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+index	question	choices	image	answer
+201	Four one-microfarad capacitors are connected in parallel, charged to 200 volts and discharged through a 5 mm length of fine copper wire.  Wire has a resistance of 4 ohms per meter and a mass of about 0.045 gram per meter. Would you expect the wire to melt? Why?	[]	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	\text{The copper wire will not melt.}
+202	A long coaxial cable consists of a solid inner cylindrical conductor of radius $R_1$ and a thin outer cylindrical conducting shell of radius $R_2$. At one end the two conductors are connected together by a resistor and at the other end they are connected to a battery. Hence, there is a current $i$ in the conductors and a potential difference $V$ between them. Neglect the resistance of the cable itself.  (a) Find the magnetic field $\mathbf{B}$ and the electric field $\mathbf{E}$ in the region $R_2 > r > R_1$, i.e., between the conductors.  (b) Find the magnetic energy and electric energy per unit length in the region between the conductors.  (c) Assuming that the magnetic energy in the inner conductor is negligible, find the inductance per unit length $L$ and the capacitance per unit length $C$.	[]	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	\mathbf{B} = \frac{\mu_0 i}{2 \pi r} \mathbf{e_\theta}; \mathbf{E} = \frac{V}{r \ln \frac{R_2}{R_1}} \mathbf{e_r}; \frac{dW_m}{dz} = \frac{\mu_0 i^2}{4 \pi} \ln \frac{R_2}{R_1}; \frac{dW_e}{dz} = \frac{\pi \varepsilon_0 V^2}{\ln \frac{R_2}{R_1}}; \frac{dL}{dz} = \frac{\mu_0}{2\pi} \ln \frac{R_2}{R_1}; \frac{dC}{dz} = \frac{2 \pi \varepsilon_0}{\ln \frac{R_2}{R_1}}
+203	A toroid having an iron core of square cross section (Fig. 2.17) and permeability $ \mu $ is wound with $ N $ closely spaced turns of wire carrying a current $ I $. Find the magnitude of the magnetization $ M $ everywhere inside the iron.	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	M = \frac{\mu - 1}{\mu_0} \cdot \frac{NI}{2\pi r}
+204	Any linear dc network (a load $R$ is connected between the two arbitrary points A and B of the network) is equivalent to a series circuit consisting of a battery of emf $V$ and a resistance $r$, as shown in Fig. 3.4.  (a) Calculate $V$ and $r$ of the circuit in Fig. 3.5.  (b) Calculate $V$ and $r$ of the circuit in Fig. 3.6.  (c) Calculate $V$ and $r$ of the circuit in Fig. 3.7.   (Hint: Use mathematical induction)	[]	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	V = \frac{1}{2} V_n; r = R; V = \frac{1}{2} \left( V_{n-1} + \frac{1}{2} V_n \right); r = R; V = 2^{-1} V_1 + 2^{-2} V_2 + \cdots + 2^{-n} V_n; r = R
+205	A capacitor having circular disc plates of radius $R$ and separation $d \ll R$ is filled with a material having a dielectric constant $K_e$. A time varying potential $V = V_0 \cos \omega t$ is applied to the capacitor.  (a) As a function of time find the electric field (magnitude and direction) and free surface charge density on the capacitor plates. (Ignore magnetic and fringe effects.)  (b) Find the magnitude and direction of the magnetic field between the plates as a function of distance from the axis of the disc.  (c) Calculate the flux of the Poynting vector from the open edges of the capacitor.	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+206	In Fig. 1.13 a very long coaxial cable consists of an inner cylinder of radius $a$ and electrical conductivity $\sigma$ and a coaxial outer cylinder of radius $b$. The outer shell has infinite conductivity. The space between the cylinders is empty. A uniform constant current density $j$, directed along the axial coordinate $z$, is maintained in the inner cylinder. Return current flows uniformly in the outer shell. Compute the surface charge density on the inner cylinder as a function of the axial coordinate $z$, with the origin $z = 0$ chosen to be on the plane half-way between the two ends of the cable.	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	\sigma_s(z) = -\frac{\epsilon_0 j z}{a \sigma \ln(b/a)}
+207	An air-filled capacitor is made from two concentric metal cylinders. The outer cylinder has a radius of 1 cm.  (a) What choice of radius for the inner conductor will allow a maximum potential difference between the conductors before breakdown of the air dielectric?  (b) What choice of radius for the inner conductor will allow a maximum energy to be stored in the capacitor before breakdown of the dielectric?  (c) Calculate the maximum potentials for cases (a) and (b) for a breakdown field in air of $3 \times 10^6 \, \text{V/m}$.	[]	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	R_1 = \frac{R_2}{e}; R_1 = \frac{R_2}{\sqrt{e}}; V_{\text{max}} = 1.1 \times 10^4 \, \text{V}; V_{\text{max}} = 9.2 \times 10^3 \, \text{V}
+208	A parallel plate capacitor has circular plates of radius $R$ and separation $d \ll R$. The potential difference $V$ across the plates varies as $V = V_0 \sin \omega t$. Assume that the electric field between the plates is uniform and neglect edge effects and radiation.  (a) Find the direction and magnitude of the magnetic induction $\mathbf{B}$ at point $P$ which is at a distance $r \, (r < R)$ from the axis of the capacitor.  (b) Suppose you wish to measure the magnetic field $\mathbf{B}$ at the point $P$ using a piece of wire and a sensitive high-impedance oscilloscope. Make a sketch of your experimental arrangement and estimate the signal detected by the oscilloscope.	[]	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	\mathbf{B}(r, t) = \frac{\varepsilon_0 \mu_0 V_0 \omega r}{2d} \cos (\omega t) \mathbf{e}_{\theta}; |\epsilon| = \omega |B| \Delta S
+209	Two concentric metal spheres of radii $a$ and $b$ $(a < b)$ are separated by a medium that has dielectric constant $\epsilon$ and conductivity $\sigma$. At time $t = 0$ an electric charge $q$ is suddenly placed on the inner sphere.  (a) Calculate the total current through the medium as a function of time.  (b) Calculate the Joule heat produced by this current and show that it is equal to the decrease in electrostatic energy that occurs as a consequence of the rearrangement of the charge.	[]	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	I(t) = \frac{\sigma q}{\epsilon} e^{-\frac{\sigma}{\epsilon} t}; W = \frac{q^2}{8\pi \epsilon} \left( \frac{1}{a} - \frac{1}{b} \right)
+210	Consider a sphere of radius $R$ centered at the origin. Suppose a point charge $q$ is put at the origin and that this is the only charge inside or outside the sphere. Furthermore, the potential is $\Phi = V_0 \cos \theta$ on the surface of the sphere. What is the electric potential both inside and outside the sphere?	[]	/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGQAZADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD3+iiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigD//2Q==	\Phi_- = \frac{q}{4\pi\epsilon_0 r} - \frac{q}{4\pi\epsilon_0 R} + \frac{V_0 \cos \theta}{R} r; \Phi_+ = \frac{V_0 R^2}{r^2} \cos \theta
+211	Show that $E^2 - B^2$ and $\mathbf{E} \cdot \mathbf{B}$ are invariant under a Lorentz transformation.	[]	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	E^2 - B^2; \mathbf{E} \cdot \mathbf{B}
+212	The volume between two concentric conducting spherical surfaces of radii $a$ and $b$ ($a < b$) is filled with an inhomogeneous dielectric constant   $$ \varepsilon = \frac{\varepsilon_0}{1 + Kr}, $$  where $\varepsilon_0$ and $K$ are constants and $r$ is the radial coordinate. Thus $D(r) = \varepsilon E(r)$. A charge $Q$ is placed on the inner surface, while the outer surface is grounded. Find:  (a) The displacement in the region $a < r < b$.  (b) The capacitance of the device.  (c) The polarization charge density in $a < r < b$.  (d) The surface polarization charge density at $r = a$ and $r = b$.	[]	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	\mathbf{D} = \frac{Q}{4 \pi r^2} \mathbf{e}_r; C = \frac{4 \pi \varepsilon_0 ab}{(b-a) + abK \ln (b/a)}; \rho_P = \frac{QK}{4 \pi r^2}; \sigma_P = \frac{QK}{4 \pi a} \quad \text{at} \quad r = a; \sigma_P = -\frac{QK}{4 \pi b} \quad \text{at} \quad r = b
+213	A conducting sphere of radius $a$ carrying a charge $q$ is placed in a uniform electric field $E_0$. Find the potential at all points inside and outside of the sphere. What is the dipole moment of the induced charge on the sphere? The three electric fields in this problem give rise to six energy terms. Identify these six terms; state which are finite or zero, and which are infinite or unbounded.	[]	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	\Phi_1 = \frac{q}{4\pi \varepsilon_0 a}; \Phi_2 = -E_0 r \cos \theta + \frac{q}{4\pi \varepsilon_0 r} + \frac{E_0 a^3}{r^2} \cos \theta; P = 4\pi \varepsilon_0 a^3 E_0; W_1 \rightarrow \infty; W_2 = \frac{q^2}{8\pi \varepsilon_0 a}; W_3 = \frac{4\pi \varepsilon_0 a^3}{3} E_0^2; W_{12} = 0; W_{23} = 0; W_{13} = -2\pi \varepsilon_0 a^3 E_0^2
+214	The radar speed trap operates on a frequency of $10^9$ Hz. What is the beat frequency between the transmitted signal and one received after reflection from a car moving at 30 m/sec?	[]	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	200 \, \text{Hz}
+215	It can be shown that the electric field inside a dielectric sphere which is placed inside a large parallel-plate capacitor is uniform (the magnitude and direction of $E_0$ are constant). If the sphere has radius $R$ and relative dielectric constant $K_e = \epsilon / \epsilon_0$, find $E$ at point $p$ on the outer surface of the sphere (use polar coordinates $R, \theta$). Determine the bound surface charge density at point $p$.	[]	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	E = K_e E_0 \cos \theta \, e_r - E_0 \sin \theta \, e_\theta; \sigma_p = \epsilon_0 (K_e - 1) E_0 \cos \theta
+216	A capacitor is made of two plane parallel plates of width $a$ and length $b$ separated by a distance $d (d \ll a, b)$, as in Fig. 1.23. The capacitor has a dielectric slab of relative dielectric constant $K$ between the two plates.  (a) The capacitor is connected to a battery of emf $V$. The dielectric slab is partially pulled out of the plates such that only a length $x$ remains between the plates. Calculate the force on the dielectric slab which tends to pull it back into the plates.  (b) With the dielectric slab fully inside, the capacitor plates are charged to a potential difference $V$ and the battery is disconnected. Again, the dielectric slab is pulled out such that only a length $x$ remains inside the plates. Calculate the force on the dielectric slab which tends to pull it back into the plates. Neglect edge effects in both parts (a) and (b).	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	F = \frac{\varepsilon_0(K-1)aV^2}{2d}; F = \frac{\varepsilon_0 K^2 (K-1)}{[(K-1)x + b]^2} \cdot \frac{a b^2}{2d} V_0^2
+217	"A charged particle is constrained to move with constant velocity $v$ in the x-direction (with $y = y_0, z = 0$ fixed). It moves above an infinite perfectly conducting metal sheet that undulates with ""wavelength"" $L$ along the x-direction. A distant observer is located in the $z = 0$ plane and detects the electromagnetic radiation emitted at angle $\theta$ (the angle between the velocity vector and a vector drawn from the charge to the observer) as shown in Fig. 5.4. What is the wavelength $\lambda$ of the radiation detected by the observer?"	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	\lambda = L \left(\frac{c}{v} - \cos \theta \right)
+218	What is the drift velocity of electrons in a 1 mm Cu wire carrying 10 A? $10^{-5}$, $10^{-2}$, $10^1$, $10^5$ cm/sec.	[]	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	10^{-2} \text{ cm/sec}
+219	A very long hollow metallic cylinder of inner radius $r_0$ and outer radius $r_0 + \Delta r (\Delta r \ll r_0)$ is uniformly filled with space charge of density $\rho_0$. What are the electric fields for $r < r_0, r > r_0 + \Delta r$, and $r_0 + \Delta r > r > r_0$? What are the surface charge densities on the inner and outer surfaces of the cylinder? The net charge on the cylinder is assumed to be zero. What are the fields and surface charges if the cylinder is grounded?	[]	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	\mathbf{E}_1(r) = \frac{\rho_0 r}{2\epsilon_0} \mathbf{e}_r; \mathbf{E}_2(r) = \frac{\rho_0 r_0^2}{2r\epsilon_0} \mathbf{e}_r; \mathbf{E}_3(r) = 0; \sigma(r_0) = -\frac{\rho_0 r_0}{2}; \sigma(r_0 + \Delta r) = \frac{\rho_0 r_0^2}{2(r_0 + \Delta r)}; E = 0; \sigma(r_0 + \Delta r) = 0
+220	A finite conductor of uniform conductivity $\sigma$ has a uniform volume charge density $\rho$. Describe in detail the subsequent evolution of the system in the two cases:  (a) the conductor is a sphere,   (b) the conductor is not a sphere.  What happens to the energy of the system in the two cases?	[]	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	"\begin{aligned}
+&\mathbf{E} = 0, \\
+&\rho = 0, \\
+&\mathbf{J} = 0 \quad \text{(for $t \to \infty$)} \\
+&\text{Charge distributed uniformly on the spherical surface.} \\
+&\text{Electric energy decreases, converted to heat.}
+\end{aligned}; \begin{aligned}
+&|\mathbf{E}| \propto e^{-\frac{\sigma}{\epsilon}t}, \\
+&|\mathbf{J}| \propto e^{-\frac{\sigma}{\epsilon}t}, \\
+&\rho \propto e^{-\frac{\sigma}{\epsilon}t} \quad \text{(for $t \to \infty$)} \\
+&\text{Charge distributed on the conductor's surface.} \\
+&\text{Electric energy decreases, converted to heat.}
+\end{aligned}"
+221	A parallel-plate capacitor is made of circular plates as shown in Fig. 2.10. The voltage across the plates (supplied by long resistance-less lead wires) has the time dependence $V = V_0 \cos \omega t$. Assume $d \ll a \ll c/\omega$, so that fringing of the electric field and retardation may be ignored.  (a) Use Maxwell's equations and symmetry arguments to determine the electric and magnetic fields in region I as functions of time.  (b) What current flows in the lead wires and what is the current density in the plates as a function of time?  (c) What is the magnetic field in region II? Relate the discontinuity of $B$ across a plate to the surface current in the plate.	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	E^{(I)}_z = - \frac{V_0}{d} \cos \omega t; B_{\phi}^{(I)} = \frac{\mu_0 \epsilon_0 V_0 \omega}{2d} r \sin \omega t; I = -\frac{\pi a^2 \epsilon_0 V_0 \omega}{d} \sin \omega t; j_l(r) = \frac{(a^2 - r^2) \epsilon_0 V_0 \omega}{2 d r} \sin (\omega t) \mathbf{e}_r; B^{(II)}_{\phi} = \frac{\mu_0 \epsilon_0 a^2 V_0 \omega}{2dr} \sin \omega t; \mathbf{n} \times (\mathbf{B}^{(II)} - \mathbf{B}^{(I)}) = \mu_0 \mathbf{j}
+222	The current–voltage characteristic of the output terminals A, B (Fig. 3.3) is the same as that of a battery of emf $ε_0$ and internal resistance $r$. Find $ε_0$ and $r$ and the short-circuit current provided by the battery.	[]	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	\varepsilon_0 = 3 \, \text{V}; r = 4.8 \, \Omega; I = 0.625 \, \text{A}
+223	Suppose the magnetic field on the axis of a right circular cylinder is given by  $$ \mathbf{B} = B_0(1 + \nu z^2) \mathbf{e}_z. $$  Suppose the $\theta$-component of $\mathbf{B}$ is zero inside the cylinder.  (a) Calculate the radial component of the field $B_r(r, z)$ for points near the axis.   (b) What current density $\mathbf{j}(r, z)$ is required inside the cylinder if the field described above is valid for all radii $r$?	[]	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	B_r(r, z) = -\nu B_0 r z; \mathbf{j}(r, z) = -\frac{1}{\mu_0} \nu B_0 r \mathbf{e}_\theta
+224	The conductors of a coaxial cable are connected to a battery and resistor as shown in Fig. 2.15. Starting from first principles find, in the region between $r_1$ and $r_2$,  (a) the electric field in terms of $V, r_1$ and $r_2$,  (b) the magnetic field in terms of $V, R, r_1$ and $r_2$,  (c) the Poynting vector.  (d) Show by integrating the Poynting vector that the power flow between $r_1$ and $r_2$ is $V^2/R$.	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	\mathbf{E} = \frac{V}{r \ln \frac{r_2}{r_1}} \mathbf{e}_r; \mathbf{B} = \frac{\mu_0 V}{2 \pi r R} \mathbf{e}_\theta; \mathbf{N} = \frac{V^2}{2 \pi r^2 R \ln \frac{r_2}{r_1}} \mathbf{e}_z; P = \frac{V^2}{R}
+225	As in Fig. 3.9, switch $S$ is closed and a steady dc current $I = V/R$ is established in a simple $LR$ series circuit. Now switch $S$ is suddenly opened. What happens to the energy $\frac{1}{2} LI^2$ which was stored in the circuit when the current $I$ was present?	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	\text{The energy is radiated in the form of electromagnetic waves.}
+226	In Fig. 1.22, a parallel-plate air-spaced condenser of capacitance $C$ and a resistor of resistance $R$ are in series with an ac source of frequency $\omega$. The voltage-drop across $R$ is $V_R$. Half the condenser is now filled with a material of dielectric constant $\epsilon$ but the remainder of the circuit remains unchanged. The voltage-drop across $R$ is now $2V_R$. Neglecting edge effects, calculate the dielectric constant $\epsilon$ in terms of $R, C$ and $\omega$.	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	\varepsilon = \left(\frac{4}{\sqrt{1 - 3R^2 C^2 \omega^2}} - 1\right) \varepsilon_0
+227	Two large parallel plates (non-conducting), separated by a distance $d$ and oriented as shown in Fig. 5.5, move together along $x$-axis with velocity $v$, not necessarily small compared with $c$. The upper and lower plates have uniform surface charge densities $+\sigma$ and $-\sigma$ respectively in the rest frame of the plates. Find the magnitude and direction of the electric and magnetic fields between the plates (neglecting edge effects).	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	E = \frac{\gamma \sigma}{\varepsilon_0} \hat{z}; B = \frac{v}{\varepsilon_0 c^2} \sigma \hat{y}
+228	If the potential of a spherical shell of zero thickness depends only on the polar angle $\theta$ and is given by $V(\theta)$, inside and outside the sphere there being empty space,    (a) show how to obtain expressions for the potential $V(r, \theta)$ inside and outside the sphere and how to obtain an expression for the electric sources on the sphere.     (b) Solve with $V(\theta) = V_0 \cos^2 \theta$.  The first few of the Legendre polynomials are given as follows:   $$ P_0(\cos \theta) = 1, \quad P_1(\cos \theta) = \cos \theta, \quad P_2(\cos \theta) = \frac{3 \cos^2 \theta - 1}{2}. $$  We also have   $$ \int_0^\pi P_n(\cos \theta) P_m(\cos \theta) \sin \theta \, d\theta = 0 \quad \text{if} \quad n \neq m $$  and   $$ \int_0^\pi P_n^2(\cos \theta) \sin \theta \, d\theta = \frac{2}{2n + 1}. $$	[]	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	"\begin{aligned}
+\Phi_1 &= \sum_{n=0}^{\infty} \left[ \frac{2n + 1}{2R^n} \int_0^\pi V(\theta) P_n(\cos \theta) \sin \theta \, d\theta \right] P_n(\cos \theta) r^n, \\
+\Phi_2 &= \sum_{n=0}^{\infty} \left[ \frac{(2n+1)R^{n+1}}{2} \int_0^r V(\theta) P_n(\cos \theta) \sin \theta \, d\theta \right] \frac{P_n(\cos \theta)}{r^{n+1}}, \\
+\sigma(\theta) &= \varepsilon_0 \sum_{n=0}^{\infty} \left[ \frac{(2n+1)^2}{2R} \int_0^r V(\theta) P_n(\cos \theta) \sin \theta \, d\theta \right] P_n(\cos \theta).
+\end{aligned}; \begin{aligned}
+\Phi_1 &= \frac{V_0}{3} + \frac{2V_0}{3} P_2(\cos\theta) \frac{r^2}{R^2}, \quad (r < R), \\
+\Phi_2 &= \frac{V_0 R}{3r} + \frac{2V_0}{3} P_2(\cos \theta) \frac{R^3}{r^3}, \quad (r > R), \\
+\sigma(\theta) &= \frac{\varepsilon_0 V_0}{3R} \left[ 1 + 5 P_2(\cos \theta) \right].
+\end{aligned}"
+229	One half of the region between the plates of a spherical capacitor of inner and outer radii $a$ and $b$ is filled with a linear isotropic dielectric of permittivity $\varepsilon_1$ and the other half has permittivity $\varepsilon_2$, as shown in Fig. 1.29. If the inner plate has total charge $Q$ and the outer plate has total charge $-Q$, find:     (a) the electric displacements $D_1$ and $D_2$ in the region of $\varepsilon_1$ and $\varepsilon_2$;   (b) the electric fields in $\varepsilon_1$ and $\varepsilon_2$;   (c) the total capacitance of this system.	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	D_1 = \frac{\epsilon_1 Qr}{2\pi(\epsilon_1 + \epsilon_2) r^3}; D_2 = \frac{\epsilon_2 Qr}{2\pi(\epsilon_1 + \epsilon_2) r^3}; E_1 = E_2 = \frac{Qr}{2\pi(\epsilon_1 + \epsilon_2) r^3}; C = \frac{2\pi (\epsilon_1 + \epsilon_2) ab}{b-a}
+230	(a) A classical electromagnetic wave satisfies the relations  $$ \mathbf{E} \cdot \mathbf{B} = 0, \quad E^2 = c^2 B^2 $$  between the electric and magnetic fields. Show that these relations, if satisfied in any one Lorentz frame, are valid in all frames.  (b) If $K$ is a unit three-vector in the direction of propagation of the wave, then according to classical electromagnetism, $K \cdot E=K \cdot B= 0$. Show that this statement is also invariant under Lorentz transformation by showing its equivalence to the manifestly Lorentz invariant statement $n^\mu F_{\mu \nu} = 0$, where $n^\mu$ is a four-vector oriented in the direction of propagation of the wave and $F_{\mu \nu}$ is the field strength tensor.  Parts (a) and (b) together show that what looks like a light wave in one frame looks like one in any frame.  (c) Consider an electromagnetic wave which in some frame has the form  $$E_x = cB_y = f(ct - z),$$  where $\lim\limits_{z \to \pm \infty} f(z) \to 0$. What would be the values of the fields in a different coordinate system moving with velocity $v$ in the $z$ direction relative to the frame in which the fields are as given above? Give an expression for the energy and momentum densities of the wave in the original frame and in the frame moving with velocity $v$, show that the total energy-momentum of the wave transforms as a four-vector under the transformation between the two frames. (Assume the extent of the wave in the $x-y$ plane is large but finite, so that its total energy and momentum are finite.)	[]	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	"\text{Lorentz invariance of } \mathbf{E} \cdot \mathbf{B} = 0 \text{ and } E^2 = c^2 B^2; n^\mu F_{\mu \nu} = 0; \begin{align*}
+E_x' &= \gamma(1 - \beta) f(ct - z) \\
+B_y' &= \frac{\gamma}{c} (1 - \beta) f(ct - z)
+\end{align*}; \begin{align*}
+w' &= \varepsilon_0 \gamma^2 (1 - \beta)^2 f^2(ct - z) \\
+g'_z &= \frac{\varepsilon_0}{c} \gamma^2 (1 - \beta)^2 f^2 \left[\gamma(1 - \beta)(ct' - z')\right]
+\end{align*}; \begin{align*}
+G'_z &= \gamma \left( G_z - \beta \frac{W}{c} \right) \\
+\frac{W'}{c} &= \gamma \left( \frac{W}{c} - \beta G_z \right)
+\end{align*}"
+231	For steady current flow obeying Ohm's law find the resistance between two concentric spherical conductors of radii $a < b$ filled with a material of conductivity $\sigma$. Clearly state each assumption.	[]	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	R = \frac{1}{4\pi\sigma} \left( \frac{1}{a} - \frac{1}{b} \right)
+232	A condenser comprises two concentric metal spheres, an inner one of radius $a$, and an outer one of inner radius $d$. The region $a < r < b$ is filled with material of relative dielectric constant $K_1$, the region $b < r < c$ is vacuum $(K = 1)$, and the outermost region $c < r < d$ is filled with material of dielectric constant $K_2$. The inner sphere is charged to a potential $V$ with respect to the outer one, which is grounded $(V = 0)$. Find:  (a) The free charges on the inner and outer spheres.  (b) The electric field, as a function of the distance $r$ from the center, for the regions: $a < r < b$, $b < r < c$, $c < r < d$.  (c) The polarization charges at $r = a, r = b, r = c$ and $r = d$.  (d) The capacitance of this condenser.	[]	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	Q_{\text{inner}} = Q, \quad Q_{\text{outer}} = -Q; \mathbf{E}(a < r < b) = \frac{Q}{{4\pi K_1 \varepsilon_0 r^2}} \mathbf{e}_r; \mathbf{E}(b < r < c) = \frac{Q}{{4\pi \varepsilon_0 r^2}} \mathbf{e}_r; \mathbf{E}(c < r < d) = \frac{Q}{{4\pi \varepsilon_0 K_2 r^2}} \mathbf{e}_r; \sigma_P(r = a) = \frac{Q}{4\pi a^2} \frac{1 - K_1}{K_1}; \sigma_P(r = b) = \frac{Q}{4\pi b^2} \frac{K_1 - 1}{K_1}; \sigma_P(r = c) = \frac{Q}{4\pi c^2} \frac{1 - K_2}{K_2}; \sigma_P(r = d) = \frac{Q}{4\pi d^2} \frac{K_2 - 1}{K_2}; C = \frac{4 \pi \varepsilon_0 K_1 K_2 abcd}{K_1 ab (d - c) + K_1 K_2 ad (c - b) + K_2 cd (b - a)}
+233	A surface charge density $\sigma(\theta) = \sigma_0 \cos \theta$ is glued to the surface of a spherical shell of radius $R$ ($\sigma_0$ is a constant and $\theta$ is the polar angle). There is a vacuum, with no charges, both inside and outside of the shell. Calculate the electrostatic potential and the electric field both inside and outside of the spherical shell.	[]	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	\Phi_+ = \frac{\sigma_0 R^3}{3\varepsilon_0 r^2} \cos \theta , \quad r > R; \Phi_- = \frac{\sigma_0 r}{3\varepsilon_0} \cos \theta , \quad r < R; E_+ = \frac{2\sigma_0 R^3}{3\varepsilon_0 r^3} \cos \theta \, e_r + \frac{\sigma_0 R^3}{3\varepsilon_0 r^3} \sin \theta \, e_\theta , \quad r > R; E_- = -\frac{\sigma_0}{3\varepsilon_0} \, e_z , \quad r < R
+234	The switch $S$ in Fig. 3.24 has been opened for a long time. At time $t = 0$, $S$ is closed. Calculate the current $I_L$ through the inductor as a function of the time.	[]	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	I_L(t) = 0.05(1 - e^{-10^7 t})
+235	In the circuit shown in Fig. 3.21, the capacitors are initially charged to a voltage $V_0$. At $t = 0$ the switch is closed. Derive an expression for the voltage at point A at a later time $t$.	[]	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	V_A = \pm \left(\frac{5 - 3 \sqrt{5}}{10} V_0 e^{-\frac{3+\sqrt{5}}{2} \frac{t}{RC}; V_A \approx \pm \left(1.17 e^{-0.38 \frac{t}{RC}} - 0.17 e^{-2.62 \frac{t}{RC}} \right) V_0
+236	"Show that for a given frequency the circuit in Fig. 3.38 can be made to ""fake"" the circuit in Fig. 3.39 to any desired accuracy by an appropriate choice of $R$ and $C$. (""Fake"" means that if $V_0 = IZ_R$ in one circuit and $V_0 = I Z_L$ in the other, then $Z_L$ can be chosen such that $Z_L/Z_R = e^{i \theta}$ with $\theta$ arbitrarily small.) Calculate values of $R$ and $C$ that would fake a mutual inductance $M = 1 \text{ mH}$ at 200 Hz with $\theta < 0.01$."	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	R \approx 251 \, \Omega; C \approx 0.016 \, \mu \text{F}
+237	In Fig. 3.37 the capacitor is originally charged to a potential difference $V$. The transformer is ideal: no winding resistance, no losses. At $t = 0$ the switch is closed. Assume that the inductive impedances of the windings are very large compared with $R_P$ and $R_S$. Calculate:  (a) The initial primary current.  (b) The initial secondary current.  (c) The time for the voltage $V$ to fall to $e^{-1}$ of its original value.  (d) The total energy which is finally dissipated in $R_s$.	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	i_p(0) = \frac{V}{R_p + \left(\frac{N_p}{N_s} \right)^2 R_s}; i_s(0) = \frac{N_p N_s V}{N_s^2 R_p + N_p^2 R_s}; t = \left[ R_p + \left( \frac{N_p}{N_s} \right)^2 R_s \right] C; W_{RS} = \frac{1}{2} \frac{N_p^2 V^2}{N_s^2 R_p + N_p^2 R_s} R_s C
+238	In the electrical circuit shown in Fig. 3.36, $\omega, R_1, R_2$ and $L$ are fixed; $C$ and $M$ (the mutual inductance between the identical inductors $L$) can be varied. Find values of $M$ and $C$ which maximize the power dissipated in resistor $R_2$. What is the maximum power?   You may assume, if needed, $R_2 > R_1$, $\omega L/R_2 > 10$.	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	M = \sqrt{\frac{R_1 R_2}{\omega^2} + \frac{R_1}{R_2} L^2}; C = \frac{R_2}{\omega^2 L(R_1 + R_2)}; P_2 = \frac{V_0^2 R_2^2}{8\omega^2 L^2 R_1}
+239	"A two-terminal ""black box"" is known to contain a lossless inductor $L$, a lossless capacitor $C$, and a resistor $R$. When a 1.5 volt battery is connected to the box, a current of 1.5 milliamperes flows. When an ac voltage of 1.0 volt (rms) at a frequency of 60 Hz is connected, a current of 0.01 ampere (rms) flows. As the ac frequency is increased while the applied voltage is maintained constant, the current is found to go through a maximum exceeding 100 amperes at $f = 1000 \, \text{Hz}$. What is the circuit inside the box, and what are the values of $R$, $L$, and $C$?"	[]	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	R = 10^3 \, \Omega; L = 0.95 \, \text{mH}; C = 27 \, \mu \text{F}
+240	A network is composed of two loops and three branches. The first branch contains a battery (of emf $\varepsilon$ and internal resistance $R_1$) and an open switch $S$. The second branch contains a resistor of resistance $R_2$ and an uncharged capacitor of capacitance $C$. The third branch is only a resistor of resistance $R_3$ (see Fig. 3.22).  (a) The switch is closed at $t = 0$. Calculate the charge $q$ on $C$ as a function of time $t$, for $t \geq 0$.  (b) Repeat the above, but with an initial charge $Q_0$ on $C$.	[]	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	q = \frac{\varepsilon R_3}{R_1 + R_2}\left(1 - \exp\left\{ -\frac{R_1 + R_2}{(R_1R_2 + R_2R_3 + R_3R_1)C}t \right\}\right); q = \frac{\varepsilon R_3}{R_1 + R_2} + \left(Q_0 - \frac{\varepsilon R_3}{R_1 + R_2}\right)\exp\left\{ -\frac{R_1 + R_2}{(R_1R_2 + R_2R_3 + R_3R_1)C}t \right\}
+241	In the circuit shown in Fig. 3.23, the resistance of $L$ is negligible and initially the switch is open and the current is zero. Find the quantity of heat dissipated in the resistance $R_2$ when the switch is closed and remains closed for a long time. Also, find the heat dissipated in $R_2$ when the switch, after being closed for a long time, is opened and remains open for a long time. (Notice the circuit diagram and the list of values for $V$, $R_1$, $R_2$, and $L_0$.)	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	45.5 \, \text{J}; 500 \, \text{J}
+242	The velocity of light $c$, and $\epsilon_0$ and $\mu_0$ are related by  (a) $c = \sqrt{\frac{\epsilon_0}{\mu_0}}$;   (b) $c = \sqrt{\frac{\mu_0}{\epsilon_0}}$;   (c) $c = \sqrt{\frac{1}{\epsilon_0 \mu_0}}$.	[]	/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGQAZADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD3+iiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigD//2Q==	c = \sqrt{\frac{1}{\epsilon_0 \mu_0}}
+243	Consider a plane wave with vector potential $A_\mu (x) = a_\mu e^{i (\mathbf{K} \cdot x - \omega t)}$, where $a_\mu$ is a constant four-vector. Further suppose that $\mathbf{K} = K \mathbf{e}_z$ and choose a (non-orthogonal) set of basis vectors for $a_\mu$:  $$ \epsilon^{(1)}_\mu = (0, 1, 0, 0), $$  $$ \epsilon^{(2)}_\mu = (0, 0, 1, 0), $$  $$ \epsilon^{(L)_\mu} = \frac{1}{K} \left( \frac{\omega}{c}, 0, 0, K \right) = \frac{1}{K} K^\mu, $$  $$ \epsilon^{(B)_\mu} = \frac{1}{K} \left( K, 0, 0, -\frac{\omega}{c} \right), $$  where $\epsilon^\mu = (\epsilon^0, \epsilon)$. Write  $$ a_\mu = a_1 \epsilon^{(1)_\mu} + a_2 \epsilon^{(2)_\mu} + a_L \epsilon^{(L)_\mu} + a_B \epsilon^{(B)_\mu}. $$  What constraints, if any, does one get on $a_1, a_2, a_L, a_B$ from  (a) $\nabla \cdot \mathbf{B} = 0$,  (b) $\nabla \times \mathbf{E} + \frac{1}{c} \frac{\partial \mathbf{B}}{\partial t} = 0$,  (c) $\nabla \times \mathbf{B} - \frac{1}{c} \frac{\partial \mathbf{E}}{\partial t} = 0$,  (d) $\nabla \cdot \mathbf{E} = 0$?  (e) Which of the parameters $a_1, a_2, a_L, a_B$ are gauge dependent?  (f) Give the average energy density in terms of $a_1, a_2, a_L, a_B$ after imposing (a)-(d).	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+244	A very long air-core solenoid of radius $b$ has $n$ turns per meter and carries a current $i = i_0 \sin \omega t$.  (a) Write an expression for the magnetic field $\mathbf{B}$ inside the solenoid as a function of time.  (b) Write expressions for the electric field $\mathbf{E}$ inside and outside the solenoid as functions of time. (Assume that $\mathbf{B}$ is zero outside the solenoid.) Make a sketch showing the shape of the electric field lines and also make a graph showing how the magnitude of $\mathbf{E}$ depends on the distance from the axis of the solenoid at time $t = \frac{2\pi}{\omega}$.	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+245	"Some isotropic dielectrics become birefringent (doubly refracting) when they are placed in a static external magnetic field. Such magnetically-biased materials are said to be gyrotropic and are characterized by a permittivity $\varepsilon$ and a constant ""gyration vector"" $\mathbf{g}$. In general, $\mathbf{g}$ is proportional to the static magnetic field which is applied to the dielectric. Consider a monochromatic plane wave  $$ \begin{bmatrix} \mathbf{E}(\mathbf{x}, t) \\ \mathbf{B}(\mathbf{x}, t) \end{bmatrix} = \begin{bmatrix} \mathbf{E}_0 \\ \mathbf{B}_0 \end{bmatrix} e^{i(\mathbf{K} \cdot \hat{\mathbf{n}} \cdot x - \omega t)} $$  traveling through a gyrotropic material. $\omega$ is the given angular frequency of the wave, and $\hat{\mathbf{n}}$ is the given direction of propagation. $\mathbf{E}_0$, $\mathbf{B}_0$, and $\mathbf{K}$ are constants to be determined. For a non-conducting ($\sigma = 0$) and non-permeable ($\mu = 1$) gyrotropic material, the electric displacement $\mathbf{D}$ and the electric field $\mathbf{E}$ are related by  $$ \mathbf{D} = \varepsilon \mathbf{E} + i (\mathbf{E} \times \mathbf{g}), $$  where the permittivity $\epsilon$ is a positive real number and where the ""gyration vector"" $\mathbf{g}$ is a constant real vector. Consider plane waves which propagate in the direction of $\mathbf{g}$, with $\mathbf{g}$ pointing along the $z$-axis:  $$ \mathbf{g} = g\mathbf{e}_z \quad \text{and} \quad \hat{\mathbf{n}} = \mathbf{e}_z. $$  (a) Starting from Maxwell's equations, find the possible values for the index of refraction $N \equiv Kc/\omega$. Express your answers in terms of the constants $\epsilon$ and $g$.  (b) For each possible value of $N$, find the corresponding polarization $\mathbf{E}_0$."	[]	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	N_1 = \sqrt{\epsilon + g}, \quad N_2 = \sqrt{\epsilon - g}; E_{0x} = iE_{0y}, \quad E_{0z} = 0; E_{0x} = -iE_{0y}, \quad E_{0z} = 0
+246	Linearly polarized light of the form $E_x(z, t) = E_0 e^{i(kz-\omega t)}$ is incident normally onto a material which has index of refraction $n_R$ for right-hand circularly polarized light and $n_L$ for left-hand circularly polarized light. Using Maxwell's equations calculate the intensity and polarization of the reflected light.	[]	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	\text{Polarization: elliptically polarized}; \frac{I''}{I} = \frac{1}{2} \left[ \left( \frac{1-n_R}{1+n_R} \right)^2 + \left( \frac{1-n_L}{1+n_L} \right)^2 \right]
+247	Given a plane polarized electric wave  $$ \mathbf{E} = \mathbf{E}_0 \exp \left\{ i\omega \left[ t - \frac{n}{c} (\mathbf{K} \cdot \mathbf{r}) \right] \right\}, $$  derive from Maxwell’s equations the relations between $\mathbf{E}$, $\mathbf{K}$ and the $\mathbf{H}$ field. Obtain an expression for the index of refraction $n$ in terms of $\omega$, $\epsilon$, $\mu$, $\sigma$ (the conductivity).	[]	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	\mathbf{H} = \frac{n}{\mu c} \mathbf{K} \times \mathbf{E}; n = \sqrt{\frac{\mu \epsilon}{2 \mu_0 \epsilon_0}} \left[ \sqrt{ \left( 1 + \frac{\sigma^2}{\epsilon^2 \omega^2} \right)^{1/2} + 1} - i \sqrt{ \left( 1 + \frac{\sigma^2}{\epsilon^2 \omega^2} \right)^{1/2} - 1} \right]
+248	(a) Write down Maxwell's equations in a non-conducting medium with constant permeability and susceptibility ($\rho = j = 0$). Show that $\mathbf{E}$ and $\mathbf{B}$ each satisfies the wave equation, and find an expression for the wave velocity. Write down the plane wave solutions for $\mathbf{E}$ and $\mathbf{B}$ and show how $\mathbf{E}$ and $\mathbf{B}$ are related.  (b) Discuss the reflection and refraction of electromagnetic waves at a plane interface between the dielectrics and derive the relationships between the angles of incidence, reflection and refraction.	[]	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	"\begin{align*}
+\nabla \times \mathbf{E} &= -\frac{\partial \mathbf{B}}{\partial t}, \\
+\nabla \times \mathbf{H} &= \frac{\partial \mathbf{D}}{\partial t}, \\
+\nabla \cdot \mathbf{D} &= 0, \\
+\nabla \cdot \mathbf{B} &= 0.
+\end{align*}; \nabla^2 \mathbf{E} - \mu \varepsilon \frac{\partial^2 \mathbf{E}}{\partial t^2} = 0; \nabla^2 \mathbf{B} - \mu \varepsilon \frac{\partial^2 \mathbf{B}}{\partial t^2} = 0; v = \frac{1}{\sqrt{\varepsilon \mu}}; \mathbf{E}(\mathbf{r}, t) = \mathbf{E}_0 e^{i(\mathbf{k} \cdot \mathbf{r} - \omega t)}; \mathbf{B}(\mathbf{r}, t) = \mathbf{B}_0 e^{i(\mathbf{k} \cdot \mathbf{r} - \omega t)}; \mathbf{B} = \sqrt{\mu \varepsilon} \frac{\mathbf{k}}{k} \times \mathbf{E}; \theta = \theta'; \frac{\sin \theta}{\sin \theta''} = \frac{\sqrt{\mu_2 \varepsilon_2}}{\sqrt{\mu_1 \varepsilon_1}} = \frac{n_2}{n_1} = n_{21}"
+249	As in Fig. 2.3, an infinitely long wire carries a current $I = 1 \, \text{A}$. It is bent so as to have a semi-circular detour around the origin, with radius $1 \, \text{cm}$. Calculate the magnetic field at the origin.	[]	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	B = 3.14 \times 10^{-5} \, \text{T}
+250	A plane electromagnetic wave of frequency $\omega$ and wave number $K$ propagates in the $+z$ direction. For $z < 0$, the medium is air with $\varepsilon = \varepsilon_0$ and conductivity $\sigma = 0$. For $z > 0$, the medium is a lossy dielectric with $\varepsilon > \varepsilon_0$ and $\sigma > 0$. Assume that $\mu = \mu_0$ in both media.  (a) Find the dispersion relation (i.e., the relationship between $\omega$ and $K$) in the lossy medium.  (b) Find the limiting values of $K$ for a very good conductor and a very poor conductor.  (c) Find the $e^{-1}$ penetration depth $\delta$ for plane wave power in the lossy medium.  (d) Find the power transmission coefficient $T$ for transmission from $z < 0$ to $z > 0$, assuming $\sigma \ll \varepsilon \omega$ in the lossy medium.  (e) Most microwave ovens operate at 2.45 GHz. At this frequency, beef may be described approximately by $\varepsilon/\varepsilon_0 = 49$ and $\sigma = 2 \, \text{mho} \, \text{m}^{-1}$. Evaluate $T$ and $\delta$ for these quantities, using approximations where needed. Does your answer for $\delta$ indicate an advantage of microwave heating over infrared heating (broiling)?	[]	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	K' = (\beta + i \alpha)e_z; \beta = \omega \sqrt{\mu_0 \epsilon} \left[ \frac{1}{2} \left( 1 + \sqrt{1 + \frac{\sigma^2}{\epsilon^2 \omega^2}} \right) \right]^{1/2}; \alpha = \omega \sqrt{\mu_0 \epsilon} \left[ \frac{1}{2} \left( -1 + \sqrt{1 + \frac{\sigma^2}{\epsilon^2 \omega^2}} \right) \right]^{1/2}; \beta = \alpha \approx \sqrt{\frac{\omega \mu_0 \sigma}{2}}; \beta \approx \omega \sqrt{\mu_0 \epsilon}, \quad \alpha \approx \frac{\sigma}{2} \sqrt{\frac{\mu_0}{\epsilon}}; \delta = \frac{1}{\omega \sqrt{\mu_0 \epsilon}} \left[ \frac{1}{2} \left( -1 + \sqrt{1 + \frac{\sigma^2}{\epsilon^2 \omega^2}} \right) \right]^{-1/2}; \delta \approx \sqrt{\frac{2}{\omega \mu_0 \sigma}}; \delta \approx \frac{2}{\sigma} \sqrt{\frac{\epsilon}{\mu_0}}; T = \frac{4n}{(1+n)^2 + \frac{n^2 \sigma^2}{4 \epsilon^2 \omega^2}}; \delta \approx 1.85 \, \text{cm}; T \approx 0.43
+251	Beams of electromagnetic radiation, e.g., radar beams, light beams, eventually spread because of diffraction. Recall that a beam which propagates through a circular aperture of diameter $D$ spreads with a diffraction angle $\theta_d = \frac{1.22}{D} \lambda_n$. In many dielectric media the index of refraction increases in large electric fields and can be well represented by $n = n_0 + n_2 E^2$.  Show that in such a nonlinear medium the diffraction of the beam can be counterbalanced by total internal reflection of the radiation to form a self-trapped beam. Calculate the threshold power for the existence of a self-trapped beam.	[]	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	\langle P \rangle = \frac{\pi c \varepsilon_0}{16 n_2} (1.22 \lambda)^2
+252	Consider a possible solution to Maxwell's equations given by  $$ \mathbf{A}(x, t) = \mathbf{A}_0 e^{i(\mathbf{K \cdot x} - \omega t)}, \quad \phi(x, t) = 0, $$  where $\mathbf{A}$ is the vector potential and $\phi$ is the scalar potential. Further suppose $\mathbf{A}_0$, $\mathbf{K}$ and $\omega$ are constants in space-time. Give, and interpret, the constraints on $\mathbf{A}_0$, $\mathbf{K}$ and $\omega$ imposed by each of the Maxwell's equations given below.  (a) $\nabla \cdot \mathbf{B} = 0$;   (b) $\nabla \times \mathbf{E} + \frac{1}{c} \frac{\partial \mathbf{B}}{\partial t} = 0$;   (c) $\nabla \cdot \mathbf{E} = 0$;   (d) $\nabla \times \mathbf{B} - \frac{1}{c} \frac{\partial \mathbf{E}}{\partial t} = 0$.	[]	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	\mathbf{K} \cdot \mathbf{A} = 0; K = \frac{\omega}{c}
+253	Consider electromagnetic waves in free space of the form  $$ \mathbf{E}(x, y, z, t) = \mathbf{E}_0(x, y) e^{i k z - i \omega t} \, , $$  $$ \mathbf{B}(x, y, z, t) = \mathbf{B}_0(x, y) e^{i k z - i \omega t} \, , $$  where $\mathbf{E}_0$ and $\mathbf{B}_0$ are in the $xy$ plane.  (a) Find the relation between $k$ and $\omega$, as well as the relation between $\mathbf{E}_0(x, y)$ and $\mathbf{B}_0(x, y)$. Show that $\mathbf{E}_0(x, y)$ and $\mathbf{B}_0(x, y)$ satisfy the equations for electrostatics and magnetostatics in free space.  (b) What are the boundary conditions for $\mathbf{E}$ and $\mathbf{B}$ on the surface of a perfect conductor?  (c) Consider a wave of the above type propagating along the transmission line shown in Fig. 4.1. Assume the central cylinder and the outer sheath are perfect conductors. Sketch the electromagnetic field pattern for a particular cross section. Indicate the signs of the charges and the directions of the currents in the conductors.  (d) Derive expressions for $\mathbf{E}$ and $\mathbf{B}$ in terms of the charge per unit length $\lambda$ and the current $i$ in the central conductor.	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= \frac{\omega}{c}; |E_0(x, y)| = c |B_0(x, y)|; \mathbf{E} = \frac{\lambda}{2\pi \epsilon_0 r} \mathbf{e}_r; \mathbf{B} = \frac{\mu_0 I}{2\pi r} \mathbf{e}_\theta; I = c\lambda
+254	(a) $X$-rays which strike a metal surface at an angle of incidence to the normal greater than a critical angle $\theta_0$ are totally reflected. Assuming that a metal contains $n$ free electrons per unit volume, calculate $\theta_0$ as a function of the angular frequency $\omega$ of the $X$-rays.  (b) If $\omega$ and $\theta$ are such that total reflection does not occur, calculate what fraction of the incident wave is reflected. You may assume, for simplicity, that the polarization vector of the $X$-rays is perpendicular to the plane of incidence.	[]	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	\theta_0 = \arcsin \left( \sqrt{1 - \frac{\omega_P^2}{\omega^2}} \right); R = \left( \frac{\cos \theta - n \cos \theta''}{\cos \theta + n \cos \theta''} \right)^2
+255	A cylindrical wire of permeability $\mu$ carries a steady current $I$. If the radius of the wire is $R$, find $B$ and $H$ inside and outside the wire.	[]	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	\mathbf{H}(r) = \frac{I}{2 \pi r} \mathbf{e}_\theta; \mathbf{B}(r) = \frac{\mu_0 I}{2 \pi r} \mathbf{e}_\theta; \mathbf{H}(r) = \frac{Ir}{2\pi R^2} \mathbf{e}_\theta; \mathbf{B}(r) = \frac{\mu I r}{2\pi R^2} \mathbf{e}_\theta
+256	A harmonic plane wave of frequency $\nu$ is incident normally on an interface between two dielectric media of indices of refraction $n_1$ and $n_2$. A fraction $\rho$ of the energy is reflected and forms a standing wave when combined with the incoming wave. Recall that on reflection the electric field changes phase by $\pi$ for $n_2 > n_1$.  (a) Find an expression for the total electric field as a function of the distance $d$ from the interface. Determine the positions of the maxima and minima of $\langle E^2 \rangle$.  (b) From the behavior of the electric field, determine the phase change on reflection of the magnetic field. Find $B(z, t)$ and $\langle B^2 \rangle$.  (c) When O. Wiener did such an experiment using a photographic plate in 1890, a band of minimum darkening of the plate was found for $d = 0$. Was the darkening caused by the electric or the magnetic field?	[]	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	\text{Electric Field}
+257	A plane electromagnetic wave of intensity $I$ falls upon a glass plate  with index of refraction $n$. The wave vector is at right angles to the surface (normal incidence).  (a) Show that the coefficient of reflection (of the intensity) at normal incidence is given by $R = \left( \frac{n-1}{n+1} \right)^2$ for a single interface.  (b) Neglecting any interference effects calculate the radiation pressure acting on the plate in terms of $I$ and $n$.	[]	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	R = \left( \frac{n-1}{n+1} \right)^2; P = 2 \frac{I}{c} \left( \frac{1-n}{1+n} \right)
+258	Consider 3 straight, infinitely long, equally spaced wires (with zero radius), each carrying a current $I$ in the same direction.  (a) Calculate the location of the two zeros in the magnetic field.   (b) Sketch the magnetic field line pattern.   (c) If the middle wire is rigidly displaced a very small distance $x \ (x \ll d)$ upward while the other 2 wires are held fixed, describe qualitatively the subsequent motion of the middle wire.	[]	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	x = \pm \frac{1}{\sqrt{3}} d; f \approx -\frac{\mu_0 I^2}{\pi d^2} x; T = 2\pi \sqrt{\frac{m}{\mu_0}} \frac{d}{I}
+259	Consider the propagation of a plane electromagnetic wave through a medium whose index of refraction depends on the state of circular polarization.  (a) Write down expressions for the right and left circularly polarized plane waves.  (b) Assume that the index of refraction in the medium is of the form  $$ n_{\pm} = n \pm \beta, $$  where $n$ and $\beta$ are real and the plus and minus signs refer to right and left circularly polarized plane waves respectively. Show that a linearly polarized plane wave incident on such a medium has its plane of polarization rotated as it travels through the medium. Find the angle through which the plane of polarizations is rotated as a function of the distance $z$ into the medium.  (c) Consider a tenuous electronic plasma of uniform density $n_0$ with a strong static uniform magnetic induction $\mathbf{B}_0$ and transverse waves propagating parallel to the direction of $\mathbf{B}_0$. Assume that the amplitude of the electronic motion is small, that collisions are negligible, and that the amplitude of the $\mathbf{B}$ field of the waves is small compared with $\mathbf{B}_0$. Find the indices of refraction for circularly polarized waves, and show that for high frequencies the indices can be written in the form assumed in part (b). Specify what you mean by high frequencies.	[]	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	\mathbf{E}_R(z, t) = (E_0 \mathbf{e}_x + E_0 e^{-i \frac{\pi}{2}} \mathbf{e}_y) e^{-i \omega t + i k_+ z}; \mathbf{E}_L(z, t) = \left(E_0 \mathbf{e}_x + E_0 e^{i \frac{\pi}{2}} \mathbf{e}_y \right) e^{-i \omega t + ik_{\_} z}; \varphi = \frac{1}{2} \cdot \frac{\omega}{c} (n_+ - n_-)z; n_{\pm} \approx 1 - \frac{1}{2} \frac{\omega_p^2}{\omega^2} \left(1 \mp \frac{\omega_B'}{\omega}\right)
+260	A solenoid has an air core of length 0.5 m, cross section 1 $\text{cm}^2$, and 1000 turns. Neglecting end effects, what is the self-inductance? A secondary winding wrapped around the center of the solenoid has 100 turns. What is the mutual inductance? A constant current of 1 A flows in the secondary winding and the solenoid is connected to a load of $\text{10}^3$ ohms. The constant current is suddenly stopped. How much charge flows through the resistance?	[]	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	L = 2.513 \times 10^{-4} \, \text{H}; M = 2.513 \times 10^{-5} \, \text{H}; q = 2.76 \times 10^{-7} \, \text{C}
+261	A plane polarized electromagnetic wave $E = E_{y0} e^{i(Kz-\omega t)}$ is incident normally on a semi-infinite material with permeability $\mu$, dielectric constants $\epsilon$, and conductivity $\sigma$.  (a) From Maxwell’s equations derive an expression for the electric field in the material when $\sigma$ is large and real as for a metal at low frequencies.  (b) Do the same for a dilute plasma where the conductivity is limited by the inertia rather than the scattering of the electrons and the conductivity is  $$ \sigma = i \frac{n e^2}{m \omega}. $$  (c) From these solutions comment on the optical properties of metals in the ultraviolet.	[]	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	E''_{y0} \approx 2 \sqrt{\frac{\varepsilon_0 \mu \omega}{\mu_0 \sigma}} E_{y0} e^{-\alpha z} e^{i(\beta z - \omega t - \frac{\pi}{4})} e_{y}; E''_{y0} = \frac{2E_{y0}}{1 + (1 - \omega_P^2/\omega^2)^{1/2}}; E''_{y0} = \frac{2E_{y0}}{1 + i(\omega_P^2/\omega^2 - 1)^{1/2}}; \text{Ultraviolet light can generally propagate in metals since } \omega_P < \omega \text{ for ultraviolet frequencies.}
+262	A semi-infinite solenoid of radius $R$ and $n$ turns per unit length carries a current $I$. Find an expression for the radial component of the magnetic field $B_r(z_0)$ near the axis at the end of the solenoid where $r \ll R$ and $z = 0$.	[]	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	B_r(0) = \frac{\mu_0 n I r}{4R}
+263	A dextrose solution is optically active and is characterized by a polarization vector (electric dipole moment per unit volume): $\mathbf{P} = \gamma \mathbf{\nabla} \times \mathbf{E},$ where $ \gamma $ is a real constant which depends on the dextrose concentration. The solution is non-conducting ($ \mathbf{J_{\text{free}}} = 0 $) and non-magnetic (magnetization vector $ \mathbf{M} = 0 $). Consider a plane electromagnetic wave of (real) angular frequency $ \omega $ propagating in such a solution. For definiteness, assume that the wave propagates in the $ +z $ direction. (Also assume that $\frac{\gamma \omega}{c} \ll 1$ so that square roots can be approximated by $ \sqrt{1+A} \approx 1 + \frac{1}{2} A $.)  (a) Find the two possible indices of refraction for such a wave. For each possible index, find the corresponding electric field.  (b) Suppose linearly polarized light is incident on the dextrose solution. After traveling a distance $ L $ through the solution, the light is still linearly polarized but the direction of polarization has been rotated by an angle $ \phi $ (Faraday rotation). Find $ \phi $ in terms of $ L $, $ \gamma $, and $ \omega $.	[]	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	n_\pm \approx 1 \pm \frac{\gamma \mu_0 \omega c}{2}; \phi \approx \frac{1}{2} \gamma \mu_0 \omega^2 L
+264	Calculate the resistance between the center conductor of radius $a$ and the coaxial conductor of radius $b$ for a cylinder of length $l \gg b$, which is filled with a dielectric of permittivity $\varepsilon$ and conductivity $\sigma$. Also calculate the capacitance between the inner and outer conductors.	[]	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	R = \frac{\ln(\frac{b}{a})}{2 \pi l \sigma}; C = \frac{2 \pi \varepsilon l}{\ln(\frac{b}{a})}
+265	The space between two long thin metal cylinders is filled with a material with dielectric constant $\epsilon$. The cylinders have radii $a$ and $b$, as shown in Fig. 1.19.  (a) What is the charge per unit length on the cylinders when the potential between them is $V$ with the outer cylinder at the higher potential?  (b) What is the electric field between the cylinders?	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GlmOlVzZXJDb21tZW50PlNjcmVlbnNob3Q8L2V4aWY6VXNlckNvbW1lbnQ+CiAgICAgIDwvcmRmOkRlc2NyaXB0aW9uPgogICA8L3JkZjpSREY+CjwveDp4bXBtZXRhPgqlvVS6AAAAHGlET1QAAAACAAAAAAAAAMsAAAAoAAAAywAAAMsAAHiNufVFLwAAQABJREFUeAHs3Qm4bUdZJv5CW9ue2wGHbiAXRFtU2hZBZhNICIPIEBICEUiAJhBICAkohikhzB0GCUMSICYQZkFAQ5BJgsRAIKBAoB0IQYG20ba7xXZs6P3/fp//Os+6O/ucs9a5Z9jn3G89z87aZ++1alW9VTf7rbfe76sbzOJodRQChUAhUAgUAoVAIVAIFAJ7FIEbFOHdoz1bzSoECoFCoBAoBAqBQqAQSASK8NZAKAQKgUKgECgECoFCoBDY0wgU4d3T3VuNKwQKgUKgECgECoFCoBAowltjoBAoBAqBQqAQKAQKgUJgTyNQhHdPd281rhAoBAqBQqAQKAQKgUKgCG+NgUKgECgECoFCoBAoBAqBPY1AEd493b3VuEKgECgECoFCoBAoBAqBIrw1BgqBQqAQKAQKgUKgECgE9jQCRXj3dPdW4wqBQqAQKAQKgUKgECgEivDWGCgECoFCoBAoBAqBQqAQ2NMIFOHd091bjSsECoFCoBAoBAqBQqAQKMJbY6AQKAQKgUKgECgECoFCYE8jUIR3T3dvNa4QKAQKgUKgECgECoFCoAhvjYFCoBAoBAqBQqAQKAQKgT2NQBHePd291bhCoBAoBAqBQqAQKAQKgSK8NQYKgUKgECgECoFCoBAoBPY0AkV493T3VuMKgUKgECgECoFCoBAoBIrw1hgoBAqBQqAQKAQKgUKgENjTCBTh3dPdW40rBAqBQqAQKAQKgUKgECjCW2OgECgECoFCoBAoBAqBQmBPI1CEd093bzWuECgECoFCoBAoBAqBQqAIb42BQqAQKAQKgUKgECgECoE9jUAR3j3dvdW4QqAQKAQKgUKgECgECoEivDUGCoFCoBAoBAqBQqAQKAT2NAJFePd091bjCoFCoBAoBAqBQqAQKASK8NYYKAQKgUKgECgECoFCoBDY0wgU4d3T3VuNKwQKgUKgECgECoFCoBAowltjoBAoBAqBQqAQKAQKgUJgTyNQhHdPd281rhAoBAqBQqAQKAQKgUKgCG+NgUKgECgECoFCoBAoBAqBPY1AEd493b3VuEKgECgECoFCoBAoBAqBIrw1BgqBQqAQKAQKgUKgECgE9jQCRXj3dPdW4wqBQqAQKAQKgUKgECgEivDWGCgECoFCoBAoBAqBQqAQ2NMIFOHd091bjSsECoFCoBAoBAqBQqAQKMJbY6AQKAQKgUKgECgECoFCYE8jUIR3T3dvNa4QKAQKgUKgECgECoFCoAhvjYFCoBAoBAqBQqAQKAQKgT2NQBHePd291bhCoBAoBAqBQqAQKAQKgSK8NQYKgUKgECgECoFCoBAoBPY0AkV493T3VuMKgUKgECgECoFCoBAoBIrw1hgoBAqBQmALEfjmN7/ZZrPZFj6htW/5lm/J15Y+pAovBAqBQmAXI1CEdxd3XlW9ECgElh+BT3/60+1rX/ta20rie/Ob37zd7GY3a//kn/yT5QekalgIFAKFwA4gUIR3B0CvRxYChcDuRuCv//qv22c/+9n2hS98of393/99+4u/+IsVFff3fu/38u//9//+XzbyL//yL/Oajaq87rvBDW6wJmD/4l/8i/bP//k/z+u++7u/uyHA//pf/+uV+3z/H/7Df2jf8z3f0250oxvleb0y13xgfVkIFAKFwC5DoAjvLuuwqm4hUAhsDQKI5Z/92Z81ZHZITj/zmc+0D33oQ6nS9s+R3P/23/5bQ2Ypt/7ux//+3/+7/cM//MN+ZfT7+jVTzv3etQhq/8613/7t397+1b/6V6n29s+/9Vu/NT/7ju/4jiS7vvddL/uHfuiH2n3uc5+GLLNH/LN/9s+SMCPKvYwpda5rC4FCoBBYNgSK8C5bj1R9CoFCYMsRoL7+zd/8TfvjP/7j9sUvfjFJq7/f8Y53tP/1v/7XChFUEeotcuv7fiCKndR20jj8rr8/0POw7DHEs1+PtDr63+7t93/bt31bQ4CH3//bf/tv2yGHHNL+6T/9p0l4/+W//Jfth3/4h9t//I//MYkygvyjP/qj7fu+7/vKK5zI1X8KgUJgtyFQhHe39VjVtxAoBFZFAJH9gz/4g1Rcr7nmmvY//+f/bNdee20S1v/7f//vyn2I4De+8Y32V3/1V+3rX/96EkN/I8DD69ygTK9OHnsh83/3z9c7D8nnetd67mpHJ7DqMXy/2vXDz/v1/TN/dxLsPS8wkvud3/mdqRgjyd6zTcwfrkewH/jAB7ab3vSmeT3CjBx3JXn+nvq7ECgECoHtRqAI73YjXs8rBAqBTUMAIURYEVveWef3v//97e/+7u/af//v/z1V2f/xP/5HXjMkj0hiJ6zDz9kT5g/L+7e4xS3av/t3/27FLsALi9CxCCDKzkMS+bu/+7vtV3/1V1MtVt6P/MiPtDve8Y7tP/2n/zQpsIxV4sorr2zve9/70j6hzkjnUUcd1W5729uOKotCjfz/2q/9Wk4E1JPtgZf3lre8ZfvSl77U/ut//a8rinVvh/Oi1zw+/kZ4f+InfiJJMXIMM57hH/zBH0wLBfXY3xVUtwi9+qwQKAS2A4EivNuBcj2jECgENgUBBJCV4Pd///fbJz7xifbnf/7nDaFFbr/yla8kwUXgEFdEFEH0fkhqe0V818ld/6yff/qnf7rd+c53TiL7b/7Nv8nl/Rve8IapgiK3lEsv5E75iFwv62//9m/bs571rPaGN7whSeq+ffva4x73uHb44Yc377vdoD9rtbP6vfvd725vfetb2wc+8IFsmzrc/e53b49+9KPTYtBV2bXKMBF4+9vf3l71qlflRIB94f73v3+7xz3u0W5yk5ukZeMjH/lI+/znP5+2Bu1Sx+uuuy4xlmGCrxmG6uTobR1iiES7r7++67u+Kwkwtfd7v/d7k1zDy3VHH310+4Ef+IHEd7W61+eFQCFQCGwmAkV4NxPNKqsQKAS2BIE//dM/TdIlxRc/LcL7qU99KhVdtgQvVgQEbN6SMKwQ8iV7QV+aR6CR5eE9luVPPvnkJKg8ra5FEr13IHud1Hk/JH1INvL4tKc9Levn+2OOOaaddtppqfIiy2MPxP6pT31qe+c739mQePcedthh7aSTTmp3utOdRtkF4ILsvu51r2tXXHFFPvpWt7pVO+uss9od7nCHLBNh/8M//MPMOHHjG9+4wQiRZu+A8R/90R+1D3/4w1mHRROH1dqjjI4Tovv93//9WS7CK0COas4j7HN2ifXI+2rPqc8LgUKgEBiDQBHeMSjVNYVAIbAjCFAZkT0kkpJ79dVXJ+GlOAoiQzCRsK4+duWxV9bSOusBO4L3ArG8795SRNpSv/RiykBun/jEJ7ZHPOIRKwFanbTNl92fMTwj4meffXZ7z3vekyQcofulX/qlVFP7M4fXr/WeF/mUU05ZIaosAU9+8pPbPe95z6y/eq11wIa14iUveUnW5//8n/+T9oKnPOUp7aEPfWijXPc2IdfIP2LaiafPqNXsENqA/CrT97e73e2yLIQabvoDhuwl/nbMq8HdzqDenk3hvfWtb50p1ODEJmKyYXLRr12rffVdIVAIFAJTECjCOwWturYQKAS2FAFKK9JEdUWcfvu3f7v9zu/8TvvoRz+aBBKx6kruooogtVJpWfpH3pAnPlX+Uu9//Md/vFlqR6iUj8w985nPXCGVvr/wwgvzOvdPPS655JKGUKo/RfZRj3pUO/HEE5u0X51IjikT+VQWsor4Iul3u9vd0iqBKHaiulZZ0qO97W1vay9+8YtTpYUNq8arX/3qti+sFWPKMKmAPQsFxdfBj/sLv/AL2SaWEiTYZETqNuo7Yi1dGz+1dgyfM1TD9YEJhv74yZ/8yUZdplyrGwsEUgxDinAdhUAhUAgcKAJFeA8Uwbq/ECgEDhgBxAh5klGB55TqSmGkwCJuSFRXDvvDECmkiUUBKZJDVpAUcnnkkUfm0jyS53MkuBOsTjwRa4TwGc94RubYpTA+/elPb8cff3xe358z5ozIIXmPfexj27ve9a4keoceemh7znOek8v23UIxtixK9umnn56qqnvuda97pSrLdzuGACKhgt0uuuiiDJ7zN1L5hCc8od3vfvdbsWesVR9tohDzEJ933nmp9trNDfn9+Z//+VSZuxXEuXt99Rk1mBXDhGLYb0PC671Df+gfEwxqvH4Q3GeSQvH18n3PEbxWneu7QqAQKARWQ6AI72rI1OeFQCGwpQggPJbMqbbUw9/8zd/MIK0vf/nLSX4RJa9OjOYrw1NL+bzLXe6Siq4gM5YFHtTuCUWKO8Ed3q9cQVpnnHFGZnVwDYJK3eUpHaqSw/tWe4/wIXhIKsLHvkBZlU1huOPZavcPP5dh4rnPfW47//zzUyWlUPMA3/ve9852jambOgicY60QzEcVRsYpzhTVMWVQd5FdmFx11VVJOk899dT2mMc8JonpfBm9r/pERftf85rX5MTFtQitCYj+1OdIuKOX43P94KUPYajeVGl+X6Qf6TV56PcMcav3hUAhUAishUAR3rXQqe8KgUJg0xFAdJApy+Af/OAH004gMIpX1zJ4Vw0RoE6UVMJ9nfz6nAIo+OlhD3tYEqkeWLYeGVKGZyGDZ0XwFgUZUUYQf+7nfm6yf1R51E2ZB2SO8LdyXvCCF6Q6uYhwrwaqeynciKmti6mdxx13XAbRWfJfz7fbcRKo9rznPS+D+5BEwW7Ua+0cUwbyykrywhe+sF1++eWZiaLbPZDPtcrQBjvWaT9lWH8isHy/FGrKug0+KPrIsbHgmk6Ah9hQ5RFf9/P7ut+L3cGEZ4zaPSyv3hcChcDBi0AR3oO376vlhcC2IoBEITXILUJGNfzc5z6XuWqpmvOEB6lCahAtJBYBpAg7KLi8sf/5P//ntm9Cqi/3Irj8sRdffHEuuSNPv/iLv5hleb8eYVbG8EDYEEMv79UH0eNHpWhOOezy9qQnPSkJoYAwquYJJ5yQ554lYr3y4Eu5lrsXkUTEEWh5e8eWgbBKY/bSl740CeqP/diPZb0o1utlmmA/MZmAB2sDhRvhZh2RBk1WCGRX3QT5sYAYB5TorvwaKw7kufcHZVe/szioh0A3kx7lI8Z1FAKFQCGwJgLxP5Q6CoFCoBDYcgRic4PZi170olnko52FbWAWZHAWpHYWhOZ6r1j+nt3+9refBXGcRSqy2bOf/exZBDKtXP+zP/uzs1AgZ6EQTq53kLFZ2B9mQf5moR7OQjGchaViFiRrcllB1GeRI3cWJDfrFirz7I1vfOMsVMwNlRebVcxCyZ0FgZuFn3X2+te/fhbkcHRZ2nDBBRfMQoXNMoIczl7xildkfaY0ThlB2LOMIJSz8DXPggSPqsell146O/bYY2ehyub9QbRnQb4X9lUQ3Fmo7bMgxrO3vOUts4c//OGz2KQj7zMu4sdrv7Hhb2MjrCx53eMf//hZBMvNYhIzqm5TMKhrC4FCYG8hYAZdRyFQCBQCW4IAAoYonXnmmbPwyM7+/b//97NQCPcjMYhNLPsn+UR2IstBksbw2M4iEGwWdoFZBFrNQuHL+5DV8Ibmd1MrjXSHmjuLZf4kqBHINYud2WahNk4tKglWZGOYRQDXLJbWs24PechDZuGf3RD5+uIXvziLTAxJxBHesFvMrrvuulkooqPrFkF4swj4yslEeHVnoezO4DiljFCIZ6GgztwfindOUCKH7ywU+HXroa/D4zuLTA7ZpyYCoRRnX601oVA/5DeU/9l973vfFTwXEd4+QTJZCsU32xu2llnkCp6FJWZSW9dtUF1QCBQCewaBIrx7piurIYXA8iCA3MRy9SwCr2YRVDaL4KMkukjK/IsSGLuHzcJmMAubw+yrX/3qLJbFV0hjpMDK+5FiJCwyDySpnELiIIMMUQQjk0MqiEhv5NydhY1gQ8BRcX/jN34j1UZ1o4T+1m/91iwyTkwuD+GODSqSYCrL5CAyJEwqi9odft+sB4zDCjF773vfOwubxej6uDasBysqc2xOkQpx2CtGlUGRpy5Tz5HR8DLnOBjbVxRu6r37tYGqH5aMWfh/V0jw/Pih+FLWw94wC5vLDDnfyARmVAProkKgENi1CBTh3bVdVxUvBJYPAUQ3vJizc845Zxa+zZkldeonEjckKkjKj/7oj+YStmsjUCuX3amIQyVQWVRYBIjqaWmdSjtGbZxHJ7JAzCLwKctip0DmxiqX82WxMkTA3eyud71rto/6HH7XDVkZkLMIDEtyBydWhsiOsB/pn3/+or9jG+LEu9shWCum2CGUqYw73vGOOTm50Y1uNIu0arM/+ZM/GaWasp5EJolZpBBLNV5fRR7lWfiuF1X3ep+Z5LA0aD8cTJJiw4tZpDabffKTn5z98i//cqrH4d1dIcR9TLney4ToZ37mZ3Iiw2qyEcvL9SpWHxQChcCeQKAI757oxmpEIbDzCFBm+UUth1NRWReQkL4E7ewzBPbMsDhEsFKS19isIBW5IdHtreH57faDyFiQVgfEaOpBdaXmxoYUWadIdZWknLq76LnrlY8EPu5xj0tFFnmnyPKibqSsyFaR6m63RcRuajlpGKuKqisbxYMf/OC0MrABPOhBD5pFkN8kpZO6HkFyqcxS3WO3ubRDjFFLWU8oyh3fm9/85qnuj/UyewY7BjKLsOtrNpYIZss2mOCwtsQWyKmiU6FNmEyE+vjSbgTYZIZH3IQmtnjOMVbEd70RXd8XAnsfgSK8e7+Pq4WFwJYigIjE1r/pvY3tb1eClToR6WfqaqTKSs9s5NpNBRORWUTsfEb17QSIXQDJ4XNddP16DeQj5W1FKpGySNG14bKozuwXscFFlofcC9TaiJWBUswG0APykDRq5tiyEGwBW3yzSB7Cx0LCasGGMJaAI5w8w8owSXngAx+YZYxRZz1DwBkc3MteENkzkiyPVeKpw6wLgggRXl5mGA/tGPpdebAxfthHYiONVLUR3+73hYF6+Exw2xFHHJGBfBXYtt6/kvq+ENjbCBTh3dv9W60rBLYUAUvmyCQ1rhNABLcvNTtTQGVmsExPBUVi1iOtrhFcRmlUBtWYp3UMAZtvMIIqE4MALNYDXtmPf/zjG17uRiYFVikLEaf0UmnHkstePxjEznKZDQERtxyP/FJLx5ZFuUS2BYfB2SvSrWWg4HoY93o4s3t0KwOieO6552bmijFlUHERZH2l7wWQXXbZZTmhGT5jtfeC1WJ75xVvdaRAm7385S/PsbLa831ussDugGzzeSPc2j8ce4gvxfenfuqnZpHubRZ5kkdPJlarb31eCBQCuxOBIry7s9+q1oXAjiJAPUSskD1kAplE2pCNTniRDyTq+c9/fqpxFDYK3XpkDqmVFis2SUi1z/nXf/3XJymWQ3CkNKP0UQ6pn+qNpG3kEIh30kknpc+UkinY7mMf+9gk64DnwkCGB6o17OBG1VT+WFVUGQgz3yyrCLxlifDZ2DLURV+aUGiPekhHRrEfO7mAZ1d3pVR785vfnBOA1ciqZw4PpJXvlvcXQTWZgOkYlRvhZ3Fh39AXyhgS3j4W4cMTLCDORMrEawpGw/rW+0KgENidCBTh3Z39VrUuBHYEASQLKUNyEDREEpkYkgxLy8glr+4rX/nKDHpCntYjuhpkaZ2SSxGmNCr3kY985OjAqXlQkEokl8pHQY0te9MXuhGyQ8X9lV/5lbRGqBsi/rKXvWy0kjmsG6Im6I3Nw0RBgBisphBxZbzuda9bCXaLTR1msb3x5Pogt4IL9Zm0cSYIVPExhFV9pWVD2pHL+9///pk3eYzvFx7ujw0q8rmeT93tzx8zXjqmvL7GDNXdmEH+u+Lcx6byEWI4eYaAuim2j/6sOhcChcDuRKAI7+7st6p1IbDtCCAgloRPO+202S1vectczkciEJ3hC8GwxG55HuGcQi7lcRVoRG1UJlJpyd6y99QDQUWmkHIECBkTmDX0hY4tE/mjMvele15TQWKCqMYQw+FzkEEbXVDHlYOMe8+XOrYsZdis4Z73vGcSZsoo36wAwLFl6E94y9XbvbPKuPrqq0epq+5/05veNOPbRtpZWkwI/uIv/mLU5AYmNqSQcsykSXaG2N55cjo27RUsKVDOeGQz4f3WLmVrmzHZx6hrKNFUbXl/YTZljA77st4XAoXA7kGgCO/u6auqaSGwYwggnF/4whfSB2lTAQRySCI6mXCm9llaRySmqHRIh4AtJAUp8QzkWvaHsSRuCJCUY+wW1FjL2WwSU8jYsCzEUJYH5E69YEDd3Qh5Zu34tV/7tcxXqyx2AB5aiu3Yg8/3BS94wUoGCwqxHLZjbQiewzLAj9ztCAgnO8IYjPSrCQX7AdUUaT/55JMnZYaQIeP000/PIEL9TaG1e95UTE2qjDfEVl/f6la3msXWyjkh0EfKFYwH6z5OjV0K8AMe8IDcze662ODDc6eM17F9VdcVAoXAciBQhHc5+qFqUQgsJQIIgGXnd7zjHZl2ypI34oAwLHpR+mwJfOWVV05SzRBa2R7OPvvsVHcRIFkV5NwduzzeAVRnBNWObTY/QMhOPfXUlRRX/bqxZ0RUTlsWDcQOMRT4NnUHM88TaCVgjpe0B73x8doUYyzZggelWio0eCN6gr4Qv7ETA89S/76zm7rwJo/1tiLcr371q1M9Vwe+X+0aS7g9XxYGqqzxxFKhvDFke9hvJmKsIFYcjBnk3USA8o7QI+VWJaR6s8Xx0H7TJ2fuke9XLuTK5DBEt94XAnsLgSK8e6s/qzWFwKYigFCIuLdEzGZg6bwTXWoaAtEJsO9cIyiIN3LKgVR7jl26EBe5d9kREMSph3tkjkBk1M0OXB/96EdHk7Hh8xCzP/iDP0gFEXnWZumz3vOe90wuj4LNa9qVWUSRZ1XA1Vii6jqKtxy5PVCQIj412I262gPm9BuMeHnHBIqpgwnNj//4jye+cuZShqfkR0ZE2TGMH5jKsqANUyc3+lX7EXZ4UmznM3AoE2asMYgxZVebEV5j2Xtp4Wx6oV/VrSwOw38F9b4Q2BsIFOHdG/1YrSgENh0Byub73//+VDaR0L4c7IykUGBZBhAexMFnVFCq7FgC1yvNLvHYxz42FVQqqtRWSMpY1bOX43qbMFA/1ceLv3Ojyh0lk6+VJQJ5RvL4VDdSnkCwM2PDDaomkoWwUqF74FRvK7IFey/vYek7L/UR7KY+MKdeyyk8xePseYLdbnazm2UZiDx1dazKrA7sC/pJO6jVf/RHfzS6z01I7OAmH7KxxIJAsR6rDve+Vg5LhGBE9TB5ePGLX5xbRXcs+7X+hhErCVLcM1IMx7RxbPwqU3uK9Hb06lwI7A0EivDujX6sVhQCm4oAP6PE/paB58kugmT5m4qKmFLMXIO48JGOUQmHlaUMvuENb8joeYqfzRdsOjGVNHdCSGEWuIQQ2nEMmd4IeVGeSH6+XYSKlcFGB9eF33NM3VzjBQ9kS4AUNRJxRrQQPruLKc/ObV5sCR/+8Idzuf/CCy/MZXYTCEFu0nfxpEq/pQx1us1tbpPqNQzHtJHaqU3dAiCjhuCusQFziP7555+fWRXg27dnHktW1ZFPF9lWf4RdOyn88yR1OEYWvbcNMpILC31ja+f1+lo/2LyEx1cwozZ00uu9OvncuC7Suwj1+qwQ2L0IFOHdvX1XNS8EtgQByiJShJxRSBECZMALIRVJjwwgGHe+852TcFAc+UgtlU89EBBBR56FTFNBpwYueSZiaVleBH4nUx/4wAcmK4e9/pRQKbd4ZGFw17veNb28Y8kdooq4//Iv/3IqorAyOehYWoL/kR/5kVTKqeVeAqxsmSvLhfRZyDZy6jtnwWk99ZY2HhLBc9K2UVy1dT0LCMIq+K6XAXP2BH2+3qFs20HLxmCCox3Ib1eo17sfoeWtfuhDH5rjCKasGRvZPQ/B127jRT36Nshj2qGeJhbu6UqvMjrx1TaWGhaHjawyrIdDfV8IFAI7g0AR3p3BvZ5aCCwlAhQwpLGT3U4EnKUIo1IiCxdddFEGpyGDyO5xxx2XCuVUla4HFPFQItO2gRU4NbUcYCJTdnxDJNX3+OOPz882UpbyBFX1/LQUY3/bWW5YHsUU+bdRgu/t6CZoD358zywQFEPEjAVAvdZ6IaDD7zsJG342fK+tSJvy9c9P//RP57MFo1GjX/Oa16RirH7vfe97M+WbwENk2b0/93M/N2qSos3IH/sCRVVfPfrRj56UH9mERGAYPDwfRiYEY0mqPumHyZYJgbooR5aLKZMkirIx21cCYDrEWv1YHEx4ivR21OtcCOxuBIrw7u7+q9oXApuGAMKAOFAyu7KLBFj2FgBma2BqHpVQDloqGKJw5JFHZtDS1IAjiiFbBCsEVQ3BYImYWg4AkCYWjJ5+CuncyA5oHUyBaspA7GBgiVvkv4AmHlqeV9vviu4/7LDD0vs53Fq5k6cDPcO+v8aU1a9FBPUP6wDizZtq+d/kBJlTlj42KRgTbCaDBjuFMt3LQsB3O5assnbICmFCgGh7vfa1r53kPe59QxG2M5v6Kwf5nZoCT65hqjmchrjCr/9tbPMHn3jiiTnJG050el3qXAgUArsHgSK8u6evqqaFwJYhwIpgEwDL7n252w8/Iko1tINXD9RCiof5aGVTmEo4kF0bOSAulvkplFJ9CTibSiwQddH6iCcCQ7VDppDzjRxInAwGfbkbDsgRtc/GE/BAJA8JOwHih3QhkZ1IdsK00fMwi0AnsEMitla5/XrXDJXgRfXzmawYyB/lWjDaIm8yPCizJgDGA6LJJ00lHXu41i53MFU39gzK+KLnrVWmyRD7S+8bHuJPf/rTo4m3sinN0pT1YEs2ERt/UMStMAwnezDktRa4iPRPHZtrtaW+KwQKge1F4AYeF/+TrKMQKAQOUgRi84EW/s8WimiLFFktyKiJcAti0mLZuL3kJS9pQQRaELEWGQFaKKktlqJb/Pi32L2sBXlosXTfggyNQjCIaAtVrkXQUYtArBae2BbZHto555zTgsCMLsfDIrNAi8j7FnaCFsStBSFqsRlClh9qbwvCMqpOLlKPyDec5Skrsiq0IGR5fyi9zcvfQZhaBF8lRr6c/18o3OaPIOItvMX56t8rK2wYzXehnCbeoaS3O97xji1sIy2IZouAtrxG3eYPzw2S2iLwqwXpa2FHyT6Zv26tv4PctQh8y76FlT5UF/0R2SSyrZ/5zGdaTIZabPncYnLR4BqTnhaK8br4qndsANLC69uUE3aVFvaVFup4i7RkLSZXa1Vvv++0N4L3WmwV3SLIrgVRbZG3uYWNpYW1JvHb74YFfxgfT3rSk1pMtlpYFfKeCNpr4edtQaJb+K5bZHpoYevJsaQIuMSErMU20C0CBlt4h1tMqhaUXh8VAoXAMiNQhHeZe6fqVghsMQKxzNwi2CxJSSzXr/zI+4EPJa3d6173aqHsJaEIv22LQJ4WS8ot1MEW6ZtaeECT+EwhLh/60IfaU5/61CTNoZAmwQsFrYVyOokAIdwIcwRhtYj8T+L3X/7Lf2lhkcg6jSHgiKt2I/sRkNW0EclEapU/PDpRRYCQ31B4WwSdNSQ1FO8kRp0Y92v7/e4xYfByhOKZpM9z1fPQQw9tkZathZrYwnaQ5BshNjlAGhG1RQdS7P7YsGG/a9TfxAUh1iZk03uk2LWdpDsj3OrXD21Qj0iblgTfpCLUzSSHyPjjH//4JH7I8lqHso0VpNREQhtCUW5nnXVWO+yww0aT1OEzwn6RY1X7kNywa7SwHexX/+H18+8j13OLAL8kzIh77OSXbdGHcIBP5ANuYV/JSVQo2yu4hpKf/RxZJfK5/q6jECgEdg8CRXh3T19VTQuBTUUA0YsMAi1ysqaiiPw5kNdYvm+xzNsiEKohNsgfJTeCoBrSEfaDJJqUXd/PE7zVKorExcYL7bzzzkvlMoKg2gknnNAiyKpFUNdqty38PDZxSCL18pe/PAkkxTB23UqFcj2yqz1h42iRAixf1EvlIZgdh+FDkTfKZARcpfKJIFFGkVOKqO+QRs9d9Gz49BciSpGlLF577bX5OSIY3uAkmZ18emZ/DesyfO97x/x12gBrz6KKhlUkyRzSS8XX7kjhlcTe/b3/lOO9CU0/fAYvBDOW/bPfxyicYYFJpdTEyCQCMbVCoL8R//7M/pwxZ3VBnJ073mPKUX/km7obuaWzjNjsooU/N/sU2XUoF26Ir/4Ia0sSYJ95jjEatpYkyiY565H+MW2qawqBQmCbEIh/4HUUAoXAQYjA61//+szjGoreit8ziMgsVLxZLEPvl+JKnlzpsoIYpH/XrmhBniZ7GqW1iiXpzL/KPxrEd0PeSIFWtpQVjBWkI4Ox+Iz5Tdc75LTVHrt7aatAN75lntYgUfu9lK2+UmBJwRX2jwzWku+VRzgIZQbZBaEajYXAN5tXdB8q/AVGBclar+qjv+/1CaK2kgdYfT1burS3vOUtK/mFg8ittHn4fh4LWSYEKNqxbD2cg5RmcJ/UX3LtesmKEAR/sm93dKPXuFA/PfvZz84d1fQz76+gxlCKF94FP77mmEyt5OuFh3tlFDk+gv34xpVbRyFQCOwOBMxo6ygECoGDDAEBQzItCMjpRM9ZaqsXvehF++1W5Uc9vLorwWXyuApSQ6amHLGsngFHCKbod5kPpKVCjqYeociupJUSpGYzBjuZISqrHQilACc7r9nWVuAZEheK7Arh6yTPhg6hRGYwkwA4eYmlY1MGkhQK6mqPWfdzpE9Krz7RMMmQPmw18rVugRMuUG9kHZELlXol0K63ey3Ca3zI0mDcmDAgz6uNAZMKO8DJMwxjGSxk+Qh7xoTaLr5UYKO+tllGf8EUgZU5wndDLLXZd3e6050ywBD5Dr/49VLMzT/Nff6dGKe9r+BkvEitBsP5NHXzZdTfhUAhsDwIlKVhm5T0ekwhsCwIxA95C9KXwTmWuv3t4Nk86qijctlZsFr8uOfSruCyU089tcWPe7v3ve/dYjvcFlkL2hQPI68pL2eQxywnskG0UMky6E3Q1ZTDsnwQrhbEPK0YofKm/zW2jF24xKx9kWYsg654MtkXLOfzxva2a6tldsvUbApHH310BtAF0UlvsLZavnbdgR6f/OQnW5CorFMQ9PQD87UGIVupw2YvlQs2s6TPjysALXZ4S6tDEMP9msN2EHl6c+me11dgl2viJyuv037WBuODnzty4Laf+Imf2M+OwvLCKyvYkXVDmUGS007A+sEaMPXwfGNVv/GAD+ukrJiUZV295zMW2NaD6rTjaU97Wnvzm9+cdpxIjZZ1ixzLC+0nyuiH5/BZn3LKKRnQxtrgCPLfQu1OH7sAP/92NtKu/pw6FwKFwNYjUIR36zGuJxQCS4UAEiNYBylBhBwIFr9upJtKfy6Ch2SEwpVeXp5P/kWZFPh3RbRP+YHn4RQJHwpcRrjzggp4412dQiL5N2MpuV188cUtNsFIgsgTKpBqEZnqbYgl/PRkCtITMIaA+86ztRXJlZWAD1ggFBItcG9KG8d0MgIVanGLLY/TQ+we/lHk6ZAIgvNM34X6vB+JHFP2/DXItHbyasOfJzWU+TzHNsbpVYWBAw4wEPCHwCGpCLJgQNciyiYH/XqYCdg7LILPjAeeZoFu/MswNrEJ20Zizev8/Oc/P8nxIn/zfL3n//ZMk5ywUmQ2Ee2A4/DobfWZ55mwIOSIqaA9kysYwDfS6GWdxwZaanvsDpfPNv76geQKgDPRijRr+/me+zV1LgQKgSVCIP5nUkchUAgcJAhYgr4odkmznG+JOghdvoLsZR7SYa7RIBWzCy64YBY/7Hkt24ANGYL4TEKLZcGmBT1nrXy7cr9uZHnbUjmrgdypltd5Si1Xr2aLsPtakPvcMY1PN4jdSpu9DwI0i3RTucRti13Xy+u7ljViUuPnLrZELm+xZfWOvXqwZWgPjEJNT38on/JG6wFbthPYhHqcm4kEoc32WpLvz46fIow3c9KeccYZsyCHeR+7QhDE9PpG9oi0JISym/e53v1BerPOkWEi8dM3fMI2E7F5CRuA9sh5u5Etpzt02vKe97xnFkR8xfcMM1aJYZ/2esmvyy+sLl6RZiytOzBnx/hS7OS3mhWjP7Of4a9d/OvDfy8dv9ve9rbZXs+poxAoBJYbATP2OgqBQuAgQQDhQkY6UUAcBGaFgpWBap3MIgQID5Lhhz5yyOa2wsjglANh+NSnPpVBQp5jty/bEyNzUw9eYj5QO4chUzatELi2iGyoJ89tZAjIugu201Yv75E3pN9mA2ExSC/meoFYU+u76Pqwh+T2x7Do9Zk/I2xhE0iSt5HAQBMVgWUmBjbJ4JlGDj0HURs+z98mNJGaLr29Qwz0HWxD4c0d+BDxPmnpZbhfX5iAhNUld59DgE0kEGyTm8gKMXmS1LEzkTFm7dCmDZ5n7NryOVTcJLbGJvLtOy9/80gbY50sCzr00tfDNvbnrHY25hBmGPU293OvSyjyWe5qk67Vyq7PC4FCYHsRKMK7vXjX0wqBHUUAKUFGkNj+wx2pxTIAZ0gcKXKR0zYD1fyw20KX+jlVcUQ6Ysk3CSZSItBn6q5sHTA7wVGZBXmFz3QWy+QLt3xFPGxRLEMAskfR7G1FdsN/OnvMYx6T1wh6Gqv29Xps9Aw79QobQBI0dVIf7UHAOyn1uf6J5fJU1KfWD6kTZCgwcEj0lasvOxbOyCOyi9T2yc6i9iF+lFHkjyLe6zosTwCkfqGkwlxfvfGNb0zFfFGZYz4L/23umkf97vW/z33uM3vve9+bGR/UyQ5uguK6Akv1D79uBq4NSbs2TiG77g37T07W+hhC7vu/nd72sKLk9sZ9J8Ix7aprCoFCYPsRKMK7/ZjXEwuBHUHAD7h0Sn60/Vh7IaGxCURmL+jECrlBzNgc/LgjG5Gjdk1CtKhBlMbYBS3vRxgOP/zwTIm1ESVMdoTIW5sKI3J47LHHpi1inqRpI2WXit2JfW8rYinFWOQenoU/NRVA12/XYXvd5zznOUnCkTfYU2BtsYzMP+95z0usOrHbt2/fLHa1W9WusVq9kUSEHuHV9r7UP3zf+5WNAanrfb9amT53jbJlQkA6e1q1jq/n9GexaBhXG53c9HoYd5GreWWCoO/DT76fHQappvp3Imq1gjVjfmz0MsecjQsTvAh2S3VXG7UpfMGZzo1C39ttUkE9lgHkQJ45pl51TSFQCGwcgSK8G8eu7iwEdhUClse7RaH/WEtDFon4V1Q4P/RSLcXOZ2l1QGqoskjwlEM58r3Kk4uIUFVj++KV50wpC4mI3a3SgoBcdOVwkS3CZ1Rs5KQTR22lOiIrsWXsmum0ptRr6rXIGzLWJxwIaWyxnMSb8kiBZNPoZAr2sYXvZMKrr2KDhfStansnof29/rDsH1kz1k3ltqiNJiy83JRV1gLl9bL7s+RYls5t6riZfx47jDFrwuQlbzJ/cT+MDfYFVgt1oDBbmdjIakQv01m95Vw26TCOtAvJl1ovtkVOC4fn9Zf0ayYPm5lLeVifel8IFAIHjkAR3gPHsEooBHYFArG9aybN9yPtR9yLeuZHvCt8cpha4mYFQMwohRshDwiDRP/dKyyX6UZzll4XXmJEBxG0dK0dlMZ5ddaS8plnnpne0a729XZGiqxZbBl7wATsQDoaeeNp7f5duVyppV0VlF+254pVbwq1pfspijhM5FGmePbndAyc9T3rgQkEJXwew7Htcx/iqS94oU1EOvnzHD7kZz3rWXnNRp+hLjCLzBFJdiniJjsmbv0wzmLr65VJAsVcnQ6UaBtfsdtg/hvQHpgJnOMJjm2H04s+HGMmVCYrH//4x1f6s9exzoVAIbAcCBThXY5+qFoUAluGAMJhOf2II45YIQadBLE4+AFHeBEvO6whSwgMQnbNNdeskOGxFaRyXXLJJSuWiNg2OJeYpxC3/iyKrcAztgp1ojzbOKET9H4d/zGrwiHhpxwSEe2k7LIwdGLZ79nOM0xe/epX58YelEoe2Pve9777EUJL9RTFXv+phJeCzEZAte8e297P/cwSYOOQYTaOA8EB7iwFfRe+PpnSVzb36F7ajT6jE17laVOkn9sv4FE7IiVYEmLfGx+C3ObHx5Tna5OdBK1K6AuTNn7xSE+WEwRWHc+x41rvK2dqt6wmB0q2p9S1ri0ECoHxCBThHY9VXVkI7EoEEF5eSqobQtKXnUWe2y5XgJofceRWxLkfeJYAW+9StKYcniWNEzJHYUSwKGNTszv0Z1IrkVgkkdIn+8B8WYgsEnxoZAdAjLrS6B6ZCpAm7dvJg7pt5zE+YvWDPRI1xNcSOhKFnLrGxIMFYy2iDm+BW3aP45G2tK/d7qeI8mEL4oqcxxnEp7/tSrZWmVNw8nyK65ve9Ka0SfS6ez7CjvQeiLdV37HFaJO+paL2tGLOUs71gDbjBKYmdxs9jJPLL788sYSfl7Hcn9nLpZDLONKx1l71kMmC8g2XOgqBQmC5ECjCu1z9UbUpBDYdAWoXhRPZQnY74eXjtGTOP+oHHRlCmBBVQV+2/Z2qlCEbrAy9nHkVc2zjEAYZFGJHtyQdyPrrXve6hbYIy8/8oq4ZEi7kiGVgGRQ3E47Y1GPFv4sMyniALCKf1MPHPe5xK4QYgZIZQ7+t1gcw8j2VnqrbvcH6N3aMywmL4EPL7IgjTzUytllkt/eleqi/QELt6n3gbJVgntj3+8acbSHNpoBYKs9EzHMovTy1yu+k07PlDEboV8NsvWf2fuKfptryBAsonM/uYHJoxQQh1lde3rOkmKRsZDVjvbrV94VAIXBgCBThPTD86u5CYOkRoCJSFzsh8uOMPPBeWkbn0bXcfoc73CFVNMQBSVkUFLZWY6ljSLIAHqQZUVH+Rn78PZvvlzdSXSmUVNx5sobYIHRSfVEAXetFpY7d2DKPLEK200fsOpYZIpAi9YMP5VIeYLmETQyQq07sLM/H7nAry+jz9bfsjsxS5BH9YdtZSEwOkGETEGRNH8Buq7BQbuwgl17r3kbjTDupvCZUG3k2nzGV32St9y11nKe2pz/rn8NOOraN+mitTFwUm7KYLCgL6fXvxgrIfN2tMggMNLHrtgb1UC+rCvqnjkKgEFguBIrwLld/VG0KgU1HAHm0rD1c7vfjTA0Tbf+GN7wh1TJEggXh0LAGDAPZxlQIIUCwLDEjawinHcU2sryMmMWWtqneIRMIOMK4qCyBapbzu7qrXdp5u9vdbkM5bMe0dSPXsIewF3RCq57IoA0bEN8heYOfNFf6Zl5ZhDMCJrsDBdsyei8TTg95yEPS9sHbupUEdxEGxllsPZ1eVnXqymdsO5z1Hdo3Ft2/6DOTKN5kxL5P2GA3JJn+9rLRBX/ydRHkOFXhdf073/nODOKEv2cJkFvNjqEfpJizSjKsiz61KkHxrqMQKASWC4EivMvVH1WbQmDTEaA2iWRHQoaWBsFGFFnR6MgComgTCgR43ie7XqU84/Wvf/0MuUEYqIyyIkwlHpRIZPuoo47KJWLE46STTlrVdypAiapHVexWje5NXiaVjWLevaidCDrrEyQJYfM30irNli2BEUTEqh/sD3L2UoX5R00qkC336V+ZKGzZ7LqpuPdnHMhZXT/60Y/mSoH+UC99QvUU5DV1xUBdlAkH5b7gBS9IEiqwT7YOkwKZIGDr9ZrXvCYtLFPHrucYcyZrPNT6xFkQ5FpjyISOb7j3gfZ6r25sNnUUAoXAciFwA9WJ/ynVUQgUAnsUgSAaLQhoi2T8LYhQtjJ+nFsESbUgEy3IQgtPYgui2h74wAe2SLbfQnlsrhlzBEltkekhy3nb297WgqS28J+2U045pQUpG1PEyjXqGgFQLbINtPCbtlBqW6RJa5GW7HplhfrXwqPbgiC2IL7ZtiAcLbblbUG+W/ham7+X4YgNJFoE3LVQrhPXWApvoU63IKdEh5Uqhg2khUrbIvdsC9V3pQ9CMWxBylpkAWjhEW0RBNfgrn0xSWlB/lrYIppyY+Kyct9Kwdv0JlKrtciq0SK3cwslugVhbbFqkP2nT0KRnlwT+ITS3UK1Tvz0tTaGBacF4cz3Co2JQ2Jm/I0du+6DY6wg5LgLYp1lhIe9PfnJT24xSWlBgF12vSPSn+XY/PznP99CTc/vPVed9LfzlHpc7wH1QSFQCGwqAkV4NxXOKqwQWD4EViO8fuRjubhF6qgklwhieBZb+GWTPIxtSXiA8wc+lu1beC5beIOTmN35zneeRDiR8VCFkziHPzXJUuTVTUIbmzS0UEH3qxJyFUF3LbyUK+QqlMV23HHHtdgcIInWfjfs4B9hx2ixPN5CgU2CFj7nFhtNNG0YEt573eteLTykSe6RJUQKMTZZiY07WqjvLdTDJPe+D99vO/HEE9sJJ5zQInfyquRsu5quvmeddVZ7+9vfvjIJQU5D9Wz6VLv1ozZHgFi2Q73123qH8WEsm+houwmB+zqpdJ4fI+uV6fuw4mSdP/jBD+b4RVQjKK5FzuQWKx+rlhmWkxarD0nCkWaHOmiPf1tIs7bXUQgUAsuBQBHe5eiHqkUhsGUIIAnh4b2ewhvBRKnMIl4U3Xvc4x4NwQw/7AqJWK9SsXzcEIUIsGqxjXAStVi+bpGRoMXy/OhyECCKbuyS1SLgKgls5HZN4hDpuRYSOSQwbBlJrpEgZVD3KNTh5ZxE2tdr54F+r26RLaJFPt7EhPLtb0TJd/2AWSd/vqO8X3755S2sDA3Bouy6nhofnuAWmQraIx7xiOy/ZVGzqdCIedgykrAjgcZUWABaZFhIEnjddde1CJRMMh+7z6WiTaHd7sP4NTkKO0SLrCDZH1RyuN72trdtkeM3x14EsCXxhTHFGrHWhkhD1q688soVhVf9I8AuFfewWyQp3+421fMKgUJgFQTif551FAKFwB5GYOjhDfKR3sr4wc4AtSBX6SGVJSAI66SMCvyV0kbJpiBoTOCVHdEEr031kNqYQUYH/scgFRkhLwAqyPqqPSP906Me9aj9PLB8rQK6BDvt1gOu8JBGLNTbzBrQ/bqw8T7U80yXFQrxZKy3GhcBhne5y11WgiSNNRkPYjKVnlhZQaQVE7DHs8yjLR2Ydm/nEROKWZDVzLnLd97/bfg3wXccSm96pQWhCfDknbZtddh2ctth7eFZ5/nVxv7y7yAU9zX9v9vZznpWIVAI/CMCpfCuMhGojwuBvYLAapaG3j5+USoh9W2KKmtpnaobwVItcp+mZzZyyaa6NWUp1zJ4BM+1SD/VIlI+1bPIcdoiXVeLPKurqsS8rNTg2NUtPZ7xv7RGiaMuUrRX8172di/b2ZI9Ty/ll1WD55d6SPn2HaXUMj7Fm/WEZYTS63Nt9+pHkK982z/r5/698/CaRd8Prx37nte2+2H5q6nU6kcZpZYaK+9+97uz36jVPL482lTeCBRbaYvr1c/YcD9MXNvraXzBxN/9s7F17NdZ2Xjuc5+bCjq/cS/L84aHvyMQMuujXhRcdYuJZCrU8yp998K/7GUvy2uHZdX7QqAQ2DkEivDuHPb15EJgWxBYi/BaPhecw6/IQtBJ0HoVQw5e/vKXN0FqrAVIQGyAkH7aTlzWK6N/zwNsGTyU2fRoIkaISKiEa5LWTniRXqQDGRHA9a53vatFuqgkSv0Zu+GMgD3vec9LXy8rAz+0oEJEz6GvYre5dvLJJ7db3/rWaR+BO2I/H/wWGzTk9YiiZfteRsfBPUgcMmfislHS2MvrZz5lhDdy4Wb9O1H3PbuJevNpe2av04Mf/OCcaPlOvZBmY0gbvvKVr6Q1RRDYsJ779u1Lsol0Dolwr8eYM3wFAvr30esCh3nCq6xFny/6zLUIr39P/n3onzoKgUJgORAowrsc/VC1KAS2DAE/6Is8vB7Ix/uMZzwjVUOEZMzhh/6rX/1qi2XeVMeQGiQVWYvcsJMC1TwP6aAwI0sUWgFDvJEIz1rHFVdc0WKHtVR4EV5HLEU30fOyHSDAu+lA6sKikdkIEFU4e/XDZIR/VKAa8utvxI8fOOwPK4qn6wW+CfQzmdBXSGQvz32U4lvc4hZJ7j75yU/mve5zzSLC5ztHr0+/Zni998Ya5RZR733Sr3U/ZbZ/3suyquDoyqnPtU//wUF9KbDu6/cgldRfr/5ZFjLhP8pzfz96OcP6Dr+b/9z185+5vhPeUng7enUuBJYDgSK8y9EPVYtCYMsQQECkJZORATl1+KFGLgUSPeABD1iXXA4rpzxpxyxNW25HdiNvbhJVquHUQ+YCdgppp2QpUKcxCi3CS93tCi8CgmywRiDQSNNuOqQsgwPlsZOvfl5ErLRNexFCKq5r+/VIMHKJ6HrNK5jIpGscVNJ+uH+1Z7mml9+vGV6/6Dv39Gv7/f3vRdf371zrGJa/6O+86P//z3x5Y64fPm/R/b38+XqsVXYR3o5anQuB5UKgCO9y9UfVphDYVAT8UFNODz/88FwC7sTHD/1NbnKTFlupphd0it+Vb1cKMkvwFFVKbwSujSKpixonZReVlypIsYxAoFHWCkvj1NzYkCBJm7ZRqc8444y0aexE1P+i9o39jDpqGRxhl3dX33USpowhOVutzH59v3bR3/07Z6oq3IaE2efIMIXd9/1616ljJ8v9c8/w3kQIee6TKnXs3/X69r+RdOOvj7v5sla71+f9Wu9ZWJShbsaNusmEof7S7FFxqd9IP5uIdn72s5/N1GbqYlLEPoGkulb7ev5g5fej17v/7bzoM58rSz7rUnihUUchsDwIFOFdnr6omhQCm44AIsBji/B2UuMhSMO+IJcXX3xxbgqAKIw5kBrL7jYWQBDudKc7JcFcz2+7VtmIg3p6IS9DQrPWfQiywKjHPOYx7Qtf+EISLe2w8YScr9qHWO2mg7prEiLnrjZJ5+VAPKXLWg8bWDpWu873MFKeYEUbQcC9e2Hz5vgP6wSrQQ/W8rnreIX10ZAI93vk1aW6w95718+Twv58vl2TJM9Zra693OF5vjyrFP3odWJT0EZlu96ESl3kMzZJYpcxjo0NwXLyTsu3ixTbRMKEQ8ox9/RDOWwgzkO7yaK6d4W3PLwdvToXAsuBQBHe5eiHqkUhsCUI+HGO9EkttknNH/ThQ/wwU0dja+FR2RkEgwkus/SOICGUrAMIJ+K06Md/+LyteI/wslMMN3DQrgc96EFJXLo/dCuevRVlIlR8t14wplLDFckc67Fer169PNhQOD1zqMq6H2FkiXAeHsik++c/dw3CKABSloye9WB4r/fu4682jiiw2rXeoW5WE0zYbFwxfPZwzA3fz5epDBtM2JXPbmryNvOb852bIMEWDiYc559/fnvFK16Rn/m3YRVD2donsHIYPDf/HH9rk50B/XvZiMVnUZn1WSFQCGwCAvGPvI5CoBDYowiECjqLTSD2y1UbP94ruXiDsM5iq9Z1c6DKrRs7R2UO2FDGMvdubDYxi3RkO5oHNvy/syBBmbu3tysIUeZQ/dSnPjUpr/CyDIFQFhPTIJd5DrK26WfP2OwjSOns3ve+9ywmHJmTtveHszETQXSz2BBk9tu//duzII+jHh/q7CxWE2byRMfGKLPLL798cp9qq3zFsSFK5opWF/V8z3vek3meh1iolzEd/vTZb/7mb2ZOafd6xUYZs7A/rOTb7e1T3vCl/eGLn4UaPqqNdVEhUAhsDwJmtXUUAoXAHkUgbAezUJpWfujnf6RjWXsWKaTWJa2xA1puLoFMxvJvlhlK1wwp26kjlqVnSLcNDNSrEyvkIxS7WaSGmoUtYEfruFPYbPdzjbPTTjst+yIUzv0Ir/4Iu0ESztgtbvSmIMgnchx2nNwkJRTpWWTlGH1/x0DdhuPEphLve9/7cmOIIdnt1xvTNi7x8t79f/iHfzgLRTjHVSe3w/HWP3O28cTxxx9fG1OxIjQAADhNSURBVE90QOtcCCwJAmVp2ASVvIooBJYVgfhBb7EbWmZpGOZqjR/rrLIlV5sB2FZ4tfy5lpLvfve7pxdYeaecckr6IKXHGi4vj8HAUjdPpTyttsq1dB//L1y51dKyDRUse6/lWQ0i0kKhSw9yKHErvsreLgVKyyXrwemnn9727UI/7wooS/6GXUB6ONtC877qG0fvV2PE1tW279W3Y7NnsBfwwZ533nlp74gdz9IKYeONseNOXYKsZlYRvnO2BB70s88+e8WqsB687A8vfvGLW+z8l2PXGD366KPTr/zHf/zH+3l9lcVSIw9vBa2th2x9XwhsMwJLQryrGoVAIbAFCFCw2BFsgdpV0KEyRY2LPLyziFxfqPKyRLz97W/PrVbdf9Ob3jTVsSDBk2sbQUOp0D3rWc/KJeXIFZvL3JS7/vr+7//+XA6+8MIL11z2jhRms9htbBakO7d2DRKVNobwna4sL2ub7WEjCGlGjYZFHZuPwJe//OXZfe5zn1Rxh0qnceYVk6pZBIalLWBsH0SWirQURFDkTN+yCURmkMk2gfBBz84999yZcWX8xs59uYW2cT3mYCcJn3iqu+qhfbbPfvaznz0L4p3bJw/b3BXeE2pr4THw1jWFwLYiUJaGbYW7HlYIbD8CoarObnOb2yQx7CRk+CPNzxjpva7njfRjH+rw7LDDDkvSYVn6qU996iwi8BeS47VaFumeZqHwzW53u9vlsnekvFrxFQ/rgqRG5P0slMD0V65W5oc//OFZqM65xIwMxS5xs7POOmsWKmC2s5eJpESe4CQ5LBDaVMfmIRAK/SwCH2eRYmxlQtWxN9Yi6G5229vedha7r83Gkky10788t8aCPtS/7A3sBWMPfR1ZF5Ksqodxws/Oazx2HPAQx852WQ/tUg6yG1km0tqDRPf29jNLQxHesb1U1xUC24dAEd7tw7qeVAjsCAJUrtvf/varEl4eWGQRkR0qcJHhYRZR6TPk1I85MokAjw04GjZWYBwPJDLQSQIiQ3H7oR/6oVQB++dIL2+xei86qH/qFTaFLIt6F5kiZpFyahYbYmRZnXw4Iyk8lYKUqMzDNi4qvz5bHwEYIo6xtXSOC57p+cmUftS/lFle6rEkU7+HzSaDEZVB/T/ppJNm+n3KgWBHxohcnVDOzW52s1nkpB49fo3z2IUuybaxqYzI+5srHpHZIYn4cJz190V4p/RSXVsIbB8CRXi3D+t6UiGwIwhYzl9L4UU8qbii0JFcB3KC0FDn/NhTxyKFUy4pb4QwChIS7NZJLXKASB933HEzAXFHHHFEkiME6cd+7Mdmr3rVqxYGJ3l25HnNJXJ1ig0G8l7R+wjO7/3e781iV7mVIL1OQiJtWl7367/+67Pwho4mXzvSYUv+UIFcJhexBXT2FbIL53nCKzhMdgWTJAFgYw79G7l80yKBOCr7Vre6VdoKPHfsgazGhhOz+93vflmG7AqC6ii2Yw7jH0l/5CMfmVYNbVOGfyOCQG9+85vvN5b7OHMuwjsG4bqmENh+BIrwbj/m9cRCYNsQQCD4c/sP9Dwp6T/UvLCxEcDsq1/9aiqgiEHsqJZqqXv4FaX5mkI6ho38rd/6rf0i+D0X0eaHRJwiP+osNgHItFURpDSLLYsXKrHsGa6n1rmfOhx5U5PIaCvCLp0UktSJWG8jcoyAvf71r5+xN3RyP6xnvV8dAfhSX6+77rrZiSeeuOKL7fgOxxYv9R3ucIdUatlZxh4mZ5EDN/tVGdR7Y2Nqiq+vfOUrs+c+97mZWYTCf//73z8J8FiVuavDJmAmaV4sNLJMaLsUa73d8+civGN7u64rBLYXgSK824t3Pa0Q2FYEKGsUVP5bhCRiYvPVyUk/IxdI5Atf+MJcOpb7lCrshx5xfOc73zmLLVs3XHeEReASMoAg9Of6m3KGuCLcVDVL18jV/EG1E4Ak7y4Sw9LA54mADa9HsORRvfWtb53X9Wc5x+5bSYaf9rSnJTFG7MeSoPn6HCx/wxYBjIwEObmQY5ZibmwYTx3f4dgygYpMCJOsDMYqK4NANZMTYxZRZUOYMtFCyq0odD+3oDkrBtow5tBe9p7IxJDjRzsFa1522WWpPnc7w7DtHQNndS8P7xik65pCYHsRKMK7vXjX0wqBbUXAj/wZZ5yxonb2H2ak0w/5UJ1CIpENAWyReix/uKmogtooq0NSuZFG8GHyYw6f2d+zJ0QqsrRRLHqOz1gskGbXellulkN4kadYFgn2hVvc4hZ5bX+Os3ZGyrP0FF9yySUzWQbGLrlvpN27+R5Ek+/5N37jN2b3vOc9Z4dE1os+aYGl8dSx7WPL5MmYYU2YgmvvX5OSbmXQh1OUeEFtFP7YIS3rqa8PPfTQJOuLxtWivjEJ0t6u7iLeAtWsCjizavi3M2x7x8C5FN5FqNZnhcDOI1CEd+f7oGpQCGwZAsiCNGAIoh/orsL50abC9WX/Tlb8WLM/+N6PN/WVZ3FKdPyixiDe7ATIg3I7WUCoKWIUtMc+9rGreiypvqeeemqSEPcLHkJW11KdffeBD3xg9vCHPzyXtgUd9XY6I0PUYuRI8BVSf6DtXNT23fgZoksplS1BQCO1fDiGOo5DlbOPLQGHlPjVlPpFeFDZY/vrHAfIJPXeeEAyxxJV5X7pS1+aPeEJT1gJVLvxjW+8nzd90bOHn3kWf7LVBv821EXA5zXXXJMTwZ6KTPuHbe94OJfCO0S03hcCy4NAEd7l6YuqSSGw6Qj4AbckLA8vothJiWVppETKrq5WDX+0vafUWVLmqzzQ40Mf+lCqg8NnUfIEmMkDjHAiK6vZC+QC/uEf/uGsk7pRdy2xr0eGKIyu4/tF8DvZVgYs1Ec95ASW6YHXuEjvLJVzEyWqOzXcWOiYDYne/Ht/97zOU2wIsngYk916I+3X7/zO70zuC4qwQEuTG0GRVjcEKa43Tvr4Zr256KKLVtKsmfC9973vTZVZqjyTJDh0LPr74RnhPb52WuuQ1rkQWBoEivAuTVdURQqBzUfAD/21116b/twh2ZQqyoYUPJPUVd8hg8MXwvDGN75xMulY1Aoe4O/5nu/Zr3wk/Mwzz0wVUSQ/Yi5XL78lm0EnKQiraPuuDlsuF1A3dbmcl5lPeYhDb6/P5HyVIQLZUl8kbMozFrV7t3wmny7/tEwcvKs/+ZM/mVk1KPAdI2fEztlyPzIsr/JwlYDt4aMf/ehovyx8YGyyoUxElfdWOjEK85TD9r/y7AooU28TpI985COjxy9F+tJLL511jy7iakMNft5nPvOZK+n5Oh6wMKaNm+G/n7I0TOm1urYQ2D4EivBuH9b1pEJg2xHgb5X0H3n1A02B86KQ/umf/mlGrrMadG9tV6r8qLM1fOITn1hVdZ3SGOqtILihQoYYICUUOcQJgUKCvZCublegzlIZkQobECC7q2VxWK1OyDNCPcxHPFQnh+1GrD2H99MyO3V5I5ttrFaXZfpcgB9VFMmnYFLBEb0+KRhi5DNZEx73uMclMeSfFpzVJyL6KLYYnpy6jm3CRAPZlbruSU960ppq/yL82FGe8pSnrKRJ492WQmxK3mWTLnmcjUvjQXsuvvjifPVJYR8nzsaS4Ee+8uG4LkvDoh6qzwqBnUegCO/O90HVoBDYMgR4eG3B23+QO+GVDgwJ5a21g9WjHvWoFQW2/6jzbApemxI0tFpDEG87clki7kqh5yBRiE5/+dsL8RE8hIQgQ5bUteH5z3/+hvPo8iIPLRxDMtfb3M/qQCU8JIK0kCeEEKGS0kxw1WrWi9Xavyyfs2t87nOfy+2WWQ+OOuqoJPdsHd220DHoY8XflEwYIMfXRVYMfSMfMmz0HbxMTOS+nWJlMAbZZrqVgUKs3LEZFTquAtW62iyDhAmT1GRj+4mab7WhrwAY+4gs2w/frjZ2XJwRf5uf2MxEphAqd/++LA29V+pcCCwXAjdQnfgfWx2FQCGwBxEIstpiObaFdaEF6TTBzVaGMtdi+bqFitVcE7l6W0Smt1e+8pUtVLG8Ln7AW+zC1uIHvUUu1BakpwVZXRWlUFFbKIYtfJAtyGILctuU0Y8gN+3FL35xC29mC5tFi0wKLchR/zrPQRxaLG23UINbpLVqYb1oH/zgB7Puxx57bIvNA1qQ1hYEZL/71vtD28PP2V73ute1UANbkJgWO7+1WL5uERjVIgCuhcWjBdHaryj19wpC2ILItCBTLUhwi2Xspq779u1rD3zgA1uQxbxP3bV9pw99ANsguIlzKNQtlPFs69e+9rXEHyaxjJ/938eFc29zrAq0IIAtAvvave51r8Q9Ahqz3e6LvMkt1Nm8P9ThFpORxBNOY48XvehFOTbDZ5vPCYW13eUud2kx4VlzrA3Lj9zROVbCB57tDRtCe8hDHtLuete7juoL4zZyP7c3velNLVTrLFq/RtBci1RkLWwR2cY+lv07eOITn9jCc5xjKWw4OX78O3IEWW7HHHNMe/nLX96CyOdn9Z9CoBDYeQSK8O58H1QNCoEtQ8CPMOKIaCI/ndiE1zHJZPgd89nIZ0SitwhUapGDd4WIIpYInutjV7QkfYsqq9xQ/tqb3/zmFsn5kyg/+clPbkhTPxAwzwiFtEUkfL7Cn7tSJ0QxsgG0yMCQhCd8pS2Wz5OUxUYSWbdYRk7y2clHL3utM0KDDCH9sRNbtgHhj8CidpOb3CRJ+pVXXpnkDRlXN1jNH8i+l3qGopmkO6wgTd06AVd3bXANkhzWiJVrp9R5/tmr/R3+18QPoQ2LStY71NcWVpSceCDwYQ3JSUxYOvK9tvWxEApoFj2sW1hZWqSna5FtIeuPfEae5GyPdrsnArlarAo05BnZf85zntNgajwNy1qt3j6/6qqrkjjGhiZ5T6wm5MQqMius4LnW/f27yLmcz49tgLOeJkXh+R5dl1ClW6yCZP8j8tp/+OGHZ7+FcpzjzxjSLu1/0IMelP8eYPL5z3++xcYnSXj1haMT3pe97GVFeHsn1bkQWAIEivAuQSdUFQqBrUJgNYU3lufb6aefvkIKENYIEmqxRNti84kWVoLmR96BzMWuWUl4qVqLSA1V+C1veUuSyvDXNsSUmooQDg+qIuJLgURoEYxOwj0H2VE+EhQ7ZSUJcT3CHWnJUpFeS2UePqu/j+XqFqmqGlLr+bFjVgufaBLVsElkO5HCCJRLlfdjH/tYQ8Qpe0ik56tjJ3LDs7ooo3+GLHXChviEDzgJtTb5u1/nHBsiJEFDPinsVEXXIVX9iGX5Flkyrqc8+x7x/MxnPpP1g7+Xz5Bc9+n7Tm71pbb73rM75v3sM8olVZRai+xS9/WffkHg+31ILoWTYuwZlHITKqp5V7p7/Vc7wxTBpaoad4cddlgq8Ig25XzsgcQbJ5EFJHEwPo1rZLRPQtYqCybhcW9hT0jVG176MPzkTdmUZ5jBKby9LVLcJeGNoL7sT2OGOmxlxOqG6/Qz1b8I71rI13eFwPYjUIR3+zGvJxYC24bAUOH1494Py/tDwutzP9aIXqRlyh/wIRm1hG/5n73B8ra/ESAH8oJUUpIju0GSnkc84hEtkvSvqnAhYIiEVz+Uh6QgHeH3TfJMrUTEkArPRSamHNocgUdZFypoeE6TtCAuwzYoUztcz3phmTy8zfkemULOfb/e0ZVfbfFiB0CEkFtErmPmTP2OAL1sb/hqU0lHMOcJr37Qj45+v/ewo06qV8fT5/oRhs5eiw7lWG73PESVGk3JRXgjS0JaN5DX+cmFiUH4eFsEa+VYgaH3LATsHsP6LXpu/4zSzxLhjOSbgCGrLCHzz+z3zJ+NjQgqbBGclsQ0vN45PiOH7n4rC/P3Df82sULWTfS6lccYgwUyC8d+RHBljkuTAbYNbdW3JnaRASQnGfqhCG9HrM6FwJIhEP9DrKMQKAT2KAKCfxbttPbUpz51YaaDIFaZzSAIa6ZbCvKRwThBRDOwKJTeWfzAZyR+h0wGA8FcItmDJGXgj9ylQRb6JaPP7pFNoedS9fxQyzJFWBC80eX0Cy+//PLZkUcemZkHBL3ZlEDarLXqJk1WEJkMelKXUDD3210MFl7qtt4ryE8GvzmL/h++ZM4INTEDwgRtBfHLvwX29VcQysR9eN/wfZDj/eoQJCz7a7V6+V4f7YuNHQSZSdUm361gs5jsZCqwINAdvv3O8Lcpg9zJ2uMZAs6kA1sLz2EhQQhnUqCFQpztVYaNQZQL9ymHMWaTC/0Kh5NPPnkWKv7CnfcWlWs3PoGItrUOBXsl6ExZyuwY6mvZRKTLi8nHSro8Zcok4nObtfQxoX/C3jE5rdqiOtZnhUAhsHkIUADqKAQKgT2KwFTCi5C4xwYMETy0ks6s//gjOiLpEUlpzUIVm0VQ2SyC2pJUhoo5+9mf/dlZLHvvRwzGwiv6PzyRSbaRs1DaMi2UDQHUbcqBvIefM9NLISM2l7DBxdjduzwPmY/l9mwbDEJtzkwP8tQiOT2Nmh29ROd3nDbrvB6BnX/O8Hp9hTAjYJ0Y+z7U5lkoskkyYQEnJHc9fI0LGRRkQVAewh7K+yRihxgjqgikPtG/trJGHKcccvTqWxMGdYF/+McXTuJWK1cGEFtpm2woY4hdx9Xn0pN5Vqj+18v64N+AHL0dE/cV4V0N8fq8ENhZBIrw7iz+9fRCYEsRQGbOiq1hKVZ+0GOBKV+UrdVy2SI+iOf73ve+WdgI9lO/lCGFFdU0LAyzsD/kpgER/JUERromW/6GNWByu5ChCGSa2ViCCok8R+BbKq2rqY5rPSQCilZy/yKqYbHIDS3GlgUHBLmnqkJkpLuSmkvu2LBKZI5jeY4ppSYCNk2QxsqWxZ6J1HUi1c9IFEUROeqfrXbu/eXcr3E/Mjt8wV2KMGnXvNRB30k71nPcul99bBOMdE5RVPWNjUoQZXXXN8qG8RQ8jTnb9qq7dkh7R1meot7rF2PTBMY4QbyN5+siXdrYuphAmaRR1dWjYzuPM0Jti2ObciyqI3XbqoGx0csw8SmFd61/mfVdIbAzCBTh3Rnc66mFwLYggHgipV197D/KaxFeFUMqqG7yjCJvftC76uWsvAhqyuVgZKsTVGSK6uX+qYctjE866aQkIcpD2uSMHUtihs9D5iKQKBVABA1Rs4nGFCKuPu5DqOBG1Y1UU2nnUD7S1F+U0gggm11xxRW5u5fNKtwbHtkkVDBDNuFI1YSp7yiwzsgxpXH4gsGQFHvvM3YHOLN99BfS5ZmIuN3FvCiYJh82lOhleZbNEmzUMLaPXGd73gsuuCD7HEE0wZG/meo79jD5shrgXmVos8nDVHUX5saJiZdyDo0NQqw4KH/sIW+vzUU6LvM4+1vfsNOsNQb1O4UXru7x0sdFeMf2RF1XCGwfAkV4tw/relIhsO0IIItIECI1/FFfzcM7X0FLx9Q05K0rlv2HHdnoL59ZVqYmTyEe/XmIE28tIogYIpm8kVMIVS+LGqnNyCCya/cwRIsvd+yhDBtlHBIbT6gP/GAWQU6rEnAKIELthcQhYZbukSo4mRjA0Q5gH/jAB2aRAm4W6bxye2e+6BNPPHHGO91fvKWUVGQbvlR66i2MI71aEjFkzMsmC57Zn+/MKxsBWSsEUxuQX37dRWrlatjoA8TUs7VFOXZbQzynHCwBEZiWbVKO3f6mbA7hWcg31b17Zim0dsNbZDdYrW7Gp00l5idxfTKovxFYdb366qvXnCSZCNjAAznu/y6K8K6GfH1eCOwsAkV4dxb/enohsKUIIDZsAhslvCqHIETmgly6RQSQt/7jPjxTzHg8BQNNOZAYS+PsApRjhCPy2aZ/dqwKOXweX3HkYV1pc2xEkMvmU8qyhD0MiIrcq7PI8zq6bXC3Kxz/J7y0S514o6mrFGKElEIoEMrEIrICZD0t8V8Xy/MCwrpyqAyWBT7VsQo6b6wy2Ac6poILp0xIYGZnOR5WRA7ptktf5FqeRJq1NzY2WSHfAhxNpHw+9lAXeOlPeCLNAu/0FYI/5jCR0QddZR6OX4QXzhR4/Y3srlc/k4HYPCMng/3fRRHeMT1R1xQC249AEd7tx7yeWAhsGwKbQXh7ZRGfxzzmMalUdtVySBgEQx0ay8usBIK9xlgRkBgEUKAavyRFFhmi4iEnUw9kjlpq2R8BEUwUu2VNUorViUVAe5ShLMv58xH6a9UNIRQQRaFVhkC+yDmb3mjlr3fEjl+z2NBixXvNPmILWyR5zP3UbB5V9yG7CN4555yzqm97tfpQYFliZHVQDjJIoV6PCA7LMw5iZ70cGwgzTAS7TcFTefo2ctuurDRQ8GVlGFMXmMGEsi7rxlA572MYiWZbee1rX5uZJ8aQaGRbxgn2il5OEd5h79f7QmB5ECjCuzx9UTUpBDYdgc0kvEiDwCXL5BRYBKH/yDsjdojEIWEDoNZa/vf8tQ7KJrsBTyoSbWmYv5hKO/VAkPlW+9I78syWQBUcQxL78yiovQxtjC2Yk7CNIfC9jNhuNi0eMKGuI3gU3LH1EASHXMKV8iiQj61gDAlTBwF1gtVgoE9k3KAcj32+MlxLlbX8j6gidQK4LONPKQdJ1359izQj8huxMggQ65YXdYHxGNKsruoQm5ckJvDouPbxq16xIUmm15vibzbeeoaSXlYRXqOnjkJg+RAowrt8fVI1KgQ2DYHNJLwqhTxIOSaYDRHqS/b9x76feXBlLRDYtBZR/NCHPpR5WJEEhBcZQmymEKoOFvJDmbWErx6xiUKWtdbz+739DC9ZBLoFBAmKzRFGE03lIPHUXfVQjjpp01iyel3YGSjlXYWMDT+SwK6WVaPXvZ/ZT4455pgV1ZEFAeGcYmVQFlL6C7/wC6lwI7w8xXL2TsGTrzh2ZMsJhDJMhmIr4NFYqIc+gYkAMmXoW5hQ0deri+fHDoA5xmJTi5yU9THavdFsI4LM3vWud01WwHmHebutBvRyi/DqtToKgeVDoAjv8vVJ1agQ2DQENpvwqhgyyqdrUwbL2/LUdiLiR797IZE9yq2NL2IntuupvbIgCNyy3I7ssjTEtsaTiVmvE/W553dFxDeSesuSdyfxFNa3vvWtk4LdEDD2BwF+1F2TAqR/CtmEiQA39yPNMhKMTd2lX3hKuxJKVf2lX/ql9GAbC2MP9WUriS12V2wm0rpNCVQzTiz5C9TTDkQQadXvUw5WBKnfjA/jy3h5wxvesGZ2B2o/W42+kCoOqaXidlLqTCWWWo1SzENuVWEKRtpgEvOSl7xkpb+VW4R3Su/WtYXA9iFQhHf7sK4nFQLbjgACZlka4RjmdD322GMzsn0jSmpvBFJBdRRIFdvEps/TD35/Tie+iCO1VdCW6xA6xBaR67lUkePDDz88CdLUOiEqlvv5ZBFvy/h27xrrd9UeRDG2Rc6ALMRIG37+538+rQxjSZAyYrvm/fLewmbMsrs6IJPUQkqqCQAs4YW4jyHMrAY81siu/tYOuXilKBurLqsHQirH8u1vf/tUqBE4FhUq9Vgs1Ndk4b73ve/KBAJRlQ5sSl0QfRYXpLX3C1sFe8h8XTzThEUGCcF61HlYwNJYHI5L2R0QeF5p7fXvZOq4g5XDBKOnrvMMz2Mh2Ygt5x9LrP8WAoXAViBQhHcrUK0yC4ElQcAP+YfCNsCLOvzRRxo2uhvasGlIAsIgNdb73//+JDnSZiGyiGcnvd1LitgKpBKYRgVFDhAqSqhUYlPIkHog3R/72Mcycl85lDyEWk5c3405ECVEzLbJbASwoorK2zuGaHoG8iVVWFer+WcFWCHd88RstTrBr6cxo2bK7yozBOI0hoxZuu9Baog/K4WMBDYRGXO/evE78yzrP1iwDvC+yvQxtm/gTtVGdqmoyKBAMROKKXUxAbjwwgtzNzvjx+u4447LlYVeF5YFfa3Pjz/++LSSCFRUdxhQyY1BkweBdwLMBA+yVbBsCHgbi81q/SYtGgLtOV6eTTmeooavVnZ9XggUApuHQBHezcOySioElg4BZEt+W2TQj3FXuRC6sZ7Q9RqFMCDWyAOVk7UAqZBPVnBbJx2dEPjbCwnxGRKMHE1VItWL0idlFgsAQoS0/v7v//5ocqYMCuyTnvSkJGfqw3uMvI4lu9pPiaRYd8IsJdmU3LBIolRYvZ/YAHiHpb0aQ8i0marp+SYR8OS35Scecz8cHDbWuM1tbrNiQZAZwoRiLBbKkOdXblr5j/WxneqQwilkV53ZIZDYPllDKk3ejDP1kTaMnQBuVHH2Dcp2H1f60nsrDBT/iyLbBOsCi4Qyxk5EtGm1w7jXNiS7P1d9+cC1t45CoBBYHgSK8C5PX1RNCoFNR8CPOq9t9z920rneTmsHUhHkzY890sgHahviTkSQgvkXonpIBDPJr3ruuecm0RtDRhDVSy+9NEm1MpAOnuIpm1UgTpRcu7ohinCSSxhRHHtQGxFF6i4ij1xNId3wQvaps+5H3gR6IWZjySqC2bM6sCJow1hluLdT6rB73OMeK9kUpP1iS5hSDsXVEr+JB4UV+WNlmbrZxWc/+9nclOMHf/AH08qgLLheF8FrPLfai9TL/Yzo6v9OOPv4MpFiSzGmZAyRfUFfjcW047LW2UTH9tdU7P5ck5baaW0t1Oq7QmBnECjCuzO411MLgW1BwI87IsNCgEx1wssrulkK72oNQS4s6wow4qu0y5fd2KiQnRz0M8KCNCBZMgMgWsjEagolosqvybMqQr4TK6rgWELjOhkNnvvc56a6i5Tzqso3PIZwazeFj7eVVxYpY9NQd8RvTD1c437qsOd7UZuvC2I3pg7up3IjuZ6PbFGXtWvM/cO+U29kW19QZfWDYENtHHtQ9wWmmThoi80yXvGKV6wZYDZftlUCQWqyS/Sxom3Kla7t0MhgYac146UTXeOoj202Cu2g/Momoj83w7owX09/m0wag8ZfH8tFeBchVZ8VAjuPQBHene+DqkEhsGUIICt8nNTDISnYDsKrUQgZhZBfkmppK12KHz8lYjCsk/dIko0ebACAcFHnbNFrKXpIIpFhxFC7kCKeWWrv2KV3ZFAUv+VoPlWESoATbydyNObQNv5lajl1GfmiKC7KSLGoPPebEPDqsmRoP8LPtzumHe7nueVfRfoFdd3tbndLT+vYNvR6SfFlGV45yCrsr7jiiklqubbYQATJ1Y8yPGgbEjyWfGsTNZZXl3Lbx4czS4PUYsYNNb5/h+j6m+/YpIqVhtWBlcdKwxTC3vEYe74uJiY8zkh2J9zIbym8YxGs6wqB7UOgCO/2YV1PKgS2HQHEiSqGJPhB7h7erbQ0rNZIaq1NHQQv8YZSJZFbRLGThX5GYKillrSPDx8noiwQCtEVCIbcyurgXmST5xX5RJjGHIiQDS96oBpyhaRMKQO2ovypjdRz9WDhQMzHHKwMFEK5h5FVZFPA39iNDxA5gW7IvucjqiYIY7NC9DrCjCVDO9Tjdre7XW77C6OxeLoOwbRBBiuBtgiaY03oAWb9eaudkWKZJrSBQqtNxmsfE338Dv9WX+OEV5yXW5CbPlHOmEnDanUZ+zk12g52yHgn4EV4x6JX1xUC24tAEd7txbueVghsKwJ+9KVfomB2woBE7ATh1XDECJHicZVui0prkwaKb8+V2gmNeiI9PqfsIafSflmyZz3wOZJhV7QpWxEjmrIOUOYsi8NGLuEPRUDUWDVQGcgckkXNRHJ4SqdkvkCuKaDd//mABzwgcRlTBzgi/pbtPR9OVFFq6pj7h4OQIk0ZVY66wGWqJUKAnh3H+IhNQpB4gYtjyD/SiKTz+SKP+kJd+njt42H4N6JLFRdgh1jrf9Yd5RjzY4n6EIeNvPccBB3pHhJek7QpPvCNPLvuKQQKgWkIFOGdhlddXQjsKgQQMwFM3WPYycNOEd4OHjVPcBlbgSwAtgB+8IMfnF5jpAuhUVckor8QU8QC+aUgInldkZSRANkZ2h76s+bPSCnFuOcAttGEpfgpBIWVADmTiUAdBE8h8PAec3TSLb8sNRt5f8c73jHaQqCd7BfdCkEpf+Mb35hZMsY8v1+jD0455ZSVyQbfLG/0lMA/pE+wIDVeWyjdj3/842fXreJD1nY2F0o2JVb/S6nG581WQiHufT4/BnzOPsBjjOhSuHl0BfiNtU30tm/WWfo56nqvc3l4NwvZKqcQ2FwEivBuLp5VWiGwVAggAbyYnUR0wrtdHt4xYCBA1ErBWwKnTj311CQ+SASS24nEojPSi/zyvlImL4rUU2wPSC0lWdle/aD+XXbZZSu7wyGa0nlRB8cSJuQKwZZ9gprJDoH8js27iiBSRKnUyJG+kXVgrJ1Ce/h8bebh+V6C3vikx7YBHny+3d+NtJtMsDaYhExRSAXNCSTrfQUXG24g5dRm9WVrMKFAcKUTe9rTnpY+YcoyOwI7RfdBz/ez9pmwIfWsDogxUu65iPmUuvZxsJnnTniNRXUvwruZ6FZZhcDmIVCEd/OwrJIKgaVDAOG48sorl8LDux44iAsyiQwi6ZbE2RgQIYFpCBVS0Un78IywuY41wpI40iVwiXVBejRkEgFTLnLYPZcU1ikbXqjj+973vtwBDdG19I54TglUUxdtQ+C0h6rJdzrWioBY82Uj+l1dRoCHxH4M1iYYNvygyqqHZXjtGOu59Qx2BJYZKrn+gMfTn/70JOSIM+sKn7L2vfSlL80cxyYn2q6/hv059OtqV59MsKyYlFxyySXp40Z0p9RxPSwO9PtOeJFdGJSH90ARrfsLga1B4AaKjf/R1FEIFAJ7EIEgQe3iiy9uscTcQtEzwc1WhqWhhR+2BfFr8SO9dC0P8teC1LRQa1uQuRaKagui14K8tyDELZTM69VZ27QlyFKeQyFuQUpbEJEWymALMtZimT1foSi3INAtCF975Stf2ULpHYVDWBlaeDZb5IJt3gdxy/sjLVkLgna9Os1/EKpzi+CuduaZZ2a71DU2AWnhBW5h5Zi//Hp/B2lvYQHI6yNzRQt1uEVatRYBdy2I1vWuX+0DYyF2VGtBQhNXWIWto8V2vJPKUZdHPvKRLYhyM9aC+LbYZSzLCELd4BwqbPZX2BhapMLL9/qvj8U+/nr/wTEsIi2yZ7TwArcgyC3IcZYdE5/s39XatROfhyrewovdwlKTbTLOjjnmmOZz/VNHIVAILAkC8T+ZOgqBQmCPImCJW/Q8Ba4rUFSonfbwToGb6kvVC7Ka2RlsfWvrVpYHCqF29bb19/NnqhvrANWwq4pURL5TXlAZG9ZTSCmrLBMUR6oohVeKtSn5jCnMgrvUpT/fjmpjrQgUWNkktEdb5KadakGgjhoTPbuD8SCVF3zH1oPSDQ+bQVjC7/hT4Y01fUOVH/ZPv6b3jed69b/5odlZXvva16YyL3COz3es8j1lTG3mtUOFV1vK0rCZ6FZZhcDmIVAK75JMPKoahcBWIBD/q2iUtiOOOKJFSrAWRCUfQ+GlKi6rwrsaFrGE3qiclEIKq1eQyFQ9fRdL6I06vN4BF0cQ11SBIxAu1dogYC28rC0IYAvLQKq+QWIaBfQzn/lMi0002rve9a7EMdKqNTj+zM/8zCjVMQhli00YWvhbU/mkhp5xxhktSGOqz+vVWVsj7VYLgtXCo9yCWLUI2mo/9VM/1YJYrnd7fq/dEeTVIlCthQ+2hae5RaaDLJOiSvXuBxU4PLepXLqOsh4bezTKsrpQ4GESpDSVzY4pDB3zf/fP+vcU7UMOOaRFerkWmToS49itLvuDWk39XvbDmNOnEXTZKNja3BVe/VQK77L3YNXvYEKgCO/B1NvV1oMOAcvMCFYE+rRQSldIyLJbGlbrqE6inL20z7I5AoygIWC/+7u/m1aI8O/mcn2/Z75MnyNfXkhtJ2KW1COIKsmwe3yH/HoG0hce3Fyyj0CtJKuI4r59+9YknZb1I1tGEiMTEKToxBNPbE984hNbZFpYefZ8HfvfSH74YFesDIhpqLtpSZhCqhC0UFBbBI0lQTMBuuc979nC85wEuj/PmU0BlqwkJhHaEIFneR+yCz/WhH50nDuOPh9izDbiOZFlIbG6y13u0hDcPtlAcGHtGJaRHyzpf4wJlpjwizd2Fe3Vt/qmCO+SdlpV66BFoAjvQdv11fCDAQGEhAoYOV6TsHRSslsJ76I+0yYv5A0hQ4CdkV8khPIWaa9SlUSKkTVE2T2rEatOvDzPNRRUWHqG+5AzSnAsw6dKHruLrRBeBDbSZuX3kfosr48cv0l4I+At+wGBjkwZ7aEPfWiSZwQWoVT28OBZ9Vze5cg12yL1WCrcyONZZ53Vjj322DW9w9pP0UXUEViK7Uc+8pFUaZXreepLbdXmISaILl9qv069evs7bsPre921xaQBZlRoCnRkY0g8eHJ971mIrvZ538sbtn03vDeeeHX5qOcV3vLw7oYerDoeTAgU4T2YervaetAhgITEBgmprFmG7qTEUvoyB61ttKO0r5MyijZlEimJrXNz+Z46+7nPfS4xoXYixv5Ggtc6lDtPyhC1/qJaeu+wHI9AOiOm7kU4w2u7svzPSoEMUzgRwNiwoYVPOes+rAdSqP6sGgL4kHnluT/SeSVZ7c91n+8cva7u1UYKMetBV2kRfofrexv63/3ejmNe+P//Z758f6s7hVudqM2RWaPd9KY3TSUX8RXYpx3e+76XP9aGMXz+sr3XfsQ2tndO5V/9ytKwbL1U9SkE/hGBIrw1EgqBPY4AVc9ScuxktbIEvVs9vFO6qpMz5+7rRXL5X/mZkVx/sxggxJRMhJiaSt3s93um952oLarD8DvvkUjn/jnyOFRKlUElRvq8EOb5Z7oGQVR39XS/cvrRLQD9GT4f1tnn/u7Etb/v9w+v72Ws1073yHwhcwJfM7IbadUyg4J2ILX7gvzKquC9cmHRyW1/zrAOu/l95D5OSwNbg4mFowjvbu7RqvteRqAI717u3WpbIRAIWNZGeCPh/36Edy8qvOt1OEKHQHby6Uz9RIIRQ+8p4jDr5DK2600LAJJMGXUP5bQHa633zPW+76RQufNHJ4jq0t/PXzP8W/sc/dpFf/fvXDf8nkIriBGR7gfrBbWWLaHbD6jX0oYh6cgvcuteh7I7kR8+p5e3187sIuedd16S3u6RLw/vXuvlas9eQaAI717pyWpHIbAKAn6I73a3u7VPfOITBz3hXQRRJ8G+QywpdT0oy2eyK7AUUMoRXoSZX5MVovs2XedAgpHnbhn4x083/t9OSJUwhkD26/u1w799RnWVHQJp9Xf/Hkljr4g0bSvKrGcitftCse3eW/cgtz6n2g7VW9cfbAdVXpaGF77whTkWtL8rvOXhPdhGQ7V32REowrvsPVT1KwQOEIFOeCm8fWl/LwWtHSA817sdCexE0JfUXGm5kFifU2Jhygox9EW71t8yGyDNwzJ8N3/4Xpmupay690tf+lJ+RiX1GQUVqaIu+8zf+lCgmaA5nlxlzBPYTniHz0RU+WltwkGVHRJewWXILouC5/T7EVoeY35knw0/H5Z9sL43QZKNIXabywA/OHTCW1kaDtZRUe1eVgSK8C5rz1S9CoFNQgA5Y2kYKrx7NWhtkyBbtxikFwlGPofEFvmkBg8tEasV5j7eXESXuopA27kMiUUyKavy1PKJxuYUqby6znNj04i0GniOMhBV5HStgyWhpwDrFoR+PbXWM33eSW3/rs5rI0DJPfvss6+301oR3rVxq28Lge1GoAjvdiNezysEthmBRYT3YAha22aYVx6HkCLEQyK88uXcG9chycgo4krt7X5dn3lRmHmLEVF/+57i6r37/c2qsN6BELuOglvH5iFQhHfzsKySCoGtRKAI71aiW2UXAkuAQLc0DBXesjQsQcdUFfYEAp3wyvBhklNBa3uiW6sRexCBIrx7sFOrSYXAEIEivEM06n0hsHkIUNcRXnl4bdKB8PJDP+QhD2nnnHNObS28eVBXSYXAASNQhPeAIawCCoHlRmCRpaE8vMvdZ1W73YEAf7UsDfLw+nfmsNnIc57znHbCCSekL3p3tKRqWQjsfQSK8O79Pq4WHuQILCK85eE9yAdFNX9TELB99fnnn99e+9rXZjChQim8j3zkIzNzg/d1FAKFwHIgUIR3OfqhalEIbBkCZWnYMmir4IMcASnoEN5LLrlkhfCWh/cgHxTV/KVFoAjv0nZNVawQ2BwE5HG18cSnPvWp2nhicyCtUgqBRMC/qQsuuOB6hPeYY45Jb6+toesoBAqB5UCgCO9y9EPVohDYEgQE0dgp7I53vGPuANZTZR199NHtpS99aeZvrbyrWwJ9FXoQIHDZZZe1Cy+8sF166aW5O58my2d897vfPUmwDUHqKAQKgeVAoAjvcvRD1aIQ2BIEENxrr722HXbYYblbl6hyx0knndTOOuusdsMb3rA2GtgS5KvQgwGBK664or3qVa9qv/qrv5r5krXZDnjPfOYz28Mf/vDMlXww4FBtLAR2AwJFeHdDL1UdC4ENIoDwfvGLX2xHHHFE+5M/+ZPcpEBRT3/609sTnvCEjCgvhXeD4NZtBz0CJpPnnXde2hpsDuKQpeEZz3hGe/SjH12E96AfIQXAMiFQhHeZeqPqUghsAQJ/9md/llsLf+5zn1vx8L7pTW9q97nPfTJJ/hY8soosBA4KBL70pS9lSjKBa0PC+7znPa897GEPq7RkB8UoqEbuFgSK8O6Wnqp6FgIbRODrX/96egqvvvrqFcJ7+eWXt9vf/vbt277t2zZYat1WCBQCn//851Phveiii9rf/u3fJiDf/d3f3c4999x21FFHjdryuVAsBAqB7UGgCO/24FxPKQR2DIGelgzh/cY3vpH1ePe7390OP/zwUqB2rFfqwXsBAWnJ5rM0ILx2X7vf/e5XhHcvdHK1Yc8gUIR3z3RlNaQQWIwAhVdask9+8pMrCq8f5Ic+9KGtosgXY1afFgJjEFiUloyH9+yzz87NJ77jO75jTDF1TSFQCGwDAkV4twHkekQhsJMIfO1rX0vCa/n1m9/8ZlZFUM2pp55aQWs72TH17F2PwCLCaxL5i7/4i+20004rj/yu7+FqwF5CoAjvXurNakshMIeALA2C1WRp+PM///PW8/CeccYZ7fTTT2/f9V3fVWnJ5jCrPwuBsQgMd1r7+7//+7zNv6kXvehF7dhjjy3L0Fgg67pCYBsQKMK7DSDXIwqBnUQA0T3yyCPbNddcs6LwPuUpT0kFqgjvTvZMPXu3I7CI8PLwvvKVr8wsKN/+7d++25tY9S8E9gwCRXj3TFdWQwqBxQj0oLVPfOIT+xHeUngX41WfFgJjERgS3r/7u7/L277v+76v/cqv/EquqlQWlLFI1nWFwNYjUIR36zGuJxQCO4pAEd4dhb8evocRmPfw2sTlkEMOadL+3fjGNy670B7u+2ra7kOgCO/u67OqcSEwCQGEl6VhqPCWh3cShHVxIbAQgaHCy8P7Ld/yLW3fvn3tqquuSn/8wpvqw0KgENgRBIrw7gjs9dBCYPsQWER4y8O7ffjXk/YuAvOEtyu8H/zgB1PprW27927fV8t2HwJFeHdfn1WNC4FJCJSlYRJcdXEhMBoBGVBsK2yntb/5m7/J+3h4/W1jl/LwjoayLiwEthyBIrxbDnE9oBDYWQSK8O4s/vX0vYuATV1e8YpXtHPOOaf95V/+Zab9k6XBZ7XT2t7t92rZ7kSgCO/u7LeqdSEwGoFFloby8I6Gry4sBFZF4Nprr23nnXdee9WrXtX++q//Oq+70Y1u1N72tre1W93qVu1bv/VbV723vigECoHtRaAI7/biXU8rBLYdgUWEtzy8294N9cA9iMCnP/3pJLyXXHJJ62nJ5LZ+9rOf3U444YTaeGIP9nk1afciUIR39/Zd1bwQGIVAWRpGwVQXFQKTERgGrXXCW1sLT4axbigEtgWBIrzbAnM9pBDYOQSK8O4c9vXkvY3AfB5erf3O7/zO9vznP7897GEPK4V3b3d/tW6XIVCEd5d1WFW3EJiKQCe8V199dfvGN76Rt7M01E5rU5Gs6wuB/REYEl55eB2C1s4999x21FFHtdpaeH+86q9CYCcRKMK7k+jXswuBbUBgkYe3gta2Afh6xJ5HYGhpGBJeWRrue9/7FuHd8yOgGribECjCu5t6q+paCGwAgUWEt4LWNgBk3VIIzCEwT3htNPG93/u97cILL2xHHHFE5eGdw6v+LAR2EoEivDuJfj27ENgGBLqlYbi1cFkatgH4esSeR2BIeAWt2Vr4Jje5SXv/+9/fbnazm7XaaW3PD4Fq4C5CoAjvLuqsqmohsBEEivBuBLW6pxBYH4Ghh7cT3n379rWrrroqvbzrl1BXFAKFwHYhUIR3u5Cu5xQCO4TAIktDeXh3qDPqsXsKgaHCy8NL4e2EVz7eOgqBQmB5ECjCuzx9UTUpBLYEgUWEtzy8WwJ1FXqQIVCE9yDr8GrurkagCO+u7r6qfCGwPgJlaVgfo7qiENgIAkPCO7Q0fPzjH2+l8G4E0bqnENg6BIrwbh22VXIhsBQIFOFdim6oSuxBBFbz8Bbh3YOdXU3a9QgU4d31XVgNKATWRuDrX/96u+Utb9m+/OUvt9lslhcfffTR7aUvfWn7gR/4gYokXxu++rYQWBWByy67LFOQXXrppe0f/uEf8t/SjW9840b5LYV3Vdjqi0JgRxAowrsjsNdDC4HtQ+Cv/uqv2p3vfOd2zTXXtG9+85v54JNPPrk9/elPbze84Q2L8G5fV9ST9hgCV155ZbvgggvaW9/61iZoTRoyQWtSABbh3WOdXc3Z9QgU4d31XVgNKATWRmCRpUGWhic+8Yn5o1y5QtfGr74tBFZDgKXh/PPPb5dcckkS3p6loSwNqyFWnxcCO4dAEd6dw76eXAhsCwKLsjRUWrJtgb4esscRGAatVVqyPd7Z1bxdj0AR3l3fhdWAQmBtBBYR3kpLtjZm9W0hMAaBIrxjUKprCoHlQKAI73L0Q9WiENgyBLql4eqrr27f+MY38jm1tfCWwV0FH0QILCK8hxxySCtLw0E0CKqpuwaBIry7pquqooXAxhDohFcgTQ9aK8K7MSzrrkJgiEClJRuiUe8LgeVGoAjvcvdP1a4QOGAEivAeMIRVQCGwEIEivAthqQ8LgaVEoAjvUnZLVaoQ2DwEFnl4K2ht8/Ctkg5eBBZZGqQlu+qqqyot2cE7LKrlS4pAEd4l7ZiqViGwWQjIw3vkkUc2Ht6hpeG0006rtGSbBXKVc1AiUIT3oOz2avQuReD/AwAA//8tqguxAAAyKElEQVTtnQmQVNX1h8+wioAgCAQ3MGiIYBR3xS2sBhM3UFySKFpqBUEjgwY1SuofQXGLSAoFFRPFEgQUhQI0iuACRlYJS3DHIGLAjSFRtoG/v2vdSTM+hu6Z7ul3+31d1fQy7917zndeF78+fe65RTu+vRk3CECgIAno47127Vo744wzbNmyZVZaWur8vPnmm624uNiaNGliRUVFBek7TkEg1wQWL15so0aNsrFjx9qmTZusRo0a1rp1a5s3b577bOV6fsaHAATSJ1CE4E0fFkdCIDQCW7dutQkTJlj//v1tw4YN5r/fInhDiyT2xpHAokWLbPTo0QjeOAYHmyBQjgCCtxwQXkKgkAgoozt79mw7++yz7ZtvvikTvDfddBMZ3kIKNL7khUBqhnfz5s1lGd4333yTDG9eIsKkENg1AQTvrtnwFwgET2D79u22YMEC69Kli3399ddlglcZ3gEDBlDSEHyEcSCfBBC8+aTP3BDIjACCNzNeHA2BoAhI8M6fPz9S8FLDG1QoMTaGBFIFLzW8MQwQJkEghQCCNwUGTyFQaAQQvIUWUfyJEwFqeOMUDWyBQMUEELwV8+GvEAiewIcffmjdunWzVatWmQSwbtTwBh9WHIgBgdQMLzW8MQgIJkCgAgII3grg8CcIFAKBr776yrp37276zzm1LRk1vIUQXXzIJwEEbz7pMzcEMiOA4M2MF0dDIDgCGzdudIJXtbypgpca3uBCicExI5AqeKnhjVlwMAcC5QggeMsB4SUECo3Af/7zH1fSgOAttMjiT74JUMOb7wgwPwTSJ4DgTZ8VR0IgSAISvCpp0O5P1PAGGUKMjimBqAzvQQcdZPThjWnAMCvRBBC8iQ4/zieBgBe85TO81PAmIfr4mEsCqYKXRWu5JM3YEKg6AQRv1RkyAgRiTQDBG+vwYFzABBC8AQcP0xNHAMGbuJDjcNIIUMObtIjjb3URmDNnjj300EM2YcIES83wqnyoSZMm1WUG80AAAmkQQPCmAYlDIBAyAQRvyNHD9jgTeOqpp+yxxx6zmTNn2tatW61GjRrWunVrVy+P4I1z5LAtiQQQvEmMOj4nikBUScPgwYPt2muvtb333tuKiooSxQNnIZAtAi+88IKNGTPGpk6dalu2bCkTvCxayxZhxoFA9gggeLPHkpEgEEsCUYJXWamePXta/fr1Y2kzRkEgBAJaCDp69Gh78skndyppQPCGED1sTBoBBG/SIo6/iSMQVdLw0ksv2SmnnGJ16tRJHA8chkC2CLz++uuuhnfixIk7CV5qeLNFmHEgkD0CCN7ssWQkCMSSQJTgHTlypP3617+2hg0bxtJmjIJACAQeeeQRe+KJJ+yNN96ghjeEgGFjogkgeBMdfpxPAoGSkhJr3769rVmzxnbs2OFcvuSSS+zOO++0Fi1aUMObhIsAH3NCQLXwkyZNsnfeecdt2616+AMOOMDUroxFazlBzqAQqDQBBG+l0XEiBMIgsHHjRle+sGzZsrKd1oYNG2ZXXXWVNWrUCMEbRhixMoYE7rrrLlOnhqVLl5YJ3latWplqexG8MQwYJiWaAII30eHH+SQQ8CUNCxYscP8py+ehQ4da3759EbxJuADwMWcE7r//fhs3bpzL6G7bto0uDTkjzcAQqDoBBG/VGTICBGJNIKpLw+9//3vT1sK0JYt16DAu5gQQvDEPEOZBIIUAgjcFBk8hUIgEogTvzTff7ASvfnalD28hRh2fqoMAgrc6KDMHBLJDAMGbHY6MAoHYEkDwxjY0GBY4AQRv4AHE/EQRQPAmKtw4m0QCCN4kRh2fq4OAujQ8/fTT9u6777r6eL+1MBtPVAd95oBAZgQQvJnx4mgIBEcAwRtcyDA4EAJDhgyxCRMm2MqVKxG8gcQMM5NLAMGb3NjjeUIIIHgTEmjcrHYC2mFN23Rr58KtW7fSpaHaI8CEEEifAII3fVYcCYEgCUjwduvWzfUGLS0tdT5o0VpxcbHrFcqitSDDitExIDBz5kzTbmvPPvssWwvHIB6YAIGKCCB4K6LD3yBQAASiMrw33XQTgrcAYosL+SUwZswYt7Xw3LlzTX14a9WqZW3btrVXXnnFtfzLr3XMDgEIpBJA8KbS4DkECpAAGd4CDCouxYKA79KwaNEiJ3ibN29uvXv3tjvuuMPq168fCxsxAgIQ+I4AgpcrAQIFTgDBW+ABxr28ERg+fLiNHz/eELx5CwETQyBtAgjetFFxIATCJEBJQ5hxw+r4E/AZ3sWLF7sMb506deywww6zF1980Ro3bhx/B7AQAgkigOBNULBxNZkEyPAmM+54nXsCTz75pD3++OM2a9asnbo0zJs3zy0Izb0FzAABCKRLAMGbLimOg0CgBBC8gQYOs2NPYM6cOfbQQw+5XrybN28ua0uG4I196DAwgQQQvAkMOi4niwCCN1nxxtvqI6Da3VGjRtnYsWNpS1Z92JkJApUigOCtFDZOgkA4BKjhDSdWWBoWgdQ+vFu2bCnL8LK1cFhxxNpkEEDwJiPOeJlgAmR4Exx8XM8pgdQ+vKk7rVHSkFPsDA6BShFA8FYKGydBIAwCO3bssA8++MC6du1qq1evtu3btzvD2XgijPhhZbwJjBgxwsaNG1fWlqxGjRrWunVrI8Mb77hhXTIJIHiTGXe8TggBCVy1TJLgLSkpMQlg3bS18IABA9haOCHXAW7mhkD5tmQI3txwZlQIZIMAgjcbFBkDAjElIIG7fPly69atm61fv95KS0udpRK8xcXFCN6Yxg2zwiAQJXhbtWpllDSEET+sTBYBBG+y4o23CSSwdu1a6969u61cudI1xxcCBG8CLwRczjoB9eBVh4bXXnutrA8vgjfrmBkQAlkhgODNCkYGgUB8CaiUQYJ34cKFZRleanjjGy8sC4fAc889Z3/5y1/s+eefLxO81PCGEz8sTRYBBG+y4o23CSQQ1ZaMGt4EXgi4nHUC2nTiiSeecIvUtm3bZjVr1rQ2bdrY3Llzbe+99876fAwIAQhUngCCt/LsOBMCQRBA8AYRJowMkED5Gt499tjDOnToYNOmTbPGjRsH6BEmQ6BwCSB4Cze2eAYBRwDBy4UAgdwQKC94mzZtameddZYNHz7cGjRokJtJGRUCEKgUAQRvpbBxEgTCIYDgDSdWWBoWgfKCt3nz5ta7d2+7/fbbrX79+mE5g7UQKHACCN4CDzDuQQDByzUAgdwQQPDmhiujQiAXBBC8uaDKmBCICQH14VU7MvXh/fTTT8t2WmPRWkwChBlBE0DwBh0+jE8YAQRvwgKOu8kiIMG7YsUK69ixo23cuLFsp7Xzzz/f1Rm2bNnSioqKkgUFbyGQJQKXX365qTXZl19+6T5b6szQo0cPGzVqlDVs2DBLszAMBCCQDQII3mxQZAwIxJSABO97771nnTp1Mm1Aoa2Gdevfv7/deuut1qxZMwRvTGOHWfEnMHDgQHvmmWds9erV7rOlRWs9e/a0e++9l0Vr8Q8fFiaMAII3YQHH3WQRkMBdsmSJdenSxb766quyDK82ntB/1k2aNEHwJuuSwNssEujTp49NnTq17LOlhWonnniiTZw40Ro1apTFmRgKAhCoKgEEb1UJcj4EYkxAGd7ly5db165dbf369TsJ3uLiYgRvjGOHafEn0KtXL5sxY4Zt3rzZGas+vEcddZQTwfThjX/8sDBZBBC8yYo33iaQgBaradGaFq+VlpY6AixaS+CFgMtZJ9C3b19Xw7tu3bqyGt7TTz+dGt6sk2ZACFSdAIK36gwZAQKxJlBSUmLdu3e3BQsW7CR4yfDGOmwYFwCBAQMG2OTJk+3jjz92Nbz777+/XXnllXb99ddbvXr1AvAAEyGQHAII3uTEGk8TSkB9eJXhnT9/PoI3odcAbueGwBVXXGFTpkyxzz//3GV4DznkENOvJxdeeKHVrVs3N5MyKgQgUCkCCN5KYeMkCIRDwAteZXi3bdvmDNd/ymR4w4khlsaTgNr7TZ8+3TZt2uQMbNeunQ0bNsz9olK7du14Go1VEEgoAQRvQgOP28khELXTmro0IHiTcw3gaW4IqAWZFq1t2bLFTdC+fXu75557XBtABG9umDMqBCpLAMFbWXKcB4FACPga3oULF+5U0qD6Q9qSBRJEzIwlAQRvLMOCURCIJIDgjcTCmxAoDAJqS/bRRx+5Gt4PPvigbOMJShoKI754kV8CErwqaSif4e3cubOR4c1vbJgdAuUJIHjLE+E1BAqIgDaeWLZsmevD+9lnn5X14UXwFlCQcSVvBBC8eUPPxBDImACCN2NknACBsAhowwm1JZPw9X14qeENK4ZYG08ClDTEMy5YBYEoAgjeKCq8B4ECIhC1aE0ZXmp4CyjIuJIXAgjevGBnUghUigCCt1LYOAkC4RDwbcnowxtOzLA0DAKUNIQRJ6yEgAggeLkOIFDgBBC8BR5g3MsbAQRv3tAzMQQyJoDgzRgZJ0AgLAJRJQ3U8IYVQ6yNJwFKGuIZF6yCQBQBBG8UFd6DQAERiBK81PAWUIBxJW8EELx5Q8/EEMiYAII3Y2ScAIGwCFDSEFa8sDYcApQ0hBMrLIUAgpdrAAIFTgDBW+ABxr28EUDw5g09E0MgYwII3oyRcQIEwiIQVdJADW9YMcTaeBLwgnfr1q3OwPbt29s999xjnTp1Yqe1eIYMqxJMAMGb4ODjejIIRAleaniTEXu8zC0Banhzy5fRIZBNAgjebNJkLAjEkACCN4ZBwaSCIECGtyDCiBMJIYDgTUigcTO5BKjhTW7s8Ty3BLzg3bJli5vIlzR07tyZkobcomd0CGRMAMGbMTJOgEBYBBC8YcULa8MhgOANJ1ZYCgEEL9cABAqcQFRJA4vWCjzouFctBKjhrRbMTAKBrBBA8GYFI4NAIL4EogQvi9biGy8sC4cAgjecWGEpBBC8XAMQKHAClDQUeIBxL28EKGnIG3omhkDGBBC8GSPjBAiERWDDhg3WrVs3W7RokZWWljrjleEtLi62Jk2aWFFRUVgOYS0EYkIAwRuTQGAGBNIggOBNAxKHQCBUAtu2bbNZs2bZRRddZF988YXt2LHDudKrVy+7//77bd9990Xwhhpc7M47gXPOOcemT59ufuOJNm3a2KBBg+ySSy6xunXr5t0+DIAABP5HAMH7PxY8g0DBEZDAfe+99+yss86yd955x7Zv3+587Nevnw0ePNiaNWuG4C24qONQdRE499xzbcaMGebbkrVt29aGDBliZ555ptWpU6e6zGAeCEAgDQII3jQgcQgEQiZQUlLiShoWLlxYVtKgLg0DBw6kpCHkwGJ73glElTTcfffd1qVLF/rw5j06GACBnQkgeHfmwSsIFByBdevWWdeuXW3FihVlGV7akhVcmHEoDwTo0pAH6EwJgUoSQPBWEhynQSAEAqrhffbZZ61v37471fDSliyE6GFj3AkgeOMeIeyDwP8IIHj/x4JnECg4AqrZnT9/vl188cW2atWqsgwvXRoKLtQ4lAcCXvBu3rzZzc7WwnkIAlNCIE0CCN40QXEYBEIlsH79euvRo4e99dZbZTW8CN5Qo4ndcSIQVcN7zz33WOfOnanhjVOgsAUC3xJA8HIZQKDACWzcuLFs0ZpKHHRD8BZ40HGvWgj4DK/v0qAMrxatIXirBT+TQCAjAgjejHBxMATCIxC1tTCL1sKLIxbHj0CU4FWGt1OnTmR44xcuLEo4AQRvwi8A3C98AlGCl0VrhR93PMw9AV/S4Dee8DW8CN7cs2cGCGRKAMGbKTGOh0BgBCR4tbXwggULjJKGwIKHubEm4AVvakkDNbyxDhnGJZgAgjfBwcf1ZBDwglfdGkpLS53T1PAmI/Z4mTsC6oBy3nnnua2FEby548zIEMgWAQRvtkgyDgRiSoCShpgGBrOCJqANXfr06WMvv/yy+ZKGww8/3C1aO+2006jhDTq6GF+IBBC8hRhVfIJACoEowXvnnXfalVdeaY0aNbKioqKUo3kKAQikQ0Abuvzf//2fLV++3P1y0rBhQ+vVq5fddttt1rJlSz5X6UDkGAhUIwEEbzXCZioI5IOAL2lIreEdPXq0XXTRRab/pLlBAAKZE5g1a5YNGjTI9bdWbfwee+xhXbp0sT/96U/Wpk0bq1GjRuaDcgYEIJAzAgjenKFlYAjEg4AXvKk1vH/84x+tf//+1rhxYzJR8QgTVgRGoKSkxO1g+NJLL5lqeCVwO3ToYMOHD7cTTjjBatWqFZhHmAuBwiaA4C3s+OIdBCyqpIE+vFwYEKg6gdQ+vBK4p556qj366KO2//7780Wy6ngZAQJZJYDgzSpOBoNA/AhECV768MYvTlgUHoFUwat6+AsuuMAtWmvQoEF4zmAxBAqcAIK3wAOMexDwJQ2pNby0JeO6gEDVCGzatMkJ3BdeeMGVNLRo0cL69etnAwcOtHr16lVtcM6GAASyTgDBm3WkDAiBeBHwgje1hhfBG68YYU14BN5++237zW9+Y3PmzHEbuuy1117Wu3dv+8Mf/mD77rsvJQ3hhRSLC5wAgrfAA4x7EIgqaaCGl+sCAlUjsHTpUrfw84033nBtyerUqWOdO3e2kSNH2oEHHkiXhqrh5WwIZJ0AgjfrSBkQAvEiECV4qeGNV4ywJjwCK1eutL59+9rcuXNdhrdmzZp20kknmVr+HXzwwQje8EKKxQVOAMFb4AHGPQggeLkGIJB9ArNnz7bf/e53tnjxYpfhleA9/vjjbdSoUdauXTsEb/aRMyIEqkQAwVslfJwMgfgToIY3/jHCwvAIjBs3zoYOHWrK9G7fvt0keDt27GiPPPIIG0+EF04sTgABBG8CgoyLySaA4E12/PE+NwRefPFFUy38kiVLXIZXfXhPPvlkGzNmjLVq1YoMb26wMyoEKk0AwVtpdJwIgTAIRJU0sGgtjNhhZXwJvPrqq3bDDTeUlTQUFRXZkUceaffff78dd9xx7LQW39BhWUIJIHgTGnjcTg6BKMHLorXkxB9Pc0NgypQpNnjwYFuxYkVZDa+2FNaitbZt25LhzQ12RoVApQkgeCuNjhMhEAYBX9LAxhNhxAsrwyBw33332YgRI2z16tWuhrd27drWpUsXe/zxx22fffYJwwmshECCCCB4ExRsXE0mAQnerl27mgRvaWmpgzBo0CC7/vrrrWnTpjTIT+ZlgddVJDBkyBDXkWHt2rW2Y8cOt2jtlFNOcYvWWrduTYa3inw5HQLZJoDgzTZRxoNAzAiUlJRY+/btbc2aNe4/ZpnXs2dPl51iR6iYBQtzgiGgHrzjx4+3DRs2uM9VjRo1XJcGZXhZtBZMGDE0QQQQvAkKNq4mk8DGjRtNmadly5aVZXivueYau/XWW91Pr1psww0CEMiMwC233OI6Mqxbt84JXpUxXH755ab6eG0zzA0CEIgXAQRvvOKBNRDIOgFfwzt//vwywav/lIuLi61JkyaUNGSdOAMmgYB68GqTiU8++cQJXv1act1111m/fv2sXr16SUCAjxAIigCCN6hwYSwEMicQ1aWBtmSZc+QMCKQSGDlypGnh2kcffeQWrXnBe/XVVyN4U0HxHAIxIYDgjUkgMAMCuSIQJXhpS5Yr2oybFALTpk1zZUG+VAjBm5TI42eoBBC8oUYOuyGQJgFf0kBbsjSBcRgE0iAwduxYu+OOO+zdd991pUJe8FLSkAY8DoFAHgggePMAnSkhUJ0EvOClhrc6qTNXoRO4++67TWUNH3/88U4lDQjeQo88/oVKAMEbauSwGwJpEvAlDfPmzXP/Mes0anjThMdhENgFgdtvv90efPDBnRatDRgwwKjh3QUw3oZAngkgePMcAKaHQK4JeMFbPsOr/5zp0pBr+oxfqAQkeKO6NCB4CzXi+BU6AQRv6BHEfgjshgCCdzeA+DMEKkEAwVsJaJwCgTwSQPDmET5TQ6A6CPgaXhatVQdt5kgKAV/SoK2Ft2/fbixaS0rk8TNUAgjeUCOH3RBIk4AXvOVLGth4Ik2AHAaBCAJsPBEBhbcgEGMCCN4YBwfTIJANAlElDSxaywZZxkgyAUoakhx9fA+RAII3xKhhMwQyIBAleNl4IgOAHAqBCAII3ggovAWBGBNA8MY4OJgGgWwQ8CUNqTW8N954ow0cONCaNm1qRUVF2ZiGMSCQKALU8CYq3DhbAAQQvAUQRFyAQEUEvOBNreHt06eP2yWqRYsWCN6K4PE3COyCADW8uwDD2xCIKQEEb0wDg1kQyBaBqJKGM8880x544AG3spwMb7ZIM06SCFDSkKRo42shEEDwFkIU8QECFRCIErz9+/e3W265xZo1a0aGtwJ2/AkCuyKA4N0VGd6HQDwJIHjjGResgkDWCPiShtQaXnVpUA0vO61lDTMDJYwANbwJCzjuBk8AwRt8CHEAAhUT8II3tYZXXRrow1sxN/4KgYoIUMNbER3+BoH4EUDwxi8mWASBrBKIKmmgD29WETNYAglQ0pDAoONy0AQQvEGHD+MhsHsCUYL3mmuucTW8++yzDzW8u0fIERD4HgEE7/eQ8AYEYk0AwRvr8GAcBKpOwJc0pNbw9uzZ0/785z9by5YtEbxVR8wICSQQJXh/+9vfWr9+/axevXoJJILLEIg3AQRvvOODdRCoMgEveFNreI899libMGGCtWrVCsFbZcIMkEQCvoZ37dq1tn37dtfi77rrrkPwJvFiwOcgCCB4gwgTRkKg8gSiBO/RRx9tkyZNQvBWHitnJpyAF7yffPKJ7dixA8Gb8OsB9+NPAMEb/xhhIQSqRCCqhlcbT4wcOdL2228/MrxVosvJSSUQVdKgDO/VV19NSUNSLwr8jjUBBG+sw4NxEKg6gSjBq1pDtSZj0VrV+TJCMgkgeJMZd7wOlwCCN9zYYTkE0iLgSxpSF61de+21dGlIix4HQSCagATvgw8+aNTwRvPhXQjEjQCCN24RwR4IZJmABG/Xrl1Ngre0tNSNft5559nw4cNd3WFRUVGWZ2Q4CBQ+gSFDhtioUaOc4FUNrzqe6JcTtfyjS0Phxx8PwyOA4A0vZlgMgYwIlJSUWPv27W3NmjVucY1Obt68uU2ZMsU6dOhgdevWzWg8DoYABMz69u1r48ePtw0bNrjPVaNGjeziiy+2u+66yxo0aAAiCEAgZgQQvDELCOZAINsENm7caKeeeqotXbrUtU/S+Keddpo9/PDDdtBBB1nNmjWzPSXjQaDgCdx66602ZswYW7dunftctWjRwong66+/3vbcc8+C9x8HIRAaAQRvaBHDXghkSCBq0drpp59uDz30kO2///50aciQJ4dDQARYtMZ1AIGwCCB4w4oX1kIgYwJRglcbTzz11FP04c2YJidA4DsCCF6uBAiERQDBG1a8sBYCGROIErxHHHGEPfPMM9a6dWsyvBkT5QQIkOHlGoBAaAQQvKFFDHshkCGBKMHbs2dPGzFihFtZTpeGDIFyOAS+JUCGl8sAAmERQPCGFS+shUDGBKIEb/fu3d2iNWp4M8bJCRBwBBC8XAgQCIsAgjeseGEtBDImECV4jzrqKJs0aRI1vBnT5AQIfEcAwcuVAIGwCCB4w4oX1kIgYwISvN26dXMbT2zbts2drxreyZMnU8ObMU1OgMB3BKIErzae6NevHxtPcJFAIIYEELwxDAomQSCbBKIEr3Zee/TRR2lLlk3QjJUYAtqx8MYbb7SxY8faZ5995jae2Hfffd1OawjexFwGOBoYAQRvYAHDXAhkSiCqpOHcc891WwtTw5spTY6HgNmWLVvcJhNPP/206fOlrYUleK+77jq7+uqryfBykUAghgQQvDEMCiZBIJsEojK87dq1c9uiHnrooVarVq1sTsdYECh4AhK8/fv3t4kTJ5q27k4VvGR4Cz78OBgoAQRvoIHDbAikS8AL3vnz55t+itXtxz/+sfvPWo8I3nRJchwEviPwzTffWJ8+fWzq1Km2adMm96bP8CJ4uUogEE8CCN54xgWrIJA1AlElDfrPesiQIfThzRplBkoSgc2bN1txcbHbrfCrr77aKcNLSUOSrgR8DYkAgjekaGErBCpBwGd4FyxYYL5LwxlnnGGjR4+2/fbbj53WKsGUU5JN4P3333f1ujNnzjSJX0oakn094H0YBBC8YcQJKyFQaQJe8KaWNPg+vGwtXGmsnJhgAtOnT7fBgwfbkiVLysqEKGlI8AWB60EQQPAGESaMhEDlCUQJXnVnmDJlih122GFWu3btyg/OmRBIIAFt2jJ06FBbtmwZgjeB8cflMAkgeMOMG1ZDIG0CUTW8devWtWnTptmJJ55IC6W0SXIgBL4joHZkuxK81PBylUAgngQQvPGMC1ZBIGsEfIY3tYa3qKjIZsyYYSeffLLVr18/a3MxEASSQIAMbxKijI+FRgDBW2gRxR8IlCMQleGV4FUdIoK3HCxeQiANAmR404DEIRCIGQEEb8wCgjkQyDaBKMFbo0YNJ3hPOukkMrzZBs54BU1AHRnU4WTEiBH27rvv2vbt252/ftEaJQ0FHX6cC5gAgjfg4GE6BNIhEFXS0KxZM9c0v0OHDqZ6Xm4QgEB6BP7+97/bsGHD7NVXX7UNGza4lmQ60wteNp5IjyNHQaC6CSB4q5s480GgmglEZXj32msvJ3i105oyVmvWrLH169dbnTp17JNPPinLXKn0oWHDhnbIIYe4jg577rmnW+Sm95Ql5gaBpBDQ50gLPVW/K7H7xRdflGV3xaB169Z2yy232MUXX8yXyKRcFPgZFAEEb1DhwlgIZE4gSvDWrFnTRo4c6bYV/vLLL+3jjz+2devWlQned955xwnh8oK3QYMGJrF8+OGHu//g9957b9tjjz0yN4ozIBAIga1bt5p6WOszIbH75ptvmnZX0zbd+nzo3qRJEzvmmGPs5ptvthNOOIHtugOJLWYmiwCCN1nxxtsEEogSvPpP+qKLLrIPP/zQ1q5da998843pP3a9v2XLFvfao5I4rlevnim7q6yuBO9pp51mqv9VhviHP/yhe4+MryfGY+gE9KuHdlBTFvfzzz+3Bx54wObNm+c+Lxs3bnSZXR2jz4t+7Tj++OPtZz/7mcvuNm/e3L0fOgPsh0ChEUDwFlpE8QcC5QjsSvA2bdrU/vvf/5ZtjVrutLKX/j92/4YEsDK7qlls27at9ejRw4477jjTZhbKAEsEcINAaAR0nWvrbf3i8dlnn9m//vUvV7qghWmvvfaay+rq7zpON30O9OVPGd3LLrvMPf7gBz9w74fmO/ZCIAkEELxJiDI+JprArgRvFBSJVd1TF7LpP3hlu/x/9P48n/k96KCD7Mgjj7QLL7zQOnbsiOj1gHgMhoDKE/Q5Uf36zJkz7cUXX3TPVduu9/XF0N/850MLP/Urxy9+8Qs7/fTT3ZdAvux5SjxCIH4EELzxiwkWQSCrBNIRvL5kQYvWlLVS9wYJWn+bPXu2ff311070KsulEgjfjqlWrVpO5Oocid6ePXta48aNdzrfj8MjBOJEQF/iVMKjbO5LL73kNmNZvny5/fvf/3bvSwjrpuMkZvU5adSokcvmnnXWWe6XDWV1db0jduMUWWyBwPcJIHi/z4R3IFBQBCR4zzjjDFM7JYlV3fx/znqUsFWG6uyzzzbVH+qm2tzUmtw33njDiQIJgE8//dSeeeYZV9voBYHO0eK1Vq1a2a9+9StXH6wSh9q1a+tP3CAQKwISsLp2lblVbe748ePd52PVqlW2adOm79mqz4mub31OVKurMgZd6yrhSf2cfO9E3oAABGJDAMEbm1BgCARyQ0DlCOobeu+995aVJug/cN21EO3ggw+2Sy+91C240WtlbpXJSr1JNCvDq5uyuw8//LC98MIL9sEHH+zUi1T/+SvjpS4O1157rStx0Jip2eLUcXkOgeokoIWZyuhq4Zk6L+iL2z/+8Q+3GE3XuL4Q6nOhm65lXbdalKaFmeqve9RRR9kBBxzg3kPoVmfkmAsCVSeA4K06Q0aAQKwJKJv10Ucf2W233eZ+qtVr3SRqf/rTn7p2Sq2/7SHaokWLsv/sd+eQah2VDZs8ebKNHTvW9fDVuLpLMKg0QkK6Xbt2dsMNN7gSCbK9u6PK33NN4MknnzTdtTBN3RdUo+vLc/znQjboWlVtuvpPd+/evawjiT4zCN1cR4nxIZAbAgje3HBlVAjEioCythK9qYvPlL3SwhvV7FYmA6ufhNXSTPWPEhCvv/66jRs3zr32zutnYHVwePzxx11mzGfP/N/9o8SGMsj//Oc/bcqUKfb222+7TLO6QJx77rmublKZY98azZ+XrUf9jK2V+eo8oefKAO6zzz6V4pItmxgnOwR0ban9nrK5ug51bSnT67+caRb10a1fv74rU9DGERK6+lwou6syH3Ul2dW1mx0rGQUCEMg1AQRvrgkzPgQSQEDi97333rMJEybYfffd51o4ebeV7b3iiits6NChTrj69/2jxKVqhCWYX375ZVcmocb+EukSGsq0qWuEHk888UTXEeLAAw90grSq2Tb9jL106VK3Ml81zqrN1HvaZEAZai3EU1bPix1lwlXfzGYbPnq5f1QJglqDvf/+++6aKCkpsWXLlrnrQTW4Eqra4ldfViRQfaxkma4h9dKV2NViNH1B83XsEry6vlSmcN5557nx1KpPcdfCtNRxcu8lM0AAArkmgODNNWHGh0BCCEiYqNRBC4CGDBmy0+YVypbqp2S1cfJiUUJX/U21Ol5iV+dqe2OJZ4kR3SVovahVdlfZNo0l0alV8scee6wTOpmIE427YMECmzt3rivL0HNlvzW3xpYgkqjSgiQJIHWh8Lf99tvPTj75ZCeMtflG6t/8MTxmh4C+9MyaNct9GVK9rYSrYqfsrJ4rA6tY6dcJXXu6PlSKkHot6Hj9bfXq1e5Rr/1NQrm4uNi6dOli7du3L6vL1fWWOoY/nkcIQCBsAgjesOOH9RCIFQGJVZU4aGeqUaNGlS10k4DQzm66r1y50pUuKCunYyU2JWC80PUOSZyUFx5ejEjsaCGRfnpWBwr1QtV75Y/3Yyk7KAE1ffp09/O26o+1nbJEt8oxJJxS5/PP/Xj+tcS6ykBatmzpFuapBlpt2KhP9qSr/qgvG8r0qxeuOiiozlb1tsrW+jj4R82m56k3HzP/N73Wuak3dVrQFyZ1XVCpjH5BSD0v9VieQwAChUEAwVsYccQLCMSGgDJwKm+48sor7c0333RCVsZJKKosQZlU1cvqOIlc3b0gUfnDYYcd5nZw85ndV199daefojWWxImyqxKgyvZKuKjWV90hytcjP//88/bYY4/ZunXr3E/jEr7K+vmftv3cGndXNy+wNK/s0l0ZwjZt2tjPf/5zu+aaa1wdKKJpVwR3/77ioGy7Nn6YOnWqu4Z8aYuPkY9D1GhRfyv/3k9+8hPXOUR1unquEojy10vU2LwHAQiETwDBG34M8QACsSOghV9jxoxxnSEkcL3wkEhNFbiphitLevTRR1v//v1d9taLx4ULF9qSJUts9rebX2hDANVtagx/U42tMq7HH3+86wGsOlzNI1GtUgnVFc+ZM8dlmyVyo8ST5qpoQZzOk0hOnVfnyGb1G+7du3dZf1aJdm6ZEdCCxcWLF9tf//pXV2qiRWZaYKlY+etAXHXXlxo9+vc1k77MqD+0X4zmZ9d1py8nErb6JUDlKBK6WgypL0upY/hzeIQABAqTAIK3MOOKVxDIKwEJFZUuqCWZfpr22dTyRilLqlIEPWqh0C9/+Ut3T118pJ+z1e9XmV6VQEgYSRCpDMILImXptNuV6jG1sE2vJXhVI7xo0aKdegV7G7wQUp2u6nUltiV6o0SQBJkWTqkWVMIqdXMCiV71ZlVN7yWXXOJqineXNdTc6gyQ6qe3K46PEvoqQdFdItLf5LsWi+3OX3981KPKS7RoUfFVb2fVcqcKVwlTfamQ0FX5wRFHHPE9wasvQn53tPJzKJ7irEy8SmD0vLxgLn8OryEAgcIjgOAtvJjiEQRiQUAiUS3GbrrpJlcv6zOrMk4iRIJPGTcJGIldL1i1MEyC0N8ktpTtU22n7qrr1CKmV155xQlhZXx105gax4tIiSYdLzu8SNMxEk0SqJpPfYI1n55LKEt4R93Uq3XFihWupZUyzuri4Ntb6XhllCXcTz31VFMHid0JQP1dIk7ZxkMPPdQtxpNtcbuJnbKn6nCglnESlZ6lbJVwVCcL9XDWlwZ1OKioljrVP31pUAx115cifZlQCYPippsy98rEqmRFixOVuVcmX/OUZ6VzdE+9xvxcOla81ZFBtbqp15Y/hkcIQKDwCSB4Cz/GeAiBvBCQMFI5w6BBg2zGjBmuFEHvKSuobguq1dUiNglNCSe9L7FUkSCRoNFCMy1Ce+6552z2t2UOEqJaeOazvbtyVkJY2chjjjmmTDypJZWyul6w7kqoamyJPwkyiT91eJg0aZJbcCcx7G+aI50FUBJhEm4qw9CWzhK9Eo3yX+ene5PI0xcC2SC2qS3U5IvuFfHc1TzyV18WJHKVUVcdtHYk8756walHLR7UXTHt1q2bE/LyQV8iosSpxlb2XYvRbr/9dleuIlHtha5sUkxUH33hhRe660N8NJ6uE24QgAAEKkMAwVsZapwDAQikRUDiRoJUHRvUFUGvtXhNmVC1gqpsz1NlfJVtVNnEU089ZdOmTXOZyCijJJI05ymnnGLnnHOOm1fiTKLMZ4Ojzot6T/ZL+KqsQT+/q+uDSiYk2FIzn1Hnln9PQlQCV9lmtUPTjl7KdouLMtXKNkcJcM3jF95pcaCeSzxKMCpr7M9RBl3j6i5fd1WuUd4uZV4VK9U9P/vss46xygzUn1j+6+YFr2xRyYGEtjjLF4lcZVMl5iVUywtu2amMrnrpvvXWW46nxvVjyW9tVtKjRw/3ZUCxo962fJR4DQEIZEoAwZspMY6HAAQyIqAMpASUzw5KGEmE+cxqRoOlHCyBJHEmwTl69Gi3zbEvb0g5zO2edemll7pFZRKTElTlRVjq8ek8l08Smqot/uu3C620w1z5+tZ0xtExskUiVSJcWV51m1CphbLP4iSxp7/LXwl91TRrMZ5E9tNPP+2y6D7DK2ErMaq7stnKomucVq1auecaqyLhq/FVqqGeybO/zZ4rm62xvdCVDbqlCt7U57JTd2XrJXrLZ3j9+bJdmXqJX3++zvnRj37kRL9avXXs2NExqWqsnMH8AwEIJJ4AgjfxlwAAIBA2AQkyZXqHDRvmhKCEqBdoyuCqbKJfv35O9Else4GVDa+1GE8L6O666y6X8VX2V8JNHR30uCuxJvsk1nVP/SlfYlGiV3arNladBbRYS2JYfqptl8pDtCucXivTrLn8zQtK+Sjx67OtypIqa6qMq3rQSowqK6v5/E22a+HYE0884R5VdiAB7G/yR5ln+eQZ+vnkh75siEf5v/nXGkfH+9f+XL2WLfL3qquucjvpSaBnmn33dvIIAQhAIIoAgjeKCu9BAAJBEZDQUl2vhO8jjzzifn5XXe5ll13mflrXQjIJtlzcJF61eYZKLFTnqtpT1b2qPEHZZC/wUueWWFVdrLpIaGtj2a+7F4E6VudK/EpkKjOrrLJqlTWPsqOpx/qx/Xvl5/Q1yhKRqrfVVrqdOnVyXwLERedNnDjRRo4c6bK65csXdJ6yzuq6IfHtx9d5Euwq71BNtRae6bVs1V1/98fKRv9a74mb7JKAVqmJsvBamKYyj1Qh7n3jEQIQgEBVCCB4q0KPcyEAgVgRUKZx1bdtrnymsXXr1hX+hJ9t41XWoKyqhKkWWUnQRd0kBpWdVW2s6o9VRqDsqs5TVlXCUDf/qOepwlGvddN7ylp7geiP1/heQPv3dLyeS+Cq1lflA1pkJmGu7O6dd95p6kCRmjGW0FZdrgSpaoxVZqBsbOpNwlW+KPusmlz5pNpiCXllfTWn7NFNdvr5Veaiump9GenVq5drCyexG+Vn6nw8hwAEIFAZAgjeylDjHAhAAAJZICCxqE4Wythqcd/f/vY3V4usGlefIfXTlBeCeq1SBfX+VfsuL3p1vGp8JaDVq1gCWncvgP04vpZawlxz6YuCvjD4vyvz+tNvt06+4IILXBmEX+jn7Sn/qKy1OjtoDJVDKOut1yoxkRDWPKoplmDWYkWJYoltiVxfq7yrEpDyc/EaAhCAQKYEELyZEuN4CEAAAjkgIFGqcgUJQS0ak/jVa1/jKyGqulz1DVbZhBalSewqU1u+3lWCU0Ja2VotrFOJhep+1b9YItvffPbXi1y99s+VfR0wYIDrlayOD/59f25FjxLQslsiW4/KXEtg+xpgLZxTVrmiBXQVjc/fIAABCGRKAMGbKTGOhwAEIJBDAhKLEqkqL1Cdr3YhU22s7+CgHcMkQFXjq0zp7rKiqsdVZweVEKgVmDYDUfZXgjNK8KoMQ50izj//fOvatasTqZmI3RyiYWgIQAAClSaA4K00Ok6EAAQgkBsCysKq/nXt2rWuNECCVdlR7Tqm+luJXInQ3Yldb52vo9WYEtMqn5g8ebLbQENZZC981SlBglqbYVS2R7Kfk0cIQAACcSKA4I1TNLAFAhCAQAoBCV+VBegucauygHRFbsowOz1VBln1ttoeWTupqZevxldtrbK62olOW/hqLjK7O6HjBQQgEDABBG/AwcN0CEAAApUhkJrxVSs1iWAJXPXppS1YZYhyDgQgEHcCCN64Rwj7IAABCOSIgISvb4OmbK7fqS1H0zEsBCAAgbwRQPDmDT0TQwACEIAABCAAAQhUBwEEb3VQZg4IQAACEIAABCAAgbwRQPDmDT0TQwACEIAABCAAAQhUBwEEb3VQZg4IQAACEIAABCAAgbwRQPDmDT0TQwACEIAABCAAAQhUBwEEb3VQZg4IQAACEIAABCAAgbwRQPDmDT0TQwACEIAABCAAAQhUBwEEb3VQZg4IQAACEIAABCAAgbwRQPDmDT0TQwACEIAABCAAAQhUBwEEb3VQZg4IQAACEIAABCAAgbwRQPDmDT0TQwACEIAABCAAAQhUBwEEb3VQZg4IQAACEIAABCAAgbwRQPDmDT0TQwACEIAABCAAAQhUBwEEb3VQZg4IQAACEIAABCAAgbwRQPDmDT0TQwACEIAABCAAAQhUB4H/BxRkpRCK5xdtAAAAAElFTkSuQmCC	\lambda_i = -\frac{2 \pi \epsilon V}{\ln(\frac{b}{a})},\ \lambda_o = \frac{2 \pi \epsilon V}{\ln(\frac{b}{a})}; \mathbf{E} = -\frac{V}{r \ln(\frac{b}{a})} \mathbf{e}_r
+266	(a) Find the electrostatic potential arising from an electric dipole of magnitude $d$ situated a distance $L$ from the center of a grounded conducting sphere of radius $a$; assume the axis of the dipole passes through the center of the sphere.  (b) Consider two isolated conducting spheres (radii $a$) in a uniform electric field oriented so that the line joining their centers, of length $R$, is parallel to the electric field. When $R$ is large, qualitatively describe the fields which result, through order $R^{-4}$.	[]	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	\varphi(\mathbf{r}) = \frac{1}{4\pi\varepsilon_0} \left[ -\frac{ad}{L^2 \sqrt{r^2 + \frac{a^2 r}{L} \cos \theta + \frac{a^4}{L^2}}; \text{Potential} \approx \text{resultant of fields due to a point charge and a dipole with moment } \left(1 + \frac{a^3}{R^3}\right)P \text{ at each center of the two spheres}
+267	The potential at a distance $r$ from the axis of an infinite straight wire of radius $a$ carrying a charge per unit length $\sigma$ is given by  $$ \frac{\sigma}{2\pi} \ln \frac{1}{r} + \text{const.} $$  This wire is placed at a distance $b \gg a$ from an infinite metal plane, whose potential is maintained at zero. Find the capacitance per unit length of the wire of this system.	[]	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	C = \frac{\pi}{\ln \frac{2b}{a}}
+268	Two similar charges are placed at a distance $2b$ apart. Find, approximately, the minimum radius $a$ of a grounded conducting sphere placed midway between them that would neutralize their mutual repulsion.	[]	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	a \approx \frac{b}{8}
+269	Two large parallel conducting plates are separated by a small distance $4z$. The two plates are grounded. Charges $Q$ and $-Q$ are placed at distances $z$ and $3z$ from one plate as shown in Fig. 1.42.  (a) How much energy is required to remove the two charges from between the plates and infinitely apart?  (b) What is the force (magnitude and direction) on each charge?  (c) What is the force (magnitude and direction) on each plate?  (d) What is the total induced charge on each plate? (Hint: What is the potential on the plane midway between the two charges?)  (e) What is the total induced charge on the inside surface of each plate after the $-Q$ charge has been removed, the $+Q$ remaining at rest?	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+270	Take a very long cylinder of radius $r$ made of insulating material. Spray a cloud of electrons on the surface. They are free to move about the surface so that, at first, they spread out evenly with a charge per unit area $\sigma_0$. Then put the cylinder in a uniform applied electric field perpendicular to the axis of the cylinder. You are asked to think about the charge density on the surface of the cylinder, $\sigma(\theta)$, as a function of the applied electric field $E_a$. In doing this you may neglect the electric polarizability of the insulating cylinder.  (a) In what way is this problem different from a standard electrostatic problem in which we have a charged conducting cylinder? When are the solutions to the two problems the same? (Answer in words.)  (b) Calculate the solution for $\sigma(\theta)$ in the case of a conducting cylinder and state the range of value of $E_a$ for which this solution is applicable to the case described here.	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+271	Consider the static magnetic field given in rectangular coordinates by  $$ \mathbf{B} = B_0 (x \hat{x} - y \hat{y}) / a. $$  (a) Show that this field obeys Maxwell’s equations in free space.  (b) Sketch the field lines and indicate where filamentary currents would be placed to approximate such a field.  (c) Calculate the magnetic flux per unit length in the $\hat{z}$-direction between the origin and the field line whose minimum distance from the origin is $R$.  (d) If an observer is moving with a non-relativistic velocity $\mathbf{v} = v \hat{z}$ at some location $(x, y)$, what electric potential would he measure relative to the origin?  (e) If the magnetic field $B_0(t)$ is slowly varying in time, what electric field would a stationary observer at location $(x, y)$ measure?	[]	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	xy = \text{const.}; \frac{B_0 R^2}{2a}; \phi(x, y) = -\frac{B_0 v}{a} xy; \mathbf{E} = -\frac{\dot{B}_0(t) xy}{a} \hat{z}
+272	An isolated soap bubble of radius 1 cm is at a potential of 100 volts. If it collapses to a drop of radius 1 mm, what is the change of its electrostatic energy?	[]	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	5 \times 10^{-8} \, \text{J}
+273	Let a particle of charge $q$ and rest mass $m$ be released with zero initial velocity in a region of space containing an electric field $\mathbf{E}$ in the $y$ direction and a magnetic field $\mathbf{B}$ in the $z$ direction.  (a) Describe the conditions necessary for the existence of a Lorentz frame in which (1) $\mathbf{E} = 0$ and (2) $\mathbf{B} = 0$.  (b) Describe the motion that would ensue in the original frame if case (a) (1) attains.  (c) Solve for the momentum as a function of time in the frame with $\mathbf{B} = 0$ for case (a)(2).	[]	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	"E \le cB; cB \le E; R = \frac{c^2 m E}{q(c^2 B^2 - E^2)}; \begin{align*}
+p'_x &= \frac{c^2 m B}{\sqrt{E^2 - c^2 B^2}}, \\
+p'_z &= 0, \\
+p_y'(t') &= q \sqrt{E^2 - c^2 B^2} \, t'
+\end{align*}"
+274	A parallel-plate capacitor is charged to a potential $V$ and then disconnected from the charging circuit. How much work is done by slowly changing the separation of the plates from $d$ to $d'$ $(d' \neq d)?$ (The plates are circular with radius $r \gg d.$)	[]	/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGQAZADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD3+iiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigD//2Q==	\frac{\varepsilon_0 \pi r^2 (d' - d) V^2}{2d^2}
+275	An electric charge $Q$ is uniformly distributed over the surface of a sphere of radius $r$. Show that the force on a small charge element $dq$ is radial and outward and is given by  $$ dF = \frac{1}{2} Edq, $$  where $E = \frac{1}{4 \pi \varepsilon_0} \frac{Q}{r^2}$ is the electric field at the surface of the sphere.	[]	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	dF = \frac{1}{2} Edq
+276	(a) Derive the repulsive force on an electron at a distance $r < a$ from the axis of a cylindrical column of electrons of uniform charge density $\rho_0$ and radius $a$.  (b) An observer in the laboratory sees a beam of circular cross section and density $\rho$ moving at velocity $v$. What force does he see on an electron of the beam at distance $r < a$ from the axis?  (c) If $v$ is near the velocity of light, what is the force of part (b) as seen by an observer moving with the beam? Compare this force with the answer to part (b) and comment.  (d) If $n = 2 \times 10^{10} \text{ cm}^{-3}$ and $v = 0.99c$ ($c =$ light velocity), what gradient of a transverse magnetic field would just hold this beam from spreading in one of its dimensions?	[]	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	\mathbf{F} = -\frac{e \rho_0 r}{2 \varepsilon_0} \mathbf{e}_r; \mathbf{F} = -\frac{e \rho r}{2 \varepsilon_0 \gamma^2} \mathbf{e}_r; \mathbf{F'} = -\frac{e \rho_0 r}{2 \varepsilon_{0}} \mathbf{e}_{r} = -\frac{e \rho r}{2 \varepsilon_{0} \gamma} \mathbf{e}_{r}; \left| \frac{d\mathbf{B_0}}{dr} \right| = 1.21 \text{ Gs/cm}
+277	Given two plane-parallel electrodes, space $d$, at voltages 0 and $V_0$, find the current density if an unlimited supply of electrons at rest is supplied to the lower potential electrode. Neglect collisions.	[]	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	j = - \frac{4\varepsilon_0 V_0}{9d^2} \sqrt{\frac{2eV_0}{m}} e_x
+278	Show that the electromagnetic field of a particle of charge $q$ moving with constant velocity $v$ is given by  $$ E_x = \frac{q}{\chi} \gamma (x - vt), \quad B_x = 0, $$  $$ E_y = \frac{q}{\chi} \gamma y, \quad B_y = -\frac{q}{\chi} \beta \gamma z, $$  $$ E_z = \frac{q}{\chi} \gamma z, \quad B_z = \frac{q}{\chi} \beta \gamma y, $$  where  $$ \beta = \frac{v}{c}, \quad \gamma = \left(1 - \frac{v^2}{c^2}\right)^{-\frac{1}{2}}, $$  $$ \chi = \{\gamma^2 (x - vt)^2 + y^2 + z^2\}^{3/2}, $$  and we have chosen the $x$-axis along $v$ (note that we use units such that the proportionality constant in Coulomb's law is $K = 1$).	[]	/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGQAZADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD3+iiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigD//2Q==	E_x = \frac{q}{\chi} \gamma (x - vt); B_x = 0; E_y = \frac{q}{\chi} \gamma y; B_y = -\frac{q}{\chi} \beta \gamma z; E_z = \frac{q}{\chi} \gamma z; B_z = \frac{q}{\chi} \beta \gamma y
+279	The inside of a grounded spherical metal shell (inner radius $R_1$ and outer radius $R_2$) is filled with space charge of uniform charge density $\rho$. Find the electrostatic energy of the system. Find the potential at the center.	[]	/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGQAZADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD3+iiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigD//2Q==	W = \frac{2 \rho^2 R_1^5}{45 \epsilon_0}; \varphi(0) = \frac{\rho R_1^2}{6 \epsilon_0}
+280	The Lagrangian of a relativistic charged particle of mass $m$, charge $e$ and velocity $v$ moving in an electromagnetic field with vector potential $\mathbf{A}$ is  $$ L = -mc^2 \sqrt{1 - \beta^2} + \frac{e}{c} \mathbf{A} \cdot \mathbf{v}. $$  The field of a dipole of magnetic moment $\mu$ along the polar axis is described by the vector potential $\mathbf{A} = \frac{\mu \sin \theta}{r^2} e_\phi$ where $\theta$ is the polar angle and $\phi$ is the azimuthal angle.  (a) Express the canonical momentum $p_{\phi}$ conjugate to $\phi$ in terms of the coordinates and their derivatives.  (b) Show that this momentum $p_{\phi}$ is a constant of the motion.  (c) If the vector potential $A$ given above is replaced by  $$ A' = A + \nabla \chi (r, \theta, \phi), $$  where $\chi$ is an arbitrary function of coordinates, how is the expression for the canonical momentum $p_{\phi}$ changed? Is the expression obtained in part (a) still a constant of the motion? Explain.	[]	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	p_{\phi} = m \gamma r^2 \sin^2 \theta \, \dot{\phi} + \frac{e}{c} \frac{\mu \sin^2 \theta}{r}; \dot{p}_{\phi} = 0; p'_{\phi} = m \gamma r^2 \sin^2 \theta \, \dot{\phi} + \frac{e}{c} \left( \frac{\mu \sin^2 \theta}{r} + \frac{\partial \chi}{\partial \phi} \right); p'_{\phi} \text{ is a constant of motion, but } p_{\phi} \text{ is not.}
+281	The figure 2.21 shows the cross section of an infinitely long circular cylinder of radius $3a$ with an infinitely long cylindrical hole of radius $a$ displaced so that its center is at a distance $a$ from the center of the big cylinder. The solid part of the cylinder carries a current $I$, distributed uniformly over the cross section, and out from the plane of the paper.  (a) Find the magnetic field at all points on the plane $P$ containing the axes of the cylinders.  (b) Determine the magnetic field throughout the hole; it is of a particularly simple character.	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	H_y = \frac{I}{16\pi a}; H_y = \frac{I(x^2 - ax - a^2)}{16\pi a^2(x - a)}; H_y = \frac{(8x - 9a)I}{16\pi x(x-a)}; H_y = \frac{I}{16\pi a}
+282	In Fig. 5.10 a point charge $e$ moves with constant velocity $v$ in the $z$ direction so that at time $t$ it is at the point Q with coordinates $x = 0$, $y = 0$, $z = vt$. Find at the time $t$ and at the point $P$ with coordinates $x = b$, $y = 0$, $z = 0$ (see Fig. 5.10)  (a) the scalar potential $\phi$,  (b) the vector potential $A$,  (c) the electric field in the $x$ direction, $E_{x}$.	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	\phi = \frac{e}{4\pi \epsilon_0 \sqrt{(1 - \beta^2) b^2 + v^2 t^2}}; \mathbf{A} = \frac{ev}{4\pi \epsilon_0 c^2 \sqrt{(1 - \beta^2) b^2 + v^2 t^2}} \mathbf{e}_z; E_x = \frac{e(1-\beta^2)b}{4\pi\epsilon_0[(1-\beta^2)b^2+v^2t^2]^{3/2}}
+283	Two semi-infinite plane grounded aluminium sheets make an angle of 60°. A single point charge $+q$ is placed as shown in Fig. 1.33. Make a large drawing indicating clearly the position, size of all image charges. In two or three sentences explain your reasoning.	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charges symmetrically distributed on the two sides}
+284	What is the least positive charge that must be given to a spherical conductor of radius $ a $, insulated and influenced by an external point charge $+q$ at a distance $ r > a $ from its center, in order that the surface charge density on the sphere may be everywhere positive? What if the external point charge is $-q$?	[]	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	Q \geq \frac{a^2 (3r-a)}{r(r-a)^2} q; Q \geq \frac{qa^2 (3r+a)}{r(r+a)^2}
+285	A point charge $q$ is located at radius vector $s$ from the center of a perfectly conducting grounded sphere of radius $a$.  (a) If (except for $q$) the region outside the sphere is a vacuum, calculate the electrostatic potential at an arbitrary point $r$ outside the sphere. As usual, take the reference ground potential to be zero.  (b) Repeat (a) if the vacuum is replaced by a dielectric medium of dielectric constant $\varepsilon$.	[]	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	\phi(r) = \frac{q}{4\pi \varepsilon_0} \left[ \frac{1}{|r - s|} - \frac{a/s}{|r - \frac{a^2}{s}s|} \right]; \phi(r) = \frac{q}{4\pi \varepsilon} \left[ \frac{1}{|r - s|} - \frac{a/s}{|r - \frac{a^2}{s}s|} \right]
+286	A charge placed in front of a metallic plane:  (a) is repelled by the plane,  (b) does not know the plane is there,  (c) is attracted to the plane by a mirror image of equal and opposite charge.	[]	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	c
+287	A long conducting cylinder is split into two halves parallel to its axis. The two halves are held at $V_0$ and 0, as in Fig. 1.17(a). There is no net charge on the system.   (a) Calculate the electric potential distribution throughout space.  (b) Calculate the electric field for $r \gg a$.  (c) Calculate the electric field for $r \ll a$.  (d) Sketch the electric field lines throughout space.	[]	/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGQAZADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD3+iiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigD//2Q==	V = \frac{V_0}{\pi} \left[ \frac{\pi}{2} + \arctan \frac{2ar \sin \theta}{|r^2 - a^2|} \right]; E_r = \frac{2V_0 a \sin \theta}{\pi r^2}, \quad E_\theta = -\frac{2V a}{\pi r^2} \cos \theta; E_r = -\frac{2V_0 \sin \theta}{\pi a}, \quad E_\theta = -\frac{2V_0}{\pi a} \cos \theta
+288	An electric dipole of moment $P$ is placed at a distance $r$ from a perfectly conducting, isolated sphere of radius $a$. The dipole is oriented in the direction radially away from the sphere. Assume that $r \gg a$ and that the sphere carries no net charge.  (a) What are the boundary conditions on the $E$ field at the surface of the sphere?  (b) Find the approximate force on the dipole.	[]	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	E_n = \frac{\sigma}{\varepsilon_0}, \quad E_t = 0; \mathbf{F} = \frac{6 a^3 P^2}{\pi \varepsilon_0 r^7}
+289	Two conductors are embedded in a material of conductivity $10^{-4} \Omega/m$ and dielectric constant $\varepsilon = 80 \varepsilon_0$. The resistance between the two conductors is measured to be $10^5 \Omega$. Derive an equation for the capacitance between the two conductors and calculate its value.	[]	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	C = 7.08 \times 10^{-11} \, \text{F}
+290	The cube in Fig. 1.7 has 5 sides grounded. The sixth side, insulated from the others, is held at a potential $\phi_0$. What is the potential at the center of the cube and why?	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GlmOlVzZXJDb21tZW50PlNjcmVlbnNob3Q8L2V4aWY6VXNlckNvbW1lbnQ+CiAgICAgIDwvcmRmOkRlc2NyaXB0aW9uPgogICA8L3JkZjpSREY+CjwveDp4bXBtZXRhPgoGKlX1AAAAHGlET1QAAAACAAAAAAAAAQ0AAAAoAAABDQAAAQ0AAJpS5Wtr0wAAQABJREFUeAHsnQeYXlW1/rf/e5Wi0lS6EEAISuhe6SQQahJqCNICIRBBegcBJfQWIHRCCUkAIRBI6BBaKAFEBUR6r1K8totXbz///Vu45jk5OW0mM5OZ8737eWbO952yz97v2fs7692rfSmJJagIASEgBISAEBACQkAICAEhIARyEPiSCEMOKtolBISAEBACQkAICAEhIASEgCEgwqCBIASEgBAQAkJACAgBISAEhEAhAiIMhdDogBAQAkJACAgBISAEhIAQEAIiDBoDQkAICAEhIASEgBAQAkJACBQiIMJQCI0OCAEhIASEgBAQAkJACAgBISDCoDEgBISAEBACQkAICAEhIASEQCECIgyF0OiAEBACQkAICAEhIASEgBAQAiIMGgNCQAgIASEgBISAEBACQkAIFCIgwlAIjQ4IASEgBISAEBACQkAICAEhIMKgMSAEhIAQEAJCQAgIASEgBIRAIQIiDIXQ6IAQEAJCQAgIASEgBISAEBACIgwaA0JACAgBISAEhIAQEAJCQAgUIiDCUAiNDggBISAEhIAQEAJCQAgIASEgwqAxIASEgBAQAkJACAgBISAEhEAhAiIMhdDogBAQAkJACAgBISAEhIAQEAIiDBoDQkAICAEhIASEgBAQAkJACBQiIMJQCI0OCAEhIASEgBAQAkJACAgBISDCoDEgBISAEBACQkAICAEhIASEQCECIgyF0OiAEBACQkAICAEhIASEgBAQAiIMGgNCQAgIASEgBISAEBACQkAIFCIgwlAIjQ4IASEgBISAEBACQkAICAEhIMKgMSAEhIAQEAJCQAgIASEgBIRAIQIiDIXQ6IAQEAJCQAgIASEgBISAEBACIgwaA0JACAgBISAEhIAQEAJCQAgUIiDCUAiNDggBISAEhIAQEAJCQAgIASEgwqAxIASEgBAQAkJACAgBISAEhEAhAiIMhdDogBAQAkJACAgBISAEhIAQEAIiDBoDQkAICAEhIASEgBAQAkJACBQiIMJQCI0OCAEhIASEgBAQAkJACAgBISDCoDEgBISAEBACQkAICAEhIASEQCECIgyF0OiAEBACQkAICAEhIASEgBAQAiIMGgNCQAgIASEgBISAEBACQkAIFCIgwlAIjQ4IASEgBISAEBACQkAICAEhIMKgMSAEhIAQEAJCQAgIASEgBIRAIQIiDIXQ6IAQEAJCQAgIASEgBISAEBACIgwaA0JACAgBISAEhIAQEAJCQAgUIiDCUAiNDggBISAEhIAQEAJCQAgIASEgwqAxIASEgBAQAkJACAgBISAEhEAhAiIMhdDogBAQAkJACAgBISAEhIAQEAIiDBoDQkAICAEhIASEgBAQAkJACBQiIMJQCI0OCAEhIASEgBAQAkJACAgBISDCoDEgBISAEBACQkAICAEhIASEQCECIgyF0OiAEBACQkAICAEhIASEgBAQAiIMGgNCQAgIASEgBISAEBACQkAIFCIgwlAIjQ4IASEgBISAEBACQkAICAEhIMKgMSAEhIAQEAJCQAgIASEgBIRAIQIiDIXQ6IAQEAJCQAgIASEgBISAEBACIgwaA0JACAgBISAEhIAQEAJCQAgUIiDCUAiNDggBISAEhIAQEAJCQAgIASEgwqAxIASEgBAQAkJACAgBISAEhEAhAiIMhdDogBAQAkJACAgBISAEhIAQEAIiDBoDQkAICAEhIASEgBAQAkJACBQiIMJQCI0OCAEhIASEgBAQAkJACAgBISDCoDEgBISAEBACQkAICAEhIASEQCECIgyF0OiAEBACQkAICAEhIASEgBAQAiIMGgNCQAgIASEgBISAEBACQkAIFCIgwlAIjQ4IASEgBISAEBACQkAICAEhIMKgMSAEhIAQEAJCQAgIASEgBIRAIQIiDIXQ6IAQEAJCQAgIASEgBISAEBACIgwaA0JACAgBISAEhIAQEAJCQAgUIiDCUAiNDggBISAEhIAQEAJCQAgIASEgwqAxIASEgBAQAkJACAgBISAEhEAhAiIMhdDogBAQAkJACAgBISAEhIAQEAIiDBoDQkAICAEhIASEgBAQAkJACBQiIMJQCI0OCAEhIASEgBAQAkJACAgBISDCoDEgBISAEBACQkAICAEhIASEQCECIgyF0OiAEBACQkAICAEhIASEgBAQAiIMGgNCQAgIASEgBISAEBACQkAIFCIgwlAIjQ4IASEgBISAEBACQkAICAEhIMKgMSAEhIAQEAJCQAgIASEgBIRAIQIiDIXQ6IAQEAJCQAgIASEgBISAEBACIgwaA0JACAgBISAEhIAQEAJCQAgUIiDCUAiNDggBISAEhIAQEAJCQAgIASEgwqAxIASEgBAQAkJACAgBISAEhEAhAiIMhdDogBAQAkJACAgBISAEhIAQEAIiDBoDQkAICAEhIASEgBAQAkJACBQiIMJQCI0OCAEhIASEgBAQAkJACAgBISDCoDEgBISAEBACQkAICAEhIASEQCECIgyF0OiAEBAC3Y3A//7v/4b/+Z//CX/961/D73//+/DHP/4xJEnSrmZ86UtfCvPMM0/453/+5/BP//RP4d///d+tjvnnn79tf7sqzJz8//7f/wsLLbSQ1c9n2kwbv/zlLwf/nrmk7Svn0jf6yOf55psvzDvvvOFrX/ta+O///u/wf//3f23npj9QP8f/67/+K/ztb3+z8+gnfeK+9Jfvc1LACsy8HdTnGHKMtv3Hf/xHu5/HnLTJrwVX2kJfvdAe/sCkbIzQdvrCH7gXncs9KH6c68CV5+T38XvnbTmfP9rJfbiG7ZwU6qPQhrLi44PtV77ylVnGAvtoB/MArOgTfaVu9lXVzX3BjusWWWSRtuvL2qNjQkAINA8BEYbmPVP1SAj0SgQQbBCm//znP4df/vKXYerUqWH69OntFroQmJZeemkTwr/+9a+HF1980er43ve+FxZffPHwjW98o9340DaEJgoC/kYbbRS+9a1vmQBLmxHEllhiCRPW+M752cK+zz//PPz2t781MvSf//mfYaWVVgrLLLNMWHPNNcOnn34a2JdXED4/++yz8PHHH4dXX33V7ofwvPLKK1s7llxySRMA866ts4++QT7AxtuBULnwwguHBRdc0IgNfXz33XfbBOg69XbGObTtq1/9qj1P2oegC5a0B/IEJkWCuffLyQZjK+9c+spzBWf+KIwdcEWo/vvf/264+LFsv7ge0kc7aeOf/vQnu4Zt3ljIXp/3nX5SJwI9Y6qscA7jg3sttthis4wFCCDE+7XXXgsfffRRWHbZZa2dEICXXnrJxqSP7aJ70Bau23zzzcO3v/1tGw9F52q/EBACzURAhKGZz1W9EgK9DgGEouuvv94E/JkzZ4ZPPvnEBK/2ClwIPwhDCDn8IVRSx5xoGLjehSqEQ4RCiAn1I7gisC2wwAJ2jms0sg+AOjiP4witfKZNaCuWWmopE0hZwc8rXNuVGgb65sIuhIF20E/aBmlAmOb+77zzjrWd9rSnZM93LKnDj2X3+Xdv26KLLho22GADwxnsX3nlFftDCAZP6vFrvG18R4sDuYI0/OUvf2k7N30OfWXMpAkDzxPiybhkDDEeva1+rd+TccB9IBkQyT/84Q/2nLmfX+Nbrk230/en93GOkxAfM+xLF783+/jMOKTkaRg4Bulh6+OWNvtYzN7bKkr94zhjFQK12mqrGVEdPny4jYuqa1PV6KMQEAK9GAERhl788NR0IdAUBBCKMEE6++yzw69+9avwi1/8wgTqOe1fWqiak7qy9SB8ItAhdLnwj1CN8OQEJXs/6qCkBSwXxBDK6X+RhiFbV2d/z2sH/UO7gOBM3xA2P/jgA3su3pe67cien8bAj2X3+XdvG4L4gAEDjMQg3KOpeeGFF0yQLyIMtA9Bl+fFs0LD4+d626k/jzCwuo/WyDUMrOBnC23367kPpAuzHdcw/Nu//dscEQbqZG4g7GeL3zu7P+97HsacV7Q/rw7wo3/9+vUzjdjxxx9vfYWAqAgBIdB8BEQYmv+M1UMh0KMRYFWXVe1HHnkknHXWWWZyw2o2xYXGjnagPUJV0T3qClXeVj8/W5/v9/PSxxFYi8xd0ud19edsO7ytvu1oG73v3n6vj+8cS3/P28dx/hD8/TOCNH/epmw9fk+vm63v8y338uN+X9/HfvDgXP78Ptnz/Ttb/+Pc9D3SdXv9bL1wrtfj+8q2Xnfda4rqb289tAmC0KdPn3DooYeGDTfcMKy66qplTdUxISAEGoKACENDHqS6IQR6IwIIfKzcYl4yadIk81mAPCBwufA1J/2iHoS+OSkIVfzNaT0ucM5pPXPSl/Ze63336zradu97Xj15z7rouaXryY6P7DXe9rw2p+tJH8+7Jn1u1T29f35Num7fxznp/Xn3LKuHY2XX+LXpLffOtp3j3qZ0e9LXZT9zPqQNU60DDzwwbLLJJmHttdfOnqbvQkAINBABEYYGPlR1SQj0BgTQImC+g2nJ008/HS688MLwr//6r2b6gkCEgDOnpSfVQ1sondGvOcWl7vXeZj+/o20vq8ePpetmX/q739/P9e/pc/KuydvHtel60nX4sfS+9pzr7fJr6tSTd25ZPelj6fp9f9626B5F+/PqYB/nY5oEYdh///3DwIEDw/e///2i07VfCAiBBiEgwtCgh6muCIHeggC2+kQvIhrSbbfdZtFbcKiFRLCKiWBSJgyxIsofwktZqaqn7Fo/1l6hyq/Lbjurnmy9c/LdscauP694m/1Y+pnwGfz9GXCu+wdkr8t+T9fjx7L70t/9/n6uf0+fw7H0d87J2+f78+rwY+l60vdM78871+v0a9Ln+z7Oyduf3ldWT/pY3jV+PL31e2fPL9qfvjb9mfPRMBDda8yYMWGVVVaxqEnpc/RZCAiBZiIgwtDM56peCYEeiwBCJWZHTz31VHjooYfClClTAs6haaEVwSQr3EAQcETFhpo/It/gjFtW8uopOz/vWHuFqrw62NdZ9RTV35H9mIRB0oiK5OYp2Xq83exPPxOeB88AR1gKdVEPz5HP6ZKug/3pejiW/s7xvH2+ny2l6hq/Z/Y8rvVj2Xp8f/oa38e5FI6BFf2E+KbP/eKML+oHH4Rr/iBV1MM1YOTXsM2eA3acxx/XcA5/1EfhuLfJ6/H7Fm29Ho7zmTp47h2ph/YSoviKK64IK6ywgkWFKrqv9gsBIdAcBEQYmvMs1RMh0OMRQNAi0g7mR08++WT4zW9+02aClG58VpBB4CKS0K677mqrmwgqxJtffvnl05fpczsQ4FkQNYgQoPiQIEBmiz8H9iOc8t0FWMgaz2CNNdaw/UQTeuONNyzmP/Vmi9eVFnK9Pt9yjZ/H56JzOUbx40XXcE667vR33+9bjnnJ7uM7hfuBG3393e9+ZxG9vA1+rW8Js7rccstZyNxvfvObdt2HH35o497rQ/hmLH/nO98xMkwkKqJloW0jXCzncQ51QZIR9D3yUraNft+8rd+PY5AcTP945r6/qA/Zurw9ThhoN9GrVISAEGg+AiIMzX/G6qEQmOsIIGgQGhJ/BZJFXXXVVeHdmAQMTUNVYWWVUJXYSu+9994mXJEHwfMGVF2v4/kI8EwQHvEjQYBkRTuvuFDJsbRgiSCLxofY/BQXdj3ev+38x790HexK18Ox9HeO5+3z/WwpVdf4PbPnca0fy9bj+9PX+D7OpfAdcoXgDgFIn/vFGV+cg/aFcUpuBnCCaJCX4b333vPTTGvAOfwRKpZnABkhLKvncHBNjmspeGbURcm7d1vlqQ+0mXPZouF4+eWXw4033mhkMY8opi6d5SNtITfH6quvHsaNG2dhZ13DNMuJ+iIEhEDjEBBhaNwjVYeEQM9DAKGEaEgIKb/+9a/DtGnTTMAsaqkLOBxHUGIVdtiwYWGfffaxjLNF12m/EBACxQgwr9D+PP7444E8Cm+//bYRlLrEA8JAZnLI+5VXXmlkiH0qQkAINB8BEYbmP2P1UAjMVQRY0YQkPProo2Hy5MlmblGU3MwbmiYMrGRj+rDbbruFPffcU06WDpK2QqAdCDCnyFpNvpMnnngiXHTRRabRQFtRlzBA3pdddlkjDFdffXWb/0o7mqFThYAQ6KUIiDD00genZguB3oAA5hOsYs6cOdMEFYSVOmZIeYRh9913D8OHDxdh6A0PXm3sUQgwnyDpn3zyiQUZgMDfeuutbaZZ7SEMfWLSNjQMmBXKHKlHPWY1Rgh0KQIiDF0KryoXAq2LACuX2HhffPHFYcaMGeHZZ5+tDYYIQ22odKIQqEQA3wgc0olMRjZ1SDvaBuYZRYShEkKdIARaHgERhpYfAgJACHQuAu7cecstt4QXXnjBsjcT+QUn0bpFhKEuUjpPCBQjwDzCgfrhhx+2EMaPPfZYeP/9981/yMO2crUIQzGGOiIEhMAXCIgwaCQIASHQaQggoGCGRASkyy67LDz33HPmv4DTs0d2Sd8MQWX++ee3XYSMJNIO54kwpFHSZyHQfgSYQ5ghffzxx+HnP/95ePDBBy2jOvPMC+dQRBgcEW2FgBAoQkCEoQgZ7RcCQqDdCLBqiVYBMySSsmH6wL68gpBCyMmBAwdaJKQ//vGPZrb05z//WYQhDzDtEwI1EYAIEJ716aefNsJ+wQUXBOZVNoSqCENNQHWaEBACQYRBg0AICIFOQYD4+7/61a9M6B8/frxFQ0JoyStEPiLpWr9+/cL2229vK5xvvvlmmDBhgsWpR5DxVU+PkiSn5zwktU8IzIoAGjryarz11lvh5ptvNgJP0IEsWeAqEYZZsdM3ISAEihEQYSjGRkeEgBCoiQDCCNqEa6+91syQ7rnnHtMsuECSroa47WgWNt100zB48OAwdOhQM0MicsuRRx5pyd1EGNKI6bMQqI8AxJ3kiJCEyy+/PEDE3RzQSbjX5vMzu9+PZ7eEVVWUpCwq+i4EWgMBEYbWeM7qpRDoMgTIs4Bw8sADD4SbbropYFpUpFlAMFl00UXDjjvuGLbaaquw8cYbWxZcCAcroiNGjDATChGGLntcqrihCDBniHyElo+AA3feeadlcsanqIgYFO0vgkiEoQgZ7RcCzUdAhKH5z1g9FAKdjoCbPRD56L333gu//OUvLWQj0VhwtMwrCBuLLLKIJX7ae++9w/rrr28mSZAInJ2LCIMLKTvssEPYf//9w3LLLZdXvfYJgZZEAB8hiALzh2zqL774Yrj//vuNxHPMgwgATlaTkCUMX/nKV8KSSy5pgQvI2eDHHVi0gxwnD8OkSZOUh8GB0VYItAACIgwt8JDVRSHQ2QhACqZNmxaeeeaZMG7cuICWoawgqGCGtMkmm4R/+Zd/CUcccUSYb7757BKEEurDjAJCQGSldEFIWXjhhcM666wTzjnnnLDKKqukD+uzEGhZBJg7ODNjzveTn/zEzPnQKHSkuPbvgAMOCB988EGYOHHibGaFnMO8hTDcddddNqc7ci9dIwSEQO9DQISh9z0ztVgIzDUEWK0kTCOahOuuuy68/vrrlpzNbaTTDXOSsO6664YBAwaE9dZbzzQMCyywgGVrhghQEHrQMLzzzjth1KhRJvxgh02hjrSG4cc//rE0DIaM/rU6Apj9kYgNoj116lQjC3/5y1/a/BXS+DCPFlxwwbDQQguZVgCNBJpB1yDMO++8YYMNNgibbbZZGDJkiGkpTj31VDsnrTFMaxiY/8r0nEZZn4VAsxEQYWj281XvhECnIYBw8fnnn5sT5eTJky0Cy0cffZQbNtVXIr/1rW9ZFCSEkP79+5vwz7FswXSCVc399tvPbLDToVXTUZL23HNPIxvZ6/VdCLQSAswXfIWmTJliGjkIA+aB7M8rmBotvfTSYfHFFzdCQTK31157zQgDJAAyQbQyAhBsuOGGFukMjcUrr7xic97rdPKOhuHqq68WYXBgtBUCLYCACEMLPGR1UQjMKQKQBVYlcWzGDIloSHlx3f0+CCiYHq2xxhrh8MMPN0fnr33ta344d4sAdOKJJ4Zf/OIXFgoS4QdyIcKQC5d2tigCaPPInI6vwlFHHWUaPuZi2lchDQ1zcZllljHNwWqrrRYuuuii8Lvf/c78HTiPxIlrr7122GuvvcKwYcMC5z/55JNm4iTCkEZSn4VAayMgwtDaz1+9FwKVCDhZQJuAZuH5558Pd999dyBjrJs0eCUI+JgpLLvsshYBCQFlt912M6GE1cmygtAzevRoIwxEehFhKENLx1oRAUgBJkKYAmKOdPrpp1vOhTzNAvPNzZDWXHNNm49LLLFEOOmkk4wwYL5E+cY3vhG22WabsNNOO4Utt9zS5jVRz6RhaMURpj4LgWIERBiKsdERISAEIgKEPCV784wZM8zp+A9/+MNsRMGBQhuAU/KPfvSjsPXWWwcEFFYs65Q0YcCJE0JCSWsYhg8fLpOkOmDqnEYigEPz22+/baZIBB14+eWXzf8n21kn7j/4wQ/C6quvHvbdd18zWUIrAREgsRsFc6SVVlopnHvuuRaxDE0E/kQQhuOPP77UJOmqq66SSVIWeH0XAg1GQIShwQ9XXRMCc4IAq5mQA6IW3XHHHRaqET8DVjPzNAtEMtp1110DWoVBgwaZgzNkwZ2bq9qCoOKZos8888yAnTX7MGXCZILISu44XVWXjguBJiEAUSB0MSZC119/vZkhIfTj+Jydi/PMM09Ya621LGwxGoM+ffqYszO5Gcj8jMkfUc2+/OUvh5VXXjmgfTjllFPCN7/5TYuAJMLQpJGjvgiBzkNAhKHzsFRNQqAxCCCEIIy8//774aGHHrIQqo888shscdzpMITAzZAOPvhg0zAg2Le3oFEgWzSrppgmEQce8wtMJiAMBx10kAk4Vb4Q7b2vzhcCPRkB5gXkGTNACPU111xjeRKYo9kAAmjjFltsMQtfvMUWW4SBAwfad8yPLr30UnNUxn8B0k9kJAIR4Gt09NFHm9kgc1mEoSePBrVNCMw9BEQY5h72urMQ6LEI4OCMCdLTTz9tDs44JLMqmRVQEDAI1YgN9HbbbRcGxPCpCPQILh0paDUQWCALJKLCuZMVUO4BccAuO9uGjtxH1wiB3oAAZAHfoXvvvTdcccUVNicg8swTSnouoM3DpOjAAw+0EKlo+tAiYFL47rvvhssvvzxMmDDBoh5xPRrBE044IWC2BMF3HyMnDPJh6A0jRG0UAt2HgAhD92GtOwmBHo8AggRC+htvvGF5Fgi9SFQkTCI4lhZQIAs4VW600Ubmr0AMd5ydO0oWHBxWTiEnmEMhHC211FLmB1HXF8Lr0VYI9GYEENyZh+RZuOGGG4y8Q9whEW6G5PMRbQGaAvyHRowYYWZIiy66qGkSMF3CpPD2228PaAmpl7lExvSzzjrLzJfwNWI+U0QYevOoUduFQNchIMLQddiqZiHQqxCAECCgYxL0xBNPhLFjx5pzJGQhK6AgXGCGxIrmPvvsY6YNaAJUhIAQmHMEIAUEAUCzgJYPMyQ0BcxRSno+QtDxP2AeYro3ePBg0yxwDiZ9aOpOO+0080XiMyQD7QKaBTKn9+vXb5YGizDMAoe+CAEh8A8ERBg0FISAEDBBhAzOZG8lXCNRiliZTDs4I4AgbGDmwOrlyJEjzVyIRE9f//rXa0dDEtxCQAgUI8Cce/PNN805ecyYMZZZHfLgJMGv5DtzkShHu+++e9hxxx1NG+fZl9HS4STNXCbiEX4M1A3BWHXVVcMBBxxgwQlI5pYuThgUJSmNij4LASEgwqAxIARaHAFWMz/88EML18hK5m9+8xsTWFjRzAopmDIsssgigUyve+yxR/jud79rf27/3OJQqvtCYI4QYM5hdoQZIOZDEHgEfeZotkAW0PAh/GOGtP7665ufD+cxb8n8TKJFoitdfPHFZuaHZnCBBRYw7cJxxx1nhB+zwnQpIwxcj/kSUZjGjRtnvwW0Q0UICIHmIyDC0PxnrB4KgVIEPv/8c4uggpByzz33mOlD3gUICzgeb7DBBpb8aYUVVlAc9jygtE8IdAABzI0+++wzy7L885//3PwO0AhQ3FfBq+U7Zkg4OCO8Y4aULhAGQiAT/YgwqiwIUD8hVwmlir8RuRfyShlhoF40FN/73vfMCZvfgG9961t51WifEBACDUNAhKFhD1TdEQJ1EHAbaRI5TYiRUwjXiLCCGVJWq+D1Ea6RXAjYPG+88cYWllGaBUdHWyHQcQQwH/rtb38bnn322TBx4sTwzjvv2Hx0n4U0YUDLh6/CgBiRDFMk5iVEPl24jshIJFCEMBD1DMIPySCJGxrCHXbYIX1J22cnDHlRkrKE4Tvf+Y4IQxty+iAEmo2ACEOzn696JwRyEUAowE4ah8rzzz8/vPfee+YgmUcWEDSwi0Y4OOOMM8KKK64Yll9++dx6tVMICIH2IYAZEnkWyHeClg8CT/CBtP+QEwYIOuRg8803N/8DwhkzN/04d2YOQ0Bef/1181PAJIl7oBkg4thPf/pTi6a07rrr5ja0ijCgpWDRgDCt/A5kyUpupdopBIRAr0dAhKHXP0J1QAi0DwFWH0neRHZXQjYipLAvjywgZJADgRwL22+/vYVQRUCRZqF9mOtsIZCHABHI3n77bdPwEeKUwAP4LPhc9C2EgLmINmG33XYLW221lZkG5oUaRuCHJDz88MNt2grujekQuRlI4AZxmH/++fOaVBpWlcWDJZdc0sygrrzySvNhoF0qQkAINB8BEYbmP2P1UAi0IQAxIOIKoVNxesRsASElryCMLL300mFANH3gD6fKb3/7212WPA3hCH8K8i9gRsEKK8QEJ013tMxrp/YJgd6GAGMdp2QikmGGBGl/7LHH2jQL3h/mK4VVffwG+vbta9HJ8ENgLuYV5tCUKVPCzTffbBGSmE8I9ZgxbbrppuGQQw4xrUAR6U9rGF599VWbk34fiAu5VjBpgjAQHQ0SoSIEhEDzERBhaP4zVg+FgK1YInxg6gBJYAWSsIn4LGSLr2aiWSAZFAIG0ZAgD11ZIAistiKkEIEFswpIC6uhCDujRo3qMrLSlf1S3UIgjQBkAc0CTsmXXXaZEYXnnntuFrMiP59zEeyJZITPAfNxr732MgLh56S3zHEWAIiKdPXVV5uwz7xCm0DY1Z133jlssskmhdoF6nLCUBRW1QkD9XsI13Qb9FkICIFmIiDC0Mznql4JgTYEEDpwenz//fdNiGBFkwzOnjW27cT4gdVCiAJZYMmzwEomq4nzzTefCS7pczvzM07YCDonnHCCmWfQVoQfyAv3xt76xBNPtFVWVjVVhEBvRQDSjgaAeXjjjTeapgEhnbGeLcxHBHRMAvfcc0/zGfja176Wey7z/NNPP7U677777vDoo4/aQgFhT/E1gHATCpmwyGVagTLCwHWu7VNY1ezT0nch0GwERBia/XzVOyFgK/UkcIIkXHvttbaCT5jFvMKKPqESCdU4IsZ2J8475KHIfCGvjo7sYxWUNhHVhYhN2HF7QeCBtBx77LGzxJr349oKgd6AgBN3nJFvuukmi4pErgUckilZwuA+C5B2/Ba23npr82Eo6iv1QLQvuOCCMHPmzPDCCy9YnRAMsjqjmUDLMO+88852r3SdZYSBNuLkvMYaa5gWkASORb4Q6Tr1WQgIgd6PgAhD73+G6oEQKEQAQfyTTz6xmOtkfGVVE8EiLxEUq4esPg4dOtT+WNXvas2CNxwhhVCSrKJCGNx2GwEFwYlstsOHD7cwkl1tGuVt0lYIdCYCzEWSImIuBFEgjDGmSRTIRJow8NnNkBD2GfsI+kWaAa7Hd4HQrGRwxtwJXyXOx0kZ7cIWW2wR1llnncouOWEoCqsKgV9llVXa8jAQqlVFCAiB5iMgwtD8Z6wetigCCCOsOGKecMstt8wW291hQThBCGDlkIROCBYbbbSR+Q50tWbB24CQgv+CEwYEIIoTBkK6EnOe40XOnl6XtkKgJyEAUfj73/8eyHmC7xDOwtkwxmnCwJxDyMfJee+997ZwxmuuueYshCLbP+7B/GFB4Mgjj7TAAezDfI8wyIRSJSN0nz59spfO8h2ijqnijBkzwjHHHGOLDfgSeaGdEHhP3KY8DI6MtkKg+QiIMDT/GauHLYgAwgIvfvIsEK6R8KmsQOYVBABWCREscHDG3ACzpO4sIgzdibbu1V0IIGDjs4CW77bbbrOoRZD3bHHCAEFGk4AmAPK+3377mU9RFXFHqCfKEoSEXCkQFBYBIB6rr756OO+888Liiy9e6aTMPHzrrbcsJwRR1Fh0SGsjRRiyT07fhUDrICDC0DrPWj1tAQR4ofPSJxIS8dZZ1SR0IwTCzXwcBhdOWHUkIgox2vmMwAKJ6M5Cm9MmSS5A0Qba4hoGTDOkYejOJ6N7dRQB5htmQdOmTQtTp041sgBph0Aw97ww1imYDxFwgNV7xjmmgXwvMkPiGq5FqCcJIwED0DBATtiP7wIZ2YmsdPjhh8+W4I3r04VriJpGQjbMF9FMetv8PL6nNQwsLJDfQUUICIHmIyDC0PxnrB62EAK+Qkho0iuuuMKEcISJtIACHE4WSAS14YYbhgMPPNA0DAgo2XO7Az4Rhu5AWffoTgRckJ88ebJFRWLlPs/B2YVytAgI3x46lUSJZWSBvkBKyBKNZgGzIzSJ3Jc5jD8SztL4QOy0004Woris/7SNwAOnnnqq1YMvUbaIMGQR0Xch0DoIiDC0zrNWTxuOAKYDrBBigsTLntVGTBV4yWdJAOYKOA/379/fBARMkvKyxnYXZCIM3YW07tMdCDDnPMTpnXfe2Rbi1O+dno9OGFi5J4TqoEGDLKs6+RKqCppDIqCNHz/eSAkZ3CkQDaKbERWN4AVVJk0QDyKT4TSNGRTE4W9/+9tstxdhmA0S7RACLYOACEPLPGp1tKkI8BLHZplwjddff3247777wkcffWQ+CwgCHHcBhS2OkAgThx56qOVZIIQqBMLPmRs4QRiKnJ5pG2FVsakm2zTO2SpCoCciAGkng/P06dPNHPD2228PCPH4EzkxoN3Zucb3hRde2LQBhx12mJkl1YkGhlaAxQEWCZ588klzdob44ySNORJhisnBkL1fFjvqIYITzs5jxoyxetK+C35+ljDI6dmR0VYINB8BEYbmP2P1sMEIQAgQtgnRSLbYSy65xOyPsZ32kiYMnjkZR0gSoeEP0BNskKsIA06gmFxAHBCsVIRAT0OAeQZxx3+IPAvPP/98ePjhh9sch8sIA6QYf4ANNtggHHHEERahbIEFFijtIvWhBcBH6aSTTjIzIsgKoZA333zzMGTIENNW4PhcVTBjgizgtzBp0iQjPXnXcM+0D4MIQx5K2icEmomACEMzn6t61QIIsAKI2cMbb7wRfv7zn1tiNndwTgsnfGaFEbJAIrZdd93VbJrJbYCgUmUn3R1QlhEGBBTlYeiOp6B7dBQBF94h7WPHjrXVfswDMRnykp6T6RV/PhPBiMADhD7FhKiOxg9zQ4IakNNh9OjRRky4F8nUCMdKVmfm+1e/+lVvQu6WduEHQX6Iq6++2n5T0u1OX8S5IgxpRPRZCLQOAiIMrfOs1dOGIcBq5r333murgkQ1+cMf/mCmSNluIpCw6rjEEkuEYcOGmd8CjpVVEViy9XTldwgDUZKIDpN1tkRAIdQrIV/JEYFApCIEegoCCNGYHCG4o1W4+eabbR4yP6sKcxNNAiGNCYeK+RB+DFU+By7k33DDDeGZZ54xjQb7IAfMbZydcZqmbuZPUeEaIjeRGZpFB0yoiOLE/qJC24jkNG7cONOK9AQNZVFbtV8ICIHOQ0CEofOwVE1CoNsQwBQJM6Rzzz3XwiAicBe95HnBY5ZAdtbTTz/dVh2JoNKTihOGdOI2X4VltXW99dYzswtss8mAqyIEegICzEOIARGQsP1/+eWXzTTQ56KPYdrq+/js+5mbSy21VFh77bXDmWeeaaQeod+Pc25e4b44Jh977LHm9IyzMnUhvO+yyy5hm222CQMGDMi7dJZ9aCnxd0L4f+ihhyza0iwnZL7Qh7SGQWFVMwDpqxBoMAIiDA1+uOpaMxHgJY+wgAnBo48+OouAku0xZkiQhaOPPtqEEkwe2NcTzJDSba0iDGgYcAYdOHBgj/C5SLddn1sPAQRn7P4/+OADy6L+wgsvmIYBH4I0eU8L/nmEYZ555jHBnshIaNcISFA1NyELmCKizSBwAU7VmCeRd4H5jR8TvklViwLUg68TJIeAApAeFiHKighDGTo6JgSajYAIQ7Ofr3rXMASwLYYsEBEJwkDc9ffeey+3lxADhAYchsmz8N3vftdspasEktzKuninCEMXA6zqOxUBSDvCNT5Dt956q/kPIXhDIihODsoIA/MQs8Dtttsu7LDDDoEwqvPPP39lO4loRCjVJ554Ipx22mkWSpmL0FSggeN3gUhiJGAsK/SB3w7Izk9+8pPw8ccfF2aD93pEGBwJbYVA6yEgwtB6z1w97qUI8LJmRRDzARI13XXXXW2JoLJdwmyAaEIkZTv55JMtjGqV82O2ju78DmFQWNXuRFz36igCzEPs/BHYya4Meed7utQhDGgX+vbtGw4++OAwYsSISr8Fr5/ISERh4g/fA0yiIAdo3/BfQJuIz1JVQSvxwAMP2G/JeeedZ/VUXZMlDIqSVIWYjguB5iAgwtCcZ6meNBQBXtIICYRrhCSwoslnnJxdMPGus6LJKiWOkyNHjjS/BUgDAgU2zj21lBEGNCWEm8QpFGdLzDZUhMDcQIDV/d///vdh6tSpFr74lltuMXMgVuvTxQVr/G18tR+tANdTmIsEIdhnn33MkR8fnbQ2Il1X+jPzhMztLBpcd911Fv6Ue6FJJOwwWZ0hDXXmOv2AXOA0TaQ1+sDvBCQA7cdf//rXNnMnb4P3i3lIJnkRBkdGWyHQfAREGJr/jNXDXowAL2iEBMyQMHlgVfHBBx80oSWvW2gWSPjEC5147iRo46+nlzqEAfOLfv36iTD09IfZ0PZhDkg0JGz9J06caPPx8ccfzxX0EbgRvol6RKQiyABaQTdZwpGfY4RSRchfeeWVK1Hjt4CFA+qBMPBbQL0QanwWzjnnHMtTgmlSldkhfcEcad9997WoZK4hQQsJeaFgckVf/Rj7RBhAQUUItCYCIgyt+dzV616AgAsIvLRZPWTLHy97HBazBbKw2GKLhWOOOcYcnEnOhtlDndXGbF3d/R3CQFjVvChJ9MvzMBAusk4G3O5uv+7XbATcd4jQo4RNZR4i/LM/qxngOw7IhEo9/PDDLSgBxIJMylzjvgvMT1bp0TRwflVhzr///vsB8yHMoaiPudGnTx8LobrffvvZ4kAVWUCTgLP2HXfcYf4OmAJSaDchi/F3QrswIyZyQytC2FUvWcKgKEmOjLZCoPkIiDA0/xmrh70QAYQDXtSsJhIJafLkyebc+Je//GW23jhRYGURx0mcKDFJIsRibyALCCH4ZpB/ARMJQkSyzwUx+rfaaquZILP11lsbKZoNBO0QAl2AgJP2Tz75xKIhMReZk8xD5mh6nHJ75hvCPyZ0aA2Yj5gR8kcdEAw0D5tttpmRevwXMLFD41BWuA8+B2gZiYyEWRIaAK6DmOy+++6WqA1NQ1WBnEM2iKZ0//33Wz20G7MmAiMQqpXISyRxE2GoQlPHhUDrICDC0DrPWj3tRQi4iQ6JmbCTZvUdYSNbWE3EjGCttdYyAQS/BchCnWgr2brm1ncEL4QpTK0wq8CJNL1yi5aESE8nnnii9ZHIMipCoDsQYBwiPENiiSREzgLIrZc0YYDgQgaYf6NGjWrzBZg0aZLNYT8XwRyhHFMkiEUdUs8cIXM0pJpM7WgAqI+5gfkh92OhAG1FWeEayA4aDxy2+V3B5AizJggO/k7MM4gC5lIiDGVo6pgQaC0ERBha63mrtz0cAV7o2CnzIic8IhmcX3vtNdvHsXSBLKBF4EWP6QO+CpgIILRUmSWk65nbn+kXphqYeZx00knh2WefNftqhCQEGUyQNt544zB69GgLC4uQpCIEuhoByAJE9sorr7Qx+dhjj9kqf5q4M3YhCsw3NAskR8QvAIKLIH7ppZeaRgLBm4ITNKFPGcv44xDJzDVpZf3hNwFHa/dfQNsA0YAgQDowWWT+Vy0UQDTQkjz55JP2+0K9mChxHZmhd9ppJ9OKPPfcc0aQqgiDnJ7LnpqOCYFmISDC0Kznqd70YgQQRBAEEFLIr0BUIIgDK4vZ4gIKjpPf//73LfES/gs9OXRqtg/p776CioYBkkRseDfvoI84Yh511FEmlNVZkU3Xrc9CoL0IIERjEogJ0Nlnn23jEf8BxmlWwIfUQmIXX3xxIwoEG8A0iPMPOuggI8KYD3EdPgIDYgbmn/3sZ0b0s3XltRNS8qc//ckEfAgDoVDRQHJfzJGo75RTTjHnasz3iorXg3njL37xi4DmwwkPRGZEDO26xx57WKhX7oNGRYShCE3tFwKth4AIQ+s9c/W4ByLgjogIytdcc40JKkQxYT8v9XSBLLAyuemmm4bBgwdb/HXIAoJ0HQEkXVdP+kxfEawQtG6//XbTlmBTTd+w80ab0pv715OwVluKEWAcEg0Jofqss84y8k4GZ8gCJT0GmXOssrsfAZ/JtswYRlOGvwF1EU6Vectx/A322muvsMwyyxQ34h9HmPtoAdAyQkRY+XdzJIT8HXfc0cg04VnT7cqrmH4Rbc2JAH4M1I9GkqACP/rRj4ww8B0NhJ9X5vQsDUMe0tonBJqJgAhDM5+retULEEAAIZcCGVbvu+8+0yzwQsdOmRjpCAbZgpMjJki8qHfZZRczgWAFnpd8lcCQraunfUd4wTQJ4YyVTeLXQxIw9WDlVKZIPe2JNac9jD1MiBCiIe0I/Gj3MENCw+f5E7zHzDVW+JdccskwbNgw8yNYd911bawimBNNCcJw9913m9aQuc7cXX/99U0bQIQkBP6ywjX4S7z66quWc+Gee+6x3wo0kcwJTJCIiAapxoeprKCRQGtAf2688cbw6aef2m8MfSBYwt57720LEGgrKQ899JBpR/DfQOuZLpAkCMaYMWPMrKoO8Ulfr89CQAj0TgREGHrnc1OrG4AAwjGmR5jgYKLASiQv9mxBOEFg5kWNw++WW25pzr+sCEqIzqKl70KgfQggmEMIIOsI+gQZQEjPkgRqZS4yD7H5R+DHZwH/AfwRMAeEdEA4DjvsMCMfCPdcwx9aQTSC1157bS0fI+5PyFNMkNAuUBfEBuKBkE+CtrFjx5oGjjaVFRydr7rqqjB+/HiLsETdaDzQ3hGBjHqoE00ev0v33nuvkQgWLbhvunAdvlJkkIdgoF1REQJCoPkIiDA0/xmrhz0MAV76bmaAfTSrmqxmsjLJMf68IGiwmrjRRhsZSSBPAS91NApsOa4iBIRAxxBAcCYnARqt888/3/wNPPypz0PfIpTjZIzJEVGO8FkgKRtEACGe896NGdjJxE5iNeY0wjVztU/MlYCfQd++fY1kVLWWulhAIEEcmgFyPzDXqYs6RkR/gx/+8IemhSsjC9TDbw2/MZg64r/gGgO0dxdddJERD8gC9dBeFi3QRNBHwremNZ3Ux+IFWg0cuiELkA4VISAEmo+ACEPzn7F62IMQ4IXLCh5mSI888oglbuKljBkOxyi+RUBgJRMhZejQoWZ2sMMOO/R6X4Ue9DjUlBZFgDmGbT4mgWgE0PSRdwBTQLQEaSLOuQjSEANCmOKAjzPzN7/5TRPgHUJW4gm/iiCN+RDEAyEcwRySgT8E5juY2lUV7sn1XEP7EOBpE1qN/v37mw8EYVSrCvXgMI3JI2QBzQEaFYgHZkW0FXOmtKYSwjBz5kyFVa0CV8eFQIshIMLQYg9c3Z27CCBUYBdMaEPinePkC4HICii0kpU8VhOxe8ZkCcEDm2MVISAE5gwBhGJ8DMhHMGXKFDP9QbBGwOYvPR+5E1q+tdde25yMhwwZYlGQsiv7zGOIAqv/Hq4UQRyzHRK14QBdN4cIQj3mSPgpobWgbZCWPlFTgTMy/hKQl6pCPSxIkHPh+eeftzppN/XgMO3ZodP1iDCk0dBnISAEHAERBkdCWyHQhQgghCBE4EyJ6QMmEAgsvJx5qWcFFFYh8VUg/wCEASdnzB4QGlSEgBDoOAKY5Lzxxhth2rRp5pSMQI22wW3104QB4Zo8IJje7L///iakk5gNIpCes5AFopqRfPDII49s83/AXIdQpbvttptdyxyuKrQDcyaiNEEOWFTAXBEfCZyl8YHAHKoqhDL9cJ8K/J3w0aCfaBfwf4BEQGbQnKSLCEMaDX0WAkLAERBhcCS0FQJdhACEACGFFz+mDyQnw26a6Cu81CkufEAIMENCSMFfAfMDTAakWeiih6NqWwYB5hqCPQ7ATz/9tCVCu//++231Pu3g7IQBDR9+Qjg284eGAEE9G92I8xHECXk6Y8YMy5+C0M/1kIsf//jHZkKEdqEO4Xftx8MPPxzOO+88ax91QT4Q8K+//vpKssBDhWQQDYmFCcgOvzf8FkEQ8InCpwJNA7836SLCkEZDn4WAEHAERBgcCW2FQBcg4MIEq4VkasWWGJMkBAqO8UeBMPCHUIHJA4LB8OHDzRQia/rQBc1UlUKg8QhAFnAgRrA/99xzzan473//+2z9Zk5C0CHtW221Vdh5550DoYshC8xFJ/d+IYI5WorRMXszmkP8GCg4RCOYj4gmSvgeZa/z67NbtAJoEa677jrzX6DdmEShqfjBD35g2oqqBQT6ADG66667rM9ESIIIQIC23npryw4Nicj7bRFhyD4RfRcCQgAERBg0DoRAFyHAah5aBWyQiXZC+FTCNWKa5ETBt6wgkh2WlUwEFOyTMT/Ie6F3UXPnerVgQUQWHFFZAYZUsfqJhgXha5FFFpnrbVQDeh8CjCvmHPOQsKlEDGL1HsE4zxwQkx3GHHMQO38cliHy2ZV4kIAssAAAScDPCJNDxi/kgBwNo0aNCltssYVlgK5CjnaiiaQOIhrRVjQE7MdE8bjjjjNTIpyuq34XuIbACkRhY7ECLQNtxQ8KooA/xjbbbJPbpDLCwAXMRUKxEgnKQ7HmVqSdQkAINAoBEYZGPU51pichwOolEU54WaP+JwkTL+N04cWOmQIriDgy4hxJuETIQ6sVCAJCHaTq8ssvN/MRItGgaVkuJqkilGPdVdpWw079LUYAcyMEbwINYOLz+uuvG4HwK9JjCuK+6KKL2phDywdhKCus/iOQsxhw5plnGlngfOohChGaDBYB6sxnyAtkg8SNaBjQSLIPbQLRlc455xwT9CEiVaZNzKW33nrLCAvtAwPahNbktNNOs7m05ppr5natjDBwXzQtECoIA0Smjl9G7o20UwgIgV6FgAhDr3pcamxvQAASQJjUF1980QQGSMNHH31kK3wcyxZeuoMGDQrbbrttGDhwYEuaIbH6SRhJkmAhfBEhBmEJYaRPtLPGtIMVXOyvEXxUhEAdBFixx0zoqaeeMrIAcWAfY8uLEwYEcwRh/IZwEmY1vsqxmFwJp59+enjmmWdsYYC6GZ8I+GgIIQwQkKp6aAuCOmP/4osvti1mTgjokOWddtop7LPPPjYXqrQLTrwxvyIs68svv2xdJTwzJOiCCy4woT8dStWx8HYUhVXl3vSNeghDy0KHihAQAq2BgAhDazxn9bKbEIAQYP6AmcL06dPtpcpKH3bJ2YIwgKkDq4+77757GDBggAksLsBkz2/yd4QcorhgLsEKK2EkKWAESdh0001N4FNo2SaPgs7rG/MQARyBnkzJCPQTJkywfZDTNHH3+TbffPOZ+RD5DdAsIAz7sbyWUT/BC4g2hKCPKRHjGEEcbSHk45hjjrE5XuVzQP2QjSeeeMIyKEMWMGeEfKChYF5gQoTQX1VoF1pNNCqYNkG+EfSph6hrhHNmkaKob1xfRBiYj/xeQRiuvPJKM09in4oQEAItgED84VQRAkKgkxCIJgpJXNFLoro+iaYDSbSHTuILNfcv2kQn0QExiavqSTRXSqKw0Umt6H3VgFs0RUqiU6dhFYWZNszAEJw4HslY7+ucWtztCDCXolYvufvuu5MoKCcxslHbeGI+Mr78j+9RoE6i+Vty8sknJ5HsV87FSDqSmOQtueOOO5J+/frNUnf0tUmi6VMSczxU1uPARI1HEiMtJTfddNMsbY2aiSQ6XifR7yKJ/j1+eumW8/j96d+/f0Jb6B/17L333kkMulA5h5iL0ccjiaRnlrY4TlFjkkS/jCSGfk3iQkhpW3RQCAiB5iAgDUMLkEJ1sesRiD8J5rBL/HTspF977TVLlMSKY9r8gZbEF6+tmrMCSchFVv6IwsL+olW/ru/B3L0Dq5qshBJKFg0DeFLAA7MksDrqqKPCgKiFYXVURQgUIYC9PtoqfADItUDCMlbvmYtefHzxnXnHmGIFn2hGOClXaQSoC0dnfG2IRIQ5HWMVx2h8F3A2XmONNUpX8r0tbNFAohEgkRwmSWgpaQPmSJgpUh/O2FXmSMwjNJpXXHFFmDRpktVL//h9waSJfBCYSJXV4xoGckBgzkXI2HRBgxJJkt0Dc0HNxzQ6+iwEmouACENzn6161o0IIKRghkTIxtExvCICC+YQ2YJQgekDzocIJhCGFVZYoVJAydbTtO9lhAGzDCLW7LvvvmYqgtOnihDIQwBBHuGbeXjDDTcYaSDYQJa0pwkDhNQjGm2++eYWujSv7vQ+d3bGgRhzJEzomNuYz5EUDb8GhOoq4kGdtIXfCqIi4Xdwyy23mMM/vxNEM8Icj9+UqkI9RBkjwhimSDfffHMbicGEKGoYLAJbNulctt4ywsA9fD5CSkgoiZmgihAQAs1HQISh+c9YPexCBHiB8oLFmXLy5MlhypQplpwNgSIrpNAMVgkJSUj25iOOOCIQBQihAmGjlQsYop1JaxgcE1ZIicyC4HT88ceHvn37tjJU6nsBAsw37P6JshVNiyybM/Mybx4ybymMMXwVVl55ZUu4xpZQoWUFHwgEfEKzovUiIRrjF0GajND4I/GHrb+P4aL6/PcDn4VDDjnEtAMESGA/gviBBx5o2jWCIlQVfnPIYE3gALQfzCfmDu04+OCDzZmbyEhVbXLCwFzLahhoV5owsNghwlD1ZHRcCDQDARGGZjxH9WIuIIDgQDQkQiESEen2228PZI6Nts0WESn9YuYzK3sQBJJBkYAJ4ZiXb/q8udCNHnHLKsLAyi2YYZqBCZeKEEgjgCCLGQ+r/eRZIBIQ8xBtQ9784nwK848MyuRaYGyh+WOslRXGKoL5I488YpG7uAeaDYg/Avlhhx1m5Ja5XlUgM/x+IOBDGNBMoiWgLgR9HKrRrqEhKCv0h3bwO3TQQQeF9957z7QeLFCgBYBAsVCBiVNVEWGoQkjHhUBrIiDC0JrPXb3uBAR4QRN9hTjnhBhkNZOXvZe0oILNMGYPvPiJp060k7xEUH5tq20RUop8GMAR8ww0C+BcFD++1TBTf79AAGGZ8fNuzOFx0kknWYQgxhKEnpKeh19c8YUZEPsJdwoRxYyIaxlnZYV7kUEZsyFMf8aPH2/1UxeaCjQBmAMhqLO6X1VoN2ZIDz74YLjwwgstVwvXQTYIy3rppZeaxqOqXfQVk0j8f1iI4LcJUyvIEP4/RDQi8SEEqao4YcjzYaD/aQ2DTJKq0NRxIdAcBEQYmvMs1ZNuQoBVQcjBSy+9FM4//3xbzUNY4UWbdqx0QQXNQp/oHIhDJbkWWOljX5njYTd1pcfcBuxEGHrM4+g1DUGARctHrhNs6glLiokQSRM5RvF5mO4Ux9gPiWcVf5111qnMrM41mP2wen/GGWdYfgMEdAR8zHJwmiYL84gRI2qRBX5HMG3C1wL/BfpA/ffV5hkAAEAASURBVPw2xAhHYfDgwWGPPfaw0KVVvxVoVzCHZAEDwsJ8ggzRLxYpCKXKAkUeFmlc+CzCkEVE34WAEAABEQaNAyHQTgSIuEIUpCeffNK0BdhNpwUUr46XM6txCyywgK1i7rLLLkYY+F5n9dHraYWtCEMrPOXO7SMCPOPm3UjWScw2ZswY+4zwTKkiDJj9ED0I8yU0DKzAlwnUCPg4UGPXjzYCgoufACv5mA+RK4HISDhO1yksLpDH4aqrrrKIRvyOoCng94HFhaFDh4ZNNtmkliaSdl1yySVGGDCLpO4YStZIDBoUAgZAROoUzwdx3HHHWVbstNaU66kHh24iRGHipChJdVDVOUKg9yMgwtD7n6F60I0IuGDLKt6NN97Y5q/gwolvaRJkAQdKXq5EU8E+ukoo6cau9KhbgWuR0zNCnJskIVzJJKlHPbq50hjmGYItq/2nnnqqOTqzQs/+9Bzkcx4JYMUeYReigHPvd7/73dzz0p1j9R+/BcKoMvfRbFA/gjl+BkRGgoAwz6sK1xFZCeGeuu655x675Otf/7qZ3iHgs8CAliCv/V4/9fjcIYgCPhz4RHDNsssuGy677DJLIke9ZfV4fa71eOihh8KRRx5pdVG/FxY6IEdoLZS4zVHRVgi0BgIiDK3xnNXLTkCA1T8cKYnvjtCA8MDLlJc2ha1/ZtURMwWyxrLqyGohL21WNVVmR8CFHo+ShOCCgON/mFMQwSYmpBJhmB2+ltsDWSC/AiZIEydONBNB5mZac+fzMb3PgWIeDog5PWJCQAvVW0fIR3MRE6uZgI9GA60ixIMFAUgsK/L4JuHLUFXQAJAZ+qKLLgqPPfaYhYFlgQETKbIx//CHP7S2VZki8ZtEVKV7773X/B3IwQCxgWgwX6if0KzUXadwLVGm3KEbnLmHF7CEiEAY8Ceq01e/VlshIAR6NwIiDL37+an13YQAL3gcCQl/eOaZZ5qwwss5vWrnZIGXPOSAVUfso4nAgqYhT3Dppub3+NtAGMp8GBBM8P3A7AJnUJXWRYC5CDkgzwB/zz77rAnJzL+8+Zje56ihFcA/gERmRN3CDKiq4OyMEzKCMtGMaAearyFDhpgAPWrUqLDQQgtVVWOLCgjiMSO8RTTid4T+QGIQ8nfddVdL1ob2o6owb8g5gS8VQj7+G/z+EIaYhQq0L8ybOr894If5EQ7YJJAbO3bsbLen7j7RH8sJA8RERQgIgdZAQIShNZ6zetlBBHiJIigQrpA8C7zkUfuz2kiytrQwwrm89Ikcwsv+gAMOMPMChN2qlcIONq8xl5URBrDD1GOnnXYKCGUILCqtiQAr4IQgnTBhgkUpYj6yj7nHX3Y+glJ6H58h8xtuuGEYPnx42H777c0HoUygpl4EfHwX0HDhoMz8Z1yiEcB3gvmOlqLOPGesExkJh+nRMSEbQjqr+LSLZI4I6kRJqvI5cPMhiAL5IPCBAAsiNG222WYWsQlH7Kq8Ej6S6CdaD8LC4qOFpiFb6B/zT4Qhi4y+C4HmIyDC0PxnrB52EAFe4kQxQeVPkqa77767LSISL+usgILQwUoljooIEHvttZe9+DFPUilHoIwwYE6BjTmZaocNG1ZbACq/o472NgQQhlmNR6OAGRICLXPTi89HSAFzjtV/tvgKuFkNxxDGMRWEgCKgVxXqZdGA3wDIwp133mnaBczkVlppJXOaxiSJ1fYy4uH3wZQJEyIiGmEyBBlhjGPqQ3sIu1xn5Z45g8YTwkAUJDSgtJX+QYRwnEawx2+qqnAd7YAokH0efyIISLaIMGQR0Xch0DoIiDC0zrNWT9uBAC9QVv4effRRU88TSQWhg/1e+Oyrl2xZ2SPzKSuOaBlYFVeph0AZYUDoQ/DBRpwM2YrKUg/TJp3F3Pv444/N9AbnZuz+MQlKF5+PCN+MEcx7EJ7vu+8+E6Y5F4G+T1whP/bYYy0EKv4HVYXFAczlSH6GZuD111+3etAukITx6KOPtgzPVfX4cZyl+T2BMDzwwAP2u4KJFGSYMKiYSfFbUlboazofxLXXXmu/RWgz1113XSPXECIEfP+NKqsPfN+N0abIKePaCvqdLSIMWUT0XQi0DgIiDK3zrNXTmgjw8mTlEjMkXuy8SBEY0sWJAy9jXqKsCG655ZZmz8wqIZqGqpd+ur5W/gyWCFGsHBPpxaPduKADYUBjg5AHYaizYtrKeDap75ACtHwI6pAEAg5gp4+w7AQh3V+0ChACtFFEUMJ8CcGc1XPIAlmcselnZR9THQT1soLQTM4VxiQZlPnMSj6mh4xJSCwCep0xSXshxqzeQzIwbcR3gd8PIg+dddZZZsKINo19ZYXfKBK1EZmJPpJEjv7hu4BmE2du5orPobK6OOZaD/C944472rQV2evShIGIZXU0Idk69F0ICIHeiYAIQ+98bmp1FyHASx2BANtoIrBAGBBQMIdIv3w5j8I+BFpWNAmDyCohTpQIFBRWO3mRp6+1A/rXhgBCGRjjaEl8e2zF08Ig+GLyQZjHATGyDavGKs1HAB8hBNk33ngjzJgxIxDqE40f+7yk5xXCLKv+CNwHHnhgmDlzZpg+fbrNZQR15iJkgqhBZFWGPLCvrEBYMPvB3+Dggw82rSNjk2s32mgjC5dMnXWytnPd559/buQDwvCb3/zGCAQkB9MmQqBSF9HV+M0oKtTD7xHEw3MloPVwYR7SvcEGG1iwhaI60vupDwKGuRUhXiEy1J9X/B5o/EQY8hDSPiHQXAREGJr7bNWzdiLAixNnRoQDXpzTpk2zOOSs5nEsLZxQNft4gUIWiEiCIyWrjggTHEPYWHHFFU3bgFCgko8AOGGPPn78+HDLLbeYdgf8KGAOxssss4zZnbPKK1OvfBybtJcxgYYAm3qcgCENrKgj+HtJz0cE/0UXXdRIZd++fW3+XXfddeHWW29t81/AXGefffaxJIqEOXZS7/XlbTFLxNwHDQdBDyAxaA/RJjLfCWzA+KxT6BOC/aRJk0w4J9ISZBiCQ12QZX5LysgC96Ee8CBx5E9/+lPTUkC60ZYQQQxBnvCudVb/mWfu0E1eBX736LPPv2y/0oSBaFF17pGtQ9+FgBDonQiIMPTO56ZWdwECvCRx9ENoxcGZVU0EBPbzQk6/yNnHHy9QXpqYAhAlhRVOVhs5H6Lh3xEMWqUgvIEBfQcjstmCIwXtAIKeZ7V1bD/55BMzHXnppZdsFRb8OM//EIawSR80aJDVgVAD9twHbMGabLfUR+EYgh2OpN1daAMmVmiqGDNEu4FEtnph1ZrnjoAKNmWF54/WCRMgTJFwXOaZs98LY4OxhpDNc8afAEGeaEOEGiVnAgnReAaci9kQAjaZj1khZ4yUFcYU43J0jGSEWRNjk3oWW2wxi9a11lprWSblsjr8GGOCPpO/gVCnmBExRhi//fv3NxMicpDQ9qoCjmha6BvO39SD+SP1oD05/PDDbexXaU+4D+3CLOq2226zBRIcqCEkRQUs+0QtCPiJMBShpP1CoJkIiDA087mqVx1AAGEEfwXyLGATjFmSF16sCAte+E5J7/NjvKg5zh8CAYJJmXCSrZt6vH4+592D/XVKZ9XDvfLamW0DbWXlFmLg+RIQthD2OMbqLwVsnYzxnc+Ymrg2J3svroUYLBez84IvQg5bhEAwZuWZFVsXKGkDNurYl88JfrSNkm3PF3vz/7ugiXDMc4fsIND6s+iM9uTfufP3epu95o62neeCwIzQjfkL2Yi9+D28br7zxzNFeE1rFfxcruX5Q9ZZoV9vvfVMu8B4gFygXYD0Y+ZGvYwdxgMmhgi7EPz0AoC3xbfch/GIRoCoQfjX0BbIH88SB2gILP4QdQpjAvJDZme0ZN4n8jag7dh5553N56CO3xNzCU0AhIjfKQgYYwyigNP0pptuatjUaRd9wj+LTPRoVtHolBXGc59/EAaZJJUhpWNCoHkIiDA075mqRx1EgJc6K38jRoywVXFWrL0gQLhAwz4XXNL70vv5zDH/43tRydbNeV4/n7P3YF/d0ln1cL+8dha1A2HOtSoIRy7I+740WfC6020tuhf1gofXhwDDd85Pr4yyj2Mey35OMPQ+FrXJj6e3jCX+KAimtNtLe+rxa+bWlrZ6cZw7iiV4+HN3bKjb7+H1+ne/b/q7f2YckRgRQrj77rubdg/HYcYaPjAIz5jtoCEAe4gmgjkmSX2iwMvYKCu0D7Jw/fXX2x9aMq5Ba8YqPmZSkI46Zk20md8SNJcI+GgFKJADCDSEhCRyfHcMitqGdoF+4e9APXynf2g3ic4GGaKNZWTI62YOQWLQxuy///5tvlp+PG8LBuDHfUQY8hDSPiHQXAREGJr7bNWzdiKAkIAjIgII9tKs5HnhpZ9+mbvgkt7Hub6fz9lj7MsWPz99ru/zc9PHfF97ttQ3p3Vwv86qp07bO+tePake2kLpjGdRB8POOMfb7HV1tO1l9fixdN3sS3/3+7MfYRjNAvlOMEMaPHiwmXyhaULzBOk/5JBDbA7jZIwgTrZ1BHPOx6SoqrBqjyCNczT5FzCPgqSgNeO+ROyqExmJ+yCYo21Cu/H8889bKFX6gHZh4MCB9nuz7bbbVjXJ5h/9wXcBf58pU6YYFvhmEGjhjDPOMI0H9eZhl70B5IrfOzQLxx9//GwmX9nz+S7CkIeK9gmB1kBAhKE1nrN6WQMBJwzEQa8iDFSXFWpc8PFb1Xlp+zXpc30f9aT3e73t3Wbb2d7rOd/b1BntqXP/zrpfT+p7Z/WpDn6deY63mzo7+vzTdWTryXtGefu8T2iNWFE/9NBDLXwqAQVoFwIweQQQgHEgdh8SfBzIfHzeeeeZv4Nruby+7BYBn1CuRGUi4hBkgbohKYRrxdcA4lBHu0DdXIvZz8iRI23Lqj5aAXK1EEoVs6blogakqtAuNB1oN/BhgNBQjwcEIDIUAQHqPiNMwy655BJz6CaRHNqfqpImDPJhqEJLx4VAsxAQYWjW81Rv5gABJwxoGMjDkNYwzEG1ulQICIFOQoCVeTQERBWC2LMy7wIyAvCECRNMAGb1HUEdcoGvAXb95CxAyK8y1yFSGsQD/weyLmP2wzUI5qNGjTKNAOZICM9Vhd8Uoj1BYn7yk5+YiRT14QRP0ji0DtRbpa2AQKFdwNwK7YabW0GWiNB22GGHhQE1Qw57XfiTQKLIMQGhAUcCBeAPAmHCfCpbwBOncaLBnXLKKeY/lD1H34WAEGgmAiIMzXyu6lUHEEgThjINA4ICL1eECFb4+OxCCy9jL77Pv6e3nMf9WDXkPOrhM38U9nEfPyd9T/ZxvZ+brjf7uW57stflffe6yvqVd1179nm/8Efw+6T77nWBF+eCRVHx9nLc60qf69ez5Y9zeKbcL1uy5/pxbxvf/bnwmXr8nlzLs2JL8f32pYf/8zZ7Mzva9rJ6/Fi6bvalv/v9wRsnZ8gC5jzY0lPAnpV7hHJCoJI7gX2Y62y++eaWMwGNRFXhOSEsE0oVIR/iQUG7wL3QMJBBuY6/AddBDjAhwtl53Lhx5vDN2CXvAlGWzj77bCML7mvDNXmFvuDUj/M1pIXISOyDeGAidf7551tY2ap6qJvrWBBBqwBhACvGK2QK8oJWBQLBMZ6DPx+upd+YgEEYyEvBdxUhIARaAwERhtZ4zuplDQR4kZb5MPBS9agsJFfCuZCXPkIJ9tN5Ak7ebXkBsxrKixohhxc1Jg6YPvDHd+okhwPnYIaACQa2ycSaZ2UQoYY66pCGvDb0xH3gj603fSOKEt8RSMCBvhPlBox5BjiLYnLiUV3SQk2dvrlgiGMrOGKzzj1YvcaZNls4zr1wXsVOnnbQNtrEs6cgZKGVQqilHiJF0QeEO55hbywuMPoWYbeocE7a8Tx9Xvb5pOeKH8vuS3/3urg/TscIqwjwjA2eJVGXEMxHxxCojB0nnAjAl19+uZ1Xlb+DdvCcmXOs2LNFSKcd1MO+jTfe2OZqXtu8jb71duFvgPM0Yw2zH+Y22ZgRuomOhJBfVR9j/YYbbrDwriRYg4hwHeZMaE9Y7U+TV29D3hZsaAvaGCIt0Ucfs2grIDGMdfwaOJZOlMd5kB3ajjkTc1FFCAiB1kBAhKE1nrN6WQOBOoQBgX277bYzwZ3kSAiXvDQRHqte+t4EBBOEyPfff98IAi9+BGDCQfKHUIRQgZDCOUR64b6ETsQeG3MEBFeE0yYRBhewEP4wk0CwAVdMN5wsgTECep8YqQVBhmy3LnA6vnW23Aui8G4Mo4upBwIY5hjgi215tmDe8tZbb9m5EBoKzw3TFNpIGxCuMGeBWFIPZibcB2EPjVVvK/QJAdf/6Bd5AorGOefx7PLGZPYZpevgfK7leULGeO6cnz7HsWNuIKwivEPWIQHMW8x+SLQIOXDzGp9XaAsIhcoYKiu0A8KO0zRRliB5jA3mN0Lyz372M3OeZuzVKT5mrrnmGkvU5kSTxQZW8SE8ZGQuI2HcBywYc5gvoT2ZEfPD0GeexTbbbGN17LfffnWaZOeAM87XaCXwhaDP+HWAJeZInm2dLNJgyfj1AmGg/7RdUZIcFW2FQGsgIMLQGs9ZvayBQBVh4MW+5pprWpIjVo8RSFQ6FwGEI4gQWhQELgQZBENh3bk416kNARpiirAKEUDzxYo2QmO2uFDrib/4Xrcw79AsserNijdCOtfXJQyQDRKiIeiiIYQI0kY0gAi2F198sRHuvHan28h4w+SHqEgI05B3xp+vqBMxCfKQ1650PXym/VxPcjX6hPkPBVLKb8i5555rWFY5YFMP7YLYkr/h17/+tS02UBckCDMntCx8rlPAGuJCuzBt8ueEL8SA6AMxZMgQ03pA2NEw4DPB8/AiwuBIaCsEWg8BEYbWe+bqcQECIgwFwHTzbgRVSAPCjJuBsVXpfgRY7U9rGNB8FRXORUh2IbTovOx+zkfD8/HHH1v2YEyKIAB5gnlaw4DgjaCMJoBs0GRxZrWcutD64OOAALzrrrtWZlCm7dj1kxCNfAm0AUEdgrDjjjuaoy85HOoSV65F6wHJeOKJJ0xrwRhmFX/YsGFt+SDy+pjGh98k6rn99tvDlVdeaSv+HKffaFpw5HYtV/q6vM/gzPOhjzh1Y+LEPkgL2kzMpPANoT6OizDkoah9QqB1ERBhaN1nr55nEBBhyACir0KgmxBwcyDMXHA2RkDOE6azhAEfEsxrIAxkaMckjHmMuQ6CPsJ5//79AyvoZQWSgc8C90eQRrOCMI1GgHClRAYih0OVRoB7cB0mh5gOkkGZ1XqEflbnyQdBfYMGDTLBvKxNHIN4QF5o1x133GGmbbQBTQ8aAc8HkYdVtm4wxmeKyE+0CdMmCuSK+tA47LLLLmYiNXPmTBEGQ0f/hIAQaEMg/ripCAEhEBGIq4xJVPknMQxjEgWFJK4Itv3FF3ISX9RJFBySaKueROdIYSYEhEAnIRCF2SSaEiXRfCeJDs0J8y09//xzNItKot1/ErUASRTIk6gVSKL9frL++uu3nR99XJLovJtEU6Qkmt8kkUCUtpJ7R41WEs2pkqiNaKuH+R7t9ZMYXjWJhKK0jvRBfhuib0ASzZqS6DeRRJJjdUbSksQIS0n0IahsE/XxexRNtZLJkycnUaOQcD04RC1PMnz48CSSqiT6F6RvXfiZPnJuJFdJDEmbRHMtqyuSmCRmyE5OPvnkJGp17Hr6Gs2ykphFO4l+U214cG8wiSZQhhOYqQgBIdA6CEjD0Ead9KHVEZCGodVHgPo/NxHAGdd9CPBHyFs1dw0DIVKx3ceU6OijjzaHdJzOo1Br2gWciffYY4+w/fbbmxlRXl3eV1becUrH5OeBBx4wcxy0AfhAEJKVVXzuVbdgTjfhH/kgbr75ZtMSsIpPJDQiGp166qm5fcvWDx5oW9CeELmICE60iyRv5IohwhKfwaSqYFaGpgLNAeFS8WOgfpzzyVNx4oknWrhaNDZoNaRhqEJUx4VA6yEgwtB6z1w9LkBAhKEAGO0WAt2AAMI/UcHuu+8+c/DNE/KdMBBWldC12OQTMYlIYgjFEAaiEO2www5mkkSG56riZj8//vGPzUcAYRpfBXwkiGaE6Q9BDuqUuNZofhQnnHCChUBFSIeQkC8Bcx9Mm6J2oLIq6qFvEA78CSZNmmQkA1OruPJvPhDkg6hbMNXCpOm2224zfIl8hGkTOS1wDMfJG38N8BNhqIuqzhMCrYWACENrPW/1tgQBEYYScHRICHQDAgiyd955pznflhEGwohCEl588UULp8p1COYIwSussEKIJjYWXYvPZQWSgX8Bmg1CqRINit8BwhhDNsaOHWt+DKzsVxXuj5BP6FMcsIn0hW8EQjgr92gWVlllFWtXVV0I7R4ZCV8IiBT1oPUYOXJk2HLLLY04VNXDcSdi+EFcd911FpGKPrp/xjrrrDOLf4YIQx1UdY4QaD0ERBha75mrxwUI8BLFgRJHScI8orL3woofq5skNiL7K6uYVY6Ufq229RAAYwQ4TC8QBhGQCOXJ6i6CIH8qzUYAAZuV8B/+8Ie5ZjsI7pjQEP0IB16EaUKNMmYorJKTG2XMmDFmRoQWIq8w1hCMIQhEZGLek4gM4sG4I5oR5kjUw7zPIy/peiELmCJBPmg/uR8Q+CmMYUyHyKNAjg/qLisI+OQXgXjgyI25FE7Y9J1ryWaNpgLtQFWhn4SZJVQs2grCu9JH9qP1gMRAGDCXclIELuRnOPLII60PnO/FSQtaCbQe4K0iBIRAayAgwtAaz1m9rIEAL2qED6Kh8JLlpZouvFCJJkLWVjIvs0Kn0nkIIHRhDoKwhMAFQSA5HnborPhC0lSajQCEgQhJEIb2FgR7BPM6ScVYHCAcK/N9dMwOjaaCAjEgdCyRlcjqjH9EVeF3gsUFsiM/+OCD5vPgvx0I2IxbzJsY04QsrSrkPcDPgCR0rvGgXSxQUA9hUakTv4iqQj89ez0+HpAaL7Rl6tSps2kqeAbkaSDMqked8mu8HWB81113VYar9eu0FQJCoPcjIMLQ+5+hetBJCLiGAdvgKg0DAqw0DJ0E/D+qYRUVs4nnnnsuxMg0thehiBjxrKiSuApBiRVblWYigIaJFX+yKnsStnRPXRBnn6/6s2WlG80DztCslrP67ivm6ev9MwI+q+isuCM0I0xDODBhQhjGnyFGD7I/v6ZoC9FF20H+hmeeecayOnMuxINcCYRQRVtBm8q0ZNRDHgkcnVm9J3M1q/30A+KMr8baa69tGgHmAGSkqIATmoGnn37aSBGhVCEi/MaBFckQMcGKEZPM8Tldj2sY8N9AS1KkYcC8SRqGNHL6LAQajkD8YVERAkIgIhA1DBZWtW/fvkl0LrTQjlEYsW38GbDwiFEASOLKpIVGFGidh0AUFJNozpHE5FhJ1OIkUUhCvWMhHRdZZJEkOrEmMRNwElc8O++mqqnHIRCF1SQKucnQoUOTaIo2yxxkLjIm/M/nJmMlmh4lMe9CEvML2Dyu6ljMk5BMnDgx2W677druEx2dLeRo1Dgk0Rehqoq24/xuvPXWW0kUsJMYBamtzbSf8RyduNvOLftAPW+//XYSNQtJJBg29ukjYWKjZiGJ2oskahySSCzKqrFjnBMzdCfjx49PIvmxOiLBsN+w6E+RxAhSFpI2ahNmq4uwsNwrEqfZfgcjqUqiWVUSHbgtFO1sF2uHEBACjUUAswsVISAEIgIiDHNnGMRVzyQ6dSYxrGUSV2FNqEkLhQhyW2yxRRJXnCWkzJ1H1G13bS9hQAiOq9wm6N96661JXKGvbCvkFME8JlBL4kp9m2DOIkFcxU+ihqt23gUE87hyb7kaojmU5SlAyGfMQnwhCyww1Cn0/cknn0yiOZblOqAeyBB5D2LUJWtzHbLAvTiP++6///5GNqgHrMgLAVmAlOTVxT5ISfTTshwUUcPXRoBojwhDnSepc4RAMxEQYWjmc1WvOoBAmjBkE7chwEZzAkvcJg1DB8AtucRXaKPdtq1eItiANwIKnxG+SCIVnTYtEVdJVTrUyxFAaI5hRC3BWTT7s+fPGPA/J5I+PhD4EdQRgqMPQaUGCoGYZGjR9C2JkYbatFhez1lnnZVEJ+NaWgqgZjU+5m5IonNyEs3l2sYrGoERI0aYVgxCUVXoN+2fMGGCJZ2L+RGMLEBiBgwYkMTIUSbIV9XDceYTySWjH0ISIz2Z9oW55H289NJLk5jbIbcqyDvJ7kigR3I3CINjz1aEIRc27RQCLYGAfBjim0dFCIAA9r3uIEhkkrSDYPw1MBtnnA6JZU7knijICrhOQADc34mOztiAX3311WY3Dd5RyLHasS0nugzJqohhj225SjMRwIcBH5Zzzz3XEpZh058ujIt0ieY65ghMQjRCqVYVHHqj+VAgMRz3iZoG8wWgHiKg7bvvvuZwHYXrtvFXVid+N0Q/IqIRfjc4CVMXeSDwuxk1alSt3wl+a/CpoI4o0Fs9UStgzv70DTyiaV6pD4S3M5IPaw+RkfCFYG6BG/4G0dwyXHbZZaFPnz65QQSYizha47yNDwP945l4oU1cW8ex3K/RVggIgWYgIMLQjOeoXnQCAiIMnQBiB6oQYegAaA29pD2EAUKJE3w0uzFn4G222aYUFQRpwqdCFM444wxzMMb5GSGYcKUkW8NJGaE6rqaX1oUA7uQDokKd5EqIq/thwQUXDMcdd5w5J5NxGsJbVhj/hBGGKFDPI488YvXgNA1ZoI5DDjmkVnhX2hV9F8K4ceNC1FZYSFbvI/1af/31jSyBW5EDNqSH7NL0AUKVdnoWYSh7kjomBBqOQPyBURECQiAi4CZJMdpKkjVJQqXvJkmo+zFFUOkcBMAdm/K4UttmkgTebgqBKUWMrZ+cfvrp5uvQOXdVLT0RgSqTJMaF/0XhNYkRtJJrr702idGJKrsTBWcz7YkRmMwJ2MdYFMzN5C1qCWr5QHAjTJvi6nsStQJmMoQJEb8P/GHKQ5tiqNZapk04Hsd8Esmuu+5q/gaMd0x/MHGKkYySGEa1sm9+AnMJfyD8M3z+sMW0CNOmSJQqHbppT9ROGCaR/MxSD/3Dp4K2Rq2I31ZbISAEWgAB+TC0wENWF+sh4IRBUZLq4dVZZyF8IXwgsMVwjyYQxnWaNj8GhBScoU877TQRhs4CvYfWA2GoEyUJYT+GNTYBm8hIMW9KZY/wJcB+f6+99jJ7fsYYDtObbLJJEvMtJEROiqv9lfVwAr8Vr7zySnLiiSeac7AL5xAHHPSjpiDBubqqcL8YkjWZPn26kR/GOnXRN5ymZ86cmXz88cdV1dhx5hF9RNgnilGaWOEPcvzxxyevvvpqZbucMMSEbrZw4vWwlQ9DrUehk4RAIxEQYWjkY1WnOoKACENHUJvzaxB00NiwIksoRwQTEYY5x7U31lCXMCC4QuwR/tH4cV1ZYW7jzHzwwQfbyjnXM85YxY8ZjZPJkydX1uH1M16JJBRzOBjZIPKQC9Mxj4OFV33zzTdzoxB5Hb5l3EcTpCRmb7YIRtSD5gQtxeDBg03zEE2C/PTSLX386KOPTIsQ8ytYmyAfaFA22mgjc/QmXGwZKaJvhGONflrmTA5xoU3+J8JQ+gh0UAg0GgERhkY/XnWuPQiIMLQHrc49l1VNVmzJc4FwIsLQufj2ltrqEgZMbGJG9uTiiy+u1C4gBGOOBCElvwFaAMYYwi8RlmLmdotmVCZIp/GjjeQEic7DZtqEgE99mBJBeK+N5kjRJyF9SeFnNAKXXHJJwmq+hzClnuiAnUS/hdomUtwA8oG2JfpymNaDNkEYyFGBiRK5FaoKv4FEgSN/A9oXJ1bU5ZgpD0MVijouBJqJgAhDM5+retUBBJwwyIehA+DN4SUQBswlYmQZE3Jc2EHgkQ/DHILbiy5HGC8Lq8p4IJEZ2oWxY8faaniVoM+8JrHa+eefn6y00krmZ4AgHB2dLXwr5kNVGgqHEPJBrgfuvdtuu7XZ9xP6N0bvslCqaB/qmCNxTzQRaDggMbSJ/uE/xT4ITt12cR7nk4wOrQlzhrowcerXr5+RBTQxVYV2408EGYIIUUf6Tz4MVQjquBBoLgKKkhSXMlWEAAhEwUNhVefSUIgCj4V/3HPPPcOvfvUrFjLawlpGQSpEQS9wLDpbhqWXXnoutVK37WoEqqIkRSIZFl54YQuBOnLkyLDzzjtblKOidkUB30KDRu2VRQ2KuQksIlEUfK2OjTfeOOy3334hmhIVVTHLfuqLPgUhkg+LuBTNidrCskbHfItqRNQkxixtLSqMb0KpRmftEIV8C9UcNQQWuWjxxRcPMTtzGDFiRIhEorR/Xj/XEpaV8K4xl0TwyEiEYl111VVDJDg2b4jgVFbA/50YhvX+++8PMYndbKdGEhH6KKzqbLhohxBoBQREGFrhKauPtRAQYagFU5ecVEUYEHoInzlkyJCAQKXSTASqCAMC6yqrrGLkMUb9sRwMZUggOCNEI0wjSDPOEPrJlRA1BEZAyb8Q/RDKqrFjCPlRExZigjXLr4BgTc4C2hR9DqxN5CfYbrvtKuuiDe+++67lV4iOzSFqB6yeaD4U1ltvPWvbtttuW4sscLPo9G2hYiEgMVu0LX4QlhVCRKjYo446KkR/hMp2QTzIRUMOh+jQPdv5IgyzQaIdQqB1EGiu8kQ9EwLtQ8BNkvKiJKGKj4JKsld0siScIueqdB4CZT4MmHvEePQWPYdINirNRQDTGjdJwrQG0zT/wzSGzMdRkDbzG+ZhWYlCuWUtJnvzTjvtZCY21IW5Ds7JY8aMseOY4dQpjFGiFp1yyilJJK1m7kN9hB6NuRJqRzTityOSjWTatGlmIkWfosRhPgxkNL/mmmuSl19+uU6TzLGaCFG0izkSE0q2mRAttdRSZobFsTq/V+CF03TUbiTuNO3Y+xazKfkw1Ho0OkkINA4B+TA07pGqQx1FoIwwIGTElT9zRCQEKC9Xlc5DoIowbLnlluYUXTdiTOe1TDV1JwIQhqKwqhAGIhKRA+D3v/99pRDMHPXISP379zfiQR1EDUIgjlmQzUeg7lzGcXrq1KlJNI0z4oIQHVfcLRzq9ttvn0SNQS2fA/oYV/GNGEA2qIO6oqlVMmjQoOShhx4ywb0O7vhv4GB98803WxhWFjaoC5LNwkfMnm7tqvLz4F6cg/8Ccw3/DicJ6a0IQ52nonOEQDMREGFo5nNVrzqAQBlh4AVMaEISKUlo7QC4FZeIMFQA1CKHqwgDQvUee+xhOROqIPExxao9eQgQfCH+5PRAkMbhuG6BVODMfOaZZ7Y5TlMfkYRGjRqVXHnllbXaxP1iJmUjHoRS9bClkBjIAonV2pMPAryeeuqpZIcddjDtAm2CNEAWhg8fbpqYOmSB/nFfEuCtueaabZGk0mSBzyIMdUeMzhMCzUNAPgytY32mnlYgEF+sZr+LbTOOjTglesFJMkbwCdgoxwRiZgPtx7SdcwSi4DOL03MUYMxpNAop5ggaw06GE044weyxcXpVaSYCZT4MjAWcdqNgHWIUnxBNeQpBoB5s8fFdiKFXQ4xsFLDPjxGIzAk4JnAzJ+C6vgtRyA8xmlKIWolw6623hihc27jEAf+II44wXwp8IeLCQmGbOBAXJcJnn31mTsg497u/QTS/Cvvss09Ye+21rX+R2JTWw8Eojlg7Hn/8cfM3iNqBEBczQgzPGqJGJURNQRg6dGitIAG0i+sj+Qg4bcdkcoZXthFRQ9Pm9Hz11VeHSJiyp+i7EBACTUWgeRxIPRICHUPANQx5YVWJkR4dCC0pkzQMHcO37CpWSqMzqcWjZxWT1UzMR/hjVZhVz3HjxpmJSVk9Ota7EWAcuA8DWgEfA2wx3YlRf2ppGDAbZNU/OkZbGFauZ+U9RvhJhg0bZpnF6yLF6jtmP4RSxU/A20IoVPI64COAH0HVSj710C4ymmMShVaBPqFlQOsRiYhpBPgdqlPwvXgn+kLg80Bb0IIyd/h80EEHJZFImL9VnbowtyJPAxmv0eKkcU9/BsMVV1zRzMLoi4oQEAKtg4A0DE1lgupXuxFwDcPuu+8eou3zLBoGVvxcw3DqqadKw9BudMsvAHtWNQnlSFSbmDzKVlC5KgpBFlY1mqIEno3CqpZj2ZuPdpaGIWY0tqhIMSmaRTaKr3SbszGpmc1jIm6xEl+n+O8CIX0jcbDfBcZkFJxtPKKRjDkYLLxqWX2s4hMN6fLLLw+Ed0WLidYkEiPTUKA1WWKJJUxzUVYPx+gPWhNW+X/961+H22+/3S5hxZ/fqRExJOuOO+4Y+N2KAn9pdfQPrceNN94Yoi9EiMnfDLO8iyLBadMwXHXVVdIw5IGkfUKgqQi0DjdST4VAOQLSMJTj05VHWX2NhCHZK0ahYrWVlVJf2UTDEGPcJ6effnry/vvvd2UzVPdcRgANgzs9EyXJxwBbVuNxEibiEeOAVfG84r4L+Ba4poqVcSIIHXfcccmUKVNqOSdTdxSmkyhMJ/fee6+t3FMP7SC5GhpHfCFwwK4qjG+iOk2fPj3ZbLPNTFNCn9AKoD079NBDa2d1pq5oXmU+GPvuu68FY3B8yOr8ox/9KIl5FKqa1HacuojKhE8F0aOYb2nc05+lYWiDTR+EQMshIKfnlnvk6nARAk4Y8sKqyum5CLXO2x9XhU1wwkkVwhAXaUzgQ0iBRETfERGGzoO7R9aUJgwI+Aj86T/mIYL6HXfckbwTzXGyxYln9FFIBg4caGMIgRezn5jLwwR/CADn1SmQkrvvvjsZPXq0mTbRFgRqBGvCj2IWVKcuhPLnn3/ewpySqRrSQV2YJUEWopYggejUKZCYqJ1I7rvvPnPApg7qYs4wT4qwyaubtv/xj39MJk+ebOFq01jnfeYeCquah6T2CYHmIyCTpKaqjtSvdiPgpgeYGJSZJMnpud3Q1rogCmfhgQceMJOkGCPfnC6jsGfOrZhZHHPMMeZ0XsdRtdYNdVKPQwCTpGeffdYSmuGwTGK0dIkCqzm+u6NxDP+ZPmwJy9566y1z3MWp+PXXXzeTtmWXXTbESEIhrsgHrokkdJbrir7g3HzRRRdZRuYooJvTMo7XgwcPDjH3giUTjIJ10eW2P4oRZsb0SMwK/dhjj4ULLrjATIowFyLDNJmmMbdjXDPeq0okVTZHYvjVgPN2FPjNtIm6Vl99dUvgRgK4Og7J/OaBEXi+9NJL4cMPPyy9fdokSU7PpVDpoBBoHAIiDI17pOpQRxHg5fnb3/42RLMYs6GPJgRtVfFydx8GEYY2WDr1A8IiNt5EowFjCAQCCoIU2WoRahD26ghCndowVdZtCNQlDDG8cVhrrbVsPHjjEMwR8F999dVw7LHHmiCMnwC+CtGkLURTnUD2ZPwE6hR+D7Dtx2cJv5qoIbAs0UQ0GjlypJFX/ASqSlzFD/hURPOlEM2twsSJE40YMI6JikRdO++8s/kbVJEP7kW0p2hyZH4L0bzKyAi/T9TF30knnWTRpCBXZQW8iKpENKm9997bfCr4XlZEGMrQ0TEh0GwERBia/XzVu3YgwIud1clofmCOhG+88Ubb1WnCIKfnNlg69QMCDKunrCqzEouTKCvBMWNtiJFfbDWW73WEqk5tmCrrNgQgDBDGc88918YAjr3pghBMaGMIQ7T9tzHhxyGYOBPjBHzFFVeYMMycRsDfZJNNwjnnnGOfmctVheu4N2FPme/Rxt/GZjQnMmdnQrUut9xyYckll6yqyq4jZCmaBH5f0F4ieC+zzDLm5B/zu5hmoO64hhSdffbZpl1AwKettAsyxKIG94mmW5XzJJpAWf/AK+Z/MOIBSSoracIgp+cypHRMCDQPARGG5j1T9aiDCPDijdla7WVMPHJU9F5EGByJrt1CGoh5j5kEwgsEAYEPgUimSF2LfU+ovQ5hQNtENK20hoGxgmkOQiymSBAH6mLexjDJRhhOOeWUEH0ZTFiv6itkNTpWh+gPEIi0hMCPuRCmPpj9YFYEkY3+A6VV8ZuCphLNGYI8Jj+Mb3JIrLTSSrY4scoqqwRMpuoUCDVtOf/88y1CEiSDP/JLkMcBbDC9qmNyRTtuu+02M7caP368aS6Yf2VFhKEMHR0TAs1GQISh2c9XvWsHArzceaET3vDhhx+2lUq/XITBkdBWCHQdAh0hDE4yIfgHHHCAaShoIYI0Sf7wD2DlnbCodYrXB/FA04EZEWSE3wASCG6xxRbhwAMPrEVgvT/4L1AX9SDMQ2IQ7i+88MLaJnb8PhF6+Prrrw/REds0MPQRrQtmVtSF9oXPdXwhaMuJJ54YYt4LM8Ws0i6AnQhDnRGkc4RAMxEQYWjmc1WvOoCAEwYcCXnBIzB4SRMG+TA4KtoKgc5FwAVshGucnvNMkhC00z4MzFt8DWbMmBHQIuDDgCDNnI0RfSyrMtu6q/iuXWDRIIZhDTEpm5nHoZ3YeuutbQWfVfw6vjSYD8UIRPYXE7zZKj5aieHDhxthIK8I7axT6CfaBUyknnnmGesn5CNGRjLtAjkm0HpU1Uc9bm515plnmrkVpk2uqYAQcZzfwGxJEwY5PWfR0Xch0GwERBia/XzVu3YgUEYYeDG703PMB6DEbe3AVacKgboIQBiqoiSxiu5RkogMxMr4e++9F6ZNm2baQTcfIppRDKUaYsZnE6TrCPi0E18I/CggDD/72c8sohEr9vjRbL/99mHo0KEhhnY186ayfkE80Ahg7nPDDTeY/wL7aNeRRx5p2oqYOdo0BGX1cAytBz4HmOrh0I02heSGkBi0Hj/96U/NRKuO2R54ubkVEaDAyzUVmFyNiEnfqHvSpEmzNUuEYTZItEMItA4C8YdIRQgIgYhAfJEmUfBIYvjOJK5izhL/Pa7aJeQHOPjgg5O//vWvtWKvC1QhIATah0BVHoZI3C1RGQnT3nzzTas8ro5bQrRI6JPoG2DzNkZGSqKjcxJX0BPye8TFgFoN4bwoLCdRA5BEH4m23wByQkRBOokZlZNo+19ZH/WQ7yH6VCRbbbVVW16RKFlYAjlyO8RV/Mp6vNHgEv0gkuuuuy6Jmc4T+hdNkZLoOJ3ECEdJDBRgOSH8/LIt+R6itsPyLkQSZLkqqCtqJ6ytMbRxEsMat/U9kom2z5ynPAxl6OqYEGguAtIwtA43VE8rEHANg/swpE2SWFlD3Y+jJY6VrOSxT0UICIHOQ6BKw4Cmz6MkrbHGGhZp6LXXXguPP/64heIlwhZ1oE3YZZdd7I98CYRWrSrMf8KfvvLKKyFmPbYACB999JH5AxARiX2s5mMCVOYjEMUF0wag9WAFH1OkF154wVbxcXZebbXVLGITW5z56xTPUUJEI+rEhIhISGg6NtxwQ9O4gE1Zu7gPGg6iND3xxBOWqwKfLTQX/J5RDxoPtkSHOuSQQ2ZrGv4Sffr0sWegKEmzwaMdQqDRCIgwNPrxqnPtQSBLGHg5e0EI4AVNKEfiqccVR/vux7UVAkJgzhFI+zAQWrfIh4EoScxFImhNnz7dBGAEaUxrEJoXWWQRi6RE7gUcn6sEaVqOME3YU5yATz75ZDMnQlBHECcy0oQJE0Jc3bcIR2U95XeEyEiEYsUHgjrxsaANLDoMGjTIhHH8KhDA6xR8ITCtIh9E1HJYW/kNIhEdBApTqTqF/mDyhbnV6Bg+mt81fB7w7yD/zLBhwwxDEigedNBBs1WZNkkSYZgNHu0QAo1GQISh0Y9XnWsPAmWEgRclL1USI+EULQ1De5DVuUKgHgLtJQxoEsivQPIxnHQRyvERYKUch2JyE9QhC7SOhGhkc0Ygnzp1quUlgCxATBDKCXbA/ao0i/SBBJBoKNFKfP755+ZnATnAYfv4448P0bzRSE0VKgj0tAvfBVb88a1A6Md3oW/fvhZalXwOkKKqQl34VJx33nmWhA7SQOHazTbbzKJIbbnllpbADRxEGKoQ1XEh0FoIiDC01vNWb0sQqCIMvJghDJgsiTCUAKlDQqCDCCBsu9MzGgZMjNIFoRvh/dBDDzXTGOZstLc3gZpcBxzHcZcQqkOGDDGTnfT1RZ+pB23GrbfeGsieTChVBHUEczQCCPqEUuU7WoyygkBP2FO0AeRwoB5IBhqB9ddf3xypcdau44Tt7cKsCcdmzKWoa/HFFzfzSLQqhFGF2JQVyAKmR+/GPDM4chNJCsdp+gJee+65p/VzvfXWM4dnEYYyNHVMCLQmAiIMrfnc1escBJww5IVV5cWKmQM+DBMnTrSIKVUv6ZxbaJcQEAIlCKQJA2FViwgD+RYw+8F/gQhEmOwQ/QezQXwMxo4da4nREKarCsI0Scyef/55yxB90003WV1cx5zHPAnfBTQNVdoFrqHNtA/TJnwEqJ9Qqvgb8Hf00UdzWq2S1rh4mFn62L9//zB48GAzIyJpW1UBG3wXMLOMgRtM04AJFtqX733ve+Hyyy+3ELREgiKCUh3CoLCqVajruBBoFgIiDM16nurNHCBQRhhYucRJkdVNYsSzOljX1GEOmqRLhUBLIVCHMKDlGxFDf5KNHSEax2SEXwg8oY8h9Zj9YGpTlZMAcJn3hBFltZ760HAwt/GPwAE4Rk0zEsKcL9MuQAzIxPzOO++Y+RDCOaSGNnz7298ORx11VOjXr59pGeo8VNpFcjU0LZg2QT7QXkA+ICQjR44Myy+/fC0/CLQc+HqQuRofrBjpza4jgRx4nnHGGUaO6LcIQ52no3OEQOshIMLQes9cPS5AoIww8NL3PAxK3FYAoHYLgTlEoIowsMKPA/LOO+9sjrvY4UMWKJgLYYbEPMV8qE5kJK5DyI8hWsMJJ5xgvhAI/JCPPjEa0I477hj222+/QJSkqgJhIHoR/guQDDQWCPiYL+JvMDo6GWOKhJBfp4AFwjt9hDCgRaGvaD2oH9JQRWL8PlyL5oQkchAtCAT4DBgwwMytqI+ITZ6jQRoGR05bISAEHAERBkdC25ZHwAmDh1VNR0lKEwYyrdYNh9jyoAoAIdAOBNImOHlRkljhx2yGCENoBdAuUNx34f+zd2a/UhXfF6/fow/64jfGYCI4IYZonB6MCMgoooIoBjQg4giCIqBxRAYhiApCUAQTEJDBCaIgEESFIGqCSlRQMUzqgwpi/BPqtz47Vqfvpfucc6ERbveu5NJN9zl1qtYZeu/aa+2N0U8UkJSrRehDGMhoFzDuyTjEexwI0p927tzZVt4x8IvoDegLcTIUqWXLltn4klGODgIRNv0WGRfOBxWmiQagp4AGyWfQkXA6yBJFhCEr4pFgR7sAdWvBggU2NpwannU4HjzLoFsRPWVcOCTgWsRh8CxJCWF/dQQaAwF3GBrjPPssCyDgDkMBkI7jJhhEcMnJhU82GIwXHDVEmRg3RVdmj+MQvevjjECew8DhMcKhG5F9CGoNRjMGPdqFKVOmWATijDPOyDWmud7YHxoSGY3mzJlT6o/0qWRamjFjhmVdwiHJajw76As6E/oJRMpoGdAXkKp00KBBgXoQREGKNJwWKEjMh/SsLF4wT+ZFX/3797foQF5fzJH7acOGDeZ88IpjQyYpnCocLKphI8imf77766+/wscff2xOCRinCA7Hwqlo53UY8mD37x2BukTAHYa6PK0+qaNBwB2Go0GtdvtgrPzxxx9h//79YdGiRbbSi4GFQdO+ffvQu3dvM1iKrKrWblTe03+JQJ7DgAFc3rgW4N1jSCMonjhxYoCXX6Rxv//555+W9Wz79u3mOGAc45AgcMZhwGAv0jDwERXjKLAPxj6f4ewSuRgyZIgZ2nmOB8dijlCIyIhEFIG+iArgPHMfqHq1aSHI2pbXmCMRg7lz54YtW7aYI56Mfmo3jBw5sgndKh2bbRFnMydoVamlfYnieIQhoeKvjkCDIKAHhDdHwBEQAjJYo6qzRvF5o9IoRhkjpT9RAaIoCnHs2LFRP96O13FAQCu0UcWpooptRa0gR4k7o1Zoo1Z7o7jpUTSJKBHocTiyd3myICAjO4qCE2+99daoVe/S/ZfuRf0s4zHYX/qMe7Nbt25RxnoUjafQVLjXZQzHjRs3RjkaUTqDKMfDjsf19uabb0at6hfuS05uHDduXFQ9gyj9g/Ul0bRdy1rVj3KECvXFRqIQ2VzkeETRr6wvOQtREYEoB8LGzTZ5Tc5CVITA+lImJLuXmCNz5X5SNCRyzzVv0jdERRiinIIoClWTcyCHJ4oOFlVFu+K+zfvy/zsCjkD9IMBqhjdHwBEQAu4wnNjLQKuqUdlaolY+zejCMMQoVJQhimcdxQuPKjx1YgfpRz+uCLTUYcAAxqgeOHBglFg5YuwWaRjwWsGPixcvjhJRRwxy+hK1yQxzCY1t8SCvL4xyjG6Mb65b0aLsmqU/aQ2iKE1R9RjyumnyvWh5UYXjoiovm9PMfSDNVFRRtfjMM89E7hOeVXkNLFV3Ia5evToqvWzEscLgV8amOHTo0KjIhTknzfvBGWH+3HM47Mkx49UdhuZo+f8dgcZBwClJehp7cwRAgPA94f9KdRigA3iWpON7nZCCEjoH+euhiEAPkZFigtYLLrggyMgx4SgpKr3VJwJQktABkLoYbUHzOgz6aS5NnGsD+hAUJOhD06ZNs+xGMvxL21R7A82GytDr16+3ys6Ip6ELIaameBnUJmhO9J/VZLgHRSVtzIowGMWJ5wgaAVKoMg+0N2gEijT2JZUqzyDqHECZ4hhkWiJbEwXkbrrppkKF2tAfbNq0yQrIkTKWzEgka+A5poiM6RcqYQWVCmoVmZmgRdFPauWUJK/DkFDxV0egMRBwh6ExzrPPsgAC/Fjv27fPCjVRpZWMJ6klY4IfbIocFcmakvb113wEMBThWo8fP94EqHCnOR80jJSzzjrLKtHyPUadt/pEIBmr1FGgEnG5sdp8xjgMiJ9JsUqmHxxKrpWshsOBPoDUogh74eqTQQjBMhmIyIx0/fXXh7tU5wGjv1p/9MNY0dysWLHCtAFkFqIfnhU4CeggcBhwFoqInbkH9uzZExRdsFSqOM1oF9L1Tzpnnj9c/9XGxdxxMFj4QCyt6ILhyPOMz0keAE44DVTDrtSY1yeffBJGjx5tGgYcjdRwMKhPgYaBNK3UhPDmCDgCDYJA4wRTfKaOQDYCWtGOu3btilqtjG3atClxpfUoMLqCVhyj0iMaLzi7J/+2JQjIMTBdCJxxFZEyrME8/UEVgc/er1+/KCOyJV37tq0MAegwWvWPqnsQtbpfugbStZBeocdAsVHkKSrlaGHaD1QkqEvoDVTgrdR/usYkUI5oDqAFZTWuWWUfMq6/RPlN+oH336NHj/j444/n9pOOQX+KsMV33nknyjm2uTFXxkV/V111VVTmsLR55mvSIKDFkjDaxgZe4CnRdC5e7A8lCq0DFKSEOa/0A22ra9euRo3KHIh/6Qg4AnWFgGsY6up0+mSOBQGtwJkxoRznZkzw45j+EDIqV3m85557CnOIj2UsjbYvzpoiDHHAgAEmcsZQSgYKRosKX8UJEyYYJ7vRsGmk+Wp1O37xxRdRtJtM0TO6FoTRS5cujUoDWki7wP2N0FkVj02noNV2u8a0Wm+OB319//335rxiwGc1HA8MeAT6LC7wnOA6bdeuXVTmIRNuM668fjgG2yDW1op9fPjhh023wPVPfzgPiqCY3qJIsgXmeOjQIdM6KEOTaTOYH0kE7rjjjqjCbbl44bSJyhQVIbGxpGcgr/TFHJUq1kXPWReIf+cI1CEC7jDU4Un1KR0dAvzYVsuSlIxWsoMgFhQH+ugO4ntVRADsRe+IKm5lxlu5w4CzhphUlIyoyrcV9/cP6wMBHIa8LEkYrWQgGjNmTBS1qJCzADr0/d1335nQmZV3hMQYwWTjIivaZ599FqUZyAUSAx/hsWg7sVevXhHHg37Kr1PExlzTRRr6HmNnAAAaBklEQVTbcVxpMKIqS1t0gf5wikQdikpvasfDqc5rKYIiOlFJyM24mC8RD9WbqCh0Tv0yNzIrrVu3LkqDcYTDwHPQsyQltPzVEWgsBNxhaKzz7bPNQCDLYWC1mx9LfkQ3b94cJZLM6Mm/OhoEoHhgBEK/AOsUYSg3xNxhOBpkW88+eQ4DhrS0BVHCZIsuFDXKQYBsRqTthXZEFiOuL16hNakYmq28FzHKGePu3bujhMnmdODAMC76IrNQWsUvijor+lDtrrnmGotW0B8OMxRICY/jqlWrCnWFsc8ccXyIJjAm+sEhgkK0cuXK3H5SpE91UIx6xH1IP+nPHYZcCH0DR6BuEXDRs341vDkCIKAfXBMLzps3z0SHVFdNTU8AEzN27NgxLFiwoEWZT1If/pqNAFmSJk2aZFmSwF7GoO0gI8WEnoo+mGDTsyRl49iav0X4m7Ikbd269YgsSTKmA/fgnXfeaZWOERbnNe5dUX7Ct99+G2bNmhV27txpAns+RwRM5WTExLwifJZxXLVL9iGL0cKFC02cj6iYRjYl6S6seJyoc0GpXnMzGbGfDHRLtIAIm8xMohMFMCCbEeJmqkYjoKbydF5Lz6+U5Y17iLmQYUmaCsswJh1QZjeItslOJafDsKJP5pwa+IuSZKJnL9yWUPFXR6AxEHCHoTHOs8+yAALpB7eSw8Du/IhTdRiHAaOVH2JvtUPAHYbaYdlae8JYxrDHUCZTj3QATaaC84hxL51RkGjZjOkmG1T4D/c16UnpD4eB7GekVcX4VX2CIN2AZQ3q1KlTZvYhusZ4JjMSKVxxPLZt22aVpsmoRDpWqk2TyYu+izRFFyztKWMj9Sn3gKIClv2JZ838+fMtQxjPnqzGuOhr79695nSLemUV03EYSA8rzUGgsjPpVKs1+lCUL0h4bU67NB1HbOoOwxGQ+AeOQOMgoIeEN0fAERACiZIE1xdOM+H89EdGFhkURpmB4ysjxDGrMQLllCRoSAl7qB5UqoXj7ZSkGoN+knUHJUYGvelVtLJeugbKrwXuw3fffTcqBXKh0cPrp3jakCFD4plnnlnqkyxA0N9U96NwJWbue6o6kwUJXQBUHa5PqjBDVUS4X7TxvKEQIcUKVUvC+mGePGvI4ETyhcOHDxfqjjlSiI4K1Wgq0v3DK5nH+I7nVrXGvNBlyQmyivaIrRPm5a/0B4VLKVld9FwNTP/cEahTBDzC0Di+oc80BwH9aDYp3FZOSdIPpRduy8HvWL8ujzBInGmUJFZIEyVJvGyjojgl6ViRPnn3h6IjfUAQhz689957gYJq5Y0VbiIMY8eOLRRhoD/6gPIjwzxIjFyqbSAnNBBVkG4mKN1o+WEqvociR3RB2ZGsqBn9QnWiFoGqRQcoOlybRWu0EBGg7gtRBBn6VsOBZxDRBGULs6gAVKK86AKDJWKydu1aK3hInRhqJ0CTYl5yGML06dMtasG9VKlxXKI5yhIVHnroIcNMqWWP2FTOQ4mS5IXbjoDHP3AE6hoBdxjq+vT65FqCQHOHAaM1Na0iusOQwDhOr80dBoy9cocBDQPcdXcYjtMJOAm6LackUVitEiWJIm3QfjDS0Q1kNQxpHH+t/lsVce5xLf6ZMU2Btv79+4fevXsHRR6yurHvJHa2vqAPzZ0717QM9KX0pWaUQ1WE4lSksR96ARwZ9BDQgLjWMcjRVTz66KNB6VnN+eCzvAaV6IUXXjCHAf0Bzg00KapCU6RN6aAzq1Zzr0FnShWeFdmoeMhySpI7DBUh8g8dgbpFwB2Guj21PrGWIpDlMBBhYKWO1U1WKln14wfeW+0QcIehdli21p5wGFjBp0Iy4ttyw5X7jdX8nj172vcY+Vmr7xjlCJSJVuD8i8ZksGCAw+unkjGGNAY693deY8Udw15ZkAKCbJwRxoNhz3MBB6RodIFnDdEOjHzVnTA9BKv/iJuZn9KrmiOTp4VgjlSDpqqzCrUFtAtUsmY+VEfnM8aGc5XVF3NBwA1GOGqVogvg4w5D3lXi3zsCdYyAHjjeHAFHQAgkDQMVUvUjW0olKEPFOMHKzhKHDRtmFVm1IueY1RiBcg2DjCdPq1pjfFtDd6QsRVMwcOBAq7XAvZf+ZOhbSlW+Q8siIzdzSjLKrbaH6EtWvT31I2M6oo+QyNgqMXPf5zW2QW/w0ksvWUEzdAb0R0E0PpMDkTuedAzGRRE2Cr/JyShVY0YLQdrm5557zupLsF1eY1zULyFlKoUl6UNGvekYSPFKxWY5Jpk1IdLcZs6cGa+88spSHYiEV/kr96XXYcg7K/69I1CfCHgdhvo8rz6ro0CAH04Kt1USPfOjiaFBISUKt4kjfBRH8F2yECh3GMAaA5E/jCAXPWchVz/flTsM1CFI1wCvGMKnnnpqVLafXBEviGBwI4ymvoGoQtYXfVCXgDoOCISLtGTgU4H6rrvuMoOafvij3xUrVsQ9e/YUFk6z2MC4EG4zR651ni+KllghuKIF5Bg7eFG8joJvFLMDpySapqYJAvKsxtwUTbBiecOHD4/SPdi8ynEvf89YXfSchah/5wjULwJOSarj6JFPrWUI6Mezah0G/WhaiB9aElxlUqpWExC27Ki+dUKgnJLkdRgSKo31Kqfd7sE1a9aYTgBRcHlDS0T6UlU/DlqNr6pngdqEeBpOPhRCtBB8BoXowgsvDJMnTw6InpXpqLz7iu95LjAO6iuQ8pX3PA8QFA8dOtQEylCJEBnL8K/YR/mHaBcWL15s6VQRdiNQliMU+vbta3oDtDo8X2Scl+92xHuZJZaGFeoW1KPff//daFJoFxgXSQKYI31Xa8xN0RpL6Yr2gfnxWbUmJym0a+d1GKrh4587AvWMgDsM9Xx2fW4tQiDLYeCHEgNBIXvLEc+PMJ95qx0Cf//9txlloqQYpxvjkYZjRhErL9xWO6xP1p64B8lEtGnTpjBjxgyrmVA+VoxopUI1UTB1Ctq2bVv+dek9GYhwFjZu3GjZi8hmxP3apk2boBSo5oz873//C6ecckppn2pv6IuaC+gdlDbVMiOxH9oAVWK2V1GTqu3e5HOMfHQVODFK9Wr1DrjOGct9991nOikcBxyjvIZQGScBETYOFI4IfSHCRp9x9913W2akLMeDPqhLoahq2LVrlzkPWcd1hyELHf/OEahzBOo3eOIzcwRahoB+bI2SVEnDAC0GagO50eEfe6stAlAroHV07tzZqBl67LqGobYQt4reFAWISu0ZVUwtatW+pF+AsgM1htoJgwcPNt4+21ZrchCiBMVW3wAaDftDRZIRHZXG1PQGck6q7V76nGNwXaIRQK8gg9koRGggHnjggcIaCDrkeNRCQKPBs4TxMCc5H1HOT1QRuCgHIFNvkAZGX1D4FKmwcdAPf6eddprViGC8efPje0X14mbVj5AjZdQ/cMr6cw1DOgP+6gg0HgIeYahzh9CnVxwB/YA2qcPgaVWLY3esW7IyymopOeBZeaUyL+dDxkuTCIOnVT1WpE/u/bkOyB5Eth7qGhw4cKA0YK4FGcSWjejVV1+1tKEykkvf80Y/4UbxYbX8jTfeCG+99ZZlDWI7MiNB3SFKSGrWIhFCsgetX7/erklSqfJ/ogtEKbp3725VlYv0w9i4nlPF6RQ94TMiApdddll4+eWXLQJSJNMSOBGJIVJB9INoCpE4MkcpMUPo06eP1ZjguNWanHTLSMVz7qmnnrJsS4wnq5VHGDytahZS/p0jUIcINJ6P5DN2BCojkBVhQEjI6jcZVzzCUBm/Y/1UPPN4//33R6WAtJVcPW5ttZMV4osuusiq/3ql52NF+eTen3uQVfbly5fbOS9f7WYFnVV+KjYrdWjFicjgjVxHqm0Qr7vuOotSsR+CYrIIKWVoFPUtd/U9dc4K/NNPP21iZFbXGY80AhblkAORNiv0SrTihx9+iKIPRdUSsb6IXHK9i0JUuKozcyRDlFKoWjY30ZlKkQr6+vDDDy0zUt6gRGGKcsqiqFAmdmZuYEXEg+cd78vx571HGPJQ9e8dgfpFwLMk1e+59Zm1EIHkMFTKkkT2kC5dusRx48a5w9BCXItuLm63GU5kosJJwGDhD6PKsyQVRbF1b8c9SJpQMg9xztM1wCt0oCyHIRnSWnGPqpQczzvvvJLDKaFuHDFihGVXyqIylaPHWFTN2VKfnn766TYWxiChtI2PtKgtadJCREUrbFw4MMwp0aSktTB6U5H+oO9JnBxxWFRrwYx77pEOHTrE22+/PUpnUSjFK46VohHmmHG/MTfVpIiK4kUVfDOs6bf8HLCdZ0kqcpZ8G0eg/hBwSlIdRo18SkeHAOF4pUwN8+bNC59++qlVdU096YezVOlZedIzC0alffy1ZQggTJ0+fboJQSlmhSCTJiPFBOeInvkjI423+kSAe/DQoUNWmXnq1KmW6SjNVCvcRkmCbjN79uwgI74JrUg/z0Y/go6E6BeBMgLjdP1AZ5NBXej6oS/EzgiCEQ/v2LHD6HFkQiL5wWuvvWZVpqETFWn0hyh53bp1Vq2ceTIfpUI1MTVZjaSLKJR5jXFJ72CCbmhB3Dfp+YQQe8qUKbnPJzlNJnCWE2XPOYq9MR4oTaNGjbJzQIE68IO6lFo5JQnKWBH6VNrXXx0BR6CVI1B/PpDPyBE4OgQ8wnB0uNVqL/LBq5KuUTagRZSvKkMHW7ZsmRXPqtXxvJ+TD4GsCAPXAyveCIYpSLZ///4mE2AFnxoG0gKY+JcVc2g0RAdvvPFGS2hQtH4KUQg5CVGZkazWAv1A0+nUqVN89tlnjT7EWIs2KETS5kQ5xKXrmhoMd6mug5yISG2Gog0qEcJtcEj3CZEXOVjxo48+yq0HwbF+/vlnKxB3zjnn2HigGhFFIYrKvMGXSB8iao8wFD0zvp0jUN8IeIShlTt8PvzaIZAiDAgqN2/e3CTCwCqlfkBNMMnKpygFtTuw92QIEFFQRhoTva5duzYcPnzYVjdFgbDVXDkNtgrrq5r1e8FkRRiYNSv8V199dZCuwOopqHBaCQxW2pU1yATKq1atsggB9y0r9z169LDoFfctq+RZTY6AXXtEuYgmck1Kt2Qia1VmDv379w9yQAqtrst8sGsYsbMcXnumvP/++zYGImUPPvhg6Natmz1XssbEd/RFzYaffvrJ+kIYTjSG+UgTYQJo6sRQW0JGftXuiFBQb4EoDSlZqVEhZyiI0mRCaYThciiCHCOL8CizU6kv+m33bx0GFz2XYPE3jkBjIFDf/pDPzhEojkCKMFRKq+qi5+I4HsuWMhgjK6iscq5evdrSRpLWUs7DsXTr+7YSBLgHs0TPVHru169fFO3IUoKmabFqTgV2UXuiCrOZOJeoANsTXSDFatGIAJEKUrvOmjWrlGqUFXj0Auib0C6wTZHGMdHmUCWaKBmpYmVZWL8qPBdVoC4eOHCgSFcm1EZ3sGTJEtNV0A+r/6SaldNh90xepIL7i9SuGzZsiJdffrlpKOgHTQW4IoJGFC5KZlQmKYswgGP6c9FzoVPlGzkCdYmAi57r8rT6pI4GgSyHASqEKsxafngMWn54vR0fBMAWg4xsVGTDgR6SZwgdn5F4r/81AnkOA8Yxwl6M8OQA8Hrw4MGoqslR6U5LRj5Grjj55ixA1SnSuPboWxoFEwQnQ5nMSDfccEMUr7+ws8DxuI5xFqZNmxahIGFw84dAWZWYzTkqQpNiXFD2yIyEYa9VfnM8FEExwx9DH7F4XoMaRR2I559/vpQJiWcbQmZFU6I0G3bfucOQh6R/7wg0HgLuMDTeOfcZV0Egy2Hgh7ljx45mRJBq0Q3YKiD6x47AMSCQ5zCQxad5WlXuxQNapZ8zZ04pMxIr7/D7ScerWgyWVajIsMhA9Ouvv5qOplevXrayTl+iPsXx48fHLVu2FOnGtsHIx+EVPcqeG2REYjUfTQV9q/ZBpMBckWcJuODIoNFQHQnTG+DMiJ4Xr732WtMu8H1WYzwcD50QhfGSM0R0QdWzo5I9RFGcLMOSOwxZSPp3jkBjIuAOQ2Oed591BQSSw1AprSo/rjgNCAGhPhRZFaxwCP/IEXAEMhDgHsxKq1rJYcDI3759u9VGUNYio+lwr5JWlWiE9AOlaETGoW0b6Dg4BdCaMMZxFogIQN+hhgIGd9FGZAxHhtotRCiSCBuB8syZM834L+IscDz6+vHHH42OBM0qjQuKE8JpnIW8vnAYSLnK9sqmZH3QD5EPajGQ2pVGVASHASeCcbNN+gNXT6tqMPk/jkDDIeAOQ8Odcp9wNQTcYaiGjH/uCPw3CLTUYcBIxggmgxY0nZQ1CGMf6s7rr79etchb8xmxCIDR/Mgjj9gKPo4C2iVVYY733nuv6Wgw3Is0jHMikRLvx9tuu80WG9KKPoXW0OdQ44H5Fmk4KpMnTzZaFGPC+SCr0ZgxY2zujItjVmscJ0UoiJSm7EfMkWJvX375pUUX2N8dhmoo+ueOQGMj4A5DY59/n30ZAu4wlIHhbx2BE4BAnsPA6jzcfyIBbAsn/+uvv44vvviiCXhZAWc1nJVx1U8wBwDuf5GGGHjp0qVWtAz6EP1A1+nbt2+cOHGiifGzjPLyY7Ad9B60BVScpq8UpSTywQo+xyvSX+qL+SCUZo78tW3bNr7yyitx69at5Yeu+B7HCqoV9Ch0HYwHpwNNSPfu3W2syRlyh6EihP6hI9DwCLjD0PCXgAOQEEgOQ6UsSXCPWY0jlF+0kmrq118dAUegGALcg9WyJGFwEznAgP/mm29sxR964PDhw40qyD2ajHLqCyg9cm5NgjQqjGSlK7XoArSnRB9iFZ+6DgiX8yg/qS9emQfZvaD/ULGacdEndJ4nn3wy7tu3r1B0AWchZQ3D8YByxXMIo793796FaVI4TcuXL7cK2DhDCUv0IGg/cLyS85IcBs+SVH5G/b0j4Ai4w+DXgCPwLwLuMPil4AicWASKOgxk+qH4GKvrqssQ27RpY4JiVs7h5EMhSpz8vBlhKBOxQAw8YMAAoyFh3BOloFAbKUhbQh9iDqQ/RQuBDoDxYKBDlyLTGiJsog/JQM8aH33hFL3xxhtGjcLYJ6vRJZdcElXDwcaFhiOr4egwfjIjQT9if8ZDdEFVoQ0n+kjjcYchC03/zhFoXATcYWjcc+8zb4ZAnsMAdxgDwEXPzYDz/zoCNUKgJQ7Dtm3booqHWQYjVt2JMGAMkxkJ43/v3r2FRpXoOk888YRFEFM0EcrPiBEjLFJQqKN/N4Lag0AaehN6hUSTInKBrmLnzp0WNSjSJ4a8iqzF0aNHWx0IDH2yLBFdIDJQRIRN9IDaEaNGjYopeoJDROanlStXGk7gnpo7DAkJf3UEHIFyBNxhKEfD3zc0AslhqJQliR99DBEKQ/3zzz8toic0NKg+eUegBQhwD2ZlSUoaBmiBCJp79uxZymbEPQrlZ+DAgWYEQ+XJazgLrPZv3rzZCpURDSBKQSYiuP1EF/LSlTY/BsdduHChORtoIFJ/1HFglb98Nb/5vuX/BwsiFdSXYF4paxORD1W6jgeUgSmPJkUfYKWqzRaJwbHij3mqYrXVdUjahXTs5DB4lqSEiL86Ao4ACPwf/2hFxZsj0PAIKCQfFD0IykceJEoM4kmXMNGKXDj//PODcqCHuXPnBlEDAp95cwQcgdohwD0oAz7IgA9Tp04Nu3fvLnWu1XW771TVOEgHEJSBKEjEG/bv3x9k9AY5DHZ/KgVqkEEd5FwERRxK+1d6I+M4KBIRtIofJk2aZMcW3z8oMhBEdQoSOweJlIOM9Uq7H/GZDPSgquRB+okgMbY9R/hMK/tBeoGgtMxh0KBBR+xX6QM5FkFahyBqU5gwYUKQIxLARzqGoExOQbSrIMcmyCGptDuLgYG5gM+MGTNsPNJVBDkMQRmlws033xwUQQnSezTZn+N+/vnnQXUignQdQeLs0vccS6lcAxgzR2k8DPfSBv7GEXAE6hYBdxjq9tT6xFqKQJbDgLGiVblwxRVXBK0emgHAD683R8ARqB0CWQ4DR8EB0Gp7UGQhSMdgf2nNC6N+2LBhQYkJwuDBg3OdBfZTtDBoBT+ojkOQKDhgLIt6GCRUtmMoIlB4cvSn6uRh165dYdy4ceaE4JAwZhYblixZEkRzMiM7r1P6Et0oKP1qUMrTsGjRosAziDnidOAs5DkezEWZkcKOHTuCKE3WH/gq6hE6d+4cpk+fXtEZynIYGDdOCvjghHAuJMDOm45/7wg4AnWAgDsMdXASfQq1QSA5DKycscLJCmF5k2gxKCd7ePvtt20FEsPCW+0QwEgS39pWUkW3MGOOlWPljQ+iYRQytGo3Gu/pRCDAPXjw4MGKEQbGg9HMfUj0QFWUbfWbz7gXzz33XDNiWf1mFb7ayjv9cK1hzHOdia4TvvrqK4sucnwMYCIYEhaHrl27snmhRiThl19+MSN/wYIF1jdRSJwE0XsCzgfjyltoYGwY7fQlemSQuNv+mM/ZZ58dVHshdOnSxZ5F1QZGH+Czfv16c4ZE3wqqM2E4pXkxb+khjoiUJocBDJpHGOiXSI7qOFg0R7Sm0KdPHxuXR1yrnQ3/3BGoDwTcYaiP8+izqAECWQ4DP5T80OMwsOoHZYEfW2+1QwCDCzoKlA6JNO09DgMrxsqCEzp06JBpBNZuJN7TiUIgz2HgPkwNR4HGKwYshvDs2bPtNc945TgqrBYkTg4SO9sqPA4E9zgGPrTD9u3bmxOSjpf3Kj2B9Td//vzwwQcfBGkxzEC/9NJLAzSqxx57zCKTef0kYx861siRI8Nvv/0WpKMwQ51IBY7HxRdfHNqJVlSt0Qf3kbIrmcOwZs2awP0FlZLoDBEGaE2VWp7DAN7ghPNzyy23BJwGIg70TQQknZdKfftnjoAj0HoR+H8AAAD//zqlpQ8AAEAASURBVOzdB7w1RXk/8E0zMTGJKSZqDLwQFWyo0aggTZqACFJEQFGULmChSJEOIh0EEQQUkC4gKCJiAxu2RFHBhgj2mqjRFNP2P9/h/1z27nvK3vbec+6Z+Xzu3T1bZmeeac/vafNbdUpVSYUChQLV//3f/1Xf+973qnPOOae69dZbq3/8x3+cooph8ru/+7vVU5/61Opd73pX9Zd/+ZfVH/zBH0zdLydzp8C//du/Vddee231+c9/PtP4P//zP6vf+Z3fqf72b/+2WmeddaqjjjqqeshDHpKvzf1rJYdRpIAx+OMf/ziPv+OPP7762te+Nq2YzeXqt37rt/I9fWTVVVettttuu2r33Xevli1bNu2dXj9+85vfVLfffnv1wQ9+sLrqqquqb3/725X8jOs11lgjzwF/8zd/U/3hH/5hr9eXu6Zc+u+HPvShap999ql+9rOfVf/1X/9V/emf/mm100475b9/+Id/qH7/939/uXfbF/77v/+7+sIXvlDddttt1amnnlr9y7/8S37kz/7sz6qnPOUp1QUXXFD91V/91cCyyeNb3/pW9epXv7r67Gc/W/3iF7/I9XvEIx5RHX300dUTn/jE6lnPelb70/m3cn/yk5+sDj300OqrX/1q9atf/WrqOfUMupsPH/awh1Urr7xy9ZznPKd60pOeVG211Va5jr/927899U45KRQoFFgaFPitNAEUwLA02rLUYo4UKIBhjgSc4+s///nPq7PPPjszOB/4wAcqTA+mBBMHMGAggYcHP/jBc/xSeX1UKTAbwKCPYFb32muv6vnPf3718Ic/fGj1/v3f/7163/veV7373e/OTD6QIp/HPOYx1bOf/ezqmGOOycywa8OSJRQAwaB/+MMfrg4++OD827uY6Ze+9KXVDjvskIFMl/zkBSwo38UXX1z967/+a/WgBz2oeuxjH1s97WlPyyDioQ99aC5vr7Ipzy9/+cvqrrvuqvbff/8MwP/nf/4n5wFMnX766TkvdW0n76LNxz72sVyPe++9NwOheM79AAyOABAg8/SnP716whOekOn/qEc9qvrjP/7jDJbi2Xi/HAsFCgXGlwIFMIxv25WSzzMFAjC85S1vqT7ykY9U//RP/zT1BQulxb6pYegiLZzKoJwMpACGhnZnjz32yJodDE8kdA+GcIsttujEEMa75TheFDAGf/KTn3TSMKgZhhQzveGGG2awSYI+TPNnLJO4k9Rfcskl1Xe/+93MFNMmbLPNNtULX/jCaoMNNhgowW9SNeaNCy+8MDPnN998c74N6G655ZY5v0022aT5ysBzmop3vOMd1WWXXZbzAyAw4K94xSuqZzzjGdW2226b69wvE0AbWPjEJz5RvfnNb67uvvvu/Chth3GknP20J//7v/+bNTw0Ja95zWsyXYzNSE3AENfi+Cd/8ifVaqutVr34xS/O31l77bX7gpp4pxwLBQoFxocCBTCMT1uVki4wBWLhL4BhgQndI3tMzn333VftsssuGTD4HdJJgIF0laR2xx13rEgwS1qaFJgJYNA/MNLMYdZaa61qv/32y4z0IHOYAAsY4ne+853V+9///qwNYNZEG7Drrrtm8yFaCteGJeUFPphOHXfccdU3v/nNrGlQtmVJms+sZ80116we//jHD8sqm0QyP7rjjjuqK664orr++uuzOZBy6PNvfOMbsyRfvv3qaNwA3kz7mE4qFw3F7/3e7+V3N9poo0wnGop2/dCGlo+JFjOmK6+8sgIgXI/UDzC4bpz+0R/9UQb0aPmSl7wkf3P11VeP18uxUKBQYIwpUADDGDdeKfr8UmAxAIOF1nfZ61uc/UkYAhoMC317YZ/fWo9GbuymmT8ABXxHmowJRuTRj350llzuvPPO2SxpNEpdSjHfFJgpYPjzP//zSp8geWf2MyyRljM/uvTSS7PJDym8sUa7wD8AYNh+++2zliIA66A8jVcM+pe//OXqyCOPzNoKTL+xC+SecMIJ2V9gpZVWGpRNvhd58au47rrrKmZ5Er8d5j4nnXRS9eQnPzmDpF5lM2bMI0ACUyaACAAAItSPloPJFl8PebYT2v/whz+sTjvttOqLX/xiNotqP9Mcl817rkvKhZ5//dd/nQEDU0JmVGFCZSyXVChQKDCeFCiAYTzbrZR6ASgQgGFFOT1bZDHKFnUOmBgPzpIS9T67YHbGzAeWekIHNuBNwKDOGJAmYHCfH0NJS5MCxmBXp2eMKcn7KaecUj3ucY/LZjCDqGK8kbbfeeed2dwGQP3nf/7nDMgx9AcccED2leH03DX9x3/8RwYeQC5TH2MZwCdVD38DpkBdQL+8OBvz1WFGhHnX9wEZ5kG0A5yMe4EF5VU/8we/jAAcrjHZWmWVVbJJEwfsXtqToM1XvvKVau+9987AR13ayXO9vu+6FPe0DVDCvwFwOuigg3IZaEe60KL93fK7UKBQYPEpUADD4rdBKcGIUGBFAQYSP46F3/nOd7L5AaDADIFpA/tliR02e2DmFmyBMQpLeaEdBBjUm4aBBPnlL3951UVaOyJdqhRjhhToChgwpLQLTH1IxPUJkYMGJdoFIEEEIuAgIhkB5/I58cQTM0Dv4jTtO8oqD4Dlc5/7XP7D9HPK33TTTStRkV71qlfl38FI9yuf/k8zQOOhPvw4zAU0jMytmDsBMsraL9FQABkXXXRRNrX61Kc+lRl4jDuzKJqYF7zgBVnb0C6Pd5kEMkViRgW08Z1op66AwXvGLU0LXw7aDWCBhgSAYLIEyJRUKFAoMD4UKIBhfNqqlHSBKYAB4AB51llnVR/96Eezw2F80kJJ2td0eh7mXOldC7E/DIH84xxDYHEmCQy7Z/cl38IQYYBIBF/0ohdlKeNSXWDVtwkYOJu7JmFsMB6YDQ6pIuGQlpa0NClgDPzoRz/K0YaY83z961+fVtHoF8YixlNEIxL5v/iLvxgKqIH0T3/605mxFwUJc48hp7GiDeC7RCLeBZgrB4b6G9/4RvYJEApY/q7zqyClZybFBMg3BiV15uR/0003ZU0jcyKmRRKGm0P3m970pqxp7Dfn+C6AgemnIaWpoEkxfggbmCFtvfXWOa9eZfE9WhK+HeY/woteyXfkaX5SNiDMX8xdbSAiD8/SstCUEn5wKAdgmEmhjXnNsde7vcpQrhUKFAosDgUKYFgcupevjiAFMPMYlNe+9rU5ysj3v//9aaXESJDyXX755dkUAmMwKGGCv/SlL2XzgmuuuSZrFMLkyLcwHBZ5Ggd/7WRBBlAssAceeGBmZtrPLIXfmBDMFnOIPffcM0uA2/XCVAANaM9Uq6SlSQHjAhOunUUKAuB7JcwmB3h/QEM/Rtq7+hdTJFo8knpjMsYhif1mm22WmXtgtGvIXuOVBN/eIPLF8PuOOUKkpnPPPTdrGID+QYwwRpvwgM+AeYe28de//nXOS5//u7/7u8zkv+ENb8gOxf3AjPqdeeaZmemnpTCvmH88zzwK4HDsZd4YwOf888/PdFeXAAC9aA+sMQUL88HPfOYz2RRr0DtAg/e0kz90VjaaQ2CmazjcXuUp1woFCgVWDAUKYFgxdC5fGQMKBLMijjqmwmZOzWSBo1IXwcTC23YctGCStrH9Jb386U9/mplf9shiqjMX6GUX3PyGc9+xuHIUJKUEGIRUHGSO0M5jnH5jtNDLJlE23mIy0kwYLuCJidbb3/726u///u+bt8v5EqKAMXjPPffkSD3auj0GjQumSIC7ELvPfe5zM1M9SIpvTAL/nIjtQWA8GqsAP+0ChhUw33zzzYdqA5Baf8VUC73MtMm4xnQrAw0FU6QjjjgiOzuLGjQoKRvfHT5M7PwBGcy1sQ5sGP/+jAsAwr12QjOgg9M10yiaBdeMGQw5WinPIx/5yCzpb77v+1EXIO0973lPrl/zmfa5fAEZ8yQBi+8BOb4JpKCHzd5oKdAZvXolbcmUDN21JTMl5mDAoLqWVChQKDBiFEiDuaRCgUKBRIG04NWJQalf97rX1WnRrxOjOvWXhm2dFrh8PUk968TgTqNZWhjrJCWvk19CnWyI69e//vV1ihBSJ+amTozEVD7NPJ3L119cT2ChTsxCnRiZOtkb1wmc1El6mMs27YNL7EdiuOoEGKbo3qQLuiczpDrZg9eJmVxiNS/VaVLAGPzBD35QJ+a1To7MU+PC+EjMcp1AdJ20CnUC43Vidpuv9jw3LhPjWqe9EeqkiaiTaUzOMzGkddrpuD7kkENm3KeS+U6dTJDq5LtQy0e5jNtkq5/HbNIW1ImB7lme9kV5KVvaHTqPe/VMDHm97rrr1snUqk5O2QPHvvol5rxO2o46CRbqZJqVy6NMiQHPdEwAqWce3k1goU4agjqZPdVJCDKN3jEntY8JaGVapshQmbZRp6R1qZOGpD766KPrtP9Erk977mvOddGmSdtQJ61hncKw1rfddludwF1kWY6FAoUCI0SBomFIM1hJhQIokBbQbAJBfc+HoSnpTmN2KmLJ1VdfncMGkoSx/RVpRVhFPgns70kMSdxI7pjakOJ5v1dyndSQJJLJDbtsJjcknzZZInHrYp/dK+9xuob2HC1JbElJ0dC1xFTkPxJXUmBmFySmJS1NCkQ/uPXWW7NvAkfgSPoCW/jnPe952U6/i8bN+KS5Soxodeyxx2ZTHZJw+fAPYtL0xCc+cTnJe3yzfTReSc6FLOUPYeM35aL1EMXomc98ZtYGMLuhKRyU1JVmQB6k+6T1TJ3MKxz8lY3D8yAzKXWhkbFngo3eQiOTwEL2y2DKKCRrrzzCZJL/RWLyK+FgXRuUzFXMkWj5bHzX3s/B+wnwTWlX+UWYE5mZaQtzIXo1kzzVmcYnHKK1ifZB10HmZs18ynmhQKHAwlKgAIaFpW/JfYwoYAG/LzkNinfOPpmqPVIABouv8InU+xZhYIEKnh3vxz72sczsMkWykLcXxsgrju5bDKn4AQM2xphhDoEWfCFVhzEdkddSODLHOPzwwzMtAbCgITqhNZMktAccSlqaFOgKGDgoD/MhQiG2/B//+MczYDj55JMz0ZjC2CeAvww7fOfGYJekT3LK9n2Mto3fjFHzgbyAfZGIuiTM9b0pahPGG7NvLpEw4UwQ5YeB7mduZU7ChDOftKOz/RsAEOY8QrGut956eed05kO9kncJRgB0m8IxCxyWMPfMiNRTubWBa80U5QLUmFrxqQAc+FkQpAAN/tpJPoAcWgIMQsnyBxFlyTzZ/k77/fK7UKBQYGEpUADDwtK35D5GFMAMYFSFH+R8aIGLZBG0YLEr5qBHA4DJeO9735sl42HHbCHE9EjDAINFcP3118+LIztqiyNtAobGtyYJLKAXyS1JJ/BFKqk9pCZgwKQUwJDJsiT/hdR9kIaBzXsXwGDM0loJU8oxmc+BvoQpFa74xS9+cbXVVlt1ZkSVjRTeHJFMiKYclDH0GFyOzquuumpmcIc1jrIRLNjN2Y7MohMZ88ACoQHAIDqauaBfAjhoF9AqmUBOaTNpXoQfttMywNH2tYr8MO9ve9vbMmAQrW2YdiHeAxKU8bzzzsvahn6aHuOXxsS4BkxoUJRVVDhaiH7JvGduVHb7a9hIj6bF3FhSoUChwOJRoACGxaN9+fKIUcACJ1oJRsKCZkGNFICBpJsjIabDwmYR5OBHkukZf5GagME5yZ/FlSaBRoG2Ql7OmR9Z2C2Uk5oKYJjUln+g3sYgsxqMNIaUaVqkYPa7AAbjEODn4HzYYYflfEjzMfck5Pvuu2+V/ASyJD7yH3YkDMDsClkqOhJpvmQMA7HCuwL9XcYw8KE8oh8ByKTxykar+MIXvrDaeOONs6axOYe0y0dDILLYhz/84ayZQztzDEYb4GDWxAm7l4ZCXcxx6kH6bx6L94EeTtzuY/hDABLfJygJgLQsmVEOY+RDk0KD6DtMN/0xU/KdZv4xfwJKyi4kLNraMVo45eR3krWNg4BUlLMcCwUKBeaXAgUwzC89S25jTIFhgKG5eMfC1rym6nHduXv+AAtAA1gQXUlEEAAB4+NeOw/vTmIaBBhC4ij0IwYC3QalYEKKGcMgKo3ePYws5pnkm9S7KYk2TgD1LoDBWLYxInOb/fffPzP3+gRQjtk9++yzs9kfG/muiT8SvwXRlvRDPkr6JeaeiQ6tAyZ3WDJHYJRpKnbdddfsNyUvcwRJOm0B8zvgY1BSHvUjtRcuNujDFIk5Uz/TKN8n4LjrrrvyfhG0L941VtBXfZRHXT2nTSJ5F7NuozuAjrkTpr5rAnJoU5Kjd/4TNY5gRr7xJ6/mnAig8A1hZiX0LRMl7WgOUOYyxrtSvzxXKDA3ChTAMDf6lbeXEAUCMHC266VhaC5iqm2Ba17zu5ksrLQHy5IU7mUve1leXDkMkshZBIeFXGzmNQnnTcBA6olRCfqSkqIdW2vMGSlxPymj95h7kLYOk35OAl3HqY4k2oINCH/KhCj2S1AHfQFDy+l5mEkSe3xM6Q033JC1FRhf/UHf8ccB2vgbBjx917iWH5+mq666KpsQmR/MF8oj5Kk8AZkuYxrTzN+J2Z1dojHMwAxfCjsin3rqqcs5EytHMymTMgilivEnscc4M5Xcb7/9qvWTqWO/8MPGB0m/HaHVR8hZdMD403ryI3Lf5nb8KrRJJN9tAgbalZkAhqAlraxvADzakkknurgfYz6+6Tdg5o9vF3MoG+3Zf4O/A7q134l3y7FQoFBg/ihQAMP80bLkNMYUsGBjTkjbOENiOEnwIvVayHpds2iTFAIEJGFMDEjhtt1228zkWlzdLwtcUPaBI/qnMJeZ+WFqgSELOmFS0FPbsGvGOPQDDBgctusYxGBmIh9fAz7kJTILrc8gCaU2ZlKBmWG/TjKM+ZS8h4nR1r4VyTuewWTqV5gxZVUu75Bq6wPexWA2yxZ59Dqih7IAVs7nmnyXPXpXxjm+p36+TzqM+VRH9UNXeRk36q5+QVu/1T/+goby9C7Gm/2+d4xBTDO793AE9pzydgUMyiCaGYaY063vo7l9G+xrwKHWt7ok9UVzpj82YOTojMlXX1oAG65hYP11yVPdr7322tzPRUhSNv2H1pFvBRAwCHgoj/rxX7B3gyPTLf3QXHN08gOihevl7Bzvctjm24E2aKwu5iomPyl8cW4DEcuYdWnjSN7XXqFhmClgiHzkyXmcwzYaKL9yAC/6lj7VTvqSPqKcgA2QtkoyUwKM9OMutG/nWX4XChQKdKdAAQzdaVWeXMIUwBBiUEi2MSsYgiZTZqFsM3btaxZSTAnpN2k404D1k6TPOSlYqNCXMBlnXTUMBBOSPfbYI0sdSSDb9A0pKHMEmgP07pUCMGCgAjDEc9oQ08HZFeOB6fCcvHslfYCtOntzEm87DwMz8vGetmZmxhk+ku+TnrJ3d46RYaoCECm7jfjYiQM9/Fkwa8MSWqAJIEQ6jcmca1IuTCrmT7na/btf/miCkUQPR2VBZ22CpvwGtCVptzZSdgwhMxdA3F+ES8UEAgEig5EYYwSZJAmfOxfAgFbMhmz+Fu0AHGKGAQbAoQvd0QDzqj60AfwXmBKhlTaVFz8E5e6Sn7wwxt6hFTDfoCfa7bbbbhl0CKrQBKDtdjBW0JPvw6GHHjplbgWIAgrMuQDiXgy0b2HUmQUx1QpAADz7bto/IfdJQAIQ0nbN5Pd8AAZ5KgvgQ1PCd4ymhJmTftLPARvdjVW01p76GyGDPqy/9RvHzTqU80KBQoHZUaAAhtnRrby1RCgQC6gwqpgBzA5JIkavl5SrXW0LmMU9optQly9LJkgWb9IvjCHpFyBR0vIUwICQ2mPKhb8U0hazjf7thNaYoABmIb1uP6dNAT7MQy8JvrbA4JGOstemsdBm7YQxw6Arlz8MDUlzOLsqB6ZR+2K4I+k3mGKMoTwwNxgyZdJXMDkAhiPnVMxiL+aumR/thv6pHJxF+zFU8c6wI1oqP8DDXp5kG9PPhG5QUh/fpwW46aabphhOdFZHjKp60z4AAsHAKT9ggQYk7GFqpByAF/DEWdcuyRhI0ceACs9H8mwXDYP+pIxC8NqfQFmUA7BjZkMT4FtRtsi/31F/kh8GWx8QQc27+g/zReaG6Dgs6evqDnAyicIkM8WJdgAiAEjM76CyqZ++cMstt+Q6YrA97z0AmMBDf+yVBwYd0ADGTjzxxCntgXYLvweAgv+CfHql+NZb3/rWrMVog/Je7/S7FqDBN7W7uRd9tL25uNc8IC99wbgydgBwdPNH2wBIuF5SoUChwDxTIE1iJRUKTBQFEkNXJ4Yr78ycmJs6SUrz7rFpwa0TI5d3bU3M6NSOqc7TAjXtd1o08w7OiVGqk1lCvfbaa9dJxV8nZrdOi9xE0XMulU0MaN7ZVxskW/A62SRnOrfp3W6Prr/75ZOYjToxynUy6agT87RcFfSRxFzlXXD33nvvvGN3Yuym9YGuZYjnlMWfvqPfJOamtitwYmiX+37zQmIQ8y7YyTY9757r/chzLkf5JAa8Ts6keUdxuxcPS2iSzGnyrryJMetcjqh7HJvlds3vBLzqBODyWDIOE5CYlr/yJiCev50k4z2Lqt0SOKmT6VDedTnonQB93nndjsjq0DXJLwGdOjHQtfkBvZQ1gaM6aQ/rtPfB0PaLbyXmOO9i/I53vCPvYi0fdVK2pGGpE5Ocd232zUFJ3ZP/Qb3ZZpvlfiQf/WmbbbapEwhYbhf6yMv3E1Cr08aUdYoEl+uBPuhsV+2k1amTNibnkSI1TaO9b/jzvLHz5Cc/Oe8uncBzZD/no3kzafDqtCdFvcsuu9RJK1sncL9cOZTBX5QpgfA6gYU6haGtb7zxxjqZOeU5eBgd51zgkkGhwIRRoGgY5hmAlexGnwLMj25LO7+yn73iiiuyNJhqntQ2LTI9NQtpXpgy2UiLfJZWshEWmpGkmDkF6SdJK4lhSYMpgJ4kpUx8mHrQKpC4kkKTYjfpPTinwXf75aMNmYptuOGGOYwlZ9Nm8h5J+bvf/e4crUdkHNfmkuL9xOxk6S/tU2IeB8bu9w4JOWkyaTlHXn10vhI6sMNnC087pj8PSkx9zjnnnGz2wkxHW3VJUfd4Fg0ixb3EAGZNi/qRLLse9zzrHWNsUJSk0C4w1eGkrIwk0UyvEvDL79KiNL8f5eh1NFeQenPOPeOMM7IJDS0RDRWtDI2F38o+LJlfaIgOPvjgLD2nPaFdQfPE/GdNBel4v7zQgoaAdofZkd2mlU8bMnk84YQTsoaG5sO1ZvKu79GUMMu6N5nY0Z5J3hXKleaFxuzo5ANhXOr/7SQf8xttxmyiJLXza/+mcTAH0EihFbMte6/oD9Hvo09EGzpqY7Sk2dXWzLvK3g1t6pbfhQJzo0ABDHOjX3l7DCiAqcFIWITiyP6aecF73vOevJDGIqQ6sRA1q+Z+LEwYDgumMH9MAJhTOG8v0s33y/l0CmCeODgCCezVxd7H3EUKesfv2R575aMdMRcAn9CTm266aWYumt/wnv7yvve9LzNmHF2DYWk+N5NzeUoYQt9nFoPx03/6mVB4hxkUm3PglqnOXMvRLLM+y1RHKE/hRjm9DkoAw1lnnZWZOOY08wkYMKIAt/bBIBqrGMhIrmOo+0VJUhb9iI9BML3AFhM0vgbqaLwyH+ya1BeoAxg4UPsGcx+mbPYGwHx3SdqR6ZB2fPWrX537ljoyZ+NPk7QD1UYbbZTNuvrl1+wLl19+eZ679CWmYIQWTIz4MOhLaNVM6Mjkh7PzgQcemE2hMOYS8zhBGQBofQsQYDKG/r2S7+krgOOy/29+2eu5uVwDhLSj+YFT9H333Zd9eJRZXZSzXUffM64AJvUhxFEnZQQoyvw8lxYp7xYKJAqkSaikQoElS4G0uGSTAWrqFJKzfuUrX5lNCZLNblatp0Unq7cNhfiLa82je2lxzmpyeSSJc52YhyVLt4WsmDZJ0s1sGpGkgHWy389t0KY3mjevzea8Vx5MKpLNeTZDY4bDLK2dEkNSJ4lsnZw/6xQrP5sCaf/ZlCHeif7FtMn3E1jJJiDJrr39+Wm/E/OUTZdShKhsCjPXckR55MO0JmkW6sTI1knqPO27vX4kBrpOGqFswsIUJPIadoy6x7H5fLQRs5rE5NVJ4p7LlBjzafkrb5KA9zVJYqpjjG+99da1skW+iYHO5irJr2RG5oL6QLKtr9Mu7Lm9gu7JuTabBCXpdy8S9bymDVO42Ey7yEc/TH5O+ZqyGReDkvuJca5T9KJszqZ++lJiiOu0B0TuS/3eT4x2nYQjdQoqkPtyk/7MrJK2pE4goEarxFhPo3vzWfeSZiybPynLsL7brzxdrscYRLekMagT6Mvt32zbZtma555JWqBseqVfG8slFQoUCsyNAkXDkGbdkpYWBdKQyNIozqkkxJzoqOJJsEmuOB5S7ZMWelaKo/O08DhMS+6TgHIQFSOehoH0qqTuFEBDmgXmDhwmOVaSIjKVIDFspsRUZck7h2SmHySx6N8laVcSUtJI7UzCSHIdST6kzEwxtCMJdK+8lYmpmig7otLoN8pP6qwvKSNHS/2MtF09fFvShzgyy9856TKNCkknKTcnU5oqZkCkooOkn8ohb2ZbnEE53ZKco6O8vS9CDHMMEnh0Jh1GA2Z3+j/zEs+Sjitz0JN2QxlJzF0b5HytXqTi8hMkICTRxpS8SZ6XJVqjB6fvZorx5Tll5CRMEo4eEvr7TXugzfQNGhV1jeRdJkm9NAzaxbNHHHFEjjykvRKDneu7fopURhsg6g86y2dYUl5tT8JNIo+O6s5kJzZ+M/79HpbkpS04YYuK9K53vSv3HX2gqV3o1Qcjb3mgCzMrplU0KaE9Sf4Eee8FGop+DsjqImIUbYn2Qy9Jvr6rX6if69GH49uOaJaY8KyNsks2TYbN1FwzDhYqaUP9S1/Xr9Dv9ttvz0e/3euVlFd/NM5pl0Sso3HQ15V50HjrlV+5VihQKJDmgTRh3M8xFWoUCow5BXRlix6Gjn0upo6dr8VexA0MH+bLc22moTkM2veQxX0LKwbv0ksvzWAB41NSdwpY/JnXYHyPTnbSwfy2c8CAYF7RGlMi1CNaB3PZfr79Wx/Q/trbH9MfDFEkzIL8AQUMaK/2jmcDNGC4MGwYKnUAIuSDWQMWMDSe8e1IGBamauqDuUsS2cysJAf5zMiok3J1YbiUw3cxnvo1AIApVnb1WCVF5MIsYpD0VYwUGrABt0GY9yT1VWZH/ZkfBXMWwKwLfZXDtwFwNv3yRRflAMoAaqYvaNJMMb4859u+yRQG2ImxBTCw5VdPvhrnnnturmPkE++2AYP3tbNwrMyO2Pgro+sY+pe85CWZaUyOvpHV0KN6YkhvTbsoi2ikr2pvG4WJ5MSMDuDrQjMMOLDIxwBABrbkxRTMzsX8aDC1g1KUx6Z27PPRXV9TP+/y2Yh2befj+9oDwGPeo18Yi1KzXdrvNX/rK/or/4AwXwO4tcmKSMoJNDMNuy35n/FvMAaNOW3vftSlWR7tg86EDvyUAMcYd83nynmhQKHAcAoUwDCcRuWJMaCABZUU1yJCgsdR0SLNDt3i6H4sKI7thS7uqWr7nmvuWzRJ1q677rq+cc49W9LyFEA/iztfAIs+R0aMpnZpJrTHBFnc2XU7Yohd79UuzXeb502GCHPWfjd+x7H5bvtc2aN/xLn8vatPqEPze/G++74tec9z8U58N47xzqBj89uRn+flAXTE0bV4FrPoL+jsuSY94neU07vDUnybBie+4x3fl49vxfd65RXPtYFSlB8YSVGAMtg3hiO5D2y0nZ7RnkCAXb8/gEq5PE+Dwk+EXftMNIKYcVoOYAHgAmKAGz4e9nAg5VeWYQkdAA9AgWM5YAk86jccp0n9lZF2aFBC6xQBKI8dOyMDhMoDJAgryvm62a6RFzoACLQ1wuDaw6PZNu5LaNUvYbqBO5oxPhsBTNrt1+/9+bwOsIe2DphD1+uvvz7PJfp5r6SctAqc+238qPztIAe93ivXCgUKBaZToACG6fQov8aIAhY+0iUSzfuS9BbTQFUvRjngQNPANKO9GAYzoaoWEws/SSsJrYUYg2CBbi5A3gnAAJAwJ7BglzScAhZ5jB8prR1uOZuTlDbpKxftROLOGdlmTMCZ83b7Df9ieWJcKYD5N4YxgSTitCiR9IM2YPA8BhwItW8A7QLm3rg2RknEUxjRDBZolbok/dX8YfMyWgEMd0jzkz9Dtf322+eN5oaZb/mW9/R3eZ188snZVEuZmWTp3zQVNCuD8jL3qKNn1VPABnl4L4Uizow85/1eyRxpbrTHg/0XaGGaaRBgQG9aMow2LR+Ag9FGVwz4YiTlRVPaBn1DXyGECC2yOb8JiKKMMbfQ5tAy2Om7pEKBQoGZUaAAhpnRqzy9yBSwYMSiYWG34Q8GnzQQULC4Y05jIVTcXgwn5t8fpt/iHZv/0EiQ4DkCDZHkVwBDUKP70eIdDB1TgquvvjpLgHvlgL5s8UkySYWbfge9ni/Xlh4F9JcwBTr++OMzyIxa9gIMmEcMMY3i6173ugz4MdOk4hhczOFhhx2WmesuWhTjHDOa9lfIZi8iQrkmP5qAtBdGtcsuu2Rg22teibLG0RyibLQDoixhaIEDoVSZNikbDdqgBFjzz1A/gMG5by9L/iLMtph3mcN6JXMknwXlBoLQtplinmzXxW9zI7DAZ4NviG/085Fo5rmizpUdPQEh0cO0GRChT/RK5hdaJlHRRHgqqVCgUGBmFCiAYWb0Kk8vIgUwE9TRQALnP6YLzIM4WDJ3sThiFiywsRBGcWNBJHkkNbMjKDMFNtOY1IhdbsE56qijsqqb9CqS/NqAYZBUMN6b5COaYVCABPsYAHQ0Qr00C5gTDBkHU5JXZgNdGLxJpu9SrLsxDvQzN+kHGJo+DDSCJPjClbLjj0QTYRftnXfeecrRNe4NOmI2CRwENiC1ZsIjMcmxVwFJPnt488iwpJ8zQSKAuPjii7MQQv34mZhj+OfwPxjUz81n5qEbbrihOv/88zNDbFzxpbBvgnLypeg1FzH5o3EhUDk6+QxhrttjL+bJmB/VSd0AA07CKUJY9kvxPaBpUFmH0WMh7qMnUEbLrJ40k/pPr5CwtCL8mWhJ+u1ivRBlLHkWCiwVChTAsFRaconWw4Jm8scYcNzzx0aZ42wKl5cZURJBC31z0WsuhBY6CyomwpG9sE19YuM1i6NF1+IDMLAHFo3DNyLJrwCGoMbwI0aHJJT0l105DRCQ106YE06IzCuAuBSyNjMoK9Khsl2m8nvxKGAMYv5sVMeEh5lhJOPbGA7AQANl7KedujNjjwn0TEiS2au/9KUvzcx+F0bXGMdkh9DA+GfC413Sdfb7NAMA7bAUeZlHREcCms1R5iJS7hT+NTP8TCH7gQ95mPeUgcbNJoJoIw9Sf2XBIDMRatfPu+EzxPFdVDKMtevNFL9j7nRE19jLAEhS3vAjar47Kuf6DEESOjE1ArDaUbqUVR1oL2mTAbaSCgUKBWZGgQIYZkav8vQKpgDGk5QOOBCdiMSMZgGIcC8WPMWKRc95XA9pmQUfSAAMmCr02gXUwoPJpa4m4bTYR5JfAQxBjeFH0kw26GiI+cOItaWbcqHtYZpBWkoivCyZWbhW0mRSwJi+5557svkOx+emls/4DsBgjOontAGYb86vwm0a7yT4QoyKisT2vmvybQIJfVb0Itox3yRkoPECfAHZLv3TXGLe4j8B0PDZkRfmnpkUib/IVG1Gv1lW5VEGEYEOP/zwXFdMv+/vsMMO1Y477pjnsV4mTeYrtMEYAwyYaWVqp5gnY+4MKTxbf/4bNH/9AE07r8X8rR40C0CmULjm72ZSP8EU9AlanZlEzGrmU84LBSaZAgUwTHLrj2jdLZQkRKSLVPERRx4zT6JI6mbxs0jEgqcqseg5t8hZnEU0IRHk/EhSZvEnQcN4AADNFICBCQHHQiruSL7TBgwW05KmUwCdMDVAHbtnjJK21KbNtsIoCXeoXcR1B+j8aZ9xYFCm17r8mi8KAJVMgfgOMGPDBEYyvmmjaBg4ANMAYMYBizBLxPCukkLMMm1bc801M1Me7w876recrTnmM3FiPic/4X1JpgETc8cgJj++ob8bAyTemHXMe8wfyrZ+2hvC/DQoAdmYfWZRGGEml8YG0z1Rml72spfleaw9Xnyb2SY6cnYGpsybxl9zjvTtGJPKFv4K8qb5sF9HO+9B5V3Me+rB7+yyyy7LNOMv0kxtwLDTTjs1b5fzQoFCgQ4UKIChA5HKIwtLAZM9Zt2CSG1v4aZRsODRKoiuQ73eNjtSqljwLAgWPX8kbhgLdrdCc5JeU+GTMA1aAJUhpIIWacxuJN+JBb9ESQqqLH9Ep3ByFq+dGZJ2ayZtgPGi6bEnwatf/erMPGHOSppsCugrxl3aTTozyrF/BKoY44A+vyPmRzQKzHQIFTDEkn6F0cXcOwKlXVL029jcDLOvLOYSQgdSaf0UoB2W5EUDyrcC880sDzNLM6C/k9xzVFbWfkke5ry0O3P2/RGGWP193+ZjQDZzq14J6AKm7PcAWJk/zW2SPJrJd4xH0cloPPgt2OAOmBkngYh6MEvi06beQGQzqXdTw1AAQ5M65bxQoBsFCmDoRqfy1AJRwERPY8CExQJroSYRwwRYAMKR2XP+ei14isaul/MyLcL6SXon9KFzix6JoL/2u+0qhVTQgkmrQSoYybcLYAhq9D9iVtCOzTRmh811M2kD4S3Fs2dSYadbvwcBueb75XxpU6ALYGAuc+SRR2bmkJkQsyX9zhhflkzamLjREnbtV8Y2bYIIRHZCJhAg3XedszNtB8BgPunST5WFdhTwOfjgg6d22QaQ2c9z5h42H/k2oQlQwEQrzKP4X9mHgkmSaD+9krJjnG1aKYJQbGLn2V5zILDAAdt45NQNlHWpZ69vL9Y19CqAYbGoX747KRQogGFSWnrE6mmCBwaozm9L4TY5Mgv7x7TANUyn+4OSRY0EkCkLJz1mA3wUSMqYEdAyzCQBDMwHON5a8JvmEPKxyDNvYrYwbhK4mdBhLs8G6GIa4I/GJhL6kfJh6vbYY4/MpJCWul5SoQAKAAyf//zns4aBuRFmNxJm15gGNu0/IJSmsUjYQIJOgm+fBMy96D5dJeTmIvMOUyQgl/27chBCMP8RncjcgrHukjDs8uILQUMKjCg3IQbGHAjoxbhH3sojD5oBZkfmRhoUGjhjh0CDJoDWtJ0IX8xdV155ZQY+zDjl1SsZd3wy5KlMygbUEIyMW2oDBpqiZkJvc0/s+l00DE3qlPNCgY4USAOtpEKBFUaBtLDXiamsk9lRnRwM65tvvrlODop1sp+t0wImhMe0vzTR1/HnnvMEFOrEDNRpAa+TvXKdHNjqFImkTqr/OkmZZl2XJBmsk8NcnRiSOkVOmvqub/p2WkjrJL2sExOcyz/rDy3hF9EwSXzrJOGtExioE5OT6ZiYrzoxTXWKhFTvtttudZKY1okpW8KUKFWbDQWSkKBOEbXqbbfdtk6gfNoYNO71IeMz7cBcp/CmU/fdM2aT6U6dTBlr/bBrMh8laX6dBAV1EjTksS4/84vxngBM16zyc8mMqk4mQ/ld/V5eSTtRp0hHuW7DMlOepJmr3/e+99XJl6BOZkg5D3VPQKFOmos6mTgtl406J+BTJ6BeJ01Bfs+cGvNXzKMxhyaAVScTqTpFf6qTcKROZlTL5TkuF6wryRQyt38KnjDVL6LO2iBFYst1RZ+SCgUKBWZOgaJh6AisymNzpwApIP8Edsk2MxK+0A6opPphfpS68LQPpQl/6jeJGBtekqKnPOUp2bmRTTApIFtlUn/SMc/NJoV03AZJbO+bEVqUq22S1MWeeTblGOd30IlEMzFg1cUp9ryIJRw3aYE4OIteIxY6aSZ6Ntt3nOtdyj4/FBikYfAFUn/Seg66zHTCVMecwFeJ30z4K3XtW/wNaDSFTQ3Nor4p7DKtAG2FOWZY0vdpE+Ql3Km+b9dpmgFOxPwu9H35DkrKY160gzFJubnRnOZddZSPSFDKGMnciha+LSw0bS0NqeuSsqGHP5oX2hL5iQZlXIamLzHWkeVYHdUPnWh2uvgwlChJY9W8pbAjQoECGEakIZZqMUzkTIswAkwHTOrU5MwJLM4md+r2JB3LJPB8M1nALIz+2CRbKDkzi4DCDMkmSoBCV3OBZt7tc4BBmdgd86NIGoupR5RLGZgkhdNzAQxT5Jl2go4YJeYi6CjiDOaEWQcHUuDB3hddGbppmZcfS5oCwwBDzAeYcPOKP9cAiI033rjaf//9c19zv0vSV5k9CbDAkZjfkvkIUy2Uqmv6LF+GYQlzLi9zmnCmfLLkzyeAA/Zpp51WLUvmP8o6KPk+Z25+CCJFASHmGsIR/hmijzVDqfoukE7wwpyLf4fAAzGn+pb5y3gDPMyXxh/TLfUb5oA9qKyjck/9CmAYldYo5ViqFCiAYam27IjUi00tW1wSewyk6B3s2i1m8dcuahM0kCiSznFotnCTTFvIMe8WP8eQnLXzmelvizsGl/QJ4wDgROoFGLraSEcek3REL8wc5oe0k600/xLticErYGGSekP3ugIM/aIkyaU5N/itH5kDaBxpCICGLsx95CV6Eak0LZhQnKT78rSRIG3YGWeckTWavjEsmc9oFThJ23uExN8cQchAsAHM0ITo/72SupkvaTbf/OY3V5dcckkGAq5zdj7uuOOm5r/QogIL6sC5meaBhqHp5BzfkYd6EbhwbAYW2PMDIpFXPDuOR/UDGEqUpHFsvVLmcaFAAQzj0lJjVE6LLi0CRpHEnuRLtBwSt4iXHtWJhSx+O2IqSaEtrtT3HJhpFUjpXMd4LkQCGCz4AIPyYnYjKSemoalhKIAhqNP/iAEk7RRCclAYyf45lDuTRIGZAgZjMnZuJ3mnyeraz4xpggGMOIYbs20O8P56662XJfr2UQiQO6gdMO4EDEyJlMO8R+pPK/r85z+/2nrrrbPAY1DZQkPBWfqiFBaUgMU1JliEJPJlPhTaOQDFPGt+tZM0M08gxfVmAlDMVcw2zaHMrGgVgIalkgpgWCotWeoxyhQogGGUW2eMymbCtlBZ8MUPT46LeQG7LUVAipjmvaTK3ovroTGwQNqJmWaBGt7CRuK30Ax6AQyDO5y20r7R1p7GjDD/KFqDwbQrd7tRYKaAwZxAqCDUqk3KmOp0lZibr4QstcM4wBBzEQ0FU53koN83dGm7NrRphAwf/OAH82ZthCaSvJKTf45CtCyZIw3SVJh/+HWJ1MRk014wxhXtKtBhHwhzouRZpkrKDaScfvrpWTviejsBPIQsTALNp/amAbLmw4yz/a3F+q3tioZhsahfvjspFCiAYVJaegHrSQpGikw6b5GjWXAEHDg5W0ylAAbNopjoLYpU43wSAIV111032+qSzvnDFKwIhjQAg5B7XTQMk+TDoJ1oXPgjcGi2CzbGjD02eolRD9SVVCgwFwoADP3CqspXP4xkTmCPv+eee2Zn4C233LLnHBPPN4/GunCl+nGKuJS1n+6HMzCTIAw+U7phyfxH0p+iIOWyp+hGuZwEHzQVO++8czYDGgQW1AsAoCU46KCDqhRBLv/2DuDi2vppfxljTNnNT+ZbIImJp+ebtFFm8y2NBpBxwAEHZGdw566hnb+lktS9+DAsldYs9RhVChTAMKotM+LlMkGT0AEEFl57J7A9ZgvMBtdi5r7nYiFrAwaSaYCAtIttregmtAkigVCdY8gHLbLzTaICGHpTFEME/GFM2AgDDMzLMBxMxdhCsyEH+EoqFJgLBULDwEHYfgjNnZ7l25xLzB+AKlMdUX44BHdN8R17PdhFmabB/MTch/kPPwQmPINMiKI8TI+8Hz4EAI+8aBdssGZzwvUTsz8oKc99KcgCQH744Yfn8WbcATCEKByZzY80KBENiRbXHhFoxPehmXzf/Mn0CG1oJ1II6s7+Hc28xuFcv2ASJrIUjQvA10zowcSVuak1pkRJalKnnBcKdKNAAQzd6FSealGA1oBWgTaBYyBVunOLJ8bbBB2pucjHNcwm6Z1oRzQKFjbqcpsvdTUpiLzm61gAQ29KMq8Q+UXEFjs4k+RhZrQxwGcTKWYdKXZ+7wzK1UKBjhQgZLjjjjuqM888MzPPmONmirnE/IEB5N+U9mDJwHUmGj/aMhsL2ilaQAZ9mumO/DgoC4tKkDEsKS9Gn4DksMMOy5J/mgJghtBDPVZbbbWBkZHUieOyTd7sNi0KmzEnDyCc8/XJJ5+c50VzLqb4hhtuyOZPvmUstpN3AR6bvAFSzJEWa15tl22hfluT+I6Yp2hUmqkAhiY1ynmhwOwoUADD7Og2kW9ZxEhvLJCkaNTwnAYdSbhi8bIA9gMMMXHbkdWOzFT21OyAgvCDGIHmuyuS0AAD0COWOwYACIqkTrQdk+T0jBERy/3222+vmFkwl2D6gEmStJM2Yz9Oy8AkpKRCgblQwBg0n7Dhf9Ob3pQl9838AjBgiO34vMkmm+S9BGgozR3DkveBBbb/wALGm5BDn6ZNsLNyaMy6+EzRsBobHJXtmYChVw47JtOUMncCPJS3X1Im4+roo4/O4IWZVJSHQGWdddbJdQQkaPZuS35hNLq+hV7tZC4FMjbddNNq/aTZoAWkqVisebVdvoX4jYY0DKJTddEwlJ2eF6IVSp5LnQIFMCz1Fp5j/TCNsaCKrX/TTTfl0KiYSAu7qEeRYjH3OxYni6fFkvSOBNA5u3cSaYCBup3kK56PvBbjqK5AgqgpJH1CwEZSt0kCDLEAowfmjVRTmzfbyTmw97znPa960YtelKPABL3KsVBgNhQwBmkVmCMdf/zxOSRzM5+YY8wlwiwLEUqz1dWB1/vCjprHRBbSr/VjcxCNZ9rtuXr5y1+eTZO6SOQxqSIaAQz2TgBGlI0ghGSfpqK5Z0KzLnEOHDDjPPDAA/OcQ2iBDnwgtthii2zuBwAwnSLIAHa8oy7t8WieZaaFJmjDHEk+Sz2hBbNJDuOf/OQnM62adUanpklSAQxN6pTzQoFuFCiAoRudJu4pEzC7WvaxJFoWMZIb+xRQ31uwLGqei9Q8D6BAAs0meFlyILSHApU/8yPSOwvyivRRiHL2O5LWAQnU+EIsciyMpG6TAhjU1eKLqcKcMN3AGGnzJoOijbXroYcemqW9mJOSCgXmQoGugIE2ANPnz7zS1RxJ/jSkJ510UgbA4YvD30C4UVoyUnl9e1gyX5gj7P9AwEB4Yoxg0PfZZ59sK7/ZZptlYUm/vORBi0djC6zQHLhmnBlbZ599dgY473jHOzJYILTxDck4jfHoSBjDqdnGk7QbQsyOijCmX/3n8zott/WJJpSWuJnQpwCGJkXKeaHAzClQAMPMabZk37BQUXOTktEe2P3UgijOt8XQQusYIQN7EcLETCXOfteC5Y8dLrW88IC0C6MaTUf9wySJHXXTJEldLb5MksRHF52li8lCLxqN8jU0YB5hs72LL7442wRzZg8mJcoOPAlnCSSQoi5LzA2H0ZIKBeZCAQw9BrqfhsH8Qpug7zEdIkknUe+iDZC3+Q1I0Gc5KhOIYLT1XxJ+JkBdgK+8jBPMKT8FtvPMk8wJysZx2VyBgR9UNtpbEeVuvvnmvFEboA6sGEuclJkVoceNN97Yc+4NoGA+4sxLa7vjjjvmebaLD8Zc2mrU3iXgoqlhlrTffvtNK14ABn0GnYqGYRp5yo9CgU4UKIChE5mW7kOkVJhBC6AFD8NMysWOls2syDgWMff7JZOxP+pwfxY7ccNJ6tgZ+z1o0eyX74q+ro5NkyRMc6ReGoauUs3IY9SP6oiBIS39yEc+kh2cMVj6h3tStDVnZ/bjnCn33nvvqVCNo17HUr7RpoAxaP7BiJ9wwgnTzAKVXP9jk29uwRhvvvnmnSuEobQnDPMhG7LRmkm0oHwOTjzxxCzcoG0YlowJQgV+FvZeYEaF0ce4M7Nk1oh5H6SpUFeAhe8DDQIAo4zAOC0swMAvjJCGxrOZYjzKX/lt6MaUSiQlQGUc5ttmfebjnLAjzM123XXXaVnqN00NQ4mSNI085UehQCcKFMDQiUxL8yELFvMiNp80CsACSZdrGEeLVZNZbFPBYgUg0BhYxEnnAASaBAseSSCmelwWLwsOlTbHR0CJ+j/SUgcM6gccYNTYYgvvaPFFEykYFG1pE6j1E8O211575QgwmCQLckmFAnOlgP4GtF9zzTU5+hGtZjPxB+AbgOFn6oip7poABFG+hH7m7Iw5pw21zwHgy+nYnDVsvjIWRDUSkpU5nrmTsMVciFkXoUekJeOiX5IHQQztguhIymOulYwleQEO6OEv7kV+3vccZ290ANpFmfNNGpNJTOhUAMMktnyp84qiQAEMK4rSI/AdEyqJloWKqVEsWuxnSfXsp8BPAVgAJtyX2swgoEDCzFaX2pvJEVMjsfj9kdBhKi287XdHgAx9i4A+pIYiOJEYYgIioYUFXP2uvfbaXMdhzozx7qge1Yl5mbrqD45iu2OEaBmaTIpntWe0N1MQf0I3Ym5KKhSYDwroc7QAFydzuKuuuioz4818jTlhmI855phs+tPFvFHfNacxGwIYjHFaBuMdw81vgZkKqfQwM0PzYkRZMlbE+ydYAD4w6kIMc9Ym6TdH9krKQxjDpEkdewUUiPc8K7XnUWMRuDEfAQwk5jQark1q0p7mMFGrdt9992lkQD/twVEesGqbLE17uPwoFCgU6E2BNCGVNAEUSAtdnSTIdYroUe+xxx51mkCtRDP+S2ChTotSnRwN6+SkVyeH2DotoEuCgmnRrxMTUCcmoid90iJdJwlinWyg66SFGfs6J+asTsxZnXaLrZOtda1tB/UJ7Z6ittTJYbROQKPWp0oqFJhPCqRY+nXa86NOEX7qBAaW64+Joa8ToK+T0KPzZ43rBBLqpBGrk2BjKk/9PWko6hQFrE5mP0P7s/6ehAg5r+TnkOfB5nhRNuVOAKI2tvoldUyazDqZItXJeXuqPM28Bp2bu5MZUp6DU1CCOgl7+n1qoq5r56QlrxOI60lTdDO3p523J4oupbKFAvNFgaJhSDPzJKTUYbIa/W1ve1uWrtmxN5J7JDCRnJOWMStiXiTOvpCDpMkSDQNJVmgZSPlIvMY9kVBx9Cats78ESWIkNGpqGPhljLOGwSZHTD9syHbKKadkEyxS2GbSD2iROHGSzDGzUG+2wBxNm32m+V45LxSYLQWMQeaAwmOKENQMPKC/mXeE8T3vvPP6SvCb35Yf7enHP/7xvFsyTRrNIVNJfZqvlfmNhnSYpoz2QxQ1JpzMl2hrXTP3Mcl86Utfms2b5Olav/ERplG0eMz/jEWp1/PmHcmcKzLUsuSczfzIvOybtLvqMqzsOZMl/k9b8/fopWFQdXSikdlggw2yj8kSJ0epXqHAvFOgAIZ5J+loZmjhscBRyXNotiBHagIGixawwBaWXa8oRxZAi1OSxsUrS/JoweFcuOeee05FUImKBmBgo8wZHH2GmS/Eu6N4BA6ETGVDbRdZTAtzi0jRDwBFfikvfOELKyEiLbq9GJt4rxwLBeZCAX2QqQ5HYqFPmSdF0u84+HJ0fstb3tIJMOjX8uDEL3KR0JvGMiGHiDmi5ZjjAJFhSV7GjJ2EfT98nAgOCFfs9Cw6HAfkfkn9zMOx1wtzUKBD6jWulFUCCFZaaaXsnH3UUUfl8y7mWPnlCfmHtv18GJCAvwrTs/WT/9URRxwxIVQp1SwUmD8KFMAwf7Qc6ZwsPF0AAym6BdRCSpJHq2CidX2pS7EsOPw4hEnESNskKdJSAgzqIlTjaaedlu25hbAMxiTqGxomYGHffffNGgWahV5MTbxTjoUCc6V6BYTCAABAAElEQVQA5lkYZ5GD+ArRCESaKWDQpznyX3nllZnRv+KKK3JWQIfdk81xW221VZ7XSPCHJX4HyaQzRzQSHAGAMC8CCBynMaEAtrHTKykP/zHzCmdpecgzxl6vseWeb9Ds7b///nl/BUwvYcVS0Or2otNsrw0DDNavlVdeOWuWzjrrrNl+prxXKDCxFCiAYUKa3sIzDDBYgEitONHZRIgD3yRJsQIwYKQ5fzNPihQL91LQMKgL50CLpj0WxC2PhGmxsGp3kjgRaZhoYbKWOmAMGpTj4lEAYMBIk+AzLWFOFGmmgCHMkTgmc3SmGZAH5nubbbaptt5668oOyl2T6HHnnHNOxaxTZCRlpXFj4kIby5F20N4H5hfRleyYfuSRR2ZtpjIaj1IbMPjNDIljtrCvTJE4NtvboQvA6VqvpfLcMMBgfROMQzhofQKwK3RcKq1f6rFCKJAmq5ImgAJpMq0Tk1gnVXh2zEsTZXZydUwLUz5PPgl10irUyURlAiiyfBUTA1Ank6Q6LSh1shGeok/QKDHMdZLu1YlZqJNpw/IZjMkVfYHTaDJLq9NmVdPqmaSZddIq5X4Qzt2eL6lQYEVQIEnta468HJtTtLVpfTMxfHViyOtkSjTU6VmfFYwhAeI6+d7UyZwn56V/J/Oh7HBsrHdN5obkW5HHC8dZ+ShPAtZ1iopUJ9BdJ23BwOzkkTYWqxMYqpMWd6pu5t+Yg5vzctLs1mnH5hykgtP2UgkuMZBIc7iZwFde45IWaIq2TXpqr6QlrRNQzM7RHNhLKhQoFOhOgaJhWCGwbPE/krrEQA1DmlizVNnmP6TKQmZOWiLtI93cZZddOu3DMM4+DOpK48Q84sILL8wS2MRkZRtf5hWJUclSU+ZoJHMlFQqsCAqQ2nMsZpJkLwbBByKRuHf1YWAuRHt22223Za2Avi70KWn9GmuskTUY/LL6hT6NbzqaO5k2CX969dVX56PxQ0K9LDkh27zNeJG3ebRXkge/IeFc+WZweKZtkNyT1E+Sh7w4NNvTgUaBmShfiTIWM4l6/jN/DfJhQF90FbyBFpn52DjP4T2JUC4WCiwgBQpgWEDijlLWXQCD/RNe9apX5c2HRBCZtIQJwEAzwWE73StK0lIwSYp2xZzZrA9jxplT/cW4Z17BLpvpRmFQglrluCIooA9yUk7hmqvLL788A/f47kwAA+dmmw+mkKl5rwORifRlTKL+DSRjHrv0b0CDI/Yll1ySzfdEFouyiLrD52mQo7PyG2vyEGHp2GOPnRaVrAkY5Mv0b1kCIkAIR20RnAClkgZTYBhgCCAmKtbpp58+0ZvcDaZkuVso0JsCBTD0psuSu1oAw/AmnTTAgCLqTBqLoZFITTFR/jAvJRUKrEgK6IcilZ1//vk55OhsnZ75G5D8y4e/jn6OEbehGsBAwsw/YFjChAoQcOedd1YHHXTQlOZRXjRxrgHZg3y9zL3CfQoTy5eCpsK1AApxxNDyiRCyOO0VUL3oRS/KTrqcnstYHNZSVY7yNkjDgI60SptuumnWOvXTBg3/UnmiUGAyKVAAw4S0u0VpkNOzybNoGCZLwzAhXb9Uc4woADAINsAhn5MyZj1SSPWHhVUFgGnOOE7TCth3wfwndKq9Ephc7rDDDn2jGcX3HOVF6yj86dFp7wWhVIEP2re11lorR0ayT0k/8EHTIeoTEyS7OovCZm+JJgBQNr9jzxPR6dZbb71cTmVuPtssWzmfToFhGgaAQdQ/gEHfKKlQoFBgZhQogGFm9BrbpwtgGN50k6hhGE6V8kShwIqjAPMfvgc2ExTamJAjUhfAYJ5jfiQSUYRm9Z4/AhGmKMKSLksmP10kzPwObK722c9+Nu9hk3Y4z3bvq622WtYsiHbEXAgz2k7mE5oF79u7RZmAF4xtGwTQWAj5KTIdrQXGFoAoqTsFCmDoTqvyZKHAbChQAMNsqDaG7xTAMLzRCmAYTqPyRKHAQlJgroAB03jfffdVJ554Yt7FPEX6yuZ1wIK9Fw4++OC8uVqXXdrlRcMhnCnA4ByjL3QqkyGaiu23374n8PAucyq+EhyvbZYJfJiHpQAMjsoCwLz+9a/Pzs1CqAIQXQDNQrbFuOVdAMO4tVgp77hRoACGcWuxWZa3K2AQS5xtbnF6Hk+nZwwXqSxJpj++CCLB2Jmaf0IwKrPsRuW1QoEFpYD+y/wnNAxs0iPpu6TuTHaYlPSKcMSE6O67787AgN8BEyDSfwz5C17wgmr33XfPO9b30gjEdxzNl/K65557qj322CMz/LQL3uOELHqRaEvrp71K2ikYV+/yo1AfJlIBFjwf49CYZFcvr0MOOSTv4Mwxu4CFNlWH/w6633TTTdWuu+663AvarpgkLUeWcqFQoDMFCmDoTKrxfrANGKjJI7lnAbNQiZI06YDBDrBdoiRxUBylREMiVOMNN9yQmSYMC6ZKtBXMEsakS1SYUapTKctkUaAJGD760Y/mMJlBAXMU859+gME8ZidljsW7pNDINAJAM6aco/PrXve6au211x7ooBzfwnxylr4taQeOOeaY6mtf+1qeI/kqMEeyeVva26Gy+3k78Vv4yEc+kkGGDcI4YAMfbcAAFADyfDLsOL3xxhtXwhiXNDsKmP+GOT0HYDj33HNn95HyVqHABFOgAIYJafw2YEibdk3V3D2LF7X9pGsYmDCQTjFriDjpCIVGJFSjGFYVk5U2hMrOohdffHF17733ZjtuzJJ2BRTYRdvBWzz3Ahqmun45GTEKNAEDH4aZaBj09w9+8IN5rwNO02kjtdzXV1999Sl/A6FUh2kXkATTH5oOu74rBzOhxz/+8dm06bDDDsvMfuQFYPCdMH/wnXAEWAgeOHKbP/xJxl/aGLJKG8hVe+21V8Vp2hhl6lQ0C5lEs/pXNAyzIlt5qVCgMwUKYOhMqvF+0GJl0WNTa/Og66+/fqpC7gVgmPR9GEgS99lnnyyh/9GPfjSNRqMIGEjVMEZsrMWHF7qRRDPCpKoAqexRRx1VPfOZz8x21wUwTDVrORkxCgAMs3V6pl0AmEUkuvbaa7NUn8R+zTXXrNZPpkOHHnrolCnQoGqbD+3B8vGPfzy/I6qRMWaTLxoKUXZ22223aXsjMFeyyZwxaGM2AgfvNFMABvnYt4HwgdM0oNDFp6KZVzlfngIFMCxPk3KlUGA+KVAAw3xSc4TzslhZUG+88ca8edBb3/rWqdK6V0yS7o/j/d3vfjfbHTOHwLhEQqM2YFhskyQLJC2IuPUcJjEpJJrBmETZhWYEgkSH2WKLLbKkNO6VY6HAKFGgqWGYiUkSgGzsHnjggRkwGAfGB5OfV77yldks7/nPf36nqsqL74OwrjSuQLkxZRzJ6xWveEXWCjS1C75tTmUORcsR74Svgg/HHCIkK5MppoLKRHPRfK5TIctDy1GgmCQtR5JyoVBgXilQAMO8knO0MyPxEtqPXe4b3/jGqcJayApguB8wfO9738ub+tx6661ZExNEisW+aZK0mIAhwIL2tKOtsI1ixIvE0kyYGqZmHCrZcYvsUjQMTQqV81GiAGbdvgUREpXUPpI5qpcPg7Hw85//PGvZ7KLM2dk4IMlfZZVVcsQkpnh8D4Yl45x2AVigYWDa5FpoYAEI2gUbtRlHmFSaSGUWmYk5oD/vSAEEHDlsr7rqqtWWW26Zw6cyS3r0ox9dxuOwRul4fxhg0F4Pf/jDq0022aTiW6J/FBOwjsQtjxUKoECa2EqaEAokG986ma7UCSzUaQGb+tMN/E6TaX3CCSfUaSfSCaHI9GqmBadOvgB1co6sE2M9RR+0QaPEfOfrSZpYo+VipcQg1YkhqpM0s95///3r5MhXJynltPIqc1og68Sk5DKnyCF1AkO1OpZUKDCqFEiAoU7O+nWKklQn2/5pfToxd3VyMq5f8pKX1ElbOlUF76QoRHVi2OvEkOd39P2kXag32GCDOmne6uR0PPX8oBPjI2kn6hR+tU6R4nJexn5ynK4f97jH1cnkL3/bGPSXwEWdBDB12jk6fy/mVe/EvOpaEi7Uyf+hTj4LOf+u5RlU1nJvOgX0A22XzG6n9ZtoE/O3NU7/Sftj1EmbNT2D8qtQoFBgIAWKhiHN6pOQUi/I5iuXXXZZlsTZdTSSeyFBm2QfBpJKGgYhGyPKSZNGpPVNDQMJ1YpOykiT8I1vfCP7JTgyvyCZbSbSNA6e/BbEnhfbnYTT9ZIKBUaVAvqxnZVjp2eRiiIlxi9rGJo7PZu7OBvTBjDLa/sbCA/d9jeI/NpHY4ufF4dlY4ZZku/77qMe9ahsjpQASDYl8l2aBWZTTJGMQ+/GOHRfMq8yZeLYzF+BpqMEHmhTfn5+c3rnn2fupmnqlWiFbY6XBGN5Pw5tU1KhQKFANwoUwNCNTmP/lAVMfP4LLrggT6rtsKoBGCY5StKoAwZtKHrLl770perLX/5yjlUvEguGqZmAAuFUn/jEJ2bAoE2ZJS0GwGmWq5wXCgyjQDg9J4l9Np1s7/Tc3ocBg85/gJklwMCnRx7CnwIWwgnzE/B7WJIXcyIBBIRSBQiYNmEyMfyHH354FhgwcwLa7a3AFJCDNdMp7wdQcAQ0ODN7njlg0gbmaEjMmSYxoQmzoUjo006ueS7o6Hf8ebb5fvNdzzMlAxZEtQI4eyUhdtdaa63quOOOy/Oj/hTJ/B/f9h2O7K4BFdZHKcoVghdtLsiEPudc8ixne74pXfpdfqn8KxQYAwoUwDAGjTQfRTTRWXxJw+w62gYMJuVJ34chAMM555xTjaIPgwWJNoH/CUka4NBkUvQT7QgsCNko7ryQkrQLseDNR18qeRQKLBQFAjDYuI30vg0Ymj4MGDlMIifjtr+B/RE4J9uRme8C5m1YAsaNext/0cQC4saN2P1CEp9xxhkZeBtjn/70p7M/mI3ZBJMIZjG+Yb6lkWQzv+OOO+YdoQF4DOukjkU0akaOatLB3IuuGHHn/iTPRNuhqf0seqVY3y666KIcrCKZ1fZ6LNNf1CwaCG0agCEAgjI61xcARn1Au4W/g3vKCQh41v3PfOYzGUACDsrtWQDTemoeDnDRs0DlYqHAGFGgAIYxaqy5FDUm1AIY+lPRZD+KTs/azgLGRAIz8853vjNLQjFT7kWykGGiNtpoo7xz7Pbbb58ZnEmVaAZdynF8KAAwxP4Hw6Ik6evNUNHXXXddZjBJd5/ylKdksLDNNtt02t/A2Oc4zVTz6quvzoDcmMPgiy5mM0thWT3D/OiWW26pvv71r1f2isBEtseh92j1aDiYMWFSw1F6fFpj7iVFV6ZCzLzMX6JIYbQx0WhkzpJck2hzSPYBA/cw30wrPe+a9kbvSPG+37RBhGEYfaZpvZJ8OJ7TOhGmEK4oo2+aT0NboB8Co46eD6DnOedApHrRaBHcAEL6i34AKIrOJRoWUGLvDr+90wRJvcpXrhUKjDIFCmAY5daZx7KZyIqGYTBBRxUwWCCZHpFknXzyyTmMai8zJIur3WcPOOCAbDoREs3BtS53CwVGhwIzAQyAAVMge4xgSO2/gCHDqG277bYVsLDhhht2qhyGlWkT/6WL014OgIH5wDe22267bFIEgNMskF7T0EZUsibT6mPKgEFMTtLZtImU+RGPeESnciy1h7QnPxBALPb/CTAA8KGdtck1zDzJPcYfA+6eZ2xqh6YYchtUahfvtOnehXbeYSZG82Ou1L4SLRFAY54FCiIpE6AHBDhXNu8DAeZgACY56WfA0yyP8tpfQ+hcoaw9z3eCtqT5XHynHAsFxoECBTCMQyvNQxkLYBhOxFEDDNrMgssMiTkEpuiTn/xkvqaskUi82EkLmcpp3TnJWVmcgkLlOC4U6AoY2Khj7myUxrzEOYkv0IxBZ6NOumssDEvGGcbvhhtuyD4JQqoaXxhEjOX5559frbzyyhkofPjDH86mSKTPnvHXZAC9AyzY94TfwjrrrJOl5q5PWiLouC/tDcMnBKj74Q9/ONAkCX0w2trDn4S2mHXJtdBEOG/SPT/Q8V/kqU2c+9OO8m5ri2QZbee5+K451zueB3Yk95vJe/oj4EB4I+yuULrM5UoqFBhHChTAMI6tNosym+i6aBhe/epXZ+m06CKTliwAzShJJGKR0M/C1YySRH2+kMliBCwACmeeeWY2Q7r77runfRIooLJfb731sunELmlDKL9jkZ32cPlRKDDiFAAYYqfnXj4M+jZnZgDahoWY+/POOy9L+41R9/ns8IFgR455H5aMe5qKc889N+9pEpoKzB5zFD5DmD57Q2B+7bngHSkYSOfGHB8Luzjb4E05Jjkikrb82te+ls22jj766AzKmvRCs3Yadj+e7/pcPN/rKA+pzej3enbQtUH5yNs6QcNgDgdmmaqVVCgwjhQogGEcW20WZTapNQHDe97znqlc3CPZMZFNelhVjAM/D5uhYRwioVEbMGAoFjJReYvCcs0112QHUOrwZtJmpFUYk1NPPTWr2JljlFQoMK4UaAIG/gHmrEiYLww5wMA0z7i45JJLMnAg5TU+SXJp2kRZ6hqhBjAXdexlL3tZNktiakQ6TLsgLPEaa6yRbdsBE2YxzWReUC5jkXkLExS7TT/rWc/KIKP57KSdaxNmlEAdUy90RS+pH5M+7L53uzzjuWFpReWjL9mgTyjXrlqvYWUv9wsFFoMCBTAsBtUX4ZsmxyZg6BclaZI1DGjEllVYPtE2MOuR3GsDhoXQMGCYaDnY015//fVZ2kqSGjbVUR5lEYXDrrFbbbVV1i5gkCKiSDxXjoUC40SBJmDopWEAGJj5vOY1r8nOyVdeeWU2cyHxD38DTsq77rprNgcZVncAgPMyR2thWZkmYXQBAGYnTPsiIg5tn+80mV3nbNxpIvbcc8+s1QBaRN8xRic5MfG5L5kkMRsDotJmadM0Mr1oY55t0rfXM651fa7f+5GHY5fvzTafEMTRTBNE0XgtxLoxqHzlXqHAfFGgAIb5ouSI52OC7QIYaBhEBJlEkyQ0Ygct6gWJmNCKkdxbaMBggaVV8H0g4fLLL8/RPkT9aCYLnEUHY5J2Lc3OnaShYWvbfLacFwqMEwUAhkFRkjjBkuK/+MUvrt773vdWN9544xQTD0xg2mkYRMEZBp6Nac61/IKYHzJj4ptA49BkIj3XTHHPeOMACywwQ7LZm0g4xUb9fmoBV3xLbMQnEAPnZ7SVgob3P/nA/6B1+374F+gf/Z6JXLwbc6Fn45txP47D8pEHht9RHr7dKw3KB+hkljZTrVev75RrhQKLTYECGBa7BVbQ901qTcBQTJKWJzwakTh2BQzzaZJkQRIBhP326aefngEDZsaiGwtSlNgCFjvHAnfsYi1sJRUKjDsFmhqGtklS1M24Aw6Mj4imQ7uAMTv++ONzSFXatzbTGe/H0bjC0NpLgW8CzSLG1PXmu83xF9eNN+Z/NgED2u31YEyWQANB3fuP5jWmSPbKEIK0aZY0/cn+v7QJrav1S0SifgBADtpHX2Beq91EPNLG5tGZJO0L+NEe+VNuviszSeZpGoV99903A0r9o8zTM6FgeXbUKFAAw6i1yAKVx+RZAMNg4qIR0x+L2xVXXJElmPGGe20Nw3wCBgsbSSd7X/ssCPEYC2MwKRYgiyE7WNoFjpVCDhaJZrRSOY47BYYBBuPQODAWjQ9/mDDjwP4jTCrZixsngxIGEgOLCeTvYH8A/ksB0GPMycM3I7kOFIh2I2yqTdlIj4EH5kuFIQxKPXBk4mVfBMIYf016PvBU/zNtgmHnw6XNBjH/0T7hvwJs0BrN9JvyoT3Sj+RF80xDMpOkL3jfHhwAjP7R7Fczyas8WygwChQogGEUWmEFlMGECTBccMEFWf3e9mEwuRWn5//Lm/5wpLz55pszAx9Ng34LCRgshuyxbRpl8yHAJZJFxh+AwuRhhx12yNGaxPceZnYReZRjocA4UKALYGjWw7gwBkShsbOzvReAh2EJI8l3gX29iEui+UQy1puMXZPZBFYwfmuvvXaOq7/ffvtl88ACFIJ65VgoUCiwVClQAMNSbdlWvSx6mFAMqcgV73jHO6aeiAWSGn+SfRhIriK8onjrw6IkzafzGtOKi9OGUfwm+C9wvpYCLHCitHut9mHDTU0eUrSphiwnhQJjTgGAoZ8Pg6o1mfcYGzRs66+/fnXSSSdlQN1lXPIV4v9g7wXO1Rxym/n3AgzAwqMe9agM1g877LCsZehi+pQzLv8KBQoFCgXGnAIFMIx5A3YtvoXWInnTTTdlyTmn3khNwDDJUZIABray55xzTnXrrbdmTUyTRm0NQxfGJN4fdgQYaDYABvsuBGAguYydRW0Etddee2Vb6QIWhlG03B9HCjQ1DO0oSerTBgzGJK3bBhtskJ2Wu0QnkgcTF2ON6SGzpBhvkX8bMBiH/CaA9nXXXTc7V9ubYT7NEsexvUqZCwUKBSaHAgUwTE5b53CBFkd7DLzuda+bqrlFspgkVdk2trlxG9OgSGjUBgzzySwwScK8XHXVVdnxOUySRNlYaaWVcshHZhfspUsqFFiqFGgChl5Oz8HQqz+mno24MKo0DEcccUQnshAM2HXYhmwEJ01wIAPfaF/zHfsx7JI2Rtx+++2Lv0InSpeHCgUKBZYSBQpgWEqtOaAuFkFSNGp4zrXnn3/+1NPuFcCwuIABoyQ6k/COTMbEg9cmJKbLli3LjIqIG+ynSyoUWKoUmAlgMD6YCB133HF580IRw4almAebe620wUETMPiGcScCk7CpHJ0BeOZJJRUKFAoUCkwSBQpgmJDWtgiSWlPDCyHIwTZSAQz3UyJMkkgdP/KRj2Tn4yaNFlLDINoL7YZoImy4RQPBrDCDwBSJK1/MkKI1ynGpUqArYAjtAkaeCSFQbS+SYckY569w3XXX5Y0R+Sr1Awyu0yKuvvrq2RTpqKOOyuCBtqGkQoGlQgFrj3EnWXMikEZ7XCyV+pZ6zJ4CBTDMnnZj9SZQIEoSzQJTmxIlafnmW0zAoDTaSBlEcHGUTNomcaZJJRUKLHUKdAUMGHmRijbbbLMcHYkmzjgZlIwvYT0FFbBT9N13351DZbYZoxCg8FESO/+YY47Jjs6Au2+0nx/0zXKvUGCUKWCdifDCzoFhINwxgMMol7+UbcVSoACGFUvvRftaAAbb0wMMvTZue8QjHlGRoonx/6xnPWvRyrpYHzZhLpYPw2LVuXy3UGCUKNAVMNC22e3Zpmn8err4EwHi3/zmN7OP0CGHHJIFKOLrtwEAUMCheZVVVqm23HLLHKrVvgtFw7e4PcX8rL3sUfODH/xguXbrUjrroH0hfvnLX2ZNk/Nm+zsHFLW38LyiYPlbiiZosUkp4MyvURJxTAAB/nJ2MC+pUKBJgQIYmtRYwuddAINJ8swzz8y7llLDT1oqgGHSWrzUd9Qo0AUwYOowNgI32LwQI99k+nrVyfwnEplNGfkJ2XsBwyS138Uw8lWw4RZNhChM8xkRrVf5yrXhFMDcC3tt74wvfOELy7Xb8Bzu1+LqB0DHN77xjbypW7P9nTMDfeYzn5k3yLRJ5lOf+tQscWeSulSS8UCzcOmll+bw4cKtS/Ziss8PE9j1UyCBJm2WSt1LPWZPgQIYZk+7sXqzC2DgzHf22WdnwGC31ElLBTBMWouX+o4aBYYBBuXF0D3hCU/IoU3ttDxM+mvu47+FyTz33HOrO++8s7rnnnuW20kdc0RTsfLKK1f2WVhttdWyttW1YeZOo0bHpVQe7QcsfOc738n+KoJD3HvvvbmKs2FoaZp+85vfZADJfl9q5gMY6GPM3AjRXv7yl1ePecxjqi5O9TmzMfiHpt/+9rervffeO5vmoScaAMa0C7vuumsGDmX38jFozBVYxAIYViCxF/NTXQBD0TAMN0kSh/3aa6+tHvawh+X9Efq1KXpbjGJBwtRgOgrj0Y9i5XqhQJWdLzH2p5xyStUrrCqmhunkOuusUwELdjtvMnttGhqHzFiYsHzgAx/IgAFYCO2C571vXAIGNBdMMm0Cx2eBaVJJi0sBbciEyG7cIlUxofnRj340sN27lFi+Ur/+o0+QuO+zzz4ZLGy66aZdsh2LZwjHjAM7owNiv/71r3O5rVNRZ0DJOjcMkI9FhUsh54UCBTDMCxlHPxOTI6fnQT4MJorXvva1OSLIxhtvPPqVmucSdtEwYCbe/va359CK/ZgJtLavgljv1L5+m3jtzkxyVVKhQKFAbwoM0zBw/mcqdNBBB2XGnpBjUAIWABBhVIEQoaVJmINZ9C7GkFkTCTInanMfKatv9WMmB32z3JtfCtAGCDXNlIwDOpMic/Vc2yb6QL98XH/IQx6SbfoBVGvjUknoB3jp68y8mkmdX/GKV1Q777xzHmMl4EaTOpN9XgDDhLS/ybELYHjVq16VbTaf+9znTghlHqhmF8DAVOvEE0+snvSkJ2WnyAfevv+MRuEnP/lJdq60qzZTCLQnFcXoPO1pT8tSyyK1aVOu/C4UGK5hYDIhOtLRRx9dGYuAeK9kLBt7zC5siMgMye7txqfxGMyicQj4M0N66Utfmuc+/ls0DUUb2IuyK/4ac6TPfe5zGTAIykEaviIBw4Ybbpg1WvxZlkoKwLDRRhtlwBCgSZ/X93ffffc8HkQJW0q+G0ul/RarHgUwLBblV/B3uwAGi2+oXzfffPMVXMLF/5xJlDMcP47bbrstSyajVOiHueDnAVStu+66mblo3icdtZhRndsc7+STT65+9atfZeZEjPiddtop7xLL/rpIbYJy5Vgo8AAFjCFR3IwdWgEbGDaTcI+kvRhHzIxN1SIZo94HCmgWgAV52dEZiKf1ixTj+cEPfnAOI8mxlfSaFrBLxKXIpxwXngLaFOCzP4121ydoHYLJnW0J9AGpXz6YZxpha+Gzn/3s7DMz22+NynvqTMMGhH31q1+ttt5662mAwRonKpRgArukXc1ZHRTh1qi03uKXowCGxW+DFVICE4WJ9m1ve1uW1LDDbyaTJgenmBz33Xff5u2JOMdofP3rX8+q57vuums5VS0aYShe8IIXVNttt13V1MJQk7/3ve/N4WpF8WBz+4tf/GJqPwUxrYENISDPOuusvpLRiSB0qWShQB8KYGRsmgiUC3GM8W8m0k4aAJFcmFM84xnPmLptDF5zzTXVHXfcUb3vfe/LAEF+xqGxTSAQCRO0LG32JgoOxkhUJL9d78dAxrvluGIpYO0CEJjOXHjhhZXN9pgnzaadAiSoQZz3yick7Zydmb85Mkcd56S+tG7o54+PkDDDAJmEDjR4BFoEh0ySClgY5xaf/7IXwDD/NB3JHE0WmFgL6qc//elsh98sqMmCNEXc8bXWWmtJSFOa9etyjqkQao9jnUgcJJTNhEYAw/Oe97zqRS96UbZ3xoRgVESZuOGGG6obb7wxv4tRaSaAYZUU151Z0qmnnjpNMtp8rpwXCkwyBYwb2r39998/j6mmVgBdAjDQ1jGnAMCNW5o9Y1d4SGOX+RFJajNhAkW+YaNNO8H/QSQkAgAmSa73Yh6beZTzxaGA9YvA65Zbbsn+DF/+8pdn1VYBEpq1cK3d7tFX9At7fTApFV53HJNxwHcHAOdX99GPfrS6/fbbs8bGuAmaoAENnsAee+21V9aIo0NJhQJBgQIYghITcCSloYa0SYsY5pFiwqSKJNnj/NeUnsdzS/2I+TepnnPOOZnhIMWKhEYmTyYQ1LjbbrttlnCKtkJdftFFF2UTCsxKpOYiRHsjtrV3Rdsom0AFlcqxUOABCpB2Mj3hoIyxaZskAQxPf/rTM6BgRmRzKUyPd0477bRs6+6dpmNzjEOmRjak9P4RRxyRx2CRoD5A+3K29ChgTaNV+OxnP1u9+c1vzrucizBlfADaTbBgnFinCLVoFwBpJnsxfpYedUqNZkqBAhhmSrExfr4AhsGN1wUwmFBt6kPDgPmw8Q0zJrbSIiJhXiKZaDE47EABBRJR2htOloVRCSqVY6HAAxToChhErFljjTWyxuCyyy7LWoWbb745+wwFWAhmyFgD9JkvCcXKpEnQAtcLM/QA7cvZ0qGAvs+igHksIdY73/nOqfCpof32TIyRGAfWK2OFcAtgWD9t3gY0lFQogAIFMExQPyiAYXBjdwEMJk82nky3MCwcpO+7775sPoFRaSYMyUMf+tBqWbKN3mOPPTJYGHc72Gb9ynmhwHxToAtgoFmw4RS7cgwOySnNKdAejI9yYYb8ps0zBpkS8n1gZmJcNp+d73qU/AoFFosC+j1TPpoEJrI05UyRA0g3y9UGDO7RxAEKQgxvv/32eayUnc6bVJvc8wIYJqjtSRb6mSQxtyEJL2FVv1e95S1vyY6XGJBIwXz4zR9B6DnggU2oiRjYkGICds4mGoPCzppGAuNSNAsoU1KhQG8KAAzDNm575CMfmcMTE4DQ6pnTOEcbh20QwCZbGFaavf322y+PyaJZ6E37cnVpUICZLIdmZnp2Nv/pT3+ancZ71S7Wq+a4cQ408PHh8E1AxowPOC9psilQAMMEtf8wwGAhPvbYY/MEgcmdtBQahmGAwYQKNJhAMSox6aJXAAumS0wfxLOmieAXUsDCpPWoUt+ZUmAYYJAfIC5MsWeNPz4LYY8djI+xxlH1sY99bAbtjmyzC1iYaYuU58eNAqKC0Xzbu4IfkKAczTWqWZ+4HuMm7hEgMp194QtfmE35CLxKuOGgzuQeC2CYoLYneQgNwyGHHDJVc5OGCYKq/rzzzsuqfir8SUtdAQO69Jto3aN5AL6EfWSKZIOp4uSMMiUVCgymwDDAEOMucmkyOu75bS4D2JkuPec5z8nmS0yQCmAPqi3uUTu123FxS/TA1/Wdfsn6EP0tjtHnvBN1al6L5/rlOd/XAWdab/soAAwBpvt9J8rcq5zWMRGT1ltvvaxpMKbKGOpHycm4XgDDZLRznsxsIvaBD3wgR/OxF0Akk4aJUqhB+zMAC8IPTloKwNAvSlJ7Um0uDEErpkqkMjQKHJ0xKjQR7Xfj+XIsFCgUeIACAMOgKEnB4HijPabcw9DQPti1ef1kh83R2Vw2iBF84OvlbCEpwGSMtFuIz2ZwiIX85kzyjr6DUaZBlvQpZaXJEm1I6HH2/J5xTX8liXdkHucapt287xlM9opK1i9+C/YxsVmhMMPKMijFeGqPJe+4RtDF2oA5nz1LhAYvaXIpUADDhLS9iUHUhOuvvz5HTrABTiT3LKgk4dddd13WNKzIiS7KsdjHuQAGkyvGBNjabbfdslmX3aALo7LYrVq+P04UwHjxHbLT88c//vHlwqoGg6NObSbHWMPQYWowOMCCDdlKWnwKAAsY7rvvvjvvuo25HrUEMDzqUY/KTHIABmsCwOCPtB44AAT4xnAsZuYrqpCj+66pq+c8Q4DkvnPX2n12PmkAHNg7yH5AzGq/9a1vTWVvbFjTfR8fEOMojv3KRdjFh0GYVZoGWruypk2RdeJOCmCYkCY3MZike+307J5JgIbBxkeYXhPdpKW5AIYHPehBOczqJptsMmUC0W8SnjS6lvoWCnSlAMDAlIKEVEjINmMZDI78muPLOckvhoZ2zz4LpLzB+HX9fnlu/imgzTDcNgy1V8ZXvvKVvN9Nry95ttmuvZ5xretz/d6PPBzje5hjm7ORqodWuBdg0M88AxzorzbzBBh+9rOfTWkdXAMS+NHQNGO6majKd6ESoIK2559/fgYNP/jBD6Y+FXuQqOsnPvGJDGrcjPEUNJh64f+f4AuMI2GIX/GKV2Ttubz6Pd9+v/xeWhQogGFptefA2pjgLMZ2QT3uuOOmnjVpmBhMbocffnieHEQVmbQUgGGY0zO6tCdai8iGG25YbbHFFjnW+4rU0CgLczPM1X0pxKtwkyStFjULmXscRT3HIc5zFnDXlNtR3UmomAz4k4SABYQGJflTg4vE4T3SXfk1Aad8PUOyxU9GuUqabAroEzZJZJ6C0Yq++J3vfCfPUUKl6reYoGaKcRfXMC4kw/qVsSd06rIk8PDnemFsglKLc9Re2vimm27K7XrllVfmecC80StF+w5qty7P9Mq7fa2dj2+a7/SbphRdH9RfgQMMv3uOrsnD846eM486d991c539eoDYgw8+OGsn2uWYj9++aW4XHYl/orFlvY9E+233ZmU644wzKv6MkvekQfQGuh/2sIdVr3nNa3IQD2O1SR/vow2wYgfur33ta3ndcT2SPIAOAUDKGhBUGb9jAQzj12azLrFJOpye2zs9mwBKWNX7d3qeDWAgdaGyJUVa0Ts5W6QwVz/+8Y+zyp80i/rbYmUit2ADMBYHanMMWlyjXreYyMOCB0jIywLCpEO9vBcLYbPzuS60JUkWRzvviUYDrJCwRbKwfve7380mCczeBoEpC5pvtxlF1yw6FuLm4ibveNZ99fXbc5L8Is8oj6NnvOsPkxDP+61OsZB61tjwTfeCWYhyoEt807Pt5D3PkjbG99g5N1M8I2/f7cdMNd9pnnsP8JOatIln5IlBiDoFCESDXu0a783XUZm0jYRWyuHbzCeYqQCT+qA6ALw2mrr88sv71qVZLnl7DzOy5557Vptvvnllx/qSRoMC2tqcQ7PN1Ow973lP7t+9+qkSRx/td7/rM11q3+Vbc81Hv4+wpCeddFKe+8xH852MY3T+4Ac/WO27775ZeGOMRTInH3DAAXkuPP7447MmxL2uNDA+hVjlTO3cnCOZ04xp87/9HuwobfyaQ5vJnMMXwpry+Mc/Pq8PNBeRT/PZcj66FCiAYXTbZt5LVgDDYJKadElmZgMYgnEJ+1YT4aBFL0rSa8KOa56ZSR4WCJN3SMniGyb1WKTUMRjFYKSVNb4ZDKSFblmS0kqYTWCAxKpdHu/JP/L0nvziezmD9C/uY577LRKus/eVfvKTn+Qy+Z4/4GellVbKscEx375rUbJIAiyeWZbKiwn1G/j1nPyAl2CS5Y1G3//+97OmBbMK5AAy6u679gEwVvxWH/l4H3OrHKuuump2rHUNbTgX3nvvvbKelqLcygVMyhuou/322zM9PBzPiKqF8VUntsfK2CV5HzNgMdb32nRHJ5qfz3zmM7n90JjmSL0w59Gug74VfcMzvjfT5Fto7F27oqOtc30i/pRb2dQbDQK0tr/VLIt78mZ3vn5ycH7DG96Q29q1kkaDAtpLnz/11FOrL37xi1kCro379aNo33731arLM11qvyLyUQ/zhzH3pje9Kc8dTWFKl3J2ecYcbC57//vfnzUJ6hb1874y2IjNGOPjEPNLPDOI3t7vBRjMj+ZfGoWjjz46C4X8Nn4jX+9K8je/0TyLvMSB2p5P5tP2nHX/G+X/KFKgAIZRbJUFKlMXwMBZkPr0uc997gKVYnSzNQHOFjBErZoT5bBJ2DvxfPPZuBZ5Nu/FtZkc5TfTPDBd1NCSBQDTSTI+03xmUk6LGamTb1h4IvltwRP9JhhrddKfqeExJJ6x0RAg4HfYEMvPIhUaBHlaLD1Dy8KUapVkRgWMxAJItd4EOBY69PC8cvgO2riGJkCKftNOyoSJx9CSrKkT7Q5AIn8p6iY/2hx1oo2J++0827+9z0SAqh+AadYzngX07rjjjgxu0Dh2SEYr7RrmCfF88zgffVGZ0FhZAww5jxTfaF9r/u71LCYG3WgXmH2QrKKhOpY0GhTQtvq8DcREv8LQBmDsVcJefaH9XJdn2u/0+r0i8tGHQwOGBsxxmuaavco1m2sBGG6++easaWvnYW6wrisPs+SYX7rQwDvmURoKO6wbd5K5w7wCCPJN0c5NM6h2Gfw2PgkPAIbXv/712Qx6kMa5Vx7l2uJRoACGxaP9Cv8yxq+fSZJJgSof6p90wDDbsKox+UbDoumwFO80n41r3m1eH5ZXv/vym2s+Uaa55tOvjO3r8/W9Uar7fNWpTauF/h3l9p3Ztn8zj3Y+vdqo1zXvRT4YIFoV+yy85CUvycCBGV5Jo0cBjCXbelGvSNnbJnnNEvdr9+Yzzrs+136v+Tv60mz7dOQ1KB/gFah92tOeVl1yySWZ8V4IiTrAwCyoH2CIsraPg8oezwL8NLavfe1r875ChCZA3z333FMdeeSRWQDC9yjyivf6HdFkWdK6HnrooXkzRSZKJY0HBQpgGI92mnMpDWZOp+9+97uzScQFF1wwlad7Js1JBwzoQOJsLwpqW87hJmIpaDRFtB7XPNNMXRaieKf5bFyTV/N6M++ZnPcq+0ze92yUaT7K0+Xb8/W9Uar7fNWpC/3m85kotzxn2/7NPNr59GqjXte8h3mhZVpnnXWyv5DQxeYt2p5e2hXvlLS4FDCHCrTAdOXGG2/MmrZekuhmHxnUz+I5Rz5XbOYxsDSE+gCJNQYXE0ubSKIPtPiTr98iAtLMed577tHskZITrLWTb5HKK3esCfGMe5hgfZAE3dFv32GKtPbaa2epOv82QHchkjKg8Yc+9KEs9KN5DbOjQd/zntSP3uoBiBMivvzlL6+22267vBZwbma6++EPfzibQs1E++xbTJGe/vSn5/1Stt122/zbt0oabQoUwDDa7TNvpYsJ5dJLL82OSVddddVU3u4ZxEw+DjzwwGxjuMEGG0zdn5QTdGCnbhK0X4VN7ky8FpSgUZMW7Wt+N1O/Sbj5TLzTfDauea55vfneTM7b5ZzJu/FslGk+yhN5DjrO1/dGqe7zVadBdFuIe1Fuec+2/Zt5tPPp1Ua9rvk20wgmVS94wQtyVDJahpJGnwKYbGZ7QnpGlLZepY5+MqifxTPeJwTjaIvJ9w3Muj4i4h8JOKYZw8snBrgIBpgjMmARIJO5IXM5fgC9TPTkDZRYD8Kcp1l+WgPfBkKYIfoO/ymahfWTfw0zRr5PC8UUowlafPSjH81RkoCfXqCsWWbnQct+9FYvAJ0mb4cddsgBPdCUHxbtArDmu/KRh78wjUQPtEK7tlYJ3YWw3X333TNo0F4LoXlp17f8nhsFCmCYG/3G5m0DmvREjGbRKmgaIrlnIluW1IRvfetb84LMpnsSE1qQNpkQb7nllurtb397tl2PCTFo4rfUnmjjeq97+YXWv3i+mU9ci0eb9+LaTI7ym2sevjdf+XQp+3x9a5TyURZpPtqiCw3n45koc+Q127IPyifuNfN2rfnbOefurbbaKvuD7Ljjjpk5K0xGtMzoHwleMJDaNtp8rqWWTzDwkae+ol9gVF2ztjm277eZd8+HcKhdLkwyxhioADyayfcwx2z7MdcRuEH+GGNlcb7QfRUdBBW4+OKL835KfJSGpSZNej2rXvwNMPZrrrlmjvgEODExEyb2m9/8ZqaHfNCBuRKnZn5bTI1s1AcofvKTn5xqp/gOYMURG/j3R+tQ0mhToACG0W6feSudAQ0wAAQR3i4yd89ktkpyTLziiivycSEiOcT3Rv1o4SCh4e8hDKBzEzEpCVpFZAc08+d5k6h7/iSTZ/yRuLBjJcXy10zxTnPximu98iHBsnj5I1ULFbgymKxJaiLJR5mZWbmvPJ4nefLntwXNxO23xWFZAo3qFOXxHdI5kjVld08e+ocFUh5xz0Lqt+vKIVqRMpCuUc97T0Qh5UYP31Q+jCDHQEdgzTvKhKb+2kkZog0867vBNLSfdV+ZMAK+63vOlUc+XZI8JPlI3ldOSXvE9Xyh8U+Z0CbojQ7aKJ6XT9RRuUhCtYHv+W28qptrpHG+6bo81CUcw91XH9dIR6MvNooy9FSZSFy1m/aWD22bMkb9ZRL9wjeZAvmm/jUsySPy8a2ggfd8o3ktnnVNG+kLq622WmZWbMyGGeHo3LX9hpWt3C8UGEYB82eMOXNiO+mL5jdjaLEYX2UUre2aa66pLrzwwuq+FAVtWGqOyV7PGucAgD0cnvnMZ1arr756ntNuu+22bI3Q1MhY58wfHKMjop3IcMpE8MbHwpwSyZy/ftK+2DvFTtJoV9JoU6AAhtFun3krnYlhGGBg18kUx2BfrElv3io8Dxlh9MSWBhZE98D8YW4wZyY7CwQGCmMYjG5MwD4fTBCmkrSFpKUt9YnnmwxUXIsqNPNhNuZbGDoSL8y5/P0m2cJIRVJWEzQmHROprCZl/YBZgHwxY+qD+cSI2rBPvSyAyoEGJn2gyYQvD4w99TomVh7q5c9z7ls0LDKiAcmD2Yi+pU/R2gAeGEDfRFMMoDKQzimbdwASjKu/dgoABuyoo+9azAelAD7yQ4tlCRhZDGeTLMxRTrbS6twrKRM7arRWVwtuE4gru7YECjyjTGgU7UY6p276GtMGjDl6yQMNmVxEG3rXNX1CnvKYSWq2GybAdyz06tpMvifpN+yzlR2wHpZ69el4J+5F3q675rd+CEiRRDKTRJ9+9I78yrFQYBIpYKyah22Sx7nc/BBjqx894n5z7DWfNUcC6UCASG/MAa0DfCX233//PNeEsCbWuYsuuigLiWIuo4Ww87r1QJkiWWdEN9tkk01y/taVkkabAgUwjHb7zFvpTAxNwNDLJEkseoCh7MR4P9nRDNPnDzNmQsasYFgdTbIx0bYZq2bDxTsm1phcm/e7nssnmGRli/JgqjCI7rWZYM+ERMw7nnUtyhtMmfedBwiKMsV3mmVXDt+Rl3fiXuTpunww5pJzZfMeACJP7/umv6hXlM07zuO+383km95xlHxXnsNSM78o+7B3+t1v1rXfM8qENr7reXTw3WZyL2gcNHLf80HXaJcov7o7j3Z1X5+M7zjOJikbcBJljvx75aUM8c1o517Pzcc15QJQ/PluSYUChQLLU8A8QkDEggCDftddd03Nt8s/ff+VmDdjLm0/Z4wLMHDMMcfkvWoIdggSCH5ETYq5xrhcloQWhCKnn3561iC7Jn/CEpp6mg/vRTKuaSkJQ5hKOy9ptClQAMNot8+8lc7ALYBhduQ0KWKiJBNrmymfXa7lrUKBQoFCgUKBQoH5oYA1nkCGRjw2yiPdHwT8BwEGAgxmlKI88VegCSZQ4MchIMhrXvOaqYJj/mmdaQzsyRB+HPKnhfzUpz6Vd/sGGiJZS2kVaMXtBE5jTShQ0uhSoACG0W2beS1ZAQzzSs6SWaFAoUChQKFAocDIUYB5qpDgNA1Mk5g7BjBoFzautzUMtANMAXfaaadsUiqcamiNZwIY4ntMJWkpzjzzzLiUj0AJzYRyMlMFOkoaXQoUwDC6bTOvJTMxsG886KCDss3xnXfeOZW/eyQExYdhiiTlpFCgUKBQoFCgUGDsKEAjzgzIGk8zcF9yfva7V+oFGIAFpkdCz55yyinZp5HGwHXain6AYZUUNEUkJdqN0DDENwGGY489djnAIE9aDGZMAMPjHve4eKUcR5ACBTCMYKMsRJFMDBxXqRGpLG2iE6kAhqBEORYKFAoUChQKjDIFMK38yjChYSq6UOUleRcMgi0/J16CtXFIfKAETbBXgvXeH1oFQIg6xO/QMGDgBcYQ+MTGaieeeOI05h/tv/3tb2eTJD4MvhP8w2wAg+8CDMyYRGAquz5Hy4zmsQCG0WyXeS+VQc2Hwe6MVJUiKUSKAV80DEGRciwUKBQoFCgUGDUKYHoxwjZrO/fcc/M+AOF4O9Oytpnl9vuYWczzhhtumPcisCOxcNDAwzikiNJms7wTTjghh7n+f+2dC7BVVf3HV9lDyAcPAQEFJB4+AtMEUWLCB4iEoqaAgmgPS01Dy2gamqYcrXSaNBMHbRTI14wDWqNmakPOYCioJRKoCIoaiqSIoaL2mL+f1X/d2fdw73lwH2efcz9r5nAee+211/4s7t7ru9fvgblStmQZcL5EYJs0aVI49thjo+8CkeuyIgnWmDhh8kSSVyK3cRzqKBiyZOvzs4KhPsd1h7NKgiHlYchGSaIyF4sBH9oSEi+ZaEk4IFkkIAEJSEACeSBANC7MagnpSZhrkoGl8MZt1T/s9gklyhN3wvqefPLJ8d5YC6KByT3R/XhAiGnRY4891igPAvd8zg+RgCkQKymEiSaEMU/7iZaIEzL1UmEegRMzGaUxb8ZqAUdrfBEQDIVOz2m/5nwYaBtn6quuusoVhgQrx+8KhhwPTmt2LQmGefPmxQsIYc5SYVv6w73iiivixYM4+hYJSEACEpBAtQmkiSrRdhYuXBgWL17cEP53Z/tGm5TshLipttiOORKTakxnuDeSc6AWCisyhFflQSEPCcmhkAqrAl26dIkTdZyaiVhEaNOjjjoqrqJgntRUQbiR6RnBQBQm8r7QVlNRktL+CoZEorbfFQy1PX5l956LI8uHv/rVr8Jf/vKXcN999zXsmwRDiopAgpYZM2Y0bPeDBCQgAQlIoFoEeFpOEkScY5cuXRpWrlzZ4q6UKxg4EKKByTThP7k/cq8sJTRa3MFWaKCYYGBFgbwJhE0lCRuTfkQCvxcrCoZidOp7m4Khvse34ey4OPJ04fLLLw+rVq0K2DWmkgQDWYNJ0z569Ohw/vnnp82+S0ACEpCABKpGAMGAOdK1114b7ecff/zxFk/YKxEMTKT33nvv8Otf/7rmBMOaNWsaVhheeeWVOIaIHfwzJkyYEO/3F154YdljW6lgYOwwHWPuwQPLbKEfKUqSTs9ZMvn8rGDI57i0eq+4OJKhkZUDwqKx2pBKEgzYK5IGHltNYiZbJCABCUhAAtUmwD0Ke3xMYRYsWBDuuuuudhMMTGrxWcBGn6AhZCbGRKlWVhiSYMAMOSsYCH167rnnxvM54YQTyh7iJBhmz54d1q9fH30aijk9Ux/TJXIwsEKTLTDEh4GVIwVDlkw+PysYcjYuLCGS3p2LY2sVFD4CAVvGn/70p2Hz5s1h+/btDc0nwUAWR/5ojzzyyEZZHBsqlvmB4+EItW3bthhBgQsCTlGpkCkZp2ouMhYJSEACEpBAKQIp6g9+DKwwkFtg69atMcwn0X94cZ/jHtpcYYLKfQ6TIu5DfE+2+oQI5Uk47dAG26jD/Yun4DxIO/300+PnWnB6hgHn8dRTT4VrrrkmhkJ97bXXIhrOGUfulDANx+5yS1OCgfYw2eKBI36QMMNigblFyvRMQJWmMj3jG4KYwMmaKFSW/BJQMORkbPjDIsYxQoFEKyy/tlbhorF27dpo94nvAk5K2ZIEAxdB/miHDx8eMzxm61TymeNxMccEiovFiBEjYjQG2uAijI0kFxYcx4jSwG8WCUhAAhKQQDECPIziHokwILcA90kEBA+nCPeJfx4Pw6jXVOHBFWKBpGQpr0K6/3D/JT8R7SNO0r2KfATcr1id50EXgqNWCueEuLryyitjVKmUwI2HdYiEBx54oOKIiAgGTJq///3vR17c4ymYONEmDyVxgGYuwdwCEXb33XdHR/UHH3ywAR19QFgwP8BUiQhNlnwTUDDkYHy4uLGqQNgzljwxHeKPrLVKEiNcPBALfM+W9J2nBDxR4ZWNAsH2dFHN7pf9nNpIv3FOPLHhHSGSnuKwnQsuCVpwuDrvvPNiVsnsCkRqw3cJSEACEpBAlgD3Gu4t3M94OMXknkksTtFz5syJJrckFyss3IcGDBgQxowZExOacc/J3pfSfZi2UkIy9sF0B3NdJsRMckvdCwuPW83vnAuTdHwSsSyAFYXzHjJkSNxWaQh1mCPWWDG44447wsaNGxuSt8EIvsOGDQsnnXRStCwg9ComR+TPyEZpgi1zgPHjx4dvfvObMWJTNVl57NIEFAylGbV5Df6osQUkrjR/WNgZlmOSlCbpLb2ANddOc783ByTVZ3u2T+n39Fu6cPNkYdasWdEMKitQmmvf3yUgAQlIQAKFBJjgIxK+9a1vxcks99PCwqT/0EMPjWFDyYBcOPnnPsUDNSbEfOaFqODelBUWhe3m+TsCgVWEc845Jz6URGRRWiIYYI0VBOZF+CTwgJPfuL9jMYAQIQksJlwwxgzqtttui4IlO69hiFJM2AAAIR9JREFUPEgQh//EtGnTGj2kzDPTjtw3BUOVR5+LEjGK77zzzvDoo4+GW265JdpQltMt9qWkiXg5+zRVp7l2mvu9qTb4LdXnc7ZP6ffsb1xIeNpzyimnRMer/T50KLNIQAISkIAEKiXAPYYVhiQYMMHNFu49Xbt2DdOnT49RjnjvCKUtBAMrMZiEEd72sssuC08//XRc4cne38thS96Hs88+O5p6sSLBg0RLvgkoGKo8PlzoMEe69dZbo0nSokWLGpYNS3WtqYl4qX2a2k47Tf2xV9p+qs8xsu2l37O/IRiwX5w4cWK4+OKL4xOJpvrmbxKQgAQkIIFiBLjHIBhYscZcppRgOOOMM4o1VzfbkmD4+te/3rDCwH2YyTqT9Ntvvz307t274vNlpWLTpk3hN7/5TUwEe++990YTsew9vlijrESwCoFJ8plnnhlXF8rdt1i7bmtbAgqGtuVbsnUudKwwIBTwYcAmkGVRlvhKlaYm4qX2aWo77TT1x1pp+6k+x8i2l35Pv/HOcuSAD1cYTjzxxLhcymeLBCQgAQlIoFIC3GMUDDtSw9x5yZIlMeohvgY4hGOOhN8Cztxz587daWdj2kIoJN9Lvqd7/Y49+d8v3PvxkcTXgeN/5StfCWSZttQGAQVDDsYJcUCEh+XLl4errroqPh1J8ZKLdS/9caaJeLG6xbbRTlNtVNp+qs+xsu2l39NvREnCf4EMk9/5znfi0wVWHCwSkIAEJCCBSglwj1Ew7EiNuQV5l3ggefPNN0c/DybskydPjubA48aNK5nZecdW//cLzAmf/uSTT4aZM2dGXwVEQ7FCwJOhQ4fGoCfkgBg0aFBMiFdsH7flh4CCIQdjwR8eS4dEE8AuECchzJRKlcKJeKn6zW3PtpP6wvEJl4bTFzGoy4lixDIljmeskCRxkI5JCDviNHPBQDAQdo0XERUUC4mS7xKQgAQkUCkB7ltZHwYi8mQL9yMyNZNsjLDhY8eOzW6u289wwYIBPwN8JHkwyQrDwQcfHDmwsl/Ovb05QAgSQtvecMMNkT+fESjMHciRQaF9cjJggsw9n4eFmCPxwBDTKOYDltogoGDI0Tjxx4dwYBmRV3sXLi68iGRAFATCsGFryNIh7/QvFS4CXHiywoCEN0R6SrGeU13qEZqOBC1cOBAPvGiDpx0WCUhAAhKQwM4SSIIh+TDgx5At3KdIVEa8f55wV5KoLNtOrX7GUZlJfIoAxSQds+CWFrhz3ycqFdmcySr90EMPRf+GFNqWuQPsEQqjRo0Ko0ePjuLNyIgtpd/++ysY2p950SPyB0hJ70Urt9JGjsXSIi8KFxcuLLxYNeAJBU8LeHLAhZeLDRdcLgKsGqSSLh5ZYZG2sYpAFIQkMpLQSO+pnu8SkIAEJCCBSghw7+Hp9re//e2YTGz16tWNduc+g3Pvj3/845i0jYlrRyvc11OBR2vde2Gf5gqIB5Lo8dARnwmOgWCAPX4LvBAqzAda6/jpnHxvewIKhrZn3KpH4I+eyTtLi5gu8Yfa0sIfPLaH/LEXFgQDSeQ4Jhdk/sgxKyIMap8+feIyIysH/OZqQSE9v0tAAhKQQFsTSILhe9/7XjS/WblyZaNDct8ikzBhV8nFcNxxxzXa7pfWIcA4YB3BfCJZGjAv6N69exQOLTF/ap0e2kpLCCgYWkKvCvtissSSH9EJFi5cWFaCt7bqJisG2CSS8ZH37GpDWx3TdiUgAQlIQAJZAkxUySJ86aWXhlWrVoVly5ZlN8cHXZjA4OSL39xFF13UaLtfJCCB0gQUDKUZ5aYGqws87Sf2MXkbsBdEzbd0aY+LLaWwneZ+T3VTxAMEA+ZJ3bp1i+34jwQkIAEJSKC9CHCvYtWdh2grVqyI4cmzx+be1tFNkrI8/CyBnSGgYNgZalXaB8GAGdL1118f5s+fHwi9iklS4US/0u41Jwya+5328UVAIBBx4pprrommSTg0WyQgAQlIQALtSYB7Vcpn9Mgjj8T7Y/b43CN5qEXeAZyeidJjkYAEKiOgYKiMV9Vrc1FcsGBBjKnM0mu1VhhYXcAO9KSTTorxnFnubalwqTpcOyABCUhAAjVHoBzBMODDEKLz5s2LATv4bJGABCojoGCojFfVa+OYTDxlsjfeeeedMfQpORN42k/0Ip7y8/S/3JJWEahfOOFvaht1EAtDhgyJIdIOP/zwGHUCfwaLBCQgAQlIoL0JFAoGHqplC/etAR+KBFbnU4S/7HY/S0ACpQkoGEozylWNFCWJuMdXX311jH9MkhoyJpLrgOQoOyMYCsVC9qS5GKftvHfp0iUmXeHCy/EQEGl7dj8/S0ACEpCABNqaQBIMixcvDs2ZJCkY2noUbL/eCSgYanCECXVK2DIyW+LTgHhAMBDjuD1MgwiThmhgRYMYy5UIlBrEbZclIAEJSCDHBBQMOR4cu1Y3BBQMNTyU6SKJcNh3331j9mRMg1iFIHkaDtG8SMhGohRiILMSwH682JbqZTFQj1UDBAH78bJIQAISkIAE8kgg3QtdYcjj6NineiGgYKiDkWTSnyb1iAV8Ggi/+vLLL4cNGzaEe+65J0aIYEmW1YkkIohbTXIVTJpoAzFBO3379g3HHHNMmDBhQjQ5YjUhtV8HuDwFCUhAAhKoIwJJMCxatKgsk6T+/fvX0dl7KhJoHwIKhvbh3C5HQSyQln3p0qXh4YcfDps2bYrC4Zlnngl77rlndIxGLFAP4UD6dlYfEA38hmDgRV38Ez73uc9FUyeEQ9euXaPJU7uciAeRgAQkIAEJlEmgHMFgHoYyYVpNAs0QUDA0A6YWf0YMIBKuu+66mMAGIUDY1VKFiy0FsZAKKwpkbj7wwAPDnDlzYiZnzJ4sEpCABCQggTwRKEcwEBTknHPOCYcddlgMB56n/tsXCdQCAQVDLYxSmX18//33o3nRL3/5yygYWDVIYqBYE9TJioVUN4mGyZMnB8KnnnnmmWmT7xKQgAQkIIFcEEiCoZgPA6vkM2bMCCNHjgynn356LvptJyRQSwQUDLU0WiX6mgQDmZcXLlwY/RJaIhiIftSzZ89w6qmnxovs9OnTS/TAzRKQgAQkIIH2JVCuYOAehmA444wz2reDHk0CdUBAwVAHg5hOAfMjnJznzp0bs0GT5A0zpVKluRUGQqYOHDgwXHLJJTE524gRI0o15XYJSEACEpBAuxJQMLQrbg/WQQkoGOpo4LlovvPOO+HJJ5+MkSJwfCZiUo8ePaLDMmFSqYOj8yuvvBKef/75WB9zJPZDYODw3KlTp9CnT59w1FFHhaFDh4ajjz5ap+c6+n/iqUhAAhKoJwJJMBSLkoRJUlphcLW8nkbfc2kvAgqG9iLdTschPCpiYO3ateGPf/xj2LJlSyA6BEKApG5cWN9+++3w4osvhjVr1sTPCIa33norCgkcw0gA169fvzBx4sQYJekzn/lMIL+DRQISkIAEJJA3AuUIhu7du4ezzz47sFJ+2mmn5e0U7I8Eck9AwZD7Iaq8g1w8EQ6ETsXxGV8EREFybE7bt27dGuuxnc+sMrAawQrDHnvsEcjojOOzORgqHwP3kIAEJCCB9iFQjmDYZ599ws9//vOw//77h2HDhrVPxzyKBOqIgIKhjgazuVPhYop/w/bt2+PqA34N6TdEAeZHSUxgtkSmZ/wXLBKQgAQkIIG8EygUDAsWLGjUZe5vJCS94oorwgEHHBAOPvjgRtv9IgEJlCagYCjNqOZrsMpAkjZyNKxYsSL6KnBSXEQxPzr00EPjygI2nhYJSEACEpBALRFIgqFYWFVMc3/0ox/FAB6jRo2qpdOzrxLIBQEFQy6GoW07werC8uXLw5IlS8Itt9wSxQNHTIKBHAvEpf7iF7/Yth2xdQlIQAISkEArEyhHMHTr1k0fhlbmbnMdi4CCoQOMN/kZ/vSnP4V777033HzzzWHbtm3xrBEM+Ctgz4kzGI5gOEfj02CRgAQkIAEJ1AKBcgRDNkqSeRhqYVTtY94IKBjyNiJt0B98F+6+++5w5513RtGAc3O2IBqmTp0apk2bFsaMGRNFRHa7nyUgAQlIQAJ5JZAEg2FV8zpC9qseCCgY6mEUS5wDguG+++4Lv/3tb8Ndd90VoyGlXXBuHjJkSDjrrLPClClTYghWoyIlOr5LQAISkEDeCZQjGHr27Bkuuuii8NnPfjYcd9xxeT8l+yeB3BFQMORuSFq/Q8kk6fe//33AKYw8DDhCEyGJ3Aw4PbPCMGnSpPgdUyWLBCQgAQlIoBYIlCMYevXqFWbPnh0jJJGU1CIBCVRGQMFQGa+arI04IOMzmZ0JN0cyN37jAkps6gkTJsSVBRLb6L9Qk0NspyUgAQl0WAJJMBSLksQKwwUXXBAfkHHPs0hAApURUDBUxqsma3MxJVLS5s2bA6sMhFhFMJCkjYvoEUccEVcWzL1Qk8NrpyUgAQl0aALlCoaLL744miSNGzeuQ/Py5CWwMwQUDDtDzX0kIAEJSEACEsgFgXIEAwlKL7300piHYcSIEbnot52QQC0RUDDU0mjZVwlIQAISkIAEGhFIgqFYlKR+/fqFa6+9NgwdOjQMGjSo0f5+kYAEShNQMJRmZA0JSEACEpCABHJKoBzBMGDAgHD99deHwYMHh/79++f0TOyWBPJLQMGQ37GxZxKQgAQkIAEJlCCgYCgByM0SaAUCCoZWgGgTEpCABCQgAQlUh0ASDClK0k033dSoI4QKd4WhERK/SKBiAgqGipG5gwQkIAEJSEACeSFQKBjmz5/fqGuFggF/BosEJFAZAQVDZbysLQEJSEACEpBAjggoGHI0GHalbgkoGOp2aD0xCUhAAhKQQP0TUDDU/xh7htUnoGCo/hjYAwlIQAISkIAEdpJAEgzFwqrqw7CTcN1NAv9PQMHgfwUJSEACEpCABGqWgIKhZofOjtcQAQVDDQ2WXZWABCQgAQlIoDEBBUNjHn6TQFsQUDC0BVXblIAEJCABCUigXQgkwZDCqholqV2we5AORkDB0MEG3NOVgAQkIAEJ1BMBBUM9jabnklcCCoa8joz9koAEJCABCUigJIFyBcO8efPC4MGDQ//+/Uu2aQUJSKAxAQVDYx5+k4AEJCABCUighggkwVAsShLJ2q6++uowdOjQsP/++9fQ2dlVCeSDgIIhH+NgLyQgAQlIQAIS2AkC5QiGPn36hEsvvTQcdNBBYeTIkTtxFHeRQMcmoGDo2OPv2UtAAhKQgARqmkA5gqFbt25h5syZUSxMnTq1ps/XzkugGgQUDNWg7jElIAEJSEACEmgVAgiG119/PeCj8MQTT4Tf/e53jdr9yEc+Enbbbbcwfvz4MGbMmDBr1qxG2/0iAQmUJqBgKM3IGhKQgAQkIAEJ5JQAguHVV18Nl19+eVi1alVYunTpDj3t1KlTOPTQQ8PRRx8dTZN2qOAPEpBAUQIKhqJ43CgBCUhAAhKQQJ4JIBjefPPNcPvtt4fly5eHW265pVF3WWHo0qVLOO2008KoUaPC2Wef3Wi7XyQggdIEFAylGVlDAhKQgAQkIIGcEijHh6Fr165h+vTp0YeBd4sEJFAZAQVDZbysLQEJSEACEpBAjggoGHI0GHalbgkoGOp2aD0xCUhAAhKQQP0TSIJh8eLF4ZFHHgnz589vdNKYJGVXGM4444xG2/0iAQmUJqBgKM3IGhKQgAQkIAEJ5JSAgiGnA2O36oqAgqGuhtOTkYAEJCABCXQsAgqGjjXenm11CCgYqsPdo0pAAhKQgAQk0AoEkmBYtGhRNElasGBBo1aTSRKmSGR51um5ER6/SKAsAgqGsjBZSQISkIAEJCCBPBIoFAylfBgUDHkcRfuUdwIKhryPkP2TgAQkIAEJSKBZAgqGZtG4QQKtRkDB0GoobUgCEpCABCQggfYmoGBob+IeryMSUDB0xFH3nCUgAQlIQAJ1QiAJBsOq1smAehq5JKBgyOWw2CkJSEACEpCABMohoGAoh5J1JNAyAgqGlvFzbwlIQAISkIAEqkgAwfDmm2+GW2+9NaxYsSLcdtttjXqToiTh7EyUJBO3NcLjFwmURUDBUBYmK0lAAhKQgAQkkEcC//rXv8KLL74YZs+eHZ599tnw9NNPN+pmoWAwSlIjPH6RQFkEFAxlYbKSBCQgAQlIQAKVEGAi/+9//zv897//bXa3j370o+FjH/tYYJWAunzmtw8++CD+1uyO/7+B/d55552wdu3aMGvWrPDSSy+FLVu2NNotCYYpU6aEESNGBN4LC3XSsXmn0Hbqx3/+85+GXTgfjsGLc9x9991D//79wyc/+cmwyy67NNTzgwTqiYCCoZ5G03ORgAQkIAEJ5IAAE+l//vOfYdu2bVEIMPkuLEzSmWDvuuuucdO7774bOnXqFD7+8Y/HfYsJjdQWdd56663wzDPPhEsuuSS8/vrraVPDO8fZc889w4knnhiGDx8eTjjhhIZt6QN1OnfuHI9NH/iOSKD/nAuvVBA2zz//fNiwYUN4++23Q9++fcPo0aPDHnvsEc+Fc+LFeVgkUC8EFAz1MpKehwQkIAEJSKDKBBAG7733XjQLuv/++8NDDz0Uv2ef0DMZp7CS8IlPfCJ07949ft+0aVP8vNtuu8WVAibmhSUrPFI7TOZZZXjuuecaTeyz+7Jq0KNHj7gasNdee8VNtJXaoC/8zrGpl1Y5/v73vweEDMIhFfbbvn17fHFeCI199tkn9OrVK/Tu3TsMGjQoDBw4MIwZMybt4rsEap6AgqHmh9ATkIAEJCABCeSDAJPprVu3hiVLloQ77rgj/OEPf4iTeX7nRUmTdJ7CIxiYqLPt1VdfjZ95Uv/CCy/ElYnCsypso3B7ud8L26Ev9APzor333jv2EXMkfCMQI1nBkD0G7XAO9BnBgHA46KCDwrBhw8LUqVPjNsSHRQK1TkDBUOsjaP8lIAEJSEACOSHAE/c1a9aE8847L6xfvz784x//aBAKhZP01GUEBC/2ZXLNK7sikerx3lwb2TrlfG6qndSP7AQ/9SPVL2w7/c4+7M87JlajRo0Kc+bMCQcffHA0hyrcz+8SqDUCCoZaGzH7KwEJSEACEsgpASbYf/vb38KXv/zlaFZEuNNU8DdIk/L0W/a91HbqMkHnlZ3UZ9so93Pyj2iLdjB/wlfi/PPPDxMnTowrD+X2y3oSyCsBBUNeR8Z+SUACEpCABGqMAIJh9erV4atf/Wp0Cn7jjTcazoCJPoKhuVJqe9qv3HqpflPvtEEp1p+m9iv8ral2MG/Cj4HwrTNnzgz9+vUr3M3vEqg5AgqGmhsyOywBCUhAAhLIJwGe3GOK9MMf/jA88cQTYd26dQ0dLTXRL7U9NVRuvVS/qfemJvpN1Sv1W1PtYJKEKdKFF14Yxo0bF52oS7XjdgnknYCCIe8jZP8kIAEJSEACNUIAwYDz8k033RRWrlzZJoKB6EmEbOU9TdgxLSIPAqFMmbATOYnthD1NdZpCyLZyVxlYPeFFuxynqbCprC507do1Coavfe1r4ZBDDtGHoSnw/lZzBBQMNTdkdlgCEpCABCSQXwKIBkKRkkRt48aNrdpRJvhELVq2bFnMucB3XoiFfffdNz7N32+//eI2zKEQLUzwCwv7UMoVC9QnUhLnRbs9e/aMx8q2Q1uIFfwXhgwZEo499tjCw/pdAjVLQMFQs0NnxyUgAQlIQAL5JMCT+Pfffz++WruHtE2ytmwytcIVBkQCYVERF2lS39J+lLPCQD/I5UDyN1YaLBKoFwIKhnoZSc9DAhKQgAQkUGcEWK3gRSH6UFMFQcCLCX1LC6sEmBWVu/LQ0uO5vwRqhYCCoVZGyn5KQAISkIAEOggBBAArBIRlZZUAsYDJUWEYVOqxHV8F6rZENCASSMLWt2/faOKEcLBIQAL/I6Bg8H+CBCQgAQlIQAJVIZCEAX4BDz/8cJz4Y2rE75g0IQIQAzgYFwoGJvjUYztO0K0hGDAnwlGZKEf4ISgaqvLfwoPmkICCIYeDYpckIAEJSEACHYEA5kaIhbVr14Yrr7wybN68ucHvAMGwdevW+B3BsM8++7TaCgNCg5I1PeIzfgfHHHNMOPXUU8Pxxx8fPvWpTzWq0xHGxHOUQFMEFAxNUfE3CUhAAhKQgATanACRh+bNmxcef/zxcP/990czpDSZ5z35MDCZxyyJ33jxPU32U71KzJHYh5LaSCeKydOee+4Zxo4dGyZMmBCmTZsWnZjTdt8l0FEJKBg66sh73hKQgAQkIIEqEyDa0U9+8pOwfPnyGCqV6EaFk/hsF5ub6GfrlPO5WDuEaD3iiCPC+PHjw7nnnmsehXKAWqfuCSgY6n6IPUEJSEACEpBAPgngdzBnzpwoGJ566qnotFxtwYDjM34MrDJ897vfNTxqPv/r2Kt2JqBgaGfgHk4CEpCABCQggf8RIMLRokWLwooVK8KNN94YTZJKsWF1oJioKLU/24utMOy+++7hlFNOCaeddlo46qijYk6Fctq0jgTqmYCCoZ5H13OTgAQkIAEJ5JgAjs1Lly4Nf/3rX8PVV18dtm/f3pB3obluM9lPvg1EVMIhmmhGhSFXm9ofPwf24T0rPBAgtEFbvXv3DlOmTAlf+tKXwoEHHhhDrTbVlr9JoCMRUDB0pNH2XCUgAQlIQAI5IsCknVWGjRs3hsWLF8eISXwvVvBzSGFUn3322dC/f/8wYMCA0Llz56IrD4iMLVu2hNWrV8dM0Vl/CRyq+/XrF9s6+eSTw/Dhw8OnP/1pxUKxgXBbhyKgYOhQw+3JSkACEpCABPJFgKf9+DKQhwEh8O677xbtIPVT7oXnn38+9OnTJ4Zc3XXXXYsKBsQJx1m3bl3cPysYWF1gZYHQrccee2zM+bDXXnsV7YcbJdCRCCgYOtJoe64SkIAEJCABCUhAAhKokICCoUJgVpeABCQgAQlIoP0JsCLwyiuvhNdffz2wmkBStcLsz+3fK48ogY5BQMHQMcbZs5SABCQgAQnULAHEAv4HZIR+6aWXoljYY489op8BeRPwQWjK6RnzJfblRaEe9YmEhBlSS6Mt1SxQOy6BCgkoGCoEZnUJSEACEpCABNqPAFGNXn755XDdddeFP//5z9FpmYk/+RK6d+8eBg8eHAYOHBidnrOiAZHwxhtvBPwc2J9tPXr0iEnZZsyYER2lWaVQNLTfWHqk2iWgYKjdsbPnEpCABCQggbomgKPytm3bwpo1a8Ls2bPDc889FzZt2hRXB1gh6NSpUxQNCAdComYn/0RFIuISKxNklGYbAmHQoEExx8JBBx0UxQNtWCQggeIEFAzF+bhVAhKQgAQkIIEqEWDSj8/C448/HqZNmxajG2XzJ+xMtxAI48ePD4cddlg4//zzzeS8MxDdp8MRUDB0uCH3hCUgAQlIQAK1QQAfhNdeey089thjATMiwqm2tGDOhAkTguEXv/hF6NWrV0ubdH8J1D0BBUPdD7EnKAEJSEACEqhNAqww4IeASdIPfvCDuNpANuhUWG0gbwO/IS74Tkmfeafgv0BkJV6YL5HBediwYeHiiy8O3bp1i3X8RwISaJ6AgqF5Nm6RgAQkIAEJSKDKBJIoeOaZZ6LD8/r16xt8FXCI5nd8G1h9QGDwIgEc2957773o70BkpL59+0ZHZ8yRJk+eHL/ze9bvocqn6uElkFsCCobcDo0dk4AEJCABCUgAAogAHJjTakKiksQEjs2rV6+OdcjmvGzZsugcjbPzF77whTB27NiAkzOhWLt27RrI4kyUpWxUpdSm7xKQwI4EFAw7MvEXCUhAAhKQgARqgACC4f3334+RkB5++OG4soCT9EMPPRQ2btwYIyxNmDAhTJo0KfoskH+BSEkWCUigMgIKhsp4WVsCEpCABCQggZwQ+OCDD2IEpSVLloQbbrghbN26Na5GkIOBVQkEBWZHe++9dzjrrLPCIYccEsVDTrpvNyRQMwQUDDUzVHZUAhKQgAQkIIEsAZyd77rrrrBo0aLw4IMPRpOl7HY+46PQuXPnMHLkyDBq1KhwwQUXRMdn8jZYJCCB8ggoGMrjZC0JSEACEpCABHJGAEfnuXPnhhtvvDG8+OKLgZWF5gr5Fz7/+c+Hn/3sZzE7tKZJzZHydwnsSEDBsCMTf5GABCQgAQlIoAYIVCIYcHIePXp0uOyyy6IDNP4MFglIoDwCCobyOFlLAhKQgAQkIIGcESBy0vz588PNN98coyThAI3vQmHZZZddQu/evaNgmDNnTthvv/2imVJhPb9LQAJNE1AwNM3FXyUgAQlIQAISyDkB8iw88MAD4Z577okvwqjyW7bgw0A41eOPPz4ceeSR4Rvf+EbMzWD+hSwlP0ugOAEFQ3E+bpWABCQgAQlIIKcE8Fl44YUXYvK2Rx99NLz66qth3bp1Db1lZaFnz55h3333DYcffnhM3DZixIiG7X6QgATKI6BgKI+TtSQgAQlIQAISyCkBsjq//PLLYcOGDWHp0qUNvSQS0v777x8OOOCA0K9fv5iszehIDXj8IIGyCSgYykZlRQlIQAISkIAE8kqA1QZeWZMkzI4QCOmV177bLwnknYCCIe8jZP8kIAEJSEACEpCABCRQRQIKhirC99ASkIAEJCABCUhAAhLIOwEFQ95HyP5JQAISkIAEJCABCUigigQUDFWE76ElIAEJSEACEpCABCSQdwIKhryPkP2TgAQkIAEJSEACEpBAFQkoGKoI30NLQAISkIAEJCABCUgg7wQUDHkfIfsnAQlIQAISkIAEJCCBKhJQMFQRvoeWgAQkIAEJSEACEpBA3gkoGPI+QvZPAhKQgAQkIAEJSEACVSSgYKgifA8tAQlIQAISkIAEJCCBvBNQMOR9hOyfBCQgAQlIQAISkIAEqkhAwVBF+B5aAhKQgAQkIAEJSEACeSegYMj7CNk/CUhAAhKQgAQkIAEJVJGAgqGK8D20BCQgAQlIQAISkIAE8k5AwZD3EbJ/EpCABCQgAQlIQAISqCIBBUMV4XtoCUhAAhKQgAQkIAEJ5J2AgiHvI2T/JCABCUhAAhKQgAQkUEUCCoYqwvfQEpCABCQgAQlIQAISyDsBBUPeR8j+SUACEpCABCQgAQlIoIoEFAxVhO+hJSABCUhAAhKQgAQkkHcCCoa8j5D9k4AEJCABCUhAAhKQQBUJKBiqCN9DS0ACEpCABCQgAQlIIO8EFAx5HyH7JwEJSEACEpCABCQggSoSUDBUEb6HloAEJCABCUhAAhKQQN4JKBjyPkL2TwISkIAEJCABCUhAAlUkoGCoInwPLQEJSEACEpCABCQggbwTUDDkfYTsnwQkIAEJSEACEpCABKpI4P8AWtC/yjOXCxMAAAAASUVORK5CYII=	\phi_c = \frac{\phi_0}{6}
+291	For a particle of charge $e$ moving non-relativistically, find  (a) The time-averaged power radiated per unit solid angle, $dP/d\Omega$, in terms of velocity $\beta c$, acceleration $\beta \dot{c}$, and the unit vector $\mathbf{n}'$ from the charge toward the observer;  (b) $dP/d\Omega$, if the particle moves as $z(t) = a \cos(\omega_0 t)$;  (c) $dP/d\Omega$ for circular motion of radius $R$ in the *xy* plane with constant angular frequency $\omega_0$.  (d) Sketch the angular distribution of the radiation in each case.  (e) Qualitatively, how is $dP/d\Omega$ changed if the motion is relativistic?	[]	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	\frac{e^2}{16\pi^2 \epsilon_0 c} |\dot{\beta}|^2 \sin^2 \theta; \frac{e^2 a^2 \omega_0^4}{32\pi^2 \varepsilon_0 c^3}\sin^2 \theta; \frac{e^2 R^2 \omega_0^4}{32\pi^2 \varepsilon_0 c^3} (1 + \cos^2 \theta)
+292	(a) Consider two positrons in a beam at SLAC. The beam has energy of about 50 GeV ($\gamma \approx 10^5$). In the beam frame (rest frame) they are separated by a distance $d$, and positron $e^+_2$ is traveling directly ahead of $e^+_1$, as shown in Fig. 5.8. Write down expressions at $e^+_1$ giving the effect of $e^+_2$. Specifically, give the following vectors: $\mathbf{E}$, $\mathbf{B}$, the Lorentz force $\mathbf{F}$, and the acceleration $\mathbf{a}$. Do this in two reference frames:  1. the rest frame,  2. the laboratory frame.  The results will differ by various relativistic factors. Give intuitive explanations of these factors.  (b) The problem is the same as in part (a) except this time the two positrons are traveling side by side as sketched in Fig. 5.9.	[]	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	"\begin{align*}
+\mathbf{E}' &= -\frac{1}{4\pi \varepsilon_0} \frac{e}{d^2} \mathbf{e}_z, \\
+\mathbf{B}' &= 0, \\
+\mathbf{F}' &= -\frac{1}{4\pi \varepsilon_0} \frac{e^2}{d^2} \mathbf{e}_z, \\
+\mathbf{a}' &= -\frac{1}{4\pi \varepsilon_0 m} \frac{e^2}{d^2} \mathbf{e}_z.
+\end{align*}; \begin{align*}
+\mathbf{E} &= \mathbf{E}' = - \frac{1}{4\pi \varepsilon_0} \frac{e}{d^2} \mathbf{e}_z, \\
+\mathbf{B} &= 0, \\
+\mathbf{F} &= \mathbf{F}' = - \frac{1}{4\pi \varepsilon_0} \frac{e^2}{d^2} \mathbf{e}_z, \\
+a &= \frac{F}{m \gamma^3} = \frac{a'}{\gamma^3}.
+\end{align*}; \begin{align*}
+\mathbf{E}' &= - \frac{e}{4 \pi \epsilon_0 d^2} \mathbf{e}_z, \\
+\mathbf{B}' &= 0, \\
+\mathbf{F}' &= - \frac{e^2}{4 \pi \epsilon_0 d^2} \mathbf{e}_z, \\
+\mathbf{a}' &= - \frac{e^2}{4 \pi \epsilon_0 m d^2} \mathbf{e}_z.
+\end{align*}; \begin{align*}
+\mathbf{E} &= - \frac{\gamma e}{4 \pi \epsilon_0 d^2} \mathbf{e}_z, \\
+\mathbf{B} &= - \frac{\gamma v e}{4 \pi \epsilon_0 c^2 d^2} \mathbf{e}_y, \\
+\mathbf{F} &= - \frac{e^2}{4 \pi \epsilon_0 d^2 \gamma} \mathbf{e}_x = \frac{\mathbf{F}'}{\gamma}, \\
+a &= \frac{F}{m \gamma^2} = \frac{a'}{\gamma^2}.
+\end{align*}"
+293	As can be seen from Fig. 1.12, a cylindrical conducting rod of diameter $d$ and length $l (l \gg d)$ is uniformly charged in vacuum such that the electric field near its surface and far from its ends is $E_0$. What is the electric field at $r \gg l$ on the axis of the cylinder?	[]	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	E = \frac{E_0 dl}{4r^2}
+294	A particle of mass $m$ and charge $e$ is accelerated for a time by a uniform electric field to a velocity not necessarily small compared with $c$.  (a) What is the momentum of the particle at the end of the acceleration time?  (b) What is the velocity of the particle at that time?  (c) The particle is unstable and decays with a lifetime $\tau$ in its rest frame. What lifetime would be measured by a stationary observer who observed the decay of the particle moving uniformly with the above velocity?	[]	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	p = eEt; v = \frac{eEct}{\sqrt{(eEt)^2 + (mc)^2}}; T = \tau \sqrt{1 + \left( \frac{eEt}{mc} \right)^2}
+295	A solid conducting sphere of radius $r_1$ has a charge of $+Q$. It is surrounded by a concentric hollow conducting sphere of inside radius $r_2$ and outside radius $r_3$. Use the Gaussian theorem to get expressions for  $(a) the field outside the outer sphere,$ $(b) the field between the spheres.$ $(c) Set up an expression for the potential of the inner sphere. It is not necessary to perform the integrations.$	[]	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	\mathbf{E}(r) = \frac{Q}{4 \pi \varepsilon_0 r^2} \mathbf{e}_r \quad (r > r_3); \mathbf{E}(r) = \frac{Q}{4 \pi \varepsilon_0 r^2} \mathbf{e}_r \quad (r_2 > r > r_1); \varphi(r_1) = \int_{r_1}^{r_2} \frac{Q}{4\pi\varepsilon_0 r^2} dr + \int_{r_3}^{\infty} \frac{Q}{4\pi\varepsilon_0 r^2} dr
+296	An infinitely long perfectly conducting straight wire of radius $r$ carries a constant current $i$ and charge density zero as seen by a fixed observer $A$. The current is due to an electron stream of uniform density moving with high (relativistic) velocity $U$. $A$ second observer $B$ travels parallel to the wire with high (relativistic) velocity $v$. As seen by the observer $B$:  (a) What is the electromagnetic field?  (b) What is the charge density in the wire implied by this field?  (c) With what velocities do the electron and ion streams move?  (d) How do you account for the presence of a charge density seen by $B$ but not by $A$?	[]	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	"\begin{aligned}
+\mathbf{E}' & =
+\begin{cases} 
+-\frac{\mu_0 \gamma iv r}{2 \pi r_0^2} e_r, & (r < r_0) \\
+-\frac{\mu_0 \gamma iv}{2 \pi r} e_r, & (r > r_0)
+\end{cases} \\
+\mathbf{B}' & =
+\begin{cases} 
+\frac{\mu_0 i\gamma  r}{2 \pi r_0^2} e_\varphi, & (r < r_0) \\
+\frac{\mu_0 i\gamma }{2 \pi r} e_\varphi, & (r > r_0)
+\end{cases}
+\end{aligned}; \rho' = -\frac{v i \gamma}{\pi r_0^2 c^2}; \begin{aligned}
+v'_e & = -\frac{v + U}{1 + \frac{vU}{c^2}} e_x, \\
+v'_i & = -v e_x
+\end{aligned}; \begin{aligned}
+\rho'_e & = -\frac{i \gamma}{\pi r_0^2 U} - \frac{vi \gamma}{\pi r_0^2 c^2}, \\
+\rho'_i & = \frac{i \gamma}{\pi r_0^2 U}
+\end{aligned}"
+297	A metal sphere of radius $a$ is surrounded by a concentric metal sphere of inner radius $b$, where $b > a$. The space between the spheres is filled with a material whose electrical conductivity $\sigma$ varies with the electric field strength $E$ according to the relation $\sigma = KE$, where $K$ is a constant. A potential difference $V$ is maintained between the two spheres. What is the current between the spheres?	[]	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	I = \frac{4 \pi K V^2}{\ln(b/a)}
+298	An electron (mass $m$, charge $e$) moves in a plane perpendicular to a uniform magnetic field. If energy loss by radiation is neglected the orbit is a circle of some radius $R$. Let $E$ be the total electron energy, allowing for relativistic kinematics so that $E \gg mc^2$.  (a) Express the needed field induction $B$ analytically in terms of the above parameters. Compute numerically, in Gauss, for the case where $R = 30$ meters, $E = 2.5 \times 10^9$ electron-volts. For this part of the problem you will have to recall some universal constants.  (b) Actually, the electron radiates electromagnetic energy because it is being accelerated by the $B$ field. However, suppose that the energy loss per revolution, $\Delta E$, is small compared with $E$. Express the ratio $\Delta E / E$ analytically in terms of the parameters. Then evaluate this ratio numerically for the particular values of $R$ and $E$ given above.	[]	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	B \approx \frac{E}{eR} \approx 0.28 \times 10^4 \, \text{Gs}; \frac{\Delta E}{E} \approx 5 \times 10^{-4}
+299	A parallel-plate capacitor of plate area 0.2 $m^2$ and plate spacing 1 cm is charged to 1000 V and is then disconnected from the battery. How much work is required if the plates are pulled apart to double the plate spacing? What will be the final voltage on the capacitor?  $$ (\varepsilon_0 = 8.9 \times 10^{-12} \text{ C}^2/(\text{N} \cdot \text{m}^2)) $$	[]	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	8.9 \times 10^{-5} \text{ J}; 2000 \, \text{V}
+300	Consider an arbitrary plane electromagnetic wave propagating in vacuum in $x$-direction. Let $A(x - ct)$ be the vector potential of the wave; there are no sources, so adopt a gauge in which the scalar potential is identically zero. Assume that the wave does not extend throughout all spaces, in particular $A = 0$ for sufficiently large values of $x - ct$. The wave strikes a particle with charge $e$ which is initially at rest and accelerates it to a velocity which may be relativistic.  (a) Show that $A_x = 0$.  (b) Show that $\mathbf{p}_\perp = -e \mathbf{A}$, where $\mathbf{p}_\perp$ is the particle momentum in the $yz$ plane. (Note: Since this is a relativistic problem, do not solve it with non-relativistic mechanics.)	[]	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	A_x = 0; \mathbf{p}_\perp = -e \mathbf{A}
+301	Determine the electric field inside and outside a sphere of radius $R$ and dielectric constant $\varepsilon$ placed in a uniform electric field of magnitude $E_0$ directed along the $z$-axis.	[]	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	\mathbf{E}_1 = \frac{3\varepsilon_0}{\varepsilon + 2\varepsilon_0} \mathbf{E}_0; \mathbf{E}_2 = \mathbf{E}_0 + \frac{\varepsilon - \varepsilon_0}{\varepsilon + 2\varepsilon_0} R^3 \left[ \frac{3(\mathbf{E}_0 \cdot \mathbf{r}) \mathbf{r}}{r^5} - \frac{\mathbf{E}_0}{r^3} \right]
+302	A sphere of dielectric constant $\varepsilon$ is placed in a uniform electric field $E_0$. Show that the induced surface charge density is  $$ \sigma(\theta) = \frac{\varepsilon - \varepsilon_0}{\varepsilon + 2\varepsilon_0} 3\varepsilon_0 E_0 \cos \theta, $$  where $\theta$ is measured from the $E_0$ direction. If the sphere is rotated at an angular velocity $\omega$ about the direction of $E_0$, will a magnetic field be produced? If not, explain why no magnetic field is produced. If so, sketch the magnetic field lines.	[]	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	\sigma(\theta) = \frac{\varepsilon - \varepsilon_0}{\varepsilon + 2\varepsilon_0} 3\varepsilon_0 E_0 \cos \theta; \text{No magnetic field is produced because the polarization and thus the dipole moment do not change.}
+303	Suppose that the potential between two point charges $q_1$ and $q_2$ separated by $r$ were actually $q_1q_2 e^{-Kr}/r$, instead of $q_1q_2/r$, with $K$ very small. What would replace Poisson’s equation for the electric potential? Give the conceptual design of a null experiment to test for a nonvanishing $K$. Give the theoretical basis for your design.	[]	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	\nabla^2 \phi + K^2 \phi = -4 \pi \rho
+304	A dielectric is placed partly into a parallel plate capacitor which is charged but isolated. It feels a force:  (a) of zero (b) pushing it out (c) pulling it in.	[]	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	(c)
+305	(a) Write down the equations of conservation of momentum and energy for the Compton effect (a photon striking a stationary electron).  (b) Find the scattered photon’s energy for the case of $180^\circ$ back scattering. (Assume the recoiling electron proceeds with approximately the speed of light.)	[]	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	\frac{h\nu}{c} = \frac{h\nu'}{c} \, \cos \, \theta + \gamma m v \, \cos \, \varphi; \frac{h\nu'}{c} \, \sin \, \theta = \gamma m v \, \sin \, \varphi; h\nu + mc^2 = h\nu' + \gamma mc^2; h\nu' = \frac{h\nu}{\frac{2h\nu}{mc^2} + 1}
+306	A plane monochromatic electromagnetic wave propagating in free space is incident normally on the plane of the surface of a medium of index of refraction $n$. Relative to stationary observer, the electric field of the incident wave is given by the real part of $E_x^0 e^{i(kz-\omega t)}$, where $z$ is the coordinate along the normal to the surface. Obtain the frequency of the reflected wave in the case that the medium and its surface are moving with velocity $v$ along the positive $z$ direction, with respect to the observer.	[]	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	\omega_2 = \left( \frac{1 - \beta}{1 + \beta} \right) \omega
+307	Two large parallel conducting plates, each of area $A$, are separated by distance $d$. A homogeneous anisotropic dielectric fills the space between the plates. The dielectric permittivity tensor $ε_{ij}$ relates the electric displacement $\mathbf{D}$ and the electric field $\mathbf{E}$ according to $D_i = \sum_{i=1}^{3} ε_{ij} E_j$. The principal axes of this permittivity tensor are (see Fig. 1.27): Axis 1 (with eigenvalue $ε_1$) is in the plane of the paper at an angle $θ$ with respect to the horizontal. Axis 2 (with eigenvalue $ε_2$) is in the paper at an angle $\frac{π}{2} - θ$ with respect to the horizontal. Axis 3 (with eigenvalue $ε_3$) is perpendicular to the plane of the paper. Assume that the conducting plates are sufficiently large so that all edge effects are negligible.  (a) Free charges $+Q_F$ and $-Q_F$ are uniformly distributed on the left and right conducting plates, respectively. Find the horizontal and vertical components of $\mathbf{E}$ and $\mathbf{D}$ within the dielectric.  (b) Calculate the capacitance of this system in terms of $A$, $d$, $ε_i$, and $θ$.	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	E_n = \frac{Q_F}{A(\epsilon_1 \cos^2 \theta + \epsilon_2 \sin^2 \theta)}, \quad E_t = 0; D_n = \frac{Q_F}{A}, \quad D_t = \frac{Q_F (\epsilon_1 - \epsilon_2) \sin \theta \cos \theta}{A(\epsilon_1 \cos^2 \theta + \epsilon_2 \sin^2 \theta)}; C = \frac{A(\epsilon_1 \cos^2 \theta + \epsilon_2 \sin^2 \theta)}{d}
+308	A $C$-magnet is shown in Fig. 2.18. All dimensions are in cm. The relative permeability of the soft Fe yoke is 3000. If a current $I = 1$ amp is to produce a field of about 100 gauss in the gap, how many turns of wire are required?	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lVzZXJDb21tZW50PlNjcmVlbnNob3Q8L2V4aWY6VXNlckNvbW1lbnQ+CiAgICAgIDwvcmRmOkRlc2NyaXB0aW9uPgogICA8L3JkZjpSREY+CjwveDp4bXBtZXRhPgp5jy8MAAAAHGlET1QAAAACAAAAAAAAAIwAAAAoAAAAjAAAAIwAAC1DLxHwoQAALQ9JREFUeAHsnQn4nNP1x682RVNLijRSUgklshQJikTwWGKJtWlpLUEWsVQbuyCqohIVsTWpJSHEFiEoUYRKK4JSWqIhSGgttTYpXXS7//M5/973eWcyM7/5zbzzzjsz5z7PzPvO+97l3O+9c8+95557zipegrNgCBgChoAhYAhkHIFVjGFlvIWMPEPAEDAEDAFFwBiWdQRDwBAwBAyBhkDAGFZDNJMRaQgYAoaAIWAMy/qAIWAIGAKGQEMgYAyrIZrJiDQEDAFDwBAwhmV9wBAwBAwBQ6AhEDCG1RDNZEQaAoaAIWAIGMOyPmAIGAKGgCHQEAgYw2qIZjIiDQFDwBAwBIxhWR8wBAwBQ8AQaAgEjGE1RDMZkYaAIWAIGALGsKwPGAKGgCFgCDQEAsawGqKZjEhDwBAwBAwBY1jWBwwBQ8AQMAQaAgFjWA3RTEakIWAIGAKGgDEs6wOGgCFgCBgCDYGAMayGaCYj0hAwBAwBQ8AYlvUBQ8AQMAQMgYZAwBhWQzSTEWkIGAKGgCFgDMv6gCFgCBgChkBDIGAMqyGayYg0BAwBQ8AQMIZlfcAQMAQMAUOgIRAwhtUQzWREGgKGgCFgCBjDsj5gCBgChoAh0BAIGMNqiGYyIg0BQ6CWCPzlL39xHTp0cB07dqxlMZZ3lQgYw6oSQEtuCBgCjY3A+++/74YMGeK22morN3XqVGVcjV2j5qXeGFbztq3VzBAwBMpA4LLLLnMnnXSSGzBggLv//vvd2muvXUYqi1IPBIxh1QN1K9MQMAQyg8AJJ5ygK6tBgwa5++67z6211lqZoc0IyUXAGFYuHvbLEDAEWgyByZMnu1NOOcXtuOOOyrBshZXdDmAMK7ttY5QZAoZACgh873vfc1deeaWzFVYKYFdZhDGsKgG05IaAIdDYCBx99NFuxowZbuDAgbrC6tSpU2NXqImpN4bVxI1rVTMEDIHiCHzyySdu4cKFjj2sV1991fXo0cM9/PDDbuONNy6eyN7UFQFjWHWF3wo3BAyBtBH4xz/+4a699lo3e/Zst3jxYvfBBx8oCeuuu66bP3++69u3b9okWXllImAMq0ygLJohYAg0PgKPPPKIu/DCC91jjz3m/vWvf+VUaL311lOG1adPn5zn9iM7CBjDyk5bGCWGgCFQIwT+9re/uenTpyuz+tOf/qSlrLLKKo6P914/nTt3do8++qgzhlWjRkggW2NYCYBoWRgChkB2EcDs0llnneWmTJmiRH7mM5+JmNQee+zhunXr5q677jpnDCu7bRgoM4YVkLCrIWAINCUCmFtCdf2///2vrqioJPc9e/Z0t9xyi/v973/vhg0b5hAJ2gor213AGFa228eoMwQMgSoQWLFihTv00EPV5BLiPwIiQBQrZs2a5Xr37u2OOeYYVcKwPawqgE4pqTGslIC2YgwBQyBdBP7617+64447zs2cOTOn4PXXX9/ddtttbuedd9bno0aNctOmTTORYA5K2fxhDCub7WJUGQKGQBUIPPXUU+6MM85wv/zlLx3q6ltvvbV77733VCQ4ceJEN3jw4Ch3Y1gRFJm/MYaV+SYyAg0BQ6BcBNib+tnPfqa2AZcuXaoiP5QtdtllF4em4H/+8x+35ppr5mSHaPCwww5z66yzju1h5SCTvR/GsLLXJkaRIWAIVIDAK6+84i644AJ38803K2NCA5ADwhtttFHJ3Dg4jHWL1VZbzc5hlUSq/i+NYdW/DYyCAggwE/7www8LvHE6U1511VXd5z//effFL36xYBx72BwIsA/FYV8sUqCOHgKKE7gB2X///V2XLl3cp59+6nbYYQf3/PPPa584+eST3YgRI1zXrl1DkqLXt956y22++eaOPjVfLF187WtfKxrXXtQXAWNY9cXfSi+AAGKdyy+/3J166qm65wDzIoRDnuF+ww031AHGbL8pPE35NWHCBD1DVaxytD1Mhj6D6jrWK44//ni37777Fkuy0nNWZngb/ve//+1+9atfue22226lOPYgGwgYw8pGOxgVMQSYLaPBxcY5Aa0umBUHQBlYXn75Zb1H5HPNNde4L3/5y7HUdttMCNxzzz3ukEMO0RUUK6qjjjpKVdQxVksYOXKkHghmdVRpeOedd9ymm26qK3aUNFB1t5BNBIxhZbNdWpoqGNauu+6qlrSZQc+dO9etscYaOntGBAjj+vvf/65qyGyUEzBoyt7F448/rrNtnPAx0CEmCudvWhrUBq08IsETTzzRPffcc2pVHVcgu+++u66qEBFeddVVDi2/agIMa7PNNnOrr7665mummapBs7ZpjWHVFl/LvQIEYFi77babMh8OeN599926IU5WiAe/8IUvqFWCkPUbb7yhYiOsFsQDs+4rrrjCjR49Ov7Y7hsQAfasmHi8/fbb7utf/7pj34mDvs8++6yaVqqmSsawqkEv3bTGsNLF20orA4H4CotZL7beQmDggmGNGzfODR06VF1EnHPOOW7JkiUapUOHDrrCIh4fVmBs2iNKtND4CCAiPPjgg90///lPx2oLLcDPfvazVVUMJhhWWIgEbYVVFZy1TSx/aguGQKYQEPGeF++vXnp+0Y8MVkrzpEmTojiyx+GFkXmZeXuZjevzTTbZxIutuEzVz4ipHIEzzzwzats777yz8oxiKYVheRE5a79ZtGhR7I3dZg0BW2HVdj5guVeAQFwkSPJ+/frpHhZ24dDk2mCDDdzkyZPVHtzw4cPd9ddfr6XwnNXXa6+9pqJDzt/cdNNNbscdd6yACkuSNQTYu0QZ57e//a3r3r27e+ihh1RZolo6TSRYLYIpps8aBzV6DAFWWAMGDNAVkpjQ8e+//74XRuXfffddz2xYLBZEIF155ZVexIbRKkv+Onove19e3J9H8eymsRAQkZ8Xv1Ve1NUjwsV9vZezd9q+RxxxRM67KFIFN7If5mWi48WEk7cVVgUAppgEOb8FQyBTCMRFgmPHji1J21133eVFc1AHMdEa0+tXvvIVv2DBgpLp7GV2ERCVdS9HFryskP3VV18dEco9ExKxSOF/8pOfRM+rvTGRYLUIppfeGFZ6WFtJZSIQZ1hyzsaLZmDRlKJQ4b/0pS9FDAumJRqGnr0tOXTqX3jhhaJp7UX2EBARrhcRsLYnK2fR8lQiWVXLGSx9LufyvPitSox4Y1iJQVnzjIxh1RxiK6C9CMRFgqLd5/ldLMh5LC+GTXUgQ9EiKFsE0eB+++1XLKk9zxACiOXEUoUXLU9tyy222MLPmzcvEv+KyaVIHCiWKEpOYtpbLRMJthex+sU3hlU/7K3kIgjAoLbffnsduMSuW0mGRRaiiuxF4ULjB0bFldXWaaedVqQUe5wVBJ544gkVAYa2k8PiXqyc5JAnB4ejycgJJ5yQ867aH6J0YVqC1YKYUnpjWCkBbcWUj4DYg/Ni3UD3pph187ut8Itf/MKzGhMLF75Hjx4eZY2LL75YlTXaSmvv00UgKFIwMbnssssikS6KD9/+9rf9/PnzVyLoo48+8ueee64XNyBetEBXel/NA3FDokoXnTt39i+++GI1WVnaGiNgau0yrbOQPQRQYZbzU26bbbZxHAYuJ8igpla9sT2I2nO1B0rLKdPirIwABmg5aoBJLQ5404YEzGlxHOHJJ5/UIwkYncWKCdZLsJYuzEsdK2LRIs0wZ84cNeOFexHZG3PbbrttmsVbWe1BoMYM0bI3BAyBFkOA4weDBg1SEe35558f1V5sPXoxl5UjumXP8YADDii4qooS1vhm5syZEV3i/LHGpVn21SBgK6z2cHeLmwkEfve737mf//zn7nOf+5zOjHEzYiE7CMj5Kfetb33LydECd+SRR7oZM2a4O+64Q43ULl++XP1ayaDFdoQatr3kkku0LetVA2xQcgCdA+tyTMIdeOCB9SLFym0LgWq4naU1BOqBwDPPPOMxuSR924tV98T3NOpRp2YqEyUGsS6i7cP1wQcf9J06ddLfcU1OcQvjly1bVveqo0ofVn6c67OQXQRM6SK7bWOUlUDg6aef9hwQhmlh9UBmxyVi26s0EYBh7bTTTto22OjDggTtFA52c4+Cg6ysPBYt6h1gWLJaVxplP6ve5Fj5JRAwkaD8eyw0JgKIb0RrTH1hIVY66aSTGrMiTUY1IkEsqj/22GORl2hhVmpFHwWagw46yB177LHq8ywLVRe1erfnnnuqPyxEzVtvvXUWyDIaCiBgDKsAKPaoMRDALbqY6HG4F0HDCzcicuC0MYhvYipF6UL3sOIMi+rix4pJBftbWdPglGMRTsSWrn///k3cMo1fNWNYjd+GLV8DZuv4RZI9ETd16lQn1i0yhwmq22GQxpeTSD1WohGHk6h0867Wqt35NLDyCfRBGKrpTAgqCRxHYMUiRos1OXXB+7Oco3I9e/ZUX1ZyBktd0reVP3SgDAFtYvhWV9NMTsATy/1cQwj0B6zj74jDezDGmj8YY92f8OGHHzo8G8d9pmHBXcx6lY0BeS9evFiPYMhZMvXDppnbV6IIGMNKFE7LrFIE8CD7xz/+sd0DNYMhmmdoeZEHGoOc58ElCYPyJ5984rp06aIDFQMws3/xm6XuShhQOe+FSxIGMgYxsdbt5OCxMj/iMlhSBgMaAYeQDLblMBTOHYlSgXrJJa8tt9zS4SIF9xghj8C4yG/TTTdVWhks8bQsxl8dZ5WIm1RANAcmeOoFH8qFBs6u9erVK/otii3u448/jn6H+hI33BeiiXevv/66E0sVUVqYoRzo1g8rYLELqEwDBsE72qVQntAKfi+99JKTfTBd/aAhCjZ//vOftb+AZ0hLHMIHH3yg7cS5vPAOullBgTEiQBghDJAyaCc+w4YNU+/UXbt2dSeffLJqNvK+rUDefEJgxT9+/Pjw064JImAMK0EwLav2I8BgfOmllzpUi5n5tieEwZMBD8bC4MI9VzHvo4MQDEmUM1RkyIwbpgjTYQCFwTHwrbnmmrp/weDGewY+Zt/cB8bC4N6xY0edpTPglhrIoIv3rABIV2nA23KSzKpSOipJF8eHNslaoK0Dk4kzNdqYCQ+TIHEWWXCFRd1C2nClT8EgxZSYmzhxottnn32yVuWmoMcYVlM0Y2NWglXLD3/4QyeW1aMBoNqaMJhkcYCstl6NmL6atkDExjk7VkLc8wmBiQDPCYHxsELmebltH5hOYFbkBfPhIwecVWnk1ltv1RU5cQmIIjlbdtttt+mEhLQXXnihGzJkiK7QmVzAuIKoURPZV6IIGMNKFE7LrFwEEHsdc8wx7r777tMkYeApNz3xGEBYDTHIkB4RVhBjMdixiuIaZsGF8mYVw+osHicMiIiGWIGh9YaoUfxuqUiPFRYDI2nj6UL+PEPMSBxETaFuXAm8z78Pz7hCM2WRfxgsQ95pXaGD8kUtXT/QwW8+BFaOAYN8mmhbFGAQPRIfZQtML8F0yDc/hLqH5+SLWBbM33jjDWUA0MFzAu2BmHDJkiWq0Ucbodn33nvv6ao5YBvyi1+hgZXzvffeq/nlx0VM+Jvf/EbpjafjnhX6mDFjVNGH34gYUSxBRGkhHQSMYaWDs5USQwB7bewRsJfDgBEGMTlP5cS3lQ4kDE7cI9qDQTCjZgbLgAMz4Lec5XFf/epXNT4DKmKcM844Q/co2B8R47eaR8g/RkJ0S17kH+JAD3nDxNhDYp+LPZnNNttMy2ODnoGYwYvBLaSLMvzfDWJG6kDc/EExP278N/nBiKk7gz17PPUI0AHWMM/2BvaQsBbx+OOPK7MSa/oRo2tvXqXi0wbQ2N4gTkHdRRddpMnibUN70c7YOmTCkB8KaT8iPhQDze1q4/x87Xc7EJCOacEQSAUBEQF6ke/roVHpopG7iPXWW8/fcMMNnvcyCOlHVjkV0STnaLwMYr5Pnz5eGE1FeVii6hCQFVZk6QKbglkJMtlQdzMyIYj6XuiHMuHRg8P44aIfFgqyMoucS4b4MkHywugKRbdnNUCAGaIFQ6DmCOAeQjaidVBgkAgfEeV4vAYnFWRWH1ktSNKNelL0tUI+ssLye+21l7YxppmyEHBJsu+++0b9LvQ/WUGq00hZaek76JaVfEGScfRIfw1Mjuupp55qDKsgWrV5aAyrNrharjEEZE8gGsAYGMLgIBYPPLPxJMOrr77qRZSng0pwr55k/pZX2wiw4mAgZ0DPAsMSDVSPU8g4o+Ge1dGNN97oZa9M3/FMDjYX9WbMil1Ehho3rLBYkbFys5AOAsaw0sG5ZUuRA70RAwl/clEd1sFCNskTx0X2n9QJIIMPnmkRMVpIHwGYAW1QT4YlZ7T8VVddFdkyDBMlDCdfffXV6twT5hpWTdCLw9BifWbWrFkRYwt9GfHzsgwY8E2/hetTojGs+uDe9KUiApSNbfUAzEAQPqLVp4NFrQBgsBk5cqSWx6xaFCpqVZTlWwKB0047ra4MSzQJvRwEjvpd6H/sqcVF0PSXvffeO4pXSsT3wAMPeFFhVwYYmB9SAjnrVwIJe5UkAsawkkTT8lIE3nzzTb///vtHg0D4c3/zm9/0YgGh5ijdfvvtqnjBSq7YBnrNiWjxAk4//fS6MSxEgGLpRMsPfU+OOKjCD/tr+UGOV0R9FcvtbQUxvaTxEQcmLdJuq+xWf28Mq9V7QML1Z2NaVJpzBgtmt/itKjRYJFy8Zvf88897UTn3xrBqgW55edaDYbHSYVUvKuk5/Q9fXKX2M8OKnH5ajsfho446SvMfPHhwUQWN8lCyWO1FwBhWexGz+EURkMOYvlu3bvpnDiIYZraIWVh1pRXkfJcxrLTALlJO2iJBOYPnR48eHWmIhv43YMAAf/fddxeh8v8fxxlWOQ4cxWST9nEmYbaCLwlt4i+NYSUOaetlyD5RofNVOPF79NFHUwcEhsXqylZYqUMfFZjmCov2Dmr0QQQoB8K9GKH15Sj2xBlWW8yNCuIwFIa42267GcOKWjydG2NY6eDctKWIWRx/+OGH655RmNWiQcWfOc1VVRxgsehtDCsOSB3u02JYiPDCMYbQ/8T6ib/jjjvKrnV7GdZ3v/tdZVi77767MayyUU4mojGsZHBsyVzEX5BqTYWBgit7R+eff35q+1WFgBfXGB5rBtBiIptCCNX+WRoiwcsvv9xjJSXe/wYOHOg5i9eeEGdY5YgEOapBmWgcmoZge5CuPq4xrOoxbMkcxPComj/ijxvEMDCIadOm1R2P2bNn64AiDh1Nrb1OrVHLFZY4iPRonIqtxYhZIf4Vy/8VnYmKM6xyRIKBYfXu3dtjrslCeggYw0oP66YpiXMsYoFbB4vArMTYq58yZUom6igGSZU2TEFxkNhC+gjUimEtXLjQixv7iFExYRJ/Z56jDJWGOMOaM2dOm9lMnz5dy2eP1lZYbcKVaARjWInC2dyZiUsJZUpiSTyHWWFodv78+ZmoPDRymJOB7OyzzzY7b3VqlVpYusA2JBOj+Kp+++239xzorSbEz2FNmDChzawmT56sNOy8885erPG3Gd8iJIeAMazksGzanN5++23PjBlNLIyFMmCEzyGHHFKRGKZWYKGxKG7QlT4GFgvpI4Dx2LBqgaFUE9Dyo+8NHTpUFWlCv+MqLmrK0gJsq/xvfOMbUX/mDKG4limZJMQX9zb+xRdfLBnXXiaLgDGsZPFsutzEl5EXt9/RH5qBAqYlnlY96sRZE4lgG27x4sUeg7vlqDQ3XYNloEK4hsEmH30FJYhKAnngKkb8muX0Pc75sU9K3xPnmJVkvVKaoKYOvSNGjFAbgytFij0ICiXbbrttXZWLYiS1zK0xrJZp6vZXFGbVvXv3nAGjS5cu/sc//nH7M7MULYVA2MNin6e9gVUyqycsVMBEwqdnz56ePpl0GDVqVFTG97///aLGb0O5MExo2mOPPczSRQAlpasxrJSAbqRiEOmw/wNzCoMFV8Q7zz33XCNVxWitEwKBYbG/ibmucgMq6cFWX+h7HFHA8n571dXLLTOILymvHIaFliDKRr169TItwXJBTiieMayEgGyWbGBWY8aMyWFUuFBggxlRmwVDoBwEgtiMQ73YdiwnoH263Xbb5fQ9/E9xOLitfaVy8i8WJ86wSrkXCelxWQJzY8VXr8PxgZZWuxrDarUWL1HfN954w5944ok5AwYzSUSASe0XlCjeXjURAoFhIVJetGhRyZrh4mPmzJmR0dqwsmL/i8PptQ7tZVj333+/Sh8wgltLRlrrejdi/sawGrHVakAzruU333xzZVbhbBUzyJtvvrlNmX4NyLEsGxyBIBLs0aNHSYbFAXQG/mBhHWbVoUMHj/kjJlBphDjDKkckiGIPonF8bllIFwFjWOninbnSmN0+KgZqsb8WZrZccX7ITNKCIVAJAuWssLBYgUfieL9ba6211GIF5+nSCnGGVY5IMC26rJyVETCGtTImLfVk/Pjx0WHMMHBsueWWHgOyFgyBShFoi2ExGWIFH/ocV/avHn744dRX9MawKm3l9NMZw0of80yUiJV1rBHEDwKjjXXsscf61157LRM0GhGNi0AxkeBHH33kx40b51lJwaSC+BmlnrREgPmoxhlWWyJBlJIwA8V5LVTvuf/444/zs7TfNULAGFaNgM1ythjs5LR+GCzCLPdHP/qRnSvJcsM1EG2BYW244Yb+pZdeUsoXLFigZ5fi/Q6DyQz+9TzkHWdYpUSCTPLYbwvmofjfcP+d73zHf/jhhw3UOo1LqjGsxm27iiifN2+e33rrrXNEMcx2zz333DZP+FdUoCVqSQTmzp3ru3bt6ocNG+bff/99dVGf7wpkm222qdoOYBLglsOwULSYNGlSzv8mTPS4chQkzX23JOrdiHkYw2rEVquAZsQteAXGZT1/MGa5YaZ76aWXVpCjJTEESiOAOjtnlg444ACPU0/6XbjCJOolAsynmhVeYD7FRIKYIIMBE2/VVVf15513nucAMfYEeYY25NKlS/Oztt8JI7AK+QngFpoYgfvuu8+JryAnqrhOtAKdMComKk5mvO6CCy5wItJw4lK8XQiQXmaUTlSQncw+NU/ZA3PizsOJnF/zl/0xJ39uvZfzKlp2eCa24hwf0kBPoUD+5B0C9yJC0nS8kwPNmp57ygn14jd5F8s35EcdxKeS5gPdMphqnXgf6hTihiv1JZCO/MEzHsiH8gnEpX7kBT3UHWygm7TEzQ/Lly93YgHciSgt/5X+Jg/oJr9Kg+y5OBELOxlkFTexROFon0022UQxENGXExFdpdlr/cjjuuuuc7LSctQpHmQ14kT87MSHVfxx3e5lL8rJpE3LF5Gg3tMX4oH6dO/e3QnjcuKLy916663avmLWyYmpJr0X24dOvBDHk9l9wggYw0oY0CxlJ3J1J7NAJysrt2LFCiUtDOIMegxY/AnXX399J+dgdCAsh37yYBCWvQkns04dYBmYxaGdk1mzE4+/Ohgz6Ir5Gh3URevQffDBB058Fzk57+XEQoAOiltssYUOkvnlMtiL2rPSDTOiPAY+2ZzXwfaVV15RmkWj0YkFDi2HNNQLusTCvDKFUN/8/PkNsxG/Xk5WnUoPTJu0BPFUXJAu6KcMEWcpwxcFlQg3Brlly5a5l19+WcsWB5JODAcrPjAIsGbSwEQBhkcdyAsaw5V2gmFtsMEGSkd4zpUglh+cHOJWDOLpeBficl8qkP8777zjxJCsMlHuYbLQRx3AmbYKIZ5v/D68j1/De675zFxEz072gJwYTm73BCleRtL3ctbQDR8+XDEoxrBEWUTxgdnvt99+Thw9KlYXXXSRGzt2rGIvB+ydaEcmTZ7lF0dAOpaFJkSADeKDDz5YxRXS3iqKkcEouspgF73jvX1aC4P89i/0m2fheaF7ntGnwrtwH+9n3NO3ZFLkZaWfyX8ah+NlwqV0FhMJYumlX79+Gof6opyBDzjsa4b/zsUXX5zJ+jUTUbbCkt7WjEHst7kBAwboSiGp+iHKkgGooCgrXgZxiMsMm5VRCCE9v+VPpCuL8K6cayERWqF0ofwgbmRFIoNMoahtPoN+PqzegpiR/Kkbdah1oCzKh/4gSoxjxztoCe8qqWc8v/h9qBtlkH/Ak/IQIRICJryPiykDHeQnSj5O9rJ0VRryzNI1vsIS02ROPFYXXF0LQ3Ki/RiRLo5MVUpAXamnrbAiaGp2YwyrZtDWN2PxF+QGDRqk4iUo4U+FiI6BBVEQfzbu+aOF93qT98V7RGYwC/FNpPsOTz/9tIrqGMgQYSFODAMUAztiunXXXdeJdpi+RwSFqEzcMegeFHnyCWnyiiz4k4FbfFy5NdZYw7Hnwl6OOGpU8RjiOzGTo+kQOyHqpHzxV6TPfv3rX7errEAA9CEC4oN4791339VBm7wR8SFyZU+KfY0QwESshCiNcQYbr2+h+/xn5AeWYP76669rm1Eu8eJxYRKIMdl/Yn+vkhDPL34f8qJO4A4tXKm7OC5UOhDbIlJeZ5119BkYPfvss0ozeUET+0OjR48O2WXuGmdYgwcPdvfcc4+KbPMJRYzN/tVTTz0VvQp9mLoaw4pgqd2NAG2hCRHA1ln8vAhnRTCFI/smiZ61ktl2WejJwFpWPIvU+AhgLFlGLP0II43OYWW1ZnGRID6uShl6/sMf/qAuSLAGw/9LGFak+Wgiwdq3MLMkC02IAB5ZgzUBBg88BFswBNJA4Oqrr44Ylqx2M+9G/pZbblFVdf4nGN0tNgkTSYF/8MEH9ewYRnuxFEMamBbXSy65JA14W7oMY1hN2vyiqeZFjBUNHGeeeaYX0U6T1taqlSUERHMu6nei7ehFhJYl8laiZcqUKWohHqYjYnSPx+P8wH9HNAm1XiKO9iI69P3794/qKaJSL6LQ/GT2O2EEjGElDGhWspN9BvWIyp+QD7PBYjPHrNBsdDQHApj4Cv2OSROua7IcLr/88ohh7bPPPgVF5jAsOXuV858Kddx7771r7mQyy/ilSZsxrDTRTrEsOUeT471VDg6nWLoV1coIBI+8DOi4qWHvNMvhtttui9TaTz311JKSCLwnIzZExf3II4/0119/vcegr4V0EDCGlQ7OqZeC/TbRkotmuueJKRkLhkAaCEydOjXqd+xhteVxOA2aSpURV7oodg4rP71ogJZkbPnx7XcyCBjDSgbHzOViDCtzTdIyBLUCw2qZxsxYRY1hZaxBkiLHGFZSSFo+7UWgkRlWKfci7cXB4iePgDGs5DHNRI4wLNw3hI1hEwnmNoscBvZY4BYberkv8n4Rh48prOQBU+JnIzOsvfbaq6DSRX512bcyR6f5qNT+tzGs2mNclxL4Q+2www7GsPLQxzU7NhbxcMtnyJAhunGez7g4x3b88cf7nXbaST84vJw9e7Yxrjw8C/1sZIbVt29fz3mrtgKHhNmfe+KJJ9qKau8TRMAYVoJgZikrNoUZZMMK6wc/+EGWyKsLLWIx3m+00UYRJgEbvN5yTi0MVGICKjJ0GuJwxbLBTTfdVBfaG6lQzjUF3Lp37555pQvaFB9X0CzW9aN+UApztAmJj+NTO99YCqlk3xnDShbPzOSGWru4zogGjlZnWDDwuPV6vN+KP6YIH7Gr6MWfkSfegQceGD0X+32ew69hAGYGXk937pnpYCUIaQWGFaxccDWGVaIzJPzKGFbCgGYlu/w9LGaCrRywZXjccccp42EWvXDhQo86M24vgmmd6dOn+xdeeCHyyiwGgj0iRNSysWwQmNaVV17ZylC2WfdGEwlWssIKDMssyLTZHRKNYAwrUTizk1k+w7rmmmuKEtcqhmnZ18MocHDNLhbecywXiFM+3ZMIjAkmFcKMGTMiI6dokrVqoK+ItXy1qYchWPyuoZQSD+KeI2Lu4vDSI4rNcjCGleXWyaXNGFYuHk3zK59hnXPOOaoRh6hQ3GJ49mnEtbdnVSGuH9Q4LgN4KwWYuHgZ1sFVvCB7zFmJKxL9zarrsMMOi+AQFx+R1uXAgQOj5612c/vtt6uIVFyf6EpU3Iqo8gErePoSVi7EK3K0akXser1Yg8hyMIaV5dbJpc38Ycl0uhkDLs7Fxpm6q6d++Kjq06ePw6U74dVXX1V/Tvrjf1977rmnuvvGz5Ps1TCZ0TdcZQCPR825x1+TrFrUBxTO+kiP/ygcJ8p+T5SWfHD9jv8sEb0VdJKXk3EbP8gPP1lirNTh/0tUz9UlvShHqC+w3r17F80B/1liN05d1lM3Yd7qJl20vtTxJfni3+iUU07RPMBTTPE4ERG67bbbzj355JNR3tBx7733urfffjvyMZaPVxzDQvf5z8icPMJzrvnP+B3ex+9JR3vQBqJM4MQQsrYDcekD+K4i4NeKZ1y7du3qli9f7nr27Knu68mDdqROYIHfL/xeiRkjt3jx4pw21czyvgLtq6++uhMRqhs5cmRejOz8jPvDEnGxow/IRKYkgSIKdGLk13EVTwgRHiUT2cvqEZAOa6EJEWCFFUwzyeDhUSqQ3pLzkYFIZ8K85573QRlBnD3qTBqFAwyYci304R1uTEJ6VizMvtGoQ/su5E353PMeRQbKCu9Iy3uu8fvwnneFPrzneX69+H3QQQd5VpOFApvkJ510UpRu99139+IEUqNiqJX05ItoKwTwxMgp73CLHg+IGoVRaxrqTh2gjbihDtyHugW6KaPY+xAnYEL6kF+4EqfUfXjHNf4hXUgbfx7u23ofaCp0JW14Tn70AVbyWQ5x00xbbLFFWVqC7F1Rv7Fjx5rSRYqNayss6XXNGFgRsILAO7AMItFqKdSVZ/Hn3MtArrPvzp0757i2l/5YcAZJmi5dujgZsPW9DFQOj7/M1JmN4zEXb8Oy76EzfGb2rH5kz0M9ulIeqzDy54oXYfKUM1Hq2ZhZPyshPArzPD/E6aJsAs8o+/DDD3dHH310wVWc+DRyovKvKzPoYdUAVgRRxnAi8tN0kyZNcsLY9Dl4Dhs2zIkm4UorLGgXS97qaZeVCPSzOqF+rPqE2ekKBm+84EEI9YFecKKuxCN9CMQhD2jEQzSBZ/F6F7sP8UKaUB75hRCexX/H34e04T0rY1YfS5cuDY+KXmkP8sLjMCusESNGFI1b7xfiD0tX159++qkThqV9oK0VljAqN3HiRJVIiHX6qD3rXZdmL98YVpO2cJxhUUXcyfOHZMBkUESMlh9gGDNnznRyWHYlBpcfl9+yQlCGRVkEBqm1117byUa8k5WaPmPAFlVxFS0x6OJiHQa02mqraRnQwcDGlfLJAzoZMDp16uRWrFihNOcPrpp5gS/Sw7CKBdzJDx061OHaHeYqTvdyxFWywnI77rijJscdOsyMesKAYFiFRILFygrPYeDUBUYtFjZWGtwCjjB+mF+8rmADnXyyEGTv051wwglu2bJlTiypODnXpmJEJiUEaAfDOXPm6O9mZ1hyHktFx/E204rbV20QkBmahSZEIC4SlJ6j/rBk38rL/oNqwk2YMMHLAKwfrD3IgOhlIF9J46uZoMGaxaGHHhqJw3BzLns0OVXEwgXO+MBMmHwkVsSiAWJSnrey0gVggRkOQoWJFzRthZIFOPFpNJEgfSKIh3M6Rt6PIBLcddddCzp8zItuPxNCgFmuhSZEIJ9hFfKHJbN3lb9jJ49BCBXlZg3U9cYbb4wc9cmM2Hfr1s2fffbZ6tp83rx5akOOg8M48WOwJc7pp5/uH3nkEY+NuTAIczDWQnEE0EBlL68RGRaTFBhxW+Gss87S+nEYXSQCbUW39wkhYAwrISCzlk0+w2r1g8MMKrvssosOMiI2jFZZgQmJKNPjnI8AQ2JlEN7Fr1gPERFf1po7U/TgKj4wLNES9Ndee22m6MsnBrV2EVFrn+D64osv5kdZ6beIRbV/7LHHHmUZy10pA3tQEQLGsCqCLfuJZF8pMs3EAC0by9knuoYUsorEOZ/sk6ndOBiS7CupNiODK5p/4UCx7Kf5H4jtRQavwKyIIyrfen6thmQ2RdZxhiVKOZ7Va5aDHEmINFpp87Y8JLPiln1SZXBoeorShWkKptTApnQhI1IzBs7PiKUGJ7NFVWSYNWuWQ4mglQPKIA888IAqNqCV179/f4fmngywevZKDrxG8KAswvkcOQyrSiPDhw93Yt1dlVeiSHZTEAEUMzirBobCAJxYNncnnnhiwbhZeLhgwQLHGcSgqcoZu379+hUkjf4iRyZUWxJFCxmnVYOT/5es4AumsYcJIpASY7RiUkYAszmsCKSr6IezJhbajwAb8MGKe/tTt2aKZ555JhK5sjLFFUeWw5IlS3SlzX+FFTj0FwsoLbH3Gf5XXPE7F8TJxdLZ82QQMJFgMjhmLhdEguHgMH8qDL+Wo/2UuYoYQQ2HAJqWQZyK6BWTTVkOssKKLPcj4pPVUlFymbzEHaPy35Izf0Xj24tkETCGlSyemclNxBteRIDRTND89mSmaZqekFdeecVvvPHG2vcaQa39zTff1P1MtELZ773iiiuKtpGcC4x8pREfhiWHoovGtxfJImAMK1k8M5XbuHHjIoaFSrcFQyANBFBrZ+BnMG8ELcF33nlHGRb0woRKMSzO8g0aNCj6X1HPUp4Q0sC7lcowhtXErS2mifSPxZ/wrrvuauKaWtWyhABagojWGoVhPfTQQ9ExBv4rbfk7Gz9+fFQ/9rzEekqW4G9qWoxhNXHzHnHEEdFMMOsb303cDC1XtbhaeyOIBIN7EZgVSiK4UCkV8I0GoyK+WMNXp592eLgUYsm9M7V2mQY2a8D2HbYBCXKuyJ133nl6b1+GQC0R4JiAKPyojcisuxfBVuOoUaOcmJNSSIQJ6T3/nblz57r58+fn2HbkPbYSMQIsw7C+QwUe25nYexSHlWroWTwSqGsaMedVS6hbL+/keJ/llDUE4issDsJaMATSQAClix49emReJIj6uvjp0n02Vksy+qu2ICtEgpzNiiQUvGvv56c//WkacLdUGbbCauI5Cg4HRdlCa8jqilWWBUOg1gjgnBOL91inF5Fg5tyL4D3g4Ycf1pXVW2+9pXCI8oSuCMeMGeNwK4MFfaQTN9xwQ1G4hFO4rbbaygV3PByUxp2PeK9WdzG4uOGdhQQRaCn23GKVtRVWizV4RqorTMCLpQtdkWRNSxDzW8cff7yuqmQY1X2osLoS5uPRGLSQXQRM6SK7bVM1ZcawqobQMqgAAXHwGFlZyRLDEuebvm/fvpEVDhgWHw45Y5XftP0qaOyUkxjDShnwNIvD31X4U4pIMM2irawWRiBrWoLiXNLfeeedarA2rKrC/6JXr15qTZ44FrKPgDGs7LdRxRTaCqti6CxhFQjkHxyeNm1aFblVlxSnpWK42IsHa528BfFfx44d1anpokWLqivAUqeKgDGslODGgWDawRhW2ohbeSCASJCVC6sYzinVy+ElbkBE5TySMoRVlVjpz7zLE+tJhRH4PwAAAP///W/CcQAAQABJREFU7Z0J3DVj+cfvtn8qlYq0yWtrobwVKlGUkJ20IdkSkWgRUXnpta9lly2k3rS9ltBGUkRos7SQlGjVZq/m//ten67pPvPMnOec58ycM+e89/X5nGfmmbnXa2bu6772R2SCkKAxDNx+++1h3rx54e9//3t45CMfmffz0pe+NGyyySbhUY96VH6t7pNtttkmnHXWWdbsnDlzwn777Vd3F6m9hIEpGPjlL38Z1l577cC7D7zrXe8KJ598sp0P48/9998fTjnllLDvvvuGe++9NzziEY8IvsxttdVWYe7cuWHWrFnDGErqo24MQLASNIeB4447jg3BlN9Tn/rU7IYbbmiuY7W89dZb5/2KWDXaV2o8YcAxcN1112XanOXv3jvf+U6/1fjxu9/9bqaNYN63f3svfOELs9NPPz37z3/+0/gYUgfNYYCdR4IGMXD55ZdnCy200JQPaOGFF86uvPLKBntOBKtR5KbGKzFw/fXXZ5Ic5O/8MAjWrbfemu26667ZM5/5zLxfiNVjH/vY7G1ve1t28803V453JjcS4ZsJ1gavkwjW4Djs2gIv9l577WUfjkQT2f/93/9lL3/5y7P9998/+/e//9217qA33/GOd+Qfr0SCgzaX6icM9IQBCNajH/3ojPcdorHjjjv2VG8mhfiGrrrqqmzVVVfN33XnqiT2yySOr/U7++Mf/5iddNJJ2d57750deeSRtRPCmeBgQaqTCNYQnjac1OKLL24f1GabbZY9+OCDQ+g1cVhDQXLqZAoGhslhSR9lm0CIlBNIJBp77LFH9rOf/WzK2Aa5gLhxpZVW6iCMz3nOc7KPf/zj2UMPPTRI06lujxhIBKtHRA1S7JhjjrEdJx8VH9iw4O1vf3v+cX3iE58YVrepnwUcA+iwnHjwztctEpQBU/bTn/7UdLSI/Jyj4vi4xz0u+8hHPlL7pvDhhx/O1l133byvWOQJN8n39a9//WsBf/LNTz8RrIZxDDe1wQYb2IvOzu/ss89uuMf/Nf+Wt7wl/8AOOeSQ/91IZwkDDWLgJz/5SYZRkROS7bffvpbe4GK+/OUvZ0sssUT2mMc8Jm+ffpZffvlsrbXWys4999xa+io28o9//CNbf/31s1e/+tX2PR999NHZhhtumOvqnv70p2c33XRTsVr6v2YMJIJVM0KLzf3ud7/LVlxxRfu4sFRCBj4siK0EP/axjw2r29TPAo4BmbVnSy+9dE5Q6uCwaFPm8bmkwokhHNVHP/rR7A9/+MPQsS6XkZxwyow/g6glaBYDiWA1i9/stttuyz/eNdZYo1YF8HRDn1SjCwxZHnjggb5+KOfhdov1psMhYp777rvPdBRx3Vj8Q9vco324gLJ+4rp+Tjn5DNnPr3GM255ufG28j8Xe8573vJxgDWp0ceKJJ2bLLbdch5gRgvWKV7wiO++88zLEdcMG9GPLLruszRHxIBxXguYx8Ai60MNP0BAGvvWtb4V11lnHWj/++OPDTjvt1FBPU5udRMdhnFFlpRV+/OMfm0OodCVTJ/7fK7za3Oe4zDLLhDvuuCOIGOTlRfjCKqusEp7ylKcEzosgsVOQmCfIiCBocQp//etfrYgIVJBYKjzrWc+yur/5zW+snHQZ4QlPeEIQ0QlaRK1vb9PHwv9+jiM5DuX0I11M3vazn/3sII44PPe5z/XqY3W8++67w1vf+tZwxRVX2LhFsMyRt99JSDoRTj311CBxdsAZ2J8leN5ll12CLF8N//22O2h53qF3v/vdNjbaetOb3hQk6g8S+Q/adKo/HQb08SRoAAP6aDNEBhtvvHG+C/vABz7QQE/VTcYiwUlwHIb7KFpp6f3Od/KTdP7a1742+9Of/lT9cFt856677spWX331/Ln0KxKEg9bmLlthhRXyNvzZIl7nu6LMqAADCzcqgZO88847RzWUBa7fJBJs4JH/5S9/yTBff/zjH28fnHv9Y9p+4403NtBjeZOTJhJERyBuyBYLcOqLhi9m3Y6UL/t1q8O9Yp1ufXpZynQrV9UndWiD++hmrr322vIH2/KrEKzXvOY1ObHpRySIBeBhhx1mfouOf47iXLM3vvGNmTjrkc7+hz/8YSYO2OaG4ceZZ5450vEsaJ0nkaC+hrrht7/9bdAHG371q191NC1LonDJJZcE4ggOAyZNJEhcOMRk99xzTy4eWnTRRU0M5yI9LfpBztkmlgPHiI8Q5f3tb3+bgnLqPPnJTw6yMMvFd9RH5CNdVJAuJvzzn//sqEcdEZXw4he/ODzxiU808Z4WjSAz6yCCmo+LGJEyPAjapAREiN2A9ugH8SN90x6/Qw89NHzoQx/qVrWV92YqElQ0irDddtuFa665xubPswAP4PCTn/xk2HzzzRuNvTkdMqVzDDvssEP4zGc+Y0UZj6wS7X2brm66XxMG9EIkaAADF154ofmDKABnxg8rvW9/+9sN9FTd5CSKBKVzynfuhLc655xzzEGU0Dv8brnllky6KjMx5hwT6zXXXNPqwMH4T5+PKc3PP//8KeIlxE1XX311vpOO66BgP/jggzMRzQ7Ev//97+/gqjBz/vrXv95Rpts/cI9arPO5MT5EyIxl3KBfkSBGK8T5W2qppfLnxPz5YX3XFk7ztNNOy83YeQ8OP/xwezQY2ozjcxq394rxsoNJMKEYmDSRINZgxIXzxUzcUfa9732v8umxEEo5n0HYYnEdjp4veclLjCiVVdYOP0OHBKGiHkf6RASELlBc0JRq6DVYxLwsPnfHHnvslHLdLqCb8blx3GeffcZyISyKBDFHrwI2F0SlQOTHnB1/iNMxV//9739fVXWo13/xi19kRLVgjP4u8T861dmzZ2fihIc6ngW1s0SwJvjJSySYL4CyqBr7mUKwZH2Wzwk9z9e+9rXSeWH0EnMsLDJODFgIMSkvAibmskrLdY++eFIPA4Aqp1S4LTgBX3C9Htcwie8VcCr3MXL86le/2mvVVpUrEiwirpQRebhYTNN9zo43Ym1edtllrZrTRRddlI/Txxsft9xyy7HcXLQKyT0MJhGsHpA0jkVYICRjzz8yOINxBwhWHL2DHS5ivyJAxOCg4gWF81e+8pXZ5z73uVLrO5T5KPXhjCjriyfBihHnynS92I39j4GNcizldbwebSC+5H6vUOSwLr744l6rtqpcUSS45JJLmj+iD1K63Wy33XbLNwb+nOBQd955575w5m02fWRTcsABB5gxCelL+LbYBHKOJAN/ywTNYyARrOZxPJIe+MBWW221fNGeRA6LaAryy8rxC9f0xS9+0UL3+CLIEfESVptVKSaw/Ipx5XWxBsNptYw7oFMZcxgBdVGgi4qoD+FD14VYslcoEiwZ6PRatVXlihzWIossYrH/4DY/+9nPZi960Yvy99JxTVoQnICxEmwzwLnzbfHsAc7bPuY247PfsSWC1S/GeizPQkraA1kMVi54PTY1o2IogePgt5NIsFDSg18AYgRRgniwCLoIkAgJX/jCF0qjIeDndMIJJ5iOizrOHRFQFdFjt2jfLFzOwVLPiZX3S9y5KkJX9UAnlWDxTMhVBcfp+HFcw8GiL/zOd75ThZZ0PWEgx0AiWDkq6jvBkdCt2QjKSZBMlPJ//vOf6+ukh5Ym0egi1mFhTIF1GcYNnrjPF0IIENG1iUFXBmwoYl8hr4f4inxHWH5Vgcya8+cbEzpvg2ss0P1CkWBNgkgwxonjyq8h0oWrkrtCv6hK5RdQDCSC1cCDLwb/5EPFwgwihi4JU2oU/E0Ci4BCQuWiF6INEClinAEdFrtx8Ok79ac97WlT8iFByNA7VQUaxuXARYC+eNImUUlIjVFloozpOakraN8XX478MABhTN4e1on9QpFgjatIEO5zDcXNBC+OE45+znUMUtpmWNHv80rlh4+BRLAawjkL37bbbmtpD+KcPSxoEC+ICakSfv3rXzcyAjnKZiuvvLItGiwQ7PjbTrDgajBuQMznP/7HlwrxKuF60EeBw3jxY37+w8yYRHtlQERvCA7m8JR34kL0DK53i/iNyBFLMO/H68qR2cyy4bp8bJRZkAkWEgY5xxuu/Dk5wQI3iKoh/gkSBvrFQIp0oS+oCCI2FtyUyBTabVtkA8pIJwGBz4vrI7SoC9J1WDQDIiYQpFMWQ+aRL9m9BWlVRtKgj9jqaaHL2+A+QVlf9rKXBaUeCYpLFsRBBHENeRnvjL61aFrEBvoFGBvXpPjNx8h1xii/kfCVr3wlD9j6pCc9KYirsKgQIphBup08WCdRIPhJHNbRL+MjWoPEZwEvf++XPvoBxv6jH/3IokpI72TRIMSFWuBX8AHQNpEsZEGWR53gOnORL06QtR3/Gngd7jk+xeEEOWgHmfIHiZq8aH4k8LDEhxbINr+oE+m9gizT8gDF8T3OxdUFGV6EI444IhDkNgaiHuy5557h+c9/vuFaFoxWnjIER5V+LC4+7TkBVCXGzctdeumllePKC7XwRCbgYaONNspHFj8nxQIMl19++UiC1uYDSidji4FEsKJHx6LMojdv3rw8ZI923baQs8gTOodI3A4sltSBYEA8IDQszh4GiEWYMlLuW6gf6vkCy5E6MRDqhyjgHrnb73lZ6cDyBdHvlV3zexypC7Bo9AvUJXQR85lJ/X77m6484/H5UJYx8SM8E2GMlChwShPi1IIMTuyZEv6I+tQB10TOh+CwMSkDortLhBtk2WbP2cuwuaAuUcjFVdll+UwFmcXbc6Z9iX+NiBHRvVcoEiyIpCJodMy517aaLke4KcJX+TsOYefa97///bDXXnuFG264Id/ggA/wzvtOaK33vOc9Fv2e/wm7JKvBvGzVuKnP8yNyPt8cdQlxtthii1kUfr5NninfIONgoyXrT+tPVov2jRKVn40amyW+Z74zQncRggtQ0kl7brTjwPfMho0NF+V53oT6on82i0SUl4+efbc/+MEP7JzQYERuV7JHG5O3lY6DYyARrAiHX/rSlyxeWXSpltN4kfUF06/FH3MtnUWNsJjQvoP3FV/ze+NyBG+OOxaNV73qVUasFB18yhQUBSPISTiQ4iUGOFm4XjiiMmBBVDigoAgMAW47BhlyhE996lO2QMXXr7zyyiC9TE7YwDHtQ4RYwHqBIsFi8YXjgvNlrrQJ18sCCccuc/HwjGc8I2/anysbJNKcODGlAJyrx2JUAGZbUCG8EGXp+nKc5o2VnLB58XiJLOAQJcYgnZ4t3mwOIBYQL949B8blz8zPmQfnlOPc73ud+MjcIQAQDDZoDhAb6tMnP9rwd542ITYcqc/P+6KsA3Xi/xW1IsgQJCAJAOQmYelDKOf4jetyjT6AuB3+l4+WbVo4T1APBhLBivCIaG+99dabErQ2KtL3qX+I/rKXvfjdGmUnyAJAPc69Pa9Du37NOTPnAvmA/CPiY+UD58Nl98lCr9iGJuaivqzsbPfJ/SLEfRTvzfT/Ypv0yyLLjwUXTpPduOON8bMTlt7PxK70i+jvm9/8polS43HI3yfMEVd1xhlnWFt+D/zJYdUIEe2XAUFsFRIpyPk4Jz6UY2cOtwUXhfgxBjhQ8j8hwgOXPmYIAuMDt73Apz/96bDtttv2UjSVmSEG/FuhevEd9Gvve9/7wlFHHWU9IFqfO3dumD9/fmCz8oIXvCCwTshh3cT9/qzh9NhIONAP78Qw899535N8TASr8HRlQWbiI3a17D7ZlcYvuRdn8WdXzxGIX37Ky0ggsMPnhS8COzJ23SyggCIw2G6MRRmgLX7sXtGPyOjAdtJlC1/cr+/02FnKmMNEVuyeAXZ7H/7wh61fdsq0xS7do5FDKLhOe6MC8AE+0QMilok5BMbE7hqcs1gARYIFJ4VoUFZqtphYIf2hHXR4Rx55pBEcdutFQN9HRHD0j+AOAJ/gBU6JhUdGLB3VWLhY3NBtwbXEuONZbrHFFkY0/Tl3VC75h3eGRQ4xNFyeg79j/r8/87g/v1d19HfY61IuPq+qx3XepyqgXTisqrFwnx/34zJ+vardquveVtX94nXKAzwP+u9FvM3mhHUAThzgfWSzxJrAewmXifiPxKyOm1VXXTUoEHOOC/pFVO3ftDWU/gyMgUSwSlDo4gOO8UdWLOoEonhdUbrDm9/8ZiMGzuFQBn0G8vpNN93UiBQ7cIAFqbgo2Y0B/iBnf/3rX5+LtGQFZ2KwAZoceVWeh4LfmsiGwSC2YZGHIJHyAd0JGXwdWDTAAbogCL9zoH6fI+XlI2e/WNzEZoGdNYYV1POFz+vCTZH6g8zHDpTx94U0Gaecckpfz5W6ECrEi4in4RRZIDHKYQzetvfX9JF3ks0SmwB/jxmDz5P3H5y/973vtbEVx8f/EGvmAJ5Z3B2PzKe4IWlqPowBXMptwHSC6N58DnGffo3s0kgfuukfEYciAvZ3Jon/Ykw2eK6XKkHNGNBOHTbFfvqozXFYi5eFp9GHX3Nv5c3hg+TOy4yFqAzaXZYXHpOrEo3mwW+1uGTawZq/lcS4ZubOPLnOUbthcyr2EDplU8StIHYepp52xJmIVKVpPCbbpBJxXyzKe59+roU++/znP1/W5VhdIw4i7w3z8h844icuJDv55JNLI4i0bZIS81rMP8Jl8ayYi8+Db4RnRXBjv6bNTUZ4qW6gzYyV97aUHy1lHu6GsJrusTNKUDMGpJA2J1RxUpkU6UOPcMF0WGyIeu0fIY6a/QRirRklAzcHscLZWuK5fKFgsWBDwBydaHBOkFuZTlf2qZ2+RceQUUOOH+pJbGihmoh5VwYSAXYQOO9TotRs1qxZeXoR7egtHFRZG+NyDb8zIoX4++NzlYg0k5VfZQSRts2P4Mj45hXnAfGSmDcParzWWmvlZaSnmpZgkauMNnkHnQh2S3XTNryM63iSSFBvXRPgIpQqsWETfcZtoufZYIMNTCfDdYwMsIzD4ALxCObEdQF6MHR1+nCtSX0MpnNDFIPoB7NixD+ImNCdcd8BMRF6I3SFAHo0dAWUxeoMHRw6HRe9ySk43C4zY/rydvycI1Z16KqwsCsD9FMKShuUjC/XP1BOkRmConFbpuhiPXQWlD/wwAM7jDgoh/n6QQcdZPoK2kD0xdi1azcfr2Jb4/A/Y9977707jI/ALX58H/zgB83HSgt166eCgY4inlg2aH9HGDTm5nwLZAXnOt/q6173unDFFVfYnNBdIRKMLTDjyVIeXarSo3S8hwqlFd7whjfERdN53RgYV0qbxl2NATgBWQHaDlAfZM59cM7un10hIi1+7Jj5+f9lx+nuiyjlu1O9n3m/iMYIbso1+qZf6TPyfulLhGxKXa5RjjreXnykHX7eJvek5zERIFxYFZDPClGWj4cjcyPOY5XoUH5FmfRgGXMpjgFOg4gcAFyZFrq8bS34VcNo7XXpZTL5lmX+PB3/cKJEnh+X6BSIAMmFVpwH7z4RTQh6HANieuJ9+vOdTiRIeQ8s7e8idYnsn6BZDCSRYLP4HUnrMjKwj88XdV/YfQHyo3+gdRz9w/Vj3Ed8XtYX96vq+fWyo7cLQZGfUSWu5dyZ7b777kYE4/7RW8h4orSeuEZbpEkxEtfhnHBMxP2LRYcylsgQJXlZgh6PS44kQmLJsMLm5eP3IwkWyS+GGHUc4LjjjjPxrI/fj+KIMhlDVQY1Jruzl+1FJPjzn/+8Ix4l4b2qQoKNA97GZYyJYI3Lk+pjnOyG/ePzoy/u/v84H5mLz4fdv8zZS7Ejq0JL2Aj3Fc8XDk7+TpXpQ+CaZJLeUYf66LhIPIh+pwjUKRI3dEBVnFux/qj+lzm+6QXZEMQ44n9FDskIZDsOAP7JJO0cvc+FZ4K+aTr9LckZvQ5cOJuc6eCYY46xOsRNJN4l71uCZjGQdFh6SycN0AmhpyHEFPoXB+K7YQru5vpa9Dv0QF6ueNQrmOunivckdjEHX/RK6J7om/YBjujOkPljJo4vFH1iCoyuB91XlZ9bsR9vD5cB923DgVepQDri73k9IlXg/KkMw37Jjuge8EfDQZyxFAFHX8IhoTOL8YOfDfXiGHlxXfpCvxMDeCN6hcRH8eXWnKPrI94hzyyeK/EsiYWonF7mh9aaAZcMhHcLl4ZDDjnEom3E89h6661NF0eMz+kAnRb6LoBoF4okP228Q3CnoNL2fHnOCYaAgWbpYWp9VBjALDdOE68F10RUiHawuKvr57tK5PpA3D6ipumgn3Ggn5J/W74TRjT3q4IoENEcu2VyLenzyX/oM+AY5AxeOiTqHXbYYZniClodLXx2lJGItYc5exkw72984xuZghhbeTgTr8tRgWDLqo30GuJOEaspejlwRBoaBRse6fh67VybpEw+YFP0oNokZYoa0lcm4JjDwtRdG6pph0H2AN4xovgnGA4GkkhwOHgeei/oV+J8WPgqTScWGfog++wQ4uDKbhYKcYsZi5aDLLvMT8tN3Z1goU+SI26lzxDGBrEvl9fDFaBbJlzERgqe26Hcd2KFMYecajv0XD7OUR3ZQIAHcoEVRYByYs/IE+Ybj1GNsdd+xUF3bMh4ZhjxyDI2416/sP/++xvxoR3cInohWOjLKI/4OMFwMJAI1nDwPPResOhiwfXFV+a2lQkNhz64ATqU6C2fE1wUhg3kzEJ/ITNku+dEg7mTlBH9QhmwKJGtuFiPdnEM7WZxKJPmDGdR+qA/CID/uEYusjYZKrBZwQLQ34cYR2wCwOG4AJyNolDkuGdO6J0woJGIeUbTiDmsNddcs+uz9w4Sh+WYGN4xEazh4XqoPSFqix0/4SDabgAwHYIQPyKyYoGCOGBqjjly7CDtC7HyLhkxquIqEQ3ihFxU0rND76ZAh4hJV5WLHOnP+4wJFtZ1PINRAzi75pprMpzYnVj5EdEZHJfS44x6mD31j2GF9FKW3dnnwBExMQ7Cg0BMsLAS7MXYRDosw2kSCQ6C+f7qJoLVH77GpjRiEfxJ/MOWIjnDE5+dNFyJDB8s2zHmuYRxwjeFY9mv2z3KE/KJnS36JAUJtY+dOvyPFRqcDBwfZcnqi58YepKydrnGmBDTQThYOBgzGYfxl8I/izk5kfD5xUestliky4BxskgTuimugzhJiRwz9DtVwLgIVeT1fAwcEU9CsPwehHXUAN4V7zDHmY8NE+ytttpqbMzueb+UfDOT03uOX+YiQx7LpN3tmfX6DGKRIP5004Vmol23EkwiwV6xPHi5ZCWoN78pIMgmSd70mKwL6QfMSo9EcU3CBRdcYNZLWuhzSzjGQDBPIkkQYJWkheI+zFKP61psK4dEXS3Kpfe5h7Ue0edFoHKLQKwHsQYUV2dpF2gfq0AsB4l8QaQNImEUgX60k7Z6tInlIePFko0j4GONx0W71CVCg3yuSiN5YAEoEWC45JJLrC3K0wYRD7RgWQSEqsgkRLqQzsKSAjIGr0tQXdKRYEWo8D55VuJddtklkOV4VEBwXhmR5LnAfLxk/CUqPVE5xgFIwoh1Js8sBvDNMyO4MXMbFGIrQZ6pQntVRrqgL95FUtWQG00cllkqDjqGVL8HDOiDTdAABuAMFMHZnDFnKc4cO3pEMHA6+vga6PF/TSLW0qO3Hb8+5lzHwrVx/sHBxD/mxv/MCd8qxDrKBfY/RPz3DLHY+eefn2HxF88fvyoC2VZZAFIdzpAyxYgc7O6VWiSPqYexQuw4DLc2CoCDRLdS1MsxbziB2EhlFOPrtU/wyTODc42fGc9BxKXrM+u1j7hcUSQ4HYeFfhLulbGhJ+UdS9A8BpJIsCEcY86MmCn+2PycaOBNvuAE9aQvFnTv0wmX/9/U0fuJ+66zr7L2lbIlE/dU+iTR22HJVwx0S5QLonR3ew5Ke5+hiyqOH5HjZZdd1lEX3ZbSUuRlcSMYtg5LcRIzxVLseO6MHQMFiO646KqUwj6TH5iFzYpxzzMjmHQT0K9IEIJFaC7GhxXquOC2CdwNs80kEtQb1wRIf2CBMMnXhAhLC6N1IyJmgVRJCtgUEPQTMQoJBgEt8rlYEjEbYiHEk/F1zqtAL2Sl2IV6OCcjIkEEirjPgb5kEGEJ8HDEJSgsuYZIoEguMESE2vF78WmPjDl26GVc4BEHWJI5xkBZgrieeuqpuViM+2SGJUkiokNFQYir5OcktiSX1eGHH25jdzwhypU1oiWBJBtyDFrAbCzgHlCEcEvgCQ6aBnFV4cwzz7ScXh6EGNwA0lXZu6DFvulhDNw+7xHPDFEf4uwYEPOSLBMRcRPQr0hQmxFzNMZhWdailpdNrgxNDC21GWEgEawIGXWfor8iysH1119v+ho86SU+MJ1Ola6kjjFAPPjgZcYcLpcsHkDmv59SvKO7IhOqL2h2c4A/LOYQKggERJmMrgDto8ci4jWLuYwpjOgR8QLCxeJPPQh7r0CbLBBEtwDQgUEgiEofA7ozCAsZYFkEHZi7FOVBhhOmc/Pr8VGBU21hRN/lOGKO6LnAH1EgyoC5k8jQ9VZkJybjdJmerqz+TK+hNyQ5pwxJgsSh+SZE4smAHm2bbbaxCCMzbX9Y9Xhf99hjj0Akk/iZzZo1y54lhJf3qSmICRa4EwfdVYfFOMhCTHLLzTbbzDanvCcJGsaAPsoEDWEAcZNbNmGZFQdLbajLjma1WOUiKvRaWI2NO4hjyueEnib2sRIBtACnRTEeERzwQ8M6sQoQHdK2Py99dtaPCGumtCJdrQdpUwQ7UyijfGyY2jcJ6OpErDNxHHmfPmYiNYjTarL72trW5srmQdQSHz9HdFXogAc1V+91oJ6Qkb6xru012gfPPcHwMJA4LL2hTQExzuBypN8wqzX5/lTu7JsYA+nkiScIILbAerApkUoT4y9rk5xUcBQAnCI7cjg2heIJN910k+2MwbeDFj6LlydfndKU7AqrZFyakm6aWMdFt9RXihbLgSVHUm+u8ii9i6VMdxEnokd23oxtENBSYJwFeb606QnSjQa5CpjVpKJwWG4zbx8OkniG9Ivota3AnK688srw2c9+NoAvOFHnzBkz3LdSdQT5jg3le2E80vuaxR/9841glQinlaBlGBgebVzwevKspHrkmcRJHUr6YWADJ0v65qekdSPJfFz3PI8++mibj8Qv5vT7xje+0SwvfZ5+ZJeswLeZzKJLhyCxU0YalmKEdZnomxUafl/drAeLjZJuhDH5z8dR1xFOCv8g6cTyZ+ptY3QinZv5vBXH1bb/kTrwLRQtNkXYLRI+eCef1TCBMbnFHzglLiT+hAnah4HEYekNbQIk/gtKYRHOO+880yGgY8BPZ1iA8QMclmdRxcgB7oSdfwx6JfNI6n6da+jY2NHDrbjOCz2VnH9N94QhCdwD+inK9wP4ZqG7wn8LvzAyCnMEZG2VG3hILBPgStHNMG6yJTMHpRMxQxbvl6MbtjDuN73pTVZOC0/psNAposDHIAblOYCuiR01Oi6yz/YDcK4yYzeDE/QYjMfH1k87zAHwut4Wx5jz8+twj0QLxw8M3WDbAWMWDGTkAG7z8WeGnkpxF43LYW6jAIkETVdG3/glfuELXzC9b9VYeDeV3DPAmfN9yHI0KI3NUDjCqjEtCNcTwWroKSO2IT0DCy6KeqyfeLGHASiwxXmEH/zgB/ni74tgWf+k/UCc5EBZFnDS2UNYsIjjGsQJEQ7EGGKFBRwGHt3a9jbjo3zUzEKQNnAgZiGDOAIQrOkgXth9gWNBV3R6U9xjaFAGjBWCp6gJ1qcvmCjzMdJQdIpSh+OytriGdR5pXHBGBk+0By74kVaFtBZOaLhG//wPoWbcEEvpaKwsztKxhSXte3tOoLjGOW3wbCCuTVqb0l8dwPuCaBpixXfheKdtRHGkcyEt/SghNrrgfZcPmKUZKRsT76j0awGRbAwY3WBZOgzL0LjfBepcH1KCmjGAQpzspi720C54qD45ZD7VSzzFcVgLRe54q4Uvv0/ZYf/o3/uMz+MxTnfu9RAn4RMjHVblk8TghAC5Xsf7RtSGvxXPrB8gzBQx7Lw9xkqbHAnfhGiLMFQo7/1HdHfEjPzPPZxTGTNxDbVTt5QYxKfDMTZ2/KVN+vG+xAlWhp7qZw7DKKsNjqXfIHq944ejOOpMrhfmmD2McUzXR+w4TCBdxl0F+PX5+4MI2Z+9NnmZ9HJV1dL1GjDAbjBBjRhgAcJplBdZ4il7sXEsxBlyWEAcPV/g/OgflX9o43xkLr6IY31JenNxf5XoFadpKSMcF8ydZ0Pkh+uuu66yXtUNiYLM6pB24jbRMclYoOtYqtqMr5MmRZynvTu073PlnD4l6s0kajYiBxEsi8nocRuxfiQAsP9PXL5f/TeHmDs2i2PriCFJe+j4qFP1g9iiH5R41YguRzIxQ3y/9rWvZQpZlOGMy4bA3zUfP9ErGH+bICZYPEdJKUqHB+48+oZEmRnPas6cOXkeNYW8mtaitLThdLEnDCSRoL6mOgGxEnHninDGGWeYTqt4vYn/8WNBJk/sO8QxgBYLs3pDT4MuCv2H3pCBuqc+cdfQG2HxhfMu8n9EjIjEsPzCV4W+ETEiAkT8hvgM8aKMBawsDsQKLGu6sW4D0sJtIiUtEjZ22kMfgliJMZQBmYBlXNGhX2JsiG6wputHfIMujQzGWOLh68W8wAHjwIpvzpw5Nu+ycfR6DX814vxh8ejt+5E24nOc0GdJ/4OIkXHw474D/+OkjQgR8SP/89wRwaJvYT6KAGLPCZEkQBnwjBMsz8Wvebt+H/EmlpG0TVnEozx3dGk8c96xMkBMTizDKv1iWZ1hXBPBMj87+gInZBAmK3UREG1qo2N4Qict7tzeIRz18RHE7/ArX/lKkGtFsWr6vw4M6AVMUCMGyJMknVWG5Rbx5uC0sFhjlz9M0IJiMc70jtgOF98krK8IISQiluGzNOiPPhxI/cDuvcjpUIYfu3n3WaHfuC5tUI9r043JUzowLyzmEL2WATthOc7myRUdD3IAzmS0UVal6zVEisQO9HBbWsANr+y2CRdEDL86AE4c0RLtO2flx/ia9+/zatuRMfuPsSIShIvpJW1HHXjst42Yw+KZwi2WgQhWLprdbrvt8iJyILb3AVEuWRESNIMBdgoJasYAiy4iFZw3Sa9BKo9RgIwP7CNiMZuEjMPg8OSTT87nxMJeTEEP7uX/1iGKYv4Qt2233XZGWZdJdUIw2yJRQFdVt/nzF7/4xTx1fduJUhEfxf8Zv88BPS6ix7ZCHEuQDWYVYSU1j4s52fyw+QMQSzP/RLCafcJJJKi3bFJBBCvIP8imp0gPJuYYlqViUzglxh8iQABxHuIXF92QguSggw6yeYpw5UMgrp/8bPq2qEN0ue+++1rqCDe31+do4k0p3s00vm58YqKOaMmB/hD9EZMR8S7m/4hXEa1yj5+IghWPzxGRIp5FLIsYELEdokPEgFiRipu1OrSllPAmMuScMoj3vE0KcQ18IsYF4nt2IfrDPdrGnUP6wdwiECtZnLfbCrGVIGJzxM6x5ayPG9GqNj7h3HPPNVEwYcEQhWNVCF6x3sSFBZwmaAADeskTTCgGYsdhQhOhQB93iDksuCZStcBV4bgrwjSFC1pnnXUyxIP9AuJNMgvrk8t/iLhkOm8JIIsizX7bryqPIUjcJ/3JfNosCxG7Yl0Ix44xBT8R0innXHPxrIt/4/7g/inDD1FnE+AiMhEwm48IVhPd1NYmzsyOd6LbI9qvAjhu6Q7z8l6PY+KwqrBWz/UkEqwHj61sBRGYf0zrrruuLWKtHGgfg4oJFjECMTFGNIfVn8+VI7pDTN2rRDvdulTA4ExhmTrag1jJz6Y2XVVV/1jXxXNRZPmqoq2+jh4HC05/JjwL12G2ceCePZjxYiWIFWQ3YH5rr7225biDKDthTgSrG9YGv5dEgnpDJxGw8CIyPFGnEdMg3iBFwxqyQItBC7FlCkbcg2WXR53Q7tscXxEPySfFMiUjDpGPilVH1ISXf12AtRntcawC5oEFGqImzvX624/y/A9wTWGoLPoD2Wix4OsVyMCM1SHR4MGD94EDMOlIiPKOeK1JQKxEVBLEf8yFVChYJo4bkAYGMbQ7Q2OpiYOwP6e2zYeoJ8SOBBDxkQWAiPtlgHUkaVwQzyJ2RdxJJgZEoTjCU5fsCAkawMDgNC+1MCgGsDDDtweHURGYQZszERlKYDgQvTL5j/+JnccPsYefY/mGFZcWYyvr9YhU/sQnPtGukZ2XMvqY7adQSXm7cR/DONeil+9o43O4IKUrz0hk2C9ce+212YYbbmiWbT4HRI4i8EO1+tLmIH8OjGNcOSx8tOA2mAPPaP78+f0+kqGWd2d7xss7XmXVi7WrQn9lfBt8P0phY/58vHvUle6qNc7QQ0XgkDpjF5dgBBhAn0R0A/kDZeIEMvnL2AuPOIJoCIMAiy9Exxdzjv5B8VF1+1GW+36crmxcjvNef95HXJ4x9vOL+2aRUeifvp020X+RpoPFJ54r7cl3rjEdT9XzhWCxMfC5jSvB4t32SC8s7sMOaFuF36rrMcEikkg3UbLCYeXvijj4/Jz3h+DMCZrDQCJYzeF2Sst8BJgty8otk7jBwtPEiyR+W+9617tmZHodd0b0huKH5Atg3F9d53BmTbZfHCd9eX+kpVe6kRlFKmfTsMMOO5i+K+4DLm0mETDiZzDTcwxEnNNlTONKsGIOi81Y0f1gpvhpqp7SneSEh3eqm6EOmwoFSM7L85yQUiiu5BT/wqbGu6C2m3RYetuaBMyByf1D3iZy7Ehc1RHgVRyF6SwIVivDCMtbRcSAQQDTZcx0iXSBabYWdzMvxlwX73z6RB8lTizIis76RzdDFHSuExWdH6bQ3XRKjJG2Kccc0ZPxv7g7i9SA/ou+HPSRWRQBojkQ5YK20TGJu5m2H9qgLfJBMS8A020ZKZiZMf32A0SSwDSdSAUOjJ/o5+haMCUfBfB+kM5+3HVYBPXlfSb4M0A0dgIF9/uchvUMZEQRVlttNeuOSBe4gxCVowoUEsu+FyL/E02EuaI7jd/3qrrp+gAYWFApdZPzRswkpXN22GGHZVjnuR5IjynflbHrnD17tsVbI24ZdWYCZZZXXMP8GVGj90mwUeK9iUjkv6JpNvfK2pvJuKgT9+Xnfn2mbcr/JZ8TOqZLL720r6aI9EGAUnIeOW60yJj+qpspc1+dDFB4UkSCvM9kXXYcI15tM8QiQRGsnjlC3usEw8NA4rD0RZWBAsiatQ+7+H6B3aUCgAZi+gHxrpJzPV6zNmNHxk4e6yIs9LAscsskdmpY+pGOAS4E51eleA/s7HxMWPZhsQQ3BFcDYOlGGWLDeXoR+sOiCS4IzmacgTxF7oBadByebl7kL5K/Tc5JUh5c4mwMVwWeRw1wJDwjf3fG1UqQeIVw87yz4BjpAlabbYWYwyLOId8v31WClmFgeLRxfHqS13qmnDj57lCPbEbn7Nz9J0Jlehf+9/Niu1yXWCrDAo9j7MfC/0W9VLF+8X/vi+twWD/5yU/G5yFUjFQm5/mzgMMiNUgvgLMnUfNjHIFfBWKdEv+wl/aaKoNT74tf/OJ8nJOgw8IACA6mzRBzWHx/RJxP0D4MJKOLkmcSp8uOFzjOndhwjP+Pz7nnhMqPXs+JSHzdrxX78v+9L+8jvu7t+tHbpUzcLgYdbbfUKnkUUy7FjsMQrIsvvnhKmfgCqTLIg+XE33Gp3XPGxqRtgHgYFwIfJ5EvxhEQieM6wXvIc1Lm61ZPIyZYfCtYjvYCRAohqkiC4WAgEawSPBO0lpA+WPKxeGBqzjlhcpxYcGTnGP/fy7kvRE5geqlTLIO58HTcFh9dXI9FY1SWbyUonvEl8k35vCDIVQnzWCAl5stWWWWVvLzX22233TKlM5nxGJqsyKaCKB0+VnSg4wjkiXLdLfPBCq/NQHQTxznfigx7ph0uvloS62cymDKd8bQVUoGBMZB0WHpLy4BIB1jbEfEBKzi9xGbJxnV0R1os7RplRHxMLxW3E19DD4XuRYuotRmX41zGF0HRooP8VUwXRfvUB/SEO87pFytCrMiwQAS8LOeUpwxWf+T4kRk9l+1/5PT0Nc5AUFJ0I+j80I0QZJW8Vg4yqjBLwg984AO5hRr30BUSyHbNNdcM2niYZZfXadORCAo8I+YBbLrppqZLbdMYexkL3wm4VpoOK441pgcp7qX+sMuQ7l7R161bvndtjIJicXYdxje/+c2g8EwWGQN9MVamCRrGwMAkLzXQEwawyEOPgriR9AXuKKzHa9wSabm3UTqQX80gUGvVANDPaFG3neOk6LDw7yGtCHhjJxyLBOFORLymcJ9EqxgXnQRWgrEfFtmFxxEI1ItkgueEOLbt+lM4QMbKD/01js/TAQ7+WJvit0Ug4gTNYyCJBJvH8ZQeeNExFlBsv2z11VfPPxQ+lo022mhK+ZlegGC56BDRZtsXjV7mqdQNuW4OYowjNosFEQZ8gRTHaThlU8AGYdDIIb2Mq64yk2LWzuZMcfXsOWAm3nb9aazDmqVI7L2MV9a4RqzYbCaCVdcX0L2dRLC646fRu/iqsJjCJRCfDOuwOg0BFMg157D4qMhmO+5w/PHH2yLoRAmc4e+DPguC79eZ76mnntrqpIFlzwIOO+awxtVKkBQoZN3mmYxDaKaYw0L/qzxrZY+n4xoEyzksUrUkaB4DiWA1j+OeeiCoJk6tdUJMsIiVJ/+wOpsfSVsnnHBCB2FiQfQfxIqf9D6tNaqoQhrm7PK7s7xezhUzr3ElWGzG3OBl3AgWcSR7MVBC7Im1aeKwqt7q+q8nowutCpMKxx57rDnEYsSBUzKGH6RDGGcgm6u40XwKIlD5uaIO2D3CUmF0gmFGk0DfOGorRqQZyyy11FJmCCNxkjmDx2PTp9thHEN6Fpy75fMTMIYhXBXGMjh942xLeX7j6jhMiC+JuwMO+GRlxliGNC1thdhxmPQupOUhVUg3wBGdkEw8Q5zypyvfra10rzcMJILVG57GspR0WEawWLjJTXT22Wfb4jGWk/nvoIklqDQg+RRiosDFJZdcMidWRSKRVxrghDYB+uWHNR8xE7FYlCjJiKSC6toxHls8Fs6x8OQHkYLQVoEig4d58+ZV3W7tdfKWYUEnEadFEMFKkP/bCtJhGYFlfDKKMgI7HQEiPqh0zkHm+2atilVkgoYxoI8nwYRiIBYJ4rslE+Oxn6l2wmYdqM8iFw2KMOQO3X59Uo4KQzWWzwz9Dmk6/DlgLNNmiHVY2vT0FP3/M5/5jL13GJWIeLV5ehMztqTDmphHOXUisZUgTpxEHxh3QNcTB/X1BbHtR6I+YP6Mkh69hyc3xJKOsFuMH/NvLB8JDcT/lB/XhRAdVhz8thcjhlG+m7GVIATowgsvnHY4OK2zWcIadc6cOWNn4DPtBFtYIIkEtTJMKsQiQcQciGUmIaAnzqikjffUKf08P32DAV0T4h6cW2XNZo66OIY3BfIbC+Jw8wDF9IPj9+9//3sbB2NCh4VIkYDH6N/kBxS04JuTc1PjarJdxJ2k68ChFiBtPE7QbYVYJMizIu09OrgqYF7bbbddQF8JUEfRMoJcK6qqpOt1YKCFRDQNqSYMxCJBQvyQsHCSwFOW9HucJBy0dS44yhPOTGuU/XqNzTeq+bhIEI6JMZMUtBt8+MMftnJenjptj5fYbT7jci+JBMflSc1gnLFIUEYXE0ewZoCSVGVIGIBguVk7i/m4iAQhQMQIPeqoo7piSgkpjWDh/+dES+GdutZJNwfHQCJYg+OwtS3EHBbBfCUCa+1Y+xmYrB7Nz2qcIlj0M79JKDuuHBbEldBfhxxySNfHMHfu3A4OizptSADaddATcDMRrAl4iFVTiAkWkeaVfr2q6Fhdl3m+RU941ateNbEhcb7xjW9k++yzTzauERTGlWA5t0Sk/26ghJQdBEv6urF9Vt3m2bZ7iWC17YnUOJ5YJEgA2LvuuqvG1kfX1FZbbWWLxSzFfLvttttGN5CGemaxf+c732lzrFv3Q+ocOcXmP/QuTXDe4yoS9BBfH/zgB7s+3W9961smCvTyxABFl5qgWQwkgtUsfkfaesxhKbVDRjLDuoGP9Prrr8922mmnbP3117fgvXy8G2ywQfbe9763kcCz73nPe3KCRey9SQM5ImfbbrutzZFQVHUAoYYIWQWRx8XBfwRFJuYfHEOdMO4cltLTdEUHYc48QSVcGdxwguYxkAhW8zgeWQ8xwXrFK16REfusbmCHjt8Ksv+yH8ntCIRaJxx88MHWFw6ek0iw2FhA8MHnSSedVAvqWFDLno9fIx4ehLIuIDZmbHRRN6dY1zi9naKV4HQEywPfgj9S91xwwQXeVDo2iIFEsBpE7qibjkWCTTkOn3HGGXlEeMQjOL+y43RRicLV1C6KRCHOQgG3MIkEi8UQES5zPPnkk2t5jT72sY9ZezwbNhhsJDi6zgYxK86+dQG6txVXXDEnkm23EsRgAnz7exuLBMlygE5Rflb2I5vyueee28FhEaQYJ2/KIC5UaKq6UJnaiTCQCFaEjEk7hWDFCRyV+bj2KZKPihTomALvt99+lkeItOF8/CyGhx56aO190qYTLPJHTRpg/YgSnzmSIqUO4Nnj2sBzch8j70PBaTMSY84U3A8urk8CRMKBMQd+bSdYvglyAu4cFoSMjRFWgES08B/JQ31ufqQM+OW3xBJLGFGLcZLOB8dAinSht21SQQt7kCjIgquS9lvK9iAxjf1PBHeiKyjxnEWMUMggizrdLy6IaIDXP9G5STFOewQ5lc4kSFQSlOvLIsX30y7RA4hiAWgByavqdbcgs8qJZYF8lTIlaOcbFLMuLzMJJ9KPBIWfCiJcQQkowyabbNIxLaJkPPDAA0GLZ5AOylKzE6mDIMciHlYWXGnhDAoBleMQnP7mN78xfNEHKev5f/bs2fZuiDvu6Cduj+dAhHkicTgQ5FccrkVk5/nzjhHdgggepI8XkbLAwJQ/77zzOqLsexujPIIjJTUN1157bdhzzz2DuELDFdff/e53B+kPA0F8d9111yAuK8ejj1ncWH6NOuCeI0CE+lNOOSWIy/Ti6VgDBhLBqgGJbW1CHE8g1YZ/RDLVDcr1Y4sUi5523fYhkh5DflrhgAMOsMWLhSoGPkxZ49kHqV2khQ5SGvG4SH4unYt97FyAOBKSB8ICkIqDBQ4gJBIfuLgzWwQVT8/us3hI92bE1AqW/FG+qADBJa3DpZdeGl760peWlBrfSxBsiD8LaC/Aorjwwgtb9HfwAoBbQj3tv//+QWJZu+Z/eB8U+86eNwSP8/e9731+244Sa4X58+fbRoQLRKNn8Sb9CcSLNhhn8V3paCT656yzzgpbb711dGW0p+DpuOOOM/ywyYoBIi/H4bDFFlvYZcWvtDBefAe9ALgB98oD1kvxVKYfDAi5CSYUA8qHlYsEEXVoBzxFjKF3Jb9GEFYy+GI1xk/5i+y4wgorWEBWgrIi5lEsvtLMyFokzVqQNklCGEfoxgcMww99yPZjPJRz0YoW3FyfwnXuV/18zIxjUnzL4lcQ/Ucc6dxx5XjxY3zdceI4439EVFqU46btXFxVrl9SnrRMRKejDP+jk/E2i8div96nX4//92sinK0x+0bvufnmm+f6Kh8jmZ732GOPnpI3diAs/TM0DCQOS1/jpEKcwJHdIbvuIuhjzS/prbPcPlzgOrt2OCGOiHvYTSNG5Jwd6DbbbJPX5QSR02tf+9ogM3cL3IpYiLqAfMDCDjvsYLty2kZkgsiKPvnfj5QTEbI6XOsGIlgBTmDWrFndio3dPTgZWQlaIsfpBk9CzhNPPDEgzovxxTn4JRkhotkY4JxIDIkYD/HqzjvvHN+2c7huxIZlXAXPC5EkYr7TTz/d+q16tyjLPZKHikhM6WeYF8AJYnE4SoVRsq793SMo9N577x3k/5aL+YY5ttRXjxjQQ0wwoRiIrQT1YVq6ipe97GVmyQe35dyNXhXbTbPb1sJi3BPpFW644YaMnD9YRUnWn0lcl5155pmZ9FKlGMPE3dO7H3HEEVPKSAxp7ZDmBLPnMsCnS5HlbTyMEc4Lrg4/MnyTdtxxR+P6GDMcFrvlSQOs0hwHRPPAiRgfN9J1iDhncALgBiu/6UIIleEGnznwRztXXXVVWZGerkmUZuOiLZ47z4q0KUo6ac+L94v3jvujNrrA8vKjH/1oPh4fF2PDbxA/tQTtxwC7owQTioHYD4sPUzvxTApxs+TDioscQAceeGD2jne8I0NkM2hsPnx9WAikszLiNlO0QrSUPiSTMUfGOJUyPtOOPm/uoIMOskVwUv2wIFhKU2FzPO2002zeOOLin0VkDyz6+N10002VhD9HVuFEnFO20korWdtsUGh3EIAQkBcKU25/VrQn/Vae54t3b1R+WIiplco+Y66MI/5B/M8555yOd2sQXKS6zWMgEazmcTyyHmIOi900H24ZSAFddrmva+hF0H+xIMhgoJFwPz6g2Kx90jmsuvywHHekxXDugo1KFafr5Wd6lEVhJuvDnECMgsOSkU+2++67GyfJe+nzRo8qcXZPWYVnOv9UrxkMJILVDF5b0WpMsPDGZ9fbFBxzzDHmo8LCMBMxVT/jcp8ZdsiTSLCI90fkCXAJV1wnIK6jXUR4TabDGDXBYm44RzPX+MemCu49wXhiIBGs8XxuPY06FgkSMw49VFMAEWEHiw4DXVeTMOmhmQhSTDoYOIGLLrqoVlT+/Oc/Nz3g0UcfPbA4sNvAeNc81h4EY1giQSwc4cDZoMWECgkDOa4QYSYYXwwkgjW+z27akRc5rCYJ1v33329x7+peYMsmKd8yW4xYECcx0gV6F3SNcFp1iGuLOCyasRfv1/E/OrY40sX5559fR7Nd26DPXXbZJXflcIJFah1ZM3atm26OBwYSwRqP5zSjUQ6TYM1ogDOsJHNqs5bDV0hOnTNsJVVrEgPF0ExyHG6sO0XfyDBO8SDMrqsiRBKR/RWRo7G+U8PDxUAiWMPF91B7G6ZIcJgTg0NAd4WeJEE7MQC3g3jYuRwccpvg7LCo9FQs3hdHRXQxrqqJPtuJ8QVjVIlgTfBznlQOa4If2cRMrchhES2+TuKBqJSI6YsvvrgRReeqiO4BAcPkP8HkYSBFutB2bFIhjnRBtAPl/AkKuTSp003zahEG5BweFB3eIpwwLDmghy233LKWERJ0l3iT2pAF4vyJWLHxtjiZirIelDi0NEJHLZ2nRkaLgcmjwWlGjgE4LE8v0rSVoPeZjgkDYKDIYSnwci0c1rx58zIFO85FjVo97ZyIIFV+humJTA4Gkkhwcp7llJlg/u0ECzPfJq0Ep3SeLizQGMBp1x3JISq77bbbQAQLfaViAGYkIqU9FwEqIrpFaUn6zAXjdUsEa4KfM4n6/MNOBGuCH3QLp3bHHXdY7ErngCSmmzHBwsBmu+22mxL7kogqcUaAFqIhDalmDCQdlr6oSQWS0h155JEm3yfvkWIHJh3WpD7sls1LgZMtQSTJHAFxWEHRUPrSLZEpgGjyCric51GjLSLTo6eiTZmycynBgoKBmglgaq5FGEAMo/fYfonDatGDWQCGUtRh9cthkSmgLGAtXBV6rAQLJgaSSHCCn3ucTiERrAl+0C2c2iAEi2gpyuPVoatSZmpLKjmJCTtb+PhaO6REsFr7aAYfGEpq12GhrCYPVYKEgWFgAA7JfaTg8gmZ1M0Pi/QxEKPtt98+j67u0gE4LXyumghTNQxcpD7qw0DSYU2w7HfXXXcNJ5xwgs1Q0bnD1VdfHZQLaYJnnKbWFgwoMWRQ0smgJI82JDIoy0AiKKljxxBlTRg+//nPm1+VUtSEe++91+4vtNBCYfnllw/LLrus6WEVuaKjXvpnAcVAfbQvtdQ2DJDzR6+1/ZIfVtuezmSPh6jonjWZd5C8VEUOi8mkXGUAAAZgSURBVHQ3m266af6O+rsqIpXJ2CJxVJP9isxodonDmuCNihL0hbPPPttmKB1WinQxwc+6bVOT+C6sttpq4ZprrrGhYdVHdApAmZPD3LlzjeOCq3JACqB8XUHR+MPSSy/tl9MxYSDHQCJYOSom70QcVlCUbJtYIliT93zbPKOHHnoorL766kG50WyYEK/58+cHxfgLRxxxRFC6kY7hL7HEEuHwww8Pm2++eYBwJUgYKMNAIlhlWJmQazGHlfywJuShjsk0Hn74YeOwnGApKG3YcMMNwxVXXBHwr/L4f0xnvfXWM64q6VfH5OGOcJiJYI0Q+U13HXNYECyC3ypcTtPdpvYTBsLdd98d1lhjjaAMx0acQImUFoYZJ1ZwVQofFjbeeOMgK9aEtYSBaTGQCNa0KBrfAjHBeuQjHxnk32IRtMd3RmnkDz74YLjnnnuCkhNaxIcYIzJqMP0Q1xZddNGAWE4x9nJupqwOVnyLLLJI3MyMzuGaZJpu3BPjULbkgJUq+ioIFD9A2ZTtuNFGG1kUC4hWgoSBXjGQCFavmBrDcrFIkOHvs88+Yeedd7aFTlZcYckll7SFj8UGM2KOSjvfoUP4+9//HlCgK8hoXxj4wx/+YKkfMFtWAN7w+Mc/3hYrzJohnixuLGKIjljUWGCB3/72t0H+O4EUEqSOWGyxxawe7Sy88MJWh/HwY0FWnDlbwBE5LbPMMrZT9528D5h+mBvllbY93+n7/aoj9RgHCzAhgG6//XYjAJhas8jTj88BTuL+++/PF+aqNge5Dh4JdXTzzTdb/7Nnz84JAOOAON144402rhVXXNHwd+uttxq+IRSENHrBC15gz5exM69bbrklrLDCCjnOnaD0M07akqNw4BnRP0QV4Nn6s2B8nPOerb322olY9YPgVDbHQCJYOSom7wRxi6Jd2MIEkVC0ACNIT3jCE2xxgUjMmjUrKFCpEQClGjfCxMLI4sIic99999k9jDZ6Xcx88WQBp03+Z3dPmyjU+R/iwZggPBAmFwlBWCAGEEqIGtepRzssdtRlofVf8alx38HnwP+cA/F9uzDNH69XLBa3U1WmWGdB+h/8OI78vYHoz5kzJ8g52DYwCxI+0lzrwUAiWPXgsZWtnHjiiRYkFKIAcfCFo5WDTYOaaAxgWHHYYYel4MsT/ZSbn1wiWM3jeGQ9/PCHPzSFduzrMrLBDNAx3Nkqq6xiJtGInXznHnNQxea5B3eGjgROD5EhnCMiT+ojEp0JODflY/A2nv70p5v4EK6VzQFcItzknXfeadEbnvvc5xq3etddd9nGYZY4WwwTEJ/RFiJXxJVsKhBzwtlSBmMZuE1Ed8stt5y1SxnmwnV0UGxI6I+2fXyMAY6UyBGIAukHPACUgWMGJ3C0/O/zic99bn6NPhkDAP4YL9dioCx90xecO/1QB06f+SRIGBgEA4lgDYK9MagL0SJFA4sZC4mDL0IcAV+w/D5HFkYWffQe+M9Qf+WVV851IHHZOs4ZCws3uij0MfQNsXL9FPotT4neS3+IQBFDIX50UaTr4jBcqBNYmCEgjBk8obMDpxAURJvo4txggnnyvxMbxkE9iBOA3oyylGH+nEMgnvGMZ5hY1wrpD9chbIhH6Y/24ueJvpAyiIDRJ4EHgDJcg9iAz16BeUGkAPAHIawCiCi6Scbl86oqm64nDPSKgUSwesXUGJer0vf0MiUWKRZ7FjwWYM4TJAwkDCQMjAIDiWCNAuupz4SBhIGEgYSBvjGQCFbfKEsVEgYSBhIGEgZGgYFEsEaB9dRnwkDCQMJAwkDfGEgEq2+UpQoJAwkDCQMJA6PAQCJYo8B66jNhIGEgYSBhoG8MJILVN8pShYSBhIGEgYSBUWAgEaxRYD31mTCQMJAwkDDQNwYSweobZalCwkDCQMJAwsAoMJAI1iiwnvpMGEgYSBhIGOgbA4lg9Y2yVCFhIGEgYSBhYBQYSARrFFhPfSYMJAwkDCQM9I2BRLD6RlmqkDCQMJAwkDAwCgwkgjUKrKc+EwYSBhIGEgb6xkAiWH2jLFVIGEgYSBhIGBgFBhLBGgXWU58JAwkDCQMJA31jIBGsvlGWKiQMJAwkDCQMjAIDiWCNAuupz4SBhIGEgYSBvjGQCFbfKEsVEgYSBhIGEgZGgYFEsEaB9dRnwkDCQMJAwkDfGPh/eeTeOC1iifEAAAAASUVORK5CYII=	161 \text{ turns}
+309	A cylindrical thin shell of electric charge has length $l$ and radius $a$, where $l \gg a$. The surface charge density on the shell is $\sigma$. The shell rotates about its axis with an angular velocity $\omega$ which increases slowly with time as $\omega = kt$, where $k$ is a constant and $t \ge 0$, as in Fig. 2.14. Neglecting fringing effects, determine:  (a) The magnetic field inside the cylinder.   (b) The electric field inside the cylinder.   (c) The total electric field energy and the total magnetic field energy inside the cylinder.	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	\mathbf{B}(\rho) = \mu_0 \sigma \omega a \, e_z, \quad (\rho < a); \mathbf{E}(\rho) = -\frac{\mu_0 \sigma a k \rho}{2} \, e_{\varphi}, \quad (\rho < a); U_E = \frac{\pi \varepsilon_0 \mu_0^2 \sigma^2 k^2 a^6 l}{16}; U_B = \frac{\pi \mu_0 \sigma^2 a^4 k^2 l t^2}{2}
+310	(a) Given the following infinite network (Fig. 3.11):  Find the input resistance, i.e., the equivalent resistance between terminals A and B.  (b) Figure 3.12 shows two resistors in parallel, with values $R_1$ and $R_2$. The current $I_0$ divides somehow between them. Show that the condition $I_0 = I_1 + I_2$ together with the requirement of minimum power dissipation leads to the same current values that we would calculate by ordinary circuit formulae.	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	R = \frac{R_1}{2} + \frac{\sqrt{R_1^2 + 4 R_1 R_2}}{2}; \frac{I_1}{I_0 - I_1} = \frac{R_2}{R_1}
+311	A cylinder of radius $R$ and infinite length is made of permanently polarized dielectric. The polarization vector $\mathbf{P}$ is everywhere proportional to the radial vector $\mathbf{r}, P = ar$, where $a$ is a positive constant. The cylinder rotates around its axis with an angular velocity $\omega$. This is a non-relativistic problem $-\omega R \ll c$.  (a) Find the electric field $\mathbf{E}$ at a radius $r$ both inside and outside the cylinder.  (b) Find the magnetic field $\mathbf{B}$ at a radius $r$ both inside and outside the cylinder.  (c) What is the total electromagnetic energy stored per unit length of the cylinder,    (i) before the cylinder started spinning?  (ii) while it is spinning?   Where did the extra energy come from?	[]	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	"\mathbf{E} = 
+\begin{cases} 
+-\frac{ar}{\epsilon_0} \mathbf{e}_r, & r < R, \\
+0, & r > R.
+\end{cases}; \mathbf{B} = 
+\begin{cases} 
+\mu_0 a \omega r^2 \mathbf{e}_z, & r < R, \\
+0, & r > R.
+\end{cases}; \frac{\pi a^2 R^4}{4 \varepsilon_0}; \frac{\pi a^2 R^4}{4 \varepsilon_0} \left[ 1 + \frac{2 \omega^2 R^2}{3c^2} \right]"
+312	A conducting sphere with total charge $Q$ is cut into half. What force must be used to hold the halves together?	[]	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	\frac{Q^2}{32\pi \epsilon_0 R^2}
+313	An air-spaced coaxial cable has an inner conductor 0.5 cm in diameter and an outer conductor 1.5 cm in diameter. When the inner conductor is at a potential of +8000 V with respect to the grounded outer conductor,  (a) what is the charge per meter on the inner conductor, and   (b) what is the electric field intensity at $r = 1$ cm?	[]	/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGQAZADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD3+iiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigD//2Q==	\lambda = 4.05 \times 10^{-7} \, \text{C/m}; E = 0
+314	Which is the correct boundary condition in magnetostatics at a boundary between two different media?  (a) The component of $\mathbf{B}$ normal to the surface has the same value.   (b) The component of $\mathbf{H}$ normal to the surface has the same value.   (c) The component of $\mathbf{B}$ parallel to the surface has the same value.	[]	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	(a)
+315	Design a magnet (using a minimum mass of copper) to produce a field of 10,000 gauss in a 0.1 meter gap having an area of 1m x 2m. Assume very high permeability iron. Calculate the power required and the weight of the necessary copper. (The resistivity of copper is $2 \times 10^{-6}$ ohm-cm; its density is $8 \ \text{g/cm}^3$ and its maximum current density is 1000 amp/$\text{cm}^2$.) What is the force of attraction between the poles of the magnet?	[]	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	P = 9.5 \times 10^4 \ \text{W}; \text{Weight} = 3.8 \ \text{kg}; F = 8 \times 10^5 \ \text{N}
+316	Assume that the earth’s magnetic field is caused by a small current loop located at the center of the earth. Given that the field near the pole is 0.8 gauss, that the radius of the earth is $R = 6 \times 10^6 \, \text{m}$, and that $\mu_0 = 4\pi \times 10^{-7} \, \text{H/m}$, use the Biot-Savart law to calculate the strength of the magnetic moment of the small current loop.	[]	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	m \approx 8.64 \times 10^{-26} \, \text{Am}^2
+317	A spherical condenser consists of two concentric conducting spheres of radii $a$ and $b$ ($a > b$). The outer sphere is grounded and a charge $Q$ is placed on the inner sphere. The outer conductor then contracts from radius $a$ to radius $a'$. Find the work done by the electric force.	[]	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	\frac{Q^2 (a - a')}{8 \pi \varepsilon_0 a a'}
+318	A square voltage pulse (Fig. 3.15) is applied to terminal $A$ in the circuit shown in Fig. 3.14. What signal appears at $B$?	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	V_B = 5e^{-t}u(t) - 5e^{-(t-1)}u(t - 1)
+319	In the inertial frame of the fixed stars, a spaceship travels along the $x$-axis, with $x(t)$ being its position at time $t$. Of course, the velocity $v$ and acceleration $a$ in this frame are $v = \frac{dx}{dt}$ and $a = \frac{d^2x}{dt^2}$. Suppose the motion to be such that the acceleration as determined by the space passengers is constant in time. What this means is the following. At any instant we transform to an inertial frame in which the spaceship is momentarily at rest. Let $g$ be the acceleration of the spaceship in that frame at that instant. Now suppose that $g$, so defined instant by instant, is a constant.  You are given the constant $g$. In the fixed star frame the spaceship starts with initial velocity $v = 0$ when $x = 0$. What is the distance $x$ traveled when it has achieved a velocity $v$?  Allow for relativistic kinematics, so that $v$ is not necessarily small compared with the speed of light $c$.	[]	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	x = \frac{c^2}{g} \left( \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}
+320	As in Fig. 2.15, you are given the not-so-parallel plate capacitor.  (a) Neglecting edge effects, when a voltage difference $V$ is placed across the two conductors, find the potential everywhere between the plates.  (b) When this wedge is filled with a medium of dielectric constant $\varepsilon$, calculate the capacitance of the system in terms of the constants given.	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	\varphi(x,y) = \frac{V \arctan \left[ \frac{y}{x + \frac{bd}{a}} \right]; C = \frac{\varepsilon w}{\arctan \frac{a}{b}} \ln\left( \frac{d + a}{d} \right)
+321	A cylindrical capacitor of length $L$ consists of an inner conductor wire of radius $a$, a thin outer conducting shell of radius $b$. The space in between is filled with nonconducting material of dielectric constant $\varepsilon$.  (a) Find the electric field as a function of radial position when the capacitor is charged with $Q$. Neglect end effects.  (b) Find the capacitance.  (c) Suppose that the dielectric is pulled partly out of the capacitor while the latter is connected to a battery of potential $V$. Find the force necessary to hold the dielectric in this position. Neglect fringing fields. In which direction must the force be applied?	[]	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	\mathbf{E} = \frac{-Q}{2\pi \varepsilon Lr} \mathbf{e}_r; C = \frac{2\pi \varepsilon L}{\ln \left(\frac{b}{a}\right)}; F = \frac{\pi \varepsilon_0 V^2}{\ln(\frac{b}{a})} \left( 1 - \frac{\varepsilon}{\varepsilon_0} \right)
+322	As observed in an inertial frame $S$, two spaceships are traveling in opposite directions along straight, parallel trajectories separated by a distance $d$ as shown in Fig. 5.1. The speed of each ship is $c/2$, where $c$ is the speed of light.  (a) At the instant (as viewed from $S$) when the ships are at the points of closest approach (indicated by the dotted line in Fig. 5.1) ship (1) ejects a small package which has speed $3c/4$ (also as viewed from $S$). From the point of view of an observer in ship (1), at what angle must the package be aimed in order to be received by ship (2)? Assume the observer in ship (1) has a coordinate system whose axes are parallel to those of $S$ and, as shown in Fig. 5.1, the direction of motion is parallel to the $y$ axis.  (b) What is the speed of the package as seen by the observer in ship (1)?	[]	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	\alpha' = \arctan \left( \frac{8}{\sqrt{15}} \right); \frac{\sqrt{79}}{10} \, c
+323	A perfectly conducting sphere is placed in a uniform electric field pointing in the $z$-direction.  (a) What is the surface charge density on the sphere?  (b) What is the induced dipole moment of the sphere?	[]	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	\sigma = 3 \varepsilon_0 E_0 \cos \theta; \mathbf{P} = 4\pi\varepsilon_0 a^3 \mathbf{E}_0
+324	A dielectric sphere of radius $a$ and dielectric constant $\varepsilon_1$ is placed in a dielectric liquid of infinite extent and dielectric constant $\varepsilon_2$. A uniform electric field $\mathbf{E}$ was originally present in the liquid. Find the resultant electric field inside and outside the sphere.	[]	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	\mathbf{E}_1 = \frac{3\varepsilon_2}{\varepsilon_1 + 2\varepsilon_2} \mathbf{E}, \quad (r < a); \mathbf{E}_2 = \mathbf{E} + \frac{\varepsilon_1 - \varepsilon_2}{\varepsilon_1 + 2\varepsilon_2} a^3 \left[ \frac{3(\mathbf{E} \cdot \mathbf{r}) \mathbf{r}}{r^5} - \frac{\mathbf{E}}{r^3} \right], \quad (r > a)
+325	A spherical conductor $A$ contains two spherical cavities as shown in Fig. 1.14. The total charge on the conductor itself is zero. However, there is a point charge $+q_b$ at the center of one cavity and $+q_c$ at the center of the other. A large distance $r$ away is another charge $+q_d$. What forces act on each of the four objects $A, q_b, q_c,$ and $q_d$? Which answers, if any, are only approximate and depend on $r$ being very large. Comment on the uniformities of the charge distributions on the cavity walls and on A if $r$ is not large.	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	F = \frac{q_d(q_b + q_c)}{4\pi \varepsilon_0 r^2}
+326	A capacitor (in vacuum) consists of two parallel circular metal plates each of radius $r$ separated by a small distance $d$. A current $i$ charges the capacitor. Use the Poynting vector to show that the rate at which the electromagnetic field feeds energy into the capacitor is just the time rate of change of the electrostatic field energy stored in the capacitor. Show that the energy input is also given by $iV$, where $V$ is the potential difference between the plates. Assume that the electric field is uniform out to the edges of the plates.	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	P = \frac{dW_e}{dt} = \frac{iQ}{\pi r^2 \varepsilon_0} d; P = iV
+327	The frequency response of a single low-pass filter (RC–circuit) can be compensated ideally:  (a) exactly only by an infinite series of RC–filters   (b) exactly only by using LC–filters   (c) exactly by a single high-pass (RC) filter.	[]	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	(c)
+328	What is the average random speed of electrons in a conductor? $10^{2}$, $10^{4}$, $10^{6}$, $10^{8}$ cm/sec.	[]	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	10^{6} \text{ cm/sec}
+329	A cylindrical capacitor has an inner conductor of radius $r_1$ and an outer conductor of radius $r_2$. The outer conductor is grounded and the inner conductor is charged so as to have a positive potential $V_0$. In terms of $V_0, \, r_1, \, \text{and} \, r_2$,  (a) what is the electric field at $r$? \, ($r_1 < r < r_2$)   (b) what is the potential at $r$?   (c) If a small negative charge $Q$ which is initially at $r$ drifts to $r_1$, by how much does the charge on the inner conductor change?	[]	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	E(r) = \frac{V_0}{\ln(r_2/r_1)} \frac{1}{r}; V(r) = \frac{V_0 \ln(r_2/r)}{\ln(r_2/r_1)}; \Delta Q = \frac{Q \ln(r/r_1)}{\ln(r_2/r_1)}
+330	A cylindrical soft iron rod of length $L$ and diameter $d$ is bent into a circular shape of radius $R$ leaving a gap where the two ends of the rod almost meet. The gap spacing $s$ is constant over the face of the ends of the rod. Assume $s \ll d, d \ll R$. $N$ turns of wire are wrapped tightly around the iron rod and a current $I$ is passed through the wire. The relative permeability of the iron is $\mu_r$. Neglecting fringing, what is the magnetic field $B$ in the gap?	[]	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	B = \frac{\mu_r \mu_0 NI}{2\pi R + (\mu_r - 1)s}
+331	A long, solid dielectric cylinder of radius $a$ is permanently polarized so that the polarization is everywhere radially outward, with a magnitude proportional to the distance from the axis of the cylinder, i.e., $P = \frac{1}{2} P_0 r \mathbf{e_r}$.  (a) Find the charge density in the cylinder.   (b) If the cylinder is rotated with a constant angular velocity $\omega$ about its axis without change in $P$, what is the magnetic field on the axis of the cylinder at points not too near its ends?	[]	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	\rho = -P_0; \mathbf{B} = 0
+332	(a) The capacitor in the circuit in Fig. 3.10 is made from two flat square metal plates of length $L$ on a side and separated by a distance $d$. What is the capacitance?  (b) Show that if any electrical energy is stored in $C$, it is entirely dissipated in $R$ after the switch is closed.	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	C = \frac{\varepsilon_0 L^2}{d}; W_R = W_C
+333	A thin metal sphere of radius $b$ has charge $Q$.    (a) What is the capacitance?   (b) What is the energy density of the electric field at a distance $r$ from the sphere’s center?   (c) What is the total energy of the field?   (d) Compute the work expended in charging the sphere by carrying infinitesimal charges from infinity.   (e) A potential $V$ is established between inner (radius $a$) and outer (radius $b$) concentric thin metal spheres. What is the radius of the inner sphere such that the electric field near its surface is a minimum?	[]	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	C = 4 \pi \varepsilon_0 b; w_e(r) = \frac{Q^2}{32 \pi^2 \varepsilon_0 r^4}; W_e = \frac{Q^2}{8 \pi \varepsilon_0 b}; W = \frac{Q^2}{8 \pi \varepsilon_0 b}; a = \frac{b}{2}; E_{\text{min}}(a) = \frac{4V}{b}
+334	Suppose the input voltages $V_1$, $V_2$, and $V_3$ in the circuit of Fig. 3.1 can assume values of either 0 or 1 (0 means ground). There are thus 8 possible combinations of input voltage. Compute $V_{out}$ for each of these possibilities.	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	V_{\text{out}}(0, 0, 0) = 0; V_{\text{out}}(0, 0, 1) = \frac{1}{12}; V_{\text{out}}(0, 1, 0) = \frac{1}{6}; V_{\text{out}}(0, 1, 1) = \frac{1}{4}; V_{\text{out}}(1, 0, 0) = \frac{1}{3}; V_{\text{out}}(1, 0, 1) = \frac{5}{12}; V_{\text{out}}(1, 1, 0) = \frac{1}{2}; V_{\text{out}}(1, 1, 1) = \frac{7}{12}
+335	"Consider the motion of electrons in an axially symmetric magnetic field. Suppose that at $z = 0$ (the ""median plane"") the radial component of the magnetic field is 0 so $\mathbf{B}(z = 0) = B(r) \mathbf{e}_x$. Electrons at $z = 0$ then follow a circular path of radius $R$, as shown in Fig. 5.18.  (a) What is the relationship between the electron momentum $p$ and the orbit radius $R$? In a betatron, electrons are accelerated by a magnetic field which changes with time. Let $B_{\text{av}}$ be the average value of the magnetic field over the plane of the orbit (within the orbit), i.e.,  $$ B_{\text{av}} = \frac{\psi_B}{\pi R^2}, $$  where $\psi_B$ is the magnetic flux through the orbit. Let $B_0$ equal $B(r = R, z = 0)$.  (b) Suppose $B_{av}$ is changed by an amount $\Delta B_{av}$ and $B_0$ is changed by $\Delta B_0$. How must $\Delta B_{av}$ be related to $\Delta B_0$ if the electrons are to remain at radius $R$ as their momentum is increased?  (c) Suppose the $z$ component of the magnetic field near $r = R$ and $z = 0$ varies with $r$ as $B_z(r) = B_0(R)\left( \frac{R}{r} \right)^n$. Find the equations of motion for small departures from the equilibrium orbit in the median plane. There are two equations, one for small vertical changes and one for small radial changes. Neglect any coupling between radial and vertical motion.  (d) For what range of $n$ is the orbit stable against both vertical and radial perturbations?"	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	p = -eBR; \Delta B_0 = \frac{1}{2} \Delta B_{\text{av}}; \ddot{r}_1 + (1-n)\omega_0^2 r_1 = 0; m\ddot{z} + m\omega_0^2 nz = 0; 0 < n < 1
+336	"An electromagnet is made by wrapping a current-carrying coil $N$ times around a C-shaped piece of iron $(\mu \gg \mu_0)$ as shown in Fig. 2.19. If the cross-sectional area of the iron is $A$, the current is $i$, the width of the gap is $d$, and the length of each side of the ""C"" is $l$, find the $B$-field in the gap."	[]	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	B = \frac{NI\mu_0 \mu}{d(\mu - \mu_0) + 4l\mu_0}
+337	A system of conductors has a cross section given by the intersection of two circles of radius $b$ with centers separated by $2a$ as shown in Fig. 2.13. The conducting portion is shown shaded, the unshaded lens-shaped region being a vacuum. The conductor on the left carries a uniform current density $J$ going into the page, and the conductor on the right carries a uniform current density $J$ coming out of the page. Assume that the magnetic permeability of the conductor is the same as that of the vacuum. Find the magnetic field at all points $x, y$ in the vacuum enclosed between the two conductors.	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	\mathbf{B} = -\mu_0 aJ \mathbf{e}_y
+338	The diagram 3.18 shows a circuit of 2 capacitors and 2 ideal diodes driven by a voltage generator. The generator produces a steady square wave of amplitude $V$, symmetrical around zero potential, shown at point a in the circuit. Sketch the waveforms and assign values to the voltage levels at points $b$ and $c$ in the circuit.	[]	iVBORw0KGgoAAAANSUhEUgAAAc4AAAECCAYAAAB3zDd/AAAMTGlDQ1BJQ0MgUHJvZmlsZQAASImVVwdYU1cbPndkQggQiICMsJcgIiOAjBBW2BtBVEISIIwYE4KKGylWsG4RwVHRKkNxVUCKC7VqpSjuXRyoKLVYi1v5Twigpf94/u95zr3vfc933vN93z13HADoXXypNBfVBCBPki+LDfZnTU5OYZF6AAJIgAYMgQdfIJdyoqPDAbTh89/t9TXoDe2yg1Lrn/3/1bSEIrkAACQa4nShXJAH8Y8A4K0CqSwfAKIU8uaz8qVKvA5iHRkMEOIaJc5U4VYlTlfhi4M+8bFciB8BQFbn82WZAGj0QZ5VIMiEOnSYLXCSCMUSiP0g9snLmyGEeBHENtAHzklX6rPTv9LJ/Jtm+ogmn585glW5DBo5QCyX5vLn/J/l+N+Wl6sYnsMaNvUsWUisMmdYt0c5M8KUWB3it5L0yCiItQFAcbFw0F+JmVmKkASVP2ojkHNhzQAT4kny3DjeEB8r5AeEQWwIcYYkNzJ8yKcoQxyk9IH1QyvE+bx4iPUgrhHJA+OGfI7LZsQOz3stQ8blDPFP+bLBGJT6nxU5CRyVPqadJeIN6WOOhVnxSRBTIQ4oECdGQqwBcaQ8Jy5syCe1MIsbOewjU8Qqc7GAWCaSBPur9LHyDFlQ7JB/XZ58OHfseJaYFzmEL+VnxYeoaoU9EvAH44e5YH0iCSdhWEcknxw+nItQFBCoyh0niyQJcSoe15Pm+8eqxuJ20tzoIX/cX5QbrOTNII6XF8QNjy3Ih4tTpY+XSPOj41Vx4pXZ/NBoVTz4PhAOuCAAsIACtnQwA2QDcUdvUy+8UvUEAT6QgUwgAg5DzPCIpMEeCTzGgULwO0QiIB8Z5z/YKwIFkP80ilVy4hFOdXQAGUN9SpUc8BjiPBAGcuG1YlBJMhJBIngEGfE/IuLDJoA55MKm7P/3/DD7heFAJnyIUQzPyKIPexIDiQHEEGIQ0RY3wH1wLzwcHv1gc8bZuMdwHl/8CY8JnYQHhKuELsLN6eIi2agoI0AX1A8aqk/61/XBraCmK+6Pe0N1qIwzcQPggLvAeTi4L5zZFbLcobiVVWGN0v5bBl/doSE/ihMFpYyh+FFsRo/UsNNwHVFR1vrr+qhiTR+pN3ekZ/T83K+qL4TnsNGe2LfYQewMdgI7h7ViTYCFHcOasXbsiBKPrLhHgytueLbYwXhyoM7oNfPlziorKXeqd+px+qjqyxfNzlc+jNwZ0jkycWZWPosDvxgiFk8icBzHcnZydgVA+f1Rvd5exQx+VxBm+xduyW8AeB8bGBj46QsXegyA/e7wlXD4C2fDhp8WNQDOHhYoZAUqDlceCPDNQYdPnz4wBubABubjDNyAF/ADgSAURIF4kAymweiz4DqXgVlgHlgMSkAZWAXWg0qwFWwHNWAPOACaQCs4AX4G58FFcBXchqunGzwHfeA1+IAgCAmhIQxEHzFBLBF7xBlhIz5IIBKOxCLJSBqSiUgQBTIPWYKUIWuQSmQbUovsRw4jJ5BzSCdyE7mP9CB/Iu9RDFVHdVAj1Aodj7JRDhqGxqNT0Ux0JlqIFqMr0Aq0Gt2NNqIn0PPoVbQLfY72YwBTw5iYKeaAsTEuFoWlYBmYDFuAlWLlWDXWgLXA+3wZ68J6sXc4EWfgLNwBruAQPAEX4DPxBfhyvBKvwRvxU/hl/D7eh38m0AiGBHuCJ4FHmEzIJMwilBDKCTsJhwin4bPUTXhNJBKZRGuiO3wWk4nZxLnE5cTNxL3E48RO4kNiP4lE0ifZk7xJUSQ+KZ9UQtpI2k06RrpE6ia9JauRTcjO5CByCllCLiKXk+vIR8mXyE/IHyiaFEuKJyWKIqTMoayk7KC0UC5QuikfqFpUa6o3NZ6aTV1MraA2UE9T71Bfqampmal5qMWoidUWqVWo7VM7q3Zf7Z26trqdOlc9VV2hvkJ9l/px9Zvqr2g0mhXNj5ZCy6etoNXSTtLu0d5qMDQcNXgaQo2FGlUajRqXNF7QKXRLOoc+jV5IL6cfpF+g92pSNK00uZp8zQWaVZqHNa9r9msxtCZoRWnlaS3XqtM6p/VUm6RtpR2oLdQu1t6ufVL7IQNjmDO4DAFjCWMH4zSjW4eoY63D08nWKdPZo9Oh06erreuim6g7W7dK94huFxNjWjF5zFzmSuYB5jXm+zFGYzhjRGOWjWkYc2nMG72xen56Ir1Svb16V/Xe67P0A/Vz9FfrN+nfNcAN7AxiDGYZbDE4bdA7Vmes11jB2NKxB8beMkQN7QxjDecabjdsN+w3MjYKNpIabTQ6adRrzDT2M842Xmd81LjHhGHiYyI2WWdyzOQZS5fFYeWyKlinWH2mhqYhpgrTbaYdph/MrM0SzIrM9prdNaeas80zzNeZt5n3WZhYRFjMs6i3uGVJsWRbZllusDxj+cbK2irJaqlVk9VTaz1rnnWhdb31HRuaja/NTJtqmyu2RFu2bY7tZtuLdqidq12WXZXdBXvU3s1ebL/ZvnMcYZzHOMm46nHXHdQdOA4FDvUO9x2ZjuGORY5Nji/GW4xPGb96/Jnxn51cnXKddjjdnqA9IXRC0YSWCX862zkLnKucr0ykTQyauHBi88SXLvYuIpctLjdcGa4Rrktd21w/ubm7ydwa3HrcLdzT3De5X2frsKPZy9lnPQge/h4LPVo93nm6eeZ7HvD8w8vBK8erzuvpJOtJokk7Jj30NvPme2/z7vJh+aT5fO/T5Wvqy/et9n3gZ+4n9Nvp94Rjy8nm7Oa88Hfyl/kf8n/D9eTO5x4PwAKCA0oDOgK1AxMCKwPvBZkFZQbVB/UFuwbPDT4eQggJC1kdcp1nxBPwanl9oe6h80NPhamHxYVVhj0ItwuXhbdEoBGhEWsj7kRaRkoim6JAFC9qbdTdaOvomdE/xRBjomOqYh7HToidF3smjhE3Pa4u7nW8f/zK+NsJNgmKhLZEemJqYm3im6SApDVJXZPHT54/+XyyQbI4uTmFlJKYsjOlf0rglPVTulNdU0tSr021njp76rlpBtNypx2ZTp/On34wjZCWlFaX9pEfxa/m96fz0jel9wm4gg2C50I/4Tphj8hbtEb0JMM7Y03G00zvzLWZPVm+WeVZvWKuuFL8Mjske2v2m5yonF05A7lJuXvzyHlpeYcl2pIcyakZxjNmz+iU2ktLpF0zPWeun9knC5PtlCPyqfLmfB34o9+usFF8o7hf4FNQVfB2VuKsg7O1Zktmt8+xm7NszpPCoMIf5uJzBXPb5pnOWzzv/nzO/G0LkAXpC9oWmi8sXti9KHhRzWLq4pzFvxY5Fa0p+mtJ0pKWYqPiRcUPvwn+pr5Eo0RWcn2p19Kt3+Lfir/tWDZx2cZln0uFpb+UOZWVl31cLlj+y3cTvqv4bmBFxoqOlW4rt6wirpKsurbad3XNGq01hWsero1Y27iOta503V/rp68/V+5SvnUDdYNiQ1dFeEXzRouNqzZ+rMyqvFrlX7V3k+GmZZvebBZuvrTFb0vDVqOtZVvffy/+/sa24G2N1VbV5duJ2wu2P96RuOPMD+wfanca7Czb+WmXZFdXTWzNqVr32to6w7qV9Wi9or5nd+rui3sC9jQ3ODRs28vcW7YP7FPse7Y/bf+1A2EH2g6yDzb8aPnjpkOMQ6WNSOOcxr6mrKau5uTmzsOhh9tavFoO/eT4065W09aqI7pHVh6lHi0+OnCs8Fj/cenx3hOZJx62TW+7fXLyySunYk51nA47ffbnoJ9PnuGcOXbW+2zrOc9zh39h/9J03u18Y7tr+6FfXX891OHW0XjB/ULzRY+LLZ2TOo9e8r104nLA5Z+v8K6cvxp5tfNawrUb11Ovd90Q3nh6M/fmy1sFtz7cXnSHcKf0rubd8nuG96p/s/1tb5db15H7AffbH8Q9uP1Q8PD5I/mjj93Fj2mPy5+YPKl96vy0tSeo5+KzKc+6n0uff+gt+V3r900vbF78+IffH+19k/u6X8peDvy5/JX+q11/ufzV1h/df+913usPb0rf6r+tecd+d+Z90vsnH2Z9JH2s+GT7qeVz2Oc7A3kDA1K+jD/4K4AB5dYmA4A/dwFASwaAAfeN1Cmq/eGgIao97SAC/wmr9pCD5gZAA/ynj+mFfzfXAdi3AwArqE9PBSCaBkC8B0AnThxpw3u5wX2n0ohwb/B97Kf0vHTwb0y1J/0q7tFnoFR1AaPP/wIw5IMgGpF8LAAAAIplWElmTU0AKgAAAAgABAEaAAUAAAABAAAAPgEbAAUAAAABAAAARgEoAAMAAAABAAIAAIdpAAQAAAABAAAATgAAAAAAAACQAAAAAQAAAJAAAAABAAOShgAHAAAAEgAAAHigAgAEAAAAAQAAAc6gAwAEAAAAAQAAAQIAAAAAQVNDSUkAAABTY3JlZW5zaG901OZeaQAAAAlwSFlzAAAWJQAAFiUBSVIk8AAAAdZpVFh0WE1MOmNvbS5hZG9iZS54bXAAAAAAADx4OnhtcG1ldGEgeG1sbnM6eD0iYWRvYmU6bnM6bWV0YS8iIHg6eG1wdGs9IlhNUCBDb3JlIDYuMC4wIj4KICAgPHJkZjpSREYgeG1sbnM6cmRmPSJodHRwOi8vd3d3LnczLm9yZy8xOTk5LzAyLzIyLXJkZi1zeW50YXgtbnMjIj4KICAgICAgPHJkZjpEZXNjcmlwdGlvbiByZGY6YWJvdXQ9IiIKICAgICAgICAgICAgeG1sbnM6ZXhpZj0iaHR0cDovL25zLmFkb2JlLmNvbS9leGlmLzEuMC8iPgogICAgICAgICA8ZXhpZjpQaXhlbFlEaW1lbnNpb24+MjU4PC9leGlmOlBpeGVsWURpbWVuc2lvbj4KICAgICAgICAgPGV4aWY6UGl4ZWxYRGltZW5zaW9uPjQ2MjwvZXhpZjpQaXhlbFhEaW1lbnNpb24+CiAgICAgICAgIDxleGlmOlVzZXJDb21tZW50PlNjcmVlbnNob3Q8L2V4aWY6VXNlckNvbW1lbnQ+CiAgICAgIDwvcmRmOkRlc2NyaXB0aW9uPgogICA8L3JkZjpSREY+CjwveDp4bXBtZXRhPgq72ddOAAAAHGlET1QAAAACAAAAAAAAAIEAAAAoAAAAgQAAAIEAACUoJslCjQAAJPRJREFUeAHsnQu8VUX1x8f3W1MUTRMxDAVNS8MHpaISZYgmPrIyRDHAxyfwVQaifkrTQFTUNFETRaUMnwiIaYBpqaHiGxUBn+QL3+90/uu7/M/pcL33cs/lnLP3Ofc3n8+559y9Z8/M/q295zdrzZo1y0RLQUkICAEhIASEgBBoEQLLiDhbhJMyCQEhIASEgBBwBEScehCEgBAQAkJACJSAgIizBLCUVQgIASEgBISAiFPPgBAQAkJACAiBEhAQcZYAlrIKASEgBISAEBBx6hkQAkJACAgBIVACAiLOEsBSViEgBISAEBACIk49A0JACAgBISAESkBAxFkCWMoqBISAEBACQkDEqWdACAgBISAEhEAJCIg4SwBLWYWAEBACQkAIiDj1DAgBISAEhIAQKAEBEWcJYCmrEBACQkAICAERp54BISAEhIAQEAIlICDiLAEsZRUCQkAICAEhIOLUMyAEhIAQEAJCoAQERJwlgKWsQkAICAEhIAREnHoGhIAQEAJCQAiUgICIswSwlFUICAEhIASEgIhTz4AQEAJCQAgIgRIQEHGWAJayCgEhIASEgBAQceoZEAJCQAgIASFQAgIizhLAUlYhIASEgBAQAiJOPQNCQAgIASEgBEpAQMRZAljKKgSEgBAQAkJAxKlnQAgIASEgBIRACQiIOEsAS1mFgBAQAkJACIg49QwIASEgBISAECgBARFnCWApqxAQAkJACAgBEaeeASEgBISAEBACJSAg4iwBLGUVAkJACAgBISDi1DMgBISAEBACQqAEBEScJYClrEJACAgBISAERJx6BoSAEBACQkAIlICAiLMEsJRVCAgBISAEhICIU8+AEBACQkAICIESEBBxlgCWsgoBISAEhIAQEHHqGRACQkAICAEhUAICIs4SwFJWISAEhIAQEAIiTj0DQkAICAEhIARKQEDEWQJYyioEKoXAp59+GmbNmhU++OCDsN1224U11lijUlWpXCEgBJYSARHnUgKoy4VAORC47777wg9/+MPw7rvvhokTJ4ZevXqVo1iVIQSEQAUQEHFWAFQVKQRKReDmm28O++yzj182evTocOyxx5ZahPILASFQJQREnFUCWtUIgeYQmDJlSujTp0/47LPPwvDhw8Npp53WXHadqxICn3zySXjttdfCqquuGlZfffWw3HLLValmVZNnBESceZaO2tZmEJgwYUI4+OCDQ4wxdO3aNRx11FHhK1/5Slh77bVD9+7dw7LLLttmsMjLjc6ePTtcf/31Yfr06aFDhw6hS5cu4ZBDDgkbb7xxXpqodmSEgIgzI+CXVO1///vfsPzyyy8pm87XCQIjR44MJ554YlhmmWX8jlZaaSX/veKKK4aBAweGk08+Oay22mp1crf5v42LLroonHnmmeHll18OvIsMXPjsvvvuYcyYMeFrX/ta/m9CLawYAiLOikFbesFoG9OmTQuTJ08ODz30UNh8881d43j66afDXnvtFfr37y9TUemw1sQV1157bTjooIMKbcUkiKctzwQkeswxx4QzzjijcF4/KofAI488Enr37h1eeOEFf9822mgjN9e+9957/v8pp5wSRowYUbkGqOT8I2AvplIOELC5rTh27NhoL2k0LSNaxxlXWGEF/22aZ9xqq63ivHnzctBSNaESCEyaNCmaRhOtx4j9+vWLt912W/zZz34WzVTrx9q3bx+ff/75SlStMhsgcN5550XT/P2z5557xieffDKa9hk7d+4ct95664islNo2AoxolXKAwNy5c/3F5IWl87T5rbj99ttHc0rw/zfddNM4Z86cHLRUTagEAjfeeKPLGdlDmmYejK+++mo89NBD/TiDp7PPPrsSVavMIgTeeuutaJp/AXNkwaD2o48+is8++2w0LTSaw1DRFfrZFhEQceZE6uPHj/cRLh3nLrvsEu+99964cOHCaHMp/hJ/9atfFXHmRFaVaMajjz5aGCTdcccdhSquu+66wnNh5trCcf2oDAJJDgxgsfzcc889hYogUD5KQkDEmYNn4P33349DhgxxguRlNceEaPNb3rK+ffv6cWmcORBUBZuwaNGiuNZaa7ms//73vxdqsvWdfowB1dChQwvH9aMyCDAdsskmm/hghamSu+66qzIVqdSaRkDEmQPxvfHGG/GAAw7wDnLNNdeMzzzzTKFVFn7Nj6NxMteiVJ8I2FrB+KUvfcllfdNNN/lNot3Ymk4/hgYk4qy87C3kYTz66KMdcwYrgwYNii+++GL829/+Fv/0pz/Fv/zlL/H111+vfENUQ64REHHmQDzvvPNO/PnPf+4vK1qHucAXWoUzAi8wo+DHH3+8cFw/6gsBNM5EnLvttps7oFxzzTVxiy22cPnjLHb++ednctNpfi+TyjOoFNzRNnnvbAlQ3GabbeK6664bV1llFXfWuuWWWzJolarMEwIizpxIA8cPXtSVV1654LX3n//8J2Ki5bgtSYi2VCUnra1+M95888149dVXLzaoaKwVaGm2aD3++c9/jjh61Epibo1OGs0SksQpjP+Tp60tTcpE03n77bejhf+L2267bbRlGG3CMYZn7cADD/T3jncvyYDfFhYxPvfcc7XyWKmdFUJAxFkhYEst1gJ7RzwneTktQombbnfddVcn0uRpu//++2fSeZZ6L+XOzxzw8ccfH9dff/1oEXWaJcQLL7wwfvnLX44bbLBBtKAC5W5Kxcpjbs12RCl01jwH6dOuXbt4xRVXVKzu5grGRMlgDvJgEGdrGZvLXjfn5s+f71YgBjDcu4XbixbZKeL9LgehuhFzq29EARCsd8pDMnIIJ5xwQiBiiRGlRykxqfoi+NQ+IgndfvvtwQg1HWoT32Y6C2bKDmBkpkvHgEXpjSWCCBBMAOy++93vBjOrBaLv5D19+OGH4YILLvBF99ZRB1sG4RFrevToEWxJSvjmN7+ZyX1cfPHFYfDgwQ6fTReExx57rE1EMOL5MW07PPzww75jDaEPbR2nByTh/VRq2wiIOHMkf5vrDMOGDfNtpcxM6x0l8TEJtUb0IDqucePGhS233DJHra58U84999xw3HHHeQD0zTbbzGOHEse1sWRaebAlHH4K0rn11ls98k5jefN27OOPP/Z7pF025+nNo8MmchBkmkUyDd7j5lJ3x44dA1F1CHbekmQmTW+7WQpakj2XeYjeREqD2Vw2Uo2qOgIizqpD3nyFaB73339/MFNRMGeEsMMOO/imxoTgQ8syc1lmnWjzLa/c2XPOOce1cToxYoTacg0PgN5Yjead7AMPzpmTTZg6dWrNEGdj95P1MSwgRx55pDeDZw/iZCDXVDKP8GBm5WDBAoI5s/nzShlmbm7qEh0XArWHQKuNvLqwYggQNca0D3fESPMpHEu/K1ZxTgvGcQqHGXu7PCBEc6HnmAcmHx+8U20gktO7qo1mMWec8GSO0zbabrThONQQ/ciCoLsjG16pzA0SQlLe4I1CpoM1jICcg2pYeG2l6SLO7CS9JOIkLKDNg8Zvf/vbEScmBjg4s0GaEC5LONqyN3h2klPNlURAxFlJdFV2WRAQcZYFxlYVUkycBOFIGjxrj4njuscee7g3MESZCJPf6X/I8/LLL29V3bpICOQVARFnXiWjdhUQYOF/MtWynrGlptqePXsWytCP1iFw2WWXFUy1G264ocdLhjD79OkTiXKFXBJRNvYNcY4ePbp1lesqIZBTBOQcZG+2UssRsPBjAS9JlsYUJws24Meacxwpzt/cb5yALMC9e5iyPynLUWbOnOlLTGytY3jwwQdDp06dGi1iv/32CxYAwc/hkDJgwIBgHX7AY9WivwSLAlNY6mMdfTBTo9fDuWotM6Aei8bjjja2TtCdv/BAXW+99fzD/dl89hecwKwPKbSR3yTKang83UdL8lCPEaC3gW8c0MDl3//+t8sAD+XZs2d7XTZv6fhZyLlggxdfLpPq9wxN/LEBjO8nStnU19LEM8Y93HnnnQGnOeri2bMt9tzpyKJs+flZs2YFnj/O8cExaeONNw62ljewhyYy5llYsGBBsJ1NvHrKNg062PrZxZZ8FbeN+nBGK8czXVyuftc+AiLOnMuQDpalKLYQPUyYMME7DzoFlqTQCUEykAq71NPx0qnQwZGa6lCLzzWXxwuxP3QgdEwPPPCAd0J4+rJMgs6V+jlvMT59k1+WTtAujjWXiuttmI9z1Mc3y3LMIcXL5P8OHTqEf/zjH/7d8Dr+T8tRUv2s4eTDtXSWDTtBcCM1HAj4wQr/oVOHpExrcyJFbnxYlkRK95CawT2kY/xOeRoeLzUPddIGrkN+JDCHZCCsVBfftLf4/1SXX9TIH/JSPs8L36UkyuYai+NbqJP/GWww0OGb589CVHo7kTNkylIeC1/oAwIGTODJEhoIn/wkyuZ9gVTT/TTWNgZao0aNCl27dm3stI61UQREnDkWPB3X73//e18YD5HQCZBSZ5uankbRHOezpM4sXVfKN50LJMM3JEMdiXRKKaeleVNnlr6pj98tXceZ8jdVX8IolU++dIzfHC/+n2PlSsV1Nldmqr+l+Zsrq6XnqLNhfakdlFGMS/HvpsovLqu4nOL8SyqnuIx0Hc95SpwvLiP9TvWl/1M+ruMcH441lTjHgKJ3797BgrsHi6DUVFYdb2MIiDhzLHBMjocddphrX8UvOaZHSAvtKXUKaAa2JMBH6EQ8YfQN0Vr4OX/hG2qB6brUOTBK5zcjcrS69u3bu6kOk9ymtn6PDoQPo3/WlzIST9owJi+InetSGWhTHCOhIZMwR1IenR7toyOizZjwqI92o1FgDkZjIC91ctx2kHGts6XrOMEL0+PAgQObXPPpjSr6Q2QitBMwQHNh7SztQbtHE3viiSf8PGU3lhhQIBvupSkNFpkQfcfmal1jaqwcIh/dfffdBe2uV69eHgUJzQo5ggtmSHCnLQyc0JyShkjZJJ6RpH3xfGDmJj/lvPLKK54/DcYatoN8yNf2hXV5pHtOzw35i383vD79T3up1/aYdZny/5ISdSELnheePZ4j2v/SSy85rjzT/E8QDJ4N2zXIsaJcnis0Ue6dSD88Y7SzJQn8uA75T58+3c28XEvUJqYM0FCVhAAIiDhz/Bz87ne/CxZY219mSIC5op122sk/vOR0ECnRydHBQDSQDKRKp0gHm8xvKW/DbzoqCIxOjU6DeSLqo1PCVEpHBRFAeBALnVMi7zR/hKl2nXXWKZhUaQ+dG2VDQiTaRZkco52QEtfRsVIf+amD+6DDS3mZ4zQHIS+7pRon9XXr1i3YptBLvH/yklIHmwgB0uG+U/sZDKR7+vyKxf9yT9xLsTa0eI7P/wND8jWVTj311HDmmWcW2sMACq0H+dA2ZAVe4JdSOkfHXyzvdC/pm/z8hpiQNfmbSpRJ1CZMlciMxLUk/i8u0w828oc8hx9+eLDt0fx5pcyWJNrFffJM8YzwvINbep74n8EV5xjMpfaBPffPvTGAWZIsittC2xKOvHuXXnqp4yPiLEZJvx0Be7CVcorAWWed5bvQm6CiaXPxvvvui0ZI0ToV/1jn4Bte880x60wK3/xO/xfna+p3KpNv8lgH4t+U0dg1nE950u9iGNMxvlNK+RuWV5w35Unf5LUOrLAu0IizWa9acw6iZ/dPjx49HK9Uf618//Wvf3WP1XQf06dPX6zpYFONRD0WP7eAJ4HOu3fvHo3MCseMsHwZSlPf3INNN5QcvCPJn+/0Sc9N+j99p+MNvzlfSkrl8c1OPDZg8vs04oymoZdSlPLWOQKMGpVyigBu/2Ye8peXNXRtdSNrC7RdGECYqbZZ4qyHyEFsmGwWA5c7hNSQOKv5uI4fP76wFMjMptG8naNp8XHnnXcuDGZMq2tySQrEadpzNZtclrrYsDrtj8qWaiLOssBaN4WIOHMsSnOzj2YSLRDnnDlzctzayjXN5gTbFHGOGDGiQEoQp8XmrRy4SyiZbcXMNO/PYMeOHT3kHlYJW6ISTzzxRA+BmDTjhgRK2zk3ZsyYJdSSv9MQp3kCe/tFnPmTT9YtEnFmLYFm6r/qqqsKJjtG+22VONnk2ebzvBMr1VRrc5LNIJzPUyeddFKBOCGeLIkTs3EiRojT5hkdNMyiYItsBg0a5Ht2pnzJbMv/NkfsMWzziXTTrWIj9KRxylTbNE5t9YyIM8eSt8XnhZcXU21bJc7WapwEHGdOuNaSOUMVNrXOWuO88sorC8TJ4K1hkHfmA83pK44dO9bD7yXtNGmbbChuAR1qTQRRGmfNiayqDRZxVhXu0iozb0bfaYKRu4jzc3PhkuY4bVuxQkdvSyC+0NGXJoFscjOnmRxwsiZO2xKsgGdjxJkQMg/uaF7I7gjEs5q0T7Q1W0aSstXMNxqnTLU1I66qN1TEWXXIW16hRQoqePZhJrN1hC2/uI5yttRUa0sToq15LHTamHXnzp1bc0hMmTKlYGmAgLI01RInOJFgsam2KVDR8HFqGzJkSOzfv3+0Nakle9Q2VXY1j/PuyVRbTcRrqy4RZ47lZSHtoq2h9I7LFuHHBQsW5Li1lWsaxMlcWdK8LQBAo5XRae+zzz6Fjt5CA0Zb7N9o3jwfxAu12OSZJXFOnDixMN+anIOWhB3OQwxibK2oL4laUv48nmcP0aQ5yzkojxLKtk0izmzxb7Z21m0m4txxxx19LqnZC+r0JOSX9ntkpw3WljaV0MrZCgtNCfxKXcvXVLnVPI4XqgWA8AFA1qZaiwtccMyCQGrR2ao1srvlllsKS8FEnK1BsL6vEXHmWL50/DhXJE2rra7jhPxYR2e7XrgW05zIyIvmyQfPz1pMN910U8FEj+xZN5lVQru3qEXx61//ehw3blxWzah6vfKqrTrkNVWhQu5Zz5TXxHZK5uzicUXNMSPY3FfYYost8trcirfL3qxCaLWKV5ZhBaeddlog7J4Rv4dOZGccQi1mkcCcXUUI0UfoxeIwf1m0p1p1EubxqKOO8rB/2223Xbj11lt9R5Zq1a968o2AiDPH8rGoLf7yEqOzS5cuTpw2z5TjFqtp5UDgkksuCUOHDnWyIqg9nbbNt5Wj6FaX0VYGLQkgm1cPtll3ML8C35Fn8uTJHjQ+ndd320ZAxJlj+c+YMSMceOCBvvMFu0ugcTbcTzLHzVfTWomAxSgOw4YN88Dm7HQCcWrA1EowW3mZeQaHfv36+U4y7CVqc57B4vS2sjRdVm8IiDhzLFE2it577719hxK2toI42bpLqb4ROPnkk8Ppp5/uO3WIOLORNVu7WUSkwk40aJzf+c53smmMas0dAiLO3Inkfw2COG15he+LyRwXxMlWSkr1jQDzm8xzMsfJnPbUqVOlcVZZ5BDn4MGDfSs8tpWDOM2zu8qtUHV5RUDEmVfJWLvMq9aJkz0xv/GNbzhx4qChVN8I/Otf//L5NZxypHFmI2sLuefEyZ6gDFYnTZokjTMbUeSyVhFnLsXyeaP++c9/hr59+/o8iy0HcOJk13ul+kbAAggEnIKSY8q0adMydw6qb8S/eHe2H6c75rGpOpuOM8eJn4GSEAABEWeOnwML8h4GDBgQeHmZ26QDbcvLUXIsqrI2DQ/WTp06hfnz54d27doFlqNYzNey1qHCmkdg5MiRYfjw4YFBzHLLLRduuOEGtwI0f5XOthUERJw5lnSxqZb5FeZZmG9Rqn8EWH4CcWKqZY6TdbxK1UPAAiCEI444wp2DeOfQOOUcVD38816TiDPHEip2Dvre977nplrbLDjHLVbTyoUAGue8efPcwsBylE022aRcRaucFiDAOk482hm8yDmoBYC1sSwizhwLvJg4iV6CV2379u1z3GI1rVwIFBOnvGrLhWrLy7H4yGG33XYLFvtYxNly2NpMThFnjkVdbKq1IO9OnCzGVqp/BIpNtQqAUH15L1y4MPTo0SM89dRTTpwy1VZfBnmuUcSZY+kUEydzXGgezHkp1T8CIs5sZfzaa6+5xonJVnOc2coij7WLOPMolf9vU7GpFtMdptrOnTvnuMVqWrkQkKm2XEi2rhy8afErsL1QZaptHYR1fZWIM8fiZSH8vvvu6+s411lnHY9Z2q1btxy3WE0rFwLSOMuFZOvKefvtt0OvXr3CvffeG9Zcc033aJdXbeuwrMerRJw5liou8cTL5CXeaKON3FRLIASl+kdAxJm9jAl3efPNN4s4sxdF7log4sydSP7XoGJTreY4/4dLW/glU222Un7vvfdc4yR6l5ajZCuLPNYu4syjVP6/TcXOQWwrhXOQIgflWGBlbJo0zjKC2YqiiA+96667uletYtW2AsA6v0TEmWMBFxOnlqPkWFBlbtpnn33mIfeIVavdUcoMbguLw6t2jz32CA8//LBMtS3ErC1lE3HmWNrFptqtt97aHRQU5D3HAitT0x577LHQs2dP34cVzZN1nAR9V6oeAh9//LHvTAT2MtVWD/daqUnEmWNJPfDAAx5Y+qWXXgrrr7++d6BsL6ZU3wjMmTPH1xBiLiRS1G233Ra22Wab+r7pnN0d2BM5CFmIOHMmnBw0R8SZAyE01QT2BBw4cKB71S6zzDK+jvP73/9+U9l1vE4QmDVrVthzzz0D5kLW7aL1KMh7dYULcRI56Mknn5SptrrQ10RtIs4ciunTTz8NixYtCgcffLBvKUUT2Wpqv/3282MszF555ZUDZKpUfwjMmDHDZc0zoDnObOQrjTMb3GulVhFnjiTFvMrjjz8errrqKt97k9EuJAppQpLsC7j66qsHgiBgRoJIN9tsMxFojmRYjqbMnDnTZfv666+HDTfc0DVOrd8tB7ItL6OYOPGqJVYtW/spCQEQEHHm5Dl48cUXwyWXXBIuu+yy8Morr/gGunhXNpYg0OWXX96DIhx77LFuzl1hhRUay6pjNYjA7bffHg444ADfC5IB06hRo8Jxxx1Xg3dSu00uNtUqVm3tyrFSLRdxVgrZEsq95557vGO8//77A1onGiaJMHtolWiZdKBEECKSCcRK4thKK60UDj300HDMMcfI89JRqa0/77//frjuuusC2uUHH3zgc2pPP/10wKOaeKkkPKl33nlntzQgcxKDqi5dugTNeTscZf9TrHHKOajs8NZ8gSLOjEX46quv+oa5rNmkM0Sb7GjBDugQIUSWI6y44oreSkiVtX0sVzjnnHMCXrckzqOhoK1CpEq1gQBEOXr06DBmzJjw0UcfuVn+k08+8eeAZyGRJAMpnotVVlmlcIzzECrX/+AHP6iNG66hVrIfJ85B8qqtIaFVs6n2UiplhIBpFPGEE06Iyy67bLRO0r8HDx4cTeOI7777brT5zS+0jGNGoNEWZkdboO3X2fMSzVQbrQP+Qn4dyC8CNmiKffr0wbxQ+PAcpP/5XfxJx9P3aqutFidMmJDfG6zhlr3wwgvR1s66LHg/r7zyyhq+GzW93AhI47ReKItkxOga4m9+8xv3oKUN1omGSy+9NKy33noFzaKptqFxPPPMM27KfeSRRzwbmurpp58efvKTnzR1mY7nCIF33nknMEeNzI0gCy2zl9x/Fx/jAMfTMX6zWwfbXml+uwBdST+ee+658NBDDzmuaP9gisWG37Nnzw4XX3yxT49QKBYd3isj0SbrwFEP83mSUZMZdaL2EbCHRSkDBGxvzWhLSnxEy7eZZeP8+fNLaomRZ7Stx+JJJ53k5dgLG20LpGhzpSWVo8zZIWCe03HLLbcsyA8ZWq+y2P8cS8fTd/fu3aNteZVdw+ugZrT1VVddtdGPTX8U5IA8sOg0lTcd/+UvfxmxIinVPwLSODMY+6Bp2EsW/vjHP3rtjFRvvPHG0LVrVx+tok3ao+fnrKNsdpRL3jfffNP37bzzzjv9mhEjRgQ0WaX8I4Cc2T7OTPSFQBfFsi++g3R8jTXWCNdff33Yfffdm302iq/V7y8igH8B7yDzmLxnxQnNEietDTbYIGDRYbeUhnlSft5BNNXzzz/frUZN5Uv59V37CIg4M5Dh3Llzw1577eUelFTPvn90hDiGEFR63LhxgeUpvLzrrrtu6NevXyDUHt61xYk1njiN0KH+9re/Daeccoqfxqlh+vTpxVn1O8cI4PSFmZ7Qesg8EWTDDpjjfA4//HB3KDJNJ8d3lf+mgSVOWXwaYk3rOY4Z/MMPP3SHrebuCLnhBZ8c+ZrLq3N1gIA9PEpVRgDHHtuY2k1BRnzx17/+tTsDmZYY7eWLmIlsnaZ/MBFhfrXQe3HevHne0oULF8YLLrgg2nxmtDkaP3bNNdd4efZIRvPEjRbftsp3peqWBoFp06ZF01oWcwayztgdxtI3srWlEdEGRUtTla4VAkJgKRGQxpnB4Mc6ydC7d29ffmCekR6VBHPrj3/8Yx/d0iRGuqzjM/l6C/mfQN/EMGVz3bvvvtvPbb755oEF8zY/6ktY3njjDQ8Iz9pARTrJQLitrBJrA5qkeW8WSijWgtJzcNhhh7nTCgEwlISAEMgGARFnBrjjCck6TTpL1uZdffXVgfmWQYMGhXbt2rkH309/+lPfRJd1eoThI2EOSoSKmZbE9Zh+WUhPmXjaMi+D6XennXbyPPpTGwhgXj/ooIM8wAWkWUyczKOxbvPaa6+VXGtDnGplHSMg4sxAuI8++qgvWn/++ed9TuS8887zTXPRHIlJyt6bzF/RWT7xxBPBTLmuYb711lveWpxDiGFqnpUePGHvvff2oAjMkz377LPSODOQaTmqxFrA8pRxNsddTJwNtU3mtZWEgBDIDgERZwbYP/XUU06caId0kEcffXQ499xz3XSLVlncMUKeePSxtVRy+PnWt77lziQ4C6GBYrYjzi0aK50spIqjiS1zyODuVOXSIIB3dd++fV2OSeNEplgWbF7bnxv2Zk3nlqYuXSsEhEDrEBBxtg63pbqK4AcsR7nooou8nF122SVMnDjRAx80VTDznZh2SRAlhJkSMWyPOOKIYA5Cfmjffff18iBhpXwigKl90qRJBe9pLAXsv4nZPS0rSuQIcSJL5rPXXnttN9kyaOpoAS84Rsg95sqVSkMA/AmC0PA9YdqDwS3ezgw+kQM7FaX3r2EtyKdDhw4eLxr5KNU/AiLOjGR8xRVXhP79+3vtzEkSZ7a1MUcJDm/h93wdINoqDiY4GinlFwELXuBrbxlE0TGz5IEOGAsDpMqxRJzcBefSsfRNh4/2ecMNN4Rtt902vzebw5YRHYh1sKzRLLbwgC2DVEiTlGI/szSluYQsjjzyyHDGGWcUrmkuv87VNgIizozkx0gXoiRgOy8dRAfhNRz9Lql57JTCDip33XWXZ+3UqVNgtxXWfyrlFwGIk7lpgmGQktzRalKnnYgT0mwqYXnAhC8P6qYQavw4RMiG8GyuUJzAHLwh1uYS+fBDYMCTHPWw9LCXrtbXNodcfZwTcWYkR15O4sqeeuqp/uLZWs2Ak9AhhxxSUovOPvvs8Ktf/aqwBdXIkSPD8ccfv5i2UlKBylwVBNBqGOAQ8CKRJs/EokWLPH4qGyfTedNBs2k5miXni8kUksXTdtiwYaF9+/ZVaXc9VfLggw8GBjANE1o/hIpnOhYBcMdpL5ltIUpbh+2byGNiZykYViOiPxH9S6n+ERBxZihjvCiHDh1aWLtH5BH21fzFL34RINLmEpGFWKrCCJelLCTKsri1vqSluWt1Lh8I0AEns2xqEZ02hIoVgT06IUo0ym7duqUsi31DupgTE6EudlL/NItAMos3zARR8m72sAhchOMjXXjhhYsNasGdD2Xw4TdRg/hWagMI2EOilCEC5gwSbZeLQtQftooyR59oS1UabZV1pnHWrFlx//339whD9oj6tTZfE23z3Uav0cHaQsCIM5qpvfBMGHHW1g3UQWt5l8zxqiAD28GmDu5Kt1AuBKRxZjw4MkG6aQ5tcebMmd4aNAi89JgzwQSU5lDQKjAfYRpCy8TcxxzXVltt5SPiHXbYQZpHxvIsR/XMvyFLtrwiETADc61S9RBA2+/Zs6dvL0atLPcispOSEAABEWcOngNMPbi/DxkyxMmTjhOShBQbmn5wHCE/iX07LYatm5AsPu1i3oE5uC01YSkQMItCIGwiz8Edd9wh4lwKLFtzKQNaZMBAlcSeqQMGDGhNUbqmDhEQceZEqLyoL7/8shPn5Zdf7vFn0/wX5+hA+SbZ/p3hRz/6kS9nIawecyucV6oPBFjLydpeC+bvNySNMxu5Ms+ciFMaZzYyyGutIs6cSQbzK556ePyNHz8+TJ48uWCqZSuyXr16ufm2hzku4ExUvAYtZ7ei5rQSAdvZJmy//fYeHIEiRJytBHIpLxNxLiWAdXy5iDOHwkWzRNs866yzfI9NzLPMeRJdiB1SMN9qd4wcCq5MTUL+7NFKZBuZassEaiuKSeZyLpWpthUA1vElIs4cC5c1mSNGjPAF8ZtuuqnHq+3cuXOOW6ymlQsB4g6PHTtWxFkuQFtRjoizFaC1kUtEnDkW9KhRo8Lw4cM9RibOP1OnTg0izhwLrIxNIxIQ+66SWMeJaV6puggUE6fmOKuLfd5rE3HmWEIEQmBHDEx3a621lmucO+64Y45brKaVCwEsDAsWLPDipkyZ4huYl6tsldMyBFgCNGPGDM/8hz/8wWPRtuxK5ap3BP4PAAD//6DH/9wAACYLSURBVO1dCZQVxdW+KLuyLwKK7IIIKmpCcCFoErckKKKiRkAR1MgqKAgHRYIoEI8kB40SFYEkGshRiFEQVECCIRoFIagckUWQRRQEF0RQ+7/fzV99ep5vmNczr94087465013V9+quvVVT319b9dSLtAgDIlEYNy4cYLfwYMHpXHjxjJ//nw56aSTEqkrlcouAs2bN5eNGzdKuXLl5KWXXpLzzjsvuwUwtyIRuOSSS+TZZ581uUcffVT69u1bZBoK5AcC5UicyW3oSZMmyZ133ikHDhyQZs2aGXG2bt06uQpTs6wh0KJFC9mwYYMR58svvyznnntu1vJmRpkh0L17d3nmmWdM+LHHHpMbbrghs4SUKvMIkDgT3MQTJ06Uu+66y4gTFsi8efOExJngBsuiaiTOLIJZzKwuv/xyefrppy01ibOYIJbRZCTOBDfs1KlTZejQobJv3z4hcSa4oTyoRuL0AGrMLKPEOXjwYLn33nulatWqMXOheFlEgMSZ4FZdtmyZ4J/3o48+InEmuJ18qEbi9IFqvDyjxDl58mQZNGiQHHHEEfEyoXSZRIDEmeBm/c9//iMYoLB9+3YSZ4LbyYdqJE4fqMbLs1u3bjJ37lxLRFdtPOzKujSJM8Et/Prrrxtx7tixg4ODEtxOPlRzo2qR96JFizg4yAfIReR5yy23CD6XfPfdd8JRtUWAlWe3SZwJbnASZ4Ibx7NqJE7PAGeQfb9+/eTxxx8XzNgjcWYAWB6JkDgT3NgkzgQ3jmfVSJyeAc4g+8suu0zmzJljkiTODADLIxESZ4Ibm984E9w4nlXjN07PAGeQfXRwEL9xZgBYHomQOBPc2LQ4E9w4nlWjxekZ4Ayyjy6AMG3aNLn++uszSEWRfECAxJngViZxJrhxPKtG4vQMcAbZR4lz2LBhtvxllSpVMkhJkbKOAIkzwS1MV22CG8ezanTVegY4g+yjrlosfjBixAjO48wAt3wQIXEmuJVpcSa4cTyrFrU4Fy9eLF26dPFcIrNPRSBqcY4dO1ZGjx5N4kwFKU+vSZwJbnhanAluHM+qRS3O5557Ti6++GLPJTL7VASiFieWvrzvvvukYsWKqWK8zkMESJwJbnRanAluHM+qRS3Ov/3tb7b0oucimX0KAlGLc/z48TJq1KgUCV7mKwIkzgS3PC3OBDeOZ9WcxYliZs6cKT179vRcIrNPRSBqcd5///224QL2R2UgAiTOBD8DJM4EN45n1aLE+dvf/lZuu+02zyUy+1QEosTZp08f+d3vfifVqlVLFeN1HiJA4kxwo5M4E9w4nlWLEiesHUyHYMgtAldeeaXATY7Qq1cvefDBB0mcuW2CxJZG4kxs04ikEufChQsFHSpD2Ubgiy++kPbt28umTZusolhsHNZOhQoVynbFE1S7nTt32gYL//73v00rEmeCGicBqpA4E9AIhamwYsUK+eUvfynbtm2TSpUqyY033ij9+/e3t164jD777DP59NNPpXHjxkUOk//yyy/l4MGD8u2338qBAwekYcOGgl1XatSoIdFJ3fv375e1a9fajhBOLyxyjW87OCIU9Z3Hybv06Y6pMtCrfv36Vg90WigDv127dtnmwZ9//rmccMIJVucXX3xRvvrqK2nSpImceuqp8s0331gRkAcmb731lpxxxhmCfFDv3bt3y9FHH211Rr1RVqZ1OPLII2XlypWyd+9e6dy5c4hBap3eeOMNqVy5snz88cdy1FFHmTxGYJYvX950atOmjW0Nh/0cly9fLieeeKLFr1q1yurcoEEDu//mm28K4ubPn2/thXJq1qwpHTt2lFNOOSW1WC/XaBu8oAH7WrVqCYh8z549htsxxxxj2OMaGAJLtAsGM61fv15at25teuOlz8lAyTp16hgmrq28KJ6FTIE//qfwf4D6fP311/a/gG/MDz30EC3OLGBcFrIgcSa4Fd977z3rrLGRNQI64nr16pnlAbIDeeAfvHr16iHRRMkN5+jYECCHa2yRhM4LhAkyQp5uiD3u4x46zNIIIBl0xiB4F6AT4nB0mwjjvrtGGpy7gHPUGfGoKwKOyAPpcYwbkB/yRZ6FBYcz5Jy+ThZxIGBXPjB2dXFEgmv8kA9+URnoj/T4Of2RJ4IrKxofPc9EJirv8kNZKBc6oaxoecjTYYtzVzcnjzjUISrj8sG91IC8nQ6p9wq7ziRNXBnIQ28cEaL6DxkyxKaj4OWIgQiQOBP8DMDyGDhwoDh3EVRN1xm4f3TX6bkqoUM77rjjzFp1MrgHOVidiENHEL3n0ubyiE61UaNG1gGj44IljDd9WFqwEF0H5vSE/vjBooEliPvHHnvs91yZIFjkDYsdLwp4wcg0oCzkjzz27dtnlgZeVrZs2WJWGPJDPCwpWCiwNIE3PAN169b9HuaZlgt9N2/eLKtXrw4taejdqVOnnLcVyBv1xRF4w9qsWrWqfPjhh/YSgbbByxueJbQDsIKcC6gL3Muw9mvXrm2kBOsVL2rA0rWnk0/qEfpi1SB4MRiIABAgcSb4OQAhoBN9++23i6UlOi64cdF5RTspdG7oDBGXeq9YBZUwEfQEcUIv6AQXKyxkkBNchYUFyMA1C7KFqzPaaSONq/Mnn3xipAlSixNAjCBwlAP3qyMNEDp0A2kgDvdBnLBI0cmCJFJ1iVMu9AVRgvAR8I1z0qRJJcozTvlOFvhBB+CLAOJE/eABQV3xggCyxA/tAKyi9Ua7Qh7ECZwQIINnDvcOp4AXzMNN58MJ38NNVxJnwlsMnZezuIqjKjqyaGfm8nCkku6ek8nlMapHHN0ykYVMNP+49Yqmj55H83F6IK4kZSE98mrZsqVs2LABl1Kao2rT1cvFRevp4kzhlD9RuZRbvCQChyUCJM7DstmodFlHIDodZeLEiTJ8+PCyXmXWjwgcNgiQOA+bpqKi+YRAdMm9CRMm2De2fKo/60oEkowAiTPJrUPd8hYBWpx52/Ss+GGAAInzMGgkqphfCOCbNr5xbty40SqOBcbvuOMODk7Jr8eAtU0wAiTOBDcOVTu8EcBI01dffdWmsmBKydatW22gF0akNmvWzKavYHrGBx98EI4Axj1MP5o8ebIt3gAEsHhCjx49pEOHDkUCgkE6GPGLlYcw6pWBCBCB7CNA4sw+psyRCNgUjscee8zWmMWUDEzHwLxQFzC1A/M+MeUF80CjAdM/olM7MCoVUzggn0nAtIlf/OIXRr6YpsNABIhAdhEgcWYXT+ZGBAwBkB8G9YwePdquQX5uWgZcse4cFqKbH4hzN60jKh+NR2aQd3LuGM0DMliSEcsAtmrVCpcMRIAIZBEBEmcWwWRWRCCKABZymDVrljzyyCPyzjvvGFmC6LC+LtZ0XbNmjS1uAZJEPFYhwhq2WAoR90CwiMeCC3DVwmrFOrfRlaROPvlku494LESAgPxGjhwpd999t1mqUZ14TgSIQBYQ0H9MBiJABDwhoG7Y4JprrsHip4ESWnD22WcHuoh+gPhu3bpZPO7pYKBgwYIFgS5IHwwdOjRQC9Lu6YpFgbp8AyVTu9evX78wzfHHHx88++yzgX47DZo2bRrGX3TRRRbnqUrMlgjkPQJ4o2UgAkTAEwJTp04N1GI0UtNdRAK1DAO1JAPdMizQ3V0sHqQ3b968QJdBDHTd1+DCCy+0eB0oFAwePNjioN66desCXXvY7oFQ//SnPwVqZQZLliwJdPF/i9eBQWEZnqrEbIlA3iNA4sz7R4AA+EIAliXIEhYlrEOQo377NMvxiiuuMAtUR76GpAk9Zs+eHYD8kKZLly6h5ajr4QZ9+/a1NLh30003GaHqIuxmxcKaVVduMGbMGCNgX3VivkSACOj3E4JABIiAHwTgRgWhwe365JNPhoQGstOdRYwc4XqF1ejCPffcY/G6UHzwwgsvmHWKe7rQf6Aja+2efh8N9JupJZkxY0ago20t/vTTTzdSdnnxSASIgB8EODhIX98ZiIAPBDCPU121NjXl5ptvtkE8KAeDfrC/4/bt220Bd2zI7cJrr71m97Bpea9evcIpKNhgWb+J2mAhrF171VVX2fmoUaNs5xRs8aXkLGqluqx4JAJEwBMCJE5PwDJbIgAEsFclAuZyRgO2IgOBYl9KjIJ1AdNYsF0ZtkDD3E0XEL9ixQrbzqtdu3bhPbU4ZcqUKQKiveGGG0Kidel4JAJEIPsIkDizjylzJAJeEADRIrg5mzgHAe/atUvq168fkiniGYgAEfCHAInTH7bMmQjkBAH9ilPAas1JoSyECOQxAiTOPG58Vp0IEAEiQATiI0DijI8ZUxABIkAEiEAeI0DizOPGZ9WJABEgAkQgPgIkzviYMQURIAJEgAjkMQIkzjxufFadCBABIkAE4iNA4oyPGVMQASJABIhAHiNA4szjxmfViQARIAJEID4CJM74mDEFESACRIAI5DECJM48bnxWnQgQASJABOIjQOKMjxlTEAEiQASIQB4jQOLM48Zn1YkAESACRCA+AiTO+JgxBREgAkSACOQxAiTOPG58Vp0IEAEiQATiI0DijI8ZUxABIkAEiEAeI0DizOPGZ9WJABEgAkQgPgIkzviYeU3x7bffysyZM+Uf//iHjB07Vtq3b1+gvJEjR8p///tfufbaa+Wqq64qcI8XRIAIEAEi4B8BEqd/jGOV8N5778m5554rO3fuNOIcMWKEHHnkkZbHm2++KZdeeqns2LFDzjrrLJk7d67UrFmz0PwPHDgge/fuFWx0fMQRR5jcd999Z/kdddRRgvN9+/ZJ5cqVpXz58oXmE73xzTffWLqKFSuG0cgf107P8Iank/379wt+qJ8LqF/VqlWtnl9//bXpU65cOXe7WEfUq0KFChljU6xC0iQ6ePCgAOcopnihcvhCL4SS1i9N0YwiAkQgAwRInBmAlEuRpUuXynnnnSfoKGFd/uY3v7GOGwTYvXt3WbRokREhzp966inr2NPpB/K4//77Zfbs2ZYXSAUd7ZdffinVq1eXjh07yldffSUrV66UNm3aGAG7DjldfohDeugBsm3YsKHpgXika9u2rfTp00cqVaqEqKyHzz//XF577TVZu3atvP/++4IXjC1btoTloH4dOnSwlwDca9asWUg0oVDME7xY1K1bV7p27SqnnXZazNTxxVevXm11W7VqlXzyySfSuHFjwxUvUbhu1aqVPQvr16+3tqhRo4bUqlUrbIfUEtFeaGPUA/ikBqTv3Llzoc9QqjyviQAR+B8CJM6EPQkgzp/85CdmcYA4x40bZwQA67Jnz57yxRdfSNOmTeWZZ54xokinPjrKJ598Um6++WbrOEFszjpx57Awce4sGXc/XX7ROKTBz1mw7h6s1r///e/SpUsXF5XV44IFC+zFAfqifu4IvV2dYJHh2tUpGwogvyZNmshDDz0kP/3pT7ORZdo8XnjhBRkwYIBs377d9HcYA+dUzFF/BOiGX1HB4ZMqB2v6nnvusXJT7/GaCBCBQyCg/1QMCUJgyZIlgRIAfHGBEmegnWSwbdu24IILLrA4Jbxg8uTJgZJDoVqrm8/SIg/tWO2nlknQokWLoF69epYP7rkf8sR9XKvFGJx99tmBkkV438mlOyJ/F/+Xv/ylUJ1KeuOJJ56wclx9XJk4NmrUyPRVC8rO1doM1IUd4FqJx9KpxRWoezrUNZq+sHNXFo7Dhw8vaRUOmX7IkCFhWxWmj494fRk7pF68SQSIwPcRoMWpvVGSwiuvvGIWJ6wm7azNVTthwgQZP3684NsXXKLLli0zF11hen/88cdy9dVXy8svv2yW4bBhw+RXv/qVuWM//fRTs2r0UQiT41saXH74dlqlShVz3UJu06ZNaS0axEP2ueeekzVr1pheyAyuY18DlubPny8XX3yx6QxLqUePHmZxt2vXzlyacBHDnVmtWjVzSwID4PXZZ5+ZBXf00UcbFrhOF5QczbKDu7SpWvSw6m6//XbRlxYTv/XWW+WBBx5IlzQrcfiWPWnSJMMbbfOzn/3sewPDEA89EVz7Ob2j8dFzyDoZWOS7d++WOXPmCNoXoXfv3jJ9+nQ75x8iQAQyRED/ARkShIASZwALUJsv0AFAwR/+8IdAv0maNQKr6cEHHyxS27ffftvy0A4zUFIMXnzxRbNQYb3CUoVFmvqLxqOA6HWqrH4/DXRwTvCvf/0raN68eWjF/fWvfy1St+IKvPTSS1YO6gQ83n333QB6QDfUy9Uten6oOqTWyV0jTyXc4KOPPjL80Q4oU18+iqt6RunUFW/WsbOQ1XUb6PfJrP/0+3Sg38fDNrvkkksO6b3ISHkKEYE8QwBvrgwJQiDqqoXLFu5FdNzowK+//vpAB/cUqa1agWHHqNZZANLxEd544w1z/0I3/NTi9FGM5Qnyd+XoyGIjFG+FacZqvQb6vTYsc+jQoT6LC55//vkCrtoNGzZ4K0+tzLBeIFG8NDAQASKQOQIkzsyxyokkiNNZHY4wQRj4Zqeu14x0KOvE6ft7I0CGRT1w4MCQYHwT5+OPP25luTbfuHFjRm1dHKFevXqF9dKR0MXJgmmIQF4jQOJMWPPD0oAr0llXOMJ1e/nllwc6ojYjbXWBhDA9rNYndGCNjwD3YnSw0bRp03wUY3nqiN2wTieccEKgczi9lYWMYdmDVFw7wKXpM/z6178Oy4J73Sdx6vfvsCz9Ju2zWsybCJRJBEicCWtWfGNDZ4YO21kfGHGZiYvWVSVKnHDVLly40N3K6lHnVQYYwerIRafAZDX/aGZRV+2pp56aE+KEa9zVbfDgwVF1sn6u04vC9j7nnHOCXbt2Zb0Ml2HU4rzuuutcNI9EgAhkiACJM0OgciUGSwqdmeuwTzzxxEAnwMcqXhcAsKkYyMPnN87NmzcHp5xySqhrrr5x6mIE3olTR9+GLzDA0berVpdYDIlTV44KdPRrrDaPIxwlTrwcMBABIhAPARJnPLy8S2NEp/u2ptMiijWwRyfRBz/60Y+M0OD2y/TbaNzKYQQrOnlH8rkYVYuyTj/9dO/EiRG5Y8aMsbrB8vc9qhbE6b5t68pRJM64DyPliUAOESBx5hDsTIuCC/SOO+4IFi9eXKwRjzrH0hYx8G1xoj7RkadlyeLESFNHnGXZ4sT3TrwAMRABIpA5AiTOzLHKmSSsHczhK+40ARAn5oDmgjh//OMfhxZnrogzF984Yflj5SZgiJ/vkbyl5ao988wzA11/OGfPNgsiAmUBARJnWWjFlDpELU6frloUGyXOXLlqdS1fW6QgpdpZvdRF5QNdbclIE67aK664Iqv5p2ZWWq7aTp06kThTG4PXRKAIBEicRQB0ON7OpcVZGq7aW265xbt7MXUeZy6I042izuU3TnwLp8V5OP6XU+fSRIDEWZroeyo7l8QZtThz5arFdA24Un0GuMnvuuuu0FWby1G1IDNda9db9aKjarF5QHE/CXhTkBkTgYQjQOJMeAMVR72y7qrNxXSUKHHmclQtRtZiwQufCyBEiRPWLaxrBiJABDJHgMSZOVY5k4Q1VZLOLJfEGXXV5uobZy6mo5QmcYKofa5Ve+2114aWNKzbPXv25OzZZkFEoCwgQOJMUCti0v19990X/PznPw/OP//84Lbbbou9+AGqEyVOnwsgoKwocfp01brdUTDCNVcW55133hkSjO95nLpFW4FF3n1ZnJh60rVr17BeTXTf1bVr16IpGYgAEcgQARJnhkD5FsOKQf379w90P0xz1WGNWYyIxfe8d955J1bxWNEH67mCZJAH5oP6Crn6xonNu93UEBCn7+9yaA/dIzMsE/MdfX1XRb5Ycg9uWvxgcWKhfldHTE/CUozYEqykP7ycXXTRRVYvlIPn7NFHH7UlHeHlcFu1RZ8X6Bct1+kFEi5s2hTwi6Yp7BxlFibrC+9o3XhOBIqDADey1t44CQEbWKslYBsva+eJFxpTC+cXXnihYDNr7ahsw2ldt9buY/Np7fxMDvLqcrNNnLUTFmxejTjtGEWtWNscu0aNGqLblIXySAuZaB7uPIqJk8E9bBaNIzaMXrFihZXz/vvvm3jfvn3lpptuErVy7RoySKsdrW2irR2hbaCsRBCW6cpBPaGrdqLfu6dTQ6yc119/3e7VrVtXHn74YWnZsqVLnvaonbJtRN2oUSOpXLmyyWzdulW2bNlieqVNpJHQBRs9K1mL7stpZdapU0duvPFGaaqbXEP/bAXUWd2ytjm57m9q2aKddX6lqOchbO8PPvgg1AVCwBUBbeHaB9ep51EZ/XYqqP/y5cvDOqCsY445Rn74wx8KcIIM8D3uuOOs3aCfWr/2Q72Rvy6zKA0aNBAlQ9HFOqRVq1ahPMpDGn3Zs7Jc+TimBpRdu3ZtwSbjqB/SuYB7+vIneKZ0PWQXzSMRSAQCJM5ENIPIzJkzpXfv3qZNtDNERwUiQucGImjfvr11/OhYTjrppLDjhJy63KRhw4by1ltvCcgGAXmBNNAhoiNCh4i0roN1R8hGz3HtgotHx7Zy5UrTR1181gFDJ9zHD3o6Yka56PDQ2aoVI61btxYQvm6yLWqlWNaQcUEtY1Fr28g/Go/7yANpobcLkEW9UG40OF2RB+RBxMgb1/hBl2g+0bTRc+QDWRdwXalSJSNVF5etI/TBy4XTC2UBa7SZe4nCPXe/JOUib+DpMMY1AspyGOGIcl1AuUjjAnRzeiEe51F5yCE+E31dmelkUQ6IUzdvd0XzSAQSgQCJMxHNIDJlyhQZNGhQ2AGhQ3OdW7RTQWfirnEeDa4TwxFpXR6uc0zXwUXTZ3KOvBGQlyvPpUM5riwngyPioCuOLr1LEz06naNx0XPXOaeWE5XJ9nkuyyyNstyzlG3cspUfXianT5+ereyYDxHICgIkzqzAWPJMdOsv0T0fzapEBwpyiBJJ1apVzSpwJYGA4PqMyuAcVhhcX87idPLuCKsJ7rFt27aFxOzuwYpDRxq1tNy9wo5w1zkyhMXprNvjjz/e9IU7GXVJDa5+qfHpriG7bt06c+ehjrpfqZxxxhnhS0Y0jcsX9XDWL6xVBNSvQ4cO5mY+FGGgDGAwZ84cs7CRFq5JuL9dXRGXrYD21r1NzYJH2dBt1KhR0r17d9EF+02Xpuoi1u+TJtOmTRsBvtBF53uaex7ehubNm4suZmDuXbiWgQWeA7jU4TbHue60I7o/qx2hf/369UV3SBHdV9VkUD5eciAHLwHK/PDDD0WXcDTc9fu5vPvuu2mxLwoP6AM9dMcf0R18zB0ObwA8E6iH7jdrXhS4/nGOZ0e/x1pdi8qb94lALhEgceYS7UOUhQ7pyiuvtG9GUTF0qro/p3WicNPiGp0bvouh83FWJzolnOv0Avue6MgPsgi4jwAZkCcID/cQ745w1+E6lVSiMsgD8vihc9M5gbJq1SpEy4ABA8xqdi5byKCskgbo88gjj4gufG9Z4RvbokWLwm+pheWP8hFc3XEN3Vx8YekQD1IaN26cfR/GNTp7uMB9Bd2oW3r06GHZQ1+0bYsWLUx3XLuXKbh00Ya4RnB1g76IxzXq5+qIa9zDNc6B5XXXXSezZs2y9Pi2qcv92TPj0uAG5Fx+OHeuXJy7/CyDYvxBvsgHP5Tp6gb9cA/54xzxrtxiFMMkRMAfAvqAMiQAAe1EgqVLl9penPodMlBLIFDLwqakYFNjjDCEjPthZKOSo41IxKhE99NOx2rj5NIdIZAuPm4cyoqOqp0xY0aYb7YhzfVG1sA3Oh2lbdu22a5SgfzcIu9KJHjD8TqPM7oAApfcK9AMvCACGSGANzuGhCCAzhrD9nX0aLBs2bJAB9LYcP+EqJdWjS5dulhHj85+9uzZaWWyERmdx9mtW7dwqkY28k6XB9oiuuSeDsRKJ5a1OLfIu1pZNh3F5wIIUeLkIu9Za0JmlEcIkDgT2Niw5PCDBZj0ECXO3//+997UBXE6aywXu6OkEqdvizN1AQQSp7dHiRkTgRIjQOIsMYT5nUHnzp1Di3Pw4MHmPvaByKuvvmqLQ8CybdeunbmmfZTj8oQbHKsFoTz84Db3GWCt48XAvRz4JM7okntYvhCfAhiIABHIHAESZ+ZYUTINAlHi1EEnAVam8REWLFgQkhiWicM3XZ9BR+IGOocwLFMn+fssLtDBTwWIc/369d7Ku+aaa8J64SVEF4TwVhYzJgJlEQESZ1ls1RzWKTo4aPjw4eZi9lG8+8YJi0wXgwh0pRkfxYR5wlUe/cYJgvEZ+I3TJ7rMmwhkFwESZ3bxzLvcot84b7/9dm+Ddhxxwm2qU0O8b76Mb5xjxowJLTMODsq7R5sVJgKFIkDiLBQa3sgEgVwR5z//+c9A54Qakenkf9sBJhP9iiuTOjiIxFlcJJmOCJQ9BEicZa9Nc1qjXBGnriYT7viiKyMFunqN13qWZeKMDg7ifpxeHyNmXkYRIHGW0YbNVbVySZy6BJxZnLqUXuyt1uLiUZaJE6Of3WhhtJ/vgVZxsac8EUg6AiTOpLdQwvWLEic23gbh+AirV68OdOcX6/B1TdZAtzfzUUyYJ+pRVlcOwlSXPn36BLA2sRcnAxEgAvEQIHHGwysn0pgKsXHjxrRzInfs2GHLsek6sTnRpahCoqNqfQ4O0rVpwzmOmBqye/fuolQr0f1cW5y6Vq3VLxcrB2FhDV3wPdCF1dM+YyUCjomJQB4gQOJMWCPrXpXBiBEjbOQo5i6mBl0IPgBx6ObUtn5t6v1cX+fK4ly8eHEAUoGLEd84daNkr1XNtcWpG0Lb4KdcLIDgFThmTgTyAAESZ8IaWbeACjtQTIeIuj4xSR6kgc5Vd7UI9uzZU+ra58riBLHo1mohcZa1wUFYvadmzZrhIgg+Vw4q9YeGChCBwxwBEmfCGnDJkiWhZQXLE7uiIOieiIFupxUO6ujfv394rzSrUBoWZ40aNQLddstrtXNtccJtCuJ0g3ZInF6bl5kTgRIhQOIsEXzZTwyXpO5JaB2o7j8ZkiMGcbh43ZfT67ZTcWoVtTixcpCvAFwcqejGxzkfHIRFF3wG7Ijj5qminiROn2gzbyJQMgS4kbX2UkkKr7zyiujuH7aZ78iRI+Xee+8VtTald+/etnmzumll+vTp0rNnz3Cz4tLUXy1Ogc4IXbt2tc2s69WrJ7osXgG19DE1fXVkrOjAFNm/f79ATt3NooOhwo2ZCyT6/wudLiF//vOfZfTo0RajC67L8uXLbfPldPLZiNMl92wj67Fjx5retWvXlqlTp4ouhGCbc6t1KLVq1ZKdO3eKWqcmgzSNGjWy+qCOaCvUu3LlyoL02Ph77969Fo97qNfWrVttQ2f9ni3jx4831ZFGiVP0BSEbVWEeRIAIZBkBEmeWAU2XnY4AFZ3AL7q/pnWW6DR1ZKPoIB8B8WDXexeixDlkyBDRKRGi8+7kqaeeMjLVRdXl+eefF/3W6ZKU6tERJ+qEeugcS1FXquhm3Gn10lV/QrIEyei0EtE9SI1M0ibQSJCsDgYS3bHEiKhDhw6iFpqUL1++sCQljgfJqTtcZs6cGeoGoq9bt65UrFjRiLBBgwaiC6SHxIk2PfbYY404HUFCEcgjHs8BXhQQdKCT6ECwMD0wAJEikDgNBv4hAslFQP9JGTwigI2pBw0aFLRs2TKoU6dOoFaKfcvC9ywsHTd//vwCpStxBkoI5paES/buu++2QTFKTObKmzVrVgH50r5wrlrop0+5/XCOEbDpfqgbXM74ufN0cqlxLm8cL7vssgKDpnxggG/LavGHdXLlu7oVpn+6OkG2QoUKVudD1cuVgQUeNm3a5KNazJMIEIEsIECLU3srn0G32ZILLrhAdFRo6I7UdrMiYZlNmzZNLr300lCFpUuXhq5a7WTNzQdXJsKAAQNkwoQJZtWFCUr55I9//KNMnDjRLCeoUr16dbOYcA5LCz8loTAO8QjAQEnofxcZ/oUrFFbelClTRAk7w1TFF1u3bp3ceuut5jbV+bNm+aI+sAxh8UfrBevRtaursxKm4ZFaz8Lqjni0uX4rloEDBxbwRBS/FkxJBIhAthEgcWYb0ZT80Lk+/fTTsmbNmrAjRAeJ72JnnXWWnH/++aLWSJgq6qp1HS7kdSqGzJkzx+RD4QScgETWrl0rc+fOtTrpxsjmhgbJwa2JlwMQP+pb0oA8dZCOfT8FKfkOwB0uVLhgddsv+9YM9zJItG3btuZ2hRsZZLd582ZzpUNWPQt2D2122mmnWfsir6ICZKpUqSInn3yytXdR8rxPBIhA6SBA4swB7iBPdKipAZ2/uvYKRKMDBvng2x86ZHSmINCrr75aHn74YalWrVoB+SRcoG6oI0KU0KA3fpmQRqb1iOafaZpsyDnr0tUHekTbNHruZHCMqy/SoN0ZiAARSC4CJM6EtQ0snI4dO5qFig4UHbKuzSrz5s0TXeQ8YdpSHSJABIhA/iFA4kxYm8Oy0QW4bfoFiBMWC6akDBs2LPY3wYRVjeoQASJABMoEAiTOhDUjiLNfv34yY8YM0+zMM88UzPFLyvSThMFFdYgAESACOUeAxJlzyA9dIAbAYFTlAw88YINEdH1a6dSp06ET8S4RIAJEgAjkDAESZ86gzrygVatWycKFC+Wcc86RH/zgB7EHmGReEiWJABEgAkQgLgIkzriI5UAeA4IwfQMjbjnCMgeAswgiQASIQAwESJwxwKIoESACRIAIEAESJ58BIkAEiAARIAIxECBxxgCLokSACBABIkAESJx8BogAESACRIAIxECAxBkDLIoSASJABIgAESBx8hkgAkSACBABIhADARJnDLAoSgSIABEgAkSAxMlngAgQASJABIhADARInDHAoigRIAJEgAgQARInnwEiQASIABEgAjEQIHHGAIuiRIAIEAEiQARInHwGiAARIAJEgAjEQIDEGQMsihIBIkAEiAARIHHyGSACRIAIEAEiEAMBEmcMsChKBIgAESACRIDEyWeACBABIkAEiEAMBEicMcCiKBEgAkSACBABEiefASJABIgAESACMRD4P+0P/Lz/uUkiAAAAAElFTkSuQmCC	"V_b = \begin{cases} 
+0 & \text{when } V_a = V \\ 
+-2V & \text{when } V_a = -V 
+\end{cases}; V_c = -2V \text{ at all times.}"
+339	Refer to Fig. 3.25.   (a) The switch has been in position A for a long time. The emf's are dc.  What are the currents (magnitude and direction) in $\varepsilon_1, R_1, R_2$ and $L$?  (b) The switch is suddenly moved to position B. Just after the switching, what are currents in $\varepsilon_2, R_1, R_2$ and $L$?  (c) After a long time in position B, what are the currents in $\varepsilon_2, R_1, R_2$ and $L$?	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lVzZXJDb21tZW50PlNjcmVlbnNob3Q8L2V4aWY6VXNlckNvbW1lbnQ+CiAgICAgIDwvcmRmOkRlc2NyaXB0aW9uPgogICA8L3JkZjpSREY+CjwveDp4bXBtZXRhPgpK0hpkAAAAHGlET1QAAAACAAAAAAAAAIwAAAAoAAAAjAAAAIwAACyQKdBCjgAALFxJREFUeAHsnQm8VVX1x7eNWmIKgiGYgSUqYliWmog5gYpo5YCKmBOmkppjDhgm+qFySM3p44xDJILhUGKkOBSmKYpAzqEpWU45ZIkN57++y/++77z77n3vvse97513zm9/Pueee8/dZ5+9f3ufvfZaew0rJJaCkhAQAkJACAiBgiOwgghiwUeAmi8EhIAQEAKOgAiiBoIQEAJCQAgIAUNABFHDQAgIASEgBISAISCCqGEgBISAEBACQsAQEEHUMBACQkAICAEhYAiIIGoYCAEhIASEgBAwBEQQNQyEgBAQAkJACBgCIogaBkJACAgBISAEDAERRA0DISAEhIAQEAKGgAiihoEQEAJCQAgIAUNABFHDQAgIASEgBISAISCCqGEgBISAEBACQsAQEEHUMBACQkAICAEhYAiIIGoYCAEhIASEgBAwBEQQNQyEgBAQAkJACBgCIogaBkJACAgBISAEDAERRA0DISAEhIAQEAKGgAiihoEQEAJCQAgIAUNABFHDQAgIASEgBISAISCCqGEgBISAEBACQsAQEEHUMBACQkAICAEhYAiIIGoYCAEhIASEgBAwBEQQNQyEgBAQAkJACBgCIogaBkJACAgBISAEDAERRA0DISAEhIAQEAKGgAiihoEQEAJCQAgIAUNABFHDQAgIASEgBISAISCCqGEgBISAEBACQsAQEEHUMBACQkAICAEhYAiIIGoYCAEhIASEgBAwBEQQNQyEgBAQAkJACBgCIogaBkJACAgBISAEDAERRA0DISAEhIAQEAKGgAiihoEQEAJCQAgIAUNABFHDQAgIASEgBISAISCCqGEgBISAEBACQsAQEEHUMBACQkAICAEhYAiIIGoYCAEhIASEgBAwBEQQNQyEgBAQAkJACBgCIogaBkJACAgBISAEDAERRA0DISAEhIAQEAKGgAiihoEQEAJCQAgIAUNABFHDQAgIASEgBISAISCCqGEgBISAEBACQsAQEEHUMBACQkAICAEhYAiIIBZ4GLz//vthyZIlYdmyZSFJktCnT5/Qt2/fAiOipgsBIVBkBEQQC9r7Tz75ZDjllFPC/Pnzw3//+19HYeWVVw577rln2G+//cKAAQPCCiusUFB01GwhIASKiIAIYgF7fcGCBWH//fcPixYtKhHDCMPHPvaxsM4664Szzjor7LTTTvGyzkJACAiB3CMggpj7Lm7ZwDFjxoQZM2a4mHT48OHODf7vf/8Lc+bMCS+//LJzhnCPkydPbnmzrggBISAEcoqACGJOO7Zas9grHDJkSFi8eHEYOHBgmDVrVvjc5z7n2a+66qowderUMGzYsHDMMceE/v37VytG14WAEBACuUNABDF3Xdp6gyCIQ4cODY8//nhgz3DixInhkEMOCZ/85Cf9xtdeey306NHD/9MeYutY6l8hIATyhYAIYr76s6bWnHjiieFHP/qR511xxRXDJptsEjbbbLMwatSoMHjw4NC7d++aylEmISAEhECeEBBBzFNv1tiWv/3tb+Hoo48O06ZN8zs+/OEPB46PfvSjYeTIkWH8+PFhhx12qLE0ZRMCQkAI5AMBEcR89GO7WoHY9PXXXw+XXnqpK9I88sgj4d133/UyPvKRj4RVVlnFTTLYR1QSAkJACBQFARHEovR0hXa+9957Thj//Oc/h4ULF7qCzdy5cwPXUbS57bbbwnrrrVfhTl0SAkJACOQPARHE/PVpu1oEt8iBcT6ea0444YRwySWXBDjFmTNnhtGjR7erPGUWAkJACHRXBEQQu2vPLUe977///vDb3/42bLTRRmHEiBG+dxiLO+KII8JFF10kghgB0VkICIHCICCCWJiu/qChcINbbLGFu2zD1GLrrbcOX/ziF50AIjqdPn16ePXVV8NXvvKVMHv27LDaaqsVDCE1VwgIgaIiIIJYwJ4/7LDDwmWXXRbwToNoNGqZ/uc//wn//ve/XakG121omyoJASEgBIqCgAhiUXo61c6//vWv4fzzzw+/+93vwlNPPeV7h/wNx4gyDQ6+IYaYYSgJASEgBIqCgAhiUXo61U7EpijQ/P3vfw/z5s0L//znP51b7Nevn4tPIYw4+VYSAkJACBQJARHEIvV2hbYiJoVAkj70oQ+5+LRCNl0SAkJACOQeARHE3HexGigEhIAQEAK1ICCCWAtKyiMEhIAQEAK5R0AEMfddvHwNfPHFF8OSJUs8TmLPnj3D+uuvr7BQywep7hYCQiCjCIggZrRjslCtW265JUyZMiU8++yz4V//+pfvL0IQcQy+11571b2KmHy89dZbYfXVV6+57GXLloWPf/zjNedvVEbwWWmlldyGE68/MX3qU5+qeJ3/Ca8V92/jd9qCUhM4YBKTJztQ2gQe9Ui4FwQzlL8qhSlDaUyKYfVAulhliCAWq79rbi0T9dixY8ONN97oGqhxwkbxBm3UMWPGhDXXXNNdvhFbEeWcShMTD2RiX3vttcPTTz/tijtci+XxncRvHI6/8sorYZ111vHJjDpwVCuX+4jfSFxHiFEkLlwvT9XKqXad+7HTJNHmmI8zRzrxmwgiTPbPP/98CQuuf/rTn3a7zj/96U+OVfo+vpMnjQXtgAiCA2Yvn//850u3MMFDLNEOJkVcqGf8nr5eXnY6jxdgH+ShfaSYP373i2Uf6Txlf5V+VssDNuBByLGILTdRL470fenv5OE392AzS17wpt5gstZaa/miCFz4zjiLxDdtOkQZ9NHmm28ekHw8+eSTXu4GG2zAI8If//hHD5o9YMAAv841FmeERuvVq5cUzgAk50kEMecd3NHmzZkzJ+y8884lG8V0OUxITDRxIoUjYrKplshP3jTnVJ6XPEx4lBPLLc9T6Tf5ubejiQkVboKJNl0/ykREzLU333zTgya/88473m4CKJc/MxKlcizgYDn4f9VVV/Vqci8cDhwxZaWxo+3UhwPiB85vv/22/47PTOenQCZ5opXEezuKRaPvAwMiqVBXziyUSHDXmP5wjbZynQOMYoKIsliIi4GIAZjEg2txnPE9fT2WwzUwpZ+oDymON37zPf6O36nXtddeG7bZZptYjM45RUAEMacduzzNYiU/YcKE8Ktf/conlTi5xDKZKDbccEMPJBwnpvI8TDoQGyY/JjOiZjAZkZh43njjDZ/wmeRaS+XlVsrbkTzcQx1Z+TPJUg+4ChL/QahwacdEvXjx4vDZz37WRccQNZwXMGGTr7VEe1944YXw3HPPefm4wwM7rsPhQGDhAOPETFn8z3//+Mc//JnU8YknnvA93Igf5/hs/qcv4Hj4TluiOJE86bzx/vI6P/jgg+6kgXqwMCAWJqLxSimWWem/eK1SHq5RP7j/pUuXOoYQGhJ1x0EEgarBGgLPYuCll17ydkK8Pmv49+/fP/z+97/3cUVb6BvwomwS11hIcI3+o1wO2gTnCK6cP/GJT3heuHAkDAMHDvQxShlwjZQ7f/58XwhxjQRBHDdu3Ac/9JlbBEQQc9u1HWsYnOFpp50WHnroIZ+omWzSExzfmVTuueee0KdPn9JkVP40JicmJiYzzkxK6ZQuM329s7+nJ1TqFBP1j3WObYBgxHbFfG2duScSvMgRcQ/P4uD55an8v3QZ5Xn5TT1j3eK9lfJVu4bXolNOOcX7CjE4C6FBgwZVy97h6xE76kq7+U2K7aMdYM11Dq7HRH6OtGietlZL8X7yk+ICJpbNNe7neel+4Zncc8MNN4RTTz3VxfgQUCK/KGg2qOU7iSDmu3/b1boZM2aEiRMnOifERMEEBXdHihPMrrvuGggc/KUvfak0obXrIcqcOQRw4n7AAQcEXPqxf8bvddddN3P17MwKsZ/49a9/PTzzzDO+8PvlL3/pHGxn1kHP6nwERBA7H/NMPvG+++4LBx54YED5g5Uz2o5HHXWUa5MivoJAklCKQKRVibPJZMNUqTYRIBTYPvvs4+LFz5poEoLYCA6xzYpkKAMEkcUfGtZrrLGGc82I0JXyjYAIYr77t6bW4eSbOIiPPfaYE0M06w4//PBw0kknlfZrYkFwikr5QkAEsWV/pjlEFgl33nln4bnmlijl74oIYv76tF0t+tnPfhYmTZrknCH7J5/5zGfCpZde6hp1WbDva1djlLlDCLAggkMkHiYi0zvuuKPwHCKKTIhMMeGAILKvWk3RqEOg66ZMIiCCmMlu6ZxKXXLJJeGMM85wDUbEpNhbnX766U4Mo0JJ59RET+lKBMQhtkQ/LTJFiQyCiDavUr4REEHMd/9WbR0G94hFUdOHGKLyftVVVwWMlEUMq8KWyz/KCSIcImYyRU5pgjhkyJDwm9/8xpVrioxJEdougliEXi5r46xZs3zPEDsv0he+8IVw0UUXuQcPKcuUgVWAn2mRKXaCEMS0h5wCQNCiiWmRKYpkcIgbb7xxi3y6kC8ERBDz1Z+ttgZOEC4QmzOMkvk9atQo91cqzrBV6HL9Z5pDRGwON4RmcZFTWqlGWqbFGQkiiAXpa9xjYYDNgb0ZCTMLFGrwACLOsCADoUIz0wRx6623DnfffXeFXMW6lBaZiiAWp+9FEAvQ13CDJ554Ypg+fbq7UsOF1i677BIuvPBCt7GSKUUBBkErTUyLTLfcckvnEHG7V+SU5hD79u0bMMyXyDT/I0IEMed9TASJ448/Plx//fXuTBo3VRjco02K/04Rw5wPgBqalyaI8lTzAWD4oMW5/aJFi9z/Ks4K8GGrlG8ERBBz3L/YlZ1wwgnh5ptvdmLIqp/9w2OPPbbwe0Q57vZ2Ny0tMsXmTp5qgjsCHzlyZFiwYIHb5qJUM3jw4HZjqxu6FwIiiJ3QXxi8d/YeHREFjjzyyHDrrbe6s2KaibNiCCTxA5WEQESgnEOUYX5wg3y2FYjCoT3EOFLyfxZBbGAfo8iC1xf8g+62225hiy228BA4DXykF71w4UIXi95///1ODAlZtPfee4dzzjnHxaSNfn5Xl0/4HrgeQvukRcJo1SIyZi8I8Vf6v66uc1c+XwSxJfrY526//fbhkUce8bHCIkEi05Y45e6KTRJKDULA9u0SI0aJiSoTi7mWWKy1Bj2pqVh7gROzK0zMuJ7YOIkZWCcWxSIx4tyUKeffJk+enFisvcTC9lQ8TPSVXHPNNYlx7jlHorbm2cIpMW8sPl5MZJqYDV5tN+Y4l8UETRgnvEMW2SUxApnj1qppEQFs0ZQahMCee+7pL5RxIolxJonFWGvQkz4olvJNKSIx8aw/d9NNN00soGpikdkb+twsFf74448nTOpMZNUO+mO11VZLrrvuuixVvcvqYtx0Yj5sHS8LYpxY1Pouq0tWHrxs2bJk+PDhjsnaa6+dmNZpVqqmejQQARHEBoFrm/GJqWs3m5TNWXDy5ptvNuSJc+fOTfr165cw2UMIzNNIMm/evMTCNjXkeVkt1KKiJ+ZkwDFgcfCTn/wkMSURP/g+YsQI59jBaJtttkksMn1Wm9Jp9UoTRAtxlLzxxhud9uysPsi0TJONNtrIx5HtISZIXpTyj4AIYoP6GO4jcoYWP9BfLESncGz1TIj9Lr74Yie+kRjutNNOiUW0LxwxBFdTgkjM/Zjjve222yas9C0Cuh98N6cEidna+f+IxF5++eV6dke3LMv2EEscIpiYS79u2Y56VhqxMYtKFk7mui2ZP39+PYtXWRlFQASxAR3z3HPPOSfCy8TeoSmz+IvF70MOOaQu+xFM7vfee29y9tlnu/iPsjlMESBhdQsRKGJiwRH3w5jQfv7znyemMl86WDxEkaopOeVqb5V9Yohbe4m8GZ0nffr08fEzbNiwQonYq70jb731VmIO7x0T9ADYZ1XKPwIiiHXu4/feey/ZY489SkotF1xwQWKeYpLjjjvO9xHNS0xiHmOW66mUd9BBByXmbzJZccUV/aXdbrvtEott6JNhkZVFTKO3tLJnLxXFGnCKhzkjKImVLQbgcvVDlm5GND5lyhRX4ho7dmxiGrY1V++WW25JevfuXSKI77//fs335jljlCT06NHDF595bqva9gECIoh1HgkvvvhiabWNqGXJkiWuzWgOkxMLuOuTzrhx4zr8VFauBxxwQAJhjVyh+Z9Mnn32Wa3sDVU4JPZSwQYiCOfDZL/66qv7d8TXUekIbVy4+e6WWPCw9wkRjIsfFKfY/6Pd7KEy7mpN6T3Er33ta7Xelut8vGdf/vKXHU/2EB999NFct1eN+wABEcQ6jwRznu3cIZMuRIv9vL322iuxKAIlzoQ9LnMJ1e4no+wwfvz4klIIphVbbbWV75vFibHdhebsBib3SBDNRV1i3npchIwYme+IVIcOHep9QR9NnTq1WyBgtpWJRW9Pzj333MRsWn087b777v6ddk6bNi0xJ+0+gVsg2w4TRBZXSokvNlgcsMBgYSulmmKMChHEOvYzGqRMRrxEUcEFooXJReRKuM7x3e9+t9UnI7Zi8p5r2qPsFaIpOXr06Gac4be//e0EeykRwyYo4ZSjUs0PfvADxwZ84gFXZbEfS9w6mqdZTygKQfQQ3SEij+OJMwfKWoiG4xiDQ0R0XGtKc4giiE2ooZQlgtiERxG+iSDWsZcvv/xyn5h4iTiYrOASOSN2YUKL/2HvVW2fByNg9hx79uxZ2vtC/Ec53M8+mDnsdvV4EcPmHYh2bTR3QbTMoiJtV8ei5Zhjjint8ZonoeYFZOwXxBDDcIheHDuIemkDYwTFoLT4nDyMrfZoiqYN8yUybRoAmOWAp8wumjDJ+zcRxDr2sLlH8xcILymnnXZaYnHlSscDDzyQXHnllUmvXr1KRM0i11d8Oko3UVkmToKRs+T6eeedVxdN1YoP7+YX77rrrhJBZN8QbomJzcJfJSeffHJiEQxKfYAo7KGHHspsi1nsoJQF50f/m7Np15pF3I4IlQPvR3PmzHFTEvJgYI+DhvYoxohDbDkE0naIEpm2xCevV0QQ69SzTE5oekLAEJuyXxXt3zgjqmOSOvrooz0P+SweYYunU040CI4TIRNdFIexgk9zPC0KyNkFNGonTpzomruIjDGbwPi+WmJyZ0WfXkggtobDQqkpctko15x55pntIhzVntmo64g9o5OB6FIN5RnGUkwQTcYX9pWIi5nIMclpTxJBbIkWnmnSdojaQ2yJUR6viCDWsVexdzv00EMTxHCYX1RKzzzzjCva7Ljjjq4MU54H7UGLRuETOoQwPbHzfd999830JF7enuX5DYbsk0ZCBjFDXLzrrrv6xF+pbGzxLEqB2yIiOkwfQ4YMSTgQM15xxRVV+6hSuV1x7cEHHywthLBfTRPCSvWJ+6SV/mvtmkSmLdFZvHhxYs68/f2TyLQlPnm9IoJYx55l9Q6H15q4iknrnXfeSVDrrjTBsdpHkxTiV4lDhECQpwjp9ttvdyfdkUMGDw4I4ze/+c2qBA3TF0Sh7NHGAw1drqOExD5ia32UFWzhSqJkALd/jJ1GJHGILVEVh9gSkyJcEUHMYC+zLwQXAyGIBwQS5Qq4hqIktEHjwiASw0gg0CStJjqGcFRabHSUg+oqvF9//XU3qwAD9kPb2u9ETA/Bb28SQWyJGARx3XXX9fGnPcSW+OT1ighiBnuWiZvQUUyEHBBFjIQxOq800WewCXWpEmLNuCBIn8GESQoH6nlPKGLBEdN+tEuvvvpq30Nlb5WD/VSUs9ibJtQXB/us7Qn31d1FpkhlWDxwTr8f6e/tHScoKkVtZYlM24te982vAME2u2Yx2X5kGDVqlFfNlHTCzTffHMwvajAFkSxWtyF1Mm1KD9JqCiPNgvna6xYsakX4xS9+Ecz+riHPzkqhto/qwZ7NgUAwkby318IROR5GJIMtnoKZWAQjgP4/9TalrHDrrbcG0zitqRnGIQZzYxdMpBxMaSuY7WtN92Uhk0lTgjnDCLbnF3hPeEcGDRoU/vKXvwTbmvDf4JROBPq1veT0pRbfTVwdzAVjWLJkSTCCGHgfzRNQi3y6kDMEui8tz3fNUdCxoeYHijpwjUVL7Mn+8Ic/TNAIhUOK4lIiMnTE0093xQ9O8KabbkqIrxm5xShCBhfGCe7poqkOWs42kdfc3O4qMoULRrMbO8yoSQwGOClA+Sp+53f6AB+U21pLEpm2hk5+/xOHmNEFTppDNK82wTyqZLSmja2Wad0G208NFvjXuaLNN988GJH0a0YUGvvwDJVuilTh1VdfDbaPGEwhqwXHbCLkcPjhhwfzzRpswRBMISmYqUZNLeiuHCIcszm5D+bUPpjTi2BBn4OJSYOJkYMpTXnbbTHl1yMQ3GNi5QDHveaaa8bLLc5GEINpMwczZRGH2AKdHF/IL63v3i0jJI8NOz/acvPWvVvadu0xnYhYnHLKKYXRsi1HBikBXDMasuUHmsfsH4IT5/a4buvOe4jYX+I4/w9/+IMrFOGs/Xvf+57jAPc8YcIEvw7HzAEuJk5tU+Iis4vy0VeM31KqyWg/p0WmIohNBHHGjBkZ7bGurRaE0vZVnRDgSH7p0qU1V6i7ikxjA1kMoEDDgoHD9tsdB8TLKCHF6/Ec72vtLJFpa+jk9z8RxIz2rQhiU8ekOURTpGn6Q9+aIYDfViKrEBSZyb/W1N0JYnk7b7vtNieIeCcyBaHyv2v6DUGUp5qaoMpVJhHEjHanRKZNHRPj0jHB3XnnnU1/6FszBOCS3n333XY7HejOItNmAPz/D/y/IjpG8eicc86plKXNaxKZtglRLjOIIGa0W8UhNnVM5BBNCUKBWptgqdu37s4h4qAB708cRIqJ/oIhiHyP/8V8iJfbShKZtoVQPv+XlqktJbOY7rjjjmDBhb1qRdYyBYBNN93UtSvXWmsttwfD3kypfgjcd999wXzkuh2ixUMMFqWlfoU3sCSbkn08XHbZZW6fi70h9pgPP/ywa+Ty2zz8hOHDh7u9Jvm5ZtFPgrlADGauUbV2aJmau7xg5hkBDV6T2MgOsSpaOfojn3S++7cqzSES+67IKYpMjSAWyv6ws/r86aefLrkpI5pKd0lweuyZojwTD+wRbXpudsT/4hkXiPgSbi2lRaZ4ReK3Uv4REIeY0cUNXljMgbXXjvPMmTMzWtPGV2vjjTcOjz32WLAgyQHOecstt2z8QzPyBOzp8LpipgVh9uzZbHEE20sNZk4Qhg0bVpdamn/cYEb/wXyhhq9+9avBYkoGM2qvS9mNLgS7TFOiCdikmgMD5/qwRwSndIrcI+PoG9/4RjBnF81sOdN5+Y79K9wy3KZFW3GvNRaQOZj7vPKs+p0nBPJP87tnC6OmnI01D4HUPVtRn1qzogcHVuqPPvpofQrNUCl4XCECR3nIMPbDjjrqqARH5jbJl7ggOB0zuk8uv/zyurSCQNb9+vVzjLfaaqtm/kDr8oAGFoIiEfhFDNknjL/Lz4RWwwYRn6e1pIMPPrjEaeINh3BQSG6U8ouAlGoy2rdEtejZs6e/kEyKRU5EiocgIjI1jzW5goJJ+vjjj0+M20u+853vNIuR+cQTTySrrrpqCwfnKIsYx5PUS7y5cOHCUuy/epWZh05irOFQnQUI4w/MMcUwDjoPzVMbKiAgglgBlCxcghOCI+JFLLph/hFHHFEiiEzeeUpEuR8wYICbCGBWYo65k3PPPTchBBgc44knnugxIeOEzKTMd/y74uO2HolYkUz8lGsKJ/UoMhdlwH0SYQbvSPFdBH9T8vIoI7lopBrRDAERxGZwZOeH7ZX5ilQEMUnMX2VuCSJivSOPPNKdU9PXcH84pcaBOcGgiQk5bdq0pH///o5BJIbXXXddgtuyeiQmfYug4eUjnkZUq/QBAnjBYWEyZcqUxPawHSMkN/PmzRNEOURABDGjnSrD/KaOOemkk3JLEGklsfxuueWWxNT8fb8wikTZt+rVq1diSkUerSFyh4iO2+OrtAnJyt8s7FPJDyrE2BzJJ8uWLaucuaBXWXxYyCgfh2iyyoVgPgeCCGJG+1UcYlPHTJw40SciFD/ytocYW4kJAV5m2Dc8+eSTffK1eIbebggknGEkiHBxKIfUK+HmbfTo0f4MnoMCDw6yEedmJYEN9cF5N99JiDQtbqErupgtZQJhb1SySCMlsTIYWYSNRj1K5XYhAiKIXQh+a4/Ge78ZFfskVfQ9RPZwIAbEtJvbQd+UrWGdpf8gTojoIIz33nuv7x+jcBOJIpPxpEmT6h7xA/dtUdMUrNnP3HbbbduMG9gZ2C2xKBUollmA3mSTTTZx7zP4a508ebKLehFlsqdqjiwct+WtE1qoHGmPNhDctNia5yvlDwERxIz2KcbSqNszAYogfkAQwaIozr0hjOxfscdo8f2S008/Pdlggw1c6QYN5HonnnXppZf6wgOCyIFocO+99673o9pV3ksvvZSYpxkn0CwKOCDWLI7MPrDENTM20AZFS5Z7OpouvPDCZPvtt/fD4iEmiOvZL7RYkyVtU8TY2kPsKMLZvk8EMaP9g3/JVVZZJTMEkYkZZYtyW7nOgC9yiEUiiOW4RpHhCy+8UHfukGchfrznnntKyj0QRPA2JwjlVenU32jcRu8zEEIIYiTYnCGC7LFyUF+4RRSOOpLmz5/v9p08j4OyIbprm8JRfBd5BpxzrbaMHamH7uk6BEQQuw77Vp/MHiIvH0dXc4g4R95nn32SNdZYIxk/fnwCsUbJgEm0MxJ7iFFkSKy7oia4RuwWX3vtNbdXxAH1okWLfD8Rw/64t9ZefJBGnHnmmS4yhchErBl7u+22W3uLq1t+OGMculOPlVdeOfnxj39c0jimjhAtTHJww4bkIG4x4M6tI4nIGJRJ2fFIE1/qAWdqvlM7Urzu6QYIiCBmtJOypGUK8WMiYEJA87Fv376uhIEqOsSxoxNxrdBHDhEOgYVCERNan7Qd0d2YMWOS9ddf3+0X0TjdYYcdkv33398XTrNmzWoXFw9R3XzzzZ0Ton8hAJw54ISIsdhVydzVuXiUurB3iDYuPkUhWlzjjJINiQXBeuut59fN5ZovHNpbb7BjL5Ky04Qwfuc6BBpCrZRPBEQQM9qvt99+u7+YvIRdzSEiJkWRg8kgEkbESajoQxyZkCFaTz31VEPU9SkbHHhWHl23tTUEIVrjxo1zDohFAdjHSZozhIGFStxbQ0MUAtFWWrBgQYLjdLghygFjDogse2lLly5tiHi2rXrF/3/961+X9u3w2GN+Sz2UEyGd8BjDvmqUUtx4443u1Yf6YzhfS/vjc+IZJRrc4aXFoxGTiA/1QLSslE8ERBAz2q9o/fXo0cMnqK4miECEqI7V+Zw5c5LDDjvMXY0xMTNhMCGz17Luuusm++23X8JEhpg1raW3PDBHswsm6rx5qmkLF/aqEAFC8MAaDsacvScHHnigc4WczTG3K2BBEMnDogW7xtYS4lcIZxQNcuZefKQShBmOlDxdmRANb2W+VakXB+JR6gSxY/HFvjYJc4vNNtuslG+PPfbocN3NmXqCdAZc8SDUu3dv3yqIixBwOuCAAzpcflfiqWe3jYAIYtsYdUkOXHcxOTERZIEgAgKTEdqIiEgRG2HADYeB0gH1ZBXNxI0dGy7ArrrqqrpgFzlE7PKKFoYncklgi3Ppq6++2hcb9EE8WHxAPE499dSSiBHtSPqqtcTiBi6fsiMHhBJNW/e1Vma9/7v++utLPn1ZbEWOME2sUTSCeDEGWZQtrxZuHOOIaHGAAKeM5inlc/BeFm0c1rtfs1qeCGJGe8YCk5YcLmeFIJZDBRfBZIyiC74emVQjxwHXyF5XPRKq/0xEqLsjNitKYvI///zzve0QLrg+OJhqycI3lRYn2ORFDqpafpRRUJYC28ghYmuHzV1WEuJ6jODZO8UuM50wysdUBDE6CjG4wGMsRqKZztvR75HwIkKOrtsY59OnT+9okbovwwiIIGa0cxANIiJkssoqQURNHeNoVs9RGYH6ciBiQnOxHgkRVeRi2hIF1uN5WSkDTgXn3uCJOLQtcwL20eDOyW8x/2raz4UDwuA99hs4sz8H919PwrI8mCJ6h7inOVeu4bBgpZVWctExizPy1EtMX15fwj4hPo044V9WKX8IiCBmtE8RZ8U9uqwQRCYbXIYxMY8YMcK1+tg7hBtkokA1Hn+PaJ+ieIAYrx4JV2aRgyma2QVxMeEOwRdxIEofSA8Q2XEgWkcbE6UbuDsIGuPmyiuvrAl6OCBEjDvuuGOJu6cMFjg4Fo8cUk2FdWImOOVBgwY5LrvvvnvdngzRRXMVggeGF198se+pso/LOAcb+kIEsW6QZ6ogEcRMdUdTZVBsiISmqwkihJAVMiIpVNshfHFyYOKEk7VI68kVV1yR4PMRMVd6Nd/Uqo59i3424ZKKFqCVRcV2223nkzCTMQoziI7hBIm6wIFWJHu3/M/5tNNOq8kUBo8uFkHexd4QWrgtyoiLD7R6586d27FOa/BdEMRoZkF765XQ7u7Tp49jilIbYx3N0rRXHPqAvV2l/CEggthKn7ISx+CXfQpC5DRKHFOpCqjER6PkY489tlKWTrvGpIwbOQhSXCEzaWCnhpEy2BBTr7X9reWp7IQJE5wgQHjz6ty7NXxwE8Y+KoQQ7iT2Aef4HcJITEOIQ63hm/APCjEF3xgPMe4BUy6LHkTiWUxpgnjGGWfUpYpor2KyAcYRh/Q5Yg0njimMUv4QWIEm2QBQKkPA9iSCTULBODUWDcE4oWBcUNh5552D7bmEDTfcMNiEUXZX/X6aZ/9gYqzA2faDgokK61d4O0uyySeY+CjccMMNjoXt3YRddtklWDDbYOI8x8EmjnaWWnv273//+8Em5mAEMRiH6NjXfnf3z2l7eYHxaEokwRYnwSbmZo1ifBpBDKbtG4yrC8bNNPu/2g+z5wvnnXdesIVOMI7e+zaWbaLSMHDgwGDG6sHE4NWK6LLrtjj18Wci42AEMZgm8nLXxUTQ/o6bolgLjCkcTMDWJCXBbCB97C/3Q1VAthCAICq1RIAVKKYDrBCtx/xgb4ZVOkoHRhjdcwhalo1QPrj77rtLe0dEUW8rse/B3l094+Sln4kYlLI5aHM9RaLp51T6jjkBfYDZBa7KiprAHClFpYP/2rvfxx4ZuEYuCA4ofkf0yv5lI8Z2PfovzSHWS3lr5syZLjZOYxLx4Aw+4GILtHo0QWVkEAFxiDb6qyW4MwsEGkxBJJg4JVhInvD222/76hHu0NSwfVVugV2DaVoGEz8FMz8IJk6sVmTN1+GERo0a5fnhRk3rtOq9cA9wURdccEEwZZcwderUYPseVfN39A8bv35r5CI6Wk577zv++OPD2Wef7djaHk+weIDtLaLb5zebQx97tTTEFm7BNCJbzWp7vcGiOYQHHngg2GTveelf+hZOyLwPBTMtCLaP1mo5XfWnLdCcc+UdPe6448KkSZOCKXw5J12tTkgzeD+rtYl32+w3g9k+VsQabMDIHIkHWywEC5dV7VG63k0REEFspeMY/IhmOMxTSzAPFsF8dwYmJ5Jp5wXzkhFs1egH18yPYjC7qWCb8fzscDIfkj4pma1YGDx4cDDOqGpZiHgOOuigcNNNNwUmQ4ulGIYOHVo1f3f7Y+TIkcGUGHyyZpI2rcLu1oTlqq/ZXgbT7A22b+XlxIk5LkwiIeNPiJkpfQTbHwymjFNR9Ec+xIOI/kwSwc9myUIoBdOuDOYvtdn1LP3gfUR0b47Jg4WHCrbHHcwkJ/C+VEssEtmGMAN/v7dSPsq1WIe+VQKWHOBrJkb+rnMPC4hrrrkmmGZvpSJ0rTsjYJ2tVCMCiGlwpRXFk3jHsEnJxU7xjKPkjvhRLK+CrdxLvhmNIJb/7aIsNARRZsGtGhqgNg5d5IXo1Pb7OkUBBfsvxKlg06hknLK3jfYVJR5ixBJssfNEoQkll1oORPtbmcuz1gzzEYWiZYp2MLjG8ct3FHMQy2Y9oWyE2Hdt85QEPtSdA41QPCjZQsqPGBqK/xB5Yr6Cwly1xFiOXoDieezYsaXyKUdmF9XQ697XxSHa6K4lwSXCGbJ6RMGE1TpiG+t+58rYbDdfi8GMyIO52Kq6Mq/lWeSBy2M1a+6jXIkkLTJFRGoeTLweiH/gCs1LSTB3al4fC4Pjj0EJBfFPPVf6Nlk4twZngYIHK3QwoP020ThnjEgJkZuFi6q1ua3m+9a3vhWuvfZaV/5AZIp4uigJZRdE8kgnYkLsh9gYDsl8egZbpPkYgANiHNAftjAL5qvUr8f7ys/kQ2nMQnoFI46lMUu/mZG/c17l92TpN8pGjAukI7QFhTfz0BPMHMMVsBiTJN5buGy2IWyfMHAf74V56anYHDCH+04rzVk0Ed+K4DrPQgqE0p1SzhCwzlWqgoCJS9xVGDZaNim5k19skNhg50wInn333TdhMx6DdVbk3FOPxOoX+ycbbontITYrEjMITB5Y1VMXjvidM/dwUMd6RvYmbh4G3NgesiJntR2fD+fCb65ju4X3ExyU1yMdeuih3h5MPR5++OEWRbKKZ8WPw+dKB33TnROSgIMPPtiVivBA8/zzz7sUAu4RBSdcsHGAA9IJjloD2MIJYvOKFCI9hvhN2K8sJ6QTxGtkrGMziCs3rkUFI97FeMD1MR6j+zXbb2+hMMR9s2fPdqxxYI+5FW7jcBeIK7z0ewVmSvlDgNWOUhUEmIgw/sVgGTFUfPEQ4f30pz/1SZiJpxHiJfwzYhjNM8tFpjwPN114i8Fom+gHaL9GYsh9tg+UmCJKXcS3wIOYmDIhfNQJWyx+I5rjIAYdYqroOgxCiWutV155pQq6tV/GDpNn0r5KrtvoC9oMwSw/wMX2mLo0rl/tLa2cE/Em4wx3fhD3ei264tMgBHgfQtQYcab/WAhmOUH8EItSZwjikiVLWq0uxvTR6w8O48vF/PhwNUUZX9ixuOO9Z1HJ2GKRx3M4WKDigEIpfwiIILbSp3BXGDzzEkB4rrZIA6wg2bfjZaz3xJSuCob5kSCWc4jkgyiyd2iacU70CBBLPbnnrrvucuNs6liPBCcCUYrEEC6RwLFwJZEjgVNhTwo3YnFfCk7SRL/LVQW4IYLDxsmIIK7lKXIJMU/5mXoTQqq7JwhjIxKLHWIMQgQilwiGLDSynMCDEFbUlboTsonxB0eXdk5A++D2cCtIXrhEQjyVp7POOsvLiVIPznGRGc9cMxFzC+6yvCz97p4I/B8AAAD//wNTjQcAADpxSURBVO2dB7gctfX2BaEECN0QAqGD6aEmAQI4FBMwwZhuqund9Go6poWSgOlgYjCmBhN6N7ZDqKH3bnrvvf71nd/hO3vnrmf73t3Z3aPnmTt7ZzQa6ZVGr87R0VGIHgoi8N1338Wrr746Dhs2LL766qvx+++/jz/++GPB+PW8MX78+DjVVFPFEEJcfPHFiyb9ww8/xH322Ufj9u7dO3799ddF41d68+OPP46LLLKIpr/CCivE5557Lv7000+pyYDPqaeeGieddFI9Lr/88tR45V787LPP4u9+9zt9N1j8+9//nujRZ555Jg4dOjQefvjh8bTTTovHH398POCAA+Kf/vQnPTbddNP44osvTvScX4jxgw8+iAMGDIi/+tWv4iSTTKIHOPfp0ye+/fbbmYfowQcfjNNPP722j8knnzzOOeeckW/g97//fVx55ZXjSiutpN/PDDPMoO2RMq6++urxvffem6hsf//73+Nkk02Wa7vWhu0MLuB08cUXT/SsX2gPBEJ7FKPnSgHZQIz/93//13MvSUn5xhtvzJEAZEQ+CgVI6G9/+5t2DDvttJPmt1Dcaq6/++67ccYZZ9T80NG88847BZOBPPfbb79c3mslRN690EIL5dJLI0TI+ZtvvtGDuvr222/jV199pZ09Hf6nn37a8PorCFCGbjDAY/ACCdDZc0Aq/fr1i2PHjm0JzKj7UaNGxUUXXTRON910OoiE9CAxyjLNNNMoiXFebLHF4qGHHqpkmPY9P/HEE3GeeeZRHGxwkDyDD/9vscUWGapFz0o9EZiExKSiPWQIAencw9lnnx32339/zdVMM80UZFQa/vrXvxbMpRBHkE4srLrqqmG22WYrGK+aG+Rn11131Tz84he/CNtss00YNGhQEAk2lxzN6PXXXw9CgOHmm28OPCOdS7j99tvDggsumItX6Y+nnnoqSAcd3njjDX302muvDeutt16lyXj8FAREAgwiRYVXXnklSEfP4Dj85S9/CZdcckmgzVHXrRBksBheeuml8L///S98+eWXQTQGQQZBQTQrYZZZZtEiCHGGFVdcUdvilFNOmVosIckwevToIAO6XHtLi7j00kuHO++8UzFKu+/XWhcBJ8QM1R3kMW7cuPDkk08GiOC1117L5Q5SgYTmm2++sOGGGwYZ/ebu8YPOTCTFIKN97dy63azDP6KaCptssonmiXfLaDz88pe/zKXM+0W9GURC03zMP//84dxzzw2rrbZakNF6Ll6lP2655Zaw/fbbB5FK9dERI0YoIVeaTrvFB+u77747iDo5zDXXXFUVj7oS1XI444wztI4gBNoWGE877bRVpdmsh6z9c6YcnGl3ybYHwSf/T8sr39AjjzwSHnroIR3YiTpWifXKK68Mjz/+uH5btHuZStGBWloafq2FEZCG46EGBNJUL5Ukh8rn+uuvj1tvvbWqa2T0qiosU9VI08qpcLj361//OoqEFGUkW3fVaLF8o14Tso7rrrtulA5BVVLSwUQ7yC+qt7nnnjuKBBnvv//+quZbwWPMmDFxzz33jOuss05ceOGFVfVF+mCB+vT888+Pn3zySUuo9IphWss91NJzzDFHZH4UNTVBJLt40003VZTsHXfckZurBl8hwnjwwQcrvhUl1MTIfIOoyd9//339JpheKHYwxVAs0AZRvb/55puqXiXto446qptq+bLLLiuWhN9rUQRcQiwxmDGpKxmNaxMmTFBpDskFaemPf/yjjtZlriIZtehvRrLnnHNOOOmkk1QCIl1pR0Wf4SZSoEzuB5kvDDInou8v+VAdIkhHET7//PPw9NNPB34nA/lm9I20grqN/JUajSefJz0x1gmnn356kAFCEMLTd4BRMqDaI20xnAhCziotVishJdNttd9rr712uO2221QlKKSmEh0qQdofKs/ll1++LE0BUqIYIqk0L4ZjCgMS0JprrhmGDx+eUzlmFR8ZDITjjjsu3Hfffaoupe0Va3d8Y6hRxfAqyOCqaLFo07Q3At/pvvvuG4Qc9X+mBgYOHKi//U8bIdCiRN6QbCPlHHnkkfG///1v7n2MPDFEkPkxHVkjtSExMaG/22676agyF7nID0azQoRRPuCcZR9SEOnIPGCU+UI9TEriPdLsuh1TTDFFPOigg6LMmxR5U/1vMYKWjiX1qEZixiDmlFNOUUwxhDBpML+8yf+l04tgIgORiEVupwUMX8BDSDB+9NFHUQYSOc3CscceW9AKOA0npCEkRSwxwR5skfbPOuustOiZuoYVON8BeTZtRakzZUOariRg5DbrrLPmvr9ajcUqebfHbRwCLiFKr5IWREWoBgaMPJdbbrlw1VVXhdlnn11HzYMHD9a5MptLY1KfOR35MMNWW20VRKVXdJRK2oxQxTI0N+JktLrHHnsE5t5WWWWV3MiUvDGXiFTGfBqGLNddd10QdY7GIQ/bbbedpieWoGlFqds1pDiMFQhIqWK6rlIdo2hR34V5551X52+4L01Y81pKYhZr0CDLJXQEjrTCcwRwwChCVKZBOiJNl/vPPvuszu88//zzWn7ejYTIPFgxoyNNtI3+YGhEe6C9jRw5UqVl6bRVUqStrrXWWhWVlrpFKrzrrrsUV+rhD3/4Q3jggQcqSqfRkceKIZlYfebmmHv16qVaE77JtCCDp4Ax0aWXXhrEejstin5bzBciTdLOiXfDDTeEww47TKVQHhKVadhss81Sn/eLLYxA47i3td6E2f4yyyyjI0JRP6kUxtqlpZZaSq8hyZ155plROowoxg1xo4020uvyQcaHH364aGHvueeeKOSq8aXpRNb2kQ4jdSSv/IDUhWTKEgJRWcZ//etfut7KJKmpp546jhgxIv+xuv4PHiztkE5SpTIwWWKJJbQczGUx18c1JDYO4olKKb711lsF80GZmK9CwgYHjplnnjmKdW0UowaVtllTCS4cNk8EVrvssktu7gscWKv56KOPFnxXu90QlaniJSSm0mDfvn31/3LaXz4WSOhITNYmrV3JAC0/aub+p02gIdh5552jGJxFpGNrL2lnsVaOrFtFy5EWxLBN1zCynpF2zZlv/je/+U2ujfK93XrrrWmP+7UWR4ARuYcUBJhQt8XoGDAQrrjiCjU6oOOmI4IkTH0oFpX6waDGu/DCC1NS/PmSLE2IYradUwtCumJVWvADTUsIIkGNK1JU7iPloxXz+bToNV+jjP/85z+VgFBN5R90oBz511FNyci64PtFwsnhCaYMMkTa0cEH7yykfuUeA4OTTz5Z15jxLO9Gvfzhhx8WfF873RAJUOuegQeEZv/L/JgOJsotK2s0WVfH4narQ/CkPYkUXm4yTY3HIJL2wOCLb7JYoE0ValfgKMtOtC1ZmzZM7H+w4fvFYYSH9kPACbFAncqaJp0z4EPAwozAAmBGh3wUO+64Y+5JpBisIrnOfEaxuRc6fIiCuKJi1M6LDr7SwDMQLyRCWhACEmtPBEbaoi7K5Zv3MYfFImckPIho9913jxtssIFKh1iCMlpHapH1YalZwgtKH/GGQlocLPxnUIE1a7mBfDF3ZnUCrmJgUdSJQblpZz0elsbghlQODmussYb+j4SN95ZyAgMrPPswb0tatHXOMkVQdbss571ZjcPCfL4nI8H8AR7XmZ/EiroQqWa1bJ6v8hBwQiyAE9LWAgssoB0E6jhUMaip+CDoNOjsGV0TZLG4esTgOp0zape0AHEyoiceB8Y5aSrStGfTrkEesmA+15FBUqhVeyLgMQa12iGHHBKPPvpoHY2jrmJUzaicM3jwfpnvjDIHoybraWRPmZHuDEs6ZJkDrIgMrYxgesIJJ+Q6dersscces9tte0ZtTn3LXJiWkcEQbUqcMij+5RSc+urfv78+Z2SI1oH6S6u3ctJs5ThImKhIwRE88g+usyxF5mhbuZie9yIIOCEWAAfLTdyU8REwUkQVigRiHUey48FvJvE48JNYyOoT4jQXaMxJ1GPO6+WXX46yaF/fjXsq3tETgRExBAwJchQLxC3WoUJi+Jg0zOiUC2FW7D12D/WVDV6on56eT7X3NvOMVCjGVrlBBBggLbM+jsFJOYF6NB+4tHHqQwyUypYwy3lHK8Wh3R544IGKA+0oX0IEHyRI1gB7aE8EnBAL1CsfBypJOgjUoNZ52xmCHCv+HgmYYBOP+cBik+0sLbC0xJI0t6BaE6nyD8SDE2vLFx1cJWrHKl9b02M42mauizxjUFOPDgYiMFX0kksumZPea8poxh+mjSYDJFlp3WOghLMH6sIkIoy8MBTrxCBWzKoytu/JzjZgwLk3Uyce2hMBJ8Qi9UrngrUj81I4zcaykUNciek1m1inI8ICFe8pxVSgRxxxRE5NaIY6RV5f1i0Ikfk7+3CZy6y0UyzrRXWMxLyVdTCQVz12VcAIirTAARUs69M8lEaA9iqLznOaC0gRVTbzwP/5z39KJ9BmMfiexG1iHDRokDoMR4WK9S242De29957t1mpvTiGgBOiIVHgzAeCagk1X/IopTbMT445SeYi7aOCWOsV6Lgs3T//+c8lLe3q9V5Lh4EAOBHACFWeDRYsTvJsSwTIM3OzGHfUGqgPnBQYDhj6eCgPAQZ0aDZwEmH4QQAYfWE4xfxxJwXasrVjpjWY7zZcOMv6w06Co6PK6oTYoOpGgjQJho9qr732qtubsYi1D5ZODBP0RgUMMDDuEOcAkSUlqI+Ze8XYJ1+lZ3lKzh+aUYjdq+XMEg8byXunVRmSSIo77LCDtiMwtANJEa9KrRYwGGJ/wyPF05SthcWKme+u2PZllBNrU6Tmiy66SKdNsJ6274s9Spmr9dCeCDghNqheIQckGFMVbr755nVTbTIPZB8szp4Z8TcqYHXK3B1zqKiaUAVTRoxcXnjhhdRsyA4Yufwyr1qvMFbmdI0QWajdKQGJBvdtSOrVBiR69gukHRmGrE1kCVGhgU2172rEc6xxRdXJHPUxxxyjzubnFsfzEBpratMC5WR9Lw4nMJ7BlR0YMO9vmNDOZTeMtMf9Whsg4ITYwEpEPWhrvjBvL0QYlWaJdI0Qmets5ByiuA7Td9PZIC0yv0JeWF5SSBWK9GYdjGwpVVS9WgkWbB5s6XYKIbLM5R//+EfsI2s6kdQvuOCCVAmIeLLHplrgog5MBv6nDWEoZvhBBKgKGzm4Suap1t9YW6MCZnCGVIjhFgYxlLHQel0kRwzjeAYc7OB/Dto1PoZteqDWPPrz2UPACbFOdVIOCV1zzTU64uTDYr0iDoNrDZjYmzs5Pna2RmrkB8tcKOXB2TkSohEilq+FwrBhw3IdLypeDGLqEZA2yQsdGY7W2z3I7iARaRspCEMYDiQgsM+3EgVz7rE0Rza37QYNrgapP7DjgBQYXLQqGVI4vjUkPEhR/BHn5pfBqhAhsnbWHF0YGSbPYIPmg4Gfh/ZEwAmxinpFtYIVIyNz5ir4QJB0UB8WMyb54osvtAOzjoeF/qi6agmyBVDuI8Z8HjdwjQxGgKYytf+LESIqJ1uPCYlffPHFNWcZdaEtMifNfEKo+QUZS4A5P9TT5twAtbW5X+Mag6Tknpl4FKLdoaG4+eabu5UGo6zf/va3eh/SpD4KSffdHszwP0aIqE3ZtcbaRjFC5DsGQ3BKEqH95jrYslbRQ3si4IRYRb0yZ8c6OlQw9957r1ri0SHJ7uW6/KJYkoy8TQVD51TM12exdLgHwaLCMYLFJyUE3chgBIiEQcez/vrra37YlqhQYBE+a90s3/jhrFUawWEzXkRIk06t0TgUKmtPXcdnKwYvlJe2iBEIGOBS0NoXAyRUoRiJmBYBgsh3CMG8GQMa0kL1zVq8Vg98Zwy6IHjWE5vBEP/jFSkt0AYZONhaYfAwLDlDjFzDOK6UYU5a+n4t+wg4IVZRR1deeaV+GHwc7O6OgQy/WVZRykQdizd2hiA+B0SCMUg1gZGqzUky8mVU3OjAjgiUw0bi5mSa5R/FAju7m5SI+hhXZLUElgcYptRHrQRbS14a8SzqUtSflBkrSAYAaC7oqOn8rVNncIBfWWsnSIIQZDIkCZGdShhotXpAg4PKFIkO61KkabBCe3DeeecVLB4W2uzqgtqYb8raFGeTFCFHDHNa0dioYMH9hiLghFhFQ0ClZB8KhMiSA/7HSq/UyJGPCHXesssuq8/wkTEqr4QQIFVMypPrxlh3V4v7sypg0EdGyLZTbGg8ZMgQ7ZRR4WJNW8xjDw/i/1R2IM/hiPs5OuZqwrhx43LeVpB0kNrbPSAhmlQH6dF+rIOWXeTVm4rNC5pkQxtlSyPmypKB9mg+PEsNZJLPZfk3S5GQnMGG7aHYqQaCxHE57g6LBQZTDGzxfoTEyHy0bf9kWLJFWaurlYth0Kn3nBCrqHmcdxshIt1Zx16OhMjrmP+hA0PlSjp8ZBiXMHIt5YeStX6oSZNkiDosXw1WRbGqeoQ5U1yx2dpHykYZOJcK5Nk6dTBAOim0O0ahtJB2UM9aRyUbL7e9dAgWGE6ZQRNtiEFI0pgKIy/aKdsZWVvlnEaISQmRwU07BBw1oCrFIT0ERzuFGGlzNnAoVU4Ij7aM0ZcNYJEOwZFv3gmxFIKtd98JsYo6Q/qxTgbpxBwkl0uIvJKPFNWrjczp0BnNbrjhhmoMwagdU3nIhk6fuGz5A3Gaz06eYW82PvJkZ1hFkWp6pNwOJv8l5BnDJMoNnnQ2qFzpoEsNDJCQWGKAZGmGJSz4L6Wyzs9DK//PZrcss1l00UVTnbozKEFjgQrZBl9pPnTbkRCpVwYFSetv8Kj0O+H54cOH61wkbdQGXljtemg/BJwQq6hTrPSMEFGZDh48WP/HJLsSv5yMMJnrYJLePjTIjjk1JEAIlrk59rjjGvcsHnMhdIaVbi5cRXFLPsKcE554IPBKAwODk046KTcfBrmh6gJTBhu4gSNdDgiArZ3wboNRDp284YFkg6q0WnKuNN+NjA+pMejhQN1nZeSM6hlsikkrSDh4EEL1d9111+WetzK0o8rUylbLGany8MMP1+/PvnfODOAwIPPQfgg4IVZRp8yT8WFAVCwhYBIeSY/F4MWWXaS9io4M60CetTkf+/iss7f/ObNOinkQFk0zZ1jpiDctD7Vcu+eee5S88JDDgntGzuYqK5kuEh+dCHjld96ot1B1JsuPUQhGN6j8kHA4WHhOHAYHproCE+KAYTlq2mSeWuE3A42BAweqahn1Muph6r4SrzQQJ5hTB/nYg4ETYnpLYJ9NM6xJfovbbrttSQ1Geop+NesIOCFWUUOo6/CEwYJfJBxG6HT01Zr602FBbhg7YLDD/AQLru0jpPNnfg3SuOuuu+Krr76aiXky5qgYCEBeSK8cdCDs4o4RQ7LzZfE3Fo4sFUhb2AwpIgFhIQnh2SAAiRELSY6khMx9XGzhfQVfm80eGFTRjEo+ggcZdkixctMewAOMjxQfnSYpWkK0i2oGBe2qMjVcqj2bi0G+P/sWGbh2klq+Wuxa9TknxCprjs4+2Qknf1eZpKbHnAUqyOTSDlSIqGkhDTq8/I6w2vfV8hySy4ABA7SjoLOAFG2eig6kV69eaqGHSo+AdxTicaAKTQtgiOSDGhojETZbxpghmS4u71ZeeWW1AJwwYUImBgZpZanHNSRtBheQf+/evSMbUXPmf7QTI0eOVMcOqJBx8sB8KqrksWLoVUkb6QQJke+GtlXuoBVpGmncBmazzjprZNsyLHg9tC8CTogZrVvcutnHOLcsy2D7qCwFrF0hJvLIYmcWgNMxo861fDPPiSUkEggOlrmO+XopS1I6LzokpGYGBxga8Swke8cdd+h1BiSVdPpZwq7cvED4tvieHRbABJW0qYuZZ8YZBHNaSI4MNriH9JiUzku9rxMIkX1NWVKC2r2ceX6895jBG23vxBNPbOvBV6k20in3nRBrqOnnn39eDT0YNZo1W706aSxZrePjw8xfO1ZDtuvyKISIxSKdxWyzzaZzp3TCtrkq1+mgUXWiKmWhM9cgd56tJNj2O6hSURkXC6izWdKCirbVAwZEtqDenC5AkpAgWNI+rI3wPxIiVrrM61YSOkFlykCC9sMcfDlrfiFNLLjBlYPlGx7aHwEnxCrqGMtO5hKYw0Klh9/OddddN2688cbquoyF+uwHiIeMoUOHxq233lrdRVUyv0NnyJoxPkZccFXayVVRrIoegdRsX0NcpuF5hoDakzWJSRdYJrlQFgxDsBatJLC/onVMuOQqFtiuiI4Py128ubRyYDcUW6d52GGHaVEYcJl7PDChg8fgaIQ4SGAwglFXJe2MRFtZQsSCFktkBkLFgi2NQqpGy1AqgDMqe8O41ECsVHp+vzUQcEKssJ7obI466igdudsInbMZlXBmVM+cGq61UBvyP78r8aBCZ4jLLT7IfELkY2W/t4022kidFjOXxxrF5BkDnHLnSyqEQKMjDWKSbkTF72SAFK+//vpubuqIyzKSSiXESggRdSHvgRRbfVTPoIhyUB58lBLo/G0ekXktXIhBBmgoqtVOtCohjho1SqVi5pVxTsEgjLWprNvN99rEgIFvEJV9mlFXsu3abzOq4fvDaM5D+yPghFhhHdPpIIUYEdiZzokPExJj8TwHSwQ4oybk45og6q5yA9INz5I+KskkmUI2W265ZTcSThIyvyHieu5Gn5Zv5gIhYVR4GAHlB0gTYyDmbpjjoixI1JXuwM7eioZzKQmRuUwkUg7mLVs5oIlgfpCyMJeIZMMu7ualCIOb/I6/mvK2qsqUeVXmr00DwSCU/9GssAwI1SiaFdopA0QGptwrlxBNQsSA6cEHH6wGWn+mxRBwQqyiwvAew84SEB4m8EgwEALLMOhc7OBj5Dcj8OSC6nJeiYUhar80QsTalL3/mOOAjLCG4wyBIlHw4TNvx3t7MjA4wIoUic/mUPPfh0RNp41zZQYFrOGsVJIpRogsTcAlFzjT0e2+++7aQYIbxjjsD8nAoBUdVrPrhPnQRAuBhEOHb/OGECPLf2oNYGeq2VZy3YalM2symZ5gjhpfwtQ7BMmgkG8BC2Xaj8278l1USojg3eh9RmutU3++OgScEKvAjQ6djhiVFqN2pDmkIebPIIC0o1ISIL7tHIHKJikhkmXWP2J5Cjkzj8IomPywvAGDHJwbk496BCz0INdCS0vIK8SI70icFKRJLVhIotqrJk/FVKZIgVifQhxIUYzm6RCtU4RAIBLWK7ZaoE1B9uxqgvYBqd8kZTvjtm3PPfdUYkRzAM6VBgjRLCpbybk37Y7vgG9xgmhfcM6ACpkdWBgs0AbACUKzQQQq+3IJ0VSmpIEz/ULtv1K8PX52EXBCLFE3fHTMxdHZ5AcjQOIgIbHPGvsb8pHWGvhobdSO4QSe9/MD700elh9Ipx4fL+UYNGiQ5oORNSNxOun8QNmPO+44Ve9BPqjyJlSgHs5PL/9/28uPjilfNYv7OnYxsMNIg84QCYGOEZIcIXNIrRioSwYYDHhYv2nGXJSJA28+tA8GTWwrBkGagVO55UWCBj/wZR0jBNNqwb4D2iLfKuTIIAjvSUiPhhfuELEOLyfYsiLU/aVU9eWk53Gyj4ATYok6wnyfToaRc7FtY/DaYp0yapxaA/4rTWXK/CTrohod8LOK9GUS11ZbbVUwCywLQE1Fp4pUVg9Vnr3M1jaSj/x0kUxZcM3B8hcWr5MHLF+Z67V7hVS69o6sn+nwIUfIig7fyoXaEAKEKM19XqUGIBAtAx5w69OnT9ahKCt/4EWd0z6SeDG4LXewiPoYTPj+0JJ4aH8EnBCL1DEfFeooOmJGibgjKxSQXIwQkJDosGoJzHnZOr98K9Na0q3kWdSfpmrCuMOkLOY38YZCx2udC4Yym2yyiXYg4LXXXntV8qqicU1lijRUyqmyWb6S33LM64u+uEVuGlHS+XNYnZSb/Va1Mi23fNXGM5Up3187rGutFodOes4JsUhts17OHE6jCkQKLBRQw9gyCaQTtoypJeAf1SSjfCvTWtIt91k6VvMQwygZwx1ID7P/vn37qgoKbFC30QEzeECtS1wOOpN6BTOqgeSY7yoWMMVHVcr7kZ48lEagVY1qSpesthhmZcr8dKVSd21v9qebhYATYhHkkTZsuUD//v119E10SIFJdrbUsfkW5tZYCoF0BCEwtwVJVBsY9UM8pNUMCREHxuZdhjwwf0h5MNqB8LlGWZEKzYLzqquu0uvcw8CFea96BJMQkVaxUi0WyAsdPO+uBf9i72i3ey4hpteoSYhYbbNtlof2R8AJsUAdI/WYCpAOfpAYlxAgwG222UaXWyCxsBbKApagzDcQn9FlmrWlxS11pjO33c6bQYi4rkoas+y9996aZRwCUG7KyME6RDM4Qm1s15Ee6zXvYoSYttt7Go4msabd82sTI+CEODEmXDFCxDCrlGYiPQW/2moIOCEWqDFcYLGInA4eSQhTbgKT8kmiWHPNNXOSCJZtmHXzDB8TasdqA4Royy6aoTJlntDKSfkx2iCwRxyWnCYJU06TEDGsMUJkTdiEOlmamsqUpQEsVvdQXwRcZZqOpxnV8P35HGI6Ru121QmxQI1CCJix08Gz+N4kQYjSrD+5h5rUAoRoC6n5mFpZQqScNodCOfHbigRso2YIkYOFz+zMwV585i+S+JS/XipLkxCxhHRCtNZWv7NLiOlY4nyDtuxGNen4tONVJ8QCtcoaPOYN+SAw0jjvvPM0JusDbc0W99i416z6cK7MaJLrLNOoVUJspsqUwuKY3OZQmUdBDYpxkZGhSYlIbgweTJVKXBtAFIC3ostOiBXBVXFkJ8R0yPBZ7ISYjk27XnVCLFKzu+22W041uP3226vEx75oSUJgKQCSE9Igu5vbwnAWBNciITVbZQosbDmFZEinkCyzLcXgevIevyFQHI2X2n2gCOwT3XKV6USQ1PWCq0zT4WR6gHbvKtN0fNrxqhNikVrFBZpZVLJAffDgweq31MgBYuA32z9xj8l3SAGSHD16dJGUy7vFLuik14w5RHKI5IsPRxba5xMfZU9zJ4YnkGIODMorefdYTojd8aj3f06I6Yg6Iabj0s5XnRCL1C6eLtjbENKDEPCmjwRk/3ONg2vcs/8xwMEBdy0huQ6xGVamlnfKMXLkSHXfZupTVJgs0keCZN0fHlJQme6yyy5xzJgxORWypVHr2VWmtSJY/HlXmabjww4ZfNM+h5iOTztedUIsUas40GaBfJIE+T23bOnEnBoGN/yPxMRvyAGDnFoDUpbte9csCdHKwMAAgyE8v7D4nr0auYYEyZkF8Dg4xzsP6yfrHVxCrDei3dNzCbE7HvafS4iGROecJ6GoMgryUAAB4BFSDOK4O8iu2RpLrC+DLEMIYkQSxMdokBF2ECIIsiYviPo0iOVlEJIskGJ5l0mvX79+QUgoCCEGWdIQxPFyeQ/3QCxwkHlNBlBBJMWJysf1WstcKNtiuBRkP7ogxjtB9lcMopYtFNWvV4GAbFMWNt988yDbeAWxDs618yqSaqtHxF4gDBkyJIiEGMRfbBBHFW1VPi9MCgLSkXkogQAGLmyrgwT00Ucf6W8zmMFDDfdYsF9P6Yj0m21lWgKWht12lWnPQu0q03R8WXsrXaarTNPhacurrjLNaLVCiM1cmJ8lWFxl2rO14SrTdHxxUM90iFuZpuPTjledEDNaq06IXRXDHn2M1N1TTRcm9fzlhJiOJru9OCGmY9OuV50QM1qzrjLtqph9991XCdE91XRhUs9frjJNR9OtTNNxaeerTogZrV0nxK6KYWNiJEQnxC5M6vnLCTEdTSfEdFza+aoTYkZr11WmXRXD7iKuMu3Co96/XGWajqgvu0jHpZ2vOiFmtHbzJUTcw3VqwCWeE2LP1X6SEPHB6+FnBCBE2h1GNb5BcGe0CifEjNYzyznWWGMN/SBxG8fGvJ0abBcN9pr0jqn+rQCHC7ZLS58+feruaaj+OW5MimwQDiHikvG+++5rzEv9LU1FwAmxqfAXfjnOwldZZRX9INlFgs13OzWsuOKKigNbTY0fP75TYeixcl9xxRXqf5fOH4te1tV6iOqKEEzw5Xv77bc7JB2AgBNihis5uQ6xk0eotg5xrrnm8v0Qe6C9iqcadUVI588+lh5+RsB2tkF6ds1EZ7QKJ8SM1rMb1XRVDHtO0llDiOw56aG+CCTnEJ0Qu7BlDhGH9vgodgmxC5d2/uWEmNHadULsqpiBAwcqIbLN1ueff951w3/VBQGWXTDYcAmxO5xGiJNNNlm89tpru9/0/9oSASfEjFarE2JXxWy88cbaWaM6/fjjj7tu+K+6IIDK1AlxYiiTyy4eeuihiSP4lbZDwAkxo1XqhNhVMebcG9dtTzzxRNcN/1UXBHBYv+SSS7qEmIdmkhAffvjhvLv+bzsi4ISY0VqFENdee23tpJq5QXAW4DFCdE81PVMbn332WVx66aW1rfk6xC6M3VNNFxad8ssJMcM1jbd95nUgxE5emM8GzeDgzr17prE+8MADcd5551WM3aimC2OTEN3KtAuTdv/lhJjhGt5iiy1yhMg8T6eG1VZbTXFwCbFnWsC4cePiHHPMoRi7hNiFMRIiu13MMMMMEcMjD+2PgBNiRusYlaltEIzrqE6WEPfff3/trF1C7JnG+u6778YlllhCMXYJsQtjJMRJJ500Tj311HHMmDFdN/xX2yLghJjRqk0SYqfPIR522GEuIfZgO3355Zfjwgsv7BJiHsZIiKxDnHzyyePo0aPz7vq/7YiAE2JGaxVC7Nevn3ZSnU6I/fv3d0LswXaaXJjvKtMuoE1lioR42223dd3wX22LgBNihqt2l112cUKU+jHXbT6H2DON1fdDTMcVQmRRPgZdl19+eXokv9pWCDghZrg6Dz30UP0Y2eWhk41qfNlFzzZS5qdtYT5aCQ8/I5AkxFGjRjksHYCAE2KGK3nTTTdVQux0oxqTEN2opmca6wUXXBDZSQRJiDbn4WcEMKph/hBcLr30UoelAxBwQsxwJW+99dZOiFI/Tog920jZ1QHjETp+9uD08DMCToid1xKcEDNc5wcffLB2Uq4y/b3i0Iw5xE8//VSXvBRyGffjjz9G4hQK3333Xbz//vvjW2+9VShKfPXVVyNrAZ955pmCcXryBh2/EaIb1XQh7SrTLiw65ZcTYkZrGivTzTbbzCVEqR/b/qkZKtNjjz1WF2bjyeWkk06K33//fa7FvP322xFvQn379o2oHfMDG+2eeuqpuuM6G+8OGzYsfvHFF92iQabrrLNOnGaaaeIiiyzSlG2GkBDNeMTXIXZVD7i4yrQLj0745YSY0VpOrkPs5DnEDz74IC666KI6MGg0IT722GMR6RxVIh5LWP7y4IMPaov58ssvIyrtKaaYQqWrWWaZRQkv2ZzGjh0buc7zLPCebrrpIlKHhZ9++imeffbZut+evQOfoi+99JJFacjZCTEd5kMOOSQnOV922WXpkfxqWyHghJjR6qSzTHqqwd9kJ4Znn302t5s7lpDPP/98Q2BAFXr00UcrEUJmHJDi+uuvr1tQsYP6jDPOmCNLCA3yO+ussyKDGQLkZ0THs/xmAbyV4ZVXXonLL798tzi8B1X5Dz/80JBy8pKTTz45JyGuuOKK8dtvv23Yu7P6IvbdZP9N6ozjmGOOaWidZBWXds/XJBRQKtxDxhAQySjIbhdBtp0J0047bdhnn33CgAEDwuyzzx5kd4Igu3gHkRwZ0JSVc+mQ9TmRaPTZtIeII2q+QBxRoQVR54VPPvkkiJ9LvfbVV1+F999/X9851VRTab743wLPpwXySJozzTSTpilkr2lytvRE+gqy12EgjZlnnjkIMQTpmMP48ePDTjvtFMS9WOjVq1cQ1WRYaaWV9N1p7yp1jfTBlrOoKRUT8kA5p59++iCkq7hSdiGrIOSleSFdyiFzbUFUp+Hxxx8PF198sd7jOukJEQbKcc011wRRrQZReYf33nsvlyXiECiPkG04/PDDw4UXXqjp8iz3SUuk0nDGGWeETTbZROOTX9miSX9T79wnHxZ4Zsopp9R32rVyzryPOhg6dKiWid+iGg7XX399WGihhbQ85aTTyDiUlbbJYYF8E8BQVJx2OcigRn8T97XXXtO2TbtKC6RL++TbIh0ZrITddtstTJgwQaOvueaa4aKLLgri6Dvtcb/WJgg4IWa0Il988UUlRHGrpTmkw+ODXWCBBcKHH34YxEw+zDPPPLlOiw/aOlTreO0aCdAR0LGK140AmRG4T7D4nL/++mslLzoWiIKDd9IR01m88cYb+hwkLU6Pw5tvvqlpJN+lFxJ/uAchilGMEhsd1YILLqidsRiUaHp0xO+8847mk06HDp+8PPfcc+H111/PdW7co7MGCwvF3p0fBxzIM2WlDBAhnaWoQBWb3r17hx122EExFpdxQSQ1zZ+9g+coC51wsiPmPaRNPNmdQ9Ol7ohPB5u8T91BtuPGjdM0eIZOm3eRBvEhVlHJap5knaDmkbSou7nnnrsbIRBf1LFaBssn77PfnAk8nwz8zztF2s3VI3kTKVHTs3wnn7E0k9fyf5cTp5pnSJcDDKh/2iTfBfVHoCwMaqycMl+r18FGNCzansA3LZAumPNt8ZvBmMwRBzGK0v+POuqoIJK7vi/teb/WHgg4IWa0HpFAZJG0fpTJLEIUdFR89IU+7mT85G8+dIJ1GMl79ps4dp/fvMukEfvf0iBeWqdpaSXPxOWwPFje7XkjAp6xe/Y+e4Z7pMF9ztUGe6flx/4nPcqKJAppm1TGIGLQoEFh5MiRASmZYM/ye8MNNwyi2g1iJcq/mj/ybPmm80bqZZBjgfcYoXLtwAMPDOJCLUB+FiBe3kNeLI/8b/hYPM7J/CSvl/ObfFheiU/eSC+rgbxZ/jgbNpTBrlve7Vp+Ge1+8gyuxDcs7Eycq6++Wus5Gd9/tx8CTogZrVNGpmKuryNbRr75H3qxbPMhI+EhSTF6poOTtXy5D51nuYZ0RictVpyqPiyWZrPuUW7yiOoKdaYY2HQjEvKFxICqNxkoH9IOUgKdYT5+qDTFaEZVuHSExOcdqDBN1UZ684rkivpylVVWUTXp9ttvH1544QVND5wXW2yxcO2116q0cscdd4Tdd9+9W1523HHHIMYZKtGJkU2QnTtyKlueR0rlnajHySt1vscee3QbCJF32dE+yJxW2GijjbSukp01+eT//DJyvVBAPU35jUyIJ3OiStxIzah6wYQDlTmSExJ7Je8o9G67Tp5R+y+11FKaPlhw7emnn869n/+pA9qyDSC4RuC7oAzJtk0domlYdtlltV1QPuoXaQ9th8wNqgQP1rfccosOZGSnj7D66qvru5EmKTtqaeJwZkA0//zza3uyvPu5PRFwQsxwvdIBlDOyTSsCHRcdgXV4yTkXi8890udePTs6S79eZ/JoHRsddH4g79ZJJu8Vum5xID57jrh0+rIEQjtZ4nDtvPPOC9tuu61iRD6GDx8eZN1eToW56667htNOO03vI1EeccQR4ZxzztFXoBaVpRbaAXOB94nHE1XJkhaB+VA6ZsibQBzSO+CAA/R//jCXKIYv2jkz0CFftQbKTR6s/KRHezHMrN3wv11Lxq31/fa8DUZI28pl9Z0fx/63s5Uh2bbJNwftxNIjPteIz8E9zmDNu/jf0rCy2pn8Eeys//iftkXACbFtq9YLVikCdJKoxoYMGRJk6YMSkViNqgrV0kIqefLJJ1W1iSpULIFVqrL7SFcYpSBdiNeXwJxksjNFyoLwLhIDDSQP5qYwlkoGJBzygQER0sspp5yiklSyg0/G99+OgCNQHwScEOuDo6fSJgggNchaQ5UAUSXPN998E5UMaYN4EFTSqtEiQpqQayFpjnlIjIWYI5TF+DnpxJ7nWdIgDnOPWBY7GRo6fnYEeg4BJ8Sew9ZTblEETJWYr3arZ3EgVUJSesxPnzgQoZHhFVdcofOVqGWZS/XgCDgC9UXACbG+eHpqjkCPICC+UIO4VVPDn8GDBwdZ9F9wPWmPZMATdQQ6AAEnxA6oZC9i6yPAvON+++2nxiHbbLNNOPPMMzNrGdz6aHsJOhUBJ8ROrXkvd8sggAoXTyl33XWXqk/PP//8sN122xVVt7ZM4TyjjkCGEHBCzFBleFYcgTQEWLDP0gusTyFGXMPhds6DI+AI1BcBJ8T64umpOQJ1R4BlF7iRY63c6aefHnAO4MERcATqj4ATYv0x9RQdgbohgP/Y9dZbT52c47EFbzf4MvXgCDgC9UfACbH+mHqKjkDdELjtttt04T7rEnE6jgcbPOrg7gzH1h4cAUegfgg4IdYPS0/JEag7AldeeWUYOHCgLtC//PLL1e/pPffco95ucCruwRFwBOqHgBNi/bD0lByBuiKAk+k999wzXHXVVerg+thjj9VdN7A6XWuttcINN9ygfjjr+lJPzBHoYAScEDu48tu16Pgave+++3SXBva4w2couztgmcmOGbhDa2RA7ckGx8sss4zu2oDLtmR49NFHdecRjGbYWYJ4hBEjRoSdd95Z3cShHp1nnnnUnRv3cCmH9WmpDWtxE3f33XerKzrUruxowe4Q7EfpwRFwBPIQEL+JHhyBtkFANv+NslVTlC2homzlE8UAJS688MJRiDEKiUTZ/DaeffbZUaSshpT55ptvjrPMMovmR3yjxocffjj3XnHNFmX3iyhEF4W0o+x4ob/FqjTK9l9RFuOzz1EU1225M7/F3VsUUo2yE0curbQfl1xySVxttdWibOSs75cNdfUsW1ZFcVreMAzS8ubXHIEsIoATYg+OQNsgAElALBAJxCFSVxSfpPrbyESkpHjZZZc1pMzHHXec5oX8iIQaZZeL3HtffvnlKM69c4Rn5AeRn3rqqVH2XYyyT1+UXeD1gAQtDmU699xzc2nl/7jxxhuj7DWoZecZ2WtQ0xCH4/o+MIAwPTgCjkAXAk6IXVj4rzZAQDbQVdIQtWg89NBDlVhkL8HIsemmm+bISTbqbUhpZXun3DshpqOPPlrfi3Q4cuRIJWquywa0URbdR1GZanwkWlH9RplHjA899FB85JFH4pFHHpkjONkWKsr+i6llEDVpFEMcJT4GB1tuuWUULzeaBpgYsULGsoF0ahp+0RHoRAScEDux1tu0zJ9++mns06ePEsq6664bv/32W1U9on7kuPXWW3PktO+++zYEBSRCJENID2kViZFA3sT7jF6XfRWj7KEYv/zyyygL75X0kABRnRJQ73LIcou41157Rdl4WMkUUk0LqGGRAHmnrGGMsgdjlO2qNA0w4r3kReYldaCQloZfcwQ6EQEnxE6s9TYtsyxH0DkyiGDQoEHxm2++yZUU9STXuMdxyCGH5O5V80M2AC7rMeL1799f3wlJyRZO+hwk1a9fP70umwxHMfrR62+//XZkjo88ikeaid5BmZgn/f777ye6ZxfE+bc+36tXL5UM7bqd77zzTlWn8o69997bLvvZEeh4BJwQO74JtAcASFBnnHGGEgEdPfNwGNcgDW2wwQZxoYUWisyfcQ/jFtl8NyJhiScYlaBKoSBLH+L6668fZe2fHiuttJKekcCGDRtWUH1JugceeKC+F6nsxBNP1FdBiKhIyc/aa68dP/nkE71OnlBxch0DoGLEpw/k/RFL0ihLMvR5DIpQueYHscCNc845p8aRraTyb/v/jkDHIuCE2LFV314FR2piHg4i4UANidoREuLAwAZSXGedddTSEwK96aabonh8UdKU/QaLAoKUh+ozmZ79xoq0mMWn7EyheYKQjznmGH3P559/HmWTX72++OKLRyRDAoRoEiXziffee69eL/fPiy++GBdYYAFNF0JlPjE/iHNwxQectthii/zb/r8j0LEIOCF2bNW3V8ExPIGg6OQHDBigqskdd9xRrSu5hpHN+PHjdZ4OMnz//fdVAjNLVObuigXis1wDVas42o6ya70em2++uUqIzAkWCsQlD7JmMKKuJCRVpkiZJiGSDpIt8cV3aXz22WcLJZt6/YMPPojLLbecPg8RpwVwMOMdWfifFsWvOQIdiYATYkdWe3sVGoKTzXOVBLC+hERQHUI6ZlnKWjyMaiwQBwnS1vgddNBBdiv1jIp1yJAhceONN1aJErLFcpW1gkZmqQ/KRaxDIbjZZ589jh07VqORN1SlXF966aWVoLmBitQMg2SBvhrf6ANl/uF5CJZ0l1xySVUJ5z8q/lBVfcy6RPLvwRFwBH5GwAnRW0LLI4AFJXN7kADzckhJFiAtrCkhvz322MMuq4oSIoIQOUoZ2SB1kg5qTw6WLqBCxVAGNSwWoIUCz5I3pDKWPxAgbCxduU56F154oV5//fXXc0Y1EGa5AdUo86GoYu19qHLFS023JJ566ild/M97WZIhmw1HDH/A0IMj0OkIOCF2egtog/Kzlo5F6HTyLEtIzpuxuN3m1JZddtkccTFXh/qSRe88d/DBBxdFgvV7xIUAOSAxnuNgblJcsxV8ftVVV9V4SIhjxozJxYOsTEKFLC+44IKIChM1Ltd5ZzkB7ze8g3Jy4PWGfJHGILGsZckJAXUs0iHX7UCVjIp1+PDh7rmmHLA9Tlsj4ITY1tXbGYWD2OjgIQHZHaJboSEBDGe4B5GJ/8/cfdSmZm1ZihAhPBbS491l1KhRcejQoao6xTUa15D4CoW+ffvq+5HYbr/99lw0DGmMLMk/7uZs0TyEi9u3csJOO+2UU/8aDpSXg3nICRMmaDJIgua4wO5zhoBZAoIa14Mj0MkIuHNv6RE8tDYC4rElyPxeEEvRIEsg1PF1skTsMi/r7dShNTtEiESnt2VeMMgawCBqyiAq03D88ccnH5vot5Be7ppImEHmLgPXcB4uBJa7l/9DjHHCOeecE2R9oW7bJNKsRpGOJ+DYm7zhgDsZZDlEkIX5QQgyeTn1N47MxdWb5oM8PfHEE0GkUXVk3rt3b3UQLstQAnmWOcwwevRozbuQp6ZHPthKao011ghCjqnv8IuOQCcg4ITYCbXcAWVkNwtRDQbIxjp6K7Z4gAn3339/kIXqQYxuclsmQYgy5xjeeOONIBJiOOGEE+yRup5FMtPdLmTObqL8QVKyZCTIUggldMiJHSxkLWJgp45yAiTIpsFiZaukJ0Y+urMHRC1SZxDjmVwyxCU/vCeJk/g6zeGSi+w/HIEOQ8AJscMqvJ2Lm9/JJ8sKEUAASQmoUYRIPsgbIUlCekH+cA9JkzwSxACoLMlQI6f8KfaulOh+yRFwBP4/Ak6I3hQ6FoFKVaYdC5QX3BHoEAScEDukor2YEyPQSAlx4rf7FUfAEcgaAk6IWasRz0/DEHBCbBjU/iJHoCUQcEJsiWryTPYEArLsIsiSCDVmEU81QRxv98RrPE1HwBFoEQScEFukojyb9UdAtoQKsjNEwCpTnHPr0oP6v8VTdAQcgVZBwAmxVWrK81l3BGTRfmANH1adK6ywQtG1hHV/uSfoCDgCmUPACTFzVeIZaiQCyaUOjXyvv8sRcASyh4ATYvbqxHPkCDgCjoAj0AQEnBCbALq/0hFwBBwBRyB7CDghZq9OPEeOgCPgCDgCTUDACbEJoPsrHQFHwBFwBLKHgBNi9urEc+QIOAKOgCPQBAScEJsAur/SEXAEHAFHIHsIOCFmr048R46AI+AIOAJNQMAJsQmg+ysdAUfAEXAEsoeAE2L26sRz5Ag4Ao6AI9AEBJwQmwC6v9IRcAQcAUcgewg4IWavTjxHjoAj4Ag4Ak1AwAmxCaD7Kx0BR8ARcASyh4ATYvbqxHPkCDgCjoAj0AQEnBCbALq/0hFwBBwBRyB7CDghZq9OPEeOgCPgCDgCTUDACbEJoPsrHQFHwBFwBLKHgBNi9urEc+QIOAKOgCPQBAScEJsAur/SEXAEHAFHIHsIOCFmr048R46AI+AIOAJNQMAJsQmg+ysdAUfAEXAEsoeAE2L26sRz5Ag4Ao6AI9AEBP4fWE9VNt2+9eYAAAAASUVORK5CYII=	I_{R_2} = 0; I_{R_1} = 0.5 \, \text{mA, leftward}; I_{\varepsilon_1} = 0.5 \, \text{mA, upward}; I_L = 0.5 \, \text{mA, downward}; I_{R_1} = 0.25 \, \text{mA, rightward}; I_{R_2} = 0.75 \, \text{mA, upward}; I_{e_2} = 0.25 \, \text{mA, downward}; I_L = 0.5 \, \text{mA, downward}; I_{R_1} = 1 \, \text{mA, rightward}; I_{R_2} = 0; I_L = 1 \, \text{mA, upward}; I_{e_2} = 1 \, \text{mA, downward}
+340	A circular loop of wire is placed between the pole faces of an electro-magnet with its plane parallel to the pole faces. The loop has radius $a$, total resistance $R$, and self-inductance $L$. If the magnet is then turned on, producing a $B$ field uniform across the area of the loop, what is the total electric charge $q$ that flows past any point on the loop?	[]	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	q = \frac{B \pi a^2}{R}
+341	A source of current $i_0 \sin \omega t$, with $i_0$ a constant, is connected to the circuit shown in Fig. 3.31. The frequency $\omega$ is controllable. The inductances $L_1$ and $L_2$ and capacitances $C_1$ and $C_2$ are all lossless. A lossless voltmeter reading peak sine-wave voltage is connected between A and B. The product $L_2C_2 > L_1C_1$.  (a) Find an approximate value for the reading $V$ on the voltmeter when $\omega$ is very small but not zero.  (b) The same, for $\omega$ very large but not infinite.  (c) Sketch qualitatively the entire curve of voltmeter reading versus $\omega$, identifying and explaining each distinctive feature.  (d) Find an expression for the voltmeter reading valid for the entire range of $\omega$.	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	V_{\text{meter}} = \frac{1}{\sqrt{2}} i_0 \omega L_1; V_{\text{meter}} = \frac{i_0}{\sqrt{2} \omega C_1}; V_{BA} = \frac{i_0}{\sqrt{2} \left| \frac{1}{\omega L_1} - \omega C_1 + \frac{1}{\omega L_2 - \frac{1}{\omega C_2}} \right|
+342	A solenoid having 100 uniformly spaced windings is 2 cm in diameter and 10 cm in length. Find the inductance of the coil.  $$ (\mu_0 = 4\pi \times 10^{-7} \, \frac{\mathrm{T \cdot m}}{\mathrm{A}}) $$	[]	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	L = 3.95 \times 10^{-5} \, \text{H}
+343	Consider a space which is partially filled with a material which has continuous but coordinate-dependent susceptibility $\chi$ and conductivity $\sigma$ given by ($\chi_\infty$, $\lambda$, $\sigma_\infty$ are positive constants):  $$ \chi(z) =  \begin{cases}  0, & -\infty < z \le 0, \\ \chi_\infty (1 - e^{-\lambda z}), & 0 < z < \infty; \end{cases} $$  $$ \sigma(z) =  \begin{cases}  0, & -\infty < z \le 0, \\ \sigma_\infty (1 - e^{-\lambda z}), & 0 < z < \infty. \end{cases} $$  The space is infinite in the $x$, $y$ directions. Also $\mu = 1$ in all space. An $s$-polarized plane wave (i.e., $E$ is perpendicular to the plane of incidence) traveling from minus to plus infinity is incident on the surface at $z = 0$ with an angle of incidence $\theta$ (angle between the normal and $k_0$), ($k_0 c = \omega$):  $$  E^I_y (r, t) = A \exp[i(x k_0 \sin \theta + z k_0 \cos \theta - \omega t)] e_y . $$  The reflected wave is given by  $$  E^R_y (r, t) = R \exp[i(x k_0 \sin \theta - z k_0 \cos \theta - \omega t)] e_y , $$  and the transmitted wave by  $$  E^T_y (r, t) = E(z) \exp[i(z k' \sin \gamma - \omega t)] e_y . $$  $A$ and $R$ are the incident and reflected amplitudes. $E(z)$ is a function which you are to determine. $\gamma$ is the angle between the normal and $k'$.  (a) Find expressions for the incident, reflected and transmitted magnetic fields in terms of the above parameters.  (b) Match the boundary conditions at $z = 0$ for the components of the fields. (Hint: Remember Snell's law!)  (c) Use Maxwell's equations and the relationships  $$  D(r, t) = \epsilon(r)E(r, t) , \quad \quad \epsilon(r) = 1 + 4 \pi \chi(r) + \frac{4 \pi i}{\omega} \sigma(r)  $$  to find the wave equation for $E^T_y (r, t)$.	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+\mathbf{B}^I &= (-\mathbf{e}_x \cos \theta + \mathbf{e}_z \sin \theta) A \exp \left[i(x k_0 \sin \theta + z k_0 \cos \theta - \omega t)\right], \\
+\mathbf{B}^R &= (\mathbf{e}_x \cos \theta + \mathbf{e}_z \sin \theta) R \exp \left[i(x k_0 \sin \theta - z k_0 \cos \theta - \omega t) \right], \\
+\mathbf{B}^T &= \frac{c}{i \omega} \left[ \mathbf{e}_z E(z) (i k' \sin \gamma) - \mathbf{e}_x \frac{\partial E(z)}{\partial z} \right] \exp \left[i(k' x \sin \gamma - \omega t)\right].
+\end{align*}; \begin{align*}
+A + R &= E(0), \\
+k_0(R - A) \cos \theta &= i \left( \frac{\partial E(z)}{\partial z} \right)_{z=0}.
+\end{align*}; \frac{\partial^2 E(z)}{\partial z^2} + \frac{\omega^2}{c^2} \left[1 + 4 \pi \left(\chi_{\infty} + \frac{i \sigma_{\infty}}{\omega} \right)(1 - e^{-\lambda z}) \right] E(z) - k'^2 \sin^2 \gamma \, E(z) = 0."
+344	The pulsed voltage source in the circuit shown in Fig. 3.27 has negligible impedance. It outputs a one-volt pulse whose duration is $10^{-6}$ seconds. The resistance in the circuit is changed from $10^3$ ohms to $10^4$ ohms and to $10^5$ ohms. You can assume the scope input is properly compensated so that it does not load the circuit being inspected. Sketch the oscilloscope waveforms when $ R = 10^3 $ ohms, $10^4$ ohms, and $10^5$ ohms.	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	v_0 = u(t)e^{-10t} - u(t - 1)e^{-10(t-1)} \, \text{V}; v_0 = u(t)e^{-t} - u(t-1)e^{-t+1} \, \text{V}; v_0 = u(t)e^{-0.1t} - u(t-1)e^{-0.1(t-1)} \, \text{V}
+345	In Fig. 3.41 a box contains linear resistances, copper wires and dry cells connected in an unspecified way, with two wires as output terminals A, B. If a resistance $R = 10 \, \Omega$ is connected to A, B, it is found to dissipate 2.5 watts. If a resistance $R = 90 \, \Omega$ is connected to A, B, it is found to dissipate 0.9 watt.  (a) What power will be dissipated in a $30 \, \Omega$ resistor connected to A, B (Fig. 3.42a)?  (b) What power will be dissipated in a resistance $R_1 = 10 \, \Omega$ in series with a 5 Volt dry cell when connected to A, B (Fig. 3.42b)?  (c) Is your answer to (b) unique? Explain.	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	1.875 \, \text{W}; P = \begin{cases} 0.625 \, \text{W}, \\ 5.625 \, \text{W}. \end{cases}
+346	"Switch S is thrown to position A as shown in Fig. 3.30.  (a) Find the magnitude and direction (""up"" or ""down"" along page) of the currents in $R_1, \, R_2,$ and $R_3$, after the switch has been in position A for several seconds.  Now the switch is thrown to position B (open position).  (b) What are the magnitude and direction of the currents in $R_1, \, R_2,$ and $R_3$ just after the switch is thrown to position B?  (c) What are the magnitude and direction of the currents in $R_1, \, R_2,$ and $R_3$ one-half second after the switch is thrown from A to B?  One second after the switch is thrown from A to B, it is finally thrown from B to C.  (d) What are the magnitude and direction of the currents in $R_2, \, R_3, \, R_4,$ and $R_5$ just after the switch is thrown from B to C?"	[]	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	i_1(t) = 0.59 - 0.19e^{-0.34t} \, \text{A, upward}; i_2(t) = 0.12 + 0.28e^{-0.34t} \, \text{A, downward}; i_3(t) = 0.47(1 - e^{-0.34t}) \, \text{A, downward}; i_3(0) = 0.47 \, \text{A, downward}; i_1(0) = 0; i_2(0) = 0.47 \, \text{A, upward}; i_1(0.5) = 0; i_2(0.5) = 0.37 \, \text{A, upward}; i_3(0.5) = 0.37 \, \text{A, downward}; i_3(1+) = 0.29\, \text{A, downward}; i_5(1+) = 0; i_2(1+) = 0.145 \, \text{A, upward}; i_4(1+) = 0.145 \, \text{A, upward}
+347	For the circuit shown in Fig. 3.35, the coupling coefficient of mutual inductance for the two coils $L_1$ and $L_2$ is unity.  (a) Find the instantaneous current $i(t)$ the oscillator must deliver as a function of its frequency.  (b) What is the average power supplied by the oscillator as a function of frequency?  (c) What is the current when the oscillator frequency equals the resonant frequency of the secondary circuit?  (d) What is the phase angle of the input current with respect to the driving voltage as the oscillator frequency approaches the resonant frequency of the secondary circuit?	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	i_1(t) = \frac{V_0}{\sqrt{R^2 + \left( \frac{\omega L}{1 - \omega^2 LC} \right)^2}; P = \frac{RV_0^2 / 2}{R^2 + \left( \frac{\omega L}{1 - \omega^2 LC} \right)^2}; i_1(t) = 0; \varphi = \frac{\pi}{2}
+348	As shown in Fig. 3.26, the switch has been in position A for a long time. At $t = 0$ it is suddenly moved to position B. Immediately after contact with B:  (a) What is the current through the inductor $L$?  (b) What is the time rate of change of the current through $R$?  (c) What is the potential of point B (with respect to ground)?  (d) What is the time rate of change of the potential difference across $L$?  (e) Between $t = 0$ and $t = 0.1 \, \text{s}$, what total energy is dissipated in $R$?	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	i_L(0) = 1 \, \text{A}; \left. \frac{di_L}{dt} \right|_{t=0} = -10^4 \, \text{A/s}; v_B(0) = -10^4 \, \text{V}; \left. \frac{dv_L}{dt} \right|_{t=0} = -10^8 \, \text{V/s}; 0.5 \, \text{J}
+349	A circuit contains a ring solenoid (torus) of 20 cm radius, 5 cm$^2$ cross-section and $10^4$ turns. It encloses iron of permeability 1000 and has a resistance of 10 $\Omega$. Find the time for the current to decay to $e^{-1}$ of its initial value if the circuit is abruptly shorted.	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	5 \, \text{s}
+350	Calculate the energy in the 3 μF capacitor in Fig. 3.17.	[]	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	E = 0.42 \times 10^{-6} \, J
+351	What is the attenuation distance for a plane wave propagating in a good conductor? Express your answer in terms of the conductivity $\sigma$, permeability $\mu$, and frequency $\omega$.	[]	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	\delta = \sqrt{\frac{2}{\omega \mu \sigma}}
+352	A plane electromagnetic wave of angular frequency $\omega$ is incident normally on a slab of non-absorbing material. The surface lies in the $xy$ plane. The material is anisotropic with  $$ \varepsilon_{xx} = n_x^2 \varepsilon_0 \quad \varepsilon_{yy} = n_y^2 \varepsilon_0 \quad \varepsilon_{zz} = n_z^2 \varepsilon_0 , $$  $$ \varepsilon_{xy} = \varepsilon_{yz} = \varepsilon_{zx} = 0 , \quad n_x \neq n_y . $$  (a) If the incident plane wave is linearly polarized with its electric field at 45° to the $x$ and $y$ axes, what will be the state of polarization of the reflected wave for an infinitely thick slab?  (b) For a slab of thickness $d$, derive an equation for the relative amplitude and phase of the transmitted electric field vectors for polarization in the $x$ and $y$ directions.	[]	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	"\begin{aligned}
+E_x' &= \left( \frac{n_z - n_x^2}{n_z + n_x^2} \right) E_x, \\
+E_y' &= \left( \frac{n_z - n_y^2}{n_z + n_y^2} \right) E_y.
+\end{aligned}; \begin{aligned}
+E_{1x}'' &= \frac{2n_z}{n_x^2 + n_z} E_x \cdot e^{i K_1 d} \cdot \text{coefficients determined by solving the system}, \\
+E_{1y}'' &= \frac{2n_z}{n_y^2 + n_z} E_y \cdot e^{i K_1 d} \cdot \text{coefficients determined by solving the system}.
+\end{aligned}"
+353	The direction of the magnetic field of a long straight wire carrying a current is:  (a) in the direction of the current   (b) radially outward   (c) along lines circling the current	[]	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	(c)
+354	A plane polarized electromagnetic wave traveling in a dielectric medium of refractive index $n$ is reflected at normal incidence from the surface of a conductor. Find the phase change undergone by its electric vector if the refractive index of the conductor is $n_2 = n(1 + ip)$.	[]	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	\varphi = \arctan \left( \frac{2}{\rho} \right)
+355	Calculate the reflection coefficient for an electromagnetic wave which is incident normally on an interface between vacuum and an insulator. (Let the permeability of the insulator be 1 and the dielectric constant be $\varepsilon$. Have the wave incident from the vacuum side.)	[]	/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGQAZADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD3+iiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigD//2Q==	R = \left( \frac{1 - \sqrt{\varepsilon}}{1 + \sqrt{\varepsilon}} \right)^2
+356	What is the magnetic field due to a long cable carrying 30,000 amperes at a distance of 1 meter?   (a) $3 \times 10^{-3}$ Tesla, (b) $6 \times 10^{-3}$ Tesla, (c) 0.6 Tesla.	[]	/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGQAZADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD3+iiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigD//2Q==	6 \times 10^{-3} \, \text{Tesla}
+357	A plane wave of angular frequency $\omega$ and wave number $|\mathbf{K}|$ propagates in a neutral, homogeneous, anisotropic, non-conducting medium with $\mu = 1$.  (a) Show that $\mathbf{H}$ is orthogonal to $\mathbf{E}$, $\mathbf{D}$, and $\mathbf{K}$, and also that $\mathbf{D}$ and $\mathbf{H}$ are transverse but $\mathbf{E}$ is not.  (b) Let $D_k = \sum_{l=1}^{3} \varepsilon_{kl} E_l$, where $\varepsilon_{kl}$ is a real symmetric tensor. Choose the principal axes of $\varepsilon_{kl}$ as a coordinate system ($D_k = \varepsilon_k E_k; \; k = 1, 2, 3$). Define $\mathbf{K} = K \hat{\mathbf{S}}$, where the components of the unit vector $\hat{\mathbf{S}}$ along the principal axes are $S_1$, $S_2$, and $S_3$. If $V = \omega / K$ and $V_j = c / \sqrt{\varepsilon_j}$, show that the components of $\mathbf{E}$ satisfy  $$ S_j \sum_{i=1}^{3} S_i E_i + \left( \frac{V^2}{V_j^2} - 1 \right) E_j = 0. $$  Write down the equation for the phase velocity $V$ in terms of $\hat{\mathbf{S}}$ and $V_j$. Show that this equation has two finite roots for $V^2$, corresponding to two distinct modes of propagation in the direction $\hat{\mathbf{S}}$.	[]	/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGQAZADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD3+iiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigD//2Q==	"\mathbf{H} \cdot \mathbf{E} = \mathbf{H} \cdot \mathbf{D} = \mathbf{H} \cdot \mathbf{K} = \mathbf{D} \cdot \mathbf{K} = 0; \mathbf{D} \times \mathbf{H} \neq \mathbf{0}; S_j \sum_{i=1}^{3} S_i E_i + \left( \frac{V^2}{V_j^2} - 1 \right) E_j = 0; V^4 \left[ \frac{1}{V_1^2 V_2^2 V_3^2} \right] 
++ V^2 \left[ (S_1^2 - 1) \frac{1}{V_2^2 V_3^2} + (S_2^2 - 1) \frac{1}{V_1^2 V_3^2} \right.
++ \left. (S_3^2 - 1) \frac{1}{V_1^2 V_2^2} \right]
++ \left( \frac{S_1^2}{V_1^2} + \frac{S_2^2}{V_2^2} + \frac{S_3^2}{V_3^2} \right) = 0"
+358	The electric field of an electromagnetic wave in vacuum is given by  $$ E_x = 0 , $$  $$ E_y = 30 \cos \left( 2\pi \times 10^8 t - \frac{2\pi}{3} x \right) , $$  $$ E_z = 0 , $$  where $E$ is in volts/meter, $t$ in seconds, and $x$ in meters. Determine    (a) the frequency $f$,   (b) the wavelength $\lambda$,   (c) the direction of propagation of the wave,   (d) the direction of the magnetic field.	[]	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	f = 10^8 \, \text{Hz}; \lambda = 3 \, \text{m}; \text{direction of propagation: positive } x; \text{direction of magnetic field: } z
+359	(a) Write down Maxwell's equations assuming that no dielectrics or magnetic materials are present. State your system of units. In all of the following you must justify your answer.  (b) If the signs of all the source charges are reversed, what happens to the electric and magnetic fields $\mathbf{E}$ and $\mathbf{B}$?  (c) If the system is space inverted, i.e., $\mathbf{x} \rightarrow \mathbf{x}' = -\mathbf{x}$, what happens to the charge density and current density, $\rho$ and $\mathbf{j}$, and to $\mathbf{E}$ and $\mathbf{B}$?  (d) If the system is time reversed, i.e., $t \rightarrow t' = -t$, what happens to $\rho$, $\mathbf{j}$, $\mathbf{E}$ and $\mathbf{B}$?	[]	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	"\begin{aligned}
+\nabla \cdot \mathbf{E} &= \frac{\rho}{\epsilon_0}, \\
+\nabla \times \mathbf{E} &= -\frac{\partial \mathbf{B}}{\partial t}, \\
+\nabla \cdot \mathbf{B} &= 0, \\
+\nabla \times \mathbf{B} &= \mu_0 \mathbf{j} + \frac{1}{c^2} \frac{\partial \mathbf{E}}{\partial t}.
+\end{aligned}; \begin{aligned}
+\mathbf{E}'(\mathbf{r}, t) &= -\mathbf{E}(\mathbf{r}, t), \\
+\mathbf{B}'(\mathbf{r}, t) &= -\mathbf{B}(\mathbf{r}, t).
+\end{aligned}; \begin{aligned}
+\rho'(\mathbf{r}, t) &= \rho(\mathbf{r}, t), \\
+\mathbf{j}'(\mathbf{r}, t) &= -\mathbf{j}(\mathbf{r}, t), \\
+\mathbf{E}'(\mathbf{r}, t) &= -\mathbf{E}(\mathbf{r}, t), \\
+\mathbf{B}'(\mathbf{r}, t) &= \mathbf{B}(\mathbf{r}, t).
+\end{aligned}; \begin{aligned}
+\rho'(\mathbf{r}, t) &= \rho(\mathbf{r}, t), \\
+\mathbf{j}'(\mathbf{r}, t) &= -\mathbf{j}(\mathbf{r}, t), \\
+\mathbf{E}'(\mathbf{r}, t) &= \mathbf{E}(\mathbf{r}, t), \\
+\mathbf{B}'(\mathbf{r}, t) &= -\mathbf{B}(\mathbf{r}, t).
+\end{aligned}"
+360	(a) On the basis of Maxwell’s equations, and taking into account the appropriate boundary conditions for an air-dielectric interface, show that the reflecting power of glass of index of refraction $n$ for electromagnetic waves at normal incidence is $R = \frac{(n-1)^2}{(n+1)^2}$.  (b) Also show that there is no reflected wave if the incident light is polarized as shown in Fig. 4.5 (i.e., with the electric vector in the plane of incidence) and if $\tan \theta_1 = n$, where $\theta_1$ is the angle of incidence. You can regard it as well-known that Fresnel’s law holds.	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	R = \frac{(n-1)^2}{(n+1)^2}; \theta_1 = \arctan n
+361	A current element $idl$ is located at the origin; the current is in the direction of the z-axis. What is the x component of the field at a point $P(x, y, z)$?   (a) 0, (b) $-\frac{iydl}{(x^2 + y^2 + z^2)^{3/2}}$, (c) $\frac{ixdl}{(x^2 + y^2 + z^2)^{3/2}}$.	[]	/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGQAZADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD3+iiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigD//2Q==	-\frac{iydl}{(x^2 + y^2 + z^2)^{3/2}}
+362	A long non-magnetic cylindrical conductor with inner radius $a$ and outer radius $b$ carries a current $I$. The current density in the conductor is uniform. Find the magnetic field set up by this current as a function of radius  (a) inside the hollow space $(r < a)$;   (b) within the conductor $(a < r < b)$;   (c) outside the conductor $(r > b)$.	[]	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	\mathbf{B} = 0; \mathbf{B}(r) = \frac{\mu_0 I}{2\pi r} \cdot \frac{r^2 - a^2}{b^2 - a^2} \mathbf{e}_\theta; \mathbf{B}(r) = \frac{\mu_0 I}{2\pi r} \mathbf{e}_\theta
+363	In a region of empty space, the magnetic field (in Gaussian units) is described by  $$ \mathbf{B} = B_0 e^{ax} \mathbf{\hat{e}}_z \sin w , $$  where $w = ky - \omega t$.  (a) Calculate $\mathbf{E}$.  (b) Find the speed of propagation $v$ of this field.  (c) Is it possible to generate such a field? If so, how?	[]	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	\mathbf{E} = -B_0 e^{ax} \sin w \, \mathbf{\hat{e}}_x - \frac{ac}{\omega} B_0 e^{ax} \cos w \, \mathbf{\hat{e}}_y; v = c; B''_z = B''_0 \exp \left( -\frac{\omega}{c} \sqrt{n^2 \sin^2 \theta - 1} x \right) \exp \left[ i \left( \frac{\omega}{c} n \sin \theta y - \omega t \right) \right]
+364	Consider an electromagnetic wave of angular frequency $\omega$ in a medium containing free electrons of density $n_e$.  (a) Find the current density induced by $E$ (neglect interaction between electrons).  (b) From Maxwell's equations write the differential equations for the spatial dependence of a wave of frequency $\omega$ in such a medium.  (c) Find from these equations the necessary and sufficient condition that the electromagnetic waves propagate in this medium indefinitely.	[]	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	\mathbf{j} = i \frac{n_e e^2 \mathbf{E}}{m_e \omega}; \nabla^2 \mathbf{E_0} + \frac{\omega^2}{c^2} \left(1 - \frac{\omega_P^2}{\omega^2}\right) \mathbf{E_0} = 0; \omega^2 > \omega_P^2; n_e < \frac{\varepsilon_0 m_e \omega^2}{e^2}
+365	An electromagnetic wave with electric field given by  $$ E_y = E_0 e^{i(Kz-\omega t)}, \quad E_x = E_z = 0, $$  propagates in a uniform medium consisting of $n$ free electrons per unit volume. All other charges in the medium are fixed and do not affect the wave.  (a) Write down Maxwell's equations for the fields in the medium.  (b) Show that they can be satisfied by the wave provided $\omega^2 > \frac{ne^2}{m \varepsilon_0}$.  (c) Find the magnetic field and the wavelength of the electromagnetic wave for a given (allowable) $\omega$. Neglect the magnetic force on the electrons.	[]	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	\mathbf{B} = -\frac{K}{\omega} E_0 e^{i(Kz-\omega t)} \mathbf{e}_x
+366	Let $\mathbf{A}_\omega, \phi_\omega, \mathbf{J}_\omega$ and $\rho_\omega$ be the temporal Fourier transforms of the vector potential, scalar potential, current density and charge density respectively. Show that  $$ \phi_\omega(\mathbf{r}) = \frac{1}{4\pi \epsilon_0} \int \rho_\omega(\mathbf{r'}) \frac{e^{iK|\mathbf{r-r'}|}}{|\mathbf{r} - \mathbf{r'}|} \, d^3\mathbf{r'}, $$  $$ \mathbf{A}_\omega(\mathbf{r}) = \frac{\mu_0}{4\pi} \int \mathbf{J}_\omega(\mathbf{r'}) \frac{e^{iK|\mathbf{r-r'}|}}{|\mathbf{r} - \mathbf{r'}|} \, d^3\mathbf{r'}. \quad (K = \frac{|\omega|}{c}) $$  How is the law of charge-current conservation expressed in terms of $\rho_\omega$ and $\mathbf{j}_\omega$? In the far zone $(r \to \infty)$ find the expressions for the magnetic and electric fields $\mathbf{B}_\omega(\mathbf{r})$ and $\mathbf{E}_\omega(\mathbf{r})$. Find these fields for a current density $\mathbf{J}_\omega(\mathbf{r}) = r f(r)$.	[]	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	\nabla \cdot \mathbf{J}_\omega - i\omega \rho_\omega = 0; \mathbf{B}_\omega(\mathbf{r}) = \frac{i\mu_0 K e^{iKr}}{4\pi r} \mathbf{\hat{r}} \times \int \mathbf{r}' f(\mathbf{r'}) d^3\mathbf{r'}; \mathbf{E}_\omega(\mathbf{r}) = -i c \frac{\mu_0 K e^{iKr}}{4\pi r} \hat{\mathbf{r}} \times \left[ \hat{\mathbf{r}} \times \int \mathbf{r}' f(\mathbf{r'}) d^3\mathbf{r'} \right]
+367	Four identical coherent monochromatic wave sources A, B, C, D, as shown in Fig. 4.2 produce waves of the same wavelength $ \lambda $. Two receivers $ R_1 $ and $ R_2 $ are at great (but equal) distances from B.  (a) Which receiver picks up the greater signal?  (b) Which receiver, if any, picks up the greater signal if source B is turned off?  (c) if source D is turned off?  (d) Which receiver can tell which source, B or D, has been turned off?	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	R_2; I_1 = I_2; R_2; R_2
+368	A sphere of radius $R_1$ has charge density $\rho$ uniform within its volume, except for a small spherical hollow region of radius $R_2$ located a distance $a$ from the center.  (a) Find the field $E$ at the center of the hollow sphere.   (b) Find the potential $\phi$ at the same point.	[]	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	\frac{\rho}{3 \varepsilon_0} \mathbf{a}; \frac{\rho}{6\varepsilon_0} [3(R_1^2 - R_2^2) - a^2]
+369	The uniformly distributed charge per unit length in an infinite ion beam of constant circular cross section is $q$. Calculate the force on a single beam ion that is located at radius $r$, assuming that the beam radius $R$ is greater than $r$ and that the ions all have the same velocity $v$.	[]	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	F = \frac{Qqr}{2\pi \epsilon_0 R^2 \gamma^2} e_r
+370	A perfectly conducting sphere of radius $R$ moves with constant velocity $\mathbf{v} = v \mathbf{e}_x$ ($v \ll c$) through a uniform magnetic field $\mathbf{B} = B \mathbf{e}_y$. Find the surface charge density induced on the sphere to lowest order in $v/c$.	[]	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	\sigma = 3\varepsilon_0 v B \cos \theta
+371	Figure 1.10 shows two capacitors in series, the rigid center section of length $b$ being movable vertically. The area of each plate is $A$. Show that the capacitance of the series combination is independent of the position of the center section and is given by $C = \frac{A\epsilon}{a-b}$. If the voltage difference between the outside plates is kept constant at $V_0$, what is the change in the energy stored in the capacitors if the center section is removed?	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	C = \frac{A \varepsilon_0}{a-b}; W - W' = \frac{A\varepsilon_0V_0^2}{2(a-b)} \frac{b}{a}
+372	A waveguide is formed by two infinite parallel perfectly conducting planes separated by a distance $a$. The gap between the planes is filled with a gas whose index of refraction is $n$. (This is taken to be frequency independent.)  (a) Consider the guided plane wave modes in which the field strengths are independent of the $y$ variable. (The $y$ axis is into the paper as shown in Fig. 5.14.) For a given wavelength $\lambda$, find the allowed frequency $\omega$. For each such mode find the phase velocity $v_p$ and the group velocity $v_g$.  (b) A uniform charged wire, which extends infinitely along the $y$ direction (Fig. 5.15), moves in the midplane of the gap with velocity $v > c/n$. It emits Čerenkov radiation. At any fixed point in the gap, this reveals itself as time-varying electric and magnetic fields. How does the magnitude of the electric field vary with time at a point in the midplane of the gap? Sketch the frequency spectrum and give the principal frequency.  (c) Any electromagnetic disturbance (independent of $y$) must be expressible as a superposition of the waveguide modes considered in part (a). What is the mode corresponding to the principal frequency of the Čerenkov spectrum considered in part (b)?	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	\omega_m = \frac{c}{n} \sqrt{\left( \frac{2\pi}{\lambda} \right)^2 + \left( \frac{m \pi}{a} \right)^2 }; v_p = \frac{\omega_m}{k_x} = \frac{c}{n} \left[ 1 + \left( \frac{m \lambda}{2a} \right)^2 \right]^{1/2}; v_g = \frac{d\omega_m}{dk_x} = \frac{c}{n} \left[ 1 + \left( \frac{m \lambda}{2a} \right)^2 \right]^{-1/2}; E(t) = \frac{A}{t}; \omega_m = \frac{m \pi}{a} \left( \frac{n^2}{c^2} - \frac{1}{v^2} \right)^{-1/2}
+373	Consider a uniformly charged spherical volume of radius $R$ which contains a total charge $Q$. Find the electric field and the electrostatic potential at all points in the space.	[]	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	\mathbf{E}_1 = \frac{Qr}{4 \pi \epsilon_0 R^3}; \mathbf{E}_2 = \frac{Q}{4 \pi \epsilon_0 r^2}; \varphi_1(r) = \frac{Q}{8 \pi \epsilon_0 R} \left(3 - \frac{r^2}{R^2}\right); \varphi_2(r) = \frac{Q}{4 \pi \epsilon_0 r}
+374	For a uniformly charged sphere of radius $R$ and charge density $\rho$,  (a) find the form of the electric field vector $\mathbf{E}$ both outside and inside the sphere using Gauss' law;  (b) from $\mathbf{E}$ find the electric potential $\phi$ using the fact that $\phi \rightarrow 0$ as $r \rightarrow \infty$.	[]	/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGQAZADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD3+iiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigD//2Q==	\text{(a) Refer to Problem 1013 for the electric field vector } \mathbf{E}; \text{(b) For } r > R, \, \phi = \frac{R^3 \rho}{3 \epsilon_0 r}; \text{For } r < R, \, \phi = \frac{\rho R^3}{6 \epsilon_0} \left( 3 - \frac{r^2}{R^2} \right)
+375	A particle with mass $m$ and electric charge $q$ is bound by the Coulomb interaction to an infinitely massive particle with electric charge $-q$. At $t = 0$ its orbit is (approximately) a circle of radius $R$. At what time will it have spiraled into $R/2$? (Assume that $R$ is large enough so that you can use the classical radiation theory rather than quantum mechanics.)	[]	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	\tau = \frac{7\pi^2 \varepsilon_0^2 c^3 m^2 R^3}{2q^4}
+376	A particle of charge $q$ is moved from infinity to the center of a hollow conducting spherical shell of radius $R$, thickness $t$, through a very tiny hole in the shell. How much work is required?	[]	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	\frac{q^2}{8 \pi \varepsilon_0} \left( \frac{1}{R} - \frac{1}{R+t} \right)
+377	Find the potential energy of a point charge in vacuum a distance $x$ away from a semi-infinite dielectric medium whose dielectric constant is $K$.	[]	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	W = \frac{(1-K)q^2}{16 \pi (1 + K) \epsilon_0 x}
+378	Suppose that the region $z > 0$ in three-dimensional space is filled with a linear dielectric material characterized by a dielectric constant $\epsilon_1$, while the region $z < 0$ has a dielectric material $\epsilon_2$. Fix a charge $-q$ at $(x, y, z) = (0, 0, a)$ and a charge $q$ at $(0, 0, -a)$. What is the force one must exert on the negative charge to keep it at rest?	[]	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	-\frac{q^2}{4\varepsilon_1 a^2}
+379	Two large flat conducting plates separated by a distance $D$ are connected by a wire. A point charge $Q$ is placed midway between the two plates, as in Fig. 1.40. Find an expression for the surface charge density induced on the lower plate as a function of $D, Q$ and $x$ (the distance from the center of the plate).	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	\sigma(x) = -\frac{QD}{4\pi} \sum_{n=0}^{\infty} \frac{(-1)^n (2n+1)}{[(n+\frac{1}{2})^2 D^2 + x^2]^{3/2}}
+380	As can be seen in Fig. 1.32, the inner conducting sphere of radius $a$ carries charge $Q$, and the outer sphere of radius $b$ is grounded. The distance between their centers is $c$, which is a small quantity.  (a) Show that to first order in $c$, the equation describing the outer sphere, using the center of the inner sphere as origin, is  $$ r(\theta) = b + c \cos \theta. $$  (b) If the potential between the two spheres contains only $l = 0$ and $l = 1$ angular components, determine it to first order in $c$.	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	r(\theta) = b + c \cos \theta; \Phi = \frac{Q}{4\pi\epsilon_0} \left\{ \frac{1}{r} - \frac{1}{b} + \frac{cr}{b^3-a^3} \left[ 1 - \left(\frac{a}{r}\right)^3 \right] \cos \theta \right\}
+381	A charge $q = 2 \mu C$ is placed at $a = 10 \, \text{cm}$ from an infinite grounded conducting plane sheet. Find  (a) the total charge induced on the sheet,  (b) the force on the charge $q$,  (c) the total work required to remove the charge slowly to an infinite distance from the plane.	[]	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	-2 \, \mu C; 0.9 \, \text{N}; 0.09 \, \text{J}
+382	(a) Two equal charges $+Q$ are separated by a distance $2d$. A grounded conducting sphere is placed midway between them. What must the radius of the sphere be if the two charges are to experience zero total force?  (b) What is the force on each of the two charges if the same sphere, with the radius determined in part (a), is now charged to a potential $V$?	[]	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	r_0 = \frac{d}{8}; F = \frac{QV}{8d}
+383	A parallel plate capacitor (having perfectly conducting plates) with plate separation $d$ is filled with two layers of material (1) and (2). The first layer has dielectric constant $\varepsilon_1$, conductivity $\sigma_1$, the second, $\varepsilon_2$, $\sigma_2$, and their thicknesses are $d_1$ and $d_2$, respectively. A potential $V$ is placed across the capacitor (see Fig. 1.21). Neglect edge effects.  (a) What is the electric field in material (1) and (2)?  (b) What is the current flowing through the capacitor?  (c) What is the total surface charge density on the interface between (1) and (2)?  (d) What is the free surface charge density on the interface between (1) and (2)?	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XhpZjpVc2VyQ29tbWVudD5TY3JlZW5zaG90PC9leGlmOlVzZXJDb21tZW50PgogICAgICA8L3JkZjpEZXNjcmlwdGlvbj4KICAgPC9yZGY6UkRGPgo8L3g6eG1wbWV0YT4KI0yFiAAAABxpRE9UAAAAAgAAAAAAAADqAAAAKAAAAOoAAADqAAByt0U4HfoAAEAASURBVHgB7J0HuFXF2bbH3igBFUGRYqHZsURRFOwFEGOMghEjauxoxIqakBh7Nxpr7L3FAkZjAUtEsSE2VDqIgoAottjOv+/J955/zmLtcnZf+zxzXYe196yp96y9mGfKO0vVpZyTEwEREAEREAEREAEREAEREAEREAERSASBpSTkE9FOKqQIiIAIiIAIiIAIiIAIiIAIiIAIeAIS8noQREAEREAEREAEREAEREAEREAERCBBBCTkE9RYKqoIiIAIiIAIiIAIiIAIiIAIiIAISMjrGRABERABERABERABERABERABERCBBBGQkE9QY6moIiACIiACIiACIiACIiACIiACIiAhr2dABERABERABERABERABERABERABBJEQEI+QY2looqACIiACIiACIiACIiACIiACIiAhLyeAREQAREQAREQAREQAREQAREQARFIEAEJ+QQ1looqAiIgAiIgAiIgAiIgAiIgAiIgAhLyegZEQAREQAREQAREQAREQAREQAREIEEEJOQT1FgqqgiIgAiIgAiIgAiIgAiIgAiIgAhIyOsZEAEREAEREAEREAEREAEREAEREIEEEZCQT1BjqagiIAIiIAIiIAIiIAIiIAIiIAIiICGvZ0AEREAEREAEREAEREAEREAEREAEEkRAQj5BjaWiioAIiIAIiIAIiIAIiIAIiIAIiICEvJ4BERABERABERABERABERABERABEUgQAQn5BDWWiioCIiACIiACIiACIiACIiACIiACEvJ6BkRABERABERABERABERABERABEQgQQQk5BPUWCqqCIiACIiACIiACIiACIiACIiACEjI6xkQAREQAREQAREQAREQAREQAREQgQQRkJBPUGOpqCIgAiIgAiIgAiIgAiIgAiIgAiIgIa9nQAREQAREQAREQAREQAREQAREQAQSREBCPkGNpaKKgAiIgAiIgAiIgAiIgAiIgAiIgIS8ngEREAEREAEREAEREAEREAEREAERSBABCfkENZaKKgIiIAIiIAIiIAIiIAIiIAIiIAIS8noGREAEREAEREAEREAEREAEREAERCBBBCTkE9RYKqoIiIAIiIAIiIAIiIAIiIAIiIAISMjrGRABERABERABERABERABERABERCBBBGQkE9QY6moIiACIiACIiACIiACIiACIiACIiAhr2dABERABERABERABERABERABERABBJEQEI+QY2looqACIiACIiACIiACIiACIiACIiAhLyeAREQAREQAREQAREQAREQAREQARFIEAEJ+QQ1looqAiIgAiIgAiIgAiIgAiIgAiIgAhLyegZEQAREQAREQAREQAREQAREQAREIEEEJOQT1FgqqgiIgAiIgAiIgAiIgAiIgAiIgAhIyOsZEAEREAEREAEREAEREAEREAEREIEEEZCQT1BjqagiIAIiIAIiIAIiIAIiIAIiIAIiICGvZ0AEREAEREAEREAEREAEREAEREAEEkRAQj5BjaWiioAIiIAIiIAIiIAIiIAIiIAIiICEvJ4BERABERABERABERABERABERABEUgQAQn5BDWWiioCIlBaAnV1de7nn392P/74o/vpp58c35uiW2qppdwyyyzjuGZzMLK/pZdeOqc42dIs533qyB/tbp+pR2Mc9ed5Ib4xID3jsuyyyzYmuaKHpRyUhzbN1RGeP5zVic/4WT35HucsP644i0+8OGfhuWdtYHH5Ht4P43PP6mRhLF4YrpDPVnbSCNPG3xz+1v5WfjhZ+PC3hF94z9LI5UqeYb5hHMs39NNnERABERCB2iYgIV/b7avaiYAI5EiADvZXX33lJk2a5B588EH3zDPPuG+++cbHppNsjnDR73Yvzj/0I1y6+NFw6cJGw5EeLurvPSP/pMs7jI9QaNmypevZs6f7xS9+EUlhya8ImPnz57uPP/7YbbDBBm6FFVZYMlCV+lDX1q1bu3bt2rlp06a5FVdc0XXs2NF16NAhrWCKVgVRtmDBAvfqq6+69u3bu9VXX92nOXv2bM+EQaHevXs7xHwubRRNv9DvlI/2mTVrlttoo43c8ssvnzXJH374wc2YMcPNnDnT/wa6du3qmSxatMhNmTLFNW/e3KeVLqH//ve/7t133/VcqH+3bt08l2bNmi0RhfJ9/vnnPt3vv//e84fhp59+6ssKs++++8698847jvvmEMerrbaa23rrrX1bffHFF27q1Km+njyTxXA8yzAjH54V6k55VlllFdepUyefBb+pxYsXu/Hjxzvq17ZtW9emTRv/Hlm4cKEvM2XkOaOuX375pfvoo48821zLSN78Fkm7e/fuDaJRHtrU8raBjQaB9EUEREAERKAmCUjI12SzqlIiIAKNJYD4+PDDD93rr7/u7r//fvfyyy97AREVX+nEcLZwlCcaN52flT0uvN2zuPY9mr/5h9doenzHWVyu/CEKEAwItmwOcYLAmzdvnlt33XXdcsstly1K1dy3QQuEI8IbQbTmmmt6YW9MshUWhgjR9957zwu4Vq1aedE1d+5cxx+ikkGRSs3K0z6IXITxeuutl1P7IL4/+eQT/4eI7pQSrQx2IELhtPLKK7v1118/LRoEN6KX54L6d+7c2cGFeFEHP9JloIHf4FprreXDMjjCs0Q7kB7ilwEGc7QdaW688cZeZCOmKZsxt3CFXHkeqCcDWwhkykh5VlppJf+cWNpff/21H2jAH9G/6qqr+vpTL8pMGVu0aOGDU04GSGiPXB158lsk7XXWWadBNO4x4MA9njPEfi6DNQ0S0RcREAEREIFEEpCQT2SzqdAiIALFJoAAuOqqq9yYMWPcSy+9VL8slnzoLJtLJ4bjwlmcfOITN11e0fSieVu+0Wu69HKNH02P76SJC8vkPXL8J1qmHKPlHKzS5SukfoWWPWdIeQa08hE9n/ZPFz/KLPqd/DLFDctj4aLlM/8wrKUbhs01HHFxhM83vuUVxo9L02f0f/8QlpUkCPxDDz3U9e/f3w8yMKggJwIiIAIiUNsEJORru31VOxEQgRwJTJ8+3Z100klu3LhxfibSOtVEDzvWjemoW9b5xCduuryi6RE29ON7nEuXHmFziZ8uzULj55t3XHmiftaO+eYRZRZNP9v3QuIXWvZsZSv0vpWPdPLhmy5+lFn0O/llihuWx8JFy2f+YVhLNwybazji4gifb3zLK4wfl6bPKPIPqxeYjd9///3dDjvs4PbYY4+ct4dEktJXERABERCBhBCQkE9IQ6mYIiACpSPA0t233nrLnXbaae6NN97wS5GtU02uYce6MR11K3E+8YmbLq9oeoQN/fge59KlR9hc4qdLs9D4+eYdV56on7VjvnlEmUXTz/a9kPiFlj1b2Qq9b+UjnXz4posfZRb9Tn6Z4oblsXDR8pl/GNbSDcPmGo64OMLnG9/yCuPHpekzivmHJfWbbrqp69WrlzvkkEO8bYIkbXWJqZK8REAEREAEMhCQkM8AR7dEQARqnwCdZ/Y4P/300+6CCy7wRqq+/fbbjEIh7Ghb5xtSufrnEo700omCuPihH3HjXLr0CJtL/HRpFho/37zjyhP1s/bJN48os2j62b4XEr/QsmcrW6H3rXykkw/fdPGjzKLfyS9T3LA8Fi5aPvMPw1q6YdhcwxEXR/h841teYfy4NH1GMf8Qn2X2m2yyiTv22GPdPvvs4w3zxQSVlwiIgAiIQA0QkJCvgUZUFURABPIngDGuyZMn+/3xDz30kDeWRYfYOtWkbB1rruEfBrcsnIXJvySVj2n15hrWM1PJwjhhOOOCXyY2llcYt5ifrRyZypApv3zKRxyMzFncOEvi3LO/dPlTZsKU0lkeXO1zXJ52n7JYubmaP7+FxjpLh3gW3/ImXXOWj323a1xYuJuz36eFsyv3LU2rs8Ux//C7fSaspUk+YRkJY+mH/ubHffM3P/vOPVwm/2jY/8Vo+C/xmYHHqOGBBx7ojjnmGG+or2EofRMBERABEagVAhLytdKSqocIiEBeBBDyWKu//PLL3SOPPOKtr5OQdar5TOcdy9AcIYVRKZawYsWbDjOWuTmOKs4iN3GT4rBUjqVwrGl/9tln3vI21tw5Ui2dgx1HbBGe48rMkRarHBCwsIo7dszC1toVgYe1cgaHsFjOc7HhhhvWn3dOfXm2sNDOsXBz5sxx8Io6uHEMHqtDONqv2I5nmrJhTR+r6xyZhghkm0nU8jsiEqvp9rxjBZ9nhfbFQjsW07HsnovYDOthrCgDv6HGxg/T4jNcsbJP+Xguu3Tp4r9TP6zF81ulfjjKTrlhgBV5yhL+5n2g1D/mR9ngg1V9/MLn3cLGXcP4cfdDv1zDWrgwLp/xNyE/aNAgN2zYMAn5KCR9FwEREIEaIiAhX0ONqaqIgAg0nkAuQp7OMUKH49XsLG469D169PCCBqGadLGKmOQIOYQlV0TOGmus4c/1Tkc1FP+cw24OsRQKeTt6y+7X8pXnCcH4/vvve7FO3dm3zDNkDsGF4GTQhCPNwmPVLAwDRwwaIUIRmsV2CHmeWUQ0Ipdj9xg8sHKFZSIsQp0jCRHwtC3PCGKY3wVG1jjnnHCNcbBi0MOEfGPjR/OC6zfffOP5Uz4GUBgIoX42+BAKecrNAAIDeSaOMw0mwKdjx44+LMfhUX7CwyFfx2+IP7hbGeBAXjwzsMGfchOOASCeCT5bXSxvwknIGw1dRUAERKD2CUjI134bq4YiIAIZCNAZp1OeaUaeWceDDjrI/fa3v/VnNWdITrdSBBAUJgRtJrMpgaHuX331leeAEGM2OyoQmQFGlIUCLmSEmOMIMcIhRkvhKBvlQhSyt5rP/B4QiCYqLV/CIvypG3+EITyC00Snhc31as8JdSX9Yjh4UT7Ywp36UL9ovazslIHBFOrP7Hw44BItD3EIQxwGIFhRQbkZ9MrHUSbSYNABY5s4KxcDBvwxmAZrBhtYKTFlyhT33HPP+TJPmjSpQTtRrlDIH3fccZqRz6dhFEcEREAEEkJAQj4hDaViioAIlIYAnelsQp5Zxz/84Q/eEjSf5UQgGwEEpblMM81hOAtvV4uXKYyFzfeKcEQAcjXH9zhHeeyeXYkXxo2LVwk/mBk/8qe8VmYrj5UboW/1MD8LE71amqTPu4Pw5hcNm8t30uCPwYfQ2Wy8MQ8HIz755BM3ZswYN3LkSL+FwOrFVUI+pKjPIiACIlDbBCTka7t9VTsREIEsBHIR8syKDR8+3B166KGuVatWWVLUbREQAREoDQHEOlsbnnnmGXfKKae42bNn+1Ub5GZCvnPnzm6//fbz7yy2PMiJgAiIgAjUJgEJ+dpsV9VKBEQgRwII+WzG7hDyJ554ojvssMO8wbsck1YwERABESg6AbYNvPDCC+7000/3S/KZrcch5Fnqj/2Ovfbay5199tl6XxWdvhIUAREQgeohICFfPW2hkoiACFSAgGbkKwBdWYqACORNwIT8iBEj3IQJE/zSfBIzIc/A48477+wuvvhif6pA3hkpogiIgAiIQFUTkJCv6uZR4URABEpNQEK+1ISVvgiIQDEJZBPyHFs4YMAAd9ZZZ2krUDHBKy0REAERqDICEvJV1iAqjgiIQHkJSMiXl7dyEwERKIxAJiGPsTuOLTzggAPc8ccf748FLCw3xRYBERABEahWAhLy1doyKpcIiEBZCEjIlwWzMhEBESgSgUxCnj3y7du3d/369XN//vOfNSNfJOZKRgREQASqkYCEfDW2isokAiJQNgIS8mVDrYxEQASKQCCTkF9mmWX82fFbb721u+mmm5yOyywCcCUhAiIgAlVKQEK+ShtGxRIBESgPAQn58nBWLiIgAsUhkE3It27d2vXu3dtdc801bvXVVy9OpkpFBERABESg6ghIyFddk6hAIiAC5SQgIV9O2spLBESgUAKZhDx75Ndbbz03aNAgd9xxx/nZ+ULzU3wREAEREIHqJCAhX53tolKJgAiUiYCEfJlAKxsREIGiEJCQLwpGJSICIiACiScgIZ/4JlQFREAECiGAkJ8xY4a79tpr3d133+3mzJnjk+NMZnOcyzx8+HB36KGHyniUQdFVBESgIgQk5CuCXZmKgAiIQNURkJCvuiZRgURABMpJ4Oeff3bz5893Dz/8sLv44ovdlClTfPZRIX/SSSe5oUOHSsiXs3GUlwiIwBIEEPLPPfecO+2009zbb7/teIfheGfZ8XP77befO/HEE3X83BL05CECIiACtUNAQr522lI1EQERyIMAM/KzZs3yFp5vvvlmN3v27AapLL300q5z587u5JNPdocccohbfvnlG9zXFxEQAREoJ4HvvvvOjRo1yv3+9793ixYt8gLe8ud91apVK7f99tu76667TsbuDIyuIiACIlCDBCTka7BRVSUREIHcCTCbtXDhQjd69Gg/I//hhx+6H374ob5zzAxXly5d3AknnOAOOuggt8IKK+SeuEKKgAiIQJEJMCP/7LPP+u0+H330kWMwEseMPOfIr7nmmm7PPfd055xzjsOCvZwIiIAIiEBtEpCQr812Va1EQARyJEDnlxmu1157zZ1yyilu4sSJ7ttvv60X8szAd+vWzR1zzDFu8ODBrlmzZjmmrGAiIAIiUHwC33//vXv11Vfd+eef75588kn3448/+kxsab1ZrR82bJis1hcfv1IUAREQgaohICFfNU2hgoiACFSCAJ3fxYsXu7Fjx7rTTz/dTZo0yYt4/M21bdtWxu4Mhq4iIAIVJYBwx5bHbbfd5i677DI/EEmBJOQr2izKXAREQATKTkBCvuzIlaEIiEA1ETAhP2bMGDdixAgv5ClfKORltb6aWkxlEYGmTQAhP23aNHfnnXe6iy66KK2Q1znyTfs5Ue1FQARqn4CEfO23sWooAiKQgUA2IY/xqE6dOrnjjz/eHXzwwa5FixYZUtMtERABESgtAQn50vJV6iIgAiKQFAIS8klpKZVTBESgJASyCfmVVlrJbb755u6II45wHOkkq/UlaQYlKgIikCMBhPzUqVPd7bff7i699FLNyOfITcFEQAREoNYISMjXWouqPiIgAo0igJD/8ssvXdzS+qWWWso1b97c9enTx58hP2DAAIefnAiIgAhUigDG7saNG+fOPvts9/zzz8vYXaUaQvmKgAiIQIUJSMhXuAGUvQiIQGUJZBPyLKXv27evF/L9+/evbGGVuwiIQJMnwPFzL774ojvzzDP9aRvh8XMclymr9U3+EREAERCBJkJAQr6JNLSqKQIiEE9AQj6ei3xFQASqkwBC/oUXXvCnbLz11luaka/OZlKpREAERKDkBCTkS45YGYiACFQzgUx75FlGH87I9+vXr5qrorKJgAg0AQIm5DllY8KECS7djLys1jeBh0FVFAERaNIEJOSbdPOr8iIgAhLyegZEQASSREBCPkmtpbKKgAiIQOkISMiXjq1SFgERSAABCfkENJKKKAIiUE9AQr4ehT6IgAiIQJMmICHfpJtflRcBEdAeeT0DIiACSSJgQv7000/PuLR+2LBhrmXLlkmqmsoqAiIgAiLQCAIS8o2ApaAiIAK1R0BCvvbaVDUSgVomICFfy62ruomACIhA7gQk5HNnpZAiIAI1SEBCvgYbVVUSgRomICFfw42rqomACIhAIwhIyDcCloKKgAjUHgHtka+9NlWNRKCWCZiQl9X6Wm5l1U0EREAEshOQkM/OSCFEQARqmICEfA03rqomAjVIQEK+BhtVVRIBERCBPAhIyOcBTVFEQARqh0C6pfXUkHPkmzVr5rbffnt36KGHugEDBrill166diqvmoiACCSOQCjk33zzzfpz5KnIsssu69Zbbz03ePBgp3PkE9e0KrAIiIAINIqAhHyjcCmwCIhArRFIJ+TxR8ivvPLK7pe//KU7/PDD3b777uuWW265WkOg+oiACCSIgAl5Wa1PUKOpqCIgAiJQAgIS8iWAqiRFQASSQyCTkKcWiPl27dq5E0880Q0dOtS1atUqOZVTSUVABGqOgIR8zTWpKiQCIiACeRGQkM8LmyKJgAjUCoF0Qt7qx1L6Tp06ueOPP94dfPDBrkWLFnZLVxEQAREoOwET8hi709L6suNXhiIgAiJQNQQk5KumKVQQERCBShBAyC9evNiNGTPG0TGeNGmSLwb+uBVWWMFtsMEG7uijj3YHHHCAX2rvb+gfERABEagAgVDIT5gwoX6PPO8stv6wR37QoEHaI1+BtlGWIiACIlBOAhLy5aStvERABKqOQCYhz7J6ZuB33HFHd8ghh7h+/fpVXflVIBEQgaZFQEK+abW3aisCIiAC6QhIyKcjI38REIEmQQAh/+WXX8bOyCPk11hjDT+7NXDgQG+9vklAUSVFQASqloAJeRm7q9omUsFEQAREoCwEJOTLglmZiIAIVCuBbEIeQ3fMxu+1115um222qdZqqFwiIAJNhICEfBNpaFVTBERABLIQkJDPAki3RUAEaptANiHftm1bN2TIEH+GfK9evWobhmonAiJQ9QQk5Ku+iVRAERABESgLAQn5smBWJiIgAtVKINse+ZYtW7pddtnFW6zfc889q7UaKpcIiEATIWBCHuOcMnbXRBpd1RQBERCBGAIS8jFQ5CUCItB0CGQT8hi769u3rz9DXsbums5zoZqKQLUSkJCv1pZRuURABESgvAQk5MvLW7mJgAhUGQEJ+SprEBVHBEQgIwEJ+Yx4dFMEREAEmgwBCfkm09SqqAiIQByBbHvkwxn5/v37xyUhPxEQAREoGwET8rJaXzbkykgEREAEqpKAhHxVNosKJQIiUC4CEvLlIq18REAEikEgm5Dv3Lmz23///d3w4cMdNj7kREAEREAEapOAhHxttqtqJQIikCMBCfkcQSmYCIhAVRDIJOSXXXZZ17FjRzdw4EB3xhlnuFatWlVFmVUIERABERCB4hOQkC8+U6UoAiKQIALaI5+gxlJRRUAEnAn5OKv1yyyzjGvdurXr3bu3u+aaa9zqq68uYiIgAiIgAjVKQEK+RhtW1RIBEciNgIR8bpwUSgREoDoIZBLyyy+/vNtoo43ckUce6ZfXN2vWrDoKrVKIgAiIgAgUnYCEfNGRKkEREIEkEZCQT1JrqawiIALZhPxmm23mjjvuOLf33nu7VVZZRcBEQAREQARqlICEfI02rKolAiKQGwHtkc+Nk0KJgAhUBwET8ums1rNHft9993Wnnnqq9shXR5OpFCIgAiJQEgIS8iXBqkRFQASSQsCE/LPPPuuNQ02aNMkXHf+lllrKcfxcnz593NChQ92AAQOSUi2VUwREoEYJIOSff/55h5B/66233E8//eRryjuLPfJt2rRxO+20k7vsssvcaqutVqMUVC0REAEREAEJeT0DIiACTZrAzz//7BYsWOBGjRrlzjvvPDd58mTPg04xbqWVVnI9e/b0S1U50klOBERABCpJ4LvvvnNPPfWUGzZsmJs1a5bjHYYzIW/G7q699loZu6tkQylvERABESgxAQn5EgNW8iIgAtVNgE7w3Llz3YMPPuhnsKZOndqgwMstt5zr3r27P5N5yJAhDe7piwiIgAiUmwBCfvTo0d6gHYOQNuhIOZZeemm/nH7bbbd1N954o4R8uRtH+YmACIhAGQlIyJcRtrISARGoPgJ0gr/88kvH0vozzzzTRZfWN2/eXEvrq6/ZVCIRaLIEwqX1EydOXGJpPUfO9e3b111xxRVaWt9knxJVXAREoCkQkJBvCq2sOoqACKQlgJBfvHixGzNmjONc5qiQZ488nWL2yPfr1y9tOrohAiIgAuUgYMbu4s6RZ0Z+5ZVXdliuv++++9waa6xRjiIpDxEQAREQgQoQkJCvAHRlKQIiUD0EJOSrpy1UEhEQgewEsgl5zpLv0aOHe+yxx1y7du2yJ6gQIiACIiACiSQgIZ/IZlOhRUAEikVAQr5YJJWOCIhAOQhIyJeDsvIQAREQgeonICFf/W2kEoqACJSQgIR8CeEqaREQgaITkJAvOlIlKAIiIAKJJCAhn8hmU6FFQASKRUBCvlgklY4IiEA5CEjIl4Oy8hABERCB6icgIV/9baQSioAIlJCAhHwJ4SppERCBohOQkC86UiUoAiIgAokkICGfyGZToUVABIpFQEK+WCSVjgiIQDkISMiXg7LyEAEREIHqJyAhX/1tpBKKgAiUkICEfAnhKmkREIGiE5CQLzpSJSgCIiACiSQgIZ/IZlOhRUAEikVAQr5YJJWOCIhAOQhIyJeDsvIQAREQgeonICFf/W2kEoqACJSQAEL+yy+/dGPGjHEjRoxwkyZN8rnhv9RSS7kWLVq4vn37uqFDh7r+/fuXsCRKWgREQASyEzAhf/rpp7sJEya4n376yUfinbX00ks7zpHfYIMNdI58dpQKIQIiIAKJJiAhn+jmU+FFQAQKJaAZ+UIJKr4IiEA5CZiQZ+AxnZDv0aOHhHw5G0V5iYAIiEAFCEjIVwC6shQBEageAhLy1dMWKokIiEB2AhLy2RkphAiIgAg0BQIS8k2hlVVHERCBtAQQ8lpanxaPboiACFQZARPyWlpfZQ2j4oiACIhAmQlIyJcZuLITARGoLgIS8tXVHiqNCIhAZgIS8pn56K4IiIAINBUCEvJNpaVVTxEQgVgCEvKxWOQpAiJQpQS+++4799xzz3njnBMnTpSxuyptJxVLBERABEpNQEK+1ISVvgiIQFUT0B75qm4eFU4ERCAgEL6vTj31VDdlyhT3888/+xDcM6v1MnYXQNNHERABEahRAhLyNdqwqpYIiEBuBDQjnxsnhRIBEag8AY6amz17ths9erQbNmxYvYinZKGQ1/FzlW8rlUAEREAESk1AQr7UhJW+CIhAVROQkK/q5lHhREAEAgII+VmzZrlRo0Z5IR/caiDkmZEnTLt27cIg+iwCIiACIlBDBCTka6gxVRUREIHGE5CQbzyzSsVAxNBetpTYyoHfDz/84P1XXnnlJe5buFJdl1pqKbfccsvFJm/lXWaZZfx9vv/444++HmGEMA2rT3i/WJ/Jh+XX/MEzyjKaz7LLLuuIY+WO3ucef9nSIR7h0nGKpmv5cY06WFJ+0ivEUWbSt7YpNC1jUUg62eJ+//33btKkSe5f//qXw2p96KgLXGDctWtXd9ddd7n27du7lVZaKQxW0GdY8Ude9nuMayPKQTiY8Lzj8OMP7hY3U2GIa+lkCqd7IiACItBUCUjIN9WWV71FQAQ8ATqhOn6uuh8G2ghL3YsWLXLffPONv4YlRsQzS4nI6dmzpw+LUCiHQ2wweNCxY0cvOqJ5UrYFCxa4li1buuWXX95hqOyTTz7xVwtLGogtRBeOOrJ8utiOfFZYYQXXqlUr17x5czd//ny3cOHCtNlQ3jZt2vh6wX/u3LkNwpLeiiuu6BD7X3311RKDEw0Cp76Qd4cOHTwH4mZy5AeDb7/9tkEwxCHlb9Gihefe4GYjviAuFy9e7J+VNdZYo6BBAYTp119/7etFHUvlyIc2u+WWW9xrr73mHn300QZZ8TuBK3+tW7d2v/vd77yg5zdRDAd70oU/n+fNm+ef1WgbIb4J84tf/MIz4fmHN78TnjvC8yzxW4gbBLCy8vzRzoW2j6WXhKu1X7rfB8+AOcKE382fK21gacA4XTjCWjgbeLHv3JMTARGobgIS8tXdPiqdCIhAiQnQyaFDP2bMGG8FmtkunHWK6Uj27dvXDR061PXr16/EpVHyUQIIgBkzZrh77rnHvf32214UI+hDR1shCuiArr766l5cmJDnHi7fzqk9B2F+4WfSXWWVVVznzp2X6DwTl8EFxDLCBsFLOT/++OMlhDwiZ+211/blRBTOnDmzXuTkW/awnHwmHYQ3YqxZs2bus88+yyjkEaVt27b19bIBiGiaDEDkKuTJu1OnTrFCnrJZW3FFyMMA0Re2AXkhEPmDu9WLq8WP8wsZEo4BFhPyVkeLb2HtO+nhov5WZp41E/LUMRruf7H/Fz9M08JxPxd/xBgDJm+++aYfzIoOwpCGpQknBmFMPJu/lSV6tfyj4UJ/hN5qq63mVl11VZ8PYpx6M/AUxkNEEobnjHKEQp73KeHnzJnj25j0w3JbuUiPlQW0s7WP3bOrlY3vYf52P9vV4ucTN1va+dynHAx0YN+A3ye8rYxceWZ5F/IZxvzFDXbxm9x444394CBhaKdp06Z57tFykSd5MViyzTbbuI022sgPOhJPTgREoPoJSMhXfxuphCIgAiUkQKdIQr6EgAtIGoH0+eefu9dff91dfvnl7t1333VffPGFFzNxydLxRUgh/mwGyjrC+XbWiZ8pLvfIE7FB/qEjrglGRCeiBmHPrCpXc6SBaEZ44RDNzHYWWnZL367kgzhCTNHZhyWrUdI5yosgo1NPeRFkUUe5qTfiLJtjhhXBwDXqjDF1Nm4wQNDz3e6TF8IDntQBZ/eMl/lFv/vAqX/wZ4CIMtM+CE7qaOHj0rM0uYbh+MyzxjNHveDbmPikh7M0+Wzxo/6E4dlAmNlAFWHMcT+Mm83f7nO1/KPxQ38YsbKE54fPPA+0D2UK43EPQWrheL/Cm98J7UYcfgOwJ/105eb5Ix0GwUgz6qxs+If5R8Ol+27x84mbLs1C/CkHzzb2DeBk7xMrJ7wY3OJ5gwd/DIjw7IWO3wWDAQzikCa/IwYA4n6j3Cccv8tevXq5XXfd1XVKDbbxXU4ERKD6CUjIV38bqYQiIAIlJEAnSUvrSwi4gKTpoL766qvu4Ycfdtdcc40XAI1NzjrB+XbWiZ9vXMpaSPxCy95YVo0Nb+UjXj6M0sWPMot+J79MccPyWLho+cw/DGvphmFzDUdcHOHzjW95hfHj0vQZxfwTzduCpPO3+3aNC5euTBaHa1w8u5/pnsXlGq2zxc92zaV8mdLIVr5Mcct1r1x1ZBBhyJAhbqeddnL77LNPuaqnfERABAogICFfADxFFQERSD4BOkmaka/OdmSA5ZFHHnH33nuve/rpp/0MXmNLWq5OcFy5ipE36eYrcuLKVEw/q1++ZYyLb35hnfELv1sd0oWNlicuvsXNFjbXcKRjYcOyml+Yj/mF4dLFN/9oWPyjjnTjwqXzD+M3tkzRuHH5EibXvNPFD/OJ+5yu3HFh4/xyKV9cvHL6lauOrCZhNcCee+7p/vrXv5azispLBEQgTwIS8nmCUzQREIHaIEAnSUK+OtsSIf/QQw+5u+++240dO7be+nVjSluuTnBcmYqRN+nmK3LiylRMP6tfvmWMi29+YZ3xC79bHdKFjZYnLr7FzRY213CkY2HDsppfmI/5heHSxTf/aFj8o45048Kl8w/jN7ZM0bhx+RIm17zTxQ/zifucrtxxYeP8cilfXLxy+pWrjmxlWHfddb2Qv/jii8tZReUlAiKQJwEJ+TzBKZoIiEBtEKCTJCFfnW1Ju4wePdrdd999fkY+3PselhgRYJ3d0J/P5l+IUCgkLmVobHzC2376fOITpxzO2JJXY+tInLj45sf+X/vMNS59/AjHnuEwbLQ8cfEtfLawuYYL6xOWNS6++YXh0sU3/2hY/KOOdOPCpfMP4ze2TNG4cfkSJte808UP84n7nK7ccWHj/HIpX1y8cvqVq47MyHfv3t3tscce7txzzy1nFZWXCIhAngQk5PMEp2giIAK1QYBOkvbIV2dbYtALg1oTJkxwV111Vb217tC4Fp1PDHBhyAmL3lFnHXUThtkEg3WaLZ3wO3Gzxbd4drX87XumK2ljPA5L3Rxnh3VyDIM1Ns9MeRTzXpRNXNqECcOFYcyf+tE+5mhTGHA6gRlEs3tczeAdYTDUxdGDWE83A4ekx58J/HT8zN+ucWUNyxiWIdNnSy8axvzDfPAL/YnDd8vXrnHhwvTDcJaG3eee5WF+cde4cNF0jSnx7V5cPEufe9a2cWWwNAgT3jd/S8fu4R/es892n/DhZ75bGD5HHfei4aNhKv09fK4z1SVdOXOtI4YFBw0a5PfI77fffumSk78IiEAVEZCQr6LGUFFEQATKT4BOTpyQpyR08LC83KdPH3/8XP/+/ctfwCacI22DkMVK98svv+w++OAD/xnhttZaa3mr5Vh3Rvzix1FM1uk1bLQhQh8rzFjKpj2Jw+w+ItAsQxOP54C8MPqEmEREYvHZOvpYJUdgYxXaxInlU4wr+ZAH5cKC/dSpU/OyC5CuLPCkTjCljlavdOEL8be8EOPZrKyb1WyEBFxZjUAbMTBDWbGu/8knn/g24fgzOz7PLHu/9957fsCHNsXKPu1D+8HPrLuHdSUPLKHzBwfKilV+VoDwHIVhuWcu6h9+tzBcsc7OM0dbWnvynPGMUR+eKY6Oo548l9SDP3OE4YhCBqew9k55OVYRPtSNkxzwJz2e/fD0Ab6T95prrmnJFeVKXgyWTJ8+3f9xdCHfKUd4AkOYGXwoD3WzNo5aoDe+tFeHDh18WOLBxwbn2rVr5+tNGbC+Tn4Wz65hW5AW+cCeQT9+9+kc8cO46cJVyp9n4cMPP/S/W55l2hoOVu9s5cqlboThd4DV+oMOOshtuummfmY+W9q6LwIiUHkCEvKVbwOVQAREoIIE6BBpaX0FGyDHrBEMCKBPP/3Uvf/++/68Y4QNooWO7aRJk9zkyZOX2EePCELUdOnSxU2ZMsUhCpjJRbRzpbOPo5OM4KTTjFhEgNCJ/uijj+o7+oiRzTff3A8GIBZK4SgvaSPY6LTn2mHPpSykhdhFIFNH8iqVIy+EGMdjmRCJ5kUYykA70D6IVcQtflxt0AERT5vTJp07d3bt27f3YhlOtBvHEvJc0KYMtPBMIKZfeeWV+oGQUNCQNmnwBweeH8pK+0+cOLG+vSlvyD9MA//wu9UNP4QrafO8UA5EpZUV9jxTDBjw7FFvBiYYgLD8KAvloP0RopSXesOHtBiwwp+6I8DgQ9lx5M0zvuGGG/rvxfqHvBDX48ePd6+99ppvU84mZ6AGoRzHgvohztdee21fx65du/oBOOpjzvjCqWfPnj4caTGQwWocBgw4So025R3AUZTwoc1wFj/Mn98O/LnyTExPDT6kc+naMV34cvtT17Ep+yD8bnkfMWjF/1e0fzoHC9jDlD8+h3wsHnWHKVcGDg877DA3cOBA//yU8t1g+esqAiJQOAEJ+cIZKgUREIEEE6ATIyGf4AZU0UVABMpOgEGGG264wQ+WPPjgg0sIRYQjYhrr57vvvrsfMCl7IWsoQ/6fYsDm7LPPdi+99JJ755130taOAS8GcjbbbDO31VZbpR3UYaCMARMGYxh0Gjx4cP0KpbSJ64YIiEBVEZCQr6rmUGFEQATKTUBCvtzElZ8IiEDSCbCs/vHHH/dC/tJLL11CyNtqg5tvvtkv02Z2XC5/Avw/xYqkSy65xI0ZM8a98cYbsYkxgMLqhX333dftuuuubrvttvOrNKKBSY8/tikwK88MPNs85ERABJJFQEI+We2l0oqACBSZgIR8kYEqOREQgZonwNLucePGedsVZ5xxRgMhj5hk28smm2zibr/9dr9UO1xOX/NwSlBBE/JXXnmle+aZZ9yrr74amwvs2YJxwgkneKN1W2yxRWw4eYqACNQGAQn52mhH1UIERCBPAhLyeYJTNBEQgSZLgGXZGBNEzA8dOrSBkEe0d+rUyW277bb+tAmWbcsVRsCE/BVXXOGeffbZjEIeOxHXX3+9XwlRbKOHhdVCsUVABIpNQEK+2ESVngiIQKIISMgnqrlUWBEQgSogwHsTA2wI+V122aWBkGePNvuz8T/ttNO8wbUqKHKii2BCnm0MLK3H6F+cY0aeQZRbb73VrbfeelouHwdJfiJQQwQk5GuoMVUVERCBxhOQkG88M8UQAREQAfZXI+T79u27hJBnSfduu+3mhg8fLiFfhEeF/6dmzpzpl8xzokE6S/wIeU44MCGPNXo5ERCB2iUgIV+7bauaiYAI5EBAQj4HSAoiAiIgAhECEvIRICX8ynF7HOP4q1/9ylua5xjDOCchH0dFfiJQuwQk5Gu3bVUzERCBHAgg5DlrmOWKGG3iPHIc/nSKWrRo4fr06eP3gfbv3z+HFBVEBERABIpDgPeQ/VmKvJdwXO2z3SvnNZuQx2r6SSedpBn5AhuF9ueUgPHjx7shQ4a4BQsWeGvzccnyPHRKLa3ntIAuXbpoaX0cJPmJQA0RkJCvocZUVURABBpPgJkOOkajRo1y5513nps8ebJPhM4TjmOTNt98c3fccce53/zmN95P/4iACIhAKQnw/sEy/MKFC90HH3zgOLf9p59+8seEtW7d2h8phnXyVVdd1QvlqFX4cgj8//73v7FL65dbbjkvIrfffnt38cUX+3doKVnVetq0+6xZs9z999/vzj33XMdsPH5xjnbnmTjyyCPd7rvv7nr16hUXTH4iIAI1QkBCvkYaUtUQARHIjwBCfu7cue6BBx5wl112mZs2bVqDhOiUdu/e3e/1ZDZETgREQARKTQCr8LNnz3bvvvuue+qpp9ynn37qZ2F5H7Vv3961atXKrbvuuv6vWbNm9WJ+xRVXdIh6wmF0DmHHH9+L7RDyL730kttxxx0bJE3+a621lheRN954o5PV+gZ4Gv2Fc97ZF4+hu/vuu8/xbGRytDtH/x177LHuoIMOyhRU90RABBJOQEI+4Q2o4ouACBRGgJkvW1o/YsSI2KX1GHPiiCUtrS+MtWKLgAhkJ8Dg4rx589x1113nbrnlFm/kzFYIhbGXWWYZh4g30c4Mfc+ePd3aa6/tOIKsa9eubvnll/eCHgvmhF966aX9XzFm7NPNyCMkMXbH0vqTTz5ZS+vDRsvjM0L+vffec3//+9/988CWhkyOgRTa/5RTTnGHH354pqC6JwIikHACEvIJb0AVXwREoDACEvKF8VNsEagVAnFiOVPdsoWPE8vZ4rBkmq0+zz//vLv77rvdE0884ZfYx6WFH+KcKwIdAde8eXMvnBHTzITjz5XtQYg7BD1Hw6222mpe5GeqX7Z76YQ85WAwgWXdDEZoRj4bycz3GdiZM2eOe/jhh/1xft98803GCGwH22qrrdwRRxzhDjjggIxhdVMERCDZBCTkk91+Kr0IiECBBCTkCwSo6CKQcAIIJfYdszLHRBJilGXqcY6lzexZZ6Y0nTBHQDMbzhJ4HLOopM2+93Rx8Cccy+gR8s8995x766236g1vxpUl9CN+nOCnHj169HAdOnTwS/G33HJLP3O/xhpreOEfptGYz5mEPHkh5K+99loJ+cZAjQnL88ngzpNPPumOOuoob/guJpj3ov1btmzp9t13X7fffvv5VRHpwspfBEQg+QQk5JPfhqqBCIhAAQTo/C5evNhbrc+2tL5fv34F5KSoIiAC1UYAkYRBuXfeece9+eab7qOPPvLCGTHErHLU8b5YtGiRe+ONN7z4R8yHzsQ0y92Z9UbMWhwMaTKzagMAUdFNWRD7n3zyibfbYQbNLM0wn7jP6cKF/gwwcLb48ccf73r37u223nrrWPEfl37UT1bro0RK853n4vPPP3fPPPOMN7rK8xd97siZtmUlRqeU1foLLrjAbbjhhn4VRmlKpVRFQASqgYCEfDW0gsogAiJQMQJ0ciXkK4ZfGYtAxQjw20dYX3HFFf5oLwzLIU7DpeqEMWfCG2HFbDTX0FlYwlkaCCscYRFfJuLxs/T4jCM+fwh4E/HmHw3rI0T+IW5cuKg/Zdpoo43cLrvs4o14MmiBCGysSyfkGcTAQCi2Rc455xxZrW8s2JjwPA8YP7zkkkvcCy+84I3fhcFoP1Z/sNoC7uyNx34CWy/kREAEapeAhHzttq1qJgIikAMBOrlxxu6ISqdY58jnAFFBRCCBBBDXH374oTdkOWXKFPfZZ58lsBaNL7LNyvfp08edeeaZ/qg4thI01oVCPoyLeGzbtq2f7cdY3yqrrBLe1uc8CPD/FLPyt912m3v00Ufd2LFjG6TCvviddtrJ/7HSAqv1EvENEOmLCNQkAQn5mmxWVUoERCBXAumEvM1iIeRltT5XmgonAskhgJB/++23/XnbLK9n77v97q0WfDcXznZHw1mYqH9j4lvYMB/SjaZpeUWv6cLF+WOAbtttt/VCHsNotnIgmmam7+n2yFN+xPumm27qHn/8cT8znCkd3ctOgDZk5RjGD++880732GOPNYjEqorhw4f7Z5kTA+REQASaBgEJ+abRzqqlCIhAGgJ0kOJm5K3zKyGfBpy8RSDhBPiNsx/9yiuv9DOc7JGPntFNGHOhwMafme3Qz8LZlTDh8vswLPf4bn5cLS8+h/EsrKWb7pouXOhP2hi/Y8bWltazBDufpfUY7hs3bpw/R97qQdmY3ees+2222cbdcMMNMnaXrsEa6c/ACbYZOIYOMR+6X/ziF/64ud12282fShDe02cREIHaJSAhX7ttq5qJgAjkQIBOrvbI5wBKQUSgBgmwPHzmzJleIGEl/l//+pc3NIdowvF+MBeKVfaBr7vuun5fMke+4Sws+5mxMo5RsunTp3uxTngENHvkyZMrS58RYMymciwc8YmLRXyM7xEOP/7CvK080WumcMTnj7x22GEHN2jQILfxxhv7fPMR8ZRz7ty57uWXX3a//vWvG5QPa/0MFLDUm6X7LPuWK5wAzySnGFx99dXujjvuaJAgz9Gpp57qrdSzEkJOBESgaRCQkG8a7axaioAIpCFA51dCPg0ceYtAEyDALDx75V955RX34IMP+ll6ZptxvB/MhWIaYd6tWze36qqrejsaYVhE7rx587w1fPbe4xC3LGcnLwQ6V2auW7du7QcDSIu8EPgs83/99dfd/Pnzvaj/9ttvGwhln2DMP6GQp6wMFLBknoEGxDplXn311d2ee+7p9t9/f2/RPF+RTTkxvoaQHzx4cIPykSfLu5kdZrl3umP8YqogrwwEJOQzwNEtEWiiBCTkm2jDq9oiIAL/IyAhrydBBESgmgjwTmI2/5577nF33XWXe+211xpYuw/LajPt0Vl1BgnatWvnjyDjPHH7zvnuHTt2DJPI6zNC/uOPP/ZL6yXk80LY6EgI+YkTJ7qrrrpKM/KNpqcIIlCbBCTka7NdVSsREIEcCdBp1h75HGEpmAiIQFkIIJQ5Go9z7VnyPzZlpZwZemb7zSHO11xzTb9EfoMNNvCz+7ZqAGHP3neW0rNfHX9WBTA7no9hO8vTrrw3v/rqKy/kmXm3fLlP+hyDtuuuu7qTTjpJM/IGrcArz8S0adPcNddc425JnQbAFgzaAWdL62kLLa0vELSii0CCCEjIJ6ixVFQREIHiE5CQLz5TpSgCIlA4AYQbYg0jfC+++KI/Hi80goeQ55g3zoTv0aNHAyFP7gh3whRDuMfVhhlijN1xqoeEfByh4vrR9gzuXHvtte6mm27y2zfseeAM+ZEjR3rDgwzqyImACDQNAhLyTaOdVUsREIE0BCTk04CRtwiIgAhkICAhnwFOiW5hz4UZ+RtvvNHPztsKDWwfIPBZCcEKDDkREIGmQUBCvmm0s2opAiKQhgBCXsbu0sCRtwiIgAikIYDRvnQz8jJ2lwZagd5sA0Owm5C3GXnsIYwaNcqtv/76bpVVVikwF0UXARFICgEJ+aS0lMopAiJQEgIS8iXBqkRFQARqnICEfHkbmNn3GTNm+Bn5m2++2RtE5P8vHFss/vnPf/qTFFq0aFHegik3ERCBihGQkK8YemUsAiJQDQQk5KuhFVQGERCBpBGQkC9vi2U6fq5Nmzbu9ttv94YP+SwnAiLQNAhIyDeNdlYtRUAE0hBAyLNc8dlnn3VnnHGGmzRpkg+JPwacmN3AmNPQoUNd//7906QibxEQARFoWgS0R7687R0KeUR76LBaz/9fu+yyixfz4T19FgERqF0CEvK127aqmQiIQA4E2GM4b94899BDD7lLL73UTZ061ceSkM8BnoKIgAg0WQIS8uVt+mxC/tRTT3U6fq68baLcRKDSBCTkK90Cyl8ERKCiBOxInzvuuMNdd911fg8iBZKQr2izKHMREIEqJyAhX94GkpAvL2/lJgJJICAhn4RWUhlFQARKRgADQh999JG74oor3MMPP+xn58ksTsj369evZOVQwiIgAiKQJALZ9sjvuuuu7qSTTnIrrrhikqpVtWVFyE+cONFdffXVjoFn/o8yx9L60047zcF8k002MW9dRUAEapyAhHyNN7CqJwIikJkAM/Kffvqpu/fee91VV13lpk+f7iNIyGfmprvFJxB2zO0zdhr4kxOBaiOQTsgvt9xyrkePHq5Pnz7unHPOcSuttFK1FT2R5bHVY5wjj9V6toTZe4Jz5DmSrmfPnm7NNddMZP1UaBEQgcYTkJBvPDPFEAERqCECdI4WLFjgHnnkEXfRRRe5yZMn+9pJyNdQI1dxVXjOfvzxR/fDDz+4r7/+2nfOv/nmG/ftt996Ad+yZUvXqVMn16xZM7f00ktXcU1UtKZGIJ2QX3bZZV3Hjh3ddttt5wdHV1555aaGpiT1ZfXYrFmz6o+fW7hwYb2QX2ONNdzdd9/tNtxwQ7fqqquWJH8lKgIiUH0EJOSrr01UIhEQgTISQEhhtX7MmDFuxIgRslpfRvbFyIr2YzAGIYywoLNrjnvmlllmGT8zyJW/SjjKQ/koK2W2z1988YX77LPP/CDS6NGj3bRp0/zf8ssv7zbffHM3bNgwt80222iJciUaTXmmJZBujzwrSBh42myzzdyoUaP857SJ6EbOBDLtkW/Xrp1n3aVLF7fKKqvknKYCioAIJJuAhHyy20+lFwERKJCAhHyBACsUnXZDuH/11VcOIfziiy+6l156yc9YhWKe4jGTzYzVAQcc4NZZZx231lpruXLOElJW/r777jtvTPHNN990c+bMcbNnz/b2GZhZW7Rokfv8888ds/EIfWbpcRx/uO2223obDu3bt3csW5YTgUoT4HlevHixGzdunNt9990bbP/gGe3WrZtfWn/++edraX2RGiuTkGcW/oILLnC9e/d266+/fpFyVDIiIALVTkBCvtpbSOUTAREoKQHrkEZn5JkxtXPkd9xxR3+OvIzdlbQpck4coT5//nz3wQcfuKefftqLYI4NZCYbQUzbmaN9rR233HJLt8EGG7itttrK7bDDDo4lwKV2lIUyUbaZM2e6Z555xg82MPiAPzPxiHdEPgMToSMus/LMbHJuNMuV+S4nApUmgKh8/fXXvZDHoF247UNL60vTOqGQx9hd6Fq1auXOOussx/9VG220UXgr78+8O0MnWx0hDX0WgeogICFfHe2gUoiACFSIAJ0VBNW///1vN3LkSPfhhx/6koQCsG/fvhLyFWqfaLa0CyL41Vdfdc8//7y34MzMYCjewzjWGaUTusIKK3gjXHvuuaffRlEOa9p0vnmmeL4mTJjgHnzwwfql9WE54z5TdkTRxhtv7O68807XuXNnCfk4UPIrOwG2IzG49PLLL/tnMxR5iHpmiNkWcs8997jmzZuXvXy1mGEuQn6nnXby++QLrT8rghgsZYCRFUK0KZbxeYeybUJOBESgOghIyFdHO6gUIiACFSKAAGSJ82233eat/mJMCCchX6EGyZAtbYIROJbzYs9gxowZvrNpYj0uqt1DaLA3HuvOdHax/JxuL6nFIb1QoMSln8mPdFg2j5j5+9//7lg1EJ11zxSfe2wB+OUvf+luuOEGt/baa5dlFUG2Mum+CCDyzj33XPfKK6/432P4O+Ezgo/VL5wGoi0hxXleMgn5Nm3auH/84x9+9Q775QtxrHhi9RDbIsaPH++mp05yYTDmkEMO8YMz/fv3L+i9WEjZFFcERKAhAQn5hjz0TQREoIkRQMh/8skn3uIvYotOCw4RRoeUPco2I08HRq5yBKytGHS5/PLL/Z5y20uerlQmymkzASDhAAAyd0lEQVRLZpVWW201L+Svu+662JklhPbcuXP9HnWEP+GZuQ+XDqfLK+pPed9//32/muPdd9/1S+ijYTJ9J3/29B944IHu2GOPdSyfNcFk9bL45m/fdRWBUhHgN/L222/7o+VYZcK2kejzZzO4++23nzv66KP9c5xu4KxU5ay1dEMhz2qI0DFAee2117otttjCD/iF9xrzmXcWp7iw1eyPf/yjF/QMnmL3gK09rA668MILvZ2RcqxoakzZFVYEmiIBCfmm2OqqswiIQD0BOi6cI8+sabZz5CXk67FV5ANtxUwRHVb+WN6bzZngRWiwTJ3ZwV133dVdcsklDWbkCUdHmWeBIwhZTsp+9A4dOvhOK2dhR8VKprxJj73vbAEYNGiQ3wtP+RvjKC/7XY866ihvqI8lrQxcUG/SZuaMMiH4KR9LX/MZcGhMmRS2aRPgGeb5w9bDlVde6e1UMPAV99tgVp7l9X/605+8AMTgpFz+BDIJeQYcGdzkdAu24OTreKewKu3+++/3M/IY4ORdRvvSnt27d/fbmVhtwSC3nAiIQGUJSMhXlr9yFwERqDABOqbMyCPkr776as3IV7g9MmVfiJBH7LJvl/3x++67r9ttt93qLcCbOMGaPM8ABvSYhWIGEeNRp59+ut9bj1jO1REfK/qPP/64X8bPXtPGOgYSWFZ/2mmn1RvnYxvIAw884Pfcs7yZerVt29Z34Jn5DGftG5ufwotAJgL8TrAnMnHiRHfEEUf4QTXEpQm9uLgtW7Z0Rx55pH+OBw4cGBdEfjkSyCTkGcQ79dRT/Xtt0003zTHFJYOx2uI///mPf+e99dZbfnDT2pdBQk784DjM/fff3w+KLpmCfERABMpJQEK+nLSVlwiIQNURYAZiypQp7m9/+5s3RMbsEs46L+HSelmtr2zzmZBnWXyuM/KUmCWgHMk0ZMgQ16tXLz87yN5z2pjO8UcffeQuu+wyP7vIkmFmu7lHxxWRTMd1++2392IkVwLMWiK42SM8duzY+uPkovGZ6SKvOGdCng46FvfZj/zYY4+5Rx55xM+KwgNHOPbFmhE/xJOOqYsjKr9CCHDU43333eefaY57NBFv78q4tBloYhUMA1I33nijt/kQN3sfF1d+DQmEQj5qtd6EPKuNchHyce8cG6h59tlnHScRMMBtW5doM9qya9eu/v9KTtLgPSMnAiJQWQIS8pXlr9xFQAQqTAAhj5BjWSICad68eb5E1jmVkK9wAwXZ5yPkEeMs6e3Tp4/fa86SUJbL40gPwc3y97PPPtuvxvj444+DHJ3vrLJHfeedd3YDBgyIXULcIML/fcGyPpbm77rrLm8wiucsdCybZzCBGXTC8hftXCPG6ZQz+0kHmpkyZviZ6bcONmlSRzryHKnHc2z7+sP89FkECiXAbwWDatiowOaDPdP2rkyXPu9QhDwDW6xykZBPRyqz/9dff+0HBW+++Wb3z3/+s0HgXIU8bcXqINLij8EZe+/wPuT/P04iuOKKK/zqC2tjE/I9evRwN910k+vSpUusjZEGhdIXERCBkhOQkC85YmUgAiJQzQToqDAjz/54jgZjjzTOOqcS8tXTeibkmY1nVh5hkc2xr5PZ9JGpowWZ1WZWyRz74NkPj9im/ePSQ0wzm499BNJg9jsXh8EoZiAxSsV595TdHMKb2Sz2v2+77ba+44w4Z8YtdIRbc801/bn31APDYhjPi3OEpZPNTB0DFZoti6Mkv0IIMNiEQVDEPCdG2DNt78q4tLnHb2irrbZyo0eP9uKPZ1WucQTgiMjGLgH2CRh8DF02Ic/AH38I9+kpg64ciWl/Jta5T7uyKm3OnDk+efLFIeRpx0022cSvyGClkozdeTT6RwQqSkBCvqL4lbkIiEClCdAZxaDPv/71Lz8ry+w8zjqnoZCXsbvKtpYJeY6Oy1XIs6+dvbmIf4zF2WwgaX322Wdu1KhR7uSTT26wVD2sJc8BRy/R9sxStW7dOqtBOdLGYNR5553nxTzfQ4co33rrrf3ed8Q3zx42GliuHM60kzeih9l7HB3uaFqWblTI07GXE4FiEmCgi9nYW2+91b3zzjs5zcjze7MZeQyohb/BYpat1tPiXYCQ5x2USchj+yO6tJ4BSwYT33jjDT9oOWnSJP++Y2beRLzx4/1CXuF7hu+8g1jZhPFC2p93YjgoavF1FQERKC8BCfny8lZuIiACVUaADguz8HfffbeM3VVZ20SLQ6eTs9gvuugiL3yZXcrmEPIsiccGAiLchDxGnVgezJ7zc845p4GADtOkE8tyYOwjkAYG8+JmFAlnafNMIeQ5Z/v666+v97d0mdlCwB922GFujz32cOxJZS/9c88916AcpEle/FnHGr84JyEfR0V+xSSA7Yh///vf7uGHH/a/P35DuPDZj+aHAMSKOgNXN9xwQ84rWqLpNPXvMEbIs3UGIf/aa681QGIz8lEhz8Ag24V4vxAHOxsYyaTtoiK+QYLBF/Jm8JEVRKxqwp4I77C492AQTR9FQATKQEBCvgyQlYUIiED1EqAzw/Jqliw+9NBDflkhpbXOKTNIvXv3docffrif2a3emtR2yWgPE99nnHGGF725WIKnA8receK0adPGzyKxJJR2ZTk7e85ZLpzOkS972RHyPCPsP7eZKCsTS+IROQh5lt4Tnk63CXnChY4OMGXBIj5H0zFT9uSTT/q99OGMPHEYRGCZPKtGMnW+SZOjoZgt69Spkx+0CPPUZxEolAAzu8zmcsY4JzlwMgOO59sGsaJ58HvAMBrHol166aXR2/qeIwEYs+T9ggsu8O8+ttmEjnfECSec4Pbaay9/ljzhaS9OGXjhhRf8cZsMXC5evDiMltNn0mJAlPcVtg54l5I2/3faO4/3T7pnIKdMFEgERCAvAhLyeWFTJBEQgVohQIfk9ddf950glotiACh0zCixRxrL4QcffHB4S5/LSACBS0eW5eeHHnpovWX5XIrA7BHinc4mHdKePXv6bRS0NUfNsQSeTikdVv6ijjjMdLESAJFsS90R8GzFQIhjiM5mH3fffXdvfI5lsMxCsiQ5mi6dXsrFQAN14zmMinjyZQZs77339obzpqf2ttq5ztEyUrf11lvPrxrAoB/HRMmJQDEJsCqE2dzx48d7w5GIwuhzHc2PZxzDaAh5fgty+RGAM7//o446yq8k4hjK0DF4yBai3/72t36VD+8SVi8x6IIFeltGH20vE99R/zBtPvOewp4HS+s5DpOl+qyIwp93IqudGByVEwERKC8BCfny8lZuIiACVUaADg8GxM4//3y/bBQjZTjr2CCQMB524oknukMOOUSdlQq1H+1BZxThfOGFF/oTBqKDLnFFs3a0DqsNzPzhD3/wM0z4I8TZo87KDM5ODh3x6SQz04UwZ58ocZiBZwCIkw6eeuopPwPPs8LMGEfc/f73v/eDDo8++qgbN27cEiI9zCPuM53inXbayXeeBw8e7A1TsXqAmfv33ntviWWx5M2MPHuY11lnHb8FIC5d+YlAvgT4LTDgxFLtSy65pP64Tvzt9xVNm73UBx10kF9aj8iUy48AjBkQ5H3Cuwq7GqHDDsGxxx7rbXkwa85qCex/EJaVZtH24X3Be40tPrRn9LSOMG3yRrCz956tRQwwMpBAHvjz3mH70i677OL3zkfzCtPSZxEQgeISkJAvLk+lJgIikDACzMRivTfu+DmqQqeE2U2WLQ4dOtQfF5awKtZMcZkRZFaeY90QEgsXLvTCIlMF6YTirHNpM4TMUnHuOh1Tzktm2S+Cnn3qoSN+uEeemScc5eAYrieeeMILdQQOedCxZUacWStmLBH7HBdFp9fKEqYf95nBho4dO/qVB6weoIOMxXA65hgMQ8zb/mSLT8c8tFovY3dGRtdiEuAZZrATy/UYkMTKOX72+4rmxXPIuxNxyaoWufwJMJDJ+wRjn5y0EbroHnkGOXlP8o5itVDYPnzmndauXTsv/N98802/fz7dsnval/cmtg640v727jV/Vg3ts88+fhsF70A5ERCBMhFI/UDlREAERKDJEkjNyNelZjjrUjOodanZ1rpUJ8f/pV7BKED/h39qb2JdqgPTZDlVS8VTgrgutby+bosttqhbffXV69vL2i16tTbEPyV261Iz5nWppe91qaWhdaml8b5aKVFel9rzW5cSzEukR/xUp7du//33r0vte6/jeUl1kuuef/75utTRcHWpTmuDOOSR6iDXpbZi1KWW7delBgbq2rdvX5faK+zzj5Yv/E7clIivS+3Dr0vNXtZNnz69jvriUp34utSRU3UjR470dSBsGDe1b78uZYyqLrWioC61/N7H0T8iUGwCqcG0utRpD3WpFUx1nTp18s8gv5HwWQw/t2rVqu4vf/lLXWrwqdhFaXLp8Q5IGaurGzJkyBK84UybpES555IS5XVXX311XWprjv8/LGyTlPiuS82i16WMbfp3WurozbrUkvkl0rQ4mdqXMLx7UgOPdamVF3W8S3lHyomACJSHgGbkU28oOREQgaZLgBl5lmunm5GHDMuphw8f7mdIUx2mpgurSmrOsk4szU+cONFbYaZYqf8yY0uHf6qz6f9YSso+T2aPUp1hv0SUe8xEsVR17Nix/li7MCHihzPyzHyxN559wsxARWexUgLbb8XAGBhGEjGOx3JYZtF5zqJL9y0vZuEJy554zmr+3e9+51IDAN6wHmWkHMzqY3mabQHsUeW7OfINZ+RZ4i8nAsUmwHPIEm+2lGDMkWfafmNxeWHUEWOSzMinBr7igsgvRwK8d3h/pAS6u+OOOxrEshn5XXfd1W288cZ+lRGnbLByghl03iHmeJ+xXefAAw/0q4fYVkbY6CofwtO2uDC+9wj+IQyz8Cy9p1xsRWOmXk4ERKD0BCTkS89YOYiACFQxAQn5Km6cNEVjWSd7P9kS8fLLL/uj3rB1QIeS5fcIXK6IW/Zz0gnF2B3G4DgGi73nffr0qTdaxzLU1Ay7N3zHgE7oSJOOL+fIY7WeDjNGnjjG6Te/+Y3/HIanA9u1a1c/0IC1bgZ+sDCNhXyMT7E0lvPrKR/inbyx7I3wZm87Qr5bt27eYJWV3dKnjiyDZS8s++TZp29OQt5I6FpqAjx3GIkcMWKEty/CbyRO6PF881vAtgRbRDS4VFjL5CrkOSaOPe+8yzAwyDsmbB8GNFMrjPyJGYhvBkVpozhH2+LC+NFwhKGtGYBkyX+nlPE7CfkoJX0XgdIQkJAvDVelKgIikBACEvIJaahIMek80kHlpIFbbrnFH7OEH51djNZxxQAUs0PMFrEfFKNbfGfmO3TsPWV2n/3uZ599dv2Z7YQhzVDI85lOMkc6DRs2rIGYprOLkTpm/TE6x0oOc6SDACIfzuJmsIFBAWbWmbVEvBOP8jHoEOcQ8gwKsOeYdKi/OQl5I6FrqQmYXRFO8WBgimc7KvT4zu9vv/32c6eccopbd911S12smk+fdxp2PNgjz/730DFgeOaZZ/pBSlbmzJw50xsFvf7665doHwYOGTDceeed/cw8gp8045y1LXFwfMceSOjwk5APieizCJSPgIR8+VgrJxEQgSokYJ3SbEvrsVqf2lOo87mrrA2Z2UaI05nEhUIeoYwwppOJ0KUzyjUqOoiLMTmswrOFgjPgLT2uiHfOkb/sssv8PWad/vnPf/oZdvI3Z0J+u+22W0LIWxieN+sIE57vXDmb3sppYaNXwjKrz7OKJWoM7pmLCnnqLicCpSDAc8hg2RFHHOGFPCtUor8pvjMD/+tf/9of3SkhX1hL8B5iS8PDDz/s7r33Xj/oGKbYtm1bf48VEAwmYoSQ4zKvu+66JYQ8bcPgJoY+2fLAqS38xTnCMoNPOOJQBoznhY6y8f5idt9m5E34h+H0WQREoPgEJOSLz1QpioAIJIgAndJMVuupCjOrEvLJaFTak6X3XJnZZlYQkZvNMbs9evRo386ffvpp/ax8KORZgspsOtbjOc8eAcN9c+TDbD/WuS+++GKXMsZnt4pyZdCAstFZZt/x9NS50uYk5I1EMq7hc5NPiaPCOZ808o1D2VmVcvLJJ/stJtOmTUsr5AcNGuQHx9g2Ipc/AZjzXuMEDN4/bAUKHSuOGIhk+xDvvTlz5tQvrceOR/R54X1BOE5kMSv0YXp8JgxinzQPPfRQ/06krRnQZD+9DWJSNgn5KD19F4HyEJCQLw9n5SICIlClBCTkq7Rhylwslroj5DEkx3F0YSeVGSnOkedIOWa5MHRHhzbqmIVi5vGAAw7wy+6LvSeYMtHpxngeBqqmTJlSXwQJ+XoUVfsBwcNzxh+rSPJ1iCaeNWZeKzXzyXPIwBa2IrD/ECcUGdRKnQbiVzKxMkYufwI8O6wUYi/7M88841InWDRIDEOCbA3i/YNAxw4Hy+Uxdjdr1qwl2qdB5DRf2OfOMv3tt9/etzVbg1jazxYlZuZtZZGEfBqA8haBMhCQkC8DZGUhAiJQvQQQ8rJaX73tU66SIa6Y0YoT8hid23HHHR17ghHzzHaxhD90CGmEC1ajU8dt1VucD8MU+plnFSN3Z511ll8RkDpmrj7JqJAv9iBCfUb6kBcBxA5CiFMHxqZOR8BoYVT8EgYX529+XBlY6tKli/vVr37lUseI+dnQvApVQKRFixb5c+QR8liwt/JZ+RlgQATefffdLnU0WcUGHAqoYlVF5dlAnGNwE0ODcUKekzcQ8ryvWGHEGfK33nqrH3gM2yfXipHOHnvs4QYOHOgNe5IGVvMZqOQdaINRlE175HOlqnAiUFwCEvLF5anUREAEEkZAQj5hDVai4mYS8gin1Bnz7sgjj3R//vOf/cAPy1zNMUPKUXFDhw71R85ts802JREuGLujI3388ce7t99+u4HFfAl5a43qu5qIx1Ahs9hs5WEQJhRXJuIpfZx/6IdIXnvttf3xhxg+ZAa23A6hyMAXp0aw1DosH58pE1bMWQaOvYbwfrnLWiv5wZwl9RjSxEZG6NjGc+2113ojdiyXZ+k7g0bwv+CCC8KgOX/mvYeNA4Q7J33QhgwkssweI51sLcJJyOeMVAFFoOgEJOSLjlQJioAIJImAhHySWqt0ZaVTijDBFgJG5GxpPZ1X9onuvvvufrk8nWg6yCxr59nBNW/e3BuDYhnxhhtu6C3kl6KkOn6uFFRLnybPEsuiWfr8xz/+0ds5oC2j4tbEfJx/6MegDc8kVscRaawEwRBZOR0rUrBYP27cOL9XPiwfA1ss9eaoR34vCEK5wgnAPN058q1bt/bbbXr37u1Xa/BuYkk9hulGjhzptwsxWJmroz1Z1cNZ89g52Gqrrfzzyuo13pFsL7LBTBPynF8vY3e5ElY4ESgOAQn54nBUKiIgAgklQIdHxu4S2nhFKjZCixlShDwGvFjCaqKK2U86qOyRx6I9Ih+L9Ri9w9I9ogpjUMyMmsXoIhVriWRMyB9zzDGx58hvsMEG7o477vCztbJavwS+inmwl5gVFFdddZV74IEH6o0khuKXwtkzF+cf9eO5w4Acs+GcG17uPeiUlcEvhDzLr8PyI9z33HNPv2KAGV2dKe7xFPxPKORvv/32Bunxez/11FO9oU2sx+N4r/G+Yp884TGOyTsEl+5Z8zdT/9BmbIlgldHgwYO9UTzuYeSQ5f1Yzp89e7YPTloydudR6B8RKDsBCfmyI1eGIiAC1URAQr6aWqMyZaGDzLns7DHlHHmbaac0nM98+OGH+6WlzIByj5kt9jtbZ5hOL7PyXKOCq5g1ohNOORk0YJm2LW0lT/azckQUM6CcS893ueoggJCnvRBAHB/GEmmeneizYn7422dqEH7mO/cZYGL1x9VXX+0FPTP05XY8j5MmTfLnxPNcMhiGH8v+DznkED+T26lTp5xOjSh32ZOYX2OFPHVEzDNzji0DDNWxKoSj6Xh/cY/3RPgcIsg5paVPnz5u77339oOUvE/wJzwrkc444ww3NmXnYf78+R4jz6eEfBKfKJW5FghIyNdCK6oOIiACeRMIhTzWwFkCi6PTYo4zellOyN5AljDK1RYBhBYdVIQ8S5/p5Jpj2TIG7nbYYQfXs2dP867IlWeVWTUsVz/44IN+iTYFoRPNUuYBAwb4ZbQcuYfxKbnqIGBCnnbjHcMADOKHWXVziCmWx6+yyip+TzknJ/CuCQW6CS6u+G+77bb176RKDNxQB6zXY3yNc8iZoeV4xM0339z17dvXXxngsnJbXXXNj0Ao5Fl5EzqbkcfYps3I233eGzxP/NFO/B9nVucR6WH78Jk2Y5URxgp5lzBohCMdBm6OOOII9+677/o08Of/St434TnyWoUBGTkRKD0BCfnSM1YOIiACVUyAzoms1ldxA5WhaHREESRPPfWUtwhPh9eEFkbsRowY4Xr16uXWX3/9MpQmfRaUidk1Bhwuv/xyN3nyZG89HxGH9XKWwXI0lHW806ekO+UkgJBnbzMz8lh451xvXCigEELMZDMbyqAMQqlz587+z8pq4Rm44blkhQjbPsIBAQtbziuz8OzHnjp1qheKlIs6IALlikcgXyEfloB3CNbm2RZEejxzuT4//F/JFhHeMQwo2oAnacpqfUhZn0WgfAQk5MvHWjmJgAhUIQEJ+SpslAoUiecAAc8Zzffff79fIsxsFXt9mV3EKnSuHd5SFp9OM0IQY1PMrjH4wBJr9kn379/fny1eyvyVduMJ2BL0G264wR8JhojCmTDnM5bGOaqtU2opOts5iINgD8MQzhzPIrOehEnneFZwXC0du6aLk68/g2H88TtC1FG+UuWVbxmTHq8YQt4Y8Ezw15h3Gu3LqgsGEbH1wH55HOlIyBtZXUWgvAQk5MvLW7mJgAhUGQE6nmbsTkvrq6xxylgcOqPMMLF/9J133vGCpFmzZt4CNIbEKrF0OV31EXkMOmCUj1l5tn4wk8uKgcZ0zNOlL//iEuAdw4w14gcr86z+iIooZkYxomhCvpASkDbPCPmwb528eZbbtWvnn5VqepYLqWdTi5tJyDP4c9ZZZ3lbHgzslcIh5Dk//m9/+5u755576o3d4Y+Q19L6UlBXmiKQmYCEfGY+uisCIlDjBEIhz7JX2yNPZ9gcIok98ocddpj2yBsUXUVABHIigNCxrRt/+MMf6k9FCGesWYqOdXGW0/O+4Rz2uBl54mQarEHAMyCFtXIGKGfOnOmX9bO6BIGH2Fp33XUzzuTnVCkFKjuBUMhHrdZjM+Giiy5y2223nd/fXorCmZBni0go5Pm/kmc1FPLa3lOKFlCaIrAkAQn5JZnIRwREoAkRkJBvQo2tqopABQjkIuQxdIcQYkZ+++23d1tssYVfYo+gDx2CCcNmLKtnFjR0vMtYqcHZ4ZdeeqkX8N9//3390mdWbnDO+MUXX+zPnpfYCulV/+dMQp6BICzSM0hTqhUXEvLV/4yohE2PgIR802tz1VgERCAgQOdXxu4CIPooAiJQVAKhkGdlj636CWfkmWXHYj3CHaGO5XDba86Mp4UlzC677OJtIuy+++715eQ9xv5l9uFztvvrr7/uj7kjb+KTPmkj9CgDcZn5l0sOgVDIR63WI+QxglkOIR9dWs/zxcAShhfvvPNOPxilQaLkPFcqabIJSMgnu/1UehEQgQIJ0AHm6DGWC7JHleOTcHROzNHhHT58uD/qib2IciIgAiKQKwHENO+VUaNGuTPPPLP+/G0T55aOvXPi/M1v5ZVX9tbqmVk/6qij6mdfEXkYP2Sf9GuvvVY/WEDapEt8xDzW7ok3ePBg/9ny1rX6CWQT8szIr7POOvXPRLFrZDPyUSFPPgw+bbnllu7666/3JxZEV4sUuyxKTwRE4H8EJOT1JIiACDRpAgh59pHeeOONjn2HoSVeAyMhbyR0FQERaCwB9q2z6ueWW27xM+aLFi3ySZg4t/RyEfLE4Vi3nXbayV144YWuY8eOXqR//fXXfkn9ySef7I+uszS5SsiHNJL7uVqE/FVXXeX3yGNEEcds/CabbOJXeZx22mklG0hIbsup5CJQOgIS8qVjq5RFQAQSQMCWvWLoDovSzM7jrFPNZ4S8jN1BQk4ERKCxBDhHntlyZitZEv3ll1/Wi+swLXvnxAl88+PKsvs+ffq4888/35+qgB9C/sUXX3S5CvkDDzxQM/Ih/AR8DoV81NhdOfbI83wyCMUS/muuucY/0zzLHM05aNAgxzPF8vpMRyImALOKKAKJIiAhn6jmUmFFQASKTQAhz97S2267zc/KMzuPs041nyXkoSAnAiKQDwFb9XPvvfd6y+IcCcf7xcS5pWnvnDh//PhjyTKijX3y55xzjjdaR3yE/EsvveROOeUUf3wi7zVzlle4tF5C3ugk55pOyPNcsGXi8ccfL+nSekh99913burUqX7QiP83v/jiC2+Uceutt/ZL61u3br3Ec50cwiqpCCSPgIR88tpMJRYBESgiATrZdo68jp8rIlglJQIi4Akgqj/77DNvVZwZ8/nz58cKeWYy+YtapDeBjxBnj3y3bt1c37593RlnnOHT5/63337rxo8f70aMGOGt1fPdnIS8kUj2FSH/xhtv+Nnw0Ngdz0yn1GkHjz32mL9GTzoodq15npmJZ/CIa7NmzeoNNBY7L6UnAiKQmYCEfGY+uisCIlDjBBDyslpf442s6olABQmwR/6DDz5wN910k/9jFhMXzrxj5bt79+5+zztngSPMEPShYzaeZfWcB4+g58i60LHs+b777nNPP/20N9xps/JxQl7G7kJyyfi8ePFi9+STT/rtGYh2HM8QNhM4uvDmm292a6211hLHEpaidja4ZFfKET7PpchTaYqACCxJQEJ+SSbyEQERaEIEJOSbUGOrqiJQAQLskZ84caLDSNhDDz3kEGS4UPiwfefyyy/3Ah4xhlAPnQklZl85gi6Ma+F4l3GOPEfPsR//ueee8zP1EvJGKLlX2nDGjBnu6KOPdu+9954zQ3PUiAGetm3buj//+c9u2223deuvv35yK6qSi4AINIqAhHyjcCmwCIhArRGwpfWXXXaZX5poZzzbTAP1bdOmjTvhhBPcIYccorOXa+0BUH1EoMQEEPITJkzwR1yyfeerr77yOYZifO211/az6MzEF3LEJXm988477tprr/WWxclLQr7EDVyG5FldMXnyZDdw4EB/soo9Q5Y1x7+dfvrp3nYCFuTlREAEmgYBCfmm0c6qpQiIQBoCLHtlhuPcc8/1S1IXLlzoQ4ZCHgM+LEX97W9/67baaqvY2bA0yTfwJs0w3QY3gy82+xZ46aMIiEBCCZiQv+KKKxxCnr3FJq6tSszCY4l83XXXrbcmH74rTPTb1eJFr7zPOHnjrrvu8gMHLOO3vGTsLkorOd+jQt5WdVgN+D/qr3/9q9thhx38Fg3z11UERKC2CUjI13b7qnYikFgCdD6xkMsfs+alcOSBsZ5XXnnF/elPf/LLFb///nufVdiJxngQ+1d32203v7SRval0irM5Ot0se2T/KzMo06ZN87MpGC0K0ycdwpImhoPozHfo0MGRb7aOe7Yy6L4IiEBlCeQi5FkujyV6Bgp/85vf+GO+MJDHwCJ75ZmxR6zxx3uCdwpxoi5XIc/AJGnKJYMAQh5bLvvss4//PyQq5Nmacffdd7uNNtrIrbrqqsmolEopAiJQMAEJ+YIRKgERqC0CCEzELDM5CNaVVlrJdxrLWUs6LeTPTPmCBQscwrcUjnwQ2CxFxVAQn/HDhUIbMU7niDNymZVvjJBHjNPhplM+ffr0eiEfVx8T8l26dPH7HDlmis52qa0Qx5VFfiIgAsUhkIuQ5x3DEWIYstt7773rhTwG7OweS+55DyHsObubwUWWVIeDfdmEPNuEeIcdfvjhrnPnzmUxjFYcik03Ff4vsqPnODZw7ty5flVHSIR2xZI9/0fxWU4ERKBpEJCQbxrtrFqKQE4EmPnm2CIEJwaT2rVr58+lRUwyAxR2GC1BOhl0VBH/dDYQoxhkInw+ApQy0Hl988033ciRI73IDmcfTGDHlcXKZNe4sHF+hMc/TNPCcS/qH/1OGFzUHxZYFKbzPWfOHM+HgYJouP/F/v+z8sRBxO+8887uqKOO8h3uqAVri6OrCIhAdRMwIX/llVf6pfW2vzl8D1ADe+fE+ZsfVwYGt9hiC3fSSSf5WXyEvjkT8szOkl+4tJ64DMz27NnT/eUvf/GWzlu2bGlRda1SAvyf+PHHH3sbCrQb/x9GV6nRjscff7zbc889/bNhz0uVVknFEgERKBIBCfkigVQyIpB0AnQAEZvPPvusu+iii/ySTsQ4ZxYfd9xxjiORmP2JOvZ7sjT9iSee8EfjMFPETA/nHDOzFLf8M5pG+J2Z61tvvdW9/PLL7vHHH/eDBDZLTrh0nd0wDfscFzbOz9INOz8WjntR/+h3yy/O3wY24GtpxoUL8+E+gyEMoBx77LF+uW2vXr0sG11FQAQSRKCYQp5q827gPbv77ru7v/3tbw0s3GcS8ha3Y8eO7sILL3S//OUv/YBhglA2yaLy/Lz22mvuvPPOc//+97/9/4lREAzmdO3a1R1xxBFu0KBB3mBi+P9MNLy+i4AI1AYBCfnaaEfVQgQKJsAo/wsvvOANvl1zzTV+9tjE5O9+9zs3dOjQeiNMltk333zj3n77bTd69Gj/9/777/s93quttprbfvvtvQE59nQ2xjGYcMEFF/jBgfHjxzcmas2FZSntvvvu648UOvjgg2uufqqQCDQFAqGQf/jhh5dYFt1YBgwO8l7ddddd/TFz4VF1oZDHuB4z8uYQdoRlHz5HlWHdnHPp5aqXAIPYLKXn/+YzzzzTTZ06tX77V1hq2paVX4h4bCwwSBOu1AjD6rMIiEDtEJCQr522VE1EoCACzITfdttt7qWXXvJL+EiMzgFiEiNvGINj77Y5ZpeJw7nIDzzwgBs7dqzvYBCHDsRmm23m6LRyvm1j3OzZs731XWbk33rrrQaz4ZYOeZNPJmez34QJw5p/6EeYaJoWLi5+GDdTOOLiouGj3/8XqmE4/FjNgBXi3r17u1NPPdWC6SoCIpAgAgh5Bjyvvvpq/05EXLM0OnwPUB17l8T5h368X3mvDhgwwK+eYrm8OYQ8RjXvvfded+mll/ptSvZuIw3EHgbTWJav88aNWvVeeXYmTZrkB9g5Xs6MscaVmOcAg4k8F9hBYEWdnAiIQG0TkJCv7fZV7UQgZwKM+v/jH/9w48aN87PrRKTjx3J6lnCGQp5ZAqzJT5w40Z1yyinemi7xLQ7G4Lbcckt33333Nfrc9c8//9w9+uijfgYCA3TWufWJ/98/1jEN/aKfw3hhJ9j8Qz/iRtO0cNwLwzYmHHFx+cQnDstnf//737ttttnG7bHHHv9LTP+KgAgkigDvS6zPMzh54403elHPyiNEd+jsnRO+L7gfvnNYJYUxM7baIOywUs4MvTnCsrrq1VdfdRhGmzdvXn18wnHMHcuvDzroIFmtN2hVfOX/WQbJ+WM7RCaHTZo+ffq4fv36ucMOO0xCPhMs3ROBGiEgIV8jDalqiEChBGbMmOHOOuss38mcMGGCT44OJaKcpZhXXXWV7zQyQ8A5xczEjxo1yr377rveQB7+OGYBevTo4Ww5fmOXbpIOgwJYrP/73//u/vOf/zjEvbl0nV27b1cLx/ewY2z+oR9h8A/9LJzF57v5RTvOhAmdhTM/S9f8o9/DcHTUMVyEocGddtrJz6yss846fmWEhdNVBEQgWQQQ7QjsWbNmeWOiGC9DpNk7Idfa2Gw8gpxVT+GyetIgPYzpsaeaZdY2wMo93jussELojRgxwu+pxl+uegnQlqyUYxDo9ttvz1hQDKLyfy+ruM4//3xv2DBjBN0UARFIPAEJ+cQ3oSogAsUhgKX60047zQtzjmMzhzDHQjL75jnaBqv2zNozs/TII4849smboyPBbBHCn+ONmB0Il31auExXOqKI+ZkzZ/oODMb3WMIfOsKYGA79w89hBzkMa/6hH/GiaVo47hGW7+bHd4tvfoQzF/pZOO7hb2nZ1eJYOIQ8+185iootDXS6dZyQUdJVBJJNgCX1n376qRfY4bsz11oh5HkfMEDKip2o4x2DAVJOHdl///2XEPKssGJ1zx//+EcJ+Si8KvzO4A8r0zAoe9ddd2UsIc/Geuut522qcGJBdJAnY2TdFAERSCQBCflENpsKLQLFJ8ASTFtaz0w7DnEZ7pFnTyUzSeecc45f6vfBBx/UFwQB2qFDB3fMMcd4Q3eIfzkREAEREIHyEUDIs4+aFU39+/f3J5HYACLv6E6dOrmTTz7Z32PVj1x1E+BIV7ZJjBkzxh8ZGD12Liw9A+ndu3f3NlVYht/YQfQwLX0WARFIBgEJ+WS0k0opAiUnECfkyZQZHKwjYzEXQ0nPP/+8t0bPDD6zBTgEP4bZ2LfJTA8z982aNfP39I8IiIAIiED5CJjl+iFDhvhl/KxoYjsQ7+TNN9/cb5NC0Evola9N8s0J+woLFizwx7seffTRGU88YKBmzTXX9PZpOMK1sUe/5ltGxRMBEagcAQn5yrFXziJQVQTSCXk6Axxlw0w7++Wffvppd8cdd/h96zY7QCeR2Z0DDjjAh6OTKCcCIiACIlB+AryXP/nkE3/uOFuUWEWFyGM5PoOsI0eO9J/xk6t+AszKP/HEE367GqKeFRZxjqX1a6+9tv//mq1vWlofR0l+IlBbBCTka6s9VRsRyJsAQp5RfI6fw2q8OToNLVq08KP87I/HEF5opInZeDoMW2+9tbvssstc586d1YEweLqKgAiIQAUIIOYRfYsWLfLL63lPMxDLCqtu3bpVoETKMl8CbJUYm7JaP3z4cMd2NhtAj6aHPRvs07CCjrBYsZcTARGobQIS8rXdvqqdCORMgGXy7MN76qmnvLV4i4iQZ+aGTiDL/OhUhDMCJuIHDhzoj0pjVoBOo5wIiIAIiEDlCCD4eGeHwo/VUzpfvHJtkk/OGH994403/PFzo0eP9sZg49JBuGOxfq+99vLHz/F/tpwIiEBtE5CQr+32Ve1EIGcCzLbTWaCjwNE1uTgEOxaUBwwY4C0k77jjjrlEUxgREAEREAEREIEsBBg05xQCDN799a9/dS+88ILDBkKcY4Bmyy23dLvssos75ZRTNCMfB0l+IlBjBCTka6xBVR0RyJcA+/BYtseyegzW4WzmPd0MOyP+LNMcPHiw+/Wvf+2X1eebv+KJQLEIMAuJY/YxX2fPvl0LTS/fciieCIhA0yXAagqOK3zxxRfdn/70JzdlypQGKyxCMuHxcxdffLG3g1DIOzBMW59FQASqk4CEfHW2i0olAmUngJD/8MMP/dnwuQh5OghrrbWWGzp0qD/vnL156jSUvdmaVIaIavuLqzj3mK1iBsuMe8WFy+Zn6fCbIC3bX4yxsEzPeLoBr2z56f7/J2AM7fr/7zT+E+1orhjpWVrluMY959ShVPUIWVn9onkRxvzss8Uzf4ura3EIsFIOA7OcFnP55ZenFfHkRhswuN6lSxd30003uY4dO7rWrVvXF0RtVI9CH0SgZghIyNdMU6oiIlAYARPy4Yw8KVqHLUwdMdOyZUtvWIfOBUfe6Li5kJA+F5vAN99847d+zJgxwxtcjEufmXiE96xZs/zRWhhezEdokA42IxYuXOitf/O8t2rVyq2zzjouzgYEfnSY11tvPR35FNcwOfox+IIxtjXWWMO/UwoRHjwvDEzieDfRdpkGYXIsYsmDMQP7+eefu3fffdfbI7EMKftqq63munbt6sVavmywcfLFF194zpw7juN554g6DJ7Onz/fv9tXX311bwGd+8T58ssvvZFTDJ9ybN3cuXP9Xnv2b2NQj99auuPO7DdIWuYaU/64/4MsnfAalw/3ySvuXjr/MM1Kf+YddPrpp7t33nnHvfLKK1mLw3PSoUMHd9FFF/nnheX2/BawZs87ir9M9W5Mu2QtjAKIgAiUnICEfMkRKwMRSAaBxgh5Ogd0FtgTf+mll+o84mQ0cSJLSQecZxMBz6wU4mz8+PGxdUEEffXVV2727Nn+mUS8WQe+MR3UUMiTFgKTDjDpxRkKQxAhsrp3764BrdiWyc0TzghIjrJs3769555bzIahaHMGdBDDfEZ8MkvJgEs5HGKKZ4K8EcG5OsKzogTx9uabb3rhbHFhgz0Sjo9j1tUGJagTzyt/2Rzp81tioGDVVVf1e6gpJ2XkiDr+EPMMprDaqlPqGFGLg1gnLgO4CHmWexMXIU96lAvOUUd8ZpWtfJSbujTGEBu/a+Jl+g2TD/UgrOVFPvxRTsQsYXDWPlwpWzU7Th5AyE+bNs2/A7OVFUYMhJ144om+ragj70QGWmyADD+eM/5oB65ww1ge7YtfuX4r2eqj+yIgApkJSMhn5qO7ItBkCOQq5OkotG3b1i+pZ288HWQ6BtXu6MRZR67YZbW0YWN58Nm48FkuPwJmsXnYsGHuvffe8x3yxqQUtkdj4v0/9u4mRXUgiAN4jjLgThDEjQtB8BjewRO6mlu48ABe482v4Q9NTzITM+/hg+mCmKS7quujSaiPNh1c9Evn72/wJsdS/tHhX52j31IZx+jTVuusrb6PPlO4rTxj9KH9DncunnHgeuYFtCqgAqTb7aarQHTImLlP/1ftLS4aSSUJJIGaFSQC2DE849btrgW3klOWX6cSr+pe4+ExJZO+gADwcDgUWQTONQigfaBNQMo2/p4iUbPb7Wq0yWs2tErA7iiONsCMfLZE9X6gi8QCOfBxSEpYnp5gXrC6Wq2KLHZqaXWeFOZFHdFxqZzo2V6Cht6SOP5r/3g8hs1mUxKfbLbf74fL5TJst9uSqF/K70Vm6my7BX6lBXog/yunvSvdLfDZAgL5OR+74wTZau58Pg+n06k4hJ9H+39aOIIqXJZbv3/sxUtPjk3rpLRtcZ5oUuO2eBzI+/1enCJOKqeaQ20JLDut1+vh7aOy1eF5CwjiVaKu12v50JMlwam2zR0t81jP4VxaeO18P0P7U/qfyv6srM/iRz50S+w7Rd/avL3H7yvaWp7gtfKlvcbNuDXuXDy0AH4qwe7rinw7bn0fWuex9rYteHh5Jhx4j+FNtaNNRV9F1tHSR/+2Hf8aBPPGa4Fc3rl5bgWUeEokBKbk068PLf5oWwits/cFXHqA6IfOexoOiAzOKvLf6VaIXvgTuZfKGRvVeqcKLxnkmt2stBDoH4/Hsg+9VTFt4uSFZuisuwW6BUYs8AcAAP//z+m8DgAAQABJREFU7J0HmBRF3sbLeOaAiaCIiqhg9szZUwHhwJwDyYwJPVDOeGfGiJ7x7oyYE+acI4iCOYKiGE48E0bU+fpX9/33qe3tCbs7M90z+9bzzM5Md8Vf1fTWW+Ffs+Qi5+REQATaPIGff/7Zvf322+7OO+90xx9/vOdhj4dZZpnFf5911lldhw4d3JAhQ1zfvn3dWmutlWluM2fOdP/5z3/ca6+95iZPnuyee+4598svvzgrl2U+/G5l5Z5dt2v2nXt2jfg++OAD98UXX7j55pvP/fDDD+63335zyy67rOvVq5dbe+213QYbbODmnXfehjCElytOALbvvvuuu++++9xJJ53kvv/+++KBYj6szqy+YreLfiV8S8MSeWvCtzbvRQvXSg+WP6JpCaN84ePM4t9Jr1DYMD/mL54/ux76tXhDv6X6IywO/y0Nb2mF4ZPi9Akl/ImnbV7yXbf79p7kL1+eLAzvSeHsfqF7Fpb3eJktfLH3UvJXKI5i+SsUtlr3qlVG/r8vssgibv3113cjRoxwa665pvvDH/5QrWIqHREQgRYQmCV6QEjItwCcgohAvREoJuT5J48YRbyfcsopboUVVnDt2rXLLIbff//di+u77rrLXXTRRe7999933333XYMAiHcc4x268NEY+i3VH2HoFG266aZu+PDhbrXVVnNzzjlnZnllMWMMxFBv999/vxfy3377bUP9lZpfq8ewDksNi794fTcnbGvDtzbvzc1rc/1b/gjXEr75wseZx7+TXqGwYX7MXzx/dj30a/GGfkv1R1gc/lsa3tIKwyfF6RNK+BNP27zku2737T3JX748WRjek8LZ/UL3LCzv8TJb+GLvpeSvUBzF8lcobLXuVbOMs88+u+vWrZsfrB80aJBbYIEFqlVMpSMCItACAhLyLYCmICJQjwQQ8sx+jh07tmFGnnJaR4eR+TXWWMPtt99+rn///v4fPOI+q47Z3PHjx7tDDz3UvfPOO+6nn35yiPt8nSIrp5XH/PE97GQ2xx/CfamllnL9+vVzxx57rFt44YUter2XQADW1NuLL77ohg0b5t566y33448/NtRhCVE0+A3rsJRw5ide33Y9fCfusL3YPbtWKO189ywscZkfu2bfLZ1qv1s+7J388LLvhfJjeTe/9h6/bs8W7vOy+/Zu10nLrvHZ/MavcS90+DMX9xv/Xoo//FicxcIn+csX3q6HcXItyVnZ4/fyXQ/9NTdP8bD58ldq2vnCh+kkfc6X7yS/SddKyV9SuGpeq2YZ+Z+1zjrruBNOOMHPzM8999zVLKrSEgERaCYBCflmApN3EahXAr/++qv7+OOP/ezn3/72N78knQ4ErznmmMMtueSSbrPNNnOHHXaYW2mllfy1LLOgPBMnTnQjR470gp7ZXFy+ThHXw86k+SNM/Hr8O35w8evMbsANIU/HSEL+f5ya85fBF9rlTTfd5J588kn/eerUqe6bb77xdRnWU6F4w7qJ++MeHVjqCwHJyg2cxR2GtWvcxz91Otdcc7kvv/zS0ebYVhEOGOEvDM93HL+p+eef3y244II+zf9dbfyXeAjLi3QZbOManeukOBuHLv838kAZZ8yY4b766iu/QoftJJSDPH3++ed++wP3kxyMl1hiCV928k95PvnkE8/MygN/4lp88cU9FwbkSAvGhOeeXbN6CsOSF/zClc/kGX9TpkzxeSdfYR3y3cLb9fh3/ODi1+079yxs3F++66E/PuPMbxivXY9f8wFifwif5C/f9TB4obTxlxSvhS8Uf6F7SeELpWP+7d3yzPd4uPCe+U96LyV/SeGqec3KEi9jqXkotYz8vlZffXW3ySabuIMPPth16tTJzTbbbKUmI38iIAIpEJCQTwG6khSBLBJAINBhZh/5ueee68aNG+c72nQCWELPKP3WW2/tWG43zzzzNOk4Za1MCCo675dffrm77bbbvGBgdjdfpyje2TF/lCvsQDXHH2JtxRVXdHvuuafbf//9tUyxhY2EJfaffvqpe/DBB/3qCtrmZ5995gUdwhJBSL3YC+72siTDOrRr9o54pE3TkSUcdhUsLvxYWH4jtCG+EwYR27lzZy8ascFAPsgrecIRB87C+y///x2xiVils8yAQJILw5M29heIf6GFFmoSZ1L4cl8jP5SfQYsPP/zQbx1BmFMORDMrJriHvYgkx9Ycfg82EEF5XnnlFV+Pxgj+lI/lvTDGz0cffeTjp464Z9cYOMBZWDiSH5YDw3XRRRf1dUB+nn76aZ8O/o0rn3EW3q7Hv//PV35/dj8pPM8hnqvUmw1SED9+LR3C850BCuqZMDhY2OASfhFV1lbwY+3Me47+xOMsdt3u23tSeK7hLM+Ug3ySNnnlflI4i5N3ykHe+X2R/3i5+Y4f7sMovB/GE/9seeN6GIbr9lsln+SZwaXQv8UVzzv5Iy/GnniJizLD3PJKPi1uiyvpnfhYzWZlJx+EI13ek5zln3SNMf7CMiaFy3ctXkYrA/minHznxW94p512chtvvLHbZptt8kWn6yIgAhkiICGfocpQVkQgbQL8w6ej8fzzz7sTTzzRC2E6L1tssYUfoe/evXum98WH/CiLCYUxY8Z4wcASbTpkOOsUWacp3tnhuznzy/d8/kI/9hmhxzYEBkaYuaXzJ9cyAnRorePM6goM3/Fith4BiYjmRftdZZVV/JaGpZdeuqTEqC863NQPgoN2k+RIb8KECd4v9g8Qm8z80iEmT+Qv7HgnxWHXSAdBSxux9mL3kt5pdxY/oqCUMEnxtPYaeUDMw5nBCMQ15Sd/cOP3xfaHJAdjhDjv5J9ny/Tp0z0z88914rPBCtIjLRNXlJ1r1EW8ngjLYAF+yJsxIk8MMFA31Xaky+8fWw/UNSKJeo878sgWIEQ/g1aUl0GiLl26+GcH7YW2xlYdHCtSWJlSTYcgZvvVe++95393DJCQ7/gzMcwTdUEZFltsMb+Si/xT/6Gjvjt27OgNhMKIMK1x1DOrMF544QXPkoGgO+64o5GNFIs/zDuM27dv75ZZZhm33HLL+RfPBNofBlMpL3nlPoNXcGAAL5+jDikXz6MePXr4gSUMd06bNs3HyUAUbTnuyBP5J93//ve/DQM7cX/5vtPuw/818LDfAtdpfzy7GFTD1g3lpk4YBNssWnXHO+WUEwERyD4BCfns15FyKAJVJcA/fTqJzJTRiaBTwT97RBGd9rCDUNWMtSAxykKHnw4TgoGOFx0nyoRDCLACgRedYoSFOfPDd+sE8U6HB7FA5wcX+oMN9+m0rrvuun6Z4qqrruqt1tcSN1+wDP+hXqkrXohK6pFrdh0xgJDjVaqjbu0VtoMwPNcR7Pijk27tgO/cC9tCGC7pM2FoE81pF8TPqzlhktJu7TXjTD6sHMRp3Lif5PAbijjKkiRk4v6Il2s4KzvX4umEeTF/hMmXDvcq7RjUePbZZ30bZYUA4py2E3eUhXYMDwakKIu1YfwbExNY5i8eTyW/Wx75Dbz66qvujDPO8MIevlY/lj7fWcm1zz77uK222soLZH4v4QBL6NfKynM1rDvz09x3+JBPWPL8P/nkk93LL7/sByDCuCzvpMlzmy1QDFgj6Pl/h6OtIaoZyKBcXKdOqNt8g1aEI0788TyyAQoGdnhmEacNguA3dHAm74h5Birvvvtu///pzTffDL01+UzeSIftXAMHDvTPJ/LH4COz7ZSPAQobOKGM1AnheDGAYgNtTSLXBREQgUwSkJDPZLUoUyKQLgHruNiMFyP05ehcpVUqOmt06FgyTdn4jkPkI+Ifeugh99hjj/kBDO7jzA+f6eTQwaTT0yWaXWJWyWbVzJ91hui4MVvLVgRmYugsMXsjJwIi0PYIICiZgUWcsSqHZf+1/CylBhG02B9huxDvPAN5/oWO72xvODFa2cVRpWk+AxHP2Ep54okn/KqHMJ/knfpAxCJyr7jiCj9wnaa1dvLEwAGCny1Et99+u18RcO+99/rBnjD/4Wf+RyHi2ed+9NFHe/GOkH/ppZf8ZwaSOBaV/1EIdsS9nAiIQG0TkJCv7fpT7kVABFpJgE4pMxZYRWf5JOIeZwKdz3SQmOlgpuaggw7yM0xpdkzJk5wIiIAIpEGAwc63337bDRgwwD878wl5VnGxrQDjaQjHtBwry5iRf+SRR/wzPswHeef5zuqBDTfc0F166aV+5jr0k+ZnBoAYgH7qqaf8yScs5edakmNVw+abb+769OnjBg8e3OotCklp6JoIiEC2CEjIZ6s+lBsREIEqE6BThOXs6667zl1yySXeiBdZCIU8SynXXHNN9+c//9kLeWbja31WrcqYlZwIiECdEChFyPN8ZBvBeeed5+0CSMi3vPJZTca2gFGjRrl77rnHr4hIik1CPomKrolAfROQkK/v+lXpREAEihBAyLN//s477/QdJfbR40Ihz2z8Rhtt5HbYYQc/01EkSt0WAREQgbolgJDnObnvvvv6GXmWb8eX1jPLzVJ1ZrgZBOUZmpar5Rl5mLFqbNKkSe7ss8/2y+z5nuQk5JOo6JoI1DcBCfn6rl+VTgREoAgBBDuGhdgjzz5KLKDjQiGPtWiWK+6yyy7+TPgiUeq2CIiACNQtAZ6NGGE75phj/DGlWLIPhTyfEe6rrbaatxaPbYDwfrXBIOT//ve/u4cffti9/vrrjZKnLOHS+ssuuyxTS+vJbDgjj+G7UoT8kCFDtLS+UU3riwjUJwEJ+fqsV5VKBESgRAKlCHms/R5wwAF+TyjGguREQAREoC0TwBgbRtgwFnrxxRc3EuoYjsOeCPu12ZtuhkHT4lWqkGfVVdb2yGMs8cMPP/SG+o477jhv/C4cZA6ZMiPP8Ya9e/d2Bx54oI6QC+HoswjUKQEJ+TqtWBVLBESgNAL5hHwY2o5R2nvvvf0sU3hPn0VABESgrRHgRJMHHnjAC/mzzjqrUfE53myNNdZwW265pV/lhMBM09nSembkMWgad8zIY+29X79+3so+Kwiy4jiijv3xjz/+uB8UMWOsSfnjaEcGmjkx5bTTTvOnp6TNPimfuiYCIlA+AhLy5WOpmERABGqQAEKe83oLLa1HyLOsfo899vBnwtdgMZVlERABESgbAYQ8z0xm5E899dRGM/II+T/+8Y+uZ8+e7sgjj/Rnx5ct4RZEZEI+n9V6jmNbccUV/YorrL2nefRcvHgcQYeI54Wxu2KO1RDdunVzV111lePUgCwNShTLu+6LgAg0n4CEfPOZKYQIiEAdEShFyC+xxBLuiCOOcIMGDXKcxSsnAiIgAm2ZQD0JecTvqquu6k8k2Wmnndy8886bmaptrpDHFsEyyyzjhXzXrl2djknNTFUqIyJQEQIS8hXBqkhFQARqhUC+pfVcN4eQ55x5DAgxOy8nAiIgAmkQCJ9LpJ+WETmE/KOPPpp3Rn7ttdd2W2+9tTvqqKMyMSNfyNgdQh7DfAcffLDbcccdMyfkWfnweIkz8ibkr776aichn8YvVGmKQHUJSMhXl7dSEwERyBgBCfmMVYiyIwIi0IgAR2RysgbHvLFHmq1ALAdnCTjCjX3QGJSbZ555HOe3V8PVo5A/5JBD3Pbbb18XQp6l9Qh5BqHlREAE6peAhHz91q1KJgIiUAIBCfkSIMmLCIhAKgR4PiGax48f7yZPnuyPT5s4caI3ZMasNwbOllpqKX9mO4bOTMyHM/V8Dr+XoyD1JuQ5657tU3379vUMy8GoHHGES+vPPPPMolEykMPS+iuvvFJCvigteRCB2icgIV/7dagSiIAItIIAHeVixu6Y1cBoE4aQZDyoFbAVVARqiADPhmq4uMi2dH/77Tf30Ucf+ePdHnzwQX/0GGeKY8kcwYZRORxinnPbO3fu7Nq3b+86duzoevTo4a9hkZ2Z+w033NCfKx6K+ni6zSkrQr5ejN2xomGTTTbxlt5XXnllv9qhOSwq6Ze6fuWVVxyG+k444YS8Z8iTB7O+zwDPOeecI6v1lawYxS0CGSEgIZ+RilA2REAE0iEgIZ8Od6UqAlkkwDJ2zkhnGTvvlXaIaQQ5Avybb77xIp3l85wfPm3aNH/02A033ODeeecdv6zeRH48X4j5BRdc0M0///z+nfgQqMTPO8bcMHzGQCTL8LHSjr0P/LfE1ZOQZ488VvYZrMXSPqsasuIYzPnss8/ck08+6Y499lg3depURxtNcrQjjp7DNsHQoUP9FgHEvZwIiED9EpCQr9+6VclEQARKIFBMyNMRZobr8MMP91brNSNfAlR5EYEaJcBS5g8//NB98cUX7vPPP694KXi+IMCZQUe4sxee49KYeZ80aZI3Jvf88887BF0xx7OM+OIOMbfYYov5M8aZtUfAI/aWW245f346s/mESwobj8u+15OQx97A8ssv748XxeBdlo6fg/fMmTPduHHj3N/+9jcv6Jmljzvqjnz369fP7/PfZptt/EqNuD99FwERqC8CEvL1VZ8qjQiIQDMJ0Pml85x0jjydIzq5G220kV9Wv91221XNmFQziyHvIiACrSDAcwARz/7zM844w4vo6dOnO66bC4WuXS/HNWaEEdesAEC0IeKJH/HOi2thOpaf+DthkvxxnaX49kLY81wjTfaGn3zyyX6wkpn7Ul2t7ZFHBLM8/fXXX29URNjAY5FFFvHL6y+66CI/6NHIU8pfyOPXX3/tnn76aXfggQe6L7/80reRMFvMxvN/iiNS+T/VnLoM49FnERCB2iIgIV9b9aXcioAIlJkAnaRCQp5lluw53H///f1MB51uOREQgfoiwHJlBNLtt9/u96S/++673sgczwdzoUjmevjd/MSvlxIeIYnwYqYV4R5fOh2P09KKv+fzF79OvlmKT5oYykP8sUd8lVVWadh3H487/r1WhDwsWZrOTPuLL77oVz2EZYEN/BnUwI7AZZddljkhT34Z3GGv/F577eU++eSTJts+FlpoITdixAi/0mL11VdPbJthufVZBESgPghIyNdHPaoUIiACLSRAR47Zjocfftgdf/zx7u233/YxcR3HTAfLXpkJ2XXXXf1Mlr+hPyIgAnVDAMH3wQcfuPPPP9/deuutXixROHsO8DkU7lwPv3MfF7/enPDmNx5vPM7/pdT0bz5/+a4TAwOTzMrvueeern///n5mPp5+05Sc36//wAMP+KX/Z511ViMWPDMRk1tuuaX761//msrsMPWJrQFWOfBMZ8/4lClTvO2DsDywQcizvYEB2wsuuMAPbmRtRpvycGoB/4PY+sGgU+iwiUC7XWmllRyiXk4ERKBtEJCQbxv1rFKKgAjkIWAzNhiUohNHZz7uFl10US/kBw4c6I/2id/XdxEQgdomwEw4v32sfY8dO9Z9+umnvkA8H0IXilxEYK07yoPxO5Zl9+nTx688QogXcwx+Xnzxxe6FF17wvEL/CGNO+lhvvfXc1Vdfncq57Aj4m266yQ/QXn/99WH28n5mjzkz9+wzJ+9ZcrQ12ueQIUPcW2+91TDQZHkMhbzsuBgVvYtA/ROQkK//OlYJRUAEChCgg0SnlNkl9lHGZ+QJyv7JAQMGuL333tsvPy0QnW6JgAjUIAGeAyxfxio4R74hmhCprNTBgj0Oo2gIJsQvzwyWlzMAYM6EvYl9+8798Brx8QrD4gf/iOh5553XW61nz36SYTP8JjnCWzrh/fh1/LBfnplbjLyxpHyDDTZwa621luvUqVNJdkCY7b7nnnschvjOO++8Rukyy88y/S222MIfmcZAQbXdV1995Th3/YknnvD1mC/9kA35xuo7z/rtt9/eG49L4pkvrkpeJ59sETj11FP9XnmW2ePIH22GUwiuu+46t/TSS6eyAqKSZVfcIiAC+QlIyOdnozsiIAJtgAAdpGLnyEvIt4GGoCKKQESA5wEiFdGEkH/00UcbhDz7yplpZsY5ScgDMBSG9p13HKIL8c4xc4THiF3cIeJZAYSI57mE/Q78YkXfjODFw9j3eNrhdfJM3Bw3xzuzz5SFY+nWX399v30IEYjAL8Vl3Wo9lv85d51j21577bW8RQqZwQgG2EPZY489GgZt8gau4g3y+Z///MeNHj3aG+0bP368T502RV2yPeKKK67wWyMoh5wIiEDbICAh3zbqWaUUARHIQ4AOUjEhz9FNdO4GRDM1yy67bJ6YdFkEREAEChPgfHiMlbF0H7HO88ccogyja126dPFiH/HOCoHnnnvO3XLLLd5QG+I/DBOG5Xo+Ic6sbffu3d1qq63mxXu3bt28aGUmtyWuHoU8HBjoOOCAAxzbqFitkI9nS5i1Jgx1myTkyR8DMptvvrlfGcGgs5wIiEDbISAh33bqWiUVARFIIEAHSUI+AYwuiYAIVIQAYp6Z+SRBzmwqM//szeeFcGcZPoJ+woQJ7sorr3RvvvmmHwRg2T3+O3bs6BZffHG/pHqNNdbwW4Ew1sbAAO/cZ+adJe4IepaQs02AsLy3xGVdyLO0ftSoUX5pPcv/8znqAE443s0eCoO2WPSvBSFP3bONgS0OEvL5alrXRaA+CUjI12e9qlQiIAIlEihFyDNLhrVglluyDFVOBERABKpFgGcUy/2nTZvm96Rjvdz2zyPG2bePAGUAAPHJ0nk+4xDqLL1GzCNKTbS2Nu9ZF/IMzl577bV+GTpHCuZzoZCHFQMhGJTbcccdM7dHPmlGnvpkFQGnBFx11VW+nq3u85VZ10VABOqHgIR8/dSlSiICItACAqUIeY4m6t27t9tll138EU0tSEZBREAERKDVBJjNZ8k977wQ51gpR6xX02VdyLOK4cEHH/RGTC+99NK8aEIhP8888/jnO0fx9erVK2+YNG6QzyQhT14Q7uzt57SFZZZZRsbu0qggpSkCKRGQkE8JvJIVARHIBoFShDwd5Z133tntvvvubuONN85GxpULERCBNkmAZxbO3pmVLddMe6lA61HIMxjCefN9+/Z16667bqkoquKvkJAnA6y4uP/++70NlzROCagKBCUiAiLQhICEfBMkuiACItCWCBQT8iy3ZJZjn3328cvr+SwnAiIgAm2ZQNaFPBb+X3zxRXffffe50047LW9V8fy3QRBWXh166KGuT58+bu21184bJo0b+YQ8eWcrBcf9jRkzxh8fqKX1adSQ0hSBdAhIyKfDXamKgAhkhEAxIc/sBpaesWTM0nqMRcmJgAiIQFsmYEIeQ3KnnHJKgxiGCc/IP/7xj65nz57uyCOPTGWpN8YEP/zwQy/kjz76aG8wkGd93NW6kGdrBaeqmLE7bCXIiYAItB0CEvJtp65VUhEQgQQCxYQ8Vp+Z7TjwwAP9jDzf5URABESgLRNgD/ozzzzjj8bjvHab1YZJFoQ8+cCq/7hx49ypp57qz5Mnz3FXD0Jex8/Fa1XfRaDtEJCQbzt1rZKKgAgkEKAj9+2337rHHnvMjRw50r311lveF9dxzHh07tzZHXbYYf5sYZZfyomACIhAWybA0XgY3eOM++22266JkGdp+tZbb+2OOuqoVGbkqRtm5T/44AN38803uzPPPNN9/fXXTaosn5BfZ511mvhN8wL5xNjd+eef7y3xjx8/3meH/08IeZuR1/FzadaS0haB6hOQkK8+c6UoAiKQIQLFhDzHO3Xp0sULefbJV9s6dIZQKSsiIAIi0ECAfejPPvusF5HxGfksCHkGGz777DNvvX748OFu+vTpDXm3DybkyT8i+LjjjvPl6dGjh3nJxLuEfCaqQZkQgcwRkJDPXJUoQyIgAtUkQAeJM4fzzchzJBGd0v3228/tsMMObs4556xm9pRWGyNAezQXiiO7pncRyAoBzrJHyG+55ZZNZuTT3iMPI4T8f//7X/fUU0+5gw8+2M9oh78v/PCdWW2MmjJge/3117uuXbu6+eabj9uZceQz6fg5m5HffPPN3XnnnecHIzKTaWVEBESg4gQk5CuOWAmIgAhkmQAdpEJL6xFTSy65pDv88MPdoEGD3EILLZTl4ihvNUyApcAYEeN8cByGFrFALSvUNVypdZp12ujUqVO9kN9rr72aCPkszMiDHjHP8nqW+ZNf+21ZtfD8Z9UVz/X11lvPXX755X6pOgI5S86EvJbWZ6lWlBcRSJ+AhHz6daAciIAIpEigmJAna+xBHDZsmBsyZIhr165dirlV0vVIgDb4/fffuzfeeMMLI1sC3L17d7fccstl7kzreqwDlal5BFhW/9JLL/k98limD1ePYOwuK0KeUn388ceOGWus2OcT8jzjWVlwzjnnZHJWu5CQX3zxxRv2yMtqffPasXyLQK0TkJCv9RpU/kVABFpFoJiQp4Pavn17L+QHDx7sFl544Valp8DlJUD90TnnxexbkmPGjS0Rac+y5csreWfZ7J133un+/e9/e8FBXhEWCJChQ4c2EkpJZdQ1EagmAVaOPProo17IYxW+loU8K14waNqvXz93/PHHZ/IZLyFfzdattESgdghIyNdOXSmnIiACFSBAB6nQHnk7fu6ggw7y58jr+LkKVEIzo6TO7EXdccQUpw1MmzatSUx00tn7+qc//cktvfTSXsyHoqNJgApdYJCBLRzMYpLfr776yqc0c+ZMP2P4/vvvO17MzOOXPLJPF3Fx4YUX+s9pD0RUCE2bjpZ2bC78bNdKeaetVLtN2znyWK1PEvJZ2CNv7D766CP/+883I88g31prreUHa7fZZhu/pcXCZuWdtlHtPfJhe6x2+8oKd+VDBLJOQEI+6zWk/ImACFSUAJ2VQnvkEe6rrbaaP0d+l112Se0opYpCqJHIqSuEO0cvjR071oteBMW7777rvvnmG4fxrdDhnw7o/PPP75eob7DBBn6Wm2W/1XLkAdFOfl955RVveOvLL79sWOKLaGeZMnmnLKFDYGy88cbupJNOcmuuuabaXginxj9jD4Hj0F5++WXfPqh/BnloA/Hl3/mKyiBVx44d3eqrr+5f2PJg9Uk1HPnM+ow8vz24vv76626nnXbyA2ZwDx1+eMZvtdVW/mg3ZuarxTDMR7HP5LNax8/xTKJ+P/nkE/+/kbytssoqflWTBH2xmtJ9EaguAQn56vJWaiIgAhkjQAepkJBnv+fKK6/smJHfddddHVbs5dIhQAeTs6tvu+02d+WVV3pRjwhmJp6Zbeoy7riGRWr2jm6yySZut912c717967a6QPk65133nH/+te/GvYUI9SS8hrPO0KewQeOxFp//fUl5OOAavQ7dY/AZBXJk08+6Y9FQzhhAZ532kwxh6CiXSPeMdK26aabelsKtJlquGJCnhlutoYcffTRqbVbOM+YMcNNmDDBcXQowjSfkO/Zs6e76KKLvD2UWhPy5dwjbyKeVQw2QMpKoA033NB16NDB8f9QTgREIEMEogednAiIgAi0WQJRxyUXzYzlbr/99txKK62UizrI/hU9plGF/hUZQsqdccYZuWgmtc1yykLBf/nll1wkdnw9RYKloa6szpLerQ6j2ctctLQ+99e//jX32muv5aIOfcWLRBqTJ0/O7bHHHrnFFluspPyGZYis1ud23HHHXHQWdlXyW3EgSsATiER87vnnn89FK0Ny8847b0O7sLYatgE+cz1+LfweCfpcNNCTi6yz56JBgKpQjraA5CKbDrljjjmmSf74bUYzuLnItkMOf2k5fn+RobtcNIiWi8RuLhLo/hUJ0xwvYxjNyOc222yz3EMPPZT78ccf08puwXT5P8VzAN7rrLNOQ94pU2TDxT9jokHOgnEUu0ka0XF9ubvvvtu3zUi0+3SiLT65aDVa7tVXX83xDJYTARHIDgHNyEf/IeVEQATaLoHocVxwRp4ZLqyHMyO/++67u6jj3XZhpVhyZopYisye3H333dcvM+VaMUf94phV4oipPn36uJ133tkxA8eMZqUcs+7MAEaCzY0YMcJ/LmWm1fJDfhdZZBHXv39/v0e+WjOtlr7eK0PAnje044EDB/oVJtaOra1GArNR4lyPXws9MIPMM+r000/3KzgWXHDB8HbZP0dizp+wwAz2xIkT/VaXMH+0Xbaz9OjRw59tTt7SWMkEN/IaCWD/3MAGBZ+ZpY8GPfxKHp4BnBvPqgaMmfKby/KMPGfFP/LII+7FF1/09Qp3WLO94uqrr/ZbLdhy0RLH6qYXXnjBx3/uuef61SG0TeoTRhdffLG3JbDAAgu0JHqFEQERqAABCfkKQFWUIiACtUPAOtaPPfaYGzlypF/uSu6tU00HFMNN++23n99nKUGVTt0ijD///HP3zDPP+LqgM24CqFCOrB7pnEez4l4YI+RZZt/SDm+h9OweS6cROQ888IAbNWqU7xTbvVLeTWAw8HDmmWeWEkR+aoAAbRZ7Diyp5/x12rE5a6uhKOYe1+PXLAzvJuSjVUNeyFdKaJGPaMbaDz7ce++97pprrnHRihP/u4znj99Wp06d/CBWr169/JL1aIVJmO2qfCbPJuZZLm5CHsN3bMkhn8suu6wfdGArQCUH91pTYMrx6aefur///e/+GRitKvLRwZ3l7iussIK7+eabvfX9lv6PYrsE25YefvhhPyhg+SVtlu9fGW1nWnfddXUEq4HRuwhkgICEfAYqQVkQARFIjwCdlHxW6+kk0SnmCLBBgwa5vn37ppfRNp4ys9l0vp944gkv5EvFQf0yo8SADLNW+++/f8OADPcQVrzYO2ufqXfCIJDsVWp65o/VAwid6667zu/RJf7mOGbZ2Mu/2Wab+TxbWPKMMAn32ZNfXuRVe1iNVDbfaWPYeaAdDxkyxBtstJxStzjqMnRcj1+z+1zHWBsCC6GF8TvaQSUcv0HsPZD3E044wQ9I0K7z5Y98YDyOI90YDGVmXq5lBGA8ZcoUt/fee7v33nvPt6EwJur9/vvv94MSLRkwIX7aJas6nnrqKW/Pg/i5jguFvI5g9Uj0RwQyQUBCPhPVoEyIgAikRYCOSj5jd3SSQyH/5z//Oa1stvl0EREsh22ukKcOWWqM1WWOluIYOgxxIaii/aAOC/LMKmLYCevyzPozo8VRdcsvv7x/IUaaszSYNhXtzXXMkGLkjiWrzXV0xjF0hzXt4cOH+w41s/zTp0/3S5mx3M9gAY5BB7YNcLoCWwbIa1ZnFpvLod78U4fUXbS/3P3jH/9odNKCiSYT7fbOdfsc50E74WQDtmCw9YcjC2kPlXCsHrjpppvcDTfc4H+HtlWkUP5oi6x+Yek6gl6uZQRgzAoCjAeyrJ4BldCZkF9uueWadXwe8fLi2Eu2AR177LH+dI3wmcX9UMi3a9cuTFqfRUAEUiQgIZ8ifCUtAiKQPgE6KUkz8gg9Os8I+S222EIz8ilXVSjkmVUvxTEjiLV6Th3gxAHEPKKcjij71x988EEv4JnpZzaKpaW0BZbb4ofOa5foDHrOcmePaGT0sJRk/SABy3hPOeUUd/nllzcRVrQrbC2w1J9ysdSadENHHhhMYPCIAQGWBHOMFseV0ZEnz+QXh3BD0FE2xD+zn5QVcZ9PAIZp6XP1CLCaYtKkSY6l6Wy5YKm6OXvmMMPOcm/a7TLLLGO3E98ZdOrWrZuv78hYZ0UHcBjwpD1fddVVfguSrTIh3/kGDxhQoj1y6gLllWsZAf5P8Qw49dRT3dNPP+3FdhiTCXnaTaEZeeqKeqQd8szBoj+Dg7yY8WcrEIOZ5kiXF88+Vnyw8kMz8kZH7yKQPgEJ+fTrQDkQARFIkUA+Ic91E/JaWp9iBf1/0gje5i6tZ5k5BreYpY6s1fslyMTDzDt77THexF5TzmdOctR/ZBHaHXzwwf54L8RIKcKYthMK+XgY2z/M2fCI8bffftuvNojngQ759ttv78+3xjjafffd5w1RsbTWRFQYBtGE8CMML4QgQi+efhhGn6tLgC0RCCb2IbPSwgZjyIU9cxiAYYZ922239bPthXKIgEb4V2NLBQLw0ksv9YKOFSzWBi3fSfkkX4g/fjuI0DQc4hXO5NPyym+FV74BiKz9Zsg3z6nRo0f7ZwCrOkJXTMjT7phlZxXS1KlTvW0G4rvxxht9e2T/PfXJwJLVK/GTLi6ckZeQ90j0RwQyQUBCPhPVoEyIgAikRYCOStKMvHX4wqX12iOfVi05P3PdXCHPrPdm0R5zltMfdthhPg4sV2PYkNlBOq8Ie+usJpWOzj6GpFiWz2AAcRbr5BNfISGPuGHmnAEClvbfcsstLjr6qknyCLStt97aHXDAAe6kk07ye2NZTh92tOOByC+DD8R/4okn+hUFLTV+FY9b31tPAFFpxu7Y7xw3doewZDCG9slMNgbjirli7bFY+FLvI4bvuecebxAtOq7T/3YIa8/KpHhYWo/BRoQ8v8FqO/LGAAT7x2HNdwbSWIIO5yRRym8IP/lEfrXLQHrkuyVCnnBm7A/xf9lll7k333zTD2zw7OMebZKXpeM//P8fwuNsRj46+i6R2f9715sIiECVCUjIVxm4khMBEcgWAToqdPSSrNbTQQ6FvPbIp1d37C1m9hxr30cddVRJGWG/MKspEPLRmda+I8z+3uuvv94vby4m4i0R2kB05rcXIsRVaOkqYegUFxLyLPnv0KGDFzcshcW41LPPPmvJNbzT/hAazLYxiwuDQiKegIRBiLClgP31hxxyiF96DQu59AmYkKfO99xzzyZCnvpDNGEIj/pj1UZW6o72xz5qVoZccMEFDfv7eYaS7yTHb4eBKPbIs8Kgmo7fN3vJMThJntkHjiOvDDAwUMZvMcw7g17YmmAgjC01/Jay4GCMkD///PPzzsizLD5cWs+zgi1EbIcYN26cfyaxz54BGe6ZSC9WPjhttNFGfqsQq3yKPf+Kxaf7IiAC5SMgIV8+lopJBESgBglIyNdGpdH5pDPK/tBSjWbRWd9www39sniOD2SP6T//+U8v5NkTWkpHFj/MoLPnHEGyyy67NAgr7rFclRcCDUGAEKDji5BnKTGd6LjDHzP7dLpXXXVVP6jw6quvxr357wgNZgeZOSslvxaJ5ZnjqjDuh7CXS58A7YRVGAxIcY58fEaetsHSelb/MAjFrDxiOBSbYSkQmrRzXpUWnbRB9vezLeDkk09u2N9Pu8yXPwaiRowY4YU8Ru+q6fhdci76aaed5nmH9ggsH/G887th0I5BFGxxZOVcefJZTMiz6sCM3eGflWZvvPGG+9vf/uY5sKWoJY4TNBiE+ctf/uKNfxI3K4PCgVDaHs8+Bp14XtEesrSioSXlVhgRqAUCEvK1UEvKowiIQMUIWIeHGXmWTrPsEMd1OiPhjLyW1lesGopGTCeUmXRmrnkvxVF/zB5hfZ6OOR1L6jm+v7RQXLQDOqgYEkN4DRgwwLcJwjC4gOG5l156yXeysY6PP5bDM1DA8uh///vf3l+hNJLukVc60AghxASrERAm5kLhRB6THMb0jjzySD+QwZJYufQJIH6wicDsKUe4heLS6pG65cWAEO3XhFE897RLBoNYKcTydUQcAz+VcjYIwe8H45E2w23PyqR02ebB75X2R3mq6cjfHXfc4Y9sy5duUt757bEqgq0Au+22m9/eEP7e8sVVyevkszlL6xkgYhUCpwzceuuteQdaSskzK4IYDNhyyy19e8Tg5oUXXugNHjJYAC8Mc7J6ZI899nBLLrmkH1iSdftS6MqPCLSOgIR86/gptAiIQB0QwBAQMxeIHqz4sofVOngS8tmo4JYIeXJOB5zZIhMRNoNeaqloB3RUCc+yUvaYsreWeOggY32cwQWWqtosOLP/rARg0AA/7CtGwDXHMStrlvbZo4+RMQYMWCpLm2SWnfSY+X/llVf8jH08fhPym0V2AphllEufgC1Pv+uuu9wll1zSsDydnNHWcCYaeQ8/+5vBH+7RFpgtpa1suummXvQHXsr6sSVCni0k2IBAyPM7qqZrqZAnjwyIYOCN3w6/NbaoxJfhV7MszRHyPGuYnYe7bSmwdtTcPJMuz77u3bv7YzyJG2ObbEfj/yZtAj82I097RMizgolVGwxCVrvem1tG+ReBWiYgIV/Ltae8i4AIlIUAnRH2Ug4bNszP1mLZl86JdZRltb4smFsVCYMrzK5hbZ6z2Ut11CMu7MjSIWdpu3XM6WiyNJlOKukw027O2gGzoszsc/QWs6AMLJxzzjl+fzuz5Tg6s/jBiNlee+3lB4cQ+ljHR8A1xyEimBFk6f2KK67oO+WsFuFoKDrLzPwzI8vsLobHEC1WVtKhTBhKY1kz+1vpWMulT4B2QBseO3as3+YRrrKw+gvbKjm2NpiUe5Yyb7fddl7IM2NKO62Ua6mQZzALIR8vV6XyafG2RsgTBwNl/P54YZdjqaWWSm1/OG2glBn5LtFxmTy/rrjiCj+AyFakQu3HWOV7JyxtiucRzzeekRgJDV0YP88d/HIkIivcOLHAVpWEYfRZBESgPAQk5MvDUbGIgAjUOAEsoiOcMObEmeLWOUE0ScinX7ksQWZGGiNhxx13XIOV5WI5ox5xJiIQ78x2I2ypWzqpzDixLBmRzN7l+NFadE7pxCKeWSrPLCMrOJgJDfc4kwbCitl49sYjBNjXP2jQIL8vupihOisLeWRAAMNWvLNsNckhAtkDzHJW9v8jtHDkw0QIe+RZ8qplrkkEq3+tWkKetsCedtoc4iufo63Q/vkd0O4KOeJkkNOW1lvbt2dlPCxxMzvL8m5WhPC9mq4UIU9++G1ThiQDcPz2sS+BbYxDDz3UD+JVswyWFvkrJuSZfWfwDqHN6jKeUR9//HHD/zKLqznv8ednUth4/VubWn311f1xeZ07d5aNjiRwuiYCZSAgIV8GiIpCBESg9gl88MEH7vDDD5eQz2hV0smmI4swZsCFzipLO4u5sCOKUGG5OTPUHOeGoKfTaS86vhjDY0kqIghHeMKx/x1L1iyHZu86e+MLCXkEPwKApfDsJ8VaPp9NbCflm3wgKtiTyow+x9OxRz5plpV8MfPGwAYDBbCxspr4IH9HHHGE69q1q5a3JgFP4VpLhDzZpG0kOQaOdt55Zz+YwwASbZW2i3Xyu+++2w9KIbzzhactsw8cq/Js4aDt5HO0L8QxhhlZdcK2DgYJuB6Pn++seunVq5f/rbGqpNquFCHPIAZH4/G7ZIsKK3LC3yjlwA+DYWeddZa3aM8gWbUdjIsJeVb/8Ex76623fHugLDwjk+qn1PwTFhev3zB8vvgZKGW1CM9NTmGQEwERKD8BCfnyM1WMIiACNUaAziidOKzyMuuLAR/rnGhGPhuVSX0wK8/KCWa7meXDcnJoLCwpp2FHlCWeWAHHONiBBx7ol9MTho47nV5WY5x99tleHNsgAeER18wsEu7YY4/1/lkevc8++zQY/CIeRBDCmyPqmE1niSliAr/XXnutN1iH1e98jvytscYarkePHl4o2T74JP/kmVl4lvqTZ1hYWckvKwzY17v99tv7fCTFoWvVJ1CKkKcdIRYxuMYeY+o1SUgh2vGzzTbbuJ49ezpmPnEIPpZUM5iE2J46dWpiePySDsufWXW08cYb+/ZHvEmOfPCs5CjEo48+2q9esXYXzx/feXYymDRy5Eg/mJQUZyWvlSLk+b0OHz7cD4CwRYXnf7jdgfwxkLZMZBeDQTy2CLANp9oO9sWEPAM3bLfhGbPvvvs2bBGKtx97TjHQwox9OHARLxdhcfH6Df3F47d7tCMGcDA0yjNKTgREoPwEJOTLz1QxioAI1BABOiF0+DBYdswxx3ixFc5i0NlhBnfw4MG+U5qvk1tDRa7ZrFJXCCGsJp944onug2gVBTOPdESZsecVd4Sx5fMsL+/fv78Xt8xe2kw3M5jvv/++N053xhlnNJo5JzxiB3HNzDdGxZhZf/TRR71ACQcSaBssu+f8afKHCMNhGIpONjOjY8aM8e0NQWT5pWON+EaIMTvKYANWyPM5ykubZeaNpfPkxfJBXMzKMYOIVXT29zJrK5cNAqUIedoCAp2BHLZz5HM2wIS4pJ4RW7Rl2gUDPAh52h5tuJAQY8aZ3wODAcy0s/oEQZjkiAtByUAVbTnf0m0T8jvttJMXygwsVdsVE/L8XhHosEKcM0B4zTXX+IHceF4ZlLvyyiv97D0DFNV2xn306NF5z5G/8847fd6fe+45/1ywZ0JY/9QL9YvxOlYnPfTQQ37gwp5F8XLBiBfheGYlif4w/jA813l28jy88cYbw1v6LAIiUCYCEvJlAqloREAEapMAnQ1m4B9//HEv5OkE47iOowPDUmeWKHP8GDM4cukSoIP6+uuv++XtHG3FrCCz05zPHXcIWzqsCFvEymb/b4UaEWSOo+KwRo/QRnCHnVXqH0HOjCUziwj16667zouYiRMnNohx4iJOZqBoJ7ysw09bYpaP7QAs26fDzcABthiIHxGBYBs6dKjbYostfHr5hBTpIFBYUk+HnYEHG3jiHgNPxMGSVpZcM8svlx0CxYQ87QHRSPvp3bu3H9QplHsTWrzTzhDuDOxgaIw2Zm2DeAs5GxTgOcfMPAMDSY40+J2xBYXfDCtkuBaPn+8Ixh133DGTQp788bvmd4KRU57rTzzxhP8N8ruMu1oQ8qxSQpjzTMSyvD3HwvrhecAKDgZY2HJzwAEH+BUWSc9O2hT/+xhU4jnK/0baV9yF8Yf3uC4hHxLRZxEoPwEJ+fIzVYwiIAI1RIDOBkKeo8IQanEhT1HoyGA8iFl5Cfn0K5c6Q8xTb8yOY3SLjisvZgu5j6MTibE4OqPMqCOsqT+boWYWig4sy5A5J5nZfYx5hQ4xgiBGyGMVHPF+9dVXezFuWzDMP2KII+r2339/P7Nu6dh9ZrQwqEc6DD4QHodoJ18MAvBuKwUsnL1TLptx5WgnViawzNkc5WWfM0v+yTNneNMBl8sOgWJCnvrCuOFpp53ml7znM3SYVCLaMzPk7JVmmxBp0WZ4xYV2UngGgWjnDCKwJD7JERe/GWb7WWpeSMgz6MWAQlrbOwrNyMMDGxYMNGDEjt85g7l8ZmAv7rIi5FkJ8cgjj/hBzDCPDEqwAgf7BZSDQZwkIc/qC55j1C+rJLALw9YLTuGIOwYYWaWxWTT4SdtigICtGrQBnl08iwoNFOFPQj5OVd9FoLwEJOTLy1OxiYAI1BgB65QwG8PSeo74wnHdHEKeWRuWVttyabun93QJUE902BG0CPnQoBydVgQ89ceRcaGYoWOKaKcT++CDDzbZZ26lIixHT7G9gjjYR3vzzTf72Ts6saGj04qlZvams58+LuTxS34ZhGCGnnfyxMwXYRloCPMYxk04jNvR4cZSPQMPDDqFeSA98okQYwtBuOogjEuf0yNAnXMyAu2IAaFwPzZ1jJDnmDNEGas0GIwptKqC9kI7p/3wGQHHGfXsYTdHvPnaVeiHOPi9YEwSY4tJjrhog9h8YJk3v7uk+EkPuxIMOGHwDtFcbWdCnoEt8hg68sdWG36nDHogWlmNA/f4YB7hEPIMXmAYj60r1Xbkn0HAM88807cfBvFCR5547jCQw2AjNl94xuHC+mHQEMOGiHm28px66ql+NVPSTDvPI07EYNUCop2VSAh5BggY7GAAFUEfH9C0fJEubUpL642I3kWg/AQk5MvPVDGKgAjUEAE6G8xcYQ2d2RjOBLeZDCsGS7OxII6Qp5MtV9sEqHOW4jO7xQAORu7ijo4+nVCMzyFYukTnM2NHAevLSUtvEWB0plm2inVr2kw5Z8MRJawaue2223yHOhSA5J3BAPJ4/PHH+5lcZublskcA0cMJBuzFZmtEOBATzy11SjtiRjTfoAwiHmN1WAbn2UR7vv/++/1JCfH4in2nzTNwgEHHgw46KK932h6DSQhHZoD5PcUdcZF3BgUQ0hyLVm3HbwZxzm+Wz/F88vtkj/yV0d536oVVVxw9mVQnlIXTJ9iek0ZZyPsHkU0QVoW9/fbbfsAy5MlqCgbvWMFB/i+44AL/fy3005zPtD0GYhgQYvl96IgfTgycPvDAA35ACn5JjkEohDxtXk4ERKACBKKHg5wIiIAItFkCkWjPRbMRuXvuuScX7QvNRR2YXNQJpWfq36PjmXLRXtVcNAubi5ZGt1lO9VLwqBOamzx5cm7EiBG5aGlpLhJCvp6pc3tFnc9cJIxykSG5XLSvPRcJlxzhohnwXCSqclGn3vuNhEAu6kDnopnTXCR+cpG4yUUiPxfNhJUNF+0z6iTnog5zbs8998xFS4BzpGt5pb1Gs525aIlwLpqF837VTsuGv+wRRasqcpHQzkXbL5q0PZ459twJ65c2xitacdHkxfMpEpa5aNY098477+SiWf7cgAEDGrWReJwWd/hOm6IdRSuPctHS7ILlpk1GK19y++23Xy5agdIkz8QVDYLlVllllVxkdyJHmdNw/A75/UYzyZ5RtGWl4XdjZYddZG8iFw3k5iJDk56v3Qvfo5U5/n9ENFufRlFyMKcskQ2DXGTvo1E5okGeXLTfPRcNSPp6ieyH+LJEg3neXyn1H5aV+otWK+QiAZ+LlvE3KS/Pw2gQKnfKKafkohVqvq0lpUF7igY/ctHgUpM4dEEERKA8BDQjHz195ERABNougehR6mdrOCKM2QeMqDHjwPWoc+OXO7NvlNl4lmHK1S4B6pTZROqYPcjMcMf3hlLn7JfdeuutvUGoHXbYwReYsFFH2odjWStLWG3GtFu3bq5v375+5pQlxFFHuGyQaItsF2Am/o477vD7+aNOfUP87KdnhpDly5SJvFMGuWwSsD3y1CUG42iP5mhjuHj92bPI/MXfWTmC5XqMz7G0fsKECX55PculaT/YZsCxrJ8Xs9NxR5rMOjMTz75oZvkLOfbJs2ye1Sy8wjzT/lmdstpqq3lL8KwUyLeioFAarb0HN7ajsGqAmWxmtCm/OX472NBgyTxL63nnlTS7HO6R5zdWbUdZ7LQA9shjmBMHd2a92YbBrDez6NjfoC1g9JCVE5Q5rJ9ieee5hn0DVqHxHGRVUuiI77777nMPP/ywb8PWvsI0WCmCvZBI7PstSWmcWhDmWZ9FoF4JSMjXa82qXCIgAiURoIPE/j/OD2avJGfw2jJMOibsE5SQLwll5j2ZKEbAU9fshQ1FMQWgE8veUTqx0Qy43+fONV7sOWVPPUIJWwp0oLGGz754OvrlduSNPJJfjrMj7bgIo8PMcXW0Uew4IKIsvwg8uWwRqISQR5DSBjBGxkASQgsjdOyVRswj7Gj7LIVmEOuNN95oAoVnHW2Y7UWc+018hRwDYOeee64X8QhLnqPmaHf8JogHuyP8TtJ0bIXhRAhELb8hHOXFsCQDcAzgIs4pB1b7kyy4Z1XI83snb5xUcd555/n6p64ZtEDYc+xbtFKjYXC6WD0QH7Y2EO+c/Y5le/4HmuOZhLFOjr1k8JvnoNW9CXmePwzeYFuE4wyTbIVYfHoXARFoHQEJ+dbxU2gREIE6IUDHh/2czC5hyIfOSVzI0+mTq10CCBrEDudfM6NFhzfJsd/UjuDCD7NdzHTRqeWddoGo551OK51fXuV2zNa++OKLvkPN7FdcxFt6GLBib3O0lNnv68dKP0Jq991399/Nn97TJ4CQx9bC2LFj/Wwm383ZM8e+23u+63af2W6EN8bIqHuEPe2TtmsiC8Nkt956qxd3GNtLchh2RMhjCK2YkCduBB2DWlg+55lJe+V3wGDCLrvs4l+sFOA3kqaDMb8fZtvhjiOfrGRh/ze/E2bkEaacOJFkAyMU8qGwrVa5qEdm5OPnyFMO6o2BPIS8GWOl/qkTbL5cfPHFfiUP3ws54qJsGPTDTgJHEDJQaALdRDz77zlGk1VJpBO2T+LAiCADARhE5DPX5ERABCpDQEK+MlwVqwiIQI0RYAbLhDwdOeuchDPyEvI1VqlBdhHBiHdmqLDqjQXo+Gy8eUcYIdjpvNNRpaPMLD0dXI5tQuhX2gA9LYAAAEAASURBVCGUmD3EeNnpp5/uZ9i4luToaJMnOvHknTbL4APbQVgxkIbwSMqnrjkvrqlXZof/9a9/eaOLLE3meWPPHDhxjYEnZtTD6yFDBBIzySxbRsgNHz7cL2mPCyfavg0ecDQdz7q4o91wKsMZZ5zhBVyxY+/IE/Ei5jDcx+AAQpHZd5blMxjA74Ul2iYE42lW6zu/G4yzsdycgTzyCSPKe9xxx/m8MhiGwVMM42EIM3w24JcZ5ssvv9yXLY0ZZng3R8jjnwEMykq5GKhmmwHlYjUF7YtyIbT5f0ddwoP6o+4322wzPyBjgzAWH4b2WM3ECjbaJ4571DHxRTYb/DYfnjsYQ4Rr2vVfrXamdEQgDQIS8mlQV5oiIAKZIkBHZEp0jBLLKuMz8nTaONKLDh5WgemsyNUWAeqXziozRMzIcW58qY6wtg8di/QsKaXzW2nH8mg64ByNh5BvjjPhQZtlaSuDEnLZIYCYwu4BS58jw4sN+7Zpa+YQYRz1hV0GrieJIcQ3g0xYUkc4b7rppr6tWhy8ExZhisV1ZqVZ4RF3tBcGe1jFccUVV/gBLGZiS3FsS2JgwI4mY2ABWyKcmoCIz4pjRQJ5ZCCP7QUIVPLIHu7u3bv77xzZxow83M12AdwRowyMcRoFAjWNrQLUYz4hj22DcGl9IeYMaiDqKR/PtS7RSRcMcrCFh5MP4JLU1hjQhAv2QbCjYIMBpGXt056TbANaa621/FGGhfKieyIgAq0nICHfeoaKQQREoIYJ0AmhU0MHJb5HnmLRyWU2luWjAwYM8DNgNVzcNpl16phlwIgZ9sGyHLhUR1g6t+yn3WSTTdwll1zijYKVGr6l/jC4xTFijz/+uF8a25x4aLMIPJY3MyvGEVty2SKAmEcEI5CSHNdpA8yi5nPUM/vRmQVlaTjCPu5IA+HK8wvBhqiPO7OzgGEzjmBrrlClLDxDeUcEkg9+M+QvKw6ezE4z6MDqAQYcELEM0sKQvLI3HoORGMczTlxnpUufPn3czjvvnMrRczDkOZRk7I78xffIF2NOPVmc1BNsiB8hns8x+86AIoOLrBLCvzk+U++0GwQ8x3qyzadQfBZW7yIgAq0jICHfOn4KLQIiUOME6ITQCQ2N3dF5to6KdU7YS7nTTjv52ZkaL3KbzD6iiA48M3LRUYN+WajVcSEg+EGYMKvNigzOaUfUV9qx9JVVIgh5xAUDEfmW1od5sRlExDuWuqMjtfy+6dCPPtcGAQSWia58OUbI8UqaRaW9REcm+iXlzEbzG6BdhY7ZZsRXdHydF6ucwIC4q0cHDwY2EKWUkQEMViIYO+6bQUn84bjH7x8xz95/eKXheA6VS8g3N/+0m7vvvtufTc/S+vhJH+QNTvyvZMXCOeec47dnyNhmc0nLvwg0n4CEfPOZKYQIiECdEaDTxiwMVnYR9HRcrHNiS+sRRXR26TTL1R4B6hir3Yh4ZuVZssxyUgZtGMihnsO6pf5xdFCZvcPQHUJ+1113rYoVZgTcN99841eKXHrppb59sjwYscE99rSSt/h+XcqA4GApMHllFUE1Bh5qr0XUd44ZBKCNM4OKsGJPPtdCh5hlmwgrN7D/wZ52Zvflskcgn5CnDjHaR/2x7afcv3UGflidgAV7jCViW4RnUOjsfyXCneP8sDXD0XMMCvHsDJ+rYTh9FgERaD0BCfnWM1QMIiACdUBAxu7qoBKLFAEhw2wSnVFmllgiyvsH0Z5RZpKSZtu41qNHD79UFEv2ScuXiyTb4tt0kBlkoG0yAMFsIbOJ7J+2fb7saw4ds2JYHF9vvfW8mFcnOqTTdj4zGHnzzTd7S+zse2fQJ3R8x0AiS6DZLsIKjmoYcQzzoM+lEzAhH7daz/J1nk/77ruv22uvvZoM7JWeQlOfDBjyvGTbGdsKzPBi3KcJea4zsMAJGgh6jvXjmVmqvYV4vPouAiJQnICEfHFG8iECItAGCEjIt4FKjopI55QZJV4IYmac+Ixgj4sdiHAN8c79tDqk5I+VAwxE8KLjbEuk44MP5JdrzI7F77WNGm7bpaRtsFqDY8ew+cEgFdsy4m3bZnJ79+7tTjrpJL90XIM+2W07+YQ89Yi1ebZ9Yd9goYUWKlsheD4+Hm3tYVk9R/cxqJjkQiHPffLEs4dVTBxVxyCRDG4mkdM1EWg9AQn51jNUDCIgAnVAIJ+Qx4gUxyntt99+bvvtt5cBnzqoaxVBBOqVAANVrDh57LHHvEBnWTSz83Ehj2jHSBpbL1gKjUFP9oszKx/3W6+saqlchYQ8R+P169fPH6VXzhM1EPIPPfSQP+ljzJgx3r5AErO4kDc/GNxkAIAl9gw2yImACJSfgIR8+ZkqRhEQgRokwMxV/Bx5ikGnltkErD5zLnc5ZzxqEJOyLAIikGECzJqOHz/ejRo1yh83xzGG+YQWM6eId5Y/c3Qdx4+tuOKKeS3gZ7jYdZ81E/JYhMfGB3WMswGZUo+faw4o2tIzzzzj7rvvPn9yhrWleBzkDRcOAJGvjh07un/84x9eyHPUn5wIiED5CUjIl5+pYhQBEahBAvmEPEVhZmHYsGH+LPlyznjUICZlWQREIKME2HbBMnqE1/Dhw/0Se2bo8wl5ioH4Yp+1nczA8mwEPfuu5bJDIA0hT5qs5uDYQgzBTpw40WFw09qU0QmFPO2JASLOtseI4siRI70BPq7JiYAIlJ+AhHz5mSpGERCBGiQQLq3nmJ/QsQSVDu6QIUPKbhU4TEefRUAERKClBJhBnTBhghfyZ5xxRhPr4oXiRYBhpAzBttlmm7k11lijkHfdqzKBNIQ8RcQ+B6d73HvvvW7SpEne2CanabAiYPr06X7fPG0HmxyId7ahscqD4/q22mort9FGG6VmW6TKVaTkRCAVAhLyqWBXoiIgAlkjEAr5L774ws9ikUeWCLIHkaX1AwYM8MfpZC3vyo8IiIAIYOSO0w0efPBBh6V6c4hAxFYxx8qjQw891G255Zb+5INi/nW/egRMyMet1vP/iXrbfPPN3XnnnecFdCVyhXFNTvhAxGN34dprr3WTJ0/2qz5Ij2MwMW43cOBAnwfEfPfu3SuRFcUpAiIQEJCQD2DoowiIQNslkCTk6fzSIaGTxP54zuqVEwEREIEsEgiF/JVXXtkwGFmKkOdZhyA85JBDJOQzWLlpC/kMIlGWREAEIgIS8moGIiACIhARyLdHnnO5WWZ6wAEH+LN0WUIoJwIiIAJZI8AeeSzWM3M6duxY99RTTzm2CbFvPp9jRnfBBRd0q666qltvvfX8MWasQGKZtFx2CJiQTzJ2xwCMGbtjSbucCIhA2yEgId926lolFQERKEAgn5DHCBQWd4cOHer23HNPfzxTgWh0SwREQARSI/DLL7948T5u3Dh/BjjLoHm25Vtaj5BfeOGF3ZprrunWWWcdb+iOZdJzzTVXamVQwk0JFBLy2HAxIb/ooos2DawrIiACdUtAQr5uq1YFEwERaA6BfEKeOJjxkNX65tCUXxEQgTQJYFn822+/9XuYv/zyy7xZQcizfYhjNXmXyyYBCfls1otyJQJpE5CQT7sGlL4IiEAmCCTtkbeMIeSxWj948GBZrTcoehcBEcg0ATsmjPdCjtl6BD0vuWwSMCGfZOyObRCakc9mvSlXIlBpAhLylSas+EVABGqCgIR8TVSTMikCIiACbY5AISHPQHOlrda3OeAqsAjUCAEJ+RqpKGVTBESgsgQk5CvLV7GLgAiIgAi0jICEfMu4KZQI1DsBCfl6r2GVTwREoCQC2iNfEiZ5EgEREAERqDIBE/JJVutl7K7KlaHkRCBDBCTkM1QZyooIiEB6BPIJefaPdujQwRu74yx5LDzLiYAIiIAIiEC1CEjIV4u00hGB2iIgIV9b9aXcioAIVIhAPiGPAaill17aHXbYYW7AgAH+zOUKZUHRioAIiIAIiEATAibkzz77bPfYY4+5CRMmeD/8f9I58k1w6YIItBkCEvJtpqpVUBEQgUIE8u2Rn3vuuf0Zy/vvv7/baaed3B/+8IdC0eieCIiACIiACJSVAEL+448/diNHjnTjx4937777ro8fIR8urV9kkUXKmq4iEwERyDYBCfls149yJwIiUCUC+YQ8HaXOnTu7ww8/3O2zzz6aka9SfSgZERABERAB5xDxP/zwg5+FZ0D5k08+cTNmzPBo+P/Edq/111/fXXLJJX52nmtyIiACbYOAhHzbqGeVUgREoAiBfEKeYDpHvgg83RYBERABEagIAYT8119/7R5//HG33377uW+++cb99ttvPi1suMw777xu1VVXdZdeeqnr0qWLm2eeeSqSD0UqAiKQPQIS8tmrE+VIBEQgBQL59siTFYT8sGHD3JAhQ1y7du1SyJ2SFAEREAERaIsEEO2fffaZGzt2rBs+fLifnY9zWHTRRd2FF17o1l13XW/TJX5f30VABOqTgIR8fdarSiUCItBMAhLyzQQm7yIgAiIgAhUl8Ouvv7r33nvPPffcc+70009377//vvv999+bpIntlo033thv/+rfv7+bb775mvjRBREQgfojICFff3WqEomACLSAQCjkp0+f3qiz1L59ez8jP3jwYM3It4CtgoiACIiACDSfAMvoR48e7SZNmuQeeOCBxNl4Yp1tttm8LZeDDjrI7bXXXo4Zepbdy4mACNQ3AQn5+q5flU4ERKBEAtojXyIoeRMBERABEagKgU8//dRts802joHmb7/9tmCaCyywgDvkkEPcvvvu6zp16uRk9K4gLt0UgbogICFfF9WoQoiACLSWgIR8awkqvAiIgAiIQDkJcOTcBhts4KZNm1Y0Wgn5oojkQQTqjoCEfN1VqQokAiLQEgLh0vovvvjCH/lj8cjYnZHQuwiIgAiIQLUIfPTRR/5oOYR8saXyWK/fc8893R577OHDsNxeTgREoL4JSMjXd/2qdCIgAiUSkJAvEZS8iYAIiIAIVIVAc4Q8x87tsMMObuedd3Y9e/Z0s88+e1XyqEREQATSIyAhnx57pSwCIpAhAhLyGaoMZUUEREAERMA1R8jPNddcbvPNN3d9+/Z1GGadc845RVAERKDOCUjI13kFq3giIAKlEeBYn4EDB7rx48e7n376qVEgLAAPHTrUDRo0yC211FKN7umLCIiACIiACFSCAHvk11tvvZL2yHME3YYbbuh69+7tjd7xXU4ERKC+CUjI13f9qnQiIAIlEpCQLxGUvImACIiACFSFwCeffNJgtZ6j6Ao5ZuS33HJL169fP3+evGbkC9HSPRGoDwIS8vVRjyqFCIhAKwloaX0rASq4CIiACIhAWQn897//dX/961/dq6++6p599tmCcc8333xuyJAhXsSvvPLK/mz5ggF0UwREoOYJSMjXfBWqACIgAuUgICFfDoqKQwREQAREoFwEmiPk5557bj97v+2223qDd3PMMUe5sqF4REAEMkpAQj6jFaNsiYAIVJdAKOSnT5/ufv/994YMtG/f3g0bNswbEGrXrl3DdX0QAREQAREQgUoRQMgfe+yxJc3Ic/zcbrvt5l8bb7yxZuQrVSmKVwQyREBCPkOVoayIgAikR+DDDz90hx12mHv++edd0jnyRx55pBfyCy+8cHqZVMp5CTDwksvl/FnLs846qx+ICQdj4gE5Y7nYuczxMMRvcRKWdKrlSPvXX3/1ZdTe12pRTy8da8vp5UApZ4HAV1995U488UQ3adIk99RTTxXM0gILLOCN3O27776uU6dOVX0+FcyYboqACFSMgIR8xdAqYhEQgVoiICFfS7XVOK+//PKLP6bpyy+/dEsssYRjsOXbb79177zzTmOP0TfEN3tJl1tuOUfHtzlinNMM3nrrLT/TteCCC/oTDJIGA8JrCLLmuDCshfvtt9/84BInKrBapH///o70yXvcvwSgUavddwZsvv76a8e54Lzk2i6BH3/80T388MPuiSeecOeee25BEBLyBfHopgjUJQEJ+bqsVhVKBESguQTCpfVJM/IsrceQkJbWN5dsef2baH/66afdDz/84L777jv38ssvu88//9x/Z3kpe0UR3YheE9ImeHlnRnuRRRZxHM9UTMiHwhiBRdsgDGHjAwHETfrMhi2++OLe72effeawNm35yEeDFQIMQCy//PJ+oAF/CHjCTpkyxX366af+9fPPP7vOnTv7MpI+AxKEI+3vv//evf32234wY4UVVnCrrLKKe/PNN/2gBvGRb45SJI1qCMTZZ5/dsybPpI1V7cUWW8znlbJRd8w42ioH/MCP+gmvk3fKR54JDyvCEO9//vMfXw/ETb2HDj8zZszw7YLwtpqGdBnosXQJw35iwuNn2rRpburUqe7dd9913bp18zwZOCE9BnKIa7XVVvP1Q16szXG9NY42Qn4nTpzoLrvsMl+3LJHedNNNHSwLuZkzZ/oykQf4MVhVzNGeEYr8VmALQwYQuEZZCznSoI3riLNClFp3j/qhLZ500knu9ddf90ejFoqR58Ghhx7qNCNfiJLuiUB9EZCQr6/6VGlEQARaSEBCvoXgqhgMoYMIY2b6nnvu8cIV4cF2CPaSIvIRFogyhA2iyAR0KLIQRQgd3sPrSUUhvPlBfBIn30kD4WP3CIsQnX/++V2XLl1chw4dHCL+o48+8nmzfCSlwTXywiAR4psOOf5JD0GLOCcuhDrXSAMhhb+VVlrJD0qQNvdZgstAAvGsvfbaXhTCCIcfViz06NHDC7cw795DGf8YI+qDARcTvEsttZRnhkihzhgY4TMOPwsttJBni0APhTZ5p7wdO3b097lHeTlnG/FNffIyzqSPHwZCEO04ys510uVl6XLNxC/ilIGT9957z7322mueI2lSNwheRDZ54WxvwlNviHzEPPHg7J3Plp/wul0L/XGf/Fp7PueccxyDMVtvvbXr1atXUcFM22dFCnEyIEGezJFePC3u8Rvh9wRH2CLmiYM2zrV8jrho+9QlaRE/THhRhzjaKeWx74ThhV9exh6/+fLHPcLHf2dcL7cj79Ql+bI8hmlwjzaCv2o42FEPb7zxhjv66KMd/59o64UczwVE/IABA1zXrl397ySp3u2avReKU/dEQASyTUBCPtv1o9yJgAhUiQAdpUJ75DUjX6WKyJMMnWvECrPvhxxyiDf+xPdijnC4lnZaC4mMYmlzvzXhW5v3UvLXGj+WP+KI8+U7gx2hkEdoI4oRQ4hIBilYSYFowT/XEfIIplDIkw6CDqHCIAWiimsIHQZKWGVA3Ijp0CEmEcYIecIzm48jXQQr93GkS5rEj5Dn7G4GH6x9ISR5kSYCl7zil/CUERFsQp57+LN3n0D0h+/mwvvx6wwWMMhAvskTcdsqhtCvxcU78ZFXwlEW8mpCvlBaNthFWSkPQp5VLHDlmsXNe5g2n0ljySWXbFgFYXXXJRrEQgwz8EQZGNCCPZxIg5l+Bleot9BZPsNrfKY99OzZ09d5/F65vpN3BoNY6cIgTlj3lJW8U45VV121gWu50s4XD6sixo0b50aNGtXwrAvrICkc7YVj5zbYYAM3cOBAzy6+SoU4qGd+l/iXEwERqG0CEvK1XX/KvQiIQJkIaI98mUBWKBpEBzNSGHzaf//9vRCk81/MmZ9ineB88eQTGPn8h9fLkTbxtTTvYV4q8dnKly+P5JsXQh2HYEKE4wiL4LN7Vkbe8Wci2/zadUShOcISB9cIw8vyZPHhx+LCH9f5bteIi2vmHz+EIR572X3ew2sWlnQtPPf5jjO/5i/0Y9d4N2f+eSd/lq7Fb+HNf/hu5cQP/uN5sO9hGEuPtCwNrln58ct3XDxtvhtP/Nh3q19jbPFavix+458vfp9o9IfwDBrE07f7xcKbv3zvYd4pD/kKy2/h0piRZ3CGQQ/eLZ+Wn6R3GDHoAC8GluL1QxiusZJinXXWcRtuuKHr06dPw28yKU5dEwERyDYBCfls149yJwIiUCUCEvJVAt3CZBDyzOJh9Akhb0KgWHTl6ugXSyfpfjnSJt58IiYpzWpes/K1NI9J4e1aWGauhd+tjPn8xvOTFN7CFvNbqj/iMb9hXu1amI5dC/3lC2/X4365HnfEm+Qv3/UwfHPzFA+blC5+Sk07X/gwnaTP+fKd5DfpWin5SwpXzWvlLCNCntUF2HhAyB988MF+hj5poKeaZVRaIiACLSMgId8ybgolAiJQZwQk5LNdocy8sgz7ueeec0OHDvXLiEsR8+XsBDeXUDnSJs2Wipzm5re5/q18Lc1jUni7FpaZa+F3y2c+v/H8JIW3sMX8luqPeMxvmFe7FqZj10J/+cLb9bhfrscd8Sb5y3c9DN/cPMXDJqWLn1LTzhc+TCfpc758J/lNulZK/pLCVfNaucsIa5bVr7jiiu6WW25x7du392K+mmVSWiIgAuUhICFfHo6KRQREoMYJaI989iuQWXn2Tt94443+KCb28xazrl3uTnBzKbVGKLQ2783Na3P9W/4I1xIhli98nFn8O+kVChvmx/zF82fXQ78Wb+i3VH+ExeG/peEtrTB8Upw+oYQ/8bTNS77rdt/ek/zly5OF4T0pnN0vdM/C8h4vs4Uv9l5K/grFUSx/hcJW614lysgMPDYBLrroIm/8kuX2ciIgArVHQEK+9upMORYBEagAAQn5CkAtc5R0aDEGhiXnO+64wx8R9v777zdJBcGPQTPqFGd7RhH+8f2vdGgx/IQRNYxAYTQtdIU6+sSFQS9eGAhLcvHwLG3FgBnpkC4rQchvkmtOBx6/5Ac+pEG5+I7jO3tny+0sf8RrQoxrlMf2v3OdcpIfXqGz8Pi1fcDc57rFl/TdrvGOi/sNr1kaoR/u2/XQr10P/Zbqj7C4pLz/707TfIbpWFjek67Hr1mc4Xs8bbuX77rdt/ckf1zDFUo/KVyhOO0e76XEH/qPfy5H+EJli6eXxvdKlJE9/8sss4y79NJL/ekILLeXEwERqD0CEvK1V2fKsQiIQAUIIPpktb4CYCsQJUIRw3dYmH7hhReapIDFZ+4988wzXjxiwRvL5u+8804jwUhARC73//jHP/ojxsyyeZNIEy4gQDnnmb37DBIkubjIoQNNp5l0sOJN/hHfSa45HXhEO+U2a+cIdzjZQEV8gCIpveZes/wRzsQQ2x0Y1MC6O59t4AIxHx9MIDwv8o3FdYvP4rLvli+7zvdC98x/ofcwPPGG3wln1ygDn3nB2FaAUC6WJ9vgRBjeBlR4t+uEt3hpA7AgjtDhlzA2EGJhebeBEd7zOfxZOqGf+HX8kLbl3doJ1+J1FMaT77PlMyltwhCvxQ0/ysjLnOWPd3iTn0IG7iwc7xaGgSCz0J4vH2E4OFr7tPzwPXTEQx1b3rlvZTV/fCftpHvmp7XvlmYp5UpKi/BhWD4zaMnxhldddZU/fcBOOUgKr2siIALZJSAhn926Uc5EQASqSEB75KsIuwxJ0fmm8xzvfBM11xCGDM7QCecIK46XevXVV32n28QQHVoE5iKLLOKWX375RsKs1CyaCAiFSbGwCChepI9oaa2jo048HKnGCgU66bwYIEA0Un6OCqu0Ix8INQY3sGfAZ/guvfTSnj95iju4cZb8m2++6UWSiZa4vzS+007YymFH25HPV155xZeL2cxll13Wcw7zRv5ZDTJhwgT/Ht6jvhHKhOsSHdPGQA7XzBGWo/ImT57s2y7pcw2hSL2SF451y+fwG8Zn/uLXaRMcA8jKEOoH9u3atfNthOXWJvAJZy4pXu6Zn6T73CMu4uY31q1bN2/jgoEe2oaFtXg40x52lH/99ddvEOaWh/g74fmt094ow8Ybb+wHAPjNF3L8VhjoY/CNlTjUKwNg/H5CR111797ds1pppZW8P+rCHOlzVN2kSZN8ew/vmZ9yvIecWhIf4cP6oVyIeHidccYZvg2H91uShsKIgAikQ0BCPh3uSlUERCBjBCTkM1YhrcwOIgghSwcV4cILAUGnNuwYIzTo2DKbV8udWcqEQGF2GyHDC5Fj5UewVcMhzBFpiBo+w5fZVRibQAzzYflGEIX1EvpJ67PlDZbkHb60IcpFe6FcSaKRtocgx3/cGQ/C0ybjjrDUIW2XdHDkg3RZ+fHII4+4W2+9teFYsjA8/pLaMNfhz+ABgnSjjTZyq6++uh9cwT+rJ7hPeWgnSXGE6TTnM3ERNy8GchDMtEsrWxgX160NM0Oc1F5C//aZ9gYfBqwIUyz/8IAxaVFe3u1lcfJOXBzjxqw87/iJ55vvDEBYew/Dt+QzaXDkHOWHGfEzKBluFcoXL21n6tSpfmAjfPax+oeBJ/jT5tgPT1tggI1BpVI550tX10VABNIjICGfHnulLAIikCECEvIZqgxlRQREoBEBm3l+4IEH3IUXXug+/fTTJjPISUKegQbEKjPiWClfe+213ZZbbumFvJZTN0KciS8MCCDcWcXAAAL1zsoBXmwNKuQQ8qzc+CBaiWQrHhgMYCsPK45YWYKQR9SzIoM05ERABGqbgIR8bdefci8CIlAmAnR+tEe+TDAVjQiIQEUIMNN/ww03uGeffdZdffXVjdKIC3lmWpmN3WSTTdxBBx3kxRxHjWkGthE2fREBERCBmiUgIV+zVaeMi4AIlJOAhHw5aSouERCBShBg6TWzrvfee6876qijGiURCnmWl7McnNn3c845x58Vzuxs0laARpHoiwiIgAiIQM0QkJCvmapSRkVABCpJQEK+knQVtwiIQDkIsNSavfJ33323O/TQQxtFGRfyLKXu06eP++c//9nEKF+jgPoiAiIgAiJQkwQk5Guy2pRpERCBchPQHvlyE1V8IiAC5SaAkOfoRYQ8W4EQ7+aShHz//v39EWPmR+8iIAIiIAL1Q0BCvn7qUiURARFoBQEJ+VbAU1AREIGqEMCKOcfQ3Xfffe6II45oOImBxCXkq1IFSkQEREAEMkNAQj4zVaGMiIAIpEkgXFqPheDwmCEMRA0bNswNHjxYln7TrCSlLQJtnABiHYN3Dz/8sBs+fLg/bsyeVbybITv2w3ft2tX17t3bjRo1qo1TU/FFQAREoD4JSMjXZ72qVCIgAs0kEAr5L774otGS1SWWWMIL+SFDhkjIN5OrvIuACJSXAEeLPfXUU+6YY45xEydO9EeUkUI4I4+hu549e7pNN93UHXLIIeXNgGITAREQARHIBAEJ+UxUgzIhAiKQNgEJ+bRrQOmLgAiUQqAUIc/gIzPxPXr0cGussUYp0cqPCIiACIhAjRGQkK+xClN2RUAEKkNAe+Qrw1WxioAIlJeACfmRI0fmnZFHyJ9//vlupZVWciuvvHJ5M6DYREAEREAEMkFAQj4T1aBMiIAIpE1AQj7tGlD6IiACpRCQkC+FkvyIgAiIQP0TkJCv/zpWCUVABEogICFfAiR5EQERSJ2AhHzqVaAMiIAIiEAmCEjIZ6IalAkREIG0CWiPfNo1oPRFQARKIWBCvpCxu3bt2vnj6dZaay3Xq1evUqKVHxEQAREQgRojICFfYxWm7IqACFSGgIR8ZbgqVhEQgfIS+OWXX9wzzzzjTjjhBPfcc88lWq1HyHNkJkIe6/VyIiACIiAC9UdAQr7+6lQlEgERaAEBCfkWQFMQERCBqhOYOXOmN3J3zjnnuNtuu83xHRceP7f44ou7U045xa2yyipunXXWqXoelaAIiIAIiEDlCUjIV56xUhABEagBAtojXwOVpCyKgAi4X3/91U2ePNldc801DjH/008/eSqhkMdq/Xnnneet1iPm5URABERABOqPgIR8/dWpSiQCItACAhLyLYCmICIgAlUngJCfMmWKGzNmjD8rPp+Q1/FzVa8aJSgCIiACVSUgIV9V3EpMBEQgqwQk5LNaM8qXCIhASOC3335zU6dOdTfccINfPv/jjz/62+GMfIcOHdwFF1zgVlxxRT8rH4bXZxEQAREQgfogICFfH/WoUoiACLSSgPbItxKggouACFSFAIId8f7888+7bbfd1s2YMcOna0J+9tlnd8sss4y7+uqr/Tv75eVEQAREQATqj4CEfP3VqUokAiLQAgIS8i2ApiAiIAJVJ4Bg5wi6cePGub59+zYR8rPOOqtbaqml3GWXXeaWX35516VLl6rnUQmKgAiIgAhUnoCEfOUZKwUREIGME6BjjPGooUOHuhdeeMF9/fXX3gK0ZZsZrSOOOMINGjTIaXbLqOhdBEQgDQK///67f0Y9+uijbuDAge7777/32bAZ+VlmmcV17NjRXXTRRa5bt25uhRVWSCObSlMEREAERKDCBCTkKwxY0YuACGSfAHtOX331VTdkyBD38ssvOzrKoVt00UXdgQce6DvNLFmVEwEREIG0CGDs7o033nAXX3yxu+KKK/zsfDwv7du3d6NHj/b741deeeX4bX0XAREQARGoAwIS8nVQiSqCCIhAywkwi/XDDz+45557zg0fPty99tpr/ngnrpvjKCdm5AcPHuwQ9XIiIAIikBYBe2axR3677bZrtLSeZfVzzDGHF/C3336769Spk/+eVl6VrgiIgAiIQOUISMhXjq1iFgERqBECv/zyi5+RP+qoo9xLL73kvvvuu0ZL6xHyw4YN8zP27dq1q5FSKZsiIAL1SmDmzJluwoQJrmfPnv55RTkR+Aj5Oeec0/Xo0cPdddddDuv1ciIgAiIgAvVJQEK+PutVpRIBEWgmARm7ayYweRcBEUiNgIR8auiVsAiIgAhkhoCEfGaqQhkRARFIiwCd4tdff90xI88s17fffttkRv7II4/0S+sXXnjhtLKpdEVABETAE+CZxeqhfDPy3bt314y82ooIiIAI1DkBCfk6r2AVTwREoDABlqNyJjNHOY0YMcK98sorjqX28T3yEvKFOequCIhA9QhIyFePtVISAREQgawSkJDPas0oXyIgAlUhgGBnT/yTTz7pjjnmGPfmm296ES8hXxX8SkQERKAFBCTkWwBNQURABESgzghIyNdZhao4IiACzSOAYGcGftKkSe4vf/mLP35uxowZTWbkZeyueVzlWwREoHIEEPIydlc5vopZBERABGqBgIR8LdSS8igCIlAxAibkWVLPHnnOkZeQrxhuRSwCIlAGAhLyZYCoKERABESgxglIyNd4BSr7IiACrSOAkP/555/diy++6M+RZ2aePfPxpfWakW8dZ4UWAREoHwEJ+fKxVEwiIAIiUKsEJORrteaUbxEQgbIQQLCzR/6xxx5zI0eOdG+99ZaPNy7kZeyuLLgViQiIQBkIaI98GSAqChEQARGocQIS8jVegcq+CIhA6wiUIuQXXHBB169fP7fLLru4bbbZpnUJKrQIiIAItILAb7/95qZNm+ZuueUWd/zxx/sVRETHs2zWWWd1c845p9Pxc60ArKAiIAIiUCMEJORrpKKUTREQgcoQoPPLufHxGfkwtQUWWMD17dvX7brrrv49vKfPIiACIlBNAr/++qt7++233b/+9S938cUX+61Blv4ss8zihXyPHj10jrxB0bsIiIAI1CkBCfk6rVgVSwREoDQC+YQ8180ttNBCbvvtt3e77767+9Of/mSX9S4CIiACVSfAsvpXX33VjR492t1www3+1A0yEc7IS8hXvVqUoAiIgAhUnYCEfNWRK0EREIEsEShFyC+++OJu6NChbtCgQa5Tp05Zyr7yIgIi0MYIMCM/efJkd80117izzz7b/fTTT56AhHwbawgqrgiIQJsnICHf5puAAIhA2yZA57eYsTubkd9tt900I9+2m4tKLwKpE0DIT5kyxY0ZM8aNGjUqUchrj3zq1aQMiIAIiEDFCUjIVxyxEhABEcgygVKEPHvke/fu7XbeeWe33XbbZbk4ypsIiECdE5CQr/MKVvFEQAREoEQCEvIlgpI3ERCB+iQgIV+f9apSiUC9EpCQr9eaVblEQAREoHkEJOSbx0u+RUAE6owAQj7Jaj3XzTEj36tXL3/8HEbv5ERABEQgLQL2zHr88cfdnnvu6b7//nufFa7b8XMydpdW7ShdERABEageAQn56rFWSiIgAhkkYJ3i+PFzEvIZrCxlSQREwFun//nnn924ceP8cZgzZszwVCTk1ThEQAREoG0RkJBvW/Wt0oqACMQISMjHgOirCIhApgnwzPrxxx/d888/77bddlsnIZ/p6lLmREAERKBiBCTkK4ZWEYuACNQCATrFxazWy9hdLdSk8igCbYPAb7/95qZOnepuvPFGd/LJJ3tRT8nDGXlZrW8bbUGlFAERaNsEJOTbdv2r9CLQ5gmUIuQXWWQRt9dee/n9qGuuuWabZyYAIiAC6REwIX/TTTe5v//9742E/CyzzOJmn312t/zyy7sbbrjBde7c2TEQKScCIiACIlB/BCTk669OVSIREIFmEChFyC+++OLu8MMPd4MHD3aLLbZYM2KXVxEQAREoLwGE/GeffebGjh3rhg8f3kTIzzbbbG6ppZZy//znP13Xrl395/LmQLGJgAiIgAhkgYCEfBZqQXkQARFIjQBCvpjV+oUWWsj169fP7bbbbt56fWqZVcIiIAIiEBHA2N348eNdnz59/NYgoPAsY0Ye1759ezd69Gi34oorupVXXtlf0x8REAEREIH6IiAhX1/1qdKIgAg0k0ApQt72yO+6667euFQzk5B3ERABESgbAZ5Z33zzjeOkjb333rvR8XO2tJ6Z+Ouuu84tvfTSbuGFFy5b2opIBERABEQgOwQk5LNTF8qJCIhACgRKFfI6Rz6FylGSIiACTQj8/vvvbvr06e7+++93Bx10kPvhhx+8H55lnCM/xxxz+Jn4W2+91XXq1MnNNddcTeLQBREQAREQgdonICFf+3WoEoiACLSCAJ1fWa1vBUAFFQERqCqBX3/91U2ZMsWNGTPGjRo1yv30008+fRPyc845p5PV+qpWiRITAREQgVQISMingl2JioAIZIWAhHxWakL5EAERKIUAzyzOjn/66afdLrvs0mhpPTPyEvKlUJQfERABEah9AhLytV+HKoEIiEArCEjItwKegoqACKRCYObMme6ll15yPXv2bGTsTkI+lepQoiIgAiKQCgEJ+VSwK1EREIGsEEDIF7Naj7E77ZHPSo0pHyIgAvms1puQ79Gjh7vrrrtchw4dBEsEREAERKBOCUjI12nFqlgiIAKlEZCQL42TfImACGSDAOfIf/rpp+6OO+5wI0aMaHSOvIR8NupIuRABERCBahCQkK8GZaUhAiKQWQL5ltZjGdrcggsu6Gfkd955Z7f99tvbZb2LgAiIQNUJIOQ//PBDd8MNN7hTTz21QcjzzJptttm0R77qNaIERUAERCAdAhLy6XBXqiIgAhkhkE/Ic92cnSOPkN9uu+3sst5FQAREoOoEZLW+6siVoAiIgAhkkoCEfCarRZkSARGoFgEJ+WqRVjoiIALlICAhXw6KikMEREAEap+AhHzt16FKIAIi0AoCCHkZu2sFQAUVARGoKgET8tdee23ec+Rl7K6qVaLEREAERCAVAhLyqWBXoiIgAlkhICGflZpQPkRABEohICFfCiX5EQEREIH6JyAhX/91rBKKgAgUICAhXwCObomACGSOgIR85qpEGRIBERCBVAhIyKeCXYmKgAhkhQCWnj///HN3yy23uHPPPddNmTKlSdbmmmsut9pqq7n+/fu7Y445psl9XRABERCBahGYOXOme+mll/yy+jvvvNPxPe6WW24598QTT7hOnTrFb+m7CIiACIhAnRCQkK+TilQxREAEWkYAIf/FF1+42267zZ111llu8uTJTSKae+653Zprrukt1h955JFN7uuCCIiACFSLAMJ94sSJfuCRAci4kOcs+a5du7pHH31UQr5alaJ0REAERCAFAhLyKUBXkiIgAtkhUKrV+l69ejmdI5+delNORKCtEuAceVYOXX/99e700093P/30k0fBswwRP+ecc7ru3bu7u+66y3Xo0KGtYlK5RUAERKDuCUjI130Vq4AiIAKFCJQq5Hv37u2FvM6RL0RT90RABCpNgGfW119/7R5//HG3zz77uO+//94nKSFfafKKXwREQASyRUBCPlv1odyIgAhUmQCd3x9//NG98MIL7uijj3avvPKK++WXXxzXzS2wwAJOQt5o6F0ERCBNAjybmIV//vnn3bbbbutmzJjhsyMhn2atKG0REAERqD4BCfnqM1eKIiACGSPAHtPXXnvN/eUvf3ETJkzw58pLyGeskpQdERCBBgI8szB417NnT/fdd9/56xLyDXj0QQREQATaBAEJ+TZRzSqkCIhAMQIffPCBO+yww/ws1/Tp0zUjXwyY7ouACKRGQEI+NfRKWAREQAQyQ0BCPjNVoYyIgAikQYBZrJ9//tnPxI8YMcJNmjTJ/fDDDxLyaVSG0hQBEShKgJM2GGy877773NChQ/3zikA8y2aZZRY322yzuS5durgrrrjCLbvssjJ4V5SoPIiACIhAbRKQkK/NelOuRUAEykSAzi975MePH+/3yCPkEfZcNzfffPO5jTbayO2www5u4MCB3jK03dO7CIiACFSTAFbrp02b5jh67vjjj/fPL9I3IY+YX3LJJd1FF13kunXr5o+iq2b+lJYIiIAIiEB1CEjIV4ezUhEBEcgwAZapYuTuqKOO8vtOMR4VCvk55pjDz2pttdVW7oILLvDHO3HMk5wIiIAIVJvAr7/+6o+fGzNmjBs1alSj4+cQ8bgllljCnX/++W6llVZyK6+8crWzqPREQAREQASqQEBCvgqQlYQIiED2CXAu8+GHH564Rx7RPtdcc7kNNtjAXX755a59+/buD3/4Q/YLpRyKgAjUHQEGGTFw9/TTT7tdd9210fFzEvJ1V90qkAiIgAjkJSAhnxeNboiACLQlAh9++GGDsbsvvvii0Yw8nWNm5ddbbz3373//23Xs2NEL+7bER2UVARHIBgGEPGfHP/vss26nnXZqdPychHw26ki5EAEREIFqEJCQrwZlpSECIpB5AqHV+nxCft111/Uz8p07d3Zzzz135sukDFafAPuX2arBKo7ZZ5+9kT0FjJRx/jdLo3EYJWOAiOuE42VbNhBrXMcPqz/wF273MMFW7RL+X3vnDnJH0cfhrSwUL/EGQQwJKoqixkQMQRRREEQLESuxtLWwtRYsxSLBwl4ULNQuiooi3lEwQY0XxIhGId5Kq+975uMXJvPtnnffc3aTvMdn4OScnZ3/ZZ7ZN+xvdneWHImdPE93/HWKB0vGd7OF4+LPP//s3nzzzbJmB6KewvGR44Jb65955pnu+uuv72666abNhrC9BCQgAQlsAQIK+S0wSKYoAQnMT2CjK/KccF977bVlQbx77723u+yyy+ZPyghbhgAiircdfP31190bb7xRHr+49dZbi5BiH2KLxzeee+65ciX1n3/+6W644Ybuvvvu644dO9Z99tln3ZEjR4odxxqrkuMPIfbYY49199xzTxH6+GH/xRdfXMT96QKEeOR27uPHj5e427dvL3elRDierjzWIQ4CnnU4fvnll45JwXPPPXdT3WIi6Jtvvil3Bx04cKAszomDWshv27atrGjPMfjAAw9syr+NJSABCUhgaxBQyG+NcTJLCUhgZgKsAv3UU0917777bvfll1+Wq6EJydVHPpdcckl35513drfcckt30UUXFSFz1VVXlSuvabuVvxFlfLgCfOGFF5YryydOnDilS+yHxfnnn19WxubuBURJrgrWjWlLu127dp28Uljvb38jcLjSiGDkTQKIRUTOOeec0zY967bJ96OPPuo++eST7u233y7HB1dCWWyMuzd+/PHHjsmi119/vXzTV9ZaYHKIPnP8/frrr4UXQh2eiH3acMzdeOONZTwQ9/BHqOGX4zCimnUcYIegQ+xlTOBHO15Fhg3tKIhz2uKPWH/99VfJkzsKqCcWOV966aUdb25gIgIByfGxd+/eMrnA+GA/VPCDP/pLDCYofv/995IfeVx33XXF3yIfQ77bevpDHGLymw/HIDwXHUPY0C6f1u8q2+TCWzDIhT7C9Isvvug+//zzMuaMLX8fTOqkYAMr2vMh/5QsdPfpp5+WVek/+OCD0mf2Jwa/L7jggu7RRx/t9u/f3z3yyCNUWSQgAQlIYM0IKOTXbEDtjgQksBwBRBQr0r/11lvd+++/X8RAPHGCT+EbIXT55ZcX8cHJ8h133FHq0narfyMczjvvvO6KK64oYhoh1xZuGYfBnj17uqNHj3aI+T/++KNtVnhx5wKv7gvD/2tUVSD4fvrppyJoEZWIG648b/aKZeXytP0k35deeqm8xhCRhdjd+d93eSOemRQ5fPhw99tvv5W+1UnBBeE2VGDNcYZw57Z8RCE21CGuec0YnBDqbBMDQUdbRDPjyTF75ZVXlnFgMooPMRGFtOW2fSYAGGsmI5iUQNwypmwzWcV4I0C5awB/d999d3nLAyIfe/LEVz7pD37wTd5MLHC8MMbEgMv9999fJi8WCe34WvRNXI4fPvQLIUwdIpgJA3jxDQ8K+ZBb7GhHP2iTiQf2wZrc2NdXiIUv7GEQDvFPDCZqaIevv//+u3vllVe61157rYzVgw8+2HHV/KGHHjrpHhva4Yt86tiMK8/G83/U888/XzjGkDElBoUJtIcffriMOa/MtEhAAhKQwPoRUMiv35jaIwlIYAkCiJgnnniirFrP7cO1uMrJcdxGDFDPyXb255t2Q/b1yfaidtnX53OjOmz7ytjY+E8fERV9hf30HYGC37q/dXt81UKk3tf3m3jxhzhKHn1tz6Y6co54gwmF3PnQD/qFMOQztoRpxiPb2FOXevznd/yHYdoyVkyKMLFyzTXXlDy4k4JcEX2IayZk6mMfH4ja+KcPfIjFpMHu3buLTyYGmLDgVnF8IjZT+M2VfCYV2BcO+Gayg0kIRDaifpVCnvjnaj+TBIhnrn4zKcUkBK9gY7FKJh7IgQkK2mKDaGZygjsbbrvttnJHDvuYeCBHHm/gzokwJ0/yhx3cPv744+IXriyESewPP/ywfNN/rr6TC/1kUopJw6zDgX9y4o0Y8U/+3PlA7owX48M+SvwxcdROnpFT2uHzySefLGN01113FVv/kYAEJCCB9SKgkF+v8bQ3EpDAkgR+/vnn7umnn+7eeeedcvWUk+KUnByzXZ8sZ3uoXVsfn62/tl22h2LFPv5on7rY9n0P+RtrP+RzVfsxuffFHlMXRsvGaJmNiZk2U8TG17K5J4/4QJAzqYJAJLdMOFDPJARXsRHEYwoTFIhSJgi4Ys3vTGRkMgE/iGaEKbESL/7pF7kkr9S3zNtt2oUtv/FDTGLlSjy/+cQ3Ew/ctUCu2CKCySft6E+u3CPgc1U+OZInbSh1bIQ1ojpc8Y9f6uKfOxKIAyvyoR7/GVdsEfkp9AXhn9yxS1v2ZUIEn3WpObHYHe+YZ6KECReLBCQgAQmsHwGF/PqNqT2SgASWIMAtySwcxa3177333ikn6zmJxm19spzthGvbtfURABu1i91QrNjHH+1TF9u+7yF/Y+2HfK5qPyb3vthj6sJo2RgtszEx02aK2PhaNvfkMdd3+rdsjn32qav7TF29nf4MtW3z6bOPbds2vvOddn3x0ybfY+MM+VxUv5n4tOWRi4MHD5Y7CXg0wiIBCUhAAutHQCG/fmNqjyQggSUIcCvtiy++2B06dKg8w5qTalzVJ9HtyfqidkljGXtsh2K1/mhb17HdV4b80XaM/ZDPVe2Xjd2XT1uX8Vk2Rsus9b/R9ir2q+a+UW6r7k9++FmG75B9y6zdJt4i2zqftGvzS33dNn7rtmPbYUuh/bL2iVXb9/ksgXr+wZ67BrjCz6MAL7/8chH03GlgkYAEJCCB9SOgkF+/MbVHEpDAEgS4Jfe7777rXn311bJ6PbfX9p1Yb+ZEPWnUJ+Zj7bEdatv6o21dx3ZfGfJH2zH2Qz5XtV82dl8+bR19PpP5tczb/BZtr5r7It9T7Et++FpmDIfsW2btNvEW2db5pF2bX+rrtvFbtx3bDlsK7Ze1T6zavs9nCdTzD/YIeW7v57l+FtTjuf/WX4+pVRKQgAQksAUJKOS34KCZsgQkMD0BnjdlASpeP8ct9t9//315tpdnVfOsK8+n5kSdE2aeYa2fX62foa1PynMiTV1OtulBtvlNm7Sr96U+bbNdt+mzp64urX220ya5Z3vMN7nQfxbs4hli+PDsL89K8+wwMRaV5FD3CaYIEa4i8pwxPim0xWe2iUnOi/JmTHk+G1tipGATe+LxYSKHcSb39Ctjm/zwQxvssWG777ny7Cc+nzo2v7GN70Wc8E+p7dOH9ruOiV1s23YbbROLK7rkDes88812W+oYY3Ica4/f2l+7jZ+h2KmPfbudHFLPdtrym/p2m3pKW19v/6/FavbJqfXb5pRY7TftOA5YuO/mm28uV+R5faFFAhKQgATWk4BCfj3H1V5JQAJLEOBEGGHFKtsvvPBCeR3XV199VVaZZmVrrtJHSLK4FytKsyI2wuzfWBCjrI7Nq+q4lReRy2QI70Tn7oY+8beIEyKECQFW/uYZX16zhRCnMEHAgoRMrFCIidhHaA4VRDl51AuLIZKyQjljSDw+rCTOAmjkzniywjuvfKtvS2bsiU9MPvQPO1ZkT6EP2LB4GYucsTBZLczwnVfF4eOHH34o+cW+/h4SdnUbfqdPrG7O5Af9JTfsyZlPfLW2sScvckfEs1AaefO3wDEOF1Ziz7EfH8TFju+6j9lffycX6ohD+zqn2p76Rdv4WGTL/tinHblTl0/q67b87otNPSU++d22o45Cfb2PccgY8M3fTNrV/lLHd1uPXcaTffHRtiMu48dbBHjl47PPPlv+PvFpkYAEJCCB9SOgkF+/MbVHEpDAigQ4ac4K3Agj3p/N66R4zRQiH3G5d+/e7vHHHy+3sEZM1ifWnFSntPXtdl876mpBkG2+++zrOtr0lSF/tB1j3+cTO4QZgo6C6CAODMeUNidsIiqZGGA/hSvfx44dK0KamAh9BHMttEvD6h+E6LfffnuKUMYWG+wR8sQiZyZpmKxBmFOHkEcQ0TZs6BMCl6v51JMfr1xrhTzHA2Kdtnzqgm9etYboxg/HE8J7lUJ+TE7gM6ux0yeOYSaiWMixzrGNBQdezUZ/8YOQZxICfkxm8O54/gboawpiknfT79y5s9voqi+cmIQ5ceJEYb5jx44SJ77m/Ob4YQw4DjIuTALNVThOmcxigovYHLPwO3r0aHmt3Z49e8r4I7g3KtjjD+74YEwYn3379p18lV3tA5+7du3qrr766m7//v1lPPnbtEhAAhKQwHoSUMiv57jaKwlIYCICnEgjQnhfNB8WxUN4IQZuv/32f/UV+YkQj3KDiEZoMx4IV654IyZzdbLPCQKS8ULU1gXBE3t8IZgYU4Qvgj7CGNFUC64IK2JmAgCRmLsEiIEt+7BFCLcinf1MAiAq8YPwbvOrcx37mzzxSUz8kSv9Z2KizbH1iS3imjsT+M03nGFOrvhATCIkUxCITEgw4VG/Oi3762/8YAtb/Oc1cHWbuX5nzJjIyLis+s76oVyJRV/pJwzZ5k4G+CHu+XC3CUzJZUzJcX/8+PFyfGasmARivOuCz0xAMcmy6G+jtvO3BCQgAQlsTQIK+a05bmYtAQmcZgKclLcFUWaRwNlMoO+47ct3o2N5yM9GdnUsfGymfW276u/kfybiJ/aqfRhrfyb6ODY320lAAhKQwHQEFPLTsdSTBCQgAQlIQAISkIAEJCABCUhgdgIK+dkRG0ACEpCABCQgAQlIQAISkIAEJDAdAYX8dCz1JAEJSEACEpCABCQgAQlIQAISmJ2AQn52xAaQgAQkIAEJSEACEpCABCQgAQlMR0AhPx1LPUlAAhKQgAQkIAEJSEACEpCABGYnoJCfHbEBJCABCUgKfXFkAAACTklEQVRAAhKQgAQkIAEJSEAC0xFQyE/HUk8SkIAEJCABCUhAAhKQgAQkIIHZCSjkZ0dsAAlIQAISkIAEJCABCUhAAhKQwHQEFPLTsdSTBCQgAQlIQAISkIAEJCABCUhgdgIK+dkRG0ACEpCABCQgAQlIQAISkIAEJDAdAYX8dCz1JAEJSEACEpCABCQgAQlIQAISmJ2AQn52xAaQgAQkIAEJSEACEpCABCQgAQlMR0AhPx1LPUlAAhKQgAQkIAEJSEACEpCABGYnoJCfHbEBJCABCUhAAhKQgAQkIAEJSEAC0xFQyE/HUk8SkIAEJCABCUhAAhKQgAQkIIHZCSjkZ0dsAAlIQAISkIAEJCABCUhAAhKQwHQEFPLTsdSTBCQgAQlIQAISkIAEJCABCUhgdgIK+dkRG0ACEpCABCQgAQlIQAISkIAEJDAdAYX8dCz1JAEJSEACEpCABCQgAQlIQAISmJ2AQn52xAaQgAQkIAEJSEACEpCABCQgAQlMR0AhPx1LPUlAAhKQgAQkIAEJSEACEpCABGYnoJCfHbEBJCABCUhAAhKQgAQkIAEJSEAC0xFQyE/HUk8SkIAEJCABCUhAAhKQgAQkIIHZCSjkZ0dsAAlIQAISkIAEJCABCUhAAhKQwHQEFPLTsdSTBCQgAQlIQAISkIAEJCABCUhgdgIK+dkRG0ACEpCABCQgAQlIQAISkIAEJDAdAYX8dCz1JAEJSEACEpCABCQgAQlIQAISmJ2AQn52xAaQgAQkIAEJSEACEpCABCQgAQlMR+A/oOoaO5e91PAAAAAASUVORK5CYII=	E_1 = \frac{V \sigma_2}{d_1 \sigma_2 + d_2 \sigma_1}; E_2 = \frac{V \sigma_1}{d_1 \sigma_2 + d_2 \sigma_1}; J = \frac{\sigma_1 \sigma_2 V}{d_1 \sigma_2 + d_2 \sigma_1}; \sigma_t = \frac{\varepsilon_0 (\sigma_1 - \sigma_2) V}{d_1 \sigma_2 + d_2 \sigma_1}; \sigma_f = \frac{(\sigma_1 \epsilon_2 - \sigma_2 \epsilon_1) V}{d_1 \sigma_2 + d_2 \sigma_1}
+384	A classical hydrogen atom has the electron at a radius equal to the first Bohr radius at time $t = 0$. Derive an expression for the time it takes the radius to decrease to zero due to radiation. Assume that the energy loss per revolution is small compared with the remaining total energy of the atom.	[]	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	\frac{m^2 c^3 a_0^3}{4e^4}
+385	In the equilibrium configuration, a spherical conducting shell of inner radius $a$ and outer radius $b$ has a charge $q$ fixed at the center and a charge density $\sigma$ uniformly distributed on the outer surface. Find the electric field for all $r$, and the charge on the inner surface.	[]	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	\mathbf{E}(r) = \frac{q}{4 \pi \epsilon_0 r^2} \mathbf{e_r}; \mathbf{E} = 0; \mathbf{E}(r) = \frac{\sigma b^2}{\epsilon_0 r^2} \mathbf{e_r}; -q
+386	A sphere of radius $R$ carries a charge $Q$, the charge being uniformly distributed throughout the volume of the sphere. What is the electric field, both outside and inside the sphere?	[]	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	\mathbf{E} = \frac{Q}{4 \pi \epsilon_0 r^2}; \mathbf{E} = \frac{Qr}{4 \pi \epsilon_0 R^3}
+387	Čerenkov radiation is emitted by a high energy charged particle which moves through a medium with a velocity greater than the velocity of electromagnetic wave propagation in the medium.  (a) Derive the relationship between the particle velocity $v = \beta c$, the index of refraction $n$ of the medium, and the angle $\theta$ at which the Čerenkov radiation is emitted relative to the line of flight of the particle.  (b) Hydrogen gas at one atmosphere and at 20°C has an index of refraction $n = 1 + 1.35 \times 10^{-4}$. What is the minimum kinetic energy in MeV which an electron (of rest mass 0.5 MeV/c²) would need in order to emit Čerenkov radiation in traversing a medium of hydrogen gas at 20°C and one atmosphere?  (c) A Čerenkov radiation particle detector is made by fitting a long pipe of one atmosphere, 20°C hydrogen gas with an optical system capable of detecting the emitted light and of measuring the angle of emission $\theta$ to an accuracy of $\delta \theta = 10^{-3}$ radian. A beam of charged particles with momentum of 100 GeV/c are passed through the counter. Since the momentum is known, the measurement of the Čerenkov angle is, in effect, a measurement of the particle rest mass $m_0$. For particles with $m_0$ near 1 GeV/$c^2$, and to first order in small quantities, what is the fractional error (i.e., $\delta m_0 / m_0$) in the determination of $m_0$ with the Čerenkov counter?	[]	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	\cos \theta = \frac{1}{\beta n}; 29.93 \, \text{MeV}; 0.13
+388	A charge $Q$ is placed on a capacitor of capacitance $C_1$. One terminal is connected to ground and the other terminal is insulated and not connected to anything. The separation between the plates is now increased and the capacitance becomes $C_2 \ (C_2 < C_1)$. What happens to the potential on the free plate when the plates are separated? Express the potential $V_2$ in terms of the potential $V_1$.	[]	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	V_2 = \frac{C_1}{C_2} V_1
+389	Calculate the net radial force on an individual electron in an infinitely long cylindrical beam of relativistic electrons of constant density $n$ moving with uniform velocity $\mathbf{v}$. Consider both the electric and magnetic forces.	[]	/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGQAZADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD3+iiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigD//2Q==	\mathbf{F} = \frac{e^2 n r}{2 \pi \epsilon_0 \gamma^2} \mathbf{e}_r
+390	Given a uniform beam of charged particles $ q/l $ charges per unit length, moving with velocity $ v $, uniformly distributed within a circular cylinder of radius $ R $. What is the  (a) electric field $\mathbf{E}$  (b) magnetic field $\mathbf{B}$  (c) energy density  (d) momentum density  of the field throughout space?	[]	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	"\mathbf{E} = 
+\begin{cases} 
+\frac{qr}{2\pi \varepsilon_0 R^2l} \mathbf{e}_r, & (r < R) \\
+\frac{q}{2\pi \varepsilon_0 rl} \mathbf{e}_r, & (r > R)
+\end{cases}; \mathbf{B} = 
+\begin{cases} 
+\frac{vqr}{2\pi \varepsilon_0 c^2 R^2l} \mathbf{e}_\theta, & (r < R) \\
+\frac{vq}{2\pi \varepsilon_0 c^2 rl} \mathbf{e}_\theta, & (r > R)
+\end{cases}; w = 
+\begin{cases}
+\left( 1 + \frac{v^2}{c^2} \right) \frac{q^2 r^2}{8 \pi^2 \varepsilon_0 R^4 l^2}, & (r < R) \\
+\left( 1 + \frac{v^2}{c^2} \right) \frac{q^2}{8 \pi^2 \varepsilon_0 r^2 l^2}, & (r > R)
+\end{cases}; \mathbf{g} = 
+\begin{cases}
+\frac{v^2 q^2 r^2}{4 \pi^2 \varepsilon_0 c^2 R^4 l^2} \mathbf{e}_z, & (r < R) \\
+\frac{v^2 q^2}{4 \pi^2 \varepsilon_0 c^2 r^2 l^2} \mathbf{e}_z, & (r > R)
+\end{cases}"
+391	The electrostatic potential at a point $P$ due to an idealized dipole layer of moment per unit area $\tau$ on surface $S$ is  $$ \phi_P = \frac{1}{4\pi\varepsilon_0} \int \frac{\tau \cdot \mathbf{r}}{r^3} \, dS, $$  where $r$ is the vector from the surface element to the point $P$.  (a) Consider a dipole layer of infinite extent lying in the $x$-$y$ plane of uniform moment density $\tau = \tau e_z$. Determine whether $\phi$ or some derivative of it is discontinuous across the layer and find the discontinuity.  (b) Consider a positive point charge $q$ located at the center of a spherical surface of radius $a$. On this surface there is a uniform dipole layer $\tau$ and a uniform surface charge density $\sigma$. Find $\tau$ and $\sigma$ so that the potential inside the surface will be just that of the charge $q$, while the potential outside will be zero. (You may make use of whatever you know about the potential of a surface charge.)	[]	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	\Delta \phi = \frac{\tau}{\epsilon_0}; \sigma = -\frac{q}{4\pi a^2}; \tau = -\frac{q}{4\pi a} e_r
+392	A charge $q$ is placed inside a spherical shell conductor of inner radius $r_1$ and outer radius $r_2$. Find the electric force on the charge. If the conductor is isolated and uncharged, what is the potential of its inner surface?	[]	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	F = -\frac{ar_1q^2}{4\pi\varepsilon_0(r_1^2 - a^2)^2}; \frac{q}{4 \pi \epsilon_0 r_2}
+393	Charges $+q$, $-q$ lie at the points $(x, y, z) = (a, 0, a), (-a, 0, a)$ above a grounded conducting plane at $z = 0$. Find  (a) the total force on charge $+q$,  (b) the work done against the electrostatic forces in assembling this system of charges,  (c) the surface charge density at the point $(a, 0, 0)$.	[]	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	F = \frac{(\sqrt{2} - 1) q^2}{32 \pi \epsilon_0 a^2}; W = \frac{(\sqrt{2} - 1) q^2}{16\pi\varepsilon_0 a}; \sigma = \frac{q}{2\pi \epsilon_0 a^2} \left( \frac{1}{5\sqrt{5}} - 1 \right)
+394	The mutual capacitance of two thin metallic wires lying in the plane $z = 0$ is $C$. Imagine now that the half space $z < 0$ is filled with a dielectric material with dielectric constant $\varepsilon$. What is the new capacitance?	[]	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	C' = \frac{\varepsilon + \varepsilon_0}{2\varepsilon_0}C
+395	A conducting spherical shell of radius $ R $ is cut in half. The two hemispherical pieces are electrically separated from each other but are left close together as shown in Fig. 1.31, so that the distance separating the two halves can be neglected. The upper half is maintained at a potential $ \phi = \phi_0 $, and the lower half is maintained at a potential $ \phi = 0 $. Calculate the electrostatic potential $ \phi $ at all points in space outside of the surface of the conductors. Neglect terms falling faster than $ 1/r^4 $ (i.e. keep terms up to and including those with $ 1/r^4 $ dependence), where $ r $ is the distance from the center of the conductor. (Hints: Start with the solution of Laplace's equation in the appropriate coordinate system. The boundary condition of the surface of the conductor will have to be expanded in a series of Legendre polynomials:   $$ P_0(x) = 1, \quad P_1(x) = x, \quad P_2(x) = \frac{3}{2} x^2 - \frac{1}{2}, \quad P_3(x) = \frac{5}{2} x^3 - \frac{3}{2} x.  $$	[]	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	\phi = \phi_0 \left\{ \frac{R}{2r} + \frac{3}{4} \left( \frac{R}{r} \right)^2 \cos \theta - \frac{7}{32} \left( \frac{R}{r} \right)^4 (5 \cos^2 \theta - 3) \cos \theta \right\}
+396	Consider an electric dipole $\mathbf{P}$. Suppose the dipole is fixed at a distance $z_0$ along the $z$-axis and at an orientation $\theta$ with respect to that axis (i.e., $\mathbf{P} \cdot \mathbf{e}_z = |\mathbf{P}| \cos \theta$). Suppose the $xy$ plane is a conductor at zero potential. Give the charge density on the conductor induced by the dipole.	[]	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	\sigma = -\frac{P \cos \theta}{2 \pi (x^2 + y^2 + z_0^2)^{3/2}} + \frac{3Pz_0(-x \sin \theta + z_0 \cos \theta)}{2 \pi(x^2 + y^2 + z_0^2)^{5/2}}
+397	Consider a long cylindrical coaxial capacitor with an inner conductor of radius $a$, an outer conductor of radius $b$, and a dielectric with a dielectric constant $K(r)$, varying with cylindrical radius $r$. The capacitor is charged to voltage $V$. Calculate the radial dependence of $K(r)$ such that the energy density in the capacitor is constant (under this condition the dielectric has no internal stresses). Calculate the electric field $E(r)$ for these conditions.	[]	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	K(r) = k r^{-2}; E(r) = -\frac{2rV}{b^2 - a^2}
+398	When a cloud passes over a certain spot on the surface of the earth a vertical electric field of $E = 100$ volts/meter is recorded here. The bottom of the cloud is a height $d = 300$ meters above the earth and the top of the cloud is a height $d = 300$ meters above the bottom. Assume that the cloud is electrically neutral but has charge $+q$ at its top and charge $-q$ at its bottom. Estimate the magnitude of the charge $q$ and the external electrical force (direction and magnitude) on the cloud. You may assume that there are no charges in the atmosphere other than those on the cloud.	[]	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	q = 6.7 \times 10^{-4} \, \text{C}; F = -4.05 \times 10^{-3} \, \text{N}
+399	A capacitor is made of three conducting concentric thin spherical shells of radii $a$, $b$, and $d$ ($a < b < d$). The inner and outer spheres are connected by a fine insulated wire passing through a tiny hole in the intermediate sphere. Neglecting the effects of the hole,  (a) find the capacitance of the system,  (b) determine how any net charge $Q_B$ placed on the middle sphere distributes itself between the two surfaces of the sphere.	[]	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	C = \frac{4 \pi \varepsilon_0 a d}{d-a}; Q_{1\text{inner}} = -\frac{a(d-b)}{b(d-a)} Q_B; Q_{2\text{outer}} = \frac{d(b-a)}{b(d-a)} Q_B
+400	Two square slits of dimension _a_ and 3a are arranged along a horizontal line _L_ on an opaque screen. The separation between the edges of the two slits is equal to 2a. The slits are illuminated with collimated monochromatic light of wavelength λ and uniform intensity _I₀_ coming from infinity. A lens is placed on the right hand side of the screen to collect the diffracted light and focus the diffracted light onto a screen for viewing the diffraction pattern.    (a) Calculate the intensity distribution of the diffraction pattern due to the slit of dimension _a_ alone (as a function of the coordinates of the diffracted beam on the screen. Choose the origin of the coordinate system appropriately to simplify your answer!)    (b) Do the same, but now for both slits.	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	I(\vartheta, \varphi) = I_0 \, \text{sinc}^2 \alpha \, \text{sinc}^2 \beta; I(\vartheta, \varphi) = \frac{I_0}{100a^2} \left[ \sin^4(2\alpha) + \frac{1}{4} \left(\sin(4\alpha) - 2\sin(6\alpha)\right)^2 \right] \text{sinc}^2\beta
+401	"familiar toy consists of donut-shaped permanent magnets (magnetization parallel to the axis), which slide frictionlessly on a vertical rod. Treat the magnets as dipoles, with mass $ m_d $ and dipole moment $ m $.  (a) If you put two back-to-back magnets on the rod, the upper one will ""float"" - the magnetic force upward balancing the gravitation force downward. At what height, $ z $, does it float?  (b) If you now add a third magnet (parallel to the bottom one), derive an equation for the ratio of the two heights? (You need not solve explicitly.)"	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= \left( \frac{3 \mu_0 m^2}{2 \pi m_d g} \right)^{1/4}; 2 \zeta^4 (\zeta + 1)^4 - (\zeta + 1)^4 - \zeta^4 = 0
+402	A very thin, long, electrically neutral wire is fixed in the laboratory frame and carries a uniform current, $ I $, in the $\rightarrow x$ direction. An electron moves outside the wire with an (instantaneous) velocity $\mathbf{v} = v\hat{\mathbf{x}}$, with $ v \ll c $. The (instantaneous) distance from the electron to the wire is $ y $. It just so happens that $ v $ is also equal to the magnitude of the drift velocity of the charge carriers in the wire, $ v_d $.  (a) In the lab frame (in which the wire is at rest and the electron in question moves to the right), calculate the force on the electron due to the current-carrying wire.  (b) In the frame of the electron (in which the electron is at rest and the wire bodily moves to the left), calculate the force on the electron. (Do not neglect relativistic corrections.)  (c) Compare your answers to parts (a) and (b), and comment on the nature of the force in each case. What qualitative differences (in force magnitude and force “origin”) would you expect if the force on the electron were measured in a reference frame moving to the right at velocity $ v' = v/2 $ with respect to the fixed lab frame?	[]	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	\mathbf{F} = -\frac{\mu_0 I e v}{2 \pi y} \hat{\mathbf{y}}; \mathbf{F}^{\prime} = -\frac{\mu_0 I e v}{2 \pi y} \hat{\mathbf{y}}
+403	A current $ I $ flows down a long straight wire of radius $ a $. If the wire is made of linear material (copper, say, or aluminum) with susceptibility $ \chi_m $, and the current is distributed uniformly, what is the magnetic field a distance $ s $ from the axis? Find all the bound currents. What is the net bound current flowing down the wire?	[]	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	"B(s) = \frac{\mu_0 I}{2\pi s}
+\begin{cases} 
+(1+\chi_m) \frac{s^2}{a^2}, & s < a, \\ 
+1, & s > a. 
+\end{cases}; \mathbf{J_b} = \frac{\chi_m I}{\pi a^2}; \mathbf{K_b} = -\frac{\chi_m I}{2\pi a}; I_b = 0"
+404	Imagine an iron sphere of radius $ R $ that carries charge $ Q $ (spread uniformly over and glued down to the surface) and a uniform magnetization **M** = **M**z. The sphere is initially at rest.  (a) Find the electric and magnetic fields.  (b) Suppose the sphere is gradually and uniformly demagnetized by heating it above the Curie point. Find the induced electric field and the torque this exerts on the sphere, and compute the total angular momentum imparted to the sphere in the course of the demagnetization.  (c) Where does this angular momentum come from?	[]	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	"\mathbf{E} = 
+\begin{cases} 
+0, & r \leq R, \\
+\frac{Q}{4 \pi \epsilon_0 r^2} \hat{\mathbf{r}}, & r > R.
+\end{cases}; \mathbf{B} = 
+\begin{cases} 
+\frac{2}{3} \mu_0 \mathbf{M}, & r \leq R, \\
+\frac{\mu_0}{3} \left( \frac{R}{r} \right)^3 [3 (\mathbf{M} \cdot \hat{\mathbf{r}}) \hat{\mathbf{r}} - \mathbf{M}], & r > R.
+\end{cases}; \mathbf{E}_{\text{ind}}(r) = 
+-\frac{\mu_0 \dot{M} r \sin \theta}{3} \hat{\boldsymbol{\phi}} \times 
+\begin{cases} 
+1, & r \leq R, \\
+(R/r)^3, & r > R.
+\end{cases}; L = \frac{2}{9} \mu_0 M Q R^2 \hat{\mathbf{z}}"
+405	An iron rod of length *L* and circular cross section (radius *R*), is given a uniform longitudinal magnetization *M*, and then bent around into a circle with a narrow gap (width *w*). Find the magnetic field at the center of the gap, assuming *w << R << L*.	[]	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	\mathbf{B} = \mu_0 M \left(1 - \frac{w}{2R}\right); \mathbf{B}_g = \mu_0 M \left(1 - \frac{w}{L}\right)
+406	At the interface between one linear magnetic material and another the magnetic field lines bend. Show that $\tan \theta_2 / \tan \theta_1 = \mu_2 / \mu_1$, assuming there is no free current at the boundary.	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	\frac{\tan \theta_2}{\tan \theta_1} = \frac{\mu_2}{\mu_1}
+407	Electromagnetic radiation polarized in the plane of incidence is incident upon a planar interface between two regions with dielectric constants $\epsilon_1$ and $\epsilon_2$ (it is incident from 1 to 2.) In the lab frame the dielectrics are moving with speed $ \beta $ away from the radiation source in the direction normal to their planar interface. The angle of incidence relative to the normal in the lab frame is $\theta_I$. Express the reflection and transmission angles in the lab frame, $\theta_R$ and $\theta_T$ in terms of $\theta_I$, and calculate the effect of the motion on the reflection and transmission coefficients.	[]	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	\tan \theta_R = \frac{\left(1-\beta^2\right) \sin \theta_I}{\left(1+\beta^2\right) \cos \theta_I-2 \beta}; \tan \theta_T = \frac{n_1\left(1-\beta^2\right) \sin \theta_I}{n_2\left(1-\beta \cos \theta_I\right)}\left[\left(1-\frac{n_1^2\left(1-\beta^2\right) \sin^2 \theta_I}{n_2^2\left(1-\beta \cos \theta_I\right)^2}\right)^{1 / 2}+\beta\right]^{-1}; R = \left(\frac{1-2 \beta \cos \theta_I+\beta^2}{1-\beta^2}\right) R^{\prime}; T = 1 - R
+408	A perfect dipole **p** lies a distance **z** above an infinite grounded conducting plane. The dipole makes an angle θ with the perpendicular to the plane. Find the torque on **p**. If the dipole is free to rotate, in what direction will it come to rest?	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	\mathbf{N} = \frac{p^2 \sin 2\theta \, \mathbf{\hat{x}}; \text{Pointing directly towards or away from the plane.}
+409	An interference pattern is produced by laser light (wavelength λ) passing through two slits. One slit has width$w_1=10 \lambda$and the other is $w_2=20 \lambda$ wide, and the slits are separated by d = 1000λ. The pattern is observed on a screen a large distance L away.  (a) What is the separation$\delta y$ between adjacent interference maxima (neglecting the slit widths)?  (b) What are the widths ($\Delta y_1$ and $\Delta y_2$) of the central maxima of the diffraction patterns due to each slit independently?  (c) How many interference fringes are contained in the central max?  (d) What is the ratio of intensity maxima to intensity minima near the center of the pattern?	[]	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	\delta y = \frac{L}{1000}; \Delta y_1 = \frac{L}{5}, \; \Delta y_2 = \frac{L}{10}; \text{Number of fringes} = 100; \left(\frac{I_{\text{max}}
+410	Consider a metal with a density $n$ of conduction electrons that are free to move without damping. Each electron has mass $m$ and charge $-e$. Suppose that an electromagnetic plane wave is sent into the metal with frequency $\omega$.  (a) Derive an expression that shows how the wave vector $k$ of the plane wave depends on frequency $\omega$.  (b) There is a threshold frequency below which plane waves cannot travel through this material. Derive an expression for this frequency.	[]	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	k = \frac{\omega}{c} \sqrt{1 - \left( \frac{\omega_p}{\omega} \right)^2}; \omega_p = \sqrt{\frac{n e^2}{\epsilon_0 m}}
+411	A cylinder of length $ L $ and radius $ R $ carries a uniform current $ I $ parallel to its axis.  (a) Find the direction and magnitude of the magnetic field inside the cylinder. [Ignore end effects.]  (b) A beam of particles, each with momentum $ p_0 $ parallel to the cylinder axis and each with positive charge $ q $, impinges on its end from the left. Show that after passing through the cylinder the particle beam is focused to a point. [Make a “thin lens” approximation by assuming that the cylinder is much shorter than the focal length. Neglect the slowing down and scattering of the beam particles by the material of the cylinder.] Compute the focal length.	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	\mathbf{B} = \frac{\mu_0 I}{2 \pi R^2} r \, \hat{\phi} = \frac{B_0}{R}(-y \hat{\mathbf{x}} + x \hat{\mathbf{y}}), \text{ where } B_0 \equiv \frac{\mu_0 I}{2 \pi R}; f = \frac{2 \pi p_0 R^2}{\mu_0 q I L}
+412	A quadrupole is a magnet in which the magnetic scalar potential $ (B = -\nabla \Phi) $ is given by $ \phi(x, y, z) = B_0 xy/R $ for $ x^2 + y^2 < R^2 $, where $ R $ is a constant (pole radius) and $ B_0 $ is the field at the pole.  (a) Demonstrate that for relativistic charged particles moving along the z-axis, the quadrupole acts as a lens. Is the focusing the same in the $ x $ and $ y $ directions?  (b) Consider a “realistic” warm-iron quadrupole of length $ L = 2m $, $ B = 1T $ and $ R = 20cm $. Determine the focal length $ f $ for 20 GeV electrons.	[]	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	f_y = -f_x = \frac{p_0 R}{q L B_0}; f \approx 6.67 \, \mathrm{m}
+413	A rectangular loop of wire is situated so that one end (height _h_) is between the plates of a parallel-plate capacitor, oriented parallel to the field _E_. The other end is way outside, where the field is essentially zero. What is the emf in this loop? If the total resistance is _R_, what current flows?	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	\text{emf} = 0; I = 0
+414	A particle of mass _m_ and charge _q_ is attached to a spring with force constant _k_, hanging from the ceiling. Its equilibrium position is a distance _h_ above the floor. It is pulled down a distance _d_ below equilibrium and released, at time _t = 0_.  (a) Under the usual assumptions (_d << λ << h_), calculate the intensity of the radiation hitting the floor, as a function of the distance _R_ from the point directly below _q_. $$  \text{Note: The intensity here is the average power per unit area of the floor.} $$  At what _R_ is the radiation most intense? Neglect the radiative damping of the oscillator.  (b) As a check on your formula, assume the floor is of infinite extent, and calculate the average energy per unit time striking the entire floor. Is it what you would expect?  (c) Because it is losing energy in the form of radiation, the amplitude of the oscillation will gradually decrease. After what time _τ_ has the amplitude been reduced to _d/e_? $$  \text{(Assume the fraction of the total energy lost in one cycle is very small.)} $$	[]	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	I = \left( \frac{\mu_0 p_0^2 \omega^4}{32 \pi^2 c} \right) \frac{R^2 h}{(R^2 + h^2)^{5/2}}; R = \sqrt{\frac{2}{3}} h; P = \frac{\mu_0 q^2 d^2 \omega^4}{24 \pi c}; \tau = \frac{12 \pi m^2 c}{\mu_0 q^2 k}
+415	Consider the cubical arrangement of fixed positive charges $ q $ at the corners of a cube. Could you suspend a positive charge at the center in a stable manner (not counting quantum tunneling; in other words, is there any potential barrier to tunnel through?)	[]	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	\text{No, a positive charge cannot be suspended in a stable manner at the center due to the potential being a saddle point. Laplace's equation forbids a local minimum at the center.}
+416	Seven antennae, radiating as electric dipoles polarized  along the $\hat{\mathbf{z}}$ direction, are placed along the x-axis in the xy-plane at $x = 0, \pm \lambda/2, \pm \lambda, \pm 3\lambda/2$.  The antennae all radiate at wavelength $\lambda$ and are in phase.  (a) Calculate the angular distribution of the radiated power as a function of the polar and azimuthal angles, $\theta$ and $\phi$. Neglect any constant multiplying prefactors.   (b) Consider the direction in which the radiated intensity is maximum for this array and for a single dipole antenna. How do these intensities compare?	[]	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	\frac{d\bar{P}}{d\Omega} \propto \sin^2\theta \frac{\sin^2(7\delta)}{\sin^2(\delta)}
+417	An infinite plane conductor has a small protrusion in the form of a hemisphere of radius $R$. A point charge is placed directly above the protrusion, at a height $h$ above the plane. The conductor is kept grounded, and the electric field vanishes at infinity.  (a) Find the electrostatic potential.  (b) Find the total charge that is induced on the protrusion.  (c) Now take the limit $h \to \infty$, $Q \to \infty$, keeping $Q/h^2$ fixed, so that the effect of the charge $Q$ is to produce, far away from the protrusion, a uniform electric field of magnitude $E_0 = Q/2\pi\epsilon_0 h^2$. How does the protrusion modify the electrostatic potential?	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HgAV7OXYVr1LuKOYwYuDDMtVGAwfJ1Mt2ASEnMNkgpISNQjqItATbbJVRw6KSCHqFAsALCtHTTikH+eMpSQhMT0QVIBCYnpRWXKcsozoJz4etQzgBkMyloaqIB21GoLH/OLnLFyJSQkeMi4AhISNYBXfIJqlJawLhAkW2Ivt8/ABLq2+ris3KqJ1iAhIeGEtApISNQMtdKOjFiUSy94J8EKhJktI3zhYQFJ/S4hMSuQVEBihuDUMdLM64PK2EA1wRP5nGeSEHD7BfySSTOAhMT0QS4QSMwEXMdxwSdcgodzS/0Mlz7DxUleKCExi5BUQGI2wTvHgeQE9QR/3TyTmlt6BkhITDckFZCoF0g2UG+o25m6tCJISNQW0ldAou4gY8hI8JAtQUJiuiGtAhJ1CmkeqE/IGbmExJ0HaRWQqF9I88B0o2SwYVn5EhJzAZIKSNQ75Ak00wEfo0u5sYclJCRud8gFAonbAHKxoLao3/qUxENCYjYgrQISM4Hb4iwZQcL6mRDL6Ezlom5fpYREfUJSAQkJADd1W28LEzMvzwwUx1d7zahi3ZNOCYl6g6QCEvWLWdfEdcUGuAC9MyHSdJfiayUiVS0VcKLXvy1KQqIeIKmARD2ifhRwXbEBqFHN+GQyM8/rqqBR4Q/yZgLeP3hsNrktVqYkJGYdkgpIzBCcgzIbuOVg7Y+Z5CIVlFURexBaQoCkhAAQVDK1A3XF5CQk6hNyB4HE7MBn83o1Y3fR2nONGEZt87nDIupXHy4asT/guSxACLEK/5EaOhVISEhQSKuAxMxhuq21TrVUE3N3TaaVgmz1tu5QGSp7m8JNpLAkYAMRO1URWUSFDxUUKCEhUQKSCkjMPirmB0FurF7pTpPavt3ZQBWsjoA9tUeFrARzQMEnwAIAAIVeQ8gmAqRav0IJCYliyAUCiVlADVcEZgDTJ97tu1jguvey3Cx4+wDPDKiZgBTcA1yKvk0rTUKibiGtAhJ1AbZ2MCu0wF+1TPf0fQ7Gw2EP7Fa3iCYghFYNEuf/lApgdAe7nc7BJiExu5BUQGJG4TWoTbcPgf/2uSpzCHJ7xffemXCrEOESKqwjTFUeIYDAIoS5F9yBCtK1qchzuSSmG5IKSNQXZnhhfgaUdMkibschflo9QC0CdN8gxhgAJiYmdD2vYDWXy2FVSSYSqmoPXJwQt2M1loXb3blEop4hqYBEHWFaB7tZHEl97L0zHNy3huXSHMonBAQAEHMOsHcGENtSQAhYhCDEthUQy9AnMhldN7PZbCyZjMcTLCeLEPpaKWm43VGyMiUbkJgmSCogURfgd9lBYEXlMzd1zaeaobayUdj1udjnGeMBTi4ya0rFjZZQakAQAABBYAGoU+/OOnPqxH//z0ufHurrvmvDrie+3NrWWsiJEGJZFiGKosyY+LMOyQYkpgN3ApWWkBDAK+CA01aWcgYiH8wwnKGNaigGIzTB9JNbkEH7LyEIEN1YgAAhQASIQSbTa1ev3HLPZgBQtdC89gVI03KmWXgMUtWz1NVmhOCS1I/MEncMpFVAovaowMvJOX2v2DDgus/NPzdnDrWaePHzb1bKzMzqShZX28cMIhGLIcwusKUCO6owFQwRywRkAgJEDGQaRjY7mc3OX7qkdV5LGMDCmABYGGOMEMGVrQ7cYeGeJCSqgaQCErMMJ28Q5molh+kgLmxe7MRnfaG2apJxgtlyVMQYs4qdiYUJWxQodvRndADZkYYQIoTzFQAAC8AyLQwGCmHAMD46cmNwUAuF1t69vikeBQCMEACYCDRA9HPxlgQEqLz9BbcdG7jtBJaoc0gqIFECFSuPIKOV19YpugpMy8UY12rUq1INVzn+8pyAfS2L9PjL5iOn04bPeEnNNYqLVYb/1/GjVbjMHUOACACgQj7mZGb8wtmziqaiaPhmziSDtzQFQVNMi0UREE0MVEgIECCAUHlhiqVylZjLkFRAwhP+2qWGcK4OWJZFqQDGgcy/t9dZtEJsHMYMKq5kwdGBz8qVE0xfXXnkTNy8BYW7CqGE6AMoWAGiAGCwzIlM+tjRIyTVdHloyMoeUc5fx8Rsvnv50jWrLcvQsAbAaX1CCLGoSaDcyqyfPSYSEjMMSQUkZg1U5Tsd6anuL8cZrQjTRwu8IhNUrL9L5uz1k5dsAp+oWLCaakRPHoCAxQlCBE3Z+BGibUADMMG0Ll25cm3k5pru7nAkEsEqMa2+w4dCuaGWriUpHDKIpSJELILoIQUI0bBEZXmHSEjMccgdBBK1R0AtzhYCqAGAv11RFFVVVVVVFCWIWnJulitf6hJw9TOoWKOwZyeE0BUQgRLRXw3DME2TJvOXjcE1Ny8ZvC5W/FxuRfqLgZipwrLjCtjUQQHTAB0OnzyhN0RX9ay7q7Nz4/q167rX9F++8vvfvzU6MhoGxbRMwzTzuRyh2woQAoQQ9lwd8HlrcoFAYs5CWgUkZhM+Kif43NQ1k5JbEmbefc8pANO7XlYB3nAiLJRUrLcCMpgKnRgQN7v3ucjMFvQLArAIoYyQnVJECGRN41b61MUL4YXzVvasW9HeEQdQ49GbQ0P96JaCkAaQQ4hYYJqmhVVFofYFT5HvJGOAdG6QqCEkFZAIhHIHHZ/0TLcx9ebqK2CapqZpbG2bDnzBtwBUKX+tbhd2rAnqnBkGBOMH85pk9eNqaBFm8D4uAsDVYZB9BNU4M7qSgan4gjDFA/jsOT8Bgmz/f2KQ6xev3hgda+1ePn/pkigAAFw8eW58fHT15tULm9oBQMMqIGKpKsJ2qKICkxDtAiUtK2U9poTEnQRJBSRmFIKtmzdlM11lWZau65ZlYYxptPnp2AIX3KWgynJ9vC/Zg5umydgAXRcAAGHrBK/ywa4uRiZYGnqXl7ul4Ffo46MAlRMChJBT79KQQbY/n52Qu4eGFwJS2DuAwDRN3Tpz+sJIZmJ19+q2ZCsGgMHMsU8OEgU23n13DGDCNGKKCgiFbNZI86QUiRfb/01LHiAxxyGpgMSMwsvKrev65OSkaZqhUCgcDkciEZ+7GPwN7FNqwHttuJrF/uCJeaVLNTfy3iSJMdY0DUrpJ5anT9hdtiGTUQR/OYWdCNXAjcQU9ggg7r+p9IwYEEIsCwiCXN7IG4ePHx/PTK7u7EqEowBw5dKlvZ983DK/fd26u04NXTUms6sWLVMQLqoEVIhZyIgHYwYlRfWBQMUkJO4kSCog4YlqNCUDb+vmx1DTNOkVOifOZDJjY2O6rsfjcdM0U6kUTabrOsbYVdvxSsvJBpyTb6iFhnNmUlIx8OsCzE2SGTzYddM06ZV8Pp9Opy3LikQibImEJSNcxAUGepFWFLMuGIbBrAuKogRZWuaXD4I8WkDwVgLkIAFTyQr/EiAWsbBuGJaeP3f5qqaGOtuXRkAFAteHBs9eu7Thvs1LFi85dup0CCvL5i3AoRCgqRZSYAIAuBQJqAxykV7izoOkAhLTC2b25y+Ojo5euXJlbGwsn8+rqhoOh/fu3ZtJZyxi9W7qbWhsmJiYMAyjra1t8eLFyWTSdUbrxVR8hmlmWi8ptlcmXjzAdQnD1QJPN0cIF8fGxigToglCoZBhGDdv3szlctS1QlEUjLFpmmxDAb2oaVokEkmlUs3NzbzthBILZ0H8ngXX53JWDqu0qvRfqZsR8x2g7gIYEYRHR8cnCbnrrg2t4cYIAJighbWOziU4Fh7svxbGSktTSzgUAgLEstDU4yOMg4pa2UNJNiBxh0FSAQk/oBoFpBMUzM2bN0+fPn3x4sXh4eFYLNbe3v7v//7vhmFQC/L8+fPPnz8/PDzc09PT0NAQj8cpY6jVAXQ8h6jM8uHj8w/eQQLYdgDhQbLZ7PDw8Keffnru7Nn2jo58Pr9///6TJ08ODQ2l02ld1xFCoVBIURTDMKgXBb1RUZREItHS0tLR0bF48eLly5d3dXUtXbq0paUlHo+HQiHB9mCaZi6Xo6swmqbxtgqnR6HT/XC69R+yoxRjuiFQUUYmJ2JNTd33bEmFo2EAsEiyqWH9lk23JtKXLl5auWrVovkLVKyYlpmZmNDoQ3H0607aLyAhMa2QVECiBKZj9I9Goy0tLYZhNDQ0hMPhVCoVi8Vu3rypqdrixYubmpoAoL29fcmSJalUStO0IEqoYkXlNBW4Li6wr65ugEFs7xR0cwT1DRwaGjp8+PC5c+dCodDx48c//uijZcuWLVu+fPfu3QMDA21tbU1NTblcjhCiaZqiKKZpGobBlgMwxrlc7syZM6dOnYpGo7FYLBaLtba2dnV1dXd3r169etWqVY2NjXyEBuqEIUjLzAy8nD5PNB2r5oRY1LcPY6ypGgCooVDzvLaHH310cW93YyhKQw80tjb3btl8Mz3WmGxob21NxmIAAAQwtQOQom0DJXnebT2zv62Fl6g3SCogMe1wKsu2trZIJLJ69Wr6NZvNGoaRncx2b+retm1bOBymmi8cDkejUa91bn5Vu1ZCunr4eyVmYrgmM02TEMIm5dlsNhKJIIR0XT927NjevXvffPPNvr6+XC7X2Ni4bt26RDyOsWJZVnd394YNGxKJRFNTUywWYyGDwNZtlExQWmAYRj6fHx4evnLlyqVLly5evHjt2rXXX3/9xRdfJIQkEokNGzZ85jOfue+++9atWxeLxXK5nGEY8XicF5L5FlCvgiCRnmvIBpxrLjRPrCqtizr+oPVzWjScVzUAAoik2lrXtTWZxMIIhzQNY0wNLeFwmLlNIETtCzKOkIREUEgqIDG9oAfiCRdVVaVTf4p0Oq3n9cnJyXw+T/VfOBzm0/uo5NoagYPoCVYoctujz+Thze90On7hwoW33377ww8/PHny5MWLF2/cuIExXrx48cqVKxcvXkx5Q2Nj46pVq1auXNnc3Bxc7HQ6febMmZde+p+7uru3b9/e399/8eLFI0eOHDt27OrVqx9//HFnZ2d3d/fWrVvvvffelStXAgBzM2TbEV2NAV4krIaHRdkRB5AiUBAEiqbGtQTY4xRREA6F+L0ldNGFrrkU23WAECSwgRqSgFnnE7MugMQdBkkFJKYdwhxaMLADAMaYbiZUVTUejxNCqFWcLnX7G6udmBmXLmZFsCyLrf3rum4YBuKi/1L5T548uWfPnldfffWtt966detWU1NTb2/vn/7pn27atCmZTKqqms1mJycnr1658uhjjy1atChG7d6O5wLHdLwwgca4ra3t1MmT0Wjs//j2txVFsSxrdHT06tWrH3744TvvvHP06NH333//xRdf3Lhx48MPP7xjx47u7m4AmJiYUFWVqfOyqpqXp0qPQqC7KxWlsJ0QCD1m2DBM3dBDqqaqCgACRbEs0zAMyyKYA09N+FwLcYpq1B5c7Ua1QlmkVvIAiZpDUgGJGYXrhgLDMHL5nG7ohw8f6u/vX7hwoWEYdHCvYOQta2Zf8qIXnBZywkULoPoVAM6dO7d3796XXnrptddey+fzXV1dX/nKV+67776enp5169Yx48f4+PgHH3wwMTGxePHitrY2GlcgiAC00HA43NzcnEymotFoW1tbNBqlpW/YsOGhhx764he/eOjQoY8++uj9999/5ZVX3njjjYMHDz7xxBObNm1avnw5e2rKvQIukYCHa2FlsHNAAACFMEMAACYhumlS14HCUwPYeygwgIrsjZo+Thu1VZyzroZnXQCJOxKSCkjUHj4zRVcr9AsvvNDf348xHhwc3L9//9e+9jXeP8BpsnZ+ZmmCD5RsklfyoitoeAC6ss7kpCZ3+vXSpUsnTpz4xS9+8etf/9qyrLVr1z700EM7d+6855572FI9g6ZpF86fBwDqJsmK4Df++etdy7IIAEKI3xoAALFYrLe3t7e394knnvjkk0/ee++9Dz744O2333733Xe/+MUv7tq1a926dUuWLKE5U2dGYd+Ba9XxwtR4ooymdhWGNEVVoir3OBjjcDhC3xAhgAAxw1LNBJglBGGikgdITBMkFZCoMfztxq5j2ejoaCgUIoQAIdQ27mWpZqZgPrdq5qZefMX/LmJHCqIGAHadbv0fHh4+dOjQur0IcAAAIABJREFUT3/609dffx0htGLFiu3btz/++ONr1qxhURR59UkIURSloaFBVVXeHkAIMU0ziNG+MDm2a56GMaY/Ue9CRVGampoefvjhhx9++NSpU88999wrr7zy85///KWXXvrKV77yx3/8xytXrmxpaWEzbK+nBvvVOA9TqI2WQggAFeIDAmBHhAAECOGppRmwjRk1KFpCYg5DUgGJquClNoJoU+DWC0KhEEJArKnxHWwFI7gauAbJmZXZEuLC/LGLZ8+e/dGPfvTKK68MDg4mk8ldu3Z9/etf7+7uZpYAdhoTn5WqqlooJMzF+b0DAgTVizEOhUI0Me9xSSsqHA6zejZNs6Oj48/+7M8ee+yxH//4x2+88carr7565MiR7du3f+1rX1u2bFkoFGJysszpB8pLKMkQXopTpGrAHEoIQtj2/eMzpzyMEIIRRoGjCdU/vIxS0hggMd2QVECiEgRcU/fZckYnr1TftLe3h0I0wi6aN28e2GM9AAhH9vFZVeDpVhZcDRv8BgFiH55E01y+fPnDDz988803f/Ob36TT6T/8wz986qmnuru7FyxYQG+hOwDBjgQsOBkoGKuqShxxhVka1zpnCTDGpNhhntgAuz7p6QapVCqVSnV0dKxYseLJJ598/vnnX3zxxcuXL587d+7RRx/9zGc+09HRQVcKqGDU74GRCafK5yuhhqBWokK0Ado4uIcqMBXM1hPuHEjFLzHzkFRAohIEWdcsmQObbj799NPHjx/7yU9+eu+999577738r8KwSD3GecUzkzyAbuhnjuvs+vj4+Llz537zm998//vfHxgYeOyxx3bt2nX//fevW7eOv52qf+phIMzpAQAVZ+v/XJ7WAo80dE+BQD4WLly4cOHC1tbWTZs2/eY3v/nhD3+4Z8+eP/mTP9m+fXtnZyc1Y1g22OKF01cfbGJUW6eBKX8E2+xAlw8QQgBT51zXqjgJibkMSQUkKkRwNuC1Hs+OI8IYb9my9Sc/+SlThP6L1tWsDfsYKkreSKf1bG2CGcZ37979/e9//8CBAxjjJ5544jvf+c4DDzzgmgny3YjPqzfXyXcpyf1myHycg3w+b5pmOBxWFKWnp6enp6e7u7utrW3v3r3f/e5333333T//8z9/5JFHaEp6F1u8cI2dDFyUBR9n/mCYImGFHBCyrQFgX6g2mIGEhAQPSQUkKkeVtgF+VpfJZFxzYyvrgmmaFG/ory18KAivBa9fv37o0KGDBw++8847+/btW7Jkybe//e0dO3YsXrzYK2e/iSxCgBBdAgdvulPCWsDN2l0XZehFuvGBr71t27YtX778tdde+/nPf3727Nl/+qd/6uvr27Vr14oVK2gC6orINkx6CSAsZFSjsPl7GT0ipAa+ohISEgIkFZCoCtWvFJSEsGWA2qJpxFwFY5iOJWqPbYq8ChweHj569OgvfvGLX/ziFxjjBx98sKenJ5VKXb9+nR6swNYCAhYqlFsBEAJCQFg94T0GoNj/n5EG0zTHx8eHh4ej0WhPT8++ffteffXVgwcPTk5OPvnkk0uWLKG+hOzI45IKuIqVAgRQ4gQsuWVAQqLmkFRAolqUZAPCbN59lEeAMAJUlADZAWVNy8QIY4QJFMXHtYAQi7CAtXZkmkDwkgRNxbEvuKcJjgv5fH5gYOCtt97as2dPf3//tm3b2traOjs7McaHDh3q6uqi3n9USKpuvVRX0cO6yRD4aaZu5O/iPR4Itx2Dm2QTah6IRqOZdPrXv/rV5nvu+fKXv3zPPfecPXv2Bz/4wc9//vOnn376mWeeicVi2WyWnnZYUgbhg4SERJ1DUgGJGiAIG+A/O5UEom5zqOjAAqa3EMYIYZrMNE3DMsNaCAAMy5qYmIiHI6qmAQABQgD5aype1JJsgDoHUEZCZ8O6rp87d+7jjz9+4YUXPvjgg507d/7FX/xFe3v7+fPn9+zZk8lkhKBDbOujT83wDgIlTwNy9Wcs5AMuOthpSGfmB2YtQAjRuA7pdLq1teVLX9rV2NjY19f37LPPvvrqq9/73vdGRka++93vCq/Y1euiYh5g+wL4PTXL2asSJCQkKoOkAhK1AZto+qTxX0XGuLBHXCAWpmVNZieBkIgaUsMhRVEURTEJyWTSWFVD4TC2jfDEDl+P7OJodhU8Du8Bx5vE8/n8vn37XnrpJQDo7e19+OGH169fH4lEFEU5cuQIQog/SpEtZ/jXRsEIYX8JKJ5T2oCP5srbFEWJRKOAoLm5ZdGiRQCwZcuWZ555ZtmyZb/85S//53/+Z/v27Rs3bmTunLwy5vcUVMAAAv7kJHDOe8sq3ZXKSEjMTdQFFZAc/46Bj3nAX1dhjBRciKkDXGMghJjEwhhbpqXn9Xw+n9VzecNUFKwoOBYOR7TQVOkAxF4lYB7nFbQqYh8EzNsD6E+3bt3avXv3b3/727/+679+7LHHVq1aRdfRGxsbE4kEQiiRSLAFAvD1ExTqqrBpPph47l8RQtxRkF6qjucNLDENOQAAiqLQXQOKotx///3t7e26rv/Lv/zLP//zPz/77LPxeJyet0S4KE/EjrNU1hK+57OiErTS340g4AsvaaaSkJhTmH0qMN1OZxIzjEodCQuzaOS4Oj4ycurkqYHBwdGx0Uw6gzGORqOapsZj8ZaW1oULF8QSicaWZoxAAawgTEd15lVQrhxMU1ISwO/Bu3Tp0iuvvHL69OnOzs6tW7fed9999CfTNFVVpfH+QqFQ8H0NwevKK6V4sdgVgKVx2vCZLi+e4k/t8AQAjPGyZcsefPDB3bt3Hz169Le//e2WLVs6OzsjkQgNQMQyrKyqy8X0FSHZgMQcxyw74koecEfCawG+5G0AQOxkbOOAgpV4LD40dOP5n7/wH//13I2bN1YuX97a3AKmte+d3b947r9+/MJPTly/fD09auR0ZCEaZwcB8lkaEAxRxI5nTOzDBRRFYacLUkxMTLz22mt/93d/l8vl/vZv/3bdunX81gZ6O7UilFzv93x+3zpyXYb3Mcs7/QN4CKcosesKxpqmMUKjqmpvb+93vvOd9vb2733ve7/+9a+JHb6QbuIA27uz5qoUORDklorLquxGCYk7A7NvFZC4I8FrWf6it9W3sEzuHJIbm5oam5rGM+nrP/5BKBF55HOfv//eewHASE+8j0Jvvv7G/k8/hNULPtd73zwcB4OAigAThJFrSa7L6ky9eSXI5XIHDhx49dVXr1y5snPnzq985Su8eZxwklNDgpdN3qnSpr6iQmgB1/phidl8XViw92cDbMnAS61OXUbi9YULF+7YsePo0aPvvPPO7373O+o0gOzNERXDfxWg5I01hOQBEhJ1tD1XWgjuSAi6x0sVkeKguQCcTsqbYEHfoUM3MmO9D9y3umsV6MSyLDOn/8H27T1r7ro6OPDqR++bCgphDfIm3VzvIxLhwKQSZGa/0lMDBgYGnnvuub179z755JPPPPMMXRpHnNOcqqpYUVyfjrjBq658xGZpnJXpcyMrjv11LZ3ZBlwTJBKJnTt3Pvnkk0ePHv3Rj340NDTEjkKmwQZcSwwCl0fwvVWqbQmJ6UAdUQHZye9slLDxEgDRfd5eKcjlYDh99fIVNR7dtO2+luYWyOYQQoDxhJk7f+bstf5rtybSCVCB4ClSMfXHRRJwmCuYeOwD1fGUCvT19b311lsY469+9at33XWXrutChmw1IQgP8JrBl9UDyrKc+1MQ3leAkKmaoasAAKCq6r333vu1r30tGo2+/PLLhw4dyuVy/L0MbJ2lwuk+KfrqRLl5+pVV/EFCYi6jjqiAxFyA14BOgBBCkFN3E4LV0NDlq4P9A9GmhlAiBgBAMDGt0dGRY7v3X7tx/ZE/+OzXHv1iQ7IBMICKQMWgKpRIeA3z/CSYv8KD7gkMhUKffPLJf/7nfyKEvvWtb/X09AAAO8kXfM0eguGhpD6rWC0JApSVp6CzGQ1i50aCfZRiT0/PN77xjVwu98Mf/vDYsWOapiGE6L4DCp4H3BZGPskDJCQoJBWQqA8QO8S8DWRfBlW5dvHS0PXrTfNa1VgknclAJjvZf+P8lUtv7HknbeZ3PPro1+/f0aDFiIpAU/wjDjr1sZd5AAAMw5icnPzd73736quvLl++/I/+6I9WrlwJHuoWea/0B57aVqmZPF36vYouXjWY8mZg5ykjbq1k+fLl3/jGNxYtWvTGG2/s27dvbGyMpmFZCSSgYjZQWwOATynTXYSExO0C6TYoMWsQ5o683iB8oNxcbvBq/+DAYGh1Nw5r1y5dDl8bPXj+5MWxG21LFnZvvHtN793z1LAChCgEFQUbZEfZFYHpANfzdgHAMAxVVS3L0jTt7bff/tnPftbR0fHkk0+2tbW5PgXLxKcs16/CT8yWUIWWEqf4xA6i7JQZRG09ZVeg2weoSPyixsKFC59++ukf/OAHL7744sKFCx977DGakk9zW9gDJCQkeMyyVUAS8zkLYRJJ6Bo1IQSIVYgUVEA2nR7o7x8fH0s1NGih0PXBwQvnL3zwwd6PDx7sWLJox+Nf6lrRGTYtpBsWIiZmGRGwAKjF2jZc+0jCX6GTXboc/vbbbx84cKC3t/erX/1qNBqlCYQJd0l7eAB7AE3nKVIQED4LrmgonmcHseEL+yDYSkEymXzqqae2bNny3nvvvfnmm+l0mv5KnQd91ikCP4KkERISs4DZXyAIOkpK3FkovHQaDqhYL2EAAGTZm91vDt08c+ViNJXcsKZ79bLOBcuWLFyxdMNdd+njmcOHDk8SAyOsapqmqtTrjeYN1P+goB/La110pmua5q9+9avXX3992bJljz/+eFtbWzwe5xMEf9IKUlaqSiuUZKoPuiVhrgPhcLi5uXnnzp2rVq165513XnvtNcMwMMa6rtMcBA5xG/kNSEjMZcw+FZCYy+C4gAWFOXzhp8LaNYGBa/2n+y+3LVmwddXda6Bh2cJFK+/r/cz27Qmivvf2OyfOnh5OjxFUCE2AgCCxCLpj34VuCleY0qKaPpfLPf/885988snXv/71J554gnCxB/zz4a+XodHR1C0VM2P/27xUclFxLo6bBAAMw6ABiXO53M6dO3fu3Hn06NFf/vKXV65cAQAapJmm59kAb/WRhEBCom4hqYDErKFI7VG1T4AQiwBYABZVbCacOHb8wvBg14a71q1YGQHAmgZRTTHMa6fOT46nAeMcMU3TpP4FLnGF3Lz5mGYSVC/zHjBN88033/zggw/Wrl37hS98IRqNujoWEO7kX17nVab2ULVugy7wcuJDHKCUwUBVVT6eoKIon//85zds2HDkyJHXX399eHg4mUx6lS5JgIRE/UNSgTmHaR2Xg6xD8+BN+QBAwDJNywRiAlgAYBDIw/G+vuuT490b717U1JY3jByYV0dvnjh8+NTJvgXzOto62tVI+MborZGxUcuwMEHUxsBUvauQXsKwz6dOnfrhD3948+bNb3/72/fffz/7FSFkWZau62yvnTCJ94rBV7fq0N8IQeyzGVVVZecVAcC2bdu+9a1v5fP5n/70p+fOnaMp+Q0F7Pby2MAMVlLdvhEJiZmHpAJzCBU6ozkQMOegZRU8BgrJqRrXwcoYucHLV4Y/7bs20I/DGiEwkR43JrMAioEgT6xkOBWLxcbHx4dv3hwaGhofHwcAUKhW89NtdrEuE2L66/j4+O9///sPP/xw/fr1jz76qKqqhmFQ3U/sQwoEI4Ezk3qDqyOCCwng1wqKH4RGO6Z+A5FI5HOf+9yaNWs+/fTTt956iy4Q+IQiLmvJY8YqsLLuMB2SSEjMLiQVmCvgh7AqhzOBE3iZoIMXxPwHgQBCgAgxjPzY2K2PPz34Hy/81/WRW/Fw9Ninh08fP4GxEgZoTTQs7erc9ugjBMHpY8fPnT4zPjJqGHrBBsAZvr129zl1IX0iqsyuXbv2q1/9Stf1b37zm11dXTSBYRjCmUNO9caOQyzplzBNKOk2WK4jgjMxnfrrur569eqdO3dSw8Du3bvBDkLMDi2k5gT2N2C5bJ0luJDlwrX1Bryx3FskJG4LyLgCcwI+StrfOFxutvxPbAU9iA5ACBXiDhMglgV5Q9FJqrGxfdWyL3Uu1MNqoiGlqSpBhADEsTp/6eLP7vrCmf7LikmwYYUToZCmoUqZLSUB1PSt6/qBAwcOHjy4atWqRx55JBwOM7s3U6W8iwD3DADciX/lCwFQHMdw1uH6IPTBdV2PxWLbtm1bsWLF4cOH9+7d+9nPfpamNwwDcZEJKi6db121IlIVa3HhRsZ1aiCThEQdQFKBOx/+w59TVVdvMxBy9mEDwpJDIZlFworakmpY+tmHHvzsQyxxXtdN09BNQ0E42dz0wPZH1qfHw9GopirhcCQajeJiLuBVqOt1KoWqqv39/b/97W/Hx8e//OUvz58/HwAURTFNk54ywHsIumTiVSkBgBAiABcvXero6Kgim6pA3Db2s1dE/9J4w7FYDACWLFny6KOPXrp06dixYzdu3GhpaQEHGXK1B7gyUX9mWcVjlUBJtur5uiUhkLhTIKnAHY5yx9Ba8QD21V93ckCEALL9CKOhCL2azecMw1QARcLhkKaBphHTMgxDC4c6Fi0UdKb/En6J4hECANM0L1y4sG/fvpaWloceeqixsZFGHmRW7lLZVF57WMEA8MGePVu3bKk4Eyd8eJ47JaKHQTjuYosjtDYAwLKs1tbWRx555Pe///3Ro0cPHz788MMPO7P14QHgUMN1aHmXywEScwHSV+AOB+Lg9ZNwscriKpCNallCCAFCd6WzNJFQOBGLRWNRpGBCCBBAGGseVvSy1qQFSRRFsSxrdHT0xIkT4+Pjmzdvbm5uVhRFVVVwTG1daQGyHSArBAEAULXK2bmrb4SYJlj9CIyBviPqHsHOHKKVsGbNmo0bN544caKvr4/dyAwJTkrB1laYJD7uqNMKn64hJPPPYRpEk5CYaUgqMIeAiuGfrJpSAkpS9BnR2MNAw9PQnyxC8pZpEgsAgBDLNE3LnIrOS7WnNbVzEBzju7/NWfg1n88PDw/39fVhjB988MGGhgYfl3jXfKoMDICqzaEME4j7a/KoLRY1CNl7KScnJ6mT4OLFizdt2pTNZg8fPpzL5SzLoskq1O7FwR7KbYol76o+28pykJCoc0gqIOGOKtmAz3DppYSoVQAhhDAmhIYaAhVjhXoAIIQVhTcY0MhEpmUSYlUmraCuMMZDQ0MfffRRIpHYvHkzPXyITWT5op05EEKCa+JpRPX6yUN9s7dJP7ANFKFQaPny5atWrTp+/PiePXsUReF5A72XLty4MgMUwDBQUu+6NjbXKz6ZSEjMZUgqIOGJ4FOf4PMknzTEDjQEhegClhA90KUIAqZtsA4ip0e5hOn7/v7+kydPtre3r1y5kp44YJom2x3nkwNQLTy7yqbq0ks7dCBK1TCjAqZpzp8/f/PmzRcvXnz//fcBgHImQcd7LRk4BQj+IoO0Ovar5AESEj6QVECiPPhYSv31ZQCuUJYisPPkFE/Z99qn99LPmUzm6NGjANDV1UUPIWRaLZC+CcCFnKqxbsFLWLQI4lCuzc3NK1euHB0dvXjxIgDoui44BvoXhNghRm52F3BbyoHAb5x/hCDpJSTmJuQOAonaoCQPKHF78b5CgV743I699XTJQpG9pE1T3rp168iRI01NTd3d3Wx/v+u6gGsR/iv9rvVDggVdCIggboM+ILxZhr/IfaCsiHehIIQkEomlS5cihG7cuDE2NsZ8LQtSlfWApNAQ/FNN9xQ/iAFDQuJOgrQK1AtmfdZSzTy1Sh4AUOAC4JiAlrxXKXYgqABUsVmWNTw8fOzYsYaGhp6eHmoVIETc0eBESTO1s2KFCXdxdpU+xrTBacbgzx7EGKdSqSVLlnR0dFy/fv3EiRP8RgOaPuj6UbERwst8Etwe4Kz2gDcGSRYQt4sRSGKOQ1KBAuqho86uDK6DtVOk6RCSGy2L9EfNCwKHhmBfLcsaGho6f/58Q0NDd3e3pmn5fL6klwCPIBU4vSph+n0FuKIKoQUAIBwOL1iwoKura3Bw8MCBA5Q5sRgPUOxyWFIA4qY+Z6xrCG1jZgqVkJh1SCpQLwi+6D4DYBN0cNsO4BymXV0HKEqP/oQAgKIqxM0JP9BsshwIuVEPOADIZrOXL1/OZrONjY2pVGpmSnf8DPVoFvAGawapVGrVqlU3b948ffq0cGCj07dAgGma+Xw+l8vRrOihR65doMrXUcG9NaRucrlBop5x+/kKkGBRQgNqINdxKkgO1U9e/Uth+7OryTyIeF71KYTtY7kFmajxyQLKmclkTNPMZrOCSCVft0/OQXwIWCWPjY2dOXMmkUi0tLTQQwdohN0gGbIEzqd2VgWyjzAo84FKowZEwkMBl3yb4XB4+fLlY2Nj/f392Ww2EomwsFH+N5qmOTExkU6nAWA8nQaAXC7HJ7Asq2TkKNf6FEoPWOGuMlfzvqbvdQuYvlJmRn6J2cVtZhVgtlyvncoFK7P3PmYhmVcO/rMBvgjXHIIL4AxiQ4rhL4NrAn/xhGQ+4nnd6C9/Bcjn888//7xpmvv27Xvn3XeCCOCPkrXnLGJkZISuDixfvhw7diWUy2z8Uc8Dq6A+2cyegjgAAJZlaZrW0dGBELp165au6+Bw/PQpLpfLjYyMjI6O/uyFF4CQ37/11smTJ4PcC8VxHappMHxxNTcFzQCCNPhpynk6Cp3J/CUobiergGufd12dZV06SG5CMqrhfKya/OjjlcA/B14AV1At7hP0XuifzkfwEU9I6fWArj+5lu6T0h9MTl3Xb9y4YVomEBgbG6s4Q9f8vWwebLpJv46NjV29erWpqWnDhg2VHQ/oNWL6T44d4lUx8KEq9xBMlS0YTqYSuNFHhJCmaclkcsGCBZOTk9TCj+y4Av6vUlEUygYojQCAfD6fmcgIN7pm4uzC1bQc1wGB7wjVGAYqu9Epj1ca/kMNeUzJnJ0DUW1ZFOOaUGovT5Wl3Hbkr+a4DawCFRNen7u88mTXXc3jQprKpPIXAIq7n38C//z9EwuExj8Tp9j8T9XUA9jbylVVtUzLsiwFK/7piQP+ybx+ZTYVQkg+nx8fH79y5UosFlu5ciX1HvC367jnSdxtJF5DZM0HoJpkV1JUYfQHAEVRotFoMpkcGRkZGRlhxzr7vALWxTRNC4fDoVAoHA7bT1Fe3OIqWyB49AK+j/g0pGmSLUjpTIDqa6CCnGteYhB5pinbGX6WOkS9WwWEN1STjseUhM9UgyVznXBT+Mx7/Nc1iU01XKUVhgDX/Ik3/We3B1zYdhbhHIPYk/JXeP9wV/HY55IKDyFkGAaNaU8niF4yg6MN+L9E158Eo4tlWdlsdnx8/Nq1a/PmzWtoaDAMQ9M0XdeFLfL+oHXj0/hKex7M+nBEiM82BKHBs2UUagPTNG1ycpLuJ1y6dGmpcgi1ygBALBZrbW0FAGaMMU3T2facPdH5lnnzgGsb8GqrxHZ9dRWVfXBdM3LtbsHbKn+L12jjb58DrheX7A6sPl0z9Kpk+oG3U/KjQZBHcybzeX0+aWqLckeqOxh1TQVcuxMDG8eZ4chVqznz9NG1/ERQcITm5fHpAEKJrgIwHsCuCAKwwYUfMX3ydP7Ky8yvVjgrQRg+WIUIle98dq8aEAzIyNttir9oWZZpmsuWLXvggQf8R9WSQ7wgpFC9/MF69KJhGJOTk4SQRCLR3NwcCoVYpIFyhwZCXKL0uMIz52rWByq/tZxS3Oz2lAo0NTXl8/nBwUFd1ymFEl4EexdM2SOEQqFQU1MTIYTeEovFkslkSTItXAEHDxAMe3yrds3QuR4naDvBk1cYBEjxOoVrIxTkLAlhiHDtqnzv8DLgu+YpPAJxYxLC7XwNCGNIQAG8hGF58mOdU3jXImoIr5FqLqDGVKDctl4yK69xn2+OVFkSe7ZHrbuuOTi7Db2L3uLTbYQPyF47ZAJQkdiZ7rRBs+KcT8Fn6BxEhOGGV66saP4R2C3ss8D9fTqVl6pGnI+YMIY6OzBfA2wI5ivBtWgelAqsWL6io6ODL8X5ClzzFIZI/nw8oaIIIdR8zZJls9l8Pt/Y2PjUU0/Nnz9/cnIyHo8jhPjgRag4LqErCCkcoVQ5qp8CVdn1AlAZXv3TD3RDZjQa/dKXvjQ+Pt7W1pZOpyk5oDXMdhOYpsnrG9r1hFe8Y8eOrq4ucDRyTkaXxiz8yq/+CL3Ji7675uksV7jdtT2QYpdegSsIBTn7Mt/q2FIL4gBcYxYKZaMfL7MgiVMGvq6E/L3GLtdKI46ZGMuBl0EQW7hFENK/s9cWc5YHQG2pAN+ly6rTIOmdrRnZVgGqRcAmlewv+HZyli2v7ZwuAl7jDuvAghc9666uArj2K9M06YjpJYBX0cIjsJTsqBj+otdTCAMcYzNC/m6VNyWhsKzO1wBwnd/rLUejUSdvQMUbF10HL4GvsDoUGgmxGRUzCbD3Qje1m6bZ1tb2jW98g1oI6PRUVVWvSmA15nhT1SnzKgei6geyUhl4vUHLsuLx+Pbt2y3LUlV1bGwsFAoJL503s1GYpslvN6C+AqlUSjBE8x+c7VnIH4pNa2woYPBpzHzL4ckEX5DPaMDSsxFJqC7XgY7vbnQoUBTFOTkhxYYBL01MimcFTgOk17Ozp2YRovhsnY8gXAwogM+NYA+nbCgQhjV/CBXrNKZK+KMuFggQQu+88+65c+cKfkOE/qH/8O3G/q3wlRnuaPsrag4IIXtgI/T71I0WcUa1K7RgAgBg0UEEIYQd/bboC2FXqb8YRth5iyt4BVYQg0qLpvr/VM9nSTggJsyUXiMI4aIeIc5geKlJ4X986XYhvHJl1Tp1Y5EwnF4FghDCCNP83JYEpjJgI5mmqZlMJp/PR6PRgcHB53/8Y5PG+EOAABEgU89P3xQQKKxo29oCwLJMGrqehTDZAAAgAElEQVQY2XNQ+6kQrSkmYQEWIUCIVRi1EUIvv/JKX9/hRYsW/eeP/pPeXnQgstuKCXIYVAIOW9OJatlEuTewGkilUs8///xzzz3X0tr6+K5d8+fPNwyjQJhwoVdM1RV9lZy7SSqV+uijjwCg78iR/37xxUw6zZJNiYWQq9GCMUKTUmrLAoRw8bnSPpMNbiSxWG5Oqlf47rFAQG+npJgKiex2KBQtyEFHNcL1Zpq1UBxvDOSLJ8WGHELIlNW0XGpIySzNcIp1TAnOd7riOgBuNKJJWWpEgPi1q+IXSsdeeocoAh0Kkcur5AebbDbbs7Gnt7e39PMWzzd8WshcQF1QAQB49v979uDBgyWTFWuj8hJ4/sQzD/dMS8rlAcT+1AJlZVSqWbuxC+Fnt/FrigAAYewFTV1y3CgOENywh4QEzc0tQ0NDf/VXfyWKxlgPmrqF5y6EFUC40Ux8bZxkCNjxRxaZshMQAqdOnUokEh6VYj8SZ5AQ2IDPcUQzgap5CPdegqUnxDRNOpdNJpP9AwO6YfT39//rv/4rP6Vj/4Ctq+gnp1LUNO3Axx8f+PhjcCyElfhLs0Al2nXlCDpKEJdrhS9ugxL3X3lwqGXnr1PfXL4EGx9KixEwHX9HyXuQy6ei766Xpy4+/vjjAakAzHkGwFAvVODP/+L/+Yf/9x8VVSneS0aEf6aosD3eAxDLKpxtj7GCFYX+OEWoi/QT69CFeSEdpSzLsoiFABRqE55i1o5WQgoT0sIwZ2se5pSuKoqttoraWNE02Z6QC6oI7MN1CCEiJ0bcrYxr2/+z7GwQQoqq2OUX/hJHV6Ff7Acg9HZ6nZ40MzW38JxdoKkXYVmE226uaRrGmNbT1Dy+MKsBjHCB2VOrC0IYo5AW6h8YuHTpUiqZXLNmjUltszSEEbXhcPraphVTpAJjfPny5cuXLwNAe3t758pO0zAJTBldGDXgTRlgvzhWSiaT2bFjRzwed53cC3ZRUryoyewQVaEGg1JVdKACKsNm3rqub1i//vTp0w122GabBXC7Eih5csqLAGOcz+c//PDD1tbWdevW6YYBMDVOM31PCm1a3OmAqHWdLg/Z7gvM1CzOLfnyOZMANWMwMzUf5RAV96Gi6bBtUDQMw7RMRk+woogza3aXsBxuW9HZ8pxFCEaIrfS5TYQRIQTZlcwegS5MYIzBPvqZ1U9RZdn/8A8SCoXOnTt39epVAFi0aNHiJUtM267jLgOAbcWEAkFH6ODBg3TRp6enJxyO2OMvGxSBEHssEN4BIYqqjty6dfz4CQBoaGjovqvbNEzMjYGsObgJUrg4MjKycdNG4rYWI+GDeqEC2x7Ytu2Bbc7r3Ixtah0dY0wbPQ1dPj4+nslkDMNoaWlpa2sraERFURSF9+NjupF2dcMw6O0TExNjY2N0D9uiRYvourWqqnSpmC0ZIm5ZnSpLKkA2m02n0+Pj47qux+PxhQsX0jGIKXXWOXkBAMCyLF3X0+l0Op2m8luWNW/evMbGRgCg29iEeOxMAHb4m67r2Wx2YmJifHw8l8upqrpo0SIaMZfdzrwpneZK0zQzmcz4+Hg6nc7n85ZlNTQ0zJs3r0BrVFVVVWHUY7VBv+q6nslkMpnMxMQEHUkXLlxIJ9Z8DbCx1Stu0ssvv/wP//iPmzZu/Pu//3tnG2BFC26J9Eomkzl//vz+/fuz2ez69et7e3ubm5t5H1LDMISd7vQt0Nt1XZ+cnKQNIJPJjIyMRCIRwf3KC8Rt6XT24LuXMSDKGT/ps9NGkslkdu3atWnTpo6OjkQi0dDQoKoq3/hZZwQPtZJOp1d1dT344IP/9m//xtLwKfmWwBo2sR1BRkZGCCEXL15MJpONjY3JZDISiQgMG2yySzOkwwht7ePj44ODg6qqRiKRW7dupVKpVCoVDodZT2Q9l5XIGiTt7/39/WNjY5FIhJbS0NAQjUYVmxCwAYR/KNo7qAD5fH5gYGBiYqKhocE0zVgslkgkQqEQG75Y6YhzWKZWGXpxfHx8ZGREURT64KlUinnhABRxWV4AtkZGCDl27NgHH3ygKMrmzZsXLlxIawDs7uYMJk0IoduAaW1ks9k9e96/fPlyS0vLww8/Eo1GaQ0IgwbYwyCyfa1oDgAwNDT01u/empicWLt27bp16xKJBHuJ/Ojh2n746hUeU6Ik6tGxglf/wDUaCtotVVVVFIXuO5qcnPz0008HBwdpvw2FQqz3Oj1HkL0MrCiKpmm0s127du3AgQPUYSccDmuaRscOblrMDJCIaXra5VKplGEYR48ePX36dDQaVVU1FAoxKsBrPv4D7Vr0EeLx+MjIyMcffzw6OqppGo244vMILFtaD6FQyDCM8+fPHz16lNUAu9frKZgMoVAoEolMTEwcP358aGgomUxSAfhH4GuPDQrsV6o1b9y4cezYMQCgrwbsDWNMZiaG6+tWVLWhoSEWj/u3Db4l8PLMmzevp6dnzZo1CxYsiEQiFhdJ0NmEmDC0DVAzxuTk5PHjxwcGBlhZvPzAaSaf8aXqoWd2Ry7kZgcTwXNTsB+ZdoehoaEDBw6A3URZ8xD6gpc/F3OeBTce4Cou7QKaplHaOj4+/sknn1iWlUqlmNen8PaB421UPEplIpFIPB4/c+ZMX19fe3t7PB7n/Ub59y60PVq0aZpNTU3pdPrIkSOZTIbuShVai+tX/hEsy7py5crx48dpvCYqgFAJiHOVZZWg2chkMmfOnBkaGmpqaqK9mK8rVwFoR6CDxvz589evX9/V1dXc3JxIJLwEcH0LNIfOzpWrVnWtX79BVdVwOOysQ2cXpm2DhpmKxWKr16zu7u5eunRpNBqloSb4Er04N18nRJoEyse0UIGKX4MwyvAZsjGFH9Aphc9ms2+//fbQ0FBbWxvtlkyR87pQaNP09nA4nEgkrl69+rvf/S6VSsXjcdonBSoN3OjGt2zaAQBg//79hw8fXrBgAVXGPHsVVDJ/O8Y4Go3SzVdvvvlmNpttbm5mRIQXABUrYF6AWCwGACdOnNi7d29HRwel4SyZIAB2TMojkUhjY6Ou6wcOHLh582Zra2soFKLakeXgFIDnIolEIhaL3bhxY//+/clkMplM0nmArut0cGe3OEufGpQRCofDmqoKRJAl4Ict3sJBh/JYLDYwMHDhwoVwOByJRPL5PNgqh9lRcDFobrTBaJqWy+U+/PDDmzdvxm06Qo0ZTlGFhlF0ZfYHoGrNAkGsG85+ijGmbWDfvn10Jgc2lxIavCsPoO+iQAV8eQDfPJgaZrR+aGho9+7dpmk2NDTQI5Fc3zvLgTUnQghtOQcOHHjttdfa29ubmprYoUo+VcEou2ma8Xj81q1bb7/99vDwMJ2RC/GpBBXIehBtz6FQKBQKXbp0ae/evdFoNB6P87rcXwB6byKRmJiYOHDgADWNUPmxG5XnXxxt/5QNRKPR8+fPHz58GGPc2NhIBXAOnnyGtJLpjCIajWYymY8//nhkZIQKwPdWKGYDwDUJymNCoVA8Hj979mxfXx8ANDY20nmd8Ba81AT7VfgrEQTTskBQGSnzeW2uQwP7ahhGf3+/ruu0Q/I/oWK4ZosxzmQyV69ejcViU6FPixfzXHNgPYoQMjAw0NjYyHo+n9LZ+oWcAUDXdbpExwKz8MnYZ143C5LcunVrcHAw7jar9u/JVB0CwPXr1+nBgE4BnA/FrrChNpvNDg4O0pkQ+4nVsLNJCPwdFbMcoWheWvrZ4sKS09FwdHT0+vXrpmk6M2E38gMEiz3A5oUDAwPLly9nbcB1xGFPx34q0na3vU1yygTt+jNTotSExidTFIX2I0qmnU2OXmE62LVdsXt8qlHo3exzKBTK5XKXL1+ma9V0kk1s2zLfAMDZ/OzmOjw8fObMGbBXPQy6mcVbEqFv5vP5q1evZjIZsJs9a6i8qM4Hp1BVNZ1OX716ldeUzlhJLD0uNpirqqrr+uDg4Pz58/kKx8WmQYGf8WLQjaCDg4NMbIvb5SHUIV9vrCfquj4wMEB35ApP6hyIhCGR5jA8PDw0NOQ0Dt3mPaveMV2+AuWygZI8wCe9oigNDQ10csyClvA2QCETJ2EMh8PNzc1MkQujVcmZASEkHo8nk0l2hTESVMzBWV/iJ74AoGlaY2MjnUsx8fgETibBgy40CK7vPIlxlZm/Tmd1tAaojuT3RrtmwlSsYRiUhzEBLMvSNI1/ZC8ewP7iAqsosULPj7xsFzgdcw3DyGQylM0I5wk5B18htC2du8RiMSo2fWX8jIo1CWeeUw2pLqwClYPKjtw2a/HgWy+fkuoMaipn82/eP8AuRVQn/E8IFfxlvYUs6DZXqahBi7Zby448BsWN0HVoYhScToVZWexxnLQGils1bXLhcDiZTPLdVhh/fB6NtklqZqdBuF1zEEY2IQcqs8iu3BSwaz0QQqihhR4VzQZA4GxszhrguxXYbYC6LvEy+Fg4mDDMuYTVANg9lKXke66QiZCb12NKOFEXboP8uOA1DxPSC8qeGvaB0y7Mpd911ODnlACgaRoNMMfSMC6MvRe5eQnD4TAbQcD2BnI1ibNf+StUE9PmjmxXGjZtdXZmoSdgjKl5k7h5sbkKIITgQAhRWxwAmKbJu0w6DXRQrBpZbtRJgtW8T425ViIWgiKIv7vbhMBWD4QQGiwIHCEBguTGaoA9l9cjoGLPqanrNZi4VGXPJFV7DZYlvlAJtMswTczl6W6N82MDvsW5qlXaAGgjpFYBV23hQuAAwGaTuVwuHo9TRs7Se80EnDlTGhqNRlnEM/o4rk/qfDpKBagmpo/g+pjsovNZ2Hocf92rSp0XKfunBn9nlEPhXtc86ajF1gdLdiXXHBBnCwE3Xe5sCcCN/K6PJlESdUEFqgTVAbTzMAbtP7HAxTHITNPMZrP8EMbYbkkeQKHrOl2fZrf73MgEYDJQAZz9HznmBOyRBV1IN0SQYtOfTw0IH+ismtejfJqSNYAQovMAygn4buwvCZ8DVnBJqwCD//AapB54+zaxtxIw/wafQv1ISUDpPeWuegib5rVRV1XEfmIxBngfi7IQqLO5gba6fD5vGIbXOlrJoulIIggfcASgoBYyppZYLw5SOjNu0cm9V0rGMJxp6Aopv6gRUI+y22kNsDp0VeHOXsA+07fASEAFL5O2IoPbxOgzipbMSnKC4LgTqAAA0NYDxSqc/uRsEIiz0tMrdDcLb5KCAOsCfIY0B/6KjznBeZ32H2EMEhYC/VHYHh/YTUaQgb+d9f+ShIZPxu8IcrJ15ysgxfF5MEJKwYbiMgdyBT/egW1FxHbYVNdg7LwAvPGfPj7TZK6P7GpxER5qtoeeqomA7xqH8Cq9aqlKKuBvmvAhl7QFEnsHKf+y+NHAv1EJJg2vslxBdy87cxDk9+lQxA6bXZZRjX8jwccBL0mYPbICAfhFBFcPoSDgLY5QTv17SSURBPW4mZDBZ2zl1wiYFy6UMw3lewu1iaHig3eDsE72mYUNd5XTeV3Qsq4k2osHsDmH6yPw9/rAqXHZI/gsTPhnKOTpP+wKT1cgT8UjYPDOjGxnbH4w4hUS1fFeUgmzqOCMShQiWMPzrJwaODxXm4PXA/A9y7VVsBZIHGdSeOXmUrpvHZbs3a4tli/LXyrs5rtaFtgOBXAc0VlSBkIIE6AyNYaK99f4tHaf7om810SCgDrhsmYg7Mj1kkoYygR3hyAod7ySEFAXVIB/eRWQQdYBwM385dP5+cQ0PfMmK6kMhCmmQAVKtkghASo+B4+/7iMALyeLglKBGnNSgYBPwd8upCfcSSQ+gw7/mY5AZcnMPhN7axmzCjjT+4+AUN1oUtld4oBY3SA2Mzun6JPy2oJp6Mos82L+pRL4kDls73EVEjtbi2sb4JVQkEFAlNzeGkfcPH/9S2d1GJAKuCZA9nYY9gjONLwATkkQtyfItdyS1SLQKVc+5JMDQojN6yRmEjWjAhVooNpmKOjmCrIKyAC8knkJQLigvP4i+TyCE67P6JpDyedy1ZElBXAOIv7pXVFS9ZYkQ1COCncdIvkHF15cgCcoIgHlVlq9wV96H+FZ+3HWgJfac/2KEAI3OhukYyJvi0VZqOZ2xpMgQNumEOotyCzCJys+jX8+1TRFrzfow3LKytAf1VSRhBfqwirgBS8d5mwKFhcemE/mkzM4lCVfVkl9L8jg1PfBNZNr5s5Zl/+95foKOLNiS7xBxhF/YYB7/ODz7ABMrAwBwIOs+AjjfKdllYvYHw+U5n/VcoVp5xnOXsZfZ/BvugKEPuvVUkpmxXqNwC283njJ1xFkbuAlBpRym/fv1JUpM54cQzneTrwAXurcOUIKCZwyVDCSlCyIFzV4thIlUS9UoIL3KvRw1xwCDvrgNqt2widNkMVRAV5ykmK/Aa9b+GQsQcVsQMiZl8prxHQ+QjVLjIQAPRYpuJC8DK4jvmvzQB4+WYiLTckX4ZqbF3ySBNFkhBDBd3XGUaEGYvEDhGosT5sWXmHlQzwfJ1RoxuWJ4Nv4/W9n1nUfPuQzkvirT39i7XxkmtjnKYR+ROwzVoSIGsKeIK9yhf7o8yA+KMnIXWvAp6Dqh8S5gHqhAlXCtdd5tUWvlsG6BM+sg9zr39QEbe01OPpPpJx6V+gtgvCuOTh7bMkHCcKQvKYyiIPP7byA5S53C8reZwBi8yTXgqE4bD77qTxPeOTp/R5kMKKe5/fff38ZJTrKCZRoGkZG1rqcdRgcKLDmcE2GuTPAfFL6qxnsiHFbVhtwpQIlbwFuzHFS1bLolMDI/WVw1bLC6yPcsU+8kK4SMiYhPF1wuI4Y/iOn673OHMoSYw6ijqhAwObrBPVTde2xQsPyV/aoeIOZf+sp+SuFV8sGbnVTKNFLx/NyepXo+tVVJQt5Evv8QD5/n2d0rSv/IdgfhHguEPBjpSAA+4kFZfKicYLAbgIUnXTnfAp/NuaPIClp5S9dujRgnk4EGe7Ym/Lgo4FycG2ThDNKBRyynW3Sa5HFtSM7u7wzqoEgiaDpnR2T9QKeN3s1GNeLTsucT23wnRS4ocx1ZGApUbEZn5+yC9UivCyhOGezJHZwCGEwYX/ZW+B7vZCYye/a7Et2HOcbdDa5ChhGWennIOo0rkBJMsvrWmJHpXAm89KazuIo+H04VvHpdmCrE75fsRYvFMR0Kp9A6JNevd01pSuf4MkT+8x205HAUT6QbZrmQwx51R67hZdEuIgq3o/nKyHhdvqh4qhq/Emp4KhDL4H5zOkozEIjCHex0sGncZZv1XCKQQO+VoyS1c5XoNvtgUqxiuPqs37BNHFlbx9Rs4pH5GNkR6FgjE2YfZqmqeu68AbB0ZIZKRSus+Ai/A4aL1HZ+CNMoFloCv4i253LPwX/UMIj+EcmEGQQqshrXuQcDVwbM60EPgdWitNe4mQD9BH4KE+uAxcri9/vw6rFyUXYryXZgNcr8x/NJKCurALB4WwlLMAW/9f/Xr6NmqZJYwWWHAWQ22yYhjnjO7DraMhIhlMAXdez2Szf/dg01+tBeAnpCEKDFbKgp86Rwge0DoNbBfgbGRWj4Q7BQVP8bw8oIbKnTSwECi8nG0N5KiAodVb/rmMosY9SZFJV4Prg8zhetKyYbQAf9bZcBKzMgATR9UZwq0BkW5Uty9J13Yd1BRHJRzKBmfG9jOZAOzJfqGsvcKoo1tdoM/Yql8/TtR4IZ1dgiaG41/MhvISCaCPkRxL/XiyMMzRnGvFQyFZ4di8BwB5MBDrCupXQ75yRAyhBn5iYYKeQOPuaz9Mhe1rivy7jWifOx6mgKc5Z1BcV8JiplH6Flh1djinCkgXxuiGfz9PZGIs7W9ZwSWPu0u7Hxz8vKQP9QAWYmJhgx6hAgFVqgUnkcrlcLkcIoX+FIgQ4hzCwIwsJwgesfCrA5OQk4YLN+dchP6WgFwCAeLsNspHX1QBL7BDuzkfgwb904ToA0NkMjaAOHgrASzb/BEJB3j+RQ4cO+efgg7LIXzVFuNIpup09n8+zCB/+bRhxqEAMp/kB24F7nQJ7CcA+W/ZxG7QzeiWD4nboFADbZ3CA3SpcCb2gj9lnKgBTrq6tna8B4eloXARiH3HCd0YnG3AlBJT+8gL4tHlnJSCEotFoKBS6ceMGf8Kn8/HpB2cdCsddVgPkb8OTKEbNFghQjWzCznxKvktN0+bNm0enU8FjU7BsMcbJZLK9vd25IuCqElwFaGtroycT+jtMMT0klBKJRNrb2+lBXmw0Ib5GLf5XjHFjY2Nra6uu60JfCtITCCGhUKi5uTkajYI9pJa8iwfGOBaLtbW1Bawxpy6352SeplEfHU8vJpPJpqYmWodl9X+amLaiaDTKW4aEfFz1Fhs06REMQYpz5Wp0/O3v7w8uuZBtNputJlIe1R/OObFQipeSsCwrFot1dHQIzc/1XXgNFwhgYmLCXwBhYioI0NTURA8J9CeFArB9FF5DQ0NbWxsry1UAcLNXUwGi0WhTUxMz7bAEQcSgz9XQ0NDQ0FDWMh//q6Zpzc3NqVQKHOpfuMWrKyUSiebmZv5kUa+BiLUBvj2HQqGWlhZ2u7Pokkgmk7qu8zkEh6u0fKOVzMAL9egrUPJt0b7BZrGpVGrz5s3JZHJiYoIeVVySD/IaS1GUzs7Ohx56yDCMcDiM7MVI8B7IoLibpVKpe++9FwDS6XQikWDDhI/e4jU9xnjx4sWPPPJIIpEwDIPyegjQcFmCRCLR3d3d0tIyMTHBBjIfCAMBISSVSvX09DQ1NeXzef6EXxzgYEZVVROJxIoVK4Bb/ysXGzdubGub19jY4JWAH24EeWiJK1asSKVSlAti7ghjAYjzCGGgg/g999wTj8cnJyfj8bjzrpLrBW1tbQ899FDA+nde3Lp169mzZ7dv317ydi889dRTZ8+erfj2hlTDkiWL6VH3AgSl4myZlmVls9m2trYHHniATVj9G4/zuqZpmzdv7unpKSkqTwiYMLlcrr29fcOGDVQRQrChn9hO79Si0NnZSd8+PZ/Tp3QhBwDIZrNNTU20J7LryOGT7xQAuDFt2bJlNGKga1lOGfjXkcvlNE1bt27dsmXL2JksJZk9/2s+n58/f35HR0c8HqenIiG3IJKs/nHxQQP0ysqVKxcvXlzZUJDP5xcuXNjS0kJHcr5ECMYqnGlqMke946H8zd/8Ta3y4lvttJIvxAEACCH/f3vXst00D4Tt3OvYPaUJYUFhA6zYw+Ep2PD+G16BOk5J638xf3UU3TySxo5l5ltwaGuNx+O5S7Jubm62221VVVDX4u8ORBaLxW63u7m5qapqJp1x3rkpSLBRFAVU1UVRiEBrCx66oGaz2f39fVVVVVWJ05ZlBnSPIIfG2Wy2Xq/3+/16vS7LUlxpZEAvSWHCryiK7XZbFAXIUDwCRgKLxUIwUBSF7H0w7wLe4OFwuL29tZUyuicSP8Jap7Isb29vF4vFZrMBGRrdqFGY4Dffvn27Wq3W6zWcWK0XZLprk8u+T58+ff36NbdXUW4JVFX148cPkUp6DQd8/vz527dvAQOBgfvd/c+fPz9+/NjpOoVfFvJ5fn6u63q9Xr9582a328G3Y2XtxfCwWq1+/fr1/fv3TgnIgVD8W9d1VVWn0+nLly/QostMy+VsBM/nc9M0ZVkeDof9fp9dnstllIAihOPxOJ/PN5vN4XC4u7uTF9LbeJDNpG3b4/FYluV2u314eBCHKrn5ly84nU6QkL1//z6/PI/A5j2yy7roz58/8/n84eHh7u4OPtIgXqKu/IoQZrPZ379/4S18+PABjix3MK8wBvSPx2OWZfv9HpyJ0IRcg00gChzTEwwZxCu9M3RTnRAwS/38/KycNa7DOPUAFvj09JTnuUgFFGfkfpzz+VzX9fl83mw2kMwaJ8ttStm2bdM0MMdfluVyuWylDTnZpckZSYlDlufzOYQxjATEZTAc1i1CQpB5vkdYrgUBtSgKzDQNUvFsLkz+PayTEsezFkUB85TImNq+rtXK87xpmuVyKfI593DbIyTna/BOQG4Iyz765eXldDqBIoECuD9lT8Kz0j8/nU6LxeL379/v3r0rikK05dyRQ1wDqQAsX4e+grxFwj0WfgQJ1HW9Wq2qqlI2DtiGA0Qq0LZtXde73W7WdbKfbgsQibPs/8Wn4lwS93A56X98fGyaZrVaLZdL5Q3qlti+LobIXptt5/P58fERemwiEXEzoHT7mqap6xpqm+VyGRD7bY8pIzkLHQD0qcDAaLV5d6+EEeZHRTvu6elpdnnEX+YMikBBGAwEFdsphUZSYr0S/AhLZ40fTZMh5wQvl6eawto3mwtWvKegIFwGbCWKOREEzhrHLL/H6J5N7A7/IkSKzAP0u4BWuCWgeFKFQkK+JsADKEFIjiXZ5VfA+0sFMimWQDSS+/kiUGEY0I1IyTMwmtxKGwsFS7bhusx1bn1dWXapdbql23iQI7qQoXgEmyErgVy4EWE1mLXDMgXFbKFVKTwJpwJ9Y1w7CCIh7N8L+i5k3zsq9uC4XtfpTgq61trSc4BtybED+M+TYdAphHjkr0sx9CelMnI5VXLLU3+nCTmasErALZyATZhh0PN145/CKCvpsvt6/e5uIWDYo30EcgqdlEn4j6HgQOoFcB8Y47JBL8R74Xiz1GOzLw/yWEfstxUTDmZ0dD5LgAxbn/mU8QMTA3LqzygNDyT/RvV2iyh39tWpIN/aZjX42lr3JDHvt3O4I48JRpgZ2l5WgABjvLHx4l6zgdTdFC2STwVk+L5avYFp7Ak7+mOZVlJDb98xp6AQUWYExaZ2G8PK3TOtCOssRzptYPZ6vBtenvKVXvs58e5ShnsUfjOk7TLhBN1sGPm/un8JiCu+Ltsdg21ckUvG/YJyny1kMXHIRj/MfLzQSqvqfMcilRxPSv+lbx6mJBPxjQ03OBuQkXxlEwNdFdrL7cKOUCQHez3BF3/tDK4Cd/IAAAQ2SURBVGb6BXLT1Uah8xpkLqIwI34cpqoz3l3AcXdjKJIfGf/4tiuRLpK2Lx2DYEMOawIZKXTyQCgffW7CqLQBhmB8HHc9kF1mSEqUdVDo5CHgYt8Ih9EctxeydRQwLLXaYi/5PwFNDp0+5jLOCVJdK+CewQ1+/RinJiurruK+KuUoK4MzYiGcMDngl3p1zqMH3N3xS3FTnQfFgxivdCBYl/JLIG9HC5K34IXOuGgDYSccw1IYzTAmdcULy7GE5crwvbXXIyjai7ypGItkCU+BUJ+9PMDARjQ2pJoKOEDyRvGePaCodVNo0TuhvfjppKZ4hE4GCC3HK52y/VXm/9/J8a/lv2Rpe7lRKvPMLo3UYYZIZZBNQHkiX3XSuwK+DSrdJ2DGhuXBCvAW5GVreH4ijRefQhnHxtw6aaSdCujvO/JdiuF4S1BKcGRBgAnk8SaRRWQGGOL6/4OBT0EGYCkVj5AKnwri35TDTMYgE5ISUyaCMQr9SILIbIDkykj/4zWcSuyRFBJFqmsFFLaNqbRXUDF+0sd2X2QnAG8nus0HB+PctNYBTw1fvmRS3tO+bqpuh1qJE9nA9CI12h4DbRKWFg++becYssgOnE358UqolxOdlbfRI/k6IpmU+L88yk2Byhh1fygPjOEh99wPMlqT7w9pdwUEYvLBnnLJsAmC+KaWV1AnZIBEjCPEP+gUksBg74W8Ae4FTG9P/ysJM4O19Acg2BPNKWEiXQEjvGxYzoIx6Wdn9eBbCsijgmtZY+MUSc3LVPTGAP5eVIhpArlJkdAcBpH2S/KAmBZdT2x4FfEBNL0K2bBaXCHlWxA7OosBbMQYAkmfxkEkuCsgDyTsJk4MqaYCmX1WHjlbrw8BkMx+hVXk8WNjOPEFYSSO54E8pCXkC2JMuO/HTNTz4jNjwlzEFtSRIdDo9+JnXvpzpEgGkASRoxJVyAGQcCpACF8Npq1FYuxHj4UDx7PBFgcwHAi24jGkAqnrT9/dqbDiJHWp+oJTgUhwKhAOjoKMUcHXlsewwHMaFhTQiewkOHw5njowORmnAjZwKsBgTA1j9ncctBjXRbo7hnrFpM4gYDAY2bh92Zh5YyQEbsrSgrsCDAaDwUgG8Y2l4H0KEwanAgwGg8FIBlTrNMewB2o84FSAwWAwGMkgZgM2wwZeK8D4V8BFAIMxPbAhk4BTAcbEYet78bIjBiN1sAlTYSJnEDAYCsI+3s5gMBICmzAVOBUYGqy7AwCTBzAYjNTBXQEq8LLBDhB+Ryzy88as9G4gNVl/oSzY/kB7SARjDPK8+szaGIQwPUw8FYg8ce5aZ9+RH5Q31TW3eO11S2Aa0hgVpqdy1/1OIq08w55lJMXJ1XORSSLVVCCe7eATCOMP+3ITpP1mO8nHNEbiAmR49QBs4GyAHKM9cSDyzJ7rZjZUvoj8DGK2msngP2s+zUECDyD6AAAAAElFTkSuQmCC	\Phi = \frac{Q}{4 \pi \epsilon_0}\left(\frac{1}{\sqrt{\rho^2+(z-h)^2}}-\frac{1}{\sqrt{\rho^2+(z+h)^2}}+\frac{R}{h}\left(\frac{1}{\sqrt{\rho^2+\left(z+R^2 / h\right)^2}}-\frac{1}{\sqrt{\rho^2+\left(z-R^2 / h\right)^2}}\right)\right); Q_{\text{protrusion induced}} = - \left[ 1 - \left( \frac{1 - (R/h)^2}{\sqrt{1 + (R/h)^2}} \right) \right] Q; \mathbf{p}_{\text{protrusion}} = \frac{-2 Q R^3}{h^2} \hat{\mathbf{z}}
+418	A hollow metal sphere of mass $ m $ and radius $ R $ is electrically grounded, and is connected to a spring (spring constant $ k $) such that it can oscillate horizontally (x-axis) around $ x = 0 $. If a point charge $ q $ is fixed at $ x = 0 $, show that for $ q < q_c $, the sphere can be considered a simple harmonic oscillator for small amplitude oscillation. Find the oscillation frequency and the critical charge $ q_c $. Ignore all frictions. Assume the sphere slides on the floor without friction. The spring is in its relaxed (equilibrium) position at $ x = 0 $.	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	\omega = \sqrt{\frac{k}{m} - \frac{q^2}{4\pi\varepsilon_0 R^3 m}} = \omega_0 \sqrt{1 - (q/q_c)^2}; q_c = \sqrt{4 \pi \epsilon_0 R^3 k}
+419	A rotating electric dipole can be thought of as the superposition of two oscillating dipoles, one along the _x_-axis, and the other along the _y_-axis, with the latter out of phase by 90°:  $$ \mathbf{p} = p_0 [\cos(\omega t) \hat{\mathbf{x}} + \sin(\omega t) \hat{\mathbf{y}}]. $$  (11.2.1)  Using the principle of superposition, find the fields of the rotating dipole. Also find the Poynting vector and the intensity of the radiation. Sketch the intensity profile as a function of the polar angle $\theta$, and calculate the total power radiated. Does the answer seem reasonable? (Note that power, being quadratic in the fields, does not satisfy the superposition principle. In this instance, however, it seems to. Can you account for this?)	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+420	A dodecahedron has twelve regular-pentagonal faces. All the faces are grounded, but one, which sits at a potential V. What is the potential at the very center of the dodecahedron (i.e. the center of the sphere that circumscribes the dodecahedron.)	[]	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	V_c = \frac{V}{12}
+421	Magnetic fields from current loops.  (a) Find the magnitude of the magnetic field at a position $(0, 0, z)$ above the center of a circular loop of radius $R$ with a steady current $I$. The loop is in the xy-plane and centered at the origin.  (b) Find the magnitude of the magnetic field at a point $P$ on the axis of a tightly wound solenoid consisting of $n$ turns per unit length with radius $R$ and carrying current $I$. Express your answer in terms of $\theta_1$ and $\theta_2$, as shown in the figure.	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q1WrVbX19ePj4/v7e1xHLe8vGy328+fP9/d3d3V1WU0GrPZLM6JCr6vpOsQqUsv62h6yEMl+LKsJvYTQZojWsofuquKu81jTL8Og3aFfnV0CFcq26aUDn+3BVHk5PfAKBOJxMbGxr1793p6eqampqLRqEKhaGpqOnXq1JUrV5qbmxFC6XT67bff/sEPfpBOp2trazOZzMLCglQqPX/+/KVLl7q6ulQqlc/n6+npGRwcnJ2dbWhouHbtWjwe/9nPfsay7HPPPXfhwgWFQhEMBl999dVbt26dPHny+eefN5vN6XR6Zmamr6/PYDD89m//tsvlevfdd4eGhlQqldPpvHr1alVVFUJoZmZmfn4+HA7r9fqOjg6lUjk7O7u9vQ2elhCoF4/Hd3Z20uk0Qkgmk6nVakDxbDZrs9ksFgvDMIVCIZ1Op1KpQCBAZsSWSCQQ9SGVygqFfDqd3tnZicVigUAgk8lUVVU1NjZWVVVptVqxWJzJZNLptEgkymazY2NjfX190WiU4zitVtvV1aXRaGZmZoLBoFKp1Gq1FosFITQ1NbW1taVSqXQ6HUjeELABeJzP5+PxOKg9AcNYls1ms+ANazab6+vru7q6nE5nMpkMh8Mvv/zytWvXOjo65ubmpqamFhcXLRbLE088YbfbM5mMXq+32+12u12v1yuVSoQQRO4LBD5SVfBA8IC9bQWP3307OYqu9RPEwkN6q8Dh40oV6fCRpFIhj1RnCfiUwCPmQUeBngXcEPcZCAT6+/vHxsZCodDx48cvX77M8/xPfvKT1157DURDrVYLYBOPxz0ez+/8zu9YrdaFhYXBwcHBwcGpqak//dM/PX369PDw8Ouvv15VVfUHf/AHnZ2ddXV1wWCQpmkQJQOBgEwmi8fj4M9SXV3t8XgsFguELgQCAUjCsrOzE4/HKYoCBAKolkqlRqPx+PHjqVQqHo9Ho9FoNErT9F4kYjabA4FAKpUCXxKZTMax3ODgPVgvyxZsNtuJkycKhcLS0tLQvWG2UJDJZaHQ7ujIaNENiKIp2tvqXVtbj0TC5C61d7aLRKKtrS1AHaPRKJPJxGJxNpvNZDLZbBZUzUajkaIokFaHh4c5jlMoFDqdTi6Xi8XiSCQikUjq6+u1Wm0mk1EoFFqtVqfTQVi9VCqFe6RWq0Ui0ebm5tTUlMlkOnv2rFqtzmQyIpFILpcbDIbq6mqZTBYKhdbW1vr6+jiOgzNHf3//v/3bv01OThYKBY/Hk8vlAoGAyWSyWCy1tbX19fXV1dVVVVVga6QIJ+GDUPDoBkK+XIT+x6RD9LG4wRG7OqSfioD4uFIFDh8BEsQYlG2DERHbe3DWsaN3XvZXHNJXNunlysrK+++/L5VKX3zxxSeeeAKMc3K5fHh4WKVSra2tJRIJuVzudrt///d/v6qqqrW1VaFQuFyuqqoqo9G4u7tbKBSCwaBIJGppaXG73c3NzQqFYmNjI5vNHjt2rLa2FuYASr/Ozs5jx47J5XKfz7e4uIgQKhQK7e3tG+vrb735pkQqTSaTSqXSbrezLBsOh0HhKWYYsUQSCUf+8R//MRKJiBmGZdl4PHHi5Inqmur33nkPkIOiqFwun81mi8cIhBD60Q9fRdRH/8G64f/g/UNRFIWosdExbFKDIwSiqGw2q1KpJBJJKpXSaDTHjh1TKpUajSabzUI2GblcDsA2NjZ29+5ds9l8/Phxm82mVCrxjROLxYCgu7u7Gxsbu7u7Lpfr9OnTHo+n9K4Fg0Eo8dHZ2Wm320vvo06nE4lE3d3d3/nOd5LJ5F/8xV+cO3euUCj86Ec/Gh8fP3ny5FNPPXXr1i0Q94eHh3U6XXt7+/nz52tra00mE2hfyz4k+DSGfYYPT3xz9JSz+JLDGxylWQXDKnQ4VeDws04C5VIpkRCFmRF8AyrNh1ZDkb0BCyNzpAHcZjIZsJ9BNNvu7m4ul2toaHA4HFiVVygU9Hq90+lUKpUsy6ZSKY7jqqqqXnzxxUwmk0wmA4GA1+s9fvx4Pp8PBAL9d++KGAaAnWXZvt7ecHhXxDA8z2czWW9ra0NDw7vvvBOLxcANUiKR7OzssCyLiuLah7dugxwjEolgYRRFsRybSqU5jstkMsCOBwcGB+728wgVN5ei0Ee4B38qFIrmlmMURYkYRiqRIuoj3s+ImGQqNToyihBvMBm8Xm8ulzt58qTD6chkMplMZnd3d2dnRyaT5XI5juM+97nPffWrXwWtLJw/QA8JBFEQIpHo8uXLNTU1ZW9QMpkcHx8fHR1VKpVWqxX6AccluCnpdFoikRgMhtu3bysUiitXrrjdbpxwhyrmRtBoNF1dXS+//PLt27eXlpa6urq6u7s3Nzfn5+dlMll3d/fJkyfBX2liYmJ+fn5wcHBxcdFut1dXVzudTovFYrFYjEajUqkECCTlRYGn1SFGRIjGwdqLI6pA7yt63lc6rFCFDqEKHH7W6XC5UKAI5UsqBx3SnrwQlUvJxhOJSyAQEGIB8/k8+FyAZ8fnP//5XC63vLwcCoXAdgWX3PzgxtTkpEKhAIg5f/68zW4HsCmwBZ7jaZru6+3dDmxDZALikYgRRSKR8O4uFjhgRA6ED57neb73Tk/vnTuIQjRFYy4vEokYsZiiKLlc3tbenklnEM9DG5DgaIrOZrNT09PYMbKxqdFitWQzWY7neB5BXwjxPIcKhUI2l2EL3P/x4m81NjVqtVqFQgELh1kVCoVMJjM3NxeJREwmU11dnV6vR8VscLlcLpfL7e3taTSaxsbGV199FWIzVCpVLBYDUCSzEJjN5pqamv7+/tXVVRIO8X0BZ91oNDo5ORmPx5ubm+vr6ymKIt16VSpVLpc7e/bsW2+9dfv27e7ubsjaA3AFJxgwf1oslosXL/b19YVCob29PZ1O19HRcf78+Xg8Pjw8fPz48cbGRpfLde7cOb/fPzMzMz09fe/evTfffFOj0Xi9Xq/XW1NT43K5rFYr2DIf1Hz4oO3JC4/S5leNiBUp83GlChw+MoQP3Udphh6EL5RtiQEJH+c5jvMtLoZCIZD5KIqanp4aHR2RiCUcx3H8RxpahCie42gRvbG+ns8XotEo9PD666+hfbJXcSBYFFa47UdlmqY5nqd5nuc4HqH29o4nrlzRaNRSqZRhxDRN8xyXLxQQz4vFYpbjpFJpdXW1QqGQy+UQvPGRhY+maZoeHxuLxmIsy3Is19rWCsllYDmQCBshlMvlQqHQyspKIpGw2Ww6nU6j0cjlcoBD2JlcLicWi6uqqtLpdDqdpihKp9OhYuELnucZhnG5XAzDOJ3Ou3fvDg8Pf/jhh88884xGoyndf41G43K5Pvjgg6WlpfPnz0N6UpzQDjSrMH+IVFlaWrLZbDiaBVMul3M4HC6Xa3NzE7x+8vm8RqPBpwr4oNPpLl26tLKysr6+3tTUpNPpQAE7NDQ0PT0NIStyuRx8X8+ePbuzs+Pz+aanp9fX16PR6ODg4IcffqjRaDo6OlpaWux2u8FgUCqVkEacOjhF30NQ6WP5cRDx6HbNQ3p+6Gsr9NmnChw+YnRfTRFP5EoGZ5ajdy4QEIGHYnGqr7f3b//mb/YPiX6paCS+QkXDG26BO+URj61wVqv13PkLer0+lUqJJWKWZRGPlEolrnzLcixIjblcLhqNSmXSCxe6IWYckIwq5gsFR4+VlZX+/n6KosAxEm8Irh1f39CwtLS0vr6eSCQGBwdbWlpqa2sRQmByA/WvSCQymUzb29tDQ0N7e3utra3YvRZnmJNIJGq1emtra3JykqZpSJ+NEMpmsxDAB6cHuMrtdk9OTg4PD7e1tYHwJ0hQl8/nrVarzWabnZ29ceOG1+utqqrCpl+c37WxsbG1tXVoaCgSiYhEInAcJbdepVLxPN/d3f29732vp6dHo9FYrVZsqAOUksvlHMe1trZ6vd5QKATypUgkamhoWFtbW1hY2N7eBgMwQohlWYVCUVNTU1NTc+XKlVQqNT09PTAw0N/fPz09PTo6qlKpjh071tra2tDQUFNTA66zCoUCRMbSp0ugcjjkORTgGVarHnKVoP0nLiNWsPCxpwocPlaEAYDExYcj4CYcx4EPy7Lf///97/+tUCikMhnP8wjxuVyuobGxra0tnkjwHEfTIhEjEjMMRdOIRxzHFgosz/NQno9HiGOL4iOF8rmcx1PrbW3leT4ajUKcAMdxJpOpqqoKfEnAvASsPB6Pr6ys7O7uRiIRCDeUSqUg/CGERCIRqDHD4fDQ0JDL5YLs2Kiol8N6Y5Zl9/b2/H7/2tqaXC632WwAh1AIAvemUqnkcvnW1lYkEgHVKAYwUvphGCYYDCYSiXA4jPbnH4fPIE06nU6apsfGxkAXClImWYk+n8+bTKbq6ure3t6enh673Q7xIWi/+1JNTU1XV9fIyMjOzk42myU1pbBRAJ+gL713715nZ6fL5Sqt1EjTtMvlamhoGBoaisfjAJkul8tms42Ojk5MTFitVugNLwGWwzAMlM64cuXK6urqysqKz+cbHh5+//33nU7nyZMnvV4vhJTo9Xq5XE4mascHF0QkISp1t8F3gQQz6qEcUD9ZRKxg4W8CVeDwkaGjqHogLj4WiyGEcJrpBxoCcxCQkwqFQiqVikQi24HA//n1r3s8Hp1Ox7FsMpWan58PBoMWi+XU6RrQ5kkkEsj1BeIax3G5XI6iqOXl5UKh0NjYCCFxgE8ikUgmk8GIuVzu5z//ud1u7+jogBh2nEgaJpNOp+fn51977TWlUvnHf/zH7e3tYKHE1ZFAl6hQKIxGo9vthqJImIfifRCLxRB+F4lESp0b8XA8z6vVar1ePzs7Oz09XV9fj7N6krdAr9c3NjYODQ0tLi5euHAhk8kolUrM6GGGLMvabDan0+n3+5PJJFxOYiFCCAIwqqqqeJ7f29sjq3Pgmw5Y4na7a2tr19bWNjY2WlpaMCjiLYX73tDQMDMzA+nLYealjw1N0xsbGzs7O3V1dUqlkqZptVpdKBSGh4dPnz4NG4jFdJLEYjE4yiKECoXCnTt37ty5Mzk5OTAwsLy8vLm5abVaRSKR0WiEYBgQl+FpLA1eJPcTJ7MVaFzxM/mgoHi43f0Q+jg4KgDyh+6nQr9+qsDhI0DkC1bKEbAgCN/n8/mdnR2e5x0OB666gDHjoCHwURor1uB7yBfj9/vn5+dpmna73SaTied5aSwWiUT6+/ubm5vBCx/nvaSKObgpioIStZubm8lksq2tzWQygQ8OCFvAyhmGSaVSAwMDzc3NEokEDHiCBWq12uvXr3Mc98orr8zNzTU0NODSE3j+NE1rtdrGxsa6urr5+XmdTgc8HRMoOT0eD03TW1tb4XCYTGNN9pbNZtVqtcvl6u/vn5ubq62thbK6ZG+QIO348eMzMzOzs7O7u7sURZGhCFg8tVgs9fX1Ozs7iUQCfiKxEBTaDMM4HA61Wp3NZrPZLCLgGctShULB5XK1tLS8//77q6urXq83mUxiGRELVWKxuKWlZWlpCTTApN8KSHuQMYfn+UgkMj097fV6NRoNy7IajUYikYyOjgYCAbC8klp3nij6yPM8hPlDlIvX693Z2VldXZ2amhofH7937x5k6pFKpQ6Ho6ury+v1QoIbwRMI6W9A6Y2LHiMiKS65k0fMG16WSLv7x9SaHE4CHP2VjlWhT5wqcPjIk+AlTyQSCwsLHMdpNBrwh+SIqvH3NT1iSyF8ube3NzMzMzk5SVFUe3s7Lg1BUVRdXZ3f7weNmdlsJj0M8dEekmszDOP3+yELjFQqxWAJzBFMTY2NjWtra0tLSy0tLQLggeGkUqnZbLbZbD6fTyKRFAoFLG1gJqvX61tbW8Vi8fT0tE6nw7Ia7gRa6nQ6u90ejUbxQIKdATNhVVVVW1ub3W4XmLKgMbBsl8tlt9unpqaWlpZOnjxZuqtQ4KK6unp0dBTiAlmWxSlYURHtwN5ZU1MDGeZOnz7NF1Mf4LlJpVKKoqqrq7VaLUAmYCGZOYjjOLlcbrVa0+n0xMQEpLmB/vG0AYxtNpvZbF5bWwuFQhqNBiymWq12/7qG4QAAIABJREFUfHx8aGjI4XDgc0npUwG3AxrAlwaDobGxsaura3l5ORgMxmIxCDXx+/0TExMikaiurq6pqam5ubmhoQES4MHpBB9rQPXNE3UoyQ0/ROQSHAc/Dj2QUFg6pbKXVxDxEaJKRYtHj0rfLpJbbW1t9fb2BoPBmpoak8mELWcCjnZI56Seyu/33717d3Jy0u12X7t2DfgmCAcOh4Nl2YGBAZ7n6+vrASkpIhsAQgjcPTY3N/v7+41GY01NDSAQXczpApeAQq+np0cul9fW1mIYI1WF4GaZSqXm5+efe+45HPiI1wWCkclkQgjd6bkTi8Wam5vxZPBw0Gc2mwVLnlarxTZIUrfGF+PW3W43BFZSxaK+GMtZlpVKpRsbG3fu3Kmpqeno6EilUmCGpIoVfVmWlUgk6XR6bm4un8+3t7fn83ksRMJAsBtisTgUCo2Ojsrl8u7ubig0Qc4KPmQymc3NTZ1Od+zYMchKA8pVmBKI3clk8saNG8Fg0OPxQJAiRVH4AAGzEolEYI6FIFEYAgINFQrF2bNn8d6So/MlEfRAID7KZDKLxeLxeJqamo4dO1ZfX19VVSWXy7PZrN/vHxkZ2djYSCQS2WwW1ACkyRM/ong5PEGCRx3/STZ4INQ5BMAOaX9EKoXACiI+ElSRDh8BOvxdEnCHzc3Nubk5lmVPnDhRX1+PpYGjvPmlA21sbIA05na7sWgIejOpVNra2upyudbX18PhcHV1NSqJVgSbos1mE4lE4+PjZ86cAYFVYBmSy+UdHR1NTU0+nw8i4YBxQ7AjCEkikUin06nV6kQisbS05PF4wEhJ8kfQOnIcl0qndnZ2UDl/Csy1pVLp4uKi1WqVSqUajYbU40E1CYvFolAolv3Ls3NzX//6/4Uvx+IITdNyubyqqkqj0aytraFioEWhUMC9gSbQarXW1NQEg8GdnR2wEVL73YARQlKpFGIbotHo8vIy9qYREGzg1tZWPB7XarWoGNKOiAIUJpOppaVlYmJibW2tq6uL1M3i4bRarcFgWF5eXl9fb2trk8vlSqXy2LFjkPR8e3s7l8vZbDaMT6SoKnjkEBFWjxeuVCqNRqPL5ero6NjZ2RkfH5+dnQ2Hw++88w7HcVKpFJKjgtRosVgKhQLLsuBXjPbDleAmkpuGT0Jl90pAZMuDLiEfy9Ivy7Y8YvsKffbpQGNShT7LJDgyA3Ect7e3t7m5uby8DE4Ne3t7EIFAykZlD92lBNlbNjc3Q6FQQ0NDS0sLyGfgvQKKMqvVeurUqUQiAdhDTgxGBFHJ4XBYLJbJyclIJILKmUKlUmlVVdUTTzwBxZhisRiMRREZAMRiMWTKZhhmZGQESxKlJiWapkU0LZfJ8Zel6eWUSqVCobh37x5UMcRwgucmEon0er3FYqFo6vbt24C7mONTRf0eoGZ9fT2kAwWhENLxYIkHFZ1upFLp1taWQqEAgCHjH+BPh8Nx4sQJhNDk5CTGMNKzBjpMJpN+vx/cWami2pZUMxqNxkuXLul0umAwiMFDwKMlEgnYVre3tzc2NiCS0uv1Pv/880ajcXV1NRQK4QngfQb7H0UQvqG44AnP85lMBiJTFQqF2Wxubm5+7rnn/vAP//BP/uRPvv71rz/55JMajWZ+fv6HP/zhN7/5zX//939/8803p6enwbYK3YJ1kyoh/NgI9uRBEYgvIUGD0kEPp0NaVtDxUaGKdPjoEX57+f2ZtSGxZyaTgcRgkCcav+ek9qksfxQQ+HRkMhmz2Xzs2DGz2QwSAAyKfTXr6upkMtnk5GRzc7PT6UQl3vMURel0Oqj/HggEwCORXAjwEUhUjRCampoym80Gg0HQCUJIJpNpNBoovAABAKVtgGiaTqVSZc/v8KVEIpHL5dPT0z6fD9dKFOi4IP+1WCxmWTaTyYBmEsMhbmwymTwez8LCQjQahQIUdLEQMe6KYRhIWwNCJBBALOnOo1KpLBaLWCxOp9N4h0lOXSgUoOTv2tra7Oysx+NBBF5ioZOiKNCTBwKBWCwGullyPqAfdjgczc3NkEY1l8tJJBKbzeb1egOBACRHJTe2LLsvq6jEeAYZ+Pb29tLpNBk94vV6T548OTY21tvbOzc3d+vWrd7eXqvVWltb29ra2tjYCGGj4GCM41vQJ0dH15E+KFWQ75GmChw+YlR6niX5FEhaer0eXCrIl5PbX8cVn+sPeoEBTRmGgaxdqMhPBcEbBoPBbrffvXu3sbFRr9dD+ASeKrYMOZ1Oh8Oxurq6vb0N2aXxfODfVCoF7oi9vb2nT5/GYew8kXaOYZjq6moIlUulUuD9SEZHYAlGIpX29vb+3u/9nlKlJPcNrxr0chsbGyMjI8888wwEhJCyDsYArVa7u7vb19d37do1vMl8MWsrTdMGg8HhcCwvLwOiALSTu8rzPPSfzWZXVlYgozf+SVAhGSGkUCgAO8kecAONRtPS0jIyMtLb29vW1uZ0OmFctJ8XJxKJVCoVDAY3NzdB50n+CtnampqaGBEzPz8PgZ4IIchvYLFYwuGwVquFrYA7jjenLJbgzkEslkqlyWRydnZ2ZmZmYWEhl8udO3fu3LlzBoNBIpEolcrGxkan03n69GlwWp6fn19ZWRkYGBgZGTGbza2trV1dXW6322KxgEIYD03ebsGSj6iu5PfrSysAViFMFTh8xEjw/pOMUiQSQeCd3W7nOA5CoUmZgBQrcW8HISJFUfF4PJfLud1um81GXoKKkg3kD6utrYXIs87OTqvVisfCYekIoerq6urq6o2NjXA47HA4SLUkEHhgVlVV9fX1AUhA9T6eMDTSNA3mKK1Wy7JsLpcrzX4Ca2QYBlEIcuHwhKEOFUP0eJ43Go0Wi2Vubg7SyIG9sJRF0jRNIXTv3tC1a9fKiptyudxkMjEMs7m52dXVVSqyY09anuej0WgkEoGMbrAuMDRSFMUwjEwmk8lkkBgdtJcUEW4BrkMMw7jdboVCMTY25vP5nE4n/ISXCeMyDCOVShOJBCioS28uTdNWqzUYDL75xpst3haz2Qz9gOkuEAhAElSw/pLrxXE7qByWAOpDroPx8fHFxUXILb64uJjNZru6ukA9wPM8zndz/vx5kEfX1tYWFxeXl5cnJiaGh4edTmdzczMkRzUajThzLI6wLL0X5InnoKca7Qf1Q06EFfpNo4rt8NEj0qQBH/hiuQm1Wl1VVVVdXQ1MBDuC4msFp/tDtEZyuTwUCu3u7oLjAykUYpcN4EpNTU0NDQ0+ny8cDjMMAzEApCaQZVmXy+V0Ond2dlKpFF4FCbFQ7RaEBhLkBJITuL1IJBKwbAkEAgweTz31FM/z3/72t0mQACCEUAcoMvX0009vb2/39PTgWPVSzggr7evri8cT5FikYArlKUZHR6GcBbm9UNADgjKlUilN09jOinvAUX0ymcxoNBYKhfn5+eXlZRKbMQixLGswGEwm08rKysLCAip665DzQQhZLBbIhoPnI/AIhdJRCoVSIpHOzsyCYhzGCgQCy8vLUI6j7A7DWKROAjcDv9Y7d+68/fbbU1NTEonk+vXr3/jGN+x2+/Dw8MrKCs77ii/hOM5gMHR2dn7hC1/4sz/7sz//8z9/6qmnaJoeGRn57ne/+w//8A//9E//9Morr/T19a2treE0BfjJF8wNz+qgZ1twlytYWCFMFTh8JAleaRIqsLyl0Wi0RcKBAdhEd5CWVUAQHrC3twfZWyC+Hv9Kipg0TUPysFwut7W1hRACLxgQkvBVWq3W6XTm83mAQ77EQRGi8p1Op0qlgoRtZZMGgCqYYZjJyQlsy8TLwXYmjUZDU3Rfb9/a2hpfDLSAX0HwAkHzxIkThUJhcHCQ9HwR7InX621v7+BYTiQS2kRxSzArzs7OhkIhXD0KEfo9WZEQQuAUig1+guEMBoNGo1leXp6bmyt7myBOw2g0ZjKZQCCAikpsfH8B9fV6fW1trUQiiUajOBs4SYAcer1OrVFrNBqc95Wm6Ww2m0ql0uk0KQ6SkyklRMAPePrMzMyEw2Gz2dzV1QW5YUUiUSKRgGaQtAjay2QypVKZTqej0WihUKiqqnrhhRf+8i//8vnnn5dIJPF4PBwOT0xM/OhHP/rWt771k5/85O7duwsLC5FIJJVKQRVlcO8ibw25/6VPEXmaFPzEFemQk6KAeIKOeEmFPptUgcNHlQQyIgaPfD6fTCZBRAMi4ZC8HH8ulRchhiGZTCYSidJMb1QxEBA8OzQazcmTJ2tqara2tmKxGDB9geNGJpOxWq16vT6dTsdiMSixW5qyCyoXjo2NRaNRQXoaQDW5XA5KzpXl5ZWVFQEjxpCg0+na29s4noOof8zdIOwEXyWVSk0mE5j9ym4yXGU2m7gDkqEDE5RIJBzHQeUHVDwQwHwg9gMhpNFoQN7a2toCbo6FPyzT5PN5rVbb1NQUi8Wmp6fLclj4Uq1WQ0Ahib74tuZyOblc3tDQIJfLNzc3o9EoJJ4tXZrVaj1//lw0GsXzBFcdm83m9/sh3EWAN+RTh4nfHz6vUqmUSqVKpXI6naAinp6enpqa6uvrg/MQeReA5HK5VquFOcAmQCdPPfXU17/+9atXryqVysHBwZdffvnv//7vv/3tb9+4cWNoaGhhYWFrawsWSNYgK4vTJG7hbRe0xAs5Irbho2EFCx8DqtgOH23C5/dcLgdZS+A9z+Vy6XQa2gj4F8kd0H6fGuAmwJIgsQgENqCi3o+MCYPGkFUEso2sr6+vr6+3tLSgknN3JpPR6/VGoxFcDbHjKFXMEgC+MxKJJJfLDQ4OdnZ2Go1Gsgcc6A01GUKhXUAUnnCnxOvied7b2jp4715fX9+zzz6LrU0URQF0oSL61tXVzc7OQmiEQNWGtyuTzXI8n8lkIHKcXBrMCso45PP5lZWVzs5OyOhGFYMx4INYLNZqtTKZDKQ6jUYDCySPKel0WqVSORyOTCYDekWaprGbDJY1QbvodDohEgZcQHEIJjQTiUSQlTuTyUSjUYFvDiaKotRq9eC9oWw2C+cYsVjscDhSqRSoviHKggdz7P4LBV1xxVrTUqnUYrHQNA1OOjs7OxaLBWJaVldXo9Go0WiE8xYAGD6p4P2HQse3bt2qra398pe/3N7enk6nu7u7l5aWNjY2/H7/wsJCf3+/wWCoqalpampqamqyWq1yuVwul0N6dzIZAiqGReItKhUNSYUH+adgmeQrI/iyQo8BVeDwESPyHMpxHIhZUqlUKpWCXKjX6zs7O8fGxrB1jRSzSHaP/8RfQswcQiifz8/NzS0sLKhUKpxuBjejinpaLHCIRKLq6uq1tTUIhkMlTjoQrqDRaGKxWCaTEVQm4ot6V7VaXVdXt7CwAEUbsGcHaaqkirVzVSoVRvdSzerZs2dffvnle4P3nnnmGUTwrI9KDSMEPZw+fRpUl6lUSqFQ4FRhJMszmYwUhf7H//jb//k//1aACpAjWyqV1tXVgdsIhGdQxeh1vlgvHpJ0ZzIZo9FoNptxTgOSIPkchN9BoAKGQyBQKUOCU71ePz09DSlVBfcUksBJJJLOzs5cLlcalELeUB4hCiGR6KOMd2Kx2OPxSKVSyOuNSsy3ZYlsoFKpxGLx3t5eIBCYmJjY3Ny02+1QEEMqlWItMU6wB9+QAScDAwM3btxwOBwXL16srq6mKEqhULjdbrfbDQ3Gxsbu3LkzPz8PWZNSqVRDQ8OTTz55/Pjx6upqXOEEfI9R8ayAD3ao5EXgixns0P7qH4css0KPH1Xg8BEjvphPGSEE3pXpdDocDq+vryOEGIY5ffp0fX391NTUzs4OaO1KAwEpwrtEcEYGaSCTyfj9/tXV1draWgjWFjACiDEgYQN8SsGPEVv+8AdQuymVyvX1dTKoTkAqlaqhoQEiFBOJhEKhgOAz6IdMjLK7uzs9NdXa2nrQ2VwkEqmUqsXFRb/fD2WVyOXDEuRyeWtr6/T0NFTxBa9OtF8s4Hn+ueeee/PNt8bHx3d2Qna7rfSOABw6HA6ouEveKVRkr2KxGCJMFAoFeDkJxFmAOlBQq9VqmqbBJxO3IQ8fNpvNYDAMDAyAelYwH4qiYBperzeTyZRKOSTl8/l0Os0wH1XUEolEDoej907v7Vu3/+7//juDwXCUuig84QAMltRsNqvRaLxe76VLlyBFzr/+678i4gHGukqBt1c8Hg+FQiqV6tlnn+3s7ISgFBAlcT3kmpoaq9WayWRisdj4+Hh/f7/P5/vOd77z7rvvXrhwoaOjw2q1ggYCUjfk83k4MpbdBwFAHh3zygqLFXp0qQKHnwI99FuERUO6WKg2n88vLi7+53/+59zcHGTgTKVSJpMJREMw+ZDsrDTugid808G5EYIcCoUCRMsBRxY0BgIlJF/0eNzd3V1ZWcEKPfKUDVJOMpn0+Xznzp1DCOEoPcwKC4WCWq222+25XG5qaurChQtGoxGHKJDu/gzDNDY1vvrqq5976imj0UhKoqS+S8SIEIXyhfwhh32KomKx2Orqql6vx/IKRRTngx2gaUoikZb690MDmUwGBRyWl5cXFxdPnDiBBVmMvgzDgLXvm9/8pkQi+eu//mtyDlhMZxjGaDS2tLRsb2/zPK9SqXANRXJQlUrlcrl0Oh0U88J3lrxBIIJPTU3V19eTz4DgJuaLenVSn1woFNKZzM0Pbn75K1/Gt55cctn9RMWnCHZDr9dDuKFYLIaYVJw3FUyeZBQHUC6Xm5mZ8fl8dXV1FosFXKPxzuCCzzBQLBZjGObatWsvvvji0tJSb2/v1NTU3bt3e3p6DAaD2+0+duxYQ0MDuCIDBoNzb+kzgMopSEmtCSo5VpIHrIN2o0KPFlVcaX7dJLBPPNCFpJsAQgjcHMbGxqanp5ubmz0ez717977zne8MDQ1BpVywKZJehSBjkUYmIHxgB42WSCSSSCTAfSjCUiiYM2lxAc/AlZWV7e1tRLiT4HHFYnEikVheXo5GowghHACAh4BLwHF0bm4OBM1UKiXgxfDnlSufy2SzMzMzuBPBdsnl8ovdFxFCInqfrg/kDFRU5yYSiWAwuLS0REazkQI0Qkij0Vgs1kKhUJbvwRlCIpGIRKLV1dXZ2Vl8IV1MMg57q9PpGhoawHnnzp07kKVTMHmKoux2e1tbm1arBXtwWU8oqVTqcrlqampInym8KOgW3Ih+8F8/TCSSWOqFm7j/PlKZdObmzVskMFA0xbIfFc7Eu0FGHAoIgzocgxwOh0gkmp2d3dnZMRqNBoNBrVbDFoH2Ox6P7+3tweTxfADhxsbGgsHgyZMn9Xo9T+RiBd9XcCWFvYUURWAWdTqdL7zwwh/90R997Wtfu3TpkkQiGRwc/I//+I+/+Zu/+Zd/+Zef/vSnk5OTqVSqrLsyfjAgOw+cBUnPIBha4L+KF35QhxV65KgiHT6ShJWl6XQ6FApRxaRchUIBrH2QoBnK7ZZyMSyLCDrEn0ECU6vV+Px+0GuP5TalUmkymeLx+NbWFhRFwm2ARXIcB/UNtra29vb2SJMYT2R/1uv1TU1NS0tLgJoAyeSI8Gc6neZ5DnuslMVpg9FQ+iXphwmibSAQWFxc5IuJZkjhAGBAqVSeO3furbfeLK08hftRqVSw25lMJp1Oq9VqLNbwxahQ6Fkhl1MIYc/SUmEF6sgvLS3Nzs663W6we0HwIj43iEQip9NZXV0NI5ImRqyBhJONWq1Sq1U4KKWMkEchjufIdLIMw4BvUVlpuCwiUvv9hLVabXNzs8/n8/v9Pp/ParXGYjGNRtPV1SWTycbGxsbGxhwOR2dnJ2lFTiaTc3Nzi4uLNputpqYGBEpE5CgX5EnA+nOEkFQq1el0Foulrq6uu7s7lUqFQqHx8fGJiYn5+fmBgQG73Q4Z541Go8Ph8Hg8kJ2O4ziwGeMKHqSKG49LhqWWypGH7EyFHiGqwOGvlR5UIiSJKhYYwgwdXmYwMn344YcURWm12qtXrzY1NWWzWafTCQwRIYQzipEdHoRzhUIBnEghBo6UmUqnhC8xGo2NjY3j4+NbW1sC3w3wVqUoqrW1taamZnV1NRgMQuI3RKhhAU5UKtWpU6disRgUMQY/UkTwGqrosQlJvQVTIjl+vnicxxfyxfJM8CeEosdisfX1dZ7noaYS9p7FzLd4FR0MBiFnGF447h+qNsIBIh6PA6SVbhTMiqKQVCIh1aTkTaFpem9vb3h42OPx4FQ4uVyOYRiAf/hss9kcDgckagfxVHBnYZdyuRyk3SHPAbBLwOJBaTk9PZ1MJiG7KUVRly5deucX73BEIj1y8/n9yQ0Ea4TIyAsXLgQCgdnZ2W9961tOpzORSFRVVV2/fl2hUNy+ffvnP//55z//+cbGRiiwBTclFotNTEwEg8FTp06ZTCbIQSPovBSBEJE4kKIocCuFw1ljY+MTTzwxMzMzMjLi9/snJydHRkZkMpnNZqurq6urq3O73WTlEDi0gQ8XZESCROTkMQh/iV8fgdrmEAG0Qp9xqsDhr48+DhYClbJO4NQQAwAJTUKhkN1uBxYDSjPsjUIyX/JDqWgFEX5ardZms2EWWfqeY4mH53mFQgEJrJeWlkKhEHjWkOflQqHgcDgMBgMUy8VwiGcFrFkqlVZXV0PF4HA4DNEIpUOzLCuVSJPJ5CHbxRYKPM8DX+MJWyAeDoImm5qawO8Rm98wVGA4BBx677336urqBAvnizZXl8u1tLQUiURg57Efo0DVqdFoEEVxB9iPYZ9lMplOp4MkPlhCwoNSFAUHHTjrZDIZMt832adIxMQTiZ/+9I0TJ04IFABYsXnq1KmRkZFoNIpjRkUikdvt5nl+b2+P3+9VhDspI2UWHwkImPF6vdls9oMPPhgbGxscHOzq6uru7gYrJk3T2Ww2kUhgkRf8S3O5HJRCdDqd4BwrsECXJXy/8J+gDwfXJIfDAXVC/H7/4uLi1tZWOBwOhUIffvjhzZs3tVqty+Xyer1NTU1arVapVELRbPLO4tHxS4QV4AJFAtp/TqpIio8cVeDws06kZkbwgkkkEjAf0jR9/Pjx9vb2N95444033gCTTD6fBw89sNmA5YPsoexBGxVfeyiA53Q6ISQAsxuOyBeDIQGMZEqlslAoQGQ0eFGSBJ4ycrl8bm5ufn7+2rVruCv4FyCE4ziVSpXNZn0+XyAQMBqNpXoqhNCxY8fUavV///d/X7x48aCtA5Y6NjYGweA8UcUeFeHQYDA8++yz8/PzWC4UMHo4+LMcS9M0RziL4k3ji5lLm5ubZ2dnl5aWBInFyY3ief7q1au3b9/Cal68q1i2AN/OixcvQuUsm82G77XgvqfTacijRg5HcmSOY0E5ubCw0NDQgJ8lctyurs729vaFhQXs4clxXCaTEYvFNz+4+aUvf8nlcpH7LzhYCJ4ivMMWi+XJJ59samqan58Ph8MNDQ1NTU2wwx0dHSsrKyqViiay0ebzeY7jICctONai/QE25G6TxyPseIybkTU+YbZqtbqtra2lpQUs3KFQaHt7e2FhYXh4uKenZ3Z21mazicVilUrV1dXV1dUFPlxisRjOByAyJhIJCBbCeIkfJJBu8QRKEyNU6JGgChx+pokvxg7jb0hUACnB6XSeOHHi1KlTra2tCwsLs7OzkJUG2CVAAiqJqSCpFBfBB0cikZB1drCqVgCrkISaYRgoh5RIJEg3GTxbcHO32WwMwyQSCeDjIN/gQYGRQWh/KpXCwh9VdOfB49psNo/HsxMKHXIMv3jx4uuvv/6DH/zg/PnzOKhf4O8ql8sbGxt9Pp/P59PpdFg3KyCRSIQoJJfLsWpXIA1QFGUwGORyeTAYBMMbdkQSwJ5YzCBETU1NXb9+HcujHFFNEPww3W737Ows2AXRfgDAUAGyL3Dn0ltZRI5fqoixBZEj0shRFFVbW7u0tETOluO4QoGlaIrUVJP7hocTbD5eCMMwEokEYuQFm2k2mwF+yFKO+Xw+l8tBiSu1Wl16TwU7L9gNQTMBXmJsk8lksLcIoWQyOT4+7vP5MplMPB6fn5+fnp4eHx9/9913PR5PbW2t1+ttaGhACMEBLh6PSySS5ubmY8eOQZg/ILFYLCZTVZRauyuS4qNCFTj8TBNP2E5IzgusEGxyZ86caW1tBa/0Z5999sKFC5FIZGBgQKFQkExB4BbB71fW0cWCSqjIZyFUgyzuQ167XwT5KMZZJpOp1WqGYUgGjZuBcauurq6trU2tVkPCaIBDkkGLRCKpVAqh3IKIN5Ip80VT3yFbB7Hku7u7S0tL4GpEbiNeBcdxq6urmUympqbG5XLx+z1fQC32xRdeGBoagsRp5CjQIeirQb4pFArJZBLU16VoQdM0zyMKodHR0VgsBqUtsNDDFXOrglMoQCNmtYKuQBzP5/MQbiFQhuP2+TwLnZAKXjx5+DKVSmYyGdKTSKfTVVdXr66u4tgGvPmHcHa+mOEMks5gaMTp0yDOASc6x26xIH5BvIdSqcQZAAQr4os5DQT7Tz7nFKHihuWQsZu4DQx04sSJ48ePQwoLMDEODg5OT08PDw8bDIbu7u4XXniBoqgf//jHN2/eTCQSZrP5+vXrFovFbDbDawjOrvCBK6bRF9gaD9quCn3WqAKHvz4SMKP7Ek/YaUgeBNCF+Utzc7NcLodYY3i3+/r6BgYGyjIvzNfwIbqUu4FaNRQKAfc5yoSBH0mlUoVCwRVT25C/4lGsVqvD4eB5PplM4sws3P4k0WKxWKfTJZPJUlmHJJZluWIQArk63ODmzZt+v59HH1n+yrJy2IRcLjc5ORmJREAxSPJc2CutVnvlySf/87/+a3V1tbq6+qB90Gq1JpMJ7kXphH85BwrJZGWiGPHdAd9OUsrhiARjVNGZSCKRgGQjlUqz2SwOM8dnHZVK1dhYPzU5TdrAKMINhPrITycfjUZv3Ljx0ksv4T358le+9M1/+X/LysqHEHkv4EEC1TF0nd8eAAAgAElEQVT8CVW0otHo6uqqRqPBWgS+WPpDINghQiWA8bUsYVsv7BsMBJdg52qe50FmTafTkUgkmUwCgEFMkdFovHz5stfr3dzcHB0dHRoaunnz5tLSUj6fHx0dXVxcjMfjZrO5ubl5b28P/NeCweD6+vr29nY8HlcqlfX19VAN+yAP5Ap9xqkCh79ueiC1CXkqJ3vAKRllMhmc30ECAI5jMpmMRiMkBynbIT4+l1XjQNBVNBqFHFdwCj5IQKQIaxzMIZFIrK2tnTx5El+CyzyB9386nV5fXwfmIhD4UFGOtFqtuBjQQYRVbXh6/H7bWG1trVgsTmfSZREdz1+n09XW1g4PD4NulgzRw8IHyH+oeD7gShKEKpXKVCp17NgxkEoPOUOUjTXEXqxkMwiDg3uKbxYptiKEpqenBwcHn3nmmUQiQRW9Y8jduHT58uKij6IOrJqLEMpmMtG9vfW1dbyf+Xy+vb3d6XQWCr88cPBERiTBoYEntPf4S3zfeZ7HBT0QQnt7e1NTU2azmczgAx2C2RIXvuCLmeJR8XEFEZycPMxKIpHI5XIIPYK0eZAXIhwOZ7NZnueh0gtIdYFA4K233pqenoYjBSqaG1UqVXd397Vr19rb2y0Wy3vvvfeLX/wiGAyqVCqwZ4M2O5/Pb21tLS4u3rp168aNG+Fw2Ol0tre3Q74hKMNZ+qRV6LNPFTj89KkshyKp7E+laiLwl0EIabVai8WCFaqCsbB0eNBkOI6DRNtkRVxyUEF7PAfIGxKNRsF+hhAiHUYgPzW4REYiEUgpAhEdZJ9gQYTqVGQsf1nBLhqLJRIJlUpVdjk1NTX19fVjY2NgjCy7jaDd8ng809PTgD2lKTr5/USq40jZRSaTVVdXx+Nx6lBv+9ra2tq6Or/fX7qrpD6AK4Z+g92L/BUVY2wYhlldXZ2ZmXnmmWf4orMoiV48z7Msy4gZmewjhAZDL07NCo3TmXQ8HueKywEzHtwaen+oHwhbWOaj9qfvIZvhL7HXKPh8gc0YksVAjCa2yOZyuUgksrW1JZFIpFKpTCbLZrOQAxbqY7AsGwqFIG4ELwEVDbeQ9CedTm8WaXt7OxQKgX/sqVOnnnjiCfBLCgQCd+7cuX37NjyNUAITHHTX1tby+fz6+vobb7wxOzsrkUg8Hg94eNE0rdFowJQul8vtdrvX602n0xRFeb3etra2hoYGmAPY3Q96biv0maUKHH76dDgQHsTHUTl7EoTuSSQSs9mcTCahIkHZ4ch/EaFAA063sbGxs7Oj1+uxDCS4HLMhUsSE4/nu7i5wTAEkwJFZKpV2dHQsLi7u7e0B9uCFYA8RCFTAYgEmgQ5TKpXGotH+/v6nn36a3BNySk8//fTw8PCtW7fa2trK7iF402g0GqVSCfCMiDg26Aqr2qBPhmFIJ0YSwxBC6+vrUHq37A2CbXE4HEtLS6W7KrhNIIuQnZMCN5RuwPIN+EyRHpW/VLTy3L1796xWK0QuIkLOA9xKpVL5QgHiTSUSCUhyu7u7EomkUMjjJ5AqRmqSy4E7RT6osVgsEAhkMhm5XA4ohRAaGRkZGhoCL6FMJnP8+PFcLjc+Pp5Kpc6cOaPX6/P5/Orq6t27dwcGBhiGMZlM6XQ6Ho83NTVdvXoVnKF2d3d/8Ytf9PT0wC1LJBLZbBYS+3V3d0P5jp6ent7e3r29PcgDx/P83t5ePp/3er2g7YAqiRaLxev1QraE9fX1SCTidDrNZnMqlXr99dfz+Tx4mYKxM5fLJZNJMGrq9XqNRgORi2fOnPna175G1vOCR/oQk3aFPstUgcPPLpFYdd/Gvzzpp9MURUERXXx8xm1QCRCSw/E8n06naZoOBAKxWAxHrJfOSiAwwU/gWQo5o9F+oQfrA6VS6bFjx+LxeDKZJOUYUqICZR1XzKZWutKPRJBihFnZTUNFhR7LsqOjo4dsHZg8IVlrLpcjs8mQsMEjHpYggHnyfFAoFNbW1hoaGiBztKBsMio65eeyWYqIYyNvDb47dLHoPD6mIEJAxL/K5XJwR4KZw7T3uSlxXC6bfetnP2tvb3e73Vh644vp2vP5PCRbkEjEqVQql8splUqKorLZrFgiTqXSkCsO3xq0P84EvlxbW/P7/SBgbW9vz8zMiMXiEydOnD59GiHEsqzf73/nnXcikQgkRGVZVqlU2mw28AZCCKXTaThIqdVqvV7vcrny+XwsFlOr1dvb2z6fT6/Xy+XytrY2RZESiUQikQBNKbjDgHeM0WgMh8O5XE6r1apUKhB24WwHuR1isVgoFNrd3WUYRq/X2+12u90OyG232202G/j7WCyWxsbGZDJ58+bN0dFRlUql0+lcLpfJZJLJZOA/jN2hcdwqfjtQRTR81KgCh59pOvrrxBHhgGCA2d7e3tnZqa+vF7TkCbMfKhE7QOEGlRnAXR7tV9ORI/L7nXEUCkVDQ4PL5eIOqGUPPFomk4E8IRaLsQMIlkHBQ1WhUCiVSrA2CbKF/VIwBTghviTZEI5lBHZZunwgAC2JRJJKpXw+H67ggREae2SkMxmKpjlCTBQsDbYL/EF4ni8tYoWv4jgeFSv8kduOLX80TSsUColEAmGjqFj7CcIBAZzgxMBxHBTDAtEECvlChSmoiJtMJtPpTCqVmZ+fh/AGnucBkMA8mc1mzWazWCxeWvL7/f5UKoWTczIMEwwGU6kkpBiVy+WQZi+ZTEIdKKjLkUql7t2799Of/jQSiRgMhlwuB6oFtVpts9kAPOrq6k6fPg1pCjiOUyqVXq8XXFegZoXH4/nKV77yhS98AWoXK5VKcDeFZwxWLRaLz5w5c+bMGXhgwGUJp/aGB9Lj8Xg8HkjShotbwS719vbOzs7OzMyEw2FQyMdiMYqi2tra2tvb6+rqXC4XKAkgshM2SqPRvPjii88++yxAr8lkAkFcIChX6DGgChw+YkRqKQVfAoH6Dqo0bG9ve71e/BN5FWbNwLuxSCQWi1OpFE5nc1AlBFJGBKEEQAvqACMivSQ5ParoBJROp0HOgMo7ApFOKpVCHVdRsVhdWe0Tx3Ecz3M8j/34UVHAIttj7w9whUf7w7SxuyNEnp09exaydgn2imXZGlc16M1K9Z9U0dUTtgsXXiZHx8jHsiyPeET0AdIwX8xmgIpWWNH+QhbgJwITBuTLZrNKpTIYDP785z/P5/NOp9NqtZpMJijgkEql4vH4f7/9diaT5TiOZbnBwcGtrS23293U1CQSiaCsVSaTGR+fEIvFwWBwdnY2Go2Gw2GWZauqqhhGtLMTnJkJ+f3+5eVlCLyDysPt7e1QporjuN3dXbVaff78eZZl9Xq9TqfT6XSQ5EWv10PaW4/Hc/36dUjIrlKpjEajWq2G2o1UMYEc6W4DX8IOiIpE7gbIrNAevFJhJpubm6FQKJFIhEKhpaWl1dVVeNhwGgqpVNrQ0OB0Ot1ud319vcPhAN0APO34pIgfFZVKBT4+2Wy2UCiQNRRhXDIehnwkfj2iYUUM/QSpAoePDB2k9kT73fwguwrHceFwOBKJiIpVdeDX0nAuwXsL8hB0COls8IgCOMQtSVlTo9E4nc5oNErqMAVDALoAuwG0gAhC3AwO9YFAYG1traurC7i/gN1wHJfL5zlChhOogjki3yYeVxAijTWKYGTleZ4M1iSEOY5l2VOnTtU3NBgNhkQigbWmmE2D/1EqlTIajSaTidRqwgcAMxDjEOIRQouLi4AKSqWS1EamUqmlpSXw4L9586bVas3n8+CI63a7ZTIZ6BV9Pt/MzMz29vbi4uLY2Bhu8PTTT3/+85+H2sjpdHp3N5wv5DmW4zh2aGiov7//qaeeguCcbDYLfkwej3tgYEAsFmu1Wr1eb7VaOY4Ti8WpVNpsNtfX11+5ckUmk42Ojr7++uvb29vV1dUmkwlkI5qmnU6n0Wg8ceIE2B0RQhDFCII+7CQ4oQAmgaqTvJs8z2NEwXdQcO9QUe0BvkXYAyuXy4EiZGdnZ3p6uq+vb319HdKtQei9wWDQarU6nc5kMjmdTo/HA45aIAWSQl6pFoS8j+DyQ54j8QEI7VfPHOJI9QlSWZ1NhT4OVeDws0v8fidG8j0sPXuS7p0gbyUSiXg8DlYQARyShOU8OIxjpR+wCQyffDGzCR5X0BVEYlEUBXVZQddadl1YMYgQAkeMTCYDXiHgxQ4lcBcXF9Vq9ZUrV3Q6Hfi4AwJBG5ZlL126BAWeyCXglQLnhSkxjAhHLGDexxElhYHUajUo7gR3AXcVi0Zz2axWqwVZRCqVQsouqA2JI7Ln5+c3Nzd1Oh3DMDzPW61Wj8cjFovhgMLz/NTkNMOIR0dHYUs1Go3ZbG5oaHA4HBzHLS8v9/f3Lyws+P3+H/7whzqdDsp1fe5zn3vppZcUCkUsFvP5fO+88874+DhN0zqdjud5MHpVV1cbjUYsviCEKApRFEXRlFgsvnLlSmdnp91uB2QCBBKJRE8++eRPfvLT6prqM2fO4BSv8Xh8Y2PTZDJVVVVBEWCIwIPCFK2trRA2SlEU+JjAEwJLhjgHivDPYhgG2nDF8iZ8MWafKkaPwH0Ejx5QcoLHEA7YSCQSqVQqFovt7u6C8lYqlS4sLAwNDUFZaVDyGwyG5uZmKHnmcDggHwKIngcVAcbvFNxuVHSnwvZjRJS8xldhJ2TQPPPlAnnLqtY/carIiJ8IVeDws0t8kfA3FFGkEO0PbxcQyBOxWKxskTZU7v0BOIT2HBEXj4c+ZDjcp0gkUigUwGQFmlVMoCLji6k+wZOeJtLigKEIMnZC4hLgaGT4Yz6fv3jx4ve///2dnZ1oNAqcDpgvKB5hCSdOnKiurt7dDWcyGYC6fD4PBkvAxXQ6vbKyMjk5mclkdnZ2BgYGIIE4zNNsNgM83O3v/8EPfrC7u9vZ2Xnt6tVAIADpxTs6OpxOZ6FQ2N3dnZ+fHx8f7+npgSR5TqcT7Ftnz5793d/93aqqKrAChnZDmWwGuPPc3NzMzIxWq21paVEqlRaLBRvJwBaYy+VAvlGpVGazGQSUbDZrt9u/8pWvXL58eWZmZnd31+v1dnR0wIVarVYmk8HdNBqN58+f/+9fvE1RFCMWNzQ04AAJgHO4ralUKl/I26xWkKioogMtRVFgxIVvJBKJTqejKMrlcpnN5lgsFovFIB2gWq02GAxKpRLuDi4ZjYiTlsABB4bAOMQVU6mBohisdxRFRSKR5eVlsDhGIpHFxcW1tTUILpTL5XK5fHd3F0IDIdShrq7OZrOp1WqdToez25CEPZgOOq6R3+OTlkALIkC+g94L8v39ZLHqoJe6gogfhypw+Jkmjoh6xi8kPq7yRKV7nGELhC2wG8XjcYjcwh3ioqZYlsJWNOghk8kAFwaNJYYoar9BDgi8GUk9LUwSrCn4zYTjNgZISB0ATAeUaViGAKUZ8HRIuQLXlgbewTIbGxsLhQIoIaEl1GHHm6bX61966aX/53/9r/fef7/7wgVYDsi+PM+Dw9H3v/99sDBBzWG32w3CkN1uP3XqFHgG3b59e3t7CyEqnUotLS2Njo5CMUKz2QzScCAQ8Pv9fr9fq9XCbJ1OJ8S9WCwWWLhWq+V5Xq1WWyyWUChUV1dXU1Nz7tw5mUxmNBotFgtMu6amJp1OLy4uBgKB9vb28+fPQ/lcqKML0qTJZGIYJh6Pb29v7+7uOhyOlpYWRFRp5ouR7y0tLe+8+y6PeEYkglMF5uO4JdwOvii4Y1Mrj375gMG+QbQ7xI8GAgEoKLi+vu71ej/3uc+1tLRAiCd+ZlDRm0kQJINK4AFU6Ht7e8lkErT0MzMzfX19fr9/b28PxD44bBkMhvr6ervdDhnhwRMK8gGB/w7uE55qgSEZi3Glb1bpc06V1LEil4CIbN2H5wuk9lfA+P/Ze+84ua76bPzc6W2n7s7sbO+9SKu2K62asWQbbAzGgMEYsOmQAD8IIT+TECC8hIQ3CUkABxLTQrFxk3CR1bAkSytpVVar7b3Ozu70Xu7M3PP+8dUcnb0zO1qtZFsy83w+lmfvnHvuuefeOc/59htEVk36BiFLh7cu0qp0EJWPimcGI5+J2zcpbU83oze8tJ0MFj5YwU0mE+j66HUT9tQ4WWyd1NgDN1FwN/B6vRDmBYXUYd0kSzDolKanp+12u1qtDoVCi4uLoByDhQy8Ou12+9TUlN/vdzgcZ8+erayshMVdIpFAwSmO4wKBQCwW+9CHPuTxeE6dOjU/P+9wOGD1r6+vhwyuAoHg8OHDP/zhD4VCodvlevnll202m0KhKC8vb2trKygogCGFw2HI0UVCI2A2iLpMIBDcc/fdXq9ncnJSKBIqFArwzjcajSA7chynUCjq6+vz8vLcbncoFGpsbIQqRQKBADyDYDVXq9USiaS0tNRms5lMpqKiIvrpgKQlFosLCgqAV8B0ByZD0owY3kA+83q9wWAQfCyJClqQLAiciMeFAgFikDAZdEi/J7ToBt/CwyWaTIFAQLZQQGxAiijp7Gq1Wvv6+sD7Zmpqqri42Gg0An/Dy0NLUcQXVCKRRKNRh8PBcZxarfZ6vd3d3f39/VDKEeypQ0NDZ86cicViZWVl4B+Un5/f1NRUXV2t1WpVKpVCoSA2V/IDIblD03IPicyhKTAzyO8F9luCZCYB+JXRPJraITmXDO/GGTHLhW8csnR4S4O2VdAGjNQflYCKYZfL5eDgB/UooAHLsnTgBOE5CBwmqz+wWkNDQ19fH5Tgwck8kGAO5DgOsniAxyAswcTBz+Vy+f1+juMWFxdBe+l0Or1eL0R0RSKR6enpY8eOjYyMSCSSgwcPjo2NWSwWv9+/e/funTt3gratt7f38OHDCwsLkUjkN7/5DVQhKCkpqampEYvFQC1OpxNjDA4jgUDA4/H4fL5YLAb1NIjcXFJSUltbOz4+DoIFrNFEvAax7O6777bb7WNjY2KxePPmzVBzA4xMGo0GCKCtrW3Dhg3f+MY3JGLJunXrGhoawMlQr9eDdAKpbZxO5x//+Ee73d7S0gJ6RfKAyBoql8vBlQa4n2iAwYwKwwaS9vl8kUgEclvTBZ5gQYc7AtMa0f2C+pEOGGUYhhEwCCHBCgsxUY0Swx6TdJQF2ZF0RSxkMHuQlsXpdELWveeffx7C59va2u68886WlhbQTpNhQ1AjhHaEQqHh4eEzZ854PB4Qr0+fPj0zM1NZWQn1IpRKZXNzM0TK5+fnGwwGlUqVk5MDqmDYQqFkEA4t5/HSvnPLszLBLmH1XEiQSCQglhFMxRA3CZ44PDeutNNLsDbd6eopMKsvvRFk6fDWBfxoiW4TLTdFoCT5ccn8meSXCWsoTvqAwPYfYsVAkUgUYlwyBQxs22EpBItdPB4HblOr1UA/kKqGpMgCHgVvvdLSUrVaHQ6Hh4aGLl68CIsFGKLm5uYcDgfUN0cIBQIBl8sFqs6FhQXoFlS7RNEHFQ8g8A6cYzmOA+mNLPRisRj+NBqNZrMZSJpJunWA/JRIJCoqKj76sY99+1vfUqvVe/bsIc6QZNHUaDQbNmxwOp0Oh0OtVm/evJnWtiGEgKJgF7L3rr0XL14sKyujAxlpdVwikRgZGVlaWgIL3xUlJMbg7gtcIpFIhEIRQhgYjqMynBHXHljWIRkKrcBESbmNSWYYgLymLMuS8fAXxOVGL7oZTRUajebSpUvWxcXCggJahcA7BaYOvlUoFFVVVVDG8tixY6dPn/b5fC6XSyQSQcoYsN7BXEEmUuB4yHw9PDzc398fCATgCZaWlm7fvr2lpaW2ttZgMMBD5Lm90EZHmvbITnEl+YyembWxBQRazMzM2O12MLuKRCIIzNfr9QaDgRdmuhIIca6et7Li4JuGLB3e6qDXMnr9whhD0BjQAPFhCQQCNpvNYrEEAoH5+fne3l6IxV5cXIRFFnKvoCQrQNqqhYUFr9cLdjtIBn3u3DmdTgeOiEKh0OFwdHd3nzp1CsxjZrPZYDCYTCYQEw0Gg1qtZll2aWlpZGTE6/VijCsqKsCBpaKiAjJ9yGSy/Px88MiHGuXNzc0QvFVSUqLX6wUCQTQabW1tve+++86fPy8Wi5ubm8vKygQCQV5eHiw9sBgVFxcnEolf//rXc3NzX/rSl8CTHiF0Jdd2cu0TCoXxWEwgFIIsmzbNDSQ9dzgc4LsIdEh2HsQayjAMgxiVUiWkainTCdtAjgRrFpPMbE6ro0lwJ+/5ErGGLNZSqTQ/P18qlYbDYb1eT8I/iEcusbaCZxChw7SawCufmWX+U3CDxAjNQIaEZL0tuHuiUSdaeoVCwVAlk0CGKy0tzcvLgwB8s9nMsmxvb++JEyeIOhFkesgOCk7Ccrm8srKyra0NdBgGgwH+NZlMoCGAnEqw1WCWV5gis03+zGC3S6Uc+keUdqOQ2hhuX6fTdXd3P/nkkyqVCiy1sL9paGjYu3cv0GFakqMnnD6+GkbMcuGbiSwd3k6g1wIo6u12u/1+P0II/AM9Hk8oFBIIBB6PRyqV2u32gwcPWiyWiYmJ4eFhCCaDnFUomRWFYRi1Wl1SUmIymQTJDCyQiTuRSLjdblAQFRUVrV+/XqlUOhwOnU6Xn59fUFBQUFAArivguK/Vat/znveYzebDhw+XlJTcf//9IpEIdIbE1RBK5Ljdbp1OV19fD+omuCmy3hUXF2/cuHFpaUkikezZs6eiooLMAMiOQDkIoenp6cnJSbPZDLIUQkgikcB6yiWTWYtEIqFAALUP004prM4QOBgIBMiF6FABGJhQJATFIyzrYrGYEBWdpRoy1YGxk2avqwrM5QMgx8myDgwtEAji8TjMMEpqtjHl00jTIRgdwWq4TE5ikldBy1xzMQUQfTra20GCR0nZkWhlBckSxGBaJhZKeBZ5eXmtra2QCzQnJ2dsbGx6enpkZATUyCipd1UqlW1tbTt37qyoqDAajUajkdRkTiRrMDHJohyQ+QXGwCQrCxJVJ2g+BEnQrwfvl8IDuV+yM0i7R6FB5gF8u+bn5zs7O/fu3VtYWHju3LkXXnghGo22t7fn5eUR59i0/aQVuDMjy4VvMrJ0eDuB/Ggho1h/f//Q0ND4+HgoFELJeuIgJoJlJRAIjIyMxGIxs9lcVFQEawFYPnAyhk8sFhcWFra3t9fV1TEMQ0SNffv2YYxramrAuV+hULS2tu7evZsMAHKACQQC4rlDPiiVypqaGp1OB6LAVRpgGDB3kVqvAHrjD7tst9s9MTEBzpmIUkhCMxLyDLZDr9drMBhoBSY9VwzDMIIVvephQYxGow0NDaDkhOM8zRt8bqhvqKqsghkmUQqkPdyIRCLR6XRQKnZFqYVBaGW5BJZ+lUoVCoVIqhRuebJQMm90Rp60I0/EwTUGMUnmIGIKiH1XqAghjnJUjsVi8XgMcp8SNSBEE/p8PkiQ7XK5XC4XvFHBYFChUFgslqNHj05MTDgcjpKSkvr6+tLSUqlUGolERkZGFhcXDQZDWVlZSUmJQqFIJBILCwsSiQTci9LOFZO0BYK2mdw1pvIo8dpfk0JoeTdVd5pqBRRQhTtyc3Obmpr27t1bW1ubm5vLsuz09DRo9VEyT40gmVoo7aXTfs4w1OtlxLWpgrMAZOnwlkbqjxMEApZlVSpVRUWFQqEoLi6G1P4gOqhUKpKJGOQh3vpI3EQRQjKZTKvVggYMJWMhwKkdSqSCnU8kEmk0GpT8wQMfpJa8F4vFkJ0LXOFTk48wSQsZCGHhcBjWOPA2JGs9CGoghsLKEolEiGxH1jKMMUh1r7/++nve8x7eYHjiUWZEIpHKykqv15uqSaPhdDqj0ShkoUu75MEmAxLH8I7z+swwKOKpQV+FJxTyeibLeur6rlAooE0sFqO1dmSVRwglOA7sx3AKPOVINBoKhULhMJGSwf4H+UsnJyfPnTs3MjICWXhcLtfCwoLb7Y7H4/X19Wazubi4uKioKD8/X6PRhEKhrq6u8+fPezyel156CcaQn5/f0NBQVlZGkoYD9ZKgGpw0byPqHcZUUHzapT8DH9A7JPqXxft90VNN/8txHJS52L59O8Mwbrd7cnJyaWkJiqnxHvQ1x7BKXBcjZrnwBpGlw1sUZMVH6Zwg5HJ5VVVVbW0t3QzAMAz43UWj0UgkAnk90PKFkrQH5xqezEGyMoLQSX8LYQMZhg1cFQqF4FzaOkI+QN4ZUO2SfGY8wi4pKWlrawN3fJSMOySXID3DMkQ7kpAbvMoQiD97KGUFRFTGUXIQU8UroEN/wD86OtrR0ZF6LXLvkUjE6/XyKgCTxZ25MiwGMcxKlCgSiRQKhVarraurA5coYkKDBrQFlKhGYfCpQnBHR8cvf/nLKBsFnTORC6ElcSiNx+PBUNButwPtsSzr9XrdbvfI8PD83BxEsg4PD3d1dVmt1qNHj+bk5MTjcZlMVlNTAzuw4uJi8P6FaiqQTQ2updVqP/GJTzz22GMOhwMcSru6ul599VWISPngBz94xx13QHZTjuMg7oXeHiGEILSGYRjIIIqTif0yWA3TgnBqKhGSx5RKP9AsHo8vLCwsLS2dPHnS7/ezLDs7O+t0OsHKgKjKX2l/tmvGKrWsWS68cWTp8BYC+RURkqM3yEwSsNSC5Yb2LBUm6wFBmLlMJoPcjNA57XpAAy4HEfdAnJDsCpLCkCTFUKsBpVCvcHmxXFCd+f1+p9MJ4RlgbaKXLRIO4XQ6UwtuIIQSiQTEp8/OzgKt0kRF7mJgYODs2bNoeRQ/Sh+vmWaSybVgZiB6kjQDOxBRwELnIpFIKpPSM0msa+QIZLeRy+Wk0C4tjl9djhHC3NVQTrgKMdGBVbK6utpisYAuNDWMHQBaRPIt7xFjjM+ePetwObd3dhYWFNBJ0ej5YaPRRCLBRtmFhQWMMbiqvvLqqza7fWpqamFhYW5uzmazRaNRmUxWVFQklUoLCws7OjpaW1tzc3OVSiXsV+BOIQSFFAaBmQwGgy3lTE8AACAASURBVOCDumXLlvLy8o0bN54/f/7MmTNOp/OFF17o7e1taGioq6szmUy8UHqv1zs+Pg6VnoqKimhjLZN0ccLXGV2w+sa0YhZy483Nzb322msgCldWVu7evbutrY3YXIlaNe1v7UaQuoFL+1UWN4IsHd4qIK94qsCXCkJ+abRwyd8hb+Oc2fuOVCZikumyIPSCSRpaAISSEUXPdFdwIlQ5J9V9U/fgJEIAjvAUX8DN9A3yOBg+QFISopZM24YHchd0S9ANklvO0IlAIBAKMokjsBTCvNGPhq+aS1naeDMZjUYtFsvi4iJOljdKe0c4GfmgUqlAp03nlYXBuFwujuOmZ2bm5+f1ej1tpQMZDh4WQmhxcXFubi4YDCKEIpHI4OAgg5BAIIBKgXl5eeBZCmRWWVkJnUB6vNTbIfcO7AUJS+FBFxcX5+fnb9my5WMf+9jQ0NDx48f7+/vHxsa6urp27tzZ2dkJdaMSiYTdbj9x4sSzzz7r8/lqa2urqqp27NjR2toKm8I1UM71EidJqBQMBvv7+8fHxyORSFlZWV5eXjgcrqioaGlpKSoqorUXN50IU5HlvzcIWTq8JZBqDQLQywqv/Uq/OpzMGsNb9NNel+6f5H0GGYIsXiDfMMtjBtJ6psClgVSIDyR9U1f5YPkY+MIKy3q9Xq/XS8iJJ1/CWaBQPXnyJE+qToerzMS7OjAuyEOgJORSUntfbZwUROh5S70omTH6osvOQggtfzq8vb/H4xkbG7t8+XJTUxNP/ianoGQWcnDe8fl8SqUScpwSWS0Wi4nFIozx9PTMqa6unTt2aDQaELXj8Tg4xQSDwTNnz0YiEYvFMjw8HIvFoN6kSqEIRyJ5eXkNDQ1yuVyhUKhUKnBzhXK7IPcTeYjsmUAmJmMmSdroKQX/IJFItH79+urqaijw63K55HL50tKSTqfT6XRWq/XYsWMDAwMSiaS2tlaj0YyOjmo0msrKSlL0kZ60VZJEZk0mfRx0yHDE7XZ3d3dPTU3pdDpIKw9JycHJGSc9XZkVkrplcVsgS4dvPXhyIQ+pjHhNKwJKrg6C5fkyeHYRvNxlQEClIwFlnVQqBU0dHWyQYd0hyyKQKImVJtxAXw4ns16lAs7lOA5kF7RyxRyMMEbLZi/tLgFC6FaaOjjo8/kgvQvN+rw2UqlMq9GmHQmiFGuQGI+ebT7hLT+RfrKEOAOBgNvt1mg0EOhCtycjFIvFarXabDY3NzdDejMydRD4AVImxhghzLLs6OgoOGHJZLILFy4cP35cp9N1dnYuLS0lEgkBw0A4uVQqBePlSy+/bDAYKioq1Go1ZJGF65JYi1RTGbM81TtOmirTzhjDMBDJXlRU1NTUBObkQCAAr43FYjl9+rREInnooYfq6uqsVuuRI0dGRkZmZmZKSkpS6RBdi4Q4KgHvSj8iYp6ApwCUD7lth4aGOI5rbm4uKSnR6XS8nungjQxjyOJWRpYObxXwSDFVhEr7mXcuopZUXqwbrzH52dNmJ/gXQrvAhAN1i8BaSZudUpW0dOdQ945ePdHylCuwHhFRjDAH9CaVSlUqlVgsDofDUDB2JU1vKBjCGMcT6WkVwHEcMBW9GvLaMAzjcrkg1xq5kdRZRQi1tLSklXRJe9hJgMTAuwRKx8dkYskIIZEbyE96vT4UCkHqV5zMk0csqZAUDQgYXEugw1AoBNnPfT7fa8ePYcwhxMRibG9v7+DgIES/WK3WxcXFmpqaYDCoVCoTiXhpecUdd9wB1AuE2nX6tFany83NJUngoH/wYQECIPbO1LmlNyiYsqiBFoHmVCZZgEmtVkMsI0LI5XJNT0+XlJQ0NjaWl5dXVVW53e4XXnhhbGwMSjSj5WHyKz3ctE8z7WjpNvDTgKn2+XxLS0tLS0sGg2HHjh0krIJ0wqQkh8uS4u2ILB3eKki7Y02rXaTBO2Ullkq9RIYNMlQPrqurc7lcUCyC7MTTLnbkCFG0kizPHFUTlaz7KOktQvJwMsm0I8JkLXiJRAJSDs/DhcbAwMCFCxcQQgq5IpPEzKQhId60wPpLO5fyLgr+lpf7++7ee1fq6bwJAb0ZWv44yLfJZRczTBo1KRHQYT8Bc0JmCbYUQC0cx0EKb6fTCdlNYdcyNzc3Ojoaj8cNBoNIJIrHE8lbEObn58P0Qv7PnJwcMDeWlZUdOXqkoKCgqKiIyHanz5xxu90GvV6pVKY6TOHlGW0yvKKCZD4dTPlzEl6kd4Hw5oAPDkIoFouFQiGHwzEzM6PValmWDYfDYOCEzOlMMgKVN9srPeW0G5QM7cln2JYBW0N1SV6ztJvCLG47ZOnwlgPvd7v6beZqzqJ1lUReYdIZPDZs2DAzMxMKhYLBoFqt5u2d08o6YKyCbTXQIfgikrzSpKVIJAIDFfwpSGbDESTLwMJnUiGdd49wdXAA0el0kBxgpdtn0LIUX0Q4ptuDYczpdBLvHt4SD9GERmPeSkEd5DPHcaFQKJXn6LExwNDL29APhWVZqINhs9lIQh9aBAFNstvttlgs/f39Tz75pNFohLiUsbGxwcFBnU63adOm0tLSRHI/oVQqN2/aBHcK9A/dzs3NDQ4OJhIJjDDUBIbBjI2OxuNxUneQN04yRamZAeg/yYnM8vwvoNdN64FCJgEyFtlstuPHj4+OjoZCoaGhIbvdDiZGyPtDn0g/hWv+atJqCHifmaSBlmVZsVhcVVXFsqzVai0rK6P3eTyQFywrIN52yNLhWw+e6IBWIRRes8NrfkVvqHm6SvhQUFAgl8vtdjvJW3ZNEA8OtVoNxhWcDOkjma5QUsoRLa83xFA2J4yx1+u12+0YYyIroJRYkeLiYpCH0mZfI8AIcctnFSdTsYCFTyQSBYNBKJXMLS+AQEMgEBTkF1zsuUg0dWj56g8roFgsLikpIZLcspEkhwFuJ3wTIqVPZlk2EAhAXQsyWqjsaLVap6ambDZbJBKx2Wx9fX02m81ms5WWlsLuIRaLqdVqqBWsVCorKioGBgerq6q2dnRoNBpIBxMOh4GNOI7T6/UHDr6KEJJKJDhZ1AIh9K577z156lQkGsXLIwdwEmkD4emdB308Lf3QHaaSmSCZ7s7n84nFYr/fD95VkF2WaOBXI5kxy/UiqQNLff/pBmKxOD8/v6Ojw+VygXV5JfkvKxfe1sjS4S2Bm8KIqzwl7U4fQPJ9CAQCqDJhs9nA8z7tukMvZBhjiUQC+j1Qu0F277TjIftu+ggxfXEcNz8/39fXBzVdUVLpCgRGLmcymdatW3fhwgUi06C06uIk2fP0cuSKAoFgaGior68PMoqBWo8MBlP+sbFYzO/zpxpcSUvwbdm8eTOiUn2SBiT0EFOGzESybjNpBg2mp6c9Hg/DMBMTExDYPjs7Ozg4CO7+VqsVvG1FIlF7e/vmzZtzc3P1ej14poDfI4xze+f2waFhUu0LFneS+UUgEDhdrv7+foZhMF5WKSLg9weDQUgWkFbmS8uFaY+nBaZ0p/RxMmmgJy8sLNy1a1dFRYXT6Tx37pzFYnE4HENDQxCxSjMTLbOudNG0hLfSmHHSWK7X65VKZVlZGcuysMlIFQ2zRPg2QJYObxUwKRrL65UO1yZN0owI4hGU0ItGo3K5nM7dxdNl8QCcBL1B4jeWZXl5REk/INWl7Qf8a5xO58zMTF1dHSnVxFuAGIaZmpo6e/YspAin9/g8gJ2JjcVWaiAQCGw228zMTGFhIdFMwle89sFQsKm5iVmuaiZzCFEHMpls/fr1sJQzlG4WegCdcDwW4zguFo/BnyDrhMNhv9/PMExOTg4UEsIYLyws7N+/Hx6H2+12u90SiWTbtm0ikSgUCi0tLQWDwT179jzyyCM4mfGAp8CEsl+xGAuZbKHsFIjFxNArlcpYlkXo6hOJRqPf/ofveDweqVSSehepOlLeXGXmpJUeBPmKftM0Gk1FRUVjYyPkN4A05R6PB9ySo9HoSikIUnG9vyyYIoi2TE1JuMrbyeI2QpYObyGk1dtc85Qb/CnSCzrt/CmRSDZv3pw2dRmi3AVT+2EYJpaOe8ifIpFIr9dHIhE65wu5X6JZhXK4aUsyAegYDN5KR8/eCy+8kJOT09HeTpMcLZARkyei1JUA+nMgGDzx+uuPffxR2s2VeFdijMELFyIceJ6WZG6hhGEkEuE4bn5uXiQUKZVKp9PZ398/NzcHuWdjsZjb7fZ6vYWFhVCpA7ptamoi5QDFYvHU1NRTTz116tQpjuPEYrHdbod4edp3KakTZu7Y/Q5EZRGDUYH7q1Ag4DgOJoNMkc/nm5+fB9GQ+MJwK1eZp5F520S3SQXGV+2X8Cb4/f7Z2dnq6mqZTOb1ep1OZ01NTWlpKUSmBoNBKC62Uh0J0i3vz9X8vpgUP2oAyTdEt0wrQGdxeyFLh7cc3uQfEi2V0g6EAoGgvr4eEqMgagVZaU2kCQmSvNDOhCipLQSroVarJVmq0fJbpvPjkKLnaYNG6uvrW1tbh4aG6E5SNbout8vjcVutVijODuBRGrA+WdHSeklIxOI733GnkrJlwuXAqgeCNXChz+fT6/VkJGDzA3kxGo36fD6OwxyHFxcXA4EAxrivr+/EiRMjIyM+n08qlZrNZgg3LCoquv/++++9916yIwFTIoRe5ObmQkEPEFwg+wEp2oUxhqcAzkk11dWI2sQQaRskdXWOyuP1ktuHgEUuwSGE2OVpeq4pga0B9P4P9kDAbUql0mAwcBw3OTlZWlqam5vrdruVSmVJSUkoFHrttdeg2vCmTZtIYWdeh2T3RsZPt1kNrzOUpZm8/xzHpao9aJ1BFrcpsnR42+PGf4GpelqUXJj8fn84HIbPmZN3w3oEyjpQsaYKdjjpWQMx/rxYZhrAMaST1OHB0iOTyYA7yY3wLocxfvd97x4YHKRXRroZx3Hg3A/Vi+jMAHRMG1D7utZWqEFP2JRkkRYKhVAAGchPqVSCgEvMhD6fb2pqyu122x32sfExhmGCweDY2NjAwMD09LTT6QRf0Obm5ubmZoTQ0aNHbTZbTU1NIBDQaDRwUeIRChOu1+sJU6rVakiUSu4RrK0QqgipwMmOgRZ6NBrN7t137Nv/AnjqgkAWjUbf9773xVhWKpEQ55rVi4bX9U7SDxeiLeG42Wy+88475+bmLBbL/v37wfV39+7dLS0t4+Pjvb29CoXC5XKdO3du8+bN9F6H3oFl0LWsnr3oGQO5cKVyVKu/6yxuQWTp8G2L69LepH4LAQMul0un0wWDQZJfhl5VebICFLKAYvHABKmXgAVFKpXq9XqdTkc8R1KZDLbhGcbp8/nGx8ehNtBKN2W1Wn/8kx/XVFXX1taiFFrFGIOJFBK1YCpRDvAxPYZQKNR1umvDhg3GPGPqvQP5CQSCWCwGEf1+v39paWlqaqqnp+fixYuBQKC0tLSysnJgcMDn98uk0mAwmJube8cddxgMBrPZLJfLY7GYQqEwmUxOp7Ovry8SiTQ0NDgcjlR9eDgc9ng8ELouEomi0Si44NJDYhiGjbFHjh5lGAGX9A6lAz1JnKhcLkeIaWluAQb1+Xxer7ejvR1uPxKJkMTZGUArDFfPNMBYdGOSLLCwsPCuu+46f/78gQMHLly4wDBMTU3N3r17N27cKJPJ2traEEKHDh26dOkSlD0h+UV52yYyvNWMJ+19kZwDzPKcO1m8zZClw7ctUu0Z1wWxWKxSqaLR6OzsrNfrhUpMqcsBvZaBBKNSqaAqLFquQSUpuTmOA2EFJQMTeV0RbV5OTg5opYCMecvQ2NiY0+F85JFH0jrsAPr6+jweb0FBIcmalpZ6wX+HhEvCtUjdXSgw+eJLL/7+97//zne+I5PKwD8FJc1Icrk8EAgMDQ2B/NfX17ewsDAxMTE/P2+z2VwuF8uyubm5Op0uLy9PqVTiJQ5hVFhYqFQqJRKJXq/Py8uTyWSQ+xti8IHmw+GwXC5nkqWsyFoPOmeO43JzcwsKCmKxGMjutNSCMU7EE6FwWCAQrLSAw0tyua9v08aNd999NzwdkUi0sLBgtVqbm5tJVlJ4IplJMa2aITMyECfsmaqqqrZu3VpUVMRxXHl5eWNjo9FoZBhGqVTOzs4GAgGtVgtPLTVfPL1ruUEOu+ZuIIu3AbJ0mEV6SKVSyFg2NTVlt9uNRmMikYAlmLQhQgbIfGBTAXmFJzwxyRBynCyeDjt6SBgNbXh0KBKJDAaDXC4nHqq8DsFmpjfoM9yFRCoBSZPYgXjjh0A9v98PjELSW8MtwEji8TjLsna7PcFx8Vg8GAxCmmzAxMTEgQMHenp6EEJQWeLkyZNQIFCpVBqNxnXr1pWUlOTm5spkMrlcLpFKxsbHEjhRXVOda8gF/gOeo9PagYRttVrLy8uBDgmXQwIacDc1m80VFRWpYjS5U7FYxCTz5KWlBJfLNTo6cvddd4FnDcZYLBbPzc319PS0tLQQ7xtSHIo8o7S9XS/r8HQDtPkWLHalpaWFhYVQLEwsFsvlcmAmGKTD4SgrKwMdMt0JoUC6fvINDjWLtz2ydJhFeoAtMDc3d3p62uFwEKNOasADcZsUi8U+n89qtUJdBZ7tkEn6SoDTB7EjwreYCgAn675arVapVCs5lx48eBBjHI/FM0kkGGGEolGW0DavJRA8ONNXVFRoNBqUVKIihIAg3W630+kUi8UI41cOvFJTXWO1Wm02G/B0KBSanp6ORqPl5eUajaawsNBoNMIN5ubmFhUV6XQ62iQmlUkxxohDOaocshXgAWoICwQCiUQCriVEMgPuBNqORCIikQhyBvF6IPSZiCcYhlGrNWSeSQPA6ydPMsnEcjAbTqczEAjk5OTodDq1Wk1Ec/Jc0grZ1wXyIOhtU6r4znNsJiOHOJyBgQGv1wsbGrrBSjx944rTLN7eyNLh2xk3oryCc4uLiy9duuRwOJjlHvz0Lp5QmkQigRBprVbLC0InIIGM8C/s64mlkKy2KOlxs1I/CKGpqSmoaJFhmQOJx2DQR6NR8O0kKlCyFguSJQNramrA8AnDCAaDMzMzoOocGhrq6uoCY6Qxzzg1NTUwMODxeFQqVXl5+a5duxobGwsLCycnJxmGWbdunVwul0gkUBdJIBCAGRJuLRgKYozD0XDS8/NKBnNaC+33++12u0QiMRqNoVAIOIkwByQ3iEajkUgE9KuEM0i9Q/KM2Gh0+/btBWYzSsmhA3M+OzsrEAj0Oj18m0gkZmdnE4nE+vXrCwoKiNWQaJvJruJ6Xy360hkeGf0tSsq1iApWicViw8PDXV1dLpcLfLIQlb4gw3iyLJhFZmTp8G2O67Ug0usUxthkMkkkksnJSZvNBgmgARylfkTJhUYgEEAdnE2bNqEVVjpSYpdl2VgsluofD4AwDHAXTLuKYYylkqt1NshBXmO/348wvu+++0gEAh1biRCC4Pfh4WGXyzU8PAyCYDAY9Hq9s7Ozvb294XC4s7PTbrd5vV6GYTRqjdFo1Gg0W7duBcLLy8srKipSq9WBQODUqVOBQOAd73iHWq2mzXi0iAPi7PrW9ZAMmnifkuh4jLHb7Z6YmKiqqpJIJJAllX4uQOfz8/Pz8/OQhpuX/oaWutQ56r137uHJYaSfKxzDMDt27IDj0WjUbrd7vd49e/YQzSRK5pWlR4KpfD2rB4/tMoBsy8hF4d94PD47O3vp0iW73Q7iLIS16PX6zM7PaxgqypLonxOydPhngetSbYHQAAo6tVotkUiGh4eHh4cJHdKaLoQQ2PkikQjDMIuLi9PT0x0dHSsNAwQaXkgiDwzDsCyr0WhAdZl2hFfKA+GrxRTJyMnwwuHwM888gzHm5UcliMfj4Md/6NChhYWFX//61/F43Ol0JhIJyMjjdrtVKhXLshs3bXJ7PDab7a677yowF2g0GpPJRIc9BIPBxcVFm81mtVohrQ9dmJ6+tf3792OMP/6xj4N5jMfosEtwOp2jo6OFhYUIIYVCwTAMSIEMw0DqH6/XOzAwMDw8vG3bNpCAuWRtB8IiIEhxmCOSJT0YYOt4PB6PxyorK/Ly8jDG4XDY5/MFg0G73Q4eOrTMytM3rpknMm/RyPh5l6DVvGq1ury8XK1WMwxjNBrB24g4994sAssS4Z8bsnT4Nge9l4cPmX/kZDMO7VUqldFovHTp0tDQ0K5du9L2gJOReQihYDAIBWbhKy5ZzhBOgXD1cDgMciH9Fd0trINQhzbtHV3xHGEQZMGmFbykWTweP3jw4PT0NELI6XTa7XbCUhBm7vf7HQ7H5OSk1WodHh4GLo/FYoFAoLCwcOfOnZAiDmjDZrc5HI7W1tbWllaNRkO8PWH9BV9QhmHUanUoFIrFYiRfGsl9CvwUCAQu9V7KNeTW1daBdEXSqhFXVafTOT8/zzCMVqtFFD1gjOPxONgOw+Hw3Nycx+MBZSaEhdBiIszt6dNdbpdrJRkOnGYj4Uh9XT2MEHYAbrdbKpWSSD7em8OTPlcP3gaI7g0t32PRB3lkDBO+fv366upqhmGgUrFCoQD5OzWZXxZZrB5ZOvyzwzUlRSZpYGNZVqlU1tbWnjx5cmRkxGKxFBYWEvKjpRCEkFgsBmHCbDbn5eWR3ojfKYg4GGO/309C2WARR5Q0ABY+SAVOrFkggBIzG7SMhMIKpaK9vT0SiQiTIMsoZLaEMczOzsbj8Wg0GgwG3W435BYIh8OgFI1EIhhjo9EIFZHUanVpaWlTU5Nef8VndXFx8Uc/+hEo5UDpStStZCYDgcDo6KjX662rq6NjErhk2m5oOTQ85HQ6CwoKotEolFkWJGtaERqwWq2Tk5MNDQ0NDQ0IIahkBPwKNkgwcIbDYSi/R88z/RwFAoHX65VIJJAGncwn2ZpAFM3AQH9BQUE8HlepVBKJxO1222y2uro6qI8BrwF5JcgbsgYuRCvsyWj5OK04yDsuk8mKiorozlmWhTeEF3SYRRbXhSwdZrEMvFVJIpEUFxebTCZIF1lYWMhR9RwQtTKKxeL5+Xmn02k2m41GI/mWthUB/9nt9ng8zvOHpJN8AlfRNYTB75GMCmPcc7FndHT0ww8/jDEGaiF2OEiHDcl04BIOh2N2dnZ4eNhmsyUSCRB9oGZeOBxeWFiQSCSNjY3bt29fv349LLUcx4XDYRABFQqFwaBnEGKjLJ2RBEyhMEter3dubi4YDJrN5lS2IEeUCiWmSlugZKoXWkNos9ksFktFRUV9fT2iCJXme7/f7/F4tFotBOTRalKCSCRy7NixjvYOlUrFs7DiZAy+z+dj0JUsQlBAcWxsLBAI1NXV0VGGN0KEqwdPECQMSg8DzKskPQJ8myHwNIssVo8sHWaxIsCPQy6XV1ZWWq1WiD0gGT5ptSoE4Hd3d58+fbquro5Ihzzdl1wuD4VC8/PzCoVCp9NFIhEwv5EcYAghoVAIyVxIdScippCBsSxrsVgwwoyAsVqtUF/Q5/M5HA6r1epyuaC8cCAQABEjEAgEg0GBQFBdXd3a2lpeXg6ZUcFO9sQTT0il0nvuuae1tZWMHILr4XMikYhEIgijbdu20fIHkWKj0SgUaFxcXISoRJQUbngstbS0hDGGVKUoHbuAH43L5aqvry8vL4dJI2QplUrh89zc3OTkZFVVFUTKE0qg3T59Pl8gEOBRL7nQFesmQhjjcCiUSCQsFsuRI0eOHTum0WgqKyvp1+AGXiKElst5ZDCpwl+q4pQ3RTiZPpQuRJVFFjcL2Vfqzw6r2d3T1j6VSlVZWQmiQzxZWp1epAQCAZSTHRgYmJyc3LlzJ9HgpSIUCkEqTshSTXujkA6Xlpamp6e3bNmSk5MDWlliE4KKEIFAYGlpCWNkt9uHhoaGhobArjY1NfWnP/1pfn5+165du3fvZlkWYyRXyFtaWqqqqnJycnJyclQqlVKpBAnP5/MtLCz87ne/0+v1mzZtMhqNRPJgku4ewIU7d+6qqandsGFDqksOx3Eej2dpaSkQCEDOUpLQjkkphPT8C88jjN/7nvfyIg4JAYBmWCaT6XQ6ItXRnjJg+4RnYTQa9Xp9OBwmowJt6lWDMceFwiGOqrOIkjsYULeGIxHMcUKhyG63z8zMnDp1ymaz1dbWFhQU3EQpkEnnO0OTHD0PvI0CT31KUsOTxEBZZHGzkKXDtzMy+O9lBlmD5HK5XC7Pz8/v6enp7++vq6srKSlBSRmRNI7H4x6PJxAI5OXlVVZWQsl1knySo4pggMVOKBTm5OTQ+bJphEIhn88H2s5YLObz+cC5A+yOkGD62LFjGKP5ufnBwcGpqalEIlFQUABiTWNjY319fW5uLohin/vc5xobG2UyGcSo0cuoTCZzuVxarXbz5s20kY80AHKKRqMlJSXV1dUSiYQX1YAQikajU1NTo6OjCKHS0tK8vDwiimEqtwAgGAjK5YpHHnkELTfikmbxeNxkMm3durWqqgrIlTwOMFuCvVOlUm3fvr2qqioYDNIul2iZClcsk8m2bNlCIu6hTSAQgOmNRCIOh0Mul+v0umPHjoE3aUtLS0tLC/ivru3lSQtm5aBAWs1AuJBYiHmNYRIyRKNmkcWakaXDPy9c7xoH7fV6PcQ+z87OAh3S7g8IIZZll5aWEEK1tbVVVVVisTgUCgEpMsl8m6RDhUIBUeqwooGHCJOsSeTz+ex2eygUCgQC4XBYJpOFQiHQDU5PT9vtdshMFglHEMZ5xrz6hvr6+nqTydTe3l5VVcVxXCgUcjqdbre7v78fI6zT6QoLC4maETKugc8qx3ELCwsGg2Hz5s3hcDgajfJ8WYVCYSAQ+PWvf93V1XX//fc/9NBDUqmUFyUCDikzMzNyubygoAAyasJXZIkn1MgwzNatWyHUhFdIEjgsHo8XFRXl5eXp9Xq3202GQWjY7/dDXvXdu3dLpVKr1Zqbmws7DCbp7ApuMvv2vRAJh+OxOMuykUgkHotFWRaCKGw2G1SLjMdifp9/fGxsUQ2DBAAAIABJREFU3mKJRqN33XXXtm3bQGMMomra0g1rwyrfvbRqZPIKpTrLrORxk0UW14ssHb5tkUE9tcrTyQ4dknMGg8Gpqany8nKtVgulCmOxGFj1IDwgPz+/sbExPz9fJBJBUk3iXQmXnpqaOnDgwOLiIpSwJ1VehUIhKGOJ/S8YDPb19T333HM5OTk+n296enp4eHhxcTE/P7+8vBw8PBHCBoNh06ZNJpMJ4iMRQiKRCOTOUCh0+vRphDHGy9gL5FSO48AdEVKgmc1mtVqdVuBgWVahUOTl5eXk5BA5BlgHWArCKoxGo0wmM5lMYrEY+gQ3WkL5KBnk19bWRsezM1RFPXB+sdvtpaWlWq32wIEDiARpMIxAKGQYJh6LQfVgsViMEcIcJ5VKiSsNjFAml588cWJ0dIRhmB/+27/JZfJEIg6ax3g83tjUpFCpIJGeOicnwSXkcvnGjRs5jmtoaDCbzUSR+2ayC5Mxg1Lag2lNkhmQof+b0j6L2x1ZOnx74qZwIaz4oDxUKpVisdhisfT19TU0NAAdRqNRaADK0uLi4tbWVijbRCfdJiwilUq3bt3a3t5eWVlJRDGv1zs1NXXs2LGuri6fzycUCj0eD1QvWlhYqKysNJlMBQUF69atQwgVFhaazeZYLNZ16pRGo73vvvtyc3N5Ih0J+LPbbMXFxVVV1aFQCCVzm4GgBim2Qe0mFoshAw6xwBHtItRczM/PTyQSROwDKo1Go6DhDIVCWq0W3HNUKhVk1IRrges/XNFut3/ve9+bmpr+8Y9/vLi4WFxc/Mwzz4RCISIjMoiJxWKzc7MIIZFQqNfr7Q4HeWYMgtL0Vz4zzFUBip5kZrnNDf7QaDVKpZJLJBBCoVAII2SxWGKxmE6nMxqNn/v8FyoqK2DAer2eNmq++QpJ8pbylKs8CyJKcbdZ/SVWSXJX7a/Zor5/NsjS4dsHa7YUrtQb6VClUrW0tGCMbTbb5cuXIR4OUcsluFaqVCqDwSCVSiORyBUqRQyHOSiflEgknE7nonWxuKTYZrNBwheHw3H48OGzZ89C7VmIYVer1evWrWtqatq2bVtjYyPJQ8ZxnM/n8/l8fr9fKBDuvesuqNkLaka4BEIIOEylUrW1baipqQZZCmgCCtfF4/FIJAJFprRabW1tLYxfLBZLJBJw5Y/FYtFoFHLE6PV6iUSSk5MDDBoOh6enpxcXF4VCoYBh2Fjs6NGji4uLuYbc9o52OC4Wi8UisUgMLpCiRCLxi1/8YmZmBiHk9Xp//vOfL59s5sp/6ArXxeMJu93R2toyPj4eCobKy8tlMhlG2O/3LywsYIQRZhiECwsLP/LRj7LRKAItokAgFomkUunl3t4Tx0+Y8k1jo6MlpWWf+dzn4NagPMjZs2e7u7sFAgH4965bvy4/P592QCUg83YT36sMgH0DfWQlKlrDq77Knm8Ksvrb2xRZOry9cXMpMG3/GGO1Wt3R0SGXy59++unR0VGIUiCZzzDGoVAoGo3CcYxxMBj0+/1QDiIQCExPTcXjCYxw76Xeo4eOPPSRD4E3B8uyoVDI6/VWVlbW19eXlZWdO3fu2LFj5eXlDz74YFtbW25urkgk8nq9LpcrEomAehNuWSQS5RnznE4nCJSgt3Q6HD6fHyEM1W4feN8D0Wh0YmICyk7JpFJGIIDMOBzHiYTCM2fO9Pf3S6XSvLw8o9F4/tw5y4IlP998zz33YI4LhcMY45MnT1osFrFYDLmrEUaIQUNDQywbxRghkkEc40XrYl9fH7pSRQOmj/f/q/MK/zMYDFKpDGMsEgpZlrXZbOTL/HzTZz77WavVal1Y2NLeLhQK3W63xWIZHR2VSqWYw8FgoKi4uKSkBJK0SaVSiKf0er3xREKlVqtUKsgkIBaLoTaIUqlMJBKlpaVOpxOi+E0mE5TxAp9V8NwhWc6BDt/M2PZUd9MMjHi9as+0B1dDtzdyrazG9TZClg6zSAPiYAkiF8hGVVVVlZWVvb29vb29mzZtUiqVsFyCkSwvLw/kQr/fD84vCoVicGBw//P7rFYrsQxptNpEIgG+oz6fD2Os0+n0er1KpYJSt+Xl5Xl5eX6/32azQVSfxWJZWlqCGEGNRrO0uDQ6Mupxe5YWl0wmUzgcFjACDnPdZ84eO3YMpEyEEMawBuFlyxPDz+gG/166dIkoHy8zlw8fOnR1XSbdISSVyhKJBIc5gUCwpb29qLDI5/NdvHAxFAwJRcJ4PC6Tydo2tIHdlCRJEQlFfX19I6MjYrHE6/UihMz55tZ1rSKRqKmxSavTgtkvEolc7r3MYQ68Os1mM8xMQ0MDKDBnZmYuX74sFApra2uNRiNEd/T29ra2tlZWVkIGuIsXL05OToZCIYjB2LFrF9TlyM/PFwqFWq1WLBY7nc7+/v68vLyWlpaysjLaUkjn/SHqgbdEW8isnNeU91WWabK4WcjS4e0NYpa76T2TlRFjDElhNBrNjh07HA7Hyy+/XFlZGQqFIM/1/uf3LSwsJBKJ5tYWr9f7yksvjwyNXLrUKxaLo9EIZBbFGEOOUXDLBP2nTqtjY2w8Hvd6vQ6HA5wtqyqrRGKRxWKJRCKW+fnLvX0erwchNDU+6XK7JBIJC8XtMP7DU08/9funrtw7xleNSsBhFA/CB4ZBCCOxRCwRSxCDwqEwscbt2r0715CLmGXREUKBYN++ffF4HCOEMNq0aeNDH/oQpCeNRqMk23VlZSXLsqAgzcnJMRgMOp1OLpeD6AxOnh1bO+x2eyAQOPDKgeHhkQ8//GGVSgV5BnJyclwu18TExOLiolgihlgRmUw2NTV19OjRtra2xsZGGKTb7X799ddBu1tdXR0MBru7uw8dOvTAAw98+MMfBjH62WefvXjxYl1d3ac+9anm5maLxXL27NmBgQFIe11fX5+Xlzc6OupyucrKyurq6sAQizEGdTSdRZaXUfbNB3Otgk035RJvXOdZ3HbI0uHbARm20jcCQbIYL0IIcptVV1c3NTWdO3cOITQ6MjozPW2Ztxx85VVof/xPx9RqNWQKxQhFEwmSZRshOIYCfv9Tv30KYw6OE4cUTOpOMIgEXVxRNFE+JNFoFMEShnFOTk7r+nVXgjQ4LBQJEUJisbi/r29xcVGQLJa0YeMGgyEXrIASiXjHjh0arVYgEPzXT54IhkP1dXUCofChhx4CEQ1sbAghiPmTSCSzs7MymSwWjxv0Bq1WC6GHkG50cHDw+PHjbrd78+bNJpNpfHx8fHy8trZWr9cTBx+v1wv+Rz6fz2QydXZ2ghxsNBqLi4sLCgoQQuFw2GKxLCws6HQ6rVZrNpv9fv/Jkyd7enosFgvHcbDtcDgcEonEkIRWqzUYDBaL5bXXXoMUazKZ7PLlyz6fLzc3t7CwUCwWm0wms9k8Pj4+ODhos9m6u7uNRqNWq+3o6Ghra8vPz4doCph88i7xXoA3gZZWwkoXBUH+Bt/5DHf0Bv2gsrjFkX3qb0/cRB90uoISy7JWq9XpdBYXF//q57/c99wL6Xuj/3+1y2XciBBCmMkvMOt0WliOrQtWt9uNEEaIYQRMfX29QCgQicRQqEin05WUlpw/dy7KsgijmZkZjUb9ve//Y15enkKhwBiHw2EwSTqdTq/HwwgEsVgsHo+Db6pIJIK4fiZZGsJutysUCoQQxKRrNJqCgoKioiKlUhmNRgcHBxcWFsDqZjQa1Wq13W53Op2QJhTS7ly4cOHxxx93uVzf/OY3d+7ceeTIkVOnTimVysLCwo6Ojvr6+lAo1NPTc/78+YmJCa1We8cdd1RVVVmt1vn5eb/fHwwG5XK5Wq1eXFycmJgwGo07duxobGzU6/Uej+fo0aPd3d3gkRSPxxOJBFSVqq+vb2xsNJlMCKHx8fHjx48vLi6OjY2Nj48XFRWZzeaamprOzk7IwR2PxwOBgMViGRkZmZ6e9vv9IpGopqampaUlPz9fpVKBbxFKMh9dHgtldO98a3G9ytI1OFpf7y8ow7Wu6/Qs3kJkpcO3J27iz4+4jwJplZWVlZWVBYPBltbWyfEJhVIJayhGOBQMVdVU1Tc0BIPBeDyeSMQ5DkNkXveZs4FAQCwWJ+JxiVS6fkNbTk4OxriouAgKKbAs6/P5LPPzwJ85OTkFhQVQvgf8Iefm5qampopKil0ul1Kp1Ol1ly72XDh/4f733A8RgVKp1OfzjY+PLy4ulpeXFxUVzczMTE5OBoPB0tLS2tra2tpajPGlS5cmJiai0ahcLtdqtSqVymaz9fT0SKXS0tJShFBtba3D4Thw4MD4+DiEhYBHz/Dw8NGjR8vLy7dv365Wq10uV19fX35+PiQXVavV9957b3Fx8ZEjR1588cWenp5NmzbZ7faenh6tVrtnz57169cbDAZw74zFYufOnTt48KDf78/JySkqKqqpqamtrSVlNHQ63YMPPrh9+3ZIQTc7O+vxeIxG4+7du6EmMDyRqqqqqqqqmZmZS5cuWa1WjUZTV1dXW1sLNM+yrEAg0Gq1Wq22vr4+HA7DzoYUuCcJg8jzpd2JU2MYeF+9hbgR6W0Ng7/B+33LpyuLVSJLh1kgtLpfLENV70MIde7o3LZ9G8TVsSwbCASmpqYGBweXbEttbW1FRUUgTuXm5s7OzhqMuXfetaempsbhcECymOaW5vr6+mg0Go/H3W731NSU1Wo1FxRUVFQ4nc6hoaHoVLSpqQliDEKh0Pj4+Ojo6Pz8fDgcrqysbF3XWltbW15RDp6lDMN4PJ6RkZEDBw7Mzc099thjVVVV4IrpdDovX748Ozu7c+fOWCx24sSJy5cvY4wrKioaGhpqa2uLi4uVSuXp06f3799/8eLFu+++OxKJTE9PQ+K36upqqVTKsmxJScm6deuWlpb27dvn9XrD4bBOp+vs7GxpaYFMPRKJpKioqLm5ORAIDA0NPfnkk2KxuLCwsK2tbdeuXZCOPB6P6/X6mpqajo4OoVAYCoVkMhmY8SorKyGaExCLxeRyeWtra3NzM8uykA0gJyeHcCFRYut0une+852QJyEQCBCRjhR/AKOgTCYDjTHLsiRTHS3/MVR2usxkc0uF4hHHn8zNrnfAa2bcrKfP7YssHWZx3QCfFxAKIVAPQiwgXVkikaivrzcYDCaTCSLW+/r6JiYmNm3aVFxcjJJpuGG5h7XM6/VCLYUHHnhg165dLMteuHDBZrOBfq+trS0SiXg8HrvdXlJSUlFRkZubazQaJRJJPB4Hp1Or1Xr+/Pnh4eFwOFxfX19cXJyTk7N9+/bCwsKurq4TJ068+OKLR48eRQiFw+H8/PwdO3Zs3rzZbDYjhBiGgdBDhND09PQvfvGLnJycioqK5ubmjRs3Qq5UhmHWrVvX0NDQ09Nz7tw5hUKh1+urq6vXr19PqgmCO+iuXbtqamomJibm5uZkMllJSUlxcTHJVA4mOrPZ/K53vWv37t2Q+lUul4OhEYJAoA1kAoJsNbxoB5DhQMkpEonUajVEUkqlUkKoOFlbmLj5kAuBoRGKYBBXLJ4seE0yeMvjB+gR0kO9iQN7Q82TWdyCyNoOs7huYIwh4B0nk5CBIDI4OHj06FGHw9Hc3FxXV6fX6xOJxMjIyJEjR8Lh8MMPP7xx40a/33/q1Kne3l6xWKzX6/1+P4g+oMTr6OjYtGlTMBg8f/58V1fXhQsXJBLJzp07zWZzd3e33W6/55579u7dC6FyCwsLJ0+e7O3tnZmZWVpaCofDBoOhra2tvb29qampsLAQRruwsACVp3p6esRicXt7e2dnZ3NzM9AYQgjoIRqNRqPR+fn5qakpuVze3NxcUlJCHEygcDwUoweWikajUASKTt0CIZigAoUgP7vdjhDS6XR06hwwXpIYSthSoGQ9itQs4TzQFZUzPCOi+SQtcbIkJFouC64Ua7+axeEtXPFTWZCHG7d6vuWsn8WbiSwdZsHHakxEREMFSWFgQfd4POfPn79w4cLU1FQ4HIbIudnZWZfLtXPnzne/+93gSDk/P//yyy9DLaFgMJhIJPLz8+++++49e/aUlpbCGh0Oh0dGRs6cOTMwMGC322UyWUtLS1tbW1VVVUFBAcY4GAxKJBKpVNrT0/P8888vLCzU1NS0trY2NDSACRAGCerBSCSyuLg4MzMjlUobGhoKCgpisVgsFiPx+9AeZFnIcQP520jFXdqZCOQtyBRKovRIoB58BrMcEelYlgVJGjw5IdcrqQMFEw4hnuDdCoIdnRSGZ9ijqxDDsEGspAsB0j4yQMBEoCRKbzLmtAR8u9BhhnGmWkCzyGIlZOkwizRYvfEDUpnAChuLxSDE+/Dhw5cuXQoGgwqFoqKiYv369Vu2bKmrq4OI70AgMDw8PDAwYLFYwHhmMplaWloaGxtVKhV0G41GocZhLBaDGrZqtVqpVNLMBCIapFIDVxqZTEYUgIjKvErsZ2i5qIQoAZd377yATp5HCW9OaOLJMJ80sfGsdEyyGAVK1jCiLwSqUSKUp1Y4opk47RGaSnknpq3LSI8tM95apiEPcaUGWTrMYvXI0mEW6cFbaNIuK0S8gDShEolEIpF4PJ5Lly4NDg4GAgG5XF5TU9PU1ETi8K64oWIcDAYhVZher9doNCDTED0hsCwoJ4HhQJ4jcYFkAJCDFEQxWs0I5AGBCkQVSbJ7p62lDv2Q0hA82uAxIl3EEZiMrgwMgxcIBNcsHAhDIq6eKJ3qEieLEhNJLrOmFFH8l1nvmrnZ7UKHaIWh3oIhIlncysjSYRbpQRZKWqrgUQL5CjiJaOqg4AOYqUBoI6st7dkPSzyt3KPJjFjIaHUfs3IKTZqxcNLThEkCIbSSWwpPoiL0wDueKkRmaEBrJq9pCETLMx6gdMs3mRCGQoZu6WeXuXEG0faai8OtQDMrMSI9tlthnFnc+sjSYRbpQbiBLJfMckd8oo5DlBqQzvuclgJR0i0FJCc4CwpF0dIVXcCdMCJavr4TyQwscyAF0uHkNO2BxY5Y5lCyBiFa7lSCUuiBx0NwcCWGI1VqM0jVqZIffTxV+8dTgfLmgW5Gf8vTkWZg0MwcnPY2V2r/VuG2oO0sbn282fXMsrhdAKsnb/1dSSVFQMuUGdbZ1K54BEMv37TQltoVUC8QIe9bHluk7TNthysNmFBj6rd0m7RfpfIiWjlCgFwoVeJJ2w/vIP2Bx4s3BdeUTd9k3FKDyeL2RVY6zGJF0IIRWoGiUkUrTHlaouUrMk/Kof/MzEDwJ4kcv+byt5J6k/c5tau0I8FJfxNyZKUx0NIhcVHJMOBUCRul7CSuuZlYSaqjn1RaEs3QVYZl4ZblnpX2am/+SLK4TZENw88iE1IrsqKUdYdWzaXKcyQegAbdLINXCFnEicS5ytUtLYswSQsiuSjdJoM4y6Q4Xq4kqtJlQHjXzQD6unTPGU7ktUx7p/TnVc7bNWf4VmYX8lLxjmSRxSqRpcMsroEM+j2eIo6nrCPCXGo/tOIxlREJ+fFOzCBNXnMRJFfM7L2ZOmzSZ+omIO1d85BBLuQNO7OeJpX8Vr/WZ2hJLsr7sNJm4tbH7TLOLG5BZOkwixVxTd3aSmdlEFwQJTvS4KkKeYSX2TkTsBLPIYp7MmsOMysVeWRM90mUw6kbgutanVN7oMd/c7F6Js4STBZ/JsjSYRbXB5rtMohHmaUiQh5MMoqO1wA+pBXU0ir0mGTG6rQN4E9wt6Gtobw2JE7/mjNAjyTtRddGIWvbf9BtbuS6aS+U5cIs/nyQdaXJYo1YwxLMc8zBy6MX0HKjI7p+6Wo1A1tJcs0s0a50IZ6SlmZHtIKoSl8ug46XJt2V2qQ2WMMtZG6QpcMs/nyQpcMs3iTQkQNp/S15XIjWSod0DdvVaFlXg7QCJUpnQaSxeqPdKm9zleLjjewhbrCfLLK4fZGNO8zizUCqsfCNvhyJeXhDwSRxzYOpJ9KNV3mtVY4qdXqvOedZ5lszeDubLG5fZOnw9kDaBe4tGckbjTXwRGoPaz73ugx1K119Ddcl56555BmAuVWt1wwFlLyRlXYVq/fEeduDYRg2yqJ07se3Dsg7cINt3t54Q+iQjbKrfC3oB3DLvkk8rG2cN3h3DMPMzcyeOn6y+/TZM6dOB4PBN2g7/0b8JGhDGr3U8hrQbUBNSvKo0S2J0jXDirx6UuF1AmedOHb86OEjx/70pyOHDjudTt6AGYY5133uT0f/lKrnvK6Hwhtk2s/EHpmh52trUBnksNtffH7fknVxNQMjl/vvHz0xOjyy0kXPdp0+cvDQSgMgcLvdRw8duV1+3WvDH1/447ce/5Zl3rI2RmRZlktc3XZgjP0+P28jcoPaDkbAzM3MvvzCH70eT4Y24yNjr+x/KRwK3ci1bhzLfpVvIkm/IduZwweP/se//lihUIjEIpaNxWMxsVjMIARV3IRCoVgs+srXv7yurRUhtLiweLm3v7ikqL6x7qaP5KaA47BAwCCELpzvyclR1dRWk68yrFNDA0MD/YMajVoqk23p2ExXf10Dpien/uV7P2AEDEKIw1xhYeF7P/C+IwcO1zbU7bln7430DBjsH1ywWJpamvLN5hvvjSBVjwQzNj013X3mrFQmk0ml23Z0qtVqtHwyL13skcnkdQ1XXwlI8kKyw5zpOiOWiMUikc/n37FrB0IIc5gRMMTbM8bGMMLdZ7oNBn1DUyNK97BS+WxxcfHJn/73mdOngY8xxkKB8AMffqigoODlF1/6q6//dZ4xDyH05b/44uDAUHNL83f/8btyheImzhg9S2OjYxPjEw2NDSWlJas5JcO3XSde/z9/9/dCgeCrf/v4rjvfsZoxPPHD/zx29E8/+cX/GHINaRt86qOP9fde/u1zT1dUVa7UyaFXD/3z//m+3+srKCw0mU3f+8E/6g3pe7utMT01/Y2/+kZhUeE///s/r+H0y5cu/93X/zYSjWo0GpZlJRJJx7b27jPdS9bFusb6B97/wMbNm7Q6beZd0TXx/FPP/OpnT6o1mse/+/f1jQ1p2/z0P36y75nnTfmm7/zgH0vKrv3WvXHgOK7r9S6jyVhTV/OmXVT4rW9966Z3WlFZrlarn336eZvN7na6P/XZx9553z1tG9bv2N2p0Wq6Tp5xuzxbOzvKyktZlv30xz535NUjs9Oz99x7900fyY0D4ytc+Iennvv2331XqVQ2tTT+9VceHxoc7ti6ZaW3839/9Zv/+vFPF62Lr7z4yqEDhw4fOFRUUlRcUryGqzMMMzY8+oN/+Kf1G9s+8dlPrtuwfvvunTlq9Y//7T/n52bLK8thrb8R9PVe/soXvnTq+OuGvLzG5qa1dZJ2OeYdxBgLBIJ9z73wnW/+w9Tk1GD/4O9/8/s//P4PhlxDXUMdmczus92f/PgnGxob6hvr9z2/71c//1VTS5NSqSS97X9+37//yw+3dm4Ti0XffPxvA4FAU3OTWCK+Ktb8189OnTwlVygunDv/yosvu5yu2rqatPlxAHBW76Xezzz6yZnpmQ986IOf/tznOnd03vOud1ZXV//o3//z2J9es1gW3vf+B6EiY45affy1Y3ab/YH3vw+KON5cMAwzOzP76EcePXnipEgo3Ny+5QY7NJnNfT099iVbeUVF8/p1GVrCHL70wv59f3jme//6g6KS4rSr8Pzs3M9/+rMYG8s3m1vXr0vbJhqJfvIjj8Vj8f/7H//y/DPP2Zds733/+1K3Pmvw6c2MzK7FbwS0Om1Ta9PL+1+2Ldk2btl4vaeb8k01dTUXz1/o7xsIh8Pf/IdvPvjQ+0vKSnfs2vH6ayd++8v/7Tpxcu89d8nl8hthRJM5/8zJLo/LvX7ThpKy0rRtjCbjoZdf9Xq8O++8w2gyru1CNwi4x33P7v/+d74fDUe2797+pl365itL4Wbuvf+dD37wAS7Bbe1s//BHH2rfunnnHds3bdn46Cc/+tyLTxeXFMXjMYSQRCLp6GzXaDQPfOC9N30kNwUMw8Ri8S//xdf+/V9//JWvffHzf/kZvz9wrvvCc8+8MDkxlfaU3//2qWeffu6f/uX7//XkE79/7ncPPfzBhQXr1778td6e3jVcHSH0P0/8LBQOve+hB82FBTV1tWXlZbvesWvL1vZIJCIU3oQnmG8219bXlldWbNux7cZ7WwnwYixYLD//2c8f/+bjTz3/9O+e/f13/+m7Ab//23/7LduSDZqdO9v96Y9/6gMPfeCB9z+AEKqpqT7x2vG/+crXUXI2Dh44+ORP/+f/++uvdGzraF2/7jvf+4fnnn72R//2n6TBD/7xn21Ltr/40l+uW7/u81/8wgc//NDY8Mi5s+cyDAwhdPHCxc998tPRaPSb3/nWo5/8RGVVZUtra21d3d577v6nf/0BwzASqnJhaWkJQkgul79xC67eoO/Y1iGTSQuLCm+8N4lEYsjNRQiJJeLMLRmGWZi3/Pbnv2xZv66qtgatQCqD/QORcFQgEHS9fmqlNfqFZ56LRCKb2jdt29H5v8/87m+/8/eFRYWD/YP/9aMneFyIriXdrgFvGhfCyGvraguKCk4ePzk8OLyG0zds2vDVv/krjHFRUdH2nduFQuGWji3bd+345VO/bt/aMTo69oVPfZ5LcDdyU3qDQaPVIoTSFvsEFBQVKlUqhNBNWVjWAHiXEonEH373DMJIrrz5qpcMuPn3TLTntfU1mMNciuZXp9c+9umPR6Ms/Pnlr33xuVf+sPOOHSt1mNlo/ybYJP73l789133hy1/9iwcefA9CSCIWl5aVaLQasTjNWzU+NvGjf/sxF+fKK8oRQnqD/vNf/Hx9Yx3HcZMTk2u4+oXu8yPDw1qdhqdluve97w4Gg16Pjz64Bk8QzOE8Y95//uwnP/3V/xQWFd0UTf1KXvtul+vh9z9stVqbW5rh4H3veffuO++Ix+Mv7X8RIcSy7Df//28yCO2564oGuKGp8eGPPjw2MnrwlVcRQgsWy7/+079EItHX2iz4AAAgAElEQVS6+npo0NzaIpFI/rhv/+jIKEJocGDwxX1/7NzeSerubt+1Y+877zrx2vFUSyRK/vwmJyY/8+gnYiz74Afev33nDt4ttG3YsOfuuzC+usJGo6xwTUEgqwTHcSqV6vv/9/sHXzv0nvdde6e4mucei8Wu2QwaPPXr3yS4xEc+8WiGng8fOCiXySQSyfDg4PTUdNqu9j+/TygUfuBDH0QIVVVX3XPvPQih/37iZ386fHT1d7GGH/hNdEdajccQudZX/+arDMP84me/uK5LkNOhThkUjiZXlEqlf/13f4MQGhoc9Cw3+13vzGCMYyzLcRxCK57IRtl4PL5az483wJ0KZuPUiVOL1kVGwCD0pjo8vyFbALilUDDEcRyXXIPo+aqpq25sqkcIYQ77vFcWdFiI0wZRgW0ZPvt9/kgkQk6Ba0WjUfoUr8dLXimCDA8sw1cet+fZZ/YhhDZuaoMjWp32l7/57+f2P5V2226ZtyQSCbvd/sxTz9LHOY6DMu7X+w4xAsbj8Vzq6T3fvUy+KSoueuSxj8nkVzR1AX8AZfSqwBh7PV6ovc7rPx6L+3zLaNXr8cZisbTjWWk7D90GAgGobghPk+cqabc5vB5vIp747yd+Rk4RMAglM2sffvWQdWGhoalx4+aN5BItrS2xWOyp3z6FEPrjvheDwVBZRXluXi70oFAo7nrX3ZFI5A+/fxohFAmHI5HIyy+9TIssS4tLwWCQLojB81X56U+eiMViOeqchz/6EZTOyrilvV0mk7HslT0cg5CAKuiY+Tmu9G2G4Aewsns9XhghuFGsoZ8028cMAwUnSZYdGhwUCkVFJcVohTdqZGhYIpE89MjDarUaI3T00OHUa4VD4Vg8IRKJ6Fer9+KlC93ntVptJBwJBoOp5SHTDikSjsDPn3drGGOvN80vfZVYzeYAJgR4KHUqeD2Y8k3FpcXhcHht3MBxHMIYpWRdkEqlDMNIJVLyvvl9vtTxZPC1IePhuATHJdL6MVwdM7xOON1Xy9szDBOPxz3u9JOT6RIrNeAwQqj7zLnXj53c3L6JYcBO9ebhjU3SxnEcqenKMMy5sxeikUjnzm1FxVeIxOfzfeIjnzYXmB/7zMfXb7hqgXj+6ecddqdYLM5Rq5Qq1cGXDo6Njj3+7ce37dj691//ltVqfewzj955952MgFmYX/jRD38yMzXzic8+dsee3QihGBv7wie/KJJIPvOFT9Y31B4+eFQkEt31zr0KhRwu2nXqzMXzl/KMeV6vt6mpYWtne4Zn+fJLB71eP2IYoVDYd3ngdNeZzZs3rmtrJaVreedu39n55b/6Ul9vX3VNFTmYoIrZgirglRdfXte2fjXWxLaNGyqrK8+dOffZRz/15a995b0Pvk+hVMBFH/rIh9mkkP34V79eUlbSuXN7VU312a4zkXAkHA7vuecuU74JGgcDwU9/9FG1RvP5L/9laVnZ4QMHlUrlnnvuksqk5850f/sbf3/H3js/8ugjBYUFsVjsi5/6PEboU1/4TOfO7Re6z48OjwSDoaaW5o7ODiaZ0IthmJmp6cP/r73rjKvi6Ppn91bqpXfpSDMqWAARO6Ji7yWJUaMmanqMUYy9d429V+wVEJGOdBVUqvSmIp1Lu2133g8D66VIjI8mPs97/x/4XXZnZ2fOnJ0zp8yZe8FsNpvH42lpa9dUV1/xvdLFzHTL7i18Pr8993e16/rHulWx0TG9+r7xrzB+HgCQSMQEATzuG54BgIaGBplM1tjYSJJkY0NDk6jJ3sGex+PhsBqCIEiSFEvEjY2NAGBmYa6qqno/8F6dUPj9Tz/YOzokP07yPXdh3sL5bXyHTEfq6+ofJiRSFKWrp6erpwcdfdvuHu6VFRWqqirMw/IpAgiCqKmuCQwIZHM4FEXV19U593Z27uUszyF3/QObRCIuh1NTW0vTtFs/165dbQCgvKw8JjqWx+NJpdKqqip1dXVPL081NdXMjMyFc79x93Bf8O18K2srXE99ff2NK9caG5s0NTWEtUI7R3usyxIEIRaL798NlEiklExWXVXl5T3K3NJCPioV/ZUsxLh7+05tVXUvlz7ypzG3weF9B9gs9vzF39RUVwfdDXryOLk90fxv+70uLWWz2ZvXbUqMT5wzf+7jxEc7tmzHIUJeg4YbGBqcuXQWT83NOsGDmPy8fC0trYaGBnML876ufXFV506fu3PT7/PZs0aPH/0k6UleTp67h7ultaVIJFqy4DsWi5y7YJ7HwP4JcYk52TkNDQ3de3zm5u7WzF0I4fWE3y0/qVSGECovKx84ZKBjNwf5BtdU1wQF3udyuY2NjfX19WPGjTYyNsIFAv0D92zbPXHapFlfziJIIu5BnFAoJFmk91hv7M+Wr4em6IryiseJj9/DgwiMG7W1SpT06DEBgBBisZsZ+LcfftXU0vIcMdy5b6/I0PCqyqqutl37DegPAMmPHsdHxxqZGItF4jqh0Gv0KBPTLkwLaQQURaU+TenRyzn47r1XL16aW1kOHDq49fC1Wl3hDubn5gX539M3NJCIJRqaGl6jR+Dyjx8+3rJ266Chg6Z9Pk1DQxAZHlVdVU3JqEHDBhqbGOdk5yY9TAIgEKK9vL00NAQ43u1tfSdIora29uiBYxu3r48Mi0p6lAz/7HbYj2ggRgjRNJ2Xm48XuU+Snn4777s7N/3ly6ipqxkYGTxPf37hlC+0DMn6PzaePnb61ctXhQUFJ4+c2r9zv46utnNv54b6BgDoYmZSXVVzcO9hSkYBgLpAvaamprCg6ODeQ3gUOVyOSReTwvxCn6WrFs5ZcmT/8f27D50+cRa/MeR+2C/f/16QX2hrZxMaHPHjkt/8bt/tpBeNjU14ROLjEruYmjg6OqxeucFn2eq3dZkkyemzpm3ctsGplxMTPI0omqIoZsUVcMd//R9rN65Z/y40BIAVa1apqquVl5X//tPS/r1d+/dx27F5W3VVNQBweVxc0tDIMOx+yDqf1ScPH7N3dPisZ/cH4ZHTxk68de0GLqCiqmJsYpKblbP0u5++nbPg5JHjB/b8efnCRQDQ1ddjkWRoUHDcg1gA4HA4xl1MSoqLV/3mM2/WV3V1dX3dXIIC7v28+Megu0G4NoIg8vPyf/nul6RHyeVl5SlPU04fOxUdEe01ygsQys3OhXbzI+7L+Enjt+3ePnjo4DaLWVyUJFkIgYyiWz8IeKwxJGJxfX09yCUXlUqkMqkMv05bW3vO/LlSqTQqInLG5GkzJk377adf3dz7jRrj3SGFCYIIDLhbXlZGU5SDQ8fhdgghDoczaepkgYZGS9xHq4w5NdU1P33/06kTp9TV1bS0NK9fvbHsl9/DQsMZIvgsX3U34F7v3s529rZSieTKpavLlq6gaVooFPosX0VRdE+nHqamprnZuccOHz984DBCSFtHR01NLSoiKsDvLrQIvCULFh3YdyA/N8/W3i4yPOK3H37JTM/AbfA9c27Hxi26erpmFuZR4RFzZ3x+/ODh9qPwlyIxKfERAPR2dYVOzINA2Nh1BYDuTj1JknzyOLkgv60f3aSLCZvNZnPYbDa7p1NPXT1dNodt0sUEgFAXCPoP6O/az41FvlmgBN0NWuuzhsvl9vPoV5BXsMZnbURYJL5lbGKCEDp76tw3c77ZsHrjhbO+S39aBgB8Pt/YxDg/v3Dl73/MmTVPLBa7uLn43w74cfHPQYH3mfHNysyaMGri84znfV37mHQxTnqUtGT+kpvXbjKvjgqPmjJuan19vYtbXw1NjUD/wKnjpyXEJeK7hkaGNE1fv3x92vhp50+d7+Hcg0bo2KHjK35d0dTU1Ia8tva2CKGmpqa/oHKHQIAAaJpmxB4A1NTUbF23mSCIP9avUlNTwxctrCwjQ8NXLVsxd8aXOzduPX3k+KkjxwEgJvLBL4t+eJ7x3MbOFgfFfDVl5qP4xDdvoChKRt33DxSJRPbdHDU0Nc8eOzll5LisjDfbabBqiFp+EwRRmF/49ax58bHx5pbm5eUVJw6fOHbgGC6sq6vL4bDDg8MXfLHgwO4Ddg62mlqaJ46c/GLK7H07/6ysqHR1d+HxeedP+f7+k49IJHqbLIQWRvU9c9HUzFTfQL+qsookSYL4R12YH1McAqIRnZOd6zVkzPRJX86e+TVCCMepNxdAiCTJoZ5DgABVNVV80ffMxQfhD8ZMHLt606o1m9f0dukNBHiP916/fd3wUZ4A4DnSkwBQV1fHM6iqmuoyn6WAEF9Jial5+ChP/N0PHT748Mn93bo76urqAkBocPhqnw09nXvs2LO5p1P3C5dP2jnYbly77emTlLf1gsUiEQJAkJ2Vq6EhcPdwmzp9UvD90PWrN8Hb80xikCwSAG7fuJ2c9ERTU3PgoIH4uqqqKkXT2K3dOfDq3sra6uL1y3r6+mwOp6qy8mVxyeH9B0cN9bpx5Y09dvgoL4qiKIoaMGSQpbVVVzvbQ6ePOXRz3Llp653rN3FVw0eNwJzuPdZ77+E/HRwdNLU0AcC6q3XP3k4EAXw+j6kNfxIegwYOHjbEuquNz7o/AODy+Uu4AE3TK39dUSesW71x9VKf335Y+iOiaVU11QVLFu4+tMfMom3cWht3Dv4XIRQZFhkSFIIQ8ho1AgAA24raO4iBMSLhbYutdzGSBEmSZMuX88VXXy758XuSJAFBdlZWQ319T+fOYikrKyooipJR9ITJk942Cu1+EwRBMO189PBRSVGJgb6B10iv4SOGb9+1jSTJzeu3YHdmRXlFbHSslZWlmbmZTVebuV/PcXF1YbPYJEk+THxcUVHp4tbX0Miwp3OPNRtWI4SUlJQAQF9fz93DHQBwPKFQKFw8/9v0tIwFixZu3b29p7PTpGlTEEJVVVUAIKwVnjl+EiFw/KybSz+3Q6eOc7ici2fP+d28JUdFgHcw4uH4oPq6OmgvSgEA4HHiI4lYPGHKJAAY6uVpZGwkkUjuBQRCa/HZz8Pd1s6Oy+H+/NsvYyaM5fF43mNHz5k/lwCwsrHeuH3Tj0t/ZLd434PuBm3buNWpl/PUGVM1NDS+/+V7SyvLbRu2ZT/PBoCBQwYINAQIIXUNwdHTR0aN8XZwtMf+Ea9RXliXGjDIY+DgATZdrVeuWQEILl+4jGvOzcld+PW3tbW13/38namZqZu727EzR1VUVfbu3JeelgEAUREPfJatNDIxmrdgrpGxkfeYUQePHUAIbdu4tbysHAD6uva1sLakKFpJWfnzOZ8bmxjP/GKGUy+nZ09S0lPS2xDH1d31vYM/MZPn5eZtXrc5Oio6KiLq6MEjwz2G8ZX42/bs8B47mqHw6PFjsKjo4eR07vqlfgP6D/Icmvwo6Y+lyy2trfYc2e/QzXGQ59A9Rw8ghHZt3lZRXo5fQdE0RVE2dl2VlJS6mJmOmzLxh2W/1gmFB3btwUtMrBo2m20BCILIzc6ZPfVzmqaOnTvh1Nt5yc9LvMeNDg0K8b/lDwCW1pY9nHrSNM1isydNn2RmbuY1arjXqOFSqfSq71VRk8jUzHTcxDFW1pavXr68fcPvrX1HCADiouPiouNXbVgJLRkW/2Fj6cfWDhGPz1v8/TdTpk20srZEgLCGh0E028ckAM3aQemr0iu+VwFALuqBIIDIzX4ThCIWi1Frw4+ZhZmtvW2jXM1isRghBID6D+xn3dVq76GdU6ZPBICL56+y2ezPZ8/Axdhs9k+/LGGz2a9Ly97eC2w7QJNbYl+nTJ9kYWVx65bfn3sOdtJ9rP3UCetWr1xD09Tvf/wu0BDgW0M8h544f8pnzcpO6feGSgghMwvzW/f8Lt+6unLt6j4ufdXU1KRi8db1m4IDm9U1UZOIksm6mHZxde8HLUuNr79diBA6fewk9q+IxWJAYGVjPWvOl3aODjsP7h0zYRx+nJK2csAwgU7mlub4h1MvJ109XSbe7OrFKy9fvKQoqq6uDgAa6uvFYnFudm5lRSVBEKqqqh36gOV7hP9d7bMKIbTMZ5lJFxNonrHbe8IIkiQJkgUAJEly2Bw2q5WRn81i87g8Jl4uJzsnPSWtV+/eTr2c2Ww2QZLr/lhzv4VQ7SGjKIqiaZrOzMjobCRa94UAgmmli6tLrz69HD9r3vFiZWOlraNNkmRVZRUAAAEkSURGRj16+Ph5ZhYALFq88NCRPwFA1CQSicTnz/pmZ+cUFhSyWKyDR/cvXLQA1yOVSqAlmCA6KjrlWaq+gf6UaVMxiQQCgYGRoZaWFgCoC9RHjx9n52iPwwLVBQLPESMQgo723f+FRKQpiiAIbDTuEJfPXbCwsdLV1wMANps9ZPiwJlFTXHQstBafMpmMAOBwOIZGb3ayYrVJXtfH8D3rS9No6syp+F8+n//1N/MoisLxxhKxRCKW0DTdu0/vLqZdvv95yfot67CVFQtFAgiGUV3cXHR0tRkt5M5Nf6lYOnHKRLyqwIy3cPECALh07iIAXDx3ESE0bcY0pjFGxkbjJ41/+fJVYIuMl0qkNE1paAg0NTVxmWHDh0qlUnk1DgOHw7x3XAlqFgwIAERNIlNT03Vb1vuF3B02whMXaA6VEInxWnDA4AGm5mabdm2b9dUX50+eAYBxk98EXhkaG02aPrX0xcv7AffwFZqS0TTlNWYUU6a7Uw83D/fMtMyE6NjmMjRNywVA3rxyQygUTpw+mYlJnj1/NgBRVFCE/5VKJDSiVVSVjYyN8JXhIz1pmu7RqycOkEQIIQJYLFZkWGSHkXp4UGpraq9duvH1t/Oae0o2JzZ+P0q+Hz6m7xABQqiPS+8vvpoJAJOmjvf5bZWGVluVCCHEhA9p62gbGRvlZOXwec0RIhw2G9p5iduTiKKo1lcRQsihm4ODoz1zKfVZWkF+IZvFvuJ7TV1NlWSRAMThAyfYbLaenM7avnmYQZnQEi6XM3rMyN079uXmvDVSFEsjUZNo8rgpUol09/5dw4YPY24RBNHTqSfz+22VMAVwGWMTY2MTY5d+bvMXLcxIS1//x5oXxSUvSkqaSwKSyWQ4epB5pKtdVx1dHZp+M/sQAPoG+h3swGvPeAShr6/3WY/ub+hA04ztwtzCnKZpkFHYgKOqpiYWi8USqXx9b5OITK/nzPqqvKzcZ/XKGV/MeNNhGtGo1RlMBAEEQbJIAgBYJMnhcNq0n81i83nN4jDredbcWbNVVFWDIoIBIPlx0p6du/Oyc3dt29HHpS/Whttg8NAhB/bsoxC6eunK1BnT3zYKbX5j9RZfVFNX27Jjy8sXL9f4rCHZrPy8/NpaIUmSLDYbAHR0dMZPHH/75p1lv64AAHMLs28WLejTtzcAuLj1uXz52v2gkKB79wEhT89hcxfMkY+DJ1rYmt1cla6auhpuxuBhQwYPGwIAOHbp1xXLAOD2tRshQfeVlZVzc3IAUIfbKjrnOpFYrKevhx1RHT5bXV1T+qp027pN9fUNEqk0IS5eJBJFhEXk5eZZWlm2GhcOm8vlto7JItp/vUkPkwryCwkCzp8+z+PxEEKqqqpx0XE0TWtqawEAApDKZDSNPL2GtXmWAIIAQs9At3uP5lhlmUxG0TSeUurr6uNi4gAAt4Hp9ZBhQ3Zu3aWqpvbq5avnmc8BARMkhTF6nPf1y9cZWy5FURRFD/EcwhSQSCSyt0TqvrcsBABAYGVjtXzVivZ1thoyAkiS1NPXcx/QvCcvJys7JysLACSSVhFwI8Z6X7ngy2pxK2DtUNq6jNfokbFR0aTcN8WIZGFtbWR4hEwmDbjl19PZSUdXh8/nhd0PJwhghB8NNE3T/Qf2Zxw3EqmUpmnvMSOZClkkiyRJLofbYaAo7tq1S9e9x44c0LLLkM/nkSSJbX7vrXD/XXxcy2wbzti4bd2SH79tX4xo8R5zOJyvv50LAMH3gndv2X1g18HEuAQej9vHta1fut3UDai1yESAEGp1paKikiQINputqaVZ+up1fl5Rbk5ePw/XtRtX9nTu/rYuiEQi+dVei+uIQAjx+B0nmmEGb9a0z4sKi7bs2Dx8RPO2ASapSkuz/2KMCYKQSqWVFZVMyAyGvaPDnPnz+Hw+EySGEP5o30g+mqZV1dQsrKzahN3KOgwZ7egTNjA0xAGcTGOY5rr0c/UYPICiqG0btu7Ztnvv9r1iscRjkMfbMpi06RQALP568eOEx0uXL30jC1viS9sdQ/FGO0QIcThsDqdVjC6Xy+FyuXjfy/7d+7hc7sHjh/Atp17O+w7ut7KxqhPWBd/rWEF07OY4bdYMQKgNoeQbLBFL4mPiGuqbc+O9CQBvoZvfbb8Vy1YkJyUDjRy7OeIFCUOv735YPG7CWDaHraGpkZebv/Tn35f/5kPTtI6Ozp/7dxkbG3LYHJJkBfjfnTh2yq2bd95GOqplZSPPOZhcCbHxC76cu2Pz1rpaoY6eXkVZefvgGea/TqZsHo9XWVGZkdbWDIgfyUzLqK+rMzE1tbC2supqbWVjNXn6FE1NTZlUGhEaJl8zAcBisVlsdiuGb257K7YvKyvDFwQagpLikrzcvGdPU7R0tFdvWMUsZ3G1qEM2JUDfwECeURn9TCgUvi593cETeGnFZlVWVErE0vb6HEmQ8ldwVkAHuUwuCCEZRXUsDlsOVHk/EATZXntu65TBvgKSYAiSm5VTX1dPEG3t4QRBIBox02VLSF+riZHPV2rVYCwLEQCAsFb4quQlTSNNLc2a6urc7JyszCxtba05C+aMHDuypTgChGxsbYAZJoRohGj5EFkS2hxr2gZ1wrqQe6EPEx4fP3Ti4L7DJw6ffJTwmCDI6MiYiNCIf0xH/IjaIV7CM4TGQoLNZnco6okWShl3MREI1HX19ZRVVAJuBzj1dlr00yIDQwPmKYQQgZrdRczjEom09RGy0H7L46AhA65fvl2QXzhu4mgn5x5tGvC2BUjvPs6+56+8+cgJAgCaGpuw+GnzIF6n43/PnDyrrKycnJ6Es5ZUlFdUlJfbOdh3qGp0gozU9HU+q5etWt7H1UW+/Gc9u7NYLLp10lf5AiRJCmuFqU+fqap1YLpsD6JNEQQyadsQdvnGTpg8IT0lXUtL60XJy+RHyfO+/XrmlzOZTnX+xrDg0Jrq6uDoEJz5or6+viCvoFv3blxsAROJmR4RBKGiokwQBM6jqKSkRJIsqbQ5YzIuJpXJWCyWqEkEAJSMMjQytLK2ZmoQaAh+81k+7/M5TU2i9i3Br+jv0f/iuQvZz7NC7gcPG+7ZflwaGxsexiVYWluptASXYhUcu4ePHDxy7co1ExMT32u+KioqAJCell5a+hpXUldXp6qq+t0Pi+fMm62qqnrtyvV9ew5ER8fVCesEGgKBhuCc7+nGxkaKolcuX5UQn5gYnzh+wljmLViIIISAIKQyKeYxaGG2FnqG/PHbCoKAk77nutrZAkBdbW10RCRuQPPWl07GQw54O1B2RmabPF64quMHD3e1s127daP8LZlMtnXjliMHDo8eN0ZPX1/uCYJpP7S+in+kpqSamZuN8B5x7dK1osKiydMmd+veTf51zb8BuByulN2BNoYA0TQtba3bMTAyNvIeO+rOTT+8amSGFS8uhbXCbt27OX7mkPosVUm5lRaCN0vITegIIVo+QAahtqttDB6fJy8G5McI3uV7x0P9DiHA2HXNEOQzp+7aOjqVFeX81h0Ri0RI7nQXHKqjpKwkX9XDuAT5BQHJYrFYLPy4iWmXyTOmXLt0bdDQwWNaeLJNd1gsFpvNlsnp3wQQ0Cb95191SE1drVdf5+jIGKKlOEJAkmRlRWVMVNygoYP+kiAfBB8lKw3+gTUhrlzQPKNayZfkK/ERALM98eLZS9o62jv2bVv43YI7IbfXbVtnYGgg/ziLZCEgKBnFjHHKk5SCvAKBhoCpma/ERwgxJjWmSTwlHpfHfZqcKt9gmUwmEonexqZ9XXobGOizWSzG8yeRSP3uvAlGJQiirq7+2OETDxMfMax/2ffKnp17d+zZzufzsdQ8dfxUXGw8Lk/T9BXfywF3/N9l1SOVSimKSohNYEiHuyORSOjWCk3zSlAOV30vNjQ0MDuWcIwGl9uBUsvhsgEAZyADACzC2XJ5BgiCIFksdkvwfU11zf7df86cPdNn3crt+7aHxIZgWfguiAqP+v3H31dtWK1voI+Jc+PK9ZD7IQDgNcrLytoqIy0jIe5Nfx8/TAIAHDo/btJ4Hpd71y8Ah5AAQFNTU6BfII2Qc59eACAWixsamhMQM5OChoYA0XSHiTZwgWFew6fNnMHjcreu31ReVtZ+XB4nPNLU1NJuyYSADQMESWKKhYWGAcDc+XOxLAQAgiABgYGh4fVrNyaNmzpp/NTkpCe48OSpk4YMHQwIVFRV/P3uTp/yBU3TysrKamqqO3ZvJQiCsXfhxYGyijLgKQZBXnYuk14H+yaLi4oBICI0AgCmzZqJZSEAqKiqAgG6+nrPMzLSU1IAAH+Jyi0tfBuampoQgFpLKjWGkgBQU11dVFg0atwY5gr+6z1ujLKKclVllXxCFhabxSJJiqJUVN8kFhGLxUQL9QDgWfKzstdlBEEoKSspKysnP2resIHpHxkWWZhfCAB8Pl9FVYXP56vLtap59uDzEaLlzctsNptFshgrMZ/PJwBw/C0zrP63A6BF8GOjAs4YxRS4eO4StBioCYLAe07UBerQEtagpq5GEIR6ayoBQOrT1FaihSQLCwoP7z981+/u22QhU1hDQ4MEgs1md5I1prlTSnxAiGSxGDFvZGyMY31TnzyT78jVC5cAgNVSIV6GPE1KZqoqK3195bwvQggbVHl8PofL5XK5As1mr5ampqaGQJCVmSXfgOzM7KTEJPwWFWUVHo/HLNEwoUiSYKIj8dSBw206ocCvK345ceH4Cd/jZ6+euRV0Y8wEb5qmR3gP91m7vHNqfEB8lKw0YrHk/JmLe3YeIEgyLTXj4vkrAX732tgJoWXMkozk+xYAAA9TSURBVB4mA6DY6Lhb124DwNhJY/LzCuZ/uTDgVsDjxKToyJiw+2HxMW8mR6c+TrZ2XV+/eh0ZGonrCb0fRhBQVVX1ICIaX0mMS0QIZWY8Dw+JBDnmmDv/SyUlpbDgyIiwaJFILJVIY2MSD+47XllR9VYCkYTXyGEsFut+YAi+kvIs9UXJS00tjSXfNxt+/9x9YOe23TeuNoduX710bdWK1U2NTVMnTO/f12Og2yAPlwEnj53Cnx8A3Ll5Z+0fa3dv2/Uu9KQomUwmDQq4e3T/IYZuNE3v2bKTpqiutm/y2xIEUVxYtH/nHvxvTNSDk4ePkQDf//YzXhk8jE8AAlKfpcRGRcu/orKiIjM9EyG4f/ceDr54nPCQAMjKfB4REo7LBPoHVpRXZKQ/jwqPAgANTY0eTj3/3Llvnc/a2AexsQ9iw4LD7vkHFuTld64aRoVH/rLkZ4qmlsxfPMx96HAPz2H9h27ftB2PEIfDmT1vNkmSCbHxuHxebt7Zk2csLMx/81kGAIZGhmMnjqNkFN7rBgBPkp7U1tQMHzl89LgxAODc27m2uubwnweBUeWbmk6fON3Dqef4SRM7bBJu7brNG6bNmiGTSo4fOpqWksp0QSaTxT+Ira2pmTxzKovNwtdTn6UCQGND481rNymKUlNVI4DISM8AAJqm9+89UPqqFCHkfzsgLCQCAOrq6vbs2ofVi8aGxoz0TLwPITn5aUlxyYmWPCaPHj4mSNLR0YEgCFGT6NmTZ0AQYSFh+Xn5niM8Pb08AcD33AW8q6GwoHDD6nW52TkAoKTEJwgiMz0du4WEQmH28+cAxIPwiJtXrnE4XJlMlp6SCgDhwSElRUWdrMPMLC0QQnk5rbbKEASRm52zY+NWAOL1q1Jm+UgQhEwmy0hL53A4XC53+6atEaHNDJObnZubk0vJZIF+gS9fvMQXraytCIJIe5ZaUV6RnppOUZS+gT4ALFi0UEVFNfhe8IPwB2KxWCKRxEbH3bnph31+Wc+zEY2UlJQC7txlznLBfxPjE2kaZaRnhAWH4VfcvnGnvLwiM+15zINYAJg1e5aZhVnK09QDew7gw0kiwyJPHD2pq6c3Z/5XAPDtd9/y+fzb12/7nrvY0NAAAGdOnIkIi3By7jlu4jgAyM3JxQGu1y9fLy8rZ7FYJcUld27cJgji6qWrVZVV8sTErkp5JD1KOnbo2BqfNdGR0dAR8OccGhzqe86XIIm83LyrF6/glrwNj+IfIoCyV6V+N24ziTW+WjCPx+MH+d+9cr65I+dPngkJDOru3JOJmKuvqycATh85npGahq8c3XeApunBnkP7Dx4IAOkpafXCOi6PF3DzjrC2FgCmzJru1Nu5tOTVpbMX8Za5ooKi677XysvLAaC6qrqooIjH450/eSErM5skyeqq6lvXb5Mk6XcroPRVKQAUFhTlZefRNJ39PLsgv7BDCuDPSltHS0tbi8PlJMQmZD3PRghlpGUW5BV0QooPi4+Swrumumbf7kNaWhp29nbq6urxsQn19fWeXkPa247r6+pjHsTq6OmqC9RYLJaru0tVZZX/Tf96YV1i3MPw4PDoiOi46PgHYVEURfVosXBa21oH3L6b+jR16qwpeTl5QQH3y8sq6oR1ocHhX877giTJ+4EhGpoCdYF6RXnFgMEezHt19XR6OHWvKKt8/bq8vra+qLDkSXJK/4H9bO1soCPgBZ1jN/uUp6n374VizeOHxb8qKStdunqui6kJLpCTnVtS/GLshNH2DvYAcOvGbZqmbe268pX46gKBhkAgEAj09fVGeo/E++5fvHiRmZ7pNWoEs1m4EzQ2NhYVFpp06RIfHXvt0uWigkI+X2nDH2sz0tJ/X+UzaFize7+4oDAsOAQIKCoodOnnpqWtPXvqLHV19a17d7n0c8P1PAiP1NLSVlJSqqmu7j/oTVa83Kzs3OwcC2urstLX+ob6FlaWYfdD1dTVBQJBeVn5oGGDpRLp6aMnNDU1BQL1yspKbLt4nPgoPTWjsKAwPCQiMiQiJjI6Pibunn+Qq7urppbm29bCwfeC6+vqbO3tlJT4Kmqq6gJ1VVVVTS0tr1FeVjZWAGDvaJ+TnXvz6g0zC3ObrjafT5mppqa2fusGfQP95uHo3i0iNOLWtZvDRnhKJJJF875x/Mzxh19/wrpXH9e+oqYm37MXgu8Fa2hqxERFL57/LQFw/NxJZud+myYRLZGuHgMHCGuEcTExj+ITnz15qsTnx0RGB/r5C2uFU2ZNxyYH/PjDhIcymczA0LAgv6Bf/35m5qalpa9FTaKy12XPnj7LzsoxMDQwMTXJz8s3Njb6ZtECUZMIIXj9ukxZWfn2Lf+K8opvFi/oYmqiqqxSVFQsFApphGqqa69dvWFoYPjdD4u4PG5hYdGT5Gfm5uY1NbUsFqunU88hw4ZY29rEx8bn5ea9Li296xegpKT0xZwvSZI0MDQoffVKKpOVvS4jWWRS4iM3D3eJRFJTXSMSNU6cNvVFcXHasxQLK6uammp1dYGtvX37ocEwszC/HxBYkJfn5T2SWcABQGhQcE5WtrmlRVFBoWP3z7BihPnq8L6Dunq6dg72AFBbUztg8ECSJFOfprx+VWpuaVFeVp6dlW1oaKClrW1obGRuafGi5EVlRVVCXIKTs5ONrQ1CyMBQv3vP7pUVla9Ly4S1wsL8gmfJKdNmTcWnGWSmZzY1NZmampYUF1t3tdFqiYcSi8XhIRHq6urq6mplZeVDPYdIJNKjB47q6OhoaKrX1NQOHDxAWVlp0JBBL4pf5ObkvX5dXphfEPMgVlNLY9uuLQaGBjRN6xvou/V3zc8ryM3OLS8rS32WGh8T3+0zx217t+F9R0+TnpYUv7C1sy0uKrG0sjQ1N30QERXzILbbZ45FBUU2tjby2amC7wVTFLVg8QImiYFYJL7rd5fFYvVx7WPboru3AU3Te3bszcvJc+zuqG9gkJaSVltT69DN4W2ZEMKDQ9kcjoGR4YuiYlf3fjjlhbaOTt9+rsUFRbnZORVlZRmpaQkx8V3tbDfv3clryTL/oqiYx+UaGBu9KnlRVFD4MD4hLyfHzaP/0lUr8CT55FFSTXW1dVeb169KLW2sdfV0lZSV+nm4C2trK8vK62rrKsorkhOTuvXoNnTEMAAoKSx5UfzCzNyMIAldPR0LK4uM1Iz790Js7bu+evnK2NjI0toyPSX91ctSC0tzPp/XxdTE1KyD3CPyX+WLkpfHDhzncDjmFqaNjU1SibRnO9/WR8KndV5lRXnl3BnzevV1njB1Al7IcLicmqqaI/uPNjU07ju+z9K6OXQtLyevIL/QfUA/bC5IS0l7UfJKIFDv49q7E4etPGRSGQLUSeoNDDwD1gnrHj5MBkBisVgmkzk79zQ2MWKcZO/uC2xjLv5LyFdYUlScEBsXFHBPKBSOGD3Kzd3N1sGeKRMdGbXy1981NDSOnDulb6BP0/TjhIcO3bth810nDWt/6108mjev3ty7bfcvK341NDISi8UEEMqqytHhD/xv+Xd37rF1z9Z3fFebu9ASPRQeHG5obJjyNEUgUPceN7oNhaurquNj4srKyqRSqb2DvfuA/tCatgV5+YnxCTev3jAwMhw5elT/gR7Kysp/+XY8msmPkyRicXhwqEQsNTU3de7Ty8bOVllZGRCC1pGx7SERS4AAeSkiD5lMBgiAaLbCyWfowGoQw43tX0FRlDxjNzU28vj89k5EmUyGaMRiszr8Ct6RUdevXJX2NOWS3015svwtJmlzF4dvyNsA8UFvHdbT5sN8P/7ssDBFUVKplDmBpH09UomURrRceFoHX2sbd6B8MUpGzZk1R0lJ6cjpI/IF8nLzlv+yfMr0KZOnT37HZkskEjab/Y5TWfvuSCVSiqY66SlCSCwSkSwWw6sddrbNRZqmZTKZ/CN/OTTt09D8Lc55l0c+JNCnhLSU9GFuw/1u+Le5fvroae+B3ru37Mb/yh8A2x6d330PdFghjoH8VyDfHuZ3fHTs4D79vp45u5PCHxCb124a2GdA++tTR08d7u6ZlpJGvy/kCSsUCtv3ginQ1NjY2ND4jg1+l/FqQ6sO6fyJ4D0I++6VhwbdnzpqbMi9oI/X/v9JbFqzaZzXOP/bbaevOmHdgL4DLp6/9K+0SoF3x79zisfbgHNCZj3PbnO9uLAYIcQcfNX5SuGDryM6rPBvLdw+LFoF3bX8rqqsJAhCWFNb1jqy/COtqrS1tQkgniQ9YRIoUxSVlZlVW1NjZWPVZv/Z34I8YZmsVPK9YArwlZTaxMi9Y7VvQ4e+7Q5v/etg/Gdt0GEx+JvtHzLc09DE+Mi+AzhVNPqUDEifIDB9ZDJZXEycvYO991jvNrciQiOUlJT6e3zE09MU+CD4tIylAOB/K2Dv9j9d3V3cB7iJmsRcHicqNCo9JX352uVuHn/taft/i6VLfkh+lEQAdLW3331k/9vsdR8KYrF47e+rE+MfOvV2GjR0EEmS8bEJifGJ9g72m3dt5vK4neTq7RyfmuD5rwPzRb8fJRF2h2dlb1i5WkVVdeeBfcypKQp0gjU+a/Jz8nfu3ym/AxIAXr0s/XnJzwsWzR88bDD6x4x+CrwXPiFxyPBK2euyOmGdVColgECAuByuQFPwLvu7/z+j/HUZ3ZzQhTY0NCQ+pvJKtxzhVFRYhBDC523hYGtDY0MOh/NJyUL0N/21CuAvMfVpyp0bN+cv/qaThG0KYMRExRw7eGz3wd3tg8iEtcKqyipTc9N/0Z6kwDviExKH8E+6TBX4z9B+pBhGer9B/HjjrhCH7wH5QVR8lX+JkuISNTU1nGdcnlYKMv534dMShwr89+I/YSTFNKHAfy8YW4hC4P23QyEOFfgAeG8uUkwfCvyHaMN7Co5S4L2hEIcK/Kf4uyykmLAU+CDohPEUPKbAe0AhDhV4f/wt5lHMUAp8QLwL7ylYToG/hY953qEC/6N4dymomI8UUECB/xYoxKECb4UiOkaBTxMKm5YCHwOKrTAKdAyFLFRAAQX+X0EhDhXoAIrVtwKfMt5lvaVYkynwd6EQhwp8YCimIQX+dSiYUIH3gMJ3qMCHhGIaUuDfhYIDFXhvKLRDBTrA+80piplIgX8YnRxCooACfxcK7VCBDwPFTKTAP4lP+fgtBf5LoRCHCvynUExGCvyLULCfAh8Kiqw0CnSGDtlDMQEpoIAC/3tQiEMFFFBAAQUUUITSKKCAAgoooADA/wEEJHQzMEFqcQAAAABJRU5ErkJggg==	\mathbf{B} = \frac{\mu_0 I}{2} \frac{R^2}{(R^2 + z^2)^{3/2}} \hat{\mathbf{z}}; \mathbf{B} = \frac{\mu_0 n I}{2} \left(\cos\theta_2 - \cos\theta_1\right) \hat{\mathbf{z}}
+422	Suppose you have a double convex lens made of glass $(n = 1.5)$ such that the magnitude of the radius of curvature of both sides is $R = 42 \, \text{m}$. One of the sides is painted with a layer of silver and thus acts like a spherical mirror. Assume the thin lens approximation and thus, that the lens and the mirror are essentially at the exact same position. An object lies to the left of the lens a distance $d_o = 84 \, \text{m}$ away.  (a) What is the focal point of the lens by itself? What about the mirror by itself?  (b) How many stages are there in this optical system. For each stage, state whether the light is incident from the left or from the right.  (c) For each stage, calculate the image distance and linear magnification. Make a diagram for each stage separately.  (d) Where is the final image located and what is the total linear magnification? Describe the image (i.e. is it real or virtual, upright or inverted, bigger or smaller?)	[]	/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGQAZADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD3+iiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigD//2Q==	f_{\ell} = 42 \, \text{m}; f_m = 21 \, \text{m}; \text{Three stages:}; d_i^{(1)} = 84 \, \text{m}; m_1 = -1; d^{(2)}_o = -84 \, \text{m}; d^{(2)}_i = 16.8 \, \text{m}; m_2 = \frac{1}{5}; d^{(3)}_o = -16.8 \, \text{m}; d^{(3)}_i = 12 \, \text{m}; m_3 = \frac{5}{7}; \text{Final image is located } 12 \, \text{m} \text{ to the left of the lens.}; m = -\frac{1}{7}; \text{The image is real, inverted, and smaller by a factor of 7.}
+423	Calculate the force of magnetic attraction between the northern and southern hemispheres of a uniformly charged spinning spherical shell, with radius $R$, angular velocity $\omega$, and surface charge density $\sigma$.	[]	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	\mathbf{F} = -\frac{1}{4} \pi \mu_0 (R^2 \sigma \omega)^2 \hat{\mathbf{z}}
+424	You have just performed an experiment demonstrating that the actual force of interaction between two point charges is $$ \mathbf{F} = \frac{1}{4\pi \epsilon_0} \frac{q_1 q_2}{r^2} \left( 1 + \frac{r}{\lambda} \right) e^{-r/\lambda} \hat{\mathbf{r}}, $$  (3.1.1)  where $\lambda$ is a new constant of nature (it has dimensions of length, obviously, and is a huge number - say half the radius of the known universe - so that the correction is small). Assuming the principle of superposition still holds, reformulate electrostatics to accommodate your new discovery.  (a) What is the electric field of a charge distribution $\rho$?  (b) Does this electric field admit a scalar potential? If so, what is it? If not, why not?  (c) What is the new version of Gauss' law?  (d) Draw the new and improved triangle diagram (like Griffiths Fig. 2.35).	[]	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	\mathbf{E} = \frac{1}{4\pi \epsilon_0} \int \frac{\rho \, \hat{\mathbf{r}}; V_{pt}(r) = \frac{q}{4\pi \epsilon_0} \frac{e^{-r/\lambda}}{r}; V(r) = \frac{1}{4\pi \epsilon_0} \int_{V'} \frac{\rho(r') e^{-r/\lambda}}{\hat{r}} \, d\tau'; \oint_S \mathbf{E} \cdot d\mathbf{a} + \frac{1}{\lambda^2} \int_V V \, d\tau = \frac{q_{enc}}{\epsilon_0}
+425	A plane polarized electromagnetic wave travelling in a dielectric medium of refractive index $ n $ is reflected at normal incidence from the surface of a conductor. Find the phase change undergone by its electric vector if the refractive index of the conductor is $ n_2 = n(1 + i\rho) $.	[]	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	\text{phase shift} = \pi + \tan^{-1}\left(\frac{2}{\rho}\right)
+426	Beams of electromagnetic radiation eventually spread because of diffraction, among other things (e.g. scattering). Recall that a beam which propagates through a circular aperture of diameter $D$ spreads with a diffraction angle $\theta_d=1.22 \lambda_n / d$, where $\lambda$ is the wavelength in a material with index of refraction $n$. In many dielectric media, the index of refraction increases in large electric fields and can be well represented by $n = n_0 + n_2 E^2$, where $n_2$ is some positive dimensionfull constant.  Show that in such a nonlinear medium, the diffraction of the beam can be counterbalanced by total internal reflection of the radiation at the boundaries of the beam thus forming a self-trapped beam. Calculate the threshold power for the existence of a self-trapped beam. Assume the radiation to be plane waves.	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	E \geq \sqrt{\frac{n_0}{n_2}\left(\frac{1}{\cos(\theta_d/2)} - 1\right)}; P_c = \frac{\pi \epsilon_0 c D^2}{8} \frac{n_0^2}{n_2} \frac{1-\cos\left(\theta_d/2\right)}{\cos^2\left(\theta_d/2\right)}; P_c \approx \frac{\pi \epsilon_0 c}{64} \frac{n_0^2}{n_2} \left(1.22 \lambda_n\right)^2; P_c \approx \frac{\pi \epsilon_0 c}{64 n_2} (1.22 \lambda)^2
+427	A point charge $q$ is at rest at the origin in system $S_0$. What are the electric and magnetic fields of this same charge in system $S_1$, which moves to the right at speed $v_0$ relative to $S_0$?	[]	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	\mathbf{E}^{\prime} = \frac{\gamma \, q}{4 \pi \epsilon_0} \frac{\left(\beta x^{\prime}+c t^{\prime}\right) \hat{\mathbf{x}}+y^{\prime} \hat{\mathbf{y}}+z^{\prime} \hat{\mathbf{z}}; \mathbf{B}^{\prime} = - \frac{\beta \gamma \, q}{4 \pi \epsilon_0} \frac{y^{\prime} \hat{\mathbf{y}} + z^{\prime} \hat{\mathbf{z}}
+428	Find the force of attraction between two magnetic dipoles $ m_1 $ and $ m_2 $ a distance $ r $ apart and which are aligned parallel to each other and along the line connecting the two. [Extra: if $ m_2 $ is misaligned by an angle $ \theta $, what is the torque it feels and if it is free to rotate, but not translate, what will be the equilibrium orientation?]	[]	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	\mathbf{F} = -\frac{3 \mu_0 m_1 m_2 \hat{\mathbf{z}}; \mathbf{N} = -\frac{\mu_0 m_1 m_2 \sin \theta \hat{\mathbf{y}}
+429	Four identical coherent monochromatic wave sources A, B, C, D, as shown in the diagram, produce waves of the same wavelength, λ. Two receivers, $ R_1 $ and $ R_2 $, are at great (but equal) distances from B.  (a) Which receiver picks up the greater signal?  (b) Which receiver, if any, picks up the greater signal if source B is turned off?  (c) What about if source D is turned off?  (d) Which receiver can tell which source, B or D, has been turned off?	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	I_1 = 0, \quad I_2 \approx 4E_0^2; I_1 = I_2 \approx E_0^2; I_1 \approx E_0^2, \quad I_2 \approx 9E_0^2; \text{Only receiver } R_2 \text{ can determine which source, B or D, has been turned off.}
+430	Two long coaxial cylindrical metal tubes (inner radius *a*, outer radius *b*) stand vertically in a tank of dielectric oil (susceptibility $\chi_e$, mass density *ρ*). The inner one is maintained at potential *V*, and the outer one is grounded. To what height, *h*, does the oil rise in the space between the tubes?	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	h = \frac{\varepsilon_0 \chi_e V^2}{\rho g (b^2 - a^2) \ln(b / a)}
+431	A rectangular waveguide made of a perfect metal sheet extends from $x = 0$ to $x = a$, $y = 0$ to $y = b$ (with $a > b$) and is infinite in the $z$ direction. For an electromagnetic wave of frequency $\omega$ propagating along the $z$-axis,  (a) find **E** inside the waveguide $(\epsilon = \mu = 1)$, and the dispersion relation,  (b) find the phase and group velocities $v_p$ and $v_g$, and show $v_g < c < v_p$, but $v_pv_g = c^2$,  (c) show that there is a cutoff frequency below which no electromagnetic wave can propagate through the waveguide.	[]	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	"\begin{aligned}
+E_x &= E_0 \cos \left( \frac{n_x \pi x}{a} \right) \sin \left( \frac{n_y \pi y}{b} \right) e^{i(k_z z - \omega t)}, \\ 
+E_y &=-E_0 \frac{n_x b}{n_y a} \sin \left(\frac{n_x \pi x}{a}\right) \cos \left(\frac{n_y \pi y}{b}\right) e^{i\left(k_z z-\omega t\right)}.
+\end{aligned}; \begin{aligned}
+E_x &= E_0 \cos \left(\frac{n_x \pi x}{a}\right) \sin \left(\frac{n_y \pi y}{b}\right) e^{i\left(k_z z-\omega t\right)}, \\
+E_y &= E_0 \frac{n_y a}{n_x b} \sin \left(\frac{n_x \pi x}{a}\right) \cos \left(\frac{n_y \pi y}{b}\right) e^{i\left(k_z z-\omega t\right)}, \\
+E_z &= -\frac{i a\left(\omega^2-k_z^2 c^2\right)}{n_x \pi k_z c^2} \sin \left(\frac{n_x \pi x}{a}\right) \sin \left(\frac{n_y \pi y}{b}\right) e^{i\left(k_z z-\omega t\right)}.
+\end{aligned}; \omega^2 = \left[k_z^2 + \left( \frac{m \pi}{a} \right)^2 + \left( \frac{n \pi}{b} \right)^2 \right] c^2; v_p = \frac{\omega}{k_z} = c \sqrt{1 + \left( \frac{\omega_{mn}}{k_z c} \right)^2; v_g = \frac{d\omega}{dk_z} = \frac{c}{\sqrt{1 + \left( \frac{\omega_{mn}}{k_z c} \right)^2; v_p v_g = c^2; \omega > \omega_{10} = \frac{\pi c}{a}"
+432	A circularly symmetrical magnetic field (B depends only on the distance from the axis), pointing perpendicular to the page, occupies the shaded region. If the total flux is zero, show that a charged particle that starts out at the center will emerge from the field region on a radial path (provided it escapes at all). On the reverse trajectory, a particle fired at the center from outside will hit its target, though it may follow a weird route getting there.	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UAggNU/rhATjFadOaQ/PgoZyYCSAs3KJ7NOPkCwAYFXDYIKCAg8K9bJwK+15aoh7XlgMxwFUX/VEFvyjqZpFotlw6HAK3fkNwB1IHtgOAwmk0lMPTabzSj8OxwO8gZYeRcrnzl/UugfV1oLlOy7KlsSPEDgFYSgAgICG2DDpPETUQECM1axWxJ71grnT300WujTARGzFUWhYnzJLpAdKIryFOeCEwAF70KhsNaTwaKfv9+VW26YEdk1bSkCAlsCoRUQEHgmlDSsbxhIkD9HoOXdebfqMp7xgHQvWPpLklQoFBYXF2dnZ0dGRqLR6JEjR06cOMGPGCCUEJFNMiRJkmhCMTGADRf0VChZh/2scwGkDFj1fQGBVw2CCggIrIfNh9hVN1up9aMk+cq1bD6fL/HIWxnMYBC0kkOsk5zf8DqxzmacwhEvEI9VVf3888/v3btXWVnZ1tZWUVHBXyFcBXHZkAKsdfsrT80rD8CN4AsEkWDJc+APRX9a/2nzr1d9JiXERfAAgVcWggoICGyM9ePEyjLzSkkazwMQNUmIB1c+WZZRPqcEOH92cgLAC2Tjed6Ag2++3ldSvIfwnnQAOFEul3vw4MHAwMCDBw8URTl8+PDZs2dL8v+6MVO45AmsPBe90Dm/I3of4V9/3ApppYZx/TQAW+3Jr3VVJRA8QOBVhqACAgKbwqpSOD7AlyzcGWOU92aPRxoEXcZYoVBIp9OwAYZ5fiqVwkQApMplWYYkHttYLBaPx4MWO/T0l1wVHzuxzuZBtkLMWM1jHY+NkQMgblEsFoeHh//7v/97enr6jTfeOHnypM/nA/+gnATOvqqQsASrXiQBPYGrFhdoFyI6m6+DiOguILBJCNmggMB6WHWVCVADW8mb1MxG4Q3MAME+n88jDBcKhUQiEYlEYrFYPB6Px+OJRCIejyeTSU3TCoWCoigOh4MxlslkVFVljMmy7PP5ysvL/X5/eXm5x+NxuVxOpxP2wPDzgfhuZa4eoKoEL+OH0ZDJAGNsdnb25s2bY2NjqqrW1NScO3euubmZrShYrB+VS5byK7ffvNyy5IBs7eW+KP8LCDwFBBUQENgAq/4/IkkSb2aHN5FpxwBffndVVdPpdDqdDofD8/PzCP+qquq6nkgkZmZmUqlURUVFWVmZpmnZbBY0Aj11qqouLCxkMhm73W632+HqEw6Ho9Go2+2urKy02Wwmk8nj8VRVVVVUVPh8Pr/fX1lZCdNfHpqm6bq+vkV/Op2enJy8devW7du3PR7P+++/f/z48aeLpiXlAHpu62zMY9Uwv2H+/0nphYCAABMFAgGBzWAzjBkLfYp8qKAXCgVM6sNI31AoFAqFFhcXY7FYPp/HKr+rqwvTewOBADPmAymK4nK57Ha7pmlTU1PpdNrr9TocDl3X0+n0wsLC1NTUyMjIw4cPk8mkLMsej2d+fr6ioiIQCFRVVWUymUAgYLPZkCpghl4Bg/tKFHm4YMgFbt68+X//93+yLL///vuHDh3yeDwlmz3pE+MVDGtREJAqUi+SKmJV5f9a2kDaYPMXKSAgAIisgIDAeljZQcBXrNnjnfeETCYTi8VSqdTS0tLMzMzs7OzMzMzS0pIsy4FAoL6+vrGxsbq6uqKiQpZlDO5Dxh6lARTgHQ6Hy+VSVTUcDquq6nA4ZFmGxtDn87lcrnA4PDU1lcvlZFnG1OBQKITZAS6XKxgMtre3t7e3w5EX/vx0hfAAIHvBXC738OHDoaGhRCJhsVgqKysbGhqqq6udTudTBNd1flXW0RXyoxBIvbhys/XDv6ACAgJPAUEFBAQYW7vsTVSAVrT86p8X4jFj6ZzP56PR6NDQ0PXr1wcHBzFNp7GxsbW1tbm5uba2lnz1UUeAyT8c9bPZLDSDjDGY+SANkM/nLQaKxSLKDWazWZZlXdcxmAfa/mw2OzU19cUXX4yMjASDwX379rW2tra3t1dXV7vdbhrZh2mBOGmxWFxeXr5+/fq1a9fq6+svXLjQ3t4OGQFu/4lm/q71k7JhkF7JulbtyBBUQEBgyyGogIDAmuZ0ugH2+Oofen4+014sFpPJ5NLS0uLi4sTExNDQ0NzcXLFY9Pl8Bw4caGtrKxaLmOpbVVVls9moHV/X9Vwuh9UwYwy6QqTKoatnxgoeekBIEQuFAkQJ+Cc1MuRyuWQymclk8vl8LBa7f//+2NgYRvt0dHQcPXq0uroaUgZZlnFGTdO+/PLLW7duWa3W6upq8Aafz7f+g3rSdr4n/SDW6ibYzMEFGxAQeFIIKiDwqmOd6MK35Emc6U2hUCgUCpRdz+fz2Ww2Ho/fvXv38uXLS0tL9fX17e3tLS0tNTU12ABHQyzXdT2fz+dyOVAK3jOAcuDU48e4Vjo+9qPDkN5EwgDnwmGRddA0bWho6M6dO6FQSNf1/fv3f+tb3zp48CCSAcPDw0NDQ+Pj4/F4vLOz880333S73bhN9BRQTYFS92vRplUf6bNHZTrU5mUBggoICDwpBBUQ2Nl4ljXohkdYf5GKSgG8Aa5du/bJJ59IktTZ2dnS0uLz+TDDl+/WQ9qfHHaRAKBCAzOshHgeQIMAKCdRcoNgEtRGiCMzY4BvLpfL5XII51NTU/fv3x8fH19cXKytrX3nnXd8Pt9HH300NDR09uzZCxcu+P1+TAKkW5M4A+C1CigvAJv8jRIMQEDgqSGogMAOxlYJyNcpEKwMvRDuIc2O7Prly5fD4bDdbt+7d++pU6dqamowh5fs9JG6R70fvXzkGkSlAf1xlPgT8JGeTySQyA4vKFWAs+RyORgS6LoOX6Dh4eEvv/zywYMHKF40NjaicNDU1MQM3yFSP/AyiJeO9X+pts91CgjsRIhmQoEdibUCw4Y9b6tuIHHe+yvPUqJKoyr7nTt3ent7JyYmUqnU3r17jx07Vl9f73K5GGP5fF5VVYRwRG6yE0a45SVyFHd1o6GO5wF0dsrbU+qeHIF4r2LsomkaufqDKEBv6Pf729raZmdnf//73+u6/k//9E8dHR3l5eVEL+hoJZ0RLzErAEhPYqssICDwRBD/dwnsPDzLAnFDrsCD8vMlOy4uLk5OTn711VcjIyN79uzp7Oysrq52uVxw/VNVNZFIaJomyzJU/SUigJIbKTEpQu2AAjn+hGYBxlg6nc5mszTFgPIBKFWYTCZMEE6lUtlsVpZlm83mdrvtdnsmkwmFQvfu3bt+/frCwgJKGCaTqby8/NixY11dXV6vF5mDktIAXfY2SRJsVSpIQECAIKiAwI7Ec0oXl6x9V10KY0l9586d2tra1tbWpqamuro6WZY1TcPiO5fLxeNxTdMwKYAuCQl8fgzgytspSQkQC1lJBWi5z3c5ktGhqqqaptlsNnQbZrPZiYmJ4eHhiYmJcDjc0tLygx/8oKqq6uOPP75586bH42lsbDx06NDRo0eph7DkST4RhXoiPOmRn04d8vyuX0BgF0BQAYGdiufBBqiLb9W/JhKJnp6evr6+ubk5k8l08uTJo0ePyrLMiwCQnE+n09Tsx1/SytIAuglQNaDhvCQCYNzUPsR4TdPAOfhBhYwxs9mMjga4FEBICOXg+Pj40NDQgwcPFhYWKioqjh07dvjw4cbGRkVR5ubmhoeH7969Ozk52dzcfOLEiZaWlurqakmSkJlY6V68tXi6usOTdihsYUeDgMCuhKACAjsYG7KBJ10LrkUF8vl8Op2+ffv2//zP/ywsLJw7d+7MmTNut5s0gFarVVEUsgHQNA0NhOtcs2SMBUJFABQBoZ0cC5AhAFEgRwHqRGDcsEFwEYRwuAtrmrawsDA9PT09PT03N6frutfrhaahsrIStkV2uz2bzQ4ODg4NDc3OzqZSqRMnTrz99tuBQKCkYbLkKdEtPEtwfTER+umyCAICrxQEFRDYDdjM1/hZYsDY2NiVK1empqZsNltVVVVjY2N9fb3D4YAWDw17NDWY4nfJ5YGXlMgFGDfhkHfbpaiPRsSVpXqJcxYitQEuo1AoLC8vj46O/uEPf/j6669ra2vPnDnT1NRUXl5eUVFRXl5ut9tJwIhRSdFodHh4eGRkxO12t7e3d3R0tLW1USckXRJOzTcalPzpifBSqMDzPp2AwE6E6CAQ2A2gXPqWHxlqu7t37/b09Hi93u9///uHDx9WVXV5eRmRm3L7+Xye70SAlRAJ7ig/QaIBOgV5CJK6kLQC/E1R+aCEMdBfaZdsNvvw4cNvvvnm888/HxgYUBSlvr6+s7PT7/fD2ziZTOJcmqYxxrxebyAQqKur6+rq+uqrrz788MOenp6//Mu/PHjwIE9iwAz4Z779Y+qqXwmhGxAQKIGgAgK7Byt/3zdZil5LIa9p2sDAwLVr1xKJxJEjR/bs2eP1elOpFOYLw75XVdVMJkMVfb4NT+em7fGXwXcTUDKgJJFQIjCkXaipAWzDZDKhHmEymRRFkSQpkUiMj49/8cUX165dM5lMJ06ceP3111taWpxOJ8YfWywWjDWicUTwPPB6vcFgMJPJRCKRxcXF3/zmN+Pj493d3ZWVlRA00LWVNBc8wSe04qN5WRBsQECAh6ACArsZ6/zclzT1lTTvMcYwC3hwcPD27dtVVVXvvvtuR0dHNpuNxWJot4NcHy18aPdnRgmfJIG6Yf/HS/1LrgEb80co4RD8xvwuaClEQgK8BKMQ5ubmRkdHZ2dn9+/ff+bMmaNHjzY0NJjN5qWlJV3XMZQIp5BlGdJCVVVnZ2dzuVwgEPiHf/iHmzdvfvjhh9PT09XV1aACT/GEN491Wiqe5RTrsw3BBgQECOaf/vSnL/saBAReNBCkecU+3qHBfYlEor+//8aNG7FYrLm5+dChQ3V1dRaLJZvNQpSHbDmCKKYJkHdQyUJff3yUAJ2dNqZufoj2EdpxzHXy23zlHrOR0DeIWUROp7OlpeXEiROHDh2qqalxOp1Y2VMZQjcGIpBQETRIlmVQCsw1zmQy8Xjc5XK53W62deHziVICzyhEeB4HFxDYZRBZAYFXFIjTq9YUEonE3NwcqMDevXsvXLhQXV0dj8ej0ShjDAl2+Adomkasgh/Yg9dkAkjv8NkCng1InGcwM6oDpAagigMdkKoJ+CdmEeF9i8VSXV3d0NAAgyOr1aob/Yo4DggBjT1kjCGjkE6niY7U19cHAoGRkZFr165NTk76fL5AIMAYy2azONczRlDpSawDn+vyfZMlJAGB3Q1BBQReRUjGaABK2tM6O5/PDw4O9vb2xuPxjo6O9vZ2uPIhG49FPI0H1I0ZAfxBKGzzp2Oc7o9XDiLq05v8tdHxGVcR4AkH/1fdmI3EGLNarS6Xy+VywZEwm82mUilqQ8Al6UYHAWMMFgjgCoyxQqFgt9tdLlc6na6url5YWOjr69M0ra2tzev1YgO+kvLUHwF7boqBlytEEBDYcRBUQOAVAr8ElB731iUkk8m+vr6rV68eOXLknXfeKS8vV1V1cXERCXOK2UQC+DQ7M5INtHyXjFYCxGnJaPnDcbAZqQVJZ2C1WrGap1ECzNAQ8KML6eCUJMDGuq5ns1ld1+12uyzLNAURBwGhoY5HPl2BC8jlcsh8+P3+jo4Oq9U6NDQ0Ojr6ox/9yOfzMWN+8ZaspKXHpZTrb7NJCB4gIPCkEFRA4FWBzvXFrfwrpH9jY2PDw8Oqqra3t7e2tlZUVNjtdvLdo7iLSMy4oM6LAPgXRBEKhYKmaZRRkLj2QqrcS4bHH0I+lQAoTvPsgU9IIKjjTT6BUSgUYD5IVki4WeQ26Cz8k4EWEk/DarXW1tbquq6qaiQSuXLlitPpbGxspIFMGz5ttulAvlaS4Il4gCABAgJPB0EFBHYn1okK+oreAcTUYrF48+bN69evnzx58tvf/rYsy4lEQlVVu92Opju4CfGZdt4TkMr8jEs/ICrjXLlcDu+AUrDH4xwt1jEEWTI8iSm64xoKBnB2UAFcPII62AaIC/iH2Wx2OBxQI0I0wBiD3AHvkFYRy32bzWYymTDd2O12t7S0VFZWTk5O/vu//7vVav3Rj37kdDrZ47OatgpPnWkQJEBA4FkgBZt6xgAAIABJREFUqIDArsWG2jSKx7DpvXfv3sTEhMvlqq6ubm5uzmaz6K9TFIVf6/PrXYmbLMwfc+VZEJ5pWjGp/KjvAAfkpQNUO5BlGQMIkDzAQcixmDFG/AC8gRnGR7zGkL/yQqGgqip4Bt0Xr2OgxIPZbIZuoFAoyLI8Ozt7586d1tZW6jAsaY7gH/6qT2NrsSXHF5pBAQHRTCiwO0GCAPrnSjAugT88PPyrX/2qWCx+5zvfqaqq0nUddsImk4kyAXQofiQg3zvAH5leIBKbzWaMD4ZGz+l0Ug8CH9fRQ6goCtr/0um0JEkej0eW5Ww2i8HHaBrEah4lAFwh31+gaRpOBOeDdDqN2I9LzefziUQikUjgvihVgIwCkRukKDRNw7UhkXDv3j1d11tbW8mWGBqIlWyAPbcoqxsGjltyNEEFBAS2MrknILANsTJE8etjxlihUJiZmbl7924ikairqztw4IDf70+n0yjtI+DRmpsxBlMBciAoGmArmAedjjGGqIz1PXkSS0azAOPcBmkWkcR1K/DXj7oAqQHIHAliQ+r0I1rA9zQyLplR8g6vfKRCQy6XAwVRFOX48eN1dXUYdTgxMaGqaskQxRcAXo2xJQcUPEBAgIlxRAKvCFbqAxCPTSZTMpn84IMPent7u7u7Dx486PP5rFYrKexoR0raS4YbP5bjJMKnDkDGBRiaH4hIj17/YrEIq6KVUgOEOgR7/miUaSjpU6AGRSIQFCxpG7AEvlLA3xF7vPCBGwFrQfIAAwzxz1AotLi42Nvb63K5vv3tb9fW1j7nz+0xPI8fK0EFBASY0AoIvAooWUfyYY8xNj09PTg4mM1mu7q69uzZMz4+7vF4oLmDjE6WZcbZ+zDGqC0QCnyeCuAUJekBqu7jaMQhFEWBc7Bu6BCh3dMNsyCMGURnoM1ms1qtSOaDjtCORAUkbvKhruuqquKkiqIwQ7eYz+cxwNBisdB8ZCpS8M9NMjoUkISQZbmysrKhoWF6enpkZGR8fNzr9Tocjq1VDq4FwQMEBJ4fBBUQ2M2g9S6fxOZfjI6OXr582e/3v/baa2azOZFIICsuGU7AWE8zY+2OFxDr2e12TPvNZrNUNeCX3ZT5RzxGX2I0GqX0O4r6ZP1rMpk0Tctms7IsI/BLkoR9KdtfEhHpBvkoTikELO51XSdXRGb4E+QNEK2hlAPez2azOBoUjngmjLFCobBv375UKnX37l1d17u6ulwuFyUzntcHKSAg8DwhqIDAbob++Cg/eh8x22w29/f39/X1vf7666+//nomk4nFYsxY9EPEh8ApGdp+Zsjvi8UiojXWzZJhN1QiRKBQDdlBPp9PJpNms9ntdkuShDIBaAE5BORyOUgKkANgRq8gM/oC2OMpfd1Q+5NegaoSNptNURRN09LptG6MTETmAJMJyZ+AuAhvPQR9A3Uq4uCapjU2NsZisc8//1zX9YaGBpfLRXTnRX2wAgICWwlBBQR2OUpSAvl8nhr9v/jii+Hh4b179+7du9fhcDDGoOdHJEZigI7AWxTbbDbGWLFYRIh1uVyUACjJOdOOWJqbTCZ49zKDcFDtH8UIi8XidDrROsgLCJjBZhDC2eMjECltQCfFf8FawDb4+gj2giaAcYQJ/0UtALQAskGTAWZIEOrr69vb2+/du/fNN98Eg0Hqt3xOEJImAYHnCsHiBXY/+EBCBr3ZbPbatWuhUKirq6u5uVnXdYR/rJ5J6k8MwGSM77NYLA6HA6Y9oAJ2ux2xcOUsQURc1PVBBdxuNyx6QAWgMCCHH/Tx8+2CxAPoXkgwSIoHcAirAbw2m835fD6TydAoRZ6mYBdFUXA6ckfWdR1KAqfTifIHOhUpK6DreiqVCgaDhw4dWl5evnfvHqY0UbJhk5/I5qO74AECAs8bIisgsJvBr+YBSAEsFsuNGzfC4XBLS0t9fb0sy6qqojsOXnuUIdc50DFp2Y0ojko8jQAu6SSkRbyiKFADUGsivyV2xHmpv5/a/RFl0XRAGfuiYVHMywbpTkEXyH6AZyqkOiQFADNiOQkjkH7ANVMqAmQI9ot+v//IkSPj4+PXrl179913HQ4H1BU8f1ofG8Z4aevMAwQEBNaBoAICT4O1fqC3myRbMgb2UAg0m82xWMxut1+5ckWSpNdee62yslLTtEwmk81mnU4nmv00TUNolwzbf4mbGkDvQHMAn39mGBYRcF5I9O12u81my+VyyWQSEZ2P3MQJisUiHH9JMyhJEkYKweoA5X+yFaJuAoCKEbxikbIIZFdsMpmgQsCNIAXCKxDxPmyRFEVJJpOapkGHCNpRKBRsNtv58+dnZma++OKLAwcO7Nu3DxRnC0UDggcICLwYiAKBwBOgZH286gYv8nrWwsosPa2wEXRv3rwZDoebm5tra2tNxuAf6v6n5kCTMQGIFtYkHuSDN6gA0vIUjPk0Pv6paZqqqljclzxGyQCORhoFfmqAyRheQEfg7QSKhvMgfAYBXkjI6xJMJpPD4XC73SgogKbgdHRwXBjODtdkKBWy2ayqqqiM+Hy+lpYWxtjQ0FAikaAhzht+QHzWZGXeRUBA4AVDZAUENoUnquy+xNwAr7MruYwiN5fv97//vc1m6+zsdLlcaAdAAEPoVRSFqvVk50exn/R6jHMHwghjlOexF1/IZ4yhS7D4+AgfnRtOSK16xEWQ3tcNUyNU9PP5vKqqJDJA7gHXQA4BODglJ0rkCAjtDocD96jrusPhkCQplUpRjQOxv1gsZjIZlAlgh5DJZEAyIDXQNK2zs1PTtL6+vvr6+uPHj/P5gFU/hQ0/vu2WWBIQeBUgqIDAxtgFyzVeZt/b2zs7O9vV1YWUAFLlJZV7fi9eoIcNSBzHS+ulx918CXReFOZLjIH57AK/Fx2kaIAP/LTKp75BSiTwwZh4AEkLwXgymczg4GAmk6EZgzabzeVymR63KqKHgCuE9pD0CsgooLxy9erVBw8edHR0wMtoQ/AHX/W1gIDAi4SgAgIbYMf9OlOI5d9ELEylUpIk/fa3v/X5fIcOHcJKl+T9sP9D1bxET0fHQYo+m83mcjnk1ZkRrbFYJxkBH9gQXBGV+eEFdHyJG55E04p1Yw4hFThIJ0i0o2hMQkKMpxeUzGBcp6LJZILib35+/pe//OXo6Ohrr70mSVI4HG5oaHjrrbfcbrfD4SCJA0SUzCgTKIoC6YCqqqACONqBAwdmZ2cnJydDoVBjY+M6n8s6nxr/BAQEBF4whFZAYBeCX5rrnPdONpsdGxubn5/fs2dPQ0MD5G/MWNxLnI8QxWB+1V405gfybX5U40cPAv7EHvc0pOCNxDvZBtAxecEd1H80PgAEgh9DTJdEpQGiBczIBDCueIFrpqJDoVAIh8O9vb1zc3MNDQ1lZWXDw8P9/f3xeJyv9PPPhCYoUkdlLpdbXl5OpVKQE2YymYGBgdu3b6OZAkfg6cg6PIByGwICAi8LIisgsB52XEqArehZxwIXqjdJkr7++uv29vZDhw7Z7Xb6K2MMXXOZTCadTrvdbjjokfKOSACOiTWxJEkw8EG45cX8xA90w2OYLgNjBbAjH9SZUaTg3Y0YYxKnW8TFUGKA/koXAA5hMpmQt8DFkICRMZZOp4vF4tzc3OLiYmNj48WLF8fGxj744APceMEYlGyxWCAkTKVSkDhIhjciPInj8XgkEikWi1ar9dGjR59//vng4KDH4+no6KipqXG5XIwxTdNWtjiWVAT49/mPbMu/FQICAutAUAGB3YZVS/6MsXw+v7S09ODBg5MnT7a0tMDWVzfmDpM+H29S+R/lefyT4j3qCEi8k56ATs03EyKI6o/PI5a4YUL8FTJuQjG9z9cR6GJMK9wL9Mfth2mWEl08uRfncrnp6enx8XFJkv7whz+MjY3FYrHu7m63260b7Qk0IgFdCSbOljiVSi0sLDx48OD+/fsTExOhUCgajdrtdp/PF4lEhoaGHA4HqACyGis/iM18guzJG1YFgRAQeGoIKiCwJp7ut3W7lXtJwJ9IJO7cuSPLcmNjo9PpRFq7WCza7XbJ8Pax2WywGEqn05LRL2AymajLn4x3qBGffHXQSYggir2godM0Detjp9OJdTb69a1WazabRcCmdgBI86igQM4BRc52kHSIPBXA5CFKKqAYQX0H2DKdTttsNlVVo9FoeXm5z+f78MMPzWbz+fPnv/e979XU1GSzWVwqY4zsDXDZ8BQymUzhcHhwcPB3v/vdxx9/rGkaY6ympua73/1uV1dXLBbr7e1tamqqra3FlfAWh0/aUFCiItxwx5ITCQgIbB6iRCewOnbi7+mqAn4gm81GIpHBwcHy8vJAIIB4iWQ4JdiLxaIsy5i6i/hNa32r1QqzYVT6kXiHhJ4yCrzvL71DIj5m6AGx7KYxwQjY2MXE+QdjCgCvACCigL0owUDnQssf/oojkAkx/sQYw/TFhYUFn8/X3Ny8vLzs8XguXLiAAYMkMNR1XVVVOCXjSvL5fCqVWlxcHB0dvXfv3ujoKG6qvLz8zJkzr7/++pkzZ/bt2xcKhUKhEKYq06ymkg+IV2CsD4nD5r8Gm99+J37JBQSeB0RWQGAV7PSfyJLCMwr2s7OzoVDo4MGDlLTnFf5I+FNeHSV2iOD4igBcCGkDkAnwCcnoDoCwDrtDrwdukclkFEVxuVywB2CMoaFfN5yLwDnoRJlMBhMEKNPAGEPGHtJFvlJAAKchjwHcFHUSxuPx27dvj4+Pt7e3v/vuu6qqDg8PT01NhUIh5DxAkkyGURLOoijK8vLyl19++fXXX4+Ojk5OTobDYVmWW1tbX3/99VOnTu3ZswdPqaGhYW5uTtf1TCaD7gP+U9huGSMBAQFAUAGBXYKV+QDdGC6MNPvCwkI2m62vr+c99fgGfbj3wFKXLPopMw9DHmjpoTNAsAcVwKHoGqisrmkaVucI7TDwz+VykUhE13WfzyfLMvz7sPpHg2KhUMhms+l0OpvNMsZsNhvJHsED8F/eBoBGJFMzgm4MVCTaYbFYQqHQ0NBQOBx+44033njjjfHx8Z6enunp6ampKWQFkDwgwpHL5RKJRCgUGh4e/uSTT3p6esrLy1tbW5uamlKp1GuvvfbDH/5w79696XQ6FApZrdaWlpaHDx9mMhlqRKTPYq1PjV5vLVGQhEuBgMCmIaiAwFbiZS37Vv3RlwxjnHw+PzExMTs729TUFAwGrVZrLpdD9JVlGYEfDv+SYfhP8kDqxMOsXtT4MREA+5KjALQCoAtEDux2O3iG2+12u92aps3MzDgcjrq6Ok3TZmdnU6mUw+GgzbCv1+stLy9XVXVhYSGXy7ndblggkEoRtQaqa9AinnHzEaTHZyPh/Xg8ns/nA4GA1+u12Wz79+/fv38/0g9ut9vv9yPbwRizWCzZbHZ+fv7WrVsffPBBf39/e3v7n//5nx87dqyrq0uSpEgk4na7GxsbUbZwu93owrh69Wp/f//Jkyfz+TxyDMzwWWJrf0NeyjdHZCkEBABBBQRKsUPXUnz+ucS5L5fLDQ8Ph8Ph48eP+/1+SZKWl5fRI1firu90Om02G5bjMOADCcC0X1mWoY3H7hAW4E8oMaCXDx7DkiQhhKdSKVVVPR6P2+1OJBLRaHRiYiISiczPz8/NzS0tLaEMYbVaXS5XWVlZIBBoampqbGx0OBwwMsKwgGQyiUyAZMxYQoqCGhH5XgPGOSHypCGTyXg8nr1797rd7mw229bW1t3dHY1GqYfQYrHkcrmlpaXZ2dkbN2788Y9/nJycrKur+9GPfvTmm2+ePHnSbDYjV9HQ0ABdJASGTqfT7/fncrloNHrnzp1z586lUqmSychshXhQBGMBge0AQQUEHsMO5QEE6tzjYwyW14yxqqoqSOEQQSHcw1KbXPexxKeBAoyz/2OM8Uq6QqGQSCR0XUc/AjUBWiwWZOPxX8TsBw8eTE1NDQ4ODgwMTE1NxWIxNCyYzWbkJ7C2xtrdZrP5/f4DBw6cOnWqpaUFVgdut9vr9abT6UwmgxORHxGZGTDOuQjbUM0CWgSv13vgwIHm5uampian0+l0Os+cORMKhaqqqkBrpqam7t+/f/369Rs3biwtLVVVVb333ntnzpzp6uqqrq52uVyFQgGdF6ROQCYDUxg8Hk9ZWdns7Ozs7KzP51sr5K9qLfCCIViIgABBUAGB3QaTYcjPjEAYj8eTySTW5cvLy1j4Wq1WROJ0Oo3obrFY4KgDiyFU6yGagz9gLpeDdbHH45FleWlpKRqNejwen89XLBbT6TTsiuEjBJ6RTCbHx8d7e3uvXbt2+/btcDjMGCsvL9+7d299fX11dbXX60UHP5QKcO8ZGRkZGRnp6+v7zW9+09XV9f3vf//06dNOp5NmJpFbAHoEqBkBf6URxvrj04ksFkt1dbXf77dareXl5S6XK5fLdXR0HDp0SNf14eHhmzdv3rhxo7e3V1XVYDB49uzZ7u7uQ4cOBYNBp9OZy+XS6TTJHdAmAC6VSqVkWfb7/W63u7W1dWBgoL+//9y5cxI32Vla1y1AQEDgJUJQAYH/j2f8mX7pKzx+DUrv5PP5UCi0tLS0d+/eiooK+OdD4Q8dH+XbGWM0xA8j+MjgD7vQKZAtgD0AYwyjh9PpNLrwGWPJZBKy/NHR0WvXrvX29hYKBa/X29nZeeDAgT179lRWVtrtdigSIBSAeNBut1sslnA4/OjRo7t37965c2d4ePhf//VfP/300x/84Afd3d0Wi8XpdGazWVQlIGZE3yMqHQUOuGDqk0QHo8fjQS0jkUhAHgirgI8//vhPf/pTOp2urq5+5513vvvd7x4+fBjkw2KxwFaZtIRIPJCTIMkMJUkqLy9XFGV0dPSNN95gK74V1Lvx7N+WZzmISAkICPAQVEBgl4B+3InQIFYVi8WFhYVoNBoMBgOBAJx3Ie9PJBJWq9Xj8ZhMpmQyyRiD9i0ejyN5ANlgMpmEhFBRFEzrwTxfr9fr9XqTyWQkEkHrQVlZmdPpzGQyk5OT169f/+KLLwYHB81mc3V19cmTJ0+fPl1XV+dwOJxOJxbW8Xhc0zSs6THdBx0BDQ0NtbW1Bw8efPvtt69evfrBBx/89re/nZ+fHxkZuXjx4pEjRyKRSCQSoWkFMASEORI/rcBkDBGAcRAI0PLyMowNEonExMTEyMjI3bt3BwYG4vG4oijd3d04RTAYxIofnsS5XA7mBDgdnIlJHoHnDK5gNpsrKipmZmZUVaUmglU1g88Sj0kh8eyHEhAQEFRAYFeBl86R6/7MzIwsyxhJjLy6LMswEcLGUNVRIoFeIFtAroKFQoHmFmJOMVkVYbFeLBYnJiampqZu377d09MzMTEhy/K5c+feeeedffv21dTUMMbi8Tgti1F6oN5FRFksrxljFRUVtbW1gUCgurr62rVrPT09P//5z2OxGLSEkuFkrBuWwzA9pClE2IDMi3Rdh7Ihl8vFYrGZmZmxsbGenp7h4WFMKz5//vzZs2c7OjoaGhpkWU4mk4uLi/zYRugecJFkqaQ/7qmMXomampqbN29Go1EqamytqcDK9NXK46+T4hK8QUCgBIIKCOwqUFs//XdhYWF+fr6mpqa6unp5eTmTyWAJ7vV6HQ4HiezQCAdTIFmWA4EAgqvFYkEfAWMMhQNd12k6XzweLxaLLpfL5/M5nc7x8fE//elP33zzzczMjNVqffvttzs7O9vb2xsaGtCviPMipY8CBDNGEkDJCOUdLA1wAcFg8P3339+/f39jY+OtW7c+/fTTgYGBt9566/z586gs6MZUAnJHxhpdN2Ycw35A07R0Oh2JRObm5u7fv9/T0xOJRGpqat555526urrGxsb6+vqamhqUKjRN8/v9hUIhFosVCoWKigpZlvP5PO+5RDkJcjVAhaKqqgoiypmZGbCf5/ERr/W+UCQICDwFBBUQ2AJsn2UWRQIs7rPZ7KNHj1KpFNrnlpeXyT4P/4XzDybsERWw2WxOpxMFeMkYAgRPIUq8Y2OkzeFVnMlkRkdH0VXv8Xj27dv39ttvnzp1qlgsJpNJtAkUi0WsrcnY2MQNR0bWgayKSKZgt9v3799fX1/f1dX1H//xH5988onVat27d29zczMuhtoHcONYyjPGYP2rqmo8Hp+enn748OGtW7fQGhAMBru6ut55552zZ8+Wl5fDtyCZTKL1Ec+HFvroNUgmk6hEMKPkT3ZGlEoxmUxQXLrd7kePHnV2dkJxybY6MbAWBAkQEHgKCCogsKtAvv0IPOl0em5uTpblPXv2aJrmcDgoyME7iDr1sQv9SVVVGknMp9x5F0KstrHN8PBwX1/fN998MzExAdnd6dOnKyoqkskkaASOgPDJjEwAHZ8MBDOZDPL8YAzgH2AnNTU1Vqs1Go0uLCz09fVdvnzZ6/Xa7XYQERwBkn4wA/IsmpiYuHfv3uXLl69cuZJIJOrr6y9duvTDH/7wyJEjiURicXExn897PB5YHKIQQNyCKiCwYMK982pKKmrAdgnpB03TgsHg9PS0qqpQV/CfUYnG88XjxZASAYEdBEEFBJ4V2+1XldeoZ7PZ5eVlm81WW1ubyWS8Xi/iOgIntAJY5qL2j0Q3bIV4YRp156MojlE9VONPp9NDQ0O/+93vJiYmFEU5fPjwhQsXDh06FI/Hw+EwCAeqEiAZVL8AcSGfYFwGMg12u103xh5CkReJRDRN6+rqOnfu3GeffXbt2rWDBw+2trbC1YAZM5SpuJBMJqenp0dHR2/dunX79u1cLtfU1HTixImLFy/u3bsX3keMMaRGyGUIXQbgECgxMMbyBuhpgAHQNAdcP/k067ru8/l6e3vRXbky9L7074xgAwICPAQVEHgabLef0VUF6oxLmPt8vnA4DJ9gXdch+EcaANEOYQxt+sjVM24ynr7Cyw9Dh+12OyR4Q0NDg4ODTqfz4sWLp0+fdjgc0WhUkiSY+qmqKssyWRjxdX1ahdtsNkmS4AGMlAA2RtUAAkafzxcIBP76r/+6pqbmX/7lX/74xz+2t7e73W7cKTyDzWZzMpkcGxvr7e29fv16X18fYywYDJ47d+7SpUvNzc24NZwO14b7snBAlwTKGVj64wnTlVDWgS9PQEBAHkSJRAJ84hk/RAEBgecNQQUE/j+kjSa4bM+faRL5l4zEZcZaHyOGsZRH9CX5GyIZXtO9U0MBGfcyozeBZImooCuKMjk5OTQ09PDhw2Qy2d7e/tZbb3V2ds7Pz8/Pz/t8PrvdjjwEqADqDuRXyIzqAAnxcGE0XZAICtgDhirput7Z2ZnJZG7dupVKpbCsx4UtLS09fPiwt7f3yy+/HB4eDgQCx48fP3LkyPHjx6uqqmCpFAgEJEmKxWKpVAoPDTdI449NJpOqqvA0xPPBdSJlQrIA/BVEAf8EUXA4HG63G9UNTFakEQn6CiPIp8CG39JNQiQGBAQIggoIbBbb83ezpL8coCgbj8ej0SjmApuMIb8I85STZ4yhNs8YQzaeCvnUp8cYUxQF4U3XdfTRwZn44cOHn3766dzc3OnTp7u7u6uqquBVwBgD+QARwVqZDIVwMXgfgZ/GH0PQgFU7RiCSnw+qDCaTqays7MKFC319fbdv325ra1teXo5EIoVC4d69ex9++GFfX5/f7+/q6uru7j59+rTf78e4BLvdDnmgJEmgBTgpMzonqXWwWCyiQoF/mrgRiFTXKBojH3GdjDEUXBRFQb7E4XDMzc01NTWZjFlEWwXBBgQEthaCCgg8hlV/ZHfczyU57cRisaWlpbKyMsYYojtCl2RM76XVv9VqpSgIEQCV6uFSDNsA6h602+35fD6RSAwODn755Zf19fXvv//+yZMnXS5XJpOBVm5xcTGdTldUVLjd7lQqlUqlbDab1+ulIQgIzIlEAnMOFUVBxNV1HfpB8jZArp4mDjidzu9973sjIyNffvnl22+/nc1mv/rqqy+++GJgYMBsNh87duzP/uzPLly44HK5EKehhUSPAGNMURS3243BS7T6pyU+DBldLpeu6/F4HNoF4kZ4wkQFkC2AlRByAKACTqfT6/XOzc1ls1kQhQ3z/0/0NRNNgwICWwhBBQTWwzYnAaumBHggqlVXV2M1Tz0ClBVASOMb8VH5pqQ3Mx4C32JAiv3+/v6vv/7aYrFcvHjxwIED5eXlkjGeBwZ/drudMQaLHsR4iOodDkcqlZqYmJifnwcbGB4enp2d9Xq9NTU1TU1Nra2tFRUViqKgZk8GyYqiSJKUSCRkWXa73WNjY//2b/82Pz8/NjaWy+Wam5tff/31kydPtrW1VVdXQ52ASYl0ARjQDGKBC+OT9rwxEfQHSJPwT4CSLtT3SGZNpBswm81ut5u6JOjzwr1s1ReALvupOYFIDAgIMEEFBFZid/wykimQy+VqaGhAUx9UddQTT8I9ZpQGMJQIyQBm1MIRKfkphdD3xWKx69ev37x5s6ur66/+6q+8Xq+maXa7XVVVKOYwXxjTepCTh42xyWTCBKPJycnPP//89u3bs7OzyNtDw9/Y2Hj06NHu7u7W1laiJul0mpT809PTS0tLPp+vv79/cnKypqbm2LFjFy5cOHjwoM/ns9lsEBDgIcBiGbkECA7y+TzSA0SAGDfaGLUJciagcgBqJWAJfPslNAGMMTgTo/tAkiSHw4GZzjxIMfACvwsCAgIbQFABgd0JXuWnKAoCOYn+sPbFC75RkJoJ+UNRQQHb4OCpVGpkZGRwcDCfzx8/fry+vh4+QlR3oBwDJR5wRkjrY7HYlStXfvWrX01NTdlstvr6+s7Ozj179kSj0UePHo2Ojv7iF7+4fv36P//zP1+6dElV1VgsZrPZcrlcKBSanp6+du3arVu3JicndV1va2v727/92zfeeMPv98OQGLUApCWwrMepkRggMyVcVYl60Wq1KopCHYmkIoTbAU1nxpPB7fAPFk9PVVWr1ZpOp1E/S/i/AAAgAElEQVQicbvdz64WfH4Q1ERAQFABgZ0KyglTmOGr0RSi4CdI63tSBSLqk7idhhNiA0pik0UgCt6URUilUvfu3ZuZmWloaDhx4kQ0GqWuPMaYLMt4QeaG4BwIw48ePRoYGPiv//qva9euvf766z/4wQ+CwWBTU5Pdbk+n01NTU7Ozs7///e8/+uijn//8552dnXv37k2n00tLS/fu3bt58+a9e/eWl5eRw+jo6Dh58uTRo0dramoSiUQ4HOYHGUN+CBUChiBD4Q92gqlCRFYo9lNDoK7rEAGQzRFGFWuaJhkmjACfKgAVsNlsi4uL8Xj85MmTVVVVzHB/Wj+Tz//1SaUDQjcgIPDUEFRAYDeAqABZ+cqynE6nY7EYDfAl5xwqZmOaDhnnIZIheNMgItLMYwOs+BE4JyYmksnk0aNH9+zZA30Awip4hm54BdrtdkRimjIwOzt7+fLlqampw4cPf+c733n33XcxQTiRSNhstoqKio6OjmAw2Nvbe/ny5V//+tfvvffe/fv3b968efXq1ZmZmWKxePLkye7u7kgkMj4+jmEB6XSaMUY5CWYs2VFxQJWB6BGqFSANfLkddRMU/nlGhXsvsTemwgE2oBQLXttstnw+H41G0c/Jf0xroSSWi8W6gMALg6ACAjsSay0B+f7AbDY7NzeXy+VsNhtK+GgrMBkjfKhwDjE/7Pppvg7jUgskNiRnYsZYLBYzmUzHjh2jojiFWARUEhxgti8W5Xa7fWZm5vbt23V1dT/+8Y9Pnz5tt9tRa6cUPUQD6IH8xS9+8cUXX+RyuaWlJavVeunSpWPHjh08eLC6uhpDkHEj8C3I5XLZbBYtD2gHgJ0wzAmcTif+CVMEk8mUTqfhq0gVEMgIUCbQdR37Yh5xsViEdxC6GMB7GBez8UKWZQwscDqd0WiUVw6us3Bf9U8vjA0I2iHwikNQAYGdh02mgjVNSyQSqJTT+pUWrzRWgDLb2It0hYxbKCP881mBZDKZSCTKysra29sxaxi7gzGQ+ABvIiSDGSSTyfHx8cXFxQsXLrzzzjuBQGB5eRnDijAU0WKxzM3NffbZZ9PT05qmDQ4ODg4OHjp06NSpU2fPnj1+/HhLS0uxWAyHw4VCIZVKIeGfyWRQyMcFIOdBSgiMEeJzA6RjQLaf1JHkuwBfAUxGAL/JZDJIGGBj0hnQx0FCQlATp9NJhg30MNkappDrfNaCDQgIPG8IKiCw87BOYZjiOmX1IXNLJBLwGoKwDnEXowFsNhtCKZa/0PlTmp2mFkFDgK48SZJmZmYSiQQU+8gukFUA1d0dDgdkdPF4HJHGarWOj48PDw/7fL6DBw8qirKwsICwarPZkD+QJCkajd6/fx+CAMbY/v3733333YsXLx45coQxNj8/jykJKAeUlZXxbQs0K6hQKCAeQ0UI6R/y/BaLBSV/pBAosU95flw2MRhkDmB9iOcMO2TakhmhlHoNcEfQRjCOB5RgM6zuxQRpwQMEXmUIKiCw47GWftBisdjtdnLQy2az6KZDFR/VfYkbNghnQGaYDGKNSy+wsEblW5KkqampdDpdXV2NuQYAM3SFEBxgcZxMJmmsgMlkmp2dhX8AbPgikQgE9kjpI5r6/f4TJ06EQqH79+9XVlZevHjx7NmzdXV1uIxUKpXP55eWlubm5gqFAswEcS/Q+eMFqRZwSaR/pH4/lDBIEyBxRsuSMbmRkgp8qwU9E8qpUAcBYwy0A2xMURT6mEiz+ZyCrlAOCgg8NQQVENjZoEw+4xZ2qAiYzeaysrJQKGS1Wu12O/EAGqqL7RHdEQVVVdWNGUUIopRXlwzjP0mSVFWdnJykcn46nVYUBa/RiYdaAEVTRClN0yjNjhwAeQkjD0/VB7vd/hd/8RfJZNLn8508efL8+fO1tbUul4tcit1u9/z8/O3btxljoAI4JpoUcFNoGcAxkSGA5zHpGJDDwAWT4RIz8v9UKYBuANkOSpDgr3jaYB6kK9Q0LZlMwl0ReQtmxGlwBQEBge0GQQUEdgNI7U9sAA2EyN4jQlOGAGGM0s6IVdREl81myWeX9IM4Mt40mUzZbHZ+fj6fzyNJjjZ6u92Oc0G0T1N9QUoQR9HrrygKuvWQSMfGCN4gB4uLi2j9P3Xq1I9//OO6urp4PA5BH67HbDaHQqGhoaGmpia32w3ighYJxGzJcBdAbh8boDMQ/gd4E5MYC8YoZN5jEfwAfEWWZRRBKP/P/5UeO16goJDNZjOZDFImOKDEDY9+gV8NAQGBjSGogMBuwMrMsGSYB1CUJdkggh/56YIKMMNiiNLjjEs50PwhxO+iMa0Ai2Y+UiL9jnIATk18An0ENTU1brd7amoKeX5N05CloM5DJDNmZ2czmcyRI0cqKysxShgtkU6nU1XVcDj8+eefp9PpAwcOINtPzj/gHwVjipLEDRCisYf0cHRdV1VVMkD9h5JhP6wbXgt4gBTLiQHgUGS6ABEiChYmkykQCDgcDvqM6JnzH9N2kAsIdiLwikNQAYHdCSjgkKDOZrMw20f5nHFqAMbRCBrRS2kDZuQbSFJHKkIEV6jnHA4HGvMQQSmIojURK2/wCU3TGhsbg8HgyMhIOByOx+OZTMZut6Ngkc/nXS4XLmNycnJ5ebmmpkaWZbQS4ESYejwzM9PT0+PxeLq6uhhjqA7Qql03JiiaOOi6jgwBuR6ZTKZMJoOUBun7QF8Q3UGJiFggE0A0glb5IEO6roPcyLIMUwGTyVRZWYk2S7qwl/V9EBAQWAeCCgjsBqy1uMR6PZFIYO2LcI7/ZrNZiOwwMQjLfYRt0gBKnO0gFPtYSWezWcRsxpiqqjiLyXDwpf9SyOSrA16vd9++fXfv3r1x40ZjY2NLSws2o4k+xWJxenp6aGiopqamoqKiWCwqiuJwOLxeryRJoVCov7//gw8+GB4efvvttxsbGz0eDwI/7U7OxxLnj0TLfZyOuiQoyQ8NAfUy0BNgBnPi3ZTBiqjaQsILPAqcKJlMrpxItA3X39vwkgQEXjAEFRDYtdAN5114DvJLZKjbsHJ1Op2o9yMYo9GOj+UoKKBOj17EXC7n9/vJdQdyOVooUzECxQKQALQw+Hw+uAXX1dXduHGjubm5o6MDvQbEGAqFwuDg4P3790+fPu10OjOZjNvtVhTF6/XG4/Hh4eGvv/56eHj4rbfe+vu//3uMH8T9UmmjZP1NIn9a7kMgSYUAbID0CfSVjLF0Oo0kP63+cVikEHA0Eg1Q9yDmLDPGMG6xpINg1Y9pMzWCTUbrp2giEDxAQIAJKiCwK4HcuK7rkAouLS3ZbLZkMomqPLkC43XRmNaDWM6M+jrjzHepmgCpvNvtrqqqMplMqVSK0vtYK1NSocgNQS4aMw/R5V9fX9/d3Z3NZu/evfuHP/xh//79e/fudTqdDocjm80mk8l8Pm+321taWrxeL2IbAvPY2NjHH3985coVRVEuXbr02muvUf2CGSGfcf0U1AqBpTl6Jfi4zjhHRQIzWAXpAUFu+AIKqQcYY9AnmrhRC7qux2KxXC7n8/nwQeBzoSsswcvqAxQ8QEAAEFRAYOdhw7BRNEYKweRnaWnJ7XYvLi4qioLwbzKm7aHzDct3lM+pg043eugR82gvRVEqKyurqqokSYpGox6PJxaLkV0xdsReSDNAluhyuWALmEqlysrKLly4oOv6hx9++LOf/ezv/u7v9u7dC7F9NBpdWFiwWq319fV+vx+HUhTl0aNHf/rTn65fv76wsODz+b71rW+dP38e1AFGSXz3BEVfkACwECQzdMMkAFfLWyBIxlgBekRgGIj0SLHY7XbUEYhJ8BLCojHIOJ/PRyIRi8VSVlZGc57YuqF3HTbwRAH7ZbEKAYEdDUEFBHYe+J/7VX/6dcMbAO1z2WwWEatQKKiqCrs9xhjiH8R0yJwXjVm92ACSeFLFo6KPJHlFRYUkSbOzs8lkEmUIlMx5+T3VICBBsFgsKEM4HI62trZ0Oj02Nnbnzp3//d//ffjwYXd3d0dHRygUWlhYiEajZWVluq5Ho9FwOPzo0aNbt25dvnw5Ho9fvHjx0qVLR44cqa6uxtF0o4sSIdPEDQzE0+D7J4vGvCXkMMh1gPokGWMI/BLnJEhPtcSBgOcf+BMOqGlaOBx2OBw09OjpWgCebtXOp0a28LACArsYggoI7EJQ0xqp+eLxOCzxEckQqmkyYT6fh5cAFtmI3IwxhE8S01FFP5PJlJWVybI8NTU1Ojp69OhRFPLR9WexWCAqRIsgTSZcXl6mLgaLxdLW1vaTn/ykra3to48++tnPfvbVV1/t27cPTQczMzP79++Px+OqqmKicSqVampqev/998+cOdPZ2Wm325eXl6lNAHEd904pAWolALmBvSDOjiwI4zopqNMSWQFm6CTwJkgSmA21XPIsAefCcTRNU1U1Go16vd6iMSiSOjaZUYxYaTe0tQv6tY4meICAwEoIKiCwO4EwYLPZvF5vMplcWFgIBoOMMYR8WP1TUZ9iG5bIIBAkEdC5TnrGGNr3PR5PVVXV4ODgxMTE0aNHKZ2OcKtzwwwZY1DvU8IAUcrtdnd0dHg8Ho/H09PTMzk5efXq1WQyaTKZZmdn5+fnZVlWVdXpdFZVVXV0dJw/f/7gwYPI6ieTyRKFP4AzUpSljD0RIF4fwD8o9rhtM59UkB73ZqZyA/21yE1yQmsGFA81NTXrhPYN8wTPHrNF1BcQ2CQEFRDYkdiwRoAw4HA4mpqaZmdnx8fHGxoaJKPvn/wGTMa4XvLkZ0ZQ1DQtnU6jUR7VgYIx8NfhcDidzoMHD/b09MzNzSUSCSQYIJjHvgjJVqsV+kRmxFSkFigzX1lZ+d577505c2Z+fn5iYqK/v//+/fuKojQ2NqIpv7m5uaurq6WlBXmIbDabTqd53R/1RKxM2uMakDywWq2QI+CmIPSj3VE9ocIKX2WgugPyBOS+jINTZQG3D6+CdDqtqmpdXZ0kSag+lERlutS1PlYRxQUEXiQEFRDYqVinJExrcbvd3tDQcOvWrcnJSSj7EK6KxqghRGusZaHyIx8hfl4R1QvAFaAxPHDggNfrHR8ff/TokdPpRKR0OBw0KYDqC1D28bOOyADRZDL5/f5AINDU1NTW1pbL5RYWFs6fP3/mzBn4C9ntdugNY7EY7IAQWWFbRBl49njinQgB5SEwSgAZfrIOlLhmQj7kY63P8wB6qrw4EY2FzBj6gCep63oikcjn87j+zWgGV352AgICLxKCCgisgpL4up1/nbGOLIlS9CdJkioqKjwez9zcXCwWKxaLPp9PMux0oI9DboDPn4MEoAOQxASSMVAHBXjGWG1t7cGDB/v6+m7evNnZ2YmjuVwuiAk0TcN/seZmjCGpwBgjqyLyKoAPUjwej0Qidrv9zTffDAaDkUjE5/M5nU5iJCX5f7aigZAZOgk+ACNam0wmKP+R4S9JKmBjKoUwY/wguSRJhi0xHRl6CzQQyrJMagC32720tFQoFMrLyz0eD08jBAQEtifEoDCBUqwqyN9ZDVq8ol5RlLKysuXl5YWFBSj7kGPPZrMI+XhNvnuMsVwul8lkKGqyx8fykgguEAgcPXo0FArdunUrnU7D2xjVBJpslMlkiEYgGQBvH8ZYsVhUVRUjjFOpVCwWW1xcDIfD5eXlx44da2xsxHqdMZZMJmOxGPwQ+SoAr0UgYb/ODVamHD60EeifRMcjlQCIN5RUBHh3BOlx0AWAiOC50TRks9m8vLxss9k8Hg+mNbLHyxb0XdpZXyoBgV0MkRUQeAzr67zYtlzerbwkft0sy3IgELBardPT0wcOHCj5q26M2mPGDZZY9fEqejLkR3DVdb2tra2trW1kZKSvr6+trQ3e+1R05/P2dGGQHSB2KopCF+B0OtPpdCqVOnv2rKqqZrM5EAggTlNyAgfBup8P4Yzr7+cth2kzfqpCiWYQwZsCP/VD4rLx5sonTKkRmq2MvIWmaTMzM7FYrKamBp2cm/m8BAQEXi5EVkDgyVAiL98m4Bed/D8R9oLBoMvlevToEbLZNFaAGuqKnJc+r8xnnNYP+XnIBVAXVxRlz549x44dW1hY+Prrr5eXl3VdV1UVUwQlQ6LIL7ItFgvceRGqabwQWhDRH9jR0RGNRlVVLS8vh+oQzIOfAESyQUo2EJuByoHoAlEBchWkyG0y5hCShhGlECRLiGeQWwAlG+iJZTKZRCIBG0ecS9O0iYmJVCrV2NhYMn2APc6KSj4yAQGBlwiRFRB4SujbbPB8CRVgRvSVZdnv99vt9lAoRMlqyoRLhtqfYjYzVti6riMikiCOIisEhjabLRAIHD58+LPPPvv0009bW1tdLhcG8NB4YtAIdB+QGlGSJDLwR24gm80+ePDg0aNHlZWVPp/PbDYjMYA1N3IMvMEfnxXg2QljDHUKEgPSyp5a/6GKwOQCUAFU/UnnSI2RAGUR6KS6MaqRGWbGMDbA3IFQKGS1WlHgWPnpbEluadsmqAQEdigEFRB4emznX2Sds8qx2+1ut3t6ehrzeMhRB4lxaiAs8cXDERC84ZonGZI6mAcg6u/bt+/AgQMffPDB6dOna2pqgsGg1+tFboAZk/qojk7jB6Hhx0ntdnsmkxkYGJiamjp8+DC0eOg7AGMAe6CuP57K0AKd3iefYJMxKVHnXAKpGsILI6BsoEU/dl/pI8TXO0zGtAUoIdAhmU6nY7FYIpHweDzV1dXrfzGe/Wuz3ciogMDOhSgQCDyGJ/1t3c6/xRS5HQ5Ha2ur0+m8e/cupPsIhIgl6Iij+Mq4ujt7XExn4sAYA1EoKyvr7u6uqan55ptvbt68iSEFMN1DIJcMt/9MJkNLcKy8ydZQ1/VkMrm8vBwMBiknwbiAXXJhpN3DoSjYM8asVqssyyg6IFWAJATaDqlmwU8f4E/HHk/jk86gYEwotlqtaHngWQXIRCwWi0QimUzmwIEDGG/Ig3+8W/K12c7fPQGBnQVBBQRKsflf2O38W4wwiRw15gLX1tZevXqVMQY/QfTlS5IEvyDy2zevAFnrlLyTTqeTyaTFYunu7n7vvfcGBga++uorVVURidEsgHgMKpBKpWBYBIkAjfRFbR57VVRUUFSGRAD9CHRqkzFBEYSGRAyUG3A6nWhoTKfTqI/g7FAq4IAoi6iqajKZENeZQTvALeiTJS0hmITFYnE4HB6PR5ZlcjLG+/l8PhwOh8Nhs9l84sQJ6XHfp+chMdlughUBgZ0LUSAQWAWS0ay/zq/ttuUB/CIe75hMpoqKij179qAeX1VVRe3ylHKnBTqvGKDnQAGSdmGMYd1vs9mqqqrOnz9/69at+/fvf/bZZ06nExOHIQWw2WyI+gj8iJ3IHCC+Wq3WdDqdyWTa2tr8fj/cimgVTroH6tkzcYMH0VyQyWSY0ehPt0z6PmYYDSHk01KeGgdosY4NmGFXoHNNhowL57QLXlNeIRwOz8/PNzU1VVZWkvCw5EPZwq/Ntv0GCgjsOJh/+tOfvuxrENiOoBQ0e7xNn3+9PYH4VHKR8NlVVXV6erq2tlaSJIzcJes9TBckOx3sRbEfWXdm1PjNxsBi2P/pul5VVaUoyieffDIwMNDQ0NDe3u52u7H0d7lccPxlxowfk2Hi+//YO8/4tqqzgZ+rdbVly7Ys7z1jJ07iDIcsQkIIBEgIm5a92rJ3CxRooYyXMksZL1BGGS3jpRBIIHuRhDiJ7XhvW17ykG3tfd8PT3R6LMmy7DjOOv8P+SlX95577pGs5znPdDqdQqFQLpdDOuKyZcu0Wq1Wq+XxeNAvkRT82LyPQwjhERBCTqeTz+fLZDKhUAg2Bp6v7zB254tEItA/YGSZTAbJC1hmYz0DWwWYgPJN4C+AyER4F7wMLMvabLYjR450dHSsXLkyKioKjBw8onEDN7KD4jFyMn8DKZRTDuogoIwB+Zt7qvz++hkzQCbFxsZmZ2e3t7dDh0DsQcCRg3jfH/jI2GWOfA51HJbvdDotFkt0dPTixYtnzpw5NDS0Z8+eAwcOdHd3Qw4eXA6bcrAKkJ4IkPo6nc7hcGRlZUG3JL+nwLMi5TTyKT1kHAMW26C7gMEAlz0m9TkwIcB/8UzIyETyX6yRgB4A2ZJwC9ClHA7H0NBQX1+fSqXKyckBV4Xfp+BnY8AHJ+A4OFW+hxTKqQK1ClBON/xi03BCP8TKlZWVRUZGRkdHQzMC2NeS0fX4chBREF6HA+nhoNvthgh/XECQZVmZTJacnOzxeEpLSysqKhBCKpXKZrNBhJ3FYjGbzcjXGpHzNUpGCHV0dGzduhUhNG/ePDBLQEAingYZ848D+/GcoXwhNgMgoo8ADgiAmzK+zgLYO4CzEMHIDzfyswAFekYQQtDcCCYDrZkbGxurq6vPPvvs3NxcMJx4fS0f/T6U0QwDVMBTKCcKGitAOd0IFDY4wi4iIiI2NrazszM+Pl4ul+NEOJ6vioCf8EM+szlCCKQmKSZZlhWJRLDtNpvNERERK1ascDqd5eXle/bsEQqFMplMo9Hw+Xy1Wm2xWEwmE4QoMgwDtxYIBEajsbKysru7OycnBxQOi8WCJw+qCReQNcfzdTGA1AAwb2CNgYwJwE+ERwOPBjwOVCCA/b3D4YBcR3he7NHAmgcMhWMscFEEq9Wq1+tbW1vFYnFBQQHyRSowIyNO/BwNgR9c4GNSKJSpgVoFKKchpMwGUYpN8Xw+v7S0VCKRQAtdhBCE0PN8HXthBFwuEG9/sTjEeYBKpRJi6eF8u90uEAjUarXX621oaNDpdCCklUqlSqWyWCyDg4MMw8jlcogKdDqdTqezpaVl8+bNDoejpKREq9VCeUH8FKT9HEt0bB7AYQdk0AMIb7BYQFwhPkKqPrgwEYhz6CcEtRBwkAG8Bs0A2xJwsiKoLDB+XV1dRUVFUVHR3LlzeSP7D+EERXzET0sjj1BVgEI5IdBYAcppAik4/Zz9WJjx+fzCwkKbzdbZ2QmpfZyvhDDO2cOx98jXMgBSAHABAOQrWwS1BUEhYBjGZDIZDIaUlJTVq1fPnTvX4XCUl5dXV1e3t7ebzWaLxQJ9j6C6AELI4XAYDIaqqqqKiorIyMisrCyQ8Th5j/RZ4NB9rJHgOoaQH4jlN1yL3SKg6IDgx3WNsOMfhsV+B7xigeAwAhxgYbPZoL+R2+3u7e31eDwzZswgszDAuOId2dAIESaBwBcUCuWEQK0ClNMEvw2ln8MbZCTk9Ov1+uHhYZZlo6KiFAoFmNnJbj2kYxuH5kE+Iey2QXZCA0MIoYeTQaXw+loadnV16fX62NjYmJgYcMyDEIV6gnw+v729fePGja2treeee25xcTFoHl5fswC/HTMibOxkAAFkAUAcH64biGU28lUmhumBax8qDIIFAt4COwEoEKCpwCNAPgLjK8WIR4OngEmWlZXV1dXNnDmzuLiYZVm/9R/vZ0cNAxTK1EOtApTTjaDeaIjvg4j3mTNnCgSCzs5OSMeHnEAQb16iFxEoAS6XC1oYw+Yb+fIJPR4P1Ae02+0Mw0DSILQUEggES5cuXbNmTVxcXFdXV1tbW2dnp9FohGvNZrPD4QBJ2dXVVVVVxTBMVlaWQqGAXT6uBkj2TcZWATwriFsELQdLd9AkwOUPpYTIAkEQQ2Cz2cBRApoBDIVLITG+/gigWMDje4leiNDW2ev1QhvG4eHhyspKq9U6f/58hUIBS4pGRgb44ZcyQPUACuWEQ8MGKacPWIST2gA2VuN9rUajSU5ONplMjY2NVqtVq9VKpVKQptg1HjgmruPL81UdBq85bL7hcojVh0FSU1MvuOACt9tdWVkZHx8PtgG1Wq1UKlmWdbvdOp2urKzMarVOmzYtMjLS4XDYbDbo8wubdfDxg1qAUxjADEC2KUK+bkCgGeCwPtL+jxMKYMcPoQN4fSBwAUtoeEbQJ0CB8Pq6FuH4Sng9NDTU2NhoNpvz8vK0Wi3MJISkJ9+iQYIUyskDVQUopxtktCDyKQRkIpxCocjKympoaGhoaBgaGlKpVCqVymw2w44WxwrgfS02wmMXgNVqdbvdcrlcJpN5fX1+7Xa7SCSSy+V8Pn94eFilUq1du9ZoNL7yyiu1tbUDAwM5OTkKhUKlUslkMsi+q6ioEAgERUVFEokEDAw4VgD5BHzQx4FsRpgk1DHkOA5aLOJGiDghAiwNMEPctBA8HeD4gIxEWBwojwiWBuQzLeCESbArgC7idDoNBkNFRYVUKp09ezaYTPAJiAgYxB9NYExACOMBhUKZMqgqQDk9CXQTYHmjVCqzs7OHhobKy8vdbjfE8YGPAMzy2BiOrwXfPC6bQ8bxcUSdH0TIbLFYrFarZ8yYERcXp9Pp+vr6FApFbm4u5PLZbDaj0Tg0NMTj8WJiYmw2W39/v0wmw6kBEA8IO3I8/0BrB/I5MsjHJGdC5vXhI2SEYOAqkW5+uATXOYAzQRnq7e3t7e0ViUQpKSmxsbHkWqFg0p0bWcrabw4UCuUEQmMFKKctfiINO/4ZhlEoFFFRURzHWSwWKP4D2+KgBYVwWR6EEDQOBnkGXnPYajO+PgVguoegBJfLlZaWtmDBArPZ3NjY2NPTA5tmiDf0eDwQP8iy7NDQUEdHB+gijK9zMQyC9804jAD57Pa4fCF496FmEWgt4N1HCIGNAQwAYBrhfP0LyPoBeMVwQCKuVQBuBdCWwHDCsuzw8HBNTY3BYMjMzMzPz4f6x3jRQrj/yVjOcYUWUiiU4we1ClBOf7BwAqEO/42JiSkqKmpvb6+rq+Pz+dHR0SCGcZcBuJbxpd6ByASzPIwDAhjXIeb5WviA1Z3jOLfbHRERsWDBgqamps7OTpfLpdFoxGIxjvBXqVQxMTEpKSkWi8Xr9SqVSq+v7RDswnHQH+MrFQxHQJCDtOZ8aYFkw2KOAPls9XiqjC85EK8GroiM70WOjHyZgbhU0fDwcF1CK+YAACAASURBVH19fXx8fE5OTkZGhlQqxUs92qfAELWGqBJAoZxUUKsA5bQlUBxCCQF4NyYmZvXq1cnJyQcPHmxvb1er1VKpFHzqEFQPW2HsNcAOcmjGg//rcDjsdjtZixALWtj3z5kzZ968eTKZjGXZhIQEaIgslUpFIpFGo5k7d25hYaFQKFSr1VqtVq1WQ5cgq9VqNBqNRqPNZvP6GgTjrgH4v7hCABbwaGS1f9KwwRCdBciSwH79EcgVgxuBBUIsFuPiQkajsaOjIyIiIjs7OyIigufrkETeJfATwYtD9QAK5aSCqgKU0xksnLAExfH/EOKXnZ0tk8k6Ojp0Oh3LslKpFLL/wU+PK/rxR4LL++BQRL9YAbyZFgqF8fHx06dPT0hIGBoaMhqNuJKxzWZTqVS5ublyuRz0AKhlhP0C5JYdZyvgWn5+EYXcyMgGP5c8LpaARlZcIGsPYIMEKafJTkWgDTgcju7u7v7+/vj4+IyMDJVKhXz+FzIVkySEv4BCoZwM0BJDlNMTLA7xThS/BSHxcFChUIjF4qqqKr1eP2PGDJlMZjAYlEoldBbG/ngs/kEk4+qEuEAhHhmn20GhISjjY7fbW1tbq6urs7KyUlNTOY4bHBwsLS1lGGbevHlCoRDSCnDuAONrLQg3ghfQP4kMbEREzCCoCwzRqQgRDRQ4IvsAruUTrQjJksM4bYH0LMDjQB/n3t7e2tra7u7u5cuXFxUVYXsAGqmgBIXqARTKyQm1ClBOQ/x80kH3qWDolsvlc+bMUalUzc3NXV1dOJ8QZD9s0MndORwEkQn/4n0zIkwC4FwAuY4Q0mq1OTk5/f39lZWVRqPRbrf39/ebzWbQAEwmEygfdrsdFw4KLIfMBDQpJuMB8TzxCnC+igI4PJAjYvvhv2D/gBPItQr0LIBy0NfXV1dXZzQaY2JiiouLIyIiQNHx+poQho4VmMSPmEKhTCI0bJByWuEnikYLT4NIfpFIxHGcXC5fsGDBzp079+7dm5eXFxUVZbPZnE4nNPbF5fawRwBv/bHgJzfiID5x42OWZSUSSURERGJiokQiMRgMfX19UHJYKpVCSySGYcxmM4wGMQq4IBKeP04QQL7KB/heeIuPfAIei3OerxkxCgjd53zpkbAO2N4AB/E5uFchKE+HDh366aeflixZMm/ePLFYjBBiWRb3QMJrEtpHQKFQTjaoKkA53cDaAOkUIN/C/gIsHadPn97b21tWVoar7UJ2HK7rh/sC4KrAyJeGR3oicL4fSFao+aNUKiUSSVJSUmRkpF6v7+vrEwgEra2tcrk8LS0NrjKbzXhkp9OJB+GImgFgLUC+goOk3CXjBsjnQiOVIT8zCU6SBMcHxD/CmNitgFUNl8tlNBqbmpr0en1iYmJubi7yKShktgVoRTQwkEI5taCqAOW0IhwJxBGVBOGIRCKZNWuWSCRqamrat2/frFmzUlNTEUImk4lhGIVCAUIOC11sBsCSGOzzIFNBvkKiAWzKnU5ncnJyXFxcc3Pz4OCgTCZraWmZP39+fn4+2AAsFgvs7HHNPtxBAAIIGF83gdBmD1Lq44fFFn6/gAmGqCKAT8B5kgghgUAgFot5PJ7L5RocHDx06BDLsldddVVGRgY3slTRuNafQqGcbFBVgHK6ETpsDbvAyZ20QCBISUmRSCRtbW11dXUZGRlQfBfegiKADocD1+1BRO08HHyHEIJIAuSzEECGIZQ2iomJ0Wg0ZWVlg4ODHMdBZeL4+Hi9Xo/tCrBBx/kCyFfyCAci4ObF5JPiKeEnwvPElyAipg9kPxgecPlhsECQtQTgv1DJwGw2GwyGlpaW/Pz8devWQZOCoOtMVQEK5VSEqgKUMwuQ334SC47I5fLp06ezLGs2m7dv3x4XF6fVaoVCocVi4Yhqg2QGPylxQbKSt8D5dUKh0Ol0KpVKqVTa2dk5MDCQlJSk0WhMJhOMiRDCJ+MbwQiIKObvZxXATgScUwBGCDKaAY8AGgZOUgD1BVIDsOUAV0YCewDDMFartbOzs7a2lmXZ4uLitLQ0sVjMH9mxiZxSoFOGQqGc/NC/W8oZB97E+6XCSySSOXPmLF++3OPxbNu2raamBhzhw8PDg4ODEN5vs9msVivE+XNEEUPIGgB3O65BhB3nQqHQaDTKZLKIiAidTtfc3JyXlxcbG9vd3Q0VjUBy426BEDEA4yDfdp8bWUYQPwgTUMWPDAjAVgFcnRD5VB/sICC1EOwpEIlEHo/HYDA0NDQcOHDAarWuWLGisLCQ1APAleC3GuS7IRIKKBTKyQO1ClDOLEipiYisOZCCLMtqtdqEhAS9Xm80GsvLy6EKoVgsxh50MK1jYEDQBiDDkGEYqD/I5/OhuCEkFkL/wNbW1tjYWI1GExkZCeIf1/bBu/9AqwNHZAkiX3YA5+smACkAMBqchk39OOoQdAuGiG3EVRSxF4PzVQqSy+XR0dGDg4NtbW1tbW3x8fEFBQURERF+K4kVqUC/AFUCKJRTCGoVoJxKHONG00+gggwjUwERQkKhMCcnZ8GCBQKBYPfu3UeOHBEIBCAFPR6PUCiERkGk/GOI3DwoMOx0Ou12u1AolMlkHMdZrVaGYUQikd1u1+l0fD5frVarVCqWZaHYEa5jiHyqAC4z7Ofvx4F+AEQmymQyaG3gcDiwswArFvCANpttcHDQYrGA8d/r9cLJoMRAh8bh4WGoczw4OFhfX79///5Dhw45HI5ly5bNmzcPIYTtFqB2wL3IGsZ+nxENHaBQTgmoVYByYhiXtPAT/xyRMjfe2wXascn9N/w3Ojqaz+fb7XbwBbS0tFitVqVSqVAoEEJYEjO+Lj7YdE/uxbmRQKkAk8nkdrvj4uKio6NZloVMRbAH4Nx9OIJ7GIKcRgiR3YZwDCCpQPiFETC+kkRwPvnUeJLgMoBpgP4RFRWl0Whqa2u///779vb2uLi4oqKigoICXNKAvAUinBdoQkoAF5AQEc5VFAplcqGqAOUEQAqAEMIjtAHAT/KFcy2WWDiyL9C4DdWE1Gr1jBkzkpOT6+rqDh48GBsbu2zZsujo6KGhIVyREOQo48szBNeAzWYD1wBCCCrx8Xg8lmUdDgc4DqKionJzc6Ojo0H8Yz0A9wJwuVxQ3gD5duG4azBpfiArCcJWnvE1SkaEnMYjQ7gfaAYOhwOsERKJhMfjWa1Wj8cD5Y0ZhjEajTqdrr6+XigULlmyZP78+VBXAA+OfGoQufJY6QnqLxjzEySPUIWAQpliqCpAOVnw0wkmxREw5mlBI93A+x4VFRUVFWW329vb2+12e2dnJ44EhKucTqd3ZG9iMLZjszls8SUSCRgAHA6H2+3WaDRpaWkSiQR2/Li6HyK6A8DgiAj6QyN35ByRGgDaA8dxuGcxrjlIhgeShgfOl3SAp8qyLKgyFRUVe/futdvtc+fOnTlzZlFREdRkhNhGMmaQXDq8AhP9xMb4XCgUynGFqgKUqWZMgTEBiTKuS0gf/5jjJCcnL1++vLW1taKiora2Ni8vLy4uzuVy2Ww2kFjQLghv1mE3j4FQfHDVg3dAq9VqNBqGYcD7AA573MgA4vw9Ho/JZMISEUtxrGEghCCGEY30feCSAPjuWDmAlso4OBH8Dk6nEwonyGQyvV7f2tp6+PDh2tra/Pz8lStXpqWlIYQgtxAKDAcqBOQcJuayCXo51QYolKmEqgKUM5TRJI2fQFIqlUqlUiAQdHV19fb2MgwzPDwcHR2tVCoRQtCGB6zuiIgewAUAGF+DAIZhuru7ZTJZWlpaREQEeQ4OLMDNjUByg33Cr90RaBtgCYBJYmsBzAGbLpCvuQDyJThAFALOIGB8dY4hyHHfvn179+6NiYm57LLLCgsLExMTka+OAl4WsCLgxUEj7QFMyHZEJEE9RH7in2oDFMqUQVUByhlECHsAPu5n90YIcRwXGxu7cuXKysrKHTt2HDx4cMGCBXPnzo2IiIC6vFAbAIL7sCDHSXpgXZfL5Q0NDampqbm5uVBJELoOwuWcr2oheATAi++XocD5UgdB88AlB7wjmwd6fX0TkC+gAfkcChzH4fBAHo8HgQJGo7GsrKympsZisSQlJRUXF59zzjlSqRT5FB0yrwHqDJIrFjTuL3wR7nc51QYolBMCVQUopzlhRh742ahJIQT+fqlUKpPJXC5XZWVlY2Njb2/vzJkzCwoKoOQAxPwzvnrD2E8Pu3+Hw2Gz2To6OubPn5+UlATyG2oMI19iHp4npCySPQiw8YAhyhiAsAfngt+D4EgC/NRkRgNcAskIJpOpp6enubm5vb19xowZK1euTEpKgpaDoKCQLQeZkV0MyHULXHAUhkIQjgmBagMUyhRAVQHKGQFpuw4aIuD3Lj4HdsbwWqFQrFq1qqCg4Ntvvz148KBOp6uoqEhJSUlOToYiATj4DkQ42OEdDofVai0rK3M4HGq1WiKR4B5FUOiXLHqIY/pw80Mswr0EUDAYT5ghmhPiEoSIMCGQZwqFQmidrNfrN2/eXFdXl5KSsm7dOqiFDC0ZEUJ4bpyv/lJQkRxCTlMpTqGcKlBVgDLVhO9RPk4ETRwIehpZ9xcf12q1a9asKSgo2L59+65du7q6utxud3x8vEKhUCqVIOZxogEkEJrN5rKyMoFAEBMTg/sMwWheot8gnA8X4h4EWBuAk8G1j4giwYyvfgCZhoBVAc5XohghBLECHMf19va2tLR0dHQYDIakpKT58+eXlJQEBgMiopFx0BXzixsIf/3DPxlRlYJCOf5QVYByOhOmCGF8jX/8AgVAlPoNIhQKExISYmJi5HJ5YmIiNOzp7e2VyWRxcXHp6elyuRxqCUBLw4GBAZvN1tjYGB0dnZ+fLxaLHQ4HrtjjF2CIYwVgPmAeIP302LyPo/+QT2CTqgBWArC/n2VZhUIBiQy1tbVbtmyx2+2XXHLJihUrZDJZUEsJzlcMGh9AxTOFctpAVQHKCWBqDAN+smq0m2KZhwI2oGScARa6TqcTToNYgf379+/du3dwcFAqlXIcFx0dLRAIoLIQyGAo6NvV1ZWQkJCXlwfFhmELTu74sWgnvRVgM4CygDAgFs9wBCsN5JyxUx8aBclkMqlUOjQ01NnZWV5efvDgQZfLNW3atJkzZxYWFsrlcuQrYADBAbidARk2OOZSTyB3gEKhnCRQVYBy+jDmPjVE4gA3Spk8vyNQJwD5JC7LshkZGR6Pp6Wlpbu7u6qqqrKyMjExcebMmampqVar1WKxmEymtrY2l8s1ffr0pKQkKEwEbYo4XxVhRKgdGBz/DxWE8HzwPLHxH3QCvw5GCCEIADQYDLW1tdXV1dXV1Xa7PSYmpqCgYMGCBWlpafjpcKEk8nlJv8OYhKMNjHnCaPeiPgIK5bhCVQHKiWFyDQPHIifIiPdwIuOwtZzjOIfDERsbq1arZ82aZbFYDh8+vGnTpv3793d3d2dnZyclJSkUCrvdXldXx+fz8/Pz5XK53W7nOA4aAsFrLLzJyABYHAhCBB8BGUiIAxFAA8BlBHGMglAo9Hg8PT09PT09dXV1DQ0NPB4vJSUlKysrNzc3Pj4e+iSRJY39HtOvrnCYKxmYHBj+5RQK5URBVQHKCWNStIFJ2SyOpgSMeRUUBxQIBBKJRKVSqVSqwsJC3NOvvb0dLPNlZWXR0dEZGRkIIYfDwXEcOP6hBBBUL2ZZViAQ4IIBDMMIBAKoPeD19SiCKAHoFIAVCI/HY7PZcGiC3W43mUx6vb67u7u+vr6trU0gEMTGxhYWFs6YMSM2NhYMEoioFxTUFjKxhR1XICETMq2DQqFMGVQVoJxIjlEbmHr54Se6hEIhuNXBkg8VfKOiouLj43U6nV6vb2ho2Lt3b0VFRVZWVkNDg1Qq1Wg0YrEYgglEIhGUEoLNPTYJ4NYDOB8BygJCXSCxWAymAqg5CCdYLBaj0WgymXp7ezs7O1taWoxGY3x8/IIFC1JSUhISEqKjo2UyGfkgDJGCiEYK73AWNrTRfmrCQSgUyqRAVQHKCWbCMuOE6wEYXEUAIeRyuViWzc/Pz87ONpvNFRUVlZWVTqdTqVSWlpa2tbXFxcVBGwKpVArGfJFIJBaL5XK5RCKBwD3oTAjdDUDk4yaERqNxYGAA6glCgYHBwUG9Xt/T09PX12ez2fh8vkqlSk9PT05Ojo+Pj4+Pj46OJgMRcA1j/Bo/FFm4MMwFOcZPgRoDKJSTAaoKUE48ZKTbSctoGXRgyUcIgZ1fKBQiX7OAiIiIrKwstVqdlpZ24403chxnNps7OzsNBkNnZyfHcUNDQwghjUajVqtB8IvFYolEIpPJ5HI55BZCVWPwGrhcLohDNBqNRqMRqh339fV1d3cLBILk5OSMjIyYmJjExMT8/HyVSoUQstls0I8YjUwLhDSBwGdBRBDl8VxOCoVyEkFVAcrJwnjdzMd5OiOAPfRoN4UkfvIcxtfFuKOjY3BwMDMzc82aNTKZzO12Nzc363S6vr6+oaEhPp/vcrmcTqdOpxsYGDAajaANKJVKhULh9XrNZjP2PkD/IWh5zPgqCMnlcpVKlZubm5CQABkKeFZwIVQPtNlsyBcJiJMDRwsRgPUfUxsI/e7kKnZUL6FQjitUFaCcdIypE0ylYCBlfIjSOn4JfsiXX9Dc3GwwGKZPn240GqGzQHZ2dnp6Oq4cbDQa29rauru7LRaLzWaz2+0ulwuaAlssFojsg6rG0BRALBYrFIro6GiNRhMREaFUKtVqNa4iYLFYxGIxFvl4wtDRYLzBgKNpA1MZB0CVAAplCqCqAOXk5YSLATKvL1AuBtUMINQfDhqNxiNHjphMppycHOg/hBByOBwQWAD1CaBG4WgTAMuBQqEI+i7uVARzAxcDIvIScWBgOGWCAp8dvw5qPwjz2glzwj99CuXMgaoClDOR8UbLhx6BBO+8eTye0+msq6tjWXbWrFlQ7QchxLIs7j8UWkKDeQD5TP2BJwStB+znqgjzQYJqOWj8gYHHqARQ8U+hnBCoKkA54whaBiec4kJBLyeP+6UYDAwM6HS6mJgYqDeMT3O73Q6HAyEEtQSQL8yQvB3UHgBDQtBJkiIfYgAh1wCfMy53AFnpKMS7oUcI814kVPZTKCcDVBWgnFlMQGKRrvHQegMuECQQCCwWS3V1tdvtTktLk8vleFuPPfe4sVCYcyAnH+j4J4sE+J0W5mP6PSN5fMxaQONdVaoBUCgnFVQVoJxBhJBYoUPkAkMCg1rUyfENBkN5eTnUGAh0BEDXnxB6AC4iBMmKgaGUgbPFBQNQSJUl6LTH9P1PivCmGgCFcnJCVQHKGUSI0PdwpFToDTHUFcCNg3t7eysrK+VyeXFxsdfrtdlsOp2OZdmoqCiZTBZOxz+yvRCewGhzIP0Cfv+d2HON64RJvIpCoUw9YRknKZTThkBpGr4VnRkJPg4R+351+jo7OxsaGjQazaxZszweT1dXV2lp6aFDhxoaGvR6vdPpJC+HhkOBtwMPQjjT4wjCeZbQjxn0vyEWignGMU6DQqFMGdQqQDkTmYAHfczRSBv+wMBAQ0ODRCIpKiqCXsNSqVQmk1VXV2/cuDEnJ2fNmjVZWVl4BNyqOOjcwrT2jzaxCTCaNhB0Ysd4rxDQoocUytRArQIUSlgEyiRSeIPjH464XK6Wlpb6+vq0tLQFCxYMDw/zeLzY2NiCgoKurq5PPvnkww8/rK2tJf300IsIbAOBUXsQNAD5h6PNLcT0goJvNOZWflJcDBPgeFQx4kZn0u9FoZxCUFWAQgmF344/6Lu4eSAWrh0dHa2trYmJiVlZWSDChUJhfHx8RkZGamqqWCxubW2tr6+3Wq1+5nc/yTQxKTWmfT7EmOMS6qEX51gYLZ3hWAYMPRTVBihnMtRBQKGMAROy5DBCCPoEejweiUQC0f7d3d29vb3FxcUqlQqnCbAse/HFF+fk5LS2thoMhj179ixfvjw5ORkh5PV64UKyWgC+Y5i1Apmw2wiFCJ8kxwlntFPCgB+mmKf+CMoZC1UFKJRwwULaT2BgRQFeNDU1HTx40G63R0VF4UaFDMMIBILMzMzMzMzm5ubt27fb7faWlhY+nx8ZGSmRSJiRWYuQRjje+LvwT8Y3CpqdePy2++EwuRv0cY1GtQHKmQl1EFAo4RJYPAD54vxZlpXL5V6v12q1bty48bvvvhOLxWq1Gs53uVykjImLi1u1alVRUVFNTc2GDRv0ej285Xa7kS/yAOIDpv7pTjjHdRo0LIBCCQpVBSiUceMnTnCRAI7jhoeHS0tL+/r6oqKiYmJi4AQy6M/tdkskkri4uMzMTK/Xq9PpWltbLRYLmV6IpmpHfvLsgEOE7x2L8J70ASmU0xLqIKBQxgab00O8ixASi8UWi8VoNCKEUlJSUlNT8TlQgAjcBHBEKpWWlJQ0NjZWV1e3tLSUlJTk5eXh88GzAArEcRXYExg8aAmEY5nD8ZPNfh9c6HmePIoRhTLFUKsAhRIu2HkfYgvrcrnEYnFOTs706dNjY2ORz4OAgtkGioqKZsyYYTQaDx06pNPpIBMhMJlwtPmcPLlwk+7dn9znCifkguoBlDMZ/pNPPnmi50ChnBr4SZSgaQVms1mn08XHx1966aUajQbyAkAbgJrEOPAQjAR8Pp/jOAgbNBqNIpFIJpP5ZRgGnQwpLMcbXXgs+AVMBAYbHvvgfkxWDKNfGCYzkmMcnEI5paEOAsrpSWBw32SNTMbe+yUUWCwWmUxWVFTEsmxhYSFEC3IcR7Yd8lMglErlggULUlJSysrK9u/f7/V6IcLA6XRCmUJ8r8DeRXgOYRYnnizItQ2dZhkm2NAyKVMacz5U8FMoflCrAOV0Y0yP/qSANQBSFfB6vUKhUCqVxsTEQPrAaC2FyF01y7IQZGCz2bxer9ls5vP5MplMIBC4XC7cyxi3OfB7UnImY06bXJyJRQmQMz9OG2s/9SKE4SGoM4Xu8imU8UKtApTTitCe9cmSEIECye12e71eyCpMS0tzuVwOh4NsLuyH1wefzxcIBBKJJD09ncfjtba27t+/3+VyRUdHI4QcDofb7ZbL5QKBAM4XCoVkKNyYDgu/eZKCPJxgOj8DADey9lHQpQixUGMyWkBiOLYHv6lO7sQolNMbqgpQTh/GtDBPojZACidw+YP7HyEErx0OB8dxOAXA7744XAD+y+fzY2JihEKhxWIZHBzs6elpaGiIj4+XSCQQRgAJCKQjgJSRXLDCR6FnTs4kqKD1iwnwu1fg+WhkXwN85FgWPFDRCXpf8l08gdBfhkn8JlAopwFj/MFQKKcKYX6TJ1cV8BvT6/U6nU6O43DGIAAiPDBiAPksCgghkUjkdrvb2tpqa2v7+/s9Hk9+fn5xcbFAIIByQ9geQA7iFzk45r6ZG9lPmRTqgXKXtCL4yfjA6IRAZ3/4bgu/Z8GXkyoFFt6ByxjaHhA4pcDXFMoZDk0mpFCOiUDpwvnKDPvtTQPlHI4bAOOBQCBITEwsKCiIjo42m81tbW2tra02mw3rFkFlM1gLEEIej8ftdoejEvnpDYFCkTwBpzhCyyUUTA9AwSwfE8Zven5+Db8z0TgFfDg6E4VypkGtApTThzCl4OTezm9AkJogLEGIgrQOYcPHl8BoXq+3ubm5oqJiYGBALBZnZWXNmDFDIpF4PB6HwyESiUAtAJcBOQi4JFiWDdG+CNctCKfFEefrj4yvRQgJhUI/m4ffaoTp1/czQoxm3vB7KzCNIujg5FB+0xvzcgrlDITGClAoEySoQ5qUVXj3HHobCpfgqAIej5eYmOhyuWpqapqbmzmO02g0aWlpWBC63e7AfTnYIUgRG9RUjuccjrMcpg16DH6coFdhA37gguC38IWgjmBdhCMIXCuwRpAWlHDEOZ4w+SxjXkWhnLFQVYBCOSZCbzcDj492PrbGcxwHxgCGYaxWq9lsrq6u9ng8aWlpYrGY4ziz2SyVSv32xwzDQK1i5NMqQGr6edaxHgCdD0G6B0prDM5jRKP4BZBPWnNEOCF5WqDNA8wMpFnCL4iBPA4lGmEacA52iISANJmM5lwITaBOQ5UJymkMVQUopw/MyILzo50wuXckI9fGHD8wMs7vNU5KFAgEycnJFoulubm5p6fH4/FIpdL4+Hh4Fz8pWAiQr6uhQCCArobIl8jAEY2PyRvBVhsfCWpIxxt9kN9CoRB3XfKbduDl+FryvuTg4D1BhDkkhO2ENBv4Hfe7BJ/jZ0sIevJoULcp5UyDxgpQTkNG+1Yfv41dmA5yFDIZDwVY2p1OZ1tb26FDh4aHh1NTU7OysuLi4qRSKZxss9msVivDME6n02Kx8Hi8yMhI6JXs9XrFYnE4s+U4zul0Op1OoVDIsixCyO12wy4cXkONBLvdLhKJcNtlzhfq6LdHh509aWYYzcFvs9nsdjsIbCiyFGgnAHMCaTDwU4PgBHwQIeRyueCmEEQpEAgg8wJXcQjfv+AHtQpQTmOoVYBypnBif8r9NuUhHAoMw7hcLrvdLpFIxGJxcnJyb2+v0Whsbm62Wq1CoTA5ORlOdrvdRqOxv7/faDR6vV6WZQcGBhQKRUREREREROjJgAzm8/kul6uioqKuri4jI2P27NkikQjkrkgkQgh5vV6j0djR0eFwOFJSUuByj8cTVFhi+Y0zDvh8PnZbIEIF8Xg8JpOpr6+PZVmpVOqXJwl+AfwaawNopNUBSjFCpgY2V3g8HijYjJ0geAJYQQn9SfnNFo20kYR5LYVyakFVAcppiJ+9Gh1/PSAce0CYJyOEBAKBWCyGzbRIJMrLy2NZtra2tq+vr729HYQ9wzAKhaKrq+uHH37o6enJz88XCoXV1dUCgWDt2rWLFi0KIbpAwHMcFxUV5fF4uru7a2pq5HI5CGChUOhyufCWWq/Xr1+/XigU3n777XC53W5nWRZELGnGAL8+CG/QJBBCTqcTWjEhX29GcPWLUQAAIABJREFUkUhkt9sPHDhQV1c3Y8aMwsJCmUwGD4ttCZCk4Ha7YRowgsvlcjqdsCZwC7vdjojwQIZhsC2Ez+dLJBJcpRFHG2BHQwh/RODHR5UAyukN7UFAOZ0J7YGeGkjZg0bXA/zOgY6FdrsdRL5SqTSZTAMDAx6Px+VysSwLVQhbW1u/+uorl8t13XXXLVu2rKqq6scff9RoNPPmzTMajXw+3263Y2s/rhBgNpt7enqGhoZAdiqVyszMzMzMTKVSyePxnE6nw+FwuVwIIR6PV1dX9/777/f3919xxRXgDhgYGACzAbm8brd7eHjYZDLBVaAoOBwOo9HodruFQqHH4zEajU6nUywWC4VCrVZbWFgYHx8PglYkEjmdTrPZ7PV6YaMPyZN2u93lcoEqYDab+/v7wffB4/HAcxEY0ggaAwRPgPEAIjD8lhoI/XH4eXOoQkA5XaFWAQrlxOMXXgcveDyeRCKB11KpND8/Xy6Xd3d3t7W1yWQylUolEonghOHhYZfLJRaLIyMjPR7PwMBAQ0NDV1dXVFRUe3t7RkaGRqPp6+urr6+3Wq1arXZoaGj79u0ul+vSSy8tKSnp6emprq5OT09Xq9V6vb6pqUmpVBoMhv7+/lmzZslkMpZlYZsO6sjAwMDw8LDD4dBqtbm5uQqFAiFktVr37dun0+ny8vLS09P7+/s7Ozs9Ho9YLJZIJFKp1OPxgLAXCAQzZ870er2HDx+22WwlJSVWq7Wjo8Nms7W1tZnN5sLCwqysLIPB0NfXhxDq7u4WCATZ2dlNTU2HDh1asmSJXC4fGBiA8YVCodlsVqlUGo2msbGxr69PpVIZjUaVSmWxWEQi0axZs1QqVVNTk9VqTUpKio6OBv0gRIeIoPGnVA+gnMZQVYBCOb74yZUQ1ubR3oJNbVxcnEwms9lsNTU1g4ODLpfLaDSKxeKYmBjYbff29up0Othzl5WVdXV1xcXF/fLLLzabbdq0aXV1dT/++GNPT096erpQKGxtbVWpVGBj0Ol0hw8f5jiusLCwsbFx3759eXl5TU1NZWVlarU6NTU1NjaWZVmHwzE4OHjkyBG3293S0tLe3l5QUJCYmAiqgMVi2bdvX2lpqcfjUalUpaWlO3fulEqlmZmZKpUKIQTSV6fTWa3WxMREtVpdUVHR2dlZXFw8PDxcUVHhdDorKip0Op3H41Gr1e3t7V1dXRKJ5PDhw2AIOXjw4Ndff52RkZGcnFxXV9fY2KhUKoVCYVNTU1RUVGFh4a5du8rLy7OyskABMhgMEokkLS1NpVI1NzdDIAX0ecKlltBIewz5qdGQasqZA1UFKJSpYMxgAjLwPvBdOCiTyZKTk6EGkUQisdvtSqUSBPP69esjIyP1ev2iRYtKSkrAQj40NDQwMFBeXp6bmwvJCHPnzr3pppsGBwc/+OCDwcHB2NhYsPM7HA4IGtixY4dSqZw2bZpYLPZ4PNHR0R6PRyKR8Pn8rq6u5ubmurq64uLirq6u4eFhg8EAznv8jCKRKCoqKiEhoaqqyu12KxSK/Px8mUxmMBh6e3ttNtvAwIDZbHa73WDPGBwc7O/vb2lp6e7uTklJycrKgnKKlZWVbW1tmZmZSUlJbrfbZrOxLMuyrEwmk0qlHMc1NTXxeLyioqKBgYEjR440NzeD82JoaGjp0qVQkenbb7/dunXrrl27XC6XyWQi6zCSbqPRqiZQbYBy5kBVAQplquECCumgkeH3fnWB+Hw+1BVGCCUlJWm1Wkjxh5g4iI+TyWT5+flLly5NTEwUi8XNzc16vd5sNns8noMHD15yySURERGRkZHz5s1LTEwUCAQJCQnR0dHTpk1zu90Qwy8SiTo6Ovbs2XPXXXdlZGRER0fn5+er1eq6ujrIwWtvby8vL6+rq1u0aFFxcXFubm5kZCTLsh6PBzIFEhISOI7Ly8vTaDSZmZkZGRnTp0+fP3++SqVqa2urrKzs6enh8/kikYjP58tkMq1W29DQoNfry8rKWJZNTU2dO3duT0+P2Wz++eefu7q6li9fnpGRAbUXh4eH09PTi4uLtVqtSCTq6enJzs7OzMyMjIw8cODAli1b1Gp1SUlJU1NTUlJSWloauB527dq1detWPp8vFovT0tKUSiUiOkmika6Z0RiXa4DGGFJORWg7IgrlBOBnnQ5qo0YB/YcgHA8kN0JIJBINDg46HI7ExMSSkpJZs2bl5OTExMS43e6ampqenh6VShUbGyuRSGJjY+VyOQ4GFIlEIpFoaGiov7/f5XKp1WqFQgGKhcPhqK+vB+97YmKiVCo1mUxGo9FqtTocDuiNlJqaetZZZy1cuDA7O5tlWRgT+XL9nU4n5AoajUaGYVQqFagRLS0tVqvV6XR2dnZ2dHQ4nU65XO52u8H10Nzc3NDQgBCKjY0VCoUmk6mnp6e+vt7pdAoEApVKJZFIvF7v0NAQNGLwer2Dg4MIIT6fb7FYOI6LiIiAm0LyAsuy6enpM2fOHBoaOnz4MJ/PT0pKksvlMFWy7hD5EUzuh0uhnCpQVYBCOTH4CSHSZE2GEDK+yn0Quwd9kL1er8vlkkqlZrO5r69vYGAgMjIyJiYG4u0bGhp2797d3t4uEAjg3a6urp6eHpPJ1NXVxXEcy7Jut/vIkSMQuOd0Omtra1taWlQq1fTp0/fs2fPVV1/98ssvNTU1Q0NDkBpgsViioqK0Wq3FYtm/f39ra+uRI0daW1vJCgTDw8M6na6xsbG1tbWmpqa+vr6trc1mszU0NPzwww87d+40GAx2u722tvbIkSODg4MCgcBmsyUkJMTExNTU1GzatEmn04E6IpfLnU7nN998U1lZ2d7ebjKZvF6vXq8vLS3t6ekRCoWRkZH19fUVFRV6vV6v1ycnJ8+ePbusrKyhoQGWiMfjKZXKlStXRkdH19fXi8ViiHgglzew1LHfB3ScvwIUyskCdRBQKCcAslQOGumWDixowxENAqAGMMTzezwe8NYPDAy0tLQUFhbK5XIIj9fr9UNDQ/Hx8ZA3uG3bNqvVKhKJXC7X0NCQXC5PSEiIjY3t6+traGg4cuRIQ0NDenp6TEzMnDlzvv766+3bt1dVVSUnJ69YsSIiIiIpKYlhmJiYmIKCgp9++unNN9+cN29eZGRkfn5+SkoKuDMEAkFUVFRMTAxCaGhoSCQSJSQkqFQqmA8Ib41GA9oJNFqEM1UqVW5ubk5Ojslk2rJlS25ubkxMzMyZM202W2Nj444dO3g83sKFCzMyMiIjIyH+n8/nZ2ZmQpWFuLi4uLi4tLS09PR0uVyenp6OEHI6neCGSE5OhmrNcXFxsJi4IHHQDyVQG6NQzgRoXQEKZaoJIWYCpRTeueKOPuDqhjx7m80WHx8/ffr0jIwMtVoN5XuhRpBEIoG9slqtzsvL02q1WVlZBQUFSUlJLMuKRKLExETwuwsEgqysrJKSkszMTJlMJpfLtVptQkJCSkpKXFwcyNSoqKjMzMz09HSFQsHj8bRabV5eHoQU4J7FQqFQo9EkJSVFRkZGRkZmZmbm5+drtVpIc8jNzc3KysrMzCwqKgJ539zcvGXLlmuuuUatVqenp8fGxjocDoVCMW3atIyMDJVKJZfLcTuGpKQkoVAYERGRmpoaFxcXEREhl8thtsnJybm5uWq1OjIyMjc3NykpSSaTQU2F/v5+g8Ewffr0efPmQYMGjuiNFDQwkAlonTCBogI0XIByakFDZCmU40LQ2EA01nbT7xIyrYCMdIMzofYOjjGE3gEgyex2u8lk4jguNja2q6srPj6eHNbtdtvtdqjih8sCIp/JAazrEOEPCYQGg8FqtWo0Gqh5DOkG0AoBT8br9VosFovFAlOFOEShUIgNGF6v1+12w5n9/f02m62qquqzzz575513xGIxrikEZQwQQgMDA4ODg1KpNDo6GiZpMpmGh4e9Xi+Y+oeGhvr6+sDyLxKJHA4HDA7+hcHBwY6Ojr6+PrvdPmPGjOTkZLvdDq0dya1/YKxGYFGBcakCo4V9UCgnM9RBQKFMPiGCAUOkqAWeGfgaZ74hhKAiIYwGeQeMrwAwlBGE3LmIiAioWgh7YtjmQmYdyE7YKMMJAEhuKOYfGRmpUCggsx/PAS4E+Q2yn8fjyeVylmVhPqBn4PmDGQPMFb29vY2NjW1tbVqt9tJLL4UYRnKzDpeo1WooTAQ6BCQdSCQSaMbIcZxEItFoNDBJhBCoC+A+4PP5ra2tmzZt4vF4JSUl0EUJYi3DWeRjh+YRUE4tqCpAoUw+E0hJDyo58MGgQYW4eSAU3cNl/CGUD1fjl0ql0LkHxDa+liF6BpKdAvAL/BorAQCugQhymkzWJ20MQXG73Waz2WKxGAyG/Px8sNvDtMGQgHw+EUiSxBeCagKCH/olQitFXFEYHg2WAiHkcrksFotCoYiJiZHJZOQ80UgtLajYZka2VA4T8kOn2gDlFII6CCiU40WIMDS//45ZgAgR2gA5LG4KTDYLDpRh0EuQzEcgR4MTsAMChKtf1AJ5U9w2EPlSHEcLxAvE6XRarVYoYJyQkBAREYF7BWFVBsbHKgIZNYmnwfn6H4LSgJ8dfBw4rwFm63A4SFdIYBxA4Gr7MS7vwLguoVBOBqgqQKEcdybrr4yULrh0LplcQG70SYFNyn4SUkXAu2po5AP7b9zHCO+2OY5zOBxYAIMe4Kc9BKZHwiAul8vPcgCj4fZF0DAJ3sI2D5Dr4LZwOBxCoRDv+yH4AEwXPB4PmxNgZKiECB2QyZGZkQRd6nHpakGvoqoA5RSCOggolFODoEZsUpj5CTYsEYNeC4D4xAoEjk9EIwvxkiYHxtdBGJ/DEe378Iug8w9a3BfaAsFxsEyAIwOfTI4PZRbx3eF88r7kamC/RtA0gdCiegKCnG6rKKcu1CpAoRxfjodJAAVzRU8sdj2wgMF4J+Znww99ZjgzJDf3Y97Xz6oRYkzSdBFCZZkwQRWOSRyfQjl+UFWAQjm+TMqf2DEKlRAyHqwCk3ivYwdHP4Q+YVzbetIV4jfysaf/hfiIT/hiUijhQFUBCsWfyU0NDz8MLZwkwzHn5hfEjgjJGrh1huA78i7hjDyuLbXfVWGCZx56zn6RkmMOGGg/OEbv/pj3paoA5ZSA9iCgUP4LSM3A11NDoNgLx+oOYGt50IPjfRbSZTBZizCxCYR4/MC3Qt8iqB9hwqJ66r8eFMrxg4YNUihHCfrLPjH3+XjvRd6CmVBGOzksCDywBATa//3uS26sye0+Q6QdkuOTRybXfBI4t9FGZkYv2+D3eeGlCDFPhoh8DJMwlQBqEqCcKlAHAYWC0HF2906iGXk0qTZaDJ2fCyC0mWECEjH8gMFJdLgELgK5Rx/zMSd833GdT/UAyikEdRBQKGP8yk+Bujwptxgz1GByHdvj8j6EHnlcxvZxRSpMFlQPoJzeUAcB5UwnnF/54+QmmAAhbOPhcDweZGKBgYGXhw/0IJjAvcLnWMY/Sb4qFEr4TIVVIPw/KuqtCA229I7GsS9gYNzZiR3nJOEYf9xPuGxgCI7f4FN5eeD5fkfC/MpN+hd1zGBGzntq/y2cWowWADTeC4N+aqf6zxrJFMUK1NbUDxgMKqWS4TGI46w2+9HOKBwHrdM5zpuekUZ2H0EIcV6O4Z2M+rXXy/ECJjaB/dYELunQdTY2NEVERkilkq7O7nff+oeIFV31q8ujoqNmzS6a8LAkzU3NLz7318ysjCuvuTI+IR75OsGMd/B33ni7raXlVzdcl5ufO5Wy0G+G5OSDnhzmsMf4COHcaEwreujnwp57FOBHD/MW4+I4DTuxOXDBeg2HOavdO/Z88sEnUVHRt915S1JKkv+YAb9CoYcN+m5jXcMrz/112bnnnHvhKrlcHs6szmT8vuoT/kHDF5YdPOR0ODmO4wsEqWmp0ZqYcMY8Ulbx5qtvXHDx6mUrl/vJJoy+R/8/f34+Kjrqmht+lZyaMoFJniRMkYOgs7PrhedeNhpNsPpqdaRSqfB6vUKhsK21HSGEEPPmO69MK8hDCP3rsy937fx5xbnLLl67emqmFz7wBeLxGKfT+dRjz1y0dvW8kjlNDc2JyQnQnnW0r5fZbHn7b/9bVVUtkUh4PN6cecXX3nDNBEKXrVbrG6++3dTYjBCHEIpURzI83huvv9On79XEahYtXnDfQ3dPYFiSskPlFWUVFWUVzY3Nf3vnbwghHo+3Z9eezz7+tGThgmuuvSbMcfr7+kp/Ka06UvXRF58olcrRTpt0kzWM9skHn+zctuuCi8+/6JKLjnFAmCH572RMc9x2dYZhXE7Xxx98cvDAwbWXrlm+8pzAE4KOdiwTDtRgGF8x4EkZ/xjxc5f4/TfMFf55197a6jqE6hKTE26/6zaGYZxO50fvfVx+qGLdFZcsXrbI7/wQ34HRjrvd7oba+sbaeovZ8utbrg/jyc4U8GKSq8owTGtzy8fvfcCy7C13/CZSHXksI7/49HNbftx06dVXZOVkv/b0sw6H86U3X8vKyR5zBKfT2dzQ9Nr/vOL1cheO8jNSW1Vz8EAp4lBDXf37n384gXmeJExR2OA5y5e++4835HIZQig7J/Ozf//jn5+9/+E/3/n403fffu/1ufOKGXQ0bkjf0/vmG+9WHqmpr2ucmrmNC/hu7d974OpLr6uuqolURzQ2NN107e1PPPo0Gv2HoKK8cu3qy3t69EuXLcnNy/llX+kbr771/jsfhrgkKBzHZedkffGfT3513ZUch5JTkjdu/Xbzju+/Wf+vjz9/32Q0ffTBpw/c8wg6No/yJZetfeTxRxBCXmKEskNllUcqK8rKwx/nsqsuRwwacxIw1eHh4Uk0nA70D/ztpb+VHyrbsWXnsY/m+9B/GTQMTroeMC6am5o/eO/DIxWV7W3tQU+YAqlMBvCHufMeV4DhxCCliN9N0Vir/dBjD5y7agVCCO/+mxtbPv3gs6qKqg5dR+CcJ7DIudPylpyzFCHEjf0HcQYB0tpqsdqsVr9V/fH7DXt27Nr602aT0TixwWHAl597cetPmx/64x9u+s2ti5ctXXv5pQ67/ZXnXwxnhNlziwuLpoc+Z8k5S5967s8c4rynuLNg6jIIkpISV1+0ikNcQUG+QqHg8Y42C8nLy3nx5b+cvXyp2WxGCMVqNU/9+bFfXXvlLbffMGVzCxP4Rdi7Z//D9z0qkYi/+u5f2TlZZpOZ47w/79prNJpGu/BPjz9jMpquuPqya2+45s57f/vGO69yHPfWG/97YP/BcU0A/7UsXHIWQojP50OLNoRQekba5p0/zJ4za/NP2x6+/zE0UakAz3j+6lUqlcput+PjCxcvvOzKy+976P7wh4KmNTz+2NOora69/3f3mkyjLuB4iYqOev6V5y+5Yt3ay9eEPjNMYaZr7/ifp1+ATncnkJy8nN8//vBNt9145a+uOLEzGRfHVUGZlMH5AgHi/lu7MCcv+75H7rn+luvG/P6EDw+aPDE0aeu/wGf3/J/+8vW/v/J76/Jrrrzmhmt/fdP1kWr1hMffvmnr5g0/pmdlnL3iqAltzvy5F16yZs1l68IcwdeaK/h3DH4tFy9bkpqWarVYJzzPk4EpzSAAE7rd4Qh86+xlixE6utxLzl645OyFKLxYgTENtpNo0YVx/v762whxr735Enw/tHHaCy5cFamOFIvZoFd5vV6BQIA4ZLMd/a4Uz52Vmp7S2twG2s8EsJgtHOK8nNfv6aRSCUJo25YdRqNJqVRMYGQYjcfjCUQiL7FNnzFzxoyZMxBCnNfLjO56J/F4vYhD4eyCvvzsC12bTqk66kQI7d0fE7h88bLFi5ctJkcb7ZsQzj71y8++GDQMxWpj8SVjfqnG9RThDAh/DqtWn+cbf0TAynHKcfCLTgjcfI9rnKBBNsAxzp+0M/vdNKzLISCXg9ccYtAFay4YLVaAnGrgtEf9mnm9HMeFaRUY72qEntLJCcyzu7Nr/897Z88tPnrQyzE8xuv1RqrVv77pevLgBAbn8XkMgxSK/3ons/Nys/NyUdirRHb6DgSPIBAKPZ5J28mcEKZURfV6PKOZ7GYXF80oKkAIWSyWHzduPhpAwKDAM4EjFVU7tu9GCDEMs3P77kMHy8h3m5tayg5VwGvwsG76cUtNVa3fIH6mP7vNTr4V9BE2rP+xQ9epjFDxBQKvl7PbHdq42Icevf+W39woEomCXsXj8V589bmPP39/dvEsOPLtN9+3trSxLJuSmux3r2M0n8JGXCgU8ANqs3s8njE1D6fTabUe1Vc473//BhwOx55de8BIwPjEKh7fYrGQg4z3EXZu3bF7xy6RiN3w3YbdO3ZbzBYej2cymTau39De6m8Gx9oJx3EWc/D78ng8u92+acOmLT9tdTldfnrA7u27+3r7yKvIX4TyQ+Ub1m90uVzkmLt37P726+/4fP76b9bv2r7bZDIFSh273U4aUUAPGB4a/v7bH7o6u/2ewuVykT/cEEJL/ugEXUOGxwwNDm38/seebj3y7VT27dm//+f9yPerZDaZQw8SiNPpHPPWAI/Hc7vd27dsr6mqCXqC35+21+s1m8wOn+rPcRyPx7S2tJb+EsQYxjDMgf0HdO0d8F+Hw2Ee5fPFuFwul9OFfKYdq9W6cf3GpoYm+K/b7bZZbYGX+/3Jw7eIzE6Edd7w3UZ9tx4hvEM5its1YliGYWw226YffmpraUP/tXhbNn63QdemG3nfIGsFAwZuKBmG8Xq9u7fvrDjk75IL/t1gmP0/79+3Zx/C3wTziG+C1Wq1BlsNjMVsIT10QZcL09LUsm3T1t07dm/fsr26spocJPQ8nU6n2+3Gc646UvnScy8yDNNQV//zrj31tXUg8nk8Xm1V9fbNW4+6ongj/ty6O7t+/H5DTWVViHvBIjTVNzAM09PdPTQ4iBBqb237/pvv6qpr8Al+f8I4RYs4zvkpDMQH57KYj369vZzXe4onhkypVYBDCHFHTS7wSTz5x7/MmFGwdt1FOKq2u0v//LMv8xjmd3feunbdRfCnVVtT/9rLf3c6XXwBnxWxrFhUfriC4zjn7+9bsXLZM0+94HQ6L1xz/n0P3oUQKj9ccf/dj9hs9qt/fcXv7roNIWQ2W556/C8Mw1x+1bqEhLh/ffpVXLz2gUfuSUxKQAi5Xe4nHnu6T987a86s7Vt3zi+Zc88Dd44WILZ9604GMUKBwOv1btq4ee+e/Wnpqb+6/io+nx9CzYQbYT58/2OO46645tL0jDS4qqG+8dk/v3DTrTectagk7OU82ugd/7+psbmmqg4h5s57fiuTy46exDAIoW+/+b78cIUmVrN187aU1OTf3HFrWnoqIgRhY0PTay//TSIWL1q6MDU1ZfNPWwYGDIlJiTCIxWz5w4O/VypVF19y0c2334KH/ecHH5eXlRXPKS795UBnR+fF69ZecfWV5NJx3BjO0ZrK6meeeJrjkMPheOm5vyKE3v7w7fTMjI423YvPvMjn86+75XqX0/Xd/31XMKPw/t/fp1AqEEIfv/fx4YNlc+YX7//5l05d59rL11x93dXkfd95/Z1/ffJvhNDNv7nphttuwMdfef6Vr//99UXrLm5ubBaL2b+89KxYzILYdjgcjz/0+O4de+Litbu27Wxv0z3+58dy8nI+//jzN175O4/Hc7ncLz33MsPjvfHu67n5uXjMTz789P+++GbpOUsQQju27Fi2Ytk1N1wNYZLP/un5Pbt+livkN9x83aBhcMP6H+cvmPfw4w/u2Lrzg3c/UkUo3U53ZLT6kccejIiM2Llt178+/cJmta08/9xrrrsq6HI11De+9PzLfL7ggd/fe8655yCEXv3r6/oefclZ8y646Pz+foO+R39g34FoTfQf//SYWCIO/QXatnnbO2++O3feHKPRWFVZvWjJwjvvvSN0aKTFbHn6yb8gjrto7UXpmWlffP4l4pDVZp1dPOvG226KjdVgW8g7b/5v9ZHqkoUlzU3NnR2dzzz/tCpChRD6edfPr7z42srzz73sykvX/+f7PTv3rLxg5V333YkQevuNd2oqa85afNaK81b06nudDufe3T/PP2v+oqWLsnKyRmhshyuee+rZ3Gl5QoHg4IFDDzz6QMlZ8/t7+//yxLMIoSt+dUXxvOL21rYOXecve39ZdeGq626+Fi7Ej7Zn588fvvthXkF+rFZzcP+hisMVeHCO4xrqGl569mWhQPDwEw+BbQkhtG/Pvhf+/ELx3OKklKRdW3dm5+fc+/C9AqGgT9/3/FPPcRz3u/t+t+6qyxBCr77w6qbvNzI83gOPPrjq4guIgf0tFi8/84LdZk9JT92+eWtaRvo1N12Ho9AdDsfzTzzjcrnOv3h1Vl7OF5/8S6FU/u7+O7Nzc4J+NH/76+t9vf3zzpp/3gUrh4eHu7t6Sn85qIpQ3XjbDUnJid98+R+b1Xaw9HBCQvxDjz2AHYsIoe++Wb9t8/Z5JXPLD1c0NTYvX7nslt/czBDVmnVtumf/9JzVapWIJRKpWKFQNNU3erweHo+HOOTxeObMn7PknCX6nl59d/feXXuTUpMe/dPjfj2mN67f8N6b7yxYvHDQMNje2vbnF55JSkl+9omn+/v6hULB1p82b9u0ZeHSxY888Sic/9XnX+zevvO7r7559Okn1FFR+IP77IOPP/vwnyKRSMSK0jLSz1l57rLzVgT9utqstq0/bWIYpr+37/brbk5MTGqsr3e73RzHrbl83S2/ux1/Cp9+8PFnH31yzsoVLU3NVov1Ly89HxOrIYcix2cYplPX8dZrf/d6vPmF0xgez2wy1VRWp2dkBP1cThX4Tz755JTd7MD+g2VlFUODwyAa//H+P9d/uyEnLxtnwSGE1FGRTY0tuo5OlUq1cFEJwzCtLW13/vbBlNSkq399RXpG6qaNW3u6e+578M5zVixLz0yLiFA5nc4jFVV2u2PNugsRQtq42I5uIIYbAAAgAElEQVSOrsb6JoZhVl+0CiEkkYj7evvrahuqK2tam1vtdkdrS5tEws6eMwshdNdv7y/df/CBR+5ds+7C+pr677/dODQ4XHLWvKBfr13b97S2tFnMlojIiDXrLsrNz374/ke3bdmx9pKLxqz3jhCqq61/6N4/NNQ3zi+Z++TT//Xof/jex5s3bRvoN8CEx6S1pe3HDZtFQtEFF66SSMR2u/27//zw21vv4QsE99x/x1XXXIaIX72tm3f84aE/nrVw/m/uvDUiQvW/b73/xb++zszKSEtPhRO2bNp6x613ezyeJ5/+45y5xQql8s3X3zIODSckJaxavQohJJFKent6K48cEQqFK88/aqBuamz80+NPJSUn3fPAffGJCZs3bvp59x6ZXJY/bRoMazAMfP+f9UKhcO1l6yAuJBCJRCISiSoOV0ikkvt/f/+qC89Pz8oQCoXRMdGV5Uc6OzoPlx7q7xsYGhpqqm/MyMpIz0xvamh64pGnklIS73vkvoSkhB+//2n39t1yuWza9Gl48aM1MVartbmxWROrWbJs8VHPzqtv/vuTLx589IEbbrvBZDT956tvyw+VLV62mBWzLpfr7tvu/mXvgetvuf6FV19QqVQf/+Of27fsuOTySwqmF4jEbNnBMolU/MCjD6xeszozK1MkEsGYX37+1Vuvv33h2tU33XbjrOJZNpvto/c/7u8fWHL2YoRQbFxsfV2Dvqvnl/2lw0PD/b39DfWNefm5i89eZLXZNm/cYjAM3nzbjbn5OQghAZ//4XsfmU3miy+5KDk1OehywbL09vbGJ8TPKp6FEOLzmNJfSjt0HYcOHLrq2qtWnLe8vq5h08bNnZ1doJ2MxtDg0P13PWjoNzzzP0/PnjN7766f9+z62WQ0zSuZG+I7LJaIjcPDtTX1tTV12rjY81efXzS7yGqxbVi/oba6dvXFF8C1H73/8QfvfXDLb2+5aM2FERGqd996d/fOPcvPXS4Wi7Vx2h++/aG6snrX9l2rLjhv849bKiuqlp6zRB2llspk2zZv07XpjEbjw489NHN2kdvj+furf1//zfq1l64RS8Tw99VQ13DbdbcnJCU++tQf8gunffHZFxu+3VBYVJhfkN9Y39je2l5VUWUyGm+747aSRSX/+erbbZu2xWo12bnZyPfn9s4b//vScy/n5uc8+OgDM2cXeTye3dt3cxxXOLNw9tzZsM6lvxzs7+1PSUsuml3EMEzp/tK7b7uH83ieeO7JxWcvLis9vGPzjjklc2JiY1QRqsb6Rl1rm1KlXLxsCUJIGxdbU1k90NcfGxc776z5sHS7tu5obW6ZMatohu/nbvtPWz58+70ly8+++sZrZXL5p+9/9N1X32Tl5SQmJyGEhEKh0+msLD/SUFdffaQacai9td1hty9c6p/RADA85uAvh7o6ug4fLLvk8kuWn3dOa0vbD99t+Prf/zdj5vRVq8+bVTyzsaF56+bthgHD/LPmwVWGAcMDdz8skUn/8MeH0zPS9v68f/f2PS63e1bxTDCu9Op7b/n1LXK5/Mbbbsidlrtvz76O9o5rb7r2gotXL12+VKlS1tXUtbW0VR+pvuLXVy45Z+nh0kM//fBjf3//wiX/nef2zVuf/P3j889acO/D98cnxn/+0adbftx01uKFy85dXltVbRgwrLzgvOtvvWn23GIcGaBUKbds3NTX27fqwguUKhV8cB+8/e4n//ho0dlLbrv7jvkLF+zbuaeuqubcC88P6okTCoUWk7mmsioxOenG229NTU89b/X5Yom4qb7R43afd+FRFe2f//jor8++cMkVl95x391SqfRfn3y2c/uOZSuWS2VShNBP32/s1ffOWzA/KzcHflEryspvu/bmXr3+0T//cck5Z+cV5L/56hu9+t4YTczay8MNQTgJmVIHAYc4DqEevf7PTz13+613/fvzrxBCEmLvAnpockoSwzDg9uY47rVX3uTzeAsXL5hfMmflecvTM1J5PJ4mVrN46VmpqckIoYysdMQweB+MELr51usZhiHVUth/c17vH/740Lcbv7z3wTshF+uxR56sqqi+5/47FiyczzDMo08+ctGaCzas/7Gmui7oI3i9Xo/H43a7QZvRxmnvuf+Oyoqq66652Wwyj+kb3rJpe0V5Jcch+J7hR15+7rL4+PiLLxlf8mRPj37r5u19vf0P3ffYU4//BSH01NOP+ukBCKGtm7cjxEDU0oqV59x93x0IMa+8+Dd4d3h4+JmnnkMMevbFZ5KSExFCEon48qsvQyOtZxlZGQghqVSKj+zbs4/jEGwvCgoLfv/Eowhxb772Rl9v79EzOBTaOcp5OblCfvbysxHiRKzonJXL55bMlUqlnJdjGCYhKQEhxHHo5bde/mrDV3c9cFfB9AKE0N5dexnEiYRChFDhjMI/Pv04Quj1v/7NMDAIw3q93oys9AcffYDHMHz+0U/ko/c++vyjz1etPu+idRchhK789ZUP//GhwwfLvv/2B4TQvb+5r/xQxbnnn3vbHbcihHLzcwUCgdlk1rXrRKzovPNX8ng8kUi08vxz586fI5PLwJT6w7c/vPnqm7NmF/3mrtvFErFYIr7p9hunTZ+2cf3G//vyG4RQ4fSC5OQkDiGhUPjOh299+cMXd91/R1pGGkLoV9ddPXf+HAYhHG0qEAgkEsnd998JMaFBlovjWFaUkJjAY3hi8dEs58zsLB7D4/F4V1xzRVZ2JkLolt/erFQqK8oqgg6CKT9cbjKZUtJSomOiY7Wap559ks/n/9+X31SPYvxHvu9DekYGg1BSUuJv7/zt4rMXL1229MlnnkhMTjzwy4HX/voaQujfn/37zdffXLR00fJzzzn6Gf3p8fY23Vf//gohFKOJSU5NFvD5GVkZay9b++nXnzz4hwditVqEUHZ2FjjtfnPH7XDHtZeuWbV6lcfjefTBx1wuF4/Ha29rv/lXt/B4vL/89Rl1lDoxKeGr778UCITPPvksQig9Mx0xDELorgfuksqkQqHwgd/fhxCqJf6c//mPTz5+75+RkZF/eu4p0FDPv2jVeatXInT0G4sQYlk2Ll7LIU7Esgihqoqqe26/l/N6n3v1+aTkJITQtOnTWFbEcUftyanpKQzDSGRSWKWs3OybfnuL1+sBh93R1QuwY+/cugP5AtOWrVx+/e03Mwi99/pb+IT0zKMbzd8/9dgn//nXPY/cd+ElF4/26WRmZzIMYhhm3RWX/H971x0YVZX1z33vTUubJJNkZlJmMkkmvYeE9EJAeqi6oq5lXb/VdVddPwt+llUXUVZR17bqigUbKghSA0QChJAQAiGNkJDe26RNps+8+/3xMsMwKUTcRXDn9wfM3Ln9nnvuueeecxISFgwA99x3l7eP2GQy1dc1MHniEmIRQocOFDRcuMikVJypRABsNhsAZIGy5196DhB8tfWriw0TDlxvbX5bo9HOTZublpmWMz8nIDDAaDQ6OjlGx0WHR4aHhofqdDq9Xr/m1jWMEvGBR/4IAOfOXnqxPVNW/tSjT/pK/J5/+UUulxsRFfnRl5+MK8c/ePufUpm/r0SCEIRFhMcnJgQEBVqmKCAokGJRBElYmOq2z7/88tOtRpPxT489EhEdGTcnQeDpwdzyJ88GkygLCsQYOzu7ZORkLViyKGFuYnBoKAA4Ok8oofft2v3qhpfjExMefvxRiqJyFuRufvcf/b19X3/2hXVVTAMIofM1tY/c/2eapp976YVAeRAAUBS17q7bMY2NM1oVXP+4tg8EGDDG4RGhH/7rbbVK/d23Oz/95MvRkUu+IszpZTAYkPlzbU1dw4VGhJBRbzDnAYTQyPCIpZROq0MIrG8yXkJPL6GX0fziCwBarQ5jLPGXBMkDAWDlmjwAGB0dO3emiiAJHysFvn+Av6Ojo8n8oGUDE00bjUa+K9+iyVhz86qvvvimvOzMpx9//qeHH5h5Bh740333P/j7F57duG/PgbxFazb/Y5M8JAhjHB0btTt/+yym8DI4OPCiY6M8vTye3/B0SfGp55956anH/vruh2/Ez4m1vtg98r9/iogMy8xO12g0PB4vIFCGANhsFiMu5O87pFKpklPnhoWHWoogsL0X6rQ6mx23+pY1zi7OoWGhJpNJqVQ6OjlijClbgwk8g/8U8wSoZJ63aaxWqRkJiUnX6wwYQ2JyosBDAACrblnFlFpz6xoXvnNIeKjRaBxXjjs6OwIAi8Wy8GWGd2i1WoIgLAMpKykDBH5SP0vrUpm/yWTS6/QAUF1VDQhuXreW+YnFYj357JM6nc7H1wcAlEolRVEEQYyNjjG2jUwPy0rLASA8KgLMrAch9D8P3vfQHx6uKD+3au1KANDr9YAhLSOVx+PxeLxVN68EsyXBXffeebr0dGFB4fKVSwFgeHjYXeC+bOVSmMamaWJ3GI2IICy/6nQ6RBBsFhWfOGGJ4uLi7Cf1HRwYnHrSzcjIznh+w3MkRY2MjGAMCCGBwH2gf8D2TXtSB3Q6HUJI6i+hWJSln3fe89tn1j9bXn4GAIqLTgICieSSYiMpOYnH5Rr0l/Yji8VevXYVAMgCZLIAGZOo1WppGnt6CgKDL+lab7tzXf6+g1XnqkeGRjyFnlUVVTRNS6QSD08PJoOzi7Obu6tapQEAZjW5DjySmrgGBAYHMQtqWaOqc9UY8Mq1K5j+M9lojG0sh5iINMxsNDY0AkBkTFRiciLza9ycOASIIQ8AMBpNBEkSgCyzJA+R0zRttGIj5tovNfHHR/8cHRedmpWh0WgAwMPLAwBY7Euqe51WCwBRsdHxSQkAsDhvKUxvQ6fT6hirCUfzY6uDg4O7QNDU2JxqfnbUabUEIjDgttb24FA5AGTnZhqNBm8fMU3TIyOjJEm6uDgrlUpm4G2t7adPlSOELPzQaDLqdbre7l7mq1Kp1Gg0Do4OEVGRTIqXUCjy8bYm3rKSUwBYIr0UfsfHzxcAGJMLg0GPAFnsbC4RtlY38XJvrqq2stpkMqVmpjs5TxhEL129QqvR2LxEWNej0+qABmtmrtVqrHdW8fETBEHIgi7Rm1Tmz2axDZeOG2SmAgCAxvqLtIkOiwhLSU+91BYgmqZn2Dg3BK713yDAgMPCQjkcDofD+Z/7fycSizw8BJOzIfNyRUaFJyUnlJ8+x/gdaLU6vc6AELJ+60JMCavTizHFuvyOjjHGQfJAZxdnC//K33dofHycxWJ9uuVzxaCCIAiDwXBwf4EsUCaxOjOsYTAYjEajTqfTaLXM4UeQRGhoSHVljcEwhfRgY0bO6NyefWH96bIz3d29r7z02pat71+1ua+vn688OBAA3N3dli5f1Nrc9tEHn/7t+Zd37v3GOpuHp2DdHbe89/aHO77d+Zvb1u794QAAEObrstFkZMwOLus2pvHlIQGY89xC7RhjHo+Xt2rFgb37H3rgzxRJmGgam3nupHJXwOVM+DJERk8ctBYzH54DL2/NigO7Dzx4z4MUi0WbaACwaOyt60RmoqiprKmtqkWAtm/bQZCkg6MDxnjX9p0ESSQkxQOAA5enNBgpauLA4PK4K9ZciijC0BtFUdbyZkdbB2Ovx/BrS+sRUeEAwGJRlm4A4Ji4aOtRMCQREhbs7iGoqqiur2sICQv+7usdGWZ9wAwkQRAEYSUKAAAikFAsYlQCDIwG48wKKoYsc2/K3bNrb97ClU7OTggh9bgK2cjU0wEhhtot3ViybMmml/7u4ODQ1Nh0pOCIo6Nj/v58gYeAz3dBgDo6Ol1dXS3nKIvFoliU9Zk3MVcAGGODwajVai0vSrJAWe7C3B/zC9gcNgDs+OZ7AGhva9/w3Eux8bEAuL6uYaB/cM2tq4FxWgHImZ/DRMkEAK1GYzMengMPrOjf3Da2ubVbf2V0AxbfB4xxgDwwQB4I5jUlCZIkSWv5WaPRmEz0ZWRtdaQwpTy8PFf+Zu1n72/5+rPPXfgujM0dmuRtaHPUzWBLjxBiXsQsKcqxMU8vTyvaYDgrYtQAmMYkSS5cctPJEyU3592q1WhJilSrVBYCk/pLFizKzd93UGU2bBweGtbr9WERE9cGk9Go1qglMolFyMYYG3Q6DpvNfB0ZHtm1fRfGcLKo+K3X3vQPkJEkeepkKWCcPT/b0qfpRmQN5oUoIjoKzEuTmDLXej6nKoRtj2grhtTV0XnoQD5C6Mf8w76+vp5eXhRFHSs4wuFwki+d9Ais/KDYHDaNaZs9QtM0noGF3SC4xqIABjzBOpnFy1uxBGZ0MQKAO+5aV3763LavdxwtLBpSDGs12iXLFqVnplrnsSmMEKJYpO3lFGPG2tNCNFJ/CUKIIIkVq5ZFx0aq1RqEiITEeA8PAct8abbpDDkVh6UxPd1PBEE0N7UUnyglCCI7J8PHd4JDMZ6HP9NP3WAwWHcyNSP5ow8/7ezovlDXEBp2KZbWgX2Hnl3/Ao/HXf/MY/Fz4poaW3p6eizzwJyWk/+6weQznOGWzGeEUGVF5bPrn9ao1Vk5WatuXnPmdPknH31Mm0zWvGx2vlN4yuaYn7SXLxlCqPJs5TOPP6tRqXNuylmxZkX5qTNb3t9iok1T8AKzLKDX65ktfdOSBbkL5ykGFYDhuQ3PicQiJ2cnxiOAJAkOhw1TMSaECBaLTZEs5gfFoILFZhEkwTga2ORnrMGRVYgnDMBc+2xyIoSWr1z22Udb9+zax2JR52vrHnn8oSvP1oRAafkMCCHaZDQajTby3AwgCKKjvePpx59paWnNyslcsnyJUql85cVXbK6t03fA9kAiSIJFsXRanZfQSyKVjAyP5ORmZ+Vkjo2OAUCAPGDtrWuczZc5iqJYLNYUFteTmClD3lwOB8wkKg8Oamxo9JX43rxuLULIaDSGhIXcfvftIrEQYMIn0PK2OCE+2tRJ0zAb9wqMaRpbAk8ghBCaOCBtjMgAgKRIiqIQQVga5fJ4zAkxzQQiADi098DrGza5urmt+s3am5Yt3rb1y+OHCy3KLQt+UuwaikVZh8hFCAx63WWsDCFktopHBGprbX/mib/29PSmpievXJPX19v7+qY3rcd47x/uPZR/eN/ufRqN2tHBsbqyevGyxTHxEzpRE03rdDqL25F55i512MXFRR4iLz9VlpA0Z+XNq8eV4wA4JCzk4cf/IrC6BFomtLW5RSrzn044QOjSBWXyKkxZwuY7hksCmbvAPTAoqKWpOTs3Z9GyJaOjowRCoeFhru6uLnw+k4ckL5O8mQdP22BoE2KkXRSYBRhaZNztLO8ull9t5QCMMcaU+X5ZX9fg6+dz5923CoVe32/fk5mVmjg3Aay2ut5gwBhb88Guzu7+/kGxWGxJQRO1XrbNklOThCKhUqmUyiRibzHMAqvWrig5WcZis5lQIQghvV7f0dbBYrMNk94UmB4WF5W8tulNhMDd3Y0RBUiSZHpuNF7l85L10WhJZBRuJpOppPiURRS4UFf/7PoXANBr/3hlbkoiAKz9zaojBYUURY6OjnK5XIpFoalOKZuQAOZL+cTXsdHR9Y8+oVGrHnrskdU3rwUAP6nkk39toU20Tqfr7+vzEgoBIQzAKJ9nMyTm/5NFJx2dHGPiYiaav3x/jY2OrX/kKbVa/fBjD62+dTUASPwlW97fgmms1Wj7evssrv9g1d34xPiwyLDaqlqhWCQSi0RikU3bBEFQLHbDhQbmId9GCiQIxOVyOBw2h8sFgJ3f7QoICpi3ICc5be7JohKbKAuM8YEt+55mBlasXv79tzvz9x0sLDgaHRvp6uZ65YmyPcYQs6d+qm7p2fXPNTe3rFid9/hTjzEpn23Z2tPVDRgUCgXfhU+xZmIONs0VFhSOjo3SNO3k5DQ3OelY4XGhUOTh6eHp5Tm5LJvFYh5cpqyZpEiLSgAh1N3VXZBfQBCE0WAEgJwFOQf25nM4nJCwKQzprZUu1inWkhltfsphvjJrzWKxrKcVIURjTNMmRkI1GAwkSbLNN93JwCaaRVFcLhfMGpfz1bU0jSdF4MCWs6muunbz315BCJ7e+HxUXAwA5C686fjhQopijSuV48pxkbf4J63pxAalsYk2kWBRJCArHSsAuox4jAbjC89s6O3pvfWOW37/h3uYxC3vfzI6OkbT9ODAoIenR09Pb+783MiYiPDI8K1btj79wtMLFi24bEiTQjEiK1mVIInMnKzyU6f5fL5EOoUx7MSxihAAXKg9f/jAwT8/9hcmZeLRzTxler2eoqiWpmYwL6hFUzjdRBEkQZKkzSrQJhPQNADwHBxSMtK6O7u8REKhWCS0ZQsAAGw2h8vlWhQzCCGKpGyfJC4P7fozw6L8UrhGf5mQWarOji4AYE1/d2EmlKQojDHjPA0ANdXnSZL09fWRBfj/7xN/ZuQAsNreXkIvGuPe3n6LB/O5ikpMYycrQ0Lmls9ogK0h8haRJPXjoaPWic2NreNK1ZTkFRoWIhAIOGy2xUqxrbW9oaGRy+Uy7nkAcPDA4bzFa04cL7a6Q+DFSxcuXnoTk2FgYHB4eAQw9jPbKLS1tt+57t733vpghmm0Bo/HA0A2FGkwGpkWncxGMapx1eCAAhAKCJIxcgCTiBBydHQcHFDs35O/eOkiADh5osTi0g0AHDYHMFDUpfpZLBYGbNF7j40p1WoVILRo6RImpfpcJcaYw+XQtKmw4AgAMJIfMqtkp5OaTSYaABBMmFKOjymHh4YBgKIojCcMmixllWNKtVqNEFqUN+HIUFVRBRi4HI7BYDhy8Ih1zdZ2ChFRERjjvTv3WmfY9OKmb7/6ztnZaf7i+Ww2u6SohElHCA0phl7f+DrzJooxZrPZer1hSDEEAEVHi5g34KiYKIzxj4eOWBzNDQbD11u3AQbLAxPzYsKcbZNnwIXvwuha9Xr9bXdO7UB4aTjM7iBJjDHLfCyxWCxMYwSENTGQFDnzKaLT6fp6+wEgb+VyJqWlubWnq5vp6rEjx1Rq1QzFAUPl2Uprgvnmq294PF5oeCgA+Er8HHgOJ4tOWo93+7Yd+3cfMPeZTZIkYy982ZwghBBSKpX9vf2Wn77/dqder/eT+DnznQHA2cUFAJouNpWcKLGUq6yoeurR/wPzPPf09IL5sGcMXZn3I6bCRUsXAob8fQctbQJAb08vwGXERhIETdPMq4RILKIoVn1dvcXaDgBaLja3NrUyn8W+3iwW1WfV7o/5BRjTjo6OYNZnkBQFABzOhJX00KACAKQBMkYOAACVahwAOzo5DPQNlBQVg9luwHobzgAWiw0YIxJZiywsiiKtmB6LxWJU2QxZqjXqgb4BALzEHLeq8WLT6OgYk/PokWMAUHy8uKaqRh4slwXI/vrSX23kAA6HQxKEDUsnSNJajvTwFBAEOnbkaIdVtOz9u/e+8cprAKDTajGeMM+srqxubW6xdBUBAox5ZlNlP6mExWafLillAsAghGiaLi48bh3PwwYcDoeiSOvuURRlMpkI82YRicVcLq/k+EnrSg7u2b97+07ms6OjA4/nYDGXTk5L9fAQXKitq6q4FO+Bx+MBBkudBEEoBhX3/fbeF59+YbqOXYe4Fs6ECKGuru7f3fPHU6WnEUItza3Hjp5obGxOS0+enFOhGHrt7//Q6fSdHV3j4+OJSQmhofIt/9q6d/eByorq40dPHDr4Y/6Bw9VVtQkJsQzB+fh6X6xvrK2to1hUbFx0T3fv319+Y2xM2d7WMTw8nJqWTNP088+8NDY62tTYPD6uSjE70gBAWkZyednZpostA30DfD5fMTi0Z+cBxeBQeFTYZGsUjDGPxyUIdOF8Q01VbXpWKkVRr//9rZ7u3vvu/93td97KZHv4wf/t6uyOjI6Iio4EAKFIWFh4vLuz21/mL5H6jY0pb7/57qFBRVpGyiubX2Ja2fLhp0cKjgKCvJVXcCLQ6w0bnt/0xdZt40rV0NDwhfP1fDe+j7c3IpCnp8eBfQfHx9XDQ8Or1+Z9+vEXpcVlKWlzt321fXh4hCTJ+ITY+gsNJ44VV1fV9vf2F/54zE/qm5qe4i5wKy0p27t7v8DDPTgk+OyZivfe+ufY6Gh3V7e/vzQgMMBgMGx8cePY2FhLc4tKpZqbPJckiR92/qDT6Xp7e0NCQ0ZHR3ft2NXc2KTTaouOFXG5nIzsrE8++ri+7oJerz939lxqetp0bu4CD8HF+ouNDY0AqL7uQuXZyrt+f5diUPH3DZtMJvrc2XMuLi7hkeEWCtmzc69Op+vr7g2NCB0dHt353a6mi006ne74kWMcLifL7EGn0Wi2ff5NkDwoIycDAJJSEjs7Ok+XlB07ctzNzXVsbOztze/UVtfedudtAg9BSFjIqZNl3Z3dA30Drm5u/b19W9772MPDIzM3EyHk6uY6PDTS3tox0D8wNjpWWHB09S2rvYRekdER6nF1WenpI4ePuPBdMMbvvPFuXU3dqltWPfDQ/QBQdPTER+9/DAjKT5ULhUJ5iHzK4R/KL5DLg+69UqRthFBbS9s7b7yHMa44e07gIQgKDnr/nQ/b29rHRkcbLjRkzcsiCGLji6+cOnlqTKlsa21Py0yd0qiKoqgjBYWKQUV7a3tYRBhtondu33Whrp6m6ZLikqGhobxVedMJE3XnL5SXlZtMpqbG5pS0lPq6C5s3vV5/vj49M/3ZF58BgLj4WI1ac7G+qba61tHJyWAw1NXUlZ8qn7cgx83drbKiau+uvRjj0uJSXz9fa0POoUHFzu27MMb5+w6mpKcIPATvv/3Bti+2ubi4vLPlHVc3V4yxUOQVGh5SkF9wOL+AJElnZ6cfDx159433Fi5ZGCgP+NuzG3RaXXtr+7hSOTd1bk9XzxMPr1cMKKoqqhwcHaJioxBCflK/ro7uijMVpcVl7gJ3gYdgxzff/7B9NwBUV9Xw+S7hkeFNjc2vbdwMAKdLy0XeouzcLG9fcXVF9cmik46Ojg4ODmdLz5QWnYqMjXRycQIA/05lgBoAAAzCSURBVED/YwVHL9Y1uAncfHx9igqP/+vdD0wmU825akcnx6jY6JbGpjde3owQnCs/6y5wDw4L0ajVB37YOzo8wuVxw6OjGurqTxeX1p+v6+3uKT5WFBwWGhET9Y9XNg/2D/R09fR0dadlTe1DaMH7b/2zs71TOTZeX1eflplGUuRrGzcXHS9WjasaLzYtWDQfAN589S3F4BAGPDQ0vGBRLofDKfzx2MjwSFdnd3CIXK/X79m5h/G2KCku0Wm1uTfNi42P+eCdD/ft3l9WWnb8yPH9ew/s372/tLh0TtIcDofz6sZX+3r7FIOKtpbWnAXzAGD9X56sra5RDCoG+vszsjMBQBYY4OTiXFpccvjAQQdHRzab9f2323d+u335qhX+ATI+n3+0oLC9tc1PKvnq0y/koSHMO/2Obd9WlJ/FmD5TdnpOcpKTs3N84pz+3t6ujs6LdRf4rnzAeM93O/t7ehPTbM8RCz7+54eKwcGBvv7uzs6UjDQAePVvLw8pFB1t7VKZv3+ALDImymDQNzVcrDlX7eLiAggKDxbUnKvOXjDPXeDefLFp387dJElWnT0n8PCQ+Eu5PK5ILD5dWlZwqAAAvH19OtraX9v46mD/YH9fv5dIGBYRDgA/7Pjh661fjY2N3nH3b2detesH1yiugF6nNxgM83Kzc3Iz4xNi3dzdgkOCgq0MnSzQ6XQuLs5p6ckxsVEhoXI/P59tX21vqG905fO7e3p7evqGFEOdnd2NF5s6O7uystOZUvEJMaUlZX29A8vyFvf39XM4bLVKPTAwgAgib8VSo8HIYrPSMlLj4mP8/HwY01mY8M7ipKQlubm7ubu705jW6w0Cd7es3HTm2dgGDHOMiArv7+uvrqyhabrkROmxI0V33LXud/fdacnm7S0OCw/NzEp3deXTNO3s7LTgptwfdu05fPDHC3UNb25+u79/ICMr/c13X6WoCRtsPp8v9hYtXrLQJhjRZBgNxnfe+qCrs9vbW0xSZH//YEiIPDQ8mCAINpsVGR3R2d7Z2dHd09Pb3dnzp4f/4OnlGR0bGRDo7+bm6i+T1lTXZs/LSstIkQcHyQJlGVnpXl6eYRFhy1YsJQnS1Y0vkUqqK6v9JH7jynGFQjE2NrZ42WLaRLPZrNS01NjYGB9fX3mwnM1mx8XH+0n9XF1d2Wz2kGIoe1724qVLfCV+Un9pSlqqj6+vQW8Ij4xISUsRicVhEeFT6lcxxgRBpGWlCzzcKZLU6/Vz5s7xlfipVWqBwD0zJzM0IlTqL7UcGBwOJzYhTiKV8F1duFyuYlCRPT97ad4SX6mv1F+akpHiK5kIi6TRaLZ9vi0oODAjJ4OZ5IzsDIGHQCgWmmh6dGSMYlH3P3R/oDyApmkHB4fUjFR3gZu7QGAymbRqTXCoPG9tHhMDlSCI2PgYgYfA01OgUqmWr1oWPyeOqTMxOVEkFjGvEkOKISdnpwWLci0BbZobm0PDQ3IXzJOHyGUBMm+zpYg1RGLRkcOFBEHkzeLvcGq1Ok9Pj7TMVHmwXCL18/bxNhmN0THRCUkJIrEoLDyUIIghxVBcfOzc5CSRtzg0PGQ6XWVcQqyPr4/YW0ySpHJMGRYRtu6OW8Vikb9MOicxIUg+xd5kUHe+7nTZGYIkUtKS5cFBO779vuJMxd333v3gw39kLmoIobg5cR6eAoGHACFCrVKrVar5C+czwRL0er2X0CslPcVP6isLkFm/ICgGFbt2/EAQRFRsVFJyosBD8OmWz+Qh8k1vvuIl9LIoF/2kfrHxMd4+Yg6XqxxTjo+rsnIylq9aplFrnJyc0rPT4+fEBYeFSP0ler1er9dnz8+OiAqT+kulMilTSVZupguff3DfwSHFUHRs1LhyPCwirKerZ2RoWCQSpmamajUaoUiYsyAnOFQeECjz9vUOlAcuWr7I0cGBw+UY9AaMcWRspDRwwiqeJMmQ8JDyktPj4+McDufcmYq0zLS+nr7hoSGhSJgxL0ur0QpFwqz5OcFhof4ymbefj4eXZ0hEmH+gjO/q6iuRXKg9nzk/Z07KXFlQkFTmn5qZ5ubuDhgnJCXGxMeKfbzlocEza3pMJlNUbHRCUoJQJAwOCyZJckgxFJcQl5qR7O3jHREZjhDCGOISYuYkJYSEyv0D/AmCiImLFvuIPTw8KBY1OjoWFR25+pbVYh+RRCpNTE6U+kt2frerprKG78of6Bvo6e4ZVgx1d3W3tbadrzk/76Z5PB4vITEhMTnJ28cnPDIcYzwyNDQ3NTkpNdnbxyckLITpc2R0ZEBQoLevD4uilGNKnVa3Ys2q1Mx0APD29YmKi+G7umjU6uCwkLXrfsNoYvQ6XWBwUGpGutjHOyQslNENzE1L8RJ6eQq9WBRbp9O5CwSp2RmM0nEyjAYjRZHRcbGRMdFCsUgeEmw0GEiSTEpNjo6LdXJy8g8MAID4xASxj49QJGSxWTqtDgHKzM32D5QBgMFg8PTySkxJksqkPhI/hlalMv+VN68+efyEYmAwJj62o61DKPRiXkUH+geWr8ojSdLJyUkkFi1ftdzf7B1zAwD/52ExsLxi+uSUslNncrOX7d61D2Os1eq0Wh1N0/39A3fe9vuctEWlJ09Zl1KpVCZzbGOj0ahWqXU63cytTNe3K45Fo9H09w0MDgxqNFrrn6wrZDpjSWluannphU3vv/OvkeER6yKWPtt8ng5arU6j0Wg1WrVazVgOMlVZGlIqlZ2d3TatT4fpWmQmUKPRTDmBV1Ht7MlgirImeuZKJkMxqEiPy9jwzIaZC848S5PXdPKv2Dwh1jCZTCaTySbRaDTRNG0yXpbe2tx63533t7W0XXFElkmYKWUWewrPjsymw45vv1+QufDJR58yD8rIEAkzasu/1rD0ZIruWQ2hvq4+NS5tUfZijVrD5NdqtVfd4clFbNZap9NZtg/GWKvVatQavV4/G4KcEgaDgTZdGqNOq1Or1Vdd4U9iTbNcd9s8k+jHBk0XmxZkLPz4g08wxkxobZPJNK4cf+B3D8xLzunv67+6vlnSpyYJmp6SsGfPQKZM/El8bLqOTZmZ+UmlUmnUGob+Z1PkesO1MBucyRz0SilajYamTYw4Zrmpe3p6xMXHtLW019ZcsA6OZh0AhyTJ6aTF2ZmeTg2LuQqXy2WshBhg85XlcnMzwjpFFuD/f889MbmI9b1tNvYmM2gsmDqdnJyYQM54eoOaK7Y4ywmcfbWzJ4MpypoNS6/Y9P7d+5sbm+++725GY8+Y7s9Q0GaNpuzbzL/iaWLCT9UWAgBEoBPHiisrqpYsXyQLlL3/zocUi/Kbxnn1sjonedlMkTKLPQWzI7PJYMiJx+MihJycJsLpEARhbeU3XYvTpVsPwcHBgQnlxDWbEVhsLK6iw5OL2Ky1xTKASbGMYvKCzrJ1xnLZUpxt3qdXV+FPtBmc1brb5rnS3/hh/HeYgAeW+XF0cpybMre+buogbLPp25XTp3QG+in1z2ZCrrpOPMliESFkOX1+zvnyC+JaxxX4qZDKpCRBfP3ltwKBm9RfotPpCYIoP332YP6R4FD5ujtuvvZdmiXlXV09PxNTOAL8l2HLPz/u7ent6e41GgyAMRNH9nrDD9/vPlteUVtVO++med1dPeufewJmJ7f94sAYl506TRCoqrK6uOhkWkbqlcvMeminSk4RBDEyPLL148/X3XGrJfDAf3Raru4QvZYV/oLw9hbzXfl7du4NDAoIlAca9AYWi1VTXXNw30GJVOLm7vZLd/CXgWVBb9yVnYxr+jcIfiowxq6u/JTUpKLjJzs7urq7empr6urO1xf+eEwq9Xv19Y0cDoembwAGasc1A2OYqVaphhRDt99z+1pzAMHrClJ/yfDQCAZobmx+8pnHg0PkNofl9UbSlnutalx1puyMUCR0cnJSqdRzU5JmX8kVB1VaXEpRpMRf0tvdOzc1aTqllB3XBhhjHo+XmZ1Rfqq8palloH/gfE1dQ119UWER35W/4dUNDg4ON4T8asdsgKZUb14/sCY1JhKRdYqdEO24Iv7TRPJTd9DkU59JmVzPdULblo79zJmcuezkyu27+xfHZGZ7Wco0IZDtuBFxvYsCdthxnePn7CDro+76FwV+Dq6Tsdhhhx1T4sYLimSHHb8O3CiGHT+/Y9ft0Oywww4Gdq2AHXb8XFzFJrqitvyKea49rppXXG8DscMOO2xgFwXssOPfgNnvoxv9XPypHONGH68ddvw3wC4K2GHHvwez2Uq/pnNxlqzj1zRkO+z4tcJuK2CHHdcCCKFf2aE4qyA2v64h22HHrxV2rYAddvybcX2+9P/nMB0P+e+ZATvsuNFhFwXssMOOfwOsOYldCLDDjhsL/w8iJkbKpMKfCQAAAABJRU5ErkJggg==	\mathbf{L} = -\frac{q}{2\pi} \int \mathbf{B} da
+433	A thin uniform donut, carrying charge $ Q $ and mass $ M $, rotates about its axis (the $ z $-axis).  (a) Find the ratio of its magnetic dipole moment to its angular momentum. This is called the **gyromagnetic ratio**. Note, since masses will enter in, it may be advisable to use $ \mu $ instead of $ m $ for the dipole moment.  (b) What is the gyromagnetic ratio of a uniform spinning sphere?  (c) According to quantum mechanics, the angular momentum of a spinning electron is $ \hbar/2 $. What, then, is the electron's magnetic dipole moment?	[]	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	g = \frac{Q}{2M}; g = \frac{Q}{2M}; \mu = \frac{e\hbar}{4m_e}
+434	A charged plane lies at $ z = h $. Centered at the origin is a conducting sphere of radius $ R < h $. Consider polar coordinates on the plane with $ \rho $ as the radial distance from the z-axis. The surface charge density on the plane is  $$ \sigma(\rho) = \frac{R^3}{(h^2 + \rho^2)^{3/2}} \sigma_0, $$  (4.7.1)  where $ \sigma_0 $ is some constant.  Calculate the pressure on the plane as a function of the position on the plane.	[]	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	P = \frac{R^6 \sigma_0^2}{2 \epsilon_0 (h^2 + \rho^2)^3}
+435	Consider a coaxial cable with a solid inner conductor of radius $a$, and a thin outer shell conductor of radius $b$ (the conductors are highly conducting). The region between the conductors is filled with a dielectric of permittivity $\epsilon$. A current $I$ flows on the inner conductor and returns on the outer conductor.  (a) What is the inductance per length of the coaxial cable?  (b) What is the capacitance per length of the coaxial cable?  (c) What is the characteristic impedance of the cable, and the speed of wave propagation through it?	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	\frac{L}{\ell} = \frac{\mu_0 \ln(b/a)}{2\pi}; \frac{C}{\ell} = \frac{2\pi \epsilon}{\ln(b/a)}; Z_0 = \frac{\ln(b/a)}{2\pi} \sqrt{\frac{\mu_0}{\epsilon}}; v = \frac{1}{\sqrt{\mu_0 \epsilon}}
+436	A rectangular loop of width $a_0$, length $\ell$ and resistance $R$ sits a distance $b_0$ away from an infinite straight wire carrying a constant current $I$ (both lie on the same plane). The following things happen simultaneously for $t \geq 0$: (1) the loop is moved directly away from the wire at the constant rate $\dot{a}$, and (2) the loop’s width is increased at the constant rate $\dot{b}$ and the length $\ell$ is unchanged. If there is to be no induced current around the loop, solve for $a(t)$ and $b(t)$.	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o0WiyUYDEqSZDabV65cuXTpUngqkXvEdICpPX3ppkXJQqKcbkQvB3r1JUV4UNNgMNjY2HjgwIHW1la4ZSkQCJhMJqvVCoe10t0MlFtmBMGXDMOEQqGmpqZt27ZZrdbvf//7+fn5kIzjOJZlfT7fjh07jh8/7nQ6x44dS3dFWU+O+3Xo/mn8qcRLlKG/poMEdCyjFMvSS0xVlwjgasYjR45UV1fn5OQUFhaGw2GPxwO/6kwNUe9a1RmZaGudTqw6YMBn8KFLkgRHW1dXV1dUVCxevBhiB0hUWBLeX+PVBisG5xqplrlEQ6aLOlnJPhiERIWO0aYB9KVrrrnmvPPOy83N9Xq9wNFkToop0HKCiwYkcTgcHMc1NTWtWrXqq6++CgQCdrsdIcQwjN1uF0Xx8OHD69atO3ToUCAQuOqqq0pLS5WCJQglrfcBqypdGVoE1C9QJXQjk5KY0pMitEqnASeMggExd+7cW2+9taSkxG63e71ekoBkKONlZGBxkn5E6a6RzTiJGmOMwc3CMIzH49m1a9eqVatYlg0GgzCt1DfS+30gT2f0Baf3S70naAQZdOcZ5zLC1wihoqKiefPmFRUV2e327Oxs8MDQxdGcTp4lvkiMMdj1xcXFy5Ytq6urg+uMw+EwuF9aWlq+/PLLL774or6+3ul0zpw5s7Cw0GKxKBegkgWD1ZWK4pCxUSpFk0WMMVLLNtayjKePQ6vNZrPD4XC73RzHTZw4keM4l8vldDrB1Y6oxR7V/I3UrVI2mZ2OImosCALY4OA9FwQhJyenqakpJycHfIPA5mQZQEnudCnp6YvrXyTK6X02f4wDWi1t3DbXh04mNIMDQEcxxhzHeb3ecDhstVpRhMGNX7hBCmUYRhAEr9cLa60IoWAwaLFYPB7PRx999MILL7jd7pKSkq6urrfeequiomLMmDE42eGM/dL6staRsYa+f0D5+ABC3EoLTCpF1iSdTidCiBz4nmwxo0BmYpNjLAVBCIfDIKeR6TX5Bkdbgh5qGJy+l7QCzcIo4vIGWrfZbPTNCUrTRpYPWUSFnuD1eru7uzmOg5zBivf5fK2trd3d3WVlZSUlJTabLRAIBAIBnZwTgYzWU9q1lJkraVpGGUoeTHr/T+4igU7ryz4YLxrWaSRJ4nk+GAxC1CAoHjLgXVGtXtUBJqqXhnZCknLhHldYsyXZksjIqO1F3HFRBVB90Hj6gYKUc/pAr7WofQypKQfxlsicEuDcNJlMsrhDnch02eOIYiscOQEYOoDVapUkyeFwnHHGGQ6HY9u2bcFgcNmyZZWVlcOHD9efVUR9X33BDFrrdMfTesQ4v6DeNposw76ZQGCMep20G08OvU7+Uk2jxaRGTFpiKID/OsEjo2NqHa0E8C+9Rc4UgWwLtOob6WCw0nRMSAKnp7P7JSbIvNiApKsReFqIswV2sRrPhCTrueOYZVHEqDGbzRhjp9M5efLkgoKC1tbW2tra6dOnT5s2DSw1VYvMiCmUXOhXaRz1ST4QS1DHco+jiGgSJJyBgUVIFOMoper9A8YkxrJsOIzJp686vdCpWNVoK9pgJ8pJ291KITOIitTa6QNizIw699R6KmpPUGowLPrTmkr/GxPXgNjK6QIsNMHqE8/zsgQxvKFhGM9Wf/gnpKxMQ+zxqHYi3f91rNqBaNApa89gbaCI7hGvOqKOG1LaxaQhZAmQdmwM6QuqYyrdpvQYTB6BhVPa90Kv32q9fuIYiGoQFUPRny7TqpQWgShdBN2Vncqic5av/pRcSXCyjgRlkUUnIoPOU3Eg1m5mZPKuZHZZfRophaw9aD2YtP7ch5wQn8BQmcSeIIpHRkpZI5Kqk1VR0imV0DrZnEHGEi2dz1jrUZEcTlet68ExAOq4JoxrmCpVkZitqLEHqgKA3pMLVFHvGAZZehIZZkRO46DdAnFMNbRkUHobJOooQboayYXOqvUj28ClI7+OMFHl7VNSjwuqFKk6TUTG6kSrwqM+pZNeoqCUUFl6HOQ+RMaDoWinyxCT2R6TbyTV+eAIdJ6ig2q0slJ+r2Ujq6bRmgEop+E66clnYk7SL6js3kYs98QnZFqv0DeIiYOijqY62kIS6NMlVvhY6J9kH2Q/6YuXCNvGOodTFj04rE+CpHH6wJoWGWe3qPlo2Sx0bdBpoF+p+iWjCiObCMscFLSBQ6xaEkCJ4w1OV+U1pSmNelvTOrnRRyCQiTapFsLpMIPRP4JVn3OT1Vf7pdsbGVZlKaM66wwqAFZziyvTRP1G/yd6eJAisfNGNsTRnWuQ0XFSkCo7faDUtb7lgpIxX1OlWkSZqwlShv7wQE+rEywlagKdrktKxxibTCYdT53+EfOSJAUCAY/HY7FYHA4HnOGnKoCM9wcWYpI5qjmFewO+hDgokoD+oKOQtDrJvoxVSJnJjzXOJdXJMOo3QxPJ5PSBZaoTRFUFg35GnWxlNpdqx0gRjMx8ZTAumKq1rpqGNseiegBkj9PmvyAITU1NTU1NNpstJycnLy8vKyvLYrEg7XdMCrnr0VzcmRpDfIypTEBPhhBCZNu9/ixTv0pjgnLySj7IpmuxZhW3SESAwTQepMROH0wV1JeIqlt0AtrxojXqGOwhdCYxQYdKiEi03Q0XMkAUHc/z9Nl7SlEJ9UiSBI9IksRxXG5ublNT01NPPdXW1rZ8+fJ58+YVFxfDCfKIoipVaeN7zQEBfVpPk7cmQsrkSfCIggzh0Egmp9MUk6llHcj84PEBR4Je6GxR7y0bRiRR/axlnWllq/qT8puDBw9u374dTs0OBAJwqgFsuUJqtE6zsCiK4XAYIZSXl9fW1nb48OHt27d/++23y5Ytu/HGG6dPnw6Jo57RGh+z6+lzijXdeG+KahDQjj6dWpJpRRL7spaSgNclKf1CB1oKPMjIaqjHvcjc2ToqlYaeJVl/ozkdvqH7rWrnVOV00ueVJeoQohEnT3V19dq1a3met9vtoVAITtAm8YhaeaLeC8Jw6Hx9fX0gEGhvb9+2bduCBQuGDRtWVlYm21yugzRszdRB1U1B/DBxMFrU4T8m4Mg6U6o5fYhgqHN6VCgdAnErMU1MOmmMG2Uyf2h8/YG262kjTr9oegCQlav8E3ITRXHp0qUzZ84MBoOwbxAhBJxObyBULQ4SWK1WjHEoFNq/f/+6detcLtfMmTOXLFmycOHC4uJi2Ldi/IRL5XBoJKXiN5QKQz3pQ45EgRSB1F4t6mxbq32NyEA+y2YJZICRNM7X1cEgs7ITx9DldLIsE7XzpFRpyEQhKd4YpGtfw2kBcAAey7JwgQaKhEAkl0fIIEH6vCRJDoeDWOWq5KIlPAwAdrtdEITjx4+bTKY5c+ZceumlCxYsgOs+gAjidstq8Xua8EX6ODNVNSRx8VRtnVTY7ENhfpY0Th+gNSUjnZSWFXXF0kjfoKXVsblIWRAJDvco8Tzv8Xg8Hg9cG5+XlwecThIbn4yrmurKOQ0tJ8bYYrHYbLaometAEAS73W632ysqKmbPnp2Tk4Oo4TmRnAlizadvuDYO3pQ1iow302SQoLsevSla6UhMCpR9PE3qIYkYona6qh+5b2BkPhtrhlFNXSgCbhbu6uqCW33Lyso4joPTHPXF0ypXxwOjFA8EAItbitzZRIxrHbqRIsEz8JTVajWbzRs3bty6deuSJUumTp3qdDptNpvsRQY6tJxa6fmOiZAv8a3hCJIrm6yslPZ3mZnVLxiinJ4spEI/aFdM4lNacisexI00NTU1NzdLkmSz2ViWBU5PgtDaotKLlt9+++1nn30WCASA3yVJslgs4E9XngdAXgGkNZlMMCaxLNvc3Lx+/fr6+voNGzYsXrx4xYoVU6ZMKSws7I+OpH53XeoQn8FuXFHjY71k+V6UTjD9902w3NRNAvpxAB60nB53ncbUAVKExAWAt4B4cPA1C4Lg8/k+/vhju90+YsSIadOmIYQgpjsVIDVPPnAc197evmbNGr/fD7Er4AKSrZHKZhvwInCZQygU4jjOarUKgtDa2hoMBnfu3CkIQn5+fnZ2dk5ODlzTSp/2hdLVsE0Exv1jslaQIjBSSkz1lj4e//5CilYa4sCg5fSoUF2TIV9q/RrfIKH8UsdDol8E3Ut1MiHHlpKzGGGBdO/evePHj580adKIESN0xDACLSXWEi8UCs2fP/+2227LyspyOBxA0BD3QuRUchC57gOuWxMEwWQy1dbWvvHGG42NjTNmzFi0aNHcuXPHjBmTrAnH4IPqcpGOphk01QfokJmsSTANnerqe1pPDqf3u2Erg748yilSKupdv88kqwjll0CCZGmU3FUmCILFYpEkKTs7u7y8HBLHFPwXtWglaHPbarVmZWVddNFFdrvdZIquePSYRNJLktTc3FxYWGg2m00m08KFC0ePHh0Oh2FgkHofyUuONEldp0ppZ9XhViNjf1J6ZdSqG4gWeqrXXZUJ+rKKBrmdrlWb+mukBhsgwT4TlW6MdCctMWjfNHzDMIzH4wkGgzk5OcXFxVAz9A3XxhHH5B1HLmDKzs6WJInneUydaKY6K6K/h92hEL1jMplKS0snTpyYlZUFEZkQS0OfDk8+90FfGlh8ZtD3kuq1RNUS+12GOJCGEg5CTk+wlpVKH3XSmvg4HIf6SoqodnqQIEfcgRMGXBZ1dXVdXV12u51hGJ7nwaERq9vUyItEnaDQJwAjtdeX5UAGHpZlc3NzbTYbRL8oH6Gn1akOouhfJKh1xr18fYYB11jG+2xfmuqDkNP1YcQtY2QylUyZDEM5lqimAReEjOPAznW5XD6fLxQKAasad7wYt82N667MkFeWqJoVy7J2uz1qKTFNthLqb6nsqonYqvovRWyXmN49QXmS1XHSwZUfnxGWImFoDDZOT2TkNLgulPTwKVVq03IZyQJCCGQZ0hYxsHkoFBo9evTkyZM7OzsDgUBubi4pRfVO96S8mlYyIymVrUO/KVkwID+RMcz4uEJyS1uncBKtB1pzkpUnShmxGlnJ7MdWS0OXC8Fg43Tj0OdW44h1tUrVd5ygaiqnF6RQskZqMpmGDx9+xhlnhEIhq9WqvJ0DJdY/U927wIMEUxDZ9ELpgDKYYZJE6589MomvgiSl3RMRINYE6YM45hwDzPeSnqsZqlypL2qsYRKJGHrx9VXaB00MUsgKwr1pSTDGJGLEbDabzea5c+dKkiQLS4djTkk+9OPJbVY6f52qU/XDkPSqJwwPYqi2ghFl09dJ2ZxPtc6VBdGtJns2anFRpdVPkIFBDFE7PSbzJ74BVtWLotVzYoKMtUkmyp07dAL4oLXJiK4QHfdF3JadKiupskbUnKPam+npRUkEKX0jHUJHCupPRVkDFDFZPH351gldL5LOiGqM901ZqiWqOsGjCqbqNyelq/rWJepsAEmSRFHkOA42cBovl85N9bNBRH1ffT84mZco31EnT4NITCUGhoGpP/tRVmkSDWc6Q51sZS2bOh5U7X1xwPgCUuJlGccQtdMBtBMDRTOoo8KgDaKVBsdyJiLqLTwAnBKqXhQ6JcR0awkgE1KWIY1Yba7ENVvLDI+bx1UnCoMDqpxFj5rK5jNommhVmv54LEVCb7WSaQmsL1IcSMRfqkTS/ZOJY+hyumpzxkTuMtNGn6yRgXiPWDUM0pOjDWlO1youqi0ckwBxIGp9RhVPp54Tlm5QQbk6QqBMqcXRyR1BdXoWPWD0GfqA1vteLZPmexlYPSpuXlPtD6qfkwipN2Ty4MiGTHLtkSRJPM9DYp7njeQvy1OZJsH21WITLYeAqqMGq13BSuccx6CYhC6d4PN9hZhetu9tz/j8IUlx8SeYA0ozO2Po2umJILkTrqgNr+oVoX8lBjt8A92DGD5k2gtnFmoZRP01KmvJo+Na7TPH6+CDwZE1FVWaDvasqgCpsNb7UScHLacni3ZpMlXas/rTSWVWcS/O0DNoOkPZyePwJRyBAr0X7vBECl+qcVcypnxHWkNLUrpETIl1BrkMZCArIrT6gctOUotxSt10U+snpYoORKSJ8Mnk9ORar4nLoFPFOut+OrSrYulp2QAAIABJREFUM8E32Jx0/rG6C5QdT4yAXvaBz8Qep5dDZbQe9aXoB3XGgH5R5TTpP2kLWbPKhn/U+6I41We1+ohqYn3IstIqlHas0Y9ENZUSV4akZJImSLKdrjRd0xbEI4HUWjSmwckgO0uRY8218lfdo6+VLWRF91K4ORr+5DiO4zi4UZoWQOaQUUqoVeKAaNPBgRT1IIk6VR8Zm1Mqv4QPssmi8kv93OiuR48fymx1qiKOWup3i7NvkPz49AHX+WkjV/VXHTcZsXSizglkUPpSZLa2znRBmZI+Zha+IWukHMfRvU4nT6Wxn4EBSEmMTyc1n4r6j8qSMmgl0yFZGehyZQqv7FbKiYVWL1B22Iy60hiE/nQjLiCdnkMrk1ZWseqQRIVnAOC2CkSdjGjEmUjrPROBKIqwh8hkMkmRExmdTqfdbrdYLE6nE2MsCAKZ2EJiekF1wA3DgwY6ipTEdgHVgiulTCaTkcM4Y3UMRs1KCTKnhL4g2zNh0JErUVPPqDMP+sMg1vlByOlRIZsGyv7UeTBBPcCR/T6yzUH6bh+tea7SOQ5ZiaLY2tp67Nix7u5uSZIaGxudTqfL5crKyiLaT9bHUO/hTVbWINb7fkcfm5bEklAGPvVXK9M1QHqE7DITLSNdy9Iy/i6DWL2HIqcDopKpjp0eU/505yFnCoqiyPM8y7JwexxJSfvHCaBDSpGN/hhjs9nM8zzP83A9G9g4HMdZLBafz/fee+99+umnzc3NOTk5b7/9dl5e3qWXXupyucj5tCSSXfbig96ESQf0vaOANrphVmcymTiOIxM+rZUVlDyDXeZpQb3vrgLTSufAImSs3gYxUxvH0OV0pdIAaMeL8lf9rFS/lDGmlu7ShSpBZqnkG2JzmUwmi8WCEAqHwxaLRRTFjo6Ow4cPNzQ05ObmnjhxYuLEibDziOd5I5PcTMdIKTAVR6DPU4k3BMkBJojAoWTkjsmqjbVo1fmlLAHdxVSnnnFcrJjBkON05cqMqiuGqBcY0Vq9y6DCkXFCEARBEOh7k2Pyp9NgGAYun7NYLMDpILnD4Zg/f359ff3atWv37t1bXl4+Z86cwsJCRFnoGSQTCfCd/hCeLDAMY7FYzGYzsYsRQrKb/1IK1dekNZ9YJ+RLWAGSReKi5IVmDeKhYshxOoCYBjIVUfYl0CrVHZhG1IJecYVHBEEIBAJ+v9/tdjscjnA4TPdwmVeEFAc+FiKzyWTied7v9/t8vkAgYLFY4PB0hJDVaq2qqlq4cOHWrVt5np81a9acOXPgZmctgQexfg9QJOL0ozOBD1LkSE6Yw8GNKKFQCCZtYGRgtXMXZBkqFyRVp7NaC0I4cqamFAkZYFkWouZ9Pp/P54Obx+FX8EkarJkMm9MYhJwea2fQcSYihIhdI/sppnkrUWKz2Qz3O/v9/paWlqysrGAwSPcl0rXIN2RjEaKuarPZbBzHhcNhv98PndPtdufl5UEOeXl5c+fOXbp06dixY6+88spJkyYRQx4GJ9R7Xq/FIBknTHxIkHTII/ruONVCVRMLghAMBnmet1qtDQ0NRUVFwWDQ7XZbrVZwrINRTBbwZYvnsskr/SvtNlGtASkSiKWcE0NZ4XBYkiS4IxfWh4DNiRGjWjNGKmTIYhByekyQ6Yeq/05G68qn9POHmC2i/RB/snHjxq1bt5pMJhJlKDNhZIYPPZZIkgQc7ff7q6urwQaXCVxcXHzWWWdNnTp12rRpDocjqtiyKUgGxiGr06TXoRFa1y8UVlxYlt27d++TTz45bNgwhFAwGATfHW2nqz4um9Qqi6ZZnn5EdlAoipgstMLzPC8IQkNDA8dxRUVF4H4hA0Cf0fdgGieGLqdrueSUBgVS7LCPqSD6WZ7ny8vLly1b1tbWBv5Ncrcc2bpNegjuDRnpm0wmp9M5b968MWPGhEIhWYc0mUwzZ87ked5sNpNpLD1UaL1+htbjhqzqaEqKm56kaMeORwUoFcMwp59+usVicbvd4OKw2+2EeUlZtPWAelOwqm7AzA/uiUW9Z7EQDo8jEYogBo7szMAYw7Y4k8lkMpnGjx9/2mmnVVVVkdtakr7wM3R0e7BxetzNRtYtiZmgmiaR8RyKmDBhwpgxY3iedzgcMsXVEp6mBkTZTeB+MZvNwWAQLHcChmGcTidCiD5rV+u9lGXRc+fBZMKkCDIqRNpR/3HkGbUJ6KKVvkHw9SGEZs2aNXnyZBS5v1CZp6r6GRHeyIM6TktBEDiOAzmJiUPuRu8DDDINHzycnvggjBW+bIQQMXLjyx+GAdI/rVar1Wp1Op3gOqTD1VHv6C7CrcTMwRjDFdIQWQymFtmMpyyXPj2GxAIbr4ohYtQkDJWzAZJVdXEMCcpJHkIIgqNEUQQPDMuysLkBU+uiMq83bUYo7XfZOxKlRb2tASI/3a1U85F5Y+iruHQGg1ihqtWDjNDRwOL0lLIM6BD4FiVJgumk2WyGg7FQbyOX1nKlN4PISQdjEXYGHjeyP1sLsme1vChg8qh2SCMYfLqeaijt5UTqkB6D9fORKR7toyOUjTG2WCwkJYmjVR3m6eKMzO1igk5uUFaCIQlRS0+8adIcA4DTk0jlsl5H2xcAMJ+lyLYgWEGCDkAnk9T2DRGNhB6lSugkmSRJ4AQHf7cyGhf1HhvgT7KPlJYHxiEIUNOqsaT3zAxUEdV7Ricj1rRWbrE2GTF1iaYprWmEUCAQCIfDgiBYLBar1UoHqpP1UuU4IdM6mVlDTytllYApkATghYfiTCYT7Yck26rjqAGDtZT0PNMKac3pKTLM6YFapvRkrmq32+FLlmXr6+tLS0tpVSAhX3RWZA5L9wpRFIPBoCRJdrsdztgiZdlsNkEQvF4vxjgrK8uI5AzDBIPBQCDgdDrBK4oQglj1Qa+paQ6iDHQTSxqucFVTmv4p8TFYdXLGsixELiLKUKCFJJa7ctKplEeH02Xdin5Her0URcwjWMxX2lgZxIH05fSkELqOfpCeQ5vDZAs16KUgCC0tLceOHSsoKGBZlqgdnTmxyunvccSL7fP52tvbOY4rLCx0uVzEH4IQ4nm+vb29s7OzoKAgKqeTcSIUCnV0dPj9/sLCQoh2x1TwDP12SmNQSTFKk0pfDC2o2oNDAfCqmLoDFr6H8VuH0AmvyehbS+11uFUVYAXDg6DVYBTD2cuSJGGEkMlEzh0iYsjy159GKBNjhc9aloaJXK6EevhdkiQ+4A8gB5L1rwziQ5pyeoosdBpKZyWO+BwDgcDRo0ebmpr2799fW1s7duzYCRMmOJ1O4G6JumBI1hNkk1aWZTs6Ol5//fWampolS5bMmTOnoKAAbO3Ozs6GhoZt27bt37//sssuy83NNZvN5P4KmR2HIudzmc3m+vr6Tz/9tL293el0VlZWTp48ubi4GGYVpNJUJx9KKCtZi4ZiQlIyGVjwer2HDhzcuXMHMJrT6fzhRRcJgoAxYnDvHQ8YiaJEIvaw2rK8zmAA/8UkJl7NdhZFEWO09Zutu3ftQhgLAl9RUTln7lyn07nt2207dmyXJJgmWn+0ciWGoEOGQQgjHPN6rNaUQofWRVEUBRFhdPDAoc82fw4dShDEH/zwe+WV5cZLz0ALacrpKQLWWCHBGANBg0XT1dW1bdu2zz//fMeOHS0tLZdccsmJEydycnLA5QKhVyTsV3ZmAHwDjM+ybEtLi9frPXbs2O7duydPnnzZZZdVVFQ0Nze/995769atYximqqrKbDYfOnQoKysrFAqhSAwM6TBgQ0GYFxy76HA4vvzyy61bt06dOvX888+fO3duZWUl2f5HQCbX9JeqPE4qIVn1PChpXVVzEEIWi/nSiy8mLIsQwhi98NxzGPfwZOR/GMMQSzLp+YyU2dKNJElk1iVJEoK/UM9ozWCMEcWq4KfmhV4QRWnsuHHz5s175eW1DMNgBjMMgxnm5TUvw5AT+edk6AsC2VGPfL0/n3zT3hWEiFFBJaDGKoQkURQFsbdsoihKCKHOjo47775j2LBCY62hKHywr3waRzpyuo6RniwCUj4uCALP84FAABzo+/bte+211zDGw4YN27t3b1tbG1kphekqos66o50wsttBOY7z+/1er7e6urqmpiYQCFRUVFRXV2/durWmpqaiooLjuNdff93j8QApy/aUIoXtbzabzWZza2trfX19Z2dnV1eXKIojRoyA3aS0k1RpQ+kQOkpsX0wcTw0aSAiNHTuWZdn29naEEEbY4XTYbLYevsb4JK0jwo5ST8P2/C0RgsdUtogm9JNsLkVywQwh9EhDiz2kyQdDIY/bEwgGBFFyZbsqKyt9Pl9lZWV7ezvGGLNMljMLVibh4ciEImKrE4Fp4RECESVJknE6jkjbG73VSepxpguCKIoCx3HubncwFJJExLJs6YhSs8KFaKj+kxpuNAiQjpyuhVi5I9amFQQBYlF4ng+FQhhjq9VaXFxcUlJSWVkJv9KDCllQIp5rREVDwn45juNaW1s7OzvNZrPT6SwqKiovL+/u7j506JDdbjebzcXFxS6Xq6CgANz3soh1iVpGA48txtjv95tMpoKCgnA43NXV5fV6yWkwtDdTqd8yXyctNj1sDPEuESvC4fBTzz6LENq0cSNCiGHZiVVVsP9e5lchGgKRslLkDhNIRkwEkjOxEiA9juzqpCMUlfJAKX6fb+/evR0dHTzPn7V0KexsQAh9vGmTKEoMw0yaPKmkpEQ26quegUHUhtgZIA/RVRSxdWgFRr2VSuYPRAjxvLB71+6W5hZJQiPKSidPmZRIgG8GBOnI6Vhjw4uW50TrWR16ovOBz3DLBGjVpEmTKisrZ86cCb1i7NixP/3pTyG8BHog2Oykp9G+dTrO3WazdXd3v/HGG16vt7y8fPr06cuXLx8xYsTpp58+ffr0zZs3Nzc3l5eXX3TRReBPD4fDdEQjdDDwvUD+4If94osvWlpaCgsLR44cOWvWrKqqKlhixZF92LKpA6I6p1bdJoJU5JmG0NIljBAcjXnaokXk4BQy5UKKQEDg7mAw6Pf7WZYNhUI5OTk2mw0hJIoiRBmazWaynE5WU+F4FhTZG0yfI0QgRc5zZk2m6aecQg8A8OsZixfDESsQkQUFyTJRDhg0ucNSMGF/+nHSNfSrDvdEiOGp06aAStPxixkkiHTkdB2oNrxSY7QohnxPDFvoA6BSJFq8tLT09NNPnz9//vbt23fu3BkOh+vr64uKimApkuM4t9uNMXY4HPR2JEzFbMHBcpCSZdmqqio4zgJGjqKioosvvvjMM89cu3atx+MJh8Nw6ims0MrMukgHYCBbCH8sLS099dRTKysrR40apVUhMgeOVvB70hl5qHXOiNuhx6aOulkXmlgUxVAo1NrampOTk52dDT9BoBTP806nk8SiwOHMoihmZWWBBuqUEnFunFyDRQjJNIpORg8MSl+fqvAIoXA4HA6HbTabzWajlS0QCHAcBytPqjxOAOnB4UlreBzAGmH4QxZpyukGiSZq+6kaMuQD2TIKmk2Mbr/fDzb77NmzJ06cyHFcbm6uyWSC9M3Nzdu3b4dDsgoKCqAPkGmjRB26ZDKZiouLzz//fEEQIKKcmNIsy+bn519wwQWiKA4bNoyY5FJkY5HMnw6fYQPq/PnzZ82aVVRUhBAigWikaHoCSyYQ+nWbeDcY4h0JR+5zoM9jQLohnqB1X3311dKlS8HuBk4E3QNVgdYMh8Otra0QvTp8+HDYIqQkTQBx49Al0h4Vco8KiqgW0/twXRno28kBLMv6fL6urq7S0lJybEY4HEYINTc3nzhxYubMmXD4qNKSoGsD5ivknKJEVAhrbwUYgkhTTkfRaD2O9pM5mpW/EooPh8NAuyzLZmVlEcWFvuF2uw8fPmyxWCZMmFBQUECMJtrYAcBP2dnZtHITTjeZTGBlcxxHqFmiVllF6ig7mq/h0iKYAtNzfJ1aUibQn81kukeskFGYqHavLA2r1dre3u52u10uF8MwHMd5vd6uri5BEKxWK4zugUCgvr6e4zhg9ra2ttzcXNR7T79szJZZ2fRcjfyq6rbWkhZyg0AvmCaGw+HOzk7ygoIgdHd3NzY25ufnS5IUDAY7OjocDgdW2zahrDGdBDEho7EE6cvpSNexbjwTmqFkdhO9/QHKAt0FJwz5nixXIoRMJlN2dnZ+fj7Lsk6nU0tr6TkvXSgxt4lIMPe0Wq0QTiMLhQSpSHociW0gjktiYan2EKwW/owUdo1ylUKV1mlq0K7vDBDSJiwyF7TZbC0tLQ6Ho7OzMxwOB4PB+vr6jo6OkpKSYcOGwR7jEydOvPPOO2PHjl26dCnDMLW1tcFgkFw/i9TWHpULRbQk+k4VWh9AA8ElKIqix+Px+/2wDMBxXHNzc2VlJZyG5Pf7Dx8+vHXr1tmzZ0MoQX19/fDhw8lZvihjJfQt0prTkRotJks5GOpEOkSt/8jOuyA/ERngdhifz/fdd9+NGzeutLQUZpoksUjdM4d6z3yJh0f2jjgS0iCKIoSyAL9DqIxqndB5Kr8kTgDZNFyWieqzdLaq0HlqCEK1FmQDJPkMLheGYXw+X21trcfj+fLLLwOBAFx95XQ6CwoKXC4Xxtjn84HLxWazORwOl8sVDAbBVJeNx/SfUZtVB8r1G+gO9fX1MIrU1dV5PB6WZRsaGubMmQOnU/j9/kOHDjU0NPA8b7fbCwoKvv7664KCggkTJpAJbrI4PWNVGMHAuHEYU0gwK5m6y8wTAtBm1JtwEUJgTYOL87333tu4cWNzczN9RjnqrXlgUCsPhyF/gg1OzvAKhUKNjY1HjhzZv39/dXX1iRMn6JzpgzLoTFQJXfmCSmT6RoIwUn10JZPrIw4cOHDkyJGqqqrFixe7XK5vv/12y5Yt1dXVcP4PQggCYyZPnjx58mRRFC0WiyRJTU1NOBL+ROes9CvG1LKqRgbLssFgsKmpac+ePTzPu1yuhoaGhoaGtra25uZmWMVlGCYQCBw/ftzpdObl5YE1c+LEie+++w420BGptByeMu+QDpTz3QxU0Z+cbrw5Y4XMyqY/K3WdjvYl8So8zweDQVkyk8kUCAQOHDiAMZ4+ffr48ePdbrfP53O73a2tre3t7V1dXcorh6BQLU7HlBO2paVlx44d4XDY5XLBhNdsNvv9/s7OztbWVrfbLbN3VIc6mfM07jrUR2YwMA5aw4kbLRQKORyOUaNGjRkzpqSkxOFwQEQTsQ/gslm73e5yuUg+YE9oxXEn0pWIIknUwTX19fWbN2+GOJba2trdu3fDlejEaIBppdvtLi4uLi4uttlsMOfw+XzK8w/ili2DmNA/nC6j8r4ZdbW8ikThTCYT+FVQ5O4V5UqXz+fbsWOHzWY788wzL7roouLiYoRQV1dXY2Pj8ePHT5w4QewscmyvzK1Jv7uM6Pfs2bNp0yaM8ejRo3Nycsxmc1FRUUtLS319/ZEjR5qamqCzhUIhcjKMKnEna06jROpyHrjQrwyp99ZiONsrEAi4XK7y8nKn0xkOh/Py8qZNm1ZeXp6fnw9hLRCoHgqFILQRYwxnb2VlZXk8nt6lqy97xN2niIIJgnD8+PENGzZUVFRgjHft2rVv376srKzc3FwyzAiC0NnZyTBMWVkZUL/X683Nzc3Pz9eyq+JGRusMoq/96VqqlvRVFKwR3qT1vSRJcANRSUlJUVGRIAjg1gT2BFM6HA7X1NSEw2E4phFjPGzYMJZlPR5PXl6e1+sNBAJkygm9V2lZywYzSZIgyMHtdu/ZsycYDFZWVnZ3d2/fvt1qtUqSFA6HISq5u7sbNokgDZc6XUpilZfpP8mBFFlspKdu8KXVanW5XD6fr66uzuVynXrqqdnZ2e3t7bB9TBTFQCAQCATAZy2Kos/nE0WxoKCAPu4cpaalyI5WmK3u2rUrNze3q6vLbrfDlCIrK8vtdmdnZ8P2pZKSksLCQpDEYrGUlZWVlpaCC17mKlQ6eWJy/ceafmiiT+10fdsh6da6KqGrfo8iCpeTkzNx4kQIMcSRFU5wxSCE/H5/bW1tXl7esGHD6uvrYSOSxWIJBALDhw/Pzc2FoDQyfSaGuZZUEnV9gcfjaWtra2lpOXr06I4dO/bv3x8MBoPBIMY4Nze3uLgYTk6XItfyKuVPiiMrY4bHBKDsqMlI0xBKMpvNNpvN5/M1NTU5nc6pU6fOnTsXtgSHw2HwYMDEEa6ag5OI4MRmupVV/W+k0DjeiKwAYYydTufIkSO3bdvW2tpqs9kqKirKysrATm9pafH7/RDAM378+Ly8PNiIZLfbR48ePWLECPqICx2RYtW3jH5GBXv//ff3TUlGNKwPWkvZB0ioIqxkFhQUlJeXy/aIgorD1rvc3FwwnF0uV35+vtVqbWpqcrlcbW1tXV1dcHgL5Kyqwai3BwNHFmDBJG9vb29ra2MYZuTIkeXl5Xl5eWCb+3y+zs7O/Px8m81Gnx+gHDASqcNMb9GBqoVYOXHiZVdeRe4n0YKyxWHjT1ZWVk5OTmFhIRykDAwOFy7b7fbs7Ozhw4cXFhZCVIzD4RgxYgQ5k5mhDosmUul8MA66jxQUFIwePbqioqK4uHjEiBGjR4+2Wq1wgAHsI4WRBjZqdHV1hcPh7OxseCMwq5neVwvEKkwGsaLvTupIE06XgT4giUSmK5MRr6gkSR6Pp6mpyWKxjBw5ElZNv/rqq8LCwo6OjlAoNGHChHHjxqFI4DmEJ0qR+HHV82/hrf1+PxwAwnEc7MqzWq0cx7W1tZnN5q6uLo7jKioq8vLyyLkfKHJ5tM78wwiS7vgaTEjQryVbMqEtCbgWkXwDh8S1t7eHQqFhw4bl5OTA9zzPezwer9ebnZ2dk5ODMQ4Gg7AhTjbnkxRBjfHJrA+e5xsbGzs6OgoKCgoKCuDSREmSurq6mpubTSbT8OHDnU4nmeZmLOs+Rh/509M59oi2eZVbmWVhJBhjh8MxbNgwJnJVdFZWVnFxcUdHB5yVSM7uoE8LIGfvkazobOEDWGomkykYDMJ2DzDP/X5/S0tLMBgcNmyYw+GgvS7KBdj4MJi6XBL9rapKG+v4p9U0yr1g4PTIycmBm0KJF55lWTgUF9ZXEEL0bdGot4oaFyw+gOuvsLAQThWltdpms+Xn55tMJnIIDMq4SvoD6bXnqI8NRmJEEBuK53mymZOJXGlEp4E9I/TufIxxSUlJZ2eny+UqKysjnI4VUS40sGKpFs6TwRjT5zTZbDaXy1VfX282mwmnE8NfuQabQbKgbDUyWiRY53SrQWwVkCM0K5wkAY44UDZyEzTEYsHBMnRWBt9FVWYt9yAADhqDwQaOcoQzLex2u91ulyQJonHgEfgSUZNarH3eSwapQx/5XgyW0sf0pJwYqvZkrWmsSN0R2t7ebrVas7Ozyb5t8jit30ZekDa7YItTR0cHQig3N9disdCdRNS403IoI1l2ug6nJ54/USqJOhYUUQcuKo0JpOau0eF0mYQ6AstWXLVERYq6lSQJFnJVMwevYIbT+x5D2p8eU/9X9QySYzFIhsoOENPUGGwfJnK7BdY4cYlOn2HzVEB/dO+XOgcGl4VFIo2elTp/OoFM+VHvKsp40vsLQ53TjZeo7FGqaWTfxPFGtBGnmlWGx/sA+uraL8aHatHkJ500KZKWXGeh+msSFzYyiAl950/Hxo5ETweokiZW3CIke4QYTTF5WpDaETR0ieRyJdgJolxxzWCAQjaT029Q4mTTSqDl6I9PT+iuqroOT1seqkXo/5pB6tDXPKtTXH/ZPjGZ6vqPSBHE6uPWUX36KLGoiTNIIlKtqzJPXVROVy03av9NRFQj8wMjQ1HcAmQQB/rHdk6KjyKJMiSxdDqqIW4TKdMN0gHpY39oIaWEbqT0NKmHDGj0sz+kv9RCNrWk54kxyUMzOOr9OvF50pVfZrpNPyI9W8R4n+13UY0gMzYkF/0cn54mbRnfwEb70Onv45ulZpCGSMNFIIPy9OMqbn/JkAEgvfYc9RliDTHUyQdpbEBFsbO5LA4yQdkyGOgYQAasMlLLuOQD5R0HCtLODOlj6JvYSck5o7IDHalTEiPlak379JEsIVO07JRB6jBE7XSCFKmp8ZEyQ/0ZqEIWeB6TeqSC0NGAmjcMZWR27vYz+n1QySAq+jcoi3xD1m8yyEAHGU5PCXie/+Cd9+Gzfj+sOXrs8IFDxrurkWRk5fbA3n1fbfki1Pti1QziAE3r27dt275tG7k+MCkQeH7Du+801NXSmqDP41p7IAaZKS2K0r69Bz9av7m/BRkwiMefXr17z+233sGazUhCSJIEUWRZhmFYs8lsMpsmT5503Q1Xjy8f39Lcsu3b7YXDCqafMk12slV/wefzvf/2+yaWFSWxcuKEKdOm6CR++cX/IIStVusps2aMGTfGeCmSJAX8gRWLz87Ny7Pbbed+77yrrr9Gua3u8f97bMP7H/q8voA/sHnbF1pbQ+nQGiOBknSDvvjMv5/511Nnrzj3xz+9oXj4cGViURT37K4+tP/AjNmzxo4fZ/wdhzIeffjhD95797wLLrjuxhtdrpyk5BkKBi//3rlFRcWX//iGhWeehaI58XWc7KlYE0pF5gYRDATPXvwDq9Uyeeqkvzz+UF8WHQqGdu2s7ursnj5jalHxsL4sOhHEY6dPmlz17vq3O9raOzs6p06f+uFH7775zmtvvPPqXx9/ZOy4MW1t7TwvIIRWPfXso3/6y6aNH4eCoWSLHQ88Hs8f73vwyMHDoigeOXj4/x56ZMunW7QSL1+41O/zd3d2/eXhR2+57ieP/fmvOjlLvYEQsjvsL7/9ak6Oq7G+8fPNnzY3NikNrq+/+KqpoWl4Senbm97X7yrkOo5YB+BpM04ZPWaMx+0WBfX71cKh0M3X3vjk35/Yu7s6ppyHMk5deFp+QYHH7RF4IaZGkSkJDdZkWvGDH3Z1dcJ1KKq+F/LaDpQiAAAgAElEQVRZxzZPLufGsW016bDZbf959dlAMNTZ2dXHRR87WnPv3fe/+vLrtSfq+7joRBDPGimc633d9dc+u+rfs2bNINdjjhs/7t7f/fqrL7+BCzkvv/LS0aNHnbl0SbYrO1nixr1KE/AH/vzgnxYtOWP5ecslSXJ3u19+cc3br701omyE0gZffvrSlVdces2N1yGELr585V233rnh/Q+nTJty5tlnGS8xvyB/5ZWX/um/H+7u6j5y6EjR8GKEEMZYEAQ4hlTgBYTQjFkznFlZ+lnFHSXNsAxrYnVqzGK1PvSXPx8/euy8H1wQR/59Bp7nX1n9SlaW83sX9r+ckSuY489BhZQRMpnMOllGVfu+saD7xbFjd9iQ1A9Fjxo98u577rRYzLPmnNLHRSeC+P3pmGEkScK947ILCgtGjioDq3D0mNGXX3XZ8BKVKX98UN3gYxA8z3+39TvM9GzZz8nNGTFyxK4dO3fv3CVLuebF/wQDoZ3bd8C1GA6Hfeop08IcB6fQqUJV20wm09Tp0xBGTY1NH773Pi2Jz+d769U3liw702a3S0iKekmxzHMaQ+QvQhhjBmu2MsMwC89YdMV1VxvMsL/AcdyzTz6TNguEmMEM1q5Vzcd0TwHCvVMi7T/7EnTR/SWGJEkSklCfN7/D6Vh2zplnnLmoj8tNEAmskUqShE7OIuH2BoTQtOlTp06fghDatPHjjzZ+7PF4yRM8z3MRBAKBTzd/9uorryOEjh45+sqadXW1Jyc4r73yemNDE/lz1b9WffvNt4IgQA6EXkVR5DgOLieCK1c0pcXI6/Ou+tfTRw4dRgh1dnTurd47f9GCM85aLEs4Y9YMs8W8a8dJrpckSRJP5gyGdtSY5UAg8OG7H1x/841nrzinuam5ob4BHuE4zufzLThjYW5eniRJkiiCawVFhiuO47gwB5fa0C/1ycZN69/7wO12C4LAhTkuzEmStOqJJ3mOg7MboX5ksgGhQxE8z3Nhjh5CeI5b9cRT1Tt3w59HDx9Z++Kauto6kEqZHkEjhjn4v9fj3bTho7dff1Or1lc//9KWTz8Ph8PkKVKl8HYgsxQpAhqUNDR8z3HcrdffEggEN3+8efXzqw8dPEQyEQSB53pan+d4+sVX/XPVtm+2we08ysokZRExdu/c/cyTq2Dl85knn961Yyck9vt8H63f8PLq1bUnTpysVYZlGAZRe8Rosekaqzl65I11a5saGqA+4W4s1bqSEJIo4sIYI0niqWxB7Ymm8TzPhcM9rxYOk0L37923bs3LTY2NYqQRQT202khW88qKeunfL3395dekl0E3P1n/PE9aAZ56Y92bH2/8JBjoWZnf+s22J/+xijaJ6usaXvr3y8eOHhdFCSQMK9RMFEXoBaIo8hyPdPlckqQIDfSSUOtNee6kwhBSgqegBuCnlubWNS++crymljz76cefb/xwk8ftIRVFfoK3gL6pY//1AeKPT5eQJIkSvJXX613z0su7d+356+OPkgRfffn1x5s2n3nW4tt+fku2K1sQhLt+fveePXswxjwnYIxNJlPhsILi4mEMwzzxt39u+HDjHb+8fdLkqheee/G5Vf/+88OPvPb2OjDz17y05sV/vzR12lSEUPWu6sVLF//X73+HEPrmq2/+69f/VVFZEQqHao7VPPzow7PmzFKV1mq1XnzpxS8+9+I1l10z79T5ubm5x44eveSKS10ulyzlhKqJG7dsol4TCQKPUI/Pp6uz65E//gkh9Itf35WXn08/qOIhwcjhcFRNrvroww2ff/LpxZetBA4Ph8Msy4ISS9T8A2Pc2dF5x09u7e5yf+/CCz7dtDkUCt3+/35x6sIFCKGtX33z3lvvjB03bljRsB3bvuN5/tqbrv/P8y+9+Ozz006ZPvfUecFAcOeOHbm5uVddf215ZQWIZLZYvv166+ebP7Pb7V9/8eXmjz554OH/WbLsLNj4yvPCf55/6bVXXr31jttWXHB+3YnaJ//2xMsvrp532qkjRpadqDm+8f31N9z6kwsvudhqtSKEeJ6/46c/O7jvAHxGGLEsW1Jakl9QcNrpC5XV/s7rbzbUN1RNnmSxWnZ8twMhtPmbzxFC9XX1d99+l9Vimbdg/q4du1Z877zv/fAChNCTj//rjVdf/94PLmhrbfv8k89/+/vfnnHW4meffGbn9p0MZr7a8lXN0Zqi4qKKygqEUGdH5xN/feLA/oOjRo/at2dfdnbWg488OKJsBBT9n+fXvPTsS1OmT509f1Y4HP7y8y8D/sBDjz40aswoSPDK6rVrXvpPMBAQREGSJIZhGJbBGF134/Wrn3/x5ZdW33jzTy6+9JITx0/8930PSJJYe6L2l7/+FTzLMIjeObxrx467brv1xzfdtPO77Xurd197000XrlwJhnx9bd2zT/zjzbVry0aOrDl6xGK13vfQn0aNGaOqpQhh2lz/eMP6p/72t8nTpjmysj77+OPZ8+ffdtcvc/PyoPJ/ftONB/cduPr667/csuXwwYM//fnPL7pkJUKo5tixx//y2NqXVs9bsKC4pGRv9Z6G+vqLL73k7HOWW6zqoQo+n++ZJ1dt/WrrKTNP+eyTTyVJuv8Pvz9lZo/D4fVXXm9va580ZZLZbN61Y/fc+XMf/stDCKGG+sbV/17N8bzL5dr8yWelpSW33XlLRWX5xvWbdu+s/v6FF9x2580Wi+VXd97r9/v//exLW7b2dKvWlrZVT/77Py++Mu/U2aPGjDxxvO7D9zZee8OVl1/5I4fTgRASBGHVk88//8yaG356DRfmnlv1IkJI0ub1wweP3nnbb8aMHWm12bZt3T5pysTHnvhf+rIOGh++t/Ffjz/r8XhGlJU++rc/PvPk8+vf/wghNGPW9D/99cEXn1vz4nNrrFbLz35x87jysav+9fyGDzbdcvtNs+bMQAht2/rd+vc3jR4zOi8vZ/fO3T5/YP3mt80WcyAQuO7yG+tO1F1y5crV/15z4cof3H3PL7SkTTXit9NhlH78sSf+9cRTf37o0Weees5mt9EJzlp6ZmFBATErfvHzu3fu3LVx8/oNn3x41bVXOJ2Ofz3zxOpXXlx4+sJRo0fNmjNTEnt486prr5w5ewad1XU3XIcktKd6z+mLF81fMK+hvgEh9O03395/7/3nnn/u408//sjfHpk2fdp//ep3Rw8fVZXWYrFc/eNrxo4f5/f5P1q/cd3Lr4wZM2b5iuVRX9Pd7d629buc3JzJUycjhLq6utzdbne3u6O9Q79yYL7ocDgqqybwPH/sSI9gcFnwyVvoqMm4u9t9+023ioL4xoZ3rr/5pkefeGxC1YSXnn2hoa4eIbRk2VllI0ceP3rsF7+5+4KLL8zJzb3yx9f8+Kc3IoRO1By/4rqrr7/lpvv+8PuGuob7fvXbo4ePIIQkCTGYYVmWwcyKC8578JGHR40d/bv/dw+48hFCJrNp5RWXsgzLsiaE0LiK8gVnLOzq6rJYLT/40YW/uf+3c0+b/8/H/tHc2AQvdcdPf7Zn9571Wzat37LpR5dfkpef9+x/nn9m9b9HjR6lWg+XXnWF3WHft2fvaacvXHzWkqLiIoRQQ1393bffVVRc9NyaF6676fpTZs548u///Hjjpueefnbt6pdv/+WdN//8lvsevD8nN/eB3z4giuJNt/7kxz+5njWZ7r737lffe3Xp8qWQ+a4du7d+9e3Ky1f+z5/++94H7gmHuXt+ca+72w2/XnvTtQjjfXv3Llp8+g0/veG+B++rq6178vEn4ddXX1739D+f+sWvf/n+J+vvvvfXNpvt17+75/1N609deBpC6OofX4sQYlgWITRxUtU/nn5SFEV6JgZ2OhM5ffOFZ54RRPHya659+K9/vfyaa57+x+MPPfAApBwzftyMOXM72ttcuXmLl52NEAqH1EMGJNRDWuCf+eLTzU8+9tcLL7vst3/44y/uufe3D/5h+9atG99/D6Zld/zkJ0cOHdr45RdX33D9359+6oILL/zX3/++Z/duEHj2vLldXd2Tpky+8tqr//Dnh2fOnn3fb377zptvaVnr9XX1699bP/WUab/41V0PPfpwbl7efb/+rwP7DsCvV157pcls3lu9d9HiRYsWL4Ted+J47V0/u8vj8d5z369vu/OWhx550Ov1vf7Kmz6v74cXfz87Oxv8nAihTVs+sFgsLFV9pWUlS89eEggEBEH84UXf+90Dv1p69pJ//n3V4UNHEUKCINxxy6+eferFp5//27XXX37jzdc88tgfVMUmWLf2je5u9x/+fP8jjz145y9v2bN73+03/0or8bnnn/3jm65yOOzlFeNYlv1/994JMS3/+3//gxC65vorJk2ZWDqidPmKpQUFeWcsWSihk2t4py9ZOKKstPZE7aQpExcvPSM314UwCgVDV6+8rrG+6fNtn9x2x833//F3b7/x7mOPPK4vc+qQiO8FSaJYUFiQk+PyeD02u03ke804hIhLgWGZA/sO7N2ztyeeT5REUQxz4V2RKT8MD7SFcu5559rtdmL18rwgISkvP++iSy568E8PPvH0P1qaW1Y/v9rhcJy68FSEUE5OzoUrLxRE0efzacnb2NCAJKm8onzkqJEWs2Xjhxuff+Z5/Shjn9f32CN/bWxoXH7euSUjShFCY8aOufXOn91658/GV5RrVgx1OYYgisNLShYvPfO7rdu2bP5MFMVQMGg2mx0OB8MyuPfB6M/886kTNcdXXnkZ/FlQWHDuBedX79z1/lvvYoxFURR4vqJqAmbwz+66/Y0N77IsKwoCRvjya6+KPFL46/vvPXbk6PNPP4dgno4RZnDFxAqT2YwQ+tFll8jmEpIomsg6qiQJoogQHjtunNPpRAidveIcZ5YTUu7ZVb23em+kRXhREoOBUPXuapPZPFKD0wVBkETkcDhXXn7pA3/871fefi0UCj339LMdbe3nrDgHIWSz2c4+9+yy0SMfeejPLzzzQmnZiGnTp8FoN3rsKBgqoD4tFoso9hI9K8s5aswolmUC/kDVlKr8gvzGhkYy74b5r8PpHDtuDELI5XKddfZZYOt1tHfs3LFLEATw7Qi8wLKm1S+sDoVCE6smwtthjElFFRYWLFi4kON6csbo5IUn8O/wkpKykSN5jvO43WctPwchdOTQQaINAs/n5RcuW7Hi+ltuW7XmlfIJEzT05qQpWn/ixJuvrB1eOmLajJmgIbPnzZs4efK/HnvM5/O99Oyz1bt2XfXj6yExy7I/uuyyro7ORx56GBpU4PlTZs6cMKkKEvz8rjsqJkx48IH/CWrsVLBaraPHjsrLzeV5ftz48ePGj2vv6PB5fScbUZKysrMvvvTi3z/0+xdeed7r9T7/zAuhUPjsFcsgzfjycacumPfe2x/sqd6LFDb1NT++kqcjryQkiSKDmTFjR7lyXAihs85enJPbE0mx5qVXt327Y96pcyZWVcI3E6sq9cOLioqHjRo9wtPtcbs9y89bJknSvr0HNFMjdPqS08aMHV29a28gEEAILV+xFCG0+ePPEUJ+nx8j9MAf70UISRKSe4QEURJFBuPl5y375W/ueP39tWaz+R+P/Wvf3gNXXXcFQghjPH/BvIWnn3bsSI2OAClFAr4XScIMc92Pr1552Y8uvfySD977kHC0MqXD6czKyuru6u7s6BQlKRAIIIQdDnvvZCc/C7yARGK4IIQkSRQvvuRiksDr9R47eiwUDB06cGjS5EkIoaNHjuXk5tpsveYKRID6uvr7fnPfyFGj/vev/1tXW/fnP/x5985dT//jqdLSkqXnLFMVOxAIvPHq6x+v/+jqG6694eYbyfeVEyuNVA5h9qzsrMqJEz7e8NG333x72hmL9u/ZV1wyfPTYMSzLIowY5iSnb9/2HWtmaW9g2ciyGbNnkh4iSeLY8eNsNrusOIF6xGqzjRk3lgwVoigtWHTa8NJS+JXjOFEQqYpFmGFYcDogBPsVJkyaWDVlEslZFHtaxuF02O12n8/n7nZnZWcF/UGMsV0hTC9gJIjCjy6/hAQs8Ty/e+cunud376o+7YxFAi90dnRZrTZ3t8fn881bMI/M9h75+6OkMk0mk9VqZXsvyM+eN3v6zOkfvrv+ycefamlqPlFzQla4hBDxxYHdAK4Ns8Wc5XQihDwej9/v93m9HM8VFhb2PojtpIkhSYjnOXpNhcEMnfiX99zT2dHx7ltv1R4/zvO8JCHMnLzRTRTFYcVFrpxcvYo6SekSQqi7u6u2pqZ4eIkonrSTlp27Yue2bQzD7PxuO0KY5042ujPLecGFFx49egQkh0UUieKjGbNmHDygSXOjx4z+v8f/emDfgX8//ZzX6z24/2DvCkCiKK68fCX5MxQM7dm9h2VZ2nE8a+7MTRs/UaVenuMlqfcUAeMxY0fNnN3j3uF5XoiQvollMcaTJp8c+QQxinv6+puuvvTyi57653OShFiWQQgxDNZJn5ubU1ZWum/P/uamltIRJW+/8b7Valn9/MuLz1q07dvtbW3tJaWakR28wC8950zwEQG+/vIbhmG2f7eju6tbEMTWltaujq7xFf222yPB814kYuees2L5OXJXRk/zSqI0clTZqQvmf/j++ldfed3d7T565OikSVXTpk+l0iJ88gmEmV6ORUlCoiTRNrUoiOEQl52VHQwEv9rylSAKw4cX3//gfaqbgwReeGPdG8Fg6J7770EIlY0se/TxR19+6eW/PfJYZ2en1ru999a7r6559fqbb7z+pzeIohgMBh0Oh1ZiVUgSkiSRYZipp0wrHVF6cO+B6l275y9cAFc4MgxLQiEQDDwn6mQ7jySERFGi6gJLvYY6FVit1sKiYaRrYYwFkY4ZkGS9C2OM8cnlPoyQKIikg8G4BJ/HlY9fft45r699bd2atfMXnHro4KEp06ZM1t23BTn2WrOSJI/bw7ImjPDnn3wmiALGzHnfP39C1YTX1r6mZYwBpzMsUJUUCoesFuvePftee/nV2hN15ZXlY8ePPXzoCJhd5EUQQhOqKqlvet4xOzt74eJF33373Refbqk5WnPs6NHi4uIrr72qlwcWkypBGCOMmV62J8aE84LB4DtvvPnqyy8XFBZMmjyZwRhRTQT/FQXRSNgG+OsQQsFA0N3tHl46gmZWj9sNUbAN9XVIsSwvUs2KMWYoCRFCpWUjtKJWRFGsq61b/fzqndt3lFeMH15S2jsGpwc8f7L3SZLk9XhsNlsvXZUkWHaKdPuTz2JWvtSEEZaQJCNrWkdllr4kaca9cGFu00efvrz6VbPZXDWpEmOs30EAy849c9fO6hefWzNyVNnisxa1t3V8vnnL0cPHjh4+9tPbbtB6CvKVLXR7vV6T2VRQkP/l519jBrMMc+2NV1VOrIgqQ4oQP6ebTCaEMda+cxkjjCSJZVjwrEmSOHP2zKpJE48cPlJSOnz5irPzI2uMQNkYI5JbfV19MBgi19dKSBIFkW6p/IL8BYsWHDpwaMasGbPnzY4iK0Y2m9Xlys7N67GVGIZZsHDBxxs2QdhlS3MLw+D8/AJgDYTQtq3bvvz8y6dfXJVfkI8Qam5qPnH8xLxT5yGEPG631+srKCzQ3xzLsizDYIZhEULDS4ZPm3HK+2+9u/bFNcNLSmDhF0wJBrNg8WGM55126pefbXG73SSTgM/f3NQkoako0ocxg5VRdAxlFTbWN+zesfv0Jaf3tEGP/R2hbIZFGDPUvcBYeY8lxsTMYTCDMCYGckFhwex5sydUTfxyyxdnnn3W2SuW5+bqmZ8MZqQemXsyNFssS885++3X36qYULHigvPgy2AwaDKxxcOLIZjn5Ls0NJaUliDgdLvVbDIjhJoam1pb20aOKnvlP+u2fPb5/Q/ed9rppyGEqnftaW/vMJlMtcdrR44eCX2b5MYwDGYwivCew+GYNGXyxEkTGIZxZjlPX3zGuPKThpUoikg6uQoaCAQb6usLhxVG6geBFwheasd33z368MNjx479+1NPIYTC4fC7b/YEArW2tDCY6RkBdC1HqHXyb25e3qgxY3w+H+18r961CyJY5syb987rb3ZR5oggiDVHj9IDCaZmEhzHffnZFi1O9Pv877z5zttvvHXLz2+54porEUJej/d4TQ3Lsk2NTcXDizFzUjBSe2cuO/Oj9R8R/wxCqK21rauzSxTF7OwsWHAmPx0+dATLxgncs9gDfzEYuIJBCMGSdWfHyR1GrO7F7gf2H/rbo08wDPvKW8/DSv4ra16Hn04crx01eqTqU+UV40eOGvHtN9s/+2TLDy46v662/vNPtjzwuz+cs2LZwjMW9MgY6T6YtnhEsUfgCC6+5KKnnlg1Ztzoc84/G74RBKErskPK4/EGA4G8/DytNdukI05/+t49e7d/t10Spfq6+kMHD3V1qWzx6urqCgVDhw4egqjEhvrGispyi8Wy5KzFpy1a0NnRdeJ4T5BQTq6rpHR4Q11De1s7QojjuE8/+UwUxUMHD0MNNjU0iaLY2NhIaspmt1VUVkiitHP7LlCsjvaO7779zuv1KiXBGBcVFQu8uH/vfhJi1dTYVDx8+NjxY9ta2576x5NvvPpmINhj5X3y0Sf/7/a7g8HQxg83rnnhPy8++8JzTz8L64Rut3vdmnUvPfdiS1OzakE9nyS0f+/+ttbWlqbmgD+QX5B/2ukLbQ57MBiEQLH62rra47Ucx7U0N7e1tsKDK75/viPL+fnmz+pq6xBCHrfnvbfecXd3l1dWIoS6u7oDgWBHW3tLU7PU2823Z3e1x+2WJOn4sZr33npHFPhpM05BCHk9Xo/H293V1drcIoqix+1uamjEmNm7e0+PmJLU0twSCgWbG5uCwWAoFOrs7PJ5vc2NzRzHBQOBpqamMBc+uP8gzLI//eTTyqoJVqt12bnL5y2Y397aXl9bp6MnrS0tfJhvbmxubWmBb1iWrZhQybLs5k2bW1taQchPP94siuLUaVNaW1oP7DsAA21DfcOG9zYAKRcVF5lYU1d3VzAQ/OyTzwSe97g97a1tZWVlefl5/7+9O41t47oTAP7mIocUKXIo3ockS3asy5Zlu3Zi53C6ydaNY7dNm6Jt0AMFghbYRRdYYIGiWOwai2ax2C7QLXa7CNAL2SJtnTTdOHLt+JAjV7asSNZFkRIpUaIO3udQPOfeD+MyQmzZaWrLNfl+gD5oJA7evBn+5817//cGAJBMJGk6BySw4A9cOj8gSVI8FgcAJGKJ9dy6/Gs2k6WztDy4fWP0Ri5HUxS1Z2/fJ5/9K4CABf9Ctdid3V08z1cHCQMLC8GlYI6m8/m8fCJKxWImnZbLH1xcQhBkz/6bnTyRcBgAUC6V3JOT0xMTHMflaLpQKCRicX7zwRtRkpLxOMuw8VisUi5bbLYDhw6nEomxkeulYhEAsLgwPz0+3tHdg+P4Xx871mQ0Dg8N+efmAACiKJ7r75+Zch88fLi6w0gksrK8LIpiqVg8d+b3E+Pj+w7sx7HbhJVyuRxaXTMYDE6XEwBAZ2n5Ul9ZXrn47kWmwsgXTzwWl7+eAACcwHc8sh1IyPWh63J9xqKx/rfPNOoam4xNPb09KpVqzuuTbwPZTPa9i1cAApaDK/LHWZZNpzLFQiEWjbEsx1SYSDjKMuy8PyCKYmfXTrPZODQ47PfdPCOzXr+cdHjbHMG1tTDDsD27bw4ezPsCQAICz/tm5wcHhjar8Eaddu/+PTiBLwdXrVbLo4cOdHQ9ElmLChv6/TmOo7N0pVROxBLy/N5cbr1ULKWTqUQ8We2L6+rpcNhtk2NTcja2IAiTN6ZGro2Cm1/hc+/87szGW9T9hp08efJjfOzXr5+a9y84XQ6FQpnNZJuaDCbTh9dDmJmeoWmaZTlXs7OtvW1tNfTmb347OjLqcXuvDQ2PXBuZ9c4ZDAarzUqSpEbTcPUPw5VK5RMH98/7F8ZGRhPxhG/Od/S5TylJ5bmz55VKJUkq7U6H1WoBACgUCofTASQpR68TCkLghcX5xXV63elyyvfqjRAE0TY2ppLJyxcGSqUyhqFXr1wbHxs/8NiBJ4886ff5r18d1lNUb1+v3PT+8X/+tyiKxWLR6/bMzfr8c36GYZ546gmny5mIJwYHBgVe2N3Xu1kTFUEQnudPv/V/67k8QBC7025oMmAYVi6VO7s7P3HwAIqhgwPvBebnSRVJkqQoSh1dHSiKNrc0K5XK5eCyyPMYjnvdHo/b8/znTjxz9FkMw7xuTyqZIlWk0WRytTTLDzHuyemJGxMrwZUdHY84Xa4zp/unJ6aOv/CZz3/pRRzHg4Gl8OoaSar0Bn1zS/PK8srU+BRBKBiGPfDYQQCAIAiDly6rNRqVWu10OVmW9UzPqNRqPUW5ml3ZbHZqfFKSAMuwe/fvIwhiNbjyxq9OjY6Mzky5h/9wbeTa8Lx/wWgyyQkttxq6MgQQSalUWG1WOcsQRdHWba0AQUKrqyiKISgy7/PzvHDo8UMtba0KhbJSrqAoWi6VfbM+s8Ust7i1Wu36eh6IEoIiqytrR545olAQ2SxN0zmdTicI/GJgSZJEAicYhrHZrDu7dl46P0CSKpIkbXZbk9HgnnQHg0ECJ/SUvnVbayKe6P/d6SuXBz0e7/vD169fHR4dGVUoiLbt7QCA5pZmn3fuynuDbe1t6WTKOzPjcc+Ew2GOZTu7uhcDgVQqRapUBoPB2ezCMHR1eYXAie6ennw+H1pdLZfKSpJEUHTb9nYUxbwzbpVKracou9NJqm4//CAIwtDAQEODRq1W2RwOs9VqdzoL+XwinsAwrFKpvHfxAkEovvWd75gtFovNptU1Li8uMQxHKIiVpeDAhQuHn3zim996mVAo6Gz2xsj7i4FFURR7+3r9Pv+bvz7V3NLyD9/7bpOx6dYeGAQgpXI5HotptY2UgQqvhXK5HI7jHM+bzeauXV1DV66iGKoklVabTX5swjCspbVFFJ5DN5wAAAffSURBVMW1tZA8ev/+9dFMOvPS17+yq7eHJJXZbPbS+csGA1WpMJ4Z78y0J58vrK6sHTt+FACQyWQnb0yRalKj1bianYVC4cbYBMuyHMft2de7ra1FT+krDHP+3CWFUqlWq8++8+7yylo2nVWpyN29H+7rQ1E0HIqIokRROhzHp6c8SlJJqkiO41taXW3trbetcAAAw7DJRKqjc0dndweKoYSCSKcyR489a7VZ5H9Yz+XHRycaGhq0Wo3T5WjQNHg9s6lkWkkqTWaTw2WXv4MOp0NPUelUFscwhYKIxxKhtUhrW7PZYkrGUxNjk6IodvV0VHMN7rePOencPeWWn9/lx3aHwy43lzYKhcL59TwAwGAwJBOJf3vlB8+feA4BiNzxV6kw/W+fcbkc//qDVxo0DRzHT09Op1PpRw8fXM/lg0vBaCRaLBS+/NUvq1Qqj9sDEARIksVqkR+B5UuzUqlEQpHqZepwOjbLwAUAJBPJq4NXM+lMo04LAGgyGfv29VEGKp/Px6IxtUpttVvlk+Rx31z8BLn5A3Act9psOr2OqTCRSAQAYLPbbjseKxMEwTvjwVAMJ3CzxaLT6yqVSjQc1ekbm4xGSZKCi0ulYgnFUCABlmX37OurHsXsjFeeJoMgiEardTjtSpIEAERC4RydkyRJT+mtdpv8ZP3Ln7/281d/eujxw197+RvtO7ZPjU9yLLtn316VWiUfcjqZAgjQaLVWm3U9tx6PxSQJCAK/q3c3AEAURd+sD0NRFEMtViuCImsrqwiCqtUqi83KsVw0EhUEgee57l09numZV05+/4UXPy9KoiRJCEDyhfy5/rMdXZ3/9P1/Vt0uWi34F3ieE0XJZDaaLZbqdlEU/5hCI6EoZnPYKIoCADAMk0qkOI5DAIKgSDWXHACQo3OJeILnBY2mwdXiAgDQWToSjgiCKAiC0WTUaDWpRJKpMGaL2WQxzXrmUBSRJMlsMVMGQywSpWlakiSKokgV+ep/vcrz3M7ODo7nEAAwHDvbfzZH5378k/9xupySJMktAJPFbDKbOI6NRqLJZNJoNB56/DDDsDmaBkDS6fQWmxVFUf+cT+D5JpMRACBPP07E4xiG2Z1OSRRDa6sIQBo0GrPFotzkmhFFcX5uTv6s2Wpt1OkAAOu5XGh1VRQEUZIwDDOZzSaLpXqdzHm9Ai/IswRIUuVwObVaLQAguLj4o//4YTwWe+GLLz534vlEPB5YCHT3dNsdjs0u10qlEpgPiKKgVjc06hoJgshms8VCscnYZLPb5v3zoiBKkmQym0zmD5puPMf7fX553hCKopSBslgtBIEDAIrF0oVzFxUKhd1hR1EkmUxFQlEcx77ytS/Jf11eWkZQVKlU2Ow2URDC4SjHcjzPd3bvlNtkNJ17+61+s8Xct683Ho3HYol4NG62mj997DYZDcGl5VKxzHGcxWrGCRzH8VgkLkmizW69NS5Vrefy8XiisVFrNpsQFEmnMqlkauMATLlcCS4GURRVKJVWm0WtVkXC0RydkwCgKL3Fat44Th5cXEbkoRQEqBvUcn6kfD0DAEwW09atYyhtiVO/euPZJz+1cQvP8yf/8V9OHP3s9Wsjd/24eIuPXZJMOhNaC7EM+7H38NHdWuw/s/C3+uXPXjuy//E3Xz91D/e5mf/92WtPP/rUxi2VcuV7f//dLx7/wsTY+BYU4F7xuD0vfeGl02+d3rjxFz/5xdOPPXXq9d88qFLdK0uBxb99+dt/9+2/CS4tPeiyQA/AFq2f3rqtFQBw+eIH8zMD84vFQrF9e/uOnXcfIL6HC01QBsrhdBAK4l7t8A6QTdyTncvnLzAfAAD4ZufCayHpPi+I0ba9HQHIlcuDch+6JEoDFy6xHLdj5yMP1zq9lIGiDNTkxKRvzifn5EyMjUcjEYvV2rdv74Mu3Z8rl8vFYrFYNDbnna1sSASC6sQWvY+UqTDnfv9uJp2R++MkSaJpulAoHv/MMXnLXW0s5wNc0ugvh1whP/r3Hxby+Uad7sgzT+/asxvcz8opl8tn3zmbzWS0jY1arUYUxXAoTJLkp48/t1l/+l8mURQnxiamJqcIHNdTeoIg4vF4Jp05duJYxx/n6Ty8vDOe3556A0PR7t27n37mk3dOTIJqz9a9Y5pl2WKx+MHEDQTgGC7PIvuIpD/9xYy1qnrWqgltKpVK7qu9r/XDsmyxUJSkmwnYCILiBC534z5cBEEoFovVZb/k56c79L0+RFiWLeQLCAJwHFc3NGAb8laherB1MR26tzY7cfCeB0H1DL6PtKbAgA5BdQ7GdAiCoNoBY/rDCjbJIQi6FYzptQNGeQiC4Bjpww3mAkEQtBGM6XUBZvdDUJ2AfS+170O3bXgXh6AaVrPt9Opx1XmzFKaxQ1BdqcGYDqNY1Z1Pbh1WCATVvFrre7lDFJMXvdrKwkAQBG2xmorpMGRvdNfagNUFQbWnpmL6RwEDGQRBNazuYjoEQVANq52YDhvgEARBtRPTYRYHBEFQ7cR0CIIgCMZ0CIKg2lF3Mb1+umjq50ghCKqqu5gOQRBUw2oqpsOW6Z8EVhcE1Z6aiul3BaMYBEG1rdZi+h2idh0GdFgbEFRvai2mQxAE1bMajOm3bYHWbbMU1gYE1ZUajOnglphV5yGszg8fgupKDb4To0qSJBjOquDbqCGoHtRyTIcgCKo3/w+SH1GwHANVZAAAAABJRU5ErkJggg==	a(t) = a_0 \left( 1 + \frac{\dot{a}}{a_0} t \right); b(t) = b_0 \left( 1 + \frac{\dot{a}}{a_0} t \right); \dot{b} = \frac{b_0}{a_0} \dot{a}
+437	We consider a dipole antenna of dimension _d_ much smaller than the wavelength $\lambda$ of the emitted wave. This antenna can be modeled as two charges at the two extremities varying sinusoidally with time, $q(t) = \pm q \cos(\omega t)$, and the average power emitted over $4\pi$ can be computed relatively easily to be proportional to the average of the square of the second time derivative of the dipole moment, $$ \langle P \rangle = \frac{\mu_0 (qd)^2 \omega^4}{12 \pi c}. $$   (11.1.1)  (a) If we neglect the propagation time along the dipole wires, what is the intensity of the input current to the antenna?  (b) By comparing the average of the current squared and the emitted power, argue that the real part of the antenna impedance as seen from the input circuit (that is the dissipative part) is  $$ R = \frac{2\pi}{3} \sqrt{\frac{\mu_0}{\epsilon_0}} \left(\frac{d}{\lambda}\right)^2. $$   (11.1.2)  (c) Compute the numerical value for $d = 0.3\lambda$ (which, strictly speaking, is outside the domain of applicability of the above formulae). This explains that for TV stations around 100 MHz, a dipole of the order of 1m is approximately adapted to a coaxial cable of impedance 75 $\Omega$.	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+438	The electric potential of a dipole (with moment $\mathbf{p}$) is    $$ V_{\text{dip}} = \frac{1}{4\pi\epsilon_0} \frac{\mathbf{p} \cdot \mathbf{\hat{r}}}{r^2}. \tag{4.6.1} $$  Calculate the electric field in spherical polar coordinates (with $\mathbf{p}$ aligned along the $z$-axis). An electric charge is released from rest at a point on the $xy$-plane. Show that it swings back and forth in a semi-circular arc, as though it were a pendulum supported at the origin. The expression for the gradient in spherical coordinates is    $$ \nabla f = \frac{\partial f}{\partial r} \mathbf{\hat{r}} + \frac{1}{r} \frac{\partial f}{\partial \theta} \mathbf{\hat{\theta}} + \frac{1}{r \sin \theta} \frac{\partial f}{\partial \phi} \mathbf{\hat{\theta}}. \tag{4.6.2} $$	[]	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	\mathbf{E} = \frac{p}{4 \pi \epsilon_0 r^3} (2 \cos \theta \mathbf{\hat{r}} + \sin \theta \mathbf{\hat{\theta}}); \mathbf{F} = mg (2 \cos \theta \mathbf{\hat{r}} + \sin \theta \mathbf{\hat{\theta}}); m = \frac{qp}{4\pi\epsilon_0 g r^3}
+439	Two infinite conducting planes are  arranged in a parallel configuration, with one in the $ x = 0 $ plane, and the other in the $ x = D $  plane. Both of these conducting planes are grounded. A point charge $ q $ is introduced between  the two planes, at the position $ (x, y, z) = (a, 0, 0) $. We would like to calculate the result potential  between the plates. This problem can be solved using the *method of images*.  (a) Determine the series of image charges that can reproduce the potential between these plates.  (Warning, infinite series may be in your near future.)  (b) From these image charges, derive the potential function between the plates.  (c) Determine the surface charge density as a function of radial position, $ r = \sqrt{y^2 + z^2} $, on the surface of the $ x = 0 $ plate.  (d) Compute the integral of the surface charge density, $ \sigma $, over the whole $ x = 0 $ plane. You  should reach a complication. Use Green's reciprocity theorem to resolve this issue. The  theorem says that if one problem contains a charge distribution, $ \rho_1 $, creating a potential $ V_1 $,  and another problem has $ \rho_2 $ and $ V_2$, then   $$ \int \rho_1 V_2 \, d\tau = \int \rho_2 V_1 \, d\tau $$  where the integrals are over  all of space. [Hint: for distribution 1, use the actual situation; for distribution 2, remove $ q $,  and set one of the conductors at potential $ V_0 $.]	[]	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	\text{Place a charge } q \text{ at } x = 2nD + a \text{ and } -q \text{ at } x = 2nD - a \text{ for } n \in \mathbb{Z}.; V(x, y, z) = \frac{q}{4\pi\epsilon_0} \sum_{n \in \mathbb{Z}} \left\{ \frac{1}{\sqrt{(x-(2nD+a))^2 + y^2 + z^2}} - \frac{1}{\sqrt{(x-(2nD-a))^2 + y^2 + z^2}} \right\; \sigma (r) = -\frac{q}{4\pi} \sum_{n \in \mathbb{Z}} \left\{ \frac{2nD + a}{[(2nD+a)^2 + r^2]^{3/2}} - \frac{2nD - a}{[(2nD-a)^2 + r^2]^{3/2}} \right\; Q_{1t} = -\left(1 - \frac{a}{D}\right)q_1
+440	It may have occurred to you that since parallel currents attract, the current within a single wire should contract into a tiny concentrated stream along the axis. Yet in practice the current typically distributes itself quite uniformly over the wire. How do you account for this? If the positive charges (density ρ<sub>+</sub>) are at rest, and the negative charges (density ρ<sub>-</sub>) move at speed v (and none of these depends on the distance from the axis), show that ρ<sub>-</sub> = -γ²ρ<sub>+</sub>, where$\gamma=1 / \sqrt{1-(v / c)^2}$ and c² = 1/μ<sub>0</sub>ϵ<sub>0</sub>. If the wire as a whole is neutral, where is the compensating charge located? [Notice that for typical velocities, the two charge densities are essentially unchanged by the current (since γ ≈ 1). In plasmas, however, where the positive charges are also free to move, this so-called pinch effect can be very significant.]	[]	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	\rho_{-} = -\gamma^2 \rho_{+}
+441	Calculate the terminal velocity for an ideal magnetic dipole, with dipole moment $\mu$ and mass $m$, falling down the center of an infinitely long conducting (but non-ferromagnetic) cylindrical tube of radius $R$, thickness $t \ll R$ and conductivity $\sigma$. Assume that $\mu$ aligns with the central axis at all times. [You will need the integral $\int_{-\infty}^{\infty} x^2 (1 + x^2)^{-5} \, dx = 5\pi/128.$]	[]	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	v_{\text{term}} = \frac{1024 \, m \, g \, R^4}{45 \, \mu_0^2 \, \mu^2 \, \sigma \, t}
+442	A rectangular (or elliptical) loop of wire has width $2a$ and length $\ell >> a$. At the center of this loop, and coplanar with it, there is a square loop of wire of side-length $a$. Suppose the small loop carries a current $I$. Compute the resulting magnetic flux through the large loop. What is the mutual inductance between the two loops?	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	\Phi = \frac{\mu_0 a \ln 3}{\pi} I; M = \frac{\mu_0 a \ln 3}{\pi}