Pansquam_TCGA.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Install packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from sklearn.decomposition import NMF\n",
    "from numpy import asarray\n",
    "from numpy import savetxt\n",
    "import matplotlib.colors as mcolors\n",
    "import matplotlib.cm\n",
    "import matplotlib.patches as mpatches\n",
    "import umap\n",
    "import matplotlib as mpl\n",
    "import scanpy as sc\n",
    "import scipy\n",
    "import kmapper as km\n",
    "from kmapper import jupyter\n",
    "from kmapper.plotlyviz import plotlyviz\n",
    "from kmapper.plotlyviz import *\n",
    "import plotly.graph_objs as go\n",
    "import sys\n",
    "from sklearn import ensemble\n",
    "from tqdm import tqdm\n",
    "from ripser import Rips\n",
    "from ripser import ripser\n",
    "from persim import plot_diagrams\n",
    "from sklearn.metrics.pairwise import euclidean_distances"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Read in data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Data shape: (23862, 1229)\n"
     ]
    }
   ],
   "source": [
    "pd_data = pd.read_csv(\"sc_Normalized.csv\", sep=',', header = 0, index_col = 0)\n",
    "np_data = pd_data.values \n",
    "\n",
    "pd_hnsc_data = pd.read_csv(\"hnsc_Normalized_na.csv\", sep=',', header = 0, index_col = 0)\n",
    "np_hnsc_data = pd_hnsc_data.values\n",
    "N_hnsc = np_hnsc_data.shape[1]\n",
    "\n",
    "np_data = np.append(np_data, np_hnsc_data, axis = 1)\n",
    "labels = np.append(np.array(pd_data.columns), np.array(pd_hnsc_data.columns))\n",
    "\n",
    "pd_data = pd.DataFrame(np_data, index = pd_data.index, columns = labels)\n",
    "np_data = pd_data.values\n",
    "print(\"Data shape: \"+repr(np_data.shape))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>TCGA-56-6546</th>\n",
       "      <th>TCGA-85-A50Z</th>\n",
       "      <th>TCGA-18-3409</th>\n",
       "      <th>TCGA-52-7809</th>\n",
       "      <th>TCGA-21-1080</th>\n",
       "      <th>TCGA-77-8008</th>\n",
       "      <th>TCGA-66-2780</th>\n",
       "      <th>TCGA-56-8083</th>\n",
       "      <th>TCGA-85-7843</th>\n",
       "      <th>TCGA-63-A5M9</th>\n",
       "      <th>...</th>\n",
       "      <th>TCGA-CQ-5323</th>\n",
       "      <th>TCGA-CV-7263</th>\n",
       "      <th>TCGA-CV-6945</th>\n",
       "      <th>TCGA-P3-A5QE</th>\n",
       "      <th>TCGA-CV-7423</th>\n",
       "      <th>TCGA-CN-5364</th>\n",
       "      <th>TCGA-CQ-A4CD</th>\n",
       "      <th>TCGA-CN-A63V</th>\n",
       "      <th>TCGA-CV-A45R</th>\n",
       "      <th>TCGA-CV-7178</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>TSPAN6</th>\n",
       "      <td>3180.613507</td>\n",
       "      <td>4703.080581</td>\n",
       "      <td>6705.466751</td>\n",
       "      <td>3713.704395</td>\n",
       "      <td>3814.302200</td>\n",
       "      <td>1573.335345</td>\n",
       "      <td>2857.464784</td>\n",
       "      <td>2662.462678</td>\n",
       "      <td>5782.545432</td>\n",
       "      <td>4361.557659</td>\n",
       "      <td>...</td>\n",
       "      <td>1021.100269</td>\n",
       "      <td>1466.900840</td>\n",
       "      <td>2144.201236</td>\n",
       "      <td>1733.959094</td>\n",
       "      <td>1096.718307</td>\n",
       "      <td>2096.943466</td>\n",
       "      <td>1833.868831</td>\n",
       "      <td>1527.335057</td>\n",
       "      <td>2819.439259</td>\n",
       "      <td>1940.753958</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DPM1</th>\n",
       "      <td>3781.097860</td>\n",
       "      <td>2319.455297</td>\n",
       "      <td>1864.633379</td>\n",
       "      <td>2833.243722</td>\n",
       "      <td>1800.001604</td>\n",
       "      <td>1266.256912</td>\n",
       "      <td>3216.634485</td>\n",
       "      <td>1508.695491</td>\n",
       "      <td>3513.054393</td>\n",
       "      <td>2490.653460</td>\n",
       "      <td>...</td>\n",
       "      <td>1588.109661</td>\n",
       "      <td>2394.488379</td>\n",
       "      <td>2403.343983</td>\n",
       "      <td>1547.867124</td>\n",
       "      <td>2721.404388</td>\n",
       "      <td>2046.606271</td>\n",
       "      <td>2315.854840</td>\n",
       "      <td>1263.007786</td>\n",
       "      <td>2108.765802</td>\n",
       "      <td>692.570945</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SCYL3</th>\n",
       "      <td>480.843966</td>\n",
       "      <td>503.410487</td>\n",
       "      <td>637.085032</td>\n",
       "      <td>1398.868769</td>\n",
       "      <td>777.626168</td>\n",
       "      <td>855.090701</td>\n",
       "      <td>736.469487</td>\n",
       "      <td>1065.784931</td>\n",
       "      <td>472.680063</td>\n",
       "      <td>831.569911</td>\n",
       "      <td>...</td>\n",
       "      <td>753.777945</td>\n",
       "      <td>630.294418</td>\n",
       "      <td>258.178407</td>\n",
       "      <td>997.197964</td>\n",
       "      <td>638.783985</td>\n",
       "      <td>537.439032</td>\n",
       "      <td>652.389446</td>\n",
       "      <td>457.053390</td>\n",
       "      <td>818.712218</td>\n",
       "      <td>1422.743321</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>c1orf112</th>\n",
       "      <td>664.255908</td>\n",
       "      <td>581.650216</td>\n",
       "      <td>378.189488</td>\n",
       "      <td>1400.235732</td>\n",
       "      <td>624.310367</td>\n",
       "      <td>409.618975</td>\n",
       "      <td>700.903288</td>\n",
       "      <td>1117.774455</td>\n",
       "      <td>428.289652</td>\n",
       "      <td>1545.047152</td>\n",
       "      <td>...</td>\n",
       "      <td>498.952471</td>\n",
       "      <td>442.215564</td>\n",
       "      <td>400.385580</td>\n",
       "      <td>986.846130</td>\n",
       "      <td>867.278540</td>\n",
       "      <td>836.942126</td>\n",
       "      <td>932.572739</td>\n",
       "      <td>489.935937</td>\n",
       "      <td>293.403503</td>\n",
       "      <td>921.423417</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>FGR</th>\n",
       "      <td>1961.311697</td>\n",
       "      <td>2535.247808</td>\n",
       "      <td>1215.023137</td>\n",
       "      <td>399.744952</td>\n",
       "      <td>555.042656</td>\n",
       "      <td>1062.657755</td>\n",
       "      <td>785.929771</td>\n",
       "      <td>242.950898</td>\n",
       "      <td>1222.517650</td>\n",
       "      <td>599.236106</td>\n",
       "      <td>...</td>\n",
       "      <td>231.862926</td>\n",
       "      <td>1008.671889</td>\n",
       "      <td>152.462647</td>\n",
       "      <td>406.202706</td>\n",
       "      <td>75.825798</td>\n",
       "      <td>557.931328</td>\n",
       "      <td>234.319789</td>\n",
       "      <td>321.957888</td>\n",
       "      <td>459.678622</td>\n",
       "      <td>446.185776</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ENSG00000281789</th>\n",
       "      <td>7.766299</td>\n",
       "      <td>3.558203</td>\n",
       "      <td>5.713695</td>\n",
       "      <td>13.494845</td>\n",
       "      <td>7.373036</td>\n",
       "      <td>7.554291</td>\n",
       "      <td>9.528246</td>\n",
       "      <td>19.996060</td>\n",
       "      <td>3.424476</td>\n",
       "      <td>13.977688</td>\n",
       "      <td>...</td>\n",
       "      <td>9.426400</td>\n",
       "      <td>4.892826</td>\n",
       "      <td>9.375999</td>\n",
       "      <td>3.647902</td>\n",
       "      <td>3.883333</td>\n",
       "      <td>0.801538</td>\n",
       "      <td>21.089220</td>\n",
       "      <td>4.723877</td>\n",
       "      <td>3.192649</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ENSG00000281849</th>\n",
       "      <td>9.841254</td>\n",
       "      <td>2.387838</td>\n",
       "      <td>3.443572</td>\n",
       "      <td>23.330929</td>\n",
       "      <td>10.172457</td>\n",
       "      <td>3.737742</td>\n",
       "      <td>5.180793</td>\n",
       "      <td>14.997090</td>\n",
       "      <td>7.027841</td>\n",
       "      <td>1.582234</td>\n",
       "      <td>...</td>\n",
       "      <td>9.402240</td>\n",
       "      <td>1.305676</td>\n",
       "      <td>8.437996</td>\n",
       "      <td>8.223248</td>\n",
       "      <td>0.962755</td>\n",
       "      <td>4.243175</td>\n",
       "      <td>1.161711</td>\n",
       "      <td>7.027676</td>\n",
       "      <td>4.245588</td>\n",
       "      <td>1.958544</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ENSG00000281896</th>\n",
       "      <td>23.410909</td>\n",
       "      <td>25.728023</td>\n",
       "      <td>15.941094</td>\n",
       "      <td>35.656925</td>\n",
       "      <td>46.186697</td>\n",
       "      <td>51.737766</td>\n",
       "      <td>15.571968</td>\n",
       "      <td>28.994117</td>\n",
       "      <td>59.287531</td>\n",
       "      <td>41.874191</td>\n",
       "      <td>...</td>\n",
       "      <td>29.941487</td>\n",
       "      <td>24.643996</td>\n",
       "      <td>18.699313</td>\n",
       "      <td>23.712000</td>\n",
       "      <td>26.252187</td>\n",
       "      <td>27.307912</td>\n",
       "      <td>20.193091</td>\n",
       "      <td>10.632666</td>\n",
       "      <td>24.361902</td>\n",
       "      <td>39.262258</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ENSG00000281903</th>\n",
       "      <td>3.794517</td>\n",
       "      <td>3.561565</td>\n",
       "      <td>6.851476</td>\n",
       "      <td>2.575533</td>\n",
       "      <td>18.483294</td>\n",
       "      <td>16.742106</td>\n",
       "      <td>22.600684</td>\n",
       "      <td>2.999324</td>\n",
       "      <td>1.305884</td>\n",
       "      <td>3.220589</td>\n",
       "      <td>...</td>\n",
       "      <td>5.580770</td>\n",
       "      <td>4.111562</td>\n",
       "      <td>24.347269</td>\n",
       "      <td>7.331523</td>\n",
       "      <td>36.974288</td>\n",
       "      <td>6.776358</td>\n",
       "      <td>7.882718</td>\n",
       "      <td>9.442742</td>\n",
       "      <td>28.563100</td>\n",
       "      <td>14.394650</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LINC01144</th>\n",
       "      <td>78.973246</td>\n",
       "      <td>56.085071</td>\n",
       "      <td>51.126795</td>\n",
       "      <td>123.333648</td>\n",
       "      <td>98.837383</td>\n",
       "      <td>21.196043</td>\n",
       "      <td>45.077840</td>\n",
       "      <td>141.971480</td>\n",
       "      <td>28.084079</td>\n",
       "      <td>23.743449</td>\n",
       "      <td>...</td>\n",
       "      <td>58.478587</td>\n",
       "      <td>50.772073</td>\n",
       "      <td>28.989851</td>\n",
       "      <td>84.011089</td>\n",
       "      <td>6.794528</td>\n",
       "      <td>15.303489</td>\n",
       "      <td>13.496457</td>\n",
       "      <td>17.680469</td>\n",
       "      <td>32.840077</td>\n",
       "      <td>28.088488</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>23862 rows × 1229 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                 TCGA-56-6546  TCGA-85-A50Z  TCGA-18-3409  TCGA-52-7809  \\\n",
       "TSPAN6            3180.613507   4703.080581   6705.466751   3713.704395   \n",
       "DPM1              3781.097860   2319.455297   1864.633379   2833.243722   \n",
       "SCYL3              480.843966    503.410487    637.085032   1398.868769   \n",
       "c1orf112           664.255908    581.650216    378.189488   1400.235732   \n",
       "FGR               1961.311697   2535.247808   1215.023137    399.744952   \n",
       "...                       ...           ...           ...           ...   \n",
       "ENSG00000281789      7.766299      3.558203      5.713695     13.494845   \n",
       "ENSG00000281849      9.841254      2.387838      3.443572     23.330929   \n",
       "ENSG00000281896     23.410909     25.728023     15.941094     35.656925   \n",
       "ENSG00000281903      3.794517      3.561565      6.851476      2.575533   \n",
       "LINC01144           78.973246     56.085071     51.126795    123.333648   \n",
       "\n",
       "                 TCGA-21-1080  TCGA-77-8008  TCGA-66-2780  TCGA-56-8083  \\\n",
       "TSPAN6            3814.302200   1573.335345   2857.464784   2662.462678   \n",
       "DPM1              1800.001604   1266.256912   3216.634485   1508.695491   \n",
       "SCYL3              777.626168    855.090701    736.469487   1065.784931   \n",
       "c1orf112           624.310367    409.618975    700.903288   1117.774455   \n",
       "FGR                555.042656   1062.657755    785.929771    242.950898   \n",
       "...                       ...           ...           ...           ...   \n",
       "ENSG00000281789      7.373036      7.554291      9.528246     19.996060   \n",
       "ENSG00000281849     10.172457      3.737742      5.180793     14.997090   \n",
       "ENSG00000281896     46.186697     51.737766     15.571968     28.994117   \n",
       "ENSG00000281903     18.483294     16.742106     22.600684      2.999324   \n",
       "LINC01144           98.837383     21.196043     45.077840    141.971480   \n",
       "\n",
       "                 TCGA-85-7843  TCGA-63-A5M9  ...  TCGA-CQ-5323  TCGA-CV-7263  \\\n",
       "TSPAN6            5782.545432   4361.557659  ...   1021.100269   1466.900840   \n",
       "DPM1              3513.054393   2490.653460  ...   1588.109661   2394.488379   \n",
       "SCYL3              472.680063    831.569911  ...    753.777945    630.294418   \n",
       "c1orf112           428.289652   1545.047152  ...    498.952471    442.215564   \n",
       "FGR               1222.517650    599.236106  ...    231.862926   1008.671889   \n",
       "...                       ...           ...  ...           ...           ...   \n",
       "ENSG00000281789      3.424476     13.977688  ...      9.426400      4.892826   \n",
       "ENSG00000281849      7.027841      1.582234  ...      9.402240      1.305676   \n",
       "ENSG00000281896     59.287531     41.874191  ...     29.941487     24.643996   \n",
       "ENSG00000281903      1.305884      3.220589  ...      5.580770      4.111562   \n",
       "LINC01144           28.084079     23.743449  ...     58.478587     50.772073   \n",
       "\n",
       "                 TCGA-CV-6945  TCGA-P3-A5QE  TCGA-CV-7423  TCGA-CN-5364  \\\n",
       "TSPAN6            2144.201236   1733.959094   1096.718307   2096.943466   \n",
       "DPM1              2403.343983   1547.867124   2721.404388   2046.606271   \n",
       "SCYL3              258.178407    997.197964    638.783985    537.439032   \n",
       "c1orf112           400.385580    986.846130    867.278540    836.942126   \n",
       "FGR                152.462647    406.202706     75.825798    557.931328   \n",
       "...                       ...           ...           ...           ...   \n",
       "ENSG00000281789      9.375999      3.647902      3.883333      0.801538   \n",
       "ENSG00000281849      8.437996      8.223248      0.962755      4.243175   \n",
       "ENSG00000281896     18.699313     23.712000     26.252187     27.307912   \n",
       "ENSG00000281903     24.347269      7.331523     36.974288      6.776358   \n",
       "LINC01144           28.989851     84.011089      6.794528     15.303489   \n",
       "\n",
       "                 TCGA-CQ-A4CD  TCGA-CN-A63V  TCGA-CV-A45R  TCGA-CV-7178  \n",
       "TSPAN6            1833.868831   1527.335057   2819.439259   1940.753958  \n",
       "DPM1              2315.854840   1263.007786   2108.765802    692.570945  \n",
       "SCYL3              652.389446    457.053390    818.712218   1422.743321  \n",
       "c1orf112           932.572739    489.935937    293.403503    921.423417  \n",
       "FGR                234.319789    321.957888    459.678622    446.185776  \n",
       "...                       ...           ...           ...           ...  \n",
       "ENSG00000281789     21.089220      4.723877      3.192649      0.000000  \n",
       "ENSG00000281849      1.161711      7.027676      4.245588      1.958544  \n",
       "ENSG00000281896     20.193091     10.632666     24.361902     39.262258  \n",
       "ENSG00000281903      7.882718      9.442742     28.563100     14.394650  \n",
       "LINC01144           13.496457     17.680469     32.840077     28.088488  \n",
       "\n",
       "[23862 rows x 1229 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1229, 2)\n"
     ]
    }
   ],
   "source": [
    "reducer = umap.UMAP()\n",
    "UMAP = reducer.fit_transform(np_data.T)\n",
    "print(UMAP.shape)\n",
    "\n",
    "savetxt('sc_umap_logscaled.csv', UMAP, delimiter=',')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "UMAP shape: (1229, 2)\n",
      "Primary shape: (1229,)\n"
     ]
    }
   ],
   "source": [
    "UMAP = pd.read_csv(\"sc_umap_logscaled.csv\", sep=',', header = None)\n",
    "UMAP = UMAP.values \n",
    "\n",
    "Primary = pd.read_csv(\"type_sc.csv\", sep=',', header = 0)\n",
    "Primary = Primary.values[:,0]\n",
    "Primary = np.append(Primary, [\"TCGA-HNSC\"]*N_hnsc)\n",
    "\n",
    "print(\"UMAP shape: \"+repr(UMAP.shape))\n",
    "print(\"Primary shape: \"+repr(Primary.shape))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "frame1 = sns.scatterplot(UMAP[:,0], UMAP[:,1], s=10, hue = Primary, linewidth = 0)\n",
    "plt.title('Pansquam - UMAP')\n",
    "#plt.xlim(-30000,25000)\n",
    "frame1.axes.get_xaxis().set_ticks([])\n",
    "frame1.axes.get_yaxis().set_ticks([])\n",
    "plt.ylabel('UMAP2')\n",
    "plt.xlabel('UMAP1')\n",
    "plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Distance Matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from manifold_utils.mSVD import eigen_plot, eigen_calc_from_dist_mat, eps_projection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0\n",
      "0\n"
     ]
    }
   ],
   "source": [
    "np_data = np_data.T\n",
    "N, d = np_data.shape\n",
    "print(np.amin(np_data))\n",
    "np_data = np.log10(np_data + np.ones((N,d)))\n",
    "\n",
    "print(np.sum(np.isnan(np_data)))\n",
    "\n",
    "dist_mat = euclidean_distances(np_data, np_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "savetxt('dist_mat_pansquam.csv', dist_mat, delimiter=',')\n",
    "\n",
    "dist_mat = pd.read_csv('dist_mat_pansquam.csv', sep=\",\", header = None)\n",
    "dist_mat = np.array(dist_mat )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1229, 1229)\n"
     ]
    }
   ],
   "source": [
    "print(dist_mat.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Witness complex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n = 1229\n",
      "d = 23862\n",
      "shape of dist_mat: (1229, 1229)\n",
      "Timing computation of density filtrations...\n",
      "\tk = 10, p = 0.01:\n",
      "\t0.002000570297241211 seconds\n",
      "\n",
      "\tk = 10, p = 0.05:\n",
      "\t0.0010004043579101562 seconds\n",
      "\n",
      "\tk = 10, p = 0.1:\n",
      "\t0.002000093460083008 seconds\n",
      "\n",
      "\tk = 10, p = 0.2:\n",
      "\t0.0020003318786621094 seconds\n",
      "\n",
      "\tk = 100, p = 0.01:\n",
      "\t0.0020008087158203125 seconds\n",
      "\n",
      "\tk = 100, p = 0.05:\n",
      "\t0.0010006427764892578 seconds\n",
      "\n",
      "\tk = 100, p = 0.1:\n",
      "\t0.002000093460083008 seconds\n",
      "\n",
      "\tk = 100, p = 0.2:\n",
      "\t0.002000093460083008 seconds\n",
      "\n",
      "\tk = 1000, p = 0.01:\n",
      "\t0.0010006427764892578 seconds\n",
      "\n",
      "\tk = 1000, p = 0.05:\n",
      "\t0.0020003318786621094 seconds\n",
      "\n",
      "\tk = 1000, p = 0.1:\n",
      "\t0.0009999275207519531 seconds\n",
      "\n",
      "\tk = 1000, p = 0.2:\n",
      "\t0.002000093460083008 seconds\n",
      "\n",
      "Timing computation of landmarks...\n",
      "\tk = 10, p = 0.01, pp = 0.05:\n",
      "\t0.0 seconds\n",
      "\n",
      "\tk = 10, p = 0.01, pp = 0.1:\n",
      "\t0.0 seconds\n",
      "\n",
      "\tk = 10, p = 0.01, pp = 0.2:\n",
      "\t0.0 seconds\n",
      "\n",
      "\tk = 10, p = 0.05, pp = 0.05:\n",
      "\t0.0 seconds\n",
      "\n",
      "\tk = 10, p = 0.05, pp = 0.1:\n",
      "\t0.0010006427764892578 seconds\n",
      "\n",
      "\tk = 10, p = 0.05, pp = 0.2:\n",
      "\t0.0 seconds\n",
      "\n",
      "\tk = 10, p = 0.1, pp = 0.05:\n",
      "\t0.0 seconds\n",
      "\n",
      "\tk = 10, p = 0.1, pp = 0.1:\n",
      "\t0.0 seconds\n",
      "\n",
      "\tk = 10, p = 0.1, pp = 0.2:\n",
      "\t0.0 seconds\n",
      "\n",
      "\tk = 10, p = 0.2, pp = 0.05:\n",
      "\t0.0009999275207519531 seconds\n",
      "\n",
      "\tk = 10, p = 0.2, pp = 0.1:\n",
      "\t0.0 seconds\n",
      "\n",
      "\tk = 10, p = 0.2, pp = 0.2:\n",
      "\t0.0 seconds\n",
      "\n",
      "\tk = 100, p = 0.01, pp = 0.05:\n",
      "\t0.0 seconds\n",
      "\n",
      "\tk = 100, p = 0.01, pp = 0.1:\n",
      "\t0.0 seconds\n",
      "\n",
      "\tk = 100, p = 0.01, pp = 0.2:\n",
      "\t0.0 seconds\n",
      "\n",
      "\tk = 100, p = 0.05, pp = 0.05:\n",
      "\t0.0 seconds\n",
      "\n",
      "\tk = 100, p = 0.05, pp = 0.1:\n",
      "\t0.0010001659393310547 seconds\n",
      "\n",
      "\tk = 100, p = 0.05, pp = 0.2:\n",
      "\t0.0 seconds\n",
      "\n",
      "\tk = 100, p = 0.1, pp = 0.05:\n",
      "\t0.0 seconds\n",
      "\n",
      "\tk = 100, p = 0.1, pp = 0.1:\n",
      "\t0.0010006427764892578 seconds\n",
      "\n",
      "\tk = 100, p = 0.1, pp = 0.2:\n",
      "\t0.0 seconds\n",
      "\n",
      "\tk = 100, p = 0.2, pp = 0.05:\n",
      "\t0.0 seconds\n",
      "\n",
      "\tk = 100, p = 0.2, pp = 0.1:\n",
      "\t0.0 seconds\n",
      "\n",
      "\tk = 100, p = 0.2, pp = 0.2:\n",
      "\t0.0 seconds\n",
      "\n",
      "\tk = 1000, p = 0.01, pp = 0.05:\n",
      "\t0.0009996891021728516 seconds\n",
      "\n",
      "\tk = 1000, p = 0.01, pp = 0.1:\n",
      "\t0.0 seconds\n",
      "\n",
      "\tk = 1000, p = 0.01, pp = 0.2:\n",
      "\t0.0 seconds\n",
      "\n",
      "\tk = 1000, p = 0.05, pp = 0.05:\n",
      "\t0.0 seconds\n",
      "\n",
      "\tk = 1000, p = 0.05, pp = 0.1:\n",
      "\t0.0 seconds\n",
      "\n",
      "\tk = 1000, p = 0.05, pp = 0.2:\n",
      "\t0.0 seconds\n",
      "\n",
      "\tk = 1000, p = 0.1, pp = 0.05:\n",
      "\t0.0 seconds\n",
      "\n",
      "\tk = 1000, p = 0.1, pp = 0.1:\n",
      "\t0.0010006427764892578 seconds\n",
      "\n",
      "\tk = 1000, p = 0.1, pp = 0.2:\n",
      "\t0.0 seconds\n",
      "\n",
      "\tk = 1000, p = 0.2, pp = 0.05:\n",
      "\t0.0 seconds\n",
      "\n",
      "\tk = 1000, p = 0.2, pp = 0.1:\n",
      "\t0.0 seconds\n",
      "\n",
      "\tk = 1000, p = 0.2, pp = 0.2:\n",
      "\t0.0009999275207519531 seconds\n",
      "\n",
      "Printing numbers of landmarks...\n",
      "(10, 0.01, 0.05): 0\n",
      "(10, 0.01, 0.1): 1\n",
      "(10, 0.01, 0.2): 2\n",
      "(10, 0.05, 0.05): 3\n",
      "(10, 0.05, 0.1): 6\n",
      "(10, 0.05, 0.2): 12\n",
      "(10, 0.1, 0.05): 6\n",
      "(10, 0.1, 0.1): 12\n",
      "(10, 0.1, 0.2): 24\n",
      "(10, 0.2, 0.05): 12\n",
      "(10, 0.2, 0.1): 24\n",
      "(10, 0.2, 0.2): 49\n",
      "(100, 0.01, 0.05): 0\n",
      "(100, 0.01, 0.1): 1\n",
      "(100, 0.01, 0.2): 2\n",
      "(100, 0.05, 0.05): 3\n",
      "(100, 0.05, 0.1): 6\n",
      "(100, 0.05, 0.2): 12\n",
      "(100, 0.1, 0.05): 6\n",
      "(100, 0.1, 0.1): 12\n",
      "(100, 0.1, 0.2): 24\n",
      "(100, 0.2, 0.05): 12\n",
      "(100, 0.2, 0.1): 24\n",
      "(100, 0.2, 0.2): 49\n",
      "(1000, 0.01, 0.05): 0\n",
      "(1000, 0.01, 0.1): 1\n",
      "(1000, 0.01, 0.2): 2\n",
      "(1000, 0.05, 0.05): 3\n",
      "(1000, 0.05, 0.1): 6\n",
      "(1000, 0.05, 0.2): 12\n",
      "(1000, 0.1, 0.05): 6\n",
      "(1000, 0.1, 0.1): 12\n",
      "(1000, 0.1, 0.2): 24\n",
      "(1000, 0.2, 0.05): 12\n",
      "(1000, 0.2, 0.1): 24\n",
      "(1000, 0.2, 0.2): 49\n",
      "saving\n",
      "[787, 134, 960, 949, 791, 347, 150, 547, 842, 512, 569, 220, 1113, 933, 3, 549, 490, 1097, 637, 109, 499, 956, 1131, 485, 607, 718, 1096, 848, 254, 745, 632, 191, 212, 246, 288, 1150, 175, 860, 529, 1071, 375, 930, 1118, 1105, 965, 1092, 127, 789, 790]\n"
     ]
    }
   ],
   "source": [
    "from time import time\n",
    "import numpy as np\n",
    "from tda_utils.density_filtration import sort_distances_per_point, indices_for_density_filtration\n",
    "from tda_utils.witness_complex import *\n",
    "\n",
    "dist_per_pt = sort_distances_per_point(dist_mat)\n",
    "\n",
    "# Load in ILC data\n",
    "sct_sparse = np_data\n",
    "dist_mat = dist_mat\n",
    "n, d = sct_sparse.shape\n",
    "print(\"n = \"+str(n))\n",
    "print(\"d = \"+str(d))\n",
    "print(\"shape of dist_mat: \"+str(dist_mat.shape))\n",
    "\n",
    "# Load in distances per point\n",
    "distances_per_point = dist_per_pt\n",
    "\n",
    "# time computation of density filtrations\n",
    "print(\"Timing computation of density filtrations...\")\n",
    "density_indices = dict()\n",
    "density_filtrations = dict()\n",
    "ks = [10, 100, 1000]\n",
    "#      10000]\n",
    "ps = [0.01, 0.05, 0.1, 0.2]\n",
    "for k in ks:\n",
    "    for p in ps:\n",
    "        print(\"\\tk = \"+str(k)+\", p = \"+str(p)+\":\")\n",
    "        start = time()\n",
    "        indices = indices_for_density_filtration(distances_per_point, k, p)\n",
    "        density_indices[(k, p)] = indices\n",
    "        mask = np.zeros(n, dtype=bool)\n",
    "        mask[indices] = True\n",
    "        sqr_mask = np.outer(mask, mask)\n",
    "        density_filtrations[(k, p)] = np.reshape(dist_mat[sqr_mask], (len(indices), len(indices)))\n",
    "        print(\"\\t\"+str(time()-start)+\" seconds\\n\")\n",
    "\n",
    "print(\"Timing computation of landmarks...\")\n",
    "landmark_indices = dict()\n",
    "landmark_mats = dict()\n",
    "pps = [0.05, 0.1, 0.2]\n",
    "for k in ks:\n",
    "    for p in ps:\n",
    "        for pp in pps:\n",
    "            print(\"\\tk = \"+str(k)+\", p = \"+str(p)+\", pp = \"+str(pp)+\":\")\n",
    "            start = time()\n",
    "            landmark_indices[(k, p, pp)], landmark_mats[(k, p, pp)] = choose_landmarks(density_filtrations[(k, p)], pp)\n",
    "            print(\"\\t\"+str(time()-start)+\" seconds\\n\")\n",
    "\n",
    "print(\"Printing numbers of landmarks...\")\n",
    "for k in ks:\n",
    "    for p in ps:\n",
    "        for pp in pps:\n",
    "            toople = (k, p, pp)\n",
    "            print(str(toople)+\": \"+str(len(landmark_indices[toople])))\n",
    "            if toople == (1000, 0.2, 0.2):\n",
    "                print(\"saving\")\n",
    "                landmark_inds = landmark_indices[toople]\n",
    "                dense_inds = density_indices[(k, p)]\n",
    "                true_inds = [dense_inds[ind] for ind in landmark_inds]\n",
    "                print(true_inds)\n",
    "                to_save = np.vstack([sct_sparse[ind, :] for ind in true_inds])\n",
    "                np.save(\"PanSquam_landmarks.npy\", to_save)\n",
    "                np.save(\"PanSquam_Racute_landmark_indices.npy\", true_inds)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualize Landmarks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[787, 134, 960, 949, 791, 347, 150, 547, 842, 512, 569, 220, 1113, 933, 3, 549, 490, 1097, 637, 109, 499, 956, 1131, 485, 607, 718, 1096, 848, 254, 745, 632, 191, 212, 246, 288, 1150, 175, 860, 529, 1071, 375, 930, 1118, 1105, 965, 1092, 127, 789, 790]\n"
     ]
    }
   ],
   "source": [
    "landmarks = np.load(\"PanSquam_landmarks.npy\")\n",
    "\n",
    "landmarks = true_inds\n",
    "print(true_inds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1229, 2)\n",
      "(49, 23862)\n",
      "(49, 2)\n"
     ]
    }
   ],
   "source": [
    "N, d = np_data.shape\n",
    "genes = pd_data.columns\n",
    "\n",
    "UMAP = np.array(UMAP)\n",
    "print(UMAP.shape)\n",
    "\n",
    "UMAP_landmark = np.zeros((1,2))\n",
    "data_landmark = np.zeros((1,d))\n",
    "\n",
    "#Going through all of the cells, if index in landmarks we should pull the associated gene expression data\n",
    "for i in landmarks:\n",
    "    next_cell = np_data[i,:]\n",
    "    next_cell = np.reshape(next_cell, (1, d))\n",
    "    data_landmark = np.append(data_landmark, next_cell, axis = 0)\n",
    "        \n",
    "    next_embedding = UMAP[i,:]\n",
    "    next_embedding = np.reshape(next_embedding, (1,2))\n",
    "    UMAP_landmark = np.append(UMAP_landmark, next_embedding, axis = 0)\n",
    "\n",
    "#To get the indices to work out I have a row of zeros at the top that I need to omit\n",
    "data_landmark = data_landmark[1:, :]    \n",
    "UMAP_landmark = UMAP_landmark[1:, :]\n",
    "\n",
    "print(data_landmark.shape)\n",
    "print(UMAP_landmark.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "frame1 = plt.scatter(UMAP[:,0], UMAP[:,1], s=1, c = \"silver\")\n",
    "frame1 = plt.scatter(UMAP_landmark[:,0], UMAP_landmark[:,1], s=1, c = \"red\")\n",
    "plt.title('Racute - UMAP')\n",
    "#plt.xlim(-30000,25000)\n",
    "frame1.axes.get_xaxis().set_ticks([])\n",
    "frame1.axes.get_yaxis().set_ticks([])\n",
    "plt.ylabel('UMAP2')\n",
    "plt.xlabel('UMAP1')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Persistence Diagrams"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1229, 23862)"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np_data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\users\\hmkri\\desktop\\riesenfeld pearson\\lib\\site-packages\\ripser\\ripser.py:257: UserWarning: The input point cloud has more columns than rows; did you mean to transpose?\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "ename": "ValueError",
     "evalue": "num must be 1 <= num <= 2, not 3",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-15-52f192230b51>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[0mplot_diagrams\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdgms\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mplot_only\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0max\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msubplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m121\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      6\u001b[0m \u001b[0mplot_diagrams\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdgms\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mplot_only\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0max\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msubplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m122\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 7\u001b[1;33m \u001b[0mplot_diagrams\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdgms\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mplot_only\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0max\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msubplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m123\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32mc:\\users\\hmkri\\desktop\\riesenfeld pearson\\lib\\site-packages\\matplotlib\\pyplot.py\u001b[0m in \u001b[0;36msubplot\u001b[1;34m(*args, **kwargs)\u001b[0m\n\u001b[0;32m   1028\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1029\u001b[0m     \u001b[0mfig\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mgcf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1030\u001b[1;33m     \u001b[0ma\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mfig\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0madd_subplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1031\u001b[0m     \u001b[0mbbox\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0ma\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mbbox\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1032\u001b[0m     \u001b[0mbyebye\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\users\\hmkri\\desktop\\riesenfeld pearson\\lib\\site-packages\\matplotlib\\figure.py\u001b[0m in \u001b[0;36madd_subplot\u001b[1;34m(self, *args, **kwargs)\u001b[0m\n\u001b[0;32m   1417\u001b[0m                     \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_axstack\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mremove\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0max\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1418\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1419\u001b[1;33m             \u001b[0ma\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0msubplot_class_factory\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mprojection_class\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1420\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1421\u001b[0m         \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_add_axes_internal\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0ma\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\users\\hmkri\\desktop\\riesenfeld pearson\\lib\\site-packages\\matplotlib\\axes\\_subplots.py\u001b[0m in \u001b[0;36m__init__\u001b[1;34m(self, fig, *args, **kwargs)\u001b[0m\n\u001b[0;32m     63\u001b[0m             \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     64\u001b[0m                 \u001b[1;32mif\u001b[0m \u001b[0mnum\u001b[0m \u001b[1;33m<\u001b[0m \u001b[1;36m1\u001b[0m \u001b[1;32mor\u001b[0m \u001b[0mnum\u001b[0m \u001b[1;33m>\u001b[0m \u001b[0mrows\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mcols\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 65\u001b[1;33m                     raise ValueError(\n\u001b[0m\u001b[0;32m     66\u001b[0m                         f\"num must be 1 <= num <= {rows*cols}, not {num}\")\n\u001b[0;32m     67\u001b[0m                 self._subplotspec = GridSpec(\n",
      "\u001b[1;31mValueError\u001b[0m: num must be 1 <= num <= 2, not 3"
     ]
    },
    {
     "data": {
      "image/png": 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GPJ1XUBtvrdzYoUOHaNCgAY8//jjGGG3SVUopOxn/VRIpx7IBWLwjjU9W7eO+K5pXeGxl9+Oie3bfvn1Zs2YNHh51fz2Luv8VVENsWADXXnRmtoGezcPpEhvqwIqUq0tISKB169Zs27YNQAOfUkrZ0fGs0kunHcvKK/78RHY+q//MYHfaKe6ZvpaWzyxk0NvL2HvkzITMy5Yto2XLlsyePRvAJQIfOM/o3Vr379u6cGv3WPItVnq3isTL0zX+QZXzKdmHr1WrVo4uRymlXM6iLam8/t+deIow/i/t+FvPOP75XeEv2cF+XtzYpXAWuAPHsxk2eSWpJ3Lw9JDibl6/p53isc838vVDl5Xqw9e/f3+HfU324LahT0To3SrS0WUoF6eDNpRSyr4OHs/mkdkbybMN2hj96W+sHNefDo1C2Jtxmp7Nw4kNCwDg45V7ST1ROBGzpUw/r437j9P5gUR2ffIMTV1g0EZF9PGWUnYyf/58DXxKKWVnqSdyigMfQHa+hfRTuRw6mUN6Zm6pPvtenpV3rSnIPMLmaePwCYlyycAHbvykTyl7u+qqq0hMTGT06NEa+JRSyk7aNQwmLsyffUcLB260bRDMF+v288HPewBI+HEXo/u2YMyAVlzcuPL++17BEYQNvJ9LrhjokoEP9EmfUjVu+vTpHD58GG9vbx599FENfEopZUfGQLB/4X3W00Po2iSU6Sv2FO8vsBre/d8fPPDJen7dc7Tc+SHHf8dyaCcA9S6+kvuv7lo7hTuAhj6lalBCQgJ33XUXb775pqNLUUopt/DZ2v1sOVA4167Fapj1637yK5iTefGONKKCfUtty0lOYueM8URu/Zy3br6Ibx++nCGdY2qjbIfQ5l2lakjRoI2hQ4cyYcIER5ejlFJuoaqrbvh5ezCiV1MOHs/h640HyNmfROpXL9GiWVMWzv/WZZt0S9InfUrVgJKBb/bs2dqkq5RSteTmbo1pGh5wzuNuvzQOX29PXhzSgXf6+rJ/9vO0aNbUZQdtVERDn1IXKDs7mw8++EADn1JKOUB4kC/fP9Kbd4d3JsT/zP3Xu0TCiQjy5b7eZ1bkmDp1qkuspXu+tHlXqQtgjMHf35/ly5cTEhKigU8ppRwgLTMXL08PZt57Kf+av409GVn0axvJZS0iOJaVx6D2DWgQ4le85NrUqVM5ceIEERERji69Vrl16Fu/7xgFFivxTcPw9NBlsdT5SUhIYNWqVcycOdPtbhxKKeUsVv5xhJHT15JXYMVTBIspnHR59q/7aREZxL22J3zLli3jySef5LvvviMqKsot79tu27w7YtqvDJ28klunrGbIe79gLTMzt1JnU9SHz2qtWgdipZRS9jH1lz3kFRTei4sCX5E/0k4BFC+tlpmZiTHu+/PeLUPfjkMnWbYrvfj1loMnWbT1kAMrUnWJDtpQ7kZExorIVhHZIiKzRcRPRMJE5EcR+d32sb6j61TuKciv8kbLS5qFlVpL19368JXllqFv35Gscts2pxxzQCWqrnnvvfc08Cm3IiIxwCNAvDGmI+AJDAfGAYuNMa2AxbbXStW6f1zVhnqVBL/Z3/2oga8Etwx9Xp7lt9Xz1R/e6ty6du3KyJEjNfApd+MF+IuIFxAAHASGADNs+2cANzioNlWHLUhK5fVFO0q1vgG8tmgHF//zB/q/tZRN+4+f9RpRwX6V9ss/4VWfq666SgOfjVuGvosqWHuvV0v369Cpqm7Dhg0A9OrVi48++kgDn3IbxpgDwJtAMpAKnDDG/ABEG2NSbcekAlGVXUNERonIOhFZl56eXtlhys3MWLmX0TN/Y9LS3YyY9isLk1IBWLz9MJOX7uZEdj5/pp9m9MzfKr2G1Wq4Z8ZajmXll9qel74XY7VwbY8OzJs3TwOfjVuGvsycgnLbsitas0UpCvvwde3alfnz5zu6FKVqna2v3hCgGdAICBSRO87nGsaYKcaYeGNMfGRkpD3KVHXQwi2ppV4X9a0/dDKn1Pa0zJxKB1/sP5bFz78fKbXNkrKVIzOfoMvhRTwyoFUNVlz3uWXoi6nvT+P6/sWvQ/29adsg2IEVKWdVNGhj2LBhXHXVVY4uRylHGAjsMcakG2PygXlAL+CwiDQEsH1Mc2CNqg6KCwss9bpJWOGqGv3aRFE/4Exryg2dYxCpuPm2np83JVt2c5KTSP3iBVo2b8b7r79Q80XXce47T1/J3xoEKvl+Um6sZOCbNWuWNukqd5UM9BCRACAbGACsA04DI4CJto/fOKxCVSeN/0s7jmfnseXASS5tHsZD/VoC0CjUn28fvpxFWw4RHuTDDZ1jKr1G/UAfujcNY82eo+QkJ5H25YsERzTUPnyVcMvQd+BYNinHzzw+Pp6Vz9aDJ7lM+/Upm02bNmngUwowxqwRkS+B34ACYAMwBQgC5ojIPRQGw5sdV6Wqi0L8vXn/zvgK98WGBXDfFc0r3FfSPTPWsnbvUUx+LunfvoZ3SBQzv/peA18l3DL05VvK9987fjrXAZUoZ3XxxRezYMECBg4cqIFPuT1jzAtA2bayXAqf+il1wTJz8nnmqy1sSz1JrxbhPHdte7w9z94D7fVFO1i8vbBXgXj7EnPz83w//iY6tYqrjZLrJLfs07d+T0a5bQu2HHZAJcrZ/Pvf/2b58uUADB48WAOfUkrVglfmb+fbTQf5I+0UH6/ax5Tlf57znN/2HSMnOYnM3woH2XlEt6Z9iyb2LrVOc0joc/Ts7iWbdoscOlF+wmblXhISEnjkkUeYNm2ao0tRSim3sjv9VOnXaacqPC4n38KSnWms23uURtl/kvbli2T+tgBTkEfT8IBK5+tThWq9ebfE7O7tjTHZIjKHwtnd21M4u/tEERlH4ezuT9mjhorWS80v0Clb3FnJQRsffPCBo8tRSimX98nqfXy/+SCx9QPo1SKCdfvOrIzVv92ZaR9nrUnmncW78PH0wMvTgz1HTpOTnMTReS8R0SCGZn97jeZNGjLlzm6O+DLqFEf16Sua3T2fM7O7Pw30te2fASzFXqGvituUe9BRukopVbv+u/UQz329BYDVHGVA2yjeGHYRWw8W9um7skMDAHYdzuSZr5NKTbhRNErXq14Uq39ZTvMmlY/uVaXVeugzxhwQkaLZ3bOBH4wxP4hIqdndRaTS2d0vvIjyj3899YmwWzLGsG7dOg18SilVi7YeOFHq9ZaDJ5g6snu5IeCpJ3IoOy9zfsZ+vOpFE3P7BGIaNbBvoS7GEc27JWd3Pw58cT6zu4vIKGAUQJMm1euweTInr9y249n5FRypXFlWVhYBAQHMmDEDY4wGPqWUqiWXNAtH5I/iQNejeXiFx3VpEkqgjyen8yxY83Pw8PYjuMs1hHYexKs3d8PXy7MWq677HDGQ44Jmd6+J5XyOniof+k5VsDSbcl0JCQl06dKFtLQ0vLy8NPAppVQturxVBJNv78YNnRvxcL+WPHV1W+6dsZbLX/sfT89LKp5a7dCJHLLzLeQkJ3Hg/XvJPbCD8EBvNr10LbfExzr4q6h7HNGnz+Gzux/JKj9697SGPrdRsg9f/fp2GySulFKqEnuOnKZVdBBXd+wCwJjZG/jJNufe7F+TaRIWwIN9W/BH2imy9p3pw+cVGs34a9oT5OuW0wxfMEf06XP47O5HMss/6cvTkRxuQQdtKKWUY708fxtTf9kDwPDusUwcehHJGadLHfP+8t1MXvoHLa3JxYEv+rYJdGoZx9BujR1RtktwSFR29OzuOXnln+pp5nN9H3/8sQY+pZRyoOSMrOLAB/DZ2v38rWdTruzQgE0pZwZ3HM/KJy99L1s++TuRDRsz/MUPiY6O5sE+LRxRtstwy+ejIX5epJ22lNqmg3dd3+DBg3nqqad4+eWXNfAppZQDfLPxQLltVmN4qF9LGtf3Z8ehTOas3U/G6Ty8w2MJ7nYdox97jBduvcwB1boet1yGDY/yX7aGPtf17bffkpeXR2RkJBMnTtTAp5RSDjJ1xZ5Sry9uHELHmBAAhnSO4amr29Iz6AgFp44iHp40HHg3N/fu5IhSXZJbhr5An/JDvL3d8m/C9SUmJjJkyBDee+89R5eilFJuz1NKP2IZ0jmGBUmprNx9BIBly5bx0bP30mT7LMYNbsu3D19O+0b1HFGqS3LL5t0/K1jTL1c79bmcxMRExo4dy7BhwxgzZoyjy1FKKbe2ft9RckssedqlSSgzVu1lX0YWAP1D0vn8lYeIi4vjq1nTiY6OdlClrsstQ1+uzsPs8koGPh20oZRS9pWTb+GL9Snk5lu4qWtjwgJ9yh0zbm4Sp3JLDqQ0xYEvJzmJ6V++SJsWzVmyZIkGPjtxy9CnD/VcW1paGi+++KIGPqWUqiGncgtYtOUQvl4eDO7YAC/PM32irFbDiGm/smbPUQA+Xb2P+Y/0ZnvqSf5IO8WlzcJoHhlUJvDBhuTC0brGGI4tnY5XvSg++uI7DXx25JahzwvQh32uKyoqitWrV9OiRQsNfErVABFpA3xeYlNz4HkgFLgPSLdtH2+MWVDL5Sk7y86zMGzySnYcygTAx9ODod1ieHlIR7w8PUg9mVMc+AD2ZmSR8MNOpq7YC4C/tyef39+DGzrHMHnZ7nLXFxGihj4HGFo21Tn47Mkthy/kOroAZRcJCQm89tprALRt21YDn1I1xBiz0xjT2RjTGegGZAFf2XYnFO3TwOea1u07Whz4APIsVmb/up9PVu8DIMTfG3/vMwMkBfhqw5mpWbLzLXy6eh/TyozczUlO4sj8tzCWfDwDQ+nZsQURQb72/WLcnFuGPm3edT1FK22sW7cOq1X/hZWyowHAbmPMPkcXompH/YDy/fMADhzLBiDI14v/u70LMaH+hPh74yHC0az8cseWHMSRk1y4tFreoT+w5mbRKSaE9/7axX5fhALcNPQp11J2aTWPCuZhVErVmOHA7BKvHxaRzSIyTUQqXMxaREaJyDoRWZeenl7RIcqJdYwJoUfzsFLbRODqjg2KX/dvG82Kcf3566VNsBhT6tjIIF+8SsyUVhT4vOpFccvzU9j99nC+G3M5UcF+dv06lIY+VcclJibq0mpK1RIR8QGuB76wbZoMtAA6A6nAWxWdZ4yZYoyJN8bER0ZG1kqtqmZF1ysdyNo3rEd807Byx8WE+pfbln4ql2W7MoDSge+iUW/zwQOD8PHSKFJb9G9a1WmBgYHcfPPNGviUqh2Dgd+MMYcBjDGHjTEWY4wV+AC4xKHVKbsZ3LEBJedVviU+ttwxxhjaN6xH0/CASq8jXj74RDZjwgdzWPXyTfhXsFiCsh+3HL2r6r6UlBQaN27Mfffdx7333ouILqSnVC24jRJNuyLS0BiTant5I7DFIVUpu7u6Y0Nm3HUJa/Zk0LFRCIM7NSy1/7Nfk3n26y0UWE2F5xecPIJXvQh8G7WhwR1vcNegLnh76nOn2qZ/46rOSUhIoHXr1mzcuBFAA59StUBEAoBBwLwSm18XkSQR2Qz0A8Y6pDhVYzJz8hn/VRJ3fLiGT1btLbXvitaR/OOqtsWBL7fAQnpmLgeOZTH+q6RKA19OchIHP7yfzE0/4OMlvHVLZ8J1lK5D6JM+VaeUHLTRoUMHR5ejlNswxmQB4WW23emgcpSdjJubxPdJhQ9vf/njCBFBvgzu1JATWfl8tHIPeQVW/tKpIW/8dyc//34EizEEeHtQSd4r1YcvoGV3Xrq+I0O76Vx8jqKhT9UZZUfpah8+pZSqWZsPHC/1elPKCQa1j+avH65m68GTAHz48x7yLGemX8nKr3iarJKBL/q2CVzSrjk3do2xX/HqnLR5V9UJ//3vfzXwKaWUnXUvMyL3kmb1ST2RUxz4gFKBrzKW08dIm/tSceC7vkc7vnigJ75eOnDDkfRJn6oTBg4cyOTJk7nnnns08CmllJ1MuLETDer5sS8jiys7RNO/bTRZeQXU8/PiZE7BuS9g4xlYn/CrHsYv7iK6tW3Gv27shIeH9r92NA19yqlNnTqVQYMG0aRJEx544AFHl6OUUi7Nz9uTJ69uW/zaYjXM/e0A/dpGsTH5GFYD+20rcVQkJzkJY6z4x11McIc+/PyPfsSEVT6Fi6pd2ryrnFZCQgL33nsvb7/9tlyYpHwAACAASURBVKNLUUopt/T0vM089/UWvtl4kH1Hszl8MqfSY4v68B1fOp1ODYP59uHLNPA5mSo/6RORXkDTkucYYz62Q01KlRq08cYbbzi6HKVcit7P3duhEzlsOXCCVtFBxIUHlts/77cUFiQdIjbMn+82Hii1L89SfphuPT8v0nZtKB60cfdL/2HyfVfYrX5VfVUKfSLyCYVL7WwELLbNBtCbhKpxOkpXKfvR+7l723rwBMOnrCYzpwAfLw8++Fs8fVqfWRrvfzsO8/icTed1zbRdGzgy95+ERjXi9Wlfcu+VXWu6bFVDqvqkLx5ob4ypZCYepWpGbm4un376qQY+pexH7+du7I1FO8m0DcjIK7Dy/rLdxaHvj7RMxn5+foEP4PT25XgER/J/n37DbX071Wi9qmZVNfRtARpQuKC2UnZhtVrx9fVl8eLFBAYGauBTyj70fu5mvt+cypSf/8RqNSQdOFFqn7/3mSlUnv9mKyey86t8XWOsiHgQNugBrLlZeAfXr7GalX2cNfSJyHcUPvYPBraJyK9AbtF+Y8z11XlTEQkFPgQ62q5/N7AT+JzCfiZ7gVuMMceqc31V9yQkJPDTTz8xb948QkNDHV2OUi7HXvdz5bxy8i3szTjNI59twFLBkhmeHsK4wYUjddMzc9m4/3i5Yyq9dnISR396n6hhL+JVL4KWsQ0Y1C66xmpX9nGuJ31v2ul93wEWGWOGiYgPEACMBxYbYyaKyDhgHPCUnd5fOZGSffg8PHRAuVJ2Yq/7uXIyJ7LzuXfGWtbuPUZkkG+FgQ/g8pYRtIoOBmD0p+vJyrNUeFxZOclJHJn7T+Li4hh/40U0iG7A5a0iCPHX1hlnd9bQZ4xZBiAirxljSgUwEXkNWHa+bygi9YArgJG298gD8kRkCNDXdtgMYCka+lyeDtpQqnbY436unNPkpbtZu7ewoSz9VC6eHlIc/MICvPHwgBaRwbwx7CIAFmxJZe2+qjWsFU3L4l+/ASt/XkZ0tD7dq0uq+lhlUAXbBlfzPZsD6cBHIrJBRD4UkUAg2hiTCmD7GFXRySIySkTWici69PT0apagnMGkSZM08ClV+2ryfq6cUNl+ea2jg7izRxy9W0VwNCufI6fyWbf3KIu3H2Zw4nJGf/pbla6be2B78bQs3UYnaOCrg84a+kTkQRFJAtqIyOYSf/YASdV8Ty+gKzDZGNMFOE1hU26VGGOmGGPijTHxkZGR5z5BOa2ePXty7733auBTqhbY6X6unNBtl8QS4FM4QMND4K7LmrE7/RQ//36k+BiLgfFfbWH7ocwqX9crLAb/lj2Ivm0Co3RaljrpXH36ZgELgVcpHcwyjTFHq/meKUCKMWaN7fWXtmsfFpGGxphUEWkIpFXz+srJrV69mh49etClSxc++OADR5ejlLuwx/1cOaGLGoey4JHe/JZ8jNbRwSzensbK3RnljqvqnD15h3fjHd4ET/96RF7/D/q0juCOnnE1W7SqFWd90meMOWGM2WuMuc0Ysw/IpvD7JEhEmlTnDY0xh4D9ItLGtmkAsA34Fhhh2zYC+KY611fOLSEhgZ49e/LFF184uhSl3Io97ufKeTWNCOSmro3pGBNS4TQsUsXr5CQncWjmkxxbOo3+baN4Z3hnZtx9ac0Wq2pNlfr0ich1IvI7sIfCzr57KfyNsbrGADNFZDPQGZgATAQG2d5nkO21ciFFgzaGDh3KDTfc4OhylHJL1bmfi0gbEdlY4s9JEXlMRMJE5EcR+d32USdqc0K3dG9MsG9hw54Af+nUkB7Nws55XtGgDa96UYT0vIVpI7szpHOMnatV9lTVyZlfAXoAPxljuohIP+C26r6pMWYjhbPClzWgutdUzq1k4Js9e7b24VPKcc77fm6M2UnhL+iIiCdwAPiKwmZinWrLyby2aAffbTpI4/r+vDHsYto2qMeCR3vzxfr9+Hp60DEmhA+W/3nWa5QMfNG3TaD3RS1qqXplT1UNffnGmAwR8RARD2PMEtsQf6XOafv27TzxxBMa+JRyDhd6Px8A7DbG7NOpthxj/9EsMnMKaNMgGE+P0g21X284wOSluwFIOZbN43M28sUDvfhi3X7e/d8fxcd5nqV91xTkc2T+W3jViyL29gk89JfuPH5lm8pPUHVGVUPfcREJAn6msFk2DSiwX1nKlbRr144ff/yR3r17a+BTyvEu9H4+HJht+7zUVFsiUulUW8AogCZNtPvghZiyfDevLtyBMXBF60imjYjHy/NMT619GVmljt+XkYXFapi8bHep7RYDof7eHK+ov5+XN1FDn8czqD4v39abv/bQQRuuoqrz9A0BsoDHgEXAbuA6exWlXMO7777LokWLAOjfv78GPqWcQ7Xv57YVlK4Hzmsklk61VTNy8i28tmgnxjbsdvmudJbsLD1f7YB2Ufh4nfnRfnXHBngI+Hp5UlbZwJeTnMSJNV8C4BPdnOjISIbFx9bwV6EcqUqhzxhzGogF+hpjZlC4bm6ePQtTdVtCQgKPPvooM2fOdHQpSqkSLvB+Phj4zRhz2Pb6sG2KLXSqrdphTOmJVnann2LLgRPFrzvGhPDF/T0ZcnEjwoN8WLD5IFOW/8krN3Q863WL+vCdTlqMR0Eut18Sy/JxA0oFSFX3Val5V0Tuo/DRfBjQAogB/oMOvFAVKLm02rRp0xxdjlKqhAu8n9/GmaZdODPV1kR0qi278/P25Kmr2zJxUWHzrp+3BxMX7gDg+s6NOHw8h9N5BVzSNIyFW1LJsxQGxFcX7uD+K5pXet2ygzb+b0RPBndqWCtfk6pdVe3T9xBwCbAGwBjze2V9N5R707V0lXJ61bqfi0gAhdNp3V9i80RgjojcAyQDN9d8uaqk+/u04OLGoYz46Fdy8q3F27/deLD48y0HT5Y77/1KRuuWDXyXdWqhgc+FVTX05Rpj8kQKh/uIiBdVn8xbuQljDDt27NDAp5Rzq9b93BiTBYSX2ZaBtvjUuj0Zp8ktsJ77wCooOJmGV0gDooe/Qtc2TZlx9yU1cl3lnKoa+paJyHjAX0QGAaOB7+xXln35ArmOLsLFZGZmEhwczOTJk7FarXh5VfVbSylVy1zqfu6K/kg7RcKPuziRnc8DfVpweasI1u87yl0freVUbgGNQv0v+D2suVl4+AYQ1HEAge2uoGWDUD6599IKB3wo11HVHprjgHQKF+W+H1gAPGuvouztbPMTqfOXkJBAp06dOHjwIB4eHhr4lHJuLnU/dzVHT+dx46QVfJ+Uyi9/HOGOqWv4cdsh7pm+jpM5BVhN4fx7LSIDaR4RiEc1fp7lJCdx4P17yUneDEDbRvVZ/Pe+1PPT1hlXV6WfzsYYq4h8DXxtjEk/5wlOLsBPyMrW1umaULIPn07FoJTzc7X7uavZdvAkmTmlp038aMXectssVsN3Yy6n04s/nNf1S/bh8w6PxVNg2sjuF1y3qhvO+qRPCr0oIkeAHcBOEUkXkedrpzz76NWqfJ/lBkH6SPt86aANpeoOV72fu5pTufmUfXgXXc+XuIiAUtu6xYUR7OfNFa0iqnztsoM2LmoVx7pnBxJTP+DcJyuXcK7m3ceAy4DuxphwY0wYcClwmYiMtXt1dtIopHx/iOgQ/aY/H7NmzdLAp1Td4pL3c1eyZGcaD83aUGpUTYvIQJ4e3A4fz9I/rnPyLdw5dQ1ZeZYqXTv/yP5Sga97u2Z89/Dl1A/0rcGvQDm7czXv/g0YZIw5UrTBGPOniNwB/AAk2LM4e4msIPRF1tNv/PNxzTXX8Oyzz/L8889r4FOqbnDJ+7kr+XbjQSzWM5HvkmZhzLm/JwDhQT6ljl24JRXrefRS8gqPod6lwwjufDXNYhvx0chL8KhOh0BVp53rSZ93yRtEEVs/kDr7kz7Uz6fctsigCx8N5Q7mzp1LdnY2oaGhvPzyyxr4lKo7XPJ+7kqi6/mVet0oxI8Ci5V5v6Wwft+xUvuqGvhyUrZScOIwIh6EXnYb4266lEWPXUFIgP6Tu6Nzhb6zLc1TZ5dhi6pX/pu9UahfBUeqkhISEhg2bBiJiYmOLkUpdf5c8n7uSsb0b8mV7aOp5+dFlyahbEw5TqtnFvL4nE2lJmKuqpzkJNLmPE/GD5MAaBsdxEP9WhHgozMsuKtz/ctfLCLlp/YGAepsSqpoTktPD11f8GxKDtp44oknHF2OUur8ueT93JX4eXsydlBrgv28eO7rLWxIPl7taxUN2vANjabnyGdp17wBL1zfoQarVXXRWUOfMcYlh7TGhpUftNEsItABldQNOkpXqbrPVe/nriKvwMpd039lxR8ZiIC5gFnFSo7SvfWFD5j+0JU1V6iq09zy8VZFo51y8qs2AsrdHD16lFdffVUDn1JK2dGP2w6z4o8M4MICnzGG4ytmFY/Sbd+iSQ1VqFyBWzbsh1Qw63jZDrSqUFhYGKtXryY2NlYDn1JKOTkRIerGZzCWfAZ0acWY/q0cXZJyIm75pK9JeAD92pxZPaJT4xC6Na3vwIqcT0JCAs888wzGGJo3b66BTyml7OB4Vh4f/vwnm1Kq338PbE26X/0La34uHn5BdG4dx/S7L8XfR1v11Rlu+aRPRPjgb/FMWrqb3AIrD/ZpoYtMl1CyD5/VasXTU/9ulFKqpmXlFTB08kp2p5++oOuU7MNn8rK5qnMT3r8zvoaqVK7ELUMfwLh5SXy5PgWAbQdPMHVEd52okvKDNjTwKaWUfWw5cLJGA1/0bRNoFttIA5+qlFuGvv1Hs4oDH8CSnels2H+MbnFhDqzK8RITE3WUrlJK2VmBxcr4r5L4YdvhC7pOzv4tpQJfeHgkPz5+RQ1VqVyRw0KfiHgC64ADxphrRSQM+BxoCuwFbjHGHKv8CtXn6+VRbki8Nu9CgwYNGD58OB9//LEGPqWUqkE/bTvMtBV7CPL1omVUEHPWpZz7pHPw8A3Ep0ErIoc8hWdgfZY+2U9/lqmzcuRAjkeB7SVejwMWG2NaAYttr+0iqp4fT1zZBrG15o7s1ZSOMSH2ejunt2fPHgCGDx+uT/iUUhUSkVAR+VJEdojIdhHpKSIvisgBEdlo+3ONo+t0RrsOZ/LgzPWs3J3BD9sO8/GqfRd0vfzjhzDG4BPVjLg7XqVlXGNWjetPaED5JUaVKskhoU9EGgN/AT4ssXkIMMP2+QzgBnvW8FC/lqx/dhC/PjOAF914lvLExETatGnDmjVrgMJBLkopVYF3gEXGmLbAxZz5pT3BGNPZ9meB48pzXjsPZZJvOdO0dCq3oNrXyklOInXaQ2Su/w6AX54exJIn+tIwVNePV+fmqCd9icCTQMkF0aKNMakAto9RFZ0oIqNEZJ2IrEtPT7+gIsICfYgKdt/5+RITExk7dixDhgyha9euji5HKeWkRKQecAUwFcAYk2eMubA5RtzIxY1D8fe+8B+3JQdtBLbrTWx9fyKDfWugQuUuaj30ici1QJoxZn11zjfGTDHGxBtj4iMjI899gqpQUeDTQRtKqSpoDqQDH4nIBhH5UESK1q58WEQ2i8g0EalwwtOa/GW9Lqof6H3BCwCUHaXrGVifrx66rIYqVO7CEQM5LgOut/X98APqicinwGERaWiMSRWRhkCaA2pzC0uWLNHAp5Q6H15AV2CMMWaNiLxDYb/r94CXAWP7+BZwd9mTjTFTgCkA8fHxF7DIWN1x7HQeExfu4OCJbBqF+LE3I6va17JknyRt7kvFga9L6ybMvK8nwRWsLqXU2dR66DPGPA08DSAifYEnjDF3iMgbwAhgou3jN7Vdm7vo27cv06ZN44477tDAp5SqihQgxRizxvb6S2CcMaZ4zhER+QCY74jiHO14Vh5enh4E+Z75kfrIZxv4+fcjNXJ9T/96RFz7d3wbtaFTyzi+HdO7Rq6r3I8zLcM2ERgkIr8Dg2yvVQ2aMmUKv//+OyLCXXfdpYFPKVUlxphDwH4RaWPbNADYZmuVKXIjsKXWi3Owl+dvo/NLP3LxP3/goxV7irdvTjlR6rjqzP2fk5xE1h+/AhDQqgfBoWHMfbDXBdWr3JtDQ58xZqkx5lrb5xnGmAHGmFa2j0cdWZurSUhI4P777ycxMdHRpSil6qYxwEwR2Qx0BiYAr4tIkm1bP2CsIwusbZv2H2fqL4VBz2I1vDx/G0dP5wEQH1e6e6P1PBu1i/rwHf/5U4zVAsB/x/bRtXTVBXHLFTncTcml1TT0KaWqwxizESi7vtedjqjFWWTlWUq9thpYuzeD9/63m9/TMqt93VKDNm75J8H+Piz+e98LHgyilNuGvlO5BXz2azL5FsMt8Y0JD3LNYe9l19LVJl2llKoZ8U3r07N5OKv+zADguosa8thnm8jOt5zjzMqVHaV714CLee66Dnh7OlNvLFVXuWXoK7BYuePDNWzcXzjN1Jx1+5k/5nICfV3rryM/P5+5c+dq4FNKKTvw9vTglRs6cMv7q8k4nceK3RkXFPgAsv/4tTjwvfW3PtzSPbaGqlXKTUPf/mPZxYEPYM+R0yQdOEGP5uEOrKpmFRQU4O3tzaJFi/D19dXAp5RSNWjrwRM8/81Wfj+cycmcwhU2ivrzVYexWhAPT0L73U1Ir1u5p38HDXyqxrnl8+KwQB/8vc90hvX0EBqGuE5fiYSEBAYNGsTp06cJCgrSwKeUUjXIGMPd09eyft+x4sB3IXKSkzg49SHyj6UiItQLCeWpwe1qoFKlSnPL0Bfi783/3d6FuPAAGoX48frQi4gLDzz3iXVAUR++iIgIfHx08W2llKppp3ILOHwyt0auVdSHT0Tw8PHD39uD5U/2w89bR+mqmueWzbsA/dtG079ttKPLqFE6aEMppewv2M+bS5uFsWZP4cxiHnL+U7JA+UEbgfXqs2Jcf8IC9Rd2ZR9u+aTPFb3//vsa+JRSqhYYY5g6Ip6xA1vRoJ5vtQJf7sGdpQKfT1B9Fo3tS1iga84koZyD2z7pczV9+vThwQcf5J133tHAp5RSNazAYuXT1fv4dc9Rftp+GBC6xYVyqJrNvN7hsQS06U39viPo3rYp0++5lHq6lq6yMw19ddzy5cvp3bs3bdu2ZdKkSY4uRymlXI7Vauj9+hJST+SU2GpY9ef5LxyVm/o73uGxePgGEPGXx3igT3PG6aANVUu0ebcOS0hIoE+fPnz66aeOLkUppVzWj9sPlwl81ZOTnMTh2eM49r8PAWjXIJgx/Vtd8HWVqip90ldHlRy0MXz4cEeXo5RSLiugBkbSlhy0MWzUWEZd1ZUezcMRkRqoUKmq0dBXB+koXaWUqj29W0fSOTa01KT+56Nk4Pvhp5/o27l1DVeoVNVo824ds3v3bp588kkNfEopVQsOHs9m3m8pxIUFVOt8YykgY+E7eNWLosFtEzTwKYfSJ311TIsWLVi2bBndu3fXwKeUUnb0Z/opbpq8kuNZ+dW+hnh6ETXsBTz8goiKcq25YVXdo0/66ojExETmzp0LQK9evTTwKaWUHWXnWfjs1+RqB76c5CSOLf8EYwze4bH4BNVnwaO9a7hKpc6Phr46ICEhgbFjx/Lll186uhSllHJ5s9Yk0+GFRUz5eU+1zi/qw5e9ayV+Jpc7Lm3C1peuJqqe66zxruomt23ezS2w8O3GgxRYDddd3IggX+f8qygatDF06FA+/vhjR5ejlHJTIhIKfAh0BAxwN7AT+BxoCuwFbjHGHHNQiTVi/qaDjP8qqdrnl11abeurN+Llqc9XlHNwzqRjZ1ar4e7pa1nxRwYAH6/ax1ejezndAtclA9/s2bO1SVcp5UjvAIuMMcNExAcIAMYDi40xE0VkHDAOeMqRRVbmRFY+//xuK38eOc2AtlHc1K0x0cG+pQJZvsXKE19sqvZ7lA18b4/oo4FPORW3DH3JR7OKAx/A9tSTbNp/nEubhzuwqvIOHDiggU8p5XAiUg+4AhgJYIzJA/JEZAjQ13bYDGApThr6npq7mUVbDwGwcf9x3vpxF62jg5h1Xw8iggrXu83Jt5BTYK32e1iyT+IV2pDoW19m9Us3EVO/eiN+lbIXtwx9If7e+Hh6kGcp/M8tAuFBzrPI9fHjxwkNDeWNN97AYrHg5eWW/0xKKefRHEgHPhKRi4H1wKNAtDEmFcAYkyoiURWdLCKjgFEATZo0qZ2Ky9hx6GS5bbsOn+I/S3fz7LXtAfDxqt5TOWvOKTz8gghscxkBrXpwe4+mGviUU3LL5871A3144+aLCPH3JtDHk+evbU/LqCBHlwUUNum2a9eOvXv3IiIa+JRSzsAL6ApMNsZ0AU5T2JRbJcaYKcaYeGNMfGRkpL1qPKvLW0VUuD2nwFL8ua+XJ75e57dCRk5yEin/uYfs3esQ4PnrOjLhposupFSl7MZtE8WQzjEM6Rzj6DJKKdmHLybGuWpTSrm1FCDFGLPG9vpLCkPfYRFpaHvK1xBIc1iF5/DCdR1oFOrPyt0ZrN6dQYHVUD/AmxE9m5Y6rl3Demzcf6JK1yzZh8+nQQvmju5F1yb17VC9UjXDbUOfs9FBG0opZ2WMOSQi+0WkjTFmJzAA2Gb7MwKYaPv4jQPLPCtvTw9G923J6L4t2Zdxmj1HTtOhUQiRwWe69qQcy6J5ZFCVQl/ZQRtP3nCJBj7l9Go99IlILPAx0ACwAlOMMe+ISBguNvS/qubMmaOBTynl7MYAM20jd/8E7qKwi9AcEbkHSAZudmB9VRYXHkhceGCpbdNX7OGl+duwGvDz8jjrgI78YwdLBb7re7RlzABdXk05P0c86SsA/m6M+U1EgoH1IvIjhaPC6sTQ/5r2l7/8hZdeeolx48Zp4FNKOSVjzEYgvoJdA2q7lrM5lVvAZ78mk28x3No9lrBAn3OeU2Cx8q8F27GawtfnGsHrFdqQkMv+SlDH/oRHRPHO8K41UbpSdlfrAzmMManGmN9sn2cC24EYYAiFQ/6xfbyhtmurbZ999hmZmZkEBgby3HPPaeBTSqkLUGCxcvuHa3jl++28tmgHQyev5HRuQRXPNec8Jmf/FvIzUhARQi4dSt/OLVn+VD+di0/VGQ79ThWRpkAXYA1lhv4DlQ79F5F1IrIuPT29tkqtcQkJCdx22228/fbbji5FKaVcQvLRLDbtP178es+R02w5cIIlO9PoMWExHZ5fxOiZ68m1jdhNy8zh7R928uhnGzhX5MtJTiLtixc4+uNkAAT4+O5Lqeenv6yrusNhAzlEJAiYCzxmjDkpUrVh8saYKcAUgPj4+HP/auaEigZtDBs2jPHjxzu6HKWUcgnhgb74e3uSnV8Y6jw9hCA/L/427VdybU22C5IOkZP/G/++rQs3/2cV+zKyznndkoM2Iq57Ah9P4euHelHVn1tKOQuHhD4R8aYw8M00xsyzba4zQ/8vRMnAN2vWLG3SVUqpGhIS4M2k27vyz++2km8xPHFVawJ9vIoDX5HVu4+w83DmeQe+no+8w7QHBtIsIggPDw18qu5xxOhdAaYC240xJds2v6WODP2vrhMnTvDWW29p4FNKKTvp1zaKfm3P9A6yWA3NIwL588jp4m2tooNpFOKPpwgWc/YGo5Nr5uJVL4rBT03im39ca7e6laoNjnjSdxlwJ5AkIhtt28ZTGPbq3ND/qjLGEBISwqpVq2jQoIEGPqWUqgWeHsJ3Yy7nnhlr2ZZ6kthQf568ui0GQ4MQPw4cz67wPGMMIkLEkKeI9jfMeOjKWq5cqZpX66HPGPMLhX1gK+JUQ/9rSkJCAnv27OGdd94hNjbW0eUopZRbmbfhAGv+PIoBtmZncvuHa/D2EPKtFT/ly0lO4sTqL4gcMo6QesH88GR/QgPOPfWLUs5Ox5nbWVEfvtTUVCwWy7lPUEopVaPeXfx7udG5Zwt8aV++iOVkOqYgj/+7vSv1qzDXn1J1gS7DZkdlB214eelft6vKz88nJSWFnJwcR5dSbX5+fjRu3Fi7Hqg6x2o1TF62m3V7j9IpJoQCi2FL6kkubRbGA1c0Jye/ar9wl11abfzQS7midYWzhylVJ2kKsZN33nlHR+m6kZSUFIKDg2natGmdnMbBGENGRgYpKSk0a9bM0eUodV4++PlP3vjvTgCW7Dwzf+vyXen8fjiTzJxzT9Ccs39LqcD37LAe3N+npd1qVsoRtHnXTpo3b85f//pXDXxuIicnh/Dw8DoZ+ABEhPDw8Dr9pFK5rw3Jxyvdt/1QZpWu4RlYH99G7Yi+bQJTHxiogU+5JA19NWzXrl0AXHfddcycOVMDnxupq4GvSF2vX7mvrnGhle9rEnrWH3T5Rw9gjME7LIbo4a/w+PWXcGWHBjVfpFJOQJt3a1BCQgL/+Mc/+N///scVV1zh6HKUUsot3Ne7OcbA2r1H6RQTiohhy4GTnMotYPav+ys9r6gPX+QVf+WGEaO5+7JmXNo8vBYrV6p2aeirISUHbfTs2dPR5SillNsQEe7v04L7+7Qo3pZ2ModLJiyu9JySgza+TnyGnh1bVHqsUq5CQ18N0KXVlFKqduw6nMnqPzNoFRVMzxbVeypXMvCNmjhdA59yGxr6LtCKFSs08CmlVC2YtSaZZ79OomiKvQk3duKvlzap8Nioen482LcFk5fuLrXdmnua9HmvFI/SvebSdvYuWymnoaHvAvXq1YvZs2czdOhQDXyqWN++fcttu+WWWxg9ejRZWVlcc8015faPHDmSkSNHcuTIEYYNG1Zq39KlS+1UqVJVIyJ7gUzAAhQYY+JF5EXgPqBonpTxxpgF9nj/tMwcXvh2CyXnVP509V5W7D7C4u2HaREZxOTbu5F8NIt/fLmJzJwCRl3RnOl3dWfkR2uLz/HwDSRiyFP4RDWjXfNYrtZBG8qN6Ojdapo8eTJJSUmICMOHD9fAp5zCwoUL6devH8899xxLliyhT58+/P3vf3d0Wcp19DPGdDbGxJfYlmDb1tlegQ/gz/TT5FtKr6KRmVPAN1IoqgAAEetJREFU95tTycm3svXgScZ/lcSDM9eTeiKHU7kFvP3jLvy9PbmsZTg5yUmc3v4zAP7NutKjfTO+ffhyPDx01LpyH/qkrxoSExMZO3Yso0aN4v3333d0OcoJne3JXEBAwFn3R0REVPvJ3uLFi1myZAmvv/46CQkJ/PTTT8yePZtt27bRvn37al1TKWewft/RUq89PaB70zD2HztQvO3QyZxyEzEfOZXHXc2zmTvmJaJimjDllYdpFxNGbFhArdStlDPRJ33nqSjwDRs2jPfee8/R5ShVijGFT0LCwsI4deoUFosFY0zxdqUugAF+EJH1IjKqxPaHRWSziEwTkfoVnSgio0RknYisS09Pr+iQc/p41b5Sr++5vBkjejXF1+vMj7HOsaFEB/sWv44J9ccc3MqQ666lebOmrF2xjCs7NdbAp9yWhr7zUDLw6aAN5YwGDhzIgAED2L59Oy+++CJXXnkl69ato0OHDo4uTdV9lxljugKDgYdE5ApgMtAC6AykAm9VdKIxZooxJt4YEx8ZGVmtNw/0Kd0w1bh+ABfHhvLtw5fz3LXtefYv7Zj3WwqHM3MBaB4RyJMXW7h16BDi4uJYsmQJ0dHR1XpvpVyFNu9WkcViYcGCBRr4lFMbPHgwgwcPLn69fPlyB1ajXIkx5qDtY5qIfAVcYowp/gYTkQ+A+fZ6/3/d2In7P1nHyZwCereK4Jb4WADa/H979x9cVX3mcfz9EMAYDGACIhghgSLIz4DUFtlxFVYFRG2RdtDtDs6yuuPvH3W6ZhlndGdHZ3FtqG3XX6hlEWmrhcIIimh309rdVvEXEAWhGCBiiQZWQBqF5Nk/7rl4QQg/cu459+Z8XjN3cs/h3vM83+Tk4ck533PP6cWc1esUfvybDQdd5LHt07/w5h/+oIZPJIOavmPwxRdf0LlzZ5YsWULHjh3V8IlIophZF6CDu+8Onl8M/IuZ9Xb3j4KXfRtYm60cxg4o5Y27L2JP035O7dL5wPqtO/Zy+U9eZefefQfWefM+RvU/nXuuvYc777yT4uLibKUlklfU9B3FnDlzWLhwIStXrqRr165xpyMiEodewOLg/swdgWfc/UUzm29mlaTm+9UB/5jNJDoVdODULp1pbnH+edEalq/9iOYWZ+8XzQdes79+LXtWPsTNzy/DzNTwyRHt27eP+vp6mpqa4k7lhBQWFlJWVnZcB6LU9LUicw7fySefHHc6IiKxcPdNwMjDrP+7GNJh4Wtb+MWqr95TN32njcFf68+Avr1jyEzySX19PcXFxZSXlxP8QZM33J3Gxkbq6+upqKg45vfpQo4j0EUbIiK5afuurx6ZSTd8xT16aw6fHJOmpiZKS0vzruGD1P2mS0tLj/sopZq+w5g7d64aPhGRHDVpWG9O7lRwYPnrXXbS+Kt76Xl6GWtf/x81fHLM8rHhSzuR3HV69zAmTJjAzTffzIMPPqiGT0Qkxwzp05UlN43jv9c30LekiPP7d+P7237PPffco4ZPpBU60pfh5ZdfpqWlhYqKCh566CE1fCIiOeqsXsWMPOkTxp5ZRFFREQ8//LAaPpGjUNMXqK6u5qKLLuKJJ56IOxURETmKmpoaxo8fzy233BJ3KiJ5I+eaPjObaGbrzWyjmd0VRczq6mruuOMOpk2bxjXXXBNFSJGsePTRR7nhhhsOWjd06FDWrVsXU0Yi4aupqWHy5Mn069eP2bNnx52OSJtEWbdzqukzswLgp6Ru8zMEuMrMsnqX+MyGTxdtSL5bvXo1o0aNOrDc1NTEli1bGDhwYIxZiYQns+HTVbrSHkRZt3Oq6QPOBTa6+yZ3/wL4OXBFtoJt2bKFqqoqNXwSua079jLjydeYOOe3zP3dptC2u2bNGkaPHn3Q8llnnUVBQUEr7xLJD83NzVx//fVq+CQWP3p5AxPn/JZ/mLeKhsN8bNCJirJu59rVu2cAmZ+4WQ98I/MFZnYdcB1A37592xSsb9++vPrqq4wcOVINn0TqxmfeZHX9pwD867L3GHDaKVw46LQ2b7e2tpapU6ceuJR/z549TJkypc3bFckFBQUFLFu2jKKiIjV8Eqlfv/Uh1S+/D8C6P+/m8/3NzJ/5jaO869hEWbdz7Ujf4T50xg9acH/M3ce4+5iePXueUJDq6mrmzZsHwJgxY9TwSeQ2Nuw5aPlPhyyfiK1bt9KzZ082b95MXV0ddXV1TJ8+nREjRvDZZ58xY8YMrr32WhYsWNDmWCJRqqmp4fbbbz/w6Qpq+CRq2ajZ0Hrd3rRpEzNnzmTatGmhxILca/rqgTMzlsuAbWEGSM/hW758Oe5+9DeIZMGFg788qte5YwfGfa1Hm7e5evVqhg4detC6d999l+HDh7No0SKmTZvG448/ztKlS9scSyQq6Tl8K1asYNeuXXGnIwn114N6UtDhy+NSFwxu+5kZaL1u9+/fP/RPFMm107uvAwPNrAL4EJgOXB3WxjMv2nj66afz+pO4Jb/98LsjGdanG9t3NXF5ZR/O7t21zdtcs2YNQ4YcfN1TbW0tI0aMYNWqVQwfPhxA8/skbxx60Ub37t3jTkkS6uvlJcyfeS4v1W7nzJIiZoztF8p2W6vb2ZBTTZ+77zezm4AVQAHwpLvXhrFtXaUrueSkjgVcf8GAULe5Zs2ag+aB7NixA3enV69elJWVUV9fT2VlJS0tLaHGFckGXaUruea8AT04b0Dbz8pkaq1uZ0NONX0A7r4cWB72dvfs2aOGT9q1Q+fqlZSU0NDQAMDUqVO56aabWLZsGZdddlkc6Ykcl7179zJo0CBeeOEFNXzSbrVWtxsbG5k1axZvvfUW999/P1VVVW2Ol3NNX9g++eQTevTowd13301LSwsdOuTaNEaR7OvSpQtPPfVU3GmIHFW6Zk+aNIlLLrlENVsSq7S0lEceeSTUbbbr36bq6moGDRrEhg0bAFQ8RERyWE1NDf3792fRokWAarZI2Nrtb1R6Dt/48eMpLy+POx0REWlFeg5fWVkZ48aNizsdkXapXZ7e1UUbIiLhMrM6YDfQDOx39zFmVgL8AigH6oDvuvvO4922LtoQiUa7O9K3ePFiNXwSi3z/3Md8z18icaG7V7r7mGD5LuAVdx8IvBIsH5fNmzer4ZPY5HPdO5Hc213TN3nyZGbPnq2GTyJVWFhIY2Nj3hYQd6exsZHCwsK4U5H8cgUwL3g+D/jW8W6gX79+PPDAA2r4JHL5XLdPtGZbPg42bcyYMb5q1SoA5s+fz6WXXkpJSUnMWUkS7du3j/r6epqawrsJd9QKCwspKyv7yh9LZvZGxpEdSSgz+wDYSerWmI+6+2Nm9n/u3j3jNTvd/dTDvDfznunnbN68mZqaGrp160ZlZWVUQxA5SL7X7ROp2e1iTl96Dl9VVRX33Xdf3OlIAnXq1ImKioq40xDJpnHuvs3MTgNWmtm6Y32juz8GPAapP9bTc/jOOeccampqdHckiUUS63ben95NN3xXXnkl9957b9zpiIi0S+6+LfjaACwGzgW2m1lvgOBrw9G2s3v37gNz+J599lk1fCIRyuumb/v27QcavoULF2oOn4hIFphZFzMrTj8HLgbWAkuBGcHLZgBLjratjRs36qINkZjk9endhoYGNXwiItnXC1gcHJXrCDzj7i+a2evAL81sJrAF+M7RNtS5c2c1fCIxyesLOczsY2BzGzfTA/gkhHTyNX4u5BB3/FzIIZfj93P3nlEmI+3XEep23Pt/WNrLOEBjyUXHOo4j1uy8bvrCYGar4rwyMe74uZBD3PFzIYekx5dkay/7X3sZB2gsuSiMceT1nD4REREROTZq+kREREQSQE1f8NlRCY4P8ecQd3yIP4ekx5dkay/7X3sZB2gsuajN40j8nD4RERGRJNCRPhEREZEEUNMnIiIikgCJbfrMbKKZrTezjWZ2V0QxzzSz/zKz98ys1sxuDdaXmNlKM9sQfP3KDctDzqPAzN4ys+djit/dzJ4zs3XB92JslDmY2e3B93+tmS00s8JsxjezJ82swczWZqw7Yjwzqwr2y/VmdkkWc3gg+BmsNrPFZtY9mzmIAJhZnZmtMbO3zWxVsC7SGhSWuGtZGMxsUPCzSD92mdlt+TaOtKjre7aY2a3BGGrN7LZgXZvHkcimz8wKgJ8Ck4AhwFVmNiSC0PuB77v72cA3gRuDuHcBr7j7QOCVYDmbbgXey1iOOv6PgBfdfTAwMsglkhzM7AzgFmCMuw8DCoDpWY7/M2DiIesOGy/YH6YDQ4P3/Eewv2Yjh5XAMHcfAbwPVGU5B5G0C929MuMzx6KuQWGJrZaFxd3XBz+LSuAcYC+peyvn1TggtvoeOjMbBlxL6v7WI4EpZjaQMMbh7ol7AGOBFRnLVUBVDHksAS4C1gO9g3W9gfVZjFkW7CzjgeeDdVHG7wp8QHARUcb6SHIAzgC2AiWkbif1PKn7iGY1PlAOrD3aeA/dF4EVwNhs5HDIv30bWJDtHPTQA6gDehyyLrIaFOI4Yq1lWRrTxcDv83UccdX3LIzjO8DcjOW7gR+EMY5EHunjyx0jrT5YFxkzKwdGAX8Eern7RwDB19OyGHoOqZ2nJWNdlPH7Ax8DTwWnmOda6gbukeTg7h8C/07qPqEfAZ+6+0tRxc9wpHhx7Zt/D7wQcw6SDA68ZGZvmNl1wbqof//CEGsty5LpwMLged6NI4fqe1utBc43s1IzKwImA2cSwjiS2vTZYdZF9tk1ZnYK8CvgNnffFWHcKUCDu78RVczD6AiMBh5291HAZ0R4qD2YA3EFUAH0AbqY2feiin8MIt83zWwWqakHC+LKQRJlnLuPJjW95kYzOz/uhE5QrLUsbGbWGbgceDbuXE5UHtT3Y+Lu7wH/RmoKzovAO6RqdJsltemrJ9U1p5UB26IIbGadSDV8C9x9UbB6u5n1Dv69N9CQpfDjgMvNrA74OTDezJ6OMD6kvvf17v7HYPk5UoUzqhz+BvjA3T92933AIuC8COOnHSlepPummc0ApgB/68E5g6hzkGRx923B1wZSc8fOJfrfvzDEXcvCNgl40923B8v5OI5cqe9t5u5PuPtodz8f2AFsIIRxJLXpex0YaGYVwV8304Gl2Q5qZgY8Abzn7j/M+KelwIzg+QxSc/1C5+5V7l7m7uWkxvwbd/9eVPGDHP4MbDWzQcGqCcC7EeawBfimmRUFP48JpCZfR/Y9CBwp3lJgupmdZGYVwEDgtWwkYGYTgX8CLnf3vYfkFkkOkixm1sXMitPPSc23Wkv0v39tlgO1LGxX8eWpXcjPceRKfW8zMzst+NoXmErqZ9P2ccQ9YTGuB6lz5O8DfwJmRRTzr0idJlsNvB08JgOlpC6u2BB8LYkglwv48kKOSOMDlcCq4Pvwa+DUKHMA7gXWkfrPZj5wUjbjB7+sHwH7SB0dmNlaPGBWsF+uByZlMYeNpObupffFR7KZgx56kJoH907wqE3X3jhqYEjjibWWhTiOIqAR6JaxLu/GEeQdaX3P4jh+R+qPiHeACWH9THQbNhEREZEESOrpXREREZFEUdMnIiIikgBq+kREREQSQE2fiIiISAKo6RMRERFJADV90mZm1mxmb5vZO2b2ppmdF6zvY2bPHeE95WZ2dcbyNWb2k6hyFhFJKtXs5FLTJ2H4i7tXuvtIoAq4H1KfvO/u0w59sZl1BMqBqw/9NxERyTrV7ITqGHcC0u50BXZC6i9DUh8APczMrgEuBQqBLqQ+DPRsM3sbmBe8p4+ZvQgMABa7+w8iz15EJFlUsxNETZ+E4eSgEBQCvYHxR3jdWGCEu+8wswuAO919CqROFZD6dPtRwOfAejP7sbtvzXbyIiIJo5qdUDq9K2FInyoYDEwE/jO47+GhVrr7jla284q7f+ruTaRuP9MvG8mKiCScanZCqemTULn7/wI9gJ6H+efPjvL2zzOeN6Mj0SIiWaWanSxq+iRUZjYYKCB18+7W7AaKs5+RiIgciWp2sqgrlzCk54cAGDDD3ZsPf7bggNXAfjN7B/gZwURiERHJOtXshDJ3jzsHEREREckynd4VERERSQA1fSIiIiIJoKZPREREJAHU9ImIiIgkgJo+ERERkQRQ0yciIiKSAGr6RERERBLg/wHt9qH1nOurxgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 864x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "dgms = ripser(np_data, maxdim=1)['dgms']\n",
    "\n",
    "\n",
    "plt.figure(figsize=(12, 4))\n",
    "plot_diagrams(dgms, plot_only=[0], ax=plt.subplot(121))\n",
    "plot_diagrams(dgms, plot_only=[1], ax=plt.subplot(122))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot_diagrams(dgms, show=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_landmark.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "dgms = ripser(data_landmark, maxdim=1)['dgms']\n",
    "\n",
    "\n",
    "plt.figure(figsize=(8, 4))\n",
    "plot_diagrams(dgms, plot_only=[0], ax=plt.subplot(131))\n",
    "plot_diagrams(dgms, plot_only=[1], ax=plt.subplot(132))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot_diagrams(dgms, show=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Eigen plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "from manifold_utils.mSVD import eigen_plot, eigen_calc_from_dist_mat, eps_projection, eigen_plot_numPoints, eigen_calc_from_dist_mat_withNumPoints\n",
    "from manifold_utils.iga import chakraborty_express, iga"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "787\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "134\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "960\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "949\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "791\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "347\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "150\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "547\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "842\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "512\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "569\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "220\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1113\n"
     ]
    },
    {
     "data": {
      "image/png": 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Fi9Ta2qpZs2Zp27ZtioqKCsNLAgAAg53LGGMiXUR/BYNBeTweBQIBzkcBgKtILXwj0iX029kNeZEuAQOoP+/f3IsHAABYh4ACAACsQ0ABAADWIaAAAADrEFAAAIB1CCgAAMA6BBQAAGCdfn9RGwAAA6Uv393Cd6UMD6ygAAAA6xBQAACAdQgoAADAOgQUAABgHQIKAACwDgEFAABYh4ACAACsQ0ABAADWIaAAAADrEFAAAIB1CCgAAMA6BBQAAGAdAgoAALAOAQUAAFiHgAIAAKxDQAEAANYhoAAAAOsQUAAAgHUIKAAAwDoEFAAAYB0CCgAAsA4BBQAAWIeAAgAArENAAQAA1iGgAAAA6xBQAACAdaIjXQAAoH9SC9+IdAnAgGMFBQAAWIeAAgAArBP2gPL555/re9/7ntLS0hQbG6vJkyfr2WefVVdXlzPHGKPi4mL5/X7FxsYqJydHp06dCncpAABgkAp7QHn++ef1yiuvqLy8XP/93/+tjRs36oc//KFeeuklZ87GjRu1adMmlZeX68iRI/L5fJozZ45aWlrCXQ4AABiEwh5Qfvvb3+ob3/iG8vLylJqaqm9+85vKzc3V0aNHJX2xelJWVqb169dr4cKFysjI0Pbt23X58mXt3Lkz3OUAAIBBKOwBZcaMGXrrrbd0+vRpSdLvf/97HTp0SPfee68kqa6uTo2NjcrNzXWe43a7lZ2drerq6h6P2dbWpmAwGLIBAIChK+yXGa9bt06BQEA333yzoqKi1NnZqeeee04PPfSQJKmxsVGS5PV6Q57n9XpVX1/f4zFLS0v1zDPPhLtUAABgqbCvoOzevVs7duzQzp07dezYMW3fvl0vvPCCtm/fHjLP5XKFPDbGdBu7oqioSIFAwNkaGhrCXTYAALBI2FdQ1qxZo8LCQj344IOSpClTpqi+vl6lpaVaunSpfD6fpC9WUsaPH+88r6mpqduqyhVut1tutzvcpQIAAEuFfQXl8uXLuumm0MNGRUU5lxmnpaXJ5/OpoqLC2d/e3q6qqiplZWWFuxwAADAIhX0FZf78+Xruuec0ceJE3XrrrTp+/Lg2bdqkb3/725K++GgnPz9fJSUlSk9PV3p6ukpKShQXF6fFixeHuxwAADAIhT2gvPTSS/r+97+v5cuXq6mpSX6/X8uWLdM///M/O3PWrl2r1tZWLV++XM3NzZo+fboOHDighISEcJcDABhi+nIvorMb8m5AJRhILmOMiXQR/RUMBuXxeBQIBJSYmBjpcgDghuJmgb0joNipP+/f3IsHAABYh4ACAACsQ0ABAADWIaAAAADrEFAAAIB1CCgAAMA6BBQAAGAdAgoAALAOAQUAAFiHgAIAAKxDQAEAANYhoAAAAOuE/W7GAIDrx40AgS+wggIAAKxDQAEAANYhoAAAAOsQUAAAgHUIKAAAwDoEFAAAYB0CCgAAsA4BBQAAWIeAAgAArENAAQAA1iGgAAAA6xBQAACAdQgoAADAOgQUAABgHQIKAACwDgEFAABYh4ACAACsQ0ABAADWIaAAAADrEFAAAIB1CCgAAMA6BBQAAGAdAgoAALAOAQUAAFiHgAIAAKwzIAHlk08+0SOPPKLk5GTFxcXptttuU01NjbPfGKPi4mL5/X7FxsYqJydHp06dGohSAADAIBT2gNLc3Ky7775bMTEx+vWvf60PPvhA//qv/6pRo0Y5czZu3KhNmzapvLxcR44ckc/n05w5c9TS0hLucgAAwCAUHe4DPv/880pJSdHWrVudsdTUVOe/jTEqKyvT+vXrtXDhQknS9u3b5fV6tXPnTi1btizcJQEAgEEm7Cso+/fv17Rp0/Stb31L48aN0+23365XX33V2V9XV6fGxkbl5uY6Y263W9nZ2aquru7xmG1tbQoGgyEbAAAYusK+gvKHP/xBmzdvVkFBgb773e/q8OHDevLJJ+V2u7VkyRI1NjZKkrxeb8jzvF6v6uvrezxmaWmpnnnmmXCXCgAYolIL3+h1ztkNeTegElyvsK+gdHV16Y477lBJSYluv/12LVu2TP/4j/+ozZs3h8xzuVwhj40x3cauKCoqUiAQcLaGhoZwlw0AACwS9oAyfvx4ffWrXw0Zu+WWW3Tu3DlJks/nkyRnJeWKpqambqsqV7jdbiUmJoZsAABg6Ap7QLn77rv14YcfhoydPn1akyZNkiSlpaXJ5/OpoqLC2d/e3q6qqiplZWWFuxwAADAIhf0clO985zvKyspSSUmJFi1apMOHD2vLli3asmWLpC8+2snPz1dJSYnS09OVnp6ukpISxcXFafHixeEuBwAADEJhDyh33nmn9u7dq6KiIj377LNKS0tTWVmZHn74YWfO2rVr1draquXLl6u5uVnTp0/XgQMHlJCQEO5yAADAIOQyxphIF9FfwWBQHo9HgUCA81EADCl9ufoE4cFVPDdef96/uRcPAACwDgEFAABYh4ACAACsQ0ABAADWIaAAAADrEFAAAIB1CCgAAMA6BBQAAGAdAgoAALAOAQUAAFiHgAIAAKxDQAEAANYhoAAAAOsQUAAAgHUIKAAAwDoEFAAAYB0CCgAAsA4BBQAAWIeAAgAArENAAQAA1iGgAAAA6xBQAACAdaIjXQAADBephW9EugRg0GAFBQAAWIeAAgAArENAAQAA1iGgAAAA6xBQAACAdQgoAADAOgQUAABgHQIKAACwDgEFAABYh4ACAACsQ0ABAADWIaAAAADrEFAAAIB1CCgAAMA6Ax5QSktL5XK5lJ+f74wZY1RcXCy/36/Y2Fjl5OTo1KlTA10KAAAYJAY0oBw5ckRbtmzR1772tZDxjRs3atOmTSovL9eRI0fk8/k0Z84ctbS0DGQ5AABgkBiwgHLx4kU9/PDDevXVVzV69Ghn3BijsrIyrV+/XgsXLlRGRoa2b9+uy5cva+fOnQNVDgAAGEQGLKCsWLFCeXl5mj17dsh4XV2dGhsblZub64y53W5lZ2erurq6x2O1tbUpGAyGbAAAYOiKHoiD7tq1SzU1NTp69Gi3fY2NjZIkr9cbMu71elVfX9/j8UpLS/XMM8+Ev1AAAGClsK+gNDQ0aPXq1frJT36ikSNHXnWey+UKeWyM6TZ2RVFRkQKBgLM1NDSEtWYAAGCXsK+g1NTUqKmpSZmZmc5YZ2enDh48qPLycn344YeSvlhJGT9+vDOnqamp26rKFW63W263O9ylAgAAS4V9BWXWrFk6ceKEamtrnW3atGl6+OGHVVtbq8mTJ8vn86miosJ5Tnt7u6qqqpSVlRXucgAAwCAU9hWUhIQEZWRkhIzFx8crOTnZGc/Pz1dJSYnS09OVnp6ukpISxcXFafHixeEuBwAADEIDcpJsb9auXavW1lYtX75czc3Nmj59ug4cOKCEhIRIlAMAACzjMsaYSBfRX8FgUB6PR4FAQImJiZEuBwD6JLXwjUiXgL9wdkNepEsYdvrz/s29eAAAgHUIKAAAwDoEFAAAYB0CCgAAsA4BBQAAWIeAAgAArENAAQAA1iGgAAAA60Tkm2QBAIi0vnxxHl/mFjmsoAAAAOsQUAAAgHUIKAAAwDoEFAAAYB1OkgWAMOBOxUB4sYICAACsQ0ABAADWIaAAAADrEFAAAIB1CCgAAMA6BBQAAGAdAgoAALAOAQUAAFiHgAIAAKxDQAEAANYhoAAAAOtwLx4AAK6iL/dYOrsh7wZUMvywggIAAKxDQAEAANYhoAAAAOsQUAAAgHUIKAAAwDoEFAAAYB0CCgAAsA4BBQAAWIeAAgAArENAAQAA1iGgAAAA6xBQAACAdcIeUEpLS3XnnXcqISFB48aN0/33368PP/wwZI4xRsXFxfL7/YqNjVVOTo5OnToV7lIAAMAgFfaAUlVVpRUrVui//uu/VFFRoc8//1y5ubm6dOmSM2fjxo3atGmTysvLdeTIEfl8Ps2ZM0ctLS3hLgcAAAxC0eE+4G9+85uQx1u3btW4ceNUU1Ojr3/96zLGqKysTOvXr9fChQslSdu3b5fX69XOnTu1bNmycJcEAAAGmQE/ByUQCEiSkpKSJEl1dXVqbGxUbm6uM8ftdis7O1vV1dU9HqOtrU3BYDBkAwAAQ9eABhRjjAoKCjRjxgxlZGRIkhobGyVJXq83ZK7X63X2fVlpaak8Ho+zpaSkDGTZAAAgwgY0oKxcuVLvv/++fvrTn3bb53K5Qh4bY7qNXVFUVKRAIOBsDQ0NA1IvAACwQ9jPQbli1apV2r9/vw4ePKgJEyY44z6fT9IXKynjx493xpuamrqtqlzhdrvldrsHqlQAAGCZsK+gGGO0cuVK7dmzR2+//bbS0tJC9qelpcnn86miosIZa29vV1VVlbKyssJdDgAAGITCvoKyYsUK7dy5U7/4xS+UkJDgnFfi8XgUGxsrl8ul/Px8lZSUKD09Xenp6SopKVFcXJwWL14c7nIAAMAgFPaAsnnzZklSTk5OyPjWrVv12GOPSZLWrl2r1tZWLV++XM3NzZo+fboOHDighISEcJcDAAAGobAHFGNMr3NcLpeKi4tVXFwc7h8PAACGAO7FAwAArENAAQAA1iGgAAAA6xBQAACAdQgoAADAOgQUAABgHQIKAACwDgEFAABYh4ACAACsQ0ABAADWIaAAAADrEFAAAIB1CCgAAMA6BBQAAGAdAgoAALBOdKQLAADbpRa+EekSgGGHFRQAAGAdAgoAALAOAQUAAFiHc1AAABhgfTmP6eyGvBtQyeDBCgoAALAOAQUAAFiHgAIAAKxDQAEAANbhJFkAwxpfwgbYiRUUAABgHQIKAACwDgEFAABYh4ACAACsw0myAAD8FTjRemCwggIAAKxDQAEAANYhoAAAAOsQUAAAgHU4SRbAkMXJixhq+vI7fXZD3g07zkBiBQUAAFiHgAIAAKwT0YDy8ssvKy0tTSNHjlRmZqbee++9SJYDAAAsEbGAsnv3buXn52v9+vU6fvy4/v7v/17z5s3TuXPnIlUSAACwhMsYYyLxg6dPn6477rhDmzdvdsZuueUW3X///SotLb3mc4PBoDwejwKBgBITE8Ne22A4eQgY7jgBFuiZzSfJ9uf9OyJX8bS3t6umpkaFhYUh47m5uaquru42v62tTW1tbc7jQCAg6YsXOhC62i73OmegfjaAvunLv1NgOOrL+1Ok3ueuHLMvayMRCSiffvqpOjs75fV6Q8a9Xq8aGxu7zS8tLdUzzzzTbTwlJWXAauyNpyxiPxoAgKsK1/vTQL7PtbS0yOPxXHNORL8HxeVyhTw2xnQbk6SioiIVFBQ4j7u6uvSnP/1JycnJPc7/awSDQaWkpKihoWFAPj4aCuhR7+hR7+hR7+hR7+hR39jSJ2OMWlpa5Pf7e50bkYAyZswYRUVFdVstaWpq6raqIklut1tutztkbNSoUQNaY2JiIr/svaBHvaNHvaNHvaNHvaNHfWNDn3pbObkiIlfxjBgxQpmZmaqoqAgZr6ioUFZWViRKAgAAFonYRzwFBQV69NFHNW3aNP3d3/2dtmzZonPnzumJJ56IVEkAAMASUcXFxcWR+MEZGRlKTk5WSUmJXnjhBbW2tur111/X1KlTI1FOiKioKOXk5Cg6mlsVXQ096h096h096h096h096pvB1qeIfQ8KAADA1XAvHgAAYB0CCgAAsA4BBQAAWIeAAgAArENAAQAA1iGg/IWXX35ZaWlpGjlypDIzM/Xee+9FuqSIKS0t1Z133qmEhASNGzdO999/vz788MOQOcYYFRcXy+/3KzY2Vjk5OTp16lSEKo680tJSuVwu5efnO2P0SPrkk0/0yCOPKDk5WXFxcbrttttUU1Pj7B/uPfr888/1ve99T2lpaYqNjdXkyZP17LPPqqury5kzHHt08OBBzZ8/X36/Xy6XS/v27QvZ35eetLW1adWqVRozZozi4+O1YMECffzxxzfyZQyoa/Woo6ND69at05QpUxQfHy+/368lS5bo/PnzIcewukcGxhhjdu3aZWJiYsyrr75qPvjgA7N69WoTHx9v6uvrI11aRMydO9ds3brVnDx50tTW1pq8vDwzceJEc/HiRWfOhg0bTEJCgvn5z39uTpw4YR544AEzfvx4EwwGI1h5ZBw+fNikpqaar8PIjAwAAAZhSURBVH3ta2b16tXO+HDv0Z/+9CczadIk89hjj5nf/e53pq6uzlRWVpozZ844c4Z7j/7lX/7FJCcnm1/+8pemrq7O/Md//If5m7/5G1NWVubMGY49+tWvfmXWr19vfv7znxtJZu/evSH7+9KTJ554wnzlK18xFRUV5tixY2bmzJlm6tSp5vPPP7/RL2dAXKtHf/7zn83s2bPN7t27zf/8z/+Y3/72t2b69OkmMzMz5Bg294iA8v/cdddd5oknnggZu/nmm01hYWGEKrJLU1OTkWSqqqqMMcZ0dXUZn89nNmzY4Mz57LPPjMfjMa+88kqkyoyIlpYWk56ebioqKkx2drYTUOiRMevWrTMzZsy46n56ZExeXp759re/HTK2cOFC88gjjxhj6JExptubb1968uc//9nExMSYXbt2OXM++eQTc9NNN5nf/OY3N674G6SnEPdlhw8fNpKc//G2vUd8xCOpvb1dNTU1ys3NDRnPzc1VdXV1hKqySyAQkCQlJSVJkurq6tTY2BjSM7fbrezs7GHXsxUrVigvL0+zZ88OGadH0v79+zVt2jR961vf0rhx43T77bfr1VdfdfbTI2nGjBl66623dPr0aUnS73//ex06dEj33nuvJHrUk770pKamRh0dHSFz/H6/MjIyhm3fAoGAXC6Xc7Nd23s0OL7vdoB9+umn6uzs7HYnZa/X2+2Oy8ORMUYFBQWaMWOGMjIyJMnpS089q6+vv+E1RsquXbtUU1Ojo0ePdttHj6Q//OEP2rx5swoKCvTd735Xhw8f1pNPPim3260lS5bQI0nr1q1TIBDQzTffrKioKHV2duq5557TQw89JInfo570pSeNjY0aMWKERo8e3W3OcPy7/tlnn6mwsFCLFy927mZse48IKH/B5XKFPDbGdBsbjlauXKn3339fhw4d6rZvOPesoaFBq1ev1oEDBzRy5MirzhvOPerq6tK0adNUUlIiSbr99tt16tQpbd68WUuWLHHmDece7d69Wzt27NDOnTt16623qra2Vvn5+fL7/Vq6dKkzbzj36GqupyfDsW8dHR168MEH1dXVpZdffrnX+bb0iI94JI0ZM0ZRUVHdEmNTU1O3hD7crFq1Svv379c777yjCRMmOOM+n0+ShnXPampq1NTUpMzMTEVHRys6OlpVVVX693//d0VHRzt9GM49Gj9+vL761a+GjN1yyy06d+6cJH6PJGnNmjUqLCzUgw8+qClTpujRRx/Vd77zHZWWlkqiRz3pS098Pp/a29vV3Nx81TnDQUdHhxYtWqS6ujpVVFQ4qyeS/T0ioEgaMWKEMjMzVVFRETJeUVGhrKysCFUVWcYYrVy5Unv27NHbb7+ttLS0kP1paWny+XwhPWtvb1dVVdWw6dmsWbN04sQJ1dbWOtu0adP08MMPq7a2VpMnTx72Pbr77ru7XZ5++vRpTZo0SRK/R5J0+fJl3XRT6J/iqKgo5zJjetRdX3qSmZmpmJiYkDkXLlzQyZMnh03froSTjz76SJWVlUpOTg7Zb32PInV2rm2uXGb82muvmQ8++MDk5+eb+Ph4c/bs2UiXFhH/9E//ZDwej3n33XfNhQsXnO3y5cvOnA0bNhiPx2P27NljTpw4YR566KEhf+ljb/7yKh5j6NHhw4dNdHS0ee6558xHH31kfvKTn5i4uDizY8cOZ85w79HSpUvNV77yFecy4z179pgxY8aYtWvXOnOGY49aWlrM8ePHzfHjx40ks2nTJnP8+HHnCpS+9OSJJ54wEyZMMJWVlebYsWPmnnvuseYS2nC4Vo86OjrMggULzIQJE0xtbW3I3/G2tjbnGDb3iIDyF370ox+ZSZMmmREjRpg77rjDuaR2OJLU47Z161ZnTldXl/nBD35gfD6fcbvd5utf/7o5ceJE5Iq2wJcDCj0y5j//8z9NRkaGcbvd5uabbzZbtmwJ2T/cexQMBs3q1avNxIkTzciRI83kyZPN+vXrQ95EhmOP3nnnnR7/Bi1dutQY07eetLa2mpUrV5qkpCQTGxtr7rvvPnPu3LkIvJqBca0e1dXVXfXv+DvvvOMcw+YeuYwx5sat1wAAAPSOc1AAAIB1CCgAAMA6BBQAAGAdAgoAALAOAQUAAFiHgAIAAKxDQAEAANYhoAAAAOsQUAAAgHUIKAAAwDoEFAAAYJ3/A/qefICIN0hOAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "933\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "549\n"
     ]
    },
    {
     "data": {
      "image/png": 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Oud1u7kcBgOvoPXdLmz1X5cIxbfZcaL9a8/rNb/EAAADjEFAAAIBxCCgAAMA4BBQAAGAcAgoAADAOAQUAABiHgAIAAIxDQAEAAMYhoAAAAOMQUAAAgHEIKAAAwDgEFAAAYBwCCgAAMA4BBQAAGIeAAgAAjENAAQAAxiGgAAAA4xBQAACAcQgoAADAOAQUAABgHAIKAAAwDgEFAAAYh4ACAACMQ0ABAADGIaAAAADjEFAAAIBxIkNdAACg/es9d8tNx1QuHNMGlSBcsIMCAACMQ0ABAADGIaAAAADjEFAAAIBxCCgAAMA4BBQAAGAcAgoAADAOAQUAABin1QFl165dGjdunFwul2w2mzZt2uTra2xs1Jw5c5SRkaFu3brJ5XLpmWee0TfffON3jaysLNlsNr9j8uTJdz4bAAAQFlodUC5cuKC+ffuqqKioWd/Fixd14MAB/exnP9OBAwe0YcMGnThxQuPHj282dvr06aqurvYd77zzzu3NAAAAhJ1Wf9V9Tk6OcnJyWuxzOBwqKSnxa/vVr36lH/zgBzp9+rR69erla+/ataucTuctPafX65XX6/Wdezye1pYNAADakaDfg+J2u2Wz2XT33Xf7ta9du1bx8fHq06ePZs+erbq6uuteo7CwUA6Hw3ckJycHu2wAABBCQf2xwO+++05z587VlClTFBMT42t/6qmnlJqaKqfTqaNHj2revHn6/PPPm+2+XDVv3jwVFBT4zj0eDyEFAIAwFrSA0tjYqMmTJ6upqUlLly7165s+fbrvv9PT05WWlqYBAwbowIED6t+/f7Nr2e122e32YJUKAAAME5S3eBobGzVp0iRVVFSopKTEb/ekJf3791enTp1UXl4ejHIAAEA7E/AdlKvhpLy8XDt27FBcXNxNH3Ps2DE1NjYqKSkp0OUAAIB2qNUBpb6+XidPnvSdV1RU6NChQ4qNjZXL5dJf//Vf68CBA/rd736nK1euqKamRpIUGxurqKgo/eEPf9DatWv12GOPKT4+XsePH9esWbPUr18/PfTQQ4GbGQAAaLdaHVD279+vESNG+M6v3rw6depUzZ8/X5s3b5Ykff/73/d73I4dO5SVlaWoqCh98skneuutt1RfX6/k5GSNGTNGr776qiIiIu5kLgAAIEy0OqBkZWXJsqzr9t+oT5KSk5NVWlra2qcFAAAdCL/FAwAAjENAAQAAxiGgAAAA4xBQAACAcQgoAADAOAQUAABgHAIKAAAwDgEFAAAYh4ACAACMQ0ABAADGIaAAAADjEFAAAIBxCCgAAMA4BBQAAGAcAgoAADAOAQUAABiHgAIAAIxDQAEAAMYhoAAAAOMQUAAAgHEIKAAAwDgEFAAAYBwCCgAAME5kqAsAALRO77lbQl0CEHTsoAAAAOMQUAAAgHEIKAAAwDgEFAAAYBwCCgAAMA4BBQAAGIeAAgAAjENAAQAAxiGgAAAA4xBQAACAcVodUHbt2qVx48bJ5XLJZrNp06ZNfv2WZWn+/PlyuVzq0qWLsrKydOzYMb8xXq9XeXl5io+PV7du3TR+/HidOXPmzmYCAADCRqsDyoULF9S3b18VFRW12L9o0SItWbJERUVF2rdvn5xOp0aNGqW6ujrfmPz8fG3cuFHFxcXavXu36uvrNXbsWF25cuX2ZwIAAMJGq38sMCcnRzk5OS32WZalN998U6+88oomTpwoSXr//feVmJiodevW6fnnn5fb7dby5cu1evVqjRw5UpK0Zs0aJScna9u2bRo9evQdTAcAAISDgN6DUlFRoZqaGmVnZ/va7Ha7hg8frj179kiSysrK1NjY6DfG5XIpPT3dN+ZaXq9XHo/H7wAAAOGr1TsoN1JTUyNJSkxM9GtPTEzUqVOnfGOioqLUvXv3ZmOuPv5ahYWFeu211wJZKgCgjfWeu+WmYyoXjmmDStAeBOVTPDabze/csqxmbde60Zh58+bJ7Xb7jqqqqoDVCgAAzBPQgOJ0OiWp2U5IbW2tb1fF6XSqoaFB586du+6Ya9ntdsXExPgdAAAgfAU0oKSmpsrpdKqkpMTX1tDQoNLSUg0ZMkSSlJmZqU6dOvmNqa6u1tGjR31jAABAx9bqe1Dq6+t18uRJ33lFRYUOHTqk2NhY9erVS/n5+VqwYIHS0tKUlpamBQsWqGvXrpoyZYokyeFw6LnnntOsWbMUFxen2NhYzZ49WxkZGb5P9QAAgI6t1QFl//79GjFihO+8oKBAkjR16lStXLlSL7/8si5duqQXX3xR586d06BBg/Txxx8rOjra95g33nhDkZGRmjRpki5duqRHHnlEK1euVERERACmBAAA2jubZVlWqItoLY/HI4fDIbfbzf0oADqcW/k0THvFp3jCW2tev/ktHgAAYBwCCgAAMA4BBQAAGIeAAgAAjENAAQAAxiGgAAAA4xBQAACAcQgoAADAOAQUAABgnFZ/1T0AIHjC+VtigdZgBwUAABiHgAIAAIxDQAEAAMYhoAAAAOMQUAAAgHEIKAAAwDgEFAAAYBwCCgAAMA4BBQAAGIeAAgAAjENAAQAAxiGgAAAA4xBQAACAcQgoAADAOAQUAABgHAIKAAAwDgEFAAAYh4ACAACMQ0ABAADGIaAAAADjEFAAAIBxCCgAAMA4BBQAAGAcAgoAADBOwANK7969ZbPZmh25ubmSpGnTpjXrGzx4cKDLAAAA7VhkoC+4b98+XblyxXd+9OhRjRo1Sj/84Q99bY8++qhWrFjhO4+Kigp0GQAAoB0LeEDp0aOH3/nChQv1F3/xFxo+fLivzW63y+l0BvqpAQBAmAjqPSgNDQ1as2aNnn32WdlsNl/7zp07lZCQoPvuu0/Tp09XbW3tDa/j9Xrl8Xj8DgAAEL6CGlA2bdqk8+fPa9q0ab62nJwcrV27Vtu3b9fixYu1b98+Pfzww/J6vde9TmFhoRwOh+9ITk4OZtkAACDEbJZlWcG6+OjRoxUVFaXf/va31x1TXV2tlJQUFRcXa+LEiS2O8Xq9fgHG4/EoOTlZbrdbMTExAa8bAEKl99wtoS4hpCoXjgl1CQgij8cjh8NxS6/fAb8H5apTp05p27Zt2rBhww3HJSUlKSUlReXl5dcdY7fbZbfbA10iAAAwVNDe4lmxYoUSEhI0ZsyN0/DZs2dVVVWlpKSkYJUCAADamaAElKamJq1YsUJTp05VZOT/bdLU19dr9uzZ+v3vf6/Kykrt3LlT48aNU3x8vB5//PFglAIAANqhoLzFs23bNp0+fVrPPvusX3tERISOHDmiVatW6fz580pKStKIESO0fv16RUdHB6MUAADQDgUloGRnZ6ule2+7dOmirVu3BuMpAQBAGOG3eAAAgHEIKAAAwDgEFAAAYBwCCgAAMA4BBQAAGIeAAgAAjENAAQAAxiGgAAAA4xBQAACAcQgoAADAOEH5qnsAAG5H77lbbjqmcuGYNqgEocYOCgAAMA4BBQAAGIeAAgAAjENAAQAAxiGgAAAA4xBQAACAcQgoAADAOAQUAABgHAIKAAAwDgEFAAAYh4ACAACMQ0ABAADGIaAAAADjEFAAAIBxCCgAAMA4BBQAAGAcAgoAADAOAQUAABiHgAIAAIxDQAEAAMYhoAAAAOMQUAAAgHEIKAAAwDgEFAAAYJyAB5T58+fLZrP5HU6n09dvWZbmz58vl8ulLl26KCsrS8eOHQt0GQAAoB0Lyg5Knz59VF1d7TuOHDni61u0aJGWLFmioqIi7du3T06nU6NGjVJdXV0wSgEAAO1QUAJKZGSknE6n7+jRo4ekP+2evPnmm3rllVc0ceJEpaen6/3339fFixe1bt26YJQCAADaoaAElPLycrlcLqWmpmry5Mn66quvJEkVFRWqqalRdna2b6zdbtfw4cO1Z8+e617P6/XK4/H4HQAAIHwFPKAMGjRIq1at0tatW/Xee++ppqZGQ4YM0dmzZ1VTUyNJSkxM9HtMYmKir68lhYWFcjgcviM5OTnQZQMAAIMEPKDk5OToiSeeUEZGhkaOHKktW7ZIkt5//33fGJvN5vcYy7Katf25efPmye12+46qqqpAlw0AAAwS9I8Zd+vWTRkZGSovL/d9mufa3ZLa2tpmuyp/zm63KyYmxu8AAADhK+gBxev16osvvlBSUpJSU1PldDpVUlLi629oaFBpaamGDBkS7FIAAEA7ERnoC86ePVvjxo1Tr169VFtbq3/+53+Wx+PR1KlTZbPZlJ+frwULFigtLU1paWlasGCBunbtqilTpgS6FAAA0E4FPKCcOXNGTz75pL799lv16NFDgwcP1t69e5WSkiJJevnll3Xp0iW9+OKLOnfunAYNGqSPP/5Y0dHRgS4FAAC0UzbLsqxQF9FaHo9HDodDbreb+1EAhJXec7eEugTjVS4cE+oScJta8/od8B0UAACC6VZCHCGm/ePHAgEAgHEIKAAAwDgEFAAAYBwCCgAAMA4BBQAAGIeAAgAAjENAAQAAxiGgAAAA4xBQAACAcQgoAADAOAQUAABgHAIKAAAwDgEFAAAYh4ACAACMQ0ABAADGIaAAAADjEFAAAIBxIkNdAAB0FL3nbgl1CUC7wQ4KAAAwDgEFAAAYh4ACAACMQ0ABAADGIaAAAADjEFAAAIBxCCgAAMA4BBQAAGAcAgoAADAOAQUAABiHgAIAAIxDQAEAAMYhoAAAAOMQUAAAgHEIKAAAwDgBDyiFhYUaOHCgoqOjlZCQoAkTJujLL7/0GzNt2jTZbDa/Y/DgwYEuBQAAtFMBDyilpaXKzc3V3r17VVJSosuXLys7O1sXLlzwG/foo4+qurrad3z44YeBLgUAALRTkYG+4EcffeR3vmLFCiUkJKisrEzDhg3ztdvtdjmdzkA/PQAACANBvwfF7XZLkmJjY/3ad+7cqYSEBN13332aPn26amtrr3sNr9crj8fjdwAAgPAV1IBiWZYKCgo0dOhQpaen+9pzcnK0du1abd++XYsXL9a+ffv08MMPy+v1tnidwsJCORwO35GcnBzMsgEAQIjZLMuygnXx3NxcbdmyRbt371bPnj2vO666ulopKSkqLi7WxIkTm/V7vV6/8OLxeJScnCy3262YmJig1A4AgdZ77pZQl9BhVC4cE+oS0AKPxyOHw3FLr98Bvwflqry8PG3evFm7du26YTiRpKSkJKWkpKi8vLzFfrvdLrvdHowyAQCAgQIeUCzLUl5enjZu3KidO3cqNTX1po85e/asqqqqlJSUFOhyAABAOxTwe1Byc3O1Zs0arVu3TtHR0aqpqVFNTY0uXbokSaqvr9fs2bP1+9//XpWVldq5c6fGjRun+Ph4Pf7444EuBwAAtEMB30FZtmyZJCkrK8uvfcWKFZo2bZoiIiJ05MgRrVq1SufPn1dSUpJGjBih9evXKzo6OtDlAECb4P4SILCC8hbPjXTp0kVbt24N9NMCAIAwwm/xAAAA4xBQAACAcQgoAADAOAQUAABgHAIKAAAwDgEFAAAYJ2hfdQ8A4YLvOAHaHjsoAADAOAQUAABgHAIKAAAwDgEFAAAYh4ACAACMQ0ABAADG4WPGAICwcysfDa9cOKYNKsHtYgcFAAAYh4ACAACMQ0ABAADGIaAAAADjcJMsAKBD4kZas7GDAgAAjENAAQAAxiGgAAAA4xBQAACAcQgoAADAOAQUAABgHAIKAAAwDt+DAqBDu5XvwgDQ9ggoAABcB1/mFjq8xQMAAIxDQAEAAMYhoAAAAONwDwqAsMUNsED7xQ4KAAAwDgEFAAAYJ6QBZenSpUpNTVXnzp2VmZmpTz/9NJTlAAAAQ4TsHpT169crPz9fS5cu1UMPPaR33nlHOTk5On78uHr16hWqsgC0E9xfAoQ3m2VZViieeNCgQerfv7+WLVvma3vggQc0YcIEFRYW3vCxHo9HDodDbrdbMTExAa+NL+YBzEdAQUd0K689gfq7EYzXuda8fodkB6WhoUFlZWWaO3euX3t2drb27NnTbLzX65XX6/Wdu91uSX+aaDA0eS/edEywnhvArbmVv6dAuLmV155A/d0Ixuvc1Wveyt5ISALKt99+qytXrigxMdGvPTExUTU1Nc3GFxYW6rXXXmvWnpycHLQab8bxZsieGgDQQbXla08wn6ZuAIkAAAnNSURBVKuurk4Oh+OGY0L6PSg2m83v3LKsZm2SNG/ePBUUFPjOm5qa9L//+7+Ki4trcfyd8Hg8Sk5OVlVVVVDePmoPWAPWQGINJNZAYg2uYh0CswaWZamurk4ul+umY0MSUOLj4xUREdFst6S2trbZrook2e122e12v7a77747qDXGxMR02D+EV7EGrIHEGkisgcQaXMU63Pka3Gzn5KqQfMw4KipKmZmZKikp8WsvKSnRkCFDQlESAAAwSMje4ikoKNDTTz+tAQMG6C//8i/17rvv6vTp03rhhRdCVRIAADBExPz58+eH4onT09MVFxenBQsW6F/+5V906dIlrV69Wn379g1FOX4iIiKUlZWlyMiO+1NFrAFrILEGEmsgsQZXsQ5tuwYh+x4UAACA6+G3eAAAgHEIKAAAwDgEFAAAYBwCCgAAMA4BBQAAGIeA8meWLl2q1NRUde7cWZmZmfr0009DXVLQFBYWauDAgYqOjlZCQoImTJigL7/80m+MZVmaP3++XC6XunTpoqysLB07dixEFQdfYWGhbDab8vPzfW0dYQ2+/vpr/fjHP1ZcXJy6du2q73//+yorK/P1h/saXL58Wf/wD/+g1NRUdenSRffee6/+6Z/+SU1NTb4x4bgGu3bt0rhx4+RyuWSz2bRp0ya//luZs9frVV5enuLj49WtWzeNHz9eZ86cactp3JEbrUFjY6PmzJmjjIwMdevWTS6XS88884y++eYbv2uE8xpc6/nnn5fNZtObb/r/SE+w1oCA8v+tX79e+fn5euWVV3Tw4EH91V/9lXJycnT69OlQlxYUpaWlys3N1d69e1VSUqLLly8rOztbFy5c8I1ZtGiRlixZoqKiIu3bt09Op1OjRo1SXV1dCCsPjn379undd9/Vgw8+6Nce7mtw7tw5PfTQQ+rUqZP+8z//U8ePH9fixYv9fkoi3Nfg9ddf19tvv62ioiJ98cUXWrRokX7xi1/oV7/6lW9MOK7BhQsX1LdvXxUVFbXYfytzzs/P18aNG1VcXKzdu3ervr5eY8eO1ZUrV9pqGnfkRmtw8eJFHThwQD/72c904MABbdiwQSdOnND48eP9xoXzGvy5TZs26b//+79b/A2doK2BBcuyLOsHP/iB9cILL/i13X///dbcuXNDVFHbqq2ttSRZpaWllmVZVlNTk+V0Oq2FCxf6xnz33XeWw+Gw3n777VCVGRR1dXVWWlqaVVJSYg0fPtyaOXOmZVkdYw3mzJljDR069Lr9HWENxowZYz377LN+bRMnTrR+/OMfW5bVMdZAkrVx40bf+a3M+fz581anTp2s4uJi35ivv/7auuuuu6yPPvqo7YoPkGvXoCWfffaZJck6deqUZVkdZw3OnDlj3XPPPdbRo0etlJQU64033vD1BXMN2EGR1NDQoLKyMmVnZ/u1Z2dna8+ePSGqqm253W5JUmxsrCSpoqJCNTU1fmtit9s1fPjwsFuT3NxcjRkzRiNHjvRr7whrsHnzZg0YMEA//OEPlZCQoH79+um9997z9XeENRg6dKg++eQTnThxQpL0+eefa/fu3XrsscckdYw1uNatzLmsrEyNjY1+Y1wul9LT08N2Xdxut2w2m2+HsSOsQVNTk55++mm99NJL6tOnT7P+YK5Bx/2+3j/z7bff6sqVK81+STkxMbHZLy6HI8uyVFBQoKFDhyo9PV2SfPNuaU1OnTrV5jUGS3FxscrKyrR///5mfR1hDb766istW7ZMBQUF+ulPf6rPPvtMP/nJT2S32/XMM890iDWYM2eO3G637r//fkVEROjKlSv6+c9/rieffFJSx/hzcK1bmXNNTY2ioqLUvXv3ZmPC8d/N7777TnPnztWUKVN8v+TbEdbg9ddfV2RkpH7yk5+02B/MNSCg/BmbzeZ3bllWs7ZwNGPGDB0+fFi7d+9u1hfOa1JVVaWZM2fq448/VufOna87LpzXoKmpSQMGDNCCBQskSf369dOxY8e0bNkyPfPMM75x4bwG69ev15o1a7Ru3Tr16dNHhw4dUn5+vlwul6ZOneobF85rcD23M+dwXJfGxkZNnjxZTU1NWrp06U3Hh8salJWV6a233tKBAwdaPZ9ArAFv8UiKj49XREREs7RXW1vb7P8gwk1eXp42b96sHTt2qGfPnr52p9MpSWG9JmVlZaqtrVVmZqYiIyMVGRmp0tJS/fKXv1RkZKRvnuG8BklJSfre977n1/bAAw/4bg7vCH8OXnrpJc2dO1eTJ09WRkaGnn76af393/+9CgsLJXWMNbjWrczZ6XSqoaFB586du+6YcNDY2KhJkyapoqJCJSUlvt0TKfzX4NNPP1Vtba169erl+zfy1KlTmjVrlnr37i0puGtAQJEUFRWlzMxMlZSU+LWXlJRoyJAhIaoquCzL0owZM7RhwwZt375dqampfv2pqalyOp1+a9LQ0KDS0tKwWZNHHnlER44c0aFDh3zHgAED9NRTT+nQoUO69957w34NHnrooWYfLz9x4oRSUlIkdYw/BxcvXtRdd/n/UxgREeH7mHFHWINr3cqcMzMz1alTJ78x1dXVOnr0aNisy9VwUl5erm3btikuLs6vP9zX4Omnn9bhw4f9/o10uVx66aWXtHXrVklBXoM7usU2jBQXF1udOnWyli9fbh0/ftzKz8+3unXrZlVWVoa6tKD4u7/7O8vhcFg7d+60qqurfcfFixd9YxYuXGg5HA5rw4YN1pEjR6wnn3zSSkpKsjweTwgrD64//xSPZYX/Gnz22WdWZGSk9fOf/9wqLy+31q5da3Xt2tVas2aNb0y4r8HUqVOte+65x/rd735nVVRUWBs2bLDi4+Otl19+2TcmHNegrq7OOnjwoHXw4EFLkrVkyRLr4MGDvk+o3MqcX3jhBatnz57Wtm3brAMHDlgPP/yw1bdvX+vy5cuhmlar3GgNGhsbrfHjx1s9e/a0Dh065PfvpNfr9V0jnNegJdd+iseygrcGBJQ/8+tf/9pKSUmxoqKirP79+/s+chuOJLV4rFixwjemqanJevXVVy2n02nZ7XZr2LBh1pEjR0JXdBu4NqB0hDX47W9/a6Wnp1t2u926//77rXfffdevP9zXwOPxWDNnzrR69eplde7c2br33nutV155xe9FKBzXYMeOHS3+GzB16lTLsm5tzpcuXbJmzJhhxcbGWl26dLHGjh1rnT59OgSzuT03WoOKiorr/ju5Y8cO3zXCeQ1a0lJACdYa2CzLsu5sDwYAACCwuAcFAAAYh4ACAACMQ0ABAADGIaAAAADjEFAAAIBxCCgAAMA4BBQAAGAcAgoAADAOAQUAABiHgAIAAIxDQAEAAMb5f5orQIYT6IuIAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "490\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1097\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "637\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "109\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "499\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "956\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1131\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "485\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "607\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "718\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1096\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "848\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "254\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "745\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "632\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "191\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "212\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "246\n"
     ]
    },
    {
     "data": {
      "image/png": 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rkiSv1ytJcrlcAc9zuVz+fefLyspSfHy8f0tISAh22QAAwCJBDyg1NTW67rrrlJmZqV69emns2LF69NFHtXTp0oB5Docj4LExptbYOTNnzpTP5/NvJSUlwS4bAABYJOgBpV27durWrVvA2NVXX62jR49KktxutyTVWi0pLS2ttapyjtPpVIsWLQI2AAAQuYJ+kmy/fv108ODBgLFDhw6pU6dOkqTExES53W7l5eWpV69ekqTq6mrl5+dr/vz5wS4HAPAjcdVehEPQA8rjjz+uvn37KjMzU/fff7927typ5cuXa/ny5ZK+/WgnPT1dmZmZSkpKUlJSkjIzMxUbG6sRI0YEuxwAANAABT2gXH/99Vq3bp1mzpypZ599VomJiVq4cKFGjhzpnzNt2jRVVlZq/Pjx/gu1bdmyRXFxccEuBwAANEAOY4wJdxGXq7y8XPHx8fL5fJyPAjRSfOzQ8HAlWVzO+zf34gEAANYhoAAAAOsQUAAAgHUIKAAAwDoEFAAAYB0CCgAAsA4BBQAAWIeAAgAArENAAQAA1iGgAAAA6xBQAACAdQgoAADAOgQUAABgHQIKAACwDgEFAABYh4ACAACsQ0ABAADWIaAAAADrEFAAAIB1CCgAAMA6BBQAAGAdAgoAALAOAQUAAFiHgAIAAKxDQAEAANYhoAAAAOsQUAAAgHUIKAAAwDoEFAAAYB0CCgAAsA4BBQAAWIeAAgAArENAAQAA1iGgAAAA6xBQAACAdQgoAADAOgQUAABgHQIKAACwDgEFAABYh4ACAACsQ0ABAADWIaAAAADrEFAAAIB1CCgAAMA6BBQAAGAdAgoAALAOAQUAAFiHgAIAAKxDQAEAANYhoAAAAOsQUAAAgHUIKAAAwDoEFAAAYB0CCgAAsA4BBQAAWIeAAgAArENAAQAA1okOdwEAgMah84wNl5xzeN6geqgEDQErKAAAwDoEFAAAYB0CCgAAsE7IA0pWVpYcDofS09P9Y8YYZWRkyOPxKCYmRqmpqdq/f3+oSwEAAA1ESANKQUGBli9frmuuuSZgPDs7Wzk5OcrNzVVBQYHcbrcGDhyoioqKUJYDAAAaiJAFlBMnTmjkyJFasWKFWrZs6R83xmjhwoWaNWuWhg0bpuTkZK1atUqnTp3S6tWrQ1UOAABoQEIWUCZMmKBBgwbp9ttvDxgvLi6W1+tVWlqaf8zpdGrAgAHasWPHBV+rqqpK5eXlARsAAIhcIbkOypo1a1RYWKhdu3bV2uf1eiVJLpcrYNzlcunIkSMXfL2srCzNmTMn+IUCAAArBX0FpaSkRJMnT9abb76pZs2aXXSew+EIeGyMqTV2zsyZM+Xz+fxbSUlJUGsGAAB2CfoKSmFhoUpLS5WSkuIfO3v2rLZt26bc3FwdPHhQ0rcrKe3atfPPKS0trbWqco7T6ZTT6Qx2qQAAwFJBX0G57bbbtHfvXhUVFfm33r17a+TIkSoqKlKXLl3kdruVl5fnf051dbXy8/PVt2/fYJcDAAAaoKCvoMTFxSk5OTlgrHnz5mrdurV/PD09XZmZmUpKSlJSUpIyMzMVGxurESNGBLscAADQAIXlZoHTpk1TZWWlxo8fr7KyMvXp00dbtmxRXFxcOMoBAACWcRhjTLiLuFzl5eWKj4+Xz+dTixYtwl0OgDCoy51x0fBwN+PIdjnv32FZQQGA70P4aLzq8v+eENM4cLNAAABgHQIKAACwDgEFAABYh4ACAACsQ0ABAADWIaAAAADrEFAAAIB1CCgAAMA6BBQAAGAdAgoAALAOAQUAAFiHgAIAAKxDQAEAANYhoAAAAOsQUAAAgHUIKAAAwDoEFAAAYB0CCgAAsA4BBQAAWIeAAgAArENAAQAA1iGgAAAA6xBQAACAdQgoAADAOtHhLgBA49J5xoZwlwCgAWAFBQAAWIeAAgAArENAAQAA1iGgAAAA6xBQAACAdQgoAADAOgQUAABgHQIKAACwDgEFAABYh4ACAACsw6XuAQQNl7EHECysoAAAAOsQUAAAgHX4iAcA0KDU5aPEw/MG1UMlCCVWUAAAgHUIKAAAwDoEFAAAYB0CCgAAsA4BBQAAWIeAAgAArENAAQAA1iGgAAAA6xBQAACAdQgoAADAOgQUAABgHQIKAACwDgEFAABYh4ACAACsQ0ABAADWIaAAAADrEFAAAIB1CCgAAMA6BBQAAGAdAgoAALAOAQUAAFgn6AElKytL119/veLi4tS2bVsNHTpUBw8eDJhjjFFGRoY8Ho9iYmKUmpqq/fv3B7sUAADQQAU9oOTn52vChAn68MMPlZeXpzNnzigtLU0nT570z8nOzlZOTo5yc3NVUFAgt9utgQMHqqKiItjlAACABig62C+4adOmgMcrV65U27ZtVVhYqJtvvlnGGC1cuFCzZs3SsGHDJEmrVq2Sy+XS6tWrNXbs2FqvWVVVpaqqKv/j8vLyYJcNAAAsEvJzUHw+nySpVatWkqTi4mJ5vV6lpaX55zidTg0YMEA7duy44GtkZWUpPj7evyUkJIS6bAAAEEYhDSjGGE2ZMkX9+/dXcnKyJMnr9UqSXC5XwFyXy+Xfd76ZM2fK5/P5t5KSklCWDQAAwizoH/F818SJE/Xxxx9r+/bttfY5HI6Ax8aYWmPnOJ1OOZ3OkNQIAADsE7IVlEmTJmn9+vXaunWrOnTo4B93u92SVGu1pLS0tNaqCgAAaJyCHlCMMZo4caLWrl2r999/X4mJiQH7ExMT5Xa7lZeX5x+rrq5Wfn6++vbtG+xyAABAAxT0j3gmTJig1atX669//avi4uL8KyXx8fGKiYmRw+FQenq6MjMzlZSUpKSkJGVmZio2NlYjRowIdjkAAKABCnpAWbp0qSQpNTU1YHzlypV6+OGHJUnTpk1TZWWlxo8fr7KyMvXp00dbtmxRXFxcsMsBAAANUNADijHmknMcDocyMjKUkZER7B8PAAAiAPfiAQAA1iGgAAAA6xBQAACAdQgoAADAOgQUAABgHQIKAACwDgEFAABYJ6Q3CwQAIBw6z9hwyTmH5w2qh0rwQ7GCAgAArENAAQAA1iGgAAAA6xBQAACAdQgoAADAOgQUAABgHb5mDKBO6vK1TQAIFlZQAACAdQgoAADAOgQUAABgHQIKAACwDgEFAABYh4ACAACsQ0ABAADWIaAAAADrEFAAAIB1CCgAAMA6BBQAAGAdAgoAALAOAQUAAFiHgAIAAKxDQAEAANYhoAAAAOsQUAAAgHUIKAAAwDoEFAAAYB0CCgAAsA4BBQAAWIeAAgAArENAAQAA1iGgAAAA6xBQAACAdQgoAADAOgQUAABgHQIKAACwTnS4CwAAoCHrPGPDJeccnjeoHiqJLKygAAAA6xBQAACAdfiIB0CdlqiBSMNHM3ZjBQUAAFiHgAIAAKxDQAEAANbhHBQgwnF+CYCGiBUUAABgHQIKAACwDgEFAABYh3NQAAC4CM7hCh9WUAAAgHUIKAAAwDp8xAM0YCw/A4hUrKAAAADrEFAAAIB1whpQlixZosTERDVr1kwpKSn64IMPwlkOAACwRNjOQXnrrbeUnp6uJUuWqF+/fvrTn/6ku+66SwcOHFDHjh3DVZYkbsENAAiuYJ0vFqz3nobwPhe2FZScnBw98sgj+s1vfqOrr75aCxcuVEJCgpYuXRqukgAAgCXCsoJSXV2twsJCzZgxI2A8LS1NO3bsqDW/qqpKVVVV/sc+n0+SVF5eHpL6aqpOXXJOqH42cDnq8rsKIHIE670nXO9z517TGHPJuWEJKF999ZXOnj0rl8sVMO5yueT1emvNz8rK0pw5c2qNJyQkhKzGS4lfGLYfDQBopOrzvSeUP6uiokLx8fHfOyes10FxOBwBj40xtcYkaebMmZoyZYr/cU1Njf73v/+pdevWF5z/Y5SXlyshIUElJSVq0aJFUF+7oaAH36IP9OAc+kAPzqEPP64HxhhVVFTI4/Fccm5YAkqbNm0UFRVVa7WktLS01qqKJDmdTjmdzoCxq666KqQ1tmjRotH+8p1DD75FH+jBOfSBHpxDH354Dy61cnJOWE6Sbdq0qVJSUpSXlxcwnpeXp759+4ajJAAAYJGwfcQzZcoUjRo1Sr1799aNN96o5cuX6+jRoxo3bly4SgIAAJaIysjIyAjHD05OTlbr1q2VmZmpF154QZWVlXr99dfVs2fPcJQTICoqSqmpqYqObry3KqIH36IP9OAc+kAPzqEP9dMDh6nLd30AAADqEffiAQAA1iGgAAAA6xBQAACAdQgoAADAOgQUAABgHQLKdyxZskSJiYlq1qyZUlJS9MEHH4S7pJDJysrS9ddfr7i4OLVt21ZDhw7VwYMHA+YYY5SRkSGPx6OYmBilpqZq//79Yaq4fmRlZcnhcCg9Pd0/1hj6cOzYMT344INq3bq1YmNjde2116qwsNC/vzH04MyZM3r66aeVmJiomJgYdenSRc8++6xqamr8cyKtD9u2bdM999wjj8cjh8Oht99+O2B/XY63qqpKkyZNUps2bdS8eXMNGTJEX3zxRX0exo/2fX04ffq0pk+frh49eqh58+byeDx66KGH9OWXXwa8RkPvw6V+F75r7NixcjgcWrgw8GY9we4BAeX/eeutt5Senq5Zs2Zpz549uummm3TXXXfp6NGj4S4tJPLz8zVhwgR9+OGHysvL05kzZ5SWlqaTJ0/652RnZysnJ0e5ubkqKCiQ2+3WwIEDVVFREcbKQ6egoEDLly/XNddcEzAe6X0oKytTv3791KRJE23cuFEHDhzQggULAm4nEek9kKT58+dr2bJlys3N1SeffKLs7Gw9//zzWrRokX9OpPXh5MmT6tmzp3Jzcy+4vy7Hm56ernXr1mnNmjXavn27Tpw4ocGDB+vs2bP1dRg/2vf14dSpU9q9e7dmz56t3bt3a+3atTp06JCGDBkSMK+h9+FSvwvnvP322/rXv/51wXvpBL0HBsYYY37+85+bcePGBYx17drVzJgxI0wV1a/S0lIjyeTn5xtjjKmpqTFut9vMmzfPP+ebb74x8fHxZtmyZeEqM2QqKipMUlKSycvLMwMGDDCTJ082xjSOPkyfPt3079//ovsbQw+MMWbQoEFmzJgxAWPDhg0zDz74oDEm8vsgyaxbt87/uC7H+/XXX5smTZqYNWvW+OccO3bMXHHFFWbTpk31V3wQnd+HC9m5c6eRZI4cOWKMibw+XKwHX3zxhWnfvr3Zt2+f6dSpk3nxxRf9+0LRA1ZQJFVXV6uwsFBpaWkB42lpadqxY0eYqqpfPp9PktSqVStJUnFxsbxeb0BPnE6nBgwYEJE9mTBhggYNGqTbb789YLwx9GH9+vXq3bu37rvvPrVt21a9evXSihUr/PsbQw8kqX///nrvvfd06NAhSdJHH32k7du36+6775bUePpwTl2Ot7CwUKdPnw6Y4/F4lJycHJE9Ocfn88nhcPhXGRtDH2pqajRq1ChNnTpV3bt3r7U/FD1ovNfp/Y6vvvpKZ8+erXUnZZfLVeuOy5HIGKMpU6aof//+Sk5OliT/cV+oJ0eOHKn3GkNpzZo1Kiws1K5du2rtawx9+Pzzz7V06VJNmTJFTz31lHbu3KnHHntMTqdTDz30UKPogSRNnz5dPp9PXbt2VVRUlM6ePau5c+dq+PDhkhrH78J31eV4vV6vmjZtqpYtW9aaE6l/O7/55hvNmDFDI0aM8N/JtzH0Yf78+YqOjtZjjz12wf2h6AEB5TscDkfAY2NMrbFINHHiRH388cfavn17rX2R3pOSkhJNnjxZW7ZsUbNmzS46L5L7UFNTo969eyszM1OS1KtXL+3fv19Lly7VQw895J8XyT2Qvj0P7Y033tDq1avVvXt3FRUVKT09XR6PR6NHj/bPi/Q+nO+HHG+k9uT06dN64IEHVFNToyVLllxyfqT0obCwUC+99JJ279592cfzY3rARzyS2rRpo6ioqFopr7S0tNa/HiLNpEmTtH79em3dulUdOnTwj7vdbkmK+J4UFhaqtLRUKSkpio6OVnR0tPLz8/XHP/5R0dHR/mON5D60a9dO3bp1Cxi7+uqr/SeIN5bfhalTp2rGjBl64IEH1KNHD40aNUqPP/64srKyJDWePt6ry8wAAAMjSURBVJxTl+N1u92qrq5WWVnZRedEitOnT+v+++9XcXGx8vLy/KsnUuT34YMPPlBpaak6duzo/zt55MgRPfHEE+rcubOk0PSAgCKpadOmSklJUV5eXsB4Xl6e+vbtG6aqQssYo4kTJ2rt2rV6//33lZiYGLA/MTFRbrc7oCfV1dXKz8+PqJ7cdttt2rt3r4qKivxb7969NXLkSBUVFalLly4R34d+/frV+or5oUOH1KlTJ0mN53fh1KlTuuKKwD+JUVFR/q8ZN5Y+nFOX401JSVGTJk0C5hw/flz79u2LqJ6cCyeffvqp3n33XbVu3Tpgf6T3YdSoUfr4448D/k56PB5NnTpVmzdvlhSiHvygU2sj0Jo1a0yTJk3MK6+8Yg4cOGDS09NN8+bNzeHDh8NdWkj87ne/M/Hx8eYf//iHOX78uH87deqUf868efNMfHy8Wbt2rdm7d68ZPny4adeunSkvLw9j5aH33W/xGBP5fdi5c6eJjo42c+fONZ9++ql58803TWxsrHnjjTf8cyK9B8YYM3r0aNO+fXvzt7/9zRQXF5u1a9eaNm3amGnTpvnnRFofKioqzJ49e8yePXuMJJOTk2P27Nnj/3ZKXY533LhxpkOHDubdd981u3fvNrfeeqvp2bOnOXPmTLgO67J9Xx9Onz5thgwZYjp06GCKiooC/l5WVVX5X6Oh9+FSvwvnO/9bPMYEvwcElO9YvHix6dSpk2natKm57rrr/F+5jUSSLritXLnSP6empsY888wzxu12G6fTaW6++Wazd+/e8BVdT84PKI2hD++8845JTk42TqfTdO3a1Sxfvjxgf2PoQXl5uZk8ebLp2LGjadasmenSpYuZNWtWwJtQpPVh69atF/w7MHr0aGNM3Y63srLSTJw40bRq1crExMSYwYMHm6NHj4bhaH647+tDcXHxRf9ebt261f8aDb0Pl/pdON+FAkqwe+AwxpgftvYCAAAQGpyDAgAArENAAQAA1iGgAAAA6xBQAACAdQgoAADAOgQUAABgHQIKAACwDgEFAABYh4ACAACsQ0ABAADWIaAAAADr/B9HH6+f+FOyDgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "288\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1150\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "175\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "860\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "529\n"
     ]
    },
    {
     "data": {
      "image/png": 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QkKCYmBj9+c9/1qpVq3TXXXcpKSlJBw8e1JNPPqmhQ4fq1ltvDd2ZAQCATqvdAWXXrl3Ky8tz9s9fG1JYWKiSkhK9+eabkqQf/vCHQa/btGmTcnNzFRMTo/fff18vvviiGhoalJaWpoKCAj3zzDOKioq6knMBAABdRLsDSm5urowxF+y/WJ8kpaWlacuWLe19WwAA0I3wLB4AAGAdAgoAALAOAQUAAFiHgAIAAKxDQAEAANYhoAAAAOsQUAAAgHUIKAAAwDoEFAAAYB0CCgAAsA4BBQAAWIeAAgAArENAAQAA1iGgAAAA6xBQAACAdQgoAADAOgQUAABgHQIKAACwDgEFAABYh4ACAACsQ0ABAADWIaAAAADrEFAAAIB1CCgAAMA6BBQAAGAdAgoAALAOAQUAAFiHgAIAAKwTHekCAACIhAHF6y855siCgg6oBG1hBQUAAFiHgAIAAKxDQAEAANYhoAAAAOsQUAAAgHUIKAAAwDoEFAAAYB0CCgAAsA4BBQAAWKfdAWXr1q2aMGGCUlNT5XK5tG7duqB+Y4xKSkqUmpqq2NhY5ebm6sCBA0FjAoGAZs6cqaSkJPXu3VsTJ07U8ePHr+xMAABAl9HugHL69GkNGTJEixcvbrP/+eef1wsvvKDFixdr586d8nq9uvPOO1VfX++MmT17ttauXavVq1dr27Ztamho0Pjx43Xu3LnvfiYAAKDLaPezePLz85Wfn99mnzFGixYt0rx58zRp0iRJ0ooVK5ScnKzXX39df//3fy+fz6elS5fqtdde0+jRoyVJK1euVFpamjZs2KCxY8dewekAAICuIKTXoFRVVam2tlZjxoxx2txut0aNGqXt27dLkioqKtTc3Bw0JjU1VZmZmc6YbwsEAvL7/UEbAADoukIaUGprayVJycnJQe3JyclOX21trWJiYnTNNddccMy3lZaWyuPxOFtaWlooywYAAJYJy108LpcraN8Y06rt2y42Zu7cufL5fM5WXV0dsloBAIB9QhpQvF6vJLVaCamrq3NWVbxer5qamnTy5MkLjvk2t9ut+Pj4oA0AAHRdIQ0oGRkZ8nq9Ki8vd9qampq0ZcsWjRgxQpKUnZ2tHj16BI2pqanR/v37nTEAAKB7a/ddPA0NDTp06JCzX1VVpb179yohIUH9+/fX7NmzNX/+fA0aNEiDBg3S/Pnz1atXL02dOlWS5PF49Oijj+rJJ59UYmKiEhISNGfOHGVlZTl39QAAgO6t3QFl165dysvLc/aLiookSYWFhVq+fLmeeuopNTY26rHHHtPJkyc1fPhwvffee4qLi3Ne86tf/UrR0dG6//771djYqDvuuEPLly9XVFRUCE4JAAB0di5jjIl0Ee3l9/vl8Xjk8/m4HgUALDCgeH2kSwiLIwsKIl1Cl9Kez2+exQMAAKxDQAEAANYhoAAAAOsQUAAAgHUIKAAAwDoEFAAAYB0CCgAAsA4BBQAAWIeAAgAArENAAQAA1iGgAAAA6xBQAACAdQgoAADAOgQUAABgHQIKAACwDgEFAABYh4ACAACsQ0ABAADWIaAAAADrEFAAAIB1CCgAAMA6BBQAAGAdAgoAALAOAQUAAFiHgAIAAKxDQAEAANYhoAAAAOsQUAAAgHUIKAAAwDoEFAAAYJ3oSBcAALDbgOL1kS4B3RArKAAAwDqsoAAAcAGXs3p0ZEFBB1TS/bCCAgAArENAAQAA1iGgAAAA6xBQAACAdQgoAADAOiG/i2fAgAE6evRoq/bHHntMv/nNbzRt2jStWLEiqG/48OH66KOPQl0KAOAS+I0T2CrkAWXnzp06d+6cs79//37deeeduu+++5y2cePGadmyZc5+TExMqMsAAACdWMgDSp8+fYL2FyxYoO9///saNWqU0+Z2u+X1ekP91gAAoIsI6zUoTU1NWrlypR555BG5XC6nffPmzerbt6+uu+46TZ8+XXV1dRc9TiAQkN/vD9oAAEDXFdaAsm7dOp06dUrTpk1z2vLz87Vq1Spt3LhRCxcu1M6dO3X77bcrEAhc8DilpaXyeDzOlpaWFs6yAQBAhLmMMSZcBx87dqxiYmL01ltvXXBMTU2N0tPTtXr1ak2aNKnNMYFAICjA+P1+paWlyefzKT4+PuR1A0B3wUWyV46fur98fr9fHo/nsj6/w/YsnqNHj2rDhg1as2bNRcelpKQoPT1dlZWVFxzjdrvldrtDXSIAALBU2L7iWbZsmfr27auCgosnyxMnTqi6ulopKSnhKgUAAHQyYQkoLS0tWrZsmQoLCxUd/f8XaRoaGjRnzhx9+OGHOnLkiDZv3qwJEyYoKSlJ99xzTzhKAQAAnVBYvuLZsGGDjh07pkceeSSoPSoqSvv27dOrr76qU6dOKSUlRXl5eSorK1NcXFw4SgEAAJ1QWALKmDFj1Na1t7GxsXr33XfD8ZYAAKAL4Vk8AADAOgQUAABgHQIKAACwDgEFAABYh4ACAACsQ0ABAADWIaAAAADrEFAAAIB1CCgAAMA6BBQAAGAdAgoAALAOAQUAAFiHgAIAAKxDQAEAANYhoAAAAOsQUAAAgHUIKAAAwDoEFAAAYB0CCgAAsA4BBQAAWIeAAgAArENAAQAA1iGgAAAA6xBQAACAdQgoAADAOgQUAABgHQIKAACwDgEFAABYh4ACAACsQ0ABAADWIaAAAADrEFAAAIB1CCgAAMA6BBQAAGAdAgoAALAOAQUAAFiHgAIAAKxDQAEAANYJeUApKSmRy+UK2rxer9NvjFFJSYlSU1MVGxur3NxcHThwINRlAACATiwsKyiDBw9WTU2Ns+3bt8/pe/755/XCCy9o8eLF2rlzp7xer+68807V19eHoxQAANAJhSWgREdHy+v1OlufPn0k/XX1ZNGiRZo3b54mTZqkzMxMrVixQmfOnNHrr78ejlIAAEAnFJaAUllZqdTUVGVkZGjy5Mk6fPiwJKmqqkq1tbUaM2aMM9btdmvUqFHavn37BY8XCATk9/uDNgAA0HWFPKAMHz5cr776qt5991298sorqq2t1YgRI3TixAnV1tZKkpKTk4Nek5yc7PS1pbS0VB6Px9nS0tJCXTYAALBIyANKfn6+7r33XmVlZWn06NFav369JGnFihXOGJfLFfQaY0yrtm+aO3eufD6fs1VXV4e6bAAAYJGw32bcu3dvZWVlqbKy0rmb59urJXV1da1WVb7J7XYrPj4+aAMAAF1X2ANKIBDQn/70J6WkpCgjI0Ner1fl5eVOf1NTk7Zs2aIRI0aEuxQAANBJRIf6gHPmzNGECRPUv39/1dXV6bnnnpPf71dhYaFcLpdmz56t+fPna9CgQRo0aJDmz5+vXr16aerUqaEuBQAAdFIhDyjHjx/XlClT9OWXX6pPnz665ZZb9NFHHyk9PV2S9NRTT6mxsVGPPfaYTp48qeHDh+u9995TXFxcqEsBAACdlMsYYyJdRHv5/X55PB75fD6uRwGAKzCgeH2kS+j0jiwoiHQJnUZ7Pr95Fg8AALAOAQUAAFiHgAIAAKxDQAEAANYhoAAAAOsQUAAAgHUIKAAAwDoEFAAAYB0CCgAAsA4BBQAAWIeAAgAArENAAQAA1gn504wBAOhOLueBizxQsP1YQQEAANYhoAAAAOsQUAAAgHUIKAAAwDoEFAAAYB3u4gGALupy7i4BbMUKCgAAsA4BBQAAWIeAAgAArENAAQAA1iGgAAAA6xBQAACAdQgoAADAOgQUAABgHQIKAACwDgEFAABYh4ACAACsQ0ABAADWIaAAAADrEFAAAIB1CCgAAMA6BBQAAGAdAgoAALAOAQUAAFiHgAIAAKwT8oBSWlqqm266SXFxcerbt6/uvvtuffrpp0Fjpk2bJpfLFbTdcsstoS4FAAB0UiEPKFu2bNHjjz+ujz76SOXl5Tp79qzGjBmj06dPB40bN26campqnO3tt98OdSkAAKCTig71Ad95552g/WXLlqlv376qqKjQbbfd5rS73W55vd7LOmYgEFAgEHD2/X5/aIoFAABWCvs1KD6fT5KUkJAQ1L5582b17dtX1113naZPn666uroLHqO0tFQej8fZ0tLSwlozAACILJcxxoTr4MYY/e3f/q1OnjypDz74wGkvKyvT9773PaWnp6uqqko/+9nPdPbsWVVUVMjtdrc6TlsrKGlpafL5fIqPjw9X+QDQqQ0oXh/pEvB/jiwoiHQJVvD7/fJ4PJf1+R3yr3i+6YknntAnn3yibdu2BbU/8MADzp8zMzOVk5Oj9PR0rV+/XpMmTWp1HLfb3WZwAQAAXVPYAsrMmTP15ptvauvWrerXr99Fx6akpCg9PV2VlZXhKgcAAHQiIQ8oxhjNnDlTa9eu1ebNm5WRkXHJ15w4cULV1dVKSUkJdTkAAKATCvlFso8//rhWrlyp119/XXFxcaqtrVVtba0aGxslSQ0NDZozZ44+/PBDHTlyRJs3b9aECROUlJSke+65J9TlAACATijkKyhLliyRJOXm5ga1L1u2TNOmTVNUVJT27dunV199VadOnVJKSory8vJUVlamuLi4UJcDAAA6obB8xXMxsbGxevfdd0P9tgAAoAsJ6108AIDQ4/ZhdAc8LBAAAFiHgAIAAKxDQAEAANYhoAAAAOsQUAAAgHUIKAAAwDoEFAAAYB0CCgAAsA4BBQAAWIeAAgAArENAAQAA1uFZPAAAhNnlPD/pyIKCDqik82AFBQAAWIeAAgAArENAAQAA1uEaFADoIFyHAFw+VlAAAIB1CCgAAMA6BBQAAGAdAgoAALAOAQUAAFiHu3gAALAAd3kFYwUFAABYhxUUALDI5fwvGugOWEEBAADWIaAAAADrEFAAAIB1uAYFAIBOojvd6cMKCgAAsA4BBQAAWIeAAgAArENAAQAA1iGgAAAA6xBQAACAdbjNGABCgJ+ohy26yq3IrKAAAADrRHQF5aWXXtIvf/lL1dTUaPDgwVq0aJF+9KMfRbIkAGiF1RF0NZ1hlSViKyhlZWWaPXu25s2bpz179uhHP/qR8vPzdezYsUiVBAAALOEyxphIvPHw4cM1bNgwLVmyxGm74YYbdPfdd6u0tPSir/X7/fJ4PPL5fIqPjw95bZ0hWQLoOKygoDsKx+dcez6/I/IVT1NTkyoqKlRcXBzUPmbMGG3fvr3V+EAgoEAg4Oz7fD5Jfz3RcGgJnLnkmHC9NwD7XM6/CUBXE47PufPHvJy1kYgElC+//FLnzp1TcnJyUHtycrJqa2tbjS8tLdWzzz7bqj0tLS1sNV6KZ1HE3hoAgLAL5+dcfX29PB7PRcdE9CJZl8sVtG+MadUmSXPnzlVRUZGz39LSoq+++kqJiYltjr8Sfr9faWlpqq6uDsvXR50N89EacxKM+WiNOQnGfATrzvNhjFF9fb1SU1MvOTYiASUpKUlRUVGtVkvq6uparapIktvtltvtDmq7+uqrw1pjfHx8t/uLczHMR2vMSTDmozXmJBjzEay7zselVk7Oi8hdPDExMcrOzlZ5eXlQe3l5uUaMGBGJkgAAgEUi9hVPUVGRfvzjHysnJ0d/8zd/o9/97nc6duyYZsyYEamSAACAJaJKSkpKIvHGmZmZSkxM1Pz58/Xv//7vamxs1GuvvaYhQ4ZEopwgUVFRys3NVXQ0TwKQmI+2MCfBmI/WmJNgzEcw5uPSIvY7KAAAABfCs3gAAIB1CCgAAMA6BBQAAGAdAgoAALAOAQUAAFiHgPINL730kjIyMtSzZ09lZ2frgw8+iHRJHaK0tFQ33XST4uLi1LdvX91999369NNPg8YYY1RSUqLU1FTFxsYqNzdXBw4ciFDFHa+0tFQul0uzZ8922rrbnHz++ed66KGHlJiYqF69eumHP/yhKioqnP7uNh9nz57Vv/zLvygjI0OxsbEaOHCg/u3f/k0tLS3OmK48J1u3btWECROUmpoql8uldevWBfVfzrkHAgHNnDlTSUlJ6t27tyZOnKjjx4935GmE1MXmpLm5WU8//bSysrLUu3dvpaam6uGHH9YXX3wRdIyuNidXxMAYY8zq1atNjx49zCuvvGIOHjxoZs2aZXr37m2OHj0a6dLCbuzYsWbZsmVm//79Zu/evaagoMD079/fNDQ0OGMWLEJNlW8AAAauSURBVFhg4uLizBtvvGH27dtnHnjgAZOSkmL8fn8EK+8YO3bsMAMGDDA33nijmTVrltPenebkq6++Munp6WbatGnmf/7nf0xVVZXZsGGDOXTokDOmO82HMcY899xzJjEx0fzxj380VVVV5g9/+IP53ve+ZxYtWuSM6cpz8vbbb5t58+aZN954w0gya9euDeq/nHOfMWOGufbaa015ebnZvXu3ycvLM0OGDDFnz57t6NMJiYvNyalTp8zo0aNNWVmZ+d///V/z4YcfmuHDh5vs7OygY3S1ObkSBJT/c/PNN5sZM2YEtV1//fWmuLg4QhVFTl1dnZFktmzZYowxpqWlxXi9XrNgwQJnzNdff208Ho/57W9/G6kyO0R9fb0ZNGiQKS8vN6NGjXICSnebk6efftqMHDnygv3dbT6MMaagoMA88sgjQW2TJk0yDz30kDGme83Jtz+ML+fcT506ZXr06GFWr17tjPn888/NVVddZd55552OKz5M2gpt37Zjxw4jyfmPcFefk/biKx5JTU1Nqqio0JgxY4Lax4wZo+3bt0eoqsjx+XySpISEBElSVVWVamtrg+bH7XZr1KhRXX5+Hn/8cRUUFGj06NFB7d1tTt58803l5OTovvvuU9++fTV06FC98sorTn93mw9JGjlypN5//3199tlnkqSPP/5Y27Zt01133SWpe87JeZdz7hUVFWpubg4ak5qaqszMzC4/P+f5fD65XC7n4bfMSTB+Y1fSl19+qXPnzrV6knJycnKrJy53dcYYFRUVaeTIkcrMzJQkZw7amp+jR492eI0dZfXq1aqoqNCuXbta9XW3OTl8+LCWLFmioqIi/fSnP9WOHTv0j//4j3K73Xr44Ye73XxI0tNPPy2fz6frr79eUVFROnfunH7+859rypQpkrrf35Fvupxzr62tVUxMjK655ppWY7rDv7tff/21iouLNXXqVOeJxt19Tr6NgPINLpcraN8Y06qtq3viiSf0ySefaNu2ba36utP8VFdXa9asWXrvvffUs2fPC47rLnPS0tKinJwczZ8/X5I0dOhQHThwQEuWLNHDDz/sjOsu8yFJZWVlWrlypV5//XUNHjxYe/fu1ezZs5WamqrCwkJnXHeak2/7LufeHeanublZkydPVktLi1566aVLju8Oc9IWvuKRlJSUpKioqFYJta6urtX/ALqymTNn6s0339SmTZvUr18/p93r9UpSt5qfiooK1dXVKTs7W9HR0YqOjtaWLVv061//WtHR0c55d5c5SUlJ0Q9+8IOgthtuuEHHjh2T1D3/jvzzP/+ziouLNXnyZGVlZenHP/6x/umf/kmlpaWSuuecnHc55+71etXU1KSTJ09ecExX1NzcrPvvv19VVVUqLy93Vk+k7jsnF0JAkRQTE6Ps7GyVl5cHtZeXl2vEiBERqqrjGGP0xBNPaM2aNdq4caMyMjKC+jMyMuT1eoPmp6mpSVu2bOmy83PHHXdo37592rt3r7Pl5OTowQcf1N69ezVw4MBuNSe33nprq1vPP/vsM6Wnp0vqnn9Hzpw5o6uuCv4nNCoqyrnNuDvOyXmXc+7Z2dnq0aNH0Jiamhrt37+/y87P+XBSWVmpDRs2KDExMai/O87JRUXq6lzbnL/NeOnSpebgwYNm9uzZpnfv3ubIkSORLi3s/uEf/sF4PB6zefNmU1NT42xnzpxxxixYsMB4PB6zZs0as2/fPjNlypQuc7vk5frmXTzGdK852bFjh4mOjjY///nPTWVlpVm1apXp1auXWblypTOmO82HMcYUFhaaa6+91rnNeM2aNSYpKck89dRTzpiuPCf19fVmz549Zs+ePUaSeeGFF8yePXucO1Iu59xnzJhh+vXrZzZs2GB2795tbr/99k59S+3F5qS5udlMnDjR9OvXz+zduzfo39pAIOAco6vNyZUgoHzDb37zG5Oenm5iYmLMsGHDnNtsuzpJbW7Lli1zxrS0tJhnnnnGeL1e43a7zW233Wb27dsXuaIj4NsBpbvNyVtvvWUyMzON2+02119/vfnd734X1N/d5sPv95tZs2aZ/v37m549e5qBAweaefPmBX3YdOU52bRpU5v/bhQWFhpjLu/cGxsbzRNPPGESEhJMbGysGT9+vDl27FgEziY0LjYnVVVVF/y3dtOmTc4xutqcXAmXMcZ03HoNAADApXENCgAAsA4BBQAAWIeAAgAArENAAQAA1iGgAAAA6xBQAACAdQgoAADAOgQUAABgHQIKAACwDgEFAABYh4ACAACs8/8AG3NwMILurcoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1071\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "375\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "930\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1118\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1105\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "965\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1092\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "127\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "789\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "790\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(len(landmarks)):\n",
    "    print(landmarks[i])\n",
    "    center = landmarks[i]\n",
    "    plt.hist(dist_mat[center,:], bins = 50)\n",
    "    plt.title(center)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "radius = np.array([75,90,75,85,65,80])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "#for i in range(len(landmarks)):\n",
    "#    print(landmarks[i])\n",
    "#    center = landmarks[i]\n",
    "#    radii, eigval_list, eigvec_list = eigen_calc_from_dist_mat(np_data, dist_mat, center, radint = .01)\n",
    "\n",
    "#    rmin = radii[0]\n",
    "#    rmax = radii[-1]\n",
    "    \n",
    "#    eigen_plot(eigval_list, radii, rmin, rmax)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|                                                                                           | 0/49 [00:00<?, ?it/s]\n",
      "  0%|                                                                                           | 0/16 [00:00<?, ?it/s]\u001b[A"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "787\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      "  6%|████▉                                                                          | 1/16 [18:51<4:42:53, 1131.55s/it]\u001b[A\n",
      " 12%|█████████▉                                                                     | 2/16 [37:45<4:24:10, 1132.18s/it]\u001b[A"
     ]
    }
   ],
   "source": [
    "for i in tqdm(range(len(landmarks))):\n",
    "    print(landmarks[i])\n",
    "    center = landmarks[i]\n",
    "    radii, eigval_list, eigvec_list, num_pts_list = eigen_calc_from_dist_mat(np_data, dist_mat, center, radint = 5)\n",
    "\n",
    "    rmin = radii[0]\n",
    "    rmax = radii[-1]\n",
    "    \n",
    "    eigen_plot(eigval_list, radii, rmin, rmax)\n",
    "      \n",
    "    landmark_loc = UMAP[center,:]\n",
    "    radius_UMAP = np.zeros((1,2))\n",
    "    for j in range(dist_mat.shape[0]):\n",
    "        if j > center:\n",
    "            if dist_mat[center,j] < radius[i]:\n",
    "                radius_UMAP = np.append(radius_UMAP, np.reshape(UMAP[j,:], (1,2)), axis = 0)\n",
    "    radius_UMAP = radius_UMAP[1:,:]\n",
    "    \n",
    "    frame1 = plt.scatter(UMAP[:,0], UMAP[:,1], s=1, c = \"lightgrey\")\n",
    "    frame1 = plt.scatter(radius_UMAP[:,0], radius_UMAP[:,1], s=1, c = \"dimgrey\")\n",
    "    frame1 = plt.scatter(landmark_loc[0], landmark_loc[1], s=2, c = \"red\")\n",
    "    plt.annotate(center, (UMAP_landmark[i,0], UMAP_landmark[i,1]))\n",
    "    plt.title('Racute - UMAP: '+str(center)+' Radius: '+str(radius[i]))\n",
    "    #plt.xlim(-30000,25000)\n",
    "    frame1.axes.get_xaxis().set_ticks([])\n",
    "    frame1.axes.get_yaxis().set_ticks([])\n",
    "    plt.ylabel('UMAP2')\n",
    "    plt.xlabel('UMAP1')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
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