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1d_Gaussian_mixture_hmc
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{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"name": "1d_Gaussian_mixture_hmc",
"provenance": [],
"authorship_tag": "ABX9TyNOaf5ehKy8W7e193JCqG8V",
"include_colab_link": true
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
}
},
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"<a href=\"https://colab.research.google.com/gist/Isa-rentacs/c5d8d9bf01e0746f06e6ae2faffd4aba/1d_gaussian_mixture_hmc.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "AYKOC4bWE3Zf",
"colab_type": "text"
},
"source": [
"# An Example of Hamiltonian Monte-Carlo for 1D Gaussian mixture\n",
"\n",
"This notebook is an implementation of HMC and an example of its application for 1D Gaussian mixture.\n",
"\n",
"The distribution we use is a mixture of two Gaussian distributions $\\mathcal{N}\\left(x|\\mu_1, \\sigma_1^2\\right)$ and $\\mathcal{N}\\left(x|\\mu_2, \\sigma_2^2\\right)$ with a weight parameter $\\pi$. For simplycity, the variance parameters are known as 1.\n",
"\n",
"Likelihood $L$ for $N$ data points $X = \\{x_0, \\dots, x_{N-1}\\}$ will be\n",
"\n",
"$\\displaystyle L = p(X|\\mu_1, \\mu_2, \\pi) = \\prod_{i=0}^{N-1}\\left(\\pi\\cdot\\mathcal{N}(x_i|\\mu_1, 1) + (1-\\pi)\\cdot\\mathcal{N}(x_i|\\mu_2, 1)\\right)$\n",
"\n",
"We use normal distribution for the prior of $\\mu_\\cdot$, beta distribution for $\\pi$ and assume those parameters are independent each other.\n",
"\n",
"$\\begin{align}\n",
"\\mu_\\cdot &\\sim \\mathcal{N}(\\mu_\\cdot|0, 10^2) \\\\\n",
"\\pi &\\sim \\mathrm{Beta}(\\pi|2,2)\n",
"\\end{align}\n",
"$\n",
"\n",
"Then the posterior is:\n",
"\n",
"$\\displaystyle\n",
"\\begin{align}\n",
"p(\\mu_1, \\mu_2, \\pi | X) &= \\frac{p(\\mu_1, \\mu_2, \\pi, X)}{p(X)} = \\frac{p(X|\\mu_1, \\mu_2, \\pi)p(\\mu_1)p(\\mu_2)p(\\pi)}{p(X)}\\\\\n",
"&\\propto L \\cdot \\mathcal{N}(\\mu_1|0, 10^2) \\cdot \\mathcal{N}(\\mu_2|0, 10^2) \\cdot \\mathrm{Beta}(\\pi|2,2)\n",
"\\end{align}\n",
"$\n",
"\n",
"Negative log-likelihood of this distribution $S$ is:\n",
"\n",
"$\\displaystyle\n",
"S = -\\left(\\log L + \\log(\\mathcal{N}(\\mu_1|0, 10^2)) + \\log(\\mathcal{N}(\\mu_2|0, 10^2)) + \\log(\\mathrm{Beta}(\\pi|2,2)) \\right)\n",
"$\n",
"\n",
"This $S$ will be used as the potential energy in HMC (function ```potential_unknown_mixture``` in the cell below).\n",
"\n",
"In each step of leap frog, we need to calculate partial derivative with respect to each parameter $\\mu_1, \\mu_2, \\pi$. (function ```dh_unknown_mixture``` )\n",
"\n"
]
},
{
"cell_type": "code",
"metadata": {
"id": "f-RoJrkLqeQf",
"colab_type": "code",
"colab": {}
},
"source": [
"import math\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"import pandas as pd\n",
"import seaborn as sns\n",
"import time\n",
"from scipy.stats import norm, beta\n",
"from typing import Callable, List\n",
"\n",
"plt.rcParams[\"figure.figsize\"]=(16,9)\n",
"\n",
"def potential_unknown_mixture(params:List[float], observed:List[float]) -> float:\n",
" # params: [u0, u1, pi]\n",
" assert len(params) == 3\n",
"\n",
" likelihood_part = 0\n",
" u_0 = params[0]\n",
" u_1 = params[1]\n",
" pi = params[2]\n",
"\n",
" for obs in observed:\n",
" likelihood_part += math.log(pi * norm.pdf(obs, u_0, 1) + (1 - pi) * norm.pdf(obs, u_1, 1))\n",
"\n",
" return -1 * (likelihood_part + math.log(norm.pdf(u_0, 0, 10)) + math.log(norm.pdf(u_1, 0, 10)) + math.log(beta.pdf(pi, 2, 2)))\n",
"\n",
"\n",
"def hamiltonian_unknown_mixture(params:List[float], p:List[float], observed:List[float]) -> float:\n",
" assert len(p) == 3 and len(params) == 3\n",
" return potential_unknown_mixture(params, observed) + sum([0.5 * _p * _p for _p in p])\n",
"\n",
"\n",
"def dh_unknown_mixture(params:List[float], observed:List[float]) -> np.ndarray:\n",
" u_0 = params[0]\n",
" u_1 = params[1]\n",
" pi = params[2]\n",
"\n",
" denominator = lambda x: pi * norm_u0 + (1 - pi) * norm_u1\n",
" u0_numerator = lambda x: pi * norm_u0 * (x - u_0)\n",
" u1_numerator = lambda x: (1 - pi) * norm_u1 * (x - u_1)\n",
" pi_numerator = lambda x: norm_u0 - norm_u1\n",
"\n",
" dh_u0 = 0\n",
" dh_u1 = 0\n",
" dh_pi = 0\n",
"\n",
" for obs in observed:\n",
" norm_u0 = norm.pdf(obs, u_0, 1)\n",
" norm_u1 = norm.pdf(obs, u_1, 1)\n",
"\n",
" dh_u0 += u0_numerator(obs) / denominator(obs)\n",
" dh_u1 += u1_numerator(obs) / denominator(obs)\n",
" dh_pi += pi_numerator(obs) / denominator(obs)\n",
"\n",
" # partial differential for each prior\n",
" dh_u0 += u_0 / 100\n",
" dh_u1 += u_1 / 100\n",
" dh_pi += (- 2 * pi + 1) / (-1 * pi**2 + pi) \n",
" dh_u0 *= -1\n",
" dh_u1 *= -1\n",
" dh_pi *= -1\n",
" return np.array([dh_u0, dh_u1, dh_pi])\n",
"\n",
"def leap_frog(params:List[float], observed:List[float], L:int, dt:float, calc_hamiltonian:Callable, calc_dh:Callable):\n",
" assert len(params) == 3\n",
"\n",
" # Sample p from standard normal\n",
" p = np.random.randn(3)\n",
" params_hist = [params]\n",
" p_hist = [p]\n",
" hamiltonian_start = calc_hamiltonian(params, p, observed)\n",
" # The first step of leap frog for params\n",
" # Proceed params for 0.5 * dt\n",
" params = params + p * 0.5 * dt\n",
" params_hist.append(params)\n",
" for i in range(L):\n",
" dh = calc_dh(params, observed)\n",
"\n",
" # Proceed params for dt\n",
" p = p - dh * dt\n",
" params = params + p * dt\n",
"\n",
" params_hist.append(params)\n",
" p_hist.append(p)\n",
"\n",
" # The last step of leap frog for p\n",
" # Proceed p for dt\n",
" # Proceed params for 0.5 * dt\n",
" dh = calc_dh(params, observed)\n",
" p = p - dh * dt\n",
" params = params + p * 0.5 * dt\n",
"\n",
" params_hist.append(params)\n",
" p_hist.append(p)\n",
" hamiltonian_end = calc_hamiltonian(params, p, observed)\n",
"\n",
" return params, params_hist, p_hist, hamiltonian_start, hamiltonian_end\n",
"\n",
"\n",
"def hmc(calc_hamiltonian:Callable, calc_dh:Callable, observed:List[float]=None, num_samples:int=1000, init_params:List[float]=None, L:int=20, dt:float=0.05, debug:bool=False):\n",
" if observed is None:\n",
" observed = []\n",
" if init_params is None:\n",
" init_params = np.array([0,0,0.5])\n",
"\n",
" ret_dict = {}\n",
" samples = []\n",
" params_hist_arr = []\n",
" p_hist_arr = []\n",
" count_accept = 0\n",
" params = init_params\n",
" time_start = time.time()\n",
" for i in range(num_samples):\n",
" cand_params, params_hist, p_hist, h_s, h_e = leap_frog(\n",
" params,\n",
" observed,\n",
" L,\n",
" dt,\n",
" calc_hamiltonian=calc_hamiltonian,\n",
" calc_dh=calc_dh)\n",
" thresh = np.random.uniform(0, 1)\n",
" if debug:\n",
" print(\"Diff of H:\", abs(h_s - h_e))\n",
" if math.exp(h_s - h_e) > thresh:\n",
" count_accept += 1\n",
" params = cand_params\n",
" samples.append(params)\n",
" params_hist_arr.append(params_hist)\n",
" p_hist_arr.append(p_hist)\n",
" if (i+1) % (num_samples / min(num_samples, 100)) == 0:\n",
" print(\"sampled {}/{} times({}sec/sample)\".format(i+1, num_samples, (time.time() - time_start) / (num_samples/min(num_samples, 100)) ))\n",
" time_start = time.time()\n",
" ret_dict[\"samples\"] = samples\n",
" ret_dict[\"num_accept\"] = count_accept\n",
" ret_dict[\"params_hist_arr\"] = params_hist_arr\n",
" ret_dict[\"p_hist_arr\"] = p_hist_arr\n",
"\n",
" return ret_dict\n"
],
"execution_count": 53,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "DUS7wHDQxa7Y",
"colab_type": "code",
"colab": {}
},
"source": [
"observed = []\n",
"pi = 0.7\n",
"for i in range(50):\n",
" r = np.random.uniform(0, 1)\n",
" if r < pi:\n",
" observed.append(np.random.normal(-3, 1))\n",
" else:\n",
" observed.append(np.random.normal(2, 1))\n"
],
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "iYi4EsM-9JFb",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 551
},
"outputId": "9e6e9d3c-6569-463a-e9af-a028495c6c4c"
},
"source": [
"ax = sns.distplot(observed, label=\"Observed\")\n",
"sns.lineplot(x=np.linspace(-10, 10, 100), y=[pi * norm.pdf(_x, -3, 1) + (1-pi) * norm.pdf(_x, 2, 1) for _x in np.linspace(-10,10,100)], label=\"True dist\", ax = ax)\n",
"ax.set_xlabel(\"x\")\n",
"ax.lines[1].set_linestyle(\"--\")\n",
"_ = ax.set_ylabel(\"probability\")"
],
"execution_count": 54,
"outputs": [
{
"output_type": "display_data",
"data": {
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J0glIWmEbRVErcBPwR2Al8NsoipaHEG4JIRxY5fjfgALgzte19ZkILAohvAA8CnwjiiILW0n9X1srbFoM5XPiy7CnGh7+MuxaH18GSZKkbkjqO7ZRFD0IPPi6fV845Oe3HOW6p4GpycwmSb3S9uXQ0gCjYixsWxrhiW/B4FEw84b4ckiSJHVRMh9FliR1V/XCjm15jO+4lp4MBcPsZytJkvoMC1tJ6k02LoT8oTB4THwZ7GcrSZL6GAtbSepN5v8TXPGTjuIyThXnQN0W+9lKkqQ+wcJWknqT0nEw9ty4U3QUtlmFUGOXNUmS1PsldfEoSVI3bH0JNi2BqVdCVn68WUrHwWfWQbr/MyFJkno/Z2wlqbdYfi/87h/iTtEhBItaSZLUZ1jYSlJvUb0Qhk2Of7b2gA3PwQ/Ogp2r404iSZJ0TBa2ktQbtLfBpsXx9q99vbzSjr66656IO4kkSdIxWdhKUm+wfSU074PyXlTYlo6DguH2s5UkSb2eha0k9QbbV3Rsy2fFm+NQB/vZPmE/W0mS1KtZ2EpSb3Dae+DTVVAyNu4kh6uYB/u2wa61cSeRJEk6Kpe8lKTeIn9I3AneaNQZMPU9zthKkqRezRlbSYpb4y74zTUdqxD3NsMmwRU/6XjfVpIkqZeysJWkuFUvhlcehNamuJMcWRRB0564U0iSJB2Vha0kxa36eQhpMHJm3EmO7N6Pwo/PizuFJEnSUVnYSlLcqhfC0MmQXRB3kiMrroTaNdBcH3cSSZKkI7KwlaQ4tbd3PIrcm9r8vN6wyUAE21fFnUSSJOmILGwlKU6NtVA2AcbMizvJ0Q2b3LHd9nK8OSRJko7Cdj+SFKf8IfChP8ed4tgGj4GsAti2PO4kkiRJR2RhK0lxiiIIIe4Ux5aWBud/AYaMjzuJJEnSEVnYSlKcfnJex2PIF3017iTHNvfDcSeQJEk6Kt+xlaS4NO2BzcsguyjuJMfX0gSblkDT3riTSJIkvYGFrSTFZdNiIIJRs+NOcnybl3TMLm98Lu4kkiRJb2BhK0lx2fJix/ak6fHm6IqhEzu2rowsSZJ6IQtbSYrLjlVQMBzySuJOcny5xVBUDttWxJ1EkiTpDVw8SpLiMuYsKBkbd4quGzbZlj+SJKlXsrCVpLjMuC7uBN0zbDJUPQytzZCRFXcaSZKkgyxsJSkOLY0dn77wGPIB098LY8/t/X13JUnSgOM7tpIUhzWPwzcroXpx3Em6bsh4GDsf0jPjTiJJknQYC1tJisP2zkWYhpwcb47uevVPsOaxuFNIkiQdxkeRJSkOO1ZB0UjIGRR3ku555BYoGNbxSLIkSVIv4YytJMVh+0ooOyXuFN03bIorI0uSpF7HwlaSUq29DXa+CmUT407SfcMmQ90WqK+JO4kkSdJBFraSlGrtbfDWb8Lkd8WdpPuGTe7YbnfWVpIk9R4WtpKUahlZMPN6GDU77iTdN2xKx9bHkSVJUi/i4lGSlGrbV0HU9tfZz76kYCjctAhKxsadRJIk6SBnbCUp1Z74d7j9qrhTnLgh4yEtPe4UkiRJB1nYSlKq7eijKyIfsOE5eOBTHe8KS5Ik9QIWtpKUSu1tsONVKDs17iQnrmY1LPwJ1K6NO4kkSRJgYStJqVW7Ftr2w9A+2OrngGGTOrbbXo43hyRJUicLW0lKpR0rO7Z9sYftAWWnQkiD7SviTiJJkgRY2EpSao2ZB++766+znn1RZi6UnmzLH0mS1GvY7keSUimvBMZfEHeKnhs2BfZtizuFJEkSYGErSam19DYYOglGzog7Sc9c8VNb/kiSpF7DR5ElKVXaWuF3/wDL74k7Sc9Z1EqSpF7EwlaSUmXXWmhr7tsrIh/QtBd+cw28/D9xJ5EkSbKwlaSU2X5gReQ+3MP2gOxCWPsErH8m7iSSJEkWtpKUMgcL21PizZEIIcCwya6MLEmSegULW0lKlR2rYPAYyMqPO0liHChsoyjuJJIkaYCzsJWkVHnXD+GG38WdInGGTYb9e2BPddxJJEnSAGdhK0mpkpENg0fHnSJxTpoOo+bC/r1xJ5EkSQOcha0kpcKu9fD7z0JNVdxJEqd8JnzwTx0zt5IkSTGysJWkVNi8FJ77f7C/Lu4kiec7tpIkKWYWtpKUCjtWAQGGTIg7SWL98XPwk/PiTiFJkgY4C1tJSoXtK6G4ArLy4k6SWBk5sOVFaGmKO4kkSRrALGwlKRW2r4ShE+NOkXjDJkPUBjtfiTuJJEkawCxsJSnZ2tuguR7KTo07SeIdWDhq+6p4c0iSpAEtI+4AktTvpaXDJ5d3FLhJdvtzG5J+j0OltWfwnpDOihcX8WLTmSm9dyq8d24/as8kSVI/5oytJKVKWnrcCRKuPS2T10Zfza7CfrYoliRJ6lOcsZWkZFv4U1j3FFx5K4QQd5qEWzzps3FHkCRJA5wztpKUbGsehy0v9Mui9oCs5t0QtccdQ5IkDVAWtpKUbDtW9c8VkTuN3XgPVz58DnlNW+OOIkmSBigLW0lKptb9UFPVP1dE7rQvrxyAon3r4g0iSZIGLAtbSUqmmtUdfV778Yzt3vwKAIrq18YbRJIkDVgWtpKUTC2NcNL0v/Z77YeasofQkp5PUf26uKNIkqQBylWRJSmZymfBhx+PO0VyhcDeggoK69fHnUSSJA1QFraSpB5bVfF+otD/+vRKkqS+wcJWkpLpJ2+Gyvnwln+NO0lSrR9xSdwRJEnSAOY7tpKULC1NsHkppPX/f0NMa29h8N5XyGzZE3cUSZI0AFnYSlKy1LwGUTsM7b+tfg4o2reGtz11JSftfCbuKJIkaQCysJWkZNm+qmNb1n9b/RxQlz8awJWRJUlSLCxsJSlZdqyCkA6lJ8edJOna0nOpzzmJQgtbSZIUAwtbSUqWslNg1gcgIyvuJCmxN3+MM7aSJCkWFraSlCynvQcu+fe4U6RMXX4FRfvWQRTFHUWSJA0w/X+pTkmKQxRBcz1kF8SdJGVWj7qCTUPnAxEQ4o4jSZIGEGdsJSkZ9m6Cr4+EZbfHnSRldhedypaysyH4Py2SJCm1/O1DkpKhZnXHdlB5vDlSKLS3MmL7Xxi895W4o0iSpAHGwlaSkuFAYTsAVkQ+IAppnL30k1Ruuj/uKJIkaYBJamEbQrg4hPBKCGF1COGzRzj+yRDCihDCiyGEh0MIYw45dn0I4bXOz/XJzClJCVdTBZl5UHhS3ElSJ6RRlz/alZElSVLKJa2wDSGkA98H3gpMAq4JIUx63WlLgVlRFJ0G3AV8s/PaEuBfgbnAHOBfQwjFycoqSQlXsxpKxkEYWIso1eVXWNhKkqSUS+aM7RxgdRRFa6IoagbuAN5x6AlRFD0aRVFD59dngQMvo10EPBRFUW0URbuAh4CLk5hVkhJr6nvgjI/EnSLl9uZXkN+4ibT2lrijSJKkASSZ7X5GAhsP+V5Nxwzs0XwQ+P0xrh35+gtCCDcCNwKMHj26J1klKbFOe3fcCWKxN7+StKiNgoaN7C0YG3ccSZI0QPSKxaNCCNcCs4B/6851URT9OIqiWVEUzSorK0tOOEnqrv11sONVaBt4s5aby87hgbPvpi5vVNxRJEnSAJLMwnYTcOhvNuWd+w4TQngL8DngsiiK9nfnWknqldY9Bd+fDZuXxZ0k5ZqzBrOncDxRWmbcUSRJ0gCSzMJ2ITA+hFAZQsgCrgYO6wERQjgd+BEdRe32Qw79EbgwhFDcuWjUhZ37JKn3O9jqZ1y8OWIyZvMDjN7yh7hjSJKkASRp79hGUdQaQriJjoI0Hbg1iqLlIYRbgEVRFN1Px6PHBcCdoWPl0A1RFF0WRVFtCOHLdBTHALdEUVSbrKySlFA1qyG3GPJK4k4Si5M33EmgnQ0nueafJElKjWQuHkUURQ8CD75u3xcO+fktx7j2VuDW5KWTpCSpWQ2lJ8edIjZ1BRWUb30k7hiSJGkA6RWLR0lSv1JTNaAL2715FeS07CKreU/cUSRJ0gCR1BlbSRqQLvkW5A/cldrr8isAKKpfy86s6fGGkSRJA4IztpKUaKdeAqPmxJ0iNnsLKgAoaKiON4gkSRownLGVpESqqYLdG2DMPMjIijtNLPbljeLOtzxFS2ZR3FEkSdIA4YytJCXS8rvhV++E9pa4k8QmCukWtZIkKaUsbCUpkWqqoGgkZOXHnSRWYzY/wIyV34w7hiRJGiAsbCUpkWpWQ+m4uFPErnjvKsZvWECI2uKOIkmSBgALW0lKpJoqKLGwrcuvIL29mbzGzXFHkSRJA4CFrSQlSkMtNNYO6B62B+w92PJnfbxBJEnSgGBhK0mJkl0INz4OUy6PO0ns/lrYros1hyRJGhhs9yNJiZKeCSOmx52iV9ifVUJ9znDS2xrjjiJJkgYAC1tJSpSqR2Dfdph2ddxJ4hcC9537Jwgh7iSSJGkA8FFkSUqUJb+Ex/9v3Cl6D4taSZKUIha2kpQoNatdOOoQI7Y/zoXPvI+M1oa4o0iSpH7OwlaSEiGKOlr9WNgelN7ezJDdL1LoAlKSJCnJLGwlKRHqtkBLA5Taw/aAvfljAFdGliRJyWdhK0mJUFPVsXXG9qB9eaOJCBa2kiQp6VwVWZISoeJs+NTqjl62AqAtPYf63BE+iixJkpLOwlaSEiEEKCiLO0Wvs2XIWbRm5MUdQ5Ik9XMWtpKUCE9/D7ILYOYNcSfpVRZO+ULcESRJ0gDgO7aSlAiL/xtWPxx3CkmSpAHJwlaSeqqtFXatc+GoIyjes4J3PPoWhtY8H3cUSZLUj1nYSlJP7V4P7a0WtkfQlFVCftM2V0aWJElJZWErST1lq5+jaswZRmt6LkX1a+OOIkmS+jELW0nqqYadkJ5tYXskIVCXN4rC+g1xJ5EkSf2YqyJLUk9Nfy+cdhUE/63wSOryxjB432txx5AkSf2Yha0kJUJaetwJeq3NQ8+hIXdY3DEkSVI/ZmErST312+vh5LfAjPfHnaRXWlP+rrgjSJKkfs7n5iSpJ5obYMW9ULcl7iS9WmhvJa1tf9wxJElSP2VhK0k9satztd/ScfHm6MWy99dy1Z9mc3L1/8QdRZIk9VMWtpLUEzWrO7auiHxU+7OKaUvLcmVkSZKUNBa2ktQTBwrbEmdsjyoE6vJGU9iwPu4kkiSpn7KwlaSeSM+G8jmQXRB3kl6tLn+0M7aSJClpLGwlqSfOugk+9FDcKXq9uvwx5DduJrS3xB1FkiT1Q7b7kSQl3eayc2hNzyMtaqWNzLjjSJKkfsYZW0k6UY274TvTYfm9cSfp9XYWn86KcR+iLT037iiSJKkfsrCVpBNVU9XR7ic9K+4kvV8Ukdu4ldymbXEnkSRJ/ZCFrSSdKFv9dMulT7yTSWt+FncMSZLUD/mOrSSdqJrVENKguCLuJMe0q76Z5Vv2smLzHvbtb6MgO4OCnIyObXYGhTkZTBhWyKDcJL77GoIrI0uSpKSxsJWkE1WzGgaPgYze9yjy9r1NLN+yl+Wb97B5dxMAJw3KYXhRNvv2t7F1TxP79rfQ1NIOQHpaYHZFMfMnDE1agVuXP4aSPcuTMrYkSRrYLGwl6UQNmwSDR8Wd4jCNzW3cs2wTL2/aA8DokjzeOmU4k04qorQg+w3nt7a1U1vfzFNVO3l+bS0L1+1i1phi5k8oY3BeYgv2urzRjNr6EKG9hSjNlZElSVLiWNhK0ol606fjTnCY59fW8t1HXqOuqYXzJw5l9pgSio4z+5qRnsbQohzedXo5504YymOv7mDRul0sWreLWRXFXDxlONkZ6QnJV5c/hrSojYLGTdTlVyRkTEmSJLCwlaQT094GBEiLfw2+1rZ2vvvwa3zv0dUU52XxkfnjKC/O6/Y4xflZvOv0kZx7ShmPv7qDhetqqd7VyHVnjqEwp+czrNtKZvP0aV+nKau4x2NJkiQdKv7fyCSpL9r4PHztJFj3VLwxaht4z4+e4buPrObyGeXcdN7JJ1TUHqo4L4t3Th/JtWeMYXtdEz/6yxp27tvf46wNuSexbuSltGQO6vFYkiRJh7KwlaQTUVsFrU1QODy2CEs37OJt332C17bt47vXnM633j2N7MzEPDYMcOrwIj509liaWtr44eNVbKxt6PGYJXuWU7r7pQSkkyRJ+lUXjE4AACAASURBVCsLW0k6ETVVkJbRsSpyDFZvr+MDP19IcV4WD958DpdNG5GU+4wqyeMj88eRk5nOT59cw6qte3s03uzlX+a0176XoHSSJEkdLGwl6UTUVnUUtempX6pgy55GrvvZ82SkpfGrD85hVEnPHj0+niEF2Xz4TWMZWpjDbc+uZ9G62hMeqy5vNIX16xOYTpIkycJWkk5MzRooHZfy2+5uaOa6nz3P3qZWfv6B2YwpzU/JfQtzMvnQOZWMKyvgnqWbeHVb3QmNU5c3mrzGLaS1tyQ4oSRJGsgsbCXpRJz2bphyZUpv2djcxgd/sYj1NQ38+LqZTBmZ2kWYsjPSed/cMQwrymHBwo3U1jd3e4y6/DGk0U5Bw8YkJJQkSQOVha0knYh5N8O0q1J2u5a2dm66fQlLNuziP6+ezlnjhqTs3ofKykjj2jM63iu+7dn1NLe2d+v6urzRABTWb0h4NkmSNHBZ2EpSdzXthfqdEEUpuV0URXz+npd5eNV2vvyOKbxt6kkpue/RlORncdXsUWzb28TdS6uJuvH3sLtoAg/N/W+2l8xMYkJJkjTQWNhKUnetuBf+bRzsWpeS293/wmYWLNrIx88bd3C2NG4ThhVywaRhvFi9h6dW7+zydW3puewomUVLZmES00mSpIHGwlaSuqt2DaRlwqBRSb/V1j1N/Mu9L3P66MH8w1smJP1+3TF/QhmTRxTxh+Vbqdqxr8vXDat5jjGbH0hiMkmSNNBY2EpSd9VUQXFF0lv9RFHEp+96gZa2iP94z3Qy0nvXf7JDCFw5o5zSgmx+8/wGdjd0bTGpcRvvZtqr301yOkmSNJD0rt+SJKkvqE1Nq5/bnl3PE6/t5J8vmUjlkNS09emu7Mx0rp07hrb2iN8u2kh7F963rcsfQ37jFtLa9qcgoSRJGggsbCWpO6Koo7AtSW5hu2bHPr764EreNKGMa+eOTuq9eqqsMJtLpp7EupoGFq/fddzz6/JGE4goaKhOQTpJkjQQWNhKUne0t8JbvwmT35W0W7S2tfPJ375AdkY637ziNEIISbtXoswYU0xFaR6/f3kLdU0txzy3Lr9jAazChvWpiCZJkgYAC1tJ6o70TJjxfhg1O2m3+H+PVbFs426+/M4pDB+Uk7T7JFJaCLxz+khaWiMefGnLMc/dm28vW0mSlFgWtpLUHbVrYfMyaG9PyvAvb9rDdx5+jbdPG8Fl00Yk5R7JMrQoh/mnlPFC9R5e3VZ31PNaMgdx3/zf80rFtSlMJ0mS+jMLW0nqjsX/DT+7ADj+Iknd1d4e8X/ufomS/Cy+/I7JCR8/FeZPKGNIQRb3LdtEc+vRi//6vHKitOSuKi1JkgYOC1tJ6o6aKiiuhLT0hA9999JNvLRpD//8tokMzstK+PipkJmexjunj2RXQwuPrNp+1PNO2vEk0175dgqTSZKk/szCVpK6o3YNlIxN+LANza382x9XMW3U4D73CPLrjS0rYMboYp5cvYOte5qOeE7p7peYvOZW0tuOfFySJKk7LGwlqava25PWw/aHj69h2979fOHSiaSl9f5VkI/nbVOGk5OZzj1Lq4/Y2/bAysgFDRtTHU2SJPVDFraS1FV1m6G1KeEztpt3N/Ljv1Tx9mkjmDmmJKFjxyUvO4NLpp7Exl2NR+xte7DljysjS5KkBLCwlaSuyi2B998DEy5K6LDf/MMqogg+c/EpCR03btNHDWZUcS4Pr9xGS9vhC0nV5XW2/LGXrSRJSgALW0nqqqw8GPdmGFSesCGXbdzNvcs286FzKikvzkvYuL1BCIGLpgxnb1Mrz1TVHHasJbOQxuwhZDfvjimdJEnqT+y1IEldte5JaG6ACRcmZLgoivjy71ZQVpjNR889OSFj9jZjhxQwYVgBj7+6g9kVJeRm/XU16XvP/RNRWmaM6SRJUn/hjK0kddUzP4CH/iVhw/3uxS0sXr+LT194CgXZ/fffGS+cNJzGljaeeG3HYfstaiVJUqJY2EpSV9VWQUliVkRuamnjG79fxaSTirhiZuIebe6NRgzO5bTyQTxVtZO9TS0H9w/f+TTzF32c9NaGGNNJkqT+wMJWkrqivR1q10JpYlZE/tUz69m0u5F/uXQS6f2gvc/xXDBxGG3tEY+u2n5wX1bLXkbu+AuFtvyRJEk9ZGErSV2xtxra9idkxraxuY0f/WUN54wfwpnjShMQrvcrLchmdkUJC9fVUrNvP3Doysi2/JEkST1jYStJXVFT1bEt7Xlh+5vnN7Bz337+7vzxPR6rLznv1KGkpwUeWrkNOKSwrbfljyRJ6pkuFbYhhLtDCJeEECyEJQ1MY+bBxxfCyFk9GqappY0fPl7FmWNLmV1RkqBwfUNRTiZnjRvCi9V72Ly7kdbMAhqzSpyxlSRJPdbVQvUHwHuB10II3wghnJLETJLU+2RkQdmEjl62PfDbRRvZXrefT5zfP9v7HM+bxpeRm5nOn1ZsBWDn4Gm0pWXHnEqSJPV1XeovEUXRn4E/hxAGAdd0/rwR+AlwWxRFLcccQJL6usW/gOxCmHL5CQ+xv7WN//dYFbMrijlz7MB4t/b1crPSmT+hjD8s38qGmnqemPnduCNJkqR+oMuPFocQSoEbgA8BS4HvADOAh5KSTJJ6k2e+By//T4+GuGtxNVv2NPF3548nhP6/EvLRzB1bQm5mOo+9uuP4J0uSJHVBV9+xvQd4AsgD3h5F0WVRFC2IougTQEEyA0pS7NrbYNe6Hi0c1dzazg8ereL00YM5++QhicvWB2VnpHPmuFJWba0jVD/PW5+8gkF1r8YdS5Ik9WFdnbH9SRRFk6Io+noURVsAQgjZAFEUHXUllRDCxSGEV0IIq0MInz3C8TeFEJaEEFpDCFe+7lhbCGFZ5+f+bvyZJCmx9myEtuYetfq5Z2k1m3Y3DvjZ2gPOGltKVnoaz1c3UFz3KkX71sYdSZIk9WFdLWy/coR9zxzrghBCOvB94K3AJOCaEMKk1522gY7Hm28/whCNURRN7/xc1sWckpR4PWz109LWzvceXc1p5YM4d0JZAoP1XXnZGcypLOGhrfkAFDZsjDmRJEnqy465eFQIYTgwEsgNIZwOHJhmKKLjseRjmQOsjqJoTedYdwDvAFYcOCGKonWdx9pPJLwkpcTeTR3bE5yxvW/ZZjbWNvKvl052tvYQ804ewjNVNexKK7aXrSRJ6pHjrYp8ER0zquXAfxyyvw745+NcOxI49J/gq4G53ciWE0JYBLQC34ii6N5uXCtJiTPjOpj8Lsjq/pICbe0R3390NZNOKuL8iUOTEK7vGpSbyemjB/PalmGM2rcu7jiSJKkPO2ZhG0XRL4BfhBCuiKKoZ8uBdt+YKIo2hRDGAo+EEF6Koqjq0BNCCDcCNwKMHj06xfEkDSjZhSd02Z+Wb2Xtznp+8L4ZztYewZsmlPGX6tOY3tYYdxRJktSHHfMd2xDCtZ0/VoQQPvn6z3HG3gSMOuR7eee+LomiaFPndg3wGHD6Ec75cRRFs6IomlVW5ntrkpLkgU/Bi789oUt/9uRaRpXkctHk4QkO1T8MKcjm8eHX8/Hd76OxuS3uOJIkqY863uJR+Z3bAqDwCJ9jWQiMDyFUhhCygKuBLq1uHEIoPrDqcghhCDCPQ97NlaSUaWuFxf8N27v/n6BlG3ezaP0uPnBWJelpztYezfwJZexvbef5Nfa1lSRJJ+Z4jyL/qHP7pe4OHEVRawjhJuCPQDpwaxRFy0MItwCLoii6P4QwG7gHKAbeHkL4UhRFk4GJwI86F5VKo+MdWwtbSam3ZwO0t57QwlE/e3IthdkZvGf2qOOfPICNz6rlxdwP85Wq62k++W/Jyujqgv2SJEkdjrcq8nePdTyKor87zvEHgQdft+8Lh/y8kI5HlF9/3dPA1GONLUkpUbOmY9vNVj+bdjfy4Etb+Jt5FRRkH2+dvoGtMbuMgqieke2bWby+ljPHDYk7kiRJ6mOO99vW4pSkkKTeqrZzzbpuztj+8ul1AFx/VkVi8/RD7elZ1OeOYErzDv579U7mVJb66LYkSeqWrqyKLEkDV2sTFJVDQddb9dTvb+X25zfw1inDKS8+XstvAdTlj+FUtrF7Vwsrt+xlyshBcUeSJEl9yPEeRf7PKIr+PoTwv0D0+uNRFF2WtGSS1BvMu7nj0w13LtpIXVMrHzy7Mkmh+p+6/ArG7lpKcW4GT1fttLCVJEndcrxHkX/Vuf1WsoNIUn/Q1h5x61PrmDmmmNNHF8cdp8/YXDaPtrQszkkbxP3La9i0u5GRg3PjjiVJkvqIYy49GUXR4s7t48AzwC6gFnimc58k9V9tLfDTt8DLd3f5kodWbGNDbYOztd20pewclp36SaZXDiMrI42nV++MO5IkSepDutRTIYRwCVAFfBf4HrA6hPDWZAaTpNjt3gDVC6GlscuX3PrkWsqLc7lw0rAkBuuf0lsbKGQfM0cX82L1HuqaWuKOJEmS+oiuNgv8d+C8KIrOjaJoPnAe8O3kxZKkXqCmc0XkLrb6ebF6N8+vq+WGsyrISLcXa7dE7Vzx8HwmV/2UM8eV0h5FPLe2Nu5UkiSpj+jqb151URStPuT7GqAuCXkkqfc42OpnbJdO/9mTaynIzuCq2aOSGKqfCmnsyyunqH4dQwqyOWV4Ic+tqaGlrT3uZJIkqQ84ZmEbQrg8hHA5sCiE8GAI4YYQwvXA/wILU5JQkuJSUwVZhZBfdtxTd9Tt58GXtvDuWeUU5mSmIFz/sze/gsL69QDMO3kI9c1tvFi9O+ZUkiSpLzjejO3bOz85wDZgPnAusANwuUpJ/VvBUBh/AYRw3FN/u2gjLW0R154xJgXB+qe6/DEUNGwktLcydkg+w4tyeGp1DVH0hm5zkiRJhzlmu58oij6QqiCS1OvM/6cundbWHnH7cxuYd3Ip48oKkhyq/6rLH0N61Ep+4xb25Y/irHGl3L10E2t31jPWv1dJknQMx+tjC0AIIQf4IDCZjtlbAKIo+psk5ZKkPuPRVdvZtLuRz18yMe4ofdr24pksmvhZWjLyAZg2ajB/WL6Vp6pqLGwlSdIxdXXxqF8Bw4GLgMeBclw8SlJ/tuMV+NYpsPrh4576q2fXM6wom7fY4qdH9uWP5tWK97E/uwSAzPQ05laWsGrLXmr27Y85nSRJ6s26WtieHEXRvwD1URT9ArgEmJu8WJIUs52vwr6tkDv4mKdtqGngL6/t4OrZo8m0xU+PFdRvZFDdawe/zx1bSloIPLumJsZUkiSpt+vqb2EtndvdIYQpwCBgaHIiSVIvUNPZ4ax0/DFP+/Xz60kLgWvmjE5BqP7vrBc+w4yV3zz4vSgnk8kji1i8YRfNrbb+kSRJR9bVwvbHIYRi4F+A+4EVwP9NWipJitvO1VAwDHKKjnpKU0sbv124kQsmDmP4oJyjnqeuq8sfQ1H9usP2nVFZSlNLOy/Y+keSJB1FlwrbKIp+GkXRriiKHo+iaGwURUOjKPpRssNJUmxqXoPSk495yu9f3sKuhhZb/CRQXf4Y8pu2kt7WeHDfmNI8hhfl8OwaW/9IkqQj61JhG0IoDSH8VwhhSQhhcQjhP0MIpckOJ0mxGXsuTLzsmKf86pn1VA7J56xx/ucwUfbmVwBQWL/h4L4QAnPHlrBlTxMbaxtiSiZJknqzrj6KfAewHbgCuBLYCSxIVihJit15/wxnfOSoh5dv3sOSDbt539zRpKWFFAbr3+ryOma/C+vXH7Z/+qjBZGek8eza2jhiSZKkXq6rhe1JURR9OYqitZ2frwD2tZDUP7U0Qeux28vc9uwGsjPSuHJmeYpCDQx7Cyr5y+n/yY6SGYftz85IZ8boYl7atId9+1tjSidJknqrrha2fwohXB1CSOv8vAf4YzKDSVJsXv4f+Opw2LXuiIfrmlq4b9kmLps2gsF5WanN1s+1pedQPfx8mrKHvOHY3LEltLVHLFrnrK0kSTrcMQvbEEJdCGEv8LfA7UBz5+cO4Mbkx5OkGNS8BiENio48G3vP0k00NLe5aFSSFO9ZQfnWP79h/9DCHMaW5fP82lraXURKkiQd4piFbRRFhVEUFXVu06Ioyuj8pEVRdPQeGJLUl+18DYorIT3jDYeiKOL25zYwZWQR00YNjiFc/3fyxjuZ8/KXjnjsjMpSdje28MrWuhSnkiRJvVlXH0UmhHBZCOFbnZ9LkxlKkmJVsxqGjD/ioRer97Bqax1Xzx6d4lADR11+BTktu8lqfmPf2oknFVGUk8Gza2piSCZJknqrrrb7+QZwM7Ci83NzCOHryQwmSbFob4PaNUftYXvHwo3kZKZx2fQRKQ42cBxtZWSA9LTAnMoSXtu+j537jr3AlyRJGji6OmP7NuCCKIpujaLoVuBi4JLkxZKkmLS1wJv/BU552xsO1e9v5f5lm7hk6giKcjJjCDcw7M3vKGyLGt5Y2ALMrighLcBzztpKkqROXX4UGTj0ZbJBiQ4iSb1CZg7M+zsYc+YbDj3w4hbqm9u4Zs6oGIINHPV55bSHdArr1x3xeGFOJpNHDGLxhl00t7anNpwkSeqV3rgyypF9DVgaQngUCMCbgM8mLZUkxWX3RiCCQaMghMMO3bFwA+PK8pk5pjiebANEe1omfzhrAftyRx71nDPGlvLSpj28WL2bWRUlKUwnSZJ6o+PO2IYQ0oB24AzgbuB/gDOjKFqQ5GySlHpP/gf88Ow37H51Wx1LNuzm6tmjCa8reJV4u4tOoTWz4KjHK0rzGFqYzXNr7WkrSZK6UNhGUdQO/FMURVuiKLq/87M1BdkkKfVqVkPp+DfM1i5YuJHM9MDlM44+i6jEKd39Eqe9+l8QHflR4xACcytL2LS7kepdDSlOpz6tvR3sgyxJ/U5X37H9cwjhUyGEUSGEkgOfpCaTpDjsfGOrn/2tbdy9pJoLJw2ntCA7pmADS/GeFUyp+jG5TduPes7po4vJTA8876ytumrzMviPifC1EfCj+X/dv/xeWHQrvPpH2PoytLXGl1GSdEK6+o7tVUAEfOx1+8cmNo4kxWj/Pqjb/IZWP39avo1dDS1cNdtFo1Kl7pCVkRtzhx/xnJzMdKaVD+aF6t28dcpJ5GalpzKi+ppNi+FX74LsQTDrbw5/GmDhT2HdE3/9PuoMuO6+jsXkJEl9QlcL20l0FLVn01HgPgH8MFmhJCkWNas7tq8rbBcs3MjIwbmcffKQGEINTHX5FUBHL9ttpXOPet7cylIWrd/F0o27OGuc//fRUTQ3wO1XQ85guP5/oXjM4cfffy/s2wZ7N8HG5+FPn4NnfwDnfDKevJKkbutqYfsLYC/w3c7v7+3c955khJKkWAweDVfeCqP/2upnY20DT67eyScvmEBamotGpUpDzlBa03MpOkrLnwNGFudSXpzL82trOXNsqQt76ciy8uDyH3f8o9XgIzx5kZ4Bg0Z2fEbNgSETYOy5qU4pSeqBrha2U6IomnTI90dDCCuSEUiSYpNXAlOuOGzXgoUbSQvw7lnlMYUaoEIadXmjyWvcctxT51aW8D9LNrGupoHKIfkpCKc+Y/0zsHs9TLsaxp3X9esmXNixrd8J25bD2PnHPl+SFLuuLh61JIRwxoEvIYS5wKLkRJKkmKx9AjYvPfi1ta2dOxdv5NxThnLSoNwYgw1MD839OU+e/h/HPW/qyMHkZKbx3NqaFKRSn7HuSbjtCnjy29DafGJjPPhp+M3VHYtOSZJ6ta4WtjOBp0MI60II64BngNkhhJdCCC8mLZ0kpdKfPgcPf/ng18df3cG2vft5zywXjYpDa2bBG9ouHUlWRhozRhezfNNe9u13NVsBax6H266EQeVw3f2QkXVi41z8Dcgtgd9cA3uP//SAJCk+XS1sLwYqgfmdn8rOfZcCb09ONElKoSiCmqrDWv3ctbia0vwszp84NMZgA9egulc548XPkd+w6bjnzqkooS2KWLx+VwqSqVeregRufw+UVMIND0DhsBMfq3AYvPcOaNoDd1zTsQiVJKlX6lJhG0XR+mN9kh1SkpKubgs07zu4InJtfTN/XrmNd54+ksz0rv4boBIpo7WRsZvuZ9C+1cc9d2hRDpVD8nl+bQ3tUZSCdOq1Ni/t+P/j6/8XCsp6Pt7wqXDFTzseR374lp6PJ0lKCn9bkySAna91bDtnbO9btomWtshFo2J0oOXP8VZGPmBuZQm7GlpYvX1f8kKp9zvnH+GDD0F+Ats/nfq2juL2TZ9O3JiSpISysJUkOKSHbUdhe+eiaqaOHMSpw4tiDDWwNWcNoilzMIX1XXswaNKIIvKzM3hujYtIDUjbV3W8Wwsd7X0SbeqVkF8KbS1QvTjx40uSesTCVpKg45fWv/kjFI1g+eY9rNiy19naXqAuf0yXC9uMtDRmjSlm1dY6djec4Cq46rsevgUWvB/21yX3Pn/+IvzqXR3v3UqSeg0LW0kCyBkEo8+AELhrcTVZ6WlcNm1E3KkGvN2F47u0MvIBcypKAFi4zkWkBpTNS+GVB+CsmyC7MLn3mnol7N8Di/47ufeRJHWLha0kATzzA9jwHM2t7dy3bDMXTBrG4LwTbBGihFk45V95ZM5Pu3x+cX4WE4YVsmh9LW3tLiI1YDz6dcgthrkfSf69RpwOY8+FZ38ALU3Jv58kqUssbCWpdX9HD9uqh3lk1XZq65u50seQ+6y5lSXUNbWycsveuKMoFTYuhNf+CGf9HeSk6J34s/8B9m2DF+9Izf0kScdlYStJtWshaofS8dy1eCNDC7M55+QErqiqE5bbtJ03P/dBRmz/S5evmTC8kMG5mTy/tjaJydRr7NsKZRNhzo2pu2fl/I6Z21f+kLp7SpKOycJWkmo6Wv3U5o3m0Vd2cPmMcjLsXdsrNGcWMrz2eYr3ruzyNWkhMLuyhNU79rFz3/4kplOvMPHt8LFnILsgdfcMAa5ZAFffnrp7SpKOyd/cJKmzh+19G3Joa7d3bW/Slp5Lfc7wLveyPWDWmGLSAs7a9nev/gnaWru1wFjCFA6DtDTYvw8i3+eWpLhZ2EpS7RqiguH85oXdzBg9mHFlKZz50XF1p+XPAYU5mUwaMYjF63fR0taepGSK1dq/wO3vhmW3xZdh81L49iRY81h8GSRJgIWtJMHbv8uKy37Hq9v2ceXMUXGn0evsza/omLHt5qzY3MoSGlvaeHmT/Ub7nSiCR78GhSfBaVfHl2PoJMjIhSe/HV8GSRJgYStJkJbGb1Y0kZOZxqXTToo7jV5n5+Bp7Bx8Ghltjd26buyQfIYUZPOcjyP3P2sehQ3PwDn/CJk58eXIyIYzPw5rH4dNS+LLIUmysJU0wDXU0nrPx1m97AkunjycopzMuBPpddaNfDuPzf4hrRl53bouhMDcyhI21DawZU/3imL1Ygdma4vKYcZ1caeBmTdAziB46j/jTiJJA5qFraSBbeerZLxwG7nNtT6G3NudwAI9p48eTEZacNa2P6nfCfvrYP6nO2ZM45ZTBLM/BCvuh90b404jSQOWha2kga1zReT6gkrOGlcacxgdzYXPvI9ZK77a7evysjI4rXwwyzbuZn9LWxKSKeUKyuCjT8P0a+NO8ldnfAw+9GcY7D+OSVJcLGwlDWj7Nq+kOUrnzJnTSUuLoWWIuqQ9ZDC47rUTunZuZQnNre0sq96d4FRKud0b/z979x0eV3mmf/x7Zka992ZLsoot914BY0wxndACpJCQQiCE9E2yu9nNbvqSbH5plBQSNgkllJDQS8A2uHdjy5ZtFatYVu9tpJk5vz9kU91kzcyZcn+uy5exZuZ9b+sS8jx6z3me0dNamx3sDqvTvCMuHSYssDqFiEhYU2ErImGtpaacWjOb6xYUWh1FTqE7voikvqqzuhx5QkoMuUnRbK7uwNS80eD20rfgN8sDc26sacKzX4bXvmd1EhGRsKTCVkTClmmatHb10B47iYK0OKvjyCn0xBcTNdJN1PDY75U1DIMlRWk09QxxuH3AB+nEL/rb4eDLUHYFGAF4dYVhjJ4mb34ABjutTiMiEnZU2IpI2Npe28lN/V+n/sL7rY4ip9EdXwRAUl/1Wb1+1oRkYiLsbKpu92Ys8ae9T4FnBGbfYnWSkzv3yzDcB1sftDqJiEjYUWErImHriW0NxEbauXxWrtVR5DS6EiZTNeFahiMSzur1kQ4b8wtSKG/spmdwxMvpxC92PwrZMyFrutVJTi57JpRcBJvuB5fT6jQiImFFha2IhKWBYRfNe17jb4k/I27giNVx5DSGotLZPPO7dCWWnfUaiyelYpqw5bBG/wSdjmpo3BHYp7XHLbkTBtrg0CtWJxERCSsqbEUkLL20t4liVyVlfZshMt7qOHImTA9RzrO/lDgtPorJWQlsrenA5fF4MZj4XGoR3LE+OArbSStg+Tcgc5rVSUREwooKWxEJS09sa2BWTCtmTArEaX5tMFhY/n0uX3fduNZYUpRGr9NFeWOPl1KJ32TPgNhUq1Ocnt0BK/8d0oqtTiIiElZU2IpI2KnvGGBjdTvz49ow0kqsjiNnqDeugJjhDqKGz77jbGlWPKlxkWoiFUwOr4O/3Q59LVYnOXMeD1S+BrUbrE4iIhI2VNiKSNh5akcDhgE5rgZIK7U6jpyh7vjRE7DEs+yMDGAzDJZMSqW2fYDGrkFvRRNf2vkXOPASRJ1d4zBLGAY8/1VYe4/VSUREwoYKWxEJKx6PyZPbG1helIw9YzLkzbM6kpyh44VtUl/VuNaZX5BKhN3QqW0wcPbBvmdg+ocgIsbqNGfOMGDmjVCzFnqbrU4jIhIWVNiKSFjZVNNOQ+cg1y0shE8+B4s+a3UkOUMD0dmM2GPPepbtcTGRdmZPSGZ3QxeDw24vpROf2P8sjPQHR9Oo95t5I5geKH/a6iQiImFBha2IhJUntzeQEOVg1fRsq6PIWBkGO8u+Rn3WheNeaklRGiNuk+21Irs1+wAAIABJREFUGv0T0HY/CskFkL/E6iRjlzFldK7tniesTiIiEhZU2IpI2OgdGuHFPU1cOTuX6LXfh99eAKZpdSwZg8r8D9OStnDc6+Qmx1CQFsummg48+hoITKYJuXNgyedHL+0NRjM/DN0NMNhldRIRkZCnwlZEwsbzbx1lcMTNjQsmwNHd4BkJ3jfMYcrhGiC9cyd29/gbPy0pSqOjf5iDzb1eSCZeZxhw8XdhyR1WJzl7iz4LX90HMclWJxERCXkqbEUkbDyxvYGSzHjmTkyG1grInGZ1JBmjzI5tXLLpVlJ6Dox7rem5iSREO9hQpSZSAcc04fB68AT5PdARMWCzj47/0ZUBIiI+5bA6gIiEt0c21/lln9ZeJ9trO7l0ejZPri/nxp4j7BzKYb+f9hfv6I4vAiCpr5K2lDnjWsths7G0KI1X9jXT1DNEdmK0NyKKNzTuhIcuh2vuhbkfszrN+NRvhcdvhY88BjmzrU4jIhKydGIrImFhR10nNgPm5ie/PS6mO0EzbINNf0wuLlv0uEf+HLeocHT0z4bKNq+sJ16y+1GwR0HZlVYnGb+0YuhvVRMpEREfU2ErIiHPY5rsrOtkclYCCdERuOwx1OReSWfCZKujyVgZNnriJ4175M9xsVEO5uansKu+iz6nyytryji5hmHPk1B2eWjcmxqbCiUXwZ6nRi9JFhERn1BhKyIh71BzHz1DLublpwDQlVjGxtk/YjBGI3+CUXd8CYleOrEFOKc4HZfHZHO17rUNCJWvwmBHcM6uPZmZN0BvI9SutzqJiEjIUmErIiFve10nsZF2ynISAIgY6VYjlyC2f9KtrJ/zE6+tl5EQxZSsBDbVdDDi1oma5SpegLgMKB7/vOKAMeUyiIjT5cgiIj6kwlZEQtqA08X+oz3MmZiMwzb6Le+qN65mwb4fWpxMzlZXYhltKXO9uuY5Jen0O13srte8Uctd9Qu47UWwh1B/y8g4WPV9mHG91UlEREKWClsRCWm7Grpwe0zmF4xehhzlbCd6uIPe2HyLk8nZMjwj5B99iZTufV5bszgjjuzEaDZUtWPqNN9adgekh2BjtwWfgqLzrU4hIhKyVNiKSEjbUdtJblI0OUkxAG930+1KKLEyloyHYWPJW9+m8OgL3lvSMDinJI2mniGqWvu9tq6M0d8+BxvvtTqF77Tsh7d0ObKIiC/4tLA1DONSwzAOGIZRaRjGt07w+HLDMHYYhuEyDOOG9z32CcMwDh379Qlf5hSR0HS0e5DG7iHmHTutBUjuPQSMNiCS4GQadnriJnlt5M9xsyckEx/lYF1lq1fXlTPU3wZ7HofBTquT+M7W38Mzd4Oz1+okIiIhx2eFrWEYduBe4DJgGnCLYRjT3ve0OuCTwCPve20q8B1gMbAI+I5hGCmIiIzB9tpO7DaDORPeGRmS1FeJMyKJoah0C5PJePXEF5HopZE/xznsNhYXpXKwuY+WniGvri1n4OBLYHqg7Aqrk/jOzBvBNTjaIEtERLzKlye2i4BK0zSrTdMcBh4Drnn3E0zTPGya5lvA+9tQrgJeNU2zwzTNTuBV4FIfZhWREOPyeNhV38XUnERio95pQlOfdTG7S+8Gw7AwnYxXd3wx8YONOFwDXl138aQ0HDaDDVUa/eN3+5+DxAmQM8fqJL4zcTEk56s7soiID/iysM0D6t/154ZjH/Paaw3DuN0wjG2GYWxrbdWlYyLyjoqjvQwMu5mf/96LPZoyllFZcJNFqcRbuuOLAbx+ahsf5WDOxGR21HXS53R5dW05BWcfVL0+elobyj90MgyYccPo37VP71tERLwpqJtHmab5W9M0F5imuSAjI8PqOCISQLbXdpIY7aA0K/7tjzlG+kjtLsfmdlqYTLyhKX0Jf1/xMh1J77/DZfzOLUnH7THZWNXm9bXlJJy9MP1DMP1aq5P43ozrwR4JTbutTiIiElJ8WdgeASa+688Tjn3M168VkTDXMzTCweZe5uanYHvX6U9G1y4u3XAzad17LEwn3uByxDEQkwuG9/8Zy0yMZlpuIhur2+kdGvH6+nICiTlw3W+hYKnVSXwvazp8swZKLrI6iYhISPFlYbsVKDUMY5JhGJHAzcAzZ/jal4FLDMNIOdY06pJjHxMROa1ddV2Y8IHLkJN6KwF1RA4VhUeeZfLhh32y9vmTMxga8fCXTXU+WV/exT0CLRUQLvODDQMiRsePhc3fWUTED3xW2Jqm6QK+wGhBuh943DTNcsMwvmsYxtUAhmEsNAyjAbgR+I1hGOXHXtsBfI/R4ngr8N1jHxMROSXTNNle20l+aizpCVHveSy57xADURkMRyaf5NUSTPJa1jLl8F98svaElFhKM+N5cF01QyNun+whxxxeB/cthsrXrE7iP90N8MB5UPGc1UlEREKGT++xNU3zBdM0J5umWWya5g+Ofew/TdN85th/bzVNc4JpmnGmaaaZpjn9Xa/9g2maJcd+/dGXOUUkdNR3DtLa52R+wQcnhCX1Vem0NoSMdkY+gt096JP1z5+SQVvfMH/dWn/6J8vZq3geImKh8Byrk/hPfDZ014/+3UVExCuCunmUiMj7ba/tJMJuMDMv6b0PmB6SeqvoTii2Jph4XXd8EQYmiX2HfbL+pLQ4FhSk8Ju1VQy73j+VTrzC4xkt7opXvnN5bjiwO6B01ejsXre6b4uIeIMKWxEJGcMuD281dDEjN4noCPt7HjMwWbPgXqomXG9ROvG246fvSX1VPlnfMAzuuqCExu4h/rFL/Qt94uhO6G2EqVdZncT/yi6HwU6o32R1EhGRkKDCVkRCRnljN06X54SXIZuGnZa0RXQn6FLkUNEXl4/bFkmM03fzQFdMyWBqTiL3r63C7VGjH6+reB4MO5ReYnUS/yteOTr2p+IFq5OIiIQEFbYiEjK213WSEhtBYXrcBx5L79xJXvNqC1KJr3hsETxx8Sb2F93msz1GT22LqW7t5+XyJp/tE7bO+TJ8/GmITbU6if9FJcB5X4f8xVYnEREJCSpsRSQkdPYPU93az7yC986uPW5y7aPM3/9jC5KJL3lsET7f47IZORSlx3Hv6kpMjWfxruhEKDrf6hTWWfFNmHaN1SlEREKCClsRCQk76joxgHn5H7wMGSCpr1IdkUNQTut6Vmy9A5vb6bM97DaDO1YUU97Yw5qDvrvsOey89QSs/4VmuXYfgcZdVqcQEQl6KmxFJOh5TJMddZ0UZcSREhv5gccNzwiJfTV06f7akBPh6iW3bT2J/Yd9us+H5uSRmxTNr1/Xqa3XbH4Ayp+GE1xhEVYevxWe+4rVKUREgp4KWxEJejVt/XQOjJywaRRAwkA9dtOlE9sQ1B1fBEBSX7VP94l02LhzRTHbazt1ausNPY1wZBuUXWF1EutNuQwad0DPUauTiIgENRW2IhL0dtR2EuWwMS0n6YSPJ/UeAqArodSfscQPemML8WAj0Ucjf97tpoX5TEyN4Z6XDuBRh+TxOXCsE3BZGI75eb/jxf0BdUcWERkPFbYiEtSGRtzsbexm1oRkIh0n/pbWkHUhz573DD3xxX5OJ77msUfSF5fvs1m27xbpsPHViyez/2gPz+3R6dq47H8OUoshY4rVSayXUQYpk1TYioiMkwpbEQlquxu6GHGbLDjJZcgAps1Bb/wkv3TQFf9rSZnHiOODI5584erZeUzJSuBnrxxgxO3xy54hx+MBmwOmf0j318Lo56DsCqh5E4YHrE4jIhK0VNiKSFDbdriT7MRoJqTEnPQ5Mw/dS07rOj+mEn/aMvO/2Tzr+37Zy24z+PqqKRxuH+CJbQ1+2TPk2GzwsSdh5X9YnSRwLL0LvrQbImOtTiIiErRU2IpI0GrsGuRI1yALClMwTnLyY3M7mV75W9K7dvs5nYSqi6ZmMi8/mV+8dpChEbfVcYLPcP/o7zqtfUdiLiTmWJ1CRCSoqbAVkaC19XAHDpvBnInJJ31OYn8NNjx0qSNyyIp2tnH5m9dSeORZv+xnGAbfuLSM5h4nf9p42C97hoyRIfjfMlj/S6uTBJ6aN0dH/7hHrE4iIhKUVNiKSFAadnnY3dDFjLwkYiMdJ31e8rGOyN3qiByyhiJTiRtsJK17r9/2XFKUxvLJGdy3poqeIRUiZ6x6DTh7IGua1UkCz1AX7PsH1G20OomISFBSYSsiQWlvYzdDIx4WFJ68aRRAUl8VbsNBb+xEPyUTvzNsdCaWkdKz36/bfmPVFLoGRvjdG76doRtSKp6FqEQoXG51ksBTvBLsUVCh7sgiImdDha2IBKWthztIi4tkUtqpu+FGO9vpiS/CVEfkkNaZOJWUngoM03/3vM7IS+KKmTk8uK6G1l6n3/YNWh43HHgJSi8GR6TVaQJPZBwUrYADz4OpOckiImOlwlZEgk5L7xC17QMsLEw9adOo4zbP+h4vL3vMT8nEKh2JZUS4B0nor/Xrvl+9ZDJOl4dfvnbIr/sGpSM7YKANplxudZLAVXY5dNVBc7nVSUREgo4KWxEJOtsOd2IzYG7+yZtGvZvm14a+tuTZ1ORe6fd9izPi+ejifB7eXEt5Y7ff9w8qKQVw6Y+h5EKrkwSuyZdB7tzR+5BFRGRMVNiKSFBxuT3sqOtkak4iCdGnLliTew6wfPvdJPbpHshQ1xs/iY2zf0RPfJHf9/7axVNIiY3kP/9RjsejS0hPKj4TltwJMae+Lz6sJWTB7WugYJnVSUREgo4KWxEJKvubehkYdrOwMPW0z03tLmdCyxo8hk5sw4JpEjXc6fdtk2Ij+OZlZWyv7eSpHQ1+3z8o9ByF3Y/BkE4iz8hw/zvzfkVE5IyosBWRoLL1cAfJMRGUZMaf9rnJfZW4bNH0xeb5IZlYbV7FPVy19gpLGu/cMG8C8/KT+fGLFXQPavzPB1Q8B09/DvparE4S+Hoa4Z4i2PWI1UlERIKKClsRCRod/cNUtvQxvyAF22maRgEk9VbSnVAMhr7VhYPuuCIiXb3EDR7x+942m8F3r5lB58AwP3vlgN/3D3gHXoS0EkgvsTpJ4EvIgcRcOPiS1UlERIKK3u2JSNDYXtuBAcwvOLN79JL6KumOL/ZtKAkYnUnTAEj18zzb42bkJfGxJQX8eZMaSb2HsxcOvwmTL7U6SXAwjNHPVc0b4OyzOo2ISNBQYSsiQcHtMdle28nkrASSY08/A9PmHqY/Jo/2pJl+SCeBoCu+BI9hJ8WiwhbUSOqEqlaDe1iF7VhMvnT0c1a9xuokIiJBQ4WtiASFiqYeeoZcLJp0+qZRAB57JK8u/TOHCm72cTIJFB57FN3xxaR277MsQ1JsBN9SI6n3atwB0UmQv8TqJMGjYBlEJepyZBGRMXBYHUBE5ExsqekgKSaCyVkJVkeRAFZe/FnctihLM1w/bwKPba3nxy9WcMm0bJJiw7wr90X/BUvvBnuYfx7Gwh4BV/8K0kutTiIiEjR0YisiAa+9z8mhlj4WFqZgt52+aRTAwr3/zfnb7vJxMgk0dTmXciTrAkszjDaSmk7X4Aj/9Wy5pVkCRlya1QmCz/QPQdZ0q1OIiAQNFbYiEvC21HRgM2DBGcyuPS6jcydwZkWwhA7D4yKtaw9xA/7vjPxu03OT+OLKUp7eeYRndjdamsVSb/4MnvoMeDxWJwlOB1+GihesTiEiEhRU2IpIQBtxe9he18nUnEQSo8/sUkaHq5+kvmrak3TaEW7snmEu2fhRJh15xuoo3HVBMXPzk/n203to7Bq0Oo419jwJvU1g09uNs7Lu/8GaH1mdQkQkKOhfGhEJaHuPdDMw7GbxpDO/lDGlZz8GJh0qbMOOyxFLT1yhpZ2Rj3PYbfz8pjm4PSZffXxX+HVJ7qqDlnKYvMrqJMFr8ipoegt6wvjUX0TkDKmwFZGAtqWmg7S4SIoy4s74NWndo/c16sQ2PHUmTrVslu37FaTF8Z2rp7OpuoPfr6u2Oo5/HTjW0XfyZdbmCGbHP3fqjiwicloqbEUkYDV1D1HbMcDiSanYjDO/X7Y3Np/KidfjjFLDmnDUkTSNuKEmopwdVkcB4Mb5E7h0ejY/efkA5Y3dVsfxn4MvQloJpJdYnSR4ZUyB5ILRe21FROSUNO5HRALW5pp2HDaDefkpY3rdkawLLO+MK9bpTCwDIKWngqaMZRanAcMw+NF1M1n1806+/Ngunr37XKIj7FbH8r28BVBy0dt/fGRznYVhgtf8pHPIaVjP85tqMI13vm4+sjjfwlQiIoFHJ7YiEpCcLje76ruYmZdEbNSZ/wzO5h4OmJM6sUZ70kz+uehB2lLmWB3lbSlxkfz0xtkcaunjxy9WWB3HP1b+OyzVyK3x2jX5Szy3/Nn3FLUiIvJBKmxFJCDtqu/C6fKweNKZj/gByOjczvWvn09m+1YfJZNA53LE0pK2CJcj1uoo77F8cga3nVPIQxsO8/TOBqvj+FbrAXANW50iJLgdsTCGWzFERMKVClsRCTimabKlpoOcpGgmpo6tODneOKozcbIvokmQSO3ay5SaP1kd4wP+9bKpLC1K45tP7mFzdbvVcXzD44GHroBnv2h1kpBRUvc4qzbcDGaYddYWERkDFbYiEnDqOwc52j3EokmpGGM8qUjtLqc3diIjEUk+SifBILt9I/MrfkLESI/VUd4j0mHjgY/NZ0JqDJ/7y3aqW/usjuR9R7ZDfysUX2h1kpDhtkWS1l0eEGOsREQClQpbEQk4m6vbiXTYmDMhecyvTesupz1phg9SSTDpTJwKQErPAYuTfFBSbAQPfXIRdsPgUw9tpaM/xC7ZPfgiGHYovej0z5Uz0phxHiYGeS1rrY4iIhKwVNiKSEDpHRrhrSPdzMtPIWqMnWOjnO3EDR2lQ/Nrw97xzsipPfssTnJi+Wmx/PbWBTR2D3H7n7YxNOK2OpL3HHwZ8pdCzNi6mcvJOaPSaE+eSV6rClsRkZNRYSsiAWXr4Q7cHpOlRWOfQeu2RbFp5nc5krHcB8kkmAxFpTMQlUlKT+B2IJ5fkML/3jibbbWdfPOptzBD4f7Jrjpo3gtTLrU6SchpyFxBWnc50UOtVkcREQlImmMrIgHD7THZXNNBaWY8GQlRY369KyKe6gnX+iCZBKOOpGkk9VVZHeOUrpqdS13HAD95+QC5yTF8Y9WUMd9XHlAS8+C2lyB1ktVJQk5D1oXEDTZhM11WRxERCUgqbEUkYOxt7KZ3yMV1c8d+WguQ1baRgZgceuMKvRtMgtKmmd9nJCLe6hin9fkVxTR0DnL/mir6nS6+c9V07LYgLW5tdihYanWKkNQTX8TWGf9hdQwRkYClS5FFJGBsrGonLS6S0qyEsb/YNFm2+1+ZXvU77weToDQcmYRpjO0+bSsYhsEPPjSD25cX8aeNtXzxsZ04XUF4z+1QD7z4LWg9aHWS0GV6SO0ux+Z2Wp1ERCTg6MRWRAJCQ+cAdR0DXDkrB9tZXIoZM9RMzHA7HYnTfJBOgpHN7WT+/v+hKX0p9dkXWx3nlGw2g3+7fCppcZH86MUKugaG+c3HFxAfFUT/TFf+EzbfD1OvggzvzZE2TZP+YTftfU7a+px09A8zOOJmaMTD0LHfnS43bo9JhN1GhN1GpMMY/d1uIyE6gvT4SNLjo0hPiCIu0h60l3tnt29i5dbPsWb+vUCp1XFERAJKEP2LKSKhbGPV6Iifefln10k1rbscQKN+5G0eWyQTm/6JzXQFfGF73OfOLyYtPopvPvUWt/x2Ew/dtpC0+LHfb26JAy9AbBpMXHzWS7g9Js09Q9R1DNDQOUBL72gxOzTiefs5BhAdYSc6wkZ0hJ0oh52kmAjsNoMRt4cRt0m/082we4QRl4feIRfudzXmio6wkR4fRX5qLEXp8UxKjyMmMvBP9gFaUuYzYo8ht/UN4GNWxxERCSgqbEXEcsdH/CwsTCV6jCN+jkvtKcdj2OlKnOLldBK0DIPOpKkB3Rn5RG6YP4GU2AjuemQHNzywkT9+ciGF6XFWxzo11zAcfGX0tNZ+5m8tRtweatr6qWnrf7uYHXGPFqFxUQ5yEqOZPSF59LQ1Por0+EiSYyPHdA+y22PSNTBMW98w7f2jhXJLj5OthzvYUNWOAeQmx1CUHkdxZjzFGfEBe4+zxx5FU/rS0Xm2pglBevIsIuILKmxFxHLjGfFzXFrXXrrjS3Dbo72YTIJdR+JUymr+D5t7GI890uo4Z+zCqVk8/JnFfOqhbVz2izf51mVlfHxJAbYALbioXQfObii74rRP7ewf5kBzLweaeqlu62PEbWIzRovLBQWp5KfGMjE1lpTYCK9cMmy3GaTFRx07+X7n/n2X20N95yDVrX1UtfazobqdNyvbiIu0M2tCMnMmJjMhJSbgLls+krGCic2vj45Vyp5pdRwRkYChwlZELOXyeNhc08HkrLMb8XPchtk/Inq4w4vJJBR0JE7FbrpI6qukMym47r+eX5DKi186j3/92x6+80w5L+w5yk9umE1+WqzV0T6orwUSJ0DxBR94aNjlYVttBy/uOUpFcy+tvaONj1LjIllQmMqUrAQmpccRYfdvP0uH3cak9Dgmpcdx4dTRnFWtfeyq72Lr4Q42VreTHh/JnInJzM1PISU2MH4w0ph53uh/HHxJha2IyLuosBURS5U39oxrxM9xzqg0nFHjW0NCT2fiNPpi8oga6bI6ylnJTY7hodsW8sS2Br733D5W/fyNwDy9nX0zzLrp7Utjm3uGWHOghdUVrayrbKPP6cJuM5iUHseiY8VsWnxkQJ2GRjpsTM1JZGpOIkMjbvYe6WZXfRev7W/htf0tzMhLYnlpBnkpMZbmHIpK59XFD3Hx0kstzSEiEmgM810NFYLZggULzG3btlkdQ0TGaPk9q+l3uvjKxZPPqhsyQHrnTjI7tnOw4CO4HAF4miVB6yOL862O8LbGrkG+9bc9vHGwlUWTUvn6JVNYWJhifXHocuI2ItjV0MXqilZWH2ihvLEHgJykaFZMyWRlWSYNnQNEOYKjSdO7dQ0Ms6m6nc01HThdHooy4lhemkFpZryln/tA+toUEfEXwzC2m6a54ISPqbAVEau81dDF1b9ez5WzclhWnH7W68yp+F+m1D7CExdvwmOL8GJCCXeBVjyYpskT2xr44Yv76RoYYWZeEp8+dxKXz8wh0uHfS3mbe4ZYX9lG3PofMbn9dS4Z+jEeWwTz81O4oCyTC8oymJKV8Hbx98jmOr/m87ahETdbD3ewvrKNniEX2YnRXFCWyYzcRL8XuIZnhFuG/gqZU2H6tX7dW0TESqcqbHUpsohY5ndv1hA1jhE/x6V1l9OZMEVFrZxQUf3TTKt+kOfP+zumLbj/2TMMgw8vnMhVs3P5284G/rCuhi//dRc/enE/ty4t5JZF+aTG+eZe0K6BYTZWtbOhqp0NVW1UtfYD8Fr0WlyxWfy/6xZyXkkGSbGh+f9hdISd80ozWFqcxlv13aw91MqjW+rIT43lshnZFKT5r3O1aYuAvX+DpDwVtiIixwT3v/AiErTqOwZ4Yc9RlhWlnfWIHwBMD6nd+6jJu8p74SSkeGwRJA7UkthfQ3dCqdVxvCIm0s5HFxdwy8J83jjUyoPravjJywf46SsHKMtOZFFhCgsKU1lYmEp20tg7hbf1Odl/tId9jT3sO9pDeWMPVa19mCbERtpZNCmVmxfmc356D8WP18PyL1A6K9cHf9PA47DZmFeQwpz8ZHbUdvLq/mZ+80Y103MTWTUtm/RxNMEbk7IrYOOvYbATYsb3w0ERkVCgwlZELPGH9TUYwLKSs78EGSCx/zAR7n7ak6Z7J5iEnONfG+ldb4VMYXuczWawYkomK6ZkcrC5lxf3NLGttoMntjfwfxtrAZiYGkNxRjwJ0REkRjtIjIkgIdpBQpSDXqeLzv5h2vuH6Tj2q6l7iJZjnYsB8pJjmJqTyNWzc1lWnMbsicnvdDBe/8vR38su9/df3XI2w2BBYSqzJiSzrrKVNw61sf/oQRZNSuWiqVnERvr4LVbZlbD+53DoVZj1Yd/uJSISBFTYiojfdQ+M8Net9Vw9O5ekmPFdthg/0IDbiKAjaYaX0kmo6Y0rZDAylcyO7VRNvN7qOD4zOSuByVmjc1pdbg/7j/ay5XAH2w530Ng1SG37AD2DI/QMjTDifqe/RnSEjbS4KFLjIkmNi6Q0M4GpOQlMO9YhOOVUlzZXPD86ciY5sO5F9qdIh42VZVksLEzl9YoWttR0sOdID1fMzGH2hCTf3X+bNx/is2H/sypsRURQYSsiFnh4Sy0Dw24+c14Ru+rHN4alMXM5T1yyGY8RfN1WxU8Mg9bU+WR2hE+DQYfdxswJScycMNpc6t1M08Tp8tAzNEJ8lGN8J4tL73p7xE+4S4iO4Jo5eSwsTOXvu47w+LZ6dtZ1cs2cPN/c92yzwYzrob/F+2uLiAQhFbYi4ldOl5uH1h/mvNJ0puUmjruwBdQ0Sk6rNnsVg1GZ2DwjYf/1YhgG0RH28d3bfty0q8e/RojJTY7hjvOL2VTdziv7mvnFawe5sCyLc0rSsXt79vClP/TueiIiQcy/swFEJOz9Y1cjLb1Obl9eNO61DI+LlVs+w4Tm17yQTEJZfc4qtk/7VtgXtV619yloq7Q6RUCyGQbLitP5ykWTKc1M4KXyJu5bU0lT95BvNhzq8c26IiJBRIWtiPiNaZr87o1qyrITOHecTaMAkvqqyG7fjN3tozeLElIMj4u4gSNWxwgNzj54+k7Y9qDVSQJaUkwEH1tSwEcX59Mz5OLeNZWsO9SKxzRP/+Iz9dp34ZdzweP23poiIkFIha2I+M2ag60caunj9uVFXmmoktpdDkCHOiLLGVj21r9y4ZZPWx0jNFS9Bm7n6MgZOa3puUl86cJSJmcl8MLeJv6wroaugWHvLJ49EwbaoH6zd9YTEQlSKmxFxG9+90Y12YnRXOmleZdp3eUMOxLojQ2JO3GZAAAgAElEQVTfjqxy5tqSZxM/eITYwSarowS/iudHZ6dOXGJ1kqARH+XgY4vzuW5uHg1dg/zy9UNe6TFAyUVgj4T9z41/LRGRIKbCVkT8Yu+RbjZUtfOpcwuJdHjnW09qTzkdSdPA0LcyOb3m1AUAZHZstThJkHOPwMGXYPJlYFcPyrEwjs2+/eLKUjITonl8Wz1/3VqHc2QclxFHJUDRCqh4Drx5ibOISJDRu0ER8YvfvlFNfJSDmxd56XTVNOmPzuVo2lLvrCchrzuhlGFHApkd262OEtxa9sHwgC5DHofUuEg+e14RF03N4q2Gbu5dU8nR7sGzX7DsSuiqheZy74UUEQky+lGriPhcfccAz+85ym3LCkmM9lJXWsNg3byfeWctCQumYac1ZV5YzbP1iZzZ8I0qcERbnSSo2W0GK8syKUyP5a9b67l/TRVXzc5lQUHK2HsQHP8hQ1Ke94OKiAQJFbYi4nP3r63Cbhh85rzxj/h5m+nRJcgyZuXFn8budo5esumFBmZhKzrJ6gQhoyg9nrtXlvL41nqe3nmEmrZ+rpmTS5RjDHOG49Jh/id8F1JEJAjoXaGI+NTR7kGe3NbAjQsmkJ3kvROeJXv+g4s23eq19SQ8tKXMpTl9iYras9W4Cx5cBc37rE4SUuKjHHzynEIunJrJ7vou7ltdRXPPGMeYDXbC1gehWyOtRCQ8qbAVEZ/6zdpqPKbJHecXe29R0yS7bRODUZneW1PCRmb7VvKaV1sdIzhVPA8NWyA+y+okIcdmGFxYlsWnzp3E4Iib+9dWsfdI95kvMNABz38V9j/ju5AiIgFMha2I+Exrr5NHt9Rx7dw8JqbGem3dhP7DxDpbaEpb7LU1JXxMq/kDcw783OoYwaniechfCnFpVicJWcUZ8dx1QQlZCVE8sqWOV/Y14TmTbsdpxZA5TWN/RCRsqbAVEZ/5/bpqRtwe7lzhxdNaIKt9CwDNKmzlLDSnLCCpv5ooZ7vVUYJLRzW0lKsbsh8kxUTw2fOKWFCQwpoDrfxp42EGh89gJFDZFVC3Afr1tS0i4UeFrYj4RGf/MH/ZWMuVs3Ipyoj36trZ7Zvpj86mL3aiV9eV8NDy9jxbjf0Zk71Pjf4+9Sprc4QJh93GtXPzuGZOLlUt/dy7ppKm0913W3blaGO9gy/6J6SISABRYSsiPvHHDYfpH3Zz1wUlXl+7LucS9hbfrgZAclY6kqYxYo8hs1Njf8YkrRQW3Q7JXppFLadlGAaLJ6XxmfMmMeLy8MCaKvY1nuK+25zZkJQPLfv9F1JEJEBo3I+IeF3P0Ah/XF/DqulZTMlO8Pr6dTmXen1NCR+mLYK25DmkdZdbHSW4TP/Q6C/xu4K0OO66oIS/bK7l4c11rJqezS2LJn5w3q1hwF2bIDLOmqAiIhbSia2IeN2fN9bSO+Ti7pWlXl87uecACf21Xl9XwsvG2T/k1cX/Z3WM4NGwfbTrrlgm8dh9tzPyknipvIlvPPkWwy7PB594vKg9k4ZTIiIhRIWtiHjVwLCL379ZzQVTMpiRl+T19Wcf/AXLt3/B6+tKeBmKSse06aKlM+LxwBOfhKfvsDpJ2Iuw27hp4URWlmXyxPYGPvbgZjr6hz/4xKfvgGe/5P+AIiIWUmErIl71yOY6OgdG+IIPTmsNzwiZHdvVDVm8Yk7Fzyir0antaTVsge46mHG91UmE0Xm3F03N4hc3z2FXfRcfunc9lS2973uWAeV/B5fTkowiIlZQYSsiXjMw7OKBtdUsK05jfkGK19dP6y4nwj1Ac+oir68t4Se1u5zCI5r5eVp7ngRHDJRdbnUSeZdr5uTx2O1LGBh2c+19G3jjYOs7D864HpzdcOhV6wKKiPiZClsR8ZqHNhymrc/J1y6Z7JP1s9o3A9CcpsJWxq8ldQEpvQeIGDlFl9lw5x6B8qdhymUQ5f1GcDI+8/JT+McXziEvOYbbHtrKnzYeHn2gaAXEpsOex60LJyLiZz4tbA3DuNQwjAOGYVQahvGtEzweZRjGX489vtkwjMJjHy80DGPQMIxdx3494MucIjJ+3YMjPLCmipVlmcwvSPXJHlntW+hIKGM4Mtkn60t4aUldgIFJZsdOq6MEriPbYaANZt5gdRI5ibzkGJ68cxkrJmfwn/8o5zv/2IsLG8y4Dg68BEM9VkcUEfELn3XOMAzDDtwLXAw0AFsNw3jGNM1973rap4FO0zRLDMO4Gfgf4KZjj1WZpjnHV/lExLt+90Y1PUMun53WAqyf+1Nihlp8tr6El7bkWbhtkWR2buNI1gqr4wSm/CXwxV2QmGt1EjmF+CgHv711AT9+cT+/e7OGmvYB7lt5M/FxGWC6rY4nIuIXvjyxXQRUmqZZbZrmMPAYcM37nnMNcLxzx5PAhcYHhrKJSKBr63Pyh/U1XDkrh+m53u+EfJwzMoWuxCk+W1/Ci8ceRUPmBbhs0VZHCWypk8ARZXUKOQ27zeDfr5jG/1w/kw2VbXzob33UzfgCxHi/34GISCDyZWGbB9S/688Nxz52wueYpukCuoG0Y49NMgxjp2EYaw3DOO9EGxiGcbthGNsMw9jW2tp6oqeIiB/ct7oKp8vDVy/23Wlt4ZFnmXz4YZ+tL+Fp/dyfsmeyxked0P7n4LGPQn+71UlkDG5amM+fP72Ytj4nH753NVVrH4E+vUcSkdAXqM2jjgL5pmnOBb4KPGIYRuL7n2Sa5m9N01xgmuaCjIwMv4cUEWjsGuQvm2u5fl4eRRnxPttnct1jFBx9yWfrS3gzPCNWRwg8ux+Fhm0Qo3vag83S4jT+ducypkS1U7z6Tva+8gerI4mI+JwvC9sjwMR3/XnCsY+d8DmGYTiAJKDdNE2naZrtAKZpbgeqAN8dBYnIWfvV64fAhC9e6P25tcc5RvpI7S5XN2TxOsN0c9XaK5h16NdWRwksg11w6JXRsTE2u9Vp5CwUZcTz/75wM4cdRYzsepx7V1dimqbVsUREfMZnzaOArUCpYRiTGC1gbwY+8r7nPAN8AtgI3AC8bpqmaRhGBtBhmqbbMIwioBSo9mFWETkLNW39PL6tgY8vKWBCSqzP9sns3I7NdNOUtthne0h4Mg07Q5GpZHVsO+Hjj2yu83OiwFBU/zRL3MO8ZDuPjjD9HISC1LhIEs+/lcLX/osvv7KW2vZ+fnDtTCLsgXrBnojI2fPZd7Zj98x+AXgZ2A88bppmuWEY3zUM4+pjT3sQSDMMo5LRS46PjwRaDrxlGMYuRptK3WGaZoevsorI2fn5Pw8Sabdx1wUlPt0nu30TLlsUbcmzfbqPhKeW1AWkdu/D7hqwOkrAKDz6PL2x+XQkTrM6ioyTY9aNAPyw9ACPb2vgk3/cQvegLr0XkdDj0x/Zmab5gmmak03TLDZN8wfHPvafpmk+c+y/h0zTvNE0zRLTNBeZpll97ONPmaY53TTNOaZpzjNN81lf5hSRsato6uGZ3Y3cdk4hGQm+7ZgaMdJHS+oCPHZ1ZhXva0ldgM10kdG1y+oogcE0aUldQEXhx0GDCoJf0gQoOIdzIqv43xtns6Wmg+vv30B9h36QIyKhxZeXIotICPvRCxUkRDn43PJin++1edb3wPT4fB8JT60pc/EYDrLbNtGUvszqONYzDPaW3GF1CvGmm/4CMSlcbxjkJsfwuT9v49r71vO7WxcwN1/jgEQkNOgmCxEZszUHWlh7sJUvXlhKUmyEbzc73uzE0Lcr8Q2XI5bdk+/maMY5VkcJCJntW7C5h62OId4Umzp6+m6aox2TP38OsZEObv7tJl7Yc9TqdCIiXqF3iiIyJi63hx88v5/CtFhuXVro8/3m7/8xy7ff7fN9JLztL/oUzWpORnx/HRdt+TST6x61Oop429YH4f5zwOOmJDOepz+/jOm5iXz+4R08sLZKHZNFJOipsBWRMXl0Sx2HWvr4t8unEunw/beQ3NZ1Pt9DBCCxt4rstg1Wx7BUwdEXAajLXmVxEvG6mGRoKYfa0a/xtPgoHvnsEq6clcOPX6zg357ew4hbt3yISPBSYSsiZ6x7cISfvXqQpUVpXDwty+f7xQ4eJWGgjuZUza8V35tX8RMW7f3uO5e/hxvTpLDxeZpT5jMQk211GvG2yZdBRBzseeLtD0VH2PnlzXO564JiHt1Sz6ce2krPkDomi0hwUmErImfsV68domtwhG9fORXDD91Ss9q3ANCcpsJWfK8uZxXxg0dI7dlndRRLJPceIKm/htrcy62OIr4QGQtTr4R9/wCX8+0P22wG/7KqjHtumMXGqnZuuH8DDZ3qmCwiwUeFrYickZq2fv5v42E+PH8i03OT/LJndvtmhiJT6Uoo9ct+Et4aMlfiMRzkH33Z6iiWmNC8GrcRQX32xVZHEV+ZeSMMdUHlax946MMLJvKnTy3iaPcQH7p3A7vruywIKCJy9lTYisgZ+dEL+4m02/jaqsl+27Mldd6xWZr6ViW+NxyZRFP6EvKbXgnLy5H3ltzBi+c8gTNS419CVtEKWHIXpE464cPLStJ5+vPLiI6wcdNvN/LS3ia/xhMRGQ+9WxSR09pQ1cYr+5r5/AUlZCZE+23fqok3sK/4M37bT6Q2exUxzlbiB+qtjuJfpgmGQU+C7+dSi4XsEXDpDyFz6kmfUpKZwN/vOoepOYnc+fB2fvdGtTomi0hQUGErIqfk9ph8/7n95CXH8OlzT/xTfl+IG2ggcrjbb/uJwOh9tk+tXEtfXL7VUfzH9HDJxo9SWqsRP2HBNKF+CzRsO+lT0uOjePSzS7h8Rg4/eGE/3/77XlzqmCwiAU6FrYic0iNb6th3tIdvXlZGdITdb/vOrfgZl274sN/2EwFw22NwRcRbHcOvcto2kt69hxFHgtVRxF+e+jSs/uEpnxIdYedXt8zlzhXFPLy5jk//3zZ61TFZRAKYClsROamW3iHueamCc0rSuGpWjt/2tbsGyG1bx9H0ZX7bU+S4pN5KVm24hbSuPVZH8YvJtY8wGJlGXY5m14YFwxhtIlW9BnqOnvKpNpvBNy8t48fXzWRdZRs3PrCRxq5B/+QUERkjFbYiclLff24/zhEP37tmhl/G+xyX1/oGDvcgtTkaOyL+NxCdSXJPBflNod8dOb6/ntzWN6nMvxGPLcLqOOIvcz8Gpge2P3RGT795UT4P3baQI52DfOje9exp0G0iIhJ4HFYHEJHA9MbBVp7Z3ciXLiylKMO/l2YWNL7AQFQmranz/LqvCMBIRCJN6cvIP/oKO6d8bfSEK0RNrnsU07BTOfFGq6PIGD2yuW4cr3Zwfsa5pG76Pf+I/vAZ/1DjU+dO4v82Hua6+9fz4QX+G/3max9ZHEb31IuEMJ3YisgHDI24+Y9/7GVSehx3rvBvl1SHq5/c1nXU5azCNPx3T6/Iu9XlrCJu6Chp3aF9OXJN7pVsm/avDEZnWh1F/OxgwS3YPMMk9lWd8WuyEqO58/xishKjeXhzHa9XNKtjsogEDJ3YisgH3Le6ktr2AR75zGK/NowCcDnieP68v+uySLFUQ+YK3EYE+Udfpj15ltVxfKYzaRqdSdOsjiEWOJp+Dn+/4J+47TFjel1CdASfPa+Ip3ce4Z/7W2jqHuKG+ROJdOisRESspe9CIvIelS193L+2imvn5rGsJN2SDH1x+QzE+K9Zlcj7jUQksq/407Qnz7Q6im+YJrMP/IKk3kNWJxGrGLbRotb04HD1j+mlEXYbN86fwGUzsilv7OE3b1TROTDso6AiImdGha2IvM00Tf796T3ERNj5t8un+n3/KGc75+78Kkm9B/2+t8j77Sm9i7qcS62O4RNZHVuYXv17UrvLrY4iVjI9XLr+Jubtv2fMLzUMg/NKM7h1aSGdA8Pct7qSmraxFcgiIt6kwlZE3va3HUfYXNPBty6bSkZClN/3z296hfymV4HQbdYjwSXa2UZ6506rY3jd5NpHGYpIDtnCXc6QYaMjeTqFjS8QOXx2nY6nZCdw5/klxETa+cO6GrbWdHg5pIjImVFhKyIAtPY6+cEL+5mXn8zNCydakqHg6Et0xZfQnVBqyf4i77do739zzq5/GR2NEiJiBxvJa15N1cTrcdujrY4jFjuYfwsOzxBFR/5+1mtkJERx5/klFGfG8fSuIzyz+whuj5pKiYh/qbAVEUzT5N+e3kOf08X/XD8Lm83/J6axg0fJ7NxBbc5lft9b5GTqsi8hbqiZ9K63rI7iNaV1fwXgUP5NFieRQNCVOIWWlHmU1j6GYbrPep2YSDu3Li3kvJJ0NlV38Mf1NfQ7XV5MKiJyaipsRYSndhzh1X3N/MslUyjNSrAkQ8HRlwBU2EpAaci8ALctkvyml62O4jVuWzQ1eVerQZu87WDBLSQMNpDdtmFc69gMg8tm5nDD/AnUdQxw35pKmrqHvJRSROTUVNiKhLkjXYP89zPlLCpM5VPnTrIsx3BEArXZq+iLs+YyaJETcUXE05h+DvlHXwmZy5H3lt7J5lnfszqGBJD6rAt5Y+7PaUpb6pX15uWn8NnzinB5TB5YW8W+xrO7f1dEZCxU2IqEMY/H5BtP7sZtmvz0xtnYLbgE+biqiTewfu5PLdtf5GTqsy8h1tlCSs8Bq6OMj2mS3rkLTN37KO9l2iJoyL4Q0+bw2poTU2O5a0UJmYlR/GVzHa/sa8Kjrz0R8SEVtiJh7C+ba1lf2c6/XzGV/LRYy3LE99dh84xYtr/IqdRnreTvK16hM8n/I7C8KaNzJ5ds+jiFjc9bHUUC1LSq3zOt6vdeWy8xJoLPnlfEgoIU1hxo5aENh3XfrYj4jApbkTBV09bPD1/Yz/mTM/jIonzrgpgm52//Auft+Ip1GUROwe2Ifed+1CC+HHla9e8ZdiRQn7XS6igSoJJ7DzKt+g/YXQNeWzPCbuO6eRO4dm4eh9v6uXd1JQ2d3ltfROQ4FbYiYcjtMfna47uItNv4n+tnYRjWXYKc3HuApP4ajmQutyyDyOkYppvztn+R2Qd/aXWUs5LduoG81jcpL/4sbod1V2dIYDtYcAuRrl4Kj77g9bUXFqbyueXFYMBv3qhma00Hpi5NFhEvUmErEoYeWFvFjrouvvehGWQnWTvHsuDoi3gMB/XZF1uaQ+RUTMOO2x7N5NpHiHJ2WB1nTAyPi3kVP6E3ZgIHCj5qdRwJYG3Jc+hIKGNy7aM+uRc7LyWGL6wooSh9dN7tUzuOMOwK3qsgRCSwqLAVCTNbajr42asHuWJWDlfPzrU2jGlScPQlmtKX4IxMsTaLyGnsLbkDu9vJ1JqHrI4yJvGDDUSO9LCz7Ot47JFWx5FAZhgcKriZlN6DZHTu8MkWsVEOPrGskJVlmeys6+S+NZU092gkkIiMnwpbkTDS1ufk7kd3MDElhh9dN9PSS5ABaNhG/GCjZtdKUOiJL6I29zIm1z1GlLPd6jhnrDeukGfPf54G3VsrZ+Bw7uUczrmMEUecz/awGQYXTc3itnMm0T/s5r41leyo7fTZfiISHlTYioQJt8fky4/tonNghHs/Oo/E6AirI0HefF5Z8ifqsy60OonIGdlb/Dlsbidlh/9sdZQzktm+FZtnBLc9Gqz+QZYEBbc9hg1z7qErsczne5VkxnP3yhImpMTy5I4GntzeoEuTReSsqbAVCRO/fr2SdZVtfPfq6UzPTbI6ziibjbaUubh8eDIg4k298ZNYP+cn7J90m9VRTiu+v44Ltt7OrIO/sjqKBKG4gSMUHnnW5/skRkfw6XMnvefS5CZdmiwiZ0GFrUgYWF/Zxs9fO8h1c/O4aeFEq+OMqt0Iz3+dqGFdfibBpT7nEoYjA+SHQ6cw98D/4rFFUlH4caujSBCaWvNHluz5T+L7632+1wcuTV5dycbqdnVNFpExUWErEuKae4b40mM7KcmI5/vXzrD+vtrjdj0Mux/DZY+xOonImKV2l3Pxxo8T7WyzOsoJZbVvZmLz65QXf5ah6Ayr40gQ2lv8OTyGg1mHfu23PUsy4/niyhKKMuJ4dncjf95US5/T5bf9RSS4qbAVCWEut4e7H91Jv9PNfR+dR2ykw+pIo5y9sO8ZKLti9N4/kSAz7EggrXsP06oftDrKBximm3n776EvJlentXLWhqIzOFD4MQqPvkByT4Xf9k2IjuATSwu5clYOh1r6+NVrhzjU3Ou3/UUkeKmwFQlhP3yhgi01HfzwuhmUZiVYHecdWx8EZzcsut3qJCJnpS8un5rcKympe4LooVar47xHlLMDjy2CXVO+gsceZXUcCWL7im7DGZHInIO/8Ou+hmGwrDidz68oJibSzh83HOaFPUcZcauxlIicnApbkRD1l021/GF9DbedU8i1cydYHecdwwOw8ddQvBImzLc6jchZKy/+HDbTxfQAO7Udis7g5aWPUJe9yuooEuRGIhIpL76d/uhsDM+I3/fPSYrhrgtKWDwplXWVbdy7upIjXYN+zyEiwUGFrUgIeuNgK995ppyVZZl8+4ppVsd5L9cQlF0By79hdRKRcemLm0hN3tWU1D9BzFCz1XEAyGtePdqQzbBpvI94RcWkT7B1xncwbdaMiIuw27hmTh6fWFrI4Iib+9dU8lpFM26PGkuJyHupsBUJMYeae7nr4R2UZsbzy1vmYrcF2Jvb2FS46hdQsNTqJCLjtrf4drZN/RbOyFSroxA30MC5O7/GrIO/tDqKhKC0zt1kdOywbP8p2Ql86cJSZuYl8dr+Fh5YW0WLxgKJyLuosBUJIW19Tm57aCvRkXYe/ORC4qMCpFnUcYf+CfVbrE4h4jX9sROoyr8Rj0WnWW8zPSzY9yNMm4O9JXdYm0VCj+lh6Z5vs7D8exim27IYsZEOblqYzy2L8ukcGObXqyt581ArHo0FEhFU2IqEjKERN7f/aRttfU5+f+sC8pIDbIyOewSe/wq8/G+gNyESYkrqHmfGofut2dw0mb//HvJa32DX5C8xGJ1lTQ4JXYaN3aVfILmvksLG561Ow8y8JL50YSmlmfG8uLeJB9ZW0aTTW5Gwp8JWJAR4PCbffOotdtR18bMPz2H2xGSrI33QW49DVx0s/xfd+ychJ7n3IDMr7yf/6Et+37u44W9MqX2YisKPc7DgI37fX8JDffbFtCdOY+ahe7G5h62OQ0J0BB9bUsBNCyfS0T/Mva9X8s/9zbjUOVkkbKmwFQlypmny3ef28Y9djfzLqilcPjPH6kgf5HHDm/8L2bOg9BKr04h43c6yr9OaMpelu/+V7NYNft27LvsidpfezY6yr+uHRuI7ho3dU75E/GAjJfVPWJ0GGB0LNHtCMl+5aDIzJyTxekULv15dSV3HgNXRRMQCKmxFgphpmtzz8gEe2nCYT587ic+vKLY60omVPw0dVTqtlZDltkezdv6v6IkvZvnOL5PW9ZbP90zpLsfmdjISkUR5ye2jnZBFfKgpbSl1WRdjBtjXWlyUgw8vmMgnlhbgdHn4zdoqntndyNCIdfcDi4j/BdZ3JhEZk1+/Xsn9a6r4yOJ8vn3FVIxALRqH+yB/GZRdaXUSEZ8ZiUhk9cIHGIxMI6Nzp0/3Su0u56LNtzGv4ic+3UfkPQyDdfN+xqGCW6xOckJTshP58oWlLC5KY3N1Oz979SC76rsw1ddBJCwYofI/+4IFC8xt27ZZHUPEb37/ZjXff34/183N46c3zsYWaGN93s80T3ha+8jmOgvCiPiOw9WPyxE3+oeTfN2PR3x/HZds+jguewyvLPkzQ9EZXl1f5LRMD/lNr9CcughnlPWjrk7kSOcg/9h9hIbOQYoy4rh6di6ZCdEnfO5HFuf7OZ2InC3DMLabprngRI/pxFYkCD28uZbvP7+fy2dmc88NswK3qDXN0RE/Ho8uQZawcbyoTevczcWbbiVquNNra0c727hg6+fA9LB64QMqasUS8QMNLNv9Lf5/e/cdHkd17nH8+2pVrWKr2ZLcJAu544obDthgOoQSkmBIggkhgQRTbsIlOKQQEi6hhBAIaSTcSwkQIBQTqkMxxYAbbjIucldxkWz1Lp37x6xt2ZZsgyXtrvT7PM9as3NmV691dnbmnXPmnLFrfxvoUNrUNzGGa6Zlc8GYDApLa3jwrTzezN1OfaMGlxLpqpTYioSYfy3J56cvruLUob25/5KxhPuCeDdePw/+cTGsfiHQkYh0ujDXSGL5Z0xf/APCG6va5T2nLJ9DTH0J8094iIrYzHZ5T5HPqzJ2ALmDrmJQwdyAjAR+tMLMmJSVzA9PH8Lo/j15d90u7pu3lk+37tHctyJdUBCfEYvIwR7/aDM3PbecKYOS+eM3xhEZHsS7sHPw3t3QcwAMOz/Q0Yh0ul1J4/lwzL0kln/GSUtvPKYpUsKa6gBYMuwW3h/7O0p6jWqvMEW+kFXHXU1xz+OZuOp2etRsD3Q4hxUXFc5Xx/fn6pMHER8dwbNL8vnL/A0aPVmkiwnis2IR2cs5x/3/WcfPXsplxtDePHLFBKIjfIEO6/A2zYf8RfClG8EXEehoRAKioM90Phn5S9JLPubEFbd8rtdacyP9i97ktI8vZ8qKnwBQHp9NUerUjghV5HNxYREsGP0bzDUyecWt3sXMIDcwOZbvT8/mq+P6UVrTwJ/nb+CZxdsoKqsJdGgi0g7CAx2AiBxec7Pjly/n8uhHW7h4XD/uuvj44O5+vNf8eyA+HcZ8I9CRiATUpn4XENlQTlrJR/vWjcj7C2Vxx7E9ZfL+gab8IhrKOG7b8wze8hSxtUVUxvRla9qZnR22yBFVxg5g4chf0OiLDZlxFMLMGDcwkRF9E5i/dhcf5BVzyr3v8u2pWVwzLZueMboQKxKqlNiKBLH6xmZuenY5c5cXctWXsvjJOcOCd6ColmrLoKIIpt4AEa2PQinSnazN+hbrBs4EILyxmmGbHiWysYImC2dX0ngKUk8mv88Mqnr0ZdimRxm54WG2J01k8fBbKOw9DWdB3qZJoAEAABwXSURBVENDuq0tGefuW7bmBlxYaCSGUeE+zhiRxoTMJNbvrOBP727gyU+2cu0p2Vw+JTP4e0WJyCE03Y9IkKqub+T7Tyxl/rpd3HzWEL4/LTt456ltTV0l+CIhPPKwm2m6H+mOrLmB1D3LyNj1Phm73qdXZR4Lh/+UvIGXEF1XTHRdCaUJQwIdpshRO27LP8nZ9gxvTnmCJl9MoMP5XC6bNIDcwjLufn0t89ftIqNnNDeePpiLx/XDFwoXk0W6kcNN96PEViQIFZTWcPXji1ldWM4dFx3PpRNDZI695ib45C8w/gqI7HFUL1FiKwI9agppCI+lIaJnoEMR+ULSihdw6qKrWTfgEhaP+Gmgw/lcWs5ju2BDMXe9tobl+WVkp8Zy/YwczhuVoQRXJEhoHluREPLRhhK+/OAHbCmu5uHLTwidpBbgw9/DG3NgXfBO/yASjKpjMpTUSkjbnnIiazK/xeCt/yRj53uBDucLOzE7hRevncofvzEOX5hxw9PLOPP+95i7vJCm5q7RGCTSVSmxFQkSzjn+98NNfPPvn5DYI4IXZ09lxrA+gQ7r6BUsgXfugOEXwoiLAh2NiIh0smWDb2BPfA6TVv6M6LriQIfzhZkZ5xyfzus3nMxDl40jzOD6pz5VgisS5JTYigSB2oYmfvTscn758mpOGdKbF6+dSnZqXKDDOnp1lfCvqyAuDb58f8iMjikiIu2n2RfFgtF3Ed5UQ5+SRYEO55iFhRnnjvIS3D9cNhbDS3BPu28+Ty3cSm1DU6BDFJEWNCqySIBt213NtU8uZUV+GTeelsP1p+aExsjHLc37GezeBFe8AjGJgY5GREQCpCw+h7nT36AususcC8LCjPNGZXDOyHReW7WdP8/fwJznV3LfvHVcOTWLb0weQEJ0aIwGLdKVKbEVCRDnHM8s3sbtL68mzIyHLz+B04eHUNfjlqbMhvTRkDk10JGIiEiA7U1q++54h6iGUjb26xq3p+xtwT3n+DQWbCjhz/M3cNfra/jjO3lcNnkAs6ZkktErtEaEFulKlNiKBEBxZR1znl/JvNU7mDwoid9+fQx9Q/FgWFcJkbGQnO09REREAJzjuG3/ImPXezjC2NTvgkBH1G7MjKnHpTD1uBRWFZTxl/c28vB7G/nb+5s4a0Qas07MZEJmYmhN0SfSBSixFelk81bvYM7zKyivaeSn5w7jyqlZodf1GLypff7xNUgaBBc+FOhoREQkmJjxwdh7OXnJdUxe+TOchbG575cDHVW7G9m3Jw9eOpYfnzWExz/ewtMLt/HKyiKGpydwxdRMzh+dQXSEL9BhinQLGjxKpJPsqarn5ueW893HFpMaH83L132Jq04aFJpJLcAH98HWBZD5pUBHIiIiQajJF8174x9gR/JEpqy4lcyClwMdUofpl9iDOWcP4+M5M7jzK8fT1Oy4+bkVTL7zLX7179Xk7awIdIgiXZ5abEU6WFOz4+lFW7nnjbWU1zRwzbRs/uv0HKLCQ/gK7oa34Z07YeRXYfTMQEcjIiJBqskXw/zxDzJt8WySyld3yVbblmIifVw6cQAzJ/Tnow0l/OOTrTz20Wb+/sEmJmQmMnPCAM4dla5WXJEOYM51jbm4TjjhBLd48eJAhyFygKVb9/CLl3JZWVDGxKwkfnn+CIalJwQ6rGOT+6I3tU/KYPj2qxDT65je7slPtrZTYCIiEqzCmupoDosEM2/ZFxXokPa5bNKADn3/4so6/rUkn6cXbWNTcRUJ0eGcPyaDr4zrx9j+vXQvrsjnYGZLnHMntFamFluRDlBcWcfdr6/hmcX59EmI4vczx3D+6IyucfDq2R+yT4GvPHzMSa2IiHQPexPZ2OptnPbJd/h06A/Zmn5WgKPqHClxUVw9LZvvnTyIjzfu5ulFW3l2cT5PfLyVrJRYLhzTl4vG9mVAco9AhyoS0pTYirSjPVX1/PX9jTy6YDP1jc1cffIgrpuRQ1xUiO9qzsHGdyD7VOg3Hr7xbKAjEhGREFQXmUxVTDonLr8FoNskt+CNpjwlO5kp2clU1Dbw2qrtvLC0gPvfWsfv/rOOEwYm8uXRGZw9Mo3eCdGBDlck5Kgrskg7KK2u5+H3N/J/H26muqGJ80ZlcONpOWSnxgU6tGPX1ABzr4flT8Ksf0PWSe369uqKLCLSvYQ3VjF98Q/ovWcp6/t/jU+H3kRjeOBaKzu6K/KRFJbW8OKyAl76tJC1OyowgwkDkzj7+DTOHplOWk8luSJ7Ha4rshJbkWOwp6qe//1wE498uJnKukbOPT6dG07LYXCf+ECH1j7qq+DZK2D9mzD9JzDtZmjn7tRKbEVEup+wpjpGrf8DwzY9ymdZV7Bs6A8DFkugE9uW8nZW8MqK7by6soi1O7yRlMcPTOT04X04bVhvslPjusZtTSJfkBJbkXa2qqCMxz7azEvLCqlrbObskWnccFoOQ9NCfGColqp3e/PUFi6Fc38LJ1zZIb9Gia2ISPeVunsppfE5NETE06NmO7WRSTT7Ijs1hmBKbFvK21nJayuLeD13O7mF5QAMTO7BjKFekjshK4kIn2bulO5Fg0eJtIOGpmZeX7WdRxdsZvGWPcRE+Lh4fD9mTclkSFoXaaFtafP7sGMVfP0xGNa1p2cQEZHA2JU0DgBzTUxbci3mmlkw+k5KE4YGOLLAO653HNfNyOG6GTkUltbw1pqdvPXZDp74ZAuPfLiJuKhwpmQnc3JOCl/KSSUzuYdac6VbU4utyGE458gtLGfu8kJe/LSAnRV1DEzuwbcmD+Rr4/vTs0dEoENsXzWlsOVDGHqu97y8CBLSO/RXqsVWREQAMna+x6RVvyCyvpSVOdfyWdYVuLCOb4MJ1hbbtlTVNfJBXjHz1+3ivXW7yN9TA0C/xBhOyknlxOxkJmUlaQAq6ZLUFVnkc9paUs1Lywp4aXkheTsrCQ8zpg9J5bJJA5g+uDdhYV3simhTAyx+BN79jXdf7Q9XQ2xKp/xqJbYiIrJXZH0pE3J/zcDtb1DScyTzxz9IbVTHHo9CLbFtyTnHlpJq3s8r5v11u/hoQwkVdY0AZKXEMjEziYlZ3qNfYoxadCXkqSuyyBE0NztWF5Xz9pqdvLVmJ8u3lQIwMTOJOy4ayTkj00mM7dx7fjqFc7DmFZj3c9i9AbKmwRm/7rSkVkREpKX6yF58OPZe8gtncNy2Z6mLTAQgqXQVZXGDaArg6MnByMzITIklMyWWb00eSGNTM6uLylm4aTcfb9zN67nb+efibQD0jo9iTP9ejB2QyNgBvRjVryc9IpUKSNehFlvptsprG1iQV8zba3byztpd7KqowwxG9evFmSP6cP7oDPoldvEDaFk+/H4MJA2CM34FOWe0+6jHR6IWWxEROZywpjoufOd0jGbWD/g66wfMpCa6d7u9fyi32B5Jc7Nj7Y4KFm3ezadbS1m2rZRNxVUAhBkM7hPPyL49GZGRwIiMngzPSCAuSsmuBC91RRYBdpbXsnDzbhZt2s3CzXtYs70c5yA+OpyTB6dy6pDeTBuSSkpcVKBD7Ti15bDuDShaBmfe4a3b+gn0HQ++wBzIlNiKiMhhOUdK6TKGbnqM/jveotl8bMk4h9zs71IRm3nMb9+VE9vW7K6qZ/m2Uj7duofl+WXkFpZRXFm/rzwrJZahafEM7rP3EUdmSqxGYJagoK7I0u3srqont7CM3MJyVhWUsbKgjC0l1QDERPgYPzCRG2cMZvKgJMYNTOzaX9Y1pbDudVj9EuS9BU11EJ8OJ/83xPSCAZMCHaGIiEjbzChOHMsHiWOJq9rGkC3/YFD+C2zodzEVsZn0rFhPfNVWdiRPpCGiC85S0M6SYiM5ZWhvThnqtXo759hZUeedNxWUs6qwjM+Kynk9dzt7278ifMaglDgGpcaS5e/6PMj/Mzk2UvfuSlBQYishyznH7qp6NhZXsXFXJRt2VbFhZyWri8opKqvdt13fXjGMyEjgm5MGMiEriREZCV07kQWoKgFfBEQnwGcvw9zZkNAXJnwHhl8I/SZAWBf/G4iISJdTGdufJcNvYXnObBrDYwHIKpjL8E3/R7P5KO41iu3JUyhKOZGSXseD6Vh3JGZGn4Ro+iREc+rQPvvW1zY0kbezkvU7K1i7vZL1OypYu72Ceat30Ni8v8dnfFQ4fRNjyOgVQ0avaDJ6xdC3197nMfSJjyK8q593SVDo0K7IZnYW8HvAB/zNOfebg8qjgMeA8UAJcIlzbrO/bA7wHaAJuN4598bhfpe6Inc9zjnKahooKqulYE8NBaX+x54a8ktr2FJSRWl1w77tI31hZKb0YGhaAiP7+u8VSU/omoM+tdRQA+vnwfaV3ryz21dC2TY4+x6Y9D2vxbZ4vdfdOAiTWXVFFhGRY2HNDaSUriC9+EPSiz8iqSyXuoievDDjXZz5GLTtBcKa6ymPG0RZXDZ1UUkHvL67dUU+Vo1NzeTvqWFTSRWbdlWxpaSKgtJaCktrKCyrOeDcDLx7edMSokn3J7q946NIjoskOTaSpNiWy5HERYWr9VcOKyD32JqZD1gHnA7kA4uAS51zq1ts8wNglHPuGjObCVzknLvEzIYDTwETgQzgP8Bg51xTW79PiW3wcs5R19hMdX0TVXWNVNU3Ul7TyJ7qesqqGyitqWdPdQOl1fXsqqjb/6iso6HpwM9nZHgYff1XAvsn9SA7NZbs1DiyU+PomxiDr6tNw7PXjtVQUQgVO6CiCMoLIH0MjJ8FdRVwZz/vqnRyDqQdD2kjYfBZ0HtYoCM/IiW2IiLSniLrS0mo2kxx4hgAzlxwKcllq/aV10b0Ij9tBgtH3gbAZfHLICIGYlMhro83M4Cvi81T34mq6hopKquhcG+yW1pzQOK7q6KO6vrWT+kjw8P2JbnJcVEk9YggPjqCuOhw4qPDiY8K95ajWq6LID7aW9/le+RJwO6xnQjkOec2+oN4GrgAWN1imwuA2/zLzwF/MO8yzQXA0865OmCTmeX53++jDoxXWvj3ikIqaxtpaGqmvsnR0NRMQ2Pzgc/9j/pGR11jEzX1TVTVN+5PYOv2P29qPvwFlAif0TMmktT4KHrHR5HTJ57U+ChS46LonRDlJbOJMaTERgVmDtnmZnD+Bw6am7yfkV43KGr2QEMtuCavrLnRSzSTsrzywmVQsxsa66GpHhprISoehpztlb93D+zZDHWVXqJaVw5po+C8+7zyR8+D6pL98UT3gsg4bzkqHq5+H1JyvAOziIhIN1Yf2YviyDH7nr8x5Ul61O4goXIjPSs3kFC1kaqYjP0vmHsd1JYe+CbjZsH5D3jL//wmhEd7x/zIOO8xYDJknwJNjbD2FfBF7n+ER0HPfpCQ4ZWXbYMwH4SFg/m85chY75jd3OydE1iY/2EHLoeg2Khwjusdz3G9277fuaa+iZKqOnZX1VNSVU9JZT27q+ooqfSe766qp6Syjs3FVVTUNlBR23hA9+e2hIcZMRE+oiJ8REeEEb33Z7hv33JUhI/ocB9REWFEhBkRvjDCfWFE+IzwsDDCfbZvOcJnhPvCCA8zwsz2VYkZGHZAFZkZxv5q21tu7H/NgKRYhmckfLE/rBxRRya2fYFtLZ7nAwePUrNvG+dco5mVAcn+9R8f9Nq+HRdqJ7kry0tqWho3C876H2hqgLsyD33N5B/Aqbd6idPvRh5aPu1mmHqDN23LQ60MAnTabTDxu7BrLTx86qHl59wLYy6F/CXw2Pn7Vp9S34hz8KOG7/NG8wSmhOXycMRv95Wb/58f+27m04ixTGMxd9fe12Jn9nbgxwffz57kMYzeM49T1v+PV+Z/sRns+trLxA0cTezKx7E3fwqVDiqBIv8v+sECSMyABQ/C43ceGv+NK7wrq+/cCQseOLT85k0QEQ1v3AqL/uat29tLISwcbi30ll+aDcue9L/IedvE9IIfb/ZWPTsLPpt74Hv37A//5b8C/NyVsOHtA8tTh8G1/o/xq/8N+QsPLO87fn9iu/4/ULoVovwHzOgEiE/bv+1X/uqtj0/zriYfnMCmjzr0/y4iIiJgRnVMGtUxaWxPPfHQ8u+9C5U7oWonVO6Ayl3Qe6hX1tzkXXiur/IuPtdXQkM1nHi9l9g2VMEzlx/6ntPnwPRbvPd8YMyh5WfcASfOhpI8eGjCoeVf/j2MvwIKlsLfZuz9j/hPogy+8hcYeTFseh+euPjQJPiSJyDndG8mhGevOPT9v/k8DJwCq/4FL113aPmVr3vnFksehdfnHPr+V78Hydnw0R/hnTsOff31n0Jcb5h/D3x4/yHFMTeto19iLP2W3A0LHz6o1OAn+d7iKzfB8qdw/mv5zjmaI+JYfdlCKmobyXz/Jnrne3crOrzTt8qIZO4d8hR1DU18c9vPGL57EXtTYuegICydWRH3UtfYzANNv2KMW0vLlDnXZXJJ/c8BeDbyNobZgT3LFjYP5cqGmwF4NXIOA2zHAeXvNo9hdsP1AMyPvJFkK99XFuEzGH0xXPCQt+Ke47xbyloa+004+y7vosdv+h/6t510Dcz4mTfTxX2t9Mw76Udw0g+hvAj+0ErD5oyfw6SroTgP/jrtwLKh53rnnCGqI7sifxU4yzl3lf/5t4BJzrnZLbZZ5d8m3/98A17yexvwsXPuCf/6vwOvOeeeO+h3fA/4nv/pEGBth/xn2k8KUBzoIOQAqpPgpHoJPqqT4KR6CT6qk+Ckegk+qpPgFOz1MtA5l9paQUe22BYALS8z9POva22bfDMLB3riDSJ1NK/FOfdXIGQuK5jZ4rb6hEtgqE6Ck+ol+KhOgpPqJfioToKT6iX4qE6CUyjXS0feYb0IyDGzLDOLBGYCB/XlZC4wy7/8VeBt5zUhzwVmmlmUmWUBOcBB/ThFREREREREOrDF1n/P7GzgDbzpfh5xzuWa2e3AYufcXODvwOP+waF24yW/+Ld7Bm+gqUbg2sONiCwiIiIiIiLdV0d2RcY59yrw6kHrft5iuRb4WhuvvQNo5W70kBYy3aa7EdVJcFK9BB/VSXBSvQQf1UlwUr0EH9VJcArZeumwwaNEREREREREOoNmMRYREREREZGQpsS2nZnZ18ws18yazeyEg8rmmFmema01szPbeH2WmX3i3+6f/oG3pJ34/6bL/I/NZrasje02m9lK/3aLOzvO7sbMbjOzghZ1c04b253l33/yzOyWzo6zOzGze8xsjZmtMLMXzKxXG9tpX+kER/rs+wdb/Ke//BMzy+z8KLsPM+tvZu+Y2Wr/Mf+GVraZbmZlLb7Xft7ae0n7OtJ3knke8O8rK8xsXCDi7C7MbEiLfWCZmZWb2Y0HbaN9pROY2SNmttM/3eredUlmNs/M1vt/Jrbx2ln+bdab2azWtgkG6orczsxsGNAM/AW4yTm32L9+OPAUMBHIAP4DDD54UCz/oFnPO+eeNrM/A8udc3/qzP9Dd2FmvwXKnHO3t1K2GTjBORfM83h1GWZ2G1DpnLv3MNv4gHXA6UA+3sjrlzrnVndKkN2MmZ2BN1J9o5ndBeCc+3Er221G+0qHOprPvpn9ABjlnLvGzGYCFznnLglIwN2AmaUD6c65pWYWDywBLjyoTqbjnQecF6Awu6UjfSf5L5xeB5wDTAJ+75yb1HkRdl/+77ICYJJzbkuL9dPRvtLhzOxkoBJ4zDk30r/ubmC3c+43/oumiQcf680sCVgMnAA4vO+78c65PZ36HzgKarFtZ865z5xza1spugB42jlX55zbBOThJbn7mJkBpwLP+Vc9ClzYkfF2V/6/9dfxLjZIaJgI5DnnNjrn6oGn8fYr6QDOuTedc43+px/jzScugXE0n/0L8I4Z4B1DZvi/56QDOOeKnHNL/csVwGdA38BGJUfpArwTe+ec+xjo5b9QIR1vBrChZVIrncc59x7eLDQttTx2tJV3nAnMc87t9iez84CzOizQY6DEtvP0Bba1eJ7PoQfBZKC0xclka9tI+zgJ2OGcW99GuQPeNLMlZva9ToyrO5vt7xb2SBtdYY5mH5KOcSXwWhtl2lc63tF89vdt4z+GlOEdU6SD+bt9jwU+aaV4ipktN7PXzGxEpwbWfR3pO0nHksCZSdsNCtpXAqOPc67Iv7wd6NPKNiGzz3TodD9dlZn9B0hrpehW59xLnR2PHOgo6+dSDt9a+yXnXIGZ9Qbmmdka/5Uu+YIOVy/An4Bf4Z2Q/Ar4LV4yJR3oaPYVM7sVbz7xf7TxNtpXpNsyszjgX8CNzrnyg4qXAgOdc5X+7q8vAjmdHWM3pO+kIGTemDHnA3NaKda+EgScc87MQvoeVSW2X4Bz7rQv8LICoH+L5/3861oqwesSE+6/4t7aNnIER6ofMwsHvgKMP8x7FPh/7jSzF/C6AurAeAyOdr8xs4eBf7dSdDT7kHwOR7GvXAGcB8xwbQzIoH2lUxzNZ3/vNvn+77ieeMcU6SBmFoGX1P7DOff8weUtE13n3Ktm9kczS9H96B3rKL6TdCwJjLOBpc65HQcXaF8JqB1mlu6cK/J3yd/ZyjYFwPQWz/sB73ZCbJ+buiJ3nrnATPNGrszCuxK1sOUG/hPHd4Cv+lfNAtQC3P5OA9Y45/JbKzSzWP9gIJhZLHAGsKq1baV9HHR/00W0/vdeBOSYN3J4JF6XprmdEV93ZGZnATcD5zvnqtvYRvtK5ziaz/5cvGMGeMeQt9u6GCHHzn//8t+Bz5xz97WxTdre+5zNbCLeOZcuNnSgo/xOmgtcbp7JeINIFiEdrc2ectpXAqrlsaOtvOMN4AwzS/TfKnaGf13QUYttOzOzi4AHgVTgFTNb5pw70zmX6x/xeDVet75r946IbGavAlc55wqBHwNPm9mvgU/xDpzSvg65x8PMMoC/OefOwbu/4AX/d2w48KRz7vVOj7J7udvMxuB1Rd4MXA0H1ot/dN7ZeF+mPuAR51xuoALuBv4AROF15QP42D/irvaVTtbWZ9/MbgcWO+fm4h0rHjezPLzBQWYGLuJuYSrwLWCl7Z827ifAAADn3J/xLjB838wagRpgpi42dLhWv5PM7BrYVy+v4o2InAdUA98OUKzdhv8iw+n4j+3+dS3rRPtKJzCzp/BaXlPMLB/4BfAb4Bkz+w6wBW9gVcybsvQa59xVzrndZvYrvIusALc75w4ehCooaLofERERERERCWnqiiwiIiIiIiIhTYmtiIiIiIiIhDQltiIiIiIiIhLSlNiKiIiIiIhISFNiKyIiIiIiIiFNia2IiIiIiIiENCW2IiIiIiIiEtKU2IqIiIQQM5tgZivMLNrMYs0s18xGBjouERGRQDLnXKBjEBERkc/BzH4NRAMxQL5z7s4AhyQiIhJQSmxFRERCjJlFAouAWuBE51xTgEMSEREJKHVFFhERCT3JQBwQj9dyKyIi0q2pxVZERCTEmNlc4GkgC0h3zs0OcEgiIiIBFR7oAEREROTomdnlQINz7kkz8wELzOxU59zbgY5NREQkUNRiKyIiIiIiIiFN99iKiIiIiIhISFNiKyIiIiIiIiFNia2IiIiIiIiENCW2IiIiIiIiEtKU2IqIiIiIiEhIU2IrIiIiIiIiIU2JrYiIiIiIiIQ0JbYiIiIiIiIS0v4fUrfmvDHyqOQAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 1152x648 with 1 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "FNT2Ja7oxspB",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 1000
},
"outputId": "1fd50f87-7963-4f0f-b042-0553e1401b5b"
},
"source": [
"unknown_param_hmc_result = hmc(calc_hamiltonian=hamiltonian_unknown_mixture,\n",
" calc_dh=dh_unknown_mixture,\n",
" observed=observed,\n",
" num_samples=1000,\n",
" L=50,\n",
" dt=0.01,\n",
" debug=False)"
],
"execution_count": 13,
"outputs": [
{
"output_type": "stream",
"text": [
"sampled 10/1000 times(0.5513622999191284sec/sample)\n",
"sampled 20/1000 times(0.5492487907409668sec/sample)\n",
"sampled 30/1000 times(0.551176643371582sec/sample)\n",
"sampled 40/1000 times(0.5578527450561523sec/sample)\n",
"sampled 50/1000 times(0.5475445985794067sec/sample)\n",
"sampled 60/1000 times(0.5505130767822266sec/sample)\n",
"sampled 70/1000 times(0.5771337032318116sec/sample)\n",
"sampled 80/1000 times(0.548284387588501sec/sample)\n",
"sampled 90/1000 times(0.5502357959747315sec/sample)\n",
"sampled 100/1000 times(0.5471829652786255sec/sample)\n",
"sampled 110/1000 times(0.5593499183654785sec/sample)\n",
"sampled 120/1000 times(0.5668631076812745sec/sample)\n",
"sampled 130/1000 times(0.55431649684906sec/sample)\n",
"sampled 140/1000 times(0.5472422122955323sec/sample)\n",
"sampled 150/1000 times(0.5472617387771607sec/sample)\n",
"sampled 160/1000 times(0.5606219530105591sec/sample)\n",
"sampled 170/1000 times(0.5567830801010132sec/sample)\n",
"sampled 180/1000 times(0.5610764503479004sec/sample)\n",
"sampled 190/1000 times(0.5422102689743042sec/sample)\n",
"sampled 200/1000 times(0.5443647623062133sec/sample)\n",
"sampled 210/1000 times(0.551986575126648sec/sample)\n",
"sampled 220/1000 times(0.5528671264648437sec/sample)\n",
"sampled 230/1000 times(0.5476746797561646sec/sample)\n",
"sampled 240/1000 times(0.553111481666565sec/sample)\n",
"sampled 250/1000 times(0.5528491735458374sec/sample)\n",
"sampled 260/1000 times(0.5389492750167847sec/sample)\n",
"sampled 270/1000 times(0.558059549331665sec/sample)\n",
"sampled 280/1000 times(0.5684660196304321sec/sample)\n",
"sampled 290/1000 times(0.5606884956359863sec/sample)\n",
"sampled 300/1000 times(0.5447774410247803sec/sample)\n",
"sampled 310/1000 times(0.5471237421035766sec/sample)\n",
"sampled 320/1000 times(0.5474431276321411sec/sample)\n",
"sampled 330/1000 times(0.5449186801910401sec/sample)\n",
"sampled 340/1000 times(0.5553054332733154sec/sample)\n",
"sampled 350/1000 times(0.5510136842727661sec/sample)\n",
"sampled 360/1000 times(0.5348914861679077sec/sample)\n",
"sampled 370/1000 times(0.5405498504638672sec/sample)\n",
"sampled 380/1000 times(0.5469263315200805sec/sample)\n",
"sampled 390/1000 times(0.5536019563674927sec/sample)\n",
"sampled 400/1000 times(0.5630254983901978sec/sample)\n",
"sampled 410/1000 times(0.5591370582580566sec/sample)\n",
"sampled 420/1000 times(0.5421874523162842sec/sample)\n",
"sampled 430/1000 times(0.5400131940841675sec/sample)\n",
"sampled 440/1000 times(0.5575704097747802sec/sample)\n",
"sampled 450/1000 times(0.5595711708068848sec/sample)\n",
"sampled 460/1000 times(0.5692451953887939sec/sample)\n",
"sampled 470/1000 times(0.5502549171447754sec/sample)\n",
"sampled 480/1000 times(0.5531431198120117sec/sample)\n",
"sampled 490/1000 times(0.5454210996627807sec/sample)\n",
"sampled 500/1000 times(0.5600160598754883sec/sample)\n",
"sampled 510/1000 times(0.5425496101379395sec/sample)\n",
"sampled 520/1000 times(0.5606476783752441sec/sample)\n",
"sampled 530/1000 times(0.5454223155975342sec/sample)\n",
"sampled 540/1000 times(0.5539846897125245sec/sample)\n",
"sampled 550/1000 times(0.5558640718460083sec/sample)\n",
"sampled 560/1000 times(0.5628155708312989sec/sample)\n",
"sampled 570/1000 times(0.5597005367279053sec/sample)\n",
"sampled 580/1000 times(0.5500614166259765sec/sample)\n",
"sampled 590/1000 times(0.5484118938446045sec/sample)\n",
"sampled 600/1000 times(0.5507491827011108sec/sample)\n",
"sampled 610/1000 times(0.5445457696914673sec/sample)\n",
"sampled 620/1000 times(0.5534426450729371sec/sample)\n",
"sampled 630/1000 times(0.548730731010437sec/sample)\n",
"sampled 640/1000 times(0.5443217754364014sec/sample)\n",
"sampled 650/1000 times(0.5419971704483032sec/sample)\n",
"sampled 660/1000 times(0.5559844493865966sec/sample)\n",
"sampled 670/1000 times(0.5448656558990479sec/sample)\n",
"sampled 680/1000 times(0.547739052772522sec/sample)\n",
"sampled 690/1000 times(0.5401161193847657sec/sample)\n",
"sampled 700/1000 times(0.540514612197876sec/sample)\n",
"sampled 710/1000 times(0.5482651710510253sec/sample)\n",
"sampled 720/1000 times(0.5448983907699585sec/sample)\n",
"sampled 730/1000 times(0.538712477684021sec/sample)\n",
"sampled 740/1000 times(0.5620675325393677sec/sample)\n",
"sampled 750/1000 times(0.547161865234375sec/sample)\n",
"sampled 760/1000 times(0.5487202882766724sec/sample)\n",
"sampled 770/1000 times(0.556964373588562sec/sample)\n",
"sampled 780/1000 times(0.5637707948684693sec/sample)\n",
"sampled 790/1000 times(0.5580365180969238sec/sample)\n",
"sampled 800/1000 times(0.5407766580581665sec/sample)\n",
"sampled 810/1000 times(0.5392672777175903sec/sample)\n",
"sampled 820/1000 times(0.5534862518310547sec/sample)\n",
"sampled 830/1000 times(0.5651037454605102sec/sample)\n",
"sampled 840/1000 times(0.5530963659286499sec/sample)\n",
"sampled 850/1000 times(0.5483020305633545sec/sample)\n",
"sampled 860/1000 times(0.5415844678878784sec/sample)\n",
"sampled 870/1000 times(0.548154067993164sec/sample)\n",
"sampled 880/1000 times(0.5465356588363648sec/sample)\n",
"sampled 890/1000 times(0.550841212272644sec/sample)\n",
"sampled 900/1000 times(0.5441557407379151sec/sample)\n",
"sampled 910/1000 times(0.5559996604919434sec/sample)\n",
"sampled 920/1000 times(0.5632436513900757sec/sample)\n",
"sampled 930/1000 times(0.5532380104064941sec/sample)\n",
"sampled 940/1000 times(0.5400418281555176sec/sample)\n",
"sampled 950/1000 times(0.5614359617233277sec/sample)\n",
"sampled 960/1000 times(0.5520702123641967sec/sample)\n",
"sampled 970/1000 times(0.5511296510696411sec/sample)\n",
"sampled 980/1000 times(0.5549504518508911sec/sample)\n",
"sampled 990/1000 times(0.5562551259994507sec/sample)\n",
"sampled 1000/1000 times(0.5439979791641235sec/sample)\n"
],
"name": "stdout"
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "Ht1Ne1Qz6N8-",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 646
},
"outputId": "1c5d7726-972b-43c7-80b9-ca24e1ad9a61"
},
"source": [
"samples = np.array(unknown_param_hmc_result[\"samples\"]).reshape(-1, 3)\n",
"df = pd.DataFrame(samples, columns=[\"u_0\", \"u_1\", \"pi\"])\n",
"df[\"index\"] = [\"First 100\" if i < 100 else \"The rest\" for i in range(len(df))]\n",
"g = sns.pairplot(data=df, hue=\"index\", vars=[\"u_0\", \"u_1\"], corner=True)\n",
"g.fig.set_figheight(9)\n",
"g.fig.set_figwidth(16)\n"
],
"execution_count": 57,
"outputs": [
{
"output_type": "display_data",
"data": {
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\n",
"text/plain": [
"<Figure size 1152x648 with 5 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "7T6mbvfv6lpA",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 568
},
"outputId": "a49ed1a9-2e39-439f-d283-7b412801e79e"
},
"source": [
"sns.distplot(samples[:,2], axlabel=\"pi\")"
],
"execution_count": 58,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x7fb3f47af4e0>"
]
},
"metadata": {
"tags": []
},
"execution_count": 58
},
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1152x648 with 1 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "koosjlH5pVqV",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 34
},
"outputId": "ce7b347f-d5d8-4c42-81e9-a7b8cfee6768"
},
"source": [
"unknown_param_hmc_result[\"num_accept\"]"
],
"execution_count": 34,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"984"
]
},
"metadata": {
"tags": []
},
"execution_count": 34
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "fNmSR3n4WDCx",
"colab_type": "text"
},
"source": [
"Posterior predictive distribution $p(x^*) $will be approximated as\n",
"$\\displaystyle\n",
"p(x^*) = \\iiint{p(x^*|\\mu_1, \\mu_2, \\pi, X)p(\\mu_1, \\mu_2, \\pi|X)d\\mu_1d\\mu_2d\\pi} \\approx \\frac{1}{N}\\sum_{i=0}^{N-1}p(x^*|\\mu_{1i}, \\mu_{2i}, \\pi_{i})\n",
"$\n",
"where $\\mu_{1i}, \\mu_{2i}, \\pi_{i}$ are $i$-th sample for each parameter. To draw a sample from $p(x^*)$, simply follow the definition.\n",
"1. draw $t \\in [0, 1]$ from uniform distribution\n",
"1. If $t$ is less than $\\pi$, draw a sample from $\\mathcal{N}(x|\\mu_1, \\sigma_1^2)$, otherwise draw it from $\\mathcal{N}(x|\\mu_2, \\sigma_2^2)$\n"
]
},
{
"cell_type": "code",
"metadata": {
"id": "Lm6o0RLtsdlA",
"colab_type": "code",
"colab": {}
},
"source": [
"x_range = np.linspace(-10, 10, 100)\n",
"num_samples = len(samples[100:])\n",
"predictive_pdf = []\n",
"generated_samples = []\n",
"for sample in samples[100:]:\n",
" u_0 = sample[0]\n",
" u_1 = sample[1]\n",
" pi = sample[2]\n",
" predictive_pdf.append([ pi * norm.pdf(x, u_0, 1) + (1 - pi) * norm.pdf(x, u_1, 1) for x in x_range])\n",
" if np.random.uniform(0, 1) < pi:\n",
" generated_samples.append(np.random.normal(u_0, 1))\n",
" else:\n",
" generated_samples.append(np.random.normal(u_1, 1))\n",
"predictive_pdf = np.sum(np.array(predictive_pdf), axis=0) / num_samples\n",
" "
],
"execution_count": 35,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "sjplADAYwG5G",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 537
},
"outputId": "1e20c046-69c1-4301-d3b7-2268911bd19c"
},
"source": [
"ax = sns.distplot(generated_samples,label=\"generated samples\")\n",
"sns.lineplot(x=x_range, y=predictive_pdf, label=\"predictive dist\", ax=ax)\n",
"sns.lineplot(x=x_range, y=[0.7 * norm.pdf(x, -3, 1) + 0.3 * norm.pdf(x, 2, 1) for x in x_range], label=\"true dist.\", ax=ax)\n",
"ax.lines[1].set_linestyle(\"--\")\n",
"ax.lines[2].set_label(\"generated samples\")"
],
"execution_count": 59,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1152x648 with 1 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
}
]
}
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