diff --git "a/optics_dataset.tsv" "b/optics_dataset.tsv"
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+index	question	choices	image	answer
+664	The pattern of intensity $I$ vs. position $x$ as shown in Fig. 2.60 below is measured on a wall 20 meters from a set of $N$ identical, parallel slits. Light of wavelength $\lambda = 6000 \,\text{Å}$ passes through the slits, each of which has width $a$, and which are spaced from each other by a distance $d$.  (a) What are the values of $N, a$ and $d$? (Give a reason for each answer.)   (b) Give an expression for the dashed curve which is the envelope for the large maxima, and explain its physical significance.	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1sul6NtWKPbtGlTVlZGEERNTQ3P8wzD9OzZ8+23337jjTcOHjw4ZcqU5cuXd+nSJVQHgLnNwLLk7Y9Wq4UOCk3uCfXNQjWvw+GorKwEjzmqxiaK4nVuc0hRlHeqJU3Tjz766OLFi5OTk3/99dcpU6bk5+dfz6PC3EJgu+TtCeTPSCs5+sSjGoXBYDAYDHV1dQ6Hw+l0Bv9sQFIg2CJRtQswgGo0GpVKJZ09yLnQUFKxFIb1LrpBEATDME899ZTb7Z48eTIkfSPnOAYjBfe9uQ1hWfa99967fPny7Nmz27Rp05yPgKSJVpBQFTSDBQuVTRNFkef5qqoqgiD0er1ery8qKrJarRB5HhJ4ni8tLYXt6OhomUwGSrfHIQE0TT/yyCN1dXVFRUVY48Y0BrZL3m5wHPf1118vXbqUYZihQ4dC8HZje0L9XYgxlBoH6+vrKysrU1NTgzkSqZWTIAij0Qhp44IgwFywdFoslhDaJd1ud2VlJWy3a9cOMnzQRUBFidD+ERER48eP9zhgDEYK1rhvN06ePLlixQqHw/Hiiy/+/e9/93N/bTZbSUkJz/MajaZTp05StRfqTgZZG0Kq5xIEUVFRAfKpR2IP2C5DZQ+laRrZQFu1aiWXy3meNxgMoIm7XC7chxbTUrD35raiuLh40aJFFy5c6NWr19SpU5tszICSuGNiYjzeQuWCAsYj0Kcxp01o44Hcbjdo9ARB6PV6iqIgcxyU7ry8PMjI9APLsiDehvCoMLc0WOO+fXC5XGvWrPn555/1ev2oUaMSExP931yPwhbeam+Qz0ZZWVl5eTlBEAzDMAyTlJSkUqlAmgt51BECHEToX5AcUcp2Q0MD6Pt+Rvjxxx/Xr18/ZsyYwYMHhzBfE3PrgjXu2wSe5/fv3//ll18KgjBkyJDhw4c3WfrMO9PG42EI8tkQRRF83DExMdHR0Tk5OU6nE+RW6VxgGw3hcyiNKvc4L6vV2qTv/syZM3v37s3Ly5PJZI888gj+gmCwxn2bcOrUqdmzZ1dUVAwcOHDatGkh7KkdPCBLghTJ83x9fb303by8vOC1e4Qoih7jSzEajWaz2f8IQ4cO/fvf/56fn79ixYq8vDysbGGwxn07UFpaunjx4tOnTyclJU2cOBEc1k1+Cu0jk8k8wgwJgvCoNRkMHjo1y7LSf1UqFUVRoZrLbrcXFBRIpyYIQi6X0zTtcrkEQeA4zv9cHTp0mDFjxssvv3z48OG5c+e+8847ycnJITk2zC0KliVvBwoKCg4fPiyTycaNG3f33Xc3/4OwXiQmJur1eoIgNBoNCKEul6uwsDBUh6dUKr3VeVQOvb6+PrQOHO+o8sTExMTERIIgeJ6Hbmh+oCjqgQceWLJkSXx8/H//+9/58+cbjcYQHh7mlgPbJW8H4uLiBgwYEBMT88ILL6CEliaxWq0Wi4UgCIVCwTAMSZLR0dHR0dEEQdA0HRkZGeSzgT7etm1baYVwWDFjYmLi4uIIgghtjx00DkVRKPEmJiYmNjY2NzeX47iqqqom52IYZvjw4Vardfbs2V9//bXBYHjzzTdRUU7MnQbWuG8H2rVr98knn0Ax3ebfUJRgg2KtGYaB6BmO4yorK4N8NtDHNRqNKKlGDuo2wzDh4eGg6fM8H0LtHjYiIyNhxYe5UAmMJn3cAMMw//rXv4xG47Jlyz799NPw8PCJEyfeVNZezHUDa9y3CRqNpqUtCtDahMRPpVIZExMDy1mTcYVN4rEYxcfHe8i5SqWSoiiWZYuKioKcyxulUild1ODKuN1uqdXSP3K5fMyYMSNGjLDZbJ9//nlOTk7IDxJzS4A17jsXo9EIFresrCwwHRISjdXlcvE8H0z9HrPZDA5lULErKyudTichyRZv3bo1tNkxm80h17ilMUAqlcpgMMDq36IqHvHx8QsXLgSjbXJyMv6y3JlgjftWpaqq6s8//2zTpg0kFwYwgtlshi6v0H/GI8i8oaHB5XIF02/W6XTabDZC4uNGqj1seOjgAU8kxWewukKhiI6OJkmS47jCwkKbzdZ83Tk6OnrBggVwtPjLcmeCNe5bEp7nP/vss5deemnp0qXBF+9JTU1FSSYxMTEQGBQZGdl8R5BP4uLiwD8DKBSKEHYBCwyIpgSRtvlQFHXDjxxzA8Ea962HKIo5OTmbN292uVx33XUX9HENYBykkBoMBlgZCYLo0qWLXC53u93BLw0oWRAmgpKX0nmROh/a+pLSMdG/6enpCoUC9djBjz2m+eBfyFuP+vr65cuX5+bm3nvvvSNHjgxYKXY6nd4qZNu2bUOVvOxROc1gMEh7LRAEAU0mCIJoMh8msNmlZ4cCm4J33BuNxpycHDAmYO4EsF3yFsPtdn/55Zdbt25NSUmZPn16QkJCYHdQEAQk3EkXFLTmWq1Wl8vlsa61CGmWiyiK8fHxCoXCarWi6SIjI8HHXV5eHqrn0EObRsPSNC3+r8kysPFtNtvEiRNzc3NfeumlV199FcukdwJY477FOHz48HvvvedyuZ577rm777474Nsnk8nCw8NBp/YudSEIQmVlpc1mA/duYFRUVEBNIBgcEhMJicILfwVBsNlsoXoOL1y44LOKZXp6ulwut9vt3ifbIliWLSgoOHPmzLp16+65556OHTvib9BtD9a4byWKi4tXrFhRXFyckZHx7LPPBlO5VhCE+vp6P60URFEMstECwzDSQCLv1QSlx4SwowNUIfIG/STU1taaTKaAx9fpdCtXruzTp8+FCxfmzJkD/SAxtzdY475lYFl2+fLle/bs0Wg0L7/8cnp6ejD3zu12X7lyBdYUqQZK07RGo4F1JMgAHZfLBcV+tFotSZKQBEkQRFhYGAwbGxurVqsdDse1iAQC75P3sDabDbT+wManKOpvf/vbnDlzRo8evXPnTq1W+95770GSD+Z2BWvctwxnz57dvHkzx3GDBg0aPnx4kD4WkiRBgpPL5QqFAimhUtd2kL5gyD6kKKpdu3bIvklRFPKnNzQ0sCwrCILRaBQEIZjYTOmksGEwGKCQJfzLMAyI3haLxWq1BvnY9+3bd9asWbNmzfruu++6dOkybty4IKOmMDczWOO+ZQgPD8/IyBgwYMCUKVMMBkOohtXr9fHx8WjV0Gg0sbGxBEFwHNeY9toitFptXFwcSZI1NTWwJiKPNpQC4jiurKwshEo3oFAopK4nnU6XlJREEER9fX3wLnWlUjl69OhJkyZRFLV8+fLNmze3NAYTcwuBNe5bhrS0tH//+99arTY+Pp4IacM/qWZKURTU76murq6urpaGhbcUGNNisdTW1oqiKJfLQVqU5t5Is3FC+yh6j4mk72YWvPAPRVGvvPLK5cuXN23aNH/+/Pbt2wfZTA1z04L7cd8y0DTdrl276zad2+0OvuAFIfEChYeHe+jUIMbW19cj18q1QyaTwa9LCDEYDHPnzrXb7efOnQttiUzMTQW2S97sgOYLpsMQDisIArho/ETGBGmXRIsjVJqQ1p6ADb1en5WVlZ2djWJ3Ap7LG4/zgvZkBEGIohjCTjtpaWnvvfdeaWlpwNn0mJsfLEve1AiC8N133/31119Dhw7t2bNnCEd2u91QjdyPqhuMWspxXF1dHcdx4eHhqH6tKIoKhULaIAGU7oaGBo7jgqk/1Hx4ns/NzWVZVloYOBiSk5Nxy4fbG2yXvKm5cOHC/Pnzc3JyKIrq0aNHCEcWRREkuPDwcK1WK30MpMpvwI+HTCbT6/Vo4UNrMcuyxcXFHsWBjEZjdXV1SNYadMAKhcIj3wadF4p/Cn46nweAhcrbDKxx37w4HI61a9fm5uaGhYUFk2bjE5ZlL126RBBEZGSktHkDTdPIYxOMxi2Koslk4jiOZVmk4UJskDT3BjZYlnW73SE5QTSywWCQnhfDMK1atZLuFvInXxTFvLy87OzsTp06paam4jJCtw1Y475JEUVx37593333HZTngZzoEH6xRVGEAjkqlUqawyMIQkNDQ/DjC4IAXRjr6+ulzSEYhmnTpo33wQQ/owckSUrXKZlMhsKnQtjYluO4kpKS/Pz86urqoqKivXv3Hjt27O677165cmVmZmaoZsHcWLDGfZNSWFi4cOFCyIM2mUwzZsxwuVyPPfZYaKOXSZLU6XRSjZuiqJiYGIIgnE5nMM1moe82NI2Av3V1dbA8oSoYUpNoqCKBUKEjQRAEQfBpPTh//rzT6Qy+9JEoivv37582bVpBQYEgCG63m+d5nucPHDiwevXqhQsX6nS6IKfA3AxgjftmxGazrV69+vjx4+iLnZubO23aNKfT+eKLL4ZWooTgQTSmTCaLiooiCMJoNNbU1AQ8F8RdkiSp0WiioqIoikLVgpG/nqZpsEWiKhjBnxHS641GY11dHaz4MAWKQ6qsrOQ4LvjpCgoKli5deubMGY/XWZb98ssve/To8fzzz18flxTmmoJNJzcdoij+9NNPW7Zs8UhHKSkpWbJkyV9//RVC8Z8kSQ+NGxKuiVDUYYTKbFqtNioqiiRJnudBuFOr1bAPrJIkSYYkHwawWCwQuqhSqTza28bGxoLSXVJSEhKle/PmzYcOHYLtsLAwqdxqNpsXL1588ODB4GfB3HCwxn3TsWvXrrlz55aVlXm/lZeXt3Pnzk6dOoUqigUhrXaB7IbBaMEomDwsLCwiIkIURajCC/XTkPAYHR0tl8vF0DWbLSgoABe20+lEtdoAtG6C+Bz8dC6XCwaJiIiYNm1aYWHhZ599ht7Nz89fvnx5+/btQx7NjrnOYFnypuObb77xqMeFcvsEQSgoKLimaR4URYWHh4dwQIvFYrFYCIKAmkCiKMK/xNXKGlB60mazXesfbI8+PMFjtVphRU5KSnr88cdfeuklCFwHBEH45ZdfZs+eXVtbG8JJMdcfbJe86bj//vuzs7OTkpJOnTpVXFxMEAQUScvOziauxvqFPE2lsX8DnkgaaoOif0DvbmhogLc4jquurnY6nVVVVTk5Of369Qs+egZFAsXFxen1eunx0zQN9S9gpQ5exKutrUWdfGQyWUpKSlJSUmlpKUEQKSkpXbp02bt377Zt2x566KFnnnkmyLkwNxCscd90DB8+fNCgQRUVFY899hi88vTTT5tMJlgly8rK3G538HetoaEB2T09RpP+G4zGXV9fT0jcKQBN07GxsajaRUJCgkqlcjgchYWFEPMU4Pl4HTBIqT7PhWXZy5cvhzApHk4tOjo6OTn56NGjoihmZmYuWbJEEIQ9e/acOXNm2LBhoZoLc/3BDribDpqm9Xr98ePHa2pqCIIwGAy9e/fOycmBd5H8EiR5eXlNFrOAaPDAcLlcly9fJghCo9GEhYX53IckyfDwcPACHz161G63h9zeKgWVRicaL2nefKSFhWBYuVyu0WhQ5HxiYuLSpUuffPLJfv36BTkX5saCNe6bFChMSxBEenp6ZmbmlStXZDIZz/NQPTf4uyath+hT4xYE4dKlSwHnO5NXq/xC3KJU43Y4HGhGpJgnJCQolcrgz8uPuSA8PFyn03mk/QRMXV0dipbX6XQwMhoTzj0rKysjIyMk1YUxNxCscd8UuFwujuNUKhVSOUHWI0kyNTU1JiYmKSlJo9FYLJaqqqrS0tJgmnYhILU5KirK4xnwELgCe0K886kBmUym0WikweSw0bVrV3B2B3YuCBCQaZpu1aqVx2gMw0BMPlRHD3IulHlJUVT79u0NBoPUb+5wOOx2O1SEw1+xWx3s477xmM3mVatWjRkzBvIRCYIQBAE0a4VC0aNHD5VKpVKpIIyRZVnILAwS9NXVaDQeb0FmN0EQQeq/MIVWq9VqtY3tgyqKN6aVtwin05mfn+92u2UyGYonRzAMk5qaStO02+0uKioKfjoA4vBBYETicKhSiTA3A1jjvsGIovjrr78uWbLE4XBAjUKIjLly5QrP8wzDQKaKwWAwGAy1tbVQqzwkmikEkCckJHiMFhYWptVq6+rq0J4BjC8IQlVVFWyDQRAKqTEMEx0djcaMiYmJiYmpqakpLy8PSfE0lOHjU6dOTU0Fw0VIrBYIxJu1PAAAIABJREFUNFe/fv2++uorq9VqMpnq6uoSEhLQPjabbffu3Xa7/cknnwzJTwLmuoFlyRtMVVXV+vXrzWZz586dBw8eDAKjw+GAkhMURUEXGoVCAZIdy7IhqUbRHIJJUOF53sNDEhUVlZGRIYqi1GuEmpGFpPUNRVFarfb6FOPxKS2mp6d7dK1AFBYWvv322+PHj//000/RUo65JcB2yRuJ2+1es2bN3r17s7KyFi1a1KFDB7gd0HOGIIjw8PD27dtDlAlk17lcLovFEvxdQ1bCmJiYxiKBkDExgPE9lipRFBmGgdyboqKi7t27h3Au6SxutxtWW/+jBd/6pry8HIRlqBjikYpuNBo9TJ9xcXFZWVnnzp375JNP+vTpg5vk3EJgjfuGAbr2f/7zH6VS+frrr993333eBWx0Ol1sbKzPbOsgZ0dhjBC84vGWdJ/A5uI4rqKiQjpOQ0ODyWRyu90lJSXSKWCjpqYmeC1YJpNptVqQ5vwcOVgDQP0PbCJRFCsrK2GVlMvlbdq0Qa5z2MHpdDqdTukBGAyG2bNnnz9/Pjs7e82aNZmZmWD8xdz8YI37hnH69Ok333wzNze3b9++jz/+uE+THCR1EARBURS0i6FpWrpcBgykOdI0HcKmtR54aNAul6uiooKm6dTUVO+dS0pKQhLDaLfbm8zg5Hm+qqoqmN5nJEkqlUrUyRbdO5lM5kffT09Pf+ONN7Ra7bZt21auXBlMOCrmeoI17htDbW3typUrz549m5aW9sYbb+j1eumNgEqFsC1VjWUyGcdxqMhCMBQXF7vdbrB1eoym0WjA8R0SLRiNA4KbTCaD4hfoLdjQ6XTBB824XC5UW8hnXBEq2mYymUwmUzDFOmtrayG5SDoXlB2CtmuE14WlaXrIkCH79+//8ssvP/vss969ez/wwAO4pPnND9a4bwA8z//www/ffPMNTdPjx4+/5557PL4qNTU1RqORIIh27drBFxuEFxRlEuRdA4WR53m1Wg1lzaTvQhw4HGfw0ddQiYckSYfDgaRLNCaSwqqrq2G6YOZyu93gGIGK6N6jpaeny+VycI7ZbLaApxOvVhH2mEsul4OA6XQ6i4uLvZV6rVY7fvz406dPnz17dtq0aevWrfvb3/4W2DFgrhv4d+wGACE+GRkZI0aMGDZsmLc0YTKZQB1DnVsoitLr9bAnqqkTMNCHgOO4sLAwb43b4XDA7AUFBcG35DYYDBC6iFJ6UIQQIanTE5I4UIZhYFVqrLKRVquFwwC7YZDTIbyH4nm+sdvUqVOnMWPGqNXqc+fOffjhh/BziLmZwRr3DYBhmGHDhvXp00en03no2gRB8Dx/5coVWKdgZYQd2rRpwzCMy+XKzc196KGHgjkAaLcAHmFv/V2tVoPps66uLiRlH8FNpFAoKIqCiG40ptlsBh25rq6uoqIiMTExmIncbjcybvq0FcTGxkZGRtbX13v7oAMG7CEwlEwmS0xMPHfuHEEQtbW1PM97m5tpmn722WcrKyvff//9ffv2Xbp0KTo6OvjDwFw7cLWLG4NCofBukgWIV7ssEATRunVrpLKp1WqQg0JYXxIVE5MC0l9ubm6oZgF8GuCioqJA0gw+NIfw6nTmjUajQYV4gwzPRFK2TqdD8jhN0yiSHOoB+8xfCg8PnzRpklwu53m+U6dOwRwG5jqA7ZI3HaIoorqtKKhFukPwtkJpMRtppRwgMjIyMTGRJMna2trgG8Cio/XeIAhCqVSmpaWhX4JQzUU0cpVISWPFYC6j2+0uKCiA7eTkZGknH9TPFsJaG5siMjJyxowZRCM/HpibCnyHrhOiKFZUVFy4cKHJzBm32w0102iaRvJjaEH1w30il8vBU1RWVhZC451cLvc+F4qiQpiu53K5UL6QT8lUJpNBPzKe5202W8DiJJgsYBssCWh8VA4dKir5GQTlHWFucrBd8jpRXFw8derU/Pz8mTNnPv300/53tlqtBEGEh4dDyjbK64CN4KvwSkWqxmJ9RAnBzIVGsFqtYCvwGBP5i61Wa5Bz1dXVocWL8LVQolXM4XDk5+cH7FWHyuSwjQIP4F90YaGhLv5+3QZgjft6UF9fv3Dhwh9++EGhUDT5zXQ6nSdPniQIQqvVonqIBEHEx8fL5fKGhoZLly4Fedfq6+vRatKY4umtHQcGGgESb7zHBKsC1A8fMGBAMHN5rEo+NW60qJ07d45l2cDSbwRBAHnfYy7Iu9dqtVartaWZSxzHyWQy/H28CcEC/zVHFMVjx47t2rWLoqhnn332gQce8L8/RVGwcHAcJ3XUpKWlpaenEwRhs9mCP6qQFDxvEUlJST5dK+np6eDiCD4XRaVSoTa2TRJMyQlRFH3GLZEkqdVqA0iOunTp0tSpU//973/jQhg3IVjjvuZcunRpwYIFVVVVgwcPnj59unfVWw8EQYD1gmVZp9MpVeXgs9XV1TU1NcEU4m1OjQmkCIdK425Mx4+IiCAIwuVylZaWBjkXiitCE3kfjDTfJuCz8zkybCBrBqRLRkVFNWfAixcvrl27VqFQqNXqoUOH4vLmNxVY4762FBcXv/3224cPH+7atev8+fN9JoR4A185iMjxLgzhXUmhpXg4gr2Hgq6wHju3iOLiYhCLpK5t6aRoTyi3oVAooK5HAHNJARlZpVKFhYV5j6ZQKEAeRwQ2I0mSSMwHnR2NExMTYzAYqqqqHA5HcXExOIuapGvXrv369fv555/fe++9tm3b9ujRA38xbx6wxn0NsVqty5cv37p1a2xs7Jw5c7p06dKcR7+urg58o5GRkR6SyHWr3hoZGQkCUcDfVYip9njR52h6vV4mk7lcLtQBLXjIq1VCvF+XypLBRAKhikcZGRnSoEilUolCMpuvPrdq1WrJkiWdO3c+efLkG2+8ceLEietvEsE0Bta4rxUWi+WDDz5Yv3495Fo88MAD5P82Pm2M0tJSiBaKjo6WZubI5fK2bdui3UJ447yHgtaGUDsnsHwYaRtbqfJOkqS07w1BEPX19bBzSKp4AE6n02cVTpIk4+LiwsLCbDabxWIJOLNIWksJLKHe9Ts4jisoKOjfv38zx8zKynrllVemTJny22+/LVu27OOPP26mto651mBZ8lqxd+/eVatWsSw7YsSIadOmBV/uDNTSkBxbk/Y4KIHBcdyVK1dCMiNCLpd76Lzt2rULuM5jYyiVSp9yN0mS4eHhkG6Um5sbcJY6z/MePm7p1CCuchzXohxthmGeeeaZ0aNHK5XK3bt3r1mzBgLCMDccbJe8JkA/VYIg7r333gkTJkBXhmaCMpEhLsT7BtXX15vN5qSkpIAPz2q1Sr+BPiNmYCPgyrjoU8jECefCcVxpaal3JBARiqgjBFTh9DkairZpaGgwGo2BOcFYli0sLIRtOEGpXTIzM/PIkSPwb4vOKDIycubMmQ6HY8OGDcuWLYuIiHjllVeuaY9yTHPAGvc1gaKoYcOGpaenx8TEpKSktOgi5+XlsSwLuW4eJRfhm2+xWMxmczA3DlX9iYqK8lnV0cMJHsAU8CmFQoHaVCB/ut1u9xizsV4xgU1KEIRGo5FWsZSi1+ujo6Nra2sdDkd1dXVGRkYAE1EUhcpltmrVClrpwlskSUJXCbiwLT2j2NjYqVOn1tbW/v777xUVFTgu/WYAV7u4VjAM06tXrwA+WFFRIQgCwzAdO3aUSiI0TXfq1AkslcF8cyCWCGRJqDPkvQ+KOgxeF/aopkGSpEcnA4VC0apVK6PRiBaXgOeqq6tDFXAbE+KUSiU6u2AyFFGEfEREhHQukiShn60oinV1dWLLi4G2a9du1apVly5datOmDRYkbwawxn1zIYoiVHVUKBQeHWVBXbXZbDKZDNaCwO4dz/MVFRUgS0ZERPjM90hLS5PL5YIg0HSAT4h33A+KOvLIPpLJZCqVShTFsrKympqaFlknPLDZbBBy7yfvhabp4HX8uro6qcXWYxDovcGybHFxsSiKAaz7SUlJwVhUMKEFa9w3Hcjx6u0T1+v1UVFR5eXlQWrcqEyZXq/36XmHnGuO4y5evDh48OAAphCv1ltEbnqkcSuVSumMUu0+yHKW6LNQ8NHnUNHR0VDPkeO4wsLCe++9N7CJpF16PCZKTk6Wy+VQegOrzLcB2McdMmw2W1lZWZDFvUVRhGBJkiS9Kz+q1ermZ+D5n8Vjw4OoqCiZTMbzfPA1gTymoGkaCkoiKIqCMw3JggIjtGrVqjFbgVwuBzWW53lo5xsMMpnMOzCTZVmIFa2srERhlcEgCELwrdMwAYM17tBgNBoXL1587NixuXPn3n///cFXxILCi43dHZZlg/EIow/Gxsb61Lj1er1Wq3W5XN59aFs0Bc/zJpPJI/fG228O/9bU1NTU1ARTrhxdE4hU93nkPqcOGJ9xCImJiVCinOM4juOCnIJl2c8+++zMmTNvvPGGNGAWc93A3psQIAjCF198sX79elEUg29KA1AU5UdsPH/+vMvlCknLWZ80NDTY7XaO46Q9alpEY7IPx3HIwYIAcQx53m8hdDqdTqfzeBF1cXA6ncGfETQp2rhxY01NzbvvvuvntxNzjcB2yWARRXHPnj2rVq1yOp3Dhw8fMGBAM3NsfGK1WqHYjEdGhwdQYjLgWTw+6DNHBTYCbrRQVlYGpgNp7g285REJJJfLu3fvvnv3biJopVv68caGIkkyLCyMoihBEEwmU5DPP3jMPQZJSEhQqVQWiyUk3XWUSuXo0aPPnDmzfft2juOWLVvmEZaPudZgu2Sw5OTkLFq0qLS0dMCAAXPnzvWWLFpEQUEBtApo3769dxQIsoIFKU0gFdi7dxUgl8vBrme32wMLl5HL5T4PFXRw6SsKhaJLly6hqoID06EWC95AaSXoUwaFeEMyr5To6Gi4eiGxtJIk2aZNm2nTpsXFxe3cuXPmzJkFBQVYuLmeYLtkUGRnZ0+bNu3IkSM9evR46623Gmv41XysVivUx4UQHI+7YzAYDAZDTk5Ofn4+y7LSwg0BoFKpDAaDT/tdZGRkeHh4dXV1SUmJy+UKwGV05coVZJKTRgIxDOOtM8LJwoIVzAOJPltbW9uYQZAkydatW8tkMo7jKisra2pqUA+G5pOfn48qWXjfJo9XQvIV+/vf/z5r1qy5c+d+//33LMsuX768Xbt2wQ+LaQ5Y4w6cmpqa+fPn79mzJzk5ed68eb169QqJixYGAZujx4BarTY2NpaiqJqampDIKahFqgcKhUKhUIDDPTCl21vzhQ3olO2t8kOse3l5eUg0boZhfOYUAe3atYNIHZfLJa3g2Xzg+ntMiiBJ0mAwlJSU+Hw3MORy+UsvvUTT9Jw5c3bt2qVQKN5///0gG/NimgmWJQPEYrEsX778xx9/VKlUU6dOHThwYPB+bVEUq6qqoI5s27ZtvdtpyWQyuVwuiqLJZLLZbEFq93K5XKvV+jzs4B3B8BGZTIZi4/2IV8ghjqKgWjodGgdp3N69IRFSO0NgoQJxcXHSSCOPEeRyeevWrU+ePGmxWCCTKiT2BJqmn3vuOZvNNmfOnD179pw7dw5Hnl8fsI87EOx2+7p169auXcuy7AsvvDB8+PBQNcPjOA7sgD5DcGQymVqtpijKYrEE7DwNuTLoB4VCIQ1e8V4uQ3skSOxtrNQFANcwmImcTicyaPqZiGVZm80WwousVCqff/55q9VaXFwcvHkH00ywxt1iRFE8cODA0qVLrVbrww8/PGPGjCabNDR/ZIfDgRKEvZU1mqaTkpIgRzhg7zNU5UEzNmeQACaCcHS5XB4ZGSnVuKFmpfd5SZeSwM5LEITKykr48RAEwc/10ev1UnEygOlQTUwoCORnhCCjEbyJjIycPn06x3FgEgnVsBg/YB93i0HWum7dus2ZM6dVq1Yhn4JhmLi4OJ8OaLAkIpEzADiOa05CiEajCWx8giDcbndOTg6koHj0pJbJZB7VLgiCiI+PT0hICHg6AJzXEBjgvxF2WFgYatzof88miY+Pj4+P934dnWNxcXGQ6VjeyGSyCxcu7N+/X9rkB3PtwHbJFmM0GktKSqBoQmFhYWZmZqgaLSDRgGGYmJgYn1qhwWBAzacCvndoosasclAX/ejRo2i3Fo0vk8kgx5EkSWQfLCsrA0HP295KXm3AUFVVxfN8Y/FJ/uF5vrKyEqVU+jE4ajQauIZGo7GmpiaA8ENUTSMuLk7aDRhQKpVSB7QfC2kAOJ3Ob7/9duHChWazediwYW+++WZCQgLHcRRFhcrsg/EA2yVbRnl5+bRp03766Ser1VpdXT1+/PiJEydOmjQpJAulKIpQ3Vqj0TQmyoFNjeO4CxcudOjQIeCJPDY8IEkymMQemUyWmJgok8ncbjcq94tCL/3oiRA/FNgqKYqizWZrTvwjOgCo6BHYXARBUBQVERHhnW4viiLSxOvq6jiO894nMERR3Lt377x58yCods2aNTabbdSoUfn5+QqFYuDAgbgJxLUA2yWbC8/zPM+vW7fu22+/RWpadXX1ypUrO3XqNHjw4OB/yV0uV15eHnG19o/PWwOzuN3ugINmmky88X49gIlAetJoNAkJCfDxhoYGaTMcj7nglWCK6Eg/BfJdY+NQFBUbG1tZWenffOkH6Jnjc2qCIGQyWXJyslKpdDgcTf4wtIja2tqPP/4YlkiCIHie/+qrr/bv319VVSWTyUaPHj1nzpxgWhBjfII17qbhOO748ePnz5/v169fYWEhLJFgHxQEwWg0Hjhw4IEHHgg+qxpqecF2YwpjQkICTdPQqjuYOhQEQTAMI+0o29huRBCRQC6Xq76+PjU1lSAIlUoFeYF+wrALCwsDLg8h/ZTPOCoETdPh4eEEQVgsFigL1NIZjUYjLH8+bxNJkhqNRpp6FJJvmSiKu3fv/vPPP+FfhmE4jnO73VeuXAH14t///rdSqQR3YvDTYRDYkNEEHMft2bNn1KhRr7322q+//pqfn08QBE3TI0eOHDZsGOxz6dKlIJ0AgCAItbW1hN8vFfi44bsR2Cw8z5eVlRFXM3l87kNRFKj8drs9sJAjWERYlkUehvj4+CaThYK8jOi6VVVV+feZgJPH5XLZbLYABL3mJ26GsGFsfX39d999B+VUdDrda6+9hnxEPXv2/Ne//sXz/EcffTR//vzgK8JhpGCN2x8sy27fvn3mzJl5eXmZmZkajaa8vJwgCK1WO2zYsNra2m+++UYUxePHj9fV1Wm12iCnQ8pmREREY21bPFJZApiF4zhY+GialjZskSIIAuwD1cygbG3zEQShvLwcTH7oOK9cuQKFPLyPHL1it9sDLsQLdknY1mq1jaUVEQRBkqQ0ayWAK4kKdjT2WfRiSUkJBAO1aHyflJaWXrx4EbbT0tKGDRu2b98+SIpv3br1nDlzoqOjV61atW7dupqamtdff71r166hyo6/w8Ead6PYbLZNmzYtXry4urr6/vvvnzdvHkVR8FCmpaW1bdsWumYTBMFxnNjy9iZ+iIyM9OimglCpVBERERaLJbCkEYIgZDJZREQEbPsZRGpDbOlEUOAWlGvk4ZUufx4DRkVF6fV6KOIQ8HlB9QrYhpyixsaR+qChf0aLrCUcx6Ekbmje4L0PWp7g1yIkz0ZtbS20t6Uoqlu3bh06dOjdu/e5c+cIgigqKlKr1ZMnT3a73R9++OHmzZsvXrz43nvv9evXD3/Bgwdr3L5xOBxr1qyZO3duWVnZE0888eGHH/bu3Rv5XkFXDXlzktraWmhrk5qa2piPOzw8HDrDOByOwPyzpaWlFy5cIK5l4o3dboefELVa7V1LwqchL/iDAc9ySz8VQGUzm81WXFzM87xCoWjfvr3PfVDfCJPJ1Fjn7pZSV1dXV1dHEAQ8IUqlEl1bs9nscDiioqJmzZo1efLksLCw06dPr1q1KlTVTu9wsMbtA5vN9vnnny9ZssRutz/77LPz58+HbLALFy6AEAG5Iqmpqa1bt4aiBkQo/JgXLlyorKwkrxZA9KMwgm3RYrF4R2g3SX19PSxhFovFYrE05kmHtTiwCokmkwkMrDzPu1yuxvRrBOpUUV5eXl9fD66VlkLTNOoshtRhn3tKX4fDa9EJQgYRbDMM4/OzYWFhYIHxmUMVAKIoWq1WEPCVSmWfPn1IkoTSJ5B0ZDab4+LitFrt5MmT9Xr9rl27evTo4dFiCBMYWJb0pKysbMmSJQsWLLBYLMOHD1+8eDFKmP39999dLhdN0+np6SHpP+MBRERDJ+4md7bZbEHWwYY4GJ9vMQyTnJxMEITD4QBjYovQ6/UQj6JUKpvjbw0PD09MTKQoymq1ImW2pbjd7qKiombujApQgsYd2Ix+QDk5gV1Ab9xud15eHkqLTE5Opmk6IyMDKp6Ioog8NpGRkRMmTNiyZcvrr78eqjjNOxxsl/wfiouL/+///m/79u0Mwzz33HMLFy6ExQKAaD6GYbKyssDshSxuZWVlwacqWiwWqB8THR3tJ0AHQiaD7xJjMBhiYmJ8TiSKIlqCA1CHUc9rl8tlsVg8sg+9B1QoFFqtFgXNBBwJhFzk/uNvGIZJTU1VKBROpxNkyRbN6HGEPj+LbhP09e3WrVvzx28MdEfCw8PBHpqSkpKQkGAymViWzcvLQ/0gaZr2qBfF83xoU4DuKLAs+T8UFxcfPnxYr9fPmjXrgw8+kC6RCJlMBuZItVodFRVFkiTHceD7DpLmKEcURUGVHT+SYDPxk3lCkqROpwssB4a4qqcTBOF0OmFDyjXSAXmeb6ZwTZIk8ro4HI4AypW36BSC70NJEITL5QJrMkEQiYmJkOul1+vB+il91xtRFPft27dp0yZU5QTTIrBd8n/o1KnThx9+qNPp7r77bg+bTllZWVFRkSiKERER7dq1E0VRrVZnZGTAUhJkI2mgoqLC7XaDMtjYaGq1um/fvhs3biSCrvAKHgafI5AkGR0drVKpoMdpS2eRdsWShi6hHfwMGMB0AEVRqAcGDOJnHIZhwA0NqdwtCsNuTvKSQqGAToocx1VXV4fELolsEeDBF0VRo9EkJSXBdl5entls9mnShXLRZ86cefDBB2fMmNGtWzccIdQisMb9P+h0uqeeeorwpUaVl5cXFxcTBJGenq7X62GHVq1aQcgh6qcaMG63GzweMpksJSWlsdE4joN48oaGBofDEcykSqWysTqMJEnKZDKKohoaGoqKilpagQKNqVKp4uLiPPRfPzo1y7JFRUWNOY7943a7c3NzYdtsNguC4OeYExIS4uPjL1++7HA4XC5Xiy6jIAhS8dPnZxmGka68IfmWIftpZmYm/JQqlcpOnTpt3brV6XRevHixpKTkrrvu8v6gVqt94oknLl++/P333xcXF0+fPn3IkCHYZNl87mhZEsxYPh8X78tiNpshrgJ6S4lX6x3AOHl5eUFeSbPZfP78eaj1EBcX58c/C29B9Fwwk4Je3JhlE9YyCC8PwAsMGwqFQqfTST/L87wfp7koipWVlYGdFIqER8fvZxxRFFHefUtTuaurq6VmBP+f5TguOzvb7XYHbL4A7HY7/EgTBJGUlIRi5uPj4+FERFFsTAxXKBTjx4+Pi4tbtmzZqVOnJk2adOzYsfHjx0PmKKZJ7ly7ZG1t7SeffLJo0aLmpHOJolhcXAx9u9q2bYvi8nQ6XaiUF6imgaZrbDe5XJ6VlUXTtCAIqBZsi0CD++9/rVKp4IsdzELc0NCAFhQYR6VS+XRzwbtOpxPCpAMA+ijAtsvl8n9laJqGmygIQkt90NKqlH7C0SFv3e12nzlzxrsFeUupqalBwY+wSsJ269at4USgsW1jN0uhUAwfPnzDhg0PP/xwTU3N6tWrJ0yYcPTo0WvRQvL2407UuF0u119//bV69eqffvpJp9Pdf//9KM6uMZC0CAY71HcQpC2oecGyrHdv2OZjtVoh5VnqPfeGJMmkpCS9Xl9VVQW6cEuXaTQyxMY3+QAEUK8B7azRaNAU0hd9BpbDhtvtDuyZlPrQoCaIn3FiYmIghx2cb4HNyDBM27ZtG/ss/JqiKkdBftEKCgrA1QaWEDRaampqdHS02Ww2Go0nT57s169fY6o0TdPdunVbvnx5dHT0V199tWPHDoIgNm7cGEDI7Z3GHVdf0mQybdiwYe3atfn5+UlJSS+88EJzrGDi1cqPCoUiIyMDyZJdunSJiYkpKioKfpVEPmudTuffZsQwDEh5EDnU0onAZkcQRFRUVHOiPm02W8DOdPJqeV0Ey7Jgfg05giCgnNEmgXpIcDz5+fkohqY5iKIIFwTVBPFJeHh4CEWQ6upqkPvS0tKkHW/CwsKioqLy8/Mhjb1JwT8jI2PZsmVJSUl//vlnt27drkXY7+3HnWKXhK/Q8ePHV69evXPnToqi+vfvP3Xq1P79+/spi4BwuVyXL18mrsYYov31ej3kRIP2GkwtXovFAgVrDQaDSqXyb1ODjby8vACW5traWvBspKamNlbtgiCIsLAwjUZTU1OTl5fndrtbZOxHYyKTmfRFn+YzaXJhSDzC/m2p6C2e5yF/vPmD2+12pKT7mQWqtxFX4x+CPCm4CwRBxMTExMfHo9HA1/fXX38RBHHmzBmXy9XkndLr9XPmzKmvr1epVNCSs6Ghobq6Oi4uLsgO77crd4pd8vfff584ceLw4cN//PHH2NjYGTNmfPHFFwMGDGimuioIApii1Gq1T/HBarWiotyBgZ576CXtZ08koQSWplJbW8vzPHhI/Qg7UVFR4KUNJtxParf1L1hBj+yAJ/KmmXIcx3GVlZUtGlmpVMIvE9rwCapXUl1dHWQpM1EUkSU0LCxMagylaTolJQW2jx071sybRdN0dHQ0PMmCIHzxxRcPPfTQW2+9dfTo0ZBEd95m3P52SYfD8emnn65cubK4uDgsLGzw4MH/93//17dv3xZVRrBYLFCTEexZ6KLJZDKwaRYWFhYWFgbT/NN00GIpAAAgAElEQVQjUMbPfQkPD0dV2gLIVIHluMlZUPaIx+E1B8gLIggCEtI9Putz3rCwMPJqC4TAbBdoTIVCERER4T/VhKZpaTmflp4deGPi4uIiIyOb/KzL5Qq4ZDLQ0NCAel106tRJakmUy+WovhHLstXV1TExMS0a3O12V1ZWVlVVrVy58vvvvx8wYMCYMWM6d+4cpFP+duL217iNRuN3331nNBp79eo1YsSIJ554AhJsW3TiJSUl4GGMjIzUaDToszRNQ34Oy7LeZR1ahNvtlhZk9DOUTqeD/LP6+nqbzdZSNR/pv83USSsqKloa6Y10UuiG6qFx+5wXXhEEAap4tLSiJfG/SjT0mPQjkqvV6tTUVJlMBmFALTo7l8sFUjw4UvxENcEG1P4I5tkoKyuDonCQwS0diqKo9u3bx8bGQuHh3NzclnZDgjihjIyMH3744cCBA+vXrz9y5Mjo0aOHDBkCzYsCPuzbhttfloyNjV20aJHVas3MzGzVqlVg5wuVsqBSjrTaLkmSSE8MOAEZqKmpAQcRxHY0R8rLzc29ePGiz06nfoAMH2m/gcZmgY2SkhLQ0Fs0CyCtrgh/KYryWZMRifb19fVWq7WxIup+sFqtYLnTaDQxMTFNfr2lykRgZyf6rYaJXoc6csE8G9C5AbZRnQ5E69atU1NT0SoZwESxsbH//Oc/H3vssZ9++mnu3Lnnz5+fMWPGli1bXnzxxZEjR+L489tNqDYajadPn9br9V26dIGlRKFQ9O3bN8hh0bfdwyfIMExaWlqQgwPgJScIIisry/9zGRYWBjYvt9uNqnM3n7q6OqR0B3y0/kEjZ2ZmekQUQvCz90fatGkjl8thQQngpAiCKC0thQ/KZLLmVNWFDEKWZe12O8uyzV8LUIwhLOgedSUQMpksPDw8JA59JJuHhYV5F85QKBRwvoIgQCm8AO4sSZLh4eHDhg2Li4tbvXr1vn37Dh06dObMGafTOXbs2Dt8obxNNG6wZ508efLjjz8+cODAE088sWbNmlDdWqfTeeLECZZlVSpVz549pVeMJElwcbAsW1ZWxnFcYBqKNHunpqbG/zharRZZpgJwnoKe2KLPBpx7A/ED0s8qlUrUVVGKtDZ7c6aD/mgEQaBiQtJU+uaMEB8fDxp3eXm52Wxupo7P83xxcTFIdnV1dVartbGJ1Gp1SkoKtHtDHSACADIaQM+Iiory0LjhRUgD5XkeutcF/OTTNN2/f/+MjIzvv//+o48+qqysrK+v95/FdCdwO8iSOTk5R48e3bBhw/nz5xsaGrp16zZq1KgQ/vqxLGsymURRVCgUWVlZ0rdIklQoFFDUACJsArbjoJhEqGXQzE9BMGNeXt65c+eUSmWvXr38VF1DpxOwBt1SpBGdYLeFi+nt5qIoSnrpRFEsLS3Nzs42m81hYWE9evTwcEp8/fXXGzduVCgUL7744sMPPxxM0yFkZ2wOgiCggFO1Wu1HaOU4DgnFFy9edLlcgYXTwroMsqRarfZ+sGmaTktLQz3jTCaTd334FpGYmDhu3LiHHnqotrYWRg5mtOtAdXX1lStXMjMzgwnF88OtapeExLKSkpItW7Zs27YtNzfX5XIxDDN69OjJkyenp6eHcC7pD6mHxZAkyfj4eJ1OF1hcoRQ0LOiezdnZ5XKdPXs2IiJiwYIFJ0+eVCgUjz766Pvvv48slRzHofgkpVKpUql4nge5pkkft8d0IFCAcgoqnnQp53kezAUKhULqXIa1D/4tKSlhWZYkSZvN5j0vCESQh2c2m0+ePDl9+vRjx46Be+ruu+8eN27cww8/DCtpRUXFV199deDAAYIgDh8+/Pzzz8+ePVtaTLc5p4Z2gLJASUlJbre7oaFBFEW4VtKzI662spGOrNPpwDXvc3yGYdBqBQU1AvuugZAID2F6erq3XRJeh1XSbDZbrdaWmqp9Tpqenu79PTKZTKWlpeHh4QkJCTeDGm6xWA4cOLBmzZrLly+PHDnyjTfeCCazozFu9l8Jn4iieOjQofXr1x88eLC8vBwJAjRNq9XqyMjI4BPCpNTW1oJ1SavVegdL0jQN60UwfkxBEFB3lOY8fHB2brf7yJEjZ8+ePX78OCxhP/3009///vcJEyZQFOVyub777rtPP/20qqqKYZju3bs/88wzbdq0qaiogEFaJH8JgvDnn39+/vnnx48fz8rKeuCBBx588MHExESSJM1m844dO44dO+Z2u3v27Nm7d29keZROkZiYCKfm8yrJ5XJYmGpqao4cOXL48OGDBw/C8mSz2fbs2ZOTk+NwOJ588kmapk+ePHn69Gn4oMVi2bBhg0Kh0Ov1KKiwRTcC+cS3bdu2evVqs9ncvXv3V155pVevXjRN19TU/PzzzxaLJSMjo2vXrmq1Gg2uVCr93Cy5XI5WmaKiIml4E8/z4IL31jwgBQv9tBAEwXEcumWNyUoZGRlyudzhcFRUVJSXl6PYoJBgs9lMJlN8fDzP8ytWrFi3bp3BYBg0aNDAgQM7duxoMBiar/qEEJ7nT5069cknn3z//fcmkwnCSK/RkbTALglmoBZ1m7tGWK3WRYsW/fzzz0ibYxgGSsKsWbPG4XC8/fbbPrNTIeLM+/XKysrffvvNarX26tULHjjpu0VFRWBdMhgMHhVuiKtdYaurq0GjBI2ssrLSYrGkpaV517ItKirauXOnyWSKjY39xz/+ASV17Xb7mTNn0D5N3pS2bdtCqe0TJ05I93c4HBs3brz//vvT0tLWrFnz7rvvVlVVQbTKuXPn9u/f/+ijj4J0KZfL09LSmhMJBAJpTU3Nq6++CqVez549u23btocffnjmzJkZGRnvv//+ihUrQLtUKBQdOnRISUmBWUpLS1mWBZeXXC6XWh49pgPvAUEQPM/v2rXryJEjsET2799fEISDBw8WFRW9/fbbHTt2bNWq1f79+2traxmGGTBgwLlz58rKyjZt2hQVFQWPKMzS5DVEB2M2m81mc05OzooVK44fP04QRHZ2dk5OzpYtW6Kjo997770PPvjA4XAkJyc/9dRTM2bM8LhKfiZCAimKpqqoqLh48eKuXbvy8/MTExOff/75nj17IjPxhQsXvvzyy5KSkrZt2z7yyCM9e/aEC1JVVYWO2eeMSUlJOp0OylYVFBT07ds3JBE8VVVVP/744x9//HH58uUOHToMHTq0c+fO0dHRly9fvnTp0pdffpmVlTVw4MC77767ffv2Go3Gf2xGqHC5XCaT6auvvvrss89yc3OVSmWHDh0mT5787LPP+sklCwqxeZhMpsWLF48fP37Lli1HjhwBe1MzPxsMTqfTbDajoqqA1WqdPn06apcaFxc3duzY1157LTk5mSRJnU63YMGCwsJC6RG63e6jR49+/PHHO3bsMJvN0tGKi4ufe+45+C1KSUl5++23i4qKpJ/94Ycf4LfhscceA2u9lMLCwu7duxMEkZycfOXKlUOHDt1zzz3R0dERERGdOnVaunRpaWkpGq2wsHDQoEGQGaZSqfr373/mzBnoy4osnlu3bm3ysnz00UeNJZORJDllypQDBw5kZmbCv/fdd99TTz0FSxWqhaNUKj/44AM/U5SXl999990EQYSHh+/bt++TTz7x+IGkKKpXr16vvfYatLiBLgLwhUc/DGlpaSBiw2UMCwsLDw//9ddfvaez2+3PPfccfArF6CgUis2bN2dnZ/ft25ckSaVSOW/evF9//RViVNu1a/f7779PmzYNnThstG7d+q+//mryGv7xxx/wU0pR1KZNm/bs2SP9ZVWr1cuXL//555+l9lCtVrtw4cJRo0bBvz179oSAAZ84nc4333wT9jQYDMePHz948OCAAQN0Oh2cIEmSnTp1ysnJgf3Pnz/fu3dv+IVmGKZ3795nz56FH90+ffrAOHPmzEHtzKSYTKbOnTt77wPdcnbv3l1aWtrkBfHAaDSOHTs2LCwM7iZJkgaDYdKkSTt37pw9e/Z9990HiepyuTw6Ovof//jH1KlTd+/eDbnk145Lly699dZbd911l0qlYhimXbt2CxcuPH/+PKoqci1o7ipZUFBw7733UhSlVCqTk5OffvrpzZs3FxUVmc1maMoeEjiOczqdJpOpsLDwl19++eijj1544YWHH37422+/9djz7NmzED1L0/TkyZOdTifLst988w2UzKNpevDgwZcuXYKdBUH45ZdfMjMzZTJZXFzc7Nmz0cNtNpsnTZoEP7zoAX3kkUfA4yyKotvtXrZsGXz5X331VTDqScnPz+/RowdBEDqdbu3atf3795cuJUqlctCgQb/++isYUidPngxDwV+SJJ944onS0tLi4mJYazQazY4dO5q8UHv27EE/EmiNQFFKBoPh3nvvha9i165dz58/X1JScs8990j3l8vl8+fP9zOF2+1+8sknCYJQqVSrVq0aNWoUHHNycvKoUaO8Ezx69+79zTffPPLII9IXW7VqhVbJvXv3QptcdG2l2Gy2ESNGeIyZmJj4+++/C4Kwbt06sHUkJibefffdFEVRFDVixAibzfbLL794HEx6evrZs2ebvIZGoxFF1Tz++OMbNmyQXlKSJFNSUlBRW4VCAQ9JWFgYUnszMzPLy8sbG1+6Ssrl8gcffBApwkisVigU8+bN4ziO47jFixfDEwjvymSyZ555pqqqqrq6GnUW+fTTTz0kBsBqtUL1aIIgnnzySViqjEbj+++/36NHD51ON3ToUKiI0Uzg4GF9VCqVSUlJ8Kus0Wg2bNjAsmxJScl33303btw4KJYOVywmJmbDhg3SBQFCEXwec5MIguB0OlEWPDBlyhTIrerUqdOCBQtOnz4dwPpjtVrBSi6KIs/zOTk5O3fuhMKmPvn/7SDNAczkbdu2hahgjUaTlZU1YMCAefPmQXe3gCkvL//rr7927969Zs2aiRMn3nfffYmJidACCRJO33nnHen+PM9v2rQJRJvk5OQTJ07A606nc+PGjSBRymSykSNHgsxrNpufe+45JGvIZLJx48bV1NTwPP/pp5/CdyM9PX369Ont2rUjSVKlUr311lt2u10QBIvFAosFQRBjx45taGjwOPjTp0+D1CaXyzMzM5EcFBMTo9PpwGbftWvXPXv2fPHFF5ByS1HUkCFD/va3v8lkMpVKtWDBgpycHIgoSklJOXz4cHPuhccq2aFDhxUrVqCUXnSyr7/+usPhYFn2448/lgqDGo3mq6++8jMFy7LPPvssCAuDBg2C3ySKop5//vnq6up33nlHOhrDMAsWLHC73SdOnJDmfrRq1aqmpgYG3Llzp1arjYuLu3Llivd0drv9tdde81glu3btmpubKwjC+fPnUclY+E6GhYWtX79eEASbzfbqq69KQ8SjoqLgZ8k/Vqt1xowZsOSp1epevXp5GxnhMqpUqunTp0+fPt3DkhsVFZWdnd3Y+A6HA62SxNWCeHCLp0+fPnDgQFh2H3nkEZvNdvHiRdBIGIaZMGHCQw89RNO0RqNZsmQJNGKCQT755BMwoXpgs9kmTJgA+7Ru3bqwsJDjuHfffVeayTpt2jR4pIG6urqdO3d+++2333777fHjx6VvCYJw/PjxjIwM+ODLL7+ck5Mzc+ZMWCgfffRR8PLDvMePHx89ejS6dN26dTt16hS8W1tbu3LlyjfeeGPFihXffvvt1q1bDx48ePbs2YqruN1u73NxOp2VlZUXLlzYtWvXwoULv//+e6fTid798ccfZ86c+csvv1RVVTkcjibvsjcsy65atSozM/Ozzz4D/2f//v3DwsJmzJjhcREQzZUlAafTefLkyfXr17/66qv33HNPVFQUwzBqtXrZsmVo+T906NDYsWNHjhw5cuTIV155Zdy4cYsXL16zZs2WLVt+//33o0ePevyw5ObmDhkyJCUlBdyFkJuh0+natGkDvst9+/ZJ9RqHw3HixIlBgwbBXRk6dKhUC2ZZdsuWLVB/OyIiYvny5XV1dRs3bgQ5C4UKRkRELFu27MCBA6DnKhSKVatWcRz3ww8/QOev+Pj4Xbt2NTQ01NbWIvlo/Pjx3rLklStXwH4kJS4u7j//+c8XX3yB7PcpKSkon6RPnz5lZWUbNmyASouZmZn/+te/4DlLSUk5evRokzfi2LFjHsHMEydOzM/PR6oZYtasWU6nUxTF4uLi++67D72u1Wq3b9/uZwqj0divXz/YWSaTwVeaYZi33npLFMWCggJpeHNKSsqFCxdEUeQ4bsyYMciIDqskDLhq1SroBlNVVeU9nd1uHz9+vMfB9+7d+8qVK6IoNjQ0jBs3TvrWkCFDoJ+MKIqnT5+WhhZFRUXt27evyWsoimJJSUnv3r2JpujZs2d1dbXJZHrmmWekr0dGRsJZ+8Tlci1cuNBjqMTExM2bNwuCsGXLFljCEhISQDiAB6BDhw4lJSVHjhwB+TEhIaF3797oN68xWdLtdn/88cewT0RExC+//HLixAmP7g6dO3cGyRda8s6cORPEc5lM9v+1d+ZhTV1pA79LcrMRICRhx2AEXLDulio4Oi7V0TJ2xlY71XbGajvqM9UOrXZsrV/bqVvbcdzHulVtXerI2M607ooLLihVWxVZBAIICASSQLabu31/vE/vkydgxC2k9vz+8MGbu5x77rnnvu95t+Tk5LfeequqqgrOZrVas7KyQJA0Go3ff/899BWswERHR3vfdXNzc1ZWlrgMSlHU/PnzeZ4XBOHcuXNQMRx+IggiMjKyW7duGRkZGRkZw4YNW758ufhC1dbWLl++/JVXXnnuueeGDBnSvXt3qJsyYMCA4uLi1rdst9u//vrrdevWrVu3bvPmzVeuXGlsbLTZbCC6+kigPn21du1akiQTEhKWLFkyfPhwgiB0Ot3KlSvvJPPe2ywJ8DzvcrnMZnNOTs7ChQvnz59fUlICP7nd7r///e9g9gVIkpTJZAqFQqlUhoWFPfnkk+JCDHDlypWMjIzExMTExMR+/fpNmzZtxYoV586dKy4ubmlpgc+FuLPJZHr//fe7dOkiChQ7duzw6ZHm5uYZM2bADpGRkdOnTwcLCYZhgwYNmjx5MghBarU6NjYWxl9aWlpBQYEgCE6nc+HChSCYDBw48JVXXpk7d6442j799NPW4r3H4/FRMzEMmzx5cktLi8fj2bFjh48+qFAoYKxXV1eD+IB5rcQZDIYLFy7c9RGUl5eLYiOwadMmlmUXLlzo7Qkhk8m++uorsQOzs7PFpTeVSrVlyxY/l2BZduLEiT6L8X369AF7ektLyx//+Edx/fHll18GHxpBEI4cOSJ6aHtr3IsWLYICD2fPnm19OZfL1VqWHDFiBBzO8/w333wjlr7Ccfxf//qX+Nzdbvenn34qKsLh4eEHDx7k27FuzrLsX//617vmPVmwYAEs6fzjH//w3h4bGyuO/DbZtm2bT8aQl156CT7q1dXVvXr1EoeE+NRgB7vdLpqJxEcglUq3bdvWpoLJ8/y3334L065UKh07duygQYPg0iqVCqYbtVq9YsWK0tLSLVu2pKen+6xry+XyKVOmXLp0yWq1Ll68WPwGZ2ZmNjU1wZrA22+/TVGUVCqdOnUq1DFnWfbo0aMgWIitHThwoJjvcuPGjaNGjbqTybdXr143btxgWZam6UWLFimVSp8cJTiOjx07FuI1WJYF2xSwZ88eg8Gg+In4+PiePXsOGzZs7ty5GzZs2Lt3b2FhYU1NDYirPt1VVFTUv39/WOkmCMJgMGzevNnHXOHN/ZiE4P3HMKxnz57iDGI2m0HiGDt2LIZhZ8+ePXLkCHiEeGeNb2hoKCsrEzOpEAQRHR29bNkyGDosy4aHh8PNYz9Z1SsqKiDFS25u7ooVK3Jzc8U2g19YTk6OTCbr1KlTbW0tWFohVTWkSNm0aRPsTJJkbGzsyJEjjx07dvv2bTHXGUmScXFxNE2DITssLEyhUDAMc/HiRUjbJ3Lz5s3jx49DAFx4eHhDQwPHcWazuayszKeLQkJCzp8/D6aknj17njhxgv/JHK9Sqdxu94kTJ5xOp6iniL5+Vqt17969YMD18wgKCwvF/P5Afn5+QkKCT4J+iqKuX7+u0WjEEt7ivOZyuTZs2FBTU6PT6eArQpJkSkpKY2MjFAZoaGi4ceOGz/AgCKKyshIqW3hPx+Xl5UePHgXZ5Pbt2+LUYLfb//Of/xgMhsrKyhMnTsBtrlmzJicnx+eOPB7PqVOnfDZWVlauWrUKomtA9RZ/OnjwoNlsFi9UXV0t3lpLS8uWLVvy8/PbY2+9evXqncrtihw4cMBsNjscjh9//NF7O03TmzdvvpNDFcdxoPiLW3AcLygo+Pjjj+VyOU3T4nW962qcPXv2pZdewnFc9P4RvAKK1q9ff/To0S5durQeHgUFBfC+MAyzf/9+72bAxNrS0vLhhx9u3bq1sLCwdXo0t9u9e/fuS5cuJSQk5OXlwSPGMOzixYuvvPIK9OSNGzfgxd+xY8f169fj4uIEQaipqfEusywIwtWrVxcsWAALL7du3bJard6urN6Ul5fPnj07JCQEXrfWpTVwHC8pKZk1axY8aKfTKTrMNTc3g54B/7116xbU0QUvWpVKZTQaYR182LBh06dP956p4+Pju3fvfvnyZbfbHRcXt2TJkkmTJvkJMcL5e0xD7XK5Zs2adezYsdY/aTQakPI8Hk9xcTF8ZlvftkajEfMdyGQysSq0IAgMw0AgoLcfg8fjgTHhcDhgvvc+G+jpsE4q1lYW7pC3mSRJlUrVOvk22GfBSQ3iiNvsL4qioK9htQ78NAVBcDqdPtOTtydd69AOpVIJr7TT6Wz9iopX8QPLsj5DCo5qvV0mk4nTGc/zIPF5HwXhQ9hPnUnTNLwJgiDAIqz32cQOx7xiBGG7OFn4dD7YIlmW9Xg8cLMEQbT5DYDV9Na9Ac+X/ynFJ+BzEhg84uEkSbYzYgS0s7vuBqGWrV8Wb/em1oAg47NRzB/azkuLwB2xLNvmRXmev9NkdNcT3tNRcKD/0spi//up+R4wUlNTd+3a5b3+kJOTM336dJCKfv3rX+/evdt/dpV7jr2B3mFZ1nuMwmOzWq3gvodhGM/zYI4AqdDhcFAU5bM6DqFyYn0SeF1bu86LW9RqtX9HaHA0SUxMLCoqCg8P53ke5i8cx7VaLTha4zjetWtXl8sFRWZaI+Yl8wEkGlGCgypdJEkWFRXZ7fawsLAuXbrU1dVBGkpvYPoW3xaSJDt37ux0OmtqanwsMOJdJCQkQFAaQRDx8fFxcXEajcZqtYoDDgxzUVFR4rp+exAEoaqq6k5JZ6Ojo7VaLdS0av8574rD4bh58yZN03a73WKxYBim1+uTk5MhLyfUtNLr9TzPh4WFWSwWtVrdrVs3sKLe3xVVKpVGo2lqaoJ64gaDobi4uLy8vF+/fgzDNDQ0kCRpNBpv3brldDrB08VoNMJ4ZlnWZDKRJFlfX08QhFar9SMKgbKGYRhFUXa73e12G41Gq9WqVqvb/AzU1NRUV1dHRERAbqqKigqappOSkhwOB9hqMAwDfSgiIsJkMnnPLyRJ9uvXT6/X19bWmkymhISEB88rDioaPBQMw6xWa1lZWVJSklKpLCwshFaBU21NTU3Xrl1JkmxqatJqteHh4WASfJCr19bWwsuSmJjY0NBQVVUl1sDQaDQREREVFRU6nQ5KoVmt1qqqKvBlFgShtLT06tWreXl58FqJnw0wk8A0kpyc3KtXr8jIyCeeeAKsshiGgUfg4sWLxYKUzc3Ndy01fD9x7BaLxWKx+JT18JFXaZoGV1gQy6ELfF7pxsZGgiAeenEiiqLg+TEMU1FR4XA4pFJpcnIy9C92Z7ngrhAE4X0UTN+iBOQtF3vTWpL3/w0HQVU8LXyWW3+9PR6PaFRpP36+7WDaehTRC3AvBw4cmDlzJkEQ27ZtGzZsmCjrMQwDQQHQvTiOg3PyvUpG3kBkPUmSHMdRFLVr166PPvroiy++6N27N4hvMpkMBD24qLd0Bmnl4OpwBv8Xwn56xHAtyLDX5lsHnS9KwWArgHsX4xdhH6lU2vr2od4RyIz3lEP6TkA7vW8QCkLgOC4OP5B8xQwaEJcBcQr3MXV4Iw5FqVRqMplmzZr18ssvP/vss6KdEB6EOE68s3iwLJubm7tgwQKWZWNjY/v16wfqV+fOnfv06QOCoVQqpSgK3hHRb//06dMzZ86EfIM9evTIz893OByrVq2aNm2any69n3XJO0lbPngHk7aZP9m7rPsj4q7FER8cP/WhHulpH9F1HwXQ1OjoaBisarW6TSHahwcMExZVEPhY1tfXt7S0+NRCaPNA2P4gaXX8/OStKrW5p7jPnRpAEMTDTT/hfTbxb59L3Gn7A15X7A2n03np0qW+fftOmjRJ3OjTAz7tHDp06M6dO8E8fdckFzDLcRxXUlJSUVGRnJz84Ycfjh07ds6cOTt27MjLy5s8ebK/BxeAiCIEAmtVsiLAV/d4PEVFRaNGjQrwdRHtAfyaKyoqWJZtZww0RVH3WkBFIpFkZmaGhIQYjcbevXtTFPXmm29GRkY+++yzfrKWYD/TbBcIxL1CEER7FCBEh1BaWsowDAQgPNILRUZGeju9pqamLl269K5HPSZZeBHBj7dHS4BHnSAIEMGJRntwAouwoGsH4TNCGjciQPjY+gJ5aY7jSJK8a35iREeh1Woh/AQL+NhoD7+UetyIXywMw1gsFgjt7+i2INqmc+fOEomke/fujyKH7oODNG5EgPB29uR53m63cxxnt9srKipKS0vr6upMJlNiYuL06dPvwzkM4uLNZnP//v0zMjI0Gg34zYD7F3jaB17TR7QTcCiOiIjwU7m3A0HWG0SAqKysZBgGx/Fvv/22rKzs8OHDFRUVNpvNbDaD66LH4wkLC5NIJL///e9Ft02VSiUG88lksjbjc3iez87OXrp0KU3TcrkcnO0NBkNSUlJycrLb7dsgoAEAABmNSURBVIbcukGoyiEAsdoahJl0dHN8QeuSiAABE5zL5Vq9evWd9rFYLIsWLfr3v/8tugHL5XIxzg/cm1sfBcEhIDA6HA7IhuATg69SqcrLyyGrDSLYaGpqAuf2DvESuytI40YEiKSkJIqi3G53fHw8+JnTNF1bW+sT5C6Xy7t37w7pf1iWrampiYqKkslkPM9XVVU5HI7WZxYEob6+/k7XhQAMCLNBoz04MRgMUqk0eG3cHd0AxC8FMUR3zZo1nTt3xjDM7XYXFBRAMG95efmpU6cIgpg7d+6UKVPEOmIulwtyo7SZVQRgWfbw4cPvvvtuTU0NpAswGo2pqalJSUk4jsfExHz99dcnT54U8/gigg0wrEHIZke3pQ2Qxo0IEDabjeO40NDQ9PR0MQHlwIEDYc2RZVmXyyUIglqtFkPTINWT+LefQLQXXnjBYDCcOXPGYDD06NEjPj5eDIDjOK68vPzkyZMYWpoMVuC5hISEeBePDB6Qxo0IEJBjFf72HnWwWi+RSMTQtPaMSbvdLpPJvDMUDBo0aNCgQa33hIwSJEmK6U4QwYaYL8ZPkscOBGnciAAhl8vvKiYwDFNUVATp6eLi4hISEtrMUVRfX79s2bKYmJhZs2aJNdHuBEEQoaGharVaFGARwQYMDNA2gtCtFWnciEBzJzum3W7fsGHDhg0bIIe80WicO3fub3/7W5/dWJbduXPnunXrdDrd4MGD72q2hsVNl8vlcDjQaA9Ompub4TFhQbkqgmRJRIAAb7g7/cpx3K5duxYvXtzY2KjT6Wiazs3N5Xk+NTXVaDR6vzk0TZ88eZKmaYPB4J2d707wPF9dXY3jeBA64iGAurq6Dk9p7ge0LokIEBaLBdwe24yB8Xg8ly9fbmxsTExMfP/99y0Wy8KFCy9cuHDmzBkwiIvcuHEjPz+foqjx48cbDIY2BzBUlaipqQFbUEpKyh/+8AetVnv9+nWoyxYbG9ulSxeVSgWl7sAx86GktkXcBx6Px8/Y6HCQxo0IEHFxcWJm79ajjmXZsrIygiCGDRs2adIkhmGOHj26f//+y5cvT5w4UTTs8Dx/+PBhs9ncrVu3SZMmtbmGxTDMyZMnN2zYcOrUKalU2rNnzxdeeGHevHkrV66ESpMej0en0w0YMODFF1+0WCwHDhygaTotLW3atGkBSNuMaA0U9dNqtWJ9l6AC6SCIAFFWVuanUgrHcU1NTVKptHv37nK5XCaTDRw48MiRI7W1td66WENDQ05OjsfjyczMpGnaarW2zhp5+vTp1157raqqSqvVNjc3Hzp0qKCgICYm5sSJE1BlBMOwlpaWioqK48ePu91u8FQ/fPhwWVnZJ5988tBLjCDuCsyPkPOio9vSBkjjRgQIWKHH7qxVqVQqkiSjo6Ph18TERIlEYjKZvIsj3rhx4+rVqxiGnT59euvWrUOGDFmzZo13aRCn07l9+3aTydSvX79//vOfjY2NW7dulUqloaGhYobXbt26aTSa/Pz8xsZGDMMMBoPb7a6vr8/Ozh49evRzzz33iHsC4Qs4ADU2NkK1oo5uji/BKN8iHkvEClxtatwURSUnJ1+4cMHlcsGv4pQq7k/T9HfffQfyIBTvPnDgwNmzZzMzM8XzOByOkydP4jjev3//IUOGCIKQkZEB54G6uCkpKevWrZPL5S+++KLJZIqOjl65cuWPP/64ePFil8tVUlKC3ojAYzabwfk/OLNdoPySiAARExPj5wUgCEIul9M0XVRUBFvKy8sZhomOjhaPqqioOHjwoPdRLpcrLy/PWzLleb6lpYWiKDB/4ziu0+l0Op3T6YQsk/3793/qqafUajWsdWZkZAwfPnzixIntKViGeEQE+ZcJadyIAHHr1i1YYWxT4yZJMjk5WRCE4uJiyBBz5coVhmEMBgNUBoYz+JQ7ZximpKQEMlnAFoIgoK73jRs3mpqaKioqSkpKhg8fLpPJQkJCwMNcLpeLbQgLCyNJUqvVigZu9EYEHuhzjUYTnBlJgk64RTyu3LWw9ZAhQ4xG46lTp959912O406fPi2TyZKSkjweT1lZmUKh6NOnz6uvvnr8+PHm5uZbt26Bbq7Var0lEaVSOXz48M2bN2dnZ1+8eNFut7vd7vHjx//lL38RTTcYhtE0DaYkEFRdLpdPuXNEIFGpVARBGI3GIFS3MbQuiQg8d4q9SU1NHT9+/Lp169avX49hGEVRgwcPHjdu3KlTp955552+ffuuWLHigw8+mDlzZnNz8/bt22F58Te/+Y13FKNKpZo2bdrly5cvX75cXl5OkqRcLud5XiyrIpVKxeoOOI7Daiksh5Ekqdfr0RsReCCrXnCmusCQLIkIHqRSaVZWlkajOX78OE3TGRkZkOnHZDIJghAVFSWVSuVyeWJiIoZhs2fP9ng8SqVy6NCh3ifBcTwtLW3Tpk3r1q0DP6G0tLRRo0bp9fqFCxfm5OSMHz8ew7DOnTuPHTu2pKRk3LhxMplMr9dPnTq1rKxszJgxHXLvv3DaWYO7o8AfdQFcBAJYsmTJBx98EBkZefnyZa1We6fdBEEAi6dOpwP9i2XZmzdvGgwGhULxIA3gOI6maTE7BkRMiikw3G43y7J+krMhHh1XrlwZMWLEhg0bJkyY0NFtaQOkcSMCRHh4OEmSHMc5HI7W6XnAq9xut8fGxkZGRnr/BK7mD94AiUTivezl7WWJYdgDTsEIP9TX1xcWFvI8r9FotFqtXq+XSqXe6yQ0TXu7fAUbSONGBAgoX+N0Oq9fv67Vai0WS2lpKU3TZWVlTU1NlZWVRUVFTqdz1KhR8+bNCza/HLCJe7/YPM8/orcaPAEkEgnHcQRBgLb3iHytYW7y/q94X7CY++CXoGl6zZo1n332mThLRkVFJSYm9urVq1+/fhA70NDQEMymM+QJhAgQDocDklAsWLAgPj6+vLy8qqqK53mWZbmfwDCsuLg4PDy8T58+er0eRD+appubm7VaLUxSdrvd4/GIkqDNZrPZbN4X0uv1LpfL7XYLguDfsH4nwIxDEERDQwNMUi6Xy+l0JiQkuN1useAfjuOt4yMfEI7jqqqq3G53UlKS3W5XKBQ2m83lciUkJKhUKp1OZ7VaIbPcg8PzvNvt9k7Q6Xa7LRZLWFgYjuM2m02v17eeKHEcVyqVbRYgahO73X748GEoTGQ2m0tKSjAMg6TICoUiLi6uc+fOtbW1drs9OFNdYEjjRgQSsCaDAfpO+9hstvfee08ul8MsKZPJ3G53S0uLXq+HHVpaWhiGgVlSEASbzQZZewGCIPR6vcPh8D9LchzHsizYuOEoQRAoioLtMEtSFFVbWwuzJJRkiYiIgMoTUFIcSn4/xP4BQP2Uy+Ucx+E47nQ6CYIgSTI8PFyr1TY0NPjUU3sQRFdTmPpZlmUYBtwAWJb1TpIklUphH4VCoVKpzGazRCJhWRZ8A/yfuampyedXjuMg6WdTUxOEnOI/8bBu7SGCNG5EoAkPD4e5iWVZq9XqYz+USCR9+vSJi4uDF8ZoNKpUKrfbDQLOw2pDU1NTWVmZRCJJSkpSq9VKpZKm6aSkJIZhysrKBEGQSCTR0dFNTU1QwBYgCKJLly4OhwPKkMGxD6tJbeJ2u00mk1qtdjqdnTt3drvdtbW1iYmJDz3JW3V1tdVqhdw8raEoKjExsbq62uFwGAwGjUZTVVWlUqlu376t1+vj4+N99ud53mq1KpVKuVxeUVGxfv16MUQK3P4VCoVerw8NDQXXq7KysmvXrj3cO3qIII0bETgEQVAoFO+9996AAQMwDHO5XNXV1Tdv3oSsE42NjRcvXkxLS1uyZImYU/LRCRcw8oNTeHmc4Hl+wIABx44dKy0t7dSpk06ni46OVqvVer0e/sVx/NixYxMnTgxejbujG4D4BYHjuEKhGD58eO/evWGLuC6J/VRWOzQ0VKPRBGDyQvNjYCAIokePHl27dvV4PFCmrXXPw6p00D4RtC6JCChKpTIhIUEcdSRJeq9q+aQlD35YloVlRAzDoBR4R7coSPFxw/KhuroavpTBOR0hjRsROPznl/zZ4XQ69+3bd+TIEYfDQZJk9+7dJ02alJKS0mbdR4QfjEajVCoN2oGBNG5EQAHjZke34uHw3XffvfHGG42NjRRFgTqZk5OzcePG5ORk7914nm9ubgbXGbVaHRoa6v2rIAgMw/zChdDm5ub789kKDEjjRgQO0V358Rh1FEVFRET07t178ODB+/fvv3LlSn5+/vnz51NSUsR9BEE4f/780qVL8/LyCIJ48sknX3rppREjRpAkWVxcDDnSq6qqevXqlZKSYrfbi4qKBEHo2rVrSkpKEGbtfkSAI0HwegIFp4iLeCwRBMHpdFZVVXXq1Kmj2/IQGDly5Pbt2xMTE/V6Pcuy165dk8vlERER3u9UXl7e7NmzL1++LJPJaJr+3//+d/78+ZUrV968eXPjxo1utxvs+zqdzmg0trS0QBLinj17zpw5c+rUqcGZSeyhYzAYwLcpOKejX8QzQAQPPM8/RKfojkWlUqWlpWEYVllZefbsWY/Hk56ePnjwYHEHt9u9c+fOH3/8sWvXrlOnTi0pKdmzZ49cLlcqlQUFBbdu3RIEITQ0lKIos9kM0SmhoaE4jl+5cmXZsmW9e/ceOHBgcIpXDxeLxQJ++x3dkLZBGjcicIiD7XEadXa7fe3atefOnUtNTYXMb+LdVVdX5+bmsiz7pz/96c0333Q4HOPHj4+IiBg4cODu3bsxDBs7duyMGTMYhnn99ddramp0Ot2CBQtsNttHH31kMpmKiop+IbMkRPsEr8bd0Q1AIH7GcBy3Z8+ezZs3K5XK+fPnZ2RkeL/nDocDjDadOnWCYhLPPPOM9+EDBgwYPXo0RIjX1NT06NHj+eefr6+v3759e2lpqXeJ3ccbnU6nVCohTXIQgtYlEQFC9CuEsqId3ZyHgCAIubm5H3/8sdPpnDVr1oQJE8QSPYBer9fr9cXFxdevXzebzRRFsSwLlXZgB7ErwNc6NDQUyu16F+F5PPrKP2LVzOC8WaRxIwIBx3E3btzweDyhoaFRUVGPx6irqKiYP39+SUlJWlrazJkzIWWGt7NkeHh4ampqXl7eF198kZeXx3GczWZ7/fXXJ0+eDDuAtAi9QRBEbGwsrEvCr8GshD5ccBxnGAbyj3R0W9oAadyIACHqj8HsGdd+GIbZtGnThQsXBEGoq6tbunSpy+Xq0qXL3LlzxRQYSqVy6tSp586du379emVlJY7jMpns9u3bOI6D8bqurg4S7fipVP5LICoqavbs2WLcarCBNG5EIBCHGcMwNpvtMRh1Npvthx9+4HleEISysjKTyYRhWFpaWlZWlvfdDRgwYMeOHbt27bp06RJFUX379p0yZQpJkr/61a+Ki4tHjRqlUCjsdrvRaCwoKIiMjBQEQa1Wx8fHm81myNn+GPTVXYmOjp47dy5FUcF5s4/JChEiyOE47vnnn9+3b19MTMy5c+cMBkNHt+hB4TjuwoULBw4cEPPRqlSqIUOGjBw5srU8yPO8zWaTSqViXR23211VVRUfH69QKARBqKysLCkp6dGjR2xsLM/zV69era+vT09P906Ri+go0CyJCAQcx02aNCk7O7tTp06XLl3yUx3s54VoksK86tZ2bJMQDx2kcSMCAUEQ6enpZ86cycjIAOmpo1v0cGgdf/3Y3BpCBFWaRQQIu91+9erVLl26+JRIRCCCHKRxIxAIhD9QIjwEAoHwB1qXRCAQCH8gjRuBQCD8gTRuBAKB8AfSuBEIBMIfSONGIBAIfyCNG4FAIPyBNG4EAoHwB5IlEQgEwh9oXRKBQCD8gTRuBAKB8AfSuBEIBMIfSONGIBAIfyCNG4FAIPyBNG4EAoHwB9K4EQgEwh9IlkQgEAh/oHVJBAKB8AfSuBEIBMIfSONGIBAIfyCNG4FAIPyBNG7E/cBxXJs1igmCIEkS/uZ5HsdxHMcD2zQE4iEj6egGIH5+8Dx/6NChgoKC1j+FhoYOHz7caDTiOJ6bm+t0OtPT09Vq9YNcThCEuro6q9UqCEJ0dHR4eLifmdfj8dTU1LhcLq1Wq9frxT1dLldVVRXHcaGhobGxsWjuRrQfpHEj7hmn07lv377PP/+c4zgMw6RSKUVRNE2zLCuVSufMmfPhhx9WVFTMmDHD5XLt2bNnwIAB930tt9v93//+d+PGjbdv3yYIIikpac6cOUOGDGk9zfE8n5+fv3Xr1osXL9I0HRcXN2PGjGeeeYYkyWvXrq1cuTIvLw/m2Tlz5owZM0YiQSICol2ggYK4Z1Qq1fvvv19dXX3o0CGe559++ulJkybl5+fv2rWroaHh0KFDWVlZCoXCYDBIpdKIiIgHudahQ4feeuut6upq+JxfvXq1rq5u79690dHRPnueOnVq9uzZRUVFsbGxVqv12rVrFoslPT1dIpEsWLDg4MGD/fv3J0ny4sWLWVlZSqVy+PDhD9IwxC8HCVI9EPdBXFycwWDAcZyiqF69eqWkpNy6dSsrK2v58uUNDQ02m81oNK5cuZKiKNgNjnK5XDRNkySJ4zjLsgRBqFQqcR2zTX744Ye6ujpBEHr16iWXy/Pz869fv15YWBgTE+O9m81mW79+fVFRUWZmZlZW1r59+zZv3pyQkCCVSg8ePHj06NGnnnpq69atEolkxYoVq1evXrduXb9+/TQazSPsI8TjApIlEQ8Ex3EnT548fPiwyWTasmXLn//8ZwzD4uLicnNz165dq1Qq//a3v6WmpmIYVl1dvXr16tzcXJVKFRISUllZqdFo5syZM27cOD/n79Onj1artdvtU6ZMuXbt2vfff+/xeEwmk/c+giBcuHDh5MmTMTExkydPlsvlGRkZBoNhzJgxSqXym2++cbvdaWlpsbGxMplszJgxn3/+eXFxcX19PZolEe0BrUsi7hMYORzHnT17FsOw8PBwpVL5zjvvYBgml8sLCwv379+PYVj//v179OhRW1v7zjvvfPnll3K53OVyCYIgkUjCwsIKCgrGjh3r5yojR47cunWrIAh6vX7nzp08z2u12tjYWO9xy3FcYWFhXV2dXC5fuHChw+GQSqVPP/30s88+a7Vaa2trVSrVkCFDKIoSBAEkWZfL5Xa70eBHtAekcSPuE3HkeP+hUCjg78zMzA8++MBmszEMg2HYxYsXv/nmG7Va/dprr2VnZ5eVlQ0YMOCdd95p0w7jjUqlGj16NMuyixcvLiwsjIiImDdv3q9+9SvvoxiGuXnzJoZhbre7oaHhqaeeKi0t3bBhQ1VV1RtvvGGz2UiSVCgUcAg4J1ksFovFggY/oj2g2BvEA4Hj+NChQ9PT08FHR9yuUqlCQ0Phb0EQnE6ny+XS6XTDhw+Pj48nCKJXr16ZmZneh9wJQRAKCgq2bdvGMExmZubzzz9PUZT3DhKJpFOnThiGkSQ5Y8aML7/88qOPPlIqlSdOnLh06ZIgCIIgsCwLp2poaHA6nXq9XqvVPsyOQDy+II0bcZ/AyFEoFJMnTx44cGBJSUlqamrr4SQIAo7j0dHRarXaZDLNnTu3tLRUq9WOGzeunWOvqKho3rx55eXloaGhVqt1xowZb775ZkZGhrgDSZIJCQkymYzjuNjYWIVCkZycTBAETdNyuVyv11+/fv38+fPDhg2TSCRNTU0ul0sikUgkaPAj2gXSuBH3A8MwYuwNwzBPPPFE7969fXZoaWnBMIxlWZDgHA4Hx3HXrl3DMOzpp58ePHgwjD2Xy3X06FGJRDJ06FClUulzIYvF8n//939Hjx4VBMFutx88eBDH8czMzCFDhrS0tOzevVsikUyZMuWJJ55ITk6+du3ahQsXRo8effnyZZqmZTJZYmJi3759T548eerUqenTp4eFhVVVVWEYFh8fr9Pp0OBHtAsBgbhHeJ7Pzs5OSUnBMAzH8Z49e3722WdgkxF3+Oqrr0JCQnAcHzNmTHV19YYNG7xHnUajefvttxsbGwVBOHPmTFxcXHx8/KFDh1pfa/fu3T5auU6nO3HiBM/ze/fu1el0RqMRDN/Lly/XarVyubx79+6RkZEKhWLGjBlNTU3nzp0zGo0KhWLChAmvv/66Xq+PjIz86quveJ4PXJchfs4gpQNxzzgcju+++85sNoPHeE1NTXZ29qRJk2QyGezA83xBQYFKpaIoqrm52Ww2l5SUYBhGkqRMJuN53mKxrFq1ym63L1q0KDw8XKPRSCQSrVbbejQyDBMWFkYQBM/zDMNIJJIRI0b07duX5/nw8HCdTtezZ8/o6GiJRDJ9+nSapteuXVtXV6dUKhcuXPjqq6+Gh4f369dv2bJln3zySU5ODoZhnTp1euuttyZMmID9tGiAQPgHbzNnAQLhH7PZbLVaxf+GhIT4BMO0tLTU19cLgiCTyZRKZWZm5vnz5+Pi4p577jmr1ZqdnW2326Oios6fP9+pU6eqqiqSJGNiYgjC15zo8Xiqq6s5jnM6nWVlZXq9vmvXrjqdDsMwQRB++OGH2NhYMV6bYZiamhqYTGNiYsRZG8Ow27dvOxwODMPkcnlUVBQKT0S0H5QTCPHIcblcixcvXrVqFcMwiYmJNE2bTCaKol544YXVq1eHhIR0dAMRCH+gWRIRCBiG2bt379atW+vq6jAMk8vlv/vd71588cWEhISObhoCcReQxo0IEIIgNDY2gp5OUVRCQgIyMSN+FiBZEoFAIPyBbNwIBALhDxShiEAgEP74f2PkFRGauKfNAAAAAElFTkSuQmCC	N = 4, \, a = 0.6 \times 10^{-3} \, \text{m}, \, d = 3.0 \times 10^{-3} \, \text{m}; \left[ \frac{\sin \left( \frac{\pi a}{\lambda} \sin \theta \right)}{\frac{\pi a}{\lambda} \sin \theta} \right]^2
+665	 A 35 mm camera has a lens with a 50 mm focal length. It is used to photograph an object 175 cm in height, such that the image is 30 mm high.  (a) How far from the camera should the person stand?  (b) Estimate the best resolution obtainable on the film using light of $\lambda = 5000 \text{ Å}$, if the lens aperture is 1 cm diameter.	[]	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	u = 297 \text{ cm}; \Delta x = 3.1 \times 10^{-3} \text{ cm}
+666	 Consider an opaque screen with 5 equally spaced narrow slits (spacing $d$) and with monochromatic plane-wave light (wavelength $\lambda$) incident normally. Draw a sketch of the transmitted intensity vs. angle to the normal for $\theta = 0$ to approximately $\theta = \frac{1}{5}$ radian. Assume $d/\lambda = 10$. Your sketch should show the maxima and minima of intensity. Approximately what is the ratio in intensity of the least intense to the most intense peak? Approximately what is the angular distance of the first intense peak away from $\theta = 0$?	[]	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	\frac{1}{25}; 0.03 \, \text{rad}
+667	One side of a disk, 1 cm$^2$ area, radiates uniformly and isotropically (a Lambert’s law radiator) with a brightness of 1 watt · cm$^{-2}$ steradian$^{-1}$ at a single frequency in the visible.  (a) What is the total rate at which energy is radiated from this face of the disk?  (b) Given a fused quartz lens ($n = 1.5$) whose diameter is 10 cm and whose focal length is 100 cm, show how to image the radiator onto a disk whose area is $\frac{1}{4}$ cm$^2$.  ( c ) Estimate the total energy flux reaching the $\frac{1}{4}$ cm$^2$ disk to within a few percent.  (d) By changing $n$ and the dimensions of the lens, you may increase the energy flux reaching the $\frac{1}{4}$ cm$^2$ disk. By what reasoning might you determine the maximum energy flux into the $\frac{1}{4}$ cm$^2$ disk that can be achieved?	[]	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	\Phi = 3.14 \, \text{W}; \Phi' = 8.7 \times 10^{-4} \, \text{W}; \Phi'' = 0.785 \, \text{W}
+668	The Space Telescope, as currently planned, will have a mirror diameter of 2 m and will orbit above the earth's atmosphere. Estimate (order of magnitude) the distance between two stars which are $10^{22}$ cm from the earth and can just be resolved by this telescope.	[]	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	d = 3 \times 10^{15} \ \text{cm}
+669	 A sound field is created by an arrangement of identical line sources grouped into two identical arrays of $N$ sources each as shown (Fig. 2.62) below.  All of the radiators lie in a plane perpendicular to the page, and produce waves of wavelength $\lambda$.  (a) Assuming $r \gg d, c, \lambda$ find the intensity of the sound produced as a function of the maximum intensity $I_m, \lambda, \theta, N, c$ and $d$, the distance between the centers of the arrays.  (b) By taking an appropriate limit, derive an approximate result for the interference pattern produced by two slits of width $a$ whose centers are a distance $d$ apart.	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	I = \frac{I_m}{N^2} \left(\frac{\sin \frac{N \cdot 2\pi c \sin \theta}{2\lambda}}{\sin \frac{2\pi c \sin \theta}{2\lambda}}\right)^2 \cos^2 \left(\frac{\pi d \sin \theta}{\lambda}\right); I = I_m \frac{\sin^2 \left(\frac{a x \sin \theta}{\lambda}\right) \cdot \cos^2 \left(\frac{\pi d \sin \theta}{\lambda}\right)}{\left(\frac{a x \sin \theta}{\lambda}\right)^2}
+670	 Describe the Fabry-Perot interferometer. Derive an equation for the positions of the maxima, and indicate their shape. What is the instrument's resolving power?	[]	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	2d \cos \theta = m\lambda; \frac{\lambda}{\Delta \lambda} = \frac{m \pi r}{1 - r^2}
+671	Light from a monochromatic point source of wavelength $\lambda$ is focused to a point image by a Fresnel half-period zone plate having 100 open odd half-period zones (1, 3, 5, \ldots, 199) with all even zones opaque. Compare the image dot intensity with that at the same point for the zone plate removed, and for a lens of the same focal length and diameter corresponding to 200 half-period zones of the zone plate. Assume the diameter of the opening is small compared to the distance from the source and the image.	[]	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	I'/I = 4
+672	"For a camera lens, ""depth of field"" is how far a point object can be away from the position where it would be precisely in focus and still have the light from it fall on the film within a ""circle of confusion"" of some diameter, say $l$. For a given picture derive a relation for the depth of field, $\Delta q$, as a function of the object distance $q$, the focal length of the lens, the $f$ stop and $l$. (You may consider the object distance to be much larger than the focal length.)"	[]	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	\Delta q \approx \frac{l}{F} \left( \frac{q}{f} \right)^2
+673	"A retro-reflector is an optical device which reflects light back directly whence it came. The most familiar retro-reflector is the reflecting corner cube, but recently the 3M Company invented ""Scotchlite"" spheres.  (a) Calculate the index of refraction $n$ and any other relevant parameters which enable a sphere to retro-reflect light.   (b) Sketch how you think Scotchlite works, and discuss qualitatively the factors which might determine the reflective efficiency of Scotchlite."	[]	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	n = 2; \eta = 0.75
+674	 An opaque sheet has a hole in it of 0.5 mm radius. If plane waves of light ($\lambda = 5000 \overset{\circ}{A}$) fall on the sheet, find the maximum distance from this sheet at which a screen must be placed so that the light will be focused to a bright spot. What is the intensity of this spot relative to the intensity with the opaque sheet removed? Indicate how you arrived at each answer.	[]	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	r = 500; I' = I_1 / 4
+675	As shown in Fig. 1.29, the image which would be cast by the converging lens alone has a distance of 0.5 cm between top and bottom. Calculate the position and size of the final image. Draw a ray diagram showing image formation for a point on the image not on the axis of the lenses. Using at least 2 rays. (The rays need not be the same for both lenses.) Explain how you arrive at the ray diagram.	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	10 \, \text{cm}; 1 \, \text{cm}
+676	Find and describe a combination of two converging lenses which produces an inverted, virtual image at the position of the object and of the same size. By a sketch of image formation make it clear that your scheme will work.	[]	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	9f_1 = f_2
+677	" Figure 2.63 shows a phased array of radar antenna elements spaced at 1/4 wavelength. The transmitting phase is shifted by steps of $\pi / 6$ from element to element, i.e., element ""0"" has 0 phase, element 1 has $\pi/6$ phase shift, element 2 has $2\pi/6$, element 3 has $3\pi/6$, etc.  (a) At what angle $\theta$ is the zero order constructive interference transmission lobe?   (b) Are there any secondary lobes?"	[]	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	\theta = \arcsin(-1/3); \text{No, there are no secondary lobes.}
+678	(a) Show that for Fraunhofer diffraction by a slit the direction of the first minimum on either side of the central maximum is given by $\theta = \lambda/w$, where $w$ is the width of the slit and $w \gg \lambda$.  (b) How wide must a rectangular aperture in front of a telescope be in order to resolve parallel lines one kilometer apart on the surface of the moon? Assume the light has $\lambda = 500 \times 10^{-9} \ \text{m}$ and the distance of the moon is 400,000 kilometers.	[]	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	\theta = \frac{\lambda}{w}; w = 0.2 \, \text{m}
+679	(a) Three identical positive lenses, of focal length $f$, are aligned and separated by a distance $f$ from each other, as shown in Fig. 1.49. An object is located $f/2$ in front of the leftmost lens. Find the position and the magnification power of the resultant image by using tracing method.  (b) Looking through a small hole is a well-known method to improve sight. If your eyes are near-sighted and can focus an object 20 cm away without using any glasses, estimate the required diameter of the hole through which you would have good sight for objects far away.	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	\text{Position of image} = \frac{f}{2}, \, \text{Magnification} = -1; d < 0.12 \, \text{mm}
+680	 A laser beam ($\lambda = 6.3 \times 10^{-5} \, \text{cm}$) is directed at grazing incidence onto a steel machinist's ruler (which is calibrated in $1/16$ inch). The light reflects from the surface of the ruler and is projected onto a vertical wall 10 meters away (Fig. 2.61).  (a) Derive the condition on $\theta'$ for interference maxima on the wall. Assume for simplicity that the laser beam is initially almost parallel to the ruler surface.  (b) What is the vertical separation on the wall of the zeroth and first order spots of the pattern?	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	\cos \theta' = 1 - \frac{m\lambda}{d}; x = 0.28 \, \text{m}
+681	A plane monochromatic wave (wavelength $\lambda$) is incident on a set of 5 slits spaced at a distance $d$ (Fig. 2.55). You may assume that the width of the individual slits is much less than $d$. For the resulting interference pattern, which is focused on a screen, compute either analytically or approximately the following. (Hint: The use of phasor diagrams may be helpful.)  - (a) Angular width of central image (angle between principal maximum and first minimum.)  - (b) Intensity of subsidiary maximum relative to principal maximum intensity.  - ( c ) Angular position of first subsidiary maximum.	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Lh48eLly5cnJyez2WxKDSnGEH8KiCDI6OgoOFhjsFMSjUYbswSz2+12ux1BkDmMBITQk/7+/q6uLp/PNzAw0N7ertPpQqFQMBgk561cLjcrK4vBYCiVyoSEBI1Gk52dXVRUlJ2dzWAwOBwOm82m0+mkiEQLH8ng4ODFixdxHJfJZJs2bZr6ICsrK1Uq1ejoqNlsHh4enlABo0FRVCwWi0SikpKS9evX/+AHP7DZbN3d3UNDQ4cOHWpubu7u7m5qatq7d69SqczPz4eJamZmZmFhIbkqp5jnxJ8ChsNhvV4PeRdzPZYJYLPZfD4fSp6AEYSsmToLgBciEok4HA6LxXL+/Pmenp5AINDV1aXX64eHh6FSIfgfQNQUCkVmZmZ2dnZOTk5qamppaSkoINgxo8UO/jH5Zcdx/NKlS319fSiKrly5Mi8vb+qDl0qlGzZs6Onpsdvtp06dWrp06dQ9XQwGQyAQJCQkZGRkEASxdevW3t7e3t7erq6uxsbGxsbGkydP1tbWMhgMtVq9YMGChQsXFhYWLly4kJwbTn2cFDcT8aeAyGU7oM/ni8F4wHA4DCqj1+ttNlt0zPYMqbbVajUYDOFw2GQyNTY2ejwek8lUX18/OjoaCARgPQsheCqVKi8vj81m5+fnFxYWqtXqwsLC1NRUCDlmsVjktHq812KK4Dje2trq9Xp5PN7mzZuvadrLZrNXrFjx/vvvezyeM2fOBAKB6/b1s9nsgoKCgoKCjRs3BoPBoaGhxsbGI0eOWK3Wrq6us2fPHj58mE6nJyYmlpWVlZaWwgVRKpVisZiKN5xXxJ8Ckt2XYVE218MZSyQSgSjF0dHR559/XiqVOhwOKIyh1Wqvu08IGWUSDoeHhob8fv/Q0FBtba3T6TQajXq9PhwO2+12r9cLCXkQhKVWq0UiUXp6emFhYX5+fnp6ekpKCsTicTgccufXrXfjGR0dPXDgAIIgWVlZpaWl17TSpNFoCxcu1Gg0Fy9ebGpqam9vX7x48Q2Oh06n8/n8nJwcjUZz//33h8Ph7u5us9nc29t7/Pjxurq6r7/++osvvmAwGDk5OSqVasmSJTU1NXl5eZCLEsutvimmhfhTQAjUIJdycz2csTCZTIlEQqPRgsHgV199Bc8PrILD4fA1PU4EQTgcDpvNBnax8+fPw9r23LlzgUAAx3EIMATl4nK56enpMplMKpUWFRVlZmZyudyKigqVSkWn02GKR6PRplHsJqSjo2NgYABF0dLS0szMzGv9ekZGRmlpaUtLy+jo6OnTp29cAcfAZDKLioqKi4tXrVq1devWgYGB+vr68+fPm83mrq6uS5cunThxgs1mKxSKVatWVVVVicXiBQsWJCYmTsWdTRGPxJyCxDtisfhnP/uZXC6vq6sjC96hKJqYmPjUU09NGBkPLaUhIWxwcDAUCmm12t7e3u7ublIBvV5vMBgk57wQZF9cXCyVSisqKgoKCgQCQUZGhkwm4/F40JgJZG5CZ8UMQRDE6dOnPR4Pm82uqam5Ds8PnU5ftmzZZ5995vf7z5w54/f7Z8h9RKPRBAJBYWFhYWHhE0884fV69Xq9xWKpr69vampqaGjYvXv3zp07YW6YlZVVWVm5fPnywsJCPp8fm6V5Ka4P6oecZmg0WnV1dUlJicViuXjxIqyIuVwuJPnDFAyqqA4NDZlMpkAg0NHR0dTUZLfbOzo6XC4XeGYh2wyiNzQajVqtTk9PX7JkCSiCUCjMy8uTyWSQWQEVWOfcNeTxeE6dOhUIBKRS6fLly69vJzU1NWw22+v19vT0GI1GjUYzvYMcD4qiAoGgpKQEQZBly5YFAgGbzXb+/PnTp09fvHjRaDTW1tYeOHBAIBAoFIrVq1cXFBQUFRUlJyenp6fHoB2G4pqgFHBG4PF4mZmZGRkZIHler9dgMNTW1o6MjHR3d/f09DgcjqGhIavVCh3WoXMuaJlYLM7JyWGz2RUVFSUlJSwWS6PRKBQKFosFlilk3DI2RmxVBoOhr68PQZCioqL09PTr24lSqSwvLz906FBXV1dLS8ssKGA0EAIJPuV7773XarUODQ21t7drtdqLFy+ePHly586dkUhELBYnJSWVl5fX1NRUVlYmJiZyuVwul0t5UeIOSgFngx07drz22msWiwWMmDQaDdyvKpUqKSmJx+OlpKRkZWXl5eXl5eVJJBJwy4IgIjNptptGCIJobm7u6emh0Whr1qy57sbwCQkJCxcuPHToUCAQqK+vv+222+YqjpJGoymVSqVSWVZWBu2unE7n6dOnW1tbOzs7W1tbd+/evWvXLsgILCsrW7duXXV1tVKpTE9Pj9mCoBRjoBRwNnC5XC6Xi8ViZWdn5+fnL126FGKMQQEh8o6MNI4LvRtPMBisq6vz+/1qtXrVqlVMJvP6ToTFYi1evFgkErlcrvb29lioKQvudSaTyePxtmzZcu+993q9Xp1O19raOjw8fPjw4YsXLx47duzw4cNqtVqpVFZUVJSXl1dVValUKolEMp+7xMQ+camAkBU316O4CuFwGMdxmMT98Ic/XLVqFYvFAhctWTQhTsVuQgKBQFNTE4IgSqVSrVZf935oNFpqaqpEInG5XH19fYFAIAb9sHw+v6SkpLi4GMOwp556qqur6+DBg52dnf39/V6vd9euXTt37uRwOMnJyStWrCgtLS0uLk5OTk5JSYn9+3a+EX8KOD7tLNbw+XyfffbZd999h2GYSCRKSUkZHBxMS0t78MEHZTIZEjNmu+nF4XBAz18oZXoju8rNzS0qKurv7zeZTF1dXTe4t5kDRVHIRYGK1jiOW61Wl8vV2Nio1+tra2s7Ozvfe+89HMdhsp+XlwcFbyoqKqRSKcQnzfVJzHdiWkomBMdxm80Ws1V3MAzbu3fvz372MwiFgVaZwWCQTqfb7faXX355ztd0M8Tp06dNJhODwYC6LDeyq4SEhAULFhw8eDAYDJ4/f/663cqzDGk31Gg0GIY988wzLS0tHR0d/f39Z86cCYVCBw8eNJlMO3fuzMnJWbJkSVlZWU5OTkZGRmpq6k35UowL4k8BSWJzQeF0Ovfu3QtJIAkJCUwmE0oP4Dh+4sSJYDB4UyogjuNdXV3BYJDP52/cuPHGn+e1a9e+9dZbXq+3t7cXw7DY/K2vBMwNRSLRsmXLbrnlFhzHR0ZGIpFIS0vL7t2729vb+/v733vvPYIgIGMnJSUlNzf3tttuy8vL43K5HA4nvs43roljBYRM+LkexVgikQikanC53Ndee23lypVHjhz58Y9/7PP5bqYS+WOw2+2nT58Oh8MKhSItLe3Gd6hUKrlcrsvl0mq1brc7us963AFzQwRBkpKSVqxY4ff7jUbjhQsXGhsb29ra9Hr9hQsXcBx/9913s7OzMzIywIuSn58vFovHdxykmF7iTwExDBsaGkIQxOVyud3uGGwXByiVynXr1qWmpjocDpVKBYFyNyujo6PQDrGwsHBaOkKkpKQsWrRo//79vb29AwMDca2AJCiK8ng8LpcrlUpLSkoeeOABl8ul1+svXrw4MjJit9s//PDDlpaWzz//XCaT5ebmSqXS3NzcZcuWlZSUyOVyLpdLqeG0E38KGIlEjEbjXI/i6qSkpMAUFQIp5no4M0tHR0dHRweCIMuWLZuWZT6LxcrJyUEQxGg09vb2QsLGTQaTyZTL5QqFYtGiRZFIBEXR7du3NzQ0gFtZr9efP39+//79b7/9dkpKSn5+/rJly8rKyrKzsxUKRXRhC4obIf4UEEXRGAyPGM/NveyNhiCIwcFBr9dLo9HS0tKmxYbF4XCWLFny7rvv+ny+7u7uSCQS4wEANwKNRoN3ZHFxcVFR0f333280GkdGRqBSQ1NTk9FoHBgY+Prrr8VicVZWVnFx8dKlS3NycnJzc6ECOWU3vG7i765isVipqalIVAeimALKjiIIAvWpov8kl8tvyjvV6/XW1tYSBAGe0GnZJ4qiMpmMw+F4vd5Lly6FQqGbWAGjgZWyRqPRaDTV1dXbtm1zOBz9/f0Gg+HQoUPDw8ODg4OfffbZrl27mExmenp6enr68uXLKyoqsrKyhEIhVfv6Wom/uyocDhsMBgRBFApFbPaKU6lUUHoEHlqFQqFUKru7u1EUjc1OSTdIKBQCy2xiYmJycvJ07RZakdhsNq1WO09m02Og0WjQFwWu6n333RcIBPR6fVtb2+nTp48dO6bT6Xp6eg4cOCCTydLT08G8uHLlyvLycrFYTOWiTIX4U0AodA7/iMEplc/nczqdOI6np6fD0kYoFCqVShRFR0dH53p0M4JWq9VqtQiCqNVquVw+XbuFGWV3d3dfX5/FYokL08eMgqIoh8PJz8/Pz8/ftGmTzWbT6XTNzc2Qjm2320+cOHH48OF33303PT29urq6rKwMatgkJiZed5r2TU/8KSCKojEYBEPCZrO5XC6KogqFAlbBQ0NDPT09BEGIxeKb0pcHuWt0Oj07O3sanbZyuRyyQSAqEBwjFMjlMPukpKSkpKRly5ZBeXCbzXbixIkzZ86cO3dOr9d3d3e/9957kKGYnZ29aNGiysrKtLS0pKQkaFQ/1ycRK8SfAsY4bDYbCpSSW/h8Pp/PRxAEakfP3dBmBBzHzWYzhmEsFis3N3ca90yj0WAeHYlEOjs7N2zYMI07v5lgsVhqtVqtVufn5z/88MNOp7Ovr+/SpUtnzpyBOrvNzc379u3jcrkSiWT58uULFy4sKSlJTk5OS0uDt/Vcn8FccjMrIPRRAvWZQ5xOJ3R2HxgYuPnsWT6f79ixY4FAQCAQXHdNwAlBURQq6AQCgXPnzt3c7uBpgbQbJiUl3XLLLY8++qjD4ejq6oIeyg0NDTabbdeuXR999JFcLk9MTCwqKlq0aBG0lFIqlUwmcx5e4Zv2hP1+/3/+5392dXVt3759/fr1s/bTkr0xyeRlqVQKYds+n292xjCbOJ1OSAFkMBjT6AYBNBoNk8n0+/12u93v98ey9SMG4XA4MDdcunRpIBCwWCwdHR2nTp06d+5cZ2dnW1tbc3Pz559/zmKxUlJSampqFixYkJOTk5eXl5ycPF3xhl6vN8a9f3GpgFO5plar9bvvvjt37pxWqy0tLZ32h/NKQMNvHMd7e3sjkQiCIFwud87nodMFtDTx+/0ul6utrc3v97e1tbW2tiIIEolEzp07l5CQQBaOR1FUKBROsvCHTmxMJhMqicFGcHBB45RAIAAbOzo6WlpaKisrYzD+KfYhmylnZ2ffeuutFotFq9V2dnZCFe7u7u7+/v6uri4EQXg8Xm5ubl5eXmpqalVVVVFRkUql4vF4133ZwSs4rWczzcSfAmIYNpWcELVafe+992q12u7u7vr6+u9973uzMDYEQXg8HsRkxfgPP3X8fr/b7TYYDODSaWlpgdx+n89HEARBEDC39Xg8zz//PFnHH0EQNpudnZ09udFdKBTm5uYODw8PDQ1BtUSosdzb22uz2ZxOJyRZDw0NvfrqqyUlJTk5OQKBALmcUEEm28jlch6Ph6Iol8uFD8CQqGjhMUAPVbVavWTJkkgkEgqFnE7nkSNHTp482d7ebrPZent7m5ubwdnC4/FKS0sXL15cXFycl5eXlpZ2rfGG0No7lutgxp8CEgQxlSQzFov15JNPtre3f/jhhwcPHrzrrrtmp6kNVBKe8C4BU8ssjOFaASGDyR0UH4MoPJfLpdPpBgcHTSbT4OCg1Wr1+/3I5fqGUN4OWkEhCAJ2hkgkAooDe2tubqbT6eRnxhCJRAiC+Prrr6E+NkyZJ3xaIpHIl19++eWXX5IXlslkKhQK0rghl8v5fD7kC0GUKJyIRCIhY5I0Gg18ProWN4fD0Wg08N0xR4cpqkwm43K5sD26Sxz5SehnQA4sXhwLZI+thISE7du3b9u2zWKx2O32gYGBCxcunDhxorW11e12Hzt27NChQzQaTaPRZGVlFRYWVlZWLlmyRCQSCQQCsv/qlQAvWSw7AONPAaG4/FQ+CR0n3n//faPRGIlE5rytl81miylPiM/nczgcbrfbYrEMnq8ESAAAIABJREFUDg62tbWdPXvWbrdbLBa/3w/rUFif4jhOo9FkMllSUpJcLpdIJElJSZmZmQKBYMeOHbAKXrZs2Z133pmenp6amophmE6nGx0dTU1NlUqlXV1d422gGIZBF1Cn05mQkMDj8YaHh71eL1gVgWAw2NnZCdNAHo+Xlpbm9XrZbLZQKLTZbHa73ePxEATB5XJHR0edTieoEvm8EQQR/XxOeAPAMvxKjyiKokqlkgymS0xMTElJGf9hjUYDtW+5XK5arSY/kJCQwGAwHA4H5IZnZmZKJJIp/jqzDIPBgPCa4uLi9evX//CHPzQajX19fSdOnDh//nxHRwcspw4dOsRisZKSkpKTkzds2JCfn6/RaJKTk690XtFrgtgk/hQQmfJrFsMwi8WCIIhWq21vb6+srJzhcf0/4DnEMGzMdIbP58/my5D0yQSDwXA4jGGYz+czGAw9PT3QAq2zs9Nms42OjtpsNofDgWEYFLaDIv4ikWjhwoUQ4JKcnAyVn0UikVwuFwgEEPfn8XgOHz7c2trK4/EeeeSRhx9+GH4aFEWrq6vJ06+pqUH+fuYFjN8SDAah0DRsHx0dffnllz/66CMEQVauXPmrX/0qHA7DtAUUEILMeTwem80mvxiNz+fr7OwMh8PkUQiCMBqNkMQyHrfbHYlEbDYbTEgxDBsYGCD/2tnZOebz0NSU/C+LxRKLxeSxoEAkKCCbzc7MzJwwXhI6CzocDqVSCTItEomys7NDoRApvtH3vEAgSE5OJi81giCkiJNNomk0Go7jMD8l9zAVgwBZ3FAsFhcWFt5+++0mkwlCapqbm48ePWqxWPr6+rRabV1dHbyWUlNTS0pKVq1aBZ1OIcIGxmO323Ecj2VDRFwq4BQxGo3fffcdgiBarfb1119//fXXZ6GUls/nc7lc8PSGQqHoP+Xm5s70KhjHcZPJBGPo7e01m80QTNfW1mY2m8PhMIwKwzAQaA6Ho1AohEIh9AUXi8XJycmlpaWZmZksFgu6/CAIQqfTYeTjbTrgrIBQmBt/23M4nMTERPIQarV68+bNX3zxhc/nk8lk+fn5oAgQKDP+6+OHB6t75O91FjoyT9hxNBAIEATh8Xjg5WG323U63RiTbvRRLBZLf38/aA2CIF6v1+12g/mf1HeJRGK1WsE5hiCI0+mMzg6CiSqDwQgGg2A1g+0sFutK2sFisaIzZBgMRmZmZvS9TafTuVyu1+uFNT5cNC6Xm5KSAr9j9BJeIBCMabwDFgYcx0E9pVJpTU1NVVUVQRBDQ0MNDQ3nzp1rbW1tbW21WCydnZ2dnZ1HjhzZsWOHSqVKS0tbsmRJWlpaQUGBWCzu7++P8QK3N7MC7tq168KFC2Cj+fbbb+vr6zdt2jTTB3W73SMjIwRBgP83HA6PjIxAPOB03QfkjCYYDELz9aampkuXLoXDYYfDcf78eVBAs9ns9/tpNBocl8ViMZlMsVicnZ2dnp6elpaWmZmpVCoVCgWdTlcqldGOhSvN18aPRKfTIQgiFotnooQfiqLkxDl6qhX9gfFCNmbYENgx+dyT3AjFDcHMAruqrq4ev88rfR185WD3JD/m9/utVisoHUEQYHkgv+jz+bhcrtPpHBgYwDDMarVarVZIgGlra4s2oaIo6vf7+/r6vF4vOeEFYwVkyiOX+3ONuUog93Q6HSx3Y4YtEAiEQuEYBZTL5WSfL+Ty/DE/P5/BYPT19fn9/qysrMHBQWgFgSAIhmEQ9wpNo2BNLRKJ9Hp9jLsEb1oFdLvdZ86cwXH8nnvuEYvFf/nLX15//fWFCxfOWljMwMDAG2+8wePxzGZzf3//jewqHA6bzWaXy4Xj+PDwsF6vh2VaR0fH2bNnvV6v3++HRwUsd0KhUK1WZ2VlSSSS1NRUmJ1pNJqioqLMzEwowg5GfXgerrtL58jICBRGTUlJSUlJuZFzvBIymUwmk3k8Hp1OF70qjE3gqpITVeTyHDApKQm5wnUmCAJWrGAjJggiEomwWCyCIMZ4kCDAAJouwE7C4XBnZye4p+C7/f39pCoBGIb19/ePjo6S7zCCIIaHh+FwsNFmswkEgmAwSNpSL1y4ML4VD0wJI5EITA8n6dUTiUSirQexTPwpIIZh5BvvSuA4vm/fvvr6erFYvHXrVgzDPvzwwxMnTvzbv/3bL3/5y6ysrFkY5/Dw8Msvvxy9ZfLqWOR6zePxeDyeSCSi1Wp7e3u1Wq3dbm9vbx8dHY1EIkNDQ6FQCMdxMP2A61kmk2k0GrlcnpubKxaLc3Jy0tLSmEymRCKBGiHkUaa3JXFvby88SGTU97STk5OTk5PT399PPpw3GeRLiDTYcTgcOFM2mz1m7kma+cjt0V2WJpyown0FRl74E4Zhw8PDoF+w0eFw8Pl8v98PixUcxwcHB2GpDjdbKBTSarU+n89sNsOtOMbCc1VidiEcfwoYiUTIQNkr4fV69+/f73Q6161bV1NTE4lEbr311q+//nrv3r1qtfrVV1+dueGx2eyMjIxz586NuUUEAkF5efkYOyBBECaTyWw2j46OgnUZuu62traCrQoitgiCAGNKenp6fn6+TCZLTEzMyspSKpW5ubmZmZkikYgURFj20mi08U/LtAMLHDqdnpSUNEMuPxaLBaEqwWDQ7XbHrC81ZoHIPuTvX35kmYkJzR3gQ/N4PF6vNxQKmc1mt9udlZWl0+kwDJNIJG63+5puKiaTqdFopvGkppH4U0BYwU3+GS6X+8gjj6Slpd1+++1Qre+VV14hCOLYsWMzHY8iEolefPHFtWvXwhLG4/FYrdZz585VVVUtWbLE4XCMjIxotdrDhw97PJ5wONzT0wMrXLAe0ul0iNISCoUJCQlQbqC4uFipVLJYrKKiIrlcLpVKxxh0pndmN3VA5cHoM3NHgYmM0+kcHh6eljZMFAAsvSORSDgc9vl8drs9GAzqdDqr1drT0zM4OAhboAkyeHWnuGc6nS6RSKqqqgYGBi5dukSj0WK200v8KSCGYaTh40owGIwNGzasXLmSzWbDbCg3N/edd97p7u6e0Ic4OWBtAYMXuPkVCgW8VyORiNVqDYVC5AzI4/H4/f6MjAwOh1NSUgIevcHBwXfeeefnP/95W1sbGJLJfEkcxxkMRlZWVlZWlkAgKCgogAJwEDkB0WpkyjoZgBoj60HokBm9gpt2ouONY+Ss4xd4kXg8HpvNBhFRXV1dOp1Op9O53W6r1YpcXvZC+FT0BZfL5TQaDXKNdTqdzWa70lHEYvGaNWseffTRysrKF198ERrIxCzxp4BXDUMHSCcgCfg9r+OIhw4deuGFF0ZGRsgBkAoIzrvoBW8gEAiFQkKhUCgU/upXv7rvvvsQBNFqte+88w4ZA6FWq/Py8vh8flFRUUVFRUJCQl5enlAohC5i0Wc3009+MBjEMOy6G9RC9Z0ZXeOw2ey0tDQGgxGJRHp7eyG0kGI8IFhkfCLY/vr7+/V6vcFggFxSg8EAQZQQTelwOCAbB15gkJENZW7hxsvIyKioqIAJvlgsttvtFy9eBNEcPwA6nS4Wi1euXPn4448vXrwYJn1FRUUxnsodlwo4yx0yZTJZQUGBwWBobGwMBoPQrYZciZMFS0iLm81m83q9QqGQTIQoLi5+5JFHPv30U7PZzOPxXn/99XXr1oHZDmQ6Orp1dmY6wWCwsbHxq6++GhkZKS8v37hxY0ZGxjXZ8iDgHHKeZq5qCxTERVEUXjYzdJR4BCpHmEymQCAA8QYej2dkZESv1wcCga6uLo/HY7fbQ6EQGd0NFcaYTKZKpUpMTCwrK0tLSxOLxRqNJiEhISkpCRockonVYJOBNdC+ffv2798P/pAxXmD4jTZs2PDwww8vXboU1i7wJ5g5zvKVuSbiTwEheA1BkEmc8ZMAMcPd3d0pKSkKhQKi5CY3LFZWVv71r39ta2u76667RkZGtmzZ8vLLL4/5SrR4DQwMnDp1isFgyGQyaCGEIMjmzZsNBsO+ffvYbPaCBQvAoj9Xy7pIJPLBBx/89re/1ev1CIJ88MEHmzZt+vOf/zzFdENyJ0ajEZyMM3qXazQaFosVDAaHh4dn7igxCHjDYE0KQaCQ0HLy5El4y3Z2dg4MDEDlK7fbDTZu8IPBjQ3es8TERJlMBmaW3NxcgUAAqX4QDM9kMsd7QjAMc7lcly5dOnbs2NmzZ6EWxvgnjk6nS6XSW2+99b777rvllluEQuGYtzi8vZAYtmDEnwKSdHV17dq1C/olRaf+IBP5tsh/uFyu3//+90eOHIHlFdREA7+qXC5nMBgKhYLP54+JIOHz+YFAABIG3G43j8cj35Pjj/vZZ5+99NJLY4yVNBoNolWDwWBbW1t+fv5MXZcp0Nzc/Otf/9pgMCiVyqKiosbGxoMHD+7Zs+eHP/zhdWgZl8udxvYg44HY8kgkctUoqHgnEAg4nU673U6+Sjs7O0dGRrq6unp6esAOEwqFyFlYOBwG25xQKExMTORwOEqlEvpV5efnZ2dnJycns9lssIYzmUwwK0cfccysH8dxl8vV09Nz/vz5zz//vLm52efzhUIh+DoZhwhf5HK5S5cufeGFF8CSM8kCAsMwSO6OQeJSAeFn6Orq+v73vw8ZPFNXQJi5gDxZLJaGhgYIFxAIBKCA0FqhqqpqxYoVpaWl5H4sFgu8kLu7u81m8xgFJAkEAkeOHIEcABqNxmAwyBQOGo0mFApTUlJmISp7ZGTEZDIVFhZOeF9+++23ZrNZJBK98sor69ev/4//+I8PPvjg0KFDjz/++JXOazxkYlkwGJydJlAxnl1wVSKRCIZhEGgCb9NAIADryoGBgeHhYYPBAB5YiEexWCwejwfeSTQaDVoD83i87OzstLS0lJSUpKQkHo+Xnp4ukUikUinkOMLsbypZ2ACO41AAra2t7dChQ01NTZBDieM4zBOzs7OlUqler29paYGoLJlMtmLFii1bttTU1EzFO4/jeMxaMOJPAcn6gHADhS5D/rQMBoPP5weDQfBqXXWHsJ9AIED6OlAU/fzzz+++++4dO3ZwuVzY2N3dDasMyEW70t5cLpfJZIIUqHvuuaewsPDixYu1tbWBQCAjI+O//uu/cnJyZnoCiOP4m2+++be//e3nP//5HXfcMX6NDwZKhUJx++23K5XKzZs3f/7552az2eFwTF0Bh4aGoL4ArLmm9xRuDsB7AzlwXq+3paVlaGhodHT0zJkz/f39sKqFlQEY6XAcFwqFPB4PVqn5+flKpRKa0LPZ7PLy8qKiIljkgtcCJnRkNvG1rjTBVXLhwoWDBw/W1dVBRnkkElGr1cuWLUtKSlq7dq1IJKqrq/vf//1fk8mE47hKpVq/fv3jjz++cOFCgUAADrSpHBecZjFI/CkglO5AECQlJeWxxx6Dbi9QJQk+AG9Ct9sNmRVjvh4KhT744IOmpibkcrYjg8GAUndMJhPWDlCZAxJmyYN2d3eDz3dgYACWsVdaMILsSiSSV155RaPRnD59urm5ub+/XyAQFBUVdXZ2ikQiaPo+Q9BotI0bN+7bt+/f//3fU1NTKyoqov9K1ozxeDyfffYZm80+depUIBAYHR11uVzXNDBYi6Wmps5omo1SqZz6kzabQLoFvEGtVitMip1OZ0tLS1dXVyAQANUDBfT5fFarFcQLJnRQuzAlJSUtLU2j0YjFYjqdnpqaKhaLQQHBJ0veZhPmhCDXWJEQwzAowAMzviNHjnR0dPj9fiaTKRAIqqqqVq9evXbt2sLCQp/P9/HHH7/66qvd3d0EQSQnJ69YseKRRx6pqam51tzE6OVzrBF/Cshms+EpXbhw4b/+679CKR5yrodeBrYQf18hDn4GgUDwzjvvRCKRnJwclUqVmZmp0WiUSiWXyyU7JEAcH2k0cbvdNpsN7jyws0zFXgaf8Xg8sEjEcXz37t2vv/76/fff//vf/56cXc4EFRUVzzzzzE9/+tNdu3YtWLAgeo6G4zgswcxm87/+678iCAIxsdd6CHIuHAgEZnR9mp6ezmAwCIKw2+1Op3MOY2s9Hs/Q0BC8gL1er8Vigfjhzs7OlpYWuIaQQ0ZWKEBRVCaTJSQkZGZmLlq0KC8vLz09XSQSFRcXg5GOcRm4WyA8ZSbyeUKhUH9//7lz544cOVJfXz80NOT3+yORiFQqLSwsXL169e23315QUAC1Fw8ePPjHP/7xwoULfr9fJpOtX7/+Rz/6UXFxMVlKdopAtABUC5+uE5le4k8B4YdE/r4aMzlZI5cDk7w5t2/fvnz5cnCTjfk5o1cT0SFyEonk6aefPnv2rNPp3LRpU1VV1dQHrFKppFKpw+GAOjF2ux0CiWdUAZlM5p133rl37969e/euXbt248aN5AWh0+lw3UDKURQdGBiIrks6RaxWK9gNgsHgjL7hyZHDvH6GFBDmKXAuOI5DBygMwxwOR0NDA4T1Op1OsNMhCAJZtGABgJkaFAdUKBQSiSQnJ0cul0NVaqVSKRKJlEol5PlMWFRmhi4gvO1sNtuZM2dqa2vPnz+v1WqDwSCPx8vIyFi4cGFNTU1BQUF6enpGRkYkEnE4HN99992bb7559uxZv98vFovvuuuuRx99dMmSJRDwdK3jHBgYiEQiNBptkgjquSX+FJCsIHDdQG/va73zqquroRYxJOFe6YukdYYkOTk5JSVFp9OxWKzi4mIulwsWtJmeyyiVygceeOAnP/nJH//4x/LycrVaTf4JKvc++OCDzz//PJ1O/8Mf/vCb3/wGnIZT3z8UGUQQRK1Wz04rvulq5whVr+FGMhqNZOVEk8mk1WohCaytrc1ms8Enw+EwzHYhGl8kEqlUqtzcXC6Xm56eXlJSwuPxIKoOIuERBAH3K5R4Id+yM5Q6PSHBYNBsNjc2NtbW1h4+fBhsfAwGIzs7u7q6euPGjUuWLBGLxRwOB+bXJpNp3759H374YUdHh9PplMvl69ate/LJJ2tqaqLj+64VuDegVdP0nuB0EX8KOGtEIpH29naCIMAjTEYSTP4QisXi6DrpyOU8OdhDamqqRCIxGAx9fX2FhYUzOn4URdevX79gwYJTp04dPHjw4YcfJv9UVFTEZrNra2sfeughlUrV29uLomh2dna0Sk6dySMhpgW4nhMWv5sEMpgOQRAwdOr1+r6+Pqj5DhuHhoYgqycUCnk8nug1KSwyMjMzocuaSCTKyMiQy+VisVilUkE5xYSEhCtVGJtNvQNgAT4yMlJfX//ll192d3dDfwKo3b98+fJ169YtXLgwIyODtIqQ2rd79+6GhoZAICCRSLZu3frAAw8sW7Ysug7r9QGuFfDb3PD5zQhxqYAzun4k0el0Tz/9dCAQ2LlzZ3FxMZvNLioqslqtBQUFk3xr/BzQ5XJBTjGCIAsWLHj66aeHh4eh+vxMk5SU9Pjjj//oRz/atWvXxo0byaTAxYsX5+bmXrx48Z/+6Z+EQuHBgwfZbPaaNWuu70Wt0+lmtN4Eh8MpLCysq6uzWCwWi2V8FQaI54BQTbPZbDabIexJr9ebzeauri7o6unz+QKBAFlxBxysKIqCokml0oSEhNTU1Ly8vIyMDIlEAmtYLpcL7jL6ZWIwxBfq8bW2th47duzAgQNg42Oz2SUlJUVFRWvXrq2pqVEoFGA0J7/ldDqPHz/+7rvv1tXVeb1epVJ5zz33PPbYY+Xl5Xw+n06n3/g5QncwGo1242I6Q8SfAkLHmRnaOUQnwFEGBgZ6enr4fD4Ec0Ki8RjXynjAfjRmqkLeSTwe74UXXiAIYnbaNtFotLVr15aUlJw6dWrHjh1lZWVVVVVSqVQulz/77LO/+tWv6uvrMQxLSEi4++67b7vttuubtoATc3pHDqtUKLns9XrLyspOnDhht9vPnz8vkUj6+/tHRkagH5PD4YB4unA4DJWxoSQ9uGhxHOdwOODr53K5UCIbEnLS09NXrVrFYDDEYrFQKAQFBNcEjGGGPBLTBWnja2hoqKurO3XqlE6n8/v9fD6/tLR0xYoVS5cuLSsrk0qlMOOLrhg4PDx84sSJTz/9FK6qRCJZt27ds88+W1NTw+fzp/FkDQZDOByOzRaJQPwpIIZhV2pzc+P09PQcOHDA6/WWlpZ+8sknDoejoqIiOnzvqlnJpM2IhMViRbtiURRtaWmRSCQZGRmzkDKpUChSU1MbGhp++ctf8vn8X//610888QSTydy+ffvixYtPnTpls9mWLVtWXFx83ZaarKysabnFCYKwWCwgYcPDw263+9KlS1qtdnBw0Gg0gnfiH//xH7lcLoQWIwgCJUyQy3UBOBwOtPcmK2PT6fSKioqKigqo28jlciFXDEEQFEWjozpicGZ3JaDjVXNz86FDh+rq6oaGhiKRiEQiKSsrW7Fixa233pqXl8fhcCZ8y7rd7m+//fadd945d+5cMBhUKpUPPvjgtm3bKisrb8TedyWuOmOYc+JPAVEUBWPz9OLz+Xbs2LFjx46Ojo5wOCyTyUZGRhgMRnV1tUQiIR8M6Pg1yX6gYzc4B+G3h7w98gPt7e2PPPJIeXn5W2+9NQvm4ba2tp6eHpgvBAKBb7/9dtu2bWC9ysvLy8vLQ6734SelZOo6Dm5WiKGDhsJOp9NsNmu12ra2Nrfb3dPTMzw8bLVaoQbneKsfJGlBQzuxWLxgwQJ4IdFoNOjOo1Ao4N8pKSkQF0Wj0ch6sUAciR0JjuNQovns2bMHDhxobm7W6XQ0Go3NZi9dunTNmjVLly6Fpp0TVtmAWKKTJ0/u2bPnm2++8fl8crn80Ucf3bp1a3V19cwZ6Xw+X4xf5/hTwPGGtmnh4MGDr7zySjAYrK6ulsvlWq0WEiTWrVsX/bFQKDQ4OJienn6l/XC5XLLbDkwxottsIwjidruNRiO4R2ZaAUOh0IkTJ9ra2sgt05i+xmazx9QfmxCo6QL1S0DdoJVwT08P+GFBDWHiDElXCoUienYGc0MoQlNZWbl48eK8vLyioqLExEQofwsfg6onY8QOiZ8W5ldidHR0eHi4sbHxu+++O3v2LLRJkMlk1dXVW7Zsqa6uzsjIgPiEK+3B7/efOHHizTffrK+vd7lcSqXye9/73mOPPbZgwQKI74txkZpR4k8BQ6HQhOXJbgS3271z506bzfYv//Ivzz33nFgsfvvtt3/6059WVVXBLAlBEBzHIbNncnckTE8gb3zCVyts93q9Ho/n+uoVTh0Wi1VSUiIUCsnWYiBG01LMiizt5XK5IO0BtCwcDptMpmAwODg4qNVqL1261Nvb6/f7zWaz3W6HDgcwL2Oz2RBMl5GRodFo0tLS+Hx+YWEhGasE2O32xx57bGRkRCqV/uIXv9iwYcO0ZEfEMuFw2O129/b2Hj58+OTJk729vT09PVAV6c4771y+fHlxcXFeXh60aSfPeoyQ4Thut9vr6+s/+eST48ePW61WmUz20EMPbd++nczruGmu2HUTfwqIXO5ZNY2YzeYzZ84kJiY+8MADSqUyEAg0NDQEg8Hly5eTUXtgSofl5FT2CZFW47enpaWJRCKr1drd3T1zLh2Sqqqq2267bc+ePZAgCOXkrntvEB9nt9vBSAexwSdPnnz22WeFQmEwGOzp6XG5XBD+DbmusOYlywsrlUpo+K1QKEpLS/Pz8wUCgUQi4fP5ZPGSMcvqkZERsVg8MjIC0Sc3eEFiHL/f393dffz48T179mi1WmiPpVKpVqxYsXr16rvuugvSQK+6bvV4PAcPHvzrX/9aX18/OjqalZW1ZcuWBx54oKioCKw0s3M6sU/8KSCKotMef4thWCAQSExMTExMRBBkdHTUaDQKhcKysrLoxQXU6YS6DFcCNAJBEIlEMuFtCnUDHQ7H9dU3vFZEItEjjzzyzTffwDRwiusdyNXHMIzsIzEwMNDS0tLY2GgwGBwOh8fjcTgc0FrM4/F88cUXSNTMDqbA6enpSUlJGo0mKSkpKysLajdBxqtQKJwwn39CCx0MBrkWg2N8AaGIJpPp4MGDTU1N9fX1BoMBarKtWLFizZo1y5cvhwItpI1vkt/R5/NdvHhxx44d+/btGx0dTUlJefjhh7dt2waNuuZkwYth2HUkHc0O8aeAMxdfPjw8fOjQodLS0iNHjly6dCkxMTG6TADY78Lh8MWLFwOBwJXCWUZHR6HnEQjB+A/w+fwf//jHFy5cKC4unomzGE95eXlZWdnRo0cn+Qy4sC0WSyAQ8Pl8Op2uv7/f5XJptdqBgYHBwUG/3w+VeCbsXC6RSIqKilJTUzMzMwsLC4VCYXFxMVTfBIfJhPWapgj5wCckJNxkc0CHw3Hp0qW6uroDBw709fW5XC4ajZaYmLh58+YVK1ZAgRbwbiNXEz7wdTQ0NHz11VdffPGFzWbLyMjYtm3b9u3bCwsLORzOHL4/IpHI4ODgXB19cuJPAcPhsMVimd59CoXCwsLC+vr65557TqFQDA0NORwOGo1Gms8Igvif//mf8+fPRyKRPXv23HLLLffcc8+EtxSbzYaAbbPZTLZkjf4kk8nctm3bfffdNzuZZAiC8Pn8pUuXggJC8RKRSOT1em02W19fn8fjgcjH4eFhs9kMFU3gH7AmJZvzMRgMkUikUCjS09NzcnJCodDHH3/scDikUumbb765evVqkUgUXfR/uqYbkUgE7IxMJnN2guFnlFAo5Ha7dTrdgQMHTp8+3draOjIywmKxEhMTN2zYsGTJkpqampycHMhcnMo1hOtTV1e3c+fO48ePe73epKSkH//4xw888EBxcfGs3WaTE7POlpi4OnOOUqn89a9//cc//rGvr48giOrqapPJlJmZGZ1+YDQa4VeEiIQ77rhjwmmgz+cbHR2FnARYDnO53MTExDEr4rq6OoIgVq9ePXOBCDiOu93uQCDQ19cHCoIgiMvleuKJJ3g8XldXF3gtYKiRSASSwKDibH5+PgSUZWZmJicnZ2dnQ3ZEbm7F5Zd0AAAgAElEQVQu2buut7f32LFjDodDKBSuX78erPIzAY1GEwgEtsvEbOfZySEIAvoWnThx4rvvvuvs7PR4PNAka9u2bSUlJevXr4eQ7Gtaqzocji+//HLv3r2nT58OBAK5ubn33Xff9773vbS0tNmJup8KNBptRvup3giUAiIIgtDp9BUrVixYsACmfmq1enh4mM1mg1kQQRAURauqqj7++GOfz4eiaGZm5pVerVDcjUajGQwGl8slFot9Pt8Yq5/JZHrppZdwHC8tLYWeJ9cHPCcgtdAbzG63G43GgYEBo9Go0+kGBwc9Hk9fXx9phcFxvLGxkclkslgsaAmQm5sLpdVLSkqSkpKgjU5ycjKsvMgksPEOR9JlAebC6z6LqwJhfQiC0Gi02TGeThcEQfj9/pGRkZMnT9bV1TU1NQ0MDNhsNjabnZubu2bNmtWrV5eWll6HOsBc/syZMzt37jxw4EAgEEhOTn7qqafuuuuu3Nxc8orFyMwLyiDO9SgmhlLA/w+UGkcQhCCI8V7a8vJyHo/n8/lUKlV+fv6V5m7hcBiq77lcrt27d6enpw8PD7e0tIz/TFdXV1tb27UqYCAQAA8stLUOBoNDQ0N6vb6np8fhcBiNRp/PR/phITkMSjPJ5XI+nw+OiIyMjEWLFqWlpSUnJyckJEC6a7QT9pqen9HR0d7e3uurqjAVMAyDOaxSqbymXk5zC/iODh8+fPTo0d7eXijNkpubu2rVqjVr1tx2221SqRRKyCDXKFUul+vEiRPvv//+0aNH3W53QUHBpk2bNm/ePKYQJMVUoBRwqqSlpUEIlUqlmqQ3gs/ng+De0dHRn/70p9F/IqdRkCXS2dl5pTJfxGX8fn8oFGpvb4eUCa1WCw1AEAQxm816vZ6cE0FjQxAyhUKhUqmysrLUanVxcXFSUpJQKAQFlMvlkN08fmDXPV8gk6lnCLAqIAjCZDJjZ2U3HijQ4HQ6W1tbv/rqq4aGhq6uLrfbDW5x8GyUl5cnJydD76fr2L/T6fzuu+/27Nlz8uRJ8PM+8cQTjz76aF5e3rQUMpheoJQn2Fj6+vqWLFky1yOagDhWQKhRPJW0hNlEKpX+5Cc/sdvt41s7FhcXQ2wNk8lUq9XhcLijo2P16tWwEQq6YRg2MjJiNptNJtPo6Ojx48e7u7utVitkF0F5KPJGZ7FYarWax+MlJiYWFBTk5+cnJydDvXWJRALlTEAyZqJEXXTG1eDgII7j0Q4fiApCr7GRJpwdeADIpVxzczO8VDweD2TLRS/J4SjTHuBGns6Y8yL/Gl2WnCAIrVbb1NR0/Pjx1tbWjo4Ot9sNTvO0tLStW7feeeedBQUFkyfekr9s9GfIl5PL5aqrq9u9e3dtba3L5WIymQ8++OBTTz1VUlJyJT2FKzPhn8gDkWcBb9zo3wuuLXG5yddVrzB8PrrGNVgAwNDc19c3pkRCdNYjeanh3+RvCqMijz7hbwH7gUfjOlzec6OA8J6MjqsgHycI14RyLORGiKeVy+USiUSv18MysL29/dNPP12xYoVAICA/Gf1sMBiMMQ0KJvzYmC3I38+Gom9BhUIxMDDAZrPBCjOmeSD53ZKSkvfee490PsBGDMOgpaTX64WMdBzHP/roI7fbDSbFzs7O9vZ2UEDIsoDEfjj98bNFOp2en5+fnp7O4/EqKirKysogIQzEt7+/X6FQGI3GUCiUnp5usVhkMplSqTSbzYODg9HWNBRFWSyWRqPh8/l9fX1sNpvP58OzShCEx+Mxm80ZGRmQtAt3JHxxeHgYQhy8Xu9LL710/Phx6OkDfzWZTAaDQaFQPPPMMwsWLLjSnRCNxWJ5++23W1paxGKx3+9XqVQKhQLH8cOHD0NrJ51O99xzz5H1S1AU9fl8er0e+nwjE01mlUpleno6zI9wHNfpdBwOh1TS6KOT301ISFAqlSdOnOByuTQaTa/XZ2ZmjklFh8tI/hfDsJ6env7+fhhnNG63G/oQpaWlPf/881VVVRPO1Do6Ot54443xQQ4pKSkCgaC3t9dqtTY1NUEAJoIgDAZjeHj497//PfT/hY1j7tuBgQG5XE56z8kTxHHcbDYLhUI+n280Gt1ut1qt7u/vD4fDbDY7KysLUuWgzRME6KxduxYKaowZXiQSqa2tbWlpgfmpXq+H5ututzsUCvX19TU2NiIIEg6HP/jgg7a2toKCAtgJiqJOp7O/vz8hIcHn8+Xm5tJotI6OjlAolJWV5fP5aDSaUqk0GAw2my0/P5/H40GXR7VaDXlEyGXVNpvNBoMB2qIlJyffcccdGzZsmLo1AAW5nSTH6KorpinGtUZv3L9//9NPPx2tESTwDhkfdAZZn9A5G1IOEATh8/kikehKJjmFQgGFv696FaYCQRBWqzUYDDIYjIKCAgaDQfaWG4NSqfzkk09ycnLI2crg4OCBAweg8avT6Wxvbx8ZGYEa6+RdBfVOwO+pVCqhwElBQQGHwwkGg3/5y1/GXy7yViADVkjC4TDZqJPBYMCe4R8TBvSBERD6zyJRHQIg0Q3upzEqDHPS6LcUvBtgC7yWmUzmL37xi3/+53+OvmvJPYzZ8tprr7300ksOh4PD4cAAYKhkJZgxZw0uaTjTK81QxmSRh8NhFEWhAS6cEdhAoy8ajuNcLtfv98OEyOPxoJeL45LDIAuvRo/qSs6xYDCIYRiPx3vrrbceeeSRCZ+L119//Wc/+9l4AYXhwbEgwRyKzpNjBsdxJBIZ/8xDkvWYLeD0B4ceeJZgC3k60eZgsiTt0qVLP/nkk9TU1DGDHxgY2L59+9mzZ5HLtwqZmg3t3secafQg4f6h0+kYhpE3GNyuyOUZDPz08IvDNGL8RY7+LVAULSgo2L9/P2TuT3jLjdG6uZkDLliw4Pnnn/f7/S6Xy+fzsVgsnU4HQbNkaSmVShUMBsmXHgCvceg5wGQy+Xy+VCrNysqyWCyDg4PZ2dmDg4M+n08mk9Hp9EgkolQqIQMX/PFQya6vr2/CAgFQdQaCSCYcNpkhR76r4c0Djwd5t2VnZ0cH7gYCgVdfffXPf/4z3BDk48Risfh8Pjw5eXl5arU6NzdXKpVqNBq1Ws1ms9VqNXhmnE5nWlrayZMnJxSvyaHT6WKx2G63nz592mw2oyhaVFQEobaT+D3Gb8EwrK+vj8/nk/5xn8/3ySef9Pb2IgiSnJy8ZcsW6Bjn9XrJrwsEgk2bNk3xhbxp0yaRSGSxWBITExUKhcfj0ev1Npvtb3/7m1arxXFcqVRu2LAhJycHCrur1epox8jk83pyO47jDocD5uMGg4HH40G5QIgzVSgUPp8Pfmj4OhSRFggETqfz6NGjZ8+eJXUKYpVzc3NvueWWsrIyiAcas5KFIBin06lQKO68884rnfuWLVvIpQ9kUHz11VcwW2cwGEVFRevWrSstLZXJZOBKJm8wFEW9Xq/Vak1NTSVNgeMXNLDFbrc7HA6ZTGYwGMi7EbmaRtBotOLi4glddgqF4rnnnoPiQ9HXnIxS2LNnT3t7O41GW7Zs2fr168f8WJMfd/IPX2lLQUHBNfnW50YBU1NTn332WeTy8pBOp4PwRZ88uXKB/5JnaLPZHnrooVOnTpWUlPzlL39JS0uDvm7hcJjFYoEDFNKzQJvI9xg0WoWZzpWqG4D1YYql2DEMg8KcMpkMx3HobYggCIvFGpO1IpFIFixYALvNzMwsKSmBGVl1dXVJSQk4Mch8svFTWpFI9Oyzzz7xxBOTDGaS6FkQ/e3bt0OX9N/97ncrV66MfpdO8Q6DCVR0B1GTydTf349hWHV19SuvvALKTs58/987dsoRuRqNJjs7G6aroM7QfzIUCv3pT38iCGLVqlVvvfUWOSOA+dF1rFrAXEXeXeSbAOq5k1Mn0g7Q0dFx9uzZurq6xsZGv9/P4XCSk5PLyso2btyYl5dXUFAAb7IrDQa6pJNvvglJTk7+h3/4B4IghoeHv/7662+++cZisTCZzMLCwjvvvPPhhx9OSUmB22NCuyeMfPKzhu/C2ZGv0ikqUfRMORoej3f33XdHv5ijdwjL7e7ubgaDcdttt/3kJz+ZfHjTooDwmI8f6pWYM08IrFwIgiDz4aP/Ovk5kyXhyPiVyb84c2t88sU45mNjiqQ+88wzW7duhXtUpVKRRqWrHj36coGqTn3Y0WftcrmsViuCIOFw2G63j8msmOJZkwIHW5hMZlJSEqxikMvdl656IpMzppYfXDFyCsnhcMDqP4ncTwXyYY5+VOAE4RGCOkBer7e+vv5vf/tbfX39wMAAiqJ8Pr+mpubBBx9csmRJXl5e9GW80jIcubJ8REMQxOjoaF1d3Z///OfTp09DK9d77rln27Zt2dnZ0YoMboHJf5orQboUyMftmpToSvsckzsfvUORSARvzTFldGdOAa864DHEsS+Yy+Vea+fm2aGlpeWzzz6DFQ1Jamrqww8/DIuvWYYgiAsXLkBh7WAwGF0u8AYRCoWzlm3KZrNnurcUjuM2m62jo6O1tbW2travrw9muGq1etOmTRqN5tZbby0uLoZO5zciwdEQBGEymY4dO/bRRx+dPn3a6/Xm5eWB9qWmpsZaqMP1wWAwZi5c9AaJYwVUKBRzIiiT4/P5/vCHP3z44YdjnhAOh9PX1/eb3/xm9tsGer3e2traaCv+dO0ZXHs3Um7rqsAqEkEQsJbOxP4jkYjdbm9sbGxsbDx69GhHR4fVaoWC+8uWLdu8efOiRYsKCgrIUMRJpnvXBI7jVqv1yJEjO3bsOHPmDIZhmZmZ991339atW8na3dOls3POdF20aScuFTCWC4S43W69Xg83LtSGcjgcbW1tgUDg+lwZN47H4+np6YF/s1isadSRBQsWsNlst9tNuhSna88kgUAAetHxeLwbySCcEJfL1dLScvz48b179xoMBr/fD/lb69evv+WWWxYvXpyamioQCMDxMr2HNplMtbW1O3bsaGlp8fl8OTk5999//3333ZeWlnZzzPvihfhTQPAhzPUoJoMsiPDiiy/ee++9tbW1TzzxRDAYnMbJ1zXR0dFhMBjg3xiGTWNlHbL7IrQ3monsd6g0MV17A1eA3+/v7e09evRoXV1dQ0OD1WplMpkSieThhx9eu/b/tnfm0U2c5/6f0Wi0Wast74uw5A3bmKCYBjBbIGVfGgwkxtwCOUla0nNS2uaGtmlvz21um5sm9Oam5Z4mEAIhpbQlKQmBAOESg4NZbXYbMN5tWZZkrdY2I838/nh+UX2NccDI0gi9nz84Rh5pXo2l7zzv+zzv830iNzc3Ly8P0g5hFz6GYZxOZ01NzZ/+9KdTp04FAoGsrKx169atWLGiqKgIv4f2f4jwwmkpGZZvdGvjCGKxeO7cucnJyVCvOyQ3EkkoihKJRC6XiyRJuVwe3tb8sA7Y29vb29s7FgpoMpkgh4Pf5/aSIQSDwe7u7ubm5nPnztXU1Fy+fBlq0bVa7eLFi8vLyx9//PFQvjV8w/8nUMZw8uTJTz755PPPP3c6nXl5eWvWrFm5cqVGo0H7eaNF7CkgQRAcXP4bFohVIWF9t/LpCKDX6ydOnFhXV/dv//ZvU6ZMmTJlSrhemc/n63S6vr4+r9cLJiphx2azQfmnQqG439V0qKQZGBiwWCy7d+8+duxYd3e3xWKRSCQ5OTnr168vLS0Fp6FhC7bDRSAQcDgcn3/++Ycffnju3LlAIKDT6TZt2rR06dKSkpJRdEaIIZRKJcc7e8eeAmIYdmfpPGIEHA5HS0tLXl5eVVUV9HQI1/cNvHuw/7tPNry4XC4oUE9KSrp3l9RgMNjV1dXY2HjixImDBw8ajUZ4kSlTpjzzzDPQkyohIeFe6lQeEJPJdODAgT//+c/gPFNcXLxp06YFCxZAQpmz+YFwMXYxdbiIPQWE/YbRHsVdCfkFh7ZqJSYmRnfaXlNTYzQalyxZEnZrOpIk8/PzMQxzOBwGg2HYjesPCFihYxiWl5c38lSRpmnYZXTr1q1PP/307Nmzt2/fdrlcIpEoNzd30aJFRUVFs2fPzsrKAtUb07AL+jYfOnRoz549tbW1NE1nZmY+88wzy5YtKykp4bgohJFQp3TOEnsKyOfzuVkGCMjl8pSUFBzHs7OzIWctk8kiXwETwuv1njhxIikp6cknnwx7klEgEEyaNEkgEFAU1dnZCds5wvj6wWCwvb3d6/ViGCaTye4mHGAseezYsePHjzc2NtrtdmjjmJ+fP3HixKlTp86ZMyc1NTUCER9gNpsPHDjw0UcfQX1fUVHRypUrly9fXlRUhNb7uEbsKSBN07AwxE1Ck0GVShX6uEfxnt/Q0FBbWztx4kS9Xh/2F+fxeLDVGsOw1tbWsBfEQMUcBBH5+fmD5YOiKLfbffPmzaNHj0Invra2NtgqXlZWtmzZsqlTp2o0muTkZKjji8BCWyAQsFgs0L/v5MmTwWBQq9VWVVU9+eSTRUVFof0YD+uSX4wSewooEAiKioqiPYq7An3qYV0s6p91iqI+/vhjk8n0+OOP3/si2n2Rmpqampra3t7u8/nCvhQIRZTwMwTULMuaTKbbt2+fPHny+PHjly5dGhgYoCgqKSlpypQpCxcunDVrVkFBAehyJG88Xq/3k08+ee+9986cOeP1ektLSysrK1etWpWbm4viPi4TewqI4ziXZ8EikQiq5BQKRdTrFtvb248dO1ZcXLxq1aoxOgWfz4cg6+bNm36/f3Tdj++G2WwO7eGrr6//+OOP//d///f69eutra1GoxG6Rubn50+bNm3VqlWlpaVqtXosqpdHAOorL1++/OGHHx47dszpdGZmZq5du/bpp5/Oy8uL8GC4TLSKYb+R2FNA6Dcb7VHcFaFQCALtcDhgBwj0so78SDwezzvvvNPR0fHqq6+OnVMXWMphGNba2mowGMKS84Gujna7/dChQw6HAx7cvXv3vn373G43wzAymWzGjBlarXbu3LkzZsxISkqSSCR3dkwZUyAaPXLkyAcffFBfX+92u0tLS1944YWVK1fqdDru50AjCXxnp0+fHu2BDEPsKSA2qFkIN4EVnztTYJEMCRmGOXr06AcffJCfn79gwYKxywCkpKSkpaVduXIlGAze1wZhaJAJJhIYhvl8vu7u7t7e3tbW1osXL96+fdtut0OlIRwPSeHCwkK9Xl9ZWTlr1iyJRAI9Wcfkjd2dQCDQ19d36NChvXv3nj9/PhgM6nS6J598srq6OvfuJoLxSaj9/Zg6yTwIsffX4vP5mZmZ0R7FXSFJElKumZmZ8GUAg13sHuo5wkgwGOzr6yMI4umnn77T9y6MSKVSaI5P03R9fX15efndjgQPqe7ubqPR6PV6vV7v7du3u7q6uru7fT5fY2Ojz+cDlztw/hxylqVLl65cufLRRx9NTEyUSCTRqrM1Go2ffvrp9u3boaV7eXn5+vXr58yZk5WVdacFFSI1NZXP54MNQ7THMjyxp4DY/23rxllCWVGPxwOdskLN/SMAn8+H0rNJkyaNaQkIj8cDWwmPx3Pw4MFly5YxDAOzfr/f39jYSFGUy+W6detWR0eH1Wrt7u42mUxgKArd6kMds2Hfm0QiSUhIAIv03t5e0JSpU6e+/fbbIVP2yO+cZb/2Ktq6devp06cxDNPr9XPnzl2zZg18t9Gcd1jcbjd0bx2jLUMPTkwqYEzQ3t4O8zupVAr1gCaTKWLfWxzH09PT09PTx0gs7Ha7xWLp7e1tb2+vr6+HKeoXX3yxaNEih8MR6mUAUghiRxCEXC4HLx5wI8IwTC6X5+fni0QirVYL9kxKpTI9PZ3H412+fPn555+/ffs2SZKPP/54FKvKDQbD8ePHd+3adeXKFbvdXlhYuGbNmnXr1imVStTHZWRCnwTOLg5wdFgjwLLsmDakCxeDk1+xsvcTmvFBN3wMw3w+n8PhsNvtdru9vr6+sbGRZVl4F0ajsbe3t6enZ/B+Zwj6wNAKvL7y8vIyMjKEQqFOp0tJSUlPTxcKhcnJydCgYeROvyEHOLFY/K1vfSvyQRbDMLCnbc+ePefPn8dxPCcnZ+PGjVVVVQUFBREeTEwDE4Voj2J4Yk8Bg8Eg2hccRiwWi8vlMplMFEX19/dDAxW/309R1I0bN4xGo8PhYBiGoqjBGW2pVJqUlJSXlzd+/PiBgYFr167BBH/WrFlPP/30+PHjpVIpeLSHJrn34jk7GKPRCN7w4CEV7vf9DfT19Z08eXLr1q2XL1/2er0lJSU//OEPZ86cmZaWBs3xuX8/Q9wLsaeAfD6fy92xQlHSwMAAiEJoZ2ska6QhlAs5DWEYZjAYwDgU/PZaWlrA/9disTidTrPZDG1U4GAQLPg3KysLvNOys7NzcnLy8vIUCoVcLler1cnJyQKBwGg0PvPMMw0NDRiGlZWVVVdXw9zw3l1Q7oRl2dbWVtj8k5+fD3ZuESAQCAwMDNTV1f3hD384e/asz+cDe4OVK1cWFhaixb5Rw9ndwbGngBzH5/MNDAywLNvZ2VlXVzdr1qyWlpbOzk4Mw6xWq8ViCe+XOeSlC9NVm80GTVCgTLerq2tgYKClpcXn87nd7tDqATwLGhlIpVKVSiWRSHQ6nVgshn8LCgrS0tIKCwvBoQkq/sB7l8/nD7bZZFlWoVBMmzYNFDBc+Hy+M2fOgByD204YX3xYWJY1GAz79+/fs2fPzZs33W63TqeD/n05OTmhFvmI+wI+KlzeyYoUMMx4PB6bzcayrNVq3bhxY0lJidfr7ejowL62K7yvV4OexhDQQfQEZXQWi6WlpcXpdH711VddXV0Mw4QW7EABoQwbbOYhFywQCGQymU6nk0qlSqVSp9PBtlm5XJ6YmEgQRHp6OiQrsLt7cWHDBXEEQUB8xLJsW1sbNGQd9QUEKIq6evUqDHv69OlDzO3CC03TfX19R48e/ctf/lJXV8eybGZm5ubNm5csWQL7L1HT5lEDxeGhLmocBClgmOHxeLArDmIKcGjDMEwmky1evDgrK+tuTwSHRpBIj8dz48YN8Hrv6OhwOp23b98GJ/KBgYHbt2/7fD6KoiApBBlngiAkEglU58EiHSRY8/LywONcp9Op1erQehz8ELJhxB5gYYvP50+ePDkzM7O7u7u+vt5msz34HmSj0dje3o5hWFJSEtgrj5EGdXR0/P3vf3/vvffARDw/P39w32YkfA8IVMNEpiXP6EAKGGaUSuUPfvADtVo9OG+gVqtnzZpVXl4eDAahPoCmaZfLBd6VMNe7du0alJVgGOZyuaDgNlRMD+VyUFANkRqfz4cgjiAInU6XkZEBC3bJycmggGAjO0Q7xqg9iVqtVqvV3d3dTqezp6dHo9E84AuePn0a5k2ZmZljUQAPdu8HDx7cvXv3hQsXIM/73e9+d9myZcXFxTFRcBoTGAwGzq4AAkgBwwyO4/PmzZsxYwaEgaHJ44ULF956660rV65AyOZyubq7u0PFwxiG0TQNUgihnEQi0Wg0QqFQJpOlp6fn5+fLZLL8/HyFQiEWi8eNG0cQBJ/Ph7srTHUH32kjPHGTyWRQuQLOnNOmTXvAF7x27RpcqKSkpFAhdLgwGAyfffbZjh07rl69GgwGH3nkkeXLl1dWVo4bN24s7O4QXAYpYPgJbZMIKaDL5fqv//qvTz75BP8agUAAm+czMzNVKhX0zkxNTc3NzVUqlWq1msfjJScni0QiuVw+OBUwbBAX9cZzcrm8sLCwrq4Oauge8NVsNtvVq1dh9pSXlxeuRUBYlzhw4MBf//rX+vp6hmEmT55cXV39xBNPaDSaWKnZjEVYlg3t7+YaSAEjAY/HmzFjhsfjkUqlEMSVlJRMnjxZKBSmpKSE2qtAAQo2KO0QdWm7R0Qi0VNPPfXxxx/bbLbGxkaj0Xi/rkaDsdvtVqsVwzCxWDx//vwHj8tYlu3p6amtrf3jH/94+fJlmqYrKiqqqqrmz5+fkZHB5VWqhwOKokJ+rVwDKWD4CQaDzc3NtbW1Tqcz5ACr1WrffffdlJSUkMcuxr1Q7kEoLS3NyMiwWq1NTU23bt0atQJCIVFPTw+GYYWFhZMnT36QUQUCAZPJdOzYsffff//ixYtCoXDOnDlVVVXTp08fISuFCC8CgeDBl4bHCKSA4eezzz575ZVX2traBte+CIXCtWvXvv7661Ec2JiSkJBQWFh47dq1/v7+W7duVVRUjDqfAN0TMAzT6/WjTiuDkn7yySd79uxpamoiSXLOnDnPPvvs1KlToaI+Ru80sQgk5aI9iuFBChhmTCbTu+++29TUxLKsWCwmCIJhGGgM9dVXX3G2S9qDA65JH330UTAYrK2traqqGl0rb4qiGhoaGIYhSXL27NmjWARkGKavr+/AgQM7d+5saGiQy+WzZs167rnnKioquLyb6KEkIyODJEmGYdA6YLzQ0dFx48YNlmUTExNffvnl0tLS9vb2X/3qV5ytiQ8XJEnq9XqlUmm320+dOuXxeEangB6P58yZMxiGZWdn3+924GAw2NHRcfLkyZ07d164cEEkEi1atOi555577LHHkPZFBZZl4WbG2SY6SAHDDLRXwTBMIpGAQ/n169eTkpIeegXEcTwrK0utVtvt9v7+/ubmZrVaPYrXaW5uhlpojUZz74tHNE13dnZ+/PHH+/btu3LlSkJCAsx5p0+frlKp0KaOaNHb2wtfB85uqUYKOFZ4PB6oaEtOTk5JSbl16xZJkpz9HISFkpKSCRMmwPaVw4cPT5ky5X7fL8MwNTU1/f39PB6vrKxMoVB841NcLldHR8fhw4dhP69MJlu0aFFVVdXs2bOhLPzhvuYxQTAYtNvt0R7F8CAFDDMCgWBIM0ihUAiLWVqtluMOJw8IjuN6vf7QoUM0TZ8/f95qtd5vMbPD4aipqaEoSiKR6PX6kZfP/X5/c3PzH//4xxMnTrS2tiqVysrKyrVr11ZUVHC2G118AltFoz2K4RWSNa8AAB5XSURBVEEKGGZUKhX0kroTq9VK0zRnPwphYc6cOb///e9tNltDQ8OlS5fmzJlzXyFYd3c3GAGq1epJkybd7TC/33/mzJkjR47s27evvb1dqVSuWLFiw4YNU6dOha0pCE6B4zjMhzgIUsAwAy2kMAxTq9VDxM5sNnPWNTVc5ObmFhQUnD171mw219bWzpgx497DXoZhTp8+3dLSgmHYY489NqzBk8fjOXfu3K5duw4fPmyz2ZKSklatWrVu3bqpU6dKpdKYLqh8iIH+RtEexfAgBQwz0GwKx3Eofo72cCKNQqGYOXPm+fPnGYY5ePDgiy++eO9JWJ/Pd/LkSZqmCYJYtGjRkFQywzDNzc27du3avXt3X1+fTqd7/vnn16xZk56e/uCtaBBjyv22B48kSAHDTKhHdHyuwYtEooULF+7cudNsNre1tV25cmX27Nn3+Nyurq6LFy9iGKbT6SZOnAhXj2GYgYGBS5cuffTRRydPnrx58yZJksuWLXvppZfKy8tJkkQRH/cBh+Voj2J4kAKGGblcDinIaA8kOkAyZOLEiceOHRsYGDh27NjMmTPvZXMIwzAHDhxobW3FMKykpASmwDab7fz58zt27KipqbFarTKZ7Nvf/jb0MkD1fTEESZJjalr9ICAFDDMul8tqtT70630jIJPJpk6devLkSYqijh8/vnHjxntp8NfZ2fnpp5/6fD6hUKjX64PBIDSwOn36tMlkgjxvZWXlnDlzYJEBhX6xBXLLjBfEYnFoST4+wXG8srJy586dXV1dV65cqaurq6ys/MYw8NSpUzAFZhjmxIkTp06dOnv2rMPhEIlE06dP37Bhw9KlS1UqFepdiggvSAHDjNPptFgscR6haLXa8vLyrq4uj8dz9OjRRYsWDSnQg+sTCAQCgQDDMEajcfv27W63G8MwmqaPHTuGYZhIJJo0adL3v//9+fPnZ2dnx/klRYwRSAHDjEQigYam0AA12sOJDlKptLKy8tChQ36//+jRo7W1tfPmzQNnzt7eXrfbbbVabTYbZEu8Xu+VK1cuXboUejpBEJMmTVqxYkVlZaVWq0X9+xBjB1LAMEMQBGwCT0hIiLcpGzhw0jRN0zRshvf7/d3d3S+88EJ5eTnLskaj0WAweL3egYGBgYGBO19BKBQWFxdXVVV95zvfycvLgwfj9kaCiABIAcMMOPNiGGaz2YZUgQYCgYepOxbLsoFAgKIos9lssVisVmtnZ6fJZILWBs3NzeDbybJse3t7e3s7CBmsiCsUitTU1LS0NIFAcPPmTXDUw3F89erV//7v/56VlcXZhXPEQwb6nIUZhmHAx/LOdSuLxWI2m5OTk6MysFEAbsUQ1oHJut1uhz0bLpfr2rVrN2/edDgcJpPJYrE4HA6n08myLEmSsA9EIpF4PB5IiysUioULF+r1eq1WS5KkXC5XqVRpaWk0Tf/oRz/at28fhmH5+fkvvPBCbm4uWvJDRAykgGGGoqi7NYMcVhY5hd/vd7vdZrM5GAz29/cbjcaOjg6z2dzc3NzZ2WkwGEKtLsG4nSRJkiTBnzM1NVWlUslksuLi4sLCQolE4vV633nnnRMnTmAYlpmZ+etf/3rcuHGDgzscxxsaGurr6zEMIwiiqqpqhL3AiFhEIpFwfC0oJhWQywtDSqUyLS1t2L+6UqmMeh0vhHIgxMFg0OFw9Pb2dnR0NDc3m81mk8lkMBhMJlMgELBYLC6XC1QbNjuLxeK0tDTw7czLywN3drlcnpycTJKkVCpVqVSwDAp/oEAgoFQqW1tbu7q6urq6amtrdTrd4MHQNL1r1y7oBpibmzt//vyHu3dOHMLZ5vghYk8BeTxeUlISZ9eJeDweQRDDxnr9/f0WiyU9PT2S4/F4PG632263O51Oq9V669at3t5emJkaDIaamhqHwxGa5IrFYoFAkJiYKJPJcnNz09LSCgoKVCpVYmKiVqvNyclJTk4GWztwcA/9FYYtUSYIYu7cucuXL3/nnXdcLtfWrVunTJlSVFQUuoFdvHjxyJEjLMvyeLzZs2cXFxdz+d6GGAVOp5PjuwM4qiMj4/f7OXtZ7Xa70WhkWba/v//q1asajQb0Bft6WS28p4OW1IFAAMdxmqb7+/shD2M0Gq9du3bjxg2z2Ww2m0MKODAwQBBEqImhRCLJzs4uKipSKBTFxcXZ2dlJSUmggEKhMDU1NbSnfVh/u2/cm0GS5Pz583fv3u1wOK5evbp3796f//znoKEej2fXrl23b9/GMCwlJWXDhg2owcHDB8eXfbBYVECGYVwuF2cVMBgMQsK3qalp6dKlSUlJEokEtruGBYqiIJZ0Op0YhhmNxp6enpaWFqgrrq+vh2a8MAyKogiCSExMTEpKSk9P12q1aWlpWVlZZWVlUGcnk8lSU1OhdBHCOpi/h7HNVHl5eW5u7qVLl2ia/uCDD/R6/eOPP06S5KFDh/bt2we3hHnz5pWVlT34uRCcZdjiJy4QewoYwmq1WiwWrqVWSZIMbd6y2+2gRzweTygU6nS6kdu+g60MRVEMw/h8vp6eHsiltre3t7S0NDc3Q/WJ0Wg0m83wkbLb7X6/H8MwoVDI5/Nh3ioUCvPz83U6nUajEQgEqampycnJMplMIBAkJSXxeLxI+hQrFIr58+dfvnwZ7Cufe+65yZMnkyRZX18PlpgZGRlPPfUU6ur8EBMIBOCGzUFiWAHlcjkH502JiYk//vGPk5KSAoFAaMUtPT19woQJ3/72twdb/8CkGOrpzGazy+WiKKqjo6OxsdFqtYLnHEVR2Ne7xyCgg4lnTk5OXl6eSCTKzMwUiUQikaikpCQjI6O0tBSaJAsEApjtDhle5BfaRCLRs88+W1dXd+rUKYZhLBbL559/Hpo+83i8lStXzpw5M8KjQkQSuDdHexTDE8MK6HA4HA5HSkpKtAcylJkzZ4JJUCjyl0gkBEFcv379+PHjgUCgsbHR7Xb39fX19PRQFGUymSCmC03wIfcKeqdUKnU6nUgkKi8vHz9+PJQX5OTkgBOrTCaDw7C7rNBxoY2KTqfbsmXLli1bvvjiC9B0DMP8fj+Px9Pr9c8//zwKAB96OFsTE8MKmJiYqFKpoj2KYQhtCoaVNQzDWJY9ffr0hg0bent7MQyDkmmGYQKBgEgkUigUQqFQKBRqtVqZTCYWi8eNG5eXl5eWliYUCgsLC5OTk+E1SZKET1LURe1+KS8v3759e2NjY09PDySRL126hOP4smXLxo8fH+3RIeKXGFZAj8cDRbnRHsgwhIwR4NseCARMJlNfXx+O4xKJJCUlRafTJScnFxQUjB8/Pi0tTSQSBQIBnU4HIZ5QKAx7RiLqSKXSb33rW6H3snjx4ofp3SFilBhWQEiJ5uTkRHsgQ7l27dqZM2eg0JfP52u1Wrvd7nA4XnvtNa1Wq9PpVCoVRHOwpyK0NocUAfGw4vF4oj2E4YlhBeTmJjOGYbZu3free++F7AGhQJpl2Xnz5n3wwQcwpYVfcXD8CES4gN4ZGIZRFNXc3PzEE09Ee0TDwNHlyZHJyMiQSqXRHsXwOByO9vb2we6o0FyAZdkzZ86cO3cuimNDICIJRVFdXV2BQABWvaM9nOGJPQXk8/nZ2dkcrIMBSJKUSCSw/LdixYo//elPr7zyChg/UhTV09MT7QFGGZ/Pd/PmTdi4gni4IQhCKpVCYcOQLeHcIfYUMBAI1NfXG43GaA9keKDLAMuyMpnsF7/4xbPPPrtx48aSkhIMw3Ac51r9doRhWfbo0aMrVqx4++23ORsUIMIFVLzCvm/Ohiyxp4AYhoG5RLRHMTwMw8AmjZSUlLS0NIIgHA4H9AoVCASc9QyMDMFgsLOz8+bNmxcuXIjDNVCGYdxud9j3hnMWgUBwtz5J3CGGMyHcRC6Xw66M5ORksViMYVhiYmLUm2JxBD6fP27cOOiMEG/QNH3ixIkjR44UFhY+/fTTnF3IjjeQAoYZt9sNiX+bzeb1epVKpVgshj0PSqVSqVRGe4BRJrSDJa7wer3bt2//j//4D4vFMmHChKlTp8LCCCLqcDpAjUXS09Ozs7NhNxvEgCFkMtnInRHiAbFYPOSyxANffvnlli1bzGZzXl7ed7/73ThfDOEUSAHDjEqlysjIgDZTQ4IdHMfjMPwZQnJycrylgy5fvvy73/2us7MTw7CkpKSFCxdCbQCCCyAFDD9I5hAhPB7P7373u6+++gr+29DQ8Le//S26Q0IMBq0DIiJKMBgkCEKj0XA8RRguQm0ysK/7uY0bNy7ag0L8E6SAYw6fz09ISECBIWCxWGw22+CtgQ83YrE4IyODx+NJpdL333+/uLh4cI9IRNSJYQXkrFnSEMDKIw7L34ZFpVLFVTrIarVevnyZpuni4uI5c+YoFAr0SeAUsToT4fF4xcXFGRkZ0R7INxMMBqFGGoFhmEAgiCtLTKPR2N7ezuPxnnjiiThMgnOfGFZAhULBzeaAQ0hISMjOziYIItoDQUQB6AspFosnTZoUEx/XeCNWFTAQCBgMhpiYUPD5fKlUGifLXt+I1+v1er12uz0m/nYPCMuyLpfL7/enpqZClWi0R4QYSmwspQ1LDEVV6OYPsCzb0dHR2dkJ9p7xkA7WaDQTJkzIzc2N5wRIyIWVg8SqAgqFwhi6qcbnVrA7wXFcJBLxeLw4uSA4jpeVlf3lL39JSEjgpqdNZFAqlVlZWdEexfDEpAKCqW53dzfLsjHxRfL5fPEw6bsXwBtAq9UO/sNBupym6UAgEAwGJRLJw5Qtyc7OjvYQxpZAIMDj8UaI8qAgLJJDundiTwGDwaDX6+XxeNCINNrDuScUCgVnZwGRB8fx3t7ea9euud1usM3zeDy3b9++ceNGc3Nzf39/dXX1iy++GCvVTvEMy7IGg+HAgQM4jmu12nHjxmVmZsZWyjv2PmQEQSQkJDAM43A4YiIGZFlWpVKF3EKiPZzoQ1HU3r17T58+PTAwEPKRcDgcoQN6e3tv3LgxYcKEoqIiWELFcdxqtdI0PbI99L2bI4tEIqVS6XQ6NRoNSC3DMDRNi0Si0CsMiVKHPDj4EXBG9fv9gxt/3bvv1T0OG05EEAR8lgKBAJ/PB89VMN4aYhgNP4SWy6EoNbQkB4EbjuNg4QBPGby2Du4OsF4R6mk4ZJzBYPCNN954++23MQxTq9XZ2dkZGRkFBQUTJ06cPXu2RCIJ2UNzlthTQAzDQPuMRmN/f79arY72cL4Bn89XX1/v9/tdLpfT6Yzn9aAQPB6PYRiGYaxW650dQ41G444dOwQCQSiHHjo+FBiC9QRN0wRB3FlwDsePMACCIIRCod/vD50CXnB06TW5XJ6fn9/d3Z2ZmTl2WS+CIEQiUWJiYnp6OsMwfX19MpmMYZiOjo6srKxhe1BKpVKoxGJZtq+vz2KxqFSqzMxMlmW7urpEIpFQKOzp6YFrJZFINBoNXAE43mazQT9Hg8Fgt9vvfH2v13v48GG4+Gaz2Ww2NzQ08Pl8kiRVKhWfz3c6nTRNj9EFCQuxp4B+v7+5uRnDMJFIFBMTJfgmwy0axYAYhhEEsXz58p/85Cdut/vKlSunTp0yGo1NTU0ejwd8lktKSpYsWSKVSjUaDVwx6Cc6+Or5/X6v19vd3a1UKh0OB8SSEEyB4bLX68UwzOPxtLW1aTQaqVTKsmxvb6/JZCopKTEYDH19fSzLKhSKvLw8iqJaWlq8Xu+QMGrwf2UyWVpaGthgweMkSSoUCrvdHggEAoFAenp6yCcau0sMeGe4N+xhRqOxs7NTqVT6fD54I6ODz+eLxWI4qd/v9/v94N3BsqzT6YQYEDxbWJbl8/kSiSR0p/H7/RAUEwQBP8Oe7mAwONgI7M4oD66G1+u995A8isSAgtxJcnKyWq2uqKjg5v6qIboM4QaGYeAOHKVBcQUejycQCIqLi/V6PY7jFRUV69evDwaDfX19bW1tJpPJbDbPmzcvPz8f3KZCojZEmyBsgalcKNwLqcngB/1+v0AggF+FprrwLYUD4Lc0TX/jLYokSZqmB3+xRwg2H2QWDOOEdw2vP2S1Z+Sp+rBnx3Hc6/X6fD6VSsWybE9PDwiixWJhWdbn80ETB5vNZrVac3NzYbJst9uhoJWmaZvNlpKSYrFYWltb4ZVZlj1w4MDly5dDF4EkSY1Gk5CQkJycLJPJzp0719PTQ1GUy+Xi5uwn9hRQIpFs3rx57dq1paWlQ74YHEGhUAw7mfL5fJz1jY4YcPcK5YVgVRf7eiI5rGoMm0SCIwUCAcuyoas9+OmhByGtHHpN6NRCkuSQsww5DBskTIMVKtTo5RtDuXt55G6H3XnekR+HH+7r7LB8dF9nv3PwGIaVl5dv2bJFoVDMmDFDKBTK5fJHHnlEIpFAF8g1a9b09PQ4HI6enp6cnByMe8SeAvJ4PK1WO6ScglPYbLZh3XBUKlVSUlLkx8MphEKhSCSK9igQ4QHH8UWLFs2YMQNqM7Cv0ykglB6PZ1h15hSxp4DcZ4RpEaqJQTxkEAQxeDFqcFxCkqRarSYIApZQozG6bwZ9IcOPSCTCcZyiqPjxRbx3YD0+2qNARAKSJNPT03k8HtQeRXs4w4MUMPxArtDn8w1OmSEAqJmI9igQkcDv93d2dtI07fP5Btd7cgqkgOEHhE8mkz1MW7vChVAoFAgEaDUgHggGgyB8AoGAs+ZQaB1wrLjTGQ7VA2IY9sgjj7z22msTJkyI9kAQkQNKoKI9iuFBChh+7rYLGFrjcbMqKmIolcrq6mrO5vER8QZSwPCj0WhIkrTb7aEl/4SEBB6P53a7BwYGojs2LhBDjR0RD0JMGGSj5Zjw09jY6Pf7e3t7Yb8RhmFerxc2G6HsMCJ+gCwwx0UQKWD4gUxIqOUGhmGJiYkEQUgkEs52SUMgwg7s7YMdx9Eey11BChgJQA0piuJ4nwwEIoyIRKKFCxcWFhYuWLCAs00DuavNscudYT9MfsViMdoQhogfcBxfu3bt5MmTtVotZz/5SAHDz5254Pz8fJIk0SwYEW8kJCQ8+uijGIf3BaNZcPjx+/0w7e3r66MoiqIo6AMKyZBojw6BQPwTFAOGH2hpabfbX3rppSeeeALDsIMHD/r9/v7+fovFMmwvXwQCERWQAoYfuVyOYRjLsnV1dXV1daHHoa1x9MaFQCCGghQw/FRXVzc0NLS0tIQSIDRNe73e2bNnc9Y1FYGIT5AChh+9Xr9z506j0RgMBnEcF4vFfr/f6XQWFxejDqkIBKdAChh+CILQarU6nS5k5gk9ETheHI9AxCEoFxwhkPwhEBwEKSACgYhfkAIiEIj4BSkgAoGIX5ACIhCI+AUpIAKBiF+QAiIQiPgFKSACgYhfUEU0YjS0trb29fUNbnkEPxMEUVRUpFKpWJZtaWk5derU9OnTtVrtA54uGAz6fD6WZYVC4QgNh30+XzAYDI1KIBCQJAljczqd0Lubpmmz2azVajnr34iIJEgBEaPhtdde++ijj+5s+kaS5Jo1a379618LBILf/OY3f/3rX7/3ve/95je/eZAWwTRNf/bZZ1988YXT6SwoKJg3b155efmddks+n2/btm0XLlyAFmQEQZSXl69fv14mk7W1tf34xz++fv069rWYvvTSSz/4wQ84a+GIiBhIARGjYfXq1deuXTt79iyGYdnZ2YWFhTRN19fXOxyOTz/9dN26dUVFRTiOSySS9PR0CMRGh9/v37lz5y9/+UuLxQLeY3v37n333XcrKiqGHNnc3Lx169Zbt27Bf/l8fl9f3+rVq2UyWW1t7eHDh0PWfQqFAkOWdQgMw5ACIkbH3LlzzWbz1atXPR5PZWXlpk2benp6jh49+uabbxoMBoPBoNfrX3vttfXr15eUlDyIUc6lS5fefPNNi8VCEERJSUljY2NTU9PevXv1ev2QuNLj8Xg8HoFAoNFoMjMzJ0yYUFVVpVarMQzLzMwUCoXBYHDKlClqtXrJkiUrVqxACojAkAIiRgePx0tJSREIBB6Px2Aw7Nu3b9++fZs2bVqwYEFNTQ2GYZ2dnX/+85+9Xq9UKlWpVDiOsyzrdrutVmuoUTaO4wkJCYmJiSNsmvZ4PBD9aTSa73//+6+++mpvb+/Vq1cpihqigH6/3+/3p6Sk/OQnP1mwYMHg2BNWAMeNG/ezn/2stLQ0MzOTIAjO9m1HRBKkgIgH5Ysvvvjyyy8HBgZsNttvf/vbpqam6dOnNzQ0/Pd//3d/f39/f/8bb7whFovb2treeOON/fv3UxQFT8Rx/NFHH/3www8hUhuWyZMnv/DCC6dPn/6Xf/kXjUYDDxIEcTe/gZ6enl/84heHDx9+8sknKysrId1x/fp1v9/f2tpaXV1dUlLyox/9aMGCBSgTgsCQAiJGB2RXQctsNhuGYWKxmGXZ/Pz8/Px8HMdLSkrGjx9/4sSJpqYmiqICgcC//uu/7t+/X6FQBAIBl8uFYRj4Ro3cNUcqlf785z93OBwKheL111/v7e3Nycn54Q9/qFKphhwpFApJkhQIBEKh8MiRI3V1dS6X6/nnnydJMjU1VSQSicXirKysCxcuPPfcc5s3b37xxRc5a2CGiBioHhAxGliWDUVhEonkTj2Sy+UpKSk4jpvNZpZlrVZrfX09SZK/+tWvNm/eLBaLhULhT3/60x07dnxj11ipVJqenv7ll1/u2LFDLpdv2rRp7ty5dx42fvz4p5566uWXX96/f/+LL75osVjefPPN8+fPsyw7c+bM6urq//mf//nHP/4xY8YMu93+/vvv9/b2huVSIGIapICIUeLxeMAAfunSpT/96U+zs7Ozs7NDvxUKhampqTweDxIOEomEJEk+n08QBI7jwWAwLS3tO9/5TmZm5r2c6/z586+88orFYnnmmWemTJkCqjrkmLa2NoPBIBKJioqKpkyZwufz29vbb926xbLs/v37GxsbaZpOTEyUSCRg4+d0OsN3MRCxCpoFI0YDy7IOhwMUUCaTfe9731u9enVaWlroAB6PB4kIjUZDkiTLsjwez+Px/PKXv8RxnCCI1atX63Q6OBgyJKmpqUKh8M5zmUymLVu2XL9+HQqtq6urZ8yYsXXr1oSEhP7+fpvNlp6ezufzIRtz9erVpUuXdnV1BQIBPp8PY6itra2pqVEqlbNnz3a73digYmlEnINiQMRoGBgY6OjogJ97e3udTmdOTs5g/XK5XH19fcFg0GAw2Gy2/v5+t9vNsqzdbrfZbDKZ7LHHHoPwcGBg4NVXX129evW2bdt8Pt+QE1EUtW3btgMHDjAMY7PZtm3b1tbWlpCQwOfz3W73z372s6qqqu3bt+M4rlKpGIZxOBzHjx+vqalhGKa0tLSsrAzHcYhGm5qafv/739+8eZPH4y1evHhwxIqIX8DbG8y8Qz+E/jvkkWEfvJdH7nbYsOeNzFki8+5GODgW33XowbfeeitkfMzn8/V6/VdffRVyhWcY5m9/+xtkeKVS6b59+y5evJiSkjL4g5eTk7NlyxaPx9PR0TFt2jQcxzds2AAqOfi8TU1Ner1+8BPFYvG2bdtomjYajRBFVldXMwzT0dFRWVlJkqREIhEKhTqdbufOnTRNsyx78eJFvV7P4/EEAgGPx6uoqDh79my0ruGDnHeE8XD8kzPq8471WdAsGDEaioqKlixZ0tzc3NPTIxAIKioq1Gp1KKvLsqxWq12xYkV/f39GRsb48ePr6urcbjeEY3w+32q1dnZ2/ud//ucjjzxSUVHx8ssvX7lyZd68eXdunsvIyID5MsMwGIbhOK7VahcvXkwQhFwu/+1vf9vZ2VlWVoZhWHZ29uuvv15QUNDW1lZWVjZ9+vRp06bxeDwMw0pLS7du3bpv3z6LxVJcXLx8+fKCgoLIXjAER8EZhoFqVQzDQj/8/9997XP2f55wx4P38sjdDhv2vJE5S2Te3QgHR+DsYX/XoQcZhvF6vcFgEIqNIewKHQMnhQMIghCJRJs3b37rrbckEsnGjRszMzP37t1bV1fH4/H27NmzatUqlmVpmiZJEubFQ4ZH0zSU3cDjPB5PLBaHRgiWpPBEHMcpiqIoSigU8ng8kL/QkX6/PxAICAQC2A7M8U/OsOcdYTwROHtU3vVYnwXFgIjRwOPxEhISRv7UDg7o1q1bd+vWrWPHjm3ZsgUmIGKxeOrUqXq9Hnb7DpsDAUCzhv0c83i8IeWEI6Q4hELhCGdBxCdIARGRoKSk5A9/+MPRo0cvXbpkt9sxDCsrK6usrMzNzY320BBxDVJARITIycl59tlnv3HmgkBEElQNg0Ag4hekgAgEIn5BCohAIOIXpIAIBCJ+QQqIQCDiF6SACAQifkEKiEAg4hekgAgEIn5BCohAIOIXpIAIBCJ+QQqIQCDil/8HH/4JUesdZjoAAAAASUVORK5CYII=	\theta = \frac{\lambda}{5d}; \frac{1}{25}; \theta = \frac{\lambda}{4d}
+682	A useful optical grating configuration is to diffract light back along itself. (a) If there are $N$ grating lines per unit length, what wavelength(s) is (are) diffracted back at the incident angle $\theta$, where $\theta$ is the angle between the normal to the grating and the incident direction? (b) If two wavelengths are incident, namely $\lambda_1$ and $\lambda_1/2$, is it possible to monochromatize the beam with this configuration? How?	[]	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	\lambda = \frac{2 \sin \theta}{mN}; \text{Not possible}
+683	 Two stars have an angular separation of $1 \times 10^{-6}$ radian. They both emit light of wavelengths $5770$ and $5790 \text{ Å}$.  (a) How large a diameter of the lens in the telescope is needed to separate the images of the two stars?  (b) How large a diffraction grating is needed to separate the two wavelengths present.    Be explicit and complete in your answers, explaining your reasoning.	[]	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	70.6 \, \text{cm}; 289 \, \text{rulings}
+684	Two positive thin lenses $L_1$ and $L_2$ of equal focal length are separated by a distance of half their focal length (Fig. 1.32): (a) Locate the image position for an object placed at distance $4f$ to the left of $L_1$.  (b) Locate the focal points of this lens combination treated as a single thick lens.  (c) Locate the principal planes for this lens combination treated as a single thick lens.	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	\frac{5}{11} f; \frac{f}{3}; \frac{f}{3}; \frac{f}{3}; \frac{f}{3}
+685	An object is placed 10 cm in front of a converging lens of focal length 10 cm. A diverging lens of focal length $-15 \, \text{cm}$ is placed 5 cm behind the converging lens (Fig. 1.27). Find the position, size and character of the final image.	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	\text{Position: } x' = -22.5 \, \text{cm}, \text{Character: upright, virtual, magnified 1.5 times}
+686	A plane wave of microwaves having $\lambda = 1 \text{ cm}$ is incident on an opaque screen containing a circular aperture of adjustable radius. A detector having a very small sensitive area is located on the axis of the aperture 1 meter behind it. If the radius of the aperture is gradually increased from zero, at what value of the radius does the detector response reach its first maximum? Its second minimum after the first maximum? At the latter radius find the positions of the maxima and minima along the axis.	[]	/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGQAZADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD3+iiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigD//2Q==	0.1 \, \text{m}; 0.2 \, \text{m}; r_1 = 4 \, \text{m}, \, r_3 = 1.33 \, \text{m}, \, r_5 = 0.8 \, \text{m}, \ldots; r_2 = 2 \, \text{m}, \, r_4 = 1 \, \text{m}, \, r_6 = 0.67 \, \text{m}, \ldots
+687	A 55 year old man can focus objects clearly from 100 cm to 300 cm. Representing the eye as a simple lens 2 cm from the retina, (a) What is the focal length of the lens at the far point (focussed at 300 cm)?   (b) What is the focal length of the lens at the near point (focussed at 100 cm)?   ( c) What strength lens (focal length) must he wear in the lower part of his bifocal eyeglasses to focus at 25 cm?	[]	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	f_{\text{far}} = 1.987 \, \text{cm}; f_{\text{near}} = 1.961 \, \text{cm}; f_{\text{glasses}} = 33.3 \, \text{cm}
+688	Illustrate by a sketch the position and orientation of the image of the 3-arrow object (Fig. 1.16). The length of each arrow is 1/2 unit and the point O is located 3/2 F from the center of the convex lens, (F=1 unit). Work out the length of the image arrows.	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of image arrow a} = 1 \text{ unit}; \text{Length of image arrow b} = \frac{1}{2} \text{ unit}; \text{Image of arrow c extends to infinity}
+689	A Fresnel zone plate is made by dividing a photographic image into 5 separate zones.  The first zone consists of an opaque circular disc of radius $r_1$. The second is a concentric transparent ring from $r_1$ to $r_2$ followed by an opaque ring from $r_2$ to $r_3$, a second transparent ring from $r_3$ to $r_4$ and a final zone from $r_4$ to infinity that is black. The radii $r_1$ to $r_4$ are in the ratio $r_1 : r_2 : r_3 : r_4 = 1 : \sqrt{2} : \sqrt{3} : \sqrt{4}$.  The zone plate is placed in the $x-y$ plane and illuminated by plane monochromatic light waves of wavelength 5,000 $\text{Å}$. The most intense spot of light behind the plate is seen on the axis of the zone plate 1 meter behind it.  (a) What is the radius $r_1$?    (b) What is the intensity at that spot in terms of the intensity of the incident wave?    (c) Where can you expect to find the intensity maxima of the axis?	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+690	A rainbow is produced by:   (a) refraction of sunlight by water droplets in the atmosphere.   (b) reflection of sunlight by clouds.   (c) refraction of sunlight in the human eye.	[]	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	(a)
+691	A glass cube has a refractive index of 1.5. A light beam enters the top face obliquely and then strikes the sidesmall fish, four feet below the surface of Lake Mendota is viewed through a simple thin converging lens with focal length 30 feet. If the lens is 2 feet above the water surface (Fig. 1.8), where is the image of the fish seen by the observer? Assume the fish lies ofn the cube. Does light emerge from this side? Explain your answer.optical axis of the lens and that $n_{air} = 1.0, n_{water} = 1.33$.	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	v = -6 \text{ ft}
+692	A dye laser (Fig. 3.2) consists of two nearly perfectly reflecting mirrors, M, and a gain medium, G, of bandwidth $\Delta f$ centered at $f_0$.   (a) What are the allowed frequencies for laser operation in this optical cavity? Express your answer in terms of the time, $\tau$, it takes light to make one round trip in the cavity.  (b) Assume that the laser operates on all possible cavity modes within the gain bandwidth. Also, assume that these modes are all stable in phase, i.e., there are no fluctuations in phase. Also, assume that the phases are adjusted so that all modes are instantaneously in phase at $t = 0$. How will the laser output vary in time?  ( c ) If it is desired to produce a pulse of one picosecond ($10^{-12}$ sec) duration at a wavelength of $6000 \, \text{Å}$, what bandwidth $\Delta f$ is required? How many laser modes would this involve? (Let $l = 1.5 \, 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	f = \frac{n}{\tau}; E(t) = \sum_{n}^{N} \left( A_n \cos \frac{2\pi nt}{\tau} + B_n \sin \frac{2\pi nt}{\tau} \right); \Delta f \sim 10^{12} \text{ Hz}; N \approx 10^4
+693	Incident parallel rays make an angle of $5^\circ$ with the axis of a diverging lens $-20$ cm in focal length. Locate the image.	[]	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	\text{The image is a virtual point image in the focal plane 1.75 cm off the optical axis.}
+694	 An undulator consists of a linear periodic array of magnets of alternating polarity. Each repeat unit in the array of magnets has length $d$ and there are $N$ such units. An electron of speed $v \ (v \sim c)$, passing through this undulator, travels a path with only small deflections, as shown in Fig. 3.5. The motion of the electron along this path produces radiation which is most intense at a certain fundamental frequency corresponding to a wavelength $\lambda$.  (a) Indicate for which parts of the path electromagnetic radiation in the forward direction will be generated.  (b) Find the wavelength $\lambda$ using the condition that this forward radiation from successive sections must interfere constructively.  (c) If the undulator consists of $N$ sections of length $d$, what is the spectral width $\Delta \lambda / \lambda$ of the radiation produced by a beam of mono-energetic electrons?  (d) How does the intensity of the forward radiation produced in the whole undulator compare with that for a single section?  (e) If the velocity of the electrons differs from the speed of light by 1 part in $10^6$, calculate the wavelength of the radiation produced by an undulator with $d = 10 \text{ cm}$.	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	\text{Electromagnetic radiation in the forward direction is generated where the tangent to the path is parallel to the axis.}; \lambda = d\left( \frac{1}{\beta} - 1 \right); \frac{\Delta\lambda}{\lambda} = \frac{1}{N}; I \approx N^2; \lambda \approx 1000 \, \text{Å}
+695	Incident parallel rays make an angle of $5^\circ$ with the axis of a diverging lens $-20$ cm in focal length. Locate the image. *(Wisconsin)*	[]	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	1.75 \, \text{cm off the optical axis}
+696	The first free-electron laser (FEL) was operated in late 1976 or early 1977.  (a) What does the acronym laser stand for?   (b) What is the output of a laser?   ( c ) How is the output produced in the FEL? (How is energy fed in? How is it converted to its output form? etc.)   (d) Identify a particular advantage of the FEL over previous types of lasers.	[]	/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGQAZADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD3+iiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigD//2Q==	\text{(a) Light Amplification by Stimulated Emission of Radiation}; \text{(b) A highly coherent, both in space and time, and highly directional beam}; \text{(c) A beam of high energy electrons passes through a transverse, undulating magnetic field; the electrons suffer transverse acceleration and deceleration and electromagnetic radiation is produced by Bremsstrahlung. The initial electromagnetic waves may also be provided by a laser. If a synchronism condition exists between the electron velocity and the phase velocity of the waves, energy may be transferred from the electrons to the waves. The waves are built up in the cavity between two mirrors and finally a laser output is produced.}; \text{(d) FEL is tunable, allowing coherent radiation production at any wavelength from microwaves to visible light and beyond. It can provide high peak-power, broadband, and coherent radiation.}
+697	 A He-Ne laser operating at 6328 Å has a resonant cavity with plane end mirrors spaced 0.5 m apart. Calculate the frequency separation between the axial modes of this laser. Estimate whether this laser would operate at one or at several axial frequencies given that the linewidth of the Ne 6328 Å line observed in spontaneous emission is typically 0.016 Å wide.	[]	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	\Delta f = \frac{c}{2 \times 0.5}; \frac{\Delta f'}{\Delta f} \approx 4
+698	 The index of refraction of glass can be increased by diffusing in impurities. It is then possible to make a lens of constant thickness. Given a disk of radius $a$ and thickness $d$, find the radial variation of the index of refraction $n(r)$ which will produce a lens with focal length $F$. You may assume a thin lens ($d \ll a$).	[]	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	n(r) = n_0 - \frac{r^2}{2dF}
+699	 Sunlight is normally incident on the surface of water with index of refraction $n = 1.33$.  (a) Derive the energy reflection and transmission coefficients, $R$ and $T$. $(R + T = 1)$  (b) If the incident flux is $1 \, \text{kW/m}^2$, what is the pressure that sunlight exerts on the surface of the water? Be careful: part (b) may not follow from part (a) as directly as you think!	[]	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	R = 0.02, \quad T = 0.98; p = 3.34 \times 10^{-6} \, \text{N/m}^2
+700	Estimate the intensity of moonlight on earth. (a) In watts per cm$^2$. (b) In photons per cm$^2$ per second (in the visible range).	[]	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	3 \times 10^{-6} \, \text{W/cm}^2; 7.5 \times 10^{12} \, \text{cm}^{-2}\text{s}^{-1}
+701	 Explain the physical principles involved in the following phenomena:   (a) the blue sky   (b) the red sun at sunset   (c) the rainbow   (e) the twinkling of stars.	[]	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	\text{The sky appears blue due to Rayleigh scattering, where shorter wavelengths (blue) are scattered more strongly.}; \text{During sunset, sunlight passes through more atmosphere, scattering blue light out and leaving a red appearance.}; \text{A rainbow is formed when sunlight is refracted by water droplets, with refraction varying by wavelength.}; \text{The twinkling of stars is caused by random fluctuations in air density.}
+702	 Describe briefly how a photomultiplier tube works. Can such a tube be used to distinguish between two photons whose energies differ by 50%?	[]	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	\frac{\Delta N}{N} \approx 2 \sqrt{\frac{2 \ln 2}{5^{10}}
+703	A typical molecular gas shows absorption bands over the entire electromagnetic spectrum from X-rays to radio waves. In terms of atomic and molecular structure state the absorption process responsible for absorption bands in the following regions of the spectrum: - (a) X-ray, - (b) ultraviolet and visible, - (c) near infra-red, - (d) far infra-red and radio.	[]	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	\text{X-ray: Removal of an electron from the inner shell of an atom to an outer shell or out of the atom.}; \text{Ultraviolet and visible: Transition between the energy states of an orbiting atomic electron.}; \text{Near infra-red: Transition between the vibrational levels of a molecule.}; \text{Far infra-red: Transition between the rotational levels of a molecule.}
+704	Choose proper values from the given values below:   (a) The critical angle of total internal reflection in water is    5°, 20°, 50°, 80°.    (b) Energy flux of sunlight at radius of earth's orbit is    $$10^6, 10^2, 10^{-1}, 10^{-5} \text{ watt/cm}^2$$.    (c) How many electrons per second flow through the filament of a light bulb?    $$10^{10}, 10^{15}, 10^{19}, 10^{25}$$.	[]	/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGQAZADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD3+iiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigD//2Q==	50^\circ; 10^{-1} \, \text{watt/cm}^2; 10^{19}
+705	On a clear day the sky appears blue because of: (a) reflection from the sea,   (b) density fluctuations of the atmosphere which cause scattering,   (c) cobalt vapors in the atmosphere.	[]	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	b
+706	 Give a description, including the physical principles involved, of the following optical systems:   (a) A lens or mirror arrangement for converting a 10 cm diameter spherical 1000 candle-power light-source into a $10^6$ beam candle-power search light. (Neglect lens or mirror light absorption.)   (b) An instrument capable of producing circularly-polarized light and of analyzing light into its circularly-polarized components. (You may assume that the light is monochromatic).   (c) A system (in either the visible or radio-frequency range) for estimating the size of a distant (stellar) source of radiation.	[]	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	\frac{\theta_0}{\theta'} = 31.6; h = 1.22 \frac{\lambda}{\alpha}
+707	"(a) What is meant by  - (i) the Doppler line width, and    -  (ii) the natural line width of a spectral line?  (b) Describe an experiment for making ""Doppler free"" measurements of spectral lines. (You need not be quantitative, but your answer should make clear that you understand the basic physics involved.)"	[]	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	\text{Doppler line width} \propto T^{1/2}; \Delta \nu = \frac{\Delta E}{h} \sim \frac{1}{\Delta t}; \text{Doppler free if }\mathbf{k}_1 = -\mathbf{k}_2
+708	Estimate the efficiency (visible watt/input watt) of 2 of the following light sources: gas light, incandescent bulb, light emitting diode, fluorescent tube, mercury or sodium arc, laser.	[]	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	0.02; 0.09
+709	 Consider the earth's atmosphere (consisting of $O_2, N_2, CO_2, N_2O, H_2O, O_3$ etc.). Discuss whether the atmosphere is reasonably transparent or strongly absorbing for each of the following frequency regions. If absorbing, say what are the most important mechanisms.  - (a) $10^8 - 10^9$ Hz. - (b) far infra-red - (c) near infra-red - (d) visible - (e) ultra-violet - (f) X-rays - (g) $\gamma$-rays	[]	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	\text{Strongly absorbed by } O_2, H_2O \text{ and } N_2O; \text{Strongly absorbed by } CO_2; \text{Strongly absorbed by } H_2O; \text{Transparent, but some absorption by } O_3; \text{Strongly absorbed by } O_3; \text{Transparent}; \text{Transparent}
+710	Sunlight travels to earth in approximately: - (a) 1 hr - (b) 8 min - (c) 8 sec	[]	/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGQAZADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD3+iiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigD//2Q==	8 \, \text{min}
+711	In a compound microscope the focal length of the objective is 0.5 cm and that of the eyepiece is 2 cm. If the distance between lenses is 22 cm, what should the distance from the object to the objective be if the observer focuses for image at $\infty$? What is the magnifying power? Answer within 10%. Derive all necessary formulae from the lens equation $\frac{1}{p} + \frac{1}{q} = \frac{1}{f}$. Normal near point of eye is 15 cm.	[]	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	p_1 = 0.51 \, \text{cm}; m = 290
+712	The width of a certain spectral line at 500 nm is $2 \times 10^{-2}$ nm. Approximately what is the largest path difference for which interference fringes produced by this light are clearly visible?	[]	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	3 \times 10^{-4} \, \text{cm}
+713	A $\text{TiO}_2$ film of index 2.5 is placed on glass of index 1.5 to increase the reflection in the visible. Choosing a suitable value for wavelength, how thick a layer in microns would you want, and what reflectivity would this give you?	[]	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	d = 0.055 \, \mu m; R_{\lambda_0} = 0.376
+714	 Monochromatic light of wavelength $\lambda$ is normally incident on a screen with a circular hole of radius $R$. Directly behind the hole on the axis the intensity of light vanishes at some points; how far from the screen is the most distant point at which the light vanishes? Assume $\lambda / R \ll 1$.	[]	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	\frac{R^2}{2\lambda}
+715	Find the thickness of a soap film that gives constructive second order interference of reflected red light $(\lambda = 7000 \text{Å})$. The index of refraction of the film is 1.33. Assume a parallel beam of incident light directed at $30^\circ$ to the normal.	[]	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	d = 4260 \, \overset{\circ}{A}
+716	Consider the Young's interference experiment shown in the diagram (Fig. 2.7).  Assume that the wavelength of the light is $6000 \text{Å}$, the slit widths are all the same, $S_0 = S_1 = S_2 = 0.2 \text{ mm}$, the slit separation $d = 2.0 \text{ mm}$, and $L_1 = 3.0 \text{ m}$.  (a) About how long must $L_0$ be in order to produce a well-defined interference pattern on the screen? (b) What is the distance between the central and first bright fringe on the screen?	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6tBpGpOTo6xsfGrr746cuTI+Ph4sKMBdJNEIikoKFDe18Bms728vFgslsYF9MbGxrKysoKCAgqFQqFQbt26RRZAUZRsakVFRVlZWUJCQk5OjpOT09y5cz09PX18fMAmCLKYRCK5c+dOXl4eQRA4jqelpZFvnpGRkXJhFVQ62dB1nQwqbXTlVulER2AES9/0AXQF8vJFsCCEEs/pEKwBHHfU1NS0bt06Z2dnctcvg8FwcnJatGhRfX09hmGnT5/28vKaMWNGYWEh+e8lJSXz5s1zdnYeOXLk5cuXu7q63nrrLZWUCxwO58cff5TJZARBlJaWzpkzR2U0GBsbv/POOyCHMo7jFRUV7777rvP/MmzYsG3btoG8QsooFIqCgoIFCxY4ODjQ6XQGg6EcgWttbd3S0kIQhFwuT01NDQsLI7fAIQhibm7u6+t7+PBhqVRK3lF1dfX777+vHoeLIAiVSl25cqVcLu/9ZC/tzxXTE30wz9bSqGsspo2u8cZ70tUb9kxd43UHpqsfgfZMXYeNGUBXaHwXBk0fkkGrj6ZcIpF89NFHGtPDoyj6888/8/n8+Ph4BEFoNNprr71WXV1NEER7ezt5FCGNRtu8eXN7e3t8fLz603716tXd3d3FxcUzZszQuF+ATqd/8cUXUqlUJpPt3btXYxkGg7F69erm5mbyruVy+cWLF/38/Hrag0Ca8tzc3NGjR2ss4+Tk1NzcDPqhvb39/fff7ylNPpVKXb16tXrnq7wLQ26CdaUP5qdCo66xmDa6xhvvSVdv2DN1jdcdmK5uvJ6p67AxA+iKwTHZPelDMmj1LoKFIIgnT578+uuvIAuaCsCjwmKxhg8fnpSUJJVKExMT3dzcpk2bdufOnStXrgDHtLW1dVBQkImJydKlSzMyMp4+fUr845SwtbUNCgqiUqm//PLLlStXVNJBACgUClhObGlp+fvvv0lnN5VKRVEUvGEymeznn3+2sLDYtm0bSOxQXFy8b9++wsJCBEFoNJqXlxeYdJeUlDQ1NZGVi8XiP//8MycnR+N1R4wYAUJc5HL5wYMH//Of/4Crs9ls8PUCZILWooMhEMiLiPqzhVB73Gmp9+vZIhKJFi1apNFxRqPRtmzZ0tnZieN4UVFRbGwsCCtkMBgmJibk7NXS0nL79u0gU75EIklISCCTajIYjC+++KKrq+vx48fKB1YpQ6VSFy5cWFFRQRDE7du3QXoHBEHAg2H9+vXz5s0zMjICIo/Hy8jIwHFcLBZv3rwZzMepVOqyZcuysrI6OzsbGxuXLFkCCoNZeWZmpru7u8ZLe3t7JycngwRvYrF4+vTp5KV37Nhx69at27dvr169mmwnnJUPpq6xmDa6xhvvSVdv2DN1jdcdmK4+D32mrsPGDKArBjab1pU+JINW7yJYMAxrbW1VqQ1BEAsLiylTpmzYsAEkrvTy8vr888+bmppyc3NlMhl5FLeZmdmePXvmzZsHjoNiMBiRkZH29vbV1dUIgjg5OcXHx3O53KqqKnItVBkGg/H666/v3r3bzc2NIAgMw8hk9q+99tqhQ4dMTEzKysoKCwvBtLqqqio7OzswMBDHcZAaArThk08+cXFxQRCETqeTudxAp4tEora2NvXr8ni89evXT5gwATzGmpubQTEKhTJ58uSNGzcaGxtjGPbo0SPwLyiKMplMlW5UoadXDVQf8KDSla6x2ID1vt/4gPWerjsIum4r729XqL80yPrgD059jGBB1PD29t63b9/EiRPBKiJBEBQKJSQkZNWqVRs2bCBjDREEiYiImDt3rrGxscYFbjqd3lOWSxRFbW1t586du2HDBuXU+CTBwcFcLhdFUTqdTnrDlWMNSSgUCiip8SoaxTlz5uzcudPFxQUEXOI4np6enp+fD2qztbU1MTFRGTocDic6OvqZoQvqrxqoruWg0l5XbpVOdARGsPRNH0BXIC9fBIve+crV8fb23rt3b3x8PI7jCoWCDPpGUdTDw0PFNLu6uqqvE5KdTqFQVAwiqYeEhOzYsSM6OppOp5MnCiq/W+QeURBiqP57T5B2X2NJBoMxY8aMzz//3NnZGXxBA2/V06dP+Xw+KEMQBNls5SZpTEEHgQwh5FqOVCotLS2Vy+VUKtXc3NzZ2ZnL5YJz2oa6jS8m+m7KXVxcwHFQtbW1N27ckEgksbGxPB4P2LuioiLStQJQKBQqxppKpfJ4vHv37iEIUlVVdfny5Q0bNqiYYHd393379o0ePfry5ct1dXWmpqZTpkyxt7dHUVR95NnZ2fn5+WVnZ2MYZmtr6+fnB+w++YwhCKKjowOk32QymYGBgXQ6XS6Xe3t7q0RGoigaHx+/Z88eKyur9PT0hw8fWltbT58+ncVigUEPjHhTU1NXV1dPmUUhED1BLBYfOHDg6tWr4PfKykowKzIzM/P19Q0NDR0zZszEiRNf1DSzQ4vemXI6ne7p6Umj0UBsCYqiVVVV+/fvT0pKevjwoUKhmDRp0r///W8XF5fMzMyff/5ZJdDlzp07+fn5wcHBpMLhcCZNmnTp0iWRSCSTye7fv9/Q0MDj8Xg8XkFBAShDo9EeP378559//ve//+Xz+Uwmc/v27Rs3bnRzc3NxccnNzVW+BFhlVf4dRVEGgxEcHAxMtlAoPHPmzIYNG6hUaktLy927d4HDHbi2raysrK2twTlbNBoNw7CrV68+efIEnIllZWXV2dn51ltv+fr6WltbNzc3YxiWmZn56NGjsLAwsBxKtoT040Mg+sDNmzcPHjyovhTU0dFRWVl57do1V1fXzz//fO7cuS/waT5DBqHEc1q17+/6bHp6+qhRo8gWstls5VOghg8fXlRUVFVVFRYWpp4zlk6nr1ixorGxUXmV+cmTJ+AcQgRBqFTqhAkT6urqvvjiC3Kei6IoGe0H/ty4caNEIuno6Bg3bhwQN23aJBaLQYWrV68Gl7axsUlKSgJnwhYWFgYHB4NZvJmZ2axZs5YvX+7v70+OWltb25aWFqFQ+Mknn5APAwqFwmazyTIoiq5bt04qlTY2Nk6cOJH8ThASEnLo0KHDhw97e3uT3fLNN9+od77Ku6B9IISe6IMZDKBR11hMG13jjfekqzfsmbrG6w5MV4/ZUNcVCsW2bdvAjJvJZDo7O7v+g5OTE/lRHT58eH19fb8aM4CuGFjkia70IRm0/z+/h14hl8tTUlKCgoJUnBs0Gs3b2/v3339XKBSnTp0C8dcoivr5+b3//vvu7u6gPIvF2rdvH9gzCZBKpV9++aWpqSmox8TE5M8//2xqalq7dq3KQa40Gs3c3DwuLi4tLQ3H8Y6OjrFjx4KXJkyYAOIgcRxfs2YN6Uz/7rvvwJZLHMcPHTrk5+fX04zD2dkZbP/p7Oz8/PPPyfaQRpzFYs2ZM6eyshLHcQzDkpKSlLMe0mg05W+mVCp1zZo1g/3eQCA9UFNTM3HiRDAyFy9enJ6envEPN27ciIuLA+PW3t4exO9CdIs+zspBy27cuBEcHMz6Bysrq2XLll25cgXY6OTkZHNzcwqF4uHhcenSJalUmpycTM7lJ02axOfzlVvV3t6+efNmMA339/cvLi4mCKKjo+PYsWOhoaHm5uYcDsff3//tt99OTExsbGwEPvfOzs74+Hjgtp47d65QKAS1HTt2DBhZe3v7K1eugFk5QRBisfj+/fsffvgh2OnDUsLS0vLTTz+VSqWgZEdHx9atWy0tLckCo0aN2rVrV1lZGbh9giAEAsHatWsdHBw0rpcymcxvv/1WvfNV3gX1Vw1U135QaalrLKaNrvHGe9LVG/ZMXeN1B6aTrepFT0lJAR8KZ2dnkCmIBMOw//znP2Dc+vj4NDU19asxA+gKje/CoOlDMmj11GOFomhkZOR///vfmpoaoHC53JCQEDIYMTQ0dNOmTUKhcPLkyUFBQQwGY/z48du2bfvss886OzvHjBmj7JNBEMTc3HzLli2Ojo7FxcVxcXFeXl4IgpiZmS1atCgiIqKqqkoqlbq7uzs7O5Pbf8BFd+3aFRQUxOfzZ8+eTUaMzJo1S6FQPHr0aNy4cTExMaSpZTKZr7zySnBw8NKlS6uqqgilBVgOhxMSEkL6cMzMzDZt2hQdHU1GUvJ4PF9fXzKkCUEQIyOj7du3x8XFJSUlqazuIghiY2Pzxhtv6KCvIRBdIJPJwPrWsGHD3N3dyUUdHMcbGhr+/vtv8CdYWBqyVr64GPDZnnK5HMMwFotF6hiGdXV1KRQKNpvN5XJVWoUgiFwuVygU6tHlKvWr6DKZDMMwBoOhHKNCEIRUKlVxevReTx914n+jVnEc17hTHzhk1Dtft43RH31wBlUvunKrdKIjL1BcuVQqXbdu3Y8//ojjuLu7+/jx48mPmFQqffDgQVlZGYZhFApl6tSpZ86cUZ4wPbMxA+gKBMaVGxDqFplCoZiZmSH/jDB1gOXt6dVeLqQ+j6BQKOpJbp8HYF0U6Xm4QyBDzv379xMSEnAcRxCksrKysrJSpQCKonQ6fezYsTt37lSx4xCdYMCmHAKB6ANisfjEiRNPnz7tqQCNRnN2dp4xY8bixYtHjhw5mG17eUBxeM4vBALRApD3/8mTJwiCODg4REZGmpqakt8gCYLg8Xjjxo0bM2aMumOzq6tLJpOZmprCfUNaoo85WHSuqzRMz/Ve/JIDcHrqyU1prw/5oFLpbe115EXxlXd3d4NFTgaDsXbt2lWrVqEoqlyYSqUCF6Vy5RiGpaen79u3Ly8vb926dW+//TZIgafNLT8n33d/9SEZtNDBAoFAtKKioqK2thZBkICAgClTpmiMOFCnuLj4gw8+yMjIQBDkwIEDoaGhoaGhKmW6u7sVCgU41/c5Nf6F4RmpoCAQCKQXgJME5M+IiYnx9PTs4z82NzdXVFSA30UikXJGCkBjY+PHH388e/bsu3fv6rDBLyrwWQeBQAaOWCwGuepAbudnJgpVhug5lqyhoeHTTz/9+eefORwOmSIU0gtwVg6BQAZObW1tQkICgiDm5uahoaE62f7T3d29f//+X375Bcfx8PBwMg8SpBf07hQh8AvIekyn08nY7YHVo/7YHwQd7N8FB4FqWX9fxGfqQ9IJOtQVCkVpaWlXV5eXlxcIjdByMAxY11hswPqAO6Tvek/X1aGO4zjYigy2X/Rysyq6ei+Rn/0zZ86cPXtWJpONHTt2165dlpaWA/jgDI5l60kf/MGpdxEsGIYVFxdfvnw5KSnJy8tr4sSJrq6uRkZGnp6eTCZTuXx7e3tZWRm4oomJiZeXF5nYXqV+EnDoD51OJ/dtAgVFUQaDAbaPkjuPcBzv7OysrKwEopubm4mJCfhHMOyampoaGhpANKeFhYW7uzuFQunu7k5NTS0tLXV1dY2IiLCwsOilPRp1Qm19XKVX+6X38aL6rGdnZ69cubK5uTkkJOTzzz8PCAiAESx90VUaoI3ey5g0MjKKiIgoLCycNGmSn5+fxpvVWLlyAZCGCCipqal79uxpbm62tbVdvXo1SKsHI1gMLIKlpaXljz/+OHLkSHFxcXd3961bt86dO2dubm5iYhIbG7tmzRo3NzcEQYRCYUpKyoULF1JTU0H32dra7tq1Ky4uDphaqVQqEolwHLewsCCtNo7jCQkJ58+fnzx58rx581gsllAoPHHiRHJysqmpaWBgYH5+fmNj46JFi2bPni0QCBITE//73/+Wl5cjCEKn0728vN58880pU6YwGIyKiorExMQ///wTvIogiIODw/Lly6dNm5aZmblu3bqqqiobG5sVK1Zs3boV7m3TBqlUeuzYsSdPnhAEkZiYuHz58oCAgKFuFOT/cHR0/PHHH5ubm52dnVWSffYXqVSal5e3b9++6upqBoMxd+5ckMyO+N/5L0QzhBLPKRtc3/N7rV+/HpzkoN5OJpP573//G6TsOXLkiI2NjUp80rBhw27evAnqOXr0qLe3N4/HO3v2LJm2sL6+Pi4uDkVRe3v7GzduYBh26tQpS0tL5J985cDox8XFFRYWLlq0COQAUMbZ2fmdd9759ttvR48ezeFwVNrJZrP3zmbaHAAAIABJREFU798fExND6o6Ojvfv31e/X5WO6ik3nsbC/dW1T7A3tPrDhw+Vc81fvHhxqJLPaSymjd77u699B2q87sD0XsbkgMfqzZs3wacPQRALC4vk5OQjR464urqiKEqj0d555536+voBd4XGd2HQ9MEfnLheZUZsbW0tLCzs6uoi/vme4uTkZGxsXFlZKZfLLS0tHR0daTTao0ePfvrpp+bmZgRBgD8a9GBxcfF33303atQoMzOzhw8flpeXYxj2008/RUdHg9ybeXl5wLDy+fzKysqIiIjGxkZw4glBEBKJhMVicblcR0fHq1ev/vbbbyCJFZvNptPpEolEJpPV1tb+9NNPNBpN/Whm5B//PkiEC5S2traWlpZB68AXEoIgQL49yAtMd3f3V1999fjxY/C5Dg4O3rx5s4ODAwHn431Gj0y5QCBobm4m3zwKhRIYGLh27drs7OzGxsagoKCYmBiZTHbixImcnBwEQVgsVlxcnJubW0NDQ2JiInDIpKamTps2jazTycmJ/NInFovVY1dJvLy83nnnnbFjx1pYWHzxxRfAjltaWm7cuHHMmDEPHjxISEjIzc2VSCQa7TiCILa2tuTxFxAIpHc6OjrIh7REIrl+/Tr+TxIRLy8vGo0mkUiI57Dbk0ql0un0F+9zqkcRLCYmJuBkZCBiGJacnMzn82NjY9977z0PDw8URWtqau7fvw9GwNixY48cOWJnZ9fY2CiRSK5cudLR0fHLL7+MHz8e1MBisUJCQvqSCpHD4WzdunXBggVUKjUtLe3KlSsIglAolBUrVqxdu5bNZkdGRs6ePTs9PX3v3r0lJSUq/06lUu3t7bdv3x4TE/PDDz+ovKp8p+ot6V3vi/hMvb8X1TddGfAc7fug0q2usdiA9WfeuPZ6T9cdBL2XwgqF4smTJ999911XVxep40rJoBITE2tqalRO+NIV9vb2mzdvdnd3V2nn4Fs83ep6FMFiZWW1dOnS/Pz8qqoqUI9EIrl9+3Z6evrvv/++b9++6OhoiUQiEokQBKHT6WFhYTY2NsD3vXLlyrS0tI6OjoyMDBCRgvRnzwI4Gxq4a+RyObAXFhYWUVFRIMEsnU739vZ2cnI6f/68uikPDw//8ssvR40aRZ4joQx5p32cXKjPKVR6tV/6AGY0eqUrKziO5+bmxsfHKyepH9hgG4Cu0irtdeSFiGDpSVcXxWJxa2urVCq9cePG4cOHc3NzezL37e3tqampGl/SHnNz8/nz53t4eCBKXYfACBbdMn36dDab/csvv6SkpIBDJBAEkcvlT5482bBhw759+2g0WnV1NYIgdDodBP+Bf/T19XV1de3o6MD/N9GjNm5WIyMj8KggBxyKoioPBhaLFRoaum/fvpCQEPWxa2RkBJ4EEF0BNohDDAgcx0UiUU5Ozrlz57Kysrq7u4uLi9VPxaLT6b6+vuqxBn1HIBBUVFSQM32wygV+p1KpHA5HJBIZGRmFhoY6OTkN+Cp6i36ZciaTOXXq1HHjxmVkZKSlpd25cycnJwccjpyfn7958+YPP/zQzs6uq6sLw7DKykocx0HYSWtra0dHh0ptYFI/f/58cIwc3s90vgKBoKmpCcfxntxq9vb2q1atmjdvnru7u8bK3d3dwcMfohMoFIr6UX8QvQVs2sjMzDx9+vTVq1cbGxt7Wmei0WgzZ87cvXu38rnkCILgOA6O/eqLa5vP5584ceKLL74QiUQ0Gm3BggVLliwBL1GpVDabLRKJTExMXF1dgUF4wdAvU87n81NSUlpaWpycnD788MPFixd/++23P//8M5iL1dbW1tXVWVlZlZaWSqXS7OxshUJBoVAEAsHFixfBKaDe3t7koxjH8QcPHhQWFo4ZM0YkEpFO9t4hNxC1t7dfu3Zt7NixHA6npaUlMzOzqamprq6OLBkWFvbuu+/S6fSMjIzExESCICwsLBobG8kCKIqSUe2QgaGSxhpmyDMIhEJha2vruXPnUlNT8/LyyJ10JCwWC/9nmyiCIK6uruvWrQMn7pLI5fLExMSLFy/OmjVr+vTpGh0ayiKHw6FSqSC0gUKhODs7R0ZGqpRHNLmDXgz064Px008/7d27VyKRGBsbjx8/3sjIKDU1lfxOHRER8eabb1pYWOTk5HR3d6elpX355Zf+/v6pqanHjh0jCILBYLzxxhtcLhe4yDEMKy8v/+qrr958880nT54cPXq0J9+cMn5+fuHh4ZcvX0YQ5NSpUy0tLQwG4+bNmwKBAMwyyJI3btz44IMPOjo67t2719nZSRAEjUZTPoezq6tLeWEHMgB8fX19fX3JrVgQfUahUFRXVxcUFJw7d+7mzZsdHR3qDjFTU9OAgIDo6Oiurq6ffvoJLH05Ozurf3+9ffv2xo0bKysr8/LyfHx8yO0FPUEQhEQiIZ8ZEokEw7CXZy6lRxEsCII0NDQAF7lYLP7111/J2phMppub27x586ysrCZOnBgUFHT37l2BQPDpp59SKBS5XI7jOIVCCQoKioqKolAoEydOPHv2LJhBX7x4MSUlhcyODwBPZvL5TP5CEISpqel7772Xl5dXWVkpEAh+++038r8oFIqHh4eLi0tqaqpCoQABM//XlTSak5NTU1MTab7lcrlMJlO+U/VnSe96X8Rn6v29qF7pIpFI/btU74MKlBeLxSiKMplMCoUCVjj6OAh70TUWG7De+43rRO/pujrUMQzDMKy5ufnhw4fXr19PS0srLy8nd4cgCEKhUIyMjFgslqenZ0xMzMiRI8PCwqysrFJTU0+ePAlMOSimXD+fzz979mxFRQWNRvP19bWystLYq8oiQRCkHVcoFHl5eXw+39zcXKXxemXxdKjrUQQLgiAzZ85samoqLS0tLi4m578mJiYLFy5csWKFt7c3lUrl8XhffPHFpk2bHjx4QJZhMBjh4eG7du3y8fFBUTQyMvKjjz767LPPnj59imEY2AdE4uDg4OnpiaKoh4eHra1tc3PzsGHDgJMORVEajRYbG7t37969e/fm5+cDu4CiqKmpaWRk5Nq1a52dnX/44YfTp0+3traCoYOiKIvFmjt37uLFi7du3frgwQNwIQsLCwsLCxjBQhBES0uLQqGws7NDUbRf9QgEAoFAoHJrPQ0qmUxWUVGRmZnZ0dGRm5vb1tYWEhLi5OQUFRXl5OQEnDMDHpwqva29jhh4BAuYqdy9ezcjIyMpKSk/P18oFCo/dykUioWFRUhIyLJly9zd3V1dXc3NzWk0GniystlslaAAsn6RSHTw4MELFy4AH/quXbvA56j3W8ZxnDweGvze3NyskgQJ0WmkSk963weVDnX9crCEh4ePGDGiubm5uLiYfNqYmJgEBQUZGxsDhUKhjB079ttvvz1x4kRtbW1GRoa9vX1ERMSSJUtGjhwJbozFYr311lvGxsZHjhzJzc0Fq6OhoaHu7u5UKnXy5MkREREoik6ePPnrr79+9OjRzJkzeTwe2QwqlTpr1ix/f//ExMSKigocxzkcTlRUVFRUFBgZu3btmjRpUnp6+qNHj7Kzs2NjY2fMmBETE4MgCI/HI0058uI65vpFU1PT9u3bKyoqtm3bFhUV1a/vvA4ODra2tn0p+eTJk0OHDt2/f7+qqor8BvbHH3+wWKygoKC5c+cuWrSI3CkOGTBSqbSrq0sgEBw9evTx48c5OTkNDQ3kqxQKhclkOjo6hoWFubu7R0dHe3l52djYkF+MyE+Em5ubm5ub8uITgM/nf//99wcOHBAKhWPHjt25cyePx+vjsufDhw/JPxsaGurr6319fXVwz4aAfplyBEFMTU1BmkPkf585ymVQFA0ODh42bBiGYWKxGCxPqyRKZrFYCxcufO211zIyMiorK7lc7qRJk7hcLoqi5II4i8WaN2/ezJkzGQyGctAhgiA0Gi0gIMDHx0ehUIBmMBgM0gYZGRlNmjRpwoQJCoVCJBKx2WwOhwNcPSNHjjxz5szz7iUDgiCIrKyshISE1tbWKVOmRERE6Nx9SRDE48ePN2zYcOfOHQzDVF6VSCTp6enZ2dl8Pv+jjz7SSULtlxO5XJ6RkZGSknL27NmWlhaBQKAcU0ihUKytrYODg2NiYl555ZVRo0ZRKBQWi9VTbXQ6Xf1oZgzDjh079tVXXwmFQn9//+3btz/TRU6SnZ2t/FB52dA7U9532Gw2QRBGRkY9WXwqlWpmZhYXF0cqyt+DyDKgHo2XoNFoYLOoxkkBSNDM4XBU/oX8HU7JAaampiCCsL/xoIBnbvKqqqraunXr7du3CYKg0WgODg5BQUFjx47t7u5OTk5+/PixWCwmCILP5/f0RkN6giAIqVTa1taWl5d39erVhISEuro60osCHJJsNpvH473++uvjxo0bOXIkmaKuX1dBEEShUCQnJ//444+dnZ2mpqZr166Ni4vre2ZEhUKh/CAnXrLsPQZsyvUcFEVtbW1hhlsURY2NjUE26gE821AUNTMzo1Kp6tNtAI7j6enpwI4jCBIQEHDw4MFRo0aBb2CLFy++dOlSUlKSv7//ypUrwTZRbW/ppUEsFj98+PDatWtJSUllZWVgPwfpEabT6aNHj46KioqOjubxeA4ODqQfvC+dTBAEWaytra21tTUzM3PTpk1FRUUcDmfdunVz587t1/FyKnR1dV2/fj0yMvIl2aYHTfnzgkqlOjs7kwvoLzNubm6urq5tbW0gTVK//pcgCBBV1lMBFEVBQDGCIBQKJSAgIDw8nEajge9SPB5v3bp1S5YsMTEx6eXLPoQELGamp6dXVVXl5uYmJCQ0NTWR8QVUKpXJZFpbW0+ZMiUqKmrcuHEODg4D85gJhULy0M6Kioovv/zy3r17hYWFYHfPunXrTE1N+/XcLS8vV44VBkmctmzZAk05RCsUCsWjR48aGhocHR2Hui1DD4qi4EgmsHmvX/+rMbONcs2urq5WVlYgAK6srKyoqGjYsGHkNwAqlWpjY6NsFORyeUtLi1wuNzMze045mwyR1tbWysrK1NTU7Ozs1NTU9vZ2DMNIb7iJiYmNjU1YWFh4eHhYWJibmxt5qtfAMDY2Jju/u7v75MmTIHtSXFzcxo0bB7CDPzc3VyUfQC+ZUF88oCl/jqg4715aqqqqQIq0nvZta4mxsbGFhUVlZSVBEBkZGf/6178mT548duxYBwcHHo+nMmeUSqUXL178z3/+I5FIRo4cuXXrVldX1+fRKoOAIAiBQFBeXl5UVHTq1Km8vLzGxkbSxUylUkE8uKen56xZswICAjw9PZV9hlp6q5T9J2BshIaG7tmzp+9Lncqof9YEAkFZWdmYMWO0aaShAE055Lmj7BXVhp687Twe71//+temTZtAPrW0tLT79+9zOBxvb+85c+bMnj2b3Ekol8vPnz+/c+fOmpoagiCePHni6Oi4c+dO7dtmWBAEIZfLq6qqSkpKLl68mJycLBAIwBmKoACFQrGyspo0aVJQUNCMGTPMzc25XO7zzprAZrPBgX8Dm+xbW1urHAuDYVhnZ6fuGqjXQFMOGSRQtbyS/QVEIqvrFApl5syZ5ubmJ0+evHXrFp/PVygUAoEgKysrJycnMzPzyy+/BFPvjo6OEydOgOSaCILIZDL1uOYXGBzHxWKxQCC4fv36jRs3srKynj592traShZgMplGRkYuLi7Tpk2LiIgYN24cl8tFtJ599wUul7tkyZJZs2Ypf4tSKBTZ2dn5+fmjR48ePnx47yZ+xYoVJSUl165dA98qfHx8Nm3aFB4e/rxbridAUw4ZJExNTT08PLQJKjc2Nu4pp525ufnrr78eGxv75MmTY8eOlZWV5eTk8Pl8uVx+4cIFZ2fnzz77DISNgvw8AwuLNGj4fH5mZubJkyfv3r3b1NQklUqVPRKOjo4BAQGjR4+eN2+era2tsbHxIGegjI+P37lzJ9iCR/Lo0aOVK1eWlpbOnDnzyJEjvceD+fv7Hzt2bMuWLcePH2cwGLt27Zo5c2Z/F2YMF/3KwfL8dJWGPT9dvZhyyf7W3xfxmfrgd4LGN4XD4dja2qrE9felHuU/NXYm+YuRkdG4ceNCQkIEAsEff/yxc+fOxsZGgiDu3r0rlUrZbLaZmdmmTZtEIlFKSor6VZ45qHoqPzD9mTeuvY7jeGdnZ2lpqVAoPHPmzPXr12tra8lXqVQql8t1cXGJj48HqY2UvSh9HJM96f0qbGNjM2PGDGtra+VXKysrv/nmm4KCAi6XO2LECJVAUo23bGlp6eHhQaFQGAzGsGHDQCCTynVfVIunXzlYnpOu0rDnp6sD3Lv9qof4J25XpaqeLte7PvidoK6DX0QiUWNjI5livo/1KCttbW3t7e1gGzd4VSaTlZWV2djYkNtSCIIA0XKzZs06c+YMyDlMpsphMBjjxo3bvHlzUVERuTOwj4NKpVXa64imXCs96f3qcLDezufz09LSLl26lJiYqFAohEIhOQ1ns9keHh6jRo2aOnVqcHCwi4sLGY6icTj1MiZ70vs1Vv38/CIjI5X9b2KxeP/+/RcuXGAwGGvXrn377beVPfV9HDPk72R5RKe5VnrSh8TiQQcLZJDg8/kgoc2AfSxNTU319fWjR48Gf+I4fuHChf3797u7u3/44YehoaFkyZaWlj/++KO4uBhBEBRFPT09yf36KIpaW1ur7NF9McBxvKOjo7m5+fTp03l5ea2trSA7IHgVRVEWi2VpaTl+/Php06aNHDnSzc1NT2KuURRVttQikej48eO//fabXC6fP3/+unXr4P6MZwJNOcRgsLa2tra2Jv/s6Oj47LPPCgsLHz9+3NDQsH79ek9PTwqFUlFR8euvvyYnJ4PoBUtLy7lz5+qJzXpOiESirKys+vr6H374oaioSCU7CoIgVlZWPj4+kydPHj16NLmYObBAkeeNXC4/evToZ5991t7e7urqOnPmTN3G/kul0paWFhaLZWVlpcNqhxxoyiEGg0AgEAqFygp50EdGRsayZcvs7e2pVGpdXR154gGXy509e/bEiRP102xpg0KhAFn479+/f+XKlcuXL3d2dpL58ZF/XOEODg6vvvpqbGxsQECAk5MT6cRQcfXqCSCW9PDhw21tbe7u7rt27Xr11Ve1DHxSRqFQ/P777z/88IODg8Pnn3/u6ekJ9Orq6jNnznR0dMTFxcXGxurqcoMJNOUQg0EsFivv3+NwOOvXr798+TJY1ZRIJGS6agRBqFSqtbX122+/vXTpUpUt4CwWy6A38RME0draev369d9//72urq68vBzEX5IFgBNp+vTpr7/+Oo/Hc3V1BUdwDGGb+0heXt7mzZvLysrs7e337t07Y8YMBoOhw6dOaWnpt99+m5GRgaKoj4/Pxx9/zGaz6+rqNm/enJCQoFAoCgsLg4ODDdGfA005ZPDofQt+f2Gz2atWrYqPj3/8+HFdXd3169fT09OBRbOxsVm0aFFYWFhISEjvrhXDynnb3d39+PHjzMzMa9eu3bt3j/SDI/+4whkMxogRI0JCQiZPnhwWFsbhcPqyOK8PEARRX19/8ODBjIwMCoUSExMzc+ZMnW9Kqq2tLSoqApc7depUaGjo8OHDt2/ffvHiRZA2QCgUdnd3Q1MOgfRGcXGxVCrVbaivk5OTs7MzhmFLliwRiUTAcqEoamJiAiKj1ed04AwzBEG4XG50dLQOG/OcUCgUT58+LS0tTUhIOH36tFAolEqlZGg8m822sbEZNWoUyFA4ZswYIyMjw1obkEqlqampJ06cSEpKQlE0Li5u165dIL+0bi8UGBgYHBx88+ZNBEGqqqrWrl1rbW398OFDuVzOZrMnTJjw7rvvOjg46PaigwM05ZDnCIZhra2t+fn5wKktEomam5ufR+JfKpXK4XC4XK5yeFZPhZ2cnFxdXQsLCxEEAQuAegiw1DKZrLS09Lfffrtx40ZFRUVbW5tyghRTU9Pg4ODp06eHhobyeDyV/TUGRF5e3po1axoaGlAUDQsL++STTzRu6+0LNjY2vYRImZmZTZ8+/c6dO6Aby8vLwQngTCYzKirq3//+N7iufi4k9A405ZDnSElJyQcffHDv3j1wPmdycvK//vWvrVu3hoWFDeFR6I2NjSDeXG+pra3NzMxsaGioqKi4evVqZWUlucCLoiidTvfw8AgPD4+IiJg6daqxsbFuHcqDT1dXFzjc3NHRcffu3cHBwQOuKjo62tPTs66uTqNbiU6nz5w58+zZs5mZmaSIouiiRYvWr1/v4uIy4OsOOdCUQ54jNTU1t2/fJk9Vl0qlycnJPB4vJCRkqCK7FQrFlStXSktLh+TqvQAyyj59+jQ1NfWXX355+PChsisc+Sdvwfjx42fMmDFs2DBfX1/wODRoI64Mg8GYMWPGmDFjtHnM29raRkRENDU1OTk5aSxgYmKiEt3o6uq6fPlyf3//AV9UH4CmHPIccXBwsLe3LysrIxUURcGx60PVJLFYfPv2bd0uwGpPa2sriClMS0urqqoCTn/wEoVCcXBwGDZs2Jw5c6ZMmdJLIhqDhkqlLlmyZPPmzSrPeIFAwOfzLS0t2Wx2X9Zvc3Nz09LSTExMyO8xKrS2tqo8I0NCQsh9Z4YLzMGiY129mHLJ/tbfF/GZ+uB3Aqnb2dl5eHiUl5crBzsHBQWprGj1Uo/K8Yzg86nNYADPEqCbm5uDs2H7WI/GYgPTMQzDcbyqqqqxsTErK+vGjRtPnjxpaGggy9BoNAsLCx6PB87rCQ4OJg8K7+9oHBK9X4UpFMorr7yyZcsWBwcH5QL19fUHDhy4d+/ejBkzVq9erbyW29Mt37p1q7Cw0MjIqKWlxcbGRrm8QqHIy8v7+uuvnzx5ovwvIpFI/UQUg7N4MAeLLnV1QDRFv+ohLY5KVT1drnd98DtBWbe2tvb3909JSVE52Fdj/gqN9VRXV4NjKxAEwXG8rKxMLpcD1/DABoORkdH69eu7urqePn26ZMmSoKCgPtaj0tsD1hUKRV1dXVpaWm1t7blz56qqqqRSqUwmIxPF0Gg0Ozu72NjYpUuX+vj4WFhYUKlUcFrxAEajTvRexmRPer8u6ubmtmvXLnd3d+VXm5qaPv3009OnTxMEMWXKFOVh00tXgG7EcVz5VdDOmzdvbtq0KT8/X2V+AM4vjY+PV04lhsIcLBCIMiq+FFdX134FJ5CpshAEsbKyAjN6LZsUGBh45MgRqVRqa2s7OHHlBEGAnZl1dXXnzp27fv16fn4+uSUVwGQy7e3tX3311YiICC8vLy8vrwEcimaguLi4jBo1Stk4NjY27t69+9ixYyiKLl++fNWqVVq+U3fv3v3www/BfJxOp4NvY3w+nyCIp0+fHjp0KDQ01EDDEAHQlEMGFRMTk365epVdw46Ojl5eXjpphq2trfJM6rnS0tKSkZEB9tZLJJKuri6VBCkgV/iYMWPmz58PdmZSqdRBaJj+oLIZtampaceOHSdPnlQoFGPGjHnvvfe0j7PMzc0tKSlBEITNZi9evPidd96RSqUbNmx48OABgiD5+fnt7e3QlBsGBEFgGEahUPqyeALRFSq9bWRk1K/pFYVCmTBhwoMHDyQSSVBQkHI6Lb2FIAipVCoSifLy8pKTk7Ozs+/evSsWi5XPu6DT6ba2toGBgRERESEhIWSu8JfKggNoNJqvry8ZVSKTyY4dO3bq1CmpVOro6LhmzZrhw4drf5Xo6OiYmJj09PR58+bt3LnTxsZGoVB88MEHH330UWtr65gxY8gvfwbKS2TKHz9+DJa2J0+ebBAW4cXAy8uLwWAA7ySVSvX19bW3t+/7v6Mo+uabbwYFBREEwePxTE1Nn1tLdQCO43V1ddXV1UlJSXfu3CktLW1pacFxXNmIm5mZ8Xi80NDQ+fPn+/v7czgcOp3+Mk8vcByvqanp7u4G1jwnJ+f8+fMSicTW1nbHjh2vv/66TjrH19f38OHDVVVVfn5+wGrTaLT4+HgPDw8+n+/u7m5nZ6f9VYYQAzblEonk/v371dXVYWFhZIaznhCLxf/5z39+/PFHLpf73XffLVy48OU5KWpoGTFiBJPJJIP/6HR6f6OGuVxueHi48gqP7lupNWKxmM/nX7x48cyZM9XV1U+fPlVeW6NSqQwGw9vbe+zYsZMmTRo5cqSdnR2Lxerj4vmLDUizDhZ+c3JytmzZkpuba21tvWPHjuXLl+tw+76Tk5OTk5Nyb9PpdDBLQPQ15W/fMVRTLpfLjx07tn///ubm5hkzZhw5cqR3D2x+fv6ff/5JEIRMJpPL5QaRJe7FwNbW1snJqaOjA0EQOp0eEBAw1C3SMWVlZQUFBX///XdiYmJTU5NYLFY2PZaWlhwOJzw8PDIyMiIiwt3dHcRH6+cDaaiwtLSk0+lPnjxZu3ZtWloaQRDz589fsWLFEO4/MDgMtafkcnlGRgYIU0tNTZVKpb2Y8u7u7uPHjz99+hRBEDqd7ujoOIS7xl8YgNNAffFQoVCArNlgmkOlUkkvJIqiAoEAbOJnsVjkA1VlckrWprdvU3d3t0AgSE1NvXv3blpaWnFxsbIrHMzBnZycvL2933zzTRcXF19fXw6HY+jzvucElUql0+k5OTm7d+++e/cuiqLBwcFLly5VOcwT0juGasqVUT44XB2CIG7fvv3nn3+CT5qrq6utre1gNe3FhCCIkpKSJ0+egKejCvX19VlZWaR7AcOwvLw88LtEIjl06NDVq1cRBBkxYgSPx+v965G3t3dUVNQgH/3eO0KhsLi4+JdffsnIyADHHys7Uuh0uoODAzgqevLkyY6OjkZGRuAeoVVSgcw+j2HY1atXMzIyqqurCYIYPnz4vn37Ro4cOdQNNDAM1ZRTqVRnZ2dyPiiXy3sqWV1dffDgwZqaGgRBPDw89u7dC0eJligUim+++eb06dMgBVLfIQiioaEBnI9869atZ5Z3d3f/6quvZs6cObB26gqFQiGXy6uqqu7du3clryUAAAAgAElEQVT79u20tLTKykrllUwURc3MzMaNGzd//nwfHx9/f39yXyK04D0hFArJDfR8Ph/8bmVl9d5770VFRentFzK9xVBNOZPJDAsLMzMz6+jo4PP5Z8+eff/99zWuZFZWVoIsaFQqde7cuXFxcXCUaAmVSg0MDKyrq1M2ZxKJpKKiQmUfXX+RSqWtra2k+WtsbAQ5SIcKqVTa3Nx8+/btlJSUlJSUlpYWqVSq/C2QzWY7OzuHhoauWbPG09MTxGBAR0pfsLa2trGxAamGATQabc2aNQsWLFD5hILJex9zsLy0GHAOFn9//4CAgLt373Z3dx84cMDPzy8uLk756EKweReAIIidnd2kSZN6Oo5Apf4B6+rFlEv2t/6+iM/UdX6zYAPewoULyT8JghCJRBUVFYh2G/07OzsLCwtJL7y5uXl8fPzzGDy96GD/AUgwm5CQcO/evZKSErBsS94vlUo1Nzcnj6739PRUTgLVx89I3zt8wHpP1x0EvS+Fld1rKIqGh4cvXbpUOSuOXC7Pyso6ceIEhmE7d+50dHRUqaf3D47G3w3X4vWuG3AOFicnp/nz5xcUFLS1tTU0NABHG/gc1tXVtbe3NzY21tTUNDQ0gHVwEErxXNOPqIOiKFmyj/UQhpCDhU6ng5wYpM7lckH2Ii3rj4mJUe4EKpU6aOksEARRKBTV1dU3btz49ddfs7Ozu7u7lX134ICL4ODgwMDAmJiYcePGGRsbkymu+vsZQdTWe3vRB9CxKg3QRu9lTPak9+uiCIJ4e3tv2LABeE1J8enTp9u2bbtz546Zmdn69evJvLW9dIWyhVVeSCedservjs7152TxetcN1cECWLBgQXt7+9GjRz08PMzMzM6ePVtaWpqfn19VVQUcL+3t7WTh+vr6X375ZeHChZ6enr0ElWMY1t7e/ujRI2tr61GjRg3KfUD+D40pjZ43QqFQKBTevHnz8uXLRUVFBQUFyilSKRQKl8t1dHRcuHBhcHDwiBEjHB0d+/Igh/QRU1PTzZs3T5s2TblL29raDh8+DI76nDZt2jN31WMYVlhYeOvWLalUymQyS0tLAwICXqL3iFCC9Egouya019WL6VAXiUQPHjxYtGgRCODtfVM4nU63s7PbuHHjtWvXmpubVRqM47hcLv/jjz+GDx9uamo6fPjwjIwMsFWP+F9U2kMik8m+/vpr8nJjxowB3xV6Kq9R13hFjf/eF73vjddnXaFQtLa2KhQK9fJaDqqamprLly/Pnz/f0dHR2NhYJaKGQqE4OzvPmTPn/Pnz9fX1EolEh5+R3t997TtQ43UHpvcyJgc8VltbWydMmAD6efz48WVlZcolhULhxo0bwdmB06ZNq62tVa9HuTa5XH7u3DkfHx9yljZs2LAbN26ojBmN747O9edq8XrSDXhWThCEWCw+f/78jz/+qBz91gtyubypqenQoUNHjx6Njo6eMWPGnDlzQLABjuN8Pv/vv//euXMnOJO7pqamqqoqODj4JXqwDxb9SoZTX1+fkJBw48aNuLi4ZcuWaZ/LEMMwoVDY1NSUmpp67ty57OxsgUBAKK0EcDgcKyur+Ph4T0/PwMDAkJAQsDMT6dkFDBkwVCrVyclJOUQYw7DExMQTJ06IRKJRo0atXbu2pyOBSOrq6g4dOlRcXEwqhYWFN27cGNqjBwcTAzblFRUVR48ePXHiRGNjo8oHDEVRGo1maWlpb2/f2NjY3t4ul8vJMgqFgs/nJyQkgM0dCxcu9PHxaWxs/Pjjj//66y9ygSskJGTUqFEgT3TfWwU/6r1DEERxcfGdO3fs7OzCw8PJUyB6oru7+7vvvjty5EhXV9etW7d4PN7EiRMHdmkcx6VSaXl5+ePHjxMTE8HhmcqbM1EUtbS0DAgImD17dnh4uLe3N51Op1AocG/wcwXDMIFAQE7FCIIoKir69ttvW1tbbWxsdu7cSU7eewGknFRWiH9yl78k6J0pJwhCIpGIRCIajWZiYtLTxK2xsfGzzz47fvy4sumk0+nm5uYBAQHBwcGjR48Gp5HV19e3tLQ8fPiwvLw8IyOjpqYGDBocx5ubm/fv33/jxo2PP/64sbHxt99+AymkqVTqK6+8smfPnmemdlFBJpNlZWVpcfcvOARB3Lt3b8OGDZmZmfb29vv37yfDYHqisrIyISEBBB13dHT8/fff48aN69e5oGAOLpfLr1y5kpCQUFxcXFVVpZIrnMVi2djYTJ06ddq0aYGBgba2tmC9GoHP5ucPnU739/cnMyNWVlZu3bo1LS2NRqNFR0dHRET05VHq5OTk4+OTn59Pvl9MJvOl2tetd6a8ra3t4MGDp06dsre3f//996OiolS+WxEE0djYuGXLlvPnz5NvG5VKdXNzmzp16vLly93c3JhMJpvNJggCRVEPDw8EQaZNmyaXy8vKyn766acrV67U1dWB6GCFQvHgwYMVK1bY2tqSH++wsLCvv/46JCSkvx9jhUJRW1urg154QcFxPDc3NysriyCIp0+f3r9//5mmHOTMIf+kUCh9/3DK5fLW1taUlJSff/65qKioq6tLKBQqF6DRaC4uLn5+fuPHj3/llVeCgoJA8PKgLbdCEARBUZTNZgN7LRKJjh8/fv36dSqVOnPmzN27d/cxU7mRkVF4eHhiYiIIQkcQhMPh+Pj4vDxZXPTrPqVS6aFDh7777ruurq7a2tqVK1dGRESsWrVqypQp5Ae4ubl5165d58+fBzEG4Evx/PnzFy5cOGrUqJ7CxhkMBoPBGDFixJ49e954443Dhw//9ddf5Deytra2tra2UaNGGRkZWVtbb968OTg4eBDv+2WBIIj29nbwtZdCofT3uGEKhQKOuOz9EkKhUCAQ/P3331lZWTk5OQ8fPlQ+lBn46I2NjYcNG/bqq69OnjzZy8tLeWsPNOKDDIZh5eXl4IDN77///uDBg2KxeMqUKXv37nVzc+v7Y3XUqFEcDoc05Q4ODspx6C88+mXKJRJJSUkJeRRvd3d3cnJyVVWVQCAIDAz08PBAUfTUqVNnz54lY8UsLCw+++yzBQsWcLncviyjmZiYhIeHBwQE/Pjjj19++WVbWxv5koWFxdGjRy0tLY2NjXWy1AkWl7Wvx3AhCAKEEIA/u7q60tLSwO/29vavvfZafyvsZUpOEERtbW1eXt6ZM2cKCwtLS0vFYjGGYeTVKRSKqalpRESEk5NTZGRkdHS0iYkJg8GAFnxowTCspqamvb392LFj33zzTVdXl4WFxdtvv92vgwMRBAkICLCxsSE/0VZWVlZWVrpvrr6iX6bc2Nj4k08+cXd3P378eGdnp1QqBatk69ats7GxiYqKcnNz+/nnn8nZtLu7+86dO19//XUwv+v7p9Hc3Pzdd99VKBT79+8HifoQBLl3796JEyc+/vhjXYWsVFVVVVdXu7q66qQ2wwLH8fb29lu3bp07d45c0ZLL5eD8LQRBPDw8fHx8dHKturq69PT0ioqKP//8s7S0tLW1VflVKpXKZDLt7Ozi4+MnTZo0ZswY8J2dGMS4dYg6ys/4+vr6Tz755Lfffuvq6jIxMXnnnXfGjx/f33eHwWC4uroqZwJ4qWLP9MuUUygUPz+/Tz75ZObMmenp6SkpKTdv3hQKha2tra2trcXFxQwGg5yPg7f8jTfeGFjmPFNT040bNzKZzL1794KdROB4ivHjx0dGRupkEEgkEvLr3stGRkbGhx9+mJ+fD07CVXmVyWTOmjWrvw4WZbq7uzs6OkCewnPnzl25cgXDMIlEonItHo8XFhYWGxsbFRUFdh5A260nFBUVkbGDJSUllZWVcrmcy+WuX79+7dq15Cpo32GxWIGBgdeuXdN1Sw0DfczBwmQyR48ePXr06AULFhw+fPj48eM1NTUEQWAYRlpGCoUyderUlStXqjjHe6pfpWHgJ5PJXLlyZUdHx/79+8HMsamp6cyZM8HBwVwut+/1kNBotNDQ0IyMDLlcjqJoYGCgp6encsk+1qNR6Ul8pt7fi2qpYxiWkZGxadOm9PR08BKLxQJnxJBlLCwslAM9+9gJBEEUFBTY2dl1dHRcunQpLy9PKBRWVlYq5wpHURQ4Utzc3KKiombNmhUUFMRisTQ2uL+DU2OxAevPvHHt9Z6uOwj6MwuTS50A8JF5++23169fb2JiotxpYP2DQqGoJ7pRvgpBEMqLnMQ/qFxXDy2eTnR93+3Z3d2dmpq6evXq8PBw5d323t7eOTk5faxHpWEqemVlZVRUFDmqAgICyI1nA9h3V1RUNGPGDDabHRISor7ZrC/1aLODro+NfK56QUFBWFgY6E8GgxEQELBjx441a9b4+PiQnezo6Hjv3r2+1J+dnc3j8cj3nc1mm5qampiYqDvNURSl0+kjR458//33k5KSamtrga9cVxvqNBbTRu/93df+jdB43YHpvYzJAY/V4uJif39/5XfQ0dExJSVFuQz4vba29t133122bFlFRYWyrnIVqVS6Y8cOsraoqChyR7fKbkyV+nWuaz/YBqDrl4NFHTabHRERMXr06Nu3by9dupQ868DU1FRXy9Nubm6rVq3Kycnp7OxEEKS8vPzy5cvr1q0bWG3e3t6HDh169OiRp6fnsGHDXipvHaCkpOTRo0c4jlMolJkzZ27dutXT01MmkwEjKxaLKRTKuHHjlA103yHPKyChUChGRkZMJjMyMnLRokV+fn48Hg8cXQ/XM/WZ5uZm8uOMoqiTk9Pu3btDQ0NBTDCFQmEymTKZLDs7+/vvv//999+NjIwWLFjg7u7ex/rxl2l/EKJvvvKeYDKZGIaRq2cMBmPRokVmZma6qn/ChAmenp5gd49cLi8vL8cwbGCbC1AUdXZ2dnFx0VXbDAuxWHzhwgVgbc3Nzbdv3+7n54eiKIvFsre3J6fqY8eO1T66AEXRkSNH+vv7z5s3D3hRwN7Rl/DxaYj4+Pj4+PiANWobG5t9+/ZFR0dfuHAhMzMTwzBjY+MRI0ZUVVUdP368vLxcoVB0d3dfu3ZNJpP19P7K5fKSkhLyz5qamkuXLqnsSjE2Nvb39+9jrLphYRimXC6Xp6WlkWkOWSyWt7c3lUrV1YSLRqORx75gGJadnV1XV/dyRp5oSXd3961bt8D74u/v7+DgAD54CoUi//+1d9/xTdX74/jPyG669160QAfYFmihZZULXFAqAoIXFFEQF6goU4ZeQZaIOBAZXxxc5r0WBEUEoYBsKNBSCh2hC9I90jZNmnHO74/3w/PLJ0nTkKRNTnk9/2pfPT15552TV07e5/1+nbt3VSoVhmF+fn4JCQnWJFwul9u3b9+pU6dOnTo1KChI99b1cA7OFlVVVczEwd69ew8bNmzPnj2rV69GM8oIguDxeFqtllkg1t7ejko4mNin7mqy8vLyd999V2+lqLu7+6hRo1asWBEVFWXj52Nv7EjlbW1tFy5cYN6lcXFxtn0lBAJBcnLyX3/9hWEYTdM5OTn379+HVG4BmqaZL0/h4eHMcp7W1tYDBw6gd1pqaqrFK7AIgoiJiUlJSXnjjTfi4+N5PB4NxWbZqb6+npk2ihbxuri4UBTF5XLRFQ5m9TUqqYR+NnHrR4TD4aAjkKZpvfIMHA6npqbm+vXraCi1h2FHKscwjHlVOBxOYmLi4y4fMI3H440YMeKHH35Axxa6hGLD/T+ZdAv/NzY2olt6YhgmEAgsG7zi8XgzZ858//33AwICTNTnAWyh+xWKw+FMmTIlJCSkvb392rVrX375pVwuxzBMJBJNnTp14sSJev/Y0a0n5HL5xYsX9ZI42k9aWppIJPL19Y2Li+uy52Q3rEnluoRCoW2r5KDV/8yUNbVa/ccffxAEERkZGR0dzVSH0Js+BUyrrKx89OhRQEDAgwcPNm/eXFtbi2GYSCQaMGCAZUsB+vbt++677/bp0wcGUnoYDw8PHo/n4uLyz3/+s62t7f79+6hEklAonDt37tKlS3VL4GImUzmGYc8995zhQ6ALNljPvZTCylTe3NysVqtN3AnIShqNZufOnT/88ENsbGxaWhr62GhsbExLS5s2bRozqg4MEQTh4+NTWVmJYdj58+dfffXVoKCgnJycwsJC9ObEcVwsFpv/dtKdKUwQBHR+z4OKIzELts+dO/fNN98olUonJ6eXX3552bJl3t7e5u8NFefCOr5hW0/FvlSu0WhKS0tlMlmXFlhQq9XoFrG3bt1CEZqmjx07Vlxc/NZbb/n7+3fdQ7Oaq6vrihUrFixY8PDhQ4VCceHCBYIgdKeFyeXy8+fPT5o0ycxCtWFhYWFhYRKJpMuaDOzDw8PDw8MDXflk7kNSUVGxceNGqVQqEAjmzJmzdOnSx8rjTzL2DRdwOJywsDAbzkQ0hOO4h4cHl8tFF/EQrVZbU1OzZcuWCxcudN1Dsx1Jkk8//fSWLVtiY2MFAoFAIODxeGFhYc8++6yvr69AIHBzc0tKSjL/5JrH41mzvh84LH9/fzRTkKKoqqqq9vb2qqqqDRs2oAkOo0ePXrlyJSocb++WsgM7zspxHPfz80M/azSae/fu1dXVMRGbUKlUaAQAwzAvL68tW7YUFhb+8ssvUqm0vr6eGRzo06fP496P4kkjEAgmTpzo6+t7+/ZtDMP4fH5KSgpa3llaWhoZGflYJW7u37+P7s8HepjKyko0EKfRaAoKCiQSyZdffvnTTz9pNJpevXotW7bM09OzZw+J2JYj1mAx/NXJyWnatGlnz55Fc07LysrKy8vRlRAz96PXML24UqnMzMxkZrmiGkxTp07917/+VVZWdv/+fWYF2tChQxMSEkzvn6KoysrKxsbGiIgIZhjhsdpjNNJRsNP44z6o9XGCIFJTU1NTU3WD48eP76jBpjuTmX+G1igbbm/bg81E3OhmFsdNP3GbxDt63G6Id7oxj8djLoQUFBQsWLAgKytLrVYHBAQsWLBg0KBBRl9rvf2YeON0T2brKN79ByfH8OKA7g82iRtu9lhxdEYcGhoqFotRKq+qqrp+/XpCQgKHwzFnP3oNM4wrlcobN26gBSwkSQ4ZMsTHx4fD4URHR/fu3Ts9PZ3pL5IkdVejGO6fpunTp09/8sknjx49ev755xctWuTt7f1Y7UGPZXjeavjv5sTN7wTHjAuFQmZmkZOTE5r6Yv1BZUFcr7etj+s9EdNxCzpQrwHWxE0ckx3FO9257k1THz58KJVKKYry8fFZuXLlSy+9hOYaWHwsYR1f9uyGePcfnDRNO/RYuVqtvn79+uLFi+fNm9fW1sZc52xvb9+9e3dNTY1NHoWm6by8vNLSUvRrcHCw3jQVkiS5f+t0MmJVVdVnn3128eLF0tLS7du3M1dNgWXCw8NnzpwZEBDg5uY2evRo246qATuSSqWPHj1ifqUoysPDY+XKlbNnz2bqkjJaWloKCgp0bxQD9DjoWLlGo6mtrT169OjXX39dWFjI5/NDQ0PHjBlTUFCAFu/k5eVt3779o48+sn6CeVlZ2Zo1a5gFLH379rXmlggPHz4sLi5GP6tUKnSmDyzG5/Pfe++99PT0kpKSUaNGoWvR9m4UsD0cx8eNGzd16lTDScZNTU2rV68+cOBAWlrarl27LChl/iRwuLNyiqJKSkq2bt06Y8YMdO8CtVrd2tr622+/jR07limOo1Kpjhw5cv/+fSvf2CqVav/+/WfOnEH7QUX7DE8KzETTdFlZGXPugEZjrGkewDCMx+MNGDBgypQpPbIK0hPLycmJGTrjcrmJiYnoZmF6mzU0NHz++ec7duxobGx0dXU1fWfXJ5nDpfLCwsK33357+fLlZ8+eZW78huO4k5NTVFTUzJkzmQuJeXl53377bWNjo8WPpdVq//zzz++//54pGxIWFjZy5EiLz/QpipLJZMyZOJoTbXHzAOjBIiIiIiIi0M+DBw/+7rvv0IQCXS0tLdu2bfvmm28UCsW0adOWL1/OZH+gx7EGWLRa7cmTJ0+dOoUudZIk6erq6uTkNGbMmFdffTUwMPCdd96RSCT79u1Dt3TYu3evh4fHe++95+np+biPpdFoTp8+vXDhwqKiIhQRiUQzZ85MSkqy5lRarVYzkxqdnJx68JxomqbRzVcN19HpXZJi/tppnCRJkiTb29s5HI7uOk/Q82g0GnTOxOVyU1NTExIS9E6h2traNm3atG3bNrlcPn369NWrVwcHB9upsSzgWO8WmqbFYrFAIJDL5Twe7+mnn160aFFYWJhYLHZ2dqZp2s3NbeHChQ8fPjx37pxWq5XJZJs2bSorK1uyZElMTIz5D6TRaI4fP75s2TJmzjKfz58+ffpbb71lzcc+TdMKhYI5x+/BaJq+fPnyiRMnbFtkztfXNyQk5Pbt235+fv369evTp09wcLBt6+0AByGRSB48eIBhGPoINzx/OnHixK5du+rq6tLS0j788EPI46Y5VirncDgTJ04kCKKmpsbLyysjI8PT01PvpC82NnblypXl5eXo6qJSqdy/f79EIpk4ceLUqVODg4NNTzLRarVlZWW//vrrt99+y9wlViAQTJs27eOPP4ZVwmaSyWQffPDB9evXbXuvFjRZSKlUcjgcJyencePGbdu2rUtX9gJ7CQkJ8ff3Ly8v12g0eXl5zc3NzAtN03RhYeGWLVuqq6v79++/fPlya2YiPCEcK5VjGObh4fHSSy9RFNXRZzVBEGlpaatWrfrwww8fPnyIYZhGo7l06VJOTs6xY8f+9a9/paamhoeHi0QivZyOBrJ//fXXn3766fLly21tbSjO5/NfeumllStXBgQEaLVamqZ1Z7wCozgcTnJyslqtNjHAgmFYZWVlXV0d6lXmT0zBDQzD3NzcPDw8OBwOn89nggqFoqyszMXFxd/f37IaisDxCYVCdN2LoqimpibmuyzK40uWLLly5UpoaOiGDRtGjRoF78dOOVwqx/6uQ491vGCMJEk0aenzzz+/efMmOjGUy+V//fVXbm6un59fWFhYQEDAgAEDmGukWq02Ly/v9u3bly9f1q1F7ubmlpGR8e9//9vPzy87O/vgwYMSiSQxMXH+/Pmurq5d/1z/fxRFtbe3c7lcVowniESiFStWtLS0mFjhQtM0qnO7ceNGZn59RETEwoULmenhqKYSupGjbiovLy/39PSMjo6Gy1w9HkEQfn5+zGd2fX39+vXrjx49yuPxnnvuOWumITxRHDGVm4PP50+bNi06OnrNmjWnTp1qbW1FcZlMJpPJ0MjJ/v37dT/MUbFD3Z34+vp++umnEydO9PDwUCgUGzZs+OWXX9Rq9e+//y6TyZYtW4buFdml5HJ5Y2Pj/fv3q6qqbt68GRAQgAaIe/fu7chZjCAILy8vZiGr7p90F6T16tWrubl5165dzF9dXV3HjBnDTF3AOli5Fxsba/R8H/Q8HA6nT58+YrEYwzC5XP7tt98ePnyYJMmMjIx58+ahG0XZu40swI4aLB3Fn3rqqe++++7w4cM7duy4c+eOXqY2vJMIgu4p8dxzzyUnJ48bNw5lTIIg0P2o0D9u3769uro6IyNjwoQJRg8mvfYYfZSQkBBXV1fdLXW3VyqVly9f3rdvH7r/nEajUSqVXC4XlRKcNWvWK6+8ojeTuqOHMx03v/FdFNfdgP6bNfuxV9zoZhbHzX/iFsc7etxuiD/WxuhTvLm5eevWrZ9//rlCoRg/fvy6devCwsIs6wrDP3Vz3A4HJ62Doii9H2wSN9zMtnG1Wv3gwYP169cPGzYsNDSUy+UanU0oFAr79OmTkJAwefLkv/76q62tDc1oZPaTk5Mzbtw4Zn0QQRARERHnzp3Te3aG7WGoVKrPP/8c/TuHw5kzZ45SqTS6vVarzczMjImJ6ejLI5/P/+ijjxQKhWGvGm1MR3HzG99F8erq6pSUFOZ5JSYmSiSSx92PVqtFpSsNt++2g83oZtbEjT7xjuKGDes0bvRxLYszrTI/3unO6+rqRo4ciWEYl8t94403GhoaVq9e7e7uTpLkpEmTCgoKrOkKo69Ct8W7/+CkKIqtAyy6SJIMDw9fuHDh9OnTpVKpRCK5fv263tIhPp8/evToPn36CIVCV1dXNDFGbz9xcXE7duz4888/165dW1RURFHUw4cPT58+PXToUAtaRVFUY2OjQqEwvHBH03R2dvaqVavy8/MxDHNzc+vfvz9aTFRRUXHt2rXW1laNRtPY2EjZdH6IXfz111/MTCEMw+rr6x93/mJtbe3WrVvv3r2bnp7+wgsvwISWHkatVp85c2bx4sWHDh1qbm728fGZPXt2dHQ0ZvJbL9DTE1I5QpJkUFBQcHBwcnLypEmT0OeVbr4WiUS0yRpyOI4HBQXNmDHD2dl56dKlEomEw+FYnDgIgvD29jZaA6CpqWnbtm337t3DMMzNzW3dunWTJ09GW8rl8szMzKNHj7q7u8+cObMH3P/sxo0bzKpdDMMePXr06NGjxMREM/+9rq5u1apVP/30U1tb2/Hjx5uamt5//32Y1tLDFBYWlpSUqNVqkUg0d+5cvfLIwBzsTuUURV28ePH8+fNJSUljx45lEjSaDmE0ZaMUb+KaOJfLffbZZ0Ui0Z9//tm3b1+jt3w1B03T7e3tWq3WsDyQRCLJysrSarUEQYwcOXLatGnM9VWRSDR79uwZM2ag+1j2gBIuzNpXE5GOUBR16tSpH3/8UaFQYBimUCjq6up6wDcVgGGY3uuI8vg777yzcOFCvcljWq22uLhYJpPx+fy4uDhYBmwUizuFpulr167Nnz///v37ERERO3fuHDJkiOnc19zc/Pvvv7e2to4bNy4wMLCjzTgcztixY4cPH46q41v2LQ/Nizc6HxaNbaFt3N3dBQKB7qcOSZJOTk49IIlbj6bp5uZmlMcxDCMIIjk52ZEn9gDzoclmzK84jqenp7/++ut6eZym6XPnzi1cuLC0tDQ5OfngwYPdPEuYLVg88b6ysnLduujmPiwAACAASURBVHW5ubkqlaqgoODOnTumz9daWlrWrl37yiuvvP3221999ZXp5fUEQYhEImsmtGq12sLCwrq6OsM/RUREDB06lMPhUBR1/Pjx999//9dff62vr+95K/7lcnl1dbUNz6MNv+IAlnJ1dWWSMo7jw4YNW716tWH5ubKysk2bNt2+fZuiqJEjR1pctbTHY2sqpygqKyvr+vXr6FdfX9/IyEjTS8Lq6uqysrKUSqVKpbp//35Xf0+naVqpVBrNzp6enlOmTHF3d6dpuqqqaufOnTNmzBgzZsz27dtrampMfAlQq9VVVVUdTbJ0QLW1tWgqgm4QTcsxcw+6a6bEYjGafQx6AObenhiGBQUFzZ8/v1+/fnrbVFRULFu27MyZM2jsZc6cOTC60hFW9otKpTp69OjKlSurqqowDCMIYsSIESkpKZ0OSjjOMOuoUaMWLly4d+9edDONlpaWmzdvFhcXZ2VlrV27NioqSnfj5ubmM2fO3Lhxo76+Pj8/PyoqKjg4OCMjo3///g6+oLmsrEwikehGtFrtiRMnnnnmGXNqRhIEERUV5efnh243A0WDe5KGhoba2loMwzgczuTJkydMmKB3MJeWln788ceZmZlarXbixInvvPOOBQVQnxysTOWlpaWbNm0qKSlBv0ZHRy9ZsuSxysnafZKTs7PzBx98MHHixB9//PHSpUt3796tra1tbm7+5ZdfaJreuHFjREQEs27iu++++/rrr6urq2ma1mg0Fy9eJAji3LlzK1asQDNzHVZ1dbVcLteN0DR98uTJlpYWc14vHMdRpUz0K9TG6UlQzYb6+nqCIDw8PPTuKaFUKj/77LMDBw6o1eqRI0euWLGCuR8kMIqVb4yAgID4+Hgej4dW8Sxfvrx///6PdZ2woqKirKys61poDpIko6Ki1qxZs2fPnq+//nrixIkikUij0Rw9enTHjh3MKMru3bs/+eSThw8fqtVqNFyj1WrVavXZs2eXLFmSm5tr1ydhCkVRqHiWXjwlJcX8z10PD4/Hmg+q0WhaWlrq6+tLSkoOHjyYk5PT2NioW3UHOIjAwEDmpmB62trafvzxx4MHD2q12pEjR27atCk+Ph4mApjGyrNysVg8d+5cHMdVKtX06dNHjBhhzsssEAj8/f1JktRqtU5OTkylLfvCcTwwMHDq1KmpqamTJ0++du2aRqO5du2aSqUSCoXo2ilK6yRJenh4REdHq9XqW7duqdXq7Ozs77//fu3atQ7yXPQQBDFo0KDp06fv37+/tbWVJEl3d3d3d/e5c+ean8qDgoICAwOzs7M73ZKiqLt3716+fPn48eM5OTlo2EokErm5uY0ZM+aFF14YMGAAzH5xHK2trUzpJF1qtXr37t2rV69uaGgYPXr0xo0bDcfQgSG21mAZOHBgfHw8TdNoEU2n22MY5uvru3TpUhzHa2trJ0yY4Ofnp/tXw+0tixtuprulXC6XSqUEQYSFhaHTVWYPTk5OzHdMNPOapumcnBx0kw0cx4cOHbpkyZLExMT6+vq33347KyuLpuny8vL29vaOVhLZ6klZHA8JCVm1atXdu3cvXbrk4eGxevXqgQMH9unTx+jR0tF+mPN6vc7Ufa0pijp//vyiRYvy8vJ0z8Hlcnltbe2DBw+OHTv26quvfvDBB05OThYfhEY3szje6RO31dFol3inG5eWlpaWlurFaZq+fPnyt99+W1tbm56evn79+vj4eKN7M90Vhn/q5rjNM16ncY5ehVL0K21QudSauOFmNokLhUIzt0dwHB8yZMjevXu1Wi0anNG9M5nRJUWPGzeE4zizZVtb27Jly06ePMnhcN56663nnnvO19cXx3GtViuVSs+fP89c0Pfw8EC12qVSKbokIBAIZs2aNWbMGIIgPD09//Wvf128eFGlUp09e/b8+fPPPvus4UPb6klZGffx8Rk1atSlS5d4PF6/fv0SEhIeaz+GnYn93xvLoUMZTT3OyclBV7b5fH5YWJhQKCwrK2tsbNRqteXl5du3b3/11VeZOfuPexDqtcr6OGZwhzwTcQteiI660YI40yrz453unP57dQWCnsLFixeXLFlSWFjo6uo6f/58dGHfgq7Qa1U3x7so45mOs3KAxRroxnJ2GXeTy+WHDx9Gt8tYsWLFoUOH0tLSPD09r127VlxcXFhY2NzcjGGYp6fn008/jcZMmJs2CIXCoUOHovNTkiQDAwPRz0qlkvkAcEwkSfr7+3fpQ9TV1W3evBmVRCdJcvTo0TNnzoyNjRWJREVFRd9///3Jkydpmp4wYQJMgXBk169fR7emEolEM2bMSE9Ph/Fx8z1xqdyOXFxcFi1atGbNmtra2sbGxnPnzl26dAnd/4w5PXFxcVm6dOkLL7xAEIRara6trUWDLQRB6I4v+/v7+/v7M3N4nnDV1dVMVwQEBCxdunTYsGEYhuE43qtXr7S0tEuXLmm12rS0NFSHx66NBUYolcqioqJPPvkkOzubIIhJkyYtX74cnXXZu2msAam8+/B4vNdee00gEOzcufPBgwdNTU1arRZlapFIxOVy4+LiZs6cOXPmTFQuisvl+vn5kSSpV4cdwzBPT09vb29I5UhoaGhwcDAqMykQCMRiMfNtF8MwsVg8duxY3a9iSqWyvb0dfaC6urr26tUL5jh2P2b1nEajyczMPH/+/JUrV2iaTklJmT9/fld/k+t5IJV3K6FQ+Oqrr44fPz43N/fEiRPt7e04jnM4nP79+0dGRkZHR/v6+pqznk2pVLJozadQKNSbNWxbIpGIWc9dXFy8fv36hQsX9u3b18nJybD0QlFR0Q8//HDt2rWKioqamhofH5+333578uTJAQEBXddCoEej0ZSWlqL761IUdf/+ffTpGxQUtGbNmqSkJHs3kH0glXcho+d6HA4nKCgoKCho/PjxRq/edPSlUqVSMT/rXf13ZMy1yq5DEMTkyZPPnTtXX19P0/Thw4dzcnIiIiL8/f3nzJmTmJjIzPC5e/fuokWLTpw4wXRyU1PTqlWrrly5snr16sjIyC5tJ2Dgf2MiNE37+vouXrx46NChuh/AMplMo9E4Ozt36dlADwDfK7sKuvnsY61BNUEul589e5b5VaVS6WZ2R0bTdFtbW5e2FsfxcePGvfjii7GxsWjdQFFR0R9//PHDDz9Mnjx5wYIFUqkUw7DW1tZly5adOnVK78NSJpMdPHhw1apVDQ0NXddIoEur1crlct0KRd7e3h999NGcOXN0K6ZVVFTMmzcvMTFxwYIF8OqYBqm8q9A03dLSYuU6Q92ZWxUVFejqKE3TMpkM5SN0i1vrW9sNXFxcuu62125ubuvXr//xxx+XLl2alJTk4uKCvhJVV1f/8MMP//73v2UyGbpfFyoTLxQKk5OTx44di5pEUdTJkycvX77cRc0Deng8XkxMDFMcDc21nTVrlu4Kifb29t27dx86dKiiogLdmMJOjWUHSOVdhaZpZiqhxdzd3dGdmpVK5R9//CGVStHpzMmTJ9F5rp+fX2xsrG1a3MWam5t161NbwMSYO47jfD4/MTFx1apVBw8e3LNnz7x589DUw/b29qNHjxYUFIjF4gULFmRkZDz//POrV68+fPjwDz/8MGnSJLSHhoaGEydOWNM88Fg4HA6zSmDs2LHz5s3TzeM0TV+5cmXPnj0qlcrPz++dd97x9va2X2NZAMbKbUmlUt24cQP9TJJk7969rTz+EhISJkyYsGvXLq1We/Xq1ZkzZ7q5ubW3t1+4cAF9SKSkpLCogrM1lSmZKol6cbVaTRAEulaM4ziXy42MjIyMjBw5ciSXy0V3zZbL5Y2NjQRBjBo1KiEhQSgUovVlNE0PGTLk//2//4d2xaIryT0Jl8tNSkoKCQlhIhRFXb9+ffHixSUlJUFBQZ988kl6ejrMMjINUrktaTSa8vJy9DNaj2pleWWhUPjyyy+fPn26uLhYoVBkZWXp/tXb2/sf//gHWy4HWV9tnM/nc7lc3S86crn8wIEDra2tEydODA4O1r2MptFomIorHA6H6SV3d3dmM3QuLxaLW1tbcRz38fGxpnnAJtBdHhcvXnzjxo3AwMD169dPmTKFLQe5HbG1BsvjxvUa1nVx3TJ+6LzPmv1jGPbUU0+tXLly5cqVzIcE4ufnt2TJkilTppAk2dEwjr06weiLwuPx0Hx5CzrB6JYajebQoUOLFy9uaWn5448/1q1bFxkZyePxFApFRUXFtm3bDh48iP4rPj4+Ojra8CCprKzMzMxERZ0SEhKmTp2qu/8uei+Y/8Stj3f0uN0Q73Tjjnrpxo0bS5YsuXLlilgsnjNnDsrjFhwz3ZPZOop3f8ZjcQ0W8+N6Deu6uEgkGjJkyG+//YZ+ZaZbPdZ+0GvDRIRC4fTp0zkczubNm+/fv69QKNzd3cPDw+fMmfPiiy+i5Ysm6l10fyfoxSmKQvMmGxoa0CSEx9qP3pNitqRpWqPR3LlzB+3z1KlTjx49iouL69OnT3Z29r1790pLS9HlBA8Pj9dee83f31/vIFGpVLt37/7jjz8wDBOJRK+99lpsbKzu/rvivaAbx57sGix6G6Bfq6urv/zyy2vXrgkEgldeeeWNN97g8/kWdAUGNViAlbqijCqHw5k6dWpCQkJpaalUKg0ICOjbt6+/vz86yXVwKpWqpqYG+/sQt+GeCYIICQnx8vJCt0XNzc3Vq95OEISrq+ucOXMM71CjUqmOHDmya9cuuVxOEMSECRMyMjLgZmP2pVKpvvnmm//+979cLnfGjBmrVq2Cmjnmg2PXxlDasjk06bBv377oyiGLLgEJBILExMQff/wR1Y2xZlfNzc1tbW3MPAcej/fGG28MGTJk69atVVVV9+7dq6qqQlPWCILw9/dPTk6eMmXK+PHjXVxcdPdD0/Thw4eXLFmCxqyeeuqpjz/+2NfX15q2ASu1tLT873//2717t1qtHjNmzDvvvOPl5WXbz/6eDVK5LbW1tV29erVLH4JFSZwhFApJkvTz87NmPg9FUUVFRVVVVeHh4UxQIBAMGDBg27ZtSqXyzp07d+/eRfMdeTxeUlLSwIEDhUIhGubSTQp3797dsmULuo2Um5vbvHnzevfubcXzA1ahafrBgwerVq3av39/dXW1n5/f9OnT4+Li7N0uloFUbmOOeUMfOyIIIjk5ecGCBQMGDLByRAjNYNEL4jguEolEItGwYcNSU1OZlE2SpN7NPTAM02g0N27c+OSTT9CcUQ6HM3fu3EmTJtl88AeYT61W7927lyCI9vZ2Ly+vFStWZGRksPGUxb4glduSQCAYNGjQ8ePHMQyjabqmpkYul7No3ndXwHG8X79+n332me6lIQt0NK9cF4fD0b0QZLjBvXv3li5deu7cOfRrREQEqlWpVqthoNyO0LCYl5fXypUr586da/iBDToFh68t6VYV12q1FRUVMpnsCU/lNmQ4r/yxNDU1bdmy5eLFi0wEx/Hc3Nz//ve/GIaNGzcuPj7esJIi6B44jo8bN+61114zmscbGxs5HI6tKhr1SJDKuwpJklFRUXAJ3nFcvHjxyJEjuiWciouLZ82apVAoaJq+cOHCvn37XF1d7djCJxZBEHFxcS+++KLRu9QWFRVt3LjR1dV1+fLlqI4FMAQDUl0Fx3EXFxdWzBd0ZLqV2dva2qwpT4bKaelGtFptS0uLRqPRarUqlQrGZ+0lJiZm06ZNo0aNMvxTcXHx0qVLf/rpp19//RVVuARGwVm5LenWYAE2UVpaiqaaUBRVVlZWXV0dHBxs2a5SU1M3btx4+fJltVqtVqsvX74sl8sxDONyuSNGjJg1a5aVdQWAZbhc7jPPPJOenm44uiWRSJYsWXLkyBE3N7dXXnklOjraLi1kBUjltqRbgwXYBFOZnSCIXr16WTMz3cPDY86cOTNmzKBpmqbpxsZG9ANBEO7u7gKBwOgCRdBF2tvbmeWRIpHIMI+3tLRs2bLl2LFjLi4uH3744dy5c6ESiwlQg8WWccNfrWyPOcFO493cCTaPM1Qqle6Whi+63viJ0c5nRmMNL0d3elAZ3cziuOED2Tze0eN2Q9z0xqjoQnNzc0fbKxSKbdu2/ec//9FoNCNHjnz99dfFYrHuNp0eM92T2TqKd3/Ggxostowb/mqiPSjREwRhGDfclWEnmxnv/k4wP07TNEVRzc3Nrq6uTF919LzQHSClUmloaKjei65QKFDFlUePHnl5eT311FO6hTtsdVDptcr6ONZDa7DQNF1QUKBUKl1dXdGLpfuKM73R1NSkewlarxPOnDmzbds2mUwWGRk5c+ZMvbkrnXaF4Q67M26XjAcDLF1Io9GgS3ZarVapVKpUqosXLyoUChS5e/euWCx+5ZVXLB78ZTWapq9cubJ161apVOrt7Z2enj5u3Dh0Y2Xd4rRKpZI572hvb5fL5ejKp0qlKi8vz8vLU6lUBQUFR44cUalUjY2NHh4eX3311T//+U+7PbEnm0ajOXDgwKZNm+Ryuaura69evVJTUxMSEqKjo/l8PnPzEK1W+/Dhw472cO7cuVWrVpWWlkZFRa1bt27ixInd+yRYCVJ5V0Fll5ctW4ZhWE1NzZUrV9RqdUNDA5OY0LKU2tradevW2X3CLE3TNTU1egMUHh4eWq22ubmZJEkPDw8Tc67b29tbWlo8PDxMTwLRaDQymczNzY0kyUePHm3dunX//v3oQX/99dfVq1eTJOnl5TVkyBC0YMfHx+fSpUsVFRXo3+/fv79q1aqQkBCapiUSyfXr11tbW9GpPTPLpb6+ft++fdHR0d7e3mKxGMdxlOLd3NwMK53ptufx+wwYce/evU2bNuXk5KBfs7Ozjx49KhKJnJycgoKCxowZk5SUxOVym5qazp8/b/jvNE1nZWUtWrQoJycnOjp6w4YN48eP795nwFaQyrsKRVG3bt26deuWiW3QkmW5XG5lnSlz4DiO7mMZEhLy6NGjQYMG1dTU3L5929nZuW/fvjdu3Dh79qzu7RNJkoyNjVUqlcXFxWKxOC4uzsR6yMbGxoqKipiYGNNrJltaWh48eBAdHS0UCu/cuXPixAnmw6Otra2trQ3DsPLy8ps3b6Igh8PR/Q6u0WgyMzM7faYnT56USCTh4eHoZhSNjY0FBQXR0dGGU5J129PpbgUCwcCBA729vbOzs9GkGgzDeDze8OHDRSLR9evXmalyYWFhfn5+2dnZTG0vLy8viqKSk5N1P05u3LjB7EdXUlJSWFiYYfzRo0c3b96kKCopKSkoKIgkyYCAAIIgpFKpWq2mabqiouL69et8Pn/gwIFoZaxGo5FKpdbcHam5uVmr1bq5uemOJ6AXy8vLi9nm2rVrqPpNWVlZYWGh7h4UCoVCoaivry8vL7969SqqikPTNJo+pEur1WZlZS1ZsiQ3N9fX13fRokUTJkwwUY4f6Po/C6m7aHzQLiNHdhkOlslkTz/9tO56QnMw1UK6GnoUgUCgVCqFQiEa9sFxXCgUKpVKwynbaB28VqvFcbzTde0ajabTbWiaRpvhOI7umGzN0zGNIAjmXFutVhvtZN32mLNPPp/P4XBUKpXuZ55IJMJxvL29nfnUIQiCx+PpJlAOh0NRlN4Hht5+GDwez+iKR/R6Mc3gcrlRUVEkSRYVFaE4RVFo+E4gEPj7+0dERKjV6qKiIt2rixbQarV631rQUaH7cisUCuYe4rqfvubg8XgrVqxYsWJFVlbW+++/n5ubKxaLv/jiixkzZvD5fMvemBiMlYNuRpKku7u7p6enl5dXaGioRqO5ePFiSEhIeHg4QRAKhaKsrCw8PByNMFpwPYqmaalU+uDBg8DAwJKSEo1G4+npiSrxEgTBpAwnJydmRkdgYGBERMTdu3cbGhpIkoyOjg4PD0cHTW1tbWtrK7qWhT3OVTu9eG1tbXZ2dn19/eOecKH3NoZhGo3GRMrw8fFJTExEp422ercwT8TMeHt7e05OTl1dXUeNFAgEJqrbOzs7Dxw4sKmpqaCgIDY21svLS61W37x508fHp6SkJDo6OjAwED1QSEgIjuMajaakpMTPz48ZrKupqVGpVEOHDpVKpXfu3OnVqxeO48XFxUY/QZ2dnQmCaG5uZl4RHo/Xv39/b2/v6urq3NxcvU8dveSODp729nbL1nAplcqsrKyFCxfm5ORwOJwpU6Y899xzAoEAzsfNB6m8CwUHB/ft2xf9jFa4NDU1NTU16b4rYmNjN23aFB8fz+Fw0L2D6+vrUak/7O/zLCuruKCrhUKhEH2l5fP5aEpvR2c0AoHAycmpubkZ5UqmMRiGaTQatVptznCEaRqN5t69e/PmzcvOztaNoyne6ANGLBaHhYVVVlbevXuX+euMGTNiY2Npmi4vL79//75u4wsLC+vq6lQqVUxMzNq1awcPHmzfacg0TTc3N6tUqo5SP2byMw99xqtUqpaWFmdnZ3RTtKamJoFAIJfLxWKx3scATdNtbW0CgUD3u4harRaJRCqVqrm5WSgUEgTBDGvoPS5BEARBaDQaJo7jOHpc9O+GBwxmcCaRn59/9OjRPXv2GA6eILr3d62rq0MHmEql2rNnz8GDByUSCY7jI0aMWLBgASzQf1wwwGLLuO4AC0mSr7/++rp165h/KS0traury8/PR+/wM2fOODs7v/vuuyNGjNBd32/iRNvoOIDpePd3gplxtVqdmZn5zTff5Ofna7Vaf3//3r17Jycn9+vXDxVCEYvFoaGhp0+ffv3119Fd34KCgg4dOpSSkoLjuEql0h3BUKvVhYWFEomkoaEhLS0tISGB6UN7nZV3Gsd64mTEmpqa99577/fff9dqtS4uLuiGHlFRUTExMVwuNyQkBF0GaG1tfeuttx48eKC7N5IkR4wYsXHjxoSEBCvfyBgMsABbwXGcx+Oh+9egHu/Xrx+GYcOHD0cv+YIFC3Ac17vBzZODy+U+//zz6enpubm5NE1HRUV5eHigk0qmzjiO4xEREW5ubiiVe3l5MTev4HK56KSbOZpTUlKSk5M1Gg2Xy2XeV6Cb+fj4rF+/ftasWRRFeXt7R0ZGYhjG4XDQyQr+90WXxsZGw/JEQ4cO3bRpU//+/Y1+xgDTIJV3K1zn+qGbm5vuh/kTiCAINKPcxEklpnP6g+O46Tc5Gv2HRGBfISEhaO6Q4Z90D3W9S7tBQUELFy586qmnDP9LKpXm5OQkJCR0w0Qv9oJScF3oiT3jBsA0kUg0ZswYZk6RUCicN29eenq64ZZSqXT+/PkvvfTS2rVrOxqCBxjUYLFtXPdXdB3JyvaYE+w0bnTnDQ0Nhw8fLikpGThw4Pjx49Epkl06rdO47q+6W3b/QWV0M4vjKKJWq8+ePXv58uVx48YlJiaii5a26sCOHrcb4qY35nA4AwcOdHZ2lslkOI4PHjz4hRdeMJyyUltbu3Hjxt9++42ZOGvmG8rwT90c7/6DE2qw2DKu1wmotMjj7oc2uKii16uPFTf6oFqt9ttvv928ebNcLo+NjY2Pj4+MjLRXp5mO60aYARa7HFR6rbI+jp7In3/+uWDBgpKSkv3793/xxRfoXNUmHdhRN1oQN3FMdhQ3vXOapqVSKZoFz+Vy09LSDMdkKIr6+eeff/rpJ5VKNXjw4NmzZ6PlReZ0BfbkXfaEAZauIhaLBwwYYO9WGCeTyU6dOoWmRTY0NLS0tNi7RU8ohULxyy+/SCQStJbn9u3bXbpsynFQFIVmjmIYRtN0Y2Oj3rx1lUq1b9++devWNTU1DRw4cPPmzcnJyUY/HgACqbyr+Pn5mb6nsB1JJJKCggL0c1JSUkREhH3b88Rqbm4uLCxE6dvX1zc5OfkJvEMxRVG6IycYhtE0ffr06eXLl1dUVISFhW3atGnQoEGQx02DGSxdxdvbm5k552hUKhValcfj8dLT05kVQEZptVp090sej8cstgQ2odVqmdPwXr169enTx77tsQsnJye0thP9SlFUXl7eli1bysvL/fz83nvvvdTUVLhXX6cglT+JJBIJ+m7r4+OTkJDQUe0UmqYlEsmpU6cuXLjQ0NAQGRk5ceLEwYMHW7n6FDDy8vLQMhkul5ucnOywn/1diiRJHx8f5tf8/PwPPvggKyvL09Nz+fLls2bNgjxuDkjlT5y6urqDBw+iK06+vr6enp5GN1OpVEeOHPnyyy8vX76MvvwSBHH48OERI0bMnj175MiR3dronkilUl24cKGyshLDMC6XGxgYyOVy6f87LwLDMJqmlUolKhvp6uraY+rx6iZoVIoLnY8vXrw4KyuLJMn58+ejm8AZ9gkwBB93tqRWq5kaTy0tLY55ObGurg7dgFQgELz00ku9evUyull+fv7q1auvXLnCvJEoipJKpQcOHHjzzTcvXLjQPW8wsVjs5eWFRnWcnZ2tL//iONRq9fXr11EW69+//4QJE4xuVl5evnLlypSUlOHDh+/du/dx6w46JoIgIiIi0MieWq3Oz8/HMCw/P3/BggWnTp3CMGzatGmzZ89+Aq8cWAxSuS3V1NSgooMYhpWVlTngLZtpms7NzS0pKcEwTCgUjhw50ujoCkVRv/76a0FBAUVRqNx2fHw8qnBEUVRRUdH333/fPes1IiIiVq1aNXz48PT09LfeesthryRboLW1lbn4HBYWZvSptbe379ix4+uvvy4uLs7Pz9+/f3/PWCbD4XDCwsLQBzO6D1Rtbe2mTZvOnj2LYVhSUtKKFSuCgoLs3EpWgVRuSwEBASNGjEC1Qdzc3FBZKIeiVCovX76MRld69erV0bulrq7u4sWL6ASwV69eO3bsOH369JdffonuXUfT9O+//97a2toNDSZJcty4cYcPH87MzJw0aVJPGjY9d+5cfX09+jkiIsLoGei9e/f279/PTNpDlQu7tZVdpqWlhbnkK5PJfvzxx8zMTIqi+vbtu3r16qioKPs2j3VgrNyWXF1d16xZM27cdtc2JQAAGAtJREFUuNzc3H/84x8xMTH2bpG+9vb2Bw8e0DTN4XBmz56N7itkdLPGxkaaprlc7uTJkzMyMgiCmDp1am1t7bJly1DV3Bs3bnQ0JmBbOI4z9Wq64eG6ze+//45uChEaGvrss88aLclbVFTEpPueBA2qoBFItVp94MABmqblcnl8fPyGDRtGjRrVw17rbtBzznEcREBAwJQpU5YuXTps2DAHPByzs7MvXbqEYRiPx+uo5pEukiQDAwPRpTYejzdy5MjAwEAMw9RqtdGbmQEzNTU1MTeQc3Fx6egLXExMzNSpU318fBzwWLIGjuNRUVERERE8Hi8sLCwwMFAmk/Xv3x+td+0xl3a7E9Rg6ZI4up6jt+rBgv2YE+w0rnvdMjs7Gw22RkREhIaGGn3VaJqurKysrq5mgkzc29vbz8+PKTPdzZ1s94PK6GYWxNESGPSZimGYi4uL3twVpgExMTGbN28OCAjYsGEDWgrAvBwmOsroX7s5bnpjkiSffvppX1/fmzdvDhgwICAg4Pz58/Hx8fHx8bqVi7COn1qnb5zuyWwdxbv/4IQaLA4XR6+NBXUtjMZ1/1pbW3vixAmlUkkQBLqjmN6/MNvX1dXV1tYyQSbu6enZu3fvq1ev6m3fDZ1j94NKr7etidM03dzczNzUSbcCCfPqM9s7OztnZGR89dVXKJWjl8OcDtRrgDVxE8dkR/FOd87n84cMGTJo0CB04X369OmGJ+MWHzPYk1eDBcbKnyDl5eVo7gpN01euXNm8eXN1dXVMTAyHw6mqqkpNTf3HP/7BvJ3o/3vSgbS2tlZXV2u1WpglZo36+voTJ06gn1Uq1fHjx0NDQ5mSyL6+vmlpabp3ZuipvY3jOFOSEwZVrASp/EmBRlcaGxsxDKNpWiqVbtiwQaVSCQQCgiDUanWvXr327dvXv39/EztRKpXohj7AGlKpNCsrC/1M0/SdO3c++OADZnKOh4fH6tWrp0+f3lMzOOgKcNnzSSGXy8+fPy+TyZgImuKGVhKq1WqFQsHcLl0kEjETKnRPz9va2iy7pTrQRdO0XgVEhUIh/9vDhw//97//6c4fr6+vN/olCQAGpPInhVgsnj9//qBBg/h8flRUlO5AOY7jkZGRL7/8MlMiMT4+HtUwomlaIpEwU8glEolEIrFD63sWZ2dnE/OmPT09n3nmGd0aZxcvXkRLAQDoCAywPClwHB88ePDOnTtLSkpCQ0MVCoVUKmUu1PTq1Ut38oCnp2efPn3++OOP9vb2AwcODB06NCMjg6Ko0tJSdFbO5/MNr5oCM4WFhe3ataugoEDvEhb6q5eXV1pamu7YsV4tbwAMQSp/guA43q9fv/j4+I6u/uv+KhAI0AZVVVUff/xxW1tbU1PTZ599hoZlEhISUlNTu7PxPQlJknFxcXFxcSbmLzEvh0qlqq+vR6VaAOgIpHJgXEZGRlZWFpr7nJeX98Ybb1AUhb7m83i8p59+GpVkAV1NJpPl5+f3jCpaoOvAWDkwbsCAARs2bBg0aBAadZHL5SiPEwQxZcqUZ599FmaPdQ+apiGPg07BWTkwjiCI1NTU7777bv/+/ZmZmY2NjVwuNyUlZciQIa+88oq3tzfMqeg2zDxF5lY7AOiBVA46hON4QkJC375933nnHZVKRRCEp6cnn883WvgJdBGxWDxs2LCbN28GBga+/vrrzEoiAHThcDkFAAdXW1v7888/9+7de8SIEUYXxAOgf6Prrqg7YfcyGnoNc/C4NXUt7N74rovb/aDS623r45ixIjYdxTUaDY7jJEma34F6DbAmbuKY7Chuw8ZYcMxgUIMFAOCAOBz9IqYA6IIZLAAAwHqQygEAgPUglQMAAOvBDBYAAGA9mMHicHHbzgpwkCdlfdzuB5Veb1sfxx5nBosFHajXAGviJo7JjuIwgwWz4mCzIA4DLAAAwHqQygEAgPUglQMAAOtBKgcAANaDGSwAAMB6MIPF4eK2nRXgIE/K+rjdDyq93rY+jsEMFvPiFnQFBjNYAAAAsA6kcgAAYD1I5QAAwHqQygEAgPVgBgsAALAezGBxuLhtZwU4yJOyPm73g0qvt62PYzCDxby4BV2BwQwWAAAArAOpHAAAWA9SOQAAsB6kcgAAYD2YwQIAAKwHM1gcLm7bWQEO8qSsj9v9oNLrbevjGMxgMS9uQVdgMIMFAAAA60AqBwAA1oNUDgAArAepHAAAWA9msAAAAOvBDBaHi9t2VoCDPCnr43Y/qPR62/o4BjNYzItb0BUYzGABAADAOpDKAQCA9SCVAwAA60EqBwAA1oMZLAAAwHowg8Xh4radFeAgT8r6uN0PKr3etj6OwQwW8+IWdAUGM1gAAACwDqRyAABgPUjlAADAepDKAQCA9WAGCwAAsB7MYHG4uG1nBTjIk7I+bveDSq+3rY9jMIPFvLgFXYHBDBYAAACsA6kcAABYD1I5AACwHqRyAABgPZjBAgAArAczWBwubttZAQ7ypKyP2/2g0utt6+MYzGAxL25BV2AwgwUAAADrQCoHAADWg1QOAACsB6kcAABYD2awAAAA68EMFoeL23ZWgIM8Kevjdj+o9Hrb+jgGM1jMi1vQFRjMYAEAAMA6kMoBAID1IJUDAADrQSoHAADWgxksAADAejCDxeHitp0V4CBPyvq43Q8qvd62Po7BDBbz4hZ0BQYzWAAAALAOpHIAAGA9SOUAAMB6kMoBAID1YAYLAACwHsxgcbi4bWcFOMiTsj5u94NKr7etj2Mwg8W8uAVdgcEMFgAAAKwDqRwAAFgPUjkAALAepHIAAGA9mMECAACsBzNYHC5u21kBDvKkrI/b/aDS623r4xjMYDEvbkFXYDCDBQAAAOtAKgcAANaDVA4AAKwHqRwAAFgPZrAAAADrwQwWh4vbdlaAgzwp6+N2P6j0etv6OAYzWMyLW9AVGMxgAQAAwDqQygEAgPUglQMAAOtBKgcAANaDVA4AAKwHqRwAAFgPUjkAALAepHIAAGA9SOUAAMB6kMoBAID1oAYLAACwHtRgcbi4betaOMiTsj5u94NKr7etj2NQg8W8uAVdgUENFgAAAKwDqRwAAFgPUjkAALAepHIAAGA9SOUAAMB6kMoBAID1IJUDAADrQSoHAADWg1QOAACsB6kcAABYD2qwAAAA60ENFoeL27auhYM8Kevjdj+o9Hrb+jgGNVjMi1vQFRjUYAEAAMA6kMoBAID1IJUDAADrQSoHAADWg1QOAACsB6kcAABYD1I5AACwHqRyAABgPUjlAADAepDKAQCA9aAGCwAAsB7UYHG4uG3rWjjIk7I+bveDSq+3rY9jUIPFvLgFXYFBDRYAAACsA6kcAABYD1I5AACwHqRyAABgPUjlAADAepDKAQCA9SCVAwAA60EqBwAA1oNUDgAArAepHAAAWA9qsAAAAOtBDRaHi9u2roWDPCnr43Y/qPR62/o4BjVYzItb0BUY1GABAADAOpDKAQCA9SCVAwAA60EqBwAA1oNUDgAArAepHAAAWA9SOQAAsB6kcgAAYD1I5QAAwHqQygEAgPWgBgsAALAe1GBxuLht61o4yJOyPm73g0qvt62PY1CDxby4BV2BQQ0WAAAArAOpHAAAWA9SOQAAsB6kcgAAYD1I5QAAwHqQygEAgPUglQMAAOtBKgcAANaDVA4AAKwHqRwAAFgParAAAADrQQ0Wh4vbtq6Fgzwp6+N2P6j0etv6OAY1WMyLW9AVGNRgAQAAwDqQygEAgPUglQMAAOtBKgcAANaDVA4AAKwHqRwAAFgPUjkAALAepHIAAGA9SOUAAMB6kMoBAID1oAYLAACwHtRgcbi4betaOMiTsj5u94NKr7etj2NQg8W8uAVdgUENFgAAAKwDqRwAAFgPUjkAALAepHIAAGA9SOUAAMB6kMoBAID1IJUDAADrQSoHAADWg1QOAACsB6kcAABYD2qwAAAA60ENFoeL27auhYM8Kevjdj+o9Hrb+jgGNVjMi1vQFRjUYAEAAMA6kMoBAID1OPZuAOg5lEqlUqkUiUQ4jms0mvb2dhQXCAQEQWB/f/fk8Xi6/6VWq3EcJ0nS6FdsAIA5IJUD26irq9uxY8fZs2cHDRokEAgaGhquX78ul8v5fH5ycrKXlxfaDMfxtLS01NRUDodD03RZWdnPP/+sVquHDx+enJyMMr5jam1tLSws9PX19ff3d+R2gicTpHJgG8eOHVu3bl1ra+upU6f0/nTlyhXdX2NjY7dv356amlpVVbVs2bKDBw/iOJ6QkLB79+5+/fp1aSMVCoVEIjl//rxSqaRpmsvlpqSkJCUlkSTZ6T9+9NFHx44dCw8PT01NFYvFetfcIiMjn3nmmU73A0AXgVQObGP48OEvvfTS4cOHq6qqmGBYWNhTTz2lUqnu3Lnz6NEjNPNVIpHk5OSgVH7jxg2apmmavnfvnlQq7dJU3tjY+MUXX/znP/+RSqVM0NfX98MPP3z55Zf5fL6J/21ra/vll18kEklRUdHZs2cNx4Lc3d0PHDgwfPjwLmk6AJ2BVA5sIyIi4uuvv/bx8dmwYYNSqcQwzM3NbdmyZbNnz25vb7969erOnTsPHTqk1WoxDNNoNBiGBQcHDxkypLa2FsfxyZMnJyUldV3zZDLZmjVrvvrqK/TQXC5XrVZjGFZeXv7vf/+bz+e/+OKLHE6Hb4fKysq2tjb0s0ql0vsrjuMBAQHu7u5d1nwAOgFDfsBmSJIMCQlhxpH79euXkZGBYVhxcbG3t/ebb74ZFhamu72Xl9fGjRv/85//7N69+9NPP/X29u66tuXl5WVmZqI8juP4+PHje/fujU6uKysr9+zZU1dX19H/0jR96NAhExuEhYVt3LgxNja2K1oOgDngrBzYku7IQ3FxcUtLy4MHD95++20ej3fo0KFJkyZt3bqVWWCsUqnEYvHIkSMxDBMKhYZ7UyqV6Cyez+drNBr0M47jRjc2gaKoioqKR48eMY2cPn16U1PTggUL0Ll2QUGBRCLx8/PraA93795Vq9UEQURHRw8aNOjWrVslJSWtra0Yhjk7O7/55psjRoyAgXJgR5DKgS2JxWLmrLyhoWH37t15eXk5OTkeHh4cDuedd95xdna+cuVKZGQkRVG//fbbzz//TNM0n89/9tlnx48fz+Vy0f/SNJ2Xl3f48OGioiKSJOPi4uRyeXFxMU3TQqFw2LBhGRkZrq6uZraKIIi4uLjw8PDCwkIU4XA4oaGhTPJtamoqLS1NSUnpKB3HxMQcP368b9++u3fvjo6OlslkCxcuPHjwoFarTUxMfP7552FOC7AvDq2zcB/7eyWu7g82iRtu1s1xvYaxJW5OsNN4dzY+ICCAmTauUqm+//77lpYWZoPAwMAPP/ywpaXFxcWlvb39zJkze/fuxTAMx/GioqLExMSgoCD0j0eOHFmzZk1+fj46hWdWRSNHjx5FM0n0nr6JgyEyMnLevHmfffYZRVHjxo1LTEzMy8tjdujs7Ozl5UUQhO4edB/xzTffdHFxSUhI6NevH47jJSUl+fn5Wq3W1dV1ypQpwcHBRh/XaPNs2+Gm4x09bjfEbbtzC9443ZPZOop3f8bjdFF9CfuWy9CL6zXMweM0m2uwSCQSdM0TwzCKoqqrq3X/BcdxgiDc3NwwDOPz+WPHjs3MzJRKpTRNt7S0KJVKtMMzZ84sW7aspKREr090MUuKzDwYhELha6+9NmzYMA6HExISwuPxdu3axVzJTE1NTUhIMLGfgICAd999l8Ph4DiuUql27tyZn5+PYVh6evq0adNIkrTgPYJBDRbz4hZ0BQY1WACwRmBgoOlZfQyCIEaPHj116lR0Fl9aWlpaWophmEKhOHDgAMrjIpFo6tSp/fv3Z942np6ec+bMWbx4cVxc3OO2TSAQ9O/fPyYmxtnZubKy8tSpU1qtliTJoUOHLl68mFnE1BEej4dGUW7dunX48GGVSsXn8//5z392+o8AdAMYKwe21N7eji5OYhiG43hSUpJUKq2srDS6MY/HCw0NRfmxtbVVLpdjGKbVapubm9EGkZGRa9euPXXq1AcffIDOoCdPnrx+/XqRSKS3+v+xNDU1rVmz5ubNmxiGDR48+IsvvkhMTDT/Ce7ZswddQe3du3daWprR00kAuhmclQNbkkqlaMIfhmGurq7bt2//9NNPfX19XV1dDVMeRVG3bt1iBmQQgUAwaNAgZm9Xr15tbGxEHw88Hm/IkCFubm5mnvgbpVKp9u/f/9///ler1YaEhCxevLhfv37mV+0vKio6f/48ao+rq6uLi4vFLQHAhuCsHNiMVqstLCxkVtCQJOnr6zt58mQnJyexWGx02jiPxyNJkjmRxzCMIAhmrU19ff37779P0zSqzBUdHW3lMiKaps+dO7dhw4bm5maxWLxw4cKQkJCvv/7a1dV10qRJna7xUavV//vf/4qLi1E7+/Tp4+/vb017ALAVSOXAZiiKKiwsZM7KEWdn5+effx4zdumSIIikpKR9+/a1tbW5urqiy6F6mAunXC53woQJkZGRun+laRoNvIhEInNamJ2d/emnn5aVlWEYJhQKSZJcuXLl8ePH/f39Y2NjU1JSmC3RULjev9fX11+4cAF9jeDz+YMGDYK55MBBQCoHNqNSqXQXtdM0XVxcbLqOoFqtRoMbzc3NzBC5bo0UhkAgCAgI0Ftbf//+/R07dtTV1Y0dO3bKlCkCgcBE865du/b+++8ztb1qa2sXL16sUCgoitJoNMwnkFarvXr1alZWVr9+/caMGaOb0I8ePXrjxg30M4fDCQgIMPFwAHQrWgdFUXo/2CRuuFk3x/Ua5uBxiqIMtzT67+bEu63xCoVix44duqMoBEHExsZu3rz54cOHhttTFHXz5s0hQ4agjXEcnzt3blNTU3Nz8+jRow0PVBzHQ0JC9u7d297ejv5doVC88cYb6HMiPDxc91EMf2hoaEBfDowaOHBgSUkJ2j47Ozs2NhbH8cDAwCNHjug+8eXLlzOLmJydnX/77TfDV8H894jpV9/6F8jo41oWN3FM2vBY7ShuQVcYfRW6LW6XjAeXPYFt3Lt3b926dbW1tUyEoqi7d++uWrVq586dhtur1eqDBw9evXoV/UrTdGZmZm5urlar1R06Z9A0XV5evnLlymPHjqFKWG1tbTdv3qQoCv1Md7DGBCkrK8vNze3or+Hh4cycwvr6+kePHtE0XV1dffnyZd3xIi6Xy1y85fP5zs7OJh4RgO4EAyzANsRicWBgoGEW5vF4Hh4eRv8lKiqqT58+LS0tzK/u7u5SqVQikehuJhKJmLU8JSUlixYtEolEY8aMcXJyev3112UyWXV19fTp003P7/bx8Rk5cmRtba3ehBkMwzw8PCZPnsyMtsfGxmZkZJw4ccLd3X3IkCG6Qzpjx449fvx4Xl4eQRBjx46Nj4/vpFMA6C7/Zz00Das9HSBOs3O1J03TMpnM6Am1UCgUiUSG+6EoSiaTUX9PBCRJ0s3N7dq1a2PGjJHJZKgT+vXrN3HixMOHD+fl5TFbbtiwYcGCBVwuV6PR3Lhxo66uDt2oyPTB0NjYePr0acNUHhwcnJKSwufzdZ9Ifn5+cHCwn58fWuHJNPjOnTt37txB1zxDQ0MNXwXz3yMYrPY0L25BV2BP3mpPqMHi0HFzgp3Gu63xJupb6W7JbI/juN6sFZqmSZJkxqNJkhQKhaWlpbr519nZ2c3NDR3QJEkmJyd31B69H9zd3adMmdJRC/WeyODBgw3j6KOFuT+Gle8RwwbbPN7R43ZD3LY7t+CN0z2ZraN492c8OCt3uDjNzrNyW8UbGhoWL17MXN7EMIwgCOZ8PDAw8OWXX37vvffQOTjWjQeVXm9bH8fgrNy8uAVdgT2BZ+WG3QeAHbm7u3/00UcDBw784osv0KQUFMdxPCQkZMWKFRkZGejWmvZtJwAOBVI5cCw4jgcHB8+ZM2fo0KG3b99mBt95PF5CQkJYWBgz/AIAYEAqB46IJMm+ffvGxMQY/S5p79YB4HBgXjkAALAepHIAAGA9SOUAAMB6kMoBAID1IJUDAADrQSoHAADWg1QOAACsh1Nm39UQAACAY4IaLA4Xt21dCwd5UtbH7X5Q6fW29XEMarCYF7egK7AnrwYLDLAAAADrQSoHAADWg1QOAACsB6kcAABYD1I5AACwHqRyAABgPUjlAADAepDKAQCA9SCVAwAA60EqBwAA1vv/AH70gU9FCVGbAAAAAElFTkSuQmCC	L_0 > 0.67 \, \text{m}; x = 0.9 \, \text{mm}
+717	 A common piece of optical equipment is the viewgraph machine used in physics colloquia and seminars. A rough sketch is shown below (Fig. 1.48).  One or more optical elements are located at positions **A, B, C,** and **D.** Describe each element and explain how the elements are used in the operation of the viewgraph machine. Write down the relations which must be satisfied by the distances between the elements. Which element in this device was not available at reasonable cost in 1900?	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	\text{Objective lens}
+718	Show that Fresnel half-period zones for a circular aperture all have equal areas.	[]	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	\text{The proof is omitted here.}
+719	"Explain how the colored rings in the demonstration experiment shown in Fig. 2.17 are formed, and show that the estimated size of the rings is consistent with your explanation. Why are the rings so bright?     Hint: Mirror problems involve ""folded optics"", unfold this problem."	[]	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	r = \left( \frac{n m \lambda a^2 b^2}{d (a^2 - b^2)} \right)^{\frac{1}{2}}
+720	The radius of curvature of the convex surface of a plano-convex lens is 30 cm. The lens is placed with its convex side down on a plane glass plate, and illuminated from above with red light of wavelength 650 nm (Fig. 2.20).    (a) Find the diameter of the third bright ring in the interference pattern.  (b) Show that for large $R$ this diameter is approximately proportional to $R^{1/2}$.	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	d = 1.4 \, \text{mm}; d \propto R^{1/2}
+721	Fresnel biprism. A Fresnel biprism of refractive index $n$ and small equal base angles $\alpha$ is constructed as shown in the sketch (Fig. 2.10).  (a) A ray of light incident from the left normal to the base of the prism may enter either the upper or lower half. Obtain the angular deviation $\theta$ for the two cases. Assume $\alpha$ small. Draw and label a sketch.  (b) A plane wave is incident normal to the base of the prism, illuminating the entire prism. Fringes are observed in the transmitted light falling on a screen parallel to the base of the prism. What is the origin of these fringes? Obtain an expression for the fringe separation in terms of the angle of deviation $\theta$ of an incident ray. Draw and label a sketch.  (c） With a glass biprism in yellow light a fringe separation of 100 $\mu$m ($10^{-2}$ cm) is observed. Estimate in degrees the base angles $\alpha$ of the prism. Indicate and justify your choice of refractive index and wavelength of yellow light.	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	\theta = (n - 1) \alpha; \Delta y = \frac{\lambda}{2(n - 1)\alpha}; \alpha = 6 \times 10^{-3} \text{ rad} = 21'
+722	(It is impossible to increase the apparent brightness of an extended (large solid angle) diffuse light source with lenses. This problem illustrates that fact for a single lens.) A light source of brightness $S$ subtends a solid angle that is larger than the acceptance solid angle $\Omega$ of a telescope that observes it. The source emits $S$ units of optical energy per unit area per unit solid angle per second isotropically. The objective lens of the telescope has area $A$ and is a thin lens.  (a) Show that the energy entering the telescope per second is $S\Omega A$.  (b) Show that the product of the area of the image formed by the objective lens and the solid angle subtended by the objective lens at the image is $\Omega A$.  ( c ) Explain why the above results show that the apparent brightness of the extended source is not changed by the objective lens of the telescope.	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+723	A thin, quartz crystal of thickness $t$ has been cut so that the optic axis (o.a.) is parallel to the surface of the crystal (Fig. 2.70). For sodium light ($\lambda = 589 \text{ nm}$), the index of refraction of the crystal is 1.55 for light polarized parallel to the optic axis and 1.54 for light polarized perpendicular to the optic axis.  (a) If two beams of light, polarised parallel and perpendicular to the optic axis respectively, start through the crystal in phase, how thick must the crystal be in order that the beams emerge 90° out of phase?  (b) State precisely how to use the above crystal to produce a beam of circularly polarised light.	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	t = 14.7 \, \mu \text{m}; \text{Pass a plane-polarized beam through the crystal with the polarizing plate at 45° to the optic axis.}
+724	A pinhole camera consists of a box in which an image is formed on the film plane which is a distance $P$ from a pinhole of diameter $d$. The object is at a distance $L$ from the pinhole, and light of wavelength $\lambda$ is used (Fig. 2.66).  (a) Approximately what diameter $d$ of the pinhole will give the best image resolution?  (b) Using the pinhole from part (a), approximately what is the minimum distance $D$ between two points on the object which can be resolved in the image?	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	d = \sqrt{\frac{\lambda L P}{L + P}}; D = \sqrt{\frac{\lambda L (L + P)}{P}}
+725	"A parabolic mirror of small relative aperture (10 cm dia, 500 cm focal length) is used to photograph stars. Discuss the dominant limitations of resolution, first on axis then off axis. Roughly what is the size of the image ""blob"" for a star on axis for visible light?"	[]	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	d = 0.3 \times 10^{-2} \, \text{cm}
+726	Given the following arrangement (Fig. 2.82), where the crystal is assumed to have parallel planes of atoms spaced by distance $d$. The X-ray tube has anode-cathode potential difference $V$ volts. The angle $\theta$ is variable. What is the angle $\theta_m$ below which no X-ray intensity will be recorded by the film? Explain semiquantitatively how one could produce circularly polarized light from an unpolarised source, using a linear polariser and a slab of fused (i.e., isotropic) quartz and a compressor clamp.	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	\theta_{\min} = \arcsin \left( \frac{1}{2d} \sqrt{\frac{150}{V}} \right)
+727	 Sketch the interference pattern on a screen at the focal point of converging lens which arises from a double slit on which plane monochromatic light is incident. The two identical slits, having width $a$, are separated by a center-to-center distance $d$, and $d/a = 5$.	[]	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	I = I_0 \left( \frac{\sin \beta}{\beta} \right)^2 \cos^2 \gamma
+728	Sunlight enters a large darkroom through a hole 2 cm square, which is covered with a parallel set of wires of width $w/2$, spaced $w$ between centers. The sunlight falls on photographic plates at distances $d$ behind the hole (Fig. 2.43). The sun’s angular diameter is about 0.01 radian; describe the predominant character of the images for the following cases:  $(w, d)$ = (a) (1 mm, 1 mm)                        (b) (1 mm, 10 m)                        (c) (0.005 mm, 10 m)	[]	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	\text{Shadows of the square hole and the wires}; \text{No fringes, uniform intensity on the plate}; \text{Colorful diffraction patterns are seen on the plate}
+729	 A double-slit interference is produced by plane parallel light of wavelength $\lambda$ passing through two slits of unequal widths, say $w_1 = 20 \lambda$ and $w_2 = 40 \lambda$, their centers being $1000 \lambda$ apart. If the observation is made on a screen very far away from the slits, i.e., at a distance $L \gg 1000 \lambda$, determine the following features:  (a) Separation $\delta x$ between adjacent maxima.  (b) Widths $\Delta x_1$ and $\Delta x_2$ of the central maxima of the diffraction patterns of the two slits individually (i.e., distances between the first zeros).  ( c ) Hence, the number of fringes produced by the overlap of these central maxima.  (d) The intensity ratio between intensity maximum and minimum in the center of the pattern.  (e) An analytic expression for the intensity on the screen as a function of $x$ when $x = 0$ is at the exact center of the pattern. Show your reasoning.	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HNs0aJFMpkMHEJRNDEx8d69e2xut2/fBn0WT0/Pw4cP93rd7Mdh5wIYhtFoNO3cXQEURQFb9I6nXLp0aenSpWvXrq2qqnqo4gZ2UQCCIAiKol08BbPZzPo4kSRpMBjYcThN0/eLs8hCURRoG2xH7waDITs722q1TpgwYcmSJVKptKSkZMuWLS0tLadOnfrxxx91Ol1kZOS8efOkUmlGRsaePXtYa9ExY8Z8+umnI0aMUKlUP/zwQ8e3sd9w2Be3tbX19ddf12g0n3322ciRI9nfNRrNyZMnz5w54+bmtmLFioiICPa9aWtrO3jw4JEjRxiGsVgsW7duhVP9QwLwWWo0Go1GM3z48I4JdDrdtm3btFrtmjVrFArFyZMnf/zxx6eeeuqZZ55BECQtLe3ChQvPPPNMdHQ0iJ7GYjAY8vLy2trampubm5qaaJr28vJKSkoC9hQymWzFihXTpk17+umnvby8GIY5cuRIeXm5TqdrbGykKCosLOzAgQMKheKjjz767LPP8vLy9Ho98BZFUTQyMnL06NEVFRX5+fnl5eVjxozpj5vVkZ73MQZnvzE9PV2hUIjF4tTUVPZHlUq1fv168GHjOB4REbFr1y6z2QyOEgSRmpqakJCA47iXlxeIpTUkGJyPoH9yIwjin//8J4IgI0eOzM/P7/Ssy5cvu7u7S6XS8+fP//rrryEhISiKTpw4sa6uLjc3Nzo6GkXRv/3tb+ybwJKWlubl5eXi4sIGJhWJRN9++y1rJclSXV09efJkDMOWLl2qVquTk5MRBFm3bp3VamUYJj093dvbOyoqqqSkhL2Etra25cuXIwiiUCjS0tJ664Y8LAMwfXrz5s2qqirg+1lbW5uamlpXVweOUhRVV1fHesh0G5qmr1+/3tTUFBYWZtsF2L9//xdffGE2m//4xz+GhobevXt348aNt27dAkc5HM6TTz751VdfjRo1SqlUHjp0yE6nN5qmdTod65YP6WeA32QXYYUsFgv4aFtaWvbu3VteXs4wTENDQ0FBwYYNGwoKCvh8/ogRI27dupWRkWH7+vn7+0dHRysUipkzZ86cOTM2NvbRRx8NCAhot+5AUdThw4evX78eEBCwYsUKiUQCMmHDQ/B4PA6Ho9frQRxHQGFhYUZGBoIgDQ0Ne/bssT3Un/S3BFy+fDklJWXVqlVKpbKkpGT16tXJyclbt24Fa6RHjx5NSUk5fvx4D+PA6HS6c+fOoSg6adKkoKAg8GNbW1tGRoZer584ceKhQ4f27t07cuRIpVKZlpbGnoiiqJ+fn1wuZxjm2rVrxcXFDyyLYZjs7OxVq1bl5ub2pM6Q7sHhcNjOf9cqTJLkd999d+rUKZBMp9N98cUXFy5cYBjmiSeeKCsrW7BgwdKlS23fBx6PJ5fLeTye7HckEolKpbItiKbptLS07du3IwiycuXKuLg4DMOAF1O7CjA2xgs0TR8/fryyshLMF168eBFEdut/+nsuoLy8vKqqqqmpqa6u7vTp02fOnLFYLLdu3TIYDGq1etu2bdevX581axbTM0uPGzdu3Lx5U6FQLFu2jB3d6XS6lpYWhmFiY2M9PDw8PDwWLFiwefPme/fu2Z5rMBhAIDC1Wl1fXz9u3Liu12wtFktqaurRo0eHDRsGQnpDBoQHWmqbTKZz586xPYWWlpazZ8+SJBkcHDxlypSDBw9WV1djGHbixInExEQQXuH8+fPHjh2zWCy2L0ljY+Njjz3GhmzJy8t7//33m5ubFyxY8Pzzz4M6gBBMbPAI4D9qW5nq6mqwCWJoaKhSqWxtbT1w4MC7777b/1sh9LcEgJgZDMPcvn377NmzYCZWqVSWl5cfO3YsPz8fPA8ulwsianWayb1793bv3l1TU8OKsUwme+WVV8Cgrq2t7dChQyqVatmyZZ6enkajkY2xC0Ll+Pr6crlcDMPA9E+7Z9PY2AjWEVQq1b59+yZOnPjANVur1UqSZHNzM0mScGlgoPDw8PD09Oz0ENsMWK1WDMP4fD6YgSdJ0sXFZdWqVQsWLLhz505BQQFBEBwOBzxEDMNiYmJmzZrV1NRkm9Wf/vQn1mu7sLDwL3/5S05OTmJi4vvvv896K4NX98yZM6+++qpMJsvPz29tbQXBDpHfg6DcvHlTIpH85S9/uXv37meffbZ3796goCAQ0KWv7lFnDMz7qtFo3nzzTY1GA/40mUzffffdvn37aJpevHhxZGSkRqPJysricDg8Hi8gIMDX15c1riII4vTp09u2bbMNFIOiaHBwcEREBJfLVavVhYWFIpFIJpMlJyf7+Phs27bNy8uLTdlF0Euapo8ePcqOykCEvIiICHsuCsdxuK3oAAJit3Z6yNfXVyQS6XQ6DMNmzpwZHR394YcfkiQJNiBZtGiRt7f3e++9V1FRkZaWxuFwwHNEUTQqKurAgQPthqUCgQAkYBhm//792dnZPB4vNDSUJMkbN24EBwdLpdKAgAAej1deXp6bm+vt7X327FmCIEBcVgRBjEZjamqq2WyWy+WjR4/29/c/fPhwbW3thg0bGIZJSUnpz75Af0sA+JIZhgFh8wB1dXV79uxpa2tLTExcsWKFVqv961//euLECYqiuFxucHDwyy+/nJycDKJ04jgeExOTlJTE4/FGjhxptVrLyspIkgQxLRAEKSkpKSkpEQgE169fv3LlCp/Pf/rpp5OTkzEMY8Njgv90HDqqVKr8/HyKogIDA9VqNYiW849//OOBjwTDMKlUCiVgABGJRGKxuNNDbm5ucrm8oaEhLCxsw4YNKIru37+/uro6NDR07dq1CoUCpBk1alRaWlq7dUHgiNnpYLC0tPTMmTMkSZIk+e2336alpRkMhtWrV69aterxxx+Pioq6fPnyihUrRCJRaWkpj8eLiIgAwwcQbBpF0TFjxowcOVIsFr///vsbN26sra09ePDg9OnTbV28+5r+loCxY8cKBALQ03Z1dfXx8SksLLRYLBaLJSIi4t133x02bNjNmzdPnjyp0+l8fX3VanVOTk5FRQWPx0tJSUEQBMOw2NjY119/XavVWiwWFxeX2bNni8Vidua/pqamtbWVYRiNRgOM9i5evDh37lwvLy8QmSczM3P27NlcLvfGjRvtRgF37ty5d++em5vbpk2brly58uWXXx49ejQ+Ph6k7+K6wJ6cfXXXIF0CNlBTKpVKpXLYsGEdEwgEgkWLFoF/o6OjdTpdQkJCVlbW+++/HxMTY5uSy+XaxlDoGtAI1dXVkSRJ03Rtba1YLAYREBUKxYcffrhp06aMjIza2lovL6+ZM2euWLGCy+UyDCMSiVasWOHq6jpnzhxPT08URZctW+bn53fu3LlZs2axPdb+ob8lAESARhCEx+MtW7YsMjJy5cqVFouFz+cvX758woQJCIL4+fm98sorHh4eCQkJP/3009atW1taWi5dugQkAEGQgoKCNWvWVFdXa7VakUjk6enp4eHx5ptvzp4922q15ubmgjkYMFIgSTI/P7+xsTEgIAAM1S5fvqxSqTgczuXLlxmGYUfvRqPxq6++qq6ujoqKGj9+vKen5/Hjx6urq9evXy8QCJ588slOmwKGYcAOIoPB68s5CQkJiY2NDQwMZHc9aIdQKFyzZs3ixYs9PT25XK67u/umTZsaGxujoqLaddwIgrB/Zt7f3/+TTz4pLS1lu5MSiSQyMhK8URMmTNi1a9cvv/xiNBrDw8NjY2PZSSUMw6ZOnfr444+z7YpAIJg5c+b06dMdfzqQz+eHhYU1NTU9+uijr732WmNjo4eHR0NDw/jx4xctWgRmCuVy+TvvvAMC8lZUVGAYJhaLZ8yYAXKgKKq2traiogLE2zSbza2trSiK/vzzz9OnTxcIBLNnz1ar1Uql8urVq2BUHxQUBCaKFi5ceOLEieLi4nfeeYeiqGvXrrm4uEydOhXkbDKZiouLGYaRyWRCoXDy5MlvvfXW119/XVRU9PPPP0+bNq1TX0B2HwHIQBEREXH06FGGYbqYuBUIBKwHEdiShF0t7jYoio4YMeJ+jkkoivr7+y9btoxhGBzH27UfYPvWrn/pH/pbAlxcXFasWOHh4fH8888HBQW5u7svX7781q1bb731FpgpAYBJUa1We+XKFbPZ/Nhjj02cOBEcwnE8MTFx3759SqUStPZNTU06ne6ZZ54BM/8zZsyYMWOGVqvduXPnv/71LxRFU1JSwCgxOjr69ddf/+STTw4fPkzTtFgsXrBgwezZs0HOUqn0n//856VLl2bMmOHt7c3hcFavXh0XF3fjxg2wSHG/i4IRrAcW8LHZk1KtVoMdDTp26BiGAZZg7eYCekjv5tYn9Nz2sBveeGD3O/Cn2WxWq9W2cSnZ/3zxxRfu7u4ymezIkSPtSqFpmvodgiDAVhPtCtLr9SdOnAA+GOyPZrP5+PHjb7zxxqpVq44dOwZ0xBaz2dwuq669AA0Gw7JlywYqfChgaJn0DlRuZrN5zZo1q1atMhgMHY+q1eoJEyYIBIJPPvmkFwvtyGDLbQAWBdtF2mI3k7KFpumsrKxPP/1UrVYnJSUlJiZ27Eexv7C7ZbRDLBYnJSW1O5HP58+bN2/evHn3q17HynS91I/jOIxdPSQ4efLk4cOHV65ceb+Fd/Ai2T8d6BgMUjuWysrKDRs2lJaWRkRErFu3Dn5jkB5iNpvT0tKGDx8+b968+zUYq1evzs7Onjx5cv9XbwAZjBJgMpl2796dk5PD5XJTUlLCw8NNJlO7LbR6nZ4Y9gkEAh6PBycFBwqDwXDhwoWAgAB2E9R20DSdmpqampq6YsWK8PDwTtNwOJxnnnlm7ty5AzInN5D0fJjR62ObixcvAtMIHMejoqKeeOKJV155paGhoXu52ZOMIIhvvvnmzJkzwLXzYblz586nn37KbtrR/wy24WU/5/bLL7/4+PgsXry400E+wzAajWbWrFljx44tKSnprUK7zWDLbTD2AqqqqnQ6HYqiNE3n5+fn5+crFIqXX365U6uPXkGv13/++efAbLMba0WjR48ePXp0X1QM8kBomi4vL6+vr6+urjYYDB0DeCIIkpWVlZWVtWrVqn6OLDgkGIwSMH369D//+c+2O8nGxMSA7Wv7CBcXl4ULF27ZsuXo0aNvvfUW3EhjCEEQhE6n6yIBSZJpaWk8Hm/ChAnQiasjg/GOgEBL/Vkin89/8cUX09LS0tLSXnjhhX620IT0BD6fHxoa2sUAvqGhIScnJyoqKjY2Fop7R6Bby3+QyWRTpky5efPm+fPnoanv0GLYsGG2dmXtuH37dllZWXx8PLtRMsQWKAH/AcOw+fPnu7u7f/PNN6wXs53QNN3W1gYDhw0Uer0euGl0hCCInJwcgiBmzpwJuwCdAiXg/xk2bNj06dNv3bp1586dhzqxuLj47bffBnHgIP0PG+SjI2q1+tSpU6NHj7YNIQmxBUrA/yMUChcuXCiTyYAHoZ1nEQRx9OjRnTt3/vjjj31aPcj9EAqFbGAoAHDIRxAkJyenrKwsJiam05UCCAIlwBYQJSYwMPD06dP19fV2nkUQRH19PUVRdoYbhvQ6JpOp3VYclZWV27dvv3LlysWLF41GY0hISENDg0qlsl/ZnQcoAf+FQCAYPXp0WVlZaWmpnaewwYggAwUIFsL+SdN0RkbG+vXr33777atXr+I43tDQsHz58t27dz9w1yAnBL67/wWXy42Pj0cQpLm52c7pPYvFUlRU1Mf1gjwAhmEoigJB/jAMA/G5MjMzr1+/bjabt2/fnpGRwdiEh4GwQAloz9ixYzEMu3Dhgp2BwHAcv1/gWkj/4O3tHRwczOVy2UZeLBbzeDyGYUAoB61WGxQUNGXKFCgBHYES0B5/f/+goKD09HTbvmUXiESixMTEvq4VpAvi4+N//fXXffv2gdiQCIJ4eXnZWgqgKBoTE2NrxG2xWIqLi7s2K3QSoAS0BwQCa2xsBIHJHghJknamhNgPwzD27yiF43hAQEBgYCBrI+ji4mLrWiqRSBYuXMguChiNxs8++2z+/PmbNm26n0GB8+AUEmAymew0+GtpAwfBygAAGSdJREFUaamtrQ0ODmYYRqPRmEymzMzMrrsDzO/hQyG9BUEQmZmZO3fu/O2337pnqent7e3n58faAo0fP37SpEns0eLi4v379xcUFBw8ePBhzcAcDweXAIZhTpw4sXz58s2bN6tUqq4TWyyW//3f/01JSTl79qzVai0oKDhw4MD8+fN//PHHLqIDAo/L3q74fTEajTqdzrFNmPPy8l544YXXXnvtrbfe0mq13chBLBYHBweDlRocx6dNm2a7fwy4hwiCWCwWtVrdW9Ueojj47IhOp9uzZ8+ZM2ekUmlQUNCzzz7bRWKCICoqKsBGwyiK/vTTT2azua2tzcfHpwsvFB6P14WBeu/S3Nz8wQcf3Lt3LyUlJSUlxVEXIxsbG6urq2mavnv3rsFg6EbMKLBbHJ/PNxqNvr6+kyZNsp0I1Gg0QAIoimpsbBw7dmxv1n6o4eASYDabtVotwzAWi+WBI3YejzdmzBgURUHDfvXqVZqmQ0JCfH19uzjLYrHU19djGNZpiPHe5fjx4zt37rRYLGazecaMGY7q0QjCYCAI4uXl1cXub10THR0tEAhMJlNkZGRYWBj7O8MwWq0WRJcHkWx7pc5DFweXAKlUav87xOPx4uLiPDw82B0KcByPj4+/X6gp9qynnnrKbDbPnTu3F2rcJXV1dcBawWw2O6qVC9gngjXK6LZvj1wuDwoKKioqSkpKYncBhnTEwSWAoij2HbJnTTggIMDf35/tL3A4nHHjxnXdvGMYlpCQkJCQ0PPado3Vaq2oqHD4PQsoilKpVEACKIqyx0BLrVZfuHDB398/JiaGfdwKhWL37t21tbWPPfYY9BHsAsccTLKwpqM8Hq/rxhwQGBgYHx/PioWXl9fgWfMH2xY6/NvM5XJDQ0PBDhx6vb6d8X+npKenv/DCC6tXry4uLmZ/xHF83Lhxs2bNso1Y3xEY9NXBJcDNzQ10AlEUbedM1ikoigYGBrI7wAQHB/ddwMKHhcfjBQYGAnnCMMxRtQBFUaFQCK4uKCio6w8YAIb0DQ0ND7t8APat7mZFHQUHlwCNRsMu/Nq5Ajxnzhyw+xiGYQ9sQ/oTDMNCQkKABMjlcmfY8QKY/fZd/hiGQSdiB5cAi8UCepIkSdpp8y8SicAq1IgRIx577LFBtSecXC4H9REKhX29scJgoC9uPoqiHh4eXWxA6mw4uASwcDgcO1fvZTLZU089haJoeHi4nb3ExsbGEydO5Ofn96yOD6a4uBhEwoD0BA8PD7g/FYuDrwiw0DRtZ0gPgUCwdOlSLpc7ffp0ezrbJEkeOnRo/fr1c+bM2bNnT7fXse1Bp9PBoBf3w/75EU9PT7lcXlFR0ddVGhI4iwRgGGbn3C+KouPGjQsNDbXT1Ickyfr6eoIg1Gp1n67YOWF4Uo1GY48pNI7jHA7Hzc3Nzc3NnmxVKhW0C2ZxFglgGOahutAPu1aEYZhCoejTESbz+zbnfVfEYKOsrMwef0GJRCKVSoHRpD3ZqlSq1tbWHtfOQXCWuQAEQfp6u0iBQNBbESn0en1NTU27BtBqtRYXF9vvQusAcLlc0LcHoRkNBkNFRUVNTU27DpFGo9FqtTKZrFMrwKqqqtzc3ObmZraPRhCEU93GrnGWXgCKoiRJWiwWo9FosVgoiiorK1Or1SiKhoaGhoaG9ryI3mqf7969+/HHHxcVFf3hD3+QSqVeXl6PPPLIyJEjzWazw5sGAiQSiaura2trK4qi586dw3E8Pz//xo0bBEG0tLRIpdLNmzfHxMSw6YEzONhj07avxzBMQ0PDm2++ef369YCAgKCgoKioqKioKPujwjkDziIBRqPxyy+/PHfu3OXLl0tLS0mSJEkSmA/Hx8e/9NJLbm5u3ZslNplM5eXlDMNUVFRcvnyZx+Mplcp23yqfz+fxeBKJxLabYLFYgOWip6enu7s7hmENDQ1qtfr06dMHDx4kSfLatWsgNimPxwMTE04SmMBgMAA3nszMzGvXriEIQhCErU/Exo0bY2JigKOkxWK5cOECgiBlZWUfffSR7UO0Wq03b95MT0+3Wq2VlZWXLl3icrl8Pp/D4cBwzyzOIgEEQZw4cQLprK3+5Zdf0tPTxWIx+/ZgGNbFqAFsQI5hGE3TPB6PIAggAZmZmYsXL0ZRlA1MANKQJInjOJ/PBwHt2FlGIAEMw8jlcjc3NxRFGxoadDpdW1sbGAJQFAX+46geQfdDKBQKBAKr1UqSJFC9dk/twoULGRkZYAkAx3HwPSuVyj179uA4Dp4OsCmwWCxsv4CmaYvF4mw384E4uAS4uLiwdsESiQSY/SEI0tbWxhqTikSiSZMm2Q4jxWJxSEgIn8/vmCFBEEVFRSaTSSaTURTl4+PD4XCOHDly+/ZtDw+PuLg4Lpfr4eERFBSEYZirqytJkqWlpdXV1eB0LpcbEhLSxcKhVqvNy8tLT08HTqwYhrm7u/v7+wPhqKmpqa+vd/gZQXas7urqOnXqVD6fr9VqVSqVVqvVarU8Hi8xMTE8PNzd3V0kEnE4nFOnTu3Zs0cmk73wwguRkZGgz6VQKBAEuXnz5v79+2tqalAUlcvlAoFALBaTJJmdnQ0tLAAOLgFubm4gvC+Xy12+fPkzzzyDIAgICpabm1tSUlJSUjJz5sw1a9Z025/UbDar1eo7d+4kJibu2bOn55OOBoPh22+/PXbs2NixY2NjY/38/AICAkC2u3bt2rJli8O3YxiGAZmLjY395ptvJBKJwWDQarUg1AfYSphVcwRBfHx8MjMzhULhkiVLoqKibLOKjY1NTExsbm4GEgD2Hbpz5878+fMbGxtFItGgsv4cEBxcAtRqNVgBFgqFTz755IQJE9hDiYmJBEGYTCaRSNQTY1uwIo3juLu7e68sOojF4pdeeik5OZnP54O1SdbiZezYsbahsh0Vb29vb2/vysrKUaNG8Xg8FEUlEolEIvH19WUYpqP9zyOPPHLw4EGGYTo6g+I4HhISEhIS0u5H8OW3m51xThz8+t3d3cFaPYqi7RxCwLC8514iFEWBMUUvOpxwOJxOeyWdjk0cDxRFwVSfnSEScRyPjY3tRkGNjY32OCM7Ng5uF9APu32x4a77YcXOxcXFUeMF2sIGDgNml31XEJjK7bv8hwSO/z4BUBTtIwd7DocTHBzs6uraD54nfW3dNEhQqVQgcFNfSx5N09BS2MEHAiwcDqePetEcDiclJSU6OnrUqFF9kb8tOp3OGWxagCu0Xq+vrq7uCzM+dqMRDMN8fHx6Pf+hhbP0AgiCsNOAvBu4urrGx8f3QwwPpVIJhseOvS7Y1tYGlvrt3y7hoW6IXC6Xy+UIgnC53OHDh3ejho6Eg0sAa13D5/MdI0oEGM7YWrw4Hg8bEIWm6WvXrmVnZ9s/cQBuI8MwwAzRmXFwCWDDh3K5XAcIFMm6zej1egd+d8ESoP3pi4qKVq9e/fLLL9+9e9ee9Hq9HiziOHZnyk4cXAKsVitoLQ0Gg507BQ9mamtrQUPHdpUhDMPk5ubevHmzurq6qanJnlN4PB6YWMUwbPDEhhwoHFwCbOm7ibTCwsItW7ZcvHixj/JnCQwMBJbCOI47agThhwUYCxEE4e7ubmfIEKRvohIOURxcAkwmU9/NAgIIgjhy5Mjf//534IbUp7D+Dr6+vsAGHoJhGDAW9vX17XrrNxY+n+8kRlb24OASQFFUXweHIEmypaXF/pA1PaGlpQXMbgIPub4ubsB5WMNtO40I4DDKFgeXALFY3NeB4lEU7beJxrq6OiAB7ByHY+Pl5dUXNvxGoxFIAJfLdQZry65x8Ot3cXGxdSnrI/ptWD58+HAwj2UymZzBuL2+vt6eTtzD7q0kl8uB/6ifn58zbMfQNQ4uAaze9x04jtuzVVmvIJFIwLvu6urap9HKBwnABdOeZA/l680ODzUajTN0prrGwSWAJMm+9t6hKApEtumHvkBrayvbKjrwigBrzWFnEHG1Wg0irNhJc3MzyF+lUjlJOMYucHAJ4HA4/eMQjmGYnbsV9QR2LsCxMRqNYJgTGBhoj2fUw/qAOclMip04uASwsMHk+ggul2vnilRPcAYfIcTGaK+mpqavW2nYC3BwT8HGxkbQS/fw8AgMDOy7gkiSLCsr67v8EQRhGIbtAmg0mvr6em9v70G+NEiSpMFg6NoOVyQSWSwWMMDR6/UtLS1ZWVlA7Oycx3nYpV+aptn8d+3alZSUJBAIzGYzn8/vtDcBrI+4XC5FUeBEHo/HbvEKRmf2h3KiaRos7srl8uHDhw/47vV9KwH19fWnTp3S6/VeXl5dd9UYhqmvr6+vr/f19XVzc9NoNCqVymAwgPiZPj4+D1x4YxjGaDSKRKK2traysjIMw3Q6XU5ODgjdCeLM9+a12QBCXPT14JwkyebmZvCuZ2VlLVy4MDw8HNyWjqWjKOrt7S2RSGpqary8vBoaGtzc3Pz8/HAcpyjKarXiOF5eXk7TtEQiaWpqAm82iqJCodDDw4NhmNbWVpFIpFar7zf0APez41WDUF/gk2hra+u484ctOI4rFAqVSmU0GoHTTktLS3V1NTiFIAh7Bj4gLrj9I77m5mYQ5dlkMm3duvXQoUMCgcBisXRtL8TlckmSBFfNSgBFUSqVCsQmtrN0mqaVSiVN097e3hMmTNiyZcvAWnn1oQRQFLVt27YdO3ZYLBZ7GiuapgmCAPvDAbkF7wGI9GbPB0bTNFjmtVqtGIaxboIIgqjV6qqqqr4YrlMUVVtby+Vy+7SXgSAIl8udOnXqsWPHDAZDW1tbVlbWlStXukiPYRiHw7FarRwOBwQyZz8SIBkkSdI0jeO4bRPK3mqKosAr3g3pRFGUPeuB3zAIFtppKSKRyB4JiI2NXbduXWBgoD0GwgzDiEQi0PVAEIQkyZqamgee1RcYDAYEQZqbmx1WAkDvyGKxEATBjrhAmHfQrQKbefB4PBD4HbHxhAOfPU3TFEWBF9dqtbIqwOVyrVZr1wNjcJQ1/PD39/fy8uqLywRdAA6H0w8GQtOmTRs/fnx2djby381vF30Q0LJxOBwulwsUFgwoOBwOj8cDKsDj8YBYgO/QViwA4Em1y7mP7GrAvokKhSI0NPSNN94AC/hd4+3t/cEHH9iZP4qikyZN2rRp086dO5VKpdlsRlFUJpMZDAapVGqPR7m7u7unpyeGYVKp1GAwNDQ0IAji6enp5uZGEERZWZlOp/P09DQYDL6+vq6urmVlZRqNpmM+OI7PmjXLzg3s+w60C423s3PbRbKKioodO3bYxmaSSCQMwwiFwoCAALA2ExAQgGGYSCQyGAwURUmlUjY3o9GoVqsVCgVFURUVFaC5EAqFCoWitra2qanpgQ0UQRA0TRsMhpSUlDlz5vTFyJkkydOnT1+9evXll18eMWJEr+dvC8Mwv/32W3Z2NkmSD6U4fD4/ICBAqVQKBAIQQx0IYltbW2trq0KhGDZsWFlZGXCh9fb29vf3t/28m5ubq6qqbDX3gRsi2Nb5oYZI1dXVBoPhkUce8fT0FIvF7R5Zbw24rFarUqkEu8sBf0EwirTHkAzsNAO6nGC7WjDZDO4YeOVAA8bhcDAM61RAAXw+v4e2ST2/IX0rAd2gd3MDAwqj0WirLI7HYH4Egzm3ASl0sOXm4CsCQJ4dI14QBNIXOItdAAQC6RQoARCIUwMlAAJxaqAEQCBODZQACMSpgRIAgTg1UAIgEKcGSgAE4tRACYBAnBooARCIUwMlAAJxaqAEQCBODZQACMSpgRIAgTg1UAIgEKcGSgAE4tRACYBAnBooARCIUwMlAAJxaqAEQCBODZQACMSpgRIAgTg1UAIgEKcGSgAE4tRACYBAnBooARCIUwMlAAJxaqAEQCBODZQACMSpgRIAgTg1Dr65+FCHoiiSJDtuII+iKJfLBf8nCAJBEPZPCOShgBIweGEY5tSpU7m5uR0lwNXVdeHChf7+/haL5fDhw01NTS+++KKnp2cPi6uqqlKr1QzDKBQKhUJxv5Qmk6murk6n0+E4HhwcLBaLbY+azeaysjI3NzcfH5+e1AfSTzD3h6bpLo4+bDI7Gcy59TN6vX758uUczn9k2tXV1d3dXSAQIAiC4/jmzZvNZvPZs2e9vb2lUun333/fk7KMRuOxY8cmTJgQFBQUHBw8a9asvLy8TlPW1tauXbt23LhxQUFB4eHh69ev12q14FBTU9MPP/zwxhtvjBkz5tVXXzUajYxDPNDBfAk9zw1KwKCmvr5++vTpKIoKhcKPPvro+vXrX3zxha+vL4Ig8+fP1+v1tbW1S5YsmT59emFhYbdLoWn63//+t0KhYLsbKIomJSWpVKp2KdVq9UsvvQRkSCQSIQjC4/G+/vprgiDMZvPatWulUimfz0cQJDw8HFTJAR7oYL6EnucGpwMHNQqFwsfHB0VRDMP8/PwYhpHL5eBLu3btmlKpHDZs2ObNmz///POwsDD2LIqizGYzZUPXpRAEcfr06YaGBoZh4uLixo8fjyBIZmamSqVql7KoqCg1NdVsNotEoiVLlsjlcqvVevjwYY1Gg6LohAkToqOjaZpGEEQmk0kkkt6+H5DeB84FDBkKCwt37txZWlq6ffv25557jiRJsVj8008/HT9+3MPD43/+538CAwMRBDGZTKmpqXl5eQqFAsdxBEFwHJ8wYUJERETHOQUAjuMRERFisZim6blz5+bn5+fm5prN5vz8/ODgYNuUCoUiOjq6ubk5IiIiJSUlLy9PqVRWVFQYjUZPT8958+b94Q9/SE5OzsnJwXEclA4Z5EAJGBqYzeYdO3aoVCqJRCISibZs2YIgiEAgKCgo+P7771EU9fHxWbdundFo3LZt29atW41Go8ViAefyeLxnn332s88+azdvx4Lj+LJly7y8vBAEGT9+/Pnz5xmGcXV19fPza5dyxIgRH3/8cUJCwsSJEzUaTXFxMYZhU6dOBTORKIp6eHgIhcI+vBGQ3gYOBIYGFEWp1WrQpUdR1MXFxcXFBcOwxYsXu7m50TTd1NTEMExOTs4XX3yBoujy5ctHjBiBIIirq+uf/vSnOXPmuLi4dJG/h4fHs88+m5ycfPPmzXv37kmlUjDn1zFleHj42rVrw8PDd+/erdPpgoKCnn/++a4zhwxmoAQMDfh8/pIlS8LDw3k8Hob9/1Nzd3fncDhWq7WyspKiqMbGxoaGhsDAwJUrV44ZMwbDsCeffHLHjh2zZ8+2PatTGIapqqratm1bc3Pz/Pnzn332WR6P12lKmqb3799/7tw5Ly+vt99++5FHHunNS4X0L1AChgYcDmfatGlvvfXW6tWro6OjOyYAk3BCoZDP55eXl+/YsaOgoIDH48XHx0ulUnuKqKure/fdd69fvz569Oi4uLgdO3aUlpZ2TMYwTGpq6pdffmmxWCIjI0tLS7/66iuj0djDC4QMFHAuYFCj0+nAqjuCIARBPPvssyiK2s7qsbP9IA1YO1Cr1du3b0cQZMaMGU8//TRIYDab09LSjEbjrFmzOvbbTSbTV199dfz4cYIglErlBx980NraOmbMmJCQEI1Gk56eLhAIpk2bxuFwsrKy3nnnnfLycgRB8vLyMjIyfHx85s6dGxAQgCCI0Wg0m80IgpAkCVQJMsiBEjB4IUny22+/zc3NZRjGZDLt2rWLx+PNmzcPLLwDbt26ZTAYEASpra2trKwsLS21bZAbGxszMzPlcrlIJLpw4cKKFStQFB0xYkRcXFy7srKysg4cOABsjRsaGhAEYacDs7OzX3rpJTc3twMHDkRGRn7zzTclJSXgLLVajSBIYGAg6GiUlpbu27fv9u3bCIIUFRXt2LHjiSeeiIuLY62bIIMQ+GwGL2q1+sCBA01NTVwul8vl5ufnb9++fcaMGawE0DSdk5ODYZhIJAJmQo2NjcjvfQEEQfLz81evXn337t2//vWvAoGAx+Pdr2UuLS3V6XQcDgfHcfDFjh8/fuTIkQiCiMViPp/v4uLC4/F0Ol1dXZ3tnD8wBxCLxSaTae/evTt27EAQRCQSEQSxbdu26urqyMjI+61EQAYDKOhAdgrDMPdbSe5GMjsZzLn1MyRJnj9/Pj09HUXRkJAQsVgcHBwcExNjO7Gn1WoLCgrq6uoCAgICAgIWLlx46dIlFxeXyZMnu7q6njt3rrW11cfH59dffw0JCbl27RpN0+PHj+/oU6RUKr/99tuqqiq5XB4UFISiaFRUVHh4OIIgFoslKyvLzc1t3LhxGIbl5eWVlpYCwzIEQfh8flxcHDBbKi0tBWbFIE+pVBoZGTl8+PAHzkTaz4A80MH8TvY8NygBjgC4TJ1Ot2TJklOnTnG53Pj4eDc3t4sXLxqNxoSEhH//+99yufyhcuvdug3O3Aak0MGWGxwIOA5SqXTjxo1CoTA9PT03NxeYDy5ZsmTNmjX2f/8QZwP2AhwB9jIZhmlubr57925jY6NOpwsMDIyJiXF3d+9ebr1bt0GY24AUOthygxLgCHS8TOBDhmFYNy5/MD8CKAG9nhscCDgmKIpCLx2IPUDrQAjEqYESAIE4NVACIBCnBkoABOLUQAmAQJwaKAEQiFMDJQACcWqgBEAgTg2UAAjEqfk/6I8zJrGAwcoAAAAASUVORK5CYII=	\delta x = \frac{L}{1000}; \Delta x_1 = \frac{L}{10}; \Delta x_2 = \frac{L}{20}; 50; 9; I(x) = I_0 \left( \frac{\sin \frac{20 \pi x}{L}}{\frac{20 \pi x}{L}} \right)^2 \left( 5 + 4 \cos \frac{2000 \pi x}{L} \right)
+730	When the sun is overhead, a flat white surface has a certain luminous flux. A lens of radius $r$ and focal length $f$ is now used to focus the sun's image on the sheet. How much greater is the flux in the image area? For a given $r$, what must $f$ be so that the lens gives no increase in flux in the image? From the earth the diameter of the sun subtends about 0.01 radians. The only light in the image is through the lens.	[]	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	f \geq 100r
+731	 A Lloyd’s mirror (see Fig. 2.12) can be used to obtain interference fringes on the screen from a single source as shown. Construct (draw) a two (coherent) source system which is equivalent. The first fringe (at the point 0) is dark. What does this imply?	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	\text{Phase change on reflection} = \pi
+732	(a) Distinguish between Fraunhofer and Fresnel diffractions in terms of the experimental arrangement used.  (b) Show schematically an experimental arrangement which will allow Fraunhofer diffraction to be observed.  (c) Draw the pattern observed on a screen of the Fraunhofer diffraction from a single slit (width $a$) and from a double slit (widths $a$, separation $d$). Point out the distinguishing features of each pattern.  (d) Calculate the interference pattern that would be obtained if three equally spaced slits were used instead of two in Young's experiment (screen far from slits).	[]	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	"\text{A light source is located on the front focal plane of a convex lens } L_1 \text{, the light emerging is plane waves. The waves fall on a diffracting aperture, behind which a convex lens } L_2 \text{ is located. On the back focal plane of } L_2 \text{ is an observation screen, on which the Fraunhofer diffraction pattern appears.}; \text{For a single slit (width } a\text{): Principal maximum at } \theta \approx 0, \text{ and diffraction zeros at } \sin \theta = k\lambda / a \\ 
+\text{For a double slit (widths } a\text{, separation } d\text{): Interference pattern is shown with an envelope of single slit diffraction, maxima occur at } \sin \theta = m\lambda / d \text{ and zeros at } \sin \theta = (m + \frac{1}{2})\lambda / d.; I = A_0^2 \frac{\sin^2 \left( \frac{n a \sin \theta}{\lambda} \right)}{\left( \frac{n a \sin \theta}{\lambda} \right)^2} \frac{\sin^2 \left( \frac{3 n d \sin \theta}{\lambda} \right)}{\sin^2 \left( \frac{n d \sin \theta}{\lambda} \right)}"
+733	A 5 mm thick glass window 2 cm in diameter is claimed to have each  surface flat to within 1/4 wave of mercury green light $(\lambda = 546 \text{ nm})$, and the  pair of surfaces parallel to within 5 seconds of arc (1 arc sec $= 4.85 \times 10^{-6}$  radians). How would you measure these properties to verify the manufacturer’s specifications? Your may assume the refractive index of the glass is   $n = 1.500$.	[]	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	S \geq 0.75 \text{ cm}
+734	 A lens (of focal length $f$) gives the image of the sun on its focal plane. Prove that the brightness of the image (W/cm$^2$) is near that of the surface of the sun.	[]	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	L \approx L'
+735	 A two-slit diffraction pattern is produced by the arrangement shown in Fig. 2.9. A discharge tube produces light of wavelength $\lambda$ which passes through a small slit $S$ immediately in front of the tube. The centers of the two slits of width $w$ are at distance $D$ apart. Find the condition that a maximum intensity be observed at the screen a distance $l$ from the central plane. Assume that $D \ll L$, $l \ll L$, and that $w$ is very small. How large may $w$ be before the interference pattern is washed out? As $w$ increases, do the maxima and minima wash out first near the midplane or further away? What is the effect on the intensity and sharpness of the pattern of increasing the width $S$ of the slit at the source?	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	l = \frac{n \lambda L}{D}; w = \frac{\lambda L}{D} = D; w = \frac{D}{n}; V = \left| \frac{\sin \frac{\pi DS}{\lambda z}}{\frac{\pi DS}{\lambda z}} \right|
+736	A soap film ($n = 4/3$) of thickness $d$ is illuminated at normal incidence by light of wavelength 500 nm. Calculate the approximate intensities of interference maxima and minima relative to the incident intensity as $d$ is varied, when viewed in reflected light.	[]	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	I_{\text{max}}/I_{0} = 0.08; I_{\text{min}}/I_{0} = 0
+737	A 35 mm camera lens of focal length 50 mm is made into a telephoto lens by placing a negative lens between it and the film, as shown (Fig. 1.43). $L_1$ = camera lens, $f_1 = 50 \ \text{mm}$; $L_2$ = negative lens, $f_2 = -100 \ \text{mm}$.  **(a)** What is the distance $x$ if the system is focused at an object 50 cm in front of $L_1$?   **(b)** What is the magnification produced by the lens combination?	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	55.2 \, \text{mm}; 0.17
+738	A circular aperture of radius $a$ is uniformly illuminated by plane waves of wavelength $\lambda$. Let the $z$-axis coincide with the aperture axis, with $z = 0$ at the aperture, and with the incident flux travelling from negative values of $z$ toward $z = 0$ (Fig. 2.30).  Find the values of $z$ at which the intensity of illumination on the axis is zero (Fresnel diffraction). You may assume $z \gg a$.	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alTJ2t12aACzA8oJuK6lo+JTCZTRkbG5s2br1+/npOT87K1phRFpaWlrVmz5qeffpo0adLMmTOtMqaOCjA/oJiI0wiCgOs8W+yJWq127969P/74I9yhFQCgUCiCgoIoirp79y5FURiGdevWTalUFhcXP3nyRK/XZ2VlrVmz5ubNm4sWLXr33XdbODhCBZgfUEzEaQqFQqFQtFgeVVVVbd68eevWrbW1tWKxuEOHDsOHDx8yZEhoaOiNGzemTZumVqvlcvnKlSsHDhxYVFR048aNf//73/fv36co6tdff01LS1uxYsWkSZNacpoPKsD8gOZYc5pYLG6xEKO2tvabb75JSEjQaDQODg6zZs2KiYlxd3eXSCQUReXl5Wk0GgAAhmFSqdTW1jY4ODgoKGjIkCHx8fGHDh3Ky8vLz89fu3atSCQaN24cmumDvBbUOuMio9EIe2fgtoQtkEc1NTXffvvtrl27dDqdSqVaunRpTEwMPEQEgkfRAwAoisrPz4dJIgjCy8tr9erVvXr1WrFiRVpaWnFx8RdffOHo6Dhq1KiWKVqoAPMDap1xUVVVFRwvLysrKysrUygUzfo4o9EYHx8fHx+v0+mcnZ3XrFkzadIkqVRqLhsGgyElJQX+TNN0YWFh42IjEolGjhwpEAgWLlyYnZ1dUVGxZcuWoKCgoKCgZk02hAowP6CYiIsYhoEBCEmSJpOpWfOIZdnffvtt+/btDQ0NMpls+vTpU6ZMeaajhyTJx48fw58pisrNzTUfN2Y2aNCgpUuXLlu2rLq6+rffflu1atUPP/zQAktnUQHmBxQTcRFJknDcSiAQ4DjerHlUXFz8r3/9q7i4GAAwZsyYxYsXi8XiZ55YVlZmntPIMExDQwNN089sqi8UCidPnlxRUfHPf/5Tq9WePXu2R48esbGxzd17jQowP6CYiIvMmaJQKJRKZfPlEUVR+/btu3z5MsuywcHBc+bMUalUzz8uNTXVYDCYf4Wnnj1/mUgkmjZtWnJy8rFjx0wm07Zt24YPHx4aGtpMiYdQAeYHtBaf0+B8oua7f3Z29vHjxymKkkgkM2bM6NGjxwu/2FlZWSaTyfxrZWVlRUXFC2/o6uo6Z84cT09PAEBJScm+fft0Ol0zJR7hE1QTcVp1dXVlZWUz3ZwkyfPnz6enpwMAhg4dOmHChJedYta3b9+OHTsCADAM8/b2HjhwoLOz8wuvxDDsnXfemTp1qkQiMZlMP//8871795op/QifoJqI05p1PlFBQcGePXuMRqOjo+OUKVNesVbjnXfe2bZtW0hIiEwmW7du3ZdffmneKuB5IpFowoQJXl5eAIDi4uILFy40btm9PZIktVot6h7iGVQTcZG5F8ZoNDZuFlkQy7LHjx/PzMzEMKxfv379+vV7RYcLjuOdOnXy8fHBMMzR0dHGxubVvTPe3t5jxoyBP589e/ZlTbk3o9VqS0pK0AGwPINqIi6Chx0CAJRKpVKpbI5HwLF2mqbFYvGAAQMcHR0teHOJRDJq1CjYW5SVlXXy5EkL3lwsFtva2qKOap5Bo/hc1DgUwjCsOfIoKysrLS2NZVl3d/eBAweC1xkOb8qVQUFBERERxcXFJEleunRp8uTJlqrsdDpdTU2NOQ2oAPMDGsXntGY6jZqiqJs3b5aUlAAAhg4d6ufn91qPaMrFjo6OgwcP/vXXX3U6XUZGRmFhoZOT05un+P8+vXECUAHmBxQTcRr7X5a9rcFguHnzJkVRdnZ2/fv3f34q48sIBIKmx2hDhgxxdnbW6XQlJSX3798PDQ21yIyEZz4QVID5AcVEnNZMMZFarb5x4wYAwM/Pr0uXLk2/v7u7u7u7exOvVygUvXv3Liws1Ov1Dx8+pCjqZbMEXguKiXgJ9Vi3Renp6XCLD1dX19ddXtv02kQqlfbu3Rv+/OjRo2YaBET4AbXOOK2ZWmeXLl3S6/VisbhPnz729vZNv7/JZDIajU28HsMwV1dXmUym0+lSU1NLS0ttbW3fItX/P9Q64yXUOuO05midGY3GyspKhmHEYnFoaCiOv0ZcXFVVVVVV1cT0EAQRGhrq6emZmZmp0+mys7Mtsk+IQCAQiUQAAJZltVotKsD8gGIiTmuOmCg/P//BgwcMwwgEAmdn59e6uY2NjVwub/pLbG1tYRzEsmxDQ4NF3oitra2npyfc3lsikbTBAmw0GtVqNQDAzs6ON3tjopiI05ojJjKZTHBVqlwu9/b2fq2bw+1Kmv4SlUoFtygyGAxJSUljxoyB4czbaGhoKC0thecdtfBxA29Go9GcPn26qqqqe/fu4eHhr1go8woURZ06derq1asURanV6tLSUgBAcHDw8uXLvb29LZ1kK0AxERc1nrZn8ZjIaDQajUYAgLOzs52d3WvdXK/X6/X6pr8EbsufmJhIkmRRURFJkm9/TCNJko3X93O/AP/5559Lly6tqalxcnIaNmzY8OHDO3fu7OLi4uDg0PSbaDSao0ePnj59Gi5zgf99+PDhiBEj4BK/1g7FRFxkzpTmiIkqKyvh+n5/f3+hUNjEm+M4LpPJlEqlQqFoenowDJPJZPB6hmEs8l6euQP3C3BQUND48eMPHTpUXV2dkJBw6NChoKAgT0/PIUOGREVF+fj4CIXCv6yg7ezsYmNj3dzcbt++fe/ePYZhZDLZpEmT+vTpw/1PoCnQ2R6cZmtra/GOAJqmaZrGcdzNza3pUw1FIpFKpaJpGsZETSz9BoOhuroa/gEvLS0tKCgICgpq4muNRqP5tRiGOTs7SyQShmGKi4thTMSybEFBQUhICNz31t7e/oW97xqNRiAQmEwmkiThihOtVmswGEiSdHFxebPWotForK2tZVnW2dlZJBKxLFtRUfGyIyoBAHPnzh00aNDBgwePHDmi1+uTk5OTk5MvXrwIp1yFhob26tXL1dU1MDDwZVtc4jjet29ff3//uXPn0jQtEoliYmKWL19uqZnrVtfKaiKGYZ7fYgK2NZ5BEMTbz6NjWRbOgoF3g0XNUsfAUxQFNz98vn2Rnp5uMplwHFepVBYZ+X7mufAHg8GQnJzs5eUFwxa4U+0zV1IUVV9fn5WVlZiYePbs2ZKSks8//7xDhw4BAQGwv0Oj0Tx58kQgEAQEBIjF4pycnMYr7/V6PZzMDQB4/Pjx7Nmz3d3dm5hOg8FQXl5urolUKpVUKqUo6unTpxkZGfDR//M//5OQkFBfX29nZ/fCLZNYllWr1UKhEB6XolQqKYpqaGiANZFSqZRIJBiGubi42NjYFBQUND5u+9Vpq6ysZFlWpVKJxWKapktKSswf7AuxLAtf0vgmhYWFhYWFAAAnJycXF5ewsLBvvvnGz8/vZS+Pi4u7ePEi3G585cqVL9slqjVqltWVzYRl2eTk5P3798OBA4im6ezs7Lq6usZXYhimUCh8fX3f8okNDQ2ZmZk0Tbu6unp4eOTk5DAM4+/v//arFuDf9rKyMqlUCicZNlZVVVVRUYFhWP/+/Q8ePNiuXbu3fJwZSZKbN29eunQpwzAikUgulzs5OYnFYqlU6uPjY29vb76SZdmysrL8/HytVltbW6vT6czfNAzDRCKRObQxmUwsy8J/gdVr4yc+U8Beqynxwte+rMS+4s4wiDOHcuY7NG4Fm//SvFbazHewyPfI2dn53Llz5umgjeXm5v7jH/84fPgwTdNLliyZP39+M23SYC2tqcfaYDAcOnToxx9/bMofLgzDkpKScBxvXFYYhoF/9hvvbtO4WoFjMc//cYN/hKFbt27BH4RCIUVRz5y3Ax9H0/QzNxEKhTiOMwxDkiRBEDiOv6LcwzfIsmxJSUlFRYWrq+tfvt8mwnFcoVCYWysNDQ3miBJu3vgyz+zFoVQqYbtALBbLZDJPT8+CggKhUOjv7w8AYBgmLy+vvLwcAJCdnQ27pTAMCwgIcHZ29vLywnFcJBJVVlZqNJqgoCC5XJ6eni6Tyby9vYuKimxtbUtKShoaGhonQKVS1dbWmkym2trajIwMWK34+fm9+gtJEISfn5/BYIAd/xUVFb6+vm+wKwBBEG5ubg0NDZ6enoWFhQRBuLu7P336VKlUCoXCxk2kkpKSoqKiZ7ZPggNemZmZcJFNYziOSyQSBwcHLy+vUaNGhYeHP/OVZFk2MzNz2bJlv/zyC03TTk5OJEneuXMnKiqqJc/abW6tqcdaLBYPHz68pKSktLT0+QpUr9eTJGlnZwd/lUqlBEHY2NiYi51Wqy0uLra3t7exsTGXFYIgfH19ze04FxcXW1vb/Pz8pmzE1a5dO61W2zhAa9++PdwAv7y8PDc31/zv8CnOzs61tbVPnjyxt7d3cHDIy8t74VNIkrx27VpWVhbDMB4eHm5ubhbMI4IgnJ2dYeXbvn37oUOHhoaGmj+0V8BxPDAw0DzcY2NjI5PJzP9LKBSSJMmyrLlXiyRJmqZZlk1ISFi5cqVer3d0dPzuu+/69esHK2IAAE3TMDTDcdxoNJrvQxAERVHPfDgEQcAKOisra8qUKenp6XK5fN26dYMHD351yoVCIayG4N8YoVD4ZiEt/MMjEolIkoTJNplMAoGAZdnG/QDP/xGiKOrIkSNbt25tXCQwDLOzs3N1de3SpUtUVFRERISvr69EInm+30qn061btw5WQwCA2traTZs2/fTTTzt27BgxYsQbvBFuak0xEdxdsEePHnq9/vn/q9VqKYoyty9gcReJRObvBuwgEIlEIpHI/PcWx/HXGkxtASzLxsXFrVq1ymQyqVQqBweHZsqjiIiIDRs2yOVyi9ztmZ518zcqNDQUflFVKpWfn9/Laj3z9X/Zhezr6+vq6pqenk4QhIeHR1OqUUuBlZq53jEntXEGwVLX+FV37txZvXp1UVERjuO2trb29vbh4eFhYWHdu3f38vLy8vJq3BX4fF4LhcKuXbtevXq18dwFmUwGE2PZN2hFrSkmgmQymfmvcWN/2XvXOIrmclcfhmFdu3YViURw4s/zZxxaymuNgr0x8/3t7e3t7e3f/nFw7O/5+3OWs7NzaGioVCoNDAycOHFi7969HR0dJRJJE6dQiESiefPmmXfjhQiCeOF5UK1Xa4qJ2g47OzvYw+Xk5GTxBQ3m4pudnQ07my148+cVFhbCHjEnJycnJ6e3f5xAIJBKpRiG4Tje3MdSWkRgYOC///3vuro6d3f3Z7qomph4kUj0wumL3H/vTdf6YqK24MmTJ413j7XszV1dXVUqVV5eHjwh47XuzzCM0WiEY2dNXDr7TPetRd4OHCiQyWR2dnbcL8AEQXh6esJdvZGXaWXzidqIuro6+OeuOU6wcHNzc3d3hzVRQUGBi4tLE1+oVqvPnDlz+vRpAECvXr2mTJnylwPJJEnCWhXHcVdXV0s1M+GHo9Fonpm9gbReqHXGRTBTWJYtLS2F0/YseHOZTAZ7qUmSzM/P79atW1NepdVq169fHx8fD+cWnz9//s6dO3Fxca+eqajVauFYPkEQSqUSjjS9ZfrR/kS8hFpnXGSegKfVak0mk2XzSCKR+Pr6EgRhNBrT09P/9re//eVLWJb9/fffYWeHv7+/QqG4ffv2mTNnQkJCli1b9opZLfn5+fn5+QAAgiDat29vkTeCdo/lJRQTcZE5U2C/tWXzSCgU9uvX78CBAzqd7uHDhxqN5i8H8imKSk9Pr6qq8vf3j4+PDwwMXLp06bFjx5KSkhYtWvSKlXFlZWVw8YdUKu3bt69F3giKiXgJxURcZM4UgUDQHFvwwGnNGo0mLS2tpKQkMDDwL9MDF81GR0fDqYkTJkz45ZdfcnJyamtrG68RaYyiqJSUFLiWpWPHjpaaooliIl5CO+pzmslkevW6yjfj6+sbHBwMAMjIyLh169Zfrp6BcYdQKGzXrh2coBwcHCwQCMxbdr2Q+SwjHMdHjBjxwllgbwDDMIucVoRwCqqJuKiZpjKawdnJAACKou7du/eXp24wDFNXV0fTtPnwVfMQ/itqMZ1OB9eyOTk5denSxSJHDAFUE/EUqom4yNXVFX5vxWKxpb7AjclksqFDh8L+nd9///35yIhG2gAAGW9JREFUzQCeB1eEZWVlwV1ZmrJsPSUlpaysDADg6en5wp0u3gzDMOjAIv5BNREXGQwG2C/j7u7eHOuqcBzv3r17QEAAACA/Pz8pKenV/b5w3SyGYXCZKwAgKysLrll92fxGiqIuXbqk1Wrhsyy71zLqpeYfVBNxkXlLLdhj3RyPCAgI6Nu3r0AgqKurO3jwYG1t7SsuFggEwcHBjo6OBQUFjx490mg0d+/eJUkyICCgffv2L3xJXl7elStXKIqSSqUjR45s7vYm0tqhUXwugoEG3E9HrVZbfNtG+IiPPvro+PHjFRUVjx49ysnJefWuPUFBQSEhIdevX58zZ463t/f169cpioqIiHjhwY0sy968eTMtLQ0AEBoa2rt3bwsWs+e377HUnRErQqP4XNS+fXu44am9vb15R3qLCwsLGzJkyIEDB3Jyck6cONGxY8dXzFH08PCYPXt2eXl5SkpKSkoKy7IRERGffPLJC0fECgoK9u7dq9frpVLplClTHBwcLPgW0Cg+L6GYiIsUCgUMi8RiMUEQzZRHcrl80qRJly9fLi0tPXr06Lhx4zp37vyyizEM++CDD/z9/a9fv15WVhYYGBgZGRkYGPh82miaPn78ONycsFu3btHR0ZZ9C2hmIy+hmIjrmi+DCIJ45513Bg0a9PPPPxcWFm7btm3Dhg0vm6YIAJDJZL169erevfurdz58+PDh3r17DQaDUCj86KOPXvdwx7+EYiJeQjER1zVrBkml0pkzZ167di0vL+/QoUPh4eFTp059de8yQRCwDnphwurq6n788cfHjx9jGNazZ8+PPvrI4lsIoZiIl9DYWVvXq1evhQsXSiSShoaGDRs2/P777298K4qiDhw4cPLkSYZhnJ2dv/jiCwueSmJGEETjk0UQfkCtMy6CBzfDn5s7g0Qi0fjx4+/du3fo0KHc3NzVq1c7ODiEh4e/7nNJkjx37lxcXJxarbazs5s3b96AAQOauJvaa7GxsXF3dzffGRVgfkCtMy4qLS0175HWAhmkUChWrFjx5MmTW7du3bhx47PPPlu/fn14eHjTp3dTFHX8+PGVK1fm5+cLhcJZs2YtWLBAJpM1R+L1er35bFiAWmd8gWIiLoLnqcKTyFomgwICAtasWfPpp58+ffr0+vXrMTExK1euHDVq1F+eqMUwjFqtPnfu3KpVq/Lz8zEMe/fdd+fOnfsGZ4o1ETym7fnTE5FWDcVEXPTqY2eaA47jgwYN+vrrr9euXZuZmfno0aPY2NjU1NSPPvqoQ4cOLwuOKIr6/fffd+zYcenSpbq6OlgNrVu3zsfHp/mSjXqseQnFRFyUnZ1tPpq1JTPoww8/9PT0jIuLS0xMrKysXL9+/dmzZ99///2hQ4d26NABbqgGTxY0Go0pKSmJiYnHjh0rLCxkWVYoFPbo0eO7777r0aNHsyYSjeLzEtpRn4ustVG8UCiMjIz09vYOCgratWtXdXV1SkrK48ePf/zxx65du0ZEREil0urq6pycnIqKiuzsbJ1OB5fFKxSKsWPHLl68+IWH4VgcioP4B9VEyP+BYZinp+eqVat69uz5008/JSYmGo3GmpqaK1euXLly5ZmL4fl/4eHhEyZMGD16tKWOk0XaIFQTcZF58w1rkclko0aN6tu378mTJy9fvpyVlVVfX19TU9P4Aj8/v5CQkLFjx4aFhclksubYRwlpO1Dp4SJ4sqB104DjuJOT04wZM8aPH19eXl5XV9e4zWhjY+Pn5+fg4IC2T0QsAtVEXCSRSJpjTuAbwDBMLpf7+vpaOyH/j8lkasqOkUjrgkbxuQ5l0DO0Wq1WqzX/ij4ffkCj+FyERqlfgWXZxod0o8+HH1BMxEVo5t4rqNXqxkcAoM+HH1BMxEUoJnqFZz4Q9PnwA4qJuAjFRK9g/kAYhqmurkafDz9wYoAGeRmRSGTtJHAXhmGWOlcWsTpUE3EXQRDNcapHq8YwTGFhoVqtBgBgGCaVSq2dIsQy0Hwi7iIIAn3TGjOZTElJSevWrauurrZ2WhALQz3WXAQzhaZpmqZRBgEAaJquqqrau3fv9u3b8/PzAQA4jru6ujo6OqLPhx9QjzUXwUwRCoWenp4ogxiGuXjx4oYNG/7880+dTgcAwHE8LCxs+fLlvr6+6PPhBxQTcRHMFIZhNBpNW84gmqYrKytPnjz5/fff5+XlsSyL43i7du0mT578ySefhISEcGRNDPL2UEzERTBTTCZTVlZWm80gvV5/5syZbdu2JScnw6mMAoEgKioqNjY2KioKjpq12Q+Hf1BMxEXmTGFZtg1mkNFozM/P37Zt28GDB6uqqgAAIpHIx8dn3Lhx06dP9/LyaoOfCe+hmIiLzP1Efn5+bS2D6uvrf/75540bNxYUFFAUBQBwcXGZOnXqlClT/P39xWIxQKEQH6GYiItgpmAYJhaL204GmUym1NTUuLi4X375Be6FZGNj06NHj0WLFkVHR6Od2PgN5S534TjeduYT1dXVHT58ePPmzdnZ2TAU8vDwWLx48fjx4xUKBdqPjfdQ64yLzJli8UPlOYiiqOTk5K1bt545cwaGQjKZrE+fPosWLYqKikLNsTYCtc64yJwpFEXxOIMYhqmtrT19+vTmzZvT0tJomsZxPDQ0dMKECRMmTHBzc0OD9G0Hiom4CGYKSZK5ubl8zSCNRpOUlBQfH3/58mWj0YhhmI2NTXR09LJly7p16wbrX76+d+R5KCbiIpgp8AwfXmZQWVnZli1b9uzZU1ZWBjdg9Pf3//TTT8ePH69UKlEo1AahmIiLaJoGAOA4LpfLeZZBDQ0NSUlJ27Zt++OPP+B21Pb29gMGDIiNje3Xrx/smebZW0aaAo2dcVFpaSk8aCgzM9PaabEYiqKysrJ27dp14MABuMOZWCyOjIycM2dO//79nZ2deRn9IU2EaiIukkqlBEHQNC2RSKydFgtgWbasrOzUqVM7dux49OgRAEAgEHh5eX3yyScxMTEeHh7WTiBifagm4qKioiKTySSRSLy9va2dFgu4efPmxo0bL126BJePyeXy0aNHx8bGdunSpe1MmEJeDdVEXKTX61mWpSgK7sXTepWXlx87duxf//oXXElPEETXrl3nzJnz8ccfo+0okcZQTcRFsMuWoqiKigprp+UNURR148aNLVu2JCYmwp5pOzu7kSNHLlmyJCQkRCgUWjuBCLegUXwuatWnDNE0XVZWduLEiR9++CEnJwcAIJPJOnXqNGXKlE8++cTe3t7aCUS4CI3ic5GDgwNBEHCiTevKIIZhfvvtt7i4uN9++02r1WIY1rFjx5iYmL/97W8KhUIoFLaut4O0GBQTcZG/v79AIDCZTKD1xER6vT4tLe3EiROHDh0qKCgAANjZ2Q0YMGDlypVhYWGt5V0g1oJiIi4iCKLxZmnWTUxT1NfX79ixIz4+vqSkxGQy4TjetWvXzz77bPDgwU5OTqCVvAvEilBMxEWtqJ/IYDCkpaV9//33iYmJ9fX1GIa5ubmNHz9+6tSpoaGhHE88wh0oJuKiVnEaNcuy1dXVe/fu3bZtW35+PsuyQqGwf//+sbGxgwYNghOFOJt4hGvQKD7yJkiSfPTo0T/+8Y///Oc/Wq2WIAhXV9fRo0cvXbrUy8vL2qlDWh/UOuMiLrfOWJYtLy8/cuTInj17UlNTaZqWSqVDhgxZtGhRWFiYjY0N1xKMtAqodcZFnG2dabXae/fuff/995cuXTIYDAKBoFOnTvPnzx8xYoSrqyu8hlMJRloLFBNxEQdjIrgxwM6dOw8fPlxWVsaybPv27YcPHz579uwOHTqgOdPIW0IxERdxLSaqqam5devWN998c/v2bYZh5HJ5ZGTk8uXLe/XqhfaZRiwCxURcZM4UoVBo9QwqLi5evXr16dOna2trWZYNCQmZPHny1KlTlUql1dOG8AaKibiIIycv1tTU/PHHH/Hx8VevXjUajTY2Nu+///6iRYu6du2K9plGLAuN4nMXQRAODg5WeTRN0/fu3du4cePFixfr6+tZlvX19Z05c2ZMTIyjoyMKhRCLQzURp7V80MGybFFR0fnz5zdt2gT3rrWzs+vTp88XX3wRGRmJDmJFmgkqWNxFURRcStqST0xKSvr2229v374N91cMDAycP3/+hx9+iHqFkGaFeqy5CGYKRVGlpaUtk0EMw1RXVx88eHDDhg2lpaUAAAcHh6ioqKVLl0ZERKBjf5DmhnqsuaiFR/FramouX76ckJBw48aNhoYGDMM6d+68YMGCkSNHOjk5YRiGCgnS3FBMxEUtNrORoqjMzMxvvvnGvJJeqVQOHjx42bJlQUFBaL4i0mJQTMRF5kwhSRKeFt8cT9FqtYmJievXr09OTqZpmiCIqKioefPm9e/f387ODqBBeqQFoZiIi0QiEQCAZdm6ujqdTmfZYzBYlqVpOjs7+4cffjh58mRlZaVAIPDz8xs5cuTixYs9PT0t+CwEaSI0dsZFTk5OcNtGZ2dnuVxu2ZvX1NQcOXJkx44d6enpJEkKhcLRo0cvWbIkNDTUxsbGss9CkCZCNREXmRd54DhuwaaZRqN58ODBnj17jhw5otPpRCKRj4/PxIkT58+fr1QqLfUUBHkDqCbiIrlcbtlWM8MwDx482LZt27lz52praymKgnu8jhs3LjQ0FB3Eilgdqom4iGVZHMcJglCpVG95K4Zh6uvrT548+cMPP6SmprIsKxaLu3fvvmLFioEDB8pkMoskGEHeEqqJuKi8vNxkMtE0XVNT8zb3MZlMN27c2L1797lz59RqNcuyTk5O06ZNW7Bggbu7O5qviHAHGsXnosrKSpgvJEm+WQaxLFtVVbV9+/aEhITCwkKWZaVSae/evRcsWNC/f384GIeyHuEONIrPRXl5efDYRfBGMxv1ev2lS5d27959+fJluHzMw8MjJiZm5syZKpUKhUIIB6GYiIsEAgGO4zRNg9ePXPLy8nbv3r1z587KykoAgFwu79Onz8KFC6OiotD+ighnoZiIixqPnTU9gwwGw82bN+Pi4i5fvqzX63EcDwoKiomJGTdunFKpRKEQwmUoJuIipVJJEARFUaBpIQxN0wUFBTt27Ni3b19FRQUAwNbWNjIycvXq1eHh4XBTIZTRCJehsTNO02g0JpMJLv54mYaGhrNnz27fvv3evXtGo5EgiO7du8fExAwbNkylUqGYF2kVUOuMi/Lz841GI8MwJSUlarVaoVC88DKdTpecnLxr166zZ89WV1fjOO7l5TV16tTJkyf7+fm1cJoR5G2g1hkXaTQa85b10DMXsCxbWFi4a9euhISE8vJymqZlMtmIESMWL17cpUsXsViMshVpXVBMxEU2NjZw7Az7L/P/Ylm2vr7+2LFje/fuhc0xgUAQGho6ffr0qVOnOjk5WTHZCPLGUEzERR07dhSJRCRJ2traNg5wjEbj3bt39+7de+LECXjkhrOzc3R09KJFi+BLUG4irRSKibgIx3GGYXAcVyqV5k3L8vPzExIS9u7dW1RUxLKsUCgMCAhYvnz5+++/j3bzQFo7NHbGRWq1GgDAMExBQUFtba2Njc21a9f++c9/Xr9+3WAwAAAUCsXEiRNnzZrl7++P9nhFeADVRJxWW1t7//79q1ev/vTTT/DEIbFYHBYWtmDBghEjRlh8EzUEsRZUE3FacnLyuHHjGhoajEYjAMDFxWXatGkxMTHt27cnCMLaqUMQi0E1EafRNF1VVQUAkEql3bt3/+KLLwYNGgSXjyEIn6CaqBVQqVSffvrp1KlTPT090fIxhJfQKD4XSSQS2PgSCAQRERErVqwYMGAA3F8R5RfCS+h4Ty4qKirauHFjRkaGu7t7bGxsly5d0GQLhN8whmGsnQbkBSiKgvOnUa8Q0hagmAhBEOtD/UQIglgfGohBEMT6UOsMQRDrQ60zBEGsD8VEvEKSJDwRpDE4PGo+7hVue4RmSCKcgmIi/tDpdHv27Hn69Okz/65WqxmGmTNnTnh4OI7jiYmJeXl5H3zwQbt27d7yiQaDoby8vLy8XCaT+fv7SySSl12p0WiysrIoihIKhX5+fnCrE6i8vDw/Px8AgGFYYGCgvb39W6YKaZVYhC8qKipGjRplngMpkUgcHBzM6/Xff//9urq6mpqajh07ymSy+Pj4t3xcWVnZsmXLunfv7uXl1aFDh2nTpqWnp7/wyry8vLlz53p7e3t5efn5+U2fPj01NRX+r8zMzLFjx3p5eXl5efn6+i5evLi6uvotE4a0Rqgm4g+GYfLy8kaPHk0QBEEQs2fPvn379uHDh2EopFKpSkpKamtrJ06c2Lt378TExLd5FkmSa9asgTu02dra4jguEAjmzJmj0+meuVKv10+bNk0sFmMY1r59e6FQKBKJZs6cqVar9Xr97NmzxWJxcHDwiBEjPD09BQLBd999ZzQa3yZtSGuEOgv4A8Mwb2/vAQMGiEQisVgcERFhY2MjFouXL1/u4uJCkqRGo7Gzs1u3bl18fPyQIUPMLyRJUvdfWq22trZWr9e/+lk6nS4pKUmj0YhEolmzZvn5+VEUdeXKlaysrGeu1Gg0V69eNRqNrq6uy5cvDwkJMZlM9+7dq6ioSElJuXLlio+PT3x8/JEjR9atWyeXy/fv319YWGj5TwfhNrQWn2/gFo4MwyQnJ1+4cOHu3btbt26dOHFiSUmJk5NTcnLy7t27a2tr58+f37t3bwCAWq0+fvz4rVu34MuNRmNOTk737t2//PJLFxeXlz0Fw7BOnTo9ePDAxcVl4MCB165dAwBotVqdTvfMlXK5fN68eb/++quXl5dWqy0pKQEA2NraYhiWmJiYk5PTq1cvf39/mUwWGRnp6OiYk5Nz584ddEpSW4NqIr6BY2cGg2Hnzp0Mw4jFYoZh1q1bp9fr7ezsHj58ePjw4fr6erFY3L17d5qmN23a9P3331MUZTKZ4GvFYjFBEK8Oi2xsbFavXj1ixAiJROLm5mY0GjEMc3Nze/5wEalUunDhwm7duq1fv/7MmTM1NTX29vbz5s1TqVQajYamaaVSCas8e3t7uVxeXl5eU1PTbB8PwlGodcY3paWl8Bhrk8lEUZRKpVKpVCKRyN7eHsOwLl26hISE0DRdU1PDsmxmZuaRI0dIkpw5c2b//v0BAHK5fNasWatWrXr1yBqGYU5OToMHD+7Tp09SUlJOTo6fn9+CBQv8/f2fv1ggEOA4jmGYnZ0djuMEQeh0OljTYRgmFosbH3JrMpkyMzMt+5kg3IdG8fnGwcGBIAiKokJCQhiGoSgKx3FzLstksp49e/7xxx+wm5BhGIPBIJfL+/fvT1HU5cuXfX19P/300+DgYNC0vZAePXq0Y8cOoVD4+eefjxkzpvGzzIxGY48ePfbv3//kyZPvvvvu7Nmzn332GcMwMARjGAa+hGVZmUwmEAi8vLxQsWxr0ClDfKNWq2maFgqFEyZM6NGjx59//qlQKMy5zLKsyWSCP2MYZmNjI5fLc3Nz169fX1dXh2FYRESEt7d3E0tFcXHx6tWrk5OTx44da2tru3HjxilTpnh4eDS+pqCgYNeuXfX19RMnTuzTp8+4cePOnz9fU1Nz584dgUDAsmxVVVVtba2Tk1N5eXlJSQlBEB4eHqhYtjUoJuIVkiTz8vIoipJKpfb29gMGDIiKigKNohuapsvLy+HPLMtqNBo47n779m0AgLOz80cffSSTyeD1paWl2dnZ7du39/T0fP5ZlZWV69atS0xMZBjmwYMHV69eVavVXbp0cXd31+l0mZmZQqEwODj45MmTGzZsoCiqqqoqLi4uPz8f9l75+voqFAqxWJyTk5OamhoWFpadna1Wq+VyeUBAACqWbU7LThpAmhHDMEePHvXy8gIAYBjWs2fP/fv3NzQ0NL7mypUrCoUCABAREZGVlXX37l1fX19zYRAKhZMmTUpPT6dp2mAwfP755w4ODmPGjCkrK3v+WTt27JBKpY3Lkp+f3927d1mW3bdvn4eHR6dOne7evXv8+HFXV1cAgFKpHDp0qLOzMwCgd+/e6enpxcXF0dHRBEG88847n3zySYcOHUQi0Zw5czQaTct9agg3oLEz/mhoaDh06FBNTQ2ccJiWlrZ+/fqwsLDQ0FDzNRkZGSaTSSaTPX36NDExUaFQ1NbWYhgmEAgAADRN//zzz4WFhQkJCa6urrArh6bp5xep6XS6+/fvEwRhPn4Ww7CwsLCAgAAAgEKhEAgENE2TJDls2LCvvvoqPj4+Jyfn+vXrQqFw4MCBy5YtCwwMxDBs7dq1NjY2Fy5cSE5OFovFH3zwwZdffonOcWuD0O6xvJKZmdl4bqGbm1vnzp0bHxJbV1d39OhRAICfn5+fn9+XX355+PBhkUjUv39/f3//tLS0P/74QyQS7d69e+zYsaWlpY8fPw4JCXF1dX2+4yY3Nzc1NdX8q1Ao7NixI+wkMplM9+/fd3Z29vX1JQgCTv5OT09nGEYul4eGhiqVSvMN6+rqkpOTGxoa2rVr5+fn5+jo2HyfD8JZaC1+22U0GuPj41evXq3RaIKDgz08PPLz89PT09u1a3fs2LHIyEhrJxBpQ1BM1KaZTKatW7f+61//Ki8vJ0lSJBL5+PjMmzcvJiYG7eSPtCQUE7V1Wq327t27ubm5cCg9LCysQ4cOjRt0CNICUEyEAAAAwzAMw2AYBk98RJAW9v8BKLgXoVUY/TQAAAAASUVORK5CYII=	z = \frac{a^2}{\lambda N}, \, \text{for} \, N = 2, 4, 6, \ldots
+739	Suppose right-handed circularly polarised light (defined to be clockwise as the observer looks toward the oncoming wave) is incident on an absorbing slab. The slab is suspended by a vertical thread. The light is directed upwards and hits the underside of the slab.  (a) If the circularly polarised light is 1 watt of wavelength 6200 Å, and if all of this light is absorbed by the slab, what is the torque, $\tau_0$, exerted on the slab in dyne-cm?  (b) Suppose that instead of an absorbing slab you use an ordinary silvered mirror surface, so that the light is reflected back at 180° to its original direction. What is the torque now in units of $\tau_0$?  (c) Suppose that the slab is a transparent half-wave plate. The light goes through the plate and does not hit anything else. What is the torque in units of $\tau_0$?  (d) If the slab is a transparent half-wave plate with the top surface silvered, what is the torque in units of $\tau_0$?	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+740	 (a) Consider the Fraunhofer diffraction pattern due to two unequal slits. Let $a$ and $b$ be the unequal slit widths and $c$ the distance between their centers. Derive an expression for the intensity of the pattern for any diffraction angle $\theta$, assuming the arrangement to be illuminated by perpendicular light of wavelength $\lambda$.  (b) Use your formula from (a) to obtain expressions for the pattern in the following special cases and make a sketch of those patterns:  （1） $a = b$, （2） $a = 0$.	[]	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	I(\theta) = a^2 \frac{\sin^2 u}{u^2} + b^2 \frac{\sin^2 v}{v^2} + 2ab \frac{\sin u}{u} \cdot \frac{\sin v}{v} \cos w; I(\theta) = 4a^2 \frac{\sin^2 v}{v^2} \cos^2 \frac{w}{2}; I(\theta) = b^2 \frac{\sin^2 v}{v^2}
+741	 Consider a monochromatic beam of light incident upon a single slit. Let the wavelength of the light be $\lambda$ and the slit width be $w = 5\lambda$ (Fig. 2.44).  (a) Sketch the intensity pattern as a function of angle in the region far from the slit.  (b) Calculate the positions of the first maximum and the first minimum.  (c) It is now desired to uniformly phase-shift the light incident upon the upper (i.e., $y > w/2$) half of the slit by exactly 180°. Design an idealized apparatus to accomplish this and sketch the resulting intensity pattern.  (d) Calculate the intensity vs. angle; give the position of the first minimum and an estimate of that for the first maximum.	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	I = I_0 \frac{\sin^2 u}{u^2}; \theta = \arcsin \left( \pm \frac{1}{5} \right) = \pm 11.5^\circ; \theta_1 = \arcsin\left(\pm \frac{1.43}{5}\right) = \pm 16.6^\circ; I = I_0 \sin^4 \left( \frac{5}{2} \pi \sin \theta \right) \bigg/ \left( \frac{5}{2} \pi \sin \theta \right)^2; \theta = \arcsin \left( \pm \frac{2}{5} \right) = \pm 23.5^\circ; \theta = \arcsin \left( \pm \frac{1}{5} \right) = \pm 11.5^\circ
+742	 The plane of polarisation of plane polarised light transmitted along the optic axis of certain crystals (e.g., quartz or sugar crystals) is rotated by an amount which depends on the thickness of the material. The indices of refraction $n_R$ and $n_L$ for right- and left-circularly polarised light are slightly different in these crystals.  (a) What is this phenomenon called? Describe briefly how the rotation is explained.   (b) Derive an expression for the angle $\phi$ by which the plane of polarisation of light of frequency $\omega$ is rotated in passing through a thickness $d$ of the material.	[]	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	\text{Optical activity}; \phi = \frac{\omega d}{2c} (n_R - n_L)
+743	An excellent camera lens of 60 mm focal length is accurately focused for objects at 15 m. For what aperture (stop opening) will diffraction blur of visible light be roughly the same as the defocus blur for a star (at $\infty$)?	[]	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	D = 0.32 \text{ cm}
+744	Estimate the optimum size for the aperture of a pinhole camera. You may assume that intensity is adequate and that the object viewed is at infinity. Take the plane of the film to be 10 cm from the pinhole (Fig. 2.67).	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	d = 2.3 \times 10^{-2} \, \text{cm}
+745	" Suppose you have been supplied with a number of sheets of two types of optically active material. Sheets of type P are perfect polarizers: they transmit (normally incident) light polarized parallel to some axis $\hat{n}$ and absorb light polarized perpendicular to $\hat{n}$. Sheets of type Q are quarter-wave plates: they advance the phase of (normally incident) light polarized parallel to some axis $\hat{m}$ by $\pi / 2$ relative to light polarized perpendicular to $\hat{m}$.  (a) Describe how to combine these materials to produce a device which converts incident light polarised parallel to some axis $\hat{x}$ to outgoing light polarised perpendicular to $\hat{x}$ (see Fig. 2.71). What is the loss in intensity in the device you have constructed?   (b) Describe how to combine these materials to produce a ""circular polariser"" — a device which converts unpolarised light entering side A into circularly polarised light leaving side B (see Fig. 2.72). What is the minimum possible loss in intensity in this process?  (c) If the power entering side A is $I_0$ with wavelength $\lambda$, what is the magnitude of the torque on the circular polariser in part (b)?  (d) If the light emerging from the circular polariser is normally incident on a mirror, what is the loss of intensity of the light in passing through the polariser a second time? (See Fig. 2.73)  (e) Take two sheets of the circular polariser you constructed in part (b). Flip one over and put them together as shown in Fig. 2.74. Suppose unpolarised light is incident normally on this system. What is the intensity of transmitted light as a function of $\theta$?  (f) Now reverse the order (see Fig. 2.75). What is the intensity of transmitted light as a function of $\theta$?"	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	\frac{I_0}{4}; \frac{I_0}{2}; \frac{I_0 \lambda}{4 \pi c}; 0; \frac{1}{2} I_0 \cos^2 \theta; \frac{1}{2} I_0 \sin^2 \theta
+746	 For the combination of one prism and 2 lenses shown (Fig. 1.42), find the location and size of the final image when the object, length 1 cm, is located as shown in the figure.	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	\text{Location: 10 cm to the left of the second lens, Size: 0.5 cm}
+747	 A beaded screen (Fig. 1.19) returns light back to the source if light focusses on its back surface. For use by skindivers in water ($n = \frac{4}{3}$), of what index material should the beads be made ideally?	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	n' = \frac{8}{3}
+748	Monochromatic parallel light impinges normally on an opaque screen with a circular hole of radius $r$ and is detected on the axis a distance $L$ from the hole. The intensity is observed to oscillate as $r$ is increased from 0 to $\infty$.  (a) Find the radius $r_a$ of the hole for the first maximum.   (b) Find the radius $r_b$ of the hole for the first minimum.   (c ) Find the ratio of the intensity for $r = r_a$ to the intensity for $r = r_\infty$.   (d) Suppose the screen is replaced by one opaque disk of radius $r_a$. What is the intensity?	[]	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	r_a = \sqrt{\lambda L}; r_b = \sqrt{2 \lambda L}; 4; I_\infty
+749	(a) A coherent plane wave of wavelength $\lambda$ is incident upon a screen with an infinitely long slit of width $d$. The beam's propagation direction is perpendicular to the slit and makes an angle $\theta$ with the normal to the screen (Fig. 2.32). Find the intensity distribution beyond the slit in the focal plane of a thin lens of focal length $f$. [Assume the lens, diameter infinite.]  (b) If, instead of a screen with a slit, there is a slab of width $d$ (Fig. 2.33), find the intensity distribution in the focal plane.	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	I = a^2 \frac{\sin^2 \left[ \pi \left(\frac{\sin \theta}{\lambda} - \frac{y}{\lambda f} \right) d \right]}{\left[ \pi \left(\frac{\sin \theta}{\lambda} - \frac{y}{\lambda f} \right) d \right]^2}; y = f \sin \theta; y = f \sin \theta - \frac{k \lambda f}{d}; y = f \sin \theta
+750	A line object 5 mm long is located 50 cm in front of a camera lens. The image is focussed on the film plate and is 1 mm long. If the film plate is moved back 1 cm the width of the image blurs to 1 mm wide. What is the $F$-number of the lens?	[]	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	F = 8.33
+751	 It was once suggested that the mirror for an astronomical telescope could be produced by rotating a flat disk of mercury at a prescribed angular velocity $\omega$ about a vertical axis.  (a) What is the equation of the reflection (free) surface so obtained?   (b) How fast must the disk be rotated to produce a 10 cm focal length mirror?	[]	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	z = \frac{\omega^2 r^2}{2g}; \omega = 7 \, \text{rad/s}
+752	 (a) What is the minimum index of refraction for the plastic rod (Fig. 1.34) which will insure that any ray entering at the end will always be totally reflected in the rod? (b) Draw a ray diagram showing image formation for the lenses and object as shown (Fig. 1.35). Choose the focal length of the second lens so that the final image will be at infinity. Use the arrow head as the object and draw at least 2 rays to show image formation. Explain briefly how you arrive at the ray diagram. Do all the refracting at planes 1 and 2.   ( c ) How would you change the position of the second (diverging) lens to make the combination a telephoto lens?	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	n > \sqrt{2} = 1.414
+753	 Suppose you wish to observe reflection of laser light from the moon. Explain how you could use a large-aperture telescope lens or mirror, together with a laser and a short-focus lens to get a beam with very small divergence. What would the characteristics of the telescope lens and short-focus lens have to be to get a beam of angular width $10^{-6}$ radian (first minimum on one side to first minimum on the other)? You may assume a rectangular aperture at the objective if you wish.	[]	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	\frac{F}{f} \ge 100 \quad \text{or} \quad R \ge 0.6 \, \text{m}
+754	(a) A curved mirror brings collimated light to focus at $x = 20$ cm.   (b) Then it is filled with water $n = \frac{4}{3}$ and illuminated through a pinhole in a white card (Fig. 1.25): A sharp image will be formed on the card at what distance, X?	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R3KsbExEIz0bbcKWcckScJCE8dxpVKZmprKcdzY2JjT6YTdBAJBeXn5vn37Ll68eOTIEbCUHo+nvb19YmJi3bp1CoWCP29oaKhCoYiIiDh06NDAwMDIyMjMzAyO49CpMDk5+Xe/+11DQwPvPPdFqVTGxMSUlJRkZWUJBIIX0jC9gP5xBAKBeGp811Usy46Ojo6MjLjd7sdJPTzLiWQy2XxFYpfL1dbW1t3d3dDQIJFI9u7d67sCXgoSiaS8vLylpcVoNEIcGlaZ80/E/0wQRHx8fHR0tN1un5mZ4UPXarU6NTU1IyPDZDJdu3ZtYmICzPbMzIzD4YAqKTgCRVFFRUUpKSkURalUKrVaDQlfOI6r1eqQkBCz2azT6SYnJ+cMgyCI8PDwsrKy8vLy9evXL5ecSACCYrcIBALxv/iKPGAYxrLs0NBQc3Oz0Whc9nOxLGuz2RZc6kETXL1eD6d+0qUeRVGpqalbt25d+spYJBIVFhYmJiZiPqoXFEVlZmZmZmbK5XJIZfI1wzKZDBK7YGeSJNesWQOdFSDvmp+ggKPY6XQ6nU7fFTagUql27tz5gx/8YOPGjRqN5knnFqsIZG4RCAQCwzCMJMm0tDQoceE3ut3ujo6O8fHxZT/d7OxsZ2fn1NQUv0WhUGzZsqWwsFCpVBIEwbLs+Pi42Wx+Cs8qRVFxcXEgqei7fcEgNOhCFxQUREVF+f6W9w9jGGY0GqGOFsMwgUBQUFAQGxtrt9v56QLHcbOzs1C4TBAE1PXCdoPB0NHR4fF4QkJC5lhTyP0OCQm5ffv2xx9/fOTIkc7OzgX1Rl4AkDMZgUAgMOxR84D4+HiRSMR7X0H/yLeKdFkAN3Vvby/fRp4giIiIiPfff18mkx0/fry1tTUkJGTt2rVPJ6EMFnTOZ8FtKxQKjUYjnwyFYRhJkomJiTExMXP0JSCxGdavvunKsHrWarUWi4UvkYKdQQWa4zi32w3fIcuyfX19x44dCwoKys/Pb25u1uv1/AQCx3GXy3Xu3LnJyUmv16tSqVwuV1hYWERExJNecuCDzC0CgXipAfHe4eFhm80G2lJzkoEhHRfyiZbrpDRNt7e3Dw0N8c5VgiCio6Pj4uLy8vI0Gk17e3tERERBQQH0s3vS4xMEERkZmZaWdufOHX6uoFKpqqqqCIK4fPkytPGB7RRFJSYmhoWFzVGsBKvp9XpxHA8LC1MqlVBQKxAIwPoqFArf2DPLsnwH38jIyNDQ0P7+fpqmPR5Pa2trXV3dnj17SktLDQaD1WqFPRmG6evrg259GIa53W6Hw7FgpPkF4MXMt0YgEIgl4nQ6b9269fXXX4+Ojtrt9gcPHvCNerBHqhEdHR1gBZcliwfkLO7evTs0NMTbp+Dg4C1btiQlJSmVSlAhxnGcJMmnlhGWy+WlpaWNjY137tyB7guZmZl79+41GAz19fWjo6O8ueWVsyCrWSaTgV0gCCIqKio4OJggCKVSCZYVynXA3W2323k1DI7jbDYbpDQLBIL8/PzCwsKenh5Q6XK73Xq9XiwWl5eX37t3r7m5mT87b1xFIlFGRsb69ethJE/99QYsaHWLQCBeXliWHRwcPHr06IULF+x2OyyzfGOl0JPu+PHjCoVi//79T7fW9AVa/n377bd3797lo6FCoXDbtm2VlZVwfF9liacGIqyVlZUPHz4cHh6mKCo3NzcjI8PhcFRUVNhstqGhIQzDpFLpxo0bCwsLg4KCSJKMioqKj4+XSCQgbpWdna3VauFoQqEQ1r5JSUkajYYgCIZhxGIxNO4VCAQSiQQczhD0LS8vb2hoqK+vxzCMJEmZTCaTyZKSkjZu3Dg0NGQymfjvGcz5+vXrDx06tH79+mfRsAxkyF/+8pf+HgMCgUD4B4ZhWltbz549q9fraZrm3aG+wGJ0enpaJpNFRUXxi7+nPuPdu3d/85vf3Lt3j2/zJ5PJfvSjH1VUVCxjuRGoREml0o6OjocPHwYFBe3bt6+kpESr1cbHx9vt9ocPH7Isu379+p/+9KclJSVisRiuy2azjYyMzM7O5uTkvPbaa2lpaSRJut3u4eHhmZmZhISEAwcObNq0KSgoSCQSzczMjI6OSqXSgoKCN998Mz8/Hy6BJMng4GBIpAoLC4OFdVFRUUREhEKhkMvlSqUSxhkdHZ2fn19eXv7DH/6wrKwsNDT0Re0LhFa3CATi5QVaFGRlZQ0MDMzMzIjFYkgXAo2k2dlZiK16PJ6mpiaXyyWRSHbv3s2biifFbre3tbWdPHmyubmZz+mFOKtGo1n2VR1JkklJSbt27aIoKjIysri4WKFQ4DienJz81ltvKZXKycnJ0tLSkpISfg4hEolKS0sJguju7s7Ozs7NzRUIBDiOx8XFvf322/n5+SqVqqCgQKvV4jguEomqqqrkcrnVas3Ozs7IyOC/GVjgvvPOO9u2bTMajWq1OiUlJSgoCMfxjRs35uXlDQ4O3r17d2xsLCYmBnobqFQqONfyfgmBw1whaQQCgXipcDqd9+7du3r1qtFoDAoKgggly7Lt7e03b96cmpriX5ISieS1117727/926ysrKewCgzDNDQ0/OY3v/nmm28MBoNv1PbP/uzPfv7zn69Zs2bZjQ0szfv7+4OCgmJjY/nVM03TVquVpmm5XD6ntTvfU48gCF/7x7IsTdNzIsqwM8dxBEGQJDln/KDGxbLs/LbBcDSWZeGDy95UOABBIo4IBOKlRiwWFxYWZmdnMwxDURQYEmibA5KK/DLU4/E0NDRUV1czDBMTEwMdhJZ4FovF0tnZeezYMbDrvlnB69at27VrV0JCAuYjMbFc4DgeEhICy0roRwvbwdmLPVLRmnNeiqL4sh/foh2+Ush3f99+BguKIfNxaN/f+h7tcZ99wUDt5REIxMsONCeQSCQikQha4ohEIqgB7evr45N6oCXt0NDQwMCAx+PRaDS+jdYXBD4IrX4++uijS5cuTU5O+iorQRLv1q1bIyMjV0i8EFaW82cGK9F3AbEIyNwiEAjEAgiFQq1WKxKJJiYmwO+KYRjLsmazuaenp6+vj2VZu90+ODg4OzsrlUpBWB/wer3Dw8N37969e/fu/fv3GxoaTp06de3atenp6TkqhiDGJJPJEhMTYQ3qp8v1A/AFTk5OejwekUj0omZI8eDzFSwRCAQCgT0q2jlx4sSnn37a3t7uq28MyUdqtVogEKSlpVVVVWVlZbEs63a74VM1NTV/+tOfBgYGwE57vV6IccLHRSIRjuMej4dlWYqiMjIyfvnLX77yyisvsGLwHDiOe/jwYW1tbVtbm1qt3rZtW1ZWllQq9fe4VhCUmYxAIBALA7IPe/bsEYlEf/zjH+/du8drH9I0PTIyMjY2hmFYe3t7Z2dnRkYGTdPQgQdWwAaDYb5AEkmSISEhRUVFUqn0/v37Dx8+9Hq9AwMDOp2uuLgYJP6fP8urmbUUvF7vlStX/vu//7u/v18ikTx8+PAv//IvU1NTX+A1LjK3CAQC8VigSmfv3r0jIyP9/f2+UsMsy4J3kKbppqamlpYW7FGwdr5cBiCTydLT0zdv3nzgwAGFQvH1119//vnner3e4/F0d3dPTk4+f3MLGpYej0cqlT5PfQmWZUdGRkDJy+FwNDc3j46OpqamPrcBPH+QiCMCgUA8FoZhDAZDW1sbpEfBRl9VYfiBZdnH9bHhM5U0Gs2GDRsOHjxYUlISHh6OYZhSqTQYDCaTiWVZUI14bi9kqM8ZGxvr7Ozs6emx2WyxsbGFhYUxMTFCoRCGAQrJPPOviwfzqfnxer1Wq9XtdgsEAmjDBwtW+O3s7KzNZqNpGnoY8MnJUBSEfbff8AsGWt0iEAjEY7HZbJcuXfriiy+am5utViuGYQKBQK1Wy+VymqYtFsvMzAzI6z8OhUKRm5sbHx+fmZlZWlqanp7Oa0pERUXt378fIr579+6NiYl5TleFYSzLPnz48Msvvzx9+nRPT4/H44mMjDxw4MCrr74aERGhUqlCQkIoivJ6vWNjYwMDA5OTk76ha1CxiI+Pj4uLUygUHMe5XK6BgYHOzk6DwTAxMTE7OyuRSNLT0zdt2hQVFQX9BIeHh+vq6rq6ulwuF03TLS0tIJzJcZzH4/F6vS92LRAytwgEArEwLMv29vZ+/fXXd+7cAWOjUCjWr1+/detWjUbjcrlGRkZ0Ol17e7vBYGAYBoworwRJEERISEhZWdmf//mf5+XlSaVSoVDoqwUhEAg2btyYlJQEDdt9u+us9HUNDg4eO3bs6NGjvb29EGCGLZ2dnREREcnJyXv37o2Ojq6vr//mm2/q6+v7+vp8OzdA/6LCwsIPPvigsLDQ5XLdunXryy+/vHr1KlQ6gfBFYmLiX//1X+/fv18mkw0MDBw/fvzYsWODg4PYI30MPrYNqWTP5/L9BZK5QCAQiIWhabqtra23txdsbXh4+LZt2957772ioiKQZ3K5XDqd7urVq62trQ6HQyaTcRzX0tICnfVkMlllZeUHH3zAKwkDvm9dkUgEi9oF5SZWAo7jjEbjmTNnPvvss/7+fn5pDslf4+PjJElGRERoNJrp6emPP/64urp6dnZ2fih6ZmZmbGysoKAgIyNjeHj4888/P3funNVq9a126evra2tr27x5s9VqPXXq1Jwz8sxp8LfS34C/QKtbBAKBWBiO40D1gqIoqVRaVVX1wQcf5OTk8EFWgUBQXFycnZ09Pj4+OzsbEhLidrv/8R//cWxsjKbpqKioPXv2FBQULF7e85yjlS6X6/r166dPnwbLx8dfwakLZlUqlTqdzurq6jt37szMzPCLdd8gLsuyDocDevu0tLTodLo5tpbHaDQ2NTWdPHmSt7Vz5hYEQcTExISGhj6nr8BPIHOLQCAQC0NRVGFh4b59+yIiIiIjI995553c3Fzf9F1QIlSpVEqlEmppJicn+SZ0UqlULpdTVABlpHIcNz09/e233z548ABsbXBwcGZmZlhYmNVq1ev1drs9MTGxqqpKqVSeP39+fHwcjCLkVHu9Xr1ePzs7yx8NHMK+HeN5oMl8cnJyW1vbkSNHOjs74Yz812I2myHTG8dxiqLmSy6/YCBzi0AgEAtDEERCQsKPfvSjnTt3BgcHx8bGPq5UBpJvGYbR6/Wjo6MQhmQYBtT5n+ugFwUypAYGBsDOicXibdu2/fjHP05NTZ2cnGxoaDAajTk5OVlZWRcvXuzu7oYLEQgERUVF77//vtFo/Pjjj7u6uvhVrG9aMr8lODg4Pz8/NjY2LS0tKSnps88+a25uhkb0Uqm0rKwsPz9fIBDU1NTcvn3bt7bqxSaApl0IBAIRaAgEgqioKOg3970KDCzLdnZ2joyMcBwHEVCVShVQ0sSg5WQwGGAeEBMTs2vXruLi4qCgoLi4uPz8fGjRMzAwcP/+/fHxcexRVtTrr79eUVHx4MGD8PDwrq4uOBpFUUqlEhrl8tdIkmRiYuIvfvGL0tJShmEaGxuHhoYg+A0x2tdff33v3r2QS9XV1eV0OuGDfPWRH76X5wJa3SIQCMRi+Pa0WQSO45xOp16vn5qawjCMIIiIiIhAk0GGQcJCE0qBo6OjpVIpRG1BUZLjuP7+/v7+frCRoDGZk5MTHBzs6++lKCo1NTU7O3v+NUokErlcLpPJ3G73zMwM73zGcVwmkwUFBUmlUpqm+QJfnoD6rpYdZG4RCARieQCtBhzHhUJhQkLC5s2bo6OjA8qEgKcXCn85jhsaGqqrqwsPD+c4rru722KxaLXa9PR0WOPCRwiCCAoK4muFeQQCwaZNmzIzM+f00fNd6RIEAafjfwux3jlRXijbhbrbgPq6lhdUCIRAIBDLg0KhqKqqYhjGbrfn5ORs374dUqj8Pa7/gyCIuLi4sLAwHMcZhhkZGfniiy8GBwfdbndjY6PJZEpISDh8+HBubm5YWBhoUzAMMz4+fv/+favVqtPpzGYzXBHLshaLhXcF85fJx3HBdgYHB/ONB6CDodlsdrvdMAB+YCBzgb3QXW/R6haBQCCWB4FAsHXr1tzcXJZlpVKpRCIJtLUaoyPwEQAAIABJREFUjuNRUVHR0dEikcjhcNA03d/fPzQ0hD1K7Hrw4MGf/vSntLS0NWvW1NXVmUwmkH+anZ1VqVSTk5P9/f18E99r164VFxdHRET42kjo0MA7kEmS5BfKYG4bGxtDQ0O9Xq9Op+N3k0gkQqHwBV/d+nsACAQC8eJAUVRISAgWqGFIHMcVCsXWrVu7u7ubm5sdDgd05+V3YBhmbGzM7XZv3bq1trb2zp07HMdZLJb79++D/5lfknIcZzAYrl+/np+f72tuWZYdHx8HwUscx4OCgmJiYpRKpc1m4zjO7XZ//fXX9fX1TqdzfHwcinpRIRACgUAgnpgAtxkSiaSiooKm6Y8++qilpQXSpngoioqPjwcdx+zs7NbWVmgpuKDCIk3T3d3dExMTCoXCt1UtbzgJgggPD9+1a5fRaLx+/brRaGRZdmJiYnJyEptXPrSC1xwYIHOLQCAQLxE4jqvV6ldeeYVhmAsXLvT19U1PTzMMExISEhERodVqq6qq0tLSlErlq6++ajQaa2trTSYTmMY5tTokSSqVSqlUqlaro6Oj9Xo9TdMikSgtLS0iIgL2EQqF27ZtUyqVBEFUV1dDTwJ+JHAoiqKgd5A/vo/nBzK3CAQC8XJBEERYWNjhw4fz8vLa29uHh4cZhomOjk5NTY2Ojg4LC4OueTt27FCpVBqN5t69ewaDYXp6WiAQiMVilUoFYemgoKBdu3alp6cLBIIdO3ZAjphGo3n11VfT0tL400ml0oKCgnfffVetVvf29tpsNl+tRxjMpk2b1Gr1i73GxReUuEQ8H+bnBSyelTdfI833OL4ypL6Hnb9l2fneZELfHeYPe5GPv9iP38sJ9D3lb8sF/8RLeS4WvzeW/ij5KgbDzyzL0jQNOT5er9fr9QqFQih3Wa4bck4T2TkP7ILtCr63hwFN04/rYQflttBo1ncjwzA0TTMM4/V67XY7f9WwAyxboWsetPEJDg4OCgri64lVKlVCQoJSqSRJ0mw2DwwMuFyuqKiohIQEiUTC/5UBt9s9PT09NDRkNpsxDCNJkmEYhmFEIpFGo4mNjVUoFPO/Xgj32mw232bDCoVCJpOBhrPdbnc6nTKZTKVSEQRhsVg8Hk9QUBC03RUKhSEhIdBqye8vE2Ru/QYIfAsEAl4WzuFwQObC/J05jrPZbHa7nc9TwHFcqVTKZLLZ2Vm73a5QKCIiIgQCAfTukMvlcIdxHAdbpFLpnPK4ZQTu+AV/xXGcw+Gw2WyQjkFRlEqlEolENpvN4XBIpdKwsDAMwx7XmhvSO79XzQexKoCsnJGRkYGBAYvFAoLD8Or01ZEAMQSFQgEbZ2Zm7Ha7x+PxlZsA6V2FQgECxQzDeDwegUAgEAhYlrXb7b4Py5wx+P4WbEZUVJTNZpuYmBAKhWFhYRaLZWRkRKVSKRSK0dFRg8EQGRmZmZkJbW4X7zewxO/BbDb39fVB2z4Mw5RKpVwuxzAMGrNDbxywMXx7gKCgIAzD7Ha7b2bTnOuyWq0L/pZlWavVajQa50Rq+c+6XC5oUstvhG8mIyODIIju7m6O41JTU9VqNUEQBEHwpotlWZfLJRKJRCIRPN1SqZQgCKvVOr8TMD/JkEgkUql0dnbW5XKFhIRIpVKr1bqgmiNc19TUFP+GgdVwSEgISZIsy5pMJovFEhYWlpSUJBAIoFFgXFyc3W4fHh5WKBTFxcVZWVkwsJV7By6FF7nbUUDhG/nweDwjIyOdnZ39/f1isRgeM3gCzWbzgu8IuKtMJhPfBgvuOZVKBZ9Sq9WpqalisdhkMnk8Hr6bFXyQpmmtVhseHg5vCkh8cDqd8JDwM194UAmCUKlUYrHYYrEsRc4UEhTnC5Tzv7VYLEajEQyqQCCIiIiQy+VGo9FisQQHByclJcETNf+zOI6HhIQEBwfD4y2TyeRyOZ+FwXHczMyM0+kMCQnRaDQ0Tdvt9qVPH+ELjI6O9q3BR6wQsKIdHh6+d+9ebW1tY2Pj1NQUmNuQkJDQ0FCwmgBoI4SGhgoEAo7jpqampqennU4nQRD86xLMj1qthlva6/XyL32WZY1G4/T09ILZPRzHmUym6elp/m7XarWpqalms1mv14vF4piYGIPB0N/fDw8RSB5GRUVt2LAhKSkpIyOjsLAwPDx8kaXSIuk/MOFobW29fv16XV1df3+/1+vl7QeGYVNTU7Ozs2q1miRJg8HgdDrhaBRFhYeHYxhmMpkeZzJhXvu4rrG+ToUl/pYgCH42g323pGf+9cJfBzQd+eXBgs8jjuMikUgsFrtcLrfbHRQUJBaLrVbrIlP2OWPzzWGGX5EkGRwcLBAILBYLHNPj8czOzgqFwuzs7HXr1sXGxq5fvz4nJ0epVC54lucAMrfPCbfbPTU1BWGPvr6+o0ePfv3114ODg/wNjWGYx+N53CIPe3TP+W7xdYIRBAHKpR6Ph2VZ8H3Bb2GCrFarNRoN37/a5XLZbDapVAodOmdmZgwGA6/ZptVq5XL52NgYZPMvDpxiwTn1giMH2wkPCTx4UEq/4Gf5C4FO3fAKhl+xLDs1NWWz2WJiYlJSUjweD/8OXQoURaWnp7/zzjt5eXlo9bzSwLTvs88+++yzz/r6+lwu15x8mflifvxGuFXmx0R895lj4RaxK9i8G5JfNMNNCC5KhmH4GxUkliiKEolEWVlZH374YVVV1XyVJf7gTqfT6/WC7Z+zD8uyQ0ND/+///b9Tp05ZLBZfZxXchHxjduy7ibv89S4yoZyzv1/w/YssPhh+N9/32DOeGn6Y440nSZKiKJlMtnv37r/6q79au3bts5zlWUCpUiuOw+Ho6elpb2/v6OgIDw+vqKgYHR29detWd3f3HNuwlLvzcbtBhIOPg7pcrjn7OxyOkZER343cdyO+vuE0o9HIv2iwJcQ85rwKF4w58cACnT8v/yUseF2+F2IymfR6ve/RYMyTk5MtLS3zpyOLg+N4Z2dnfn5+VlbW49q8IJYLcHI0NjZ2dXUtMqf0F76zPf5n340sy8JsuLW1taGhoaioaL5TBJZ0XV1dOp3OYrGEhITk5+evWbPGV+wCgjsTExMWiwXufH5+4Hu6Oc/CShjR+cZpWQ4159/HHdnXuC7XLMH3IL4/Q4SY47j+/n6TyfTsJ3pqkIjjysKybG9v70cffVRdXT01NRUaGup0Ords2bJ582aHwzE9Pb349w9+IfDhqFQqmUxmt9ttNhs8meA+gh1mZmYg308oFEJ+B//0wuQOciIWHy1FUfN7c5IkCZLi8F+32+1wOMRi8fysfXAleb1eiBbz24VCIbiY+DEbDAaRSKRSqaanpw0GA0mSsB2efI/Hs+CrZ/4KGLyRMKql38nwhVAUFRoaCuLs6ClYafhAYHNzM98fZtUBAWOlUgk6/nN+a7fba2pqjhw5UldXZ7PZlErl3r17f/7zn0P4kz9CZGRkaWnp2NhYV1eX1+tVqVSQ0Mvf3lAVIxQK3W43RVHgGHiWLnU4jsNrgd9CkqRKpRIKheDClcvlEKaBGJNQKFz6BBQOJRaLGYbhHcLQmcDj8cBbC/aEdT88eiaT6XHhJ+wxLyIeSOya/1mhUEiSpNfrnfOig8uPiIjIzMwMDQ3148OOVrcrC03Tt27dunr16tDQEGRznDlzRiQSVVZW5ufnT05OLv63hwWrQCAgSVKr1SqVSrPZbDKZYF4M6Q8YhpEkOTU1NTQ05Ha7Q0JCJBLJ9PT0+Pi43W4Xi8URERFg5nk7vSAEQSgUCniV+G4nSVKj0ahUKuyRsbRarXK5fH4IRCQShYWFQf6hr5dMLBaHh4fDUwernMHBQZlMFhkZOTIy0t/fLxQKGYYBLVa4lpGREXgj8ymIC45ZKBQGBwfD9+B2u81mc1dXFz+BhU4m0dHR89NwoMgP4nDPnvmC+F7A3B48eFCtVtfX1w8ODkIgQCQSQafxOfvDJE8oFMLNIBaLY2NjPR7PxMSEr0iv3W6HZ0Quly9uIfh3vVqtxjDM6/XKZDKhUOh0OmmaFovFj7sNYM0KhjY4ODgvL6+iomJ+yQrDMO3t7X/84x+vXLkCpaVut7u6ujotLS08PBw0irFHGY6HDh2KjY29ceOG1+uNiYmBOAhvJCC/AbIghUKh1+vt6Ojo7e319cDzh+J92l6vt6ura2RkZI6xIUkyOTl53bp1cOEAmB+JRDIxMWGz2UJDQ0NCQiiK8ng8NpuNTyhZCjBahULh9XonJydBOmp2dhaCU/Dq8E22EAgEQqGwv79/cHBwQT8HXNf8FxHAsuzg4GBDQ4PBYOAX0HFxccnJyTExMXK5HFK0IJNjdnYWkgOgy/2mTZsSExOXeF0rATK3K4vb7e7p6RkbGwPzAzKhHo8nKiqqqqqKj6QuBYgkzXGZ8o+f1+udnp6G6aREIjGZTIODg9PT03K5HBTJnU7n4plEkF7Pp4POPzV/Rl8v9Pw9MQybf5Y5R4Ad+CAZbPd4PLCbwWDQ6/VWqxXH8fDwcEhBXHDMQqEwKCiIZVnImWppafmP//gP3tyKRKJ9+/bt27fPdyHOL1BgErPIJBqxvFAUlZaWlpiY+Morr/T19fX19RmNRrlcHhoaOr8RG0VRGo1GJpP19PS0tLRAu3K73d7d3W2z2WAfhmHg/Q6t7hZPgYE1okQigdQ8p9MJvg2oG1EqlY/TN2YYBmIrwcHBGo0mNTU1PDx8viVwu903b95sbGzkZRxADfGrr76Kjo7esWMHX+VCEERoaGhlZWVJSQlBEHBzznlk+Icde6SJqNfr+Qvn94mIiAgODoa4T09Pz69//evx8fE55paiqHXr1n344YcZGRnzT8GnUPjKGmNPWDPDP918QIp7hO+Dj/m8r2ZnZ61W6+PM7eNeRBiGeb3eY8eO9fT0GAwG2CIQCMrKyt555501a9bIZDKbzQZZn0aj0Ww2i0SiqKioyMhIqVQKOpFLv65lB5nbFcTtdt+/f7+7u9v3rgJN8Lt37xYWFiYkJCzXuUQiEfhF4f6WSCRarRZSPAClUgmZjYuAL6GB9rLDpz7xeSUSiSQqKoo3yYsMibf6ISEhbrd7cHBwzntQJBJFR0cHBwfP/xSyss8fSOiLiYmJjIzcsGHDnBf9HCD7NCUlpaysjCRJSKEvLS31jflB1zbwoCxe4wEJfQRBwCKYf1L47IRF7gffW3HB7FyGYUZHR1taWub4qzweT2Nj4/Hjx6Ojo9etW+d7cwoEArgtl3IfxsfHR0dHz/eEwZDcbrdOp6utre3t7Z1vwCBP2+12PwfNpqUbM6FQqFKpHufbW+Su4Diur69vYmKCnxZIJJLs7Oy1a9fChEYikYSFhXEcl5yczKdKzbH6/gJN7VcKjuNGR0ePHTvW0NAwJyXK7XbfuXOnpKQEXKzL9SfwvddJkvTvPO4p4L+Hpxs8juOTk5MWi4XfwrKswWCw2+1Q2osIEODvu0QfPkVRvk6gOR5jhULxFKuxZQeitq2trfMT410uV11dHYgaxsXF+VqRpY95kSeC47iHDx8eOXLk7NmzU1NT8w0YwzCdnZ3t7e3Z2dkL6kj4haceBjzUvgt9iEeIRCL4bgPkAhcE1T+sFG63++7duw0NDWAAYL4GtwJN0x0dHadPn+7q6kIyI8sChIQ7OzuNRqPvdrfb/b0JYohVjd8dFWDPzp8/39fXB1tIkoR2cuAQNplMp0+fPn/+vNFoXN48HZZlR0ZGvvrqq8uXL09NTUFne5lMtmnTpr1798bFxcHyfXJy8sKFC83NzQGYE/6k8G5q/r+zs7P19fX9/f2LJKYECMjcrggMw/T399fU1AwMDMAzEB8fD40hYQeHw1FbW9vU1LSgvAPiSWFZtr29vb6+fnp62t9jQbxEcBxntVpv3LjR1tYGxowkyTVr1uzdu3fbtm2gXEHTdF9f3+nTpzs6OpZ3eu1wOC5fvnzy5MnBwUF4z4SEhGzfvv3v/u7v/uVf/qWkpAQc7B6P5/bt2zdu3FjtTwfLsjabbY4ahsPhqK6u1ul0gT+xRoVAK4LNZquurr558+bMzAyGYZCKXF5e/tvf/vabb77BHq3G+vr6LBaLH1VOXhhomoa0zDmvszlzYQRiebHb7devX6+uroZoIiT3vfnmm2+88cbY2Ni//du/Xb16laZpcGjpdLrc3FxI8n92XC5XQ0PDl19+2dPTw69rKysr33vvvYKCApIkw8LCINkYwzCHwzE4OGg2mzUazbKc3S8wDMN30vUFSqID/0lHq9vlx+v1trS0VFdXDw0NwRMok8lycnI2bNiQlpbGh08YhhkaGlrt880AgXsk5ePvgSBeIliWffjw4YkTJxobG8GqiUSirVu3VlVVJSYmrl+/fteuXWvWrBEKhVBNdOXKlfr6et8OdE+N1+tta2v75JNP7ty5A5qOUql006ZN77333qZNmxQKBWSlgSIb9khPJvDXf4sDvXJhDcMDhUAajSbws1X8b26hLGRx0bVVBE3T7e3tn3/+Of8ESiSSvLy8NWvWhISEbNu2LS8vD9I9aJpubW1ta2vzlQVfXcAz7KtAi0C8PDAM09fXNzAwAO5NKBjdsWNHdna2QCCQSqV79+59++23Y2JiMAzzer03btz47W9/CyIYz3je7u7uo0ePXr9+HWyPUCgsKir6yU9+UlBQADFj8GlHRUXxJTqTk5OLKEusCmB165sOiWEYlF0sY87pyuHnQiAIdA8NDTmdzri4uNDQ0MD/yhbH4XB88803V65cAdEGgUCwfv36d999NzMzUyAQbNiw4fDhwzabra2tjabphw8fXrp0KSMjIycnZ8Ga7kCGZVmz2azT6e7du0cQRFFRUU5OjkKh8Pe4EIjnARTY6HQ6vvgHanNDQ0NhPg3ND/bu3dvc3DwyMuJ2u+12e3V1NbSc27hx49NJh9I03dvbe+TIkTNnzoyPj2MYBmqR77///tatW/kHkKKoTZs26fX6zz//HDR2Ojs77969m5KSsnh/hUDG4/FApbXvRpZl9Xp9T08P1AL5a2xLwc+veK/Xe+vWrTNnzkxPT5eXl7/yyiuRkZGB7xN4HCzLjo6O8k8gSZJJSUk/+MEPqqqqoD1kaGjovn37DAaDwWAYHR11uVzXr1/PysrSarWRkZH+Hv6T4fV6b9++/T//8z8NDQ0Yhu3cufNv/uZv8vLy/DIYjuNomp4fuEUeZsQKAQ/v+fPnR0ZGoIo3MjKyrKzMV7eIJMnY2NhXXnllcHBQp9O5XC6Hw3Ht2rXo6OiYmJjExMQnLXNnGKa5ufno0aPnzp0bHR1lWVYikZSWlv74xz8uLCyEJmCwJ0EQcXFxb7/9tl6vHx8fB8mnL7/8MjU1taKi4okEdgIESMPW6XRzdI+hVUl3d7fFYglwc+tnZ7Ldbv/mm29Onz594cKFX//616dPn56cnPTvkJ4Fj8dz586dtrY2iKYEBwdXVVVt2bIF+h5jPoIyxcXF0IrHZDKdP3/+4sWL3yvoGGiAR6uzs3N6etpisdTX1w8NDfllJKBgYDQa50TF5pfoIRDLAqQ6Xr9+vbu7G9KUgoODd+/e/f777ycnJ/vuKRaLq6qq3nvvvZSUFKgLmp2dra2t7ejoeNJIKjiEjx49+sUXXzx8+JBlWYqiMjMzX3/99Q0bNvjaWkAgEERHRycmJsrlchzHvV5vZ2dnfX39nGK51QLDMF1dXf39/QtKeYCcp18GtnT8KXPBsuz09PTIyAhIXHZ3d3/xxRdpaWlarXY1NkQDuagrV6709/fD0jYjI6OysjI+Pt73ckDKrqysrK2trbu7m6ZpnU73u9/9TqPR7Ny5c5W2pgGFWND3ef5nB5W7gYGBOVVVoKnr21MIgVgWYEU1MjICnQNEIlFJScmhQ4fWrl07RxYUinN27do1NTVlt9uHhoYgwaqmpiYtLS0lJWXpzjyO46anp/v7+6G1iUAgWLNmzVtvvVVSUgIGdf5HYB+tVgtRW4/H8/Dhw+npaQgnry44jhsfH4cg3fxfgXMrwJ90f1o1yNabnZ2Fr8/j8ej1+omJiVWq/ADOVZ1OB5MsoVC4bt26lJSUOeo5IDO2bt06KELHMMztdnd1dbW3t8/JuAtw7Hb72NgYv3b0er2g9v78R8IwDNw5Cz6Hz388iBcbCFK0tbVB4RkU/+zcuTMrK4vPBPYFmny8+eabr776KnSksdls586du3jxIq+zvxSg5XNaWlpSUlJKSsr27ds/+OCDffv2abXax5kZgUBQXFy8ZcsWqACGJgGrtB0T9vhWfdDzJ/DTX/w5PvDA8BllJElGRkYGBwevxqUty7L9/f23bt0aHR3FMIyiqNTU1OLi4gWfBJIk4+PjExISxGIx5DR6vd6BgQGTybRa5AZZlh0eHu7u7oYpAryAzGYzNPN6znNM0II3m81ztkP/ohdASQcRUEAR7YULF/r6+jiOoyhq7dq1eXl5QUFBj/sIBHErKyvv379vMBggyePUqVMqlWrXrl1LzF0iCCIsLOzQoUPJyck4jqenp6elpYWEhCzywoQI7o4dO5qamoxG46oOr5AkuX79+k2bNs3MzPjWT0KKzJyWR4GJPw0bTNb4kANJkmlpaVFRUavO3MKc8cKFC9evX7fb7TiOR0VFHThwoLCwcEHnMBQM5OXlxcXFgSsJVKj4HheBDzjTzGbzfFfE8/fnQGXzgl91gEiTI14kbDbbt99+W19f73Q6oX0NtBtZ/MUlFArXrl27ZcuW6OhoiqK8Xm9zc/Pvf//7mpqamZmZJa5xhUJhbm7uu++++8477xQXF4eGhn7v21IoFK5ZsyY+Ph4KhPzeFeepoSgqNzf3nXfe8X2vEgQRFRX1xhtvlJaWBnieFOZ3Z7Ldbnc6nXwavVQqXY0pc16vt7u7u7a2dnR0lOM4uVxeWVl54MCB6OjoRZw827dvP3jwYFRUFPZIFKmlpcVisawW/6evYwf+dqGhoc+h68h8BAJBQUFBeXl5YmIi/xxCHviWLVvi4+Of/5AQLyrQ5qumpmZ8fJzjOJVKtX379m3bts3vgDsHgiA0Gs3hw4fffvvt2NhYDMM8Hk9LS8vZs2f1ev2CEbQFNdEIghAKheA7XeKaOC4ubs+ePbt3796xY8fu3btX7xMhFouLioq2bdsG/YNB4OKNN97Yv39/dHR04K/T/CniyLKs0+kE8S3skdR44AtxzYHjuKGhoQsXLkCqoVAoLCgoOHjwYGpqKkmSi3SYio+Pf+2111paWiACZDAYLl26lJOTU1xcvHgrsUBg/osAerwscskrB0EQiYmJ7777rlKp/OKLL3p7ezEMEwqF27ZtO3jwYExMzOq6oxABC8RQzpw509zc7PV6SZIEcYm8vLyl3PkURaWnp7/99ts2m+3EiRMGg8Htdjc0NFy9ejUiIiIyMnJOa1iHw2EymaRSqUqlepbApEwm279/f25ursvlio6OVqvVq/eJEIlEUDo8NjZGkuS6desOHjyYkpICzbP9Pbrvwc/O5NDQUKVSyfckt1qtc+SnAxxYoF+6dOnUqVPDw8OQNLF///78/PzvNZkkSUZHR6ekpECwk6bp+/fv37lzZ34MEvG9UBSVkpKyY8cOWDfw+j55eXlLbPSGQHwvdrv9xo0bt27dslgsoGKxZ8+eoqIiqVS6xCNQFJWQkPDWW29B2hTUkh47duzKlSu+kk8cxxmNxkuXLv3Xf/3X73//++7u7mdsdyOVStPT03Nzc8PDwwM/pWgRCIKIjY3lw7SrJUkK8PMofUNrDMP09PTo9frs7Gy/+CSfApjt3rhxo6+vj2EYkiQzMzMXT5rggahPSUlJe3t7Q0PDzMyMxWKpqalZv369SqVCRuJJwXHcZDJBLRBBEGq1Ojw8fJUWViECELfbffv27VOnTun1eo7jRCLR5s2bi4uLn7SJLARxDx06NDQ0dPPmTSiHPXHiBMQ+lEolrGtramr+/d//XafTQXZLeHj49/qrFwFkHZ/uswGFr32FHO/AL7flCaBJAcMww8PDnZ2dpaWlYrE48DNcOI4zm801NTWdnZ00TcO0q6KiAjwbSzmCQCDYunUrwzBWq7WxsdHr9TY2Np47dy46OjopKSnwQxEBBcMwExMT0C0EVh5LmfQgEEuBYZiBgYEvvvji5s2bUMmt0WjKy8shSfhJjyYUCvPz8/ft2zc6Otrb2+t2u+vq6mQymVqtLigocLlctbW1R44c0el0DocDEu/tdvsyZt5C65TlOtrzhOM4PrkaaluW7lrwOwFkbrFHM5fVMgtjWba5ufnMmTP9/f3YoxI3Poy/lCNACfzmzZvPnj177949lmUtFsulS5dyc3M1Gk2AJ9pBA21/j+L/gOpGMLEgu7Ha+58gAgeGYXp7e/V6PUS7BAJBYWFhbm7u073rwU7s2bOnu7t7ampqenoapKZSUlLsdvvMzMznn39+8+ZNh8MBPrDExMSQkJDlMpAul8tqtUokErlcvurm9LD0hxUtZGhCxrW/x7UkAsjcQjVqZmbmMt5YKweouF27dq21tZXvvZWens634FgiBEHIZLLk5GS1Ws0X5NXW1q5fvz4jI2PFhv+sEAQRHh4+RzfOv6kKFEVlZ2fHxcU1NjZCndIqrS9EBCAOh2N8fBzuKJIkExMTKyoqnsUFBU/Qjh07dDrdnTt3aJo2mUxHjx6tra31eDz9/f0QFhGLxYWFhfn5+csy+Ya2CnV1dTqdTqvV7tix43vrlwKQOe+ZwDcWPP4UccQeZSP/71Aoas2aNXFxcYGfl4thGKhO3rt3DwTVIF8uOztbpVI96Vcqk8l27NgxMDBQXV1tNBrdbndjY6NOp4uLiwvYrlIEQcjlct+qLY/H43A4vF6vv5a8BEEoFAqpVAr57bC6DcxvD7G6YBjm/v37165dA0V3oVBYWlpaUlIyX6b4iRCJRMXFxa+99prJZOrp6aFpenh4GHRyoCEpjuPJyckHDhxP4YRmAAAgAElEQVTIyMhYFp8fTdO3b9/+1a9+df/+fY1GIxAIYNL87Ed+bviaDFDXgdXOqnjS/VkIBIhEIij6hp8FAoHfh7QUTCbT1atXe3p6OI6DZpOHDh0qKCh4ivGTJFlQUAAP282bN6GJ5rlz59LS0nJycgJz7jnnGsHDYzQaHQ6Hv2ZLNE0PDAyACChJkiEhIVKpdFXcS4hABoKFZ8+era6uhtWtUqnMzc2Njo7GntmjExoaevDgwe7u7tHRUchM5jOQIf9g375927dvV6lUy3In0zSt1+uh4enExERDQwP0on/2Iz83fL8HaPECjUlWxZPu51c51ALJ5XLsUeYRSH4HONAG6/Lly2NjYziOa7XaQ4cOvf7664uIly6OWCzOzc1NSkqCjDun01lbW3v//v1VVBbFsqzH44FZuV8GAK8SaKwEmclwXyEQzwJI0ICkOTThycvLy8zMXBZBHoIgVCpVQkKCSqWa8yuVSgVqObGxscs15wapDTiX1+ttaWnp7e1ddSqnvm8YiqICc0GyIH4eqK/8HsMwU1NTkFkayNA03dPTc+HCha6uLoZhpFJpWVnZpk2bnkXtGcdxsVicl5eXkJAA9fJms/nWrVt9fX2rq2GDf+eYvp4lhUKxGhXKEAEFNOGpq6sbGBiANl+JiYkHDhzIysparoxOHMfVavWcJSZ0z62oqEhNTV1GcyIQCNatWwchZxCOvXz5cn9//zMW9fqLBTNIAhk/m1vowTc7O8v/N/B9AhaL5ezZs3/605+mp6ehHqCsrGzpxT+PQyQSwWRWq9ViGOZ2u69fv3758uWpqanA/06wR9pyfswqd7vdQ0NDIBJCkmRqaqpGo/HXYBAvBizL6nS6y5cvQ0hVIBAUFRVBI/dlOT7HcaOjo8PDw/P9WC6Xa3R0dHm7hJEkGRMTk5CQAM22zWbz+fPna2tr53SuXEUQBIFWt0uFZVmz2Qzmls/q9u+QFgdaHN+8eXNkZARaTqampsbFxT27nAJBEDExMbt27UpNTcUwDFKUz54929zcHPjeHnBSabVafxVMg7yXXq83mUzYoyYh4eHhz38kiBcJl8t1+/Zt8GNB68w1a9ZoNJpluckhf/6rr746ceLEyMjInF8NDQ2dOnWqsbFxeR9/oVCYlZUFnWBAO7a1tXV1NZxXKpWr1HHl/9itQqEADSloLxXIcXsQMbl16xboWuA4npKSAg3kl+X4AoEgNjY2Li4Obiav1/vgwYP6+nowIYEM9CBLTU31o4oTTdN8w13ofLKKpr2IAISm6d7eXmhdh2FYUFDQ5s2bS0pK5sdZnwJoln7hwoVTp051dXXNl0byeDytra03btyAXgjPfkaAoqj169fn5eVBxTBN0yMjI6tIOBZm9kFBQavFgeyLnwuBSJIE9R+r1Qo/P0UhzXPD6/W2tbXV1tZCJ3ORSPTKK6/s2bMnIiJiWcZMkmR4eHhZWdmDBw90Op3L5Zqdnb1+/XpJSQkonQbON8N3lYD/wlTJj8/AnPcRSZKgDxo43xhidcGy7MTExFdffdXa2goP+4YNG372s58VFRU9u64CwzAWi+XixYuffPJJe3s7LJ3FYjEsnQ0GQ29vr81mc7lc169fz8nJ2b1797LYeAzDCIKIj4/fvHnzvXv3enp6WJadnJyEjJlV8bDMEUnmx7wqBu//6T/ffzHAhfcg6fybb75paWnxeDzg+k5NTdVqtcsokC0SicrLyw8dOgRS+9AU8+bNm1NTU8t1imVhjiWDOBAfg/fveHAcV6lUMpnMX4NBrHYgNlFTU3Px4sWJiQlQf6uoqFi3bp1EInnGNzvEa8+dO/f555/DrBrDMLFYvGHDhg8//PCf//mf/+Iv/iI1NRXHcYZhOjo6Tp8+3dnZuVzZTGDX165dC60/wdx2dXWZzeZVkSOCP2LOFj8Oaen439zy4DgOdbf+HsgCsCw7NjZ26dIlyF3CMEwgECQlJUVGRi7vgKFLa3l5eVpaGtxDTqezpqamra0NSpMDE3g9wYvDXwgEAqlUCj4A5ElGPAter7e+vv7EiRMQNoLK+OLi4uDg4Gc/uNvtvnz58n/+5382Nja63W6YuJeUlPz0pz/dtWtXdnZ2aWlpXl4ezBfdbvedO3fOnTvX09OzXFr8kDAVERFBkiTkiJw5cwYGsyzHRzwOP7+SfGVBAhm3211TU/PRRx+1trZCN4Ls7OxDhw6lpaUt+2udJMmIiIikpCTwzdI03dnZee/evQCPr/g3RRDSWNRqtUQigQn7xMQEen0gng6TyXTu3Lk7d+5AwrBMJtuyZcuaNWue/Q4HvbOGhoaOjg64P8Vi8caNG3/2s5/t2LEjODgYlJ5KS0vXrl0rFouhE9+JEyc+++yzoaGhZbi2R+6fqKgoaP3p8Xiam5tv374d+Dkiqx3/Zybz7R0CGZfLVV9f39XVBT2l4+Li3nnnnbfffhtcvssLjuNBQUGVlZVlZWUwm7bb7VevXr1//75/l4/z8Y3dhoaG+td/KxAIRCIRBCZAc2OVVhMi/IuvrgX2KJV37dq1y1XfybKs2+32er04jgsEgrVr17733ntbt27ljy8SibZu3free+8VFhbKZDLo8nn69OkTJ048ePDg2aVvwJ+cn58fHx8PEwiXyzU0NGSxWJ796hCL4GcRR47jZmdnYXULIwlAOS6O40ZGRgYGBkDxSqVSvfrqq2VlZdB+ciVGKxAINm7caLVaBwcHp6envV5vQ0PD+fPnk5KSnq7h17IDySMKhUIoFDqdTijVl8vlfvzb+Z6aIAioFgi0ewkR4ICuRW1trV6vZ1kWx/H4+PiDBw9mZWURBLEstxNJkrGxsREREU6nMyUl5Qc/+MHWrVshE4rPQNRoNAcOHCAIwm6363Q6mqb7+/t/+9vfTk5OfvDBB5mZmc84BoqiNm7cWFZWNjExAUJss7Ozbrc78J8X7hEL/jfA8XNHIMhBkEqlgbZu44H194ULF9rb20GMF4p/kpKSVtTsicXijIyM2NhYeNig/g+KjgIhvA1yYOC8BXMbgAkLgTYeROADvWarq6uh/EYoFG7fvr2qqmoZa7glEsmePXuEQqHFYikoKNi8efP8Ql4cx5VKZXl5+eDg4OTk5NjYGMMwo6Oj58+f37Jly7ObW7DoFRUV9fX1k5OT0Clo9YpdrBb8bG75Wtvp6WkMwwKwR6nD4airqzt37tzw8DCI8WZmZiYmJq60zSMIIjo6uqSkRKfTPXz4EDIa9Hq9zWYLCQlZ0VMvERzHAzYdCVK33G73MiaNI154+FrYtrY2KM6RyWQ5OTmxsbHLKJcGqstr1qxhWVYkEgmFwgWfIygw3b179927dycmJhiGYRjGYDAMDw/bbDYIuz7LMAQCQUpKSkJCQlNT0+rtNr+68H+qFLwWsUe9GANnhgWiFjU1NZ9//nlXVxcsbePi4oqKiiIjI1f67oRHfffu3fv37w8PD+c4bmZm5tq1a01NTQHSxYGmabfbHVDxUd/OXC6XK/BT8BABBURtWlpaoKRNJBLl5+enpaUtu4YRSZJyuRziHYvMWSmKSkxMzMrK4ivavV7vlStXLl++DOuTZwHH8YiICFAOqKys3LVrV1xc3DMe8/kgFAplMhlFUfCKdjqdyJm8JFiWNZlMcHNDE7fAeUWCXuMnn3xSXV0N+foxMTFvvPHG1q1bn4/0FcR4du7ceffu3fHxcY/Hc+PGDbVardVqMzMz/buyhE5h0ALIj8PwxbfdhVwuj4iIAN0cBOJ74TgOGjhevXq1v78forYJCQmvv/56ZmbmSsytl3hMmUxWUVFhMpm+/fbbiYkJr9d7/fp1l8tF03RFRcWziAJBAdLu3buzsrJomo6JiVkuJY0VBfLLICmSpumJiYnA72rD439nclBQkFgsttlsgZDd6ovX621vb9fr9RBXlkqlFRUVhw8fTkhIeG6OF4qi4uPjExIS7t2753K5HA7HjRs3tmzZkpCQ4N/ucqDtAnNMPw7DF4FAUFBQUFRUpNfr161bl56eHghBbkSAA3m/3d3dRqOxqamppqbGZrPhOB4cHFxZWVlaWvossRun0zk2NjY2NqZQKOLj459Cdk0gEGzZskWj0SgUii+//HJiYsLpdN69e5cgCK/Xu3PnzrCwsKceHoZhUqk0PT0dmh1hGBb4XmVYlVmtVliYeTyeQIs/LoKfdQEJgggODoZVCPwsk8kC4e/Ncdzk5GRrayuIWlAUlZ6eXllZmZyc/Dxf4hRFRUVFlZWVdXZ2tre3u93uycnJmpqa/Pz8tWvX+neBSxAESZK+Wk7+zZYSCoUbNmzAcXxycjI7Ozs1NdWP7YkQqwJokXLmzJkTJ05MTExYLBboVS4QCLKzs3fu3BkfH//UdxHDME1NTWfOnNHpdJBpXFpaGhoa+kTPCBSUp6enHz582GQyXbp0aWZmxul03rp1iyTJhISEsLCwZ3noIAOD4ziv12u1WqFz5bOrVK40fO843Ad/D+r78fPShOM4i8UClWQcxwVIrSRE/q5du3bt2jWIkSiVyl27dq1fv/75S/CLxeKKiorR0f/P3ntFt3Vd6ePAvagkAIJg7w3snRSr2ElJpCiq2pId23IsW56UtTKTZK15nsfJmofMPGSScY+KbfVGdYq99yp2sIMAC1gAot2C/8P+6y78wGJKBAlCwveQFQNXvAe3nH3O3t/+vpnFxcXx8XEw5ouNjfXy8oJOpD0ejwksPgAKMFPk5OSAB7gt1trwi4CC0dOnT9vb20mSpCojkGlzdnZ+47U1+It8++23Dx48UKlUEMCCg4NFItEbvDJMJjMuLu7Xv/61UqmsrKwEvsvLly/7+/vBbGAnryHI0zY0NHR1dRkMhri4uNTU1P0wt7x9sDBVCizlQeZi/0heGAwGmUxWXl4+ODhIEASCIH5+fsnJyeYy3notIAji7Ox88OBBkNQAyaSysrLh4WFrIQjsGSDFzeFw9pWdgw37FhiGtbe3j46O4jhuzEIApQuJRPJmVBKDwSCVSn/++efy8vLl5WUMw6Dn4o1fWKizZmRkfPLJJ9HR0Uwm02AwzM/PP3v2rK+vb4fZVJIkW1tb//rXv/7lL3/5y1/+8l//9V/Nzc02RbbdgIVlLoDeAlIJBoNhZWVFrVZbPIqsra01NjYODAyAFYGTk1NOTg4YyFtkbMCZCg8P7+rqWl1dJQhiZGRkbGwsPj7egr6P+63f3PjsEGupQpQt9NqwHmAV0NbWJpfLTb4iCGJiYqKjoyM9Pd3Dw+O1nh+CIGZnZ+/cuVNaWgrWYWAzGhERAdZhb/yOcDic/Pz84eHhqampmZkZvV5fUVERFBQkFAqhLZjL5b6BXziO4yMjI+Pj42trawaDoaurq6qqKioqajck83aOzaYdi0eN7WC/8FwA++GqkSQ5Pj7+6NGjkZERGo3GZrMzMzNPnz7t6+trqVkbQRBPT8+TJ0/KZLKqqqrl5WWpVFpeXh4dHR0REWHLmtJeJcSmpqYUCgVISjGZTK1WC7kBFxcXLpe7b7uEbbAIoC7T0tKyvrMOKpp6vf51d7ewr7158+b3338PNj50Ot3LyysrKysvL2+HtCbQvsjOzq6srJTL5RiGLS8v3717F8MwT09PBoMRFhaWkJDg7Oz8un/W09PTxcVlamoKx3G1Wt3Q0JCfn+/h4WEjG5oXlq/dYhi2H+q1ALBMqKqqampqUqlUCIKIxeJTp07FxMS8wbLRjGCz2enp6XNzcxKJZHl5WavVPn78WCwWu7q6urq6vsu7N2C7DA8P19XVNTU1TU9PMxgMFxcXDoejUqkYDIavr29UVFRmZmZgYOD+4VHbYFlA6aq+vn5sbMykmY1Op3t7e2dmZh45cuS16kfwN+/du/fDDz8MDAwQBIGiqKOj46lTpz799NOwsLCdP34oioaHhx8+fHh6enpkZAQ2pv/4xz8QBGGz2VFRUZ999llxcfFrVYgZDMaBAwfS09MlEsnCwgJBEENDQ48fP/bz8xOLxftwNW/xLdkbw/KNQCKRyN7efp+oW6hUqpaWlsePH09MTBgMBkdHx6KiovT0dMt23QC4XG5oaKibm1tPTw/4hLx48eLgwYPOzs778JXYG4DY1tOnT+/du9fa2qpQKGDqBKYivJYoirq7u58/f/7ChQsWTFHYsK9AEMT09PTU1NR6+Vg2m33o0KHf//734eHhr0WNXF1dffbs2eXLl2Ffa2dnJxaLs7KyPvroo6ioKLPsFMG/5OTJk0tLS5cvX56ZmSEIAnbnKpWqoaGBRqO5uLjk5uZuv8wEgufh4eFOTk4LCwswt9y6dQtW82bxHDQjjOWdre5dtiSjxGAwLC0tKRQK41K/BSndBEG0t7f/3//9X0NDg16vh2aAQ4cO+fr67oc8JGhapaenDw4OSqVSMOZrbm4ODw+3CI3QpCy693R8g8EwNzcHibuhoSEMwzZc9uI4LpVKKyoqsrOzfXx89sOttMGyABe84eFhaPMzBpPJhJa/8PBwDoezzeeZJElQoLt06VJvby+O4xwOJyMj44MPPsjNzfXy8jJjVhaYHBkZGZWVlVKp1PiZxzCsq6urtrY2Ojrax8dn+3+TTqez2Wxq8w3b9IqKiqSkpAMHDiAIsn8CG3DEwKyJZhQv9s8It4Alpx6CIPr7+zs6OvaJ8ROGYXV1dbW1tSBTYmdnl56eHhoauk8ykKAvffbs2ZKSEicnJ3jsSktL29vbLSXFZdlHHPoab968CaS2zVJMCILweDw/Pz9HR0ereCdt2G0YDIb+/v4nT56YOMhCnfX9999PTU3lcrnbf1rAwvabb76pr68Hxw5XV9czZ86cPHnS19fXvBVQOp2OoqhGo1lPHoadX2tr6/j4+GvJvQHdgcvlUp+AnuWzZ89MIvp+AJPJNJmTreW9tmQggaZbpVK5H24nLOjGx8dXVlZAHjksLCwtLc2MTiA7BzS2Z2VlNTQ0zM3NYRjW0dHx5MmT4OBgyrry3QFBED09PWNjY1D7B5Z7aGgo3DLqDbSzs/P39y8qKgoJCXnXLpENGwLDsKqqqrq6OuO2QyAiHTp0qLi42NPTc5t/CtQCOjo6rly50tLSArGWy+UmJSXFxcUJBILdeOQgE764uLh+5sRxvLe3t6yszN/f38vLa5tnp9PpQqHQWPSUJEmZTHbr1q2wsLBjx44ZR2LLAubAsLCwjo4OtVrN5XKtiM9lyUYgUCE2UUWxFDlZpVKVlZW1trZqtVpo/ikuLk5ISGCxWPthNUCByWT6+/t7enr29vZiGAY9S8XFxX5+fns8Tos3ApEkubq6StXeEAQJDAz88ssvk5OTjVPc9vb2wA8ATfM9G54N+xYEQcjl8uXlZeMtIBj1HD9+XCwWb7/lD2LtV1999ejRI5DEYbPZBw4cOHv2LCzvduORg+aiDbd0UGG5ceNGUFDQyZMnt6/uvl4ZBnhYbW1tqamp3t7eZhi3meDi4nL48GGFQiGXyzMyMtzd3WlWwp+y5O4WQRA3N7edqGybCyRJDg4O3r17t7+/nyRJFosVFRV18OBBi+habA0w3D127Nj09HR/fz+GYdPT093d3bGxsa/bALBDYBimVqstKFgKliYCgYDSKIcmLhaL5eXlJRaLuVyuSqXi8XgQa/fbrbTBItDr9WNjY9C3Sn1IrbCTkpK2TzIiSXJoaOif//zn06dPFxcXaTSavb19QkLCxYsX8/LyBALBrvwAGg1ybz4+PtPT0+tfQGgaLi8vj4uLi4qK2s5jD7wQT09PJpOJYRj1uV6vb25uzs3NdXV1tWxrhjFYLFZubq63t/fq6mpAQICXl5e1vNqWDLckSU5MTMzNzVncVQbH8e7u7qGhIdC1ABWnwMDAfZh7hLTPyZMnpVLpwsLCzMyMXC6/c+dOQEDAoUOHdijntn1AB5dWq7VgExeDwUhNTU1MTARTKYIgXr58OTIywuVyIyMj09PTBQKBQqHw8PBITEyMiIhwcnJ6ZyncNgAMBsPY2NiPP/7Y1NREhVtII6empqalpb2WpjGO401NTZWVlXNzcwaDgcvlZmdnnz9/Pjc3d1eJAiiKRkRE5OXlSaXSiYmJ9RFXp9M1NTXV1dV5enpupykI2tP9/f35fP7S0hK1U8RxvKur6/nz52KxeC+tWbYG0LMTEhJIkkQQZB/O0pvBwrVbjUZDPfRAF9z73RJJkgqFYmBgYGFhgUajOTg4FBUVnThxwsPDY49Hsk1AxE1OTn7+/PnMzAwI0T148CA4ODg8PHxvXgk6nc7hcNzd3Xk8Hvgn7j0QBAkLC8vPz3/58uXg4CCNRiNJUqvVwlzT3t4OvUA8Hi86OvrkyZPHjx/39vbeJ1OGDRYBjuPt7e2PHz+empqigoqdnV1OTs6vf/3rNxCNYbFYdnZ2IKISFRV14cKFw4cP29nZ7WoMACrWBx98wGKxLl26NDIyYrLqJQhCIpFcu3YtICAgJydnO+1MCIIIhUJ7e/ulpSXqQ1D6e/LkSWxsrKur637oh6RgXYEWYMlwCy3boaGhvb29KpXKUvby4GpXXV2tUCgYDEZMTMzZs2djYmL2CSF5Q4DvtFgs7u7uVqvVWq0WAoyPj8/upbBMwGQyvby8HBwc1mvg7Q1AIdnR0dEk+wc7byonplara2pqFAqFt7e3q6vr3ptM2LB/APRMUEKFT5hMZmJi4meffZabm/u64QTyKwqFYnh4GPwfU1NT98bTjMFgiMXi8+fPEwRx48aNkZERMHqhAEXlmpqayMjIbVZeN6wHQ+R+9uxZTExMdHS0bbW6E1gyokDaNjg42MHBAcLt8vLyekG13QM4/zQ0NFy5cqWvr89gMDg5OR06dCgyMnI/x1oajYYgiK+v74kTJyQSSWtrq16vHx8fv3Xrlq+vb1pa2t5UWQiCoFpdLcJTMBgM09PTtbW1MzMzJl8ZTwp0Op0kSY1Go9FoLF62sMGyMBgMlHcbjUZjMpmxsbEXLlzIzMzk8XjbiSUUHxCEHgMDAy9evAjBm8lk7qV1Hei3fPzxx87Ozj/88ENXV5dJa5BGo6mtrc3NzfX09PzFjSBk1DesW+t0utra2uzs7MDAwH1ikGqlsHBQQVGUx+NR4WGPqa0YhrW0tHz11Vc1NTVqtRpBkISEhJycnH3V/LMhgHCbl5fX1tY2MjIyNzenVqsrKir8/Pzc3d2DgoJ2e7kAJJGmpqb5+Xnqkz0OupAYrK+vp9JfsN9lsVhCoZBqXWAwGG5ubhkZGbGxsbat7TsOcHUFNjvQo06dOpWfn79Nwia0C05OTq6trXl6evr4+HC5XOP+mT0GSF6cPn0aQZDLly9Dbwz1LY7jfX19VVVVISEhv1hGAdMhNpu93kQBNkKLi4t6vd7e3n63fsw7AAuHWzqdDpbyFjn78vLyvXv3qqqqoP1OKBRmZ2eHhYVZC6GGzWZD9RTEcdbW1h4+fGhvb//hhx+GhYXtXjsajuPj4+M//vjjixcvQN4FTIrGx8c9PDz2LKQZDAaFQqFUKmHPiqKoj49PSkqKr68vMJbhMDab7efnFxoa6uzsbHXFHhvMCAzD+vv729vbFQqFwWAAreCsrCww6vnFf06SpFQqvXv37vPnz1dWVuLj48+fPx8dHW3ZTBiwnM6dOycQCP7+97+3tbVRERcy53fv3hWLxSdOnHBwcNj6Txk7/hoDzA9iYmIcHBxsW9udwPLdEZTTJOzYti+ctkNAH/fg4CAw8VgsVmxs7IEDB4RCobVMyiiK8vl8KrxBG8wPP/xAo9G++OILf3//3Vg3gOfJ9evX79+/L5fL4d5hGNbQ0PDTTz8BL2lvbAHB18x4FxsXF/eHP/whPj7epAqFIAiKohZ/1G2wICD2PHz4kDJzZbPZKSkpIBv3i8+GXq+fmpoqLS397rvvBgYGSJKcnJxMSkqKiIiwuMwCiqIODg6HDh2CxorW1lYq4sI6+Pbt215eXunp6VtIZUF9ysXFpb+/3+Qre3v73NzciIiIfV5i2/+wMDNZJpPV1dVNTU3RaDQGgwES/HtwamAjU34gdDrdz8/vxIkT+79qawxIJRm320Ky6+7du0wm88MPPwwODjb7z9Hr9ZWVlTdu3DAWioON5u3btx0dHV1cXPz9/c170s1gPHeA6sXExASfz4cwvLq6qtFoOByOo6OjQCCwZZLfZZAkOTo62tTUBB60DAYjKCgoIiLiF3dsJEkC7eju3buPHj2CdkEURb28vPaPOwidTheJRCdPngS+bnt7O6UqDD6DfD5fKBTGxcVtNiEgCOLv75+dna1QKKamplQqFYZhoKWcmJiYlZUFahJmBGjmSyQSBoPh4+MjFAr37GLqdLr5+XmNRiMSiRwcHPZszrdw3+309PTY2BisxUATePsyKDuBRqOprKz86aefRkdHDQYDk8mMj48Hd509OLu5gKJoUFBQVFRUd3f36uoqVFzAP+ubb77h8/mffvqpiWjXDgGSdb29vePj4yYtWwaDYXV1tbOzUyqV7lm4NQZBEH19fd9//72bm5ubmxuPx5PL5UqlUiAQeHt7p6SkJCYm2rJh7yaAFNnV1UVJfopEosLCwtjY2C14hfC0T0xMdHd337p168WLFwqFAixsYcO3r1bnoHt8+PBhFot1+fLl6upqlUoFbBilUvnixQuolG3GvgZT7U8++cTf37+jo6Otra23t5cgiPj4+AsXLiQnJ5uXgAl35MWLF9evX2cwGCkpKYWFhWKxeA+uJyy8Hjx4MDU1FR4efuTIkYCAgL2J9JaUtcNxXK/XEwQBYwBR7AMHDvB4vF2dFtVqdXV19XfffUeJ+7PZbLFYDBpSViEGBqDT6R4eHqdPn56ZmamoqKAEYEmSXFxcbG1tzc/Pd3JyMm9uHEVRNpsNuVmTa0Wn0yEvtzfXcD2hY35+vqqqCjTcgZAMjfAcDic7O/vf//3fk5OTraVSYNYHxfIAACAASURBVIMZAVY5z58/h3ZbBoORlpZ27NgxLy+vLZ5VnU7X1dV148aN58+fSySStbU1OJjFYsXFxWVkZEAqbl/NGM7OzsXFxaCkVlFRAYZ6EHFlMtna2toWRBnQlvLw8Dhy5Ehra2ttba1er8/MzMzMzBQKhTSz/lLIct+4cePhw4cGg6G+vl6tVn/22WdUHR2SVcCCdHJy4vF4ZnlzQYbv1q1bly9flkqlHh4eIyMjiYmJQUFB4eHhAoFgV5fjFluaaTSa7u7usrKy6elpKtw2NDSwWCydTldQULBL9GCQ9f/b3/5WXl4OJRzQvE5MTDTvRnBvAPWnnp6e3t5eY711giAGBgaam5u9vLzMeyXpdDqPx9swMYsgiKur697kJwAODg4gpAWPEOT91h+m1Wr7+/tB+mfPxmbD/sHa2trTp08bGxtBEd3BwaGgoGCLrS1Y6/T09Fy6dKm0tFQmk1F9unQ6PTQ09MMPP4yNjd0/W1sKCILY29vn5OTw+XwEQR4/fgx5LwzDWltbExISMjIy+Hz+ZhMdiqJcLpfD4RQWFubn58PShMlkmn1iBP/Q0dFRaBeenZ2trq6GrhA6nb62tjY0NNTY2Dg4OIggSHJyck5Ozs6z2SRJDgwM3L59+8aNGxKJhCCI0dHRv//970KhMDU19fe///3Bgwd31YzBMo8LtJF8++23paWl8/Pz1CSo1WprampoNJqfn99uhFsQa7x06VJrayvVo2Zvb5+fnx8TE2NxysObAQhTJhMHQRCDg4OXL192dHQsKiraZk/hdgBMSIFAIJPJTL4Cqak901ZFUTQyMrK4uJjD4cjlcr1er9VqoeZkMmAXF5e0tDQr0la1wYwARnFfXx9Y6HA4nISEhMjIyA1bSA0GA0EQ8/PzlZWVd+/erampMVaZhYf/9OnTxcXFLi4ue/5Ttgs7O7sDBw78+te/RlG0rKxMLpdjGFZZWQmkquTk5K3nOkhT7fZigiAIahEDHkfT09NxcXEoira2tl66dKm8vHxubo7BYHR2drq7u+8w3OI4Pjw8fOnSpRs3bkilUjg1SBnOzc1VVVWJxWKxWLyrhTDLhFuCILq7u5uamtYLJut0uomJCfDWMPtJh4eHv/3227t374KeOO2Vw2VmZuZruTHvK4Cf63oysE6na29vv3r1KovFysrKEolEZjkdtMMDxXH9ZnEv4xmCIH5+fl988UVsbGxlZaVMJuPxeAwGw+SJQlEUOCBhYWG2TPK7Bsij1tTU9PX1AXE3ODj4vffei4yMXP8wgJ0OTE137959+fKlTqczfsh5PF5eXl5hYaGHh8c+f5a4XG5mZiZkRx88eLC6uqpUKmtra2NiYvz8/Cy+9KSI0AiCQMu+VCp98eKFg4MDgiA//vjjw4cPFxcXoRgklUop5tebwWAwyOXy69ev37p1a3p6GqYIKIrpdDqCIFQqVV1dHTDCdq+xwjKNQJCr0Wg0Gyb3KNEWM54ReDRXr159+vQp1DPgcwaDERUVFRAQsBsJk70BMLp9fHx6enpMpFOBlKjT6Xg8XnZ2tll+I/0V3uBbswPKtBiGLSwszM3NBQcHv//++7A+xXF8dHR0bGzMyckpPDzc2dnZem+xDW8MDMN6enpKS0slEgmNRhMIBMXFxUeOHDGxIoBN7eLi4p07d3766aeXL1+urKyYkAERBAkODj5z5ozFe223CS6XC83BGIaVlZUtLi4uLS2VlpYGBAQcP378tazYzD4nM5nM8PDwnJycoaGhmZkZgiBWVlbu3LkzMjJCo9F6e3upWdre3j4uLm4764MtBgl2OPX19RBrqYyXk5NTVVUViE739/c/evQoJCRk94yxLfPQ7OWMTKPRCIKQyWTXrl378ccfoQ2AGoZAIEhKSvLx8bHeiRj4yenp6R0dHTMzM8YrGFja19fX37hxA0GQ+Ph4c+1x9wnW1taePXv27bffdnR06PX6xcXF5OTkyMhIOp0+MzPz4MGD0tJSf3//Dz74IC8vz8nJydLjtWFPQZKkXC5/+vRpV1eXXq8Hycbc3FwvLy9jJqrBYMBxfGho6NmzZ5cvX4Zl6/qdgL29fXp6emxs7N60le8cUNxJT09HEGRlZaW8vBzaCm7evOnv75+amrrN1jgo/UId11wMXqigHz9+fHp6+vbt25DmXFhYAKojdf05HE5KSsqvfvWrkJCQ9X+E4kICLxIGyWKxNhwkh8MRCoVsNhvHcYFAkJ+f/9vf/pbP58tkspGREZgqy8vLc3Nz/f39d+kWWyzcQs/PhglJM95U2iva98OHDx8/fjw7O2ucaYR8y8GDB3fVLWu3AW0Jhw4dqq+vn5ubW88VWltbu3HjxuTk5J///OecnJzdK1FDK8KeTUYkSc7Ozj569KilpQUIFxKJZGJiQq/XIwjS09NTUVHR09MzODgIKkJHjhyxNQK9OwCmemlpKXCdQKG9pKRkPcVJrVY3NjZev3792bNnGzrIgvhdbm7uyZMnfX1993ka2QR2dnZJSUlnzpyRy+UvX74EC9vr168LBIKoqKhfnA1IkhwbG2tra1OpVOHh4VFRUebiQqIoGhgYmJ6eXldXB7p4kGOgDuDxeGlpab/5zW+A+QUfgkmRVCqdnZ1dXl6GVRSTydRqtSsrKyRJBgQEREREuLu7G/80BEHEYvG5c+d4PN7MzExQUNCJEyccHR3r6+spxXXo+9JqtbunrG6ZRiCwTvP09Ozu7l7/lbe3t1AoNNfAMAx78uTJ//7v/xrLMtBehfxjx45BFceqOatQxRSLxcDdN/kW9HQaGhqam5vj4uJey9FzPTa7UNBoHxwc7OjouDcXkyCI8fHxqakpivUGrgmwNJ6dnV1cXMRxHExJBQKBl5dXSkqKVaQBbdg5MAxra2v76aefoH8U/MeSkpKcnJxMMkBjY2Pffffdw4cPKUFQEyAIcuDAgd/+9repqaksFsvq5goej1dUVLSwsPD1119LJJKFhYVbt27x+XyBQODv77/16kGv1z948OAf//jHysrKoUOH/vjHP8bFxZlrYCiKMpnMDTdXCILExcV9+eWXubm5EGspXYG2trbbt2+3t7fPz8/r9Xpgdel0OqjvRkREFBYWnj17Njg42HiiEwgEx44dS0xMnJ+fd3NzE4lEd+7c+frrrykVLQRBIiMjQ0JC2Gz2Lt1iS+5uN7SKYzAYERERXl5eZjkR5IiqqqrWyzIgCBIUFCQWi98O0W0ul+vv7+/o6GhsV2kMrVY7Nja2uLi4w5wq3DtHR0fgOFCfIwgSGhoqFov3cnc7NjZGtfdAaUAkErHZbJIkfXx8HB0d4UidTtfS0tLT0xMTE7OXfUo2WBAajaa1tXV0dBQ2TGw2Oz4+fn10wXF8YGBgYGBgs1gLVcYzZ85YURrZBOCPW1JS0tbWNj09rdfrFxYW7t+/LxQKT506BcyVzf4t5J9BDqi+vr6oqCgyMnK3mzjgmn/yySfZ2dkmGSmQ8Xnx4gV08lA/ELyeQMNSJpMFBwcHBQWZBHIWi+Xj4wPBZWZmprq6GthwtFdb7eLi4t0r3NJoNMtkRcC7asNfBUK45tLbUygU9+7da2trW58g4nK5SUlJAQEB1pUa2gwIgohEoi2WDlCc2Iyetn2gKBoWFpaQkEAFM2oA0CC0Z9laKPZQ3cYIgjg5OYlEIljtBgQEUK0aoHglkUg2W4vY8JYBw7De3t7GxkboQUBRNCQkJC0tbUM3ArCI3zDtAYHq3LlzhYWFIpHIeisR8Ebk5OSEhoZyOBxo0/j++++hK2aLOQF0HIHwL5fLm5qaKKWEXQLkyd57772ioqL1qTg6nR4YGBgaGmpnZ0e+AkEQsFSCMjyO45uZyyEIwmAw1Gr18+fPGxsbKXFpNpudm5ubnZ1tMq2ZFxb2stjw8TULkQoaqpqbm58+fSqVSk2+BcnTxMREDw8P632FjAF10y16tOl0OpfL3bkfJ3AcUlJSysvLKfc9mpG5017Sko1LxQaDQa1Wd3d3w3s4Ozu7sLBAHUySpFKpBOc1G95uEAQxOTl57dq15uZmqK2IRKKSkpKkpKT1TeEMBiMxMfHs2bNqtbq3t9ekFsNisdLS0goKCjw9Pa19omCz2UePHjUYDN999113dzeO42NjY/fv34+Li/P09Nxswwr+lQKBAESGnz59GhkZeebMmZ2HJZIk5+bmhoeHV1ZWjD8H9eakpCSQ+Vs/npSUFAzDmExmeXn5ysqKQCCIiIjw9vZWqVRKpVIoFCYmJsbExGxGACJJcnBw8MGDB8PDwxCSmUxmaGhoVlbWbnNmLRZuURQFU1JjLSQajcZgMIwdcN8YSqWyo6Pj559/7u3tNdE9gLMHBwf7+Pi8NZU80Mby9vbu7OzcUFmJzWb7+/ubhZ3LYDA8PT1B140CgiAeHh67ujY0AdxEDw8PUOaD1ffly5dLS0thKz89PW08PEdHRwtak9qwZ8BxvKOjo6GhAShyIIeSm5u74dqaTqe7u7ufO3dOr9f//e9/l0gk1K4IOP/Hjh2zIlPOLQCtrufOnVMoFHNzc1KpFMOwkZGRtra2hIQEDw+PDf8VtYyen58HtkRFRUVycvIO33QQzL979+6dO3coshJ1Rg6Hw+FwNsw70ul0Pp+fnJzc3d3d0tKyuroqEAiysrKSk5Oh8S8+Pr6goGCLxiEgc1BLK0jXffTRR5mZmZsJSpsLFgs2TCbTxcWFx+MZh1t49P38/HZYT4Vy+ldfffXixQuTpRMA/ED2sy7M6wLYUseOHZPJZN3d3ZS+K/WtUCgMDg7eIU8KADqOJnUsBoNhZ2e3l72tQLiLjIzs6+sDNXatVjsyMgIDgABMHeng4ODt7W0r3L71MBgMi4uLTU1NlDxyXFzcuXPnwsPDNwuZUIgpLi6Gdk+lUmkwGCjCf3p6+m7PwnsGWHQeP358bGzs3r17S0tLSqXy8ePHgYGBx44d25C3DxQzPz+/6elpDMOADSOXy994DDiOy2SysbGx8vLymzdvDg4OQqXPWIp1cnISaswbFstxHO/s7KyqqgJxTej1grK0QqEYGxvz9PR0cXHZbCtFEMTExASlZigUCo8fP37q1Kk9kP6wmN8tCBSYrF9QFI2IiNi56ARBEJ2dnY2NjbC8XX8Aj8cLCgoyS+zZJ4BF36lTpxgMxrffftvT04NhmFarhZ09xB69Xo/j+HbcPbfGem1kyFQ7OTltYahpdqAo6uHhcfTo0enp6dbWVtAlMBH6oNFoXC43MDAwOzs7JSXFjGKWNuxPgGIdvPs0Go3NZpeUlJw4ccLV1XULlgaDwfDz8zt9+jQUfTUaDYiR5efne3t7vx30DgCo4pSUlPT19bW0tEDounz5soODQ3Z29nruBYPBiI6Ozs/Pl0gkk5OTBEHMzMzI5XIcx9+AMGUwGMbHx2/dulVZWdnT0yOXyymHJYFAsLq6qlKpIMnc1dWVmZnp6+u7/oVVq9VVVVXQS0175SRBqVPV19cDB3bDVl3aq7qbnZ3d2toalBLgLu9BAmN/pVIRBPHy8to5JQFYx5GRkSsrK8vLyyZfubq6FhQUJCUlvTWLVgDUMgsLCzkcTnd3t1qtfvnyZUtLC0jFKhSK/v7+hYUFb2/vHZ4IZCOFQiGTyaQS9Uwm087Obs8EkwFsNvvQoUMcDqempqaioqK3t1er1RrLmPD5/LS0tFOnTuXl5fn6+r41tQMbNgR4YVVVVQ0NDcHCCwh0AoHgF0Mmh8MpKCjw8/Pr7+9fXV1lMpk+Pj4xMTFWykbeAiwWKyEhISUlRSKRKBQKvV7f2NjI4XDodHp2draJgQGdTndycjp58mRLSwskDJRK5ejo6NLS0ht4uuA4XlNTc/Xq1eHhYQzDgEssEony8/MjIyMfP37c0tJCEIROp6uurk5PT3dzczO5/vB229nZgQSj4RWodTaGYQqFguJArQeDwcjKynr58mVPT4+Xl9enn34aHx+/N4L5lpx91lOiNtzyvgEYDEZ2djaCIHq9vqamhurLpNFoTCbz4MGDFy9e3J+GHjsE0INPnTpVUlKi1+tbWlr+8z//s7KyEth6/f39U1NTHh4eO//hwDVzdHSkcjJ7rBQGgIB6+PDh1NTUmJiYhw8fGpu3sFis4ODgkydPJiUlgUHKHg/Phr2EwWCQyWSPHz9+8eIFLDEhVDg6Om7ngYcMTVRUVHh4ODzSCIKAk+Puj31PgaKop6fn6dOnVSrVkydPZDKZUqksKysTCAS+vr7R0dHrN7gBAQFisRhqf3q9vqmpKT8/39HR8XWjFFR/ZTKZXq+HGwSx9g9/+ENISAhsCSBN1dPTU1lZGRsbGxAQYBL+eTzekSNHVldXu7q6FAqFUqmkGk9wHA8KCiosLNxiU4GiaEJCwsWLF8fHxwMCAmJjY/dM/caSVCkvLy+hUGjMZzEX4JYEBQV5enpCBzR8DlKZ2dnZUVFRu2q0ZEHQX7l5sNnsAwcOnDhxYnp6GkRBe3p6nj9/7uXl5efnt8OzoCjq6+vr7OxsLEBtKTAYDKhIJSYmLiwsQLiFBgYPDw8XF5ed87Ft2P8gCKKuru6bb77p7u6mtk1HjhzZ0OwL5vr1f2SzBsW3DCwWKzU11d7eHlQsVCoVOJq8fPkyODh4PaOQwWDAdK1SqXAcb2trq6+vDwsLe136C7BzHBwclpaWSJK0s7PLz8+HzQ9IUru4uADbBsOwoaEhmUzm7+9vcqdAjNPLy2tmZgYaEGCGhy6g8PDw+Pj4LZhcMEP6+vry+XyhUAjb+tf6FW8MS1KlDhw4EBISMjAwsL4pdufQ6/W1tbUtLS1UVgGemCNHjhw8eNDBwcHsZ9xvgNxySUlJV1cXWGpMT09fu3YtNDR0fYrmdQE5OiobD1wkC65goPwjFouDgoKMP9+s2cyGtw96vb61tbW/vx9KegwGIz4+/v333zcRLgAF4JWVFTabbS7TcmsEh8OJioo6d+7c/Px8fX392tra1NTU06dPxWLxeidg6D92cHCYmZkB43dQaH/dcMtgMNLS0vLy8mpqarRabVBQ0IcffkgFfnd3d2PtIxzHN9NTZDKZ7u7ubm5u0HdLfQ5E9K1zEgRBdHR0PHz4cHJy0tPT88yZMwkJCXuUTLbU1gTEGr29vUEz2virzTqUtw9ovKuqqpqYmDAYDBAbkpOT8/LycnNzwYjN4nuyvYGzs3NSUlJtbe3q6ipQ8jo6Og4ePLhDGp7J1WMwGAkJCb6+vpa9qhsmtN+RG/2OA8Shent7Kac2FosVFxcXFBTEZDKpZwD2TB0dHRKJRCQSZWdng2if5QZuSXA4nOzsbKVSqVAo2tvb19bWHj9+DDSi0NBQY+oQiqKxsbEJCQlTU1MrKytgzE4Jum0foD134cKF5ORktVodHBycmJgIm2kg7gB9lfIngHu3hXAsBNf1X232T4C4fuvWrStXriiVStB2DQsL21Di0OywZPGSyWSCgJRarTbuddshQwwehevXrzc3N4NyvVAoPHz48O9+97u4uLjN/CLeVrDZ7IyMjLa2Nrlcvry8DMTLsbExNzc3My7omExmfHy8r6+vuf6gDTa8FmAO7ezshJkEih1RUVHGSUXK8fr27dvz8/Mg3XDx4kWLm79aCkB9KCgoGB4elsvlUql0YWHh3r17IpHo/Pnzfn5+1NYfQZDAwMATJ04MDg42NzcTBCGVSik/2tc6KZfLPXDgQHx8PGyEqEYJFEX9/PwSEhJevnw5NzfH5XJDQkLegI21NWBrPjk5CYOn0+lra2ugsr4Hz4AlEykIghgr7UE+0NPT04Qa97rQ6XSPHj26evXq2NgYjUZzdHQsLCz87LPPoqOjuVzuOxVraa+0QE+fPh0REUGn00EBANrd1vfMvDGgr/ftUJ+2weqA43hfX19DQwMYy6wXLjAYDBqNpqen59KlS/fv35+entZoNCsrK3Nzc1tQWN8FAJvsvffeKy4uFolEJElKpdJr166VlZWtrq4a7xG5XO7BgwejoqIgz7y6utrT0zM7O/sG2SMURVksFpvNNm74pEbyu9/97tSpUx9++GFJSYnZxbxgpgoICHBycuJwOO7u7h4eHntWvrXk7hYigaurK4hpAY8pMDBwh/v65eXllpaWsbExgiCgQvz5559nZGS8fTzkbYLFYkVFRYWEhHR0dKjVaplM9tNPP3l7e7u7u5ux89hWJbXBIgDxzqamJqr5h8fjHT169Ny5c9T+TK/Xd3R0XL58+eHDh+DCCSJo0dHRzs7Olv4FFgaKomKx+MSJE319ffX19SDu+Pjx46ioqAMHDlA5MNgKg1bM4uKiRqN5/PhxTExMcXGxuToqmUxmXFxcWFiYTCbjcrnOzs5mbywERktRURGNRpudnQ0ODk5OTt6zXi8LNwJBSxw1TXM4HDabvRPyAoZhnZ2dEGuBBXfkyJE9sLDYzwCV49TU1Kampv7+ftDr7+vrk8lk5lJdNxgMa2trOp1uL1USoagDGSGakYwUBH4KezYeGywCeOWrq6vlcjkwZcLCwjIzMyl5CoIgXr58efny5QcPHshkMoi1fn5+586dg24W20MCca64uFgul4+NjUEn7u3btx0dHYODg6mMIIqiPj4+zs7Oi4uLkJmvrq5OSEgIDg4210hQFLW3t4fmn126L9ALGh0dvba2xuPx9tID28Lh1sXFxdXVlcViQZF1h5eYIIipqalHjx4NDg6SJAnUxPT0dJFIZL5RWyU4HE5eXt7AwMDi4uLc3BxJkhKJpLu729PT0ywXhyCIubk5pVK5Z+EWFg2jo6MSiYTBYID4NkjS8Pl8Pp/v6Ojo7+/v7Oz8rpUP3jUoFIoHDx50dHQA45LL5ebn58fHx8PGyGAwLCws3L59m4q1sMo/ceLEJ598EhQUZIu1tFfiP2fPnlWpVJcvX56cnJybm7tx44azs/Mnn3zi7u4OCxcwD/Dy8pJIJHq9Xq/XDw4OyuVyM4Zbajzm/YMmYLFYTk5OICC/lw+AxUQcaf9vdkKj0dDpdLAafuMhgahFbW0tKElBEtXPz2/nsoXWDmCOvP/++z09PRUVFQRBdHV1/fOf/3R2ds7NzTWL0DHsNffgOsOJVCpVeXn5jRs3mpubmUymvb398vIyNPM5OjqKRCJPT8+UlJTY2NjAwEBfX1+bfOPbBzClKCsrq62tpYz2fHx8EhISwEzGYDBMTEw8fvz40aNHVKx1c3ODVLNYLLbNDBQQBPHx8Xn//fcnJibu3r27trY2Ozt7+/ZtWJoAZQkEHYuKiqampkZHR1EU5XK5VnoNLTJmizUCAaBwTRHBwbH1zYZkMBgmJycrKyvHx8cNBgOXy42NjU1KSgJqoq0bhMlkhoSEREREtLS0rKysKJXK+vr6lJSU6Ohod3f3Hf5xFEXBcGIPrjNIqoKgAfQLQuGfSiYD87C7u7u2ttbPzy8pKenYsWMZGRm2JMdbBp1OV1FR8dVXX3V3d0PVVigU5uTkgIEPCJfev3//q6++Gh4epva1RUVFX375ZWxsLBSYbDMDBZBTPnPmzOTkZHNzs1arhUW5u7v7oUOHoF0KrAzVanVZWRmdTj98+LCfn5/tGm4TFmYPGe+H4GV4s6o7+JveuXOntrZWpVJBl9iXX36Znp7+zjbVrYe9vX1OTk5bW1tTUxOO43q9vqenZ2JiYgv3jC1gLE0sEol2Lp2xHZAkOTAw8ODBg1u3bvX29up0OhiGMcuaqumurKz09fWNjo6Ojo6q1eojR44IhUJrXInbsCF0Ol1dXV1nZyeUolAUTUpKOn36dGBgICXoeO3atZGREQzDqH3tF198AQ2Blh7+fgSLxcrKyhoeHp6amoIibldX1/Pnz8PDwwMCAkDVMiAg4Msvvzx48CCO4xEREW5ubpYetdVgH5F16XT6G7NbtVptVVXVrVu3YGsrFAqPHj16+PDht8nzZ+cAr+zjx4/Pzs4Cm6y3t7eystLLy8vHx+e1/hR0VoB8D4Ig7u7uQqFwtysuUK+9c+fO119/LZVKTdRRKMKU8fE4jqtUqvr6erBVyMnJect8Kd5ZGAyG2dlZaOmBT5hMZlZWVkJCAovFWl5efvr06f/+7/+CNRasCI8ePfov//IvMTExtli7GaDAl52dPTAwoFQqgYFcU1OTkJAANRoajcZgMFxcXLKysiCr9M7Kcr0B9lG4fWOA3d6dO3egE4DNZmdmZubl5W1tufUOgk6nOzs7Hz9+vLm5eWpqCsOwycnJn376yd/f//jx46/FcoJMHbjM0un0zbTWzAuSJOfn5zs7O6enp+GM0EsGfCgQ7lAqlWBSBMpik5OTOp1Op9M1NzffvXs3MDAwIiJiD4Zqw64Cbi5kOKgnwdfXNzQ01MHBAQxQv//++76+PgzDYDlYVFR04cKF9fKENpgACrSff/45juMPHz5cXFwcGBi4cuWKvb19QUEB8HhBzslSI1Sr1SMjI4uLi25ubjs3R99LWH24BebhzZs3KyoqVCoVjUYTiUTHjh2LiYmxUVLXA5whIiIiampq5ubmMAwbHh6ur69PTk42cd74RQCvjUajGQyG5eVlE0P73QAIsC0vL1PRnc1mFxcX5+XlcbncoKAgNpu9uLgIGWadTnf//v0ff/xRKpVCa2ZXV9fMzIwt3L4FwDCspqbm5s2bkM2i0+menp6nTp2Kjo4mSbKtre2bb75pbW3V6/UIgri5uZ06deqzzz6LjIy0xdrtgMPhxMfHf/jhhxKJpK6uTqvV1tXVoShqZ2eXnZ1t2fBGkmR/f/8333zT19cXGRn5+eefJyQkWMu2ysKj3HmmF8OwgYGBrq6upaUlg8EAZhFhYWF72QBqXWCz2bm5uVSnBIZhLS0toJi6/T8CTn/QMw2bTkqrdvcA5VhjGSCDwaDVavl8vru7u1arXV1dBU4yk8kEbTbj91Cr1UL22wZrB47j4+PjcrkcFl5ca/nH9AAAIABJREFULregoAB0LUiSXFpaAhM3Go3GZrNzcnLOnz8fExNjo3FsH2w2OyEhoaioKCAggMFgaLXahoaGW7dujY2NUatqMHvQarXgXLs3A9Pr9S9evHj06FFTU9Pdu3dbWlqoasL+h+U53Ca9tq/VegvFvIaGBngIUBQNDg4uKSkBDxCL/7T9CSaTCS/SyMiIRCIhCKKvr+/WrVsBAQHbXydCVwB1MEmSsMnY1WuOIAgIv1GfgGCnXC53dXWFA9zc3BAEGRkZmZiYAGdNyo7XwcHBzs7O9lRYOwwGw/T09NjYGCy8GAxGTEzMyZMnw8PDWSwWjuOhoaFRUVEzMzNqtVosFhcWFoaFhb3LQjdvACg8nT17VqfTXb16VSKRrK2tVVdXx8fHu7i4uLi4IAiysrLS1tY2OTkpFAoDAwMDAwN3qL+7HYAXBRgTraysjI+PLy8v29vbW8V7bd3JZBzHu7q6ysrKZmZm6HS6UCg8efJkUVGRs7OzVVx9i4D+yp+5vb0dtCnW1tYqKyuPHDkSHR29n3cA0Bro4eHBZDKhQEuS5PT0tFwuN9ZSp9FoxCvAohtibUpKis1EwdpBkqRMJrtz5051dTUUj4RCYUlJCSXFh6JoZGTk+fPnPT09lUplYmJiVlaWjR/3BgDtrY8//lij0Vy+fFkul09NTf34448Yhp0+fdrb27u9vf1//ud/WlpanJycEhISPvjgg6ysLD6fv9sDo0z3SJJcXl62ItVrC4dbOp3OYrGgC8VgMFDz43aAYdjExMTDhw97e3txHOdyufHx8QUFBT4+PtaSyrcUwHyjoKCgs7Ozp6cHkgSTk5MrKytmt+AwI4Dzkpqa2tvbOz4+DkZSJEmCufQW/8rJySknJ6ekpMTLy2vPRmvDbgDDsLa2tocPH05MTIAcY3h4eHJyMigE0V6tJg8fPpyWlkYQhJ2dHYfDsU0IbwYmkxkQEHDmzJn+/v6ysjKtVtvW1ra0tOTh4XH06NHOzs7u7u65ubn5+fmpqSk+nx8cHLzb4RaWzlwuF3LIO3dr3UtYONyCLQHl2rG0tLTNpQpJkoODgzdv3nz8+PHCwgLoNX700UdRUVE2htR2APztpqYmiLIYhtXW1kZHR+fl5QmFQkuPbmPQ6XQul1tUVMTlctvb21taWoaGhuCBWf/KwaKBwWCEhYUdOnTo1KlTCQkJe6ZFbsNuAHiRdXV1EokEZCuEQmFeXh44WBsfyWAw4DHet2tHawGKoqGhofn5+QMDA9DBPDk5WVNTExUVRR1DkqRer5fJZHtA4EBR1NnZmc/na7Xa3T6X2WH53S2lKgVqQdu8YTiOV1RUXL16dXx8HGRyCwoKCgoKbGnkbQJBEE9Pz4KCgqampvb2dhzHGxsb7ezs3NzcUlNT9+2SBcrz0LlUVlb24MGD/v5+hUKxuroK6WUAmDmKRKKgoKBTp04VFRW5u7vbqnfWDhzHm5qaKioqFhYWaDQagiC+vr729vbt7e2enp7BwcHGfie2ecAsgE7cQ4cODQwMKBSKpaUlnU5XXV0dGxvr4eHh7e09MzMDfrHAmdrt8UCXAaVvY12wsIgjgHox2Gw2g7GtIWm12vHx8bm5ORzHYf2VmJgIXlr74RdZBaDBLiwsrK+vT6PRqNXqxsbG3t7e+Ph4Lpe79b81vML6D3dzyDTaqwKEq6vr8ePHYfBgi2282gVBUC8vr+joaOjFBFW/3R6bDbsH2NqWl5f39/dTCidarfbevXsqlSooKOj06dP5+fk2kSOzA0EQsVj8/vvv9/f319XVEQQxOjp68+bNkpKS6Ojo0dFRuVwO9jASiSQ6OnpvOoUoWRsryidbeHdLkiQYt9Fe9ZZsh9QA5LTh4WEwNuDz+YWFhaAms/tDfnsAjkzJycmNjY0jIyMkSYIx3+zsrL+//74td4FWlFwuHx0dnZ+fZ7FYKSkprq6uHA4HMiXwHgJNGsMwuVy+vLzs7u5u6w2zamAY1t3d3dXVBQwpGo1GEMTQ0BCCIFBakkqlfD7/8OHD+5nuZ6VgMpmRkZEREREdHR1KpVKr1dbW1hIEkZycHB4evrKyotVqJRIJKMkkJibuUiYJWo8QBLFS83LLh9v5+XmlUkl7Zfy7nX3V5OTk9evX29raMAxjMBghISGpqangAbIno357YGdnl5eX197eLpfLVSoVhmEVFRWwkv1F3wLIIO3NOCkYDIa5ubnm5ub6+vrGxsapqSmSJIODg8VisUAg8PHxyczMDAkJYbPZcGRNTU11dTWdTj9+/HhaWpot4lopDAaDVCp9/vz5yMiI8VNHkVS1Wm1vb29XV1daWhqLxbJNBeYFEJQOHTokk8nq6+shmdTc3IzjOIZhTCZTq9VqNJry8vKIiAhfX19PT8/dGAZBEBKJZGhoCPTsduMUuwrLWxSoVCrY3W6zaxPH8ZaWlvLycrlcTqPRWCxWYmJiYGDgvt2N7WegKBoUFHTs2LG+vr729naCIAYHB69evRoUFHT48OEtlpB7piRlAoIgamtr//u//7urq0ur1YIzwdTUVFVVFeQ5zp8//+WXXwYGBtJotIaGhr/+9a+dnZ0oiq6trXl4eKzn1NhgFdDpdFVVVU+fPp2fn9/smL3xf3xnwWazDx06JBKJeDze48ePFxcX19bW6uvr6XQ6vIYwmXd3d0ul0l0KtziODw4OSiSSrZsR9i32xZZ8+1M2SZIzMzPNzc2gmsvj8dLS0goLC3fp7r4LYLFYqampmZmZY2NjCwsLoNLV39+fnp4O+qgb/isTXhu1bNrV7SPkQiorK7u7u6mMIu1Vly2NRsNx/NGjR2w2+7333gsKCpqampqdndVqtXQ6vbGxcWhoKDg42BZurQ5gXVVaWjoyMmJs/QSAzp+goKCoqKj09HSb6dMuAeiHSUlJOp1uYWGhqqpKo9Gsvx1qtXr3tNtQFHV1dXVycmIwGCYOJVYBy4s4cjic7Sf6tVptRUVFWVnZwsICkFS/+OKLvLw8K1Kp3m8A+RjQuIDtLPhcDg8Pb72EpPJ4NBqNIAi5XL7bbQB6vb6xsbG1tZWKtdAaRD0/UMz7+uuvv//++5GRETc3N5FIBDKTMpnM2D3GBmsBaEj9/PPP9fX1G/Z+CASCvLy8P//5z//xH/+RmppqpVU9qwC8bikpKe+9915ISMj6Sw38j91r0WEwGFFRUQcPHnR1daXT6bDK12g01pJYtrCII9VERX2yWUoZRDAmJyfLy8slEonBYLCzs8vIyIiLi7MWBa99CxaLlZSUlJmZ+fLlSyB7V1RUCIXC3/72t+Hh4RteWzqdbmdnZ8xNA0Xi3bsRBoNBqVRWV1cPDQ1Ruoz+/v4pKSlyuby9vX11dRVULxQKRWlpqcFgCAwMpFgzer1+dXV1V0dog9kB1Jj6+voXL17Mzc2ZfAsc9ZSUlIsXL2ZkZPB4PJt0624DGDZHjhyZnJxUKBRTU1PG3wI/eWZmRq/X71IF3cHBQSwWOzk5gT4r6OLRrKTvy/KJNRRFt3OlSJIcHh6+ceNGU1OTWq1GECQmJqawsNDHx8cqLvR+BqTj0tPTg4KCgOc5Ozt7+/bt5ubmzTa4oE9i3OZI2/0nHsdx47Uzk8nMzMz8t3/7tz/96U/vvfcepRhFkuTk5OSVK1d+/vnn6elpiM1W1C1gAwWSJCcmJioqKkDc2+RbPp+fnJz88ccfp6WlCQSCbc4kNuwQoEx+4sQJkMQxvubgyzk0NKRQKHbj1LCjnZ+fX1lZgTcamn2t5b5bONwaM5OhwWMzEcfV1dV79+5dunRpbGyMRqOJRKITJ06kpKTYdILMAtB5z8jIgN5lsFUZGRkBn6X1x0Mhh7r4dDrdyclpV1P6wIRyd3enzkKn02HDmpmZ+ac//amkpMTV1ZXJZEL2eHV1taOjY2ZmBsbPYrF4PJ5N6cKKAHP3w4cP6+rqTOyqKLv4P/3pT0eOHHF0dLSWCfftAJPJjIiIOHfu3HqfUwzDmpqa+vr6dqmCC1kua5SUollc5gIkQkCLxGAwaDQavV6/fkiwomlra5uamiIIAm52YmKio6MjzaZrYSY4OTmVlJSMjIw8e/ZMpVLhON7Z2dnZ2Xnw4MH1OqiQ5aPYCuDuzufzd/VeoCjq7+/v5OQEokLAVo2NjQ0MDBSLxb/61a8cHR0HBgY6OzunpqaMhwezs6enJ5fLtT0t1gJ4AktLS8HU1vgrBoORkJDwxRdfZGRkwBLKdlv3GNASkpOTMzo6OjMzQ31OdY6EhIT4+PiY96TgY61UKqkwASUta8ldWb4RiPpfE083Y0BT3cTEBI7jdDrdw8OjsLAwJCTEtqQ1I0B3+uzZs+Pj452dnTiO19XV8fl8FxeXhIQEk0tNkuTi4qJJ99tu3w4Wi5Wenl5ZWTk5OQmkJ7Va3dvbOzs76+npmZycHBkZOTc39/Dhwxs3bvT09ICHAY1GQxAkICDAw8PDxqOxFmAY1t/ff/v27e7ubhNpQFg85ebmhoeHbxhrKb2hrU8Bh4H28r6aSayiown0d48fP76wsHDr1q25uTnqgms0mq6uLqlUavZwSxDEyMhIX18fsDKZTKZYLHZzc9v/lwuwj2afzVjKBEGMjY09ePBgaGiIJEkGgxEbG5uTk2NTazMvgHaYnp4eExMzMDCgVqtXVlYqKyuPHTsWFxdnkjIy8ZOA5K1Go9lVPxDoEs7JyWlraxseHqaWtPCyMZlMoVAoEAg+/vhjFxeX7777rqWlBZKQIPPp6elpLa/lOw7IZt24cePhw4eLi4smgRNBkNjYWErMaP2MAZqdKpVqi3ymnZ0dn8/X6/UzMzNcLtfNzW2faNIB25YgCHt7+31e+2AymVFRUe+//35fX9/8/Lyx7bxKpdqNfC+O4y9fvoQuUARBvL29U1NTrei9tvzuVqlUAh8HaKXr16Rarbaurq65uXl1dRVCckREhLe3t62B0uyAEuzBgwebm5v7+/sNBsPKykpXV1dGRoaXl5dxxKVssOA/odNmZWVlt+23WCxWRkbGyMhIVVWVWq329fU9duyY8SIa7PaOHTvGZrOdnZ2HhobodLqPj09+fr5Nd8xaQBBER0dHRUXF7Ozs+gkB6McVFRVPnjxhsVgmko0Igri6ujIYjMXFxc36vuDpFYlEWq12cHBQIBCkpaX5+flhGAZ8KyimODg4bNhHDiUwmIvodLpWqyVJEvTe4QBwPt/Q3AyqMCsrK5stBYA2geO4r69vYGAgi8UCgoLxMQwGw8HBAYwFHRwcaDQazKJ6vZ7JZDIYDDqdzmaz+Xw+rCEg/qlUqu3Ym66trcHPX/8VjuOwxDEe7czMjAnDA7oDTMrt5gJlhMBgMIKCgsRisRVJxVm4EchgMFD9msCMWFtbM6G6TUxM1NTUAMWUy+XGxsZmZGS4ubnZwu1ugM1m5+bmdnV1yeVyhUKh0+kePXrk5+d35swZY1lHFEU9PT2BlwhvGoZhkJfb1eFBs/XFixfT0tLW1tZCQ0NDQ0N5PJ7xeVEUFQqFxcXFfn5+o6OjNBotNDQ0JCSEklO2YT8DYkNtbe3g4OCGkz6GYS9evKisrDTObRgDksNb1/OoBDJBEAwGo6ysTCwWa7VaiFWLi4t6vd7T0xOCmQnA1Ry4ewiCKJVKgiCAiAfnxXF8dnZ2ZWVlw1+nVqvn5+e3cBqFZLKrq2tkZKSdnd3c3BxVFqG9ygICVQIcoOl0+vz8PGwo2Ww2m82Gsbm4uMCCGBipCoViPbt7/U9bWlpaWFjYcDWg0+lA7dVktBiGGV9qgiCmp6flcjmO42bfoFO3G/T2QULZvKfYPVg+mQzPN82oHEh9BRnLR48e1dXVqVQqFEVjYmI+++yzpKSkfZL5efuAoqiPj09JSUlXV1dDQwOO4yMjIzdv3gwPD3d1dTV+shEEsciDzmQyAwMDfX19DQYDg8HYsP0D2oITEhJiY2NpNNpmh9mwDwH1ua6urqWlpc2OwXHcjKJCer2+t7cX0jlUnDYYDFs84cYVXzjYpAC8haL4Zmk8E0xOTkqlUqDZry9OUx3GMEL4m9S3JsfQ/l9Rmq2xxZHbHDmNRtPr9ZOTk0tLSy4uLmZ87xAEEQqFxmsI6GqxFuwLe3mBQKBSqejrLApwHB8aGiorK5uYmDAYDAKBoKioqLCw0MXFxYJjfusBJZm4uLje3t6lpSW9Xt/X1yeRSNLS0n7RQGJvgKLoLzry0ul0JpO5z6tfNqwHQRBzc3PLy8vbDA9mgXnjt1kAnu2WHsUbAsfx5eXlLXbwbwbYzUPKwWAwrK2tra2t4ThuLRRICzcCGYsTgUepvb09DIkkyampqWfPnoE3HIfDSUtLy87OBh6aVdC+rRcikSgvL6+tra2pqYkgiNXV1cbGxuTk5LCwMIoLSjknAqg9geVGTdPpdFKpdGlpydXV1c3NzRZrrREMBiM4ODgkJKS7u3vD+Zr+CvCfO+TGG2ekjSnB6/+s8fbRuKXC+LxbkIq3GNuGzGrjb9ePakP29Ru8fW+89dziXFA+DwsLE4lEbzaqLYCiKJVywDBMp9Ntc8O9H2B5qpRxumNpaQkK7AaDYXFx8d69e9evX5+amqLT6c7OzidOnFhPkbVhNwC+BdBUNzc3p9frnzx54uHhceHCBX9/fxqNRhDE8PAw6KhZerD/P/R6fXt7+71798bGxuLi4sClwIrqOjYAEATx9fU9evRoT09PV1eXyR4Xeq99fHxcXFzYbLYJI8nR0dGYOAPlPSaTyeFwYGpmsViwuIeWQuA04ThuZ2en1+t1Op2Dg4O9vb1SqaSIRVqt1tHRkcVijYyMSKVSR0dHV1fXlZUVmUxGkYbs7e15PJ5er19bW+PxeOvJOyiKAvHKYDDo9XqlUslms0F9Fpy1jA/m8/k8Hg9FUeAqrq2tcblcHo+n0WjW1tZgVHw+H8MwsOXh8XhcLlej0SwuLq5foIDU5Wb7PyaTKRAIgPO1zRsEo1peXt5QI4FGowmFwsLCwvT09O2Yl78WjE8H2zNHR0dr2drSLB5uMQxTKBRAIDTms+E4Pjw8/PTp04GBAeAyxMbGRkdH7zbx1QYA1dpYV1e3uLiI4/jc3NyjR48OHjwI4RbHcYlEQjXbQSHAsgpfSqXy7t27V65cWVpa6ujoCAwM9PPzs9X4rREsFis7O7u9vV0qlRo3dNJoNBRFw8PDP/7449TUVD6fD3x4qrvaw8NDKBRSB2MYtry8zOFweDyeTqeDuAWxUKvVoigKiWudTicQCLRarVqtdnNzc3BwWFhYUCgUsG0C60Y7O7umpqb+/n4vL6+AgAC5XD40NASTFZ1Od3R0FIlE0Dvn6Oi4nmDFZDLd3d1BB0aj0SwsLNjb24NKz8zMzNDQkEwmEwqFHh4eXC7XyclJJBIxGAxgki4vL/P5fJFIpFKpgO4E2w+tVjs5ObmysiISifh8/srKytDQ0MLCgvECBUoqJqsQY7DZbDc3NxOy4dYgSVIqlVZXV7e3t6+ngzGZzNTU1F/96lehoaG7ypaAPfQWrmX7EJYMtwaDYWpqqq+vb3l5mfoE3py1tbXOzs7x8XF4tlxdXfPz8226FnsJBoMRGhqakJDw8uXL+fl5HMdlMhmEXlh3GytuUoUAS40W5GbkcvnS0pJWq5XJZOPj4yqVCtJZNlgXYLVXUlICbhNyuZyKuNCFL5fLWSyWUCh0cHAw2fGYTBHwABinXuH/CwQCOMDZ2ZnKsQE9CgQcqGeb+tDHxwemI3j+jclQwEvakDO14dioPz4/P6/T6fr6+mZmZhgMRlxcXGxsLJvNprIywE6i/qYJHwoWBPAt8KXXW1BT+9fNLvVmA94Ccrlcp9MNDAyYhFuQUz527Fh8fPxur3ShEGnSBrbPYclwC17B4+PjJqox4LP24MEDsJtgsVhZWVlZWVlgpmahwb5zgFXO8ePH+/v7y8vLMQxTqVQ1NTX+/v7R0dEmN4Iy3jJ7+mj7o+VyuUKhkM1mQx/kwsKCLdxaL5hM5oEDB2BPdvfuXZDtpL2qYly5cgU0k2GDuAWMH9TNouCG/2p90cqEebcTZgAE7Pn5+Xv37t2/f7+rq2t5eRlEyL29vX19fU2aIXU6HQh6cDicLappbm5uG2Z33yCgbgaSJJVKZV1dXUNDg0mspdPp7u7uR48eTU1NpVYzuwdoqbIuNpmFd7cgNm3SIi2Xy2/fvl1XVwdJZnt7+4MHD4rFYlus3WOAMV9+fv7Lly+npqaUSuW1a9fW1tb++Mc/BgcHGx9pIjJlEaAoymQyTbYFFhyPDTsEm82OiIj48MMPx8fHKysrKeYwuM1fvXqVTqcXFBSYt9VkM0B/pxmJIyRJSiSSe/fuVVZWQt8qjuMDAwNzc3PGLmcGg2F1dbW+vr6/v18kEiUkJGwh7GDGsLohILldW1v71VdfNTQ0GG+TIKNeXFz8xRdfhIWF7c1cvZno776FJWUuTB4Oqut8eHh4eHgYsiIcDic6OtqmUWApsNns9PT0Fy9eyGQyoHjU19efOHEiODh4w9thqXtkMBi0Wu3KyooxWXq3Zx8bdhssFisyMjIoKKi+vt64UUen01VXVy8vLzOZzKKiotcqPW4HQKHq7e2dnJyEWKjT6VAU5fP5AQEBYWFhJtaTb4bV1VXQb4J8tbOzc1xcnIeHh3HaGcOwjo6Ov/3tb3V1dY6OjsePH//Nb34THh4OiWtIbsPxu/2oQ7K6tLT08uXLXV1dxttKSP4fOXLk008/jYuLo6QUzA7j1DedTufxeK9F8rI4LEyVMmZ1A9Rq9fDw8NTUFIgYREZGfvTRR3ALLTXIdxkMBiM8PDw7O7u/v39iYoIgiIWFhdHR0eXlZRaLxWQyTQoBFoRWq11eXt7MoNcGawTUmyDmGX8OicSurq6bN2/y+fzU1FQT49UdQqvVVldX/+Mf/2hqaqIkZul0Op/PT09Pv3DhQnZ29g5jPCSEKJMP8Dg6dOiQiQKwWq2uqanp6uoCinJ9fX1xcXF4eDgYuQ8ODpIkGRQU5Ovru6s98dAqUlVVdeXKlaamJpMeZSaTmZGRcfHixfj4+L3sviMIwroyWJaMYQiCODo6wlMLizWlUllbWzs8PDw7O0uj0Xg8XnFxcWFhobOzsxUtYd4y8Pn8o0ePSiSSmzdvLi8vazSaZ8+e+fn5AeFzeXl5//QCUSPZP0OyYSfQaDRPnjxpa2sDC3Eg61IcJa1W+/z5c6AHZ2VlmYuph+N4R0fH1atXGxoaVldXjZ8ljUbz/PlzIDwXFBQYy5rSNmrD3QygiNTa2grWdXQ63cXFJTs7WywWG+erSZIcHx9vb2+fn5+nvSIHMRiMpaUlsCasqakhCOLAgQPx8fH+/v7BwcFeXl5mbxCAfqry8vJvv/22s7PTZOnj4OCQmpr6+eefJyUl7YEMjvE+3hZuXwPwkFG9PQRBSKXS69evq9VqoOmHhoampqba5JEtCwaDERYWdvz48e7u7paWFgzDGhsbXVxcGAwGl8ulWOX7AcbPidW9ijaYwGAwLCwsDA4OKhQKOp3u5OSUkJCA43hXV5dCoYAF+vLyclVVFZ/Px3E8LS3Nyclph+tykiTn5uZu3rxZXl5uEmtpr/Scnz9/LpPJeDxeUVERxYyFbtT5+XkURV1dXaGndrOzwEtUU1MDP4TBYKSmpubm5jo7OxsfRhDE5OTk7Ows7CZRFA0JCUFR9MGDB1evXm1ublYqlQaDobe398aNGwEBAYcPHz5//nx4ePhOrsD6CzIzM9PQ0PDDDz/U19eb8DMQBAkKCvr8889zcnL2oN4HOzQoXdM3cZDbz7Bwhtak5KDVaoE5BWJdJSUlsbGx1nVB30pAVj84OLi7u1uj0YCso0gkMm6WsOwIaTQah8MBZjLouWu12v0my2fDawEyyVKplCRJFEVTU1P/9V//FUGQa9eulZaWUmZBarW6tLRUJpP95je/OXLkyC9ylbcGQRASiaSnpwcCIXwIyzjqaYcemP7+/qysLLAekkqlK/8fe/cVFNeZJQ78xo7QgZyzgAZEEAgQQkJIsrBkWcGWZrSSx2HsqZ2Z3dmdfdia133erd2qrZ3amR2Px+NsWbJkW7ayhbJQJufQ0GTohobOfcP/4azuv7dBSA4XGvv8Hlxy0930Be499/u+851jt7e1tbW2tkLf6PT0dEEQYmNj09LSFsYhmMbr7e2VZpILCgpSU1MXjiv8fr/0ZwzB5u7du8eOHWtubvZ6vfByn8/n9/tbWlqsVuvatWvXrFnzfS29wb7k48ePf/jhh52dnQub/EAR47i4uOXJrYG4AGnPoXDN+aZWsojjwrJ/0r+Dmtquxp/sDwlsCqqoqGhoaICamhMTE1B5J3BD5MpWU1Or1UajUaVSwQ14KBSVRN+aIAjDw8PXrl0bGhqClMmKiorCwsLw8HCo8fTpp59OTExIlSju3LmjVqt5nv+OucqQEBT4h63RaDIzM8PDw3t7e6WurhzHeTwen883Ojr65ZdfXrlyZWJiAkqwwQ7dhIQEjuPy8vIOHz5cVlYWONENq7aDg4PQCQ0eMZvNbW1tJpMpIiJCGmBAXJduLDiOa25unpqaam5uDrqVFEXR7/dPTk4+ePCgoqIiOTn5u49S4FOdPn363XffbWlpWbSbEEwwQFrr8pxrkBpGBHTVXUXneCjmH5Ekqdfrq6qqMjIycBo5RCiVyq1bt969e3dsbMzlclmtVii7A18VHzVPXMFP6PF4pM6gkOe5gmU30Hfk8/muX79+9uzZ8fFxGPwVFxcbDAaGYfLy8l5//XWGYT799FPoy0kQhMfjuXz5ss1mc7lcO3fujI2N/dYjvMC7RpqmCwoKXn311fj4+N///veXL1+Wog6sIt++ffudd95pamrieV5av+jv7zebzQRBdHR0wK2qNMELSV6tra3QIx0e9Pv9ly9fnpubKy4ufuaZZwo2tL8+AAAgAElEQVQLCzUaDRS17ezsDIzxra2tLpdLirUwOyiFOp/Pd+7cuejo6EOHDqWkpHy7wyceLdaazeZPP/302LFjvb290lEHfUcoBRjUkm95wLQ/dgT6rliWXb9+fU1NDXb+CR00Taenp5eWll67ds1sNgcti8J4V7pbX37wASwWC+zVhgJvy7DXHsmE5/m+vj4oyp2UlHTw4MF169bBiE2hUOTl5b322mter/f48ePT09Nw9fd4PE1NTW+//bbNZtuzZ09mZua3GOHxPA+9Y4lHySW7du3atWsXLB4HPpMkSWjsOj4+Ls3rSm8C8Wl+fn5wcDAwvwHWnj/88MP29nbpJBIEAdrtwSj5N7/5TU5ODozeoKQzPA3WdDweT2Njo8Ph0Gg08fHxRqNxdHR0bGwMvml3d/eXX35ZXl7+rcMt1GdtaGi4cuVKfX390NBQ4Mmu0+lycnKmp6dhnwIRUApw+XEc98QOviEl5MItbOF69tlnCwoKsBtBSKFpOjEx0Wg0Qj/EoK+u7MytKIput1u66lEUBXvyVurzoO9I2rbg9Xrr6urq6upiYmKkr7Ism5OTc/jw4aGhoa+//lpqFeD1eu/fvw+Vlg8dOpSXl6dWq7/RxDLkJYyOjsJ3KSwsrKmpSUhIGB0dDUw8Dg8Ph+mTjIyMrKwsm82m0WgMBgPHcT6fD6owOhyO2NjYrVu3JiUlBb7/pUuXbt68GTQVBLPBdrv96tWru3btysnJIRacUwqFYtOmTWvWrLl58+bExERMTExmZqbb7f78888nJiYg8EDbvm+dtcDzvNls/utf/3rixAmLxQL9duBLMGO0Y8eOffv2Xbx48eOPP15YMFluYkDD3RUvHPstrHyZi6APQFGUTqdLTk5eXbWnfwxoms7KykpOTm5tbV1YO03ae74SH+3/x1fpA0BvcPwTWqWg0v34+LjT6XzhhRcyMzODJocVCkV8fHxkZGTQTbnP57NYLB999NHMzMzLL79cVlb29IVFRVGcmpoaGBiA0S1FUcnJyTExMTzPt7e3j4yMwIWeZdnS0tJ169YZjcaSkpLy8vLe3t7w8PCUlBSn0zk/P6/T6cLDw7Va7aZNm+rq6uLj4wOrRE1MTEhtFYJAKjJkYkM9KelOAoSFhT3zzDO1tbWQoNDa2nr8+PHBwUFpc45Wqy0oKIiLi/sWf/kwOD527Ninn37a398fNHDU6/Xbt2//1a9+tWbNmrt37wYu8327wsvfFOwUbWpqgpshmMyHuoQh0of7iVa+vfzCX5JUJ2VFPhJ6HIqi0tPT9+7da7fbHzx4AJsQpK+ubMKCIAiDg4Mwr0gQxBIdx9CqwLIs5PcSBKHT6RZWoud5vq2trbOzE5YPAsHKwsmTJ+12e01NTXJy8tq1a1NTU584t8xx3J07d/r6+qRIQ1GUIAjNzc0ffPBBa2srDPV0Ot327duhVKHP54NcodnZ2ampKdhboVar9Xo9JHZBK73A77L0PBDP89CYnaKowcFBq9UKj8O0HyQDqtVqr9d748aNP//5z/X19dLSKaw07969G35uT0kURZ/P5/P5hoeH33vvvaNHjw4NDQXGWpqmU1JStm3bdujQofz8/Pn5+aGhIdhwT5KkUqlcnnON47i7d++++eabjY2NBEHwPN/V1XX8+PGYmJh169atit5fK7zvVq/X63Q6hmGk0ZIoil6vFyYxME8qpMAc2osvvqhSqf7t3/6tqalJumpILQpW6rMJggB5oXAJgJZkeMe2qikUCsjeWPT36PP5WltbofwcSZJarZZhGKfTCeM8SDD+4osvzp07Fx8f/7Of/ezw4cNPjLiQ+hu0VuLz+S5fvnz9+nXIyqEoKjo6OiMjQ6fT8Tw/ODjY1tY2MzMDpwDxKHrZ7XYYxUZGRm7duvXp1zU4jhsbG7Pb7TqdbmxsTFr3pWm6tLQ0Ly9PqVSSJCkIwoMHDxobGwMTJqQWsE+/DAcFN+7evdvX19fd3X3hwoWgWAsL2Pv37//5z38Ou37dbrdWq1UqlW63m6KohIQEo9G4PEPbCxcuXLp0aWZmhniUnnnq1Kn8/PysrKygLcuhaSU3AkEHifXr19+9e3dwcBAehMzyu3fvJiUlJScnR0VFra4WSz9scGOuUqmC7iUhS3BhWYBlIwgCbAgmCIKiKGjlTaz0mBt9Lxb+En0+X2NjY0NDAwz+IiIitm/fnpycfP369aamJmlzCMdxHMeZzeajR4/Oz8/v3bu3qKhoiQIU4v9tMkOSpEKhoGlaEASplBVkGhuNRhj4QoLSohsaPR5Pa2trR0dHZWWldBGTKv263e7H/XHCCiVkJktlJVQqVWVlZVZWFnT6g5YAOp2OZVmougzHe/v27WPHjgXmQi8B8orPnTv35ptvNjc3+/1+n88XNIfMMExtbe2BAwcyMjJgFKvT6erq6txud3t7O0EQO3bsgMG0rOcax3Hd3d2NjY1Wq1X6RpAf19fXZ7VagxLZQtMKT7ipVKodO3b09fWdPHlSyjCcm5v75JNPuru7165du2vXruLiYsx5CREwhfXRRx/19PQEJSezLLuyqW2BlzxcjPgBE0VxfHz8k08+uX37ts/nYxgmNTX1pZdeqqqq+uqrr44ePXr79m2pYR9BENBpZ3h42Gw2v/baa+Xl5RAsF33z8PBwmKoVRVGhUMTFxRkMhtTU1IiIiOHhYeJRaSdYjoUBQ0ZGRmtr68K8IZqmIyIioFG89CDDMGVlZffv329qaoKBuM/nC8xIgkqNCoXC6/XOzc1BxWaooJSYmCg1rmdZtqqqymq1NjQ0dHZ2ms1muMmYnp4+depUdXX1E4tdzM/P9/T03Lp16+TJk01NTY/bUaNUKmtra0tLS6WJAbVa/dxzz+Xn5zc1NQmCUF5eHlTnWQ4cx7W1tUn7viTQ6x7Gu6FvhcMtVMB//fXXtVrt559/DjtMBEGwWCxjY2NXr14dHx9/9dVXi4qKsCPQyoIb/wcPHvzlL3+5cOFC0MnJsmxGRsaqmM9Bqx0kLt27dw+GtgzDpKWlxcbGGgyGPXv2JCcn/8///M/Zs2fn5+elgRp0aT137pzD4XjmmWdqampycnIWXlIYhtmwYUNHR0draytJkvn5+RUVFVFRUdnZ2aWlpS6Xi2XZ1NTU2tra2NhYkiRhd9xPf/pTvV4PZd4DqVSqwsLCqqqqwOxZhUJRW1vLMExTUxMMcMfHx6VqHjRNx8fHZ2RkhIWFtbS09PT0wOgW1t3gA/M8D90AMzMzf/nLX+7ateurr77661//CnfAgiBYrdahoSGn07lo2yKY9Dabzffv379w4UJDQ4NUJPJxoBlJ0KGtWbMGBrWBXS/lA1P0izZE4ThutZRrXfl0EoVCUVJSAq3j33//fdjTLaWznz592uv1vvLKKxUVFasr5/sHBlqevfPOO1euXAlKkoLVnQ0bNgRueEBIJoIgDAwMjI+PC4JAkmRaWtrWrVuhJbtOp6uoqPB4POHh4R0dHV1dXVL2HCz+Xbx48cGDBw8fPnzuuecKCwuTkpICG/uwLFtTU6PVatvb22maLiwsLCgoUKvVJpPp1VdfLS0tValUJpMJGvDBS7Ra7TPPPLN+/fqgjC0IxuHh4RqNJiiJNyIiYvfu3c8++yzxqHjW73//+5MnT3Icl5WVVVtbW1JSQlFUS0tLX18fBBiapuPi4vR6vd/vb25ubmlpIUkyNjY2JSVFr9enpaVJlecJguB5HhZ9F+47h6n1y5cvf/3113fv3h0dHfX5fIGxSqFQUBTl9/ufuJ+VpunlnM2iKCoyMvJxSearZc1o5cMtQRAMwyQlJVVWVtbX10unB0EQgiCMj49/9tlnXq+X5/mKigrMf1l+PM/b7fbGxsY333zz66+/DqxvRzxai6qrq9uzZ098fPwKfk61Wr0qshPRdwdTvhDPnn/++WeffVZaulOpVDU1NZmZme3t7f/5n/955cqVwD9XjuOmp6c///zz5ubm0tLSbdu21dTUQBMUCIphYWHV1dWVlZXEo/URmMitrKwsKyuDrkTwoPSeLMtGRUUtvOI/bm8MvIk005uamnro0KGEhARBENatW1dUVBQdHc3zPLTnC/wuJElaLJa33noLYnNqamphYWFMTEx7e/vAwEDgtmCNRiONR6FE1NjY2Pz8vNVqPX/+/KlTp6CnYWCghcowlZWVUVFRV69ehVqt0sz2t/w9fX9oml6zZk3g3uvVKCTCLfGoCPjCP1mYBTpz5ozX63U4HDU1NRERESvxAX+kINu+vr7+zJkzDQ0NQbGWeHS3vn379ry8vBXcewN78PFu7MeApumioqKdO3fGxcXFxMTs3LkzJSUlcKSlUqnS09MnJycXfTlcUlpbW7u7ux8+fNjd3Z2fn5+ampqTkwN7/VmWDZo7XfTBoCd86z88pVJZUVFRWloqiqIUyzmOs1qtQacbz/MDAwPt7e2QgT8zM9PS0gIZW1K2FJwIWVlZkC0siuLIyMjVq1dv3LgxMTExMTHR09NjtVqDZl81Gk1sbOy2bdt+8YtfxMXF/e53v+vr6yMIgqbpzMzMUAhyNE0nJCRERUXB8a70x/mWVrLMhcTr9XZ1dd2+fRtmkgO3hMM/HA7HxYsX5+bmZmdn6+rqvktBVPQ0YD5/ZGSkubn51KlTFy5cgHmnRSdtRFFc8ZoSsElp4W73UPjzRt8vaM35q1/9anR0VKlULizWKD5qk9fR0QF/nDBE43ne5XJJO4Ugc9hsNuv1+uLi4iNHjlRWVsL0Lwwll+2IAge70iFAuA16jsFgMBqNDMPA2DQo8FAUlZGRUVdXl5iY2N/fD0ty9fX1H374YXd3N6xxSinW0kvi4+NramoqKioqKyvz8vJmZ2elt2UYJjs7Gxaq5fwBPBWVShUdHa3VahdOsC1DkY3vxcoHLVEUzWbzO++8c+zYMUg30Gq1Wq2Woii32+1wOODGzel03rhxY3Z21maz7du372k2raPvwm63f/bZZ++++253d7fT6XzcHSXsk3a73dAlbZk/pGRhaZTVcgaibwpKK6SlpUFZ4IV5OrCXtLW1FfrzJCUlbdy4MTk52ePx3L59u6WlRdpdw3Hc7Ows7JGdnZ198OBBfHy8yWRat27dim8sCcq0h91HWVlZdXV1AwMDXV1dkLQsgR1Ku3btKiwsvHHjxvDwMOQ8wxrw45KhFArF1q1bf/vb3+bn5zMMQ5Lk5ORk4JNDpGIMTOmnpaVFRkauSEeE78WK/RzhMg1zIzdv3jx16tTY2BhJkikpKZs3b4aabYODg/X19QMDA/Drh3Kmf/nLX6ampurq6goLCyGhH6+q3yPIABwYGLh169Ynn3zS1NQUdKLCXbaUTAGTV4vmQCIkH8hFWvRLHMcNDAxAez6Yqv3Nb36zdu1aj8fz9ddfnzhxoqOjY2xsbGZmRiqy7/F4bt68effuXbVaXVRUtH///pycHIqiFApFbGxsfHw8DACW8wClKxtFUbGxsevXr09ISFCr1Xv27FEoFBcuXOjv75+YmJienoY6VomJiSaTCVoT3r17VxoCBtXxh/eUAjnDMIWFhRkZGdLOYL1eD52XeJ6H1fEQ2YcJPweY8F8tuVFBVizcQjb/+++/f+rUqZGREZ/Pp9frMzMzd+3adfDgwYyMDIIgBgcHk5OTL1y40NbWBt2efT5fV1fX5ORkU1PT/v37169fn5qausQuOvRNeb3ee/fuHT9+/NKlS/39/UGxVqvVFhUVxcbGPnz4EIrv6PX6mpqa3NzcULgFRgi21sBfL0EQLMtmZmYmJiaGhYWFhYXt2bNnzZo1bW1tt2/f/uqrrwILSPn9fr/f73K5rl27NjAwEB0dTdO0RqPJzs5ev359eXl5UlJSYAqSrCDxWK/Xz8zMGI3Gurq6LVu2wIUuISHh8OHDGzZs6Orq6uzsPHPmzMOHD2GiFbZyDAwMPK4LLMuyGo2Gpmmn0xm4ozfw5FUqlfn5+SkpKWazOTExsaCgwGg0LsMhP43VPrhayXBrNptv3rw5MDAAN6Fbt279yU9+UlFRkZCQAL/+rKys119/ff369SdPnjx//rzFYoHlB5vNduXKFYvFUlhYuGPHjh07dsTFxWH7oO8CMi+6u7u7urq++uqrK1euWK3WoJtiuBH+u7/7u4SEhH/913+F+nlQTPUb1WiViTT5BhtCQuSWHC0zjuNu3Lhx/vz5iYkJqPJdVFQUmLdcWFhoMplKS0tHRkYsFsvCHS9+v39wcNBisRAEQZJkQ0PDxYsXq6ur8/LyoAtQQkJCdnZ2UK3E7zcMsCy7detWaFmfm5t7+PDh3NxcqN0GKzswvcxxHKRV22y2u3fvQo7Vont4SJJUq9Xl5eUlJSUul+vSpUu9vb2ByczSM1Uq1c6dOwVB6OjoMJlM1dXVgbuMQs1yFm3+7lasiCOs6hcVFY2OjlIUlZOTc+TIke3bt6vVaqhSRhAETdOxsbFbtmyJj4+Pi4t7//33+/v74arq8Xg6Ozv7+/v7+/vtdnttbW16enrgFjr09GBpvL6+/t13333w4MH09HRQ/06KolJSUvLy8vbs2VNdXQ374iGpTa/XR0REsCy7stM7QakTUBNg6Vrw6AeJ47iHDx/CPpaIiIhdu3ZVVFSo1WrpLwE2jIaHhwfub2EYRqlUwgBXqqEIX/L7/b29vWazWalUKpVKtVqdn5+/Y8eOvLy8hISE2NhYuLGDYeL3NfalabqioiI2NnZ6ejomJiYiImJkZASqGE5OTvI8D6WVR0dHBwYGYB/8wiZd0qGpVCqj0VhQUPDGG29s2rTp8uXL9+7dIwO6xAeeKVA2C5a6lUol1NYIhfNo0dNZq9VmZWVFRkaGwid8ohW7KYB9VK+99lpubi5BEMXFxYWFhQvrvEDZ0uzs7B07dty4cSNwexnkFra0tMzOzt6/fx/mW6TiaitwSKsQLJ/39/cPDg5+8cUXN27ccLlcQVlR0M37wIEDzzzzTFZWlkajaWxshJJ1UmBboY//fwT+YfT29t67dy8pKQlq3KMfD7h39Hg8NE1nZGRs3rw5OTk56IIAbXHNZjPcMiYkJJSWlqakpNjt9rt37/b390PQDXxPiMROp5MkScjDSkhIyMrKyszMhNoLUHAqNzc3JiYmLCwsKLdZmnchHlOTAT62y+WSxqYcx7lcLqfTeefOnampqb6+vnv37vX29koTxTzPL8w0DqRWq/Py8nJycmJiYpKSkoqLi4uKipRK5cOHD6ULqUqlgu68gS+EXO4QLOQX9HlomjaZTHDZX6mP9I2sWLiFDdTr168vKSmB6mVBm8clUCSloaFhYcFMgiDcbndvb+/Q0FBHR4fVai0vL09LS4N1l2U5jtUK+mA3NTV9+OGHV69enZiYWLSlD0VR+fn5b7zxxp49e+Li4iiKggpwsJQOo97IyMiVPS1htsNisczMzMDQpL29/b333ktOTt62bRtmsP+oQI0zvV7vdrtNJlNSUlLQpYDn+eHh4TNnznR1dQmCwDDM+vXrf/vb3xYVFc3MzJw8eRKqQMC0bdAFBwZYXq93dHR0bGyssbFRWk2E0s3l5eVZWVnR0dEGgwH6B8DQUGrMR1GU3W4PSiomHnULsNlsUp1Cv98/OjpqNpuhJjBU2ZOaqz8RTBn++te/3rZtm9FohF4LFEVBsQs4NIqi1qxZk5ycvHAyNtQCLfEoZAR2rIGGg9nZ2auljc3K97tdumQJbNP+5JNPjh49ajabFQqFlK3AcZzT6YQiZDDM/cMf/nDhwoVt27bt27cvKSlp4eYQRBCE3+/v6+trbm4eHR29cePGtWvXYNv7omVxoqOjDxw4sHfvXoi1UEPu8uXLsGVLo9FA9faVOI7/D9LuoHcYHAXcSXz99dcmkwnK+63sJ0TLhmGY7du3w/ae559/HjYLBeI47t69e/fu3YPWdSzLZmdnZ2RkQG/aI0eOFBQUtLe3nz179tatW1J7O5gzC5p9DZoH6uzs7Ovrg9R9nU4XHR0NG8FhH7DD4QgLC2MYZtFAThCE1Fwo6JGF+2uDQBwyGo1zc3NSgVUIRevWrYO8FukUYBgGWh1YrdaUlJQ9e/bk5+dD7YilA7koilCoMmitFPYBEgSh1Wqfcr/yEqP8hd9UerIoirAJIvCoIVWWIIglfkShM98Z6ivMPM9DSyno7bx+/fqKigr4iTudzrt37zY2NkK5fJ/P19PTMzAwAP2Y8vPzdTpdfn7+wtvbHy1RFHme7+vre+uttz777LOxsTG/3y/Vo1mIpumkpKSSkhKYoicIwu/337t3r6mpyeVyKRSK4uLi4uLiFa/l5PP5rl+//vDhw8DRucvlqq+vr62tTUhIwAHujwfDMOXl5enp6aIoRkRELKx84vV6GxsbIScZsnDLysoiIyNhQjU6Onrr1q1lZWWzs7PNzc0QbhUKRWpqalhY2PT09OTk5MKxKYDoCP+22+3Dw8OBFXsgcpAk+fQj1KcEazpr1qwxm82BvUNmZmba2tpGRkZcLpe06AO5VGFhYTMzM5GRkWq1uq+vD/qfOhyOwL4OQaAhoCiKMTExUVFRMEwSRdFisVgsFpqmYWpdpVJRFLXEJZdlWb1er1Ao5ubmFi5dBYIAzzCMQqGw2+3z8/MDAwNOp1N6glqt1mg0drt9ampqfn5+0QYGUI4qLi4uFEpRhnS4hfWMBw8ewNbbiIiIAwcOHDlyBBZLPB7PrVu3vvjii4aGBvg1QBWVnp6e//7v/9ZoNNHR0YcOHdq3b190dDSUlQmRe5zlx/P81NRUc3Pz0NDQw4cPz549G9REmghIspcuB9BJGza6wXMgAEMeck5OzuHDh4uKilb8bgYKYAU14RIEYWJiYmG9OvSDp1AoYDFv0WGN3+8fGxubm5uDqdRXXnll48aNUh47TIlZrVZIQSIIgmXZ4uLiQ4cOJSUlmc3mW7du3blzZ3JyEv6uHhc7F83r+XZR9omZSjB6tlgsgU0AeZ5/+PCh1Wp1uVxzc3NwIhOPNkpNTExwHNfR0fHmm2/GxMTQNC2KYtBs9sLv4vV6SZI0Go2xsbFwHwPd2yAJPC0traCgICwsjKbpx6UKQy5ObGysVqudnJycnZ1doheCKIrz8/Msy6pUqsnJSZvNBk0DpQmGubm5M2fO9Pb2OhyOqamphWXvoPrmunXrDh06lJOTs+JXqpAo4vg4MBRrb2+32+2QLwcluaVi4s8++2x+fn59ff1bb7117949+EOB6t6zs7OTk5Mffvjh6OhoSkpKZmZmeXk5zIiu9GEtK8jyGB4ePnXq1EcffdTR0eH1eoOqkxMEQZJkTk5ORkYGSZItLS0WiwU2GyQmJkLxVXgaNL+kaXpkZKSkpKSwsHDFh7Zg4YQbzIRHRkZCrZyV+mBoRTzuwgpDTKk3c0lJyebNm2EvjfQcjuOgH63L5SJJMioqat++fQcPHoyNjfV6vZs3bz5z5kxHR4dUswn64MqEZdnw8HCv1+tyuR4XdCEsQV2LwITBsbGxiYkJeHBoaEg6RpgGh8FMR0dHZ2enNGG79L0pvLnNZhsYGJDOKenUa25ubmtrg8eXPuPgzv5pRvlSihk8Wfrk8FWn0/n111/X19cTj59MhgtaTk4OlE5a+tvJbcU2Aj0NmCRsb2+nKMpkMu3fvz87OzvwXo9hmJSUlP3798NN08OHD6W1Fggz7e3tPT09CoUiMzPzJz/5SW1trcFgiIiI0Ov1K/6jl5UoihzHTU5OdnR0mM3mjo6OCxcudHd3B+0WgNI8KpUqMzPztddeq62tHR8f//d//3eYB4uMjDSZTEFJ9pGRkc8995wgCFK/lND8E4KCANDYMTQ/IVoR0N7HbDa73W7YbCPtPAQ8z/f09IyNjYmiyDBMdXX1tm3boE47wzAlJSWZmZnz8/Ner7enpwdOFuLRUmJkZKQ0UPb5fDMzM/Pz84Gt46U1YCJgCVN6AkVRBoMhJSUlOTk5PDwczs2IiIi2trbr16/b7XbphU+8g5Qmq6QnBx6jFHqlOw/pk8ALYc4Zbk0g2kltZaWYJ70/vASuOUt8pKU/89JflQ48sJkNrI7B55SOLvAw4dgZhpE+4RLfYhmEdMiBKVC/319cXPzKK68s2uKNpmmj0fjCCy84HI7R0VEp3AKO4ziOc7vdzc3NVqv11q1b8fHxWVlZ27dvz83NDYXZ/O8X3GQ4nU6bzdbT03Pjxo1z587B5oGFPSzhzj0/Pz8nJ6eyshKaZre0tIyNjUEB5OLi4g0bNgTVlIF95ct7WE8GWZeBj5CPaVqAfuRUKtXu3buTkpLgwhIVFRX4VVEUfT7f9PQ0ZDMpFIqampqCggLp7pxl2cjIyIiICI/H09TUJF1wFApFVVXVli1bpDs8p9N57969+vp6aOADf5C5ubmRkZF2u51hGK1WS5Lk5ORkT0/P3NycKIrh4eE7d+587rnnSkpKYI6XJEme599+++2WlhaYK1apVPHx8QtnlaAIhtVq5ThOpVJlZ2fHx8cvPaiAJrJSH3FBENxuN8uyCoXC4XDY7XaWZQ0GA8uyfr9/ZmYGSqNbrdbR0dHZ2VmGYSIjI3U6ncFgUKlUHo8Hlm8WBl2lUqnT6R533aAoCpaWl4i48J7S/T0Uu56dnXU4HBqNRq1W2+12KJc0NTU1NzcH26BVKlVYWFhtba3JZAqF8dXKf4IlwNQly7Jr1qzZsmVL0JyPRBTFmZmZ0dFRqDzOMExycrJKpYLoKz4qHGqxWMbHx+H+sb29vaqqCjo/JyQk5OXlQVBZjbOOcICCIEBjJUiOGBwcbGpq6urqmpubW/SWk3zUp/bll18uLCzU6XQKhQJqZI6OjhIEQdN0bm7uqkg0o2k6NTUVrmKBj4dORiIKHZCRUFtbSxAEjHsCvwpBa3x8XKpxGBYWtrBCGUTB3t5eaPMHC4S/+MUvtm3bJj2Z47i0tEmuadUAACAASURBVLTe3l5odEbTdF5e3i9/+cuioqKJiQmFQhERESGKYkNDwx//+EfoGB8dHb179+7du3er1Wrpr9fj8UBcgQ9fUFCwb98+WPcJ/Eh+v//BgwdQfL6oqOjVV18tLS1dekRB03RERIS0bx62eEBqktPphHALaU0+n292dtbtdvM8b7FYOjo6oB1TSkpKTEwMhP/5+fne3l5ojRD0jSCTRorrCz9GXFycwWBY4qN6vV6KomBhCFaRx8fHx8bGbDabwWAIDw+Hzgpqtbq1tfX+/ftKpTI7OzsuLs5oNFZUVGRlZYXCMmJIh1uWZTdv3lxeXg41Xx536fR6vZcuXfrqq68mJiZIkkxJSTl8+HBycnJ9fT00EfL5fLBfCE4hj8fz0Ucfff7557Ckv3bt2jfeeGPjxo2wqWsVZVT5/X6v1wsdsy0WS29v78WLFxsaGmw2Gwzrl1gdUavVGzduPHLkSFVVFZzb8Lj0EpqmDQbDqhgdsixbXV391VdfQZlchJa2xP5D6Ck7OjrKcRxJkjqdLvDskAiCYDabGxsbbTYbQRAajWbXrl3V1dUGg0F6st/vh+22cEIpFIrS0tLKysqsrKz8/Hz4GDzPT09PS1USFQqFVquF5N7AbwezU6IosixbUVFx8ODB1NTUoE/F83xJSYnBYBgZGdm0adPWrVufpnFe0C0pbPqAmwxocyt9Erg5IAgiPz9/+/btc3NzNE1rtVqYWIIoWF5e/rgthUvf+36LHZuwZhyY7008SgRrbm5WqVR5eXkRERH0I9/ozWUS0uGWIAiGYSAP+XHm5+cbGxtPnTrV09MjCEJsbOz+/fsPHz6cmJi4du3adevWjY+PDw8P37x5E+ZIYb3d7XZLm0ZgOqi5uVmn08XFxZWUlKSlpS2M7qEwVBIf8Xg8vb29nZ2d4+PjHo9ncHCwra2tt7cXEgsXJg1JCx7wJZhG3r9/f2VlZeDVBMpWREVFOZ3ONWvWmEymVdHqh2GYzMzM2NjYoMcD16UQehoURYWFhaWkpKSmpjIMs2HDhoX1wEVRtFqtn3322e3btz0eD0mSWq02PT09Kioq8GQRBGF8fBxmXKDoRE1NTVJSEjSHJh6VZ+nr65uenhZFkaIorVa79O0+RVFQK23h7QLLslDXgud5aOPzLcZz0rdeeLmTHqEoyufzPXjwAHZmBh71cp5ujzu6lJSUhIQEyEoJhRFtoFAPt0vz+/0NDQ1//vOfb9y44fV6lUpldXX1gQMHsrKyYPtdSUkJdON6++23L126ND09bbPZYFO2dAsGvesvX74MJZq3bdtWVlaWkJAAU83wHKVSGR0dHR8fv/yFzaQkBVEUXS7X+Pj45OSk2WyGgezU1JRUy23Rcm40TaelpUHgtFgsra2ts7OzsIwUFxcXVGWapunS0tLa2tre3t66uronTkaFCEEQ5ufng0pikSRpNBpheWylPhhadWiazs/Pf/nll0tLSymKKikpyc7ODnoOjIBv3LgxMjIiPqqtJu2YkAiCMDc3B1cblmVramrKysoCp4tgOvrcuXMDAwMEQYSFhZWUlEB9nqDvCE1nSZKERnuwpWchWEwlZF4UEx/1K5ycnIyNjV3xonJBnlg6aQWt4j0SMEg9ffr0+fPnYW08IiJiy5Ytubm5UNYA5hBEUczOzn799dfLysqgge6tW7eCqrpI+9MHBwc/+OCDEydOwKS/dP5otdqMjIyamprq6uro6OjA80q66fvWP8nATyKl8guC4HQ6BwYGzGYztLQURdFut0Mpj8HBQdhntkT6O0VRUMf18OHD+/fvZ1n2vffe6+/vn52dJQiCZVk4gYPCbV5e3i9+8Yu5ubk1a9bExcWtlj8PqaGYBBrxQkbJajkKtOLgTrS2tnbTpk1EwGkS+BzY8elwOCCPNz4+vq6uLjc3N3BGFEpF9vT0wOZdjUaTmZkZExMT+NcIo2Q4kdVqdW1t7U9/+tPMzMyFZ2VWVlZycrLf7zeZTPHx8UsM2pbhTx2mmrdu3To2NoYdx7+RVT+6hTw0giD0en1VVdW6deuC2kVBJq3JZMrOzna73Vqttq+vD24niQVbyCE3z+12wxAw8E1Ylr1z505XV1fgqjss8mdkZEj7O7/RxR3GrF6vd25uDprwuN3u6elpiK/j4+O3bt1qbm6emJiAWAKzwTCcXSKpHZJB8vPzU1NTi4uLd+zYkZKScv/+/Tt37oyPj8P9uNFoXNhACW6fS0pK4DoSalMxjwPHm5iYqFarYTABMNCib4EkSYVCscQIiSRJvV4PG3V0Ot0zzzyzZ88emMCUngOJS7DNnabp9PT09PR0lUoVFEdTU1NNJlNfX196evrPfvazioqKhWlZsBlpamqqp6envLzcZDJ974f8TSmVys2bN0P/eTzFnt7qDrfw5w59r7Zt2/b666/n5+cvun4AWQlms7mvrw8SmFUqFbQB6e3t7evrg+1x0uLowlEjx3GNjY39/f2B5wzDMNnZ2aWlpcnJyZBmpdfrn3KfjHSPPD8/PzU1BdvYZ2dnh4aGLBYLdDVxuVwLN/AsPDSlUgkVtSBxIC4u7sUXX4Q7Za1Wq9FoOI4bHx+XWtiq1eqCgoLExMRFT5XvJdBK2/KWASyelZaW1tfXd3d3B7ZOW/pHh9C3wDBMVlbW3r17w8LC4uLiXnjhhUUrFkGCrlqtTk9P379//8JLE0VRycnJf/M3f5OVlZWWlgZ7JRZ+OyjY9Itf/MLr9Wo0msfl9y6z0Mk/WkVWcbglSVKlUkH7Va1W+9JLL23atOlxf4tQouzYsWMnT56cnJyELMF//ud/Xr9+fUNDw/Xr10dGRrxeL7TRHRkZWXTzDMdxNpstKIoMDw9fvXoVZlTUajUUjHyazw89QGZmZqBqsbRxW8q4I56i6htJkvHx8eXl5VNTU42NjQ6HA5Iy9u7du379eqliOGxah3djGCY3N3fLli1B9+PfncPhoGlaqVRC9wiGYTQazfKck5CxmZ+fbzabYRE3qAANQt8XSAs4cuTItm3bwsPDo6KiFv6Rw5aHPXv2DA8Pl5WV1dXVJScnL3wftVq9efPmqqoqkiSXKH/GMIzBYFjOW1gkh1UcbgmCUKlUu3btys7O1mg0aWlpS+QxQVbC7du3oZVNYWHh66+/XlVVFRkZuWvXrs2bNzscDr/fb7fbjx8//sEHHwQWZiP/b02WoCt4YF3yhbPQS3tir48ngh3ieXl5g4ODHR0dUL/bZrPdvn1boVCwLOt2u6H2hdSkFqa21Go1lE222+3SXoUluFwuKF8e9EzIANTpdBzHDQ0Nwey6w+EYGRlRqVRpaWmwbw/29c7PzysUCilbBB5nWdZut8OUQxDIDnM4HCzLQg9R6GO6sPEIzMPDd5Fypmw2W19f39jYGPxyg8rNaDSalJSU6OjoUNj/jlYXWL/MyMh43MolwzAFBQVQTCM8PHyJ+86nHyZirF3tQrqI49MwGAwlJSXk/y3uFQQy8i9fvtzb28vzvEql2rFjxzPPPAP1X5RKpVKphC5yXq93amrq6tWrUrhVKBTQSGt6enpubu6JNUW/39lLmLj2er2P+75QcO7DDz/kOA56b/E839raOjExceXKFYZhoNAH9AyGWw2e5zs6Ot577z2dTufz+cbHx4NKcS0kCMLs7Oz09PTCDewEQUDNcZ/PB9VzoqOjXS7X7OwsTdOJiYmwjx5qmk9PT6vVamlvn0ajiYmJUalU4+Pjs7OzC393MLtutVqVSmVUVJRSqXQ4HAzDLLoVEm4ppIQpjuOuXbsGPUympqYW5i1HRERUVVW9+OKLmZmZSx8+Qota4ppDLMgTXu1XWvTd/RDu6594b+hyuc6dO/fpp58ODQ0xDGMymUpKSqKiooISjOEfUA2VeNS5ad26dRUVFQaDob+/v6OjA8qWiqI4MjIyNja2aPh5osDUxMDHAz8PwzBJSUllZWUcx926dQsiZeDLpdf6/X7onyWFZJ7nJycnL1++LD1NmqMmCILjuM7Ozt7eXnjyU864Lj0Qh83+8ATI2IT37OnpgXwlqSi5dGNEBGwIXrqtSuCrAiu1LnwyFPeQfggdHR3QP2TRT05RVGtra1xcXGJi4sL8FIS+OxyPokA/hHC7NFEUHQ7HzZs3u7q6BEHIycmBDMCFCU2iKA4ODsI6LkEQkZGRL7744ksvvZSdnc2yrMvlGhwchIZufr//xIkTn3/+uc1mE0URyp4FpRdxHBe4UQemdiH2GAwGrVbr9XptNpvD4YABMUVRubm5CQkJBEGQJBkZGVlRUVFbWzs4ODg6OiqFWyhzqlarrVar1PpxYTiBzCmYJl04AxwYlgiCgCqp3+XSABER3iHwqFc2UynoMBeanJycmJjweDxL1CxDCKHvxQ8/3BIEwTBMTEyMwWDQ6/UHDhzYt29fXFxc0HMEQbDb7adPnz5z5gzMeW7atOngwYNr166FFAaFQhEeHg6DvNHRUY1GA0FFoVBUVFSsXbs2cITE83x3d/e9e/empqZgm0plZWV6ejok/UKB0Lm5uatXr167ds1qtRIEoVKpDhw4sGvXLuLRzhZIwZiamoKoSVFUREREbm7uxo0bo6OjW1tbGxsboZAWwzAdHR0Wi4XneShkajQaNRpNXFwczCcTS5ZJ0+l037FFks/ng4qmsDkYyoVDlXa4n1AqleHh4SzLTk9PQyUs8VGLD5ZllyhfDuA5QfsoAGy6n5+fpygqPDzc5XIFtSqDZV2n0wk155xOJ8wwG43GgoKCoqKi5S9dghD6Efrhh1vYJPfcc89BTa+9e/cuWnbfZrNduHDh5MmTMDGbmZm5d+/egoICqJgB7wMByel0Xr9+/datW9ChOjMz84033ti9e3dguHU4HB988EFPT8/U1BTLshs3bvynf/qn4uJiGAFD5HM4HDabraGhgXiUo7hmzZrS0lJ4B3iOz+dzuVwwZQ2VgV955ZUNGzaEhYVZLJb79+8TBAGbEE6cOPH++++PjIykpKS89NJLxcXFer0+JSUFEpQIgnhc3iOsoULt02/9Q4YCs1BUxOl0Op1OCLc2m216eprjOK1WGxMTo1AoBgcHOzs74SMBtVodExOzcBNwIKVSGRsbC4u+QWA/1fT0NCyV2e32hX3m7XY7LAAbjUabzWaxWERRTE5OLi8vz8vLC9kaNAihH5IffrglCIJl2fLy8rVr1xIEsWiKIMdxt2/f/tOf/nT37l2/369Wq8vKyoqLixeWaxZFcXJy8tKlSx0dHYIgJCYm7tu3r6qqKrA0uSAIXV1dDx8+nJ6eJggiPDx848aNJpMpaJOSKIpDQ0MwtFUqlWvXrl14H8BxHMxgEwTBMMy6desqKyujo6NJkszKykpNTYXHRVEMCwtTq9VNTU35+fkvvvhiVlYWxD+CIKCY8BLB7LuXgwjcoqBWqyFDhCCI1NRUqUoz3GqkpaVVV1cHTW4vHenJR5VaH7cbGKYc4FtIm6eDPl7gE6Rq7wqFAvcOIoSWxyou4viNLF0mhuf55uZm6L5OkmR0dHRpaWlCQkLQ9R2Scdra2rq6umBHSklJyfPPP5+Wlhb4TI7jLl26dOXKlbm5OZZli4qK1q1bp9frA3/UMCaD2hokSaakpBw4cCAvLy/o1+Hz+fr6+iDcsiwLDVzhe0Gza+mZGRkZf/u3fzs7O6vX641G4zJHkaAKXNK/F92P+L1/dwyZCKHQ96MY3T6RVGTc4XCsWbPm2Wef3bJly8L+i4Ig9Pf3nzlzBvJdFQpFXl5ecnJy4OUeFi+bm5uhfLnBYNi5c2dhYWFQSOB5vqmpaWhoSBRFmqZNJlNZWZk0KJTeyuFwTE9Pe71eo9FYWlqam5v7uBxaaF1pMBiwhClCCIUgDLcEQRAMw2zatGlkZKS/v7+mpqa2tjYmJmbRqmyXLl26dOnSzMwMbCgqKyuDzbvSc3ieHx8fn56ehoKi0dHR2dnZRqMxKARyHNfc3AzhFlaXF128ZFk2Nzd3+/btqampO3bsWL9+/dKlXHGchxBCoWnVl7n4XpAkmZiY+POf/9zv9+t0OkhVXfiT4Xl+dHTUZrPRNJ2dnf3yyy9XVVWpVKqgckVQyUGpVLIsW1hYmJiYSCy2yT0qKio2NlYURdhfC20jg54WGRl5+PDh3bt3R0dHR0ZGQqzFXxlCCK06OLr9XzRNP7FVJMMwxcXF1dXVNptt586dzz//fGxsbNDzKYpKSEjYuXMnx3FKpfLgwYOLFi2CngqiKI6Ojubm5tbU1ERFRS36HdPS0mAEjFPECCG0epHfsWbvjwrUFOzs7HQ6nVCSYtFcWVhztVgsCoViiY70PM/7fD6e5xetkoEQQuiHBMPtNwZFmp7YpQ5+sBhEEUIIEQSxyAolQgghhL5fOPZCCCGEZIfhFiGEEJIdbgRCCCGEZIejW4QQQkh2GG4RQggh2WG4RQghhGSH4RYhhBCSHYZbhBBCSHZY5gIhhBCSHY5uEUIIIdlhuEUIIYRkh+EWIYQQkh2GW4QQQkh2WMQRIYQQkh2ObhFCCCHZYbhFCCGEZIfhFiGEEJIdlrlACCGEZIejW4QQQkh2GG4RQggh2eFGIIQQQkh2OLpFCCGEZIfhFiGEEJIdhluEEEJIdhhuEUIIIdlhuEUIIYRkh2UuEEIIIdnh6BYhhBCSHYZbhBBCSHYYbhFCCCHZYbhFCCGEZIdFHBFCCCHZ4egWIYQQkh2GW4QQQkh2GG4RQggh2WG4RQghhGSH4RYhhBCSHRZxRAghhGSHG4EQQggh2eFkMkIIISQ7DLcIIYSQ7DDcIoQQQrLDcIsQQgjJDsMtQgghJDvcCIQQQgjJDke3CCGEkOww3CKEEEKyw3CLEEIIyQ7DLUIIISQ7LOKIEEIIyQ5HtwghhJDsMNwihBBCssNwixBCCMkOwy1CCCEkOwy3CCGEkOywiCNCCCEkOxzdIoQQQrLDcIsQQgjJDstcIIQQQrLD0S1CCCEkOwy3CCGEkOww3CKEEEKyw41ACCGEkOxwdIsQQgjJDsMtQgghJDvcCIQQQgjJDke3CCGEkOww3CKEEEKyw3CLEEIIyQ7DLUIIISQ7DLcIIYSQ7LDMBUIIISQ7HN0ihBBCssNwixBCCMkOwy1CCCEkOwy3CCGEkOywiCNCCCEkOxzdIoQQQrLDcIsQQgjJDsMtQgghJDssc4EQQgjJDke3CCGEkOww3CKEEEKyw41ACCGEkOxwdIsQQgjJDsMtQgghJDsMtwghhJDsMNwihBBCssNwixBCCMkOy1wghBBCssPRLUIIISQ7DLcIIYSQ7DDcIoQQQrJjVvoDIIQQkoUgCARBkCRJkuRKfxaERRwRQii0iaLo8XhEUVQqlTRNP+Wr/H7/4ODg1NRUdHR0UlKSSqWS9UOiJ8LRbUgTBGFubq6vr8/lcqWnp8fHxz/9ycbz/NzcnEKhUKvVeHuL0Crl9/vb29vv37/v9/tLSkry8/O1Wu0TXyUIQn9//3vvvXf//v38/PwjR46sXbuWYfCCv5Lwpx/SXC5XfX390aNHrVbrrl27Dhw4kJSU9DSBUxTF7u7uq1evUhSVnZ1tMpmio6Mx4iK0uvA839/f/9Zbb504cYLjuBdeeOE3v/mNyWR6mhc2NTWdPXu2tbW1paVFoVCwLJuVlYVj3BWE4TZEiaLodDrv3Lnz7rvv1tfX+3w+nudLSkoSExMDo2bgWkDg4263+8svv/zTn/40Pz+fl5f30ksv7d69GyMuQqsIjFCPHj167ty5sbExlmX7+vqsVqv0BFEUBUHgOM7pdHIcp9Fo1Go1TICJouhwOFwul9/vn5iY+Oijj2w220svvVRaWqpWq1fumH7UMNyGKJ7nW1pa3n333evXr8/Pz9M0HR4ertFoAp8jCILD4Zibm/N4PDqdLiIiAiaLRFH0+/02m21mZmZmZubWrVscxykUip07d0ZGRq7QASGEvgFRFG022+eff/7+++8PDAyIokhRVGJiotFohCf4fL7h4eG+vr6JiYmxsTGPx5OQkLBu3bqcnByNRkOSZERERHh4OEmSPM8PDQ0dPXrU5/OFhYUVFBTgrPKKwB96iHI4HBcvXqyvr7fZbARBGAyGqqqqjIwMiqIIghAEwe12t7W13b5922KxOByOxMTEurq6goIClUpFkqRGo9m4ceONGzfu3Lnj9Xrv37//l7/8xWg0btu2DWeTEApxoihardYvv/zy+PHjZrOZ53mKotLS0qqqqhITE+Grt27dunjx4u3bt4eHhx0OhyAIERERmzdvfumllyorK8PCwoqLi/fu3etwOHp6ejiOm5ubO3v2bF5eXmJiYnR09Eof4o8Rg7OLIUgQhLa2titXroyNjYmiqFKp1q9fX11dHRUVRRAEx3EjIyMNDQ3Hjh27du3a3NycKIrh4eEulys2NjYlJYUgCJZlq6qqdu/ePTw8bDab3W73nTt3zp8/bzKZ0tPTIWYjhEKTIAjt7e0ffPBBY2Mjx3EkScbGxu7fv3/r1q16vV4QhJs3b/7Hf/zH/fv3PR6PIAiwqOR0Oj/77DOHw6FWqysrK1NSUl577TWSJN98883BwUFRFGdmZu7evbt9+/aYmJiVPsQfI9wIFHIEQRgfHz9x4gScaRRFpaen79+/Py8vjyAInuctFsvHH3987Nixnp4el8slnWmDg4MzMzPJycnwPjqd7rnnnmttbZ2amnI6nT6fr62tbWRkJC0tDX/pCIUynud7e3uHh4f9fj9BEDRNp6en19TUwMk7Ojp65syZhw8fSqc/gISP+vr63Nzc9PR0GMU+//zzLS0tk5OTLpeL53mz2Tw9PY1XgBWBo5yQw3FcZ2fngwcPZmZmCIKgaTo3N7eoqEin0xGPzsNz5861tLQ4nU7ptIGkCdjVDhiGycjIqKurgyloQRDGxsZGRkY8Hs+KHBdC6CkJgjA5OTk3Nwf/S1GUTqcLDw+nKIrjuLa2tpaWFofDAac/TdMsy8KUFWRIXbp0qampyefzMQyTnp5eXV2dmJhIEATP86Ojo1NTUxzHreDR/WhhuA05giBMTEzMzs5KoZSiKIb532l/iqKio6Nzc3MTEhKUSuXSawFKpbKkpCQ1NZUkSUEQLBbLlStXLBbLchwGQujbEgRhamoK1olIkoyMjCwpKYmLiyMIQhRFn8/n9/vh+kCSpNFoTEtLg9tx4tEdeV9fH9xYKxSKvLw86bUzMzMjIyNBw2K0PDDchhw40+bn56VHaJqWwirDMCaT6ec///mvf/3rzZs36/X6JSIuSZJarTYsLAz2Brjd7lu3bg0MDMh9CAihbw1GqJOTk263myAImqYrKip2794NI1SaplNSUuLi4iC7mKbp/Pz80tJSg8EgvQPLsiqVCs56iqKioqLCw8PhS7CRd3JycgUO7EcPM5NDDtyBOp1OgiBIklSr1cnJyQaDQQqrSqUS0v0jIyOHh4ftdrv0wqC3IkkyPDw8MjJSqVT6fD5RFOfn510u13IeDkLoG4Hh6fj4OKwNMQyzbt267OxslmWJR+u4zz//PEmSVqtVr9fX1dUNDQ3xPA8vp2k6IyMjIyMD9tdSFBUfHx8ZGQkrSjzPDw8P22y2jIwMzJNdZhhuQ44oijzPw5lG03ReXt7mzZvj4uICzw2GYTQajVKpDMwxXnR2SKlUxsTEhIWFzc/Pi6LocrlsNpvb7cat7giFJo7jIKFJeoRlWal6K0mSOp3upz/9aVlZ2dTUlMFgCAsL+6//+i+47SZJ0mAwVFdXZ2ZmwsWBJEmFQhEREaFWq6Wb+JU4LIQbgUIMVKiw2+1er5cgCIZhioqKcnJyYDdt0JMDHxEEYWZmxuVyBT2NpumEhAS9Xg97iux2e3t7++TkZEpKCm4HQigEkSTp9/ul0ar0oFT5HGat1q5dy/O8y+X6+uuvGxsbnU4nrPI+++yze/fuhWqv8HyFQmE0GjUaDSzZTk9PT09P+/1+3IK/zPCCG3I8Hs/U1BRM+cKdqZQnFcTlcvl8Pvg3JFhJqYwSkiRpmpYiK8dxPT09ExMTch4BQujb8/v909PTDodDemTRW21Yu33w4MG7777b0tICpTCKi4tfeeWVdevWKRQK6VUwhwwTZjzPt7a2Xr9+fWpqarkOCP0vDLchR3yEIAiKouC2dNGnTU9PB8ZXabf70m8Or8K8RIRCEORJdXV1BU4mL4rn+ba2tvfff//mzZvS3Tk82N7eLu0SFEWR47iZmRm32w2P+P1+i8UC+wzRcsIyF6FFOkPgf6WswoW/JkEQFrbVk+L0Eo9I23PxV49QqIHUDY7jAvfQS2exdM4KgjA8PPzxxx+fPXt2ZmYGHuc47tq1a52dnQ8fPvyHf/iHoqIiiqJgfQrCLbxWqVSmpKQYDAa8AiwzHN2GNFiRhQSHIBRFxcTE6PX6b/SGsOqDazYIhSbIhFqzZs3CbiKBNW2GhoY++eSTr776anJyMjAwcxw3MTFx+fLl3t7eoIJT0oRZQkJCSUkJ1nFcfhhuQw6stsKwVRCEoFUcCcwRBeVTPJFarS4sLHzKprkIoeVHUZRKpXpc0x6o1Hj69Om33367u7s7MNZKTwgaGXs8HigGCW+elpaWmJgI24rQcsJwG1ogN8poNMIAVBTF2dnZwJ2yoih6vd7e3t7z589fv37darVKs0xzc3NtbW3Dw8OBFdqgBg08AhvyqqurMdwiFLJ8Pt/o6Ki0n54gCLvdLk0F8zzf1dV17tw56POz8OUURaWmpkZFRUm37JOTk1LZHIqiMjIyYmNj8Qqw/HDfbchRKpWwSc7hcPA8PzY2FnjicRzX2Nj46aef1tfX9/b2SqlSUBL5448/pijqwIEDqamp8LjP5xsbG4OnsSy7du3arKwshUKx/MeFEHoaFEVFRkaGhYVB803oWTI7Owsx0u/337t3r7u7e9FYC4XkNmzYIFWxCKpSR1FUai0tPwAAF3ZJREFUUlJSRETEch4RAji6DTkURRkMBshGhlNlbGwMtuESBOHxeC5evHjs2LGmpiYIotKGPLjtPXv27ODgIDwZhrwDAwOzs7MEQTAMk5mZiWs2CIUyrVa7Y8eOLVu2QIlWKDMnrSjBFiCapmGDXyCapiMjI2tra5999tmEhAQIt16vt6urS6raCPH4ieXWkRxwdBtyaJrOzMyMjo4eHByEhllXr14tLi7OzMyEsBoREWE0Gq1WK2RVSHlP0FU+Ly9PunWFNtRTU1OwcsMwTGxsrFQ9FSEUghiGycvL27p167179+bn56HKscViWbt2rUqlYll248aNg4ODd+7cgcqs8CpYhzKZTHv37i0rK4OlWbgC3LlzZ2RkRHpzqX0QWmYYbkMOwzBr1qxJSkp68OCBIAgOh+PKlSvbtm1LSUlRKBRqtXrnzp1KpbK9vZ0kSSjQKN2ohoeHFxQUZGZmwv9CL7+xsTFInaAoCm5sV+zYEEJPgabpqKiosLAwgiBEURwZGWloaCgpKUlPT6dpOisr61e/+tXevXuD6p+r1eqEhISoqCgpDcrv97e1tfX29kJ3IOjHFx8f/7g8LCQrLOIYcmiaTkpKMplM165ds9lsUFJ8ZGTE7/crlUqGYdLS0l5++WVYuaEoamHVRiivyvP8xMTEzZs3BwcHoY2XQqGAG1v8pSMUymC7jtFohNaZdrv9woULsHtHq9WyLBsfHx8XF7dw42zg2Q3dbS9cuNDT0wM33OHh4Vu3bs3Ly8NwuyJwSiHkwJzwpk2bcnNzpcZ5jY2N7e3tUu0YlmXVarVarVYqlYr/C14iCMLAwMDx48evXLkCmVYMw+Tm5ga1OkAIhSCKohITE/Py8qAVGM/zPT09H3/88alTp2AVliRJWKwNEnh2ezye+vr6y5cvQ8oV9DvZtm1bUlLSih3Yjxv9L//yLyv9GVAwiqJ0Ot3k5GR3dzfkJ4+Ojnq93qysLCm/f2ler/fEiRN/+MMfurq6BEGgadpkMr366qs1NTVarRYjLkKhDG6plUqlw+EYHR11u91+v39wcHBwcDA/P19aLVoCTEG//fbbN27cgNQNtVp98ODB559/PiIiAq8AKwKLOIYoo9G4e/fupqam8+fP+/3+qampa9eu7dy502QyPU1hZKfT2dzcbDabOY6Dce0rr7yya9euqKgoAss3IhTyWJatqqqCSazTp09PTEzwPD8+Pm6325/m/IUKOZOTk16vFzoFbdiwYfv27bGxsQReAVYIzuCHKJZlTSbTrl27ZmZmurq6nE5nRESEVqt9ypfzPO/z+WBcm5WV9corrxw8eFDaG4AQCn0qlaq0tJRl2ZiYmJaWFrfbnZeXl5WV9ZQv1+l0BoOBZVmO46qrq//xH/9x/fr1WExqBWG4DV1hYWH79+9PTEy8c+eO1WotKyvLzc19mngJW+sqKyu7urocDsfevXv37t2bmJiI2f8IrS4KhaKoqCg5OXl6etput8fHxz/lyiuUs9i5c6fX6xVF8ciRI6WlpWq1Wu4PjJZALiy5iUIHtAfxeDw+n0+lUqlUqqcMmYIgjI6O3r592+l0lpWVYSUphFYvqSknZEg9/atmZ2f7+/uhTjJkXcn6OdHSSJzED32BO9mf/lWCIPj9flEUoQYNnmkI/djA/TpBEHgFCAUYbhFCCCHZ4WIeQgghJDvcCIQQQgjJDke3CCGEkOww3CKEEEKyw3CLEEIIyQ7DLUIIISQ7DLcIIYSQ7HDfLUIIISQ7HN0ihBBCssNwixBCCMkOwy1CCCEkOwy3CCGEkOywiCNCCCEkOxzdIoQQQrLDcIsQQgjJDsMtQgghJDsMtwghhJDsMNwihBBCssMijgghhJDscCMQQgghJDucTEYIIYRkh+EWIYQQkh2GW4QQQkh2GG4RQggh2WG4RQghhGSHG4EQQggh2eHoFiGEEJIdhluEEEJIdhhuEUIIIdlhuEUIIYRkh0UcEUIIIdnh6BYhhBCSHYZbhBBCSHYYbhFCCCHZYbhFCCGEZIfhFiGEEJIdFnFECCGEZIcbgRBCCCHZ4WQyQgghJDsMtwghhJDsMNwihBBCssNwixBCCMkOwy1CCCEkO9wIhBBCCMkOR7cIIYSQ7DDcIoQQQrLDMhcIIYSQ7HB0ixBCCMkOwy1CCCEkOwy3CCGEkOww3CKEEEKyw3CLEEIIyQ7DLUIIISQ7DLcIIYSQ7LCII0IIISQ7HN0ihBBCssNwixBCCMkOizgihBBCssPRLUIIISQ7DLcIIYSQ7DDcIoQQQrLDjUAIIYSQ7HB0ixBCCMkOwy1CCCEkO9wIhBBCCMkOR7cIIYSQ7DDcIoQQQrLDcIsQQgjJDsMtQgghJDsMtwghhJDssMwFQgghJDsc3SKEEEKyY1b6AyC08kRRlKZ5KOpp70FFUXQ6nRaLZWpqan5+3u/3q9VqpVIZ9DSVSqXT6YxGY0REBHyV4zin0+n1etVqtVqtpmmaJMnv8XAWfk44Ovgv+cjTv4Pf75+ZmZmfnxcEwWAw6PV6lmWD3sHv91ut1uHhYYfDQZJkZGRkYmJieHg4RVFP/yNF6AcMwy1ChNPpNJvNExMTer0+KyvLYDA8zavm5ubq6+tPnz7d29s7NTXldrsNBoNGowl8DkmSYWFhsbGxqampO3bsKCkpoSiqs7OzoaFhYmIiMjIyKyuruLg4JiZGniMjCIKYn58fHh4eHx/3eDwEQajV6tTU1MTExIV3BguJoshxXGNjY319/fDwsCAIycnJZWVlxcXFkZGR0tM4jmttbT1//nxDQ4PVaqVpOjU1tbi4ODU1NSUlJT09Xa/X0zQt3zEiFPow3KIfO47jbty4cfTo0e7u7oyMjL//+78vLy9/4qt4nm9ra3vrrbcuX77s9XoFQRBFkaKohaNGkiQpitJoNPPz87GxsRzHvfPOOydOnJiamtJoNAUFBb/73e+2b98uUzTyer2XL1/+4osvOjs75+fnSZLU6XTl5eWHDh0qLCxUKBRLv9zj8Tx48ODPf/7z2bNn5+bmRFHUaDTFxcU/+clPysrK0tLSjEajIAj9/f3vvvvusWPHpqenBUEgCKKhoeH06dNRUVEFBQUvvPDC9u3bo6Ki5DhAhFYLLOKIfux8Pt/Zs2ePHz/u9Xrn5+enp6ef5qTgeX5sbGx0dNTlckGAIQhC+sdCHMc9ePDAbDY7HI6bN29aLBae510uV3d39+TkJM/zcsy48jzf39//8ccff/HFFx6PR5pMbmtrU6vVsbGxSUlJS7xcEISHDx/+8Y9/PHfunPRjcbvd165dGx0dXbt27d69e3fs2KFUKi9evHj27NnR0VHpR+f3+z0ej9VqHRwc9Hq96enpgaNhhH6EcHSLEKFQKGiaViqVubm5TzmvS9O0yWTasmWL2+02m81utxsepygq+f+1d64/Td1/HD/30p7S9pRyKVdbSmVcauWSiqxAZKCRmYXAlpi4DB7MzG1P9mDP9x/syZI90CUaMjIzk0WdZGzOwVTcNMBs5SK3tdwptKX03tNzzu/B9+fJCQJDdBfl+3rgg9PzPf0gNO9+7nl5BoOBoqjJycm5ublkMokgCM/zXq83GAzK5XKSJBEEQVGUpumKigqj0UgQW3wSn1b9Z03xsiw7ODg4MjISDoel10OhkMPhWFpa2kFueZ6fn5+/fPnyDz/84PP5pMYkEomJiQm32+33+3Nzc81m89DQkNvt3mQwsJbn+Xg8zrLsM1kOgbx6QLmF7HcIgqirq/N4PDzPv/nmmwaDYTenMAwzGo2dnZ0qlaqrq2tmZgaIDUVRx48fb25u9vv933zzzfLyMpBbBEEEQUBR1Gg0VlRUeL3eeDz+2muvdXR0lJaWSnWU53mO40AdVjAYBMdRFCVJkmEYhUKxe9HleX55eTkQCGy6LghCJBKJx+M7nGVZ9t69e3fu3PF6vU8LP8dx0Wh0amrK4/EUFhZGIpFEIiG+iqIojuMKhSI3N7ewsPCtt94ymUy7tBkCeVWBcgvZ7xAE0dDQYDKZSJLMzMxMSUnZ5UGKogoLC81ms1KpRNH/t7BjGBYMBh88eDA6OjoxMcGyLIZhQGgxDItGoysrKxqNpqSkhKKoEydOHD16NDU1FTyQ5/nFxUWn07m4uBiPx9fX19fW1liWBccVCkV1dXV9fb1Op9ul4hIEAVzw4eHhP//8MxgMgutADncOXyeTycnJyaWlJVFrKYpiGCYcDodCIdFgED+X6jGKogUFBRUVFQaDoayszGKxHDhwQK1W7/J/FQJ5VYFyC9nvACUD7tczJVBBOw0IEYt6E4lErly5guM4x3EcxxEEUVxcHI1GvV5vXl7e3NxcT0/P8PAwy7IZGRlOp1Ov11dWVmo0Gp7n19bWvvvuu66ursnJyUQiITwBPJkgiCNHjqSnp9vt9l3KLUVRjY2NBoPh5s2bFy5ccDqdouVarZam6R3O4jhuMBh0Ot3S0hI4kp+ff+jQoUePHj1+/BjcAxK0ovsuHszKyjp27FhZWVlubq5er09JSflbO50gkJcCKLcQCII8o9CKoCgqengiLMuKqUqFQtHa2pqenr6wsGCxWNxu9/379ycnJxEEmZmZcTqd4+Pjn376aU1Nzezs7I0bN7q6uh4+fLhlppNlWbfbvWVodwdkMpnRaKyqqrp27Zr0Oo7jO9dCUxRlt9sHBgZmZ2dDoZBKpWpqatLr9cB4BEEEQYjFYuvr6/F4XKqmHMeNjY1dunRJr9eXlpa2t7eXl5dvmZyGQPYVBPzWCYE8D385MkKr1Z4+fZqmaY7jfvnlF4ZhBEEACVqWZQcGBsbGxiwWS39///nz58fHx7erKgLpWzBf4pk+tgRBkCQp/T7Bcdzk5KTH49nhOTiO6/X6lpYWv9/vdrvNZnNzc/P9+/fX1tbEezAMI0mSoiilUimTySKRCIIggiBsbGwMDQ2hKHr37t1wONzZ2Xnw4EG5XL57myGQVw/YCASBPC87fIgSiYTX600kEmlpaTzPW63W2traqakp0FcDSpYCgUAwGHQ6nW63G2gtUEHpYzEMYxjGZrPl5eWJeeI9m8dx3Nzc3PLyMsuyO/idBEHU1tampaV5vd7s7Oz5+Xmp3JIkaTabTSYTwzBFRUU6nW52dhacQlE0mUwKguD3+7/99ttYLHbu3Lny8nI4Xgqyn4F//RDI3pHmVrdDjDZjGJaRkVFdXZ2TkyO6lcDTjUQiS0tLoJQJRVGNRpOeni6d+qRWq0+cONHR0WE2m/cQkXrayGg0GolEOI7b4RSKomq1uqqq6o033tBqtX19fQ6HA3whAH1Q77zzDqj5KigoAG21BEFUVFQ0NTVlZ2eDSPvKysrVq1d//fVXMCXjWS2HQF4ZoNxCIC8YUQ5BERbDMGK1MwgIb0qasiybTCbBXCpwj1wuVyqVot9JkmR1dfV7771ns9leSEgWtPyq1eq/nCqFIAiGYX6/v6en59atW2LmmCAIs9lstVrBVCm/3w86jymKamhoOHv2bGlpKfBleZ5fX1//448/pEXOEMg+BNYvQCB7B7T3SN1N4BGiKBoOh5VKpc1mq6ioUKlU4qsURUnjt4Ig+Hy+UCgkShFolkWeuKQYhuXk5LS0tBw+fFgmk72QYgsURXU6XWpq6qZ+X9A7K/1CANp/+/r6Ll26NDo6KhaFJZPJkZGR77//Xq1Wq1Sq4eFhUMAMwuMkSUr7qUCTLpx0AdnnQLmFQJ4LjUZD07SYTyVJEvTeeDyezMzMY8eOWa1WMEYKedKBo1QqxeNAbjdNfZKWOpMkabVabTabVqsF6siyrMfjcblcFEUZjUaGYXbOiQJ3WbQBQRAMw8A2BdDRiyBIMpmcmJgYGhqKRqNVVVUlJSUglL2+vt7X13fx4kWHwyEdZAGKrbq7uwsKCrKzs0dGRkAzrjhAQ+rIUhRlMpkyMjJgYSZkPwPlFgJ5LjZ5q6CA6MyZMzRNK5XK1NTUTb5sMpnclDF9upVICoZher2eYRigVRzHDQ8P9/T03L17V6VSvf32201NTaISb4dMJpPKLc/zPp/P5XKVlpZqNBocxyORyPXr17/66qtAINDa2vr++++XlZURBOFwOC5cuHD79m1xSqVIMpnc2Njwer0URUUiEaCvHMdNTEz09/cvLCyI3nlmZqbZbBZ/BAhkfwIbgSCQvSAIQigUGhwc7O3tlY7mj8fjvb29BEGcOnUqIyNDuhcW1A39/PPP09PTm8YwcRy3neJyHOd2u+fn5/Pz80mSXF1d7e7u7u7uDgQCJElGIpGcnJyjR49uWWDM83wgEBgfHx8YGHC5XNLr09PTX3/99dzcXH19/aFDhzwej8PhmJ+fTyQS165dI0nyww8/1Gg0vb29w8PDT2utCKiZKi4ufvz4cTgcZln2wYMHDocjFouBn4imabvdbrFYXlQkHAJ5SYHeLQSyFwRBGB0d/fLLL3/88UdpzS3YDgvG93/88cdFRUWixoCXfvrpJ9HzA1AU5fF4/H7/lm/Esuzvv/9++fJlHMfLy8tXV1enp6dByVIymXz48KHL5bLZbFvKLejrvXjx4u3bt71er9T4cDh869at3377bWxs7JNPPgkGg4uLi4lEgud5j8dz48YNu92elpZ27949j8ezXYkTGIxsMBjsdvvg4CCYNhWPx8VpzCRJHj58uLW1tbCwEGotZJ8DK5MhkL0AFvCBhXogAwrkBPwbDofBznnpEeAQi4vwkCep3OzsbKfTOTU1teUbge7VK1eufPHFF6Ojo8APFmuY1Wo1TdPb5W55nne5XA6HA6yhRSWAV2OxmMvl8vl8NE0zDAMcUJIktVotSPcqFAqKojbVgoGRy2q1urKysri4mGGY+vr61tbWgwcPSpuXFApFTU3N2bNn6+rqdh4YCYHsB/DPPvvs37YBAnn5ALVRq6urPp+PJMns7GyapgVBoGk6Pz+/srLy5MmTNpsNVClLD4bDYY/HEwqFOI6TyWQNDQ2vv/76nTt3hoaGtosng3GJYPdOQUHB4ODgxMQEz/MpKSl1dXUtLS2gyXW7sxsbG0DXZTIZRVFAQQVB0Ol05eXlx48ft9vteXl5giAEg8GUlBSLxdLW1lZXV5eXl4fjuCAI0Wg0HA4DwU5NTU1PTzebzU1NTWfOnKmpqVGr1QzDmM1miqLm5uZ8Ph+CIHK5/MiRI+fOnWtubv7L1DIEsh+AwWQIZC+AVXqdnZ0lJSVer1en04VCofn5eZlMZjKZSkpKwLglqcyA/TwffPBBfn4+6GHVarXt7e0mk+npQVEEQQiCIBZVAc/Y5XI1NjaePHlSqVRGIpHU1NTGxsYDBw5sJ2YEQVitVpVKBdYBraysgLg3mHWck5NTWVlpsViysrJQFG1tbS0oKFhYWDAajcXFxRqNBkXR9vZ2q9Xa39//6NGjWCyG43hGRkZWVlZRURE4CBxiHMdzc3Pb2tpSUlLAAgaNRtPU1GS328Fz/r5fBATysoDuUBIJgUB2hud5MK0Q6CXLsuIgi039uCIgbzozM+P3+7VabV5eHoIgn3/++fnz51dWVkTRlclkHMeJy3bA1vqPPvro3XffVavV0WiU4zgcx+Vy+V+WIIHKZzAAC3zeQYstSZIymQzHcfE4iFRjGCY1HuyHj8ViHMehKAqKnDEMe3qFH/CDQZEUQRByuXxTIBoC2c9AuYVA/mmA2yoIAhC2ZDI5ODjY1dV1/fr1xcVF8JEU/V0wSSM/P7+tra2jo6O4uBgs0AWP2rOYiR23u79/l+/4/LZBIK8kMJgMgfzToCi6qVW3srKSpmmSJK9evbq0tAQ8ZoqieJ6Xy+VGo/HUqVOnT582mUzAoXx+JXvWJ+z+fqiyEMiWQO8WAvlPkEgkRkdHb968OT4+HggEBEHQaDQsyzIMU11dXVtbCwqX/m0zIRDIHoFyC4H8VwAp1VAoFAwGBUFQqVTJZBJskyUIAm6vg0BeaqDcQiD/LcSlftLNQv+qRRAI5AXwbHuqIRAIBAKB7AECyi0EAoFAIH83/wOLZq+AjC+2DgAAAABJRU5ErkJggg==	X = 30 \, \text{cm}
+755	 A transmission type diffraction grating having 250 lines/mm is illuminated with visible light at normal incidence to the plane of the grooves. What wavelengths appear at a diffraction angle of $30^\circ$, and what colors are they?	[]	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	\lambda_1 = 4000 \, \text{Å}, \text{ violet}; \lambda_2 = 5000 \, \text{Å}, \text{ green}; \lambda_3 = 6670 \, \text{Å}, \text{ red}
+756	A diffraction grating is ruled with $N$ lines spaced a distance $d$ apart. Monochromatic radiation of wavelength $\lambda$ is incident normally on the grating from the left; parallel radiation emerges from the grating to the right at an angle $\theta$ and is focused by a lens onto a screen.  (a) Derive an expression for the intensity distribution of the interference pattern observed on the screen as a function of $\theta$. Neglect the effect of diffraction due to finite slit width.  (b) The resolving power $\Delta \lambda/\lambda$ of the grating is a measure of the smallest wavelength difference which the grating can resolve. Using the Rayleigh criterion for resolution and the result of part (a), show that the resolving power in order $m$ is $\frac{\Delta \lambda}{\lambda} = \frac{1}{mN}$.	[]	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	I = I_0 \frac{\sin^2 \left( \frac{N \pi}{\lambda} d \sin \theta \right)}{\sin^2 \left( \frac{\pi}{\lambda} d \sin \theta \right)}; \frac{\Delta \lambda}{\lambda} = \frac{1}{mN}
+757	Find the angular separation in seconds of arc of the closest two stars resolvable by the following reflecting telescope: 8 cm objective, 1.5 meter focal length, 80X eyepiece. Assume a wavelength of 6000 $\overset{0}{\text{A}}$. (1$\overset{0}{\text{A}}$ = $10^{-8}$ cm).	[]	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	\Delta \theta = 2''
+758	The headlights of a car are 1.3 m apart. The pupil of the eye has a diameter of 4 mm. The mean wavelength of light is $\lambda = 5,500 \ A^\circ$. Estimate the distance at which the headlights can just be resolved.	[]	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	7.75 \text{ km}
+759	"Set up on the lecture table is a demonstration that shows that it is possible to ""measure the wavelength of a laser with a ruler"". Make the obvious observations (please do not touch the equipment, the alignment is tricky), and use your data to calculate the wavelength of the laser."	[]	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	\lambda = \frac{\Delta d}{L}
+760	Given two identical watch glasses glued together, the rear one silvered. Using autocollimation as sketched (Fig. 1.26), sharp focus is obtained for $L = 20 \, \text{cm}$. Find $L$ for sharp focus when the space between the glasses is subsequently filled with water, $n = \frac{4}{3}$.	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	L = 12 \, \text{cm}
+761	A spherical concave shaving mirror has a radius of curvature of 12 inches. What is the magnification when the face is 4 inches from the vertex of the mirror? Include a ray diagram of the image formation.	[]	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	m = 3
+762	A self-luminous object of height $h$ is 40 cm to the left of a converging lens with a focal length of 10 cm. A second converging lens with a focal length of 20 cm is 30 cm to the right of the first lens.  (a) Calculate the position of the final image.  (b) Calculate the ratio of the height of the final image to the height $h$ of the object.  ( c) Draw a ray diagram, being careful to show just those rays needed to locate the final image starting from the self-luminous object.	[]	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	-100 \, \text{cm}; -2
+763	A thin lens with index of refraction $n$ and radii of curvature $R_1$ and $R_2$ is located between 2 media with indices of refraction $n_1$ and $n_2$ as shown (Fig. 1.12). If $S_1$ and $S_2$ are the object and image distances respectively, and $f_1$ and $f_2$ the respective focal lengths, show that  $$ \frac{f_1}{S_1} + \frac{f_2}{S_2} = 1. $$	[]	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	\frac{f_1}{S_1} + \frac{f_2}{S_2} = 1
+764	 A plane wave with wavenumber $k$ is incident on a slit of width $a$. The slit is covered by a transparent wedge whose thickness is proportional to the distance from the top of the slit ($t = \gamma x$), see Fig. 2.36. The index of refraction of the transparent wedge is $n$. The intensity of light at an angle $\theta$ is given by  $$ I \propto \frac{\sin^2(\beta a)}{(\beta a)^2}. $$  Derive an expression for $\beta$ in terms of $k, n, \gamma$ and $\theta$.	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	\beta = \frac{1}{2} k \sin \left(\theta - (n-1)\gamma \right)
+765	A thin, positive lens $L_1$ forms a real image of an object located very far away, as shown in Fig. 1.39. The image is located at a distance $4l$ and has height $h$. A negative lens $L_2$, of focal length $l$ is placed $2l$ from $L_1$. A positive lens, of focal length $2l$, is placed $3l$ from $L_1$, as shown in Fig. 1.40.    (a) Find the distance from $L_1$ of the resultant image.   (b) Find the image height.	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	9l; 2h
+766	Light of wavelength $\lambda$ and intensity $I_0$ is incident perpendicularly onto   (a) an opaque circular disk of radius $R$,   (b) an opaque screen with a circular hole of radius $R$.   In each case, find the intensity of the light at a distance $L$ behind the obstacle, on the path passing through the center of the circle. Take $L \gg R$.	[]	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	I' \sim I_0; I \sim 4I_0 \sin^2\left(\frac{kR^2}{4L}\right)
+767	A ray of light enters a spherical drop of water of index $n$ as shown (Fig. 1.21).  1. What is the angle of incidence $\alpha$ of the ray on the back surface? Will this ray be totally or partially reflected? 2. Find an expression for the angle of deflection $\delta$. 3. Find the angle $\phi$ which produces minimum deflection.   $$ (Hint: \frac{d \sin^{-1} x}{dx} = \frac{1}{\sqrt{1 - x^2}}) $$	[]	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	\alpha = \sin^{-1} \left( \frac{1}{n} \sin \phi \right); \delta = \pi - 4\alpha + 2\phi; \cos^2 \phi = \frac{n^2 - 1}{3}
+768	By considering the diffraction of light that passes through a single slit of width $D$, estimate the diameter of the smallest crater on the moon that can be discerned with a telescope if the diameter of the objective lens is 1/2 meter. Assume the wavelength of the light is $5 \times 10^{-7}$ m and the distance from the earth to the moon is $3.8 \times 10^8$ meters.	[]	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	380 \text{ m}
+769	You are taking a picture of the earth at night from a satellite. Can you expect to resolve the two headlights of a car 100 km away if you are using a camera which has a 50 mm focal lens with an $f$ number of 2?	[]	/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGQAZADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD3+iiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigD//2Q==	\text{We cannot resolve the two headlights of a car.}
+770	 (a) Calculate the intensity distribution of radiation diffracted from a grating whose ruling's width is negligible.  (b) Find the number of the subsidiary maxima between consecutive principal maxima.  (c) Are the intensities of these subsidiary maxima identical? Explain.	[]	/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGQAZADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD3+iiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigD//2Q==	I = I_0 \frac{\sin^2 \frac{N \varphi}{2}}{\sin^2 \frac{\varphi}{2}}; N - 2
+771	 A plane light wave of wavelength $\lambda$ is incident normally on a grating consisting of 6 identical parallel slits a distance $d$ apart.  - (a) At what angles with the normal are the interference maxima? - (b) What is the angular width of the interference maxima, say from the maximum to the nearest null? - (c) What is the ratio of the intensity at an interference maximum to the intensity obtained for a single slit? - (d) Sketch the interference pattern as a function of angle.	[]	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	\sin \theta = \frac{k \lambda}{d}, \, k = 0, \pm 1, \pm 2, \ldots; \Delta \theta \approx \frac{\lambda}{Nd}; 36
+772	Assume a visible photon of 3 eV energy is absorbed in one of the cones (light sensors) in your eye and stimulates an action potential that produces a 0.07 volt potential on an optic nerve of $10^{-9}$ F capacitance.  (a) Calculate the charge needed.   (b) Calculate the energy of the action potential.	[]	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	Q = 7 \times 10^{-11} \, \text{Coulomb}; E = 2.5 \times 10^{-12} \, \text{joule}
+773	A glass rod of rectangular cross-section is bent into the shape shown in Fig. 1.6. A parallel beam of light falls perpendicularly on the flat surface A. Determine the minimum value of the ratio $R/d$ for which all light entering the glass through surface A will emerge from the glass through surface B. The index of refraction of the glass is 1.5.	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	\left(\frac{R}{d}\right)_{\min} = 2
+774	A horizontal ray of light passes through a prism of index 1.50 and apex angle $4^\circ$ and then strikes a vertical mirror, as shown in the figure. Through what angle must the mirror be rotated if after reflection the ray is to be horizontal?	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M7NidMygHKZrF7jttxyy2RM/mcA0u2///5yXZiKKppjNP8zGoZhGEZhYktmGiUWbl3u3qpVq3kxt0r2jz76aDdjxgxZ8hKxhsjbd999Xfv27d0FF1wg+UJRRx7dR5Qh/mh+3meffWJxRzx+0MdFtwwuGjhwoOwffvjhEkZaymI7ZMgQ99BDD8mApWHDhrmhQ4fKWvH0NWWQ0bHHHivTKB166KGSh2Nx3uoHymbSe1ZgYs5PJoHXcweOg9CdN2+edCOgxrdr164ycb6WoaggpkvCXnvtJXn1s0FqesMwDMPYmJjwNEos3Lpen0kTNU3MiDfWJqcWD0HYt29fEXZaiwgIq1RxFcYh+ELRhygjHjEI+DVdmB7HcTWfptOyGfjDtE8hGqfHAPIgDrUmVMvQ4+k+W00Pmp+tHgt/KCq1DND0oOWq3zAMwzAKC2tqN0ocoWhCV2ktHs3L1FbS5E0N4znnnCNrtEfpols9FFjqD8UZ5SD61BGnohNSBRpbai9xKiDZhvHs67yhGkc6TaOfR/c1jabTMAV/mCaEcF03Hj9bdaB5cMTrZyyoLMMwDMPY2JjwNEocKpAQU7/+OkhqGnFMp6SkikVcGKZoWbqlHBVi60LLTM3PMVT0qVPUT1rShduwnDBdWE5BaXWraTRMP6uGaRoI/YZhGIaxKbG3j1Ei0Rq8yZMnS20jzchjxoyRcBVfoKIrtcYvRPOE6SA13frQ9Kn5tGwlPJcNPd6GpCloiwuPbxiGYRibEhOeRokD4aTiab/99osnbtdaPkit0VORpfl0C6EA21Axpun/ST49Zuq5KKn7IWuLI1zjCtqqPzzm2o5vGIZhGIWNCU+jRKHCSQf01K27g2ve/HRXsWJFGb0OKqx0G7KuuMIm9Zjsp7q1sba4MF9BW/Ur4X5qnGEYhmEUNjaq3ShRqPBMvW3Zx1HrqXEmrAzDMAyjeGHC0yjxFHQLm+g0DMMwjOKHNbUbJRoVnaH4NNFpGIZhGMUTq/E0DMMwDMMwNglW42kYhmEYhmFsEkpBjWdecrs2iru2LunnbxhlGXt+DaPoWN/ztz5K+vNZMu2PWUXDMIx/hfVSMgzD2FCsxrPIsRoTwyi+rO/51PjwObVn1jA2Dut7/v4rJV0frI/i+flKgPAs7Atf2Df2f6W4n7+9ZI11UdJfHOs7f+JTz2FDzml95Rf15/uvxy/qz2eUbNZ3/xQ1Rf18/leK5vkrAcIz17u1nSLT5nDh/sv0Oesqf1Owvi9+ffFFef5c9/xlKg3j7xT2/flfn5/18W8M/4Ycc33Xp7A/X2Efv6g/n2GsDe5Lnu//Yp8K+/79r8JzffmL5vkrBTWeRf3FFjbr+3xFff6Fc2MapYWSfn9u6Plv6PH+6/UpavtX2PbJ7ItRmBS2fSrq5/O/UjjPXyno42kYRQuPkE5az/rx4QT2Npl9SWdDDL+JJMMwNibrsz8l0+aY8DSM/4CKTrbqgDB1hmEYhmFE2E90w/gPhKITPzWeGm4YhmEYxppYH88S34eipJ9/yUZFZ+hX0Zmenm4CtNDvz5J+/xW2fVsfRW1fy7b9MIqa/2qfivv9WzyfP2tqN4wNQIWlPja6XbhwoevYsaObP3++69KlizvggANcRkb+iH/NY0LUMAzDKMuY8DSMDUDFI03q+uhMmTLFHX/88W7y5Mmyn5mZ6d555x137LHHyj7pqf00DMMwjLKOvQ0N41+CoFy5cqVr1qyZiE6EaG5urlu9erV74YUXJA2CUwWq/cYzDMMwyjomPA3jX6CDiLp37y41ntnZ2S4nJ0fCEJhDhgwR0anTK5noNAzDMAwTnoaxwSAitbl9wIABIjo1jBpPwqkBXb58uYQZhmEYhhFhwtMwNoDUmsuBAwfG4hLRqRD2wQcfmPA0DMMwjAATnoaxASAkVXwuWrTIzZw5U/whGj9x4sS4JhRMhBqGYRhlHROehrEBIB5VQDKAKCsrS8RlKDCB/Xnz5sX+cGsYhmEYZRUTnoaxAcQCMy/hpk+d5nJWZ/uHKBKcxKm4pN/np59+6vdpfmcgkjrDMAzDKLuY8DSMDQBhyeAhRqwvWbJERKiOcFdUnE6dOvVv/T4NwzAMoyxjwtMwNoBYPPrtmDFjRFjq5PDEqUN8Evfnn3/m5zEMwzCMMo4JT8PYQBCSeV5UDv5j8BorEmlNpza3s2Qm0y3pvm4NwzAMo6xiwtMw/gX9+/d3afwlazPZquhUP/08J0yYIGHqDMMovYTPujq64oQujDOMsogJT8PYAPRlMd4LSsRlbl5uHKbLY6oAhUGDBsmWMMMwygY8/3S1YTUztjgVnfgNoyxjwtMwNgAVldOnT5cXSHpa/iNEXGrT+4gRI2K/YRilH33W2WITGGS4atWqWHgWL8IZNwpyhrHxMeFpGBsIL5NJEyfGa7MzmxJhXbp0kX6dvFz0pbNo0V9u2bJl4scZhlG64Tnn+edH6FFHHeV23XVXd8opp0ichhtGWcaeAMPYQNISzg0ePFheMNRiAC+Ttu0udzvuvJPfiWo+icvKzHBD/vxT0qRidaCGUXr53//+534f9JvLyijnfvsNe5HhMjMzkz9Kefr/Sc1imGbNtJSjhP6IgvKFTkECFOSU1PSG8d8J7zDDMNYBxh3HoKHRo0fHNZiEUdOZkZbujjj8cBGmCnG/e5HqPeIPsfpPwyhZ6DPMj0r90bkm+YOH9t57b1nZLC8vxzVo0MD/GM3Pn2oLQPOFFJQuJMyj/n+SZ12sLx7CY/2T9IYRYsLTMNZDaFzZDh85wuXk5fKKSf45t8UWW7jKlSu7OjvUiWs7IScnV5rlC35JGYZRHNFnXp97JbW7DPE821FaHTQU1RJuvfXWMtcvAwx/+OE76ROeWp6i4VE5f3caFxLGwYb4wzCFMHW6HxLGhy4kdd8wCsKEp2FsAIhKplLSNdrT/D61nYcddpg0o+27777yItIXFOlHjhwpW6vhNIyipSCxlIrGa9rU9OyHrR2Ri0RlGOcfeVe1alW34447yr72/w7Fa37+vzv9sar7oT/VKeF+qr8gNE1BLoxXcQ3488X2Pz+WYSgmPA1jHWBEU2s5Zs+e7VauXCnhGGBeKPvtt5/EsdX0UXyu++OPP2RfMcNsGJuOUBQBfp3iSB1hqWIKNDxMq+mEPG8f8Pp9nnp1GV51JpK2ATug28jll09ZutWyw+3fjudhH6d2RvdTnX6WglxB6YE4fiRrGknvt2H3IUXT6DmqI1zjDaMgTHgaxj8gNKZTpkyJ/QwkwvCeeOKJYrBr1KjhateuLS8F4tPS0t28efPc/AULosFE/kVlGMamQ59FRNHq1avFz4wUbHGhuMORXvfzcnL9g+4L8S6R68WZ3yLCCM9ZnR2JrUSObH1GnzAScPQDpxzK1q2WLeWSL3kM4hYtWiT75ANaSX7//ff43HBaBgwbNkxm0fjoo4+kzJkzZ7pHH33UPfbYY+7nn3+Oy1aneXE6G8eQIUPcKy+97F7u/ZJbMN/bJz6ft0/R5+QDR07Pn888d+5cd8ABB7jrrrtOfnx/++237txzz3UNGzZ0l112mZs/f76UzXEMY634G8QwjPXgDa//4Z8n20MPPyzhBWciPTMjkea35StWSPgXhrhVK1YmmjVrlsjIyEh4IZrwujRRvlxm4rFHH07kZK/yBeVJOYZhbDp45rzgSnjhmRgzZkxiwoQJiSVLliSeeeaZxKmnnpo444wzEkceeWRizz33lDB9nr24THz1xZeJ8845N1GjWvVEtSpVE4cefEji2ad9mlWrfXkrE6tWLpdnOyd7hbcPqxK5OSvFLf5rYeLmG29KnHv2OYlZs2bJsSM7kuO3vuzclf6cVieefvqpRGZmZmLfffdNvP/++4kmTZrIfvny5RMdOlyRWLVqhRwnm2P49Jx/uXLlEhUqVJA0VatWTWRlZSUqVqyYqFatmuSdNGlCnIdj4ceNHz820b59u8RWW20lZVSuWClRpVLlRKUKFRNXd7wqsXjRX/KZc/1x5Bx9/myfb8Wy5eLq1asnx6lUqZLkV0dYlSpVEl4M+/NdFdtKwygIE56GsQ5UJKohZbtVra0T6RnpIj4zsjITe+69l7ykcrNzEmNHj0nUqF49Ep1J4VnOp7m3691rCE8t1zCMwiV8dk855RQRZgg1RBviTUUeYootcbfeemti1KhRiSYHHJgon+XFVWZWokI5nz5w++69T2LM6JGJ1QhD7xCbeV544rJXL0+cdOLxIugQdx07dhRBhvhFPOKyc1YkPv/8U3/MLDkm54KIw885RWKusohHRKMIQZ/vp59+itPpD1z8KgLxT506OT4ODvH6xRefeZFaxafJlHQco1yGd+kZiQr+81UuXyGxy047J0YOHZbIW+3PdeUKsVmIUET24N9+l+tDXo6r15Et58759u7dO77WZuOMtWFN7YaxHvxzEjcd0Uy1aMFCH0g/Fa8qc/PcPnvtLU1kK1evcs3POtMtXbZM0kqetHSfNM0tWbrc+zNkNDxok5thGIUPzxv07ds37sPIM+tFkoQDfp5v0j788MOuUaPd3W+Df5dma5cWuTT/e9PLWP9M57rhI4ZKF5uVK5fLQCKa4HGJRJpPlynNzjzvXoY5L9bkGEytpOeSnpbpRo8e68qXrxifD1vOzws6OZ9DDz1E0hMW5dNXdrqPj+wH4aTNyCCeaZz2dFttVUvSMHco28mTp7qzzz7brVix3B+HbgZ8bv+Z/OdxJPEuOy/bTZo6yZ117tnur6VLXDqDoUiFneJz09wvefO7DHjRKZ+N5vYvv/zSXXzxxT5HdE6GsTZMeBrGOggNKH76d4aGlxfEbrvtJga4ZcuWMn0K6AsEeCn069dP8uhLD8w4G0bhEj6rCCeEpfoJZ1urVi133nnnyehzwkjDM8tjSrz/2elLSnMXXHChCNLddttVysjNS7gZM2a655/vEZVJSv9I48/xIrJ+/fpyDjzzW265pWzTvSDVMBFy/jhyDJ9Hz6tSpUru5JNPdj169HDvv/++hAOClnz0rdTBSsq2227r2rdv7z788AP3448/Jo8V2RrSdezY0S1fvlLSkrdp06bul19+cQsWLHDvvfee28KfX54vn+6d48dNcHfddZd8FiA/DoGJnQPKpfxDDz3UTZw40fXq1UvKBD2v8PwMI8SEp2Gsh9CAjhs3TsQmRhcDzmCFI444Ql5In3zySVxrocZa3dChQ+MXCPv4dd8wjMKBZ023S5cujYWeCrOrru7gJk+e4Lp3f9L9+edg99ln/3Ply2dJHuAZrVC+gvvyyy98mqdc69atZTq1Y4491pdJC0i2/1H5rU8XHcfLMTkWAq18uYpyLKhQoULspxYySp8vPvV8XnvtNZk146WXXnItWrSIhR6CVT9LTk4kVNlnW69ePTdixAh33333uWOOOUbCKAtIw0Cl7777Lg5v0uRAqfndc889XYWKFV2z44/3+9+IXcOmrcpe7Xr3etmtWpktx+U82TJXMeer12/nnXeWwU2E67HUGca6MOFpGOsAY63QrD582HDxY3yJY9J41mK/5557RHQC4dWrV0/WmkQvCATqGqPhDcModHjW9HkrX758LIwQTs2aHefF2r0uNy/HlSuf6TKzorXVTzvtNBFgQLpHH3vUHXzwwVLjh6OcG264ScQYtZ6/DBggAhFBqZKL2sOMrEgshnZA4mIBmr/kLvEIv+bNm8d+zoHj4xQ+SlgWx+V82ZKOcPKGZX/88ceypTwEL6PPiY8cNacZUjtLOVGtaqZbsWqlNJ1TBuk4Zq1ttvEnHZVDGOcaHicV8hhGQZjwNIx1oEZX/d/26ydNXYThVq1a5Y477jgJA14Al19+ubv33nvjl4HWaEyfPn0NQ43fMIxNw5oCLiHNzzyDGRlrijtq8OJaSK+0zj3nXBFb9HUkPX0fmVIoeo4TbsmSJTIdkj7PLCpBXhWOENqQ0BGu4o4fq6TXOEXDlFAMAj9+VWySVsPVj40ijx7rhBNO8v4oLXmiz+HcoYcdERwr3Y0dN04+g7L4r79cIjkdHGkQ4KQP04RE5RjG3zHhaRjrQI24fxVgSd1vv/3mMtPzJ4PmBRW/pLxr1KiRNHltt912kg+jjmGmHJrbQQ21lm0YRuEQih9aHYAwnr29997HP4s0JXsRlobEjJ7rqlWrx8838/JWqVpV8qUnw4Cm85xcnm3WYs9zM2fNEmGalHzyPz88sQ1AM78eN9yGDvEIYZiSbyvY5ucF8uULxvzPrMdQvwph+ptGNigSphpev169OD2fKTfZpK9oiw1xpAfykkedYfwTTHgaxjpQY8r/kydNcnPnzZV9DLIadjXOLI/3+uuvy0uJ/lMazssH/4QJE+LBDWakDWPTED/DfqsO4UQNo/e5RB7x+iqMRpSThue0Ro3N5dnnSWbFoViGeaGa7n+AkgbxOWfOPCkz6r8ZpWLxCHIygnzmzOny7Ou5kJZ0mhYQdHp+EPp9bLCfnw/hp8JRIQ3xmp4fwXQR0K5Ay5cvly1E5xylr1ChvIRxHvy4LlcuEuU47cMaQpmG8W8w4WkY60ANPP/T56l8ufISFjqMN8a/d+/ebocddpCaDkaZVqlSJX4hYMx/+OGHNV4QhmEULvqMAk3Oij6zgFiMXoWRGFQxhqtatUokNoNy8l+baTJVEulXrFjh4yNxFqcT4RkRLbG7pt3QYyjYCCUM17QIWPwIY7Yap1tNB1H6KK5Zs2ZS20sYtumLL76QcNA0xE2YMFF+JHNdsnOy3a67RqP3o3jZyD6fl61eP0XTGsb6sLegYfwTvOEdO36cdLp3zArvjSzGWg397bffLn09MeyEYZwZkBCnc3luzOiRzDkvfjPShrHp4BlEHKpoSnjBSC1i9HzyLOaLPhWheXkJV6FSeZ/Zx/GcJwfiSAp2vST18lXKiEQjI76j5SiB9dqjWk9qRzOTz3x0nIKef20Ngb/HR+UQXrFiRRGIfCb2OXZ0/ChN5KLPjGrebpttpd8q+6u9oOz1Um+ZKsl/ehHVOPxffvm5T+P38nJdxQrl3RFHHimxFMNWdHXS9oEKT4799/M1jLUT3aGGYawTDCtTloDWCgAvsgsuuMDddNNNEibGPskee+whW8JwDEJYuHCh+CkvTGsYxsZHnzF9fmkeJgyxpE3PoMIpSp/8seidNicTr07RsiPRF6F9OgnTH6FSg+iPFR4PKEvjsSPaBK7lhucU+hnYpLaG4yCoNS5E9jmGL1tHoHsp7L764kvXu2cvmaUjz4vMhC/j5/4/xXOGct5M5ZSVPH+FcCCMz4k9C6+HYfxTTHgaxj9kwIABYmgxvGwx/gcddJB77rnnJExfBmqs69atK81ivBxwvFyGDBkSl2EYRuGiwgihhMt/fvPctGnTJC58pjU94Nca0tTnNUynaXjGsQGaD6Gm4Rqm+fR4jAzXNNR4jh49Ok6jhPvk++uvv+LPgps8eXJ8DGAbny81lP7voosukl3CcVe27+C6PfGEG/TrIHfrrbfKCkwcX/L5PDd3usWlZax5vjrqnjC2CPk1jmUY/xATnobxD2BUKlOmYHAx8sBL44033ogFJ4Rb+lZRyxGFRf2rmMzZB0gaNeqGYRQuPLfbb7/9GoP7dKQ5rLmNfkQqGhei4guHCGRAIWAbCFO0xlTLI06fe8rlxylh+Alnzk38esyo32hUnuYbP368z8N+NJsGNY9hnlQIP/DAA921114r/rycSIR37nSrO/KII9zjjz7mclZ7O+WL5xgPPPCA9FXX4wGfq2bNmm6bbbaJa3IPO+ywtR7TMNaFCU/D+Af8/PPP8UsEY4/xbdu2rUy3goEuyACzFB/xxJEGETp27Fhp2lLxahhG4cMziMgLhSHzXyqhyKpYMVpliGecmSr0x2P4jOMnXstC1GoadVtvvbUIXdzmm28uP1Qplzi2OPqB0/+S47N/yCGHSHmKlqV+aNCggdt3333jchjIqOcBmi6EdF27dnXXX3+9nHc57zScfbbke+KJJ2TpTS2PLeeGcMbPcpysx969e3eZr5g84bUzjH9Cmr9p7K4xjLXA44F7/PHH3W233SYvIfZpQmct5fPPP18MshputuwjVC+55BKZQgl8jGxZZm7kqFHelz9y1jCMwkFfb/ocd+nSxT377LNu9eqVsqAD4pPw6BmORNvvvw/2z/UFbsaM6V6EtfOC7R4RZxGRIKPG8IwzznS//vqra9RoN1kut0KFclKWTqnk/7lhw4ZKH0yEYkaGPuvRs68w4p1yWCueqY84FyXVPlAuYGdYMY3lNXfaaSdJpy4kOp9IHOLIN3rkKPfqq6+6yRMnulwfhjCuU6eOu6xtGxG1EJYT+smvW85T41KPaxjrwoSnYawDfTwQnY888ogYaaAGgHXbtaYjfIyo1aRpixcD6USsekOdmZnhBWumDDDKzMpfvs8wjMJDBRfPGlueYbQdYjJ8bhl5Trz/J6KKfqCkYwBOftN7JAojAcazm+bLWy1lRaPjEWE60h3Rly/SKCsi8pBGz4kt56V9wlV8ptoHPV/dkpZzYz8UrEqYXtNwHObplBhfvB4jTKth0XXIF69KmCb1HA1jffz9TjUMYw0wssOHD49FJ4aWZvfatWuL4VdIx/6ZZ54ptRj4o5ccLx1eMPStynPDhg0zY20YmwAVSyqg2NLkjVCk1pLnUJ0KvujRzBeNBT2rUZ6ofG2G1nKAcKZSIjwSpX8vgzhQ4Ui6tR0vFdLr+eLXsILQ8tiShuMxfVKa2KT8bj8az1ZdSOo+FBRmGOvDhKdhBGB41SkY198GDnIZzMmXXKt4t912i14S6fmDEPyrx910w41u/LixPi7Hv0iiNZ0j1Jg7mUjeF+SPwchUpl/JF6+GYWw8omcuEkdrijQGELFEJa/AyJGO+Gjtds2DqEQ48pznNy0rNJ/nl6tlkY+0+TYk2o/KAC1Hj8k2dBqXisZTHgIyTLu29JSvxwiPhZ9yAD/ofmpZGq95o8/z9+MZxj8hussMw4hR46rGllGjs2bNEr/GNW7cWIRnwotGak7g2+++c08//bSPj9K1bHmx69u3b/4LIhH1BWVku9a2gB7HMIzCQZ9bnkXQZxIBlerCtLoP4VbTQujXvJpG/UrqPs++pgWNC9MUhJajedeVPkwTHkfDws+pTtPoVv2GsTEw4WkYBcALQZug+vfvL9OlqEDEUNMJX4y4D2K+u/nz57tWl1wi8STbfrvt3H333Sd9tnbecSdJl+DPR9Jsr/3L9BhatmEYhYc+Z+E2dOtibfGa99+IszCPCrzCEHmUqecYHqOgYxUUZhgbExOehhGA0dUXjNYO/P777/HLhT9qKxlJKum8jUY8XnfddTLCFEHJ2nI9XnhBJlwmzV577SXlZPjEGf7vzz//dHnJWtKwBsIwjE0Dz1tBbl2sK359eYsD4TmqjVsf/zSdYWwIJjwNIwBDi4Fmq27BggXxXH7padGE0eF8ex++/4F76623RIDimKj58MOP9OkZWJDl6u60o9SSJnz+bJ931apVbu68ecnc+TUmOMMwCg+e4Y0pEjd2eZuKf3rOJfGzGcUfE56GEaCGNjS4NLUDYQhLJoZmQmgE6MzpM9yVV14pq35Qe7n77ru7O+7sIumdF56IyTp16kpe/GypFWXePhOahmEYRlnDhKdhBKSKQYQmTeMqHBGNe+yxRzw46OILL3JL/losfiajfuPNN6Vfpw/wDu2Z7g4++BCX8CKUNLjsnJxoneOktiXMMAzDMMoCJjwNYy0gCCdPniyCU4UmrmHDhrJ9+OGH3S+//CJzdbLPiPYdatcWPyBhyduwYTQQiTHwOXm5ImYnTJhI5N+ErmEYhmGUZkx4GkaAikZl4MCB0j/TMdkyQ4t8NEvgffDBB+7uu++WsIysTHfm2WeJw4+YpJR0rynTfDxFNmmi83lCuvv9999cBnOABsIz9diGYZRdsCP6w9R+oBqlCROehrEWMPZMfaQDi9indpNJ4du1ayf71F6yxvJzzz0ntZqk05HqQBocfT/ZKhPGj5dlNMNR7WG8YRhll1RbYD9KjdKECU/DCFCDzxY33gtE3cf4U/t51VVXyTrshLF05muvveYqVqwY5wXSqpjEVapUKZ6omdWPmJSeNdulXJ8+zGsYRtlFbUEoNtWOGEZpwISnYQSosWeLSPzxxx+lVlPB+NPfkzj8119/vdt1112TsRFaBvGko8b0k08+kXLC+TvpH6ri1DAMA1ug9gN7ga3BEW52wigtmPA0jAA18Lg5c+a4mTNnxuG8EPRlwD6j2zt37iyj2DVe0+pgJPzXXHONGzt2rPgRnBo+ZMgQlxuIWsMwDGwDdka32BK2Ghe6VDQsjC8onWEUJSY8DaMAMNZ//PGHNKXjRyyq4MRP0zlN7KHoDA281ogOGjTI9erVS+IzGUzk0bJ+/vmXNZrZw/yGYZRNEJn86G3VqpWrtdXWrka16u6oI49Mxq7fThCPo5zQmX0xigsmPA2jABCHCE8MNiJSw5jHk76a77//vqtbt66EkwaID6GJ/ZLk+u1MMI/hT/N/pGdVowEDoqZ2kLiU/IZhlD2wN//3f//n3njjDbdi5XKXk7tabEVO9iqXyMvxKbA36taOik/DKG6Y8DSMAsBoz5o1S5a31JoCFYbM13n44YeLAA2FaQh5rr76ajd16lSXkVzBiNpT0mr6hQsXuXnz5sXlG4ZRtsEW4Bi8CDk52TItG2BLWJBiXWh+7NLKlStjm2U/ao3ihAlPwygAaijHjRkbzeGZBON94403upYtW8b76nQfMPyffPyJe7n3Sy5ntX9x+JfFueee62655RaXnunFqku43LyES8/IdL8P/tNnzIjzGoZRdlE7ULPmlv7/PAJcdkJmEHbLlq/0toUuPfn2Ji8pNFVssqUbT+vWrd22227rRo4cGccbRnHBhKdhpKBGmqZ2YB8j36BBA3fXXXfFLwe2OOIx+toHdPrUaa7NZZeJH9FZo0YN9+ijj7ptttkmfjlo3nHjxsmWcLaGYZRd1DZkZWWuYSuAGkzsCT+G0/yPVSCGNDoACf9ZZ53l3n33XenqM2HChCid2RajGGHC0zBSwEgvXbZMOviDNo+feeaZYtghNuR+iz92Ppp+ncuWLHEZybAePXq4KlWquGOOO1ZeDkA5vBgmTZoUi04t2zCMsgl2QAUk5oB9iGo6U2suoy48GkZafuB+9dVXUgYLW5x44oliuwyjOGF3pGGkgCHv9803MpAonTqFvITUMmgfTUnjnX89RH8+PUYf0fnII4+4X3/5JXp5+DSd77hdBGdW+XKuVq1aUvsJKjRHjBgh+/ryMAyjbIONqVixkrc3WS439++Dg7AV6sTueIe9oXaTZXzVRtEXnXDDKG6Y8DSMJKH4GzZsmOxjuDHkbOkzpYYewSl+n4Ut4nTEyJHunnvucTk+bUZWljv+hBNkgvmoaSxa9eioo44SQUvZlPvTTz9F+Q3DMJJUq1Y1tgvUdsY/eJM1n5E/Ep9AfNu2beP95s2bu6ZNm4qtMfFpFDdMeBqGJzTibKdNm+ayc6I12sVwe2F5xBFHRPvJWk7tVwWrV692LS++WLaw/Q61Xc/eveSFoGXjP/DAAyUeP3mXLl3qZs+eHaczDKPsorZiypSpLieHqZPCH6Xa3I5NitIlcvNcXk6u6/7kUzJnMDapWrVq0uSuNgWbZT9ujeKECU+jzINxBoyzGmoGFmVm5HfwZ1unTh1Jp6gxx/DfcMMNbvTo0fKeKFehvHvt9dddhUoV4zRscfvss4/UfKpgJYxlOTkGLwrDMMo22IS//lokNiLffmR4GyHepO1AfLJJc5MnT3Z33nmn/DimhrNnz55u8803F3tC/lCAGkZxwN50RpmmIIOMYR86dKjUOKjhrlevnsSRns6bXka6hDf0vA0+/fRTMfakp0/W/fff7xru2tCl+5eAS88vm7yITgYVKZQ9ffp08UvZhmGUWbA32IEtt6wpIpJ9DcMuqRiNts6tWrnSXZxsaSGcaZSOOeYYsTNanuYx+2IUF0x4GmUaDHIIxvnnn38WYy37Phq36+67yT7pJQe1C2npbtnSZa5jx46RUU/PcMefeJJrfdmlIjoJi8K90accn22vffaWMqQ2wgdk+P+WLF5EgeLs5WAYZRexL97tsEMdLzxZrhfBmG+j1KZgtmhuf/zxx+VHMtSus4O79957xbYoUdpIdLI1jOKACU/D8KjB1xpI7ZSvhn633XaL/ZLOO+LbXHqpTLtEv0/6Vj377LNS25DlRahOp4QjH1QsX8HVrFlTwiBndY776KOPxK9p9LiGYZQt9Llnzl9sUSKR620FYXkuO3uVy83NljB+xk6cON499NBDkocZN/r06eMqVoy696iTH7hJW2MYxQUTnoYRgBFnaTo66WvNAYb722+/9YZ+YvRiSHbsZ+qkj//3v9jIv/LKy27zzTeTPFSLSlr/z8dKUF4iGiG/2Wab+Qcv/2UwfPgIlxM0vxuGUTZRkZjaDxz4MYwDmtbbtGkTdwe65dZOrnHjxhKnC1kAW7VPhlFcMOFpGB4MtBrrBQsWxP0wVXz+8vPPbo9GjV2D+ru4K6+80rVo0cLdfvvtEoehf+yxx9yBBzbxZeTXWIrB9/GU9eeff7qXX37ZderUyY0aNUrSRC8ESkjIYKbw5YBfz8cwjLKB2g3to8mWMOxFpUqVxM9I9ie7PekG//a7hO+7774yuBFbpT+Y1ZaENsUwigtp/ka2t5thJMGQs0LR/z7+JDL4XhRiyKmhTEtXMRnVRqg4pAsW0yTVqbOjrFCU7t8ZK1etcrNmzHTjx4+X1YmomVARK48cA5M89PFMy8xw9953n7vqqqt8mqhvqBzHXhqGUabQ1/Fnn33mzj77bKnZVHvw28BBbtddd5UfrgcffLCIzKysLOmT3mDXhnFetTNgNsQojliNp2F4MNpq4IcMGeLlZmTE2a9SqbK7vF0bd9IJJ7rymVk+MX2soprOdC8ayffLL7+4t95+273Ys6d78YUXXZ+XX3F9+/aV5nnSUXNBWTh9QUBe0r9g/vz4JaHnYRhG2YNnnyZ1/cEr3XK8TWCfH7A0satNueKKK0R0kod4rSkFsyFGccWEp2EErFixQgYXpaf5RyNpty9ueaHr0vl216vnC+7GG68Xg56bF00uz1QmBx10kAwsUsNPLUT58uWl9nPrrbd2e+21lzv33HNd586dZd329955N36x8EKh9pRaUcMwDMB+6I9hwB5hM5gYXldV23777d2dd90l8ZpOtyI683/fGkaxwpraDcOjj8H333/vjj/+eJebzZycuTIZ/P/d1cV1aHe5GPxjjz3W5eTkujxv2O+5+1531TVXi5GXGU8Syb5ViaifFWXKfgBhvEQObtrU/frrr97vj5ue5nbaaSdZcjOaKNqa2g2jrMLzT/M583Fih9QeXH755a5Xr17SZ7xChQrum6+/do332jNuTQmRfUyamRCjGGI1nobhEaHn/wb88ovMr0lTOwY9N2e19N9cvHipO+ecFi6HEe1eVO6+eyN39TUdY4GZ4cWkiEiZ/iSy9lJmih9H2QhNys+TZrRoCqc8L3TTCKHfJ+l8uYZhlB3kmff/KlWsJHYoDvPQWkJTOzWfnW+/3e29zz7iL8jGAHYmtCFmT4zigglPw1C8YZ4/b740fWP8MeAZ6VleZO7uLm51iZs9b47LThr+nr16urT0yOhrjYM2tUsTuhQXGX59EeiAJKizY91kLWkUvnp1ths3btwaLwdNaxhG2YHnvmKFCmILchN5YifY5uTlymDHw488wl13/XWR/UgS2opUgZlqhwyjqDHhaRgeNdYTJkyIDHWytqB69eru7v/r6r7//kcRiIjO++970O22WyNJD5o3REWmlOWdDETygpQtbLHFFrFAjQRruhs4aBBvEAnTfIZhlC2wPVWrV3Orc6J+5GoHsBP0/XzqqadkH4hPFZTsy49nT2hDzJ4YxQUTnoYRQL9LDDT9MNPS09yChQvc888/z9vAG/5Md+aZZ8tIUmo2gbSphh8IV+MPU6ZMkSlSvvnmG7d06VIZcIQI1ZcE/tGjRrmE96+tTMMwygYMSsTGqFjEHuB/+umn3XbbbReHpUIatR9qf9jiNM4wihoTnkaZRo0xhnnx4sVu1qxZEs4qQ4k8b8DToylMoM4OdVyP53tIExd5qIHQWkvQFwFx2vw+YMAAt8cee7hddtnFnXLKKe6kk05yder4cnr0iF8G0Usi4UaOHCn7WoZhGGUXlsFUm8L2nHPOceedd14cjgvtROjHthD/119/udGjR681nWEUBSY8DcODkf7pp5/izvqIzty83KhWMiNd3DvvvSvzdmp6+luxVQdq1Nn++OOP7tijj3GjR46SeEQq2yVLlrh3331X/KSL8iREpCJ0ISzTMIyyg9oKVipCQCodOnSQ8FA4qg0hnf6QxRFOC0vDhg1lZSNm5NBuPqDpDKMoMOFpGB6MNstW5uTmiOAU489I9aShf/jhh139+vVFmIrRTuaDUCDiV8cydtk52dGLwGeQiaCTKxZRi6ovlSh/mps1a7YbM3p0XJ69GAyjbMGzzw9aFpbgR67+WMVhe8J9UBuh4UDY1KlTZY5hajyxM5o3RNMbxqbGhKdRplHji1EeOnRo1LzOX3pUk4DBZu7Otm3buoyMNJebG3X4R0OSTg0/W/UDzfasgEQamt0pZ5tttpE4BChOjx3VVPByyBDxm1qWYRhlCB59bxpCobg2kUg4Tn/EssW1bt3aLV++XMKwXw0aNJB0oV0xG2MUFSY8jTJNJPqiGkmWvZQwLD8GPSPd1a5d27322mvyEkgkqHUoJ2moudSBQGr0FcLGjh0rW/Lh7rzzTjdmzBhZa5lw/mTaTwRs8FKZNHky7xyBOGNtcM3XvO4bxn/N/0/ZVMfZUIr6vIrrdSlaxGZge7xtyPCvZ/Y1XP0K+1o7qjaELYMhmYAeP6unMSAptDHAfmrYpqWkf/92//4XTHgaZRo1wMuWLXPTpk2LjTv9oailfO+996SvFSAgEZmkJ56BSGxx4QtCyyN9dm6OvBymTJsarevubb30E+W4XtiGsCLSWC9Oc1XIrvmeMQyjDKA2JDM5QBE7wpYaTOLURYklQ/wDeubMma5Lly7iJ0+3bt1crVq14lk4CMMZRlFiwtMo82CkGVjEaFGMPPvMl3fvvfe6evXqxcZaDTbx++23n9txxx1lcvlFixZJOGiazTbbTF4GGHyEKbUQBxxwgBs1apRbvXp1fBzSs41IuEGDBsVxcdWnsQ605qGwaiD+a/mY2ILM7L8tb1MTfvbCON/CLr9kofaDLUtjhtAvXCFe0iZthO5fe+21bsWKFWJ3Tj31VHfmmWfKD2hF8hQrSvr3X9LPv2jYBMIz9YvZ2K60U9Bn3hBX1BR0TqErWlT0/f777yIQGVyEocbot2jRIjbomo4tUyEhIAlnfs4vvvhC4kJ23nlnSYv4REgCI0tVjBK31VZbxeUrNNFzbAlTPWpsABt6X4X3YkEulbWFbwiaX8v6p64wKOg4oUtlbeEbi8Iuv3gT2hn6idPkrjaE+X8VTUc8kOadd95xn3/6mdiOmjVruu7du4stI470oZ0pvpT0779s37//FKvxNMosoTFmFCg1ChnpGWKot912W7fllluKSMTok06N/RNPPCH7pGOi53PPPTcWlwrN8++//76rXLlynJf0wD4rF1G7SY1pdA7ReZAmnM/T+LcU9gvgv5avebWctbmQ1P2ipKDz25gUdvnFH2wBdoWBiPjnzJnr7ULUDSi0JzBv3jx33TXXxnl69eol/Tslf9JFdqakUNK/f7t/14UJT6PMoaIu3FLjqWKS/YMPPngNw46f+EmTJkmtJMaf/RdffPFvLwH2iWvWrJmIS+bRYx/jjxA95phj3CeffCLCtmnTpnENqL4c+vfvHxVUkt4TxZLCNm//pfx/m7c4vcyK8/UtuWADsAcIR+wMpLsM6aLDQhPp/scxP5Jju+PDLrm4pXT5oYbzsssuc4cccojLysqSsnAlk5L+/ZfN+/efYFfGKLOEBplmcN1HCNJUHtYSqAFn4nftM4Vxb9KkieyTViGdik/KYSJ5BCsTx/NyQHTSR5Q8bPUFoaJ36pQpyZKMfwffRWGatv9avubVctblimOtiZ5bYVHY5Rd/sAMVKlSI/diHzMws9mRfYfq3Rx99VPqok4YV0uibjm3RdISXLEr692/37/qwq2OUKdSIh4wYMUJEn9ZihsJTwU/8t99+K1vEIsKTtOQJazwVwvV4OrJUj004+4cffrjUZBCclhYdY9iw4ZLG+nj+GwrbpG2s8ilnfU7vU6vlLCuofVDbAdgJajinT5vp8nIj2yH2yO/8+ccf7p577pEwbFLPnj3XsDMlj5L+/Zft+/efsgmuEocoTFfaKegzb4grago6p9BtejDSatTZfvfdd9GcmeleQHq1h5Hff/99fVwkRDXdzJmz3TfffCthCMRDDz1URsIjOkNDjz90GsYLgbS8NLRGYocddnAZWZn+JeK8S7g8fyJjxo7zOXyZnI0/BxzoORtQ0L2E+6cUlPefuE2J3JRJF4IQVfdvCT/ThriNRUFl4wx9zpl2DbuR4wVmurcR1Ter7tIyoi47NK+vWrHKXXrppWKvSHvNdde6hrvtKnZG8pOu2BJ+56ErKRR07jjjn2BXyiiTqHFnSzM4tY74MfQY7IJW+ujR4/lYMNJX84gjjoiNO2HaVK5CdG1O0+OnmZ7mMQ1ny3yivExIg1M0jVGWCF9qBTmjtCJdevyPYcAOMLUb5oD5fgnvfNttbsKECWIXmNrtNr+vohNC22EYxQmzXEaZRcXfwIEDkyFORCMGHqNPnIo9ajh79HghNuYXXnhhLDRJE241zdrQMgE//UTDFwbH4pyIU7e+Mg3DKPmo/eCZpzUFf3p6ZIvmzp0nNgf69v1apnUjHtvx3HPPid0IIY9hFEdMeBplEjXKbH/77TfxqxFnoneMuL4E4O2333Z//fWX7BPXsWNHEaf6IgjTUib+tRl+TadQ4ym1Gx7NN2DAAFmSMwwzDKPsQJ9Nnn39gTtl8kS/zZP5Pdu2vVxaW7ALF110kdtnn33EdrGvtiLVzhhGccGEp1HmwDCrmGP99HCFEIx3nTp1xB8acUai0/zNS6B58+aubt26cRmshXzrrbfKvr4koCDDH5bJljSNGzeWrb5IOM7ECRNIIOmUgsozDKN0ofYBW0Rtp/i9bahZc0vnLYbr1KmTmz9/vg9Nd7Vr13YPPfSQpFF7YnbCKO6Y8DTKFGqc2SISmb9Taxa0/yaiUv04pkBizXbNf/XVV4sf6NzPMnXPPPOMa9myZVz++tCycczzqeKXfS8/3a+//rrGuerWMIzSjdoFajajgYXRIMOqVau4X376yb36yssuLyfblSuX6d544w1Xrnz5uLYTu6U/YM1eGMUVE55GmWbcuHEysAgw9tQ2HnnkkbHRJuy1114TP2DU99xzTxGtv/zyixh+0q5atcq9+eabbvjw4VJGan8rhfJAy2fLuu6sZBSKXZbizPNlaBjo1jCM0o92v+GHaF5Orvvqiy9dq1atxGbQ/5NWloYNG2IYJJ3aFMMo7pjwNMoUoXjDUE+cOFFEIn7iKlas6LbffnsRlprmhx9+kH1EIBx77LHum2++cZ07dxaRST7ieVFo38+1occBtmlJYckAIz0m+wsXLnQrVqyI04K9WAyjdMMzrm7XXXcV0Qk5uTnuw/ffdbNnzmAEpGvUqJG7/vrrXYa3NdgQtSuhvTCM4ooJT6NMogZ68ODBca0ixnu77baT/WgkabSU5Zdffilpc3JWiyPPqaee6n7++WcJV8GICGVQ0A033CBlrQ2N4zjUagK1qEBcnku4jPQs9+UXfeUcImei0zDKCvwYnj17dnLP24q0dJfjzUyuN1uZ5cq5555/HmPhRacXnMmVJrARZieMkoAJT6NMgoHGuDMPnu4jBJkPT2sOcCtXrpS+VsTTjwpUaLIljQjIIIz+oOt7AWg8eWH33Xd35cuXFz81ppwby+DpeRiGUXbABsybN0+efbUt+OmPTqvKbrvuKmHYEXWGUVIw4WmUSTDiNGXjFEQgTd6ggo+m9/Hjx7s777xTBgHpSkVKODAJ48/2+eefFz/h/xSmQ2GAEfmoOeUY1KzqeRiGUXbgmV+6dKm0fuiKarjqm9Vwt93eWcJohSediU6jpGHC0yiTYKzpu0ktphpv/CosQ4NOn8+bbrpJltZkLk/6hQ4ZMsR9+umnIjw1L7z44ovSB3RDXgiko4ZT82gt6LBhw/5xGYZhlC4YsBjaEWpBX3jhBbFRaiMMoyRid69RJkFcslQmRhww8Ii/6dOny35o2EPDTzhClCU1jznmGPfyyy9LGeTv1auXa9GihaRdm2AknW7lpcJuXsLd1eVOl5GWHk0az5rtLuH+WrJYBhkpmtcwjNJJ+IzrIEVsFT9s9957b3fccceJDdJ0qXZG7Yr+eNZ07IdhYZxhbGpMeBplEgw2ok7XaAeaulmG7tVXX5V90mDk2WqNJvuh4T/ttNNkbfX+/fu7888/f62CMyQ0/JTSvXt3986770he+QvKGDRokOzz0jAMo2yAbahSpUpsd9inG5DOorE+O0M86UBnx1DhCevLbxiFiQlPo8zCqkUYclBjjvvjjz9iw1yQkScM8alUr15d+mhq/nURxvMiGDpkiLv55ptdVmaWF6GRGNVyeOkwL6i+LAzDKN2ofdBtaJ/o1oP7J5Ae+/LKK6+4nXfeWZYFDkWs2RSjKDHhaZRJMLz0oWSLkdeaTGoVHn744dgwExf6w63mVdjXtGtD49muWL7cXXjhhfF+Xm40F6j4/UuD2lht+g+PYxhG6SS0D6mtK9gAdRqWitoJ4vlhfeWVV8qsHEzxFopYMJtiFBUmPI0yCaJu1KhRaxhyRrD36dMnDlPW519beraUS39NTD1bCfcbn8Pd1ulWN23KFEm37357uxd6vuDTkC6/vKF/DvEBBb9kDMMofeizv9NOO4lfxaeGr0s4ahwrHV10wYUiNsnfuHHjuMaTfDhNaxibGhOeRpmEuTYxxNrvCX+3bt3cNttsU6BBLwg14DitnVC/liH7XkjqoCH2GcTU98svXe9eveTFUKtWLff++++7s88+y2VmZkl+zgsnI9v9vr0kDKNsoM/65ptvLlv2sQlsQzsQ+tWOAfalU6dOshwwdg2bFrbiAH61UYaxqTHhaZQ5MLpMiYTow/iqQW7evHmBBj6VdRnt1HAti3AcL4ily5a5jldeKcfKLF/Ovf322/KSYQJ55goNmT9/vluSnMDeMIzSDc859gI7MXr0aNlqWKrdKchPmj///NM989yzkhcR+swzz/ytb6iWaRhFgQlPo8yB0Z0xY0Y8YTsCkBWLKleuHBtw3abyb4w1ZUmNBNMk5eS6a6+5xs2dO1eE73PPPifNYD6RlN20adP4BaOOwU72kjCM0o8++9ik5cuXix/YYkPUHxLaBvzt27eXNAmf7IorrnCHHnqo1HxSZpg3tRzD2FSY8DRKNWqU2Yb+H3/8MTLOyTDWSlc/4eo039ocpO6HaDhrLXuPNKlTw5mdm+tatmoltaz6UsDVq1dP9jUvsIKRYRhlB2yPzuOpUHuJUxCiKkaxFbnZOa7r3fe4kSNHyj4/pu+++26xK5qGcnXfMIoKuwONUo2KR5BaR+/XgUVqtDHETDlCnLqQMBzD/7///U/WcIfUWghNp8eKnd8fN368jDLleExA/9hjj7n0TC8yWf4umXe//faVsvS8OR4T3eu+OsMwSi884/oDVFHRSVxoX8BbDBGc9OUkHU3rr/TpI913FLVRhlHUmPA0SjWhSFNBx3KXGHU1xGxr1qwpW0ShhitaQzBr1ix30EEHufPOO0+WrgsNv0JeLUfikmUtXrrEnXvOOTKZM6PnX3/zDZeRlb8yidK4caM1xCxl6JrtqedlGEbpInzGQ+HJ888Smio4FdITxo/pyy+/XPyITpb43W333WLbZRjFCbsrjVINhlmNuRppVhlSYahu//33/1uYQp4FCxa4o48+WmoVqFE44IADJJw8bBXNx1aO7f2kb9u2rZswYYLEsTpSnTp14uPp1p+h92e4Ro0aSTo99xEjRsTnruGGYZQ+QrsTLufLM88PZprfsSeaji19xW/v3FlmwEB0spjFDTfdKN17QttkGMUFE55GqUeMdFKsMYfm3NlzXM7qbNlH9DHIiHWQSacGHcL9c889102ePFn8TPq+3377iWEnnjJABaHmE5eXcD1feNF98dnn/mBp7tI2l7kTTz5JajN4KeSLSMpAaDp32GGHSLiWsWjRIjd3zlyfIkpLPo0zDKN0Uq1aNXnmZTq23DxpLeHZD/uAI0J//P4H9/TTT4vNoGn9xRdflLi8RCQ61T4ZRnHB7kijVJMqzpgTk/ntCFeDvO2227pKlSqJ4VYnhjspDO+77z43YMAASUs69iWdF5KUgT8VFYfjxo51nTt3ljAGMD3wwAPxscN8ep7kq1+//hoDC6jFGDlihPhJp/kKOq5hGKWDqlWrirAERqjPnj1b7EauF5RqLxbMX+AuueSSeP/xJx53tWvXduUys1xmRmZsZ9QZRnHAhKdRJkgkVw1ikM/AgQPFCKs4POSQQ8QPoXEmrv8PP7r7770vTvvGG2+4GjVqSDr21eAruk88A5AuuOACqVGtXLWKe/XVVyVcj5Hq1/JoKlO/lkczm2EYZQdqL/kBqnaC6ZUQnWozoN3ll7uFCxdKWlplzjn7HKkRxW6QKkxrGMUFE55GqSbV8C5ZskTWP0dIUhuAkWYKo1DkkYf5NpcuWepat24ttQ6ku/76692RRx/lnxovEknot6QN81KmGH0ffu2110rtKmEMRmKFovB8wnxstXZit912E7HKPm8P+nBNnTp1jfRhOYZhlD623nrraJnd5KwXYofSM1xGWmQnXnnlFff1119LHKsTPf744xKOjUi1M+HWMIoaE55GqSY0uhhj7YAfGuatttoqFn2kw2VkZrorO3SQ5i1qHVhRqEuXLtJnUwUhaHr1a83oRx99JOu+w0UtL3bNmjUT8Sp5PRxL/RCeD1M9ESfiODlA4Ndff5U4LR90axhG6QFboPYBx3POVprdk888rSm339ZZ4rAr/LAtV6G8NMlrfrUpqVvDKGpMeBqlGoytCjRqDv9avDgSdcl+UsQzsEgFnbjcPPf2W2+5Dz74QPKwohG1C+TzCfxD4426L5It6DHUzZw+w7Vvd4X0s6rfYBfp10leMfzJfqEFwYtlsT+/Fi1aSDmkz83LlS2rF4H2/STeMIzShz7bPOtqU7Svp3JXlzvd0qVLxTa0urS1O6DJgfk2xjCKOSY8jTKBl4pSMzB50iQx5NQkirDzBn2PPfaIDTZxo8eMkaXmCMnIzHC9XurttttuuzgNIhVIq2FhHKPe6Y/FdCgvv/xyLBbpnwWaNhXCaZ6fNm2a+COhG8UxopW1m/VFZBhG6QYboM97LCrzEu7XXwa45555xq1audJts+22rmvXrlFaH601noZRnDHhaZR6MMTUcCIK6StJLaaKt1122UWmLVEjzyTN57doIU1ZNMm3bNnSHXvssXGNA+m0xpJaTy2HLeV3vvU2qZ0kze233y7l46evFnn5Wxv013rzzTfFr+cjtR7+jzKGDB0qYVKOd4ZhlC7CZ5stpiYyN9ivHLd46V/usjatxZ9VLsM9/XT3aHWiZD9Q7IP9LDWKOyY8jVJNXlIYaod81mjPofk6I+o71bRpUxGMgLi76qqrpGYR6tSt6x56+GHJR21pKtQuKJT1ww8/uO7PPC37Bxx4gOuQXB4TEKn6QkGEygsieW6wYP5c167tZS4vN8e/QxIyxRMvE6nF8PEJl+smT57gPfTzyp9A2jCM0oPaBRz2AoshVoPn3bv69eq58ePHu8zy5dwZzZu7I448MrJNeT69T+KtXJQ2ICwzJHXfMDYVJjyNUk0k9SIw5KwClJkeTd6OwWYFIfzUaH744YdRX87MDKlFePW112QbvwSSLoS8xDOlSZs2baTMqtWrud69X5KpmzSvClBv/uXloPnE+PuXxmWXXebmzJrtsrIy3f333y9N9MRpOs5v7Nixsu8LjPIZhlGqUPuitiaR520FjS2JdJebk3BLlywX/xab13RPdusudgVbwFbzaBmKlOPTqB1Rm2IYRYUJT6NMgKFd8tdit2zZMjG+arBVeE6cOFHEn3bov7Xzba7BLrtIXGptJ4Zcm+vViF966aVu3rx5Uu7zzz/vtthyC/FrPA4QnerXF8JDDz3kvvqqr/QJPeuss9yVV14po+grlItEr8LIdjkXH5b6cjEMo3Sgz7ZsaUL3TiaN915aazL8j9MXer7oqlSruoZ9WBthGvxrlG8YRYAJT6NMgJH97fffRbghCHOzc0QUHnTQQTJw57zzzpMBQcQ3adLEXX311WLoVTymQjrKJP7RRx91ffv2FdHasWNHmTqJcF4YpFNjT1MYiN87Rs//8ftgGRyQ7tPu2mh3Ea3pPk/FihXdEUccEef3uaSJbbk/V/gnLxzDMEo+aj+wKdgYZr047LDD1hCR67MH5NU0/GgW+2M2xCgiTHgapR4Ved98/bUYXcCAV6pQ0W2//fYyMfyYMWNEYFapUsW9/vrrkiYUjSGkU8PNikJ33323DERiBaQ777xT0qihx4VGX8NoXmfqpIsvvlj2EZrM+6mCljCmeconIZPKf/D++7Lsp2EYpQ+1EyFqf7A7FSpUkB+6ID9uk6TaKEV/NPfs2VN+yDK4MrRHhlEU2BvMKNWoiGPbv39/McRidL2dZhqll3r1FsGHIEX0vfbaa27zzTcXYar5gTzqFGpIW1/SSsKYhL5Xr17JmAgMPPn1HIBmfhzikYFMuiLRs88957avXTsWleTdbLPN5Dy0HLZz5s7lZMRvGEbZABuBDWBO4EqVKsXPv9oX9Sukx86wve+++6T7zuDBg2UApOZVm2QYmxp7exmlGoyriE3vHzRoUL5x9gEYYubNlNGg3hgzd+fBBx8sYo98qYZZ91W8XnPNNW7SpEkyWAnRWbVq1OcqfBkompdw5hB968033fvvvy/hl7Ru5U4++WQRvqBpt9hiC3l5QF5eFLZ61Sr5LJrGMIzSj9qUCy64YA3bouGhPcCPI5yp3WiRAezaaaedFtsU+/FqFBV25xmlHgwsI8KltlGGiEbGWWsEMND77bOv1Awg/mjSDo27QpiKznfffde9/fbb4qep/oD9D5D4gvLpMcjLduqUKVEfUh++//77uwcffDBu1mf6J/qW4keMsk2WIuc7c+bM5L5hGKUd7IXaAISjzNlZAJoOpzYIf7t27WQfG0j/c7oSaZyWaxibGhOeRqmjIIPa79t+IuhYg536T/xsGS1asXIl1/vll+IaR21mx1hTEunUmMOEceNlSUxGqB96+GHupltudukZ0brKpFNxKg4RmcxH/OrVq13r1q1ldD01pByXl0laGn07GbHuXxIuOo8tNt/C7VKvvhwnIQWluz8GD3FpfmsYRukjtDOgtkzFIzYKvzqND22e2J3cPPfIQw+7kSNHSr6aNWu6G2++SewRgx5Tj2MYmxJ7gxmlDjXIoTFmGUpqMlUUau0jRpkax7p160q4GvTQMCP8NF9OTo4MCGKFI/qCvvTSS7HgVMKXA6qT+TyBMmj2oomfPE899ZQsxamQXkVvlDfhGjZsGO3TKdXD5PbhsQzDKN3o8662AdS+qQPsC/aJ7eTJk8WuaXiPHj1kYBJQntkQoygx4WmUatQojxo1SvwYYdCmbaYladWqlYSlCkhgT8sg7rrrrnPjxo2T/G+99ZY0XWk+0ukWZN9vicffr18/98QTT8g5nHPOOe7000+XdKnoObBFELPVsPnz54szDKPsobYAe6L2BrApGoejvzrTxDHbxkUXXSR2jr7lxKkNNIyiwoSnUSpR8Qf4f/vtt1gAqvGtUaOG6927d2ys14am//zzz2Vlo9U52e66G653e+691xo1lFpG6pZjzpo1SwQu51Bvl/ru8W5P+Kcv/5hhWj13/me0fHjeTDL/888/S7xhGGUH7ACENkLthtiI3DxZGvjpp7q7AQMGyI/jHXfcUaZfkrw+KflCe2IYRYEJT6PUERpVtkuXLnXTp0+XfTXeCMZXX33VbbPNNgUaYTXsCtMesToR6fbcc0936623xmWBlsE2dMCgoAsvvNAtWbJEmrsQuzpIgDL02JpfQeyGXQDYEjZs2DDZhmkNwygdpD7XqXZFw9RuQF5ONGhywsSJMpcw9iGrfDlZkAJbI3aGv2RZYV7D2NSY8DRKHaFRxgD/nlyxSKcRwX/JJZe4o4466m9GPjTuMuo9z4s9b9QvvvAiEY7kfeGFF+Ly2YbiUeG4QC3E/915l/t90G9SLuuw02+TcvQ81UFYDuW+8cYb4pfz8n/04aLbQBwWnK9hGCWb8FnGFmADCMMfbjWdblntjLjL27aVJnbyMXfnPvvsI34gXp1hFCUmPI1ShxpmDCxGd+DAgSIE1egi3m688UZJq2lSCQ37bZ07uxEjRkjaW265xe20004S5wMkrCAok2OyvvrjTzwufa1OPfVUGZiE6IwS/T1veFzm+vz0009dTm40uT3lUe6PP/4oadZ2bMMwSj7YgNBusb9W59M93b27G+TtDa05u+yyi+vs7RZxoLbClyR9PQ2jKLE70Ch1qJFVo8xgIMCIs1+nTh1xasxTCcP7ffON6/7UU5L3wAMPlMFFiD+mJdHjhITHXrlypbv88svF0NOkz8hS8kpNKmmSk8KHaH7m66TGAjLSo9payqHcGTNmyKh6/KQv6DwMwyjZsIAEIlLtVuiAcP/wi3/c+PGuS5cu4udHLgtaiJ0K0tPH0zCKAyY8jVKFGtnY2PoNg3Ew0hhiRNpxxx0nS1Myhyf7apxVwCEI6RE1e9Zs165tWwmnbyZN7OmZUZMW8T5TlD6ZXx3HpIzbOt0q05rw8mC+znLly7ucvFyXxpyfvoyM4NhajuDzXnTBhW750qWyy/FCx2cZMXyoL4MaEdaet1GqhlGa4Bln7k2e94JQW5HmbUX2qtXuwgsucCuzV7u0rEx32+2dXcPddpV4WkqwexD18jT9aRQ9JjyNUoUaarYY5+XLlrnxY6MaTwwwhnjnnXcW66sGWfNIDYKHZitqGFtdcolbsGCBpHvgoQdd7dq1xXhrPtAXAHmlJtPv4//xhx9cz549JY6Vjfbee285po6Cj/Ll11bS/E8Y7oEHH5TuAQk+g/+jppVjUi7xTFZP0z9+/ZyGYZQeeN7pq6l+nnMWn9BnHtjmeZvDimv0+ybdAQcc4K666iqJ03zqDKO4YMLTKHWExlmnFcEIq0Cjw32IpmWLeGTLRO+IvzSf94wzzpBR6YTjwvIVwtTQz18w37Vtd7k0x+++++7upptuSiaKNqwNL+XwlzwnFaSjR4129917r4Rz3k906+YeeexRqZ2lPGpMs71InTBxkhZnGEYpQm2M/tAEtuoHtT8jveB85JFHJC1zCj/zzDPiT7VPhlGcMOFplErUSP/qxSMrFjG6HGOMn+mQRPwFNY4YazHYPvy7775z3bzgQ+zRF/TpZ5+JhStpCgKRSDw1l8zXOWfOHFexYkWZ95PmeeBI4TFDKHf1ylXukpYtpQzKO/vss2V5TQYKkIdzAPzTpk1d5/kYhlEy4bnGRUvp5rdosGVfbIG3I7nZOdKHnPCMrEwZTLTDDjtIvGEUZ0x4GkWKGlkElPpDt6FoHs0/Yfz4uBaTLcacpS7FgCfTieCU/TS3cOFC16ZNG5edm+MqVarkXn/zDemsTzo16Gz1OIoKwK5du7rvv/9eBC61D0zgDJrXZ8z3B8i0S//3f9KEzvFomn/muWelJrRy5coiPkGP/euAAXL+YVmp52QYRslDbc2ECRPkR6g+46EN8h5ZBW3o0KEShr1o3769+MMfqIZRHDHhaRQpKgpxofhU/4YSGlsM8E8//RSXyaoeOhVSfJyguRs6duwotZXkpdazXr164tdz1PLDvJr/l19+cQ899JCkueyyy2RJTJrHQ9bI7z8jjmvAebJ2O+FbbrmlCF5EJ/vkOfjgg/OPn5dw472g9jtSlqJlG4ZRcuE55rlfvnz5GiISJ3bRP//Dhw2TH7m0ymSWy5KJ4tWWGkZxx4SnUaTQpIzBxNCqkVWx9V+hnEmTJkm5Xh5KGP07Uw20HNcb8z6vvOI+++wzCaNf5xnNm/vghBj3dUFZf/31V7yyUZOmB7kHvQB1KUti6jE5L14gjKzHv2jRIhGq+KWW9fXX4xGt6ph0Xs9TPo9P+3XfvnF56gzDKPnwjO+6667xM43NAqZRYyW2lnTJyc52mRmZrlOnTvEP6lQ7YxjFEROeRpGCcVRDqbWcuv9foAyMNCNBgTkwMzIzpMk6rEnkDz9N3MzRiYHfbrvtXPfu3b0w9OexllOhJpMo8nLe1157rcyvydx7fV7pI5F5uX8XrPFxvcvNi14mvETIm+XPixGqiGO5Bsl05KFfKjW2vJA4XmZ6hps0caLkNwyjdCDPfRJGqPO8E8YPdJ77if6Zb9umjRszZoyE7777bvFiGJoGe2EYxRkTnuuBB1kfZhUZ6pd9nAtcEKZppLItz/+HK8BP04lMJq5hodPw0Pl/sUtBjpfc/u38CPNx4bZAF6Tlv/D8ZEtEqkvG/y0sBT2vRIJazkh4cU0RiCeeeKI7/PDD3VdffOmWL10mA31Sr/c/ccAWI52Vme7POTcqx9/ujffY08eRwhv45Dku+WuxO++880SoMsfmy31ekYFBxNGJH8EnOYKXggxOig7l3nnnHffuu+9KkS/0fNFttvlmkUj06TmqHIZtcG5A2U91e9J9/+13MgDplNNPcy1bXeK8qpTaUE6UtBx3//33l36nlENN6srsHDdj1pyolLTkSkiGYZRoQhvxv//9z9stplmLbGW6f+5vvvlG9/6H77ncRI6rULmC6/Pqq2LbsBHkUaEKob0yjOKECc9/gD7UPOAKfhy1VhpHDRcygzCJYwocn5awhDca1JKJny26wv/lefXic4qgyPPhUoKEJcNJG7joCMk4yg8MlZ6H+sXxlwwnPeemTtJSlpxn/l/0LwpfI8YfH9Gj+xKvefUc9U/T+rL8YeJzYBtBc3HUZ4nr26FDB9evXz/322+/uVO9ANtqq62k+Yg5LM866yzpz/Tyyy9LZ3oEImiZinxG76i1ZCvrnHMiXgRyljk5q91BBzVNpk5+Dp+OUehTp04Vo82cm7q+MY5ahNCYQ/5nSJOaUlYYIs1lbdqIcCZtnD8pQFVE4zT/yJEj3R133CHpGI0qtaxe+Mblk8879qtWreqqVasmwVoG+YlnH8JzNAyj5KLPMjaSH5Zs09Mz3Oeffyn7uKefftZtv/32kk7Ts1VnGMWVNP8C07eoUQDatwa4VIgEXvTaNxHwE0e4PvD4meibScCVWK4kw1IvPfsax1b2EUiSLl+M+ADxEl4uI39CcnWaV8M55zA8jA8Jw+WzeOEoksaHc1bRZyd/dDZybv4vipWAKEKIwtNEgUb70blwjCiEcriGc+fOdXXr1hV/lCY6X2oEya7iT6ZF8uGcp54r4eXKlRPhxsjOxo0bu/32209Gkzdt2tQtnL9APgsiGCM9dtw4OU3yw31d73UPPvig7JP/y75fyfHC8kMIA86VWtlDDjtUBvrQhD9g4K8SRx6tJVU0n54/n+Wggw5yE8dPkLk5v/rqK7e3F7x0ByBe/jjHZD5gLtG33npLjk13ASa0ZzlQudf8MSW9YRglFrUTPNPz58+Xbj/AM49dAuzdySef7F577TXZD5/7VHtlGMURE57rgQceeKAxBiJiPDzshKmQAOLUTzgXFuHElnBiQiMBXH1qDakV0y9C0pKOMpLlaHgItXWh8IS/nYN3aowIX7JkiSz/iB/xsnjxErd8+QppWtYyiGMyYkikE8b55BvDzbfYQs6XmseVK1bINcIRr8eM/f7yEUdTOmuX05eRUdtLlix2o0ePcZttVl1qJr/88ss18quQIkyvPRCmafDjFD4PhGnzcryY9Ukw2s2bN5daUy3722+/dWc1P1NWCKFvZv+ff4prEMJrxrFCv+z7f5e2bu3eff89mf6IsnbdbTcR63zerOT3AmvkY99vGD3PICKaz1lp5NZbb3VZ5ctJWqBPKuinIy+1vkxsz+fD8QLi+1yjz2oyv2EYJQ+ea32GZ86cKT/IQ3uGHatRo4a0dtAKwr4++5rGMIo7JjzXgz70cM0118g8j3T6XrZsmfv888/l5Y9ooVmY6XQaNWoktW34GX2Yw1KI/PnLnL06qrHLETGbcLleFFErmpmZ5UXcSjd9+gwRZLt5AcNoRcQax+eYjJredtttRWSwjGONzWq4qlWqSs0ZYICI43jM/8b5MSClevXqIhYRlpTx559/isFi1DY1jTTdKCq2OEfSs7QkfYzob8jUHlMmT5Zzr1ixgk+bIctRcn7rvoXyf4GTjmPolvOlfC0jLAsDij91Xw2r+lPjw/IRgFpLQDzi7rbbOnl/howkP3D/A9ysObPlPJjo/aSTTpJ8ml6hPD0ecJ5vvfGmzPfJVCY0l8sydf67BNIy+EfzsCWPnttHH3zoLrroIonba5+9Xd++faWPJ2JT7xX84SuE/J988ok799xz5TsG8vMC4t6TPMlzV8LPYBhG8YfnWLd0/8EGqw0BbNULL7wgfdLVtoE+65pO8+g+pNoDsw9GUWHCcz3wwucBZctE3vh5+EEFABAeCh3Sc2mRD/qAs4+frfp1X7eg6UHj1obmC/Oq6JK4ZFbi9dzCMv1pxhDPeQPx8tkT0efXY6h4At2uDcmjNXfJ81I/yLHyohpJ/OqAvJou9KeSGs4+ZfBZomtA03X02V9+ubdr7gU3ac45+7xY8F188cUyGXNBx9BjUyZb9qm1PWC//eWHRdNDDhZBSPlcDf+JJd+asjF5LbyjWf7QQw+VWlbuJ+bvZHUkSeOz+DtC/D7xGufD8alh1n6ewDER06xYAmH6VBFqGEbxBxsBPO+0zjApPJUL+mwfc8wx7uOPP5ZnH8JnPkTtKPH6XuJ9xf768hpGYWPCcz1weXiIaSamiRjRqWHhg6sPuPqBdDSrAkIgNQ/7oZCDME1q2jXKDfy6j9Oy4rzpaWJwMDacH8fDT3nJBDJnJPnmzZsnNbjUdtJnkYnUp02ZHAk4X06trWvFx8BpWTiam7k25MWxT/+k6pvVEMNJGHNUkpZ01PLSX3TJ4kXS1D7F/7rnOKmfU69Pqj/8vOoPIS3lRZ3zo8njx44bLU3pr73Sx1155VVcJLdro91lpSFdnYh8a8DI/GTzOXHUQjc79jg3ZMgQ+TwDfxvkatWqFSX1olPPg+9dz0/hHmLwEbWU8OKLL8rAKSX8DPq59B7h+Ajl0047TeL0+9t3332ldp2w8PxTr4dhGMUftRc87126dHGPP/642A1g1bVnn33WXXDBBfJ8qysI8iuk+eKLL2RmDJrpsRHrymsYhY0Jz/XA5dGXf8+ePUWMRYImP1zhQUZUId6onaJpvPHujcRgLF+xwg3+/Xe3jQ+rVrWqmz5jhtvKCz6avSkjw+cTEef97KerOOTr8eUSHn5V6pe03kViLlPOgbLo/4nYq1ajujS7c84IUMQSjvPDZWWVi/t8Tp8+3VWvXsPnoymdz5VwK1esdNlebFWuUkXOT4yVPzbHx89ZiPki3CPnpecp8SrGo6ZnXFR2lJalIh944AF37733utU52WvUImtathxLjpcMk/NIwnViH/HItaYMugZwvrm55E248v5zLvprgZs+dZpretBBbvHipa7mVlu5b777Nl7fWN0a8HH488eFq6++2r3y0svif+31112z45vF+SRFMrvWeOZybl64co5Xtu8gIpuyWNWIJjPOEf52XPCi1+tmSU8fUgYUIHzJg5hnS9cOZgLQ6wLx+fiwAss1DKNYonaG7c033ywzXfCsYz+wbyzDy7y/+lyv7fmWd4eHck444QT3ww8/uLPPPtv17t3b7INR5JjwXA88wHqJ9GFV4fNPHtzUy5uap7Af/IKODxwXx+fj87ANz0XPc33np+nYFlQ2oi8sQ9NFx4wEGlMp9ejRQ+JzcnOivo7JsqhtRMjXr19f+qzSf5bytt56a3HUYLKsJQIewyz4rA0bNJC+rpSDQDv22GNlFOhxxx3nhg0bJiKd+TePOubo+Hz0PDkyYhO0xhrh/vGHH4nR55xat27tHnvsMcmrn5ekDBQDFZ4a/+GHUb9O4Jx//fVXV6VS5ah5PZkf4s/t0XuPvrjUbOpSnpwLW03LubDOO32N9XPI+fh49kHT6nEMwyh+6HPKllXUEIv82OQ5xo49+eSTskJaQegzD2rP6YZDNyLATlCDqvbBbIFRVJjwXA+plyd8uDf0wSXff8m/MQk/l56Hnt+GsLY8+eGREFOi4+aLPAZYvfP229KXiRHaiEz6MR1w4AHu6KOOdrs3biR9IdeHfh4p13u39CJs8eLFso8RZh309957z/34449yjCuuuEJqWRGRmk/PmZKY5xQQkIRNGDde1kunbyYiUKddUjSflJHcclzSTJkyxR1yyCEySIxjf/fddzKAjDzqFP0c5BX87tFHHSXN6drkT3pqdTUvLyXKZaT8bbfdJjXdhFOGCk89hm4Nwyh+6PMPkydPlh/cGsYzTitJixYtZF/RZx30mSdP//79ZVEOwjbffHMZWMpgU+LNHhhFiQnP9VDQ5dlYDytlF6cH/7+ej14rysgvS4Vnfs2bxgNGkX36MfHLnm4Acc2lR9MppA3zh2jZs2fPluZzSSPzjkbijGNhvJmUnumbgMFFpFOBpiDwgLyc1zFeBGO46SP1888/u+1qb/+3fJwRXRz0WMTTlYCmrl8HDZQms+eff15GplPjCpQfInmSDu7ucqd7vFs3OQdGuDbao7EIaISnptHPh8il5pcBR4yyJ544wtVvGEbxRp9/frDSmqNhKjzp48m+wnOtrSBqd/iB3KRJE2n14fn/+uuvZWEM/bGstsBsglEUrPm2Nf4GD2boIHzo/w3kxxW3h57z0c/2bz5jeI3yPxu3WP5tFsbjVLjRNxPRhCDT66PXKNVB6A8hDyPFKQcjzIAfHLWFNGuXr1jB9XjxhWiFIL9PGkU/c3hsttddc62sUIThZ6Qp/XR18FAIe5oHx4AmalUHDRok+wjO885vEZ2LTxteYeJDKIdaTprJsletkmm3Xn3tNXfyiSfFacPjE4awZcqsTp06uYYNG8qAAuClRHzqMQzDKF6Ez6iKREV/XBb0HBNHuNpTVmDT1diwByo6VZgaRlFiwnMD4WWfKjg2lI1RRmGh57Upz49jYSALcusjPE/1//HHH/EgJQ1jHzFKv0ytDQ2PocZYhagaeNZLfumVaDDRTTfd5A477LCoKT15WNKkOgnPS7hfBw6U4yH8mCWAgQH6WSOVGuUPxS/4u0NWRWp7WZuoSd0L1a73dHUNGjSQ1Y4U8lKebtVxPJrpmKuVPq0DBgyI04UiFKflGIZRPOBZBZ1pQ59r7ITG6RZII3H+jwUz+MH5anINd7r4IEJVdGID1eaFZRjGpsSEp1GkqFFVl8r64iE1jjXf1UirqMLgHn/88fHE7RhfzaPpNK0a8lmzZklfUF4Ahx1xuLvhxhsjox30C01Fy2By/datWsk+swYwQT3l0GdU+o36ZDpwiTL1+Kz37z3uivbtpcYizb8wmp95lqwHn+U/Q90dd5Tpr8I8vFR40Rx11FFSHvtAmp9+7O+OPvIod+ThR0jfUs6Zz4YDtpQBujUMo2gIbcra/BA+q/ixKTzL9JO//trrJJzV55iyjZYa8qtdwJ9anmFsSkx4GqUCNcQY398G/x43pWNgEWCMJO/Tp0/cF2pd0C8TUdi2TRu3ZOlSEXq9evXyhfm4wF5LE76HY3B8nPh9fvpZ0keLNA889KD01dI0eq6geeOtD2O0/fvvvSefpc6OdV33Z56WzyPOi97DDjnUHzx62QD5mKPvo48+cm+++aYMSOAlQ5mMsqcc+qWectLJIkJp+pc4H675gTDDMIqO8FnETukzSThObZc+u4rG0SrDUpv477//fpljWPMaRnHBhKdRRGA41zSe/wUMK8Z4zJgxIi5xPjA24NQ40o8UUo02qIEnDhNN38qf+v8k4a++/pr0P4XYgJM+sOWk0zgGLtEXlDBGlbIykp5H+AJA3Oo+W9xkL1YZnU5aakhf88euWKlSnIZyGBEf1l5Qmzt06FAJY9lPuho899xzMvUUa+qX8/HEMW/rwIEDZeUkmuHHjR0n+YnT4xuGUbToc6g/HsPnEpsgNir5vOI0zacff+xef/VVsR1HH3303yaaD8sxjKLEhKdRRHDrbZzbT40vBhdhxTrpDOxBGBJO7SM1gpBqgPGJS4ZRxrixY13Xrl0l7Dafd5+99pY4UCOOTBWp6v15Ph1pqYGcPWu2NM9TDvNqPv3005KefT1PhdpTPS4vE8TyhRddKEtxApNH79pwVxGPelzS1W+wi4zGp8lfw/7443cvQFlIgFqShLvwwgvd8OHDXZ8+r7rdGjWS8rLKl4smnvfXpu/nX7i9Gzd2F194kZsyabLEA+ejjnINw9i0qI1gq/ZB8M97RlZm3NIicays5v9hM2646SYfn+UqVq4k/cm1xYd0bLVcwyhqTHgapQI1rpMmTYpqOz3sMz3TddddJ7UHiD+c1vCBl1giINlHaDGtExM0I9D2228/yUs5YX72NT/zfWpzNlzm8zJfJ+lo2mfePCCP5tX86shLGGKXye0Rleecc47M11dQrQfTQTG9UhiutbzsE86xoPmZZ7oBv/4qtbYMTiIOB+R8//33JbzDFe2lTytlMKBJy9HzC49vGEbhET7Tqc84AyP54cgzyb6E++f1lltukZXn4OGHH5buQZkZ0UAitQWGUVywO9Io8ajQwkAjnhBOGGZEGzV/TKiu6XSrIpBaSjXs7GPAmTqJAUHPPvecpFNBp4R+0EFC99xzj0zlRPx111/nDjyoSRSRAvFhGRyXmlpdCYkVmp7s/pTEqejTzwd169aNJ9XX+IULF8m+pmErn9f/Qxifeuqp0rfzzbffcnvttZd0ckjPzBSBTTqW0qu3084yMIEpmcIXG0hZhmFsMhgcBDx7+vztUq++bHm+6WLD9quvvnJ9Xu0j9o4mdn60hmJT89ozbBQXTHgapQIVXOPGjROjq4Z3u+22K9DganrQ+E8//dS99NJL0pR1d9d7XJ26dWIDH5ahfsQZwhVYC/nBhx+S2sojjz7K3dKpk6TDkS4kNZx15S+77DLxM0H922+/LSNR1xjI5NOSh/PBURvLVgXp6NGj1njZhOjx4JRTTnE//tTfvfPeu7ICk9bkqtBkguqdd9zJ3dbpVrd4USRANa9hGIVL+KzRJx07oM84P3BVbPLc0szOKParr77aW6E0+TH69LPPRGl55pPlKIQbRnHAhKdRosGYhm7IkCFxOMaZ2k78CgY53FcYgd62bVuJZ+5LmtvJH74ING8oJBnBPm/evHj95G222UYGMsUvC59HywnLIo40OF4cHJ94RCfNZHqs1DxaDqKRvBrO4CKNA7aEe0+8HzoGPfX77ltZBYn+r5wjjs9GLShrQtepU0eW4NQaUMqTMj3qT903DOPfk/o86XOn8IyyTz92th06dHCz5syWH6lPPNnNbbnllvEPZVxI6r5hFBUmPI0SjxrZRYsWSf9KbRpHQJ111llrGFw14mwx6qwVv3rVanfRBRe6ZcuWyYAglrXUMlUchmXgJ7+Ee8dE74hPRO4bb7wh/Uo1r5aTipbxzltvyxRInAvN/KwwooJybfnJpyuRkIZ9jo9A1HLXIFlG6IT0NNfshOPd1/2+cR989KGUSTUJZXINOaduTzzhdqlf33V7/In4uupWHekgLtcwjP8EzxLPs/a3VpuAn7hc/8wxc8aHH34o+82aNXOnn356bA8MozhjwtMo8WBoEUM//vijGF6tYaSfJk3tISqO2OIYMX7tNddIv05qCt566y3pW0VcQeY7NOr4e/fsKRPWw1133SUrFK0P8uGY+ql9+/bSXM+6yjfccIMcl8+S+gIhXAUe4TS1a19W0uL4/KRT1K8h8pmSZbKN4/2WvmHffv+de/e996RsrgV9Q1mBacniJVLz2aD+Lu7DD6IXHfm1rPC8DMP49+gzybOkNZf49RljSjTsxbChQ92NLGiRmSH2iunf6CKEA3kW7XE0iikmPI1SAWKT5mYMrgq3Y445Zq1iCIOOMafGgNHn2V7EMRqUgT0i+pLpUglfDGPHjnU333xzdKyjjnZt2rSRF0GuF2zrgjKoXT3vvPNkdDovjpdfelnKIU6b0/RYwD7xsGDBAte8eXPxaxpEKOKZz7S2z8yH8nJbvNTUqh9UwLK6EzWg73/wgdt7r71dpj8XX6CUz8Ct81u0cHvvvbf7wMdz7PC8wvM1DGPDCZ9dniueS32usGv8WKVl5/zzzxfbQdizzz7rttpqq/h5ZGvPolGcMeFplGwCA8vAIl11CFnVKDl/ZWiEMcw4FVJXX3WV1CycdfZZ7uKWLaO5NUmOoEoachVzOKD83Owc1/qSVm6VN/6bbbaZe67H83IuHEuFGPhcBYpY+pMy9ROrEZF3q62jF4e+bIB98uLCMPqTjho1KjofL3Ll0+WluVEjRkf+NM43ObUS+wo7yQD1Uh4OsSvhyXM49rhjXf+ff3Iv9XnFNdh113j+QK7NmFGj3QX+xbfLzvVkST65Pj4v/yO642vFHIMe3ZcwBW+waxhG9PwpTBavzyXPJI7BRNdcd62bOn2aPG8sTnHyySdHz7F/nnDxs5ZflGEUK0x4GiWbQMz8/vvvsZCi/yIr96ghV/GoW8Ix2ky8zLJy3bp1k+UoMe6+BIlXA65+ahe0LPpjjhw5UtIzEpy+oZLXp9Utf1j/hE+vx8Uh1j7++GNJx+oivDi0e0CYP8bnIYy8DD76/PPPJVhfSgg4zp0aX1gj7z9Ej53q6Dc2+I/Bcs5cT0S6XBP/N2P6dHfdNde6nXz4i/4a5OXkyosv9Vqz1fJioktjGEYB8KxIdxf/7Cg8S3R5ee211+SHM916mIKNNNgCbIRu13jWDKOYkeZv5vw3t2GUMPT2XbFihdu8xmaxoaYmkfXJaRZWQhF09913u0cffVRqRlkb/ehjj3GsQIQYQlRR26l5QPPB11/1lUFLGPmLLrrIPfb44yL8JCX5KUbzy3/5tX00zx988MHSTNawYUPplxn25eKlEeKlm/8vys8azAwAotZDRTA1nrTsk48aksVL/5JcaWkI2aQw/Q9wXD13tq+//roMNNJmfW9AXALBnpYuAv6hRx52p512WvR5qH1mzXyfRoWzXhfDMP6OPiP6zDGlkto0FaL6rH/zzTdi31KFpj1jRnHHajyNUgFzcGKMMdiINQx048aNk7GRQQeM9IABA0R0wrnnnisDa4iXpSlRjsm0mgcw5oi9BfMXuHbt2sk+S1dS44DolDTiIn+cNygDsdmq5SUyQICR70zarjWIUOALI9lcTRyT4a9Ytlz8O++8c/I8os/EufGZp06ZEp2IJzz//4KeF+VRQ/vLrwOk1oXplji2l7guLydHhPH557VwTZsc5L7/9jvJt7HOwTDKCjwz+szpFrAfKjJpcWEhCH78rtN+GEYxxISnUWLB4KrRZf5Opk/SfRVFIDVz3ihTE7lwwULXkr6cPt3WW2/tHnnsURGqarR1XXQtB/ATxhJ0l7Zu7ebPn+/KV6wgtX+KlE8ZQb5U/u/Ou6SmkJcFqxxR46n5JK+HY4VOwxHKf/w+WAQmy3AitK+88kr5bKTTFxIrIPnSJM/GIDw/zhs43imnniprwT/+xBPx3IH+ZOQ8/vjjD5ne5YQTTogHfBXktCz1G4YRPXMFPRNqz5h3t1OnTvG+PvugW32u1GEnQqfhhlEUmPA0SiRqNNXQDv1zSBTmdzHETAIPhEkaH4Vou+jCC92CefMl7Omnn5aaRzXgoOm1fB0sg7F+oUcPad4i/rnnnhNxq03J6hT6YMWGPifX/dz/J9e9e3dJw7m19gKWctRBuB++HIYPHebuvaerlEnTG4KXY1PrSS2vpsfRlA/huWwMwnMTAepPmc9+6WWXuXETJrj7HnhABHFGkO67775zTQ440F1ycUsZSKXnFH42dYZhROjzQA0nzwqENoo+5aTRMJ41RfPqc6XPmpYzefJk6Zak6QyjKDDhaZRIVNyo0aU/J/50L4owyAiz0LgywOe+++5z/fv3FwHaqlWreLolNcr4tTy2YfjoUaNd586dpWbvzLPOcieddBKJJD7Mo37OgaNTy0qfTIQmYbVr1xbRSjo9P80DhGk421UrV8lymrqm+oMPPeSaNm0aH2unnXaS86Rstgg85t+EsNyNRXh+wCh3BCjzkY71AvSa66+XZf6k20OyJpnVkRrv3shd2qq1mz51moRRBufLVvfDcg2jrKLPLc8QP/LYx2bhP+OMM1y9evXiNLpVUvfFDvnnii2rHNH96KmnnkrGGkbRYMLTKJGocMHNnjlL5rbDT60gcUyCzsh2wGj37dvXPfHYY9IcvNtuu7kHH3wwFj4YZcBoh+KHcMIos22bNlJTwIT0jz/+eGTQ+QvSpyITsPvtFV6UzZ49W0Qry2lWq1ZN4lNfEqlQ9s033RSPnmeddZr6eQERR/49Gu8pWz4LxQ0aNEgG+hQ28ef2B0V8UjNcqWJFd2eXLm706NEyRyldE/TcEM6MyN91113dVVd2dPPmzI2uYXD91nc9DKOsoM+39gHnmec5+r//+784riD0eSJenz3s30svvSR9ykGfO01rGJsaE55GiQXDiuhhsEu5pIHGUGfn5rh9999PRlUjGllO8vLLL3ervPipVKWKe+XVPvFAJDXgaqjVIOMw2gzuYUWhYSOGS7/OV19/zVWsVDHKk7TbpNWt+sHLVterdy/3yf8+ERF80y03u8Z77hELWj12mAfYp+y+X/V1PXv1lH2pKe3xvHxezQ9169bz8dEUTGQaM2a0hENeXg7/J93GQY8bn7u/RnxOeZkR5D9nza23cs8896wb/OcfMtE9k+ozDyjfCwKVqZnq1a8nUzExkb5cN58Vmc7MAmH3hpDU62QYpQ19rvQZZ012bAG2LMv/kAv7rq8Nnht5przj2Rw/dpy79tprJR9ddS68+CIOlExtGJseE55GiSQWIX5DjSC/6jHUbKmVpO8maTLS0mUddgYEEX/fA/fLfJRALYIaeDXUavjVz5yZrImMMe/SpYvUlhJOPs3LlvSkUaNPGP0taZ7Hf8ghh7irrroqPpaix2GrZbA/Z84cd3nbtv61kSYvizfefFOWAA3zs91n332kaZt8fPZVq1a7cf64pMMVBlp2qguvB45uANS0MIvAmWeeKWKf8wTWyO/Ro4fbYYcdZGqrZUuXxteOZTr1+4zDvGPfMMoK3PM6PzCO/fAH89qehzBcZtJo1SoeeHnvvffKgheksOfJKCpMeBolFgwpzJk92+UkBQ0GmhWL+KVPPP2Zfv31VzGyJ558kkwaL/nSfbzkyC9HDTH7OJrHWWGIcJq5r7jiirjJSyEuNT/xGHpWGFq+fLmrWbOmNLFTG6vpwzzhPudP/ktat3KLFy+W83y82xNulwa7xE3sYfpjjj5KjhXli15MP/30k8RpmsJEP7Nu9ZhsCaP/J6P3EaB//vmnNMETxvly3tleKN9/730yUOrRhx9xq1mL2ucjHvEZftbiCffCupxhbDh63yM85TnyTp8HZV3PBWnh/vvvl5k0sAv0ab/kkkukBlWfV8MoCkx4GiUSNcaIlGFDh0V+L1YQZ0ccdrj80h89cpTUUiLkmDrpmWeeEX8ekjOw2VqWGnv1M2clA4OYGJ31kBWOE6L51U/eG2+8UaZ4ojaSOS+rVq0ax2taJQzjhcGa8QyWosmZmsIWLVrENR2K5qlWvboIWj5Xuhep2dk5bty4CWukLWz0WGxTPxthXC/CqWmmmX3w4MEysp/PxAT0xC35a7G7844ukubJJ58UUaroZzWMsoY+28AzoM9YQc/aGvhH8reBg6Q/Oulq1Kghzx7l4QyjKDHhaZQoQpGj299++022OPp0HnDAATLR+kVeOCLkEH/065RBPV6cxQY7udG8oHF04mcJTqC2rnLlyuIHTcOWl4LmBY7Xr18/17NnTxFcd911l9t3333jPGFaPW4clpdwvw741XXt2lXKpRmaKZ/C46mL8Vm32mrLZBgvpDwRvFpm6vEKg/D8FI7FfuoWx6jcd999133yv/+5Pffe23+E/DR/LVzkbr2lkwhQaqv5PvUa49bm12NuejCh63LFndQa2g11xZ2Czjl0xReeidRWEgZRppJ6/8tz4R0zTfD80MKgy/oC5YXboqWg7yR0RmmkJFhGw/gbaoinTJkiA1QwomqgWUaO6YsmTpwohvuOO7vIUpMqOsX5MnRwEJBPhYyMgH/iCRGRN998s+QlD0KyoNpOIC+O5nmOzXGZQJ3mecokX9inVNFjIjoXLFzoWl58sRyXtL1ffkn6d2p6Oe/keShp/kOwZrOkkdE9aSKYNQ1lS/me8LiFSXiO4VbPX87DfxeHH3aYLBna55U+IkY1DZ9/4fwF7vbbOrsd69R1z3R/Wprk42vlCbeb+vMZRmHDvcx9rbWT+Amjr7qSet+zL89Ibp705WR2iXIVysuCGUceeaSk4RnT58wwioo136KFQkG/YkqTMzYlapBV0CBcGHSjRhfBhhD78ssvxX/kUUfJoB7m9wTye7Mb+SO7LaghRqzSDwqOPfZYWZpubU1THDPVYeRpnt9+++1lvk7CwhcDDlRE8TnwM5q7datW8bRLd9xxh/RVRUsyGlw0pUc/v4Lv4EMOls8KfDrK4BwgfMmE+QoLPT+2elzQMNA04s9Id83POlNWO6IrxPbbbiszFMDq7NXur7/+km4L9evXdz1feNF/vrUPONIyjZCCbFbo/isFlVmc3PooKE/oNj3hvR3e49z3S5cuFb+i9zxbsSPe/fLLL/LDmW5IdBNChFKGOkXzFi4FXdPQrY+C8pgrPu7fsQmEp2FsPEJDCxMmTIj7A6pR1eYolnJ84cUX/OORNN6B0UXAgJZDLRvzdJ5zzjkidhCOjGaHVGMd7uPX/dtuu01qG2naZ868sF9nqpHXPFoe/a9YFQmheMQRR7iOV3ux7P3Eq6gELScuz28PO/Qw8VIOLx76Tmo3AdJpWj1mYVPQcQiLz9kj+37rzy4KT09zF150kRs1Zox7ols3t61/YZYvV94l/PdCP9C5c+e6q6++2u3iBehbb70VlwGb+vMZRmHBvRzexzz7PNOAXVm1apX4Q8ijzwA2jKnjaGLP9HYAu0KrSUHY82IUFSY8jRILNZZjR48RI0uNYDj/IzVpr77xuqteo3pUs+nD09E3ScGJGM3zXhFAPg4Dz9rn48aNE8HXs3cvmbcTP5BOXSoc7+uvv5YBSAhYBjTtscce0XkE+VLzygsjN89NGDfe3XrbrXLOW29Ty/Xq1UvySm2lP+fYBfnxy8vGC7bpM2fEn599X6QbMXy49PPicxcl4ecO/XJt6PrAXzKcfc6/ZetWbuzECe7+Bx9wW269lb8u+bXV06ZNc60vaeV2320398EHH7js5HdPjTFOril+Xz4ONEyul2EUY/T5APzYKexAOj5//y5dusyH+HB/K4f3NY77nR9n02ZMl7lzb+50i/R3j5+voGzDKEpMeBolFowtA4ty8/Kn3cH40lR9zTXXuP3231+EjRjupIAEMcA+bQgihpV1KKNjx45u/333iyZv/gfGmjk3ddolaivbtWsn54CY1fwFlcOxqK2leZ5R+OTRlY2otWQFIsoQAZrMTx4Q4ZYMe/PNN0Xw6uenzDFjxkicpiNO8xYlnAPno98H/tBpGOfNdRzjf1gwJQzrwIPmmzRxkrugxfmu6UEHue+//c7l+c+fiwj15XMtQMtRtHzDyIf7aV2uaNH7OeF/kMV+v2XqNPXj4LPPPnPvvPOO3OcHH3yw2ECw+9749xT0TITu3/Hvc/5jUk+0tDmjqEBgjZsw3mV4wYbAQJSwQs6hhx8mk5KrQQb8oQGWOJw34NOmTnMdrmgvwo8lHamxJG1q/oLA+COQaJ7ffPPNpWkrzItf91PLILxTp05u+PDhcmz8DIwSkklJE6JlsaWml1rWL774Qs5DBSoOQa5+qfksJnA+ulV/iIapaGdwRPsrO8j3zHeKKFdRz3c+cvgId9IJJ7pjjz5G5gnV6wDEc61UfKZe/7JBqr0yt6YrnnDv6/2qzwT71PAjOrmn9RkA5gumqw/Q5/3555+X50Qp6FnbNBR0zc2VHFc4FF7JhlFIqPD6wwsNNb7sszY6S0tKzaVPl+vD1TAD+dQhTtgSf+EFF0jfKAw10yCxpbzQWKcabm3+fuyxx9x3330n5VFbifhMTasQrscnb98vv3Iv9HxRmooPOuggd/3118eCyydyBZUieX085z1w4EAZeIPYIh9xytChQ6XpuaSi1wm4trxMr7nuWjdp0iSZoor+s+WzsuSzA6sjHXbIoa7FuefJADGukV5vuZ6GUUIIn+Pw/qX5nHl6c2ls90HyIyvNv8K9EL3x+hvc1MlTxM88uFtttZXkCe/9sFzDKEpMeBolDhUUjN5UvEyRms/33ntPREm0n7GGINN8gt/Q35MlLakpI/yee+5xDRo0EL+k45+mT6JxOFZE0hGjt956qzvwwANjQ59q8MNw3Jy5c6WmlPNjCTv6dWo6nNbahYTlMNiGgVDU+upnDGv6ENLTpk6VcFxJQT+/Ovp8ajgwUOKaa6914ydMcDfdcourUqlS/Plx//vf/1zj3RtJf12uEdck/PGBX9OqM4ziSni/4s/JiZa+5LZlS6sHNq9Pnz5yr5986imuefPm8TNBHn12dGsYRY0JT6PEocZ45owZsR9De/rpp7vdd9/dW2R/Y3sjnGpwZfBNEvL88MMPMkk5eU8743QZDYpf86qZxq9GnC21CgsWLHAXXXSR1Do0a9bMXXfddVJTGh4XSM++5pUaOp+/bZs2buHChRLGBPUsq0le0Px6XCA/DiiDpSc5B86X6aMQofhBz4HPF3+WZJklBT1nf/b5fq5PUohWrFhR5lgdOWaMzJsqqyD5NHqde/fs5XbecSd30w03unlz58k112vJNtVpuGEUNdzH3ItsuW9DtJmd7jMZaelSu89E8aStufVWMiUZ6HOvNgHs/jaKCyY8jRIJRpW5H6W5yRtZmpz233//WHhImsDO4lUpSZqlS5a4jh06SDl16tZx3bt3lzQ6Mj4kfgkk4ZgMCJo7Z46rtXUtEa9KfOxk+jAfcK6sIvL999/7c05z11x9jTvssMPWSI8rqBwcNRzU0tKHE6jd/fjjj+OJ6jUv58jqQPh1tLeWVRIJz53R7/4TSX/eLbbcQtayHzpsmPwQYMoZrrFOw8SLuN7OO4tIXb1yVXxP6PUF/CX9+hilD71Hw3sV28VdShhzel5w/vlu5cqVIjDp6oM9kB+3pJH/87H72ygumPA0ShQYXv01T1M3WxzG9pBDDnEZ6RleaHnjnLS6fzO1SePLiE+m5qHm7MUXXpQ+hCpa1WDrVssH0rCcJrWJwDyhrIOsrMu4U/bYsWOlWZ5ymjRp4m6/4/Y4TsGv5cj5JB0gOBG6nA9pXn/9dVlak+mb2Ne8Ir58Ft3XuBLHWk5ZP49+pto71HbPPvecCNBzzj5bul3IZ086fljstNNO0TKcyXlf+Q5CSuT1MUol3N8g93Dy+QUEJlOwsX/TTTfJ7BX82Lrl1k7x0rz8IONOJovmB7u/jeKCCU+jRMKa5kymjHjAYZD3228/b3ATMg0SwguQFl5OYnWjmgJvtN95+x2pDUS8XX/jDW6PvfaUtNRA0nwVmWlvuJPNuqHB/vbbb93jjz8uxrxDx44ybUlBaB7ODT9b+l1eeOGF0i+Tfp3P9+ixRlMYaD624XHxs/58m0svk7I4PoOR9PhVqlSJBzbJNUmkubHjxvtPjkjP7+da4tAvI4m+RAG/7ovQ9n/UXr/Yu5f7ddAgd/xJJ7lcPreP45osXrTI3dqpk9uh9g7u4Ycflu+fq0KNsJaj14mab+6b1O/BMDYVet9xbzI3L5TL8vYikeu++aave6XPK97WpcuPzhtuuCESpdzLPht3c5q3AanPi2EUB0x4GiWKqCYv4b7t1y8WYISx0hCGN9W4IkYU8k2aPMldc/XVkq5J06Yi3vCTl3K0PESJCJPA+DNY5bLLLpPRpdRW3tmlS5wHB5qerTrOk/LpB0oNBRPFv/Dii26bbbaReM0bQh6Or37SUFM6efJk8SOymT6F2g49/uGHHx6fD3kZAc78oHpOpQU+H58z/L5At4TV36W+e/OtN9033/YTcU6c/Ajx14Wpr+75v7vdzjvv7J5/7jl5SXO99JrLdfeXLC/5ttfv0TA2JdzHPL/aN5197lGa2K+9+hpp3UnPzJQp1fQHbPhcpP5oM4zigglPo8SBUWXuSxVkbGlmT6R0xE+FvlAXX3yx1JRSQ8iyluTHhcICf2y8PZRPGLWVDAiiab33yy+JsSdOBQ9oHgjLZJL3V199VQbBMBjgiCOPcGnJY5AuzIcfR/laxueffy5zhELlypVlOU8GM2leHKuUaBjnRH9Q1rIvzfC59RrpFvT745p8/uUXMrk2k/sDa8HzQp8/d54MPqq/cz331htvSk2R5pPvPPmzRWrMfZhhbCr0Xl65epXck9gC7tnp06eLDZsxY4bcp127dnX16tUTP+jWMIozJjyNEgdGmT6WamQxzDvuuGM06CQQHyDNTsmgDh06uJEjR0qNFn3+tqxZM06farDZ1zDS33HHHdKnlGMxCp158nLy8icrV8Lja376dV511VUiCvfaay/pIyr4aASOoulTywhXRiKOforU8Gq8CmNEFueq6XhZDRs2LD5HLb+0oZ8r9fNxDQjjmhxy2KHuf59+6r78+muZhSDLXxsVoLNnzpSabCbv/+H7qO8uJTFgjf7CbFWEGsamgnt3xaqVMs8v3XP40UoLDfMGw9FHH+3atrtcWlDUBhhGScCEp1GiwLgixPjFDxhcDHTDhg3XaXgZSc7E8qQ965yzZb67dG+wQcsIUUOOYwR6t27dJIy1kKV21YeTR9OkouVRu0pNKVsGMjHyFCGoYjAUrqnlIJg4JiPWaR4m7RlnnCHz9FF+mBfo60Ue0HOjWU7LpazSDp9bHdcn3EdNssTmm/4++PmXX9xJJ50kk9BLOn+NWKf/xBNPcKedcqrUqDNljXy//FGbjj/FGcbGJry/6BfOlns0/FG55VY1Xc/evZI5Ijui9kDzFkRo18I0a0tvGIXBmm8uwyjmYCBpdubXP2u0q0Gmf6OXF7FhDt2gQYPizvfUFFJjKGLDp2VLOIg4SaL+mdNnyDyRcNRRR8lURqCGXl0qHJcyruxwpdR4sk9N6dZbby3Gn7jQhahAJJzm+a+++kr269WvJ/25wmOG+WmCZ9CSwnVBpOvLJvU4pRm9LqnOMWDMu90bN3Z9Xn/dffPtt27/Aw/kC5VrRPeEfv36uSYHHOjOPvtsN/TPITIgzUfGPwTYkha/OvYNY2PB8809NW9eNActsI/DXrHgRCX/vHMvUyMa3n/xvZ6EuPAexQ9aHoTpDaOwMeFplCgwkBMmTJCXv7Z90l9TBR2oEWU7b85cd/55LcR4I1apcWRATsjajC7HoIl70YKFUj7GXtOGRpst4boP+BGN777zjjT105R7zDHHyDmmpk09vu4z3RPzTwKf8c033nTlypdfIy9oerY0F4flMdcppB6jLMFn54rh/OtXwqj99N+g23vffdzX33zj3njjDak1z8rMir+jzz/9zDVtcpBrduxxbsDPv0iTO+Fru5ap34th/BvkfvX3Et1AclZHU38B4YhOauqbND3IpWdlxjZvXRR0v5JP71e7b41NjQlPo0SBEWVkN8ZSDSpNzKA1l8ThqL264IILZDQ6/SsZFd6oUaM1DG5olDVcjTLN89qX9OXeL7lq1arF6dniCioLP0211157rexzzAfufyBOE6YN0TC2nMOll14qTeXUfnAudenHWkA+oExc48aN4zTsT5kyZa15ygTBO5XrAbKGffKaSM2x955w4okyR+pzzz0nsw1oHAZywM8/S3+600491Y0bO1auJ/eW1kqxr84wNhZas8595X/yyA9YJojv8eILLj1p6+ReTqL3t8KPLMK0DGXAgAHShB+SmtcwChMTnkbJAdvo3R+/D45WGEra0njFIu9kMJE3shhS1l4fmJxkvukhB7uOV18lxpjO+IRpOnUKNVuTJ05yd3S+XaZOuvyKdlENAyIlQPL7bdjUxXksXrw4v19n5UrulVf7xP1JgXy6lZeD94fnQBnMM8kLAhiYdPzxx8vgKS1Hy5BVibyXfRxN7QhwyuB858ye5c/Dv2QS9P1cs3Yk/xOXXuS7Ycv/0SXLn5/Vb7j+OG2yPP/8893o0aPdgw/c72pUry7T1eTIfZVw337zjdt7jz3dhedf4ObMmi3XOPwetCy5F/le1jXLQnRShvE3QlukdkGecf/s08e8UoWKLsPfzOk+PJNaeJ9c70PNy1YHVeJHxOZm57izmp/pjj32WPcOLTE+j5av6QxjU2DC0ygRiFH0jlVnxo8fHxtMxNW22277N8OLaHvkkUfEv8UWW8hURF6ayb6mCfPgEAwY6NXZq0WAMJK0du3a7q677pK0OI6HsNO8IH0A2SbPh/k6WUOZ/ccee0zK0Lw4LUuJB7Ekz4E+qffee6/4Dz30UNclOV+o5mULcTle4Oi5M4m8pmM/3QsqmVIpOJ7y95DSB58R56+IOBYIEL+/HrJYQPIasi/X0l8vvt927Tu4cf4+u6PLHVLTjQCV78f/4Pnwww9dgwYNXAefhq4cgo/LzcmRuT9VeHJg/V7/hp6YYaQg92Fyq457iFYbauN1WVjt+hHaA0XvO+5FIE3LSy5xX3zxhfixbcRr+YaxKTHhaZQoBg8eHBtVNbhh8zksW7ZMmqkljRcRPXv2dFtuuWU83ZI3tWukV8OuRpi8o8aMlvJT+4Rqvnjr/9Rws/3kk0/cW2+9JeLlvPPOc+ecc46Uk3oM/FqGhgGj11u1aiVxiEia2OmbGqJpgeOTluPRLI/Ypm8YkE6E7MCBnHB8PCP6/rg+IkK5I5LfgVxbakT9vwoVK7gbb7rJTZg0UfraVqhUyWVmlZNriuvj7w0E6O23dXbLly0XIYCA1e/bMP4Nem+GEKbPefgcazoNS90H7tWnn37avf/ee5KfpTVbtmxp96hRZJjwNEoEaiR/+eWXZE1eNJodo7rnntGSlwrNUQzMIc/ll18utYaSP88b7nSWnIuMcqoBpzwGEH3wwQfiv7vrPSJqVeCG6PmoaKGsWbNmufbtrpD0derUcU888YTEcY6SNiiHcJzmB8q4+MKLZJJowqilrVmzZpy/IEQ4+XJJI597ytQ1Xk7Z2TmyWlLYF8xYO3rduKb4cv11ZbaA227vLNeRbg+VvACVWRWys12OF/lP+u95x7p13f333udWLo/6zlGOlqXfr2H8E7hfuHd4jtWvtiP1R6iSeo+xr47Wl9tvvz0uj37MoS2C1PyGUZiY8DSKNfoCF+f3aYZGZLEPiAKa0sGbWfe/jz+REco5OTky6Oiuu/9P+kYBxhbzGhpdLQeYbJ1pl2jSOvnkk2WFIREgQRpFz0n9GO4r23eQ/p28HFgVqUKFChKuBl/RvKnu3nu6ypyh+KmRYEALZen5UgZxBdG/f3/39ptvSRquj6ZlS5ls7dWSD9ejIMJw/GGf2s222Fx+jNAHlNkOuPeAe2350qXuvvvuc3WTAnTVipVyP+p3i9P7NnSGERLeEzz75cuXj+9J4rAl6yK8r/R+Yzo4Vm0jL92AWCo2VXjC2p4Jw9jY/P3uM4xiRmyM/VZX7SAMQ6nLxdHPcuSIEWJk6VTPZO3Mm6nN5KQJDauWiRTFQC9ZskRGwFPTWatWLZkvk/BUA61lqFGXbV7CvfB8D5lvk3iaZRG94fEUPe818vtz/+Wnn90DDzwgxyMvg4tCwallsSUf56k1vsuWLnOXt2kr8YSRhrzRZ0zIZPsrV6yI8vpjER7FGQURXm+tkVbHdd2i5pbuwQcfdEP9/Xbu+S38D5sMlyA934W/j+ifW6duHfeQT7N61Wqpaed70jL12uu+YaSi9xstJxA+r+t6dlPvrfvvv98NGTJE9uvuWNfdcsstEq7lqzOMTYkJT6NYo4YRg8q0SLNnz5aXvxpL5q1EbNG/kQm/ly9fLnG8/BGl5MNpet1qOE3QCNV27dpJEzdl06+TaUuA9JonFfIjKkaNHOluu+02ERcHHXSQTKOkohHC/Pj1fGTri2D9d/p1kocaDtZhT51rVNG86hgg0/HKK6VrAVD727FjR6ndiM4hErnh2vagxzf+TniNQ7haMosA1y09TZZNfb5HD/fHkD/dWWedJdeb657w9+OyxUtkUBpN8I8++qjLzcmNRrnjktj1N1LRe07vDbUD3FvEMVPGP4H8f/75p/yYZSAR8wC/+8670uc99b42jE2NCU+jWIMBVcHEwB0Msdb08ZLXOTyv9OJr+tSpLtMb6BNOOEEGCJEOyEs56tjHkEu5Pp6lND/5+GNJi2jUSdg1DaixJj9omctXrJCaUgb0MPq5xwsvJAXfmmg+3SppPi3NtjNnzpTPwyAAVlcK0+HXfT0usGWSegYz6fXA37RpU9knnrPOyMh0Q4cOlWPp5zEiuJLqlDW+62QE/vjPR5OGwWoI0R133FFq1wf99ps75dRTXGZWlsvIzHR5/v5btGiRzEpQb+ed3Uu9e0tZ/NjAGcb6CPt0YmO0xWdtqH0gLf3b1S7QglN7hx1cpglPoxhgwtMo1mBEVQBOmTbVZefmuLQMDCx967Ld7rvv7t59+x0ZELTK/7LffMst3fMv9BBjK8LBIyLMpxeXLFPKTUsXwUe/Tgps7EXsrZ1vE4EmefMikSrpyRfkB8RDq0sucRMnT5IasCef6e5qbbuN5Jd4n5c/Mmk5/kwkTprEvfc5/0Lo27evfEZqbM84s7n0MS0IyZ8UjvgZNMCAIqAv4rPPP+cOOrip23XXXX28Py61nd7l5Oa5ceMnyjETafnC015AXKF8l4p8Zz6Cb0wuZzIMmEeW75I9+aHhv/96DXZxr7z2mvuh/4/u8COPjPsW5+TkuPlz57r27dq5hrvsIj90FLm3ko7y5FhrcUbZgHtBKZcZCU/CEKH80NYf1MA9o7Xw2AZ1tPjQFxlbcvrpp0uf9cyszPg+Bnv+jaLChKdR7NEXM83oGN2cnFwRlsC8dtffeIMYWwzpy6+84qpXry5+jC5b0oY1TKF4YylLaqWoSX2+x/OSntc/21BA+sTiJ06Ne48ePdyXX34p4c2bN3enn3a61IJF8iEqX7b8eb+cY/I8aCIfMWKENNFT/jZesD7+xBP56ThmktBPPNeA5jPmGmUFEl5I7a9oL1M38Zl32GGHZOqkaPaOuU/lMwVlGeuHq4Wjr6f09/TfH99dZnqGOK3d5rriZ8sPmA8/+tC95QUmc7jynXDHcR/SnePiiy8WAfHRhx/Jd63fOT90qCWVeV39H3OGyr3j/4yygz6nOO4Z7ivuEfZ1TmD2Fe5PvY+IY8o5unfwg4f+6t27d49/zFKW3qeGUVSY8DSKNWpkMZZ0ksfApvsXfm4uTUiZbp999nHz5s2TtC1atHBND24aG+XULaJBRASG1/uf7NbN/fTTT7J/9913u1122UX8kpbj+j+2sZFGGHjRCyOHj3CdOnWSOMQvUyeJRPDHio+XLAMIo2yJ8+UwypSR6zrn5ku9X3IVypcXf3w8j5anLxbAT/9B+m1mZGW6/Q88wN1zb1cpnzim+2HeUvb1mDKJvCcs29hwUq8f+6lh+p2deOKJbvjIEdLPju8DEcH3k+HTjxszxl3ofzgc0vRg99WXX4moJU7LIr+U7b9yvW+NsofYI28v2HI/MFBwDTAnyfuGe4YfonTdwc/9xpRs9O+E1PvUMIoKE55GsUZfwMCUQUCYGGQPNX/4N99yC/fwo4+IX+OosZSXd2BwMdJAn0fEJvssp0l/KNGI3jEIhGMo+EmnxpyBTBdddJHEUStFzSdT68gAkiAf6PE5J8qgeZ/tTUxMPm6c1ER0vKqj29sLaOq3NK2Wo+eu5RDOXKbdvGgmHYOg6OepccrBBx8s++oQ50xObxQeev31O9Rt+ys7uAkTJ7q7u3Z1W2+9dVwTz0pHw/yPqeannSZzzf74/Q+SHxCbCA7S4Yyyhz67CjWYuiJaHO63altwLPM7YcIEsVMdOnRwTZo0kbR2DxnFCROeRrEHozllyhSpJVSjGxpTDC8Tv/PLnnAMsKL7bIGapaVLlkptI6K1UpXKsjqQxFEe/2guZ+v3NR9+joMw7XBFezd58mQJa++NOyPZIcsLCkkTgJikDJye72effSbnm52b6xo1buTu6NJFjkm8HpNy1A/4WY5xxbLlrk2bNhLOi4hBA6xwBLxstAyacnUfKK9fv37iV7RsY+Og116vuX6P3H/0r2Py+bFeFHS97z5Xo0YNEaCkIf3vv/8uNaQnNDs+nv5Gy1iXM0onfLd6DwD73Ed0NxKb4qPUzql9+3XAr+7555+XfRa+uPPOOyU+1SYZRlFjd6RRrNGXK0IPIQX6MlfjfOONN7pjjjlGwtX5CEkLasC1RvKKdu2kPAw4TeT0gyINDmFKrSToa51jEUdN6DvvvOM++ijqm7dLwwbunnvuifL5Y2p++gD6HclPzVV8rv5v5owZ8cT0zDXa+6WX5HPhtAxcKhybUEbdz5gWrWxE14Ljjz9e8pFfrweuUaPdJUzPHcaNGydpwmtnFA5cW7kPPfq9IhYYBHZlx45ujP8urrvhBlfe3wMJ/6NDvxNq9Zs2OcideUZzN2nCRMlPOJBGBojZd1dm0O9eySofTa/Ej05adGSgkbcNy/yP6cvbtpX7gq42tILw/Mt9lyzD7hmjuGDC0yjWYCx54f7xxx/xi9zvej+1i5muWbNmMl0NhMItkfwDeVH7P+IffuQRmZYJTj31VBlJHr7INT9ofvJR2zh92jR37TXXyD7zbWLctdO+EubV/PIC8F4GjlxyySUymIl8995/nwwESn25yPkHYeL3jgnqWZUJtF8pLx9GtSKi42P7fZpueTlxruxzDTmulpt6DKNw4L7T78V7/M3k7+dEntS033HHHW7UqFGubZu2cj/xXamwZNAaMzZc1vpS/2NlpogLysGpSDXKBnr/sKWVhnuEeyWHGT4wDT7uxptuipfafeqpp9x2220X5zOM4oYJT6NYg/HEyDI1CJMnh0aYpnX6V67PwBLPi/q7b791D9x/v7y4a20TrU6E0ab8EBWMITTD02mfzvvkp48lq4qEQm5tyMThnv/7v/+T/plM4nz4kUeICOXYYd5UQcE+8YjGK9u3l3lKgUnmWZJT8NlTj89E8vQ71fIQodrUrmnXdc7Gxkd+ivB9JGs42dI3+ZHHHnUjRo10F7dsKT9IcPT/zPDf9euvv+4aNmggSx1yD4B9b2WH2B54G4KfwYhsxab4f/zw/OzTT93rr70m4aeccoo744wz4hYUhXsmLsswihgTnkbxBgPr3ZoDiyTCvfZaH7flVjXlBQ5qXMXAYmPZJI0tg2voG4kAq1Cponv9jTdcZUZ7+njyqSM9tQjqtLynnu7ufh7wi9QsMtemTF2UHjX9x/n8Vvf1vMV5fvypv3vsicdlbsfqNaq7Z7zoxa8vCD0+6DnruVAGInX23Lkuz6e58eab3IEHHihpEMQ07cv5JvMD3t0aNkjuQZr74/c/kzVqkeOzGIVM/lcSdeOgBjTluwJqsJ/q/pQbOXqUa3Vpa1fe36PJG11quei716D+Lu6eu+9xOauzJVzwZXGfyLyifss3at9qyUfvD55vtQeEseQt9kD6o/tw7Bp9h7Eh1bxdeeLJblFa7gufljxaVuo9ZxhFhQlPo3jjjeWKlSvdmDFj4l/wiLUjjjjCHX300VFYUtwpGFiaoXgNi7H2BvrS1q3dnDlzJP1jjz0WrXjk7TBlgRp3CA004cOGDZOO+tRSsUwiTVmIXemz58vDpRr1sLxFCxfKqHltRmVJzppeMGtf0oIgnbrnnnvOffvtt+Lf/4D9ZS14jkfNGFt1IZwrzW3aFYBjkZ9+nppWRK2xSdHvSu8bvXfUz3f2+OOPy7yrN/kfGPTX4zukeX7ZsmWy/jvdMx64737Zlzk//ffKd8k9TzqZ/9OHGSUf7okQvX/4folrc9llbv78+RJHKwxzGMs95X/UikumN4zihAlPo3jjDewP33//N+OZOk1IGE+41gIy7+YTjz0uwo2madbUPr/F+ZHh9spTywjLIQzYrly+wl3aqrXUMiFSWRqRcsLjrQtKYmUkRuUzST3rqHPuIgTXUTel54HovfXWW8XPXJB9+vSJBaemKwjCd9xpRzlnLYt8gwYNSqYwigq9v5Twu9Q4BASLC0yYNFHmi61SuYoICmrsGdnMoLY6tXeQGREW/7VY8lADrzViRumAWmzg3sCeZa9aLbYN29W7Zy/3Xb9+EkfzOn3Wed6lG4dhFGNMeBrFGswuU83wQsZpDcC2224bvbD9S1Zf3IruY4CZmoaXNPmYQ7Hbk0/y5v9bHkVf/DJRvC+b2kVqn+CWW25xBxxwgPip7VzX613L//iTj90bb70px99zzz1lIJSIQR/Hy2Ot+GMvX7pMmtipKWV1otfffENqXJVUARPCS6pp04NFqKgQwT9xwgTxryuvUbik3nvhd0EcjvuFcOZp7XTbrVJTfc0110gNKPHEMb3Yo4884nbacUd3p7+v6H+seTWNUXIJvz/8fKfYAZ5j5urs7H+QArNyMNAQdOAROcN7wO4FozhhwtMo1tCXaeHChdLPDcGGAcWx9jBgXBU1zrpdvmy5a9WqlRhqavt6vdTbla9QnkL/lk+dQvw3/fq53j4P4ccdd5zUXBKOYdc0YV51wHbu3LmyljrHZqAPtaVaA6nHLyivcuWVV7pxE7zo9ed75//d5fbbb7810qg4gdT8rEF//XXXieiU801GjR07lsTRjlHkhPcC6D4/mvjedEv/PX5AjR4zRhYvIAzHvc2gu0cfedTtWLeue8xvqZ1PvS/Ce8MoOei9wZbvEDsITA7PD410b1sYJMkPFOCeIB12U+8l0K1hFAdMeBrFGowotT36EgZqfbbffnsJU4OqL1dNQ41f2zZtpIkbsdf1vntlec0wfWiMNT8OscYqP1d17ChN4qyjztJzxHFMoHxyUwZO8nk4PrWl1Ga2b3eFiGZqIZ555pn4nOPjBKzxOXLzpEn9vffekzCmRuJFQ14+i4pXCPNxHECMMPhp2rRpsg+k49xk6Uzv13xG8ULvDf2O2bIv35d3dLd4qnt3N2rMaNfigvPjbh/071yyeIn0RWbp1549e8ZlcV9wT/D9axjOKHnQ1/3222+XpX4zsrJc69at3aGHHyZL56o91GfbvmOjuGLC0yjeeCMa9kvEuFLzB6mGVQ0uL1oG5Hzx2WcSdtIpJ7vLLrtMKv0SPgkuFX0Zk55+VfTFZLL3jMwM99LLL7sq1arGolGPo+h5qOhlj9pN5mIkjlWSTjrpJIkD8msZuiUv580+y+IxUTzT6dDXj5WVwjx6rkKyGV3jKecKL3i1ewKwZcAJTJ8+w82ePTs+V6N4od+juvh7Br7+pKu1zTbu6Wefcb8N/t2devppLjMjU8L5XmfMmikjnevVrycrZHHfar9guRf0Pg3LNoolzP2rMHPBn0OHyAwb+OvtUt/d98D9Esd3qd8n37Ns5WYxjOKHCU+jWDN/3jwRSsALk5fo/vvvL/vhi1kMr7ezbIcPHSYDM5jjjtofEW4Z9Hv6u3FWKBfHMRh1/uGHH0pt08233OL23nvvZKqofPKKUfdF6T6wpaZzwvjxspoSZTVs2NA9+uijUZ6UY4KeD3A8Bo5ceOGFUkMF1JTWrFlT/Klo3rAMzps5/RCxfB6OSXxGelSDVq5clvu2Xz+JM4on4fda0H1DrIxe9z86dtppJ6kd//77793xzY6XeL5b7p9p06dLTXm9evXca/6e0HtK74vUco3iQ0HPNt+XtmowhzF2CrtGVxxJlfxO5XvNz2YYxQ57+xjFCgxtaHT7fvWV1NYg4jCozD3Jy1ZhX+YvJI9/ESPcGJBDX6jMrCzXJ7l0HIKQ5nHSsA2PA1oLxEoyN1x/vRxz3/32czfddJO8qEkbG3UPIlYqFDinoJxV2atFONL/in5XrG7EgADyUYZ+Dj22lgeEMYBp+PDhEs6E4s2O92IiOXUTEK4OVGxzOnNnz3FXXdlR9jO9wDzu+Gbuuhv8Z/H+3ESOXKvsnDw3YuRIMvnTt1rP4oh+t7r9G/67Y2RzVrIZHvbaZ2/33gfvu77ffO0OOugguWdJQ7eNWTNmujaXXiYD47QWXub95C72fu5f9ilJw6KdqGxj08L11+8+l++DZ1yfcw/2jIUFsIPYNbFtPlzm9kyi9ok8ocP+sEXAqs1jP9waRmFjwtMoVqiBxGEYhw8bJiIyNJL0eVQBlwxMbhLuiiuucKzDDg899JCru2Nd8QMvYxxoeWzJB8yLePHFF7vs3BwRi7oqEg5jr351kJvnXw1BWdR0jvTCjuMwH6OKZNKLGPDlgH7G0H3xxRfSNIrQJN/DjzzsMjmuvlx8GaQL84fnz2enbyrsuOOO0s9vt912k33Ni9PVT1SwqzOKP3rvqdP7knuLLaLz66+/dp999pnMdVuufDn5bokbOXyEa968uTw/P37/g8vNzpFaUJkL1ItM7uX4fsrXMEYREtor/Z5ZxeqYY46R7x6n330q4TMd2gnQ/TC8oDIMozAw4WkUOzCAGEQM6p9//imGEb8ayPr168s+v9qp0VEDSrP0xx9/LC/TE088UWoeQQ1quCU/efCTH9euXTsZ9U0YqwwxZZMeE0I/sC81Dr4soJkbscrLgKXrGOCj5euxtYzUfUbAM8k8ZVWsWFGmTqIcYkm5tnLYkufVPn2kNotrwuArml+rVasmLyiuh6Yl/4wZM6UbgpZllCz43lLvg1QQl5988on7+KOP3V577SXp+THFwLc/fh/sjj+umWt27HFuwM+/8JNG7jFqSHU1LsH/ADI2PeFziR87BTzn9PlmjX+1XRsCebAzTZs2dZ07d5awtd0/hlGYmPA0ihUYUxVTGMoBAwaIX8PorxamQZyRjjXQaabGX3Prrdwzz0VLUmqZEBpZzc+WPPQDff/99+XlfPrpp7vzzjvPpWdGtUmkwaUaevY1HsHavn17mSSeqW84Ps1jmq4gNC/HZ/ATa3Gzz8pK1FiKOPTpUo+PH3R/2tRpMtUTn4fzf7zbE65BgwaSjnk/VUBr+p9//km2PnCt52aUDPj+CvoOCeM7Z8Rzf/99P/f883IvcH8m/I8T1vz/5aefZJqwE44/3v0+6DdJz48UzWsUD/g+eLb5UUktNn7c+gjvC75P5n3lBzlzG3/33XdSBmns+zY2NSY8jWIFBhBDiJHl1zlNx4QhzoCBPpoGSMeUSWeffbaEI0TpdE9tX5gO1E+4OsKYooQaAPp1ItIYEa+E6dQPHFfPiXkUW7RoIf1LCevdu7fM2xnmwa/Hh7As5uFjZSVg9Duid215NY/u01+15cUXu6VLl0oYtaycCwKUzwOs667pERZMs7TKv4R8YFyeUTrQ7xlCcdLi/BbSf/nee++VKZlARrr777//Dz+4I4880p1x2uluyuQp8X2nfZd1X/3c47pvbFzC68p3idNrjm37p6umhWnwcy/QosM9gP/MM8+M7Zdi36mxqTDhaRQr1GBiHH/77beohsYbRA1nlDp+ffmxpOU5Z53tFi/6S16kTCOjgytwpFUXovurV66S2kb6PZIf0YqBD/NKk3dwDmqgZT8v4TrdfIsbN2as5KEsmjk1P3k1v+YD4tgnnzZ7MXodEYo41Hx6zFQQvhz77rvvlummKItrwwomelw93u677x6Xwxb3gxcbPoGEGaUL/Y5xeg/hGGTGogTDvfi4y983VfyPM+aCFAHiXd++fV3jRo3cJRe3dKNHj5b7QycsJ406yoLwfjY2DuG1xfH9AVueeewUtmV9kFe/L/IxGImuQJRfp04dmS5O7wsI/YZR2JjwNIodGE2M4K+//ioiTPcxuEzCzr4aX4QmzdwYZpakRMRhbEGbuoE8OIXySEd/qRHDolHkrIneyL94Q8Ouxli3iub/6quvpIaTfQYEPfjgg3FajpZ6TIVwXuqMwKffHXFMeUNNqfTFS740CMeF588+jfD9+vWTqZpIR79QRvCXK19e0gBN9XwWmu219pMyCNOR86Db8FyNkoneJ/pd+p9n8fcLPBOVq1R2V197jawDzxKuVatXlzTUfuLeffddWWzhggsukNpx7i8tk3RadliusXGR78M7ntXwmusPcfgn1580M2bMkAFJCFDsAP2/KUfz/5NyDGNjYsLTKJbwsvtt0CCX442lGkZEKAMlMLzE8yv+jTfeEL9OXRQb6hRbSlhoYMlDPyea1SmvyQEHyqTt5FfDzlb9Sri/YMEC6ddJmAwI8ucTCzzvOJoeMzw2kIdVZhCAiOYbr79BXvb4ieM8QsLzZ0DVwkWLXJs2beRlQjgj6Hfeeec4H2XwB02aNIlqSD2kRfDOmjU7FvU4jTNKNnqfhN8l4pPnQe9cjecHznXXXy8/3FpfeqnL8PcuP1Z4Nvgx9NFHH8mPOfoPz58/X/LofQR63xiFh9oDnNqm8LtdG6Tje2TLTB3M2EF+fmjQAqJl/pOyDGNjY8LTKFZgDIEavSF/DuEtKfv6styjUWNJw1rk11xzjcTxUn3iyW6ymovOeUl+mbezAAjXuQ0pk5GiPXv3iuKSxwEMtfoVjWf6GfLTD5XzefjRR1y9+vXjl7yslezTcwrhaajB//nnn93TTz8taXdrtLu7tfNt8pKRspPXQPx+S5nqJL/P08EL3jlz5sgAKFauOee8c106g6l8HGnkPH1m/DogC9jPzU24gQN/jYSGL5UjaJxRuuAe4FmQ50HDuDeS90NuItdVrlrFPdbtCTfU/wg669xz5McTK3Zlr1otA1KYLaL+zvXcTTfc6JYtXSb5BO7P5D3D1u6f/07q9Uy9pnxvKihT44Aw4vnecQ898KB/1geKLaMLEF0t8KttW1s5hlGYmPA0ihUYQ4wiA3ZYsQiRheAinEERKs6YeojBPPhPPfVUmZ8Q4cW+on41xjk5OVJjw/b888+XGkvCWYJuG0RrkrAMRQ00jjJe6NFDmrrhhBNOkPLSvOgNDXqEz+OPwXG0toiBQFpbyUue+TbDl4Fuw/OX8pITelPLy7RRhHHe3bt3l9orvTap+dlnCiqNx9EvlOugacL0RslHv8/wO03d575gRSu23J/b195eZndguVVWQeJ+wXGfca/wQ2nHunVFzMiz5J3em+QH3Ve/8e/Q60iTON8P8N1hM8LvUCEtcXwPEu/d0KFD3QMPPCDfIS0yOi+xlgfsF1SeYRQmJjyNYgdGdNy4cXGztRrKPfbYQ37FP9XtSfddv2+lOZApYp566qnYeHozKtsQNa5aDv06//jjD9k/66yzZM5Nza8vy4KMsb4MJkyY4Drfcbv4N998c3khg+Tx2aW2wfuTJYlfHdAvderUqbJPcztN5Pj15a3pFC8jpUyOhxhnNSXSIDZZE55uBsSF+dkPYcBV/FLysLLSiOHD43RsU/MYpRfug/A+41nQ73/HnXZy7773nvv000/drrvuGvcr5P7hB+Fdd93l6u20s/xgIjwUQ1qG3UsbB64/15LvR5/ftV1j/Q5It9p/T23btpXBSECXoq233lry2HdjFDUmPI1iB4Zx8ODB8ktdjS2Gl1V4vv/hB+mn5CNcpQoVZEAO4i98iaa+BNVY477/7vuoidv7t6q1tdR24g+Po2j+EMIuuugieQGzzCAv3+qb1ZC8iMNU3au7lA/vvfOuDN7gOEzkTNOXknreoPn13Fh7e9GChS4jK9Nde/110i9U49Vpft3n2IcddpiE6Xkg6n8dOFD8KadslCG4P3TLvcE9Rs29v4lkiiVqxl94vofbud7O8jwC99esWbPcNVddLcIIgUoYTsvRco1/B9cPJ9+H3+ozzbXle9Drq+G6BX4IMNsFUyfxnJ922mkyTRt+tW9avmEUBSY8jWLJlKlTRdx56xg3kdNcfN6550ZTingjyij0A5s0iY0oK6+oigoNMX4MLoLt8rZtJYzJ5RGtOi+eGniJC7bkxYlgy0u4Lrff4UaMGCH7NJfTb0pfyKTX2k5JH0AYcyReffXV4ue4jIbXOIVjsa/HxQHl9Xn5Fff1V30lvmHDhq5Tp07xsRVND+qndvP++++XfHosrufcOXPET9nhORhlC/3uESbcC/Is+OeD+4f7+exzz3FDhw5zL774oswqwT2nAoZ7mjl0mdicxR64r4jTezfVGeuG7yK8VtgJhevKSm5cY0hNq9/dsGHD3JNPPinxtAgx8JDvLP5u7Vk3ihgTnkaxA0M6bOhQ3RFDicG8/vrr3YJFC8V/+OGHu+tuvFFqZ9TwshXh5x21kfGgHG9wMdbMscnoXNIxUrdx48aSTw2xlgP4GT0O5KXMn376SebJpDyE330P3C81jyGhUSefvCS8YKVbwEUXXuiWLFkicc8//7yrVauWfBYgnzo5dtIBx2MwFOdMGE3szDcKoQgIIQ8O0Y7YZZJ88oafVeZqTPr1WEbZRO897ie9R0R8eq/ck/7v3BbnuRGjRsrKWiy0kOHDGUTH/c3KR0cddZSs+sVMDdx7ek/pvch+GG78Hb02+h1Mnjw5vn44plvjOwrThdeTH+VMFI/dIZw+u1WqVJG40NYYRlFiwtModmAgmcMzNKgq4girte02rtdLveVlGKYJDSp+fcnh7/5Ud/f1119L2P777y+1hbqkppaRapDZ12POnTfPtWzZUsLo88ZceFpDFKJlyXEZ7OT/mBKK7gH0KyU/q4bQ9KXweUmvLkT3mRKFmkugXyhzc4b5CoJjMSk454pf06m4YBAJ4C86uH7rckZREt433OvcO61bt3aj/Q+Zx/2PMPoNli9fPnrW/A+1fl9/I88Xc4AimkK0rLXdr0ZEeJ0YFISdURD8EF5DTc/2oYcekh+UfE+XXnqpO/iQQ8ROEKdpSxYF2YSN6YyiwISnUazAgCKwpk2fFu+HRrZ8xQrurbffdpttsbnL9S87DGloTHVfDbH3yDyF/3fXXRJfqVIl1/ull6QmMJ2meY/m1+PIllrKoHyWpWT6IuKo8dm5fr24BqEgyCMvY+9oguzWrZuE1a5dW/qYal7K0+NCQefCYChWcaKs/ffbz7Xv0CHKn/73Jn3NRzlM9UQtr+7zMpJzkmM6N378ePHrMXVrGCHcF1Lz6e85eSb4QeXDmPtz4sSJrtvjj4sA1fsLxxyg9MlmgMv06dOjMoJ7zSgYvT66pVVE0Wuo15gfxWz1maem+eGHH5Zw+t5K9xofzveiaQyjOGDC0yh20KTNCjzepIqxDV9WDHTYe6+9pOmbZj41qKFhxZ/m9Vi6f1vmZufKEoArV6+SOS97vPiCq7VNLalFQMgpehwtR47tX7A0kT/y0MNyTgi9E08+SQYXydRG3oXnBmsYeB+/fOUKd3m7y+XFTf5XXs1fNYS0UicalEGYOl4gTHJP8352bo4rX7mie4H5RtGc1GL4Q/FS0XP3/61RVocr2ruF8xfJy2eLzWu4Bg0isSwvLJ83OyfPjZ8wwX9S4AWWPzm4YYDeW1HdfXTfyb3HACR++Pi7p+Wlrd2oMaPd7bffLrWf5TKzpPYTR5cQBCjdRBYuXCg/+IB14HHh/Y4D3ZZFws/OdV+8ZLFcM/qvJ/Jy3dx5s+W6i+UgzKdHfPJjnZpo0lJLyrzELJEq3SV8GvmhahjFBLsbjWIFRpIaQl0jWl98CEXmyjznnHPisPglmNwnrzqdwP22W2+NVwc677zzXLNmzSQP5YV5lTi/j8OI0zzetWtXCaOvlHbaJ7/m1fykCbeUwSh0pk4CVkaSKaF8euJwih5XIc2yJUulxgiI6+aPvc222/h8wWCm8NjJMngRvfXGmzLamOisrEz3xRefudvv6CzHJA9p+AwMVihauAbrckZxQO81vd9St7IK0g3Xu7HjxkkTL/cWYfy4y83OkUnoWSOcbiL0c5Yfff5e5TkP7/3QXxbR66nXoWqVqnIdJcz/ValS3eVw7bw/2/8oBp5pplijiR0/13iXXXaJn3W1M1p22SLVnqQ6oyiwK28UKzCONN+p8NSXULVq1aTmb13GM4wj3+effy7z1xFOUyDrmiNANR7WVh7CjGXmWrVqJX5qdjj+ZpttFtfapB4Pp2HkYY7Nd955R/ys437bbbdJvPYbhUSyCMJT41hfmWlr4LjjjhPRLeefcsp6TD3+lEmTRfDKOaUl3PM9nne77r6bO+SQQ+Vc9IWUm5sto5Xxh+duGOtC75XwfuGeQmxuvsXm7pHHHpVBSOed38JlZiR/4PlbGgH6xGOPu7o71HH33tPVrVqxMhKnyfudexNUKJVF9Fro9WU6K1pdID0tU+wiNZ2QmRk1oX/xxRdxP25mF2Bwkdo5wrRM3ZYsVCD+W2cUR+ybMYoVGEpW3MBw8iJiywutc+fOIj7XBkZVHWVMmzZNagvV8CICmZqEMgkL0Xygcbwor2zfQQZIcA6sjsSgIBVtSpzeb9VPWfQrZUlP0rPPKHZesvqZ1oaW8dabb7m3335b8jJPKVPZeO0r8YjTENJwvrSf83K/9LJLZXQrzWwXXnhhVEvs/2puuZWcgx6Dc/nzj8HxNdFrYBhrQ+615P0Twj0UPltMu/Tss8+6IUOGyLNDPu577l2mSWNFHWaG4IchYeRTwUk5UBbvx9Rrm5kedaWhhpjrMXnKZHmWEZ9cJ2bpQGjip0WGmuUQ/b7W9r0ZRlFgwtMoNuiLhiYj9bPFSb9KD8YzdBqv6Xl5USuA4Fq0aJHsU3N44IEHxvGg+VP9yuuvv+4++OADCWdlIK1tJX9YRurx2bK+dYsWLWKByHyjjPTVF7M6JcwPU6ZMcdcm16EHlsisUaOGP2B0TI4fHk+28r+TiaN/HfCry8nLlZc/o1zBH0HysexoTk4kEsjbv3//6HMk9w1jXYT3Lei9nPpcqHikpv/VV191P//8szvxxBPlRyTxPBsM1uPZZCAMNXaEcQ+qg3A/DCsr7LPvvtE1k+ubfPZ9eCKRJ92J+HGN+CScpXMZjBR+R+oPwwyjqDHhaRQ5+iLBONK8zRrsug/Mt4nwKsh4hmG8uGgGZ75PalpgX2+4b7/jDkkXulQ4B16WlDFtylSZ+xKDT/iLvXqKYNO8GPnUMjQ/0N+KZTXZZ77Rm2++Oc5HrQ9+0msZbHGan+Z91nMnPZ/lgAMOEH9Bo/Bx8sL2eXm5M+Je14x//oUeMu+fHDedms4M16DBrpI3OgfnFi9e7IYPGyYvs3CwlmH8E/R+4X7iPtOtv5lcOve63yKa9thzT/fmW2/JDx3tZ82zQDPyzOkzXLu2l7s9fZpvvvlGytP7Wp8JwF9W7k+uI45rpJ+Z/9n3IVxe99qrfeR6cS2pVcbpd4AzjOKKCU+j2ICBZZk3eSH5l4waT1YHWhvhiwijyzQuLGNJfprW8VPKP31hcUyEH03VOd5dcskl7phjjknGppAskrLlZevh+L169ZL8NJHTxK5iMyTc13MjjIFMvw0cJPus4U5tqb58iOcvTK/hDNhgnlF5Wfuwdle0k1peGZnvT1Q//V577RXXOvl/vuxMGTlvotP4N3AfKeH9I10/fJSEkCTpGu+5h3v3/fdkTt0mTZoE92KaGz92nDvlpJNFmDJ9mGRN3pfc1zxj+NWVBWT2gCTYNGqJ8xI5bubMqe7mm673oQm33XbbrdHErtcn/G4MozhhwtMoctRAYiz79eu3huhEdCHA1oa+gNgyejxc+5yl4mrvsIOU9U+MMGUwDx6T13MO9erVcw88+EAyNoJy9JiAX1+IvBTat28v4fSlfPDBB90222wjZUGYD3SfMnmxfvLJJzL3HuGEIWDDwRdxenmLRzA4iXAm7J49e7a8yKkh7nrvvS7T541qjUjJOTq3S/1dokzJMlavXiUj2wsq2zA2hPAZUz93lTh/f/Ec4PAfeFAT98VXX7oPP/zQHXjAAZKWe5dniVpRfmyecvLJMsMFZekzouWGxyobRDWZTJtEH1laUVYsW+qy/DVDdPIjm+uqzjCKMyY8jSIlNJa4ESNG+RcMfl42/vb0L6oD9t/X79NfkpfW3/uB6UuIfqA0HcNxxzdz5194AUrK3+X5L6swn74EcbzUBg4cKFORUEOYkZHlXn71NVehYsW4NhM0vTj/p2VSFtPIaL/So48+Wvp5+gTRXHr+FMLjqxgFwln/HfFIHMt9drz6KqkdoizicTpFlLhkWdQsPfXUU+7rft9Iv86q1avJSPqsjEwfF4liyUVav9l3v719ZmqPKMXHpWe6r/p+48MyXJ6cZPQZDePfwH2pW+487lm5b5Ph3I/6DBB21DFHu77+3n3vg/fdfvvtJ2mYszLD5/2u37fuyCOPdGecdrobM3qMxJFP5gD1zx5Oy9JnWdOE25KMfDb/OV169Blzs7PdbZ1ude+994FLeBt1/gUXikjnWqpTm6H5FfxSXsq1Cp1hbBL8zWYYRYYXfAlvCGWbk5OTaNhwt0RmZrlEWlpGwou/hBdIiZUrl/v4bHGalq069m+++eZEpUpVEuXLV0xsu+22iTlz5kh5BaUnPDwuzgvGRL169RLlypVLVKhQIfHKK318On9OQd4wT7ilvC5duvhjlxdXu3btxMyZMxOrslcnvBhMZOfmH0/z4bKz+UyJxNy58xO77NLQH7eSP36FxD777JdYtWq1j8s/RphP98k/ePDgRMWKFeW4nPugQYOS5SbPMZmPMPbHjBnjr2+mv7YZ/hqnyTYrKysxefLkOA3OMDYW4T2l/tR9eVb9/f7JRx8nDml6cKJKpcqJyhUrJSqWrxC7FueeJ/cv9zPPZbbPQz693+N7/v/bOw84K4qsi9+JREUkqGRUMBBMLArqZ/gpLGAOmAATKiuwiLrqCoKAGTELgooJFdF1zYpZzICLCclgAAREYYjDxK/O7Xd7apo3DGHmzQxz/kNR1RVuVffr131edVV1zK/oYD9GjBjhrmvV3XUwWb+r+O6mpaW473pqfvPmTfPXrl0bfm+3hB0TO15ZWVnhcbOyO8MxIxWDJPwX06CEJBw7/dxFT3sr69atr7/YsR38gg9miVtPCUA80i380UcfS7duJ4XbU6ZMkXbtDi2Ux/d9YNNdjHVcmb0fvlWrVvL118Hj9qSUgjLowUG6Xz96ZvFIH29tCbbzdcD/39r/zbU5RXLzsrUHB/j1YyYq3uRSq1ZtOfXUU/VxN2xiaAEWykfvD94Cg/2Gj3jYRh53s1AbOF533XWHLh2FdNhH25Efj+jVVUnX+t1NRjIyMnQxfTyugw1rD+rAjFi8+QRxcIgjpCSx744P4oB+12Jp7gyUd95+W4YPH66TBHEu4nxFHoRPO+00GXTTYJ0Nj/KIs+8jwn490foqCtgHOKxSgaWn8Hgd+xK4fP1uY7WALl266ZvQ7DhGv7d2LCwdxxGvysVrTK2nFGWi5QgpTSg8SZnin36TJk2Siy8O1qAEwU0jT5dawTIhWMcT48AgFHEBhZj6/vsfdRY5LswAF2S8IQjjMzG+Mj09EGC//PKrrg+KGfOwi9nzEGspTlhiAWaMD7UbG9JbtNhPWrduLdVr1AjtrvrrL5kxY4a+Ax0X+zp16ugF3Gbhwx7AK+tyXPtgKzUWZ4IRDu0HCFt9CKM80uD7N+LozQMgjLKWZumIg61o/jDd3dRz84NHbcH+BvuGxfWvuOKK0BYcISWBnaPRMLDvnJ2zAGGA+NdeeVUn2OH7iaEjuc4ZXbp0kTvuulOaN2+ueQFs4Py2bZzvFRH77kJ8Y9w3rnU4Vrj+ASxN9fLLL2sYYL/1+x3bb8PsmI/JlhgHj+vM3LlzpUmTJloG5f3PhZDShMKTlCk4/ezmg4vsbbfdoRdFbJswAti2vP52cnKw5JFhF1DE+baB+UZQPrjRIYxydnEPxpi67Vi8iwjzwDcCG8HrNf16bNtvC7A6kAaHuuHbfln+aDn4yOenmUC1dL+sby+Md6YQxo0ZwB6EPd7GhIXyIZgN5CMkUeD8hLNz3MjNcd8Pdy6OHj1aV3xYv3atZHnfNYx/xKtwb7/9dn07Gb5P+F7Agp77mqvg+2FUlPP7X//6lzzwwAPhNQpgMhHGkxs4FtH98Y+hgR/eHTt2VFtYnu7nn3/WH53AyleU40IqNoXvxISUAbjYQShBrNmFz8QZBCBOU6ThYmoX1Pxcd8txLi8n22V28S4MH+sCmsvPdfacyEIeuNzsrEJhpONNP7r0C2zGbKMuOFyg85zLtbBrk/U8IK+Ku9jbgrRnJdY+5LUbqN0w/P2y/dU2xsoA+L5tLYfeG3cbhbOw+diPYLIVeotgJ5iAlZeH44g6YRdtdOkqNmEzyBPct4NH++hphuhEu8wRkkhwzpmY9ElJTdHJeVf27atLrV3W5wqdwQ30u+RO8UkTX9AnHNdee62uf6vEvkNBsOD7B/zvW3nFrgHmDOwHlnuz44Xvr+2bv19+eYRxPbvssst0G2UwNAg/sFHWPzaEJAIKT1Km4KJoF79DDz00vAhqr0XsAhoIpdhDMyf0bMxkwY0qEFV2kcU6d9i28rBpQjB6Ebd4WIfTGbWxupHX2mYO6bjZwWHmOJqQmooyrrxrYLq7Uaa6AFyau2GiRwEXeNiED4c6URZxyINhpGF+52ADzsojHx7tY00/swVgB+3Ba/XQdvi2bXHaXlcOZZKdPTiEcfM+55xzdGwpFrkH2GdCyhp8z8zH7073TXYbois23D3ybh33iXMX3w37/uLH37hHxuqj40GDBum6tugpxQ8/s2eoXVcmGl8ewXAejNm27yauA7gGGP531t8fhM0hzw033KArZyDctm3bcDy3X56QRMFH7aRMwelnAg/07n25DppHnMVDmOEmg1/tIDcvV1KcsEIapKdf3nwjF2nORx6XqOlwNnEnxV3EIcIQLlzWiTSIv5hwVMEHUed8XPyxOHzVqlUka1OmPrZq3LSJu9EFj8xV5Dl7atOFrU77quXrclEImyu4UWhduKG6cLprY9WqgfDE4/Barh7E/4VJSbvuqjelnBwnxGM3Xy3vylZ15TB5Cb0/eG2milbYcz72J921u3r16hpnWNiPI6QssHMZqOh0IA5PNfCdCr42+TJn7lwZ7ETm22+/rXnsu4dfgOnuPMdbv64aODD8fgP/PPfrKW/o/jqHsddDhgzRce/YB3x/8b1GGrD9Mixer3cx8IKIk08+WfcV1xesk9qyZUsNRymvx4PsXFB4kjLFTj//NFy2bJl89tln+ss834nMjIzVMnnyu5KbmyMYc9nusMOkfv362quhk3jcxVJFnvP1ncaxbYjLKlWrB74TXRByEIm77rKrO/NdRagzdqGNXnCL+log3vIG4WDbjy9M/BtDQd6CG4SBPJYvemPZnEB0Ar9dwNrl48f5Pm7Y8OPvAyFli/Vc2o9Mc2DKx5/oo2O87UjP6dh5jR9k6U509u3bV8dKVq9ZQ8ugFxWojcJfj9BmWWPfzZEjR8qwYcPCWe34ntoESfefXsZ8/O80jlX2pizp0KGDzFswX68lGC/ao1fP4PtuQt5RXvabVA4oPEmZg1PQLnwI+6dkME7R+c4hZL6i5dyv9ninMOzBVux6CvvxTvXtueCanZK5WG8uPAtTnPDcPqL7gO2S2R9CSg47L+N9d0F43rrk1159VZcfmjVrFrr8NC3fpelTiirp0q9/f+0FhQC1cri8IKw9pY7y8h2w/R01apQMHTo06PF0Vz/0ANuqH66xhYSnlTEfYn3woMHyyJgxOk4WS8bhaRKuiRiKA/idJ2VB6dzVCNkG7OJnF0ygNwWNR4+eu/HoqerCMV9dkrt4ahb3n3O4oKrQRBh3IsQ7YAe2rZ4C29tHtHz0gr9tePsT15UOtg9os39sCClP2Hlp56t/nto2zt+c3Bw56ZSTdS3eJ598Ulruv78Oc0GPXk5Ojqxft15Gjbxbl16647bbJScrW0Un0ot/qpB47HuJJzQQnNYzC9/22f0XRMawePgQnXhqNGb0aI3DjP9x48ZpPgwZAshHSFlQ/r5xpNJiF0L4/kXRD+sF1yO6DSzOLsLmG9iOxu0IZqck7FnbE0lJHQdCSpro98G+t/45i7CJR/zwPPPss+SbGf+Tx58YL/vss4/2ZsJhRYr1a9fJbbfdJnvvvbeuaRnvOoBeRbjEfxMLsH2sX7de2BsL9HjkFbQ5enwQj7h1bj+v7PMPjcO4UPR01qhRI3jEHisTLUtIoqDwJOUKu+D6Yd/hBhONM6LxlmY+iKaVNxLdrvJ6HAgB0fOzqG3rufSvD2effbau2vDII49I48aNVYAhHcuYrf5rlfyzX39909fEiRPVBtBJOViezYmy8iDM8JYxe7QeCkYvDKyt5sA1V18tv//+u+7vzcOHySGHHKLxhJQHKDwJIYRUWExo+g6YCL2gRw8d9/nQQw+pADWBCpG2aMFCufjCi/T1m//5z380v05gcvoNq2cgDGeCLlHYPixbsbxQjyeGFjl5WUhkWhgOwwpefGGSvPDCC7p97PHHSZ8+fdSe2bHjYnUQkmgoPAkhhOyU4NE71rGFf+GFF+palmPHjdNH7SbAwOJff5MLzjtf2rdvL1OmTFHR5lI1DeGyEmkqKFG12wcVwEG0xuMNZNpDG9tGG5cvX64TqDChardatbS3F4LT2g+/rPaFEIPCkxBCSIUH4sswgWVx8CHbIDYvuOACfQSPV082bNBAH8GjpxBp33/7nZx80knSuVPncHkm304i8UWi1h+bLAmxifWJrSfWHJZc6tmzp6xZs0bzjR07VurVqxemE1JeoPAkhBBS4TGR5gMxaT4cegnRkYmXQ/S66EKZOWuWXH/99fpyBcuLMaBfff65HHv00dL9rLPl50U/h8suwUHwYT1hnYBUoqIOvZcQk8FrcGEX7TX7JkSD+lF7TFC7bcQPvnGQ/G/6N9rD2atXL+ncpUu4T1YWlGybCdl2KDwJIYTs1JjwwiNoX4xhfc9BNw2WH2fOlNNPP11FW7JzEHN4E9lbb70lrVu1kt69e8vSxUsKBJvzIUaRL9gsOSEXCMSgjVjkHXX4YtEW00cu+Ij/6IMP9bE68uKtRHePGgVZrPmxv4HNAC3rbROSaCg8CSGEVDp8sdiocSN58umn5KuvvpITTzxRUtPTtf/RBN+ECRNkv/32k2sGXq2vo4VwU3HqRB3St0fI+fUHbH473jxPIHbD3lkXzli1Wq644gqNw6twn3l2gqSlp23Wpni2CCkLKDwJIYTs9BQnvJDeqk1refmV/8q7778nHY86UntITcChpxGLsO/XoqXcPGSoZKzOCG3C3xphZ/mKzotbcuHbsi8grRx6QnUxeeeuvPJKWbFihcbffvvtunapCuNYj6dBIUrKCxSehBBCdnqiwgvbfpz1IoLDDz9cJk+eLC+++KI+uoYABehhxLvS77rrLmnerJlce+218tdff4ViEulwtm3iLl48nItSbNuwdsG3NIvzH50/8cQT8t5772n42GOPlYsuuVjDOpsffy6f5Y1SVDwhpQ2FJyGEkEoLBBjEnI7vdL4JUPh/79pFZnz3rYwZ+4jstddeGo98EJGYCT92zCPSrElTufbqa2TlypUxMZmnvaPw0UPapk0buemmmyQjIyOu+MzN3bznEfEGwmgjfGsflnrCElD/uv46nYC0S61dZeyj48K82htKYUnKKRSehBBCiIcJP/OxBNPc+fPk/vvvlwaxJZhMXMLHxJ69mzVXAQqBiTj0RPbr10/mzZsn9957r74nHgu7owwcMEHp429H06ws4jHhCYvc41Wgjz76qNSvXz8UzYCyk5RXKDwJIYQQj7C3EIvPOw9CD6Lusisulzlz5shjjz0mLVq00BtoqouH0IQARA8nBCbGXZ533nlaDq+8hMMj+osuuki6d++u+QFEpNWFvCYqjZSkgt5Xi0d49OjRMm3qVLeVJBdfeol07tx5sx5O3w4h5Ykkd3Ly7CSEEELigFtk9DZpIu/J8U/Iv//9b1m7dm1Bb6T7S01JVSGqbx1yQGhCMFq5Aw9sLa+++qo0aLBnbPyo9QEF9ZiGfPDBB9U+Fod3xZ2dPOnXr6+MHz9ebbZosZ988cUXOpsdoJ2Fej3jiFHE2T5F06PbhJQGBWcoIYQQQkJMcEKQQdCZA0jDZJ75CxfI1ddeI6npaSo08VahjZsywwXmIRBR3oQp3OzZP0n79u3k22+/1XTrAQUm/lC2WrVq4bYr5upO0sf6GF8Kwfrkk0+GedAujD8F2LZyUWyfgAplb5uQREDhSQghhBSBiTgINHMWj3CNGjVk6NChOpazT58+m4lTE4CWH0A4YjY8ZqK/8cZbsfx+byTKJMvuu++u+c1ecMuGwEyTgQOvkbZt28byB4/pfayueKB+YMJzS3kJKWkoPAkhhJA4mGgEvoD0gWhDHN6LPmrUKOnYsaMKRRN0Juosn8UhnJ2dq2M+L774Yu31DHpErRwmLkEYFvSWGgcccIDcfPPNGo7XLrMfD0vD8ACEUS98QhIFhSchhBCyFUTFHLbNQWziUTcmEfnxcIYJPFuSKS8PPY958vzzzzoxeaC+OcnlijmUs/KFX3uJyU0QjKgzWo8fBlYnfDikYRZ8kyZN5B//+Edog+KTJAoKT0IIIWQbMHHnOxN2eOUmtgMhildXpoTbJk79R9zW4/jrrz/LscceI5dffoWsXbvO5cmVRo0a6mNxX2CeffbZ2uOJMZ5mE/HxgF1gvaWo65133pGrr75aJyz973//22J5QkoDCk9CCCFkOzDxaGEIuFtuuUU+/fRTGThwoK75CYEI8Rn0WgaTfwwTk3isjt5PCMQJE57WNyctW7ZMMjLWOOGZ5dIDcQrRevTRR+s6osDqLg7UAdt4zzwe6wPY6tKli4at7YQkAi6nRAghhGwH/u0Twg69hzZxByQnp8iMGTPk9dff0Bnoixcv1jzIC6EZiL3ABoIwhzIQqbvssouccMLx8tprr4U2IRbxmLxXr166XZRYtHZFb+/dunWTDz74QMXwfvvtJ19//XVMGAd2KD5JIqDwJISUGnZx2ex2VmRCyeNf4rbmxlr4kogFvlM2u4HHA7aj+aw+xMerOxq/pfIgasPKR8sVRby80ZLJfp0Ib0Md0fbFo5AdDUf2KRRiQbxft4WTUAZxyUFPXrRe2462GT2HoMB24R5IA/mQx5mO2Ea46OOhbdNywaNteBCaeMQNM++9/748++xz8vLLL+ujbvHaE28/0tPTdfF5ANEJkXj33XeHs+ejWP2+r/G5eXLdddfJmDFj9JjV3HUXHU/avGmzMG/huoP2B7PrA3x7PlYeFLZROA2E7YnFY9PSkWJZY9liRzvwQSF7FulAfqTZuZsXy+d2NdjWzxF5gv0yG0EbCreRlD4UnoSQhBC91JTmxb6oy9rW1Fm4bDCruKhyduOC8/NYHMSB+VEQvyV8m1ZPvHaYHetxs3xWxtKtrMXZttvDgrATKLh5Yxu2fDFkdvyyCFudVj/w2wGsrN9GJZYOT+Ni0VYWzrcLEGflQzuOaF2Wz3zYgXizOOx5UcIzmPQDP9iXwIbZDI5JYKNwG1BHFKsb+eFj8tHy5ctl/BPj5emnntZ3vFs535YR1BkcZzxiHzlypPTv3z8sY+lm32xgG+9xx9uP3njtdX2TEtKx3uhjjz8mp59xhqQmB+NPrbyVS0oKzhETnghDKK9fv14demAhivfcc089pvaZ+p+TYe2xOgK7gcvKypbs7By1h23zsRYq2poEu+5vkxPfeU68Y5Z/rJkwqO+k1/wuLStrk2zcuFHWrFkrixf/Jn/+tUpynT2kwRZso63p6am6TBWOR61atWLGgv0miYHCkxCSMOxyg/uZu71peEvs6K3Av7xt7Y0lbKP6dnMvqmes4GYa9X2iN2RLt/zx8G3Eu6EDK4+bK/LozdptmxCwPJbPD8Op6MRRdv+0bLCleXCTNvzyBsJWj8VbHsQjDPx0ADEU1ql5U5wfi1OxEdhIgW0nNJyh0JbZhzWUASlWPpbH1aw+wNJErgVhG+w4WrttO4qNqXTN8fIEdjHpx+zhuEPQBMIneC3munXr5Pfff9d3tmesWi3rNqzXY5uZmalvM0L8zz//LLVr11YB+uabb6qt4sD+QXjeeeedMmDAAI1DOcSbsIKt+fPnaxjxEHAbnFAc8/DocLa99pw68YmF57EGadWqVbUnFSA92Dd7D30gBv9a+acKTttv60rcdddd9dF9mzZttCycj+2XtdPKt2vXTl89imNm8SAsb4cDm84FZ2XBZ27pQXIszbU3bINrX7BPBd8DpNuwAnym99xzt1xyySVhGWsjKX0oPAkhCQMXG3frCTY8opchvZngXxFXp+JuEGbPbijG1txYLD98v3y0rKXjhmZCJl592PYFDratjJ/fLwfMNnzfvo9f1g9HRSOAOMKNFzYNTXM3aW0HRBrMO99vL0A+5NF8Lmw2LR5YuoV9bD9ynGjDZ5u5KVPFWY1dakndunVcer5k/LVK15Zs2LCBbHIibeHCRdKkUUMd67h2/Tr57bff5Ndff9W3AqGt61zcSldm+dJl0rRpE0lPryKrV6+SVS5u9erVKvIgtuxYQ2jVrbu7XHDBBXLooYdqu6LtNPweT/QwQuxt3LhJbblYTbNjAGDfxL8dE+RFj6Kla5x37iMf8sD5xzMeKIs09DKiLf/85z/DOiwds90xY923lZyaIrnZgTBOS9n8s9c83mdtZSUpls9+cLnjbW2w/YAIhj205Y477tjMFgjzu3zmY+F8TLoCZlPDVrWLA2rJOxwWb6jt2I8UYHXnYtvFY5+xqoB9LvhOWBvhjx07Vnr0OD+w42xH7ZPSg8KTEFJq2OXFLu4adi4XAsQu9i4inhgFUeFpNvybhG/bB/EQH9abYzcc80G0nMWbzVWrVmlPFd6Fjd4dAFGDR3RLly5V8YR8a9as0TAemx511FF6Y8WjyUaNGoX1+yAfervQPvSQweGGvGLFCg2jTqyz2LNnT+2RsnZG22s3dPD666/LRx99pL1YdevWDe1b7xfANpbiQe8VZk2jfM2aNVVI4PWNfyxfIZ06ddJ4tAPHAQKjSpUqMm3aNJ0oc/7550v9+vXls88+0941iEXU9+6774aCwm7yPrZ97/33ybBhw4IeOCkQA+GeYTspOejFxJlhdmICGWIK7UMZdxqFYlrjXDp8lLF9tjDyo11t27bWtgPL44P81uOJnm7MIp86daqGg7YUCEWUtzCwdgVlXXsLkhSNTwkEUrgPsfYC3xYw++bjcxgxYoRce+21hcohvUOHDjJz5szYe90DoQvRpe2Ac1kt3soAs18IJzy1bHKwZBN6ns0Wvqvprh0ohzb07t1b7rvvPi2GvFGsjQbObZwvOBetbnz6eg3APxeX5j4nfOfS09L184ULZvLjfEwP25vizgVtkytjdefHtnGc8ZlBrMPh2MEmHrO3aLGPrjqAOGOzY0BKDQpPQkipYZcX+HAQQZMnT9bXC2I8Fh4F6oD/2M0CYglp//d//6fbn3/6mQoUzMD96aefCj3uw40LN1OEcQPEjQY+xAXqgSCCeIKwuummm6Rv377hTcqEUfRmgzjzTz31VBVTto3xbBCYuHFanC8sYBP2UDcw2yZYrW7sQ3aOa3uB1NI0CCorA1sAk0EwFs2wdAP24O6//34Vc3h0aTdgHAuAdNgLeoAKC0ILwzfb8G2/9Liibc6m9lbGwvAhcCAIUBai4KWXXpITTjhBy6kN58y+tQVlIWw/+eQTDYfxEB5eG1JiPnqvkE/txHq3kMfKAcRZHjjsY8G+B4+WrRzCjRs3VIFmbfRBvgATdcnSuXNnba+Nd3RVhfkK8gdYPRbGfuFfaqy3Udvptq0cPhMrA9/iDX/b2o/exauuuqrAXqzclClT5NJLL9Uw8uKHkH3m8LEfeEVn1qYsyfYeccOHgy0LQ3iih7hhoyZaFvuxv/vBUt3FZbnv3TuT39HvH5Z9wnfV2qdltwDajDz4juC7acA+2pnqziOcSxhmAXCsYBGHAab1eAQBFxvUpf/H4m1/Yh9VEI4dwiAtCEcprt2kZKHwJISUOOENIHZ5gY8evfbt28vy35epYEGvp80+tRsS8iGMmxC2cXNDGPGWZjdItYvJMLFt3CBh1wSS3XQRRo8HRC18YOXNN6wejMND752rTvMUtC94bGfghon8JgCsfQDbfj1waFNgJzguCFv7URaYAEUejNlDj5uBeB+rD0vsQIwAa4cPtvWYQ0TE2qdlXfvhB71DsbBrGo4Tjr3lhY+yKgRi+SwO240bN5ZvvvlGe1uxbeVsP5EfnwUmL41//HFt66YsJ1ydIDPseLlPwLWqwLc0BZsuCPvIC4GiPWEuDKG07777ysKfF+mPA/RK77lnA/0Bgnbts09z7UU++OCD5cwzzwzMuXJRgroC4YkxjrCFx/wQnjiGqanBou0Iw0cvGuxjH608fgDgfN+UuUknxaDnHGNbEY9jBlAexxnbCH/xxRdy4403Fuyrw46bHWfkwzqh6PH08+lxc9twCKNdDRs2lFV//qX1HnPMMfqDzy9jx9CPK6BAeAM7TtG8fjzCtl0UVt58nGso42orVBZh5DEB6ROeE+4P56+CYSIANrwy0fZGKa69pHSg8CSElCjxLim4gX76yRQ55ZRT9CZqN+mUtKAnyMogbDcD+JiRizQ43IABymNb093NE2VMwAKziW2rB72Vs2fP1hs3ytpNN4rVhd6ivffe28UU1A9QxpbagUP7ajjBg55btA+9q5kbN6oY2WuvvaSa83UCBSy59CpOaEBsIIw24NFwNh6FuzAEFMpVqVZVHweilxeP2gHygmibrV3Yz+eff14ffSMOwhk9xThWOc4+Hini8fiiRYvkwAMPlFatWmlv7vq16/RRPhYSR88seqGwH7D6zbRp2rZau+0muzkRh/2oU6+ujrnEcUQ5CC68oxzCE/UgHqC9hY9ZMBHH/zzdf05kpwY6wd8vL4ixnLrPMVv4P8xvcZ6P4wihByGN7UC04VwI2mHnhR1H8w2z5QsvtevyQYQG52BwTllZS/cJ69EGo/IgHiC/lcExwxAHLI/0ww8/hOdrUHfQ840w4u0cwCNiG1OpdXh1Wzn08Ovjb3f88DlNnT5Nz2cIPGCCLdpuENiwfSzoLTasjWibhS09nj0f2DJ76uPPFbHvr8VDcMIPhWURIJ/aQNjlB6FtGHZEw0bwI3LzHz6k9KHwJISUOHZZsYs5blAQLhgfiHGMEEGHHXaY5OXkyvIVy3VMHwQMFtiGQGnatGkhEYObHOyY4IFIQzjNiTh3m9KbKgQReqYwYxj1oj6UQy8XFs62mziArS3dZNBeOOSHbzdZONSLbSO47bl9jd3UzYP58OKqARyLQDxshtcU/9jBWVvjtdfyol2Wbr6VtTzAxIth5aL5rKwPtv16QLQMQB1mz/JaGsoD+ywsj29zW9Dy7g/H3q8vHqjb9n9L+ayt1j7bH4vzidqxNthxsu0oENRIu2XECLn99tu1VxLnvZ8X9eIHwo8//hjaw7k3ZMgQueGGG10OZyM2JkIFmhNS4Msvvpa///3vag/DEyZNmiRdu3YN98XaBB/CLR44pvrPmffLwWl6rJ3wUY9/jIrDt6P/a1VBfYgPbQexZCeEwpMQUmrEu7zYzUV992fbQP9HGgSK88MbD9J9W7Htom6cUayOrb05GtZ+a6+Ft8TW5tsa/GNTFFvKY2lFtSleWcsLtib/9lJUm7aFrW3Pttbl5/frKK4+SzeBjW0TbQBpEGrvvjNZl0QKHuEHQsx6+dAjjuWJHnvsMWnevHmhtSYh2DGW91//ul63nVxV+xCerlYdN33E4R1lwYIFmrfnhb3kwQcfDNsMH3VsaR+iWH74xvbY2RqsjpK2S8oXRfz8JoSQ0kVvLri/+A4TSNAP4nzb9sN6c4bT3h4XF4foTWtHb5AoG++G6N+IfZBnR+rzKc6OtQF+vPZY+aLs+PH+PpqLUpQdo6hjYvjpRdWxLfjlt1T3ttZl+aM2i7PhlzEbOTkFk83mzp0rZ5xxho4xhejUXklnEuIRSy8d1KatjB8/Xt8qhNUH0LsPzCZ8jFV2IQ2jnIFtTKDDklMA4vWee+7RsJUHfhu3BuQ335xtlzS+fbLzQuFJCEkYuOH5N5Z4N08fbBd1k4x3g0JcNP+O3MjMntnYUnvKkq3Zx+Ly7Mhx2lrseJYGpdF+2NwWu7Zv6PG0MB6PY8wwlh1q27atrrVp6eiVdDXoUkgvTJok06ZPl+7du2savhf+8YKPbYwjzslBT2fQLnscPunFF+VF5zApDON1n3rmae09tXI+27JPPtaWeGwpjRAfCk9CSKmBG5zv7Gbqb8fLF3VGNM7fLirOd9uDlYva2V57JUl5bE9xlId2lhQQW74z7LzG0kU33vBv2a9FS5nw9DO6CgPGNaO3HhOgjjvuOPnwo4/07T+nnHyyLoge/Uz98cTA70HFZC34vyz6Wfr366dtQP6xj47TcdIQuP53bkfZko2SsE8qBxSehBBCyFYCcQdBZy7eNhg9erQ0b9ZMZ5dj6SjEw6EHdP/995dXXnlFl8vq0LFDMAsfYjQmEH2HMiYeYX/hwoVqw+qFEO3Ro4cuG4V4vJnppJNO0nBUtBJSHqDwJIQQQrYRXxjCBxCIzz33nApLrLWJN1RpuvtDGlZzgCDFmqcnnniiLm/ki1UfCFEQraNOnTru/4Je1kH/vlFnvmOlh3322UdfJoC6YNEvR0h5gcKTEEII2Uog5OCighGvK23Xrp2O5cR6qZaGV39ivVMsDo+lvi666CLtiUQ6BCIwcahiMeYA4k082rJF6Ml0KRqPtVghZNEWTER6fuJEXcdW647pTWuH+YSUNRSehBBCSBx80eY7LMyOXkyElyxZIuecc46c3O0k+e7bb3UpsGSkumw1d91F/g3B+esvcuPgQZKanubuuoFwDQRk0EtqQCuGzpXXuhzwTaxiqSQspPTnH3/IRb0u1HRw6y23S4sW+4UiVtvgwrZtPiFlDYUnIYQQUgQ2jhKizxeCmzIzZcSw4dK2dRt547XXNV9aapr2VuLtU9fdcL2KUiz4jrU4ITAh/swHJgy3RhTCPkBe9H72799f304FMEnpkt6XbpM9QsoKLiBPCCGExMHEJpyJOSxXdN899+qkodWrV2ucpWflZOuj9uHDh+t4Tnscb5N84glCpINomtm0nlHYwjZepYqezqFDh6qI3W233WT69OlSf889wt5T5PPbTEh5gsKTEEIIiQNuj+Yg4saMGaPvSf/rzz8lJztHxSBEJdKwFucDDz2o78LHxCCUweNuYAJwW4Sg3ZptLU70cqIuvHdfF553QGhi7c7OnTurbV94ElJe4aN2QgghlRITd9YzGXV4bo6xlh+8/4G0O/QwuWbg1bJ82TLJccIP71fHTPJ69erp6y3f++B9fduQij5XJioCt1cMWltQHj56XE2EYrF5vJcdaajP8sIZFvbjLQxn+05IomCPJyGEkEqJf/uDmIOAM4EHf96cuXLdddfJ5MmTdVtFmv6JVKtWTf517bVy/fU3SBomDTmsnIadZz2e24O1DeIWYbMNB9GJZZXmzJmjs9ntcbwRtiFmw3zbB7NjYROtVo6Q0oQ9noQQQiotJrbgm0D7888/9b3nBx98sC5ZBELx5v4uu+wymTdvngwaPFhSUgsWaYeN0F6QfYeICkFd2xOvynT/Hn38MRW/1rMK/PpNSPo2MEkK2xDZEJ2G7RshiYDCkxBCSKUFosuEV1ZWltx8883SsmVLefLJJ1WcQaSZiOvUqZN8//338tBDD2mPo8UbCFucH7+9WLsULMPkPCzX1LdfP33EjvRCeTysLT4QqYsXL9b3xVsbTYCWRHsJ2Rr4qJ0QQsjOibu74RanksoJN3u0rLc9CLnY3Q/xY8eOlRHDh0vG6gzJyc3RssmpwdqZ++67r4waNUon8cSjNESbttvZxWN0tA+iESIYs+WxTBPSrF4/HEX3FeuOuvSNGzfKEUccIYt++VkGDhwog9FjG5scBYqyQUhJQuFJCCFkp8Vucb5vj6fznSD75OOP9fWWs2fPDno3dQRnwF4NGuiyRRdeGCzU7j/WLm3QTghBG+MJ8QmReNBBB8nUqVM1D9K3JBZRzhzGm/bp00eeffbZcNb98uXLpXr16uF+UXiSRMBH7YQQQnZqILIMiCz0dP72y6/Ss0cP6dq1q8ycOVOFneZz4qtZ8+byyNix+urLnj17FivwShu0y+rHckrWHotDur+PBqZCWZ4333xTJkyYoGHs/zXXXKOik5BEQ+FJCCFkpyYUZXn5sn7tOhk0aJC0adNGXn7pJTz2Cx/B4zH2uHHjZNasWdrLaTPdyxq0wcQlhKcP4pAer53o5UQ6HrEPvOZqFaIQ3qeccooMuWlIWJaQRELhSQghpEIC4WS+H4aQtDCAuMKM7kcffVRatGgh9957r2RmZoaCDYu0X3XVVfoe9F69eoVl8Ghbe0hj+cqCaL3R9sRrlx0POKRjKMHSpUt1vGjT5s3kkXFjJaWM94tUXig8CSGEVEhMNPlCy0QnfHOT335Hjup4pAwYMEBWrVqlcRBwyHnKaafJT7NmyS233CKp6cF4SqSZaCtLYWZtsDaBrWmPHYf83Dx5b/K7MuGZZzQe40XxuL1GjRru7l/4vfGEJAoKT0IIIRUSCCxg4smEmrFo4SI547TT5ayzzpIZM2bEYoN87dq1k48++VgmPPesNGzUUIWY2YNvQq+ssTZtCxCdOA4b1q+Xvv/4h9u1ZN2fIUOHyAGtDpSkFCes3WFCHjtm/nEjpDSh8CSEEFKhMXGGMZlwq1evloFXXSXtDj1UF4BHnPXu1dujvjw94RmZ8tmn8rf27QsJTF+IbY/gKw2sfX67imsb8uW5fb564NXyxx9/qI1jjz1Wrryyb7ncR1K5oPAkhBBSITChpI+RY+Gof+edd+q6m4+Oe1QyN20KJwjh8fKwEcN1HOfZZ5+tNjDOEeWKEp9lhe0LwLhMtMXapfvumlaQIwBpocvNk3fefkcmTnxecl1+FdvPPK1vWVJb+HMGzC4hiYTCkxBCSIUBwgoTheBDVNpj5aeeekpa7ttCbrvlVtmwbn0oTiEq/3HlP+TXX3/VJYRMyBkmOuGbECvPYiwUlzHpiTD21cI4Jhlr1ugrP21fH3/8camOcZ2O8r5/ZOeHwpMQQkiFwt6246SifPzRx9Lh8COkf99+OnMbwgsgHcsGzZk7V+6+e5TUqFkzjIdAM/Hlh+FbuLxg+2PthOj224gw0gwI6Mt699ZJVDlOkOL1mh06dNBjpuS5vN4+E5JoKDwJIYRUHJxwguD8fenvcu6558rJJ52kE4eys7ODXsvkJGncuLG89NJLMmnSJGncqJEWQw8hxJb1kPrOMAHnC7lEUly9Jj7R2YmwOdsHPGLHEIPJ772ra3YedMjBOrxA0yE4nbM68NYmQsoCCk9CCCHlllBgOaGEcYnoAbzjjjukdatW8sYbb4RCEj16WI/z5qE3y5w5c6Rrt27uDueEZYq7zcW0JfL5j9SjWFy8tESAek0YGoWEpQuj/e5oaDg3P3jErrjjM3/+fPn3DTdoHiw0/8QTT+jjdmzbfm9p/wlJBBSehBBCyg0qMp2DoDRnj4dfmDRJ3zg0YsQIydywQR87m+DEmEaM47zu+uslCeLK2TKB5Quviia4ILRNfNq+QITrI3g9LMGxwtuJ0AOMnl/EPfzww9K0adOYlcLHIogIPEISDYUnIYSQcoMvDC383nvvydFHHy2XXHyx/LJokROiwQLwEJ14l/q8efNk5N13S/WaNbQ3EKIKM793BnAMTIybyMzNyw3GbLp9tDGfVw0cKAsXLtQw3j9/5plnhuM67TiaDzuElBUUnoQQQsoNEFYQRhBJ3377rZx66qkqoqZPn64iy+jUqZOO7Rz9yBipW7+e5OUXjN2sqMLKb7eJRLxtyLB9g+9Ponr99dfl+eee097OmjVrykMPPRT2bJqdQsBOLEhIoqHwJIQQkhAgmnxnIjN0uU48OkW0dPESueSii+XIDh3l/ffeCwUnxNS+LVvKq05ovfTf/8p+B+yvwgrx8E1k2XZFw98HA8MIovEYSACXl5Mrv//+uw4zQA9vSlqq3PfA/VK7dm09ngB+tDxChWshJHFQeBJCCEkoJjQhhiwM0ZmVlSXDhg2T1q1by8SJE/WRMsYzQkjWqVNHHnnkEfn2u+/khE4n6ux1E1Tm8GjZbFZ0bB8wQ9/2CccBvZrYBhDpPS/oIRmrVqsQ7datm/YOY0IRjgXywxFSnuAZSQghJCGYYDIgNvHMFz13zz//vApOvHkoMzNThVZKcopUq1ZNBg0aJIsWLZKevXoFYzhRNiIuTZzBj9ZTEbH9gfA00ENsvcTg4Ycekm+++UbDtWrVkgcffDDcdzsWhJQ3KDwJIYQkHBVPThjhUXrHjh3l8ssv11npiEdvHfwLLrhA5s2fLzfccIOkpae7/AXiNZ6o8kVXRcf2wY4FgA9RDjDmFb3DTolqr+azzz6rj9i3dHwIKQ9QeBJCCCkxfJEEFx3HmYQ/l2XOrNly6imnyOmnny4//PCD5oNYgsOyQHPnzZNHH31U6tWtq8IKMgppGo7lK4otpZVn7BgZ2A88Nkec7feff/4pv/zyi3Tv3l02ZWVJskvHGM+jjj5a8/jlCSmPUHgSQggpEUz0+AIKYil8RJyXL3+uXCn/HDBA2rdvL++//36hdSpPO+00mTlzpjz2+OPBGpQQkOZiYzp3drCP/nG0BeBtFvtKd/yOP/54+eOPP1xm0bcTjbj1ls3GvBJSXqHwJIQQUqKY8DQHIYSZ6cOHDZMDDjhAxjthiYlEAIKpXbt2Mvndd+X5iROlafNmKqiwPFJIJdFRJjp9H0ITQHxCvOM4Ll++XB/B7163jrzwwgtxhWa8OELKAxSehBBCShQTTdbTOX78eGnZsqW+6jIjI0Pj0JNXr149GTd2nEz59FMd55mTGyyGDkLhVIn0kx03A8fJn8UO7LgCvMmp3h719U1NebFJV35eQsojFJ6EEEK2CQgkdXlezybineaBb+Lntddek4MOOkj69eun601CRKKnrnr16jJ8+HBZsGih9OjVM3hM7JxNpAnFUyXVUDgGAL2cDRo0QPevumR3XLASAOLvvfdead/ub0EajpnzKDpJRYDCkxBCyPbhdA5EEnrg0FsJP9+5uXPnSpfOf5cePXro6ywBxJKTl9K7d29ZsGCBXH311eHEGQgmOOTxZ3FXNnAMsO96rGIiEsfIjg2OH3ys1XnppZfqsbJ0y09IeYfCkxBCyFbhC0KEMd7QhFJKUrJkbwoWgD/8b+1lypQpkpudo/HolTvhhBPkmxn/k/sffEB23a2WJKUEtx+UNWALrrIKKdt3+EY0jL8hQ4ZoWIV+rAwhFQUKT0IIIVuFiSIbY2g9c9jGm4batGkjI++8S9eaRDx65Bo1biQTX3hBH7vvt99+Ws6EkgqpmAOItzoqI3ZcgH8cLKzHx/1hsXhs4/jDr6zHi1RMKDwJIYSE+ELGwrZtghMgDkLorbfekmOOOUYf/S75bXEYj3eMDx48WGbPmi2nnHyylvHFFP7HtlFUuDJjx8uOu21XrVq10HhYc4RUBCg8CSGEbAZEje/wWB2YCProo49UcJ511lnyzbTp+tpL7YFzf2eefZb8+NNMue6G691dxgmiyBqT6pwNf5vExxeXwHzE43j7QxUIqQjwjCWEEBJiIscXO8AEDt4yhLcNnXLKKTJ96jR3Ewl64VJSU2T//feX9z/4QJ5++mnZs8FeoTAyO75N3zYpGjvuOMbmQ/z7x5WQigSFJyGEkLj4YmfZsmX6PvUjjjhCJk+erHH4A82aNpXHxj0q07/5RtfjxLqSEEZIzY08ng/xgqR4IDJx/OD7Qx4IqWhQeBJCSCVHRaTnMAsd60Umub9NGzNlxLDh0vrAVvLsMxM0TdeMdK7+HnvI6EfGyE9zZsu555+vQlR74SCQICydj7UnAeIL9dCxs26L6OfgMJFpb3LKF/jmCKl4UHgSQkglxxedEDp5CLv4Cc88o6+4vOuuu2TDhg36vnBMaqlWrZoMGjRI5s+fLz179gxEZXKwxqQ5xCEvHwlvP/g8sE4nSE4KjiPi7P32hh8mpLxD4UkIIUSBoIG4+fCDD6Rjhw5yxRVXyIoVK8IxhVWqVNHH7RCcNzrhiTiIHgqf0gGfBUR+4eMbTPQyEUpIRYPCkxBCKikQLhCVJmB+/PFH6dq1q04cmjFjRtizBpFz1tlnyU8//SSj7rlHateurfHszSxd8NnYIv32GeF4Iz563C2dkPIOhSchhOyk+ILFwiY0Nd79w1jMpYuXyKUXXyJHdTxSPnz/A8nNd3mcrsFj3rZt28r7778vTz31tDRq1EgFDwSnvjfc2TDxSQFa8uCYWu8m0M/MYWLUh8efVBQoPAkhZCcGgsQXm3C2/ddff8ngm26Sgw46SCZNmiTZ2dmhkKxTp45OHPpq6tdy5NFHOUPOGNbkdP8gShHGGE7khYsKIbL9+CISC/HbMbahDaDQDwgHjz+pKFB4EkLITo4vSiBg8ErLoUOHygH77y/3jBolGzdu1F60tLQ0qVmzptzkxOjChQulV69ehQSOCSA4ELVLSg47zrvvvrtu22eAQ44hEBChhFREeOYSQshOjIlDE5APP/ywvjMdM9XXrFkTCppddtlFbrzxRlm8eLHccMMNOpEIZUxQwjdbBsVm6WOfjwlRHHL8UPDjAD8LUlGg8CSEkAqCCT8TI/62+dE0A4/SW7VqJdddd52sXLkySMerLFOS5bIrLpd5C+bLjYMHSVqVdM2PdH85JF/kkNLB/+z083FkZGTo54ThDXCpaVVkyZLf3WeRoul+XkIqAhSehBBSQYgn/Ex0+L459Fh++OGHctRRR8kll1wiixYt0kfqALbw6svZs2fL/fffL7vttpvGQ2jCQXSSxGLi3v8M7fMC2LbH7PhsDf4gIBUJCk9CCKkgQHhEgeiAGIEQ8Zc/+uWXX+T888+Xbt26yTfffBPOhIagPOSQQ+SDDz6QZ555Rho3bkzhUo6wzxifCT7TvffeW7et5xmTvo477rhCnxk/P1KRSHInOfvoCSGkgoBLtl22IUZsG8siIXb9hvUyYsQIGTNmjGzatEnzIR2Cs2HDhnLrrbdK9+7dw3ImaHwoZMoe+3ys13rcuHEaxhuj8MMBYb9Xmp8ZqShQeBJCSDliWy7JyAvBARGCd6jf/8ADctfIu3SZJBMi8GvUqCGDBw+WAQMG6DbKwZlwNZ/ipWwp9Hk6/M8DaejRhtg00Qk/3g8HQsozFJ6EEFJOsMuxCRD4ftgEhuUzJjz9jPZkLlmyJHjsLgVisn///jJkyBCpXr26ihXE+ULTt0vKB/b5Rj8Xizf4uZGKCIUnIYSUI3BJNgcgLiAmgQlHS/v888/lqquuktk/zdJ81gOG2c+YOHTbbbcVGsPpCxWKlooLPn9+fqSiwslFhBBSTvDFJsJTp06VI444Qnr06KGThSwdj9IvvfRSfa/6nDlzNB6iE+UOPfRQ+fjjj3XiUJMmTUKBYjajYVJxwGdmn1v08+PnSSoK7PEkhJAE4V9utyT+EI/eTAjLrKwsfWf6PvvsI19++aWMHDlS7rnnHo3HuE6AXk6IzGEjhocTh3xMfCLeF6KEEJJoKDwJISSB4JJrl134Nt7SWLdunfzzn/+U5557TrctDUIRDo/dUQakJCVLtWrV9BWXmDik71KPYflR3kSmb4sQQsoCCk9CCEkguOT6AhBC0gTiF198oWtvLl++PByvCWw2M7CyeK/6oH/fqGM8MXFIwZuIPFHpC04/3q+fEEISCYUnIYQkCLvcRn0IwIEDB+ramxCcFmeiFALUJhghjOWRpk2bJvs031uSYuI0Ca9VjAhK+IjzfUIIKUsoPAkhpJSIJ/oQtolAYMGCBXLOOefIDz/8oNuWZgLUQDmITqTVq1dPFi9erNu+LeshJYSQ8gqvUoQQUopAMMLZKyshFC0OM88xa/37778P08z5QFiauES+NWvWyCOPPKJhE6OWTggh5RkKT0IIKWUgCv3eyczMTO3lvPzyyyUjIyMUonC+wISzMMqbyISIbdCgQSGx6YcJIaS8QuFJCCGlhC8iAYQn1t3s0KGDvPrqq6GgjIJ4lDVnghMTjI455hj57rvv5LTTTtN8Ztt8Qggpz3CMJyGElBB6OXUC0clBt6ERKhiVvHx58803peeFvXTJJOT1L7/RS7GVg+hMT0+X8847Ty688ELp2LFjmIYyJkoJIaQiQOFJCCElhF5OnQjMzcuVJPeXjHBsKaSBA67ScZm5+QVjPA0IR4tD2Fz79u31rUW9evXS9ToB8lgvqZWDTwghFQEKT0IIKSFMBNrkIGzjVZdYm/O7Gd9qPN6jrn4sr18Ga3NCpKJns3fv3nLIIYeoHcMEppUB5hNCSEWAwpMQQkoIu5zCh5DEO9PxiHz16tWSjD5QJxLR42nCFNsmHFu1aqXvX4fgrFq1amirKGGJdEuD728TQkh5hcKTEEK2k+jl07bhDxkyRN+pjhnoAK+3VMGZHMxKx/vX8cj83HPPVcF55JFHaj6IR+TzRWUUCkxCSEWFwpMQQrYTXD5NKBpYHgm9nJ988okKTBOJ+bmxPE541q9fX9+t3qdPH6lZs6bmMVsgLOPFEULIzgCFJyGE7AB2CYUPd2SHjrrcUU5ujqSkpqoo1TzOdfl7Fzn3/POke/fum4lM3zebFJ2EkJ0NCk9CCNlOcPk0oQiH96cfd8yxGofezpq77iI9e/aUY489VkUnJg+J05J+OfgmMP048wkhZGeCwpMQQrYT//Jpj9tPP/10nVQEsTlhwgR9lG4iEs7y2bafRgghOzsUnoQQsgP4l1ATkhb2JwkBC/t5EPbzEELIzgyFJyGEbCcmGn3fLqm+mEScLfpOCCGVGQpPQggpAaKCM96lNSpGgR9HCCE7OxSehBBCCCEkIfDZDyGEEEIISQgUnoQQQgghJCFQeBJCCCGEkIRA4UkIIYQQQhIChSchhBBCCEkIFJ6EEEIIISQhUHgSQgghhJCEQOFJCCGEEEISAoUnIYQQQghJCBSehBBCCCEkIVB4EkIIIYSQhEDhSQghhBBCEgKFJyGEEEIISQgUnoQQQgghJCFQeBJCCCGEkIRA4UkIIYQQQhIChSchhBBCCEkIFJ6EEEIIISQhUHgSQgghhJCEQOFJCCGEEEISAoUnIYQQQghJCBSehBBCCCEkIVB4EkIIIYSQhEDhSQghhBBCEgKFJyGEEEIISQgUnoQQQgghJCFQeBJCCCGEkIRA4UkIIdtMXswRQgjZFpLyHbFwKcGLM9kRSvu3Ec/PsqWi/va188ba759H/D2fOHb0+7ujnxWvH6QiUzbXqgQIz1znSrkKshNT3BdjR784PD/Llh39fIu78ZfWhbWs6iWF2dHv746ef7x+kIrMjp7/2wd7PEkFZ0e/GDw/yzfFfb7lVXiC0qqbFFDa398dPf8IqciUzjUsAcKTEEJ2NuIJDsT5F2oKT0IIicIrIyGElAi8nBJCSHGwx5MQQraZ4h6xbq0ILSk7hBBSMeAYT1LOKe0bL8/PsqWiCisKz/LBjn5/d/T48vpBKjJlc31hjychhBSiQEzkuwtzfmzWMkIB8S7WUQHi8iB7UrC1OVsSLBSbhJCdFwpPQggpAlwc8/Lz3IXSXSyTClRkGHbxgTDdXHgmQXVul/AEFJ+EkJ0TXt0IIWQLJEUvk3lOaJqL87sdv+XVqSAt/1h7CSEkEVB4EkJIBOgw02LJ6LhMwqUySXs+A1GJhcNjvZZOgObl5TnngjFXXsWctauk21Ze9yeQOE8AAA6RSURBVJcQUv7go3ZCSKUBlzv/kbl/+fPTCqKDQG5ukAYRGpCrD9Nz8Rg+OVnTIT5hIyUlRfP6DpgP8vMhXAvw0wK2r0/A9gf24u0b2gisvmTX9i3h24gH0mHTt7f5vhBCSAEUnoSQSoeJxFdeeUWGDh3qhGOuCqbs7GypXbu2pKamyqZNm1y+HPn999/lr79WS1pKquyxxx5y4IEHSr/+V8oJJ5ygZWBnw8ZNMmTIEFm9erVcfvnl0q5du1DUIc/mgizWW6oC08LG9olO4F/OTWSaMMQ+QhTPmTNHWrZsqftYuE2bA3vIAxvYB2zjGMEOyMnJ0fCCBQtk33331TjbX0IIiQeFJyGkUoFLngmqZ599Vnr37q3bJtQsDYIqOQk9kxCX8FJUaKWlpUnNmjVl6dLFkuNEmMssQ266WcY9Os7ZUBMyZcrH0rp1a7UDfBEa4AvPksNEpvkmDNetWyd33XWXjBs3TsXxypUrdR82b1dh7FgZCJtIX7JkiYwcOVJefPFFtblhwwaNNweKsksIqbxQeBJCKg12ufMve6NHj5aHH35Ye+2CeIjCJOnZs4c0bLCXzJ07T9566y3Jyc1XIWfMmz/XpTeQfCfyrrn6X/L4E0+qyMvMzJTFi3+T3XevHQq7aA9gEgaLKiUrPNF+c++99558/PHH8tNPP8m7776rbYAgxT6sX79e0tPTY6W2LDwByqD8q6++Kp9//rlMnz5dvv76a7WHPFWqVJE1a9ZoXopOQsiWoPAkhFQ67LIHH+6NN96Qc889NxBSeTnSqdOJ8sor/5W8/GzJzs6Rxb8tlYsv6S0zZnwn2bk5kpZaRV597RU55ugjJTU1RWb8b4acccaZ0rzZPnLrrbfK4R2OcHaDXs2g5zR2mXViDHUkJ6cG23GAYLMey20VbwX7lSunn366vOcEZ15+MBwgqBfjUXNVeKLnFttIK6oeswcxjhxt27Z1gnu+iw8e3WOcKwa+Vq1aVVatWqU5t6fdhJDKQ8n+3CaEkAqAiSMILzg8JoZABE6GyUGHHBJ7pJwsU7+epo+mJzzzjDRu3FhSMMPdCbt5c+ZIcoqzk5wvBx3cRmbP/kkmvTjRibPWTuRlO7v5TpQ6AYaJRK4ujBfNcza1DifoYB9i0HeIR+8i2lYg+rYdlB0xYoRccMEF0rx5M7VtNrG/qMPy+X5RWDoe1V944YXSpEkTtYdjhjR7/A7bhBCyJXiVIIRUWqLCK/CTZE3GOsnclCML5i2Uzp27yvHHn6CPk596crykpwU9mPDRE4iezczM9So8Z836Uf5YuUJSXVpSMno8IfTwqDorNvvdCU9XhwlBX6zhUfXSpUslKytLt7cX25c2bdqoUJw588cwzjBxa/hhn2g8Jk09+OCD8v3336tN7Ad6PQsfP0IIKRoKT0JIpQdCzARgUlKKfPvt905oVpXhI26TlJRUFVToFT34kIPk1ltHSOPGDeWYY/9PheRtt90q9evtKUd07Cgndvq77H/AAfLzz4vUFkSpikwX/vKLL3QmfL26e0itWrV09ny9evXUYaIPZsxjtvmwYcMCgarlC0/u2RpM0KLevFh5iGbrYTXfKEp0AqsbPsqghxPOymA5KSe9C9kztrXdhJDKAYUnIaTSgyWCfJH11VdfOUG4h/znpZd18hDApKG0pGTp37efzJr5k+zdtJm7gCZL5xO7yC5OSObnJUlqapornyTVqlV3Ag8P7QOmTp0qXbue5PxpkrkpU8UflmvCbHP0dEK4Qcz5j6pNQG5JGEbx88PHvsAmxnMibOnWq2p5isK3ZXnhY2IS2oxtc1GsLCGE+FB4EkIqPRCCJqCs9w5CE6GcPCe2klOC+JRYr6hz6PlLTU2Xdu3ay4uT/uMEXqrLA4GWLOvXbYiJSCcmXb7+/QcEj7fdJbdpk6bSq1evQnXBb9asmfaENm3atEgxVxxWDnXDBb2TaGfBmp2ID9YoDeouDpQL9qVATKIOhG3bemgJIaQ4KDwJIZWWpPxAOKEHEEIsEHuBr8LKCc6kFAjKfElx4g158GjZl4QIN2++j8ufItk5eZKSlipr164LRKC7xK5du15m/jhLcrKDXs1HH39M7r77bjnggANCkYhH4Vj26LfffpM+ffqEQg8Ebdo6fDGouDahvelVq7h9wUx62E2W7OxcrWNbbQMrg/J41I5Z7agDjhBCioPCkxBSqYH4zNyY6QQVhGEgqHbdtabMmDFDTj/jdElx4hPiqkaNmtp7CQHmZKlTYM4h7MRo9erV9XG9PtJ2WmzNurVqOzc3TzZsyJTcPAi9FMlxeRs1aqTiDXWgJzLIV9BjaGLUhF4hIVkMJgrhm4MerJJeLejVdWmoc8OG9S5U2K6V3ZxYfKwdKr6dM6weE+UWRwgh8aDwJIRUGkwkmcMVMD8pXzZlbXLbGMMIwZcidevWl5Yt95Wrrxrg5JmTU04X1q69e5AHhdBbmBL0IKInEY/ZVSy6vCnOX/XnKsnLTdYxn7vvvrukpae6FLxFKEmmTv1KqlZNl4yMtaGotNdvmgsIxlQC+NYj67t4BGko6+y4hsPaxo0btY2Iw4SjNWsyXGwgIH1bFjanS0A50Zzn7Gicy2Ptw3aSO16iLmgflivV+HAfCCGkMBSehJBKRyCqAtEFPycHIizoaURcsLh6ii4fdMUVV8idd94pu+66a5huzmwBpKn4cqIL73fHNnoZ0cNYtWp1zQcRd9lll0mXLt1k1qxZKKVrYk6YMCG0A1DO2peTkxNuwxWHib4gb3CJh/D025uRgQlNgUC0eiwd26gP9Vrd6MW1dAhzlFMXOx7JSalaB/BtEUJIFApPQkilwwQcRBUE4vLly0MxBTD5xsKjRo2S/v37h4IK+S0NdiwMkWZh+Hj0Dh9lMHsdYKb7+vUb5dNPPw1F7GOPjddZ4shrAhNpTsJpOt6JPn/+fI2HQxywuqIgHc4Wd0f2jRs3xWyCZPntt8WhHcsHUD9AfVg+SntNXf7gcAU+8mIIAcLJToQiHgL0159/K9Q+8wkhxIfCkxBS6bC1KCHGMjM3ySeffKLxEEuIgxBdsmSpbiOfn98ElcWDFStW6DYcBCh6PNFrim0sCo8yEJ1WNhCRoq+aRFlciq1u98+lQcTmS9++fWXfffeVww47TN5++21NB7BrtuIR1BeI6qysbLUHgnK58scff+g24rENzN7RRx8tbdocJHvvva/MnDlT7WA/C0Rlkqxc+acLO1sqPt1+5yfLjz/+GB4f1EMIIfGg8CSEVCpMtMFfsGCBHHFEB5k3b57GmfjCLPf9999fzj//fBWlpqNQxi8PUfb111/rqyltySKkYdY64sHixYs1DSNA8bpNK+tkn74z/bzzznN1tZQvv/xS4wyUGz9+vM54h+h7+OGHNd7aGNiIDwTgLbfcoiKyYcOGhfKizRg6ADF70UUXhe1BGawpOm3aNO2BxaPziRMnattRP7j22utcuXZ6bHTSFUZ9un8IXnrppdK6dWsZOnRo2EZCCIlC4UkIqTSYMATw+/Xr58TnvNiYTkwGCiYJAQi0N954QwUcykWdCbZ7771X5s6dGz6yRnmUnTx5sqZ/9tlnkuqUGeKRnp6a5urDNuyg9zVJli1bJl27dpXPP/9c88A1atREunXrFpbr0qWLtgs2twaIVszMh2jE/qEe7Jr1XqLN2D+AXk8bz4lJSEFcvopT1IcyaMfTTz8ZPvZPSw/eYgTRGbQ5V3799Vd57LHHwvKEEBIlyV0ceHUghFQKcLmDkLIevNmzZ8v06dNdCGIuEJOBUIMAxcLryXL44YdL48ZNXDrKBuWDy2YgCPFY/csvv5a1a9dI1arVNL1Ondpy/PHHaxjLJ61c8YeG4a7oc5nsXqeOi2/gxN9Cue+++zQe73PHazN/+22Jsx08jgdI79Spkxx44IEq/sxOPOxyjrIYR4p9g5jM3LRJe3HnzZsrK/74Q/Jzg3GkBxywn757PSCwfdttd0hGRoYK3eOOO0ZtwSHtySef1DGnWCQ/iA/GoK5YsUzrgcA97rjjZMCAAWqxqHYSQiovFJ6EkEoFLnkQTRBeJqgCH+M4ka65YuGg9xHva0ecPQoPLpuBUAvsWd7gfebwAXoV0WuoYyFdeYzXfP3N16Ru/Tqab8XyP6VlyxZav80y//bb7/RRtrUPWHuR7os5PwzQBsQhf9CuoD36TvWYjXzM3nd5EMb+WBm0MMiDR+gmznNdmkvxjpXlg/h0NxDJ0TVKg7Gpga1g3CvyRttHCCEUnoSQSoOJLPgmxIrCzxsVUYizeNuOB+o466yzdGJQsJ0r1apVlU6dOmv43Xff19nvyAcbRx11lHz44YdqN3jsHbQPab74K67dvm/lfGAD6XAWtn0BFg4mORUWjyYsgV+X31awpTYSQiovFJ6lTuELPtlWePMiJQsueSamope/qMiK5o2mF4fZ7969u7z22mux8rBjacHjeghDPE5/4YUXpEaNGloGRNuJ7W1pRzRv1I4RrQcEedDj6acVfB/NRrSsv21hQsonxd2fef8pDSg8Sx0sVcJDvP0U98XnhYGUDVsjrOzyCmH5n//8R5566ilZunSxrpGJnk5M5MEC8pgRjtnthom6aC8iKEkxtzV2S6vu8gGFR+WmuPsz7z+lAYVnqcMez9KFX3yy9eByt6PiaVttIL85lINDGMQLw0UfU0frM1tbg+X1yyAMtsZGvPI+fjrYGpvlBwrPys2O3p95fmwPFJ6EEFJKmCiLN17TLr02vhNxvmirWAKOEEK2DgpPQghJALjUWs8gRSUhpLLCfmJCCCkl7He9LzYpOgkhlRn2eJY6HOO5Y/C3Edk5KK6n078UU5wSkgg4xrcsoPAkhBBCCCEJgXKeEEIIIYQkBApPQgghhBCSECg8CSGEEEJIQqDwJIQQQgghCYHCkxBCCCGEJAQKT0IIIYQQkhAoPAkhhBBCSEKg8CSEEEIIIQlA5P8BZmTYnTdB6vgAAAAASUVORK5CYII=	4^\circ
+775	A new and important experimental technique being used in several sub-fields of physics is the use of ultra-short light pulses for studying fast phenomena. The ultra-short pulses are produced by mode-locking a laser — a method to be studied in this problem. The model laser consists of an optical cavity of length $L$ with transverse dimensions $d$ formed by two flat mirrors as shown in Fig. 3.7.  The amplifying medium (it may be solid, liquid, or gas) can be characterized by a certain gain spectrum (Fig. 3.8); only light within this band of frequencies will be amplified. To simplify calculation, assume the gain spectrum is rectangular as shown in Fig. 3.9.  To be specific, consider the amplifying medium Nd glass, which has   $$ \omega_0 = 1.8 \times 10^{15} \text{ sec}^{-1}, \quad \Delta\omega = 6 \times 10^{12} \text{ sec}^{-1}, $$   and take the length of the laser to be $L = 150 \text{ cm}$.  (a) Find the separation $\delta\omega_L$ between adjacent longitudinal modes of the cavity. Neglect the modulator for this part of the problem, neglect dispersion, and, for simplicity, take the refractive index of the amplifying medium to be one.  (b) The rectangular gain spectrum will result in each mode within the gain band having equal amplitude. If the intensity of an individual mode is $I_0$, what is the total intensity when the relative phases $\phi_n$ of the different modes are randomly distributed?  (c) By inserting a modulated absorber into the cavity, one can lock the phases of all the modes to the same value, so that traveling waves interfere constructively, producing light pulses. Find the intensity as a function of time in this phase-locked or mode-locked case. What is the pulse duration, pulse separation, and peak intensity (in terms of $I_0$)? Consider only one polarization.  (It is irrelevant for this problem, but for your information, a modulated absorber has an effective absorption that is a function of time — e.g., $\alpha = \alpha_1 + \alpha_2 \cos(\omega t)$. Any cavity mode with the wrong phase relative to this modulation experiences excess attenuation, so only phase-locked modes are amplified.)	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	\delta \omega_L = 6.3 \times 10^8 \, \text{s}^{-1}; I = 9549 \, I_0; I(t) = I_0 \left[ \frac{\sin \frac{9549 \cdot \delta \omega_L t}{2}}{\sin \frac{\delta \omega_L}{2}} \right]^2; \Delta t = 1.05 \times 10^{-12} \, \text{s}; \Delta_t = 10^{-8} \, \text{s}; I(0) = 9.12 \times 10^7 \, I_0
+776	 A ruby laser emits light with a wavelength of 6943 Å, which to a very good approximation is a plane wave.   (a) Describe qualitatively how such a laser works, including a rough energy level diagram of the relevant atoms involved.   (b) What is the wavelength and frequency of this light as it passes through water (refractive index $n = 4/3$)?   (c) What fraction of each component of polarization of the laser light is reflected as the beam enters the water at 45° to the normal to the surface?   (d) What are the amplitudes of the electric and magnetic field vectors of this plane wave propagating through water, if the time-averaged power of the beam in the water is 100 milliwatts/cm²?   (e) What is the coherence length of the laser in vacuum (i.e., the distance over which the light stays coherent to 1/4 of a wavelength) if the bandwidth of the laser is $\Delta \nu = 30$ megahertz?	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	\lambda_{\text{water}} = 5207 \, \overset{\circ}{\text{A}}; R_\perp = 0.05; R_{\parallel} = 0.0028; E_0 = 7.5 \, \text{V/m}; B_0 = 3.3 \times 10^{-8} \, \text{T}; \Delta l = 10 \, \text{m}
+777	**Metallic diffraction grating.**  Purcell (Phys. Rev. **92**, 1069) has shown that electromagnetic radiation is emitted from a metallic diffraction grating when a beam of charged particles passes near and parallel to the surface of the grating.  The velocity of the charged particles is $v$ and the grating spacing is $d$. Consider only the light emitted in the plane perpendicular to the grating and containing the particle trajectory.     (a) How does the frequency of the emitted radiation depend on direction?     (b) Suppose the metallic grating is replaced by a transmission grating, e.g., a piece of glass with grooves ruled onto it, still $d$ apart. In what way, if any, will this change the emitted radiation? Explain qualitatively.	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+778	 A projective photon, with frequency $f$ in the rest frame of a target electron, is seen to scatter at $-90^\circ$ with frequency $f'$, while the target scatters at $\theta^\circ$.  (a) Determine the relation of $f'/f$ to $\theta$. (b) Determine the total electron energy in terms of $f$, $f'$, and the electron mass $m$. ( c ) If the photon energy loss would be 0.2 of the rest energy of the electron, what would be the speed of the scattered electron?  (d) An observer O moves in a direction parallel to the incident photon's direction at a speed $u$ when the electron-photon collision occurs. What expression would O use for his measure of the electron's energy in its scattered state (in terms of $m, v, u$ and $c$)?	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+779	A narrow beam of light is incident on a $30^\circ - 60^\circ - 90^\circ$ prism as shown (Fig. 1.3). The index of refraction of the prism is $n = 2.1$. Show that the entire beam emerges either from the right-hand face, or back along the incident path.	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	\theta_c = 28^\circ26'
+780	A point source, $Q$, emits coherent light isotropically at two frequencies, $\omega$ and $\omega + \Delta \omega$, with equal power, $I$ joules/sec, at each frequency. Two detectors, $A$ and $B$, each with a (small) sensitive area $S$ capable of responding to individual photons, are located at distances $l_A$ and $l_B$ from $Q$ as shown in Fig. 3.12. In the following, take $\frac{\Delta \omega}{\omega} \ll 1$and assume the experiment is carried out in vacuum.  (a) Calculate the individual photon counting rates (photons/sec) at $A$ and at $B$ as functions of time. Consider time scales $\gg 1/\omega$.  (b) If now the output pulses from $A$ to $B$ are put into a coincidence circuit of resolving time $\tau$, what is the time-averaged coincidence counting rate? Assume that $\tau \ll 1/\Delta\omega$ and recall that a coincidence circuit will produce an output pulse if the two input pulses arrive within a time $\tau$ of one another.	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	R_A(t) = \frac{IS}{2 \pi \hbar \omega l_A^2} \left[ 1 + \cos(\Delta \omega t) \right]; R_B(t) = \frac{IS}{2 \pi \hbar \omega l_B^2} \left\{ 1 + \cos \left[ \Delta \omega t + \frac{(l_A - l_B) \Delta \omega}{c} \right] \right\}; R_{AB}(t) = \frac{I^2 S^2 \tau}{2 \pi^2 \hbar^2 \omega^2 l_A^2 l_B^2} \left[ 1 + \cos(\Delta \omega t) \right] \left\{ 1 + \cos \left[ \Delta \omega \left( t + \frac{l_A - l_B}{c} \right) \right] \right\}
+781	A glass cube has a refractive index of 1.5. A light beam enters the top face obliquely and then strikes the side of the cube. Does light emerge from this side? Explain your answer.	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	\text{No light emerges from this side.}
+782	Solar energy at the rate 800 W/m$^2$ strikes a flat solar panel for water heating. If the panel has absorptance = 0.96 for all wavelengths and the sides are perfect insulators, calculate the maximum temperature of the water. If the absorptance dropped by 1/2, how would this affect the final temperature?	[]	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	T_{\text{max}} = 341 \, \text{K}; T'_{\text{max}} = 286 \, \text{K}
+783	 An electromagnetic wave ($\mathbf{E_0}$, $\mathbf{H_0}$) traveling in a medium with index of refraction $n_1$ strikes a planar interface with a medium with $n_2$. The angle the wave makes with the normal to the interface is $\theta_1$. Derive the general Fresnel equations for the reflected and refracted waves. Obtain Brewster's law as a special case of these equations.	[]	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	r_p = \frac{\tan(\theta_2 - \theta_1)}{\tan(\theta_2 + \theta_1)}; t_p = \frac{2 \sin \theta_2 \cos \theta_1}{\sin(\theta_2 + \theta_1) \cos(\theta_2 - \theta_1)}; r_s = \frac{\sin(\theta_2 - \theta_1)}{\sin(\theta_2 + \theta_1)}; t_s = \frac{2 \sin \theta_2 \cos \theta_1}{\sin(\theta_2 + \theta_1)}; \theta_1 = \tan^{-1} \left( \frac{n_2}{n_1} \right)
+784	An electronic transition in ions of $^{12}C$ leads to photon emission near $\lambda = 500 \, \text{nm} \ (h \nu = 2.5 \, \text{eV})$. The ions are in thermal equilibrium at a temperature $kT = 20$ eV, a density $n = 10^{24}/m^3$, and a non-uniform magnetic field which ranges up to $B = 1$ Tesla.  (a) Briefly discuss broadening mechanisms which might cause the transition to have an observed width $\Delta \lambda$ greater than that obtained for very small values of $T$, $n$, and $B$.  (b) For one of these mechanisms calculate the broadened width $\Delta \lambda$ using order of magnitude estimates of the needed parameters.	[]	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	\Delta \lambda = 0.2 \, \text{Å}; \Delta \lambda = 0.1 \, \text{Å}; \Delta \lambda = 0.1 \, \text{Å}
+785	Consider a gas of atoms A at $T = 300$ K, $p = 100$ Torr. The mass of each atom is $4.2 \times 10^{-27}$ kg and Boltzmann's constant is $1.4 \times 10^{-23}$ J/K. Some of the atoms are in excited states A* and emit radiation of frequency $\nu$.   (a) Estimate the Doppler width $\Delta \nu_D / \nu$.   (b) Assume a reasonable cross-section for A*-A collision and estimate the pressure-broadened width of the line $\Delta \nu_p / \nu$.	[]	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	\frac{\Delta \nu_D}{\nu} = 3 \times 10^{-6}; \frac{\Delta \nu_p}{\nu} = 1.2 \times 10^{-7}
+786	 (a) Consider the emission or absorption of visible light by the molecules of a hot gas. Derive an expression for the frequency distribution $f(\nu)$ expected for a spectral line, central frequency $\nu_0$, due to the Doppler broadening. Assume an ideal gas at temperature $T$ with molecular weight $M$.  Consider a vessel filled with argon gas at a pressure of 10 Torr (1 Torr = 1 mm of mercury) and a temperature of 200°C. Inside the vessel is a small piece of sodium which is heated so that the vessel will contain some sodium vapor. We observe the sodium absorption line at 5896 Å in the light from a tungsten filament passing through the vessel. Estimate:  (b) The magnitude of the Doppler broadening of the line.   (c) The magnitude of the collision broadening of the line.    Assume here that the number of sodium atoms is very small compared to the number of argon atoms. Make reasonable estimates of quantities that you may need which are not given and express your answers for the broadening in Angstroms.   Atomic weight of sodium = 23.	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+787	 During the days when there are no clouds and the atmosphere is relatively dust (smog) free and has low humidity, the sky, away from the sun, has a very deep blue color. This is due to molecular scattering.   **(a)** If the molecular electric polarizability due to the photon E field is frequency independent, show how this leads to a wavelength dependence of the scattering of sunlight similar to that observed. Discuss the angular dependence of the scattering.  **(b)** If in each air volume element $\Delta V$ of sides small compared with $\lambda$, the mean number of molecules is $N_0 \Delta V \gg 1$, and if there is no fluctuation about this mean number, show that no net scattering results.   **(c)** If the root-mean-square fluctuation of the number of molecules equals the square root of the mean number, show that the net scattering intensity is as if each molecule scattered independently with no interference between molecules.  **(d)** When the relative humidity is near 100% there is observed to be enhanced scattering (relative to (c)) for water molecules. Explain.	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+788	Calculate the ratio of the intensities of the reflected wave and the incident wave for a light wave incident normally on the surface of a deep body of water with index of refraction $n = 1.33$.	[]	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	R = 0.02
+789	While an aquarium is being filled with water (index of refraction $n > 1$), a motionless fish looks up vertically through the rising surface of the water at a stationary monochromatic plane wave light source. Does the fish see the light source blue-shifted (higher frequency), red-shifted (lower frequency), or is the frequency change identically zero? Explain your reasoning.	[]	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	\text{Red-shifted}
+790	Two parabolic radio antennae, each of diameter $D$, are separated by a distance $d \gg D$ and point straight up. Each antenna is driven by a transmitter of nominal frequency $f$, and wavelength $\lambda(= c/f) \ll D$. Be sure to properly label all sketches.  (a) What is the approximate shape of the pattern of radiation at large distance away $(r \gg D^2/\lambda)$ of one antenna if operated alone?  (b) What is the approximate shape of the pattern of radiation at large distances ($r \gg d, r \gg D^2/\lambda$) if both antennae are driven in phase by the same transmitter?  (c) Suppose the antennae are driven by separate transmitters, each of nominal frequency $f$. If the pattern of part (b) above is to be maintained essentially stationary for some time $t$, what is the requirement on the frequency stability of the two transmitters?	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+791	 A source of circularly polarised light illuminates a screen with two equidistant narrow slits separated by a distance $L$ (see Fig. 2.79). A thin birefringent slab of thickness $d$ is placed over one of the slits. Its index of refraction is $n_o$ parallel to the slit and $n_e$ perpendicular to the slit. A second screen, parallel to the first, is placed at a distance $D \gg L$ behind the first screen. If one of the slits is covered, the total intensity on the second screen is $I_0$ (neglect diffraction effects). With both slits open, what is the interference pattern that would be observed by someone who measures the total intensity, summed over polarisations?	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	\text{Perfect coherence at }(n_o - n_e)d = m\lambda, \text{ and disappearance at } (n_o - n_e)d = \left(m + \frac{1}{2}\right)\lambda
+792	The diffraction pattern below (Fig. 2.51) is produced on a screen by light passing through three distant slits of width $w$ and spacing $d$ (Fig. 2.50). How will the envelope width $A$ and the separation of the peaks $B$ change if:  (a) The slit width $w$ is increased?   (b) The slit spacing $d$ is increased?   ( c ) The wavelength of the light is increased?    The amplitudes of the E-field arriving at point 2 on the screen are represented on the right by three equal vectors summed with the appropriate phases for this position (Fig. 2.52). As shown, they add to zero, which  is why there is zero intensity at this point on the creen. Make a similar vector diagram showing the relative phases:  (d) at point 1.  (e) at point 3.	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	A \text{ decreases, } B \text{ unchanged}; A \text{ unchanged, } B \text{ decreases}; A \text{ increases, } B \text{ increases}; \to \to \to; \Rightarrow
+793	 Consider the modified Young's double-slit arrangement (Fig. 2.78): $Q$ is a monochromatic point source of light with wavelength $\lambda$. $S_1$ is a screen having a long narrow slit and $S_2$ has two slits of width $a$ separated by a distance $d \gg a$, $P_1$, $P_2$, $P_3$ and $P_4$ are polarising filters. For each of the following arrangements, describe and briefly explain the intensity pattern on the screen $S_3$.  (a) All polarizers removed. (Here derive a formula for the intensity pattern on $S_3$.)   (b) $P_1$ removed, $P_2$ and $P_3$ have mutually perpendicular pass axes while the axis of $P_4$ is at $45^\circ$ to that of $P_2$.   (c) As in (b) but with $P_4$ removed.   (d) $P_1$ in place and at $45^\circ$ to $P_2$, $P_2$ and $P_3$ still crossed. $P_4$ perpendicular to $P_1$.	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	I(\theta) \propto \cos^2 \left(\frac{1}{2}kd \sin \theta \right) \frac{\sin^2 \left( \frac{1}{2}ka \sin \theta \right)}{\sin^2 \theta}; \text{No interference pattern; only single-slit diffraction images}; \text{No interference pattern; only single-slit diffraction images}; \text{Interference pattern with reversed contrast compared to (a)}
+794	 Compare the merits of the following three instruments for studying atomic spectra (in the visible range).  (1). Plane diffraction grating. (2). $60^\circ$ glass prism. (3). Fabry-Perot interferometer.  Consider as quantitatively as possible such features as resolution, dispersion, range, nature of light-source, etc. Indicate clearly the important physical and geometrical features in each case. (For the sake of definiteness, you may assume all three instruments to have similar 'apertures'.)	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	"\begin{aligned}
+\text{Resolving Power:} & \\
+\text{Prism:} & \, R \approx 10^4 \\
+\text{Grating:} & \, R \sim 10^5 - 10^6 \\
+\text{Fabry-Perot:} & \, R \sim 10^6 - 10^7 \\
+\text{Angular Dispersion:} & \\
+\text{Prism:} & \, \frac{\Delta \theta}{\Delta \lambda} \approx 1.3 \times 10^3 \, \text{cm}^{-1} \\
+\text{Grating:} & \, \frac{\Delta \theta}{\Delta \lambda} \approx 10^4 \, \text{cm}^{-1} \\
+\text{Fabry-Perot:} & \, \frac{\Delta \theta}{\Delta \lambda} \approx 2 \times 10^4 \, \text{cm}^{-1} \\
+\text{Wavelength Range:} & \\
+\text{Prism:} & \, \text{Limited by absorption} \\
+\text{Grating:} & \, \text{Avoid overlap: } m\lambda_2 < (m+1)\lambda_1 \\
+\text{Fabry-Perot:} & \, \Delta \lambda = \frac{\lambda^2}{2d}
+\end{aligned}"
+795	 Optical apodisation is the process by which the aperture function of the system is altered to redistribute the energy in the diffraction pattern. To improve the resolution, consider the example where the transmission is modified by a cosine function, $\cos \pi x / b$, between $-b/2$ and $+b/2$, where $b$ is the slit width.  (a) Calculate the position of the $n$-th minimum of the single-slit Fraunhofer diffraction pattern, and compare it with the position of the $n$-th minimum of the unapodized slit of the same width $b$.  (b) Calculate the intensity which appears in the apodized diffraction pattern halfway between the $(n-1)$-th and $n$-th minima, which is near its  \(n\)-th maximum. In each case, normalise your result to the intensity of the first maximum.	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+796	 Four perfect polarising plates are stacked so that the axis of each is turned 30° clockwise with respect to the preceding plate. How much of the intensity of an incident unpolarised beam of light is transmitted by the stack?	[]	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	\frac{27 I_0}{128}
+797	A plane wave of light from a laser has a wavelength of $6000 \, \text{Å}$. The light is incident on a double slit. After passing through the double slit the light falls on a screen 100 cm beyond the double slit. The intensity distribution of the interference pattern on the screen is shown (Fig. 2.48). What is the width of each slit and what is the separation of the two slits?	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	b = 1.5 \times 10^{-3} \, \text{cm}; d = 6 \times 10^{-3} \, \text{cm}
+798	A vertical soap film is viewed horizontally by reflected sodium light ($\lambda = 589 \times 10^{-9} \, \text{m}$). The top of the film is so thin that it looks black in all colors. There are five bright fringes, the center of the fifth being at the bottom. How thick is the soap film at the bottom? The index of refraction of water is 1.33.	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	d = 1.0 \, \mu \text{m}
+799	(a) Derive the lens makers' formula for a thin lens  $$\frac{1}{f} = (n - 1) \left( \frac{1}{R} + \frac{1}{R'} \right).$$  (b) Crown and flint glass lenses are cemented together to form an achromatic lens. Show that the focal lengths of the crown and flint components satisfy the equation  $$\frac{\Delta c}{f_c} + \frac{\Delta f}{f_t} = 0,$$  where $$ \Delta = \frac{1}{\bar{n} - 1} \frac{dn}{d\lambda} \Delta \lambda $$  and $\bar{n}$ is the value of the index of refraction of the glass at the center of the visible spectrum and $\Delta \lambda$ the wavelength spread ($\sim 3000 \text{Å}$) of the visible spectrum.    ( c ) For crown glass $\Delta_c = 0.0169$ and for flint glass $\Delta_f = 0.0384$. Show that one must use a converging crown glass lens cemented to a diverging flint glass lens to get a converging achromatic lens.	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+800	An opaque screen with two parallel slits is placed in front of a lens and illuminated with light from a distant point source.  (a) Sketch the interference pattern produced. (Make a rough graph of the intensity distribution in the focal plane of the lens.)  (b) Indicate with a second graph and a brief explanation the effect of moving the slits further apart. (c）Indicate with a third graph and explanation the effect of increasing the size of the source so that it subtends a finite angle at the lens.	[]	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	\Delta x = \frac{\lambda f}{d}
+801	A point source $S$ located at the origin of a coordinate system emits a spherical sinusoidal wave in which the electric field $E_1$ is given by $E_1 = A(\frac{D}{r}) \cos(\omega t - \frac{2 \pi r}{\lambda})$, where $r$ is the distance from $S$. In addition, there is a plane wave propagating along the $x$-axis. This wave is given by  $$ E_2 = A \cos \left( \omega t - \frac{2 \pi x}{\lambda} \right). $$  (Note that we treat both $E_1$ and $E_2$ as scalar waves in this problem.) Both waves are incident on a flat screen perpendicular to the $x$-axis and at a distance $D$ from the origin, as shown in the figure (Fig. 2.1). Compute the resultant intensity $I$ at the screen as a function of the distance $y$ from the $x$-axis for values of $y$ small compared with $D$. Express $I$ in terms of $y, D, \lambda$ and the intensity $I_0$ at $y = 0$.	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UuXMkFbiqI6OjquuoZGkqTZbAZWuVwuk8kEtiHXA71e39zc7GsrFhhQfCFXR6vVDg0NIQjC4/GysrLGrVz19/e3tLQgCCIUCiMjI6e7rkXTdHt7+759+77++muKosBOHMdjYmJ4PB5N011dXQcOHDh48CDzLIfDuWqyoFarPXnyJGjprdfrP/jgAw9pGJBrBCbOz4DASn50uVxardblcsGsT++hafrYsWMWiwVBkNTU1NTUVHd5JUny2LFjY2NjCILk5+eD4ICXZ6YoymazXbx48dVXXz1//jwQShzHJRLJrbfeumvXrrGxsaNHj7733nvMsxwOJy4u7v7777/ttts8n7yqqqq4uBh4uyCa8emnn/7617+GMnE9sFgsIyMjvrZigRFYGkRRlN1uh7ef04KiqHPnzpEkiaJoSkrKuNlclZWVn3/+ucvlwnE8Ojram7ADRVEjIyMkSba0tHz++eeff/75wMAARVEoioaEhNx44427du0KDw8vKys7cuTIjz/+aDAYKIoSi8WxsbFAdiMiIjyPI3G5XG+++abZbGb2WK3Wr7/++q677oqOjp7pJwGZkrCwsLy8vIqKCl8bspAILPFls9kqlQoWm06L0dFR4NjKZLI77rhDIpGA/SRJtre3P/vssyDYFxYWdu+99zLPToXBYDh06NCJEydsNltnZ2dHRweCIBiGKRSKoqKiDRs21NfX79+/32az1dbWgpoOoVCYn5+/ffv2DRs2KBQKb1xXg8HQ398P0jBycnJQFL1y5cqVK1e+/PLLPXv2wDlSsw6GYbBqdLoElvhCpgtFUR999BEI6WIY1tvbW11dTRCExWIpKyv7/PPPz507hyAIn8/fsmVLVlaW57PZbLY333zztddeAytpAD6ff8cdd+zatSsvL+/LL798++23mWdxHE9KSnr88cfXr1+vVCq9DBbRNH369GmQ3hAeHr53797Kysqqqiqr1Xrw4MGNGzfGx8fP6MOATInL5XK/z4B4AxRfiCdomh4eHgalvVqt9tlnn5XL5RiGuVyuoaEhkGwrEAjuu+++Z5999qrTwsfGxsrKyhhtZbFYkZGRP/3pT3fv3g0aErLZbBzHMQzDcVwoFG7cuHHPnj2ZmZnTitEbjcYTJ07o9XoURdeuXbtkyZLIyMjDhw/X1NS0trYeO3bsV7/6lefuP5DpotFoampqfG3FAgOKL2QaWK3WcTkDXC73oYce+t3vfudNO9egoKBdu3bV19d3d3dHR0ffdtttu3btSkxM5PF44ICioqL9+/eXl5cvWrQoNzc3NzdXLBZPN32ipKTk2LFjCIKw2ez169eDirvU1NTa2lqLxfLmm2+Ojo7+8pe/DA0NndZpIR5wuVxeNt+AMEDxhXgCw7C8vLyIiAitVjvuKYVCceutt2ZnZ999992eS4rdz/aTn/yEy+W2trbecMMNubm54w5QKpX33XfffffdN2ODjUbjwYMHjUYjgiBhYWEpKSkoigYFBW3ZsuXMmTMajaanp+eVV14RCoVPPPEE9H9nC9g3YwYElvjSND02Ngb7+XoPiqIbNmxISEiY6NcIBIKoqKjpLrMIhcJbb7119gwcj81m6+3tpWkax/H8/PywsDCwv6io6Le//e2XX3556dIlBEF++OGHRx55BIrvbCEQCMLCwmD3uGkRWOJrNpvBwgtcmfUegiDS09N9bYW3yOXyp556yuVyRURE7N27lwmGCIXCxx577Cc/+cm//vUvFot1yy23CIVC35rqT5AkCcuLp0tgiS+Xy01ISADNViB+CY7jt95665IlSwiCkMvl7rfDKIomJyf/4Q9/AM3g4Z3yLGK1WicGpiCeCSzxRRAE1rb5PTiOM9GGcaAoClvpQ+YJgRX6BPWssMINAoH4nMASX1jhBoFA5gmBJb4QCAQyT4DiC4FAID4Aii8EAoH4ACi+EAhkNqEoSqfTuVwuXxsy3/H/vCuSJE0mk6+t8B/MZnNfXx8oVAkKCnI4HARBYBgmFAphwRgEQRC73V5XV2exWK7aaCnA8X/x1ev1sMfzbKHX61977TUwvz00NDQhIcFkMvF4PC6Xm56eXlRUtHTpUs/dcpk8v0lrHMCzsPxhQYOiKEEQ8I94VfxffOFc1dmCoqhTp04dOHBAo9EgCDIyMtLQ0MA8+/XXXx85cuR//ud/1q1b50F/m5ubGxoapFJpRkbGuAo0kiRramq6u7tVKpVSqVSpVLAFx0IBRVHmT8nlcrOzs2H19lXxf/GFzBYURanVatAzG8dxDofDjBO22WwOh6O+vv6pp54SCASrVq2a1PEZGxvbv3//+++/L5VKb7755t27dy9btoypObx06dIjjzzS2NgYHh6enJy8c+fOdevWXUvjR7vdXlNTIxaLk5KSmJ00TYORSHCexSwilUrj4uIqKyvBQy6XCz3fqwI9C4i3OJ3O9vZ2q9WKIMidd955/vz58vLy8vLy7777bu3atUDLmpqaDhw4AMb/TARFUYlEwmaz9Xr9Z599tnXr1ueee666utpqtVIUVV9f39fXR1FUX1/f999/v2fPnl//+tdNTU0zaxRrNptffPHFzZs3P/jgg2ASB4IgFEVduHDhT3/60xtvvNHT0wNrHWcL2FhnJtD+TldXV2JiInizIpHo4MGDvrZooaJWq1esWIEgSHh4eGlpKbMf6GZubi5wdvLz87u7u6c6SXt7+8svv7xy5UqwOoeiaExMzEsvvdTb26vT6f7xj3/s3LkzLCwMSDlBEDk5Ob/97W+vXLnicDimZW1bWxsYF0QQxIEDB0iSpGm6o6OjoKAA7Hz++edBrTnk2tFqtcw8aR6P9/e//93XFi0AoOcL8ZaGhobOzk4EQcLDw92jASiKJiUlxcbGgodKpZLP5091ktjY2Keeeur9999/7rnnMjIyOBxOZ2fnSy+9tGXLlu+///6OO+546623vvzyy+effz4pKYkkyYqKiv379997771ffPGFTqejvfZVMQwD7etIkhweHkYQhKKoM2fONDY2gm2g5jP9MCD/DywWi+lYZLfbq6urwdBViAeg+EK8giTJQ4cO9ff3IwgSHh4+Tl5JkgR5nVwud/Xq1UFBQR5OxWKx4uLinnvuucOHD//ud79LT0+32+3FxcW7d+9+4oknOjo6cnJynn/++ffee2/nzp0SicTpdDY2Nu7Zs+exxx779ttvvfxVS6XSlJQUsE1RFIIgnZ2dH374IXh5XFzcli1bYHPR2cJutzOj+UCeL5jvB/GA/4svi8XyrAUQb+jp6amvr6dpWiQSbdiwYdxH2tPT09zcDJ5NSkryJksBx/HU1NSnn376s88+27Ztm1gsHh4ePnz48I4dO1599VWdTrd8+fLXX3/9L3/5y6pVqwiCGB4e/vjjj++///6HHnoIeK9eQtN0dXW1xWJ56623iouLKYri8Xg7d+7MzMyEi0KzhUAg8GaIH8Qd/xffkJCQzZs3MyMagRMEmS4XL15sampCEITP58fExIyT1+bmZnBrD3I8vT8th8NJSUnZv3//3XffTRAESZJNTU179+49deoUTdNyufxnP/vZhx9+uHHjRoIgKIoaGhr67LPP9u3bN9WaHgOKosBImqZLS0v//Oc/f/LJJ06nE8Ow2267bffu3bCz8ywyPDxcV1cHtgmCiIuLY35xkKnwf/EFQ84dDgeCIBaLpba2FqzXQ7wHJJnZ7XYEQVQqVVZW1rhn6+rqQBlhZGRkRETEtE5OkqTRaBwZGWFuVB0Oh9FoBAFZu92u1WopimKeBf/dVYMPIpEoOzsbBBb6+vr2798/NDSEIEhaWtozzzwDb4ZmFxaLxST2slis6OhoWO54Vfz/4u9wOPr7+8FPl81mh4WFwX6+02VwcPD48eNOpxNF0aVLl46bVaxWq48fP+5wODAM27hxo3tSrWcoijKZTF9//fWHH3545swZiqJQFOVwODExMdHR0TRNNzQ0fPrpp5999llrayu4ZeFyudHR0Q8++KBKpfJ8chzHJRIJ4/yCK0dISMijjz467uIBuXZCQ0MzMzMvXLgAHsKVTG/wf/Hl8Xjx8fFsNtvhcLBYrJCQEHi/OV0MBkNDQwNN02w2Oz8/3z3m4HK5Dh06VF5eDgK+sbGx3gRSaZrWaDQXLlz49NNPv//+e5DGwGazU1NTN2zYcO+99xIE8dFHH7355pv19fVAN4E/deeddz7wwANRUVEzCNey2ewdO3Zs27YNhnpnHQzDGFeXoiitVutyueAPzTP+/+lYrdbW1lYQdoDMjN7eXqCA6enpq1evZgrbnE7niRMnXn/9davViqLosmXLbr75Zg/SRtN0c3Nza2ur1Wr99NNPL1y4MDw8DMZZpqenb9mypaioyGKxVFVVffTRR99//73FYkEQhMVihYeHb968edu2bdnZ2d7fuCgUCi6Xy0SZMjMzd+/eLZFIrvXjgEzAfYAmqHiEiytXxf/FlyAIOCj+WqAo6i9/+QvQQbPZfPr06YyMDBRFu7u7T506dfToUdDqISEh4dFHH/W85F1WVrZnzx4QQzAajRRFsVisnJycXbt2bdy4USAQPP/880ePHrVareBZFEVVKtXWrVt37tyZmJjoIX14UlQqlUAg0Ov1CIIEBQXt2rUrOjp65h8EZGpGRkbAeiyCIDiOi8ViWL19VfxffEEY0ddWLGBAiABE8Zqbmx9++GFwO8nk9qIoGhsb+/LLL2/YsMFDkhlFUd98801ZWRnwiTAMk8lkP/vZzx577DEQRqiurn7//feBiw3c4aKioieeeGLlypUzCNNbrdavvvoKLLIRBHHvvff+7Gc/g4pwnaBpmikvxnHcbre7XC74aXvG/8XXHZD5AKNR08X94yJJkkk8YNbH9u7d61l5wcErVqxITU0dGhqSSqVZWVk7duxYu3atSCQCB0gkkhUrVpSVlXE4nNjY2K1bt27ZsiUsLGxmvc3q6uqOHDkCFCEtLW3Hjh3wBmhuCAkJuemmm6DHc1UCS4NomoahqOmCoujtt9+uVqvHxc1RFM3IyFi/fn1OTs6KFSuuKpEoiq5cufKrr75qbW1dtGhRWFjYuGbb0dHRH3zwwfnz50HDyemmrAFAQKO/v//VV1/t6OhAEEQsFj/33HN5eXkzOBvES3AcZ+5OtFptS0tLfn6+b02a/wSW+BIEERYWBt3eaYFh2OOPP3733XdPfEokEsnlcu/vLoGbHBMTM9UBkZGR27dvn6GhCELT9Pnz51955ZWmpia1Wg2ixuvWrVu7di3McLiuKJXKnJycsrIyBEFcLtfMGtEFGv4vQxiGSaVSFosFh0rNGC6XGxcX52srro7NZjt69Ojp06eZwIhCobj33nthScX1BsOw6S6HQvxffEEak1AovGpBKmShQ9M0aB2JIAiO4zExMffcc8/q1at9bZf/477gBvES/xdfsG4O7zoDAR6Pd/fdd7e2tup0usLCwvvuuy8pKQmu/MwBdrsdjqmdLv4vvhRFaTQacFkmSVKj0ZAkCZNg/BIURQsLCw8ePOh0OmUyGY/HgxfduYHD4cBZxdPF/8XXbrfX1taCPixMYx043c9fwXE8JCTE11YEHKOjo6DR/jhIkpxYXErTdGtra29vb3Z2tkwmm+oCiaIoWBsHnhOLxUJRFKzcsFgskiRB5hKO4wu0iY//iy8EArmukCTZ0dHBDMpjcDgcH3/88V//+teJyQ9jY2NWq1Umk3lIPZLJZMuXL3c6nZcvX7bZbLm5uQqForq62mw233DDDa2trTU1NSiKZmdn/+Y3v8nKylpwdzlQfCEQyPQALidJkkNDQ/39/RUVFYcOHWptbR13WFNT08svvzxxP8PIyIjn/6i4uJjZrqqqYrZ//PFHZru5udloNP773/9m5hgtFKD4QiAQryBJEowLKi0tHRkZqa6uvnDhwtDQkNFonHS1DSQaDQ4OjhspBGIR49pOziBA73K5QCPToKCgBef2IlB8IRDIVIC8PYPB4HK5tFrtmTNn6uvr29raSkpKLBbLVZv2JiUlvf32299///24LLS+vr533313YGAAK65/AAAAIABJREFUPERRNDc3d+fOnUyhuZeo1erW1la5XL5nz56FmNMCxRcCgfz/gP4nJpNpcHCwurq6paWlrKxMr9c7nU6NRmO1Wr1vlI6iaHh4+L333jtuv9FoLC8v/+qrr8BDDMNuueWWGQx2cjqdVqsVx/EFWt8BxRcCCVwoigJi2t/f39XV5XK5zp49e+7cucHBwba2NuRqMykwDENRFMdx9yILLpfruWny4OBgTU2Nuw3Nzc1jY2NSqXRaxhMEsaCn0kDxhUACC5qmzWaz0+nU6XQVFRV9fX16vf6bb77p7++nKMp9mN6k4DiuUChA4+bY2NikpKScnBybzfbCCy+AbLOgoCDPo6Tq6urcy01pmj5z5gzodTdLb3FhAMUXAvFzaJp2uVwmk0mv15MkeenSpcuXL2s0mpaWlra2NpvNNpV7C1axQDQgIiJi2bJlIpFIJBLdfPPNYA4en8/n8/koijocjrKysnfeeQdBkNHR0a6uroyMjEnPSVHU6OjoOH03Go0B2HoFii8E4m9QFAWywcxmc19fX2tr6w8//FBbW9vV1UWSpFartVqtHtxbMJAtJCQkIiIiJCRk5cqVoaGhiYmJCQkJBEFgGMbhcMZlF2AYxkRseTzeuBGr7hgMhtOnT08cPn3VcdT+BxRfCMQfAINFSJIEUgsiAENDQxUVFS0tLZ5DtziOg3IyuVyelpYWFxeXkZGRnZ0dFxcnl8u9yeLS6/Xt7e1g2+FwmM3mqY4cHBwsLS0dZw/wxwsKCrx6q/4CFF8IZKFCUZRarQajgs+dO3fq1Km+vr6xsbGRkREwc88DEomEzWbLZDKJRLJs2bJFixatWLFCLpdLJBIejzfdqR8WiwVMbEIQxGw2M9sTDa6vr+/r65u4v7S01OFwLNBC4ZkRWOLLZrOjoqIC6g+8EAGdIUErdBzHZzZGyM+gaRrMYSFJcmBg4LvvvjOZTBaL5eTJk9XV1aBswcOUFgzDgHurVCrz8vKAbxscHBwfHx8REcFms6/xQ5bL5SkpKaCZulgsjoyMnOpdVFVVgTF97lAUVVdXp9frQ0NDr8WMhUXAia9SqYSTLOYnTqfT6XSCJNCTJ0+2t7ez2ew1a9bcd999AdsIiaZpi8UyODio0+laW1ubmpqqqqp6e3ubmppAlpjL5ZoqpIDjuEwmk8lkOI5nZWWtWrUqKioqLCwsOjpaIBCwWKxZvKpxuVy5XA62jUajWq2e9DCSJGtrayd9SqPR1NbWQvH1W0BXM5vNtkCzsv0Yk8n0wQcf1NTUqNXqS5cuGY1GsL+hoeHWW28NEPFlfFuTyWS1WhsaGnp6ekpLSy9duqTX64eHh5lW8RNh7hJEIlF8fHxsbGxYWNjq1auTkpJYLFZ4ePj1bn3AGEZR1ETflmEq99xmsw0MDFAUFTg3OoElvhRFWa1WOENzvuFyuQ4ePPjHP/5x3LQRFEXFYrHf/xotFsvo6ChFUZ2dncXFxc3NzVVVVUaj0WAw2Gw2s9ns4RsLUgtQFE1PT7/ppptkMll2drZSqRQIBARBzJmT4XA4DAaDN0eqVKpJZ3rJ5fKIiAi//1u7E1jiC5mfgDV6Rnl5PF5OTk5+fn5wcDCQEt+aN7sw7m1HR8fJkye1Wu3Q0FBLS4vT6aypqRkbG/Pg2wJwHI+IiIiIiFAqlWvWrElOTiYIYvHixSKRyFf9ZYaHh927jk0FQRBPPfWUw+E4ffp0b28v2Mnn82+77ba777575cqV19nM+QUUX8j8gsvlPvroo7t37w4PD/en+U9Wq9Vutw8NDXV2dlZUVFy4cKGjo6O7uxvcoXtIBePxeDweDyyOxcfH4ziemZmZn58vk8lAIe98+IiEQmF4eHhlZaXnw1AUjY2NfeONN7777rsHHnjAbDajKJqfn//WW295mdPmTwSW+BIEER4evqDrwf0elUr18MMPexgvP/8BSkqS5OjoaG1tbVtbG3Dte3t7KyoqhoeHp4okoCiKYRiYtw3c2Ozs7MLCwpiYmLS0NKVSycS+55tOSaXShIQEb45EUVQikeTl5SUkJFRVVaEounjx4uDg4Ott4TwksMSXw+FERkZC8Z1vkCRptVrBtkKh8NyWZd4C1NZoNOp0OrVaXVlZeebMmebmZtDr1uFweKigZbPZCoUiOTl58eLFmZmZ8fHxKpUKQRCZTCYUChdEfs60rgcajaa5uRlBEJCJcd2MmtcsgD/qLOJwOIaGhlwuF0z1nVfodDrQ5gpF0dTUVCZpaZ4D8pH1en1NTY3Vam1pafnxxx+7u7tHRkZAk5qpggmgGRgYSpaRkREeHl5YWFhQUJCbmwtaJczxG5l7SJJkZgstiEvL9SCw3jabzQ4NDQ3YP/a8xeVyMaX98/8O1Gw29/b2WiyWgYGBM2fOnDhxYmRkhKIos9k8cVgZA4vFAmkJwcHBhYWFixYtWrNmjUwmk0qlXC5XKpUG1EI/hmEEQUycrRlQBJYM2Wy2trY2h8Ox4MY9+TdDQ0M6nQ5BEAzDVq1aNU9kCKQlgPTE5ubm0tJS0Eq8s7PzxIkTIOvW6XROdG+ZtAQ+nx8TE0MQRGJiYmpqanZ2NkEQSUlJKpUK1Jv55H1dD0wmU09Pj/fHSyQSlUo16cDjwCGwxNflco2MjARg87r5DE3T/f39Go0GPMRx3LfG2O12p9M5ODjY2tpaXV1dXl6u1+s7OjoGBweZwZGTtgQjCILFYqlUqqSkpKCgIJVKtWLFisWLF4PCBz6f78eLDU6n00MznYmANkDXz54FQWCJL2R+4v1kmlkH+LYul6utra2urs5ms9XV1YGJvP39/R6ybhEEwXGcxWIBYc3JycnIyIiKisrLy4uNjQVpCf7k23rGvbzYG4Dny6T6TgpFURqNpqamJiMjw73sGJT5gbSQmVs8D4DiC/E9AoGAx+OZTCbgPM7B/zg8POx0OoeHh1tbW69cuTI8PFxSUjI4OAimPHjodQuWDVQqFUEQGRkZS5YsKSgoYLFYQUFBQqEwYBdywdqj98f39/e7TxKalLa2tj179pSXl2/duvXll18Wi8UIgphMpsOHDzc2Nqampm7btm1B151D8YX4GBRF8/LyNm3adOzYscLCwtjY2Nl1GJlYQVNT0+joKE3T7e3tR44cMRqNzc3NWq0WHDaph8vMKEtMTExOTk5OTlYoFHl5eXl5eUwMIXDcWw8IBIJpFSK6JxdOCkVRJSUlZ8+edTgcR44c+dWvfiUWiymKOn78+LPPPjs6OqpQKCIiItavX3/NtvsMKL4Q3xMUFPTnP//50UcfDQsLi4iIuMazkSTJ5E6A+9be3t7GxsbTp0+DuKTZbAa5txPBcRzk1YaEhLBYrPj4+KysrDVr1qhUKtD6FqykXaOFfsm0PhYWi8Xn8z2HicEfwuFwjI6OggCx0Wj87rvvwBUURdFp+drzECi+EN+DomhYWFhYWNjMXg563Y6Ojo6Ojg4ODhYXF1+5cgXsbGho6OjoAE7WVGkJBEHI5XKBQMDkJAiFwpycHIIgBAJBgCTezjFKpTI9Pf3y5ctTHYBhWEJCgkgkAl3hQWj+9OnTx48fBwHfdevWLfReEAEnvtBz8Q9AbxqdTmcwGLq7u/v7+//1r391dnbabDa9Xu/hlhYs1AiFwpCQkOjo6JiYmKVLl2ZkZMhkMpFIBKLPc/lGAhOdTtfV1eXlwRRFlZWV4Tj++uuvg5TERYsWPfDAAyAKvHAJLPHlcDhxcXEBuyqyoAFq63Q6W1pa1Gp1Z2dnS0tLc3NzX18f0FwPzcCA4LJYrKSkpNWrV0dGRkZGRoJhZeDLAK/Hc4zFYhkeHvZ8DOMnkST50UcfnT17try8HEEQmUz2zDPPLF26dC4MvZ4ElviCMUJ+nG7pf1itVqPRODw8XFtb+/XXX9fV1RkMBqvVarFYPI8pwzAsIiIiKCgoLCwsMzMzIyNj8eLFEolEoVDAEpsFQXh4eF5e3vHjxymKOnfuHIvFcjqdOI5v2bJl586dfvArDizxRXyaUgrxAP1fXC7X4OAgqGvo7OxUq9W1tbVVVVUGg8HDyBwEQUCrBIVCccstt4jFYoFAsHHjRtDrFrSmhO7twgIsfoJtmqadTieGYQUFBY888sh053vOTwJLfK1WKxgjBH2feQIIF1it1tbW1o6OjuHh4UuXLjU3N+t0OrPZPDY2BiogJn0t6JYglUoRBBEIBHfeeefixYsVCkVGRgZQWz9wjiDuKJXKJ598MiMjw9eGzA6BJb6wvNjnAKm1WCx2u72mpub77783Go0ajeby5csajcabGWVxcXGpqaksFisqKmrVqlWgvzibzQ60ITR+D0EQIOEP/GBxHN+6deuGDRv85g4msMSXw+HEx8dzOBxfGxJYuFyunp4eUD82MjJy5MiRsrIy0IxRr9d7ztYUCAQSiSQoKCgmJmbNmjVisXj58uWhoaEYhrHZbJiZsEABf9COjg4PxzCzxl0uF4Zh2dnZ27dv96fV8sASXzabDZupX2+o/2I0GouLi+vq6nQ63ZkzZ5gZXyC2O/GFICwLMhNEIlFycvKSJUtSU1MTExPj4uLCw8OBy+M3jk8gIxaLVSqVZ/Ht6+s7duwY6NIZEhLyhz/8IScnZ64MnAsCQnzBUgxcart+UBQ1Njam1+v7+/vLy8vb2toqKyvNZnNXVxeYy+vhw2ez2VKpVKFQxMbGRkdHx8bG5uTk8Pl8lUoll8sJgoBqG4A4nc5jx46BoXAEQaxfv3716tV+Flbyf/Fls9lJSUlXrWWEeAkjo0BSR0dH6+rqampqKisra2tru7q69Hr9VL4t8t8aBwRBOBxOYmJienp6bGxsYWFhRkaGUCgEq9hQbf0eDxdj0M+zpKTkzTffdDgcKIoWFBQ8//zzIpFoLi2cA/xffHEcDw0NZbPZUHyvBbDoMTo62t7ertVqnU5nZWVlV1dXd3d3c3OzwWDwUOaAYRifz5fL5SwWKyMj46abbhIIBFKpNDs7WyaTsdlsGIX3A6Z1Z6nValtbW5H/Nnlg9lut1gMHDvzv//7v4ODgyMgIgiB8Pn/Hjh3R0dGzba/v8X/xRf7b1wriPcwQB4qiOjo66uvrr1y5Yrfb29vby8rKQG0S+LFN/MmBTmAgehsbG5uQkJCSkpKWlpaWlkYQxKJFi5iqUOjh+g3gqgy2vUmpNpvNQ0NDCIJgGObePn9wcPDgwYN1dXXMqbKysjZt2uRnAQeA/4uvzWYrKyszGo2+NmQBYDQaDQaDTqfT6XQlJSUXL17s7u4eGxszGo0gmDDVC7lcrlAoRFE0NDQ0JSUlOTk5Ojo6OzsbjEAXiUTQt/VvzGbz4OAg2AZjmL18oUQiWbRoEfPQPWAlFAozMjKeeeYZ907q/oT/i+9V22MHJqD7Nfiim83m1tbW4uLi6urq+vr6pqYmh8Nht9s9pCWATK+oqCgOhwPybRMTEwmCyM3NlUgksGFCoCGXy5OTk8vKyhAE0Wq1LS0ty5cv9+aFJpNpYGCAeRgREfHEE0+8++67oaGh69at27p160LvnuMB/xdfFEV5PB6GYSD4EMghCJqmbTbb6Ojo2NiYWq0+fPgw8FZMJlNnZ+fAwIDT6fTw+bDZbKFQGBERkZ6eHh8fX1BQEB8fz+Vy+Xy+VCqFM6EDGS6Xy4ydDg4OTklJ8fKFNpsNxHYBbDb7nnvuWbt2LZ/PF4vF/v2l8uf3BuBwOJmZmSKRyGAw2O321tZWu90eIHfBIHSLIAjIANPr9SAnQa1W6/X6kZERD5EEELrl8XhsNlsgECxZsiQzMzMtLS0rKysmJga2SoCMg/kucTgcRoi9YdwXCRQrzqZl8xX/F18wwRsE7B0Oh1qtdjqdfiy+NE0bjUaz2exwOFpbW8+dO2c2m+vr6ysqKsCIWQ++LYfDCQoKQhBEIpHk5ubm5OSkp6dHRUXhOB4cHCwUCmF9CmRS3BfcpoVEIvHLTAZv8H/xdYfNZkdHR/tThSIIy5IkaTAYQBuwpqam1tbWvr4+k8nU2NgICoSQCWkJjOvK4/Hi4+OFQqFKpVq+fPnixYtRFI2MjIyOjgbOrw/eFWShYTKZPI8ingrm5iwACSzx5XA4sbGxC118QXsgnU5H07Rara6qqjp//vzAwMDQ0JDJZDIajVMtlGEYJhAIcBwPCQmJi4uLjY3l8/mrV69OTk4GoVuxWOyXOT2Q+YbD4QAbRqOxra1t1apVvrXHJwSW+C5EgGsA1sp0Ol1PT8+FCxfOnDnT1NTkdDqtVqvJZJrUdwBOK47jIAYHUhGKiopEIlFOTk5ISAhIDoO+LeTaYbFYXobyQHOlo0ePAv+AoqiTJ08WFRVFRUVdZxvnHVB85yMgPU6n01kslo6OjtLS0u7ubr1e39LSAvJwmWDCRFgslkQikUgkERER4eHhN9xwQ3h4eHp6OoZhUqlUJpNBtYXMOhKJJCoqysNATIampqY//vGPJ06cAA9Jkvzyyy9HRkZefvnl/Pz862zm/ML/xZeiKJ1O53Q6EQQBbQxJknQvqpkPgDRkiqK6uro6OjoGBwfPnTvX2NhoMBg6OzuZe7RJgwk4joO3ExUVtXjx4pycnMWLF0dHR0dHR4tEItgJDDIHjIyMtLW1XfUwiqKuXLly5MgR92+y0+n84Ycfvv32Wyi+/gZFUUyRBWgyME/CmmNjY8CB7ejo+PHHHy0WS11dXXl5uclkstvtHkryMAwTi8VBQUGgeGzNmjVFRUUSiUQoFEqlUqlUOk/eICSg8LK3w6SHeejE5Mf4v/gCGAeQw+HMvRvItEEwmUz9/f0Gg6GysrKmpkatVtM0XVlZOTAwMFWrBDDBAUXR4ODg4OBglUqVkZGRnZ2dkZERGRmJYRiXy51vjjwEMhVT/foC8ObM/8XX6XS2t7d7nnR7/f5rl8tlMpna2tpAk4STJ09WVlaCpTOHwzFV0TObzcZxnMVixcbGpqSkLF26NDo6WqlUKpVKkJMAZpTN8duBQK4RFEXlcrlQKDSZTO77RSJRYWGhr6zyFf4vvohbSTEYjkvT9HVSLpCZANIPqqurL1682NfX193dXVlZqdFoEI9DHEBvPQ6Hk5KSsnbt2pCQEDAyJywsDJQ2QLWFLHRQFI2LiwsJCRknvllZWX4zFtN7AkJ8GSwWS3l5+T333OPeQvQacblcGo1mcHDQbrcPDAxcvHjx0qVLYDrZ6Oio3W738FoWi6VSqRQKhUgkKioqWrNmjUwmk0gkYILDbFkIgcwf2Gz2xF45MpksAL/wgSW+LBZLoVDMuFsH47eSJDk8PNzV1dXS0lJfX19eXl5TUzM6Oop4XDoAQxyAAxsWFrZ582aVSrV69erU1FQulwtTbiGBQGhoaE5ODpgPBMAwLC0tzf8GVVyVwBLfGVS4gZRbm802NDTU2Ng4NDREUdS5c+fa29s1Gg3oouC5PY1SqZRIJAiC5OTkbN68WS6XIwgiFovT0tJYLBbMTIAEFBiGCYVCpssggiAoik7l+YIgnsPh4HK5PB5vFpucgSQomqY5HI57eQhJkj09PQKBIDg4+Hr/NgNLfEGdmIeYLwjaggUxiqKGhoaqq6vLy8vVanVtba1GowHJYZO6t6DLLUhOiImJycrK4vP5IpFo8+bN8fHxCIJIJBI+nw/dW0ggw+FwCgsLDx48CO4UAZP+KCiKKi0tfffddzUaTUhISEpKSnp6elpaGpvNVigUIMNnxr+mvr6+1157bWRkJDc395e//CWQfoPB8O9///tvf/tbRETE3r17r3cYOrDE12w2V1VVWa1WJubL9PUwmUxarbarq+vy5cvl5eXNzc0Oh8Nms+n1eqvV6qH3B8i6lUqlSqVy7dq1sbGxQqEwNzcXfD9AZvEcvT0IZB5AUZSHpQ4URZcuXSqXyxnx5XK5Mpls4pEjIyP79u07evQoRVEgSVQgEIBFkezs7BtuuCEkJCQ8PHzRokWgUH5ajur58+c/+OADk8l06dKlJUuWLF++fGxs7Pjx47/5zW+MRmNDQ8OWLVug+F4rDodDp9OBbZqme3t7DQYDuNCNjY2dPn26vLwclJY1Nja2tLSAdIirNrrFMCw9PV2hUMTHx69cuTIxMTEiIkIul8OKMkiAADQRRVEw64/Zr9FoqqurPfRT53K57kIpEonCwsIm+jf9/f2XLl0C+8E9K9N5vaKi4v3338cwLCoqKj8/PzIyMioq6vbbb1cqlciEuXCTEhERATLeent79+3bZzabv/zyy+PHjwNxyM3NTUpKmv5HMj1Qvy8s6e3tvfXWW2tra8FDPp8fHR0Ngkcul2tgYECv13tzHg6HExISEhQUlJycnJeXt2bNGoVCAWaXQd8W4g7o8DnV3RKO4zweDwQcWSwW6CQHgpugCH4i4O4KRVFwWhRF2Wz2RO+SJEmNRkNRFIvFkslkIyMjHA5HKpU6nU4QRpvF90hRVENDA5vNDgkJuXz58tDQ0McffwwGAgHftqioaKoEBovFcuDAAWaABYZh+fn5N910k3vslabphoaGI0eOgLHZV4XP50dGRnI4HD6fv2zZsg0bNgQHB4eEhAA5ntSGX/3qV++//z6CICwWS6lUDgwMkCRJEMTdd9/9wgsvxMbGXu+Yr2/El+nUhfzXkZzqsKmeAl9BsDHxDO5NQnt6etavX9/S0nItBi9atGjlypWrVq1KSkqSy+XR0dEzyIwZGBgwGAzXYgYgPDx8YrKO2Wy22+3T7ZvjcrkcDgePx6MoamBgwGw2KxQK0E8dhLxnxeDrjVartdls4eHhNTU17jNprpHU1FSlUul0Ouvr65mbp0lRKpWpqal2u72urs5gMFgslqqqqqmaH/F4PJVKBTohgBmRXC7XZrPV19dP9WlzOBywPFtZWel0OkG5I8gcd4f5f0UiUWJiYl1dnVQqTUpKMplM9fX1TIeQ2cLhcID8dKvVOvFm0fP3cNIlE28O8wYwgYXFYt1000379u2LjY2d9MwXLly46667wChuAJvNvv322/fv3z83LdbmWnxJkmxpaamqqrp8+XJ3dzeCIKmpqampqRMvMqBZYkhIyKTnaWxsVCqVKIqePXs2Ly8vIiLC/Y/X399fXFwM6sesVuuFCxfMZvO1mC0QCJgxZSKRiPGdp0VPT8+sSEN0dPTEGJnJZLLZbAqFYlqncjqddrtdKBSCRV6j0RgeHg5OQlFUb2+vZ9GZJ9jtdpIk+Xw+qBucrdNKpVIul0vT9FXztblcrlQqpShKr9c7nU6apsG/kx4MlmSBQ4eiKEEQKIqC8h8Pzik4jHl3OI7DmbBXhcViPfDAA6+++uqkUzjVavX27dt//PFH8BBF0VtvvfWdd96JjIyco7AhPbecPn06JycHVMcyYFPgzVNTHeN+/ln/0NAZcb0NmJlhiNtUi3Enn0WDIQuCuf+jg1/rdTo5i8V68MEHmfEC7lAU1d7evnTpUveDX3vttbkUw7lecCsuLq6pqRkXx6Gn9r69ecrDMdeJuf8fvTRgZoaNe5XP3503gEKpcaFMHMeDgoKYxRaSJMEBwcHBc9l7iMVihYSE4Dg+ODjoHsZFUVShUIyNjU3sNILjOEEQNpsN3IVYrVbmKZAqzmKxTCbT6OgohmEEQXA4HLFYrNFoHA6HQqEYHR2lKAr8pxPtoWnaYrFcNc0RmAfmzE7r/dI0PTAw0NfXx5xHKpXGxMR4c3cYExMTHBwMZs6PO6fBYGhra5tuqBrDMJA1zGKxVqxY8dRTTwmFwoknb2pq+stf/lJVVeW+f46vPXMtvjfeeOPly5cvXrzoHt4CCw6eL4DuKdnu6jDxVeCqMulrp3oJMsH78xVgBLdWq42Pj+fxeL425//g8/l5eXnzqgBUJpMtWrSorq7O/ULO5/OzsrK4XC54aDabq6urnU5nbm7uxF/g9YPH4y1evJggiMrKSnedRVE0LS1tcHBQq9WOewmbzebxeAaDAUSZ3cNTBEGAN6VWqzs6OthsNp/Pl0qlERER9fX1Y2NjKSkpXV1dLpcrMzNz0r8RTdNarXa6ISnvoSjqm2++eeSRRwYHBxEECQ4OfvHFF3fu3Mn8ITwAfnQTr/c0TV+4cGHz5s1TrYe737cJhcKkpCQwHyszMzMzM1Mmk3G53MzMzImL4UB5H3vssbNnz7p/eWiabmxspK9b45dJ3sIcuzkURY2MjDQ1NV28eLGnpwdBEA6Hk5eXp1ar5XL5pKFxBEFIkqyurgbjUaOioiiKApdZiUSydu3acRfYzs7Oqqoq5mM1m80nTpxgvu5SqfSWW24BJWfuyOXygoICgUAwq2932rDZbIlEMjo6qlKp5s+sORzHFQrFfLg4ueNeJeW+0/0hOACWEV5vOjs7N2/eDBzJxMTEb775BhQWXQtNTU2bNm1qbm6m/7syD5pxEwQREhKiUqkSEhIQBFEqlStWrEhISADtVUE/66m+q0Bh33jjjQ8++AAEzQUCgd1uB3IRFRX1ySefLFu27Bot95K59nwxDFMoFAqFYsWKFYzuM5+Uh5/3jTfeCI4fd6mc+LtavXq1+xVFp9MZjcajR4+Ch0uXLn3ttdcmXcebJ84vxHuuqqpQdhcu0dHR+/bt+9e//nX58uXo6OiMjIzMzEwOhyORSHJzc0FvVXCk939lvV7/yiuvfPLJJyRJoiiamJj40EMPXbp06fjx4w6Ho6+v7+OPP87IyJgbJ8xnRRbTVbqJi0JeHsnlct393NDQUFBaPk17IRDInMLlcm+55Zbly5ePjIwIBAKJRMLj8a7RPXI4HBqNhiRJFouVmZn5wgsvrFu3btOmTUaj8fTp0yiK6vV6h8Ph5+I7Z1AUxSTljFuQgUAg8xmwejZp8fHMkMvle/bsAed86KGHsrKyUBSNjo7+zW9+IxQKhULhs88+K5VKZ+u/84z/iy9BEMztCY/HA/0bfWsSBALxCQRBrF+/funSpQRBgI4QCIIzQJ8IAAAbPklEQVRgGFZUVJSXl4cgCGg6ODf4v/i6g6IoHMADgQQyKIqCGk53MAybS9kFLDzxpWnabrfr9XqLxYLjeGhoKIfDgTFcCASysFhg4mu1Wuvr6z/++OOqqqqBgQGBQJCXl5efn3/zzTfL5fL5kxgLgUAgnlkw4muxWKqrq//5z39+9913vb29TDJZeXn54cOHQS/dl156aeINBQQCgcxDFob4ulyuw4cPP/PMM3q9HvQzYworKIoyGo1Go9FgMGzdunX16tXjXgva8cFGJBAIZF6xMMR3eHj4vffeAzWXGIatXLly9+7dQUFBdrv93LlzX331VX9/f0xMTGho6MTXgvQyNpvtXi8PgUAgvmVhiK/ZbB4aGgLb2dnZr732WlZWFlhku/HGG7dv315bW5uSkjJp83mn09nd3Q2UF3RPd7lcsziJDwKBQGbAwtCg/v5+phFPcnJySkoKk97AZrNBK42pXgv6ErDZbDCTraenx+FwQPGFQCC+ZWFkaCUkJDB9OkpKSg4dOnTlyhWHw+FNuzmSJIeHh0EXah6Pl5KS4j6tBAKBQHzCwnAA5XL51q1bW1pa9Hp9R0fHk08+KZFI0tPTb7zxxq1bt4aHh3uZ54vjOFh8u94GQyAQiGcWhvhyOJyHH36YxWK9++67jY2NIL2ht7f33Llzp06dev755wsLC73RX4qizGbzVXsHQyAQyPVmYYgvgiB8Pv/hhx8uLCw8cODADz/8MDw8bDAYrFbryZMnQTDBm+pAq9Xa2tpqt9thOQYEAvEtC8kBZLPZubm5f/3rX7/66qt33nmnoKAATLU4f/78pUuXvDkDj8dLTEyEMV8IBOJzFozny8DlchMTE+Pj4xMSEu6555729naLxdLW1ubN/A+mGf7cmAqBQCBTMd9liKZpl8tFkuS4cUcYhqWnp4NGnw6Ho7GxcWxszEc2QiAQyLSZ7+J77ty522677e677z516hQzVNVms3V3dx86dAhMgWOz2cnJyV6GcWGRMQQCmQ/M97BDSUnJqVOnSJKsr6/funVrbGwsSZLNzc1nz55taWkxGo0oiubm5t5xxx3e1E3YbLaWlha73Q7DvhAIxLfMd/ENCwvj8/lGo7GlpeXVV19ls9mgn6/T6UQQhMViFRQUvPjii9HR0d6czel0DgwMOJ1OKL4QCMS3zHfx3bRpk8Fg+OSTTyoqKpxOJ9BcBEFwHMcwbOfOnb/73e9iY2PhGhoEAllYzHfxlUgku3fv3rRpk1qtPn/+vE6nA/vDwsIKCwvj4+NncbgeBAKZATRNt7W1tbS0+NqQBcZ8F18EQVgsVlRUVFRUVEFBgft+6O1CIPMEm80GW7ZOlwUgvgxQbSGQ+QmbzWaz2Uw+EsQbFpL4XjssFkuhUMB+kvMfp9NZV1fX2dnpvhNF0ezs7MjISNgaaV6BouiiRYtiYmKampp8bctCIrBkiMvlJicnw1SHeQ5N0//85z9feeUVpokzQ3R09Pbt2++4447Y2NirFjRC5gwOh8Plcn1txQIjsMQXDH+DP9p5DkVRFRUV3d3dYF4fs5+maZ1OV11dferUqX/84x+RkZE+NBLijtlsNplMvrZigRFY4gu6mtlsNniVns/09fVVVlZSFIXjeF5eXnp6Oo7jdru9tLS0qamJJMnS0tKzZ8/u2LEDxh/mCQRBsNlsX1uxwAgI8WW8J4lEUlBQ4E3YwZs2PZDrxOXLl5ubmxEEiY+P/9vf/paRkYGiKEVRP/74489//vOOjg69Xv/JJ5+sW7cuJCTE18b6MzabTavVIgiC47hcLgfJ9RN/FzRNDw8PM1MWSZIEg2MgnvF/8SUIIjExkc/nWywWkUiUnJw86bcHNO5xuVxarXZoaGhkZEShUKSlpcHVuTmGJMmBgQGHw4Gi6D333JORkQH+BDiO33DDDbGxsZ2dnTRN22w2b4ZIQWaMwWB48803Dx06RNM0j8fLyMgQCoVr166Ni4sLDg4GoxGZIN7o6KherwcvHB4erqqqSk1N9an5CwD/VxYMw3g8Hrg/1ev1Fy5ciI2NxXGcoijw69VqtSdOnOjo6KBp2mq1VlVVtba2Dg4OxsTE7N+/f8OGDTDFbS4ZHh7+8ssvLRZLcHDwuJYdwPPyoW0Li2ndvQHnA9xhgD3nz59/6623NBoNeFhTU4MgyIEDB5RKpUql4nA4eXl5qampy5cvj4+Pd+9X5XK5LBbLbL4TP8X/xddutzc0NICGk0aj8aWXXuJwOOnp6f/5z3+++OILp9NptVp7enomdqRsbW09ePDg4sWLJRIJsxNFUZFIxGKxbDabzWbjcDg2m42mabFYPNFHtlgsNpttVt6FQCAA0RKSJE0m03SdPoIgSJKc9FUYhgmFQpfLZbVax/XtvBYwDBOLxTPQSr1e397ejiBIbm6uUqmc6jChUDjdgC9N0yaTqb+/f9Y726EoCsZjT/oB8ng8qVSKIIjJZJqzxqdGo3FoaCg+Pt5L/e3p6dHpdOnp6cXFxQaDgSTJM2fOjIyMMAeAt0aSpFqtVqvVCIKcP39eKBSGhoZKpVKTyTSLX54Awf/FF0EQ5ldB03R7e/tDDz1EEITFYmE6RUzFN99809fXFxERwezhcDiLFy8Wi8W9vb1qtVqpVPb09LhcrqysrKCgIPfXkiTZ1tYGvqbXTlJSUnh4OIqiZrO5pqZmutVEMpnMYrFMmgMPLkWjo6PA958Va8Fpi4qKtmzZIhAIvH8VTdMnTpzQ6XQYhi1btmxcSJcxD8Ow3Nzc4ODgaZmk0+leeumlTz75ZNb9MjCY1WQyuVyucU+hKBoWFpaSkoIgSHt7e1dX1+z+11NBUdS0Gkg5nU6Xy8Xj8cCQQ8QtFueBsbEx2Ed7xgSE+I7D+98eWGEvLS1l9qAo+vnnn2MYRpKky+XCcRz83o4fPz7Ry3M6nbPlZBEEARw9mqan8rA8gGHYVL8lFEUJgqAoaqJwXAsoipaXl2dnZ2dlZXn/Koqizpw5Y7Vag4KCMjMzx32kDQ0NPT09NE1zuVylUjndFVEQUxoaGroewWKm68g4UBQdGxtrbGwct5P55riD4zhN08A8HMfBlwcEWyZ1FMAfDpxt0m+F5xsvgiCYT5imaZIkbTYb+JrN7pcBMimBKL7TAkVRLpdLEMQMXssk34SHhyclJYGJc+Xl5Uaj0cOrVCqVVCptbGx01wipVCoWi0HzeA6Hw2KxcnJyhEKh+wstFsvAwMCiRYs6OzsJgli0aJHNZqusrIyKirLb7d3d3Xw+PzMz02az8fl84BMNDg52dXWlpKS4h1Y84HK5KioqvHF22Gz2ihUrQkNDvTktg16vHx0dpWlaLpcnJSWNe/bHH38EnmNkZOQNN9wwrTMjCBIeHr53796///3vBoOhoqLC4XBkZWW5fxrXyOjoaGdnZ2pqqvvZhEKhQqHo6upyV0YulxseHt7b2+suqSiKhoaGUhQ1PDyMoqhcLh8ZGaFpOjQ0NDQ0tLa2dpy2oiiampqq1+sFAoFKpaqsrJxYk+IBHMcTEhLCw8PBQ6vV2tfXB8IUPT09LS0t1dXV3d3dk76WkWxQVYzAOO+MCDjxBd9Ug8EAvsp2u93DV5bD4dx111133XVXXFzctWSe8fl8EPWjaVqj0Xh2K4AWMGvHAPAtZ1QPRdGJddIul8tsNotEIpPJhGGYSCQiSVKj0YCNsbExFosll8tdLheLxQIOjsViMZlMMpnMyyRNiqI0Go037jyGYWFhYdPtOXf27FmQZJaamhoTE+P+lNPpZNQqNTU1Li5uWmcGJi1dujQ1NRV8LDRNBwcHu1wudwfwWnA4HEajMSgoyP1sOI5zOJxxwgSu6GC1wH0/h8MBdzYIgoAgMtjgcrmTXrBFIpHD4cBxnMvlgkDttAxmFhIQBCFJ0mq1gsu5zWYzGo3vvffe3r17LRYLiqJisZjD4YDLA0EQy5YtA6qdmJiYmJiIIMjZs2cff/xxGPadFgEnvjfeeOMrr7zS398PviiDg4M1NTUVFRVMfY7L5WpvbzebzQiCFBUV7du3bwZ3uB7wZsQ9giAqlWrG/4V7MFShUHg4clyceronn3U6OjoMBgOHw9m8efM4b7SlpeXDDz8kSVIsFj/wwAMzS+nHMAxcBb38K0yXqVYIJy3q8XLwFWCqvxRzT+blvctU4DjO3EhxuVwul7t9+/bm5uampqa8vLylS5eGhoZiGLZkyRI+n4+iKPhFgA2apsfGxkJCQkCqL4fDEYlE12JMgBBw4iuTyaKiopgkRDCgU6vVMt6oy+Xq7e0FwbL4+PjZVV6IB7RabXFxMfX/tXf/MVXV/x/Az697gcvlXrmIIsivAM2UnxMhjYxcTE2dK5rmcJZZy/zZXK5stTV1OSLm2nTLijazRi43tpplZYAhqRDOH0N+iPL7N3h/APd4Ofe8P3+8v90vU2AXvNcD9z4ff8HxnOvrXuHp+7zP+4csBwYGxsfHj/zYe3t7v/76666uLpZls7Ky0tPT8Y/ibhEREfn5+YODg8HBwbTZO9aZLMuGhISEhITQ8A0KCqIPGGF8Xhe+D6CPm+bMmTPyYHR0tGPYo0J1eaO2tra//vqLbhP1+++/37hxIzw83M/Pr66urqysjI72DwsL27x58yQa7DBRLMsaDAbnP2rHL4vJZGpubk5ISHBbaR7C28N3LIjdx4w+iqR9o0aj8eDBgyzLarVaQRBMJpMoijabbfbs2QcOHHjhhRcw1WIqGxwc7OzsVLqKaQDhC1MC7Tek/+fRrxmGsVgsju7FmTNnHjx4MCcnZ0JdpQBTFsIXpgSO47Kzs2tqai5cuOB4aK7T6dLS0tRqdWho6NKlSxMTE7EWM3gMhC9MFaGhofn5+SMHYHEc5+/vTxu/6GoAD4PwhSmEDnJSugqAxwGtCQAABXhX+NLVpzCSAQAU513h6+vru2DBAtzYAriPWq3GDDdneFf4Tm5JMABwnkajcdPsbQ/jXeErimJNTc2oy9oCgEsYjcaxlkODkbwrfBnnlogGgEeBXzFneF34AgBMBQhfAHAlQRAwBdwZCF8AcCWtVjvOzqfggPAFAFey2Wx0LwIYH8IXAFwJi6k7CeELAK5kMpnoPqcwPs8PX0EQIiIi6Kw2uq0k3TsSANzBbDbTbbZhfJ4fviqVKiYmhj5+1Wg08fHxmF4M4D6CIGDZZWd4fvgyI/YEstvtk9hhGwCcFxQU5NigFsbhFeHrmG8jimJtbS2mFwO4T19fX01NjdJVTAOeH76SJDU2NlqtVua/jeIx9xHAfQRBUKvVSlcxDXh++CJwAR4nLCnpJM8PX5VKFRsbq9FolC4EwCuYzebW1lalq5gGPD98mREP3ADgMcCNpjO8InwBAKYahC8AgAIQvgDgSmq1WqvVKl3FNOBd4YvdiwHcjRAiy7LSVUwDnh++dru9q6vLZrMxDMPzvL+/P9Z2AHAfSZKGhoaUrmIa8PzwtdlstbW19KdBkqR79+5JkqR0UQAeKzAwMC4uTukqpgHPD1+GYTDJAuCx8ff3DwsLU7qKacArwhcAYKpB+AIAKADhCwCgAIQvAIACEL4AAApA+AIAKADhCwCgAK8L3+7ubky/AQDFeX74SpJkNBod39bV1fX39ytYDwAA4w3h29/fX1VV5fh27ty52OMEABTn+eHLsizH/f/bjIqK0uv1CtYD4HkEQTAYDPQXTa/Xq1QqpSuaBjw/fHU6XXJyMv2xUKlUoaGh+MkAcK3Q0NDDhw+//vrrqamp+/btmzt3rtIVTQOC0gW4nV6v37x5c3V1dV9f3+LFizdu3Ojj46N0UQAehef59PT0hQsX9vf3h4WFYdVWZ7DesNyXJEkNDQ2iKEZGRur1eiymDgCK84rwBQCYajy/zxcAYApC+AIAKADhCwCgAIQvAIACEL4AAApA+AIAKADhCwCgAIQvAIACEL4AAArw/LUdwB36+/u7u7vtdvv4pxkMhpCQEDqfmxDS0tJisVj8/f0jIiJGLjXnPjabzWw28zwfGBj4GP46AOdhejFMGCFk3759BQUFoiiOcxrLsqmpqd99911kZCQhpLKycteuXdeuXVu8ePGZM2dmzZrl1iJFUbx27dpvv/1WUVEREBDw0ksvpaamRkZGOrmyByHEaDSeP3++paVl/vz5K1aswHpM4Fpo+cKEEUL6+voYhrl//77jIM/zNJ6Gh4eHh4fpwfLy8qKiol27dkmSVFRUVFlZabfba2pqKisrV69e7b7yuru7T5w4UVBQ0N7ebrPZWJY9d+5cUlLSoUOH0tPTx2l0E0LMZvPNmzevX79+9uzZixcvWiyWOXPmFBYWLl261E0Fg3dC+MKEcRx36NChZcuW5efn19XV0ZunhISEN998k+f5xsbGv//++9KlS5IkybLc1tZGCOF5PiUlJSQkpL29XavVBgUFua+8vr6+999//8cff7RarfQIIeTevXulpaXvvvvu8ePHU1JSxmr/mkymI0eOnDp1qqury26307fW0dFhNpsJIVgPD1wI4QuTER4evmXLlsuXL9fX19NUSktLe+utt3ieF0WxoaFh796958+fZxhGFEVCiCAIa9as8fX1vX37dmRkZHJyspsKI4ScPn36p59+oskrCEJKSkpzc3NnZ6csy1VVVWVlZcnJyWPFqM1m6+jo6O3tdSQvfRGe55G84FoIX5gklUrl2BOEZdmMjAyWZevq6mpra9PT09euXVteXm61Wpuammw2myAIPj4+q1atokk96o3/qI8fJhp5sixXV1cPDg7SbzmOy87ONhqNR44ckWXZbrf/8ccfW7ZsmTFjxqiXz5o1Ky8vLyUl5cqVK0VFRXSja19fX3T4gsshfMEFCCHFxcUREREfffRRdXX1oUOH1qxZU1xcXFpampiYqFarJUmqqqq6evWqzWaLiopauXLlyM2cTCZTWVnZnTt3Hn5ljUaTlZUVHh7uZCUsyy5YsECr1VosFoZhdDpdbGxsYGBgbm6uLMuEkJs3b96+fXvx4sVjvUJwcPCePXtu3LhRXl7e2NjIMMzAwMDg4CC6HcC1EL7gAoSQX3/99Z9//rl16xYh5Oeff96wYUN+fv6VK1cyMjIEQWhubt69e3dVVRUhJCoqavbs2UuWLKHXtre35+bmFhYW0od4DxAEYefOnUeOHHFyZxqO43Jycvr6+j7//HONRrN169aMjIyTJ0/KskxPYFnWmQz18fF5PIPhwGshfME12tra2tramP/SjeO46Ojo6Oho+qc6nW7evHkVFRWyLDc3N589ezYhIcHX19disXz22WdffvmlKIoqlYr2DNBLWJYVBIHjuImOhtTr9Xv37o2Pjw8ICEhPT7daradPn6bhazAYtm3btmDBApe+dYDJQPiC6wUHB/v6+o48otfrt2/fXlJS0tLSIghCUFAQ7Xa4du3a6dOnRVFUq9U7d+7s6elxPCt74oknNm3aNGfOnLVr1050Q0adTrd+/XqGYex2+/fff19dXU1reO+999555x2NRuOytwowWQhfcA2tVuvn59fb28uMdmvPsuzChQtnzJjR0tLCsiy9qSeEVFVVdXV1MQzj4+Pz2muvDQ0NlZaWNjc3syy7fPny/fv3a7XaydVDC2hqaioqKrJYLBzH7d69e8eOHQEBAY/8XgFcAL1a4AIsy65YsSI3N5fO4h1rLAF1//79W7du0ebtyK5VQohOp/Pz82MYRqVSxcfHTzp5qaampgMHDvz5558Mw8TExKxfv/4RXxDAhdDyBdcQBGH16tXnzp27devWqlWrxukokCSpt7dXkiSWZVNSUjQajclkEkXxm2++oT3CDMPMnDkzKSnpUeppbGw8cOBAUVGRJEkajeaNN94YGhr68MMPn3/++czMzIn2YwC4HMIXXMZgMHzxxReiKIaEhDh5iSD830/g8PDwsWPHWJaVJInjuKeffnr+/PkPnEyfvDkzVkGW5aKiojNnzthsNoZhIiMj4+Li9uzZc/369eLi4lOnTsXExNAz79+/L8sybW4DPE4IX5gku91Oo42iyRgcHDzW+Uaj0bHmg+OSiooKOpGBviD9Yt68eTt37nwgwVtbW3/44Qer1frqq6/GxcWNE8GyLJeXl588edJR3p07d/bs2dPe3i7Lck9Pz8DAAD1eW1t77Ngxo9G4bdu2Z555ZmQHyM2bN00mk+M1HTOVAVyGAEycJEnnzp0b2TiNj48vLCwcGBgY9fzh4eGjR486hhksW7astbVVluXc3NyHewB8fHzWrVt3/fp1x+WiKL799tt0Tt26des6OzvHqa2rq+vFF18cK52XL19us9kIIT09PdnZ2YIgsCyblZXleM3GxsZffvnlueeec2Qxx3ErV64sKCgwmUyu+wjB2yF8YcJkWc7Ly4uKihoZcCzLGgyGnJwcOhnsAVVVVQsXLhwZr59++unw8PDhw4dHncvA83xGRgYdF0wIsVgsKSkp9I8iIiJqamrGqs1ut+fn5+v1+lGTV6VS0XnGhJD6+vq4uDh6PC0traWlhRDS3d2dk5MTEhLycFUBAQHbt2+XJMltnyt4F4x2gAkjhHR2dt67d4/5b1QZTWGj0djc3OxYV+GB8zs7O+lpHMfp9XqWZTs6Oi5cuEBGm0Nht9svXry4f/9+2v5Vq9XZ2dmxsbGxsbFr164dp3ODZdmYmBiDwcA+hOO41NTUV155hZYRHBy8YcOGsLAwnueTk5PpCA1/f/+nnnqKZVlCiONCPz8/2jdNm8ku+xzBu2ExdZiM7u7uioqKnp6ekQdpii1atOjh881mc3l5+d27dysrK7Va7csvv5yYmHj16tVNmzZ1dHTQa9PS0vR6vSzLd+7caWhokGWZ5/l9+/Z98sknvr6+Q0NDdIzwzJkzDQbDOLXZbLZLly49vFIEx3GLFi1KSkpytGoHBgauXLnS0dGxZMkSRyvYbDZfvXr17t27jgt1Op3VatXr9ampqbNnz574pwUwCoQvTBK9dXrg4PjrlBNC6C0/bUKWlJQ4wletVm/dunXjxo319fUnTpz4999/6YTgHTt25OXlPTBfbnK1MaPN/qBnPnB81MudXBQCwEkIX1CMyWT64IMPvv32W7odEc/zoaGhFovFaDTSExITE48ePbp8+XKkHngehC8oqaur6/jx41999RUdbOA4rlKpMjMzP/744/T0dEyIAI+E8AWFWa3Wy5cvl5SUnD9/vq2t7cknnwwNDc3MzHz22Wfnzp2LNi94KoQvKI/2Bff19ZnN5lmzZvn5+fE8j+V0wbMhfAEAFIDGBQCAAhC+AAAKQPgCACgA4QsAoACELwCAAv4HYTwLbhv6cGwAAAAASUVORK5CYII=	I = I_0 \cos^2 \left( \frac{\pi y^2}{D \lambda} \right)
+802	Consider the diagram as shown (Fig. 1.44). A slit source is to be imaged on a screen. The light is to be parallel between the lenses. The index of refraction of the prism is $n(\lambda) = 1.5 + 0.02(\lambda - \lambda_0) / \lambda_0$, where $\lambda_0 = 5000 \, \text{Å}$. System is aligned on 5000 Å light.  (a) What are the focal lengths of the lenses?   (b) What is the linear and angular magnification of the slit at the screen? Is the image inverted? Make a ray diagram.   ( c ) What is the displacement off axis of light from source of $\lambda = 5050 \, \text{Å}$? Approximate where possible.	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	f_1 = 25 \, \text{cm}; f_2 = 10 \, \text{cm}; m = -0.4; M = -2.5; \Delta \delta = 2 \times 10^{-5}
+803	A thin glass sheet has a thickness of $1.2 \times 10^{-6} \, m$ and an index of refraction $n = 1.50$. Visible light with wavelengths between 400 nm and 700 nm is normally incident on the glass sheet. What wavelengths are most intensified in the light reflected from the sheet? ($nm = 10^{-9} \, m$)	[]	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	\lambda_1 = 424 \, \text{nm}, \, \lambda_2 = 480 \, \text{nm}, \, \lambda_3 = 554 \, \text{nm}, \, \lambda_4 = 655 \, \text{nm}
+804	 A Young double-slit interferometer receives light from a stellar object which is focused at the plane shown in Fig. 2.23.  (a) Determine the interference pattern as a function of $x$. (b) If the interferometer is pointed at a stellar object subtending, at the earth, an angle greater than $\theta_{\text{min}}$, the pattern disappears. Explain why and find $\theta_{\text{min}}$.	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	I(x, \theta) \sim \left( \frac{\sin \beta}{\beta} \right)^2 \left( 1 + \frac{\sin \alpha}{\alpha} \cos \gamma \right); \beta = \frac{\pi a x}{\lambda f}, \alpha = \frac{\pi d \theta}{\lambda}, \gamma = \frac{2 \pi d x}{\lambda f}; \theta_{\text{min}} = \frac{\lambda}{d}
+805	" A two-slit diffraction system is illuminated normally with coherent light of wavelength $\lambda$. The separation between the slits is $a$. The intensity of light detected at a distant screen (far compared with $a$), when one of the slits is covered, is $I_0$.  (a) For the situation where both slits are open, calculate and sketch the response of the detector as a function of the angle $\theta$, where $\theta$ is measured away from the normal to the system.  (b) Now assume that the slit separation ""jitters"" such that the spacing $a$ between the slits changes on a timescale large compared to the period of the light but short compared with the response time of the intensity detector. Assume that the spacing $a$ has a Gaussian probability distribution of width $\Delta$ and average value $\bar{a}$. Assume that $\bar{a} \gg \Delta \gg \lambda$. Without performing a detailed calculation, sketch the intensity pattern measured by the detector for this situation."	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+806	 A partially elliptically polarized beam of light, propagating in the $z$ direction, passes through a perfect linear polarisation analyzer. When the transmission axis of the analyser is along the $x$ direction, the transmitted intensity is maximum and has the value $1.5 I_0$. When the transmission axis is along the $y$ direction, the transmitted intensity is minimum and has the value $I_0$.  (a) What is the intensity when the transmission axis makes angle $\theta$ with the $x$-axis? Does your answer depend on what fraction of the light is unpolarized?  (b) The original beam is made to pass first through a quarter-wave plate and then through the linear polarization analyser. The quarter-wave plate has its axes lined up with the $x$ and $y$ axes. It is now found that the maximum intensity is transmitted through the two devices when the analyser transmission axis makes an angle of $30^\circ$ with the $x$-axis.  Determine what this maximum intensity is and determine the fraction of the incident intensity which is unpolarised.	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+807	Shown in Fig. 2.49 is the Fraunhofer diffraction pattern resulting from 3 slits. The slit widths are $w$, slit separation is $d$, the distance between the screen and slits is $f$, and the wavelength of the light is $\lambda$. Obtain expressions for $x, D,$ and $I_0/I_1$ in terms of the parameters of this experiment.	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	x = \frac{2\lambda f}{w}; D \approx \frac{\lambda f}{d}; \frac{I_0}{I_1} \approx 9
+808	A straight horizontal wire of diameter 0.01 mm is placed 30 cm in front of a thin lens with focal length = +20 cm.   (a) At what distance from the lens and with what magnification will a sharp image of the wire be focused?  (b) If collimated light is incident from the left, parallel to the optic axis, and a screen is placed at the back focal plane (20 cm behind) of the lens, what diffraction pattern will you observe? Be as quantitative as you can.	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	v = 60 \, \text{cm}, \, M = -2; I = I_0 \left(\frac{\sin \beta}{\beta}\right)^2, \, \beta = \frac{\pi d y}{f \lambda}
+809	 A plane wave of wavelength $\lambda$ is incident on a system having 3 slits of width $a$ separated by distances $d$. The middle slit is covered by a filter which introduces a 180° phase change.  Calculate the angle $\theta$ for the  - (a) first diffraction minimum, - (b) first interference minimum, - ( c ) first interference maximum.	[]	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	\theta = \pm \sin^{-1} \left( \frac{\lambda}{a} \right); \theta = \pm \sin^{-1} \left( \frac{\lambda}{6d} \right); \theta = \pm \sin^{-1} \left( \frac{\lambda}{2d} \right)
+810	Discuss the difference between optics as performed at wavelengths near 100 Å with optics near 5000 Å. Specifically, contrast:  (a) Use of lenses.   (b) Use of mirrors.   (c) Chromatic resolving power of gratings of fixed width.   (d) Minimum resolvable angular separation of an image-forming system of fixed diameter.	[]	/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGQAZADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD3+iiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigD//2Q==	\text{Visible light can be focused using glass lenses, whereas X-rays can only be refracted by crystals.}; \text{X-rays can only be reflected at critical angles, unlike visible light, which can be reflected by common mirrors.}; \Delta\lambda \text{ is much narrower for X-rays due to smaller } \lambda.; \Delta\theta \text{ is much smaller for X-rays than for visible light due to smaller } \lambda.
+811	Consider the Babinet Compensator shown in the figure (Fig. 2.76). The device is constructed from two pieces of uniaxial optical material with indices $n_e$ and $n_o$ for light polarized perpendicular and parallel to the optic axis, respectively. A narrow beam of light of vacuum wavelength $\lambda$ is linearly polarized in the XZ plane at $45^\circ$ to X and Z and propagates through the compensator from left to right along the +Y axis as shown (Fig. 2.77).  (a) For $d \ll L$, calculate the relative phase shift of the X and Z polarized components of the exit beam. Express your answer in terms of $n_o, n_e, \lambda, L, d, x$.  (b) For what values of $x$ will the emerging light be   - (1) linearly polarized?   - (2) circularly polarized?	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	\Delta \varphi = \frac{4\pi}{\lambda} (n_o - n_e) \frac{xd}{L}; x = \frac{N \lambda L}{4(n_o - n_e) d}; x = \frac{(2N + 1) \lambda L}{8(n_o - n_e) d}
+812	A beam of light, with $\lambda = 5000 \, \text{Å}$, traveling in the $z$-direction is polarised at 45° to the $x$-direction. It passes through a Kerr cell, i.e., a substance such that $n_x - n_y = KE^2$, where $n_x$ and $n_y$ are the refractive indices for light polarised in the $x$ and $y$ directions. $E$ is the strength of an externally applied electric field in the $z$-direction. The cell has length 1 cm and $K = 2.5 \times 10^{-6} \, (\text{meter})^2/(\text{volts})^2$.  (a) If the light, after passing through the Kerr cell, passes through a polarisation analyser whose plane of polarisation is perpendicular to that of the original beam, calculate the smallest value of $E$ which gives maximum transmission. Assume the effect of the electric field on reflection at the Kerr cell is negligible.  (b) What is the state of polarisation of the light emerging from the Kerr cell if the value of $E^2$ is half that calculated in (a)?  ( c) Consider the following arrangement (Fig. 2.80)  The electric field is applied to the upper half of the Kerr cell only, and, after passing through the Kerr cell, the light passes through two slits as shown. There is no polarization analyzer after the slits. Assuming that the electric field affects $n_z$ but not $n_y$, discuss the interference pattern, at a large distance beyond the slits, for various values of $E^2$.	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	E_{\text{min}}^2 = 10 \, \text{V}^2/\text{m}^2; E^2 = \frac{j \lambda}{K l}; E^2 = \frac{(2j + 1) \lambda}{2 K l}
+813	 A camera (focal length 50 cm, aperture diameter $D$), sensitive to visible light, is sharply focused on the stars; it is then used without refocusing for an object at a distance of 100 meters. Roughly, what aperture $D$ will give the best resolution for this object? Give $D$ in cm.	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	D = 0.82 \, \text{cm}
+814	 In one or two short paragraphs, describe the conditions under which an observer might or might not be able to directly sense interference effects created by separated independent pairs of light or sound generators.	[]	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	\text{For common emitters, interference effects are seldom observed. For coherent laser light, interference effects can be seen.}
+815	The diagram (Fig. 2.22) shows a double-slit experiment in which coherent monochromatic light of wavelength $\lambda$ from a distant source is incident upon the two slits, each of width $w(w \gg \lambda)$, and the interference pattern is viewed on a distant screen. A thin piece of glass of thickness $\delta$, index of refraction $n$, is placed between one of the slits and the screen perpendicular to the light path, and the intensity at the central point $P$ is required as a function of thickness $\delta$. Assume that the glass does not absorb or reflect any light. If the intensity for $\delta = 0$ is given by $I_0$:  (a) What is the intensity at point $P$ as a function of thickness $\delta$?   (b) For what values of $\delta$ is the intensity at $P$ a minimum?   ( c ) Suppose the width $w$ of one of the slits is now increased to $2w$, the other width remaining unchanged. What is the intensity at point $P$ as a function of $\delta$?	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	I = I_0 \cos^2 \left(\frac{\pi}{\lambda} (n - 1) \delta\right); \delta = \frac{(2k + 1)\lambda}{2(n - 1)}; I = a^2[5 + 4 \cos(2\pi(n - 1)\delta/\lambda)]
+816	A lens is to be coated with a thin film with an index of refraction of 1.2 in order to reduce the reflection from its surface at $\lambda = 5000 \, \text{Å}$. The glass of the lens has an index of refraction of 1.4, as shown in Fig. 2.15.  (a) What is the minimum thickness of the coating that will minimize the intensity of the reflected light?  (b) In the above case the intensity of the reflected light is small but not zero. Explain. What needs to be changed, and by how much, to make the intensity of the reflected light zero?	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	t = 0.10 \, \mu \text{m}; n_1' = 1.18
+817	 Consider the following simple telescope configuration made up of thin lenses as follows:  $L_1$: $f_1 = 10 \, \text{cm}, \, \text{Diameter} = 4 \, \text{cm}$ $L_2$: $f_2 = 2 \, \text{cm}, \, D = 1.2 \, \text{cm}$ $L_3$: $f_3 = 2 \, \text{cm}, \, D = 1.2 \, \text{cm}$   (a) Trace a typical bundle of rays through the system.  (b) Calculate the position of the exit pupil and the diameter of the exit pupil. (c )  What is the function of the lens $L_2$? (d) Is the instrument a good match to the eye? (Explain).	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1cqTU1Nd3d3ng9RC7iKTOLlh0+cOLFlyxbu1jAACgLTBgBAaNTNAgiCMDQ0dHR0pPXp1asX9eQTh8M5e/ZsUFBQUFBQVFQUtWfr1q03bdokyPOqqanVdkKLxtvbm5viVFdXi7BCi0pFRYVWLh57vssSm83m7k4iqeT127dvzMyV9PHjxwsXLnB/X1VVVW3fvr3OARcvXszcr5XKwMAgPDycu38Vrepft27dmIdQr2awWCza7l9MwcHBdcYpFOpUYADFgeQVAIQm4NS6P/74w83NjX8fU1PT06dPN2nSRMCnHjBgwLhx4/j36dGjB3UTAWdnZ2ELLdGmtKqrq9vb21NbRo0aJdSAII7s7Ozw8HDydnl5eWZmpvhjilbfjQ9VVdXjx48fOXKEthcxydvb+/Hjx7179+a2tG/f3tLSkrytrq4+bNgw5lFDhw7l3nZwcBg7diytg7m5OXV/jZUrV4rzTwBQGnLdnBZAONSdG3v27CnvcBouNptN/RgZOnRobT2jo6P5JKYsFiskJETYZy8pKeFzimvXrl0/fvygHTJhwgRuBzs7u5KSElqHc+fOcTs0b948NTWV1iE+Pp47NcLQ0PDt27fChg0iS01Npf4XBwcHS2RYwVM9Z2dnwYctKCh4+/bttGnTWrRoQRDExIkTz549W1RUxOz5/v37adOmTZs27dChQzyHqq6u3rVrF9nn69evPPucOHHCwcFh4MCB27ZtI3ehEx91Dk9BQYFExgSQIBZHmO0ZAeSroKCAe+Fs9erVOM0gLxwO5+zZs35+fmw2W0tL6+HDh127dq2t88uXL4cOHco8W6aurk4ucxEhADab/ejRo8jIyCtXrnz+/JkgCENDQz8/v4kTJ1pbW7NYLGb/iIiIqKioFi1ajBs3TktLi9ahqqrq+fPn4eHhRkZG/v7+Ojo6zCctKyuLi4t7+PDh77//LtSUWRBTWloa9yQlQRDz5s0T5Dp+naqrq1+9enXjxo0dO3bw6WZvb3/r1i0jIyNhxy8rK6uqqtLV1aWWGZaG8vJyNTU12hbH4jAwMCAXbE2ePPn48ePMPygA+ULyCsqEmrxGRUVJZIkDiOzevXtfv35t166dq6sr/541NTXkflpnz57Nzs728PBwdna2sbHp06ePLAIFJUdLXr28vJiVg0GCuMlrQEAAd5IugOJA8grKhJq8FhUVkTWSAKB+oyWvwcHB3GqpIA3c5LV58+ZJSUm4zgCKBgu2QFmRZ/IAAEBK9PT0MGcAFBCSV1BW1MVbAFCPsVgsdXV1eUfREPXs2ZPn/G8A+cImBaCsRNgZHADk6+PHjzt37qyurp4xY4a+vn7Lli0FOcrc3Hz48OG1bZkGNCUlJatXr/7+/Xu/fv3Iul3NmjWTbF0wAPlC8grK6ujRo0uXLmVu7MRHUVHRyZMnr169ShDE6NGjZ8yYIbXoAICuoKDA29v7/fv3BEHs2bOnadOmU6dOnTlzZqtWrfgfmJubGxERwb1L1pcQxP3797lbtlpbWzO30qiXFi9efODAAYIyt8ra2nrGjBn+/v5Nmzat8/DU1FRaLTwARYMFW6BMqAu2CIIwNTX19/cfOHAgWfr7xo0bGRkZUVFRMTExo0ePJoss3rlz5927d2T/ioqKL1++kLc1NTU9PT3Pnj1raGgo638GQIM0a9as/fv30xqbNm3apk0bbiHevn372tjY0PrQFmxZW1tHR0dTTyWeOXPm58+f3LtFRUXkGvmPHz9y94gyMjLy8/P7z3/+I7l/kCK6evXqL7/8Qn01uCwsLGhLrzQ0NObMmUPeVldX9/PzIwhi3rx5O3fuJBtRbQAUE5JXUCa05JWkpqamqalJEER5eXl1dbVQA3br1i08PFzuVQtqamrI3S/19fVVVVXJxsLCQk1NTWZFUlJVVVVxcTFBENra2rX1UVIVFRWlpaXUf1dpaSl303ZuO1k7XYTx3717d+fOHe4V1doYGBioqKgUFxdXVVWRt0V4LgVEThZXV1cnN7zlvpHqpKmpyXP6Y3l5eVlZGXlbX1+fxWKRb2Zu/8rKyp8/f/7zzz87duyo8y9UU1OTW6/Uy8tr6NChQ4cO9fb2fvLkCbWblpaWqqpqp06dXr58SRBEaWmpIG8GFos1f/78oKCgRo0aVVdXkwvqCYLgfqoUFBRoaWmRbzAOh1NQUFDnmBJXVVVF5o4TJ05s1qwZQRBqamocDod86XR1dTU0NAiCYMZfVFQUGRm5YsWKV69eifbUZGpLfTGRvIJiQvIKyoRn8iqmjh07Ll26tE2bNgRBREZGxsbGtmrVysfHp7b+paWl5CU5CSotLb1w4QJBEKNHjyZTCoIgQkJCHB0d27ZtO3bs2Ozs7IcPH3IDVlFRCQsLu3nzJkEQnTt3/uOPP1q3bk0+2qJFC/JcMpvN/vDhA9nYrl07FotVUFDw7ds3MzMz7qXDjIwMcuqwo6Mjh8NJSEhISkq6efNmnz59OnXqlJiYeOvWLYIgmjdvTu5LWVRUdOTIEeK/ScD169dTUlIIgnB3d+/YsSM55oMHD16/fm1vbz9kyBDytrCvxsePHx8/fty1a1fuRd7o6OjExETydrdu3RwcHAiCOHfuHDejlYbx48dramrevXs3PT19woQJZMZAMjIyWrVqFfc3z+fPn4uLi52cnNhsdlJSEkEQhw4dmj59Ojf4mJgY8nb37t27detmbW2dkZFRVFS0d+9enk89YMAAJyen48ePk4mmtbX18OHDCYLIzc09ffo0QRBz5sxRV1f/9OkTOQeG26esrIx5apPm5MmTNTU1lpaWffv2JQgiLy/v+vXrgrwgDg4O3bp1Gzx4sIODg7Gxsbm5OUEQd+7cCQwMfPr0Kdln1KhRqqqq5JvZ0dHR09PT29t7w4YNDx48EOQpZMPKysrd3b2kpCQ0NJQgCBaLNWXKFPKh4ODgdu3akZ8GNTU1J0+elGeg/2VqalpRUUG+Gfr27UuehC4sLLx8+TJBEKqqqpMmTSII4urVqxJfxorkFRQTkldQJtJIXuuZ/v37BwcHFxQUbN++nXvtj0xTcnJy3r59a2dnR+4ydePGjZcvX5Ibb5J77UZGRsozdKXi7OxsbGxM3n716tWPHz/69OlTUVHBzVP56NixY2JiYmlpqZRjlCILCwt7e3uCIF68eCGX05MgG0heQTEheQVlUl1d7evrS55vgNq0aNGivLw8JydH3oEoh3bt2r19+5Z7t1evXo6OjomJidQVQlSdOnXq3LlzWloaeVq6HmvZsuXAgQOfPn0aFxdHEMS4ceNMTExmzpxJEMSRI0dsbW3v3LmDP8b6DckrKCZUGwBloqqqKvH1VSwWiztmWVmZiooKOYNWKB06dPD09OTe3bFjR01NDUEQ/v7+BgYGtR1FXoElCGL79u3Un5FDhgyxt7c/cuQId04bQRA/f/48ePAgQRCFhYUcDoeMOSAgQF9fnzbsuHHjbt68GRQUxGc6IznlkTvXlk8f8jY5bZH7UG3THwXn7e3NXJdTpy5duvTo0YPZHhsbq6WlxZ3DWlBQcOzYMYIgZs2aRc5fPH36dG5ubuPGjadOnfr+/fs7d+68ePHCxcVl0qRJZmZmbDb7ypUrnz9/7tq1q4eHh7q6OpvNjoiIiI6OJgesrKzcs2cPQRBOTk63bt3S09Orqqo6ePBgeHh4//79p0yZEh8ff/PmTbKPpLRr165fv36iHdu+fXvydHudcnJyzpw54+fnx/zLUlNT09LSqqysrKysJAhCR0eHO/F38+bNBEFMmzatrKyM9kal4r5pqfNi5UhFRcXAwGD8+PGmpqbkHJjWrVt7eXnxP8rBwWHw4MEEQXDnyZD7GxME8fz58zdv3vj7+9d27JkzZ/Ly8ubOncttuX//flxc3C+//ELOZ7169eqnT58IgvD09OzQocPp06dv3rwZGRnp4+NDFmG4d+/emzdvCIJQU1P7/fffr1y5kpCQUFpa2rhx4+HDh1tbW7PZ7N27dxMEUVRUJOykfwAlhTOvoGT8/f3JvIQgCAsLi2nTpnFLRYaGhr5+/To9PV3w0YyMjLZt2zZ58mTy7osXLwwMDGxtbSUbs2SFhITU1NSQk1D5y8nJqe3sIG3aH58+5O1Pnz49evSI+5CTk5Orq6twcUMD9v79+/Xr15MTdgXh4OBA3ZWAemqcIAgdHR0bG5vp06fr6enduHEjKSnpw4cP3KoCfCxbtmz9+vVCRa6AUlJSoqOjyXmuVFeuXMnJyfnzzz9//Pgh1IBWVlZ6enrdunVzc3O7dOlSeHg4dzY5zryCYkLyCkqGm7y2bdv2zp07zZs3pz6alpb2+vXrjRs30tYm89S0adOrV692795dWrECwH9VVFTMmjWL+8uTZGVl5erq+uuvv9I69+zZk1pDY8mSJdwSV1paWocPH/7ll1+o/R8/frxhw4aXL19mZWXVFoCvry+5kqx+i4yMHDFiRG5uLp8+urq6ffr0IQjit99+09TUdHZ2btKkCffRlStXrlmzhryN5BUUE5JXUCYVFRUeHh7kxdzVq1evXLmSZ7fy8vIHDx5cuXLl2bNnfKrG1I/TMADKoqysbNOmTf/5z39KSkqaNm26dOnSSZMmCbLzE7XOq4WFBbnKkCk9PZ07T+bGjRthYWH37t0j7w4fPnzLli117oZQP6Slpe3bt+/+/fvMYnBOTk4DBgzQ1NS0trau7fCCggILCwtymhCSV1BMSF5BmVCrDdy9e7fOGYGVlZW0rWJCQ0ODgoI+f/48Z86cbdu2cYuqAoBskGVEVVRUtLW1BTxEwOSVpqqqinv5m6wLK0K0yovNZlOnXgjFwMCAnMeM5BUUExZsgbLq2rVrnX00NDSo5TkJgpgyZcqUKVMuXLgwZswYqYUGALUSc6mf4NTU1Lj7HTRAImeuAIqvnuwZAw0QuURXNMhcAQDqdPv27ZKSEnlHAUCH5BWUFXdvIQCo30xMTAYNGiTvKBqijIwMlN8CBYTkFQAAFJq6ujp3M16QJRcXFxHqXgNIG5JXUFbU2i4AUI/9+PEjNjZW3lE0IAMGDCBvODs7U2uWASgIJK+grJg1ugGgXiotLf369au8o2hAnJyc5B0CAD9IXgEAQKFhzisAUCF5BWViYGCAE64ADQ3mvAIAFZJXUCYsFqshF24EAAAAJK8AAAAAoDSQvAIAAACA0kDyCgAAAABKA8krAAAojYEDB8o7hAYkIiKitLRU3lEA0CF5BQAApYGa+bKUkpLCZrPlHQUAHZJXAABQGlevXpV3CAAgZ0heQVnt2rVL3iEAAACArCF5BWXy8+fPR48ekberqqrkGwwAAADIHpJXUCYaGhp2dnbyjgIAAADkBskrKBN1dXXuWuOpU6fKNRYAgHrOwcFBQ0ND3lEA0GGnTVAyc+fObdKkib6+vqWlpbxjAQCoz3r06KGtrS3vKADokLyCklFRUZk4caK8owAAqLeaNm0q7xAA+MG0AQAAAPifSZMmyTsEAH6QvAIAAMD/xMXFyTsEAH6QvAIAAMD/3Lt3T94hAPCD5BUAAAD+JywsjLwRERFRWloq32AAmJC8AgAAwP98+PCBvJGSksJms+UbDAATklcAAAD4H1TRBgWH5BUAAJRGWlpaaGiovKOo5xo3bizvEAD4QZ1XUD4pKSnFxcWmpqZmZmbyjgUAZK2mpkbeIQCAPOHMKygTNps9Z86cLl26dOrUycPD48GDB/KOCABkqkmTJu7u7vKOAgDkCckrKI3379+3bdt2z549+fn5BEEkJiYOGjRoz5498o4LAGRHS0urWbNm8o4CAOQJ0wZAOSQmJnp4eOTk5FAbKysr586dy+FwZs+ezWKx5BUbAAAAyAzOvIISePHixaxZs2iZK6mmpub333/fu3ev7KMCANmrrKwkr70AQIOF5BUUXVxc3NChQ/lPb50/f/7u3btlFhIAyEtOTs7du3flHQUAyBOSV1B0Xl5eWVlZ/PtUVVUtWrQoMjJSNiEBANRjR48elXcIAPwgeQXFVVFRMXny5PT0dEE6V1ZWBgUFVVVVSTsqAIB6KvbGtAAAIABJREFU7NmzZ9nZ2fKOAoAfJK+goMrKymbOnHnq1CnBDwkPDw8MDKyurpZeVAAgX40bN+7SpYu8o6jPGjdurKKC3AAUGt6goKDCw8OPHz8u7FHr1q2Lj4+XQjgAoBB0dXWtrKzkHUV9Zmtrq6GhIe8oAPhB8gqKqKKiYuPGjaIdO3z4cMkGAwAAAIoDySsoomvXrkVHR4t27JcvX3799VfJxgMAAAAKAskrKJwHDx5MmDBBnBFCQkLu378vqXgAABqOhw8flpWVyTsKAH6QvILCWb9+vZhFAwoKCpYuXVpcXCypkABAvnx9feUdQkPx8eNHNpst7ygA+EHyKgsZGRm7d+/GLlCC+Pr165s3b8Qf58WLF2vWrBF/HABQBC4uLiYmJgRBdOjQQd6xAICcsTgcjrxjqM/CwsJWrVr14sUL8lSihobGsGHDbG1tyUeHDRvWtm1bAwMDucaoWC5dujRq1Chmu4aGhqGhYU1Nzffv3wUcSkVFJSsrq2nTphINEADkg81m19TUqKmpqaqqyjuW+qy6utrc3Jxb6rWgoABfUqBokLxKV/PmzTMzM/l0aNmy5fz58/v27duuXTuZRaWwysrKPD09Y2JiaO0tW7YMDAz08/OrrKzs37//o0ePBBxwzpw5u3btknSYAAD12apVq1avXk3eRvIKCgjTBuTs69evCxYscHV1nTBhwtWrV8vLy+Udkdyw2exZs2YxM1c1NbXDhw/7+fkRBKGhoWFjYyP4mPv379+9e7ckowQAqO9SUlLIG0OGDNHV1ZVvMABMavIOoJ5zdnbmf+aVVFFRce7cuXPnzrVs2bJfv37Ozs5ke+/evdu3by/lGBVFVFTUiRMnmO1z5szp169fbUd5e3v7+PhER0cfPnyY+WhVVdX69et9fHwsLS0lGSsAQP11/fp18oaZmZmaGvIEUDiYNiBdbDY7MDBw69atFRUVIhxuZGR07dq1Ll26qKurSzw2RWNoaFhYWEhr1NLSysrKol608vf3P3bsGHlbVVX13r17ffr04XA4x48fnzFjBs9FsgMGDLh58yY+ggEABGFgYFBUVEQQREBAAM/zAgDyhWkD0qWurr5u3TqRp13++PGjZ8+e3t7ekyZNevFfaWlpkg1SEZw/f/7nz5+0Rn19/YsXL/KZbuXo6NinTx+CIFgslp+f3+jRo3l2Cw8Pj4qKkmC0AAD12KBBg+QdAgA/OBclC2KeNw0LCyMI4vTp0+RdS0tLa2trb2/vgIAAQ0NDCcQnb9nZ2UuWLGHWdp04ceKQIUMEH2fXrl1PnjxJTU1lPrR27Vo3NzecfAUAqJOjo6O8QwDgp0F/l4eGhmZlZfXo0aNjx44EQbx+/frJkycmJibMatiPHz+Oi4sTfOSePXs6OzsnJSWFh4cXFhauW7dOgmGnpqampqY+evRo27ZtPXr08PLymjx5sgTHl7G8vDwfHx/m6WQ7O7vNmzcLNZSxsfG+ffuGDx/OzIPDw8NnzJhx5MgRsWIFAGgAXr9+Td54//59RUWFpqamfOMBoJHinNeampqTJ0/evHnz6tWr2traI0eOPHPmDEEQPXv2dHV15Xa7fft2QkKCs7Ozh4eHgCNfuHBh0KBB+vr62dnZZ8+eFTnCqqoqDoejqqqqoqJCBlxdXc1isZjn56qrq2tqagQfmRyTHFDk8ARHntmdMWOGjo6Or69v586dZfCkkhIbG9u1a1dm+4wZM/bv389sp855bdu27du3b2kdbt265eXlxfO5Tp48OWnSJPHiBQCoz549e9azZ8/KykryLkplgQKSYvIaHx+P2qWy16xZs5iYGGtra3kHIqhp06YxT4haWVndvXuXu5sDVZ3Ja2FhoY2NTV5eHvPYMWPGBAcHSyJqAID66cqVK6NGjSLP1/Tp0yc8PFxDQ0PeQQH8H1JcsEWeZwUZy8nJOXDggLyjEFRJScnNmzdpjS1atLhz5w7PzFUQBgYGQ4cO5flQQkKCaGMCADQQw4cP37hxo4+Pj4+Pz/r165G5ggKSYvIaEBAgvcGBj/T0dHmHIKjffvstKyuL1nj+/PnWrVuLM2xt772EhITIyEhxRgYAqPcWL1585cqVK1eudO/eXd6xKJOSkpLBgwe3atWqVatWWGIhVVJMXm1sbA4dOtQQCpSCaHbv3n3q1Clao4+PT7du3cQcuWfPnmvXrmVugF5ZWenn5/flyxcxxwcAAKApLCwMCwv7/Pnz58+fp02bdvz4cXlHVG9JsdoAi8WaNm2alZXVhg0bCgoK+Hf29/c3NDS8deuW9C7sNmrU6NdffyUI4tChQ8XFxTz7LFiwgMViJSUl3bhxg9r+4sULgiAcHBx0dXX79Onj4uJCtj98+PDly5cJCQlkjdJWrVo1btyYeuCbN294ls2XqmbNmsn4GUVQWFi4detWWqO5ufnevXtZLJaYg7NYrOXLl4eFhT1+/Jj2UHJy8qJFiy5cuMBMbQFAwWVlZZmYmIj/EQEgA4sXL+7evbu9vb28A6mHsMNW3TgcDpkDOTs76+vrMzu8evWKzIYdHR2bNm1KfSgqKqpHjx4yCNLd3T0qKsrBwaF3797r1q3T09OTwZOK486dO7Q62GpqaocOHZo6dSr/A6kLtnR0dB4+fEgtXkGVmZlpbW3Nc2+zuLi4hrPvLoCyKysrO3bs2Pnz59PT083Nzc3MzPbt22dkZCTvuAD+j7y8vA4dOlBn7h0/fnzKlClyDKm+atB1XgXEYrF69+7NpwNZJpYnnkWgJEhFReXPP//09/c3NzfPyspq3Lgxz/Ra0eTl5QUGBtIadXR06sxcaUpLS/mc1DczM3NxceG5t9b169eRvAIoiwkTJly5coW8/enTJ4IgsrOzr1+/rvi/0qFBMTY27tmzJ7WmzfXr15G8SgO2h5WuHTt2iD+IkZGRCcXq1asr/6u8vPyff/5p1aqVpqZmy5YtlSJzJQsAP336lNY+d+5cYYcyMTGxs7Pj02HlypU827dv3y7scwGA7JWXl48YMYKbuXJFRET069ePuac0gEK5dOnShw8f5B1FPYTkVbpoc2eFYmpq6unpeebMmaSkpCyKlStXqlNIMFrZSElJWbhwIbNdhEmoTZs2tbKy4tPB3d199OjRzPaioqJHjx4J+3QAIEslJSWTJ09mZq6k2NhYHx8fGYcEwN/gwYOpdzkcjhIVr1QiSF6lS9j1Z7a2tsOHDz9y5EhERERUVNS9e/cmTJhgbGwspfDk4ty5czzbx4wZI8jhNjY2gj+XpqbmsWPHOnXqRGuvrKxcvnx5Tk6O4EMBgIxduXIlJCSET4fHjx8/ePBAZvEA1Kl79+602dghISFC7dAJgkDyKn8sFuv3338PDw//9OnT06dPL1++7O/v37t3byXaJUsohw8fZjauW7fOwcFBkMO9vb2FerpGjRotWrSI2R4ZGXny5EmhhgIAWbp+/Tr/DpWVlQsWLMjMzJRNPAB1at269bhx46gtGRkZ8gqmHkPyKl29evWitairq5v+1/Tp069cuVJRUbFz587+/ftbW1vX+/WzPJdYBQUFLVu2TEVFoHcjs/pVncaNG8dzauy+fftyc3OFHQ0AZCAtLY3/aVdSXFwcs1w0gBzt2rXL0tKS2oJVFhKH5FW6AgMDuVVXTUxMFi9efPPmzcz/OnjwoI+PjzLOWxXZtm3bSkpKqC3m5ubTpk0TvHDj8+fPhX1SFRWVIUOGMNs/ffqUn58v7GgAIANZWVkCVnLcvXt3Xl6etOMBEJCKigrtG425CzqICcmrdLVp0yYqKurRo0ePHj2KioravHlz//795R2U3GRnZzOnrhsYGJiZmUn7qQcPHsxzQRi1pgkAKI41a9YI2DM1NfXNmzdSDQZAHE+ePLl37568o6hXkLxKnY2NTa9evXr16tWqVSt5xyJnx48fT01NpTX6+/vL4KkHDhw4a9YsZjtmIwEooFevXl27dk3w/nXOjgWQo8rKyrt378o7inoFySvICJvNDgsLozVqamrK7FT0qlWrtLW1aY3R0dGVlZWyCQAABBQUFCRUf1S+kzg2m/3jxw95R6Gs5s2bR2sJDw/Hd40EIXkFGUlOTn748CGtcfjw4TLb6crY2NjX15fWGBcXl5aWJpsAAEAQP3784LkxHh8vXrzIysqSUjwN0J49e3x8fJycnMaPH09uaQZC8fLyorW8evVK2J9kwAeSV5CR5ORkZmNtO2BJia2tLbMRHygACuX+/fsi1GCurYA0CGv79u3z5s27fft2VlbW+fPnmXkY1Mne3p65Cnn//v2RkZFyiaf+QfIKMsLcbMzX11fA2q6SwrNG7KlTp0JDQ2UZBgDw8erVKxGO2r59O89fyCCUHTt2LF26tLq6mtuSmJiIha0i6NixI60lLy9vxYoVAtbQAP6QvIIsZGZmHjlyhNZoamoqYG1XSWnfvv3QoUNpjTU1NWvXrpVlGABQm8rKyvDwcBEO/Pbt286dOyUeT8NRU1Ozbdu2+fPns9lsajuHwwkMDKyoqJBXYEqK+V1DEERERATmZ0sEkleQhaCgIObPzRkzZsg4DBaLxfNJv3z5Eh8fL+NgAIDpn3/+EaGWMykiIoJWRhoEV1JSsnDhQp4PJSYmnj9/XsbxKLvZs2fz3HWIOlGtoqIiluL9+/cyDFC5IXkFqfvy5YuCb8RaUFCAqUgAcpebm7tv3z6RD3/79i1+hYrsn3/+4fPo9u3bi4qKZBZMPdCsWbODBw8y2588eeLr63vp0qUVK1b06tWrK0W3bt38/f3LyspkH63SQfIKUnf//v3S0lJaY4sWLUTYC7eiokLM36aenp7W1tbMduaUXACQsb17937//l2cEQ4fPiypYBqUd+/e8Z908fr1a6Eq7wJBEEOHDg0ICKA1VlZWhoaGjho1at26dc+ePaM+VFxcfOzYsY0bN8owRmWF5BXkY/r06SJsrFVWVvb06VNxnldHR8fQ0FCcEQBASsT/Dfn48eOCggKJBNNwJCYmuru71zmrddOmTeXl5bIJqX7Q1NRcsmSJgYGBUEcFBQXdvn1bSiHVG0heQeqY2zqbm5szf4/KzIoVK5hFTPLz83GxBkCOsrKyRJ7typWUlJSSkiKReBoOAU94v3379vLlyzKIpz6xt7dv3bq1UIdwOJxRo0adPn0aE7j5QPIKUpeYmEhrcXFxEeG0K0EQ6urqLVu2FDOeUaNGtW3bltYYGRnJ3LoWAGRmzZo1EhkHlZuFUlRUJPj6d7y2IhChnHlZWdmkSZP8/PyYM+6AhOQV5GDYsGGiHairq+vp6SmlAF6+fCn+yAAgGknNO79+/Tr+lgW3atWq169fC9g5MTFx2bJlUo2n/hk6dOiJEyfs7OyEPTA0NHT8+PHSCKkeQPIK0pWYmEjbtlFTU7NLly7yioc0f/58ZuOGDRvy8/NlHwwAhIaGfvv2jdmupaWlr6/PbN+xYwebze7VqxfP0ZhTlYCnGzdubN++XfD+HA5n48aNmDwgrMmTJ589e1ZdXV3YA69du+bj44MpbUxIXkG6vn79mpeXR23R0NBo3769aKNVVVXl5uZy75qamoo2Ds/NEeLi4sQp0wMAkqWrq3vy5MnY2FjaX7qurq6Hh4eamlptF2QPHTokkwCVHs8K3HU6cOCANIKp3zp37izadujXrl377bffJB6PskPyCtLF3FfQ1tZW5NFKSkqo1xZdXV1FG0dfX3/QoEHMdhTiBpALnhuQtm3b1tfX197efsKECdT2du3atWvXjiAIZ2dnc3NzGYVYHyUlJYlwVFZWFmq+imDmzJk7duwQ4cCLFy+i/isNkleQory8vKioKFqjyBNema5fvy7agerq6s2aNWO2v3v37uLFi+IFBQDCqa3OAHd3eOY28aQmTZp0795dipHVa8HBwaLloHFxcWlpaRKPp95r0qTJ3Llzp02bJuyBZP3XcePGSSMqJYXkFaQoJCQkISGB1ti7d2+5BCOImpqanz9/yjsKgIbl3bt3X758oTWqqKhwL4+4u7vXdqyuri6zsbq6Gqep6vTz508R5gyQUMVJZKJNHiAI4tq1a56eng8fPqysrJRsSMoIyStIS3V1NbPScpMmTbp27SqXeGiGDBnCsz0zM1PGkQA0cDynqJqZmfn4+JC3+fxV/vrrr8zGjIwMrNmqkzjlHdauXVtdXS3BYBoOZpVxwT148MDDw2PBggXIX5G8grSUlpYytxP09vZu1KiRXOKhsbe359mOaa8AimDMmDHc2/irlLjY2NiwsDCRD7927drRo0clGE/DwXN6t1D27t3LnI/X0CB5BZmqbe6a7DVp0sTCwkLeUQAAbyJfXSUdPnxYUpHUS//5z3/EnFmBDQtE8PLly9WrV4s/jre39+TJk5OTk8UfSkkheQWZ4jN3TcYsLCwUJ5MGaLDS09OZ56J0dXWp5V15TmwltWzZskWLFsz279+/49JqbZ49exYSEiLmIGlpaTj5KpTIyEh3d/fi4uI6e5qbm2/evHnz5s3Nmzfn2aG4uPjUqVP29vaOjo7p6emSjlQJIHkFJfbt27c3b96IfDjP2XIAIEs8J6dOnz6dWoyZz5+qubl5p06dmO0vXrzAPlu1OXjwoETGwQoBwRUXF8+cOVOQzJUgiHv37i1evHjx4sX37t3jU86cw+EkJCT07duXthNQQ4DkFaSFOU3N1dXV2tpagk9RVFSUnZ0t8uFubm6YOQAgX+KvrMIWmkJhs9mfP3+WyFDnzp2TyDgNwd9//x0fHy9Iz7/++ou7JMPBwSEsLIz/FcvExMTu3buvX7/+6dOn4sepLJC8grQwf5QbGhryufwngtatW/fs2VPkw42MjNzc3CQYDwAIS5w17yQ7OzvJfrDUb+Xl5ffu3ZN3FA3LzZs3Bdz1zcvLKzAwkNrSoUOHsLCwDRs28HmTf/nyZfny5Z6eniNHjnz16pW44SoDeSavJSUl6enpOTk5cowBpEfA6yPi0NDQ0NbWFmcE5i/a169f379/X5wxAUBAJSUlPEuNzp8/X/BBOnbsaGhoKLmgGigWizVlyhRmGZZbt27VtpdhVlZWYmKi9ENTbiUlJcOGDSstLRWk89y5c9XU1GiNmpqaf/zxx/37901MTPgcW1paevnyZXd390WLFr148aKwsFD0oBWe3JLXHz9+eHt7W1hY2Nvb41dgvaS824tjIheAbBw+fJhn8ipsLUye8wLxhyyUefPmHT9+3MrKitbu5ua2bNkynofk5eXFxMRIPTIlV9ubnKeNGzdWVFTwfKhLly4fP37cunUr/y3Wi4qKtm7d2rlz565du06fPv3Hjx9CR6wMpJu85ufnh4aG8tyK4/Hjxw8ePCAIoqCgwNfXF3vNNQQKuLvdiBEjNDQ0aI0oKgmgXCZMmMBsxB+y4ObPn7958+baHh00aNAvv/zC8yG8yHUSambw/fv3d+7cWdujurq6CxYsiI6OFmRX5MTExMOHD7u5uV29elXwAJSFFJPXMWPGODo6+vr6tm7dOjo6mk/P/Pz82n5qiOPFixcSHxMEFB8fz/w/ra3qhxyZmpqqqqrKOwoA+J/BgwdL5LPi+vXrDXAVtmgCAgKYV6u5dHR0VqxYYWRkJMuQ6g1hrwCsWbOGf5XiJk2a3L59e/78+fxPwZISExMnTJgwcuTII0eOCBWGgpNW8rp3796QkBByJXhmZiazKq+Tk1PLli3J2127djU2Npbgs2/evFlFRaVz5856enqbN28WJzPOyclJS0uTwfTNeiY2Nra8vFzeUYjo/fv3ubm58o4CoP7j+dGqo6PDJ5HiqXfv3szGsrIybGHKtG3bNlpL69atufMuaDsg+vv7kwV3HR0dec7NSEhIwC8EPkJDQ1NTU4U6pLi4ePr06ebm5osWLartorSBgcG2bduSkpL+/vtvakVknsi5sNOmTVNRUVFRUenSpcuNGzfE3KJC7qSVvNKqn2RkZNA62Nra3r17Nzg4ODg4+Nq1a5Kdbv/ixQtyiklJScnSpUufP38u2jgRERGOjo6WlpZr1qyRYHgNgVJvLP7p06eCggJ5RwFQ//E8w8SnsGVtXFxcJBFOg8As79CyZcsmTZqQt6dPn059iMVi8Z9/bGBgIOaqWeApIyNj69atS5cu5dOHxWIFBQXFxMR07dq1cePGdY7J4XA4HM6zZ8+GDRs2ZcqUmJgY5d3IQ1rJa1JSEvUuzzp8dnZ2Y8aMGTNmTLNmzST41GVlZcL+0OEpOzt75MiR5GTnHTt2YAW6UGhvAEU2duxYeYcAAP8jwbqtKERK8/nz53fv3vHpQJvD+vnzZzabzad/ndktiOPcuXN1fpk6OjrGxMRER0fPnj27Xbt2Ao4cEhLSvXv3Hj16uLm5ubm5Xbt2TexgZaoe1nnV0NCQyCSEPXv2cJfpVVZW3r17V/wxG4iIiAglqp+igDNxAYBK5L2yUHCAZsuWLfxrNtFesfv37z958oQgiC9fvuTl5TH7v379GuutpUrAy5j29va7d+9+8uTJrl27BB/8+fPn0dHR0dHR48ePDwsLEzVGORBuXpHIhCraJyZVVVUdHR1qy8OHD3v06CHsOLSpAhEREeJG1mBUVFTw/7EuMi0tLVdX12fPnkljcCrMcgaQtjdv3uTn5zPb161bd/XqVeq0V9qV7piYmPDw8AEDBnBbavt8joiIKC4u1tPTk1DIyq28vPzff/9lticmJiYnJ9vZ2T19+vTOnTu0Rz09Pfv375+UlFTbdob//PPP/v3765x5KRElJSVFRUV1nnHg5tOmpqbcN1JmZqauri4ZZ2ZmJv/50MHBwenp6eQIZC2LR48ekVMQO3bsOHz4cAHfVEOGDDEzMxPnR9R//vOfGTNm0LKa2ujr68+ePXv48OHDhw9PSUkRvNRraWmpl5fX1atX+/btqxTzQGSRvA4YMIBZjUiW9u3bN2zYsPbt2wt+CHNWUHFxMT4EBST+ljm1qa6upi6l+vbt25s3b4T6n6XJysrieblkzJgx9+7d464pBKh/srKyPn/+bGtr27RpU9k/e1JSUlBQEM9fibdu3QoKCpo5c2bz5s3j4+MjIiKYRaMDAgJmz57dp08f8u5ff/3F81levHjh5eW1ceNGY2Pj1q1bUx8qLy+n7UXUpEkTOzs7Zrs4yDEJgkhISMjPz1dRUenatWthYeH79+/JDvb29uQq/rKystevXxMEYW5u3qJFC+og5LHkbQcHB3J2I7e/q6srNz979uxZVVUVQRDMhOnHjx+bNm3ieU3s27dvAwYMcHV1rW19CP8Lj+fOnXvz5s38+fOdnJzevn3LzY+nTJliZGT0/fv3U6dO8XuNhPHx48f4+HgfHx/+3S5evFhTU0MQxODBg7lL0G7dutWqVSsHBwfy9s+fPwV80j/++IPW0r59+z179giyv+OtW7fEPP2fkZFx+PDhuXPnCtifxWJZWFg8f/48ISHhyZMnS5cu5fkTkammpmbYsGEBAQH8ax0oCJbgtXOFYmdnl5KSQt7+7bff9uzZI85oMTExDx48uH79OnnXxsbG29t7+/btZPDr16/nfoSRxo0bFxwcTG0xNTW1trYmCMLW1nbYsGGjR4/mM00nNTV18ODBzIlBx48fnzJlijj/kIagqKioT58+5KcqzY4dOwT/C+Rp4cKFtKWyQ4YMWb16defOnQmCyMzMzMjIcHFxKSgooH7ampqalpSUMOsNf/r06cCBA7Vt821paRkQENCmTRuej/bp04c7Vzs9PT0qKoogiC5dutDy3ZSUlPfv33t7ewv37xRPamoqWTm8W7dulpaW1IeSkpLi4uIIgrCwsKBVCiwtLRXk+pSxsXFNTY2An4ZCefbs2du3b/39/fv169e4ceOSkpLbt28TBKGiojJq1ChBRsjJyYmIiHBwcBB84hd/RUVF1BNRPXv2LC8vF3kBqCCo3/2CmDp1KpnKfPr0SdhqjszkddCgQfHx8eRZq0GDBjk6OtIOKS0tPXDgAK3R2dnZw8OD1picnMz/R2xSUhLPy9BcLVu2bN68+du3b3lWCheWIMkr2UeqySuLxerWrZuwyeuHDx+4S0j5J6+xsbHkCUUxz/ZBnby9vQX5iwsNDfX19RXzubp3705+xYggODhYqArrenp6T58+Zf7tR0ZGZmRkCP5pLG2ySF5fvnzZsWNHkYcKCwsbOXIkn7IOjRo1ys/Pp15jYiavNPb29oGBgTyXBWRkZAwcODA+Pp75kLa2dkhIiJeXlzDhy9/u3bsPHDjg5+cnYP+qqqrTp09PnTqV1t61a9cePXpcvny5tmyPIAg2m719+/baKqdoamp6eHj079+fIIivX79eunRJQ0Nj9uzZtG7x8fG1/dBPT09nvmN1dXXJT/Py8vKysrLGjRuz2WzqFS4tLa2qqiryhISkNG3aVFNTk7xdVlZGfg0bGRnp6Oj4+/sbGBjcvn07ISGBe5GL/MX15MkT6pwHExMTnsXVqW7dupWYmBgQEEBe7QoODubW7hg7diz38hm1nRYPdbTi4mLyQpK2tjZtanh1dbUg33YaGhocDkdK00JIJiYm6urqVVVV3DeShYUFtYOPj0+rVq2qqqq4s7tmzZoVGRn57Nmz3NxcPT09Kysr8g28b98+cUq2UWMgCKJJkybV1dXSSNwBQLm4urrGxsbW2U0iyauGhkZ0dHSnTp1EOPbTp09ubm61TflgMjc3j46Opp31WLFixdatW8nPUgsLC29vbxsbm5kzZ5LfL6dPn7ayshLkPLQkcaSDWjs3OTm5tm6pqalZWVm1PVpaWnrt2jVBVjKy2WzqgQKuH7ezs/v69SvtSdevX8/nkE6dOon5ysiYv7+/IC8FAACAjJmYmFhYWAg4oVOheHh4CPIVXFNTQ/vtLZoNGzaIkACw2ezly5cL9URDhgyhDSLg739DQ8MtW7ZUVFSIEKcIZLRgi6c5c+bs27fFuMCPAAAgAElEQVRPX19/5syZgYGBWlpa1EdLSkr8/f1DQkIEGerGjRvDhw8XNoDk5OR+/fo9ePDA3Nyc28h/WavIi17lorCw8PHjx/KOAgD+P1dX1y9fvlDnbTs6OhoYGMTGxmpqanbo0IEgiKqqKu7MBAsLCwsLi/fv3xcVFREEoaOjQ87wpvaBOjVq1Kht27YEQXz58kXAivrGxsbk5X5SRkbGt2/fuHc1NTVtbGy4l/65/cvLy3nOmJIBe3t7WqXP6upq8jpP06ZNbWxsPn36lJOTI6Vnt7Cw8Pf3d3JyEqQzOTdm4MCBbdq0GTRokL6+fmxs7JcvX2rr/+bNm3v37pG3/fz83r17Fxsbm5+fn5iYqKamRs4Zk6B58+apqKhcuHCBXLDFU69evebMmSPIaCwWa+jQofv37xczqt27d0+fPl2oTc4yMjL27Nmzbt06AfuzWKwBAwYcPHhQpACJgoKCRYsWeXh4iHOlXXByS14fPXp0+PDhmpqagoKCDRs2NGrUaMWKFdQOq1atomWutra2AQEB//77L/d9zJWcnCxaGMnJyUFBQdRZXL/99tv9+/drm4y1cuVK0Z4IQLKMjIz69u0rzggcDic0NJS87eXlRZ78SE1NbdKkCc/Vpi4uLr17975+/Tp3RhBVbm7uw4cPuXctLS27devG83mvXbvG3fTO3t6ezMa+fv0qyDU4wTVr1ow2FV5Y6urqEyZMOHHiBHnXyMiI55T3u3fvxsfHOzk5URe/14Zn8mpoaEhLXrlzSywtLcnklZzsoaOjQ/Zhs9lCJa/U+Sq///47c/+q169fP3jwgHu3U6dO1B/q5PzXI0eOkDm0r6+vhYXF48ePuTHo6OjMmDGDnLvSs2dPV1dXnmHcvHmTW7QyLy+PT/FsOzs7Z2dnU1PT8ePHv3z5cufOncxql15eXoMGDcrMzLx//z45yZsnExOTf//9l5u8CjgTlDZHNj09nZa82traUtdFSGOxl1C4c2G5qquryb+ppk2b2trafvz48dmzZzNmzCD/E2kWLFjg6+ubl5c3bdo02iVmNTW1ESNGdOrUKTQ0lOem69bW1v/++2+rVq0EDHXMmDG0Yj5dunTp0qULn/7//PMPrfHHjx9k8lrbm01MY8aMkdRQEkle09LSjh49unjx4jp7/vz58+bNm+fOnXv58iX1TctfixYt5syZs2TJEuZD6urqI0eOvHTpkiDjnD9/XjbJqyzmvCYnJzN34L169Sr1XOns2bN3797Nvcuc52pjY0Ou/q6srJw3bx7trbBp0ybqi86c89qxY0d3d3eC1zICFRWVv//+e9WqVdyWJ0+eDB48mLlK4O+//165cqWw+xbKV3Z29s6dO8lX8vTp07m5uZ6enuT3n5T8+PGD+33PNGnSpKFDh9KWCjFFR0eT30Zt27Yl58gSBHHixImgoCDabEsrK6srV65Q17S6ubl17dqVOWZUVNTTp08Jgmjfvj2Z9oWGht64cYPPN2jTpk0nTpzYoUMHT09PsuXYsWPMzbfI73KCIHJycs6cOUP897uc/79RTBoaGiYmJuKMwOFwuAVlzMzMyDd2aWmppqamqqqqsKNVVFRQz+vo6OjUVm45IyODW6RGT0+P3F3v58+f3LLKEqGlpSWXRfQgoIqKirlz5/I8zfPXX38tWrSIuu3ihw8faEsnqZ/GpaWlGzZsqG0fxBs3bijdQgXp2bFjB7NyZYsWLWJiYszMzAheczQXLly4ZcsWgiBiYmJ69+7NnO9O7vAkzaiVnoqKSp25VqNGjcjtzQ4dOsRzkWKfPn2oJwiYOBzOgQMHVq9eLeyGvebm5uHh4bWtTiYI4vPnz/369fv06VOdQ02aNOnkyZNCPbuIpDQdoc45r1euXKGGMXv2bOqjtL8ER0fH1NRUaofJkydTO2zatIn6KG3Oa7t27QoLC7mPzpw5k/YiODs7l5eXU0dgrqj9448/JPC6NAw8r1Ooqak9ePBAzJE3btxIG3b9+vXSiJYgiClTpog5MgDwR1tWTxBE165dmd2YmyZGRUVRO9TU1PTu3Zv5V6ynpyerf4pyePv2LW2GHkEQ/fv353ZgVqovKCjgPsosFqmlpZWYmCiPf4oyWbhwIc9vGS4vLy9uZ2b6wVVUVFTbU+Tm5gq+LJukra1tYWExZ84cQf4J375927Jli52dna6ubm0Dampqvn37VgKvlwAUZYct2i9j6hUrdXX17du306Y8//XXXyoqggbfu3dvav3kffv20Uocp6Sk0Krf/frrr9S7GhoaglwTBBLPfcbt7OzIk9/ioP2/aGtrc8+Jioy2lzfJxMSEzycIAMhRo0aNuMU7SSwWi+dabJ5/3Q1Z27ZtuWVSJMLd3Z1WgwyY+J/7NzIyOnLkCPcunzctz7U9GRkZ69atc3Z2PnbsGP8w9PT0unfvfuzYsQsXLly4cOH+/fupqakC7shlaWm5cOHCpKSka9eu0SaokLS0tPbs2UPOz5EBRUleqe/+kJAQalUjIyMjnokjh3ISns8G1kZGRsyJ1bSyZ05OTvwL3Tdr1kz8JKnh6NKli+Dzn4Sirq5uZWXFvWtjY8NnppQ4/vjjD8l+xAOApLRt21bAUr5CVbgEEVCXtUFtOnTowKfmgKenp4BzwJ48eUKb57Znz57u3buvWLGCz/Iyko6OzsmTJ6OioqZOnerr6+vr61vbsgT+PD09o6Kihg4dSm10cHDYt29fQECACAOKRlGSV6rBgwfXOeXu9u3b1OSVnKzDk62tLbmjBsiMoaEhs/TJtGnTxB9ZV1eXWg6dvHwg/rBMtL9MAFAcL1++5LlyiKnOfURBTPioFISxsTGf6gSCf5GRa34yMjI4HE5hYaGHh8eCBQsEWZXl6uqakpIiQlEmnhwcHM6fP59KERMTw6wNL1WKmLw2atSIWtu1uLi4zs8pPtejRavrS1NVVVVaWir+OA2ZNHbWfffunVDbEQFAPVBZWVlZWSnvKJQVbcYFQRCJiYmCFGGIiYkRZ8uPBm7y5Mm17Td+8eLF/fv3U7dK5jmBmxQfH29ubq6iomJoaPjw4UM++8Xo6elNmjTp/PnzHA4nNjaWzzk+Eejq6lpQGBgYSHBwQShE8tq5c2c+58xLS0upNVzqVFlZ+f37d+5diVRmzcrKEmTnTJAxbW1tKf3NcHerAgCoT2grBwiC+PbtG/+tekkbNmyQ6tZ69ZuZmdmyZcs0NDR4Pvrbb7/17Nnz4sWLRO0TuIVibGwcFhZ28uRJAfdsUjoKkbyam5vTfgvSJiqtWrWK/3av1Cmz379/ZxaCFR9tRRcoAunNeeX/fgMAiRBtrY+Tk5Mg60L69u2LcmlMPF/zOr/gMjMzsS+GmGbOnNmrV6/aHn3z5s3UqVMnT5584cIFZlVjobi5uV2+fNnNzU2cQRScLJLXgwcPCjsx8e+//6be/fnz59SpUy9fvkyOw+FwaBMJqEv5TExMhg0bxn98nsvhaWhzNA8fPoyzcYJj/nA8dOiQxJ9FkP9HAFBYolVg1dPTo01DYn4pEARhbGxc24muhozna37z5k3y67W2SXpHjx6tc0kQ1Ony5ct8vrZKSkpOnTo1duzYW7duiTa+q6tramrqv//+yydLrh9kkbxu3ryZu5EPT6WlpbSLEXZ2dseOHaMu9y4vLx85cmTv3r0XLFhgYWHBpwquqqpqnRslC7L1Dm0e+tevX93d3ZnlBoEn5ivMs+qyxJ9FBDz3m5HIyAAgEQYGBnVurYKtsAWkqanJ3FPg2LFjp06devXqFXPbiKKiIjabfefOHeZQ3bp1QxFJoejp6T148EBK+wTt3bs3NjbWwsKC5xaJ9Yy0klfab7uJEydGRETU1vnu3bvM5XJTp0718fGhNT558mT79u1CnQEtLi5mZifXr1+v88D+/fvTCkkkJyeLuSFnQ1ZaWpqfny/ZMSVyLpxaYI9LIuv8AEAi9PT0UExUUjQ0NHgWGpsyZUqnTp2+fv1Kax82bNgff/zB/G2gqqpK29QdBKGnp7dy5UrmsjlxWFlZrVu3rr5Ob+VJWskr7YOmsrKSuTcSFc9Crfv27du3bx+18oAIPnz48PbtW1pjcnJynQfq6Ogw9/lNTk7mU1MW+Pj69Su5O6sEnT9/XrIDAoAsjR07lvYJn5eXR11xC9Ig1C+BuLi4bdu2Mds7deqEOlmiGTly5MmTJ52dncUZREdHZ8yYMZcvX46Ojo6Kivrzzz+NjIwkFaHik1byOnnyZNpko7i4OD7X3HluxWtkZDRz5szU1NSDBw/yKfBbpzorbdU2B8XLy4tZnVTYXYMBAIAnMzMzWvKakpJy9uxZWrfi4uI6VxThaongJJJ0ijZfGUgjRowQZ6KLiopKSEhIcHDw8OHDu3XrJtkyWEpBWslro0aNaLVXaZ9Qbdu2NTY2FmQoc3Pz6dOnP3jwYPLkyQI+O3Uuv7Gxcffu3WkdlixZwp0X6+joOG/ePJ7jaGpqLlmypE2bNtRGzIas97S0tNTU1OQdBUCDwKwAHRYWRt1kkSCIwsLCN2/ecO9WVFRUVFTQjpLSfiX1kpqampaWlpiDSKN0d4PSqFGjjh07Ct6/efPmbdq02bZt27Zt2woLC4cMGSK92BSfFL+h16xZk5WVRX7iqKmp9e/f39LSkvuojY3N4sWLly9fzuFwnJycRo8ezX80W1vbEydO9O3bd8uWLdRPMZ42btxYUFCQkZGhq6t75MgR6vOSTE1N7927l5aWRhDEqFGj+MxMaN26dXx8/PHjxw8fPkwQxPTp0/H7vt7r16+ftbW1vKMAaBCmTZu2ZcsWasvt27czMjJatGhR2yElJSUlJSW0DZxfvXolrRDrHTs7O3d397CwMHEGkcimiQ3W9+/fFy9eLPibdtSoUadOnWoIK7EEJMXktUuXLlFRUeR8U3V1deal+WXLlnl6etbU1LRp00ZfX1+QMSdPnjxy5MiePXvGxcXx6WZkZBQSEsJ/KMF39WWxWH5+fn5+fgL2B4Ighg4dqqur+/PnT2rj2bNnBw0aJK+QAKB+MDY2pl2447kUgVYvHKjGjRsnZvIKIvv+/fuoUaMePXokSGdtbe1ff/11zZo1yFyppHttVFdXl3+OWFuF+Z8/f3p7eyckJBAEoaOjM2PGjDFjxlhaWrJYLF1dXdoyvY4dO4q5qAskrlmzZswr74o5XZhZGgYAlMuNGzeYjQ1wIqDgxo4de+fOHZHXH0+YMEGy6+UbDg6Hc+7cOUEyVxaL5eLisnr16gY+Q4AnBZ3Yd/369fv373PvLlmyZMmSJX5+fvr6+tnZ2ZGRkdTOgwcPVlVVlXmMUIeFCxcGBgZSW8rKyiorKxWqbHhxcTF1R2kAUEYCnsQCLi0trRUrVly+fLm8vFzYY+3t7Xfu3KmiohA7dCqdffv2zZ07l38fJyenadOmjR07Fj/AaqOgbz6ep+iOHTu2Y8cOWnUkIyOjOXPmyCouEALzr+7Jkydi7noncadPn2au/AAAmeG58p1WwtnIyIi57pYrKioqLy9P8pHVd05OTqNGjRL2KG1t7b/++kvA9dZAc+DAgdmzZ/PpYGxsPGfOnPj4+Pnz5yNz5UNBk9epU6fyma3P1bhx49DQUPwHKyalmHBWZ/0dAJCq9u3bM9fUBgcHU+/q6OjwqZaYlpYmwulDIAjCzs5O2ENatWo1ceJEaQTTEKxdu7a2h7S1tefPnx8dHb1r1y5ZhqSkFDR5NTQ0fP369datWw0NDfnMZx07dqyHh4csAwMxPX/+XN4h/B8ibyENABJhZGT0+++/0xoPHTpUU1Mj4Ag8P1U6d+6MyjB1+vXXX2VwCJA4HE5tBd06d+786dOnbdu2ifBzomFS0OSVIIjGjRsvWLAgPz+/uLh427Zt3bt3b/F/7d+/f9++ffIOE4SjUPuPv3v3Ljc3V95RADR0/fr1o02F//nzJ3Nb79rw/FTp37+/Qk2vV0zGxsaCF94hCMLc3LzO+ZpQm6NHj5IFOml0dHT+X3v3GRbF9f4NfJZdQJCmFEERRFGwErBGxQpYsEWiAvYSNVZsFDWCHSX+VRQ0iSVqNLFEMNJERIwtoqBgAQtYEaWJSG/7vNjrN9c8M7Auy+7OzvL9vNo5c86Ze0CXe2dPuXDhgqmpqeJD4i7lTV5JzZs39/LyunXr1uv/34IFC9gODcRp1qzZ8OHD2Y5CnJcvXxYWFjLLsechgCLZ29v36tWLVnj48GGpO9TQ0HB2dm5cUE2ChoaGi4uL5PUvXLggv2BUm+gxHK2wXbt2bm5uV65cad26NStRcZeSrjYAKkBdXZ251H9mZqayLTjAhC9uAFgn4Xj0vLy8vLw8WqGjoyNGlEnI19f30qVLd+7c+WrN1atXf/PNNwoISfWUlpbOmDHj8ePHZIm5ufnRo0e7du2KSTvS4cCTV+Au5s4UCQkJZWVlrAQjoa5duw4YMIDtKACaFuZ7hYTj0Z89e/bixQtaoaurq2zCagK0tLR8fHy+Wq1du3arVq3CqpTSuXTpUnh4OHnYunXr6OhoJycnZK5SQ/IKcjRo0CBm4dWrVxUfSZ0SEhKYhU5OTrRtJwFA3pjvFdXV1bQt+upU5//iwYMHyySqJuK7777z9vYWMzdaXV19+fLlGJQpnaKiookTJ5KHbdu2vXr1ardu3VgMSQUgeQU5Mjc3Z37NpDxbkDMj0dHRWbFiBSvBAADVx48ff/nlF/F1UlNTQ0NDaYU8Hg/rDDTUjh07zpw506pVK+apDh06REZGenl5KT4q1bB582bqYVxcXKdOndgKRmUgeQU50tPTY35Yl+HSqoWFhbLdcnbWrFmWlpYy7BAApHbgwAHmeFaSUCj08/PLysqilXt4eMg5LtX0/fffR0RE0N6x27dvHxsbi9lvUgsNDQ0ODiYP/f39MadCJpC8gnz98MMPtJLIyEjJV3AU7927dw8fPpSu7aNHj27cuEErxAgkAFa4uroytyF48eJFeno6s3JSUtLKlSs9PDzqHBeLb7el1qtXr0ePHm3btm3AgAHGxsarV6+OjY1t374923Fx1b1797y8vCorK0WH/v7+P/30k5jhGSA5JK8gX0ZGRurq6tSS4uLiPXv2sBUPqaCggHxPIenq6rISDEATp6WlFRAQwCzftm1bdXU1bfxrVVXV7t27abtwkfC/uDEMDQ39/Pxu3LiRk5MTFBTUoUMHtiPisKCgoKqqKtFrHx+fgIAAzHiTFSSvIF+DBg1iju9pzAqOslJnDPPmzVN8JABAEMTcuXPbtGlDK4yOjt6wYcM///wj4eIDhoaGixYtkkN0ANLr1q3bkiVL2I5CpSB5Bbnz9PSklWRmZt6+fZuVYEQKCwsjIyNZDAAAmKZMmcIs3L59u5ubm4Q9/PjjjyYmJjINCkBKS5YsMTIy6tSp0/bt25mjYqAxkLyC3Hl5edG+yCsvL//8+TNb8RAEERoamp+fTyu0s7MTCLBtBwBr5s+f38gesMIrKA9HR8e0tLTExETs2ihzSF5B7rS1tYcNG0YrlMlqr926dZNuGmyd60eOGDGCNjwXABRJX19fW1tb6ubffvttv379ZBgPQCMZGRnp6+uzHYUKQvIKimBvb08ruXr1qiQrkMvJxYsXmYVz585VfCQAQDI1NW3Mw1c83wJoIpC8giIwV168e/fu3LlzmfP9G4Q5mlZCzP0kBw4caGFh0ZhgAKDxFi1aZGRkJF1brKAJ0EQgeQVFMDU1ZS5ud/r06evXrzemW+lmZtTW1gqFQlrh8OHDmzVr1phgAKDxOnbsKN3+Q7q6ujY2NjKPBwCUEJJXUAQ9Pb06v5TftGlTQ7saMmQI+Vq69WKDgoLKy8upJerq6i4uLlJ0BQAyp6enJ0WrCRMm9OjRQ+bBAIASQvIKCjJ27Fhm4YMHDxraD3X4bElJyadPnxrUPD8/f//+/bTCLl269O/fv6GRAIA8eHt7a2hoNKhJ69atN2zYIKd4AEDZIHkFBXF2dmZOBK6qqsrIyJC6z5cvX967d69BTY4ePfru3TtaIb5tBFAeQ4cOHTRoUIOabNiwwdraWk7xAICyQfIKCqKlpTV8+HBaYVlZ2ZUrVxrUz927d8nXNjY2Dfojl5OTc/DgQVphs2bN1qxZ06AYAECuwsPD1dQk/fNkY2NT5+4GAKCqkLyC4syfP9/U1JRWGBQUVFpaKnknN27cIF+rq6trampK3jY7O5v5oNfV1bVXr16SdwIA8ta8eXPJhwEMHDjQwMBArvGoqtra2nv37i1btuyXX36pra1lOxwASSF5BcWxsLBgzqh48eLFn3/+qZgA/vnnH2YhhsoBKCEJ113W1dX18vKSdzCq6unTp7179963b9/ChQt37NjBdjgAkkLyCgo1efJkZuGZM2ek662wsDA7O1vCyhUVFZcvX6YVWltbY8ArgBIyMTFxcnL6ajU3N7du3bopIB6VNGHCBPL19u3bWYwEoEGQvIJCeXh4MNfBSUhIePr0qRS9vXv37tGjRxJWvnLlCnNZWV9f3wYNPAAAxdDQ0BgxYgRzfWgqPT29FStWKCwk1fPx40fyteSDjAFYJ2A7AGhatLW1V65cGRAQQC2srKy8fPmyXJ+AFhUVubm50Qq1tLSGDh0qv4sCQGOsXr3a0tJyzZo1r1+/rrPCrl27sLarrCxfvpztEJqo9+/f79+//8uXL2SJrq7u2rVrdXR05HfRsrIy2veWBgYGLVu2lN8VZQvJq3zdvn17586dBEF4eHiYmZk5OjqyHRH7xo4dS0teCYKIiYlZuHChQNCwf5AWFhZ2dnaS1HR3d6dtTEAQxPTp09u3b9+gKwKAIk2aNMne3n7q1KmJiYm0U23atJk3bx4rUamkcePGsR1CU3TlypVJkyYxFyx//PhxYGBg586dqYUZGRlZWVkEQZibm9f3xysjIyMxMTElJWX+/Pn11UlKSvLy8qLOfiYIwsbG5sqVK23atJH+ZhRJCHITExOjrq5O/Wn37Nlz3LhxJ0+eLC0tZTs61lRXV9f5Lvn582dJms+ePZts0q1bN0mavHv3jrnKgYGBwcOHDxt3KwCgCBUVFf7+/kZGRuT/37Zt2z5+/JjtuDhPX1+f/JEWFhayHU6Tk5CQ0KJFi/rSsxYtWiQkJJCVa2pqyB3RTU1N09LSmB36+fmRdczMzOq86MOHD42Njeu8Ytu2bQ8cOCCvu5UpJK9ytHLlyvr+UZqYmAT+T0FBQUVFRUVFRU1NDdshK0hiYiJzKNv27dslaStF8hoREcH8FcydO7dxNwEACpWXl5f9P58+fWI7HFWA5JVFISEh2tra9SUJIs2bNyfr0758sLW1pXUYFhZGHbjM4/GSk5OpFWpqalJSUlq1aiXmiurq6r/99psi7r9xkLzKUZ8+fcT/u6SZNGnSkiVL/v7776ysLLZjl7tJkyYx/89ER0d/teHx48fJJp06dSopKflqE+anCG1t7SdPnsjiPgAAuArJK1uSk5ObN2/+1ayAx+ORTWpqaqindHR07t+/T+2Ttugkn8+nXfTixYuSpCKenp6K+BE0DmYXytGcOXMatEP32bNn9+/f7+bm1qNHD19f38zMTPnFxjrmIo5VVVWTJ0++f/+++IbffPMN+frZs2c3b94UX//ly5fUfFekQ4cOtLFEAADQICUlJf9SPHz4kO2IOCMhIaGkpOSr1caOHUu+5vF4Y8aMIQ+Li4vFb67OHL16+PBhSWLjxLBXTNiSowULFqirq1+4cKHOtfHFyM/P37Fjx++//25ubk4QhKenZ6tWrXr16qVKK5L269fPysrq5cuX1MIvX77s3r2bmWtKraKiwtvbOy8vj1aOzSQBABojNTV1y5YtZ8+eJUv09PQmTpz466+/0iZ7AE1ubm5oaOhXq1lYWAQGBpKHPB4vMDAwJSXl7du3opK0tDQxzS9cuEA9zMrKSkhI+OpFjY2NFy5c+NVq7GP70a/qq66uTkpKGj9+fCN/U7q6uvPmzRMNk71z544KDJC9evVqs2bNaLepoaGRnp4uptXixYvJykZGRs+ePRNTOTo6mvmTVFNTy83NlfXdAABwjNTDBpKSkuqbaTR+/Pjk5GQV+AslP7du3frqX3xzc/M6x7ZR95Lo168f9ec8ePBg8tTEiROrq6upDX18fL560RYtWiQmJsr9/mUBwwbkjs/nOzg4hIeHm5mZNaafL1++HDp0yNfX19fXt2/fvmPHjg0JCcnMzHzz5o2sQlWwIUOGxMTE0ApFa76KaVVaWkq+NjU17dixo5jKkZGRzMJVq1ZRpy0DAIDknjx54uTkxFzdSeTChQsODg7fffeddFvPNAWfP38WX8HS0vLq1at1jm2jLrj533//xcXFiV6Xl5cXFBSQp3x8fPh8PrUh9U9nnUSLG/Tu3Vt8NWXBdvbcJBQWFv7yyy9y2slJW1t7/Pjx1AU1OKSyspK5A6SFhcXTp0/ra3L+/Hmy5ldXG2DO5Rw/fnxRUZGs7wMAZO/z589YD0uuunTpQr43Hjt2TMJWEn6tPGbMGNrDPxBhzlem6tu37/Pnz+trm5qaqqurS1Zu06ZNSkpKWVnZvn37yEJbW9uCggJqq+rqaisrKzEXNTY2vnPnjvxvXWbkPuY1Li5OtAFdixYtRo8eLcOek5OTP378OGrUKLIkNja2ZcuWvXr1kryTsLAwMR9HBg4cSBAEbSFfkadPn7Zu3Zr8N/Trr7+KGXxdXFwsv8+gpaWlFy5cuH79+uTJk728vLg1LlZdXd3Pz4/87Cjy5s0bV1fX58+f19nE2tpaws7//vtv2sYE1tbWx48fp/7PBwDldO3atQULFnz8+HH9+vWrVq1iOxzV1L179ydPnohe9+vXT8JW4ucJkSIiIpKTkznzJE8JGBkZLVmyxM/PT8xU7+7du3fu3JlcNisrK8vFxcXY2Ji6U/qyZctogzqEQiFthgmVh5sOw5YAACAASURBVIfHli1buLVlj7yS18rKysDAwJCQkE+fPlVVVREEIRAIWrZsaWdnN2zYMIIgMjIymNOYRo0aZWtrSxDEjRs37t69K/4SxcXFlZWV1N3MPn36JBAIxKcmU6ZMiYqKIvdhy8vLq62tra+yvr6+UCgsKioSH4kyKCgoOHjw4MmTJ93d3X/66Sdzc3Pxe4Irj65du7Zr1+7Vq1fUwoyMDC8vrz179kjd7bNnz1auXEn75a5evVpPT0/qPgFAMe7evTt69GjRk4V3796xHY7Kog7cEr/8Z314PN7u3bvd3d3z8vI2btxInb8l6h/Jq4T09fUvXrwoyUeIBQsWUNd8/fjxo+gRoYienp7ke3kKBIKLFy8OGTKEOf9E2cnjcW5KSgp1GDgo3sGDB+Xxm5WTvXv3MmentmzZ8vbt28zKqampZJ36hg2Ul5f379+f1qGbm5uc7wMAZIO6JJCXlxfb4aimW7duUZ/wST5h6/vvvxc1MTY2Dg4OJstfvXpFy4A3bdokn9i5rc5tjXft2iVh82fPnllYWNT313/WrFnMJqJniEySrK2unOQyYSs4OPir45FBrpYvX852CA2wbNmyIUOG0AoLCgrGjx9/+/ZtKTqMi4ujTec0MzMLCAiQNkAAUJzc3Nw7d+6wHYXqS0tLq6yslKLh/v37w8LCwsLC7t69u3TpUrJcV1dXTlM7VMycOXOYhdRd08vLy6/9D7Nmx44dY2Nj6+yZx+OtX7+eWa6mpubq6korNDY25u5zcbkkrxIOiAH5EY2+4JBTp04xJ1fl5OSMHTtWzGDiwsLC7OxsWuHnz59nzJhBK/T29u7WrZtMQgUAubp27Vpubi7bUUC9WrVqNWHChAkTJlhaWpKFnz59mjRpEndXv1Gk7t27d+/enVZITudIS0tbsGDBkP/56aefmD106tTJ3d2dWT5t2rQOHTowy9XU1JiTjpycnAwNDclDX1/fnj179uzZc+rUqWVlZQ26I8WTS/L6448/yqNbxdDQ0KhzrLRAINDQ0BCtPSEQCAQC5d3fQU1NbcOGDWxH0TBGRkbUT/Ck/Px86iRKmnfv3lFHqRMEUVNTM2vWLOqKIQRB8Hg86sQ+AFBmY8aMad26NdtRQAMUFRWNHz8+Pj6eVt6g+dNNh46ODvPLxkmTJsXGxgYGBg4bNoy6U8+xY8eYPfB4vDr/yov50z9q1CjaTJgnT558+vSpuro6MzOze/fuQUFBycnJycnJp06d2rlzZ4PuSPHkkoFNnjw5MTHx8OHDhYWFZKGJiYmdnZ3owXhOTs7Jkycl7M3BwSE5OVmSmtbW1tS91AiCSE5OdnBwIA8jIyPt7e1bt25dXFz822+/keVmZmaiDzE6OjqzZs0iCOL3338vLi6mdjVy5Ehra+v79+/fvHlz5MiRQqHw0qVLEt4CQRBBQUGK+Uhqamr6888/T5w4UQHXkq1169aFhoaSc+lIW7duXbRoETnRivn+SOXp6RkeHk4rdHd359YiDABNWbNmzWhLVIICXLlyRbo/HFFRURMmTKhzVKXkM4eammXLlp04cYKaI507d+7cuXPMmvXNINLT02vevDn1m0kHBwcxy8lbWVnNmDGDmgqnpKQYGhp269aNua+v8j95leM6r48fPw6nePPmjfyupeQKCwvlnTyZmJisXr06PDz8/fv3bN+u9AIDA+vctcXb2zs/P19UZ/bs2dRTsbGxZPOwsDAdHR1a2wEDBuTk5LB0QwAgjbZt25L/hRszYevNmzdXr15dtWrVuHHjNm7c+PbtWxkGyXW0ne7nzJkjRSfh4eHMd13Sly9fZB62yti2bdtX/7Kbm5u/ePGivh5oHzamTJki/oopKSliflkkExMT5d9nC5sUyF1cXFynTp2++s9Far179z59+nRmZibbNyobsbGxda5mZW1tvXfv3kOHDlHH6BCU5PXChQvMVdL69OmTl5fH7h0BQEPJJHnds2dPmzZtqG8I5ubm+/btk22o3EVLXps1a/bPP/80tBNnZ2cxf56QvIq3efNmMT89CwuLOneIJTU0eRUKhWFhYeJXxTIxMalznR9lg+RVviorK5lrNklNg6J9+/Y+Pj4vX74sKSlh+y5ljDndSgzRSh/FxcXU8SEiampqMTExbN8NADRYI5PX/Pz8/v371zkzQSAQDBw4kPqNTZNFS14JguDz+b169dq+ffu4ceOM/3+9e/fOzs5mdpKcnGxiYlLf+zOSV/Gqq6vv378/ceJE2kwbQ0PDvXv3fnXxMlryevXqVUkuGhUV1adPHzU1+pQnPp8/YsQI5X/mKsITCoX1JwbQWOvXr9+6davUzY2MjPT19W1tbUeNGqWnpzd9+nQZxqa0Tp8+7eHhIeG/TAsLizFjxty5cycpKYl2as2aNco/6hwAmCwsLN6+fSt63aNHjwcPHki+60ptba29vT11Qeg6nT9//rvvvmtUlBx35MiRuXPnSl5/7ty5hw4dYpY/fvx44sSJz549Y556+/atubm59CE2GUKhMDQ0lDxcvHjxV5vk5+f36dMnMzNTdNi+fftbt25JvtNEVFRUdHR0dHS06NDW1nbt2rUyfNYmdywnzyrt5MmTjVn0bunSpRkZGWzfBDs6d+7cyH/YPXv2LCoqYvs+AEAa1CevBEHU1tZK3vb8+fOSvEVoaWndvHlTfreg/F69etWgIW3+/v71dVVZWblo0SLmjAVsUiA/e/fupf6od+zYwXZECiWXpbKAIIj79+//8MMPFRUVDW3YvHlzHx+fpKSkXbt2cWuvYRmKioqqc7E6ya1YsUL8RsEAoJLIZ1Ei2traU6dOnTp1Km1kUVlZmbe3d15enmKjUyKWlpaxsbHUzczqo6+vv27dOh8fn/oqqKurh4SE3LlzZ+TIkdTyP/74QwaBAsOjR4+2bNlCHpqamv7www8sxqN4GDYgL5WVlV5eXgcOHKjzLJ/PFwgEY8aM6dixI1loY2MzevRoPp9Pm5PUNB08eFDqBYNnzpz566+/1rleLwAoP+qwAT6fX1VVJfmwgeLiYgMDg5qaGoIgvv3224sXL4reUYuLi52cnGh7d925c6dPnz4yjZ1jqqurCwoKjh8//uXLF+q31ZcvXxatot2vXz9HR8eWLVtK0ltZWZmRkVFpaano0MDA4NOnT/IIu8mqra199OiRi4vLx48fycJt27b5+fmxGJXiIXmVr2nTplFXtBUIBJaWljY2NuvWrePS4BI25OfnDxw4MD09vaENzczM4uPjObfHGACQqMmrl5fX7t27G9T8xo0bW7du7dmzp6+vL3VtoC9fvjg6OqakpJAlSF5lTldXl1wlHcmrbOXm5v7888+0uRw8Hu/+/ft2dnZsRcUK5d0mSjX4+/snJCRkZWWZmJhMnz59xIgR4hcWAZKhoeGGDRvmzZtHfoiXhJmZWWxsLDJXgKZs4MCB5EwUKl1d3Q4dOpDJq62tLfW7L5BQSkrKnj17iouLg4ODaaviv3//vrq6mq3AVN7WrVtpQ10Jghg/fnxTy1wJJK/y1rFjx9u3b+fm5rZo0cLKyortcDjGw8Pj7NmzYWFhkjdZs2ZNt27d5BcSAHBXcXExdafDAQMG1LkrCohx8eLFqVOnirZCzMjIiIiIIPfyzcrKcnV1LS8vZzXApsXS0jIwMJDtKFiA5FXu2rZtS5s5C5I7efLkxYsXPTw8amtrv1rZxcVl6dKlCogKABRGhlvFRkdH37t3T/Ta0tIyJCREVj03EeXl5Rs3biQ38b5//36XLl3mzZtnaGiYl5d36NChoqIian1JlnwCyXl7e3/69OnUqVOix9tLly7dsmVLndv6qDyMeQUOWLly5VcHvXXp0iUmJgafEwC4rri4uGPHjh8+fBAdvn792sLCovHdFhQUDB06lFz/9ejRo7NmzWp8t03K58+fDQwMJKysp6f3/v375s2byzWkJuj58+eXL1/W0dFp0IY+KgZPXoEDAgICnj9/HhERUV8FGxub6OhoZK4AKiAmJobMXGUlJydnzJgxZOZqYWGBzFUKfD7f1NRUkt9Oy5Ytz507h8xVHjp27Iix2ljnFThAT0/vjz/+GDVqVH0VtmzZIpNnMwCgbGSyVmhISMjdu3fJww0bNjS+zyZIR0cnMjJy2LBh4qvp6+ufPXt26NChiokKmiAkr8AN+vr6f//9t5OTE7kjM5/P19TU9PT0PHXqlJubG7vhAYCcbNmyZebMmeXl5eXl5UKhsKqqqvx/JJzY/urVqyNHjpCHbm5ueOwqNQcHh+jo6KCgIC0tLeZZPp8/cuTIzMzMrya4AI2BMa/AMfHx8aLFX3v37t27d2+2wwEAGTt37tykSZPqPDV9+vSUlBTy238XF5dz586J30svIyPDxcWF3HarWbNmt2/f/uabb2QbcxOUmJh46dKl48ePUwt37NgxceJEtkKCpgPJKwAAKJFr166NGDFCwr21x4wZ88cff+jr69d5tra21tra+uXLl2TJjh07vL29ZRMoALAEwwYAAECJDB482MTERMLKERERT548qe/s2rVrqZnr0KFD58+f39j4AIBtSF4BAEC5SL4+KI/H4/F4dZ5KTU0NDQ0lDwcMGBAZGSn5Sk8AoLSwVBYAACgXHx8fPT297OzsP//8U1Ty4cOH4uJiAwMDAwODV69eiQqtra3nzp3br18/Zg9JSUmjR48ml9PX0dE5d+5cnXOMAIBzMOYVAACU3b1797Kzs9u3b9++ffu4uDhR4dixY+usnJub26NHD+pypCdPnvT09FREoAAgf0heAQBAdQiFwhkzZtBWh/3vv//69u3LVkgAIFsY8woAAKrj5s2bzH0Nbt26VVVVJXpdU1ODpzYAnIYnrwAAoDrMzc2zsrKY5XZ2dt9++y1BEC9evDAzMzMzM1u/fr34NWIBQDlhwhYAAKi+lJSUlJQUasn79+9PnDjBVjwAIDUMGwAAANWxdetWCWuGhYU9evRIrsEAgDzgySsoqffv3x89epQgiP79+w8dOpTtcACAG2bMmFFbW7tw4cLKykox1Xg83rx582xsbBQWGADICsa8gjJ6//798OHD09PTCYLQ0NC4evVq//792Q4KADgjOzs7PDxcKBTu2bOHeXb+/PmmpqbTpk1TfGAA0HhIXkEZ+fv7b9q0iTw8fPjwnDlzWIwHAAAAlATGvAIAAAAAZyB5BQAAAADOQPIKyk5DQ6Nr165sRwEAAABKAckrKDuBQNC6dWu2owAAAAClgOQVlJ26unrbtm3ZjgIAAACUApJXAAAAAOAMbFIAKquwsDAsLCwjI2PhwoXm5uZshwMAAAAygCevoJry8vLGjx8/Z86crVu3Ojg47N+/n+2IAAAAQAaQvIJqWrJkyb///it6nZub6+/vX1ZWxm5IAAAA0HhIXkE15eXlUQ8LCgpCQkLYCgYAAABkBckrNBXl5eVshwAAAACNheQVVNP48eNpJVhvCwAAQAUgeQXVNHPmTEtLS2pJ586d2QoGAAAAZAXJKyg7oVBYVVXV0FZ6enorVqyglsTGxsouKAAAAGAHkldQdkVFRSdOnJCiobOzs7q6uszjAQAAABYheQWV1aVLFySvAAAAKgbJKyg7HR2dCRMmSNHw6dOn1dXVMo8HAAAAWITkFZRR3759yddVVVVv3ryRopOEhITKykrZBQUAAADsQ/IKyqi0tJR8XVFRsXnz5pKSkoZ24ujoiGEDAAAAKkbAdgAAdXj48CH18Pz582/fvl21apWhoWFeXt7x48cJgtDU1Fy8eLG9vb2hoWGdnYjGvEqxUgEAAAAoLSSvoIy6du1KK7l79667uzutMDw83MrKKjg4eMyYMYoKDQAAANiEYQOgjEaMGCEQSPTJ6uXLlwEBAXWOba2qqhIKhbIODQAAANiE5BWUkb6+/vLlyyWsnJSUVGfyeuTIkbKyMpnGBQAAACzDsAFQUv7+/u3btw8LCyMI4vHjx9nZ2fXVbNOmDZ/PV2BoAAAAwBokr6CkdHV1Fy1atGjRIoIg3r179+nTp4cPH16+fJlWzcrKas6cOVpaWmzECAAAAIqG5BU4wNzc3NzcvHv37p6enmzHAgAAAGzCmFcAAAAA4AwkrwAAAADAGUheQWWJ9jIAAAAAVYLkFVRWfn4+2yEAAACAjCF5BQAAAADOQPIKKsvCwoJ6OGHCBLYiAQAAAFnhYf9MUFUFBQW+vr7V1dUEQcyaNWvgwIFqavi0BgAAwG1IXgEAAACAM/AgCgAAAAA4A8krAAAAAHAGklcAAAAA4AwkrwAAAADAGUheAQAAAIAzkLwCAAAAAGcgeQUAAAAAzkDyCgAAAACcgeQVAAAAADgDySsAAAAAcAaSVwAAAADgDCSvAAAAAMAZSF4BAAAAgDOQvAIAAAAAZyB5BQAAAADOQPIKAAAAAJyB5BUAAAAAOAPJKwAAAABwBpJXAAAAAOAMJK8AAAAAwBlIXgEAAACAM5C8AgAAAABnIHkFAAAAAM5A8goAAAAAnIHkFQAAAAA4A8krAAAAAHAGklcAAAAA4AwkrwAAAADAGUheAQAAAIAzkLwCAAAAAGcgeQUAAAAAzkDyCgAAAACcgeQVAAAAADgDySsAAAAAcAaSVwAAAADgDCSvAAAAAMAZSF4BAAAAgDOQvAIAAAAAZyB5BQAAAADOELAdAAA0IZWVlbt27SotLW1QKwMDgzlz5ujq6goE9LesqqqqgwcP5uTkuLi4ODo6yi5SAABQUjyhUMh2DADQVMyYMePEiRPStfX29t66dSstfz19+rS7uztBEHp6en///beTk5MMopS/Z8+elZeXN2vWrFOnTnK9UGZmZps2bTQ1NeV6FQAARcKwAQBQnIY+c6XauXNncnIytaSkpOT//u//RK+Lioq2bdvWqOAU4suXL3PnzrW3t7ezs3NwcPDz85PThSorK5ctW9arV69hw4alp6d/tf758+ed/2fjxo1RUVFRUVGPHz+WU3gAAFLDk1cAUJzPnz//9NNP+/btq/Osrq6u6DEqQRA3b9588uQJrYKfnx81Q33+/Dn1yaW2tva9e/c6d+4s66hl48yZM1FRUdeuXXv16hVZOHLkyOjoaHlcLj4+fvjw4aLXU6ZM+euvv+qr+erVK3d39zt37jBPGRgYTJs2rb7fFwAAK5C8AoBCCYXC48ePz5o1i1Y+ePDgqKgobW1t0WFFRcWePXvWrVtXU1ND1tHR0fny5Qt5WFtb6+bmFh4eThCEmprayJEj//nnHz6fL/d7aKCPHz8OHTo0PT2d+X4rp+Q1MTFx8ODB5eXlokMjI6Pc3Nw6a75//37QoEEZGRn1daWtrR0fH9+3b1+ZBwkAIB0MGwAAheLxeBMnTrS3t6eVb9iwgcxcCYLQ1NT08fFZvXo1tU5FRUV+fj55qKamFhoaeuTIkSNHjpw5cyYyMlIJM1eCIHJzc9PS0hT2pKCoqCggIIDMXMWorq7eu3evmMyVIIjS0tLZs2cXFxfLLkAAgEZB8goAiqarq2thYUEr7Nq1K7Pm8uXLv/nmG/Kwqqrq9OnT1ApmZmazZ8+ePXu2m5ubPEKVCR0dnd69e9d5Kjc3V+Z54e+//y7h09ykpKSdO3eSh3Z2dkeOHLl8+bKzszO1WlpaWlJSkmyDBACQGpJXAGCftbW1lpYWs9zMzCwmJqZLly6KD0mG2rVrFx8fn5aWduDAAdqppKSkt2/fyvBaeXl5ISEhElaeMGEC+Xrw4MHXrl2bPXu2k5NTVFTU2rVryVNGRkZmZmYyDBIAoDGQvAIA+/r27aunpyd6/fnz58uXLxcWFooOW7VqFR8fb2dnRxAEn8/v06cPa1E2go6Ojq2t7YIFC+bNmye/q+Tn548YMeLZs2eSVJ41a9aHDx/Iw40bN+rr64teCwSCTZs2ieZ7aWlpzZgxQ95LegEASA6bFACAErl+/fqECRMKCgp0dXXPnTvn4uJCEESrVq2io6OnT5/eoUOHXr16kZUfPXr0888/EwTRp0+fYcOG2draiu/83bt3BQUFtMLQ0FByeKi6uvrq1attbGxkeUsUPB5v+fLlhw4dklP/I0aMoK0mJmJkZEQruX///vnz58lDQ0PDb7/9llqBz+cfOXIkPj7ewcGhR48e8ogWAEA6SF4BgH1Xrlw5e/bsf//9d/z4cVF++eXLl23btomSV4IgzMzM4uLiqE1qamq8vb1FgzuPHTumpaV16NAhT0/POvu/fv365cuXjxw5kpWVJT6SU6dOcXRy/d69e+/fv1/nqenTp9NK/v33X+q6DVOmTNHQ0Hjw4AH159OqVSvmohAAAKxD8goA7Pvw4cPkyZMb1ITH45FfcxMEUVZWNm/ePHt7e+Y6r7/88svy5csrKiok6ba0tJS6oAFXBAcHr1mzpra2VsL6ovXFSKdOnYqLi8vOzqZmtM2bN//rr7/GjBkjy0ABABoNY14BQNFevnwZERHRyE7U1NRGjx5NLSkrK4uPj6dVS01NXbx4sYSZK0EQ5ubmch3fGRwcTD10dnZu/CiFxMTEFStWVFVVSVi/urqaVrmwsPDZs2fUzJUgiJKSku+++05OeygAAEgNySsAKJpQKKRuPSC1QYMG6erqUksSExOph7W1tZs3b6Ztc9CjRw/mcrCi8oMHD8bFxVlbWzc+tvpUV1dTD/l8vppao96Hi4uLPT09JX/mShBEamrqzZs3JalZXV09ceLE06dPY51XAFAeSF4BgKssLS3FD8osLy8/d+4ceejo6Hjt2rWUlJTIyEhazaCgoJSUlAULFshvtladcnJyaM87G+rkyZPUXQZ69OhhaGhIq0P9IYihp6e3dOnSuLg4f3//1q1biwrLy8vd3d39/PwaEyQAgAwheQUADqOuVEoQRPfu3eurKRAItmzZ4uDgQBCEs7MzdYitlZXVtGnT5BekGMnJye/evZO6+ePHjzds2EAtycnJKS0tpVVLTU3dtGmT+K5atGiRkpISHBw8fPjwgICAZcuWUc8ePXpUtuvRAgBIDckrACiF06dPr169Wl1dnSxp1qxZQztxcnKq75S6ujq5Rmx1dfXz58/JUxoaGjo6Og29FuvS09OHDRuWk5NDLfzw4UNZWRmtZk1NTUBAwMaNG0UjKPh8vkBAn63r6+vbrl078nD16tUDBgwgD0tKSoqKimQbPwCAdJC8AoBSGDx4cFBQ0G+//SbKWTU0NHx9fb/a6tKlS2LOamhoDBkyRPS6rKwsKChI9DoiIqK+VaU4JCQkhJa5iiEUCgMCAjIzMwmCsLOzGzhwIPXssGHDVq1aRS3h8/m0+XDM7cEAAFiBpbIAQInMnDmTIIizZ8+6urqSeacYT548EXNWIBDY2NgkJCSIDrdv325gYGBlZbV+/XpqNTc3N6kDZhFzUTDJWVlZkT8WgiDWrVvHnMT2ww8/7N+/Pzs7W+qrAADIA568AoCimZubi7YerdPMmTMjIiJ+/PFHSboSP2GrqqqKmt2WlZUtW7Zs7NixaWlpZKFAIBgxYoQk15IJGe5WNXDgQEdHR8nrW1pakivj0sYKW1hYMOsbGxtraWk1JkIAAHlA8goAisYcY2pra6utrS1FVy1atKAe7tu3j3pYVVV1/fp18T1oamoOGjRIiktLhzqQtJF69OgRHx9fQpGXl7d48eL66i9cuNDExET02tbWtmXLluSpK1euCIVCWv2zZ8++fPlSVtECAMgKklcAULSKiorPnz9TS9LT01+/fi1FVzExMdTDnJwc2kKqX/XVx67p6ekPHjxIT09vcHB1YY4czc3NFd+kqKjowYMHDx8+ZJ4SCATaFIaGhn5+fubm5nX2Q93ztlOnTtS9GBYuXPjgwQNq5dLS0sDAQDKj1dPTGzdunPg4AQAUA8krACjUixcvvLy8qAMuRcaNG8fcH0u8kpISWj8RERGFhYUN6kT8qNmzZ8/26tXL3t6+Z8+ef/31V4N6ZkpNTaVl2wRBeHh4XLx4sb4mRUVFU6dOtbe3d3BwkGTKVG5uroRrb61fv566P0Lfvn1//fVX8jAyMjI5OZk8nDNnjouLiyTdAgDInRAAQFGePn3atm3b+t6O1NXVd+3aJXlvZ8+eZXYSFxdHVrh169ZX3wN5PJ6fn1+d/b948YI6mMHW1jY/P1+Ku87Pzw8NDV20aBH1m3oqNTW1xYsXv3nzhtn2+PHjZDUNDY2bN2+KvxZtfVaq3bt30yr37t2bWkFTU3Pt2rWFhYW7d++mbl1mZGT09OlTKW4cAEAekLwCgOL88ccf4lNJNTW1W7duSdjbwoULmT2sXbuWrLB582bxlxPh8XgeHh6ZmZm0/mkPZTt06PDx48eG3nJZWVnPnj0lCcPf35/ZfMGCBdQ6ly9fFnOtt2/fMhcNoP5sU1NTqfULCwv79etHq0ZbXtfQ0PDQoUMNvWsAAPnBsAEAUBwDAwPm8vhUtbW1Z86cUVg8IkKh8M8//3R2dn716hW1XFNTk/oAsm/fvuSEJ8lVVVVJOO2JNvlMZOXKleTkNgcHhy5duojp4cCBA6JtCOpUW1tLG3igr68fERHh6uqqoaFBFpaXl5Ov3d3dr169OnfuXEniBwBQDCSvAKA4rq6uO3fuHDp0aH0VWrZsKWa+PI2VlZX4wnPnzkkeW0ZGxrp166gl7du3X7Fiha6uLp/PnzFjRnBwsOS9kXR1dcPDw8nNvQiCMDY2dnV17dixI1kiEAhmzpw5ffp0ZvNOnTodO3bM1dXVzc0tIiKidevWYq7l4eFR32wtEeZPzNDQMCIiYs+ePTwej3Zq6tSphw8fFrPjLgAAK3hCxvIoAAByJXoYefLkSUtLS9FWT2lpaTExMfr6+osXLxYzKJamsrKSfFZ65cqV1NTUadOm9evXT/TV+fnz5ydNmlRbW0vW19fX9/HxEW1JUFBQsHXr1oiICGqHzZs3Ly4upl3l9evXVVVV1tbWCqpV1gAAAi1JREFUUt4tQRAEUVJSkpWVRV6lTZs2eXl5BQUFohI+n9+hQ4fG9E/68OEDcx/XsrKygwcPfv/9946OjtSHrFTPnz//+PHjyZMnRYcjR450dnaWbv0yAAC5QvIKAKrp2LFjtC0Mdu7cuWbNGvIwLi7O2dmZWoHH4504cWLq1KmKiRAAAKSA7WEBQDW1aNGCz+dTx4Bu3ry5Q4cOPXv21NTUfPLkyY4dO2hNLC0tkbkCACg5PHkFAJW1Y8cOX19fWqGpqamWlhZzEpW5ufmlS5fEz4gCAADWIXkFAJVVW1u7Y8eOtWvXfrVmmzZtYmJiunXrpoCoAACgMbDaAACoLDU1NR8fn8DAQHK1qTp17NgxLi4OmSsAACfgySsAqL4XL17s3r2bueFWly5dXF1dPT09WYkKAACkgOQVAAAAADgDwwYAAAAAgDOQvAIAAAAAZyB5BQAAAADOQPIKAAAAAJyB5BUAAAAAOAPJKwAAAABwBpJXAAAAAOAMJK8AAAAAwBlIXgEAAACAM5C8AgAAAABnIHkFAAAAAM5A8goAAAAAnIHkFQAAAAA4A8krAAAAAHAGklcAAAAA4AwkrwAAAADAGUheAQAAAIAzkLwCAAAAAGcgeQUAAAAAzkDyCgAAAACcgeQVAAAAADgDySsAAAAAcAaSVwAAAADgDCSvAAAAAMAZSF4BAAAAgDOQvAIAAAAAZyB5BQAAAADOQPIKAAAAAJyB5BUAAAAAOOP/Ae7Hhg0tJqs4AAAAAElFTkSuQmCC	\text{No specific numerical answer provided for part (a).}; S'_3 = 0.4 \, \text{cm} \text{ behind } L_3; D' = 0.8 \, \text{cm}; \text{Lens } L_2 \text{ serves as the field lens, converging the rays before they enter the eye lens } L_3.; m = 3.4; \frac{f_1}{f_3} = 5; \text{The telescope is not a good match to the eye.}
+818	 A two-slit Young's interference experiment is arranged as illustrated (Fig. 2.2); $\lambda = 5000 \, \text{Å}$. When a thin film of a transparent material is put behind one of the slits, the zero order fringe moves to the position previously   occupied by the 4th order bright fringe. The index of refraction of the film  is $n = 1.2$. Calculate the thickness of the film.	[]	/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGQAZADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD3+iiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigD//2Q==	t = 10 \, \mu m
+819	Consider the interference pattern from the three slits illustrated  (Fig. 2.3). Assume the openings of the individual slits are the same $(\leq \frac{\lambda}{2})$.   (a) At what value of $\theta$ is the first principal maximum? (i.e., the wavelets from all three slits are in phase).   (b) The result for (a) can be called $\theta_1$. The flux in the direction of  zeroth order maximum ($\theta = 0$) is $F_0$. What is the flux (in units of $F_0$) in  the direction $\frac{\theta_1}{2}$? (Assume $\lambda \ll d$.)	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	\theta_1 \approx \frac{2\lambda}{d}; \frac{1}{9}
+820	Two telescopes have the same objective lens with focal length $f_o$. One telescope has a converging lens for an eyepiece with focal length $f_e$. The other has a diverging lens for an eyepiece with focal length $-f_d$. The magnification for these two telescopes is the same for objects at infinity. What is the ratio of the lengths of these two telescopes in terms of the magnification $M$? Give a good reason why one might choose to use the longer telescope for a given $M$.	[]	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	\frac{L_K}{L_G} = \frac{M + 1}{M - 1}
+821	White light is incident normally on a thin film which has $n = 1.5$ and a thickness of $5000 \, \text{Å}$. For what wavelengths in the visible spectrum $(4000 - 7000 \, \text{Å})$ will the intensity of the reflected light be a maximum?	[]	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	\lambda = 6000 \, \text{Å}, \, 4285 \, \text{Å}