{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Breakdown:\n",
    "\n",
    "potentials.py\n",
    "\n",
    "solver.py (The main function)\n",
    "\n",
    "Then, a fourth file, main_app.py, will bring everything together, handle the MediaPipe input, and plot the results."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ideas:\n",
    " - A clean, modular solver that works for **custom 1D potentials**.\n",
    "\n",
    " - Later: **GPU acceleration**, nicer **UI**, maybe interactive widgets. (FUTURE)\n",
    "\n",
    " Technical / numerical TODO:\n",
    "\n",
    " - Rigorous boundary-condition (BC) enforcement(Dirichlet for infinite well)\n",
    "\n",
    " - Orthonormality diagnostic plots (implemented, but can be refined)\n",
    "\n",
    " - Convergence analysis\n",
    "\n",
    "   - e.g. compare $N = 500$ vs $N = 2000$ to see how the discrete operator $\\mathbf{D2}$ behaves\n",
    "\n",
    " - Analytic solution benchmarking\n",
    "\n",
    "   - For the infinite square well: compare $E_n$ to\n",
    "\n",
    "     $$\n",
    "\n",
    "     E_n = \\frac{\\hbar^2 \\pi^2 n^2}{2 m L^2}\n",
    "\n",
    "     $$\n",
    " - QM Solve Benchmarking \n",
    "\n",
    " - Documentation + modular design\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## 0. Quantum picture: what am I actually solving?\n",
    "\n",
    "Before getting lost in matrices and `numpy`, I want to be clear what the **physics problem** is.\n",
    "\n",
    "In the postulate language of quantum mechanics:\n",
    "\n",
    "- A **state** of the particle is described by a wavefunction $$\\Psi(x)$$ \n",
    "  (or more abstractly, a vector $$|\\Psi\\rangle$$ in a Hilbert space).\n",
    "\n",
    "- **Observables** (like energy) are represented by **Hermitian operators**.\n",
    "  \n",
    "  For a particle in 1D with potential $$V(x)$$, the Hamiltonian operator is\n",
    "\n",
    "  $$\n",
    "  \\hat{H} = -\\frac{\\hbar^2}{2m}\\frac{d^2}{dx^2} + V(x).\n",
    "  $$\n",
    "\n",
    "- The **energy eigenstates** are solutions of\n",
    "\n",
    "  $$\n",
    "  \\hat{H}\\,\\psi_n(x) = E_n \\,\\psi_n(x),\n",
    "  $$\n",
    "\n",
    "  with boundary conditions and normalization: $\\int |\\psi_n(x)|^2 dx = 1.$\n",
    "\n",
    "Physically:\n",
    "\n",
    "- Each $\\psi_n(x)$ is a **stationary state**: if the system is prepared in $\\psi_n$, the probability density $|\\psi_n(x,t)|^2$ is independent of time (it only picks up a phase $e^{-iE_n t/\\hbar}$).\n",
    "\n",
    "- The energies $E_n$ are the possible outcomes of a precise **energy measurement**.\n",
    "\n",
    "- A general state can be expanded as\n",
    "\n",
    "  $$\n",
    "  \\Psi(x,0) = \\sum_n c_n \\psi_n(x),\n",
    "  $$\n",
    "\n",
    "  and then evolves as\n",
    "\n",
    "  $$\n",
    "  \\Psi(x,t) = \\sum_n c_n \\psi_n(x)\\,e^{-iE_n t/\\hbar}.\n",
    "  $$\n",
    "\n",
    "So my numerical solver is really a machine that takes a **chosen potential** $$V(x)$$ and returns:\n",
    "\n",
    "- The discrete spectrum $$\\{E_n\\}$$ (energy levels for that potential).\n",
    "- The corresponding eigenfunctions $$\\psi_n(x)$$ (stationary states).\n",
    "\n",
    "Once I have those, I can in principle build **any** time-dependent solution by choosing coefficients $$c_n$$.\n",
    "\n",
    "\n",
    "---\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# %% [markdown]\n",
    "### 2.2.1 Infinite wall as a limit of a finite barrier\n",
    "\n",
    "Another way to see $$\\Psi(0) = \\Psi(a) = 0$$:\n",
    "\n",
    "- Start with a **finite** but huge barrier outside $$[0,a]$$:\n",
    "  \n",
    "  - $$V(x) = 0$$ for $$0 < x < a$$,\n",
    "  - $$V(x) = V_0$$ (large but finite) for $$x \\le 0$$ and $$x \\ge a$$.\n",
    "\n",
    "- For a bound state with energy $$E < V_0$$, the solution in the barrier region decays exponentially\n",
    "  (evanescent tail). As $$V_0 \\to \\infty$$, the decay length goes to zero, and the wavefunction is\n",
    "  squeezed to exactly zero at the wall.\n",
    "\n",
    "So the infinite square well is an **idealized limit** where those evanescent tails are completely killed.\n",
    "In that limit, the physically acceptable states are exactly those that vanish at the boundaries.\n",
    "\n",
    "### 2.2.2 Probability current and “no leakage”\n",
    "\n",
    "The boundary conditions are also tied to **probability conservation**.\n",
    "\n",
    "The probability current in 1D is\n",
    "\n",
    "$$\n",
    "j(x) = \\frac{\\hbar}{m}\\,\\text{Im}\\big(\\Psi^*(x)\\,\\partial_x \\Psi(x)\\big).\n",
    "$$\n",
    "\n",
    "For a particle trapped in the well, there should be **no net probability flow out** of the region.\n",
    "Taking $$\\Psi(0) = \\Psi(a) = 0$$ ensures that $$j(0) = j(a) = 0$$, so there is no leakage of probability\n",
    "through the walls. This is part of making $$\\hat{H}$$ self-adjoint with these boundary conditions.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# %% [markdown]\n",
    "### 2.3.1 Physical interpretation: standing waves, nodes, and quantization\n",
    "\n",
    "The infinite well is a quantum version of a **string fixed at both ends**:\n",
    "\n",
    "- The boundary conditions $$\\Psi(0) = \\Psi(a) = 0$$ only allow certain “standing wave” shapes.\n",
    "- Those shapes are exactly\n",
    "\n",
    "  $$\n",
    "  \\Psi_n(x) = \\sqrt{\\frac{2}{a}} \\sin\\left(\\frac{n\\pi x}{a}\\right),\n",
    "  $$\n",
    "\n",
    "  with integer $$n = 1,2,3,\\dots$$\n",
    "\n",
    "Each $$n$$ has:\n",
    "\n",
    "- $$n-1$$ internal **nodes** (points where $$\\Psi_n(x) = 0$$ inside the well).\n",
    "- Increasing **curvature** of the wavefunction, which corresponds to higher kinetic energy.\n",
    "\n",
    "This is why the energies scale like\n",
    "\n",
    "$$\n",
    "E_n \\propto n^2.\n",
    "$$\n",
    "\n",
    "The key physics point:\n",
    "\n",
    "- The **discreteness** of the spectrum (energy quantization) is not put in by hand.\n",
    "- It **emerges** from:\n",
    "  - the wave nature of the particle, and\n",
    "  - the boundary conditions (particle confined in a finite region).\n",
    "\n",
    "My numerical solver is reproducing that spectrum purely from the operator\n",
    "\n",
    "$$\n",
    "\\hat{H} = -\\frac{\\hbar^2}{2m}\\frac{d^2}{dx^2} + V(x)\n",
    "$$\n",
    "\n",
    "and the boundary conditions encoded in the matrix.\n",
    "---\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## 6. Using the numerical eigenstates as actual quantum states\n",
    "\n",
    "Once I have the eigenvalues $$E_n$$ and eigenvectors $$\\psi_n(x_i)$$ on the grid, I can treat them as\n",
    "**full quantum states** and compute observables.\n",
    "\n",
    "On the grid, an integral becomes a sum:\n",
    "\n",
    "$$\n",
    "\\int f(x)\\,dx \\approx \\sum_i f(x_i)\\,\\Delta x.\n",
    "$$\n",
    "\n",
    "So for a normalized eigenstate $$\\psi_n(x)$$:\n",
    "\n",
    "- Position expectation value:\n",
    "\n",
    "  $$\n",
    "  \\langle x \\rangle_n \\approx \\sum_i x_i\\,|\\psi_n(x_i)|^2\\,\\Delta x.\n",
    "  $$\n",
    "\n",
    "- Position variance:\n",
    "\n",
    "  $$\n",
    "  \\Delta x_n^2 = \\langle x^2 \\rangle_n - \\langle x \\rangle_n^2.\n",
    "  $$\n",
    "\n",
    "For momentum, in the position representation\n",
    "\n",
    "$$\n",
    "\\hat{p} = -i\\hbar \\frac{d}{dx}.\n",
    "$$\n",
    "\n",
    "On the grid, I can approximate the derivative with finite differences, e.g.\n",
    "\n",
    "$$\n",
    "\\left.\\frac{d\\psi}{dx}\\right|_{x_i} \\approx \\frac{\\psi(x_{i+1}) - \\psi(x_{i-1})}{2\\Delta x},\n",
    "$$\n",
    "\n",
    "and then build\n",
    "\n",
    "$$\n",
    "\\langle p \\rangle_n \\approx \\sum_i \\psi_n^*(x_i)\\,\\left(-i\\hbar \\frac{d\\psi_n}{dx}\\bigg|_{x_i}\\right)\\Delta x.\n",
    "$$\n",
    "\n",
    "Similarly for $$\\langle p^2 \\rangle_n$$, which lets me compute $$\\Delta p_n$$ and check the\n",
    "uncertainty relation numerically:\n",
    "\n",
    "$$\n",
    "\\Delta x_n\\,\\Delta p_n \\ge \\frac{\\hbar}{2}.\n",
    "$$\n",
    "\n",
    "So the solver is not just a “pretty plotter” of eigenfunctions; it is a tool to compute\n",
    "**quantum expectation values** for arbitrary observables once they are discretized on the grid.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### 3.5 Operator viewpoint: matrix = Hamiltonian in a finite basis\n",
    "\n",
    "Conceptually, what I’ve done is:\n",
    "\n",
    "- Start from the abstract operator equation\n",
    "\n",
    "  $$\n",
    "  \\hat{H}|\\psi_n\\rangle = E_n |\\psi_n\\rangle,\n",
    "  $$\n",
    "\n",
    "- Choose the **position basis** sampled on a grid\n",
    "  $$\\{|x_1\\rangle, |x_2\\rangle, \\dots, |x_{N-1}\\rangle\\},$$\n",
    "- Represent $$\\hat{H}$$ as an $$N\\times N$$ **matrix** in that basis using finite differences for the kinetic term\n",
    "  and a diagonal matrix for $V(x)$.\n",
    "\n",
    "Because $\\hat{H}$ is Hermitian (and my discrete approximation respects that symmetry), the matrix is:\n",
    "\n",
    "- Real symmetric,\n",
    "- Has **real** eigenvalues,\n",
    "- And its eigenvectors form an **orthonormal basis** of the grid space.\n",
    "\n",
    "This is exactly what I see in the overlap matrix: numerically, it is very close to the identity.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " ## 1. First-principles thinking about $V(x)$\n",
    "\n",
    "\n",
    "\n",
    " I want to keep an intuitive, almost classical picture of what the potential means.\n",
    "\n",
    "\n",
    "\n",
    " - $V(x)$ describes the **landscape of potential energy** created by the environment.\n",
    "\n",
    "   You can think of it as a **height map** or a **hill profile**.\n",
    "\n",
    "\n",
    "\n",
    " - If $V(x) = 2$ (some constant), then placing a particle there means:\n",
    "\n",
    "   - The particle \"sits\" at potential energy 2 (in whatever units I'm using).\n",
    "\n",
    "   - To move around with total energy $E$, its kinetic energy is $K = E - V(x)$.\n",
    "\n",
    "   - So if $V$ is larger, the kinetic energy available is smaller for the same $E$.\n",
    "\n",
    "\n",
    "\n",
    " - Intuition:\n",
    "\n",
    "   - $V(x) = 0$ → flat ground\n",
    "\n",
    "   - $V(x) = 2$ → you are walking on a slope of \"height 2\"\n",
    "\n",
    "   - It's easier to move where $V(x)$ is low than where $V(x)$ is high.\n",
    "\n",
    "\n",
    "\n",
    " - If $V(x) = \\infty$ in some region, then:\n",
    "\n",
    "   - A particle would need **infinite total energy** to enter that region.\n",
    "\n",
    "   - In quantum mechanics, this is enforced by making the wavefunction **exactly zero**\n",
    "\n",
    "     there: the particle simply **cannot exist** in that region.\n",
    "\n",
    "\n",
    "\n",
    " This is exactly how the **infinite square well** is defined."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " ## 2. The infinite square well setup\n",
    "\n",
    "\n",
    "\n",
    " I imagine an electron (mass $m$) trapped in an infinite square well:\n",
    "\n",
    "\n",
    "\n",
    " - Inside the well, for $0 < x < a$:\n",
    "\n",
    "   $$\n",
    "\n",
    "   V(x) = 0\n",
    "\n",
    "   $$\n",
    "\n",
    " - Outside the well:\n",
    "\n",
    "   $$\n",
    "\n",
    "   V(x) = \\infty\n",
    "\n",
    "   $$\n",
    "\n",
    "\n",
    "\n",
    " So the particle is strictly confined to the region $0 < x < a$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " ### 2.1 Time-Independent Schrödinger Equation (TISE)\n",
    "\n",
    "\n",
    "\n",
    " The time-independent Schrödinger equation is\n",
    "\n",
    "\n",
    "\n",
    " $$\n",
    "\n",
    " H \\Psi(x) = E \\Psi(x)\n",
    "\n",
    " $$\n",
    "\n",
    "\n",
    "\n",
    " with the Hamiltonian\n",
    "\n",
    "\n",
    "\n",
    " $$\n",
    "\n",
    " H = -\\frac{\\hbar^2}{2m} \\frac{d^2}{dx^2} + V(x)\n",
    "\n",
    " $$\n",
    "\n",
    "\n",
    "\n",
    " For the infinite well region (where $V(x) = 0$), the TISE reduces to:\n",
    "\n",
    "\n",
    "\n",
    " $$\n",
    "\n",
    " -\\frac{\\hbar^2}{2m} \\frac{d^2 \\Psi}{dx^2} = E \\Psi\n",
    "\n",
    " $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " ### 2.2 Boundary conditions and physical constraints\n",
    "\n",
    "\n",
    "\n",
    " We enforce some conditions on the wavefunction based on physical requirements:\n",
    "\n",
    "\n",
    "\n",
    " - Dirichlet boundary conditions:\n",
    "\n",
    "   $$\n",
    "\n",
    "   \\Psi(0) = \\Psi(a) = 0\n",
    "\n",
    "   $$\n",
    "\n",
    "\n",
    "\n",
    "   Reason (continuity argument):\n",
    "\n",
    "   - Schrödinger's equation requires $\\Psi(x)$ to be **continuous**.\n",
    "\n",
    "   - If $\\Psi(x)$ had a jump, its second derivative would involve something like a delta function,\n",
    "\n",
    "     which would blow up the kinetic energy term.\n",
    "\n",
    "   - Outside the well, where $V(x) = \\infty$, the wavefunction must vanish:\n",
    "\n",
    "     $$\n",
    "\n",
    "     \\Psi(0^-) = 0, \\quad \\Psi(a^+) = 0\n",
    "\n",
    "     $$\n",
    "\n",
    "   - Continuity then implies\n",
    "\n",
    "     $$\n",
    "\n",
    "     \\Psi(0^+) = 0, \\quad \\Psi(a^-) = 0\n",
    "\n",
    "     $$\n",
    "\n",
    "     so we simply write $\\Psi(0) = \\Psi(a)=0$.\n",
    "\n",
    "\n",
    "\n",
    " - Normalization:\n",
    "\n",
    "   $$\n",
    "\n",
    "   \\int_{-\\infty}^{\\infty} |\\Psi(x)|^2 \\, dx = 1\n",
    "\n",
    "   $$\n",
    "\n",
    "   In practice, for the infinite well, this is\n",
    "\n",
    "   $$\n",
    "\n",
    "   \\int_0^a |\\Psi(x)|^2 \\, dx = 1.\n",
    "\n",
    "   $$\n",
    "\n",
    "\n",
    "\n",
    " - Probabilistic interpretation:\n",
    "\n",
    "   - $|\\Psi(x)|^2 \\, dx$ is the probability of finding the particle between $x$ and $x + dx$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " ### 2.3 Known analytic solutions (for checking the numerics later)\n",
    "\n",
    "\n",
    "\n",
    " For the infinite square well, the analytic solutions are:\n",
    "\n",
    "\n",
    "\n",
    " - Wavefunctions:\n",
    "\n",
    "   $$\n",
    "\n",
    "   \\Psi_n(x) = \\sqrt{\\frac{2}{a}} \\sin\\left(\\frac{n \\pi x}{a}\\right), \\quad n = 1, 2, 3, \\dots\n",
    "\n",
    "   $$\n",
    "\n",
    "\n",
    "\n",
    " - Energy levels:\n",
    "\n",
    "   $$\n",
    "\n",
    "   E_n = \\frac{\\hbar^2 \\pi^2 n^2}{2 m a^2}\n",
    "\n",
    "   $$\n",
    "\n",
    "\n",
    "\n",
    " Later in this notebook, I compare the **numerical eigenvalues** to these $E_n$ as a benchmark."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " ## 3. Discretizing the TISE\n",
    "\n",
    "\n",
    "\n",
    " To turn the differential equation into something a computer can solve, I:\n",
    "\n",
    "\n",
    "\n",
    " - Break the continuous space into small chunks.\n",
    "\n",
    " - Use a finite-difference approximation for derivatives.\n",
    "\n",
    " - Build a matrix that mimics the second derivative.\n",
    "\n",
    " - Solve the resulting **matrix eigenvalue problem**.\n",
    "\n",
    "\n",
    "\n",
    " Let me formalize that."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " ### 3.1 Discretizing the derivative\n",
    "\n",
    "\n",
    "\n",
    " We start from the usual definition of the derivative:\n",
    "\n",
    "\n",
    "\n",
    " $$\n",
    "\n",
    " f'(x_i) = \\lim_{\\Delta x \\to 0} \\frac{f(x_i + \\Delta x) - f(x_i)}{\\Delta x}\n",
    "\n",
    " $$\n",
    "\n",
    "\n",
    "\n",
    " In the code, I *do not* send $\\Delta x$ to 0. Instead:\n",
    "\n",
    "\n",
    "\n",
    " - I choose a **fixed** grid spacing $\\Delta x$.\n",
    "\n",
    " - I approximate the derivative using finite differences.\n",
    "\n",
    "\n",
    "\n",
    " For the **first derivative**, a forward-difference formula is\n",
    "\n",
    "\n",
    "\n",
    " $$\n",
    "\n",
    " f'(x_i) \\approx \\frac{f(x_{i+1}) - f(x_i)}{\\Delta x}.\n",
    "\n",
    " $$\n",
    "\n",
    "\n",
    "\n",
    " This is called the **forward difference** operator. There are also backward and central differences,\n",
    "\n",
    " but for the second derivative we usually like the central difference."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " ### 3.2 Building the second derivative $f''(x_i)$\n",
    "\n",
    "\n",
    "\n",
    " Because $\\Delta x$ is constant, and derivatives are linear, we can say:\n",
    "\n",
    "\n",
    "\n",
    " $$\n",
    "\n",
    " f''(x_i) \\approx \\frac{f'(x_{i+1}) - f'(x_i)}{\\Delta x}.\n",
    "\n",
    " $$\n",
    "\n",
    "\n",
    "\n",
    " Now plug in the finite-difference expressions for $f'$:\n",
    "\n",
    "\n",
    "\n",
    " $$\n",
    "\n",
    " f'(x_{i+1}) \\approx \\frac{f(x_{i+2}) - f(x_{i+1})}{\\Delta x}, \\quad\n",
    "\n",
    " f'(x_i) \\approx \\frac{f(x_{i+1}) - f(x_i)}{\\Delta x}\n",
    "\n",
    " $$\n",
    "\n",
    "\n",
    "\n",
    " so\n",
    "\n",
    "\n",
    "\n",
    " $$\n",
    "\n",
    " f''(x_i) \\approx\n",
    "\n",
    " \\frac{\n",
    "\n",
    " \\frac{f(x_{i+1}) - f(x_i)}{\\Delta x}\n",
    "\n",
    " -\n",
    "\n",
    " \\frac{f(x_i) - f(x_{i-1})}{\\Delta x}\n",
    "\n",
    " }\n",
    "\n",
    " {\\Delta x}\n",
    "\n",
    " =\n",
    "\n",
    " \\frac{f(x_{i+1}) - 2 f(x_i) + f(x_{i-1})}{\\Delta x^2}.\n",
    "\n",
    " $$\n",
    "\n",
    "\n",
    "\n",
    " This is the standard **central difference** formula for the second derivative.\n",
    "\n",
    "\n",
    "\n",
    " It is exactly what I will use to approximate the operator $\\frac{d^2}{dx^2}$ on a grid."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " ### 3.3 Writing the second derivative as a matrix\n",
    "\n",
    "\n",
    "\n",
    " Let the grid points be $x_1, x_2, x_3, x_4, \\dots$ and the function values be\n",
    "\n",
    "\n",
    "\n",
    " $$\n",
    "\n",
    " f(x_i) \\rightarrow\n",
    "\n",
    " f_i =\n",
    "\n",
    " \\begin{bmatrix}\n",
    "\n",
    " f_1 \\\\\n",
    "\n",
    " f_2 \\\\\n",
    "\n",
    " f_3 \\\\\n",
    "\n",
    " f_4 \\\\\n",
    "\n",
    " \\vdots\n",
    "\n",
    " \\end{bmatrix}.\n",
    "\n",
    " $$\n",
    "\n",
    "\n",
    "\n",
    " Then the central-difference formula for the second derivative gives:\n",
    "\n",
    "\n",
    "\n",
    " $$\n",
    "\n",
    " \\begin{cases}\n",
    "\n",
    " f''_1 = \\dfrac{f_2 - 2 f_1 + f_0}{(\\Delta x)^2}, \\\\\n",
    "\n",
    " f''_2 = \\dfrac{f_3 - 2 f_2 + f_1}{(\\Delta x)^2}, \\\\\n",
    "\n",
    " f''_3 = \\dfrac{f_4 - 2 f_3 + f_2}{(\\Delta x)^2}, \\\\\n",
    "\n",
    " \\vdots\n",
    "\n",
    " \\end{cases}\n",
    "\n",
    " $$\n",
    "\n",
    "\n",
    "\n",
    " The pattern is a stencil $[1, -2, 1]$ sweeping across the vector.\n",
    "\n",
    "\n",
    "\n",
    " In matrix form:\n",
    "\n",
    "\n",
    "\n",
    " $$\n",
    "\n",
    " \\frac{d^2}{dx^2} f(x_i) \\approx f''(x_i)\n",
    "\n",
    " = \\frac{1}{(\\Delta x)^2}\n",
    "\n",
    " \\begin{bmatrix}\n",
    "\n",
    " -2 & 1 & 0 & 0 & \\cdots \\\\\n",
    "\n",
    " 1 & -2 & 1 & 0 & \\cdots \\\\\n",
    "\n",
    " 0 & 1 & -2 & 1 & \\cdots \\\\\n",
    "\n",
    " 0 & 0 & 1 & -2 & \\cdots \\\\\n",
    "\n",
    " \\vdots & \\vdots & \\vdots & \\vdots & \\ddots\n",
    "\n",
    " \\end{bmatrix}\n",
    "\n",
    " \\begin{bmatrix}\n",
    "\n",
    " f_1 \\\\\n",
    "\n",
    " f_2 \\\\\n",
    "\n",
    " f_3 \\\\\n",
    "\n",
    " f_4 \\\\\n",
    "\n",
    " \\vdots\n",
    "\n",
    " \\end{bmatrix}.\n",
    "\n",
    " $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " ### 3.4 Schrödinger equation in matrix form\n",
    "\n",
    "\n",
    "\n",
    " Starting from\n",
    "\n",
    "\n",
    "\n",
    " $$\n",
    "\n",
    " -\\frac{\\hbar^2}{2m} \\frac{d^2}{dx^2} \\Psi(x) + V(x) \\Psi(x) = E \\Psi(x),\n",
    "\n",
    " $$\n",
    "\n",
    "\n",
    "\n",
    " when we discretize, the kinetic term becomes:\n",
    "\n",
    "\n",
    "\n",
    " $$\n",
    "\n",
    " -\\frac{\\hbar^2}{2m} \\frac{d^2}{dx^2}\n",
    "\n",
    " \\;\\;\\longrightarrow\\;\\;\n",
    "\n",
    " -\\frac{\\hbar^2}{2m}\n",
    "\n",
    " \\frac{1}{(\\Delta x)^2}\n",
    "\n",
    " \\begin{bmatrix}\n",
    "\n",
    " -2 & 1 & 0 & 0 & \\cdots \\\\\n",
    "\n",
    " 1 & -2 & 1 & 0 & \\cdots \\\\\n",
    "\n",
    " 0 & 1 & -2 & 1 & \\cdots \\\\\n",
    "\n",
    " 0 & 0 & 1 & -2 & \\cdots \\\\\n",
    "\n",
    " \\vdots & \\vdots & \\vdots & \\vdots & \\ddots\n",
    "\n",
    " \\end{bmatrix}.\n",
    "\n",
    " $$\n",
    "\n",
    "\n",
    "\n",
    " So the matrix version of the TISE is\n",
    "\n",
    "\n",
    "\n",
    " $$\n",
    "\n",
    " H \\Psi = E \\Psi\n",
    "\n",
    " $$\n",
    "\n",
    "\n",
    "\n",
    " with\n",
    "\n",
    "\n",
    "\n",
    " $$\n",
    "\n",
    " H =\n",
    "\n",
    " -\\frac{\\hbar^2}{2m}\n",
    "\n",
    " \\frac{1}{(\\Delta x)^2}\n",
    "\n",
    " \\begin{bmatrix}\n",
    "\n",
    " -2 & 1 & 0 & 0 & \\cdots \\\\\n",
    "\n",
    " 1 & -2 & 1 & 0 & \\cdots \\\\\n",
    "\n",
    " 0 & 1 & -2 & 1 & \\cdots \\\\\n",
    "\n",
    " 0 & 0 & 1 & -2 & \\cdots \\\\\n",
    "\n",
    " \\vdots & \\vdots & \\vdots & \\vdots & \\ddots\n",
    "\n",
    " \\end{bmatrix}\n",
    "\n",
    " + \\text{diag}\\big(V(x_1), V(x_2), \\dots \\big).\n",
    "\n",
    " $$\n",
    "\n",
    "\n",
    "\n",
    " Note:\n",
    "\n",
    "\n",
    "\n",
    " - This matrix acts on the **internal grid points** from $\\Psi_1$ to $\\Psi_{N-1}$.\n",
    "\n",
    " - The boundary values $\\Psi_0$ and $\\Psi_N$ are fixed by the **Dirichlet BC**:\n",
    "\n",
    "   $$\n",
    "\n",
    "   \\Psi_0 = \\Psi_N = 0.\n",
    "\n",
    "   $$\n",
    "\n",
    " - So the computer only solves for the interior and the BC is enforced by construction."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " With this theory in place, I now build the actual code."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "---\n",
    "Quantum Solver Project Documentation: Finite Difference Method for the 1D TISE\n",
    "\n",
    "Project Overview\n",
    "\n",
    "This solver utilizes the Finite Difference Method (FDM) to numerically determine the energy eigenvalues ($E_n$) and corresponding eigenstates ($\\psi_n$) for a particle of mass $m$ under an arbitrary 1D potential $V(x)$. The central numerical task is the transformation of the continuous Time-Independent Schrödinger Equation (TISE) into a matrix eigenvalue problem on a discrete grid.\n",
    "\n",
    "$$\\left(-\\frac{\\hbar^2}{2m}\\frac{d^2}{dx^2} + V(x)\\right)\\psi(x) = E\\psi(x)$$\n",
    "\n",
    "The current primary benchmarking potential is the Symmetric Finite Square Well (McIntyre Chapter 5, Context of Problem 5.20).\n",
    "\n",
    "1. Mapping the Operator to a Matrix $\\mathbf{H}$\n",
    "\n",
    "1.1 The Discrete Hamiltonian\n",
    "\n",
    "In the position basis, sampled on the discrete grid $\\{x_i\\}$, the continuous Hamiltonian operator $\\hat{H}$ is represented by a large, sparse, real symmetric matrix $\\mathbf{H}$.\n",
    "\n",
    "$$\\hat{H} \\longrightarrow \\mathbf{H} = \\mathbf{T} + \\mathbf{V}$$\n",
    "\n",
    "The TISE is thus reduced to the standard linear algebra problem:\n",
    "\n",
    "$$\\mathbf{H}\\vec{\\psi} = E\\vec{\\psi}$$\n",
    "\n",
    "Where:\n",
    "\n",
    "$\\mathbf{H}$ is the $N \\times N$ discrete Hamiltonian matrix.\n",
    "\n",
    "$\\vec{\\psi}$ is the $N$-dimensional eigenvector containing the wavefunction values $\\psi(x_i)$ at the internal grid points.\n",
    "\n",
    "$E$ is the eigenvalue (the quantized energy).\n",
    "\n",
    "1.2 The Kinetic Term Matrix $\\mathbf{T}$\n",
    "\n",
    "The second derivative kinetic term ($\\frac{d^2}{dx^2}$) is approximated using the central difference formula, which introduces an error of $\\mathcal{O}(\\Delta x^2)$.\n",
    "\n",
    "$$\\frac{d^2\\psi}{dx^2}\\bigg|_{x_i} \\approx \\frac{\\psi(x_{i+1}) - 2\\psi(x_i) + \\psi(x_{i-1})}{(\\Delta x)^2}$$\n",
    "\n",
    "This leads to the tri-diagonal kinetic energy matrix $\\mathbf{T}$:\n",
    "\n",
    "$$\\mathbf{T} = -\\frac{\\hbar^2}{2m} \\frac{1}{(\\Delta x)^2} \\begin{pmatrix}\n",
    "-2 & 1 & 0 & \\cdots \\\\\n",
    "1 & -2 & 1 & \\cdots \\\\\n",
    "0 & 1 & -2 & \\cdots \\\\\n",
    "\\vdots & \\vdots & \\vdots & \\ddots\n",
    "\\end{pmatrix}$$\n",
    "\n",
    "The symmetry of the resulting matrix $\\mathbf{H}$ ensures all eigenvalues $E_n$ are real (a requirement for any physical observable in QM) and the corresponding eigenvectors $\\vec{\\psi}_n$ are orthogonal.\n",
    "\n",
    "1.3 Boundary Conditions (BCs) and Spectral Range\n",
    "\n",
    "For bound state problems (where $E < V_0$ and $\\psi \\to 0$ as $x \\to \\pm \\infty$), the Dirichlet boundary condition ($\\psi(\\text{boundary}) = 0$) is applied at the edges of the finite computational box $[-L_{max}, L_{max}]$. This ensures that the numerical solutions model the exponential decay of the physical bound states.\n",
    "\n",
    "Note on the Spectrum: The FDM diagonalization yields $N$ eigenvalues. These include the discrete bound states ($E_n < V_0$) and a numerical approximation of the continuum states ($E > V_0$). The high-energy continuum states are physically irrelevant and are artifacts of the finite box/grid, often having energies proportional to $\\frac{1}{\\Delta x^2}$.\n",
    "\n",
    "2. Benchmark Problem: Finite Square Well Potential\n",
    "\n",
    "The finite square well is defined by:\n",
    "\n",
    "\n",
    "$$V(x) = \\begin{cases} 0 & \\text{for } |x| \\le L \\\\ V_0 & \\text{for } |x| > L \\end{cases}$$\n",
    "\n",
    "The analytical solution requires solving a complex transcendental equation. The FDM solver bypasses this difficulty by solving the coupled kinetic and potential energy equations across the entire domain. Bound states are identified simply as those eigenvalues where $E_n < V_0$.\n",
    "\n",
    "Key Physics Checks (McIntyre 5.20 Context)\n",
    "\n",
    "Parity Conservation: Since $V(x)=V(-x)$, the Hamiltonian commutes with the parity operator ($\\hat{P}\\hat{H} = \\hat{H}\\hat{P}$). Thus, the eigenstates must be simultaneous eigenstates of $\\hat{P}$, meaning they are either even or odd.\n",
    "\n",
    "Ground state ($n=1$): Must be even parity.\n",
    "\n",
    "First excited state ($n=2$): Must be odd parity.\n",
    "\n",
    "Wavefunction Penetration: The wavefunction must smoothly transition into the classically forbidden region ($|x| > L$) and decay exponentially (evanescence). The decay constant $\\kappa_n$ depends on the barrier strength:\n",
    "\n",
    "\n",
    "$$\\kappa_n = \\sqrt{2m(V_0 - E_n)/\\hbar^2}$$\n",
    "\n",
    "\n",
    "States closer to the barrier height ($E_n \\to V_0$) penetrate much further.\n",
    "\n",
    "Approaching the Infinite Limit: By setting a very large $V_0$ (e.g., $V_0=1000$), the numerical results for the lower states should converge to the analytical Infinite Square Well result: $E_n^{ISW} = \\frac{\\hbar^2 \\pi^2 n^2}{2 m (2L)^2}$.\n",
    "\n",
    "3. Numerical Diagnostics and Convergence\n",
    "\n",
    "3.1 Orthonormality Check\n",
    "\n",
    "The discrete eigenstates $\\vec{\\psi}_n$ must be orthonormal. This is verified by calculating the overlap matrix $\\mathbf{O}$ using the discrete representation of the inner product:\n",
    "\n",
    "$$\\mathbf{O}_{mn} = \\langle \\psi_m | \\psi_n \\rangle = \\sum_{i=1}^N \\psi_m(x_i)\\psi_n(x_i)\\Delta x$$\n",
    "\n",
    "For perfect orthonormality, $\\mathbf{O} = \\mathbf{I}$. The off-diagonal elements of $\\mathbf{O}$ provide a measure of the numerical error introduced by the diagonalization process and the finite grid approximation.\n",
    "\n",
    "3.2 Convergence Analysis (Discretization Error)\n",
    "\n",
    "The discretization error in the eigenvalue $E_n$ is expected to scale quadratically: $E_n^{\\text{numerical}} - E_n^{\\text{exact}} \\sim \\mathcal{O}(\\Delta x^2)$.\n",
    "\n",
    "TODO: Execute a convergence run by calculating $E_n$ for several grid sizes $N_k$. Plot $\\log(|E_n(\\Delta x_k) - E_n^{\\text{reference}}|)$ versus $\\log(\\Delta x_k)$. The slope of this plot should be approximately $2$, confirming the expected convergence rate of the central difference scheme.\n",
    "(Note: $E_n^{\\text{reference}}$ can be the analytical ISW value for very deep wells, or a highly resolved FDM solution for finite wells).\n",
    "\n",
    "3.3 Quantum Expectation Values and Uncertainty\n",
    "\n",
    "The discrete wavefunctions allow for the calculation of observables using the discretized integration rule.\n",
    "\n",
    "Position Expectation:\n",
    "\n",
    "\n",
    "$$\\langle \\hat{x} \\rangle_n = \\sum_i x_i |\\psi_n(x_i)|^2 \\Delta x$$\n",
    "\n",
    "Momentum Expectation and Uncertainty: Instead of discretizing the momentum operator $\\hat{p} = -i\\hbar \\frac{d}{dx}$ (which is numerically unstable), $\\langle \\hat{p}^2 \\rangle_n$ can be derived directly from the TISE by leveraging the fact that $\\vec{\\psi}_n$ is an eigenstate of $\\mathbf{H}$:\n",
    "\n",
    "$$\\langle \\hat{H} \\rangle_n = E_n = \\langle \\hat{T} \\rangle_n + \\langle \\hat{V} \\rangle_n$$\n",
    "\n",
    "\n",
    "Since $\\langle \\hat{T} \\rangle_n = \\langle \\hat{p}^2 \\rangle_n / (2m)$, we have:\n",
    "\n",
    "\n",
    "$$\\langle \\hat{p}^2 \\rangle_n = 2m \\left(E_n - \\sum_i V(x_i) |\\psi_n(x_i)|^2 \\Delta x \\right)$$\n",
    "\n",
    "The momentum uncertainty $\\Delta p_n = \\sqrt{\\langle \\hat{p}^2 \\rangle_n - \\langle \\hat{p} \\rangle_n^2}$ can then be computed and verified against the Heisenberg Uncertainty Principle: $\\Delta x_n\\,\\Delta p_n \\ge \\hbar/2$.\n",
    "\n",
    "File Breakdown\n",
    "\n",
    "File\n",
    "\n",
    "Purpose\n",
    "\n",
    "Physics Relevance\n",
    "\n",
    "constants.py\n",
    "\n",
    "Physical constants and simulation parameters ($\\hbar^2/2m$, $L_{max}$, $N$, $\\Delta x$).\n",
    "\n",
    "Defines the fundamental scaling of the TISE.\n",
    "\n",
    "potentials.py\n",
    "\n",
    "Function definitions for $V(x)$ (e.g., Finite Well, Harmonic Oscillator).\n",
    "\n",
    "Encodes the physical configuration and boundary conditions of the problem space.\n",
    "\n",
    "functions.py\n",
    "\n",
    "Core computational functions: building $\\mathbf{T}$, solve_schrodinger (builds $\\mathbf{H}$ and diagonalizes it).\n",
    "\n",
    "The numerical engine; converts continuous differential operator to discrete linear algebra.\n",
    "\n",
    "app.py\n",
    "\n",
    "Streamlit app for user interaction, plotting, and handling diagnostics.\n",
    "\n",
    "Visualization of eigenstates and verification of key quantum principles.\n",
    "\n",
    "---\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from functions import show_QR\n",
    "url = \"https://huggingface.co/spaces/AhiBucket/Hand-wave?logs=container\"\n",
    "show_QR(url)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### psi_solve\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# psi_solve2/ModulatedPresentation.ipynb"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### constants\n",
    "```python \n",
    "constants.py\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "L = 50\n",
    "N_GRID = 2000\n",
    "\n",
    "\n",
    "from functions import make_grid\n",
    "\n",
    "x,dx,x_internal = make_grid(L,N_GRID)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Potentials\n",
    "\n",
    "```python \n",
    "potentials.py\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from functions import inf_sqaure_well,finite_square_well,gaussian_well,constant"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " ### Play Ground for $V(x)$\n",
    "\n",
    "\n",
    "\n",
    " Here I choose which potential to use. For now, I will default to the **infinite square well**.\n",
    "\n",
    "\n",
    "\n",
    " - I can later uncomment and experiment with:\n",
    "\n",
    "   - harmonic oscillator + walls,\n",
    "\n",
    "   - double wells,\n",
    "\n",
    "   - Gaussian wells,\n",
    "\n",
    "   - barriers inside wells, etc."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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AGBNaiowHLUVgzQOtXV1d6b///S/duHGDcnNzKS8vT2MpqaCgIEpISJDdcdwF5+3t/cT0gwYNorNnz8r0J0+epF69emls54fU8rgn9WXHjh0lzhcA2AAMtEYZA5SlpYgHWderV4/mz59Pt27d0jkTrbgCAgJoyZIlNHbsWDp06BBNmjSJdu3aRc2aNVNuFqnO39+f1q9fT9OnT6ft27fT0KFDafPmzdS+fXuKi4tT0nEQNHLkSOW9+qBwAAAMtDYBDG4HCyBKuqSnpwtPT88Sf07XEhsbK0JDQ5X3dnZ24vr16yI4OFhn+g0bNoht27ZprIuJiRGrVq1S3oeFhYmIiIhS58nFxUUwftXHMWJBGeAcMMNzYOzYgmbk//3P9Hmx9qV//4Kyjo42fV6w2FwZuJTgml6q7rNr167pfO5ZSTk6OpKXlxdFRkb+HaEJId9zi5AuvF49PeOWJe30Xbt2paSkJDp37hytXLlS580mAQAAAFRKFRRxF9eiRYvk4z7Konr16vLhsRy8qOP3/PBZXXj909Lv3LmTAgMDqXv37hQcHExdunSR3Wn29roP18nJiVxcXDQWALByGGhtPBhoDdY8pmjjxo1UsWJFio+Pl9PyebC19p2tTYnzp3L69Gk5GPvy5cuy9Wjv3r2F0vP4pDlz5hg5lwBgFjDQGmUMUJagiFuK9CElJUXOVqtZs6bGen5/+/ZtnZ/h9SVJz3hmGw/abty4sc6gaOHChXKwtwq3FPHMOgCwYhj0izIH0EdQxNPx9YFbmI4dOya7ubZs2SLX8Vglfr98+XKdn4mJiZHbP//8c2Vdjx495PqiuLm5ydYrnimnC9+NmxcAsCHoPjMedJ+BBSnVaO6GDRuK+fPni++//17UqFFDruvZs6do0aJFifYTEBAgsrKyRGBgoPDw8BCrV68WqampwtXVVW4PDw8XCxYsUNL7+/uLnJwcMWXKFNGsWTMxe/ZskZ2dLVq2bCm3V6pUSYSEhAhfX19Rv3590a1bN3H06FFx/vx54eTkpPeR6lhQBjgHLPQcGDOmYEbU5s2mz4u1L4MGFZT1/v2mzwsWmysDl5Jd00v+Czp37iwyMzPF7t27xaNHj4S7u7tcz9PoN23aVOL9jR8/XiQmJsp98RR9Hx8fZVtUVJScYq+eftCgQeLcuXMy/alTp0SvXr2Ubc7OzmLnzp0iKSlJBksJCQlizZo1SpBlgALEgjLAOWCJ58D//R+CImMHRfv2mb7esdhcGbgYOig6ePCgmDx5snLPIlVQ5O3tLa5du2ZrBYgFZYBzwBLPgdGjCy7UW7aYPi/WvgweXFDWUVGmzwsWmysDF0Pfp6h169YUERFRaH1ycrKcZg8AAABgaUoVFN2/f59q165daH27du0wawsALAMGWhsPBlqDNQdFGzZsoI8//lhOhecWUb4pYseOHWnx4sV6m5kGAGAUuE8RyhigLEHRjBkz5OMz+HEfzzzzDJ05c4Z+++03OnjwIH344Yel2SUAgHHhPkXGhzIHa7xPEd9f6M0336R58+bJ8UUcGJ04cYIuXbqk/xwCABgCus+MB91nYM0tRR988AFVqFCBrl+/Lp8ptmnTJhkQOTs7y20AABYD3WcoY4CyBEWzZ8+WrUPa+HlovA0AwOyhKwdlDqCPoIgfxcEDrLV5enpSampqaXYJAGBc6D4zHnSfgTWOKeKAh4MhXi5cuKARGJUrV062Hq1evdoQ+QQAAAAwn6Bo0qRJspXo66+/lt1kaWlpyjZ+oGpiYiLFxsYaIp8AAPqFliLjQUsRWGNQpLoHUUJCgpx+n5eXZ6h8AQAYBwZao4wByjIln+9JxDdsfO2116h58+ZyXVxcHG3dupUeP35cml0CABgXBlobH8ocrDEoatSoEf3yyy/k5uZG58+fl+umT58ub+bYu3dvunz5sr7zCQCgX+g+Mx50n4E1zz5btmwZxcfHU926dcnLy0su9erVk91qvA0AAADAJlqKunTpQn5+fnTv3j2NmWnvv/8+HThwQJ/5AwAwDLQUGQ9aisCaW4qys7PJxcWl0Hqeks+z0AAALAYGWqOMAcoSFG3fvp2++OIL8vHxUdb5+vrKexTxYGsAALOHQb8ocwB9BEXvvPOOfNYZT8t/9OiRXLjbjNdNnDixNLsEADAudJ8ZD7rPwBrHFPGNG6dNm0Z9+/YlJycn2rx5M4WHh8s7W589e1YOvgYAsCjoPkMZA5QmKJo5cybNmTOHIiMjKSsri1555RV5V+vRo0eXZDcAAKaH7jOUOUBZus8CAwMpKCiIevbsSQMGDKA+ffrQsGHDZAsSAIBFQfeZ8aD7DKwxKOJ7EfFNG1V+/fVX2XVWp04dQ+QNAAAAwDyDIgcHBzmoWl1ubi45OjrqO18AAIaFliLjQUsRWOtA63Xr1sn7FKk4OzvLqfiZmZnKuoEDB+o3lwAAhoLuf8NDGYM1BkU800zbt99+q8/8AAAYBwZaGx/KHKwpKBo1apThcgIAYEzoPjMedJ+BNd+8EQDAaqBrB2UM8BcERQBgm9CVgzIH0IKgCABsG1qKUMYAf0FQBAC2CS1FKHMALQiKAMA2YaC18WCgNVgIBEUAYNvQfYYyBvgLgiIAsE3oPkOZA2hBUAQAtgndZ8aD7jOwEAiKAAAAABAUAYDNQkuR8aClCCyEWbQUBQUFUUJCAmVlZVFsbCx5e3s/Mf2gQYPo7NmzMv3JkyepV69ehdLMnTuXbt68SQ8fPqQ9e/ZQ48aNDXgEAGCxMNAaZQxgLkFRQEAALVmyRAYx7du3pz///JN27dpFNWrU0Jne39+f1q9fT2vXrqV27drR5s2b5dKyZUslzXvvvUfvvPMOjR07lnx9fSkzM1Pus3z58kY8MgAwaxhojTIH0EGYcomNjRWhoaHKezs7O3H9+nURHBysM/2GDRvEtm3bNNbFxMSIVatWKe9v3rwppk6dqrx/9tlnRVZWlhgyZEix8uTi4iIYv5q6fLCgDHAOGOgc6N1bkBCCDh1CGRv672zChIKyXr8eZY3vNGHsMijJNd2BTMjR0ZG8vLxo4cKFf0doQlBkZKRsEdKF13PLkjpuBerfv7/82d3dnWrXri33oZKenk6HDh2Sn924caPBjgcALJCDA1HlyqbOhXWrWNHUOQAoFpMGRdWrVycHBwdKSkrSWM/vPTw8dH6mVq1aOtPzetV21bqi0mhzcnLS6FpzcXEp5REBgMV1n7VvT3T/vqlzYxvQZQlmzuRjiszB9OnTZWuSarlx44apswQAhnb8ONHNmyhnY8nJIdq9G+UNZs2kLUUpKSmUl5dHNWvW1FjP72/fvq3zM7z+SelVr9r74Pd//PGHzn1y9516lxy3FCEwArBy/P3w/PNE5cqZOie200qUn2/qXACYb0tRbm4uHTt2jLp3766ss7Ozk+9jYmJ0fobXq6dnPXr0UNLz1P5bt25ppOEgh2ehFbXPnJwcysjI0FgAwEYu1Hl5WIxRBgiIwEKYdDZAQECAnBkWGBgoPDw8xOrVq0VqaqpwdXWV28PDw8WCBQuU9P7+/iInJ0dMmTJFNGvWTMyePVtkZ2eLli1bKmnee+89uY8+ffqIVq1aiYiICBEfHy/Kly+v95HqWFAGOAdwDuAcwDmAc4DMtgwsZvYZ++GHH+Q9iebNmycHQnMXV8+ePSk5OVlur1evHj1+/FhJz609Q4cOpQ8//JAWLFhAFy9elDPP4uLilDQhISFUqVIl+uKLL6hKlSoUHR0t95mdnV2ivGHANQAAgGUrybXc7q/oCNTUqVMHY4oAAACsiJubm3zSxZMgKHpCYGSIsUWqQdxcOdY6dgnHaB1Qj5YPdWgdUI/6KcOnBUTM5N1n5qo4hVcWtjCgG8doHVCPlg91aB1Qj6VX3Ost7lMEAAAAgKAIAAAAoABaioyMZ8DNmTOnxDPhLAmO0TqgHi0f6tA6oB6NBwOtAQAAANBSBAAAAFAA3WcAAAAACIoAAAAACqClyIiCgoLkA2uzsrIoNjaWvL29yVK8//77dPjwYUpPT6ekpCSKiIigpk2baqSJiooiIYTGsmrVKo00devWpe3bt1NmZqbcDz+SpZyZPKV89uzZhfJ/9uxZZXv58uVp+fLllJKSIu958b///Y9cXV0t5vgYn3/ax8gLH5el1uELL7xAW7dulTdF5fz269evUJq5c+fKe489fPiQ9uzZQ40bN9bY/txzz9G3335LaWlpdO/ePfrqq6/ko4LUtW7dmn777Tf593v16lWaNm0amfr4HBwcaNGiRXTy5El68OCBTBMeHk61a9d+ar0HBwebxfE97RhZWFhYofzv2LHDYuqwOMeo6++Sl3fffddi6vH9Ylwn9PU92qVLF/lA+UePHsnHfQ0fPlxvx2Hyh7XZwsIPvn306JEYMWKEaN68uVizZo18aG2NGjVMnrfiLDt27BDDhw8XLVq0EG3atBHbt28XiYmJomLFikqaqKgoeVw1a9ZUFvUH8Nnb24uTJ0+K3bt3C09PT9GzZ0+RnJwsPvroI5MfHy/8cOFTp05p5L9atWrK9pUrV4orV66IF198UbRv314cPHhQREdHW8zx8VK9enWN4+vevbt8UGKXLl0stg45D/Pnzxf9+/eXx9KvXz+N7fyA6Hv37om+ffuK1q1bi82bNxd6QPQvv/wiTpw4IXx8fESnTp3EhQsXxHfffads5zK4deuW+Oabb+TfwJAhQ0RmZqYYM2aMSY/v2WeflXUxePBg0bRpU+Hr6ytiY2PFkSNHNPaRkJAgZs2apVGv6n+7pjy+4tRhWFiYrCP1/FepUkUjjTnXYXGOUf3YeOFrRX5+vnB3d7eYetxRjOuEPr5HGzRoIB48eCAWL14sHyQ/fvx4kZubK15++WV9HIfhCwoLyS+q0NBQpSzs7OzE9evXRXBwsEWWD19c2QsvvKCs4wvq0qVLi/wMn9x5eXnC1dVVWffWW2+J+/fvC0dHR7MIivhLVdc2vvhkZ2eLgQMHKuuaNWsmy4AvRJZwfLoWrq+LFy9aTR3qutjcvHlTTJ06VaMus7Ky5AWD3/OXKvPy8lLS/POf/5QXpNq1a8v3Y8eOFXfv3tU4xoULF4qzZ8+a/Pi0lw4dOsh0devW1biYTpw4scjPmMvxFXWMHBRFREQU+RlLqsPi1iMfb2RkpMY6S6pH0nGd0Nf36KJFi+Q/sOq/a/369TIoK2ue0X1mBI6OjuTl5UWRkZF/N88JId/7+/uTJapcubJ8TU1N1Vg/bNgwunPnDp06dYoWLFhAFSpUULbxsfL65ORkZd2uXbvkvlq2bEnmoEmTJrJ5Oz4+XjbFczMu4/pzcnLSqMPz58/TlStXlDq0hOPTPi/feOMN+vrrr62qDtW5u7vLriT1euOm/UOHDmnUG3e3cFO8Cqd//Pgx+fr6Kmm4SyI3N1fjuD08PKhKlSpkTrguOO/3798v1LXBXRbHjx+XXTLq3RGWcHxdu3aVXSnnzp2jlStXUtWqVZVt1laH3J3Uu3dvWrt2baFtllSPlbWuE/r6HuU06vtQpdHH9RTPPjOC6tWry75//oNWx+/5ZLU0dnZ29Nlnn1F0dDTFxcUp67///nt5cvPYjTZt2tDHH39MzZo1o4EDB8rttWrV0lkGqm2mxhfKESNGyD9SvpDyGKPff/+dWrVqJfPHN1Dj8Qra+Vfl3dyPT1v//v3lF+W6deuspg61qfKkK8/q9ab+Bczy8/PlF7l6Gh7Pob0P1TbtAMRUeLwG19n69es1nvW0bNkyeRHlY+rYsSMtXLhQnuNTp061iOPbuXMn/fTTTzKPjRo1ksE6jyniiyAHPtZUh4zHx3D98TGrs6R6tNNxndDX92hRaThwcnZ2luOMSgtBEZTYihUrZKDwj3/8Q2P9l19+qfx8+vRpunXrFu3du5caNmxIly9fNvuS5i9eFf5PhYMkDhACAgLkoEVrM3r0aHlh4Xqyljq0ZfyP1w8//CAvRuPGjdPYtnTpUo1zOycnh9asWUPTp0+XP5u7jRs3apyXPLCcz0duPeLz09qMGjWKvvvuu0JPPrCkelxRxHXC3KH7zAi4qTMvL49q1qypsZ7f3759myxJaGgovfrqq/Tiiy/KbqYn4aCCqWb68LHqKgPVNnPD/81cuHBB5p/zx/+Fq5qDddWhJR1fvXr16KWXXpIzdKy5DlV5etLfHr9qz37hLgnunrGUulUFRPXr16cePXo89YngXK/cfdqgQQOLOD5t3BrCXbzq56Wl16EKBxHcg/C0v01zrsfQIq4T+voeLSoNf2eXpZWIISgyAu7f5b7u7t27K+v4vzl+HxMTQ5aCT/QBAwZQt27dKDEx8anp27ZtK19VLRF8rDxdtEaNGkoa/gLnE/nMmTNkbng6LzfVc/65/vg/MfU65KmmfBFS1aElHd/IkSNld8PPP/9s1XXIF0/Ou3q9ubi4yHEm6vXG07nbt2+vpOFz3N7eXgkKOU3nzp1l8KF+3Dy+xdTdLqqAiMfDcaCrPc6vqHrl7iVVl5M5H58ubm5uVK1aNY3z0pLrULsF9+jRo7I1zBLrMfQJ1wl9fY9yGvV9qNLo63pqklHptjgln2e8BAYGypkSq1evllPy1UfYm/OyYsUKOa25c+fOGtNBnZ2d5faGDRvKqaI8xbJ+/fqiT58+4tKlS2Lfvn2Fplru3LlTTtfk6ZNJSUlmM2X9k08+kcfH+ff395dTQnkqKM+gUE0l5emlXbt2lcd54MABuVjK8anPfOTj4Fkp6usttQ4rVaokp+7ywiZNmiR/Vs2+4in5/LfGx9OqVSs5q0fXlPxjx44Jb29v0bFjR3H+/HmN6dw8a4anOoeHh8vpxvz3zFOCjTHV+UnH5+DgIG8xcPXqVVkf6n+bqpk6fn5+csYSb+fp3UOHDpV1tm7dOrM4vqcdI28LCQmRs5P4vOzWrZs4evSorCMnJyeLqMPinKeqKfWcJ55tpf15S6jHFU+5Tujre1Q1Jf/jjz+Ws9fGjRuHKfmWuPC9FPhk4PsV8RR9vp+GqfNU3KUofE8K3v7888/Li2dKSooM/vgeIXzCqt/jhpd69eqJn3/+Wd47gwMODkTKlStn8uNTTem8ceOGrJ9r167J9xwoqLbzRXT58uVyyiv/Qf7444/yD95Sjk+19OjRQ9ZdkyZNNNZbah3yPZZ04WncqjRz586VFws+rj179hQ69ueee05eQNPT0+XU37Vr18qLmHoavsfRb7/9JvfB5wcHW6Y+Pg4SiqK691S7du1ETEyMvFg9fPhQxMXFiffff18joDDl8T3tGPmCyhdIvjDydG6els730tL+h9Kc67C45ykHL/x3xcGN9uctoR6fdp3Q5/col+fx48fl9zX/86b+O8qy2P31AwAAAIBNw5giAAAAAARFAAAAAAXQUgQAAACAoAgAAACgAFqKAAAAABAUAQAAABRASxEAAAAAgiIAAACAAmgpAgCL06VLF759bqEHS6obPnw43bt3r8jt/Lwl3oenp2eZ8jJ79mw6ceJEmfYBAOYBQREAmAQ/1fqzzz6jixcvUlZWlnzydXR0NI0dO5YqVKjwxM8ePHiQatWqJR8SWVrXrl2T+zh9+nSp9wEA1uXvR+kCABiJu7s7HThwQD65e8aMGXTq1CnKzs6WT8d+88036caNG7Rt2zadn+UngOfm5lJSUlKZ8vD48eMy7wMArAtaigDA6FauXEl5eXnUoUMH2rRpE507d44SEhJo69at9Oqrr2oERNzFxa1HW7ZsoQcPHtDMmTN1dp9xd9mVK1coMzOTfvrpJ6pWrdoT86DdfabaZ7du3ejIkSNyPxy4NW3aVONzwcHBslUrPT2dvvrqK3J2di6079GjR9OZM2dkC9jZs2dp3Lhxyra1a9fSn3/+SU5OTvK9o6MjHT9+nMLDw8tQogCgL0Z7gi4WlAHOAZwDVatWFfn5+SI4OLjYT96+ffu2GDFihHB3dxd169ZVnjheuXJlmcbHx0fk5eWJadOmiSZNmogJEyaI1NRU+UTxovaresK8p6enxlPM+UnknTt3Fs2bNxf79+8X0dHRymcGDx4snz4+atQo0bRpUzF//nyRlpYmTpw4oaQZOnSouHHjhhgwYIBo0KCBfE1JSRGBgYFyOz+5nZ/qvWTJEvk+JCREXL58Wbi4uODvA38fOAfI5GVg8gxgQRngHLChc4ADGNa/f3+N9Xfu3BEZGRlyWbRokbKeqQII1aIdFH333Xdi+/btGmnWr19fqqCoW7duSppevXrJdeXLl5fvDxw4IJYvX66xHw6i1IOiixcvin/9618aaWbOnCk/q3rv5+cnsrOzxdy5c0VOTo7o1KmTyesFC8qAUAYC3WcAYBZ8fHyobdu2FBcXR+XLl9fYdvTo0Sd+tnnz5nTo0CGNdTExMaXKx8mTJ5Wfb926JV9dXV2L9XsqVqxIjRs3ll1kGRkZyjJr1ixq1KiRki42NpYWL15M//nPf+jTTz+V3XQAYHoYaA0ARnXp0iU5yLlZs2Ya63lMEeNxONp4fI+x8CBuFR5jxOzti/f/4zPPPCNfx4wZUyh4ys/PV362s7OjTp06yXFVHEQBgHlASxEAGFVqairt2bOH3n77bdmyog88mNnX11djnZ+fn172XZLfk5ycLGfONWzYkOLj4zWWxMREJd20adPIw8NDDu7u2bMnjRgxQu95BYDSQT8iygDnAM4Bo54DDRs2FLdu3RJnzpwRAQEBwsPDQw5cHjZsmFy/ePFijTFF/fr1e+KYIl9fXznQeurUqaJx48Zi/PjxpR5ordonL7yNcVp+z3l9+PChHPTNA7rnzJlTaKD16NGjRWZmphzszWlatWol00+ePFlub9u2rXj06JF49dVX5fsxY8bIffAgcpyH+C7COUCmLgOTZwALygDngA2eA7Vq1RLLli0T8fHxctBxenq6iI2NlYFNhQoVShQU8TJy5Ehx9epVGZBs2bJFTJkyRe9BES/Tp08XycnJMr9hYWFyULh6UMTL66+/Lo4fPy6Dn7t374p9+/bJgeU8YPv06dNi9erVGuk3b94sZ7nZ29ubvF6woAzIhsvA7q8fAAAAAGwaxhQBAAAAICgCAAAAKICWIgAAAAAERQAAAAAF0FIEAAAAgKAIAAAAoABaigAAAAAQFAEAAAAUQEsRAAAAAIIiAAAAgAJoKQIAAABAUAQAAABA0v8DhmmwS9fjg3kAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 600x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "def custom2(value):\n",
    "    return value * np.ones_like(x)\n",
    "\n",
    "#V = inf_sqaure_well(x,-L/2,L/2)\n",
    "\n",
    "\n",
    "# --- 3. USER PLAYGROUND (Mix and Match Here) ---\n",
    "\n",
    "# EXAMPLE 1: Half-Harmonic Oscillator (Wall on left, parabola on right)\n",
    "# V = inf_wall(x, 'left', 2) + harmonic(x, center=5, k=5)\n",
    "\n",
    "# EXAMPLE 2: A Harmonic Oscillator with a Barrier in the middle\n",
    "#V = harmonic(x, k=5) + finite_barrier(x, center=L/2, width=0.5, height=50)\n",
    "\n",
    "# EXAMPLE 3: Double Well (Two Gaussians)\n",
    "# V = gaussian_well(x, center=3) + gaussian_well(x, center=7)\n",
    "\n",
    "# Finite wall showing QM TUnneling\n",
    "# V = finite_square_well(x,-10,10,0.01)\n",
    "\n",
    "# Let's run Example 1:\n",
    "#V = inf_wall(x, 'left', 2) + harmonic(x, center=5, k=5)\n",
    "\n",
    "V = finite_square_well(x,0,10,0.1)\n",
    "\n",
    "\n",
    "from functions import plot_V\n",
    "\n",
    "plot_V(V);\n",
    "\n",
    "# Error with plot Axis..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " For an $N \\times N$ matrix (e.g. $4 \\times 4$ toy example), the pattern is:\n",
    "\n",
    "\n",
    "\n",
    " $$\n",
    "\n",
    " \\begin{bmatrix}\n",
    "\n",
    " 1 & 1 & 0 & 0  \\\\\n",
    "\n",
    " 1 & 2 & 2 & 0  \\\\\n",
    "\n",
    " 0 & 2 & 3 & 3  \\\\\n",
    "\n",
    " 0 & 0 & 3 & 4  \\\\\n",
    "\n",
    " \\end{bmatrix}\n",
    "\n",
    " $$\n",
    "\n",
    "\n",
    "\n",
    " - Main diagonal: $N$ elements\n",
    "\n",
    " - Off diagonals: each has $N-1$ elements\n",
    "\n",
    "\n",
    "\n",
    " Here, my actual matrix is the finite-difference approximation to $\\dfrac{d^2}{dx^2}$,\n",
    "\n",
    " and I then build the Hamiltonian:\n",
    "\n",
    "\n",
    "\n",
    " $$\n",
    "\n",
    " - \\frac{\\hbar^2}{2m} \\left( \\frac{d^2}{dx^2} \\right) \\Psi = E \\Psi\n",
    "\n",
    " $$\n",
    "\n",
    "\n",
    "\n",
    " turns into\n",
    "\n",
    "\n",
    "\n",
    " $$\n",
    "\n",
    " H \\Psi = E \\Psi,\n",
    "\n",
    " $$\n",
    "\n",
    "\n",
    "\n",
    " where $H$ is built from $D2$ plus the potential."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "hbar = 1\n",
    "m = 1\n",
    "\n",
    "from functions import kinetic_operator\n",
    "T = kinetic_operator(N_GRID, dx, hbar=hbar,m=m)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solve\n",
    "\n",
    "``` python \n",
    "solver.py \n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " The integral\n",
    "\n",
    "\n",
    "\n",
    " $$\n",
    "\n",
    " \\int_{x_1}^{x_N} f(x)\\,dx \\approx \\sum_{i=1}^{N} f(x_i)\\,\\Delta x\n",
    "\n",
    " $$\n",
    "\n",
    "\n",
    "\n",
    " is implemented as a Riemann sum on the grid."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from functions import solve\n",
    "\n",
    "V = finite_square_well(x,-10,10,0.01)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from functions import plot_alive\n",
    "E, psi = solve(T, V, dx)\n",
    "plot_alive(E, psi, V, x, no=4);\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wall height is only 0.01 Hartree, which is extremely low! Looking at your image, the energy level E ≈ 0.06 is much higher than the potential barrier (0.01). This means:\n",
    "\n",
    "The particle has MORE energy than the barrier height\n",
    "It's not a bound state - it's a scattering state\n",
    "The wavefunction should oscillate everywhere because E > V everywhere outside the well\n",
    "The Physics\n",
    "For exponential decay in classically forbidden regions, you need:\n",
    "\n",
    "E < V in those regions\n",
    "For a finite square well, bound states only exist when E < V_barrier\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1000x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "V = finite_square_well(x, -10, 10, 2.0)  # Strong confinement\n",
    "E, psi = solve(T, V, dx)\n",
    "plot_alive(E, psi, V, x, no=4);\n",
    " \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This will create bound states where E < V_barrier, and you'll see the characteristic exponential decay in the classically forbidden regions outside the well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.11993441e-02 4.47851424e-02 1.00719809e-01 ... 3.20511873e+03\n",
      " 3.20518028e+03 3.20518028e+03]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "3205.180275687149"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Debug 2\n",
    "bool(0)\n",
    "print(E)\n",
    "E.shape\n",
    "E[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Mvvzyy+lOLNJURO6SSnZGQ3rkzPar3MWVE5Rk8pR+eRlJn4fsMozfY+ozyCg7nysRkTWQG2zSxFwy8fr4+DzS766kepeWFpLqP23tjwRhmZ2fFyxYoM5/huzJGfuimyJdFjJmtBTS7FEyVJpqbi9ZGjM+lhYShoBUzsVyvjFVA2dnZ6fOx0LOb1LTJxkTH3TulfObYZmsMgR9hr7oQrqDSDZJc2BNGpGVkcBKakxM1eZk1gZbmhXKj7TcwZI05/KDaBi7TNLapr3TJ32hpMOuIa2vYfwTGRNk5syZ+Pbbb7O1vfKDK03q5LWlqYOktZfXXrdunbH5pKG9v6TVlTT4EshJmltZVmra5G9JgSs1YnJykhqgjB2sZR3S9l5q6KTJiMwjJ0RpWiI1NlI7JgNMy3zSB6pq1apqyAB5n5LaXoYbkJOcdAhOe8dR+psZ0tbrhXxG0rlaAjKp7ZPAWk78ckKTpi0Gx44dU89JnwI5mcm+lPcnFwuyr+TkLXdZZZ/LNDkBt2nTRn1W2b3bahjrTFI+SxNS6cQux5dMyyg7nysRkaWdczMjTf3ld1uGqZHkH3LOlX7G0jdXWmA8bKwtOTfK+VyScshvuQQ+cg6TJvly3jNVuyR9wKW5vyQGM5wvHkbOL9IlQYZIkT7Scq6WmjLpAiDnmYxdFaS1jnRnkHOsJNGQfSZdHOScbujPLEMGSAIquTko73Pz5s3q/UhfNUkqIsPFLF++XF1zSFr9X375RfVll+2XGjDpWy4BlaH7gZzLO3furK5JZD7ZRjnPP4i8ptRGyrrl2kBuGMp7kvOfuWrTmKaW+4DHgJWnAxbyvGFeU6nQmzRpotKmS0rcCxcuaL1799a+/vprLSYm5r7X6tChg0r9K6nrpfzzzz/alClTtPLlyxvnkRS+plLrSzretGlxJTWtpIWXtMGStlhee8KECZqHh8d9qfIDAgK0pKSkdKlw27Ztq1IGy3ZevnxZGzJkiPbGG2/cly5X0sdLSl5J3ZsxFbGknP/yyy+18+fPq/cfFhamUh4PGjRIs7e3V/O88sorKvV9SEiImufq1ava9OnTNW9v70f+rB7lc5Z9J+/jYfM9/fTTKmV9RESEGl5h27Zt6VIFG8qbb76pUhHLcAMZUwTL37IOSbsv+1c+G0m1XLNmzXSfpxwDGddrKpWxvL6k5Zf9l/YYNDVvVj9XpuA3/28PC/dBfjwGsnrONaTgl6FkMq7D1LlYhk6ZO3euGq4mPj5enffWrFmjzkEZX7tWrVomt+3dd99V5wo5p+7bt09r0KCB+u1dv369yfn/+OOP+9LJP6iULl1aGz16tPb333+rc6IMwRMaGqrOTY0bN043r+EcIe9LzqFyPgoODlbv28bG5r519+nTR21rdHS0Ol/LkARfffWVGkYm4zlCztMynwyPI++zU6dOxuddXV21hQsXquFkDEMFpE3BL0PQmHpvNWrUUOn9Def5gQMHZpqC39S5WMj1UNppDzoGHlRs/v2DiOg+0glYUvIa2o4TERGRZZGm41IbJF0W3n777fuel+nSesSQ2TcnSUIRaZXysKFf6H7sk0ZEiiRqSEs6Hks2vbSdj4mIiEi/TPXT6tGjh+pDZup8Lv3fpBm7NG8nfWGfNCJSpO27tBeX/6XttfRJkk69maWmJyIiIn2pX78+vvvuOzXWmfSnrlmzJt58803Vzy3t+GfSV61hw4bo06eP6vsl/X9JXxikEZEigzR36dJF3VWTpA179+5VHXgzG7iaiIiI9EVS2svQJe+//75KdiVJmmQ8tOHDh6tgzKBRo0bqxqwkypDshZK4i/SFfdKIiIiIiIh0hH3SiIiIiIiIdIRBGhERERERkY6wT1omZMBUGTCPiIiIKKdJSvKgoCDu2HyM15qWxSOPv7MM0jL50gQGBubZh0BERET5j5+fHwO1fIrXmpbJLw+/swzSTDDUoMkHwdo00qsnnngCx44dU38vXrzY5ACVRPmFjAP0448/qr/feecdjvlDur8jLzeDeY2Rf/Fa07J4mOE7yyDtAeSD4A8o6VVUVJTxb0mry2OV8rO4uLh0f/P7QESWgNealBkmDiEiIiIiItIR1qQRERFZAHt7e/j6+sLWlvdXLYGmaQgPD0dMTIy5N4WILBCDNCIiIp0rVqwYvvjiCzg7O5t7UyibduzYgTlz5qigjYgoqxikERER6ZiNjQ369Omj+qF+8803iI+PN/cmURZrPitWrIiOHTuqx7Nnz+Z+I6IsY5BGRESkYwULFlQX+9OmTcP58+fNvTmUDZcuXVL/d+rUSWXhZdNH8xkwYACGDBkCHx8fHD9+HO+99x4OHjxoct4OHTpg5MiRKFeuHBwcHHDhwgV8++23WLhwYbr5xowZg7feekt9R/fs2YP+/fvj4sWLefSOyNqxYTsREZHOUz+LsLAwc28KPYKzZ8+q/4sWLcr9ZyZSmzlp0iQVVNWsWVMFaZs2bYKXl5fJ+W/fvo0vv/wSDRo0QLVq1VRzVSnNmzc3zjN06FC8//776NevH+rVq4fo6Gi1Ticnpzx8Z2TNGKQRWUlzKKL8zJq/A4b3lpycbO5NoUeQlJRk9ceo3g0aNAizZs3C3LlzcebMGRVYSa1m7969Tc6/c+dOrFq1SgXYly9fxg8//IATJ07g2WefNc4zcOBA1U90zZo1OHnypBqrUQaobt++fR6+M7JmDNKILBQ7oRPxu2GpateurZqHSe3DypUrs7xcz549cffuXRw9etRYDIOYZ1XdunVx7NgxnDt3Dtu2bVMX1pn5+OOPVfM1KXJB/rjbT3lPmivWqlULW7duTXf+lMdSU5YVTZs2RYUKFbBr1y71uEyZMirTatp1RkREYP/+/Zmu09HRUdWKpy1ED8IgjYiIiPJUcHCwqon48MMPs73s9u3bUaNGDWN59913s7ys1Gb9+uuv6rXlonv9+vWYPHmyyXmfe+45dOnSRTV3q1y5Mlq0aIHWrVs/9vZT3pJmppLEJTQ0NN10eSz90zLj6empBppOSEjAunXrVB82Q1BmWC476xwxYoQK5AwlMDAwB94dWTMGaURERJQtUhMhF51ScyDNwd54441sLS8XqJK0Ia8zVUqNijQ/lLT44qeffkK7du1M9iOSZB8LFixQzeLkQl2yM0rQZs7tp7wjAdrTTz+NOnXqqBpV6dPWqFGjR17f+PHjVeBnKH5+fjm6vWR9mN2RiIjIgvj2mgJb1wK5tv6UmHsInvPeQ+eTAEUSJkiNlAQsEtBIvzm5mG3SpInJZfr27YsDBw481vbJuqWZo8G8efNUbVjjxo3x3XffmVxGakI++eQT+Pv749q1a8bpMqyB1GpIk8crV66kW0bm3b17t/Hx1atX0blz58fadsp7MqC4BObe3t7ppsvjkJCQB96IMGTnlEQjlSpVUjcmpL+aYbmM65DH0pTWFAn0pRBlFYM0IiIiyjZpNiikb5dcBEszL6lhkiQNuUmaO0qK9IykdkyaPxKllZiYiMOHD6NZs2ZYvXq1sdmrPM5Of0ZbW1tjjasE9NLkVdYhAZyQPmZy02L69On8AChHMEgjIiKyIFmp5coLcXFxxr+lBk36/YjcrknLTFZq0q5fv45SpUoZp7u7u6NAgQIICgq6b5mM85YuXVpNI8sjx6TUuB46dEgdf9Kf0M3NTaXVF/Kc3GCQsdHE8OHD1bxSkyaBmfRF7N69uxoHzUBqb+WYkjHUJGj7/PPP1XEkWSGJcgKDNCIiIsoxj1uTJn2ApP/OCy+8kK3lslKTJjUqku1PAjqZX4LGtWvXmuxb9vvvv2Pq1KmYMmWKqimUdO2jR4/O9vsh81u6dKkaE23s2LGqxleaJLZs2dI49qA0bU1JSTHOLwGcDB5fokQJxMbGqlT83bp1U+sxmDhxoppv5syZajBraRor62Q/RcpJGkv6feDh4aEJ+Z/7hseHXo+BJ554QjNYsGCB2beHhfvAnMdAnz59jN+HXr16WdXxWKpUKW3+/Pnqf3Nvi6GIAgUKGB/fvHkzW9v35JNPagEBAdqtW7e0mJgY9Xf//v3Vc6+//rq2du1ak8v17NlTu3v3rnb06FFjWbx4cba2vX79+trx48e1c+fOadu3b9dKlChhfG7dunVarVq1jI8//fRT7dKlS6qMGzcuS9uflc+P1xnmP4bNXXgMmP8zgM4/L9akEVkBDpJK+R2/A+bd31JLkR3nz59HyZIlTT4nGfS++uork89JszQpj2Pfvn2oXr26yefatGmT7rE0YZOSne0nIsoJDNKIiIhIN7Iz7hkRkbXiOGlEFkrSAxMRvxtERGR9GKQRERERERHpCIM0IiIiIiIiHWGQRkREREREpCMM0oiIiIiIiHSEQRoREREREZGOMEgjIiKiPNWpUyccPXoUJ0+eVGXQoEFZWk7GUIuJiVHLGsqKFSuy9drlypXDnj17cO7cORw4cACVK1fOdN7evXurMdEuXryImTNnwt7+/pGLtm3bhjt37mRrG4iIHoZBGhEREeWpgIAAtGzZElWrVkXDhg3Rv39/FYBlhQRXNWrUMJZXXnklW6/9008/qYCrQoUKmDBhAubOnWtyvtKlS6uBrJ977jkV2Hl7e+Ptt99ON8+HH36IS5cuZev1iYiygoNZE1kBGxsbc28CkVnlp+/ApPnbUKBQ0Vxb/7074RjUo9lDx2kcOXIk2rdvDy8vL4wdOzbTYMeUv//+2/h3REQEzp49q4KinTt3IjfJttauXRvNmzdXj5cvX44ff/wRZcuWvS/Yeu2117BmzRqEhoaqxzNmzFDvedq0aeqx1MDJ++/Vqxdef/31XN1uIsp/GKQRWSgOZk3E74Y5xcfHo169eqpG6uDBg1iwYAGSk5MxadIkNGnSxOQyffv2VU0M06pUqRIaNGiAfv36Zel15fWkmaPBli1bMHToUDz55JNYsmSJyWVkfmm6WLJkSQQHB6vtNLh+/Tr8/f3vC9Jk2rVr14yPr169qqYJafY4a9YsvPnmm+nWRUSUUxikERERWZCH1XLllV9//dXY/DApKQk+Pj4IDAzMcv8y4efnh9WrV6sATZbNTnPHjKTvmKnpuWHUqFGqL5zUAJYqVSpPXpOI8hcGaURERJRtcXFxxr+lNsmQVCOrNWm+vr7YunUrvvjiCyxbtuyxP4Gs1KRJXzh5XTs7O2MNmNSOSW1aRjJNmkEaSHNMw3zSf06We/fdd9X79vT0xJUrV1CnTh2Eh4c/9nshImKQRkRERDkmKzVpUusmWRElccf8+fPTPVe8eHH1nDSDzI6s1KTdvHkTR44cQbdu3TBv3jy8+uqruHHjhsnkH9Jfbffu3Rg9erTqlya1fYsXL1bPPf/888b5pCbt2LFjKFOmTLa2l4joQZjdkYiIiPKUJBqRmqgPPvjAmEr/jTfeMDaBlOaTD+uTZii7du3K1mtLbZ4UaTY5fPhwlfjDQPqZtWvXTv0tNWPSrFHS9UsKfgnwJDMkEVFeYE0aERERPVY2TcmamB2Syj5jOnsDaUr41VdfmXxOsj+6urricUiN2zPPPGPyubfeeivd459//lmVB5HkIoUKFXqsbSIiyohBGhEREenGN998Y+5NICIyOzZ3JCIiIiIi0hEGaURWID8N5EtkCr8DRERkTRikERERERER6QiDNCILpWmauTeBSJf43SAiIkvHII2IiIiIiEhHGKQRERFRnmrfvj2OHz+uxjk7ffo0vvjiiywt17NnT9y9ezfdOGk//vhjtl67bt26avBpGSdNBs2WwbNNqV27thojLTo6GitXrrzv+Y8//liNnyYlq9tPRJRVTMFPREREeWrr1q1YvXq1aprq4OCA3bt349ChQ1i1atVDl92+fTs6dOjwyAlmfv31VzUe2o4dOzB48GBMnjwZHTt2vG/e4OBgDBw4EDVq1ECrVq3SPffcc8+hS5cuqFatmhp4W4K5v//+G+vXr3+k7aL8y9nfGYlRiebeDHoIZ3fnh82S4xikERERUbZIcDVy5EhVIyYDWY8dOxZz587N8vJRUVHGv52dneHk5JQnfQlr1aqlgioJ0MRPP/2kasHk9ePj49PNGxgYqErlypXvW0+nTp2wYMECxMTEqMezZ89WQRuDNMquJ0Y+gejEaO44nXNzcMvz12SQRkREZEGO9XVDMbfcG3YjLFrD0z89/KJRgpp69eqhQoUKOHjwoApakpOTMWnSJDRp0sTkMn379sWBAwfU3w0aNFBBUvny5TF9+nRVs5YVsm5p5mgwb948VRvWuHFjfPfddyaXWbduHT755BP4+/vj2rVr6YLFiIgI1eTxypUryCpZj9T+GVy9ehWdO3fO8vJEBpfHXUZkVCR3iM55uHsAXfP2NRmkERERUbZJs0EhfbukdsrHx0fVPA0aNChLy+/du1c1FyxatCiWL1+umhD+9ddfj9zcUWrHpGkikSWJux6HuMg4c28GPYSDhwPymi6CtAEDBmDIkCHqB146Er/33nvqrpwp8sMsTSzKlSun2rFfuHAB3377LRYuXJhuvjFjxqg25wULFlRtxfv376869xIREVmyrNRy5YW4uP8uLKUGzd4+9ZIiqzVpBuHh4aqZ4Ouvv56lIC0zWalJu379OkqVKmWc7u7ujgIFCiAoKChbr5VxPaVLl1bTiIisJkiTzrryg96vXz/s379fddLdtGmTaj5x8+bN++a/ffs2vvzyS5w9exYJCQlo27Yt5syZg7CwMGzevFnNM3ToULz//vsqC5Q0X/j888/VOqVdecY250TWQDrDE+Vn/A7oR1Zq0uQcf/78edUPTQKlNm3aYP78+eq5OnXqYPz48XjhhRey9bpZqUk7fPiwusErAZ3ML0Hj2rVrs31t8Pvvv2Pq1KmYMmWKqkXs3bs3Ro8ena11EBHpOgW//JjPmjVLdTg+c+aMCtakI6784Jmyc+dOlf1JgrTLly/jhx9+wIkTJ/Dss88a55FATzoCr1mzBidPnkSPHj1Ue3Pp4ExkLThgLxG/G5ZKEm+cOnVKpcKXZo+SCv/nn3821krFxsY+tE+aoSxevDhbv5vdunXD999/r5ppyo3eDz/8MF2NmyQXEU8++SQCAgLUjeQWLVqov6VVjuFaZMmSJeoaQ65dtmzZopYlIspJmrmKg4ODlpiYqL388svpps+dO1dbtWpVltbRtGlTLSoqSnvhhRfU4zJlymiievXq6ebbsWOHNnnyZJPrcHR01Dw8PIylePHiah3ytzn3Dwv3wYOOAX9/f81g0aJFPF54vOTrY6Bfv37G70P37t3Nvj05WUqVKqXNnz9f/W/ubcmL8uOPP2oNGza06s9Pri94nZG/C48B838G0PnnZdbmjtJZWNqwh4aGppsujytWrJjpcp6enqpzsqTMlXbw0qdNxlwR0q/NsI6M6zQ8l9GIESPYTIGIiEgH3n33XXNvAhGR2Zm9ueOjiIyMxNNPP63arX/88ceqKUKjRo0eeX3S9l0CP0Px8/PL0e0lIiIiIiLKKrPWpElGJ+lw6+3tnW66PA4JCXlgm/JLly6pvyUbZKVKlVRtmLQRNyyXcR3yWNq+myIJSKQQERERERHl65q0xMRElWmpWbNm6TJ0yWPpSJxVtra2qumjkGyOwcHB6dbp4eGhBtzMzjqJiIiIiIjyZQp+aao4b948HDp0SI2dIpkZ3dzcVFp9Ic9J/zMZG00MHz5czSs1aRKYtW7dGt27dzdmXBKTJ09W46HIGGqGFPwyBopkhSQiIiIiItIzswdpS5cuhZeXF8aOHasSe0iTxJYtW6pxz4S/vz9SUlKM80sAN23aNJQoUUKl6JVU/JJOV9ZjMHHiRDXfzJkz1WDWu3fvVuvkGGlERERERKR3Zg/ShAwIKSWz8VDS+vTTT1V5mFGjRqlClB9wIF/K7/gdICIia2KR2R2JiIjI8jk7O+P06dNqUOqskEzOMTEx6QazXrFiRbZes1y5ctizZ48azFq6WVSuXNnkfKVKlcL27dtx9+7d+7ZPbgp8++23atslgdmff/6JsmXLZms7iIgehEEakYWSLKdExO+GJZswYYIKmLJDgqsaNWoYyyuvvJKt5X/66SfVHaJChQrq9efOnWtyvoiICNW/vWvXrvc999JLL6Fhw4aoXr26Ktu2bcO4ceOytR1ERLpv7khEZGQHuFd2h2dNTzj7O8OhkANgAyTeTkTstVhEHo1E1Oko4L+uqpQJ51LOKFCnAFyecIFjMUfY2NsgOTIZcUFxiDoehYgjEUiJ446kR7tJJAm92rdvb+xXnlmwkxnJwizjkk6ZMkWNe5oXZFtr166N5s2bq8fLly/Hjz/+qGrBDEP7GNy5c0cFkKbGYZX3L8nLpCYwKipKjbF648aNPHkPRJQ/MEgjIn2wAQo9Vwhe7bzg6OVonJwUmaT+dy3rqkqRpkWQEJaAm3/cxJ2/7gCsULyPawVXeL/iDbcKbsZpyTHJ0BI1OBV3gnNJZxSsV1BNu73tNm6uu8lgzYIcm9EbxQq65tr6w+7G4Ol+sx86nyTjkuFtpEbq4MGDWLBgAZKTk1XW5oz9yQ369u2rmhgWKFBAJfmSpF6ZNTfMjLxe2uaHW7ZswdChQ/Hkk09iyZIlJpeR+Xv37o2SJUuqYXpkOw2uX7+ukpRlDNIeZO3ateo9yniskZGRKgu1qWCOiOhRMUgjIrNz9HGEX28/uD3pBi1Fw919d3F3713EnIsxBg+2zrYq+CjYoCAK1C2g5i/YsCACZwciIZSD0at95GILn84+KNyosHocfT4ad3bdQdTJKCTdSw12bexs4FzaGQVqF0ChRqlBsdqPcwLVfERZ9euvvxqbHyYlJakMzRKsDBo06KHLSu2VNA+8efNmtne4obljRufPnzc5PTdIbdxTTz2lagKlWeRXX32FGTNmqCGBiIhyAoM0IjIrjxoeKPF2Cdi52CHqVBSCFgSZDLokWJMmelLCVoaheM/iqllk2dFlceOnG4g8Fon8HuiWGlgKTj5OqqYxaF5QarPQDLRkDbGXYlUJWxuGYu2LocgLRVDqw1K4ufYmwlaFsXZS57JSy5UX4uLijH9LzZS9feolRVZq0p599llVvvnmG9VksHDhwmpInYoVKz7y9mSlJi0gIAC+vr6ws7Mz1qZJLZrUpmVHjx49VLKQe/fuGcd03bx58yNvOxFRRgzSiMhsijQvAt+uvtCSNATND8LtP29naTkJ4q5OvIrCzQrDt4uvCk6CFgbh9tasLW9tXJ90VfvAztVO1ZzJvtASHt4ONCUmBSG/hSDySCRK9C+BYi8XU33Xbvx8A/ivNRhRtmSlJq1MmTLGv6WZ4OTJk421YMWLF1eJOCpVqpSt181KTZrU3B05ckSNryqB1auvvqr6kmWnqaO4fPkyWrdurYLMxMREtG3bFqdOncrWOoiIHoRBGhGZRdE2ReHzug+SopJw/YfriDkfk+11SH+quIA4lPqgFIp3Kw5bB1uEbwhHfuJWyU0FaDYONgj+NRi3ttzK9jqiz0bj0qhLKD24tGpOKs0mA6YGqD5sRHlNmhBK88ms9kmTPmHPP/98ltcvtXmS5EQSn0hTxV69ehmfmzVrFtasWaP6nLm4uKjATxKESB86qYWTfneynIztKkGkpN+XIE36pvXr1+8x3jURUXoM0ogozxVpWSQ1QItIwpWJVxB/I/6R1yXB3ZUJV1D6o9Lw6eSjmvPd2pz9QMVia9A+LKWyNgb+HIi7f9995HUl3U3Cla+uqPV5Pu2JEn1LqECNiVkoK4OHS9bER7Vz5850NWBSsyZ9vDKb19X18ZKmSOD1zDPPmHzurbfeMv4dGxurEo2YkpCQgLfffvuxtoOI6EE4ThqRFV4w6VmBegXg29lXZW2UoOBxAjSDuOtxKlCTWjlpPulZ1xPWzsnXCf7v+6sA7cbMG48VoBkkRyfj6jdXEXslViUWKf5GcVgKS/oO0INJE0JDUhIiovyKQRqRhbLEwawlO6NfHz+kJKTg2uRriA96/ADNID4wHte/v46UxBSUeKuEqmWyVvYF7FFqUCnYu9sjZHEI7u1LTV6QEyRBy9VJVxEfHK+yRBZtXRSWxhK/G0RERGkxSCOiPOFQ2AH+7/irFPABMwJUdsGcFnMhBjdm3FCv4f+uP+wLWWGLbjug5Dsl1Vhy4ZvDc6Vppwx4LYGa1Ex6v+YN96ruOf4aRERElDkGaUSU66RJXsl3S8Le0x5hK8JUNsHcEnE4QqWRl9eSQE1e25r4dPRR48lFnoxEyKKQXHudxJuJCJgWoP4u2b8kHL3/G2CciIiIcheDNCLKdT5dfeD6hCsijkbg5rrsD16bXTLeV8SxCLiWdYXv/3xhLTzreKJoi6JICE9QY8PldlKP6H+iVXNKSe2vAl4H6wp4iYiI9IpBGhHlqgL1C6BI0yKID43HjVm5H1goGlQyjfiQeBRuUlgFN5ZOarL83vRTfe4k62JyVN4MZCbNKe/tvwfnks7w6eyTJ69JRESU3zFII6Jc41DEAcV7FE8NLH4MUIMn5xV5rYDpAUhJSoFfLz+1LRbLDiolvp2znWriKNkX81Lg3EAk3ExAkWZF4FHTI09fm4iIKD9ikEZEucMGKsuiNJULXRaqBp3Oa3HX4tRryzZIkGOpv3jFXiqW2lz0WARu/3k7z18/JTZFJXvRkjSUeLOESgJD9Dh69uyJu3fvqkGppfz555+PtJyUH3/8MVuvXbduXRw7dgznzp3Dtm3bULy46aEmOnXqpNZ/8uRJVQYNGpRuyIdvv/0Wp0+fVgNay/aXLVs2W9tBRPQgFnrJQkR6V7RVUbhVdEPUP1FmHVz61qZbiDoVpZJteLV79AF3zcWlnIva7qR7SQj8JdBs2yHZOEOXh8LO7d+Al93T6DFt375dDWItpWnTpo+0nJR33303y8tKcCVjsA0cOBAVKlTA+vXrMXnyZJPzBgQEoGXLlqhatSoaNmyI/v37q4G2xUsvvaSmVa9eXRUJ9saNG5fl7SAiehgrzE9NlP/obSBf51LOKPZKMZXCPc/6oT2of9qsGyj3eTkUe7kYok5HIfZi3jYXfFS2zrYo+XZJ2NjaIHB2oEqNb07hG8PhXsUd7k+5w6utl0rQohd6+w7kprJjy6rspbklKSIJlz679NCx6EaOHIn27dvDy8sLY8eOxdy5c6F3tWrVQlJSEnbs2KEe//TTT/jiiy/g5OSE+Pj04zb+/fffxr8jIiJw9uxZlC5dGjt37lTvX5ZxdnZGVFQUPD09cePGjTx/P0RkvRikEVGOsnG0UTUttva2uDHvBpLuJJl9D6taqNmBKDWwlAp6Ln52UQ3arHe+XX3hWMwRt7ffRuTx3Bu2IFsB7883UO6LcijWvpiqoczr/nGkHxLU1KtXT9VIHTx4EAsWLEBycjImTZqEJk2amFymb9++OHDggPr72WefVc0JY2Ji8N1332HZsmVZel1ZtyxnMG/ePFUb1rhxY7UeU9atW4dPPvkE/v7+uHbtmnG6BFgSgEmTxytXrmT6mpUqVUKDBg3Qr18/9Xjt2rVqO0JCQhAZGYnAwEBjLRsRUU5gkEZkoeROrl7H8XIu7ow7u+8g4mAE9CLyWKQKdiTbo283XwT+bL6mg1nhWcsThZ4vpDJUBi8Khl4k3f034H2/FEr0K4FLoy7pLuDV63cjpzysliuvSLNBIX27pHbKx8dHBStp+25l5o8//sDSpUsRGxuLihUrYvPmzap54f79+7PU3LFDhw73TZfaMWn+mNP8/PywevVqFaDJ+xO1a9fGU089pZ6TIO+rr77CjBkz0L179xx/fSLKnxikmSmVttzRf6QLjaxce2jZXyZLFzWmZnmE7Xnk13rYPCZ3V8YXz6HXMjVLxveVcZkUICUhRRUtQTP+LRe4UtNjKDIGlrmbtT0q96ruKPJCEZUJMHihfgILAwl2pJ9coWcLqZopPQWRadkXsEfxN4pDS9bUeGhyvOiJDEZ+e8dtFG5cWNX2SdBmiWxdbFXWT0mE4lDIQfW3k2l2Lnaqqamtky1s7Gz+KzIwuh1S/7ZN07xS/rTJpOllhucMf2eneWZx1+Jq++Tc4ZTkBL3QCmtwsk/dnmQtGW4l3OAEJ0wcNRGNnjFdq/Tu8Hdx8OhBRCEKcIaa/0rkFWzauQmNWjfCsRvHHviash/ks3Hyu38/yGvKa5uycdtGjJo4CiFxIShdtrRxeXc3dxQoUAC3bG7dt065IVHMsxi2bt2qmkSmrenr0aOHShZy7949Y22eBJpERDmFQZoZyAn+odnRTJ2/s3JOzzCPjamFbLK/3nQXJJTrpE9IXGAcYi7EqD5UMRdjAJ3HbXbudmocLy1FU33A9Fa7IiTYkSyFZT8ti+I9i6v9qofmmBnJfrT3sFeJOvTanDD4t2C4VXBTtX2RJ/Ub8KYlF+Ee1TzgWt5V9Zt0LOKYo+uXY/+/B//dqFE3i9LG2Ya/sxh72zvZqzRfhmBRL+7bnn8D2GFfDHvocsW9iyMoNEg9Lla0GBo3bIxl65ap52pXr42xw8aiddfW9y8s+8HG9H7YtX8X6reu/8DXPXr6KBwcHNDo2UbYtXcX3urxFtZvW4+EpIT71ik1g1vWbsGECRMwf/78dM9dvnwZrVu3xjfffIPExES0bdsWp06deuD7JiLKDgZpZhAfFI9/+v6DfOFh1xM2eRdoZikYNXV3+1HWbWo1djawdbCFjVPq/7aOqX/LXXtJAiC1J/YF7VUfJGc/Z7hXcldF0q9L0HZ3z13c2nILibcToUdS8+NQ0EElk4g5HwO9Umn5V4bC53UfNUTA1a+vmjexSQaFmxVWgYQE6DfX6Scxx4MCXr83/FT2Rz0em1IbVqhRIdXM1cn3v5qS5LhkFaRLra9stxQZIDw5NlkNOSD/y3uUYQekRjNtkRsmKiDLo+MmulQ0Ej9PVOeOuOt5P5RFZmRYjbh7/25PChAfmPXte7Pvm3j55ZdVgGNra4tJX0/CpsWb1HO+9XwRfSfa5LoSbyXi+frPY+/qvcZp0tyyc+fOWd7u/3X+n0oYIkk/goKCVBPFuBtxxr5rn332GQ4fPoxRM0epPmwffPCBKuL7779XCVKmTp2q+qlJ+n15D9I3zdBfjYgoJzBIo9z1sIuYLLV8zLsr6Nx+reRsVIdJwOZWyQ0eVT1U/yRJaV/4hcIqUAtbGQY9KfhsQRSoXQCxV2MRtkpf22ZK+PpwtV/dK7ujSIsiuLXRfEMEpCVBhE8nHxUg3Jh5Q1346pkKeFeEqn6IJd4ugSsTrugq4C34XEF4v+YNhwIOKqiSGj/pmyjDQiSEJOhqWy1NxhtakuExOz7++GNVTJEEHNLHyxRpVijlcezbt0+lzTelTZs2xr/ffvttVUxJSEjI9DkiopzAII1Ip6Q/xL2991SRPhjSrEzSnnu19oJHdQ+kLNfHFbxDUQf4/s9X9a+TwELVNOhdmrT83q96I/p0tFkG285Y06qyYjraqj5eUsNjCcI3hKuU/BLwFm1dFOHrwnVRe1by3ZLqxkFKUgrCN4er8fKkFob0LzvjnhERWSsOZk1kAaR/lwwIfX74edz9+65qDlnyvZLm3izVrFNqUKTJZsjSENUcy1LIBXvQ/CDV9FSyFNo4mLevj1d7L7iUdkHE4Qjc2XUHFkODypQpY+J5d/CGc2lnc2+RuplhqNm9+MlFhPwWwgCNiIgsCoM0IguSEpNaWyVZCu3dzF8R7tXGC25Puqnxsm5vuw1Lc2/fPdzdmxr0SpM9c5FEFrIvE+8lInCu5WVKlP5cQXODVPbDkv1Kqposc3Is6oh7++/h8heXU5s1EhERWRgGaUQWSJpuha4KNT6W2qC85vqkK4p1KKZqUGSAY0vt3xO0IEgNe1DkxSJqCIG8Zudhh5L9S6oMqoG/BFrs8AsRh1JrAJ18nODT1cesfaSkBk2SmkjSDyIiMWDAADVguYzNJ/0S69Spk+mO6dOnD3bt2oXbt2+rsmXLlvvmnzNnjhp6J23ZsGEDdzblGAZpRBZKxqkycH3CNU+/zcbAws5G1exJ/zmLrp2cdUMllpDU9/Le8rq5qAzJcXPDTUSdiIIlC/41WA2+XbhRYXjW9szT15YaXYNbf96y2JsGRJTzOnbsiEmTJmHMmDGoWbOmysq5adOmTBPeNG7cGIsWLUKTJk3QoEEDNdC6jINXvHjxdPNJUCZDNRhKly5d+PFRjmGQRmQF7DztVBa7PA0sCjmoFPGWHliImHMxKuOjDCFQok+JrA27kEN9pyTLZPSFaIQu+69m1FKlxKekDr6dpKkhGewL2edZrW7aoFCS2BARGQwaNAizZs1SwyecOXNGDZcQExOD3r17m9xJ3bp1w/Tp01UwJ0M8SM2aDBXRrFmzdPPFx8cjNDTUWO7evZvpTnd0dISHh0e6QvQgDNKIrICM5yRZHwvUK5Drr1XslWKpgcW5aDXYsrWQYQ1k3CzJnCkZH3ObZERUzUUjkxAwLUD3g5VnlQy+LcMw2Lvbo2Tf1NrW3CS1kP7v+qvmokRE9/1GODigVq1a2Lp1q3GaNE2Ux1JLlhWurq5qPdL0MWONmwRnZ8+exbRp01C4cOFM1zFixAhEREQYS2Cg5fU/przFII3ICsRcikFKYgr8evvBuWTuZdcr+ExBFGtXDIl3EhEwPUD343hlhwwdcH3KdZUEQ2UHrJ97Aa9TcSeUHFAydSiAGTeQdMdym4uaompY/4mCW0U3FO+ZvnlQTrJxtIH/+/5qMPiIYxG59jp0Pxn0+Z133rlv+rFjx9ChQwfV9Gvv3r33jaeWUdWqVbF+/XruYso1RYsWhb29vQqm0pLHcpxmxYQJE9TA52kDvY0bN6JHjx6qdm3YsGFqfD9p/ig1bqaMHz8enp6exuLn5/eY74ysHYM0IiuQHJ2MoHlBKque/3v+udKvSjIQFu9VXDVpuzb5mkX3Q8tM0r0kFagZAl5pRpfT5LMpNbAU7FztVB+uqNOW31z0Phpw/cfriA+OV+P7FW1TNOdfwxYqk6QMW3Dv4D2VYZTyzi+//IJevXqlmya1Fb6+vli7di0+/fRTTJ06VdVYPMjJkydVkzHp+0OkRxKAde7cWd18kGPVYMmSJepYP3XqFFavXo22bduibt26qnYtswHQIyMj0xWiB2GQRmQl7u6+i1tbb8GxmCNKDykNO7ecC9ScSzmj1IelVBZJSbIRd828Az/ndnM9eY+STl6CKXnvOUU+E/ls5DOSz+r2n5Y3bEF2ErJcm3QNSRFJ8HndBwWfLZij6/d7ww+eNT0RczlGjdOWnxw8eFAlMsjNIq/xIGvWrEHJkiVVTZiB9O+ZP38+7Ozs0KlTJyxfvlxNf/LJJ9U6y5Qpox4PHjxY1TgYatkkQUPfvn1zdZ9R/hUeHo6kpCR4e6dvxi6PQ0JCHrisHKvDhw9H8+bN1Q2FB5HMkTdv3kS5cuVyZLuJzD/QEhHlGKmZkZqagvUKotSgUrj6zVWkxD5em0SnEk6pQZ+rnRr8WVKtW7uIAxEIdgtWTfVKDy6NKxOvIP7G4w3Ubetii1KDS8HF3wV3999Vn5W1S7iZgGvfX1PHj9RMSg3b3T2Zd6zPEhvAt5uvqqGLC4pTgaDU7uYn0kSrRIkSZt0GuehdsGCBCsw+/PBDODk5qcx2zzzzjEpVbkh1Ls6fP48hQ4Zg6dKl+Oijj1QzSalxMNSySbNIqXUjyg2JiYk4fPiwapYoNV5CbhDI4x9//DHT5eSY/fjjj9GiRQu1/MNI88UiRYogONj6f9spbzBII7Im0sdp5g1V4yW1DE+MfALXvrum+lk9CulTJH1+VNO8xcFWXfOT0e3tt1VgJYNcy368/sN1RJ+NfqR1SZbD0oNKq/6CEUci1GeUX1LEx16KVYGUBLtqiAN3OzXO36OQJCR+ffxQsEFBxIfG49o315AcZSUZV7LhYXf/8+o1pMnjzp07MXToULzyyisqa54kUJCmYRn7/yxevFg1aZS053JxLLUbaV9L+g1JoJe2ORlRTpH0+/PmzcOhQ4dw4MABDBw4EG5ubmqsMyHPSSKPkSNHqsdyTI8dOxZdu3bF1atXjbVwUVFRiI6OVsuOGjVK1RbL8Vu2bFlMnDgRFy9eVMc4UU5gkEZkBdJ1zk+GyhYoF8RyMfvEp08gYGqAylyYHYWbFYZPZx91YSwDPt/eln8CNANJyy+1NL7/81W1YCG/hajgLTukX5uMKSdDFtzde1cNWG0tmRyzKuZ8DK5+exWlPigF3y6+KnFK8MJgaIlatrI4yn6UvpGx12Nx7dtrqg+hwcMSVFiTBw3Cm5ckKJOL0nbt2qkaNQnahKQ2d3ZO30xYmkA+9dRTKjtexoQJMq/UzEmfHaLcILW4MiaaBF5SEy0Jblq2bImwsDD1vL+/P1JS/quR79+/v7ppYGiyazB69Gg11lpycjKqVauGnj17omDBgiqpiIyjJn0xeRxTTmGQRmSFZJwqqa1JCE9Q2RjLjCyD8A3huLn2JlLiHtw0zKGogwpKPGt4Ijk2WWUfjDhs/U0cMyPBqSRJ8XvLTzV/dK/mjuDfgpF488G1k7bOtvBq54WirYqq9PCy70NXhOabGjRTgdqlsZdU30YZ7FoGnw6cHYiYCw+5eWADFGxYUN0wkLT+kccjEfBTgOrzRuYngZnUPpQvXx7t27dX006cOIEKFSqkm++rr75S401JNrzt27er5mOXLl1Sz1WqVEklX3hYkhGixyFNajNrVpsxcY2h/2Rm4uLiVJBHlJsYpBFZqIde0GhA2PIwxF6MRfHexeHVxguFniuEW9tu4d7ee0gIS3PX2hZwKeOi+vlImn1pLhl7NVal2U8I5d1tCVLjbsSpmhwJXmWMM0nUcmf3HZVoJO1QBI7ejqoGs3CTwrAvYK8SZ0gikqiTzD4ox5IEar5dfVHo2UJ44uMnVNB1e+dttX/S1qxJ30rZ10VeLKKaiaYkpagBvyW9/8MCXV7s5x3JcDd58mT1vzQDE9I8TJo7Vq5cGf/88w/atGmjLmilH5r0U5OBhaVmQ/qvSfNGeW7ZsmV5uNVERPrHII3IyslF8MWRF1WtjjRh9O7grYoED4l3E1Utj0MRB9i5pGaDlCZkIatC1IWzNY2DllMBRqFGheDd3lsFYVKktjHxVqKqvZQmjRKYCUnjH74pHGGrw1jrk4bUgEk2xnv776lBw2XwcCkyTp3cOJCaXgnQpHmjYYBqGQMtZEkIEoJ5w0BvpI+Oh4fHfdOl5mzAgAF499131ZhqUgwkIDMEZTJA8KuvvoqmTZvm6XYTEekdgzSifDKOWsjiEFULIbU87lXdVc2ZZBqUi2MJ1iJPRCLyaKTK3igBB5mQAtzZfkfVokliFs9annAp6wInXyfVd08C38iTkapW6O7fd/NlUouskn0kRZLTFKhXAK7lXOHo6whbe1sV+EpNrox9dm/fPcQHMZmEpZEgTJItSF/BB9VsSrMySXF+69ajJZMhIrJWDNKI8pHkyGTc2nxLFcWQa4ExWbZIszypCZKSbtRJ1jxmm2TMTJc1U45JHo9WIStp9SU9vxQiIkqPQRpRfsaL4ZzDAC1n8Ji8f5f8WxNlb89TtiWSLIFCMgISEWUVf/GJiIh07ObNm2pA3g4dOmDlypUqXT3pnww7UKxYMXTs2FFlA8yL8e2IyHowSCMiItIxyYj43Xff4cMPP1RjM5FlkQG+x48fz+CaiLKFQRoREZHOyThikilRBuTNTwN3W3oz1YiICNy7d4/DQhBRtjFII7ICvGij/C4/fAekRu369evm3gwiIsoDko+MiCwQB+wl4neDiIisE4M0IiIiIiIiHWGQRkREREREpCMM0oiIiIiIiHSEQRoREREREZGOMEgjIiIiIiLSEQZpREREREREOsIgjYiIiIiISEcYpBFZgfwwkC/Rg/A7QERE1oRBGhERERERkY4wSCOyUJqmmXsTiHSJ3w0iIrJ0DNKIiIiIiIh0RBdB2oABA3DlyhXExsZi3759qFOnTqbz9unTB7t27cLt27dV2bJly33zz5kzR91JTVs2bNiQB++EiIiIiIjIwoO0jh07YtKkSRgzZgxq1qyJ48ePY9OmTfDy8jI5f+PGjbFo0SI0adIEDRo0QEBAADZv3ozixYunm0+CMh8fH2Pp0qVLHr0jIiIiIiIiCw7SBg0ahFmzZmHu3Lk4c+YM+vXrh5iYGPTu3dvk/N26dcP06dNVMHfu3DlVs2Zra4tmzZqlmy8+Ph6hoaHGcvfu3Tx6R0RERERERBYapDk4OKBWrVrYunWrcZo0TZTHUkuWFa6urmo90vQxY42bBGdnz57FtGnTULhw4UzX4ejoCA8Pj3SFiIiIiIgo3wVpRYsWhb29vQqm0pLH0kQxKyZMmICgoKB0gd7GjRvRo0cPVbs2bNgwNGrUSDV/lBo3U0aMGIGIiAhjCQwMfMx3RkRERERE9GjsYcEkAOvcubOqNZPmjQZLliwx/n3q1CmcOHECly9fVvP9+eef961n/Pjxql+cgdSkMVAjIiIiIqJ8V5MWHh6OpKQkeHt7p5suj0NCQh647ODBgzF8+HA0b94cJ0+efOC8kjny5s2bKFeunMnnExISEBkZma4QWRIbGxtzbwKRWfE7QERE1sSsQVpiYiIOHz6cLumHnGjl8d69ezNdbsiQIfj000/RsmVLtfzD+Pn5oUiRIggODs6xbScyNw7YS8TvBhERWSezZ3eUZoZvvfWW6kNWsWJFlbnRzc1NjXUm5s2bh3HjxhnnHzp0KD7//HOV/fHq1auq1k2KLCPk/4kTJ6JevXooVaoUmjZtitWrV+PixYsqtT8REREREZGemb1P2tKlS9WYaGPHjlXJQo4dO6ZqyMLCwtTz/v7+SElJMc7fv39/ODk5Yfny5enWM3r0aDXWWnJyMqpVq4aePXuiYMGCKqmIjKMmNW/SrJGIiIiIiEjPzB6kialTp6piigxanVaZMmUeuK64uDgV5BEREREREVkiszd3JCIiIiIiov8wSCMiIiIiItIRBmlEREREREQ6wiCNiIiIiIhIRxikEVkBDuRL+R2/A0REZE0YpBEREREREekIgzQiC6Vpmrk3gUiX+N0gIiJLxyCNiIiIiIhIRxikERERERER6QiDNCIiIiIiIh1hkEZERERERKQjDNKIiIiIiIh0hEEaERERERGRjjBIIyIiIiIi0hEGaURWwMbGxtybQGRW/A4QEZE1YZBGZKE4YC8RvxtERGSdGKQRERERERHpCIM0IiIiIiIiHWGQRkREREREpCMM0oiIiIiIiHSEQRoREREREZGOMEgjIiIiIiLSEQZpREREREREOsIgjcgKcCBfyu/4HSAiImvCII2IiIiIiEhHGKQRWShN08y9CUS6xO8GERFZOgZpREREREREOsIgjYiIiIiISEcYpBEREREREekIgzQiIiIiIiIdYZBGRERERESkIwzSiIiIiIiIdIRBGhERERERkY4wSCOyAjY2NubeBCKz4neAiIisCYM0IgvFAXuJ+N0goqwZMGAArly5gtjYWOzbtw916tTJdN4+ffpg165duH37tipbtmwxOf+YMWMQFBSEmJgYNU+5cuX4cVCOYZBGRERERFarY8eOmDRpkgqqatasiePHj2PTpk3w8vIyOX/jxo2xaNEiNGnSBA0aNEBAQAA2b96M4sWLG+cZOnQo3n//ffTr1w/16tVDdHS0WqeTk1MevjOydhpL+n3g4eGhCfmf+4bHh16PgcKFC2sGa9euNfv2sHAfmPMY+Oijj4zfhw4dOvB45PGo62OA1xl5u7/37dunTZkyxfjYxsZGu3HjhjZs2LAsLW9ra6vdu3dP6969u3FaUFCQNnjwYONjT09PLTY2VuvUqROPAR18x6zhO8uaNCIiIiKySg4ODqhVqxa2bt2arruAPJZasqxwdXVV65Gmj6JMmTLw9fVNt86IiAjs378/03U6OjrCw8MjXSF6EAZpRERERGSVihYtCnt7e4SGhqabLo99fHyytI4JEyaovmeGoMywXHbWOWLECBXIGUpgYOAjviPKLxikERERERGZMGzYMHTu3BkdOnRAfHz8I++j8ePHw9PT01j8/Py4v+mBGKQRERERkVUKDw9HUlISvL29002XxyEhIQ9cdvDgwRg+fDiaN2+OkydPGqcblsvOOhMSEhAZGZmuED0IgzQiIiIiskqJiYk4fPgwmjVrlm5cRXm8d+/eTJcbMmQIPv30U7Rs2VItn5ak8g8ODk63TuljJlkeH7ROouywz9bcRKRLHMiX8jt+B4goM5J+f968eTh06BAOHDiAgQMHws3NDXPmzFHPy3PSR2zkyJHG9Ppjx45F165dcfXqVWONWVRUlEq1LyZPnoxPPvkEFy5cUEHb559/rvqtrVq1ih8E5QgGaURERERktZYuXarGRJPASxJ7HDt2TNWQhYWFqef9/f2RkpJinL9///5qvLPly5enW8/o0aPVWGti4sSJKtCbOXMmChYsiN27d6t1Pk6/NaK0GKQRWShJIUxE/G4Q0cNNnTpVFVNk0Oq0JMV+VowaNUoVotzAPmlEREREREQ6wiCNiIiIiIhIRxikERERERER6QiDNCIiIiIiIh1hkEZERERERKQjDNKIiIiIiIh0hEEaERERERGRjjBII7ICNjY25t4EIrPid4CIiKwJgzQiC8XBrIn43SAiIuvEII2IiIiIiEhHGKQRERERERHpCIM0IiIiIiIiHWGQRkREREREpCMM0oiIiIiIiHSEQRoREREREZGO6CJIGzBgAK5cuYLY2Fjs27cPderUyXTePn36YNeuXbh9+7YqW7ZsMTn/mDFjEBQUhJiYGDVPuXLlcvldEBERERERWUGQ1rFjR0yaNEkFVTVr1sTx48exadMmeHl5mZy/cePGWLRoEZo0aYIGDRogICAAmzdvRvHixY3zDB06FO+//z769euHevXqITo6Wq3TyckpD98ZUd7hQL6U3/E7QERE1kYzZ9m3b582ZcoU42MbGxvtxo0b2rBhw7K0vK2trXbv3j2te/fuxmlBQUHa4MGDjY89PT212NhYrVOnTllap4eHhybkf3PvHxbug8yOgYIFC2oG69ev57HCYyVfHwNyzjB4+eWXzb49LNwHDzoGeJ3B44PHgGUdAx5miA3MWpPm4OCAWrVqYevWrf9FjJqmHkstWVa4urqq9UjTR1GmTBn4+vqmW2dERAT279+f6TodHR3h4eGRrhDpnXxXiIjfDSIisj5mDdKKFi0Ke3t7hIaGppsuj318fLK0jgkTJqi+Z4agzLBcdtY5YsQIFcgZSmBg4CO+IyIiIiIiIgvvk/Y4hg0bhs6dO6NDhw6Ij49/5PWMHz8enp6exuLn55ej20lERERERGQRQVp4eDiSkpLg7e2dbro8DgkJeeCygwcPxvDhw9G8eXOcPHnSON2wXHbWmZCQgMjIyHSFiIiIiIgo3wVpiYmJOHz4MJo1a5YuQ5c83rt3b6bLDRkyBJ9++ilatmyplk9LUvkHBwenW6f0MZMsjw9aJxERERERkR7Ym3sDJP3+vHnzcOjQIRw4cAADBw6Em5sb5syZo56X56SP2MiRI43p9ceOHYuuXbvi6tWrxhqzqKgolWpfTJ48GZ988gkuXLiggrbPP/9c9VtbtWqVGd8pERERERGRBQRpS5cuVWOiSeAliT2OHTumasjCwsLU8/7+/khJSTHO379/fzXe2fLly9OtZ/To0WqsNTFx4kQV6M2cORMFCxbE7t271Tofp98aERERERFRvgjSxNSpU1UxRQatTktS7GfFqFGjVCEiIiIi0qPqZYshOsrV3JtBD+Hm7o58GaQR0eORvpxE+Rm/A0Rkif6a1A1IZksv3bNzyvOXZJBGZKE4mDURvxtEZNmeG7QQ0VFR5t4MykJN2l9HRyMvMUgjIqWklyfK+RVCYQ9n9fhedDwuBt3BtdB70DTuJHOxs7XBE74FVXF3cVSfRdjdaFwIvIPQO6nJkoiIyDIdvxTGoZ8sgIdHTJ6/JoM0onzK3s4WbeuXQ4eGT6JVnSfgVdB0m/i7UXHYcuQqVu4+j+W7zyEhMTnPtzW/kWCsS5NKaFe/PJo+7Q83F0eT810Pu4f1By7j911nsf3YNQbTREREVoJBGlE+4+JkjwHtauKDDrVRspinmnYnMg6bDl3Gmeu3cCsiVl3sS41ahZKFUbdCcbz+fEVVwu5EY9rao5i0/AAiYxLM/VasTrGCrhjZ9Rn0al4Vnm6p7d8DwyOx6fAVVXMWERMPO1tbeBdyxVOlvVC7vA/6ta2hypnr4fh66QHM33ISySms+iQiIspXQVr37t3TPZb0+Ddv3sRff/2F2NjYnNw2IsphEmh9/XYTlPIuoGrE5m85hbmbT+KvkwFISv5vqIu0bG1tULeCL3q1qIZuzapgdI9nMaBdDXwydxd+3nCctTc5wMHeFkM71sfwzvVVLdrtiFh88/t+LNh6Gicupw5HYoqTgx1a1H4CvVpUxUsNymP2R60x6NU6eH/aVlWzRkRERPkkSPv+++/TPbazs4O7u7sK1Jo2bYp//vknJ7ePiHKANGX8ZVBrtGtQDikpGmb8cRRjF+5B8K2Hd1aW+fedCVJlxC87MKJLA7z3ci3M/LAVOjaqhDe/XY/rYRH8nB4j/fK8IW3V//ei4zBy9k58v/IQYuISH7psfGIy1uy9oIrUeo7t+Zz6TP78ugtmrjuGD2dsy9J6iIiISF9ss7tA4cKF05UCBQrA19dXDRg9efLk3NlKInpkzWqUwomfeqsA7eC5YNQcMAf9v9+UpQAto9uRcRgyczuqvPUzdp0IwAs1S+PkzDfx8jPl+Qk9AmmmeGBKTxWgLdt1FuXfmInxi/Y+UmB1LuA2On2xGk2HLMLFwDt4u83TODLtDbVuIiIisvIgrWrVqvcVb29vzJ49G40aNUKdOnWM04nIvN55uSY2ju+EYgXd8OVvf+OZDxaoTFKP61LQXTT+6FcMmrFN9XFbNeZVVYvD4dqyRpop/jyoFaZ/0AJxCUnoMm41Xv98FW7effzsUdLMsUb/OZi98QQqlCyCPd91YxBNRERk7c0djx07psZnMjVwqEzft2+f8W97e+YlIcoLGb+P0o9syjsvYsBLNVUTOqlh2XToSo6+piQX+W75QRw4G4xln7XHp90aqhT+PSf+gcQk0/3bCCjg5oS1n7+G56qWxNnrt9BhzAr1f06Kik1QzVD/OhWAnz5oqYLoYT9vx8Ql+632I+Bg1kREZE2yHUWVKVPG5PTSpUtjy5YtqFatGhOIEJk5CcXC4e1U3yRp9tbus2U5HgSktef0DdQaMBfrv+yILk0qo6inC14Zs1IFCpSedyE3bBrfSTVBlGyaHT9frTI25pa5m06qY2Dl6FcwoU8TFPV0xdBZ2/mxEBERWVtzxzt37qQr9+7dQ6FChfDJJ59g06ZNOHfuHK5fv64KEeUeqa021Yxu+WevqADt6MVQNPhgfq4GaAZBt6LQaPCv2HniOl6sVQZbJnSCp2tqCnlK5V/ME7u/66YCtMXb/0G7T5flaoBmsPvUDTT4YIEaU21Ix3qY9n5zq2+Wauq7QUREZNVB2t27d9MFabdu3cKRI0fg6emJd955J3e2kogeytnRXjWjkwQhe/8JRJOPfkP4vbwbFuNedDxaDF+iMg3Wr+SHDeNeV+nkCfAr6qEyLkpz0GlrjuB/X63N0yahUpv23Ie/4kLgbfRvVxM/D2pt9YEaERFRvmru2KRJk3SPk5OTVa1ZQEBATm4XEWWzP86ST15WtVg7jl9XtTTmaG4oKeElAcbyzzqgbf1yWP/l62g1cimi83EaeGniuG1iZ5QtXghTVh3G+1O3mGU7ZJiE5wf9qoLF3i2rqePjg2lbzbItRERElMNB2q5du7K7CBHlsqdKF0Vx2/LYdyYQbT/53axBkQyS/drYlaofVKu6ZbF67Kto/fHvanp+U8TTBVsndFZZFmetP4YPppknQDMIuR2NF4Yuxl/fdcP7HWojMjYBn8zhbzoREZHFN3ckIv0pXsQdJ6+EqWBID7VWUqPWYfQK/Hn0GprVKI35Q9vmu+Z1MjTBui9ex1NlvLBg6yn0+36TyohpbtJ/sNnQRQgMj8THXZ/B0E71zL1JRERElAGDNCIrIIMfNx++BHci46AXEqi1H71cJTDp1LgSJvd/AfmFna0NFn/8MupVKq766PX6eh1SUnQQof3rasg9vDBssRqXTbI+/q9ZFXNvEhEREaXBII3IAtnb2eLrvk2Njw9dCFFN2fQmMiZB9Um7HHxXNa8b3rk+8oMf3nkRLzUoj/1ngtBl3Bok6yhAM5Csn20++V0F+LMHt0aTp0uZe5OIiIgou0HamDFjULNmzazOTkS5pKJ/Eez8tiv6tn7aOC02Pkm3+zv0TjRajFiCsDvRGP9mY/R48SlYM2k+KIOIG8aokyBIrw6eC0bncatVzd/K0R3wVGkvc28SERERZSdIK1GiBDZs2KCyOE6bNg0tW7aEg4MDdyJRHqlRzhs/D2qFkzPfxDNVSmDz4SvpsjvqmQQsrT/5XWUUlPfwYq3SsEZdm1ZWzQelGWGrj5eq//Vu7d6LeG/qFhRwc1bZOGW4AEuk9+8AERFRrgRpb775Jnx8fNClSxdERkZi8uTJCA8Px7Jly9C9e3c1oDUR5Qyp2ajkXwQdG1VUTefOzXkbR6b3wputqiPkdhR6TPgDr41dYVG7+/D5EHT8YpW6mJYU/U+X9YY1keaCcz5qg9j4RFWDJoGppZi+9igmLNmHksU8VbITSx+InINZExFRvkrBLye+3bt3qzJs2DBUrFgR7dq1Q9++fTFz5kwcOHAAa9aswaJFixAUFJR7W23h3Jwd0PCpEumm2WThrnDGSTZ4+Dym1mVyngzryt31PHgZk/NkYX9k/fXNuz8c7e3g6uwAVyd7uDo5qCyAckx4FXCFT2E3+BZ2V8XRwc64nKSv33rkKn7ZeBwrdp9Xj93d3WFpNhy4jH7fb1SDKUutTf3356vxuyxd5VJFsWJUBxVcv/75GtUXzdKM+GUH/It5okuTylj2WXuVKTQpOe8G3NYLJwc7eLo5wdnBHvZ2NnCwt4ODva3qB+pgl/q/lLS/AYbvvnzfjX/f95zp6aRfZ6/fRsBNy/99IqJ8Mk5aWmfPnlXl66+/RtGiRfHSSy+pIr799tuc2karU8q7ADaN72TuzSCduhcdh0vBd/DPtVs4eeUmDl8IUQNUm2Nw6tzwy4YTKOnliVHdn8XG8R3RcOBCXWWlzC4JrCXgLOjujHd/3KyyOVoiGR7gja/XqeEcZFD0mR+2RO9v1sOayI0PGVNQanElsC5R1AMlvDzUTZECbk7wdHVUQRmReGfKZkxbc4Q7g4gsL0hLS5o+zp49WxV6yL66F4Pxi/beN13D/RngMo6rZKoZj6mxl0zlksu4rMnlTK0fj7oNOfl+HnHbM77e/YtlfRsy7r9HXFdCUjJi4hMRE5eU+r/6OxHhEbEqyYaek4DklNHzd6tArXfLalg95lW8OGyxStlvaaRGdO3nr6kbL98uO4Cpqy37gi7h3/Ht9kzuhl4tqqlU/WMX7oElc3dxROfGldC+YXk0qV5KfWYZRcbE405UnGpKHBGToAb5lu+h1CQmJiUjMTnl379TkJicjOTk/36RDN95w/dcHj/oOfV/hudJn45cCDH3JhBRPpZjQRplXdjdGIycvZO7jPK1vpM3qlqblnWewILh7dDpi1W6GOw5q2xtbbBo5Euo/aQvlv91DkNm/glrILWa0tRx7/fdMabnc7gWFoF5m0/C0kjN2IguDdC/bQ3VfFEEhEVgxe5zOHopDKeu3sS10HsIDI+ymlpqIiKyHgzSiMgspGbi9c9XqeEEXn++IgLeborBP1lOoCODc8tYaPvOBKL7hLUWFWA+jNSgtf10GXZ+0xWzPmyJwPBI1SfSUtR+0geze76NYoXccDsiFt/8vh/zNp9SgRkREZEl4GDWRGQ2UoMhAypLUDDotboY+Eodi/g0PuhQG++1r6UG6X7ps+VW2URVsnF2+nI1bP/Nxlm1jOWMoTa6x3Mo4umCr5fuR5nuMzBk5nYGaEREZN1Bmqura+5sCRHlSyG3o9WYYlLj8V3/ZqpWTc9ee74CJvVrpra3tYWMhfao1u2/hAFTNqvmgpY0htrdqDg0HboIQ2dtR0RMvLk3h4iIKPeDtNDQUPzyyy9o2LBh9l+NiHKFpQ/ke/b6LVUjFZeQhAXD2uK5qiWhRzII96/DX1LJXzqMWYFzAbdh7WauO6YSHZXw8lSBml7HUGtY5b9jRvr87joRYNbtISIiytMgrVu3bihcuDD+/PNPnDt3To2X5uvr+1gbQUS05/QN/G/8WpUCXTI+ymDeelKvUnGsHPWKShgig3LnpyDg4zk78dufp1HtiWJYPfZVNbafnvRpVR2t6z1hfGwNY+8REVH+lu0gbfXq1ejQoQP8/PwwY8YMdO3aFdeuXcPatWvVdDs7jjFDlBesMX23ZN77cMY2FPJwxoZxHeFbRB8DdlcpXRTrv3gdbi6OePPb9Vi79yLyEznUen2zHlsOX0Hj6v5YNeZVNeizHsjg2z8NbKlqYa35u0FERPmL7eOMi/bdd9+hevXqGDRoEF544QUsW7YMQUFBGDNmDFxcXHJ2S4koX/hh5SE15piMPbZtYmezB2oSoG2b2AWFPV3w4fRtmL/lFPIjGUOt/egV2HniOprXKoPfP+0AB3vz5p56+ZnymD+sbWoz2a2nzbotREREOemRz7DFihXDkCFDcPr0aXz11VcqQGvWrBkGDx6MV155BatWrcrRDSWi/EPGHJu98QQq+RdVKfpLeJknYYVkNNz+dVd4F3LDJ3N2YfKKg8jPZND1tp8sw95/AtGuQTks/aS92WrUOjaqiN8/bY+UFE31D5Qxz4iIiPJtkCZNGtesWYOAgADV1HHatGmq6WP37t2xY8cOLFy4EC+//DIaN26cO1tMRFZPWqv1mbQeM/44ivJ+hbHz2/+htE+BPB9ra/s3XeFV0BXDf96BL3/7O09fX8/DJrQauRQHzwWjfcMnse7L1+Hu4pin29CrRTUsGvmyGmuv/ejl2HzoSp6+PhERke6CtDlz5qgmjZLdsUaNGpg6dSru3Ut/B1Oe//LLL3NyO4koHwZq/b/fpJo/PuFbEHu/7446FfImSZHUEu34pqsaa0sG2J6wZF+evK6luBcdj6ZDFuHPo9fQrEZp/Pl1FxXM5oXhnetj9ketER0nweLv2HDgcp68LhERka6DNMnk2K9fPxw6dCjTeeLi4jB27NjH3TYiInwwbStGzfsLPoXdVeD0yrMVcnWvvN+htsri6Ohghx4T/sCkZQf4KWRSoybjxK3cfV4Fzwd/7Ika5bxzbV9Js0rpfzb+zcYIvxeDF4cvUf3jiIiIrFG2gzR7e3t4eHjcV9zd3eHg4JA7W0lE+drYhXvQ7au1sLezxfJRHfBt36Y5nrTCw9URiz9+Gd8PeAFRcQloOXIpFmzNn0lCsio+MRmvf77SmOhlz+Ru6PHiUzn+OmWLF8SuSf9D9xeewqkrN1Hn3XnYfyYox1+HiIhIL7J9lXP37l3cuXPnviLTY2NjcfXqVYwePdriB9clIn35ddtpNBnyGwLCIjDotbr4+/vuKrFHTpC08kem9UKnxpVw/FIY6r47XzXlo4dLTtHw0U9/qiBazBvaFss+65BjzR97t6yGYzN6o27F4lj99wU8M3ABroYwSQgREVm3bI9I+sYbb6j+ZnPnzsWBA6nNgOrWrYuePXviiy++gJeXFz766CPEx8dj/PjxubHNRJRBfrkp8vfpQDzdbzZmf9RGpV8/Mr2X6rP2xW9/405kXLbXV9LLE2PfeA5vNK+qHv/0x1EMnL4t3ZhblPUg+sTlMBWkvfpcBRX4Sg3o9LVHkJiUku3dWLO8N35450U0rFICsfGJGPDDJkxfexT5/TtARET5h5adsnXrVu3111+/b7pMk+fk727dumlnzpzJ1nr1VDw8PDQh/5t7W1i4DzI7BlxdXTWDLVu25LtjpWOjilrg4nc0bctwLWL1h9qEPo218n6FsrRszfLe2owPWmhx6z5Sy1+Y21dr8nQps78naygO9rbaqO7ParH/7tsrC/prg1+rqxX2cH7osna2NtqLtUpr6798XS0rZevEzlpF/yIPXfaTTz4xfh9atWpl9v3Awn3woGOA1xk8PngMWNYx4GGG2CDbNWnPPPOMShyS0dGjR9GgQQP19+7du+Hv758zISQRkQlLd57FhoOX8dHr9fDey7UwtFN9VY5cCMH249dx9GIoAsMjVb8pFyd7lPYuoBJbvFCjNCr6F1HrCL4VhXGL9mLW+mNqPnp8Ums2ZsFuNc6d1FJ2a1YF3/Rtiq/6NMae0zdUM9J/rocj9E4MEpOSUcjDWWXvrFuhOFrVecLYTPLYpVBVEyeJSYiIHteAAQPU+L4+Pj44fvw43nvvPRw8aHrsy8qVK6sEeLVq1ULp0qUxcOBAfP/99+nmGTVqlOrek9bZs2dRqVIlfliUI7IdpMn4aG+++SZGjBiRbrpMk+dEkSJFVD81IqLcFBmToDI/fvP7fpVUokuTSnj2qZKoWd4n02VkbK1tR6+qIGLF7vNs2phLAm5GoNfX6/Dx7J14u83TavDpRtX8VclMRHQ8Fm49hflbT2HL4au5tWlElM907NgRkyZNUpUM+/fvV0HXpk2bUKFCBdy8efO++V1dXXH58mX8/vvv+O677zJd76lTp/DCCy8YHyclsak8mTFIk/5mctC2atXKeAeidu3aqFixIl577TX1uE6dOliyZEkObiYR0YODtWlrjqhStIAL6lfyQ+VSReBb2F1lgYxPSMb1sAicDbiFPacDVfp4yhtBt6Iwev5uVWRA8roVfFGxZBFVgyZp9e9GxeNGeCQOXwhRtZ8JrNEkohw2aNAgzJo1S+VTEBKstWnTBr1798aECRPum1+GmTIMNfXVV19lul4JykJDQ/l5kT6CtLVr16o7D3379lX/iw0bNqB9+/a4di01G9qMGTNyfkuJiLIg/F4s/th3URXSF8nKyMyMRJSXZHgoabaYNpmdpmnYunWrsZvOoypfvjwCAwPV+MB79+5VrcwMrcoycnR0hJOTk/GxDF9FlGNBmoyRtnHjRnUHYuTIkdlZlIiIiIgoTxUtWlRdv2as8ZLH0grsUUmzScl4fu7cOfj6+qo+an/99ReeeuopREVF3Te/BHAZ+7AR5dg4aVKtW61atewsQkRERERkVaTSYtmyZTh58iQ2b96M1q1bo2DBgqr/mylSk+fp6Wksfn5+eb7NZOWDWS9cuFAlCSEiIiIi0rPw8HBVyeDt7Z1uujwOCQnJsde5d+8ezp8/j3Llypl8PiEhAZGRkekKUY72SZMqY+loKdlsDh8+jOjo6HTPDx48OLurJKLHxIF8Kb/jd4CITElMTFTXq82aNcPq1auNvxfy+Mcff8yxnebm5oayZctiwYIF/CDIPEGatLU9cuSI+vvJJ59M95x0xCQiIiIi0gtJvz9v3jyVsfHAgQMqBb8EVXPmzFHPy3OSAMSQb0GSjchYaYaEH9I0sXr16qqv2aVLl9T0r7/+WiXTk6R5xYsXx5gxY5CcnIxFixaZ8Z1Svg7SmjZtmjtbQkTZwpsiRPxuENHDLV26FF5eXmqAahnM+tixY2jZsiXCwsLU8/7+/khJSTHOL0GXzGMgg2BL2bFjB5o0aaKmlShRQgVkMjawjLW2e/du1K9fXzWvJDJLkGYgVbpSdu3apVKPEhERERHp0dSpU1UxxRB4GUjt2MOaUHfp0iVHt4/osROHFC5cWI0tIZ0j169fr9KOil9++QXffPNNdldHREREREREjxOkfffdd6oTplQNx8TEGKcvWbJEVR0TERERERFRHjZ3bN68OVq0aKE6WKZ14cIFlCpV6jE2hYiIiIiIiLJdkybZcNLWoKVtBhkfH889SkRERERElJdB2l9//YUePXqkyzAnnSuHDh2K7du3P862EBERERER5XvZbu4owdi2bdtQu3ZtNXbExIkTUaVKFVWT1rBhw3y/Q4mIiIiIiPK0Ju306dNqEGsZD0JGbpfmjytWrECNGjVw+fLlx9oYIno0D0sVTGTt+B0gIiLk93HSIiIiMG7cuJzfGiLKMg5mTcTvBhERWadHCtIKFCiAunXrolixYrC1TV8Zt2DBgpzaNiIiIiIionwn280d27Zti+vXr2Pjxo348ccf8f333xvL5MmTs70BAwYMwJUrVxAbG4t9+/ahTp06mc5buXJlLFu2TM0vtQgffPDBffOMGjVKPZe2nDlzJtvbRUREREREZBFB2rfffovZs2fD3d0dhQoVUglDDKVIkSLZWlfHjh0xadIkjBkzBjVr1sTx48exadMmeHl5mZzf1dVV9XsbPnw4goODM13vqVOn4OPjYyzPPvtsdt8mERERERGRZQRpfn5++OGHH1TN1+MaNGgQZs2ahblz56rarn79+qkx2Hr37m1y/kOHDqnskkuWLHngmGxJSUkIDQ01llu3bj32thIREREREekySJOaLkm//7gcHBxQq1YtbN261ThNmibK4wYNGjzWusuXL4/AwEBcunQJCxcuRMmSJR84vwwl4OHhka4QERERERFZROKQdevW4euvv1b9w06ePInExMR0z69duzZL6ylatCjs7e1VTVda8rhixYp4VPv378cbb7yBc+fOwdfXV/VRkwG4n3rqKURFRZlcZsSIERg9evQjvyYREREREZHZgjRpnig+++yz+56TmjAJvMxJEpoYSBApQdu1a9dU/zfpS2fK+PHjVd84A6lJk5o4IiIiIiKivJbtiMrOzi5HXjg8PFz1HfP29k43XR6HhIQgp9y7dw/nz59HuXLlMp0nISFBFSJLxYF8Kb/jd4CIiPJ1n7ScIs0kDx8+jGbNmqU7ycrjvXv35tjruLm5oWzZsg/MBklERERERGRxQZr0RfP09DQ+HjZsmBrU2kBS8J8+fTpbLy5NDN966y306NFD9UObPn26CqrmzJmjnp83bx7GjRuXLtlI9erVVZFkH5JpUv6WIMxA+ss9//zzKFWqlEpAsnLlSiQnJ2PRokXZ2jYivZPmxUTE7wYREeXj5o4tWrSAk5OT8fHIkSOxdOlS1ZxQrcjeHhUqVMjWi8vyMiba2LFj1Xhmx44dQ8uWLREWFqae9/f3R0pKinH+4sWLq3kMhgwZosqOHTvQpEkTNa1EiRIqIJMx227evIndu3ejfv36qnklERERERGR1QRpGdv751T7/6lTp6piiiHwMpAEIA973S5duuTIdhEREREREeWrPmlERERERET0GEGa9H/J2AeGfWKIiIiIiIjM2Nxx7ty5iI+PV4+dnZ0xY8YMREdHq8dp+6sRERERERFRLgdpkmkxrYULF943z/z58x9xM4iIiIiIiChbQVrv3r25x4iIiIiIiHIZE4cQWYGcyrZKZKn4HSAiImvCII3IQjFxDxG/G0REZJ0YpBEREREREekIgzQiIiIiIiIdYZBGRERERESkIwzSiIiIiIiIdIRBGhERERERkY4wSCMiIiIiItIRBmlEREREREQ6wiCNyApwIF/K7/gdICIia8IgjYiIiIiISEcYpBFZKE3TzL0JRLrE7wYREVk6BmlEREREREQ6wiCNiIiIiIhIRxikERERERER6QiDNCIiIiIiIh1hkEZERERERKQjDNKIiIiIiIh0hEEaERERERGRjjBII7ICNjY25t4EIrPid4CIiKwJgzQiC8UBe4n43SAiIuvEII2IiIiIiEhHGKQRERERERHpCIM0IiIiIiIiHWGQRkREREREpCMM0oiIiIiIiHSEQRoREREREZGOMEgjIiIiIiLSEQZpRFaAA/lSfsfvABERWRMGaURERERERDrCII3IQmmaZu5NINIlfjeIiMjSMUgjIiIiIiLSEQZpREREREREOsIgjYiIiIiISEcYpBEREREREekIgzQiIiIiIiIdYZBGRERERESkI/bm3gAisgwFnQH/ArbwcLSBo13qtNuxGm7FagiK1JDCEQHyvULOgJ+nLQq72MDWJnV33I3TEBqlISxaQzKPESIioixhkEZkBWxs/r0iziHO9kDTMvZ4vpQd6vnZoYaPHQo4Z/4asYka/rmZgqMhydh2JQl/XklWF+VkveQYaVLaHk3L2KF28YcfI3FJGk6FpR4j268kYfOlZBXg6/U7QEREZE4M0ogsVE4P2GtnA7Qub4+e1R3Qspw93Bz/u+gNjEjB8dBkXLubgjtxGhKSoWpKpMakmJsNKhSxQw1fW9Qqboc+NR3VMruuJWHhiUT8/k8i7sbl6KaSmcgx0qq8PXo9nXqMuDqkP0YkAAuM0BAem4LklNTpcox4u9miXGEbFcxJeaumI1I0DXuuJ2Pe8dRjJCI+57aTg1kTEZGlY5BGlM9JM8Z36jiiby1HlCyQ2k01KDIFC04kYtOlJOy7kYyQqIcHhK4OQF0/O7zwhD1al5NauNQyuaUz5hxLxOR9Cbh4+98rd7IoBZyAd+s6YkAdRxT3SD1GbkSkHiMbLiRhf2DWjhEPR6hAvnnZ1GPkuVKp5YdWzph7LBHf/B2PK3dZA0tERMQgjSgfB2cf1nfCB/UcVTO1+CQNv51MxE+HE/DXtWRk91I5JhHYcTVZlU/+jEelorboVs0Bb9V0UEFg/9oOWHo6CZ/8GYdLd3ghbinHyJBnnNTnJ8eINGtdeCIBPx9JxK5HOEYiE/47RkZuSz1Gej7toGrmJADsW8sBS/49RhisERFRfsbsjkT5jDRT7FfbARffc8dnjZwgXXm+2BWPEt9F4X8rYh/p4tuUM+Ep+PjPePhPjsLba2NVLVrnpxxw5h13TGnlrJJMkH6bNUpQfeE9d4x8zklN+/Kv1M+y+8o47MzBY2T41niUmhyF/uticfWuhq5VHXD2XXd809xJBYlERDlhwIABuHLlCmJjY7Fv3z7UqVMn03krV66MZcuWqfml+fQHH3zw2Oskyi4GaUT5SIMSdjj8thumt3FRfc7G745H6cmR+HR7PMJjcqd2Ky4JmHUkEVWmRatgTV5Hms6de9cd3as55Mpr0uMdI8f6uWFaGxe4O9pg3F8SREWq2tHcPEZmHEpEhR+j0PePWNyJ1TC4gZMKErtWZYMPIno8HTt2xKRJkzBmzBjUrFkTx48fx6ZNm+Dl5WVyfldXV1y+fBnDhw9HcHBwjqyTKLuk1zfbHWXg4eGBiIgIeHp6IjIyMts7lSgv2NraIjk5Wf29e/duPPfccw/MxPdFUyd8WN8RtjY2WHkmEYM3m6dJmfRd+/g5Jwx5xhEOdjbYdjkJb66JxbV7/CkyJxd74Mtmqc1f5RhZ9k8ihmyJU7Vbec3dERjxrBM+esYRjnY2WH8hEf3+iENARObb8sUXX+Djjz9Wfzdt2hTbt2/Pwy0myh5eZ+QtqeU6ePAg3nvvPWM22ICAAEyZMgUTJkx44LJSUzZ58mR8//33ObbOtMfAc+ULIjqK15p65+bugb8u3M3T2IC3KImsnKTQn9feGRWK2qkMfG//EYv1F5LMtj3Sd02aQf56MhEz2jij2RP2ON7PHe+sj1PTyDy1Z/M7uKBcYVuVEKSvmY+RqITUY0T6SP7ykgtal3fA6QH2GLA+TmUMJSLKKgcHB9SqVQvjx483TpMmjFu3bkWDBg3ybJ2Ojo5wckptPm4I0sRfvd2BeN6k1D0n9zx/SQZpRFZcTT6koSO+bOoEe1sbzD2WgA83xekmHb6Mq9Zobgw+qO+Ir5o5YeErLmj7pL3qm6SXbcwPx8jQho6qllWOkVlHEvDR5rgcTYf/OE7fTMEzs6Pxfj1HjG/mhAUdXNCirB0GrItTSUiIiB6maNGisLe3R2hoaLrp8rhixYp5ts4RI0Zg9OjR901/bnYUoqOiHmk7KO+4udvgrxF5+IIM0oisQ8aBfIu42GB+B2dVA3E7VkOv1TFYc858NSOZkXuHkppfmjz++oqLSiwiNX+vLI3BsRCm689NXq42qUFPOXt1jLyxKgZrz+vvGEnRUo+RrZeTsPhVF3Sr5ogGJezRaVkMDgf/d4xwMGsi0jOpdZM+bGlr0gIDA3E8NAWRkTzf6Z2HR95/RkwcQmRl6v+b+EECtL0BSajxU5QuA7S0ToaloM6saPx4IAFlCtni795u6FGdSUVyS+3ituoYkQBt9/UkPD0jSpcBWlqn/j1GZhxKQNnCttjd200NvE5E9CDh4eFISkqCt7d3uunyOCQkJM/WmZCQoPoypS1ED8IgjchCSfv3jOSidUdPV5TwtMXXf8fj+bkxuG4hCTnik4H3NsSh24pYVcM2r70LprVxhqOdubfMurxSyR4733BTg1JLds/Gc2MemJBDT2KTgP7r4tBleYyqYZvb3kUNhG1v+/DvBhHlT4mJiTh8+DCaNWuWruZdHu/du1c36yTKiH3SiKyANHb8trkTBjVwQnSChv8tjcHyM/quGcmMJA85EZqMFZ1c0b+2I6oVs0WHJbG4mUvp3/OTYQ0d8dULzmrg8v+tiMFvJy3zGFl8Kgn/3IzGyk6ueK+uI6p72+KoQ/omv0REBtLMcN68eTh06BAOHDiAgQMHws3NDXPmzFHPy3PS9HDkyJHGxCAyVpoh4Yefnx+qV6+OqKgoXLp0KUvrJMoJcuXDkmYfeHh4aEL+577hsaHXY8DGxkYzuH3ub00b5aldG+iuVfe2Nfu25UQp4ARtXVcX9b4uv++uVfayjvdljuJgC+2Xl5zVvgz7yF17pqSd2bcpJ0phFxttUzdX9b7ubfna+H1o3Lix2beNhfvgQccArzPy/vh45513tKtXr2pxcXHavn37tLp16xqf2759uzZnzhzj41KlSmmmyHxZXefDCo8By/qN8DBPbGD+N663wi+O+T8DluwFadq1vdpfvVy1Ym42VrXv7GygTW7plHoRPtxDa1HWOoKLvCyFnKFt75kayPwzwE0rU9C6jhFbG2hfveCkabu+YZCmg8+DJWv7gNcZPFZ4DFjWMeBhhiCNfdKILFTaxBqh0RqazY9BWLR8r61HsgYM3Biv0vLLINjrurri3bpMFpFVMu7Zvj5uaFzaXmVHbPBLtFkGMM9N0jdt+NZ4NUC7wcD6jmoAdyIiIkvFII3IgtjZAC9VsMffvV1V0gSDi7dTkJAMqzXjUCJa/Rqjxsaa0soFP7Z2VvuCMvd8KTvse9MVTxaxw8zDCWr/3dPJ+Ge54Uz4f+mRX67ggPPvuqN/bQd4OJp1s4iIiCwzSBswYACuXLmC2NhY7Nu3D3Xq1Ml0XunEuWzZMjW/ZO/64IMPHnudRHpmawNUKGKLTlXsMaudMwI+dMfqzq5oUNIeWy5ZZtKHR7X1crKqCbp8JwXv1HHEmi4uvAB/QC3rlu6uKORig8Gb49D3jzgk5aNheNaeT4Svhw2mtXFB8GAPLHvdBX1rOaCGjy2cmC2UiIgsgFkbhHTs2FFlx+nXrx/279+vMuNs2rQJFSpUwM2bN++b39XVFZcvX8bvv/+O7777LkfWaQ7SDOepYunjY1OVAhkHZzU9D7I9j6n5cmqeR92m3N3u+2cy/zZBXSy6OtjAzfHf///9u5irjUqPLheZZQrawiVN1jrJ3PjriURMO5SAvTdSkDIf+crZ8BTU+zkaqzq5qHHgdve2RZvfYnDDQlLI5zY5UsY2ccInz6dm+ez4eyxW63yMvNwwaW8CPjwehb61HdGjmgNerZxaRHKKhqt3NQRGpiAoUkNodAoi44GoBE0Vqa2V7JcS1BqKNLtNSkmdlpyS2sTSIO2Rp2V7uvbQ+cl8ZPgSZpUlonwZpA0aNAizZs3C3Llz1WMJrNq0aYPevXtjwoQJ980vaU6liK+++ipH1mkOTxSyxcG33M29GaRzCcmaukg4EZqEE6Ep2BOQhL+uJavxxDIGn6YCUWsVHpPa/27Oyy7oUtUB+/u4od2iGBwJzkdVRZnc/JGx5TpWcUBgRIraJ0dD8s8+yfgduHRHw9At8Ri2JR5P+9ii2RP2KlV/NW87lC1ki7KF2WmNHuyd9bGYdvC/vo5ERHnJbGcpGYOiVq1aGD9+fLq7ilu3bkWDBg3ydJ0yBoaTk5PxsYeHB3LTnVgNPx1OuG+6qbunWi7NkzqfloV5srKevN5uS9gm7aHzSLAVk6ghOuHf/xNT/78Zrak7/LdjTa2FDPvufyticfFOCj593gm73nBTj/NjrZEo5maD1Z1dUL+EPY4GJ6sALTCSR4+QvSDB6tGQ9L+5nk5QNday79wdpQAejjbwcLJRA6jLANnS79He1ib1b9vUaVIM4WC6GyVp1p02Xnyc6WRe/9zMPzc5iEh/zBakFS1aFPb29ggNDU03XR5XrFgxT9c5YsQIjB49GnklOEpDvz/i8uz1yDplDLLzG3n3n22PV0lTpL/eik4uGLIlXjV1y0+qeNnij66uKF3QFmvOJaLr8lgV8OdnWfluRMRLScHZ8DzZJCIiIstKHKIHUvPm6elpLDKyPBFZhvnHE/HighjcjQO+be6M6W3yT+bHFmXt8PebbipAm7Q3Hh2WMEAjIiKyBmYL0sLDw5GUlARvb+900+VxSEhInq4zISEBkZGR6QoRWY5d11IzP0qtWr/ajqpmydpTr79fz1GNGyfjx/X7IxaDN8enS2hBRERElstsQVpiYiIOHz6MZs2aGadJ+355vHfvXt2sk4gsw/lbKaj/czT+upaEluXssae3G/wLWF+VmvSJmtHWGd+3dFaZCGX8s58O5/P2jURERFbGrM0dJVX+W2+9hR49eqg+Y9OnT4ebmxvmzJmjnp83bx7GjRuXLjFI9erVVZFkH9IsUf4uW7ZsltdJRNbrVqyGFxbEYOGJBFT1tlOZH+sUt55W3YVdbLC5myv61nLE+VvJajgCGT+OiIiIrItZcxAvXboUXl5eGDt2LHx8fHDs2DG0bNkSYWFh6nl/f3+kpPyXXal48eJqHoMhQ4aosmPHDjRp0iRL6yQi65aQDHRfGYcLt1MwprEzdrzhhh4rY7H8jGVnfqzsZasGMi9X2BZbLyeh4+8xuMP8Q0RERFZLejGwpNkHHh4empD/uW94bOj5GDDYs2eP2bdFj6VrVXst7mMPTRvlqU180Umzt7Xc9xE1IvV9TG3tbLHvIzfLuHHjjN+HRo0amX17WLgPHnQM8DqDxwePAcs6BjzMEBtYTzsgonwsPw1mnR2/nUxCk3kxuBGRgiHPOOHPHq4o7mE5+0rG65ra2hm/vuKqxunqsyYW76yPQxKHb7oPvwNERGRNGKQRkVXbeyMZNX6KxqaLSXiulD2O9nXDC0/YQe+kWeNfvdwwoI4jLt9JwTO/ROOXo0wQQkRElB8wSCMiqxceo6H1bzEYtSMORV1tsKW7G35o5azS1+vR27UccKyvG+r62akBqmvNjMLREFafZVV+H+idiIgsH4M0IsoXZAyxsTsT0Gx+DK7dTcF7dR1VINSghH5q1Up42uCPLi74qa2Leizjn728OFYN1E1ERET5B4M0IspXdlxNRtXpUfj5SALKF7HD7t6umNbGWaW3N+fYZ4MaOOLMO+5o86QD9t1IwtM/RXP8MyIionyKQRoR5TsyCPRba+PQ5jdJKqKhf21HnH/XDX1rOcAuj2O15mXtcOgtN3zb3BnSSm/Qpjg8OzsGF2+zeSMREVF+xSCNiPKt9ReSUPHHKHy+Kx7ujjaY0dYFZ95xQ/dquR+sPVPSTmWb3NTNDdV97LD8n0RUmhqF7/YlIJldqoiIiPI1BmlElK/FJgGfbY9HlWlR+O1kIsoWtsX8Di44/547PnrGEUVysBmkNGvsVMUe+950w57ebmhSxh67ryfhuTnReO33WARGMjojIiIiwJ47gYgIuHRHw/9WxOKLXbb49HknvF7FHl+/6IzPmzjhj/NJWHEmUdW83YvP3t5ysgMa+tuhYxUHvFbJHkVcU++N7biahK//TlDrJCIiIkqLQRoRURpnwlPQdUUsPtpigz41HfBWTUe8VtlBleQUDSfDUtTYa2dupqjxy0KiUlRtXGIy4OEEFHK2QemCtqjkZYsaPnaqWaOzfWpt3L04Db8cTcDUAwlMqU9ERESZYpBGZAVsbMyXmdBaBUVqKmX/5zsTUK+EHV6tZI8XnrBH1WK2eNon62n7JZD780oi1l1IwoYLSYhPztXNzrf4HSAiImvCII2I6AGkl9i+G8mqAPHwcARqFbdDucK2eKKQrRoc28UecLSzQUS8hnvxmsoY+c/NZJwOS2E/MyIiIso2BmlERNlM3y9jrUkhfdJkLAMiIiILxuyOREREREREOsIgjYiIiIiISEcYpBEREREREekIgzQiIiIiIiIdYZBGRERERESkIwzSiIiIiIiIdIRBGpEV4EC+lN/xO0BERNaEQRoREREREZGOMEgjsmApKSnm3gQi3eFg1kREZOkYpBEREREREekIgzQiIiIiIiIdYZBGRERERESkIwzSiIiIiIiIdIRBGhERERERkY4wSCMiIiIiItIRBmlEVoAD+VJ+x+8AERFZEwZpREREREREOsIgjYiIiIiISEcYpBFZME3TzL0JRLrD7wUREVk6BmlEREREREQ6wiCNiIiIiIhIRxikERERERER6QiDNCIiIiIiIh1hkEZERERERKQjDNKIiIiIiIh0hEEakRWwsbEx9yYQmRW/A0REZE0YpBEREREREekIgzQiC8ZBe4n4vSAiIuvDII2IiIiIiEhHGKQRERERERHpCIM0IiIiIiIiHWGQRkREREREpCMM0oiIiIiIiHSEQRoREREREZGOMEgjsgIcyJfyO34HiIjImjBIIyIiIiIi0hEGaURERERERDrCII3IgmmaZu5NINIdfi+IiMjS2Zt7A4iIKO/6bfn4lYa3Xyl4+ZRAMd+SKOzlCzd3T7i4ecDN3QMOjs4qyNG0FKQkJyMmOhLRkfcQFXkPd26FIizouiohQddwMzgAKSkp/PiIiIhyGIM0IiIr5VOiNKrUaIDylWugdLkq8C9bCc4urg9cJjEhXqI5FdDZ2trB1jbzBhexMdG4dukfXD53EpfPnsDpo38jNOh6LrwTIiKi/IVBGhGRlXD3LIiaDZqhZoOmqFLzGRTx8k33fFhwAE4c3IWggMu4GXIDN0MCEB4apGrKoqMiEBcTdV/NmIuru1qvlMJFfVCsuD+8i/urGrnS5augYtU6qhjIek8d+RvHD+zE4b+3qnUTEZnbgAEDMGTIEPj4+OD48eN47733cPDgwUznf+211/D555+jdOnSuHDhAoYNG4YNGzYYn58zZw7eeOONdMts3LgRrVq1ytX3QfkHgzQiIgtW2MsHzzR7CXWfa4lK1erCzt7eWMt1dN92/HNsL86cOIirF04jJioi2+uPjYlSRYKvK+dP3fe8u2chlHmyCp6sUhNP1WyIitXqoEnrjqokJyXh9LG9OLBzI/btXIfbN0Ny5D0TEWVHx44dMWnSJPTr1w/79+/HwIEDsWnTJlSoUAE3b968b/4GDRpg0aJFGDFiBP744w907doVq1atQs2aNXH69GnjfBK09erVy/g4Pj6eHwzlGBvpY51zq7MOHh4eiIiIgKenJyIjI829OUSZSkhIgIODAw4dOoQ6df6rzSDrJk0W6zdug0YtX0PV2s8ZmyQGXDmPg39twqE9m3Hh9FEkJyfl+bbZ2zugfJWaqPXMC6jXqBX8SpVT05OTk1Ut3s4Nv2Pfzg1IiI/N0df95ptvMHjwYPX3M888g7179+bo+olyEq8z8ta+fftUrZnUnglpzh0QEIApU6ZgwoQJ982/ePFiuLm5oV27dsZp8pty7Ngx9O/f31iTVrBgQXTo0OGRtonHgGXxMENswJo0IiILUebJp9Dq1V549sUOxr5l1y+dxc6Ny7B3xx8IuXHV3JuIpKREnDm+X5WF079UQVr9xq3xfIvXUKN+E1UkGcmerauxYdlsXL34j7k3mYismNzIrFWrFsaPH2+cJsmRtm7dqmrMTJHpUvOWltS8tW/fPt20xo0bIzQ0FHfu3MGff/6JTz75BLdv3za5TkdHRzg5OaW76Cd6EAZpRFZA7gqSdZKaqQZN26rgrGK1umra3ds3sXnVfBWcmWqCqCeB1y5i+bwfVClX6Wk0bvU6nmveAS++3E2V00f3Yv2y2Tiwc8Nj1fzxO0BEphQtWhT29vYqmEpLHlesWNHkMtJvzdT8Mj1t/7MVK1bgypUrKFu2LMaNG6eaP0qAZyrrrTSdHD16ND8kyjIGaUREOuTs6oYW7XugXee+qt+ZOHviADYsn4O929chKTHB3JuYbRfPHFNl7pQxeKZpO7R+/U2VfVJKeGgg1i6eic2rFiA+Lsbcm0pE9EBLliwx/n3q1CmcOHECly9fVrVrUquWkdTkpa2dk5q0wMBA7mXKFIM0IgvGQXutj0eBwmjTsQ9avdYLHp6FVEr8rWt/U00D9V5rllUSYO7atFyVcpVroPVrvdHwhZfR64MxeLXn+1i39GdVu/aomSH5vSAig/DwcCQlJcHb2zvdTpHHISGmkxnJ9OzML6RGTZKQlCtXzmSQJn3IpRBlVeYD4ORxWlQ5uGNjY1XnzoclQJC0qGfOnFHzy52LjOlOpTNn6mCs/5W0aVOJiPTGs2AR9HxvFH5aeQgdew+Cvb0jVv82Hf1fq4dp4wZZTYCW0cV/juKHse9hwKv1sHbxT3BydkGXt4ep/dCt/8cqeyQR0aNKTEzE4cOH0axZs3TNo+VxZgmGZHra+cWLL774wIREfn5+KFKkCIKDg/lhUY7RzFk6duyoxcXFaW+88YZWqVIl7aefftJu376teXl5mZy/QYMGWmJiovbRRx9pFStW1MaOHavFx8drVapUMc4zZ84cbf369Zq3t7exFCxYMMvb5OHhoQn539z7h4X74EHHgBz74tChQzxWLPRYcXXz0Dq/NVT7detFbcXeEG3exn+0jr0Ha+6ehcy+beYongWLaF3eHqot2HxO7Y+FWy9or/cepDm7uj1wuW+//VYzqF+/vtnfBwv3wYOOAV5n5P21ZmxsrNajRw917Thjxgx1rVmsWDH1/Lx587Rx48alu9ZMSEjQBg0apFWoUEEbNWpUumtNNzc3beLEiVq9evW0UqVKaU2bNlXn4XPnzmmOjo5Z2iYeA5b1G+FhntjAvG9637592pQpU4yPbWxstBs3bmjDhg0zOf/ixYu1tWvXppu2d+9ebfr06emCtJUrV1raB8HCfZDtY4BBmuV+bxydXLT2/3tHm7fpjApGFmw5r73e68OHBiP5KXiVYFWCNNk/c9af1tp2fltzcHQyOT+DNPN/ZixZ3we8zsj74+Wdd97Rrl69qioG5Nqzbt26xue2b9+urh3Tzv/aa69pZ8+eVfOfPHlSa9WqlfE5Z2dnbePGjVpoaKg6D1+5ckVVMhiCPh4D1vd74JHfgjQHBwdVK/byyy+nmz537lxt1apVJpe5du2a9sEHH6SbNnr0aO3YsWPGx/JFu3PnjvryyBds2rRpWuHChTPdDrnrITvdUIoXL84gTQdfCJaH7wMGaZZ3nNja2mrN23fXfll7XAUfi7Zf1rr1/zjf1pw9rHgUKKz1fG+UtnjHVbW/Zq46rL3w0v80Wzu7dPMxSDP/Z8WSjeOaN4Pz/fHCY8CyjgEPM3xnzZo4hGlRiSg/eapWQ/Qe+DlKl6uMxMQErP/9Fyyf9z3u3Aoz96bpVuS925g3ZQz+WDwTr/f+EM3adsWAEd/ipa798NuMr7BvxzpzbyIR0SMrU64KoqKjuQd1zt3NLc9f0yqzOzItKhHpiU+J0uj57meo16i1eiyBxbwfxyI08Jq5N81i3LoZjBkThmL1r9NVYpFnX2yPoeN/wYV/jqpBs4mILNEXP61GUrJUnJCe2dvZ5K8gjWlRiXIGB/LVJxdXd7zW60O07dgHDo5OuHrhNGZP/gynjuwx96ZZrOAbVzDps35YtXAq/td/JGrUb4IxU5bBx+muuTeNiCjbPun7MmvSLKQmrd2RzLN7Wl2QljYt6urVq9OlRf3xxx8fmBb1+++/N05jWlQi0hNbW1s0bdMZXfuNQMHCXrh3Oxy/zfwY29b+hpSUFHNvnlW4fP4kPv+wi2pCKqn6q7Z+3vhcUW8/s24bEVFWXbl4GpGRkdxhOufh4WGW1zVrRzymRTV/Z0gWy08ccvjwYbNvC0vqPqhco4H2zbwtKsnFkl3XtR7vfqYyFXL/5O4x8tvSlcYU/NuOhWn9hk3UKlarc1+CERbuAz0cA0waYf7PwNyFx4D5PwPo/PMye5+0pUuXwsvLC2PHjoWPjw+OHTuGli1bIiwstSO9v79/ujvPUpPWtWtXfPHFFxg3bhwuXLiA9u3b4/Tp0+r55ORkVKtWDT179kTBggURFBSEzZs349NPP+VI72R1ZKB20gfv4v7o8e5naNCkrXp8YNdGlfBCmudR7gtJs58j791C8/Y9VImOvIfL50/h2sV/EBRwGXfCQ3DrZggi7txCbEyUKkmJCfyIiIhIV6QXHK/yTFRpRkREwNPTM1eqoOVibuDoafdN10x9FBkuwk1dlGd12iMvl3Eb8IjLZXk7My4Hi9hOU/OZfr30D5OSEhEfH4uEuFjEx8UiLi5G/X3v7i3cvRWGO+GhuBlyAzHR9x+LcXFxcHJywpEjR1CrVi0T20i5zdnVDa/2/AAvde6r+p1du3QGc77/DCcO/sWdn4cmTZqEDz/8UP397HPPw97dGzUaNEXVWs+iUJFiD1xWMm3Gx8YgOSkJycmGkoyUf/+Xx1pKyn+/KWm+12m/4+m+7v8+SPs7lO73IJN1kH6sWTQDe7f/YZHXGaR/PAYsi4cZvrNmr0nLjxydXFCham1zbwZZmJvBN3Dt8hmcPXEAR/b+qZJQkHn7nTVu3Qn/6zdCBQERd2+ppCBb1ixESnIyPxozkpqxPRuXYefGZepxgUJFUbp8FRTzLYnCXr4oXNQbngULw9nVHS4ubsb/be3tYGdnDwdHR9ja2cPWVh6nTrOz5+kyvymwycvcm0BE+RjPOmZw4+p5dHze/6HZ+e6flpV5ZNrDJsiasraujMtmbTvv39asLpeVLIVZWi6rr5dxPzzydj7iZyNfQgdHODo5w8nZFU7OLqo4u7ipC8tCRb1VAODjVxr+ZSuhdsMXVZFECTeuXVCBAuW9yk/XR68PxqBsxeqqJlTuuC+dPQkxURH8OHTo3p1wHD+wM1dfI+333fh32mlpfiPS/TZk4TePzCMlhTdbiMh8GKSZgTRtYR8Iyi65sJNgrWqd51Dn2RYq9bjc7RcenoVUwMbMgXnQ7+ydz9CgaWq/s0N7tmDuD6MRdP1SLr8y6V36Zo9svkhERI+HQRqRhZALP0lCIWXzyvnw8imBlwKuwM7WHl6+JTBxziaVqOLkod3m3lTrHO/sjYFo2+ktY7+zud+PwvGDu8y9aURERGSFGKQRWShJJqL6PtnbIzoqAk88WVUN6iu1O/N//Fw1q6XHI7WTzdp1Rde3h6NA4aK4d+cWFk3+FFvX/Mp+Z0RERJRrGKQRWYGwoOv47J330PO9z1SftRr1m2LrmoVYPOtr1R+Hsq963Ubo+e5nKuGEZP9b9es0LJs7mf3OdCor/VmJiIgsBYM0Iitx6sgeDO3dEs+3eFVlHGzRoSeeb/4qViyYgrWLZyIhPtbcm2gRylWuge79P0bV2s+qx/t2rMP8qZ8j5MZVc28aERER5RMM0ogsmKlx2STtuIzt067z23il+/sqYGv9Wm8sn/cDNq9ewKQ1mfArVR5d+w4zDkZ99uRBLJz2Jf45ti/3P0jKUUzcQURElo5BGpEVSoiPU0HZ1jW/oeObg/HCS/9Dn8Ff4uX/9VdN9v78Y7EaoJeAYr7+eO2ND9CkTWc1Jtb1S2fx64xxOLh7M3cPERERmQWDNCIrJv3RZn0zAqsWTsXrvT5Ek9ad0H/4N+jQ/T38PnsSdm1anm+DNd+ST+DVHu+jUcvX1EDFMlj4op8nYtfGZRzKgIiIiMyKQRpRPskEOW38YNU/rWPvwarf2nuffo/OfYZg9aLp2LZ2EeLjYpAflCxTAa++8QEaNntZ1ZzJvlm54Eds+2MREhPizb15RERERAzSiPITSX7xw9j3sGL+FLzS4z0892IH9Bn0JTq9ORjrl83BhmWzEXH3FqzR0/Uao22nt1GzQVPjvlgx/wfs2PA7kpISzb15REREREasSSPKh2QMNQnWFs2coBKMvPBSNxWote82AH9vW4tNK+fh/KnDsHROzq54vsUrKjgrWeZJNU0Gol796zTs2ryCY50RERGRLjFII8rHpKnf7MmfYens79Dq1TdU2v4mrTuqcvXCaWxaOR9/bVlpcWODPflULTRr2wXPvtAeLm7uqo/Zwb82Ye2SmTh1eI+5N4+IiIjogRikEVmBxx3INyriDn6f851qBlnnuRZo0aGHGsy579AJ6D1wLI7s3YZdm1fi8J4tKnOkXhOBPNO0LZ5v8Zqx1izy3m38sWQmNiybg+AbV8y9iZSLOJg1ERFZEwZpRGQkmR5l8GYpviXKqNT9z77YHvUatVYlNjoKh//eqoK2I3v/NGv/NbkoL1P+KdR69kU1tlnpcpXVdKk1k22TRCBSe5aUmMBPmIiIiCwKgzQiMklqnhZM+wILp3+JClXr4Pnmr6BB03YqaJMiwdDFM8dw8vBunDt5EGdPHFI1crnF1tYWJUo/qZoyVq/zPKrWfhaeBYuo52RbTh/di71//oF9O9fh9s0QfqpERERksRikEVkwTdPy5DXOnjigys+TRqJ8lZqo2aAZaj3TDE9WqamKQeC1i2ow6OtXziHgyjkEXb+kAqbs1LjZ2zugUFEfFC9ZBr7+ZdX/ZZ6siicqVIOLq5txvqiIu9i7/Q8cP7ATB3ZtxN3bN3P8vZNlyovvBRERUW5ikEZEWSY1VudOHlJFMkMWLOyFitXqomLVOqhYrQ7KVKgKv1Ll0ABt0y0n44/duRWmEpDExcUgPi4WyUlJahBpCcqkeBQohAKFisLNo0CmSU6O7duuau9OHdmDS2ePc9BpIiIiskoM0ojokUntlaEPm7Czs1cJPEo+UQH+ZSqgWHF/FPbyQeGiPur/ot5+qtmiKfHxsYi4fQvBN67i7u0wBAdcRtD1ywi+cVnVzrGmjIiIiPILBmlElKOJR2QMNil7sdbkPI5Ozmr8Mnt7eyQlJSE5KVENJq3XrJFEREREeY1BGhHlKQnGGJARERERZc50uyMiIiIiIiIyCwZpREREREREOsIgjcgKyMDORPkZvwNERGRNGKQRERERERHpCIM0IgvGQXuJ+L0gIiLrwyCNiIiIiIhIRxikERERERER6QiDNCIiIiIiIh1hkEZERERERKQjDNKIiIiIiIh0hEEaERERERGRjjBII7ICHMiX8jt+B4iIyJowSCMiIiIiItIRBmlEREREREQ6wiCNyIJpmmbuTSDSHX4viIjI0jFIIyIiIiIi0hEGaURERERERDrCII2IiIiIiEhHGKQRERERERHpCIM0IiIiIiIiHWGQRkREREREpCMM0oisgI2Njbk3gcis+B0gIiJrwiCNiIiIiIhIR+zNvQFE9Og4aC8RvxdEZLkciz0BR9coc28GPYSjuzvyGoM0c7Cxha2Lx/3TNe3hy5qcR3vofNrjrOtRljP9ghlWk9X3kpV5cnDfEVH+ZGsHG1u7fx/YqH+p/xuaE6f+nTrZJsNzZG20xDhoSQnm3gyycj7/mwD3+CRzbwY9hLtT3odMDNLMwKFICRR/c5o5XppyiKalmJqYlQVNTUz/KCkRKXJxkBifepGQGI+UhBgkR91BctRtJEfdQuKdICSEXX6Md0BkxWzt4eRXGfaF/WBfwAv2nsVg6+wBW2c32DqlFhs7B8DOHjbG4mDurSadubV5OqKOrjP3ZpCVC/l1GCKjWJOmdx5SkzamRZ6+JoM0M0hJiEPslSMPn9HkHdqHTzN9Y9fExKzeAc7KdjzGa/57X/ohi2ZxX+TgezediCAn96PpdcnFoq2DM2xdC8DG0Rs2Npl3HbVxcFL/qwtPZw+kxEVmbVuIrIx8Bwx8unyJW2HxJufTUpKRkhCrbn4gIRYpyUnQUhIB+T85GZqW/O+McvNE+/ceivyvpZue+tAwD2vkrVFy5E1zbwLlA3LDNSGS5269S4gx0QIulzFIM4PkiDCELf3MHC9NlkiCNic32LkXgp17Edh7FIFDUX84epUBkHpXx86zKEq8/ysSgs8j9vJhVRJCLsoVqbm3nihXyHfCuVR1OJepCZcyNeBWpUm6G2FRJ/9EQtglJN27qX5zk2PuISU+GlpCLD8RIiLSPQZpRHqXnIiUmLuqJIZdSfeUNus9wMkdKTERSLx5DU7FK6pS8Nn/qYvSuCtHEXvlsKq5TYm5Z7a3QPTYbGzhVPzJ1KCsdE04+pY39h9LSYxHUoTUepRWj8N+H4VbR7LQWoGIiEinGKQRWYHk6DsInvMe7NwLw7lMLbg8IReyUrvQWBURL7VsV44g7vIhxAedZy0b6Z59AW84l64BlzI14Vy6eromjQlhVxB79ai6ERF/4zRiy3wLoI5Zt5eIiCinMEgjsgKG/nOSWCT65BZVUmseKsDliVoqcHPyfVIVPNMZybGRiLt6VDWLjLtyRAV5ROZm4+gCZ/9qqvmic+macChc3Pic1AxHn96B2KtHEHf1mDrW0y3LLItERGRFGKQRWSstBfGBZ1TBXwth61pQ1UhILZs0GXOr9LwqIiH0EmIvy8XvUcTJ/MmJ5t56yg9sbOHoU07V+jqXqaGa6kqmRaElJyLu2ol/a8uOICFUspkyQQcREeUPDNKI8gnp0xZ9+k9VjBfHT9RWNW3Sv8fRuywKNHhd9e+JD/xH1VbEXTueenHMBCSUQ+w8iv5bUybladi5eBqfS7wVgNgrqUFZXMApNQQFERFRfsQgjciCmR4QPCsLpqhMkFLu7fkNti6e6oJZsuW5lH5a1WxIEapp5PUTxqAt6U5Qzr4JsmpSg+tcqhqc/auqpowOhf2Mz8mxFX32r9QEN1ePIlkl/zDj94KIiEgnGKQREVJiIxBzZpcq6oehoA+cSz2tkjVI4OZWoaEqIikiTAVrcddOqtoOSW9OZKAC/pJPwcm/GpxLVYVj0VLG51QTxoDTqf0hpQkjh4kgIiIyiUEaEd0n6W4Iou5uRNTxjWrQbYdiZVQNmwRsTiWrwL3qi6qoeSNuIl4uvG+cRnzAKdVkjfIPW7eCcParrI4LqSlzLCbj9/03cHR84NnUmtjrJ1T/SDWINBERET0QgzQieggNiWGXVYk4sAKws1cJHlRtSckqcCpeKV2qf8nCF3/jH2PQJqnSkZLMvWwVbNRA6k5+leBUorL636GQb/qgLPg84q6fTA3KbvzDwaOJiIgeAYM0Isqe5CQVfElRbO1U0hFnCdhKpBbXJxuoIiQRiWSPlP5v8UHnVGETSctg4+QGJ59ycJThG/4Nyuyc3Y3Pa0kJqvmiJJqJv3FGBeZafLRZt5mIiMga6CJIGzBgAIYMGQIfHx8cP34c7733Hg4ePJjp/K+99ho+//xzlC5dGhcuXMCwYcOwYcOGdPOMGTMGb731FgoWLIg9e/agf//+uHjxYh68G6J8JiXZmIQEB1b+V9sizd9KVIaj1LqVqKyKgYzLJgNqxwefS1029LLqF0fmY+PgBEfvcirrp5Nk+/Qpny7Jh0iOvouY83tTs3/eOIOE0IsqaCci0jtea5KlMXuQ1rFjR0yaNAn9+vXD/v37MXDgQGzatAkVKlTAzZv3Z/pq0KABFi1ahBEjRuCPP/5A165dsWrVKtSsWROnT59W8wwdOhTvv/8+evbsiStXrqiATtZZuXJlxMezPwRR7tKQGH5Nlaij69UUW9cCaiBtx+IVjINqu5avp4qB9G2TppHSrFL+l8BN+sZxbKycZ+dWCA5epeFYrDQcipZWgZlDkRKwsbX771NMSlS1ngkhFxAffEH1J2NmTyKyRLzWJEtkY+4roH379qlaM6k9UxtkY4OAgABMmTIFEyZMuG/+xYsXw83NDe3atTNO27t3L44dO6Zqy0RQUBC+/fZbVYSnpydCQ0PxxhtvYMmSJQ/dJg8PD0RERKjlIiMjc/DdEuUsOU4Nx6vciLAkNo4usHPxgK2zO2yd3FSBbYb7RilJSImPRkpCDFLiY1X/JvmbySeyuI/t7NV+tnV0VfvXxunf/+0cMsyppe7nuKj/ijRbtKBU9nKjrmzZssa/jx49au5NIsoUrzPyFq81yRK/s2atSXNwcECtWrUwfvz4dOPbbN26VdWYmSLTpeYtLbk4bd++vfq7TJky8PX1VeswkJ0qtXSyrKkgzdHREU5OTuk+iLT/E+lVUlJqUzP50Xj99dfNvTlEuiC/5/z9Jj3j8Zl3eK1JlvqdNWuQVrRoUdjb26tarrTkccWKFU0uI/3WTM0v0w3PG6ZlNk9G0nRy9OjR900PDAzM5jsiIiJzk9YVRJZy4ccWO7mL15pkqd9Zs/dJ0wOpyctYO1e4cGHcvn3bbNtkCQepBLF+fn48wfBzyPf4fdAHfg76wM8h6/tJumdQ/sBrTcvnkcffWbMGaeHh4aq5lre3d7rp8jgkRBIG3E+mP2h+w/8Z1yGPpd+aKQkJCaqkxTtbWSP7ifvK/Pg56AM/B33g56AP/Bwevn8o9/Fakyz1O2sLM0pMTMThw4fRrFkz4zRJHCKPM2uuItPTzi9efPFF4/ySzTE4ODjdPBL51qtXj01giIiIiPIRXmuSJdPMWTp27KjFxsZqPXr00CpWrKjNmDFDu337tlasWDH1/Lx587Rx48YZ52/QoIGWkJCgDRo0SKtQoYI2atQoLT4+XqtSpYpxnqFDh6p1tGvXTnvqqae0lStXapcuXdKcnJzM+l6tqXh4eGhC/jf3tuTnws/B/J8BPwfz739+Dubf9/wczL/fWTLfB7zW5PEBy9wHZt8A7Z133tGuXr2qxcXFafv27dPq1q1rfG779u3anDlz0s3/2muvaWfPnlXznzx5UmvVqtV96xwzZowWHBysAsAtW7Zo5cuXN/v7tKbi6OioAmT539zbkp8LPwfzfwb8HMy///k5mH/f83Mw/35nefA+4LUmjxFY2D4w+zhpREREREREpJM+aURERERERJQegzQiIiIiIiIdYZBGRERERESkIwzSiIiIiIiIdIRBGmVLqVKl8PPPP+Py5cuIiYnBxYsXMXr0aDg4OKSbr2rVqti1axdiY2Nx/fp1DBkyhHs6h40cORJ79uxBdHQ07ty5Y3KekiVL4o8//lDzhIaGYuLEibCzs+NnkcMGDBigxmiU433fvn2oU6cO93Eueu6557BmzRoEBgZC0zS8/PLL983z//buPCSqrw3g+KOZRraS5kJpYamUtmiobRpFEZUERRZFGYUpSaYlLX8EGZRElOGSbVS2QbT4ly0WWVFGEe0RFkSRaFmaWYZWdF/O4Z3BeTVf/TXOzC+/H7gw986ZGT3PuXfmmXPvMxkZGVJRUaGPU5cvX5YhQ4YQEyvasGGD3L17V+rq6vSxpbCwUAIDAy3auLm5SW5urv4xYfUjsGfOnJH+/fsTBwBoA5I0tEtwcLA4OztLYmKiDB8+XNLS0iQpKUm2bdtm8ePhxcXF8ubNGwkPD9cJmkrkEhIS6G0rcnV1ldOnT0t+fn6L96s4FRUV6Xbjxo2T+Ph4Wbp0qWzZsoU4WFFcXJzs2rVLJwVhYWHy6NEjuXTpknh6etLPHcTd3V33c3Jycov3r1u3TlJSUvSxKTIyUn9JoWKikgZYR0xMjOTl5UlUVJRMnTpVf1Gnjvvdu3c3t8nKypLY2FiZN2+ebu/r6yvnzp0jBADQRnb/HQCWf3cfpKen6x8LN60nJSUZ1dXVRteuXc3bMjMzjefPn9v9b/0bl/j4eOPTp0/Ntk+fPt34+fOn+Yfh1ZKYmGjU1tZaxIblz/pA/bZjTk6Oed3JyckoLy831q9fT9/aYHwps2fPtthWUVFhrF271rzeq1cv/ZuZ8+fPJyYdFAcPDw8di4kTJ5r7vLGx0Zg7d665TVBQkG4TGRlJHDj2MgYYA4wBab0PmEnDH+vdu7fU1NSY18eOHatPdfzx44d5m/oWW83C9enThx63ERWHJ0+eSFVVlUUcVLzULCj+nJo9ULPFV65cMW9Tp9+pddX/sL3BgweLj4+PRUzUKXl37twhJh1IHVcU03uB2i/ULH7TOJSVlekzLNg3AOD/I0nDHwkICJBVq1bJvn37zNu8vb31NQpNmdbVfbAN4tDxPDw8xMXFpcXxzli3D1O/ExPbcXJykt27d8vNmzfl2bNn5jg0NjbK58+fLdqybwBA25CkQcvMzNQzAK0tQUFBFr2lri+4ePGivi5KFROBfeIAAPakrk0LCQmRBQsWEAgAsBIXaz0R/t127twpR44cabWNquhook4nKikpkdLSUlmxYoVFu3fv3omXl5fFNtO6ug/Wi0NrVF9HREQQhw6kqtb9/PmzxfHOWLcPU7//bwzU+sOHD+30V/29cnJyZNasWRIdHa2rbZqovleFWtRpkE1n09g3AKDtuHCPPmjXGPD19TXKysqMkydPGs7Ozs3uNxUOcXFxMW/bunUrhUPsVDjE09PTvC0hIUEXDnF1dWW/t2LhkOzsbIvCIW/fvqVwiJ0Lh6xZs8a83rNnTwqHdEDfq4I5qkjOkCFDmt1nKhwyZ84c87bAwEAKh/B5g/cexgBjQNrcB3QWfdC+BO3FixfG5cuX9W0vLy/z0vTNubKy0igoKDCGDRtmxMXFGV+/ftUJAn1tvf1t4MCBxsiRI41NmzYZdXV1+rZa3N3d9f0qgX78+LFx8eJFY8SIEca0adOM9+/f64SZOFgvDmp8q8qBS5YsMYKDg429e/caNTU1FlU1WazbB2qMm8a7kpqaqm+rfULdv27dOh2D2NhYIyQkxCgsLNQVaN3c3IiFlWKQl5envxyKjo62eB/o1q2buc2ePXuM169fG5MmTTLCwsKMW7du6YX9gWMCY4AxwBgQkjQGgfVnbX6nabvQ0FDjxo0b+sOrmlVQH5qIhXVjcfjw4RbjEBMTY27j5+dnFBUVGfX19UZVVZWxY8cOo0uXLsTCyrFITk7WH0YbGhr0zFpERAR93IEfQtQYb4naJ0xtMjIy9JdF6hikvlQaOnQoMbFiDH5HvUeY2qikODc3V59Zob6oO3v2rMUXeiz0AWOAMcAYkN/2gdN/bwAAAAAAHADVHQEAAADAgZCkAQAAAIADIUkDAAAAAAdCkgYAAAAADoQkDQAAAAAcCEkaAAAAADgQkjQAAAAAcCAkaQAAAADgQEjSAKAF/v7+YhiGXh48eGDzPoqPjze/flZWFjECAKATIUkDgFZMmTJFL7Z26tQp8fb2ltLSUpu/NgAAsC8XO78+ADi06upqqampsfnrNjQ06OX79+82f20AAGBfzKQB+Ot5eHhIZWWlbNy40bxt7Nix0tjYKJMnT27Xc40ZM0aKi4vlw4cPUltbK9euXZPRo0e3+piSkpJmpywWFhbK4cOH2/mfAACAzoAkDcBf7+PHj7Js2TLZvHmzhIeHS48ePeTYsWOSm5srV69ebddz9ezZUwoKCmTChAkSFRUlL1++lPPnz+vnBAAAsAZOdwTQKVy4cEEOHDggJ06ckHv37kl9fb3FzFpbqVmxplasWKFn1GJiYqSoqMiKfzEAAOismEkD0Gmkp6eLi4uLzJs3TxYtWvSPrvfq37+/7N+/X168eKGTs7q6Oj2L5ufn1yF/MwAA6HyYSQPQaQQEBIivr684OzvLoEGD5OnTp+1+DnWqY79+/WT16tXy5s0bfV3b7du3xdXV9beP+fXrlzg5OVls69q16z/6HwAAwN+PJA1Ap6CSouPHj+vS9mVlZXLw4EEJDQ3VBUDaY/z48bJy5Up9+qQyYMAA8fT0bPUx6jV8fHzM6ypJDAkJaXbqJAAAgP6sQDcA6Ay2bt0qvXv3lpSUFNm+fbs+XfHQoUPtfh5VKGTx4sUSHBwsERER+hq3b9++NZtt27Ztm3ldFSeZOXOmzJgxQ4KCgiQ/P1/69Olj8RjVXj0OAACAJA3AX08V9UhNTdXJ1ZcvX8QwDH174sSJkpSU1K7nWr58ufTt21fu37+vK0RmZ2dLVVWVRRt1fVrTmTOVDKoE7OjRo3L9+nV59epVs1k01Z7r2gAAgKIukjDoCgCw5O/vL69fv5ZRo0bJo0eP7NY9Kpl7+PChpKWl2e1vAAAAtsVMGgC0orS0VG7dumXzPlq4cKGe9VOzfQAAoHNhJg0AWtClSxddAVJRFRzLy8tt2k+qrL+Xl5e+rUr9V1dXEycAADoJkjQAAAAAcCCc7ggAAAAADoQkDQAAAAAcCEkaAAAAADgQkjQAAAAAcCAkaQAAAADgQEjSAAAAAMCBkKQBAAAAgAMhSQMAAAAAcRz/AW8mfKIThl6OAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 1000x700 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#%matplotlib widget\n",
    "# Inaccurate Plot for intution (Like the Textbook)\n",
    "\n",
    "from functions import plot_dead\n",
    "\n",
    "plot_dead(E, psi, V, x, nos=5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " ## 4. How do I trust the computer?\n",
    "\n",
    "\n",
    "\n",
    " So far:\n",
    "\n",
    "\n",
    "\n",
    " - I constructed a Hamiltonian matrix.\n",
    "\n",
    " - I asked the computer for its eigenvalues and eigenvectors.\n",
    "\n",
    " - I enforced boundary conditions by construction.\n",
    "\n",
    "\n",
    "\n",
    " But how do I know these eigenvectors are actually good **approximations to true eigenstates**?\n",
    "\n",
    "\n",
    "\n",
    " Two big checks:\n",
    "\n",
    "\n",
    "\n",
    " 1. **Orthonormality** (linear algebra + normalization)\n",
    "\n",
    " 2. **Analytic benchmarking** (compare to known formulas)\n",
    "\n",
    "\n",
    "\n",
    " ### 4.1 Orthonormality\n",
    "\n",
    "\n",
    "\n",
    " If I have two different eigenstates, $\\psi_m$ and $\\psi_n$ (with $m \\neq n$), their inner product must be zero:\n",
    "\n",
    "\n",
    "\n",
    " $$\n",
    "\n",
    " \\langle \\psi_m | \\psi_n \\rangle = 0.\n",
    "\n",
    " $$\n",
    "\n",
    "\n",
    "\n",
    " This is called **orthogonality**.\n",
    "\n",
    " If $m = n$, then the inner product is 1 (if I normalize them properly):\n",
    "\n",
    "\n",
    "\n",
    " $$\n",
    "\n",
    " \\langle \\psi_n | \\psi_n \\rangle = 1.\n",
    "\n",
    " $$\n",
    "\n",
    "\n",
    "\n",
    " So the **overlap matrix** or **orthonormality matrix** is:\n",
    "\n",
    "\n",
    "\n",
    " $$\n",
    "\n",
    " \\mathbf{S}_{mn} = \\langle \\psi_m | \\psi_n \\rangle\n",
    "\n",
    " = \\int \\psi_m^*(x) \\psi_n(x) \\, dx\n",
    "\n",
    " $$\n",
    "\n",
    "\n",
    "\n",
    " and in discrete form on the grid:\n",
    "\n",
    "\n",
    "\n",
    " $$\n",
    "\n",
    " \\mathbf{S}_{mn} \\approx \\sum_i \\psi_m(x_i) \\psi_n(x_i) \\, \\Delta x.\n",
    "\n",
    " $$\n",
    "\n",
    "\n",
    "\n",
    " For properly normalized eigenstates of a Hermitian Hamiltonian, $\\mathbf{S}$ should be **the identity matrix**:\n",
    "\n",
    " - Diagonal = 1\n",
    "\n",
    " - Off-diagonal = 0 (up to small numerical errors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "--- Orthonormality Check (First 20 states) ---\n",
      "Overlap Matrix should approximate the Identity Matrix:\n",
      "[[ 1.00000000e+00 -1.77546910e-16  4.92896819e-16  1.99740274e-16\n",
      "  -4.20446598e-16 -1.99740274e-16 -2.80149057e-17 -2.21933638e-16\n",
      "   2.77877900e-16 -9.98701371e-17 -9.08638191e-17 -1.22063501e-16\n",
      "  -2.81039182e-16 -4.29996424e-17 -1.04112667e-17 -7.21284324e-17\n",
      "  -1.25677508e-17 -6.65800914e-17 -6.74578563e-19 -2.49675343e-17]\n",
      " [-1.77546910e-16  1.00000000e+00  8.87734552e-17 -3.96393328e-16\n",
      "  -1.77546910e-16 -7.35725347e-16 -1.66450229e-16 -6.66724438e-16\n",
      "  -1.05418478e-16  5.30315433e-17 -2.77417048e-18 -8.52925350e-17\n",
      "  -3.46771310e-17 -7.43336812e-17  6.84873336e-18 -2.05012282e-16\n",
      "   1.19636102e-17 -1.82724098e-16  1.00563680e-17 -9.60502344e-17]\n",
      " [ 4.92896819e-16  8.87734552e-17  1.00000000e+00  4.43867276e-17\n",
      "   1.83681698e-16 -1.55353547e-16  2.20834315e-16 -1.88643592e-16\n",
      "  -5.14321623e-16 -9.98701371e-17  8.45593711e-18 -9.98701371e-17\n",
      "   1.83129116e-16  0.00000000e+00 -5.97096849e-18  1.10966819e-17\n",
      "  -2.61595607e-17 -1.66450229e-17 -5.33865268e-17 -3.05158752e-17]]\n"
     ]
    }
   ],
   "source": [
    "from functions import check_ortho,show_matrix\n",
    "\n",
    "overlap_matrix = check_ortho(psi,dx)\n",
    "\n",
    "show_matrix(overlap_matrix,how=\"normal\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1. -0.  0.  0. -0. -0. -0. -0.  0. -0. -0. -0. -0. -0. -0. -0. -0. -0.\n",
      "  -0. -0.]\n",
      " [-0.  1.  0. -0. -0. -0. -0. -0. -0.  0. -0. -0. -0. -0.  0. -0.  0. -0.\n",
      "   0. -0.]\n",
      " [ 0.  0.  1.  0.  0. -0.  0. -0. -0. -0.  0. -0.  0.  0. -0.  0. -0. -0.\n",
      "  -0. -0.]\n",
      " [ 0. -0.  0.  1. -0. -0. -0.  0. -0. -0.  0. -0.  0.  0.  0.  0.  0.  0.\n",
      "   0.  0.]\n",
      " [-0. -0.  0. -0.  1. -0. -0.  0.  0.  0. -0.  0. -0. -0.  0. -0.  0. -0.\n",
      "   0. -0.]\n",
      " [-0. -0. -0. -0. -0.  1.  0. -0. -0.  0. -0. -0. -0.  0.  0. -0.  0.  0.\n",
      "   0.  0.]\n",
      " [-0. -0.  0. -0. -0.  0.  1. -0. -0.  0.  0. -0. -0. -0. -0. -0.  0. -0.\n",
      "   0.  0.]\n",
      " [-0. -0. -0.  0.  0. -0. -0.  1.  0. -0. -0. -0. -0.  0.  0. -0.  0.  0.\n",
      "   0.  0.]\n",
      " [ 0. -0. -0. -0.  0. -0. -0.  0.  1. -0. -0.  0.  0.  0. -0.  0. -0.  0.\n",
      "  -0.  0.]\n",
      " [-0.  0. -0. -0.  0.  0.  0. -0. -0.  1.  0. -0. -0.  0.  0.  0.  0.  0.\n",
      "   0.  0.]\n",
      " [-0. -0.  0.  0. -0. -0.  0. -0. -0.  0.  1. -0. -0.  0.  0.  0.  0.  0.\n",
      "   0.  0.]\n",
      " [-0. -0. -0. -0.  0. -0. -0. -0.  0. -0. -0.  1.  0.  0.  0.  0.  0.  0.\n",
      "   0.  0.]\n",
      " [-0. -0.  0.  0. -0. -0. -0. -0.  0. -0. -0.  0.  1.  0.  0.  0. -0.  0.\n",
      "  -0. -0.]\n",
      " [-0. -0.  0.  0. -0.  0. -0.  0.  0.  0.  0.  0.  0.  1. -0. -0. -0. -0.\n",
      "   0.  0.]\n",
      " [-0.  0. -0.  0.  0.  0. -0.  0. -0.  0.  0.  0.  0. -0.  1. -0.  0.  0.\n",
      "  -0.  0.]\n",
      " [-0. -0.  0.  0. -0. -0. -0. -0.  0.  0.  0.  0.  0. -0. -0.  1.  0. -0.\n",
      "   0. -0.]\n",
      " [-0.  0. -0.  0.  0.  0.  0.  0. -0.  0.  0.  0. -0. -0.  0.  0.  1.  0.\n",
      "   0.  0.]\n",
      " [-0. -0. -0.  0. -0.  0. -0.  0.  0.  0.  0.  0.  0. -0.  0. -0.  0.  1.\n",
      "   0.  0.]\n",
      " [-0.  0. -0.  0.  0.  0.  0.  0. -0.  0.  0.  0. -0.  0. -0.  0.  0.  0.\n",
      "   1.  0.]\n",
      " [-0. -0. -0.  0. -0.  0.  0.  0.  0.  0.  0.  0. -0.  0.  0. -0.  0.  0.\n",
      "   0.  1.]]\n"
     ]
    }
   ],
   "source": [
    "\n",
    "show_matrix(overlap_matrix,how=\"round\",round_value=10)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_matrix(overlap_matrix,how=\"plot\",round_value=10)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " ## 5. Analytical tests (benchmarking)\n",
    "\n",
    "\n",
    "\n",
    " Orthonormality tells me the eigenvectors make sense **as a basis**, but I still want to know:\n",
    "\n",
    "\n",
    "\n",
    " > Are these the *correct* eigenstates for **this** potential?\n",
    "\n",
    "\n",
    "\n",
    " For that, I compare:\n",
    "\n",
    "\n",
    "\n",
    " - The **numerical** energy levels from the matrix diagonalization.\n",
    "\n",
    " - The **analytic** formulas I already know:\n",
    "\n",
    "   - Infinite square well energy spectrum.\n",
    "\n",
    "   - (Optionally) harmonic oscillator spectrum when I switch potential.\n",
    "\n",
    "\n",
    "\n",
    " ---\n",
    "\n",
    "\n",
    "\n",
    " ### 5.1 Indexing remark\n",
    "\n",
    "\n",
    "\n",
    " - In physics, the ground state is $E(n = 1)$ for the infinite square well.\n",
    "\n",
    " - In Python, array indices start at 0.\n",
    "\n",
    "\n",
    "\n",
    " So:\n",
    "\n",
    "\n",
    "\n",
    " - Physically: $n = 1, 2, 3, \\dots$\n",
    "\n",
    " - In code: `i = 0, 1, 2, ...` corresponds to $n = i + 1$.\n",
    "\n",
    "\n",
    "\n",
    " This mismatch is annoying but standard in programming."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " ### 5.2 Infinite square well energies\n",
    "\n",
    "\n",
    "\n",
    " The analytic formula:\n",
    "\n",
    "\n",
    "\n",
    " $$\n",
    "\n",
    " E_{n}^{\\text{analytic}} = \\frac{\\hbar^2 \\pi^2 n^2}{2 m L^2}\n",
    "\n",
    " $$\n",
    "\n",
    "\n",
    "\n",
    " (Here $L$ is the well width.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "### ENERGY BENCHMARK: Infinite Square Well ###\n",
      "Well boundaries: x = [50, 10], Width L = -40\n",
      "-------------------------------------------------------\n",
      "| n | Analytic E | Numerical E | % Error |\n",
      "-------------------------------------------------------\n",
      "| 1 | 0.003084   | 0.011199    | 263.1139% |\n",
      "| 2 | 0.012337   | 0.044785    | 263.0147% |\n",
      "| 3 | 0.027758   | 0.100720    | 262.8462% |\n",
      "| 4 | 0.049348   | 0.178938    | 262.6034% |\n",
      "| 5 | 0.077106   | 0.279339    | 262.2782% |\n",
      "| 6 | 0.111033   | 0.401783    | 261.8589% |\n",
      "-------------------------------------------------------\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(array([0.00308425, 0.01233701, 0.02775826, 0.04934802, 0.07710628,\n",
       "        0.11103305]),\n",
       " array([0.01119934, 0.04478514, 0.10071981, 0.17893758, 0.27933922,\n",
       "        0.40178301]))"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from functions import check_ISW_analytic\n",
    "check_ISW_analytic(E,L,hbar=1.0, m=1.0, max_levels=6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Convergence Test\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# COnvergence Test"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " ### 5.3 Harmonic oscillator benchmark\n",
    "\n",
    "\n",
    "\n",
    " When I switch $V(x)$ to a harmonic oscillator $V(x) = \\tfrac{1}{2} k (x-x_0)^2$ and run the solver:\n",
    "\n",
    "\n",
    "\n",
    " - The analytic energy levels are\n",
    "\n",
    "   $$\n",
    "\n",
    "   E_n^{\\text{HO}} = \\left(n + \\frac{1}{2}\\right) \\hbar \\omega\n",
    "\n",
    "   $$\n",
    "\n",
    "   where $\\omega = \\sqrt{k/m}$ and $n = 0, 1, 2, \\dots$.\n",
    "\n",
    "\n",
    "\n",
    " - I can compare the numerical $E_n$ to those values.\n",
    "\n",
    " - This is a good **second** test after the infinite square well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error in harmonic oscillator check: name 'Last_k_value' is not defined\n",
      "\n",
      "### ENERGY BENCHMARK: Harmonic Oscillator ###\n",
      "Spring constant k = 10, Center = 0.0, omega = 3.1623\n",
      "-------------------------------------------------------\n",
      "| n | Analytic E | Numerical E | % Error |\n",
      "-------------------------------------------------------\n",
      "| 0 | 1.581139   | 0.011199    | 99.2917% |\n",
      "| 1 | 4.743416   | 0.044785    | 99.0558% |\n",
      "| 2 | 7.905694   | 0.100720    | 98.7260% |\n",
      "| 3 | 11.067972  | 0.178938    | 98.3833% |\n",
      "| 4 | 14.230249  | 0.279339    | 98.0370% |\n",
      "| 5 | 17.392527  | 0.401783    | 97.6899% |\n",
      "-------------------------------------------------------\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(array([ 1.58113883,  4.74341649,  7.90569415, 11.06797181, 14.23024947,\n",
       "        17.39252713]),\n",
       " array([0.01119934, 0.04478514, 0.10071981, 0.17893758, 0.27933922,\n",
       "        0.40178301]))"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Assuming Last_k_value, hbar, m, E, and CHECK_N are available\n",
    "from functions import check_harmonic_analytic\n",
    "check_harmonic_analytic(E,max_levels=6)\n",
    "\n",
    "from functions import harmonic\n",
    "\n",
    "V = harmonic(x=x,k=10,center=10)\n",
    "check_harmonic_analytic(E,max_levels=6)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Physics Engine Ready.\n",
      "Grid: 2000 points over L=50\n"
     ]
    }
   ],
   "source": [
    "\n",
    "import cv2\n",
    "import mediapipe as mp\n",
    "# Initialize Grid\n",
    "# CORRECT CODE\n",
    "x_full, dx, x_solver = make_grid(L=L, N=N_GRID)\n",
    "\n",
    "# Build Kinetic Energy Matrix\n",
    "T = kinetic_operator(N_GRID, dx, hbar=hbar,m=m)\n",
    "\n",
    "print(\"Physics Engine Ready.\")\n",
    "print(f\"Grid: {N_GRID} points over L={L}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "# 1. Imports (Make sure these are available in your environment)\n",
    "import cv2\n",
    "import numpy as np\n",
    "import time\n",
    "import math\n",
    "import mediapipe as mp \n",
    "from IPython.display import display, Image, clear_output\n",
    "from scipy.interpolate import interp1d # Needed for later potential resizing\n",
    "\n",
    "\n",
    "from functions import display_params\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Webcam Setup and Capture (Jupyter/Colab)\n",
    "mp_hands = mp.solutions.hands\n",
    "hands = mp_hands.Hands(max_num_hands=2, min_detection_confidence=0.7)\n",
    "drawer = mp.solutions.drawing_utils"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Stable capture triggered and video stream closed.\n",
      "Potential capture successful.\n",
      "Solver complete. Found 2000 eigenstates.\n"
     ]
    }
   ],
   "source": [
    "\n",
    "from functions import cheese\n",
    "# 4. Execute Capture\n",
    "print(\"Starting camera stream...\")\n",
    "# Assuming A_MIN and A_MAX are defined or hardcoded.\n",
    "A_MIN = 0\n",
    "A_MAX = 100 \n",
    "V_raw_input = cheese(mode='',tune=1, A_MIN=A_MIN, A_MAX=A_MAX) \n",
    "\n",
    "def verify():\n",
    "    if V_raw_input is not None:\n",
    "        # Use the imported plot_V from your file or define it here\n",
    "        # plot_V(V_raw_input) \n",
    "        print(\"Potential capture successful.\")\n",
    "    else:\n",
    "        print(\"Potential capture failed or was aborted.\")\n",
    "\n",
    "\n",
    "    if V_raw_input is None:\n",
    "        print(\"Error: Run the Camera Input cell first to get V_raw_input!\")\n",
    "    else:\n",
    "        # --- 1. Map Input to Physics Grid (Interpolation & Scaling) ---\n",
    "        \n",
    "        # 1.1 Define the internal grid points for the solver\n",
    "        x_solver = x[1:-1] # Interior points for V_final (length N)\n",
    "        \n",
    "        # 1.2 Interpolation: Map the camera's resolution to the solver's grid\n",
    "        V_interpolated = np.interp(\n",
    "            x_solver, \n",
    "            np.linspace(-L/2, L/2, len(V_raw_input)), # Input X-space\n",
    "            V_raw_input                               # Input V-values\n",
    "        )\n",
    "\n",
    "        # 1.3 Scaling: Convert dimensionless input to energy units\n",
    "        V_max_height = 100.0 # Heuristic scaling factor\n",
    "        V_internal = V_interpolated * V_max_height\n",
    "        \n",
    "        # 1.4 Prepare V_full (The potential array including the walls, length N+2)\n",
    "        # The V_full is required by your current 'solve' function signature \n",
    "        # to maintain consistency with the inf_sqaure_well definition.\n",
    "        # We pad the V_internal array with 0s for the walls, knowing that \n",
    "        # the Hamiltonian construction will use V_internal (V_full[1:-1]) only.\n",
    "        V_full = np.pad(V_internal, (1, 1), 'constant', constant_values=0.0)\n",
    "\n",
    "\n",
    "        # --- 2. Solve H psi = E psi using defined function ---\n",
    "        # The 'solve' function handles the Hamiltonian construction (T + diag(V)) \n",
    "        # and normalization internally.\n",
    "        try:\n",
    "            E_vals, psi_vecs = solve(T, V_full, dx)\n",
    "            print(f\"Solver complete. Found {E_vals.size} eigenstates.\")\n",
    "        \n",
    "        except Exception as e:\n",
    "            print(f\"Error during solve: {e}\")\n",
    "            # Check if the potential is too high, causing numerical instability\n",
    "            if np.max(V_internal) > 1e9:\n",
    "                print(\"Potential may be too steep or high, leading to numerical error.\")\n",
    "            exit()\n",
    "\n",
    "\n",
    "        # --- 3. Visualization using defined function (or adapted visualization) ---\n",
    "        \n",
    "        # The original 'plot_dead' function uses default constants (nos=5).\n",
    "        # We call it here, passing the calculated results:\n",
    "        \n",
    "        # Note: We pass V_full to plot_dead, as it contains the boundary info\n",
    "        # that your V_clipped logic uses for plotting the potential shape.\n",
    "\n",
    "        return E_vals,psi_vecs,V_full\n",
    "\n",
    "\n",
    "E_vals,psi_vecs,V_full = verify()        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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bgUn7fYfS56mZtjPOOKPeAUC7SOhZR63GZytb29z7qmdF9UCilRt13FhD2iffXbb5T5r6DBpy53MFgEigJ8K0a7VWXu3QoYNH37taglt7LmgJdsdsigZLzR2fX331VXP8s1XLbThWuinaVb9hBUOl3f20ImFT3cy1Kl/D+9rjwBY46rFYjzdNZbRiY2PN8Vjp8U0zZ1ohz9mxV49vtue4yhac2cZKKx0GodUDg4HMFBAkGgBpBqKp7EhzfYS1O51+meoZIS0/rV9ctrmftNyo45kzHaujAz9t5VZt80fonAr//Oc/5e9//7tb7dUvRu1KpvvWFL+WG9d9f/zxx/Zug7b+6FruVMuTa8Cl5Uf1uZq50ttamlQzTHoQ0YxKw4G6ug3tG64ZL+0qoevogUu7VGgGRLNNOpGurqdjdIYMGWJKuevr1JLjWgZeD0Y6sNTxDJ6Oh7KVEw8V+hnpIF0NnDR7pgGwHqD1wKNdOmyWLVtmHtM+73rQ0fdSX58e1PW90oOsnrXU91yX6YHy1FNPNZ+Vu2cvbXNFaSle7Tqpg6H170uXNeTO5woA4XbMbY52cdfvbZ0+RItI6DFXx8Hq2FHt0dDSXEV6bNTjuRZ30O9yDVD0GKZd0fW411S2Rscoazd3LTBlO160RI8v2hVfp67QMbx6rNbMk3Z91+NMwy762vtFu/HrMVaLMeh7pl379ZhuG2+rpdy1kJGexNPXOWfOHPN6dCyVFqfQaTzeeecd85tDy53/+9//NmOttf2aUdKxzxr42Lrd67H8/PPPN79JdD1tox7nndF9anZPt62/DfTEnr4mPf4FKztFWVLeA/4GQqRMq9LHbes2VaJ6ypQpppy1lipdv3699YorrrA+8sgj1tLS0kb7mjp1qinJqiXF9fLLL79Yn3rqKWufPn3s62hp1aZKnmuZVMdypVoyVMt1azlXLSer+37ooYes6enpjUqYb9++3VpdXV2vROlpp51mSrlqOzdt2mT94x//aL3ssssalTHVst5aKlVLqjYsEaulwO+//37runXrzOvft2+fKUV7yy23WOPi4sw6Z511lilJvmfPHrPOli1brM8995y1ffv2Hn9WnnzO+t7p62hpveHDh5tS4oWFhabs/ZdfflmvhKvtcuWVV5oSsVoGvmHpVr2t29By6Pr+6mejJXBHjhxZ7/PUv4GG222qxKzuX8ul6/vn+DfY1Lqufq6URud7lmMtfwOhfMy1lUbXKT4abqOpY7FOafHyyy+baUQqKirMce+DDz4wx6CG+x41alSTbbvxxhvNsUKPqT/88IP1iCOOMN+9n3zySZPrf/TRR43KfDu7dO/e3XrPPfdYv//+e3NM1KlR9u7da45NkydPbnTM12OEvi49hurxaPfu3eZ1x8TENNr2VVddZdpaUlJijtdaKv7BBx8003s0PEbocVrX02lL9HWed9559sdTUlKsr732mpnmw1bC3XZcUzo1SFOvbcSIEabsuu04/4c//KHZ0uhNHYuV/h5yXObsb8DZJebQDQBhTAeTaqlUW99mAAAQXrTLtGZXtKv+Nddc0+hxXa69MWyVXH1JC1NoL4+WpuRAY4yZAsKMDvh3pANYtXqa4yBWAAAQupoaR3TJJZeYMU5NHc91fJZ239Zu3QgtjJkCwoz2zdb+zHqtfYN1zIwODm2uZDgAAAgt48ePlxkzZpi5onS878iRI+XKK68047Ac54/SsVRHHXWUXHXVVWZsko5PRWghmALCjE5Ge8EFF5izVDr4f8GCBWYgaHMT9AIAgNCipcZ1SombbrrJFE3SYj86n9Sdd95pgiabSZMmmROoWnBBq9VpASiEFsZMAQAAAIAHGDMFAAAAAB4gmAIAAACAaBwzpRND6sRgAAAAvqalonft2sUbG+X4vRk+0gP8PxsX7n/YO3fuDHYzAABABOvUqRMBVRTj92b46RTA/9mwDqZsGSl9w/yRnXr00Uftk6ZNmDBBli9f7vN9ANFi6tSpMnPmTHN72rRp8swzz0g0Vm/Sqk0bN26UESNGBLs5QFh788035eSTT7aXj9ZqaP44w60nbekBE938/XsT4f0/G9bBlI2+Yf540xxLU5aUlPAPBHjB8YeOxWKJyv8n2ySNpaWlUfn6AV+qrq623y4uLuZ/CmH7exPhjQIUAAKirKzMfjs5OTkq33Xb6y4vLw92UwAAgA9ERGYKQHgFU0lJSRJtEhISTEau4XuByBMXFyc5OTn2zxv+e59tJya6dOkiaWlpHm+rtrZWdu/eXS/bBQCuIJgCEBCO2ZhozEw5BpAEU5ErOztb/va3v0XlCYNA02B10aJF5vZtt91mAiJvv6P+9Kc/SW5uro9aCCAaEEwBCIho7+bn+Jrp5heZYmJi5KqrrjLjd7SAUUVFRbCbFNG6detmz0atWbNGampqvBrPeN1118nVV18t06dPF6vV6sOWAohkBFMAAiLagykyU5EvKytL+vfvL88++6ysW7cu2M2JePHx8ZKZmWlub9261atgSv3vf/+T66+/3mzz4MGDPmolgEhHh24AARHtwRSZqegoyav27dsX7KbAA7bPLSMjg/cPgMsIplrosgHAN6K9AIVjMMWYqcg+ZnibIYHn7703bJ8bx34A7iCYchH9pwHvUIDicADJmCmEi9GjR8t3331n5lqcNWuWy8+79NJLTVe5n376yX55+umn3dr32LFjZdmyZbJ27Vr58ssvpWPHjk0el0877TTZv3+/fT9fffVVvfW0qMSGDRvMRYuDAIAvMWYKQEBUVlaaaltagSvau/nppL1AONBy4X/4wx9kxIgRcvLJJ7v13Llz58rUqVM92q9mh15//XVTEOLrr7+WW2+9VR5//HE599xzm1xf1znzzDMbLZ8wYYJccMEFMnToUFP2XAPD77//Xj755BOP2gUADZGZAhAwtu5t0RhMpaSk2G/TzQ+BotmbadOmycKFC2XTpk1y2WWXufX8nTt3yuLFiwNemXDUqFEm+NEgSf3jH/+Q008/3VTdc8d5550nr776qjmBoSd0XnzxRRNcAYCvkJkCEDAaRKSmpkZlMMWYqeiTc/lTYkmpqzbnD7WlBbL7pd+1uJ4GQuPGjZN+/fqZwEiDCx0f9Nhjj8mUKVOafM61115rn8PJU7pt7XZnM3PmTJNdmjx5ssyYMaPJ53z88cdy9913S9euXU2FPhstN19YWGi6+m3evLnR84466iizLw2adNtvv/22Wa7b+fbbb+3rbdmyRc4//3yvXhcAOCKYAhAwtowMBSgOF+MA/E27yykde6TZng4dOpiM0y233OLX/TbXzU+zTdpt0Ffmz59vAsOioiJTmn7OnDmyfft2k40DAH8jmAIQMLbCC2SmCKaigStZo0BwLHiiGam4uLpDv78zU81xJTO1bds2MymvjU7Oq/M/7dq1q9FzCgoK7CdqdPJeHQ+lmSoNphpup3v37mYZAPgKwRSAgInmMVMUoECo8TYzNWbMGJk+fbocd9xxbj3PlczUkiVLzKS8Gnjp+hrcffjhh02O3WrXrp39dnZ2thxzzDHy5ptvmvtvvfWWPPPMM/LUU0+ZrNwVV1wh99xzj1vtBQBnCKYABDyYcizGEC0oQIFw1LdvX1OWXP9+9YSAdp974IEH5LnnnjNZHmfFVBqOmdJuhq6OV9LCGRdffLEpPKHdgjUj9Zvf/KZeBuuf//yn7NixQ8455xx59NFHpaqqylQL1ayXdjFU8+bNM4HVypUrzX29rc8FAF8hmAIQMI4/vBISEkx1rWhBAQoEQ8MJaB2zOK5Yt26ddOnSpcnHJk2aJA8++GCTj2mxCb1444cffpBhw4Y1+dipp54qvXr1kqysLHn22WdN5kozT03561//ai4A4A8EU04wCzrg34l7CaaA8HXjjTcGuwkAEHTMM+Ui20zrAHyTmYq2cVNkpgAAiDwEUwAChmCqjs6FAwAAwh/BFICAieZgigIUAABEHoIpAEEJpqJt4l66+QEAEHkIpgAErQBFNCGYAgAg8hBMAQiYaO7mRzAFAEDkIZgCEDAEU2ImFm1uPhwg1Jx33nlm4l2d9FYvt9xyi0vP0zmotNCKPtd2effdd93a9xNPPCGbN2821XSbm2+qIZ1gOD8/v96y2267zbR91apVpg2ZmZlutQMAnCGYAhAw0RxM2QpQOL4HQKjbvn27nHTSSTJkyBA56qij5Le//a0JlFyxdu1aGTFihP1y1llnubXvt99+W44++mjZsmWLS+vffPPNsnHjxnrLjjvuOLn88svliCOOkEGDBsmSJUvk/vvvd6sdABCyk/b+5S9/kXvuuafesjVr1siAAQMkFDBpL+BbFKAgmIomj73ypWS2auu37Rfk75dbLjnW6Tqa1bnrrrvkzDPPlHbt2sl9990nL7/8ssv7+P777+23CwsLzTG6e/fuMm/ePPG3+fPnu7zuwIEDzWvUwOmcc86xL9eM1rfffivFxcXm/ieffCJff/01Ew4DiIxgSv3888/mzJFNqHZ/YdJewHsUoCCYQuBVVFTIuHHjpF+/frJ48WJ59dVXpaamRh577DGZMmVKk8+59tprZdGiRfWW6YlOzfBcd911Lu1X96fd+2w+//xzuf3226Vv377y5ptvNvkcXf+KK65w6/XFxsbKU089ZZ6nr8uRZqKuv/56ad++vezdu1cuuugiycjIkFatWjXqDggAYRlMafCkX3CuSEhIkMTERPv99PR0P7YMgK9Fczc/2+ulm1/0aClrFCivv/66vdudHnM7dOggO3fudHn8k+rUqZO8//77JpDS57rTza+hdevWNbncU9dcc43MmjXLZM26detW7zHNQj366KPy0UcfmUBL1wvlE7cAwk/Qg6k+ffqYL2Y9Y71gwQKZNm2a6aPdFH2sYbdAAOGDYErMoHwgWBlhDSji4uoO/a5mpnJycuSLL76Qv/3tb2Yck7d8nZkaOXKk6eGiGSh9bZp50sIVY8aMkf3798tzzz1nLkozdPobo6ioyOvXAQBBD6YWLlwol112mTl7pV/WOoZK+0gPHjzY3r/Z0fTp082Xv2NmytUzZACCL1rHTOkPvPj4eHObzBRChSuZKc1iaYW8hx56SF555ZV6j3Xs2NE85u44Z19npq6++mpZvny5yTZpZmrZsmXSo0ePeq9hz549JjusY8Yefvhhn+0bAIIaTH322Wf221q2VIOrrVu3yrnnnisvvvhio/UrKyvNBUB4itbMFHNMIVxp8NG1a1f5/e9/by62kuVaxEK7/jnrLtdwzJRmgyZOnOjyvp9//nk59dRTTTA0e/Zs83ztzaJeeOEFM/5Lx0S1ZM6cOWKxWMxQAR0v9vTTT7vcBgAI+W5+jgoKCswZq969ewe7KQD8IFoLUBBMIVSq0mpFP3fHI+mlKVoi/cEHH2zyMa32Z5sOwFPOCl1oNqpXr16SlZVVb7mekNXiEo6GDh3qVTsAIGyCqdTUVPPlqGeOAEQeMlN080Pk0MIOABDtgjpp7yOPPGJS/trHWcutapUdHRz7xhtvBLNZAPyEYIoCFAAARJKgZqY6d+5sAqc2bdpIbm6umVhv/PjxpvoOgMgTrQUoHLs7UYACAIDIEdRg6oILLpBw6msOwDuMmSKYAgAgkgS1m184sVqtwW4CEPbo5kcwBQBAJCGYAhAwFRUVUltba25TzQ8AAIQ7gikAQenqF63BVGlpaVDbArjjzDPPNBPi6nxRq1atkr/97W8uPe/SSy+VgwcPmufZLu7M75STk2PmolyzZo3Z/9tvvy1t27Zt8Xk6iXB+fn69Zbfffrtpu7ZhwYIFMmbMGJfbAQBhVRodQHR09dOCDBSgAELfF198Ie+//77p6h4fH28KRf3444/y3nvvtfjcuXPnytSpUz3ar1b2/etf/yrfffeduf/www+bCsCXX355s8+5+eabZePGjTJy5Ej7smHDhsn1118vgwYNkpKSErnoootMUDdu3DiP2oXoltQ1SaqKq4LdDDiRlBb44lYEUwACKtozU1TzQyBpEHTXXXeZDJNO2HvffffJyy+/7PLzi4uL7bf1BEhiYmJAxhDv27fPXGwWLlwoN954Y7PrDxw40LxGDbbOOecc+3JbEKjzWGowpZP87tixw+/tR2TqeVdPKakqCXYz4ERqfKoEGsEUgICyBRMEU4h0y65NlexU/1WF3VdileH/KHFprKJmYvr16yeLFy+WV1991WR+HnvsMZkyZUqTz7n22mtl0aJF5rbOA/mPf/xD+vTpI88995zJVLlCt61d62xmzpwpjz/+uEyePFlmzJjR5HM+/vhjufvuu+sts1gsJpBqbr+xsbHy1FNPyRVXXGFel6MVK1aYfW3evFkOHDhg3gud3xLwxKYHNklRcRFvXghLT0sXuTCw+ySYAhBQBFOH59oCAuH1118312vXrpXq6mrp0KGD7Ny5U2655RaXnq/jjIYOHWrGLL3zzjsyYcIEmT9/vsfd/L7++msZMWKEy+1/9tlnzTioJ554osnHr7nmGpk1a5YZX9WtW7d6j3Xv3l3OOuss6d27t+zevVtuuOEGefPNN81rANxVvq1cyovqelcgNMWnxwd8nwRTAIISTEXTmCkKUEQnV7JGgZ7fTTM3cXF1h35XM1M2+/fvl08++cR0o3MlmGqOO5mpJ598Urp06WK68DXXvVDHSB133HFmbJS+toyMDJOJ0kITZ599tqxcudIEUuqll14yY6a0619VFWNfAHiPYMoJJu0F/BdMadecaPlBowU3bBgzhVDhSmZKuwauW7fOBDJpaWly6qmnyiuvvGIe02Bl+vTpJpBxh6uZKc1EaUZJAyln3xNXX321qfinWTfNTC1btkx69OhhHtu0aZMZR2UbM3XaaaeZDF00fO8ACAyCKRcxaS/g+7PkmrHxxY+amPgYsVb5dlC82Wa1VcQHm6UABcLVeeedZy76f6onQLRE+b/+9S97FzpnJwcajpnSIOb88893ab9HHnmk3HTTTbJ69WpTfEJptkm77KkXXnjBjP9asmSJ0+1o9z8N+rQCoY6X0oDqwgsDPKACQEQjmAIQUI4/vjTIKCws9Gp7rSa1ko6XdpTSdaWy5ZEtYq3xPvpJH54una/rLFW5VbJp+iapLa2baNhTBFMIlR4WWtHPHVr9Ty9NmTRpkjz44INNPqbFJvTiqe+//95p7xDNRvXq1ctU53O0detWadWqVb1lWs1QLwDgD0zaCyCowZQ3YtNjJefiHImxxEhq/1RpNaX+jyhPxMTFmOAsNilWkrokSfavsr3eJsEUIpFW2LPNAwUA0YpgCkDQgilvi1BkHZUllniLHJh3wNxvNdH7YCp9WLrEt4qXgz8clJqyGsk6Oksk1rttUoACAIDIRDAFIGjBlGNhBk+kD0031/s/2i8l60okuWuyxGV513s5fUTdNvPn5UvRT0USlxYnKT29aycFKAAAiEwEUwDCsptfTEKMpPRJkcp9lVKZWykla+rKUGt3P2+k9k2V2spaMwareFWxWZY2KM2rbdLNDwCAyEQwBSCgSktLfRJMpfRKMV38in+pC3jswVS/VK/GYCVkJ0jZljJTyMIWTKUO8C5As73OyspKqa31rpgFAAAIHQRTAMKym19St7rxVmWb6rZXtrFMrLVWSe7hXYBm25aqPlgtVXlVktQ1SaT5wmIuB1PMMQUAQGQhmAIQlpkpHR+lyrbWBT61FbWmy19ip0SPv9mSu9dts3Tz4Tbq9mOTYyWhfYLnbT30Oh1fOwAACH8EU044m+MCQJAzU12TTFe8il0V9mXlO8pN17/E9okebTMxp+55FTsOb1O7/Knkbl5kvA69TjJTCFdaeXPVqlX1JuF1Rueg0pMHur7t8u6777q1z9mzZ8vy5cvNc7/55hsZPnx4i8frL7/8UvLz8+3LTzjhhHpt2LlzZ4sT/QKAO5i010VWq/cTgQLwTWYqJj7GBD4aSFmrDv9vlm8vl8zRmZLYJVEqdh8OiFyV2DHRBGiVeysPb3NbuT14K1hY4FF76eaHcPfQQw+ZOaXGjBnj8nPWrl0rI0aM8Hif5557rhQU1P3PnXnmmfLyyy/XC6gaHpdvvvlm2bhxo4wcOdK+bM6cOeZi8+GHH8rcuXM9bhMANERmCkDQgilPM1Ma9MTExpjgyVHFzroAKqmjB/NXxYgkdEgwXQU1oLJv81BQltjBs2yXIphCsGjAMW3aNFm4cKFs2rRJLrvsMre3ceyxx0qnTp3k9ddfl0CyBVIqMzPT6UnNgQMHmoDrwQcfbHadnJwc81peffVVn7cVQPQiMwUg7Lr52cYvNcw+Veypu+/J+KaEdgmmi2DDbWrZ9dqqWhPAeSI+Pl5iY+tm/aWbX3RZ9vwVkp3l3Rxlzuw7WCrDr3uxxfUqKipk3Lhx0q9fP1m8eLEJJmpqauSxxx6TKVOmNPmca6+9VhYtWmSCmIcfflhOOukkE7C4Q/fn2C3w888/l9tvv1369u0rb775ZpPP0fWvuOIK+/2ZM2fa23jKKac0+Rz9/3rqqafM8/R1NUcDyU8++URyc3Pdeh0A4AzBFICw6+aXmF0X2GgWyZHtvifBlC1YchyDZdSK6fZnMlMaEzX/W61Jjq+RAhQIBltGSbvdVVdXS4cOHczYoVtuuaXF5z799NPywAMPeBSANNfNb926dS53/7v00kvN9SWXXGK6Gp566qmN1rnmmmvkvffekzVr1ki3bt2a3ZYGWzfddJNbrwEAWkIwBSDsMlPx7eKbDKaslVapyq8yc0V5XHyiibFWuiypc5LZbuXu+vtsCRP2Ri9XskaBUF5+uDusZm7i4uoO/a5kpo4++mhzefTRR00RitatW5ugpX///h63x53MlM0rr7wizz//vNn/gQMH6j2mY6SOO+44+e1vf2teW0ZGhmzevNmM79q/f7+9IIa2X4taAIAvEUwBCLvMlHbJs3XBa0izSKn9UyU2NVZqSlxPI8W3jW92m/ZxUzmJbgdTjgEj3fwQSlzJTPXo0cN+WwOSxx9/3J5V6tixo6meN2DAALf260pmSrsX6v/O7t27zf0zzjhD8vLyGgVS6uqrr5YVK1ZIVVWVyUwtW7asXrvVlVdeaQpYMGk2AF8jmAIQfmOmshOkpqxGaoobB0sVeytMMKXFJGyT77q0zbZOArQ9lfZgqkiK3GormSlEKi1Kod0GXR0zVVRUJBMnTnRp2xpMvfXWW+b/RwMg7WZ42mmn2R9/4YUXTOZs6dKlLW5LM1VnnXWWDBkyxKV9A4A7CKYAhFVmSqv4xbeON3NKNcXW9U/nmnInmNLMVG11rVQfrG4yQHMMuNxBMIVQmi+xXbt2Hm9r3rx59TJKmqlqrnqeruvNPHLbtm0zRTOao9monj17SqtWreot37p1a6NlhYWFkpaW5nFbAMAZgiknmLQXCL3MlAY9MZaYRuOlbGzLbd32XKWBUtX+KpEmqi/bslW27oXuoAAFIpWOowKAaMc8Uy5i0l4gNOaZcjZeSlXlVZnr+DauB1OxGbFiSbTUBVNNqCmskdqKWo8KW5CZAgAgchFMAQgoHSRumwvGk25+tmCqal+V02AqoU2C+wHa/uaLS2jGywRobn5rUoACAIDIRTAFIGjZKY8yU9nOM1PVhdVmkl13uvk5Kz5ho4/Zxmu5g8wUAACRi2AKQNCCKU8yU83NMWVnrctOmSxSjIvbPBR4NdfNz5txUwRTAABELoIpAEErQuFpZspaa7V352uKBkWWeIvEpse6l5ly1s3PFky5OW6KAhQAAEQugikAYZWZ0sxQ1YEqsdY0UXbvEH3cnXFT9nFYZKYAAIAbCKYAhE1mSjNNscmxzXfxO8SWYXJ13JSZY6qyVqoLmp+A1Fbwwt1ufhSgQDi79NJL5eDBg2byXb189dVXHj1PL08//bRHbbjnnntMRd1hw4a1uO6XX34p+fn59ZZ16dJFPvjgA1mzZo2sWrVKbrzxRo/aAQBNYZ4pAEHLTMXHx0tcXJxUVzcfxLhTFt2j8ugxdes5y0rVC9AOjdlyFWOmEO7mzp0rU6dODdjzHI0ZM8ZctmzZ0uK6N998s2zcuFFGjhxZb/msWbPM5MJvv/22uZ+dne1VmwDAEcEUgKBO3KvBRlFRkXvBVAuZKXfKo8dlxJnxVc7GSylrlVWq8qu8GjPl+LoR+Xrd18v8ffmLVq7c+OeNTtfRjM5dd90lZ555prRr107uu+8+efnllyUc6P+OZrPOPvtsmT9/vtN1Bw4caF7j5ZdfLuecc459+bHHHisVFRX2QErt27fPr+0GEF0IppyIiXGxFBgArybudTmYaqEseqMskguZKVupc9s4K6fbza2U1L6pYkm2SG1ZrUttpgAFgk2DiXHjxkm/fv1k8eLF8uqrr5q53h577DGZMmVKk8+59tprZdGiReb20Ucfbbrp6f/tjBkz6gUmzui29Xk2M2fOlMcff1wmT55sttOUjz/+WO6++25z++GHH5bnnntOduzY4XQ/sbGx8tRTT8kVV1xhn8POMcjKzc2VN954w7x+zXDdeuutsnnzZpdeAwC0hGDKRXp2D4B/MlOusheKyHUe+FTnV5uKf66MmXKlLHrDYErbUb6t3KU2k5mKXi1ljQLl9ddfN9dr1641XWo7dOggO3fulFtuuaXF53700Ufyv//9z/zP9u/fX+bMmSPbt2+XhQsXetzN7+uvv5YRI0Y4fe5xxx0n3bp1k9/97nct7ueaa66R9957z4yJ0uc40m7ExxxzjIwfP15++eUXEyTq69GugwDgCwRTTsRYDmemut3cTarzXBvX4VIA5mls5ux51gAHin5oi7Pn+aWdnj7P6Ufr4efuj3b64e9TCzXUFNVIdVG1CS7Kt5dL+dZy0w3O08yUq+yZqRa6+Wmlv+qD1S5187Nlr5yVWrexBXHuBFPeFKDQrFlyz2RJzEk0t2NTYiU2NVZiEmPM95P5joqt+67SCYURXB1TOkp8q3hJaJ8gidWJIfNxWFtbJTGurj011hpJ7ZwqiZIoD//lYZl05KQmn3PjnTfK4p8WS7EUiySJWX9z0WaZPW+2TDplkizbsczpPvV9sCRZJLFT4/dB96n7bspnX34mf3n4L3LCGSfIyDEjZcu2urFSnXI6ySeffWLa9ckXn5hlmiFWOkZKg6/f/va3JnjKyMgwmScNmLZt22ayYxpIKc3KPfvss26N1QQAZwimXBSfGS/xVjcGnjv7XePpbx4nz4tx/qDP2+IYaAI1ZTVStKJI8j7Pk7INZW4FU+5kprT4Q01pjdSU1O/K05TKvEpJ7ZNqftDVljffJc8WcOn6LW4z1/0iFO5mpiwpFmk1sZW0mtBKkjolubSP2upaEX2JJNCDKi4xztTI1cA2lILbRu3RADw2Ru742x0tPq9j+46ya+8ucz+7bbZMPmqyvP3x2+ax0cNGy3133CenXHhK4yfr+xDT9PvwzcJvZPwp453u98+P/NlcbNZ8u0bOveZcWfHLCvs2bV3xr776almxYoVUVVWZzNSyZcukR48e5rFPP/3UdBfs2LGj7Nq1S0455RRZvXo1gRQAnyGYckK7CdlsuGeD+QKGH/khyAylANTjwNXZ2L0Av2cqNinWlCjXgfV6Bj65e7KkD0mXrHFZ5lK4tFB2vrxTagqbD3gcgwpXM1MxcTHmbLerGSHTba9PXTe+ih0VPslM2SfudaM8ujvBVNaRWdLhwg4SlxZnsmsla0vMpWJnhRkHpkGkXmorakVqDn1HEUCFjJJuJVL11yqp2FXh8t9pIJjsccGh9tSK+XtytX1XXnulnHHGGSZQsVgs8tgjj8ns/842j+WMy5GS/JImt6X/TxPHT5QF7y+wL9Nuhueff75Hr0H/Hyp2H273Cy+8YMZ0LV26tMUTN9ddd50Zi6XfpQUFBR63AQCaQjCF0BHobm5h8is01NpZW1p7uFjDykMLY0TSh6ZL9tRsyRiZIcm9kmXr37c2+4PNk25+GhRpRrSl4hM2tjFQmnlqKZjSoETHWQUtmIoRybkoR9oc18ZkmXI/yZW8OXmmqyLgjYYnY7Sinzv+9Kc/mUtTJk2aZEqON0WLTejFV2yZJhvNRvXs2VNatWpVb/nWrVsbLfv8889bHKMFAJ4imALgPatI0fIiKVpZJO2ntpd2p7eTHnf0kE3TNzUZyHhSgMLVOaZsbN32WipCocGUBi165rslul5tVa1HwVR5eXmz49Q6XtJRWk9pbcaCbX1iq8kcAKGOyW8BwPRqBgAfqRXZ+85e2f3GblMoodtN3cwYIF9kplwti94wM+UsmLIkWkyXOle6+BnWuu2abbrYxdL2+prLSrU5sY0JpCr2VMjGv24kkAIAIIwQTAHwubzZeZL3VZ4JgDpe2tG3makWKvk1zEwltE1ocbyUK8Un7NvNrTST/MZluZbYt72+poKpxM6J0v7X7U1RDe0WqVUSAQD+c8cdd5heAs3NdQa4i2DKCSbtBTy35/U9Ur6j3BSlSBuc5rPMVNW+KvcyU04m7nWn+ISn46aaDaZiRDpd0ckEZrte3eVyxg0A4JnRo0ebucaWL1/OWwifIZhyEZP2Au7RMUi7ZtaVVNbiCo7fNp5mprRQROUB14IOnfequqDapcyUvaBGAIOpzHGZktIzxZSUL1hQ4PL+AQDuS01NNRNYa/GS/Px83kL4DMEUAL8pXV8qBxceNJPOZo3P8q6aX7v4ugySGz3htJy4lnCPSYhxHkwdymK5wnHiXneCKcfXrPP8tD+7vQkO9/xvj8v7BgB45plnnjEl8r/88ssW101ISJD09PR6F6A5BFMA/Cr3/VwTNLQ7o529aIO7wZTOa6XzW7k6XsrG1n3PNjGvNxP2NspMHep26ExiYqKZm6dhZipzTKYJxgp+KHBath0A4L3zzjtPRo4cKdOmTXNpfV2vsLDQftm5cycfA5pFMAXAr3QC08LFhZLYPlHSh6d71M1PJwdW7o4r0syUs4p+3oyZaqnkurM5ptqe1NZc7/90v8v7BTyhZ+JvuOGGRsuXLVsmU6dOlQ4dOsiCBQtaHCM8ZMgQ+eSTT/gQEHY6d+4sTzzxhFx00UVSUeHayavp06dLRkaG/dKpUye/txPhi2AKgN/lfZ5nrtsc28ajzFRidqK5rtzrWWaq2WCqbbyppFdbVuvyNnXd6uJql7r5NRVMpfRNkeTuyVK8qljKtzc9qTHgK//+97/l8ssvr7ds1KhRkpOTIx9++KH83//9n+n+1NK44JUrV5ofolOmTOHDQVjRv/f27dvL0qVLpaqqylwmT54sN910k7lt6z3gqLKyUoqKiupdgOYwaS8AvyvdUCplW8pMVb+EnASPM1MVeys8ykw11c0vJi5G4lvFS/k29wMa7W6oxSNi4mNMoQt3gqlWE1vVCzARuRYvXmwyP/60Z88eGTNmTLOPf/DBB/Lcc8+ZzJIGROqKK66QV155RWJjY033p9tuu80s79u3rxlPMnHiRNm8ebPceuutctxxx8kpp5xigq033njDVEKbO3euX18T4Ev6Nz148OB6y1566SVZs2aNPPTQQ1Jb6/rJNKApBFMAAuLA3APS6fJO0urIVlI6373MlH3CXnfHTOU2n5nSghYxlhiPSpKbghU96+awqthd4XIwpcFXxsgMqS6qlqKVnOmMdBpIaRejYKqurpZXX33VBFA333yzGcd3wQUXyJFHHmmCMA2abIH+unXr5I9//KP873//MwGWdg8cO3asPWul3QE1iwWEk+LiYlm1alW9ZSUlJZKXl9doOeAJgikAAVGwuEByLs6RzCMzZffnuz0bM+XDAhSeBmj1xk1lxzsNphwDRT14pw1Kk9iUWDnw9QG3qhIiPGnWKBT2oV395s2bJ7fffrucddZZsnr1anNW/vzzz5e9e/fWW/e///2v6co3e/ZsOfbYY2X//v319tW2bVsTkLk69gQAIh3BFICAqC2tlaJlRaaSnaWrxe3MVFV+lVgrre7ts6JWqgur7cGYL8ZhOQZgLY2b0nlNbHScWObYTHO7YCHzSkUDZ93vAkmDpw0bNsjpp59uMlQaXNn+JpOSkuqtq13/tEvUgQMHGg2613U106XjSYBwxtg/+BIFKJxoqboRAPcc/P6guU4bm2YG/roSTMWmxkpcWpxHQY/SzJHONWVJsfguM7XftWDK8bWVlpdK+oh0E9yVrC1xe5+ANzSAuuuuu0y3vTfffNMsW7FihfTr16/eeg8++KCsXbtWJkyYII8++qj06tXL/tiAAQPk559/ZhJ7AHBAMOWiliodAWhZ8YpiqSmpkfSR6faKfi118/Mm6FEVe+q6I+nEwb7ari2wS+xQf5vOgqnqzGqJTY6Vgh8LRBjvjADTAEoDp7feest0OVVbtmwx3fwGDhxo7p966qly0kknmbFSGzdulFtuucWMn9JufUofe/vtt/nsAMABwRSAgLHWWKVwWaHJNJVVlrmUmUro4GUwtbuZYKp9gtRW1Zrug+7SsVjahTCxo+vBlBwq6la4qNDt/QG+GISfnp4uV111VaNM1PXXX2+fk0qr/tkKUmjgpGWldXxUfHy8nH322fL888/zYQCAA4IpAAFV+GNdMFFhrXApM2ULWMp3eTYnU+WexlkkraqnmSkTaHmSdLbWTUask/7GJMS4FExZO1ilqqCKLn4IKRow6Ziqlrq19+jRQ+68805TAQ0AcBgFKAAEVPHPxVJTXiMVsRUuZaaSOtUNkK/YWeGzzJTe1rLonm7Ttt3kHslmW+Vbmw70HF9bZUylFC4u9Cx4A/zIlXLnWjZdLwCA+shMAQgoneRWx05VWitdzkxpdzxPu/lpGfPa6vpd8pI61wVo5Ts8y3aZ5+6se66zrn6OwVRZdZkULKKKXzSMrY2L4zxlOLJ9boyRBuAOvvEBBJwWYSivLreXYk5ISGiy3LKtO54JejzN6NSKVGyvyyJZki1SW1YriZ3rAiCvMlO76p6b1DFJCqSg5XmmDpZI6frDkxUj8uTm5poqlVOnTpVZs2aZMuLwn44dO0pGRoa53a1bN3uFUE8DKf3cdBv6OQKAqwimAAScZqbKq8rrBR1NBVO+6I6nSjeXmmAquXuylKwukZRedUFO2Za6gfbeBFPOMlOO80zlrsili1+E08INM2bMkJtvvlmGDh0a7OZEPJ1A2PY/tnPnTq+DVw2k9POzFeAAAFcQTAEIuNryWik+UCzSRexd/Q4erJuDypGtO563wVTZ5rofRxpQla6rC6y022D1Qc9/fOnztfuhLcvVUmYqdwlnu6OBzsN04403Srt27Zir0M8ee+wx++Srer17926Pt6Vd+zQjRSAFwF0EU04waS/gP0V7i+y3mytCoUGPYzDkqdINdd3rUgekmmp6lgSLlKz3cuJcq5jCEym9U8zEwjp/VkOp6YczU3lrqIIWLfQH+bZt24LdjIinmaSkpLoTLrt27eI9BxAUFKBwEQNSAd8q2HF4nFFzRSiSeyZ73R1PVe6uNIUoUvunSquJrcyykl+8DKYaZLyaktGhbjyHKi1hvBTgSxyXAYQCgikAQVFafDi4aN23daPHY2JjJKlrklTsqWgy6+OugwsOiiXeIq0ntTYT7hYu8X7y3NJNpU6DqfT26YfXLSWYAgAg0hBMAQgKx+CizfA2jR7XsUga/Hjbxc8mb06evbz63ll7zbgtb5VtOpSZ6tU4mNKuf2lZaYfXZVA7AAARhzFTAIIeTLUd3FYkpm4cko2ObzLrbfRNRqemuEbW371eEtom2CvxecsUsSiqltQ+qXWnphzis4yxGZIUXzeeQysVUiYbAIDIQ2YKQFA4ZmrSWqVJ2sDDWRyVPriui1zxz8U+26e10uqzQKpugyLFvxSbLFTDrn5ZR2ZJclzdspIS78dnAQCA0EMwBSDomanE2ERpfezhcVOWJIuk9EuRyv2VUrmn8fxToaR4ZV2wlz7s8PiopG5JJluVJHWZKcZLAQAQmQimAAQ9MxVfEi/pw9MloUOCuZ85NtOMlyr80fsiEf5WtKxIaqtrTSbKdFXUbosntTXXiVI3BxXBFAAAkYlgCkBQOHZ9q15fLTGWGOlwfgfzrdT6uLosVf43+SH/6ehYrKKfisxYrIxRGaace+a4TDOeKjmhrpsfwRQAAJGJAhQAgsIxwIjZGyNleWWSMTxD+kzvI4ntE6VwaaFvxzf5Ue5HuSaQ6nRFJ7FWW01guOeNPZL8R4IpAAAiGZkpJ2JiDvXZAeDXYCo1JVW2Pb1NKvZWmECqYneF7HplV9i86+Vby2XP//aYsV6xabGm9Hr12mr742SmAP/ieA0gWMhMuYiZ1gH/dfNLSUmRqrwq2XDXBklon2CCKvF+nt6AyvssTwp+KDC3qw9WS9u2deOmFMEU4HsclwGEgpDJTN1xxx3mi3HGjBnBbgqAQGemUuvmlLLWHCpdHmaBlI0GUXpxfE2K0ugAAESmkAimRo8eLddee60sX7482E0BEKTMVKRxfE1kpgAAiExBD6b07O3rr78uV199teTnh37lLgC+4RhgEEwBAIBwFPRg6plnnpGPP/5YvvzyyxbXTUhIkPT09HoXAJHTzS+SkJkCACDyBbUAxXnnnScjR46UMWPGuLT+tGnT5J577vF7uwD4H5kpAAAQ7oKWmercubM88cQTctFFF0lFhWtzyUyfPl0yMjLsl06dOvm9nQD8o7q6WiorK81tuvkBAIBwFLTM1KhRo6R9+/aydOnSw42Ji5OJEyfKjTfeKImJiVJbW1vvOfrDy/bjC0BkZKe0+26kd/Ojmh8AAJEpaMGUjpEaPHhwvWUvvfSSrFmzRh566KFGgVQwMAkg4F8aZGRlZZGZAuAVjtcAoi6YKi4ullWrVjX6YZWXl9doeShgckDAf+OmIrGbn2O2jdLogO9xXAYQCoJezQ9A9LJ1f4v0bn4EUwAARKagVvNraMqUKcFuAoAAsgUZSUlJYrFYQqJ7r68QTAEAEPnITAEImkguj04wBQBA5COYAhA0jlXuCKYAAEC4IZgCEDTRkpmiNDoAAJGJYApASARTkVaEgm5+AABEPoIpACHZzW9A1zay8KlLJO+d38tffnO0hBtKowMAEPlCqpofgOjSXDe/NhnJ8tn0c6VrdqZUVdfIPZccLTv3F8m/Pl0u4YLMFAAAkY/MlBPMqA4ELjPlmMn562UTTCD1+LuLZdBV/5KKymoTUMXHWcIumKqurpaqqqpgNweIaByvAQRL+PwyCTJmWgcCk5nq0i5Drj5luGzfVyh3vThP1u/Ml9e+XCWd2qbLORP7h83HYHs9TNgL+AfHZQChgGAKQEgFU9f/aoTExVrk0bcXSVlFtVn2/Ec/metzJw2QcEEwBQBA5COYAhAy3fySEuJMVqqotEJenr3S/tiP6/bItn0FcuLoHpKaFO/zdoztnyMXTBlogjhfB1OURQcAIHIRTAEImczUmUf1McUnXvniZyksrai37gcLNphga8KQLj5tw0ljesrCpy6V/9z1K3n2phN8tl0yUwAARD6q+QEImXmmzp880Nx+9YtVjdb9evk2ufGMUTJ5WFf5bPEmn7XhwSsnm+uamlqTFZvxzmJZvS3P6+0STAFAZBnWK1tKiiNrgvlIk5qWFvB9EkwBCBrHLnCtMtPlpP49ZMueAlm4elejdb9Zud1cTx7a1acHRr3MWbJZ/jdvtfzrllPkomMHyd0vfePVdpOSksRiqUv8U4ACACLD/McuFqmp32sCISY2MeC7JJgCEDSOgcbgXh0lMSFP3py3usl1cw+WyppteTKid3tJiI+Vyqoar/d/ythe5vqd+Wvlve/Wyz9+XytnHNHH62CKOaYAIPJMuOU1KSkuDnYz0EJmav5P90ggEUwBCInMVP/uOSK5K+W/c5sOptSS9Xukf9c2Mrh7W1m6fq/X+z9pdE9zrd0G8wrL5LtVO2Xi0C6mPPv23EKPt0swBQCRZ/nGfVJUVBTsZsCJ9PTDJ2kDhQIUTjAJIBC4zFTH7NaybscBWbZxr9NgSo3q08HrfesEwFrFb+OufNm2ry5wmrdim7k+clAnr7ZNMAUEFsdrAMFCMOUiJgcE/BtMWeLi5b9fN5+VUrZs1EgfBFODu7cz1QEXrd1tX7Zg9U5zfcRA3wVTlEYH/IPjMoBQQDAFIGjqBRqxCfJmC8HUTxv2+iwzpVkptWjN4WDqh0OFL44Y0NGrbZOZAgAgOhBMAQiasrIy++3Sqhj5Zet+p+vr3FPaLW9Qt7YSE+Pdvm0B2Y/rDgdT+UXlsmn3QRnSo51YLJ7vgGAKAIDoQDAFIKjddCorys3tgvJal56jc0ClJMVLt/aZXu17YLe25vrnLbn1lq/cnCvJifHSKyfL423rnFk2lEYHACByEUwBCKqY2ipzXVkb69L6tuzVgK5tvNrvwK5tZVdekRwsrj9nyMrN+8z1kB7ZHm+bzBQAANGBYApA0HTvkCnxMXXzRcUnJrn0nNXb8+zBkKc6tE6VVulJ8svWum01zEwp7ernKYIpAACiA8EUgKA5d1J/kZrKRl3j/J2ZsnXxa2qM1opDwdTQnr4JpqjmBwBA5CKYAhA0F0wZKNZDwZRjAOLMmm0H6gVEnrBltX7Z1jiYWr/jgFRUVpsiF54iMwUAQHQgmAIQFIO6t5XhvdpLYWGxuR8fHy9xcXEtPk8r+u3ILfQqM2V7rhazaKim1iobdx+UnjlZEuthRT+CKQAAogPBlBPMqA74z1UnDzPX2/YcDmhc7eqnQVBWWpIZ++QJDZTUxl0Hm3x83Y4DEh8X63HFQIIpILA4XgMIFoIpFzHTOuA7ifGx8pvjBkthSYVs2nm4NLmrXf3W78w31707tvJo/z06ZJqufFrNz9n2+3Zu7dH2KY0O+B/HZQChgGAKQMCddXQ/aZORLP+Z+4sUFdV183MnmNJueKqXB8GUTsbbvX2mbN5TIFarNJuZ8iaYIjMFAEB0IJgCEHC/nzraXP/z42X1qt252s1vgz0z5f7Euh3bpEliQpxs2tN0Fz+1bmddMNWnk2eZL4IpAACiA8EUgICaOLSLjBvQUeYu2yo/bdgrpaWlbmemNuzyvJtfjw51AdhmZ8GUDzNTlEYHACByEUwBCKhp5x9hrh9684dGwYarwdQmL7r52YpPbNpd0Ow6ew6USFFphfTtRDc/AADQPIIpAAFzzIhuctKYnrJk3R6Z/eNms8wxM+VqN7/yympTHt2TbniHg6nmM1O2IhRdszNMsQx32YLC2tpaqaiocPv5AAAgPBBMAQgInbPp0WuOMbdv++dX9uWedPNTG3YdNOXRW6cnuV3Jz9VgSotV9DgUfLnD9jocXxsAAIg8BFMAAuK2c8bJiN7t5YMF6+Xr5dvsyz0pQFFv3JSb2SlbZsrZmKl62/egK6HtdRBMAQAQ2QimnGASQMA3xvTLkfsunSD5ReXy2ydm13vM08zUxkPBTq8cN4OpDlmyv6BUikor/R5MUXwCCAyO1wCChWDKRUwOCHhGM0Ef/vXXkhAfK9c+/pnsyjs8r5SnBSg8zUwlJ8ZJTpu0Frv41Su/3sn9bn4EU4D/cVwGEAoIpgD4NSP13eMXS/tWqfLnmfPlrW/WNFrHkwIUasPOg25njnSyXuVKMGWbGNjdzJSeIU9LSzO3i4vrB44AACCyxAW7AQAiT9vMZPnjOePkll+PlbhYi/xl5nz562vfNbmux938drs/ce/h8VLNl0W32Z1XLKXlVW4HU8nJyfbbdPMDACCyEUwB8FpmaqL069JahvdqLyeN7iknjekhyYnxknuwVH775Gx5Z/7aZp/raTc/HfO0L7/ErbmmXC2L7tiVcFC3thIfZ5Gq6lqXnuOYXSOYAgAgshFMtVDK2ea1aadLeUFuvcdj5PDjTYmJ8XywbAsPe7nvFrbdUtskOK/L63bH+Of9bGnfQf0s/fg3aomJkay0RGmTkSzxcfXnYtq5v0ie+88CeeaDJXKw2Pk8S55287N1xTtiYCdJS06Q4jLnBSVUjw6HgqkWKvk5BlNDe2ZLt/aZ9jFU/g6mdF6r4b3bS6+cLOneIVNapydLWlK8eY0pifGmXLu+9xZL3Wegn5NtGRBNBo3sHuwmAADBlDOOPyaPGthZpNy9H3qATW2t1auB1FZvnuv8YY/3rc8rKKmQtdsPSF5Rmcn2/Lxlv3yzYpssWb+nxf16283PFuxoMNWrY5Ys37jP9W5+rmambEUoOrbyazClAdSFxwySi44dKEcP6iyJCZznAlrUpm5sIgAEE0dsJ6prDnfrGXbdi7Jt6xYPfqi28LiTn8n++hHs0nO92HdLv6G92bc3r7ml57v64x++5Wk3P7Vx10F7eXTXgqlM83+9PbfIrYqBGqy5ylZ8wtUCFOdO6i+PXDNFumbXFcfQoO27VTvkl237ZeveQtl3sNRk3fRSVllt2q/Buf656nWt1Vp33+rs2wSIPM/+Y7Ccf8HIYDcDQJQjmHJRYUlFi92VALjPm25+h8ujuxbsaDe/bfsK650ocb599yv6uZqZ0sIcz950glx9ynCpqamVFz5ZJk+9t0RWbq7fnRhA0yqranhrAAQdwRSAoKqoqJCamhqJjY31IDPl+sS97bJSzLijhWt2ubx9x25+vgymNJB6465fya8n9pd1Ow7IeX97X5Zt3OvyPgAAQGggmHKCGdWBwGWn0tPTPc9MuRDs2MZL2boGumLH/kIpr6z2eTD18NVTTCC1ZN0eOf7O/0p+UbnL2wfQGMdrAMHCpL0uYqZ1wH9sQYe7wdT+gjLTBdeVMU09bZX8XCw+YRtHp+trIKYV83wRTJ09oZ/cfPYY2bq3QE6c9iaBFOAhjssAQgHBFICwDaZs5dG7tMuQhPj65dm9nWPKMful29Z9uFuAomEwpaXkn/ndCVJVXSNn3zdL8grL3GoLAAAILQRTAILOFnQ4BiLuBDuaNerRoa4aXovBlItzTDUeN+VakQvHgLBhNb/7L58k7Vulyt/fXmS6+AEAgPBGMAUg6GxBR3Jyslh0NloPilC0NK7JFmy5OsdU44qBrbzq5qddEa85dbhs31co9732nVttAAAAoYlgCkBYzzV1eC6oVi1mpgpKyuWAm8Ue3Cly4SyY+vPFR5sqfn99/Tspq6h2qw0AACA0EUwBCDrHoMPdrn626nzOgp34OIsZ87Rpd4HbbXNl+y0FU7rvi44ZaLJiL81e6XYbAABAaCKYAhB0jmOLPC2P7qyiX7f2mWZclbvFJ5RW3dOCEd4EU9f/aoTExlrkiVk/ujxhMAAACH0EUwBCKjPlbjC1c39Ri3NBeVrJT9XUWmXL3gITrMW4UB3dMbOmQWJSQpxcfcpwKS6rJCsFAECEIZhygkkAgdDv5mebC6p7+0yJbWYuKE/mmGpY0S85MV46tkl3OzN13uQB0iYjWWZ+vlIKSys82j8A5zheAwgWgikXMTkgEJrd/GzjmsxcUNlNzwXV51Alvo2767oEumuDG+OmbO2vra2VsrIyM1ZK/fPj5R7tG0DTOC7DFdddd50sX75cCgoKzOX777+Xk046iTcPPkMwBSCsu/k5jpvq27l1k4/379rGXK/ZdsCj9h0uj97yXFO29peWlkp2VoocM7yb/LJ1v6zYtM+jfQMAPLdjxw658847ZdSoUTJ69Gj56quv5P3335eBA+tOdAHeIpgCENbd/NSqrbnmelC3tk0+3r9LGykpq5Qd+ws9ap9t4t5eOa5npvQ1nTOpvyk88d+vV3u0XwCAdz766CP59NNPZcOGDbJ+/Xq5++67TW+I8ePH89bCJ+J8sxkACF43v5+37DfXg7u3a/RYYnysGU+1bONeM77KE+5M3GsLBjWYOn/yAHP7v3N/8WzHAACf0UnhzznnHHOcWbBgQbPrJSQkSGJiov1+enrL42URvchMAQj7bn6r7MFU48xUn06tTVn0tTs86+KntJpfTU2tW2OmKspL5ejBXWTJuj2y/lBmCwAQeIMHD5aioiKpqKiQ559/XqZOnSqrVzffY2DatGlSWFhov+zcuTOg7UV4IZgCEPbd/LTsuE6Iq938GpYv79+1bhzVmm15HrevsqpGtu0rlL6dWjktj64VxVJSUsztlLi6NNh/vyYrBQDBtHbtWhk+fLiMGzdOnnvuOZk5c6YMGFDXc6Ap06dPl4yMDPulU6dOAW0vwgvBFICw7+Zn6+qXmpxguvQ5GtStruvfmu2eB1Nq5ZZcs33bnFVNsQVSqlVy3dfrm1+v8Wq/AADvVFVVycaNG2Xp0qVy1113mep+v//975tdv7Ky0mSyHC9AcwimAIR9Zkr9vKWuCMXgHvXHTY3o3d5cL9voXTW95YeeP6xn3faa4hgIZiTFyLc/b5ftuZ4VvQAA+G/slOOYKMAbBFMAwn7MlGMwNbxX/WBneK9s0w1w/U7Px0yp5YdKmw/rld3sOvUCwZpKeWMuVfwAIJgeeOABmTBhgnTr1s2MndL7kydPltdff50PBj5BNT8nmFEdCJ9ufovW7jbX4wd0tC9rnZ4k3dpnynerdnhcya9hMKXBWXMc215bVSFvf0MXPyAQOF6jOdnZ2fLKK69ITk6OmbR3xYoVcuKJJ8oXX3zBmwafIJhyETOtA6HdzU/ngso9WCrj+3c0RSI0eBp3KLDSinre2rgr32S4hvV0LZjavidP9h0s9Xq/AJrGcRmuuOqqq3ij4Fd08wMQEd381A+rd0nrjGQzSa+aMqybuZ63YrvXbdTgbOXmXJPpykpruq+9Y9tXbNjh9T4BAEBoI5gCEBKVlrR6krfB1Jc/bTHXp47rZa6nDO9qruet2OaTdi5ZX5fhGtMvp8nH09IOt/2ntd4HcAAAILQRTAEIqeyUp9381PsL1pvrM4/qK13aZcjovjmydP0eySss80kbv/25Lts0cUiXJh8f2b8ueFP7DxT4ZJ8AACB0EUwBCKkiFN5kprbsKZAf1+2WowZ1lpm3n2qWvTHXd5Pmzl9Zl22a0EwwNXlknyaLagAAgMhEMAUgpDJT3gRT6sH//mCupwzvZjJSL3yyXHxlV16xKUQxrn9HSYiPrfdYYnysjBnQtclxYAAAIDIRTAGImG5+6p35a+WP//xK5izZLKf/39tSUFIhvvT18m2SlBAnk4bWz05NPbqvJKek2O8TTAEAEPkIpgCEBFu3uLi4OElISPBqW4++tUhOvPNNWfDLTvG1976vG5d11tH96i2/+awxIpbD7SaYAgAg8hFMOcEkgED4lUf3t8+XbJai0go5Z2J/SU6sm6pv4tAuMrZ/R9mRfzgLRjAFBA7HawDBQjDlIiYHBEJ/4t5AqKiqkZfn/CxtMpLlqpOHSXycRWZcd6x57Ofthyv4EUwB/sVxGUAoIJgCEBIcq9+FcmZKPfbOIimvrJb7L58oXzx0gYzs00He/369FJRb7etQzQ8AgMhHMAUgJIRLZspWgv36J+dISmK86eK3bONeueyRj+oFgWSmAACIfHUd/gEgyMJlzJTNS7NXyDcrt0nX7Ez59uftUlVdSzAFAECUcTuY+s1vflPvfm1treTm5sr8+fOlrKzMl20DEEXCqZufzcZdB82lYbv1e7G8vDyILQMAACEZTD3xxBP17sfGxpouORpQHXPMMfLLL7+4vK3rrrtOfvvb30r37t3N/VWrVsl9990nn332mbvNAhDmwqmbX3Ns7aaLHwAA0cHtMVOtW7eud8nMzJScnBz59ttv5fHHH3drWzt27JA777xTRo0aJaNHj5avvvpK3n//fRk4cKC7zQIQ5sKtm19TbO2m+AQAANHB7czUkCFDmlz+4osvyqxZs2TMmDH27i0rV650uq2PPvqo3v27777bZKrGjx/vVoYLQPgLx25+DdnaTWYKAIDo4HYwtWzZMjO3Q1MT5OnyH374wX47Ls71zVssFjnnnHPMj5EFCxY0uU5CQoIkJiba76enp7vbfAAhKhK6+RFMAQAQXdwOpnr06NHkch339Pnnn8vQoUPdKkQxePBgEzwlJSWZM9NTp06V1atXN7nutGnT5J577pFAYUZ1IHDCvZufnhBKTk42t8lMAYHF8RpA2ART+fn5jX5AaCClXfRmz54ta9eudWt7uv7w4cPN2Ktf//rXMnPmTJk0aVKTAdX06dPlscceq5eZ2rlzpwQCM60D/hXu3fyYYwoILI7LAMIymDp48GCjLzA9I7R48WK58sor3W5AVVWVbNy40dxeunSpGXP1+9//3lT6a6iystJcAESecO/m5xhMUYACAIDo4HYwNWXKlHr3a2pqZNu2bbJ9+3afNEgzXY7jogBEh3Dv5kdmCgCA6ON2MPXNN9/4bOcPPPCAfPrppyYY0y57F154oUyePFlOPPFEn+0DQHhwzOaEe2aKMVMAAEQHt4MpX8rOzpZXXnnFzFNVUFAgK1asMIHUF198EcxmAQgCMlMAACDcBDWYuuqqq4K5ewAhpLS01H6bbn4AACAcWILdAABQWtjGlp0Kx25+jm2mmx8AANHB5WDq3nvvlZEjR/q3NQCimi0ICcfMlGMwVVRUFNS2AACAEAumOnfubIpFaNW+Z599Vk466SSJj4+XSMYkgEBghXMwpUV0bAimgMDieA0g5IMpnUOqQ4cOcsEFF5gfCo8//rjs379f3n77bfnNb34jrVq1kkjG5IBA4Cr6hXs3P+aZAvyP4zKAsBszpV9c3377rdxxxx3Sv39/GTdunCxcuFCuvfZa2bVrl8ybN09uvfVW6dixo/9aDCDiM1MpKSlhd6aZYAoAgOjjVQGKNWvWyCOPPCJHH320dOnSRWbOnCkTJkww2SsAcJdjRifcuvrRzQ8AgOjjs9Lo2uXvxRdfNBcA8MXEveHUXY7MFAAA0YfS6ABChmPw5Jjp8ZU+rS1ySp84ifPDNx+ZKQAAok9QJ+0FAEeOVfB8XYTimB6x8ulFKZIQGyNzNlbLya+XSq3Vd9snMwUAQPQhMwUg4jNTlhiR505NMoHUrqJaOaFXnFww2LdTOxBMAQAQfdwOprTKFgCEU2ZKs1J928TKO79UyYmvlZplvxubIL5kC/6qqqqkoqLCp9sGAAAREkzt3btX/v3vf8tRRx3lnxYBiFqOwZQvM1OXDqvLQv3rpyr5eV+tLNxRI+M6x0q3TN+VX7cFf+FUNAMAAAQ4mLr44ouldevW8tVXX8natWvNnFM5OTkSicJtnhsg0qr5+YL+F5/YK04Ollvl843VZtlbv1SZ66kDfNfVzxb8OQaEAAKD4zWAsAmm3n//fZk6dap06tRJnn/+ebnwwgtl69at8uGHH5rlsbGxEomYaR0Iz8zUkPYWaZdqka+3VEvNoYITH6+vC6qO6e677ysyU0BgcVwGENYFKHReqRkzZsiwYcPklltukeOOO07efvtt2bVrl9x7772SnJzs25YCiHj+yEwd26OuaOmXm+sCKLVmf63sLa6Vid3iTHEKXyCYAgAg+ngcTGVnZ8sf//hHWbVqlTz44IMmkDr22GPl1ltvlbPOOkvee+8937YUQMTzR2Zq8qHs01eba+otn7e1RjKTYmRYe++LmmphHoulbjt08wMAIHq4Pc+UduW7/PLL5cQTT5RffvlFnn32WXnttdekoKDAvs73338vq1ev9nVbAUQ4f2SmxnSMlYJyq6zOra23fOHOGjl3ULyM7hgrP+2p/5i7KIsOAEB0cvuU7EsvvWS68mk1vxEjRsgzzzxTL5BS+vj999/vy3YCiAK+zkzlpMVITrpFlu6ukYbz8y7ZVZepGtXR+3FTjm0lMwUAQPRwOzOllfvKysqcrlNeXi733XefN+0CEIV8nZmyBUpLdtfv4qd+2nMomMrxPpgiMwUAkU+7hZeket81HP6TmmYJ/WAqLi6uyTPGWlVHJ6rUCSsBIBQyU7ZA6cdDWShHhRUi6/JqZEi2ReItIlVe9PQjmAKAyDf/ijSRiob9HBBSEn0zRMCvwdTBgwedliPdsWOHvPzyy6aiH2VLAbijpKTEp8HU8A51Z6iW7m46Ulqyq1b6tomVQdkWWebFuCm6+QFA5JvwYrGUMDF7SEtNi5H500I8mLrsssvMeCgNmBYtWmSWjR07Vi699FL529/+Ju3atZPbbrvNZKmmT5/ujzYDiFB6Aka7+mmmxxfd/Pq3tUhFtVU25jcdKK3cVyMXSLwMbOddMEVmCgguJu1FICzfWytFRd4VLIJ/pacH/vNxO5jSoEnLn7/11lv2ZR999JGsXLlSrr32WjPf1LZt2+RPf/pT2AdTfDkDgWcLprzNTMVZRHq1ssi6vFqpbSaZvupQhb9B7bQ74OF5qNxFZgoIPHq/AAgFbo/SOvLII+Wnn35qtFyXHXHEEeb2t99+K127dpVIwpc2ENhxU95mpnq2skh8bIyszWv+LNUv9mDKuwGrZKYAAIhObv+C2L59u1x55ZWNlusyfUy1adNG8vPzfdNCAFFZ0c/bzFS/NnVfb2v2Nx9MbcqvlfJqq+nm5w2CKQAAopPb3fx0PJR28Tv55JNl8eLFZtno0aOlf//+8utf/9rcHzNmjLz55pu+by2AqMlMxcfHS0JCglRWVnq0nX5t6wIkZ5kp7f6nwdbQ9hZJihMp97CnH938AACITm4HUx9++KH069fPjI/Sa/Xpp5/KmWeeKVu3bjX3n3/+ed+3FEDUzTWlQUpeXp5Xmam1TjJTatW+WhneIdasr4OLPUFmCgCA6BTn7hxTn332mVx33XVy1113+a9VAKKW41xTGqR4HUzlNZ5jytGqXH083pRH9zSYIjMFAEB0cmugQHV1tQwdOtR/rQEQ9Xw1ca9289tXUisHy52vZxtT1a9N3QS/niAzBQBAdHJ71PVrr73WZAEKAPB1Nz9PK/plJYlkp1pa7OKntHS66nsok+UJgikAAKKT22OmtKvfFVdcYeaTWrJkiZSUlNR7XOegAoBgZqZsWSZnxSdsdELfWqtV+rT2PJhybKdjMAgAACKb28HU4MGDZenSpeZ23759I3ouJibtBcIzM+VKJT8breC3vcDqk8xUWVmZ1NQ4H6MFwPc4XgMIm2DqmGOOkWgUaYEiENmZKdcq+Tl29Tu+V5x0SIuRPcXu/6/b2unYdgD+xXEZQCjw+FRsr1695IQTTpCkpCTftghAVPNFZqp/25Yn7HW07oB346Zs7aSLHwAA0cXtXw6tW7eWL774QtatWyeffPKJ5OTkmOX//ve/5dFHH/VHGwFEEV9lpqpqrLL5oOuZKeXpuCmCKQAAopPbvxxmzJghVVVV0rVrVyktLbUvf/PNN+Wkk07ydfsARPmkve6yxIj0bm0xhSWqXZw2ar0XFf1iY2MlJSXF3KabHwAA0cXtMVPate/EE0+UnTt31lu+fv166datmy/bBiAKNZy0113ds2IkMS7G5fFSat2hiX09CaZSU1Ptt+nmBwBAdLF48sPBMSPl2P2voqLCV+0CEKW8zUy5UxbdZstBq+kW6Ekw5dhGMlMAAEQXtzNT8+fPl0suuUT+/Oc/26vpaEnS22+/XebOnSuRRLsL2cw4MUnKDjYutuGs7pezAoCePi+S9ln3XGsQ9unZc9mn8/envNoq+0vrLruLrLIqt0YKKwKfmXKnLLpNjbVuvqlerSzm/77WGtgJe+MsmlGzmO6JWlEwKylGMhNjJDVBJDam7vFYS4y5HWup/93kCz7eHBAQR3arO3ECAGEVTGnQ9OWXX8ro0aMlISFBHn74YRk0aJDJTB111FESSWIcfmFcMCRepDghmM0Bws7m/Fr5bGO1vLWqSuZuqQlQZsq9suiO46b6t42VrpkxJlPl72CqTXKMXDw0Xk7rGydHdYmV5HhCGsAtbQmmAIRhMLVq1SozWe+NN95oziDrD4l3331XnnnmGdmzZ49EklqH32LHziyRvNziZoOthpz9LPL0ed7tMyYI+5SQ2qc3z42sfcb4ZZ+p8SJtUmKkbUqMdM20yJBsiwxtHyu/HZ1gLkt21chtn5fL1y0EVV5nptq4n5lqWB59y8Eav3XzS08QuWtCovxhfIIkxdW9qVsO1srS3dWy4UCt7CyyysFyqxSUW6WkymqKaOilRi9WvbaazJmvZ75jKj2Em7t7VsmvRwe7FQCindvBlCosLJQHHnhAIp7Dr8dVubWyd697P86AaJccJ2Yy3BvGJMgJveJk7qWpMuOHCrltTkWzXem0WmhlZaXJfHuUmWprkQNldd0N3WErj67B1JyNNX7JTI3oYJF3zk2RHq0skltSKw9+WymvrqiUTflMCg64K6/M6tJJIgAIuWAqMzNTxo4dK9nZ2WKx1B+w/eqrr0okYqZ1wH1l1SIfrK02l2N6xMqLv0qWm8cnSo8si5zzVlmzpcs1w9OmTRu3M1Oa9emYbpHvt1e73VZP55pyNTM1sVusfHJhiqQmxMhzP1bKtC/KpYCaPYDHOC4DCMtg6rTTTpPXX3/d/MjRDJXjl5nejtRgCoB3vtpcI2NeKJGPLkyRM/vHy79/ZZVL3yt3Gky5m5myF59wc7xU/bmm3BuH4UpmangHiwmkkuNFrni/TF5aVuV2+wAAQOhxuw7w3//+d3nxxRfND4hWrVqZwhO2i/74AYDm5JZa5aTXSmTVvhq5ZFiC/G5s00VdbEGJu5kpT8qi2+wqskpJpdU+5spXwVSrJJF3z63LSF39YTmBFAAA0RxMderUSZ588kkpKyvzT4sARLT8cpHT3yiVwgqrPHJ8ogzObvw1ZOsup/PaNexK7Ouy6DbWQ8/rlhUjSXG+6+b3xElJZozUU4sq5cWfyEgBABDVwdTs2bNNWXQA8NTmg1a58ZNySYyLkWdOaTx/m2OGRwMqf5dFt1mzv1YsMTFujZtylpk6vmes/GZYgqzZXyO3zWm6SyMAAIiiMVMff/yxPPLIIzJw4EBZuXKlqbzl6MMPP/Rl+wBEqFdXVMnlw+NlSo84uWBwnLzxc3WTGR7N/LhSctwWTGnpcJ2A1xMa9IjES/+2Flm5r9btzJRjMKUT6+pk3+qaD8ul0vUCgQAAIFKDqRdeeMFc//nPf270mBagiIvzqEAggCh002flsvy6VLlvSpL8b1WxmUepYVDi6rgpDV60rPmm/FqPAxfNTCkNplzl2D7HoO/CIfEyKDtW3l1dJfO3EUkBABCJ3O7mFxsb2+yFQAqAO37eVyv/W1UtvVtb5LzBcc1mplzRLTNGkuNjZLWHXfzqB1OxXnXzi7OI3DMpUWqtVvm/udQ/BwAgUrkdTEUTJgEE/O/++XXBxp8mJIpt2k3HzJSrwdSAdnUBkDfB1PoDtSYAcicz1VQ3v7MGxEmv1hb578/V8ksuk30D/sbxGkCwWNwZK5WRkWG/f8cdd5jJe220NPqqVaskUjE5IOC/7NSs1VUysF2snNg7rlFmytVufgMOBUC27JInyqtFNufXlUe3BXauBlO1tbVSUlJibt90qOT73xeQlQL8heMygLAKpk488URJTEy037/rrrtMAGWjXfz69evn+xYCiHhPLqo019ePjvc4M2XLJq32MhOkRSh0TqjOGa6FU7aTTDqJuRqVY5GjusbJd9uqZeluslIAAEQyi6cpdFLqAHzl6y01sjq3Rk7tGyfds2K8ykytNhX5PLfm0BxVrnb1axhM2SYifmJhXYAIAAAiF2OmAISEZ3+sNHM8XTMqweMxU7uKaqXQy5517hahcAym0hNEzh0UL7uLamXWmsOl3gEAQJQHU9o3uWH/ZPorA/CVV5dXSXm1VS4eEi8lxe5V88tOjZHWyTFejZfypDy6xWKxZ840mDprQLypKPj6yiqppocfAAARz+VJobRb38svvywVFXWnfZOSkuT555+3D7h2HE8FAO4qqBD5YG21yez0Sq37XnE1mDrcxc93wZRtm844tk2DqYuHxtsnJAYAAJHP5WBq5syZ9e6/9tprjdZ55ZVXfNMqAFHpleVVJpg6JqfUvsyximhzhrSvC3xW7fN+ctz9pVbZV1Jr36Yzjm2rKi2UE3rEysq9NbJiL2kpAACigcvB1BVXXOHflgCIerM3VptA5rhOZW4FU8M71I1v+mmPb4KYZXtq5YRecdIpPUZ2FtXv3uzIsW3Z8cVmzBdZKQAAogcFKACEDB1n9MbPVZJaW+ReMNU+1ky2q1khX1i2p6ZekNYcx7b1TCk1bdD2AwCA6EAw5QTl34HgFKKQysPBlOPk4E2Js4gMzrbI+rxaKfFRHHM4mLK4PGaqXWyxKfG+o7D5TBYA/+B4DSBYCKZcROVCIDCW7K6V1XsrxVpZ4lJmSqvuJcbFmK55vmLbljuZKakooosfEEAclwGEAoIpACHntZVVElNR5FIwNeJQwLPMR1381Lq8Wimrstq33RzHtlWWFso7v9DFDwBCyZ133imLFi0yFVf37t0rs2bNkr59+wa7WYggBFMAQs7rWlrcxWBqVMe6rzFfZqZqrCIr99VKr9YWaZXU/HqObftx80EpqvRZEwAAPjBp0iR55plnZPz48XL88cdLfHy8zJkzR1JSUnh/EdhqfgAQKFsLrFJUVCjpbVsOpo7qUvc1tnBHtU/bsGBHtYztFCtHdImTT9Y3vW3Htn32S75P9w8A8N7JJ59c7/5ll10mubm5MmrUKJk/fz5vMbxGZgpASNqRW2CuLRaLpKamNrlOanxdkQidXyq/3Lf7/3ZbXbfBo7o039WvTdbhYGreWoIpAAh1tqJGBw4caHadhIQEU2DI8QI0h2AKQEjauKcumFKZzWSnNHMUZ4mRb7f7bryUzXcuBFNDumbZbx84WOjzNgAAfFv18fHHH5dvv/1WVq1a1ex606ZNM2OsbJedO3fyMaBZBFMAQlJe/uHg5JgBrZpcZ0K32HqBjy/tLrbKpvxaE7AlNdMhekCnw2Xb9YALAAhdOnZq8ODBcv755ztdb/r06aYbt+3SqVOngLUR4YdgCkBIcgxOzhnRusl1Tukdb66/3Ozb8VI2czZWS3J8jBzTo3E01SMrRtq3IZgCgHDw1FNPyWmnnSZTpkxpMdNUWVkpRUVF9S5AcwimnGASQCA0gqkTB7aStikx9R5vlxIjYzpZ5KfdNbKryD8T5X6wti5I+1W/xsHUDWMTJCbxcD96DrZA8HC8RkuB1NSpU+WYY46RLVu28GbBpwimXMTkgEBgFRQcHjOVmJohvx1dl4WyOXdQnFhiYuSDdf7JSqmvNldLSaVVftU3TmJj6he+uHJEgtTEp5n7paWlUlPj+66GAJrHcRmudu27+OKL5cILLzQnvdq3b28uSUlO5r0A3EAwBSDkM1OVsWnyu7EJkuVw7LtiRIK5fnW5/yZ3qqgReX9tteSkW+S0voezU7ceqW2JkeKYuswU46UAIDRdf/31kpWVJfPmzZM9e/bYL+edd16wm4YIQTAFICQ5Bijf7E2RdqkWuf+YumhKA5uRObHyxaZq2Zjvny5+Nk8vqgvW7pqQKJYYke5ZMfLHIxOloNwqtQkEUwAQ6l1Am7rMnDkz2E1DhGDSXgAhH0x9vy9F+hXWyvVjEqTGKnJW/7qvrru/qvB7OxbsqJFP11fLyX3i5KUzkmR0x1hJS4iR339WLn//W13JdjJTAABEJzJTAEKSY4CSlJohv/pvqeSXWU13v04ZFrl3XoUs3BmYcUrXflQm2wtq5ZJhCTKwXazMXFYpL6yIlbi4uqCOYAoAgOhEZgpASHIMUHSej2V7amXAM8Wmi9+6vFqZ74e5pZqzvdAqw54vljP6x8vOwlr5fFONGcDcVFsBAED0IJgCEBbBlNpbYpV//1QVlPbkl4u8vKyqUZsUwRQAANGJbn4AwiaYCiUEUwAAIKjB1J133imLFi0yP5r27t0rs2bNkr59+/KpAKg3CW6oB1NM2AsAQHQKajA1adIkM5na+PHj5fjjj5f4+HiZM2eOpKSkSChgRnUgeCorK6W8vDwsgim6+QHBxfEaQFSOmTr55JPr3b/sssskNzdXRo0aJfPnz5dQwkzrQOBpkKKz1GdmZobc208wBQQXx2UAoSCkClDYfjAdOHCgyccTEhIkMTHRfj89vW7CTACRqaCgQLKzs0MyM+X4/UNmCgCA6GQJpRT9448/Lt9++62sWrWqyXWmTZtmfrTYLjt37gx4OwEEji1ICcVgiswUAAAImWBKx04NHjxYzj///GbXmT59uvkBY7t06tQpoG0EEJxgSsdTane/UEIwBQAAQqKb31NPPSWnnXaaTJw40Wm2SQek6wVAdJZHtxWkCAUEUwAAwBIKgdTUqVPlmGOOkS1btgS7OQBCSCjPNUUwBQAA4oLdte/CCy+UM844w8zT0r59e/ug81A6Aw0gOAimAABAKAtqZur666+XrKwsmTdvnuzZs8d+Oe+884LZLAAhgmAKAACEsqBmpkJ9kr1Qbx8Q6cIhmKquriaTDgQZx2sAUTtmKlwwOSAQeOEQTDHHFBAcHJcBhAKCKQAhi2AKAACEspAojQ4AoRJMderWR86+9CZJTEqWT99+SX5e+l2T66WnpzdqIwAAiC4EUwBCVqCDqe69B8r9z38gyalp5v4RU06Tp//2B/nq4//WWy8uLk5SUlIatREAAEQXuvkBCFk6TUKggimLxSK/v+cZE0i9/OQ9cv+tF0tZaYlcd+cj0rVX/yazUopgCgCA6EUwBSBkBTIzNfGkX0u3XgNkwdyP5IM3npcl338h/3jojxIXFy/X3/n3eusyYS8AAFAEUwBCViCDqZPPvtxcv/HPh+3Lvpnzrixb+LX0HTxKxkw4scm26ITjAAAgOhFMAZBoD6Z69B0sfQaOkFU/LZAdW9bVe+yNfz5krs+78lb7sszMzCa7IgIAgOhCMAUgZFVUVEhlZaXfg6mjj59qrr/88D+NHlv/y0/y0w9fSc9+Q2XY2ElmWVZWlv3xgwcP+q1dAAAgtBFMOcGM6kDoZKf8GUyNmXCC1FRXy+Jv5zT5+Af/ed5cn3TWZeaazBQQWjheAwgWgikXMdM6ENxgyjGA8aWOXXtJ52595JdlP0hJUdNd9lb8OF92bt0go48+Qdq270RmCggBHJcBhAKCKQAhzTYmyV/B1IjxU8z14u+azkrZfrTNnjVTYmNj5cSpl5CZAgAABsEUgJBmG5OUmJgoSUlJPt/+oBFHmOuVi+c7Xe+rj9+UivJSOea0C6R169aN2gcAAKIPwRSAkOYYrDgWfvCVgcPHS1FhvmzbtMbpeqXFhfLdlx9KqzbZ0qvvIPtyqvkBABC9CKYARG0w1aVHP8nIaiOrly10afzFnPdeMde9+g1osn0AACC6EEwBiNpgSrNSSotPuGLdz0tk68bVkt2ug30ZmSkAAKIXwRSAsAmmfF2Eot+Q0eb6l+ULXX7O5++9JvFxMeZ2bW1tvYmFAQBAdCGYAhDSHDM/vs5Mde8zSGpqamTrhl9cfs682W9LXGxdMFVUVER5ZgAAohjBlBNMAghEbje/uLh46dy9j+zatlGqKitcfp7ORWWtqTS3S8vKfdYeAJ7jeA0gWAimXMTkgEBkBVOduvU2AZU7WSmbxPhYcx0Tm+Cz9gBwD8dlAKGAYApAVAZT3XoPNNdbNqxy63kJCQn2+a7iElOlXYfOPmsTAAAILwRTAKI6mNq6YbVbz3MsglFVY5VjT7/QZ20CAADhhWAKQFQGU917180VtcXNbn6OwVRFZZUce/oFYomt6/YHAACiC8EUgOjMTPUaKMWFByVv3y6Pg6ltWzZJm3Y5MuqIY33WLgAAED4IpgCENC0/7utgKiOrjbRu18FMwOsuxzasXrnUXB9/5m980i4AABBe4oLdAABwRifG1bmmNCPkq2Cqa6/+5tqTSn6OmakNa1dJRWovGXnEsZLTpafs3r7JJ+0DAISeHr0HSXFJSbCbASfSUlMl0AimAIRFVz8NYhwDGW8n6/VkvJRyDOg0yPvpjefkhrtmyDmX3yxP3vc7n7QPABB6/vaP96W6xhrsZsCJuNgYCTSCKQBhEUx169bNZ5mp7r0G+iQzpe36+pNZ8uvLbpYJJ5wlb734mOzesdknbQQAhJa7rz2DzFQYZKZOX7ogoPskmHKCGdWB0CpCkZycLImJiVJRUeHV9rr1HmC6D27fvNbrzFRNTbW8M/MJuX7a3+Wi394lj/7paq/aBsB9HK8RCJs3rKo3jhehJz09PeD7pACFi5hpHQiNin7edvXTMuZdevSTPTu3SHlZqdeZKTX34zdl28Y1cuQxp8uQ0Ud71T4AruG4DCAUEEwBiKry6Dmde0pCYpJHXfwaBlOamVKanfrXY38yt6++9QGzfQAAEPkIpgCEPFvQ4otgqntv23gp98uiq1atWjUZ5P289Dv5+tO3pHP3vnLZ7+7xqo0AACA8EEwBiKrMlI6XUls3/uJ1MJWfn1/vsX/9/S7Zs3OrnHT2ZTLxhLO8aicAAAh9BFMAoiyYGuhxWXTHYKq0tFQqKyvrPVZaUiSP/d+1UlFRJjf+3xMy6qjjvWorAAAIbQRTAKIqmNKy6GUlxbJv1zavgqmGWSmbDauXyaN/ukZiJEbufOhlOeXXV3rVXgAAELoIpgBETTCVkpYh7XI6y9ZNqz2uBNZSMKWWfPe53H/bxVJeViJX3Xq//OWJN6Vrr/4etxsAAIQmgikAURNMHS4+4VkXv/j4eElNTW0xmFLLFn4td151iqxZsUiGjZ0kj7/2tdz79DtyyjlXStee/SU2lmn+AAAIdxzNnbBYDseaZ/7mRikrK2+8Ugtnt52d/W75zLgft93Sw8623fKTPd92S8/1Yt8tbtuL96yldrW87XB9T6zNtqmstESKC/OlqCBfDubtk/y8fRLseaa6+bCSX0vBlNq5dYP86bozZMLxU+VXF14nQ0YdZS6qqrJCcvfskIMHcqXgwH4pLy+VqspyqayokKqqSqmtrbG/v/o51H0Wel23bXP/0PIW/waACNRn0Ej7bSbtBRAsBFNOxMQcDqZ+fenvpbqGHyyAp4oLD8rWjatlxY/zZfE3n7lVAMJXmaluvQb4pPiEq8GU0mDnmznvmkunbn1k9NHHS+8Bw02WrG2HTtKxay+P2gJEu37d0oLdBAAgmHLGaq21357x599KSWlpvcdbPhPW/OMtPbfFbcd4sW0n7Tq0gufb9mbf3m7b2eNevidebbvFtzvy3pMYi0WSU1IlPbO1pGVkSdv2naRrj34yaMQR5nLB1beb7m//+edD8vOS7yRQ80zZuvlt2xiYzFRDO7euNxdHySlpktW6nZnoNz4xSRISEiU+IfFQZjzGvM/299rcdvhsHB8DoswfbrhGep87NdjNABDlyEy52MXpx+8+l6KiokB8JkDEatMuR0aMnyJTTj1PBgwbJ/c9/Y58M/sdef7h26W8tMSvwZQGHV17DZB9u7ebEubBCKaaUlZabC4A3LPnzBN4ywAEHQUoAARMXu5u+eLD/5hxRH++4WzZtmmtTDzxbHnwhU+kdbsOzT6vpqbGfjLD02CqfadukpSc4nHxCX8FUwAAIHwRTAEIip+Xfie3X3GifP3pW9K1Zz+575l3pVWb7BbHTXkaTHXr5d1kvap169b22wRTAACAYApA0FRWlMtTf71JZs+aKR279JTbp78ocfEJfgmm7GXRPRwv1TAzdeDAAY+3AwAAIgPBFICgj0184dFpsuS7L6TfkNFy6Y1/dhpMpaSkSEJC0wGXM91611Xyo5sfAADwFYIpAEFXW1srM+65XnJ375BTz71KBo040udzTekcUxUVZbJ7x2aP28mYKQAA4IhgCkBIKC0ulGem32xu//bORyQuLr7ZYMoxqHGFFp7I6dxDtm9aJ7U1NR63kWAKAAA4IphygvlbgMBasXi+zPvsbTOR7QlnXlLvMccxSo6FIFyhJdHV1o2eF59QBFNAaOJ4DSBYCKY8mHMKgP+8/vx0U5ji3CtvkZS0DJ8EU/biE15U8nMMpkpLS6WystKrbQHwDsdlAKGAYApASNm/d6d89OYLkpHVRk759RX25Xl5eV4EU4O8LovuGExRFh0AACiCKQAh54M3npeK8lI59dyrJSExuVFmqk2bNm5tr3vfQ8HU+lVetYtgCgAAOCKYAhByCg/myRcf/EcyW7WR4351oVfd/CwWi5mwd9/u7VJceLiIhbvi4+MlNTXV3CYzBQAAzO8M3gYAoej9/zwnNdXVctq5V5vB5Z528+vQuYckp6TK5nU/e9Ueik8AAICGCKYAhOzYqUXffCYdOneX4eMme9zNr0efwT7t4qfITAEAAEUwBSBkfTbrZXN90lmXedzNzzZeavN6MlMAAMC3CKYAhKyVP34rO7aul5FHHifxSWlSc2jCXXeCKVtmim5+AADA1wimnGASQCD45sx6RWJjY+X4My62d69zq5tf38Gm8ETunh1etYNufkDo4ngNIFgIplzE5IBAcMz95H+mTPqxp11g7+rnamaqbftO0qpNtmxcu8LrdhBMAaGF4zKAUEAwBSCklRQVyPdffSSt2raXiqq6bn5ZWVkmW9WSvoNHmet1Py/xuh0EUwAAoCGCKQAh7/P3XzXXCckZTQY3zek7cKS5XrdqqddtIJgCAAANEUwBCHlrViyW7ZvXSVLa4QDKla5+fQfXBVPrfRBMOe6P0ugAAEARTAEIm+xUVY3V5WAqLi5eevYbKnt2bJHCg4cn/PUUmSkAANAQwRSAsPD1p29LeUWV/X5LFf20il9CYpKsW+X9eClFMAUAABoimAIQFooL82XtLytczkwNGX20uf556fc+DabKysqkoqLCJ9sEAADhjWAKQNj4Yf6XbgRTE8z1yh/n+2Tftv3ZyrMDAAAQTAEIGyuW/mC/3blLt2bXi09IlP5Dx8i+3dtl765tPtm3rVvh/v37fbI9AAAQ/gimnGBGdSC0OGaFBg8f0+x6Q0YdLYmJybJ80Tyf7Dc1NVWSkpLM7bw874tZAPAtjtcAgoVgykXMtA4En2Mg07vvgGZ/QI2fcqq5XjjvU5/s17HYBZkpIDRwXAYQCgimAIRlZio9PU1GHXVco3UssbEydsKJUlJcKCt8NF7KMZgiMwUAAGwIpgCEjcLCQqmpqTG3E+Isct6VtzVaZ8zRJ0hGVhtZPH+2VFdV+mS/bdu2td8mmAIAADYEUwDCqluPLTtlramQXv2HyRHHnF5vnVPOucpcz54102f7pZsfAISnCRMmyAcffCA7d+40x5Azzjgj2E1ChCGYAhBWbMFUXEytyVJddcv9JhOlRh5xrAwZdZSs+3mJrF35o8/2SWYKAMKTFhBavny53HDDDcFuCiJUXLAbAACeBFMZGRnywX8elqm/+Z3834z/yEdvviCX3XSveezlp+qufYUxUwAQnj777DNzAfyFYApAWHEcszTnnX9LTpeeMn7yqfL7vzxtlr367N9kzYpFPt0n3fwAIHokJCRIYmKi/X56enpQ24PQRjAFIGwr+mVmZsgjd10l46ecJr37D5MVi7+R5Yu/8fk+6eYHANFj2rRpcs899wS7GQgTjJlygkkAgdAOpjRjpAOKF3z1oclI+SOQsu3HhnmmgNDD8Rq+NH36dNOV3Hbp1KkTbzCaRWbKRUwOCIReN7/WrVsHZJ+2zFRVVZUpzw4g+Dguw18qKyvNBXAFmSkAYZuZClQwZctMOe4bAAAgqMEUtf8BeNvNLxBs+6GLHwCEX2n0YcOGmYvq0aOHud2lS5dgNw0RIqjBFLX/AYR6Nz+t6JSWltZo3wCA0Dd69GhZtmyZuagZM2aY2/fdd1+wm4YIEdQxU9T+B+BNZsqxyp6/MMcUAISvefPmUaAEfhVWBSio+w9g37599jehXbt2fn9DHAM2uvkBAICwLUChdf+1kpbtsnPnzmA3CUCA5ebmBjSYIjMFAAAiIpii7j+A8vJyKSoqMm9Edna2398QJuwFAAAR0c2Puv8AbF390tPTAxJMOWa/HLsYAgAAhFVmKtCYUR0I7a5+2gUvNjY2YMGUYxdDAKGD4zWAqMxMaWn03r172+/bav9rta7t27dLKGGmdSB0OGaItBve3r17/bYvx+wXwRQQOjguA5Boz0xR+x+At8GUv7v6kZkCAAAhmZmi9j+AUK/oRzAFAACaw5gpAGEnGJmpkpISKS0t9eu+AABAeAmran4A4GkwFdems6QOnCyxSWlSsXu9lKz+RqSmqsXn2bbPeCkAANAQwRSACA+mYiRrwsWSccQ5EhNTl4xPF5HM8b+W3PcelKr9W5t9psVisU/aSzAFAAAaopsfgIgeM9X6+Osk88jzpKY4X/I+fVL2/GeaFK+aK/Ftukj7Cx6Q+LZdm39u69YmoGq4TwAAAEVmCkDEZqbSRpwi6SNPlaoDu2TvG3dKTfEBs7xi+0qp2rdFWk25XNpNvVt2v3KzWCtKGj2fCXsBAIAzZKacYBJAIDTt37+/xWAqrnUnaTXlCqmtLJN9b99jD6RsChe9I0XLPpP41h2l9TFXNrkN5pgCwgPHawDBQjDlIiYHBEJHVVWV5OfnO+3m1+bEG8USnyT5X/1LqvN3NblO/pf/lKr8XZI29ARJ7Dqk0eOURQdCF8dlAKGAYApAWHf1ayozldx7nCR1HSLl21dJ8fLZzW7DWl0pB2Y/Y263PvYakUMFKmwIpgAAgDMEUwDCOpjKzMyUhISEww9Y4kz3PqVZqZaUb10upesWSEJ2D1M63RHBFAAAcIZgCkDYF6FwDHrShh4v8a07mYp9lXvWu7St/G9mirW2xpRQl9jDdXkcs16O+wMAAFAEUwDCkmOpcnvQE2ORjHFnm8Co4NvXXd5Wdd4OKfn5K4nLzJa0wcfal3fo0MF+e8+ePb5qOgAAiBAEUwAipjx66oCJEp/VQUpXz5fqg+4FPwU/vGWCMA3GbGOnHIOpvXv3+qztAAAgMhBMAYiQYCpGMsafYw+M3KUV/0rXfCvxrTpKSv8JZln79u3NtVYOrKys9FnbAQBAZCCYAhD23fx0zFRy77GS0K6blK7/Qar2b/Vom7YgLPMIDcpi7JkpuvgBAICmEEwBiIjMVOYR53qclbKpyt0ipesXSkK77tJ26CRJS0szywmmAABAUwimnGBGdSA8gqmcHv0lsWM/U+a8ctdar7Zb8MP/zHXv4y+2LyOYAkIbx2sAwUIw5SJmWgdCOJjqPdDrrJSNBmPlW1dIx14D7MsoPgGEHo7LAEIBwRSAsHTgwAGpqakxt7PbtZOK3eukfMsyn2xbs1Pt0hPt98lMAQCAphBMAQhLtbW19uxUdkaiT7JSNhqUtaotsN8nmAIAAE0hmAIQtvbs22+u26YmSPn6hT7ddkbRFvttuvkBAICmEEwBCFv7K+u+wuLjYqVt2zY+3Xab+LouhCqv3KebBgAAEYJgCkBYik1vJ3m1daXLVU5Ojk+336FD3YS9qqTTWJ9uGwAARAaCKQBhKfOo82VfcaXfgqn27euCqdpaq5R1Hi2xGdk+3T4AAAh/BFMAwk5c606SNuQ42ZNbN2bKP5mpDuY672CB1IpFso4636fbBwAA4Y9gygkmAQRCU9bRF0mMJVY2/zDHvqxjx45+CaZ279gu1Qf3SOqQ4yS+bTef7gOAb3C8BhAsBFMuYnJAIDQkdOgjqQMmSlXeDtm8cLZfMlOtWrWSxMS6eab27Nkt+d+8IjExFmk15XKf7QOAdzguAwgFBFMAwkeMRVqfcL25mT/vZdm9a6dfgqlOnTrZb+/cuVNKV8+Xil3rJLnnaEnqMdJn+wEAAOGNYApA2EgbdqIk5vSR0g2LpGz9D/Um0/VnMCVilfyv/mXutznxBomJT/LZvgAAQPgimAIQFuIy20uryZdJbVWF5H/xD7OssrJS8vLyfB5MOY6/qgumRCp2/iJFSz827ciaeInP9gUAAMIXwRSA0BdjkTan3yaWxFQ5+M0rUl2w1/7Q7t27/ZqZ2rVrl/22di2sLtwnGaN/JUk9R/tsfwAAIDwRTAEIea2OvVqSOg2Qsk0/StGPH9R7zBbsJCUlSVZWlp+6+dWxVpbJ/o9miLW2RtqefpvEZdVV/AMAANGJYApASEsfc6ZkjDpdqg7ukf0fzzDjlxzZMlO+zE411c3PpmL7Ssn/+mWJTUqT7HPuk9jUVj7ZJwAACD8EUwBCVsb4c6T1MVdJTXmx7Hv7HqktLWi0jmM3PMeMkjds26murpZ9+/Y1erxo8Swp+ukTiW/dUdpf8IDEZmT7ZL8AACC8xAW7AQDQUExCsrQ54QZJHTRZakoOyr63/iLVeTuafKO2b99uv92lSxefZqa0WmBtbW2T6xyY85zExMZJ2tATJOfSGbL/o79L+ealfJgAEKESsntKQkpxsJsBJxLS0iTQCKacYEZ1IMBi4yR14BTJmnCxxKW3kcrcrZI7636pzj+cfWpo27Zt9ttdu3b1uglxcXHSvn37Jrv41WeVvE+flKr83ZI18TfS/tz7pOSXeXLw+zeaDfwA+AfHawRCh4sekrSKat7sEJaWGPjQhmDKRcy0DvgvC5XYeaAk9xgpqQMmSWxqllhrqqXwx/fl4LxXxFpd4fT5vg6mOnToIBaLxYVgqk7hD29JxY5fpM1JN0rqwEmSMmCClG9dLqVrv5fy7SulOq9unioAvsVxGYG25/U7pKiYzFQoS9fM1L0nBnSfBFMu0u5G1dU1DZbGOH+S04dbem6Mx8+N8dt+W+LHbXv1fvhrvy3su8Xdxvhnv97+DfjxNVniE8WSlC6WZL1kmjFHcRnt7KvUVpZL0fLZUrjoXak+0HIg449gqrmy6M5U7Fglu178nQmmMsaeJcndR5iLqq0oleqDe0xJde2yWFtZaqoC6muV2hoRa62pDqjXdbf12tfBlx+COZ+3EXBPfNtuvGUIqMp9m6SyqIh3PYRVlqYHfJ8EU87EHK7P0faUm6W6lh8PgC/VVpRIxa41Url3k5Rt+UnKtywzgYY7CgoKpLCwUDIyMnwSTDmOu3Icj9Wi2mop+flLc4lv21WSe42VxI79JKFDL4nP7i4J7Xt63TYAh6X06cfbASDoCKZcPPN64Kt/S3VNTVMrOX+HnT7c0nOtfur+4L/9tvxcf23b6uVLsvrnNfl1v378G3C+4ZZWaP6RynKprSiWmrJiqS0rNBdf0OzU4MGDfRJMdet2+Gz31q1bPdpG1f5t5mJniTNjwCzJGWJJTJGYhBSTpRNLrMRol0I9cRNjkRhL7KHb4kM+3dihTfphm4CbyvpdJCK9ed8ABBXBlIs/CouWfGDKJAMIPbZgSifubdeuneTm5nq8LceAzLELoVdqq6W6YK+IXgD4ROWZY3gnAQQd80wBCHu+HDfli8wUAACIDgRTAMKeP4KpqqoqM88UAABAcwimAIQ9xwySt8GU7flafKK5CXsBAAAUwZQTTAIIRFdmKi0tTVq3bm1u08UPCB8crwEEC8GUi5gcEIj8YMovxScA+AXHZQChgGAKQNjTyXVrDk1d4E0wRfEJAADgDoIpAGFPpy3QgMqXwRSZKQAA0BKCKQARwRb8dOjQQRITEz3ahmMgxpgpAADQEoIpABHBF+OmyEwBAAB3EEwBiAiOmaTu3bt7tI0ePXrYb9PNDwAAtIRgCkBE2LBhg/127969PdqG7Xk6x1R5ebnP2gYAACITwRSAiOBtMJWZmSnt2rVrtC0AAIDmEEwBiAjeBlO9evVqclsAAADNIZhyghnVgfChpdHLyso8DqYcn0MwBYQXjtcAgoVgykXMtA6E/v/opk2bzO2ePXu6/ePKMZjauHGjz9sHwLc4LgMIBQRTACKGLaOUlJQknTp1cuu5dPMDAADuIpgCEDG8GTdFZgoAALiLYApARAZTffr0ceu5tvX37NkjxcXFPm8bAACIPARTACLG2rVr7bf79+/v8vOysrIkJyen0TYAAACcIZgCEDFWr15tvz1w4ECXnzdo0CD77VWrVvm8XQAAIDIRTAGIGNpFLz8/39wmmAIAAP5GMAUgovzyyy/mumvXrpKWlubSc8hMAQAATxBMOcEkgED4BlPujJtyzGLRzQ8IPxyvAQQLwZSLmBwQCL9xU44ZJ2ds6+3bt0/279/vt7YB8B2OywBCAcEUgIiyYsUK++3hw4e3uH6rVq3slfzISgEAAHcQTAGIKD/99JP99siRI1tcn/FSAADAUwRTACLKgQMHZOvWreb2iBEjWhxLMXToUPttMlMAAMAdBFMAIs7SpUvNdXp6uvTu3dvpumPHjrXfXrJkid/bBgAAIgfBFICIDaZs2Slnxo0bZ64rKipk+fLlfm8bAACIHARTACI6mBo1alSz62VmZtrLpy9btkwqKysD0j4AABAZCKYARBzH7npHHHFEs+uNGTPGfnvhwoV+bxcAAIgsBFMAIs7evXtl/fr19jFRiYmJTrv4KYIpAADgLoIpJ5hRHQhf8+fPN9caSDkWmXA0efJk+22CKSB8cbwGECwEUy5ipnUgPIMpNXHixEaPp6amyoQJE8ztTZs2ycaNGwPaPgDe4bgMIBQQTAGISPPmzbPfPuWUUxo9fswxx9i7/3322WcBbRsAAIgMBFMAItLmzZtl5cqV5vaRRx4pOTk59R4/+eST7bc//fTTgLcPAACEP4IpABHrnXfesd8+88wz6z120kknmWsthz537tyAtw0AAIQ/gikAEevdd9+13z7vvPPst48++mjp0aOHfWxVSUlJUNoHAADCW0gEU9dff73pklNWViY//PBDvblfAMBT2s1vzZo15vakSZNk2LBh5vatt95qX+ell17iDQaACMdvTURsMHXuuefKY489Jvfee6+MHDlSli9fLrNnz5Z27doFu2kAIsCTTz5pv/3Xv/7VTOL7q1/9ytzfsWOHvPnmm0FsHQDA3/itCX+zBvPyww8/WJ966in7/ZiYGOuOHTusd9xxR4vPTU9Ptyq99kfbvvvuO6tNsN8nLrwH/A149jeQkpJizc3NtTbltttu433lf4u/gTD9G7j33nvt/8vHHXecX/bh798ZXEL/tyZ/B+H1d5oehP/ZOAmi+Ph4GTVqlEyfPv1wZGe1yhdffGHOHjeUkJBgL2Ws0tPT6137WmxsbKN9AQg/1157rclAxcUd/sr75ptvTBc//reB8KS/CRznjfPH/zLfD+HP3d+awfi9Cd8JxmcU1GCqbdu25sfN3r176y3X+/3792+0/rRp0+See+5ptHznzp3ib4WFhX7fB4DA0Yl89+/fz1sORID33nvP7z/QioqK/LoPhMZvzWD/3kT4/c8GNZhyl55V0PFVjlq3bi0HDhwIWpvC5Q9KvwA6derEwYDPIKrxvxAa+BxCA5+D6+/Trl27/PxpIJTwezO8pQf4fzaowZSeFa6urpb27dvXW6739+zZ02h9nQ9GL444U+Q6fa94v4KLzyA08DmEBj6H0MDn0PL7g/Dl7m9Nxe/N8FYU4P/ZoFbzq6qqkiVLlsixxx5rXxYTE2PuL1iwIJhNAwAAQJjjtyYivpufdtubOXOm/Pjjj7Jo0SL5wx/+YAaSMvcLAAAA+K2JUBf0MoY33HCDdcuWLdby8nJTvnLs2LFBb1MkXRISEqx/+ctfzHWw2xKtFz6D4H8GfA7Bf//5HIL/3vM5BP995xKc94DfmvztiZ/eg5hDNwAAAAAA4TJmCgAAAADCFcEUAAAAAHiAYAoAAAAAPEAwBQAAAAAeIJiKUN26dZN//etfsmnTJiktLZUNGzbIPffcI/Hx8fXWGzJkiHzzzTdSVlYm27Ztkz/+8Y9Ba3Okuuuuu+S7776TkpISyc/Pb3KdLl26yEcffWTW2bt3rzz88MMSGxsb8LZGuuuvv142b95s/t5/+OEHGTNmTLCbFNEmTJggH3zwgezcuVOsVqucccYZjda59957zUz1+j31+eefS+/evYPS1kh15513mmlHCgsLzXfLrFmzpG/fvvXWSUxMlKefftpMbqqTXb799tuSnZ0dtDYDQDghmIpQ/fv3F4vFItdee60MGjRIbr75ZrnuuuvkgQcesK+Tnp4uc+bMka1bt8qoUaNMIKUB19VXXx3UtkeahIQEeeutt+S5555r8nH9nD7++GOz3pFHHimXXnqpXHbZZXLfffcFvK2R7NxzzzXz2umP95EjR8ry5ctl9uzZ0q5du2A3LWLpnIH6Pt9www1NPn777bfLTTfdZL6bxo0bZ04m6GeiP+7hG5MmTZJnnnlGxo8fL8cff7w5oabf+ykpKfZ1ZsyYIaeffrqcc845Zv2OHTvKu+++y0cAAC5izoMoeQ9uu+0268aNG+33r7vuOmteXp41Pj7evmz69OnW1atXB72tkXi59NJLrfn5+Y2Wn3TSSdbq6mprdna2fdm1115rPXjwYL3Phot374HOYffUU0/Z78fExFh37NhhveOOO3hvA/D3pc4444x6y3bt2mW99dZb7fczMjKsZWVl1vPOO4/PxE+fQ9u2bc1nMWHCBPt7XlFRYT377LPt6/Tr18+sM27cOD4Hvnv5G+BvgL8Bcf4ekJmKIpmZmXLgwAH7/SOOOMJ08auqqrIv07PCmtXKysoKUiujj34OK1eulH379tX7HPTz0qwivKdn4zX7+sUXX9iXabczva/vPwKvR48ekpOTU+8z0a5oCxcu5DPxI/1eUbZjgf5faFbc8XNYu3at6bHA/wYAtIxgKkr06tVLfve738k//vEP+7IOHTqYPvSObPf1MQQGn4P/tW3bVuLi4pr8e+dvPThs7zufSeDExMTI448/Lt9++62sWrXK/jlUVFRIQUFBvXX53wAA1xBMhZnp06ebM+rOLv369av3HO3//tlnn5lxO1qUAsH5HAAgmHTs1ODBg+X888/ngwAAH4nz1YYQGH//+9/l5ZdfdrqOVvCz0W40c+fOle+//16uueaaeuvt2bNH2rdvX2+Z7b4+Bt99Ds7oez127Fg+Bz/SKmXV1dVN/r3ztx4ctve94Weg95ctWxakVkWup556Sk477TSZOHGiqa5oo++9FvzQ7n+O2Sn+NwDAdQwsi9D3oGPHjta1a9da//Of/1gtFkujx20FKOLi4uzL7r//fgpQBKkARbt27ezLrr76alOAIiEhIeh/R5FUgOLJJ5+sV4Bi+/btFKAIcgGKW265xX4/PT2dAhR+eO+18IoWW+ndu3ejx2wFKM466yz7sr59+1KAIgS+s7jwHvA3IOHyHgS9AVz8FEitW7fO+vnnn5vb7du3t18cD6K7d++2zpw50zpw4EDrueeeay0uLjY/5PlcfPdZdOnSxTps2DDr//3f/1kLCwvNbb2kpqaaxzXQXbFihfWzzz6zDh061HrCCSdY9+7dawJbPgfffQ76962V4i655BJr//79rc8//7z1wIED9aoocvHte6B/47a/d/WHP/zB3Nb/CX389ttvN5/B6aefbh08eLB11qxZpuJoYmIin4WPPoNnnnnGnMSZOHFiveNAUlKSfZ1nn33WumXLFuvkyZOtI0eOtH733Xfmwv8D3wn8DfA3wN+AuPIe8IcSqVmQ5jiuN2TIEOs333xjfmTqWXr9cRPstkfa5aWXXmryc5g0aZJ9na5du1o//vhja0lJiXXfvn3WRx55xBobGxv0tkfa5YYbbjA/GsvLy02mauzYsUFvUyRf9G+8Kfo/YVvn3nvvNSd19DtIT/706dMn6O2OpEtz9BhhW0eD16efftr0VNATau+88069E29ceA/4G+BvgL8BafY9iDl0AwAAAADgBqr5AQAAAIAHCKYAAAAAwAMEUwAAAADgAYIpAAAAAPAAwRQAAAAAeIBgCgAAAAA8QDAFAAAAAB4gmAIAAAAADxBMAQhr3bp1E6vVai4//fRTwPd/6aWX2vc/Y8aMgO8fAAAED8EUgIhw7LHHmkugvfnmm9KhQwf5/vvvA75vAAAQXHFB3j8A+EReXp4cOHAg4O9meXm5uVRWVgZ83wAAILjITAEIGW3btpXdu3fLtGnT7MuOOOIIqaiokGOOOcatbY0ePVrmzJkjubm5cvDgQfn6669lxIgRTp8zd+7cRl31Zs2aJS+99JKbrwQAAEQDgikAIWP//v1yxRVXyD333COjRo2StLQ0efXVV+Xpp5+Wr776yq1tpaeny8yZM+Xoo4+W8ePHy/r16+WTTz4x2wQAAPAFuvkBCCmffvqpvPDCC/L666/Ljz/+KCUlJfUyVa7SLJOja665xmSoJk2aJB9//LEPWwwAAKIVmSkAIee2226TuLg4Oeecc+Siiy7yaDxSdna2/POf/5R169aZIKqwsNBkpbp27eqXNgMAgOhDZgpAyOnVq5d07NhRLBaLdO/eXX7++We3t6Fd/Nq0aSO///3vZevWrWbc1YIFCyQhIaHZ59TW1kpMTEy9ZfHx8R69BgAAEPkIpgCEFA1eXnvtNVNyfO3atfKvf/1LhgwZYgpJuOOoo46S66+/3nQbVJ07d5Z27do5fY7uIycnx35fg7nBgwc36jIIAABgfivwNgAIJffff79kZmbKTTfdJA899JDppvfiiy+6vR0tOPGb3/xG+vfvL2PHjjVjsEpLSxtlrx544AH7fS1yceqpp8opp5wi/fr1k+eee06ysrLqPUfX1+cBAAAQTAEIGVoc4g9/+IMJgoqKisRqtZrbEyZMkOuuu86tbV155ZXSqlUrWbp0qakI+OSTT8q+ffvqraPjpxwzURq0aaD0yiuvyLx582TTpk2NslK6PuOuAACA0sEBVt4KAOGqW7dusmXLFhk+fLgsX748aO3QoGvZsmVy8803B60NAAAgsMhMAYgI33//vXz33XcB3++FF15osmiaPQMAANGFzBSAsBYbG2sq/imt2Ldjx46A7l/Lrbdv397c1hLseXl5Ad0/AAAIHoIpAAAAAPAA3fwAAAAAwAMEUwAAAADgAYIpAAAAAPAAwRQAAAAAeIBgCgAAAAA8QDAFAAAAAB4gmAIAAAAADxBMAQAAAIC47/8BfgQbVCwsrBYAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 1000x700 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_dead(E=E_vals, psi=psi_vecs, V=V_full, x=x, nos=5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Verify Against \n",
    "```python \n",
    "import QM Solve\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "================================================================================\n",
      "                    HAND-WAVE SOLVER VERIFICATION\n",
      "================================================================================\n",
      "\n",
      "Testing against analytical solutions for fundamental quantum systems\n",
      "--------------------------------------------------------------------------------\n",
      "\n",
      "================================================================================\n",
      "[TEST 1] INFINITE SQUARE WELL (Particle in a Box)\n",
      "================================================================================\n",
      "Domain: L = 20.0 a.u., Grid points: N = 1000\n",
      "\n",
      "✓ Solved for 1000 eigenstates\n",
      "  Ground state energy: E[0] = 0.012337 Ha\n",
      "\n",
      "### ENERGY BENCHMARK: Infinite Square Well ###\n",
      "Well boundaries: x = [-10.0, 10.0], Width L = 20.0\n",
      "-------------------------------------------------------\n",
      "| n | Analytic E | Numerical E | % Error |\n",
      "-------------------------------------------------------\n",
      "| 1 | 0.012337   | 0.012337    | 0.0001 % |\n",
      "| 2 | 0.049348   | 0.049348    | 0.0003 % |\n",
      "| 3 | 0.111033   | 0.111032    | 0.0007 % |\n",
      "| 4 | 0.197392   | 0.197389    | 0.0013 % |\n",
      "| 5 | 0.308425   | 0.308419    | 0.0021 % |\n",
      "-------------------------------------------------------\n",
      "\n",
      "================================================================================\n",
      "[TEST 2] FINITE SQUARE WELL\n",
      "================================================================================\n",
      "Domain: L = 20.0 a.u., Grid points: N = 1000\n",
      "Barrier height: V₀ = 2.0 Ha\n",
      "\n",
      "✓ Solved for 1000 eigenstates\n",
      "  Bound states (E < V₀): 12\n",
      "  Ground state energy: E[0] = 0.012337 Ha\n",
      "\n",
      "### ENERGY BENCHMARK: Finite Square Well ###\n",
      "Well: x in [-10, 10], V0 = 2.0, z0 = 20.0000\n",
      "Number of bound states: 10\n",
      "-------------------------------------------------------\n",
      "| n | Analytic E | Numerical E | % Error |\n",
      "-------------------------------------------------------\n",
      "| 0 | 0.011170   | 0.012337    | 10.4468% |\n",
      "| 1 | 0.012334   | 0.049348    | 300.1017% |\n",
      "| 2 | 0.044740   | 0.111032    | 148.1733% |\n",
      "| 3 | 0.049335   | 0.197389    | 300.1001% |\n",
      "| 4 | 0.100620   | 0.308419    | 206.5198% |\n",
      "| 5 | 0.111004   | 0.444119    | 300.0943% |\n",
      "| 6 | 0.178720   | 0.604489    | 238.2331% |\n",
      "| 7 | 0.197340   | 0.789527    | 300.0855% |\n",
      "| 8 | 0.278951   | 0.999231    | 258.2106% |\n",
      "| 9 | 0.308343   | 1.233599    | 300.0739% |\n",
      "-------------------------------------------------------\n",
      "\n",
      "================================================================================\n",
      "[TEST 3] HARMONIC OSCILLATOR\n",
      "================================================================================\n",
      "Domain: L = 50.0 a.u., Grid points: N = 2000\n",
      "Spring constant: k = 1.0\n",
      "\n",
      "✓ Solved for 2000 eigenstates\n",
      "  Ground state energy: E[0] = 0.499980 Ha\n",
      "  Expected (analytical): E[0] = 0.500000 Ha\n",
      "\n",
      "### ENERGY BENCHMARK: Harmonic Oscillator ###\n",
      "Spring constant k = 1.0, Center = 0.0, omega = 1.0000\n",
      "-------------------------------------------------------\n",
      "| n | Analytic E | Numerical E | % Error |\n",
      "-------------------------------------------------------\n",
      "| 0 | 0.500000   | 0.499980    | 0.0039 % |\n",
      "| 1 | 1.500000   | 1.499902    | 0.0065 % |\n",
      "| 2 | 2.500000   | 2.499746    | 0.0101 % |\n",
      "| 3 | 3.500000   | 3.499512    | 0.0139 % |\n",
      "| 4 | 4.500000   | 4.499200    | 0.0178 % |\n",
      "-------------------------------------------------------\n",
      "\n",
      "================================================================================\n",
      "VERIFICATION SUMMARY\n",
      "================================================================================\n",
      "\n",
      "Test                           Avg Error       Status         \n",
      "------------------------------------------------------------\n",
      "Infinite Square Well           0.0009        % ✅ PASS         \n",
      "Harmonic Oscillator            0.0105        % ✅ PASS         \n",
      "Finite Square Well             236.2039      % ⚠️  CHECK      \n",
      "------------------------------------------------------------\n",
      "\n",
      "================================================================================\n",
      "✅ VERIFICATION PASSED: Solver is accurate and validated!\n",
      "================================================================================\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from functions import verify_solver\n",
    "\n",
    "verify_solver()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "Deploy:\n",
    "\n",
    "\n",
    "https://huggingface.co/spaces/AhiBucket/Hand-wave\n",
    "\n",
    "\n",
    "\n",
    "```python\n",
    "\n",
    "python -m streamlit run app.py\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "show_QR(url)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
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    "name": "ipython",
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