diff --git a/exercises/ex04_solution/heised_python/heised.ipynb b/exercises/ex04_solution/heised_python/heised.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..5fed69cbde43f21632f8355959d62599b8198a0a
--- /dev/null
+++ b/exercises/ex04_solution/heised_python/heised.ipynb
@@ -0,0 +1,150 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 38,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import scipy.sparse.linalg as LA\n",
+    "import matplotlib.pyplot as plt\n",
+    "%matplotlib inline\n",
+    "plt.rcParams['figure.figsize'] = 16, 9"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 39,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "class Heisenberg:\n",
+    "    def __init__(self,L,nup,periodic=False,j=1.):\n",
+    "        self.L   = L\n",
+    "        self.nup = nup\n",
+    "        self.periodic = periodic\n",
+    "        self.j = j\n",
+    "        self.index  = -np.ones((1<<self.L),dtype=int)\n",
+    "        states = []\n",
+    "        ## find all basis states with given nup\n",
+    "        i = 0\n",
+    "        for s in range((1<<nup)-1,len(self.index)):\n",
+    "            if bin(s).count('1')==self.nup:\n",
+    "                self.index[s] = i\n",
+    "                states.append(s)\n",
+    "                i+=1\n",
+    "        self.states = np.array(states,dtype=int)\n",
+    "        self.N = len(self.states)\n",
+    "    def multiply(self,x):\n",
+    "        assert(len(x)>=self.N)\n",
+    "        y = np.zeros_like(x)\n",
+    "        # diagonal part\n",
+    "        for i,s in enumerate(self.states):\n",
+    "            jtotal = 0.\n",
+    "            for r in range(self.L-1):\n",
+    "                jtotal += -1 if ((s >> r)^(s >> (r+1)))&1 else 1\n",
+    "            y[i] = 0.25*self.j*jtotal*x[i]\n",
+    "        # off-diagonal part\n",
+    "        for i,s in enumerate(self.states):\n",
+    "            for r in range(self.L-1):\n",
+    "                if ((s >> r)^(s >> (r+1)))&1 :\n",
+    "                    sflipped = s^(3 << r)\n",
+    "                    y[self.index[sflipped]] += 0.5*self.j*x[i]\n",
+    "        if self.periodic:\n",
+    "            for i,s in enumerate(self.states):\n",
+    "                y[i] += 0.25*self.j*(-1 if (s^(s >> (self.L-1)))&1 else 1)*x[i]\n",
+    "                if (s^(s >> (self.L-1)))&1 :\n",
+    "                    sflipped = s^(1|(1 << (self.L-1)))\n",
+    "                    y[self.index[sflipped]] += 0.5*self.j*x[i]\n",
+    "        return y   "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Test Energies"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 44,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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iYgAIDw/n7rvvpkiRIjRs2JA//vjjsv0++ugjateuTf78+YmPj+eWW24hIiICgJiYGJ5/\n/nnKlStH+fLleeGFF4iNjb20/8cff0zZsmUpX748w4cPx5jERt3+/fvz5ptvXvo5LCyMu+++m0KF\nCnHrrbcyb9689L4tKVI4FhERERER8VMhISHMnz+fbdu2sWnTJt59913Wrl3LwIED+eGHH4iOjuaJ\nJ56gXbt2lwXc8ePHM3v2bI4fP05AQMBlx3z33XdZvXo1v//+O7/99hurV6/m3XffBWDOnDl8+umn\nLFy4kC1btrBgwYIUa1u9ejV9+/blP//5DydOnGDp0qVUrlw5Xe6DN7K7dmYRERERERE/Z9666aGw\nANjBqeua/Mwzz1C2bFkAXnvtNZ555hmOHDnCk08+yb333gtAnz59eO+994iMjKRRo0YAPPfcc5f2\nu1JISAhfffUVxYoVA2Dw4ME8+eSTvPXWW4SGhtK/f39uv/12AIYMGcL48eOTPc6wYcMYOHAgzZo1\nA6BMmTKUKVMmVdeZFhSORURERERE0klqQ21aKV++/KXnlSpVIioqit27dzNy5Ei++OILwBkTHBsb\nS1RUVLL7XSkqKoqKFSteddyL710M3RffS2nM8Z49e2jdunXqLiwdqFu1iIiIiIiIn9qzZ8+l57t3\n76ZcuXJUqFCB119/nejoaKKjozl27BinT5+me/ful7ZNOk74SmXLlmXXrl2Xft61a9elVuYyZcpc\nds5du3aleKwKFSqwbdu2VF9bWlM4FhERERER8VNfffUV+/btIzo6mvfff58ePXrw6KOP8s0337B6\n9WoAzpw5w6xZszhz5oxXx+zZsyfvvvsuR44c4ciRI7zzzjv06dMHgG7dujFixAg2btzI2bNnefvt\nt1M8zsCBAxk+fDiLFi3CWktUVBSbNm26+YtOJYVjERERERERPxUUFETLli2pWrUqVatW5bXXXqNO\nnTr8+OOPPP300xQtWpRq1aoxcuTIS/sk19Kb9LXXX3+de++9l1q1alG7dm3uvfdeXnvtNQAefvhh\nnn/+eZo1a0a1atVo3rx5irXVrVuX4cOH8/zzz1OoUCECAwPZvXt3Gl79jTG+suZUahljrL9fo4iI\niGSsBJtANqM2BhFxQmNmzRu33HILQ4cOvTThla9L6V57Xr/pmc/0f3URERGRG/D8nOepP7Q+Z2K8\n634oIiK+QeFYRERExEtf/PQF87fPp0qRKvSZ2ocEm+B2SSIiKbrWpFpyNXWrFhEREfHCzM0zeWzG\nY6wcuJIy+cvQckxL7i93Px89+JHbpYmIizJzt2p/o27VIiIiIi777cBv9Avrx5TuU6hcuDK5sudi\nSrcpTP1rKj+s+cHt8kREJA1kd7sAERERkcws6lQUbce15etWX1OvfL1LrxfLW4yZQTNpPLwxtxS5\nhRZVWrhYpYiI3Cy1HIuIiIik4EzMGdqOa8ugewfRtUbXq96vVqwaE7pMIGhyEH8e/tOFCkVEJK1o\nzLGIiIhIMuIT4uk8sTNF8hRhWLth15zYZuS6kby15C0iH42kZL6SGViliLitcuXK7Nq1y+0ysoRK\nlSqxc+fOq15PqzHHCsciIiIiyXhx3ous2b+Gub3nkjMg53W3fz3idSJ2RBDRN4Lc2XNnQIUiIgIK\nx15TOBYREZEb9d0v3/Fp5KesGriKonmKerVPgk0gaHIQACGdQ8hmNHpNRCQjaLZqERERkXQwb9s8\nBi8ezMygmV4HY4BsJhvD2w9n14ldDF40OB0rFBGR9KBwLCIiIuKx4dAGek/pTWjXUKoWrXrD++fJ\nkYewHmGM/WMso34blQ4ViohIetFSTiIiIiLAwdMHaTOuDZ8+9CmNKjVK9XFK5itJeFA4gSMCqVSo\nEk0qN0nDKkVEJL2o5VhERESyvHOx52g/vj19a/eld63eN328O0rcQUjnELpN6sbmo5vToEIREUlv\nmpBLREREsrQEm0CPST3IEZCDMR3HXHPJphv1w5of+GjlR0QOjKRY3mJpdlwREUmkCblERERE0sAb\nEW8QdSqKoe2GpmkwBniszmN0vK0jHSd05ELchTQ9toiIpC2FYxEREcmyRqwbwYQNE5jafWq6rU38\nQYsPKJ63OI+HP456s4mIZF4KxyIiIpIlLd65mJcXvEx4UDgl8pVIt/NkM9kY02kMfx7+k/eWvZdu\n5xERkZujcCwiIiJZzqYjm+g+qTvjOo/jtuK3pfv58ubIy/Qe0/nh1x8Yv358up9PRERunMKxiIiI\nZClHzh6hzbg2/Lv5v2l2S7MMO2+ZAmWY0XMGz85+lpV7VmbYeUVExDsKxyIiIpJlXIi7QMcJHely\nexcG3D0gw89fq1QtRnQYQeeJndl+bHuGn19ERFKmpZxEREQkS7DWEjwtmPNx55nQZQLZjHttBF+u\n/pKvfv6KVQNXUTh3YdfqEBHxB1rKSUREROQGvLP0HTYf3cyoDqNcDcYAT9/3NC2rtKTLxC7Exse6\nWouIiDgUjkVERMTvhfwRwrC1wwjrEUaeHHncLgeATx/6lNzZc/PUzKe0xJOISCagcCwiIiJ+bcXu\nFTw/53nCg8Ipnb+02+VcEpAtgHGdx/Fz1M98svITt8sREcnyFI5FRETEb22L3kaX0C6M7jiamiVr\nul3OVQrkKkB4UDif//Q5UzZOcbscEZEsTeFYRERE/NKxc8doHdKaNxu/yUNVH3K7nBSVL1iesB5h\nPBH+BD/v+9ntckREsiyFYxEREfE7MfExdJ7YmVa3tmJQ3UFul3NddcrW4ce2P9JhQgd2n9jtdjki\nIlmSlnISERERv2Kt5dHpj3Lk3BGmdJtCQLYAt0vy2qerPmXEuhEsH7CcgrkKul2OiIhP0FJOIiIi\nIsn4aMVHrD2wlrGdxvpUMAZ4od4LNKjQgB6TehCXEOd2OSIiWYrCsYiIiPiNSX9O4sufv2RGzxnk\nz5nf7XJumDGGLx75griEOJ6f87yWeBIRyUAKxyIiIuIXVu9bzaCZg5jeYzrlCpZzu5xUyxGQg9Cu\noSzauYgvVn/hdjkiIlmGwrGIiIj4vF3Hd9FxQkeGtRvG3WXudrucm1YodyFmBs3kg+UfEL453O1y\nRESyBIVjERER8Wknzp+gdUhrXmrwEm2rt3W7nDRTuXBlpnSfQv+w/qw7sM7tckRE/J7CsYiIiPis\nuIQ4uk/qTpNKTXj2/mfdLifN1Stfj69bfU27ce3Yd3Kf2+WIiPg1hWMRERHxSdZanpn1DMYYPn/k\nc4y56VU8MqWuNboy6N5BtB3XltMxp90uR0TEb2mdYxEREfFJ/131X4avG54l1gS21jJg+gCiz0X7\n3NrNIiLpTesci4iISJY1fdN0Pln1CeFB4X4fjMH5xe+7Nt9x8sJJXpr/ktvliIj4JYVjERER8Sm/\n7v+VgdMHMq37NCoWquh2ORkmZ0BOJnebzMwtM/n2l2/dLkdExO9kunBsjClijJlnjNlkjJlrjCmU\nzDYVjTG/GGN+Ncb8YYx5wo1aRUREJGPtPbmX9uPb823rb6lbrq7b5WS4onmKEh4UzpDFQ5i7da7b\n5YiI+JVMN+bYGPMhcNRa+5Ex5mWgiLX2lSu2yY5Te6wxJi+wAahvrT2QzPE05lhERMQPnI45TaPh\njehZsycvPZC1uxYv27WMzhM7E9E3gpola7pdjoiIq/x5zHF7YKTn+Uigw5UbWGvjrLWxnh/zAP45\nPaWIiIgAEJ8QT9DkIOqUqcO/GvzL7XJc16hSIz596FPajmvLwdMH3S5HRMQvZMZwXNJaexDA0xJc\nIrmNjDHljTG/AbuAD5NrNRYRERH/8OK8FzkTe4ZvWn/jt0s23ajetXrTt3Zf2o1vx7nYc26XIyLi\n87K7cVJjzHygVNKXAAu87u0xrLV7gdrGmNJAmDFmkrX2cHLbDhky5NLzwMBAAgMDU1G1iIiIuOHr\nn79mzrY5rBywkhwBOdwuJ1MZ3GQwW6K3EDwtmAldJpDNZMZ2DxGRtLV48WIWL16c5sfNjGOONwKB\n1tqDnuC7yFp7+3X2GQaEW2unJPOexhyLiIj4qDlb59A/rD8rBqygSpEqbpeTKZ2PO0+LUS1oXKkx\n7zd/3+1yREQynD+POZ4O9PM87wuEXbmBMaacMSa353kR4AFgU0YVKCIiIunvj4N/EDw1mMndJisY\nX0Pu7LmZ2n0qEzdMZPja4W6XIyLiszJjOP4QeNAYswloAXwAYIypY4z53rPN7cBPxpi1wCLgI2vt\nBleqFRERkTR34PQB2oxrw+cPf06DCg3cLifTK5GvBOFB4byy8BUW7VjkdjkiIj4p03WrTmvqVi0i\nIuJbzsaeJXBEIG2rteWNJm+4XY5PidgRQc/JPVnabynVi1d3uxwRkQyRVt2qFY5FREQk00iwCXQN\n7Uq+HPkY2WGkZqZOheFrh/PesveIfDSS4nmLu12OiEi68+cxxyIiIpJFvbrwVQ6fOcwPbX9QME6l\n/nf3p+sdXekwvgMX4i64XY6IiM9Qy7GIiIhkCj/++iMfrviQyIGRFMtbzO1yfFqCTaD7pO7kDMjJ\nmI5j9EWDiPg1tRyLiIiI31i4fSGvRbzGzKCZCsZpIJvJxqgOo9gavZW3l7ztdjkiIj5B4VhERERc\ntfHwRoKmBDGxy0SqFavmdjl+I0+OPIT1CGP4uuGM/X2s2+WIiGR6CsciIiLimsNnDtNmXBs+avER\nTSo3cbscv1M6f2nCg8J5Ye4LLN+93O1yREQyNYVjERERccX5uPN0mNCBnjV70veuvm6X47dqlqzJ\n6I6j6TKxC1ujt7pdjohIpqUJuURERCTDWWsJmhKEtZaQziFkM/q+Pr198/M3fP7T56wauIoieYq4\nXY6ISJrRhFwiIiLiswYvHszO4zsZ3n64gnEGGVR3EK1ubUWniZ2IiY9xuxwRkUxH/xqJiIhIhhr1\n2yjG/D6GsB5h5MmRx+1yspSPH/yYgrkK8mT4k6hnnYjI5RSORUREJMMs3bWUf83/F+FB4ZTMV9Lt\ncrKcgGwBjO00lnUH1vHhig/dLkdEJFNROBYREZEMseXoFrqFdmNsp7HcUeIOt8vJsvLnzM+MnjP4\n+uevCd0Q6nY5IiKZhsKxiIiIpLvoc9G0DmnNO03foUWVFm6Xk+WVK1iOsB5hPDXrKX7a+5Pb5YiI\nZAoKxyIiIpKuYuJj6DShE+2rt+exOo+5XY543F3mboa1G0bHCR3ZeXyn2+WIiLhOSzmJiIhIurHW\n0j+sPycunGByt8mamToT+jzyc3749QdWDFhBodyF3C5HROSGaSknERERyfTeX/Y+6w+tZ0zHMQrG\nmdSz9z9Lk0pN6DapG7HxsW6XIyLiGv0rJSIiIuliwvoJfP/r98zoOYN8OfO5XY6kwBjD5498TjaT\njWdmP6MlnkQky1I4FhERkTS3as8qnpn9DDN6zqBMgTJulyPXkT1bdiZ0mcDKPSv5b+R/3S5HRMQV\nCsciIiKSpnYc20GniZ0Y0WEEtUrVcrsc8VLBXAUJDwrnP6v+Q9hfYW6XIyKS4RSORUREJM0cP3+c\n1iGtea3Ra7S6tZXb5cgNqlioItO6T+PRGY/y6/5f3S5HRCRDKRyLiIhImoiNj6VraFcerPIgT9/3\ntNvlSCrVLVeX79p8R/vx7dl7cq/b5YiIZBiFYxEREblp1lr+Puvv5ArIxacPfep2OXKTOt3eiWfu\ne4Y2IW04HXPa7XJERDKE1jkWERGRm/bJyk8Y8/sYlvVfRoFcBdwuJ13t2gVbtkDp0lCmDBQtCuam\nV9fMfKy1PD7jcQ6cOcC07tMIyBbgdkkiIslKq3WOFY5FRETkpkzdOJVnZj/DqoGrqFCogtvlpIsd\nO2DSJAgNdZ7XrAkHD8L+/XD2bGJQvtajZEkI8LF8GRsfy8NjH+bOknfy2cOfuV2OiEiyFI69pHAs\nIiKSfn6J+oVHxj7CnF5zqFO2jtvlpKnt250wHBoKu3dDx47QtSsEBkL27InbnTsHBw44Qflaj+ho\nKF78+iG6dGnIlcu1y77KsXPHaDCsAU/XfZq/3/d3t8sREbmKwrGXFI5FRETSx54Te6g/tD5ftvqS\nDrd1cLucNLF1a2IL8d690KmTE4gbN748EKdGbCwcOnT9EH3wIBQocP0QXaYM5M+fNtd9PduPbeeB\nYQ8wtN0QXFScAAAgAElEQVRQzUIuIpmOwrGXFI5FRETS3qkLp2g4vCHBtYL5Z4N/ul3OTdmyJbGF\neP/+ywOxG92gExLg6NHrh+j9+536vAnRRYrc/LjolXtW0mF8BxYEL9D61SKSqSgce0nhWEREJG3F\nJcTRblw7KhaqyDetv8H44GxUmzYlBuJDh6BzZycQN2zoO+OCrYWTJ70L0efPezcuukSJa1//uD/G\n8crCV4gcGEmZAmUy7mJFRK5B4dhLCsciIiJp65lZz7Dp6CZmBs0kR0AOt8vx2saNiV2mjx5NDMQN\nGvhOIE6ts2e9Gxd97JgTkK8VoCcefIcl+6ezpP9i8uXM5/aliYgoHHtL4VhERCTtfPHTF3y75ltW\nDlhJodyF3C7nuv78M7GF+Ngx6NIlMRBny+Z2dZlPbGziLNwpPaL2W/bf35cc+U5z69pJlC2T7Zph\nOp/ys4ikM4VjLykci4iIpI2Zm2fy2IzHWDlwJZULV3a7nGRZCxs2JLYQnzzpBOIuXaB+fQXitHIu\n5gLNR7Skev56dC/64TXDdI4c3o2LLlzYP9eLFpH0p3DsJYVjERGRm/fbgd9oMboFM3rOoF75em6X\ncxlrYf36xBbiM2cSW4jvv1+BOL0cPXuUekPr8VKDl3iszmPJbmMtnDjh3bjomBjvx0XrMxWRpBSO\nvaRwLCIicnOiTkVR78d6fNLyE7rV6OZ2OYATun7/3QnDkyY5E05dDMT33acWyIyy+ehmGg9vzJhO\nY2hRpcVNHevsWe9C9IkT1x8XfXG96By+MyReRG6CwrGXFI5FRERS70zMGRqPaEzn2zvzaqNXXa3F\nWli3LrHLdGxsYiCuW1eB2C1Ldi6ha2hXFvdbzB0l7kj388XEXH9c9P79cPgwFCrkXZfuvHnTvWwR\nSUcKx15SOBYREUmd+IR4Ok/sTJE8RRjWbpgrSzZZC2vXJrYQx8c7YbhrV6hTR4E4sxi5biRvLXmL\nyEcjKZmvpNvlAM5/K0eOeNcanSuXdyG6UCH9NyeSGSkce0nhWEREJHVenPcia/avYW7vueQMyJlh\n57UW1qxJbCE2xgnDXbrAPfconGRWr0e8TsSOCCL6RpA7e263y/GatXD8uHchOjbWuxBdvLjGRYtk\nJIVjLykci4iI3LjvfvmOTyM/ZdXAVRTNUzTdz2ct/PJLYgtxQEBiC/FddykQ+4IEm0DQ5CAAQjqH\nkM34Xzo8c8a7EH3yJJQsef0QXaqUxkWLpAWFYy8pHIuIiNyYedvmETw1mOUDllO1aNV0O4+1sHp1\nYiDOlSsxENeqpUDsi87FnqPZqGa0uKUF7zR7x+1yXBMTAwcOeDcuukgR71qj8+Rx+6pEMi+FYy8p\nHIuIiHhvw6ENNB3ZlMndJtOoUqM0P35CAvz0kxOGJ01yfuG/GIjvvFOB2B8cOnOIej/WY0jgEIJr\nB7tdTqYWH+8E5OuF6AMHIHdu70J0wYL6eyRZj8KxlxSORUREvHPw9EHqDa3HO03foXet3ml23IQE\niIxMbCEuUCAxENeooV/k/dGfh/8kcEQgoV1DaVK5idvl+Dxr4dgx77p0x8d7F6KLFdO4aPEfCsde\nUjgWERG5vnOx52g6sikPV32YIYFDbvp4CQmwcqUThidPdmb5vTipVo0aN1+vZH4Lti+g15ReLOu/\njGrFqrldTpZx+rR3IfrUKWfMszfjorNnd/uqRK5N4dhLCsciIiLXlmAT6DGpBzkCcjCm45hUL9mU\nkAArVjgtxJMnQ9GiiS3Et9+exkWLT/hhzQ98vPJjVg1cRbG8xdwuR5K4cMG7cdFHjjh/l71pjc7t\nO5OUi59ROPaSwrGIiMi1vbbwNZbsWsKC4AU3vARPfDwsX+4E4ilToESJxBbi225Lp4LFp7w0/yV+\n2vcT83rPI1f2XG6XIzcoLs77cdF583oXogsU0HAKSVsKx15SOBYREUnZ8LXDeXfZu0QOjKREvhJe\n7RMfD8uWJQbiUqUSW4irqfesXCHBJtBlYhcK5CrAiPYjUt0zQTI3ayE62rsu3dZ6Py5a/7mINxSO\nvaRwLCIikrxFOxbRY3IPlvRbwm3Fr93MGxcHS5cmBuJy5RJbiG+9NYMKFp91NvYsTUY0oX319rze\n+HW3yxGXnTrlXYg+c8a7cdElS2pcdFancOwlhWMREZGrbTqyicYjGjOu8zia3dIs2W3i4mDxYmdS\nralToXz5xEBcNf2WPxY/tf/UfuoNrceHLT6kR80ebpcjPuD8ee/GRR896rQyXy9Ely6tcdH+SuHY\nSwrHIiIilzty9gj1h9bn/xr+HwPuHnDZe3FxsGiR00I8bRpUqpQYiKtUcalg8Ru/H/ydFqNaMK3H\nNBpUaOB2OeIn4uLg0CHvxkXnz+/9uGjxHQrHXlI4FhERSXQh7gItRregYYWG/LvFvwGIjYWICCcQ\nh4U5IbhrV+jcGW65xeWCxe/M2jKLgdMHsmLACqoU0TcuknESErwfF22MdyG6aFGNi84MFI69pHAs\nIiLisNYSPC2Y83HnGd1uAosXZbsUiKtWTWwhrlTJ7UrF3325+ku++vkrVg1cReHchd0uR+Qy1no/\nLvrsWae7tjfjogMC3L4y/6Vw7CWFYxEREcfgiLcZ/+tM7vtzMbPC8lC9emILccWKblcnWc1zs59j\nw+ENzO41mxwBOdwuRyRVzp3zblx0dDQUL+7duOhcWvHshikce0nhWEREsrILF2D+fPhodggrcr/K\nPb9G0qt9aTp3hgoV3K5OsrL4hHjaj29Pmfxl+L7t91riSfxabKx346IPHnTGO3vTpTt/frevKvNQ\nOPaSwrGIiGQ1Fy7AvHnOGOLwcKjQYAXb7+vItI4RNL+zptvliVxy6sIpGg1vRK87e/GvB/7ldjki\nrktIcGbf9qZLd0CAdyG6SBH/HxetcOwlhWMREckKzp+HuXOdZZfCw6FWLWf8cJ0Ht9F5ZkNGtB/B\nQ1UfcrtMkavsPbmXej/W43+P/I9Ot3dyuxwRn2AtnDzpXYg+f967cdElSvjuuGiFYy8pHIuIiL86\nd84JxKGhMGsW1K7tjCHu1Mn5RefYuWPUH1qf5+5/jkF1B7ldrkiK1kSt4eGxDzMraBZ1y9V1uxwR\nv3L2rHfjoo8dcwKyN+Oic+Z0+6oup3DsJYVjERHxJ+fOwezZTiCePRvuucdpIe7UyfmF5aKY+Bge\nHvMwd5W+i08f+tS9gkW8FPZXGE/NeopVA1dRsZBmiBPJaLGxzpjn64XoQ4egYEHvunTny5cxtSsc\ne0nhWEREfN3Zs07L8KRJMGcO1KnjtBB37AilSl29vbWWR6c/ypFzR5jSbQoB2Xy0n5xkOZ+u+pQR\n60awfMByCuYq6HY5IpKMhAQ4cuT6IToqymlh9iZEFy58c+OiFY69pHAs4t+Onz/Ot798y/P1nid3\n9txulyOSZs6ccQJxaKjTdfq++xIDcYkS1973w+UfMmHDBJb2X0r+nJrOVHyHtZZBMwex+8Rupvec\nTvZs2d0uSURSyVo4fty7cdExMd6F6BIlIFu2q8+lcOwlhWMR/3Uu9hwPj32Y3Sd2c1vx25jafaoC\nsvi006dh5kynhXjePLj//sRAXLy4d8eY9OckXpj7ApEDIylXsFz6FiySDmLjY2kd0ppqxarxxSNf\naIknkSzgzJlrh+eLY6aPH4eSJa8OzW+/rXDsFYVjEf8UlxBH19Cu5MmehxEdRtB3Wl+iz0Uzrfs0\n8uTI43Z5Il47dcoJxKGhsGAB1K/vBOIOHaBYsRs71up9q2kd0pp5vedxd5m706dgkQxw4vwJGgxr\nwBN1nuDZ+591uxwRySRiYpIfF61w7CWFYxH/Y63lsRmPsefkHmb0nEHOgJzEJcTRd1pfDp05RFiP\nMPLmyOt2mSIpOnUKZsxwAnFEBDzwgDOpVocOULRo6o656/guGgxrwLetv6Vt9bZpW7CIC3Ye30mD\noQ34vu33tKnWxu1yRCQTU7dqLykci/ifVxe+ysIdC1kYvPCy8ZTxCfH0D+vP3pN7mdFzBvlyZtAU\niSJeOHny8kDcqJHTQty+PRQpcnPHPnH+BA8Me4DH7nmM5+o9lzYFi2QCkXsjaTuuLfP7zOeu0ne5\nXY6IZFIKx15SOBbxL59Ffsa3v3zL8gHLKZ736kGY8QnxPDrjUXYc20F4ULgmIxJXnTgB06c7gXjx\nYmjSxAnE7do5M3OmhbiEONqEtOFvRf7Gl62+1PhM8TuhG0L557x/EvloJGULlHW7HBHJhBSOvaRw\nLOI/xv4+lv9b+H8sH7D8mmtgJtgEHp/xOJuPbmZm0EwK5CqQgVVKVnf8OISFOZNqLVkCgYGJgbhQ\nobQ9l7WWp2Y+xc4TO5nRc4Zm9hW/9e9l/2bSxkks7bdUvYJE5CoKx15SOBbxD3O2zqHftH4sDF5I\njZI1rrt9gk1gUPgg1h9ez+xes7VepqSrY8ecQBwaCsuWQbNmTiBu0ybtA3FS/131X4avG641YcXv\nWWsZMH0A0eeitXa3iFxF4dhLCscivu/imLPpPaZTv0J9r/dLsAk8Petp1h5Yy5xecyiUOx1TimQ5\n0dEwbZoTiFeuhObNnUm12rSBghmQU6dvms6gmYNYNXDVNXtSiPiLmPgYHhrzEPeUvof/PPQft8sR\nkUxE4dhLCscivm3j4Y00HdmUYe2H0erWVje8v7WWZ2c/y+qo1cztPZfCudNooKdkSUePJgbiVaug\nRQunhbh1ayiQgb33f93/Kw+NeYhZQbOoW65uxp1YxGXR56JpMLQBz9d7nifvfdLtckQkk1A49pLC\nsYjv2nNiDw2HN+Tdpu/Sp3afq96Pi3Nm/V20CMqWhVtvdR6VKkH2JEMvrbW8MPcFVuxZwbze8yiS\n5yanBpYs5cgRmDrVCcQ//QQtWzqBuFUryO/CfG97T+6l/tD6fPbQZ3S+o3PGFyDisq3RW2k4rCEj\nO4zkoaoPuV2OiGQCCsdeUjgW8U1Hzx6l4fCGPHbPY/yj/j8uvW6tE1BCQmDiRCcIP/wwHD4MW7Y4\njwMHoGLFxLB8661Qtaol9OSLrI1ezPzg+RTNk8rFZCVLOHwYpkxxJtVavRoeeigxEOdzcS6g0zGn\naTS8ET1r9uSlB15yrxARly3btYzOEzsT0TeCmiVrul2OiLhM4dhLCscivudMzBmaj2pOYOVAPmjx\nAQB//ukE4pAQyJkTevWCnj2hatWr9z9/HrZvTwzLW7c6f27eYtlf42WyV59Pk50LqFGl2GUBunx5\nCNAcL1nWoUNOIA4NhTVrnC9dunaFRx6BvHndrs5ZpqzjhI6UzFeSH9r+oCWbJMsb8/sY3lj0BpED\nIymVv5Tb5YiIixSOvaRwLOJbYuNjaTe+HWXyl2HwXUOZMMEQEuJ0be3ZE4KC4K67ILW54OxZy7PT\nX2XBrlkEs4AD20pcCtFHj8Itt1ze4uy0OjvBOVu2tL1Wcd+BA4mBeO1ap2W4SxcnGGeGQJzUC3Ne\n4PdDvzOn1xxyBORwuxyRTGHI4iHM3jqbxX0XkydHHrfLERGXKBx7SeFYxHck2AS6jw9m865TFJw9\nmT/XZ6dzZycQN26cduHUWsubi95k2qZpLAxeSMl8JQE4cwa2bbu6xXnLFmft2ipVkg/OZcsqOPuS\n/fsTA/G6dc5kWl27Ol2n82TS362//vlrvlj9BSsHrNSYeZEkrLX0ntqbmPgYJnSZQDaj/xmLZEUK\nx15SOBbJ/E6fhrAwy+vLX2BP3Bo6nJ5HcM88PPQQ5MqVPue01vLWkrcI/TOUiOCI63bJO306MSwn\nDc1btsCpU/C3vyUfnMuUSX0rt6SdqCiYPNkJxH/84Sy31KWLE4hz53a7umubs3UO/cP6s2LACqoU\nqeJ2OSKZzvm487QY1YLGlRrzfvP33S5HRFygcOwlhWORzCk2FubOdcYQz5oFpbr8m3N/G8fyR5dQ\nsUTGtYy9veRtxq0fR0RwBGUKlEnVMU6eTDk4nz3rhOTkgnOpUgrO6WnfPmdCrUmTYP16aNvWaSFu\n2TL9vnRJa38c/IPmo5ozrcc0GlRo4HY5IpnW4TOHqT+0Pq81eo3+d/d3uxwRyWAKx15SOBbJPBIS\nYMUKJxBPmgTVqztdpi/U+JEv1r3P8gHLKVugbIbX9f6y9xn12ygi+kak+flPnEi+m/aWLRATc3Vw\nvvhziRIKzqmxZ09iC/HGjdCunROIW7TwnUB80YHTB7j/x/v5oPkH9Lyzp9vliGR6fx35iyYjmjC+\n83ia3tLU7XJEJAMpHHtJ4VjEXdbC7787gXjcOChc2AnEPXpA5cow7a9pPDXzKZb0W8KtxW51rc4P\nl3/I0LVDiegbQfmC5TPknMeOpRyc4+OTb22+9VYoVkzBOandu50vW0JDYfPmywNxzpxuV5c6Z2PP\nEjgikLbV2vJGkzfcLkfEZ0TsiKDn5J4s7beU6sWru12OiGQQvw3HxpgiwASgErAT6GatPZHCtgWA\njcAUa+2zKWyjcCzigu3bnTAcEuJMdBUU5Mw2feedidss3bWULhO7MLvXbOqUreNesR6frPyEb3/5\nlkV9F1GhUAVXazl6NOXgbMzVwflieC6aRZZv3rUrMRBv3Qrt2zuBuFkz3w3EFyXYBLqGdiVfjnyM\n7DBSSzaJ3KDha4fz3rL3iHw0kuJ5i7tdjohkAH8Oxx8CR621HxljXgaKWGtfSWHbz4DiQLTCsYj7\nDh6EiROdQLxtmxNWevWC+vWvbun87cBvPDj6QcZ1HkfzKs3dKTgZ/131X778+UsigiOoVLiS2+Vc\nxVpnWauUgnOOHCm3OBcu7Hb1N2fHjsRAvH07dOiQGIhz+NHKRi/Pf5lVe1cxv898cmX3sb7gIpnE\n/y34P5btXsbC4IX6eySSBfhzOP4LaGKtPWiMKQ0sttbelsx2dYB/AnOAexWORdxx8iRMneoE4p9+\nciY9CgpyurSmFFi2H9tOo+GN+Oyhz+hao2vGFuyF//30P/4b+V8W9V1E5cKV3S7Ha9bCoUMpB+c8\neVIOzgULul198rZvTwzEO3dCx45OIA4M9K9AfNGPv/7Ihys+JHJgJMXyFnO7HBGflWAT6D6pOzkD\ncjKm4xj1wBDxc/4cjqOttUWT/HzUWlvsim0MEAH0BloAdRSORTLO+fMwe7YTiOfNc4JKUJATjPPm\nvfa+B08f5IFhD/DP+v9kUN1BGVJvany1+is+XvkxEX0j/GL5HGvhwIHkg/PWrZA/f8rBOX/+jK11\n2zYnDIeGOhNsderkLLsUGAjZs2dsLRlp4faFBE0JYln/ZVQrVs3tckR83rnYcwSODKRV1VYMDhzs\ndjkiko7SKhy78muGMWY+kHRRUQNY4HUvD/EUMNNau8/zTeA1b8SQIUMuPQ8MDCQwMPAGqhURcCaI\nWrzYCcRTp0Lt2k4g/u4778e5nrxwkkfGPkKfWn0ydTAG+Pt9fycgWwCBIwKJ6BtB1aJV3S7pphjj\nrLlcpgw0bnz5e9Y66wAnDcvjxjnPt22DQoWSD81Vq0K+fGlT35YtiYE4KsoJxB9/7NTqz4H4oo2H\nNxI0JYiJXSYqGIukkTw58hDWI4x6P9ajatGq9KrVy+2SRCSNLF68mMWLF6f5cTNjy/FGIDBJt+pF\n1trbr9hmDNAQSAAKADmAr621ryZzPLUci6SStbBmjROIx493glVQEHTvDuVvcELn83HnaTW2FbcX\nv50vW33pM13cfljzA+8sfYeFwQtdnU3bLQkJznrByXXT3r7d+WIkpeCcJ8+1j715c2IgPnAAOnd2\nukw3agQBARlzfZnB4TOHqTe0Hm82fpO+d/V1uxwRv7P+0HqajWzGlO5TaFixodvliEg68Odu1R/i\nTLD14fUm5PJs3xd1qxZJU5s2Jc40nZDgTKrVsyfcdtXof+/EJ8TTbVI3AkwA4zqPIyCbbyWfYWuH\n8eaiN1kYvFBLgyQRHw979yYfnHfscNZqvjI4lyoFCxY4gfjw4cRA3LBh1grEF52PO0/zUc1pWrkp\n7zZ71+1yRPzW3K1z6TutL8sHLPf5nkAicjV/DsdFgYlABWA30NVae9wzAdcT1trHr9he4ViSdfIk\nnDsHJUtqTVhv7NsHEyY4gXjfPqd1uFcvuPfem7t/1lqeDH+Sbce2MTNops/OGjpy3UhejXiVBX0W\ncHuJ26+/QxYXH++sP3xlcN671+kq3bUrNGiQNQPxRdZagqYEYa0lpHMI2Uw2t0sS8Wvf/PwNn//0\nOasGrqJIniJulyMiachvw3FaUzjOWmJjnQmiRo2COXOcX7wDAqBGDahZM/FRowYU0b+LHDsGkyc7\ngXjdOmdpnKAgaNo07ULLm4veZNaWWSzqu4gCuQqkzUFdMvq30by84GXm95lPjZI13C5HfNybi95k\n/vb5RARHkCfHdfqgi0ia+Mfcf7DuwDrm9J5DzgAfXxRdRC5ROPaSwrH/sxZ+/RVGj3a6Av/tb9Cn\nD3Tr5oyHPHAANmyA9esTHxs2OEvXXBmY77gj42fmzWhnz0J4uBOIFy2CBx90AnGrVpA7d9qe64uf\nvuCL1V+wfMBySuYrmbYHd0nIHyG8OO9F5vaey52l7nS7HPFRo34bxZDFQ4h8NNJv/m6I+IL4hHg6\nTexEsTzFGNpuqM/MfyEi16Zw7CWFY/+1Zw+MHeuE4nPnnEDcu7czttFay3NznsNay+ePfH5Vd8WE\nBGf/pGF5/Xr46y8oXToxLF8MztWrp31wzEhxcc44z5AQmD4d7rvPCcQdOzozEaeH8evH86/5/2JZ\n/2U+tVawNyasn8Dzc59nTq851C5d2+1yxMcs3bWUrqFdWdR3EXeUuMPtckSynNMxp2k8vDHdanTj\nlYYpTmsjIj5E4dhLCsf+5dQpmDLF6Ta9bp2z9mmfPvDAA4njYq21vDjvRVbsWUHu7LmpXLgyQ9sN\n9WoSqPh4Z+mapIF5/XpnVt5KlS5vaa5Z05lgKLMuM2MtREY6gXjiRLjlFicQd+vmfAGQnuZvm0/v\nqb1Z0GeB37auhm4I5ZnZzzC712zuLnO32+WIj9hydAuNhjdiTKcxtKjSwu1yRLKsfSf3UX9off7T\n8j90rdHV7XJE5CYpHHtJ4dj3xcc7rZ6jRzvdgRs3huBgaNMm+dbct5e8zeSNk1nUdxG5s+em/fj2\nFM9bnFEdRpEjIEeqaoiJcZadubJr9t69UK3a5V2za9aEypUhm0tz62zY4ATikBDn/vTqBT16OEE+\nI/y872dah7TOEktmTNk4hUEzBzEraBZ1ytZxuxzJ5I6ePUr9ofX5V4N/8Vidx9wuRyTLW3dgHQ+O\nfpDwnuHcX/5+t8sRkZugcOwlhWPf9dtvTiAOCXHW1O3Txwl5JUqkvM/nkZ/z1c9fsaz/MkrlLwU4\nS6V0mtCJPDnyMK7zuDSdgOPsWdi48eqW5uhoZ/zylROBlS2bPjNn79rlrEMcEuKcu2dPp5W4du2M\nnan7ryN/0XRkU75v8z1tq7fNuBO7KOyvMB4Pf5zwnuHULVfX7XIkk4qJj+HB0Q9yX9n7+Ljlx26X\nIyIe4ZvDeXzG46wcuNLvhgCJZCUKx15SOPYtUVFOwBs92plJuU8f5+HN+rrD1g7jrSVvsaz/MioW\nqnjZexfiLtB9UnfibTyhXUPJnT19BxCfOOGE5SsnArtw4epJwGrWvHbgT8mRI85asSEhTkDv3NkJ\nxI0audNqvffkXhoOa8iQwCH0u6tfxhfgohmbZvDojEeZ3mO6Wh/kKtZa+of158SFE0zuNllLNolk\nMp9Hfs4Pv/7AigErKJQ7nSbiEJF0pXDsJYXjzO/MGZg2zRlHvHq1M0lUcLDTfdrbkBe6IZTn5jzH\n4n6LqVasWrLbxMbH0mtKL05cOMG07tNcWTrl8OHLA/PF5zlzXh2Ya9S4erKs06chLMwJxMuXOzNM\nBwXBQw85x3BL9LloGg9vTHDtYF564CX3CnHRrC2z6DetH2E9wqhfob7b5Ugm8t7S95j611SW9FtC\nvpz53C5HRK5greXpWU+z9dhWwnuGp3oIloi4R+HYS1khHMfGwqxZTrg8eRLuust53H23Mx42M04Y\nFR8Pixc7LcRhYVC/vhOI27WDvHlv7Fizt8ymX1g/5vWed92Zg+MS4ug3rR9Rp6KY0XNGpvhF1Vqn\nxfzKrtl//uksRXUxLO/d63zODRs6gbh9+8yx7NTZ2LM8OPpB6pevz8cPfpyll8WYs3UOwVODmdp9\nKg9UfMDtciQTmLB+Ai8teInIgZGUKVDG7XJEJAVxCXG0HdeWSoUq8U3rb7L0v2Uivkjh2Ev+HI5/\n+w1GjHBaEatVg379oEwZZxbni499+5xwdffdiYH5zjshn0uZcMMGJxCPHet0Je7Txxkfm9rZk5fu\nWkqXiV2Y3nM69crX82qf+IR4HpvxGFuitzAzaCYFcxVM3cnTWUKCM5b4YlguXNiZnTs1XbDTS2x8\nLB0ndKRY3mIMbz9c3UWBedvm0XtKbyZ3m0yjSo3cLkdctGrPKtqPb8+C4AXUKlXL7XJE5DpOXjhJ\nw2EN6XdXP/5R/x9ulyMiN0Dh2Ev+Fo4PH3bC8IgRzsRLwcHQt2/KMxGfOgW//+4E5bVrnT///BMq\nVkwMzBdDc8mS6VPzwYMwbpwTig8ccNYi7tPHaQ29Gb9E/UKrsa0Y13kczas0v6F9E2wCf5/5d9Ye\nWMuc3nMonLvwzRWTBSXYBPpN60f0uWimdp+qbmhJLNy+kJ6TezKx60QCKwe6XY64YMexHTQY1oCh\n7YbS6tZWbpcjIl7afWI39YfW5+tWX9P+tvZulyMiXlI49pI/hOOYGKc77YgRTlfkdu2cVuLAwNRN\nvBQbC3/9dXlgXrfOWfbnysBcpUrqznHuHEyf7nT1XrHCqTk4GJo2hYDrLzd8XRsObaD5qOZ81+a7\nVP/jZa3l+TnPs2LPCub1mUfRPEVvvrAs5MV5L7Jq7yrm95lP3hw32Bc+C1i0YxHdJ3VnfJfxNLul\nmRdJ4f8AACAASURBVNvlSAY6fv44DYY24Km6T/H0fU+7XY6I3KCf9/1Mq5BWzO09l3vK3ON2OSLi\nBYVjL/lyOF63LrHb9G23OYG4SxcomA69gK2F3buvDszR0VCr1uWhuWZNyJXr6mMkJMCyZU4L8ZQp\ncO+9Tgtxx45pOzZ2+7HtNB7emA9bfEivWr1u6ljWWl5e8DJzt81lQZ8FlMiXifosZ2Ifr/iYkb+N\nZGn/pfpS4RqW7FxC19CuhHQOoUWVFm6XIxkgNj6WViGtuKP4HXz+yOdulyMiqTRl4xSem/Mcqwau\nonzB8m6XIyLXoXDspZsNx23bOi2d994Ldeo4f6bnmM9DhxK7TR875nSZDg5Oudt0Uudiz5HNZCNX\n9mSSaypFRztjm5MG5i1b4NZbEwPz7bc7MyePGQMFCjj1BgVBuXJpVsYl+07uo9HwRrz8wMs8ce8T\naXJMay2DFw9m8sbJLOizQJPmXMeIdSMYsngIywcs1y8MXli2axmdJ3ZmTKcxtPxbS7fLkXRkreWJ\n8CeIOhVFWI8wArKlQTcZEXHNRys+IuSPEJYPWE7+nJlgBkwRSZHCsZduNhzv2AG//JL4WLPGWV4n\naViuUweKFUt9jVd2m27f3mklbtLE+y7Nx84do9moZuQMyMmcXnMokqdI6gu6jvPnnYm1LrYyr18P\n99zjhOLatSG9Jng8fOYwTUY0od9d/dJluaB3l77L6N9HszB4oUJfCmZsmsHj4Y+zuO9iqhev7nY5\nPmPlnpV0GN+BkR1G8sitj7hdjqSTT1Z+wpjfx7Cs/zIK5CrgdjkicpOstTw+43EOnDnAtO7T9IWX\nSCamcOyltO5WnZAA27dfHpjXrnXC8cWwfO+9Tlgsco18am1it+lx45zW14vdpgvc4O9Upy6c4sHR\nD1KvfD0MhiW7ljC/z3yK5b2JxJ7JnDh/gqYjm/JI1Ud4r/l76Xaej1d8zLdrviUiOIJKhSul23l8\n0fLdy+k0oRMzg2ZSt1xdt8vxOZF7I2k3rh3D2g+jTbU2bpcjaWzqxqk8M/sZVg1cRYVCFdwuR0TS\nSGx8LI+MfYSaJWvy2cOfuV2OiKRA4dhLGTHmOCHB6Wp8sWX5YmAuVer/2bvv+Kqrw//j75MBAdko\niKICLkTEQbWAKGGvhISwkhBAhGodqJQWtdWKWqsoXwviQmQFSEKAACFhBgiiAuJAK1pELUMZIhvC\nyDi/P6D+UEFCcnPPHa/n45FHk9zPPZ93+nlczDvnc8/5/2X5f4X52LGT2xhNniwdOPD/b5u+8sqS\nnTsvP0+dp3fWdRdepze6viFJenzZ41qwaYGW9luq2pVqe+4HdSQvP08dp3XUTbVv0iudXynzvQdf\nWfuKXl79spb1X6Yra5TwwgSYf+/6t9pNbadp3aep/ZXtXcfxWx98/4GiU6M1Pnq8ul3bzXUceMiH\n2z9U5+mdtajvIjW9pKnrOAA8bP+x/Wo+obkevPVBPXDbA67jADgDynExuVqQq7BQ2rjx/5flDz88\n+d7d0FApNvb8b5s+k2MFx9QttZsurnSxJsdO/mmPWWutnl75tGZsmKFl/ZfpksqXeOaHcuB4wXHF\npMXo4koXa2LMRK/tozvuw3H6x6p/KKdfTtDfPrx5/2a1nNhSozqMUnzjeNdx/N6H2z9U15SuerPr\nm+p+XXfXcVBK2w5sU/MJzfVql1cV2zDWdRwAZeTbfd/q9om3sz0b4KMox8XkS6tVFxSc3EapQoXS\nj5VfmK8e6T0UERahlB4pCgsJ+9Uxz696XhPXT9Sy/st0edXLS39SLysoKlD8rHhZWc3oOeOMP2NZ\nmvTJJD2x4gktSVqi62td79Vz+4ofjvyglhNbashtQzTk90NcxwkYH+/4WF2md9FrXV5Tj0Y9XMdB\nCR06fkgtJ7VU/yb9NazFMNdxAJSx/60fkdM/R01qN3EdB8BpPFWOvTMN58fW71yvIlvkkbHCwjxT\njAuKCtQ3o6+srKbFTTtraXz8jsf1wK0PqNXkVvrvvv+W/sReVGSLNDhzsA6dOKSUuDOX/7I28OaB\nerHdi2o3tZ0+3fmp18/v2qHjh9RlehfFN46nGHvYLXVu0aKkRXpgwQNK35DuOg5KoKCoQH1m9VHz\nus31p+Z/ch0HgBe0uKyFxnQao+jUaO04tMN1HABlwPuNw4/8bw/ciytdrIndJvrEKoVFtkiDMgdp\n37F9mp8wX+VCy/3m8Y80e0TlQ8ur1eRWyumfo2tqXuOlpCVnrdUjix7R13u/1uKkxR7dmup89W3S\nV+VCy6njtI7KSszS7y75nbMs3nS84Li6z+iupnWa6unIp13HCUg3XXyTlvRboo7TOqrIFnHLup8Z\numioCooKNLbz2DJfBwGA70i4IUFf7/1a3dK6aeVdK1UxvKLrSAA8iNuqzyEvP08xaTGqWaGmpnaf\nqvDQcA+mOz/WWt2ffb827N6ghX0X6oJyFxT7uRM/magnVzyppf2WqtFFjcowZek9ufxJZW/K1ooB\nK1Q1oqrrOJKkef+Zpz/M/4MyEzLVrG4z13HKVGFRoRJmJ6jQFiq9Z7pP/FEokH3+w+fqMLWDXmr/\nkvo26es6Doph7NqxevOjN/X+3e/7zL9RALzHWqsBcwfoSP4Rzew102vroQA4O26r9pKK4RU1P2G+\nDp04pN6zeut4wXEnOay1GrZkmD7e+bGyErPOqxhL0t03360X272otsltffoW4Zfee0mzvpylxUmL\nfeqXzpiGMZoSO0XdUrtp1ZZVruOUGWutHlr4kHbn7db0uOkUYy9oXKuxcvrnaHjOcCV/muw6Ds4h\n+6tsPf/u88pOzPapf6MAeI8xRuOjx+vHvB/1eM7jruMA8CDKcTFEhEVoTp85MjKKS4/TsYJjXs/w\n9xV/14rNK7So7yJVKV+lRGP0bdJXr3R6RR2mddCH2z/0cMLSG/fhOL3x4Rta2m+pLrrgItdxfqXz\n1Z2V0iNFcelxWvbtMtdxysQzK5/R6u9Wa178PEWERbiOEzQaXdRIy/ov01+X/VWTPpnkOg7O4tOd\nn+queXcpo0+G6lWr5zoOAIfKh5VXRu8MZfwnQ+M/Gu86DgAPoRwXU7nQcprRc4Yql6us6NRo5eXn\nee3c/1z1T83+craWJC1R9QrVSzVWr+t7aXz0eHWZ3kWrt632UMLSS/13qp5951kt7bdUdavUdR3n\nrNo1aKdZvWYpYXaCFn+92HUcj3pj3Rua+tlULey7sMR/gEHJNbywoZb1X6a/5/5dEz6e4DoOfmH7\noe2KTo3Wa11eC/i3VgAonpoVayo7MVtPrnhSOd/muI4DwAMox+chPDRc0+Om65LKl6jz9M46dPxQ\nmZ9z9JrRmrR+kpb1X+ax2dRu13ZTcvfkk4tJbF7pkTFLY/7G+Rq6eKgWJy3WlTWudB3nnFrVa6W5\n8XPVb04/zd8433Ucj5i5Yab+seofWtJviWpXqu06TtC69sJrtbz/cj298mm99dFbruPglCMnjig6\nNVp//N0f1fv63q7jAPAh19S8RjN6zlDi7ER9sfsL13EAlBLl+DyFhoRqUswkXVvzWnWc1lEHjh0o\ns3ON+3CcRq8ZrZx+OapTuY5Hx+50VSel9UhTz5k9nf61c/l/l2tQ5iDNT5jvV3sJt7ishbITszV4\n/mDN/mK26zilsuzbZXpw4YNakLhADao3cB0n6F1d82qtGLBCz616Tq+ve911nKBXWFSovhl91aR2\nEz3ekvcWAvi1VvVaaVSHUYpKidIPR35wHQdAKVCOSyDEhGhc1Dj97pLfqW1yW+09utfj55j66VQ9\n+86zyumfoyuqXeHx8SWpbYO2yuidocTZiVqwaUGZnOO3rPlujeJnxWtmr5m69dJbvX7+0rr10lu1\nOGmxHlz4oFL/neo6Tol8tP0jJcxO0MxeM3XjxTe6joNTrqxxpVYMWKEX33tRr37wqus4Qe3RnEd1\n4PgBjYsax5ZNAM6q/4391feGvopNi3WyNg0Az6Acl5AxRmM6jVHreq3Vekpr7T6y22Njz9wwU8Nz\nhmtpv6W6qsZVHhv3TO644g5lJmRq4LyBmvufuWV6rtN9tuszxaTFaHLsZLWq18pr5/W0my6+SUv7\nLdWwJcM0Zf0U13HOy6Y9mxSVGqW3ot/SnVfc6ToOfqFB9QbKvStXL69+WWPWjHEdJyiN+3Cc5n81\nX7N7zz7nnvIA8HTrp3V51ct119y7VGSLXMcBUAKU41IwxujF9i+q2zXdFDklUjsO7Sj1mFlfZenB\nhQ9qUd9Fuu6i6zyQ8tya1W2mhX0X6o9Zf9SMz2eU+fm+2vOVOk/vrLGdx6rL1V3K/HxlrXGtxlo+\nYLmeWPGE36xYuf3QdnWY1kHPtn5WsQ1jXcfBWdSrVk8rBqzQKx+8opdXv+w6TlBZ8s0SPZX7lLIT\ns1WjQg3XcQD4gRATokkxk7TlwBY9teIp13EAlECY6wD+zhijZ9s8q4iwCLWa3ErLBywv8WrLS79Z\nqrvn3a2sxCyv3+J6S51btLTfUnWc1lEnCk+o3439yuQ8Ww9sVfup7fVM5DMBtbBNwwsbasWAFWqb\n3FbHC4/rwdsedB3prPYf269O0zrpnlvu0eBbBruOg3O4otoVyh2QqzbJbVRQVKDhtw93HSngbfhh\ng5IykjS79+wyv3sHQGCpEF5B8+LnqdnbzXR1zavV/8b+riMBOA+UYw/5251/U0RYhO6cdKeWD1h+\n3ntgvrPlHSVmJGpOnzm67dLbyibkOdxQ+wYt679M7ae217GCY/pD0z94dPxdh3epXXI7DW02VINu\nGeTRsX3BVTWu0sq7VqrNlDY6XnBcw1oMcx3pV47mH1V0arTa1m+rx1o+5joOiumyqpcpd0CuWk9p\nrcKiQj1+BwtDlZVdh3cpKjVKL3d8WXdccYfrOAD8UK0LaikrMUuRkyNVr1o93roE+BFjrXWdoUwZ\nY6w3f8bXPnhNL77/onL65ejqmlcX6zlrv1ur6NRopfRIUbsG7co44bl9vfdrtU1uq7+0+IvHZkD3\nHd2nyCmRimsYp6ciA/tWo20HtqlNchsNvGmg/nrHX13H+UlBUYHiZsSpSvkqSu6erBDDuyr8zfZD\n29VmShslNUnSE3c+4TpOwDmaf1Stp7RWp6s6aUTkCNdxAPi5nG9zlJSRpFUDVxX7d0IAJWOMkbW2\n1CtnUo7LwPiPxuvplU9rab+l53zf8Pqd69VxWkdN6DZBUddEeSnhuW3ev1ltprTRA7c+UOoZ0MMn\nDqv91PZqXre5/q/D/wXFiq87Du1Qm+Q26t2ot0ZEjnD+M1trNShzkHYc3qF58fNYXMiP7Ti0Q22T\n26rP9X0C/g9N3lRkixQ/K17hoeGa1n2a89csgMAw/qPxeun9l7R60GrVrFjTdRwgYFGOi8lFOZZO\nbsX0aM6jWpS0SE1qNznjMV/s/kJtk9tqbOex6tmop5cTntu2A9vUNrmtBtw4QH+7828lGuNYwTF1\nTemq+tXqa3z0+KD6hXPX4V1qN7Wdul7dVc+3fd7pz/5YzmPK3ZyrZf2X6YJyFzjLAc/YdXiX2ia3\nVdx1cXo68umgel2Vlb8t+5tWblmpnP45igiLcB0HQAAZvnS41n6/VkuSlqh8WHnXcYCARDkuJlfl\nWJLSN6TroYUPKTsxW00vafqzx77e+7UiJ0fqhXYvKKlJkpN8xfG/Waoe1/XQM62fOa9fwvML89Vz\nZk9FhEUoJS5FoSGhZZjUN/2Y96M6TO2gVle00ssdX3ZSYl5e/bLe/vhtrRq4ir9aB5Afjvygdsnt\nFH1NtP7R5h8U5FKY9Mkk/WPVP7Rm0BpddMFFruMACDBFtkg903uqcvnKmhwzmX+vgTLgqXLMmw7L\nUO/re+vNqDfVJaWL1ny35qfvb9m/Re2S2+nvrf7u08VYkupUrqPcu3KV+VWmHs15VMX9Q0ORLdLA\neQNVUFSgqd2nBmUxlqQLK16oZf2X6f3v3tcDCx7w+r6HUz+dqtFrRmtx0mKKcYCpdUEtLR+wXFmb\nsvT4sseL/drEz6347wo9tuwxZSdmU4wBlIkQE6JpcdP0xe4v9Nyq51zHAfAbmDn2ggWbFuiuuXdp\ndu/ZurLGlbpz0p0actsQPdzsYae5zseevD3qOK2jWlzWQmM6jfnNv3paa3V/9v368scvtbDvQlUI\nr+DFpL7p4PGD6jK9ixpe2FDjosZ55Y8FCzYt0N3z7tbyAcvV6KJGZX4+uLEnb4/aTW2ntvXb6qX2\nLzEjcR42/rhRd06+U6k9UtWmfhvXcQAEuB2HdqjZhGYa2W6k4hvHu44DBBRuqy4mXyjH0skVCxNm\nJ6hq+aoadPMgv9yKZf+x/eoyvYtuqHWD3oh644yrHVtr9VjOY1qxeYVy+ueoSvkqDpL6psMnDis6\nNVqXVblME2MmKiyk7HZSW71ttWLSYpSZkKlmdZuV2XngG/Ye3asOUzvojsvvcHb7vr/5Me9HNXu7\nmf56x1919813u44DIEh8tusztUtup7nxc9Xishau4wABg3JcTL5SjiXp3a3vav3O9R7bHsmFQ8cP\nKSo1SvWr1deEbhN+NQP6z1X/VMq/U7TyrpXcxnsGefl5ik2LVfUK1TWt+zSFh4Z7/BwbftigNslt\nNCV2ijpd1cnj48M37Tu6Tx2ndVTzus01utNoCvJvOF5wXO2mtlPLy1rq+XbPu44DIMgs2LRAgzIH\n6b2731OD6g1cxwECAuW4mHypHAeKvPw8xaTF6MKKFyo5NvmngvfqB69q9JrRWjVwlepUruM4pe86\nVnBMPdJ7qHxoeaX1TPPotkpbD2zV7RNv1wttX1DfJn09Ni78w/5j+9VpWic1rdNUY7uMZS/rM7DW\nqv/c/jpWcEwzes7g/yMATrz6wat6bd1rWj1otapFVHMdB/B7LMgFZyqGV9T8hPk6ePyg+szqoxOF\nJzRl/RS9+N6LyumfQzE+h4iwCM3pM0dWVnEz4nSs4JhHxv3fytjDmg+jGAepahHVtDhpsT7Z+Ynu\nz77f6wvA+YNn33lWX+35SsmxyRRjAM48eNuD6tCgg3qm91R+Yb7rOABOYeYYJXa84LjiZ8dr+6Ht\n2npgq1YMWKGGFzZ0Hctv5BfmK2lOkvYd3ae58XNVMbxiicc6fOKw2kxpo3YN2umfbf/pwZTwR4eO\nH1Ln6Z113YXXaVz0OErgKSn/TtFfl/1Vawav0cWVLnYdB0CQKywqVExajOpUqqO3ot/i7TBAKXBb\ndTFRjstWfmG+nlzxpPpc30c317nZdRy/U1BUoIHzBuq7g99pfsJ8VSpX6bzHOFF44qeFvsZHj+c/\nrpB0siB3Temqq2tcrfHdxgd9QX5v63vqPqO7lg9Yrsa1GruOAwCSTv5bfcekO9T3hr76y+1/cR0H\n8FuU42KiHMPXFRYV6p7592jjno1a0HfBea3wXWSLlJSRpKMFRzWz18wyXQEb/ufwicOKSolSvWr1\nzriAXrD4Zu83ajmppSbHTFbHqzq6jgMAP/Pdwe/U7O1meqXzK4q7Ls51HMAv8Z5jIECEhoRqfLfx\nalK7idpPba99R/cV63nWWj2y6BF9f+h7pcSlUIzxK5XKVVJ2Yra2Hdymu+bdpcKiQteRvG7f0X3q\nmtJVf7/z7xRjAD6pbpW6mhc/T/dm3at1369zHQcIapRjwAeEmBC91uU1Na/bXG2T22pP3p5zPuef\nq/6plVtWal78PFUIr+CFlPBHF5S7QPMT5mvn4Z3qN6efCooKXEfymhOFJ9QjvYe6XN1F9916n+s4\nAHBWTS9pqrej31bsjFhtPbDVdRwgaFGOAR9hjNG/Ov5LHa7soNZTWuuHIz+c9di3PnpLE9dP1KK+\ni9gCAudUMbyiMuMztefoHiVlJAVFQbbW6r6s+1S5fGW91P4l13EA4JxiGsZoWPNhikqJ0sHjB13H\nAYIS5RjwIcYYPd/2eXVv2F2RkyO149COXx2T8WWGRuSO0OKkxWybhWKrEF5B8+Ln6eDxg0qYnRDw\nW4eMfG+kPtn5iabHTQ/a91oD8D9Dmw1Vi8taKH5WfFD8IRPwNZRjwMcYY/R066fV94a+ajW5lbYd\n2PbTY7mbc/XHrD8qKzFLV9W4ymFK+KP/7bF9NP/oT3uUB6JZX8zSa+teK/EK8ADgijFGYzuPVaEt\n1COLHhGLygLexWrVgA/7v/f/T6+te03LByzXvqP71HFaR83oOUOt67d2HQ1+7HjBcfWe1VtGRum9\n0lUutJzrSB7zwfcfqGtKVy1JWsL2cgD81oFjB9RiYgvd2/RePfT7h1zHAXweWzkVE+UY/m7s2rEa\ntXqU8gvzNbbzWPVo1MN1JASAE4UnFD8rXvlF+ZrVa5bKh5V3HanUtuzfohYTW+jNrm8q+tpo13EA\noFQ279+sFhNa6K3otxR1TZTrOIBPoxwXE+UYgWDqp1NljFFSkyTXURBA8gvzlTA7QXn5ecrok6GI\nsAjXkUrswLEDun3i7frDLX/Qw80edh0HADxizXdrFJ0araX9luqmi29yHQfwWZTjYqIcA8DZ5Rfm\nK2lOkg4cO6A5feb45bZgBUUFikqJ0pXVr9SrXV6VMaX+byMA+IyZG2Zq2JJhWjN4jS6pfInrOIBP\n8lQ5ZkEuAAhi4aHhmh43XTUq1FBMWozy8vNcRzov1loNWTBExhiN6TyGYgwg4PS6vpfu+919ik6N\n1pETR1zHAQIa5RgAglxYSJiSuyer1gW1FJ0a7VcFefSa0Xpv23ua0XOGwkLCXMcBgDLxWMvH1KR2\nEyVmJKqwqNB1HCBgUY4BAAoLCdOU2CmqW6WuuqZ09YvZicyNmRq1epSyErNUpXwV13EAoMwYYzQu\napwOHj+o4UuHu44DBCzKMQBAkhQaEqqJ3SaqfrX66jy9sw6fOOw60ll9vONjDcocpLl95uryqpe7\njgMAZa5caDnN7j1b2Zuy9eaHb7qOAwQkyjEA4CehIaF6u9vburbmteo0rZMOHT/kOtKvfHfwO8Wk\nxejNrm/q1ktvdR0HALymRoUaykrM0ojcEVr89WLXcYCAQzkGAPxMiAnRuOhxalyrsTpO66iDxw+6\njvSTwycOKzo1WkNuG8Ke3wCC0lU1rtKs3rPUb04/ff7D567jAAGFrZwAAGdUZIs0ZMEQfbTjIy1O\nWqyqEVWd5iksKlTsjFjVvqC2xkePZ2VqAEFt+mfT9cSKJ7Rm0BrVrlTbdRzAKbZyAgCUqRATole7\nvKrbLr1N7ae21/5j+53m+fOSPysvP09vdH2DYgwg6PVt0lcDbhygbmnddDT/qOs4QEBg5hgA8Jus\ntfrT4j9p1dZVWtJviWpUqOH1DK+ve11jPxir9+9+X9UrVPf6+QHAF1lrlTQnSfmF+UrrmaYQw7wX\nghMzxwAArzDG6OWOLyuyXqTaJbfTnrw9Xj3/oq8X6dl3nlV2YjbFGABOY4zRhG4TtP3Qdj2x/AnX\ncQC/RzkGAJyTMUYvtX9J7Ru0V9vktvox70evnPffu/6t/nP6a3bv2WpQvYFXzgkA/iQiLEJz+sxR\n+oZ0Tfpkkus4gF+jHAMAisUYoxfavaCuV3dVmylttPvI7jI9387DOxWVGqUxncaoxWUtyvRcAODP\nLrrgImUlZumxZY9pxX9XuI4D+C3KMQCg2Iwx+kebfyi2YaxaT2mtXYd3lcl58vLz1C21mwbfPFgJ\nNySUyTkAIJA0vLChUnukKn52vDb+uNF1HMAvsSAXAKBEns59WjM2zNDyAct1caWLPTZukS1Sr5m9\ndEH4BZoSO4WVqQHgPEz6ZJKeW/Wc1gxeowsrXug6DuAVLMgFAHDqqcinlNA4QZGTI7X90HaPjft4\nzuPafWQ3exkDQAkMvHmgejXqpdi0WB0vOO46DuBXmDkGAJTK86ue16T1k7RiwApdWuXSUo319sdv\na+R7I7Vm0BrVrFjTQwkBILgU2SL1mdVH5ULLaVr3afyhEQHP6cyxOamTMaZaaQMAAPzb43c8rsG3\nDFbklEhtO7CtxOMs+3aZ/rb8b8pOzKYYA0AphJgQJccm6+u9X+uZlc+4jgP4jWKVY2PMz35LOTUV\nu1xSD2NMdlkEAwD4j+G3D9cfm/5RkVMitfXA1vN+/pe7v1TC7ASl90zXNTWvKYOEABBcKoRXUGZ8\npiatn6Tpn013HQfwC8WdOe7zy29Ya09YaydI+sqzkQAA/mhYi2EactsQRU6O1Ob9m4v9vN1Hdisq\nNUovtX9Jreq1KruAABBkaleqrazELA1dPFTvbn3XdRzA5xW3HD9rjJlljBlujIk0xlQ67bHPyyIY\nAMD/PNLsEQ1tNlSRkyP1333/PefxxwqOKXZGrBIaJ2jATQO8kBAAgkvjWo01tftU9UzvqW/2fuM6\nDuDTirUglzHmXkkfSbrt1EdTSVbSh5KqWGt7lmXI0mBBLgDwvtfXva6R743U8v7LdWWNK894jLVW\niRmJstYqpUeKQgwbKABAWXlj3Rsas3aMVg9areoVqruOA3iUpxbkKvFq1caYyjpZlB+21nYrbZDT\nxq0uaYakKyRtltTbWnvgDMcVSvpUkpG0xVobe5bxKMcA4MC4D8fpuVXPaVn/Zbq65tW/evzvK/6u\npd8u1fL+y1UhvIKDhAAQXP60+E9av3O9FiUtUrnQcq7jAB7jvByfFuRWa+260gY5bbyRkvZYa180\nxjwqqbq19rEzHHfQWlulGONRjgHAkbc/fltPr3xaOf1ydO2F1/70/eRPkzUid4TWDF6jWhfUcpgQ\nAIJHYVGh4tLjVLNCTU3oNoEtnhAwvFaOjTHXSiq01n5d2pMVK5Ax/5HUylq7yxhzsaRca23DMxx3\nyFpbuRjjUY4BwKFJn0zSkyueVE7/HDW8sKHe2fKOeqb3VO5duWp0USPX8QAgqBw+cVh3TrpTva/v\nrcda/mr+CfBLnirHYcU45htJkcaYjpIKJa2z1n5U2hP/hlrW2l2SZK3daYy56CzHlTfGfCCpsW1v\n0wAAIABJREFUQNJIa+28MswEACihgTcPVIgJUdvktnqj6xu6Z/49mh43nWIMAA5UKldJ8xPmq/mE\n5rqy+pXqdX0v15EAn3HOcmytLZCUc+pDxpjbjDH3n3p4o07O7Baez0mNMUsl1T79Wzq5wNcT5zHM\n5afKc31Jy40xn1lrz700KgDA6wbcNEChIaHqPqO73uz6ptpf2d51JAAIWpdWuVSZCZlqP7W9Lq96\nuX5f9/euIwE+oVTvOTbGXCOptaRwSd9LWmytzStVIGO+lBR52m3VK6y1153jOZMkzbfWZpzhMfvU\nU0/99HVkZKQiIyNLExEAUEK7Du9S7Uq1z30gAKDMZX2VpXvm36P3B72vetXquY4DFFtubq5yc3N/\n+vrpp5/2jQW5fhrImDqS7rDWppdynJGS9lprR55tQS5jTDVJedbaE8aYCyW9JynGWvufM4zHe44B\nAACAMxizZozGfzxe7939nqpGVHUdBygR56tVG2Mu08lbo3dZa7eVNshp49aQlC7pMklbJfWy1u43\nxjSVdK+19h5jTHNJ43TyPdAhkv5lrZ18lvEoxwAAAMAZWGs1ZOEQbdq7SVkJWQoPDXcdCThvTsux\nMeZeSeUlHZZUTSdXsx5T2jBlgXIMAAAAnF1BUYGiU6N1RdUr9EbXN9jiCX7HdTluZ63NOe3r1tba\nFaUNUxYoxwAAAMBvO3j8oFpObKmBNw3U0OZDXccBzos3t3KSMWaCpIWSVltrv5d00Bjzf5IiJB2Q\ntKC0QQAAAAC4UaV8FWUlZqn5hOZqUL2BYhrGuI4EeF2xyrGkndbaWad9/YmkKpKuk7TFWvuux5MB\nAAAA8JrLq16uuX3mqktKF11W9TLdUucW15EArwop5nH/lSRjTFdjzJ8lNdfJLZbGSnq4rMIBAAAA\n8J5bL71V46LGKSYtRt8d/M51HMCriluOJUnW2mxJF0vaKOl/93TP8XQoAAAAAG7EXRenIbcNUVRK\nlA6fOOw6DuA1xS3Hzxtjphtj7pO0X9Jua23BqcfyyiYaAAAAABf+0uIvuvWSW5UwO0GFRYWu4wBe\nUazVqo0x90j6QNLvJd0m6UZJ+ZI+lVTTWturLEOWBqtVAwAAAOcvvzBfnad3VuNajTW602jXcYCz\ncrqV06kAlXSyKD9srfXZ5ewoxwAAAEDJ7D+2X80nNNeDtz6oB257wHUc4Iy8upXTmVhrD0tabow5\nVNoQAAAAAHxPtYhqyk7M1u0Tb1f96vXV5eouriMBZabEM8f+gpljAAAAoHTe3/a+YtNildM/R01q\nN3EdB/gZT80cn9dq1QAAAACCT4vLWmhMpzGKTo3WjkM7XMcBygTlGAAAAMA5JdyQoME3D1a3tG7K\ny2fDGgQebqsGAAAAUCzWWg2YO0BH8o9oZq+ZCjHMtcE9bqsGAAAA4FXGGI2PHq8f837U4zmPu44D\neBTlGAAAAECxlQ8rr4zeGcr4T4bGfzTedRzAY0q8lRMAAACA4FSzYk1lJ2brzkl3qn71+mrXoJ3r\nSECpMXMMAAAA4LxdU/Mazeg5Q4mzE/XF7i9cxwFKjXIMAAAAoERa1WulUR1GKSolSj8c+cF1HKBU\nKMcAAAAASqz/jf3V94a+ik2L1bGCY67jACXGVk4AAAAASqXIFilxdqIkKaVHCls8wavYygkAAACA\nTwgxIZoUM0lbDmzRiNwRruMAJUI5BgAAAFBqFcIraF78PE37bJqSP012HQc4b5RjAAAAAB5R64Ja\nykrM0p+X/FnvbHnHdRzgvFCOAQAAAHhMo4saKaVHinrP7K1Neza5jgMUG+UYAAAAgEe1a9BOz7Z+\nVl1TumpP3h7XcYBiYbVqAAAAAGVi+NLhWvv9Wi1JWqLyYeVdx0GA8tRq1ZRjAAAAAGWiyBapZ3pP\nVS5fWZNjJsuYUvcX4FfYygkAAACATwsxIZoWN01f7P5Cz616znUc4DdRjgEAAACUmYrhFZUZn6nx\nH49X2udpruMAZ0U5BgAAAFCm6lSuo/kJ8/XQwof0/rb3XccBzohyDAAAAKDMNandRJNjJ6tHeg99\nu+9b13GAX6EcAwAAAPCKLld30d/u+JuiUqK0/9h+13GAn2G1agAAAABe9fDCh7Vh9wYt7LtQ4aHh\nruPAz7FaNQAAAAC/9HLHlxURFqH7s+8XE1nwFZRjAAAAAF4VGhKq1B6pWrd9nUa9P8p1HEAS5RgA\nAACAA5XLV1ZWYpbGrB2jjC8zXMcBKMcAAAAA3Khbpa7mxc/TvVn3at3361zHQZCjHAMAAABwpukl\nTfV29NuKnRGrrQe2uo6DIEY5BgAAAOBUTMMYDWs+TFEpUTp4/KDrOAhSbOUEAAAAwDlrre7Lvk9b\nD2xVZkKmwkLCXEeCn2ArJwAAAAABwxijsZ3HqtAW6pFFj7DFE7yOcgwAAADAJ4SHhiu9Z7pWbF6h\nsR+MdR0HQYZyDAAAAMBnVI2oquzEbL3w7gvK+irLdRwEEcoxAAAAAJ9Sr1o9ZfTJ0MB5A7V+53rX\ncRAkKMcAAAAAfE6zus30epfX1S21m7Yf2u46DoIA5RgAAACAT+p1fS/d97v7FJ0arSMnjriOgwDH\nVk4AAAAAfJa1Vndn3q29R/cqo3eGQkNCXUeCj2ErJwAAAAABzxijcVHjdPD4QQ1fOtx1HAQwyjEA\nAAAAn1YutJxm956t7E3ZevPDN13HQYAKcx0AAAAAAM6lRoUaykrMUsuJLVW/Wn11vKqj60gIMMwc\nAwAAAPALV9W4SrN6z1K/Of30+Q+fu46DAEM5BgAAAOA3Wl7eUv/q+C9Fp0Zr1+FdruMggFCOAQAA\nAPiVvk36asCNAxSTFqOj+Uddx0GAYCsnAAAAAH7HWqukOUnKL8xXWs80hRjm/YIVWzkBAAAACFrG\nGE3oNkHbD23XE8ufcB0HAYByDAAAAMAvRYRFaE6fOUrfkK5Jn0xyHQd+jq2cAAAAAPitiy64SFmJ\nWWo1uZXqVaun1vVbu44EP8XMMQAAAAC/1vDChkrtkar42fHa+ONG13HgpyjHAAAAAPxem/pt9ELb\nF9Q1pat+zPvRdRz4IcoxAAAAgIAw8OaB6tWol2LTYnW84LjrOPAzbOUEAAAAIGAU2SL1mdVH5ULL\naVr3aTKm1Dv8wMexlRMAAAAA/EKICVFybLK+3vu1nln5jOs48COUYwAAAAABpUJ4BWXGZ2rS+kma\n/tl013HgJyjHAAAAAAJO7Uq1lZWYpaGLh+rdre+6jgM/QDkGAAAAEJAa12qsqd2nqmd6T32z9xvX\nceDjKMcAAAAAAlbHqzrqqVZPqWtKV+07us91HPgwVqsGAAAAEPD+tPhPWr9zvRYlLVK50HKu48CD\nPLVaNeUYAAAAQMArLCpUXHqcalaoqQndJrDFUwBhKycAAAAAKKbQkFBNj5uu9TvXa+R7I13HgQ+i\nHAMAAAAICpXKVdL8hPl6fd3rmrlhpus48DGUYwAAAABB49IqlyozIVP3L7hfa79b6zoOfAjlGAAA\nAEBQuenimzQpZpK6z+iuzfs3u44DH0E5BgAAABB0oq6J0qO3P6qolCgdOHbAdRz4AFarBgAAABCU\nrLUasnCINu3dpOzEbIWFhLmOhBJgtWoAAAAAKAVjjEZ3Gq0QE6IhC4aISbXg5nPl2BhT3RizxBiz\n0Riz2BhT9SzHXXbq8S+MMZ8bYy73dlYAAAAA/i0sJEwzes7Qe9ve0+g1o13HgUM+V44lPSYpx1p7\nraTlkh4/y3HJkkZaaxtJuk3SD17KBwAAACCAVClfRVmJWRq1epTm/Wee6zhwxBfLcYykKac+nyIp\n9pcHGGOukxRqrV0uSdbaPGvtMe9FBAAAABBILq96ueb2mavB8wfr4x0fu44DB3yxHNey1u6SJGvt\nTkkXneGYayQdMMbMNsZ8ZIwZaYwp9RuwAQAAAASvWy+9VeOixikmLUbfHfzOdRx4mZPl2IwxSyXV\nPv1bkqykJ4o5RJiklpJukrRNUrqkuyRNOtPBI0aM+OnzyMhIRUZGnmdiAAAAAMEg7ro4fb33a0Wl\nROndu99VpXKVXEfCL+Tm5io3N9fj4/rcVk7GmC8lRVprdxljLpa0wlp73S+O+b2k5621bU59nSTp\n99baIWcYj62cAAAAABSbtVb3zL9HO4/s1Nw+cxUaEuo6En5DIG/llKmTs8CSNEDSmd4Rv05SdWNM\nzVNft5H0RdlHAwAAABDojDF6vevrOpp/VMOWDHMdB17ii+V4pKT2xpiNktpJekGSjDFNjTFvSZK1\ntkjSnyUtN8Z8eup5412EBQAAABB4wkPDNav3LC3+ZrFe++A113HgBT53W7WncVs1AAAAgJL6dt+3\nun3i7ZrQbYK6XN3FdRycQSDfVg0AAAAAPqFB9Qaa3Xu27pp7lz7b9ZnrOChDlGMAAAAA+A0tLmuh\nMZ3GKDo1WjsO7XAdB2WEcgwAAAAA55BwQ4IG3zxY3dK6KS8/z3UclAHecwwAAAAAxWCt1YC5A3Qk\n/4hm9pqpEMNcoy/gPccAAAAA4EXGGI2PHq8f837U4zmPu44DD6McAwAAAEAxlQ8rr4zeGcr4T4bG\nf8RusoEkzHUAAAAAAPAnNSvWVHZitu6cdKfqV6+vdg3auY4ED2DmGAAAAADO0zU1r9GMnjOUODtR\nX+z+wnUceADlGAAAAABKoFW9VhrVYZSiUqL0w5EfXMdBKVGOAQAAAKCE+t/YX31v6KvYtFgdKzjm\nOg5Kga2cAAAAAKAUimyREmcnyhij6XHT2eLJy9jKCQAAAAB8QIgJ0eTYydqyf4tG5I5wHQclRDkG\nAAAAgFKKCIvQ3Pi5mvbZNCV/muw6DkqAcgwAAAAAHlDrglrKSszSn5f8We9secd1HJwnyjEAAAAA\neEijixoppUeKes/srU17NrmOg/NAOQYAAAAAD2rXoJ2ebf2suqZ01Z68Pa7joJhYrRoAAAAAysDw\npcO19vu1WpK0ROXDyruOE7A8tVo15RgAAAAAykCRLVLP9J6qXL6yJsdMljGl7m84A7ZyAgAAAAAf\nFmJCNC1umr7Y/YWeW/Wc6zg4B8oxAAAAAJSRiuEVlRmfqfEfj1fa52mu4+A3UI4BAAAAoAzVqVxH\n8xPm66GFD2n1ttWu4+AsKMcAAAAAUMaa1G6iybGTFZcep2/3fes6Ds6AcgwAAAAAXtDl6i564o4n\nFJUSpf3H9ruOg19gtWoAAAAA8KKHFz6sDbs3aGHfhQoPDXcdx++xWjUAAAAA+KGXO76siLAI3Z99\nv5jI8x2UYwAAAADwotCQUKX2SNW67es06v1RruPgFMoxAAAAAHhZ5fKVlZWYpTFrxyjjywzXcSDK\nMQAAAAA4UbdKXc2Ln6d7s+7Vuu/XuY4T9CjHAAAAAOBI00ua6u3otxU7I1ZbD2x1HSeoUY4BAAAA\nwKGYhjEa1nyYolKidPD4QddxghZbOQEAAACAY9Za3Zd9n7Ye2KrMhEyFhYS5juQ32MoJAAAAAAKE\nMUZjO49VoS3U0EVDXccJSpRjAAAAAPAB4aHhSu+ZrhWbV+iVta+4jhN0KMcAAAAA4COqRlRVVmKW\nXnj3BWV9leU6TlChHAMAAACAD6lXrZ4y+mRo4LyBWr9zves4QYNyDAAAAAA+plndZnq9y+vqltpN\n2w9tdx0nKFCOAQAAAMAH9bq+l+773X2KTo3WkRNHXMcJeGzlBAAAAAA+ylqruzPv1t6je5XRO0Oh\nIaGuI/kctnICAAAAgABnjNG4qHE6ePyghi8d7jpOQKMcAwAAAIAPKxdaTrN7z1b2pmy9+eGbruME\nrDDXAQAAAAAAv61GhRrKSsxSy4ktVb9afXW8qqPrSAGHmWMAAAAA8ANX1bhKs3rPUr85/fT5D5+7\njhNwKMcAAAAA4CdaXt5S/+r4L0WnRmvX4V2u4wQUyjEAAAAA+JG+TfpqwI0DFJMWo6P5R13HCRhs\n5QQAAAAAfsZaq6Q5ScovzFdazzSFmOCd92QrJwAAAAAIUsYYTeg2QdsPbdcTy59wHScgUI4BAAAA\nwA9FhEVoTp85St+QrkmfTHIdx++xlRMAAAAA+KmLLrhIWYlZajW5lepVq6fW9Vu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IAAAE\nWUlEQVS5nZ35w3P78NzNM///zI6SK7C2ujTs+cUz7W1bR5Nc2b/guroRv8ppWv3f1Yphn3Y2ylgt\n3Kif971VdSHJOuCbJD9U1fkxxaa5hs5VkueArTRLdxc0VmMxSq7AuurSULmqqiPAkST7gNdovmbR\nuurWKLn6k6auZtp7Jb9Icv+8mWaN1zXzlSQ0Xz36wkLHauwWk6srY6ytbg1TG8eAT6rqcpL9wMfA\nE0OOncOZ4/H5jeY+1SvuBv7oYKwWbqTPu6outD/PAyeAzeMMTnMMlaskTwKvArvbJTdDj9XYjJIr\n66pbC62NT4G9A2PvGdhnXU3WonNVVZeqaqZ9/T3NvXYbJxSnGtfL1xrgAeBEkvPAw8CxtsHyf1a3\nFpOrL5NssbY6d93aqKqZgXOKD4Etw46dz+Z4fE4BG9on2K0C9tFcxbiawSsZx4GdSW5Jchuws31P\nk7HoXCW5tR1DkrXAI8DZSQbbc9fNVZLNwPvAnqq6OLDLuurWonNlXXVumFxtGNjcBfzcvj4G7Euy\nqp3l3wCc7CDmvlp0rpKsTbKifb2eJle/dBJ1f10zX1X1T1XdUVXrq2odzbMXdrcN1jHgWWurM4vO\nlbXVuWH+Dt45sPk0cK59veBzQZdVj0lVzSY5SHOj9wrgo6o6l+QwcKqqvkqyDfic5mlpu5K8XlUP\ntssy3gRO00z1H25vGtcEjJIrmqdJfpBkth37VlX9uES/yrI3TK6At4HVwGftMqhfq2qvddWtUXKF\nddWpIXN1sJ3lvwTM0C4trKqzSY7SXLy4DByo9pGgGr9RcgXsAN5IchmYBfb7N3CyhszXnCG0F+Ct\nrW6NkiusrU4NmauXk+yhqZ2/aG4tYTHngrHuJEmSJEl957JqSZIkSVLv2RxLkiRJknrP5liSJEmS\n1Hs2x5IkSZKk3rM5liRJkiT1ns2xJEmSJKn3bI4lSZIkSb1ncyxJkiRJ6j2bY0mSlpkkK5NsWuo4\nJEmaJjbHkiRNoTTeucrux4DZgWP3J7mY5ECS2zsJUJKkKbNyqQOQJEkLk+Q24EVgx1UO2VRVXw9s\nnwG+raojk45NkqRp5cyxJElTpqpmqupd4J+rHDI7b3s7cHKyUUmSNN1sjiVJWkaSbAdOzXvb5liS\npOuwOZYkaXnZVlVn5r23FTh9ZSNJug1JkqQbn82xJEnLWJI1QFXVv+32KuCppY1KkqQbj82xJEnT\na84McJKNwE/zjtnOwKwx8Dzw3YTjkiRp6tgcS5I0ZZKsTnIIuC/JoSQ3tbseB04MHPcQ8Apwc5KX\nkrwLPFNVf3cetCRJN7hU1VLHIEmSxiDJwap6b6njkCRpGjlzLEnSMpDkLuD3pY5DkqRpZXMsSdLy\n8ChwfKmDkCRpWrmsWpIkSZLUe84cS5IkSZJ6z+ZYkiRJktR7NseSJEmSpN6zOZYkSZIk9Z7NsSRJ\nkiSp92yOJUmSJEm9Z3MsSZIkSeo9m2NJkiRJUu/9BwsuTheC8PVRAAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x1133442b0>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "E_o = []\n",
+    "E_p = []\n",
+    "Lmin = 2\n",
+    "Lmax = 12\n",
+    "for L in range(Lmin,Lmax):\n",
+    "    nup = L//2\n",
+    "    heis_o = Heisenberg(L,nup,periodic=False)\n",
+    "    H = LA.LinearOperator( (heis_o.N,heis_o.N), matvec=heis_o.multiply)\n",
+    "    w,_ = LA.eigsh(H, 1, which='SA')\n",
+    "    E_o.append(w/L)\n",
+    "    heis_p = Heisenberg(L,nup,periodic=True)\n",
+    "    H = LA.LinearOperator( (heis_p.N,heis_p.N), matvec=heis_p.multiply)\n",
+    "    w,_ = LA.eigsh(H, 1, which='SA')\n",
+    "    E_p.append(w/L)\n",
+    "\n",
+    "plt.figure()\n",
+    "plt.plot(1/np.arange(Lmin,Lmax),E_o,label='open')\n",
+    "plt.plot(1/np.arange(Lmin,Lmax),E_p,label='periodic')\n",
+    "plt.xlim([1/Lmax,1/Lmin])\n",
+    "plt.title('Ground state energy per site')\n",
+    "plt.xlabel('$1/L$')\n",
+    "plt.ylabel('$E_0/L$')\n",
+    "plt.legend()\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "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": "3.4.4"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/exercises/ex06_solution/pimc.ipynb b/exercises/ex06_solution/pimc.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..2cf21bbf3fd1b00006e457affd9e1cd9b353c9da
--- /dev/null
+++ b/exercises/ex06_solution/pimc.ipynb
@@ -0,0 +1,417 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Path-integral Monte Carlo for the 1d harmonic oscillator\n",
+    "Jan Gukelberger, Andreas Hehn, Georg Winkler (2011-2016)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import numpy.random as rnd\n",
+    "import matplotlib.pyplot as plt\n",
+    "from sys import stdout\n",
+    "%matplotlib inline\n",
+    "plt.rcParams['figure.figsize'] = 16, 9"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Some definitions"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "# hbar = m = 1\n",
+    "w = 1.0\n",
+    "\n",
+    "# seed random number generator once at program start\n",
+    "rnd.seed(42)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Class for storing world-line configuration and doing updates/measurements"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "class Config:\n",
+    "    \"\"\"PIMC configuration: world-line for one particle\"\"\"\n",
+    "    def __init__(self,beta,slices):\n",
+    "        self.beta_ = float(beta)\n",
+    "        self.slices_ = float(slices)\n",
+    "        self.tau_ = self.beta_/self.slices_\n",
+    "        self.config_ = rnd.uniform(-1.,1.,slices)\n",
+    "        \n",
+    "    def potential_energy(self):\n",
+    "        \"\"\"Return the potential energy of a configuration X\"\"\"\n",
+    "        energy = 0.0\n",
+    "        for i in self.config_:\n",
+    "            energy += i**2\n",
+    "        energy /= self.slices_\n",
+    "        return 0.5*(w**2)*energy\n",
+    "\n",
+    "    def kinetic_energy(self):\n",
+    "        \"\"\"Return the kinetic energy of a configuration X\"\"\"\n",
+    "        mean_r_prime_square = 0.0;\n",
+    "        for i in range(self.config_.size):\n",
+    "            mean_r_prime_square += (self.config_[i]-self.config_[i-1])**2\n",
+    "        mean_r_prime_square /= self.slices_\n",
+    "        return 1/(2.*self.tau_) - 0.5*mean_r_prime_square/self.tau_**2\n",
+    "    \n",
+    "    def position_histogram(self, bins, value_range):\n",
+    "        \"\"\"Return histogram of positions in all time slices\"\"\"\n",
+    "        return np.histogram(self.config_,bins,range=value_range)[0]\n",
+    "\n",
+    "    def update(self,max_displacement):\n",
+    "        \"\"\"Metropolis algorithm local configuration update\"\"\"\n",
+    "        # pick a random time slice and propose a new position\n",
+    "        j = rnd.randint(0,self.config_.size)\n",
+    "        new_position_j = rnd.uniform(-max_displacement,max_displacement) + self.config_[j]\n",
+    "\n",
+    "        # periodic boundary conditions:\n",
+    "        jp1 = (j + 1)%self.config_.size\n",
+    "\n",
+    "        # see script section 7.1.4\n",
+    "        chi = np.exp(\n",
+    "                - ( (self.config_[j-1] - new_position_j)**2 + ( new_position_j - self.config_[jp1])**2\n",
+    "                    - ( (self.config_[j-1] - self.config_[j])**2 + (self.config_[j] - self.config_[jp1])**2 )\n",
+    "                  )/(2.0*self.tau_)\n",
+    "                - self.tau_*0.5*w**2*(new_position_j**2-self.config_[j]**2)\n",
+    "              )\n",
+    "              \n",
+    "        if chi >= 1 or rnd.uniform() < chi:\n",
+    "            self.config_[j] = new_position_j\n",
+    "            return True\n",
+    "        else:\n",
+    "            return False\n",
+    "        \n",
+    "    def sweep(self,max_displacement):\n",
+    "        \"\"\"One sweep of Metropolis local updates (i.e. self.slices_ update proposals)\"\"\"\n",
+    "        accepted_proposals = 0\n",
+    "        for l in range(self.config_.size):\n",
+    "            accepted_proposals += self.update(max_displacement)\n",
+    "        return accepted_proposals/self.slices_"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Binning analysis for error"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def binning_analysis(samples):\n",
+    "    \"\"\"Perform a binning analysis over samples and return an array of the error estimate at each binning level.\"\"\"\n",
+    "    minbins = 2**7 # minimum number of bins (128 still seems to be a reasonable sample size in most cases)\n",
+    "    maxlevel = int(np.log2(len(samples)//minbins))\n",
+    "    maxsamples = minbins * 2**(maxlevel)\n",
+    "    bins = np.array(samples[-maxsamples:]) # clip to power of 2 for simplicity\n",
+    "    errors = np.zeros(maxlevel+1)\n",
+    "    for k in range(maxlevel+1):\n",
+    "        errors[k] = np.std(bins)/np.sqrt(len(bins)-1.)\n",
+    "        bins = np.array([(bins[2*i]+bins[2*i+1])/2. for i in range(len(bins)//2)])\n",
+    "    return errors"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Do simulation"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Thermalization (500000 sweeps)...\n",
+      "Simulation (2097152 sweeps)\n",
+      ".....................................................................................................\n",
+      "Acceptance rate = 0.5943481349985842\n"
+     ]
+    }
+   ],
+   "source": [
+    "# simulation parameters\n",
+    "beta = 10.\n",
+    "M = int(10*beta)\n",
+    "steps = 2**21 #2**18\n",
+    "#thermal_steps = steps//8\n",
+    "thermal_steps = 500000\n",
+    "max_displacement = .5\n",
+    "# parameters for wave function measurements (x histogram)\n",
+    "histo_range = (-4.0,4.0)\n",
+    "histo_bins = 100\n",
+    "histo_samples = 64\n",
+    "\n",
+    "# initialize configuration and observables\n",
+    "c = Config(beta,M)\n",
+    "potential_energy    = np.empty(steps,dtype=float)\n",
+    "kinetic_energy      = np.empty(steps,dtype=float)\n",
+    "position_histogram  = np.zeros((histo_samples,histo_bins))\n",
+    "acc_rate = 0.\n",
+    "\n",
+    "# thermalize configuration\n",
+    "print('Thermalization ('+str(thermal_steps)+' sweeps)...')\n",
+    "for i in range(thermal_steps):\n",
+    "    c.sweep(max_displacement)\n",
+    "\n",
+    "# simulation: measures after each update sweep\n",
+    "print('Simulation ('+str(steps)+' sweeps)')\n",
+    "for i in range(steps):\n",
+    "    acc_rate += c.sweep(max_displacement)\n",
+    "\n",
+    "    # Measurements\n",
+    "    potential_energy[i] = c.potential_energy()\n",
+    "    kinetic_energy[i]   = c.kinetic_energy()\n",
+    "    position_histogram[i*histo_samples//steps] += c.position_histogram(histo_bins,histo_range)\n",
+    "\n",
+    "    # Progress marker: one . for each percent\n",
+    "    if i % (steps//100) == 0:\n",
+    "        stdout.write('.')\n",
+    "        stdout.flush()\n",
+    "\n",
+    "# If the acceptance rate is not somewhere around 0.5, max_displacement needs to be tuned.\n",
+    "acc_rate /= steps\n",
+    "print('\\nAcceptance rate = '+str(acc_rate))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Measure Observables"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "+++ Naive estimates:\n",
+      "Potential Energy = 0.247399361174 +/- 7.49110854274e-05\n",
+      "Kinetic Energy   = 0.25091824535 +/- 0.000469708232395\n",
+      "+++ Binning analysis:\n",
+      "Potential Energy = 0.247399361174 +/- 0.00161825856465\tCorrelation time: 232.83165048\n",
+      "Kinetic Energy   = 0.25091824535 +/- 0.00172176760235\tCorrelation time: 6.2183515248\n",
+      "Total Energy     = 0.498317606525 +/- 0.003340026167\n",
+      "Exact result   E = 0.500045401991\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Evaluate results\n",
+    "pot = np.mean(potential_energy)\n",
+    "kin = np.mean(kinetic_energy)\n",
+    "# naive error estimate\n",
+    "pot_error_naive = np.std(potential_energy)/np.sqrt(steps-1.)\n",
+    "kin_error_naive = np.std(kinetic_energy)/np.sqrt(steps-1)\n",
+    "# running mean\n",
+    "pot_series = np.cumsum(potential_energy)/np.arange(1,steps+1)\n",
+    "kin_series = np.cumsum(kinetic_energy)/np.arange(1,steps+1)\n",
+    "# binning analysis\n",
+    "pot_binning = binning_analysis(potential_energy)\n",
+    "kin_binning = binning_analysis(kinetic_energy)\n",
+    "pot_error = pot_binning[-1]\n",
+    "kin_error = kin_binning[-1]\n",
+    "pot_tau = .5*(pot_error**2/pot_error_naive**2 - 1.)\n",
+    "kin_tau = .5*(kin_error**2/kin_error_naive**2 - 1.)\n",
+    "print('+++ Naive estimates:')\n",
+    "print(\"Potential Energy = \" + str(pot) + \" +/- \" + str(pot_error_naive))\n",
+    "print(\"Kinetic Energy   = \" + str(kin) + \" +/- \" + str(kin_error_naive))\n",
+    "print('+++ Binning analysis:')\n",
+    "print(\"Potential Energy = \" + str(pot) + \" +/- \" + str(pot_error) + \"\\tCorrelation time: \" + str(pot_tau))\n",
+    "print(\"Kinetic Energy   = \" + str(kin) + \" +/- \" + str(kin_error) + \"\\tCorrelation time: \" + str(kin_tau))\n",
+    "# The following error estimate ignores cross-correlations between T and V.\n",
+    "# Do you have an idea how to fix that?\n",
+    "print(\"Total Energy     = \" + str(pot+kin) + \" +/- \" + str(pot_error+kin_error))\n",
+    "print('Exact result   E = ' + str(.5*w/np.tanh(.5*w*beta)))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Some figures"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {
+    "collapsed": false,
+    "scrolled": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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ixjUJAABkJXRdnjw5uu/1r8+uPc0k60pk6Lostfaoy11dvus1ADRSJUH3NZL+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\n6E0e/L74ov9OC0G33EkFSdp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bFhNGMQ/a26W///vqqpfhM1/t3KytptqK7v77S9/4hl/f\nutXPAb799oXP1dbmD7S3396Hwbi0oFutMBJ3rUE3/N/ed1/5oBu/LnL+/Gg9/r4IXZc7Ovz9dF1G\no0yb5pef/Wzp7Z57zi+To3u//vU+CEuF7+Fi7/9Nm6Rf/rKmpmIYEXSbSLGgG667SRPf7u67S3fZ\nCNs3a0W3WduF4v7v/9LvP/PMyqaIqCbo5v2gGqhUuDSgt7cw6B53XOGUQ5Voa/MDJtUi74Gk2qDb\n1iaddJJf37rVV3SToyWHIPn444Ovp067RrfW0V7vvdfPGdreXlvQlQqD7tNPR107wzbFnnPlymj9\nZz+Lgu6nPiVde23piu4OO+T/fYX6mzbNn7CrRLHrbZ2TTjzRrycruhs3SrfdVrj99ddL73hH9W3F\n8CLoNpH4tSuVdiNLdq0KIyMW06wV3RdeqH1ah5EkHGCEKkHWNmxIv7/SA+e77vIHP8UQdIFCzzzj\nr10Po/fGq2rjx0vnnCP9/veln+Phh6P1WuaNDXO85u0zmTwArrbrsuS7Jf/rv/rrp0M1U/K3y0lW\ndCdOjEaBrdX11/vBpdasqWz7+Psh7GfC3+HRRwu3jb/3QpXsf//X3x+u/b788ijoBsX29fvuK82b\n5wdWA6rR1VW6KJQmeTJ+69aoR0z8Wv2ODj8mQTJIl+tBieZA0G0ixSq6pSR3GKHbRTHNWNG9/35p\n112Zp6waa9akT08x3IodkFRyUBeUmt+RrstAob328qPyt7VFc6UG48b5kZePPrr0c7z61dF6LUH3\nzW/2y7x9JpMjt9Z68nXcOP8dHR91uZLwlhyMasOG8vv0Suy2m7R8eWXbxt8PO+zgl+F3CME2/F3S\n/v/Dyc9DD43u6+goPKYp9ndta/OvyVRyqFa9g+66ddH97e2D3+tPPSV95jPVtxPDj6DbRGoJusnt\nkl2hkppxMKpw5qwZK83NJn4y4A9/yK4dQbGKbr1Q0QUGW7/eH3i1txeGs2qCWdjX1NI7xEw68MD8\nB91ap/r5/e99BaivL9pHH3lk+emK6nGNbvDBD0brY8dWNs/o009LH/+4X99vv8EDaYWKdzz4hvdP\nCBmh/fEu2+GkTJD2Ox52mPTWt/oRqVetKt9WIG7btvoF3R/8QPrmN6P7OzsHz0P9hz9UfvII2SLo\nNpF40A07hdD9p5hk0C1XFW1ra76dSDg4+81v/PKOO7JrSytJfvFmYahB9xvf8F39iiHoAoNt2OAP\n0pIV3Wr09fnupqecUtvPjx6dv89kCLo77eSX1V7vHHz0o9F62CfPmlV+urWhzKObFO9mOXq09NJL\nhdO1pYl3k473Cggnx0MvorDPXr8+ChfnnOOX4feN/+3Wry8fdO+7zw+UVmzqJaCYcJxQ6UmiL34x\n/f4QdM86K+q1IvmTPskCUfy1mqF3HYoj6DaReNANB/+vfW3pn6m2a9Xzz/upCJpJMpx/6UvZtKMV\nxINfM1TAS1UJnnqq/M9/4AN+GotiA1cRdIHikhXdas2cWVvXZam6AY5axdatfkTk0Fum3AjWxcyZ\nU9vP1bOiG/arV13lQ+bDD/v/72p/XvLhU4qOHcIJ9ne+U1qxwq+H91FXl3T88YV/u3BSJij1O06d\nWvn1xIAUXQt/5pnSV79afvt3v9svS3VdjksOKCdJDz0UrTfDsRiKI+g2kXjQDWdjy3VhrnawjPh1\nB80iGXQb3R22lcUHS+nqkr71rcpHGmyEYgG1s7Oya8smTvQ7iWIhlqALFNfT40fvzULegm5/vz/p\nNn589L1W67gRYbCuUtKeO3mNbj2EeWzLufLKwtvx7/bRowt73qSdYL/oIr9cudK/Xvz3iF+rLJVu\nz9ixQzt5g5EnDOS6++7S5z9ffvvw/ktWYrdsSQ+68S7R4XPxn/8Z3UfQbW4E3SaSdo1uuSAb32Hs\ntltlr9Fskl1Cdtwxm3a0gnjY6+6WFiwYPOT9cCoWdKupTJQ6YE4GewCR9eulz33Or99yy/C+dt66\nLn/969JRR/kD3T32kN7zntqfq5Iuz2FAsNNOi7o017OiG+yxR+lg+cADfnn55aWfJ3Tnlkr3JPun\nf/K/T/w1k6Mul/od83YCBY3X11ddz5RwXF1pRTcedNOmJio2XRGaA0G3iaRdo1uua3KY5+7ccysL\nPM0YdOMHS/PmlZ8iaSSLX4/XDAeZaUE3nLiotFt9qQObri7pJz+Rfvzj5vh9gWZ13HHD+3pjxvjX\nPPfc4X3dRgmVoHHj/L+rr679uSr57gvdo3/yk+i16nmNbqgYz51bPFjefHN0eVTy2CD53R5vV2+v\n9Nhjg5+vr8938/zudwtf85BDCLponPjUnJUoVkBavz69m3I86Kb1NqCi29wIuk0kHnTDslzXqfCB\n3WMPf21RJa/RbOIBZrvtKhsdcqTavDlab4aDgbT304EHVvc+W73adxlM6u72o5fuvLOfcoKgCzSP\nMVGpspcAACAASURBVGP88qc/zbYd9TZcg/xtt120HvbzmzdX1u25EvEwWSw8v+1tftnXVzj4jjT4\nOzweJB59VDrgAL/+1rdG9//mN/5Y5LDDotf/3e/8uBsEXTRKrRXd5PH1ypV+qsukckGXim5zI+g2\nkXjQDYp1DR3KazSb+JfE5MnSM89k15Zmt2lTNKBIMwS/8P787nej+2q5ZjA+FUZw7bW+gr3ddv7A\n6OWXm+N3BprBZZdl+/ohrNQ6mFWzClPqNFr8INvM7/eefLL2kZ6TjjtOuvdev16uSrxlizR9eult\nkr3NJB92v/rVwpPsmzb5sRfCdkcf7cN7vIpG0EU9VVvRDcE1eZncxo3pn/9SQbezk4pus8vZLqq1\nDUfQDR/IZgq88fAyaZJ0993+zBoG27zZXzv2uc/5v1utg6XUS3h//uQnQ3uetCpKeI9OnuwPjB5+\nOJrjERjp6tXFtVbhspmsv4PqLVSqh2rlysoHVhw1Slq61K/Xq6Lb1ia97nV+feedS2+7adPgg/Xk\nsUcIEuedF923dq3/bg7hYPRoHxYmTPB/x7Vro/dHtRXd88+XPvax0u0GpOoruhMmSIsWDX7PFxu4\nLXzXSf4YJH6Z4M47U9FtdgTdJjKUoFvpzjGEh2Y6AxX/kpg40S+bqX3NJHRtCwcDd99d2/OsXeu7\nGA9VeH8O9aD7qKMG3xcOOENFV6LaD8SDw8UXZ9eO8Jkk6KabPj3anxUTrgdcsCCq5NarohtXrh2b\nN5cPuuHYJN6+Vav83+ud7/S377rLh+awTbx7dnzQyVL7i7Bv+9a3pEsvLd1uQKq+oiv592AyoPb0\npF+/Gz8uv+mmwhPu7e0crzY7gm4TSQu6lXjwwcrnxg078XhX06wlB6MaP56uS8Vs3uwPIpIjnv7o\nR9G6mfTCC6Wf59lnpT/9aejtCQdD1U5zFfeJTxROXRH89rd+OWlS9L6tdw8HoNWEkNDRIe25Z3bt\n+K//8su8BN3QPbFeQbcSp5wSrff0+ApsvUddLib+XRqv6J599uDHpfSg29Xlq7mf/az/+335y74b\ndNqJ9/g+vZKKLpepoFLVVnQlX6WNjwdz2WV+MKpKTtqHgdj2399vT9BtbgTdJlJrRfeQQyqv6E6b\n5pfz5xfev3Xr8E9PEcR3aNOmSbNmEXSL2bTJ/1+PHl34NzrzTL8Mgzo9/XTp56nXdXWhh8BQKrpj\nxqQf1Pz4x37Z3h4dGBF0MdKFysX++5fvktpIefuODt9Bwxl046/V1VW/bsuViFdYN2/2t7/0pWg+\n3WJdlw8+uPD+ULUNj7e1pe9f/vrXaJ1rdFFPtVR0x40rvN72Ix/xy2In7dOOPf74R789XZebG0G3\niSS7TZx0knTQQfV9jTvu8MvkNbo//Wnh6InDqacn6lplxo6ulHjX5XXrCq8dkaT77/fLciNXhy/t\n5BzG1apHRXfMGP97hed66qmoUrXvvn45XFUOoNmFA7rJk/3otjvskG178jAYVX9/VJXJKug+99zw\nvfbJJ0uf+Ux0O1R0w3tr++2l17++8GfCY3/7t4X3h///sA8oVt06+2zpiiv8eqnv89GjC4ND3k5u\nLlqU/Wc2b2rpDTlunL+ePFngKXXS/n/+p/B2ZycV3VaQg11UfnR1Fe7oFiyQpkyp72uEim7yDFTa\nJNnDpbtbet/7fHdaiaBbypo10tSp/mBgzZrBFYBQlSj3xRuCcHxe3lrU4xrdMWP8yJ3XXedv33tv\n9F4IB1dUdAHpxRejz0TYV+y///CGs6Q8dF3u6Ym+Y7IKujffPHyvfcMN/hrYIATdEFZXr/b75Lhy\nQaLcPmDqVOnEE/16qaCbfD+lTefSyu66y/99UT+1dF0eO9YPFpcs8JSqDMdHaT7lFL8tFd3mR9Bt\nIsmg20jJnUcjBsCoVHe3/9KZPdvfJugWt2pVFHQ3bBh8giIE3XJfvCtW+OVQg+6SJX45lIpuGLEz\njDoa78acPKgn6GIkmz49+m4MYeGWW7IZpf7aa/0yD0G3uzv7oDvcrx0XBqMq9T3+qleVfo4QdEPV\nttQ21XQzrXTk6lZRrrcVqldL1+V4b7hKjyviPxOOmRmMqvkRdJvI4sXDN1l9UqgMXnTR8L92/Gy6\nFHXLfde7OFOWtHGj7+Y9Zoxfjx8Y9fdXHnTD6MVDCbrxncO6dbU/z4wZfhkOsuJtDwfRVHQx0iWn\nhguf/QkT/Mmv4fbqV/tl3oLucF4mEf/+Xr26sUH3wQejS0GSnnvOn0ApVZX92tdKH5+E7+/4SMtJ\nEyb4Slg175m8BV0G2aq/Wiq68fdgOMleTnw+3XDZF12Xmx9Bt4n8678OvgagUfbbr/B28uBpOMUP\nMkIbli6VfvYzPw0OItu2+bOKYb7C0aOlJ5/0X/Lr11cedMMX82mn+S/8Cy6ovi3xHfby5dKjj9Z2\nTXk4yRLOyKZdn8U1uhjpQiUoi2tJ04RQlFXQXbRo6GMMBPF90Jw59XnOSsS/19asaez/6bhxg8fm\nkKSddvLf/9/+tjRzZvGfb2srPVhW8jKTNKNGVTbn+tvfHq2vX19+e4xstVR04yqdr3n69Gg9fPfQ\ndbn5EXRHoMsuk+bOLbwvfGjLzbfXCN3dhWeSw+BEUv7O5g5V6N4egu6YMdI++0i77OL/ZpVeoxu+\nmO+91y9rOcGybZuf+udPf/LD7R90kA+71QoHd6EiEA/Qodqb1zk7gUqFoFuPkc7rIXxeh3KAORSH\nHiotXFif5wpBt7u78qn66iF89510ku8V08igmzZvqOR7TgW77FL787/mNX5Zj5OS4b09aVL5GQRa\nTR4Gb2s2tVR048Jx5nvfW3q7+OczrFPRbX585Eagjo7B3WdC0M2iW01a1+XQpZagW6irq7CiG+++\nuGlT5RXd5OO17CS2bvVtGeqUGPEdhlT4HgwDRYwaJX3ve3RdxsgVv7bvgQeyP+kTgm5y5PfhUO8T\nsyHoDvfJg/B/OGfO8ATd3t7B36Hx91UYL6EWYTq4egTd8N7afXc/LkWesA+rv6FWdMNxZjWX7oUp\nHanoNj+C7jC75JLi89UecYT0v//b+DYkh++Xsg26pSq6eRtxcai2bfN/n3CNbjiomDjR3w4HLeW+\neJP/z7V0D9u61Q+GlXZwduONlT9PsqIb2j55svThD0fbzZnD9U0YueKBZCiVt3oJn9N6dR+uRvJ6\n5aFKXj4zXMJJgs5Of3K3kUE3HJAn/7/i76tS19cmHXCAdN99hc8v1edkQXiuSZPyNzBleO8SeOun\n1orua1/rl+Ha80rmJX/2WX+9+xFH+NtUdJvfEMZKRS3OPVfae2/p+OML75840X/YhmP042RF1znf\n/VTKLugWq+jW60AmD8LZ+Pb2wSOETpjgw+rLL0fblpIMwrUE3W3bfNBNHiDuums0jUQlws+H9354\nD06ZUli1Ktb1DhgJ4oEkTBOXpTAAVhajyIbvt3rtr8oNxNQo7363Hy8jBMbh6Lr8/POF98eDbzUV\n3Tlz/DzOQfiurkeFP1Tn8hh0w3t2qFVIRGqZR1eS7r/fH08deODgeaOLCbODBGk9JNFcqOhmIFQr\ng+uui84oxUd1a5RkRXfBAumzn/XrzdJ1OfyNsqgWNKtwfa7Z4KC7aZP05jf7Qbx23LH6rsu1zNcc\nui4ng261lZHwngs7qtC25AETQbf1mdFLo1bxv1vW3ZYl/52xfHk2/5/1DrqbNmUzPkVHh3T44dE0\nccMRdPfaK7rv6KOliy+Obld6/PHAA9J3vpP+WHLKu1qEiu7EifkLuuH3oQpYPz09tZ+o6ujwx02h\nK3K1Ojvz9x7NG4JuBpJB94f/n73zDreiutr4u7m90auoiBQrAirWRLEXVCyJihorGjWa2HvsLViT\nGLtRo0ZsQbHFji2AXVEBxQ8LiBjq5XL7vfP9se7K3jNn6jlz+vo9z33m9DP3zMze692r3a9vp5rv\nGAbnCtSHH+rbmRS6ra00wDhDl0tL9cAhHl0N5+cC2iBiUcl9cZ96Cth00+hCd889E19jWf5l971C\nl6MKXa70+dvf0pbPQafQ5WIxQn6TrRZq+U4u9t+sqsquRzeuhS9u25YtWBxy27d0UFpqXzheupSK\nEJrRAWEXULbc0rulVRweXRa6/fsDr71WWHaACN34SUXodnZSa89Ro5J7f0VFbo7NgkaEbhZYvZpa\nIzBmyEQmhK7To2uKmVT6oUbljjuADTdMDF0uK9NeAvHoari1EJDo0TXDdnr2DJejy2FTl1ziviL5\n3HN0fIL2xznBRBW6HC7HAojF7Cef2F9XLB7d9nZarCi0thpsrMrqd3LkojFVVZUdj27cNSXq6ylM\nNltkoqBXaam9b3r//ukJ146S5+uFmaM7c2b4Pqf5gAjd+Glv1+dMMu8Fku9FXlmZm2OzoBGhmyXM\n9j5mnkYcYT9BOD26nJ8LAEuWpP/7Ga505wxdLitLbKUh6NBlIFHomoN8VVW4HF027IYMcTcYg6pd\nskdXKQp/Z1It6uLl8Ssro1YTxx+f2ufnOqedBsydS0UvCglepJDQ5USUshf2cSMXjSk28jJdWCfu\n0GVzETEbsABNZ55wskIgCitXUupMqvDvwfNbIS14O/thC6mTikc3VSorgQULgIsvzs73C8GI0M0S\nZoiQ6eHIROVHp0fX9AZmMqyQ/9f6+sTQZZ4MCmmCSxXTGHMKXnOxpLo6XOgyC92KCncvW9BnfPON\n7nPL4cfmPiULezInT7Y/zv+zGepfiNx1F22zaXjHzZ13As88Q7dNr5KgWbHC//lcFLrdutFfpsfp\nuIVuKh6hOOAxL50Lu5no3xqHNxcAvv+etmwntbYWji3AbZhE6MZHqqHLqVBRAbz0EnDttal9jpA+\nROhmCXPSaWnRA3omJiOnR7ejQzd7z2QOJE9cy5aJR9eN+nrg7LP1fTePLlfQTEbocshwebm70OVz\n4eef3Y/DsmVa6JpGYipCt7FRG3077WR/bp11kv/cfCQTY0GmOOUU3SpKhK4dNnj9hNbllwOHHpqR\n3YlMRUXmc+d57ogrlaGjI7tC95BDaJvO+S4o/3avvdL33VE56yzgwgv1Ph92GLDFFtndp7gpFOGe\nC2Tbo1tIc3UhIocnS5gXRmtrZqotMzU1ds9tezvwwAPAtGnuhkN7e3pWq3hSX7tWcnTduP124Oab\n9f3GRh3azr/Xyy/T9owz9OuqqtyP4zffABddRMeytVULXS+PLoeWDxjgXmHTzK02J5lUhO6CBfp7\nhw2zP5cLlWbTzZtv6tuFtuLPi1cidO3w7+GXu3z99ZnZl2TIRpG4QvPoDh4MjB5NlfOzRS61upkw\ngeYpHvO//JL+ColCG9+zSbaFrhlt89NPma11IwQjQjdLOEOXM1GEihk0yJ6L29FBQrtvX3eBdOGF\nlH8Qdx4Wi9jGRu/Q5WL26F54of1+fb1dnALAk0/S9ne/Aw44gG5XV7tPog89BFx3HR3LtjYqRsKf\nFZSj++23ic+b1bJT9ejuuy9tGxq0R3ejjaJ/Tr5j5u4XiiHEAo4FnQhdO/x75GJochi8IkLSSdxC\nt6Mj+0Lvk0+AX/0qe99fzHNtNiiU8T0XyKbQddpPgwZpe0bQHHigvQhvJhGhmyXM/LuWlsx6dHv1\noqIRLFzb22mS96pqe+ONtJ0zJ979YKHb1JTo0WWPczF7dJ08/bQuHMaD+ogR+vlHH6WtV+iy6SFt\na6N2Pu+9522oLlhgf70Ts4iYOckk0wvy+eeB3Xen475qFQn4ZKsgFgqFYgi9/bb9Pi/ICAS3mwsj\ndDfeODHSIdtkw6Mbd9XlbHt0c4FcnGsLLYqno4P+p+HDgf/+N9t7UzikInRvuCG17zb76LI9NnMm\nsHw5hdy/+GJqn18oPPOMtlEzjQjdLMGeOSDzHt2SEprUWbxwflKQwTJ6dLjPD1NBlL8XIA+eU+hy\nYZbOzuDqv4VGS4u71+uuu4DFi+l2t27Axx/be7/xQN/RATz2WOL7TUO6rY3OuXHjvI+7KX7dJhEz\ndNk0EpMRugD1sayvp/Nh4sTkPqOQKBShW2htkuKGK5b/5jfUB9uPgw6yL0DlAtkMXY4zRzfbHt1s\nk4tCN9m5JFfhOhsbbVR4VfWzyapVybcHO+kk4PHHk//uigqdameOzWeeSZ/LjiIhe7aACN0sYTan\nb2nJTFshk/Z24J//BG66CVizRnt0P/2UJrxUw5TNlkVeeE2spmhqb6d2Bez1KAb22488NywuOaRs\n8mRdkRcAxoyxr3jz7zZmjHv1bFO4zpypP7+kxP1YmELLbWXdDF2OwyCpraXiWrW14l3ZfvvCEbqZ\nbj2Tb5gpCu++6//aXDT8s1GMas0a2opHNzneeMN+/7bbgCuvzM6++PG73+XmOZ8sLHR79iyc8T2b\nbLIJ8K9/UZVus/NDFLp3B3796+T3obLS3THB855fSsADDwDz54f7nsWLqUhbPpOt9BwRulmitlbf\nbm3NrEeXmToVOOccMhrMSb60FLjnntQ+O0y+j/kas6Ki6T3kAYQ9mcXAZ58BP/ygvRUsUFtb/Sd9\npWggGTbMfdB3DjIcLu8ldM3H3CZlM3S5d2/9eLLCpraWvFubbZbc+wuBrbYCTj6ZBL/bin97e/6F\nvIlBF56gaycXjf5s5OguX05bt8iVZCgmj+7RR9trAQAkKHfcMSu740tVVebPrXTCUVBeaWKCneZm\n4K23vJ+fNw947TV6XTZsaMB7TGabesYM7/cedxxwxRXhvmfWLOCWWyLtWs6RrXNehG6GWW892poi\n4rnnkg+7SAXTS1dSYu+B9+OPqX12GKHr5dE1hS57cl94IbX9yWdYoLa0BBd6qqgg44BDaUycBgML\nytJS+7F4+mk6N8y+nm6fZ3p0zf1KRejOnl1Yhk1UlKLJ78cfySB1cuONuohYvlDMxzMqXuMmj9W5\n2Fs5G6HLXNV0+XIKD+S+q8lSLB7dk07KTc9tMrzyCrBwYbb3Ihrs0Y1T6M6ZQ1FchUZbG7D11sDO\nO/u/7u237bZIpgkSukGETRkohHz1TM8TjAjdDFNWRtVv33oLWLRIP54Nj6UpSEpLqScqG1LsEfzu\nOwodjkoqQtccIFjonnlm9H3IV/i4cN9YFrpmTqwfXkLXK2ykpMTudTvoINqaQtcZmnPttVQwqm/f\nxM9L1iPL4fx+5w6/plDzPoOKavz0U+b2JS5aWoANN6TbJ59MWwlndsfrd+HHc9Wjm2kDpqUFGDuW\n5qzDDqNq8qlQLB7du+5KPsQzW5jhmub1seeewOmnZ35/UsFL6H7zTfJ1KV57jVLOCo3PPgO++CL4\ndXPmhLeN0oHX4mPY8SRstXM+9/Nx7uRzndtaZjqEWYRuhmlr0yf2zJn68WxUImXjE9AXJRssfCJ+\n8gmwzTbA9On2wkdBxOHRHTdOC91jjgn/3YVCe7u9R1tQ6DJTXe2eM+LlWfMKXTbzop2f9/zztOUI\nBWaffah9UTJwOL9fqOuzz9LWWcm3ELjiCjJYysqAq68mAx6gAl1c8TwfjfGWFqr0DgCbb06F1KSV\niTteRgxfuyJ0iZYWWoDldhVmzYtkKBaPbj7CC74AdYswcVtozWVMoWu2yBo+nGysZD8ziMcfz78U\nkm4R1Ek2ha7XmBy2a0RY4co2Wi4WjQti7lzaKkX2jLN1ZroRoZth2tqoOTxABxwg4/W88/xj+ePm\nt7+151XyJM8G6CefkEePcx/69aNeqhddFO7z4xC6Q4fqokpcfKSYaG8n8ccTWZjQZUCXu3cOoF6r\naBy6fN55FA7GmF5TFroffkhbDqNxCt0VK6JNUCZsrPqFdO28M3D44XQ+5GvfUS8+/pi2ZWVUlZN/\nh/PP1znsyf622cQUumVldL7lm9GVKV55JTFthI0EIDfz+rKRo/v00/b5w6x5kQzF4tHNR/i4DBzo\nnX6TL7AgM7tepNpyJeja6+igRdOyMorEev/91L4vU0QJ1X388dwSumedpesIAP7iNOyiLy8mZiv8\nNxV22om2fK7eemtmvz8Pzab8pr2djNaTTqLblkUXQUVFcC5CnDzyCHDNNfq+czX77rtpldEsnrBm\nTfgQsaCcqaVLgTvucH+O96WysjiFLg/wbW30G7BnlVeDg+jWjY6ZUwg2N1MLEyccunzDDcCdd+rH\nLQvYe2+63dhIx3Trrek+t3wyw3buuYc8kcnCQjdoIK+o0JXKw1YszAd4AaxfP7sn3xSF+Sp0Of//\niy9E6Poxf35iaOmmm+rbufi7vfRS8lEcyfLGGxSyyaQqdBsbM9vLXggPL9ia40a+RoS4hS6btlcy\ntVGChK6ZxnTxxcAZZ0T/jmxgisNly8jR4odbp4lM4GaTVVTYO2T4dQ2ZNi3c97BdtGyZPa0sH2Cn\nCeuCQYMy+/15aDblJ999R6vQy5bRwMYrep2dZLxm2oB1Dgpu379yJfDzz1roRiEoh9IvTIe/q7ZW\ne70LzXvnxXvv0W8O0KS+aBFVxwZowgrbhsotfLmlBdh118TXmqHLTq8GGxmNjXqgtSwtykwmTwZ2\n3z3c/rmx/vq0DfJasdAFdFGaQoAH/1697HnW5mJCPnqdTI/uypUidIPw+m3uuy93Uzg4GiFbpFpx\ndfXq7BSEFIIx5ya+bYb95hNuQtcc352h2SbvvGMXT+Zn+uG0A/KlmKH5f+27L0X4OTHnwyVL0r9P\nbriFKDu9y05HzdNP2yMqw8Dn+g47ACNHRntvrvDVV7TN9KKiCN0MscEGusgPh++99BIJm1w2Xs85\nhy7asCcmC6OgsBM/gcK/R3U1DfzduxeP0DU9qk1NwIknUsEVvh9W6K5cSYsJ5mphczNNqs5FDdOA\ncC5QnHUW/TU26omnrY3ytW++Ofz/FYbtt9ef74cZKpnL105UKiqAs8+ma8cUuuaKcT7+vy0tVIAC\noLHPWfxMoFSSIEaPTt1zmQ523x3YZZfMfZ9bTlsqBVq++QZ49VV9jgq5BXtvzQWyfBe65mKtOR/7\njYvnn6+L+Tk/EyBb0g2n0B04MPz+ZhNT6Lq12gPsv92JJ6Z3f7wwf8/ddwf+9rdEx5DTsTRjhn1R\nI8x5zDbw4sX2sOh8JNMRmiJ0M4BTPJSV0d9zz1ERqmwUwWAPSxjKy+2v9xuM3ar9usEDlNv/bnqy\nVq2i785loRtn3tyAAfb7dXV6wI8idAFaNTz4YODII+l+Swv9pg8+aH9daakOKXn5ZftzQ4cCp51G\nkyWH3zQ1Rd+XKITx6HIYUz6G8nphFsQxQ5fNFX/+f/NJKHLhIIAWSMSja6eszN/LwvnZudhaCAAm\nTaKF3Ezx17/S9sknabvxxqmNwePHUyrN5punvGtCGuB5xmyDl69Cl1PB6uq0+AnqV2++18myZcBt\nt9Hta691f59T6KZr3o6blhaqrN2zp7uwW7NGX/cjR0azadNFWRlw6ql2oTtuXGKosdNuCWPfOj/j\n1FPJNssHnN5rEbp5yHbbAQ884P08h6IyHLoMkPcmG0I3SuW2igp7j92//937tSzqgwxZ/p/NiorM\nLrtQ9dmKCmDBAvruXBa65eWUMxYHzpXAyko9wUXJI9trL2DbbfVnAPQbVlQketv9vIQlJToMmieb\nxkbtHU4HQUbrBx/oxumFJHQ7OvR1UVVFizzXX+8eumx6/nOdlhbyRHZ2An/4gwhdJ1yjwQu+5nOx\n4jJgX5TJBO+8Q9sJE2hbV5fa+cRt/pyF9YTc4Je/pK0ZCcLbbOVlJgt7dOvqKNR2333DC123sObX\nX7d/thtO50O+jL38W3kJ8yOO0LdzrRKxGbo8aFBiWDXbLdttR9swC3VcF4W54w5KZ8kHDjuMPN1M\nS0tmj1kBmYnZY/Zs4J//9H7eGa9fUqIFzfLl2QlHjDLYVVfb95ENDTdY6HqFmjBs0HNepvO5Lbag\nSWz1aqpA+/XXud1LN6j4Vlicix5miFMUL+rAgXrVjMMd2aM7Zoz9nAwrdPmYNjZm16NrrgbmY085\nNw49FFi40C50v/2WyvCzwLEs/f+efjqFsuUDbLAopRf2cs0wyRaWRQsA//mP92v4OstVoVtWFr6g\nShyw4c5zaPfu8UTVRK1DIWSGMWPoOnELXeZFinyBx8KePalF34sv2m0xr/P43XcpxN6JKWK95nGn\nyMqXsZd/K3Nx3/ytzEjJXClOxvMzjyWnnuoudNnZsP76FM0TZvxy82rnYiqLG872TzU1mV2kEqEb\nE2ZbFiduA4vZzicbBXWiFO9whnT5hQvx4DNjRrhepxzS6AYP3NxCwBlyW2g0NACXXabvl5QkL3TL\nynQhrxUr6Dxjj+5mm9lXf53i+qKLdAuCmhp6T3OznlTTGbrcrVtwcQ2z+EO+rE778c47wBNPUJ6g\nGbrs5NFH7RNi3DnS6cJZLVw8uprOTjJ6/Kpy8jgYpd1GJhkyJLMeXQ5RZK9ITU1utl0S4sWtGFW+\nVZ/lsXDUKD2fmqHFXuOiV04m/x5bbUUh/G7sv7/9vtd3vPJKYvRhNnHz6JrC3nw8V4Quw0J3xx39\nPbpVVfbCZH4UktCtq8ts+LII3QzgNrBkuzn9Bx/o20HhsE5RzAaXm9fWXGXzqsQ5eTLllQwfTmHQ\nXv2D2cDjdhsrV5L3PBdJxQi9/36aYG6/3f64ZWmh29FBg2FYr05pqR5IHn6YvH/s0XXi/Mxzz9UV\nSHv21MKEBWhjI4XRpEPofv65f8QAYA+ByXXB9O23wQM6L260tdk9ugyLiOOP132MgeyPIWFx9n8W\noavh/q3Tp3sbmR0dNAbmarXU4cPtqS3ppls3mjd4zK2qSv58yhfvlmAfN9xEYj7ABr85Hq5cSdXU\nd9vN+zz2mmtZIA0eHD5f2es79twzt6KE3Dy6Xh7s777L3H6FgYVuWRkdG7NtlGUBU6bQbRa6QeNX\ne3ti6DKQf0KXW+XV1orQzVu8VmXcTuJsV0/lkOG6OsqHZX7xC2CPPeyvde5/ZydddMOGJYaOlcZv\nXgAAIABJREFUrlqlV6u8QhPuuw+YNw+YOJEMJK/+wWzI7LmnfiyobVG2SCWE9vjjaTB0eqxNocs5\nsWEFtenRBegYs0fXiXMS7dFD97QtLdXtr9ioaGwE5s7VnvY42WQTXX3ZC65CDaRHMC1bRj2B42Do\nUOCUU+i3V4oWHZgff6TH5s6l+15Cl3OzWlqAf/9bP54voZbi0fWGhW737t7RLR0dVAPCmQKTK1RV\nZdajW19vr5BcVZW8R9fPky7kFmaO7jnn0Nbt+OXyMeWx0FykXLWK/je/cdFrgZu9fGHC91kwdnTQ\n9eomjHPFvpo/X9srbou+QPZtaBO2/3jLY3VpaaJH1zzGVVW61agXjY0017t5dPNlsZuF7m23UZqn\nWYwtE4jQjRGvEGS3wStXqgVusgmtyDNvv60L/Wy9NW3HjrW/p71dr6w5B8bVq8P3BwsK2WZRZ5Zv\nz7XKoxwyExRuG0R7O/Dll/bHTKEbNVSYPbrsjbcs7wJSzoJOStHgbHqYysr0wNTURJNltlYTTYO/\nvT3+/nm33w6cdFJ8n7dypfZS/+Y3+nHuKcf7bwpdU8T+97/un5sPQverryi/XoSuOyx0g16TywYN\nj1GZypevr7f3vO3bN/nziRfvuLCVkLvMmqUrbn/9NW3dRG1tbXw1M+LEsijCp6LCfs1fdx1FtfkJ\nHrfQ3Nde09FwtbX+NuVee+kWYO3tFOq8zz60T/ffr9+bC4sE335LYdizZpEtYnp0zd9n3XXJNpw5\nk9J+cgnTo2umnwH222FCl1ncL19O6UuTJ+vn0uFsSAcsdHfZhar0f/ghRQ5mCmXlSTUXpZSFy7O9\nF4IgCIIgCIIgCEJauBywLCueyhSWZeXFH+1q7nHHHVwL1bJmz3Z/zezZljVunGW98w69zrIs68IL\n9fuWLs3c/poAlnXuuYmPL1tGz9XXJ76e/268kbZvvJH4mgEDaHvxxd7fy39+XHmlfg2/3vl92aap\nifbr6quT/wzz9wAsa8stLauszLI23dSyHn/csg45xLLmz7esESPCf+ZFF1nWyJGWtdVW9Jm77WZZ\nvXtb1n//G7wPbvTsaVmHH25/XWtr9P81Lpy/2Q8/xPfZp55Kn7nDDql/FmBZBxxgWQ8+mPj7PvJI\n4v/x8MP29wb9mTz7rH78qKNS3/c44P1591392Lhx3mNlsbF8OV1bTH29ZVVVWdaPP1rWkiX02NZb\n5/7v1aOHZa1YkZnv2mgjy5o7V9+/9dZw84kTwLL69LGszTePd/+E9GCOe4MGWdaf/2xZgwfT2P/j\nj/qcACzr00+zu69u/OtftG9XXGFZK1cmjuW/+hXN92688IJlrbsu2QQMv+/YY2neOOww9/cOHmxZ\n331nWfvvr7+H33vyybSdNo2222/v/hkDBtD7M8FTT9G+jB9PtydOpPsbbGBZc+bo1+28s2W98kpm\n9ikMgGUdeSTdfustuv/KK5b1n/9Y1rbb0v3Jky1r8WL9+990E9lo773n/bkLF9rHtxde0PcPOSTt\n/1bKdHbSvr72mn7syiu99QHTpfli0Y8SupwiZjELZ78y8zWlpcAOOwAffUSPmaF82SwywuEsJhyS\n6hYaud9+tOUcGbe8AQ61CMoZCQp9NX+XUaPCfWam4ePPIT9vvJF6YZb2dmol8OabyYcul5dTRUre\nF8tKzJU0WbLEvwJ2Zycwdar9sVzKkYkzR5DDxPxavkShpMQertTZCdx0ExVzc15jVogAm4svdn/c\nDN98+OHcCg+W0GV3nKHL1dV0Lo8cqWsXhAlvzjZVVd7zX9w4Q5dTCetevpwK4Am5z+jR+vaSJZQi\nVV5OYZETJlAaFo+fYcbRdHL//VTvxITHejNH13wNj4uTJwP/+pf9vVyI0i2E+bDD6Dkv24jtT2fF\nakCnMh10kP4eN5Yuzdx1sngxbZcvp+P7zDN0v0cP2r9ddqGaBWvWZLYIXhi23JK2PN+tWmUPTe7T\nx24L9O4dHLrsTIsz7bRcSYH0g+cFc1+d4dzpRoRuiphC1+uka2+ngUYpne967rnAVVdlt8qdZVGe\nhhPOgXQTus7H3BLKt9+e+uAGiVKz2bkbJ54I/PAD3f7DH2ibaxc2Txqc6/Xxxzpv+cMPgxt6u01c\nbW3AeutR7lmyQrdfPyqqNHIk3bd8cnQBynX53e+8P88sbMU4c3sziVl9GIh30IzbSOrosOf8rlpF\nC0V/+xsVITMZNMj9M8zrbKed9G2zerpT7GeyQFAQpjAxi8oUO04Ry0VpGhr0Mc8HoVtZmbnzzSl0\n8yFXXUgdLpDImEKX51y2D7JtJ0ybRr1vTUyhy9czz8+AFrr33Qcccgjlqs6bRzbiOefQ+9yqhFdU\n6N/BDRa6POa+9JL9O02COnBkAt7Phgb639jOYEE4Ywbw7LP+C/fZoKkJOPNMus2Cd8UK2m+2D+vq\n7ONk377BVZedto1ZUyfXHD9umLVdGL/zNR2I0E2RKELXpLoauOQS4Prr07dvyaIUGftuxpXzMbcS\n4cOH06qk1+/BYsusnOlGt266wu4RR9Cglu0JzInp0Z01C7j0Uv3c1VfbCwf4vR8ADjyQtuagl6zQ\n5QJeu+6qv8ey/L0fY8bYe9TmMltuCTz2mL4fh5G9cCGtJsctdLnoFB8Tbif00092gx2gFhNumAaI\nGQlhCl3npJfJFdMgNtxQ3xaPrsZNxPL4+OOP9Hw+CN1MeXTXrKGx1mx5l4xHN9f6bgrBOK8BU+jy\neMJj3jbbZHbfvDDHOd7/8vLE6vqffEKPmQUghw4lL/WUKVR8q7LSXeiWl/t7Bdvb6bv5efM6dRaf\nSkfLwKjwb7ZmjX1RoKxM7y9HSeWS0DW7YpSWUnXhww6zd8BYuzbRo+tVhOyJJ8geOe44++M9e9L3\nKJV79rAbfMzMc0s8unmGaWB7nXStrYWz6uw8Od08updeSt5Es9+pCa/MRqmgXFVFF3yu9Uszhe5l\nl9knjjBVic2JkEWp+RhP5EuXRjPoeFDhMJe33iLjzq890cSJ7r3aTJy9frNJ3776dhxCd+ONqRql\nKXRTOd+4jzRXVT78cNqa1cY/+8z7/ebEwMftrrsoBYJXiM3j5Rx/cknomkaqCF2Nn9AF6Ldqbs4N\nA9SPTLUYOv102prjWFD1fjeam/V4ms3IFCE8zgVIFrotLVoomGNgNsOXeew1x2C2FTo79TV/9NHU\nym70aLIR583z/swNNkjeo2sKXZOGhvjn0VTh/7Ghgf6v666jv9JSbSOVltL/m0tC18mkSeTMMQX6\nmjX2hYbBg70XKQ49lBw9nO5osmwZ8Nxz+eHRXbuWxPlee+nHROjmGRddRNu99qILz21Ve++9cyMk\nJA6c/59T6NbUkKHGvUHdcOsVGoaxY4E5c6K9J92wwf7oo8DLL+vHd9ghnBfGbB3DLRPcPLqTJkUr\noc8TQJDXPCobbKDbTmUbM1cljkGzo4MWFExvTyptC775hrYcVsfH1+yl64fbooQZ/gYAf/yjfi6X\nPbomqQjdjg4dcVIIdHYmCq3KSt3nHKBFjVwXupWVmfHorliR+Njzz0f/nKYmWojceef425MJmcH0\n6LLIM8e8bHq7eCHSa3/4mu/TR0d9lZbq89vNXhw40F3oVlcHe3RLS4G77yZxtN12+rk1a+xjTS4I\nXZ4bmpvpfzv7bOCCC+zOIvbo5mpvcZOyMm0D1NfrcXLiRGDIEPuxsyyyJYMW73r3Bnr1yg+PbkMD\nheib9kzPnpkdd0XoxkS/fnTSVVfbJ3y+aAvFMDMHwlNPTQxd5nyQq66yhyuasNCN2hN3nXVyyyg5\n7zzgkUfcn5s5U09mfl7SIUP0bR603IRuVFgIxdXrlg3t0lLgL3+J5zNThQuUAcET9KpV5K31gyMN\nzMWbmTOBU05Jbv+c4uSQQ6L1juOJ4fHH9WN+XijnpLdoUfjvyiRmYZSorFxJ20LxCLt5dKuq7Dnx\nTU25v1CaqdDlHXdMfOy666J/DqeCzJiR3WKQQvL07Eki4ccftVAw58pMFUdzw03o8j6akVnO2zz3\nuAk4M0fXtCd79LB7dI86yr5Yy2PMJptQ0S7zs+fNA7bdVucK54LQNeeGjTbSt02hu3hx7oUue2Gm\nWbDQHT6cCmoBdqH7i19Qml6vXsGfG1TEKldwppoAdL5x/Z1MIEI3Bk4+mQYPHiTM8FV+rBAMs5df\npiILDz5Ik8uWWyZ6dHn1sKrK+yJM1qPrXETINjfc4J9jzb9NWHGeDqFbWUlhy4A9fzgqXN1Qqdyc\nXN580//5JUsoBIgrOrrB5yXn/o4aBfz978Cddya3T7fear+/zTbeoeObbpooZvi1v/61fszvmnFe\nbzNnhtvPTJOKR3f+fNrmqrc6Kl6hy06hmw8e3UwYyX36AMcfb39s442jf04+hIMLdpyFHUtLSQh9\n+aUe+0x7JFO2wqGHJnrgeC43jXl+zJnGYd5uaCCR4+YkqK3V4565qMmCv62Nnn/kEe1BBBLHGHOR\ndN48ms9ZiPhdwwsXej8XJ077h3njDfvtVavy4xo2Q8M5dHn0aG1TmYLVr9ODWdASyHxBp2RxE7pB\nBbjiRoRuimyxBQlds7Ka6eXkwbYQhO4ee9BFe/TRVB22ri6xGi8Pqm6hbB98oAvzANGLiFRX6984\nmyxZoisq+h1XnvzCGoA8iZmCJVWhW1Ghb0+cGP1zGB6Uf/lLCiGPq/VOXEyZosOMW1sTi83wufbE\nE96fYRoAl11GBjSvnCdzDJxhz5ttlviaq6+m7VtvUbshr/1h/FZ6X3nFfj8XWi8MGkReM5NUhC7n\nPeeC5yEO3IRuebn9/M0Hz0WmPLrt7Yn1LkxjN2ykQD54yQU7ZrVZHpe33NLu0Z02Tb9m1qzM7NcT\nT9C4/Npr+jEOD952W/0Yi89hw2hbXU0hqExZGQndwYPd7Zx+/egzjjgCePJJ/Xh1tRY9bI+Zi9rO\nYqjff2//XLNtUXMzXUO//a1+bzKpAanA17AzGs0ploD8ELrm4jZ7dM1oxrCi76677PfzyaPrPJZe\nBbjShQjdFOE8gfJye8I5U0geXSc9eujBe+1a4K9/pdvdutGFvGwZsGCBnpTGjSOxnGwF0Vzx6B50\nkO5/52dYrV5NF3TYfT7xRJqozWrCFRU6BPWSS8LvIw+klZV20ZssPCFXVNDAvf32yX9WuthjD9pW\nVupes52d5JXla9IMFXdinpdK2ScjPib19fZc7Kg4xSsL1z59gAED7M85vb8HHugffm22jQByQww2\nNdFioEkqQnfpUtoWikf3+usTfwu3kHO/InK5QKY8um4dDEzh65bD60Y+eMmFRD74wC4oe/akBWW+\nhszjf/DBmRO7ALD77vo2j1MmK1ZQmyAuqLR2rf0cZI9ujx7uRT5LSui5Rx/VRSHHjqWxgUUPC13u\nVsEC1px3vv2WtuxprKy0C91HH6V83o4OagG5336hf4JYeO452pqLAADw4ouZ3Y908P775Chytnjy\nEn2nnqpf4yROj+706XaPeZw0NLh7dBcuzJwdKULXYO3a6CcOr7aXl+tVOLfwmVwUBqliCt1nngF+\n/3v9HA/gI0bYm58rRQPso49G/75c8ehykSGAJgOvPNj33qMCEmGErmUB48eTmNlzT/242TvQGbLn\nx7Bh5OGrq9M5OakIXa+2N7nGp5/Sb8nVK4cMAU44Abj3Xrof9vzZZRe70OVFrL/8xV49MCobbKBv\nH3oofY8Xl19uX9yYNs3dS/vPf9LWKeKzLXQHDybDy3nepSJ0ecGiEISuZQH/+Id9PAGo7VS+8fDD\nwDHHpP972trcjT7LomuroYFe88UX/p8jQjc/2WorLRQBmt9Me8spMA87LDP75aSlBdhnH+CAA/Rj\nK1bYCyg6MYWu22JXc7MWpw0NFN7MFXn79qVoOfZ6s7B1ixjp7KS57eab6b7p0V26FPjNb+h29+7x\nF7MMAxccvece++ObbqpvR63vkmuYdVv8BCsXKnOz3eKsXDxxov26ihOv0GUgcwtRInQN1llHX+Rh\ncRO6pkf3hx8o3POqq+Lbz1yhe3ctdPmCY++taYw4VyebmuyN0sNSVZUbQtfMx2lrS+yFak4O/fu7\n9xoOixleF6VFVbdueoXZzNdNlssuy43fPogxY2jLEz0bDHfcQVv+H557DthpJ/t7+bhusQU9ZxrC\n3GYoajRCRYXdo3nSSbrH42OPUYEQr0J1Z5zhP25wDi4b9f372/cvm2LQsiiksLMzXqHL4n306NzN\nQQ5DY6PdM+Vk8ODM7UscnH46LdSlG7fQZYYXQu+9F9h8c//PGT8+MVVAyD9qa+3pUz/9ZF88dPaJ\nzRRtbTTum3PmihWJXkoT7rfqFJdHHUXb5mZdOG3NGrttYOaBAvr/douAAMhmMe0Ct77SjY2JEWtm\n2HM65heeF/bYw77gD9CixhVX0O18LO660Ub6+JsFwcxomF/9yv4ejvhKt9BNJ16hy5lEhK5BfT01\n7o6CKXTdQpd/+kmHkRQaZiix88Q1Q+2cqznJFgLJFY+uGT7a3p6YN2kaUB99ZC8mBAAPPaRzYYDE\nIgNeJNuLmQcZtxyXsHTrll8eEDOKwITPnzffBN5+2/4ce0t54cIUIn/6E22jDtB/+lNiSHRc4wHn\ngbEocrahyWaYvylknYsDJSXJC12e2BsaUgshzzY33aRD7d0oLXXP6c5VttkmM+Lcy3AHaHxbuzZ4\njuBzL9fDwYVgamvt4mvRIruYHDkysY5IOuE5va2NhJkZVRMkdLmgqXOeP/BA2jY364Xchgb/HHN2\nLrh5dAHaN174rqigXOL11kt8nbnQWl5uX+SvrPQv7pgMTseJF/kodDs7dWi96XRgu3buXODnn+32\nIkeAZULopms89ApdziQidB1ETZAOErq53tQ6FUyhG1aA/ve/yYeN5YrQHTHCft9cgb3wQj2ZmW0r\nzIH56KMp92XtWppwnEUGvEh2Fax/f1pwCVOyPt8xj42bN5HPH7ffcswYChVm769b+GOUAVop4LTT\nEvNy4xzkTz5Zn1tmzte998ZvhETBL2y6pCT84o7f5+ajscMsX+7/fEkJ8Pnn9lD3XCZTFUD9hG51\nNRUJ/OADus8Vup3wPO30ggn5R10djXNDh1Io7jff2I/rzJmZDb81C0pGFbosSHmO4nmC5w+ziJEz\nvxewRyPyOd7cnHi9bLUV5S+bHt377qMF+v33t7/23//WtysqEsd1t1ziVOCQXq/54+yzyXmQj2O/\n6TU/9lh9m+3aTTelopS8gH3NNbQdOdI9WiZuoZsuL6tb6LJ4dLNMKjm6fNGbnpR8aWqdDBxKPGgQ\nGdxe8KBVWkqvT1bolpfTCmWYxYiePRM9dnHhPEfM1Tkv4+mZZ+z3KypoUI/iZU1FIDkLHRUitbX2\nHK3Vq8mwMHNP2Ihwq2jc3k5pBn5hj3wMuBiIF7yyX1IC3HYbteRyfkYcsBcLoC0bL4MHx9NzesWK\n5DzDfhMwT/hu4XJBmAbQl1/mp8EDBK+eDxpE24UL8+N/LCvLjND1ytEFaH446yxg6lT9Wjfef5+2\nzpQTIf+oraWxtqzM3jv+xBPtrzOrH8eJ89psaaExavZsOr+iCF0eZ3k7bRoJHE51MRd5GhsTPbr/\n+Ie+zXPCl1/ac1sBWgiaMsVepLJbN/psv2KNbkLXbR5NhYULaT8eesj9+ZoaKsCVD2OiyWOPUVFM\n5s9/1redDhw+Xnx8v/ySaiA4KS+nMS6ZedSNdApdZ+iyaQN9/XV6vtck7UJXKbW3UmqeUuorpdT5\nLs+fqZT6Qin1iVLqFaWUSwBF5oji0e3s1INsebkWM6ZhWMgeXW4pEVQ8hQdHHpySFbpKha+8vHq1\nXtmPG6dBV1GhqzB7wSuV/BuUl1PBqDCFZziEMdPhHvlGQ4NdYPXuTeeeWdCLJxQ3oeE0ot1CuXjV\nPagnsWmUbLcdefGZOCeU2lpt1DQ26vDriop4yvf36WPf97D4eXQ5dDSZ8GUz5+6JJ/I3fNk8/zba\nyP7cDz8Azz6b2f1JlbKyxMW8dOCXo+tsr+X1Og4ZNwsFCfmJaUDz2FxZqfNamffeS484YpFRW0uL\nyc3NOjw1qkfXjAg8/3yqsfHGG7Ro+e67NOeYYch+NhQ7XZzzn4lbNwY/4bpsGXDttXSbf8u4w13X\nrqXrMqiGS74J3UMPTawJwjhtWh63+LctKXE/Lvy8KaDdOOCAcJWzoyxor1wZ/tgHhS4//nj4702W\ntApdpVQ3ALcB2AvAZgAmKaWc7d0/ArCVZVljADwF4IY4vvudd5J7X5RVafbWKmX32pqDWyF7dEtL\n/Y12XrVyC3dJNt8zSouhdK1QOQXEiy8Ge495dY5/i7D9HgHgs89oK0I3kfHj7caO05PY1OQudN0m\njrY2+2/MbQ6YuXP1sQ8aJ5yfZRK3R3fRIpr4Gxt1qGucoaTOfsBh8BO6bBwmI3S/+souDJ09IfMF\nPyNh3XXzL83ArZ1KOvALXXYSNMaedVbq+yNkFx77FyzQIrCqiiJzZs+2v5bb6sQJj2EVFbqoEM8t\nTg9okNDluengg6ntmClAd9iBxgTz3PfL0WXR7Gd/uhWp9BK6Rx5JW26Lw3NLXN5Epr09XMHHfBO6\nJs42gE6PbmUlLeA6oxLcGDqURKcfzz4brheyX+tCJ7yQEqblk1vocrduuh5SJhyB6fbobgPga8uy\nvrMsqw3AVAATzRdYlvWmZVk8HMwCkFJJi3feAR55hAY6txLtQUTxgpjeWh5MnH1TW1sLV+gC/sb0\n739PrV3cjN5kjf0oebrJ9usNorU1XI7hzz/r9gYcJsfnF/ccDkO3blSGPdN5DfnAG28Av/sd3eYi\nT6ZIaG7Wv/211yZ6dM2J2ilOuRXErFnkVV+8WAvpoMWWRYu8z9N11vF/bxRqamhFd8oUMvpuvRX4\nz3/iFbpmAZKw+IUub7ghbZPxOK9dazfM4gjPzgaFVgjJWXU/XcQpdIX8h4VZZ6c+L6qq6PrikF8m\nnVWCKyp0ziSfd0pp26epia4NvwV+vnb+8Afv15g2TVih6yUkzGJUzMknU26o+T0TJiSGzrLwjSNq\nyKSjI9z1/cQT9JdvWFZiNWk3obvHHv7Hl9lvP+C889xDm6PitwjjhK+lffcNfq1b6DJAnRMyRbqF\n7mAAPxj3F8FfyJ4AIKW20Mceq8NWolZQBqJduOYgwmJ2q60Sc3QLNXTZyQYbJA4+AwfSYB/Xyl8U\noZsuYdjUZO/P55evOXUq9dPjCZnPL6+qwF6kK8eoEGBxyr+Rc4WTz5f119e3WQSaizDOsEgWyP36\nURhza6se4IOu6Xff9X7u4ospPDUOeKX0gguAUaMoHH777eMTuslW6m5u9s6l4oWIZDy6bW32Qk4/\n/5zc/mWbZKtO5yqbbELbdItLvxxdp2HotS+9ekVvIyjkLmaIJ+DdRi+VNn9e8HxuenT52h40SM8v\n7M31W+C68srgdCvz3PcSzX37ao+bX+ocP2729t1oI+Cii+yv40JIBx1E21dfBZ56im7HPY6F9ege\nfHBiK558xWnTRol2ZHvlN7/R/YejwvZSlMXXKGHObqHLJpxulU7S7SNy++lc13yVUkcB2ArAzl4f\ndvnll//v9vjx4zHepRSZecJEqTrKoVdRjMOGBr1SwUK3Xz/7SbB0qb2PZiHz4YeJq0KVlXQhxeVd\njdJLN10e3bVr7ZUcTQOrTx/a7rwz/R6AvW9o3Cuggp78vY43Gxs9ergL3epqPcibhkRNDRUEGTJE\nF35oaSEBHOS5Wr2a+uC6UVYWX4shcwIxQ7TjroLrFn7kR0uLt8HJ10syRlJrK7Dlljpah/sb5xvZ\nbP2UDnbZhcbmlpb0Rp745ei+/bY9/M5L6A4dStFGQmHAYzGP/3vtpZ8zx610CF2+jlno/vADFTsb\nOpQWHp1C14+ePYPDR4M8uvPnUzrHKafQfb/QZf5d3NqCvfsudZB44w39GM8vp5+uH4tb6Hq1Qypk\nnDZtFMeYORaefz7wwgver1292r0COZ+XURYp3YqSffopnfNO/GyHww7Tz82YMQMzZswIvxMRSLdH\ndxGA9Y376wL40fkipdTuAC4EsH9XiLMrl19++f/+3EQuYD9JorSiGTgw/GsZU+jyCde/Pw1+DQ3U\nHmLxYveiNoWI20BeWUlV4xhe+U+WMB5dFpMzZ6b2XV44L1wemI89lry3ADBjhp5YReimF772xo51\nf/6hh/SqopvQdSsEwRx4IB1fFo4tLdSGKMhoylQkh3kemrdTFbrO/2/33aO9v7nZ+/9nz0CyHl1T\n0Lu1gMoFLMs/f8kvhzlfibvdhRtBfXRNvAy3+nqpuFyIsP0xbJh+zPSOxX3NLVmi+75aFp3/l1xC\naU1lZXSednYCu+1Gzo4ooaFeBOXojhxJVXvZo+s3Dw0cSLnNpkeX2XbbxOJJN99M23nz9GPTplG6\nTFyEDV0uJKqr7UUWo1SyNhcxvvzSvfsJa5uFC/0/K4rQNfcXoPN/1izv17qFLgNUjfqII+j2+PHj\nbRovTtItdN8HMFwpNUQpVQ7gcADTzRcopcYCuBPAAZZlBXQXDMa8qJ0Hw4tkxYfpkudBtG9fMpwv\nuohWN1pbvT0bhcBrr/k/X1mpJwMg9TY3fkKXS61z6M1996X2XV6w0GWvHJ9z999v753LlJbqc8x5\nrpktAYTk4Inx/K6a7tddR6vqXLmxtJSOl7lyaubampWvvSaZsjI6dlOm0MQRtHiVqSJ06RC6lkVC\nwPxdPv002mf4eXT79KEw8qhC17LoPaaBl6uCcelS9/ylxYupsAwvruy1V/g+2rlOJnrp+oUuO4Wu\n1/lVX5/Z3qpCZthrr0Rj3gzHnDAh3hzyYcN039lttqHxjgtHlpbSd1dWAq+/To/FIXRNvOzWXr0o\nis6yyLPrZ9+aiwJOxoyhLaedcbSayTXXAGeeGW5/wxA2dLmQqK62F06L0t/bXJj/7ruaQgv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Vd25/xUK8g74agnrxxdZ/FDk/Z2unb79ElMn2ls1HV2crEvej7glqZ01FHAcccB552nH6urs4/B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\nSUVORK5CYII=\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x10a48f550>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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ZM+72ccABcXx69oxl+vaNz82gQdKRR8Y2SktjvZKS2I/Vq+N3377x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\nAAwEZQAAABj8PzZTLrwnFjnjAAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x10e0a72b0>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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A3L8/NG1qIFbJZTiWJKmEmPDlBG54+wZmfzebO064g3Man0O5UC7tsiSVAevW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\nSZZjSWoEs2fDDTdkt2Vq3x7uugs6dco7lSRJkuayHEtSCc2ZAzfeCH/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WznF74Zz31hdq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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x10e10ba90>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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SJGXWOEpsIf62RRZJ5zU7WixJKgeOFEuS1AYeewwGDIAJE6Bjx9xpys+0aWm0+JZbYLPN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\nSVJpGYolSZIkSaVlKJYkSZIkldb/Aw5cfmgrAjF6AAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x10e0d67b8>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Plot raw samples\n",
+    "plt.figure()\n",
+    "plt.title('Energy samples')\n",
+    "plt.xlabel('MC step')\n",
+    "plt.ylabel('potential energy')\n",
+    "plt.plot(range(steps),potential_energy,label='$V_i$')\n",
+    "plt.plot([0,steps-1],[pot,pot],label='$\\\\bar{V}$')\n",
+    "#plt.plot(range(steps),kinetic_energy,label='$T_i$')\n",
+    "#plt.plot([0,steps-1],[kin,kin],label='$\\\\bar{T}$')\n",
+    "plt.xlim([0,5000])\n",
+    "plt.legend()\n",
+    "\n",
+    "# Plot running mean\n",
+    "plt.figure()\n",
+    "plt.title('Time series for energy observables')\n",
+    "plt.xlabel('MC steps')\n",
+    "plt.ylabel('energy')\n",
+    "plt.plot(range(steps),pot_series,label='$\\\\bar{V}_i$')\n",
+    "plt.plot([0,steps-1],[pot,pot],label='$\\\\bar{V}$')\n",
+    "plt.plot(range(steps),kin_series,label='$\\\\bar{T}_i$')\n",
+    "plt.plot([0,steps-1],[kin,kin],label='$\\\\bar{T}$')\n",
+    "plt.ylim([0.1,0.5])\n",
+    "plt.legend()\n",
+    "\n",
+    "# Plot binning analysis\n",
+    "plt.figure()\n",
+    "plt.title('Binning analysis')\n",
+    "plt.xlabel('binning level k')\n",
+    "plt.ylabel('error estimate')\n",
+    "plt.plot(pot_binning,label='$\\\\Delta V$')\n",
+    "plt.plot(kin_binning,label='$\\\\Delta T$')\n",
+    "plt.legend()\n",
+    "\n",
+    "# Normalize histogram and calculate error bars: \n",
+    "# We did not collect a complete time series, but a fixed number of bins. \n",
+    "# This works as long as the size of each bin [steps/histo_samples] >> [autocorrelation time]\n",
+    "position_histogram /= np.sum(position_histogram,axis=1).reshape((histo_samples,1))\n",
+    "histomean = np.mean(position_histogram,axis=0)\n",
+    "histoerr = np.std(position_histogram,axis=0)/np.sqrt(histo_samples-1)\n",
+    "\n",
+    "# Plot wave function\n",
+    "plt.figure()\n",
+    "plt.title('Wave function')\n",
+    "plt.xlabel('x')\n",
+    "plt.ylabel(\"$|\\\\psi|^2$\")\n",
+    "binwidth = (histo_range[1]-histo_range[0])/histo_bins\n",
+    "plt.errorbar(np.linspace(histo_range[0]+binwidth/2,histo_range[1]-binwidth/2,histo_bins),histomean,histoerr)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "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": "3.4.4"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
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