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gibbs-sampling-bayes.ipynb
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{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"<a href=\"https://colab.research.google.com/gist/kiwamizamurai/5ca91a88fa25b036d5382290b6a380e3/gibbs-sampling-bayes.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "zL0NzXeexNfT",
"colab_type": "text"
},
"source": [
"## Bayes Estimation with Gibbs Sampling\n"
]
},
{
"cell_type": "code",
"metadata": {
"id": "YBzHz4bXxM8J",
"colab_type": "code",
"colab": {}
},
"source": [
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"import scipy\n",
"from scipy import stats\n",
"import pandas as pd\n",
"plt.rcParams['figure.figsize'] = (16, 8)\n",
"\n",
"np.random.seed(11)"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "kxszjB1prS_R",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 34
},
"outputId": "ab8768c7-0d15-4b87-e979-32fbca7b0771"
},
"source": [
"np.random.normal(10,10) "
],
"execution_count": 90,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"-15.817211205927283"
]
},
"metadata": {
"tags": []
},
"execution_count": 90
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "9d8ZFxupruUm",
"colab_type": "text"
},
"source": [
"### データ\n",
"\n",
"$$\n",
"y_{i} \\sim \\mathcal{N}\\left(\\mu, \\sigma^{2}\\right), i=1, \\ldots, N\n",
"$$\n",
"\n",
"### 尤度\n",
"\n",
"$$\n",
"p\\left(y_{1}, \\ldots, y_{N} | \\mu, \\sigma\\right)=\\prod_{i=1}^{N} \\mathcal{N}\\left(y_{i} | \\mu, \\sigma^{2}\\right)\n",
"$$\n",
"\n",
"### 事前分布\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"\\mu & \\sim \\text { uniform }(-\\infty, \\infty) \\\\\n",
"\\sigma & \\sim \\text { uniform }(0, \\infty)\n",
"\\end{aligned}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "LL-L8R0isRYf",
"colab_type": "text"
},
"source": [
"### $\\mu$の条件付き確率の計算\n",
"\n",
"つまり$\\mu$のサンプリング\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"p(\\mu | \\sigma, y) &=\\frac{p(\\mu, \\sigma, y)}{p(\\sigma, y)} \\\\\n",
"& \\propto p(y | \\mu, \\sigma) p(\\mu) p(\\sigma) \\\\\n",
"& \\propto p(y | \\mu, \\sigma)\n",
"\\end{aligned}\n",
"$$\n",
"\n",
"周辺化\n",
"\n",
"$$ p(\\sigma, y) = \\int p(\\sigma, y, \\mu)d\\mu $$"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "vRuTnTqXsoY6",
"colab_type": "text"
},
"source": [
"### $y$の条件付き確率の計算\n",
"\n",
"4行目から5行目は$\\mu$で平方完成\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"p(y | \\mu, \\sigma) &=\\prod_{i=1}^{N} \\mathcal{N}\\left(y_{i} | \\mu, \\sigma^{2}\\right) \\\\\n",
"&=\\prod_{i=1}^{N}\\left(\\frac{1}{\\sqrt{2 \\pi \\sigma^{2}}} \\exp \\left(-\\frac{\\left(y_{i}-\\mu\\right)^{2}}{2 \\sigma^{2}}\\right)\\right) \\\\\n",
"& \\propto \\prod_{i=1}^{N} \\exp \\left(-\\frac{\\mu^{2}}{2 \\sigma^{2}}+\\frac{y_{i} \\mu}{\\sigma^{2}}\\right) \\\\\n",
"&=\\exp \\left(-\\frac{N}{2 \\sigma^{2}} \\mu^{2}+\\frac{\\sum_{i=1}^{N} y_{i}}{\\sigma^{2}} \\mu\\right)^{2} \\\\\n",
"& \\propto \\frac{1}{\\sqrt{2 \\pi \\frac{\\sigma^{2}}{N}}} \\exp \\left(-\\frac{\\left(\\mu-\\frac{1}{N} \\sum_{i=1}^{N} y_{i}\\right)^{2}}{2 \\frac{\\sigma^{2}}{N}}\\right) \\\\\n",
"&=\\mathcal{N}\\left(\\frac{1}{N} \\sum_{i=1}^{N} y_{i}, \\frac{\\sigma^{2}}{N}\\right)\n",
"\\end{aligned}\n",
"$$"
]
},
{
"cell_type": "code",
"metadata": {
"id": "XsYT4hl1rTB7",
"colab_type": "code",
"colab": {}
},
"source": [
"def sample_mu(y, N, s):\n",
" mean = np.sum(y) / N\n",
" variance = s * s / N\n",
" return np.random.normal(mean, np.sqrt(variance))"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "RnOFK4GkxKDc",
"colab_type": "text"
},
"source": [
"### $\\sigma$の条件付き確率の計算\n",
"\n",
"先ほど同様にする\n",
"\n",
"つまり$\\sigma$のサンプリング\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"p(\\sigma | \\mu, y) &=\\frac{p(\\mu, \\sigma, y)}{p(\\mu, y)} \\\\\n",
"& \\propto p(y | \\mu, \\sigma) p(\\mu) p(\\sigma) \\\\\n",
"& \\propto p(y | \\mu, \\sigma)\n",
"\\end{aligned}\n",
"$$\n",
"\n",
"周辺化\n",
"\n",
"$$ p(\\sigma, y) = \\int p(\\sigma, y, \\mu)d\\mu $$"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "DmqOsoyhxznf",
"colab_type": "text"
},
"source": [
"$$\n",
"\\begin{aligned}\n",
"p(y | \\mu, \\sigma) &=\\prod_{i=1}^{N} \\mathcal{N}\\left(y_{i} | \\mu, \\sigma^{2}\\right) \\\\\n",
"&=\\prod_{i=1}^{N}\\left(\\frac{1}{\\sqrt{2 \\pi \\sigma^{2}}} \\exp \\left(-\\frac{\\left(y_{i}-\\mu\\right)^{2}}{2 \\sigma^{2}}\\right)\\right)\n",
"\\end{aligned}\n",
"$$\n",
"\n",
"今回は対数をとる\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"\\log p(y | \\mu, \\sigma) &=N \\log \\left(\\frac{1}{\\sqrt{2 \\pi \\sigma^{2}}}\\right)-\\frac{1}{2 \\sigma^{2}} \\sum_{i=1}^{N}\\left(y_{i}-\\mu\\right)^{2} \\\\\n",
"&=-N \\log \\sigma-\\frac{1}{2 \\sigma^{2}} \\sum_{i=1}^{N}\\left(y_{i}-\\mu\\right)^{2}-\\frac{N}{2} \\log 2 \\pi\n",
"\\end{aligned}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "onVUTdOPzChP",
"colab_type": "text"
},
"source": [
"正規分布には従わないので他の分布を予想する\n",
"\n",
"- https://en.wikipedia.org/wiki/Gamma_distribution\n",
"\n",
"$$\n",
"f(x | \\alpha, \\beta)=\\frac{\\beta^{\\alpha} x^{\\alpha-1} e^{-\\beta x}}{\\Gamma(\\alpha)} \\quad \\text { for } x>0 \\quad \\alpha, \\beta>0\n",
"$$\n",
"\n",
"ただし、\n",
"\n",
"$$\n",
"\\Gamma(\\alpha)=(\\alpha-1) !\n",
"$$\n",
"\n",
"つまり\n",
"\n",
"$$\n",
"f(y_i | \\alpha, \\beta) \\propto\n",
"\\beta^{\\alpha} y_i^{\\alpha-1} e^{-\\beta y_i}\n",
"$$\n",
"\n",
"対数をとってみる\n",
"\n",
"$$\n",
"\\log f(y_i | \\alpha, \\beta) = \\alpha \\log \\beta + (\\alpha-1) \\log y_i - \\beta y_i\n",
"$$\n",
"\n",
"つまり、\n",
"\n",
"$$\n",
"\\log f(y_i | \\alpha, \\beta) \\propto (\\alpha-1) \\log y_i - \\beta y_i\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "jl9bE2gH04HH",
"colab_type": "text"
},
"source": [
"実に上の$p$に似ている\n",
"\n",
"$$\n",
"\\tau = 1 / \\sigma^{2}\n",
"$$\n",
"\n",
"とおいて書き換えると($\\tau$は一般的に精度と呼ばれる)\n",
"\n",
"$$\n",
"\\log p(y | \\mu, \\sqrt{1/\\tau}) = \\frac{N}{2} \\log \\tau-\\frac{\\tau}{2} \\sum_{i=1}^{N}\\left(y_{i}-\\mu\\right)^{2}-\\frac{N}{2} \\log 2 \\pi\n",
"$$\n",
"\n",
"よって\n",
"\n",
"$$\n",
"p(\\tau | \\mu, y) \\sim \\operatorname{Gamma}\\left(\\frac{\\mathrm{N}}{2}+1, \\frac{\\sum_{i=1}^{N}\\left(y_{i}-\\mu\\right)^{2}}{2}\\right)\n",
"$$"
]
},
{
"cell_type": "code",
"metadata": {
"id": "SQ-Ez005rTEE",
"colab_type": "code",
"colab": {}
},
"source": [
"def sample_s(y, N, mu):\n",
" alpha = N / 2 + 1\n",
" residuals = y - mu\n",
" beta = np.sum(residuals * residuals) / 2\n",
" # Notice\n",
" # https://docs.scipy.org/doc/numpy-1.9.3/reference/generated/numpy.random.gamma.html\n",
" tau = np.random.gamma(alpha, 1/beta)\n",
" return (1 / (np.sqrt(tau) + 1e-5))"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "ckkcqHeR349c",
"colab_type": "code",
"colab": {}
},
"source": [
"from tqdm import tqdm_notebook as tqdm"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "O5qk76gGrTGi",
"colab_type": "code",
"colab": {}
},
"source": [
"def model1(y, iters, init):\n",
" mu = init[\"mu\"]\n",
" s = init[\"sigma\"]\n",
" N = len(y)\n",
" \n",
" trace = np.zeros((iters, 2))\n",
" log_likelihoods = np.zeros((iters, N))\n",
" \n",
" for i in tqdm(range(iters)):\n",
" mu = sample_mu(y, N, s)\n",
" s = sample_s(y, N, mu)\n",
" trace[i, :] = np.array((mu, s))\n",
" \n",
" norm = sp.stats.norm(mu, s)\n",
" log_likelihoods[i, :] = np.array([np.log(norm.pdf(x)) for x in y])\n",
" \n",
" trace = pd.DataFrame(trace)\n",
" trace.columns = ['mu', 'sigma']\n",
" \n",
" log_likelihoods = pd.DataFrame(log_likelihoods)\n",
" \n",
" return trace, log_likelihoods"
],
"execution_count": 0,
"outputs": []
},
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"height": 34
},
"outputId": "e8dd240d-deae-4e0a-9c36-45de453625bc"
},
"source": [
"init = {\"mu\": np.random.uniform(-100, 100), \"sigma\": np.random.uniform(0, 100)}\n",
"print(init)"
],
"execution_count": 176,
"outputs": [
{
"output_type": "stream",
"text": [
"{'mu': -63.52864832617773, 'sigma': 10.41695812991822}\n"
],
"name": "stdout"
}
]
},
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"SIGMA = 3.5\n",
"y = np.random.normal(MU, SIGMA, size=500)\n",
"trace, log_likelihoods = model1(y, iters, init)"
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"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>0</th>\n",
" <th>1</th>\n",
" <th>2</th>\n",
" <th>3</th>\n",
" <th>4</th>\n",
" <th>5</th>\n",
" <th>6</th>\n",
" <th>7</th>\n",
" <th>8</th>\n",
" <th>9</th>\n",
" <th>10</th>\n",
" <th>11</th>\n",
" <th>12</th>\n",
" <th>13</th>\n",
" <th>14</th>\n",
" <th>15</th>\n",
" <th>16</th>\n",
" <th>17</th>\n",
" <th>18</th>\n",
" <th>19</th>\n",
" <th>20</th>\n",
" <th>21</th>\n",
" <th>22</th>\n",
" <th>23</th>\n",
" <th>24</th>\n",
" <th>25</th>\n",
" <th>26</th>\n",
" <th>27</th>\n",
" <th>28</th>\n",
" <th>29</th>\n",
" <th>30</th>\n",
" <th>31</th>\n",
" <th>32</th>\n",
" <th>33</th>\n",
" <th>34</th>\n",
" <th>35</th>\n",
" <th>36</th>\n",
" <th>37</th>\n",
" <th>38</th>\n",
" <th>39</th>\n",
" <th>...</th>\n",
" <th>560</th>\n",
" <th>561</th>\n",
" <th>562</th>\n",
" <th>563</th>\n",
" <th>564</th>\n",
" <th>565</th>\n",
" <th>566</th>\n",
" <th>567</th>\n",
" <th>568</th>\n",
" <th>569</th>\n",
" <th>570</th>\n",
" <th>571</th>\n",
" <th>572</th>\n",
" <th>573</th>\n",
" <th>574</th>\n",
" <th>575</th>\n",
" <th>576</th>\n",
" <th>577</th>\n",
" <th>578</th>\n",
" <th>579</th>\n",
" <th>580</th>\n",
" <th>581</th>\n",
" <th>582</th>\n",
" <th>583</th>\n",
" <th>584</th>\n",
" <th>585</th>\n",
" <th>586</th>\n",
" <th>587</th>\n",
" <th>588</th>\n",
" <th>589</th>\n",
" <th>590</th>\n",
" <th>591</th>\n",
" <th>592</th>\n",
" <th>593</th>\n",
" <th>594</th>\n",
" <th>595</th>\n",
" <th>596</th>\n",
" <th>597</th>\n",
" <th>598</th>\n",
" <th>599</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>mu</th>\n",
" <td>5.121341</td>\n",
" <td>5.252953</td>\n",
" <td>5.113124</td>\n",
" <td>5.256779</td>\n",
" <td>5.112567</td>\n",
" <td>5.353596</td>\n",
" <td>5.317805</td>\n",
" <td>5.491373</td>\n",
" <td>5.072294</td>\n",
" <td>5.344589</td>\n",
" <td>5.303624</td>\n",
" <td>5.486155</td>\n",
" <td>5.177728</td>\n",
" <td>5.239540</td>\n",
" <td>5.254043</td>\n",
" <td>5.310036</td>\n",
" <td>5.507515</td>\n",
" <td>5.301538</td>\n",
" <td>5.611399</td>\n",
" <td>5.25166</td>\n",
" <td>5.172611</td>\n",
" <td>5.166855</td>\n",
" <td>5.057182</td>\n",
" <td>5.170233</td>\n",
" <td>5.363937</td>\n",
" <td>5.281911</td>\n",
" <td>5.281541</td>\n",
" <td>5.174865</td>\n",
" <td>5.424195</td>\n",
" <td>5.501926</td>\n",
" <td>5.538779</td>\n",
" <td>5.395076</td>\n",
" <td>5.129883</td>\n",
" <td>5.335737</td>\n",
" <td>5.411350</td>\n",
" <td>5.125671</td>\n",
" <td>5.352181</td>\n",
" <td>5.315969</td>\n",
" <td>5.242579</td>\n",
" <td>5.276882</td>\n",
" <td>...</td>\n",
" <td>4.901483</td>\n",
" <td>5.369691</td>\n",
" <td>5.273190</td>\n",
" <td>5.329525</td>\n",
" <td>5.381022</td>\n",
" <td>5.369293</td>\n",
" <td>5.299963</td>\n",
" <td>5.209553</td>\n",
" <td>5.131411</td>\n",
" <td>5.454720</td>\n",
" <td>5.551919</td>\n",
" <td>5.097928</td>\n",
" <td>5.338960</td>\n",
" <td>5.307057</td>\n",
" <td>5.469962</td>\n",
" <td>5.287815</td>\n",
" <td>5.262049</td>\n",
" <td>5.300713</td>\n",
" <td>5.399701</td>\n",
" <td>5.061509</td>\n",
" <td>5.305844</td>\n",
" <td>5.453887</td>\n",
" <td>5.114063</td>\n",
" <td>5.295753</td>\n",
" <td>5.231326</td>\n",
" <td>5.305855</td>\n",
" <td>5.533915</td>\n",
" <td>5.263586</td>\n",
" <td>5.149858</td>\n",
" <td>5.383721</td>\n",
" <td>5.130473</td>\n",
" <td>5.227381</td>\n",
" <td>5.317560</td>\n",
" <td>5.397140</td>\n",
" <td>5.457038</td>\n",
" <td>5.398181</td>\n",
" <td>5.154811</td>\n",
" <td>5.277023</td>\n",
" <td>5.304569</td>\n",
" <td>5.400088</td>\n",
" </tr>\n",
" <tr>\n",
" <th>sigma</th>\n",
" <td>3.338913</td>\n",
" <td>3.303600</td>\n",
" <td>3.426070</td>\n",
" <td>3.246694</td>\n",
" <td>3.260373</td>\n",
" <td>3.516644</td>\n",
" <td>3.257751</td>\n",
" <td>3.191806</td>\n",
" <td>3.268338</td>\n",
" <td>3.279753</td>\n",
" <td>3.491626</td>\n",
" <td>3.328990</td>\n",
" <td>3.207215</td>\n",
" <td>3.113197</td>\n",
" <td>3.362861</td>\n",
" <td>3.364589</td>\n",
" <td>3.306491</td>\n",
" <td>3.413831</td>\n",
" <td>3.412138</td>\n",
" <td>3.22098</td>\n",
" <td>3.310952</td>\n",
" <td>3.422448</td>\n",
" <td>3.241375</td>\n",
" <td>3.241696</td>\n",
" <td>3.417434</td>\n",
" <td>3.194312</td>\n",
" <td>3.165686</td>\n",
" <td>3.302619</td>\n",
" <td>3.165154</td>\n",
" <td>3.258285</td>\n",
" <td>3.509741</td>\n",
" <td>3.311137</td>\n",
" <td>3.171383</td>\n",
" <td>3.546354</td>\n",
" <td>3.348522</td>\n",
" <td>3.521126</td>\n",
" <td>3.190818</td>\n",
" <td>3.218317</td>\n",
" <td>3.488882</td>\n",
" <td>3.341169</td>\n",
" <td>...</td>\n",
" <td>3.335784</td>\n",
" <td>3.413641</td>\n",
" <td>3.355722</td>\n",
" <td>3.687081</td>\n",
" <td>3.230906</td>\n",
" <td>3.262611</td>\n",
" <td>3.448117</td>\n",
" <td>3.386856</td>\n",
" <td>3.417484</td>\n",
" <td>3.291759</td>\n",
" <td>3.319097</td>\n",
" <td>3.179167</td>\n",
" <td>3.280552</td>\n",
" <td>3.281989</td>\n",
" <td>3.182553</td>\n",
" <td>3.384290</td>\n",
" <td>3.529515</td>\n",
" <td>3.167610</td>\n",
" <td>3.323728</td>\n",
" <td>3.309582</td>\n",
" <td>3.252536</td>\n",
" <td>3.210890</td>\n",
" <td>3.211522</td>\n",
" <td>3.269694</td>\n",
" <td>3.077182</td>\n",
" <td>3.287582</td>\n",
" <td>3.375169</td>\n",
" <td>3.336022</td>\n",
" <td>3.158726</td>\n",
" <td>3.385744</td>\n",
" <td>3.309405</td>\n",
" <td>3.348928</td>\n",
" <td>3.353988</td>\n",
" <td>3.623658</td>\n",
" <td>3.155843</td>\n",
" <td>3.138545</td>\n",
" <td>3.547806</td>\n",
" <td>3.262617</td>\n",
" <td>3.254918</td>\n",
" <td>3.288372</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>2 rows × 600 columns</p>\n",
"</div>"
],
"text/plain": [
" 0 1 2 ... 597 598 599\n",
"mu 5.121341 5.252953 5.113124 ... 5.277023 5.304569 5.400088\n",
"sigma 3.338913 3.303600 3.426070 ... 3.262617 3.254918 3.288372\n",
"\n",
"[2 rows x 600 columns]"
]
},
"metadata": {
"tags": []
},
"execution_count": 178
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "OQn4aVcA3S_u",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 34
},
"outputId": "83c1545b-1a71-426a-f2f7-5924ea7da2e6"
},
"source": [
"log_likelihoods.shape"
],
"execution_count": 179,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"(600, 500)"
]
},
"metadata": {
"tags": []
},
"execution_count": 179
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "NmGB4FeV9w4K",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 500
},
"outputId": "4628a2e0-8a9f-47de-976d-cf6b1628e80d"
},
"source": [
"fig = plt.figure()\n",
"ax1 = fig.add_subplot(2, 1, 1)\n",
"ax2 = fig.add_subplot(2, 1, 2)\n",
"trace.plot(ax=ax1)\n",
"\n",
"kwargs = dict(histtype='stepfilled', alpha=0.3, density=True, bins=60, ec=\"k\")\n",
"ax2.hist(trace['mu'], label='$\\mu$', **kwargs)\n",
"ax2.hist(trace['sigma'], label='$\\sigma$', **kwargs)\n",
"ax2.legend(loc=3, prop={'size': 15})\n",
"ax2.set_xlim(2.5, 6)"
],
"execution_count": 180,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"(2.5, 6)"
]
},
"metadata": {
"tags": []
},
"execution_count": 180
},
{
"output_type": "display_data",
"data": {
"image/png": 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kYLdcWF/SkP3JlrM0Mra9I4isIGLfBJe+FqMxDm6rCR6bmbLZpfKAnj8xitdP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\nAAAAIFb+H60jb/j5FSlkAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 1152x576 with 2 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "4YZnTu9M_Ek7",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 294
},
"outputId": "097dc034-f1d3-4eb2-9348-f3679b0c0435"
},
"source": [
"trace.describe()"
],
"execution_count": 181,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>mu</th>\n",
" <th>sigma</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>count</th>\n",
" <td>600.000000</td>\n",
" <td>600.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>mean</th>\n",
" <td>5.286680</td>\n",
" <td>3.302940</td>\n",
" </tr>\n",
" <tr>\n",
" <th>std</th>\n",
" <td>0.143217</td>\n",
" <td>0.109821</td>\n",
" </tr>\n",
" <tr>\n",
" <th>min</th>\n",
" <td>4.835356</td>\n",
" <td>3.007096</td>\n",
" </tr>\n",
" <tr>\n",
" <th>25%</th>\n",
" <td>5.192854</td>\n",
" <td>3.228822</td>\n",
" </tr>\n",
" <tr>\n",
" <th>50%</th>\n",
" <td>5.287466</td>\n",
" <td>3.296930</td>\n",
" </tr>\n",
" <tr>\n",
" <th>75%</th>\n",
" <td>5.380154</td>\n",
" <td>3.379339</td>\n",
" </tr>\n",
" <tr>\n",
" <th>max</th>\n",
" <td>5.725072</td>\n",
" <td>3.687081</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" mu sigma\n",
"count 600.000000 600.000000\n",
"mean 5.286680 3.302940\n",
"std 0.143217 0.109821\n",
"min 4.835356 3.007096\n",
"25% 5.192854 3.228822\n",
"50% 5.287466 3.296930\n",
"75% 5.380154 3.379339\n",
"max 5.725072 3.687081"
]
},
"metadata": {
"tags": []
},
"execution_count": 181
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "LTkNk_l-VExX",
"colab_type": "text"
},
"source": [
"## Mixture Gaussian Distribution\n",
"\n",
"混合ガウス分布"
]
},
{
"cell_type": "code",
"metadata": {
"id": "SuGoJ_TMxNIp",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 516
},
"outputId": "a89efacf-696b-47b1-e955-21427dde72b0"
},
"source": [
"x = np.arange(-50, 50, 0.01)\n",
"\n",
"mu1=8\n",
"mu2=-9\n",
"sigma1=5\n",
"sigma2=4\n",
"\n",
"norm1 = scipy.stats.norm.pdf(x = x, loc=mu1, scale=sigma1)\n",
"norm2 = scipy.stats.norm.pdf(x = x, loc=mu2, scale=sigma2)\n",
"plt.plot(x, norm1, color='red', label='$\\mu$: {}, $\\sigma$: {}'.format(mu1, sigma1))\n",
"plt.plot(x, norm2, color='red', label='$\\mu$: {}, $\\sigma$: {}'.format(mu1, sigma1))\n",
"plt.plot(x, norm1 + norm2, color='black', label='Added without weights')\n",
"plt.title('Not Mixture Gaussian')\n",
"plt.legend(loc=2, prop={'size': 15})"
],
"execution_count": 28,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fb8d28c0518>"
]
},
"metadata": {
"tags": []
},
"execution_count": 28
},
{
"output_type": "display_data",
"data": {
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Ijo7G3d2dadOmMW/ePCIjI+nRowdHjhwhMTExe6nvmjVr8PDwYM2aNVfsb+zYscybN48J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\n",
"text/plain": [
"<Figure size 1152x576 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "bronh9l6xNK0",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 516
},
"outputId": "12a88c9e-62d3-42a1-be84-2e76d9010477"
},
"source": [
"w1 = 0.3\n",
"w2 = 0.7\n",
"plt.plot(x, w1*norm1 + w2*norm2,color='black')\n",
"plt.title('Mixture Gaussian')"
],
"execution_count": 29,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Mixture Gaussian')"
]
},
"metadata": {
"tags": []
},
"execution_count": 29
},
{
"output_type": "display_data",
"data": {
"image/png": 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cMWKEJKm4uLjVrgkAAPyjoAIADiq+QFJr3X8a16dPH/Xo0YOCCgBAiqGgAgAOatWqVdq2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\nBRUAAAAAEAj/H/nqZmW//Od/AAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 1152x576 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "HjWtCtSrilUZ",
"colab_type": "text"
},
"source": [
"## Sampling from Mixture Gaussian Distribution\n"
]
},
{
"cell_type": "code",
"metadata": {
"id": "OV2epQ3-xNPS",
"colab_type": "code",
"colab": {}
},
"source": [
"n = 10000\n",
"\n",
"# Parameters of the mixture components\n",
"# [mu1, sigma1]\n",
"norm_params = np.array([[0, 1],\n",
" [-3, 1.7],\n",
" [7, 2.3]])\n",
"n_components = norm_params.shape[0]\n",
"\n",
"# Weight of each component, in this case all of them are 1/3\n",
"weights = np.ones(n_components, dtype=np.float64) / 3.0\n",
"\n",
"# A stream of indices from which to choose the component(distribution)\n",
"mixture_idx = np.random.choice(len(weights), size=n, replace=True, p=weights)"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "-P7pxGjHmAFH",
"colab_type": "text"
},
"source": [
"# np.fromiter\n",
"\n",
"ネイティブのように高速でアレイを作るやつ\n",
"\n",
"8バイトfloat型の0を1億回繰り返したPythonの配列(array)からndarrayを生成速度テスト\n",
"\n",
"- https://docs.python.org/3/library/array.html\n",
"- https://realitix.github.io/numpy/2017/02/01/numpy-array-initialization-performance/\n",
"\n"
]
},
{
"cell_type": "code",
"metadata": {
"id": "gVffFjywmORp",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 86
},
"outputId": "1a717886-6c00-4e2c-8e74-2ebcfb69a5d3"
},
"source": [
"from datetime import datetime\n",
"import array\n",
"\n",
"test = array.array('d', [0]*100000000)\n",
"print(test[:10])\n",
" \n",
"t = datetime.now()\n",
"np.array(test)\n",
"print('np.array: ', datetime.now() - t)\n",
" \n",
"t = datetime.now()\n",
"np.fromiter(test, dtype=np.int)\n",
"print('np.fromiter: ', datetime.now() - t)\n",
" \n",
"t = datetime.now()\n",
"np.frombuffer(test)\n",
"print('np.frombuffer: ', datetime.now() - t)"
],
"execution_count": 54,
"outputs": [
{
"output_type": "stream",
"text": [
"array('d', [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0])\n",
"np.array: 0:00:00.243476\n",
"np.fromiter: 0:00:03.632721\n",
"np.frombuffer: 0:00:00.000082\n"
],
"name": "stdout"
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "nfn6IfnRiqde",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 760
},
"outputId": "baa28acd-45b1-4dfa-d8b5-ecd5de936624"
},
"source": [
"# y is the mixture sample\n",
"y = np.fromiter((stats.norm.rvs(*(norm_params[i])) for i in mixture_idx), dtype=np.float64)\n",
"\n",
"# Theoretical PDF plotting -- generate the x and y plotting positions\n",
"xs = np.linspace(y.min(), y.max(), 200)\n",
"ys = np.zeros_like(xs)\n",
"\n",
"for (l, s), w in zip(norm_params, weights):\n",
" ys += stats.norm.pdf(xs, loc=l, scale=s) * w\n",
"\n",
"plt.plot(xs, ys)\n",
"plt.hist(y, density=True, bins=\"fd\")"
],
"execution_count": 58,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"(array([0.00029077, 0.00072692, 0.00377998, 0.00552458, 0.01817298,\n",
" 0.02733215, 0.04812204, 0.06687655, 0.07879802, 0.08025186,\n",
" 0.08228723, 0.10380403, 0.13724231, 0.14320304, 0.1049671 ,\n",
" 0.05233817, 0.01919066, 0.01221224, 0.01962681, 0.03212982,\n",
" 0.041289 , 0.05001203, 0.0565543 , 0.0565543 , 0.05699045,\n",
" 0.04535975, 0.03605518, 0.02805907, 0.02238911, 0.01061302,\n",
" 0.00741457, 0.00348921, 0.00116307, 0.00072692, 0.00029077]),\n",
" array([-9.13538357, -8.44754903, -7.75971448, -7.07187994, -6.38404539,\n",
" -5.69621085, -5.00837631, -4.32054176, -3.63270722, -2.94487267,\n",
" -2.25703813, -1.56920358, -0.88136904, -0.19353449, 0.49430005,\n",
" 1.1821346 , 1.86996914, 2.55780368, 3.24563823, 3.93347277,\n",
" 4.62130732, 5.30914186, 5.99697641, 6.68481095, 7.3726455 ,\n",
" 8.06048004, 8.74831459, 9.43614913, 10.12398367, 10.81181822,\n",
" 11.49965276, 12.18748731, 12.87532185, 13.5631564 , 14.25099094,\n",
" 14.93882549]),\n",
" <a list of 35 Patch objects>)"
]
},
"metadata": {
"tags": []
},
"execution_count": 58
},
{
"output_type": "display_data",
"data": {
"image/png": 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AOHyHLKhmFpR0t6RzJI2T9HkzG7fPZWskXS3p0X0e3y3pSufcUZLOlvQrM+t9pKEBIJnF\nYk5zaptS5vbeDiP757GCCgAAjkg8K6hTJK1yzlU558KSHpN0wd4XOOdqnHMLJMX2eXyFc25l+8fr\nJW2UVNwlyQEgSa3cuFPbmyMpMyCpQ0VJntZs2a3m1qjvKAAAIEnFU1AHS1q71+fr2h/rFDObIilT\n0urOvhYAUkll7RZJSr0V1JI8OSetZhUVAAAcph4ZkmRmAyX9SdIXnXOx/Tx/rZlVmlllY2NjT0QC\nAG/m1DSpKC9Tw/vl+I7SpSpK8iVJqzZSUAEAwOGJp6DWSRq61+dD2h+Li5kVSHpO0vedc7P2d41z\n7l7n3GTn3OTiYu4ABpDaZtdu0eThfWVmvqN0qdKiHAUDRkEFAACHLZ6COltShZmVmVmmpEslTY/n\nzduvf0rSw865Jw4/JgCkho3bm7V2yx5NLk2t23slKSsU1PC+ORRUAABw2A5ZUJ1zEUk3SHpR0lJJ\nf3XOLTazO8zsfEkys+PNbJ2kz0r6vZktbn/55yRNk3S1mc1v/2dit/xJACAJpNr5p/saWZKnlRRU\nAABwmELxXOScmyFpxj6P3brXx7PVduvvvq97RNIjR5gRAFLG7Jotys4I6KhBhb6jdIuRJXl6ddlG\ntUZjygj2yJgDAACQQvjpAQB60JzaJh0zpLcyQ6n57beif54iMafazbt8RwEAAEkoNX9CAoAEtDsc\n0eL121Ny/2mHjkm+Kzdwmy8AAOg8CioA9JD5a7cqGnOaXNrXd5RuU16cK4mjZgAAwOGhoAJAD6ms\naZKZdNyw1F1BzckMaUifXgxKAgAAh4WCCgA9pLK2SaNK8lXYK8N3lG5VwSRfAABwmCioANADojGn\nebVNKb3/tMPIkjxVNe5UNOZ8RwEAAEmGggoAPWB5ww7taImkRUGtKMlXSySmdU27fUcBAABJhoIK\nAD1gTu0WSdLk4ak7IKlDx6CkqkaOmgEAAJ1DQQWAHlBZ26T+BVka0qeX7yjdrrw4T5JUtYmCCgAA\nOoeCCgA9oLKmSZOH95WZ+Y7S7frkZKiwV4aqGhmUBAAAOoeCCgDdrH7bHtVt3ZMW+08lycxUXpzL\nLb4AAKDTKKgA0M0qa5okpcf+0w7lRXmq5hZfAADQSRRUAOhmlTVblJMZ1NiB+b6j9Jjy4lw1bG/W\nrpaI7ygAACCJUFABoJtV1jbp2GG9FQqmz7fc8qK2Sb6sogIAgM5In5+WAMCDnS0RLa3frklpdHuv\nJJV1HDVDQQUAAJ1AQQWAbjRvTZNiTpo8PD0GJHUo7ZcrMzHJFwAAdAoFFQC6UWVNkwImHTust+8o\nPSo7I6jBvXsxyRcAAHQKBRUAutG71Zs1blCB8rMzfEfpcWVFuexBBQAAnUJBBYBu0twa1dw1W3VC\nWT/fUbwYUZynqsadcs75jgIAAJIEBRUAusn7a7cqHIlpanl6FtTy4lztCkfVuKPFdxQAAJAkKKgA\n0E1mVW2RmTSlNL0m+HYoaz9qZjX7UAEAQJwoqADQTd6t3qyxAwpUmJN++08lqbw4T5JUtYlJvgAA\nID4UVADoBi2RqOauadIJaXp7ryQNLMhWdkZA1aygAgCAOFFQAaAbLFi3Tc2tMU0tT8/beyUpEDCV\n9stVFZN8AQBAnCioANAN3q3aLDNpaln6FlTpX5N8AQAA4kFBBYBuMKtqi0b3z1fvnEzfUbwqK8rV\n2qY9CkdivqMAAIAkQEEFgC4WjsQ0pza99592KC/OVTTmtGbLbt9RAABAEqCgAkAXW1i3VXtaozoh\njfefdvhgki+3+QIAgDhQUAGgi82q2iJJmlLGCmrHWajVDEoCAABxoKACQBebVbVZo/vnq29ueu8/\nlaTCXhkqystUFUfNAACAOFBQAaALtUY79p9ye2+H8qI8VW3iFl8AAHBoFFQA6EKL6rZpdziqqQxI\n+kBZUS63+AIAgLhQUAGgC/1r/ykrqB3Ki3O1aWdY2/a0+o4CAAASHAUVALrQP1dv0qj+eSrKy/Id\nJWEwyRcAAMSLggoAXaS5Nar3qrfolJHFvqMklLKiHElSzWZu8wUAAAdHQQWALjK7ZotaIjGdOqrI\nd5SEMrRvjgImVW/a7TsKAABIcCHfAQAgVcxcuUmZwYCmptv+09sLD/p0lqRB+pVqXntbevvuTr73\ntsPPBQAAkg4rqADQRWau3KTJpX2Uk8nv/vZVZg2qcQN8xwAAAAmOggoAXWDjjmYtrd+uUyq4vXd/\nyqxB1W6gnPOdBAAAJDJ+zQ8A8TrIraxvR0+W9DVNe/Uz0us1PRYpWZRag3YoR5tVoCJt9x0HAAAk\nKFZQAaALzIxOUF9t1zir9R0lIZVZgyRxmy8AADgoCioAHCHnpJmxo3VyYJECxj2s+1PaXlCrYxRU\nAABwYBRUADhCy91QNaqPTg0s9B0lYQ2xRgUVZQUVAAAcFAUVAI7QzNh4SdKpQQrqgWRYVMNso6rd\nQN9RAABAAqOgAsARejM2QRW2TgNti+8oCa3UGlTt+vuOAQAAEhgFFQCOQLPL0HuxMTqF23sPqdQa\nVOsGcNQMAAA4oLgKqpmdbWbLzWyVmX13P89PM7O5ZhYxs4v3ee4qM1vZ/s9VXRUcABJBZWy0WpSp\naRTUQyqzBu1Wtjaqt+8oAAAgQR2yoJpZUNLdks6RNE7S581s3D6XrZF0taRH93ltX0m3SZoqaYqk\n28ysz5HHBoDEMDM2XhmKaGpgqe8oCe+DSb4MSgIAAAcQzwrqFEmrnHNVzrmwpMckXbD3Bc65Gufc\nAkmxfV77CUkvO+e2OOeaJL0s6ewuyA0ACeGV2LE6PrBMOdbiO0rCK7N6SVJ1jEFJAABg/+IpqIMl\nrd3r83Xtj8XjSF4LAAmtOjZAq9wQnRmY4ztKUhhkm5WpVo6aAQAAB5QQQ5LM7FozqzSzysbGRt9x\nACAuL8cmSZLODFJQ4xE0p2G2gVt8AQDAAcVTUOskDd3r8yHtj8Ujrtc65+51zk12zk0uLi6O860B\nwK+XopM1zmo0xDb5jpI0Sq2BFVQAAHBA8RTU2ZIqzKzMzDIlXSppepzv/6Kks8ysT/twpLPaHwOA\npLbJFWiOq+D23k4qswbVuv6KOfMdBQAAJKBDFlTnXETSDWorlksl/dU5t9jM7jCz8yXJzI43s3WS\nPivp92a2uP21WyTdqbaSO1vSHe2PAUBSeyV6nJwCOitY6TtKUimzBrUoU/Xq6zsKAABIQKF4LnLO\nzZA0Y5/Hbt3r49lqu313f699QNIDR5ARABLOy7FJGqxGjbNa31GSygdHzcQGanBws+c0AAAg0STE\nkCQASCa7XZZmxsbrzOAcGXeqdkpZgLNQAQDAgVFQAaCT3oyNV4sydVaA23s7q7+alK0WBiUBAID9\noqACQCe9HJ2kQu3U8YHlvqMknYA5ldoGCioAANgvCioAdELEBfRK7Dh9LDBPGRb1HScplVoDt/gC\nAID9oqACQCdUulHaqnym9x6BMqvXGleiiOOvIAAA8GH8dAAAnfBSdLIyFda0wALfUZJWmTUoopDq\nXJHvKAAAIMFQUAEgTjFnej46VacEFinXWnzHSVqlTPIFAAAHQEEFgDjNio1Vvfrp08G3fEdJah1n\noTIoCQAA7IuCCgBx+lv0VOVrt84MzPEdJakVa5tytYeCCgAAPoKCCgBx2B2O6PnYVJ0bfFfZ1uo7\nTlIza9uHWuUG+o4CAAASDAUVAOLw0uIN2q1sXRSc6TtKSii1BlZQAQDAR1BQASAOf5u7TkNso463\n5b6jpIQya9A6V6ywC/qOAgAAEggFFQAOoWFbs95etUkXBd5SwJzvOCmhNNCgmAJa60p8RwEAAAmE\nggoAh/D0/DrFnJje24WY5AsAAPaHggoAB+Gc05Nz63TssN4qaz+/E0euzDgLFQAAfBQFFQAOYkn9\ndi3fsEMXHTfEd5SU0kc7VKidqmaSLwAA2AsFFQAO4sm5dcoImj41gSLVlcyY5AsAAD6KggoAB9Dc\nGtVT8+p0xpj+6p2T6TtOyimzBtXE+vuOAQAAEggFFQAO4G9z12nLrrCuPrnUd5SUVBpo0Hr1U7PL\n8B0FAAAkCAoqAOxHLOZ0/8xqjR9cqKllfX3HSUll1iCngNZw1AwAAGhHQQWA/Xh12UZVbdqlL59a\nJjPzHScllVm9JKmKQUkAAKAdBRUA9uMPM6s0qDBb546nPHUXzkIFAAD7oqACwD4Wrtumd6u36Isn\nlykjyLfJ7lJge9RP2yioAADgA/zkBQD7+MPMKuVlhXTJlKG+o6S8UmtQdYyCCgAA2lBQAWAvdVv3\n6LmF9br0+KEqyGa6bHfjLFQAALA3CioA7OWPb1dLkr54SpnnJOmhPNCgDeqrXS7LdxQAAJAAKKgA\n0G7jjmY9+u4anTt+oAb37uU7TlpgUBIAANgbBRUA2v3sxeUKR2O66eMVvqOkDQoqAADYGwUVANQ2\nuff/5qzT1SeVqrw4z3ectEFBBQAAe6OgAkh7zjn94JnF6puTqRvPYPW0J+Vai0rUpGoKKgAAEAUV\nAPTsgnpV1jbpW58YzeReD0qtQTUcNQMAAERBBZDm9oSj+tGMpRo3sECfm8y5pz6UB+pZQQUAAJIo\nqADS3L1vVmn9tmbd9qlxCgbMd5y0VGoN2qxCbXdMTgYAIN1RUAGkrWUN23XPG6v0yfEDNbW8n+84\naYtBSQAAoAMFFUBa2t7cqusemav87Azddv4433HSWll7QeU2XwAAEPIdAAB6mnNON//f+1qzZbf+\n8pUTVJKf7TtSWhtuGySxggoAAFhBBZCG/jCzSi8u3qDvnTNGU8r6+o6T9rKtVYPVqOrYQN9RAACA\nZxRUAGllVtVm/eSF5Tp3/ABdc0qZ7zhoVxrYwC2+AACAggogfazYsEM3PDpXw/vl6CefmSAzpvYm\nilJr4BZfAABAQQWQHiprtujie/6pgJnu/cIk5Wdn+I6EvZRZg7YpT00uz3cUAADgEQUVQMp7eckG\nXX7fuyrKy9LfrjtJI0vyfUfCPkqZ5AsAAERBBZDiHp+9Rl/9U6XGDCzQ//37iRraN8d3JOzHvwoq\ng5IAAEhnHDMDICWt3bJbP3xuiV5cvEHTRhXrnsuPU24W3/IS1TDboIBiqokNkIK+0wAAAF/4aQ1A\nSmm+rUj/G/2U7omcr4Biujn0d11b+5wyfhT1HQ0HkWlRDbFGbvEFACDNUVABpIS1W3Zr+vvr9WjL\nz1SnYp0XeEe3ZPxZg2yL72iIE5N8AQAABRVAUopEY1rduEvvVm/W0/PXa05tkyRpim3Sz0L/qxOD\nSz0nRGeVWYPmxirknMQJQAAApKe4CqqZnS3p/1PbzqD7nHM/3uf5LEkPS5okabOkS5xzNWaWIek+\nSce1f62HnXM/6sL8AFJYLOa0aWeL1m9rVv3WPVq/rVlrNu/SovXbtXj9NjW3xiRJFSV5uvkTo3X+\nMYM09NeXeU6Nw1VqDdqpHG1SgYq13XccAADgwSELqpkFJd0t6UxJ6yTNNrPpzrkle112jaQm59xI\nM7tU0k8kXSLps5KynHPjzSxH0hIz+4tzrqar/yAAktPucERVjbu0unGnVjfuUu3mXarf2qz12/Zo\nw/ZmtUbdh67PyQzqqEEF+vyUYRo/uFAThvTWiOJcGUtuSa/M6iW1TfItNgoqAADpKJ4V1CmSVjnn\nqiTJzB6TdIGkvQvqBZJub//4CUm/tbafFp2kXDMLSeolKSzxa3EgnTXtCmtW1Wa9U7VZ76zerJUb\nd37wXMCkQb17aVDvXpo8vI8G9u6lgYXZGljY9u9BvXupT04GZTRFlbUfNVMTG6ApgeWe0wAAAB/i\nKaiDJa3d6/N1kqYe6BrnXMTMtknqp7ayeoGkekk5km5yzn1kYomZXSvpWkkaNmxYJ/8IABLdnnBU\nzy2s1+Oz12h2Tdte0Rw1a3Jguc4LrVCF1WmErddw26DsPa3SHrV910BaGWybFFKESb4AAKSx7h6S\nNEVSVNIgSX0kzTSzf3SsxnZwzt0r6V5Jmjx5svvIuwBISis37NDD79Tq7/PrtKM5ovKiXN308VE6\n+c3LNMFWK9M4+gX/ErKYhtlGJvkCAJDG4imodZKG7vX5kPbH9nfNuvbbeQvVNizpMkkvOOdaJW00\ns7clTZZUJQApq3FHi37x8go9PnuNQsGAPjl+oC49fqimlPVtuz33rRW+IyJBlVoDK6gAAKSxeArq\nbEkVZlamtiJ6qdqK596mS4qkLJQAACAASURBVLpK0juSLpb0qnPOmdkaSR+T9Cczy5V0gqRfdVV4\nAImluTWqB96u1u9eW63m1qiuOqlUN36sQn1zM31HQ5Ioswb9M3aUYs4UMG6oAQAg3RyyoLbvKb1B\n0otqO2bmAefcYjO7Q1Klc266pPvVVkJXSdqithIrtU3/fdDMFksySQ865xZ0xx8EQBe7vbBTly+K\nDdcNrd9QjRugjwcq9b3QXzRiTr00p5vyISWVWoOalaUN6qOB+sjIAgAAkOLi2oPqnJshacY+j926\n18fNajtSZt/X7dzf4wBSh3PSn6Nn6I7IF9RXO/SnjLt0anCR71hIUh2TfKtjAzQwSEEFACDddPeQ\nJAApbKfL1vdav6xnYidpWuB9/TLjd+pnO3zHQhIrDbQfNeMG6KQPnWYGAADSAQUVwGFZ7/rqyvB3\nVeUG6ebQ47ouOJ09gzhig7RZmQozyRcAgDRFQQXQabWxEl0W/r62K1ePZNylk4KsdKFrBMxpuG1U\nFQUVAIC0REEF0CmrYoN0efgWtShDj2b+P40PVPuOhBRTZvWqcgN9xwAAAB4EfAcAkDwWx4brc+Fb\nFZPp8cw7KafoFmXWoDWuv6LOfEcBAAA9jIIKIC4rY4P1+fB/KVth/TXzTo0OrPMdCSmq1BoUVobW\nu36+owAAgB5GQQVwSBtdoa4Of1uZatXjmXeqrH3SKtAdSu1fk3wBAEB6oaACOKjdLktfDn9LW5Sv\nBzL/R0MDjb4jIcV1/AKkmn2oAACkHYYkATigqDN9o/VrWuTKdG/GLzSBPafoAf3VpBw1MygJAIA0\nxAoqgAP6YeQKvRybrNtCD+vjwbm+4yBNmEnlVq/VbpDvKAAAoIdRUAHs11PRk/Vg9Bx9KThDV4Ve\n8h0Haabc1qsqxgoqAADphoIK4COqGnfq+63XaIot1S2hR33HQRoaEViv9eqn5tao7ygAAKAHUVAB\nfEhza1Rfe3SestSqX2f+ViGL+Y6ENFRu9XIKqHrTLt9RAABAD6KgAviQu2Ys1dL67fp5xj0aYE2+\n4yBNlVu9JGl1407PSQAAQE+ioAL4wPML6/XwO7X6yqll+lhwvu84SGMdBbWqkRVUAADSCQUVgCRp\n/dY9+vbfFuiYob118yfG+I6DNNfLwhqsRlWxggoAQFqhoAKQc063PLVQkajTby49VpkhvjXAv/JA\nvVazggoAQFrhp1AAempenV5f3qhvnz1aw/rl+I4DSJJG2HpVNe6Uc853FAAA0EMoqECaa9zRojue\nXaLjhvXWlSeW+o4DfKDc6rUrHNXGHS2+owAAgB5CQQXS3O3TF2t3S1Q/vXiCggHzHQf4wAeTfDey\nDxUAgHRBQQXS2AuLGvTcwnp94+MVGlmS7zsO8CHlgfWSpNWchQoAQNqgoAJpatvuVv3304s0bmCB\nrp1W7jsO8BED1KSczCCTfAEASCMh3wEA+PHLf6zQ5p0tevDq45UR5HdVSDwBcyrrl8skXwAA0gg/\nlQJpaHnDDv1pVq0umzpMRw8u9B0HOKDy4jxWUAEASCMUVCDNOOf0g2cWKy8rpG+eOdp3HOCgRhTn\nqm7rHjW3Rn1HAQAAPYCCCqSZFxY16J+rN+tbZ41Sn9xM33GAgyovzpNzUjWDkgAASAsUVCCN7AlH\n9cPnlmrMgHx9fsow33GAQyovypUkVbEPFQCAtMCQJCCN/P7N1arbukePXXuCQgxGQhIoL+4oqOxD\nBQAgHfATKpAm1jXt1j2vr9Z5EwbqhPJ+vuMAccnJDGlQYbZWU1ABAEgLFFQgTfzipRWSpO+dO9Zz\nEqBzyovzVMUeVAAA0gK3+ALJ6vb4j4dZEhump8J36avBZzX4V5d2Yyig640oztXf5tbJOScz8x0H\nAAB0I1ZQgTTw08ilKtBuXRd6xncUoNPKi/O0syWijTtafEcBAADdjIIKpLh3omP1emyirg9NV6Fx\nmySST8egJPahAgCQ+iioQApzTvpx5PMaqM26Kvii7zjAYSkvzpPEUTMAAKQDCiqQwl6IHa/33Ujd\nFHpC2dbqOw5wWAYWZKtXRlCrNrKCCgBAqqOgAimq1QX1P5FLNMrW6jPBN33HAQ5bIGAaWZLHLb4A\nAKQBCiqQop6ITlOVG6Rvhx5X0JzvOMARqSjJ08oNFFQAAFIdBRVIQWEX1G8jF2qirdQZgbm+4wBH\nbGT/PDVsb9b2Zm5VBwAglVFQgRT01+jpqlOxbgr9TRwbiVQwqiRfklhFBQAgxVFQgRTT4kK6O3Kh\njrMVmhZY4DsO0CUq+rdN8l21cYfnJAAAoDtRUIEU89fo6apXP90UeoLVU6SMIX1ylBUKsIIKAECK\no6ACKaTFhfS7yAWabMt1SmCR7zhAlwkGTCOK87SSo2YAAEhpFFQghTwe/TfVq5/+g72nSEEV/fM4\nCxUAgBRHQQVSRLPL0N2RC3S8LdPJrJ4iBY3qn6+6rXu0syXiOwoAAOgmFFQgRTwe/TdtUF/2niJl\njSxpG5S0mlVUAABSFgUVSAFhF9TvI+dpsi3XiYElvuMA3aKivaCu2MAkXwAAUlVcBdXMzjaz5Wa2\nysy+u5/ns8zs8fbn3zWz0r2em2Bm75jZYjNbaGbZXRcfgCT9PXqK1qtIXwv9ndVTpKxhfXOUGQyw\nDxUAgBR2yIJqZkFJd0s6R9I4SZ83s3H7XHaNpCbn3EhJv5T0k/bXhiQ9IunfnXNHSTpdUmuXpQeg\nqDP9b/RTGmc1Oj3wvu84QLcJBQMqL85lki8AACksnhXUKZJWOeeqnHNhSY9JumCfay6Q9FD7x09I\nOsPMTNJZkhY4596XJOfcZudctGuiA5CkF2JTVOUG6Wuhp1k9Rcqr6J+vlRu5xRcAgFQVT0EdLGnt\nXp+va39sv9c45yKStknqJ2mUJGdmL5rZXDP79v6+gJlda2aVZlbZ2NjY2T8DkLack+6OXKByW6+z\nA+/5jgN0u4qSPK1r2qPdYSb5AgCQirp7SFJI0imSLm//96fN7Ix9L3LO3eucm+ycm1xcXNzNkYDU\n8Xpsopa4Ul0XnK6gOd9xgG5XUZIn56Sqxl2+owAAgG4QT0GtkzR0r8+HtD+232va950WStqsttXW\nN51zm5xzuyXNkHTckYYG0LZ6+tvIBRqsRl0YfNt3HKBHVPRvm+TLbb4AAKSmeArqbEkVZlZmZpmS\nLpU0fZ9rpku6qv3jiyW96pxzkl6UNN7MctqL62mSOAMD6ALvuTGa40br2tBzyjC2diM9DO+Xq4yg\nacUGBiUBAJCKQoe6wDkXMbMb1FY2g5IecM4tNrM7JFU656ZLul/Sn8xslaQtaiuxcs41mdkv1FZy\nnaQZzrnnuunPAqSVeyLnq5+26XPB131HAXpMRjCgsqJcraSgAgCQkg5ZUCXJOTdDbbfn7v3YrXt9\n3Czpswd47SNqO2oGQBdZ1rBdr8cm6luhx9XLwr7jAD2qoiRfi9dv8x0D6BbOOTXuaNHGHS3t/27W\nll2tMpOCZgoGTBlBU0lBtgb37qUhfXqpsFeGjDHuAFJEXAUVQGK5980q5ahZVwT/4TsK0ONGluTp\n+UX1am6NKjsj6DsOcES27g5rVtVmLVi3TQvr2v7ZurtzR8bnZgZ19OBCTRreR5OG99Fxw/qoT25m\nNyUGgO5FQQWSzPqtezR9/np9IfiaehuTTJF+KvrnKdY+yXfcoALfcYBOq928Sy8v2aB/LN2g2TVN\nisacQgHTqP75+sS4ARo3qEADCrNVkp+l4vws9c3NlMkUicUUi0ktkag2bG9R3dbdWte0R2u37Nb8\nddt075tVisTaJrofM7S3Pjl+gM45eqCG9s3x/CcGgPhRUIEk88Bb1XKSrgk97zsK4EVFSb6ktkm+\nFFQki+bWqJ5dUK8/v1ureWu2SpJG98/XdaeN0L+NKdZRgwrjuCOg4/kMlRRka/yQwg89uycc1YJ1\nW/Ve9Ra9uKRBd81YprtmLNMxQwp18aQhuui4IcrN4kc/AImN71JAEtm2p1V/eW+NzpswUEOWbfId\nB/CitChHwYBp1UYGJSHxrd2yW3/8Z42emLNO2/a0qrw4V98/d6w+cdQADevXtSubvTKDmlreT1PL\n++nGMyq0ZvNuzfjlV/RM3Yn673Xb9NOn39Olwdd0ZfAlDQ10wd8ht7MXHEDXo6ACSeTP79ZqVziq\na6eVS8t8pwH8yAoFVVaUq2UNnIWKHnJ74aGv2cc6V6TfRi7UE9FpkqRPBGbr8oxXdOL2JbJXJb3a\nxRn3Y5ikfw9JXw0+q7muQg9GztYD0XN0f/RcnRd4R/8ZekKlgQ3dHwQAOoGCCiSJ5taoHny7RqdW\nFOmoQZ3/YQlIJWMG5Ov9dVt9xwA+osH10W8in9Zfo6fL5HR58BVdF5quAdbkLZOZNMlWalLmStW7\nvnoocpYeip6lGeGpuiT4ur4eelL9jf+fACQGCiqQJP4+r06NO1r0q0sm+o4CeDd2YIGeXVCvHc2t\nys/O8B0HUNgF9UD0HP06cpFaFdIlwdd0fehpDbItvqN9yEDbou9mPKYvhZ7XbyOf1qPRj+lv0VN1\nbfA5XR96WtnWuQnCANDVAr4DADi0WMzpvreqddSgAp00op/vOIB3Ywa0DUpasYHbfOHfP6PjdE74\nx/px5DKdFFikVzK/pR9mPJhw5XRvJbZNd2T8Ua9kfktnBubo19GLdHb4J3orerTvaADSHAUVSAJv\nrGzUqo079eVTyziMHVDbCqokLamnoMKfbS5XN4Wv02Wt/6WwMnR/xv/ovsxfaFhgo+9ocRse2Kjf\nZP5Wj2TcJUm6ovUW3RS+TpscE7IB+EFBBZLAA29Vq39Blj45fpDvKEBCGFiYrYLskJbVb/cdBWnq\nrejR+kTLjzU9dpJuDD6llzNv1hnBeb5jHbZTgov0QuZ3dGPwKT0bO1GfaPmJXoke6zsWgDREQQUS\n3LKG7Zq5cpOuPLFUmSH+lwUkycw0ZmABk3zR45pdhm5vvVJXtN6iXGvWU5m36psZ/5cSezezrVXf\nzPg/PZf5PZVYk65pvVm3tl6tZsc+bwA9h592gQT3wFvV6pUR1OVTh/mOAiSUcQMLtKx+u2Ix5zsK\n0sTq2ECdH/6h/hg9W1cHX9BzmbdoQqDad6wuNypQp79n3qprgjP0cPQsfSr8/7Q0NtR3LABpgoIK\nJLDGHS36+7z1+sykweqdk+k7DpBQxgzI165wVOua9viOgjTwfPR4XRC+U5tcoR7O+JFuz3g4JVZN\nDyTLIvrvjEf0cMaPtNXl6sLwnXoyeorvWADSAAUVSGCPzKpVOBrTl04u8x0FSDhj2gclLW1gHyq6\nTyQa012tl+m61ps00ur0bNYtmhZc6DtWj5kWXKjns76nibZK/9l6vX7Q+gW1uqDvWABSGAUVSFDN\nrVE9MqtWHx9bovLiPN9xgIQzun++zKSlDEpCN9m6O6wr7n9X90bP0xeCL+nxzDsT+uiY7lJk2/VI\n5o/0xeDzejB6jq4If48pvwC6Tch3AAD79/d5ddq8K6wvncLqKdLY7YUHfKqXpDL9TMtefU9661eH\n8d7bDj8XUl7Npl364h9nq65pj36ecY8+E5zpO5JXGRbVbRl/0oRAlb7b+hWd3/JDPdiwQ6PbzyQG\ngK7CCiqQgJxzuv+tao0bWKATy/v5jgMkrDG2VsscA8TQtWbXbNGnf/e2tu4O689fmZr25XRvnw6+\nrScyf6CIgrr4f/+pf67a5DsSgBRDQQUS0JsrN2nlxp265pQymZnvOEDCGhNYo1pXol0uy3cUpIin\n59fp8j+8qz45mXrq+pN1fGlf35ESzvhAtZ7Muk0DCrJ11YPv6al563xHApBCKKhAArr/rWqV5Gfp\nU8cM8h0FSGhjrVZOAS13HIGBI3ffzCp947H5OnZYbz15/UkqLcr1HSlhDbFNeuK6kzR5eF/d9Pj7\n+s0rK+UcRz4BOHIUVCDBLG/YoTdXNOrKE4crM8T/osDBjLE1kqRlMW7zxeFzzulnLy7XD59bqnOO\nHqCHr5nC0V5xKOyVoYe+NEWfPnawfv7yCv3wuaWUVABHjCFJQIJ54K1qZWcEdNnU4b6jAAlviG1S\nvnZrKftQcZhiMadbpy/SI7PW6JLJQ3XXReMVDLC1Il6ZoYB+/tljVNgrQ/e/Va2dzRH+GwI4IhRU\nIIFs2tmip+bX6bOThqhvLr+9Bw7FrG0VlRVUHI7WaEzf/Ov7mv7+en31tHJ99+wx7Ps/DIGA6bZP\njVNBdki/fnWVdoYj+uXnJnIXEIDDQkEFEsgjs2oVjsQ4WgbohDGBNfp79BQ511ZYkaYOciTR/rS6\noL7ReoNmxKbq26G/6Pp3n5He7aZsacDM9J9njVZedkh3zVim3S0R3XPFJGVnBH1HA5Bk+NUWkCCa\nW6N6ZFatPjamRCOK83zHAZLGGFujHcrROlfkOwqSRKsL6sbWGzUjNlX/FfqTrg894ztSyrh22gjd\n9enxem15o776pzlqbo36jgQgyVBQgQQxff56bdoZ1jWsngKdMjbQPiiJfaiIQ9gFdUPrjXohNkW3\nhh7Wl0PP+46Uci6bOkw/vmi83ljRqOsemaOWCCUVQPwoqEACcM7p/reqNWZAvk4a0c93HCCpjLa1\nkiioOLRWF9QNrV/Xi7Epuj30R30p9ILvSCnr0inDPlhJvf6RuZRUAHGjoAIJ4K1Vm7R8ww5dc0oZ\nAzqATsq1Fg23Bi2JMfkaBxZ1pv9ovV4vxY7XD0J/1NWhl3xHSnmXTR2mH154tF5ZtlFf+/M8hSMx\n35EAJAGGJAHdKc6hHfeFv60iler8ZyZKz0a6ORSQeo62Gi1w5b5jIEHFnOk7kWv1XOxEfT/0iK6i\nnPaYK04YLuec/vvpxbrpr/P160uP5QgaAAfFCirg2crYYL0Rm6irQi8pyyinwOEYH6jSWleiJseA\nMXyYc9IPIlfqiehp+kbwb/pKaIbvSGnnCyeW6nvnjNFzC+r1/acWyjnnOxKABMYKKuDZA9FzlKWw\nLg++4jsKkLQmWJUkaWGsTNOCCz2nQaJwTvpJ5FI9FP2EvhJ8Vv8R+pvvSGnrq6eN0I7miH772irl\nZ4d0y7lj2dICYL8oqIBHm12+noyeoouCM9XXdviOAyStowPVkqSFrlzTREFFm3uj5+l/o+frsuA/\ndEvoUc7J9eybZ43SzpaI/jCzWvnZGfr6GRW+IwFIQBRUwKM/Rz+uFmXqmiDHHABHosD2qNzWa0GM\nY5rQ5onoqfpR5DJ9MvCO7gw9SDlNAGamW88bp+3NrfrFyyvUJzdTXziB4WYAPoyCCnjS4kJ6OHKm\nTg/M18jAet9xgKQ33qo1OzbadwwkgFejE/Wd1mt1cmCRfpFxj4LGnsdEEQiYfvqZCdq2u1W3Pb1I\nAwqydea4/r5jAUggDEkCPJkePUmb1FvXBBnYAXSF8YEqrVeRGl2B7yjwaE6sQte3fkPjrFa/z/gF\nw+cSUCgY0G8uO1ZHDy7UjX+Zq3lrmnxHApBAWEEFPHBOuj96rkbbGp0SWOQ7DpASJgTaBiUtipXr\n34LzPaeBD6tig/Sl8M0aYE16MPOnyrNm35FSW5xHqe1PjqQHXIEuivxA1/zuBT2ZeZtKAxv2eu9t\nR54PQFJiBRXw4J+xo7TMDdM1wefZFwV0kaOsRqaYFjj2oaajja5QV4W/owxF9HDGj1Vk231HwiEU\n2XY9lPETOZmuav2ONrt835EAJAAKKuDBfdFzVaRtOj/4T99RgJSRay0aaeu1MFbuOwp62K6WiL4U\n/ra2KF8PZv6PhgU2+o6EOJUFGnR/5v+owfXVl8I3a4/L9B0JgGcUVKCHrYoN0muxY/WF0EvKtlbf\ncYCUMt6qtICCmlYi0Zhu/Ms8LXHDdXfGrzW+/cghJI/jAqv0m4zfaKEr142tNyri+PEUSGd8BwB6\n2APRs5WpsC4PvuI7CpByJgSqtFF91OD6+I6CHuCc023TF+vVZRt1Z+gBfYy9x0nrrOAc3R56SP+I\nTdLtkavkHJOXgXRFQQV60BaXryejp+qi4FvsjwK6QcfqGauo6eG+mdX687trdN3pI3R56FXfcXCE\nrgy9rH8PTtcj0TN1zxurfccB4AkFFehBj0Y/pmZl6UvB531HAVLSOKtVUFH2oaaB15Zv1I+eX6pz\njh6gm8/i/NtU8e3Q47ow8JZ++sJyPT2/znccAB5QUIEe0uJCeihylqYF3teoAH/pAt2hl4VVYeuY\n5JviVm3cqa8/Ok+jBxTo5587RoEA49BTRcCcfprxe00t66ubn1jAGalAGqKgAj3k2diJalQffTk4\nw3cUIKVNCFRpYaxcbGFLTdt2t+rahyuVGQroD1dOUk4mR7qnmkyL6p4rJmlAQba+8vAcrd+6x3ck\nAD2Iggr0AOek+yLnaJSt1amBhb7jACltvFVriwpUpyLfUdDFojGnGx+bp7VNu3XPFZM0pE+O70jo\nJn1zM3X/VZPV0hrVNQ9ValdLxHckAD2Eggr0gLdjR2upK9U1wedl3IkGdKsJgSpJ0sIYt/mmmh8/\nv1RvrmjUHRccrSllfX3HQTer6J+v31x2rJY3bNdNj89XLMZtEUA6iKugmtnZZrbczFaZ2Xf383yW\nmT3e/vy7Zla6z/PDzGynmX2ra2IDyeX30fNUrCZdGHzLdxQg5Y2xNcpQhEm+KeaJOev0h5nVuurE\n4fr8lGG+46CHnD66RP/1yXF6ackG/fzl5b7jAOgBh9y4YWZBSXdLOlPSOkmzzWy6c27JXpddI6nJ\nOTfSzC6V9BNJl+z1/C8kMbYUaWlJbJhmxibo5tBjyjJuUQK6W5ZFNNrWaoEb4TsK9nV74WG9bG5s\npG4J/7dOCizXf839gjQv2sXBkMi+eHKpVm7cqbtfW62RJXn69LFDfEcC0I3iWUGdImmVc67KOReW\n9JikC/a55gJJD7V//ISkM8zabmQ0swslVUta3DWRgeRyX+STylGzrgi+4jsKkDaODazU/NgIRRw7\nWZJdveurr4Zv0gDborszfq0Mo5ymGzPTHRccpRPK++o7TyzUnFom+wKpLJ6/uQdLWrvX5+vaH9vv\nNc65iKRtkvqZWZ6k70j6wZFHBZLPetdX02Mn6pLgayq0Xb7jAGljcmC5dqmXljluBU1mzS5D14b/\nU7uVrfsyfqY+ttN3JHiSEQzo/2/vvuOjqPM/jr++M7ubkISE3kE6iIiAAcWCvRdU7KfCKUUFT3+C\nHp53Gvvp2cWKYoVD7IicBTzFU1pApPciICUQCCQh2TLf3x+JdxxHiRAyu8n7+XjsI7Ozs9n38hg2\n89lve/F3R9OwRjID385m7dZCvyOJyCFyqL9azgKestbu8y+KMWaAMSbbGJOdk5NziCOJVJzXo2dj\nMdwQUA93kYrUzSkZqzbDa+dzEjlQ1sKdkQHMs815Jvi81o8WaqaGeK1PN4qjHv00s69IpVWWAnUd\n0HSX+01K9+3xGGNMAMgAtgDHAI8ZY1YBtwF/MsYM3v0FrLWvWGszrbWZdevW/c1vQiQebS+K8PfY\nqZznTKWJ2ex3HJEqpZHJpTE5ZKtATVgvxi5gnHc8QwPvcbo7y+84Eida10vj+au7smTjDm7TzL4i\nlVJZCtQZQBtjTAtjTAi4Ehi32zHjgD6l25cCX9sSJ1prm1trmwNPAw9ba4eXU3aRuDZ62s/kk8KA\nwHi/o4hUSZnOErK9tlhdvyacibGu/C16Bec7U7jZ/cTvOBJneraty5/P68BXCzby9MQlfscRkXK2\n3wK1dEzpYOALYCEw1lo73xhzvzHmwtLDXqNkzOky4Hbgf5aiEalKwlGP179fyfHOPDo6q/2OI1Il\nZTqL2Ugt1lr1zEkkS73G3Ba5mSPMav4WfFlrR8se/f745lye2YRnv17GZ3PW+x1HRMrRfpeZAbDW\nTgAm7Lbvnl22i4DL9vM7sg4gn0hCGvfTL2zcXsyjQbWeivjl3+NQbTuaovkNEsE2m0q/yBCSCfNK\n6AmqmbDfkSROGWN44KKOLM8pYOh7P9G8TgpHNDqwZYxEJL5o/n2RcmatZcTkFbRvUJ2TnDl+xxGp\nstqatVSnQBMlJYiodRgUuZX1tjYvh56ikcn1O5LEuaSAy4vXdKVGSpABb81kc36x35FEpByoQBUp\nZ98syWHxxh30P7GluqaJ+MgxlqOdpZooKUE8GL2G772OPBgYydHOUr/jSIKoVz2ZV67NZHN+MTe9\nM5Nw1PM7kogcJBWoIuVsxOQVNEhP5oKjGvkdRaTK6+YsZqltwlab5ncU2Ycx0ZN5I3Y2N7gTuDzw\nrd9xJMEc2SSDxy7txIxVW7l33HysZkYTSWgqUEXK0bx1efywfAu/P745oYD+e4n4LbN0HOpMr63P\nSWRvZnjt+Ev0ek505nBXYLTfcSRB9ercmJtObsXfp//MO1M1OaFIItMVtEg5ennyCtKSAlx1TDO/\no4gIcJRZTpAoM1SgxqV1tjY3hm+jiclhePA5AkbdM+XADT2zHae1r0fWpwv4YbnWHxdJVCpQRcrJ\nmtxCJsxdz9XHNCM9Oeh3HBEBkk2EI80KjUONQ4U2if7hIYQJMiL4BBmmwO9IkuBcx/D0lZ1pUSeV\nQaNmsSa30O9IInIAyrTMjIjs32v/WomhZG02EYkf3ZzFjIydQ5ENkmwifscRwFq4IzKQhbYZI4OP\n09r5xe9IEm+yDmzJmOrACK8BvcIP0O9vb/JBKIs0U7Tb7847+HwicsioBVWkHGwrDDM2ew0Xdm5E\nw4xqfscRkV1kOouJEGCObel3FCk1PHYRn3nHMiwwhlPc2X7HkUqmhbOB54PPsNQ24fbITXhWU+qL\nJBIVqCLl4I0fVlEYjjGwZyu/o4jIbn5dskTrocaHz2OZPBG9nIud7xjgjvc7jlRSJ7rzuDvwDl96\n3Xg6eonfcUTkN1AXX5GDlF8c5fXvV3FGh/q0a1Dd7zgisptaZgetzDqNQ40Di7ym3B65maPMMh4J\nvqq1ouWQut79nIX2B+BI/QAAIABJREFUMJ6N9aa9s4Zz3el+RxKRMlALqshBGj1tNXk7I9x8slpP\nReJVd2cRM7x2RKzrd5QqK7cgTL/IENLYySuhJzUeWA45Y+ChwGt0NUsYErmR+d5hfkcSkTJQgSpy\nEIoiMUZ8t5LjW9emS7OafscRkb3o6cwhnxR+tK39jlIlRWIeN4+aySZbg1dCT1LfbPM7klQRSSbK\nS6GnyKCAAeHb2WLV00kk3qlAFTkI789cS86OYgadootekXh2nLMAB4/vYp38jlIl3f/pAqauyOXR\n4Ag6O8v9jiNVTD2TxyuhJ9lMBjeFbyMc1Xq7IvFMBarIAYrGPF76djldmtWgR8vafscRkX3IMAV0\nNsuY7KlArWjvTF3N21NXM7BnSy52v/c7jlRRnZyVPBZ8men2cLI+ne93HBHZBxWoIgdo3E+/sHbr\nTgad3BqjmT5E4l5Pdw5zbAu22jS/o1QZU1dsIWvcfE5uV5c7z27vdxyp4nq5U7jRHcfoaT/z9tTV\nfscRkb1QgSpyADzP8sI3y2nfoDqnHV7P7zgiUgY9nTlYHP7ldfQ7SpWwJreQm96ZSbPaKTx7VRdc\nR1/kif/uCLzLqe3rcd+4+UxZvsXvOCKyBypQRQ7A5/M3sGxTPjed3EqtpyIJopNZQToF6uZbAQqK\no/R/K5uYZ3n1ukzSk4N+RxIBwDWWp6/szGG1U7h51EzW5Bb6HUlEdqN1UEV+I8+zPDtpKS3rpnJ+\np0Z+xxGRMgoYjxOceXwXOxIbAH21tBdZGQf1dM8abo/cyhIvkzeCj9Ly+bnlFEykfKQnB3m1Tzd6\nDf8X/d/K5oObjiM1SZfEIvFCLagiv9GXCzawaMMO/nBqG3VZE0kwPZ2f2EBtltrGfkeptJ6OXsIX\nXnfuDrxDT1fFqcSnFnVSGX51V5Zs3MHtY2fjedbvSCJSSgWqyG/geZanJy6lZZ1ULjhKraciiebE\n0oJJ3XwPjc9ix/BsrDeXud9wvfu533FE9qln27r86dzD+WL+Rp6ZtNTvOCJSSgWqyG/w5YKNLNqw\ng1tOa63WU5EE1NhsoZVZpwL1EJjnNWdoZCBdzRIeDIxEw/MlEdxwQgt6d23CM5OW8o+56/2OIyKo\nQBUpM8+zPDNpKS3qpHKBxp6KJKyezhymeYdTFIn5HaXS2GRr0C88hJrk83LoSZJM1O9IImVijOGh\nizvSpVkNbh/7Ewt+2e53JJEqTwWqSBl9tXAjC9dvZ/AprQm4+q8jkqh6OnMpJsSMVbl+R6kUimyQ\n/uEhbCeVV0OPU9foAl8SS3LQ5eVrjiajWpD+b2WzJb/Y70giVZquskXKwFrLMxOX0rx2Cr06q/VU\nJJEd4ywkRITJS3L8jpLwrIWhkRuZY1vwVPAFOjg/+x1J5IDUS0/m5WuPJie/mJtHzSIS8/yOJFJl\nqUAVKYMvF2xkwfrtDD61jVpPRRJciimmm7OYyUs2+x0l4T0bu5jxXg/uDLzLWW6233FEDspRTWvw\nWO9OTFuZy32fzvc7jkiVpSttkf2IeZYnvlxMyzqpXKTWU5FK4RTnRxZv3MHKzQV+R0lY42PH8FT0\nMi5xJnOj+6nfcUTKxUVdGjPwpJa8M/Vn3pm62u84IlWSClSR/Rj30zqWbMzn9jPbqvVUpJI4150G\nwATN2nlAfvJaMiRyE5lmMY8EX9WMvVKp3HlWe05pV5escfOZumKL33FEqhxdbYvsQyTm8dRXS+nQ\nMJ1zOzb0O46IlJNGJpeuzWrw2RwVqL/VBluT/uEh1CGPl0JPacZeqXRcx/DMVV1oVjuFm0fNYk1u\nod+RRKqUgN8BROLZ2Ow1/JxbyMi+mTha91SkUjmvUyMeGL+AFTn5tKyb5nechLDThugXHkoByXwQ\nyqKOZuyVRJSVsd9D0oFXvQb0Cj9A/7+9wQehLFJNGWb3zco7+HwiVZxaUEX2oigS49lJSzn6sJqc\n0q6e33FEpJyde2QDQN18y8qzhiGRm5hvD+PZ4HDaO2v8jiRySLV0NjA8+BxLbFOGRm7Es/qiWqQi\nqAVVZC/fpL4dPZeN0Wt4puhuzH2LKjiUiBxqDTOqkXlYTcbPWc/gU9v4HSfuPRq9kgneMdwdeIfT\n3B/9jiNSIU5y5/AnO5oHo9fwXOwibg185HckkUpPLagie7DDVuOFaC9OdOZwrKPiVKSyOvfIhiza\nsIPlOfl+R4lrb0bP5OXYBVzrfkk/d4LfcUQq1A3uBC5xJvNU9DLGxXr4HUek0lOBKrIHI6LnsZXq\nDA2M9TuKiBxC5x5ZMvnZBE2WtFdfxDLJil7H6U42WYE3NWOvVDnGwCPBV+luFjI0ciPTvPZ+RxKp\n1FSgiuxmg63JK7HzON+ZwlHOCr/jiMgh1CAjmW7Na/KZxqHu0UyvDX+IDOYos5zngsNxjfU7kogv\nkkyUV0JP0sTkMCB8O8s8rYsucqioQBXZzZPRS/Fw+GNgjN9RRKQC/NrNd9kmdfPd1UqvAf3CQ2lg\ncnkt9DjVTNjvSCK+qmEKeDP4KEFi9I3cSY5N9zuSSKWkAlVkFwu9prwXO4k+7hc0dXL8jiMiFeCc\njg0xRrP57mqzTadv5E4MljeCj1Hb7PA7kkhcaOrkMDL0GFtsOjeE76DQJvkdSaTSUYEqsouHo78j\nnUIGBz7xO4qIVJAGGcl0O6wW4+f84neUuLDThrghPJQNthavhh6nhbPB70gicaWTs5LngsOZZ1tw\nS+QWolaX0yLlSf+jREp9G+vEd14nbgl8RIYp8DuOiFSgCzo3YsnGfGav2eZ3FF/FPMstkcHMsS15\nNjicrs4yvyOJxKXT3VncF3iDSV5XsqJ9sBqeLVJuVKCKADFreCR6Nc3MRq51v/I7johUsIs6NyI1\n5PLWlFV+R/GNtZascfOZ6GWSFXiLs9xsvyOJxLVrAxMZ6H7KO7EzeCV2vt9xRCoNFagiwPuxk1hk\nm/HHwBiSTNTvOCJSwaonB7m4a2PGz1lPbkHVnAxo+NfLeHvqaga44+kT+NLvOCIJ4Y+BMZznTOGR\n6NWMjx3jdxyRSkEFqlR5eTaFx6JXkGkWc64zze84IuKT63o0Jxz1eHfGGr+jVLi3pqziia+WcEmX\nxgwL/N3vOCIJwzGWJ4Iv0c0s4vbIzUxZvsXvSCIJTwWqVHlPR3uTS3Wygm9oAXqRKqxt/eoc06IW\no6atJuZVnQFlH/+4jns+mc/ph9fnsUs74WitU5HfJNlEeCX0JM3MRvq/lc2ctVV7LLvIwVKBKlXa\n4g07eCt2Jle7X9PRWe13HBHxWZ/jmrN2606+WbzJ7ygVYtLCjQx57yd6tKzN8Ku7EHB1WSByIGqa\nfN4O/ZWMakH6jJzOsk1amknkQAX8DiDil18nBKlOIUMDY/2OIyJx4IwO9amfnsRbU1Zz2uH1/Y5z\nSE1ZvoWbR83iiEbpjOiTSXLQ9TuSSEJraHIZVXgjl4bv5donP+K9pPtoYjaX74tk5ZXv7xOJQ/qq\nVKqsCXM3MGXFFoYE3qOmyfc7jojEgaDrcHX3w/h2SQ6rNlfe5aamr8zl+jdmcFjtFN74fXfSkvR9\ntUh5aO5s5K3QXykgmWvDd5Fj0/2OJJJwVKBKlVQYjvLQZwvo0DCdq91JfscRkThyVfemBBzDO1Mr\nZ7f/mau38vvXp9OoRjKj+h1LrdSQ35FEKpUOzs+8HnqM9bYWfcLDyLMpfkcSSShlKlCNMWcbYxYb\nY5YZY4bt4fEkY8y7pY9PM8Y0L91/hjFmpjFmbunPU8s3vsiBef6fy/glr4j7eh2BqwlBRGQX9dKT\nObtjA8ZmryG/uHItOzV7zTb6jpxOvfRkRvc/lrrVk/yOJFIpHe0s5eXgUyy1TegXHspOqy+CRMpq\nvwWqMcYFngfOAToAVxljOux22A3AVmtta+Ap4NHS/ZuBC6y1RwJ9gLfLK7jIgVq0YTsvf7uC3l2b\n0K15Lb/jiEgc6n9iS7YXRRkxeYXfUcrN3LV5XPfaNGqmhhjd/xjqpyf7HUmkUjvJncPTwefJtm25\nKXIbYatx3iJlUZYW1O7AMmvtCmttGBgD9NrtmF7Am6Xb7wOnGWOMtfZHa+0vpfvnA9WMMfq6VnwT\n8yzDPphLerUgfz7vcL/jiEicOqppDc49sgEjvltBzo5iv+MctJmrc7l6xFTSqwUZ3f8YGmZU8zuS\nSJVwnjuNhwOv8Y3XmdsjNxOzWs9OZH/KUqA2BnZdtXxt6b49HmOtjQJ5QO3djukNzLLWJv5feklY\no6atZvaabdxzfgdqatyViOzDHWe1Jxz1eHbSUr+jHJQflm/m2temU6d6EmMH9qBJTY2HE6lIVwX+\nyV2B0Yz3enBXtB+eilSRfaqQSZKMMUdQ0u134F4eH2CMyTbGZOfk5FREJKmC1uft5LHPF3Nimzr0\n6tzI7zgiEuda1Enlqu7N+Pv0n1mZoDP6frN4E79/fQZNalbj3YHH0qiGWk5F/DAwMJ4/uB8yNnYK\nd0dvUJEqsg9lmVd+HdB0l/tNSvft6Zi1xpgAkAFsATDGNAE+Aq6z1i7f0wtYa18BXgHIzMzUjDVy\nSNz7yXyinsdDFx2JMfrDICL794fT2vDBrLX87YtFvPC7o/2OUyIro0yHTYh159bIYNqaNby97a/U\nemLHIQ4mIvvyf4H3ieHwfOwiHDweDIxElyMi/6ssBeoMoI0xpgUlheiVwNW7HTOOkkmQpgCXAl9b\na60xpgbwGTDMWvt9+cUW+W0+n7eeLxds5K5z2tOstrq3iQhlKvTqAv1jvXlmbm9+vKcrXZw9fs+6\nh9+dd3DZDtIb0TO5L3odXc1SRob+RoYp9DWPiIAxMDQwlhgOL8UuxMXjvsAbKlJFdrPfLr6lY0oH\nA18AC4Gx1tr5xpj7jTEXlh72GlDbGLMMuB34dSmawUBr4B5jzOzSW71yfxci+7Alv5g/fzyPDg3T\nuf6EFn7HEZEE0z/wGXXI45HI1dg47+PjWcMjkavIivblDGcmo0IPqzgViSPGwB8DYxjgjuet2Jnc\nG+2r7r4iuylLCyrW2gnAhN323bPLdhFw2R6e9yDw4EFmFDlg1lru/mge23dGeaffUQTdChl2LSKV\nSJop4tbAB/wlej3vxU7i8sC3fkfao7B1uSNyI594x3Ot+yVZgTe1zrNIHDIG7gqMBuCV2PmECfBw\n4DUc/X8VAcpYoIr4roxjrnb3cex4Po8MYlhgNO1furKcQ4lIVXG1O4nPve7cE+1LF2cZbZzdp2Lw\nV45NZ1D4Vqbbw7kjMIab3XHqNigSx34tUkNEGB67mLAN8ljwZQLG8zuaiO/UnCSV1npbi3sifck0\ni+nvfuZ3HBFJYK6xPBV8njSKGBy5hZ02fpap+slryYXFDzHHtuSZ4HMMCqg4FUkExsDQ4HsMCYzl\nQ+9EbosMImJdv2OJ+E4FqlRK1sKdkQFEcXk8+JK6uYnIQatn8ngy+AKLbTPuj17ndxwA3o+dyGXh\ne3Dw+CCURS93it+RROQ3uiXw8b/XSb0pchtFNuh3JBFfqUCVSumd2Ol853Xi7sAomjsb/Y4jIpVE\nT3cuN7mf8PfYqXwaO9a3HDttiLsj1zM0chNHO0v5NOnPHOGs9i2PiBycgYHxPBAYySSvC33Cf2S7\n1ZrFUnWpQJVKZ6HXlAej13CSM5vfuZP8jiMilcztgffpapZwV6Qf873DKvz153gtOC/8MKNipzPA\nHc/bwUeoZbTGqUiiuzYwkaeDzzPTtuWq8J/ZbNP9jiTiCxWoUqkU2CQGRW4lgwKeCL6kcVgiUu6C\nJsZzoedIp5Arw39muteuQl43GvMY/vVSLgnfR6FNYlTwIf4UHK1JVUQqkV7uFF4NPs5y24jLwvey\nxqvjdySRCqcCVSoNa+EvketZZRvwTHA4dcx2vyOJSCXV2GzhvaT7qGvyuDZ8F1/HOh/S15u5OpdL\nXvyBx79cwjnOdL5IGsbx7vxD+poi4o+T3TmMCj3MFpvOJeH7mOc19zuSSIVSgSqVxnuxk/jQO5Fb\nAx/Qw13odxwRqeQamy28F7qPdmYN/SND+Dh2fLm/xvq8ndw65kd6vziFjduLePaqLjwXGk6GKSj3\n1xKR+HG0s5T3Q1mEiHJ5+B7+GTvK70giFUYFqlQKS73G3BPty3HOPAa7H/sdR0SqiNpmB6NDD9Hd\nWcRtkUEMi/Rjk61x0L934/Yi/vbFIk59/Fv+MW8Dt5zamq+HnMyFRzUqh9QikgjaOuv4MOleWpj1\n9IsMZUz0ZL8jiVSIgN8BRA7WdluNGyO3kUYRTwef15IyIlKh0kwRrwcf4/Ho5bwZO4tPYsfR/6sl\nDOzZktSksv+ZtdYyc/VW3vhhFZ/P20DMWs49siHDzm5P01oph/AdiEi8qm+28W7oAQZF/sCw6ADW\nfLGIIWe0w3E0yYZUXipQJaHFrOG2yCBW2/q8E3qYeibP70giUgUlmwh/Do7iWvcrHotewbOTkhk9\n7WfO6diAbi1q0b15LRpkJP/P8zbtKGLailymr8zlh+WbWZ5TQPXkAH2Pa851PZrTrLYKU5GqLs0U\n8WrwCe6J9uX5f8KyTfk8eXnn3/QFmEgiMdbGV2tTZmamzc7O9juGxJusjD3ufjRyBS/GevFAYCTX\nBiZWcCgRkT2bdf0qhn+9jKkrtlAYjgHQpGY1qicHCUdjhGMeRRGPnB3FAKSGXI5uXoszO9Tn4i6N\n933huZfPQxGp3KyF18+YzYOfLaBdg3RGXHc0TWrqSyxJTMaYmdbazD09pq9eJGF9EuvBi7FeXO1O\nVHEqInGla7OajOzbjWjMY8H67UxfmcuPa7ZRHPFICjgEXUMo4NCqbhrHtKxNx0bpBFxNCyEie2cM\nXH9CC1rVS2Pw6Flc9Pz3vHTN0WQ2r+V3NJFypQJVEtJcrwV3RgbS3SwkK/Cm33FERPYo4Dp0alKD\nTk0OfuIkERGAk9rW5aObj6ffmzO4asRU/nJ+B6499jCMFn+XSkJf10rCWWdr0y88hDrk8ULoGUIm\n5nckERERkQrTul4anww6gZ5t6nLPJ/O5fexP7AzrekgqBxWoklC22jSuCw+jkCReCz1OHbPd70gi\nIiIiFS4jJciI6zK5/Yy2fDx7HRe/8D2rt2iNZEl86uIrCWOnDXFDeChrbF3eCv2V9s4avyOJiOyZ\nJjISkQrgOIY/nNaGTk0yuHXMbM5/9l880vtIzu+kNZMlcakFVRJC1DrcErmFH21rngk+z7HOIr8j\niYiIiMSFk9vVY/wtJ9C6fhqDR//IXR/OUZdfSVgqUCXueZ7l7ugNTPSO5v7AG5zjzvA7koiIiEhc\naVorhbEDe3DTya0YM2MNFw7/F4s2aCiUJB4VqBLXPM/yl0/m8W7sFP7gfqjlZERERET2Iug6/PHs\n9rx1fXe2Fka4cPj3vPrdCjzP+h1NpMxUoErc+rU4HTXtZ25yP+H/Au/7HUlEREQk7p3Ypi7/uPVE\nerapw4OfLeSqEVNZk1vodyyRMjHWxtc3KpmZmTY7O9vvGOIzz7PcM24e70z9mRtPasUfpx6DlvcS\nERERKTtr4b3YSdwfvRaL4S+Bt7nC/WbP11RZeRWeT6ouY8xMa23mnh5TC6rEnV9bTv9dnJ7dTsWp\niIiIyG9kDFwe+JZ/hIZxpLOCYdEBXBP5E6u9en5HE9krFagSV4qjMW4Z8yOjpu1anKo6FRERETlQ\nTZ3NjA4+zIOB1/jJa8lZ4Ud5OXo+UatSQOKPzkqJG9uLIvQZOZ3P5qzn7nMPZ9g57VWcioiIiJQD\nx1iuCUxiYtIdnOjM5ZHo1fQKP8Asr7Xf0UT+iwpUiQsbtxdx+UtTyF61laev6Ez/ni39jiQiIiJS\n6TQwW3kl+CQvBp9is83gkvD93BEZwOb8Yr+jiQAqUCUOzP8lj0te+IE1uYW8/vtuXNSlsd+RRERE\nRCotY+AcdwZfJw3hRnccH8dO4JTHv+H171cSiXl+x5MqTgWq+OqT2evo/eIPeNby7sAenNimrt+R\nRERERKqEVFPMsOAYPg/9kc5Na3Dfpws466nJfD5vA/G20odUHSpQxRfRmMcD4xdw65jZdGpSg09v\nOYGOjTP8jiUiIiJS5bRy1vPW9d15rU8mjmO48Z2ZXPrSFGauzvU7mlRBAb8DSNWzaXsRt46ZzZQV\nW+h7XHPuPu9wgq6+KxERERHxi7mvBqcBJ1mH9wIn8eTqS+n94lZOc2bxf4H36eisOvBfrjVW5TdQ\ngSoV6vN5G7jrwznsjMR44rKj6H10E78jiYiIiEipgPG4KvBPLnR/YGTsHEZEz+P88MOc6czgtsAH\ndHB+9juiVHIqUKVCFBRHuf/TBbybvYaOjdN5+ooutK6X5ncsEREREdmDVFPMLYGP6eN+weuxs3k1\nei5fhrtxujOTGwOfkuks8TuiVFIqUOWQ+2H5Zu76cC4/5xYy6JRW3HpaW0IBdekVERERiXfpZie3\nBj6ib2mh+mb0LC4NZ5FpFnNTYBynOLNxjCZUkvKjAlUOmc35xTz82UI+/HEdzWql8O6AHnRvUcvv\nWCIiIiLyG2WYQm4LfMgA9zPejZ3Mq9FzuSFyBy3NL1znfklv9zuqm51+x5RKQAWqlDvPs4zNXsMj\n/1hEYTjK4FNaM/jU1iQHXb+jiYiIiMhBSDHF/D7wBde4E5ngHcPr0bPIivbl8ejl9Ha/4xp3Im2c\ndX7HlARm4m2No8zMTJudne13DDkA9t4MJnud+Gv0Shba5nQ3C3k4+BqtnV/8jiYiIiIih8hsrxVv\nRs9kvNeDCAG6miVc6f6T89yppJpizeIr/8MYM9Nam7nHx1SgSnmYuzaPv77wEt97HWliNnFHYCwX\nOj9gjN/JRERERKQibLbpfBQ7gTGxU1huG5PKTs5xp3NR3zvp0ao2rqMLQymhAlUOmVk/b+XFb5bz\n1YKN1GQHtwQ+4nfuRJJM1O9oIiIiIuIDa2GWbcOY2Cn8I9adfFKoVz2JC45qxPmdGtK5aQ2MWjGq\nNBWoUq6stUxeupkXv1nG1BW5ZFQL0ue45vT7V0/SNTheREREREoV2SBfXzqXj39cxzeLcwjHPBpm\nJHPWEQ04u2MDujWvpZbVKkgFqpTIyjiop+fZFD6Mncio2Gkss02oTy79AxO4yp1UMr5ARERERGR3\npWNQ8wojTFy4kc/nb2DykhyKox41UoKc1LYup7avR882damZGvI5rFSEfRWomsVX9smzhpm2LWNj\nJ/FprAdFJHGUWcbfAi9xofuDuvKKiIiIyL6VNpJkAL1LbwVuEt+Yzkwq6sK3s4/ik9m/4OBxpFnB\nsc4CjnUWkuks2f/SNZqAqdJRgSr/w1pYYA9jXOw4Po314BfqkEIRF7v/4nfuJDo6q/yOKCIiIiIJ\nLNUUc547jfPcaXjWMMe25OtYZ37wOjIydi4vxy7EJUZHs4pjnQUc4ywk01ms4WRVgApUASBsXaZ7\nhzPJ68LXXhdW2wYEiNLTmcOd7ruc4WSrG6+IiIiIlDvHWDqb5XR2lnM7H7DThpjltWGq14FpXntG\nxs7h5dgFOHgcblbTyVlJR7OCI52VtIvGSAq4fr8FKUcag1qV7DIG1bOGRbYpU70OTCm95ZNCEmGO\nd+ZxujOLc9zp1DT5PgYWERERkapupw3xo9eaqd7hzLTtmOu1YDupAARdQ9v61TmycQYdS2+t66WR\nlqR2uHimMahC3s4Ic2MdmW1bMdtrRbbXjm1UB+Aws4EL3Cmc5vzI8c48qpmwz2lFREREREpUM2GO\ncxdwnLsAKBmOtsbWY65twdzjnmXeujz+MW8DY2as+fdzGqQn06peKq3rptGqXhqt6pbc6qcnaYmb\nOKcCtZKJxjzWbt3Jko07WLRhB4s2bGfR+h2s2FwA/AmAluYXTndn0cNZwLHOAhqbLf6GFhEREREp\nI2OgmdlEMzZx3jntgZJlENdu3cmC9dtZtimf5Tn5LM8p4INZ68gv/s+knmlJAZrUrFZ6S6FxjV22\na1ajZkpQBazPylSgGmPOBp4BXOBVa+1fd3s8CXgLOBrYAlxhrV1V+thdwA1ADPiDtfaLcktfBXme\nZXN+Mb/kFbF+285//1y1pZCVm/P5ObeQSKyk27YxcFitFNo3SOfiLo3p/E1fOjkryTAFPr8LERER\nEZHyY4yhaa0UmtZK4awj/rPfWsumHcUs35TPspx8VuQUsHZrIWu37mTqitz/Kl4BUkIu9dOTqZuW\nRN30pJKf1f9zq1c9idqpSdRICZIc1NjXQ2G/BaoxxgWeB84A1gIzjDHjrLULdjnsBmCrtba1MeZK\n4FHgCmNMB+BK4AigETDRGNPWWhsr7zeSqKy17IzE2FoYYWtBmG2FEXILw2wrDJNben9LQZgNeTv5\nZVsRG7cXEfX+e9xwUsChee1U2tSrzplHNKBF7VTa1E+jbf3qpO7a//67eRX87kREREREDqFd5ljZ\nEwPUL70dt9tjFtielMpaW4d1tg5rbV3WxeqwMbcmOVsyWFinG5O3F7OjeM/LKiYHHWpUC1EjJUiN\nlCA1U0q205ODpCYFSE0KkJbk7rL9n1vJPlcTPO1BWVpQuwPLrLUrAIwxY4BewK4Fai8gq3T7fWC4\nKWkb7wWMsdYWAyuNMctKf9+U8olf8eatyyMnv5hw1KM46pX+jBH+9/Zu+2IeRRGP/OIoBb/ewjEK\niqPkF0cpDMeIeXufqCqdAmqaHTQgl24ml4ZmC40CW2j467bZQg3yMXlAHrC8wv4pREREREQSljGQ\nQQEZpoAjWP2/B+wADOxMCrHZZrCJGmyyNdhqq7OVNLZ5aWwrSGNrfhp5No2lpLHNVmc7KYQJlilD\n0DWkhAIkBRySgy5JAYekoENywCUp6JAUcEku/bnrMUHXIeAagq5DsPRnwHUIuYaA49C5WQ1a1U0r\n33+wClKWArUxsGaX+2uBY/Z2jLU2aozJA2qX7p+623MbH3DaOPDYF4uZvCRnn8c4eCQRJokIIaIk\nmQip7CSNImqvxdXLAAAE10lEQVSYnTShiBRTRCpFpJmdpAaKqMkOapp8apod1GIHNUw+NcgnYLwK\nemciIiIiIrK7aiZMU5NDU/ZdA+wqbF0KqEa+TaaAahSQTIFNpoBk8m3p/dLHC8PJFIeDFNsgRYQo\nJkgxIYpskLzS+0WEKLbBf29HcYmx99bX+3sdUakL1EPOGDMAGFB6N98Ys/g3PL0OsLn8U4mUC52f\nEu90jkq80zkq8Uznp+zDVt9euc+j0KdkM17P0cP29kBZCtR1QNNd7jcp3benY9YaYwJABiWTJZXl\nuVhrXwFeKUOW/2GMyd7bGjoiftP5KfFO56jEO52jEs90fkq8S8Rz1CnDMTOANsaYFsaYECWTHo3b\n7Zhx/LtI51Lga2utLd1/pTEmyRjTAmgDTC+f6CIiIiIiIlKZ7LcFtXRM6WDgC0qWmRlprZ1vjLkf\nyLbWjgNeA94unQQpl5IiltLjxlIyoVIUGKQZfEVERERERGRPyjQG1Vo7AZiw2757dtkuAi7by3Mf\nAh46iIz7c0Bdg0UqiM5PiXc6RyXe6RyVeKbzU+Jdwp2jpqQnroiIiIiIiIi/yjIGVUREREREROSQ\nS8gC1RhzmTFmvjHGM8Zk7vbYXcaYZcaYxcaYs/zKKPIrY0yWMWadMWZ26e1cvzOJABhjzi79rFxm\njBnmdx6RXRljVhlj5pZ+bmb7nUfEGDPSGLPJGDNvl321jDFfGWOWlv6s6WdGqbr2cn4m5DVoQhao\nwDzgEmDyrjuNMR0omaDpCOBs4AVjzN5XsBWpOE9ZazuX3ibs/3CRQ6v0s/F54BygA3BV6WeoSDw5\npfRzM6GWSJBK6w1Kri93NQyYZK1tA0wqvS/ihzf43/MTEvAaNCELVGvtQmvt4j081AsYY60tttau\nBJYB3Ss2nYhIQugOLLPWrrDWhoExlHyGiojIHlhrJ1OyWsWuegFvlm6/CVxUoaFESu3l/ExICVmg\n7kNjYM0u99eW7hPx22BjzJzS7hfq/iPxQJ+XEu8s8KUxZqYxZoDfYUT2or61dn3p9gagvp9hRPYg\n4a5B47ZANcZMNMbM28NN3/BL3NnP+foi0AroDKwHnvA1rIhIYjjBWtuVkm7og4wxPf0OJLIvtmRp\nDC2PIfEkIa9By7QOqh+stacfwNPWAU13ud+kdJ/IIVXW89UYMwIYf4jjiJSFPi8lrllr15X+3GSM\n+YiSbumT9/0skQq30RjT0Fq73hjTENjkdyCRX1lrN/66nUjXoHHbgnqAxgFXGmOSjDEtgDbAdJ8z\nSRVX+gfrVxdTMsmXiN9mAG2MMS2MMSFKJpgb53MmEQCMManGmOq/bgNnos9OiU/jgD6l232AT3zM\nIvJfEvUaNG5bUPfFGHMx8BxQF/jMGDPbWnuWtXa+MWYssACIAoOstTE/s4oAjxljOlPS7WcVMNDf\nOCJgrY0aYwYDXwAuMNJaO9/nWCK/qg98ZIyBkmuV0dbaz/2NJFWdMebvwMlAHWPMWuBe4K/AWGPM\nDcBq4HL/EkpVtpfz8+REvAY1Jd3lRURERERERPxV2br4ioiIiIiISIJSgSoiIiIiIiJxQQWqiIiI\niIiIxAUVqCIiIiIiIhIXVKCKiIiIiIhIXFCBKiIiIiIiInFBBaqIiIiIiIjEBRWoIiIiIiIiEhf+\nH+a9pZbAeT50AAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 1152x576 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "fnE-N9d-jx_Z",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 812
},
"outputId": "09159ded-e9a2-40ce-a0c9-bb2e0de225f1"
},
"source": [
"n = 10000\n",
"\n",
"norm_params = np.array([[2.5, 1.],\n",
" [-3, 1.7]])\n",
"n_components = norm_params.shape[0]\n",
"\n",
"weights = np.array([1/4, 3/4])\n",
"mixture_idx = np.random.choice(len(weights), size=n, replace=True, p=weights)\n",
"\n",
"label = []\n",
"data = []\n",
"for i in mixture_idx:\n",
" data.append(stats.norm.rvs(*(norm_params[i])))\n",
" label.append(i)\n",
"\n",
"y = np.array(data, dtype=np.float64)\n",
"df = pd.DataFrame({'data': data, 'label': label})\n",
"\n",
"xs = np.linspace(y.min(), y.max(), 200)\n",
"ys = np.zeros_like(xs)\n",
"\n",
"for (l, s), w in zip(norm_params, weights):\n",
" ys += stats.norm.pdf(xs, loc=l, scale=s) * w\n",
"\n",
"plt.plot(xs, ys)\n",
"plt.hist(y, density=True, bins=\"fd\")"
],
"execution_count": 83,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"(array([0.00023973, 0.00215761, 0.00119867, 0.00647282, 0.01390458,\n",
" 0.02349395, 0.02852837, 0.05034418, 0.07791361, 0.10572278,\n",
" 0.13880609, 0.15462855, 0.17308808, 0.16182057, 0.17069074,\n",
" 0.17045101, 0.13568955, 0.11627108, 0.0848659 , 0.06089248,\n",
" 0.05226205, 0.04075481, 0.03284358, 0.04483029, 0.05993355,\n",
" 0.08678377, 0.1023665 , 0.09996916, 0.07911228, 0.06017328,\n",
" 0.03332305, 0.01486352, 0.01030857, 0.00143841, 0.0007192 ,\n",
" 0.00047947]),\n",
" array([-8.76762089e+00, -8.35049223e+00, -7.93336357e+00, -7.51623490e+00,\n",
" -7.09910624e+00, -6.68197758e+00, -6.26484891e+00, -5.84772025e+00,\n",
" -5.43059159e+00, -5.01346293e+00, -4.59633426e+00, -4.17920560e+00,\n",
" -3.76207694e+00, -3.34494827e+00, -2.92781961e+00, -2.51069095e+00,\n",
" -2.09356228e+00, -1.67643362e+00, -1.25930496e+00, -8.42176295e-01,\n",
" -4.25047632e-01, -7.91896942e-03, 4.09209694e-01, 8.26338357e-01,\n",
" 1.24346702e+00, 1.66059568e+00, 2.07772435e+00, 2.49485301e+00,\n",
" 2.91198167e+00, 3.32911033e+00, 3.74623900e+00, 4.16336766e+00,\n",
" 4.58049632e+00, 4.99762499e+00, 5.41475365e+00, 5.83188231e+00,\n",
" 6.24901098e+00]),\n",
" <a list of 36 Patch objects>)"
]
},
"metadata": {
"tags": []
},
"execution_count": 83
},
{
"output_type": "display_data",
"data": {
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NMeuNMY+d5vFBxpilxpioMWb0KY8FxpjlpR/TyhxvZ4xZVHrPN40xqZV/OQAQGzaHzfW3\nsJ/u9KerkTnqOg4kfXtoJ+06XKTJS7a5jgIAACronMXVGONLelrStZK6SBpnjOlyymlbJd0rafxp\nbnHCWtu99OPGMsf/XdLvrLUdJR2Q9MB55AeAmPR8cJ0iCvRA5D3XUVCqf8cm6pbVQM/M3qBoELqO\nAwAAKqA8I659JK231m601hZLmiDpprInWGs3W2tXSCrXTwLGGCNpmKTc0kMvS7q53KkBIIbttfWV\nGwzSSH+umplDruOglDFGDw/tqK37j+v9L3a6jgMAACqgPMU1U1J+ma8LSo+VV7oxJs8Ys9AY83U5\nbSLpoLX26+UdK3pPAIhZr0avUpFS9aDPaGusueqi5mrXtI7+MnejrLWu4wAAgHKqicWZ2lhrcyTd\nLun3xpgOFbnYGPNQafHN27NnT/UkBIAqcsKm6pXgal3p5amjt911HJzC84weHNhOnxcc0meb9ruO\nAwAAyqk8xXWbpOwyX2eVHisXa+220j83SpolqYekfZIaGmMi57qntfY5a22OtTYnIyOjvE8LAE7k\nBoN0QPX0UORd11FwBqN6ZqlxnVQ9P3ej6ygAAKCcylNcF0vqVLoKcKqk2yRNO8c1kiRjTCNjTFrp\n500l9Ze02p6cnzVT0tcrEN8j6e2KhgeAWBJYo78EI9TdrFNvs9Z1HJxBeoqvu/u10fQ1u7V+Nys+\nAwAQD85ZXEvfh/ptSR9KWiNporV2lTHmSWPMjZJkjOltjCmQNEbSs8aYVaWXXyQpzxjzuU4W1V9b\na1eXPvaopH80xqzXyfe8vlCVLwwAatpHYY622Bb6u8g7MsZ1GpzNXX3bKC3i6YV5jLoCABAPIuc+\nRbLWvifpvVOO/bzM54t1crrvqdd9KqnrGe65USdXLAaAuGet9Gz0erUxO3W1l+c6Ds6hSd00je6V\npUlLCvSPV3VWRr0015EAAMBZ1MTiTACQ8PJsZy23nfSg/558w2q18eCBAe1UEoR6dcFm11EAAMA5\nUFwBoAq8EL1WDXVEo/05rqOgnNpn1NVVFzXXKwu36Hhx9NwXAAAAZyiuAFBJ+WFTfRTmaJw/Q7VM\nses4qIBvDWqvg8dLNHVZuRfLBwAADlBcAaCSXg2ulpHVXZGPXUdBBeW0aaRLMuvrr/M36+SC9wAA\nIBZRXAGgEo7ZNE0Ihmq495lamf2u46CCjDG67/J2Wrf7qOav3+c6DgAAOAOKKwBUwpRgoA6rju6P\nfOA6Cs7T9d1aqmndVL00f5PrKAAA4AworgBwnkJr9FIwXN3MBvU061zHwXlKi/i6/bI2mrF2tzbv\nPeY6DgAAOA2KKwCcpzlhV220rXRf5AMZ4zoNKuPOy1or4hm9vGCz6ygAAOA0KK4AcJ5eCoarmQ5o\nhLfQdRRUUrP66bqua0tNyivQ0SK2xgEAINZQXAHgPKwPW2l22F13RqYr1QSu46AK3Ne/nY4WRZWb\nl+86CgAAOAXFFQDOwyvB1UpViW73P3EdBVWkW3ZD9WjdUC8v2KIwZGscAABiCcUVACroqE3XlGCA\nrvcWqqk57DoOqtB9/dtp095jmr1uj+soAACgDIorAFTQ1GCAjqq27op85DoKqtjwi1soo16aXl2w\nxXUUAABQBsUVACrAWunV4CpdYjapu9ngOg6qWGrE07je2Zq5drfy9x93HQcAAJSiuAJABSyyF+or\nm627/Y/YAidBjbustTxj9NoiRl0BAIgVFFcAqIBXo1ergY7qBn+B6yioJi0b1NJVFzXXxMX5Kixh\nxWgAAGIBxRUAymmXbagPwxyN9Weplil2HQfV6K5+bXTgeIneW7nDdRQAACCKKwCU2xvBMEUV0R1s\ngZPwLu/QRO0z6ugVFmkCACAmUFwBoBxKrK/x0Ss02Fuutt4u13FQzYwxuqtvGy3PP6iVBYdcxwEA\nIOlRXAGgHD4Kc7RbjXS3/7HrKKghI3tmqVaKr9cWMuoKAIBrFFcAKIfxwRXK1B4N8Za7joIa0qBW\nim7ukam3P9+mQ8dLXMcBACCpRVwHAIAq9USDKr/l5rC55oe/0w8jE+UbW+X3R+y6q28bvfHZVuUu\nLdADA9q5jgMAQNJixBUAzmFCMFS+Ao3xZ7uOghrWpVV9dctuqAmfbZW1/NICAABXKK4AcBbF1ldu\nMFhDvWVqYQ64jgMHbu+TrXW7j2rpVv7/AwDgCsUVAM7ik7Cn9qqBbvdnuI4CR66/tJXqpPoavyjf\ndRQAAJIWxRUAzmJ8cIVaap8Ge5+7jgJH6qRFdGP3TL27crsOnWCRJgAAXKC4AsAZ5IcZmhdeorH+\nLBZlSnK392mtwpJQ05Zvcx0FAICkRHEFgDN4MxgiI2lsZJbrKHCsa1YDXdyqvsZ/ls8iTQAAOMB2\nOABwGlHraWIwREO85co0+1zHQVWo5FZJt0Wv1M+i92vF4z3Vzdt4yr0PVereAADg7BhxBYDTmBH2\n0G410m3+TNdRECNu8uerlgo1IRjmOgoAAEmH4goAp/FGMEzNdEDDvGWuoyBG1DcndL2/UG8Hl+uo\nTXcdBwCApEJxBYBTbLNNNDvsplv9WYqY0HUcxJDb/Jk6rnT9LejnOgoAAEmF4goAp5gYHSIraSzT\nhHGKnmadOputeoPpwgAA1CiKKwCUEVijicEQDfRWKtvb6zoOYowxJ0ddV9gOWhW2cR0HAICkQXEF\ngDJmh920Q010uz/DdRTEqFv8eUpTsSYEQ11HAQAgaVBcAaCM8cEwNdVBXeEtdR0FMaqhOaYR3iK9\nFQzQcZvmOg4AAEmB4goApXbaRpoR9tQYf7ZSTOA6DmLYbZGZOqLaeje4zHUUAACSAsUVAEpNCgYr\nlMferTinPuZLtTfbmS4MAEANobgCgKTQGk2IDlV/7wu18Xa7joMYZ4w0zp+hJbazvgozXccBACDh\nUVwBQNLcsKu2KUPj/E9cR0GcGOnPVYqibI0DAEANoLgCgKQJwVA11mFd5S1xHQVxook5omu8xZoS\nDFRhCe+JBgCgOlFcASS9/baepoe9NNKfqzQTdR0HcWScP0OHVFcffLHTdRQAABIaxRVA0nsr6K8S\nRTTGn+06CuJMP2+1WptdmpiX7zoKAAAJjeIKIOlNCgbpUrNBnb0C11EQZzxjNdqfo0837FP+/uOu\n4wAAkLAorgCS2hdhG62xbRltxXkb5c+RMdLkpfziAwCA6kJxBZDUJgVDlKpi3egvcB0FcSrT7FP/\nDk2Vu6RAYWhdxwEAICFRXAEkrSIb0dvB5braW6IG5pjrOIhjo3tlqeDACS3ctM91FAAAEhLFFUDS\nmh720kHVY5owKu2ai1uoXlpEuXlMFwYAoDpQXAEkrUnBYLXUPg3wVrqOgjhXK9XX9d1a6b0vduhI\nYYnrOAAAJByKK4CktNM20pzwUo3058o3vC8RlTcmJ0uFJaHeXbHDdRQAABJOuYqrMWa4MWatMWa9\nMeax0zw+yBiz1BgTNcaMLnO8uzFmgTFmlTFmhTHm1jKP/dUYs8kYs7z0o3vVvCQAOLcpwQCF8jTa\nn+M6ChJEj+yG6pBRR5OWMF0YAICqds7iaozxJT0t6VpJXSSNM8Z0OeW0rZLulTT+lOPHJd1trb1Y\n0nBJvzfGNCzz+I+std1LP5af52sAgAqxVsoNBqu3+VLtvJ2u4yBBGGM0JidbS7Yc0IY9R13HAQAg\noZRnxLWPpPXW2o3W2mJJEyTdVPYEa+1ma+0KSeEpx7+y1q4r/Xy7pN2SMqokOQCcp6W2kzbaVizK\nhCo3skemfM8ol1FXAACqVHmKa6ak/DJfF5QeqxBjTB9JqZI2lDn8y9IpxL8zxqRV9J4AcD4mBYNV\nS4Ua4S9yHQUJpln9dA2+IENTlhYoYE9XAACqTI0szmSMaSnpVUn3WWu/HpX9iaQLJfWW1FjSo2e4\n9iFjTJ4xJm/Pnj01ERdAAjtu0/RO0FcjvEWqawpdx0ECGtMrS7sOF2nOOr5nAQBQVcpTXLdJyi7z\ndVbpsXIxxtSX9K6kf7HWLvz6uLV2hz2pSNJLOjkl+Rustc9Za3OstTkZGcwyBlA5H4S9dVS1NSbC\nNGFUjysuaq5GtVPY0xUAgCpUnuK6WFInY0w7Y0yqpNskTSvPzUvPnyrpFWtt7imPtSz900i6WdIX\nFQkOAOdjUjBYrc0uXWa+dB0FCSo14umm7pn6ePUuHTxe7DoOAAAJ4ZzF1VoblfRtSR9KWiNporV2\nlTHmSWPMjZJkjOltjCmQNEbSs8aYVaWXj5U0SNK9p9n25nVjzEpJKyU1lfSLKn1lAHCK/DBDC8KL\nNdqfI2Ncp0EiG5OTpeIg1NvLt7uOAgBAQoiU5yRr7XuS3jvl2M/LfL5YJ6cQn3rda5JeO8M9h1Uo\nKQBUUm4wSEahRrF3K6rZxa0aqEvL+pq0JF/3XN7WdRwAAOJejSzOBACuhdYoNxik/t4qZZp9ruMg\nCYzJydIX2w5rzY7DrqMAABD3KK4AksKCsIu2KUNj/FmuoyBJ3NQ9Uym+0SQWaQIAoNIorgCSwqRg\nsOrpmK7x8lxHQZJoXCdVV17UXG8t36biaHjuCwAAwBlRXAEkvCO2lj4Ie+sGf4HSTYnrOEgiY3Ky\ntP9YsWZ8udt1FAAA4hrFFUDCez/oo0KlaZQ/13UUJJlBnTLUrF6acpfku44CAEBco7gCSHiTg4Fq\nZ3aop1nnOgqSTMT3dEuPTM1au0f7jha5jgMAQNyiuAJIaPlhhhbZLhrpz2XvVjgxsmeWoqHVtM/Z\n0xUAgPNFcQWQ0KaGAyRJt/jzHCdBsurcop4ublVfk5eyujAAAOeL4gogYVkrTQkGqp+3Sllmr+s4\nSGKjep7c03XtziOuowAAEJcorgAS1lLbSZttC430WJQJbt3YvZUintGUZYy6AgBwPiiuABJWbjBI\ntVSoa/3PXEdBkmtaN01DOmforWXbFITWdRwAAOIOxRVAQiq0KXon6Kvh3mLVNYWu4wAa2TNLuw4X\naf56pq0DAFBRFFcACWl62FNHVIe9WxEzhl3YTPXTIyzSBADAeaC4AkhIk4NBaqF96uetch0FkCSl\np/i6oVsrfbhqp44UlriOAwBAXKG4Akg4u20DzQkv1S3+PPmG9xMidozsmaXCklDvf7HTdRQAAOJK\nxHUAAKhq04L+CuQzTRg154kG5Tqtp5Xamd9o8uTVGvvOL8px30OVDAYAQGJgxBVAwpkcDFA3s0Ed\nve2uowD/hzHSSH+uFtkuyg+buo4DAEDcoLgCSCirw9ZaY9tqJKOtiFE3e/MkSVPDgY6TAAAQPyiu\nABLKlGCgUhTVDf4C11GA08r29qqvt0pTgoGyvAUbAIByobgCSBjRINRbQX8N9ZapsTniOg5wRiO9\nedpsW2ip7eQ6CgAAcYHiCiBhzF23V3vVkEWZEPNG+IuUriJNDpguDABAeVBcASSM3KUFaqQjGuot\ncx0FOKu6plDDvcV6J+inQpviOg4AADGP4gogIRw6UaKPV+/Sjf6nSjWB6zjAOY305+qw6uiTsKfr\nKAAAxDyKK4CE8O6KHSqOhhrlz3EdBSiX/t4Xaq79msJ0YQAAzoniCiAhTFlaoI7N6qqr2eQ6ClAu\nvrG62Z+nWWE37bX1XccBACCmUVwBxL3Ne48pb8sBjeyZKWNcpwHKb5Q/V4F8vR1c7joKAAAxjeIK\nIO5NWbZNxki39Mh0HQWokAu8bepqNjJdGACAc6C4AohrYWg1ZWmB+ndoqpYNarmOA1TYSH+uVtl2\n+jLMdh0FAICYRXEFENfythxQwYETGtmT0VbEpxv9TxVRlFFXAADOguIKIK5NWVqg2qm+rrm4heso\nwHlpYo5oiLdcU4P+ilq+LQMAcDp8hwQQtwpLAr27YoeGX9JCddIiruMA5220P1d71EjzwktcRwEA\nICZRXAHErY9X79KRoqhG9cxyHQWolKHeMjXQUaYLAwBwBhRXAHFrytICtWyQrr7tm7iOAlRKmonq\nRv9TfRj21hHLImMAAJyK4gogLu0+Uqg56/bq5h6Z8j02b0X8G+nPVZFS9V5wmesoAADEHIorgLg0\nbfl2BaHVSPZuRYLobjaovdmuyUwXBgDgGyiuAOLSlKXbdGlWA3VqXs91FKBKGCON8ufqM3uR8sMM\n13EAAIgpFFcAcWfNjsNaveMwo61IODf782QUako4wHUUAABiCsUVQNyZumybIp7RDd1auY4CVKlM\ns0/9vNWaEgyUta7TAAAQO5cBWP4AACAASURBVCiuAOJKNAg1ddk2DencTE3qprmOA1S5kf5cbbEt\ntMRe4DoKAAAxg+IKIK7M37BPe44UaVRPpgkjMQ33FquWClmkCQCAMiKuAwBIQk80OO9LpxQ/ovrq\nrmG5l0iTo1UYCogNdU2hrvUW652grx4vCZSe4ruOBACAc4y4AogbR2wtfRjm6AZ/gdIMpRWJa6Q/\nV0dUR9PX7HIdBQCAmEBxBRA33g/6qFBpGunPdR0FqFb9vFVqqX2asnSb6ygAAMQEiiuAuDElHKC2\nZqd6mnWuowDVyjdWN/vzNPurPdpzpMh1HAAAnKO4AogLBbapFoYXa6Q/V8a4TgNUv1H+XAWh1dvL\nGXUFAIDiCiAuvBX0lyTd4s1znASoGR297eqW1UCTmS4MAADFFUDss1aaEgxUH7NG2d4e13GAGjOy\nZ5bW7Dis1dsPu44CAIBTFFcAMW+57aCNtpVGsSgTkswN3VopxTeauqzAdRQAAJxiH1cAMW9KMFBp\nKta1/iLXUYAa1bhOqoZ2bqapy7br0eEXKuLz+2bEuUrs4332+x6qnvsCiBl8BwQQ04psRH8L+ulq\nL0/1zQnXcYAaN7JnlvYeLdLcdXtdRwEAwJlyFVdjzHBjzFpjzHpjzGOneXyQMWapMSZqjBl9ymP3\nGGPWlX7cU+Z4L2PMytJ7/tEY1gkF8E0zw+46qHrs3YqkNezCZmpUO0W5S5kuDABIXuecKmyM8SU9\nLekqSQWSFhtjpllrV5c5baukeyX90ynXNpb0uKQcSVbSktJrD0j6b0nfkrRI0nuShkt6v7IvCEBi\nmRIMVFMd1EBvpesogBOpEU83dc/U+M+26tDxEjWoneI6EuDMIVtHeeEF+tK21pqwtb602Tpqa6n1\nMwvUuklttW5cW5dk1tfgC5rJ9xgTARJJed7j2kfSemvtRkkyxkyQdJOk/ymu1trNpY+Fp1x7jaSP\nrbX7Sx//WNJwY8wsSfWttQtLj78i6WZRXAGUsd/W08ywh+7xP1TkG/+8AMljVM8s/fXTzfrbiu26\ns28b13GAGrfX1tfz0RF6Nbhax5UuSco2u3Wh2ap65rgK1Elz1+3RrsNFkqQ2TWrrwQHtNLpXtmql\n+i6jA6gi5SmumZLyy3xdIOmyct7/dNdmln4UnOb4NxhjHpL0kCS1bt26nE8LIBG8E/RViSJME0bS\nuySzvi5oXleTlxZQXJFU9tj6ejZ6g14LrlSRUnS9t1B3RKari9nyf9c9+Pt/lySdKA40c+1uPTtn\no3729ir95uOvdN/l7fQPQzooNcLSLkA8i/lVha21z0l6TpJycnKs4zgAatDkYKAuNFvUxdvqOgrg\nlDFGo3pm6Vfvf6kNe46qQ0Zd15GAajcvuETfKfmODqmObvbm6+HI2+robT/9yaWrFdeSNELStVbK\nS+2s5wqv0++ml2j2J+/oqdQ/qpXZX/EgrFgMxITy/Oppm6TsMl9nlR4rjzNdu6308/O5J4AksD5s\npc9tR/ZuBUrd0iNTnpGmsEgTEpy10jPR63V3yWPKMAf1UeqP9dvU/z5zaT0NY6Te3lo9n/pbPZ3y\nB6212bqu6FeaFVxajckBVKfyFNfFkjoZY9oZY1Il3SZpWjnv/6Gkq40xjYwxjSRdLelDa+0OSYeN\nMX1LVxO+W9Lb55EfQIKaGgyQp1A3+Z+6jgLEhGb10zWwU4amLt2mMGQCEhLTMZumb5d8V7+O3q5r\nvc80NfXnFSqsp3Odv0h/S/0XNTcHdF/Jj/XbklGy/BUC4s45i6u1Nirp2zpZQtdImmitXWWMedIY\nc6MkGWN6G2MKJI2R9KwxZlXptfsl/T+dLL+LJT359UJNkh6W9BdJ6yVtEAszASgVWqOpwQAN9Fao\nmTnoOg4QM0b1ytL2Q4VasHGf6yhAlTto62h08eN6P+yjn0TG66mUP6qOKaqSe7f3dmpq6s81yp+r\nPwaj9G/R2ymvQJwp13tcrbXv6eSWNWWP/bzM54v1f6f+lj3vRUkvnuZ4nqRLKhIWQHJYGF6k7Wqq\nR/03XEcBYsrVXZqrXnpEuUsK1L9jU9dxgCpz3KbpvuIfa4PN1Asp/6mh/udV/hy1TLH+M/Ks6qhQ\nzwfXq745ru9E3qry5wFQPVheDUDMmRIOVF0d19XeEtdRgJiSnuLr+ktb6YMvdupoUdR1HKBKFNmI\n/q7kB/rcdtAfU56qltL6NWOkxyOvaKQ3R7+JjtVL0Wuq7bkAVC2KK4CYctym6f2gj0b4i1TLFLuO\nA8Sc0b0ydaIk0Hsrd7iOAlRaYI2+X/KI5oaX6teR5zXcX1ztz+kZq/9IeU5Xe4v1r9F7NCk6qNqf\nE0DlUVwBxJSPwhwdUy32bgXOoGfrRmrXtI4mL2F1YcQ3a6WfRh/Q++Fl+mnkVY2NzK6x546YUH9K\n+ZMGeCv1aPQhfRp0qbHnBnB+KK4AYsrkYKAytUd9zFrXUYCYZIzRyB6ZWrRpv/L3H3cdBzhvbwZD\n9EYwTA/7b+vBSM2v0Zlmono25bdqa3bqeyWPaK+tX+MZAJQfxRVAzNhpG2l+eIlG+vPkGZZ7BM7k\nlp6ZkqQpS9kCHfFpTZitx6P3aqC3Qv8UmegsRx1TpKdT/qBDqqMflDys0BpnWQCcHcUVQMx4O+iv\nUJ5uYZowcFZZjWqrX/smmry0QJY9PRBnjtk0PVLyPTXQMf0u5c/Of1F5kZevxyOvaG54qZ4Jrnea\nBcCZUVwBxARrT04T7mHWqb2303UcIOaN6pWlrfuPa/HmA66jAOVmrfTTkvu12bbQH1KeUlNz2HUk\nSdLt/gxd5y3Qb6JjlRde4DoOgNOguAKICatsG31ls1mUCSinay9podqpPos0Ia5MDIZoajhQ349M\nVj9/jes4/8MY6Vcpf1Gm2avvFH9HB20d15EAnILiCiAmTAkGKkVR3eAvcB0FiAt10iK69pKWenfl\nDp0oDlzHAc5py75jejx6jwZ4K/WI/5brON9Q35zQUyl/1G411K+j41zHAXAKiisA50qsr2lBf13h\nLVVDc8x1HCBujOqVqaNFUX20mun1iG3WWv3z1JVKUaD/SnlGfowuwHept0kP+O9rQjCMKcNAjKG4\nAnBubthVe9WAacJABfVt10SZDWspl+nCiHG5Swo0f/0+PRp5Qy1MbL8v+/uRycrUHv1Lyf0qsb7r\nOABKUVwBOJcbDFZjHdYQb7nrKEBc8TyjkT0zNW/9Xu04dMJ1HOC09h4t0i/fW6PebRvpdn+G6zjn\nVNsU6YmUl7XWttZfghGu4wAoRXEF4NQBW1fTw5662Z+nVMP79ICKGt0rS9aypyti15N/W63jRYF+\nNbKr861vyusqf6mu9hbrD9GRyt9/3HUcAKK4AnBsWnC5ipWi0f4c11GAuNSmSR31addYk/Ly2dMV\nMWfm2t2a9vl2PTy0gzo2q+c6ToU8kfKyfIX6+dtf8HcLiAEUVwBO5QaD1MVsVhdvq+soQNwam5Ot\nzfvY0xWx5XhxVD+d+oU6NqurfxjSwXWcCmtl9usHkVzNXLtHH63e5ToOkPQorgCc+TLM1krbXmP8\n2a6jAHFtRNcWqpPqa2JevusowP94fs4mbTt4Qv92S1elReJzkaN7/Q/VsVld/ccHXyoahK7jAEmN\n4grAmdxgkFIU1U3+p66jAHGtdmpEN3RrpXdX7NDRoqjrOIB2HS7UM7M36LquLdWnXWPXcc5bxIT6\n8TWdtWHPMU1i9W7AKYorACdKrK+3ggG6wluqxuaI6zhA3BuTk60TJYHeXbHddRRA//XhWgWh1aPD\nL3QdpdKu6tJcvdo00u8+/krHi/nFEOAKxRWAE7PCbtqrBizKBFSRnq0bqkNGHU3MY1QIbn2x7ZBy\nlxbovv5t1bpJbddxKs0Yo59ce6F2HynSS/M3u44DJC2KKwAncoNBaqpDGux97joKkBCMMRqTk60l\nWw5ow56jruMgSVlr9Yt3V6tR7VQ9PLSj6zhVJqdtY13VpbmembVB+48Vu44DJCWKK4Aat8/W0ydh\nT93iz1UKe7cCVWZkj0z5ntEkRl3hyMerd2nhxv36wZWd1KBWius4VerH13TWseKonpqx3nUUIClR\nXAHUuLeD/ooqwjRhoIo1q5+uoZ0zNHlpASugosYVR0P96v0v1bFZXY3r09p1nCrXqXk9jemVrVcX\nblb+/uOu4wBJh+IKoMblBoN0qdmgzh6jQkBVG5OTrT1HijT7qz2uoyDJTMzL16a9x/STay9UxE/M\nHzF/cNUFMsYw6go4kJj/qgCIWau2H9Jq25bRVqCaDLuwmZrWTWVPV9SowpJAT81Yr56tG2rYhc1c\nx6k2LRqka1zvbE1eWqBtB0+4jgMkFYorgBqVu6RAqSrRjezdClSLFN/Tzd0z9cma3dp3tMh1HCSJ\nNz7bqp2HC/XDqzvLGOM6TrV6aHAHGSM9O3uD6yhAUqG4AqgxxdFQby/frqu8JWpojrmOAySsMTnZ\nioZWU5dtcx0FSeBEcaCnZ25Q3/aNdXmHJq7jVLvMhrU0qmeWJizO1+7Dha7jAEkj4joAgOQx48vd\n2n+sWKNTmCYMVKfOLeqpW3ZDTczL1wMD2iX8CBiq2BMNKnT6K9HrtTd6u/67+J9l/nVtNYWKLf8w\npIMmLSnQc3M26qfXd3EdB0gKjLgCqDG5SwrUrF6aBnorXEcBEt7YnCx9teuoVhQcch0FCeyoTdcz\n0Rs00Fuh3l5ylFZJatOkjm7q1kqvL9rKlHyghlBcAdSIPUeKNHPtbt3SM1MRwzYdQHW7oVsrpUU8\nFmlCtfprcI0OqJ5+GJnkOkqNe3hoBxVGA704f5PrKEBSoLgCqBFvL9+mILQa0yvLdRQgKdRPT9GI\nri017fPtKiwJXMdBAjpka+u56PW60lui7l7yLVTUsVk9jbikpV7+dIsOHS9xHQdIeLzHFUC1s9Zq\nUl6Bumc3VMdm9VzHAeJHBd9reKoxQRdNLfmpPnzyet106kreTzCFGJXzSnC1DquOvh/JdR3FmW8P\n66h3V+7QKws26ztXdHIdB0hojLgCqHZfbDustbuOaDSjrUCN6uutUZbZrYnBENdRkGCO2TS9GL1W\nV3hLdYm3xXUcZy5qWV9DOmfo5QVbmNkAVDOKK4BqNzEvX6kRTzdc2sp1FCCpeMZqjD9b88NLlB82\ndR0HCeSNYJgOqJ4ejrztOopzDw5or71HizTt8+2uowAJjeIKoFoVlgR6a/k2jbikhRrUTnEdB0g6\no/05Mgo1iVFXVJEiG9Hz0evU11ulXt4613Gc69+xiS5sUU8vzN0ka63rOEDCorgCqFbvf7FDRwqj\nurV3a9dRgKSUafZpsLdCbwZDFLV820flTQ4GaZca69s+o62SZIzRgwPba+2uI5q7bq/rOEDC4jsY\ngGo14bN8tWlSW33bN3YdBUhat/ufaJcaa0bYw3UUxLmo9fRMcIO6mQ3q733hOk7MuKFbS2XUS9Nf\n5rE1DlBdKK4Aqs3GPUe1aNN+jc3JljHGdRwgaQ3zlqmZDuiNYJjrKIhz74T9tNU21yORt8Q/6/8r\nLeLrnn5tNOerPVq784jrOEBCorgCqDYT8wrke4bVhAHHIibUrf4szQq7aZtt4joO4lRojZ6O3qQL\nTL6u9Ja6jhNz7risjdJTPL0wb6PrKEBCorgCqBYlQajJSws0tHMzNa+f7joOkPRujcyUJL0ZHeo4\nCeLV9LCn1tksPRJ5W55hEaJTNaqTqtG9svTWsu3ac6TIdRwg4VBcAVSLmV/u1p4jRbqtd7brKAAk\nZZm9LNKESnk2er2yzG5d5y10HSVm3d+/nYqDUK8uTN69bYHqwncuANXizcX5alYvTUM6Z7iOAqDU\nOH+GdqmxZobdXUdBnFkSdtIS21kP+O8rYkLXcWJW+4y6Gto5Q+MXbVVxlP9OQFWiuAKocjsPFWrm\n2t0a3StLEZ9/ZoBYcYW3lEWacF6ei16nBjqqsf4s11Fi3t2Xt9Xeo0X6YNVO11GAhMJPlACqXO6S\nfIVWGpvDNGEglvzvIk3dte3gCddxECc2hi30UZiju/yPVcfw3s1zGdwpQ22a1NYrn252HQVIKBRX\nAFUqDK0m5hWoX/smatu0jus4AE4x1p8pq5PT+YHyeCEYoRQFuifyoesoccHzjO68rI3ythzQ6u2H\nXccBEkbEdQAAiWXhxn3auv+4fnj1Ba6jADiNbG+vBnkrNHFxbX13WEem8+Os9tr6yg0GaaQ/Vxkm\nSUvYEw0qfMkYW0e/0VN69el/1a9S/nKG+x6qZDAgufDdCkCVmrA4X/XTI7rm4hauowA4g9v9Gdp5\nuFCz1u5xHQUx7pXoVSpSqh7033MdJa40NMd0k/+p3gou1yFb23UcICEw4grgzCr4W+YDtq4+KHpa\n4/wZSv/l2GoKBaCyhnnL1KxemsZ/tlVXdmnuOg5i1AmbqleDq3Wll6eO3nbXceLOXf5HejMYqtxg\nkB6IfOA6DhD3GHEFUGXeCvqrWCm61Z/pOgqAs0gxgcbmZGvW2t0s0oQzyg0G6YDq6aHIu66jxKVL\nvC3qab7Sq8HVCq1xHQeIexRXAFXCWunNYKguNRvUxdvqOg6Ac7i1d7aspIks0oTTCK3RS8FwdTMb\n1NusdR0nbt0T+UibbQvNDbu6jgLEPYorgCqxwrbXl7Y1o61AnMhuXFuDOmXozcX5igah6ziIMbPD\nbtpoW+n+yHsyDBaet2u9RWqqQ3o1uNJ1FCDulau4GmOGG2PWGmPWG2MeO83jacaYN0sfX2SMaVt6\n/A5jzPIyH6ExpnvpY7NK7/n1Y82q8oUBqFkTgqFKV5Fu8Be4jgKgnMb1ac0iTTitF4Jr1UL7NML7\nzHWUuJZqAo3xZ2lm2EM7bSPXcYC4ds7iaozxJT0t6VpJXSSNM8Z0OeW0ByQdsNZ2lPQ7Sf8uSdba\n16213a213SXdJWmTtXZ5mevu+Ppxa+3uKng9ABw4ZtM0Lbhc13kLVd/wfjkgXlxxUTM1q5emNz5j\nej/+19owS/PCrro78pFSTOA6Tty7zZ+pQL4mBkNcRwHiWnlGXPtIWm+t3WitLZY0QdJNp5xzk6SX\nSz/PlXSFMd+YWDKu9FoACebdoK+OqZZui8xyHQVABaT4nsbmZGvm2t3aziJNKPVicK3SVaTb/Rmu\noySENt5uDfRW6M3oEAUs0gSct/IU10xJZVduKCg9dtpzrLVRSYckNTnlnFslvXHKsZdKpwn/7DRF\nV5JkjHnIGJNnjMnbs4epTEAseiMYpvZmu3JYwAOIO18v0jSBRZogad/RIk0N+muUP1cNzTHXcRLG\nOH+GtilDc8JurqMAcatGFmcyxlwm6bi19osyh++w1naVNLD0467TXWutfc5am2OtzcnIyKiBtAAq\nYlXYRstsJ93hT2cBDyAOZTeurSEXZOiNz7aqOMoiTcnu9UVbVaxU3eez72hVutJboqY6pPHBMNdR\ngLhVnuK6TVJ2ma+zSo+d9hxjTERSA0n7yjx+m04ZbbXWbiv984ik8To5JRlAnHk9uEJpKtZof67r\nKADO09392mrPkSJ9uGqn6yhwqCga6JUFWzTEW66O3nbXcRLK14s0zWCRJuC8lae4LpbUyRjTzhiT\nqpMldNop50yTdE/p56MlzbDWWkkyxniSxqrM+1uNMRFjTNPSz1MkXS/pCwGIK0dsLb0VDNAN/gI1\nYEoZELcGX5Ch1o1r69UFW1xHgUPvfL5De48W6X7/fddREhKLNAGVc87iWvqe1W9L+lDSGkkTrbWr\njDFPGmNuLD3tBUlNjDHrJf2jpLJb5gySlG+t3VjmWJqkD40xKyQt18kR2+cr/WoA1Ki3gv46rnTd\n6U93HQVAJXie0Z19W+uzzfv15c7DruPAAWutXpi3SZ2a1dVAb6XrOAmpjbdbA7yVLNIEnKdyvcfV\nWvuetfYCa20Ha+0vS4/93Fo7rfTzQmvtGGttR2ttn7Il1Vo7y1rb95T7HbPW9rLWXmqtvdha+z1r\nLeutA3HEWun14EpdYjapm9ngOg6AShqbk620iKdXGHVNSos27dfqHYd1/4B2rFdQjW73P2GRJuA8\n1cjiTAASzxJ7gb60rXWn/zE/5AAJoGHtVN3YrZXeWrZNhwtLXMdBDXth3iY1qp2iW3qcunEEqhKL\nNAHnj+IK4Ly8Fr1S9XRcN/oLXEcBUEXu7tdWx4sDTV5S4DoKatCWfcc0fc0u3XFZG6Wn+K7jJLRU\nE2iUP1szwh7afaTQdRwgrlBcAVTYPltP74WXaaQ/V7VNkes4AKpI16wG6p7dUK8u3KLSNRaRBF6a\nv1kRz+iufm1cR0kKY/w5CuTrrWWnbtIB4GworgAqLDcYrGKl6A4WZQISzt392mjjnmOav37fuU9G\n3DtcWKJJefm6/tJWal4/3XWcpNDR265eZq3eXJzPL4iACqC4AqiQ0BqND4apj1mjCzx+WwwkmhFd\nW6pxnVS9vGCz6yioARMX5+tYcaD7+7dzHSWpjPVna8OeY1q69aDrKEDcoLgCqJC5YVdtsS10R4TR\nViARpaf4ur1Pa01fs0tb9x13HQfVKBqEemn+ZvVp21hdsxq4jpNUrvMXqnaqr0l5+a6jAHGD4gqg\nQl4PrlATHdJwb7HrKACqyV392sg3hlHXBPfx6l3advCE7h/AaGtNq2sKdV3Xlvrb59t1vDjqOg4Q\nFyiuAMpth22s6WEvjfVnKc3wjRZIVM3rp2tE15aauDhfR4v4u56oXpi3SVmNaumqLs1dR0lKY3tn\n61hxoHdX7HAdBYgLFFcA5fZGdKispNv9Ga6jAKhm9/VvqyNFUbbGSVCf5x9U3pYDuq9/O/kem3G7\nkNOmkdo3raNJefwdA8qD4gqgXEqsrwnBMA32Vijb2+M6DoBq1qN1I3XPbqi/frpZYcjKp4nmxfmb\nVDctorE5Wa6jJC1jjMbkZOuzzfu1cc9R13GAmEdxBVAun4Q9tVuNdCdb4ABJ477+bbVp7zHN/opf\nViWSnYcK9e6KHbq1d7bqpae4jpPURvXMlO8Z5TKzATgniiuAcnktuFKttFdDvWWuowCoISO6tlTz\n+ml6cf4m11FQhV5esFmhtbr38rauoyS9ZvXTNeSCDOUuKVA0CF3HAWIaxRXAOW0KW2he2FXjIjPk\nG6YMAskixfd0V982mrtur9bvPuI6DqrA8eKoxi/aqqu7tFB249qu40DSmJxs7T5SpDnrmNkAnA3F\nFcA5jQ+GKaKobvVnuo4CoIaN69NaqRFPL87f7DoKqsDkpdt06ESJHhjIFjix4oqLmqlp3VRNXMx0\nYeBsKK4AzuqETdXEYIiu8fLUzBxyHQdADWtSN00je2Rq8pIC7Tta5DoOKiEMrV6at0mXZjVQTptG\nruOgVIrv6ZYemZq+Zhd/x4CzoLgCOKu3gv46pLq6J/Kh6ygAHHlwYDsVRUO9tnCr6yiohFlf7f7/\n7d13mFTV/cfx93fKFmBZet2lShFpAiJgF3tUbCAm0WDvUaNJNEZDNGpULFFjiyWJXVERKxaKCIKA\ngoCA9N6XspTdnXJ+f+yYHyLIArt7ZnY+r+eZZ+/cuffuZ7js7nzvOfccFqzbysWHt8RMU+Akk/49\n8onGHW9/s9x3FJGkpcJVRHbLOfhP7EQOtEUcYnN8xxERTw5okMOx7Rvw3y8XURSJ+Y4j++i5LxbR\nqGYWp3Rq7DuK7KRtwxy65tfitUlLcU5jSYjsigpXEdmtCfEDme2acWFwBLo4L5LeLjmiJeu3lqhF\nKEXNXrWZL+at44I+zQkH9fEvGZ17SD5z12xh2jLdliOyK/rNJSK79Z/YidSmkNOD431HERHPereq\nS8emNfnX2AXE42oRSjXPfbGQ7HCQX/Zs5juK7MapnRuTFQ7w2qSlvqOIJCUVriKyS8s3bufjeA/O\nDY4iyyK+44iIZ2bGpUe0YsHarYyas8Z3HNkL67YUM2zqCs7u3pRa1TJ8x5HdyMkKc0qnxrw7bQXb\nS9QlX2RnKlxFZJde+HIxAOeHPvGcRESSxSmdGtMkN4unP1/gO4rshRcnLKYkGufCwzQFTrIb0COf\nLcVRPpyx0ncUkaSjwlVEfqIoEuPVSUs4ITCZprbedxwRSRLhYICLDm/JxIUFTFu60XccKYOiSIwX\nJyzm2PYNaF2/hu84sgeHtqxDi7rV1F1YZBdUuIrIT7wzdTkbt0UYFPrIdxQRSTLnHpJPTmaIp8eq\n1TUVDJ+2gnVbSrj4cLW2pgIzo3+PfCYuLGDx+q2+44gkFRWuIvIjzjn+PX4x7RvlcKjN9h1HRJJM\nTlaYX/ZqxofTV7JonT5YJzPnHM99sZD2jXLo07qu7zhSRmd1a0rAYOiUZb6jiCQVFa4i8iNfLljP\nrJWbGdSnhabAEZFduvjwloSCAZ76fL7vKPIzxs9fz+xVhVx0WEtMv9BTRuPcbI5oU5+hU5YR0wje\nIv+jwlVEfuS5LxZSt3oGZxzc1HcUEUlSDXKyGNAjj6FTlrFqU5HvOLIbz36xkHo1Mji9axPfUWQv\nDeiRz8pNRYybt853FJGkocJVRP5n4bqtfDZ7Db/q1ZyscNB3HBFJYpcf2Zq4g2d0r2tS+n51ISNn\nr+H8Xi30+zwFHdehAbWqhXl9sgZpEvlByHcAEUkez49bSDgQ4PxezX1HEZGKNjh3v3bPB07jKl7+\nYjtXTzqe2rYlcdxN+59N9tvTny8gOxzkgt76fZ6KMkNBzujalJcnLmHjthLNvyuCWlxFJGHTtghv\nTF7G6V2bUD8n03ccEUkBV4aGs40s/hM7wXcU2cGqTUW8M3U55x6ST+3qKnhSVf8eeZTE4gyftsJ3\nFJGkoBZXEQHg5a+WsD0S4yJNUC8iZdQusIzjApN5PnoSlwbfp7oV+44klPaeicWdpsBJdnvo9XAQ\n0MHu5vXhC7lgxK17eWz1fJCqR4WriBCJxfnP+EX0aV2XDk1q+o4jIinkqtBwzirpwSuxvlwS+sB3\nnPSxm6Jns8vm5eJHFGBnGQAAIABJREFU+UVgKvmP/LKSQ0l5GxAczeDoIL6LN6NDYInvOCJeqauw\niPDB9JWs2lykq/Miste6BebROzCTp6O/oMiFfcdJe6/E+lJINS4Pvec7ipSDfsHxZBDhjdhRvqOI\neKfCVSTN/TBBfat61TmmXQPfcUQkBf02+BZrqM0rsWN9R0lrJS7Ic9GTOCwwg46BRb7jSDmobVs4\nPjCFYbHDKXEaHVrSmwpXkTT31cICpi3bxIWHtyQQ0AT1IrL3egdn0Sswkyeip1MUifmOk7beiR3G\naupwWVCtrVVJ/+BoNpDDZ/FuvqOIeKXCVSTNPf35AupUz6B/9zzfUUQkhV33Q6vrV7oPz4e4M56K\nnUp7W8yRgW99x5FydERgOo1Yz+uxo31HEfFKhatIGpu7upDPZq/hgt7NNUG9iOyXH1pdHx89X62u\nHnwc78E8l8eVoeGYOs9UKUFznB0cy5h4F1a52r7jiHijwlUkjT39+QKywgEu6N3CdxQRqQKuC77F\n2sJiXp6oVtfK5Bw8Fj2DFraKUwMTfMeRCtA/OIY4Ad6KHe47iog3KlxF0tTqzUUMm7qc/t3zqaMJ\n6kWkHPQOzqJXqzo8MUatrpVpTLwzM1xLrgq+Q9Cc7zhSAVoEVtPTZvFG7GicTrGkKRWuImnq+XGL\niMUdlxyhKXBEpPxc17etWl0rUWlr65k0YR1nBL/wHUcqUP/gGBa6xkx27XxHEfFChatIGtpSHOWl\niYs5uWNjmtet7juOiFQhvVvXpVerOjw+ej7bSqK+41R5E117Jrt2XB56jwxTK3dVdkpwItXZzhux\nI31HEfFChatIGnr1qyUUFkW57MhWvqOISBX0+xPbsW5LMc+PW+Q7SpX3z+gZ1GMj5wZH+Y4iFay6\nFXNqcALvxXqz1WX6jiNS6VS4iqSZkmicZ79YyKEt69Alv5bvOCJSBXVvXofjDmzIk6Pns2Frie84\nVda0eCvGxjtzSegDsiziO45Ugv7BMWwji/djvXxHEal0KlxF0sw7U5ezclMRVxzV2ncUEanCfn9i\nO7aURHlizHzfUaqsx6JnkMsWfh381HcUqSTd7Xta2QqGqruwpCEVriJpJBZ3PDFmPh0a1+TodvV9\nxxGRKqxdoxzOPLgp/x6/iJWbtvuOU+XMiLfgk3gPLgx9RA0r8h1HKolZaavrV+5AFsQb+Y4jUqlU\nuIqkkREzV7Fg7VauOqY1phnqRaSC3XBcW3Dwj0/n+o5S5TwYPYdctnBR8EPfUaSSnRUcS4A4Q2NH\n+Y4iUqlUuIqkCecc/xw1j5b1qnNyx8a+44hIGsivU41f9WrG65OXMm/NFt9xqoyvl2xgZLwbl4Xe\np6apNTvdNLSNHB2YypuxI4g5XYSW9KHCVSRNjPl+LTNXbObKo1oTDOgPnYhUjquPOYDscJAHPp7j\nO0qV8dAn31OHzQwKfuQ7ingyIDiG1dTh83hn31FEKo0KV5E08fio+TTOzeKMg5v6jiIiaaRejUwu\nPbIVH85YxeRFBb7jpLxJiwoYO3cdV4TepboV+44jnhwb+Jo6bOaN2NG+o4hUmpDvACJS8SYtKuCr\nRQX85bQOZIR0vUpEKtDg3J+susxl8ipD+OtTL/FOxm0EzO3jsTftZ7jU98DHc6ifk8n5JZ/4jiIe\nZViMM4Jf8ELsBApcDnWs0HckkQpXpk+wZnaSmc0xs3lmdvMuXs80s9cSr080sxaJ9S3MbLuZTU08\nntxhn+5mNj2xzyOmkWJEKszjo+ZRp3oGAw9p5juKiKShalbMH8OvMt214q344b7jpKzx89YxYUEB\nVx3dmmzT/LjpbkBwDBFCvBPr4zuKSKXYY+FqZkHgn8DJQAfgPDPrsNNmFwMbnHMHAA8B9+7w2nzn\nXNfE44od1j8BXAq0STxO2ve3ISK7M2P5JkbNWcuFfVqQnRH0HUdE0lS/wHi62lzuiwxkq8v0HSfl\nOOd44JPvaVQzi/N66iKkQPvAUjrZAl7X6MKSJsrS4toTmOecW+CcKwFeBfrttE0/4D+J5aFA359r\nQTWzxkBN59wE55wD/gucsdfpRWSP/vHZXGpmhfjNYS18RxGRNBYwx+3hF1hDbZ6Inu47Tsr5+LvV\nTFm8gWv7HkBWWBchpdSA4GhmuRbMiDf3HUWkwpXlHtemwNIdni8DDt3dNs65qJltAuomXmtpZt8A\nm4E/O+fGJrZfttMxNWKMyL7Yxf1kP5gZb84nJfdwfWgoNf8+oBJDiYj8VLfAPPoFxvF07BcMDI0i\nz9b5jpQSIrE49344m9b1q3Nuj3zfcSSJnB78kjujv+aN2NF0DPxnzzuIpLCKHqVlJdDMOXcw8Dvg\nZTOruTcHMLPLzGyymU1eu3ZthYQUqaoeiZ5JDlu5UFMmiEiS+GP4FQI47omc5ztKynjlqyUsWLeV\nW04+kFBQA+zJ/8u1rZwYmMyw2GEUubDvOCIVqiy//ZYDO17ey0us2+U2ZhYCcoH1zrli59x6AOfc\nFGA+0Daxfd4ejkliv6edcz2ccz3q169fhrgiAjArns+IeE8uDH5Erm3zHUdEBIAmVsDlwfd4P96b\ncbGDfMdJepuLIjz86Vx6tapD3wMb+I4jSejc4Gg2UYMR8R6+o4hUqLIUrpOANmbW0swygIHA8J22\nGQ78JrF8DjDSOefMrH5icCfMrBWlgzAtcM6tBDabWa/EvbAXAO+Uw/sRkYRHomeRwzYuDqm1VUSS\ny5Wh4TS3Vfw5epFaifbgydHzKdhawq2ndEATMMiu9AnMJN/W8ErsWN9RRCrUHgtX51wUuAYYAcwC\nXnfOzTSzO8zsh9EVngXqmtk8SrsE/zBlzpHAt2Y2ldJBm65wzv0w+/hVwDPAPEpbYj8sp/ckkvZm\nx/P5MH4og4IjyLWtvuOIiPxIlkW4M/Q8C11jnoyd5jtO0lqxcTvPfrGQM7o2oVPe7sczkPQWMMfA\n4CgmxA9iYbyR7zgiFaYsgzPhnPsA+GCndbfvsFwE9N/Ffm8Cb+7mmJOBjnsTVkTK5tHomdRgGxeH\nPtjzxiIiHhwZnM5psfE8Hu3H6YHxtAqs8h0p6Qz5eA4OuOnEdr6jSJLrHxzDg9FzeDV2NLcEXvUd\nR6RC6A5/kSpmTjyPD+I9GRQcQS21topIErst/AKZlPDn6EU45ztNcvlmyQbe/mY5Fx7Wgrza1XzH\nkSTXwDbSN/A1Q2NHUeI0XZJUTSpcRaqYB6PnUIMiLlFrq4gkuQa2iT+EXmN8vCPD4of5jpM0YnHH\nn4fNoEFOJtce28Z3HEkR5wVHsp5cPo139x1FpEKocBWpQr6Nt2REvCeXhN5Xa6uIpIRfBT+jq83l\nb5FfU+ByfMdJCi9OWMzMFZu5/dSDqJFZpru6RDgy8C1NWatBmqTKUuEqUoUMiQ6gNoVcpHlbRSRF\nBMxxT/gZNlOd2yKDfMfxbk1hEUNGzOGINvU4pZMG2pGyC5pjQGg0Y+OdWVqgafCk6lHhKlJFfBVv\nx+fxLlwRepcc2+47johImR0YWMr1oTd5P96b4bHevuN4dff7syiOxrmjX0dNfyN7bUBwDAHivDpp\nie8oIuVOhatIFeAcDIkMoD4buCD4se84IiJ77fLguxxsc7ktciGrXS3fcbwYP38dw6au4IqjWtGy\nXnXfcSQFNbYCjglM5Y3Jy4jE4r7jiJQrFa4iVcDYeCe+cgdybWgY2VbiO46IyF4LWZwHwk9QTJg/\nRi5Lu1GGi6Mxbhs2g/w62Vx1zAG+40gKOy84kjWFxXw2a43vKCLlSnf8i6Q450rvbW3KWgYGR/qO\nIyKyz1oFVnFz6BUGRwfxWuxoBoZG+460/wbnlmmzf0TOZX6sH8+H7yXrrmkVHEqqsmMC39AkN4uX\nJi7mpI66T1qqDrW4iqS4EfFD+Na15rrQW2RYzHccEZH9ckHwE3oHZnJn9HwWxRv6jlMppsTb8GTs\nNM4NjuKYoIpW2T9Bc5zXsxlj565j4TrNMCBVhwpXkRQWicW5L3ouB9gyzgqO9R1HRGS/BcwxJPwk\nIWJcFbmOIhf2HalCbXOZ3Bi5ksas58+hF33HkSri3J75hALGSxMW+44iUm5UuIqksNcmLWWBa8If\nQ68SMg3CICJVQ1Nbz0Phx/nOteCv0d/4jlOh7omexyLXiCHhJzUivJSbBjlZnHhQI96YsoyiiHpj\nSdWgwlUkRW0tjvLwp3M5xGZzXOBr33FERMrVscGpXBV8h1dix/Jm7AjfcSrE2FhHXoidwEXBD+gd\nnOU7jlQxv+rVjE3bI7z37UrfUUTKhQpXkRT1zNiFrNtSzM3hV9BUfyJSFf0u9AaH2nfcGrmIOfE8\n33HK1UZXnd9HLqe1LecPodd8x5EqqHerurSuX50X1V1YqggVriIpaN2WYp7+fD4nd2xE98Bc33FE\nRCpEyOI8mvEoOWzjysj1FBZFfEcqFzFn/DZyDevJ5aHw42RZ1XhfklzMjF8d2pypSzcyY/km33FE\n9psKV5EU9MhncymKxvn9ie18RxERqVANbBOPZjzKYteQa17+hkgs9e/nfyh6Dp/HuzA49G86Bxb6\njiNV2Nnd88gKB3hpolpdJfWpcBVJMQvXbeXliUs4r2c+rerX8B1HRKTC9QrM5q7Qs4z5fi23vzMD\n55zvSPtsRKwHj8XOZEBwFL/U3NtSwXKzw/Tr0pRh36xgcxXpsSDpS4WrSIq5+4NZZIYC/LZvG99R\nREQqzcDQaK4+pjWvfLWUx0fP9x1nn8yPN+bGyBV0sfncEfq3xieQSnF+7+Zsj8QYOnmZ7ygi+yXk\nO4CIlN24eev45LvV/OGkdjTIyfIdR0SkUt00/lCWBa7m/hGQN/Ja+gXHl8+BB1f8/X+FLpvLIzeQ\nSYQnMh7Sfa1SaTo2zaV789r898tFDOrTgkBAV0wkNanFVSRFxOKOO9/7jrza2Vx0WEvfcUREKp0Z\n3Bd+ikPtO34fuZyxsY6+I5XJdpfBxSU3scg14tHwozSxAt+RJM0M6tOCReu3Meb7tb6jiOwzFa4i\nKeK1SUuZvaqQP51yIFnhoO84IiJeZFqUpzMeopWt4OLITYyKdfUd6WeVuCBXRq5nkmvHg+En6BP8\nznckSUMndWxEw5qZPD9+ke8oIvtMhatICthcFOGBj+fQs2UdTu7YyHccERGvcm0rr2TcRVtbzmWR\n3/FxrLvvSLsUiztuiFzN6HhX7g49y+nBL31HkjQVDgY4v1dzPv9+LfPWbPEdR2SfqHAVSQGPjZxH\nwbYSbj+1A6bRPEREqG1beCnjLg6yhVwVuY4PYj19R/oR5xx/ems678d7cWvoRc4LjfIdSdLceT2b\nkREK8N8vF/mOIrJPVLiKJLlF67by/LiF9O+eR8emub7jiIgkjVzbxgsZf6erzefayLW8HD3WdyQA\niqMxbnx9Gq9NXspvg29xaegD35FEqFsjk9O7NGHolGWaGkdSkgpXkSTmnOOv784kIxjgphPa+Y4j\nIpJ0cmw7/8n4O4cFZvCn6CXcErmYYudv0oSCrSX8+pmJvPXNcm48vi03hIZ6yyKys0F9WrCtJMYb\nmhpHUpAKV5Ek9umsNYyas5Ybjm9Lg5qa/kZEZFeqWzHPh+/jyuA7vBLry8CS21jtalV6jnlrtnDm\n4+OYtmwTj/3yYK7t20ZztUpS6dg0l0Na1OY/4xcRizvfcUT2igpXkSS1vSTG4OEzaduwBr/p08J3\nHBGRpBY0xx/Dr/F4+GHmuHx+UXw3n8c6Vdr3/2jGKs56fBxbi6O8elkvTu3cpNK+t8jeGNSnJUsK\ntjFq9hrfUUT2igpXkST1+Oh5LN+4nTv6dSQc1I+qiEhZnBL8imEZt1HTtnFB5BauLrmWVa52hX2/\n1ZuLuPyFyVzx4hTyalfj7asOo1uzivt+IvvrxIMa0rRWNv8au8B3FJG9ok/DIklo4bqtPDVmAWd0\nbUKvVnV9xxERSSltA8v5IOMWbgi9wSfx7vQtHsIz0ZOJuvL72BOPO16csJjjHhjD6Dlr+cNJ7Xjn\nmsPIr1Ot3L6HSEUIBQNceFgLJi4sYNrSjb7jiJSZCleRJOOc4y/DZ5IRCvCnUw70HUdEJCVlWYTr\nQm/zScYf6BmYzd+i53Nk8cM8Fu3HGrfvI7RvLorw/LiFHPfgGP48bAad8nIZcf2RXHX0AeodIylj\nYM9m5GSF1OoqKcXfsHsisksjZq7i8+/XctupHTQgk4jIfmoeWMNz4fsZFe/K87GTGBI9l4ejZ3NS\nYBKnBifQNTCPRns4xuaiCNOXbeLDGSt56+vlbCuJcXCzWjx63sGc2rmx5teWlFMjM8QvD23Gvz5f\nwNKCbeopIClBhatIEtlcFOEvw2fSvlEOv+nd3HccEZEqwQyODU7l2OBUFsQb8VLsON6IHcV78d4A\nNLr7M7rk55JXuxqW2D5gxurNRXy7bBML1m0FICMU4PQuTbigd3M651X+qMUi5WlQnxY8O3Yhz41b\nyF9OO8h3HJE9UuEqkkTu+2g2awqLeer8HoTU5UxEpNy1CqzitsCL/D70Gt+55kyNH8C0VjczdelG\nvpi7Dgc4Bw5HbnaYznm1OKtbUzrn1aJLfi1ys8O+34JIuWicm83pXZrw2qSlXN+3LbnV9H9bkpsK\nV5EkMXlRAS9OWMKFh7Wga76u5IuIVKQsi9DN5tEtMA8GvuY7jogXlxzRire+Wc5LXy3mqqMP8B1H\n5GepSUckCRRHY9zy1nSa1srmphPa+Y4jIiIiaaBDk5oc0aYe/x63iOJozHcckZ+lFleRJPDk6AXM\nXbOF5wcdQvVM/ViKiIjIfhhc9pGzL4114oLILbwz+EwGhMbs4bib9jOYyL7TJ2QRz+atKeSfo+Zx\nWpcmHNO+ge84IiLpZy8+5ItUNUcEptPBFvFE7HTODn5O0JzvSCK7pK7CIh7F4o4/vjmd7Iwgt5/a\nwXccERERSTNmcE1oGAtdYz6IH+o7jshuqXAV8ejZLxYwZfEG/nr6QdTPyfQdR0RERNLQSYFJtLbl\n/DPaD6cGV0lSKlxFPJm7upAhH3/PCR0a0q9rE99xREREJE0FzHFVaDizXXM+i3fzHUdkl1S4ingQ\njcW56Y1pVM8IcteZnTAz35FEREQkjZ0eGE+ereExtbpKklLhKuLBU58vYNqyTdx5Rkd1ERYRERHv\nwhbjiuC7THVtGBfv6DuOyE+ocBWpZLNWbubhT7/nF50bc2pndREWERGR5HBO8HMaUsBjsX6+o4j8\nhApXkUpUFIlxw2tTyc0Oc2c/Xc0UERGR5JFlES4Nvc+E+EFMibfxHUfkR1S4ilSi+z6aw+xVhdx7\ndmfqVM/wHUdERETkR34ZHEldNvFw9GzfUUR+RIWrSCUZPWcNz41byAW9m9P3wIa+44iIiIj8RDUr\n5srQu4yNd2ZCvL3vOCL/o8JVpBKs21LMTW98S9uGNfjTKQf6jiMiIiKyW78OfkIDNvBgpL9GGJak\nEfIdQKSqc87xx6HfsnlLIS+W3EbWXUt9RxIRERHZrSyLcG3obW6LXsTYeCeODE73HUlELa4iFe2F\nCYv5bPYabgm9QvuAilYRERFJfgOCo2nKWh6IDlCrqyQFFa4iFWj6sk387b1ZHNOuPoOCI3zHERER\nESmTTItyXegtprnWfBrv5juOiApXkYqyaVuEq16eQr0aGTw4oCtmvhOJiIiIlN1ZwbG0sFU8EO1P\n3OmDjPhVpsLVzE4yszlmNs/Mbt7F65lm9lri9Ylm1iKx/ngzm2Jm0xNfj91hn9GJY05NPBqU15sS\n8c05x01Dp7FyYxGP/rIbtTX1jYiIiKSYkMW5ITSU2a4578cP9R1H0tweC1czCwL/BE4GOgDnmVmH\nnTa7GNjgnDsAeAi4N7F+HXCac64T8BvghZ32+5VzrmvisWY/3odIUvnX2AV88t1qbjnlQLo3r+07\njoiIiMg+OTXwJe1sCUOiAyiJxn3HkTRWlhbXnsA859wC51wJ8CrQb6dt+gH/SSwPBfqamTnnvnHO\nrUisnwlkm1lmeQQXSVaTFhVw70dzOLljIy46rIXvOCIiIiL7LGiOW0Ivs9g14r9fLvIdR9JYWQrX\npsCOQ6EuS6zb5TbOuSiwCai70zZnA18754p3WPd8opvwbWa6A1BS3+rNRVz90tfk187m3nM6o//W\nIiIikuqODn7LEYFveXTkPDZuK/EdR9JUpQzOZGYHUdp9+PIdVv8q0YX4iMTj/N3se5mZTTazyWvX\nrq34sCL7qCgS4/IXprClOMqT53enZlbYdyQRERGRcnFr6CUKiyI8OnKe7yiSpspSuC4H8nd4npdY\nt8ttzCwE5ALrE8/zgLeBC5xz83/YwTm3PPG1EHiZ0i7JP+Gce9o518M516N+/fpleU8ilc45x5+H\nzWDq0o08OKAL7RvV9B1JREREpNy0Dyylf/d8/vvlIhat2+o7jqShshSuk4A2ZtbSzDKAgcDwnbYZ\nTungSwDnACOdc87MagHvAzc758b9sLGZhcysXmI5DJwKzNi/tyLiz7/HL2LolGVc17cNJ3Vs7DuO\niIiISLm78YS2hIMB7v1otu8okob2WLgm7lm9BhgBzAJed87NNLM7zOz0xGbPAnXNbB7wO+CHKXOu\nAQ4Abt9p2ptMYISZfQtMpbTF9l/l+cZEKsu4eev42/uzOKFDQ67r28Z3HBEREZEK0aBmFpcf2ZoP\nZ6xi8qIC33EkzZhzzneGMuvRo4ebPHmy7xhSlQ3O3avN58cbc1bJX2loG3gr4y/UsKIKCiYiIiLi\n2eBNbCuJcsyQ0TTIyWLY1YcRDGggSilfZjbFOddj5/WVMjiTSFW0ztVkUOSPhInxTPgBFa0iIiJS\n5VXLCPGnUw5k+vJNvPzVEt9xJI2ocBXZB9tdBheX3MRal8szGUNoFljjO5KIiIhIpTi9SxN6t6rL\n/R/NZt2W4j3vIFIOVLiK7KWYM66PXMW3rhWPhB+ja2D+nncSERERqSLMjDvPOIjtkRj3fKCBmqRy\nqHAV2QvOwV3RXzEi3pPbQy9wQnCK70giIiIile6ABjlcckQr3vx6GV8t1EBNUvFUuIrshcdjp/Nc\n7BQuDH7IhaERvuOIiIiIeHPtsQfQtFY2tw2bQSQW9x1HqjgVriJl9EL0OO6PDuSMwBfcFnrRdxwR\nERERr6plhLj9tA7MWV3Iv8ct8h1HqjgVriJl8E6sN7dHB3FcYAr3h58iYKkzjZSIiIhIRTmhQ0P6\ntm/Ag598z+L1W33HkSpMhavIHoyMdeXGyJX0tNk8Fn6EsMV8RxIRERFJCmbG387sSCho/H7ot8Tj\nurgvFUOFq8jPGBvryJWR6znQlvBMxgNkWcR3JBEREZGk0jg3m9tO7cBXCwv475eLfMeRKkqFq8hu\nfB7rxCWRm2hpq/hPxr3k2HbfkURERESSUv/ueRzdrj73fjRHXYalQqhwFdmF0qL1RlraSl7OuIs6\nVug7koiIiEjSMjPuOasToYC6DEvFUOEqspMfitbWtoKXM+5W0SoiIiJSBuoyLBVJhavIDj6NdVPR\nKiIiIrKP+vco7TJ8z4ez+X61PkdJ+VHhKpLw1tfLuDxyAwfaUl7OuJvatsV3JBEREZGUYmbcf04X\ncrLCXP3S12wv0WwMUj5UuIoAz32xkN+9Po1egVm8lHGXilYRERGRfVQ/J5OHzu3CvLVbuOO9mb7j\nSBWhwlXSmnOOBz/5njve+46TDmrEc+H7qGFFvmOJiIiIpLQj2tTnyqNa88pXS3l32grfcaQKUOEq\naaskGuePb37LI5/NZUCPPB775cFkWtR3LBEREZEq4Ybj29KtWS1ueWs6S9Zv8x1HUpwKV0lLm7ZF\nGPT8V7w+eRm/7duGe8/uTCioHwcRERGR8hIOBnjkvIMJGFz98tcURXS/q+w7fVKXtLNk/TbOemIc\nkxYV8ED/Lvzu+LaYme9YIiIiIlVOXu1qPDCgK9OXb+KWt6bjnOZ3lX0T8h1ApDJ9tbCAK1+cQjTu\neOHiQ+nVqq7vSCIiIiKpYXDuPu12PHBj6Awe+GYA7affz+Wh93Zx7E37l02qPBWukhacc/x7/CLu\nen8W+XWq8cxvetC6fg3fsURERETSwjXBYcyON+Pv0YG0tWUcE5zqO5KkGBWukpr24orfdpfBrZGL\neSt+BMcFJvNg4RPU/Of2CgwnIiIiIjsyg/vDT7GopCG/jVzD23Y7BwQ02rCUne5xlSptcbwBZ5cM\n5u34Yfwu9AZPhx+ipqloFREREals1ayYpzMeJJMIl0RuYp2r6TuSpBAVrlJlvRPrwy9K7maZq89z\n4SH8NvQ2AdOAACIiIiK+NLX1PJXxIKtcbS4s+QOFLtt3JEkRKlylytnqMrkpcjnXRa6hvS3lg8xb\ndB+FiIiISJLoHpjL4+F/8J1rzmWR31Hkwr4jSQpQ4SpVyvR4S04ruYs3Y0fw2+BbvJpxJ3m2zncs\nEREREdnBscGpDAk/yZfxg7g+cjWxuHrFyc9T4SpVQokL8kCkP2eU3MFWl8VL4bv5XXgoIYv7jiYi\nIiIiu3BmcBy3hf7LR/Ge3Pr2dOIqXuVnaFRhSXkz4s25KXIFs11zzg6M4fbwi+TaVt+xRERERGQP\nLg59xAaXw2OTzgTgrjM7EQyY51SSjFS4SsoqcmEei57Bk7HTqE0hz4SHcFzwa9+xRERERGQv3Bh6\nA478PY+NmkdxNM7953QmFFTHUPkxFa6SkkbFunJ7dBBLXQPOCnzO7eEXqKVWVhEREZGUYwY3ndiO\nrHCAIR9/T3E0xsPnHkxGSMWr/D8VrpJSVmzczp3vfceHkT/Q2pbzSvhOegdn+Y4lIiIiIvtjcC7X\nAFmhk/nb9PMpnnkXj4UfIdtK9vO4m8olnvinwlVSwtbiKE+Nmc/TYxfgHPw+9BqXBt8jw2K+o4mI\niIhIObkk9CFZlHBb9EIGltzGvzKG0MBUfIpGFZYkF4s7Xp+0lKOHjOaRkfM4vkMjPv3dUVwdekdF\nq4iIiEgV9OtJINYkAAAN20lEQVTQZzwdfpC5rilnFN/JrHi+70iSBFS4SlJyzvHRjJWc8o+x/OHN\nb8mrnc2bV/bh0fMOJr9ONd/xRERERKQCHR/8mtcz/koc45ySwYyMdfUdSTxT4SpJxTnHyNmrOe2x\nL7jixa+JxOI8et7BvHVlH7o3r+07noiIiIhUko6BxQzLvJ2WtopLIjfxcPQsYk5T5aQr3eMqSSEe\nd3z83WqeGDOfaUs3kl8nmyH9u3BG1yYaDl1EREQkTTWyDbyecQe3Ri7i4eg5TIwfyMPhf9LQNvqO\nJpVMhat4VRKNM2zqcp4cM58Fa7fSrE417jmrE+d0zyOsglVEREQk7VWzYh4MP0Gf2Exujw7ilOJ7\neDD8BEcFv/UdTSqRClfxYk1hEa9MXMpLExezprCYDo1r8uh5B3Nyx0ZqYRURERGRHzGD/qHPOTgw\nj6sjv+U3kZv5dfwT/hh6lRzb7jueVAIVrlJpnHN8vWQj//1yER9MX0kk5jiqbX3u79+SI9vUw0z3\nLIiIiIjI7h0QWME7GbdxX/Rcno+dxKexbvwt/DzHBb/2HU0qmDnnfGcosx49erjJkyf7jiFlNTgX\ngHWuJm/HDuf12NHMdXnUYBvnBD/nguDHtAqs8hxSRERERFLRN/HW3By5lDmuGb8IfMnt4Rd+eu/r\nYM0Bm2rMbIpzrsfO69XiKhWiKBJjZKwn78T68Fm8G1FCdLPv+XvoaU4NTqCGFfmOKCIiIiIp7ODA\nfN7NuJWnY6fySPQsRhYfzKXBD7gs9J4+a1ZBanGVclMSjTNu/jrenbaCj2euZktxlPps4IzgOAYE\nx9AmsNx3RBERERGpgpbG63Nf9FzejfehHhu5ITSUc4OjCf11g+9ospd21+KqwlX2y5biKKPnrOHj\nmasZNXsNhcVRamaFOLljY/pNu5xDA7MIWur8HxMRERGR1PVNvDV3R37FJNeefFvDZf2OpX/3PLLC\nQd/RpIxUuEq5cM4xd80WxsxZy+jv1zBp4QZKYnHqVs/guAMbcmLHhhx2QD0yQ8H/3eMqIiIiIlJZ\nnINP4934Z7QfU10b6udkcvHhLfnloc2omRX2HU/2QIWr7LPlG7fz5fz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"text/plain": [
"<Figure size 1152x576 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "-zaDWeNtqgtY",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 160
},
"outputId": "f3198ad4-7fa8-40df-9194-d078164c0fbe"
},
"source": [
"df.T"
],
"execution_count": 84,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>0</th>\n",
" <th>1</th>\n",
" <th>2</th>\n",
" <th>3</th>\n",
" <th>4</th>\n",
" <th>5</th>\n",
" <th>6</th>\n",
" <th>7</th>\n",
" <th>8</th>\n",
" <th>9</th>\n",
" <th>10</th>\n",
" <th>11</th>\n",
" <th>12</th>\n",
" <th>13</th>\n",
" <th>14</th>\n",
" <th>15</th>\n",
" <th>16</th>\n",
" <th>17</th>\n",
" <th>18</th>\n",
" <th>19</th>\n",
" <th>20</th>\n",
" <th>21</th>\n",
" <th>22</th>\n",
" <th>23</th>\n",
" <th>24</th>\n",
" <th>25</th>\n",
" <th>26</th>\n",
" <th>27</th>\n",
" <th>28</th>\n",
" <th>29</th>\n",
" <th>30</th>\n",
" <th>31</th>\n",
" <th>32</th>\n",
" <th>33</th>\n",
" <th>34</th>\n",
" <th>35</th>\n",
" <th>36</th>\n",
" <th>37</th>\n",
" <th>38</th>\n",
" <th>39</th>\n",
" <th>...</th>\n",
" <th>9960</th>\n",
" <th>9961</th>\n",
" <th>9962</th>\n",
" <th>9963</th>\n",
" <th>9964</th>\n",
" <th>9965</th>\n",
" <th>9966</th>\n",
" <th>9967</th>\n",
" <th>9968</th>\n",
" <th>9969</th>\n",
" <th>9970</th>\n",
" <th>9971</th>\n",
" <th>9972</th>\n",
" <th>9973</th>\n",
" <th>9974</th>\n",
" <th>9975</th>\n",
" <th>9976</th>\n",
" <th>9977</th>\n",
" <th>9978</th>\n",
" <th>9979</th>\n",
" <th>9980</th>\n",
" <th>9981</th>\n",
" <th>9982</th>\n",
" <th>9983</th>\n",
" <th>9984</th>\n",
" <th>9985</th>\n",
" <th>9986</th>\n",
" <th>9987</th>\n",
" <th>9988</th>\n",
" <th>9989</th>\n",
" <th>9990</th>\n",
" <th>9991</th>\n",
" <th>9992</th>\n",
" <th>9993</th>\n",
" <th>9994</th>\n",
" <th>9995</th>\n",
" <th>9996</th>\n",
" <th>9997</th>\n",
" <th>9998</th>\n",
" <th>9999</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>data</th>\n",
" <td>2.007893</td>\n",
" <td>1.476722</td>\n",
" <td>-4.034264</td>\n",
" <td>3.181963</td>\n",
" <td>2.321837</td>\n",
" <td>-3.626506</td>\n",
" <td>2.825216</td>\n",
" <td>1.321941</td>\n",
" <td>-1.643279</td>\n",
" <td>-0.860789</td>\n",
" <td>3.576613</td>\n",
" <td>-4.342099</td>\n",
" <td>1.037369</td>\n",
" <td>-2.404984</td>\n",
" <td>0.220586</td>\n",
" <td>-0.434947</td>\n",
" <td>-2.144353</td>\n",
" <td>-2.341086</td>\n",
" <td>2.394652</td>\n",
" <td>-3.57071</td>\n",
" <td>-2.760551</td>\n",
" <td>-0.703847</td>\n",
" <td>-3.39098</td>\n",
" <td>-2.562582</td>\n",
" <td>-1.387065</td>\n",
" <td>-6.546907</td>\n",
" <td>-1.340542</td>\n",
" <td>-4.415865</td>\n",
" <td>-3.031667</td>\n",
" <td>-3.112413</td>\n",
" <td>1.856633</td>\n",
" <td>-2.940284</td>\n",
" <td>-2.708961</td>\n",
" <td>2.637067</td>\n",
" <td>-3.179918</td>\n",
" <td>-5.159646</td>\n",
" <td>-1.69475</td>\n",
" <td>-2.57739</td>\n",
" <td>-2.67632</td>\n",
" <td>1.046988</td>\n",
" <td>...</td>\n",
" <td>-1.445569</td>\n",
" <td>2.200248</td>\n",
" <td>-4.401805</td>\n",
" <td>2.67485</td>\n",
" <td>2.452752</td>\n",
" <td>2.586784</td>\n",
" <td>-3.961637</td>\n",
" <td>-4.435274</td>\n",
" <td>-4.825331</td>\n",
" <td>-1.961034</td>\n",
" <td>-3.784201</td>\n",
" <td>-4.330992</td>\n",
" <td>1.683828</td>\n",
" <td>-5.229715</td>\n",
" <td>-0.263885</td>\n",
" <td>-2.997641</td>\n",
" <td>-2.027828</td>\n",
" <td>1.997421</td>\n",
" <td>-1.299083</td>\n",
" <td>2.204893</td>\n",
" <td>0.56796</td>\n",
" <td>-1.453882</td>\n",
" <td>-3.628855</td>\n",
" <td>3.137178</td>\n",
" <td>-5.189371</td>\n",
" <td>-1.689624</td>\n",
" <td>-3.32904</td>\n",
" <td>3.083311</td>\n",
" <td>-2.086451</td>\n",
" <td>-3.902667</td>\n",
" <td>0.17389</td>\n",
" <td>0.093511</td>\n",
" <td>0.076613</td>\n",
" <td>-4.228528</td>\n",
" <td>2.304798</td>\n",
" <td>-4.967107</td>\n",
" <td>3.023925</td>\n",
" <td>-3.372362</td>\n",
" <td>-2.142217</td>\n",
" <td>-3.573708</td>\n",
" </tr>\n",
" <tr>\n",
" <th>label</th>\n",
" <td>0.000000</td>\n",
" <td>0.000000</td>\n",
" <td>1.000000</td>\n",
" <td>0.000000</td>\n",
" <td>0.000000</td>\n",
" <td>1.000000</td>\n",
" <td>0.000000</td>\n",
" <td>0.000000</td>\n",
" <td>1.000000</td>\n",
" <td>1.000000</td>\n",
" <td>0.000000</td>\n",
" <td>1.000000</td>\n",
" <td>0.000000</td>\n",
" <td>1.000000</td>\n",
" <td>0.000000</td>\n",
" <td>1.000000</td>\n",
" <td>1.000000</td>\n",
" <td>1.000000</td>\n",
" <td>0.000000</td>\n",
" <td>1.00000</td>\n",
" <td>1.000000</td>\n",
" <td>1.000000</td>\n",
" <td>1.00000</td>\n",
" <td>1.000000</td>\n",
" <td>1.000000</td>\n",
" <td>1.000000</td>\n",
" <td>1.000000</td>\n",
" <td>1.000000</td>\n",
" <td>1.000000</td>\n",
" <td>1.000000</td>\n",
" <td>0.000000</td>\n",
" <td>1.000000</td>\n",
" <td>1.000000</td>\n",
" <td>0.000000</td>\n",
" <td>1.000000</td>\n",
" <td>1.000000</td>\n",
" <td>1.00000</td>\n",
" <td>1.00000</td>\n",
" <td>1.00000</td>\n",
" <td>0.000000</td>\n",
" <td>...</td>\n",
" <td>1.000000</td>\n",
" <td>0.000000</td>\n",
" <td>1.000000</td>\n",
" <td>0.00000</td>\n",
" <td>0.000000</td>\n",
" <td>0.000000</td>\n",
" <td>1.000000</td>\n",
" <td>1.000000</td>\n",
" <td>1.000000</td>\n",
" <td>1.000000</td>\n",
" <td>1.000000</td>\n",
" <td>1.000000</td>\n",
" <td>0.000000</td>\n",
" <td>1.000000</td>\n",
" <td>1.000000</td>\n",
" <td>1.000000</td>\n",
" <td>1.000000</td>\n",
" <td>0.000000</td>\n",
" <td>1.000000</td>\n",
" <td>0.000000</td>\n",
" <td>1.00000</td>\n",
" <td>1.000000</td>\n",
" <td>1.000000</td>\n",
" <td>0.000000</td>\n",
" <td>1.000000</td>\n",
" <td>1.000000</td>\n",
" <td>1.00000</td>\n",
" <td>0.000000</td>\n",
" <td>1.000000</td>\n",
" <td>1.000000</td>\n",
" <td>1.00000</td>\n",
" <td>1.000000</td>\n",
" <td>1.000000</td>\n",
" <td>1.000000</td>\n",
" <td>0.000000</td>\n",
" <td>1.000000</td>\n",
" <td>0.000000</td>\n",
" <td>1.000000</td>\n",
" <td>1.000000</td>\n",
" <td>1.000000</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>2 rows × 10000 columns</p>\n",
"</div>"
],
"text/plain": [
" 0 1 2 ... 9997 9998 9999\n",
"data 2.007893 1.476722 -4.034264 ... -3.372362 -2.142217 -3.573708\n",
"label 0.000000 0.000000 1.000000 ... 1.000000 1.000000 1.000000\n",
"\n",
"[2 rows x 10000 columns]"
]
},
"metadata": {
"tags": []
},
"execution_count": 84
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "pV21oddHjyCE",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 69
},
"outputId": "f8e46797-a7bc-43be-a0cd-42f35af332cf"
},
"source": [
"df.groupby(label)['data'].count()"
],
"execution_count": 87,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"0 2482\n",
"1 7518\n",
"Name: data, dtype: int64"
]
},
"metadata": {
"tags": []
},
"execution_count": 87
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "553oezSRjHhr",
"colab_type": "text"
},
"source": [
"## Reference \n",
"\n",
"- https://stackoverflow.com/questions/49106806/how-to-do-a-simple-gaussian-mixture-sampling-and-pdf-plotting-with-numpy-scipy\n",
"- http://inatim.com/numpy-frombuffer/"
]
}
]
}
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