diff --git a/learning/01 Introduction.ipynb b/learning/01 Introduction.ipynb
index bd819a3..8f3b861 100644
--- a/learning/01 Introduction.ipynb	
+++ b/learning/01 Introduction.ipynb	
@@ -41,7 +41,9 @@
     "\n",
     "# This loads some custom styles for matplotlib\n",
     "import json, matplotlib\n",
-    "with open(\"assets/matplotlibrc.json\") as f: matplotlib.rcParams.update(json.load(f))"
+    "with open(\"assets/matplotlibrc.json\") as f: matplotlib.rcParams.update(json.load(f))\n",
+    "\n",
+    "np.random.seed(42) #This makes our random numbers reproducable when the notebook is rerun in order"
    ]
   },
   {
@@ -56,15 +58,15 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 2,
    "id": "7b05be8f-9edb-4742-bbfc-e892cc09b82b",
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
+      "image/png": "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\n",
       "text/plain": [
-       "<Figure size 500x500 with 1 Axes>"
+       "<Figure size 432x288 with 1 Axes>"
       ]
      },
      "metadata": {},
@@ -104,15 +106,15 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 3,
    "id": "340a78e7-6c1d-4742-8dca-6d3bea492856",
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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yYxSNQ/W5fzfZ76Jny37vPFuvzY8cq+x4VMvdy3wPrxZ9Rp/1uR39Lm/17Rm8tAEAAADYkJc2AAAAABuSiBgAYEKU9PR0qid1jM5Vk65mr12Z6LXVZjbRbHZcovIzdbSW9jzq60i5bD9aovqqCTBXJMzMJlW+mRnLzLleva1zlka9TxLVVXqfm9FlStnvpJVtVmX7UT224vPwUXPmWUuzdiTSBgAAAGBDIm0AAAa8vLyUfpWrRldUfwFtlc8ey0bVZKIrMskuj/Wu+LU/U0f2V/Hqr+fZZ5WJ7rk/Fj2/6Fk8cnzePZnImV4/qpEzKyMcstFL32XL75bjOO4YibRiro36iDZH+tGSiXjb5RkTE2kDAAAAsCEvbQAAAAA2ZHkUAMA7iELqq0uQHpXLnJsJh88uu4razJSbSfa7YqlXVfX+WqoJn6vPoNVWby5U6x1ddtVbbrJyCcd7JY79rEaSZL+X9+zHLvccaT2rHZe3MU+kDQAAAMCGRNoAACyyItokunYmwqXleG0vmmU0qexMVEg1cqa6jXQ1iXC2b9k6Mm1ny/eeXyZpdHUL+5koo5lop2N9I3PsVu7t7S3V5ncgEunz8Ky+D5E2AAAAABvy0gYAAABgQ5ZHAQAMuFwup9fX1/84tiJZblRXNklodanQzNKVqB8rEtlmkzBnlhfNLIWKys0sQ6s+q5mxrCbArrYZtV1NkDqzpK7SzneU/Zyxj953v+f3tYm0AQAAANiQlzYAAANeXl6ayVCPf9frNbW1cqZcpNVmr95qm5l67/sR9bOqVW/v2PHvUX0jz+x0isevNw6P6pp5ZvfXZtrOjl+rT9l7j+qIrl3xmegZnYtf0bPH+juJvndW1Bkd42vy0gYAAABgQ3LaAAAs0sq9EeUqmflle8XW2dWtn29mcotkcqccIzoy5TL5gVZszT1SLtqeunVsdOxXbK2elclldF9uxTydyeEhGoGPUs3nlJX9/uPzE2kDAAAAsCEvbQAAAAA25KUNAMCAy+Xyq4SpUSLg1YlVjwkoe0loW337iCSWo8mMe4mCV4736mcWJeWN2ooSjWb71nre2ecelYueQe9YdK46T7NJprPtw4hnJQXOzH1Lo74+L20AAAAANiQRMQDAgNaW39nkr89I+jqSyPZ4bS/RazX5a6vNlmjcqkmHj3WuEiVErpbLjsfqe87Mz16S5OhcNWl09tlm+p2dp60k4T9+/HhYL2RE829FJEz2u5mvSaQNAAAAwIa8tAEAAADYkJc2AAADbomI77WSqGb0Eu+2jh3r7yWyfa+EyK1z1aS5I8cetZ1NRtsat6wo2e+jZNHRPWT623q22cSkz5oL1f7e9Ob6yjn8nvfO9xHN4Va5bH2Z+h8lZ+fr8NIGAAAAYEMSEQMADIgSEfeORWVGk/3eyyb0PbY/k8w4uq6arDabmLalei9RHVm9PkaJdzPlW21VorhGZZMvP0Mmkgp2kU0KPJokvloXX4tIGwAAAIANeWkDAAAAsCEvbQAABrQSEY/KJmJ9dM2jhK3Zdqt9q9bVS5I8WkdUbzY5cFZ2nKOxj8pXEiaP3lM0fpnEyNm5NZIEOjM/ojpGEjOPzgUYFX1vt8rB6eSlDQAAAMCWJCIGAJiQTR75nokqo2S1M4ktVyTozdTVu89MwudMZNCjuqLnd4wMqtTROjeaULjX5ujYZ5NpZ5MqR/1ZkWR1RbJmeIbou6t6zFz+3kTaAAAAAGxIpA0AwITV0Sk3rV9do63BZ/IfrMidkI2IqUZcVPs2syX26Fhmy1f7NhNtks1plCn/rLm1cqv5atv3dby9vXXrgqxMFOTIMb4vkTYAAAAAG/LSBgAAAGBDlkcBACzSWv6yItlq5tpqQt3W+dUJZFvjUU0ivDIB58jSraPes60uscoumYqe1cizz7bTqz97n9nPRLZPVVEi6R8/fkzXD0czSw4lHuaeSBsAAACADXlpAwAw4OXlpRntMvIL6fl8/vmXLXcs3zp368/9X6u/t79eP1r1rvDonu7PVY9FY7Wqr9EYtMY+O2at/lbHu1o+mjPRGI7MhWhsoucWtdUrv2JMYZXoM2BOcuSlDQAAAMCGvLQBAAAA2JBExAAAAy6Xy+n19XV50uEo8e9M2HwmSXKv/moi22pS3lY7rYS3Ub2tc5ny9+dHkxQ/Uk34HI1zNrlp1EaUDLpVR7Z8ZOb+ojZm5hbAZyDSBgAAAGBDIm0AAAbcEhFnoxuyWylnI0WeHTEwGsHQ2lL5PaMbZrbazvRzZOvqTGRJa9yyda2IzqpGGWW2bs/2rVd/NQpodLtzvqcVEZLwTCJtAAAAADbkpQ0AAADAhry0AQAYcLlcTufz+XS9Xn/+3ZzP559/x3P3jmVGQvFvddxr1VWtP1u+Wm+rv4/KPCoX3XOrP1H5qK3sc7xvt1XXfT2Pzh37/+j5rXzevTaja1qO99kbt1Y/WnVF5ar1Anw2XtoAAAAAbEgiYgCAAdlExJHRrZ1b5aKEr4/KHY/NJHqN+j2TVLk6ptHW5r26juWySYd791LdKr113TO2fc8+l2w/somFj3VV+92zSzJv9paZf7vMlxVJz/m8RNoAAAAAbEikDQDAgMvlcnp9ff2PY5kohFb5nujX05ntnlu5UTLlo8iLbMTISH9H+xH1rWpky+9M37Ltjj7b3jXZ59LKnZORjc6Knm3Ut0yepEp/+foy3xUfPV+ykYMrvtvYl0gbAAAAgA15aQMAAACwIcujAAAGtBIR3zwraWQ1+euKkPlqkt3VIfvVOrLLfLKJhTOqyZeziX2ziaFb/cjWG9URiZZf9ebJ6PjOjKnlIzwymjx8tep3Ujb5PJ+fSBsAAACADXlpAwAw4HK5nM7n8+l6vf78a7k/f/y7OZ/PP/8irXK3/27VG7XZOt9q6/78ffvHv+q9tPoRnWv9tdqK7jNbb+S+zWjcqvfZ82i8K32LZMs/Gu/efM72LZpr0TPK1h/NXfgIrXmY+Tz2vvP5Ory0AQAAANiQlzYAAAAAG5KIGABgQi/xYyYhbGZJziMrk2hWkw6P9K11bnSJSlRHr/4ogXO2zZHzxzazz6q1DOt4LpuMN2qzNx5RPx6V6bWZaadX7rgUK1Puduzt7a3UN76+7LxeWX/l/JHlUF+bSBsAAACADYm0AQAYcNvyuyUbfROVr9ZxLxvhkpH9xTcbNZSJcJnZdjprNPpm9Za62XGobuGdmUfZaJ1sf1uqEQvVe8mWjyKPfvz48fgG+NaqkWozbWS3tOf7EWkDAAAAsCEvbQAAAAA2ZHkUAMCEFctlsglkH11zLJNdwjK6VKl6z9XktiuMJIhemTR69dKp6nKg0bbu+70yoXVvqdJRNTn3yLI8iYg5ipauPqP+3jHLojidRNoAAAAAbEmkDQDAgMvlcnp9fR1KFptJCHsvu63xo+setRWVq5aP7n3F9t7Pkn0uK9qY2fZ69HnPJJ6uRvdUI2eqcytq/9lbNPM9rf7uykbFSUTMPZE2AAAAABvy0gYAAABgQ5ZHAQBMGElEfAx5zy4JuVddYtU6d+xHb4lJaynKiiVF1aSyK5aGjS7xyt5fdplRS7T0qDq+UR0jS5ai5Uit8hnZJYbVeQ2zeomDn7VsKUqIbKnU9yPSBgAAAGBDIm0AACZkf/XMJvvNRt9Uo3Wq0RszkQ6P+tjrW2QmIXJ2S91MP7JRIVFb1YibrOw8Go3Eypbvlcsc643R6NbMrf7++PEjdS1fXxSNtjIpcPX7+ln94HMQaQMAAACwIZE2AACLZXOntMpkI0Wqv8RW88Bkt3mOzo3m+MlugR7V0VKN+On1vxo9Va0jKt/b/n3lFtgz+TRWRHiN1n8vauvt7a3UJt/He+a0ib5/Pyq3DnsQaQMAAACwIS9tAAAAADZkeRQAwISVy1Dur80mYs2Wz5Qb2RI7swX0TN+qy8WiMr1EvaNboI8uA3vURqatapu9Yyvuubp0ayaRdGYpW/ZeJCLmkZGE5hkrvq8lJ/4+RNoAAAAAbEikDQDAgJeXl9JW1SsS6o5GLfTabBndBjz7C3K2TCuSZ0VkzmjfqhFQj45l2qwm732PrcSjY9l6VyS0ziTzHukb3Mt+plbXlym3um/sS6QNAAAAwIa8tAEAAADYkOVRAAATVoSojyy5OZ5bkdgyuu5RP1befzUZbsuKJUiR3lKd6hKrlc+lV+5YvjdWK553dtleph9RvdVncF/u7e0tVZ7vYyZJdqbe3nfA8dh7fA+zL5E2AAAAABsSaQMAsEg1aqKaiLWaaLa19fJM1MmKRMQt0a/KmfLZdkciS6I2q9tvR/3Inp9JqLtye+LsHHvWlsjRFujVbZJt+U3FSFRXtr5Hx3plJNr+2kTaAAAAAGzISxsAAACADXlpAwAw4HK5nM7n8+l6vf78u2kduxeVP5/P6aU+j/5udbT6cTt3/9eSOTdSR3Ts2P/j0puorcp4P5IZv6z7/rbuK/ucZ7X60ToXHYv05lh0rDW2rbGP/np9evTZaI0HRLLzb7SumfnN1+alDQAAAMCGJCIGAJgwk3R4RRutRK9R4uJWItbMluKPZJIIv8cW18djvV+fq4mZo35UkzaPzIVqQt/MffXGNEq+HF1XNTPvqv0QlcBnYr5yOom0AQAAANiSSBsAgAEvLy8/c2TcZCMpoiiBajTGiq2oq5E5kWw/RqIrKnX07qVlNPom+/yy21OPbpPdE20jHI1l9lx2zDP9yM6P6vbetkkGPhuRNgAAAAAb8tIGAAAAYEOWRwEADLhcLqfX19duudZymWri3+x21Zn6W6KlLjPLtKpLV6KlRdVlLTNJdmeS2laXFGXqap3P9ruaKLuX0Doa++xcH01e/eh8tkyv/wA7EmkDAAAAsCEvbQAABtwSEd87n8+n8/l8ul6vP/9uWsda5Y9l7stFbmXu67s/1qqj1dZRq2/RvfTqaPU3476O1nXHY636q21m76V1vjX2reta5bP3/OjeHx2L5lhVtt/RfI7qiMo/iqrJzPVeOYDdeGkDAAAAsCEvbQAAAAA25KUNAMCEkeUm1aVQo0umqv3piZbh9JbEHNvKlj+282iZ0QqZe+ktr6mOR7T0J1ry1luCNzonW31rHcssZ3q0NK26LC+qt1U+GoeZMQL4CF7aAAAAAGzISxsAgAGXy6UUERP9teroJaHNRG9ky7f62krcGh1r1ZGVKV+NjOhFXmQjXDJJdrNRJNXnEkWK9Opo3V81mXFkps1MW9l51HoGUR0SET/fyLM4HoOW7/q59dIGAAAAYENe2gAAAABs6Dcf3QEAgM/o5eWlnOj1kZFQ79s1rXqryVVn6jpemy0ftTFTx+1cpp1juWMdxyVTGdFYZuuqXpt9blG9o/NoZIxWtT1SvlXu7e2t1BZtrec/eqz1ueR7ySyhPJ2+x/wQaQMAAACwIS9tAAAGtBIR3/SS92YSEfdUEwtHyRuzbUb9zSRcHo0oqiRrzibqzWxxvSrpZbVvs2OVTTacTVKcqatnZovtaB5l+yEB8cdY+X3G9/Xd54eXNgAAAAAbktMGAGDALadNL/fCijwfM3lajuWi/vbupVVHRuteRvPu9PoR5aOp9qPXZnaMopw9o+OxIu/PiGN/e/lJMm1mc/ysuKfv/Gv9s8w822o5vqfMHPvKn22RNgAAAAAb8tIGAAAAYEOWRwEADLhcLqfX19ehLY+jZUmtUO/RZVfZJUIt0bns1tHVZVrZrcczy52yS5tmlnq1ZLYzXvFsR7YNrz7T7Fystpl53r3PRDSmfIyZz15mTvB9rfwO/4xE2gAAAABsSKQNAMCE7C9/2SiBVtLhauLdR+086lM2CudZiZYf9adXLjrWu5dqBEhUfiTaarT8igTO2bYzz3skqfKxjtXJakcTTzOnmhg8urb3HcDXN/Id/lWJtAEAAADYkJc2AAAAABvy0gYAYMDLy0tzuclIyPbtukfXRueu12upH622bnXcn7sdu/+7P/+ojtX3lx3TVt8y17buL+p3VP7+fNRWrx/R+ep9Rv1ttdmrN5oTrWO9PlWWvrTmZKvfWaOfV/Kqc+L435ZGcTrF353fgZc2AAAAABuSiBgAYMJIstNnbTe9ss3RhLrZxMEz2/1mtqLObjHc6ufMc2wlJ37U/165arLmFc92Jtn0iuTV2WcVyc5Bnm8meTRrvOe/Mx/pKyevFmkDAAAAsCEvbQAAAAA2ZHkUAMCE7DKc7JKU1jKB27Fsva1zrXLPWJIwsvRnNBls1FZviUw0ztGSnpF+t5L5Ztqs1jEjM5+e1Y+Z8cguQ4vafXt7S/WTWPb7b8USOPoy33Gf+blEy1m/2nI7kTYAAAAAG/LSBgBgwOVyGdpm+f58dG12m+xWXdU2W/2O/rLXZM1uO/1onI9GtoV+Rh33ojGtbltebas6fsdrMnMhs81zdq5H99Iq35uLtvxeqzWe0bGR74rPIPrues+2M8da1/aO7SJzn1+FlzYAAAAAG5LTBgBgwMvLy88ogaNqXpdsHpFsrpVIL1dOq1zl3Op8Ftl7bkUbZepfLXoeM9tpR3Vky7d+RT+Wm8mbFLXf+5yM1rGifp7ns+VJeYaPvvds3qnsZ+kjn181v9Yu/Z4l0gYAAABgQ17aAAAAAGzI8igAgAGXy+X0+vraPFfdBjmTIDhb16Ny2eU6mTpmE/n2jIxHKyluVG/Uj5klZ9Xz1SVyWZnnnUnc/KiuZy09Gl3C0FtOaKnU83z2JWrV5aHZOnaRvb/qvy+7LTfa+RnMEmkDAAAAsCGRNgAAi2QS5LbKVROyRm2PlKsmz60mSc5akbi4GmW0OvFu5tqZSKIVv4ZnI1FWPNNMWyP9iMa0GiH19vaWKk9sxbz9aNXP6vG61rXvee8zEWcrvn/fU/Ssdo0GGiXSBgAAAGBDXtoAAAAAbMjyKACAAS8vL6fr9TqUfHM0rLuaeLca0r566c/o0qaRJVnRkoSo3zPh8ytD76uJk7NLilYkpY7qnenHjGN9I/d5u+bHjx9L+/ZdZb8Ld1m6sjJx8i73vjoZdKa+j36ON9l736W/FSJtAAAAADYk0gYAYMJIstZMMshs+WwUyYqttqvlRn9pXp0Ut3rts7b7zSYFjurNJguNImFWROZk+vioH1F/qvcykyhVIuLne69Iq2ybvUjAUdVkv+8p+g6oRvjdn98lufSKhOm7E2kDAAAAsCEvbQAAAAA2ZHkUAMCAy+Vyen19bZ7rhcBnlozM1HEs0zMTsj+67Kq1nCUKu6+Gu2fbjI71lgmsWMaVXcoRLWuYWUaV6WNUbmacs8ssoiUc1aWDI8uoyMkmAc+cm7GyzWoS9Up9mXpXeM8k4Dt/pnbuW49IGwAAAIANibQBAJiwIkplJpFidTvrKMFrNnFntj+jiXezUUatfmaTgK7Yenf0uc0k/5ypN3NtNaJoZkvxbNRQSybiZ6Re6jJJbVdEuVWPVdvs9aNlRT9WGhm3TH0zY/QRduzTDJE2AAAAABsSaQMAsEg16iC75fGK/CSZ6IeR/CQZ2Tqe9St0dfyqUSQzzyrqb1Z1zmTbztz/TDTL6nGO+rHbNsWfXXbcR489q/5qFN9MTpvVfcuY6Ue2/cyz+mqRLh9NpA0AAADAhry0AQAAANiQ5VEAAItUk+tml2xUt4yuJsidSVh5PL8y7L5SRyapcq/eKLntTGLo6hbE1aUFKxK1ztxfVKa6BGpUr37LotbKjm11W/dqIvFH51fJfieuGI9nbZ29+nNgqeH7E2kDAAAAsCGRNgAAE0YiFEZ/qYx+fc1GxIxEV0TlM1svt+59ZhvaaqLZzDbjvXaiiKaZKKBqn1ZvUX48V41YqUYY3Ms+x+w4R221zt3a+PHjR6pe6qrfjyuecVU0h1dGoM2Um7nfldE12fqeFTX0XYm0AQAAANiQlzYAAAAAG7I8CgBgwMvLSyoJb0t1uU6m3IokwlkrQvWzSZtHQ/uzy7Ra16xY6nBff2a8solao3MrliSMjFtVNTFzpLrsr3Uvb29vpTb5T9X5Hc3X6jKp1aJ+VJMkR/dQHY+smWTk1TZGE6B/lF36MUKkDQAAAMCGRNoAACwyk+g2qqNaVzXyYuU23dlteav3kmn7UfnsL6wrntWt3LMTT/dk2prZ0nyX7epnEtdKRPwxMgnNd5Ht60z/M/XNRLs9e7xXjNHq6JcV/77sRKQNAAAAwIa8tAEAAADYkOVRAAATZhJKrgjNjhKxVpNo9kLao+S92fKjy3aeleyyupyql/A2U1826XA1UevOyVCj9rNL6lrXRmWy/ZSI+PmqyyY/egnLzDK96ndc67oViZmf9bk5Xtv7zK5YIrnSZ1kSdU+kDQAAAMCGRNoAAEzo/aJYjVLIRhqMbk1b7Uc1ee9IIuLq1ukro2micjO/ILdko2QqdT2qY3T78mwETzYaKRPpMxPdM5PM+zP+4v5V7ZqIOGvFvFrxvTDSxso6W5/pyLMTIvfKfZbvAJE2AAAAABsSaQMAsEg1Z0lWFMFTzUcT5WQZzUHzqP5qzoPsL82jUTK9/lbHtNV2Zryq0VS9eqt5IZ6VS6klutdsPqHRHCG9crb8/hijOZs+2o592k12jJ7xnJ+V92wHIm0AAAAANuSlDQAAAMCGvLQBAJhwPp9/9Xfver02l+4cl+W0ro3qeFTmmIw2Onb864muvfU/W1/vnlfK3mtm/EbafFT/o2OZcen1LZqLUf3V+Zydd9X7W/GZ6NU7WgfrVb8T+dye/dnLftd+Fl7aAAAAAGzISxsAgAGXyyUVWVL9tTgTCdKKcInarkRVRFEW2WNRv1sROdG9tPqUGe9WvVFdj5LiVtq8Lxcd641fVEd0T9nIoFYdrWcVPYNsv1eIIqVm2hTJsY+V36Hw1XhpAwAAALAhL20AAAAANvSbj+4AAMBn9PLykk7eezqdfrUE5f5YNjlidonAo6U+x3NRu63yt2OrlypkxiGTuPaR1jOoXPfoWPba0b61ZJ9L5p5bdbTmR7XenpX3fDvWG+9WuZu3t7dUP1gr+xmB706kDQAAAMCGRNoAAAy4XC6n19fXbmRC1Wi0QjVqoVXXSPljxMNIP6qRR6P3kK03ilRqyUZKtcZo5p4z/ZiJ+BndHrfXZiuBcVS+GvHTUp0zvK/oO0AUDt+dSBsAAACADXlpAwAAALAhy6MAAAbcEhGPLLs4XjMS/j+axLiapDibcLa6fGhlEtpHx6qO12aXhvX6e6w3m9y5uuyq1Y9WuWpy4l65qP7MsquZz1B1WZelNnta8Z0IX5VIGwAAAIANnSu/Rry9vf2f0+n038/rDvAO/vef/vSn//roTszwXQRfgu8iYBef+vvIdxF8Gc3votJLGwAAAADeh+VRAAAAABvy0gYAAABgQ17aAAAAAGzISxsAAACADXlpAwAAALAhL20AAAAANuSlDQAAAMCGvLQBAAAA2JCXNgAAAAAb+n8fmJJw4DAjRAAAAABJRU5ErkJggg==\n",
       "text/plain": [
-       "<Figure size 2000x500 with 4 Axes>"
+       "<Figure size 1440x360 with 4 Axes>"
       ]
      },
      "metadata": {},
@@ -155,7 +157,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 4,
    "id": "c2e63baa-8d97-41f3-9070-013aa6bf83bd",
    "metadata": {},
    "outputs": [
@@ -180,22 +182,22 @@
    "id": "8351475b-73cb-4cd9-9fe8-3b60af0b5a6a",
    "metadata": {},
    "source": [
-    "## Exercise: Write a function to compute the energy of a state\n",
+    "## Exercise 1: Write a function to compute the energy of a state\n",
     "\n",
     "See if you can write a function that calculates the energy and reproduces all the above cases. "
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 5,
    "id": "36ac021b-1da4-48d1-9cad-6ae3ba1e7e61",
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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lDjP+g2HbMnBhuDaNXJuSuDa5NtFPa2SS8ReX44y/mqy/vnxtnrfNeIJ8bsYI/dkbbdyR8aS7/ivQ1yb5tdX/v+tqHQ/dWO6FSf7V6v+/N8nPTvTzjtz7V5V/nuQFG+89LOOX/5FJHpDx14RPXZv+9hl/yXnWxLpuyfgrxdPX3ntGkpcleZsty3xRkl9Y+/vp2eFXoTnbaPX3byT5G5X7+hWr7fEnSf7FGfN+TsZfpm7LmHL3yIy/1gxJPnQ1z/MznuB/IuNF+69l/OXm2yv69p4ZLw5vSfKBq/e+J8lPbcz39Ul+de3vub8Kff4Z67+S5LVJ/s7ae9+b1a+AW5Z58Krt99pY12NWfz85Z/wqtNq/X7Yxz2ckedXa31+T5Dsn+vG3k7zllPf/a5Kv27LMh636+s4b7/9ANn4d8/I6j1dcm05bl2uTa9PJMena5LXI60r6+Okk/3Djvded/M8wDG8tpXx6kl/OeAI77deP/zKs9v7Ki5M8tZRyS8aI/pYkv1lKWV/mvhlv2yXJYzL+CrKL903y0aWUN54y7RFJbs144fn5tc/yulLKZJ7lMAx/Ukr5joz5lV+Z8dbcZ2U8Kf1pkpRSnpgxB/ARGS8SV5L80Y79XzdnG2UYhkdNNbKxLb57GIZ/sPb3R6z6+iFJvraU8tvDMHzflqa+NeNn+4mMvzj8UcZfLp6e8deQZDypD0k+fRh/UUgp5Z8m+aFSyj8ahuGuqb6uG4bh10opP5zkQcMw/MLq7Ucn+bGNWV+U5AtKKbcMw/Anc9vP+OvV1PqPSyk/kOTTM/4Cev+MvyQ+6WSe1a9zz8iY8/ng3D3G6V2T/MoOfVn3vkkeW0r5irX3bklyv1LKwTAMR8MwfFll23DZuTatcW1K4trk2sSiegUWbxqG4bfPmOfDVv99+9XrTTu0/4CMv0R8wOq/605ONrO/6Bvt/niSLz1l2quT/MWKNk/8xyRfluTxGb+k75Lk25OklPKhGX+xeFrGW5eHGb/kT51o708zXgTWrQ/UmrON5njM2v/f42IyDMPvrf73/1tVZXh6klNP3qsL8ZeWUr48423J12b8hSgZcy2TcRu/8uTEvfLrGT/nw5L81g79TsZfxY53XGbI9HY9Med4/Z4k10sp75jkYzMek+sVaH484z9enpLkVRmPi1/J+A+E05y1z5Nxvz8tpw9m27zdv81rkrxtKeVBwzC8Ye39h6ymbVvmZJ5XbyzzkpnrhaW5Nt2ba5Nrk2sTi+kVWEwqpTwi48j+p2QcaPQdpZSPOfmFZOWDNxb7kCS/tfqF5ZcyRrrvOAzDz2xZzS9nPDk8bcv0t67aWPeLGQdQvXQYhnt96Uspv5Pkj1d9+/3Ve2+X8dbpVA5nhmH4nVLK9SR/L+MX8IXDMLxsNfnDkrxsGIZnrq3r3abay3jye+e1+W/JOLjvp1dvzdlGZ5pxET7xNhl/cTqrvT/JOGAvpZRPS/LiYRheu5r8oiSfWkp5wDAMJxeYR2Y8ab1ip46f7tczDppc99gkv7n2i9Dmdn33jLmnOxuG4edKKS/PeIx/XMYBgn+8avcdMlYWecrJ/imlfPgZTb42yQNLKfcfhuHk4vGYjXl+Mcl77LDfTvPfMh7nt2Uc3JlSyntk/LXqxVuW+b2MJ/DbsjpZl1L+XMbvyrc09AX2xrXJtSlxbYprEz215lJlzGP9yYyR//rrwavpt2Q8AH5o9fc7Z6xG8MVrbdyRccDYN+Tusm5vTPK5a/N8d8YD5pMzDs75oIy/unz8avojM+Yw/vuMg8MelfEW+Ek/np0xL+/huftW30MzVgD5wSR/OePt0Sdk/PXmltVy35Ixt/LxGU+WP7bq67NmbJvPyPjLwF1Jnrj2/l/P+GV50mqdn5fxlvAb1uZ5eu6Zx/q5GX+Z+PjVZ3t2xl+TnjN3G63m2TmPNcn/kbHc27uvXn8/4y9GX702zz9Ocvva3w/OWOrtURlPON+42g4ftDbPAzJW4vjBjHmoH5mxGsm3NhyLz1v7+/2zyrldHR+flTEH+clr83xfxhzq98s4cO32jBf6J6+mPzxruaUz+vDVGXO1/zjJh6+9/zYZj/vvyvhr4+NXx+Of5dFurivjr6dvXG27R2TMN31l7pnH+oTVup6W5C9lvMX+pI19M5nHunacvyzJR2f8ZfHnkvzcxjz3OHYy/pr6+ozH83tnzKv+3ST3az2veHm1vuLaNLVtXJtcm07ed23y6vpqb+D0cnlDkt9YTf+XGW+tvcPaMp+c8UT7vqu/70jyzasD6DBjDuwzc88Bc/dJ8pUZT05vXbX5I0nee22ej8r4S8ObVwfV8zPmNWb15X3x6ss75O6Sfu++auf1q2m/nvEXrJOycw9YfeHelDEK/uKcUdJvrT+35u7ybffdmPb1qy/znRkrQ3xBpk/e98l4YfrDjKUH/1nuXdJvzjYackpJujM+xz/JeFv0Tav984sZL4xvs9Hfl679/eDV9n7jarkXJvngU9p+VJL/tNr2L0/yfya5dW3649b314xj8Xkb752U9HtrxpPTF21Mf2jGW/5vzHjh+LicPkDuMTO31aNX8780a8fvatrHZLxQvDnJf894vG49ea/e+6SMt92PMt6ufkruXdLvCRmP+6PV/vn5jL8+rW+XO87o9/0yfgdft9pfP5LknTbmucexk/HXzmdk/F68ebWPH9l6TvHy6vGKa9PUtnFtcm1an+ba5NXtdXKCOlercmMvGYbhC865K1wwpZS/m+TLk7znsLp1C7APrk1s49oEp1v8ORbQ6K9lLA/pxA3AReHaBKfYy+BtqDUMw6eedx8AYJ1rE5zuQqRCAQAAl5tUKAAAoJnAAgAAaCawAAAAmgksAACAZgILAACgmcACAABoJrAAAACaCSwAAIBmAgsAAKCZwAIAAGgmsAAAAJoJLAAAgGYCCwAAoJnAAgAAaCawAAAAmgksAACAZgILAACgmcACAABoJrAAAACaCSwAAIBmAgsAAKCZwAIAAGgmsAAAAJoJLAAAgGYCCwAAoJnAAgAAaCawAAAAmgksAACAZgILAACgmcACAABodqV2wdtvv70keWiSO/t1B4AkD0zyqttuu204745cNq5NAIs589pUHVhkPHG/omF5ALZ7WJJXnncnLiHXJoDlTF6bWgKLO5PkiU98Yu66667JGQ8PD+/x99WrV7dO2zZfran2p8xdd237tf2Yu76p5Wo/29RyNe3vovY42davXY7Jue1P9Wufx+Eu/V36s9Vu1x79qN3+S++3qX11eHiY4+PjvOhFL0r84l7rziR57GMfmytXWi5xAJyYe21qPuu+5jWvOfXkXUr5s/+/z33us3X5zWnDcPfdlTe96U1b21yfb/39XdqfWq5H+1M229y23NHR0T3+Xt/WU/3atN7P3n3ctNnnbaba21z3VP/Xj5Op5dZtHrNTbUwdCzX9mrsdN9vYtN7m+ueZWmbT1L6ae6xN/eNtvf1dtnlN+1Pnmak2dtnf2+ab6tfc+ZLxMxwcHOTatWtbl2GeK1euCCwA9szgbQAAoJnAAgAAaCawAAAAmjUnoF69evXUPO25ecqbanOae+gx/qK2/7U5+HPXtd7+3D5OtbHLtG3zTdml/3P7XGuf+3SXcS3bptWOGajV49g9z2N+bptT3/Vdjvmz9unx8XGuX7++a1fhHmrHyAG0cMcCAABoJrAAAACaNadCHR4enlludtNUekHvlIhdUpVq2tilv3PXvc+Uo12W673flkjZqdnGm+ve1CONaekUpG3rPWvdtcfQ3G3So3Tr3NS3XfbpVF/mfsdqtgEsae5xvckxCvTijgUAANBMYAEAADQTWAAAAM2ax1ic2CW/vHYMwbZptW1s6p1bXWtu3vguZVfXLZFzPzVf7RiFbZYug1vbxkUqtTp3vqnP1nuMSI9xFLtYorRx67o255Xbvn+148im1CxXe56ptfSYL4DEHQsAAKADgQUAANCsWyrULikic5+iPNXO0qXzalOmeverVxpIj+26y/q2TVtiH9aUHN2lLGPvsr69ng7eo+Rr7xSqXikWNekqPcrLTrWzy/Hakm54cHCQa9eubZ2Hea5evZqjo6Odllm6zPXcZZYowy79CdgHdywAAIBmAgsAAKCZwAIAAGjWPMZiWx7rEjn9vcvxzc2L7lW6tUeZwx555LWfe+kytb3L0m7O22M8Qa3a78MS26TG3LLHvcejnNVmbRu75LfPmW/pkrjs7vDwMFeuXKku2d1jWq/S2DUlr3fpP0Av7lgAAADNBBYAAECzvZSbrV2ux5Oea1Meap/SPLf9ufMukU61xBO0e6eF1JabrW2/5mnLtf1aupzt3H70aqNHKletHued2u+UtJOLbVuabu25sWbaPtd1FschsA/uWAAAAM0EFgAAQDOBBQAA0KzbGIteOcbryy1RFnWuJcZf9C4nOKVXidxtyy2RO7/EWIOa3OcpPcqW1u7f3mV7z9L7e7T0eIslxq70yINfegwNp9tWbnbK0sfolJrvd+1nc9wBS3HHAgAAaCawAAAAmnVLhdq0xFNpL2KJyF1SJXqXg920dNnPHrfSexwXS6cL1e7TWks/mXzpcrNz171EumRtylHNNqlNIdzFMAw5Pj7O9evXu7R3M9tWbvaiWvr6IP0J2Ad3LAAAgGYCCwAAoFlzKtRJ5Y1NS6fKLFG9o/et4h5Pzd7lc/auUtMrhW3d0k9an7u+Jaqp1Kbb7DMFYt9PNJ/b3hJpcVPz1VRo2+Vp7XNTwM6zCtGNbltVqMtQHWnuMelp8MBF444FAADQTGABAAA0E1gAAADNmsdY1JT0m8pvrskDXeLJ20vnPu97/Mi6uTnfS+fh9noibo98+bn96jHmpdcT2Wvyruf2cdMSx2uPp1P3yCmfu712OS5q9yn9bLs29RiLdp56PA1+atpF/dzA5eCOBQAA0ExgAQAANOtWbrZXGc4eqR9T5ra/76dfL52S0vs2+BLpL0uUm61pv8d+Oqud3m302L+15VTnWvp72iuFo+a73ys9RRpKP3OuTZsu6vbfZ9lsaDU3DZgbkzsWAABAM4EFAADQTGABAAA0ax5jcWKXfPnaXPq56+7Rj6XHEPQYy7BLfnbNNuqxDTbb6VEedJdjbVubteNrao/zuftm6ZzpXsfMtjaXGANUq8f3u0cp4Clyji+Wy1B2tfa7YlwFS1l6fCSXizsWAABAM4EFAADQbLEnb++zHOkSKU21asvNzm1jqr3epVxrnzJ9kbb53GOmd8naqX71eor10uk2S5d+rtX7e9RjXbWlpU/r18HBQa5duzazh+yqNh3zPNM25n7flp7GjadH+vZFuj7cSOZ+Ty/ad9QdCwAAoJnAAgAAaCawAAAAmnUrN1urtvxl75K1tZbIie+RD1477qRH+dRac9tfYpzD3O1VO3Zlrh7tLdHHi/Q9Wle73+a22Ws8zLbl5BzvX49S6Oeptv+X/XPTT8141R7jEi/aWIBt9lkufJfvXu8xo0txxwIAAGgmsAAAAJo1p0IdHh7mypUrs8t8JvNTFObe3qlNm6ktkTZ3Wo8nb0+pTQnqMd/UckukcvXof4+nfi9RtrRHilaPJ4f3KF98nqmBvb5vvVMKz/u29M2ux3dqH2qO8yVSXrnx9DiH7uIynPN6bJMlytbXnIMu2vZ2xwIAAGgmsAAAAJot9uTtdbW315a4vXOet5l6pOL0qFJT+zTH2jSBmspMS9/a65USVKO2EtpUOz1S2KamLf0E0KVTM2rTw6bmm9KSund8fJzr16/PXhf9XMQqb73avAyf7aKldLSqvZb3Xtc+27iozvN706Py02XijgUAANBMYAEAADQTWAAAAM26PXl7HyX9LuJTB5fO1V/6icRnzbttvqVz+qfWvbTaY7JH/5cYuzLVfu3YnppjoVfpwh5Pxr4oeayn9ePg4CDXrl07h97cHJYoO91jHFnNtNrxWj0+99Klq5dwWf6t0Ht9Sxyvl8E+v4u76PE4g4vMHQsAAKCZwAIAAGjWLRVqU+/SpFPTli4Hu0SZyR63uHqlSW1rp/Z2+VxLpFPVWuLJ271v8S+RcjT3lm+PY6ZXekTNbfwpSzxde26bys1eLLXf/blpur2n9XrS/UX8bJuWSAvuUVq6dV2b03pd33qs77Kk3qzb5/Faa9/r2zd3LAAAgGYCCwAAoJnAAgAAaLbYGIvacrO9H5++RKnKbe1tLrdE+c7eeelTbS6dEz9l6RzEy1KmtHdZ4trxTlPtLL29dhm3MVeP0pu1ZQEvewnHy26JUug1y9WeQ2td1M/WY7naZXqMG9znZ9tFjxLCN5LLUkq35t/HF6n/iTsWAABABwILAACgWXMq1OHhYa5cudKtDGfvtJldXJRbk3PVlqydW1Z0c74e7fd4qmRt6k2P9JQet/h79HGX5abmmyop27v9XdSk7i3xfVii7OSN8GTVG9XS6TBTLuq+7/3ZLktJ1t5q/z2zxDlo6XXP7cfS7dfMt4RdrosXZb+1cMcCAABoJrAAAACaCSwAAIBmzWMsrl69mqOjo51yunrkSvYocdkj969X/uC2HNTacQ6barb5Lnl7S5TurenX3FzGJXKpa8uWzm1j07ZpS4xdmbLEmJEe5Wxry0DObaPmuOP81ZYavpHHxtR87iVKyi4x3qlHaemadW22WTv2sHbd29Y1tb5e27/3Z9vF3M92nnqfgy5aKV13LAAAgGYCCwAAoNleys3W3kKbmrbv22tz+rHLtN792LR0SdYp+y7JukTqWI9119yOXOJ46lH6tLaNuftml9SS80ozqk012EUpJQcHB7l27VrV8rTpXQbysqj53Etsjx7pkT1Ke+4jVbbH+mrVfO7ac9xFKSF8UdMXlz5ez+Nzu2MBAAA0E1gAAADNBBYAAECz5jEWJ3qUVu21XG3p05rcvKXz12q3z9S0JcrZ1SxXO46ix1iAXnqU2V23xDiHpXMqa0vD9h4HVNt+7Xbl8ruIY3kumn1+B2rLhdde+2o+2xJldpc2d921+f5LPDagt4sypuIsNeekfe+3s7hjAQAANBNYAAAAzRZ78vY+b5kuUcZt36XhejxpeG77m3qk28w197P1TjE6q/2ln+Dco189blvuO3VviVvk27bJ0mlY+zjHDcOQ4+PjXL9+vXvbnE36071dlGt573XVrq9XenLN+nqdr7dt84tUun/ucksuc5olrsOt7V+085Y7FgAAQDOBBQAA0KxbVahelXpqUlJ6pY/MfbJ3jycNz+3Hprnrnlpuan1LP7G7RzWvXhVBatqYskS1qqWfHN57XT2+b7usY59paru0X5ve5snb56t3BaGLqjZtsDadtLZfc6/JPdbX8p3dNq21H7tM66H2c89tc4lU2R7H69L7u/ZcsvRnW4o7FgAAQDOBBQAA0ExgAQAANGseY3F4eJgrV+7dzNK59EvniS2dUzn12WrHUeyyvpr5eucTLpHzONWXJY6t3mVL9zFGoab9TTXrm/rctdu8xz6dOxZq6bxuzl9t2el9PM12STWfe+my67XTlihxvfTYtB6fu4fzLN3f63tTc7zucxsv0ZfacRpLcccCAABoJrAAAACadXvy9qalb7csfftx6TaWLutaq0dJ3Mtgl1vbPdLiljjWtq1vl1SxHqV6a7dBbQnkpdMetq1rlzZayiN78vb5WSIl8rK7DE/G7lHae99q+lx7TPYom33WvDWWaKMmBXmX9mvUbtclyp3vgzsWAABAM4EFAADQTGABAAA0ax5jcaJX/lqPnPUeue5L5KX16NfU9umdZ7prbvi25ebu0x7TepSNm1t+9KxpvcveLaH396hXabvzLO+4rZztLu3NXe4i5XxT77xzmlstUeJ8n2rLqV+GfbV0ifm5y+yyrc6zpHbNufc8+1j7fVv6GtnCHQsAAKCZwAIAAGjW7cnbtU+97VWCsma+Hk8C7vEU6Kl+7uNJmDXpHr2ejN27jdrSc0v0a+4Tx2vXPWeZqT61tNOjjSVKLG5rv0cJ4SW263nfsma+2hLCl93c89gS6SRzr4tz981FTeuq7X/vaftOAb8ozrOPl2H77ModCwAAoJnAAgAAaCawAAAAmjWPsbh69WqOjo66lSLrnbO+dC7sEjmbPXIee3zuXtuqd576Evu7V/783DZ7tLetX0uUaW6Zt1Wv8Ta169tn+6WUHBwc5Nq1a1Vts5za8XOXzdzv20UaZ3LZ980SZdJ7TIMa7lgAAADNBBYAAECzvZSb3dTj1uQS6Sk9SttNqSlXWNv+LmpKstaWtqt9QnePdKp9l9U7r9KGS6R11epRJnjpJ75vmvt96N0+l9c+y3fu20X8DBexT0tZ4hwHS3LHAgAAaCawAAAAmgksAACAZudSbnZKj/zj2nz8bfmKvXLne48tWTqXvrb92nKd6+vrlYfeo1TiRcmJP8+yq3Nze2vH3kxZoqxlbZ+3mTuuaI7j4+Ncv359p2U4XxflHMGNx7HFZeOOBQAA0ExgAQAANOtWbnbTVNrPVMpLj5SUueuu1eNpzkukseyzjO/SqUS1n7tHmlptX+am1PQqUbxtvoukNpWo17xz2ui9f89q/zLux5tRbblt2NXS6aSwT+5YAAAAzQQWAABAs+ZUqG1qn05d88Tdue3t0q+56QqXpWLD3Kdab1tmU23qU+1yNf3fxdLVf5b43NvSq5bYN1Nq035q+zz3KcdzUy7nphfs8uTt2nVzOUhBufGcZ4pij7RpuCjcsQAAAJoJLAAAgGYCCwAAoFm3J2/vosc4hym1y9WM2+hVSrLmCdFLlEPsMbZk7ja5LGVXe5RMXfpp5D32Te3+WGKZmnLMSz+tfRdzv5un7Y+Dg4Ncu3atuQ9AHz1KudcyJovLxh0LAACgmcACAABo1q3cbK8nL/cuBzu1XO+nRdf2o7aNqTZr06SWLlW6zyefb66v9gmmPfbVEmlM29rvdat+3+ub24+adde2UbvfatMXhmHI8fFxrl+/PnsZoM55phb1SLGFi8gdCwAAoJnAAgAAaCawAAAAmnUbY1Gbs75LudYe/aqZt3a8whLlO3vnhtcut8RYiR5t9iizu7lM7+3c63PXlCie6ssuY5r2Wf63dp/2+Gy1Yzhq51VuFvZn2zli6X+XzO3HWdPgInLHAgAAaCawAAAAmjWnQh0eHubKlSvdSsr2uO23dDrVPtO8LtJ2natHic5aS6fe9DgWlih1O9Ve7TE5d1ptqeHeZWqX/tz72K7A/sxNJ52a1qPUeu9zLZwndywAAIBmAgsAAKCZwAIAAGjWPMbi6tWrOTo62in/eF2PcQi1uc9L53xvqh2bMVdt7vbcknvbltlluSVK+vXYrkuXFV0ih3bbvLW5vLuse+p7tK3Ni1oeeekc6dp+Acuq+S7Wnidrr3fGVXDZuGMBAAA0E1gAAADN9lJudok0gdrynT2exLxEWkWPzz13fft+GnKPdS/R5x56PHl7bntz+7FEauDcabUpcrWm+rj0k3SX+i4eHx/n+vXrbZ0DFnFRyuDDReWOBQAA0ExgAQAANGtOhZpjifSIJars9KhINdXe3Ao5c9tfIuXlolSs6VF1anPeHsfF5nI1+7FXBaS5+6122nk+ebvHcdgjJXJqmdpjErjYaq+tvabBZeaOBQAA0ExgAQAANBNYAAAAzRYbY1Hz1OGpNjbnnZvT3COvu7Y0bA9L5OPPXccuy+wzX7RHac9e4xB6lGSdUjPOYR95vr2P+yX63PtzLzHWA7gYevybpVfZfbjM3LEAAACaCSwAAIBmeyk3W6tXClVvSz95c4mnd/d+WvgS5TVrU8x6P5W7tkxpj6c716ZaLdH+lN5ldnvY5XzRu5xt7bbrsU+BvpZIC/Xd5mbhjgUAANBMYAEAADQTWAAAAM2ax1hcvXo1R0dHk/PUlkXtkRddm8NcO4agNn96qrxtj35NqSnJWrvuHmVpdxnLMLfk69ztf1Zf5k7btu6paT3G3kzpUfJ1iWO39/Y5q81t7fQaRzFnXcDl4DsM9+SOBQAA0ExgAQAANGtOhTo8PMyVK1f28lTauekX+3z65S5pOTVl6Xpt17lpLbVt1KS59NoXPdLbam9n7/NpqkusqzalcO60Hk/GntIjZXFKbT9q07dKKTk4OMi1a9dmrRcALhJ3LAAAgGYCCwAAoJnAAgAAaLaXcrO76FGOtIfasqtT89WUO60dF1BbxreH2jLBS5Tj7TF+pPaY7J3H32O9tSWElygV22NsTO1yS4/hmGqjtrQx3Gx6fE+B/XLHAgAAaCawAAAAmnUrN7uLHiUu1299LlFyct/pL9vShWr73yudp0btU5rnlrPt8QTk2nStHqkrPVK5atfX68nt55myODe9bWqZJZ5gv639Xb/Dx8fHuX79enMfAGDf3LEAAACaCSwAAIBmAgsAAKBZt3Kz+ygJuW3eHiUtd7HE+IuaNnt97iXK29ZYovxozfiOXfQYm9GjHO/Uunps19rvYo9jpnbb1X7ftrU5Nd9U+8A8td+bi1KmvlaP6w9cFO5YAAAAzQQWAABAs27lZndJQ6hN/ehxu7NHCdslytvOTb+Yq0fJ1H3fnl3i6dfb2thUW8527vqWOGbmtlEz31n9OM9jqKbNXfrfO0VrF6WUHBwc5Nq1a1XLw2VWW6r8MqYE1Xw2KZZcBu5YAAAAzQQWAABAs+ZUqBO1qStLp83U3jKd234vc2+LzlW7P3o8qXzurdx9PNF8rotyi/k8Kw1dlv2xbd290iF6tHNRjie4zJb+ri+tR1rl3GmXZZtw43PHAgAAaCawAAAAmgksAACAZos9ebtHrvjSTxqeWm6Jkrg15U5r29+lZN3ST/quGT9Su+3m6rFvatusLSdY+52qzfPt0a8lSgP3UNOv2u+U8RZwc+h1Tdu23I1QZpcbnzsWAABAM4EFAADQrFu52V1uAdamCfQoFTvV3nmWbutRbnZquR7pGLXt16R51ardb3OX63HM1JZ1rU3XOs8Stpc9DWiJY/Ks/Xh8fJzr1683rxduVEs89b5Wj5Kyc0l94jJwxwIAAGgmsAAAAJoJLAAAgGbNYywODw9z5cqVnfIHe+Qa9i59uou54zZ6lIZbesxAUrc/euR67lIitXacQI+yn3Pb2HcZ2bljV6b0GDczd5ld1l2zTXZZpvd4mH18T4HTXZSSrLXl4Z0HuJG4YwEAADQTWAAAAM26lZvtlX6x9BNra9KYalMslrgt2uP2aW3qUI+nivdID+qhVwnW3qVce5Tg7ZUKUJMm1etJ9DXz9dLjibhzlztt3QcHB7l27drs9uBmsEsa6kXsh6dmc7NwxwIAAGgmsAAAAJoJLAAAgGbNYyyuXr2ao6Oje73fY5zA3BzEXcYCTC1Xu765665pv0cp0l3nrdF7XEiv8qA9xq7su0xtTRs9jt0pc7fdLvvtPMfb9C6xvMsxc9ZnPT4+zvXr13fuH9yslh6buW1du6xPuVluFu5YAAAAzQQWAABAs25P3t7Uo5Tk0mVXay3xlM+atJBeT4Heti17pWHVLNerfGePNnqkGfV+AvjUums/yy79qik3O+Wipu5NWSJFTrlZ2F1tevI+XYY+Qg/uWAAAAM0EFgAAQDOBBQAA0Kxbudmp0qq98vF75B7W5EVP9WPfueFT7fXI06zN1a/53LXlcneZtu047DXWYNu6ptrpsW8221ni80zZtl13+c726NcSJXhrSxvPbX+J0sZwo5s7tnGJfzfM7demmuvWvvsPvbljAQAANBNYAAAAzZpTobapTctZOp2n9xM6a8u6bqpJa6ndrlPrnlqm9inKNdt83+Vma9NTakq7Lp0u1ysdqcdt/Np+Tc1Xs+6l0wan1rdL+568Dbu7qKVca8+N26ZJi+IycMcCAABoJrAAAACaLZYKNVft7cGp+XpUoulRGaZH+sUST/auVVuZqfdTmqf0SLfZd2WeHsfa0hWvenxvar8PS++PfX+2s6Z58jbsZul0zCm154+a5VSM4jJwxwIAAGgmsAAAAJoJLAAAgGaLjbHoMRZgbjnH2tKk+y7xVtPnfT/Zu0c52Npys7XjTubOW5vH32P8Re9+TLVZ28YuejzRvEefa8do1Rxrvc4zZ01TbhZ2s89xcUuPU+u1HJwXdywAAIBmAgsAAKBZcyrU4eFhrlyZbqZX+k6PNKbaadvmq+1jj9JzU3rcPq1Na5mad4knJdc+NXuu3k8L7/VE8x7rntLjielLPEW+JuWvNnWvJaXptP8H2i2Rclm77t7/3li6/7A0dywAAIBmAgsAAKCZwAIAAGjWPMbi6tWrOTo6utf7PfLGe7Sxy3L7zMWcm4vea5xGzefuNQZibh/n6jHWYNPSefBLtF8z3maXfVOzned+ZzfbWLpEbu3xWmtu+8ZfwLKW/q5vW9cS05wvuAzcsQAAAJoJLAAAgGaLPXl7XW0JtqWf4DylRzpPj1SifT/JeO76ejx5e+kSo5vr613Sd7PNucdybbpQTZ92mTbVl9rUvdo0oN6piLVlcKcs9RT5g4ODXLt2bdbywD3tO12ox7WpR3twUbhjAQAANBNYAAAAzQQWAABAs8XGWEzllM/NIazNN5+b916bBz2Vu92j5GtNe5vz9s77PGvdc+27THCPfNW5x3Ltumu3ec3+7lVutkf7S3z/eugxJqjHPgVuXMZScKNyxwIAAGgmsAAAAJp1S4WqfaruWe20LtMjbaY2XaFHWdce6WBn9WvutNo0jR7pVb1TRHp9lrmlgee20aNc6y7HTO2x1uNJ671L8PZKLdjWfq+UrKVTuQDgvLhjAQAANBNYAAAAzbqlQvWqxtP7ScO1aqta1aaAzWnvrHVPmZt+UZtqVVO1ad8VcZZ+8vbcdmpTjubapXLV3HZ6pDRNqT3Ol6isMrdC2xLH0zAMOT4+zvXr12cvAwAXhTsWAABAM4EFAADQTGABAAA0ax5jcXh4mCtX7t1Mj/zjueVaa5+M3SMfvPap4kuXYN01r3tO+3Nz7vdddnXpsqhTasoG9/ps29roUbL2rHUv8aTv3vNNlQJeuvTz3P3h6bsA3EjcsQAAAJoJLAAAgGbNqVBXr17N0dHRvd7vnRJU22Zt6dCl00d6lKxd4knJPVzG1I+LmhbXo+RrbTpY79SxXcrg9i5L3KNsc+32qd0fAHDZuGMBAAA0E1gAAADNBBYAAECzbuVme5V1rcnrnsphri2ZunT/a/PG5/a/V7/mztcj733dErnn+85t37a+XY7xmm20y76o/Q7UHodz25+ybd4e42Rq26ndBqe1c3BwkGvXrnVpjxtDj1LrtSWp4UZkrNty3LEAAACaCSwAAIBmzalQJ2pLn+4ybWp926b1SNGqvW3c6zZ1jfN8avJFKQ+6uVyPFLke5Vprt93cab1S96YsnZoxt4+9UpBq1j13vl2fhH58fJzr16/P6yA3pCWunxelHDnsy9zrg9TAvtyxAAAAmgksAACAZgILAACgWfMYi6tXr+bo6GiyHOWU2pzyqfd7lZ1sbW/KLp+7db6zps0dC1A7rmVuG1Pr7l36tNc+7ZH/33vMzi5jXHqMXZmyz7LTu7QxpUf7S4/94ObVo+S445ObTY+xn8zjjgUAANBMYAEAADTrVm62l7npNlPvz00LWfrJzz3a6HW7rvdt8Jr91Gt9S5S6rU0xWzq9oCbdpsfT5nfp1xLHU+8njvcoZ1t7bO26Dz15++ZUWxqzd/twI9rl+Fd+uY07FgAAQDOBBQAA0ExgAQAANGseY3F4eJgrV650yWE+a7l9loOdWu/SZSbnbpNeObPb8gl7lS3d1n6vsRI126R2HMISZYJ7lIrtMXZil3XP3ae9yxBPtbNEOcHaz9ZSxvf4+DjXr1+vWp4bw9xzRO0x2et4hcui13WXs7ljAQAANBNYAAAAzbqVm10ibWaJJ0TX6JXKNWXure6lSw0uXYJ3Su2t+t5PLe/1hOht89WWda1tf+kn9S69XXt8nh5lp3t8n89aHyT137falEjlNbkRLVFqnbO5YwEAADQTWAAAAM2aU6GuXr2ao6Oje90+nXs79Tyf2rv07a9d0nl69GvpJwjXpknVHAu99um2VJYl0oU21aQX7PsJ0bXVqua2P6U2hapmuSVSCGv36T7PQdx4lkhtlP7EjU5K6v64YwEAADQTWAAAAM0EFgAAQLNu5WZrczZrn4ZYmxO6dN77EmNG5rY/9dlqxhfseyxGrd65kr3GKGz7rLvs35pjocc4jdp+LbHuqXb2WSZziTEop7V5cHCQa9euVfaSG93SY5q4MSz9b5GbhfFIu3PHAgAAaCawAAAAmjWnQh0eHubKlSvVTzWsLVM7t/2p9V2GlJ0eKU0t62udb1Nt+kiP/dYjlatW7dOde5RW3edxMaXXLeWalI4ljot9HpPcXOaeB3Y5JqVw3Nhqj4Wl088vg32n5N/o3LEAAACaCSwAAIBmAgsAAKBZ8xiLq1ev5ujo6F7vz81R65EjWlse9Kx2avQoO1nb/7n96pFTPnddu6xvbhu17S+RE987f75HXvQu22fpY35uP3aZt8eYkW3t9ejT5ry77NNhGHJ8fJzr16/P6hM3ptprgPzvevsec9lDj+OkdpmLuk1qLPFvrpuZOxYAAEAzgQUAANCs25O3l7BEikWPlKOl053mtreLHqlEU8ssXcZ3bqnVHmpTdmr7WFvariY1benbur1ul/f4bEunF9Y+6R5aKCm7f5cxxazmHFSbVn5Ztsm62n+z1Ka53kzcsQAAAJoJLAAAgGYCCwAAoFm3MRa75Jb1zn3ed2nS2tzqfZZF7VFydJfPXZNvWZvXOKXH+JGz2tzWfm2Of61t27x2uy6x7WrVHGu156CpdU8ts9S4jYODg1y7dq1qeS6vpccEXUZzv4u9278R9Ljm167rRhprcCMfI0txxwIAAGgmsAAAAJo1p0IdHh7mypV7N9OjFNkSt9OWvkU393Pvu+xnzbqXSC2ZSl3p0a+5t2T3UVK2d3rY1Pp6pDTtkspVs+4lngje4zwz97PVbp9dePI2yfzv0c2UprHU9+20Ni9SWuiUHuW2ty2zuVyP69tFdbN+7qW4YwEAADQTWAAAAM0EFgAAQLPmMRZXr17N0dHRTmVXp9Tktu2Sb3meeZQ1ue69SlzW5ALW5rH2yH+t3adz21yiVG+Pzz217qn2e+RdL122eWraLqWZe5TlrPlstd/FXZdTbpYljuvLYN9ldre1uUs/znM773N77fPfHhfJzfq5W7hjAQAANBNYAAAAzbo9eXuJpyhPtVNbDqx3ebZ93xad236PkqxTy9WWYKu9Vd8jNWbpssf7LClb22btLf4eJVmn7PuJ4DX92kdq4EUta8nFcZ7lZnuULZ2ad9/pyT1Ksl5Uc1NNa9NVt8131ryXgXN0G3csAACAZgILAACgWbcnb9emd/SwxK2p3lWINtusvTXZI9Vnidt8NelPvY6Z3k/J3Oc22GVarR6fu8ft8l3WXbO+Xt+3faZEuq3OaXapDrfNeR5btZUge6yvV4ptzTIXKU1qn/v/Rq5Utosb/fPN5Y4FAADQTGABAAA0E1gAAADNFnvy9rolngRcM99Zy81tY+mnitfmcPYYpzHXEn1c4imi2/pSWzpvibE3NW3sOu+2ZXqUeqzNK+09fmSXp3dP6Z2bvMtT3pPk+Pg4169f79oHLr4eJUD3Oa12rFiPaUuUfj7PcXC1euzTmnVtttljbONlcaN9niW4YwEAADQTWAAAAM3O/cnbPW4rLVHisscTg6fmnXtrsrYs7VQ7+y7J2vvWYY/2dklFq72lXNPPJZ7S3OM2/hJPU59qf599XjrtcZc23Wa/edSmRF6Uab3a63HN6V1udt+frVbvfbpEWutlKc9LP+5YAAAAzQQWAABAM4EFAADQrNsYi037LIO2y7qnzC1tN3fdU+3Pnbb0GI6pafvOjZy7zWv3R+2265Hv37uNKbscg733Y+1xt8s5Ym77tdurd1nrXZRScnBwkGvXrnVvm4ulx9ihJc6FtcudZ758j2tf7/PF5rR9b5/a/d26rn2sj4vNHQsAAKCZwAIAAGjWnAp1eHiYK1fu3cwSZe/W9UhdqU2B6GHft0V7f+7eT00+q82lS9Yuccu6ps3e5Wt3aaM2ZbH26dc9tkntfqspcVnb/hKpddy8epRX71UWemlLpMe2LrfEupbYrvtMfzrPY5KLxx0LAACgmcACAABoJrAAAACaNY+xuHr1ao6Oju6VH9fj0fC1Of6980eXKHc5tyRerzKc6/PWtllrW/u7lAWs7dfS27VHDnBtqcQeY4Jq8/17jB/pMRaqdkzKVBs15w9jJWhVc9zVjotauuz0EnqUp57b5hLn0CXOET3299LjJW/kY3KTMSMjdywAAIBmAgsAAKDZYuVm1y1xi26JtJkeZVeXLqE5d1qP1KFe6Rw90tvW9Xhiba/2l3ga9txpPVL3li7ju672u9LjHHGeaQJT/YKelijJehksXd5+n/1Yotz5LtN62+ejB/Zhbr9u5rQodywAAIBmAgsAAKDZYlWh1u0yraaKQo8qEFP93PcTM3tUtaqtGNU7lWtq3l5VoXpXU6ltf59ViHr0o9e6e1Rw2iUdqfdt/CW+by1Vao6Pj3P9+vWqPnFz2SVts/Zp8BdRr1ToHmmPS6Q1L9mPXZbr0ZfaY7K2/Yty/F6UfpwHdywAAIBmAgsAAKCZwAIAAGjWPMbixBLly+bmLS9RfrRHXuB5Pmmzts0e7U3psQ2WHidwUduYezz1yuWtKQfb42nzZ7VT87TcHmO5ej1V96zj5ODgINeuXZucB3Z1I5ebrbX02JIeY/eW7sc+191rvNxFKZc7d7mbbbyFOxYAAEAzgQUAANCsWypUr7J3taXbatqYWq7H7bslbvNt6+PUfJttLlH+bWrdc+frURKvto3aW5U1tzt73catKeO7RBni2mNmn+mMtSlgU9+bpbarcrPU6vG0+cvuRvosN5oe19mWdmrUpsDezMehOxYAAEAzgQUAANBMYAEAADRrHmNxeHiYK1eudCslOTXf0o+J37buXmMBasY57GKqzz22yZSa9nfZvz3G10zN1yM3ssfYmJYypXOWW+JYnlqmx5iXucdC7fmi1tzt2qsEL7SYexw6BrloLtIxeVFKCF9k7lgAAADNBBYAAECz5lSoq1ev5ujoqEdfkvQpM1kz3y7L1Za47FHub277tXo8TbjHk4yn5l1i29X046x+1dhlH9Z8V3psux7zbc5bWzq5R/tTalMbl07Dgl3NPSal5wEt3LEAAACaCSwAAIBmAgsAAKBZt3KztXrklNfmYE+1UzvWo0e501q1OeXbPvcuYw3m5ptvW2ZqvrPW3aPN2vbntjN3DEqP/bapx9iSmj7tsu6pvtSOado2367zzlmmVx56KSUHBwe5du1al/a4eS1xjQE4izsWAABAM4EFAADQrDkV6kSPpwIndekwtSk7tWkbPZ4s3UPtU5prn3g8t/258y6d0rTL+nqUn+2dzja1rl7rm2p/yrZ171J2tXcJ2F7noB5tTD1p/ax9fHx8nOvXrzf3Cdad51PqgZuHOxYAAEAzgQUAANBMYAEAADRrHmNx9erVHB0ddSszua2NXaZNmduXqf4vMb5jbh+XHiNSO/6i95iUHvn+uyzTI8d47v7oUbJ2l37Mte9+nWeJ5aXNPX/AvixxPQXY5I4FAADQrPmOxa233pokOT4+vsf7BwcHf/b/m9PmWm+j1i7r3ra+qTam+rjLNpm7vXq3sWl9uc355k6bu75ex8wu+2DbMlOfbUrNvqptf+5y+/i+ze1X7XFY08bSn3vqeN1lud7zczrb8Z5qr6e2I5DMPxeU2tvyt99++/+W5BVVCwNwlofddtttrzzvTlw2rk0Ai5q8NrXcsXhVkoclubOhDQDu7YEZz7HszrUJYBlnXpuq71gAAACcMHgbAABoJrAAAACaCSwAAIBmAgsAAKCZwAIAAGgmsAAAAJoJLAAAgGYCCwAAoJnAAgAAaCawAAAAmgksAACAZgILAACgmcACAABoJrAAAACaCSwAAIBmAgsAAKCZwAIAAGgmsAAAAJoJLAAAgGYCCwAAoJnAokIp5Y5SyrMWXsfTSykvWXIdnK2U8vBSylBKecx59wVgimsTU1zP2IfmwKKU8pzVgbr5en6PDvayjxPuaj1PLaW8vpRyv1OmHZRS/qiU8nlL96NFKeV9Sik/U0p5cynl5aWUL9lh2fuWUn61lPLsU6Z9fSnl90opD+zb4xtTKeV+pZRvLqX8YSnljaWUHy6lPOSMZUop5RmllFeXUu4qpbywlPLu++ozXBSuTfdaz6W+NpVSPrKU8lOllNeVUv5XKeU/nHyWUsq7lVK+s5TyylLKnav5/sJq2v1KKV9TSvntUspRKeW/l1I+duY6Xc86cT27efS6Y/H8JO+88fq0Tm1fNt+V5P5JPvmUaZ+S5G2TfPdee7SDUsqfS/JTSV6W5AOSfHGSp5dSPmfO8sMwvCXJZyZ5cinlCWvtfkiSL0zy5GEY7lyg3/fp3eYF8G+TfEKST03yUUkemuRHzljmS5J8XpJ/kOSDk7wpyQtO+8cE3ARcm+52qa9NSR6f5IeSfGiSv5Xkryf50tW0D8x4zfrfkzw24+f8ttW0d0zyLkn+XpL3TvLiJD9aSrn/WSt0PevK9exmMQxD0yvJc5I8b2L645K8NclHrL33JUn+Z5KHrP6+I8k3rV6HSf5Xkq9KUtaWuW+Sf5PklRkPrp9P8riNdT121dZRktcneUGSt1v1cdh4PXy1zHsl+ckkb0zyBxlPvg9ea/P+Sb5zNf3VSZ66WsezJj7zDyd54Snv35Hk+1f//3VJfnPV199dfd77rM379CQv2Vj2WRvtPS/Jc3bZRjP25z9M8rokb7v23tcm+Y0d23laklckeVCS+yX59STfsJr2N5P8apK3JHlpkqduLDsk+aSN996Q8SSeJA9fzfPEJNeTvPlk2sYy35vkuRvv3Wd1fH3m6u+/muRnV+3/YZKfSPKItflP1vWY1d9PTvKGjTY/Kcmw8d4nJvnFVd9+d7U9ruyw/a5m/N58ytp7j1r15UO2LFNWx+gXbbTz5iRPav2ue3ldpldcm077zJf22nRKn68l+Q9bpv3TJL+9Zdr7r7bzw3ZYl+uZ65nXzNfiYyyGYbgjybOSfFcp5Wop5f0ynqg+exiGP1ib9bOSHCf5oCSfn/HE8Nlr078p4y8VT0ryPkl+MMnzT26LrXIGb0/ya6v5PjzJjye5ZdXei5N8a+7+1erlpZQHJfnPSX4p4y8efzXJQ5L8wNp6/3XG6PoTk/yVjBej9z/jY39bkseXUt7t5I3VbdmPzN2/otyZ8Uv9nqv+PSXjLyAtJrfRqh9DKeXJE218aJL/dxiGt66994Ik71FKebsd+vLMJK9J8u+SfHXGE8iXl1I+IOP2/f6Mvx49PclXndGnbb42yTcmefSqj5u+J8knlFIesPbeE5IcJPnR1d/3T/INGff/bUn+NOOvWdXfjVLKR2S84H9jxv37uRn39VeszfOcUsodE818QMaLxgtP3hiG4TeS/H7GfXSaP5/knTaWOcx4Ed+2DNyUXJtGl+ja9GdKKX8lycdkPM9uTnuXVX//4ynT7pvka5L8p2EYXrFD/13PXM+YqzUyyfiLy3HGX03WX1++Ns/bZjxBPjdjZP/sjTbuyHjSXf8V6GuT/Nrq/991tY6Hbiz3wiT/avX/35vkZyf6eUfu/avKP0/ygo33HpbxpPHIJA/I+CvEp65Nf/uMv+Q8a2Jdt2T8dePpa+89I+Ot2rfZsswXJfmFtb+fnh1+FZqzjVZ//0aSvzHR959K8v9svPeeq23y6B2PjfdMctdqG37g6r3vSfJTG/N9fZJfXft77i88n3/G+q8keW2Sv7P23vdm9cvclmUevGr7vTbW9ZjV30/OGb/wrLb5l23M8xlJXrX299ck+c6JfvztJG855f3/muTrtizzYau+vvPG+z+QjV+6vLxu9Fdcm05b16W9Nq3N97Gr/fjEU6Y9bPVZ/q9Tpl3J+A/2FyX5cxXHk+vZ3e+5nnltfV1JHz+dMYVm3etO/mcYhreWUj49yS9n/NKf9uvHfxlWR83Ki5M8tZRyS8ZfAm5J8pullPVl7pvxdl+SPCbjryC7eN8kH11KeeMp0x6R5NaMF56fX/ssryul/I+pRodh+JNSyndkzMv8yoy39D4rybcPw/CnSVJKeWLG3MFHZLxIXEnyRzv2f92cbZRhGB7VsI6dDMPwa6WUH07yoGEYfmH19qOT/NjGrC9K8gWllFuGYfiTHVbxC1MTh2E4LqX8QJJPz/ir5P0z/rr3pJN5Vr+YPSNj/uaDc/e4o3dN8is79GXd+yZ5bCnlK9beuyXJ/UopB8MwHA3D8GWVbQPzuTatuUGuTc/KGDg895RpX5Yx3eq0Qeh/I+PdoocNw7Dz53E9cz1jnl6BxZuGYfjtM+b5sNV/3371etMO7T8gyZ9kvJ22+UU9OfHetUN76+3+eO4eALbu1Un+YkWbJ/5jxpPc4zN+ud8lybcnSSnlQzP+0vG0jL+gHGY8OTx1or0/zXgRWLc+wGvONprjNRlvua97yNq0XR2vXrsYMv1ZT8w5hr4nyfVSyjtm/KXrrowDOk/8eMZ/UDwlyasy7qtfyXjRPs1Z+yEZ98XTcvrAtDfP6HMybuu3LaU8aBiGN6y9/5Bs3w+vWZvn1RvLvGTmeuFG4tp0b5f12nTioUm2BVAPTfKbG4Hg+rTXDsPw+op1nnA9uyfXM+6lV2AxqZTyiIwVAZ6ScYDSd5RSPubkF5KVD95Y7EOS/NbqF5Zfyhghv+MwDD+zZTW/nDGn8Glbpr911ca6X8w48OqlwzDc62RRSvmdJH+86tvvr957u4y3oq9vWU+SZBiG3ymlXM9YiaJkHDD3stXkD0vysmEYnrm2rnc7pZl1r82Yf3sy/y0ZB/f99OqtOdtojhcneWYp5T7DMPzx6r2PTfI/Gk/IJ34940DGdY/NeDE4uehsftZ3z5hHurNhGH6ulPLyjMfdxyX5wZPPVUp5hyTvkeQpJ9uslPLhZzT52iQPLKXcfxiGkwvBYzbm+cUk7zHjHzRT/lvGY++2jAMuU0p5j4y/PL14yzK/l/FkfFtWJ95Vla8PTvItDX2BG5Jr06W6Np346CQv3zLti3Lv4OXE92Uct9KT69k8rmc3k9Zcqox5rD+ZcZDN+uvBq+m3ZDxwfmj19ztnrGLwxWtt3JFxwNg3ZPxifFrGXzI+d22e7854oH1yxkE9H5TxV5ePX01/ZMbcx3+fcXDYozLeAj/px7Mz5vM9PHffInxoxgogP5jkL2e89fuEjL/e3LJa7lsyVnp4fMaT5Y+t+vqsGdvmMzL+onBX1vJBM5bJ++OMvwQ9IuNt2z/MWq5j7p3H+rkZf9H4+NVne3bGX5OeM3cbreY5a4zF1Yxf5u9M8pcynsDelORzGo6P5639/f4ZT/z/YrXPPitjXvCT1+b5vox5ze+XcRDa7Rkvvk9eTX941vJEZ/ThqzPmT/9xkg9fe/9tVsfid2X8BfDxq2Pkz3JiN9eV8RfNN2YcyPaIjLmjr8w9c1KfsFrX01bb8NGrff3Va/NM5qSuHXsvy3gh/YAkP5fk5zbmucf+zPgL5+tXx9h7Z8x1/t0k92v9rnt5XaZXXJumts2luzbNmS/jdetrtkz7x0lu73BMPW/tb9ezwfXMa2NfNzdwerm8IavypEn+ZcZbcu+wtswnZzzRvu/q7zuSfPPqwDvMmAP7zNxzwNx9knxlxpPTW1dt/kiS916b56My5je+eXUwPj9jPmRWX/oXr770Q+4u6ffuq3Zev5r26xl/wSqr6Q9YfVHflPEf3F+cM0r6rfXn1txd9u2+G9O+fnUSuDNjRYkvyPTJ+z4ZL0x/mLH04D/LvUv6zdlGQ04pZbfRt/dJ8jOr7fiKJF+6Mf1x69twxvHxvI33TsrzvTXjieaLNqY/NONt+DdmLHv4cTl9sNtjZh6jj17N/9L1Y2o17WMynvTfnOS/r46hrSfi1XuflOS3VsfLj2f8tXPYaPcJGY/Fo4zH9M9n/CVpfbvccUa/75fxe/G61fH3I0neaWOee+zPjL9APiPjsfrmjAPvHrnkScTL6yK+4to0tW0u5bXprPlWn/85W6Y9PeMdoM33HxfXM9czr26vkxPUuVqVKXvJMAxfcM5dYYZSyt9N8uVJ3nO4O10K4Ibi2nTjcz2DvhZ/jgU3pL+WsWSjkzAAl5nrGXS0l8Hb3FiGYfjU8+4DALRyPYO+LkQqFAAAcLlJhQIAAJoJLAAAgGYCCwAAoJnAAgAAaCawAAAAmgksAACAZgILAACgmcACAABoJrAAAACa/f/bmwik/Q67DAAAAABJRU5ErkJggg==\n",
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\n",
       "text/plain": [
-       "<Figure size 1000x1000 with 4 Axes>"
+       "<Figure size 720x720 with 4 Axes>"
       ]
      },
      "metadata": {},
@@ -224,15 +226,15 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 63,
    "id": "0ad5b92f-521f-48c2-9f5b-7950f5a3f931",
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
-       "<Figure size 1000x1000 with 4 Axes>"
+       "<Figure size 720x720 with 4 Axes>"
       ]
      },
      "metadata": {},
@@ -255,7 +257,7 @@
     "            # handle the east and west neighbours\n",
     "            for dj in [1,-1]:\n",
     "                if 0 <= (j + dj) < M:\n",
-    "                    E -= state[i,j] * state[i+di, j]\n",
+    "                    E -= state[i,j] * state[i, j+dj]\n",
     "            \n",
     "    return E / (N*M)\n",
     "            \n",
@@ -278,7 +280,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 64,
    "id": "686782b5-aa37-4084-9786-538fdc89fef1",
    "metadata": {},
    "outputs": [
@@ -286,14 +288,14 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "mean = -0.0053479999999999995, standard error = 0.0037939558458158157\n"
+      "mean = -0.00036800000000000043, standard error = 0.0026727883866853363\n"
      ]
     },
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
-       "<Figure size 500x500 with 1 Axes>"
+       "<Figure size 432x288 with 1 Axes>"
       ]
      },
      "metadata": {
@@ -303,9 +305,11 @@
     }
    ],
    "source": [
-    "energies = [energy(np.random.choice([-1, 1], size = (100,100))) for _ in range(100)]\n",
+    "L = 100 # How large the system should be\n",
+    "N = 100 # How many random samples to use\n",
+    "energies = [energy(np.random.choice([-1, 1], size = (L,L))) for _ in range(N)]\n",
     "plt.hist(energies)\n",
-    "print(f\"mean = {np.mean(energies)}, standard error = {np.std(energies) / np.sqrt(100)}\")"
+    "print(f\"mean = {np.mean(energies)}, standard error = {np.std(energies) / np.sqrt(N)}\")"
    ]
   },
   {
@@ -313,7 +317,7 @@
    "id": "8da38c5b-f166-4530-b046-3600b4d84c5d",
    "metadata": {},
    "source": [
-    "If you run this a few times you'll see the mean is usually within two standard errors of 0, which gives us some confidence."
+    "If you run this a few times you'll see the mean is usually within a few standard errors of 0, which gives us some confidence. In the testing section we will discuss how we might go about doing automated tests of random variables like this. "
    ]
   },
   {
@@ -321,7 +325,256 @@
    "id": "3bd3831b-f8de-4a8e-aaf6-7aa158cf9d82",
    "metadata": {},
    "source": [
-    "## Making it a little faster"
+    "### Making it a little faster\n",
+    "\n",
+    "This project is not intended to focus on optimising for performance but it is worth putting a little effort into making this function faster so that we can run experiments more quickly later.\n",
+    "\n",
+    "The main thing that slows us down here is that we've written a 'tight loop' in pure python, the energy function is just a loop over the fundamental operation:\n",
+    "```python\n",
+    "E -= state[i,j] * state[i+di, j]\n",
+    "```\n",
+    "which in theoy only requires a few memory load operations, a multiply, an add and a store back to memory (give or take). However because Python is such a dynamic language, it will have to do extra things like check the type and methods of `state` and `E`, invoke their array access methods `object.__get__`, etc etc. We call this extra work overhead.\n",
+    "\n",
+    "In most cases the ratio of overhead to actual computation is not too bad, but here because the fundamental computation is so simple it's likely the overhead accounts for much more of the overal time.\n",
+    "\n",
+    "In scientific python like this there are usually two main options for reducing the overhead:\n",
+    "\n",
+    "#### Using Arrays\n",
+    "One way is we work with arrays of numbers and operations defined over those arrays such as `sum`, `product` etc. `Numpy` is the canonical example of this in Python but many machine learning libraries are essentually doing a similar thing. We rely on the library to implement the operations efficiently and try to chain those operations together to achieve what we want. This imposes some limitations on the way we can write our code.\n",
+    "\n",
+    "#### Using Compilation\n",
+    "The alternative is that we convert our Python code into a more efficient form that incurs less overhead. This requires a compilation or transpilation step and imposes a different set of constraints on the code.\n",
+    "\n",
+    "It's a little tricky to decide which of the two approaches will work best for a given problem. My advice would be to have some familiarity with both but ultimatly to use what makes your development experience the best, since you'll likely spend more time writing the code than you will waiting for it to run!"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6b2ed23c-32f2-40af-bf45-e60004c275a2",
+   "metadata": {},
+   "source": [
+    "## Exercise 2: Write a faster version of `energy(state)`\n",
+    "\n",
+    "You can use `numpy`, `numba`, `cython`, or anything else, by what factor can you beat the naive approach?. Numba is probably the easiest here."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 65,
+   "id": "40386cda-cc14-4fdd-8f9f-71840d1ebb40",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Naive baseline implementation\n",
+      "92.5 ms ± 2.62 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n",
+      "\n",
+      "Your version\n",
+      "87.6 ms ± 6.35 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n",
+      "Your speedup: 1x !\n"
+     ]
+    }
+   ],
+   "source": [
+    "def test_energy_function(energy_function):\n",
+    "    assert np.all(energy_function(state) == energy(state) for state in states)\n",
+    "\n",
+    "def time_energy_function(energy_function):\n",
+    "    return [energy_function(state) for state in states]\n",
+    "\n",
+    "def your_faster_energy_function(state):\n",
+    "    return energy(state) # <-- replace this with your implementation and compare how fast it runs!\n",
+    "\n",
+    "print(\"Naive baseline implementation\")\n",
+    "test_energy_function(energy) #this should always pass because it's just comparing to itself!\n",
+    "naice = %timeit -o time_energy_function(energy)\n",
+    "\n",
+    "print(\"\\nYour version\")\n",
+    "test_energy_function(your_faster_energy_function)\n",
+    "yours = %timeit -o time_energy_function(your_faster_energy_function)\n",
+    "print(f\"Your speedup: {naive.best/yours.best :.0f}x !\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a27bb821-c33f-4966-8676-4295cfd695ab",
+   "metadata": {},
+   "source": [
+    "## Solution 2"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 70,
+   "id": "26a6252d-ca67-49e0-b04e-7f001bae97ab",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[-3.9572, -3.9592, -0.0168, -3.1144]\n",
+      "[-3.9572, -3.9592, -0.0168, -3.1144]\n",
+      "[-3.9572, -3.9592, -0.0168, -3.1144]\n",
+      "[-3.9572, -3.9592, -0.0168, -3.1144]\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "[True, True, True, True]"
+      ]
+     },
+     "execution_count": 70,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "\n",
+    "\n",
+    "def numpy_energy(state):\n",
+    "    E = - np.sum(state[:-1, :] * state[1:, :]) - np.sum(state[:, :-1] * state[:, 1:]) \n",
+    "    return 2*E / np.product(state.shape)\n",
+    "test_energy_function(numpy_energy)\n",
+    "\n",
+    "states[0][0,5] = -1\n",
+    "states[0][0,0] = -1\n",
+    "states[1][-1,-1] = 1\n",
+    "print([energy(state) for state in states])\n",
+    "print([energy2(state) for state in states])\n",
+    "print([numba_energy(state) for state in states])\n",
+    "print([numpy_energy(state) for state in states])\n",
+    "[numpy_energy(state) == energy(state) for state in states]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 74,
+   "id": "c96720d4-2c0b-4fa5-b9ce-4fc7be533a62",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Naive baseline implementation\n",
+      "80.7 ms ± 974 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n",
+      "\n",
+      "Numba version\n",
+      "195 µs ± 4.92 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n",
+      "Numba Speedup: 427x !\n",
+      "\n",
+      "Numpy version\n",
+      "193 µs ± 2.96 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n",
+      "Numpy Speedup: 421x !\n"
+     ]
+    }
+   ],
+   "source": [
+    "def test_energy_function(energy_function):\n",
+    "    return [energy_function(state) for state in states]\n",
+    "\n",
+    "from numba import jit\n",
+    "\n",
+    "@jit(nopython=True)\n",
+    "def numba_energy(state):\n",
+    "    E = 0\n",
+    "    N, M = state.shape\n",
+    "    for i in range(N):\n",
+    "        for j in range(M):\n",
+    "            # handle the north and south neighbours\n",
+    "            for di in [1, -1]:\n",
+    "                if 0 <= (i + di) < N:\n",
+    "                    E -= state[i,j] * state[i+di, j]\n",
+    "            \n",
+    "            # handle the east and west neighbours\n",
+    "            for dj in [1,-1]:\n",
+    "                if 0 <= (j + dj) < M:\n",
+    "                    E -= state[i,j] * state[i, j+dj]\n",
+    "            \n",
+    "    return E / (N*M)\n",
+    "\n",
+    "def numpy_energy(state):\n",
+    "    E = - np.sum(state[:-1, :] * state[1:, :]) - np.sum(state[:, :-1] * state[:, 1:]) \n",
+    "    return 2*E / np.product(state.shape)\n",
+    "    \n",
+    "\n",
+    "print(\"Naive baseline implementation\")\n",
+    "naive = %timeit -o time_energy_function(energy)\n",
+    "\n",
+    "print(\"\\nNumba version\")\n",
+    "test_energy_function(numba_energy)\n",
+    "numba = %timeit -n 100 -o time_energy_function(numba_energy)\n",
+    "print(f\"Numba Speedup: {naive.best/numba.best :.0f}x !\")\n",
+    "\n",
+    "print(\"\\nNumpy version\")\n",
+    "test_energy_function(numpy_energy)\n",
+    "numpy = %timeit -n 100 -o time_energy_function(numpy_energy)\n",
+    "print(f\"Numpy Speedup: {naive.best/numpy.best :.0f}x !\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7d80c912-3773-4c53-a4e9-3f7ee66e2e0f",
+   "metadata": {},
+   "source": [
+    "While writing the above faster versions I realised two things, first there was a bug in my code! I had written \n",
+    "```python\n",
+    "for dj in [1,-1]:\n",
+    "    if 0 <= (j + dj) < M:\n",
+    "        E -= state[i,j] * state[i+di, j]\n",
+    "```\n",
+    "where I of course meant to have:\n",
+    "```python\n",
+    "for dj in [1,-1]:\n",
+    "    if 0 <= (j + dj) < M:\n",
+    "        E -= state[i,j] * state[i, j+dj]\n",
+    "```\n",
+    "I found this while writing the numpy version because the two functions were not giving the same results, I didn't pick it up from writing the numba code because as you can see I just copied the implementation over. So the first lesson is that simple test cases don't always catch even relatively obvious bugs. \n",
+    "\n",
+    "The second thing was that even my naive function was doing more work than it needed to! Because if the symmetry of how two neighbours talks to each other, we can rewrite the code as:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 72,
+   "id": "755ec34c-4975-467f-a559-f585f9d6a42f",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "Improved Naive version\n",
+      "35.9 ms ± 1.27 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n",
+      "Speedup: 2x !\n"
+     ]
+    }
+   ],
+   "source": [
+    "def energy2(state):\n",
+    "    E = 0\n",
+    "    N, M = state.shape\n",
+    "    for i in range(N):\n",
+    "        for j in range(M):\n",
+    "            # handle the north and south neighbours\n",
+    "            if 0 <= (i + 1) < N:\n",
+    "                E -= state[i,j] * state[i+1, j]\n",
+    "            \n",
+    "            # handle the east and west neighbours\n",
+    "            if 0 <= (j + 1) < M:\n",
+    "                E -= state[i,j] * state[i, j+1]\n",
+    "            \n",
+    "    return 2*E / (N*M)\n",
+    "\n",
+    "print(\"\\nImproved Naive version\")\n",
+    "energy2(states[0]) #run the function once to let numba compile it before timing it\n",
+    "e2 = %timeit -o test_energy_function(energy2)\n",
+    "print(f\"Speedup: {naive.best/e2.best :.0f}x !\")"
    ]
   },
   {
@@ -329,7 +582,79 @@
    "id": "81a81a81-fae9-4767-9534-e32f49058ae8",
    "metadata": {},
    "source": [
-    "## Doing Monte Carlo!"
+    "## Doing Monte Carlo!\n",
+    "\n",
+    "Now that we can evaluate the energy of a state there isn't that much more work to do MCMC on it.\n",
+    "\n",
+    "... very short explanation of the MCMC algorithm ...\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 191,
+   "id": "2586a542-35f2-419e-9aa2-2bb9e9ab74b9",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 1440x360 with 4 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "from numpy.random import default_rng\n",
+    "rng = default_rng(42)\n",
+    "\n",
+    "def mcmc(initial_state, steps, T, energy = numba_energy):\n",
+    "    N, M = initial_state.shape\n",
+    "    assert N == M\n",
+    "    \n",
+    "    current_state = initial_state.copy()\n",
+    "    E = N**2 * energy(state)\n",
+    "    for i in range(steps):\n",
+    "        i, j = rng.integers(N, size = 2)\n",
+    "        \n",
+    "        new_state = current_state.copy()\n",
+    "        new_state[i,j] *= -1\n",
+    "        new_E = N**2 * energy(new_state)\n",
+    "        \n",
+    "        if (new_E < E) or np.exp(-(new_E - E) / T) > rng.uniform():\n",
+    "            current_state = new_state\n",
+    "            E = new_E\n",
+    "            \n",
+    "    return current_state \n",
+    "\n",
+    "Ts = [4, 5, 50]\n",
+    "\n",
+    "ncols = 1 + len(Ts)\n",
+    "f, axes = plt.subplots(ncols = ncols, figsize = (5*ncols, 5))\n",
+    "\n",
+    "show_state(initial_state, ax = axes[0])\n",
+    "axes[0].set(title = \"Initial state\")\n",
+    "\n",
+    "for T, ax in zip(Ts, axes[1:]):\n",
+    "    # initial_state = rng.choice([1,-1], size = (50,50))\n",
+    "    initial_state = np.ones(shape = (50,50))\n",
+    "\n",
+    "    final_state = mcmc(initial_state, steps = 100_000, T = T)   \n",
+    "    show_state(final_state, ax = ax)\n",
+    "    ax.set(title = f\"T = {T}\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5d1874d4-4585-49ed-bc6f-b11c22231669",
+   "metadata": {},
+   "source": [
+    "These images give a flavour of why physicists find this model useful, it gives window into how thermal noise and spontaneous order interact. At low temperatures the energy cost of being different from your neighbours is the most important thing, while at high temperatures, it doesn't matter and you really just do your own thing.\n",
+    "\n",
+    "There's a special point somewhere in the middle called the critical point $T_c$ where all sorts of cool things happen, but my favourite is that for large system sizes you get a kind of fractal behaviour which I will demonstrate more once we've sped this code up and can simulate larger systems in a reasonable time."
    ]
   },
   {
@@ -339,15 +664,34 @@
    "source": [
     "## Conclusion\n",
     "\n",
-    "In the next notebook we will start making this into a python package, which will bring a few benefits, it will set up to perform automated tests, will mean our code is not spread all about a notebook and will allow us to use the same code in mulitple places. "
+    "The code we have so far is really just a sketch of a solution. So this is a good time to step back and think about what are aims are and how this software will fulfil them. I see three broad areas on which it needs improvement:\n",
+    "\n",
+    "**Functionality**\n",
+    "Right now we can't really do much except print nice pictures of states, but (within the fiction of this project) we really want to be able to do science! So we need to think about what measurements and observations we might want to make and how that might affect the structure of our code.\n",
+    "\n",
+    "**Testing**\n",
+    "I've already missed at least one devastating bug in this code, and there are almost certainly more! Before we start adding too much new code we should think about how to increase our confidence that the individual components are working correctly. It's very easy to build a huge project out of hundreds of functions, realise there's a bug and then struggle to find the source of that bug. If we test our components individually and thoroughly, we can avoid some of that pain.\n",
+    "\n",
+    "**Performance**\n",
+    "Performance only matters in so far as it limits what we can do. And there is a real danger that trying to optimise for performance too early or in the wrong places will just lead to complexity that makes the code harder to read, harder to write and more likely to contain bugs. However I do want to show you the fractal states at the critical point, and I can't currently generate those images in a reasonable time, so some optimisation will happen!\n",
+    "\n",
+    "So which of these should happen first? In the next chapter we will first make a plan for going forward. We'll then start to move our code to a python package, to document it a little and to add some testing of the components we have so far. We'll then move on to adding new functionality and making performance improvements. "
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "b1880fc9-6670-429f-be34-2511feb0e771",
+   "metadata": {},
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python [conda env:jupyter3.9] *",
+   "display_name": "Python [conda env:recode]",
    "language": "python",
-   "name": "conda-env-jupyter3.9-py"
+   "name": "conda-env-recode-py"
   },
   "language_info": {
    "codemirror_mode": {
@@ -359,7 +703,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.9.7"
+   "version": "3.9.12"
   }
  },
  "nbformat": 4,