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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"from matplotlib import pyplot as plt\n",
"import numpy as np\n",
"\n",
"np.set_printoptions(precision=2)"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"def make_spectrum(n, alpha, beta):\n",
" g0 = np.zeros(n)\n",
" g0[0] = 1\n",
" g1 = np.zeros(n)\n",
" g1[:2] = [-1, 1]\n",
" g2 = np.zeros(n)\n",
" g2[:3] = [-1, 2, -1]\n",
" fft_gg0 = np.abs(np.fft.fft(g0)) ** 2\n",
" fft_gg1 = np.abs(np.fft.fft(g1)) ** 2\n",
" fft_gg2 = np.abs(np.fft.fft(g2)) ** 2\n",
" return fft_gg0 + alpha * fft_gg1 + beta * fft_gg2"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"def mul_qh_real_symm(x):\n",
" n = x.shape[-1]\n",
" # Partition into [0], [1 .. m], [n / 2], [n - m .. n - 1].\n",
" m = int(np.floor((n - 1) / 2))\n",
" y = np.copy(x).astype(np.complex)\n",
" y[..., 1:m + 1] = 1 / np.sqrt(2) * (1 + 1j) * x[..., 1:m + 1]\n",
" y[..., -m:] = 1 / np.sqrt(2) * (1 - 1j) * x[..., -m:]\n",
" return y"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"def sample_path(rand, shape, n, alpha, beta):\n",
" diag_prec = make_spectrum(n, alpha, beta)\n",
" size = tuple(shape) + (n,)\n",
" eps = rand.normal(size=size)\n",
" x = np.sqrt(n) * np.fft.ifft(\n",
" mul_qh_real_symm(1 / np.sqrt(diag_prec) * eps),\n",
" axis=-1)\n",
" return np.real(x)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 576x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Example: 1D paths\n",
"x = sample_path(np.random.RandomState(0), (5,), 100, 0, 1e3)\n",
"plt.figure(figsize=(8, 6))\n",
"plt.plot(x.T, marker='o')\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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kCSkRcsbYpQCeBmAB8FfO+aKI9RcAeApAOYBrOOfvhKyTAWwP/Pgt5/yKVFwT0Q8wGttIZTS9g/N4/bAGk9TfTwJCEU+ZmCjG3NMNW/SIFPdQr0I8hG4v2pcrag25uXCDIH5OIp41JC3kjDELgGcBXALgOwCbGWPLOeehnQy+BXAjgP+ncwg35/yMZK+D6IeI2rCSy7D3mDpfvzaZy6a7vUW60eOxwC+6fmyfiLYZQoU9UVEXDVCxF1jDrHZXqwcMStCtrocfdtS6blCFPLcgrusg0ptUWOQ/AvA153wPADDG3gQwA0BQyDnnewPr+r72g8geRO5brpCI9xba+/zureIxpwa/i3jc6LYCC3Js1l5tlZoq4hX1hk0tKJtYLIyPa8uDx33yVDQ0j8Sao7fBD7vwuC5lKBYfeAEVU+woS+L1EOlFKoR8OIBQ39p3ACbGsb+dMbYFgB/AIs55gl0NiH6HaGwjldP0LuWz1NIzPWLEys260bX4d6YItxGa+Bo1e9Hi5N4OnbAREL28fR/K8tXbcK3rBriUodCfbBZws6+TgBEtWfF+Eukx/ewHgZT66wA8xRgbrbcRY+xmxtgWxtiWgwcP9u4VEulHXTXgPRa93JJLsfG+QPjwxA2noxlZpY4iW/BrOrvQE0XLpNdDe1+09yASe0GEDcZUl3pZ/nrMHnYLLhn4JKzwCI/v71JQu6wxzism0pVUCPl+ACNCfj4+sMwUnPP9ga97AHwC4EzBdi9yzidwzicMHTo08aslsoNVCwBFp/tHroPc6n2BaMwp0D0dLUTMtdGhIrS679ufn4LZC8/LOhEHAgl5gnHgLHBnrpgxWnc2udfjDx9jGhHWKMtfj4sGPgeHdACi4SiuVm9ajG0lkicVQr4ZwMmMsRMZY7kArgGw3MyOjLFBjDFb4PshAM5DSGydIISIXLbuI717HYRK+Sw1wdA5Qn+9Fi9Hd1xcZI2H1n1nPYLqNK20rGxiMXLs0bdpLgO1iz8BqpzAQ0XqhLMINOvcIYk9mNrAFxLzzCZpIeec+wHcAeBDADsBVHPOv2KMLWCMXQEAjLEfMsa+A/BvAF5gjH0V2H0cgC2MsX8CWAM1Rk5CTsRG5Mql+HjfUT4rMDRFYGa27wOePBW1b28XxsWz1Y0uwlagn2UeulwUJ3cpQ9RvuKxOOBNQ4XiV3OxZTkrqyDnn7wN4P2LZ/JDvN0N1uUfu9xmA01JxDUQ/4+RpwJa/6S8n+hZBbXlD5yTUHrgBLkVsP8xeeF5PXlnawQQPPaHLRSVoDumQqXNodeO1yhy4XPoPDpqbPZMqAYhu0iHZjSDiZ/dH8S0neg+deHlD5ySsOXobXMowiCx2UWJXNqMn0KHLGza1wOuJ3kaCDxWOV02fpyx/PWYPvRkOh751D5CbPZMhIScykx5oDUqkCJ14ea3rBsP65n4VFw9B9PCiLRe1aM1BZ/zjSt2tqJCehtWi//AAkJs9U6Fe60RmImoNSjHy9KB8lvov0KhErWvWJ9Oau6SSkacOxpfrmnSXA+LyPC8GJHQ+VfwZapU7Y7rZM7HxTn+FLHIiMxHFwilGnlY0jHgk0ONb7E7P1vIyM+z98rDhcpEr3Gx8XI+y/HWYPfxuw1CG9gBB7vbMgIScyEwoRp4R1H4+VOhSt8KDCv8iw4Yx2Y7I4taWj5Q2ILpGjWNk7mbxQSfcFGwQI6R9HypmjIY1N7YEkLs9/SEhJzITipFnBOLObRwXDXwOZfnrdBvG9Bdixcj3usYi2pvBsLfrh+KDXv5HdUSpZCDmzIKyicW46PqxYR30RMQ77IXoXShGTmQmohh53qDevxZCiHB6FzsWnqzlc6uDV5bcrP5up87vFx36hDHykiPAk6fCpTylu1+whjySMEtcAiDIUg9k0EWOXhX1f2cS8OytqylmnqaQRU5kJlPnq33VI/Ee65eWXboinN7FdZZzGQDvVxa6MEZe3wG07xPGwoUxci3F/YN79VsYawg68Inc7VqnOYqZpyck5ERmUj5L7aseieILtgIl+h7h9K5YWdchLV2zGWGMXFaz1iscr4JFWNVWeMQ15HlFwGMn6k8F1MjJEw4WinS3Mx2FoJh5+kFCTmQuor7qFCdPG4QxYIu+JRpGoKVrNlvmwvcnxOLmwf9z2NnRQG6BoIbce8xYxJlFrfE3CFuUTSwODqzhggmzFDNPL0jIicyF+q2nPSJX7cixBQH3LjPOsM5yN7tWLx6OmpXe0DkJq4/eDsACNeGNwc91wkmhGLnTATUJLo7cA9GDhhYzp+lp6QEJOZG56I7OZFRLnkaUTSzG2HOiE6PqdzvQcO7HQFWbKi6iEaiA6mZf8qustM71Y+RqVnqt6wbICBdSP+yodd2Q2MnyiuJOIKSYeWZAQk5kLuWzgNOvQ3h5Dgf++XrW3fAzGT2xCouzxhqBqpGF1rkwRq4MEWamCzPWjcjJAy57LO7dKGaeGZCQE5nN7o8Q1TAjmxOl6qpVy7SqMGMs1FhNTwB0j0CNJeZZ9rs1ipHHnbEuIq8oZlzcCIqZpz8k5ERm0x8awwTF26nWWbfvQ7BMa8mv1CzlNBb0WE1PwtANl0TQvi+jHmSMGFlyBKLObRWOVyEhvAbfMGNdxL3fpKwm36hpDMXL+w4SciKzycaEt1Cr+7ETgaW3hTS/0am/dremtctZP6FLsNysmz0b6s3rqtV6cVHnNmsuIGm3aBMZ63rEfB/jw6itK8XL+w7q7EZkNlPnqzdznztkYYYkvNVVq27i9n1q5jaXVTeo91h39rFRKVEoWmc0IO06ohkNBpmst0KbnFZXrfO7jUBztafZazbFqgVwyaLObUOx5ujtUBRN5E1krEdiUC+eKFpHt9pljbrudC1eTp3feheyyInMJpjwFkoaJ7yFucl/1W1pax253K2xS4hEcFl1vb/3m9Rca4owFSPXI8w615+eBiBzXe3t34nj3YzB7w9/zXFlrDtHJBUXN0KLmYugeHnvQxY5kfnoTTxLR0vtD2MBV3MPn4QDW/6m/mMW4Owb1SEafYijyKZ7czeKtwbRrHNAFWq9/voAwlzt2n7pzsBSVHS+io+P3gGOCGtbv7Nt7Iz1vCI1Jt4LiH6v1Je99yGLnMh8MiHh7ZmJvSDiEXBZFfQqZ+Bfofr1sRPVf71kxerFVa25EipmjI7vQGYS4bQQQzpb6JpX5uh+lOWvh415TO9qmLGeYIlZolCNefpAQk5kPpmQ8HaoPvF9LbmqpQWmukyv+ov6L9bM6SgCZp67NRB7753Md60W2Wrrvl5LjoGrXIRZV3s6D1/R4v4hngUP15kZACDSLI/ZY72HXOkiomrMdX4lVGPeO5Brnch8MjnhTQ9LrjoQxn0k9kjPJTdD6IeNB3erKugf3KtadT0gCFzuLkL2dshY85r6cBOX69W0qz2Az62+pnRxta9aEJW855AOwaUM09lYU0YOOzuGSQP+Gp2xzixxt11NJaFjUJ+9dbXuNhQz73nIIicyn0xLeDPCOQKY8awa56xqU5ukiG7S5bOACf8ntefvoVK22mWNkP3hDxxJW2tmXO2A+prS5XOgE+4ZmbsZxg9jDFbm0S8760MRjySufgFESiGLnMgO0jnhzYyIDBkL3LEp/mNriWxb/hspscyBHillSzhz3Qjt2lYtUAWSSd3Z/5Gkw+cAAAYUA8fCcyX2dv0QhqECCJLcQnqnt69YgQNPPgV/UxNgsQCyHPxqLS3FsLvvgnP69FS9Cl0qZozGmtfq4e8Kb/8m6iNApA4SciI7SOeEt1gtRSfclFxm+eV/BE44p7smPRVwOaWudnuBFZ4Of9TyZKw1VbxegL9ZgbXkbAz76TnA5r/hQN0A+DstqjZywJovY1j5ITiTuP6k0XoGHItOeDTTOz00ya19b17gNVqBV05VRZsxgAce5GQ57Ku/qQnND6j15D0p5mUTi9Hc2IYv1zWFLa/f2IKS0YWUvd6DkJAT2YHzeH0RyxvU+9cSidHDxFV/SY2lGBo71qirVoXYbFMZPTRXu3aOBGjY1AKvJ1rEJQsznbketDibm2EtKYFj8gVof3cpuEfN+PY3NaHpz0sAFCJo3QZ0zd9pRdPGQnQ+9BBKHnwwodeQFDEa24hj5CqhSW7te/PQ/I9CcK1RjCba3Ngbwz0eHHjyqR63yo0G5JCQ9xwUIyeyg6nz1SSxSLzH+j4+KsqeT2CsZFyUzwrE2tvVf1f9pTvj2zlC9QTkFcU+juZqT/B9rF3WqOvxzrFLpm7u7StWoPmB+arbmHP4m5rQ9sabQREPR+SiZmh74020r1gR17WnBJ0Et1AKpf3Q67cOcDikA2FtWb//fGC3iMeJv6kJO8eNx+4pU3vsfeiREAoRExJyIjson6Vmekei+Pp+WpZeUlYv1/wC6J4wpiXRXf5HVejNlLJxOeEkONFN3NshiGcHaF+xArunTEXTPb8TiHb8NM29r8fFLIoY4Z39/nLo9VtnUDB72C1hSW5yV5K37MCDUPMD83vk9YtCJbaCeEsliXggISeyB/cR/eV9HSfX6p9tA7uXWU1kW/cW5bPU7GdTzVZuiVvM7QX6ETyj+HiYFZ5KZLnHxSyKGP0MuOA2HLm8fW/qPjOaqz3VVMwYrftM6PMo1BimByEhJ7IHUTw8HeLkACB3dX+fbhPLtIeNWK52rqhJcCb7uScaHz/w5FMps8JF9JSYBamrVhvtGCQgrm37d+E6hu7s7+bNA9G0MST+b4TFEv5VgL+pKeUPMmUTi2GzRz+4KTKnxjA9CAk5QfQGqxYA/ghh0srj0gUtpm7G1b7lv009hMQbH9fc6bEscWa3o/Daa2ApLBRswWGmHK/H4sZ11cCy2w0TDRs6J+FLz0+gL84cp9j/F4Bqibc1Fgi266b0iccxrn4nxn31ZdhXa2mpcJ+e8EroVScAFCfvSUjIiexB5FoXLe9N0rk8LhLN1W4IN/UQEk983Kw73VpaipKHF6DkwQdRtrEWpU88rooVY7CWlqJ0CsO4a5pRek4brPl+9VqZgaj3hKt91YJwD4wO6iQzsTif0fYadi8fZsoSt5aWCjPSh919F5jdrruuJ7wSong4NYbpOaj8jMge0rkETXRt6dQPPpTyWbFL1wQu45o9NVj0j0Vo87ZhtvX3yPNHJyFqN/XQsjIwBihK1LYazG5HycMLogTLOX16+LIq1Up3jnTDOVLNFm/fm4fmzU5wWWy7pLREy8QDmlH9eIFyKOb1ajC7HcPuvku4Xns9Tff8Tne9vzl1w3waNrXA54n+HTIL4h+SQ5iGLHIie0jnErSp8wEpJ3yZlKMuT1cue0z//Qwl8L7W7KnBtHem4bTFp2Hu+rlo87bhpINnI8evYwlaOCpmjI4qKzMScc0KNyWyOg9HzpFulPywHdYhTv3pHgFS5mqP8fDY0DkJTOj65zhxzzJTIm4pLDT1vjinTxe72CUpZZ6I2mWNUOTo12WzW6mOvAchISeyh3QuQQOiBcRAUNKC8llq3/fcAt3VNQX5mLb5oaB4N3eEW3YTv70cVh2nnxsdqOZ/NZ3QZi0txcmrV5m3lKfOh54r2jnSjZN/6sK4nTsM48ZJu9rrqgF3m3B1Q+ckrDl6GzhEeQgyFBNlZoXXXoOyjbWm3xehi12WUxZWEIVSRHFzIjWQkBPZRbqWoOnFTOWuqAeMhk0tWDxvA569dTUWz9vQ9yU75bOAedEx65qCfFQNKUKzVXwLcXTpW6V2uQBv7XoLvubYpWWx3Ma6lM+CMNGtfR9QV20YN9ZIOH78wb0AxN6FWtcN8MPo3FY0jpohXltaitInHo+7S51z+nSUPLxAN5s9VbFyGpzSN1CMnMgu0jAW3bCpBbW774dLGQKHdCjYbrPWdQNcLUNg/+06cPCoBDBXqxcrX9qBlS/tAKAmEV0wa0yfuyhrCvIxb+hgKDE8Cq7cIxjQFV3OluttxVuPGlhoFgugKLCWlCQ+7INZxANUlt4G58zngIcXdMfnBS1ONVd7XNcSoyWumd7qXptOGSBjKH38saRi+M7p09H0u3t116UiVj7y1MFRvda15UTPQRY5kV2IRlu271PnV/dyrLxhUwvWvFYf6KUtwaUMw6qjv8bHR+8ILvN0+CsTkTMAACAASURBVGN2OQPUTO+PX9nRR1a6KtqaJR5LxAFg0wnvwc98Ycsk2YuTG5eDITjTJPwsdjtKFz2KcTt3xOdOj0Qk4oAaavngXjinT8fJq1el1tVu4vNll1wxt7F5dR4GOE9JIp61pER/hSQlnR+g12vdaDmRGsgiJ7KLsNGWEZZ5+76kB4CYpWFTC2qXNerGDBXk6OxhDi4DK1/agdpljaiYMTrKOm/Y1IL11Q3BmGTqrHhVcp8eVAiPZP75X4EMIAccHFZfB8bsfhvFB7YE1zMAMlOrww4PBD6Ylo/zT5FQmeTVwjnCeBKcNqM88DkYdvddaH5gvmHMnns8aJp7n3p4PUF97zeBcbLG18WPOACDkmpJ9mL0nuVRy8U18/EhfK0pmJZGvdb7BrLIiexD6ynuHBG9rheasASt8B68eblavVjzWn2Ydd6wqQWrXtkZlljk7ZCx8qUdWPt6fXInDLyXzVaDRjGcA5yjJMeJ+wc/gUu/vRG5XI0FMzDwyKz9AIwD19xnxe23W/HeyUfxwIYHcP4b56N8cTmmvTMNNXtq4r9ekWcmlJDOelr8WKtHF6KXGKZ1cNvyN8RsQnP3l/B6jW67HGO/fjXsYUdDHHWPj6jXqvNglmjMXFRDTr3WexYSciJ7ETZh2dcjLnYtUW3lSzvg70rVbVeMv0vB+uqG4M/rqnfplv4AwJfrmpJzyQfK5IQ3DM6x6OBhbN+7Dx998zU8n1ii3gPFYkPjqCuidj08MPxnn+JDe1c7ODiaO5oTE3at5SwzuMX53IHENBWzrvYwkdNGlJoZFRt4GDJK/HJIB1HcvFX/vG3iTPh4CX2twvyABGLmTNC4RrScSA0k5ET2YpTgluI+5/FY4RJ8YDDu+mUWT4cfa19XLfNYcfakel2XzwLyigytwsqOTvUbnxsul/6tJTKJy2MFXr/Q+CYfKexVn1WZF/MrXzCuhddc7BHEymr3Nzer+717q+GI0iA5ecDU+WjY1AK3S/93z9ClJkKK3o4YvdMTJZUxc1GZGZWf9Swk5ET2YuReTbGLvXZZowkrXJ0vPXXgn3HxwGfgkA4A4LAXWIOuR0eRDZf8cjwKpxTDzThC/xPx5bqmYGa7EUm7+i97DE5F/zqccvhrd0gHdbcLTeLiAF74CcOGU+ITKI/swdOfP21uY60WPtA7vqYgH9OOL8VpI0fg9JEj1K+fL8Bpi08Ls/aNSrUAwOq0AUtuNk6q08grAqb/CQ3uC/DxKzsgd0XPHregExcPfEYdWSr6Vctyj0xrM6ovj7emnsaY9g2U7EZkL1pC25Jf6a/XMtmnzk8q+a1hU0tMkbRaOS5y/All9k+Cy8ocG4GZz0Wde+m2/fiPz78BnN3LxnotuNydk5SLMula3vJZYHV/AORoCzQyrFzheBWrjt4JJeQWwxR/WBLXEacFG05J7PU0dzTj9FdOh8IVlBSUYM5Zc1A5Sj9FrsZRgKdPHo/mrrawi9UePbSvzR3NmLt+Lh7d9Cjum3gfKgOJXnqJYXJHB9r32oMtYA259xsAQO28DQLdZ8iTXMG549Z8Gf5O/VtzokloRmjHMmqVa7Z9bcWM0fj4lR1Rr1MbY9rXpZPZCgk5kd2Uz9LPYNdIMpNdc6kb4SiyoeKsgyjb+RkQeoMTJFU9tOKrqGX1NhlT3VbkJyjk1lwpJb2u22X9rO42SUJNQX63ex0Aj3DEh3oVmN2OU+9fgO3Tp6NmTw2e/vxptHS0wGlzwtXlgp/HdsUqXD2+JsBz189Foa0QnHO0d7VDYlJwG/Wk5t679q52VH1WBQBBMf/+9wshh8Souc+C5s3qk5ahmIckXBo97IXWlg8rPybssx4zcz5BQvvV7xw3XncbMzHzsonFYVUTGtoYUxLynoFc60T2EyuDOQk3+7rqXUKXujVXwiW/HI/ZC89D2b77TXV2A4Ajnb6oZQCwKs9v6GI34qLrx6bkJlpcIDgGY6gaUoSagnwAarMbjojYtJSjJrsxBueVM4PCUTmqEh9d/RHqZtdh/TXr8cj5j6CkoAQMDIW2QliZeXujzduG9q52AAgX8TjxyB7M+3QeavbUwDl9Olh+ftQ2XJZwoG6A+CCBuDiAmImGDulQ8HutL7wQWUbT7+5F80MPGb+IBBHFzIWx9AhojGnvQ0JOZD9aBrNeOZpGApnssRLMwsTT5BjT+5duFx6v3ibj8xwTMdkeZM5Zc2C36CeBeSQJTw9Sa51F3cu8tiKAc7jWrhOeQyTsvY3ClWBincga9XcaxH5Pvw4N7guClQwiJPiC3f40nCM9gRGsAjhH2xtv9mrM3N/UZCrxjdq09j4k5ET/wKi2XCPOTHajLHBHkS3cAhZl0Icsv3/pdry68VvDc64u8EFOICAWWXOeKJWjKlF1bpVwfUugzjzUwgxFS3YzctM2P/QQdo4bj51jx2Hn2HEYffV8vG37dZ+IuZZYJ7RGmToiVY+GjU0mKhk4pg78czA+Hrp8WPkxMIuxV+H73y80XJ8IYXXmEZhJfBO1Y6U2rT1HSoScMXYpY2wXY+xrxthcnfUXMMY+Z4z5GWNXR6ybzRjbHfg3OxXXQxBCUpjJbnSDjopHnzxNf8PAcjMirvG/uV2QLPHFyv1dSnLlZyFUjqqEM9epu25gIHu9wvEqrAiPp4d2LBMJY/NDD6HtjTfDapt5Zyeafncv5rWfL/QGxEWgcY0U+MoCX0U0dzRj2NhmfVHlDM2bnbpiXts6M2Ylg0M6qCPiKkEXOxNfm9zW1iNWuVZnrifmsZrFUJvW3idpIWeMWQA8C+AyAOMBXMsYi8yW+BbAjQBej9i3CMCDACYC+BGABxljxoN8CSIZNDe7iDh6sotKauwFOrOXd3+kf5DdH2Hptv14zaSIA8COXBlTfzEO9oJu09xWYMElvxyPS36pn6gEqA8eqerTzgSJY9risvz1mNj1V1i7XEHhZFqOgNUqnGjWVv22/gk5x3HPLEXVuVVBy1wyavYioKSgBItGXonte/fhn3v3Yfvefajbuw+LDh4WirnEOZzD9gtFVRQrjz0chUe51CNxjnSjdGIbjDrG9YRVriEMKRh4VKhNa++Tiqz1HwH4mnO+BwAYY28CmAEgGBTinO8NrIt8PP0xgJWc89bA+pUALgXwRgquiyD0SUEme8OmFvg80dYWswCTZpXpHFMcI69a/lVcKWwWxlA2sViYvCbq8Q4gOE3NUWTT7dVulnavfjJWW0i7z/Zv7VBOzAmqu5w7APVjroO0rwDjRBnXskEOgNuN879SUHl1+ENRZNZ7ZNa6bnnaplfDurFVdnRi7lB9168Ctf68cmQnmjbq9zsPjZU3dE5CresGiDu7aHChNR6Kc6QbTf9wAor+8eQUdnyLxFpSAn9T9DQza7H4c8MkIIk8QyIBUuFaHw4g9I74XWBZT+9LEIljJpP93VuBqkJdC712WaNuO1SbXccaB4Qx8s68YrS59bPURVw70SDOD9Wtb801/tPWRqQm2oNdmL0OBDPXdx9/JRRLeIKTYrFhd/HUhM4JAE1z74tyJVeOqsRHZf+Oun81Y319HT7dtR3bv/kW/+Q/wPbZ2/HR1R9F15hf9ljUsUv8goeIkIx8a75oGzVW3tA5CWuO3haYbGcs5KI8Al0EIt7TiBLfOGPYfdEU3c5vRiLeN5P7sp+MSXZjjN3MGNvCGNty8KB+1yiCMI2ZTHYuA+DdFnqImIssXmEryqnzgcgyKikHD7v/La7LPm90ER6ZeZrhNmUTi3HR9WNNHe/LdU0Jifmcs+bor2AsmLmuO1M7sPy8RauxdNv+uM8rHFqy5FeAElHe981aYHF0b3cAwZazocw50ga7oq9CHknCvKGDsf+HXsNY+WdtP4cfseP4VnhiutXDthc9QABgeTGGwyRB5IAVa2kp7BPOhtzUFJzjHpkAZ5Sd/vErsTsQEvGTCiHfDyD0bnh8YFlK9+Wcv8g5n8A5nzB06NCELpQgwjCTya4RkQhndLMSWh2RcWXG0NFlvgf1Uz87A6/9qsLUtmUTi8Ni6EYkMlBF1EUN6M5cL+CizPUjOHn7p7jn7X/izAUf4cS5NUFhN5wLHiAq2cooQfGbtdHL6qpVL0vEoJPKjk5UHWoVxsoVxvDrioF46icWyDoGMpcldLBYcXGAMQUXDXzOlFtdY1j5MQjj5LaeLesKHbBy8upV8DdFx8dDfydGjYe4jOQn8RFRpELINwM4mTF2ImMsF8A1AKKH6erzIYBpjLFBgSS3aYFlBNF7mBl5CYTFuY1uVrrZ4asWAEqEC13uwu+s5srdEnGsxtM8Zl31rriPL8pcLw64qM8t/DskOdxzoWauL8ONOz6AT+E40ukDB7C/zY37lmzHJ5N+Cq8l9rx2f1NTt1Uuyj/QQ5tWJsiPqOzoFLvYAYAxbDjVEsx5axk2AWvPXYTVk5/B6snPxDy91cpx8YCnTIo4A6raAecIw+5xqZyKZoZYCXCx8i6SnsRHRJG0kHPO/QDugCrAOwFUc86/YowtYIxdAQCMsR8yxr4D8G8AXmCMfRXYtxXAw1AfBjYDWKAlvhFErxHmZmfBARtRhMS5jW5Wum53gdiUMnMlORz6rVuNiDUNLZFtr/9LLUbOrcFJCx9Bm8cVtd6qKJhzRBWWk/LWY8yu12HxB0QoJHN9qDtafNw+GQu9P8BTZ1wN2UQ71W/m/gdW/fkVIC9GoYtmgVcVmppWZuRi1zg8UBXxHWNvgJw7QPW2aP904XAU2XBR4V/MW+La5y3QHa63p6KJMNX5LcavL5EHR0JMSmLknPP3OedlnPPRnPPfB5bN55wvD3y/mXN+POe8gHM+mHN+Ssi+/805Pynw76VUXA9BxI3mZq9qA658XsdCZ0CXKyz5TVR+prtckOzWxM03yTjS6YsrrpzKTlpLt+3HyfNqsKFRfc62Df0QTIoWfwfnwX7rDIAnNxdcyw1gLJi5vvv4ybrn4QA+GXE2/nDWNfDEsMxtsg/HPfcYDjXEUI2gBc5NTSvTXOySQW356xcy7DrpakCK7T0AAIf1iNqq1/qBqe0B1i3g5bOAnALDqWi9iSgBTunsDCa/nTzCeEyvt0MmqzyFZEyyG0H0GpEWek4BAA64jyA0+Y3J+tnmuhPKdJLdvNyCx/3xDWqJxyo3k70eiujGunTbfty3ZDt8ofNHcvTdue0h5WeMAd+P+jGUCEFWLDbsGSVIQgvwyYiz8fQZV0OJYZlbuIJDG3OE3dUAmJsXHkFlRycWHjwMu46Yn3TwbJzUsQhyjsPUsazwoCJ/cXwXMOH/dJc+1lUDcpdhwltPNIUREZkAp/WhV9ragslvJ1Tfh+OKjPM/UtWgiCAhJwh9Qi30fJ3sa58bHo++yAgz1yNEKZGRpEc6fYb92EOJJ3sdEN9Yn/hwF9y+cBHhPv166oERc8k7Jf3M9VzJhhxL5PuhcoX0KT7NvRP/fdJ/QjJRkBxzeEmCVHZ0omrklWGtYU86eDYu/Po65MkO42lqigwemD9/0cDnUFbyTXwnv/yP3d8H8iuMEt56simMHqEJcJbC6M8C93hw+sbHcOoF4uRFahCTOkjICSIWgvi2QxKXQUZZtzrJbrnMbzrZLZTXNn5r2sUeT/a66Ma6vy3aovUe/DG4En376LRIwTpyAChQ9HMAHHkcT1x9OoYX5mGG9Ck22udgj/06NNquw9M5z+F46RAkZlx2FYq/02JslSdI5bZ38dHVH2H77O1YNGkRzvvmKlhj9NFiih/j61/BhWvvwMzOu9SYuOYmN0NoFUVddTAxzyjhradatZrBKPmtZLT+Ax9AQ1RSCQk5QcRCEN+uGPA6AH2LMcq6TTLZLRQO4K63vjBdi63baU4HkeBLOoan/+iZ4Ep0nNQXUkcOACfuWaabuX7inmWYeeZwbPjJITxd8BKKcRAMgCUiX8zM4BAVcc/zpAiIaMOmFhz6ayHy5ALj7bmCcfV/R/GBLbBwqNfUNMT8rPuQ0afBDPsQjB5sjPqf9yRGyW9G7nOjyg8iPkjICSIWgvK0sry1EKXnRlm3gocBT34xhheqx47X0b6/zY273voCZy74yFDQyyYWG7o4g9fS4cdff7s2zJuwdNt+KIIkK2bp1F2u1ZEDwLDvPkdxc22w3zoUGcXNtRjWsEoVqhhZ5NrgEHWkp3E5XUIuducI4Kq/GGzA0LCpJWSKmfi3JMlejN+5GMUHtoRf046Qvhd5+qGG4Lrpf+oW/Q/ujXpvHCUeiN4Ho/7nPYle8huz2zHs7rsM3eeJtgcmoklFr3WCyG60G+uqBaplzaRg9rMNR+FFdD11VOb61PnA0tvC3etSDvIvW4AN5VOCi5Zu24+q5V/F1bb1SKcPd7/1Be566wsML8zDPT8eg5lnDsfSbfvxxIe7sL/NDQtjmJxjxVk+q+EDg7dDxprX6rH5X614bk+Lrltdg/sLdZPeikPqsA8cfxZaSiq6zWxmQUtJBYr49xi34k5TWeTOkW44R7qx883YY0wN54NHolm/5bPUznA6NHSej48X74jdO5xzjN31epiIB6/pUEhf+ssei/4cAMCEm8Lj4nXVUQ1rAODYvjyIHiaEo1Z7GGegb/6BJ58K9mXXGsQUnH4fOtzR9iK51VMLWeRExlOzpwbT3pmG8sXlmPbONNTsqUn9SUKT30Lu6sIpYO726AlqOp3dIpl55nB88eA0PPWzM4KWuhk0G21/mxv3vP1PjH/gA9z11hdBIZY5x+oCHz7P8cdsFOPvUtC6uhkDvjcuIZo16mZYIzLxrZwH68gB4JtRM3T7rX8z4uI4sslZ2JdY7F4+TN/FnlPQXYngHBFu/eqg9U03MwCEM2DowWgR1wjGr8tnATOfC7+Oq/4SLuKAbre69r15kLvEt2zRRLnewDl9umqZh3SZ8zc1wbnnM+h5EGg2eWohi5zIaGr21OCBDQ/AF7BwmjuaMXf9XMxbPw8LJy00bCWaMM7jg7FTD9cvQfIo+cCKm9UftGlrcoQwyl3qch0xmXnmcMw8U50fdMZDH8VlofsUDp/AH766wIcmr4JKdw4kIzcxGC51q2Vj9bZoq7kwLwcTRhZh2X4Wdp9mkhWw5AJQ3e4dTP+G3cFNTivOK1Kt2PJZwJvjTOzA4O+0onmz6iUJJohJOcD0p0zFqrXpZS5lKMw+PXAoeGY6w53Lue4eB558Kmi5onxW7OuIyKlo35sXmLzG0DJsAhpHXQGvrQgW2QtZylUfCmsYULMaTAJOOb8Uk68zX7GQCg48+RS4N9yVfnjQOOi9h3u/PAz9TgJEIpCQExnNon8sCop4KAoUzF0/F4BxX/CEmDpfTULyueGQDgUmXUXC0NA+AWWaUBuMMY1F1RWn4L4l26NKwBJFE+ZL3TnIMRCqHDBU6oh5Xo4FVVecgkc3/iLqvfdxGU8MHY7KY8cALsPedQQeW7SY27uOGF+kc0S32zuAtbRUd6Sm+iQR/jq0eLlzpBsKkyDNfM5wJG3twRfhkgfDzlzwcjs4co2vLwIGCRtOseDO5fqlh/rXLaCuOix80743D02bnNBEvH7MdUEvh2zVmUymqG1Qv1ynnjPZkbVm0YvRiwbnUOlZaiEhJzKaNq9xn+l5n84DkGIxD4mZV3S+hpVH70K01cFQ67oBZe23qj+GWPFhCJLgQtEs87ve+iLxa45AE+apnhzkcXFNe6RlPrwwDxeNHYqq5V/B/4MDuqXUh+RjuI/fjoctL2JU4zLUj7k+zL0uyV6MalwG/CBix5w8fXd3XTWwagGGnXAITU2qVRqO/rX7Oy04sNeBR0p/ga3vD8E98v7ge6nRsKkFa/7+FfyympDm4QN1jxULV676YKIwwKLnDDHbRlXLVA/JHfjiuynYPfFKVRS5AkjxtWTVRtamYg69EXqzyy0+l9rCNoLQGHnDphbULmuEq9Xbaw8d2QYJOZHVKFxB1WdVAHpAzMtnoQzAyltX627iUoYAeYXqzbmrQ/84XR3q+hiu1plnDg8mrqWKepuMepuMsV6Loatds8ynu3Nh8Vvx/oZmtFl8KJDzwKzR18PlPLzhOQcdkh+3ud5FW/MoNA0POFK5guLmWki5ChYfeAEuZQgYODgk2HAU7HkLPMoq2GwczNcJj5IPh6SgwjESZSP3BdzLZmFo2TwIR8/Iw/4R6lAWAGFiXrusEX5/crO+OTg2nfCeesZk26iuWgD43Gjfm4cvvpuC+hOugX90QViyYDKEirqtwAIGBk+HPyUCOuzuu9D8wHxwjweA2otesUbnKjBLd+mZVhHg71LCrm/nZ02YcfdZCV9Lf4OEnMhYzCa1eWQPnv786Z6Jl0O1LvRdhQwNh09F2bu3irOz3a3dtcIxxPyeH4+J6WIvzMtBR5cfPtn85DMzrnZN5GWXH1NgQVeegn1Ct7y6fLlyPqynjcDJuSeGCVHT8MlowmTVfEV3iN0LZ7As3+tlANT8A5cyDCuP3oWVR++G7ZxWjN6zHMUHtoTFim3e7uWh5MgybtzxAT4ZcTbcPhlPfLgL47ssQQswFXgsHfh66FYA6jCVoUf1t2t+6CGUPPhg2LL2FSvUbO/mZlgcdiieLnBfScCFfn1UomAqCR2Uowloc2NbwrF1LQeg+fcLwdva0DjqCnApWmJsdmvwgaF2WWNQxEP5blcbnr11NU69oPdj/ZkI4waDAdKVCRMm8C1bxBmiRPZTs6cG8z6dB8VMSnGA7bPNtTaNl4ZNLVj50g7ddQ7LIcweql/aFIZzhJoVH4Ol2/Ybutg11/ea+oNoanOjVFCOpkcsyzyUdqbg9Yl367rWOQdc9YsAADe32+DkKS6OCb1nhV5AYHmoqIeKfU5XG75jnRhsGw5rim57PsmLtaPeCgr5eV/JuHM5x/eChwxWWAjnZZfCtXadYdx8wzkL4LX3TWb3Jb8cn5RlvnvKVPibmtSxroKqjtufV0sunxV4s0JhFuDiXyR3TdkAY2wr53yC3jqyyImM45GNj+CtXW/FtY/Eeq7SsmxisVDIXfJgNHROij26sn1fSlzs+9vc+J+t+/HoVadFxYNDM+E1UdfEXhP/97/vwqWe3JhCN5AzcF8hWG50jkJoH/aBPDm3tS6iHueB5V77YOwYdyN2jLsxbLnPNgjH8cJYfWVMwuG1dGD9iUsAANdvfRCOrkFw5R7BrpPq0FJSEbSmvfbBqB9zHQCg+MAWtL3xZsyji5LEjC8p8MJMjIA1onZZY1KiqSW9ieLjoT0WxN6sbrgMcrfHgCxyIqOo2VMTzEaPl56yyAFg8bwNwhuSFR51cEYsMRcle0WgTSMzcrEPL8zDhrlThOuNCE0+YhJ066g5OI5ZvNg08m00Duv+W7QoHA8fPIwzXflYpZyBrkM/RxcSSyBLXxQw5oLCB8Bj6UCuYoeFh9hEnOuLqSIDTBKGAQCEeRCSFeRk0CzmRNAs8nXnPgZ/rk55JgMuuVG1sI28WXpYchmmXD+uX1rnZJETWcPTnz+d0H49aZEDavJOaNJOKH7Y1Qz2WELucwvrykPRrGojy7wpiaS4sonFwRvla9U7cHB1c1TsnIFhoGzHhd/8DIzxoGtZYuq/46VDcLaei/18QPy9Z9MeBs4HggHqFLSo1YIXHMg299oHY8fYG9Bw0r/Bn1MAi88FBgZ/ToHx/qIHBLOYtNiT/VPRkt6CryfqOoA1r9UDUD9rq/++E7LfnEEpd/GwfQkV6uxGZBQtHfozswFjsY4nlp4IsUaGupShaOi8QI2FT7hJfCATdeWAKuYb5k4Rdn8rjaMrnIil2/bjke3f4n/zfGhnim5HuBwlFxO/vTz4szY0ZW3bv2O//wwTwsOhZrhx2NAOOzsKQAn7PkW+8DjhIf8iScGTiZSjWquMQc4dEPxelHRg7XIldz7Fh/E7X8b4nS/D5jnc3fteBy5qrm8SbV653dcu3MbfpQQHqkz5+Tgwvck8Bvt+vHhH9ITBfgwJOZFRDMwVu2kXnr8wbHZ0JD3SujWEsonFBj2kGdZ4fouGcz8GTjhHfBCbA9jy38CTpwJVherXyFavIdzz4zHIy4kuSdrf5jY9HU2ENoe83ibjRac4junoGoTrtz6Ikw6eDUAdmvKV51KYETwbjuL24p/i9uKr8O/FN+Km42bj9uKfdn8/4he4ZOBTcFhboSusmiClMkTItQYz2r8+hrFuoU+QS246HWOnnoTiA1tw3sb5mLL2DvF7xpWkR6I6p0/HpFvOhaSI2/y6Wr1o2NSCsonFuHj2uLj6r3NFtepJzFVIyImMQtTbPIfloHJUJeacNUe4b6Ju+XiomDEa1lz9P6ugFaLTRzuI9xjw3t2B5jFc/briTqGYzzxzOB696jRdy3x/m1o7naiYh7rtr5A+hUM6pLsdA8OAriJM3nMNTjp4Nor9MripWwvHBQP/pr8qr0jtQf4fTSh7fAVmP3M1br/tMC4p/BMc0oHgJDVAzVIvbN2p/pwKUU8yNm3NlXDqBaVBYWLC4vLepeTBB1H6xOOwFBaiZdgEg9cppWQk6nEHNmNsw5vB35MemhiXTSyOe6ypv0vB+uqGZC8zK6AYOZFRtHv13XU+7sMjGx/B/efcL0yGa+7o+TGPWtxOmMXe6kWD/0SU5et0eQMARzHgirAyfG7g44fU77UJbM7jgy1MtWz08xatjoqZa7XTM88cjpo9NXj686fR3NEMiUlQuBL8WlJQgjlnzQnW2m9e/gI+zX0cpewQmvgQ5MONQ47tWHP0NvgR3RYU6Hazn8Y/xL+ggMO4eYkNR3Fy3npVeyUJElfCWrM2bGpBbSCJ0FFkQ0VuDcrsnwCKrF4HU6/Dax9sLjks2Riz6DiKD1a/F/6cAtj97Tj7DDvOuG5ssJd4ZNOTvmB9dQPKJhbDOX06nNOn45Nb/xcib4PN25qSkagHnnwKxS1NgCKHtZUNxd+lBBvUJIKnwx98EOjPUNY6kVFMsOhs2QAAIABJREFUe2eaoSAX2grBOUd7l77gL5q0qMcaw4RimMXOunDRgGeik9+cIwIxcuEA8PDGMhFZ7ifOrQnb0zpwG2xDPwTLaTOtX6MHjkan+xBautpQ7Jcx50gbKjs6g9oVa6AIhzo0xAIvZNh0t9G2PNX+PvZ0TUSHMhjHJI4TLizF9bPGA9AXPwl+lOZsR7NvfODY8RLdk900IRnngw9tx+Ehpxk2ogEAVlgIeL3gbndYNrpV7oAs2XWbpfQkWn24YaY45xi/82UM7/oaZRtrkzrfznHjg96RlmET1HLAHsjEtxdYcdN/XpDy46YbRlnrJORERmGm/CxHytEdpAKoQr/+mhjZ4ykglhXmsBzE7KE3dy/QRHnVAv2e7GDQFfi8IiC3AGj/Di0YgoVd/4blyvmwHbcUOYM2xn/fjLA2rYqCRw61orKjM2wztb2q3rCY2JesnkcBY/6w4SQyOPJK81E8KA/f7TwCRTfpSkGisWtL1zEgJw9y6OhVxQcGFi6qEe+BJHuFs8YTJazMDEidwBl4HTTBM3zI7HLhgs/uBSssxNgkhVwrQ9NItMmNvcCKSbPKDK32ZJvYZAJGQk4xciKjqBxViUKbcb9tkYgD6pCVnk56A0xksctDgAGBxDx7YbdlPXW+Kuqh5ORBqIju1mA8vRgH8VjOX/GzwqeQO6g2MW2I2MkvSXi0SB05GvrMX+F4FT7JeF65YbI5k6ImjFnA4Glyw33MJxBxFYd00Pi8OkiyF2O+fgdjdv49mLVt8xzG+PpXMa4+fFnp/rVhP6daxAGEJZ3ZvK0pOy6TvcIcAc0NLWzAwjnKvn5b/batLemEt2F33wVm7w7DjN6zHFLkKF8TTJpVhrKJxWGNZCLp77FyssiJjCOZpjAAUFJQgo+u/iiFVyTGyPpxFNlQYf0vlOWuBPze7rg3EB0LF1rq0Uw7vhTNOSl023KO7Xv3oZU74GF2lOIw4Dwev8QkjPlmKhxdqtCLJqjFdSpwHH/LWLS/vVf3fXNIB1DheBUfH73DcNQoU/yQ/G7IOQ5D93fUfhYFFpsCX6dVPMksxXx+2u1oKxqXtFWueQ52nXS1bkc1QP3MdbR5dZv8gCuYsvbXwR+Z3Y6Shxd0z1FPgOaHHuruZGex4Ojlt2FLe3y907XmNLGax2S7VU4NYYisonJUJbYd2BZ3m1aN3kh60zBqFONq9WINuw4Y0KbGy7UM9el/0u+7vuJOtO8Gmv7hDA4c0eOPDGDcj8MDgdcvZNhwSnITswBgSf5AfNJ2A1Yo5+ObRWqOwdV7alD1WRU8sgfXb30QA7oSaCsagZsB9y3Zjj+OOAzPkcHw826xtsKDCserKMtfjzVHb4VfT8g5j0u4I3ZGyQ/b8ekpDHOHDsZ5OxT8erk4/15BwKXJWNyZ8il1reu8ZlE82rgdKsPnp92Os7Y/qx7W48GBJ59KWMjbV6xA+7tLuxfIMpwf/gU45w8wGxoJLUkrm1iMddW7woa9hJJsa9lMhlzrREZy/zn3Y9GkRXDmOhPavzfc60C3i11UI+vnate3IFp3t0jKZ6G98CY0bRwEKBLC65zD/1m4+oc99Chwy/sc530VceOLt0SLMSwsKsFy5fywRjOVoypRdW4VJCZh0wnvRbna9RrIxCKPA7ccljHim3dw0YBn1FIzKHBIB4Jtbhs6J8EPQcMbBpy3cX5CIl44ugOfnsJQNaQI5+1Q8MuVXDfMzwG022xouf0+jKvfidLHH4O1tDRw/tgCpU42u06NF4uawISdUHXxW7qO6a62+jrCXnPxgS2JleAxhraicVh77iK1PA0wHOwSiwNPPhUcaarBPR7T/X0kC4sqSbtg1hjh9qmaZpeJkGudyHgSmYTWm+51DfGkJw6HdDBobQIMqIoeRhKZPGQWDuDQQOD1yQx7xnDMOaIe++lBhWi2WkyJD+eAd/djeOLq06OGsVz5hxsx8dvL4egaBA4FDBK8lk7kynmQErQVjPrTLz74IlzyUN39HEU2TG7+K9y1G+M4myriJT88imnHl2JUA8NtNRw5kc8/ga9Hc/LwfPlMvPza/KgjhY4lZU4n4O4A94Y/4Kw99zGh6zuS0ES7lmETsHPsz6Oz3RUfxte/GvbwYjR5zBScw+Jz4bgDW9F+8gXocEtxzywPzVoPRdiDPQJLLsOtf7ooarnw74gBt/9X4j3i0x1KdiOymspRlVh4/kJYmflIUW+61zWMur65lGFYc/Q2NHROUuPiOiRa28ugWuf/9wOOtz89gsqOTlR2dOKj75qw6OBh2BUzD0AMBbnWKBFv2NSCC/dciwFdRWBgkAK143a5AO22g4CUmKGg9aePwjlCTRQUUDFjNEa+9BIKr73G9LlYjoLPL/TjvqOluP9F4M7l0SIOdPs8nD43frf1DTQ/9FD05U2fjpNXr8K4nTswdmMtxt6oYNw1zcF/3nPHQ86JLWLgHJauY2GJdsUHtkDy6/TQl3LQOOqKsEVJJ9AFWsc2DZ+MDrcqE9rM8mdvXY3F8zbE7KpmLdHvsljcsdPUJchdPL7ObRz9ttMbCTmRFVSOqoTDxFN+KL3lXtcw6voGBMSr4+fdCW8RiG6MZsn1AwfqBqCLW3FYcUDhDBUuCb892IkSnx/M0DvH0e6OrgaoXdYIq5ITtoyBodN6DG+duRBrT3oTTPYk5Op1KUPxbMv/YPGBFwIPOCPQcO7Hwr7c9gJr0FosefBBUxYpsyhoOdeDD78vxKyP1AceM3YsA9D2xpuxM7sjeudvyf25aUt58mdzo0IEooeA0LGnLcMmQJZsSEmPesG1mhH1yKx1AGgZXoH9RbpGpS5aP/ZQjFq5rnxpB567bbXph41sgYScyBpEXd9EzPt0Xq+Keax4ORAoSxNMPxt2911JZzb7Oy34YvkP8NvGWzDK+xrO8r6Iua3PoOHrP2BAy5/AhLcEpjuIRRSXzPM7AAbsHLwRk9f/Vi2LihsGQFK9Fcdux1rrIqx5rV4349qaK2HSrDK0r1iB3VOmqm5dyaiQHZAZ8PRPLJhTMRBXrwPs/viv8PvfL9RfUVet9smPOL/X5EhXkUUda7kWf1dd173TJ14k6s7p0+G8cmZwu5biH2HXydeCxzGjXu/zFauVq/b5iNeDkMlQ1jqRNRQXFMflMle4gqrPqgCgV7q9Ad0jQkVlaUxiwpaTWvZw0/wHAXeiY0oZBrjdmPPFOwCAT0acHVyzv80NR7EieFbguOfH3YlG3k4fNr+3V3gWV+6R4PeHY2iXvcCKYx2+qFGpofi5DV/t4OA6Ks4k4KLrx2LA/76AJq3UCQBkcSc3rxV4/ifquj8/J2PIUeNrFCEH6q3DMrvrqtXqA1+CvyPOMfjQdt1Vo/csj253yjn8Um4wE16vFWpvoYnnypd2oCBPwQ/q/gXtk9w48nLIMdr26rF43oaw2Hys7PVY16XBJFX04439pyOU7EZkDYnWl/dF4ptR5zerleOin59i6sbSvmIFmh+YH5UdbAaZMfzhrGvCxNwx9j7dIR8nHZiAmUf+Ha5WL2z5ViiyAl+XguFlhWjZcxSyr/t1+KQurB31ZnBG+XlfyTit/c9Cb4KtwILPurw4yS/BGbTW9Md5isZ8Tll7h+nXzQH86Qr1OLe8zw0t8dB3QviYwRhKH39MFfO6auDdW8Nb6YbwbMv/wIwj1OY5jPM2RoRYAmVuLcU/QsOon6rzvnug5WkYKZiBbvG5MObrdwxbtEoWBg4uettgzZVw0fVjg38TPdG/3lZgwQWzxqStoFOyG9EvqBxViTxL/HO4mzuaMe2daX3iZtcTTb+fofZtfYsskk9PkfDiTyw4ao8/ImrhHHO+eAcX7tsaslRHxA+ejcnf/CzoQfB2+uHrUjBx+omYefdZmHKDFi7gcNmOhIk4AGw4xWJ4bd4OGaf7rVhn9+P/HneVuHOb6EEgzsSuY3nAdZ9w3LncWMQ9FgseP/ta/GTmH7BiZIX4NXCOpnt+h/rTytD+xzuFIq6FCswQGvMGgMJrr8G4nTswrn4nLvpkMezFg+MWWEeRLXwqW+SlcA7IXersc50udwkRSJrbMe5G8SYSMPUX43DxL8aLyzS7FKyr3hX82UyYKl68HXLGjkYl1zqRVdisNrjlaJdmvjUfHtkjLFFr7mjuEzf7ype+0l3ncsW+4T+y8RG1Kc4YYOUYK877SsYdK3hc3cjssg837vgAn4w4G9aB23S3OedfVyBHiWi+woF//s82FPy2EtaSEsy8+y44p09HzZ4avP7ptqjnAUn2glv1p6YBgJUDF3isODBwECocr2J1++2QmYmbNOcYvWd57O26LxsONzDQwOvNARwsyMdLY2cEvRX/dcZPcfneWsOoM/dZ0PwPtX2wc6TOCZzHI/ewgi6fCYs85OEkr+IcNXkvhHhqpiOt2cmC7dpXrEDTPb+LXhFo22pZvAa1yxoTq9c2eOi4ePb4MLe5qLzM2yGHhZ20MFUqrXNt1HC6WuUiSMiJrEKU8Ob2u/HopEeDncj08MgeLPpH70xH03BIB3WHj9hgHLSt2VMT1dlO7eAmx3QXRzLM3YY3358PSJ0Y4FFj2ltOAs5qtKLTOQXfnOjU9St7rE41PtvUhOZ770HzvN9ilE/C3x3AXy9kWHNafLcXJ2c4DkegfPVPjDn2GhpHzTDV+WzHuBvROOoK093cYsnogbxC3HjJ/XFceTdcYfj+84HRQp6Th/bcGVA6O4FY5WcRDyeebV9ExeFtBRZTMeKUxX8tlqBwAqprO2FRjyDy2hxFNuFx9URW+1m7Hi32nSiuVm/GjUYlISeyClHC28DcgUGB1mZy66ENVektMa8Y9gE+brk2qm+4DwWGN5NF/1iku1wT8+s+4RhyFJAKC4GODnCfeJAMA+AuHB9sGWrztmL0gW1oHHs6PHlDIcldUCzR7VBDrUauMEBRE5lyXMAtH3AUKH68V64u42YSsBQFz7UsgfW4DvDjOOQcB6y+Dvit+WIhDyz32gejfsx1AGAo5rGc0R5LDl4ef5nufgfzCnGcO7pRTyRyV/ijQvu/CnBg9wnwH1oC/2RzDUtCXwP3eNB0z+/Q+fnnOHbpLahd1hhTxB1FNsxeeJ6pcwHduRZC5PDzpUrU9VzjFTNGC3uqu1q9Uclvkdej0bCpBeurG+DpiL8cQUuMy5REOBJyIquYc9Yc3P/p/fDz8D/eTn9nUKArR1UazjWf9+k8AIm72ENvbPYCKzg4vB2y7k2h7KpKrH/eA0+E61qBVejiq9lTgzavWFA2nGLB1nI7qs6tQuWoyu5uY4KucFrJkpbt7LUPxncnXIxczxGc8c8/oStnQFSmtCR7DV3akszwi/c5Lv9UxqaTAMRqZMY5IKmiH9r1y0wHMA3FYkPjqCsSmlTGoVriL4+/LCz5DwByJIaf/WgEXvnuJ7h765uwmjD3di8fBn+nlqHNAKieIpu3NfYoT8Hx61d9jV3N22NmfltzpZglWpF8//uFhgmTwRa0OkSK+sqXd5hK2BBdZ9nEYkMBdrV6sea1+uC2sa5LKOjG1Ylxnauvoax1IuuY9OYkXaELzU6PleFut3QLoYhknvhDRf3ZW1dBZCtqk59CMXoIAdSZ63N/NDfq2kUtXkVzom2eVpy38QEA4UM+4h1K0jxsAnaKMpa1+08q53EDcV0jB/D42ddGCbjGoPwcbJs/Dav+/AqGPbcI1pj3THHZW+RDk+g16GXhrz13kanWrqdeUIrJ15mfMBY2oUyHeKegxRRzzmFzWA0zxM3EvVNRPhZroppGvB6OnoCmnxH9ClGcvKWjOxu1clQlHt30KNq79LeNFS9f+3o9vlyX+EAJra51XfUu2AqsQlepnnvdSMR/NuZnuP+c6Pju0m37sfIHUzFDacC3IyuDgnziNzVRGdIaXtug4PfFB7ZEiKJYrKJeQ9m1MV3jKSNOVzsA7CgeIxRxADhj10bsnvIYSk33uRe/pljTyQD9LPyWYRPMtXYFsPfLw8KEtkhiiTgslrhHmZZNLMbmf7Xi2IeNkK356sJAGZvN24qh363CjI+fj3kMAIYu+9DGL4lazWUTi02FBdJ9IAuVnxFZR3GB/h/zwNzwziT3TbwPdos4k1qLl0fSsKklKREPxdshB0Rc33yJbFFpVCLnzHUKRfy+JdvRWHgW6sdcH5y65bUPRv1YccvQUEFhEgfLUa/Tmu9H4egOWPP9ADgsuTLA9C2nlmETIPdRgxLN1R6Lsd/vRs3S/4eXP3wkohQPuHDfVsz54h0Tw2o4zM57M3ywEGThN466wvRDj1nRaV+xwljEAZQuejTuMab3L92O+z//Bhs923Dup3djyto7MGXdrzFl7R04e/PDePf/s3fm8VHV5/5/f8/MJDNZyLAkJICIYZFFqCwWqCIKVWsjuC/VKvR2vbW36G314lJF6kLrvVfpr/b29nqvS11xKRJTxQUXoIASQFB2IgJZTFiSkGQmmZnz/f1x5kxm5ixzJgmKMp++asiZM+ecOUnO5/s8z+f5PP2t0/TxGDG5mDn3n+moxSzcofLmY1u75OCWyjoZtOj/eG5Ly0TkGXzt4KRODp01cLvJaYs3LDZE5Wb+z92Htad18vVY4bbJtyV8r9fqjx5u53rhxoPAlUwGQqCE20C4DDXw0qpX0Ig7QtG4oyYtVZ3K+qa9Puo353Mgb3JMbZ7dfpiwkn3sTUts0J7dhxXT/2ibandFf/b9A43cvOF5/mXTS/gi2sQyidNoR8T9t3tQcnIN26yyJmZw2ltd/9DDtq8Lv79LJP7U2n1Ap2vgzzYvpSAUQALtLs2Xf+nGasMAHitMvXio4/ayrkTnTqP/47lWniHyDL52KCstY9EHiwx18pAaMhCz/m+rerluFjNvwrzYvl9kmi3+oVxRVWGbVo//XPE1RgEUSMUyXlRdPkZve9ykBl6JOyfC8Nn1hvfEysQChK8PBVdcyudFu9jRdF2s/7vd2zc9IxE1AkIhLCO4osI30V1qNEm1A5b1/iypkhXpHDtqdvZ4vQBS7SzWxn1NV0cQf717J1zP9Nf/zLbxE2JWvJYiORPntSGnpRDTRWGbZRCCkjtud3zZoJHz01ESj0e2qi2oBVDQ0ca8TS/y1z9lccn/OHNhTLe9TI/O17yyx3HtPFmw99YTWw3nCHeovPXE1oRrOl6QIfIMvpZwUifXkapenmwWY9fnmgx3lsDlUdLyhe6EjD2UK6oqYtdghpLcxMloa17ZY4hgrEgxu/0w/Q01cA3hNhfbnivBnROh37ijFJwcYFPgPLa0XEGL2o9sjhLCi/ppVHVvEvE7gpQMV99icJ+tLG++qfsEbgLVlc2OEdcghSvWTtfu7cu2kdezY9gVRDx5KQnYIFYTLtOv7d6+bB01l60j58Rqw/px3QMG4HZD2OJXQv/d8l9ycSz1PbRqGVtHfh8UT9LeMipX6Lxf29fWUTLUb0s2qaa2+a+5Ou1o/MHlOwxLxblbX8MbSWx99EZCzF7/CuDcTjmZaJ1E6PH+6ukI4jSjJnMB3PEamWdU6xl8LWGl7LbyVdeJ0sosJv69O9fV8faT21Aj1n87Zr7NXVG5S1RA0JJ9hHUnvZpgfapj1KEpzKi7mkizQl6fbM64cAjvPL3DeDC0Km48Seq+6DcvWUdhisEhIZeLt7/xc7LyTz026fJoRN5db+8YungcJdKeMAc8IQJHmnibOr44Bp3am4MHWmx/B7JzXfzoP6Ybugze/9bvHLfj2amsnfjzj9rubGY4aJH4g8t3UN1odLOrWPpr09KECoxJ4xzJ6ErverLDnR2shhrF44vuMc+o1jM44XD2oLMNzmf6djM4MYvRo3n9DzdVv6yZA5Xe1+r0IaSPFc1v78O5e67lzE8vwxvJpSXrCOsGvwrAt6ouJ6Jq+3XWCM1JLOhqJezqIK+jd+wYuwsrefFszcRFiViT36G+448diUOsj7zLkJIB1e8xcvcLli11ToaAqK5sto6ay85hVxJR3JqZTew93fnsggM7UhvK6AutcG3i72HYY6ydW8HsdyuVn4AOu57xZOhCykDIPL1gZaLT4PM7PocZumLPmk7K3Uld/njqMc+o1jP4WuL9A++ntR00Mn/jijcMaWodQgjGPTGO8188n12FlZw3d7TlsXRfaDPsKqzk0XHz+fPUebw17Elaso840ju7pBtfJA+BIL+jDzN3X8/ZVVcZfdCJTpJKOmZI6WD1KS/z9MR7+O+pN/H0xHvY3W89BeEIF/RvZNAZjTElutkKZeewK3uExJ1pu63eLLX8ZnImUUryG7dxatQXfGjVMpSkGehKpB1XqMXZeYQgnJWn+cN/wWI9PVp3lyT+HqYzHMabmxij6VF4KhIXXq82994hHly+w5LEAR4ffSFBV2I5IOjy8MToC1m6sdrxeazQleEpOgHbqdBjQ41SMKTuzf5lI0PkGXwtYVYLt9sej3kT5pm2palSRSJjNfNdJmnueJj9gd+79l7mr5wfE+LtLqzkqQkLCIn0BXQCgUc1f4CJ6P+IUbrErXqYvO8ihjVoamJFShY1HGLV/mrKWtsoGBKgaNxR3DmJD+a6okmsnrIwrYjQChLJ/vztoKZvooOUjN72ODPe+xdGb3s8NpUrO3iI0dseZ9JHj8R2La5fz8gdzyTsM3LHM5y6+0UDwR9vyM7VMhNFN9+E8Hb+Hg6tWgaqidWuSXm0PRhm57o6msrL2TVjJjW33Jp61G0aPeNLN1Zz5qIVpul0HQP9PgZdeSl/OP0KDnq11s9mj4/Fp1/BOydN5J5y84FB6UJvUzvvB6NTtpHpcNKuNmJyMd+ek/qYx0OPeSa1nsHXElae61Y95vGIT7PXtdYhhDC0pwUjQW5fdTs/5j8thVnJf+Bmg05AGxPq6uKfYmpRWOIeeiQ/c/f1uN0HGZ7zV8hZCWgtZLUfFiAjnQ8uR05kqRAlGm/7YYqDL3HSpx4ODHHuPKbDHWqN1a2NBjVGGPaJzvOGTtW65uWebSIiSwN6lkAoxFQI3YjiQ0FVMwKKEurn991PpLGR4vr17Bx2JeGspGs1OZeMwMr/Xs23/uFs+Es67m2p0umgkfjq+Zor4ZC1+5ASfr3hOfJDAeZufQ3Q2tPSaUNLBSdtZMlIJYhzeswve8hKjxC5EOI7wGLABTwqpVyU9Ho28CQwETgEXC2l3CuEGAJsA3Rlzlop5c964poyOLExb8I8U/GaVY08GbonO8C4J8aZ7mPVe64juXVM93BPxuR9F+GSX9yaWqf2SLiQN5tv5s3mm8hTDjJkXzlFkQ2x/eqKJrF15A3Oa9dRkhRqCFekg7AnN6bWBi01v7fgx1BAl9LV3UnJuwcMQLa1xQgxnuATxGxpXleyMO5zn59F59zNOe0e8tSutc+pERnz2S+YNUvr927UMjjpZEWCHmd1aPeAARRFx9CmwtKN1fxqyUdEbETSPo+LWy44Nfb9ZYe2cP1HL6JPpe8faGTephcB+NUS7f70JJl3dZiLnnL/8LPD/KmqjprGAAP8Pm654FTm3H+mrZ3ryiU7v9pELoRwAY8A5wEHgA+FEMuklPGf+IfAESnlMCHENcDvgKujr+2RUp7e3evIIIN4lJWWsbF+oyECfmX3K4wvGp/WQBSr6D4V9IEQuiLeivjzOnqbbk9GsuK8ZyAAQYtaxMfD/wmG/QCEiItU0xCgRSNeJdLOiN0vxsht+7ArqRk4Pa1WNLN9nVqUGi7L6yVv+tmWLmbF9espql/P50WT2H7qdUiTSW/6dYlIO4oaMm1V0yenbc+OsD07wsh2F2UBD4rJz6xzUWL+E40fpRlf13Y0dCUOdUWTLDMX6Xqo65G4HYkPjBJfPDHP3fYaHpMWtLlbX+PdkyZy28tbgJ4jcx1dFcQdWVFLmZC873WxvTHATc9vYv1nh7n3krGWRB5sDX+pUXlPhAHfBHZLKasAhBDPARcD8Z/4YmBB9N8vAn8U3ck9ZZCBA5gJ24KRoKlbmx2sonuwI1cZ+6NevGFxwnuHNUxk8r6LYsrxkGgnS1pbxTo7Xw9AiBiBpjN1LPkYkaz8hB7q2LGdQGrtdmZIFns5cXvXo83P77vfdj8FUI7u5u2+LmYr2Rw9HCQgACnxIchRDnFW3pNElu02PasEFp9+RYJn+/ZsLfV8fsCTMKS2A8kbvjDbsyP8pCmbAmleg13x5CfU3r2A+Gn1lv3kZosfISynwaUThetIJWyLT6fHw3OowXT/wqiaPRCK8KslHwE9T+aQfspdICiQgosCHs4PeIgI8L1ez4Ovv4XPdFmm4cuMynuCyAcC++O+PwBMttpHShkWQjQB+rLyFCHERjS/xzullCt74JoyyKBbgrd42NXMrUhVQswONnfvAK7b9xPyOnoTdLWSpXpjqfT8jj6OU8buXpIZl58W7UUP0TOGoF2Agxau+EVBOscVkXak22f6mpkHuR2Z+793DSV3301TeTmRxtRtX4WBRvb4JHPuPtMg5LrH/TxFB9ZTi3m6ut7nNx28okfnVmjL+YS+bacSlsYsQCQi+Hjw5YxuS9QGOK2Tg9HaNd0oXMfSjdW2wrbkdHo83CUlpmr5+Ba0iJTcHBf59jS6Ep0LBNkQa+DISfH31pUpiD2FL1vsVgsMllIeEkJMBJYKIcZIKQ3WFEKInwA/ARg8ePAXfJkZfBVhlRJPHp7iBPE183jzGImKsJgP/envvTya+x7ntl0bI25fxBjpOomw3W7JuZef1vlAuvUilgbnkNPRJ3oNSuxr0N0KEryRXMNr3XYEVyMMqFlJbcm3kIqnZ1uzhEDaDLFJjiyPeiHfRojd8p6WkUnlKa6jweenMaClgG+54NQEQde0/Zup/cCPVTT++OgLHZ0jHrOVVdye9ygHXJN5s/lm02OjuAxT3NLtHtDT6y6/n/533G5L4vHmLg7GdQPgEoIHLhtrGU0X3XyTwYBGAt6sO6q9AAAgAElEQVRIB+fsr4wtgCTw1Np9vPpRLQtmjzkuovOvCnqCyKuBk+K+HxTdZrbPASGEG03uckhqtnLtAFLKSiHEHmAEYMgFSSn/AvwFNGe3HrjuDL7mcDo8JV3ER+jCooNTJ+f21kg3FOkRJII8b4Cp3zsjIW23q3ADz/b7lLCSeH6PlCAlIcV4XWo4h8XbLmBHy9l0qfNUDTF6+1Naa9fuF9IXwzmBw9GeEvCF7JckehSYenJZZ31b0DnQY/1nh3l67T6m76+kY5MC0vpsdmNQkzFbWcWt7iUMFAcRAvrXr8crDhPMNq9961PcdCJPx3cdIagafikTbrkqJYHf9vJmAqHOSNXJQ9bncdmSOBA7b+1996M2NkZVGZ2+65B4/xoDoWNWNwdzQdzRw8FjV7L6AtATfeQfAsOFEKcIIbKAa4DkHNgyYE7031cAK6SUUghRGBXLIYQoBYYDVT1wTRlkoPmim9R69eEpXcXOdXUcfNTPxW/NP6Z//N/+wWncOPwXzOn7T4x4bSQ8dBpsXgLA4uKBBhIHcKuSkAUZClcbp4z5nPN6PUyu2mBtrmIFkUjYxfXrGb39SUS6PeHRxYbT8yqR9oS0ugSCHvCksq8Xgtp77rF8WY3+/3OfP1bflmi14KUbq3mpsprp+yv59YbnElryklGfhkvZbGUVd9Y8SeBVhe3Pl7Dz5f7UrCugdI/RwCYe7dl9WD1lIXVFk0zNbvTPa4agx3yKmd4LPmR+BTc9vymBxJ3i8okDHZFtwaxZuHKMyWld9JaMQCjCg8vNbYZ7EiMmF1Nw5RBe9YUIdceo6EtGtyPyaM37F8BytPaz/5NSfiKEWAisl1IuA/4X+KsQYjdwGI3sAc4GFgohQmh/Uz+TUjq3L8oggxRIZ3iKHbri7dwdZOe6GOFbCa0HO01AmvZD+S8BqFXNc8oBxbo2LUN+cqvfpjinAfHWDsJt2p+/Y1W5UAxpXv3rzmFXdqZ87Y7jxEY1af/49i4JbB0Mo41Dtkzf27jkBcuXXx0ylf86/XLD9prGAA8u38Hkqg+Yt+lFXHYLDpdMK61+U/WLHF6fF1sYRDq0xZH++SwzHPr8+FOvZeSOZxi545m0siHJiuo7l27h6bX7uk1dL1VWM+nkPo7IPNlyVkehiYUrYFuT70nc8bcttEZ1DDMDbnwxM6X0kI67XE+jR2rkUsq/A39P2nZX3L+DwJUm73sJeKknriGDDMzQHWMYHekIZJwgTJiQO4g3nEtIacejZic8ONxZCmdfdSq8faPRySsUoGLlQshLX0g25uAQiuRmENpUMx2H+o11XOtOTvNCovGK3YjP5HatoVXL2Dpqru259clsEjjYC9YPg5mb06jyR6zD9m/vX8/kz7dRGGjkaFYOSEmvUABVKCgxMaMdJETg1spn+fWG51CkRBUi9lVImXBcJUfS0aFYRvexdj0bAx79/p+59i7t3jmE3pcOneNGeyL+1BXnNz+/iQKfByGgsS0U67+OJ3gnord4KF9ApvvOpVto7dB+R+LbBs8OuuklBQG0coVPQgCJG0GWyW+F4hKxdtMvA1+22C2DDI4prFrHzOaMW8FsJGg6iCfu+EElwxomMr3qmgQSl0i8ozu0h+5rB0yPtzg7gumfro2a3K+qPBN8FSmiEqY4JVOysjkV2rP7WPYnO3Fcc4yoUl0ADb3gxhvdPPJImKweEgf7IiFyotFgQUdbbLsrhdFPJzqlg3rUnvw1/riyTZBqaaDfOzuDGv3n5Qq1EMnKd3Sl8Zmke8o/6dEkst5XrgsFQYumk+vcVqK3df1HmR5XPcaZ7qUbq3nKZH66VaeBAB66+nRGd7h4f8mO2Ghib66baVeN+GobwmSQwfEMu6lmyXPGk9GddLreUhZP3MmYvO8iw8ATgaB+e6v2TcEgLZ0eh4rcHGrdaYrLpGT+oSO4hdr5AI/+o65oUjRiNjmm1cJACEOKPV3o1q920bgr0h47fr9meO6BsD0Nut0Qds7yx6u0SV8M2ZUe6oomoQhIZ8r9znV1PFnbwJE2E7/2Y4D4aF2L0Ccw+dJLEox5BHD+/vVs6zskLcFgd7B0YzX3lH+S1n0QwHVTBscWJV/2tLNkZIg8g6899NYxsxnlVgYx6aTTk01aJJKPi1ayeqh91cjK0c0XjLbHzbxLq4mHtFphRW4OC/pZ24gqiiulbaz+TndOhAN5UzQyNamzKpF2imvXUFcy1TTNq7qytRot6ZO5U7V7RHHFIv9UsaxucFIz/zbbdPrxgaTud0UB1fhzG7r/NbYOvw7DJxdCu3+Wo7nMu+uXPf4JTxWkGJzSw9CjdT1Cf/6dFSS72se7vMXD7+uG/30UejtdTWMAf46H9lCEtjRFfWZudccbMtPPMjhh4NQgZue6Ot56YqstiesTxVQiBmGMQHB68CxKcktsRTMtWUdMt7dmN3L+i+czbuO9nH/KMCoKTwIEi3v7CZoo1QG8Li9XjjDIUKIXpL03HkXjjrKndLZ5LVaNaIKq3S8wcscz1upyxcXWUXNZMf2PMUW1FYQiQaidkbgTkZbiYU/p7JS76aM3C2bNMiXE4w2uLDU2Ltbl92tEnryP38+Emy7FcvnShZY/n4RVWb9ktrIq7fcCPHz16Tx89ekM9Pu0ckKaHgKBUATXwXrT18wEbwtmj+nKZQIagY9f+AY3Pb+J6sYAEjjSFnJM4rlZLh6++nT2Lipj9fwZxzWJQyYiz+AEghPh23vPbOfj9637jiUyIV3+0zXmZiORZoU3rngDwDQTALBu8Kucu+fahIEpIaWDtSeVx/avDTWxoMAHY/6F2r1/s7yuBd9aQFlpmel0NYC6pHR8wZAA7bUWtXGhJKjS95TOtlaXRx/muqIal0pxbSWu/BxUVzay8QjunAhF444CsFJYLB4skLJ+L0SCU5mVoOp4gXCp9J/QjOfkCJ9MvBf/w0tiA1ES9svJoWDWLPLWrLYu7ejT3AyEak2wbcFRLPb9icX8iQgKT0dmcHf4n1Jed+8cT4zM9K9OpqAl46jHR0HIqEY3E7ylIs/kFHmORyHL7aIxEHJsZmMGn0fhk4Xf6eK7vxxkIvIMThhYzRkPhANUVFWwc12dLYmDFkU/PfGeWM3bKqqOb0WxOu/uwkrq8j5FRZtzfjT7MGuGvWyopwcjQRZ9ak3iJbklnaWBSI7pPsVh48M2W2k13TfZfMWybzkJqiubfaMvZtSShYz4cAMj165h1PfqGT67noIhAQqGBAilKaxLvhYDpKT+oYdpKi8HNEFVj7rNmUAoEuGJoIkGpfbVFV0oKSJhuysrEtvXnROm+Iwmjg7O5bbQjzhj9k8tW7LCNTU0lZcz9eKh9vOw0/qsgjUt34+557qFyg2ut3jSc5/tu3weF3fPMkbHl4wfyAOXjY1F6H6fh945Hsto/Zz9leSEOwzbO4RiaOGzSqsn977H17nbQmpMcNdVEvcoggcuM592eDwjE5FncMJAJ7sH1j1AU0dnf3ljeyML/rGAf6pchF00E1I6WDf41YRte/0fc1r9NEP7WHwripXgbljDRPq3DEEgtCj/pFfZ3dcoigNoFJg/tKVk3oR5gGYdK0W74RO4VZV5R7Sob2fbNNa0fJ8WtTD6qkr8el4zX3kl4f3F9R+CkGwbOQdpJoqLQ0ukH4/8CfL6rNZmO8vOBcTOtmlYuqOrKgIVqcQ9kqSk78EttucDjfRqb7+D2vvuRzY1OTe4cYiQcNHmzqIg1BbLLhQMiYsqfX3gwoXw9kKDODEe9Xvz2PnRAHLXBrjU9y5NU8ttMwg1t92O/8orGPnZQT7uP7tHHPRaIoU07fXFrl8ImKZ8wmxlFcvUs2L76RFtqvrwJePNDWHMovW5W1/DI40LyoDHa6iPm6XVu5IBSAe9czzcPevYWMMea2SIPIMTCmWlZSzesDiByAEG1Y0hErCmcZUI75U+lxAtD2uYyMiDUwx18JFTig2q1mTBnd565pZa5JHf0YfpVZpPkpnCPdVngqhlrGJ8yOVJSVlrGzvbpvFO888J05kdUAjj4Sjt5JOnHGRqr6fIz/+IxobcGOf6S1sZdUY5A9saDe+3gj7bmT6XMIKlAKw8+iPMkoASSemeJ2j3nZJoTCMEdSVT8Td/mlJQJ0Mh0xR1VxGNs2nw+Xl89IW8e9JEKrN+Ql+lxbhzuD1BlNi010f95nzCba4Y8Uug7sPe5Ee0ffoHGqm55Vb7iwiHaXz2OYqA0UcabfvLncIdaqX2Az+1lb2QISV2fbcOXsKyDo3IXULwH1d9o1uEpr9X920Ha+OX/LgWPTssWPbJMSFxv89zzLzdvyhkiDyDEw5morfJ+y6ymWQmWTHsaQPBmrWPAez9+BDTLc6t97WbvdejZjF530XmRG6RQi3J6qwtWs1Mb4qKqda0fN9AwioePEo7Pyqa27nxDCg5wzC3iBE5K+nATaV6Iy0tqaPDcIfKioPf5Renf0DukW8yU+ZbLpT+7YZNzHtntuFzmhnQHAuEhUKrO5v8UIAGn58nRl/IO0lRYh9hJHGNtHOjpJ1PXkmQpr05MdOXcJub2g/8SMCjdp2EnPSXO4FEIlUBqit2fTVr/RQ0tMJYZ97pTqFH63oknU59/J7yTxKuYenG6oQ+9Z7Cw1ef/pUmcB0ZIs/ghIOZ6M2qFUwi2Z+/3ZRcrd5j13euR8+frjKPaq2OaX5xkrMPHoCHTqNi/KWWu+n18Ra1n+nrVtsB2qWLVnz4aaVG9uXpnLE8sOA8ILnP3jxlHg73o9bj5rr9sywXSrrOwErYlq5hTVfQ6s7mmrLfxr4f6PdBkkVoBIXWvdmxaNuVpRIJCZCdpN24J5fk+yDVnqnZ6/3luvK/K9F5xGM2Z17QtCeXW9yvMHDB3T1ObJeMH0j+qrfJiTirj4OmMNeH1yzdWB2bV96T8Ps8XwsSh4zYLYMTEGbis5Zsc9GaQNC7vX/CNq/Ly519H0Sx8JBM5blcVlpGfh9zIrcSz5lfnOCV/FwqwodYvMeiZ13KWH08Tzlofr0m26WEA2o/bgn9lAntf6G0/WnO6vgDzwWnxPYZMbmYOfefyY0XvUqe0mB5mddV3m27UNJ1Bx2KubAtpeCtB9ArFODx5fdyzv5KPC7BuSMLDfu0fJZN7YcFUY96ofmky+RHqPV8+p5Ccf16+7bALkEwY8dKJi97NGFrU3k5u2bMZNuo0eyaMTMmKkwXg//2hGlGwqw+ruPm5zdx59It3Pbyllg/uh1yPAp+nya2651j34Pu87i61d52vCETkWdwwkGPihd9sIjGdo3k1p30KjN3X28aNeZ19KYkt4S61jqKc4v5ofdfaXzDizTpWU4Wullh6sVDDYYzZmK6VAgqCvML7QePPMr5bDk8izy1NySZ1yiRdgZvfZVt9SWxemnWEJV/C/0wQfykY4DfR0VVBYs3LI7dj3l7P8bb7zMaD/4It5q4iBEI8jv6xJzuDNfvao1lO94fWsGM3deixD2WhBpOmHxmBhVSGsYIjwdyc5EWdXSBVreet+lFXEJQke3mnP2VzN36GoWBRlp9PurCvWynoH2RsG0LtLHqTYXGZ5/TnNf01rY4hGtqqLnl1lhtXzfhsRuPGnuvhTrfrj6uzye3Q+8cDxvvOt+wffzCNyzfk2p++lcRGSLP4IRFMNzpcrW7sJIzP70MX8Qs9Qh/POnJmIDtidtXE+4wps+FAudeN9KRfeOIycXU7mnsbHcTkl1F69MWumnvNT50dQw7OInpn16TUI+XUiIgbohJJSAIt7mpXtubto0umk/z4R6zkezC5QhPIzLkp73hAoaV9mXBP/4v5l1f21rLgr698fTZRv9ezzN530XkdfQ2NclJhkSy+pSXE7YlauixXAAkHhsCioec5AEzUcQTTlN5ucHvOx7eSIhfrX+G5o/+Rk64I6ayzg8EkI4TmMYyQ3eT68lHVIHSqmVsP/U6pCtJp2HZX45mx2vVOZCwX+r7rncLALZk3lRerpnemDjuHc5No5SUBKu2uKUbq23tV7sr5DsekSHyDE4YxEeSQgiDnenqU142jcoFImF6lFUNXKrOPZh3rqtj+9o40Z0UjDk4lba+DazvtSKNT6VfpPmD2dTPXQiyg4c4c+1dhv0FkNse4ZbKZ7m1Ups49sw5gtVjGvn24SVc++9h+jZLDsW2uwgqCkHgaGGlrUmOGeIXLpP3XYQ7+ZEUdXezE7uJ6H8iCFxxxC+83gSzGOgknPqHHrZs+xJgKspyTsc928duRrsKoBzdzbI8KAtIFBMb12TrYJCclvM6/qGtprX8Ll1bKMTn991vSeT6wsmMxIXXy7gFt9F7oydt/3dFYBpVL91Yzc1LNlm+7+tUF49HhsgzOCFQUVWRMAVNmkQcuwsrmbn7etP3x5N3Xp9sUzJPZx6x2UQ1GRZM3j+L9WO6QOQWsKpNpxKQ6bFnYTP8vELy49fC+EKdj/7CZvjlMsmP/x7mf74rWD1aiS0mWrKOkN+RWqAWyEqsfXf1WkGbZCboTLN7bNK+BbNmUTBrFrtmzDyuXeDAvrZeGGhke3aEiwLm9WCBiJ8iy5icFUzPexTO0F7vKTKP2LT91T/0sHn2w+WKLbLuHlTNLS9+RCjivOYvpVZDf3D5Ds4dWcg72xuobgykdHT7OtXF43F8FHwyOCFRUVXB+S+ez9gnxvKNJ7+R8PX8F8+noqqix861eMNiwyhTM9iJzXau0yLoMy4cYnjNaW08dh6LqD7c3LPRnNXnSUdA5olATsj4yBdAThj+uVxy3pYI3qhmYN3gVwkpRoVyIiSD/c/F3gMQdDtzmjODfm0K0OHyOKrdFt18E9Jz/Mcy0oJsswYMYO8ia+EkwLfnjObGP8/g53+awfTCZ2LbS85oxj+0lZ6S4VmJ4Kxq46hq7OdzyfiBPHjFN9I6n97nX90Y4Km1+2K96qk+zdcxGodMRJ7BMUBFVUWCe5pAS/MpQkGVKgVZBXREOghEOtOXeppb/5pqxGg612I2wtQK6wZbi95WLtmZMNbU43URCkbI65OtuZilMdrQKqpPS7Vug2ENE2P16uQUq+beZi8gSwdZEn70d8nslqPcf0Yue/qtp7RxMKUHp2MV8WXTzNXKW+Tlf5fFHCJ37wA8YSMhORG7GY4dCVH/0MMpibzg5AAtg5torsqJMsCXN9jUqmqtifik4XV9UAxowsk3H9tqetz4khCBxN+tkjOaySkM8fmGXpoCvxuwut+ioMBUYOguKUn4/pLxA7npeeuUeE+gJ6apHa/IEHkGPYofL/8xa+vWJmzTBUs6SSe7qlkhGAly+6rbga6ReXI63Qz64kKHXXo92BqG1s5511KVnPeD0ZYEnqzuPnvQ2bx/4H3qWuuYWHIuZzTPRoY7H892qnWvy8vFwy6Ovd/n9tEWNlf86q5xCbXxaCmhU+DWswYrQgqKV/l4of0IBUMCPHF4NC2WxCgRioudpz1B2RWXUAYs+uWLxvo4oIQDXbpWy0gQrY4afOVmLtj7Pkf3FoDseQLXU/zNHh8IQX5Hm6Wy3klMbHift3PRM2JysSWRJywWfb0hkJjdKBgSoGCUj6bR/8Hn993fmSaPCubcAwaQN/1sjr72um0K3ex+195zj3mXgNsdW4R8UfAo4mubVocMkWfQg7h37b0GEu8uVKl2OTJPlU73uryxqWHxE8qc1njDHWos4jEj7Vd2v5Kg7o6fTLa+1wqy+/TmtPppAEhUtvdba6paV4QSu854THtuWqx9Lh6mjnM2AreegowofL6hFwVDAnFe7mYQBNU83nlfgZO0coVVfdzcwCQ1kiM+0Aj8lhc2cSGreNiznD2bixy2kyXFw0Jq38YZvXQIhYDHS35HG4dze9Mx92fc1TooVredvr+SWyqfNSXy+qizWX8LC1PTK2ps1ERkaDV/qwxPdq6zSFvXDVih5O67Adg2dhyEjMI0V0FB7N9N5eXU3r0A2Wa+0HTl5SWcS58ZfqzwVfZQd4oMkWfQY3hh5wvH5LjBSJAH1j3gmMidpNNLckuYN2Fe7Jjxtq1mg1CscPRwkLFPjE3YlkzaZkj2aRe4GHlwCp/32msgcykl81fO5/ZVt6NKFX+2n/Zwe0JpIh52ojGjkrlnEelQWL3+QhiUusUp3KHy/pIdRELW19QVMxiJ1hq1beQoAITfT/V1/8xN1X2ZraziPz1/5uhnPsJtViQXp3z3qBQMDtBS6415p//72Dl0hFV+sO11+rYdSfBj93lcXD5xIO9sb6CmMYBLQERqA0PMlgwqxJzN/nXD83ik83nqMhiMpbSnXjyUt57cSvJMklBQZee6Oi1rFLAo21htT0LtPfeYkjhonwOiJH77HZr3vQUiTZ0ZuWMxCMXpwJevEzJEnkGPIbmdqyfR1NFERVVFSjJ3kk4vyS2JzQrXEW/bOqTxNMdk19Wadjpe68mlCbMoPPGaGsk3IfM8V0MPUrh1VffjomtxqqNtb7V+gKdTy9ep1yx9LRsbKXnkAX5/yhAu+uZ6WqMObVYLjaO+HAbMamJQguOd5j2vSijxhFhw5z3AXbFosqYxwEC/j3NHFvJSZXWMmHQhttXAECC2AGiYMoSBT/+XpWmNGXTV/YjJxaxcslMr/8RBjUjeekJLu48oGGQ+nU0oND1yB/UvrSVcW4u7pMQgFmwqL9eMYiwgo+Rcc9fdlmSvIz5b8uDyHd0mcQUoyPHQ2BZiwAlE3vHIEHkGPYbkenM60AVxdli8YbElkTsVtXld3tjYz3jMmzCPO1fdSViGbe1E4wm+K05sOqzOkZbXehI6BW5+w7W6CTI57ymtHNxjzp5GMq8rmkTYk9sDh5aM3PGM4/p4qgWKAMZ++in1rXkEj3gsU+ohl4s/jb6EXuEAD3v+RLILryLgl6FHgXsA4xjPMxetMCWmo1k5FJi4mDX4/LHIceb4gfAvNwAacdr1usejqbycglmzDCSuQ6pok+jOvpcRbT+DUCBhQpvwqBB5KeYJH+/gJvx+FOxbzEAj570/+AEEzLNE8Yivj9c0mu8vgIeuPj02Pc3u11Z/4ny6qOui2K86Mu1nGfQYrhxxpeN9c9w5CAQluSUsmraIzXM2s2XOFhZNW2T5HiuS1qPwVCRekltiWmvWIeL6oE1fR6CiIpEczTpsGGuaDqzO0dUIXxe45Xf00fqHYwsjlTylnum9/os/ucfiLe0g+ZGo7dXZ0pP4mtXj01y6tXPYlTb2oM5XENnth4/BxDNBoD4bGTJ/7EngP0+/indPmmhqT6ujt2iBzUti3y/dWM2Zi1ZwyvyKWBtUPM7ZX4kvZMwQCY+H8QtvZ/X8GYYIsmDWLIaveJsBD/4e4bUfG1tz2+3snDKV7OAhy33CHSrvvO5i21O92f5SMbUf+GOe8TLkshzsIhsbU5I4QpA3/WwCa1LrY/zfuyYW6S/dWG1YKOkY4PdxyfiBrJ4/g72Lynjo6tO1QTYW0IesnKjIEHkGPYY7p9zJlOIpqXdESxM/MO0B3rjijQRiLSstw59tHGuoI763XO9Dn79yfsoecT2dbkXiizcsJhS1+Fw3+FVLAhMI/nvqTTw98R5bEve6vFx96tWU5JbEFiz69/o5knutuxPhmzq4IchTDjKn6KfkebeyTD2Lc8f+P7accgpSaJ8wIuD1CXDNbW6uvs3NH2YLGnppxN7QC14fLwg6zNvZRuNSMuDAe3jbD6e0/+zp9rhEWLuy1/v8CQM8aqT5VDgB8PZCoLPGW90YsFymzN36Gllmmarc3NQtcrNmUfLbheCyEa2Fw0QaGxlatQwlYj15L+zKoa5wEjKk9NhENgDflMm2aXcdIicnJprT75uZB4zP4+KWC05N2KaTuh2ZH0vB3PGOTGo9gx7F/1zwP1RUVSQMJDGDXWvZ/G/OZ/7K+abvu33V7Wys38jrn77uuI3NKp0ej9y9A7hu30/I6+hNwHPUdt9hDRNtSTxZSGeGS/99LmERwkMWEknQ1crqU17ucoRvOVJV7UdYCnJEkKrsa6mR/fj9+Kv4t2/8grxRxnu8eoyL1UldOjtPinDtu5J+zdYp7LqiSWwdeYNlNO4KtTBy9wuw+wXe+9YiIln55geSkuLaNWlH4/E18q5AgmGc5u/DV7HY8ydzy/KmAwic1XiLLOrjTmvhOtnX3HY7hM3T59A5s3zryBtAMSF+Idgx7Ioez3Q4icQBSu5ZEPu31X1LNdDklgtOtew3N8uGnCjIROQZ9DjKSstYec1KCrIKbPdTpcpvVv/G4OBmR4CqVHl+x/OOSTxVOh00x7Zzqr4XS0vnhHpZ7isQTK+6hmENE/Fn+xMi7kXTFrFlzhbbyD/+fL5IbuyYbpkYTfuz/bH7pwgl4av+Wvx5s7LN1+R5ykFcSPqIFhQBg5SDLPI8yixlFURyLK8xHqvHuLjxRjcHLW6LPh/blDwApOTU3S/G9o3Y1dCFoK5kKnVFkxxdm47mrBzKh0xF7Yacb+7W1zhnf+dCapl6Fq2Y2+4ekXks3VhtWeMFbVEx0O/TBoaYwS7KTkLBrFm48lK34hXXr2f09ictsx4RT17a99YWDj+Db+qUhOyD1X1TpbQVql0yfqClsYuAEza9nonIMzhmuG3ybSkV5CE1xG0rbwMSCdzn8lm2VzlBfI94Kqx5ZQ9uNfHhoNeYzdTrHjWLKftncdpl3i4Z1ax46WPD+fRj/uiyKx0fc+e6Ota8soe9b7UDxujGnaUwoderhogyR3Rwq3sJf6/7Ad6SFxCKM4HiM+cIfvp3iTcpKNxTOhvVZe0z7wq1UFy/vpPwhX38oLqyUw5KiUfQ5eHPYy8G4FsN2+nX1ojwepEOhFc64seYArEUe7v0kCeM6WopJb9a8pFlOn2g38fq+TMA2Pa4xf01GSRih/i2rdSw6CqwisqFiitLIdKO7TS9hLd4vZZT5OLhmzqFIY89BmhE+/vl2y3v2+UjNkEAACAASURBVACb1LmOBbPHcPPzm0z0HFqkf6Ip1iFD5BkcQ5jN/TaDRCaYvlRUVXSLxJ2ktnUS1Ew0rHuercg8r91PWenMtK+toqqCcLPX9GzpHHPnujrDPHPFJfB4Fdpb42xjXzOvuQ8Qhwg3jycIZBcuR/E0IoR958DqMS4gMc1eVzTJdqiJEmmPReOpCD8eTgalgPaTa1fcMbMV/b6mQ+Lx8EZC3Fr5LHO3vsbjoy+k9zBz//feopWIBdnF13itPMhBG6+aDtwlJSlV7HVFk9g28nrbxVLEk6cRt0cS6VBic+gLhgRhQaMzxbzLhXf86SnT6skkbtczblYbN4OdnatdhuTrjAyRZ3BMUVZaFiNnq7o3JNbMF65Z2KVzOY3CjSRoTuK6gtzc5U10Gm2kgcUbFjMj6yemx8yzGX6RDLPpaWpE4sl286P/mN658R/mvcM1si8A4ebxhJvHA9qD9JpzG1h9+K/Utuhz0hPvjV5Df+SRMBGvHmFbpLNlhFN3PEP/aPTnlJwhPSMY85GjXUd8dH7Y24d+JxnV4Pr9S0ayCUn9QxYjXYVI26a06OabDGYrwuOh4IrLaXnvfcK1tewccRVSSf1YHzC5iYIhSffNp/18dJe3pvJy07q88HjwTpqYksSVoqIYiYO9niBd85aBfp9pTdxJRP91RIbIM/hCUFZaljBIxQyqVGO93OnCn+1n/jfnm5J4fPSd1yeb9kDYQILJiFeQWw1RSRhI4RB1rXWsG/yqwQs9pHQw9eLRjo9jNT3NsH3mXVD+SwjFD6iBgeIgq7J+ye/DV8VarQKhCI+90YeB/vlsDl7G33N9LOzXhzYhGHZwUmwIS9DVysYJ4Ja5liQuIu18lvMsf/7hJs78RHDtuzI6T9Okpipl4nGkpD27D6unLEzpC38sx5x4IyEOfuDhyMaimKtb0bij+E4O8fvwVabXoqfTdVh6vkuZUrFu/jZp+D5nwgSOfuen/GPJTsIWveTx8PokBYMixmpM+1GtrW6c9tn066u97/6YMM/l95N/4XdofM7euVBkZXHq++8lbLPrGU++b6lw7shCnlq7z3T7iYgMkWfwheG2ybelJOqukLhbuG1JPD76tiJA6OyZbsk6wrrBr8YU5E5mlDtBRVUFQgh2F1bSv3kIp9WfhTbbSmV/yWZGTP6O42N5c92mBiCGmejRhzJvL0Q27UdArHd3kNCEb4RI6JuubgzQmJ1LWWsLwxsm8tbRH6HK/NhixheJiq4s28Ulo3Y8w9TD62nKFrEo/qdrFMu3ZAcPdUbsUVJv9/bVIn44Bj3lsYvFbjkgQ4JwSHtMhtvc1H5YQG9aWVZs7DM3iwZdBQWmfdjpptUhGt0nq9bDYTY9+gbbT85PuTgFrfwy7Xunwbt5hgEqqCGtrW5c5yIl3oNdT7k7aTUrue9egATnOyt0JYp+Z3tDWtu/7sio1jP4wlBWWsa9Z91r2yfeFYRlmMUbFpu+ZpaCtkJL1hFDj3hJbgm+XHOVrDfX+TpYN61RpRrns64gECi4GPr5xNi8cyvsXFfHE7ev5pGfrTAlccuZ6OOugps/RhScZHhJF74BzFZWsSrrl1RlX4ufFra3TeOd5p8jZa+0/Nl1MxdvGC0Sj8Jq3rg71MqZa+/S0ulJEb4ufOs2LE1qQMmK2CgDEt8nIwqH1+Xx96W/5vHl98ZU7mb13abyciItLcYjejxdmv5lFd3v6n22o9/x7FwXM28YZe+73nTAfHN5ObW/ucuR05xu+pLcY292j53WxZNhtTDI1MgzyOALQHzNXB8C0hOoba3l0n+fy9T9s8ltL8DVS1JZ8gbfOHyBKQk5sVvV+89r15g/5lNZysYjfhKbmXmLDAvbVL1jcZtdqt/iIT1QHKQqW4t89Wh9Z9s0VjTPQ5LenOpkM5e+zXEvWtwu/T5a1dCttqccy5I0irPx2WdN3iFQw4J+U5qp+7A3ngQlucUZpEioo5/RcoBph3bgebGBXXE+5aYRNDgygjGDldgtpfZAwHlzk8btWvmuFwwyPUT9Qw87Uqj7v3dNzPTFrldclbJbvugDMjXyBGQi8gy+FJSVlnH/WffjdTkXeNlBtyjNbfcDgkizwjd2XGC5f9DdytGsw7Z2qxcPu5iy0jLLwR52Az+SET9dzdK8xSZVbyduu/HPM5hz/5mp6/UWD2khNAKPJ/F3mn+eHolLSXbwkMEfXaAJ4878JII3Yt4/Hs7Ko0PYC9xWT1lo6H8OuLOxXQZKifB6Kbr5pii5WNC+Kog0KORNaudznx8V+NznJ5SVOs7xRkLM2LESz8F6kJJwTQ21v7mLpvJyywhaptVG1omim28y2LUKr5esLOsFpTtLMZI4wPDzzd8Qt72pvJxdM2aybdTo1JG4EAkkDva94p8uKjO1pnUKs1p4V6P7rwMyEXkGXxr0mnZXI/POISG9kagoScQjEARdbbik2yAsWz0ktYva+wfeB7Cc9WyoR1tAr43rQiWreed2x3MsbrODifAtHjvbprGm5fvRWeLOU+khJPuCO5iz/hGyIok/RwEUNsNP/y55d9oRsqR59Fg9cBJDq5ax/dRrjS1qQpjWy32RDt4cfibn7VptXa4PBqmZr/kUoAhN6WeAoLEql1Mn1TKjRFOZz1ZWsaDmceo/7OVwZnniOesfeti6Pm4yK90JCmbNom3DBk1oJiUoCgWXXoLSnAUhk8hfwLnXjTRf4O16w7gtbrueSncShbsHDDBMS4NjFzUv3VjNS5WJxi8CuHziwBOyhxwyEXkGXzK6GpknDwlJJnEd2REf75U+Zxp9K0Kxrf3qUfSQ08xbjay2xyO+Nq7DzGfdsr4dRZbP/PM5XUwAWq181h9ibUbx0KPwFrUIW/EXknYkbUIikTQJldd9IZadepj/+q7mz25Gld4wnLLrLdNyhEBQM0gzgBm54xlt+IdJj3ZyvTxcWMDp//EAzZ4UxBCJUPubuyxIPPbBAI3AZyurWOR5lD5D2ig5owl3TljbQTgvpYRranq0Pg4auTb9bWnnvVFVmv62lGCrxdhQiXWWxqLMom93kkoXXi8DHvw9w1e8bSDxpRuraeswLi56Imo2S9lLTlyhG2Qi8gyOA+iRud0Y0vjouyXrCO5IlqHObIaWrCPsLqw0RN/xPefnv3i+6XmLc7WH4O7KetNj766sZ/q1I23PH18bj72vsJLio6dw2ueaal0oMHJKccJDN75lLsvnoiMQQShaB5eOVOQfj53r6ljzwhZaWvoi+AsShTylgSFZH7K34wxHUbiKpMIXYnt250PU3Wsj2f3L8braWD1QYfVpCs89EDY90vAD73FgmPmEPL3OW1y/nuL69ayY/kfb/STw5ylHUT9ZSnDcJczb9CLeiPUcbBkM2tfUo6WF37n/G6+IxLRxBUMCsX7rpr0+aj8sSIjQbY/Zg/VxMCdXGQxat/WBtdeBr7dRtQ401Q+gfsZM+1S6EKYzy0E3fdlMIGTMsPl9HhbMHtPtqNkqZX8ie61niDyD4wK6CA5g7BNjE17To2+duPM7+jgSmsUL2DyKhxx3Ds0dzRTnFic4v82bMM/USvbsQWcDWM55ttquo6KqwnSBMKxhIqc2TEanAKnC9rV1lAz1M2JysUHYppP4qDMHsO+TQ7F++FTits7FgP65tIe9XvtuUYv4OPhdnKTRXQSpyd3Fds8wjbwLlyM8Wto4WRB+qJeWTk+GIiS56kHaFGN9s0M5TEgBT/T5n91+mHavMeOR3X4YFVg+AVaOEcimPxCaNAW4gp9teYVeHW1d6C2X+Es1RX08iSejYEiADlx8+lF/cgMBGnx+KktG850DlSgdzkocXa2Pg01Puk1i1VRAuXmJ1jOehKZ9edSudyM7rEncPWAAw1e8bfranUu3mPZ268jNdvdI6tsqZa97rZ+I6fUMkWdw3KEkt4Ta1tqEKDw5BW6VEleJIFASesFTWbaWlZaxsX4jz+9INLl4ZfcrDD84CUgd+SdDT6mbwUy1Hu5QYw9dM2GbVGHfJ4eYc/+Zjs6fuBiwo7ZUtCfJUxqYmvcUpb7VTMn1ck9hX9qtBklj7cmOFAzZWc6OU68jIjpLAhKJIrOoK5rESXXrkcCAA8v47JSkermUhJUsPhs0iccu0Cw6hQBP77WsGnMy7560kHP2V/LrDc/hMknN233SkjOaY8ezQhiF3w64wdBDXj1wOP+8503CtbW4S0qINDYi29pMjyEKCtg1Y2ZsX7Oo1gpWqnVvqJFgVhoCyrcXaj3jcWja66NmXT5I66yGLhw0w9KN1TxtQ+KgRcynzK/ollodtAloGa/1RGSIPIPjDvMmzOOJpUv5VtXljtLnOkJKh0F9rgglpe86dArb4hGMBNn3VoAcCyLPzrVWdZul1HWkUq13R9iW6CHfPbgJcm6vPzEiZyUAFbk53FnYF9WO7ej0ZP9FucSV9LQtrqtEcatsHXEVEVUzmREI3OSzZ/i1eFQtvT7kwHq8HbBr2JXajHMhQAgiWfl8dsq1DGtwxX7OQkB2/3LCzeNjw05SpdrTRYBs5nf8MME4R8ff+o7lP/+n035428hRlseRR48SjgrgdIU74IjMzSxaAUqrytk68nqsliqG9HpS25leMkBa/1ytBG2gkbjdAJl4SDRCv+n5Tdz0/CbOHNqHvYcC1DQGHBN8xmvdiAyRZ3BcINFG1c85rVcjVXstpjfXjTvbRcvhdly9VN4rfondfRNr4apUEwayWCG+PSwevqD1SNOzrzIX7Vil1HW4e0kizcaHplDgkZ+tsHyfnbBt57o63l+yI62WOGt0RuHxJL6gX5+UJK6jclwuyjKj2Aug6MAG9o6YTQuJ9zZ+6pkASurXU1U6m7DIM+w3ed9FCQs24WrD3WtjApnfGh2kkgrCY98xISX8W+iHvJ99LgSMi4N4FbbdkBTAMPFMV7iDVgO3i9QLZs2i9r77IUkJX1y3jub+ozjQ+wzTUyak1zcvQSN8SdNeH/Wb8wm3ubDLV6RKpz+9dl8ajgqJWL2ns06vE/y/Ltmk2QjbEHvvHA9H2ux/FicSMkSewZcOcxtVexIXbsm0q0YkRBonVbVz+6oPDK1swUiQxRsW2xJ5cW6xKfkGvM3kBI1z1bNzXab1abuUOmhlgxmXn2Ywd4FEIVsyrIRt3SfwRLlWfBRekZvDL3oPoM7tQoAjEpcSclz53D1oJp6c56MkkfRZciK0qP1M359sbmJldpKc1YiPykEbQzp362v0D1hP3dNhUyVASngy8m0tEjch8eRJZ3qEnQ7CNTXU3nEnsqOj83uLSN2qxt6r9hOwIPKE7MzbC9FJPFm4ZwYn6fSukrgV9OaC6sYANz+/ifWfHebeSzp1M0s3VtMSNOpTPC6R6SPPIIPuInk4iS7GMtsOxLYlq7HtIJG0ZB1hw5DlnFx4CSPoJOey0rLYbPNkWEXcOqwEb8rJbbDDSOTDJ/Y3PY5dSl13ihtRqi0A3n9+B+1t1gSs3xcrYZuZ25s9tHq5QDVVref5Anj7vsAvivdQ647auUbJ2/ZhHa1HF4cj9G6YxND2IVyw9y+0jhMmZCFRQ4Ls4BFTMZs7lGjjaiV6M7N7jY/KAR4ffaGjqDzSYU5mUsJKdQx3h/8pYbvPo8RU2YFQhAeX7wBgjF3LltuNKy/PtK8ciJF47HuLSN2qN33nCPNuAIhmcjYv0Ug8mlav35yfuj/e5aLktwst0/4PLt/R4ySeDAkxAZ1O5g8u30HIpJUwN6tnxHRfRWSIPINuwaom23K4nXee3k7tnka2r61LiLbffnIbUsoYeVuTeGK0mFwDX7zhM0OUbRVZCyGoqKpIW/AW3mve377340NMN9lut2BIHrEaCds/BqUKN/7ZfCrUznV1vPXEVocLIGOqPB7T+V8qbniaRR/8Ljo33vljQZGS+xsOUdaqibsOqSvwi1ZcEUnBEG0fPX0rPBIZEqghF0OrlrFt5PWGkZthdzZ1RZNipi9W+3nCXoY1TExMrwtttrpO5CsHT+JXO17F3WJUaCfjyF4fvU4OxPJAR8hjQegG05p4IKTiUgSRKJlUNwa47eUtvFRTa7loGPDA/QAGkxXh9VqSf7imRjOziabjwzU14HYjPJ6EOnld0RmE3TmWn23qhAYo/yVNu6B+c5FpliQZwuu1JXH4Ytu9nlq7j0kn9+GS8QMtz9tkkjE5UZAh8gzSQjxxe3PdtAfDSIugMtyh8vH7RpWtGnG2jvfmegi5Ogg3C8NEMtD81ZPJ2SqydlIrNxO8aZavRsQvXCqqKli8YTF1rXWWbXEluSUJ531/yY6UkbRVTVyPxJ2QeLJgzQwVhYNM71kqeFWVBQcPx0gcoI9oSVB+x/dh71pWFJskVly/nh3DriCSlZ94UMUTq5Pb7efGzYzd1wEkknm0Jc7ncfHAZWMZ/K3fOHAoE3z00SnMLb7T8WePJEWEk6s+QBXCVC3vHjAggRCTa+H1Dz1s3bedVFMnHEb6fBBH5HtKZ2FV4/YqLYz4eI7jVLp+vanU9Es3Vkcr7V8cdIGcFU7U+jhkiDyDNJCcyk3VR90duLOUWA3cyrAFMJCzne1rqlq5WTSdyk5Vr4nbkaCeUtexc11dypq2WU08PUW6xCuOMi3/UUsSr8jNYXGf3tS6BTgkcUVKIgj6h1X+9UgiiUOK9q2kSDDiyTPdL74uLm32U3AxveoaIJ7MBQP9Ps4dWciDy3dwc6PCpWdczY9W/xWhWq98CgONCOBbQ/uwaX8TrR3ONQfn7K9k3qYXcZmsrJJrzPFjQeORTqROIDEitR6aIpmW9xfAWSrdSRSuw2la/Ysk+xO1Pg4Zi9YMHEAfn/nmY1vTqMdqEGn8hun75vXJTvCInjdhnqWFq07O8SgrLYv5mifDLvWtO7nFY6//Y9MoW7dntaqJ6/avJbklhpT6mlf2WF4DGD8/dC6iUpO4xCuaOa/XQ/yw/xwLEheaCr2wL7Vu54NRvKrKb+sP07J9EWOqZnNuS+JCzuKWx+DOSSRHqyEp+na9sGI3TMWjZjF530XxV8Hn6j94au2+2PjMl/uO5ffjr7YlFCkEEvik5igeV3qPxblbXzNvdUtRY9ZRMGsWJb9dqM0oFwL3gAGd3zuA5f2JfuCmvT77dHrcOZ32tDtJq7uE4KGrT2eg34dAc3bL8XTeW11kONDv4/tTBjOwmxH1iVofh0xEnkEKpC+o6oQ7S2HklOKEGjlo4zclMiEl785SLAc86CQ4f+V8w2tgTs5WtfJeWdbtZPMmzOPOVXcSlhpBDWuYyJj6M03NZz74YBv/ErrKMpUupWTznM2mr9mR8Xk/MJlUhbO56oII3+612D6NnpvD4t5+jcCdtJJF2bkkHGHekUa+29bGL0GrHYfgVvcSBohD1Mi+5IggfTBvOQMoGnc0Ib1rVv8WajhhDKq+n+kwlSjiFezJdXId7540kVsrn7W8NiX6ORsd1FmHF+Vy4Egw5vddaKWMV1XHxJhOpK54vQmCt6FVy9g6aq7x5ykE79fP4cy1u7FKvdu1llnBaVo9IiWXjE9/kMmYu15PKyOSQQ9F5EKI7wghdgghdgshDE9bIUS2EOL56OvrhBBD4l67Lbp9hxDCeu5kBl8Y9Aj8kZ+t4K0n0o/CoTOqnH7tSM69bmQsFZ3XJ5uZN4zi2zeMTthmOaUpirLSMkpyzadGmUXS8ybMwy2M69S2cBsVVRWW58jLyuPMPZfzkzUPMXP39ZbDWHzBXrY2sWbXpCOtQSdRpIrE3QQdkfiCfn2o9bhTk7iUFIQjLGo4xJa9+3njQA1lrW0EfCV4oqHUMvUszur4A6XtT3NWxx/4WD3ZNiovGBJIHEJicgfN7qk+TMVKFJCsYNfr5IaPZKNfr/eZayHMcOBIkAmDCxBoaXVpcS+7OuUMgM1LKNh9GyWn1+LOAwSIPB+KDBJpPOL4MFra3fz67FrLrJCO+UtXI+z7Lh2beqck+H2eLp3r64JuR+RCCBfwCHAecAD4UAixTEq5NW63HwJHpJTDhBDXAL8DrhZCjAauAcYAA4C3hBAjpLSST2VwrJEcgacSVCkugcer0N4asWyTGjG52JSkU87PToKVkK22tZbzXzw/wcGtrLSMRR8siqqwOxFSQ5Z18p3r6rji3Ttw4bGdigYQUqyJNbkmrh9br2+73NbHNvXGBtsWvTzXQabmPmlfC08jCi8Jq8w7bKx/gyDnwoXkLXWbmnGcpXyS8vC6+G3XsiL2lF4MSWp0XezWv349H50MI6u1yWmW4jgwDQ3j29B0vDpkCrP2rjH8ZMNorWpOEQhFWFt1hOmx2riJHWw6JBlrDTugzYwffj589Ex03KwP1DBIF7KljQiCZGLeUzrb8udqV5ZIJ5W+dGM195R/Yvpzt0JXa9aXjB/I+s8O2/q2x0MRsGD2mC6d6+uCnkitfxPYLaWsAhBCPAdcDMQT+cXAgui/XwT+KIQQ0e3PSSnbgU+FELujx1vTA9eVQQqY9Xc7SeHqcDK4oydhNyWttrXWIHxrajc3zzBTu+9cV8dbT27F7dBX3aNm89M1Dyeo6QXCMJBFP3b84siu7cwq8rZr0ZtT+GPL4+lReFBJnXzzurwsGPQdyt79g+W5GHcVR54xz2ikM6wk3OayFGm1Z/ehtSTMY1e6+c7bcMFGLXVoJXrzRnITr0OAd8ASgpBA5v91+uUAXLR3LSLK/gHFw/8bf0XMDc4pIlJ2vTa+eQlNf15A/dqQVruO5qndOYXklTTR8tdywm1+XFm9iIQESPufnaXYTUpDmUJHspLeDtpEsy2G0aF26J3j6VbN+t5LxjLp5D6Wk9Tiz3P3rO5PVPuqoyeIfCAQb957AJhstY+UMiyEaAL6RrevTXrvif0TOcaw6/t++8ltjlrD7OrZxxr6lDQzJXuyKt2qTg5GtfuaV/ZYttGZQY/Y8zv6MHP39czcfT35fbzawqY08b6ksziy8m/35rpNuwS8wr5HenFvvyMSL8ktYV6/yZS994j1TgUnsXRjdcpj2UECzfUDQbGfcJZX6+IvTwZpOuyN1f+s9m/JMqaahZB4S142JXOd0J3gnP2VzN36GkWBRlQhEFLS4PPz+OgLHdXGmx65g/rHXibcInFlC1TFjYzV4aOP3+ifXLjNTeOeXPQlUaQjtRCxrmiS5WvuUGusjS8Z4Zoads2YadtmtnRjNQ8u35F2v7jP4+LuWd2PkLtSXz9R8ZURuwkhfgL8BGDw4MFf8tV8NZFKuGZH4qlcxr5oWKnP47dbpeLBSPrdGTKik3rL4XbefGwrbz62NeE+pXNsq5R+2CIaCkvrP+GK3JyUqvTYXPaWVij/JbarmZl38eDfd9geLxWa9vr49EM3XjWUQuwmCNRnJ+RH+h7cQs3A6QlpZIlkr/9j03MJJWQqfHMKva1Mj7r1FHr/QKOtcE64w+yaNIpwi3aFRNPhkXbQEvndmUaXCMu0upSM2P2C7XvNrGDjybsrrWMuIXjgsrEZAv6C0RNEXg2cFPf9oOg2s30OCCHcQAFwyOF7AZBS/gX4C8CkSZO+SB+Crw2cRobuLCVhvy8zAreCEwe3VGr3+Pfn9cnukYlhOnRSf+fpbWk101r15oc7zA8QxlxQpKfU7YrWsfGuLa3wt5/Zk7ivD4y7imqLtDpodqbTUtTJP99ckJCOthe7JR7oUL+xhs8jEAxpPI3VvGR6PuFppHeOh5Zg2NTW0w4/27zUcoKa9UeUyJBCOJR6z+5DWqfVBQzs2E2qJJMMBvnsd//OP3+SayDvdB+yuglPhsS/ePQEkX8IDBdCnIJGwtcA1ybtswyYg1b7vgJYIaWUQohlwDNCiP9EE7sNBz7ogWvKIIp0x1rG18qTPdOPJzh1cCsrLTOtqevQSX/qxUN587Gtpvt0B1YEbAW70ajpwC6l7kVhwbT7tYXO5iWpI3GPDy78Xcpzzgndwd+zbmEk1VZBIpE2JUZte0pnW4rdzFLCTgeoJBwOyWvqz7mfK0HR2+UOUiP78bZ6OjOVTabf791bRDDUlcfjsSRuHRJ3niBv7GDcoRbCJgLA7Fw3I9auoam8POYkZ9VS4DpYz33P30FhoDFWNnCiGdDLDoWBRqRQUKSK8qafnUCkqSnteesZdB3dJvJozfsXwHLABfyflPITIcRCYL2Uchnwv8Bfo2K2w2hkT3S/JWjCuDBwY0ax3nNItwdcdxOzUpkfT0jHwW3ehHmWUfkD6x6grLSMEZOLqd3TaGopmwyJTKlq7ypCQdU4PzrF1cSjIjeXxb0LrFPqUrLg4EEtCn/oNMNsagOEC2b9AcZdxZ1Lt9ju+umiMtrv+zkiLoiNH5Xp9kUII/BEr9lO7GaGdGrkOiRwxUlZ/PrQk3y3NUiW0DIeg8RBbhBvxRYcyd9HtnwxlJwKwuOB3FykCTE2lZfDUnNy1n8/4/vTd82YaWoFKyA2Ja5/oJFbKp/l1spnqbch9eSyg67GlI2NsSxAuKaGmltupeaWWzvf6HLhv+pKSu6+O91bkYENhJUD1vGMSZMmyfXrzUUcGXTiidtXpx2JH+8EnoxxT4yz9TfXFeRjn7DuTV00bVGM9Heuq7ONzENKBzsLP2Bc4FtEmo+NMaJQ4NtzOo1hXnloAwd2WI3jlNxYfBngTKFeEgrzxoHUixVAi8SjJL50Y7WtzzXA3mtb4eVOBb2Zv7cEIgjcSFZPWWgudgse4sy1xnGgtUWT2D7y+0ils2c4IsK8M/SZBL91M7hVlXsPmrXUmWPbcyUceyqP1s8VAarEPWAAedPPpuW9923nkuvYNWMmbwy/3bJ8kjxwp6m8nAN3/Aalo/OZkDiWyAg1+nq9z8+6/qOY/Pm2aARu7ivvFP7vXZMh8zQhhKiUUpqqG78yYrcM0kcqEv+qknc87JTp8S1pJbkllvsZ+8rNH28qKu+VPsdn/TdTduZEykrL0i5dOIFUz338+AAAIABJREFU0URzj29Nq1CZSqHuVVXmHUk9nxtIiMSXbqzm5iX2JN47xwOv/VvCNjN/bwG0ZvkIurIorVr2/9n79vioyjv95537ZAIzhIsJEYqAiGioIVRAbl5aXDdGUteC1bpoW7vutr9Fa20TjBqUQlq3Vbpr1+1lla6opKwbjaOCiEhAwBKCIFcxohISbiGBJJO5nff3x8mZnJl533OZWwI5j5+W5MyZM2fOTM7zfr/f5/t8cVCDs5v8ubGXw0ypJkIJmUxYMlxcNGghc2IVQIOpKXOI6FGtW52gnd26085yEZqZEIQphff4cZjHdDB764k9/vvrLilB+Wt7sWB3bSSNPkJlXrv06V3ia4vuwU8yAGx7dY1B5CmEQeQXISRy4SE7x45Fy2dm8IzSByVlOtCbZldKr8sJvq76MFgkTkGxb8QWMfITeslfXoY4vKMFm6sPqQ5E0QwN90o7zgFQUahTGrFY1RSRyiLxipq9WL39S9VTeaLkKuD1aPMRnr/3oEAX7ix9EhP9ZtziM0fdhJTc8sSaeqyDlxXf/KIYh4bXq5rdCISgbPhQNNhtqGhVITACVaEY/8kUMAM0SBAaNgJf+8XPkqoTx34G4R4SPeX0cEs8nQEBkx57GzaLGW2+YIT8ccnX8dbNX4/s9+K6ZZG0uhpSmp+4ADPB/RkGkV9kUKuLs6ZqXchQMomRIG0nIIpEAfBV4wQEE09Px4nBR3FkeD2z/U0i9ZQTOgcUFN5xNVg5vKfxg0NkeaGwpnQ6pUATHYbngnfh7f/zoE1BoS6Hy2ZGqXkrgOiaOA+neuxQ53RbYImlhwTEbuFgfHqeC0KwZrAYwT56pi3qklHaewnDAT1lEwqh533EisXyPU5sLWHPlNeCmoYm7kLqxUm34BtWF+MRwEmBrqCArh4zlTCHOF+cdEt0rdvABQmDyC8yKLWYXQypdBaUTGIkVH5YqUjiy7Yvw+Zjm3EbfsGNcqRJW0eG1ysOXwGAcDD+tewuM4ZfOkih3q0dFBSfjKjDkRG7oBQraU2nd1EbyoI/FIehAAC039hfnPoF8HoFZ+Z1dJmi22yN2KEOpuzz5juVCWLKn7F95n4BW6/SmArvIfODwqWoam2JDH3pVa2fAazQfAlOOnNw782PMr9dx3WaqcRCaVzoplFFmNzqh53ETwYMCNpKPdKC4/sH3sGwrrMghOiKlsPEJI5vNZvjZ6crwTlwZ4enA8YY04sE0qATpVrtouUzLzoSl0Nt3KmS0nzNoTXcRYAcUqsTUUjj8hZTVrsFbaeSu7EDIol/Neggto5j90737khRqSLwohQ4I2THkLh2fG/6aHxj9xIgHODMvCYAoRAAnHB6sPKaXjvUkIldDhH9wRlkwpuJS0y45WN9FqsgBLs953C9477I0JcnQt/H3OC/4wdHfopgWFuMQwG8PPnv4eYM7TARkpQbntpC4BO7JX5kL6UY3fwRrv9KWQAoYdOoIszZ9SEmHTyAkb/+Ve/41JjveOwn0m224vfT78aVBw/gyn2fgHi0D54Z+eRSzfsaUIdB5BcBtMyqTmTi1oWG4rHFqLyukvu4WlodALrNnYqPS61OPB93gC8y7Gj1K35G2nrIKc7Yj+Otq59X3TMvFFYkcYECfwl/E0WBP+gmcY/TimcXXoNl7Y+KQz3Ar4mDAsWl/4Z7b66IamWa7XoBFsSQOaUYenoveqVtvZ8ZdwAIITg++i6MP6WPzKWRpxKcVjN+s+Dr+MVnb8MqaI8u1+UVojMQikyFkyNMKcpf25swmY9UmSA2PmSKX1QSgtPDC3Hv/rc1vYb8tN0lJbh843u4Uk7qhOCE04PaMTNwwumJWpS9fUlvvZ22acs0eb57p9FbnmIYRH4RQM2x7WKriytBadypFmy97DX+jHFQnLWfAJD6MaXZOXb88Ddz8a37ese7igEojfyPIIyrHW9hbaG6OYuWlDoB8I/mDdhi+1fcZtqi6TwJxCh89xPzRAevzz9A+1EnPn1jBPc5FhfFdx3bo7bdZtqCKVnvYqLjPYhNTtILELTkzejxECcw2QQQaxgAxbjG12EKsxdCgtmOmUdvj/xOKSAIJtUssTTyVLIWveHYLs2EJEcwTJHtsMDMyNT4gmE8vS4xa1u1CWK88kTYmg1h0HhNr3HXNLbldYTUD+zHQ99eiv+85h9w780VUYsyT5bG8aGEwDJyJEY+/WtDrZ4GGDXyCxhaWp8u1rq4EpQU6mo4MrweE058A6POT4xLxRMQjDo/EeNPFaHoCv5Ncsb8cdj4PwcUp5zJIV9oRZnxSK5rwdj06igoQkNKHUCUGcrT1v9CJf4CDzpwlmaDEMCDDhynw/B0aAFeF2Yh3+PEIzdfEWXBya6Ly17DLGBEQTtW4HdY7vgdwtSED4UrcZ3pAAgBjga+gdh4QjDbI4K3cMCMXxd9Fz/dXY3ck/UACPZfeS9T2OcIuTD+VJE4iY4ANDgYwY6JsA7ZzhW006Anylr004f/UfGaKaFNYcRnorXy0sJ8/LR6N1jusgTAoBwH+++fEBwZVwqP0xqlWpe38BEAd08fjWWl6vO//Ryvf/lCiTidoL7490mcTkxs2KX6GgYSh0HkFyi0uLZdTG1melA8tjhhIh9/qgh5neO49XQCgplHb8f6Mf+hfCDSe8u0u8yKCnauj/17T8aRuNeVpcm6vcFu02x+AgB2EoYdHQCAoaQjsv1Schq/tf8BKx2vAr6zwKZLAfPjwOQFANi94iIoLFlhjJh8Hu4x4nsgACxEwGzzvsjV7RCGMc9HEryFho3AfQfegbVHSJV7cic+G3sb00iGgETEiIAYbftPlAIAk8ypYIL/1M2Qt1yHmtV1ErG4/qt6bBpVBAr0tnnFQC1FrgSeRTwFEM61A63dYAkeg3YPdj9xU8KvK6GmoSmifo9Fu6938WKy2xFmELmB9MNIrV+gMNLpynCaE7txTvvyVlgF5ZnkjpALY/dcx3xMWmCFZTe+cJDCbGMvDOwuczyJ76mOs0/1urIwe3Q+yoYPBVXpl5ZU2bNH58PrylLeVwPMNAT4egRo7V+JWYI91QDE0Zs8XH7byQiJR52e7Ods02nmcy3BToAQdBROx7CuaAvWcY1vcJXVct91Ghbfu/9EKbqPL4QQygKlPWn3kBPdzd9B6FwhOgPhSB3bkqevLEOAqFo0r82rqc2HmVUbE6qVezhCOgA4fegceF0L9u5WfHrjTaKVaxJQKgvIFyjhdrZuhPp8SZ+DAWUYRH6BQYs6PTvH3u+mlfUnKKnXlQZwyJ9/9cnZOLwjvpectcAKBQRmOxrzXKR0egyJVw7LQZvZrGp60ntggjazGZXDclJC5lEI+sRpaXuqexXOMbBkaROLzch+CSZGn1fIYkfL8CI4N76N89boRVnuyZ2KLVKS6I2YumEZ3CAe71whOj99HB0Hq9BxsAqdnz4RNd7UFwzj4eqPsTxvru6pX6y55KxaeVObT7fwraahCZ0BtrcBAGTxRg9TinGNb0RGlSZDpEplAXkNX2kR1PzL5Qm/vgF1GETezyER93MPbMSfH96MDX/Zr0riF3ubmRb4wvybj5J6XWkAhxwEhOmex/1sOC8ZZ0ATk073urKwZPhQRetVJXT3WJPWZrlwRshGK82GQPnpWq1o/9yGT+99FKHjTYh9c8QsYMTk85qOMyGrDlYwSgA9xjCOcBBDSAeIOSb7xFnQEBDMaRTT/sQkRKnS1RCmFO9rmPoVC8ngJvZYrEhaj/CtpqEJD1d/jCCPrAF0mdUXdrS7GyefeVbTa7LOwcS51h6nNUovMeKhB/nn0NZmROVphEHk/RixbWXdnSHFaZMDPZ2eChz1fKKpTQ1gk7ZexXpkf046vXJYDgS1KFxFmi0QgvLhuZjm+GdM8f8BY/0v48Hgv+CYMAwCJTgjZCNAtctlJIGbmFYnkLeKWbJCyPtGOzOlzoMf8V7hQG+dXAiY4B7TBcja0bitaACsgr03Kre2wWk143vTR8OqgfQAcUCIVlAgYnATizYfW/zGi3AravZiXPlbGFPmxWXlXvy0ejc3VQ+I7XL5czkLdkJES9seJFL7r2loQvlre5nn4LSaUXnbVVHb3CUlMCv0kie6mDCgDoPI+zHU6uByGOn05DH+VBEmnp6ueUQpi7RnzB+n2ZQ6svBipNMB9SEogNhmZtXgxEVMwajo9A1hFmYFfoex/tUoCvwBPwv+KIrYxcidTfI84xdLVphbF1eCYp0cgNkmoP1zF3oXDcp1ckmQCAAIZ2HF7QVYVlqAhd9QUfv34MVJt2hOr7d96zbsGHutxr1FSCYxNQ1NmFm1EZeVeTHpsbfx0vYvI6RJVbImUrvc3QsmcfeRO+Tprf0DYm3cx1CrS68tj8YlDLrl77jHS2QxYUAbDNV6P0Mi07QGqjpdCW6bG+0BvmkLC1qEbnLEZj8O72jBtprPNE8siyy8nmGr07lDUACAUrjDAspbxVJA2fChqvVzqWdawvemj8bUr+Xg6XWHUNs2C97gbGb0dZtpC35rfR4WIi4qecYvrO3S4ZroMLwnXIP5lh1w43zUWmdG9kt479z/g4DoVHTI6sLGuf8Bu78V4xrfiPJfzz25Ewcm3AlqYYsaHSHRg9xmMUUI5/2Dp5j7AsBEvxlzui0YTAnooJl4f+5MWIKdoKAIW7N77GFNkXO55ORO5D/9a1xZUoIVGka8yhGmFI+s/RjhMI100PNU4SxYzQRP3/H1yPvidUXIsxbhri6019bqMmJp4mQOBEpRWpiP9tpanPjlcoR7+u6JxwPq59+3pMVEe20tTj7zrKZRrQa0wSDyfgQtLWWxMNLpbJRPK8eSuiUQoP1aahG6Sbh6zsio7Ifezy47x44Jzs0iicdE4lJKnUfMJkqx/NSZ3vYyYkaZBhEcAWAd3IARpuui+sGlf6VUamwU9oYwCwgCVdY/IYsEYMkKM9XqsQI3gQIPBv8lyjXuidD3QQCUmLbgSdv/wI3zmJBVh83nfgA/3DEnLL4nv2MoDl5xFwBEkfmVh1/l9pQDYobl02H1qKjZi2WlBXEpbTl5i9dH+lf8v5AtW3Yu5qhzeX/ibDzZQz6lhfmREaNaoVT3VkNYoKh8Yx8eWrMbMyxOzGS9bMw4WNrWhubHxBnvWkizpqGJ2+Y40uNEe20tjv+iDBB6v+9qRjojHnow7nmh48fF3zWelwE2jNR6P4KWVLrJTCJWnkY6nY/iscVYPns5PHbt9U6tQjezjSBvXPRx9ZRBLDYTZkw5xUynA8opdYcgRJM4AFABJp4PuRwEuGzCZmwtu5GZFi0tzMeK2wuQ73GCIFp5/YYwC2XBH+LY5x4IofhbPEvgRnqeFwvas/2a7v/CI8JP0OXM49bJJQhmO/ZfeS+2Tn+yx/VNJHXCGV8r9ZTToAf1HzTh+Z9txsNtTvy43YEft9nxszYHbvVZ4aYmkJ7/tEIw2zHCNA6//vFGrK7eD0BUbzutqZxfrvD6VKy/UwCFpwWw1qpWIRA3QU6P6I03rIVAfK/Nv1weReJa4C4pQfPjT8Q/TxBwfMmjuo5lIBpGRN7H0JNKH4gubclAmoomwdvoRXldOVfMdtTzCa4+OVv1ph4OULz7wn40f9aGuXdNBKCgVo8DxQ2O32DCvq1gKRfV5oozHdvcl0Kg2m6qrPGrcpQW5nMj9HNfOHFqtztm5CUFsQrIKzqnuzYOAGsD12Ft4Dr8iAButSCVkOjo/NRHmCH8GR/ix2AJE7IDQ/DP9ZUAgDBCIACyKGHuqxcEBK4wcGpjM1YDkVq1FJlrMe1JFhP9Zjg57yXI8VHQWqfmCfIoxO/IAZ02tpIIjuX8BgAIBnWn/g30wojI+xBahp0AIoH/+PkbjbayJCEndRbGtF2tKzL7ZPPxSC+5VrV6tukUJmRt5pK4UkqdOQTF6gRuelyzv7za+FU5YiP07x94hzG3msBspUwSb6XZcdt42OwIIaiR+gSzHYfHfwe/mnI3yt0/4i7MiOy/dMEKgtaNLTi8owWlhfnYWnYjjlYV45mF1yA/CTc3NUz0m1Hss/JH7gbYRKtV9MbzUB+i1Vs9Bpc8ukR1H0PVnjgMIu8DSL3h776wXzUda9TAUwdvo1dx/KieGrmEuurDAEThm9miTBgWdGNG9kvcx9VS6nFDUIgZKPkdMHkBFk9ZrOl8u0Jd8DZ6Ne0LIEJOn1cVM41PALbITQDw77Yfiqep4XUO2sN4xxmEEOpAxH5NASGrC0WDZuJWnxWkj29jJgDrX9iP3y9+P7Kwk66bkisbC9+bPhpHq4rxrGwhEHv9JvrNuMVnhYlzZSkoDgon0G2Ofu2A2Yovv71I03nwLr+0XanNLBZmj0dTpG2o2hOHQeQZhtYoHDBq4KmEt9GLyg8rFVPQWmvkcnR3hvDcAxux6eVDKkNSKG4Y/HtMyKpjn5/elLrVCXz7+YjnuVq2QUJQCGLlrpWa9o0FL5qzDI4hK5MNptv/iMqKpXHRqRKp5578CLO2VeDGD36CSQdehL37DJ9RCIEpTdG2JDdwuCwRPQoxKafKCQDqF0suf3r4gwiht3N6yXmQlPWs6J5AjIhv8llgUXjfPgK8lvc1rLzmDpxwenq77wUBuc+twN+mz8ZP76/CZWVerm0s77yl7VoibAAAIZr3TaRFzoAIo0aeYWgRRRntZKlH1UdV6OYIoyTsGP0mbvjsLph1mKNICPqVLUnFlDqDxIkZ3iwHKocN0Z5Sd48CbuodXKIXzZ3N8DZ6NZO/hBEPPYjj5UuAkMyNzmLBiMeWAwoRV2zd/eHqj5ltbvfufzuSus89uRO5J3eiZcRURWV6shDT8gSDNOhPVlfvx6mNzbCqLB78nWG8v/og/vZFK0wE0CNQlzzZY7sK5OLE5x7YyH1+EBTvOcRruGlUETaNKsL1X9Xj4V1rYOsp52S3ncY9H76M1mvuwCYUofy1vZHXAXrd3JSGv7hLStC1axfaXnlV8f2Y3e5INN68dKnivkrOcAaUYRB5hqEWiRup9F54G71YuWslWjpbkOvKxZxL52Dzsc2R3xdPWaxKRt5GL1bsWKHaU+4wO/DD27+D5ufszJ5cq92sStZ8CMyUunewBytzR6E5yD+3qJS6Mwf4xefcffNceWju1JaerPywEoD2SF4CISQqMlUqVbAgkQWrzY2Vus89uROHxt+BsE1Z1a4GqY7uIwAohRME5wjFZkcIU+fm4ycaRnnevWASVgNo3diimsoMBQQ0v9+MsDv+MafVDIfVhLOcsadNbT48uGY3ltbuwxMlV0WROMvfXwIFsMEVxEFr9HW9d//bsMRkohzhIO7d/zY2jSqKso2tfGMf15HOaTVHeatLc8XbXl3DzZxIPebttbWqpG8I3RIHoRpcofobpk6dSnfu3Km+Yz/D4R0t2LBqP3jZ3YGuSpeIWysZAYDH7kHZtWVMQpLS6WqROABUza5C8dhixWhHbRwpHxQ/zr09+tyGj0LlIBu6qULqlVJUyVvNbv+jYhTubfTqGt+a58rD+jvWa97/0xtvQuj48bjtlpEjcfnG9zQfBxCjvljSePWtx+EOxPuut4yYioNX3AXBrM/+FhAJXCLsg3b2Z2cmBL9Z8HVmSx4Lh3e04O0X98OicuukoNhlDWN8yITBlEQWEVkwwZxtwVukG3vMyql3+az0D14+iE82x19/CV2E4jl3/HfdW/Mz5sJDAFBc+m+R321mggAnfaB0jY7edx9827azT8psxpX7PsHh6TMipM4EIbjywH7+4wZACKmnlE5lPWbUyDMEqTbOInGLzYRv3TdpQKvS7193P8rqynSROAC0+dtQsaWCKeBauWulJhLPc+WheGwxDu9oAa8dOzvHjjkLroDFpv9PJtsU4yjmHoWVl4xUJnHEpNSdOaqp9OKxxXDbGCEgB3qvNU+MlIhIqbQwH7ufmIeZ40Qb0eu/qoczyP6sck/uxMRDL8MS6FAVwclx9ZyRuPSfJsL7NROXxAHRaU3PVLIJ03Ix7IZc+AhV9OUnIJgSNEd61bMoQVbPLTfcEcLN5y34WZsTP2q3Y6KfrY/wBcN4cM1u/P1P38HezfzzC8lS6rFgDXUBAEoIrv+qPvI7j8SBXje3WDQvXconcQAIh9FeW6tM4oCuz9VAPIzUeobAq40TEwa8oG3Z9mXY3qJwM1BBiIawYseKuKhcC1E5zA4snrJYdaElz5S8+4L2yCFOqd7TLtbSsEz5vKJU6ibgll9per3yaeWasxAAdNXKLXl57Ig8CZHS6vtnoKJmL765bhlsCkJEec38s7G3oduRAwoBkuSNBanHv7QwHzOrNio6r0npZa1R+d0LJqHmcjeq//cQCs9QOCl7PK6aGI8AcFMTbvGJIjYnSFT6X/4z71gUFG87g9zFyouTbsHi3WvjWgfNlGLx7rWwmU1YP7KQ+Vz5iV5W5sVIjzNSv29eulQ1XU48HhwvK1c+ds9+/RGszBEhwN3TRmOZhnJMpmBE5BkCrzZOBQxoEgeA6kPVSR+jPdCO2a/OxrLtyzBv7TwUrFL/I/PYPai8rhLFY4s1L7QmTMvF1XPYM7ijQWFHu6hUd30IgIgitZLfwZvt4teWKUVeMBSjUhc0C9uKxxaj8rpKzX3lS7Ys0dyOlj13Ttw24nAkLVJaVlqASzitbbHIPbkTE/Y/jv+a8SA2jl/N3S+2r/+Rm69QnX6mx2IVEBcILy+7ES/nheFL0v7FAjFal0fusT/zcI5QxYzDplFFWHnNHQgzvnOOcBA/aXxXteedUrEGL81Uf+/f/yLWxlVAz58HwurlqP5IRBU1e/Hgmt1xmgFKgZe2f4mKmr19dGbx6I/X76IEzzBE79jLixFax4aqoc3fhjWH1mhOGdfdWReJRvUstObeNVEkcwLIR2vKnoWrHW/hh7n3YoJ7p9gmVtkGPPQJvNkubhucQxBQdeoM1h87Hm/8ogPFY4ux/o71mtLsAhVQVleGglUFmLd2HpfU22tr0f5/NdEbCYH726VJi5SU5lTHX1lg53jx52lf3soluFjBaGlhPp6+4+uq56L35lzT0ISO7hDec2o3tEklKMT6vxo2jSoC4aSvradP6rKY9QXDsL34vLZ0uAYSB4Bwu74BR+lGRc1evLT9S8V9Vqs8nkkYRJ4hjLl6qK7tBqLhsXuw8IqFKesbliJWyZyHB95Ca+5dE/Hj/7wR2ZaziO+OJjga+EYkApdH07y6vQlg268mgXOBc7r2b+5sRuWHlUwyP/nMs6DdMedNKTo+2JzMKUaOzUPsMokAuGEPMHNfWNHAh5XlKi3MV408V+/Qd3N+et0hBAUaMbRpJ0LKFqZqkMR0StG4HNxaOYDX/+3PcFhNmrv8cjr1ey4ogbi1azvSDS0kDojXTauuIt0wiDxDOPrJGV3bDfRi4RULUXdnHSqmV2DF7BWwmhKziZQQWxfnRePcVsA91cAzVwOVHnSE2DfHDmEY8NAnUSTubfRyswUUSCmJA0CuS3/JpjvcjbK6srjoPJVCN0C8FvPWzsPkVZMRZNTdJVASv0xyhIC7PwA4duKKWS61yJPS+Kjc2+jFrFdmoWBVAQpWFWDaSzPxjWd/jcvKvFHp+IP2MP7g9uNNZ5AZnVtsvQOPkgEFRTsR8KYziO2ecMQ2VRpyk+9x4nvTR8eZ8Lw46RbmLEACYNH+t3G2K6hZc8ZbFCSK/kJENQ1NuiLtyjf2pfFstMMQu2UIPLLQM3f8YoXa7PDNx3qjPikVvmTLEs2DQuRwmp144ronUDy2GKv+tJVrzsNtBdxTLU4t65kfnm06jQ5hRPzzLdE1X6kVjofcoHp6VC8WT1msqx1NDik6bzjZgM3HNqNiEMVwRoCvJnSL9QKQrGQlQd596/jvmwIwcYglaC8CDcSHjyYzUfRhkMRsSvPDX9r+JaZ+LQelhfnwNnpRsaUCIdp7nl3hc6Dul2HuugOhc/EiMSlClkakniMUX7thZGSwChA9LMnhssDfHWLZ78e/b1C84wzi/CU2PHJzgSZxXk3PvPRNo4rwSP0rzH1G+Npw/Vf12DSqSPV4TqsZL066BY/Uv6KbgEX7nXioqtozBN7UNx7afEHUNDRpFkmmCwaRZwjZOXYmaRs1clFpHXuzlCN2YpdE5krP4cHj8KjWxQHwnfXeezJC4gAwI/slvH/uXxCCI7LNjABmXB/9p6XUCsf0UZfDPYr/mAKKxxYnTOSAGJ2vOSQKml6+nuCfayls8rucxRIldGMZ+Lx+5PXI+27ubMbjWx8HIQT+sB8z94Vx8y5l29bTg8FcQHx++beZxGd1mFTFo6WF+dj5Rati+vSn1SLR/+ZQFfM7Rkxh2C95g0nkgEjm8pS3c++XcF3ujtzwJ0zLjZtnLxG7j1DQHqV6NwGybCZQP40sLh/UKY6Vz0s/5fQwhYUEwOLdawGAS+YEiKjWn15nw5tnjuLWo9sUyTxATPBZHRgU6MIppwfOcACDGV4BIKRfTD/TK3gEoKvbIV0wiDxDGHP10DgzB8PFTYRErLwRo257fP1Meo4W1zY5WjpbIjdNHpiLqz3VIonHzA+XbFe3dXwPHcJwcaPZinc32LBt19ZIVM8dH8oZTep1ZWHlEA9aLGbk2jxY3JPm1ut0p8ftTQ3EBEBGniEaQsPJBlyPkjjznebO5sgiQI6AEIj8fN96qkgCpweLC4h/8VLIzcqI1YpuK7umqtWwZ1lpAV6rP4auIDsjI1DgF5sqYRvSxl1pELMPlsENUWTOG1/qC4bxcPXHAMC86ccSe6rxyM1XoPy1vdxWNCDa7S0W+R4ntpbdGLWtvHMBDgwdgwf21GBw0Bd1mSiAc7YsPF8wP+p4139Vj5/XvxJ/SSnFyWee7VMiT7TenQj5pxoGkWcAh3e04OD2+Bv5xOnp/eO9kFA8tphLyjz3Qfm8cbkrnImYuGn3onM34P3VB7kpdeYdtHTZAAAgAElEQVTiKiadHosJWXWYkHcUh6/bgA2r9keEuh2tfry/+iAAcXwo6705BYqVQzwoHz4UuaFwJDKvHJYTmYTWHGxHxZYKEEIQFMQbcCxRNnc2o2JLBao+qkK7vz1C9L4Q/yZDQEBBFa+XhLs2RZMpAFjCgPPfX8Fs17sAoLl3HRDFaoMUdqcAXp5jBg1bQYXoHZuHTgEhbNG0ngzX8tsnc1PslsENsA7ZrpguIASRqFwiOimNzYJkPAOwyTydkF6v8g0TVgJsMoWYYo8FAaKsWeXHe3qdDd8dVYS/P/ExFux+E8N8Z3HK6cGLk25hLgg2jSrCzznp/eDx43G96pnE0lp+vft700fDu6eZaatLgD5Pr/cXjcFFDV6PsiF0iwYvstYScRePLcbiKYvhMDu4pOQwOzDtqxLFujjTnCcmnR6HHpOXba9/FmcoEwoIeG31Fu578JkImq0WUCL+WzF8aBSJR45DQxES5yFEQ2jzt4GCRoi+zc9P2UvZDy1ag6EcAfygbuCqXWcUXycWbpsbd3+gnFL3WYANOXfiuxsdUen8lhFTcfDyhaA0/tl6M1ylhfnIsrJvgfZLajUpuInZF+VBrqaMl5zaeFPH0gnJTa/0Zz/AGRdb8U+BKLc3AuDu6aOZJCUfcfvcC0tw9r//ih/d+xzuu7kCnxbM4o5wFTgXVujx8Zd61TN5fWoamrje94CYwXmi5Crmd5YCEa/6voJB5BmAIXTTBhPHH5W3PRZKdeip527ED/asQPgc/1hRFrkyZXpsOj0KshYz3uepOOc85qYWIoQ7k7wvcWYwezuBmCLXCofZgfJp5Rh6Tvk5jhAQOlcYN0jls7G3MT3XE3VIXH775LhtlsENIGbtHQSSF7oELT3ZfUFWEkoL8zG5spw5Uc4E4L797wAQ0+nPLLxGs4OZnNi3lt2IytuuYl4HEyfDJt/uC4axtHYfZlZtVBy3mgrUNDRFMiVKKC3M5wrh+jq93v/uGBcheC0nqWhFuZjAiwy1qtN5dejxp4ow/dNvK5J4VEpWSqW3fwWlKdTe4aMwb9RITG4Q3eTCLvYiIpE55/0NL19PuFdiULeYKleD3EnP4tbWvhTb5uS35zD3S9QhkRVp2oev09xPTcNZcccoLczHitsLIu1gPMinjmUa7pISrqHLiO42HO0h42TSxdJ1kGap53uc8DitOMlpXYvdfrYriKY2X9qj9KfXHYqbxCeHPLPAy7ZI6fW+gkHkGQDPxCTMEdoMVPBsRZXsRuX9yDxcd2y+4gz4uJRsTCrd68rCvEtHYvKYUZg1Kh+zR+ejYMwolGUTNHc2R1LZ7+dVI2gKRB07aApgx+g3ua99oWDrVWac52SMCYCf1FJVMj8XOIfyunLMWzsP/rByNkre++w3995I7f5W5v7JdH/EpoCJVVuZgFIg6/w/MB8rLczHbxZ8XVNk3lcwc/zNzSk0Z2FF6fV5k5iOfTsuuVLxWOmI0msamhQ/A6uJoPK2qyK/P3LzFf0yvW6I3TKA7k52i1QoQPFf//o+LFYzujtDICYxshio40znXDqHqXSec2m8xzegbUypw+xAVjcnL4yYa81QpntdWXhs+FAEe6Krdgv/xnxkuFhbnPX57XCEs0FBEYoh9ihQCqvJgqCWBuIYEBBMy52GL85/gZbOFgy2DUZXqEu1jp4IHGYH5o+fj5rit3HP2lbmjcxMgX96iwIIY+tV7GskZVaaO5thPq+tbXDTqCJMOnMUJUe3AQCGnt6L4/lzo9LCiXZ/SALJ8Nea4Qo7ARBdKXUIVjw6927uw72CsENcslCL2tMJ3tI2neFFaWE+9pw7wvBCBKadOID/VHn+2a5gpJYtRenScfVCLaVuJgRPfyd6dGtpYT5XzHi8DxdlBpFnALweckAk81BAvKlJGeSOVj/efWE/3l99IELydpcZBCTu5+wcO8ZcPRRHPzmDjlb/Bb0IkBu/aNnOtTslJlBKUXTuBkz7qgRhTkYkO8fe2y/OUaZXDR0SIXGtMFMbAJFsnaFszG28E0Av0UdACG6fcAdz8aIGCortLdux8IqFqJheAYDdx7352Gbd7WcWYkG2LTuifo+0tU2vwOEN/LnSjpBYL996FfPhKJx3AoNV7nuSQcmMU6Lyv2XEVLTkzYir7SbS/RG1CCSAyaL/JuyyOVUJpLQwH6WF+RhTxvawD1PaZ4pnyvE3521PFaxnTjG3j/C1RXrVO/2huGElLOidWieHUkpdPgc+FvkeJ3NhNlLF/jedMIg8A5gxf5yu0ZcS5CQv74+V/9zR6o/qT5cWAe++sD+O8Ps7wfNq3KztinanlGLtxPXa2sw4/eES2nQKz6Z9eSusgi1qm1WwYdqXt8YRudvmxl8P/1XX8WOx5tAaFI4ojLTisUaSKk2C27toL9N9jTfa9JJHl6D5scfjfdd7MKgbePjMtXhuxB7mImvmvjDu2kQxSIU3CYDvf/oK/nbDuxhaI2oMeEK3o5+cwVzlwwGIXugQQhJyBpTDFz6veV/ezR9An7Wkmd1u5qIslal1FnjjcK0jR+LzKvF7J0XLSrVrCcfbfKhpaMLT6w7heJtPc/uaUkqdR+IAcMPE4UwzoTFDDSK/qDFhWi7qqg9zU+zpQizhSz3N/ZXMc125THKO9QxXtTt15XJb/gBZOt25WbE/XDco5SrUWdv1GNkoYcmWJQDAJV+P3cNsD/PYPZHnaZ1JLhl2HC8rZ062IgCm/XkHxvx0AZa7t2DcR0347iYBQ88B3RbAGVJuO5Nj6DnAZG2LuLvxhG68bJecuGNLDzxvAj3Q42UvGbKwiCmZqDIZ9EVqHRDH4bLmmMvH5MrLEhI586J0CuCRtR8jGBY/Uy0p95qGJq55T75HOdPy/kF2RuHDz1r7LLtiEHmGMHvBBMUIMRMIBQRsrj4UsYLsb1G61hq5ot1pz0CUoxs02K8+o9IfrgUyQrBSig7bWQwKxBNOOpXrAhUiCxsWIfNIK1Eyi5D5Iz9n7xAO45KnX8FKQEyD97xMVoLrWMndze5vhd8RPy3wvK0V89bOi3K6iyXuVC2a5JB847VAzeO9qSeqzCQJ9FVqnTcxL3a7VJaQwIrS7RYTQmEhQuIS1BZHS2v3MUmcZX4TC14tnEIcotIXRG6o1jOECdNyccPdE/u85czfGY5EMB2tfmz4y378+eHNeO6BjVi1ZCsO7+BYiWYAWmrkSil1AKi8rhKXnyoCr/U8om7eU63cHw4AZpvy44BIVD3/C5pM2DH6zTjlOgWFRbBh/Cn1gRQSnGYnqmZXoWp2VSRyVkJ3uBtLtiyJG0HqbfRySUzvmFM53CUlXNVzFJKIfKMsPwVgXOMbIEJ0RCt1BUgGOFIXQXugPS3CPwkeu0dzFkOCmllMpvvKeSn0dKfWE52kx2pn+9U/TIbA+YpJKfdYlbuS+QuFeolDqRYuDVHJNIyIPIOQ/JTlAxLkdey+AA33qur7Ov2uViNXS6nnufJw+akivL/6YJzDGhBTF6/9V/UTCgdggr5Uo1QHn/n57XCEXSA9/ymK3mQwEROWz1oeRRLSz8u2L1MUxsVG5lpKEMlArV6eKty1qXdYCwWNLA7MoU5suPI1xeuZDjjMDpRdm9gwmv6UYu+r1DqvRq42SQ+Ij9IBfleAiQA/X/sxAjEpdwfHzQ/g94nL8cjNV+ChNbu5vgp9EZUbRN4HUBqQwCN5rar1ZBEKCNiwShTLZTr17ra7mbVch9mBeWvnKUbiUkp925/YtfEo5y8dKfXvnDuPNYMHMV2weDgyvB7TvrwVJJwdtZ0nepO/B8kwhYWK6RUoHFGoOMK1O9yNlbtWonhssaYSRDJQq5cnC6lvfei5HmvWK+4CTL23LGqyYsIxAUeGp/yluchz5SmKAdWglmLPZAtTX6XWWTVy4nBETdLTA9biyGomCIUpwoyUu5KATi2tDqhPz+uL0aYGkfczJDoFSVLt8hYC2Tl2hPxhTZG/vA0ukxE6r2brC/vg61S+wUkp9aOt7O4AKkAUtz3DV6izUNEqLiyqBw8SV+AaCV2P6A3QThDS40r981IGQ60EkSgZySGReaoj86AJeOGb4rU+M5itWBfMdlzeVoKZ+3Zye9dTBXmbX7KQjxWNhYmQjJEAT7WuJTJOFO21tWj/v5rojYTA/e3ShCefsYRxUtSsBx6nVfN1X1ZawB2iAkBx0l06YBD5RQa1aF+v4C6TArlEa7bylDoP2dnhhBXqFa1tqGhtg9eVhaqhQ8SWNBVC1yJ6c9vcKJ9WrptQpf15kTkhBMu2L+M+P8+VlxISlyDdgE8+86yYMuWMJiMeD0wAtw8d6Bl/aXXi+cml+HToLFTN9uHtT5fj0lNsxbrfnoO7NmnrXU8EiX5GauCl2DM1Ia29thbhjo647cRqTTgy1oKTzzwbv+CjlCuA0wo9KXcWCBDl4KYFT5RcpTjp7pG/Zo7MSSraMDKNqVOn0p07d/b1aVyQiI3Yg90ChLC+74DFZsLE6bkpNaHxNnoVU8Y8SOno03/ycEsLFpsJN+S8gAmoYT6uGVYnUPI7eLNdkbYmt90Nf8gPXzj6hjH+VBHmNt4Z1VMeMgWwaeyr6BxzPKn0rAQtznYsVM2uSjkxydFeWyuSenMzLHl5GPHQg1HR1oGJbCtOCuDXRd/FplFFcYYcLz60AZ2++NqmvfsMZmx/HA8tG4XTXacRpNoFbtKtj0T+T0S6yDsWNQ1NeLj6Y4QZ92DW/O9U4tMbb2LWqYnHg4nbt6XtdQ9cOYktgCQEVx7Q77WhBD296IB4zfWOTy18cr3i1DSn1YQDT92i+XhKIITUU0qnsh5LKiInhOQAWANgDICjABZQSuP6bAghiwBIealllNJVPds3AcgDIN0F51FKTyZzTgaUERuxy4ldsohVQyggxJnQyKNhvdG7REh6SVxKRyul1IGe2vjbiZJ4T7epexRw0+PA5AUoBqLmoEt93HJIdfBpX94aSafnDBuM0tb70XHEj9O77Dg8vyWpxY9aZK72vHTBXVLCTZO219aCgt9LLs2wlpP44R0tCJmsAA1FZUJMYT/GNb6BVtcQ5AnfRrPwe8UmdUoBGnaCmH2gQQ/8p26G1TdV0fwjnSgtzOemf9NdK+cpxNNdH09G6KYXWixy5Whq8+GRtR+j8o19aPcF4cmyglKx5m0mBGFK4/4dkmVVFMT6gkJGSiVJReSEkF8DaKWUVhFCygAMoZT+ImafHAA7AUyFuOiuB1BEKT3bQ+Q/o5TqCq+NiDw9SCT1LofVboIgRA+DCZmC2DT2FZzKPwJCSMT282uDvoaPTnyUkLuW1WTFUzOfQvHYYtVzjtiwLs0RJfp6ICNvFtRU5HLc9um/YOTpaCGNxWZKaPRmLCavmhyZLa6GPFce1t+xPqnXSwZ7Zs2F9TR7rd5uy8Kdf/9kVDTK/HwphSXYiQlH/oqhpxrw2ykL8Lfr34XJpjzsRAh40PlZr9rc47Si8rar+oTEJcys2sgkGTMh+M2Cr6ft3HgRuWXkSFy+8b20vCYgLuSaKx4D9fdmz4jDgbynnky4Rq4F1yxdr8nyNR3wOK3Y/cS8pI+jFJEn20c+H8Cqnp9XAShl7HMzgHcppa090fq7AP4uydc1kAZIve5Sr3V2jh0Ol/akTdAvxE10swhW3Hjkbtz5wVIUf7gY405NQXNnM7a3bE/YIjMoBNFwsgEAUFd9WN2GFUiMxB/6hEvi3kavZhJ3mB0Y5b88bnsoIGDb65/pOy8G9LSRJatUTwY1DU0wc0icAni+YD6cVnOUcpjp0EcIzIIfuSd3ostiw6ZRRaoTy6hghf/UzQDEFOqzC6/B7ifm9SmJA/zZ5VKtPF09yXIXNS3bUwpz7/slHk/aSbymoQmdgb5p7wUy01uerNjtEkqplKNpAXAJY598AHKZ8LGebRJeIISEAfwvxLQ7M7QghPwIwI8AYPTo0UmetgEeWKl3rVE6BWWObDVB/MMdFMjR1EutBWsOrcHlp6eiu5Nv2hIV7RKzdjK3OsVIXAErd63UdCgp/X90C3vNnIqWwcVTFidUK88kKmr2YvX2L6E00DUnyxaV5q5paML5Vj8zWy7ZtQ4K+mAZ3MA9JqWISqP/28K+SaPzIJ0Lq1aezr5yre5qqUR7bW18d0OaPQgAMbUe6/yWaaTbH0CVyAkhGwCwlvyPyn+hlFJCiN6rdTeltIkQMggikd8D4C+sHSmlfwDwB0BMret8HQMJQiJCqe5tHizggOsjXHZiSpSQK2gKIGQKwBnK5h0KQG8vNdBbP+6wncWO0W/qJvcvN/iQBTaRZ+fYe0l8T7V2EnfmALf8ihuJA+rucixTl1U5W5mkncwcbQnS66zctVJ10pmSlWu6UNPQFOm55ZWwCYAf/W0N8o5dBRTmR4RK3ydWZNH4Z0lzyU+7suAYWc1sIqAU6D6+EKFzhWIa/fa+TaPz0Be18kTd1ZIBS7FOu7tx8pln0xKRS4NUFOeNm0lGSD7dmgdVIqeUfpP3GCHkBCEkj1LaTAjJA8DKmzUBuF72+6UANvUcu6nn3/OEkJcBXAsOkRvoO3w6vB6rp0STxHjX4TgiBhCn1GYhOzAE13/2XVioFUDikbpTYc54JKW+pxp4/ccaDqZO4IC6uxyAOBKXzoeV2eho9WPVkq1Jq/6lwSdqxjlyw5hMYWntPk370e5ufLn0KTywz4WmNh8m+s0RRzc5iBDCuMY3QAG8ckMQSvHDJabr8MhCfUrkvsBIznS0dPWVZ1J0JiGTiwctinVJpS71n3uyrOjoDiHI83xNAukecZpsav0NAIsAVPX8+zpjn3UAlhNCJCeMeQDKCSEWAB5K6WlCiBXArQA2JHk+BlIMXovTkeH1XNKVCJ5CiKTVYyGRuASrYMNNR+7BtC9v1Rydd1s6mRkAi430kuJ7TwLhQNw+EUz9AXDrb1VfS4KSWxogGoewSDI2syFHKo13Fk9ZjMe2PqboM97c2QxvozdjZC5vzzlny4I70MXd19xxHrdtegn/ec0/YE63BRZWqSbkQ+7JnRAAbC3g33RHZudhfRpbuFKJTPeVa5lAlmpkcvGgNGscQESLwRrMIid2nmrdRMD1eI+F1UQ0OcYlg2SJvApANSHkBwC+ALAAAAghUwE8QCn9IaW0lRDyFIC/9TznyZ5tLgDrekjcDJHE/5jk+RhIMdSIKxZygmf1UgdNAVgEK/O5BASDAjm4Xmt0zvlDMsu9lNuPKR9DI4lLIzGVol21/mxJf7BqSXyaXRK+JUvk0uuX1Sl7gfdFih0QBW0/3VUNK6fUQQCUHN2Gb35Vj22zfsvMxYet4uLtDD8hkxIL2kwi07XyTNfI22trQbviF3DJWLOyoCWdrtQvzjKWUXstuZscIGagpMVrpjojkiJySukZADcxtu8E8EPZ7/8N4L9j9ukEoH0cVD+Dt9GLFTtWRCZLeewelF1blvEbYzqhVgtmgYBEWqFie6mlFPz0r0qQ7WdblQKARbDhm5/dA4/djZ2DN3L3c4RdzO2ROex7qrkuYwBEZboGaDFe0eOWxhO4pUL4BojkXPVRFdO3XkImU+wepzXS+iP1iT+wpwaDgz5mzZwAyAoH4OCMLbX7W0EhjjdlwURMKbOgzSQyWSvPZJqbKXJDj2L90SUpq49rTaenymiHR/rGPPILBN5GLyq2VCBEe1sa2vxtKKsrQ1ldWdKDFfoDtNSCJUjknefKiyN+eYROQJDrysWYiS60rTcpK+EpwdR98zEV8yHYAvALAThCrshi4FjuPpidgMC4vzlclt4JZ0otbirKdAlqWQm90V92jp1J2sQEPPfAxpQ45Wnxh+BNm0s1Km+7Cj+t3h1JRW4aVYRNo4rw6luPc9PsLSOmImSyiYswhgkMBbj+6iyNwoUCXq081TXWTKa5mbasAMxZWSkVuWlNp1+MMOaRJ4Cqj6qiSDwWzZ3NqPywMm429IUCya1MLaXutrlhNVkjEbhS9J7nysOeRXuw/o71WHjr30X1q6vBFLDBGcqOpN5vOnIPvl9fBVOY/fXt7gzh8GtedV91FWEboJ6VyHPl6Y7+ZswfB4st/txjh9UkMxtei2+9257eudMSSgvz8dsF18Bliybe5wvmMx2xpElnYZts6hylsAQ6MPHQy8g9uZObVk9kTnh/Aquv3GE1pZyAMtlHnqnoXylrke9x9pmDXyZgELlOeBu9iilLCd3hbizZsgSTV03GvLXzLhhS12KXWjW7CnsX7UWWNUtRVCWBFbFOmJaLRctn4lv3TWKSmhIICAQfQSjAjzrfb1mIw12z+QdhpNW9jV7MWzsv8pkt275Mdf75+jvW6yaOWOMdwnj7yZrFaDGJ6Qh0ZOx7WVqYj31P/h2+N310JJ2+aVQR3hwzI07qwJp0JjeBUUqrJzonvL+gtDAfK24viJqLbSYED63ZjZlVG1NmLJLJGjkvyk9V9F/T0ISZVRu53oZSOv1iJXHAIHLd0GoEAgACFUBB0dzZjIotFZj96ux+TexaInF5LVgpNZvnygMBUY1YJVJjkVkyCMGBbR3fYz/IMHyRFjDNnc2Rz2zNoTVpm+ctLWR+/PyN3Ox/MjVzLecWoiFd3+dUYFlpAZ5ZeE2EqP5QeAdqY8hcMnuJhd+eAwrgnSnstPqFHo1LKC3Mx9ayG/HMd74OAqAzEAaF6AWeKre3TEXJ6Ra5SXVxnrjtYk6ny2HUyHVCr/hLQoiGIpG8lHoHMq8a5kFLJC4nr7AQRpY1C53Bzrj99Pp5S7XgZHzeWegQhrEfKPldJK2uRY3OgtZ0unT8ls4W5LpymdoJXs08e0jiZjHFY4tVletA4t/nZBAvEvp7tNfW4quKR2HyB2FXELm9MwV44Wb2betCj8Zj8W/vHo6LMlOlYM9EjTwTIjelungi08wuVBhErhMmYkrYI1yOvjDmUIKWNjOHxYHyunI8W/8sPHYPOoOdMBMzwrJWokQjVaU+60ThIPHzluEeFUXiiVib8hTqsaQ959I5eP3I65HjN3c2RwSRbps7MkSmKO8GfOPcbaCh6HRxKBjGi+Vb0Xk2sVGxHrtHUxkokz3lPLhLSlDc8Stc3dCKW3d58cW4e6JEbiTsx6eeWrxVyL5lXSzRuBy8mm8qFOyZ6CPPhMiNdy0IkNYxsP0NBpHrgLfRq0jiea48tHS2gBCiieybO5sxedVkbqSWSShFZhZiASEkQgotXS1o6WrB/HHzMWPkDNWIUyvkPu+xc9MjLWU6wFRu3/R4wlE4EL9Q4R1LSs3zILUtAsDOwRvRNqYdM766DS6/G9k5DgzJzcJX+88CEEWViZjGaJ1s2B8WlN5GL4Y3jceY7ltxdPwQEBD4zT7Ywg6ZhS/bU91hdlx00TjAV7BTiFPTkok2M1Ejz0T6PtftQHN7/GIh3U5q/Q0GkWuE2shKeTpZT6Qn1WP7MtWuVK83EROybdnMyO6jlo+wbNaytJwza3jLuy/wZ46z4MegqN+92S5U7f93TVEqIBLE/PHzsfnYZjR3NsNETBERoxRVd4W6NAn+1BDrlPePDU8iC9Gqcr2mMVqU60Dm2tB48DZ6saqmJs48yETNeG/8/+DI8HrsXbQ3atEkZcYuhlZPHnhub0BvvRxIrG85EySbzvS9ZMbCIvGBUheXwyByDVAbWRkbpcmHWLR0tmCwbbDqDb873I0VO1akLLrVg6qPqriPLZ+1HOV15czHMkkAE6blotn7Mj45+XXwR29EI9t0OvLzshwP1rgHAxpJXE4QsQszKdsij6pTDZ6PvJ6yQ64rV1PWIVNtaDys2LECtx59MM6jXxqwc/pSUb0v+ckPFEgEzXMqS6Zebna7EW6L/1swu1P3XWCl71MhcmMZvxCImYqBVBeXw1Cta4CaspclfCoeW4z1d6zHnkV7sOW7W/DUzKciSm4e2gPtUarpTPSiq7XTldeVg7BGS0HfHOxUYK5pKb41+BmA2X0cC4oZ2S8BALyuLKwZPEhlfxEOswNVs6si2ZV5a+ehrK4s4yNCO2xnmdvNg7XrM7RqFbSm4NOBZduXoT3QjuwA2+kvOzDkokyba4WkYOfdNRKtl/O+RamSmrbX1qL9/2qiNxIC97dLk66PswRuEolf7G1mPBhErgIthiBaogQ5see5tKWWJEFcOqF2fArKrPf3lZf1hKw6togtBnacw4SsOgDAyiEeMOdcxiDPlYf54+dj5a6VKFhVgLK6sqRU3Q6zAwuvWKj585Zjx+g3ETTFD3s55T+Bqn9di/944D08//MNiqYxWqNXrSn4VEPKdI0/VQTKoRDLYDqgonAeeDVfqV6utyWNtrOzSZQRpScCptCN0pTU4NMpArxQYRA5B95GL2a9Mku1hScRMls8ZTEcZoemfZs7m9PWd67XS91ETJp6w9ONbqo889yCbswZ/OfI780WtpWnBIlwu4JdWHNoTUpasqRrVDG9AuvvWI+9i/aianZVJCvjtrnhNPMFOUeG1+ODsa/ivK0VFBTnba044fwCOf48DArkgIAgfM6EDf+zT5HMTRoa9DOdWZGwYseKyGAd1pQ8YqG48R+u7oMz639gOb5JSKS/XKlO3V5bq/v8YpHKGrxk+HJZmRfTlvMHZA40gZscRo2cAa1iNd7ISjXE1tBzXbnwhXzcFHc6xHBq4j0WKKXYs2hPSl4/IVw2F/j8A2SbTqNDGMHZieKGwb+PRONa0B3u1n0tJFiIBdm2bLT721V1Dawar5KCPlYAd3f9E3H70BDBa6u34M3GZyOdBZIQzG1za+qe6IvMirfRi/ZAO2798lbm/HoBYdx8T0HS0+AuFqS6Xj7ioQdx/Oe/YA4UOvnMs0mnv1MldIuth584J2pELCaCkGyO6EAUuMlhELkMetqS1EZWqiH2pq62eEhl37maeI+HvorcIlj0BvAf0zCj6yW8e+4h8ERvekg8EaRSMS3/Hsj70FkCScDsPNoAACAASURBVKU6slx4p1eM1xeZFamkw3tPJpgMEo+BZKRzWZmXaUeqJ7XsLinB8Ud+znwsFcr1EQ89iONl5UBYJkhLQOjGM3zJtlvgsluiRogOxNq4BIPIe6CnZUzPyEqtkEfpvIWElGZPhjwSicSBfjTf+Sc7MGFPNd79PQWLyEnK5DrxcJgdaS0psBZ3ErETQtBhO4tBgXj7Up4wTgsSqd+nAtJ3nPeesnO0lZ4GInj95SZCcFmZVzOxmT2etCjX22trcfKZZ6NI3DJyJEY89KDuSJ+3OGn3BbH7iXlJnefFBKNGDu3TvoD0EpokiFO6uSajZtdL4lr90jOOyQtw9ZxLgbi4hOIqxztxu3uE5Mm9L66BXCC5fNZy7BqzLk4AR0FhEWwYf6pI9/H7cnFmIiaMP1UES9gWmZ4nwWIzYcb8cX1yXhcCePXyMKW6PNm5ynV/4s6Kki2rPK0uReJ6SFxtEMpAroezMOAjci0e4xI8dg/Kri1L+8188ZTFKUmzyyM6t92t2QgF0O+XnmnMvWsiAGDfluOgAgWBgKsc72Cu509x+5aZL0EZTsdtV0OmPm8tKB5bDJQCa71v46qDN8ERdoH0/OcMZWNu450AEFVTV0JfG6mMPVkYZwBDQdFt6cRtd19rpNUVIK+XH2/zgRBAiGE8LTVzrnLd50Pz0qXIeyJek6EGllqddnfrqruz+sTlGOj1cBZIX/aQJoqpU6fSnTt3Jn0cKRJXI/G+uOlpqdcrnVeiPuJA+lPIfYH7192P7S3bNe3b1ySnhlVLtjKNYc7bWrG6aKmmY+xdtDfVp6UZa958ByffNDOV6l2Odjzy7Lf74KwuXPBq5gTA51X87/CnN97EFKRJGPn0r3Wnwg9cOYkpoAMhuPKANmfGmVUbudPMBqrhCwAQQuoppVNZjw3YiFzrtK++IjSpXjpv7TzFmnnlh5VoONmAzcc2RznCPVv/rC4S99g9mpTXFyr+ePMfsWz7Mvz18F+jPvML0eqT5+7GE47Foq/q4oBotdvyFoGFQeIAkMVxtDPAR6Ke7CMeepAreAOAE79crpvIU6FWNwah6MeAJXK1aV8mYuoXUamWNLu87t3c2awpyyDHwisWomJ6RdLn2t9RMb3ionifvLGngNiiJg4YYafY+1q0uO31z2ARrNzHDZGbfiTqye4uKUHzL5dzTWDCbW1or63VReaJ2rJK3ulKynujLs7HgBW7KfmEO8wOLJ+1vM9JHBAj8/nj52sy9pAgUEHRClaOgULiFxNmzB8Hiy3++0BAMCiQg7mNdzLFb30tWjy8o0XRKz5oChgitwRQWpiPFbcXIJ9DdFK9nIW8R5couh4eLyvXbBCTqC2rVBNvavOBIl7CChh1cTUMWCJX6omeP35+vyBxQCwBvH7kdd0z0GOVwLGQPMUNEr/wMGFaLjzzutFhP8v8nKVhI7GYc+mcPvtef/DyQcXpdQLC+GDsq6im8WJFA+pI1JPdXVICz50L+QcOh3H8kZ/j4PQZqoSeqC0rr1fcTMRwJN/jxIrbCwZkXVwrBiyRK6UXNx9L3UzeROBt9GLe2nmYvGqy5ra4WHjsHsXH+0PZwEDi+HP3b/HSlEru46x6+V8P/zWNZ8TH4R0t+GQzX1QVNAWwcfxqHBlejzWH1mD2q7PTPizoYgUv/UyIKIpj+bLnPfEEiEf5fkHb2tD82ONcMm+vreUK59QMZniLDIFSfF5VPGAHoejBgCVyJRLL9HxmOXHPfnU2KrZURKag6Y3EAdE21B/ipzDTYWhjIP2Qf0/khiosUAhx6fVEvkvJ4PCOFqxaslUxEqeg+GDsq1E1/TZ/G8rqyjBt9TSD0HWC12MuUCj2mOc9ugTEoaxPoN3dOP7Iz/HpjTdFEbrUO84DS+gm9083esWTx4AVuwFi1Mrqrc7kfObYNjE9vd48EBD4wnzRSL9waDOgCWptiDtGvxnXjw0AJpjjesv16Cy04PCOFmx7/TN0tPphd5lBQNDdGYLdZUY4KCAUUG9t7bCd5QrzukJdeGzrYwD6xkb2QkRsj7mJEIRj2sF8wTAerv4YD63Z3esC11PDjrVVZSF0/HiEuN0lJeyUeg9YQje1PnHAqInrxYAmcl4PvVI0mwrEWm/qjZRMMEFQsCIN0iD3MbfNbdwULwB4G71YsWOFql+6RII3Hrk7ri9bqpVL+1x7ybUpO7/DO1rw/uqDCAXE76G/s/emLP9ZCRQUO0a/qbhPUAimbMbAQIHkyQ6I6XQWJHKPUrX3kHnzY49ziVmC3ORFqRc976kn44RuSjVxgVLDOz0BDGgi581h9oV98DZ6U3rz4EVWWg15TMQESmmkzxuA7jYzACifVq5rfwOZh14znyPD63HTkXuYj8lr5V+c/yIl53d4Rws2rNqPZDP1B3O3aXKiS8VY2YEKXo+5HHIXOIl0T/xyOdOHXY7Q8eNoXrpULMAz7mOWkSOZanW1mrgB/RjQRJ7ryuXeJFIZBSTjsgYoG9OozUuXw4jG+zf0TN+LBYUAwjBZobLMTSoI8YOXDyoK17TC7jLjln8sxIdbX4ua8MZDqhfWAwVKPeZyyMnVXVICd0lJZPiJUsTd9uoatpMbEEmpy3vEh2bbjJp4GjBgxW6Acq1YmjSWrNhGz0AWCVaTFW6bO6UDSxxmhxGN91N4G72Y9coslNWVJUy2hPOnTGCKiN6SrZGrqc+1wmIzYc6CK1A8thhPzXxKk9OcNPbUgD7Ie8wJxPQ1CywSdZeU4PKN72Hk07/mC+EUMorukpK4HvHTHeLQH6s5+jyMmnhyGNARefHYYsU6pGSBKu2rB95GL6o+qtIsXotNnWt5Pa03t/7iUncxQ6570PIZJhN9s8AbB0pAdA9UYUFKpycMAoCKrnQz5o+LDEWRrIgLVhUoPt1IrycOec2cJzTr8Ae5I1Cl9LiSnWssLCNHAuDXw102Y554KjGgiRwQa8apmDQmQS+BA4l5unsbvZpvbpRSg8QTAIucATC3yb9DagtAb6MXj219TFNKWSt46nWgV/TWOSaxaFoStqnVxB0uS0S1LinYY4mbhzxXnuL3OdWK+4GKWFV7tt2M8/4w2n0hAHxLV0mdrpRml0NKqxvzxDODAU/k0o1WKTpq7mzWVKNLpBaeyLAO6XW0QsnF7mIHa+qZ0+yE3WJnDonhRcrNnc2o2FIBQkiEgCXCtpvtcZ+5tAAE4om/6qOqlJI40Btt33TkHqY9b3ZgSMJth9te/yyiTufhW/dNSmr06OIpi1FeV851JMx0D/zFDHmEPrNqI877o8mWNwJ1xEMP4vjPf6GYTpcgRfE8sZ1RD08tBvQY01goTRqTEEu8ibSSmYgpKS93Lecp4WIcSaoVekaXAqIYsCvUlVKSNRMzwjTM/T1VkL6Xe5/1MVPsAsK4+b6ChMj2uQc2Kj5+9ZyRkfnwyWD2q7O5maw8Vx7W37E+6dcwEA0lQxYCxKW9D0y8UvWYlpEjcfnG9wAAv/Tuxx/rPo963Gk1G5arCcAYY6oRapPGADEKK6srQ1ldGTx2DzoCHQhRMS2lZVGUCmLV6jw30GvjekgcgGrPdiKIJe1kSdxCLMi2ZXNHzv5p9L1cg5gN/7MPAHSTuZQyjwMBvnVvcpG4HErlKMPEKD1Qak+TO8EBYiRvGTlSNb1+6qqpuLdqI463+UAI4HaY4bJb0dzebdTD0wSj8CRD8dhiVF5XqXn/Nn9bhMS1wG1zJ0WskkWn2kAUCUZtPDNw29xwmKNVvbG/JwKH2YGFVyxEnisv0sGwbNYy1N1Zhz2L9mD9HevjPt/Tl36GD8a+CgHxCwYaItj2+me6z4P3fbNnmVNG4krdIR67x/gepwk8S1c55NPTRjz0oKqVa3BrXUSlLlCgO0Tx87+baPimpxEGkcegeGyxpnYYPXDb3KiaXYUt392SFIlXflipS707kGvj6YCFWGA1Rc/Sltr6Kq+rjCJc6Xc9yLJkxR2jYnoF1t+xnkvcsSi7tgxHhtdz29E6WvV7GfCc2vydYRzekZq5BCt2rOA+Vnatdq8EA/oQ257GQ1ObDzOrNuL9S6cg76knFUefDu+K9v/3hwTuGFUDqYGRWmdAS4pdCYm0kqlh5a6Vus7HYXYM+HSklVgV7Wr1QKpBA/HiNenzZX3Oer5Hj894POnvSvHYYlR9VMVtR6MAVi3ZqklJLiE7x86dI/7+6oMA9Kfr5fA2ehXLGkY0nl7Eit94qXYpzb7i9ilQ6/i+/qt6bBrVO7SHp143kBoYRM6AFiU7D6kUl8mFdFrT6RIGcm1cwlOzntLlfAeo16AB7cSi53uUSte9smvL8Kdjf2XWygkIOlr9ugh4xvxxUb7qcoQCAuqqDydM5JJhEg+pzo4ZUIaaE5yUZv+z2w3KsXAlAO7d/3YUkRsq9fTCIHIOJKMKQNm8w2qyIsuShXOBc8wbv1pfOa/9LBlbV2NMqTbsXbRXt5GLXkjfo8mrJnMXY6l23SseW4zy4eLxpn15K7IDQ+Ja0kIBAe++sB/bXv9MNTqXHuONI+3uDOGDlw/qVq5L33GlTo+BnlXKNOR95rzIfMLeLaDtysLQEb7e+53h2pZ+GESuASxS13Lj12L8wTMP0ZtKl2Ck1Huh5HznsXsARH+26YTb7mYu5ghIWrInFBRHhtfjyPB6/NO2Z7n7aY3OJ0zLjYwsZeGTzceRN86jOTKXInElEjdEbn0DKdXOS7Mv2v+2ai857Vk45hsq9YzAELvpRPHYYs3io5W7VmrqSe4Od6OsrizK211ri1ksjJR6L5SuYab9E3iv5zA70vJ5yZ3QOmxnFfYUo/MNq/arCtdmzB+n+Hhd9WFN56YlEneYHYbIrY/BU7QP96m7VhJQ5Huchko9QzCIPI3QS8ZSdL5s+zLdNXFAvHkbJN4LJdV+OnrGlaA2MjfVkJPkjtFvImgKKO5PBVG4pkTmE6blwmLjq5WZveYx0DJEaKD7H/QX8AaunHJ6ND3fELhlDgaRpxGJtH91h7ux5tCahF7PsLGMhlKJgWVjmk4ofRdiszGpgNvmjvx8ZHg9Phj7Ks7bWhUXiKGAgM3V6WsT0hqJJ+N6aCC1KC3Mx9ayG/F5VTGEnqzSi5Nu0RRmGAK3zMEg8jQi07VqQ+EbDSUyoKBpiYR5UPsuSI6BBasKkiJ1yTQoNuNwZHg9VhctRd2ENbDY+H/2/s4w/vzwZmZk/sHLBxEK8G/hdhfbWEQ6p7K6MiMSv4AhEfOmUUXYNWy8Ipmfs2YZArcMwvBaTzOWbV+WcIStB1aTFU/NfMq4CcZAyZfeY/eg7s66jJ3LrFdmaU7pO8wOzB8/H5uPbY4IK+dcOifyu9vuBqU00i0x59I5WHd0naape/878V1sWLVfcZqZxWbCDXdPjIjXPnj5oMoscoqdV72B+sHvR52rMRPg4kHsCNRlW57HlNNH4nJbIRD8puhOfFowyxC6pRBKXusGkWcA3kYvHtvyWMrMSWLhsXtQdm2ZcRNkwNvoVe0lT2QCXaLnkozRUKqwd9FeHN7Rwm0n0w+K/bnbsPmyxBasyQ4RMpA51DQ0RUagUojGLw/sqcHgoFgPP2fLwvMF8yM95MaAlNTBIPJ+glRF5wZx64OWSDhTEaGSJ0EmIM9C/PnhzZoEamrwmTuw6tpHE3quEYlfuBhTpr38Y7ShJQ8lIjdq5GnC/evuR8Gqgsj/7l93PyqmV2DhFQuTOq7b5jZIXCe0mK10h7uxZMsSTF41OeXCMzmk9sWq2VUpGayiF/KWrtkLJijWy7WAgmLrZa8l9FzJT974Ll+YcNmUh63IIdm71jQ0pfGMBi6S+ismhOQQQt4lhHza8+8Qzn7vEELaCCFvxmy/jBCygxByhBCyhhBiYz3/QkPp/5XGjdDc3rIdBasKsPnYZkzPnZ7wsdsD7aj8sDKjQq0LHcVji6NU3DwIVAAFjbQBpvMaS5P2MilQXHjFwijSnDAtFzfcPZErUlMDBcUnI+pwZHi9ruc5zA5Uza7SNATGQP9ETUMTAiF9XTK+YBiVb+xL0xkNbCQbkZcBeI9SejmA93p+Z+FpAPcwtv8KwDOU0vEAzgL4QZLn0+fwNnrx2Tn+qMjmzuYIyctNO/SgO9yNqo+qEnruQEX5tHJdEXAmInQpOt+7aC+qZldFTT5beMXClEXsea48VM2uQsX0irjHJkzLxQ9/Mxffum8S9H4dg8SPreP+V/e5GFH4hY+n1x1CUNBflm3zBVFRszcNZzSwkaxF63wA1/f8vArAJgC/iN2JUvoeIeR6+TZCCAFwI4C7ZM+vBPCfSZ5Tn0IPwSbT993mb4O30WvcEDUikUE40ufDs9FN9fnFHrtwRGGUHbCaal2ucNcq3pNbDhdcMQvfOHRb3KAVFgSEsXlcddQ2+dS/RM/HwIUBJbOXfI+T69MOAC9t/xIAsKy0IOXnNVCRlNiNENJGKfX0/EwAnJV+Z+x7PYCfUUpv7fl9GIDtPdE4CCGjALxNKb2a8/wfAfgRAIwePbroiy++SPi80wUtCulUIs+Vh/V3rM/Y611MkBMYIUTToiod42n7AkqCu/GniiKDVigEEJhAQaMMdLotndg65rWolLohWhtY4PmwS7asNQ1NeHDNbsVjEIhjdQ0hnDYkpVonhGwAwLKlehTAKjlxE0LOUkp5dfLrkQSRy9FfVetKPcvpAAHBnkV7MvZ6FysSaQu7EIlLbRKfHqhN/TNwcaOiZm8kspYQ22pW+OR6nO3S3nI7JMuKJ0quMgidAyUiV02tU0q/qXDgE4SQPEppMyEkD8BJHed1BoCHEGKhlIYAXArggpU0ehu9aSHx/9/e3cfIUd93HH9/7/lw2js70Bw5arAl11FQGlu5UtQUVEEap3VJXMXCRElktUFR2/+iFtUH10aJHPlaq4r4D6FIeWiJeEjohWSlWISHCtIYcnCGg6rG9lFSLqShEJuAXRv7vv1jZi97ezOzszv7MLP3eUmr252H29/Xs97v/X7zm/n2WA+99EZegz4yWHsCl9RWOeyetodenqfQyhKoWVWOOowMjvDmuTc579kvN2vXdfeSTzNzi3z7qZVf1QZ8/APjK5Lw52+4ks/dcyR11YhfnH6bz91zhNmXXtewe52yniN/ANgLTIc/v5N2R3d3M3sE2A3cXe/+eVLu0SXpsZ6Gzokv+RJLRO9XxHsA5FV1qdo0PfSTZ08u927bcR69HtUxZO2FK3lL2cFDR5fv7lbmwCP/+eqKZbu2jzP70uureu5JHLjr8E+YuHyDeuZ1yHqO/J3AvcBG4CXgRnd/3cwmgL9w95vD7R4D3gO8g6An/hl3P2RmmwmS+AZgDviUu0cXPK6Qt6H1pCH16iHYZt6yVUPrrdPIOXQIbrgy3Dfc9l56ZXvH1o1x+u3TDVV405C51LJpXymyl23Ai9OrPytX/v33eevchdU7JCifa5dfyTS0nsTdXwOuj1g+C9xc8fqamP0XgKuytCEPkobUK5N4aaHEfS/c17T3baS6mqTTSA8d2tdLTxo2b/QUj3rdksboRf2R575HL+qP3P5Lf/q+mhPfqiXNepfVsg6tr3lJ1xdfuu7SVckgrmdnGAeuOcCtj9+auvfX7upqa1X1OfR6erzNPJceN9s8y7D5yMAIk787qeQtqcUN4sYtb2SIvVz7XNJRIs/o9qdvj11XTrSlhVLNBD22bmz5yzTNJWwjAyP68m2j6uu8m9FLB1Yl+MplldeKN2OymobNpRlOnomeiX4qZjkE14xPXL5hueDKu8NLzuJ66hc0/6cuSuQZ/eyt1XWby3Zu3lmzJw7BefTyl/jOzTtrJvKh3qFU9w+X1snaSy9/Js4tnQOCBD/1wyncnQsenE+s7Gk30uvu1Pl66V4zc4vL139XK9crj7Nr+/iqCWxxs9rVI6+PEnlGI4MjkV+yo4PB5fUHnjiQ2GvrsZ5V1yOPDo4mfnEX7frlbpWllx61zfml7JeGlQ31Dqm4jjTdwUNHYye63bJja12/a2ZuMfbSNPXI66PqZxnFzfp3d0oLpcQe2lDvUGQd5soKVdU0pJ5flYVQyvdMT1OspRn6e/oZGRhZfl/9sSetEHdrVoe6LxdLKqAyXqN3LyupR57RG+feiFx+6twpbn381tj9onriZTs372Tu53OrLlPrsz4Nqedcml76UO8Qg72DDV0eFkWzzaVd4masr4+ZsR5nZm4x9lw71N+7X+uUyDMa7hvm9PnTkeuSzotH9cQrTV09tapohr6siyfqXHp5PkR1gu/v6cfdYye0abKadFq9M9ajzMwt8tf3PhO7fv1F/boZTJ2UyDMoLZRik3iS0cHRVF/AURWxpHiSjmPaWetK3JIHcTPTk2asV5qZW2Ty/vnEc+Cfv+HKhtq2limRZ5B06Vmc8iQkkbgEr2QteVXvzWAqlXviSUlcvfHGaLJbBkmXnkVJOi8uIpJnM3OLnIypZlZraD1NT3y4v1e98QapR57B2Lqx1LfDLGLZSxER+FUijkvDUUPrM3OLyzeA6TFLTOK9ZitKoEp91CPP4NrLrk21nXriIlJkURXPKlXfDKac+BdPnsFJvi58uL+Xf7rx/UriGSiRZ/DdE9+tuU3cteIiIkURd/04BIm4+nKxWom/TD3x5lAib9D+w/trzlhXT1xEukHcZLbqRDwzt8gHpx9OVb1MPfHm0TnyBpQWSjVriuucuIh0g5m5Rd78v9X3NujvNQ7ufv+KJD55/3xiT7zXjCX35aIpSuLNoUTegOknp2tuoyQuIt3g4KGjvL20+hz3uoG+FYm41nD6cH+vhtFbRIm8AbUqUU1fM60kLiJdIW6YvDxTvTw7PWk4fVw98JZSIq9TaaGUuL7f+pXERaQr1CpbmmY4fXx0mB/uu65lbRQl8tRKCyWmn5yu2RtfN7CuTS0SEWmtWmVL0wynqwBK6ymR11BaKHHgiQOpK1WdOtucilYiIp0WN1zuNdaDhtPbSYk8QWmhxORjk3js/YxWG1s31sIWiYi0T49BxDw3egwm75+P3U/D6e2l68gTfOHfv1BXEgeWK1iJiBTZzNxiZBKHILnHDalrOL39lMgTnLlQ+6YGldKWJxURybuDh442tJ8uMWs/JfIm6bM+lScVka6RdFvWOOOjw0riHaBEnsCwVNuNDIyw//f3qzcuIl2juhBKLeWZ7NJ+SuQJbtx6Y+y6PVv3ML93nvm98zz+iceVxEWkq9yyY2vKrkzAQb3xDlEiTzB19RR7tu5Zscww9mzdw9TVUx1qlYhI6+3aPs4nr96YevvxOnvw0jzmCXVi82piYsJnZ2c73QwRka43NTPPXYd/knj9ju6j3npm9pS7T0StU49cRERi7d/1Pr68ZxvrY0qZjg73K4l3mG4IIyIiiXZtH2fX9vHlAik/PXlGpUhzRIlcRERSKSd0yRcNrYuIiBSYErmIiEiBKZGLiIgUmBK5iIhIgSmRi4iIFJgSuYiISIEpkYuIiBSYErmIiEiBKZGLiIgUmBK5iIhIgSmRi4iIFJgSuYiISIEpkYuIiBSYErmIiEiBKZGLiIgUmBK5iIhIgSmRi4iIFFimRG5mG8zsQTM7Fv5cH7Pd983spJl9r2r518zsRTM7Ej62ZWmPiIjIWpO1R74PeMjdtwAPha+jHAQ+HbPuFnffFj6OZGyPiIjImpI1kX8M+Hr4/OvArqiN3P0h4JcZ30tERESqZE3k73L3V8LnPwPe1cDv+JKZPWtmXzazwYztERERWVP6am1gZj8AxiJW3Vb5wt3dzLzO958k+ANgALgT+FvgizHt+CzwWYCNGzfW+TYiIiLdqWYid/cPxa0zs/8xs0vd/RUzuxT4eT1vXtGbP2tmXwX+JmHbOwmSPRMTE/X+wSAiItKVsg6tPwDsDZ/vBb5Tz85h8sfMjOD8+nMZ2yMiIrKmZE3k08Afmtkx4EPha8xswsy+Ut7IzB4D7gOuN7OXzWxHuOouM5sH5oGLgf0Z2yMiIrKm1BxaT+LurwHXRyyfBW6ueH1NzP7XZXl/ERGRtc7ci3e62cxeBd4C/rfTbWmxi1GM3UAxdgfF2D2KGOfl7n5J1IpCJnIAM5t194lOt6OVFGN3UIzdQTF2j26LU/daFxERKTAlchERkQIrciK/s9MNaAPF2B0UY3dQjN2jq+Is7DlyERERKXaPXEREZM3LbSJPU+vczLaZ2Y/M7Pmw8MqeinWbzOwJMztuZveY2UB7I0hnLdR0b0KMuT+WdcS4N9zmmJntrVj+qJkdrTiOv9G+1iczs4+EbTtuZqtKFZvZYHhcjofH6YqKdZPh8qMVN4LKnUZjNLMrzOxMxXG7o91tTytFjNea2dNmdt7Mdleti/zc5k3GGC9UHMcH2tfqJnD3XD6AfwT2hc/3Af8Qsc1vAVvC5+8GXgFGw9f3AjeFz+8A/rLTMTUaZ7jueuAG4HtVy78G7O50HC2OMffHMuXndQOwEP5cHz5fH657FJjodBwRbe4FTgCbCYobPQO8t2qbvwLuCJ/fBNwTPn9vuP0gsCn8Pb2djqnJMV4BPNfpGJoU4xXAbwPfqPxOSfrc5umRJcZw3ZudjqHRR2575KSode7uL7j7sfD5TwmKtlwS3rv9OuBbSfvnxFqo6d5wjAU6lmli3AE86O6vu/svgAeBj7SpfY26Cjju7gvufg64myDWSpWxf4vgVswWLr/b3c+6+4vA8fD35U2WGIuiZozu/l/u/iywVLVvUT63WWIstDwn8rpqnZvZVQR/hZ0A3gmcdPfz4eqXgfFWNTSjtVDTPUuMRTmWaWIcB/674nV1LF8Nh/X+LkdJolabV2wTHqdTBMctzb55kCVGgE1mNmdm/2ZmkbejzoEsx6KbjmOSITObNbPDZpbHzkKsTPdaz8qaVOvcgipq/wzsdfel/HwHBpoVZ4zUNd1bqcUx5kKLY/ykuy+a2a8B3wY+TTD8J/n2Nx0vXgAAAkVJREFUCrDR3V8zsw8AM2Z2pbu/0emGSd0uD/8PbgYeNrN5dz/R6Ual0dFE7k2odW5mvw6UgNvc/XC4+DVg1Mz6wr+eLwMWm9z81JoRZ8LvTl3TvZVaGGNujmUTYlwE/qDi9WUE58Zx98Xw5y/N7JsEw4R5SOSLwG9WvI769y9v87KZ9QEjBMctzb550HCMHpxcPQvg7k+Z2QmCuTuzLW91fbIci9jPbc5k+rxV/B9cMLNHge0EI7y5l+eh9Zq1zsPZy/8KfMPdy+dQCf9zPQLsTto/J9ZCTfeGYyzQsUwT4yHgw2a2PpzV/mHgkJn1mdnFAGbWD/wJ+TmOPwa2WHDlwADBRK/qGb2Vse8GHg6P2wPATeGM703AFuDJNrW7Hg3HaGaXmFkvQNiT20IwGSxv0sQYJ/Jz26J2ZtFwjGFsg+Hzi4EPAv/RspY2W6dn28U9CM4/PQQcA34AbAiXTwBfCZ9/CngbOFLx2Bau20zwpXGcoBb6YKdjajTO8PVjwKvAGYJzPzvC5Q8T1HN/DvgX4B2djqkFMeb+WNYR45+HcRwH/ixctg54CngWeB64nRzN7gb+GHiBoHdyW7jsi8BHw+dD4XE5Hh6nzRX73hbudxT4o07H0uwYgY+Hx+wI8DRwQ6djyRDj74T/794iGFF5Pulzm8dHozECvxd+jz4T/vxMp2Op56E7u4mIiBRYnofWRUREpAYlchERkQJTIhcRESkwJXIREZECUyIXEREpMCVyERGRAlMiFxERKTAlchERkQL7f9EU+jDgTZtKAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 576x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Example: 2D paths\n",
"x = sample_path(np.random.RandomState(0), (2, 5), 1000, 1e3, 1e6)\n",
"plt.figure(figsize=(8, 8))\n",
"plt.plot(x[0].T, x[1].T, marker='o')\n",
"plt.axis('equal')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Tests"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"import scipy.linalg"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"def make_q(n):\n",
" q = np.zeros((n, n), np.complex)\n",
" q[0, 0] = 1\n",
" if n % 2 == 0:\n",
" q[n // 2, n // 2] = 1\n",
" m_low = (n - 1) // 2\n",
" alpha = np.sqrt(1 / 2)\n",
" beta = np.sqrt(1 / 2)\n",
" for i in range(1, m_low + 1):\n",
" q[i, i] = alpha\n",
" q[i, -i] = alpha\n",
" q[-i, i] = -1j * beta\n",
" q[-i, -i] = 1j * beta\n",
" return q"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ok\n"
]
}
],
"source": [
"# Check that Q matrix makes FFT matrix real.\n",
"\n",
"def test_real_fft():\n",
" n = 10\n",
" f = np.fft.fft(np.eye(n))\n",
" q = make_q(n)\n",
" v = np.dot(q, f)\n",
" np.testing.assert_allclose(v, np.real(v), atol=1e-6)\n",
" print('ok')\n",
"\n",
"test_real_fft()"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ok\n"
]
}
],
"source": [
"# Compare multiplication by q.H to mul_qh.\n",
"\n",
"def test_mul_qh_real_symm():\n",
" n = 10\n",
" rand = np.random.RandomState(0)\n",
" x = rand.normal(size=n)\n",
" # Make x symmetric.\n",
" m = int(np.floor((n - 1) / 2))\n",
" x[-m:] = x[1:m + 1][::-1]\n",
" actual = mul_qh_real_symm(x)\n",
" q = make_q(n)\n",
" qh = np.conjugate(q.T)\n",
" desired = np.dot(qh, x)\n",
" np.testing.assert_allclose(actual, desired, atol=1e-6)\n",
" print('ok')\n",
"\n",
"test_mul_qh_real_symm()"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ok\n"
]
}
],
"source": [
"# Compare circulant matrix to construction from diagonalization.\n",
"\n",
"def test_compare_circulant():\n",
" n = 10\n",
" g = np.zeros(n)\n",
" g[0:2] = [-1, 1]\n",
" fft_gg = np.abs(np.fft.fft(g)) ** 2\n",
" f = np.fft.fft(np.eye(n))\n",
" u = 1 / np.sqrt(n) * f\n",
" q = make_q(n)\n",
" v = np.dot(q, u)\n",
" actual = np.dot(v.T, np.dot(np.diag(fft_gg), v))\n",
" circ_g = scipy.linalg.circulant(g).T\n",
" desired = np.dot(circ_g.T, circ_g)\n",
" np.testing.assert_allclose(actual, desired, atol=1e-6)\n",
" print('ok')\n",
"\n",
"test_compare_circulant()"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [],
"source": [
"# This function is not needed, but can be useful in debugging.\n",
"\n",
"def mul_qh(x):\n",
" alpha = 1 / np.sqrt(2)\n",
" beta = 1 / np.sqrt(2)\n",
" n = x.shape[0]\n",
" # Partition into [0], [1 .. m_low], [n / 2], [m_high .. n - 1].\n",
" m_low = int(np.floor((n - 1) / 2))\n",
" m_high = int(np.ceil((n + 1) / 2))\n",
" x_low = x[1:m_low + 1]\n",
" x_high = x[m_high:][::-1]\n",
" y_low = alpha * x_low + 1j * beta * x_high\n",
" y_high = alpha * x_low - 1j * beta * x_high\n",
" y = np.array(x, dtype=np.complex)\n",
" y[1:m_low + 1] = y_low\n",
" y[m_high:] = y_high[::-1]\n",
" return y"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ok\n"
]
}
],
"source": [
"# Compare multiplication of q.H to mul_qh.\n",
"\n",
"def test_mul_qh():\n",
" n = 10\n",
" rand = np.random.RandomState(0)\n",
" x = rand.normal(size=n) + 1j * rand.normal(size=n)\n",
" actual = mul_qh(x)\n",
" q = make_q(n)\n",
" qh = np.conjugate(q.T)\n",
" desired = np.dot(qh, x)\n",
" np.testing.assert_allclose(actual, desired, atol=1e-6)\n",
" print('ok')\n",
"\n",
"test_mul_qh()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.4"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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