diff --git a/is/UB2/ExerciseSheet2.ipynb b/is/UB2/ExerciseSheet2.ipynb
index 13b2642..7c734e9 100644
--- a/is/UB2/ExerciseSheet2.ipynb
+++ b/is/UB2/ExerciseSheet2.ipynb
@@ -80,7 +80,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 53,
    "metadata": {
     "collapsed": true
    },
@@ -88,6 +88,7 @@
    "source": [
     "%matplotlib inline\n",
     "import numpy as np\n",
+    "import math as m\n",
     "from numpy import *\n",
     "from scipy import optimize\n",
     "from matplotlib import pyplot as plt"
@@ -105,7 +106,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 54,
    "metadata": {
     "collapsed": false
    },
@@ -129,7 +130,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 55,
    "metadata": {
     "collapsed": false
    },
@@ -154,7 +155,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 94,
    "metadata": {
     "collapsed": true
    },
@@ -178,7 +179,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 95,
    "metadata": {
     "collapsed": false,
     "scrolled": true
@@ -216,7 +217,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 96,
    "metadata": {
     "collapsed": false
    },
@@ -225,222 +226,224 @@
      "data": {
       "image/png": [
        "iVBORw0KGgoAAAANSUhEUgAAAXAAAAEACAYAAACqOy3+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
-       "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3XeYXVX1xvHvSyCkAiIoIqFIQMRY0JBCKIOAkBjpvbdI\n",
-       "TYSfhCZycpAiKgqJSgmIIAgKiKKgAkoEFEEUC2IDSwJKURQTBQRcvz/WDJmBSXLXvXfmllmf58mj\n",
-       "986se3YmDysn++z9bpkZKaWUWs9yjR5ASiml6mQDTymlFpUNPKWUWlQ28JRSalHZwFNKqUVlA08p\n",
-       "pRZVUwOX9GZJD3T79YykGfUaXEoppSVTvdaBS1oOeAwYZ2YL6vKhKaWUlqieUyjbAo9k804ppf5R\n",
-       "zwa+N/ClOn5eSimlpajLFIqkwfj0ycZm9lTNH5hSSmmZlq/T50wGftJb85aUYSsppVQFM9OyvqHm\n",
-       "X8C1wEFL+JrV4xp9/QuY1egxtMs4W2GMOc4BNE7oMPiLwUkGatpxvvrnacv6nprvwCUNxx9gTqv1\n",
-       "s1JKqW4kAccBJwEHYHZb5/uNHFVd1dzAzezfwGp1GEtKKdWH31heCmwITMDsT40dUN/InZiLzWv0\n",
-       "ACo0r9EDqMC8Rg+gQvMaPYAKzWv0ACo0r9EDAEAaDfwIeB7YvJfmPa+/h9RX6raRZ4kXkMyWNRGf\n",
-       "Ukr1IL0PuBwogIvo6wbXhyrpnfVahZJSSo3jO8E/gj+L2xmzHzZ4RP0iG3hKqbVJqwBfBFYBxmL2\n",
-       "eINH1G9yDjyl1LqktwE/Bv4AvGcgNW/IBp5SalXS3sD3gBKzD2L2QqOH1N9yCiWl1Fqk5YFzgV2A\n",
-       "7TD7WYNH1DDZwFNKrUN6HfBl4Dl8vvvpWDnjgT+Y0RaZTTmFklJqDdJ44H7gbmBqpHlLSOJI4BvA\n",
-       "m/tohP0u78BTSs1PmgacBUzD7OuxUoYAnwPGAZPM+H0fjLAhsoGnlJqXNASYA2wGbIHZb2PlrAPc\n",
-       "ADwMTDBjUf0H2Tg5hZJSak7SKOBOfH33hCqa97bAvfhBM/u0W/OGbOAppWYkbQ3cB1wH7InZwspL\n",
-       "kcSJ+Oaefcz4lKfKtp+cQkkpNQ+PgP1Q56/9MfturJyReBbKKGCcGW19Rm828JRSc5BGAJcBbwLG\n",
-       "YzY/Vs6bgRvxVSr7mfF8/QfZXHIKJaXUeNKGeATsIvxhZbR57wzcBXzKjA8MhOYNdWjgklaRdL2k\n",
-       "X0t6SNKEegwspTRASDvid82zgcMxe67yUgZJnNVZO9WMS/tolE2pHlMoFwC3mNnu8i2uw+vwmSn1\n",
-       "mTHSlFEwYyQMWQjPLYDZD5rd0uhxDTjSIDy3+xBgR8x+FCvntcDVwGBgrBlP1n+Qza2mBi5pZWAL\n",
-       "MzsIwMxeBJ6px8BS6gtjpCkT4YK5MLrrvWmw/hiJbOL9SHoN3nyH4Vvin4iVswm+vvsG4BQzXqz/\n",
-       "IJtfrVMo6wFPSbpc0k8lzZU0rB4DS6kvjIIZ3Zs3wFwYvTZMb9SYBhzpHfiW+N/gYVTR5n0AcCve\n",
-       "uGdGmrdKraCyfU41rnUKZXngXcCxZvZjSecDJwOnd/8mSbO6vZxnZvNqvG5KVRkJQ3p7fwQM7e+x\n",
-       "DEjSvvi06wzMromVMhg4D9gB2NqMB0P1pdYErgc+DnwtUtsfJHUAHZGaWhv4o8CjZvbjztfX4w28\n",
-       "BzObVeN1UqqLhZ5i9yqL4Nn+HsuAIq0AfAKYCmyD2S9i5bwB39TzNLCpGf8M1ZfaArgW+CxwU6S2\n",
-       "v3Te2M7rei2pWFZNTQ3czB6XtEDShmb2O2Bb4Fe1fGZKfWkBzJ4G63efRjkcHpnveRupL0hrAF8B\n",
-       "FgKbYvaPWDmT8AjZi4GzzPhfxbU+XTId+DBwoBX2nci1m13Np9LL57MuxZ8EPwIcYmbPdPt6nkqf\n",
-       "msoYacraMH0EDF0Ez86HOfkAs49IE/HmfRlwBmaVN18h4Gh8SvYQM0J/Rio1DLgEeCuwqxX2x0h9\n",
-       "o1XSO2tu4PUYREqpzfiW+COAM4BDMftmrJyhwEXAO4FdzXgkVF/qTcBXgV8AR1ph/4nUN4NKemfu\n",
-       "xEwp1Zc0FL/jPgbYrIrmvR7wA3yKd7Mqmvdk4B58ZuCgVmzelcoslJRS/Uhd+du/xyNg/x0r573A\n",
-       "lcA5wOxIiqBKLQecChwF7GaF3R25divKBp5Sqg9pW+Aq/MDh8wnMz3bOd58CHAvsacadoUuXWhlv\n",
-       "/KsBm1phf4nUt6ps4Cml2vh894nAB4G9Ce7zkFgJuAJYA18i+FiovtRb8RTCW4E9rLD/RupbWTbw\n",
-       "lFL1pO752+MxC+VvS7wFb753AHtHUwRVag/8vMsPWWFXRmrbQTbwlFJ1pI3wlR53AfthFmu+Yjfg\n",
-       "QuAkMy4P1ZZaHp8n3x14rxX2QKS+XWQDTynFSTvja6xPxSwU4SoxCD9hfm9gshk/CdWXWh3fVfki\n",
-       "MNYK+3ukvp1kA08pVc4jYM8A9gemYnZfrJzVgGsA4RGwfwvVl9oUj+y4CjjdCnspUt9usoGnlCoj\n",
-       "vRY/4X0FfEt8KH9b4t34EsNrgdOiEbAqdRg+bXKEFXZjpLZdZQNPKS2btAk+3309cAqe/R8o52A8\n",
-       "zOpIM24I1ZZaET9xZ0tgSyvsN5H6dpYNPKW0dNKBeIzrMZh9JVbKYOB84D3AVmY8FKovtRZ+1/4o\n",
-       "MM4KWxipb3fZwFNKvZMGA58C3gt0YBZKGpV4Ix4B+yQwzox/hepLdeBTNhcAH7eij4ObWlA28JTS\n",
-       "q0lr4s33b/h8d+ioRIkt8YeVnwU+VkUE7HHAScABVthtkWsPJNnAU0o9SZvj+dsXAmdXEQG7OH/b\n",
-       "COVvq9RwPIRqQ2CCFfanSP1Akw08peR8S/wxwEeAgzH7VqycYcBcYGNgghmh/G2VGo3vyrwf2NwK\n",
-       "y1OSliHjZFNK4IeRXwFMwyNgo837TXiE60vApCqa9/vwCNnPAodm865MzXfgkv4E/Av/g3vBzMbV\n",
-       "+pkppX4krYcvEXwImIjF8rMlJgNfAD4KfLaKCNiPAIcDO1th90SuPdDVYwrFgA4ze7oOn5VS6k/S\n",
-       "9ngM61nAnGAE7HL4XPeR+Kk5PwhdutQq+I7KlfAI2Mcj9al+c+B5ZFpKrURaDjgZn/PeHbO7YuWs\n",
-       "DHwRWBXfEv/XUH2pt+F3/TcDM62wFyL1ydXrDvx2SS8BF5vZ3Dp8Zkqpr0hd+duvx5cIhg4/kOjK\n",
-       "3/4OsLsZofxtldoH31l5nBV2daQ29VSPBj7JzP4qaXXgNkm/sVf8bS5pVreX8ywY+J5SqhNpY7z5\n",
-       "3g7shcUOP5DYE3/Q+CEzQvnbKrUCflrPTsC2VtjPI/XtTlIH0BGqqeep9JIKYJGZndftvTyVPqVm\n",
-       "IO2Or+2eidkXYqV0z9/e1YxQ/rZKvR5fW/4ssJ8V+cxsWfr8VHpJw+QnciBpOL7l9pe1fGZKqc6k\n",
-       "5ZHOBT4J7FBF814dP67s7fh8d7R5j8fXdt8JTM3mXT+1TqG8HrjR1/+zPHC1md1a86hSSvUhrYbH\n",
-       "txowFrNY/rbomb9tVJy/3bklfhpwJnC4FXZT5Npp2eo6hdLrBXIKJaXGkMbizfca4DQsdviBxOL8\n",
-       "bSOUv61SQ4DPABOBXayw30XqU2W9M7fSp9SOpEOBjwFHYvbVWCk987eNUP62Sq2NR8D+ERhvhS2K\n",
-       "1KfKZQNPqZ1IK+Lxqx3AVpj9OlZOV/72AjwCNpS/rVLvAa7G59s/lRGwfSsbeErtQnojPmXyV2Ac\n",
-       "ZrH8bdFB9/zt2JZ4AR/q/LWfFfa9yLVTdbKBp9QOpK3wue45wMeCW+IFHA+cCOxvxu2hS5caAXwe\n",
-       "WA+fMpkfqU/VywaeUivzJWAfxLfFH0hwFZjEcOAyYANgvBl/DtWX2hDfGHQPsIUV9lykPtUmG3hK\n",
-       "rcr3XlwCvAWYgMUOP5Domb9thCJcVWonPP/7w1ZkhEYjZANPqRVJ6+PN9wFgEhbLz5aYik97nA5c\n",
-       "HJzvHgTMAg4C3m+F3Ru5dqqfbOAptRppCnA5UAIXVhEBezpwGLCTGaH8bZVaFV9lMhSPgH0iUp/q\n",
-       "Kxt4Sq3CI2BPAz4A7ILZD2PlvAbfUTkS2NSMUP62Sr0Dj4D9GnCSFfZipD7VXzbwlFqBtAqev70K\n",
-       "HgEby98Wb8eb7zeBmWaE8rdVan/g08B0K+zaSG3qO9nAU2p20hh8vvsW4AQsdviBxOL8bSOUv90Z\n",
-       "AftJYArwHissw+qaSDbwlJqZtBeeKXI8ZlfFSumZv22E8rdVag3gK8Az+Hz3PyP1qe9lA0+pGUnL\n",
-       "4813F2A7zH4WK6crf/s/eATsP0L1pSYC1+HLFM+0wv4XqU/9Ixt4Ss1Geh3efJ/HI2BD+dkSE/A7\n",
-       "58uB0oyKm2/nlvgj8WWCh1phN0eunfpXTQc6pJTqTC8ffnA38L5I85aQxBHATcAxZhTB5j0Ub/pH\n",
-       "AZOyeTe/vANPqVlI04CzgGmYfT1WyhD8rMrxwCQzfh+qL7Uuvkrlt8BEK+zfkfrUGHW5A5c0SNID\n",
-       "kr5Rj89LaUCRhiDNBY4Dtqiiea8N3AWMACZU0by3A34EXAnsm827ddTrDvyDwEP4BoGUUqWkUXj+\n",
-       "9p/xPJNY/rbYBt8Z+QngU1VEwJ4EzAD2ssK+H7l2arya78AlrYWvEb0UyKPTUqqUtDVwH77aY89I\n",
-       "8+6c756J76zc14zzgs17JTw7fGdgXDbv1lSPO/BPAzOBlerwWSm1P4+A/T/8v5v9MPturJyReBDV\n",
-       "OvipOQtC9aU2wjcGfR+fMnk+Up+aR00NXNJU4Ekze0BSx1K+b1a3l/PMbF4t102pZUkj8Pzt9YHx\n",
-       "mMXyt8Wb8YeNPwQOMCOUv61SuwAXA6dYYZdFalPf6uyhHaGaWk6ll3Q2cADwIjAEvwu/wcwO7PY9\n",
-       "eSp9SgDShnjzvQ84GosdfiCxOH/bCOVvd0bAfhTYD9jNCrs/Up/6XyW9s6YG/oqLbQWcYGbvjw4i\n",
-       "pbYn7Yg/J/oIcEkwArZ7/vYeZoTyt1Xqtfhxa4OAva2wpyL1qTEq6Z31XgeeJ1Cn1J00CCiAQ4Ad\n",
-       "MftRrJyu/O0h+Jb4J0P1pd6Fr3K5Djg1I2DbS93uwJd4gbwDTwOV9Bq8+Q7HV5mEDj+QeCfefD1/\n",
-       "2wg1X5U6CE8SPNoKuy5SmxqvEXfgKSUAvXz4wU3AiVVEwHblbx9rxpdDtaUGd9ZuC3RYYb+K1KfW\n",
-       "kQ08pXqT9gUuAGZgdk2slBWA84DJwNZmPBiqL7Umvr77KXx99zOR+tRasoGnVC/SCviOyKnANpj9\n",
-       "IlbOG/AUwX/iR56F8rdVagvgWuBzwDkZAdv+soGnVA96+fCDhfiRZ7H8bbFZZ73nb8cjYI/Fz8s8\n",
-       "yAr7duTaqXVlnGxKtZImAj8Gvge8P9K8O7fEH43vjDzCjDOCzXsYHkJ1GJ4imM17AMk78JSq5Vvi\n",
-       "jwDOAA7F7JuxcoYCFwLvwiNgHw7Vl3oT/qD0l8BmVth/IvWp9eUdeErVkIbiW+KPASZV0bzXBX4A\n",
-       "DAYmVtG8dwDu6RzDgdm8B6a8A08pSloHv/P9PTARs0WxcrYDvgh8DLggmCK4HHAKcDS+Jf7uyLVT\n",
-       "e8kGnlKEtC0e4fpx4NPBLfE987eNUISrSq0MXAGsjp8S/5dIfWo/2cBTqoTPd5+In5qzD2Z3xMpZ\n",
-       "CfgCsCYeAftoqL7UxviDztuBPa2w/0bqU3vKBp7Sskgj8cN+RwHjMIvlb4vu+dv7mBHK31apPfC1\n",
-       "3SdYYVdEalN7ywae0tJIG+Hz3Xfjhy/Emq/YFc/fPsmMz4dqSy0PnA3sCWxvhf00Up/aXzbwlJZE\n",
-       "2hnfWHMqZpfGShkEnAnsC0w2I5S/rVKr47sqXwLebYX9PVKfBoZs4Cm9kkfAnoEfVjIVs/ti5awG\n",
-       "fAnP3x5rRih/W6XG4imEVwMfscJeitSngSMbeErdSa/Fm+8KwFjMYvnbomf+djwC9lDgXOAIK+yr\n",
-       "kdo08NR6JuYQ/MHMiviGhK+b2Sn1GFhK/U7aBG++NwCnYLHDDyQW528bofxtlVoRTzDcCtjSCvt1\n",
-       "pD4NTDU1cDN7TtLWZvYfScsDd0va3Cw3F6QWIx2Ix7gei1ksf1v0zN82QvnbKrUWHgH7F2C8Ffav\n",
-       "SH0auGqeQjF7eQvvYHzO7+laPzO1pjHSlFEwYyQMWQjPLYDZD5rd0uhxvVL3cT4Hz58H/90ANgK2\n",
-       "xiyWvy268refxNd3h/K3VWor/LzK2cC5VvTxEVmprdTcwCUtB/wUWB+40MweqnlUqeWMkaZMhAvm\n",
-       "wuiu96bB+mMkmqmJ9zbOX8G/d4NDbog375752/EI2OPwnZkHWmG3Rq6dEtQhzMrM/mdm7wTWAraU\n",
-       "1FHzqFLLGQUzujdFgLkwem2Y3qgx9aa3cb4Vhj8Lh1b6GZ0RsNPxO+/DzDgr2LyH4ytMDgAmZPNO\n",
-       "1arbKhQze0bSzcBYYF73r0ma1e3lPDPr8fXU+kb6qemvMgKG9vdYlqbWcUoMw9eGj8FTBP8Qub5K\n",
-       "jcY3Bv0UmGSFPRupT+2r8+a3I1JT6yqU1YAXzeyf8njN7YDyld9nZrNquU5qfgvhud7eXwTN06Ck\n",
-       "YSfABr19qZJxSvTM3zZCEa4q9T58S/4s4MKc707ddd7Yzut6LalYVk2td+BvAK7onAdfDviimX23\n",
-       "xs9MLWgBzJ4G63efnjgcHpkPcxo5rpdJ6wFfXQN+dyw8+xl/ZgNUNk6JyXgY1ZnAZ6qIgP0IMA3Y\n",
-       "2Qr7YTW/hZReSYE0zOouIJmZqU8vkprCGGnK2jB9BAxdBM/OhzlN8QBT2h4/duxsYPYYmFzpOCWW\n",
-       "A04FjsIjYENLZFVqFTz7exVgDyvs8Zp+L2nAqKR3ZgNP7cv/ZXgyfuDv3pjdGStnZbzxrwbsYUYo\n",
-       "f1ul3oZPudyCJwm+EKlPA1slvTO30qf2JK2EH36wBn5K/GOxct6KR8DehjfvUP62Su2NT8scb4Vd\n",
-       "FalNqVLZwFP7kTbG73zvwO+8oxGwi/O3jVD+dmcE7LnALsB2VtjPIvUpRWQDT+1F2g24CDgRs8tj\n",
-       "pXTlb+8BbG9GKH9bpV4HfBl4HhhrheWu5NSnsoGn9uBZPGcCewM7YPaTWDnd87fHmhHK31ap8XgC\n",
-       "4RXArIyATf0hG3hqfb4f4RpAeATs32LlbIrvqvT8bSPUfFVqGnAWMM0K+3qkNqVaZANPrU16Nx7/\n",
-       "ei1wWhURsIcBHwOOMCOUv61SQ/AHlZsBW1hhv43Up1SrbOCpdUkHA58AjsLs+lgpPfO3jVD+tkqN\n",
-       "wv/i+DOeZ7IwUp9SPWQDT61HGgycD7wH2IpgAqbEWnjzfQwYb0Yof1ultsZP7fkU8MncEp8aJRt4\n",
-       "ai3SG/H56ieAcVjs8AOJDrz5ev52bEu8gA8BJwD7WZGxEamxsoGn1iFtiT+s/CzwMcwqj3AVXfnb\n",
-       "JwMHmBGKcFWpEcBleIbKeCvsz5H6lPpCNvDU/CQBM/BMkgMx+06snOHApcCb8SmTP4XqS22Ibwy6\n",
-       "D9jcCus1eTGl/lbzgQ4p9SlpGHAVcDAwoYrmPRr4Eb65ZlIVzXtH4G58tclh2bxTM8k78NS8pPXx\n",
-       "O9+fA5NYfP5qheX0zN+OzXcPAgrgEGBHK+xHkWun1B+ygafmJHXlb38U+CyB2MzOCNjF+dtGKH9b\n",
-       "pVbF7/qH41vin4jUp9RfsoGn5uIRsB8GjgR2xewHsXK652+PNSOUv61S78Dv+m8CTswI2NTMaj1S\n",
-       "bRSel/w6wIBLzGx2PQaWBiBpZbz5ropvif9rrJye+dtGqPmq1H74+vIZVtg1kdqUGqHWO/AXgOPN\n",
-       "7GeSRgA/kXSbmYV2taWENAZvvt8Bdscslr8tFudvG6H8bZVaAd/RORXYxgr7RaQ+pUapqYGb2ePg\n",
-       "/0Q1s0WSfg2sCbFtyWmAk/bE13Z/CLMrY6X0zN82lpm/LY2ZAqNmwMghrPLE/5g2aHWGvzQf2NQK\n",
-       "+0c1v4WUGqFuc+CS1gU2Ae6t12emNucRsOcAuwPvxeyBWDk987eNZeZve/OeeAHMHc1a98Aee8ID\n",
-       "b32aO1442V58KJt3ail1WQfeOX1yPfBBM1tUj89MbU5aHbgVeDs+3x1t3uOB+/E12u+rpHm7UTPg\n",
-       "ktGMvRD22QluvhBu//mqvLTusbHfQEqNV/MduKQV8GCgq8zsa0v4nlndXs4zs3m1Xje1MKkrf/sq\n",
-       "4HQsdviBxOL8bSOWv73C0GFMORTWvB8u+wE8vUHnF0YMDX1OSnUmqQPoCNXUciq9fIvzFcDfzez4\n",
-       "JXxPnkqfFpMOw6dNjsDsxlgp3fO3dzUjlL+tUuvwt2G/4PH3r8RNl8J/R3T76pRvm90yOfJ5KfWl\n",
-       "SnpnrVMok4D9ga0lPdD5a4caPzO1I2lFpIvxJL8tq2jeo4A78fXdE6po3tsC9/IvfYXrRzzcs3kf\n",
-       "/gjMnxP5vJSaQU134BVdIO/Ak9SVv70AOASLHX4g0TN/Ox4BeyKeRLivFXaHP8hce7pPmyx6FubP\n",
-       "MXvwlsiYUuprlfTObOCpb/m83pfw028+HtwS35W//SFgfzNC+dsqNRLPQhkF7G6FLYjUp9RIlfTO\n",
-       "3Eqf+oY/Hzkev/vdH7PbY+WMAD4PrIdHwM4P1ZfaCN8YdDd++MLzkfqUWkE28FR/0nD88IMNgPFY\n",
-       "7PADiQ2BG/EY2C3MCEW4qtTOwCXAqVbYpZHalFpJNvBUX9JovPneD2yO2bOxcnbED184DZhbRQTs\n",
-       "GcABwFQr7L7ItVNqNdnAU/1IU/FpjwK4KDjf3TN/2wjlb6vUa/G59hXwCNgnI/UptaJs4Kl2HgF7\n",
-       "OnAYsBNm98TK6Zm/bYTyt1VqE3y++3rgFCvsxUh9Sq0qG3iqjfQavPmOBDbFA84C5XTlb38dOKmK\n",
-       "CNgDgfOAY6ywr0RqU2p12cBT9aS34833m8BMLHb4gcTi/G0jlL+tUoPxdeHvBba2wh6M1KfUDrKB\n",
-       "p+pI+wCzgeMwuzpWSs/8bSOUv61SawLXAX8Hxllh/4zUp9QusoGnGA8vOxfYCdgWs5/HylkD+Aqw\n",
-       "ENjUjFCEq0ptjkfIXgScZYX9L1KfUjvJBp4qJ70eb57/wSNgY81XTMSb92XAGWZU3Hw7t8Qfgx9W\n",
-       "fIgVllvf04BXlzzwNABIE4Af44FS7480bwlJHIU/qDzKjFnB5j0MT72cBmyWzTsll3fgael8S/wH\n",
-       "gI8Ch2H2jVg5Q4HPAWOBzcx4OFRfaj38QelDePP+d6Q+pXaWd+BpyaQh+K7I6fiuymjzXgfPIhmC\n",
-       "R8BGm/f2+Hb6LwD7Z/NOqae8A0+9k9bGI2D/AEwgeFSexLb4+vBzgfODW+KXA04GjgX2sMLujFw7\n",
-       "pYEiG3h6NWkbvPl+EvhUFRGwM/H87b3NmBe6dKmV8PnuNfBT4h+L1Kc0kNQ8hSLp85KekPTLegwo\n",
-       "NZAkpJl4894Ps/OCzXskvj57N2BcFc17Y+A+4K9ARzbvlJau5gMdJG0BLAKuNLO39fL1PNChFUgj\n",
-       "8SCqdYDdMYvlb4uu/O278J2VofxtldoNX9t9ohV2eaS2XfnJQaNmwMghsPA5WDA7Tw4aOPrlQAcz\n",
-       "u0vSurV+Tmog6c14870HP68ylr8tdgEuBk41I5S/rVLLA2cCewM7WGE/idS3K2/eEy+AuaMXvztt\n",
-       "fWkM2cRTl1yFMtBJO+F3zedjdnikeUsMkjgLzzN5XxXNezXgW/gSw7HZvLsbNaNn8wZ/vfb0xown\n",
-       "NaN+eYgpaVa3l/PMbF5/XDcthTQImAUchG/MuTdWTvf87U3NCOVvq9S78VUu1wKnZQTsK40c0vv7\n",
-       "I4b27zhSf5GfH9sRqemXBm5ms/rjOqlC0qrA1cBQPAI2lr8teuZvG6Hmq1IH42FWR1phN0RqB46F\n",
-       "S/iX0KLQCUepdXTe2M7rei2pWFZNTqEMNNI78S3xD+FhVNHmfSBwK57dPTPSvFVqsEp9Dl/jvVU2\n",
-       "76VZMBumvWLj0+GPwPw5jRlPakb1WIVyDbAV8FrgSeB0s8WrCHIVShOR9gc+DUzH7NpYKd3zt3cx\n",
-       "41eh+lJvxO/YnwAOtML+FakfiPxB5trTfdpk0bMwf04+wBw4KumdNTfwegwi9TGPgD0PmAzsillo\n",
-       "zb5EV/7234ADzXgmVF9qS+Aa4LPAxzICNqVl65dlhKnJSW/AI1z/ic93hw4/kOjK374QOLuKCNjp\n",
-       "wKnAQVbYdyLXTiktXTbwdiZthjfvS4AzscrvfDu3xHflbx9sxrdCl/YI2LnAxsBEK+yPkfqU0rJl\n",
-       "A29HHgF7FL5M8BDMbo6VMwzfFfkOPAL2kVB9qfXxVSo/ByZZYf+J1KeUKpOrUNqNNBS4HDgS2KyK\n",
-       "5r0e8ANgEDCxiuY9Gfghftd/UDbvlPpO3oG3E480+CrwW2AiFsvPltgeuBI4C5hTRQTsh/G/OHaz\n",
-       "wu6OXDulFJcNvF1I2wFfBD4GXBBMEVwOOAWf897DjFD+tkqt3HntVfEt8X+N1KeUqpMNvNX5fPdJ\n",
-       "wAxgL8y+HytnZTx/+/X4lvhQhKtKjcHv+r8D7G6F/TdSn1KqXjbwViathB83tiYwDrNHY+VsDNwI\n",
-       "3A7saUao+arUnvja7g9ZYVdGalNKtcsG3qqkjfDm+31gH8xi+dtid3xt90wzvhCq9QjYc4Ddgfda\n",
-       "YQ9E6lNK9ZENvBVJu+CrPE7G7LJYKcvjDyn3AnYwIxThqlKr4xt7XsDnu/8eqU8p1U828FbiEbBn\n",
-       "AvsCUzD7cayc1fEt7QaMNeNvofpSm+J5JlcBp1thL0XqU0r1lQ28VUir4fnbg4CxmD0VK2cs3nyv\n",
-       "AU4zI9R8VeowfNrkCCvsxkhtSqlvZANvBdK78JUe1wGnYLHDDyQOBc4FjjQjFOGqUisCs4EtgS2t\n",
-       "sN9E6lNKfScbeLOTDgI+CRyN2XWxUlYELsBP+djSjF+H6kuNwu/aFwDjrLCFkfqUUt/KBt6spMF4\n",
-       "dvd2QAdmsfxt0ZW//TgwzoxQ/rZKdeDTLecDH7eij3OHU0ph2cCbkbQm3nyfwiNgY/nbYiu8+c4B\n",
-       "zq0iAvZ44ERgfyvs9si1U0r9p+YwK0k7SPqNpN9LOqkegxrQpC3wI89uBnaJNG8JSRyHL/M72Ixz\n",
-       "gs17ON7Dkgc4AAAPEklEQVT49wPGZ/NOqbnVdAcuX9b2GWBb4DHgx5JuMrPQXGsjjZGmjIIZI2HI\n",
-       "QnhuAcx+0Kz/j63yLfHHAqcBB2H27Vg5w/H87Y2ACWb8KVRfagP8Qen9wOZWWPjwXD8CbNQMP1F9\n",
-       "4XOwYHYeAZZS36l1CmUc8LCZ/QlA0rXAThB7WNYoY6QpE+GCuTC6671psP4YiX5t4tIw4GLgbXiK\n",
-       "4B9i5ayP78p8AJhkRqj5qtRU4PPA6cDF1cx3e/OeeAHMHb343WnrS2PIJp5S36h1CuWN+AqFLo92\n",
-       "vtcSRsGM7s0bYC6MXtuPAesf0pvw/Gzh+d3R5j2ls/4ifNqk4uatUsup1Cx8S/1OVthF1T+sHDWj\n",
-       "Z/MGf712//0sUxpgar0Dr+g/dkmzur2cZ2bzarxuXYyEIb29PwKG9ssApB3wJMAzgc9UEQH7EWAa\n",
-       "sKsZPwhdutRr8B2VI4FNrbDHI/WvNrLXn6WfqJ5SWhZJHfiS34rV2sAfA0Z1ez0Kvwvvwcxm1Xid\n",
-       "PrEQnuvt/UXEpiDCpOXwg36PAnbH7K5YOavg+duvwSNgQ/nbKvV2fL77m8BMK+yFSH3vFvb6s4RF\n",
-       "ffuzTKlNdN7Yzut6LalYVk2tUyj3AxtIWle+bnkv4KYaP7PfLIDZ0+Dh7u8dDo/M9+V3fUNaGW+e\n",
-       "U/AlgtHm/TZ8lcofgfdU0bz3Bb4LFFbYcfVp3gALZsO0h3u+d/gjML/vfpYpDXAK/Ku99w+QJuOb\n",
-       "PQYBl5nZOa/4upmZarpIHxojTVkbpo+AoYvg2fkwp88eYErd87ePx2KHH0jsha/6+T8zvhiqLbUC\n",
-       "8HFgR2BXK+znkfrKxjdmis95jxjqd97z5+QDzJSqU0nvrLmB12MQA4K0B/A5YCZmX4iVsjyeZbIL\n",
-       "sJsZofxtlXo98BXg38B+Vtg/IvUppf5XSe/MnZh9TVoeOBvYE9ges5/GynkdvjHneTwC9ulQfakJ\n",
-       "eAjW5UCZEbAptY9s4H1JWh24FvgfHgEby98W4/HmeyVQRCJgO7fEfwD4KHCYFfaNyLVTSs2v5q30\n",
-       "aQmksfhD3nuBHapo3tOAbwDTzWL53So1BLgUX8++eTbvlNpT3oH3Bakrf/sIzL4aK2UIvgpmErCF\n",
-       "Gb8N1ZdaG7gB+AMwwQpbFKlPKbWOvAOvJ2lFpIuAmcCWVTTvUcCdwCrA+Cqa9zbAffi0zd7ZvFNq\n",
-       "b3kHXi/SWngE7F+A8ZjF8rfF1viRaZ8CPmlW2S5XeHm++wTg/4B9rbDvRa6dUmpN2cDrQerK354N\n",
-       "nBvcEi+88c4E9jPju6FLlxqJB1Gtg0fAzo/Up5RaVzbwWngE7HHAScCBmN0aK2cEcBmwPj5l8udQ\n",
-       "fak347s678HPq1zCdvaUUjvKBl4tqUf+Np2RupWXswG+K/M+YHOz3nNZllhfamfgEuDDVtjcSG1K\n",
-       "qT1kA6+GNBq/830AmITFDj+QeD9+5/0R4JLgfPcgoAQOBN5vhd0buXZKqX1kA4+S3ofvapwFXBic\n",
-       "7x4EFMAhwI5m/Ch06VKr4g86h+ARsE9E6lNK7SUbeKU8ArYrf3tnzH4YK+c1wNXAcHxLfKj5qtQ7\n",
-       "8bv+G4GTrLAXI/UppfaTDbwSUlf+9ir4lvjQ4QcS78Cb703AiWaEIlxVan/g08B0K+zaSG1KqX1l\n",
-       "A18W6W14870FOAGL5WdL7AtcAMww45pQrUfAngdMBt5jhf0yUp9Sam/ZwJdG2hvf1n48ZlfFSlkB\n",
-       "+AQwFdjGjF+E6ku9AY+A/Sc+3/3PSH1Kqf1lA++NR8B25W9vh9nPYuWsgTffhfiRZ6H8bZXarLP+\n",
-       "EuBMK+x/kfqU0sBQdQOXH1AwC18HvakFc66bltQjfxuzWP62mIg338uAM8youPl2bok/Cv+5HmKF\n",
-       "3Ry5dkppYKnlDvyX+B3qxXUaS+NJXfnbVwCzsMoPP+jcEn8EcAZwmBmhCFeVGgpcCLwL2MwK63G+\n",
-       "pB9XNmqGn/6+8DlYMDuPK0tpYKu6gZvZb6BrN3kbkKYBZwHTMPt6rJShwGeBccAkM34fqi+1Lv6g\n",
-       "9LfARCvs3z0/f8wUmHgBzB29+N1p60tjyCae0sCVcbLSEKS5eKbJFlU073WAu4BhwIQqmvd2wI/w\n",
-       "U3f2fWXzdqNm9Gze4K/Xnh65VkqpvSz1DlzSbcAavXzpVLPKT3mRNKvby3lmNq/S2j4ljcIPP/gz\n",
-       "nmeyMFbOtsBV+Gnvn64iAvYkYAawlxX2/SV/98ghvb8/Ymjlo00pNTNJHUBHpGapDdzMtqthPN0/\n",
-       "Z1Y9PqeupB7521VEwM4Ejgf2MeOO0KVLrQR8AVgTGGeFPbr0ioVLCLpaFMpgSSk1r84b23ldryUV\n",
-       "y6qp1xRK60yES0I6AW/e+2P2iWDzHok/6NwNGFdF894IPyfzSWCrZTdvgAWzYdrDPd87/BGYPydy\n",
-       "7ZRSe1Ggd/UslHbBDzBYDXgGeMDMJvfyfWZmzdHgpa787TcBu2Gxww8k3oxnkdyNHzb8fKi+1C74\n",
-       "2u6TrbDLYtceM8XnvEcM9Tvv+XPyAWZK7auS3ll1A6/nIPqFtCG+0uNe4BgsdviBRFf+9qlmXBqq\n",
-       "9QjYM4F9gd2ssPsj9SmlgaeS3jkwdmJKOwKXAqcBc6uIgD0DOACYasZ9oUuXWg2frhkEjLXCnorU\n",
-       "p5TSkrR3A5d65G9jFsvfFq/FI2AH4xGwT4bqS70LX+VyHXBqRsCmlOqpfRu4tCq+xG84viU+lr8t\n",
-       "NsGb7w3AKWaEmq9KHQR8EjjaCrsuUptSSpVozwYudeVvfx04qYoI2APw5YXHmvHlUG2pwXh297ZA\n",
-       "hxX2q0h9SilVqv0auLQfcD4wA7NY/rYYjOdvbw9sbcaDofpSawLXA0/h67ufidSnlFJE+zRwqUf+\n",
-       "Nmax/G3xBnyu+ml8fXcof1ultgCuBT4HnJMRsCmlvtYeDVzqkb+NWSx/W0zCI2QvBs6qIgL2WHyF\n",
-       "y0FW2Lcj104ppWq1fgOXeuRvY5Xf+XZuiT8aOB04xIzQxhiVGoY3/bfhKYJ/iNSnlFItWreBe47t\n",
-       "kUAJHIrZN2PlDAUuAt4JbGbGI6H6Um/CH5Q+iOd3/ydSn1JKtWrNOFlpKPB5/O55syqa93rAD/G/\n",
-       "wKpp3jsA9+B3/Qdk804pNULr3YFL6+B3vr/DI2B7yc9eWjnvxbO3zwFmByNglwNOxY89280Kuzty\n",
-       "7ZRSqqfWauDSdsAX8QOHz68iAvYU/IHjnmbcGbp0qZXxo9ZWx0+J/0ukPqWU6q01GrjPd5+In5qz\n",
-       "N8EDISRWwpvvGvgp8Y+F6kttjKcQ3g7saYX9N1KfUkp9ofkbuDQSuBwYhS8RrCA/u3s5b8Gb7x3A\n",
-       "3lVEwO6Br+0+wQq7IlKbUkp9qbkbuLQR3nzvBPbDLNZ8xW74Se8nmXF5qLbU8sDZwB7A9lbYTyP1\n",
-       "KaXU16pu4JK6dj3+F3gEOMSsjlvH9fLhB6dgFsvf9gjYs4C9gclm/CRUX2p1fFflS3gE7N8j9Sml\n",
-       "1B9qWUZ4K/BWM3sHviLklLqMSBqEdDaeZ/K+Kpr3asC3gbF4BGxFzbvzQFFUaixwP37ww+Rma95d\n",
-       "42xmrTBGyHHWW46z/1XdwM3sNlu86/FeYK2aRyO9FvgWMAGf744dniDejTffnwA7mPG3QHmHSh3a\n",
-       "ef3jrbBTrbCXItfvJx2NHkAFOho9gAp1NHoAFepo9AAq1NHoAVSoo9EDqJd6zYEfCoSS/15FLx9+\n",
-       "cD0+bRLL3xYH42FWR5lxfai21Iq8g6l4dviWVtivI/UppdQIS23gkm7Dl9690qlm9o3O7/kw8F8z\n",
-       "+1LVo5AOxGNcj8HsK7FSBuPTLdsAW5nxUKi+1FrA9SzPcGC8FfavSH1KKTVKTYcaSzoYmAZsY0s4\n",
-       "JFhS356anFJKbarPDjWWtAMwE9hqSc27kgGklFKqTtV34JJ+jx/2+3TnW/eY2dH1GlhKKaWlq2kK\n",
-       "JaWUUuP0S5yspE9I+rWkn0v6qqSV++O6EZL2kPQrSS/JV8Q0FUk7SPqNpN9LOqnR4+mNpM9LekLS\n",
-       "Lxs9lqWRNErSHZ1/3g9KmtHoMfVG0hBJ90r6maSHJJ3T6DEtiaRBkh6Q9I1Gj2VpJP1J0i86xxpa\n",
-       "ptxfJK0i6frOnvmQpAlL+t7+ygPvm00/9fVLYBeIpRT2B0mDgM8AOwAbA/tIektjR9Wry/ExNrsX\n",
-       "gOPN7K34noNjmvHn2flsaWszeyfwdmBrSZs3eFhL8kHgIag8nrlBDOgws03MbFyjB7MEFwC3mNlb\n",
-       "8D/3JS5r7pcG3iebfurMzH5jZr9r9DiWYBzwsJn9ycxewLf579TgMb2Kmd0FhM4jbQQze9zMftb5\n",
-       "/xfh/4Gs2dhR9c7s5cNCBgODWPzMqWlIWguYAlwKtMKihaYdY+fsxBZm9nkAM3txaREljTiR51CI\n",
-       "nT2ZeCOwoNvrRzvfSzWStC6wCX5j0XQkLSfpZ8ATwB1mFtrn0E8+ja9Iq/g82gYy4HZJ90ua1ujB\n",
-       "9GI94ClJl0v6qaS5koYt6Zvr1sAl3Sbpl738en+376l9008fj7FJNfs/S1uSpBH4zt8Pdt6JNx0z\n",
-       "+1/nFMpawJbNluMhaSrwpJk9QBPf2XYzycw2ASbjU2dbNHpAr7A88C7gc2b2LuDfwMlL++a6MLPt\n",
-       "lvb1zk0/U/Adkw2xrDE2scfwPPQuo/C78FQlSSvg0Q1XmdnXGj2eZTGzZyTdjIe0zWvwcLrbDNhR\n",
-       "0hRgCLCSpCvN7MAGj6tXZvbXzv99StKN+PTkXY0dVQ+PAo+a2Y87X1/PUhp4f61C6dr0s9PSNv00\n",
-       "kWa7k7gf2EDSupIGA3sBNzV4TC1LfsLTZcBDZnZ+o8ezJJJWk7RK5/8fCmwHPNDYUfVkZqea2Sgz\n",
-       "Ww+Pb/5eszZvScPkB8QgaTjwXnzxQtMws8eBBZI27HxrW+BXS/r+/poDnwOMAG7rXL7zuX66bsUk\n",
-       "7SJpAb4q4WZJ32r0mLqYB3sdC3wHf9L/ZbPmC9ySdA3wQ2BDSQskHdLoMS3BJGB/fFXHA52/mnH1\n",
-       "zBuA73XOgd8LfMPMvtvgMS1LM0/3vR64q9vP85tmdmuDx9Sb6cDVkn6Or0I5e0nfmBt5UkqpRTVi\n",
-       "FUpKKaU6yAaeUkotKht4Sim1qGzgKaXUorKBp5RSi8oGnlJKLSobeEoptahs4Cml1KL+H2VQxj6V\n",
-       "FLQ4AAAAAElFTkSuQmCC\n"
+       "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xm8lVX1x/HPl0lQcDZHcADNAaeSeRDFiesETuGEmmCW\n",
+       "glrO08NjhZoz5IhjzmapmZZpSqmZWmqZ2q8gDTSn1AzMufX7Y13wYhd49j3n3jPc9X69eOU596yz\n",
+       "t6TLzXr22ltmRgghhNrTodITCCGE0DKRwEMIoUZFAg8hhBoVCTyEEGpUJPAQQqhRkcBDCKFGlZTA\n",
+       "JX1R0tNNfr0raVK5JhdCCGHRVK594JI6AK8A/c1sTlm+NIQQwiKVs4SyHTArkncIIbSNcibwscBN\n",
+       "Zfy+EEIIi1GWEoqkLnj5ZGMze7PkLwwhhLBEncr0PaOA3zeXvCXFYSshhNACZqbF/bxcCXxf4OaW\n",
+       "TqIaSJpsZpMrPY8lqYV51sIcIeZZblU1T68KXACMBHbH7P8++1EVzXMxiix+S07gkpbBH2BOKPW7\n",
+       "QgihZNKqwA+BfwEDMHu3wjNqNSU/xDSz98xsZTObW44JhRBCi0lbAU8CDwGj6zl5Q/lKKPVgRqUn\n",
+       "UNCMSk+ggBmVnkBBMyo9gYJmVHoCBc2o6OjSOOA84DDM7ljMJ2e0zYRaX9kaeRY5gGS1UAMPIdQo\n",
+       "qRNwDrALvup+rsIzKosiuTNW4CGE2iWtDNwKfAT0x+ydCs+oTcVhViGE2iRtgde7nwR2aW/JG2IF\n",
+       "HkKoRdJYYBpwJGa3Vno6lRIJPIRQO6SOwBRgH2A7zP6QFs4gYJYZb7TG9NpalFBCCLVBWgG4B9gK\n",
+       "6NeC5P014E5g/VaYXUVEAg8hVD9pE+AJ4HlgR8z+WTyULhKXA0cBQ814tJVm2eaihBJCqG7SHsDl\n",
+       "wDcxuz4tlNWB24E3gAFm1FXDYazAQwjVSeqAdAZ+psmoFiTv/viq/T5gz3pL3hAr8BBCNZKWA24A\n",
+       "lsP3d7+eFs4hwNnAeDN+0gozrAqxAg8hVBdpQ+Bx4O/4TpPCyVuis8RU4ERgeD0nb4gVeAihmki7\n",
+       "AlcDJ2F2ZVooq+CnEM4D+ptR1wdZQazAQwjVwOvdpwGXAru1IHl/Ce/IfATYrT0kb4gVeAih0qQe\n",
+       "wLXAGni9+x9p4ewPXAh83Yzbyz/B6hUJPIRQOVIfvLnmMWA/zD4sHkon4CxgDLCtGc+2ziSrV8kl\n",
+       "FEnLS7pd0guSnpc0sBwTCyHUOWlH4FHg+/gZ3inJeyXgZ8BmQL/2mLyhPCvwi4B7zWwv+bm8y5Th\n",
+       "O0NoNX2lhp4wqQd0nQsfzIGpfzK7t9LzajckAccBRwN7YfZwWjib4av224GTzfikcGyuLsDHlrXy\n",
+       "RQhtpKQELt+rOczMDgIws0+gfTw8CLWpr9QwCC6aDn3mvzcBeveViCTeBvwO3auA3vh9lXPSwtkb\n",
+       "uASYZLboi9Sbjc21BvBjvOxyZ0pstSq1hLIu8KakayQ9JWm6pKXLMbEQWkNPmNQ0eQNMhz69YGKl\n",
+       "5tRuSOvgJZMPgeEpyVuio8QU/OadHVqQvAfhu1TuBu5Kia1mpZZQOgFfAo40syclXYhvoD+96Yck\n",
+       "TW7ycoaZzShx3BBapAd0be797tCtrefSrkjbAjcBZwJTSbjLUWL5xthueL37zaShc43Hj6A9xDK7\n",
+       "JyW2LUkaAYxIiSk1gb8MvGxmTza+vh1P4Asxs8kljhNCWcyFD5p7fx6839ZzaRe83n0Unhf2w+zB\n",
+       "tHA2xssd9wLHmfFx4Vivd18IbAMMs8z+L2Xstta4sJ0x/7WkbEkxJZVQzOw1YI6kDRrf2g6oiwtF\n",
+       "Q32aA1MnwMym742HWbP9dpdQTlI3fH/3wcDAFiTv0cCvgClmHJ2YvFcFfgmsCQyo9uTdUiXfSi9p\n",
+       "c+BKoAswCzjEzN5t8vO4lT5Ulb5SQy+Y2B26zYP3Z8O0eIBZZlJP/IHhTOBQzP5TPJQOeBn2UPwU\n",
+       "wSeShs7VD/gR3pJ/hmX235T4alEkd5acwMsxiRBCHZGG4TfFXwCcm1jvXha4HlgJ2MuM15KGzjUO\n",
+       "OBc4zDKr6Z0mRXJndGKGEMrD691fBzJgHGb3pYWzAb5DZAawtxkfFY7N1RnfobIzsI1l1i5KuZHA\n",
+       "Qwilk5YCLgYGAkMwm7mEiM+FszNwDXCKGdOTYnOtDNyGb0/sb5m9kxJfy+I0whBCaaQ18FXzCsCg\n",
+       "lOQtIYmTgSuA0S1I3lvg+7sfB3ZpT8kbYgUeQiiFNAjfPnwpMAUr/sBQoju+6u6J7+9OO4Uw11h8\n",
+       "99ARltltKbH1IhJ4CKFltKBB5lDM7k4LpTe+v/sJYGszih9klasj3hC0F7CdZfaHlLHrSSTwEEIa\n",
+       "qQu+w2QkMAxL22MtsT1+3+UZwCVmFN+lkmtF4GagI9DPMnsrZex6EzXwEEJx0qrAA3jZY0BK8m6s\n",
+       "dx8L/ADYx4yLE5P3pviK/Vlgp/aevCFW4CGEoqSt8Oaca4A8sd69NDAd2BAYYMbspKFz7QlcBhxj\n",
+       "md2QElvPIoGHEJZMGgech1+8cEdaKGsDd+DHbAw1K37ujHJ1wEstB+Kr7t+njF3vIoGHEBbNL2k5\n",
+       "B9gFGIGlNchIjMBr1t8DLkwsmSwH3Aj0wOvdb6SM3R5EDTyE0DxpZeA+vOzRPyV5N9a7JwG3AAea\n",
+       "cUFi8t4Qr3e/iO80ieTdjFiBhxD+l7QFXva4FTgFs0+Lh9IVr1dvCQwy48WkoXPtit/ac6JldnVK\n",
+       "bHsTCTyEsDAtaJA5ErNb00JZC3/Q+SIw2Iz3Csd6vfsU4DBgV8vs8ZSx26NI4CEEJ3XEG3P2AbbD\n",
+       "0hpkJIbiZ5JcBHwvsWTSA7gOWA0/z+TVlLHbq0jgIQTQggaZTkA/zP6ZFs7XgG8DB5nxs6TYXH3w\n",
+       "UwgfBfa1zAp3ZbZ3kcBDaO+kvnhb+13ACZh9UjyUpYCpwFBgiBl/TRo61074yvt0y+zylNhQhgQu\n",
+       "6SXg38CnwMdm1r/U7wwhtBFpD+By4BgsrUFGYnX8IKs3gIFmzC0cm0vA8cAkYE/L7JGUsYMrxwrc\n",
+       "gBFm9nYZviuE0BakDkAOjAN2wtIaZCQG4Mn7CuC7ZhTvysy1DH7d2br4fZUvp4wdPlOuEkpcmRZC\n",
+       "rZCWww+TWhavdyftsZY4BDgbGG/GT5Jic62Ll2ueBoZbZh+kxIeFlaORx4AHJP1O0oQyfF8IobVI\n",
+       "G+KXH/wd32lSOHlLdJaYBpwIDG9B8h4JPIZfgn5IJO/SlWMFPsTMXpW0CnC/pD+b2cNNPyBpcpOX\n",
+       "M8xsRhnGDSGk0IIGmZMwuyotlC8APwTmAv3NeLdwrNe7j8Zr3mMti3//myNpBDAiKaact9JLyoB5\n",
+       "ZnZek/fiVvoQKkkLGmS+BuyF2W/Twvky3pxzPXB6Yr27G14n3wQYY5n9PWXs9qxI7iyphCJpaUk9\n",
+       "Gv96GWAH/KzeEEI18H8/fwiMwuvdqcn7AODnwLfMODUxefcCHsEvXxgaybv8Si2hrArcIWn+d91o\n",
+       "Zr8oeVYhhNJJffAHhr8B9sOKN8hIdMIfVI4GtjVLW5gp13D8HJVzgfMtK+Mf9cMCZS2hNDtAlFBC\n",
+       "aHvSjvjNN6djaQ0yEivhyfdTYF8zCm8Rbqx3fwM4HTjQsljQtVSR3BmdmCHUE//j8HHAUcCeWFqD\n",
+       "jMTm+CmEPwRONqP4KYS5lgIuAfoBgy2zWSljh3SRwEOoF/4c6iqgN35fZVKDjMQ+wMXARDNuSYrN\n",
+       "tQb+oHMOnrznpcSHlokLHUKoB9K6eK37A/ym+MLJW6KjxJl4zXv7FiTvQfjlCz8B9onk3XZiBR5C\n",
+       "rZNG4lePTQGmkfBgS2IF4CZgKaCfGWmnEOYaD3wXb8y5NyU2lC4SeAi1yuvdR+Gdkfti9lBaOJvg\n",
+       "u1TuAY4z4+PCsbm6ABfijSfDLLO/pIwdyiMSeAi1SOqGnyK4KTAQs5fSwhkNTAeONeO6pNhcq+IH\n",
+       "Wb0NDLTM/p0SH8onauAh1BqpJ/AwvgAbkpK8JTpI5PgZ3g0tSN79gCeBX+KdlZG8KyhW4CHUEmk4\n",
+       "ftP7+cB5ifXuZfF2+BXxevfrSUPnOghvzJlgmd2ZEhtaRyTwEGqB17u/DmTAgSR2PEtsgN+48xCw\n",
+       "txkfFY7N1RlP3KOArS2z51PGDq0nEngI1U5aCt+fPQAYjKU1yEjsDFyDN+ZcmRSbaxW8K/MD/LLh\n",
+       "f6XEh9YVNfAQqpm0BjADWB4YlJK8JSRxCv6wc/cWJO8t8Xr3b4FdI3lXn1iBh1CtpEF4S/ulwJTE\n",
+       "end34FpgLfz87n8kDZ1rX/xB5xGW2W0psaHtRAIPoRpJ4/HGnEMwuyctlN74/u4ngP3NKH4KYa6O\n",
+       "wJnAXsBIy+yPKWOHthUJPIRqogUNMtvgLfH/lxbODvhOkxy41Iziq/ZcKwI346XVfpbZWyljh7YX\n",
+       "NfAQqoW0Kr6/ek38MKrCybux3n0sXjbZ24xLEpP3pviK/VlgVCTv2hAr8BCqgdQP+BFwNXAGZsVv\n",
+       "vhFL4xcFbwAMMGNO0tC59sLr7EdbZjemxIbKKksCl9QR+B3wspntWo7vDKHdkMbh+6wPw9IaZCTW\n",
+       "xuvdzwLDzHi/cKzXu88ADgB2tMyeShk7VF65VuBHAc8DPcr0fSHUP6kzcA6wM7ANZs+lhbMNfpLg\n",
+       "WcDUxJLJ8sANQHe83v1GytihOpRcA5e0FtCA/xEurk4LoQhpZeA+4ItA/5Tk3VjvnoQ/cDzAjIsS\n",
+       "k/dGwOPA34DtI3nXrnKswC/Ar3BatgzfFUL9k7bAry27BTgVs+LXlomuwGXAFsAgM15MGjrXbvhi\n",
+       "6wTL7JqU2FB9SkrgknYB3jCzpyWNWMznJjd5OcPMZpQybgg1SxoLTAOOwNIaZCTWwq8t+xswxIz3\n",
+       "Csfm6gCcCkzAuyofTxk7tL7GHDoiKaaUW+klTQEOBD4BuuKr8B+Z2bgmn4lb6UPQQg0yYzD7Q1o4\n",
+       "Q4Hb8D3i5ySWTHrgN9R/AdjTMnstZexQGUVyZ0kJ/HODbQ0c+/ldKJHAQ7unBQ0yHYGvYGl7rCUO\n",
+       "xxtzDjLj50mxudbHd6k8Aky0zAqfQhgqq0juLPc+8PL81yCEeiFtite77wROxOyT4qEshZdbhuAl\n",
+       "k5lJQ+caBVwHnGaZXZ4SG2pD2VbgixwgVuChvZL2xB84HoPZDWmhrI439ryGr7znFo7NJeAEYBJ+\n",
+       "S/wjKWOH6lCJFXgIQeqAN8gcCOyE2e/TwhmI3zl5GTDFjOJdmbmWwc/+Xhs/v/vllLFDbYkEHkI5\n",
+       "ScsBN+JNbf2wtD3WEl/FG3MONePupNhc6+Glmt/jN+d8kBIfak8cZhVCuUgb4gdCvQhsl5K8JTpL\n",
+       "fB84HhjeguS9HfAb4Argq5G824dYgYdQDtKuwFX4g8qr00L5An5xw7/xw6jeLRzr9e5j8Ga6sZZF\n",
+       "j0V7Egk8hFJ4vfsU4DBgVyytQUbiy3hzznXA5MR6dzdgOrAxMNAy+3vK2KH2RQIPoaW0oEFmVfw8\n",
+       "k1fTwjkAOB843IwfJ8Xm6oVvT/wzMNQy+09KfKgPUQMPoSWk9fHLft/ETxIsnLwlOkmcD0wGtm1B\n",
+       "8t4aP4zqJuCASN7tV6zAQ0ilzxpksLQGGYmVgVuBj4F+ZrxTONbr3UcAp+GJ+/6UsUP9iQQeQlFa\n",
+       "qEFmDyytQUZic7zscRtwihnFTyHM1RW4BNgKGGSZ/S1l7FCfIoGHUIS0DH7d2Xp4vTupQUbiK8D3\n",
+       "gYlm3JIUm2tN/EHnbGCwZTYvJT7Ur6iBh7Ak0rr4Huv38ZviCydviY4SZ+HNOdu3IHkPxveW34m3\n",
+       "xUfyDgvECjyExZFG4p2VU4BpJBweJLECfgphF7ze/c+koXMdBnwHONgyuzclNrQPkcBDaI7Xu4/G\n",
+       "a977YvZQWjib4KvmnwLHmVH8FMJcXYCpwHB8i+BfUsYO7Uck8BA+T+qGt6T3BQZi9lJaOGMa479l\n",
+       "xg+SYnOthh9k9U+8OeffKfGhfYkaeAhNSb3wyw86AkNSkrdEB4kcuAgY1YLk3R94Ergf2COSd1iS\n",
+       "Uu/E7Ar8ClgKr/PdZWYnlWNiIbQ5v1XqFuA84LzEevdywPXACni9+/WkoXMdDJwDjLfM7kqJDe1X\n",
+       "SQnczD6QtI2Z/UdSJ+ARSUMtcX9sCBWlhRpkDsTsF2nhfBG4C/glsJcZha8tU67OwLnAKPwI2OdT\n",
+       "xg7tW8k1cLMFbbxd8D92vl3qd4ba1Fdq6AmTekDXufDBHJj6J6u+3RNN5/kRfHQB2LqwBjAYs1kp\n",
+       "3yWxC74//GQzrkyKzbUK3tTzPn75wr9S4kMoOYHLT2N7CugNXGoWK4j2qK/UMAgumg595r83AXr3\n",
+       "laimJN7cPP8I8xrgoHsTkrdEB+Bk4HBgdzMeS5mHcm2Jd2XeCJxumRXuygxhvpIfYprZf81sC2At\n",
+       "YLikESXPKtScnjCpaVIEmA59esHESs2pOc3NczPoDkwo+h0SPfDzu3cB+rcgee8H/AI4zjI7JZJ3\n",
+       "aKmybSM0s3cl3YOf1TCj6c8kTW7ycoZZHDpfb3pA1+be7w7d2noui1PqPCV64/Xux4H9zPiw6NjK\n",
+       "1QnvyBwDjLTM/lg0NtS/xsXviJSYUnehrAx8Ymb/ku+d3R7IP/85M5tcyjih+s2FZq/wmuf13eog\n",
+       "dZnoZ5n8jyLzlNgRP/87By41o/gulVwrwYI2+v6W2VtFY0P70LiwnTH/taRsSTGlllBWBx6U9Ay+\n",
+       "IrnbzH5Z4neGGjQHpk6AmU3fGw+zZsO0Ss1pIdJqwIN94JVJsNBJfkuap4QkjgOuBfY245LE5L0Z\n",
+       "fp7JH4BRkbxDuShhq2vLBpDMzNSqg4Sq0Fdq6AUTu0O3efD+bJhWFQ8wpX74aX5XAWf0hZ2KzlNi\n",
+       "6ca49YExZsxJGjrXXsClwNGW2Y2l/Y2E9qRI7owEHuqbdBC+z3oCZnemhbIOvlPkWeBrZsXLQcrV\n",
+       "ETgD2B/vqnwqZewQiuTOOAsl1CctaJBpAEZg9lxaONviV5adCUxNLJksj28PXBroZ5m9mTJ2CEXF\n",
+       "WSih/kirAPcBG+CXLxRO3o317qPx5L2/GRclJu+N8Hr3TGCHSN6hNcUKPNQXLWiQuRk4FSu+x1qi\n",
+       "G3AZsDkwyIwXk4bOtTswHTjeMrs2JTaElogEHuqHtC9+jvYRmN2WFkpP/EHnLGCIGe8Vjs3VAT9H\n",
+       "ZTywi2X2RMrYIbRUJPBQ+/wgtTOBPYGRWFqDjMQw/Kb4C4FzEksmy+J7w1fB692vpYwdQikigYfa\n",
+       "Jq2IN8h0APphxfdYSwg/y2QycJAZP08aOtcG+K07v8bvqyx8CmEI5RAJPNQuaVM8gd4BnIhZ8WvL\n",
+       "xFL4LfGD8JLJzCWELByfqwFv7DnNMrs8JTaEcokEHmqTFjTIHIPZDWmhrAH8CHgVf1g5t3BsLgEn\n",
+       "AkcCYyyzR1PGDqGcIoGH2qIFDTIHADth9vu0cAbid05eBkwx47+FY3N1B64BeuHnmbySMnYI5RYJ\n",
+       "PNQOaXngBqAHXu9+Iy2c8cAU4FAz7k6KzbUeXq75PX5zTrOHd4XQlqKRJ9QGaSP8wLQXge1SkrdE\n",
+       "F4mLgeOA4S1I3tsDj+E3zX81kneoFrECD9VP2g24EjgBs2vSQlkVv3zh3/jlC+8WjvV69zeBY4Gv\n",
+       "WBbn2IfqEgk8VC+/ru9U/LacXTF7PC2crfDmnOuALLHevTTeVbkRMMAym50ydghtIRJ4qE5SD7xB\n",
+       "5gt4vTupQUZiHHAeforgj5Nic62Nb018Hhhq2YKLu0OoKlEDD9VHWh/4LfAGsE1K8pboJHEBcDqw\n",
+       "TQuS94jGsW8ADozkHapZqVeq9eSzVZIBV5jZ1HJMLLRT0ii85HEaltYgI7Ey3hL/MdDPjHcKx3q9\n",
+       "+wi8ZHOAZfZAytghVEJJFzrIr6lazcyekdQd32I12sxeaPKZuNAhLJkk4ARgErAPZo+khbMFXva4\n",
+       "FTjFjOKnEObqClyCX8g92jL72xJCQmh1rX6hg/kfbV9r/Ot5kl4A1gBeWGxgCE1JywBXA+vi53e/\n",
+       "nBbOWPxOy4lmCy4OXszn+zZAz0nQoysrvmaM77g6S3/6R2CQZVb4FMIQKq1sDzElrQNsie/VDaEY\n",
+       "aV28QeZpYDhWfI+1REe8MWcfYHsznllyTN8GGHQRTO9Dz0dh733gic3e4lcfXmv/fS6Sd6gpZXmI\n",
+       "2Vg+uR04yszmleM7QzsgjcQbZK4EDklM3isA9wD98Hr3EpO36zkJpvfhy1fA2DFw93SY8dRK2NoT\n",
+       "0/8GQqisklfg8rsHfwTcYIu4NFbS5CYvZ5hFQ0S75vXuo4HjgbEk/vMgsQlwF3A3cJwZhU8hpOPS\n",
+       "3Rh1OKz9a7jqUXh7/cYfdO+WMocQyk3SCGBEUkyJDzGF7xh4y8yOWcRn4iFm+IzUDW9J3wQYg9nf\n",
+       "08LZA7gc+KYZ1yfF5lqd17s/zzsjl+eOH8CHyzb5acPPze4dlfJ9IbSmIrmz1BLKEPxUuG0kPd34\n",
+       "a6cSvzPUK6kX8Aj+z93QlOQt0UHiDOACYFQLknd/4Ak+/PQebl155sLJe/wsmD0t5ftCqAYlrcAL\n",
+       "DRAr8AAgDce3+J0LnE/CP3gSy+GNNcsBe5vxetLQuQ4BzgYmWGZ3+YPMXhO9bDLvfZg9zexP96Z8\n",
+       "ZwitrUjujAQeWpcWNMicBhyA2f1p4XwRr3c/gJdNCl9bplyd8Xb6HfH93bG9NdSMVt8HHsJiSV2B\n",
+       "i/GdIoOwtAYZiV3w/eEnm3FlUmyuVfBTCN/DD6P6V0p8CLUgzkIJrUNaE5gBLAsMTknejfXuU/Fb\n",
+       "c3ZvQfL+EvAkXm/fLZJ3qFexAg/lJw3GV7/fB85KrHf3wC8LXgM/v/sfSUPn2h+4EPi6ZXZ7SmwI\n",
+       "tSYSeCgvaQLwXeBgzJIeDEr0xuvdvwX2M+PDwrG5OgFnAWOAbS2zZ1PGDqEWRQIP5SF1AS4Ctsa3\n",
+       "CP4lLZwd8ZMtJwOXmVF81Z5rJeAW/ETMfpbZ2yljh1CrogYeSuenUj4IrA4MTEneEpI4Hr/tfS8z\n",
+       "Lk1M3psBTwDPAA2RvEN7EivwUBqpH36UwlXAtzErfm2ZWKYxrjcwwIw5SUPn2hs/BvYoy+ymlNgQ\n",
+       "6kEk8NBy0kHAOcAEzO5KC2Ud/BTCP+A3xb9fODZXR+DbwH7AjpbZUyljh1AvIoGHdH6A2bnAKGAE\n",
+       "Zs+nhbMtcBNwJjA1sWSyfGNsN7ze/WbK2CHUk6iBhzTSKsB9wPr45QuFk3djvftoPAHvZ8ZFicl7\n",
+       "Y7ze/Vdgh0jeob2LFXgoTtoSv7bsRuB0zIpfWya64Y05mwMDzXgpaehco4HpwHGW2bUpsSHUq0jg\n",
+       "oRhpP3yb4Dcw+2FaKD2BHwMzgcFmFL7pXbk64DfMHwrsbJk9kTJ2CPUsEnhYPKkTXqveAxiJ2R/T\n",
+       "whmGn0J4AXBuYslkWeB6YCW83v1aytgh1LtI4GHRpBXxBhnh9e63ioci4HC8MWecGfclDZ1rA3yX\n",
+       "yq+AvS2zwqcQhtBeRAIPzZM2xRPoHcCJmBW+tkxiKfwclIF4yWRW0tC5GvDzUE61zK5IiQ2hPSnH\n",
+       "nZhXAzsDb5jZpqVPKVSctBdwKXA0ZjemhbIGfsH1q8AgMwpfcq1cAk4EjsTP7/5NytghtDclX+gg\n",
+       "aRgwD/hBcwk8LnSoIVJH4Az8mrwxWFqDjMRAPHlfBnw3sd7dHW+n7wXsYZm9kjJ2PfKbg3pOgh5d\n",
+       "Ye4HMGdq3BzUfrTJhQ5m9rCkdUr9nlBh0vL4tWXdgX6YvZEWzqH4w86vmvHTpNhc6+Hlmt8BW1tm\n",
+       "H6TE1yNP3oMugul9Pnt3Qm+pL5HEw3zRyBNA2ghvkPkbsH1K8pboInExcBwwrAXJe3vgMfym+UMj\n",
+       "ec/Xc9LCyRv8da+JlZlPqEZt8hBT0uQmL2eY2Yy2GDcUIO0OXAkcj9k1aaGsil/c8C/8MKp3C8d6\n",
+       "vftbjb/2scx+lTJ2/evRtfn3u3dr23mEtiJpBDAiJaZNEriZTW6LcUICqQN+0fB4YBfMHk8LZyu8\n",
+       "OecaIDej+CmEuZbGuyo3wu+rnJ0ydvswdxF/EplX+NCvUFsaF7Yz5r+WlC0pJkoo7ZG0LJ58d8Dr\n",
+       "3anJexzwM+AoM7LE5L02flelAUMjeS/KnKkwYebC742fBbOnVWY+oRqVYxfKzfgtLCsBbwCnW5M/\n",
+       "isculCqjBQ0yDwMTseINMhKd8ONjdwFGm/Fc0tC5RgA3N37HBZaV+A9fnfMHmb0metlk3vswe1o8\n",
+       "wGw/iuTOkhN4OSYR2ogWNMichtnlaaGsjLfEf4SfJPhO4Vivdx8JnArsb5k9kDJ2CO1Rm2wjDDVA\n",
+       "EnACMBHf3/1oWjhb4B2ZtwKnmFH8FMJcXfGmoC8Dgyyzv6WMHUJYtEjg9U5aBn/QuDZ+nklSg4zE\n",
+       "WGAacKQZtybF5loLr7W/iCfv91LiQwiLFw8x65m0Hr7H+j1g65TkLdFR4my8OWe7FiTvIcDj+H2Z\n",
+       "YyN5h1B+sQKvV9J2eGfld4CLSXjYIbEC/rCxM9DPjH8mDZ3ra/idlQdZZj9LiQ0hFBcJvN54vfub\n",
+       "wLHAWBKbpiT64rtUfgIcb0bxUwhzdcHLLcOAIZbZX1PGDiGkiQReT7RQg8xAzP6eFs4eeEv7N824\n",
+       "Pik21+r4QVZv4M05c1PiQwjpogZeL7SgQQZgaErylugg8W3gQmBUC5L3APwslfuAPSN5h9A2YgVe\n",
+       "D7SgQeZc4PzEevdyeK18Obze/XrS0LkOAb6HH0T1k5TYEEJpIoHXMq93H4GfaXIAZvenhbMhXu9+\n",
+       "ADjGjI8Lx+bqDJyPt+MPt8xeSBk7hFC6SOC1SuoKXAJsBQzC0hpkJHYFrgJOMuOqpNhcX8BPIZyH\n",
+       "17v/lRIfQiiPqIHXImlN/LLfHsDglOTdWO8+De+O3K0FyfvLwJP4WSq7RfIOoXJiBV5rpCHAbfil\n",
+       "wWcl1rt74GehrI7Xu19NGjrX/viDzq9bZrenxIYQyi8SeC2RDsMbcw7GLOlUOok+eL37Mfwwqg8L\n",
+       "x+bqBJwNjAa2tcyeTRk7hNA6IoHXAi1okBmObxH8S1o4OwHXARlweeJlwysBt+Dnd/ezzN5OGTuE\n",
+       "0HqiBl58SrLdAAAPrklEQVTtpNWBh4DVgAEpyVtCEicAVwN7mXFZYvLeDK93Pw00RPIOobrECrya\n",
+       "Sf3xw6CuAs7ArPjNN2IZPHGvh99XOSdp6Fx747tcJllmN6fEhhDaRskJXNJO+IOtjsCVZnZ2ybMK\n",
+       "oAUNMhMwuzMtlHXxevczwHAzCt+jqFwd8YOo9gN2sMyeThk7hNB2SkrgkjriuyG2A14BnpT0E7Pa\n",
+       "aeroKzX0hEk9oOtc+GAOTP1T4gPCspI6A+cBO+FHwD6fFs5I4Eb8GNipiSWT5YGbgG54vfvNtLH7\n",
+       "NkDPSX6j+twPYM7UuAIshNZT6gq8PzDTzF4CkHQLsDtQEwm8r9QwCC6aDn3mvzcBeveVqEgSl1bB\n",
+       "G2T+g1++UHiPtYSAo4AT8V0mDyYNnWtjfNV+L3CcZVa4K9PH79sAgy6C6X0+e3dCb6kvkcRDaB2l\n",
+       "PsRcExaqrb7c+F5N6AmTmiZvgOnQp5dfPda2pC/hDwwfBXZNTN7d8F0mBwMDW5C8R+ONQVMss6NT\n",
+       "k7frOWnh5A3+ulfb/16G0E6UugIv9MdzSZObvJxhiWdUt5Ye0LW597t7CaHtaEGDzDcw+2FaKD3x\n",
+       "+yr/Cgw24z+FY3N1wLcWfhXY2TJ7ImXshfVo9vfSb1QPISyJ/FC6ESkxpSbwV4CeTV73xFfhCzGz\n",
+       "ySWO0yrmwgfNvT+P4g/9SiJ1As4CxgAjMftjWjjD8T3aFwDnJta7lwWuB1bC692vpYz9v+Y2+3sJ\n",
+       "89rm9zKEGte4sJ0x/7WkbEkxpZZQfgesL2kdebPJV/CbXGrCHJg6AWY2fW88zJrtTTOtS1oJ+Bmw\n",
+       "OV7vLpy8G/d3H4HXyw8x45zE5L0Bfl/lP/DOyhKTN8CcqTBh5sLvjZ8Fs1v/9zKEdkoJR2k0/wXS\n",
+       "KD7bRniVmZ35uZ+bmamkQVpRX6mhF0zsDt3mwfuzYVqrP8CUNsPLHncAJ2JW/NoysRS+P3sAMNqM\n",
+       "mUsIWTg+1874LfWnWmZXpMQueW59G7zm3b2br7xnT4sHmCG0TJHcWXICL8ck2hVpL/wkwKMxuzEt\n",
+       "lDWAH+Olq4PNKHzzjXIJOAk/P3xvy+w3KWOHENpWkdwZnZhtxffMnwHsD+yI2VNp4QzC75y8FJhi\n",
+       "RvGuzFzd8VV3T7ze/Y+UsUMI1SkSeFuQlseba5YG+mGpDTKMB6YAXzXjp0mxuXrj+7ufALa2zAqf\n",
+       "QhhCqG5xmFVrkzbCk+dMYIeU5C3RReIS4FhgWAuS9/bAb4DLgPGRvEOoL7ECb03S7sB04HjMrk0L\n",
+       "ZVW8ZPIOfhjVu4Vjvd79rcZf+1hmv0oZO4RQGyKBtwapA37R8HhgFyytQUaiH34K4TVAnljvXhr/\n",
+       "j8aG+H2Vs1PGDiHUjkjg5SYtC/wAWAWvdyftsZYYhx9mdZgZdyTF5lob35r4HDDUMosmmhDqWNTA\n",
+       "y0naAPgt8BqwTUrylugscSG+ch/RguQ9onHs64FxkbxDqH+xAi8XqQG/MPg0zC5PC2Vl/KLiD4H+\n",
+       "ZrxTONbr3ROBk4EDLLMHUsYOIdSuSOClkoQf4XokMAazR9PC2QIve9wKnGLGp4Vjc3XFd5hsCQyy\n",
+       "zF5MGTuEUNsigZdCCxpkeuHnmbySFs5Y/NyVI824NSk211p4V+aLwGDL7L2U+BBC7YsaeEtJ6+F7\n",
+       "rOfiN+cUTt4SHSXOxptztmtB8h6K7y3/ETA2kncI7VOswFtC2h64AW+Nv4SEA2UkVgRuxg//6mfG\n",
+       "W0lD5zq8cdxxltnPU2JDCPUlEngKr3d/E++M3AdLa5CR6Iu3td8FnGBG8VMIcy0FTAWGAkMss7+m\n",
+       "jB1CqD+RwIvSggaZjYABWFqDjMSe+APHY8y4ISk21+p4V+YbwEDLrPAphCGE+hU18CKktYFH8Cvk\n",
+       "hqYkb4kOEt8Bzgd2akHyHoDXu38O7BnJO4QwX6zAl8TvqbsZOAe4ILHevRx+CmEPvN79RtLQuQ4B\n",
+       "zsYPoqqZm45CCG2jxStwSXtLek7Sp/Ib1euLJKQj8TsnD8Ts/MTkvSG+cn4J32lSOHkrV2flmobv\n",
+       "Lx8eyTuE0JxSVuDP4pfxJnUd1gSpK35t2VbAYMz+lhbOrsBVwElmXJUUm+sL+F2Xc4H+ltm7/p19\n",
+       "G6DnJL/9fe4HMGdqXFcWQvvW4gRuZn+G+Rsz6oi0Jt4g83dgEFZ8j7VEB+AU4GvAbmb8NmnoXF9u\n",
+       "HPt64HTL7L/+vX0bYNBFML3PZ5+e0FvqSyTxENqvqIE3JQ3BzySZCnwvsWTSA7gOWA2vd7+aNHSu\n",
+       "/fHLob9umd2+8E97Tlo4eYO/bpgIRAIPoZ1abAKXdD+ekD7vZDO7u+ggkiY3eTnDzGYUjW0z0mHA\n",
+       "t4GDMftZWih98L3djwL7mlH45hvl6oQ/qBwNbGuZPfu/n+rRtfno7t1S5hlCqF7yDRMjUmIWm8DN\n",
+       "bPsS5tP0eyaX43tahdQFX3EPx7cIJjXISOyEr7xPN0t7HqBcK+GHWP0Xv2z47eY/OfeD5t+fF0fG\n",
+       "hlAnGhe2M+a/lpQtKaZc+8BrsxAurQY8CKwKDExJ3hKSOAG4GtizBcl7c+BJ4CmgYdHJG2DOVJgw\n",
+       "c+H3xs+C2dNSxgwh1BcllHkXDpTG4CvXlYF3gafNbFQznzMzq74EL/XHD4OaDnwHs+LXloll8MS9\n",
+       "HjDGjJeThs61D3AxMNEyu6XYmH0boNdEL5vMex9mT4sHmCHUryK5s8UJvJyTaHP6rEEGS9tjLbEu\n",
+       "fp7J08DhZiyivNFMbK6OwHeAscAYy+yZlLFDCO1HkdzZvnahSJ3x+yZ3xI+AfSEtnJF4Z+UUYJoZ\n",
+       "xXep5FoBuAlYCq93/zNl7BBC+Lz2cxaKtApwP9AbP4yqcPJurHcfjSfvfc2Ympi8N8G7Mv8P2DGS\n",
+       "dwihHNrHCtxb/X+Mn+GdYVb82jLRDe823RQYaMZLSUPnGo3X2Y+1zK5LiQ0hhMWp/wSuzxpksM83\n",
+       "yCwplJ74fZV/AYaY8Z/Csbk6ABlwCL7L5MmUsUMIYUnqN4FLnYCz8PNatsWaa5BZXDjD8YOszgPO\n",
+       "TyyZLIu3w6+I17tfTxk7hBCKqM8ELq2EJ18D+mGL22P9+VAEfB1fPR9oxi+Shs61Ad6V+RCwt2X2\n",
+       "UUp8CCEUVX8JXNoM3+Z3O3AyZsWvLRNL4fuzBwCDzZiVNHSunfFb6k+xzKanxIYQQqr6SuDS3vgx\n",
+       "sJMwuzktlDXwxp5XgEFmzCscm0vAycA3gNGW2W9Sxg4hhJaojwQudcQPotoP2AGzp9PCGYSfwX0J\n",
+       "cGZivbs7cC2wFl7v/kfK2CGE0FK1n8Cl5fEGmW54vfvNtHDG4405h5hxT1Jsrt54ueYJYH/LrPAp\n",
+       "hCGEUKrabuSRNsaT51/wlXfh5C3RReIS4FvAsBYk7x2A3wCX4ndWRvIOIbSp2l2Ba0GDzHGYXZsW\n",
+       "yqr4Q863gQFm/LtwrNe7vwV8E99l8uuUsUMIoVxqL4FLHYDTgUOBnTF7Ii2cfvjDyquBM8wofgph\n",
+       "rqWBK4ENgAGW2ZyUsUMIoZxqK4FrQYPMSni9+7W0cMYB5wKHmXFnUmyutfF695+AYZZZXKYQQqio\n",
+       "2qmBSxsAjwP/wDsrCydvic4SFwKnAdu0IHlvA/wWv3lnXCTvEEI1aPEKXNI5wC7AR8As4BAze7dc\n",
+       "E/vcYPMbZE7F7Iq0UFbGLyr+EOhvxjuFY73ePRHf472/ZfbLlLFDCKE1lbIC/wWwiZltju8COak8\n",
+       "U2pCEtLJwBXA6BYk7y3wa8seB3ZZXPJuvFD0s9e5uuL/0TgUGFQtyfvz86xGtTBHiHmWW8yz7bU4\n",
+       "gZvZ/fbZNWSP440s5SN1x1fOuwP9sbTuRomx+PnfJ5hxkhlLOkJ2xILYXGsBv8b3lg+2zF5MGbuV\n",
+       "jaj0BAoYUekJFDSi0hMoaESlJ1DQiEpPoKARlZ5AuZSrBv5VoHz3M0q9gceAufjNOa8UD6WjxNl4\n",
+       "c852ZtyWNHSuofje8h8BYy2z91LiQwihrSy2Bi7pfmC1Zn50spnd3fiZU4CPzOymssxI2h6/eOEM\n",
+       "4BISLu2UWBG4GegI9DPjraShcx3eOO44y+znKbEhhNDWSrrUWNLBwARgpJk1e7mvpNa9NTmEEOpU\n",
+       "q11qLGkn4Dhg60Ul7yITCCGE0DItXoFL+ivQBW9HB3jMzL5RromFEEJYvJJKKCGEECqnTToxJZ0j\n",
+       "6QVJf5D0Y0nLtcW4KSTtLek5SZ/Kb7GvKpJ2kvRnSX+VdEKl59McSVdLel1S0v2jbU1ST0kPNf7/\n",
+       "/SdJkyo9p+ZI6irpcUnPSHpe0pmVntOiSOoo6WlJd1d6Losj6SVJf2yca9I5Sm1F0vKSbm/Mmc9L\n",
+       "Grioz7ZVK33rN/2U7ln8AuSqO11QfmHF94GdgI2BfSVtVNlZNesafI7V7mPgGDPbBBgIHFGNv5+N\n",
+       "z5a2MbMtgM2AbSQNrfC0FuUo4HkofhlKhRgwwsy2NLP+lZ7MIlwE3GtmG+H/v7+wqA+2SQJv9aaf\n",
+       "MjCzP5vZXyo9j0XoD8w0s5fM7GP8wubdKzyn/2FmD0PxowoqxcxeM7NnGv96Hv4vyBqVnVXzzOw/\n",
+       "jX/ZBd8eW/iC7rYiaS2gAT+psxY2LVTtHBurE8PM7GoAM/tkcUeUVOIwq/I2/bQPawJNj659ufG9\n",
+       "UCJJ6wBb4guLqiOpg6RngNeBh8zs+UrPqRkX4DvSCh/NXEEGPCDpd5ImVHoyzVgXeFPSNZKekjRd\n",
+       "0tKL+nDZErik+yU928yvXZt8prxNP60wxypV7X8srUny4xpuB45qXIlXHTP7b2MJZS1geLWd4yFp\n",
+       "F+AN83toq3Zl28QQM9sSGIWXzoZVekKf0wn4EnCJmX0JeA84cXEfLgsz235xP29s+mkARpZrzFRL\n",
+       "mmMVewXo2eR1T3wVHlpIUmf8uIQbzCzpeOFKMLN3Jd0DbAXMqPB0mhoM7CapAegKLCvpB2Y2rsLz\n",
+       "apaZvdr4v29KugMvTz5c2Vkt5GXgZTN7svH17SwmgbfVLpT5TT+7L67pp4pU20rid8D6ktaR1AX4\n",
+       "CvCTCs+pZkkScBXwvJldWOn5LIqkleWXdiOpG7A98HRlZ7UwMzvZzHqa2brAWODBak3ekpaW1KPx\n",
+       "r5cBdsA3L1QN83sO5sjvPwDYDnhuUZ9vqxr4NKA7cH/j9p1L2mjcwiSNkTQH35Vwj6SfVXpO85nZ\n",
+       "J8CRwH34k/5bzWyRT6YrRdLN+EXPG0iaI+mQSs9pEYYAB+C7Op5u/FWNu2dWBx5srIE/DtxtVh3H\n",
+       "Gi9GNZf7VgUebvL7+VMz+0WF59ScicCNkv6A70KZsqgPRiNPCCHUqNq5Ui2EEMJCIoGHEEKNigQe\n",
+       "Qgg1KhJ4CCHUqEjgIYRQoyKBhxBCjYoEHkIINSoSeAgh1Kj/B3rn1tXOP7uAAAAAAElFTkSuQmCC\n"
       ],
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x106476a90>"
+       "<matplotlib.figure.Figure at 0x106d19790>"
       ]
      },
      "metadata": {},
@@ -474,7 +477,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 24,
+   "execution_count": 59,
    "metadata": {
     "collapsed": false
    },
@@ -503,7 +506,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
+   "execution_count": 60,
    "metadata": {
     "collapsed": false
    },
@@ -514,7 +517,7 @@
        "[-3, 3, -3, 3]"
       ]
      },
-     "execution_count": 25,
+     "execution_count": 60,
      "metadata": {},
      "output_type": "execute_result"
     },
@@ -522,96 +525,93 @@
      "data": {
       "image/png": [
        "iVBORw0KGgoAAAANSUhEUgAAAXAAAAEACAYAAACqOy3+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
-       "AAALEgAACxIB0t1+/AAAEwtJREFUeJzt3W2MXOV5xvHrwgTZyFZSwgcHWAvJQY3oUkhKQ5FSWClx\n",
-       "7Z22IkQKEVKrpsj+0EheFDVtAlbBbYSIiqqC6ZcIAaVEJKpIhIKy3tZCrCgSpiTBCcamsS1FdiCA\n",
-       "Uhpky1gJcPfDzIZZe972vMw5z5n/T0Ls2ZmdeYZlrnn2ft4cEQIApOesqhsAAMiGAAeARBHgAJAo\n",
-       "AhwAEkWAA0CiCHAASFSuALe92vaztvfZPmD7zqIaBgAYzHnngds+NyJO2j5b0tOSvhQRTxfSOgBA\n",
-       "X7lLKBFxsvPlOZJWSXoj72MCAIbLHeC2z7K9T9Jrkp6MiAP5mwUAGKaIHvi7EXGFpIskXWN7Jner\n",
-       "AABDnV3UA0XEm7a/J+lKSYtL37fNZisAkEFEeNDtuQLc9vmS3o6IX9peI2mTpL9faSNSZntnROys\n",
-       "uh1lafLra/Jrk3h9qRul85u3B/4hSQ/ZPkvtcszDEfFEzscEAIwgV4BHxAuSPlZQWwAAK8BKzPwW\n",
-       "q25AyRarbkCJFqtuQMkWq25AyRarbkDVci/kGfoEdjS5Bg4AZRglO+mBA0CiCHAASBQBDgCJIsAB\n",
-       "IFEEOAAkigAHgEQR4ACQKAIcABJFgANAoghwAEgUAQ4AiSLAASBRBDgAJIoAB4BEEeAAkCgCHAAS\n",
-       "RYADQKIIcABIFAEOAInKdSo9kDp7uiVNzUnrVkvHT0nHdkXsn6+6XcAoCHBMrHZ4X32PdN+H3/vu\n",
-       "to32tAhxpIBT6TGx7NkFaffmM29pLUTMz5b//PT+0d8o2UkPHBNs3ere31+7puxnpvePIjCIiQl2\n",
-       "/FTv7594q/znnppbHt5S+3rD9vKfG01BgGOCHdslbTv83vVTkj59Ulp9oT270O4ll6Vf73/NVeU+\n",
-       "L5qEEgomVsT+eXtaUmu79PaF0kUbpcfOlXRZ+58ySxr9ev+X/pZ03j2UUjCKXD1w21O2n7T9ou39\n",
-       "tueKahgwDhH759sDlqtekR44d/mtZZY0Tu/9S9KtkjaV/Lxokrw98F9L+mJE7LO9VtIPbO+JiIMF\n",
-       "tA0YqNhZHOMd0Hyv9/8nD0tXnie9I2mLpGtKfV40S64Aj4hXJb3a+fqE7YOSLpBEgKNUxc/iGP+A\n",
-       "ZjvEZ5+TdvaYyjiOgVSkrrBBTNsXS/qopGeLekygv6JncfQqaWw9Ih29N9vj1f150QSFDGJ2yieP\n",
-       "Sro5Ik4U8ZjAYMWWPJYPaK5d0+4BH7237IHEqp4XzZA7wG2/T9K3JX0jIh7rc5+dXZeLEbGY93kx\n",
-       "6YoveXRCc+zBWdXzol5sz0iaWdHP5FlKb9uSHpL0vxHxxT73YSk9Cte7Br71iLR3jt4rmmCU7Mwb\n",
-       "4J9Qe/XDjyUtPdAtEbGwkkYAWbRDfAOlBzRS6QFeVCMAAMuNkp0spQeARLGUHkP1WjDTvoWtUIEq\n",
-       "EeAYqPdg4Wcukz5g6YEPvfc9tkIFxo0SCobotWDm0guWh7fE/h3A+BHgGKLXgpl+f7ixfwcwTgQ4\n",
-       "hui1YObtPvdl/w5gnAhwDNFrr44Xfy7d9PPl32P/DmDcmAeOoXotmGnfwiKaJuKw5XpgIQ+AFemz\n",
-       "Te9h6ZmbCfHxYiEPgBXisOWUEOAAuoz3ZCLkQ4AD6DL+k4mQHQEOoAsnBKWEQUwAy7BNbz0wCwUA\n",
-       "EsUsFABoMAIcABJFgANAoghwAEgUAQ4AiSLAASBRHKkGZDBtt6akuXXS6uPSqWPSrv0RzJXGWBHg\n",
-       "wApN262rpXvuk36z6dM2aeO0rdNDnKBHmQhwYIWmpLnu8Jak+6QPt6Ttkn4TzisJeiALauDACq2T\n",
-       "eu7Yt1ZatmNfv6Df0A56IDd64DXEiSj1dlzquWPfCemt7pLJKul3n5J0zWn3Oz3ogawI8JrpcyLK\n",
-       "RntahHg9HJN2bZM2dveut0pHjkp7Ty+Z7Oj8uzvET0hszYpCsJlVzdizC9LuzWfe0lqImJ8df4vQ\n",
-       "y7Td2iBtXyutOSG9dVS6d0qa2y2d8bv7O0lf7Xy9VTqyV5qjBo5hRslOeuC1w4koKegE8LIQvsH+\n",
-       "2173PSC9cYP0wlLQE94oSu4At/2ApD+W9HpEXJa/SZOOE1HGoYzpff1q429J/z0fwV9PKFwRs1Ae\n",
-       "lLSlgMeBJE5EKd/S9L7d0uZ/l67dLW2+Wrpn2m7ledxObXzZ765TG+d3h1IUUgO3fbGkx3v1wKmB\n",
-       "rxwnopRr1l7oVatuSQt5e8q9auOUTJAFNfBEdcKaN31JRp3HnUWv2vhKsHITKzGWALe9s+tyMSIW\n",
-       "x/G8QC+D5nGPuy3dWLk52WzPSJpZ0c9QQsGk6RWUdZjeV2ZpB+mhhAL0sD9iftpWq2a16jJLO6li\n",
-       "VfJgRUwj/KakayV90PYxSbdFxIO5WwaUKG+tugx1Le1UhVXJw+UO8Ii4sYiGAJNuwBL9ZdMQBw10\n",
-       "NmsQdGpueXhL7evWsl0fJxklFKAmRintDBrolKRmDYKyKnkYAhyokWGlnUF7kYfkUfYpTwerkodh\n",
-       "P3AgIYMGOps3CMqq5GHogQMJGTTQGVLPKWepDoJG7J+3p9WuebMquRcCHEjIsIHOUQZBU8Kq5MHY\n",
-       "DxxIzKD9VtiLpTlGyU4CHABqaJTsZBATABJFgANAoghwAEgUAQ4AiSLAASBRBDgAJIoAB4BEEeAA\n",
-       "kCiW0gMN1qz9wXE6AhxoKA5Jbj5KKEBD9ds7fEN7f3A0AAEONFTz9gfH6Sih5MCJ2aizST4keVLe\n",
-       "mwR4RpyYjbob9ZDkppmk9ybbyWZkzy5IuzefeUtrIWJ+dvwtAs40ifuDN+W9OUp20gPPjBOzUX/D\n",
-       "Dklupsl5bzKImRknZgP1NDnvTQI8M07MBuppct6b1MBzaA+WbODEbKBmlr83f7m2PSFn/YmUZqRw\n",
-       "JiZKxTJt1F2fGSmHpWdurnuIM4iJ0rBMG2mYmlse3lL7urVdDRjczV0Dt73F9ku2D9n+chGNQv2x\n",
-       "TBtpaPaMlFw9cNurJP2LpE9JelnSc7a/GxEHi2gcqtevTMIybaSh2TNS8pZQPi7pcET8VJJsf0vS\n",
-       "dZII8AYYVCaZmuBl2kjJsV3Sto3LyyjNmZGSN8AvlHSs6/pnkq7K+ZioiX5lkpa0/eiELtNGWiL2\n",
-       "z9vTate8mzdbLG+AjzSFxfbOrsvFiFjM+bwYg0Flkv0R89O2WhO2TBvp6YR17f+/tD0jaWYlP5M3\n",
-       "wF+WNNV1PaV2L3yZiNiZ83lqqek7ng3bzW4yl2kjdXV933Y6totL17ZvH/YzeQP8+5IusX2xpFck\n",
-       "fU7SjTkfMwmTsOPZpO5mh+Zq2vs290Ie27OS7pa0StL9EXHnabc3ciFPU3Y8GybLbnYs8EFdpfS+\n",
-       "HctCnojYLWl33sdJT7Pnly5ZaZmEBT6ot2a9b9nMKrNmzy/NigU+qLdmvW8J8MwmZ8ezlWCBD+qt\n",
-       "We9b9kLJqOnzS7Oa5HMYUX9Ne9+yGyEK1asGvlU6sleaowYOjI7tZFGJSTyHESgaAQ4AiWI/cFSK\n",
-       "+eBAuQhwlIL54NXhg3NyEOAoxaCdDMX+KaWYtlvnSf9wlXTp/V3TNvngbC7mgaMUzAcfr6W/eK6R\n",
-       "fu/+0/4bs5CquQhwlIL54OO19BdPvz+p+eBsJgIcpejsZLhsxRs7GZZn6S+et/vczgdnM1EDRyk4\n",
-       "8GG8lv7i+SNJOyTd0XUbH5zNxTxwoAG6Z/08JWmPpEPSqTekF1+RbmvKB2ddD2MoA/PAgQkxCX/x\n",
-       "NO0whiLQAweQhJQOYygCPXDUFotNsHLNOoyhCAQ4xo5VmsimWYcxFIFphBWyp1v27IJ9w2L739Ot\n",
-       "qts0Dpzag2yadRhDEeiBV2SSB2RYpYksmnYYQxEI8MpMzS0Pb6l93Wr8XiFFrNKkhj6ZOmHN77mD\n",
-       "AK/M5A7IdFZpbjz91J5RF5ukXkPnwwdFIcArM7kDMnnnLKe802HqHz6oFwK8Msd2Sds2Li+jTM6A\n",
-       "TCesMgVWyjX0lD98UD8EeEUYkMkuaw29DqWLlD98UD8EeIUYkMkmSw29LqULttlFkQhwJCdLDb0u\n",
-       "pYu8A7hANwIcSVppDb0upYtJ2HQK45M5wG1/VtJOSR+R9PsR8cOiGgVkMajGXafSRZ4BXKBbnh74\n",
-       "C5Kul/T1gtoCZDasxj2gdLF31l5gTjZSlDnAI+IlSbLZKRbVG1bj7lO62Hu19GdVD2wCWVEDRyOM\n",
-       "UuM+vXQxay/UYWATyGpggNveI2l9j5tujYjHR30S2zu7LhcjYnHUnwVGkaXGXZeBTUCSbM9ImlnJ\n",
-       "zwwM8IjYlKM93Y+zs4jHAfrJMj2vTgObQKdju7h0bfv2YT9TVAmFQjgqlWV6HnOykbrMZ2Lavl7S\n",
-       "LknnS3pT0vMRcca5dJyJiTqbtlsbmJONGholOznUGABqaJTs5Eg1AEgUAQ4AiSLAASBRBDgAJIoA\n",
-       "B4BEEeAAkCgCHAASRYADQKIIcABIFAEOAIliP3AAA9nTLWlqTlq3Wjp+Sjq2K2I/+8XUAAEOoK92\n",
-       "eF99j3Rf18EX2zba0yLEq0cJBcAAU3PLw1tqX2/YXk170I0ABzDAup6nFklrObWoBghwAAMc73lq\n",
-       "kXSCU4tqgABHrdnTLXt2wb5hsf3v6VbVbZosx3ZJ2w4v/97WI9JRTi2qAQYxUVsMoI2mzFkiEfvn\n",
-       "7WlJre3tssmJt6Sj9/Lfvx44kQe1Zc8uSLs3n3lLayFi/ozj+yZRnw+5w9IzNxOyaeNEHiSOAbTh\n",
-       "mCUyyQhw1BgDaMPxITfJCHDUGANow/EhN8kYxERtMYA2imO7pG0bl5dR+JCbFAxiAolrD2Ru4EOu\n",
-       "YUbJTgIcAGqIWSgA0GAEOAAkigAHgEQR4ACQqMwBbvsu2wdt/8j2d2y/v8iGAQAGy9MD/09JvxMR\n",
-       "l0v6iaRbimkSAGAUmQM8IvZExLudy2clXVRMkwAAoyiqBn6TJBYOAMAYDVxKb3uPpPU9bro1Ih7v\n",
-       "3GeHpF9FxCMltA8A0MfAAI+ITYNut/15SS1Jnxxyv51dl4sRsTha8wBgMtiekTSzop/JupTe9hZJ\n",
-       "/yTp2oj4xYD7sZQeAFao1L1QbB+SdI6kNzrfeiYivpClEQCA5djMCgASxWZWANBgBDgAJIoAB4BE\n",
-       "EeAAkCgCHAASRYADQKIIcABIFAEOAIkiwAEgUQQ4ACSKAAeARBHgAJAoAhwAEkWAA0CiCHAASBQB\n",
-       "DgCJIsABIFEEOAAkigAHgEQR4ACQKAIcABJFgANAoghwAEgUAQ4AiSLAASBRBDgAJIoAB4BEEeAA\n",
-       "kKjMAW77q7Z/ZHuf7SdsTxXZMADAYHl64P8YEZdHxBWSHpN0e0FtSortmarbUKYmv74mvzaJ1zcJ\n",
-       "Mgd4RBzvulwr6Rf5m5OkmaobULKZqhtQopmqG1CymaobULKZqhtQtbPz/LDtOyT9uaSTkv6gkBYB\n",
-       "AEYysAdue4/tF3r886eSFBE7ImKDpH+V9M9jaC8AoMMRkf9B7A2S5iNiusdt+Z8AACZQRHjQ7ZlL\n",
-       "KLYviYhDncvrJD2fpQEAgGwy98BtPyrptyW9I+mIpL+KiNcLbBsAYIBCSigAgPEby0rMJi/6sX2X\n",
-       "7YOd1/cd2++vuk1Fsv1Z2y/afsf2x6puT1Fsb7H9ku1Dtr9cdXuKZPsB26/ZfqHqtpTB9pTtJzv/\n",
-       "X+63PVd1m4pie7XtZztZecD2nQPvP44euO11S/PGbW+XdHlEbC39icfA9iZJT0TEu7a/JkkR8ZWK\n",
-       "m1UY2x+R9K6kr0v664j4YcVNys32Kkn/I+lTkl6W9JykGyPiYKUNK4jtP5R0QtK/RcRlVbenaLbX\n",
-       "S1ofEftsr5X0A0mfbtDv79yIOGn7bElPS/pSRDzd675j6YE3edFPROyJiHc7l89KuqjK9hQtIl6K\n",
-       "iJ9U3Y6CfVzS4Yj4aUT8WtK31B6Ib4SI+C9J/1d1O8oSEa9GxL7O1yckHZR0QbWtKk5EnOx8eY6k\n",
-       "VZLe6HffsW1mZfsO20cl/YWkr43recfsJknzVTcCQ10o6VjX9c8630NibF8s6aNqd54awfZZtvdJ\n",
-       "ek3SkxFxoN99c63EPO1J90ha3+OmWyPi8YjYIWmH7a+ovejnL4t67rINe22d++yQ9KuIeGSsjSvA\n",
-       "KK+vYRi5b4BO+eRRSTd3euKN0PmL/orOeNp/2J6JiMVe9y0swCNi04h3fUSJ9VKHvTbbn5fUkvTJ\n",
-       "sTSoYCv43TXFy5K6B9Kn1O6FIxG23yfp25K+ERGPVd2eMkTEm7a/J+lKSYu97jOuWSiXdF32XfST\n",
-       "IttbJP2NpOsi4lTV7SlZUxZlfV/SJbYvtn2OpM9J+m7FbcKIbFvS/ZIORMTdVbenSLbPt/2Bztdr\n",
-       "JG3SgLwc1yyUxi76sX1I7cGGpYGGZyLiCxU2qVC2r5e0S9L5kt6U9HxEzFbbqvxsz0q6W+1Bovsj\n",
-       "YuB0rZTY/qakayV9UNLrkm6LiAerbVVxbH9C0lOSfqz3ymG3RMRCda0qhu3LJD2kduf6LEkPR8Rd\n",
-       "fe/PQh4ASBNHqgFAoghwAEgUAQ4AiSLAASBRBDgAJIoAB4BEEeAAkCgCHAAS9f963qCLZIi3PQAA\n",
-       "AABJRU5ErkJggg==\n"
+       "AAALEgAACxIB0t1+/AAAEn1JREFUeJzt3X+MZWV9x/HPh0WykN3YpKRFZCYkC7XVQZAYWxKLkyjC\n",
+       "3LZB0qjxj6ZCdv6o6Q4x2ihsLWsMkUiaytB/LAGLEjUNEgJxGLshTJEUUJRV1l0qu4nZkQgEqWQn\n",
+       "7Ka6fPvHvSN3du+d++Occ895znm/ErJ779y595nd5XOf+32+z3McEQIApOe0sgcAABgPAQ4AiSLA\n",
+       "ASBRBDgAJIoAB4BEEeAAkKhMAW57q+0nbe+zfcD2F/MaGABgc87aB277rIh4zfbpkh6T9OmIeCyX\n",
+       "0QEA+spcQomI1zq/PUPSFkmvZH1OAMBgmQPc9mm290l6UdIjEXEg+7AAAIPkMQN/PSIukXSepMtt\n",
+       "z2YeFQBgoNPzeqKIeNX2dyS9W9LK+v22OWwFAMYQEd7s65kC3PbZkn4bEb+2faakKyR9ftRBpMz2\n",
+       "nojYU/Y4ilLnn6/OP5vEz5e6YSa/WWfgb5F0t+3T1C7HfD0iHs74nACAIWQK8Ih4RtKlOY0FADAC\n",
+       "dmJmt1L2AAq2UvYACrRS9gAKtlL2AAq2UvYAypZ5I8/AF7CjzjVwACjCMNnJDBwAEkWAA0CiCHAA\n",
+       "SBQBDgCJIsABIFEEOAAkigAHgEQR4ACQKAIcABJFgANAoghwAEgUAQ4AiSLAASBRBDgAJIoAB4BE\n",
+       "EeAAkCgCHAASRYADQKKyXpUeaBx7piVNLUjbt0pHj0urixH7l8oeF5qHAAdG0A7vy26T7rjgjXvn\n",
+       "d9gzIsQxaZRQgJFMLWwMb6l9e3pXOeNBkxHgwEi2b+19/7YzJzsOgBIKMKKjx3vfv3ZskqOgDg+J\n",
+       "AAdGtLooze/YWEbZeVg6cvukRkAdHuscEcW+gB0R4UJfBJigdoBO72qXTdaOSUdun2Rw2nPL0kNX\n",
+       "nvqV1nLE0tykxoFiDZOdzMCBEXXCusSZLnV4tGUKcNtTkr4m6Q8khaR/i4jFPAYGoJ/N6/DUx5sj\n",
+       "6wz8N5I+GRH7bG+T9EPbeyPiYA5jQ00VGTDNCK/+dXjq482SKcAj4gVJL3R+v2b7oKRzJRHg6KnI\n",
+       "gGlKeEXsX7JnJLVOqcO36+O9+tRbu1Rq2QdFyK0Gbvt8Se+S9GRez4k66rcRJo+AKfK5q6V/HZ76\n",
+       "eJPkspGnUz65V9L1EbGWx3OirooMGMKrKn3qmIzMM3Dbb5L0bUn3RMT9fR6zp+vmSkSsZH1dpKrI\n",
+       "gCG8qtCnjvHYnpU0O9L3ZOkDt21Jd0v6VUR8ss9j6APH7/SuU+88LD2xUEwNPJ/nTknZferIxzDZ\n",
+       "mTXA3yvpUUk/UbuNUJJuiIjlUQaBZikyYAgv1EXhAZ7XIAAAGw2TnZxGCACJIsABIFEEOAAkigAH\n",
+       "gEQR4ACQKAIcABLFeeAAMmnGCZDVRIADGFtTToCsKkooADLodwLk9K5yxtMszMABZDD4BEhKLMUh\n",
+       "wAFkMMzl3SixFIUSCoAMVhel+UMb7+s+vpYSS5GYgQMY22aXd2s/gotsFIkAB5BJ/8u7SVxko1iU\n",
+       "UAAUaFCJBVlwHjiAQnGRjfFwQQcASBQXdACAGiPAASBRdKEAqCx2cW6OAAdQSeziHIwSCoCKYhfn\n",
+       "IMzAgS4zdmtKWtgubT0qHV+VFvdHMNsrBbs4ByHAgY4Zu3WZdNsd0u9mffPSjhlbhHgZ2MU5CCUU\n",
+       "oGNKWugOb0m6Q7pgWuIjeynYxTkIM3A0ymYlku1Sz4/s2yQ+spdg8EFZIMDRGINKJEelnh/Z1yQ+\n",
+       "spdk84OyQAkFlTBjt+bs5Y/YK3P28ozdyvs1BpVIVqXFeWnDR/ad0uEjEh/ZUUnMwFG6SS0eDiqR\n",
+       "7I9YmrHVknZtk85ck44dkW5nARNVlTnAbd8l6S8kvRQRF2UfEpqm38y41Z4Z5xaew5RIOmFNYCMJ\n",
+       "eZRQvirpqhyeBw01qcVDSiSom8wz8Ij4nu3zsw8FTTWpxUNKJKgbauAoXWdmvKO7jFLUzJgSCepk\n",
+       "IgFue0/XzZWIWJnE6yINzIwByfaspNmRviePK/J0SigP9lrE5Io8ADA6rsgDADWWOcBtf1PSf0v6\n",
+       "I9urtq/NPiwAwCBc1BiVwDGuwEbDZCddKCgdx7gC42EGjtz1mk1L7R2XvWbYc/byQ9KVJz9PS1pe\n",
+       "ipib9PiBKmAGjonrNZu+Tnrnr6W4Tzp3/b7uGTbHuALjoQsFuVg/TfBt0j1/KF3waNfX7pLe8o6u\n",
+       "8JY2ngLIMa7AeJiBI7Nes+7dnV8v7/y6pcf3rc+wJ7kTE6gTAhyZ9TpN8GZJn9MbAX6ix/etz7DZ\n",
+       "iQmMhwBHZv1q2Ouz7mulX74qhbrKKCfPsDmjBBgdAY7M+tWwn5JeaUnfXw9qZthAvmgjzIE905Km\n",
+       "FqTtW6Wjx6XVxSZdeLVXDXyndPgJaYGQBsZDG+EEtMP7stukO7pqwPM77Bk1JcSpYVcXO1zrjRl4\n",
+       "RvbcsvTQKZtQpNZyxBKbUFCaPjtcDz0uXU+IVx+nEU7E9p4LeNI2NqGgVP2uNbref4/0UULJ7GjP\n",
+       "BTxprXGbUPi4Xi3scK0/Ajyz1UVpfsfGGvjOw9KRRm1C4UCq6mGHa/0R4BlF7F+yZyS1drXLJmvH\n",
+       "pCO3N2UBc12/j+ut9sf1Rv1ZVAU7XOuPAM9BJ6wbHVJ8XK8euoPqjwBHLvi4Xi3r6xFv76xHHJC+\n",
+       "RHDXDwGOXPBxvTpYj2gO+sCRmxm7Nc3H9dJxgYx6YCcmJooDqaqB9YjmYCMPUDOsRzQHAQ7UTGc9\n",
+       "4lD3faxH1BM1cKCGWI9I3zDZSYAD4BiECmIRc0Kafh440kbbYboI8Iw4Dxyp4xiEdLGImdnUwsbw\n",
+       "ltq3pzmyE0mg7TBdBHhmnAeOtNF2mK7MAW77KtvP2n7O9mfyGFRaOA8caaPtMF2ZauC2t0j6V0kf\n",
+       "kPS8pB/YfiAiDuYxuDRwHjiqa5juEk4tTFfWRcz3SDoUET+XJNvfknS1pMYEOOeBo6pG6S7hGIQ0\n",
+       "ZQ3wt0pa7br9C0l/mvE5k8N54KgiukvqL2uAD7ULyPaerpsrEbGS8XUBDEB3SVpsz0qaHeV7sgb4\n",
+       "85Kmum5PqT0L3yAi9mR8HQAjorskLZ2J7cr6bds3DfqerF0oT0m60Pb5ts+Q9FFJD2R8TgA5oLuk\n",
+       "/jLNwCPit7b/XtJ3JW2RdGezOlCAalrvPvmVdGxOevmE9MvTpefpLqkXDrMCaqZP98mhx6XrCe90\n",
+       "cBohSsHJduXikmr1wGmEmDhOtitH95vmWdI7ez1mmO4T3nzTQoAjV/QeT97Jb5r/2Odxg7pPePNN\n",
+       "D4dZIVf0Hk/eyW+aH5S0+6THDNN90u/Nd7r95osKYgaOXNF7PHknv2le3vn1L6VXzpKeGfZsE958\n",
+       "00OAI1ed3uMd3TM5eo+L1etN83JJt0jf/48RFi15800PAY5ccbLd5OX1psmbb3poIwRqIK+r0HM1\n",
+       "++qgDxwAEjVMdtKFAgCJogYOVBgba7AZAhyoKDbWYBBKKEBFsbEGgxDgQEWxsQaDEOBARbGxBoMQ\n",
+       "4EBFcUUdDEIfOFBhbKxpLjbyoDFot0PdcEEH1N6M3TpX+sKM9CcXSGd+UO2DnMZtt+ONACkhwJGs\n",
+       "Xn3S6+dgj3MRCfquq8OeaUlTC9L2rdLR49LqYsR+/g5OQoAjWb36pG+W9Dm1Z+GjtttxNaFqaIf3\n",
+       "ZbdJd3T9XczvsGdEiG9EFwqS1a9Pekvn11Hb7ei7roqphY3hLbVvT7OB6SQEOJLVr0/6hMZrt6Pv\n",
+       "uiq293wjlbbxRnoSAhzJ6tUnfZ107L+kp56QFkatW9N3XRVHe76RSmu8kZ6ENsISsECTn7z7pOm7\n",
+       "Ll/vGvjOw9ITC036/4Q+8Arqs0BzSHr8+ib94wQ20/7/ZHpXu2yydkw6cnvT/v8gwCvInluWHrry\n",
+       "1K+0liOWhr4ALYB644o8lcQCDYB8jB3gtj9s+6e2T9i+NM9B1RsLNMA6e6Zlzy3bH1lp/zrTKntM\n",
+       "KcmykecZSddI+kpOY2mI1UVpfsepCzRH6HRAo7BhJ7uxAzwinpUkm/L2KCL2L9kzklqNXqAB+m/Y\n",
+       "abHzdUhspS9BJ6z5B4qGYz0oq00D3PZeSef0+NKNEfHgsC9ie0/XzZWIWBn2ewHUFetB3WzPSpod\n",
+       "6XuythHafkTSpyLiR32+ThshgFOwYWdzkzwPnICuKHZ9oqpYD8pu7Bm47WskLUo6W9Krkp6OiFM2\n",
+       "ojADLw+7PoF0sROz4dj1CaSLnZiNxyo/UGcEeK2xyg/UGQFea6uL7Zp3N3Z9AnVBDbzmOJYTSBOL\n",
+       "mACQKBYxAaDGCHAASBQBDgCJ4jTCGhln2zxb7YF0EeA1Mc7h+ByoD6SNEkpt9Dscf3pXvt8DoCoI\n",
+       "8NoYZ9s8W+2BlBHgtTHOtnm22gMpI8BrY5xt82y1B1eGTxk7MWtknG3zbLVvNs6Mry620gPYFGfG\n",
+       "V9ckL6kGoIIG9/mzkJ0yAhyoqeH6/FnIThmLmEBtDdPnz0J2ypiBA7U1uDzCleHTRoCjdJzHUpTh\n",
+       "yiOdP2v+vBNEgKNUnMdSpNVFaX7Hxj9byiN1QhshSkUbW7Ho808XbYRIAG1sRaI8Um90oaBktLEB\n",
+       "4yLAUTLa2IBxUQNH6cqu09IFgyriLBRgAA5zQlUNk51jl1Bs32r7oO0f277P9pvHfS6gPFyVCOnK\n",
+       "UgP/T0nviIiLJf1M0g35DAmYJLpgkK6xAzwi9kbE652bT0o6L58hAZNEFwzSlVcXynWi1xRJogsG\n",
+       "6dp0EdP2Xknn9PjSjRHxYOcxuyVdGhF/3ec5WMREpZXdBQP0UngXiu2PS5qX9P6I6PlR1HZI+nzX\n",
+       "XSsRsTL2iwJADdmelTTbdddNhQW47ask/bOk90XEy5s8jhk4AIyo0Bm47ecknSHplc5dj0fEJ8YZ\n",
+       "BABgIzbyAECiCt3IAwAoFwEOAIkiwAEgUQQ4ACSKAAeARBHgAJAoAhwAEkWAA0CiCHAASBQBDgCJ\n",
+       "IsABIFEEOAAkigAHgEQR4ACQKAIcABJFgANAoghwAEgUAQ4AiSLAASBRBDgAJIoAB4BEEeAAkCgC\n",
+       "HAASRYADQKIIcABIFAEOAIkiwAEgUQQ4ACRq7AC3/QXbP7a9z/bDtqfyHBgAYHNZZuBfioiLI+IS\n",
+       "SfdLuimnMSXF9mzZYyhSnX++Ov9sEj9fE4wd4BFxtOvmNkkvZx9OkmbLHkDBZsseQIFmyx5AwWbL\n",
+       "HkDBZsseQNlOz/LNtm+W9DeSXpP0Z7mMCAAwlE1n4Lb32n6mx39/JUkRsTsipiX9u6R/mcB4AQAd\n",
+       "jojsT2JPS1qKiJkeX8v+AgDQQBHhzb4+dgnF9oUR8Vzn5tWSnh5nAACA8Yw9A7d9r6S3SToh6bCk\n",
+       "v4uIl3IcGwBgE7mUUAAAkzeRnZh13vRj+1bbBzs/332231z2mPJk+8O2f2r7hO1Lyx5PXmxfZftZ\n",
+       "28/Z/kzZ48mT7btsv2j7mbLHUgTbU7Yf6fy73G97oewx5cX2VttPdrLygO0vbvr4SczAbW9f7xu3\n",
+       "vUvSxRGxs/AXngDbV0h6OCJet32LJEXEZ0seVm5s/7Gk1yV9RdKnIuJHJQ8pM9tbJP2PpA9Iel7S\n",
+       "DyR9LCIOljqwnNj+c0lrkr4WEReVPZ682T5H0jkRsc/2Nkk/lPShGv39nRURr9k+XdJjkj4dEY/1\n",
+       "euxEZuB13vQTEXsj4vXOzSclnVfmePIWEc9GxM/KHkfO3iPpUET8PCJ+I+lbai/E10JEfE/S/5Y9\n",
+       "jqJExAsRsa/z+zVJByWdW+6o8hMRr3V+e4akLZJe6ffYiR1mZftm20ck/a2kWyb1uhN2naSlsgeB\n",
+       "gd4qabXr9i869yExts+X9C61J0+1YPs02/skvSjpkYg40O+xmXZinvSieyWd0+NLN0bEgxGxW9Ju\n",
+       "259Ve9PPtXm9dtEG/Wydx+yW9H8R8Y2JDi4Hw/x8NcPKfQ10yif3Srq+MxOvhc4n+ks662nftT0b\n",
+       "ESu9HptbgEfEFUM+9BtKbJY66Gez/XFJLUnvn8iAcjbC311dPC+peyF9Su1ZOBJh+02Svi3pnoi4\n",
+       "v+zxFCEiXrX9HUnvlrTS6zGT6kK5sOtm300/KbJ9laR/kHR1RBwvezwFq8umrKckXWj7fNtnSPqo\n",
+       "pAdKHhOGZNuS7pR0ICK+XPZ48mT7bNu/1/n9mZKu0CZ5OakulNpu+rH9nNqLDesLDY9HxCdKHFKu\n",
+       "bF8jaVHS2ZJelfR0RMyVO6rsbM9J+rLai0R3RsSm7Vopsf1NSe+T9PuSXpL0TxHx1XJHlR/b75X0\n",
+       "qKSf6I1y2A0RsVzeqPJh+yJJd6s9uT5N0tcj4ta+j2cjDwCkiUuqAUCiCHAASBQBDgCJIsABIFEE\n",
+       "OAAkigAHgEQR4ACQKAIcABL1/z552MkEaOwoAAAAAElFTkSuQmCC\n"
       ],
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x105f235d0>"
+       "<matplotlib.figure.Figure at 0x106eb0950>"
       ]
      },
      "metadata": {},
@@ -627,97 +627,164 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 45,
+   "execution_count": 80,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[ 0.79320872  0.87751141]\n",
+      " [ 0.34859625  1.10144607]\n",
+      " [ 0.84730164  0.86600705]\n",
+      " [ 0.87178605  0.67973604]\n",
+      " [ 1.02320953  0.05223257]\n",
+      " [ 1.12153457  0.49210989]\n",
+      " [ 0.85257302  0.46268987]\n",
+      " [ 1.02866962  0.7313684 ]\n",
+      " [ 0.44710416  0.8148271 ]\n",
+      " [ 1.00715163  0.60103491]\n",
+      " [ 0.97326449  0.48955367]\n",
+      " [ 0.8782296   0.68866347]\n",
+      " [ 0.17089173  1.06423413]\n",
+      " [ 1.01157981  0.39264252]\n",
+      " [ 0.3417288   0.84054634]\n",
+      " [ 1.11146543  0.40394795]\n",
+      " [ 0.88481468  0.84173672]\n",
+      " [ 0.70515482  0.89868454]\n",
+      " [ 0.70562623  1.03892147]\n",
+      " [ 0.49678118  0.83054123]\n",
+      " [ 0.40706008  1.42381673]\n",
+      " [ 1.39657279  0.39009172]\n",
+      " [ 1.04451919  1.19192739]\n",
+      " [ 0.53297958  1.50011112]\n",
+      " [ 0.99420448  1.42983513]\n",
+      " [ 1.39050571  0.74889203]\n",
+      " [ 1.28308941  1.24967158]\n",
+      " [ 1.31448187  0.92596038]\n",
+      " [ 1.15165617  1.19119312]\n",
+      " [ 1.11444156  1.05553909]\n",
+      " [ 1.32773815  0.98155402]\n",
+      " [ 1.10494624  1.24527458]\n",
+      " [ 1.22212946  1.28531447]\n",
+      " [ 0.92884761  1.4680145 ]\n",
+      " [ 0.76518426  1.42363411]\n",
+      " [ 1.0229485   1.27350279]\n",
+      " [ 1.37170015  0.8541038 ]\n",
+      " [ 0.26667152  1.37509233]\n",
+      " [ 1.3817956   1.13790164]\n",
+      " [ 0.70795683  1.32292239]]\n"
+     ]
+    },
+    {
      "data": {
       "text/plain": [
-       "[-1, 6, -1, 6]"
+       "[0, 6, 0, 6]"
       ]
      },
-     "execution_count": 45,
+     "execution_count": 80,
      "metadata": {},
      "output_type": "execute_result"
     },
     {
      "data": {
       "image/png": [
-       "iVBORw0KGgoAAAANSUhEUgAAAXAAAAEACAYAAACqOy3+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
-       "AAALEgAACxIB0t1+/AAADx5JREFUeJzt3GuspVV9x/HvjzlO5sIgSa3cHIJNJFFsI7QaW7UeU6Ew\n",
-       "0VoTW2tibW2G+qIFalqVjlbmlb5p44XWN16ItcY2wdiIAl45ijGhIjMKDAiaIAMFtDME5orDzL8v\n",
-       "zj5xczyXvc/zzOxZM99P8mQ/z17rWes/Mzu/ec6atSdVhSSpPadMugBJ0soY4JLUKANckhplgEtS\n",
-       "owxwSWqUAS5Jjeoc4ElOT3J9knuS7Ejy8j4KkyQtbaqHMT4C3FhVb0oyBazvYUxJ0jLS5Ys8SZ4N\n",
-       "bKuq3+ivJEnSKLouoTwf+HmS65LckeTjSdb1UZgkaWldA3wKuAj4WFVdBOwDru5clSRpWV3XwB8C\n",
-       "Hqqq7w2ur2degCfxP1uRpBWoqizV3inAq+rRJDuTnF9V9wGvBe4et4jjWZKtVbV10nWsVMv1t1w7\n",
-       "WP+knQD1L/vw28culCuAzyZZDfwEeHsPY0qSltE5wKvqB8BLe6hFkjQGv4m5vJlJF9DRzKQL6GBm\n",
-       "0gV0NDPpAjqamXQBHc1MuoCjrdM+8JEmSKrlNXBJmoRRstMncElqlAEuSY0ywCWpUQa4JDXKAJek\n",
-       "RhngktQoA1ySGmWAS1KjDHBJapQBLkmNMsAlqVEGuCQ1ygCXpEYZ4JLUKANckhplgEtSowxwSWqU\n",
-       "AS5JjTLAJalRBrgkNcoAl6RGTXUdIMkDwJPAYeBQVb2s65iSpOV1DnCggOmq2t3DWJKkEfW1hJKe\n",
-       "xpEkjaiPAC/g60luT3J5D+NJkkbQxxLKK6rqkSS/Dnwtyb1VdetwhyRbhy5nqmqmh3kl6YSRZBqY\n",
-       "HuuequqzgGuAvVX1L0PvVVW5xCJJYxglOzstoSRZl2TD4Hw9cAlwZ5cxJUmj6bqEcgbwhSRzY322\n",
-       "qr7auSpJ0rJ6XUJZcAKXUCRpbEd9CUWSNDkGuCQ1ygCXpEYZ4JLUKANckhplgEtSowxwSWqUAS5J\n",
-       "jTLAJalRBrgkNcoAl6RGGeCS1CgDXJIaZYBLUqMMcElqlAEuSY0ywCWpUQa4JDXKAJekRhngktQo\n",
-       "A1ySGmWAS1KjDHBJalQvAZ5kVZJtSW7oYzxJ0vL6egK/CtgBVE/jSZKW0TnAkzwP2AR8AkjniiRJ\n",
-       "I+njCfxDwLuAIz2MJUka0VSXm5O8DvhZVW1LMr1Ev61DlzNVNdNlXkk60QwydHqse6pWvmyd5APA\n",
-       "nwNPA2uA04DPV9XbhvpUVbm0IkljGCU7OwX4vMleDfxDVb1+3CIkSc80Snb2vQ/cXSiSdIz09gS+\n",
-       "6AQ+gUvS2CbxBC5JOkYMcElqlAEuSY0ywCWpUQa4JDXKAJekRhngktQoA1ySGmWAS1KjDHBJapQB\n",
-       "LkmNMsAlqVEGuCQ1ygCXpEYZ4JLUKANckhplgEtSowxwSWqUAS5JjTLAJalRBrgkNcoAl6RGGeCS\n",
-       "1KhOAZ5kTZLbkmxPsiPJB/sqTJK0tKkuN1fVwSSvqar9SaaA7yR5ZVV9p6f6JEmL6LyEUlX7B6er\n",
-       "gVXA7q5jSpKW1znAk5ySZDvwGHBLVe3oXpYkaTmdllAAquoI8JIkzwa+kmS6qmaG+yTZOnQ5M79d\n",
-       "kk52SaaB6bHuqao+C/gn4EBV/fPQe1VV6W0SSToJjJKdXXehPCfJ6YPztcDFwLYuY0qSRtN1CeUs\n",
-       "4NNJTmH2L4PPVNU3upclSVpOr0soC07gEookje2oL6FIkibHAJekRhngktQoA1ySGmWAS1KjDHBJ\n",
-       "apQBLkmNMsAlqVEGuCQ1ygCXpEYZ4JLUKANckhplgEtSowxwSWqUAS5JjTLAJalRBrgkNcoAl6RG\n",
-       "GeCS1CgDXJIaZYBLUqMMcElqlAEuSY3qFOBJNia5JcndSe5KcmVfhUmSlpaqWvnNyZnAmVW1Pcmp\n",
-       "wPeBP66qe4b6VFWle6mSdPIYJTs7PYFX1aNVtX1wvhe4Bzi7y5iSpNH0tgae5DzgQuC2vsaUJC1u\n",
-       "qo9BBssn1wNXDZ7E57dvHbqcqaqZPuaVpBNFkmlgeqx7uqyBDyZ9FvAl4Kaq+vAC7a6BS9KYRsnO\n",
-       "rv+IGeDTwK6qeudKi5AkPdOxCPBXAt8GfgjMDfSPVXXzOEVIkp7pqAd4X0VIkp7pqG8jlCRNjgEu\n",
-       "SY0ywCWpUQa4JDXKAJekRhngktQoA1ySGmWAS1KjDHBJapQBLkmNMsAlqVEGuCQ1ygCXpEYZ4JLU\n",
-       "KANckhplgEtSowxwSWqUAS5JjTLAJalRBrgkNcoAl6RGGeCS1CgDXJIa1TnAk3wqyWNJ7uyjIEnS\n",
-       "aPp4Ar8OuLSHcSRJY+gc4FV1K/B4D7VIksbgGrgkNWrqWEySZOvQ5UxVzRyLeSWpFUmmgemx7qmq\n",
-       "PiY+D7ihqn5zgbaqqnSeRJJOIqNkp0soktSoPrYRfg74LnB+kp1J3t69LEnScnpZQllyApdQJGls\n",
-       "LqFI0gnMAJekRhngktQoA1ySGmWAS1KjDHBJapQBLkmNMsAlqVEGuCQ1ygCXpEYZ4JLUKANckhpl\n",
-       "gEtSowxwSWqUAS5JjTLAJalRBrgkNcoAl6RGGeCS1CgDXJIaZYBLUqMMcElqlAEuSY3qHOBJLk1y\n",
-       "b5L7k7ynj6IkSctLVa385mQV8CPgtcDDwPeAt1TVPUN9qqrStdCT2YuTTRvhyrVw9m44dw2sXgOr\n",
-       "D0KOwJFnwYE9cN9ueD/w0jPh3afB2v3AQTiyAQ4/DdkHT6+DQ+vgp3vh0C4447nw3PWQvbB/J3z/\n",
-       "HPjtDbDuINST8NPH4aq7qm4cp97kxZtg45WwYQ3sOQg7P1p1142/2r72bDhwFhx+BFb9Lzz4f3Du\n",
-       "H0KthYNrIKtgHbAaOFDw5GE47RCsPwhP7IKngF87c7bv/sBaZvv/Yj/suQ92v394XqklI2VnVa34\n",
-       "AH4XuHno+mrg6nl9qsscJ/txAWzaDPcX1LegtkDV0LFl6P0/gCf/Ag4v1F5Q7xg6/zeozfPG2jzU\n",
-       "PnfvG2DXBbBp9M/EBZtg8/3PHHrz/XDBpsXbtxS8u2BzwbcK/mpwbKl54wzah+/71uD46/rVMd/4\n",
-       "8Ny8Hh6tHaNkZ9cJ3gR8fOj6rcC14xbhsfhxKdw8l0rvnRe4c8f7Bq9/ukz7uH3nri+Dm0b/TFx6\n",
-       "88JDX3bT0u2vG7y+d+hYqN/7Frhequ9lI9fu4XE8HaNk51THp/yR1l+SbB26nKmqmY7znjQ2wJq5\n",
-       "88X+sFYNXtcu0z5u37nrUxfvvoANaxZ+/9S1S7evH7wu95FcqMKl+p46Ru3S5CSZBqbHuadrgD8M\n",
-       "bBy63gg8NL9TVW3tOM9Jaw8cnDt/epE+hwevB5ZpH7fv3PXexbsvYM/Bhd/fe2Dp9n2D18V+lcMV\n",
-       "zb9e7Dni8NC80vFt8GA7M3ed5Jrl7um6C+V24AVJzkuyGngz8MWOY2rITvjo5fBjgEuA985r3wJc\n",
-       "PHjdBXv+Eo4s1A7wjqHzVwOXzxtr81D73L13wu4H4doxKv4oXP7jeSP/BB68dvH2LcCLBhVdAjwy\n",
-       "OOb/aheq8OLBPe+Y13cLcNcjv5xXOvF02oUCkOQy4MPM/rz6yar64Lz2KnehdPLiZNO5cMUaOGeJ\n",
-       "XSg/2g3XAC89a7ALZR+/3IVyeHanyaHBLpQH98IvdsGZZ8Bz18227dsJd5wDF22A9U9BPQEPPA5/\n",
-       "t7JdKOdeMbt8sfcAPHjtr+5COfcKWHPOL3ehTD0MP9014i6UA/DkbjhYs7tQnloL+wa7UNYDT+2H\n",
-       "PT+C3de4C0WtGiU7Owd4H0VIkp5plOz0m5iS1CgDXJIaZYBLUqMMcElqlAEuSY0ywCWpUQa4JDXK\n",
-       "AJekRhngktQoA1ySGmWAS1KjDHBJapQBLkmNMsAlqVEGuCQ1ygCXpEYZ4JLUKANckhplgEtSowxw\n",
-       "SWqUAS5JjTLAJalRKw7wJH+S5O4kh5Nc1GdRkqTldXkCvxN4I/Dtnmo5LiWZnnQNXbRcf8u1g/VP\n",
-       "Wuv1j2LFAV5V91bVfX0Wc5yannQBHU1PuoAOpiddQEfTky6go+lJF9DR9KQLONpcA5ekRk0t1Zjk\n",
-       "a8CZCzRtqaobjk5JkqRRpKq6DZDcAvx9Vd2xSHu3CSTpJFVVWap9ySfwMSw6yXIFSJJWpss2wjcm\n",
-       "2Qm8HPhykpv6K0uStJzOSyiSpMk4JrtQWvzST5JLk9yb5P4k75l0PeNI8qkkjyW5c9K1rESSjUlu\n",
-       "GXxm7kpy5aRrGkeSNUluS7I9yY4kH5x0TeNKsirJtiRNblZI8kCSHw5+Df8z6XrGkeT0JNcnuWfw\n",
-       "+Xn5Yn2P1TbCpr70k2QV8K/ApcCLgLckeeFkqxrLdczW3qpDwDur6gJml+j+pqXf/6o6CLymql4C\n",
-       "/BbwmiSvnHBZ47oK2AG0+iN6AdNVdWFVvWzSxYzpI8CNVfVCZj8/9yzW8ZgEeINf+nkZ8OOqeqCq\n",
-       "DgH/CbxhwjWNrKpuBR6fdB0rVVWPVtX2wfleZj/AZ0+2qvFU1f7B6WpgFbB7guWMJcnzgE3AJ1hi\n",
-       "g0IDmqs9ybOBV1XVpwCq6umqemKx/n6RZ2HnADuHrh8avKdjLMl5wIXAbZOtZDxJTkmyHXgMuKWq\n",
-       "dky6pjF8CHgXcGTShXRQwNeT3J7k8kkXM4bnAz9Pcl2SO5J8PMm6xTr3FuBJvpbkzgWO1/c1xzHU\n",
-       "6o+NJ5QkpwLXA1cNnsSbUVVHBksozwN+v5X/lyPJ64CfVdU2GnyCHfKKqroQuIzZJbhXTbqgEU0B\n",
-       "FwEfq6qLgH3A1Ut17kVVXdzXWMeBh4GNQ9cbmX0K1zGS5FnA54H/qKr/nnQ9K1VVTyT5MvA7wMyE\n",
-       "yxnF7wF/lGQTsAY4Lcm/V9XbJlzXWKrqkcHrz5N8gdll0VsnW9VIHgIeqqrvDa6vZ4kAn8QSSgt/\n",
-       "q98OvCDJeUlWA28Gvjjhmk4aSQJ8EthRVR+edD3jSvKcJKcPztcCFwPbJlvVaKpqS1VtrKrnA38G\n",
-       "fLO18E6yLsmGwfl64BJmN1Ic96rqUWBnkvMHb70WuHux/sdqG2FTX/qpqqeBvwW+wuy/xP9XVS36\n",
-       "L8HHmySfA74LnJ9kZ5K3T7qmMb0CeCuzuze2DY6WdtWcBXxzsAZ+G3BDVX1jwjWtVIvLiWcAtw79\n",
-       "/n+pqr464ZrGcQXw2SQ/YHYXygcW6+gXeSSpUe5CkaRGGeCS1CgDXJIaZYBLUqMMcElqlAEuSY0y\n",
-       "wCWpUQa4JDXq/wHT38XUvMRKQQAAAABJRU5ErkJggg==\n"
+       "iVBORw0KGgoAAAANSUhEUgAAAWgAAAEACAYAAACeQuziAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
+       "AAALEgAACxIB0t1+/AAAE8lJREFUeJzt3W2QnWV9x/HvnwQaQlKpYoVIGGyi0zYLI6gIVcO2lYds\n",
+       "qfVFoTpDnYLJq5owtWpFQePY1qnTjiU6dqaRMJgy9gUWR9sQUMtWmQIGJMUAKsnUYYEgKBUTkszw\n",
+       "8O+Lcw57sjkP9+6es+fKnu9n5syeh/tc9395+OXKdV/XdUdmIkkqzzGDLkCS1JoBLUmFMqAlqVAG\n",
+       "tCQVyoCWpEIZ0JJUqK4BHREnRsTNEfFwRDwUEefORWGSNOwWVjjmOmBbZv5xRCwETuhzTZIkIDot\n",
+       "VImIVwD3Z+ZvzF1JkiToPsTxOuDpiLghIr4fEZsjYvFcFCZJw65bQC8Ezga+mJlnA88BH+17VZKk\n",
+       "rmPQjwGPZeaO+uubmRLQEeFmHpI0A5kZnT7vGNCZ+WRETETEGzLzx8A7gQene5KjWURszMyNg66j\n",
+       "X/z9jm7z+febz78bVOvcVpnFsR64KSKOA/YAV8y2MElSd10DOjP/B3jLHNQiSWriSsLuxgddQJ+N\n",
+       "D7qAPhsfdAF9Nj7oAvpofNAFDFrHedCVGojI+TwGLUn9UCU77UFLUqEMaEkqlAEtSYUyoCWpUAa0\n",
+       "JBXKgJakQhnQklQoA1qSCmVAS1KhDGhJKpQBLUmFMqAlqVAGtCQVyoCWpEIZ0JJUKANakgplQEtS\n",
+       "oQxoSSqUAS1JhTKgJalQBrQkFcqAlqRCGdCSVCgDWpIKZUBLUqEMaEkq1MIqB0XET4BfAi8Cz2fm\n",
+       "Of0sSpJUMaCBBEYz85l+FiNJmjSdIY7oWxWSpCNUDegEvhUR90bEun4WJEmqqTrE8bbM3BsRrwa+\n",
+       "GRE/zMzv9rMwSRp2lQI6M/fWfz4dEbcA5wAvB3REbGw6fDwzx3tYoyQd9SJiFBid1ncys1uji4EF\n",
+       "mbkvIk4Abgc+lZm31z/PzHR8WpKmoUp2VulBvwa4JSIax9/UCGdJUv907UF3bcAetCRNW5XsdCWh\n",
+       "JBXKgJakQhnQklQoA1qSCmVAS1KhDGhJKpQBLUmFMqAlqVAGtCQVyoCWpEIZ0JJUKANakgplQEtS\n",
+       "oQxoSSqUAS1JhTKgJalQBrQkFcqAlqRCGdCSVCgDWpIKZUBLUqEMaEkqlAEtSYUyoCWpUAa0JBXK\n",
+       "gJakQhnQklQoA1qSCmVAS1KhKgV0RCyIiPsj4hv9LkiSVFO1B30V8BCQfaxFktSka0BHxKnAGPAl\n",
+       "IPpekSQJqNaD/hzwYeClPtciSWqysNOHEXEJ8FRm3h8Rox2O29j0cjwzx3tSnSTNE/UMHZ3WdzLb\n",
+       "DytHxN8Cfwq8ACwCfhX4ama+r+mYzEyHPiRpGqpkZ8eAntLY+cCHMvMPp3sSSdLhqmTndOdBO4tD\n",
+       "kuZI5R502wbsQUvStPWjBy1JmiMGtCQVyoCWpEIZ0JJUKANakgplQEtSoQxoSSqUAS1JhTKgJalQ\n",
+       "BrQkFcqAlqRCGdCSVCgDWpIKZUBLUqEMaEkqlAEtSYUyoCWpUAa0JBXKgJakQhnQklQoA1qSCmVA\n",
+       "S1KhDGhJKpQBLUmFMqAlqVAGtCQVyoCWpEIZ0JJUqK4BHRGLIuKeiNgZEQ9FxGfmojBJGnYLux2Q\n",
+       "mYci4ncz80BELATujIi3Z+adc1CfJA2tSkMcmXmg/vQ4YAHwTN8qkiQBFQM6Io6JiJ3AT4E7MvOh\n",
+       "/pYlSeo6xAGQmS8Bb4yIVwC3RcRoZo43Po+IjU2Hjzd/JkmCiBgFRqf1ncyc7kmuBQ5m5t/XX2dm\n",
+       "xrQakaQhVyU7q8ziOCkiTqw/Px64ALi/NyVKktqpMsRxCnBjRBxDLdC3Zua3+1uWJGnaQxxHNOAQ\n",
+       "hyRNW0+GOCRJg2FAS1KhDGhJKpQBLUmFMqAlqVAGtCQVyoCWpEIZ0JJUKANakgplQEtSoQxoSSqU\n",
+       "AS1JhTKgJalQBrQkFcqAlqRCGdCSVCgDWpIKZUBLUqEMaEkqlAEtSYUyoCWpUAa0JBXKgJakQhnQ\n",
+       "klQoA1qSCmVAS1KhDGhJKpQBLUmF6hrQEbE8Iu6IiAcjYldEbJiLwiRp2EVmdj4g4mTg5MzcGRFL\n",
+       "gPuAd2fmw/XPMzOj/6VK0vxRJTu79qAz88nM3Fl/vh94GFjWmxIlSe1Maww6Ik4HzgLu6UcxkqRJ\n",
+       "C6seWB/euBm4qt6Tbv5sY9PL8cwc70l1kjRPRMQoMDqt73Qbg643fCzw78CtmfmPUz5zDFqSpqlK\n",
+       "dla5SBjAjcDPM/MvZnISSdLhehXQbwe+AzwANA6+OjO3Vz2JJOlwPQnoXpxEknS4nkyzkyQNhgEt\n",
+       "SYUyoCWpUAa0JBXKgJakQhnQklQoA1qSCmVAS1KhDGhJKpQBLUmFMqAlqVCV94MuRcTIGCzfAEsX\n",
+       "wb5DMLEpc9e2QdclSb12VAV0LZzPuw42r5x8d92KiBFmG9IGv6TSHFUBXQvQ5nCG2uux9cCMw7Sf\n",
+       "wS9JM1VkQLfvzS5d1PobS46fWXsN7YJ/zY0Rlz1oj1rSIBQX0J16s7D8UOtv7T84k/YmA7dd8L/1\n",
+       "JNh4fuvvSFJ/DWQWR8TIWMSa7RGXjdd+joxNftquN3vaepjYBOt2H/7Z2j3w6Ofbn61Tew372gT/\n",
+       "ix2+I0n9Nec96O492vbDGJm7ttV60mPra8Ma+w/Co5/v3KutMiwysQnWrTi8po8BF3f4jiT11wCG\n",
+       "OLpd6GvXm60NY9TDuOsww+S48+Iz4RrgQmD1Ee012jw8+PetgqtPOvz4w78jSf02gIDu1qNt1Zvt\n",
+       "NoxxuNa99I/Xf65u2V5z8Ne+v/U6WL2ydr/c24Hdh+CFX48YGWvXY3eqnqRemvObxkas2Q63XnTk\n",
+       "J2PbM7etqR0zMlYb7606jFH1HJc8Ay99r0p7tRpe+Sl4/Sq4vmlo48q9sPsJOHl/cwi3/kPhygPw\n",
+       "2B5Y8IRhLalZpezMzFk9ak1M5/hVY7D2EcicfLx/N6wam20tk+e4dPzw9huPS8en187F21u3c03T\n",
+       "87WP1H6nbsfWjuvV7+jDh4+j+1ElO+d8iGNmF/qmq/M4dnXthmMWND3fvBIu2Qq/0uZPwgVNx81u\n",
+       "QY2k4TKQedBVL/TN3OzHsWuqTL8DePMr4YU2bTQf6ywQSdUVt1ClF3rXS5/YBFe+A7Ysnnyv1fS7\n",
+       "F6nNEvk48De0P3b/QS8kSqpqzi8SHm0iLnwA3npGbajiaeAQcH3TEY0QXk1txsdnn4HjHoeXVsAH\n",
+       "F09O1Vu7B+7eCuddPmUO+G646ypDWhouVbKzmIAeiRhbDhuWwqJ9cGgCNu3KHHhoHTkj5DvAN4EH\n",
+       "n4dVx8IFHD5fujYbpdVMlFrPufMMFknDoUp29n2Io0rwjkSMnQfXbYaXe5brYMVIBIMP6anj2auB\n",
+       "L++BH2+FV11emyvdMDnO3WqcPeKyj7Q+h2PTko7UNaAjYgvwB8BTmXnGdBqvGrzLYUPzMQCbYeUY\n",
+       "zHjWQ6965G3Gs++G5efBzw/Cmp/Bi3th4ePdx7l7NbtE0lCoMFfvHcBZwA+mO5fvYtjeYmJwroFb\n",
+       "m4+7FMZbHXcpjM9kfuEqGFsLjzS3tRYeWQWznofceh53tTnOczEH3IcPH0fHo1N2Nh5de9CZ+d2I\n",
+       "OH0m4b8UWs4jXgKH/ZV+X+3K2xH2w4x6lv3okTe1Pu2bBkzO3PjtRfCjZ+HC++DE/f2ZAy5pvujr\n",
+       "GHTV4J2ATetgRXOoroU9j8I05y3XVP2DYWamd9OANrv37Ya7PmEwS+qkrwFdNXh3ZW4biWAM1i+B\n",
+       "4/fDwUfh8zO9QNjrHvmU1qc5jrzs0/24TZek+a8nAR0RG5tejmfmOEwveOvv9SSwJmDTlXDmFjil\n",
+       "8d4VsHemPfIprVdepVjrPY/8Vut2nLkhDZOIGAVGp/OdngR0Zm5s91kvg3c6fgF5LbXlJS8Cz0IC\n",
+       "b1kTMauZHdNbpbh8A6xsE8TO3JCGSb3jOt54HRGf7PadrgtVIuIrwPnAq4CngE9k5g1Nn2cWtpJw\n",
+       "TcT2W+GIBSHvhgNfg8VQW27yD3DgOXjq2FrS7j0IT/RygUzEZePwgfPhNmpLwF/eW/oleGYnPHGt\n",
+       "49DScOrJQpXMfG/vSmqv1bxlqM3IWAqLnoQliyBOhH3der/tLhK+sSmcbwP+EhbfBqfXd884CTij\n",
+       "twtk9h1qWuoNHAv8E9TuBXk2rLvOG9FKaqeIzZJaLWi5Es78BeS/wbJGoDZvQ9QpSNtdJGzsK3d7\n",
+       "va1rprQJvZyOB4ePV98O/PXUs3mxUFJbA7mr91St5i1vgVNWwTKYDNRmm2HlabUgPUJ99shhd/++\n",
+       "Ag5cUH++cMrPqXozHa+x3Puuq2Bse23+c8uzebFQUktF9KDbDUk0trqfbpC2mT1y90K4fDWsbOzc\n",
+       "3G4H595Mx6tp7MlR23TpyHFx+MWSXp1L0vxSREB3G5KYSZC2mj0yErFjDNa/AK+9Elb8GSyeuoPz\n",
+       "1Hnavdtlb2ITXHkmbDll8r2PAUtO6XQjWknDq4jtRluNQV8Be5/tMAa9FvbcDRtmejFvJGLsNFj/\n",
+       "S/jNpbDsBHj+OTg4AV/YlfmpdnWtg913wVUzOW/E6nvh/DdNTv5rbFXqdqPSsCliu9Eq2i1oAV5+\n",
+       "70k44cLaLI79s11p2HTOt5wDq7fAcdQeJ6yDy0ciduzK3Nb7PT1O3g+fbvG+49CSjlREQEPHBS19\n",
+       "+av/SMTYCvjIlvrUu4bmAO79nh5uNyqpumICeq4thw1nTQnnhkYAPwlLrqH2D+kFancdXM1sLiL2\n",
+       "6ma2kobB0Ab0UljU6eLjSMTYObCseebyx4HPzWJPj97dzFbSMCjiIuEgrInYfjVcNPXi4xVwYAdc\n",
+       "uhw2tFoufiHcd3vmm+euUknzUZXsLGKhyiBMwKatsPsi4FpgI7W9OnbAZ3dlth1/PhH2z2WdkobX\n",
+       "0A5xNGaOPN5mK9ROe0qXegdySfPL0AY0tJ85MhIxtgxe/R44uBKOb1wcrC9iubvcO5BLmk+Gdgy6\n",
+       "XS+41eKU98PBR+DBZ+CT7camx2D7tkwXm0iq5KhZqDLX2qwQXDES0XLjpuvh+DH42Xcyt10W8ZFW\n",
+       "bfZqgyVJahjKgO60QnBJ08XBxvb6C4Fj4K31Xveh5vcb86Orzo2evMP30kW1hSsTm5xmJ6mVoQzo\n",
+       "TisEGxcHW+z/8Wvr4Lr/hnu2wvOba7vvA7AOnn8U7u523jZ3+F7hpv2SWhnKaXadZmg09pLusAf1\n",
+       "Rc3hXH//2NPg3O5nXr6h9R2+T2u5r7Wk4TaUAd1qQ//GNqO7MrfdBVc9DM+0+u6SKeHc9H6FMeil\n",
+       "LXvubpYkqZWhHOJot3teY5rcrsxtayJ20GK2xn54vlWb1cag3SxJUnVDGdDQcfc84OVe9ormi4lr\n",
+       "Yc8EbF0Hl099v9r+HG6WJKm6oZ0HXUVjU/+pvex271dps3ah8DQ3S5KGXJXsNKAlaQDcLEmSjmIG\n",
+       "tCQVyoCWpEIZ0JJUKANakgrVNaAj4uKI+GFEPBIRfzUXRZVkJGJsTcT2yyLG10RsH4kYG3RNkoZD\n",
+       "x4UqEbEA+ALwTuBxYEdEfD0zH56L4gZtJGLsVPjnW+G1jffm2+b8ETGameODrqNf/P2OXvP5d6uq\n",
+       "Ww/6HGB3Zv4kM58H/hX4o/6XVYblsOHcpnCGlzdMmk+bG40OuoA+Gx10AX02OugC+mh00AUMWreA\n",
+       "fi0w0fT6MaYE1nzWaVvSua5F0vDpFtCzW2Z4lOu0Lelc1yJp+HRc6h0R5wIbM/Pi+uurgZcy8++a\n",
+       "jhnqEJekmZrVXhwRsRD4EfD7wBPA94D3DstFQkkapI6zODLzhYj4ALW7Py0ArjecJWluzHo3O0lS\n",
+       "f8xqJeF8XsQSEVsi4qcR8YNB19IPEbE8Iu6IiAcjYldEbBh0Tb0UEYsi4p6I2BkRD0XEZwZdU69F\n",
+       "xIKIuD8ivjHoWnotIn4SEQ/Uf7/vDbqeXouIEyPi5oh4uP7fZ8t7ms64B11fxPIjmhaxMI/GpyPi\n",
+       "HcB+4MuZecag6+m1iDgZODkzd0bEEuA+4N3z5d8fQEQszswD9WspdwIfysw7B11Xr0TEB4E3AUsz\n",
+       "812DrqeXIuJ/gTdlZst7gx7tIuJG4L8yc0v9v88TMvPZqcfNpgc9rxexZOZ3gf8bdB39kplPZubO\n",
+       "+vP9wMPAssFW1VuZeaD+9Dhq11Dmzf/sEXEqMAZ8CZivN8yYl79XRLwCeEdmboHatb5W4QyzC+ih\n",
+       "XsQyn0TE6cBZwD2DraS3IuKYiNgJ/BS4IzMfGnRNPfQ54MPAS4MupE8S+FZE3BsR6wZdTI+9Dng6\n",
+       "Im6IiO9HxOaIWNzqwNkEtFcX54H68MbNwFX1nvS8kZkvZeYbgVOB1RExOuCSeiIiLgGeysz7mae9\n",
+       "TOBtmXkWsAb48/qQ43yxEDgb+GJmng08B3y01YGzCejHgeVNr5dT60XrKBERxwJfBf4lM7826Hr6\n",
+       "pf7Xx/8A3jzoWnrkd4B31cdpvwL8XkR8ecA19VRm7q3/fBq4hdqQ6nzxGPBYZu6ov76ZWmAfYTYB\n",
+       "fS/w+og4PSKOA/4E+Pos2tMciogArgceysx/HHQ9vRYRJ0XEifXnxwMXAPcPtqreyMyPZebyzHwd\n",
+       "8B7gPzPzfYOuq1ciYnFELK0/PwG4EJg3s6ky80lgIiLeUH/rncCDrY7tuFCly0nm9SKWiPgKcD7w\n",
+       "qoiYAD6RmTcMuKxeehtwOfBARDSC6+rM3D7AmnrpFODGiDiGWkdka2Z+e8A19ct8G258DXBLrQ/B\n",
+       "QuCmzLx9sCX13Hrgpnrndg9wRauDXKgiSYXylleSVCgDWpIKZUBLUqEMaEkqlAEtSYUyoCWpUAa0\n",
+       "JBXKgJakQv0/lfRzUKDZYtIAAAAASUVORK5CYII=\n"
       ],
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x106c8ddd0>"
+       "<matplotlib.figure.Figure at 0x106a6b390>"
       ]
      },
      "metadata": {},
@@ -725,17 +792,20 @@
     }
    ],
    "source": [
-    "#X_transformed = 2.5*transpose(vstack((hstack((np.abs(x1),np.abs(x2))),hstack((np.abs(y1),np.abs(y2)))))) ### CHANGE THIS LINE ####\n",
-    "X_transformed = transpose(vstack((hstack((sqrt(x1**2+y1**2),sqrt(x2**2+y2**2))),np.zeros(2*N_half))))\n",
+    "#X_transformed = 2.5*transpose(vstack((hstack((np.abs(x1),np.abs(x2))),hstack((np.abs(y1),np.abs(y2)))))) #radius ### CHANGE THIS LINE ####\n",
+    "#X_transformed = transpose(vstack((hstack((sqrt(x1**2+y1**2),sqrt(x2**2+y2**2))),map(lambda x: m.atan2(x[0],x[1]),X_c)))) # radius and angle\n",
+    "#X_transformed = transpose(vstack((hstack((x1**2,x2**2)),hstack((y1**2,y2**2))))) #radius ### CHANGE THIS LINE ####\n",
+    "X_transformed = transpose(vstack((hstack((abs(x1)**(0.5),abs(x2)**(0.5))),hstack((abs(y1)**(0.5),abs(y2)**(0.5))))))\n",
+    "print X_transformed\n",
     "### prbly other transormation\n",
     "plt.plot(X_transformed[t_c>0,0],X_transformed[t_c>0,1], 'ro')\n",
     "plt.plot(X_transformed[t_c<0,0],X_transformed[t_c<0,1], 'bo')\n",
-    "plt.axis([-1, 6, -1, 6])"
+    "plt.axis([0, 6, 0, 6])"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 27,
+   "execution_count": 76,
    "metadata": {
     "collapsed": false
    },
@@ -746,7 +816,7 @@
        "(40, 2)"
       ]
      },
-     "execution_count": 27,
+     "execution_count": 76,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -765,7 +835,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 46,
+   "execution_count": 81,
    "metadata": {
     "collapsed": false,
     "scrolled": true
@@ -778,8 +848,8 @@
      "traceback": [
       "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
       "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
-      "\u001b[0;32m<ipython-input-46-6c4875b82fa6>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mwb_opt_c\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0moptimizeSVM\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX_transformed\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mt_c\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0;31m#plotSVM(X_transformed,t_c,wb_opt_c)  ### PROVIDE THIS PLOT ###s\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0;31m#plotSVM(X_transformed,t_c,[-2,2,-1])\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m<ipython-input-22-49e7f2f9b2de>\u001b[0m in \u001b[0;36moptimizeSVM\u001b[0;34m(X_, t_)\u001b[0m\n\u001b[1;32m     13\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     14\u001b[0m     opt_result = optimize.minimize(objective, wb0, jac=jac,constraints=cons, #the optimizer\n\u001b[0;32m---> 15\u001b[0;31m                                      method='SLSQP', options=opt)\n\u001b[0m\u001b[1;32m     16\u001b[0m     \u001b[0mwb_opt\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mopt_result\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m\"x\"\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;31m#result of the optimization\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     17\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m<ipython-input-81-6c4875b82fa6>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mwb_opt_c\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0moptimizeSVM\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX_transformed\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mt_c\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0;31m#plotSVM(X_transformed,t_c,wb_opt_c)  ### PROVIDE THIS PLOT ###s\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0;31m#plotSVM(X_transformed,t_c,[-2,2,-1])\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m<ipython-input-57-49e7f2f9b2de>\u001b[0m in \u001b[0;36moptimizeSVM\u001b[0;34m(X_, t_)\u001b[0m\n\u001b[1;32m     13\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     14\u001b[0m     opt_result = optimize.minimize(objective, wb0, jac=jac,constraints=cons, #the optimizer\n\u001b[0;32m---> 15\u001b[0;31m                                      method='SLSQP', options=opt)\n\u001b[0m\u001b[1;32m     16\u001b[0m     \u001b[0mwb_opt\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mopt_result\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m\"x\"\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;31m#result of the optimization\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     17\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
       "\u001b[0;32m/Users/Maximus/anaconda/lib/python2.7/site-packages/scipy/optimize/_minimize.pyc\u001b[0m in \u001b[0;36mminimize\u001b[0;34m(fun, x0, args, method, jac, hess, hessp, bounds, constraints, tol, callback, options)\u001b[0m\n\u001b[1;32m    433\u001b[0m     \u001b[0;32melif\u001b[0m \u001b[0mmeth\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'slsqp'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    434\u001b[0m         return _minimize_slsqp(fun, x0, args, jac, bounds,\n\u001b[0;32m--> 435\u001b[0;31m                                constraints, callback=callback, **options)\n\u001b[0m\u001b[1;32m    436\u001b[0m     \u001b[0;32melif\u001b[0m \u001b[0mmeth\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'dogleg'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    437\u001b[0m         return _minimize_dogleg(fun, x0, args, jac, hess,\n",
       "\u001b[0;32m/Users/Maximus/anaconda/lib/python2.7/site-packages/scipy/optimize/slsqp.pyc\u001b[0m in \u001b[0;36m_minimize_slsqp\u001b[0;34m(func, x0, args, jac, bounds, constraints, maxiter, ftol, iprint, disp, eps, callback, **unknown_options)\u001b[0m\n\u001b[1;32m    402\u001b[0m             \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    403\u001b[0m                 \u001b[0ma\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mvstack\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma_eq\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ma_ieq\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 404\u001b[0;31m             \u001b[0ma\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mconcatenate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mzeros\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mla\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    405\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    406\u001b[0m         \u001b[0;31m# Call SLSQP\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
       "\u001b[0;31mValueError\u001b[0m: all the input array dimensions except for the concatenation axis must match exactly"