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@ricardoV94
Created October 20, 2023 12:30
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Shifted Wald distribution PyMC
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{
"cells": [
{
"cell_type": "markdown",
"id": "db6ad00c",
"metadata": {},
"source": [
"# Implementing a Shifted Wald Distribution in PyMC"
]
},
{
"cell_type": "code",
"execution_count": 53,
"id": "8f408067",
"metadata": {},
"outputs": [],
"source": [
"import arviz as az\n",
"import pymc as pm\n",
"import numpy as np\n",
"import pytensor.tensor as pt\n",
"\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns"
]
},
{
"cell_type": "markdown",
"id": "be878276",
"metadata": {},
"source": [
"## Step 1: Implement Inverse Gaussian\n",
"\n",
"Source: https://en.wikipedia.org/wiki/Inverse_Gaussian_distribution#Sampling_from_an_inverse-Gaussian_distribution"
]
},
{
"cell_type": "code",
"execution_count": 131,
"id": "79691b26",
"metadata": {},
"outputs": [],
"source": [
"def wald_logp(x, mu, lam):\n",
" mu = mu.astype(\"floatX\")\n",
" lam = lam.astype(\"floatX\")\n",
" return (\n",
" pt.log(pt.sqrt(lam / (2 * pt.pi * x ** 3)))\n",
" + ((-lam * (x - mu) ** 2) / (2 * mu ** 2 * x))\n",
" )\n",
" \n",
"def wald_dist(mu, lam, size):\n",
" mu = mu.astype(\"floatX\")\n",
" lam = lam.astype(\"floatX\")\n",
" nu = pm.Normal.dist(size=size)\n",
" y = nu ** 2\n",
" x = (\n",
" mu \n",
" + ((mu ** 2 * y) / (2*lam))\n",
" - (mu / (2 * lam)) * pt.sqrt(4*mu*lam*y + mu**2 * y**2)\n",
" )\n",
" z = pm.Uniform.dist(size=size)\n",
" return pm.math.switch(\n",
" (z <= (mu / (mu + x))),\n",
" x,\n",
" (mu ** 2 / x),\n",
" )"
]
},
{
"cell_type": "code",
"execution_count": 139,
"id": "f0f49a66",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Replicate plot from #Sampling from an inverse-Gaussian distribution\n",
"\n",
"mu = 3.0\n",
"lam = 2.0\n",
"\n",
"wald = pm.CustomDist.dist(\n",
" mu, lam,\n",
" dist=wald_dist,\n",
" shape=(100_000),\n",
")\n",
"\n",
"_, ax = plt.subplots(figsize=(8, 6))\n",
"ax.hist(pm.draw(wald), bins=200, density=True)\n",
"ax.set_xlim([0, 60]);"
]
},
{
"cell_type": "markdown",
"id": "745f6284",
"metadata": {},
"source": [
"## Step two: Implement Shifted Wald\n",
"\n",
"(This is just a shifted InverseGaussian with a different parametrization of mu and lam)\n",
"\n",
"Source: https://hal.science/hal-01432292/document"
]
},
{
"cell_type": "code",
"execution_count": 129,
"id": "2544e9fe",
"metadata": {},
"outputs": [],
"source": [
"# Replicating parametrization and figures from \n",
"def shifted_wald_fn(gamma, alpha, theta, size):\n",
" gamma = gamma.astype(\"floatX\")\n",
" alpha = alpha.astype(\"floatX\")\n",
" \n",
" mu = alpha / gamma\n",
" lam = alpha ** 2\n",
" wald = pm.CustomDist.dist(\n",
" mu, lam,\n",
" dist=wald_dist,\n",
" shape=size,\n",
" )\n",
" shifted_wald = theta + wald\n",
" return shifted_wald"
]
},
{
"cell_type": "code",
"execution_count": 130,
"id": "bb9df0fb",
"metadata": {},
"outputs": [],
"source": [
"# Replicate Figure 2, from page 3"
]
},
{
"cell_type": "code",
"execution_count": 125,
"id": "7a7f2ae9",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"gamma = np.linspace(0.15, 0.01, 7)\n",
"alpha = 22.0\n",
"theta = 300\n",
"\n",
"shifted_wald = pm.CustomDist.dist(\n",
" gamma, alpha, theta,\n",
" dist=shifted_wald_fn,\n",
" shape=(10_000, len(gamma)),\n",
")\n",
"\n",
"draw = pm.draw(shifted_wald)\n",
"assert not np.any(np.isnan(draw))\n",
"\n",
"_, ax = plt.subplots(figsize=(6, 4))\n",
"for i in range(len(gamma)):\n",
" sns.kdeplot(draw[..., i], clip=(theta, None), ax=ax, lw=3)\n",
"ax.set_xlim([0, 1250]);"
]
},
{
"cell_type": "code",
"execution_count": 124,
"id": "f8980b1b",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"gamma = 0.15\n",
"alpha = np.linspace(22, 106, 7)\n",
"theta = 300\n",
"\n",
"shifted_wald = pm.CustomDist.dist(\n",
" gamma, alpha, theta,\n",
" dist=shifted_wald_fn,\n",
" shape=(10_000, len(alpha)),\n",
")\n",
"\n",
"_, ax = plt.subplots(figsize=(6, 4))\n",
"draw = pm.draw(shifted_wald)\n",
"assert not np.any(np.isnan(draw))\n",
"for i in range(len(alpha)):\n",
" sns.kdeplot(draw[..., i], clip=(theta, None), ax=ax, lw=3)\n",
"ax.set_xlim([0, 1250]);"
]
},
{
"cell_type": "code",
"execution_count": 123,
"id": "081faaa8",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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nEucInjbWSpVRZSbPFCAffiM94QiHIwz1Rvd7F1BYmtrigIQ4hxKOsxo7hWMLsFAIMVcI4QFuADYkzNkA3BLNrroA6JNStkxw7WPAOwCEEIsAD9Bp430oLCIYjnCqxwi4zqmY2OKA+AB52nGO/iZjXJLoIR0Hs3Cc3pZ2+5HmASO+UVeY3lqJcY50CbYZ2+26a2vSuib/PHOA/I0UMw2Gev16OUt+sWdMc8Nk1Mwt0X0FXU2DBEat2VtdMfWwTTiklCHgM8AzwH7gESnlXiHEbUKI26LTNgJHgUbgPuDTqa6NXnM/ME8IsQctaP4RqVI4pgXNPSOEI9qPqrrYG7d5UyqW1GYR5+gzFdYVpykcBRVG+5FICE6lF+cwxzeyEY50LY7I0BCRfu3+hduNs2xsV+Fk+JYsQfg0iyF0uoVQGq7bwW6/Pi6aIL4Rw5PnomKm1nZdSq2KXHF2kt5fbpZIKTeiiYP53D2msQRuT/fa6PkAcLO171QxGZzoziwwHiOr1iP9JuFI1+IAzepo36eNj/8Z5r9jwkvMGVUTBcZjzC2Zi9vhJhgJcnroNH3+Pkq8qd1pZmvDVVODcKT3uU+43fiWLmVk+3ZAqyIvevvbU15jzqgqLEtPOEBzV3U1a4WarUf7mLV0nGp9xbRGVY4rJo3TvYabKlYRng7mRoiH2gZ0qyUlfSZXVXF6sQAgIUCeXpzDLBzpWhxuh5sFpUZtyaGeQylma4RaW43rq1MH4BPxnXOOPh7dM/G2tWbhSCcwHqNWNTx8U6CEQzFpmIWjrjR94ago9FJVpD28RoMRTnSlEXvIxeKI0fwGBCfu75SNqwoS4hxdE8c5gi2GcLhq0otvxMhbYRaOPRPOH+xOPxXXTM28+AB5JB2RV0w7lHAoJo1mk3DMzEA4ID5AfjAdd1U2MQ7Q6jkqox1nwwFonjgLqW3YcCHVFKT/QI/LrOqZOM4RbDNZHGkGxmOYLY6RPXsmLDoc6jPSngvHaW6YjOJKH/nFWhuUwGiYnpbs9zdRTF2UcCgmjWwtDkhsPZKGcMRlVWXgqgKoN7Z45XRq4QhFQnSNdunHVXnpp35nWssRMlsc1ZkJh6ehAUeBFlcKd3XFub2SMdxnBMfzS9IXDiFEXFquKgQ8O1HCoZg0Tvca7o9MLY7FpgrygxNlVkmptVSPUZxewFqnzqh7mMji6Brp0tupl/vKcTtTN200s7jMsDiO9h4lEE5d3BhncdRkFuMQDge+5UaPrJEJ3FXD/cZ7KShJ3UgxkTh3lRKOsxIlHIpJIRKRtPSZXVXp+80hQ1fVaK/mZgLwFIIn/Qwu7c2ZdgpsTl330D5stEqbkT8jo2UKPYXUF2rWUEiG4vYsT0aozVjLlWFwHBIC5LvHFw4ZkQybXFUx11O6xHXKVYWAZyVKOBSTQuegn2BY86uX5bvTruGIsWBGIU6HVl12onuY4UCK4rJBU9/Lwswe5gBUnwPO6MOy9wQMdY07tX3EWCsTN1WMTOIcoU6jztU1I/P7SjdAPjoc1IPanjwXLo8zo3WqZhXhjLaJ6e8YibNeFGcHSjgUk0JTDoFxAJ/bSUO00lxKONSWYlMns3AUZCEcLg/UGHtmcHr7uFM7ho1iukwtDoh3V6UqBJShEOHubuMtlmdeHxEXIN+7d9wAeS7WBoDT7WDGHMNCVO6qsw8lHIpJIZfAeIy4CvKWFHGOQSPLKSuLA6DOaNORyl2Vi6sKYFG5sWd4qlqOcE+PvqWts7QU4U4/lhLDXV+Ps0RzI0X6+gg2J9+21iwcmcY3YsQHyHuz+h6KqYsSDsWk0JJDYDzGkuo0K8iHTC01shUOc5wjRWZVrsKRmFk1nhUQ56aqGtPTMy2EEHiXLtWP/QeTWzhD/dllVJlROwKe3SjhUEwK7QOGcMwozu5hZLY4UgbI4yyOzIPIANQlBMjHeaDnKhwzC2ZS5NYEsT/QH1cTYsYsHM6K7IQDwLtooT4eHUc4cnVVQbzF0XFigGAg/Q2kFFMfJRyKSaF9wPgUO6Mos4yqGHFdclv7xy9iGzRZHAVZttSvWKi1YwfNgjG3MDHRMWKslU1wXAjBwjLjYT5enCPUaQToXZXZC4dvsRFT8R86nHROnHBk6arKK/RQVqPFpCIRSbtqeHhWoYRDMSm095uFIzuLo640j0Kvlo3VMxyME6M4rLA4HA6Yudo4HsddlavFAellVoU6DYHKRTi8i0zCMZ7FYfpZFWRpcQDULijVxyrOcXahhEMxKVjhqnI4RJzVsad5HN+5FcFxiBeO1t1jXh4NjdIf0D5Ju4SLMl96bc4TSSezKhxncVRktQ6Ad8F8TRSBwIkTREbG9uIaHjC7qrL7WQHULjDFORpVnONsQgmHYlKwwlUFsLK+VB/vPNWbfJIVwXEw9iAHaBvbUdbcaqQ8rxyHyO7PKT2LwxTjyMHicOTl4ZkzRzuIRPA3ji06HBkI6mNfUebZWzFmmi0O1fDwrEIJh8J2RoNhBqK7wbmdgrL87B9Gq2YZn2J3NiX5FBuJ5F7HEaPaaNFB69iCue4Ro66iwpe9FbCgdIEuOif7TzIcHB4zJ9Rltjhy2wrZGxfnGCtUI4OGcOQVZu+qKqrw6em8wdGwvk+HYvqjhENhO+b4RlWhFyFE1t/LbHHsauodGyAf7QUZzeDxFIE7e+uGykXgiIpc30kYjReq7lFDOMrzst+wyOfy0VDcAIBEcrh3bNA6PsaRvUhB6swqGZGMxglH9iIvhIiPcyh31VmDEg6F7ZjjG1XFOTzIgYaKfIp9RoC8qSfBRz9sPMwpyO0Bi8sDVUadRaK7yiwcuVgcMHGcI9zdo4+dWVSNm4nLrDoYX3ToHwkhY+1GfM609hpPRXycozen76WYOijhUNhOfHwj+2AraJ9iV80q1Y93NvXGTxg29ZXKz1E4AGqMNh2J7qq4GIcvt4d5qgpyGYkQ7u3Vj11p7jU+HnGuqoMH46y2EVNg3FeUvZsqRu38Un3c0pjEQlRMS5RwKGynvd+UUZWjcACsrDc+xe5KjHNYLRzmOEdbvHDEuapyFA6zxZG4N0e4r0+L3QCOoqKs2o2Ycc+caezN0dtLqMNwg41Y5KaKUVFXgNunNUkc6gsw0DU6wRWK6YASDoXttFmUURXDHOfYkZhZZblwmCyOBOHoGjHWqsjL0VVlyqw61HNI3+MDINzTq4+dOVoboO3N4V1oxDnMhYCjA9YKh8PpiNufQ7mrzg6UcChsp9MkHFUWWByrTMKxp7mPsDnN03JXlTkldx9EjNYZVlocVXlV+vcYCY3QNGBUqod7jfhGrm6qGN6FC/Rx4KiRkjsyaK2rCmCmKc5xWvWtOiuwVTiEEFcJIQ4KIRqFEF9O8roQQtwVfX2XEGLNRNcKIf5FCNEshNgR/brGzntQ5E7XkPEwqsghvTNGTYmP6mhh2nAgzJEOU5qn1cJRUGlUn4dGoPuY/pKVwiGEYFGZEecw13OEe0yBcYuEwzN/vj4213KMWGxxQHycQ7VYPzuwTTiEEE7gR8DVwDLgRiHEsoRpVwMLo1+3Anenee0PpZSro18b7boHhTXECUeBNZ9ixy0EtFo4IMFdZVSQWykcMH5mVci0D4dVwuE1C8eR5BZHLjUcZqrmFBHLwO5uGSIwmmITLsW0wE6LYz3QKKU8KqUMAA8D1yXMuQ54QGpsBkqFELVpXquYJnQPGa6qisLcXVUAq0wB8h12C0eSzKqIjNAzalgClghHeXLhsDrGAfHCEWhs1LOd4iyOHKrGzXh8Lspqo9v3Sug4OcHWv4opj53CUQecMh03Rc+lM2eiaz8TdW3dL4RI+pckhLhVCLFVCLG1w5Q1oph8uk2fYsstsjjOnW382Led7DVesEM4Zpgyqzq0jKd+fz/haKFhkacIjzP3+0rHVeUqt0Y4XLW1OPK17rXhvj59d8FRc4zDIlcVQHWD0RK//bgSjumOncKRrDw4MYl7vDmprr0bmA+sBlqA7ydbXEp5r5RyrZRybVVVbi0aFNkzGgwzFN2Lwe0UevFerqyaVUp0C3IOtvYz6I+6P2wRDlMRYPs+wNrivxjzSubhcmj/Py1DLfT5tXhA2AZXlRACz7x5+nEszmFVu5FEZpiF44RqsT7dsVM4moBZpuN64HSac8a9VkrZJqUMSykjwH1obi3FFMUc3yjL9+TUbsRModfFouiOgBEJu2LuKjuEo3IRxBoYdh+D4IilxX8x3E43C0qNbKdYIWCo1/rgOCTGORq1f4eM+INtFocSjmmPncKxBVgohJgrhPAANwAbEuZsAG6JZlddAPRJKVtSXRuNgcR4HzC2+5xiymCHmypGvLuqB8JBUz8pAXml1izkzoPy2KdzCR0H4yyObNupJ8PsrooJR1yMo9S6tTwLTHGOI0cBGB0ydcYtsMY6BCifWYAjaiL2d44SGFEB8umMbcIhpQwBnwGeAfYDj0gp9wohbhNC3BadthE4CjSiWQ+fTnVt9JrvCiF2CyF2AW8H/p9d96DInS5TYLzSosB4jDWzS/Xx9pO9MGJ8MievDBxO6xYz96zqOKC7kQBKvaVj52dJsgpyO2IcAN75hnXjP3KEcChC0K+5FYVD4MmzTjicLgdltfn6cdfpIcu+t2Lyse43IwnRVNmNCefuMY0lcHu610bP/7XFb1NhI102Whxr5hgP0e2nepHDRUZwLM+6BywAM5bBgSe0cfs+eqvr9ZcsFY4kmVVxdRyl1q3lnW+KcRxpjLM2vPkuy9yKMSrqCulq1gSjq3mQWtO+5IrphaocV9hK95B9wjGvsoDS6N4e3UMBWtpajRetclPFiAuQH6DX36sf2mVxHOk9QsA/TGQwWuAoBI7i4nGuzBx3fT3Co/1Mwh2dDLcZAuUrsC6+EaOirlAfdzWpvTmmM0o4FLZiR/FfDCEE55o65R471Wy86CsdMz8nZpjqT9v30zvaqx+WeK375FzqK6U6X6tUD0QCHG/ep7/mLC5GOKz7kxVOZ1xm1cDhk/rYyvhGjIp6k3CoTZ2mNUo4FLZiR/GfGXOAvLm1xXjBaoujfD5EU2XpO0nviLGVq5XBcYAl5YZ1c/TUTn3sKLXeteM1CcfQCSPp0Q6Lo9JkcXQ2D6oW69MYJRwKW7HTVQWwxiQcXR2mLWOttjhcHqgwOsr2DbXpYytdVRAvHE3NRot1Z4m160B8ZtVwsyGGXhuEI7/EowtScDSsWqxPY5RwKGzF6gaHiZj3IPcPmGo4rLY4AGYs1Yc9pnRcK11VEC8c7a1GHymnHRaHKbNquMPIFLPD4hBCUFFfoB8rd9X0RQmHwlZ6h41MnbJ86x9GRT43cyu1h1ERphRPqy0OiBOO3qCxltUWhzmzqqfd6Lxjh8XhNVkcIz3D+tiOGAdAxUwV5zgbUMKhsJXeYcPiKMmz3uIAWD5TyzQqESbhsNHiCAEDUhNEgaDYY12mE0BdYR2Fbu0B6xgwHubOEustDs/s2eDSRMLvN2IOdlgcEB8g72xStRzTFSUcCtuIRCR9I4bFUWqDxQFwTp32QC2x2+Ko0oSj35TZVOwtxmlloSHgEA69grxw1HiY2yEcwu3GM2cOAEGXUaBnR4wDElJylcUxbVHCobCNgdEQsc35irwu3E57ft3Omak9UIvttjjK54LTS6/pPqx2U8WIxTkKR4xzdggHGD2rgm4j/uCzSeTLZxboLUz72ocJBcKpL1BMSZRwKGyjx+ymsulBBIarqthui8PhhKpF9JosDKsD4zF04TAlHtkRHAcjzhEyC4eFDQ7NuD1OSirzAJASetuHJ7hCMRVRwqGwjd4Rc2DcnvgGQFmBh5klPvtjHAAzlp11FkdsG9k4V1W+fd2I9E2d0HYEVEw/lHAobMNscdgV34ixsLrI/hgHwIyl9DrsF475pfNxCVd8jMPCPlVmvAu0lNyQK884Z1OMA6CsxhConhZlcUxHlHAobKNv2BwYt8/iAFg6I48CoVWpR3CCt8iehaqWTorF4XF6mFc6b3IsjoYGIg4X4ZhwCPB4rQ34myk3WRw9rcrimI4o4VDYRpzFkWevxbGszAiyDjsKwOLOrjozlsbFOOwSDtDcVeYYh8Mm4XB4vTjmGPUcHo9AOGz6/wPKasyuKmVxTEeUcChsw+7iPzOLSwzh6JUFKWbmSMks+l2G9VRi45/Q4pJF5JuD4xZ2xh3DXKPo0OOwN9PJ7Krqax8mEo7Yup7CepRwKGwjrvjPZlfVnAJjre5wHqNBmx5+Dgf9+cYDvHikL8Xk3Fjqm6P/gY76HAinfe4jUT9XH7si/hQzc8eT56KwTGt4GQlL+jpGJrhCMdVQwqGwjfisKnstDl/IKCbrlQUc7bDPd97vNj4xFw91pZiZG/Mc1fp4wCsJhoMpZudIzSx96AoM2LdOlLgAeatyV003lHAobKNn2P6qcZ2RXn3YTwGH2+17+PW7jFTV4r7TKWbmRv6o4cIZ8kqO9h21bS1ZUauPnYO9tq0TIz7OoQLk0w0lHArb6ItLx7XXVYVpY6U+WcDBVhuFA+OBXtx9wrZ1IgPGPQz54GDPQdvWCheV62PHQBeRQCDF7NwpU5lV0xolHArbiLM4bM6qMlscfRRwqM2+Pkj9phhAccchiNgT3A339+vjIZ9gf9d+W9YBCISMLCpXcIjAseO2rQVQXqtqOaYzSjgUttF7Bi2OQ232WBzhSJgBU0v1otEB6Dlmy1oRs3B47bU4/MMhfewKjRA40mjbWhDvquppHUJG1G6A0wklHApbiEQkA37jYVTss6+FBTDG4jjVM8xwIDT+/CwZDBqWTFE4ghOgZee483Mh3B/vqjrQfcC27VYDJuFwh0bwNx5JMTt38oo8ej+sUCDCQI/aDXA6YatwCCGuEkIcFEI0CiG+nOR1IYS4K/r6LiHEmgyu/YIQQgohKu28B0V2DPhDxJ5xhV4XLps64+okWBxSQmO79e6qfr9hBRTHXFS2CYeR6jvkEwwEBmgZaklxRfb4TW5FV3AY/xF7hQNUZtV0xra/ZiGEE/gRcDWwDLhRCLEsYdrVwMLo163A3elcK4SYBVwBnLTr/Styo9+Uiltid3wDxlgcgC1xjv5AEuFo3WX5OgARk8UxrJU9cKD7wDizc8M/YnZVDeO32VUFCQFylVk1rUhLOIQQvxVCvEsIkYnQrAcapZRHpZQB4GHguoQ51wEPSI3NQKkQojaNa38I/COgHKNTFPMGTkV2u6lgjMUBcNiGOEef37ACdOE4vQNscCGZg+ODPu3fg932xDnGxDiOn0AGbawbAcprlHBMV9IVgruBDwOHhRB3CCGWpHFNHXDKdNwUPZfOnHGvFUK8B2iWUqb0DwghbhVCbBVCbO3o6Ejj7SqspH/UeOgUT4bFMWo80A2Lw3rhiLM4RLSSe6Qbuqx37YQHjLWGo8Jhm8URF+MYhlCIwEl7DfqyWuWqmq6kJRxSyueklDcBa4DjwLNCiL8IIT4mhBjvqZCsS1rix7Lx5iQ9L4TIB/4J+EYa7/leKeVaKeXaqqqqiaYrLKbf5PqYbFdVv5wkV1We6ffq1GuWr2V2VQ36tD+J/d32pOTGu6q0FiB2B8gTiwDtCvwrrCdt15MQogL4KPBJYDvwX2hC8uw4lzQBs0zH9UBime14c8Y7Px+YC+wUQhyPnt8mhKhJ9z4Uk4M5xlHss1k4wiGItsmQCIYd2ifZ5t4RhvzWZlbFCUdxvfHCqc2WrgPxrqpQNJ25ZaiFzpFOS9eRUsYHx0Pap39/42FL10mksMyLO9q+3T8cYmTAXteYwjrSjXH8DngFyAeulVK+R0r5aynlZ4HCcS7bAiwUQswVQniAG4ANCXM2ALdEs6suAPqklC3jXSul3C2lnCGlbJBSNqAJzBopZWtmt62wm3hXlc0xDpObSvhKmFNh/EpanVkVl1VVvsB44dTrlq4D8XUcdbVG99qd7dZmcYWDESIh7dO+Q0gcEe1n5z9kr3AIIRI2dVJxjulCuhbHT6SUy6SU344+2BFCeAGklGuTXSClDAGfAZ4B9gOPSCn3CiFuE0LcFp22ETgKNAL3AZ9OdW02N6g4M0yqxWEKjJNXyqJqYxMnq+MccRZH5WJwREWx4wAMd1u6ltniWDRrtT7e0bHD0nXMbiqPz6n7iUcP2FepHkO1HpmepCsc30xybtNEF0kpN0opF0kp50spvxU9d4+U8p7oWEopb4++vkJKuTXVtUm+f4OU0lq7XWEJfZOZjmuKb+ArZaFJOA5bbXGYhSO/EmpXGS82bbFsnYjfj/RHW5u4XJwz6zz9tZ0d1loc/iFDOHxFXoi2bw+ePEV40N6Hudni6FYB8mlDSuEQQtQIIc4D8oQQ5woh1kS/LkVzWykUSekfNVWN2y0coz3GOK+URdWGq8pyi8PsqvIUw6zzjRctDJCbGxw6i4tZNWO1fry3c6+lLdbNFoe3wI13XnRvDinxHzpk2TrJKFe1HNOSiSyOdwJ3ogWhfwB8P/r198BX7X1riulMvKtq8tqN4Ctl4QyTxWFxZpXZ4ijxlMQLx0nrhMPspnIWFVGZV0ldoZbNHogELM2uMgfGvXkuvEuWGq8dtCf9N0aZquWYlqQUDinlz6WUbwc+KqV8u+nrPVLK303Se1RMQybVVWWOcfhKmFtZgCu6Z7bVmVVxBYCJFkfzG2CRJWAOjMf2Gl9tsjqsdFeZazi8+S58S4xA/Oh+e4WjuNKHw6X9rIb6AnHWj2LqMpGr6ubosEEI8feJX5Pw/hTTlEktADRbHHmleFwOGiqNT7JWxjniYhzeYiiuhdLZ2onQiFZFbgGJFgfAqiojnmKlcATMwfF8N94lRn3vqM0Wh8PpoHSGyqyabkzkqor99RUCRUm+FIqkmAsA7Y9x9BpjXymALXGOcCQc1x230B1dY85FxqTjr1izlqn4z1Fsr3Akuqp8JuHwHzqMDNu0f3sUc5xD7QY4PUjpfJZS/jj6779OzttRnC2csayqvFKAaJxDK++xqpZjwLQXd5GnCKcj2nKk4SLY+ZA2PvFnuDh3Y9zcGddZrLmqFpUtIs+Vx0hohNahVlqHWqkpyL32NdFV5aqowFlVSbijEzkyQuDESSNgbgMVdYU0vtEOQOcp+zbgUlhHugWA3xVCFAsh3EKI54UQnSY3lkIRRyAUYSSofUp1CCjwOO1dMInFsdBkcVi1jWycm8pTbLzQ8FZjfHKzJXEOc7sRZ9TicDlcnFN5jn7eqnqOuKyqfO2zpG8SA+SVs4yfVecp+7b8VVhHunUcV0op+4F3o1VrLwK+aNu7UkxrBhLiG0Ikaz1mIUksjqW1xoN97+k+S/ogjSscpXOgJNohJzBoyf4c5gaHjmJjrdVVq/XxtrZtOa8DiRaHZh1OZoC8apbh9e5sGlS7AU4D0hWOmK/hGuBXUkprS2QVZxVxNRx2V41DUotjbkWBbul0DgZo6/ePvS5D4mo4vCbhEEJzV8U4/mrOa0XiguPGWmurjUYNW9u2YgVxwhFtDxMXIN9rb9OG/BIPeUXa70nQH6avY8TW9RS5k65w/EEIcQBYCzwvhKgC1F6PiqRManwDYMSIB8QsDodDsHxmiX56T3MfuTKuxQEwx+SuskA4zMFxZ4nJ4pixGme0nfvhnsP0mkUzS+KzqjThyFuxQj83sns3Mrb3iA0IIeKsjg7lrprypNtW/cvAhcBaKWUQGGLspkwKBZBQ/Gd3g0NIanEALK8zHri7LRCOMTUcZswWx8lNWsfeHDAHxx0miyPfnc/yiuX68Rvtb+S0DiRkVUWFwz1rFs6yMkCzfgLHj+e8TioqTcLRfkIJx1Qnkx39lgIfEkLcAlwPXGnPW1JMd+JqOOx2VUXCYHIh4TOsjBV1xnjvaYstDm+CcJQ1QKzNugVxjmTB8Rjn1Rh9q7a25u6uSsyqAs0KyFtlpP+O7LBnX/UY1XON/8+2Y7n/rBT2km5W1S/QWo9cBKyLfiXtiqtQTG7VuOkh4y0Bh5HBdU6d2VXVT66kdFUJEZ9ddSI3d1U4oVeVGXOc44223CwOGZHx3XFNFmLeapNw7Jw84eg4MUA4bJ9rTJE76Voca4G3Sik/LaX8bPTr7+x8Y4rpyxkr/ssriXtpflUhPrf2K97aP0rHQG4B8rg+Vd6SsRMsDJBH+kyuqgThWDNjDQ6h3deB7gNx7ytTAv6wvi+n2+vE6TQeCXmrV+tju4WjoMRLYZkXgFAwQnezKgScyqQrHHsAtcueIi3iXVWT2+DQjNMhWGZKy92To7tqTGfcRMzCcSL7OIeUMt7iKIp3VRV6CllSrmU9SSTb27ZntQ4kj2/E8J2zQrOkAP+hQ0SG7H2YV881xFi5q6Y26QpHJbBPCPGMEGJD7MvON6aYvpyxBofRjCozce6qphyFI5WrCqBsLhTN1MaBAWjN7lN6ZGgIollMIj8f4R77f2hVWq45vuFJSGRwFhbgXbgw+qYijOyxNy23Zp7xf3q6UQnHVCZd4fgX4L3Af2C0Vv++PW9JMd2Jz6qa3E2cEokTjlwtjlTBcRgb58hyO9lIkgaHicQJRw4B8kCSwLiZuAC5ze6qukVl+rjpYI8lRZsKe0g3Hfcl4Djgjo63ANaUrSrOOia1AHAii2OmdQHyCV1VEN9mPcsdAeM64xYnX2dN9RpEdJPX/d37GQpm50ZKVjVuJi5AvmNHVmukS0V9oS5eI/0BetSOgFOWdLOqPgU8Cvw4eqoOeMym96SY5vRNZh3HBBbHwupCPC7t17y5d4TOwewD5BO6qgDqTcmGFghHYmA8Rom3hIVlmhspLMPsaN+R1Vr+kfFjHBAfIB9+4w1bCwEdDhFndTQf7EkxW3EmSddVdTvwVqAfQEp5GJhh15tSTG8GplCMw+10cM5M4+G77UR2D6NQJKS3VBcIijzj7CpQfQ64fNq49yQMtGW8VuK2seNhRZwjWbsRM55583BWVWrvq6+P0f3W7TyYjLrFpfq4SQnHlCVd4fBLKQOxAyGECz2JT6GIZ1ILAOMsjiQpssDahnJ9/EaWwpHYUj2WDjsGpxtmnmscN2f+QA/3mV1V4297s7Ym9zhHXHA8icUhhKDg/Av04+HN1m2Pm4y6xSaL41CPang4RUlXOF4SQnwVyBNCXAH8BviDfW9LMV2RUia4qiZ/E6dEzptjPIy2ZikcabmpYuToroqYO+MWjb/WedVGBfmerj2MhDJvDmgu/vMliXEAFFxgxG2GNm/OeI1MKK8t0Bse+odCdDar/TmmIukKx5eBDmA38DfARuBrE10khLhKCHFQCNEohPhykteFEOKu6Ou7hBBrJrpWCPHv0bk7hBB/FELMTPMeFJPAaDBCMKx9SvS4HPjcNu/FkaSleiJm4djd1MdoMPMd7cbtjJuM+nXGuClXi2P8tcp95cwvmQ9orrRsdgUMpEjHjZF/wYX6ePj114kM2xe0FkJQv1jFOaY66WZVRdCC4Z+WUl4vpbxPTpArJ4RwAj8CrgaWATcKIZYlTLsaWBj9uhW4O41rvyelXCmlXA08AXwjnXtQTA6T6qaCBIujLOmUykIvc6N7kAfCkaw65WZmcZiEo3lbxoWA5uI/RwpXFeTurkpVABjDU1+n13NIv5/BP/8543UyweyuOrVfCcdUJKVwRC2CfxFCdAIHgINCiA4hRDoP6/VAo5TyaDQ+8jBjO+peBzwgNTYDpUKI2lTXRjeUilGAirVMKSY1owrSsjggd3dVys64iRTPhOI6bRwcgo7MAspxdRzFyeM2MXINkCfb/S8ZhZe9Qx8PPv9CxutkwqylRkzq9KEeQllYiAp7mcji+DxaNtU6KWWFlLIcOB94qxDi/01wbR1wynTcFD2XzpyU1wohviWEOAXcxDgWhxDiViHEViHE1o6OjgneqsIq+id7L440YhwAa83CcTxz4Ziw+C+RHOIc8XUc6Vscuzt24w9nlm6crDNuMoouu0wfD/7pT8hQbm3jU1FcmUdpdT6g9a1qOayqyKcaEwnHLcCNUspjsRNSyqPAzdHXUpFsv9BE62C8OSmvlVL+k5RyFvAg8Jlki0sp75VSrpVSrq2qqprgrSqswuyqKrK9pXoERpO3VE9kbYMhHNtOZl6VHNfg0JPaCgByinOMt21sMirzKmkobgAgEAmwq2NXRmulajlixrd8Oa7qau399fUxvM3e+t/Zyw2r48S+LlvXUmTORMLhllJ2Jp6UUnZgbCc7Hk3ALNNxPXA6zTnpXAvwEPBXE7wPxSQyqX2q/H3onyc8ReAc/8E3r7KQ0mjWUPdQgKOdmVVaZxQchwThyMziiKQZHI9hzq7a3p5Zw8N0sqoAhMNB4Tverh/b7a6avbxCH5/co4RjqjGRcASyfA20tiQLhRBzhRAe4AYgsTHiBuCWaCzlAqBPStmS6lohxELT9e9Bi70opgjmluoldsc4zHtxpIhvgFaVfN5ss7uqO6OlMgqOA9SuAkf0/jsPwUj67rFUnXGTsaZaT0ZkW1v6lkA4HCHk1+IHQmht1VNR9A7DXTXw/PO29pKqW1iKM9oSv6d1mP4utQ/5VGIi4VglhOhP8jUArEh1oZQyhOZGegbYDzwipdwrhLhNCHFbdNpG4CjQCNwHfDrVtdFr7hBC7BFC7ELbhfBzmd60wj7iguOTWvxXOuF0cyHga0dtFg53HtSY/kSa099wKa7lSMnEbrFzZxgFhzs6dhCOpBdMDiQU/wlHMg+xQcH563EUFgIQbGpidO++tNbJBpfHSd3CUv341L7Mfl4Ke0n5kVBKmVMSvpRyI5o4mM/dYxpLtHYmaV0bPa9cU1OYSQ2OT9BuJJEL5xvuj01Hu5BSIkTqh2WMuKyqdFxVoLmrTkddR01bYcHlE14ig0FkrE7C4cCRnz/xMoX1zMibQftIO0PBIQ73Htb360jFRO1GEhEeD0WXXUbf448D0P/URvLOWT7BVdkze3kFJ6OCcXJvN8svTsytUZwpMtlzXKGYkEmtGk+j3YiZc2YWU+jVHpAtfaOc7E6/kC3j4DhAXeaZVeFBo1LaWVSEcEz8JyqE4Nxqw+pI1101GlfDkd7Pqviaq/XxwFNP2+quMgfITx3oVtvJTiGUcCgsxZxVNdUsDpfTwTpTdtWmI+kHXTNOx4WElNyt+uZMqUi1ZWwqzO6qbe3pCUe6qbhmCi68UHefBU+fZtTGPTpKq/MpqtAaRgZHw7QeUWm5UwUlHApLmcoxDhjrrkqXtPbiSKR8HuRFPzWP9kL3kQkvSWcvjmTEZVa1bU/LEvAPZW5xCI+HoisMl1v/U0+l/R4zRQgRn121V8U5pgpKOBSWEp9VZbdwmDKV8pK3G0nkgnnGg2hzNM4xEcFIkOGQ5tZyCAcF7oL03p8QGaflhk0WhzONwHiMhaUL9ffVPtJO82DzhNeYLQ5fQfoZcMVXG+6q/qefsXWPjtnLDHfVSVXPMWVQwqGwlMndxClz4Vg+s4Qin/a+2vr9HEujnsNsbaRsqZ6MjIXDnFGVvsXhdDhZXbVaP06nnsOfRYwDoOD883GWaf/fobY2RmwsBqxfUoYjmu3VeWqQob7sN+JSWIcSDoWlTGqMIwvhcDoE5881PsWm467KOBXXTIatR8J9vfo4E4sD4us53mibOP13NIsYB4BwuSi68kr9uH+jfe4qj89F7QLj/0Gl5U4NlHAoLCMckQyY9hu3veVIFsIB8e6qdALkWWVUxahbg95Bp20vBFJbOJk0OEzEHCBPRziyCY7HiHNX/fGPyLB9jQjNcY4Te5W7aiqghENhGYNm0fC6cE5QUJYzcZ1x0xcOc4D8z42dhCfYZS7jdiNmfCVQFa2pkBGjrmMcwr3ZxTgAVlatxOPwAHC8/zhtQ6m3rc0mOB4jf91afUvZcGcnIzZmV5mF49S+biJqV8AzjhIOhWVMag0HZG1xLK0ppqrIC0DPcJBdTb0p5+fkqoKM3FVxWVUZxDgAvE5vnNXxeuvrKefHWRwZBMcBhNNJ0aWX6seDL76U0fWZUFFXQH6JJoj+4RDtx/snuEJhN0o4FJYxXYTD4RC8bZHRMfnFg6nb7me0F0cyzAHyU6kf5uasqnTajSRyfq2xzevmltTbvMZlVWVocQAUvu1t+njw5Zczvj5dxqblKnfVmUYJh8Iy4gPjNmdUhfzaJkkAwgneiZsBmrl0sUk4DqUWjqyK/8zMNrZe5dgrEBq/P2i43+SqyjDGAfHC8VrLaynTjdPZ/S8VBRdeCO7o/uAHDhBsbc34e6SLOS33hKrnOOMo4VBYxhkr/ssr02omMuDiBVXEQjC7mnrpGhw/zTOn4DhA5UIona2NAwNwanxLwFw57izNfK1lFcsodGuNCNuG2zjRf2LcuXFZVQWZ/7wcBQUUrDPccIMv2Wd1zFparv+I20/0MzI4UXNuhZ0o4VBYxqQ2OMzSTRWjJN/NmmibdSnhlcNjtp3RySk4DpqoLTTSVzn8x3GnhjPciyMRl8MVt53say2vJV8noaW6Z4KW6uMxWe4qX4Gb6rnR/w8JTWov8jOKEg6FZUxug8PchAMS3FUH28edl3NwHOKF41Aq4TC7qrJbK85d1ZpcOPxDmbVUH4+CSy7Rx0ObNhEJ2GcJzFpminOoKvIzihIOhWVM9eK/RC5dPEMfv3x4/LTcnIPjAA0Xg0tr2EfnQeg5PmZKZHQU6Y+6zNxuRBot1ZNhFo4trVuIyLEtQbKtGk/EO3cu7jmaG04ODzO8JbPdDjPBHOc4ta/b1s68itQo4VBYRnyMY+q1G0lkWa2Rlts9FGD7yeTuj5yD4wCefE08Yhx+dsyURDdVunuFJLKgdAEVPu3Tea+/lwPdYzfJjM+oyu1nVXiJ4a4aevmVnL5XKmbMKdKD+EN9AbpPZ7b9r8I6lHAoLCOuwWEOn2LTwgLhcDgEly81rI6n9yTPCrLEVQUTxjki/dkX/5kRQsRZHX85/Zcxc3KpGk+k8OKL9PHgq6/m9L1S4XA6qF9i/KxPqvYjZwwlHArLmNysqtyFA+Cdy2v08dN7W5O6PwYCxh7gJd7sH+gsMgnH0ZdgNL6QzYr4RoyL6oyH+StNY62AOFdVFhlVZvLXr0d4NcstcOQIweaJO/Nmy+xl5ipyFec4UyjhUFjGdItxALxlfiVF0V0Bm3pG2NcS/zAPhoOMhEYAcAon+a7s4g4AlDUY+5CH/XAwfmfk+KrxHAQKeGvdWxHRHlk7OnbExWkARofMFkduPyuHz0f++vX68eAr9rmrZpniHKcP9xEM2NcjSzE+SjgUljHdsqoAPC4Hl5ncVc8kuKv6AvGB8WzjDjrL32+M9/wu7iVzn6pMWqono9xXzopKTaQiMjLGXZVr8V8ice6qV+xzVxWV+yir0cQ7HIpw+nCvbWspxkcJh8IypvomTuNx1Tnx7iozOddwJLL8fcb4yAtx9xFXNV5SmvNSF9WP766yMsYBUHCxEfgf3rQJaWtabnx2lWLyUcKhsAQpZVwB4HSJcQBcsqgKr0v7UzjUNsiRjkH9NcsC4zHK58LM6L4ZkSDsf0J/ycoYB8AldUaNxavNr8al5Zotjmz6VCXiaWjAPWsWAJHhYYZt3Nxpdlw9hxKOM4GtwiGEuEoIcVAI0SiE+HKS14UQ4q7o67uEEGsmulYI8T0hxIHo/N8LIUrtvAdFevhDEQJh7cHkcTrwuW3+TBInHKU5fat8jyuu6eFTu1v0sSWpuImcY3ZX/VYfRvqsi3EALK1Yqqfl9vh72Nu5V3/NaotDCJHgrrIvzjFzUSnOqND3tAwx0D1q21qK5Nj21y2EcAI/Aq4GlgE3CiGWJUy7GlgY/boVuDuNa58FzpFSrgQOAV+x6x4U6ZMY38g5FjARWe7FMR7XrKjVx3/YaQiHJcV/iZjdVcdehiGt3Un8fuO5r+UQjrjsqpebjZYgVgsHxLur7KzncHuccbsCqm65k4+dHwvXA41SyqNSygDwMHBdwpzrgAekxmagVAhRm+paKeUfpZSx3/rNQL2N96BIk/7J3Gs8HAL9gS60zZJy5Ipl1bqVdLBtgAOt2qd/y11VACX1MOsCbSzDsO9xID6rKpuW6sm4uN54mL90ytgzw8p03BgF55+PiHXLPXyYYEvLBFdkT8OKSn18bNf4fcYU9mCncNQBp0zHTdFz6cxJ51qAjwNJNzwWQtwqhNgqhNja0ZG6bbYid/oms8HhqCm11FcCjuwa9Jkp8Lq4bGm1frxhx2kgIThulXBAvLtq7++BxBiHNcLxlplvwe3Qfh77u/dzakD7s7LD4nDk55M/Sd1yG1YawtG0v4eAafdJhf3YKRzJfBWJ1VXjzZnwWiHEPwEh4MFki0sp75VSrpVSrq2qqko2RWEh5hqO6RQYN/OeVTP18R92nUZKSa+/Vz9X5rNuLZZdh/5rfvxV6G/JuaV6Moo8RVxQe4F+/MLJFwAYHbI2OB6j0LQr4MCzY9uqWEVJVR7lMwsALS1XdcudXOwUjiZglum4Hjid5pyU1wohPgK8G7hJqk5nU4JJtThsEo5LF1dRFO2xdap7hO2neunxG2uVekstW4uiGmiIxR8k7Pmt5VlVMa6Yc4U+fvbEs4RDEUIBLZFBOARuX+4WW4yiK4y1hjZvJtRj3wN9rsnqOLZTeRUmEzuFYwuwUAgxVwjhAW4ANiTM2QDcEs2uugDok1K2pLpWCHEV8CXgPVLKYRvfvyIDzDUctsc4bBIOr8vJ1aaajg07TtM72qsfWyocACs/qA/lrl/HV45bKBxvn/V2nEITh50dO2nqNGIP3jyXpYkM7tpa8lat0g7CYQZf+JNl3zuRuasMT8Lx3V1ExulurLAe24QjGsD+DPAMsB94REq5VwhxmxDitui0jcBRoBG4D/h0qmuj1/wPUAQ8K4TYIYS4x657UKTP2WBxALxnlRFKe3J3i32uKoCl7wGn1uMpcnI3RKJWQH4+wuOxbJlSXylra4zYw8tHjMpuq+IbZore+U593P/HZyz//jFmzCkiv0T7fxodCtJ6pG+CKxRWYWuyvZRyo5RykZRyvpTyW9Fz90gp74mOpZTy9ujrK6SUW1NdGz2/QEo5S0q5Ovp129iVFZPNdC3+S+TC+RVUFmoP844BP21DRoFZTg0Ok5FXCou0h2w4YPwpWlHDkcgVsw0X0usn3tDHtgjHlUYzx6G/bIqzpKxEOERckPzItvE341JYi6ocV1jC2WJxOB2Cd680ajr6zBaH12KLA2Dlh4AE4bDQTRXjsjmX6U0Pj7UbCYs+i1JxzXjq6/Cdc452EAwy8MILlq8RY8G5Rp+xw2+0EwmP3bRKYT1KOBSW0HuWCAfAtbHsKhEkjLYjn8vhosBdYPlaLLwCfKVEAkacwQ7hqMyr5NwZ5wLgDebp532F9vysit5pWB39f3gixczcqFtSRl6x5q4a6Q/QfLDXtrUUBko4FJbQM2Q0tSsrsM4/n5RhU6WwDcKxZnYps8vzEU4j96LUW2pPNbzLC8vfG29xlNlg2QDvmf8eAHyhQv2cXcJR8q53QfT/a2jTJoJtbbas43AIFq41rI5DryffjEthLUo4FJbQM2wIR7ntwmGqFC6wvkZHCMEH19YjnMbWpJZnVJlZ+SFCoybhsKiGI5Gr5l5FnisPX9CwnPJsEg73zJnknx/dhTASoW9DYkKldSxab2TCHdnRQUjt0WE7SjgUltBjamFRave2sUMmi6OgYvx5OXD9ebNwuAyLI89pvftIZ9YFhDGsDKe0p+NrgbuAq+deTV7IEA5foX0iX/Jeo8NQ32OPJ91d0QpmzCmipEpzvwVHwxzfrXpX2Y0SDkXORCKSXpPFUZY/iRZHfuX483KgpsTH8nqjMK5/0MZ7cjgIFy7QD119e2xb6sYlN+ILGq6qQYd9KazFV1yByNc2XQocOcLoHnvuSwjBovVGu5j9f7GvR5ZCQwmHImf6R4PEaq+KvC7cTht/raTUu8kCUGCPcACsmmNYTs3dDsI2FpiFXIa7xdl/ALqO2LLOkvIlzHAYWWPPtj1tyzoAjoICik2puX2//71tay2+oFbv4HJyXxd9Hao22E6UcChyxuymsj0wPtqnbYAE4C4Ad17q+Tkwo8zwlQ+NePnTAfvqBMKm5AKnLwKv2VfXWiGMT+fPtT/Nge4Dtq1V8j6jhXzf4xuIDA2lmJ3DOlV5xgZPEva81GzLOgoNJRyKnOk2Z1TZHd8Ytj++EWPAtN+4DBXw803HbVsr3G3ENVzeMGz7RbxlZSWjhgtuxDXId17/jm3xh/z16/DMnQtAZGiIvieftGUdgBWXGlX/+//SQlAFyW1DCYciZ+LiG3ZbHEP2xzdimNuNyHA+rxzu5HDbgC1rhXqN2hSnNwKhEfjLXZavE4lI/KbOuH7XEFvbtvLcyecsXwu0+EPZDR/Sj3seftg2kZq9vILiSh+gtY0/vMWeFGCFEg6FBcRbHJOZimuvcPSMGg9zGdaCvP/3l+OWryOlJNzTqx87vdHq5833QM8JS9cKDIeIPbelJ0TEoa31/a3fxx/2W7pWjJL3vhfh1dq4+PftZ3TXLlvWcTgEyy8xrI5df2qyTaTe7CjhUORMrznGYbdwDNlbw2Gma9Rwi8mwlon0u23N9Jnu1woiAwMQ0roLO/Lzccw+T3sh7Ifn/83StUYGDZEvLi7Q61OaB5v5+d6fW7pWDGdJCcXXXKMf9zz0K1vWAVj2lpm4PNpjratpkJN77UltfrOjhEORM93DkxnjMLuq7I1xdI0YwjG/TMt6GgmG+dWWk5auY45vOMvK4J3/Yby451Fo2prkquwYGTREL7/Iy+2rb9ePf7L7J7QO2VN5XXbjDfq4b+NGgu32JBr4Ct0su8jYkOuNp4/bss6bHSUcipyZ3BiHOThun6sqHAnHbeL08QtX6OOfvnqM0aB1gddQtym+UV4Osy+I7hAY5akv6S3Xc2XUJBx5hW6uX3Q9C8sWAjASGuGHb/zQknUSyVu5krzVq7WDYJCeBx+yZR2A1ZfPxuHUcnNbGvtoaey1ba03K0o4FDkzqTGOIdNObzYGx3v9vUSk9rAu8ZbwvnPnUF1stFt/ZOupVJdnRNgcGC8r1QaX/ys4o/+XzVthxy8tWWtkwPhZ+QrduBwuvrL+K/q5jcc2sr19uyVrJVL+sY/p496HHyYybE+tRVG5j0XnG3UxbzxtbZxIoYRDYQHxdRx2txsxuThsjHF0jhgusQpfBT63k1svma+f+9GfGhmxKN0z1Gms5SqPut/K58JbP2dMevafYTh3f/1wvyEc+VEhXFezLm572e9t+Z4tQeWiyy/DPUvbETrc10fvY49ZvkaMNVfO1gsCT+zpovWo2uTJSpRwKHLGbHHY3uBwwJRiWVQ9/rwcMQfGK/K0h/mH18+mqkh72Lb1+7n/z8csWStOOKpMYnjR30PJbG080g0vfDPnteKFw/hZfWHtF/A4tOPdnbttSc8VTiflt9yiH3f/7P+QQWsTDWKU1RSwcK3x+7H5sSMqw8pClHAocqZjwEjjrIrunmcbg6bgbWHN+PNyxBwYr/RpLrE8j5PPX75QP/+/f2qkuXck57XCccJhcr958uHqO4zjrffD6dzcSHHCUWIIx8zCmdywxAhg37XtLkKREFZT+v736TscBk+dsrVr7vp3z0U4NLOj+VAvp/arDCurUMKhyAl/KKzv/ud0CHtjHCG/sYmTcNgaHDcLR8ziAPjQ2lksmKGl5g4Fwnzld7tz/iQb6jAJR2XCPS2+BhbE3EgSnvxCToHy4b7kFgfAp1Z8ikK3dm/H+4/z+0bre0s5CgriYh2dd99jm9VRWp3P0rcafbk2P3YUaWO/sTcTSjgUOdFlqguoKPDgcNiw2VGMQZObqmAGOJzjz82RZK4qAJfTwR3vXxHbo4iXD3Xw6BtNOa1ldlU5E4VDCLj6O5YFyocHxheOUl8pn1jxCf347h13Mxy0PoBddvPNOEtLAQg2Ndka61h3zVycbu0x13FygH1/Pm3bWm8mlHAociLOTVVks5tqkuIbkGBx+OLrRdY2lPPRtzTox//+xD5a+0azXivUYWSKuSqTBPwr5lsWKB8vxhHjpqU3UZWnvYeOkQ4e3P9gVuukwllYQPnHP64fd959NxG/PVXrhWVezr1itn686fdH4v4PFNlhq3AIIa4SQhwUQjQKIb6c5HUhhLgr+vouIcSaia4VQnxACLFXCBERQqy18/0rJmZShWOS4huQkFWVN7bQ8IvvXMzscq0NSf9oiM89vD2rtutSyvjg+IxxMsUsCJQHRkOE/FommNPlwJPnGjMnz5XH367+W/34/j330zvam/FaE1F+04f1LXJDp1vo/tn/Wb5GjPOumkNxdKMn/3CIV39z2La13izYJhxCCCfwI+BqYBlwoxBiWcK0q4GF0a9bgbvTuHYP8H7gZbveuyJ9OgYN4ai0PTA+iRbHOK6qGPkeF3d+YBUxz9xrx7q56/nMH0iRoSHkqGatCJ8PR0FB8omefLjq28bx1vvh9I6M1kq0NsbbQ/19C95HQ3EDAIPBQe7bfV9G66SDo6CAqr/7rH7cee+9BNvsqSZ3eZxceuNi/fjwljaObLevRf6bATstjvVAo5TyqJQyADwMXJcw5zrgAamxGSgVQtSmulZKuV9KedDG963IgDPmqrLZ4kjlqoqxfm45n7tskX783y8cZtORzLYtjXdTVY77MAdgybtg/mXRAwkbv5hRoHzEJBx5SdxU+vtwuPjcGsM19qsDv+L0oPWxgdIPfADvQi1LTQ4P0/FDe6rWAWYtK4/bJfCFBw7Q35l7RtybFTuFow4wl9c2Rc+lMyedaxVTgDOWimujxRGMBOke1WIIAjGucAB85h0LuHCe9npEwuce3k7XYPr++rhU3MTAeCJCwNXfBUe0yLLpddj1cNprTRTfMHPZ7MtYWbkS0P4/frTjR2mvky7C5aL6q0bVet9jjzH0+uuWrxPj4g8toqhCa7seGAnxzH17CIesaeXyZsNO4Uj20SnRCTzenHSuTb24ELcKIbYKIbZ2mD7VKaylc/Dsszjah9uR0V+3yrxK3M7xq+GdDsF/3rBaL3xsH/DzD7/ZSSTNeEdovBqO8ahcAG8xXDw8+420A+WZCIcQgs+f93n9+A9H/sChnkNprZMJBRdeSNEVl+vHrV//BpHR7BMNUuErcHPlJ5frmX/tJwbY9Ht7tug927FTOJqAWabjeiDR3h1vTjrXpkRKea+Ucq2Ucm1Vlb3tt9/MTKqrqt/0K1BUO/68HDF3iK0tmHid6mIf3//gKv34xYMd/OTVo2mtFWwzxNBVNSO9N3jJF6A4aoAPdcCGz0IatSSDPcYDubBs4p/Vupp1XFx3MQASyZ1b7rSl+rr6a1/DUajVjwROnKDzR/9r+RoxauaWcOH7jdYxO58/xbFdNu20eBZjp3BsARYKIeYKITzADUBimegG4JZodtUFQJ+UsiXNaxVTgEkNjveZ2pmXzhp/Xo60DLXo4+qC9Fxib188g1svmacff/fpg2w/2ZPiCo1Qi7GWe2aaYugpgHd93zg+8ARs/emElw10Gz+rwjJfWkt9bs3nEFEHwKaWTfz28G/Te48Z4K6uZsYXv6gfd91/PyN791q+ToxVl82iYYXhfnzhgf0M9dmTDny2YptwSClDwGeAZ4D9wCNSyr1CiNuEELdFp20EjgKNwH3Ap1NdCyCEeJ8Qogm4EHhSCPGMXfegSI2UcvIsjtF+GI02qnP5bG1wmKnFEeMLVy5m1axSAEIRyWd/tV2vqh+P4GlDOFw1GVhRi6+GdZ8yjp/+KjRvS3nJYLdhcRSVp/ezWly+mJuX3awff3fLd2nsaUz/faZJ6QeuJ3/dOu0gHKbl61+3raJcCMFlH1lGQbTlyuhgkOd/vl9VlWeArXUcUsqNUspFUsr5UspvRc/dI6W8JzqWUsrbo6+vkFJuTXVt9PzvpZT1UkqvlLJaSvlOO+9BMT79IyGGox1ifW4Hxb6xdQGW0WfKlSiph1TZRzliFo6agvRjKR6Xg/+58VyKov8PTT0jfOV3u1K6d4LZWBwxrvwmzFiujcN+ePB66Bw/JXjA7KoqT8/iAPi7c/9OT88dCY3wuT99Lm5bXSsQDge1//5vcVvMdvzXf1m6hhlfoZvLPrZMj6ae2tfNzhesa5V/tqMqxxVZ09RrtKOoL8tPnUqaK71m4bDPTQXZWxwAs8rz+c5frdSPN+5u5T+fG/9hHmw11nLXZigcbh984P/AV6odD3fBA++FvrEtUCLhCEO9RnA8nRhHDJ/Lx/cv/T55Lq2I7uTASW577jb6A/2Zvd8J8DQ0UPU5Iw246yc/ZfCllyxdw8ysJeWce7mpqvyxI3ScGrBtvbMJJRyKrGnuMfLg60rz7F3MbHHYGN+A+BhHJhZHjGtW1HLT+cYD6b+eP8xPXhkbLI/4/UY6rtMZ31I9XaoWwU2/AbdWxU5/E/z8WuhviZs21BfQXTF5RW5c7sz6fC0qW8S3LvqWHu/Y17WPjzz1EcvrO8o/+hEKLrlYPz79pS8TaGq2dA0z5183j6rZRQBEQpJnf7qXoN+63R3PVpRwKLLG3FK8rsxm4eg1BcZLZo8/zwKydVWZ+ca1y7hkkSEE33xyPw+9Fr9XechkbbiqZyBcWbr6Zq2HD/3SqO/oPgo/fzcMGN9/sCfzwHgiV8y5gm9c+A39uLG3kZs23sTeTusC2cLhYOYdd+CaoWWYhXt7OfXJT9q2R7nT5eDKTyzH5dEehT2tw7zyiPVpx2cbSjgUWXPGLI6SetuWGQ4O6y4Yt8NNua88q+/jdTn58c3nsb7BuP6rv9/NI1uM+4iLb9TOzPIdR1lwGXzw5+CIik9XI/zyevBrrpf4wHh2wgFw/aLr+Y+L/gNXdJ3OkU5ueeoWHj30qGWpuq7ycup++AOEWxPCwPHjnLjxw4zu22fJ90+ktDqfS24wOgDs/3MLh7a0prhCoYRDkTVmi6PedotjclxVidaGQ2T/J5LncfLTj65lVX2Jfu5Lv9ult2EPtpjiGzUWFDQueRdcfz+IqBuqbTf85mMQDjHQbQ6M55b9du38a7n3insp9hQDEIgE+NdN/8rX/vw1y9qw5593HjPvvBOc2r0Em5s59qEbaPv2HYR6rA3MAyy5sJaF64zU6z/94gDtJ6yN4ZxNKOFQZE3TZFoc3aYYQekc25Y50X9CH88szNEKAIp8bh74+PmcU6c9ZKWELz66k99vbyJ4ynBduWfmvhYAy66D99xlHDc+C0/9I30dxs+quCL3n9W6mnU8eM2DLCwzdkTccGQDN228iaN96RU/TkTxO6+k/kf/g8iPxm+CQbp//nOOXPlOun7yE0tbsQshuPTDiymJdtENBSL84a6ddJxUwfJkKOFQZM2kxTiGurRW4qAFgYvta1t2rN/YR3xeybwUM9OnJN/NLz9xPstqDfH4h0d2cmyb4XrxzJ1ryVoAnHszXPwF43jrT+ltNFprlFbnW7JMQ0kDD17zINfNN3qXNvY2cuMTN/LUsacsWaPo0kuZ97vfknfuufq5yMAA7Xd+n6NXX8PgK69Ysg6AJ8/Fu25fiTdfc8ONDgX53fe3cej1VrVfeQJKOBRZMRwI0T2kpXe6HIIZRdn7zSek09QMuXIhOOz7tT3WZwjH3BLrHual+R5++cnzWVITzeCR0LHfSNP1NDRYthYA7/ganPNX+mFvu+GqKq22TuTzXHl886Jv8m9v+Te8Ts0FNhwa5h9f/ke+/dq3CUdyz1DyNDQw56EHqbvrv+L+n4KnT3PqU7fS/v0fIEPW7I9eVlPAtZ9drYtHyB/m2fv38dQ9uxnqVdXlMZRwKLLC7KaqLfXhtHPL2E5TlkvlovHnWcDxvuP6OFb0ZhXlBR4e/OT5LKouRMgIMweN5pueudauhRBw3Y+gdjWBSB7DEW3TJIcTiixwVSXyvoXv48FrHmR2kZHx9tCBh/jCS18gEM59xz0hBMVXXsm8P2yg+utf0zeBAui67z5OfvJThAescStVzy3mff+wRndbARzb2clD/7KZva80qwpzlHAosuRQm/FHOr+q0N7FzNXQNgqHlDLOP2+lxRGjotDLg5+8gLUFIXxhraVGnyefJ45bv7c37jy44SF6PCv0UyWuNhwWV33HWFy+mIff/TBXzLlCP/fcyef49POfZig4ZMkawu2m/KabmPfkExRcdJF+fnjzZk7c/NdxTSNzoaKukA9+dR3LLzZiT4HRMC8+eJDH/3N7XHrzmxElHIqsONQ2qI8XVxfZu9gkWRw9/h49FTfPlUd1vj17flQVefnPtxhpuk2FM/j8r3fw45eOWO9LL6mj97x/1Q/LOAa/eC8M2rPVQJGniDvfdid/veyv9XOvtbzGp/74KUu3oHWVlzPr3h9T+dnP6Of8Bw9y/IYb8R+2ZmtYT56LS29awnv//tw466P5UC+/uWMLrcf6LFlnOqKEQ5EVh1oNi2OR3cLRYY5x2CccifENO1uo5LUZbUGaC7VCwW8/dYB/3rCXYNjazYV6g0aqb6mrGVp2wn3vgKP2tPNwCAdfXPtFPnuusW/I7s7d3PL0LbQMtqS4MjOEw0HV7bdTe8e3IVo8GWpp4fhNN1u6IVTdojJu+Pp61rxzNiLqkh3uC/DY97dzYLN19zOdUMKhyAqzq2pxjY3CMdwNvdEUWYcbKuannp8DdrupzPgPHDAOZjfowwc2neDD922mvd+6zYw6mwzrsMwVbd/RdxIeeA/87Bp4/T7os7athxCCW1feytfO/5repuRY3zFufupmy7vrlr73vcy65x4c0bTdSH8/pz7xSfqefNKyNVweJxe+bwHX/t0qPXAeDkV4/v/28+qjh4lYLPZTHSUciowZDYY53qX5rIWwOcbR/IYxrl0JLvtat+/p3KOPF5YuTDEzd0Z2G2vd8rGredcKo8HhluM9vOu/X+WlQ7m7k6SUtB03CtlmXHcb+IyCRE78GTZ+AX64DH58Cbx4B/Qcz3ndGB9a8iG+e8l39Urz9uF2bnn6Fl46Za21U3jRW5nzy1/gjO6iKINBTv/DF2j67N9ZWnE+a0k5H/jKWspnFujndj53it9+b9ubynWlhEORMY3tg8QSS+aU55PnyaxhXkY0bTXGdWvtWwfY0b5DH6+esdq2dSIjI4YfXgiKV63gv288ly++czGx5LSOAT8fuf91vvr73QyMZr8vxWCPn5HolrFun5OyC94Jt78OK28wKsxjtOyEF78N/7UafvVhOGWNu+equVfxv5f9L/kuzSIYCAzwmRc+w/e2fI9g2Lo9N3zLltHwq4fjamIGnn2WY+//K0589GP0Pf44kaHcg/QlVfn81T+ex9xVxla/7cf7+e133uA3397Ctj+eoLfdhmSHKYQSDkXG7G42PlnZHt9o2mKM6+0Tjj5/n+6qcgkXyyuW27bW6P79ENbqGzzz5uEsLMThENz+9gX84hPnU1lo7Af+0Gsnedv3XuT+V4/hD2VeE9F2zGRtzCnWfPRFNfD+H8P/2wPX3Anz3m70uAJAwsEn4adXwMM3xceYsuTCmRfys6t+Fpdw8MC+B3jv4+/l6WNPE5HWuHo89XU0PPwrSq67Lu788ObNnP7Slzl08SWc/tKXGPrLX5Dh7GtMPD4XV//NCs6/bh4OlxELaz8xwKbfHeHBb2zml9/YxKbHjsRt2Xu2oIRDkTF/OdKlj9c1ZNcEMC0i4XhXlY3CsbNjpz5eWrEUn8u+gsaRXbv0cd6KFXGvvXVBJc98/hKuWm4EtLuHAvzbE/t46x0v8K0n93GwNf16hXaTm6q6oTj+xeKZsP5TcMtj8I9HtT5X898RP+fAE/C/F8Djn8k5DrKsYhmPXvsob6t/m37u5MBJvvjyF7n+D9fz8IGHGQjkXovhLClh5nfuoOG3j1J8zdVxBaNyeJi+xzdw8uOfoPEdl9F+550EmsbuX5IOwiFYe3UDN379fBauq8bhjE+m6GsfYdvTJ/jFP23iuZ/to79zZJzvNP0Qb4ZS+rVr18qtW7dOPFExIVJK1n3rOToHNffHE5+9iHPqSia4KktObIKfXaWNC6vhHw7atvPfXdvu4r7d9wFw89Kb+dL6L9myDsDJW29l6GWtVUbNP3+DshtvHDNHSsmGnaf57tMH41q7xFhcXcS7V9by7lUzmVtZMOb1GA9/83W6osHxq29bwbzVaez50XEIXv4e7H4k/rzLBxf8Lbz185BXOvH3GQcpJQ8deIgf7fjRGKHwOX1c2XAl1y+6ntVVqy3JbAu2tND3hyfoe/xxAkeOjJ3gcFD4jrdTfsst5K9bl/Wao0NBju3s5OiODpoOdBMKxFtRDpdg5aX1nHd1A74Cd1ZrTDZCiDeklGM+sSnhUGTEobYBrvzhywCU5LnZ/vUrcNhVNf7MP8Gm/9HG530UrrVvK9HrN1zPwR7NJXPn2+7knQ327EgcHhzi8IUX6vtpz3/uOTz14/fe8ofC/HLzSe57+Sit42RanTu7lBvXzebdq2rJ9xgup/7OEX7xtU2A9tD6xJ0X48lke9+WnfDcv8KR5+PP55XBRX8Pa27JSUD6/H38bM/PeHD/g4yGx95bQ3ED18y7hnfNfRezi3Pfg0VKyejeffRteJz+J54k3N09Zo53yRLKb7mF4nddg8ObfSJGOBjhxN4udj5/itOHe+PXyHex9poGlr11Jp48G7dbtgAlHEo4LOEnrxzlm0/uB+Cq5TXc89fn2bOQlHDXudATra246bew8HJbljrUc4i/2qD1dfI6vbz4wRcp9NiTKdb/zB9pjm6P6l28mHmPP5bWdeGI5JXDHfzmjSae39/GaHBsTKDQ6+LaVTO5cf0sVtSVsOtPTbz6iBaEn728nGs/uzq7N330RXj2G5qQmHH5YPHVUL8OqhZDfgV4i7WtbH3F4EzvU3Wfv4+Nxzby20O/1cU7kbrCOmYVzaIyr5JCdyEuhwuHcOB0OKnwVTC7aDYNJQ3MKZ6TVit8GQwy+Mqr9Dz0EEOvvjrmdWd5OUVXXEH+2vPwLV2Ke/ZsHB5Pku80MS2Nvfz5t41x8SYAp9tBwzkV1C0uY0ZDMeW1Bbi9NiaaZIESDiUcOSOl5LIfvMTRDi0z5dvvX8GN623aja/xefjl+7Wxpwj+8Yhtqbg/fOOH3L/nfgCuariK773te7asA3Dq07cz+MILAFT87W3MMO2xnS5D/hDP7W/jiV0tvHiwnWB47N/wspoiru1wEunSWmO87cOLOeeSHLoKRyKw93fw/L8ZdTUT4c7XWuDXnQd1a7R/q5ePKyhSSvZ17ePRw4+y8ehGhkOZZyYVuYtYUbWClVUrWVW1ihWVKyjxpnal+o8cofsXv6DvsceRo+MEsh0O3HV1eBoa8C5aSN6qVeStXo07ulPhREgpObKtg02PHaG/Y/xYR0Gpl9LqPEpm5FNc4aOgxEtBiZf8Eg8FJV68BS5bC1MTUcKhhCNnXjncwV//VEvRLPK62PzVyyjw2mBqSwn/9y6txgBg3afgXXdavw7QH+jn2t9fS/eo5rb473f8N5fOutSWtUYPHeLYe4xsn3lPPoF3fm4FjV2Dfn63rZlfbTmpCzrAnKCDDw5pQhtGsmN1AdUzCphVnkd9WT71ZXnUl+VRVejN7EEUCsD2X8C2n4+1QNLB5YOaFTBzjSEo5fO07osmRkIjvHTqJZ44+gSvtbyW1JWVLg3FDbqQrKpaxfzS+XpdiZlwby89v/kNPQ8+FLetbyrcM2eSt3o1eatX4zvnHFwzZuCqKMeRl7yRZDgUYe8rp9n/l9N0nhpMOicVDpcgv9ijC0ppdT7lMwuoqCukrDofp9vafKczIhxCiKuA/wKcwE+klHckvC6ir18DDAMflVJuS3WtEKIc+DXQABwHPiilTNm1TQlH7owGw7z3R3/mQDSj56NvaeBf3mNTyuqWn8KTf6+NHS74ux227fr375v+nUcOaUHg6vxqnnr/U7jTdLFkggyFOPnxTzAcbYVRePllzPqf/7Hu+0vJ1hM9/Or1kzyzs4Xre9zMiGgPke2eEM/lJ6+X8Loc1JXlUVeqiUhVkZfKQi8+jxOXQ+ByCMIRSc9wkK5BPy19o5zuG6Gld5TywUOsF/tYJE4xz9FGhWuEMscohQzhDQ8i0k2xdXq1dvkFVeAthOAojPRoe7CM9hMMDnPEKejwFdDpLWC4oIxwfgWRvDKCeaW0CsmpYB8Hew7pHwBS4XF4qCvSXF+xr5qCGsp95ZR6Syl1FOHYfYDA9p2M7NhJ4OhRgqdPax9o0kTk5+MqL8dZUY6rvEL/11VRjrNc+xqgmNPtTjo7wnQ0DdLfOZpT512HQ1BSnU9FXQGl1fkUlfkoKPNSWOqlsMyLJy9za2XShUMI4QQOAVcATcAW4EYp5T7TnGuAz6IJx/nAf0kpz091rRDiu0C3lPIOIcSXgTIpZcoUGCUcuXGqe5iv/n43rxzuBMDjcvDHz19CQ4psnqwY6YXX79Wql2U0x37dJ+Fd37d2HTS/+t077+bB/Q/q535w6Q/iOrtaRbC5mbY77mDg2ee0E0LQ8Mgj5K04x/K1elqHeO4XB2g/otXahJH8pNhPv2OyPQuSYoZ5e1kH7yhqYlnkELVD+ykcsba1iY5wIsvm0FxSwy6Pm52OELvCgxwI9hIiu3t3CRd5rjx8Lh9F0svMPgd1nTCr2U/9iSFmnOjHlSTWlBXFRcjycgIldYx4yhlxlDIqfYxGvIyKPPzOQvyuQsKu7FviuzwOCks8FJR6KCzz4cl34/I4cbkdOFwOHA6BEALh0FKNnS4HK95Wn1Q47AzprwcapZRHAYQQDwPXAeb6/+uAB6SmXpuFEKVCiFo0a2K8a68DLo1e/3PgRcC+3Mk3MS8ebOeHzx1m56neuPPfePcy60XjhW9pGVTmPatrVsCV37R0mVAkxL9t+jc2HtuIP2y0xr60/lIun21t8D3Y1kbLV77C0KbNcZ9WKz9zu+Wi0Xqsj1cfOTwmAPv2Dy/hmiXFHO8cpqlnmFM9IzT1DNPUM0JTzwh9I7lVbhd6XfhD4SRxFkE/BTzeU8DjPQ2A1gK9nH5WOo6wShxlpeMoKxzHmCF6c3oPAMgwovso9d1HqUf7JAowKgT7PW52eb3s9HnZ6fXQ7krvsReSIQaCAwwEB+gAjnqBuujXenCGBXPanSxqlixqlszskhQPQ8kwuDOtLewfQPQP4OUEXqB0nGlhhwe/p5iAt4RRbxlDBbUMFcxksGAmo3mV41wVvZ9AhN6OUXo7RoHc9lO3UzjqgFOm4yY0q2KiOXXjnI9dWy2lbAGQUrYIIdKLTikyRkrGiMbfXDKPm863ISDu9MSLRv16+OAD2p4SFuJyuGgZahkjGt+55DuWBx1d5eWMHjwUJxplN91E5d/+raXrAHjzXPGiIWD9u+eyIhoQXzAjeYV//2iQpu4RWvtH6BwI0DHop3PQjz8UIRyWBCMRHEJQXuChNN9NbYmP2pI8ZpbkUV3ixevSYhPDgRCN7YMcaBlgV3MvO0/1sb+ln1CC66WbYl6MnMuLnAvRh2sxg8wVrZSIIQoZwY+bXllIL4X0ywKG8RLGQSGjlIt+5og2Zos25opWGkQrcx2t1ImuxFsDwCcl5/oDnOsPQL/mZh0Qgia3i1MuF6fcLk653HS6nPQ4HPQ4HfQ6nAw5BJEJfh/CTsHRWjhaK3ja/JlcSvL8moCUDEPxkNTGQ1A8LKPnjHHRcPqV2M5IgPzRTvJHO8e8FnJ6GcqvZaiglpG8CvzeMvzeUvzeUka9ZUSc1iWX2Ckcyf7Xx34sST4nnWtTLy7ErcCt0UO/EGJPqvnTlEpg7G+QjXz1O/BVe5eI3tNz8KmZE062gj3s4X+wLt4wDtp9fePr8I2v272Wxj22r2DZ799uK76JdUz635V1jJuwkO09zUl20k7haALMEc164HSaczwprm0TQtRGrY1aoD3Z4lLKe4F7AYQQW5P56aY7Z+N9nY33BGfnfZ2N9wRn531ZfU929qraAiwUQswVQniAG4ANCXM2ALcIjQuAvqgbKtW1G4CPRMcfAR638R4UCoVCkYBtFoeUMiSE+AzwDFpK7f1Syr1CiNuir98DbESLYzWipeN+LNW10W99B/CIEOITwEngA3bdg0KhUCjGYmujFCnlRjRxMJ+7xzSWwO3pXhs93wVcluFbuTfD+dOFs/G+zsZ7grPzvs7Ge4Kz874svac3ReW4QqFQKKxD7cehUCgUiow4q4VDCHGVEOKgEKIxWmU+bRBCzBJC/EkIsV8IsVcI8bno+XIhxLNCiMPRf8tM13wleq8HhRD29AW3ACGEUwixXQjxRPT4bLinUiHEo0KIA9Gf2YXT/b6EEP8v+ru3RwjxKyGEbzrekxDifiFEuzklP5v7EEKcJ4TYHX3tLjGZ3QaTMM59fS/6O7hLCPF7IUSp6TXr7ktKeVZ+oQXVjwDz0NJ7dwLLzvT7yuD91wJrouMitBYsy4DvAl+Onv8y8J3oeFn0Hr3A3Oi9O8/0fYxzb38PPAQ8ET0+G+7p58Ano2MPWvHvtL0vtCLcY0Be9PgR4KPT8Z6AS4A1wB7TuYzvA3gduBCtzuwp4OopeF9XAq7o+Dt23dfZbHHoLU+klAEg1rZkWiClbJHRho9SygFgP9of83VoDymi/743Or4OeFhK6ZdSHkPLVFs/qW86DYQQ9cC7gJ+YTk/3eypG+yP+KYCUMiCl7GWa3xda8kyeEMIF5KPVUk27e5JSvgwkdj/M6D6iNWPFUspNUnvaPmC65oyQ7L6klH+UUoaih5vRauDA4vs6m4VjvHYm0w4hRANwLvAaCS1XgFjLlelyv/8J/CNg7g433e9pHtAB/CzqgvuJEKKAaXxfUspm4E60lPcWtBqrPzKN7ymBTO+jLjpOPD+V+TiaBQEW39fZLBw5ty2ZCgghCoHfAp+XUqbqTDbl71cI8W6gXUr5RrqXJDk3pe4pigvNZXC3lPJcYAjN/TEeU/6+oj7/69DcGjOBAiHEzakuSXJuSt1TmtjWBmkyEUL8ExACYu2fLb2vs1k40ml5MqURQrjRRONBKeXvoqfbouYlIr7lynS437cC7xFCHEdzHb5DCPFLpvc9gfY+m6SUr0WPH0UTkul8X5cDx6SUHVLKIPA74C1M73syk+l9NGG4fcznpxxCiI8A7wZuirqfwOL7OpuFI52WJ1OWaGbDT4H9UsofmF4ar+XKBuAGIYRXCDEXWIgW9JoySCm/IqWsl1I2oP08XpBS3sw0vicAKWUrcEoIsTh66jK0LQCm832dBC4QQuRHfxcvQ4uzTed7MpPRfUTdWQNCiAui/x+3MAXbHQltA7wvAe+RUpr33rX2vs5kVsAkZB1cg5aNdAT4pzP9fjJ87xehmYy7gB3Rr2uACuB54HD033LTNf8UvdeDnOGMjzTu71KMrKppf0/AamBr9Of1GFA23e8L+FfgALAH+AVaRs60uyfgV2hxmiDaJ+xPZHMfwNro/8UR4H+IFlBPsftqRItlxJ4Z99hxX6pyXKFQKBQZcTa7qhQKhUJhA0o4FAqFQpERSjgUCoVCkRFKOBQKhUKREUo4FAqFQpERSjgUCoVCkRFKOBQKhUKREUo4FAqFQpER/x9myZKb1l3r+wAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"gamma = 0.15\n",
"alpha = 22.0\n",
"theta = np.linspace(300, 700, 5)\n",
"\n",
"shifted_wald = pm.CustomDist.dist(\n",
" gamma, alpha, theta,\n",
" dist=shifted_wald_fn,\n",
" shape=(10_000, len(theta)),\n",
")\n",
"\n",
"_, ax = plt.subplots(figsize=(6, 4))\n",
"draw = pm.draw(shifted_wald)\n",
"assert not np.any(np.isnan(draw))\n",
"for i in range(len(theta)):\n",
" sns.kdeplot(draw[..., i], clip=(theta[i], None), ax=ax, lw=3)\n",
"ax.set_xlim([0, 1250]);"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "04c0fd1a",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"hide_input": false,
"kernelspec": {
"display_name": "pymc",
"language": "python",
"name": "pymc"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.10.8"
},
"toc": {
"base_numbering": 1,
"nav_menu": {},
"number_sections": true,
"sideBar": true,
"skip_h1_title": false,
"title_cell": "Table of Contents",
"title_sidebar": "Contents",
"toc_cell": false,
"toc_position": {},
"toc_section_display": true,
"toc_window_display": false
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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