CD8_Circadian.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",
    "import tqdm\n",
    "from ripser import Rips\n",
    "from sklearn.metrics.pairwise import euclidean_distances"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Read in data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "sample_2_1 = pd.read_csv(\"CT2_Grp1_RSEM.csv\", sep=',', header = 0, index_col = 0)[\"TPM\"]\n",
    "sample_2_2 = pd.read_csv(\"CT2_Grp2_RSEM.csv\", sep=',', header = 0, index_col = 0)[\"TPM\"]\n",
    "sample_6_1 = pd.read_csv(\"CT6_Grp1_RSEM.csv\", sep=',', header = 0, index_col = 0)[\"TPM\"]\n",
    "sample_6_2 = pd.read_csv(\"CT6_Grp2_RSEM.csv\", sep=',', header = 0, index_col = 0)[\"TPM\"]\n",
    "sample_10_1 = pd.read_csv(\"CT10_Grp1_RSEM.csv\", sep=',', header = 0, index_col = 0)[\"TPM\"]\n",
    "sample_10_2 = pd.read_csv(\"CT10_Grp2_RSEM.csv\", sep=',', header = 0, index_col = 0)[\"TPM\"]\n",
    "sample_14_1 = pd.read_csv(\"CT14_Grp1_RSEM.csv\", sep=',', header = 0, index_col = 0)[\"TPM\"]\n",
    "sample_14_2 = pd.read_csv(\"CT14_Grp2_RSEM.csv\", sep=',', header = 0, index_col = 0)[\"TPM\"]\n",
    "sample_18_1 = pd.read_csv(\"CT18_Grp1_RSEM.csv\", sep=',', header = 0, index_col = 0)[\"TPM\"]\n",
    "sample_18_2 = pd.read_csv(\"CT18_Grp2_RSEM.csv\", sep=',', header = 0, index_col = 0)[\"TPM\"]\n",
    "sample_22_1 = pd.read_csv(\"CT22_Grp1_RSEM.csv\", sep=',', header = 0, index_col = 0)[\"TPM\"]\n",
    "sample_22_2 = pd.read_csv(\"CT22_Grp2_RSEM.csv\", sep=',', header = 0, index_col = 0)[\"TPM\"]\n",
    "\n",
    "samples = np.zeros((50600,1))\n",
    "\n",
    "samples = np.append(np.reshape(sample_2_1.values, (50600,1)), np.reshape(sample_2_2.values, (50600,1)), axis = 1)\n",
    "samples = np.append(samples, np.reshape(sample_6_1.values, (50600,1)), axis = 1)\n",
    "samples = np.append(samples, np.reshape(sample_6_2.values, (50600,1)), axis = 1)\n",
    "samples = np.append(samples, np.reshape(sample_10_1.values, (50600,1)), axis = 1)\n",
    "samples = np.append(samples, np.reshape(sample_10_2.values, (50600,1)), axis = 1)\n",
    "samples = np.append(samples, np.reshape(sample_14_1.values, (50600,1)), axis = 1)\n",
    "samples = np.append(samples, np.reshape(sample_14_1.values, (50600,1)), axis = 1)\n",
    "samples = np.append(samples, np.reshape(sample_18_1.values, (50600,1)), axis = 1)\n",
    "samples = np.append(samples, np.reshape(sample_18_2.values, (50600,1)), axis = 1)\n",
    "samples = np.append(samples, np.reshape(sample_22_1.values, (50600,1)), axis = 1)\n",
    "samples = np.append(samples, np.reshape(sample_22_1.values, (50600,1)), axis = 1)\n",
    "\n",
    "pd_data = pd.DataFrame(samples, columns = [\"2_1\", \"2_2\", \"6_1\", \"6_2\", \"10_1\", \"10_2\", \"14_1\", \"14_2\", \"18_1\", \"18_2\", \"22_1\", \"22_1\"], index = sample_2_1.index)\n",
    "np_data = np.array(pd_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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       "      <th>gene_id</th>\n",
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      "text/plain": [
       "                         2_1    2_2    6_1    6_2   10_1   10_2   14_1   14_2  \\\n",
       "gene_id                                                                         \n",
       "ENSMUSG00000000001.4   73.33  78.50  82.32  80.29  74.53  76.81  78.50  78.50   \n",
       "ENSMUSG00000000003.15   0.00   0.00   0.00   0.00   0.00   0.00   0.00   0.00   \n",
       "ENSMUSG00000000028.14   5.97   4.30   7.89   5.20   4.67   5.67   5.81   5.81   \n",
       "ENSMUSG00000000031.15   0.00   0.00   0.00   0.00   0.07   0.00   0.00   0.00   \n",
       "ENSMUSG00000000037.16   0.08   0.12   0.27   0.11   0.12   0.05   0.09   0.09   \n",
       "...                      ...    ...    ...    ...    ...    ...    ...    ...   \n",
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       "\n",
       "                        18_1   18_2   22_1   22_1  \n",
       "gene_id                                            \n",
       "ENSMUSG00000000001.4   81.46  78.95  80.20  80.20  \n",
       "ENSMUSG00000000003.15   0.00   0.00   0.00   0.00  \n",
       "ENSMUSG00000000028.14   5.27   5.96   5.56   5.56  \n",
       "ENSMUSG00000000031.15   0.00   0.00   0.00   0.00  \n",
       "ENSMUSG00000000037.16   0.16   0.15   0.22   0.22  \n",
       "...                      ...    ...    ...    ...  \n",
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       "\n",
       "[50600 rows x 12 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "#reducer = umap.UMAP()\n",
    "#UMAP = reducer.fit_transform(np_data.T)\n",
    "#print(UMAP.shape)\n",
    "\n",
    "#savetxt('circadian_umap.csv', UMAP, delimiter=',')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "UMAP shape: (12, 2)\n",
      "Timepoint shape: (12,)\n"
     ]
    }
   ],
   "source": [
    "UMAP = pd.read_csv(\"circadian_umap.csv\", sep=',', header = None)\n",
    "UMAP = UMAP.values \n",
    "\n",
    "timepoint = np.array([\"2\", \"2\", \"6\", \"6\", \"10\", \"10\", \"14\", \"14\", \"18\", \"18\", \"22\", \"22\"])\n",
    "\n",
    "print(\"UMAP shape: \"+repr(UMAP.shape))\n",
    "print(\"Timepoint shape: \"+repr(timepoint.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=20, hue = timepoint, linewidth = 0, palette = \"coolwarm\")\n",
    "plt.title('Circadian - 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": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1000, 12)\n"
     ]
    }
   ],
   "source": [
    "z_expression = scipy.stats.zscore(np_data, axis=0)\n",
    "var_gene = np.var(z_expression, axis=1)\n",
    "\n",
    "top_var_gene = pd.DataFrame(var_gene, index = sample_2_1.index, columns = [\"var_gene\"])\n",
    "\n",
    "top_var_gene = top_var_gene.sort_values(by=[\"var_gene\"], ascending = False)\n",
    "top_var_gene = top_var_gene[0:1000]\n",
    "\n",
    "var_data = pd_data.loc[top_var_gene.index] \n",
    "np_var_data = np.array(var_data)\n",
    "\n",
    "print(np_var_data.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\users\\hmkri\\desktop\\riesenfeld pearson\\lib\\site-packages\\umap\\umap_.py:1678: UserWarning: n_neighbors is larger than the dataset size; truncating to X.shape[0] - 1\n",
      "  warn(\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(12, 2)\n"
     ]
    }
   ],
   "source": [
    "reducer = umap.UMAP()\n",
    "var_UMAP = reducer.fit_transform(np_var_data.T)\n",
    "print(var_UMAP.shape)\n",
    "\n",
    "#savetxt('circadian_umap.csv', UMAP, delimiter=',')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "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(var_UMAP[:,0], var_UMAP[:,1], s=20, hue = timepoint, linewidth = 0, palette = \"coolwarm\")\n",
    "plt.title('Circadian - 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": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "from manifold_utils.mSVD import eigen_plot, eigen_calc_from_dist_mat, eps_projection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "np_data = np_data.T\n",
    "N, d = np_data.shape\n",
    " \n",
    "dist_mat = euclidean_distances(np_data, np_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "savetxt('dist_mat_circadian.csv', dist_mat, delimiter=',')\n",
    "\n",
    "dist_mat = pd.read_csv('dist_mat_circadian.csv', sep=\",\", header = None)\n",
    "dist_mat = np.array(dist_mat )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "np_var_data = np_var_data.T\n",
    "N, d = np_var_data.shape\n",
    " \n",
    "dist_mat = euclidean_distances(np_var_data, np_var_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(12, 12)\n"
     ]
    }
   ],
   "source": [
    "print(dist_mat.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualize Landmarks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]\n"
     ]
    }
   ],
   "source": [
    "#using all points bc only 12 samples - BULK RNAseq\n",
    "landmarks = [0,1,2,3,4,5,6,7,8,9,10,11]\n",
    "print(landmarks)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Persistence Diagrams"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rips(maxdim=1, thresh=inf, coeff=2, do_cocycles=False, n_perm = None, verbose=True)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rips = Rips()\n",
    "diagrams = rips.fit_transform(np_data, distance_matrix=False, metric=\"euclidean\")\n",
    "rips.plot(diagrams)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rips(maxdim=1, thresh=inf, coeff=2, do_cocycles=False, n_perm = None, verbose=True)\n"
     ]
    },
    {
     "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"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rips = Rips()\n",
    "diagrams = rips.fit_transform(np_var_data, distance_matrix=False, metric=\"euclidean\")\n",
    "rips.plot(diagrams)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Eigen plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "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": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\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": [
      "1\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": [
      "2\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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YAQAAVhFG2uBi/ioAAF2OMAIAAKyKtF2ATU8Vl2t91ZEWyyvrGyxUAwBAeArrMPJxzVf6e0VVq+v7RYX1jwcAgKAI67PtzalJmtCnl891EXJpUt/4IFcEAED4CeswMrFvvCaKwAEAgE1MYAUAAFYRRgAAgFWdCiMLFy7UkCFDFBsbq6ysLL333nttbl9bW6s5c+YoIyNDMTExGjp0qJYsWdKpggEAQGjxe87I8uXLNXPmTC1cuFAXX3yxnn76aeXk5Gj79u0aPHiwz31uuOEG7du3T4sXL9ZZZ52l8vJyNTRw+ywAAOhEGHniiSc0bdo03XnnnZKkBQsWaNWqVVq0aJHy8/NbbP/GG29ozZo12rVrl/r27StJOuOMM06vagAAEDL8ukxTV1enwsJCZWdnN1uenZ2ttWvX+tzntdde09ixY/XLX/5SAwcO1PDhw3X//ffr6NGjrX5PbW2tqqurm30AAEBo8mtkpKKiQo2NjUpOTm62PDk5WWVlZT732bVrl95//33FxsbqlVdeUUVFhWbMmKEDBw60Om8kPz9fjz76qD+lAQAAh+rUBFbXKW+QM8a0WNbE4/HI5XJp2bJluvDCC3XllVfqiSee0NKlS1sdHZk9e7aqqqq8n5KSks6UCQAA2mFkbJfg38hIv3795Ha7W4yClJeXtxgtaZKamqqBAwcqMTHRu2zEiBEyxmj37t0aNmxYi31iYmIUExPjT2kAAMCh/BoZiY6OVlZWlgoKCpotLygo0IQJE3zuc/HFF2vv3r06fPiwd9mnn36qiIgIDRo0qBMlAwCAwPN9hSMY/L5Mk5eXp2effVZLlizRjh07NGvWLBUXF2v69OmSjl9iyc3N9W5/8803KykpSXfccYe2b9+ud999Vw888ICmTp2quLi4wLUEAAA4kt+39k6ePFmVlZWaN2+eSktLlZmZqZUrVyojI0OSVFpaquLiYu/2vXr1UkFBge6++26NHTtWSUlJuuGGGzR//vzAtQIAADiWyxhjf+ZKO6qrq5WYmKiqqiolJCTYLgcAgJBRuOlmHTq0Xpkjf6Pk5KsCeuyOnr95Nw0AALCKMAIAAKwijAAAAKsIIwAAwCrCCAAAsIowAgAArCKMAAAAqwgjAADAKsIIAACwijACAACsIowAAACrCCMAAMAqwggAALCKMAIAAKwijAAAAKsIIwAAwCrCCAAAsIowAgAArCKMAAAAqwgjAABAcrmsfTVhBAAAWEUYAQAAVhFGAACAVZG2C7CptnafGhoO+1znckUoLi5DLhd5DQCArhTWYWTnZ/nat++vra5PTv6eMkf+3yBWBABA+AnrMOJ291BkZO8Wy41pUGPjYR0+vMNCVQAAhJewDiMjzvm5Rpzz8xbLDx78UJs23yJjjIWqAAAIL0yI8KnpXmvCCAAAXY0w4hNhBACAYCGM+OIijAAAECxhPWekNa4TIyOhPmektna/Dh5cJ1+hKzZ2oHr3Hhv8ogAAYYcw4ot3ZMRjtYyu9sknd+tQ1Uetrh934d/Vq9fwIFYEAAhHhBEfmkZGQv0qzbHavZKkhITzFenu5V1eVb1ZjY1HVFtXrl4ijAAAuhZhxKcTl2lCPI14PLWSjt/i3KvX2d7lGzZ8TzWHt0mm0VZpAIAwQhjxyVkTWBsbj6lk9x9UX1fp134NDdWSpIiI6OYrTjwC35jQvkwFAOgeCCO+OOxumorKt/X557/s5N4uRUYmNF/ickuSDCMjAIAgIIz4cPJuGmeMDDSeeNlfXNxgDeif49e+8QmZio5OarbMO2cmxCfwAgC6B8KIT84aGWma29Kz53CdddaDp39A78gIYQQA0PV46Jkv3ss0DnEiNJwc0Tg9XKYBAAQTYcSHk7f2OmtkpGni6ek6eZmKMAIA6HqEEZ8cdmuvd2QkQGGkaWSEOSMAgCBgzohPTpszciI0BOry0okRlsM121URmRiYYwIAuqX6+oO2SyCM+OJy2nM2AjwyEuGKkiQVlyxWccnigBwTANC9ueS29t2EkTY5ZWSkac5IYEZGBg26VfUNh+Tx1AfkeACA7i0mJll9+oy39v2EEZ+cejdNYEZGkpIuVVLSpQE5FgAA7WECqy8OewJrwOeMAAAQRIQRH07e2uqMMBLokREAAIKJs5dPDhsZMYF9zggAAMHE2csHl/ek7pC7acTICADAuTh7tcEpl2m8tyAzZwQA4EDcTePT8ZO6x1Orzz7/teVa2ld1aKMkRkYAAM5EGPHB7e4pSTKmXl9+uchyNR3njuxpuwQAAPxGGPEhJqa/zh3xK9Uc3m67lA5zR8Rp0KBbbZcBAIDfCCOtSE29Tqm6znYZAACEvE5NMli4cKGGDBmi2NhYZWVl6b333uvQfh988IEiIyN1/vnnd+ZrAQBACPI7jCxfvlwzZ87UnDlztHnzZk2cOFE5OTkqLi5uc7+qqirl5ubqW9/6VqeLBQAAocdl/Lx/ddy4cbrgggu0aNHJiZ0jRozQ97//feXn57e634033qhhw4bJ7Xbr1Vdf1ZYtWzr8ndXV1UpMTFRVVZUSEhL8KRcAAFjS0fO3XyMjdXV1KiwsVHZ2drPl2dnZWrt2bav7Pffcc/r888/1yCOPdOh7amtrVV1d3ewDAABCk19hpKKiQo2NjUpOTm62PDk5WWVlZT732blzpx5++GEtW7ZMkZEdmy+bn5+vxMRE7yc9Pd2fMgEAgIN0agKr65QnfRpjWiyTpMbGRt1888169NFHNXz48A4ff/bs2aqqqvJ+SkpKOlMmAABwAL9u7e3Xr5/cbneLUZDy8vIWoyWSVFNTo40bN2rz5s360Y9+JEnyeDwyxigyMlJvvvmmLr/88hb7xcTEKCYmxp/SAACAQ/k1MhIdHa2srCwVFBQ0W15QUKAJEya02D4hIUFbt27Vli1bvJ/p06fr7LPP1pYtWzRu3LjTqx4AADie3w89y8vL02233aaxY8dq/PjxeuaZZ1RcXKzp06dLOn6JZc+ePXr++ecVERGhzMzMZvsPGDBAsbGxLZYDAIDw5HcYmTx5siorKzVv3jyVlpYqMzNTK1euVEZGhiSptLS03WeOAAAANPH7OSM28JwRAACcp0ueMwIAABBohBEAAGAVYQQAAFhFGAEAAFYRRgAAgFWEEQAAYBVhBAAAWEUYAQAAVhFGAACAVYQRAABgFWEEAABYRRgBAABWEUYAAIBVhBEAAGAVYQQAAFhFGAEAAFYRRgAAgFWEEQAAYBVhBAAAWEUYAQAAVhFGAACAVYQRAABgFWEEAABYRRgBAABWEUYAAIBVhBEAAGAVYQQAAFhFGAEAAFYRRgAAgFWEEQAAYBVhBAAAWEUYAQAAVhFGAACAVZG2CwAAAPasX79elZWVOv/885WWlmalBkZGAAAIYzt27NCGDRt04MABazUQRgAAgFWEEQAAYBVhBAAAWEUYAQAAVhFGAACAVYQRAABgFWEEAABYRRgBAABWEUYAAIBVhBEAAGAVYQQAAFhFGAEAAFYRRgAAgFWEEQAAYBVhBAAAWEUYAQAAVhFGAACAVYQRAABgFWEEAABY1akwsnDhQg0ZMkSxsbHKysrSe++91+q2K1as0He+8x31799fCQkJGj9+vFatWtXpggEAQGjxO4wsX75cM2fO1Jw5c7R582ZNnDhROTk5Ki4u9rn9u+++q+985ztauXKlCgsLNWnSJF1zzTXavHnzaRcPAACcz2WMMf7sMG7cOF1wwQVatGiRd9mIESP0/e9/X/n5+R06xsiRIzV58mT95Cc/6dD21dXVSkxMVFVVlRISEvwpFwAAtGHp0qX64osv9B//8R/KzMwM6LE7ev72a2Skrq5OhYWFys7ObrY8Oztba9eu7dAxPB6Pampq1Ldv31a3qa2tVXV1dbMPAAAITX6FkYqKCjU2Nio5ObnZ8uTkZJWVlXXoGI8//riOHDmiG264odVt8vPzlZiY6P2kp6f7UyYAAHCQTk1gdblczf5sjGmxzJcXX3xRc+fO1fLlyzVgwIBWt5s9e7aqqqq8n5KSks6UCQAAHCDSn4379esnt9vdYhSkvLy8xWjJqZYvX65p06bp5Zdf1re//e02t42JiVFMTIw/pQEAAIfya2QkOjpaWVlZKigoaLa8oKBAEyZMaHW/F198Ubfffrv++Mc/6qqrrupcpQAAICT5NTIiSXl5ebrttts0duxYjR8/Xs8884yKi4s1ffp0SccvsezZs0fPP/+8pONBJDc3V//zP/+jiy66yDuqEhcXp8TExAA2BQAAOJHfYWTy5MmqrKzUvHnzVFpaqszMTK1cuVIZGRmSpNLS0mbPHHn66afV0NCgu+66S3fddZd3+ZQpU7R06dLTbwEAAHA0v8OIJM2YMUMzZszwue7UgLF69erOfAUAAAgTvJsGAABYRRgBAABWEUYAAIBVhBEAAGAVYQQAgDDm5/tyuwRhBAAAWEUYAQAAHXrHXFchjAAAAKsIIwAAwCrCCAAAsIowAgAArCKMAAAAqwgjAADAKsIIAACwijACAACsIowAAACrIm0X0F3V1taqqqrKdhkdFhUVpT59+tguAwAAvxFGfKirq9OCBQt09OhR26X4JScnR+PGjbNdBgAAfiGM+HDo0CFvEOnRo4flatpXX1+v+vp6ffHFFxo2bJhf+/bq1UvR0dFdVBkAAO0L6zCyZ88eVVdXt1h+4MABSVJCQoLy8vKCXZbfPvroI73++uvasWOHduzY4ff+8fHxcrvdzZb17t1bN910k2JiYgJVJgAAPoV1GFm3bp0++eSTVtc75UQ8dOhQ9enTR0eOHPFrv7q6OklSTU1Ni3WHDh3S7t27NXTo0IDUCABAa8I6jCQlJSk9Pd3nOpfLpW984xtBrqhz+vbtq3vvvdfv/erq6rR//34ZY5ot/8tf/qL9+/ervr4+UCUCANCqsA4jkyZN0qRJk2yXYU10dLQGDhzYYnnTPJnKykqVlZUFuywAQBA1jZLbFNZhBL5FRUVJkgoKClRQUGC5GgBAqCOMoIXRo0dr//79amxstF0KACAIEhISlJGRYe37CSNoYdSoURo1apTtMgAAYYIwAgBAGNu/5BPVFVWpz/XD1eO8/lZq4N00AACEswaPTL1HOuXOymAijAAAEMZOZhCXtRq4TAOfTINHsheSAQDB0pRG7GURwghaqnlvj6pW7iKMAACCgjASxowxajxY2+I64dFPKggiABBGXHGRih7Yy9r3E0bC2IGX/q2jH+9vdX3fW85R7PA+QawIAGCDKzJCLre9aaSEkVYc23lQ9WX+vXjOJleUWz1G91dEXMe7tK7kxAvyIiPkOuV30N0nVrFDeysihl8RAEDX4kzjQ+PhOlUs+cRxlyoaD9Uq8Yoz/NjBI0ka8F+jrQ7PAQDCG2HEB8/RhuNBxO2y9gAYf9TvO6L6vUfUWOPfy45M4/G05XJbnEINAAh7hBFfPMdP0hGxbvWdfLblYtpX8/4eVe3dJc/RBjUeqe/wfqbh+MiICCMAAIsIIz6YE+doRTjjJO2KPj7h49j2SpVur/R/f4uTlgAA4Czky4mREZdDwkjMGYmK6BnVqX2jBvWSOzEmwBUBANBxjIz4ciKMOGVkRAkR+nzov/VVVZXfu6YMPUvJ7jFdUBQAAB1DGPHBOCyMfF64Xhv+8nKn9v1k9Zs668Lx6tmb54kAQDj6bON6HT5QqYzzzleflDQrNYR1GPnqn/tVX9ryWSKNh2olOecyTe1XX0mSkgYN1ohLLuvwfutf+X+qrz2mmor9ioqNbbYuMipaEW53IMsEAHRDm1b+RSXb/qmr7nmAMGLD0W2VbT6B1BXrjB+Pp7FB0vEwMu7/3NDh/f75jzdUv/+Yls3Ja7EuLiFRub/8rXr16RuwOgEA3ZD3RXm8tdeK2OF95G5t4qdL6nH+gOAW1EmNDcfDiDvSv+4884JvaMuq132uO1pdpaen5552bQAAZ3ARRuzomZUsZSXbLuO0eRobJUkRbv+681tT/0uX3jpN5pRHzX7455e04dXOzUEBADhPVGyc+mecae37wzqMtKaxoUF//PF9Ki/63HYpfomI9H+OR2R0dItlE2+aorHXXCdzIuQAAEJbVFycoqLtPeaBMOJDdUW548v5q/AAABBZSURBVIKIyxWhgWefG7DjxfWKD9ixAABoC2HEh6Zbe6PjemjqgqctV9O+I1W1Wr1spzYVuLWpYK1f+w44I0HZ00ZavVYIAAhvhBEfjOf48+AjIiMd8fyN4u2l2l9cL6nj76VpUl1xTBddO1SJ/eMCXxgAoNv7628/1t5PD+ryKSM0bKydeZSEER/MiZfTOGW0wNN4vN7UsxI14bqzOrzfykX/1NGaer3y+Ca5IwPXVmPa38a/Awb4eFKLSbsBOGC3F/h+CewBu+RH2N27OeCdEnj8fe5+At0ndUcbAnvATiCM+OAdGYlwxqt7mn4x43pFK+XMxA7v139wgoq3VerIiYe8AQDCk8s0KqZkm8TISPdhTpzdnTIyYrwv9vNvv29dEa/d5hNveztfwMn9O/MTC8i/agLxLwU/fg6t/moE5J8sgfh5BKhPT+evQCB+Fm0couOldYOf52nU0NTO0/57epp1+DpEp389ukVb/Pj73uohTr8dgenX01P1pz8pqv6Iel/7U2s1EEZ8aBoZcUU443Honk6+ZXjfj2er8eN/dkVJAACH6HHifzcd+Zcu05VWaiCM+HAyjDhsZMTPkZzGikpJUs9vTlTk1x77XlVXrS+qiuQJ4oVTc9o/6tM8wGnuTv0B+Ltyum047e+33Aent7vVR3lLAfgdsvw7ePp/B06fsfQ7uPPgTh3s5dKkMWef3vefhk6FkYULF+pXv/qVSktLNXLkSC1YsEATJ05sdfs1a9YoLy9P27ZtU1pamh588EFNnz6900V3NY/HWRNYT8y39fsyjTnxGPn+996ruJEjvct/9c4svVW8O1DlAQC6teNXAb5fvk066yorFfgdRpYvX66ZM2dq4cKFuvjii/X0008rJydH27dv1+DBg1tsX1RUpCuvvFI//OEP9cILL+iDDz7QjBkz1L9/f/3gBz8ISCMCzTtnxDETWI/XG+FneGoKI67I5u/nqamrkSTlDMnR2X3sJWUAQBAULtWAis904ZgzrJXgdxh54oknNG3aNN15552SpAULFmjVqlVatGiR8vPzW2z/1FNPafDgwVqwYIEkacSIEdq4caN+/etfd+Mw0jQy4oww0tk5I94wEtX816C28fjdNdkZ2fp2xrcDUCEAoNvauEI6/JVkcZ6kX2Gkrq5OhYWFevjhh5stz87O1tq1vp/8uW7dOmVnZzdb9t3vfleLFy9WfX29oqJavjW3trZWtbUnbzetrq72p8wOWzB1qtzHWi73mOMPD6sqq9Tvb5/bJd8dSI2Rg6XIM/TZOyu05/U/dXi/MTXH5JY0+6VbdCjx5C/hzrjDklv68E+/VEXt77qgYgBAd3F5/ScaIOm5v7yqOzLtDBL4FUYqKirU2Nio5OTm9yEnJyerrKzM5z5lZWU+t29oaFBFRYVSU1Nb7JOfn69HH33Un9I6JeKoVOcpb3W9ieijuthvdnkdgZK6r0Zn7fKRrtrgcUkf9qlRTY+WoyrX1m7WqLq6QJUHAOjGSqOSrH13pyawnjqx0xjT5mRPX9v7Wt5k9uzZysvL8/65urpa6enpnSm1TZ6eRtHHBrS6PjIyXu66fwT8e7uEqVdF0gZV9u3p1277+kdqpCdWOtx8eUJDlDZFnKPNsc6YxAsA6LwKV28dqLf3+hO/wki/fv3kdrtbjIKUl5e3GP1okpKS4nP7yMhIJSX5TmExMTGKien6VxnPfPa5Lv8OAADQNr9maEZHRysrK0sFBQXNlhcUFGjChAk+9xk/fnyL7d98802NHTvW53wRAAAQXvy+XSQvL0/PPvuslixZoh07dmjWrFkqLi72Pjdk9uzZys3N9W4/ffp0ffnll8rLy9OOHTu0ZMkSLV68WPfff3/gWgEAABzL7zkjkydPVmVlpebNm6fS0lJlZmZq5cqVysjIkCSVlpaquLjYu/2QIUO0cuVKzZo1S7/73e+Ulpam3/zmN932tl4AABBcLtMd3tLTjurqaiUmJqqqqkoJCQm2ywEAAB3Q0fO3M57qBQAAQhZhBAAAWEUYAQAAVhFGAACAVYQRAABgFWEEAABYRRgBAABWEUYAAIBVhBEAAGCV34+Dt6HpIbHV1dWWKwEAAB3VdN5u72HvjggjNTU1kqT09HTLlQAAAH/V1NQoMTGx1fWOeDeNx+PR3r17FR8fr5qaGqWnp6ukpCTk31NTXV1NW0NUOLU3nNoqhVd7w6mtUni1N1BtNcaopqZGaWlpiohofWaII0ZGIiIiNGjQIEmSy+WSJCUkJIT8L0MT2hq6wqm94dRWKbzaG05tlcKrvYFoa1sjIk2YwAoAAKwijAAAAKvcc+fOnWu7CH+53W5ddtlliox0xFWm00JbQ1c4tTec2iqFV3vDqa1SeLU3mG11xARWAAAQurhMAwAArCKMAAAAqwgjAADAKsIIAACwKuhhZO7cuXK5XM0+KSkp3vW33357i/UXXXRRs2PU1tbq7rvvVr9+/dSzZ09973vf0+7du5ttc/DgQd12221KTExUYmKibrvtNh06dCgobfy6PXv26NZbb1VSUpJ69Oih888/X4WFhd71xhjNnTtXaWlpiouL02WXXaZt27Y1O0YotTdU+veMM85o0Q6Xy6W77rpLUuj1a3vtDZV+laSGhgb9+Mc/1pAhQxQXF6czzzxT8+bNk8fj8W4TKv3bkbaGUt9Kxx9LPnPmTGVkZCguLk4TJkzQRx995F0fKn0rtd/WbtW3JsgeeeQRM3LkSFNaWur9lJeXe9dPmTLFXHHFFc3WV1ZWNjvG9OnTzcCBA01BQYHZtGmTmTRpkhk9erRpaGjwbnPFFVeYzMxMs3btWrN27VqTmZlprr766qC10xhjDhw4YDIyMsztt99u1q9fb4qKisxbb71lPvvsM+82jz32mImPjzd//vOfzdatW83kyZNNamqqqa6uDsn2hkr/lpeXN2tDQUGBkWTeeecdY0xo9asx7bc3VPrVGGPmz59vkpKSzN/+9jdTVFRkXn75ZdOrVy+zYMEC7zah0r8daWso9a0xxtxwww3m3HPPNWvWrDE7d+40jzzyiElISDC7d+82xoRO33akrd2pb62EkdGjR7e6fsqUKebaa69tdf2hQ4dMVFSUeemll7zL9uzZYyIiIswbb7xhjDFm+/btRpL58MMPvdusW7fOSDL/+te/AtCKjnnooYfMJZdc0up6j8djUlJSzGOPPeZdduzYMZOYmGieeuopY0xotdeY0Orfr7v33nvN0KFDjcfjCbl+9eXr7TUmtPr1qquuMlOnTm227LrrrjO33nqrMSa0/t6211ZjQqtvv/rqK+N2u83f/va3ZstHjx5t5syZE1J9215bjelefWtlzsjOnTuVlpamIUOG6MYbb9SuXbuarV+9erUGDBig4cOH64c//KHKy8u96woLC1VfX6/s7GzvsrS0NGVmZmrt2rWSpHXr1ikxMVHjxo3zbnPRRRcpMTHRu00wvPbaaxo7dqyuv/56DRgwQGPGjNHvf/977/qioiKVlZU1a0tMTIwuvfRSb52h1N4modK/Terq6vTCCy9o6tSpcrlcIdevpzq1vU1CpV8vueQS/eMf/9Cnn34qSfr444/1/vvv68orr5QUWn9v22trk1Dp24aGBjU2Nio2NrbZ8ri4OL3//vsh1bfttbVJd+nboIeRcePG6fnnn9eqVav0+9//XmVlZZowYYIqKyslSTk5OVq2bJnefvttPf744/roo490+eWXq7a2VpJUVlam6Oho9enTp9lxk5OTVVZW5t1mwIABLb57wIAB3m2CYdeuXVq0aJGGDRumVatWafr06brnnnv0/PPPe+tsqv3rTm1LqLRXCq3+bfLqq6/q0KFDuv322yWFXr+e6tT2SqHVrw899JBuuukmnXPOOYqKitKYMWM0c+ZM3XTTTd46m2r/Oif2b3ttlUKrb+Pj4zV+/Hj99Kc/1d69e9XY2KgXXnhB69evV2lpaUj1bXttlbpX3wb9ebY5OTne/x41apTGjx+voUOH6g9/+IPy8vI0efJk7/rMzEyNHTtWGRkZev3113Xddde1elxjTLN/pX39v1vbpqt5PB6NHTtWP//5zyVJY8aM0bZt27Ro0SLl5ua2WmtH6nRqe0Opf5ssXrxYOTk5SktLa7Y8VPr1VL7aG0r9unz5cr3wwgv64x//qJEjR2rLli2aOXOm0tLSNGXKlFZrdWL/dqStodS3kvS///u/mjp1qgYOHCi3260LLrhAN998szZt2uTdJhT6Vmq/rd2pb63f2tuzZ0+NGjVKO3fu9Lk+NTVVGRkZ3vUpKSmqq6vTwYMHm21XXl7uTbMpKSnat29fi2Pt37+/ReLtSqmpqTr33HObLRsxYoSKi4slyXsX0anp8dS2hEp7W9vHqf0rSV9++aXeeust3Xnnnd5lodavX+ervb44uV8feOABPfzww7rxxhs1atQo3XbbbZo1a5by8/O9dUqh0b/ttdUXJ/etJA0dOlRr1qzR4cOHVVJSog0bNqi+vl5DhgwJqb6V2m6rLzb71noYqa2t1Y4dO5SamupzfWVlpUpKSrzrs7KyFBUVpYKCAu82paWl+uSTTzRhwgRJ0vjx41VVVaUNGzZ4t1m/fr2qqqq82wTDxRdfrH//+9/Nln366afKyMiQJO8v/9fbUldXpzVr1njrDKX2+uLk/pWk5557TgMGDNBVV13lXRZq/fp1vtrri5P79auvvlJERPP/a3S73d7bXUOpf9trqy9O7tuv69mzp1JTU3Xw4EGtWrVK1157bUj17df5aqsvVvu2w1NdA+S+++4zq1evNrt27TIffvihufrqq018fLz54osvTE1NjbnvvvvM2rVrTVFRkXnnnXfM+PHjzcCBA1vcVjVo0CDz1ltvmU2bNpnLL7/c561G5513nlm3bp1Zt26dGTVqVNBvq9qwYYOJjIw0P/vZz8zOnTvNsmXLTI8ePcwLL7zg3eaxxx4ziYmJZsWKFWbr1q3mpptu8nkbWSi0N9T6t7Gx0QwePNg89NBDLdaFUr82aa29odavU6ZMMQMHDvTe7rpixQrTr18/8+CDD3q3CZX+ba+toda3xhjzxhtvmL///e9m165d5s033zSjR482F154oamrqzPGhE7fttfW7ta3QQ8jTfdsR0VFmbS0NHPdddeZbdu2GWOO34qUnZ1t+vfvb6KioszgwYPNlClTTHFxcbNjHD161PzoRz8yffv2NXFxcebqq69usU1lZaW55ZZbTHx8vImPjze33HKLOXjwYNDa2eSvf/2ryczMNDExMeacc84xzzzzTLP1Ho/HPPLIIyYlJcXExMSYb37zm2br1q3NtgmV9oZa/65atcpIMv/+979brAu1fjWm9faGWr9WV1ebe++91wwePNjExsaaM88808yZM8fU1tZ6twmV/m2vraHWt8YYs3z5cnPmmWea6Ohok5KSYu666y5z6NAh7/pQ6Vtj2m5rd+tblzHG+D3mAwAAECDW54wAAIDwRhgBAABWEUYAAIBVhBEAAGAVYQQAAFhFGAEAAFYRRgAAgFWEEQAAYBVhBAAAWEUYAQAAVhFGAACAVYQRAABg1f8HDfl0URWur5kAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4\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": [
      "5\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": [
      "6\n"
     ]
    },
    {
     "data": {
      "image/png": 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S09Pldrs1dOhQrVq1qksFAwCA8BLl7w7r1q3T3LlztWLFCo0bN06PPPKIsrOztXv3bg0aNKjdfaZMmaLPP/9cTzzxhM4991yVlpaqoaHhaxcPAABCn99hZNmyZZo+fbpmzJghSVq+fLk2bdqklStXKjc3t037l156SVu2bNG+ffvUp08fSdI555zz9aoGAABhw6/TNHV1dcrPz9fEiRNbbZ84caK2bt3a7j4vvPCCxowZo9/97ncaMGCAhg8frrvuuksnTpzo8HVqa2tVWVnZ6gEAAMKTXyMjZWVl8nq9SkpKarU9KSlJJSUl7e6zb98+vfnmm4qNjdVzzz2nsrIyzZo1S4cPH+5w3khubq4WL17sT2kAACBEdWkCq8vlavW9MabNthaNjY1yuVxau3atLrnkEl177bVatmyZVq9e3eHoyIIFC1RRUeF7HDhwoCtlAgCAEODXyEi/fv0UGRnZZhSktLS0zWhJi5SUFA0YMECJiYm+bSNGjJAxRp999pmGDRvWZh+32y232+1PaQAAIET5NTISExOjzMxM5eXltdqel5ensWPHtrvPuHHjdOjQIVVXV/u2ffTRR4qIiNDAgQO7UDIAAAgnfp+mmT9/vh5//HGtWrVKe/bs0bx581RcXKyZM2dKajrFkpOT42t/4403qm/fvrr11lu1e/duvf7667r77rt12223KS4u7swdCQAACEl+L+2dOnWqysvLtWTJEnk8HmVkZGjjxo1KT0+XJHk8HhUXF/va9+rVS3l5ebrzzjs1ZswY9e3bV1OmTNHSpUvP3FEAAICQ5TLGGNtFnE5lZaUSExNVUVGhhIQE2+UAABA2duy4SUeOvq2MC/+kpKTrzujP7uznN/emAQAAVhFGAACAVYQRAABgFWEEAABYRRgBAABWEUYAAIBVhBEAABzMyP4VPggjAABAUvs3vA0EwggAALCKMAIAAKwijAAAAKsIIwAAwCrCCAAAsIowAgAArCKMAAAAqwgjAADAKsIIAACwijACAACsIowAAACrCCMAAMAqwggAALCKMAIAAKwijAAAAKsIIwAAwCrCCAAAsIowAgAArCKMAAAAqwgjAADAKsIIAACwijACAACsIowAAACrCCMAAMAqwggAALCKMAIAAKwijAAAAKsIIwAAwCrCCAAAsIowAgAArCKMAAAAqwgjAADAKsIIAACwKsp2AQCcyRivjh59T17vcdulAI7WUH/UdgmEEQB2FBc/oY8/+a3tMgA0c7kirb02YQSAFTW1hyRJMTFny+1OtlwN4Gxud5J6986y9vqEEQB2mKZ/UlOnauiQeXZrAWAVE1gBWGFa0ggAxyOMALDKJZftEgBYRhgBYEnLyAhhBHA6wggAS5rDiIswAjgdYQSAHYY5IwCaEEYAWMbICOB0hBEAVrSspiGKACCMALCE0zQAmhBGAFjG2AjgdF0KIytWrNDgwYMVGxurzMxMvfHGG53a76233lJUVJQuvvjirrwsgHBiWE0DoInfYWTdunWaO3euFi5cqIKCAo0fP17Z2dkqLi4+5X4VFRXKycnR1Vdf3eViAYQfLnoGwO8wsmzZMk2fPl0zZszQiBEjtHz5cqWlpWnlypWn3O9nP/uZbrzxRmVl2bsRD4DgweXgAbTwK4zU1dUpPz9fEydObLV94sSJ2rp1a4f7Pfnkk/rkk0+0aNGiTr1ObW2tKisrWz0AhCtGRgCn8yuMlJWVyev1KikpqdX2pKQklZSUtLvP3r17dd9992nt2rWKiurcTYJzc3OVmJjoe6SlpflTJoCQwOXgATTp0gRW10kTzowxbbZJktfr1Y033qjFixdr+PDhnf75CxYsUEVFhe9x4MCBrpQJIJgxgRVAs84NVTTr16+fIiMj24yClJaWthktkaSqqiq99957Kigo0B133CFJamxslDFGUVFR2rx5s6666qo2+7ndbrndbn9KAwAAIcqvkZGYmBhlZmYqLy+v1fa8vDyNHTu2TfuEhATt3LlThYWFvsfMmTN13nnnqbCwUJdeeunXqx5ACOMKrACa+DUyIknz58/XzTffrDFjxigrK0uPPvqoiouLNXPmTElNp1gOHjyoNWvWKCIiQhkZGa3279+/v2JjY9tsB+AshjkjAJr5HUamTp2q8vJyLVmyRB6PRxkZGdq4caPS09MlSR6P57TXHAEAH+aMAI7nMib47+NdWVmpxMREVVRUKCEhwXY5AM6AXbt/oZKS53XuufcpfdBPbZcDoBt09vObe9MAsMP3ZxAjI4DTEUYAWNIygZUwAjgdYQQAAFhFGAFgBatpALQgjACwhCuwAmhCGAEAAFYRRgDYEfxXFQAQIIQRAFYYVtMAaEYYAWAJE1gBNCGMALCLCayA4xFGAACAVYQRAHYYTtMAaEIYAWAVE1gBEEYAWPHlFVgBOB1hBIAlnKYB0IQwAsAuVtMAjkcYAWAJp2kANCGMALCDy8EDaBZluwDgq2pqPGpsrLNdBgLA6z0uidU0AAgjCCKffvqwPtn3e9tlIOAII4DTEUYQNCqrdkqSIiJi5HLFWK4GgRAT00e9e19quwwAlhFGEESa5hAMO/eXGjjwJsu1AAAChQmsCB6mselflnoCgKMQRhA0Wq7IyYRGAHAWwgiCEGEEAJyEMILg0XyaxuXibQkATsJvfQQNw71KAMCRCCMIIkxgBQAnIowgeBgmsAKAExFGEDS+PE3D2xIAnITf+ggeLTdO4zQNADgKYQRBwzTPGXHxtgQAR+G3PoIIt5QHACfi3jQIGobLwQNAwL3zzjsqLy/XxRdfrNTUVCs1MDKCoMNpGgAInD179mj79u06fPiwtRr4rY8gwgRWAHAiwgiCRstpGkZGAMBZ+K2PIMLl4AHAiQgjCB6+G+URRgDASVhNg4A4dmyfPvjwl2poqOywzfHjRc1fEUYAwEkIIwiI0i/+T0ePvtOptrGxA7u5GgBAMCGMICCM8UqS+va9UmkDb+mwnTs2Wb16DgtQVQCAYEAYQWA033cmNnaA+vYdb7kYAEAwYQIrAoSVMgCA9hFGEBCmOYy4CCMAgJMQRhAY3HcGANABwggChNM0AID2EUYQEF9GEcIIAKA1wggCw3eahrccAKA1PhkQIExgBQC0jzCCgDC+EzUAALRGGEGANIcRVtMAAE5CGEFgmJbTNLzlAACt8cmAgDAs7QUAdKBLYWTFihUaPHiwYmNjlZmZqTfeeKPDths2bNB3vvMdnX322UpISFBWVpY2bdrU5YIRqjhNAwBon99hZN26dZo7d64WLlyogoICjR8/XtnZ2SouLm63/euvv67vfOc72rhxo/Lz8zVhwgRNnjxZBQUFX7t4hA7TvLSX1TQAgJP5HUaWLVum6dOna8aMGRoxYoSWL1+utLQ0rVy5st32y5cv1z333KNvfvObGjZsmH79619r2LBhevHFF7928QglnKYBALTPrzBSV1en/Px8TZw4sdX2iRMnauvWrZ36GY2NjaqqqlKfPn06bFNbW6vKyspWD4Q6TtMAANrnVxgpKyuT1+tVUlJSq+1JSUkqKSnp1M/44x//qGPHjmnKlCkdtsnNzVViYqLvkZaW5k+ZCEKG1TQAgA506ZPBddJft8aYNtva8/TTT+v+++/XunXr1L9//w7bLViwQBUVFb7HgQMHulImggqnaQAA7Yvyp3G/fv0UGRnZZhSktLS0zWjJydatW6fp06dr/fr1+va3v33Ktm63W26325/SEPQ4TQMAaJ9fIyMxMTHKzMxUXl5eq+15eXkaO3Zsh/s9/fTTuuWWW/TXv/5VkyZN6lqlCG2GkREAQPv8GhmRpPnz5+vmm2/WmDFjlJWVpUcffVTFxcWaOXOmpKZTLAcPHtSaNWskNQWRnJwc/elPf9Jll13mG1WJi4tTYmLiGTwUtKeiokAVlYW2y1B19QeSWNoLAGjL7zAydepUlZeXa8mSJfJ4PMrIyNDGjRuVnp4uSfJ4PK2uOfLII4+ooaFBt99+u26//Xbf9mnTpmn16tVf/wjQocbGWhUU5sjrPW67FJ+IyFjbJQAAgozfYUSSZs2apVmzZrX73MkB47XXXuvKSwRETY1HDd5q22X4LTrqLLndZ5+2nddb6wsi/ftPkstldyVLVFSCkpO+b7UGAEDw6VIYCRcff/Jbff55KF58zaVvjH5KvXtfdpp2jb6vLrxgmSIiHP3fDQAIUo7+dIqM7Kno6I4vvhaMGhqqZUydqo99dNowYozX97XLFdndpQEA0CWODiMjzn9AI85/wHYZfnn//Tn6vPTvrYJGR756p9zOXAcGAAAbuBxmiPGNcJjGUzeUpObAYnuuCAAAp8KnVKhpDhadGhnxBRZO0QAAghdhJMS0jIz4E0Y4RQMACGaEkRDTcqO5zoSRltU0TF4FAAQzwkiI8Y2M6PRzRr4MLPw3AwCCF59SocaP0zQtN6djAisAIJg5emlvKGoJFuXlW9TQUHXKtg31Fc37cJoGABC8CCMhJjqq6eaCVVU7VVW1s1P7REXFd2dJAAB8LYSREDNwYI4iItzyeo91ep9+/a7uxooAAPh6CCMhJiamj8455+e2ywAA4IxhZiMAALCKMAIAAKwijAAAAKsIIwAAwCrCCAAAsIowAgAArCKMAAAAq7jOCALi+PHj2rp1q2pqak7ZLiEhQePGjVNkJJewBwCnIIwgIAoLC/Xmm292qm11dbWGDRvWzRUhGPTo0UOpqalyuVy2SwFgEWEEAVFbWytJSk1N1fDhw9tt89prr0mStm/fru3btweqNFh21VVXdfieAND96urqbJdAGEFgGGMkSQMHDtSVV17ZbptBgwbp1VdfVUNDQwArgy0ej0eS9Morr+iVV16xXA0AmyOUhBEEREsYOdWbfciQIRoyZEigSoJl+/bt04svvqj6+nrbpQCOFx8fr0GDBll7fcIIAqKxsVGS3eSN4DJkyBDNmTPHdhkAggBhBAHRMjISEcFqcgAIJmVPvq/afRXqPWW4eow820oNhJEQ4/V6VVRU5NeEo7S0NMXHx3djVafXmdM0AIDAM/WNMvWNUqO9GggjIebtt99WXl6eX/skJSXp5z//eTdV1DmEEQBARwgjIaayslJS08XBzjrrrFO2bWho0KFDh3T06NFAlHZKLXNGOE2DrzJeu3+NAZBMY9Mfi7L4tyJhJMS0jDCMGjVKV1999SnbHj16VMuXLw+KpbKMjOBkJ94vU/kzH0gNxnYpACwjjIQYfz7Uo6Ka/nu9Xq927dplNQgcPnxYEmEEX6r5+ChBBAgSrrgoxaT2svb6hJEQ408YiY6O9n29fv36bqvJH9xzBj7N7+X4CWmKv3Kg5WIAZ3NFRcgVae80OmEkxPgTRtxut6644goVFRV1d1mdEhsbq4yMDNtlIEgYb/N7OSZSEW5+FQFOxm+AEOPv9TomTJigCRMmdGdJQNc0T5pzRXDqDnA6ljaEGCaCImy0zOAnjACORxgJMYQRhAvjGxmxXAgA6zhNE2LCOYw01jao5sMjMg1ceMIJGg7XNH0RGX7vZQD+IYyEmHAOIxUvfapj2zy2y0CAuaIYGgGcjjASYsI5jHiP1kqSopJ6KDLRbbkaBEJkz2jFjuhruwwAlhFGQkw4h5GW0zPxV6ap5+j+lqsBAGf4+L13VH24XOkjR6l3ygArNTg6jBw8eNB3r5dQUVFRISn0woi3qk5Vrx5Q44mOL01f7zkmSXJFhdaxAUAo27Hxf3Vg1781afbdhBEbtm3bpvfff992GV0SalcyPb7jc1VvPdSptpHxMd1cDQCgDYt/5Do6jPTt21dpaWm2y/Bbjx49dN5559kuwy+NtV5JUsw5CYq7oOM5ApGJbsWkJwSqLFj0Sf47+seffq/62hrbpQCQ3RF3R4cRrk4aOC2X/o5Ji1f8t7gPCaSignyCCBAkot2xOjt9sLXXd3QYQQA1T061eSMmBBdvQ70k6dIfTNE3sr9nuRrA2aLj4hQdY28VI2EkzFW/41HtvgrbZaj+s6qmL7jAFZp565vCSGyvePVIPMtyNQBsIoyEscZar44+/7FkbFfypYqqUlW83344OuI5qC+KP7U5hwoB5Pn4Q0lSZBS/hgCn47dAGDN1Xl8QSbxuiBciqfYAABFBSURBVNVaPt+3V//a8pIO/L8P5DUdL++F88TFM2EZsOnF/y7UwY+O6uppIzRsTJKVGggjYcx3j5eoCMVfbmfteIt/H3xFn1a/r9ievXRW7z7ttjlRVafjVccVGT1YcsUFuELY4HLF6eU1tXrjb6/bLgVwrLpTXP8pUAgjIabm4yM6vO6jplGP02m5WmsQ3Pujvq5OkpRx1URd8ZPb2m3zjxX/1qf/LlNUTIQig6BmdK/a41/+AgyGX4aAk7mMV+4DuyRGRtAZNXsOq7Gqzq99ymsO6tUFc7upos6pLPtCkhR1itna3vqmgHXlTefrvEuTA1IX7KkvLdXBv2xQQ41/72cAZ1bF3/6m6PpjOuv7v7JWA2EkxJjGptGOnlkppz31UldTozX33KnjDRUyQTKL9V+vVGjPO+0PydedaAojEfU18lbYXwGE7lX+2OM68Ze/2C4DcLwezf/uqP5AV+paKzUQRkJNcxiJ7BmtqL6nnldRV1mnYw1HJUk/uG+RXLK3TOXD7SXa++5RNZoU1R7reEje1digyjun6aMTpQGsDjZ5LuivI4NY2gvYsvfIXh3p5dKE0fau7N2lMLJixQr9/ve/l8fj0YUXXqjly5dr/PjxHbbfsmWL5s+fr127dik1NVX33HOPZs6c2eWinazlSqaduV5Ho7dppMHlitCQ0d/szrJO6/P9nygiar/OuzRZmdnp7bYpWbpU9a/lKbrhWICrgy3VsdIfs8pV3P+w7VIAB2u619n3v9gtDZtkpQK/w8i6des0d+5crVixQuPGjdMjjzyi7Oxs7d69W4MGDWrTvqioSNdee61++tOf6qmnntJbb72lWbNm6eyzz9YPf/jDM3IQjtI8MuKK6EwYaRqBiIiyf1O9xuYQFZcQo97JPdttU1V/WMcajin5V0t01g9+EMjyYMGSbUv07CcblDVgnK5PvsR2OYBz5a9W/7KPdek3zrFWgt9hZNmyZZo+fbpmzJghSVq+fLk2bdqklStXKjc3t037hx9+WIMGDdLy5cslSSNGjNB7772nP/zhD4SRrmgOI+pUGGla2hsRaf9snNdXS8d1m+YVNxGxsXJxIaywV6sGGZdLWSlZuiXjFtvlAM6V/5xUfVxy2VvF6DLGdHpmY11dnXr06KH169frB1/5y3XOnDkqLCzUli1b2uzzrW99S6NHj9af/vQn37bnnntOU6ZM0fHjxxUdHd1mn9raWtXW1vq+r6ysVFpamioqKpSQcOYukLRh1gPqo47vIBuMkuIGKj46Uf86/Lb2Ve85ZVsjr+q95ZIilRA3OjAFdqAh6lw1RqUq5sQmxdZsbrfNeR/XKf5Yo/43u5c+OtfePRIQGJ+4j+twdL0mHu2nbx5jzghgy1X1O9TfHNWT0d/TrQvP7KTyyspKJSYmnvbz268/P8vKyuT1epWU1HodclJSkkpKStrdp6SkpN32DQ0NKisrU0pKSpt9cnNztXjxYn9K65KUyAFK6zm021+nO5zwlqnO27lJnq6IXqqL/VY3V9Q56Z9VKu3gqe/UWtj7uHb14m6uTvHtug+UXXfcdhmA43mi278gZSB0aSzcddLNQ4wxbbadrn1721ssWLBA8+fP933fMjJyph30Fut4ZfUZ/7ndrbaxRp/XHlZMdP9OtY+KTFBk3T+7uapOMDU6mPJvHUppf86IJFX1ilBC7zhdVs0Napwgzhslj/c8rYnlIneATeWus3S4vre11/crjPTr10+RkZFtRkFKS0vbjH60SE5Obrd9VFSU+vZt/xSJ2+2W2939w/T/seK/uv01AADAqfn150hMTIwyMzOVl5fXanteXp7Gjh3b7j5ZWVlt2m/evFljxoxpd74IAABwFr/HRufPn6/HH39cq1at0p49ezRv3jwVFxf7rhuyYMEC5eTk+NrPnDlT+/fv1/z587Vnzx6tWrVKTzzxhO66664zdxQAACBk+T1nZOrUqSovL9eSJUvk8XiUkZGhjRs3Kj296UJWHo9HxcXFvvaDBw/Wxo0bNW/ePP35z39WamqqHnzwQZb1AgAASX4u7bWls0uDAABA8Ojs5zdT2AEAgFWEEQAAYBVhBAAAWEUYAQAAVhFGAACAVYQRAABgFWEEAABYRRgBAABWEUYAAIBVfl8O3oaWi8RWVlZargQAAHRWy+f26S72HhJhpKqqSpKUlpZmuRIAAOCvqqoqJSYmdvh8SNybprGxUYcOHVJ8fLxcLpekprSVlpamAwcOOPZ+NfQBfSDRBy3oB/pAog+k4OoDY4yqqqqUmpqqiIiOZ4aExMhIRESEBg4c2O5zCQkJ1jvbNvqAPpDogxb0A30g0QdS8PTBqUZEWjCBFQAAWEUYAQAAVkXef//999suoqsiIyN15ZVXKioqJM42dQv6gD6Q6IMW9AN9INEHUuj1QUhMYAUAAOGL0zQAAMAqwggAALCKMAIAAKwijAAAAKuCJozk5ubK5XJp7ty5vm3GGN1///1KTU1VXFycrrzySu3atavVfrW1tbrzzjvVr18/9ezZU9/73vf02WeftWpz5MgR3XzzzUpMTFRiYqJuvvlmHT16NCDHdSr333+/XC5Xq0dycrLv+XA//hYHDx7UT37yE/Xt21c9evTQxRdfrPz8fN/zTuiHc845p817weVy6fbbb5fkjD5oaGjQL3/5Sw0ePFhxcXEaMmSIlixZosbGRl8bJ/RDVVWV5s6dq/T0dMXFxWns2LF69913fc+HWx+8/vrrmjx5slJTU+VyufT888+3ej6Qx1tcXKzJkyerZ8+e6tevn2bPnq26urruOfCTnK4fNmzYoGuuuUb9+vWTy+VSYWFhm58R0v1ggsD27dvNOeecYy666CIzZ84c3/bf/OY3Jj4+3jz77LNm586dZurUqSYlJcVUVlb62sycOdMMGDDA5OXlmR07dpgJEyaYUaNGmYaGBl+b7373uyYjI8Ns3brVbN261WRkZJjrrrsuoMfYnkWLFpkLL7zQeDwe36O0tNT3fLgfvzHGHD582KSnp5tbbrnFvPPOO6aoqMi8/PLL5uOPP/a1cUI/lJaWtnof5OXlGUnm1VdfNcY4ow+WLl1q+vbta/7+97+boqIis379etOrVy+zfPlyXxsn9MOUKVPMBRdcYLZs2WL27t1rFi1aZBISEsxnn31mjAm/Pti4caNZuHChefbZZ40k89xzz7V6PlDH29DQYDIyMsyECRPMjh07TF5enklNTTV33HFH93eCOX0/rFmzxixevNg89thjRpIpKCho8zNCuR+sh5GqqiozbNgwk5eXZ6644gpfGGlsbDTJycnmN7/5ja9tTU2NSUxMNA8//LAxxpijR4+a6Oho88wzz/jaHDx40ERERJiXXnrJGGPM7t27jSTz9ttv+9ps27bNSDIffPBBIA6xQ4sWLTKjRo1q9zknHL8xxtx7773m8ssv7/B5p/TDyebMmWOGDh1qGhsbHdMHkyZNMrfddlurbddff735yU9+Yoxxxnvh+PHjJjIy0vz9739vtX3UqFFm4cKFYd8HJ38IB/J4N27caCIiIszBgwd9bZ5++mnjdrtNRUVF9xxwB9oLIy2KioraDSOh3g/WT9PcfvvtmjRpkr797W+32l5UVKSSkhJNnDjRt83tduuKK67Q1q1bJUn5+fmqr69v1SY1NVUZGRm+Ntu2bVNiYqIuvfRSX5vLLrtMiYmJvjY27d27V6mpqRo8eLB+/OMfa9++fZKcc/wvvPCCxowZox/96Efq37+/Ro8erccee8z3vFP64avq6ur01FNP6bbbbpPL5XJMH1x++eX65z//qY8++kiS9K9//Utvvvmmrr32WknOeC80NDTI6/UqNja21fa4uDi9+eabjuiDrwrk8W7btk0ZGRlKTU31tbnmmmtUW1vb6rRxsAr1frAaRp555hnl5+crNze3zXMlJSWSpKSkpFbbk5KSfM+VlJQoJiZGvXv3PmWb/v37t/n5/fv397Wx5dJLL9WaNWu0adMmPfbYYyopKdHYsWNVXl7uiOOXpH379mnlypUaNmyYNm3apJkzZ2r27Nlas2aNJGe8D072/PPP6+jRo7rlllskOacP7r33Xt1www06//zzFR0drdGjR2vu3Lm64YYbJDmjH+Lj45WVlaVf/epXOnTokLxer5566im988478ng8juiDrwrk8ZaUlLR5nd69eysmJiao+qQjod4P1q4Te+DAAc2ZM0ebN29u81fAV7lcrlbfG2PabDvZyW3aa9+Zn9PdsrOzfV+PHDlSWVlZGjp0qP7nf/5Hl112maTwPn5Jamxs1JgxY/TrX/9akjR69Gjt2rVLK1euVE5Ojq9duPfDVz3xxBPKzs5u9ZeJFP59sG7dOj311FP661//qgsvvFCFhYWaO3euUlNTNW3aNF+7cO+Hv/zlL7rttts0YMAARUZG6hvf+IZuvPFG7dixw9cm3PvgZIE63lDqk84KlX6wNjKSn5+v0tJSZWZmKioqSlFRUdqyZYsefPBBRUVF+ZLZyUmstLTU91xycrLq6up05MiRU7b5/PPP27z+F1980Sb92dazZ0+NHDlSe/fu9a2qCffjT0lJ0QUXXNBq24gRI1RcXCxJjumHFvv379fLL7+sGTNm+LY5pQ/uvvtu3Xffffrxj3+skSNH6uabb9a8efN8I6dO6YehQ4dqy5Ytqq6u1oEDB7R9+3bV19dr8ODBjumDFoE83uTk5Davc+TIEdXX1wdVn3Qk1PvBWhi5+uqrtXPnThUWFvoeY8aM0U033aTCwkINGTJEycnJysvL8+1TV1enLVu2aOzYsZKkzMxMRUdHt2rj8Xj0/vvv+9pkZWWpoqJC27dv97V55513VFFR4WsTLGpra7Vnzx6lpKT4fvGE+/GPGzdOH374YattH330kdLT0yXJMf3Q4sknn1T//v01adIk3zan9MHx48cVEdH6V1JkZKRvaa9T+qFFz549lZKSoiNHjmjTpk36/ve/77g+COTxZmVl6f3335fH4/G12bx5s9xutzIzM7v1OM+EkO+Hbpsa2wVfXU1jTNOSrsTERLNhwwazc+dOc8MNN7S7pGvgwIHm5ZdfNjt27DBXXXVVu0uZLrroIrNt2zazbds2M3LkyKBYxveLX/zCvPbaa2bfvn3m7bffNtddd52Jj483n376qTEm/I/fmKZl3VFRUeaBBx4we/fuNWvXrjU9evQwTz31lK+NE/rBGGO8Xq8ZNGiQuffee9s854Q+mDZtmhkwYIBvae+GDRtMv379zD333ONr44R+eOmll8z//d//mX379pnNmzebUaNGmUsuucTU1dUZY8KvD6qqqkxBQYEpKCgwksyyZctMQUGB2b9/f0CPt2VJ69VXX2127NhhXn75ZTNw4MCALe09XT+Ul5ebgoIC849//MNIMs8884wpKCgwHo8nLPohqMNIY2OjWbRokUlOTjZut9t861vfMjt37my1z4kTJ8wdd9xh+vTpY+Li4sx1111niouLW7UpLy83N910k4mPjzfx8fHmpptuMkeOHAnIMZ1Ky3r56Ohok5qaaq6//nqza9cu3/PhfvwtXnzxRZORkWHcbrc5//zzzaOPPtrqeaf0w6ZNm4wk8+GHH7Z5zgl9UFlZaebMmWMGDRpkYmNjzZAhQ8zChQtNbW2tr40T+mHdunVmyJAhJiYmxiQnJ5vbb7/dHD161Pd8uPXBq6++aiS1eUybNs0YE9jj3b9/v5k0aZKJi4szffr0MXfccYepqanp1uNvcbp+ePLJJ9t9ftGiRb6fEcr94DLGmO4bdwEAADg169cZAQAAzkYYAQAAVhFGAACAVYQRAABgFWEEAABYRRgBAABWEUYAAIBVhBEAAGAVYQQAAFhFGAEAAFYRRgAAgFWEEQAAYNX/B2TdImmkyJH0AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7\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": [
      "8\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": [
      "9\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": [
      "10\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": [
      "11\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",
    "    radii, eigval_list, eigvec_list = eigen_calc_from_dist_mat(np_var_data, dist_mat, center, radint = 0.1)\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": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}