diff --git a/Wavefunctions/Explain_Bspline.ipynb b/Wavefunctions/Explain_Bspline.ipynb
index 30f76bf..e461f94 100644
--- a/Wavefunctions/Explain_Bspline.ipynb
+++ b/Wavefunctions/Explain_Bspline.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 1,
    "metadata": {
     "collapsed": true
    },
@@ -26,13 +26,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 60,
+   "execution_count": 2,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAACXCAMAAAAs02BKAAAAQlBMVEX///8AAAAAAAAAAAAAAAAA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\nEunGIPBSNesAAAAASUVORK5CYII=\n",
       "text/latex": [
        "$$\\begin{cases} \\frac{x^{3}}{6} & \\text{for}\\: x \\geq 0 \\wedge x < 1 \\\\- \\frac{x^{3}}{2} + 2 x^{2} - 2 x + \\frac{2}{3} & \\text{for}\\: x \\geq 1 \\wedge x < 2 \\\\\\frac{x^{3}}{2} - 4 x^{2} + 10 x - \\frac{22}{3} & \\text{for}\\: x \\geq 2 \\wedge x < 3 \\\\- \\frac{x^{3}}{6} + 2 x^{2} - 8 x + \\frac{32}{3} & \\text{for}\\: x \\geq 3 \\wedge x \\leq 4 \\\\0 & \\text{otherwise} \\end{cases}$$"
       ],
@@ -60,7 +61,7 @@
        "⎩          0                 otherwise    "
       ]
      },
-     "execution_count": 60,
+     "execution_count": 2,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -77,7 +78,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 62,
+   "execution_count": 3,
    "metadata": {
     "collapsed": false
    },
@@ -85,20 +86,20 @@
     {
      "data": {
       "text/plain": [
-       "[<matplotlib.lines.Line2D at 0x7f1aaad89b38>,\n",
-       " <matplotlib.lines.Line2D at 0x7f1aaad89cf8>,\n",
-       " <matplotlib.lines.Line2D at 0x7f1aaad8dda0>]"
+       "[<matplotlib.lines.Line2D at 0x7f2ee8e8d150>,\n",
+       " <matplotlib.lines.Line2D at 0x7f2ee8e8d350>,\n",
+       " <matplotlib.lines.Line2D at 0x7f2ee8e8da10>]"
       ]
      },
-     "execution_count": 62,
+     "execution_count": 3,
      "metadata": {},
      "output_type": "execute_result"
     },
     {
      "data": {
-      "image/png": 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dp3fx0qyX+Pudvwn0t64g8yuvqNQtPlfc59NP1Q6UadMs6/L6nesUGFeATV02\n8dRjT1nWr8+yapWaEfz1l5YIU92F5sOAp4QQ+YUQgUBr4F8XdyllobijIGpd4M2EDIAuFiyAPHmM\nAbCKMZvG8HbFty01AKBypY0dq4y2z3DrFkycqHJsW0hQYBDdy3Vn7GbvLJnodmrXVpHEK1fqVpJi\nnDYCUspYoCewEtgLzJFShgshugshuiX0EWfHtBIp1aYLi39jPsuJqydYGrmUbuUS+q93jsqV4Ykn\nlNH2GWbOVDnsS5SwvOueFXsya/csLty4YHnfPocQ6iJiw/qoTruDrMbd7qD169WGi4gIEyFsBQNX\nDeR27G3G1nPNHeaCBTB8OGze7AN5nRwOKFlSLTqmIkI4OXRe1JknszzJh9U/dEn/PsWdO2pR8Zdf\nVBpcN6LbHWRrRo9WrjxjAJzn2u1rTNk5hXcqveOyMRo3VuukG3yhYuLy5RAY6NJUtn2r9GVC2ARu\nxXhXyUQtBAaqBasQe22/9WkjEBmpgjA7dNCtxDuYunMqtQvVpmAW122x8vdXRttmv7PUERKiFkJc\nOOUp8XgJyuQsw6zds1w2hk/RrZvK73TihG4lycanjcDnn6tApAwZdCuxPzGOGMZuHkvfKq5fXOnY\nUbnxDhxw+VD62LkT9u9X5SNdTL8qKnjM01zDtiRLFpV4zEZBLT5rBM6dU1tC33pLtxLvYP6++eTL\nlI+KuSu6fKwMGZTxtnnKlocTEgLvvAMBAS4fqlbBWgT4BbD84HKXj+UTvPMOTJ2qSoDaAJ81Al99\npfadP6RGtyGZSCkZvWk0/ao6nyIiufTsqWJzzp9325Du4/hx+PVX5VpwA0II+lXtx+hN9tvZ4pEU\nLKgW8qdO1a0kWfikEbh1C778UvmWDc6z7tg6rt6+SsPCDd02Zo4cKpnmV1+5bUj38cUXaqEqUya3\nDdmqRCsiL0Sy89ROt43p1fTta5ugFp80At9/D+XLQ7FiupV4B6M3jqZP5T74Cfd+nfr0UXFUt7xp\nY8vVqyoy+B3X7bBKiAD/AN6u+LZJLGcVFStCvnwwf75uJUnic0bA4VBpiU1wmDXsP7+fLVFbaP+M\n+6vwFC8O5crBDz+4fWjXMWUK1K0L+VNehMdZupbryi8HfuH4leNJNzYkTd++am3Hwxfcfc4I/PKL\nWlh0Q046n2DMpjG8Uf4N0gek1zJ+v37qd+ZwaBneWu7eVS4ETXcomdNlpmOZjnyx5Qst43sdjRqp\n+qjr1ulYh7LJAAAgAElEQVRW8lB8zgjcSxHh9dGmbuDs9bP8uO9H3qzwpjYNwcHKqP/yizYJ1jFv\nHhQqpHyVmnin0jtM2zWNq7evatPgNfj5KZ+lh6eS8CkjEBYGf/8NLVroVuIdTNg6gZbFW/J40OPa\nNNxL2TJqlDYJ1iCl+kf0c98Oq4TInzk/dZ+sy6Ttk7Tq8Bo6dIAtWyA8XLeSRPEpIzBqlKrO54at\n117P9TvX+Xrb1/Stqn9xpUULOHoUtm7VrcQJfv9d5Z5p0EC3EvpX7c+4LeO4E3tHtxT7kz69Ckby\n4BB3nzEChw7B6tXw+uu6lXgH03dN57l8z1E4a2HdUggIUMbd1rOBe7MAP/0/ybJPlKVI1iLM2TNH\ntxTv4M034eef4dQp3UoSRP83zk2MGaNib3yuKpULiHHEELIphP5V++uWcp8uXWDNGlWK13bs2gV7\n9sCrr+pWcp/+VfszauMok0rCCrJlU/+3X3jmgrtPGIHz51V0qc9VpHIR8/fNJ3fG3FTJW0W3lPs8\n8gh0766Mve0YPVp9OdOm1a3kPnWfrIuf8DOpJKyiTx9VxNwDU0n4hBGYOFFFl+bMqVuJ/ZFSMmrj\nKAZUG6Bbyn/o1Uvlgzp3TreSFHDsmEoR0b27biX/QghxfzZgsIBChVQqiSlTdCv5D15vBG7cUCki\nTHCYNYQeCeX63etuTRGRXHLmVPmgJk7UrSQFjB2rqhplzqxbyX9oVaIVBy8eZNvJbbqleAf9+6us\nh3fv6lbyL7zeCHz7rSpLWLSobiXewciNI+lbpa/bU0Qkl759ldG/cUO3kmRw6ZL6gro5RURyCfAP\noHfl3mY2YBXly8OTT8LcubqV/AvP/CVbRGys8hEP8DzPhS3ZfWY3u07vol3pdrqlJEqRIlC1Kkyf\nrltJMvj6a2jYEPLm1a0kUbqW7crvh3/n8KXDuqV4BwMGqJ1gHrTgbokREELUE0JECCEihRADE3i/\nsRDiTyHETiHEViFENSvGTYoFC+Dxx6GaW0bzfkZvGk2vir1IlyadbikPpX9/ZfxjY3UreQi3b6vC\nI5qDw5IiY9qMdC3blc83eXPxBjdSr57KcbJqlW4l93HaCAgh/IAJwItACaCNEOJB58tvUspnpJTP\nAl0Al6+OSAkjR6oLgsF5Tlw9wZL9S3ij/Bu6pSRJtWpqfeDnn3UreQg//KCKkZcurVtJkrxd6W1m\n7p7J+RveWLzBzQihDL8HBbVYMROoCByQUh6VUt4F5gBN4jeQUsb30D4CuDzd19q1cOWKKkxucJ6x\nm8fS4ZkOZEmfRbeUZNG/v7oJ8KBZ9z84HOoiYJM7lCcyPkHzYs35MuxL3VK8gzZtVBqJHTt0KwGs\nMQK5gfi5Z0/EvfYvhBBNhRDhwBKgswXjPpRRo9Qiob+/q0fyfq7cusK0ndPoXbm3binJpnFjlZr/\njz90K0mApUshKAhq1tStJNn0rdKXiWETuXn3pm4p9icwEHr39pjEcmncNZCUciGwUAjxHPApUCex\ntkOGDLn/ODg4mOAU5n3etw+2bYOffkqVVMMDfLP9G+o/XZ/8md2f4z61+Pn9k1jO49KG35sF2CiV\nbbHsxaiUuxLf/fkdPcr30C3H/nTrpspQHj2aqtoRoaGhhIaGWiJFOBsWLoSoDAyRUtaLe/4eIKWU\nIx7ymUNABSnlxQTek85q6txZxWZ89JFT3RiA2zG3KfRFIZa9uowyOcvolpMibt1Sv7NVq6BkSd1q\n4ti0SaUQOHAA0rjtHswS1h1dR+fFnYl4KwJ/PzPFdpoBA1TSwLFjne5KCIGUMlV3FVa4g8KAp4QQ\n+YUQgUBrYPEDAp+M97gsEJiQAbCCqChYuFDlbDI4z6zdsyiRvYTtDABAunSqIL2HzLoVo0apFAI2\nMwAAz+V7jmwZsrEwYqFuKd7BO+/AjBlw0SWXwmTjtBGQUsYCPYGVwF5gjpQyXAjRXQjRLa7Zy0KI\nPUKIHcB4oKWz4ybGF1/Aa6/BY4+5agTfwSEdjN402qMSxaWUN96AxYvVzYF2IiNVlanOLl8Scwnx\nU0mYxHIWkDs3NGkCX32lVYbT7iCrccYddPWqmv5v3w4FCliryxdZFrmMj9Z8xI5uOxA28l8/yDvv\nqLU47bvyevSA7Nnhk080C0k9sY5Yik4sytTGU6mev7puOfZn716VU+jIETV1TSW63UEew8SJKhbD\nGADnkVIybN0wBlQdYGsDAMr7MnUqXLigUURUFPz4o8pyZ2P8/fwZUHUAn637TLcU76BECahYUX1B\nNeE1RuD6dbW+8uGHupV4B6v/Xs2FmxdoWcJlnju3kT8/NGsG48ZpFDFqlCo1+Li+UpxW0f6Z9uw7\nt4+tUXYu5eZBfPQRjBihFok14DXuoJAQ2LxZ1eo2OE/wt8F0KtOJDmU66JZiCQcPqkSChw5Bpkxu\nHvzMGShWTBWOyZXLzYO7hglbJ7Dy0EoWt1mcdGND0rz4oqqTmsrShz7vDrp5UxkBsyXUGtYdXcex\nK8d4tZTnVLpylqeegvr1YcIEDYOPGaOiRL3EAAB0ebYL205uY9fpXbqleAeDBsH//R/ExLh9aK8w\nAlOnQoUKKhWLwXk+Xfcp7z/3PgH+AbqlWMqHHyqXUHS0Gwe9cEEVEhn4n7yKtiZ9QHr6Ve3HsHXD\ndEvxDp57DvLlg1mz3D607Y3A7dvKnWZmAdawNWor4efCvcYNFJ+iRVWmBrfuyBs7Fpo3Vz9wL6N7\nue6sPbqWfef26ZbiHQwaBMOGuT39re2NwHffqQX2ChV0K/EOPln7CQOrDSTQP1C3FJfw4YfKdeiW\nojOXLyuL8/77bhjM/QQFBtG7Um8zG7CKmjUha1a3L2za2gjcvavcaIMG6VbiHew8tZPtJ7fT+Vl7\nBjMlh9Kl1QLx5MluGGzCBGjQQOUw8VLeqvgWKw+t5MCFA7ql2B8h1MXs009Vplk3YWsjMHOmCg4z\nRWOs4dN1n9Kvaj/SB6TXLcWlDBqk0kzfuuXCQa5dU+HrH3zgwkH082jaR+lZoSefrTdxA5ZQrx6k\nT69y37gJ2xqB2Fj47DMzC7CKPWf3sP7YerqX665bisspV05tInBpCcqvvoJatXyiuPXbld5m8f7F\n/H3pb91S7I8QaoHz00/dVgzDtkZg7lwVd+NxaYJtyrB1w3i38rsEBQbpluIWBg2C4cNdFJ9z44ba\nFuojkYtZ0mehR7keDF8/XLcU76BxY3WX+8svbhnOlkbA4VCL6B99ZKuU7B7L/vP7+e3wb7xV4S3d\nUtxGlSrw9NOqyqPlTJqkqt2XKuWCzj2T3pV7M2/fPE5cPaFbiv25Nxv45BO3zAZsaQQWLIAMGVSQ\nncF5/m/9/9GrYi8yps2oW4pbGTRIuRQtjc+5dUuliPCxPcvZg7LT+dnOjNwwUrcU76B5c1Uf97ff\nXD6U7YyAlMpdNmiQmQVYweFLh1kSuYS3K72tW4rbqVFDBfHOmWNhp9Onw7PPQtmyFnZqD/pV7ccP\nf/3A6ejTuqXYH39/5U50Q8ZZ2xmBpUuVIWjUSLcS72D4+uG8Uf4NMqfLrFuKFiyNz7lzRy00+Ohu\nhZyP5KRd6XaM3uhJVXxsTOvWcPKkywtl28oISKkMo1kLsIZjV47x076fbFVA3mpq11YJ5ebPt6Cz\n77+HIkWgUiULOrMnA6oNYNrOaZy7fk63FPuTJo3aYvzppy4dxlZGYOVKlfeleXPdSryDkRtG0uXZ\nLmTLkE23FG3E35HnVHxOTIyKXPSxtYAHyfNoHlqWaMnnmz/XLcU7eO01VY9682aXDWEbI+BwqN/X\noEHgZxvVnsvfl/5m9p7Z9KvaT7cU7bz0EqRNq2q+pJrp0yFvXqhuqm2999x7fLP9G7M2YAUBAfC/\n/8Hhwy4bwjb1BGbPVjlftm41RsAKXp3/KoWzFmZI8BDdUjyCNWugSxcID1cGIUVERys30KJFUL68\nS/TZjT4r+nDj7g2+bvi1bik+gfZ6AkKIekKICCFEpBDiPzlzhRCvCiH+jDvWCyFStIH69m3lGhs9\n2hgAK9h2chuhR0LNLCAeNWtC8eKqRGmKCQlRW42MAbjPR9U/Yn74fMLPheuWYkgCp2cCQgg/IBJ4\nATgJhAGtpZQR8dpUBsKllFeEEPWAIVLKyon095+ZQEgIhIbCkiVOSTWgagfX/K4mr5Z6lW7luumW\n41Hs26eu5ZGRkCVLMj90+rRKY7t9uylu/QCjN45m7dG1pvqYG9A9E6gIHJBSHpVS3gXmAE3iN5BS\nbpZSXol7uhnIndzOL15Uu+5GjLBAqYGlkUs5e/2sV2cKTS3Fi6taxMNSkhl58GDo1MkYgAToWbEn\nu8/u5o8jrt3iaHAOK4xAbuB4vOcnePhF/nXg1+R2PmyY2g1UvHgq1RnuE+OIYcBvAxhZZyRp/NLo\nluORDB2q1nj/Tk4utH37VPi6j+QISinp0qRjWK1h9FvVD4d0X2pkQ8pw65VACFET6AQ897B2Q4YM\nAeDSJZg+PZjIyGCXa/MFpu6YSs5HcvLS0y/pluKxPPEE9OqlrutJVvobOBDeey8FviPfo3XJ1ozZ\nNIa5e+bSplQb3XK8htDQUEJDQy3py4o1gcooH3+9uOfvAVJKOeKBdqWB+UA9KeWhh/R3f02gTRuV\niXfwYKckGoBrt69ReEJhlrZZSrlc5XTL8Wiio6FwYVi8+CFrvaGh0LlzKrcT+RahR0LptKgTEW9F\nkDaNOVeuQPeaQBjwlBAivxAiEGgN/GslSAiRD2UAXnuYAfhXp2EqWrpvXwsUGgjZFEKtgrWMAUgG\njzwCQ4ZAv36JJHF0ONSbn31mDEAyCC4QTMnHSzIxLDVbrwyuxmkjIKWMBXoCK4G9wBwpZbgQorsQ\n4t72k0HAY8CXQoidQoitD+9T/caGDlU/SINznLp2ivFbxzOslqkFm1w6d4azZ2HZsgTenDNH7VVu\n1crtuuzKiNojGL5+OJduXtItxfAAHhkstmiR5P334c8/VfoMg3N0W9KNTGkzMaruKN1SbMXSpTBg\nAPz1V7zv4a1bykc5Y4aJDk4h3Zd0J2PajIyuaxLMWY1ud5DlDByoasAaA+A8e8/uZWHEQj543rtr\n3bqCl16CHDlg2rR4L06YoGpTGgOQYobWHMr0XdNNGUoPwyNnAjVrSn7/3WQKtYKGsxryQsEXeLfK\nu7ql2JLt21Xa8shIeOTORZUeYt06n6gd7AqGhg5l/4X9zHo5qa1XhpTgzEzAI43Atm2Scmb90mnW\n/L2GLou7EP5WuNmV4QRt26pSlEOu9oGbN1UReUOqiL4TTZEJRVjUehHlc5k0G1bhdUbA0zTZEYd0\nUGFyBQZUHUCrkmYB0xmOHIHmZQ6zza8CfuH7lI/IkGomb5/MzN0zWdNhDcJM9y3B69YEDM4zdcdU\nAvwCaFmipW4ptqdAfskP2XozP++7xgBYQKdnO3Hh5gXm7p2rW4oBYwS8kmNXjvHB6g+Y0niKudOy\ngpkzKZruCB9HD2DRIt1i7E8avzRMaTSF3st7c/b6Wd1yfB7jDvIypJTUm1mP6vmq82F1k9PGaU6d\nUruBfv2VtdfL0aYN7N4Njz2mW5j9GbhqIIcvH2Zei3m6pdge4w4y3Gfazmmcv3GeAdUG6JZif6SE\nHj2gWzcoV47q1eHll6G375ZktpShNYey5+we5u01RkAnZibgRRy/cpyyk8qyuv1qSuVIUd0eQ0LM\nmqVSQ2zffj89xPXrULo0jB2rto4anGPzic00ndOU3W/sJntQdt1ybIvZHWRASkmDWQ2olrcaH1X3\n7WLnlnD6tHIDLVv2nyxyf/yhto3u3m0SiFrBgFUDOHrlKHNfMQvFqcW4gwx8u+tbzkSfYWC1/1T3\nNKQUKeGNN1TR4QTSiNaooYrPvGvi7yxhaPBQ/jz9Jz/t+0m3FJ/EzAS8gBNXT1D2m7L81v43Suco\nrVuO/ZkzBz75BHbsSDRLaHS0cguNH6/SSxicY9PxTTT/sTm739hNtgzZdMuxHcYd5MNIKWk4uyGV\nclfi4xof65Zjf86cUVf3JUugYsWHNl2zBtq3V26hzJndpM+L6beyH1HXopj98mzdUmyHcQf5MDP+\nnMHJayd5/7n3dUuxP1LCm2+qmsFJGACAmjWhcWPo08cN2nyAT2p+wo5TO/g5/GfdUnwKMxOwMVFX\no3j2m2dZ+dpKyuQso1uO/fnxR1XGbudOSJcuWR+JjoZSpeDLL6F+fRfr8wE2HNtAi3kt2P3GbrJm\nyKpbjm0w7iAfREpJo9mNKJ+rPEOCh+iWY3/OnlVuoIULoXLlFH109Wro2FG5hTJlco08X6LPij6c\nuX6Gmc1n6pZiG4w7yAeZ8ecMjl89buoEWME9N1D79ik2AAC1aqnFYRNEZg2f1vqUrVFbjVvITRgj\nYEO2ndxGv1X9+L7Z9wT6B+qWY39GjYK//1b1TFPJyJGwZYvJMm0FGQIy8EOzH+ixtAf7zu3TLcfr\nMUbAZpy8dpJmc5sxqeEksx3UCpYsgXHjYNEiSJ8+1d1kzAiLFys7snq1hfp8lEp5KjG67mgazW7E\nhRsXdMvxaiwxAkKIekKICCFEpBDiP9FKQogiQoiNQohbQgizlyKV3Lx7k6ZzmtKjXA+aFWumW479\n2bNHBYT9/DPkyeN0d089BbNnw6uvwsGDFujzcdo/055Xir3CK/Ne4U7sHd1yvBanF4aFEH5AJPAC\ncBIIA1pLKSPitckG5AeaApeklGMe0p9ZGE4AKSVtf24LwMzmM02KaGc5dw4qVYJPP1VXbQv55hs1\nudi0ySwUO0usI5Zmc5vxxCNP8HXDr833PhF0LwxXBA5IKY9KKe8Cc4Am8RtIKc9LKbcDMRaM55P8\n3/r/4+DFg0xtPNX8EJzlzh2VDrRNG8sNAED37vDCC9C6NcTGWt69T+Hv58/M5jPZeGIjE7ZO0C3H\nK7HCCOQGjsd7fiLuNYNFLAhfwFfbvmJh64WkD0i939rAPzuBHntMpYZwEZ9/DjExMMBk9HaajGkz\nsrj1Yj5b/xkrD63ULcfrSKNbQEIMGTLk/uPg4GCCg4O1adHNn6f/pPvS7vza9ldyZcylW479GTcO\nwsJgwwbwc92+iDRpVOxZpUpQvLhaejCknoJZCjL3lbm0mNeCtR3XUiRbEd2StBIaGkpoaKglfVmx\nJlAZGCKlrBf3/D1ASilHJNB2MHDNrAkkjzPRZ6g0pRIj64w0tYKtYPly6NxZOevz53fLkPv3Q/Xq\n8NNP8PzzbhnSq5m6YyojN45kc5fNZElv8njfQ/eaQBjwlBAivxAiEGgNLH5Ie+PQTga3Y27T/Mfm\ndCzT0RgAK4iIUMFg8+a5zQAAFCkCP/wALVvCkSNuG9Zr6VK2Cy89/RItf2pJjMMsMVqBJWkjhBD1\ngHEoozJVSjlcCNEdNSOYJITIAWwDMgIOIBooLqWMTqAvn58JOKSDzos6c/3udea+Mhc/YcI5nOL8\neahSBT78UOV30MD48TBpEqxfb3YMOUuMI4ZGsxtRKHMhJjSYYDZKYHIHeRUxjhi6LulK5IVIVrZb\nSVBgkG5J9ubkSahTB5o3d+lCcFJIqYrQrFsHK1ZANpMy3ymu3LpCrRm1qJqnKuPqj/P5GyXd7iCD\nRdyOuU3rn1oTdTXKGAArOHxYOeJfe02rAQAQQu0YqldPrRFERWmVY3sypcvE6var2XVmFx0XdjSu\nIScwRsBDuH7nOo3nNEYiWdJmiTEAzrJ3r7ra9usH772nWw2gDMGwYcoj9dxzJqrYWTKly8SKdis4\nd+McLea14FbMLd2SbIkxAh7A5VuXqftDXXJlzMXcV+aSNk3CJQ0NySQsTEVrjRihagV7GAMGwPvv\nq1rFu3frVmNvMgRkYFHrRQT4BdBwVkOi7/xnmdGQBMYIaObs9bPU/K4m5Z8oz9TGU0nj55GhG/Yh\nNFTldZ48Gdq21a0mUbp1g9GjoXZtlX3UkHoC/QOZ/fJs8mfKT53v63Dp5iXdkmyFMQIaOX7lOM9P\nf57GhRsztt5Yn1/ccpqlS6FFC1UovlEj3WqSpE0bmDoVGjZU9YoNqcffz58pjadQJU8Vgr8L5nT0\nad2SbIO56mgi8kIkz09/nu7lujO05lCzzc1ZZs+G119XhqBWLd1qkk3Dhip0oVUrlYrakHqEEITU\nDeHlYi9TfXp1jl4+qluSLTC+Bw1sObGFZnOb8UnNT+hS1uQTcAop4YsvVFWX336DkiV1K0oxwcGw\nbJmavJw9q1JMmHuC1CGE4OMaH5MpbSaqf1udRa0XmfrbSWDiBNxIjCOGz9Z9xsSwiUxqOIkmRZsk\n/SFD4ty7Yp48qRL1PPmkbkVOER6uIouLFYOvv1Y57gypZ86eOfT6tRcDqw2kT5U+Xu1uNXECNuDw\npcNUn16ddcfWsaPbDmMAnGXpUnjmGShVSuUCsrkBAHXxDwuDXLnUP+3333UrsjetS7YmrGsYi/Yv\novaM2hy/cjzpD/kgxgi4GCkl3+76lkpTKtGieAtWtFtB7kdNpu1Uc+OGSgXdsyfMnQuffQaB3lNn\nOV06GDtWLRh36KDCHG7f1q3KvhTIXIDQDqHULlSb8pPL8+PeH3VL8jiMO8iFXLhxgR7LehBxPoKZ\nzWeamsDOsn272vZZvjxMmACZM+tW5FLOn1dbSQ8dgpkzbbnc4VGERYXR9ue2VM5TmQkNJvBo2kd1\nS7IM4w7yQH47/BtlvilDnox5COsaZgyAM8TGwvDhUL8+DB6s0nJ6uQEAlV9o/nx4+221eDxuHDgc\nulXZlwq5K7Cz+07Sp0nPM18/w/pj63VL8gjMTMBiTkef5pM/PmHR/kVMbzKdOk/W0S3J3oSFQd++\narvMjBluTQPtSRw8CO3aQcaMKsjsmWd0K7I3i/cvptuSbrQt1Zb3n3+fbBnsndHPzAQ8gDPRZ+i7\noi/FJxYnwD+AP3v8aQyAM2zfrvZMNm+u6gCvXu2zBgDgqadUGuqGDVUSupdfNiknnKFxkcbs6rGL\nG3dvUGRCET74/QMu3LigW5YWjBFwknPXzzFg1QCKTSzGndg77H5jN2PrjSVrhqy6pdmTXbugaVNo\n3BhefBEOHIAePcDfX7cy7aRJA++8o9YIqlZVGbJbtlS58gwpJ+cjOfmq4Vfs6LaD8zfOU3hCYQat\nHuRzaSeMEUglF25c4P3f3qfoxKJE34nmzx5/Mr7BeLPzJ7X89Ze6669fH2rWVP6Pnj3VdhnDv8iQ\nQXnIDh1Sa+Q1a6oUFBERupXZk/yZ8zOp0SS2dd3GyWsneXr80wwJHcLlW5d1S3MLxgikkMOXDvPh\n7x9SeEJhLt68yI5uO/jypS/Jmymvbmn2w+FQPo4WLaBuXZVf+dAhdbubPr1udR5PUJDKSHroEJQu\nrUontGunEtLZeFlNGwWzFGRqk6lseX0LRy4f4enxTzM0dCjHrhzTLc2lmIXhZHDsyjF+3Psjc/fO\n5ejlo7Qs0ZK+VfpSMEtB3dLsh5Swdava4z9vnqq12LGjSvkcZGooOMPVq2rn7HffwZ07ylXUsiWU\nLWvSUKSGyAuRjN44mvnh8ymStQitSrTileKveORsX3t5ybgaw2P5p8bwiATafAHUB64DHaWUuxLp\nyyOMQNTVKH7a9xNz984l8kIkzYo2o2WJltQsWNOke04pUsKOHerC/+OPysXTqpW6QpUooVud1yGl\n8q7NnasOPz91qlu1UgHWxiCkjDuxd/j98O/M3TuXxfsXU/LxkvcNQo5HcuiWB2g2AkIIPyASeAE4\nCYQBraWUEfHa1Ad6SilfEkJUAsZJKSsn0p8WI3Dp5iW2ndxG2Mkwlh9czp6ze2hcpDGtSrSidqHa\nBPgHuF2TbZESjh5V2zu3bIFFi9Rr9y78pUubK5GbeND+pk8PTZpAxYpQoQLkyWP+K1LC7ZjbrDi0\ngh/3/sjSyKWUy1WOuoXqUiF3Bco9UY5M6TJp0aXbCFQGBksp68c9fw+Q8WcDQoivgTVSyrlxz8OB\nYCnlmQT6c7kRuHb7GjtP7yQsKoxtp7YRFhXGmetnKPtEWSrkqkCN/DWo+2RdU+EruZw6pS74YWGw\nbZs6AgLUVaZ8eWjQwPgkPIB7nrjly//574J//pvu/c3hGTe3Hs/NuzdZfnA5a4+uJexkGLtO7yL3\no7kpn6s8FXJVoEKuCpTJWcYtpWJ1G4GXgRellN3inrcDKkop347XZgnwf1LKjXHPfwMGSCl3JNCf\nU0YgxhHDmegzRF2LIupq1L//Xovi+JXjRF2LotTjpdR/VO4KlM9VniJZi+DvZ7Yh/odbt1RV9MSO\nv/9WDuj4V5EKFVQWNINHIyWcOKFsdnwbHhQEBQpA7twJH7lymU1bCRHjiCH8XPh9j8K2k9vYe24v\neR/NS55H85D70dzkzhh3PPrP3xxBOZy+9nidEQitUxgAibz/V8mUOKSDGEfM/eNuvMcxjhhiHTGk\nTZOOoIAMBAUEkSEwiKCAIPU8MIigwCAypc3k1Wll7yOlOhyOxB/fuqWSst07rl//9/OYGHjiiX9f\nBfLk+edxvnzqMHf5XoGUcOQIHDuWuN0/dUrl7MuQIfEjXTq1FiGEOhJ77O3EcpsraQ5w3T+KG/5R\nXI87bvhF3X/tlt9F0sgMDz1aFGvFiA6vJDqOM0bAihXOKCBfvOd54l57sE3eJNrc57tb6jZDIHg2\nf07KF8gFQj1P45eGQP9AAv0DCYj7G/9I6x9o7ujjc+8Xl9jf9On/+eXGfxz/8PMBg2kA1FeiYEF1\nJIbDoe4Vbt789/1C/OPWrYTvPeL/9Q3SAiXjjoSJlXe5I2889CiTt/C/PhMaGkpoaKglCq2YCfgD\n+1ELw6eArUAbKWV4vDYNgLfiFoYrA2M9bWHYYDAY7IrWmYCUMlYI0RNYyT9bRMOFEN3V23KSlPIX\nIUQDIcRB1BbRTs6OazAYDAbnMcFiBoPBYHNMFlGDwWAwpApjBAwGg8GHMUbAYDAYfBhjBAwGg8GH\nMbAOmBUAAAUtSURBVEbAYDAYfBhjBAwGg8GHMUbAYDAYfBhjBAwGg8GHMUbAYDAYfBhjBAwGg8GH\nMUbAYDAYfBhjBAwGg8GHMUbAYDAYfBhjBAwGg8GHMUbAYDAYfBhjBAwGg8GHMUbAYDAYfBhjBAwG\ng8GHMUbAYDAYfBinjIAQIosQYqUQYr8QYoUQIlMi7aYKIc4IIf5yZjyDwWAwWIuzM4H3gN+klEWA\n1cD7ibSbDrzo5FgeQ2hoqG4JycLotBaj01qMTs/AWSPQBPgu7vF3QNOEGkkp1wOXnBzLY7DLl8Lo\ntBaj01qMTs/AWSPwuJTyDICU8jTwuPOSDAaDweAu0iTVQAixCsgR/yVAAh8l0FxapMtgMBgMbkBI\nmfrrthAiHAiWUp4RQuQE1kgpiyXSNj+wREpZOok+jSExGAyGFCKlFKn5XJIzgSRYDHQERgAdgEUP\naSvijoeS2n+IwWAwGFKOs2sCI4A6Qoj9wAvAcAAhxBNCiKX3GgkhZgEbgcJCiGNCiE5OjmswGAwG\nC3DKHWQwGAwGe6MlYjg5wWNCiC+EEAeEELuEEGXcqS+ehofqFELUEEJcFkLsiDsSWix3tcY8QojV\nQoi9QojdQoi3E2mn9XwmR6eHnM+0QogtQoidcToHJ9JO9/lMUqcnnM84HX5x4y9O5H3tv/U4HYnq\n9KBzeUQI8Wfc//vWRNqk7HxKKd1+AM8BZYC/Enm/PrAs7nElYLOH6qwBLNahLZ6GnECZuMePAPuB\nop52PpOpU/v5jNORIe6vP7AZqOhp5zOZOj3lfL4L/JCQFk85l8nQ6Snn8jCQ5SHvp/h8apkJyKSD\nx5oAM+LabgEyCSFyPKS9S0iGTkjGYrcrkVKellLuinscDYQDuR9opv18JlMnaD6fAFLKG3EP06I2\nTzzoM9V+PuPGTkonaD6fQog8QANgSiJNPOJcJkMneMB3E6XhYdftFJ9PT00glxs4Hu95FAlfMDyB\nKnHTrmVCiOI6hQghCqBmLlseeMujzudDdIIHnM84t8BO4DSwSkoZ9kATjzifydAJ+s/n50B/Eo8h\n8ohzSdI6Qf+5BKVvlRAiTAjRNYH3U3w+PdUI2IXtQD4pZRlgArBQlxAhxCPAT8A7cXfaHkkSOj3i\nfEopHVLKZ4E8QCXdxj0xkqFT6/kUQrwEnImbASZri7gOkqnTI76bQDUpZVnUrOUtIcRzznboqUYg\nCsgb73meuNc8Cill9L0puZTyVyBACPGYu3UIIdKgLqzfSykTitXwiPOZlE5POZ/x9FwF1gD1HnjL\nI87nPRLT6QHnsxrQWAhxGJgN1BRCzHigjSecyyR1esC5vKfjVNzfc8ACoOIDTVJ8PnUagYfdGSwG\n2gMIISoDl2VcjiINJKozvq9NCFERteX2oruExWMasE9KOS6R9z3lfD5UpyecTyFENhGXEl0IkR6o\nA0Q80Ez7+UyOTt3nU0r5gZQyn5SyENAaWC2lbP9AM+3nMjk6dZ/LuHEzxM2kEUIEAXWBPQ80S/H5\ndDZiOFUIFTwWDGQVQhwDBgOBgJRSTpJS/iKEaCCEOAhcB7QElyWlE3hFCPEGcBe4CbTSoLEa0BbY\nHecflsAHQH486HwmRycecD6BJ4DvhBB+qJukuXHnrzsedD6ToxPPOJ//wQPPZYJ44LnMASwQKrVO\nGmCmlHKls+fTBIsZDAaDD+OpawIGg8FgcAPGCBgMBoMPY4yAwWAw+DDGCBgMBoMPY4yAwWAw+DDG\nCBgMBoMPY4yAwWAw+DDGCBgMBoMP8/+krGcFtMiD1AAAAABJRU5ErkJggg==\n",
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Mhg0qAWN4OAQF6VbjeqZMUfEP69e7Jt3MB799QOT1SKY3nW595x5Ik9lNqJS7Eh88/4H1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\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f1aab3660f0>"
+       "<matplotlib.figure.Figure at 0x7f2ee8f4d210>"
       ]
      },
      "metadata": {},
@@ -129,7 +130,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 63,
+   "execution_count": 4,
    "metadata": {
     "collapsed": false
    },
@@ -138,11 +139,12 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Number of basis functions =  8\n"
+      "('Number of basis functions = ', 8)\n"
      ]
     },
     {
      "data": {
+      "image/png": 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MG17vl/SZkK4Qen8EasdDJtFnX+Ylh9lCGxO7xnBOi9eV5gnf7x3pcwIGDVhF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\ncDIQJGKGq8m78wARZ/Vm/5QRExazWmhgtBwxscoUyrOwhKF4saiDZW1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2ziw92xrUe1un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\n",
       "text/latex": [
        "$$\\left [ \\begin{cases} \\frac{x^{3}}{6} + \\frac{3 x^{2}}{2} + \\frac{9 x}{2} + \\frac{9}{2} & \\text{for}\\: x \\geq -3 \\wedge x < -2 \\\\- \\frac{x^{3}}{2} - \\frac{5 x^{2}}{2} - \\frac{7 x}{2} - \\frac{5}{6} & \\text{for}\\: x \\geq -2 \\wedge x < -1 \\\\\\frac{x^{3}}{2} + \\frac{x^{2}}{2} - \\frac{x}{2} + \\frac{1}{6} & \\text{for}\\: x \\geq -1 \\wedge x < 0 \\\\- \\frac{x^{3}}{6} + \\frac{x^{2}}{2} - \\frac{x}{2} + \\frac{1}{6} & \\text{for}\\: x \\geq 0 \\wedge x \\leq 1 \\\\0 & \\text{otherwise} \\end{cases}, \\quad \\begin{cases} \\frac{x^{3}}{6} + x^{2} + 2 x + \\frac{4}{3} & \\text{for}\\: x \\geq -2 \\wedge x < -1 \\\\- \\frac{x^{3}}{2} - x^{2} + \\frac{2}{3} & \\text{for}\\: x \\geq -1 \\wedge x < 0 \\\\\\frac{x^{3}}{2} - x^{2} + \\frac{2}{3} & \\text{for}\\: x \\geq 0 \\wedge x < 1 \\\\- \\frac{x^{3}}{6} + x^{2} - 2 x + \\frac{4}{3} & \\text{for}\\: x \\geq 1 \\wedge x \\leq 2 \\\\0 & \\text{otherwise} \\end{cases}, \\quad \\begin{cases} \\frac{x^{3}}{6} + \\frac{x^{2}}{2} + \\frac{x}{2} + \\frac{1}{6} & \\text{for}\\: x \\geq -1 \\wedge x < 0 \\\\- \\frac{x^{3}}{2} + \\frac{x^{2}}{2} + \\frac{x}{2} + \\frac{1}{6} & \\text{for}\\: x \\geq 0 \\wedge x < 1 \\\\\\frac{x^{3}}{2} - \\frac{5 x^{2}}{2} + \\frac{7 x}{2} - \\frac{5}{6} & \\text{for}\\: x \\geq 1 \\wedge x < 2 \\\\- \\frac{x^{3}}{6} + \\frac{3 x^{2}}{2} - \\frac{9 x}{2} + \\frac{9}{2} & \\text{for}\\: x \\geq 2 \\wedge x \\leq 3 \\\\0 & \\text{otherwise} \\end{cases}, \\quad \\begin{cases} \\frac{x^{3}}{6} & \\text{for}\\: x \\geq 0 \\wedge x < 1 \\\\- \\frac{x^{3}}{2} + 2 x^{2} - 2 x + \\frac{2}{3} & \\text{for}\\: x \\geq 1 \\wedge x < 2 \\\\\\frac{x^{3}}{2} - 4 x^{2} + 10 x - \\frac{22}{3} & \\text{for}\\: x \\geq 2 \\wedge x < 3 \\\\- \\frac{x^{3}}{6} + 2 x^{2} - 8 x + \\frac{32}{3} & \\text{for}\\: x \\geq 3 \\wedge x \\leq 4 \\\\0 & \\text{otherwise} \\end{cases}, \\quad \\begin{cases} \\frac{x^{3}}{6} - \\frac{x^{2}}{2} + \\frac{x}{2} - \\frac{1}{6} & \\text{for}\\: x \\geq 1 \\wedge x < 2 \\\\- \\frac{x^{3}}{2} + \\frac{7 x^{2}}{2} - \\frac{15 x}{2} + \\frac{31}{6} & \\text{for}\\: x \\geq 2 \\wedge x < 3 \\\\\\frac{x^{3}}{2} - \\frac{11 x^{2}}{2} + \\frac{39 x}{2} - \\frac{131}{6} & \\text{for}\\: x \\geq 3 \\wedge x < 4 \\\\- \\frac{x^{3}}{6} + \\frac{5 x^{2}}{2} - \\frac{25 x}{2} + \\frac{125}{6} & \\text{for}\\: x \\geq 4 \\wedge x \\leq 5 \\\\0 & \\text{otherwise} \\end{cases}, \\quad \\begin{cases} \\frac{x^{3}}{6} - x^{2} + 2 x - \\frac{4}{3} & \\text{for}\\: x \\geq 2 \\wedge x < 3 \\\\- \\frac{x^{3}}{2} + 5 x^{2} - 16 x + \\frac{50}{3} & \\text{for}\\: x \\geq 3 \\wedge x < 4 \\\\\\frac{x^{3}}{2} - 7 x^{2} + 32 x - \\frac{142}{3} & \\text{for}\\: x \\geq 4 \\wedge x < 5 \\\\- \\frac{x^{3}}{6} + 3 x^{2} - 18 x + 36 & \\text{for}\\: x \\geq 5 \\wedge x \\leq 6 \\\\0 & \\text{otherwise} \\end{cases}, \\quad \\begin{cases} \\frac{x^{3}}{6} - \\frac{3 x^{2}}{2} + \\frac{9 x}{2} - \\frac{9}{2} & \\text{for}\\: x \\geq 3 \\wedge x < 4 \\\\- \\frac{x^{3}}{2} + \\frac{13 x^{2}}{2} - \\frac{55 x}{2} + \\frac{229}{6} & \\text{for}\\: x \\geq 4 \\wedge x < 5 \\\\\\frac{x^{3}}{2} - \\frac{17 x^{2}}{2} + \\frac{95 x}{2} - \\frac{521}{6} & \\text{for}\\: x \\geq 5 \\wedge x < 6 \\\\- \\frac{x^{3}}{6} + \\frac{7 x^{2}}{2} - \\frac{49 x}{2} + \\frac{343}{6} & \\text{for}\\: x \\geq 6 \\wedge x \\leq 7 \\\\0 & \\text{otherwise} \\end{cases}, \\quad \\begin{cases} \\frac{x^{3}}{6} - 2 x^{2} + 8 x - \\frac{32}{3} & \\text{for}\\: x \\geq 4 \\wedge x < 5 \\\\- \\frac{x^{3}}{2} + 8 x^{2} - 42 x + \\frac{218}{3} & \\text{for}\\: x \\geq 5 \\wedge x < 6 \\\\\\frac{x^{3}}{2} - 10 x^{2} + 66 x - \\frac{430}{3} & \\text{for}\\: x \\geq 6 \\wedge x < 7 \\\\- \\frac{x^{3}}{6} + 4 x^{2} - 32 x + \\frac{256}{3} & \\text{for}\\: x \\geq 7 \\wedge x \\leq 8 \\\\0 & \\text{otherwise} \\end{cases}\\right ]$$"
       ],
@@ -258,7 +260,7 @@
        "   ⎩           0                  otherwise    ⎦"
       ]
      },
-     "execution_count": 63,
+     "execution_count": 4,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -291,14 +293,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 116,
+   "execution_count": 5,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAASsAAAAWCAYAAACYN7pzAAAABHNCSVQICAgIfAhkiAAAA2xJREFU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\ndDi3SBAEQRAEQRAEQZCFfwFbdDjud7FbcQAAAABJRU5ErkJggg==\n",
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAT0AAAAUBAMAAAANYffkAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n3q6uDrpgLrP8QsMNja5bGOHkL9ljwVrZ/xOYAAAAAElFTkSuQmCC\n",
       "text/latex": [
        "$$\\left [ 1, \\quad -2, \\quad 1, \\quad 0, \\quad 0, \\quad 0, \\quad 0, \\quad 0\\right ]$$"
       ],
@@ -311,7 +313,7 @@
     },
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAASsAAAAWCAYAAACYN7pzAAAABHNCSVQICAgIfAhkiAAAA3tJREFU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\n",
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAT0AAAAUBAMAAAANYffkAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nHmld8xQAAAAASUVORK5CYII=\n",
       "text/latex": [
        "$$\\left [ 0, \\quad 0, \\quad 0, \\quad 0, \\quad 0, \\quad 1, \\quad -2, \\quad 1\\right ]$$"
       ],
@@ -324,6 +326,7 @@
     },
     {
      "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAASYAAADICAMAAAByI7yuAAAATlBMVEX///8AAAAAAAAAAAAAAAAA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\noVP8H50KGULXv2+dAAAAAElFTkSuQmCC\n",
       "text/latex": [
        "$$\\left[\\begin{matrix}1 & -2 & 1 & 0 & 0 & 0 & 0 & 0\\\\\\frac{1}{6} & \\frac{2}{3} & \\frac{1}{6} & 0 & 0 & 0 & 0 & 0\\\\0 & \\frac{1}{6} & \\frac{2}{3} & \\frac{1}{6} & 0 & 0 & 0 & 0\\\\0 & 0 & \\frac{1}{6} & \\frac{2}{3} & \\frac{1}{6} & 0 & 0 & 0\\\\0 & 0 & 0 & \\frac{1}{6} & \\frac{2}{3} & \\frac{1}{6} & 0 & 0\\\\0 & 0 & 0 & 0 & \\frac{1}{6} & \\frac{2}{3} & \\frac{1}{6} & 0\\\\0 & 0 & 0 & 0 & 0 & \\frac{1}{6} & \\frac{2}{3} & \\frac{1}{6}\\\\0 & 0 & 0 & 0 & 0 & 1 & -2 & 1\\end{matrix}\\right]$$"
       ],
@@ -345,7 +348,7 @@
        "⎣ 0    0    0    0    0    1   -2    1 ⎦"
       ]
      },
-     "execution_count": 116,
+     "execution_count": 5,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -373,14 +376,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 109,
+   "execution_count": 6,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAN8AAAAWCAYAAABAHklQAAAABHNCSVQICAgIfAhkiAAABWVJREFU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\nmpqampq1hv8AT4E8J1fSYVcAAAAASUVORK5CYII=\n",
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPAAAAAUBAMAAABBrq01AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "text/latex": [
        "$$\\left [ 0, \\quad 1, \\quad 4, \\quad 9, \\quad 16, \\quad 25\\right ]$$"
       ],
@@ -388,7 +391,7 @@
        "[0, 1, 4, 9, 16, 25]"
       ]
      },
-     "execution_count": 109,
+     "execution_count": 6,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -408,14 +411,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 115,
+   "execution_count": 7,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAAgCAYAAAACC4MGAAAABHNCSVQICAgIfAhkiAAAB/1JREFU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\nAElFTkSuQmCC\n",
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAccAAAAyBAMAAADb+g2fAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "text/latex": [
        "$$\\left [ - \\frac{11}{19}, \\quad 0, \\quad \\frac{11}{19}, \\quad \\frac{70}{19}, \\quad \\frac{165}{19}, \\quad \\frac{296}{19}, \\quad 25, \\quad \\frac{654}{19}\\right ]$$"
       ],
@@ -425,7 +428,7 @@
        "⎣ 19      19  19   19   19       19⎦"
       ]
      },
-     "execution_count": 115,
+     "execution_count": 7,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -445,7 +448,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 85,
+   "execution_count": 8,
    "metadata": {
     "collapsed": true
    },
@@ -460,7 +463,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 111,
+   "execution_count": 9,
    "metadata": {
     "collapsed": false
    },
@@ -469,12 +472,12 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "0 0 0\n",
-      "1 1 1\n",
-      "2 4 4\n",
-      "3 9 9\n",
-      "4 16 16\n",
-      "5 25 25\n"
+      "(0, 0, 0)\n",
+      "(1, 1, 1)\n",
+      "(2, 4, 4)\n",
+      "(3, 9, 9)\n",
+      "(4, 16, 16)\n",
+      "(5, 25, 25)\n"
      ]
     }
    ],
@@ -486,7 +489,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 112,
+   "execution_count": 10,
    "metadata": {
     "collapsed": false
    },
@@ -494,18 +497,18 @@
     {
      "data": {
       "text/plain": [
-       "[<matplotlib.lines.Line2D at 0x7f1aaab7ae48>]"
+       "[<matplotlib.lines.Line2D at 0x7f2ee8c677d0>]"
       ]
      },
-     "execution_count": 112,
+     "execution_count": 10,
      "metadata": {},
      "output_type": "execute_result"
     },
     {
      "data": {
-      "image/png": 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TToEOHWDCBAW4VE8bYInkidGjQxfKAw+ElrhIKhTiIpFt3Qq33AJPPx1mopxwQuyKpJAo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\nl+NLn2hHRgAAAABJRU5ErkJggg==\n",
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ToH17GD9eAS5V0wZYInli5MjQhfLQQ6ElLpIOhbhIZFu2wK23wrPPhpkoxx8fuyIpJApx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\nscXXAAAAAElFTkSuQmCC\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f1aab1c25f8>"
+       "<matplotlib.figure.Figure at 0x7f2ee8cc9310>"
       ]
      },
      "metadata": {},
@@ -535,7 +538,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 117,
+   "execution_count": 11,
    "metadata": {
     "collapsed": true
    },
@@ -572,7 +575,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 128,
+   "execution_count": 12,
    "metadata": {
     "collapsed": false
    },
@@ -581,12 +584,12 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Interval =  [0, 1)\n"
+      "('Interval = ', Interval.Ropen(0, 1))\n"
      ]
     },
     {
      "data": {
-      "image/png": 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       "text/latex": [
        "$$\\left [ \\left ( 0, \\quad - \\frac{x^{3}}{6} + \\frac{x^{2}}{2} - \\frac{x}{2} + \\frac{1}{6}\\right ), \\quad \\left ( 1, \\quad \\frac{x^{3}}{2} - x^{2} + \\frac{2}{3}\\right ), \\quad \\left ( 2, \\quad - \\frac{x^{3}}{2} + \\frac{x^{2}}{2} + \\frac{x}{2} + \\frac{1}{6}\\right ), \\quad \\left ( 3, \\quad \\frac{x^{3}}{6}\\right )\\right ]$$"
       ],
@@ -604,25 +607,25 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Interval =  [5, 6)\n"
+      "('Interval = ', Interval.Ropen(1, 2))\n"
      ]
     },
     {
      "data": {
-      "image/png": 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EI6inogrmZuRe5/Euiq338iXiF7CcBHyL8Rn2FCQEC3Ncz8lx3EUoH/h7Ja5DLireWklV\n26lKNqI8Oitk36tR/l/o2zaKeum9hXKruneHap4VZM9Xx6D5TGFzlusu4/PQaOj0kH1p76uuNDet\nH0eje18f+GxEDek6iStnHue5vwmbyjBstnTIXr7fCfw3/YijS1CFMBgNMc37Oa89u5TnqmY1Wicv\nSJ2aGKeHfuLKFlhdLYku6EOT9ZW6WIzyadA9Oo3921RXq5PVhOsU5AxIA4rwdxnKYP71Du8ErkTG\nf8Ldvxl4I+MDPjyE3BgOz3jdtvAN9OAPdz/LUbSjj6GRmptRZTQP85Ggx7nhbkeTiy9HBfwP6EW/\nHFUS6uAClLk2oJGX3VFDYSn9NbOqtFMVPB1Vnvaiv8TB/chl5Gq0bANoPZkH0Fy7J5EoTQY+Qr9Q\ntene0zwryJ6vjkVaEDZSXXcZ34rWMtqfwbk2ae+rrjQ3rR83Ak9Di+oGqSN6ZNpy5vEjNLodXD8V\nzJagd/FctN7XHPf/kxi87zTv5zz27IqdkjgduQg+iGx4Wc7zPJPwvFqnJsbpoZ+4sgVWV4ujK/m+\na/WVLIwCn0VlDrTcxAtQgJmbSGf/rtz7Ucg7ZBZaimsdCiqYlyidSsQhvtX7TYpHBRsrePwwci6K\nHlYnDu3u4TD6OLTnWf2YZNeYsRrS4XE9cqcrylgJ52iKJvRjWDEtTscw5LnVwCXu/wtRpXC3nOf6\nAvJMiGIs53mzUpYeQrc1sSpMH4w4HMp9Vr+iX55XonnFYYEf0xKnU724Ax3ib+zlaL5SES4uePww\ncjv5X0p5WYqilhntpy3P6kTgKyl+V2cZPwP4eAnn6bIuNaEfw4ppcTq6nuemoZE2v3tg3gAUU9Dc\n7qilvqA+fSlLD6HbmlgVpg9GHGU/q0Por8W4EnlAhQUYS0OSTvXiDnZIbvV+Ec07ysMK+v7OhtiP\nftQlw2grk9E8pbAQ2H7qLuO7okjKWd3k/XRZl0w/ysNsmY5hsNMxyNXuaOR+djlwXM5zvRS52kdR\np76UoYfQbU2simHI90Z32cD4yKtZSdKpXtzBDsmNwz1Q70nW1usUrCcqjAtRZCXDaDPvRetoxdFU\nGb8WjWrmoeu6ZPpRHmbLdAyDnU5DjcOj3O+zgUcZH/01LRuBl0Xsa0JfiughdF8Tq2IY8r3RPZah\nAGTriA/ilkScTkEJjUNQ+NeJsoBq1XyOYj7EhlE1oyj6WVtZTLFJ2l3G9KM8zJbpGAY7nYAah/6l\nbh5Ai4RnYV/GRzlsAxNZD6tkGPK90V3OAu4mXx5Mo1O9uJ0ONvHVMIzucTHmBmUYRjr2QhGN/RWt\nXwJnZzzP9ahnv22YHhpGt1mOIgfv434/AHVo5SnXaXSqF7fTwRqHhmF0j6loEdw9mk6IYRid4GvA\ni93/56HlHfbKcPwq4PyyE1USpoeG0W2egzTKW7f0eBRReXHG86TVqV7cTgf4Kpq0+KGMCTAMw2iS\nXYCrKB6MwTCM4WcBWmNzDVoLckWGYw8DLqoiUSViemgY3ea1aB3HNcCnyR40K0mn1qL23i0kNA4N\nwzAMwzAMwzAMwzAMwzAMwzAMwzAMwzAMwzAMwzAMwzAMwzAMwzAMw5h4/BFGW6oiy1orpwAAAABJ\nRU5ErkJggg==\n",
+      "image/png": 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Qrii9sj97SWemfL5i98/LrHZElmApTNRnbaAaVCAd9OiihTqebfXg4Q5XDWRUOvg9eyBZ\ngjcxK3XlBf/ic5QnY8V/VGUycElcf9j4ZMtlORBsi9FhY9wSjPZ25GxHeQKfHMj0007poyp7ZWGJ\nthsQssXosFFuCUbqtBM9Z2MvKS0MaAUIt78k5EJ8yAUOBNtidNgYtwKjxqKa7Jvj/6vy8EDmn3Ja\nXacQLh/hF7qXc9tidNjQtwSjO+Ua8P+rEv2fplrnci7MPvoqltOgS1mDIbnF6LBBbgVGFfZqCt/Y\n/2n6P5QyBH1B7jAhAAAAAElFTkSuQmCC\n",
       "text/latex": [
-       "$$\\left [ \\left ( 5, \\quad - \\frac{x^{3}}{6} + 3 x^{2} - 18 x + 36\\right ), \\quad \\left ( 6, \\quad \\frac{x^{3}}{2} - \\frac{17 x^{2}}{2} + \\frac{95 x}{2} - \\frac{521}{6}\\right ), \\quad \\left ( 7, \\quad - \\frac{x^{3}}{2} + 8 x^{2} - 42 x + \\frac{218}{3}\\right )\\right ]$$"
+       "$$\\left [ \\left ( 1, \\quad - \\frac{x^{3}}{6} + x^{2} - 2 x + \\frac{4}{3}\\right ), \\quad \\left ( 2, \\quad \\frac{x^{3}}{2} - \\frac{5 x^{2}}{2} + \\frac{7 x}{2} - \\frac{5}{6}\\right ), \\quad \\left ( 3, \\quad - \\frac{x^{3}}{2} + 2 x^{2} - 2 x + \\frac{2}{3}\\right ), \\quad \\left ( 4, \\quad \\frac{x^{3}}{6} - \\frac{x^{2}}{2} + \\frac{x}{2} - \\frac{1}{6}\\right )\\right ]$$"
       ],
       "text/plain": [
-       "⎡⎛      3                   ⎞  ⎛    3       2             ⎞  ⎛      3         \n",
-       "⎢⎜     x       2            ⎟  ⎜   x    17⋅x    95⋅x   521⎟  ⎜     x       2  \n",
-       "⎢⎜5, - ── + 3⋅x  - 18⋅x + 36⎟, ⎜6, ── - ───── + ──── - ───⎟, ⎜7, - ── + 8⋅x  -\n",
-       "⎣⎝     6                    ⎠  ⎝   2      2      2      6 ⎠  ⎝     2          \n",
+       "⎡⎛      3               ⎞  ⎛    3      2          ⎞  ⎛      3                 \n",
+       "⎢⎜     x     2         4⎟  ⎜   x    5⋅x    7⋅x   5⎟  ⎜     x       2         2\n",
+       "⎢⎜1, - ── + x  - 2⋅x + ─⎟, ⎜2, ── - ──── + ─── - ─⎟, ⎜3, - ── + 2⋅x  - 2⋅x + ─\n",
+       "⎣⎝     6               3⎠  ⎝   2     2      2    6⎠  ⎝     2                 3\n",
        "\n",
-       "           ⎞⎤\n",
-       "        218⎟⎥\n",
-       " 42⋅x + ───⎟⎥\n",
-       "         3 ⎠⎦"
+       "⎞  ⎛    3    2        ⎞⎤\n",
+       "⎟  ⎜   x    x    x   1⎟⎥\n",
+       "⎟, ⎜4, ── - ── + ─ - ─⎟⎥\n",
+       "⎠  ⎝   6    2    2   6⎠⎦"
       ]
      },
      "metadata": {},
@@ -632,12 +635,12 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Interval =  [3, 4)\n"
+      "('Interval = ', Interval.Ropen(3, 4))\n"
      ]
     },
     {
      "data": {
-      "image/png": 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+      "image/png": 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       "text/latex": [
        "$$\\left [ \\left ( 3, \\quad - \\frac{x^{3}}{6} + 2 x^{2} - 8 x + \\frac{32}{3}\\right ), \\quad \\left ( 4, \\quad \\frac{x^{3}}{2} - \\frac{11 x^{2}}{2} + \\frac{39 x}{2} - \\frac{131}{6}\\right ), \\quad \\left ( 5, \\quad - \\frac{x^{3}}{2} + 5 x^{2} - 16 x + \\frac{50}{3}\\right ), \\quad \\left ( 6, \\quad \\frac{x^{3}}{6} - \\frac{3 x^{2}}{2} + \\frac{9 x}{2} - \\frac{9}{2}\\right )\\right ]$$"
       ],
@@ -660,12 +663,12 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Interval =  [2, 3)\n"
+      "('Interval = ', Interval.Ropen(2, 3))\n"
      ]
     },
     {
      "data": {
-      "image/png": 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       "text/latex": [
        "$$\\left [ \\left ( 2, \\quad - \\frac{x^{3}}{6} + \\frac{3 x^{2}}{2} - \\frac{9 x}{2} + \\frac{9}{2}\\right ), \\quad \\left ( 3, \\quad \\frac{x^{3}}{2} - 4 x^{2} + 10 x - \\frac{22}{3}\\right ), \\quad \\left ( 4, \\quad - \\frac{x^{3}}{2} + \\frac{7 x^{2}}{2} - \\frac{15 x}{2} + \\frac{31}{6}\\right ), \\quad \\left ( 5, \\quad \\frac{x^{3}}{6} - x^{2} + 2 x - \\frac{4}{3}\\right )\\right ]$$"
       ],
@@ -688,25 +691,25 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Interval =  [1, 2)\n"
+      "('Interval = ', Interval.Ropen(4, 5))\n"
      ]
     },
     {
      "data": {
-      "image/png": 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+      "image/png": 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Eww7bezb88JbK3qrfeYSNihEJa33aATH+BgF//GmOAR4PRyQc/7lIWsOkhKohtIICU4mP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\nYII=\n",
       "text/latex": [
-       "$$\\left [ \\left ( 1, \\quad - \\frac{x^{3}}{6} + x^{2} - 2 x + \\frac{4}{3}\\right ), \\quad \\left ( 2, \\quad \\frac{x^{3}}{2} - \\frac{5 x^{2}}{2} + \\frac{7 x}{2} - \\frac{5}{6}\\right ), \\quad \\left ( 3, \\quad - \\frac{x^{3}}{2} + 2 x^{2} - 2 x + \\frac{2}{3}\\right ), \\quad \\left ( 4, \\quad \\frac{x^{3}}{6} - \\frac{x^{2}}{2} + \\frac{x}{2} - \\frac{1}{6}\\right )\\right ]$$"
+       "$$\\left [ \\left ( 4, \\quad - \\frac{x^{3}}{6} + \\frac{5 x^{2}}{2} - \\frac{25 x}{2} + \\frac{125}{6}\\right ), \\quad \\left ( 5, \\quad \\frac{x^{3}}{2} - 7 x^{2} + 32 x - \\frac{142}{3}\\right ), \\quad \\left ( 6, \\quad - \\frac{x^{3}}{2} + \\frac{13 x^{2}}{2} - \\frac{55 x}{2} + \\frac{229}{6}\\right ), \\quad \\left ( 7, \\quad \\frac{x^{3}}{6} - 2 x^{2} + 8 x - \\frac{32}{3}\\right )\\right ]$$"
       ],
       "text/plain": [
-       "⎡⎛      3               ⎞  ⎛    3      2          ⎞  ⎛      3                 \n",
-       "⎢⎜     x     2         4⎟  ⎜   x    5⋅x    7⋅x   5⎟  ⎜     x       2         2\n",
-       "⎢⎜1, - ── + x  - 2⋅x + ─⎟, ⎜2, ── - ──── + ─── - ─⎟, ⎜3, - ── + 2⋅x  - 2⋅x + ─\n",
-       "⎣⎝     6               3⎠  ⎝   2     2      2    6⎠  ⎝     2                 3\n",
+       "⎡⎛      3      2             ⎞  ⎛    3                    ⎞  ⎛      3       2 \n",
+       "⎢⎜     x    5⋅x    25⋅x   125⎟  ⎜   x       2          142⎟  ⎜     x    13⋅x  \n",
+       "⎢⎜4, - ── + ──── - ──── + ───⎟, ⎜5, ── - 7⋅x  + 32⋅x - ───⎟, ⎜6, - ── + ───── \n",
+       "⎣⎝     6     2      2      6 ⎠  ⎝   2                   3 ⎠  ⎝     2      2   \n",
        "\n",
-       "⎞  ⎛    3    2        ⎞⎤\n",
-       "⎟  ⎜   x    x    x   1⎟⎥\n",
-       "⎟, ⎜4, ── - ── + ─ - ─⎟⎥\n",
-       "⎠  ⎝   6    2    2   6⎠⎦"
+       "            ⎞  ⎛    3                  ⎞⎤\n",
+       "  55⋅x   229⎟  ⎜   x       2         32⎟⎥\n",
+       "- ──── + ───⎟, ⎜7, ── - 2⋅x  + 8⋅x - ──⎟⎥\n",
+       "   2      6 ⎠  ⎝   6                 3 ⎠⎦"
       ]
      },
      "metadata": {},
@@ -716,25 +719,25 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Interval =  [4, 5)\n"
+      "('Interval = ', Interval.Ropen(5, 6))\n"
      ]
     },
     {
      "data": {
-      "image/png": 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+      "image/png": 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InJCx3UNoCsMkiZ+80W+IzHzgX0AZEYERp/RRKL+Wfmwlen2q8R2m7E/dVJuq9YKK7kcW\nmiuJRKUClIyhs35gwj4SMlqMYOPeMfsCyqggMOKUPnLlUaaMPlgZLNMlIAdZwwtqzTirQgJrkitZ\nm2L5ay75PUw1TlIYKk3qR7Bx8wF/qjInCYSa8ohT+sh1RpoK2Y5FoJkujhR/I+YFtWrbLYulvheQ\n7a+5jtV70dw/2XPfR/E3Yl5Q4VP9G35yTeY7G65l5pLrWwuJc99Hfvf1Nh/whW16LWYips7f2HD7\nbMz1453zPlZm+WRc5f817N3rNz+qpcKiSpH7Ax25d7ba576PN7KpIX8N6/2Jc7FxtuYLtrtW03us\n3HVinvM+Opg9JgX/xPn/hvCPRrGbdlEAAAAASUVORK5CYII=\n",
       "text/latex": [
-       "$$\\left [ \\left ( 4, \\quad - \\frac{x^{3}}{6} + \\frac{5 x^{2}}{2} - \\frac{25 x}{2} + \\frac{125}{6}\\right ), \\quad \\left ( 5, \\quad \\frac{x^{3}}{2} - 7 x^{2} + 32 x - \\frac{142}{3}\\right ), \\quad \\left ( 6, \\quad - \\frac{x^{3}}{2} + \\frac{13 x^{2}}{2} - \\frac{55 x}{2} + \\frac{229}{6}\\right ), \\quad \\left ( 7, \\quad \\frac{x^{3}}{6} - 2 x^{2} + 8 x - \\frac{32}{3}\\right )\\right ]$$"
+       "$$\\left [ \\left ( 5, \\quad - \\frac{x^{3}}{6} + 3 x^{2} - 18 x + 36\\right ), \\quad \\left ( 6, \\quad \\frac{x^{3}}{2} - \\frac{17 x^{2}}{2} + \\frac{95 x}{2} - \\frac{521}{6}\\right ), \\quad \\left ( 7, \\quad - \\frac{x^{3}}{2} + 8 x^{2} - 42 x + \\frac{218}{3}\\right )\\right ]$$"
       ],
       "text/plain": [
-       "⎡⎛      3      2             ⎞  ⎛    3                    ⎞  ⎛      3       2 \n",
-       "⎢⎜     x    5⋅x    25⋅x   125⎟  ⎜   x       2          142⎟  ⎜     x    13⋅x  \n",
-       "⎢⎜4, - ── + ──── - ──── + ───⎟, ⎜5, ── - 7⋅x  + 32⋅x - ───⎟, ⎜6, - ── + ───── \n",
-       "⎣⎝     6     2      2      6 ⎠  ⎝   2                   3 ⎠  ⎝     2      2   \n",
+       "⎡⎛      3                   ⎞  ⎛    3       2             ⎞  ⎛      3         \n",
+       "⎢⎜     x       2            ⎟  ⎜   x    17⋅x    95⋅x   521⎟  ⎜     x       2  \n",
+       "⎢⎜5, - ── + 3⋅x  - 18⋅x + 36⎟, ⎜6, ── - ───── + ──── - ───⎟, ⎜7, - ── + 8⋅x  -\n",
+       "⎣⎝     6                    ⎠  ⎝   2      2      2      6 ⎠  ⎝     2          \n",
        "\n",
-       "            ⎞  ⎛    3                  ⎞⎤\n",
-       "  55⋅x   229⎟  ⎜   x       2         32⎟⎥\n",
-       "- ──── + ───⎟, ⎜7, ── - 2⋅x  + 8⋅x - ──⎟⎥\n",
-       "   2      6 ⎠  ⎝   6                 3 ⎠⎦"
+       "           ⎞⎤\n",
+       "        218⎟⎥\n",
+       " 42⋅x + ───⎟⎥\n",
+       "         3 ⎠⎦"
       ]
      },
      "metadata": {},
@@ -745,15 +748,19 @@
     "# Transpose the interval and coefficients\n",
     "#  Note that interval [0,1) has the polynomial coefficients found in the einspline code\n",
     "#  The other intervals could be shifted, and they would also have the same polynomials\n",
-    "cond_map = defaultdict(list)\n",
+    "def transpose_interval_and_coefficients(sym_basis):\n",
+    "    cond_map = defaultdict(list)\n",
     "\n",
-    "i1 = Interval(0,5, False, False) # interval for evaluation\n",
-    "for idx, s0 in enumerate(sym_basis):\n",
-    "    for expr, cond in s0.args:\n",
-    "        if cond != True:\n",
-    "            i2 = to_interval(cond)\n",
-    "            if not i1.is_disjoint(i2):\n",
-    "                cond_map[i2].append( (idx, expr) )\n",
+    "    i1 = Interval(0,5, False, False) # interval for evaluation\n",
+    "    for idx, s0 in enumerate(sym_basis):\n",
+    "        for expr, cond in s0.args:\n",
+    "            if cond != True:\n",
+    "                i2 = to_interval(cond)\n",
+    "                if not i1.is_disjoint(i2):\n",
+    "                    cond_map[i2].append( (idx, expr) )\n",
+    "    return cond_map\n",
+    "\n",
+    "cond_map = transpose_interval_and_coefficients(sym_basis)\n",
     "for cond, expr in cond_map.items():\n",
     "    #print(cond, [e.subs(x, x-cond.args[0]) for e in expr])\n",
     "    print(\"Interval = \",cond)\n",
@@ -765,15 +772,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 129,
+   "execution_count": 13,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
+      "image/png": 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qbEpTCbYKnOLy5Wi3gVV6ywhpDfn+33w26mo/fKx/XT6c2wc//gF7/Cor7AD2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\n6vnr7WOLjJuxJOUtWG4ijO/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43RoD7tVirgqRA21AKuTBmwXvljUOzualvyO+FXYM85G5\nVzvxqp/QCB6tLhmfSpeZQJ2nCSns+zKdLQ+rvbikhlxDWtbxRHg9zEiWSwkxuWZYtIYhbRasmc0v\nFiwYUuh73hJKjkxqoQcBamWPYqTA58FyhXEK1gW82mhWYpWdxyOs4MONQkt0UYrsM8pAhN8tPlyh\nIHYSozReFGkGsNlVVFoLneerdTgcj/WpIgsqXGLHdzn8i5P/KdNt4Qv+aAyug/6Kvw5kCBIyP+Sq\n5j3GXjOFPG1iHWbiqiSJH+unc6cf3mNTk3u1Cxl9SPQkxLtkyAvDKYS3eZqQwr4v0+niglxwywpx\n0bbWND2wP1ItJUQSzbBsDS1tFq6ZBa2WUYVU/J6nUXJkUgM98NYrexQjBd4wLddyfoIJrbf+BoY2\n3yo7X33n9xEnGi/SMXa0z8iCSBYRRzoFsZMYpfEiqRGYLq/X4VFUWgp9Hk6v4wFtgzO98AMvspDC\nKXZ8Z+HH+NCVj+HdrwG2usYJHSNsQH/A+WpgjrS6vIu5uiRYIUdG/gozcVWSkADvdzeM6WPOT9gk\nIZL/9z/0B23ijTfKIoWpFUksryGlFy5k04hExmOeThYXT/yCHcCetGoK1RKNSS0lRGLN0KDkKhrS\n5gSaGaXMo6KpeNimMeXQpCaGmpU9ijAPlitaejJVLhGJ96zPSGkKibHWxZZVQZwWbFFS4wmpWx61\n0C1cKA3Dji8MFC7N5sEQKu1Lw9ErgUtuEszralVZKrtkvPxz7rfZvbZpyprn6Ux5Iw5yi+P5/II7\nJUqW+U4zLFnDkjbL0cyoAnlUNBUP2zSmHJrUQm+t7FGMJPgFsFzR0pOSVCJQ70WfkQXRTXNyfT6J\nWguWGDEtNV6i3RzSQjezcoQCO8ZZ+NGr+0XRbeI+lJp7NTE52MSkumTMVDxyCw1yWEvXu5GB1JGG\nPMK4CIbTxZcSpngaKlnDkkbpc+G1qJDPChqW1EJvrexRukrwW8EqxrtE0D4jC+K8iLggS2KE5Mx4\nBfJvek2xowoW/rAo+ptUVGLprL/CTkSKdkME92qm3+dcdZcMf289baFBPuvpnENj2Synm1r65eKs\nX0GaVkujb3Ph9ahWWYKxb0AvwW8DmzNCYzzpM2qAqIs7M16jju8iJ9hRRAv+d6n43XyFVyse7WB0\nyRQhbKFBphvo3G69rK62agcrAaVkDS1NMLAeN6BaYwnOvgG9BL8JrGWAxjjZZ9QAERppXBluPP7u\nJzxJ7KhTC/6fgOkdOgiv5tsZeUFWl0w+tX+zhQYpt9DhBot3NpDrNnkrqZh5X7KGlpZhRKK3oFpB\nI5I2oJfgt4AluPcLij6jBogw+YONYgvj7afybpwEduTbgn83vX4YI+HVuhtzCUrZqi4ZQbWFBlls\nons8JzYGyneQFJoVHwvWgCYyl1ZkuA3VCkvwpE3oJfgNYCvssT4J7zNqgiiKOzfees3eT8Gxo7w2\n/O/X+FskvF7/4XLjunce/alP5c03F5F9uDXa0H8E+DaI3UdgXCqijfiXWH/uO1lX6x7LlbUPQ9qK\nppX+e83VqH0j+Zdgb9Wxlf5LQC4I+XT9F6A1vFJerXNbwDVw/Emk44nOMd6i2Sdboxn9zwffDPHD\ni3s7/i0fxY+n0V6t/4L5JF9klh7X2rVdH2yNdvQ/Hnw7RDi8rm0ae1vxaqTeAX+jBj+TXHs1WJna\nWsH5KVAvi+sd6rT8XGvsgP6ng98B4kcX9z3w130Gn5XK8Grd+MG/XtT6PVlXRuPXhT/VGrug/9ng\nd4H4wcV9H/zrPoePSK3GQEHr7HYLH4FoQUl3ovTC+7pX/5p5fqdVfidqXcL3sYPm+60xRl1NzlOS\n+g0Pt4OKjK5+HqYJN4r5juu8wwDvm8zzj1mltZC8v3S8oSz8fNCGWfewg8H2W6O0VzuHIw1yesE2\nRnz6fi5hJh4321Pn0WTS7h2tN1NfK+Fd5vnHrNJaSNZmy4b0+5eFDwBt2KndDgbT741SXk1t36T0\ng+3LJrE1skqzFAH1pT4d9rSU8g3v3GrGBr5vM88/ZpXWQtKQRdWku5eFTwBtWKfVDgbLb45SXu0g\ndqUy9Bsm3Ny35bp/V11NbSW4FsU7zfNPWaW9kKzNmtXp1RZ7KznosvABoA2MrXYwWH5zlPRqQ1Ut\nqq4tPm9Dro/F6cOpC0vgw/Hb4b6Ulr8LJwWF+x12IY4pDqWjGWJKK7CbeQxUVVbBHcAuuNLVYGAp\nTOJCdlj077BKXSEhCs7BkG36TUNMKISM+RtQbwUdsrUB4jJpOhPAVUl2tMOy3G95K8dA+Ukxpkq4\nlbc46MJKN+ARG3DpY3H6A3yVxSscvx3uRYKQIJwUFO7Yb3CLNdA6vxR4yftu5tGo6qzSBVSagdSV\nP4fssOl3t0plIeE6uqegoPFqe1QohJz53qi3g47Zuh3iImXIfUjkNgDe0w6Lgr/npairjWV31cOe\nVIPYl8rW3beo1LE4/XP0x8TaVCE2HL8d7iG+eMdJxLiVXrjjdmukkt1yoth+5lGoKq0SUSkGRbv4\n7AhWEfQ7W6W+kCi1g4LqRUtEKISC+b6oG0DHbG0BuUgbujf6CVtjBsXWqQAAHaJJREFUO9phUeo3\nvRRe7VnR4QUHnsTDrxa1DoYUx0gf4VShCjHh+O1wXxRFX4aTgub76A6hTTtJyp0CKWkpvJ95FKpK\nq3QBnWJQ0r3z2ZGh39sq1YVEqR0UVC9aI/BsJsF8Z9TbQUvFWrFq+vAx3txI3Y520KK+P0Z4tdPC\nSVHT7TlU+jOPKxhyPkZ6JX04fjvcuzX04ZwNuPfeq8UVoWNycKvNv595NqEK+iK69QxidrhGSKT3\nTPeyyppMCnD0PWSffrM9Jo5eE+Y7od4HNDsCbzvODOWc+8M9zj/YyQ4Zed8azb2ar9fYCsFZyYdr\nd1yxCmk25Hwszlr6cPx2uK+iDycF4R0PshzIWQanNHRgI83G7mieTaiCYohqPYPk1Sh94LmPVVZl\nEhwm+bxcrOV5IfuCcvLe327Tc0VJBHOls8wp811QrwM9HA8wegWXBFU83moEIn/mZtZwimeMmHN/\nSrOqWu1wPtwuix3k/vz2qMFbA1fIhCEWCe7VHnDmdu6C0rdyYkv6jPBYnPX0OK/NL0LA+xr6cFKQ\nu99B+I1U0MA3b7z2NY9DtwZV0DqgW8kgZgejD0z3scoqOG6xzkRyJugSFQwR8u7Gfg6x+i1f28/z\n2UyM+S6oV4HuHv5Y55cai2eKGRBGRH3Hn+es4QyqEOVz/zFGr8bEbbDDcOrPRt4FeXA/mhPAboVN\nUrYtO3LbGMeGJh8DLfQbLQ0lYN1BXPEzCsdIL9ELWjjmEBj2YLZwhwQWvSE3nk01nxg03G70IJ7b\nguumWmjO282jeBVQUT1k2KMqMFAC4YOYOzMVvROwm1WsTJIQ/LMfCj+pkSd90JNAc3d7sYwrf538\n2Uyc+V6o60F3T/+hKKfGFUMLCdQ3fywk5GLOcLaZfazL/R4r+X7uFhdXawciQR7gR1754O2kvVo/\n0RqiIsGIimkGM934hN+T+bpOh1vyQLyuZnvXQDmAO0h8Qux8Nw6p9obEPZT9MdKL9IJdOn4bh2v8\nEKZJb8gNJwXNd6wl41Ei4bpXFkHNebt5FK8CqqCrcZ9RFRgogdGrKXovYy+rmJlkwICok3OzB9fv\nSVKE7CNRAo2fBd5XDDnNPNLZTIL5TqhXgO58y3OSH5JQDBUXqM/Yxd+/cMzDNhwxmA66j/H+hOuF\n01yEuFo7EL6lyX7j40o+Okc4Psv7kQ+X42KzNmowHK6kD4L/SHCvhkefZ67x1U1gTN0bMKcXWYCx\n/qAI/PzgGOkSvRIbjt+e7zl6LTecFBTuuKMr7b0R5ykqwSFCc95uHsWrgCrooO8BVYGBEhiyQ9BH\nAbtYJZdJUQoLXF2tQXq1oCBNKtCcX9ihM63YPW8uhOrcsj1QrwPtYZ1jY2mGWYHapXQtUNtw1GA6\nHE9tcTUEKa7WDoRvyatNnfBq4+Fa0WdwON+kbYjQGDxf+TyMRa+WZ9gfbufpBn1ymUsUPKhfPY+v\nA/Cbj8Up0Wu204SzjHDRKd5z9EpuPJsqnBh0Bgapcoo/d/RzmACU/N30umjOr83m0byWUWlrhJiA\naq1ZQnYI+sB2H6vkMilKMQJH9G3Q/X8Yz7cJDBwVJGml+Q6v18M7NUJI0qtgOJtJMt+jLGwB7Wsx\nRHmpGCKQqDGOtM+k4fB17gq5DxWMyws6JKW4WjtE/sPhdEK/1sPnM0Gd6Xw93e4TWTMEPXjMqw0X\nWrWa+RADhBioirI6uE4CKe9X9kVDzOHxgCkaM5OO1dU4tpCk7m5lQR1lW6oNcolzGnEP8Ct20IB3\no84OYhTnBvMoXm2gy9TrBZpWgVqukKUYN1gFWZ9f+JMFfw/ocTlmusqU0OfrdcUf2BKhUF4/Gqin\new8XT6oUaEM9e+S1qIfpmBpTVYbjKBaeDDsU1uQdsGQMWAn2Zz+cnjBpJH5C2INHvFp/pa2loIeR\nexN8j/gXLiNJdztiQ4VfWHlP83SYV/PdXzx57ZPK91rCxnQb5OJ3NF9uZB8H0+CHZBTd1opzg3kU\nr6DAu+7rBVpWAdfu+5aTmopxg1WQq+urdM1pkHSndeokU/3APJ7D9YXdTCVCwsMOGqihIggX9+b7\nou79eFVJeSUUIEzxqL8qw9mgjVjDDoU1ec6rHd2nNGDX6JVVsTCeeDXwREYzzzAAMqHDQDrJwnjD\nJajw3/+QgkRa1/31GK8r1uzm8Why47aRWUAS5oIzAyXKxeeIXmIEU8o1FJ1ZRX1T99gzfLO4VhR/\nXuilOCfzaJW1upSV+ix18hATyLQI9yYk0/dA6O9SeZ1+jolkhlWwLhQsFNJJxmF8273XUmayDBpY\ndeK8B/700m8gCAt3IfSBvSiPF2wEqAhtQUqvwLgzUB/OcImZWEIBqKSkU98V81hCbWVgnpGvkirl\no1Y+oIRi9Gne/jBjOFukVnGOiRINO4g1dTHpHECvFqyAPvFKu7bu6DJ4jj50DUsb4OG+QdJlppL0\nF9jFLnM9wzggq6vRuaoZQiN6uuJ1PLlbqiEbKfeN2iw35WAce8aZuunKcN5kngyvJGzv0FaBhlXg\n+4sz0aGaYOfzJqsE0GTHQtIGCm/hbgr1H3b8pMSvEaEuBw3UWBTu8csxFcDvOTa2ykJkCjKWvgL1\n6OofF+9Oi4aTMgvPhh0Ka/LQq93nCWtYsyU9fq5jQHo1SK16w0ApbgA//jlQBymTwG41etTBz7eL\ncx+ZV6toTLAdTKilzB+WlCBLl5JkQ4u0S3J1X5mTEWvbfQy9YAkf7u9DL8W5xjyqd85zVLySoEV0\nKZkKLdMtCbR1jLZIVunI+pogXzE2rJKxe2CR7nf8EfRfq2vFuLpXeh1DXOjcgIMeYkywSBg5YCDs\nRkQjLdS+u46mUnXtea4STbOcHzRln2bgLirPUUMjBAvoxbnTWsNRsS5s2QBfGHYQa+okK1ZXg3yk\nXu1+wOt1wtFCesmRS5l7DhYQkFEHmQTZ6RkiJ1f7jU0v5tV67jipPnOY72BCE4gsoK8gnKcTCY3H\nZdoFuUZfmWOffmbn0H3Enyq57bjiXDZPTqL+KiLOZXQxmQoU6JTykUFOR20VyLYwZzNSayTaKjkJ\nickc8ktqYPbkvYfVHxBp9L24pALNfHY1TEQuEVKRYTciGtdZqMM0V5JQKAB+T34qhfwgvMAP+xZN\nSXkh1DcsjtjKqjYcFYth0wb4wrADTgLGdTmZy/WrnRwSt8aAejVPEltChMNAG5DKAMGbBe8GCtgl\nA2fz0kqIN2gcbGJeLXlsogcL4pAHnaefXoosSC9cKE8nEhqPy7R5uVZfGbIfU5fIE6u6/XPo/bTt\n2OxwWmjO8QfNvdf/chIhc8SPVqJdRpfSyVCBLiswp6NhlY6sr4niNWNplZyEyCIExiMsbMRd+M5g\n/gt4tTHXqhNCz278E/pgioRBFN7DbkQ0zkINJVx9y0IBYCFRF/KDCr17r1ZUXgh1Z5vd0ZvWG46K\nxbBlA4y37YDO2zV7MYm8LmikwQ1eXHFsgAzPzknFiMscO8ZeM2WAZPcwE1clmZnAjfXTudVkj/nX\nDjKH/eaceIM2sQghsYNJiIa7yALyBoN5OpHQeFymzcvlfWWJ8UBWr00TzHOBVy4q/V65xJpzyTw5\niUvWWUaXtJahAp1WfmaQ09GwCllfk6RrxtIqOQmJxxy6+i7rI85FvPU3yAqVZI6QQgdYII5LmYuE\nkiHuRkQvAzW81ivPpQJQosWnUsgPKnT0FioqL4WeYWGA6yqvNxwVG8LSBhhv2YGsyQuk6T7ASDFO\nbx9hpf4BcuJ8gWfeOQ0xvo8gUfGQMgAy8leYiauShAR4v7thTB8DehxSFxL3aheR6ZRHDKvBfvdG\nZkFMHgM2XXy9GMjT5uVafWUoxOLl1u0Tb+fSqfpVyTw5iUteLacRxpcuC8lMkzVLTkeDV1pfQxTR\njKVVchIIk7VBLXQtB58+7kYUyA3U8EpvJqkVkKiRo80tyFp910JXszAIlA0wjaU51j7JbqsGq72j\nolMDN9vEm69un8SULZO1vT71nP2hDUxsuvB2+Z6nzco1+8pQigUS14nK4wA1Z4uS6J2VCD9li9bJ\noyPcjeACXU5gVscMNlWsNWNBmZVgAKiN0kJrKWk6shtRiBa6z9EnlVtaAYtyIT+CwDV3LXQNtZ3W\nsAEmtNC4qWK+w8rm9XNjeV3NctlSd7aDiXy58LyVDlluoTX7ypDZRbQdMA62+ZhSBdbFGP8K5slK\nNFjRqC3okH4LXVZH0yrz+hqqrA4Lq2QlaMqvj5EbTdioazYRFKgRypb8+HoTzFMEuWDTDn5RH0+4\n8YlOoyvsRLRRAiPjXo0seWCpyAPfwYS8KAS30iHbbbRWXxlyE91nGFV5lcyTk7jMfhu6n2uVbVZY\nttFeb8Mct8Bvz7KwNR+DLl91lzZAudvt8FVar5LDvZpdj6EMxQ4m9NVieCsdMt1Ia/WVATd7CHdR\n+fjS/EmLb/2umqJ3Lr3NhDai+7lWydg9A//LotNuREnknmVhaz4mbd4fsmyAUlvs8H6t10sQXq10\nPIXcwaRW4FY65L+V1uorA3ZTzYhIBlfBPBmJGWY+eiu6rXQZHXe0SkbCohW+4iX2fsOWWFTUjqi3\n5gdV5/1hwwYotMUO71d6vQTh1XynSJ6N3MEkn5K/2UqHXDbT2n1luiuYq7r0VDKPLXGJ42Z0P9gq\nG6ywaKKdXobdiAi7HcvC5vwg6rw/aNgAhbbY4f1Kr5fAx0Djwtv1jD6FIu6et0nheV3yJtqfTPQ7\nrfI7Uety2GYHze/bY0RdDdx220yRbwdUUqC8x/Aih3/UPL/TKr8TtS7fjXbQDL87Rnm1R0O303eD\nqZDfCq+VvkLFb0jSiqqV/hsgg8hWrVvpvwe1lvqv4EjIlFfzG1umBP9WaIxLxbbiwmUi/9r1O63y\nO1HrsttuB83zm2O0V+u/YJbcd4HucUPvtusfNM/vtMrvRK0L/w520Ey/OUZ7NdgRILtO/5uVbRZ/\nUUth1rP898zzO63yO1Hr8r6HHTTX742RY6Cozf/+3/fq9Abp7rTrrifLZ7cI8ZtKjJ8/nuLNMZtg\ns1XYHhufZhWKmpljVcH4NNQaHLWDfvuhMUZd7Z+cvXDeYRDkHzLMnznY97qHORjDv4dvtYD2amc+\n/VprNzxuceM3/fanxuBehm3XP2WYN5ijtVwM04Rben3L1W6Ob1H7T6htAeXVzO2XGC1sXCc37WHv\nf+iDW57YoNs/Zpj9zdFaLmAzKLnJekN2rSRtNcdKcX/J32oB5dUOxR2VYCWd3iz0rUruwlztFLaS\n6z9mmP3N0VouoI+AnGi1Mndak7eao1X+H/2eFpBebZDnPxrChknt626k+o6oeM7PvAP6YyInRx2a\n2qCfbRgjM/Y3R2258JljHpEejqk19I1Rd9hUGh4KR4vH5DEQCWQpcSnazBGF/AV+ggXYKcegkD4p\nxtJyc+9qLFAW1+a4cM7PgEd8wPWA0co+euAav5RX4b2Gea9dTFTvMEdNuQiZYxyR3oczhkyF50js\nArtBg6JwtLhmEQhkKfEp28yhpf3FfKMFRF1tzJ8pE5V0p5ds69YNBSry2jeAE+38VlF359Vc53Ma\n/NTb0deLf69h3mwXG+be5qguFz5z9BHp/YFtE2Rr7Q7OwfZi4WhxTR0IZCmZU7aYQwv7i/lOCwiv\n9iw3AXo422CoOd/AgJUKlPGyPSqd8+M/nCcskxhTu7OwO9qi/Pca5s12sZHtbI76cuEzhx+RDir2\nz7HHpuXyNb5wuiBszVk4WlxzCQSylMwpW8yhhf3FfKcFhFc7LaxyhD6qAed0wDHnW2d2pAL1Nsx+\nP3n/4fTHFx6AGK5x7Ta1gRDu7zXMF9iFYJmDe5ljdbnwmQNaeCcW6I9wkF7Fj6r3avcuHi0e6DVC\nHhMJIJqWkjlVizm4oL+n77YA92r+h9DWCc5KPly7moMqHH1/u7kjGxUz4xgLmcYfTT3C6YeX1fP4\n/Tk/84fzuL6wGhSuE3FxIa7uvp9hRjjZlx+cOGtQYRd3uC84g5xpM1ioyGm6TcGm+5hjZbkAHaNX\ncy3OtfR4mOYA++yHo8Wr6QMBWomVktls280xM/hlt/Phdsl2GVwhWwY8svXLLlqyuVd7wAHauQu+\nhTWTetwEkYOxmLzieLEj9vC7ZSzT2urVfM6P/3CmRzccyaRi8Mobr90M4w6ZvluHXxTtMl7m8ems\naW1wRGR/hXIWT7ndxxwrywXoGLyaHwtdS3+HwnGbiwUeLb6Kfj6LnJWSYLXt5ggcftV9OPXn/Nfp\ntgY2G363wu4ZpBaywp68ZHOvVug9WhpKwF9Cct3dOvJRu5GK48VuJ/Rqvuv4tNCDJ0Si9HDOj/tw\neif9mjzrbcFpE91dNYA+gydYbhotGEYoeXuhOkZLq2SX/vI8eK+WNW1QOS/yipXVSxgVrjWHtocw\nxwL8oBO9B68WZz0u0QswwGe43XBIiBwtvkSfBCcCVkpigmpzRIpfHZCHEHJjXKfDjXsE976fij/e\ndZMNkNv4hF+0+eIlm69ud5WkkFDdB3AKiY94LQ6a9lPaeuUMQoES1PRxfFzxuzs52oPrRqGvU1iI\nhBfxnB/34Yzu870lr3avK/7Qc5iE+NB2wwheZ+xC61/K21fYBWoorsKfM23UOSvywfHXmkPbg5tj\nsVxErVIgeLUw6rhIL8CA8YARHviCXQt+7uwifRIbCXgpiQmqzREpfnVgeYJfGqMjRhqf5V13h8sx\n26wlrMATHbDhMV+iZPO62iu/sGB8dRP4mWzPlCh95xe2uaEJyK9YoHg0e5o659Wu7hte5dXSOT9+\nJ3Y3/YlMF7BOQmSi5weBBWK3G0bzwr7qLXYJXi1j2gQkK/LCK7615tBejZijVC6SWjEUtsl3Z4CU\n6BUY3LYTu1vno8VL9FFqICBnlgVFfJpqcySWvzm02quNB9JsylrucL6pOoWR+HxlI5aiZAuvlmfY\nH27n6QZ9gJlLlj6YZPnwTg06tw/j+TYB7+R2Mlwg+jF6r+ZTHNG3EQ6UToqM5zXBb8LrAOL6J/SN\nk3owP6UYuhdvdtVTMe5emw2jeYWpzgRVjV2wN8lb3zQtMUxW5OsKZwylLlxuDlgGV20PYo5SuSB6\n+WDIHKht4W9tiV6BOcOR4i5P/dHiJXoifz6LPJwGlRTxabg58tYgHH9vcDicTujXeig0E+Tj+Xq6\n3ac0i/rweMCUCWKf4UKqViGefAJzFPYasQaeTgIp71dfBAKfTpRs5tV4vkaSqoAqfc/Xy43Z4fD9\nA1rTR9A3FKgFjj34D1dXc2nOL6CmHCilEklfmmHyNY64Le712pkLd6QPazCMUnKYjq5GTFFV2AXw\nBK/WWaYleHMioeGLdUQcRPQXMQfsFertEdcVhURwlwwbzEG41gWl7DqqTamIOYI1cMnzTVasNzH/\n54gO2L8zuCkGbtf70/NOygW21Mhcmf5qzWagn8BsnwlKIf6Fy0jS3Y5YT6eXLNnMq42qZURJl8Oy\n9D2ew/WFnUiupQC1jDupNC2wwiZu8mquAyfHQYpc4Dq/Qh85X24cH8ZojYU76iuG/Nlcsi0lJzyp\nKocqKKjvwauVTJsT2b9cZe8ZR4WJObpgj7CuiIqXDBvMQdlWhaXsKqJtiYg5gjU6qGCMvN2+jfe/\nR+W82tF9UAN2fl9ZFcvhvaSo29Fo5hmfAFLQMUadxBpvkCWbeTXSs9Bfj/G6Yk0SpkiKi2eUKH0P\n7C58vOADQrea3BQlUjLg5R1lxeR+nCXHQYg0VJw1jkJTf9Bzbs11euGOrpvA/Kjw86F1FlaBxygO\nA1JJ9/K02i5INnu1ommzIv3Q6yOOxydzQPVv/vkL64qcnvM/yTCZY6lcaFMhO20uFUNFK/up1DEi\nkq0UHOmSOaI1cNEpth7+LmUB9GqhIODvwVUPEDzp6NRD1bAM1/BwtiZdZurb7y+w45W6RMlmY6A4\nuXH9NV3xOp7cLQw3+PpARF1bMLDCmbwa2cuPtA4ggSmyQvNUbt3kEaRAd3WPdsow3mQYk9foaqyX\n2UtyVCUAs1dbMG1B5MkNvT5iLidzdNEeYV2RV8Zk6CbBlpRtf2/Lbueb5ZDMEa2RWutZqt/6Ar3a\nff6BfEGYzcjwc//EbFPVG4am45+AH/8cuIPkSXDwM9Qxou1FyWZ1tYqWRXZzCf573s8VloNzk66G\n6jxzVCMTuB/wep2wr7+7o4v0bsDkwEVSjjBIQIY+05vYxuhjCF56V5pSqfpBTQs01/8ilPSNwIt3\nLCYqoocIeq9WNm1WpB8pInW12CBP9qDrioJ8wdAyR7ZcBB6Ze5FOyiZ8irQkLQtm8iqWiWSNFywP\nfM61WMbi74HV1eBLZV7Ne5lY5Q3WEiOXEM0/AffFQ2wadVBJkJWeISJKNvNqvfCKyIFf+c0lROmb\nz92EmY/3HppOwMVoV3Pe6cn/VPp1UzCXL8dBiEz0T/Cl5iTBWEvp5pBz+soBKsZlw2T7XwQvD+0I\nVfMcqgRDhkJdzXdQ5k2bFzn3qwXGyRzJHjjrFafv00swhPl2su6dLxeUjw6X6aTsxKNMm9KyUC6v\nkjlC6Rix+vZ9G/QyrX/ag+tXO7m2mVtjwLyai3YDhELtgTYg1ScQvFnwblAUbe+Bs3npj41fbvgM\nPaDMq3Xx10roEh9xyMPv9ROj5oAofWc3/gnN5DM0ti7g1cYVjVus0MKgHKyYxI3SshyEyKQRLmm3\n1jiNsXuse2Ilt3djz/MOk4lc19WKhsn3vwgl3blMd/AKWVREDxGcvVrRtDmRMM8LDNPHVhUxB7UH\nJKH9IaCEYAjNhljJm1XMlwuBQTyW6ZTsyKFMG5OyQC6viDlC6ehdgYn9kIzNb39wS1QGHPfq3MR+\nP7I/W8Wt0nuYR4qPsddMfQLpSwwzcVWSZHXeT8dLNvdqJ96gTSxCKL+5hCx9w+HpVrfDfKJbf5vY\nKWuBm32fLq8XtFyvvhv4iDOabA5SJGMXVzuS2IGUzwlU8jWOuHAnptSMS4aJniLyCAHJ6/yERfvQ\nj5dFFQjl/Xk4vY6uRV8ybU4kcJyez1io4Ocp9ifCm9keaV1RUkAy7JQ58uUicbFCZTolO7Ip08ak\nLJDLK2qOYA1noVSHY3x+9cMAcwdwQscIGxMfoBid4aOlmzZA/KHUdFefADLyV5iJq5KEBHi/u2HM\nOYaVbO7VLmolD+Uyh+3NJfKlz2CxT9SSSPPsFFvzsHAnKaUZlwyT73/RvJKcN4VqRZrmwBqQ3MRf\nMTTNYbKrgLhMp2Qzjsu0LGl8yOWVxctN8KPOP3L5C+xvgejUoEHYxJ17tSk0TJd42utTzytamEvc\nV7zLi+xv2lUBYxueW7jDxGrGNmUkWuh/0bwi1bsCtSJNUG6CkO8WifophialXS4ik2xgmU7JZnyW\naVnS8JDNKwsULjj9xAPVAthfeudezfq5koYpbS4h03/TszVacDEb2DVbxhUM85n9L7Y55nVFi9lm\nmWNrudhKhwpuoc3mlWmOB/Sj0G7pRbP8vcxZgE4hLOxElGOxJp57NbLkIcekZnOJHO1XxoepclTm\n9g6SkmE+sv9lV3NsLRdb6TBft9Hm8mq7OWgZ+wv/AAtwr9aZv1dUzZpNN2j67wi7PjVj7p09eFun\nYcEwn9j/sqs5tpaLrXSYaxtpM3nVYo66MvSX6qsscEoTqlFk6UiKus0lvkr5nBzs8X74Kfg0yVQz\nFkIJSLhgmE/sf9nTHFvLxVY6zJmttJm8ajEHKSh/wR9ggYubGxYV8Z0O8VEF6jaXUGRfHAH77UwH\n8Gzi0sMCIsHCY8kwH9j/sqc5tpaLrXSYU5tp7bxqMcdCwfl79Q0WeIjF2LeG+sw3qL9GJN8jcA0l\npv3nDPNnDlYE2szBWP09fLsFYHNHpoObLMxi/pWH8u7Ci0j/NcP8mYNld6M5GK+/h++2wE2cDPL4\nVytrrcBa6b87o4X8Vjit9EKd7378x+B8tzm/Xf5BLFV2G1t+u1a7KzCai9LWiPmnDPNnDpb17eZg\n7P4evt0CR94G7b9gltzXY+5xA+u2618yzJ85WFnYwRyM39/D91vgwLdgGHFixL92XXjv4SZ4/5Bh\n/szBSsAe5mAM/x6+3wJ3vrHM2La09PvxaA16snBWv62N+WcM82cOluX7mIOx/Hv4Hgv8fxqx3Ljw\nkXH1AAAAAElFTkSuQmCC\n",
       "text/latex": [
-       "$$\\begin{cases} \\frac{x^{3} c_{3}}{6} + \\left(\\frac{x^{3}}{2} - x^{2} + \\frac{2}{3}\\right) c_{1} + \\left(- \\frac{x^{3}}{2} + \\frac{x^{2}}{2} + \\frac{x}{2} + \\frac{1}{6}\\right) c_{2} + \\left(- \\frac{x^{3}}{6} + \\frac{x^{2}}{2} - \\frac{x}{2} + \\frac{1}{6}\\right) c_{0} & \\text{for}\\: 0 \\leq x \\wedge x < 1 \\\\\\left(- \\frac{x^{3}}{2} + 8 x^{2} - 42 x + \\frac{218}{3}\\right) c_{7} + \\left(- \\frac{x^{3}}{6} + 3 x^{2} - 18 x + 36\\right) c_{5} + \\left(\\frac{x^{3}}{2} - \\frac{17 x^{2}}{2} + \\frac{95 x}{2} - \\frac{521}{6}\\right) c_{6} & \\text{for}\\: 5 \\leq x \\wedge x < 6 \\\\\\left(- \\frac{x^{3}}{2} + 5 x^{2} - 16 x + \\frac{50}{3}\\right) c_{5} + \\left(- \\frac{x^{3}}{6} + 2 x^{2} - 8 x + \\frac{32}{3}\\right) c_{3} + \\left(\\frac{x^{3}}{6} - \\frac{3 x^{2}}{2} + \\frac{9 x}{2} - \\frac{9}{2}\\right) c_{6} + \\left(\\frac{x^{3}}{2} - \\frac{11 x^{2}}{2} + \\frac{39 x}{2} - \\frac{131}{6}\\right) c_{4} & \\text{for}\\: 3 \\leq x \\wedge x < 4 \\\\\\left(- \\frac{x^{3}}{2} + \\frac{7 x^{2}}{2} - \\frac{15 x}{2} + \\frac{31}{6}\\right) c_{4} + \\left(- \\frac{x^{3}}{6} + \\frac{3 x^{2}}{2} - \\frac{9 x}{2} + \\frac{9}{2}\\right) c_{2} + \\left(\\frac{x^{3}}{6} - x^{2} + 2 x - \\frac{4}{3}\\right) c_{5} + \\left(\\frac{x^{3}}{2} - 4 x^{2} + 10 x - \\frac{22}{3}\\right) c_{3} & \\text{for}\\: 2 \\leq x \\wedge x < 3 \\\\\\left(- \\frac{x^{3}}{2} + 2 x^{2} - 2 x + \\frac{2}{3}\\right) c_{3} + \\left(- \\frac{x^{3}}{6} + x^{2} - 2 x + \\frac{4}{3}\\right) c_{1} + \\left(\\frac{x^{3}}{6} - \\frac{x^{2}}{2} + \\frac{x}{2} - \\frac{1}{6}\\right) c_{4} + \\left(\\frac{x^{3}}{2} - \\frac{5 x^{2}}{2} + \\frac{7 x}{2} - \\frac{5}{6}\\right) c_{2} & \\text{for}\\: 1 \\leq x \\wedge x < 2 \\\\\\left(- \\frac{x^{3}}{2} + \\frac{13 x^{2}}{2} - \\frac{55 x}{2} + \\frac{229}{6}\\right) c_{6} + \\left(- \\frac{x^{3}}{6} + \\frac{5 x^{2}}{2} - \\frac{25 x}{2} + \\frac{125}{6}\\right) c_{4} + \\left(\\frac{x^{3}}{6} - 2 x^{2} + 8 x - \\frac{32}{3}\\right) c_{7} + \\left(\\frac{x^{3}}{2} - 7 x^{2} + 32 x - \\frac{142}{3}\\right) c_{5} & \\text{for}\\: 4 \\leq x \\wedge x < 5 \\end{cases}$$"
+       "$$\\begin{cases} \\frac{x^{3} c_{3}}{6} + \\left(\\frac{x^{3}}{2} - x^{2} + \\frac{2}{3}\\right) c_{1} + \\left(- \\frac{x^{3}}{2} + \\frac{x^{2}}{2} + \\frac{x}{2} + \\frac{1}{6}\\right) c_{2} + \\left(- \\frac{x^{3}}{6} + \\frac{x^{2}}{2} - \\frac{x}{2} + \\frac{1}{6}\\right) c_{0} & \\text{for}\\: 0 \\leq x \\wedge x < 1 \\\\\\left(- \\frac{x^{3}}{2} + 2 x^{2} - 2 x + \\frac{2}{3}\\right) c_{3} + \\left(- \\frac{x^{3}}{6} + x^{2} - 2 x + \\frac{4}{3}\\right) c_{1} + \\left(\\frac{x^{3}}{6} - \\frac{x^{2}}{2} + \\frac{x}{2} - \\frac{1}{6}\\right) c_{4} + \\left(\\frac{x^{3}}{2} - \\frac{5 x^{2}}{2} + \\frac{7 x}{2} - \\frac{5}{6}\\right) c_{2} & \\text{for}\\: 1 \\leq x \\wedge x < 2 \\\\\\left(- \\frac{x^{3}}{2} + 5 x^{2} - 16 x + \\frac{50}{3}\\right) c_{5} + \\left(- \\frac{x^{3}}{6} + 2 x^{2} - 8 x + \\frac{32}{3}\\right) c_{3} + \\left(\\frac{x^{3}}{6} - \\frac{3 x^{2}}{2} + \\frac{9 x}{2} - \\frac{9}{2}\\right) c_{6} + \\left(\\frac{x^{3}}{2} - \\frac{11 x^{2}}{2} + \\frac{39 x}{2} - \\frac{131}{6}\\right) c_{4} & \\text{for}\\: 3 \\leq x \\wedge x < 4 \\\\\\left(- \\frac{x^{3}}{2} + \\frac{7 x^{2}}{2} - \\frac{15 x}{2} + \\frac{31}{6}\\right) c_{4} + \\left(- \\frac{x^{3}}{6} + \\frac{3 x^{2}}{2} - \\frac{9 x}{2} + \\frac{9}{2}\\right) c_{2} + \\left(\\frac{x^{3}}{6} - x^{2} + 2 x - \\frac{4}{3}\\right) c_{5} + \\left(\\frac{x^{3}}{2} - 4 x^{2} + 10 x - \\frac{22}{3}\\right) c_{3} & \\text{for}\\: 2 \\leq x \\wedge x < 3 \\\\\\left(- \\frac{x^{3}}{2} + \\frac{13 x^{2}}{2} - \\frac{55 x}{2} + \\frac{229}{6}\\right) c_{6} + \\left(- \\frac{x^{3}}{6} + \\frac{5 x^{2}}{2} - \\frac{25 x}{2} + \\frac{125}{6}\\right) c_{4} + \\left(\\frac{x^{3}}{6} - 2 x^{2} + 8 x - \\frac{32}{3}\\right) c_{7} + \\left(\\frac{x^{3}}{2} - 7 x^{2} + 32 x - \\frac{142}{3}\\right) c_{5} & \\text{for}\\: 4 \\leq x \\wedge x < 5 \\\\\\left(- \\frac{x^{3}}{2} + 8 x^{2} - 42 x + \\frac{218}{3}\\right) c_{7} + \\left(- \\frac{x^{3}}{6} + 3 x^{2} - 18 x + 36\\right) c_{5} + \\left(\\frac{x^{3}}{2} - \\frac{17 x^{2}}{2} + \\frac{95 x}{2} - \\frac{521}{6}\\right) c_{6} & \\text{for}\\: 5 \\leq x \\wedge x < 6 \\end{cases}$$"
       ],
       "text/plain": [
        "⎧                        3        ⎛ 3         ⎞        ⎛   3    2        ⎞    \n",
@@ -781,10 +789,10 @@
        "⎪                       ─────── + ⎜── - x  + ─⎟⋅c[1] + ⎜- ── + ── + ─ + ─⎟⋅c[2\n",
        "⎪                          6      ⎝2         3⎠        ⎝  2    2    2   6⎠    \n",
        "⎪                                                                             \n",
-       "⎪               ⎛   3                    ⎞        ⎛   3                   ⎞   \n",
-       "⎪               ⎜  x       2          218⎟        ⎜  x       2            ⎟   \n",
-       "⎪               ⎜- ── + 8⋅x  - 42⋅x + ───⎟⋅c[7] + ⎜- ── + 3⋅x  - 18⋅x + 36⎟⋅c[\n",
-       "⎪               ⎝  2                   3 ⎠        ⎝  6                    ⎠   \n",
+       "⎪        ⎛   3                 ⎞        ⎛   3               ⎞        ⎛ 3    2 \n",
+       "⎪        ⎜  x       2         2⎟        ⎜  x     2         4⎟        ⎜x    x  \n",
+       "⎪        ⎜- ── + 2⋅x  - 2⋅x + ─⎟⋅c[3] + ⎜- ── + x  - 2⋅x + ─⎟⋅c[1] + ⎜── - ── \n",
+       "⎪        ⎝  2                 3⎠        ⎝  6               3⎠        ⎝6    2  \n",
        "⎪                                                                             \n",
        "⎪  ⎛   3                   ⎞        ⎛   3                  ⎞        ⎛ 3      2\n",
        "⎪  ⎜  x       2          50⎟        ⎜  x       2         32⎟        ⎜x    3⋅x \n",
@@ -796,25 +804,25 @@
        "⎪    ⎜- ── + ──── - ──── + ──⎟⋅c[4] + ⎜- ── + ──── - ─── + ─⎟⋅c[2] + ⎜── - x  \n",
        "⎪    ⎝  2     2      2     6 ⎠        ⎝  6     2      2    2⎠        ⎝6       \n",
        "⎪                                                                             \n",
-       "⎪        ⎛   3                 ⎞        ⎛   3               ⎞        ⎛ 3    2 \n",
-       "⎪        ⎜  x       2         2⎟        ⎜  x     2         4⎟        ⎜x    x  \n",
-       "⎪        ⎜- ── + 2⋅x  - 2⋅x + ─⎟⋅c[3] + ⎜- ── + x  - 2⋅x + ─⎟⋅c[1] + ⎜── - ── \n",
-       "⎪        ⎝  2                 3⎠        ⎝  6               3⎠        ⎝6    2  \n",
-       "⎪                                                                             \n",
        "⎪⎛   3       2             ⎞        ⎛   3      2             ⎞        ⎛ 3     \n",
        "⎪⎜  x    13⋅x    55⋅x   229⎟        ⎜  x    5⋅x    25⋅x   125⎟        ⎜x      \n",
        "⎪⎜- ── + ───── - ──── + ───⎟⋅c[6] + ⎜- ── + ──── - ──── + ───⎟⋅c[4] + ⎜── - 2⋅\n",
-       "⎩⎝  2      2      2      6 ⎠        ⎝  6     2      2      6 ⎠        ⎝6      \n",
+       "⎪⎝  2      2      2      6 ⎠        ⎝  6     2      2      6 ⎠        ⎝6      \n",
+       "⎪                                                                             \n",
+       "⎪               ⎛   3                    ⎞        ⎛   3                   ⎞   \n",
+       "⎪               ⎜  x       2          218⎟        ⎜  x       2            ⎟   \n",
+       "⎪               ⎜- ── + 8⋅x  - 42⋅x + ───⎟⋅c[7] + ⎜- ── + 3⋅x  - 18⋅x + 36⎟⋅c[\n",
+       "⎩               ⎝  2                   3 ⎠        ⎝  6                    ⎠   \n",
        "\n",
        "    ⎛   3    2        ⎞                                               \n",
        "    ⎜  x    x    x   1⎟                                               \n",
        "] + ⎜- ── + ── - ─ + ─⎟⋅c[0]                         for 0 ≤ x ∧ x < 1\n",
        "    ⎝  6    2    2   6⎠                                               \n",
        "                                                                      \n",
-       "     ⎛ 3       2             ⎞                                        \n",
-       "     ⎜x    17⋅x    95⋅x   521⎟                                        \n",
-       "5] + ⎜── - ───── + ──── - ───⎟⋅c[6]                  for 5 ≤ x ∧ x < 6\n",
-       "     ⎝2      2      2      6 ⎠                                        \n",
+       "       ⎞        ⎛ 3      2          ⎞                                 \n",
+       "  x   1⎟        ⎜x    5⋅x    7⋅x   5⎟                                 \n",
+       "+ ─ - ─⎟⋅c[4] + ⎜── - ──── + ─── - ─⎟⋅c[2]           for 1 ≤ x ∧ x < 2\n",
+       "  2   6⎠        ⎝2     2      2    6⎠                                 \n",
        "                                                                      \n",
        "          ⎞        ⎛ 3       2             ⎞                          \n",
        "   9⋅x   9⎟        ⎜x    11⋅x    39⋅x   131⎟                          \n",
@@ -826,18 +834,18 @@
        "+ 2⋅x - ─⎟⋅c[5] + ⎜── - 4⋅x  + 10⋅x - ──⎟⋅c[3]       for 2 ≤ x ∧ x < 3\n",
        "        3⎠        ⎝2                  3 ⎠                             \n",
        "                                                                      \n",
-       "       ⎞        ⎛ 3      2          ⎞                                 \n",
-       "  x   1⎟        ⎜x    5⋅x    7⋅x   5⎟                                 \n",
-       "+ ─ - ─⎟⋅c[4] + ⎜── - ──── + ─── - ─⎟⋅c[2]           for 1 ≤ x ∧ x < 2\n",
-       "  2   6⎠        ⎝2     2      2    6⎠                                 \n",
-       "                                                                      \n",
        "             ⎞        ⎛ 3                    ⎞                        \n",
        " 2         32⎟        ⎜x       2          142⎟                        \n",
        "x  + 8⋅x - ──⎟⋅c[7] + ⎜── - 7⋅x  + 32⋅x - ───⎟⋅c[5]  for 4 ≤ x ∧ x < 5\n",
-       "           3 ⎠        ⎝2                   3 ⎠                        "
+       "           3 ⎠        ⎝2                   3 ⎠                        \n",
+       "                                                                      \n",
+       "     ⎛ 3       2             ⎞                                        \n",
+       "     ⎜x    17⋅x    95⋅x   521⎟                                        \n",
+       "5] + ⎜── - ───── + ──── - ───⎟⋅c[6]                  for 5 ≤ x ∧ x < 6\n",
+       "     ⎝2      2      2      6 ⎠                                        "
       ]
      },
-     "execution_count": 129,
+     "execution_count": 13,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -860,7 +868,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 134,
+   "execution_count": 14,
    "metadata": {
     "collapsed": true
    },
@@ -879,7 +887,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 135,
+   "execution_count": 15,
    "metadata": {
     "collapsed": false
    },
@@ -888,12 +896,12 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "0 0\n",
-      "1 1\n",
-      "2 4\n",
-      "3 9\n",
-      "4 16\n",
-      "5 25\n"
+      "(0, 0)\n",
+      "(1, 1)\n",
+      "(2, 4)\n",
+      "(3, 9)\n",
+      "(4, 16)\n",
+      "(5, 25)\n"
      ]
     }
    ],
@@ -903,6 +911,474 @@
     "    print(k,val)"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "collapsed": true
+   },
+   "source": [
+    "## Bspline for Jastrow\n",
+    "\n",
+    "For the radial part of the Jastrow factor, the derivative at $r=0$ is fixed by the cusp condition.   At $r=r_{cut}$, the value and derivatives are zero.\n",
+    "\n",
+    "Also add the grid spacing, $\\Delta$, to the knots."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'knots = '"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAScAAAAUBAMAAAA97ebFAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n/4ZmDtX/Aks2FK6SGv5JAAAAAElFTkSuQmCC\n",
+      "text/latex": [
+       "$$\\left [ 0, \\quad \\Delta, \\quad 2 \\Delta, \\quad 3 \\Delta, \\quad 4 \\Delta, \\quad 5 \\Delta\\right ]$$"
+      ],
+      "text/plain": [
+       "[0, Δ, 2⋅Δ, 3⋅Δ, 4⋅Δ, 5⋅Δ]"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "('Number of basis functions = ', 8)\n"
+     ]
+    }
+   ],
+   "source": [
+    "Delta = Symbol('Delta',positive=True)\n",
+    "#knots = [0,1*Delta,2*Delta,3*Delta,4*Delta,5*Delta]\n",
+    "nknots = 6\n",
+    "knots = [i*Delta for i in range(nknots)]\n",
+    "display('knots = ',knots)\n",
+    "#all_knots = [-3*Delta,-2*Delta,-1*Delta,0,1*Delta,2*Delta,3*Delta,4*Delta,5*Delta,6*Delta,7*Delta,8*Delta]\n",
+    "all_knots = [i*Delta for i in range(-3,nknots+3)]\n",
+    "#display('all knots',all_knots)\n",
+    "rcut = (nknots-1)*Delta\n",
+    "\n",
+    "# Third-order bspline\n",
+    "jastrow_sym_basis = bspline_basis_set(3, all_knots, xs)\n",
+    "print(\"Number of basis functions = \",len(jastrow_sym_basis))\n",
+    "#jastrow_sym_basis"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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WJVhV/wUV3tDybg0CwGrGiXGhsVlfiACpjVXSfXfegMTzJjvQYiiUvOAmxjqd\n9YmgpAoFLx5U7QCqG5brFhfvRFEVdMk+e9OUYMYnoinLWqILesBCEiSDrsHwW1hOeLwu2BuftwDZ\nc0cQVPsonOuMSvuaJ1TeerBOG5uH5pkSKZ0RQqKIeSBAKNa5IViGy7q6wvmagPc5SQVCehaqQDU5\nJ0R0AVklMDqPiolUyN+c05dGpCNI3ORJ8gXPsXiBiNYMyQXItLMpehSroseOXvWfqPh5LwKQ52ax\nflds1hsQQFudV9zwNR2rJBLHU42EnpHizOC+DpcXzKQPnAm45zBtqhcT9MzMKh5UbbXojOPGXTER\nVuTRxpEPvPa+9HYGj2tupWBKwRWyakxibcdJBFHhCRQa10oW5J0PgmrnfpgyTFr7midX3jp29q1z\nqaCUaEbjefpcKslIswE4s1Cc4I7Weh9NdQMFPRHIHuZXwLgKEbWF9CxUXLWzUYrgZLXAJHkkJkIh\nf3NMXxIRB4mbPOmcgYQQH2cerRmSCxBpZlP4TKiyjwN66X8ow1ztRsBwx/OBhFmHEUA1gVdGL/sn\nVNpnAU8VEma4s/JVhpnBfx0uLxiFdu0tZldl8oYRazCdUXesbLvefkibFb0XLNZBDd8dsNKOJnt0\nLaZX+IBv0EEzUrGTFvumZgAo2sYkXqJso8VWiRoLvAyZCoPqhUVoSWvvhO1rMZXy1vk6bU9fpYw5\n5XWKUV3aXChOcYer3Q9+KvI0PR7wSnFcRUVQzUHFVTu3hIHBuni1wHDRnEfBRCjkb47zJhGBQr2B\npGOTJ9P+aIj4ZkjHl04ENnEy4Yl9yOkV/7mENb0fARRAXSwkWJh1GAGUzL0iTe4sVNonnKcOiXTm\n41shsK/D5QU2MdaZVZcYYDI9TncZYQ+QE45TvcG1q+l3V4ikpv8IVy9khyhMBtpgqO3cz5BP6S5K\ntgdNABAkRIDnxXTD050JTDo9uk0WEK8/h0H1BrWH0qG1r3mexFtfxyjNIxTV8yB5USalMOpLm6uK\nJTe802CStBg8BU0ycLyw7soOKb0ElRAsRaB8aSHTmkgqPBomQiF7c+xFlBGBti9Ew//8GLuEeAUR\n0QyZ8MjcZjZFZEKVoNf8j4Tg5W4E/LxbJlWYdRQBlJ1GAZ8KlXgz4KlEwvDJjBRlBpGJgQ3rShtX\nmzfKvuufi6nwK/hdOiM94YIqU7lyrraveaF2zKy/XlN2BQSzpPm5ojTs+SVjYmlzVbHgFmu96x6L\nTCOl64yx4f66kyLwobCQcaSSkkfFJFbI3hx7EVWIrJMnA4Ni8TDGMHiuNkNGFPyS2cRvY1qowpuc\nXvUficLjAAIYSuzkbC9SmHUQAZTMvfKaXEqojHkqkbACRUaKM4NwCPjWibHOpJYQCIQlVe2XKREF\nnQgAACAASURBVGJR29ciGnG5Lv9mxiwsZrlqQaLfUBg3LG2ucMdrvd+0EP+4vewkAN0oc7cA1ao6\nI8A8UiwssZgZ5UDEwazChL05zluHSMVcSw2RuBky4xy3KUPmHnH6Kv+xVQcrm6bEzblrEKB5t069\nljiIAIrkdmkqtHucpxIJI0bJfBEU6tdB8281U770Hh9yW1j670vtKAoPgyqbM5bk1NrXksT2wbpO\n22DbT9aZoAUe83g3YzW3796ssYfR5KFyK9MxDiW5x789PFa1e3PZF/FWROJmSAWD9VbWJoVtK70R\n8dEIoIV7vNrDg7oqMtLuvIDy/+4RBtVO/WkK0dHa10KK+IrWaVv78eo/tN2MxoIabur/jE2uuM5B\nRaoLYohsCzB7eFYz3JvL6XsbImozZBqQnE0a11Z6I+OjEUAL93i1hwdUVWSkA3nBwP1X/0VBtWLb\nN619LYseLf+2PAZ73OLGtwT7bkYjr4p7quiZS1iXgYpUJzjpNpFtAWYPD+mjN5fV9z5EtGZIMkWc\nszYJauix2ZqZjIxPRgAN3OPVHh5QVZORDuQFA/df/RcFVdvqlAfjUdG+xiXQ8m/2bMZKYCdj+djN\naERXcV/CTv6yTZ4iAxWp9sRqisjsuQ6YPTxO+frmsvreh0hVMyTZlrWJiNh5K/3K+sEIoIV7vNrD\n41TlVR7ICyvef/MU9v7D6Iz9Rbd/EEBaBnuX6b8SqoZIQ4C+hkNIkJC/eI5KqvDL9VODu34C/Wj2\n70YTfiNUDZGGAH0Gx5AgKX/wLILq4w8VVQ/6epD9E3PbQZcOsn8CIgddOMj+CQiQDb/IFXLpm84i\nqNolub9J+8+qGS8wovvIgXPuftXREGkIUIY+jAQJ+ntnGVT7jx5X+8Y31ONeIYeO3wZVQ6QhQB/E\ncSRI0t87y6AKGxMdLMD9Iyje9vf8k4e/DKqGSEOAsvYbkCBRf+4c9/4jAP/zv38Bhv/zf9/g5a+C\nqoe1KHpt2u4WoMZ/uaMTETh8/NMIkPdvQYKE/bWzUlL9lUOFlPfK1zhTHtfc+oVQvQGVGuQaTUPg\n1yIgg+rVbL31wQ7v24ZHbEQEY3KPlso+CKp9oMDEmsfs1vu17/wwKh+cdZppDYFvQEAE1U1LYH6D\ngVIFLM2tbVIlCYM78e47+NBMBQ+oNl18ElT7QIG9O+I9uw6jsgnCRtwQ+H0IiKB6Wtdn+FxXYSCt\nWJm/bG28+w5yiGVTy2I4xSdBtQ8UQBJWmzNLx3nHDqLiBbVUQ+BPIhAH1SG7MD/u39LRJpkzJGow\now0s6VzDY2jW3WYUPXXb8ISKwt137LPTkQYABhVBAlIDiEILtCtDvsD+EtrD9L1p6eEIn+8BBer/\nkzGBizqEChfU0g2Bv4jAf/8Tjp/i+xsKPMwivLRJ5gPiwFIRlGgDSzoLqYkbw/NkdqJW9FRuwxML\nln0wLC7GxOVrDxVBAjwBRGUZhhxbMedtFQTY7QeOIBzuBAXaUuI5dIdQKfvcKBoCvxuBqKQ6ajvC\nEgL9hMVY2iTTzBHIlmsNH21gSWcSVnG2RS+pZ8s2PE5NtPvOel9sO+zoiwkGFUECtekAoqIMS45L\nJ2+sc5+ucNx4UXUXKBDMwUbxzg+gUnS5ETQEfjsCUVB9msJhwunZNWXCJpl2l1q+PaXORRR01qnU\nuyaoSj2btuEhwfHuO+v9zKKoxJk6R1DZfUMDiFKc/r4hH83+MmZRev+kkMK5YAsfVLkLFPgRgKVt\nB7G87QFUCna3xw2B349AFFQvmdnsw0JBFbu9bR2xvJANbWBJZ2iSfQ7xMB4dZxNUvR5i3LIND7YA\nW3XR7jurxnFbLON2hlDZkQAhRJxaTVvy3gZViJNkq0oc3+xNMyyxbAPFq1JhOYBKbGW7bgjsROD4\nhMedih3bXgvCoGoLTU5omJjWTvd+xurhGuwyQdhw0waWdO7mvjvduzMvZYVq/BUPqvMWRi+iyHXZ\n2EPkRAdQWUggVAUQOdpUYiXHQvwA2wFtgAYknrDyv43F21Hg242K19BSDQGJwPU0B41WIQV0ZU9u\nQt7wKsWWkPn41XA+QY8xHKuo3RaEQfXxSpv2GP1IJtgk0+5fExbXFGbawJLOuBd37fDQNahiTxro\n2cDI7ChxQYDfd8RQ4b6hEUQlwUS+AOsMReaSrYE8OzRiEwvjL/DtRoWpaMmGQIzAcOmvybphD13Z\nnW1FQz7oi+V9BqGoubDqU9j7HvImrx6m9/f1ot73rAVJKfAgDKpROyFnxA3JqfoPERWaAuDDtNv9\nBmSxOwZDKIbRGZliGi6Apdc2Va8nx9gnhea4IJgxhemklB5DhZBEEKXFmSeefJjndY81zVapG9nd\n76nGUtBsHuf4KlGpUdNoGgIOgeyO5XcsId5oRMt1nl5UZHT8NtFP51Ih1o/MiXjF5fjE+GKOpw0h\nFFMzFhBH4hwuqHImlyT18oTj9XyYxsMRoqSpwYsfkyV2lzawpDPWdOFPKpB3TFBlerKMQjHJy3LB\nEKhkMCYBeJbSGVQEiYCIS5BpIscB+B1uSZeARupGUuqhz7uHlPqR5atERZfc7jYEEgjkRkA/wi/x\nBEU4EV1Q7Pgsd+QMt3O6lMttG05YPF4PG8NdA0TSAqJPnsOS6is/WtKM+6FNMnFkpRynKiIAbWC5\nnsdXN8EIg8RvUGim3SNn1VNiFIqNrBIXlrlDpfqVlM6hIkiAN4BIl8XvGnJc6/o2AKsOjdSNEsym\nbCkWrkJLl/gqUdFEt3sNgSQCuaAa7rF8hU4irag6nu4VH+zpOseFO82m6z1a9wKIrsSYskATFN2L\ngipJjKjs5eP2Oi0wBWeeTli8m7RdVWUEoM1X7bk/zddphn6S4gG/SK8T2mP1lBilYtRQ4oKfQ9bF\nBw3ls16GltJ5M7qDpIsgKjlpya/ThDWPlK1SN4o1FYUUS0lviS9ABVoaUrCU9LTnDQGPwHC6XDCs\n9pCfJiggXu+XeZnua1XxdYfP6EnlRqyD95e4qDrcWMGSBPfzfBqhru5jVw8dJcHYUEkCzMt9re+T\nIHN2dXXdgoA2dREE1fBbSrFk7+sRIMvynod7FfvgOOJOAPd7p04B9W/MmvsGqGr93utZrXyNzqMC\na5ZbWODXbZrZL5DG1u41BHIInDBkDWYRfLMV0eUJfTM2T/Uv00C4DmfHYiL23gY12v4O9Tlx4NDC\nBzSynn2X8wQ5Fv/oUEi6+TxpJbuJcrhqAQksnIOgik2lB4+fiADG5L2K/Xsz44igKK5MAZVtqm+A\nqhbpvZ7VytfoPCodwdJtnWesyW33/jQCJqieTaQcsKP77suTawvq0y48unYWRUXV+axUcTE24jzG\nxXeOoNTRx9hOkqS6unrXb61bUPf2gqDKmtL6+9kdd/x9WIcbyFOoJ44Akp7uEJ/QZB8QWeZMEsy5\nXrGR6Hhd2+iT6hpyCqjSUcWgKkOju5j2zBl3xLOtSgNYHCqdg2XHPOPQj3b15xHAoEpfDv5u39fQ\nhcC8TIB9mFFCy1q4m30+tNg9ZPkSy5t3V2lHsoepVrLmUkHS32DJS+1wq84nLdC44ntB7z+OQN99\nTHc8zhdzynd47dahLsW8SbFYlNm9tgu9GKw3+CmgCemHoKr1P6FbZ1ex0Unl3RgWh0rnYNkxz1jq\naXf+NAIYVJd1oCouB8RHPl1M0fJhQpCLtVFRFcBTW0JZaxWQ2J7/wQkxkIckHXT7s/YB91LcmB7H\nLC1wxMlEUFKtq9Oyde6k2LjAKCmO3IH3kFqfWiqenrenaDYRizJTRbenBNpnp4AyS4X0BFRbmx1V\nG5leTArd0HWneZbGJhSo2RjD4sDwsLh5xqG0dtUQqEYgKKlCwYsHVdv7b0qqi4t3oqgKqmSfvWlK\nMCMT0ZJlLdFRD5ixLiTBW9rQrJ4G/uctMBIz/4Kg2kfhXOVj69wpz2UE8EQ3h5W/V5VyjPBj5iYg\nRJxC8QRtLG5mkJOADTBB67crnK8JY6OZAsoVCOk6VFubHXUbuWJIC906VwabQCC3MQmLQ6UjWNw8\n40BYu2gIbEDAtKleTNAzM6t4UDWrYHZPXN3HFRNh5GA4etXqGnjtfentDB7X3ErBlIIrfEExiRWD\nkwjCUtdANbSSBXmfg6DauQJKhsmvc6cRiQjgiZa7WA7JP8ylAkY7I0CSC8XYx7jOU4I6g1MdLco8\nunGqTwSyN/Mr1tWxmRIhXYVqc7NjwkamGJJCd5IrhQ2Xx21MwuJR6QgWN8+YC2vphsAWBMx8qQGW\nY4JCKhZtzryZ8AZ3emxkghq+O84U5kI1o2sxvcIHfIPupZFaLv3HSxMABImXFbXRLqu2Cgu8DJkK\ng+qFRWhJ6+/4Gbr+nk2JCOAJnr4q6W/WpDhjcilmofgCTdG03BKXEC7KPKwtPGDHND1sE3dUlkUT\nhfROg2pzs2PSRg6L0J3iSmLDpXEbk7AwVBwsbJ4xl9fSDYFKBAYYV4MjqUZYtuSE41RvcM1qr9Pz\naWIlrrjGjrAwGeuCIddzP8OnSw9Qsj1oAoAgIQI8L6Ybfr0zrl/HJgu4NJsOg+qNjUOQtO6OXefO\nXfKEiADu4TxCMT0PkKMNEpwxvRSzqthWKTomATsGeY1ipQgUuimg/q6UrkG1q9lR2ujVmpTUDbcV\nrjQ2XCCzMQ2LhoqfZ8zFtXRD4LMQcDEVKqo/ZFnQ+99NrpacMYfWuVNJ7JhZ5REuH9KdK0vCnJ8z\nZpZiVhXbhReYBLEos+qxmQLKbeikdIVxX7OjsDFQDBdSN9yUXBlsmERmYwYWxTmzOsFS96PL9LVk\nQ+DPIRCWVLUSigZJdrUZjQEq13h7MUtb6QSpu5xx41LMk22y4RLiRZlvWpivWe1VgWpXs6NiYwoJ\ndl/hqsOG2ZiBRUWF5hszM1qyIfB9CPCR14Wl/77PKE1TGFRpzphGye/RAF5+L58ebNsJzALdeOxm\nhEHANqZmJfhu7o12aVDtaHassVFato/LyHE25mDZjYo0td1pCPw1BMKg2qlFlAATWucuuFm+WLv5\ntkfj3YzdFYpiV2hWyUmg4QFlBwSFAtX2ZscaG4XmKs8kl73jbMzAcgCVlNp2vyHwZxCIgmrFlm84\noOdhZ+jWo7Q8BnuEC3yVBexm7Ib7siywd0NWwrS55OxMVqCiZQ4dTSlRZaMQso9rFUM25mA5gIow\ntt1oCPw1BKKgapvcsiD4de6yZOHDix8iYSbmhk8zV7sZYdgwHjh82B1SteySytgSPtKg2trsWGVj\nqBau9nGRmNXGHCwHUCEt7dwQ+LMIhL3/sNrW/qLbP4ihXQZ7p+G/FqpDqOwEs7E1BH4NAlFJFYpB\nPzW46ycgLW/MkLPqt0J1DJUcYu1ZQ+APICCC6uMPFVUP+nqQ/VNz1y9161Phbnb9OgREUO3Mkty/\nzk/NofHi17XVnhfv/UqoDqNShK0RNAR+NQIyqPYfPa72jS+jx31CDh2/EarjqByCtDE3BP55BGRQ\nhU2JDhbg/hFQbm4Nht0G/0Ko3oDKbjgbY0PgNyDw3//ICPo///uznvXa1NHNJvl1a3TWnq28oFNU\n3B2/plvvexDQ/HsLKprgjffeg8BGpY28IfAOBJSS6s8PFbq+obPs57048noaAu9A4MgbaLwNgb0I\nyKB63Tpbyqneu0tSvEESjJY9XFbd74VzZ2Nir/eopiHwFQjoyG58rY28IbAVARFUM2ullmRndpDK\nssYbJAGxmaGeZco/POBFXnD66V7vUWJD4AsQMK9KkZt+he1JQ+AdCIigeloX2tghHCrtqR2kstLE\nvlG4ZP+e5ay9lgNeeCHbUnu9Ry0NgS9AwLw+Re6219qoGwJbEYiD6uCjmbpnZ0F+zS5JUkS0bxQS\nnA41ADAvOr9njVT85jv7vEcjGgJvR2B9t4rcN7/1Jq4hECIQB1W/v2GwZ2fIlLyq2iVJ4xbdEjws\nagz5e96L4Xk652nf93S392hCQ+DNCLj3KuS6Jy3REPgKBKIFVUa/fxPfs7NSc90uSUJYvG+UIbjL\nJaUEY+oG8wJ2G/iuoLrTe3SiIfB2BNa8ocpN5Zt2vyHwDgSikurTRyC+Z2edprpdkoQssW+UoVCW\nKxWcqRvMi+8Lqju9Rx8aAu9HwOYNXW4q37T7DYF3IBAF1UtYPlQ2YlKUTvNzmGFz2bpdkrwA4ov3\njTIUtLu0J69PBV5sKKmSQfWagJKYtnqPSoj3YxBwFm2BgLz4JATIJobsNNOexVuca7QNga0IhEF1\njDbms3t2FmTOfXe6dzWb5YWCCnwXszFdyFJ3FXpRH1QLBunKdzGtogq8349AV7BIhWAPDwkq8O5G\nQJELGXS4KCOCyZR2/psIHJ+sLnALg+oDVspnx7pnJ7ujJWGm5q5hpQU+CNQ7j9CL+qBaMEi3ZhfT\nKqrA+/0I4E7pm9/lHh7CssC7GwEpFzcA7gdtRDDZ0s5fj8D1NMMOR/rRP7F6oT/7urvDK6ycv0NT\nGFSDxkjajbRCje/eqiBmJDm+OQzwjKuUDL2oD6ogN2dQUu0uplVajvdHENgFQc6LJGxfioB4lRe7\nJFkbt1p6H1/5fLj0V7Odr6bkDm+oVxdzmksL58n1SzQF6r3Tyw8iVQl23Ax7/8/wc+4O2unT3Ugm\nBoh/6Z+YPulylm+p/FKl+MCLTb3/GYOkGoIjw0QkyXOW9wsR2OPNHp6k4+7BFyHQxXIpN7Vxqw76\n709gdSF12J5puedkP5UbIf0QypR0uj9GZeHrPL12tzOS0PgcllRfbDoV7dkZc8TX46ubYMxA2rJF\nL1+X+Gp3s5biuRfQ+3+JLU5c5w2SaoyYPFNC03q7xPuFCOzxZg9PHgCYOJfPO3sRUOTecVEyk73b\nuNXCW/m6x7kpPXbL97hrfHxWbO4z3M6pNoXQl+FksgG7eYJJoG8vqkZBlcU/2rOTWaAm+9N8hY7V\ntFeJj7HE17/qmpCleN5KAi/ldWJeqS7Ym3mDpBrDlWfKaINHJd4vRGCPN3t48gB8GQIKsuNzfkAm\nxaxAhdaCce3x2xHIBdWXmUN5ffGV48cTtgkUj9O1alzH9Q5DlMLjCjHm/UXVIKjWfsWhYaWrxMdY\nYut4bOwmiNsxIlaCEP9ZXhTdzBB8HQICtIwV9GgPD/HuPe9FIKWvjVtNIfMN94fT5YJhtYdveYKK\nw/V+mZfpblsHe1u/vLI3PtziciUY2c/zaYRKOyso9dCl7cfXqyTAuNyfsh0SA3l/eXdRNQiqY2Xh\ncNsL2PsxsraOEXc+ueNwADmTX4j/LC+2YRVSawhAdopbWnYgIFhCxerVHh5V0IabGgLKmhT1prFx\nqxvMaKTvQeCEbaqD6Ywy+7tdngsVgUb7qgf3xvv7TSlF9ZD5H9DIemZjgyYIDvi3HhpJN58npS6N\nBVWYz+h0koiD5yCo1jZhbdNZn+NDuaxp1IxXPC2dNpNfiP8sL0Kftl0pCDwgUy3RYjM7EBAsFYbt\n4akQmyVRENDWpPgJ07J2t4cqAiaonk2hYMAh8XdfwBRBFeKg0qaIoXGCkuXCSp0oZPRBViFJ9XWt\nH9K7i6pB7//ASqovOlZ0+vvZHXf/E0JU4TlAVOT4kFZcEbP/oJ6+fC4HSAnx270QJpgbZIc9x2p0\nHneXmHXYHJmeIGYFATO4xMNhKGPToOfbN0c7DSRUZXFUQSJg6YSagFZerNxvRwA+pyFqFo1Nk8bE\nd0LX2tX3IIBBlco8WDy8++JBb4uLvPoPRVJRvMTi5j0cQ/AwLQG+uVSS9DdYVlc5lvUzmf2HplBt\nvxWUVI9XnMPl76c7HueLObGBBbqZ8eLvvlB+8SjyoJoQf9yL0L6EmpCIrkIA6G7luYxAb6LJOuYS\nfrN1gHMIJFiyFm7jOQJBGYEuXJNim2ltQlX2PX/5QwyqyzpQ9QVpPhTKBrYl6KjSG0JZsytabHv+\nBx+f4V5E0kG3v28fcG46ljcXVYOg2ge2QOPdSWmHcCZpCQDq6ov0liIuRsBdpVlMLn/vilvrj5iR\nxoNqQnzoBXZx+XKbZZH/VYMCMumFyqMBEMihC82seJl6iYBdETEaZSJMKyMgWPRXQsaas+TRmSoh\n0OG7wnfEtEoErCmlsjpS1SDMVLXk1yMQlFShlMWDqh1d/ojeLPRm+TKoNdA0HOC67vZY1tLa2uFl\nbkYkeE8Zm7W4OPvmomoQVDtfOIQxfRCKcoN1rUv2/43Mgw9CLP4vP8agWczxAkyTaW6xMkf/m7V+\nWqikIqgGXnTQgTgWR6rqBnEPZeVX59EACOSsF9ysDQisQZV1fSIm4SXc4e9RRUCw6N4ElgueTmeq\ng0DnrcoDUDiJPJamwQfLXnwK4cC/dvHlCJg21YsdLYwFVh5UZ/OVPvlPqrVn4JX3BUbF4VRL39xK\nwZSCaydJrBycReBCMd5yBdWuu0TtSZZj7/8wqF6YnicEuHAWfVLHcmdhS4Q9meP5Uq2MN5zsMvj5\nbE80qzdzIYR0JaRwL3ALwT76BKUfCYM4ofAiySNN5HJsmpu1BQHbmBiswqUF1SIC9d542wVPdwSC\nBG9NHoACsrfKpKRpZu9IevFJhCMx7fKLEbhBLQaWtcEumTuWn878ReIIH31vudEVVnEY6w2C6ugq\nn3440DoBQJJ4p4JGWhhj5Y7zW1tVw6B6i34nlN8Nb6FPPVkFXS5/L3M8bxbjvMHy93xuxTQ9bHN0\nVUmVe+GaH721SippkKcVXqR4JABeiEtxs7Yg0JtlxPzPjREoTOuKCAiWlDfOYjV2Q2GDlmjkXtRA\nkFTIJzzpeeDBP8UEAl0Vwsy7lvxyBAaYZ48jqcbnNJ1wnOoNrqmOCwEVhq+66JkwBmZ1zP0M0cA9\nR0H2WCcASBIiwPPiO9lxpUp2BIVYzrI9/d//sLEJ3cRKnCBL/90QSuYRiuSrTcry9+IDNgLW74Xx\nYnmSlcIjW1atshgoxXPOFwxMfFbhJQ0KHJVq4LHCowAQyLEXzKxtCJgVFgnsVbA0rYiAZNG94aar\nPPshUBXW5AFlTQrFtCqEuXst/U8i4GIqFIE/xYGwpMpLBlBrrtvSxFSyzrbhQFv+3o6wjR22zWKM\nN57sYucCx2xyJr8Uz7wYsVgvus5ioeZaGBRSSTXwXPJoAISC8IqZtRGBGfyJx6lK04oISBbVm8By\nlWc3BChawFeTB7Q1KaRpdQgH/rWLhsB7EAiDKk1vINlVHVWmc2mxy1tXL/6+Notx3miyi+v4JWPg\nXDeTn3nRm96uqLrMBPqkYpB/mEgpPHUAMLM2IgDtiVO55P1tCFDzJveiDgKAVIGvIg/UrUlRh3Di\nvbbbH4AAH99cWvrvA8zlJoRBtYuKhzRQl3PE6cG2iphJpPGz5PXaLJbhjcd3J0UpD5gXJp5q8Tli\nKxsUMcDlHp5VijPr30bgCAQVvEfyQA3C8pW2Ow2B4whEQdVvt2faU3OjyEn32mtQE3+JpaNmsQyv\nXFjRcRcT3gu7jn25pFphkNC6h4eEmOX10ax/GoGa90gei3MFfEfyQA3CwqZ2oyHwBgSioGprTUYu\njnl5XIp9PMtjsMct7OTK2UbNYjnei+/gy4lSnzEvrjCIIxhOrjLUGBQz7uFxMsisfxqB7ggENbxH\n8kANwu51tERD4I0IREG1m92gqgFnVPGhAbpW28RlhiYUh4OSBGoWy/DKDilirjl7L6CSWdEGWWGQ\nULuHxwtZzfqnEYAh03jg0Gl3fE4eKCPs30ZLNQTeiECwoArKNSNz36hgp6hoJuZWKR/ixVazOX1D\n4CACHMyWbgh8HwJxSbV7uKLq9xkhNR214ii/tOi77xz14Cj/d/sr9f37Hkif2p2/gIAIqp1ZPfaH\nXR8v5XaHvImf4EXewvzThsBxBPIIt6cNgS9CQAbV/ucHhfU4DfjY8QFeHHGgIfAGBI68gMbbENiN\ngAyq3Yj9/j963A70/JPhP+8FWbLn3BB4BwJ7kG88DYGjCChBtRt/eBJtz+bz7vfvp73YbzksutAQ\neAsCR95B420I7ERA9P6DHLYGzE6pH8jWs1UN95v3r0PzFhT+aRAaAjz3vwUNLrClAQGlpMoGeX4C\nRDt354g35giWFdzr109BsxMDWLjnEa2mxhfW24nCj4DQEAje1l44viI/BIa1C0BABtVreRbVtyJX\nuTtHbFO8NQksFn64rPpj0OzEQG5R8wYUfgaEhkCQwffC8RVfRWBYuwAERFCtXEP1+8CDcbNih5YK\n7TC/lm/OghxmOngFa4rk56DZiQEg93YUfgiEhkCQK/fC8f78EJjVLgwCIqie1iU+PgkfuTJ1hXXh\nxhzIMEaLO1cICUh+FJpdGED9f4JCTXAcROHnQGgIBO9xHxxvzw+BTe3CIBAHVbuznAoObX9JZ5WI\n3Vx3j5lhDQF2tyYZxYGa3Tk0saL98HSoASADDWiPbNbsqQVO492LASzRDaWa4DiEAgNhgV0xAsGp\ni2pCJkBu5fuBCDgj/UZJzAWZtGTDaRg39vVNSw9HIHA3HO/ND4FN7cIiEPf+8/0NQ4xo+0s6h0/F\n1fA8mb2qH/DhxUvVC+LwBlu3Hh/UbVASioC2Q7jBNmcxj1lEiMkrrtPQAHNksyauEjiNdScGX4CC\nBwGbqHEfguJRTcgkya189+WCL0WAjKSszuzXkkR2hdVnNv66w+ZOcPDf7Z1wvP+r0Dz96/eikuoY\nxyGPD21/SWf/JJGy9RMzP2tTvbufAvK6DUpiG+KNOezzuv1hYln2OgMNBP7QZlVCNXCSex8GYBYs\nxziIJRkPoMBAwNVgq5oSqgmZ32Ir309EwBtZWRW3ZNdlCAudzO9E8nSF48a4dsLx9vyQsPeP346C\n6tOULlVMaPtLOqtE/KbJQr2J0nxrS06ipuewX6p6d45QWLQxh33IVq8OqSuuMtBAeSi0WRVXDZzk\n3okBFKC1DSoPoOBBGLV9XaXlGHhxLkl5nXDBG2zl+4EIGIOtkduC6vZ5DThre+Fse+F4nbudIwAA\nIABJREFUd34QL63dAASioBrtKB9DRJVcOsfPg2uT02yNGxdxm+bnEA2aDMjpYlhsgKqlJ771nGWj\n/ZQjnqrLHDRkc1GQAS5rYiCinjJgK4B9AAUPwrpZdnmRBk+4zRs7zGAbD0Mhy/gWBFDZOhZiW1B9\nrhv8Zk1krphkb9qvN7EwEVm+A2gwFW9PvmGu+kGb9loQBlVbqkibYre/pG0w03TmCQ+qM5TlutO9\nMzss5/kmO4Kqmj6UVmC71HWthDLNVRaa1WaFLbqFABZMZBz1lIwJkwXG3ShwELD2MVTs/tURYcGo\n0IV1K99NPFxCgfEtCPj9hjcF1R6W1ligfbRgIvcG0ies/G9j8RIKfLvR8BoqU9fTzFsxAq7x+bzd\n/Az54VW94Hkg5sDFOE3TzRcTdlsQBtUHLOOeOdbtL2kbzAwlPlqDKq7OAgUcQKtqnOhjtEG1lj4y\nosAGcX3nkYOGbC6KNgAWTGRC6ikZEyYLjLtR4CCYuFBTqyfCglGRC7B9FwSerTxOSIHxLQigMrvf\n8KagimzYKlYwEcn8sQ4cqPyIPJ9NFVTtRiPWU7oeLv01lWXMjNnJP4XOOdaIHEmeC0vp7VoSasRu\n18WXE7IWRAYFl2Hvv28yC4jWi3X3UNoGMyDBn9/oMDltrfyZ9qB0J5jn7OHnidonc/SKPhKSY5vz\nvxokopPiM9Bwm50ERYQHLmeil4CpPKU003HnGHejEIAwzHPddqeeUDcq4cW6laTO4/xMJ3KM70EA\ndFsjNwXVG3wqvQ0emok6Gm70msaSxsA/yfHVouGl7Uzltrw3RfHuQt2q13l6JaqV/UQ15qQZfpBK\nkmR9MD7hF8ces93PnrqVMhYQR+IcllTPfNRGzEHbX9I5eL7IsrrNaabCb35zBghozoGAmV0sTzhe\nOFgF8muGXtG3Ssmz5fIWN0O4k4GG2ZwV4YDLmshEFDCAn1VhJnFnVSx7UeAgYDECd9crHp4wYZT0\nwjRV2q18EzxFrYXs8wYEmJGbgiqOArHDJlTfJBroK43YUFnKYLwHjQo9eZLcEOmLCWYn060JUk7w\nw6MWVcdneZud4XZOl3K5icPp7vv/rtiV3L+oMpu0gAtQ02FQfWXGHdL2l3QOxSlZwe7dh0MZYZzq\n+OomQC3x2xPKwhxXolf0oZASW+1G2lJ8DhqjOH6LQsQKXMlEj0WZUuiwzCXG3ShwEHBvBdYE5s2O\nUyth2ijFCww8sJVvmidWEl2XGN+CwGokqK7cptKSTZBToB0oZaKCBmgwG8umWCLnxWWJrxYNIXjr\njVxQvZsQSkH1il3bSlF1PN19o2dS/ek6J4sbjOl6P4lSnqv+pyxg/KlkFFQzpoRbZ8byRFaAH5TX\nCcVNZjvT/jRfpxkazMvH4/Y6LSV6oc/KLbH1vsUETQOLBKpGkBSfbzY3NoeuCRErgCUTvZQypdBh\nmUuMu1HgIFyn6SnbfLz1LrUSpo1SvFi38k3zOOl6osT4FgRov2GX1XVb6K4jA+CgcJEyUUEDJJgK\nX4qFNKTOJb5aNFLyK+8Pp8sFw2oPn90EhcLr/TIv0z3IROe1dIqzI/pLXFQdbqxgSVp7GDY4Ql3d\nx64eCptUiTdUkgRuL3ct/7qGA90CUpo9B0E1BDfLFz/Us0JM9b7rvfpYWBhx05Y74O9mG3rzhPjt\n0AgRXvrbUnt1KChokydj8dtBqPI0VlPFdJBIQQB+/m/P6Fc/Nu2LEODOxCr5s69Ka2iArprGnU0m\nnVDigCV8uxXe5QnjJ/nApetaOMViIgx2CIuq/V2rGeFYswc0sp6p2g4fNHzY+EeHQtLNZ6wxRMcw\nnamurloQkacug6BqW7FSpNn7350V9upjr8kMJDktHc025P4J8duhESK4/Del9+pQUNAmT8bit4NQ\n5WesporpIJGCgDaNODbtixDgzsQq+bOvSitogKqq0eibTDJB9WzaAAdsPL0H5UkQRY326zTeqKg6\nn5WqrmlNgSLt4ku8KHX0MbaTJOmurmnd3V63oM7b//7H27J2ZRrG/n52xx2ryGb2Mf8Xyo+zAqcM\n08QnNJgHIS2/Ij57rtdnZDhm3yr4pLqFn23oqGQPkG92knY7Kz0/pMoWErmUiE+c1CBBPPZc1qEz\nKyhokydj8R4EZh5Z9N1ebNHnUCBjOwUBLEDFwxmqECDpJHyrZcRnz7HKREYgpTScZatSw0+aFTSw\nlk5fCJEdPmNQpUyEgfy+hi4STKMDlrX0OnvDLMlDli+xvHkPytQP0xDAmksFSX+DhWUTx8WsJ520\nIMEV3A5KqlVjuQN2uJjueJwv5kSF55ho/7VY43yTPrHSuX9LF/4i/JTIhPgt0CRE7McAOSMcNumo\nQeEa5DJd/BYQqrzV1SRYIwQSVPrtGgTCacS6aW9HgJurq+QUPP1OONSvombqNTeoIo1BdVmHouL6\nMK4B0/K6ZeRdrI2KqkCmtoSy5gsgsT3/gxNihIckHXT7s/YBq3405cubGVjlmKUFljj3Pwiq5cqN\n0vxopYvf15zSLc8A+mtcSQB+qU9pEYOWmyu8Ba7OVXR6l4LH62xDTyjE56HRYBEivPQ9KRUHRQd0\nvvFGKqOqBoUrTZ5kxsXiQxBUwBn3miyTxWrgh1q2bpoWPi0nCI17EUBBcY03Ni1EwKjW1Amb1huq\nXxFxrBIeq2xqhohkJXmjz8J9C+yrqJ56LXUm7wQlVSiAhUF1wSIZRrbFxTtRVAUK2WdvmhJwQXZz\nGDGQCnrAQhKkk0Oz7BCuGzby5i0wajL/gqDaR+Fc8GnNj5ZIyQqOm838cvdKCccDIZEmA3AeoS9o\nEXPcALQbNm3YfbP4moL3t06JzIrPQqPCIixc5TvbuL5k2lGrOEgd0Ds60vhpx1uDAo45x7lP/IjF\nByAEgHOuMB2QOYsCmlhNp/OoCASCzMVuBJA7HlUemxYgINSZG5l/ul8RQ6wScjC8GjfpyUFYB4fO\nG2cI7auonnod2Z+7NG2qF1OdNTOrgqA6mPszOutlXLQBxQOvvS89dGgBg2tupWBKwRXydUxi5eMk\nAorEeMfWXc+osWSBFZD6HwTVzv1iJci15kdLKrOCE7Hc6St3t4qJgEcbWi308RYxxh2tdD6asr1R\n/0Tg+nU+BTXmkGFCfBYaFRYpwghntpGyzDmgljgIHViBwgleeDDeShTskmKW20jwo1TsTZ4/OOCe\nRaQ4GbOI0wkvkjwSAS7HpA8hQPOwnVRhGkcAqbg6x5VKJP3iDEJll2SrgCPBG2YI7auonnrNbS+l\nb/irPZiuoDt2V7m+dkiPZ5h5bxZhhhq+O86+ZYILH12L6RW+6BsE1ZHqZ37BcJoAIEi8pKCN1qwc\nvmDBssICL0OmwqB6YRFa0to7vvmRU8is4J4+WZ3C3SwkOI+6xrnQx1vEOHe48v3g5xZDEfZhm7TB\nFmo9J7OE+K4EjYBFijDCA9tIXfLMqRUchA6+xiLnLaPAJk86a6R4lj844I5DJjhZYJEnlWqgfZeW\nTuI8CgJeyprajwCMzDFlJS5SmsYQQEKujjOq6Qos4IOOf8m6FFsVHAkogwyhfBX61GvVq+qbA0ym\nx5kgI2wZcQK7rje4djX9u+16g6Y+XNeQHbwwKXXBGNy5n+FTpkco2R40AUCQEAGeF9MNb+9cIZab\nHqxNFnBpNh0G1RvUKQqHaH609DIrkBwoz89buxE5j77GuapvbRFj3JhBeQUibjODx2y2IZms5ewC\nNBIW1cKO2ea1JVOcWsNB6HjBgpnrWEvGW4GCKQ7Fa04L8TEICpyaL/K9BFRCDT5VeDQEAkF4sR+B\nzk0j9kKFaTECTJ3nyqUUv0JyodI8Vtiq4EBmyRtliJWA26FPveYUn5p2MRWKSj9kY7igylSqqCvN\nj9ZwO1ZWccJURs/R77tCx29xnsQa56o+2yLGuMVK55qDWEOCKZHcgE6K1zgdiwaLFAHkzDbHnE5w\nahWHWMeIlSXbm8N4q1BYJ08GxsTiuxiEuAky4PYX4r34R5gSavCm5FERQFJ+HEBAm38tTIsQYOq4\nFZm09CsiFirNc8lWBYfOG2eIyCkyKP6NpfvtXEAgLKkqP1mCP25+FAThDTPSd6FlEsJnqSvOs2GN\n87VFjHPHK53flOhOsw1T1tj7JWjqYOG25fXhU05dhUNv19nBH2vOW4MCtIZg03D+iEAQTZA6t/Je\ndEJ2V+H5agRoHjazQiYjBBjgkla7o/ilkcX3FLYqOFCOwhtlCO2rgIIGThePDfnJaz4Ut7D030+a\niWO4sSpARzhnjO6G57j5MXwaXw32teBs0OpjDw8IX1vEsty+m7PampWwBE0VLFnbhEXbqA27aTJG\nJ7O8u1EIQZBNkMIFvFHzXmLGPTxWxrciAN8P/oDV47nTr51sBpEK3nr74/fUrjUEwqDa6b9ZxKg2\nP9JD/bw2/VeFHJKwhwcqkVDOukIrSo47njBDGmvOaWjqYcnZJm3YRm34zTrg+KHneA+gwEEgwKXh\nwR0iy1kUMMDFHp5VxnciACqdutgF9XqnXzvZjAkVvAfyg+rln78ZBdXCnnBa82MWwuUx2ONWaq31\nYvbwQNHsviwLbNWQ5Z62FJi9RSaVgaYWlqxtkTroX9iBHS5wirMdsrwHUGAgEODC7vAGkWUtClnq\n3mXEQ5ffiACqJHWkPnvegwUI3MlmTKnhPZAfsu7+2YdRULVtREk06pofGbttpzLjI3gzA6OQyT08\nMLbFKKFzQqNZlVJqrLqTgaYWlm2ebaNefXiYhRZXNN6PAgOBAC+AR2RbvNnD48z4PgSMylWdU59L\n7PRrJ5uxpIb3yFeRc/fPPgt7/2Ew84Gy3MeDWLmWcMKP3wLNIRR+BQgNAZ7FD6HBBbX0ikBUUoWS\n3k8N7vqGV1LehyFrxC+B5hgKvwGEhgDP58fQ4JJa2iIggurj9xZVj7p2lP8z8txBLw6yfwIGB104\nyP4JCHAbfpk73LWfSougapfk/ilzvlLveIFR/ocOnGP3rx+HUfjnQWgI8Dx8GA0urKUNAjKo9h89\nrnb/a+tx95Rjxy+A5jgK/zoIDQH+ERxHg0traYOADKqwXMzREt1HYntzSy7sN+/fh+YNKPzjIDQE\neP5/AxpcXEsjAnHvP977n//F/7/k6NeJqT1baGGza24NnPEf6cYjr2NPD6FAwv4VEMje4NwQ4HC8\nBQ0usKUBAaWk+itGzfiXez3e8/YPIvIGrz2ELdUQaAjUIyCD6jVasKle1jspd+/AI3YjMusIHzLt\n+xDZ67V0+rjXhyBrzA2Bv4uACKpyYdAfAadyBx5pm9iPaZ2fLSlr73wjInu9Vpy2s9JrfWx0DYGG\nwLsQEEH1tC588S4FO+VAnV3bmqosLd5+BzgOrgv5jYjs9Vpx+qjXZaQbRUOgIaAhEAfVIblI/3Aa\nRtdho4mie9PSw0FXdWdNeMUOPJrwcPsdQ3FSVlHVWNV7ISK4yU7pUDe/LDHR831eK053h7wmc9q5\nIdAQ2IhAHFSD/Q0DWVdYnqMqOMFONHDURB8vXxFeswOPF8BTopMmjIuctCIdIBKtUayyBxtYqhSZ\nm7u9Fk7Dvlsbf9kyZrVHDYGGQC0CUVAd+YZOoYzrMtR9pKcrHLAI35ZDCq/egSdSE22/Y5/e90+F\nChDpp4pAhcN89y5RudNr1enugNcRqO2yIdAQqEYgCqpP2MwwcVxrB3rixKWllnhVJoTX78ATmhtv\nv2OfsmVAQ/LyVYDIXNPOyze/LMsPKHZ6rTsNG28FwttFQ6Ah8B0IvMKtFC7pIt316TbqLBrWm92O\npvk5zG6D7iyTE0481TvwkFhijLbfsY9pv2Mi3nDmiAxLTVBF4aaZgEwqayPKrV4Tn+q02+W5rL9R\nNAT+IQTeMDfyHd6mzBhfZpMdUjFmNujroVa7VLaUnrDyP/fd6d6dq8qsJHwLDxltzgXGS3FPu0Ca\nvwgQmapHJODmlwWTvI4NlIwJkiUNu70O1bSrhsCbELie5o0Ng6h4fD5vNz+XcQj21XuTZdvFJM2A\nDiI+0f/xysvuA+ok7WBiL6BgdvBJkkUPUPhWHieiwAjRfd/BEXmMtUHVbGBZMInZU0/JmCBZ4tvt\ndaimXTUE3oPAcOmvQSmuSqyZcz15PugJT/bYzIXloHi0q1KeJkqaMb2CaBM0IEbibmBP7z2LngaX\nE5UL62Iw8DLh1TyBSrjIMc6FXwuShSXm4GCI9FD6VKr/gsXtH6qbpNCDxpzxoDY2y9mY5av12klr\niYbAVyJQt497bIGp93YX6iG4ztOLAkxI2k9YQ8wewVieLCWUj6HQkj7SZpzDkvQ5U73HTu3KYfTU\n7TxAKMsa5kz2wut5HLNNZBmXbPDxkpb4pTBEliccr2fckiJY3F6gMAZA8V/Sg3qVMmMWPcrz1XpN\n0tq5IfClCOwbOn0xvecnapo8QdFGK6qOz/IeBsPtnCzkhp4Pp3u+4TJlBvSnhL39r8x0qgmsMdXa\nULl2ZXYSG1/dBNL135SYaxW+iYfLKDHWbpEtIl6EiPKrIljWDSxTJgl6+KkqISV50PkiX63XHMmW\nbgh8GQL7gurdhFAKqlco1ShF1fF0r1gv+XSd42KT6uz1XupgT5gB0s4U/VfJYbk1UjdNz7oIaTun\n+tN8nWboS6k6rPBtPExwibEPBjlMYJdeghbRK0TkcXud4lcnWNYNLFMmCfouRen9kzz4rMgXeJ12\n2utpqYbA1yEwnC4XDKs9fH4TFAOv98u8TPdk01ZoyXktneIEpP4SFVWHm1Ku7Of5NEIt3YfRHho7\ng2KkJEGly/1ZNEo1A5mnMGRAsTqu2yLVrziYpyNuAXAHeAHu+Fcijl4ViMQsJbi20qO8PTzI5712\nTne2FxGftqMh8L0InLB5cTCL4JtdeS5PGKRYF3OuazsqlhDh0w1aVfs7GxvgPMJxnQ9oZD37bqMJ\nvnz8o0MhAdlnrDcXDs0MwxLHVKhP1jlYUPiJj9lLMAONoMD5ANCXaOJtHL0qEIlZSt5vpUd5e3iQ\nz3tNTg/PU/BTjVTtaAh8DwImqJ5NSWbASvK9Pi9S58b6wYZF1fms1IhNkyKUaBdf6kR1o4+xnUJS\n7usyUKlmwJMlqvtjd4mL4v397I47VpXNhH78Z2TCP0FhHjiyILGHxwlYmbfoi3nBfNda/KSagxl8\nQRerkjh6MUQkApYnZnG6XYK8r6VHxj08UqHz2jkNr70+I4dGtKuGwEEEMKjSJ4U/+PeoTJMIKqCV\nxg0sa7FvdlnbmvSQxUssbt6DnveHaQhgraWSpL/BMprxIUNPyoyuP8fjcIePKqnuXbEZIRGrNvt3\ncFlxtmNuL/QzMt3xOF/MyUXgLCI6S/xG/HUVfeR1FQ+pSHtNTgNlC6oEVzt/NwIYVJd1WCYuuVQ9\nwGmm6EvnLiyqYr7WGkJ9+xe6anv+ByfDuB+SQOio6fFyIoQZ/dm0bhjR5l+hsgtdHRXNA3sWvlN5\nAPRrRalK570CyN4xVhHuqUpsF3GKRmHExc4QEWiDtWPmuOSYhT/T0gV61WuFR3sZYq1q8tU5DQa1\noKq9lXbvOxAISqpQcqkNqguWckaoxi9UBoJWVVfyIctll71pY+iohdRIAeKgaywkMaLKY7NyZozR\niKo+jtpkrjlD/9pIA3CDB8FFsPDdzWEQ0MQXOg8ERWWsfR0v4OhmIBgOXwZfU8saVH3XINLF0StA\nBIeoUjXEmxGz0JOU7zq9o1a9ljz8ZTjetNfkNLpY8UNFPrRzQ+CdCJg21YuJhmZmVWVQHQzHDEHV\nlRA7KKr6tlKyceCV96WHyAtPXHMrBVMKrvAtxCSrIJxFQKGYZPNz1owpCvdUsuECKI0lcJxUVDiw\n8EsL3y33chBGcUmeigCQ4I1WbR59a/ETEemfgzWSr5cC90X04ojgiDI+bRVNV1jW2ynfhQojhFNL\nrwUPfxkM5aTX5DTa24KqfUPt/7cjcIN6WDdcsI/mjt1VZ1Ha1EwazxOMuMQOVqjiu+McxS7LOboW\n0yt88jcIqiPVrv2wF5oAIEiYdqWR1j3NmwFTE4LxmhcWgp2INeFaH+MH4TVf+O7Jq50hWXCV4qlZ\nsTnFC6PgmI6Bza+dpge2WPfGdXYfyUX0ihF5cqlGgWCxapO+q/ScWvFa8PCXwXmTXq9Oo4stqNo3\n1P5/MwIDzJbHkVTjc5pOOE71BtcVddm77YGFfIuruLEjV5jEUdxzP8O3Tl6iSnvQBABBQgTmvJgO\n+uDWelEwAwazc66bCBn+6QvWl3tm3XC06/r4UF6fo951RyISCk/1is2SF0vUvHqwUgRazfpZkX0i\nekWIKJsAChajJO27Rs+pNa8FD3sZjLfG6xZUg0zQLv4MAi6mQmH5S51+hIN3pnR1fcTSdk3HEdhr\nlzUwbQXnIGhnfJE89Ss2C16xarPm2AwOxeNU7ZheZmbA2M+0qgGjECz4LOO7Qs+pVa9jHvYyGG+V\n192SfsfMq5ZsCDQE9iEwhOupagW6VXBvWiWj2rKudF0hwIzxlYNhq3mqV2xW9MWrNt+02A7TbotF\n7xgR2VGl+rPJd7s+wopUldfsZXBNFV5Dz+brhCXadjQEfgsCfBxpYem/73AZGlV5o0ZuzpiJp74T\nPW3dw7Y+D1YwzgctH3t4SGoNb43dJC84x4jQ0OWASFxs8r3bRm2UuZeR5d3ttXCo3WgINARqEYj2\nqFJLdFaWWXC6oqR6hbLTFRot1o69qii0h4c8rOGl4QjEs+HsETHtqeHA1ZScLb5vQ2rV6F5GTtMB\nr1OOtfsNgYZACYEoqGb2irvCcIhwQL0qe134rlsegz1u5Ta8PTykvIp3qiouk8jgzBDB0VuPS0Vf\n3RbfAdQNSJFp9DKyvAe8Jj3t3BBoCGxFIAqqtrFOF/KoaILEMbl40NlcFJvw9vCQjVW8ZoFX4th2\nZogMOKNKjjiW8qxNdb5vQ8rpWl9GVtMBr52elmgINAQ2IhAF1W7eX6bbqPkbyQ91eP+ziBzy+hvf\nTlPVEPhdCMRBtTPTHX6Xj100wX+jd/8qIse83ghSI28INARWBERQffy+oupBlw6y/1RW+0fN/im4\nmt6GwLsQEEG1M0tyv0v8J8gZLzXtoBlL/0lEDnudAaQ9agg0BNIIyKDaf8Dw2bS925/0uHvKoeNf\nROS414cga8wNgb+LgAyq3YhDh37PcXMrKuz26R9E5A1e74arMTYE/jQC/+//JxcXGOWtfxejnq2j\nsNuLfw6Rt3i9G67G2BD4ywgoJdXOr5b1M8j02kT9zab8tBebDWYMDYH3IMAgbcmGwHchoATV3QMz\no+2Vql0QWysFS6FWiwkJd3sRiqm/2us9amgIfAkC9S+vUTYE3oeADKrXmomYqgHq9koqZXhTbK3U\nuX2+QsINV/u92KAkIN3rPQppCHwFAsHraRcNge9CQARVZRnmWltghGvFplJSGsymDzeUgs0WDvYu\nHfBC2ld3Z6/3KL0h8AUI1L22RtUQeDcCIqie1nWPINA9b8XlRmNz9u3VEW2tBELHaEX+WE/p2nvR\n+a1pSkyHn+/zHtU2BN6PwOHX2QQ0BHYhEAdVu8coigq2OK2UrWyvVMcpWlFPhzqrvBeD2TCszoij\nVLu9R8UNgTcjcPRtNv6GwE4EXq//BJx+01i+TWlAkr7QtldKU7sn8dZK+MCHRUe2IeG9+MaN7nZ6\nj241BN6PwIbs0kgbAu9EICqpjn63PL5NaZ1GdXulMqvYWsmwKLtBlUWtFMyL7wuqO71HkxsC70eg\nOrM0wobAmxGIguoz3L843qFJVz7Nz2GG/bartldiIogv3lrJkLDFoRlLXTLwYkNDJxlUp2WlIqat\n3iM78X4MAs6iLRCQFx+FwBYHGm1D4J0IREH1Ei4obbcpLeib++5078yGzwXK8HGeb6zYuSWU568C\nL+qDat4gLz5I7WJaJeR5fwCBLm9R4Li72MNDzHneIwiQhnb+LQgcHBD0jTCEQXV8BTNU121KC+YA\ny64RUAW+i9kntKBbfRx6UR9UCwapunAL8V3eo7QC7/cjULJIhaDghcpDNwu8+xEgBe38UQhcT/Ot\nYj8izebhFRb4NJr33uufWAfbITMMqg/YB8Uf6zal/kYy5VtikyTqgxwflH53HqEX9UEV1OUMSlqz\ni2mVluP9EQR2QZDzIgnblyJQ0tqe/wQCw6W/7q2Bnl7pYZZzYWW9fStE3WF5u37P6lJh73/QGEnb\nlJbRHyAW74noWb45CPBpI3qBWOBFtyWoZgySasikDBORJJmzvF+IQNIgGHaRepd7eAiALsmc1ge8\ntQg4NS3x0Qg8YdrhzuM6Ty+97tpPxVZKPhoor3/0RVPbq7Nn98ywpHpmTtM2pXkjcJx+N0H3lu5w\nhrnEt1QWfxZRK+BeQO9/eTdXa2XeIKnGcOWZyH2ducT7hQjoBuXf5R4eAqDTmd+FgFPTEh+NwIHR\n5yeYrakVVcdnedug4Xaua3MYTne/qJ3dnL6urz5EPQyqLzedijb5DKm1q/40X6cZehw2HiW+4VW3\nuLT8XLkXgPnrJMKuamreIKnGCMkzkR6ducT7hQjoBnVZi/bwEACJoJrVB7y1CDg1LfHRCOwPqlfo\nplKKquMJ6+il43Sda0LA9Q5DmPzxMvOPrpVhyPNBI2LQ/BtccLIfSPcv3t03QdzmHnuD5Lf+JV5I\nNd6EYmof8xcisMegPTwOmX3MtQg4NS3xwQgMp8sFw2oP3/IEJcLr/TIv010032kuYIDrL1FRdbix\ngiVx9fN8GqGxwIfRHnpngqGikgSYl/szsKS3ZbPrjmgSBNUwD5OVP3Vm3oy4Jcode67kTH7xuX6N\nF0LNFlh2MmsIQG6JW1qE9DICgqXCmz08TuxOZg2BPWtSODta4icROGHz4mD6fszGb5fnUs6raDAW\nVLGJnWf9/n5Tilk9kDygkfXs+7knCB74R4dC0s3nKaprj1bZEOgkEflzEFTHoHAmgL3EAAAgAElE\nQVSYZ/z6p8wbM7TmtHTaTH7xuX6NF0LNFgB2MisIPCDPLNG6CEJ6GQHBUuHNHh4ndiezgsCeNSmc\nGS3xowiYoHo2kXHA0Zv3oACZMW3N8WFRdT4rjY4YGyco0S6+2IlKRh9jO0midXUdCqps7j9vwnrR\nsbra38/uuPtfCKIKz3t4nATC1jeNPn2xX/bli891uxdOdZAgO+w5VhOQyou3MCsImLEjHg6jJjYt\naIp0pgUWxSyOKkgELLJZNKCVFwF3nUInhHg1BOBrGSo7MUlMO38GAhhU6fPE38t7VDzoElFmWVsC\nZ58fjEMPUb7EVTS7O+tvh3KraQhgzaWCpL/Bcr7x0dsf9MPV/+FwSfWdy997AC8eJB5Upzse54s5\n+S62416E+CbUhER0FQOwjfmBs339IRHoTTS5UF0mIT2HQILFK1VS23giCDYxxxsASAS67WtSKB61\nWz+CAAbVZR2o+oJ07VAnF3vDoir4ELeEGrdYoxFc257/wclQSDro9qdvyjzGfzbvLUc7qsJqIzTe\nnaJ2BqcwlQCgrhVFerVZLF783VX91t8Mo5MHVWtEXAaCcUG8hwvWv56Da9V01aCAUqjR15vVAahl\nvkImYVolAnbxrmgQiZBeRkCw6N4wWyD/+qZ/uq/CpkKgMSsvpioP4Ie5NWOSxe38kwgEJVUoBlUG\n1cUFvLioCs5EffZwx7QsmCIr+rqsxa2gQywkQTI5NMuOzHzsyGpBm2rPQ/wTQlHtYN0beQ0hoWLx\n/6BZzPHCdxJsAOBj45pCJRVBNfCig/7BsThSVTcIsXaHiAo6jw5AJXMZgTWohuFNSC8jIFh0b5z3\nmBA84ZK77j2qEEhm/mIcbxkBY1JxtHdgeLv4FARMm+rFRDkzs6oyqLJC5kVp+Bl47X3p7ZQR19xK\nwZSCK2TkmMTCg5MI+G/1bMLGk5dyKnEMgmrnikbA/cRutLpZTcudhS0Z9oQpfKlWxhsu/j76cvcT\nUe3NXAcpXX6u3Avc7aoPY5AwB2oIrJ2OGcQphZokjzRRxqMEcxEB25gYLBijRbsiAvXeeAwETxo2\nCYFg5i+GQV5EAO2pW5PCW95SH4LADWox3XDBJq47dledfaNdxkKo4rvj7BuEGMfoWs1wWOkNotZI\ntVM/XIgmAAgSLyhso8UhR7v2ZQqD6oX9JqCqyjD9ZBX0muXvebMY5w2Wvx/YJOFpetjm5pqSase9\ncM2PHjkllTTI04qokOLRAKhmLiHQmxVvGDJooJBeRkCwpLzxAGhqoHmfVpLi71GBQCqkyg1o4Lwl\nBIC8fk0KZn1L/jgCA0zfx5FU43OaTjhO9QbXLBukDMQlJdnBS5OCBaaTzP0M4YKeoCJ70AQAQUIE\neF5YJzyOp3XRmhOV0v/9jx96ALt6hmXdyjA9j1DiXl2tXv5+bRZjvFieZIV7vd2sogwUePGCpUrr\ndtqSBgXYiaiATxUeFYBK5goEzAqLBPZqoJTO36OKgGTRvVk1mJPKUwuBYGZmbcwD9WtScOtb+m8i\n4GIqFJG/C4GwpDqxajzUmutW3ze167Mt49Yvf2+bxRhvvPh7YIuDQ87kt+OCHQEkGOeItYWarjOo\niphGAmYQFwlC3G8fuy95dADqmGsQmMGfeJyqlF5EQLKAV9Ib5moCAYVJhSBWyF4Mg7wGgdo1KQLb\n20VD4PsQCINqXDqs6qgyY3kXuxJr9eLva7MY542Wv7frGYRI1M3kZ170pmE2qi6HMtcrxSCVjt9U\neKoBoIbBjQgA21QueX8bApoXVRCwF7MRgYupCfLX0NJ/EgE+prWw9N834xMG1XjOGA3UzRk12FYR\nM4k0Rxc8W5vFcry+8z/grLjgXph4WiGqwiCheQ+PE1LBXGG2ExcmvgsBat7MvcfQMnflXkyOdz8C\nTk9LNAS+G4EwqHa+eGjaU6MBj6pxawdeTfx1/NQsluE9MmnGe2FX5S+XVCsMcsZTYg8P8XYVzJ+P\nQI0XzuMoYbZLwBfzRXkgUtcuGwLfhkAUVNl2ezjq53HJdrWhlctjsMeNt8fm7admsRzvnsVhSSvz\n4gqDOIIB9UQTnGsMChjgYg+Pk1HD/PEIHIKAXsxX5QEHdUs0BL4ZgSio2qYuY8OAM6r40ADdMtvE\nZdq5TE+PThXepWaxHO9F6xgKxSSvmBdQQa1og6wxKNa2h8fJqGH+eAS6Gi+cy3FifTFWhp5/jiAQ\nq2vXDYHvQiDcTgVW1woHVX2XGUKP7OUXJJkbn+JFxsTio4bAMQSKADeChsDXIBCVVGHB/28bzZV1\nKJrenqVVHn6IF4pl1bcaAgcRqEa6ETYE3oqACKqPjyiqHrXiKP9bMd4l7KgHR/l3Gf1Wpn/fg7fC\n0YT9MwiIoNqZJbl/2P7xUm7MzZv4CV7kLcw/bQgcRyCPcHvaEPgiBGRQ7X9+IG2PSxkcOz7AiyMO\nNATegMCRF9B4GwK7EZBBtRtxMNWPHrcDPf9k+M97QZbsOTcE3oHAHuQbT0PgKAJx7z/K+5//PSr1\nGH/PFkHYLKmnhbbGz+hx2+wAMhxCwGlsCDgoWqIh8H0IKCXVf3w80vUjetq+7w02TQ2BhsBHISCD\n6rU8i+oLPIg2NqrWEG9qBIy4/HE7GgINgYbAzyAggmrlGqrvtlbd2KhCSbypEbKYaeUVvI2kIdAQ\naAi8HQERVE/rAhdv15QXCHX2is2tpAxYmyDY2AopxmgRZ8nV7jQEGgINgS9CIA6qdmc5o2yBXQ+q\ntFYTMmnKVq1yUX9Gn0yGmxpZslNrAEji1R40BBoCX4tA3Pvv9zfEpklcZ754VBMyScpWrcrGRowh\nk5Q9U+yXIcPXHjUEGgINgfcjEJVUR79JFK51WVWRriZk1sutWtW9nRhHIhlt67RS1e0DkxDZbjcE\nGgINgf0IREH1eSZRo7ZvJz3k52pCzoTpYKtWdWOjmENex5sarRRsQVXJ0+40BBoCDYGvQyAKqn5H\n+XUz5PJ8UU84zc+hfk9XO8yAeKo2NmIwEF+0sdVKQfsmM4aWbAg0BH4HAm+YcPleICKDwqBqS51W\n4QXi6VCzSRARzn13undmD+WyyetWrZt4mNQS36Wui41JbMmGQEPgqxG4nuZbcTMRYcQ4TdPNF++G\nV/Vy+ELUe26Mz+ft5mdsxgaFQfXx8koXGDo6l3d3gt1KVkJQsmmEKG7VupWHzCvxQXRvR0OgIfBZ\nCAyX/loTUkKrR+wuX3z57vRKj5mcC8tBvWVZEzMVfvKOxAb99z9cjW9SBTeGeRZ7z/Wcmlz3hL6b\ni57hWWXCYrD58dF5iD/BC4+zfDP7dSBR7dwQaAj8KAJVW94LC2e7zzx191zn6aVXRPvpXCrD+tFN\nQk18Y3z6smj47GQK2xfalE8YFJZUz1B4pAMZcXe24FgUoz3hAKFMMUQysa1aEzykVfKuT/J8Szbk\nkvB2bgg0BL4RgX0DyK8XGIjUv6jyeYK0VlQdn+WtIobbubL1YTjdk+s6XUx8P5mufEBPGBQG1Rcb\nl4rLPLN2Awu9FuNWwvHVTaBM+Q1RmNatWtM89KYVXnhU5Nu0YTbpaueGQEPgKxHYF1SNRa76f4Ve\nIaWoOp7uvtU16cPpOivFQkl+vZ+U0iHR3U1Mp6AqDYqCKtN4naanqOxrMW4l7E/zdZqhB0kcCtO6\nVWuah4QovPCoyNf7Fhggn8CuDEakq50bAg2Br0NgOF0uGFZ7+BwnKAZe75d5me4iyKgWuHo7zpbs\nL1FRdbgp5cp+nk8j1M19UOuhtEutCEaLJMHby11GPkMe/DuvNkiDgqAahqJAwnqhxziNkt3bxXRE\nIfCyDsIR9xG4A5wAr1KOZoa2ZEOgIfCFCJywOXEwi+Cb/Y4uz6Ucc5BlOlMdGsuF2IPOv+T+LqrU\nQNMDyQMaWc/UbgClK4gE+EeHQgKyz5NSMiQWd76uJigGBUF1DMp3jp0ldsXHXUyr0r28DHQzvOq0\ndA8AecGflXY0BBoCP4GACapnEw8HbJG8B8XGrEXTukHy+gGHRdX5rNSQMTROUJpcfFEY1Y0+xnYK\nSbmvazWT+p8Ug4KgylsiX3QErooYR1ThOeDpYqaQVlwFzHt5fevwk2oKZrAFXQRK2kVDoCHwDQhg\nUKUgg8Wee1zG6e9nd9zDFruLWed5WcfZz/4DN3Y/ZPESi5v3oKf9YRoCWGupJOlvsJhofGhW0UAG\nzaBgQZXcWP/pjsf5Yk5UFo+1x9ebmKJ1qrfxPqKpXB7zy4prbwYE4EyFdjQEGgI/gQAG1WUd3/mC\ntGsozRozmqLmzQysclE4LKoCv9oQyloBgcT2/A9OhtEakkDQr+rxcivhO2HMoKCkGlb/p+ftGTcu\nxAVHMEsjM9a6f5JJ5QGQr6I6IHmx2ymaFgbDFK4AqlMICVf97ylll64qj7rgUlq6IdAQeB8CQUkV\nSmZ1QdUOoLph2+TiykRxURWMlF32po2hoyC2rGXBoGssJDGuVozNMqIw2KsGBUG151F7AhYxMUnG\nuICMzSVjb0Iw6TwQFOU61YK3g26+kYbdOn2AW7j4q28dXlPLGlR9VyCzsCUbAg2Br0fAtKleTGwz\nM6vqgqqta56xpunKhV13UYaiD7zyvvTQnwU+ueZWCqYUXCEkxiQrBDiLgEKxhspgXJhTBgVB1Zfv\nQBL20YkZVTLGcbLlTtEusEQwJXnkOtWCF8vd/RoZmb5orerRztZCM574IvrnYH3xK8YEJraLhkBD\n4MsRuGFT3GC6nO7YXeX69LOaH1gxXbDAB1V8d5x9Cx/jHl2L6RVCwA2C6kjV2gGVm4MmAAgSIoCz\n0kjrno5nWIzgeYJqtW5QGFQv/JcAGmzFak8ixnU424HInq6u7fRjQjCleJR1qiWvqwBAvOT6grWq\nBz8xF4qwD2yhXlfTks3Qga3toiHQEPgaBAaYI48jqUbYUuQE3+H1Btfsc05qvUIkNf1HuJYdO3KF\nSRzLPvczfPskFlXagyYACBIiMOcl6inzD+/WBgiqukFhUL0F7ZL48xDZLWKcVW/JoDg8xwz4XGVa\nRXMebZ1qwfuCxf7Wpl7Gi0VXXh0QhsNzs36WZh/a2I6GQEPgVyPgYioUlr/W0aD3v5ui6rtYn8CO\ndI1NsmSmUn5mZV0iU5kkj7pOdcw7YqHf9mcxfWKt6tgRNAX3hmnjVOmltHNDoCHwNQiEJdWogDeZ\n9tii4pXMjOldaJWBApfCU7VOdW9XrMFfHa4vXqv6psR2GKcwieEMBTPb44ZAQ+DTEeDjSAtL/32L\nK2FQDeeMPepi6ko22NYRnA9aPvbwWKmmsRR79LP6fOd/2ZZG0RBoCDQE3odAGFQ7XsK7QlHwWm59\nILI1AtOEiayJe3hWgWYdbIysOX1i1ELWmvawIdAQaAi8DYEoqLId84b7sizlvQ+IbHkM9rhF7bKK\nqXt4SAwu8Yrj/LP6pqriMols54ZAQ6Ah8DYEoqBqmyyN9IsZN1BURGT2bHiwKz577OFxAh+2ZTSr\n7+LGUTi2lmgINAQaAt+BQNj7D13kv6GMt5QLy9+BbdPREGgI/EEEopIqzP4qt6J+PExtgv/Hv6Jm\nYEPg1yIggurj3y+q/gIXfm1+a441BH49AiKodmZJ7n/Z7/ECqxa0oyHQEGgI/AgCMqj2nzB89gAW\nPe6e0o6GQEOgIfAzCMig2o1mD5mfMecNWm+t5/8NKDYRDYGGwE4E4t5/FPM//7tT2Cew9WzdBM2e\nXpvAqhFm7/m1b7Jk/8TDhoj6mhosKix48z3QJMX/8w+UkuqvGFWVfjHBEoFpsuyT3wVRQ0R92Q0W\nFRa8+Q5oksL//QcyqF7NBlsf6Fm0h1WlhUO8e1XntpeplCDJPgWihoh8N/swATm/OaMQTDvB+Qpo\nyKTfeBZBtf/YgarqHlbFdyJ2r4KdcQ62un4MRA0R+fr3YQJyfnNGIZh2gvMF0JBFv/Isguqpbmmq\nHwADBtDKPayKdojdq3Cjgmjp7aKQkOBjIGqIhC8Gr/ZhAoy/OaMQTDvB+QJoyKJfeY6Dqt0eT3fV\nb/ICv3g126gaMdM8nTCIqTuoGgr937T0cITP5B5W4XPtKtq9CklOhzqrMhBt9PUx0SYGmuHyngLh\nxyGyZpLV1OE0jDWdehvJPTSagj2YgMSvzCj05ui8wI4i3olUipyjc4pO3qe3sH57jGAXOG+Hhhn0\nC5P//U84Uj69v+FgdroyEJi1rIMtUdPIPKGu/YQgXEnuBcGGNnCY8E03lT2s6FHuLJrVM2ExJ2d9\nloZoo68PmBHcBw7mtSsQfhoilEnI1Cu8wopfsI3kDCZFwU5MQOiXZRTyj87YrI8bURQOco7OBXL3\nmN4C5Uf3APIbbSnK7tUk3wxNjcp/lyYqqY58o6fYK/qR6yesP/MtUWNKdv2EX+QHbGpYSe45T1c4\ngqUHtT2sPH0iFe9eZcjuxYW0EtLgdgaijb7e8PcMamS1h4TwAxGxmYRMvS5DVNlQnd1IzmRIBbsw\nAYlfmVHIPzrjesAVjVDkHJ2Z34WkfQuUHz3xPnDeDo036FemoqD6hB0CkwcF1dk0bfItUZMs9sET\nIscGcsuE86IWPuhU3cOqoLkTu1cZBrZsbEmAeJ6FCErl9b4+Ye7aWFGOIxMEhJ+IiM0kZOqVv0Dy\nQ543kjMBQsEuTEDgl2YU8m89j2bPIbbhL3OIJ8k5OvNn+TR9qjY/Otp94LwfGmfQ70xEQfWSK8Kt\nb2pYXH9RtKdVAiLXW26bDebnMLvduRMs9nZv2p2g4dEwVO1h5eQRV7x7lSGgPbUd9YZEFiL4NtdV\nviqg6WHr8sDDCisCCD8REf85o6nXp9v7tuRcQE5vr8TkFRDHNkxAPjF+dUahDAHndbf04nRqQo/O\nztYiLO4t2PxIPm4Eh9jeDk3RfiQ4OEanSkeeaK8FYVC1P6EpTeubmnwnvNhtVWHtZ1fZRvK57053\nu120QhzeMh1cWxg8e4HrUtFN4IXxVBaiyFfOp6Uf9xdWCAu2BpxbIfTMBS3vQsR9zh2a2oN7S12z\nMScv2OqdcgrqORgzJguM74IF2r/W8gqeLxBPh/I+aoQenQu2Ms/Wt7Dmx3o+JuJLoLme5qBFL9AH\nF4NvaB5eK2Axzddd3wGo4ekqV7stCIMqNn6mD/umHqMLqpW7rZqOKhBryKEgVztO1HZhbmBgphe4\nIK7vPPIQ2U458rWgYnp0wxmmWhRs5VK2Qsh4C1rehYgLqi5z9Ll2emdgQF6w1THZBCrYxsEEFBjf\nBYvN/KDX+Im/M3O5+o9mEnrbnHRvwXx7BR8ZGkGywLYDmuHSX7Nun/0PMHRUp5vj58KqT2Hve+BV\n5sLsJuJDedaCjJguDKr59kLzpnpQulb/td1W8UdVHHYzQEde9ZGBEDfqJMegKjQW5Ljm7K+Hd0BK\nz0OEBRCs1TlfM6J6E9jvphKYs9WL8GJz9NJmkpDjehci9DlbBLAvrs9+RqttglyzVfGMKdA4yPPs\nOcf4LlgoQ6znYZ4rNqck5+gMXmi2KrDQW6D8qPJlQbEPNXXEVgsN0cMZhwHljvniCK7z9EpUJ/uJ\nSv1JWekROjHL+ITfjvW4T6fZx6+MBcSQOIcLqrAfCoXevKnlCccLB2vQlqgB5eIDvblv2nRGrOk4\n8gECmnck4A4vqNkgyxArdCLyXLnc4kRA1TVyB2px7rUzMptUfGU0QtRoJM0YVLO2ehl1EApFJCCr\nZXkTIuvnvJqKrRsV3dyUOTy5aqviWYGDXM+dVVXE8CZY6M2tZyyC4Q6WhYOco3MioyiwmLfg82Nt\nBovteQs0TGhhgPj4uDtQTvBjrBZVx2d5Y4/hdk6Xcpk93XC6u9o+jF/nj+AqYUFApV2EJdWXb9JQ\niN3WT+YzoS1RQ0LxgjFDPLCOazdnHV/dBCMMEr9BoSyzfV+JQSg0MkpcVRtpgyQpPQdR5GvojRRl\nhgye+pKtTkwlhFIRSihpeRciNpNQ5pggb7uKvXNEJCLylK2KZ6uCFIfQFN8oMb4HFvKPzrgQ/K1c\nsCD0Ck4qsNi3sObHko8xJut1ia0WGia+EFSnzgXVKxTDtKLqeLJVOyZUSZ6usygNKWTXe9hhHgTV\nlAWKnPhWFFQzpsAvxOtknj9ur9PS0ZaooUTxggecZQSBdSXvT/N1mqFBuOI4449IiUEoNIJLXH3Q\nSzCBRXoWl9JzzeeRr6GLUlT/BGyghboWkkoIpSI0pKTlPYhQJnGZY5rsAIcQi/gqIk/ZqnlmFaQ4\nYkXiusT4HljIPzpfwWpfzxRGuRuEXt5JAQu9hTU/lnx06sJEia0WGid1OF0uGFZ7+Nwm+Lav98u8\nTH42AvTWuKCK8a2/xEXV4cYLlqvgfp5PI9TVfezChrVgbKgkAd7lHr+D0+MBI41WsboF68P8KQiq\nIUx5xsRT8YITdG+7vVMhi40jbhVwv0NVQE6pFNL3QyREvQ2CSNBORQoi6kxhn3et3v2IRHaXL3d6\nVhacoVBgQWpXTV1ZhWm/HBZ0W4UGCijpkUgnhG3AArTdtenyhOGZRI69NRRUsZiIfXlBjba/a6V7\nHHf5gEbWs+97nuCDxj86FJJuPmP5PzxwYAKNtlQtCMmTV0FQNW2fSdKqByJzVXEdINqpkL0uM2oG\nit7aZEAhfT9EQtQBp7OsOxUpiCgzhWWDyH5Esl5oD3d6pomqvqfAArw06NSJEab9cljQcQ0aKEmO\n6Q3iTVA9m0g54ASIOy9P4m0KqmtFPCqqzmelimvaRqBIu/iiP0odfYztJEmmq+tmbdItQLfLRxBU\nWStJfz+7404l4rI4+c0VefZqWgWL3FxUaAh80+iT6hjaZEAh3UO01W4hKmnoVsmRoHpFAaOCiJwp\nrLQye0QCcfrFMdf2eXZMpwILVmAp05CbwrQtsByzcMc3R1YfU6xAg4saYIkzcWBQJWAwJN/X0IXk\nC0aZNagua+l19iqsxIcsX2J5k2LxSmQMYM2lgqS/wWqGieNpemyTFiS4gttB739uPLJZ3kT7R+Km\nOx7nizm5Di+Nw94jvsS5zLhVoZFI2vzbcqM4wsmAunTIElRbIUn+LExeHyVECfLCMC9JT3fIBF0R\nUSXOxKwggjUoP1NYlx4gklDx+lnPyMPwnLTVPiBiBRYcFu+D6j8HC/pH3qnnSmQ6BRqc1ZA5MKgu\n6wg7XCuJjXyysyfX6OhibVRUBdGyJRRusoYIuLI9/4MTYgwKSbDbX5hqB95Oxj7HLC0w4rL/gpJq\nXZWF1rdT5YpfbJVqz014B1deW1hlSIW0vFqgJF5n11VdepdykwEZo5BehigFjxDF1OxLViMCI35l\nQ1cFImCWzevMPuFGAhFNJRMjkupbi6iEbhhZcHvKpjE9p0TC4FKzsQYWNlGbhArTfhQWHHJxCBiV\n+woRjfzFs/ty/Df0ghmt8oU4pqCkCgUvFlSXEx6vC/aFLy7eiaIqiIr77LHwi6VcygfLWqLzPWDw\nMCRBg+TQrIvxztRc8xYge+4IgmofhXOVUVlPjNGJzMWe3RxW7Ob/396VMDes6mo7cZw49pyTzNz3\nbv//L70CWyAhsXhp2qR4pvUmCekDKyC23KVjAotJ/cCxiQRxeTVL4bgBcTeXwLzxFc7lanIzHp1o\nuBDSsxBF4RGiMB2nIz7InB19KSINDXQ57gJEQBE7U5gqJMzQEaFJUvbYtZ5rAbVIW+eK4BIIg0+a\nxP9WwUImaqNQodpPwgJlHQKMbsaTs60UGJ07LDDKN9SbyqtW9VlgsjHVi3V6dmYVcaozxdxsdNVE\nM2jIh0oR66ajrfephQ4teOXCrehM0bnCVxySzJLMJAL0xObJ7Ixth1dOg1lA7D9zqv63J0Zukja9\nbdH2gyhcXtJ0j0ewPVVwxZj8PBFPJRI0fYs4W4Vw83V2ezvvyUp5GgDbZSQFTgpE+UJ6FqIoPFLU\nnAjREVNNnhl9ESI00EW4SxDx65KjTtIMV2FBEjjTJMnj+GUk1ziDSDvKpeHCZXEdV8FCJmo7mUI1\ntaC8CBZoAesfAfgXpbHnjMCLCDcvMNBP7ipJ+A219lF8Bt0NGldNZ9ccupt+qfNSqcSEG7t+MrTw\n3QFrDrmX5KJ3EdMrJHkDd9RjWM4XWZwAIEi8IBaj7U1SjwtAV6CBlyGvuFO9EA8taf0Ts76dfsjC\n5eievpXgnmUvKJO6wK5IEJdZM6IpN1uCuCMZPwwwPA2IyWRAp5aQ3pRApMIjRc2pMB1dwvELSl+I\niCv8KxEJavdWJ2mGhkgmtiati+YaJRVpx7hUXKgkc011pKDmCgqZqO1FCtXUgkKT9LyJq5iBjEWm\nzRbapLYVARPlZshAzcV39uA3ZB/5ViBTE+KYsOg8fGk9bHtwMuNUb3BPymYzwIPTozFraZGDVia5\nQHMHo2nHdoRPGF8ZyfOBEwAECRKY80S64UGxkw1erNKASpuvuVO9RZ0l45zXE2OP8EbJ4OUVzKod\nfXgf6TNnyqQvsKsmuIx4IdzGa5KWhBgSA6/N73M4pVJKL4BIh0eKsrYTHTNYzK8pfSEiJNBFuAsQ\ngRayoWKHNENDhCTJuJM3MtcCcpk2EChcOi6BsIbouAoWP1GbSJSq/TAsO4CxZklYgwKDwBMQoLwY\n30acLXv5mhvnU6FO/JoURSqs978ZShroZH07Ia6Zx8zK5/NAi3NhTRj57eiMhSmywK6a4LzgAuEO\n19nVDF0mA2La9iyla5yMJQaPFGXYiI5MSuyG0hciQgJdhLsEEajNuQoAKiTNUBAhSSJfwVnkWsgj\n0wYKyRXBJZBGdFwNi/jxVcr9D8OyHZgZJwFrWGBUZ2EWNOC9WQHqf+KW11S1CpwGQ261GYXHhFDg\nx23djwdlWrHA7jLbnHIH6+zeNO+OkwIV7f2jEohWwEN19InEryh9ISIk0EW5SxApWvdWQYQkGTcl\nfKPkWkii3CtcZbgQHVfDMk/UVrQhj34WFtP/b5WhtpUBM7NJ7qDANOo39OMZ91cAABviSURBVHgO\nid5/As+GSzqqNrP03wbpB7Jwp+rnjKWTwAG8aSr6tptjJzAbdMWxiQlizXOBSHHHwj555UogKocn\npaOmy1p6K8MFulLcxyLiktSM0J8V5JrCuI3r42Ep+ggUOPFRCazbSwym8qln7lT1Xx9mO1lPjD3P\n3Mx+DoLbNDCd4VnGOKxkwmXkUtw4OiCngPZe/YF2hCvhWQvLWnqrlwt0JbgPRsQl6YDJXeDieAkd\nFRHbuGZBTsdEkm8KC3QCQQ31Cs3ChG0KnPiohHsPNJjOh54Dp1qwI57pzzFr+a06pkc3H7eSqO0i\nehMTrjHYpLiHVRVmbmkGolXwpHTkqc53a+lnLgx0pbgPRgST1IxQn+GieCkdJeM2rkUO6phK8j1h\ngS6aeaHN5Ecg4cQnRdx7oMGEPvQcONU50JS0Fde3SxKFL+c1z+w4CdGfHNK6+01MuMbgctaTlP0v\nLtHsRQaiVfCstXAt/WLMEuhKcR+NyNrY2qwbrhCp55rMmm1cKOdjYUEY8VwKJwJTBOueEoMJfej5\n33+g4kmOcUcdjoj53Zdute1Nan4iRBURtShUWFRYzMN90ETFfsSLoKYKv23r+uffEoT8fgxJsz4Q\nooqImuMVFhUW83AnNFG5n/BCONXH51dV95q4l//3lZu9Fu3l/32IWI32mrWX/5fCYtT6YNP2oy6c\n6rwk937Bv1dCb2b37jrMXLtPOioiam5WWFRYzMP90ERFf8AL6VTbXz2udj/krdk9Zd/xYRBVRNTi\nUGFRYTEPD4AmKvsDXkin2vRmVNDnHjcx83K9rZ8FUUVELQEVFhUW8/AIaKLC3/+F4lSb/pP7qlqy\n4ML27PskiCoiajmosKiwmIfHQBMV//Yv+IIqszl+Ga23N88sDfYBRlQTKgIVgbdBQKmp/pJxmN0w\nmBVO1x7dY3QL2Fre6+cPZ1iLUaWvCFQEvg8B6VSva6egfpNykR2YcqmFewzNK7znuOr7ikBFoCJw\nDALCqeorLB+T2CopUMHU9qTKyRA76Swr5+b46vuKQEWgInAEAsKpnpZ1bY4QvldG0YY6YSLBTjrw\nOlzOP+So9xWBikBF4DAEQqfa+R1Pll1uu1PXz11X2o6+UhHcolndJFeS0ydmWzBylG2oQxiWSxFF\nPdXOKolSfVIRqAh8CwJh77/fNBb3qb3CGjfWKdEdfeO64BbNyB6nFG+CtdLLdhoKpYQ76Zj35Jci\nJK/3FYGKQEXgUASCmmrvN8czUwDMQrTXqbOLpxZur4tbNCN7ubbt4GvJwFW201AoXuykYwnk/nUh\nX72vCFQEKgKHIBA41affFhx3x70uo+VXbK9rtmhG9nItR94vtWJDHZpGuJOOfZdZWJry1+uKQEWg\nIrAHgcCpXvhSIaZBfn2Oo9nLi+zom0nQDSCw7flhfHbB0FGVv5tmp1pKHwhJsvU/u2tuoGq9rQhU\nBLIIHDCdPJtGmmCrBtyp9sFup2af2hbCANMNutBhWMDVV2Sj6pAtmg372Dane8munMM8gqqYniuQ\nYbvYTSU5S72rCFQEXovA9TTeIjsxdefTczDHolH3xSt4L1C0Hcfh6aexb9aAO9XHF1N92eXWDBjt\nyY6+jEa7WbZotuywjoDdYU2jo88e/exUS+kpL1xn2MCv16MiUBH4WQS6S3uNNRofdtOXpVMc1Dx9\nsS4WrviYWUpvw1RMSMCOJj25ReySGnB9+B3v/SchVSCb96k1c0VbQGLFrsPznqnLNrcQOFBMNPVf\nerSmTrygqNFT2sh1im3kvxYRCfVxRaAi8I0ILLUtNYXn7BFw9ON1HL6w0hrQt4NpAicPP4gpSQYv\n+6dbPmqyzf0e618JDTJCeU31TEeKLvvUmm58M3ze7eiblOi3aMZtbmEIga1IcrYpgGV6wvFlxmPp\n9Jxbu1OTQcIp5XGRqJ4rAhWB70QgNWB89qADurgT1LHUqmr/zO/k0t3OkSBDYF13goGieAzW+7UY\n4oxqgPTRM3eqJm6KB+5TO4B6piGPO/ri+8jZ+GCzg/XC3n81A2gpfnNCp2qkGdcdo4+kho9zbHPd\nGanruSJQEfgBBFJO1apzxbrWFapXWlW1P91d8zxuwOk6oqA4Ebi0O1t76fpl4r3D0j0V0yAlcHkX\nOFWiCu5T2wyDGXtqogGDGQWQOXCL5oW9PY3XYYRupOBQnOrj9nWaYvQBe3ibY2u/FqgsI0wNG/EX\nMZRU7ysCFYFvQaA7XS7Grbbw+Q1QQbzeL+M03Gkg0LWUTRSgvYRV1e5GKpaoI3QvnXpoq3vf1UIL\nHuublkqSwOPpvkQcUJAJ4z7Qpza6Bo42dcGcKnc9Kbbd7xSnultmSgDpSuzNfir3ezNMLRwppvqu\nIlAROBCBk3GanWnMzlvhXZ4wjpJUd5xHM9VEGDnEo6rt/aZUhVqo8T0gyHrGWChUNuEDN394KCTN\neDZN8OB4fn3dl6eqBgF57JY51Z4aGOM45vnLnaoPQNjhVdDHB79LcLjfxmPsqlIqAhWBGALWqZ7t\np9iZ0Zt3Vp+EKCoyLt1VQVV1PMsmb2PDk1ClnXyN10h1/U1wLUn0rq7Hs7t/mVlLcOga2FfZf//+\n43WBLiLv3pcBDvKEItv72R139wsi6fEJ8s3n0KkilTwjn55eIxnYE+T20eIntilOVzhio+aQr54r\nAhWBoxAwThWdjKmF3hfXtch3y+PP/fCmqko6eQzRQ9YvTc3yzqpGDxsIIOFSQdLeYNllcTyMNo8v\nu550VAPBpTxgNdXuFTXV4W6O88WeAsyoghtX/l9EhBsA+Ny5YAaYH5BJwZYqUa8rAhWBwxAwTnVa\nBqqaNmIw8skNPnK+NqiqgiIyEgoPSXAP7uae/84Jsepzkga6/X0F0hLAzHrb8p+dvmOWGizUiRNz\nqnrzH9fyS0hZ/yqsqUoJgHnJBC5g1JYkDDcAcNGZ1l0Bpwm21KMiUBF4DQKspgoVKu5U23k1PHCc\nzt+JqiroGfTZwxMbSmiWYGgzLTU11gPGSYy1YmgWBh9OEM9Na2DYUwdzqm3gzi0jruWXkqK/uzls\n5PuoU3VMEHfG2QCSnT6hSxI6bkDYTXgzxL4OvlxZ3U6YEVReva4IVAS+BQEbU71Yp2dnVnGn2mFz\n0lUTofaoDTDvaOt9aiFKANq6cCs6U3Su4CJDktk4M4mAOoDLHAk1s51yGqTRYU61obU45MO1/PC+\n+DzdL3HamFNlTEUr/9MlCQk33wCg99HipwGstfMoOowExPWsbyoCFYGjELiZD667mB6Yu2kknln4\nb1qcKrTw3XFGR8tV6F3E9Apf9g2cao+DCPxHjRMABImXxWK0V9vzbyKyBRp4GfKKO9UL8dCU1qzl\nt/p4spZ2wB5zqpSpbOV/uiQh5YZmgk+zIzOOh+Exh7J5XdYT16uKQEXgeAQ6GG9zA5fVw8IpJzNO\n9Qb3pDXbL5+yWfSTHLQyKZWCEepjO8Inja+M5PnACQCCBAnMefKd7BBohaH4hn2VBlTafM2d6o34\nIULr1vIjz7KXYw/V8iggEadKmQpX/idLEhJu0wFIWg7BpgKL8nXt6mwuVoKKwHsh4Hwq1Il/SHO+\noMqgNdjJWn4rlDQrpDTnSM0XfqXcLwuVSZkKV/4nSxIS7nADANWw5qIqQRWq1xWBikBFYB0CvKaq\nV+hgTaz1wUfbrz4F67PmdKNMhSv/kyUJKXewAcBN9e5n8quWU62+rwhUBH4UATpSPbP034/qCWPn\nTY0SDzZnDB/CGQfskkeZy26OlcBs0BXHJia3JGGK23f+r1CnklYEKgIVgdUIcKfayBqdX8tvleyl\nW2+dN97E5JYkTHCbDQzrURGoCFQEXoBA4FSVHfJwLb9VykyPbj5uWpQ2ImoTk1uSMMU9rKowR9Sr\njysCFYGKQB6BwKnOEUrGhmv5sYe5m3nhPzsugoYX0mybmNyShCnu2iOVRr6+rQhUBA5DgPf+w7yE\nT6zTTSuqy4chWwVVBCoCfxKBoKYK88J+anDXN8Kf33/hGxOvoisCFYE/hYBwqo/Pq6p+oEl/qoxW\nYysCb4WAcKrzktxvZUNG2X5ZKCFDVl9XBCoCFYEDEJBOtf3V42rXm9ya3VPqURGoCFQEXoOAdKpN\nb/eQeU3yL0jlVueivgDlmkRFoCKwIBD2/pvH//m/D4Ln//97gDF+DZwDhP20iFadsrtWq3eE5BDL\n383wQ4xeWzr+Nr1SU/2wUVV0BcCNeV0REcC9JyR/siwcYLTI/voghYB0qtd5q5YU0wvebd6hKtyc\nCobe7q2Z/QJENsMBWfUNiDQvhmSj+d9g+esM32jzt2T3Cz74T0pCONVNa6cej0j5DlVB2uHmVPDa\nrg4QkK24/Q2IbIYD7DwekebVkGw0/3jLX2j4Rpu/I7tXfCyVFBAQTvXEdjj4MYxgtGzZDlWhhrAs\nNtucCt738bWyQ27t/jcgshkOMOh4RJpXQ7LR/OMtf6HhG23+juzWvor6LI5A6FS7qAPqTl1fFKQf\nphaOeJLaG0140Q5VUhjfnMq+P+0JAMQRgZY1VCdedWyEA9Q7GhFYCdJl7/C8Pd1NFIoyKs+u0G8y\n/2jLieGgbEnmK5Z4M3NXm2w+Prtzatb3AQJh7z/f35ASX2F5lCLnBDvRwFFS4rx4RXjZDlVehL8S\nkXn+LXjCoqs4It3zdC4ScQTRdjgg9WMRITsLD2bnSahTpY8yKi9Dod9q/rGWs7IQW9Hd2wGNpiJ8\nKAe53mrz0dlNVKqXJQgENdU+vvDoderyVRKT5OkKx62MFlWUwgt3qEIB7hxsTjU/37EZVQIR2DXs\nZU51Kxxg/9GIQDjFrU5rhjTnF6sto3JZ2Ej6beYfbTkxHKIqg6+ve9WDK2lJQJC43Wbz8dmdULG+\nUhEInOoz7iWupXuPmAlMUynxopQQXrhDlbAp3JxqJlCWiRWckQcJRF7oVLfCAUYdjkhDILlAPvdk\np1odxDIqzyvot5l/uOXEcLPPfIFTFZZ4I3NX22z+huzOKVrfhwgETvUSX/30+hzHgvCZTaC120UN\n47Mb3QbdYcrs3glHnsIdqrwQZAw2p5oJ8t+9FxRcJRBZ51RRwUB++haZVsMBYpH3aESaAJKSZjBA\nZVwQqpQ22r5l9CvNx2SOtpwa3k0lTtWYwizJW47Kr7TZYXu00XmND6X4+fmP+zXgTrVPbNTXQktv\nKoyUnkzjf2xNuK1scz0UvoaH5WWG8WK9POMou0khssqpZhTUtdnEtIjK8G5GBGqmfHXIc/yHmFhl\nqDIqEWrYiHclPWHOJLPZcmb4UDw6ZZ0lGeWJmfwyw7fZaJ7K3rvraUwHBju2Z97e5Ir4++fzdvNF\n+gANuFN9fKXVaH00LUU4d4qDnqtGiBrha3mcFhnGfGeKk8Qv0oisiKlmFOSp4t0mpoU5w7sZkSaA\nZCgag2epMiqh1ea8lp7yZpLZbDk1/NGXOtWVlmSUp3ay6wzfZqNZIntvukt7TQeLoJc72hsz5pZ6\ncqH+NXraabyD1yqlQaHcf/+hmrCgUSDhBoStT3t5a6qY4nADRct8MPAT4WkeNb1ZgRTjmPm1QBOE\n+BQiek1ViEDZTUpBRxReZJni6SUT3IwIDamCso8in+qoNHMUC5L0IUTKvZYMkm22nJSFFurRZc3/\npCWK5aBlSnk0Qjun+EqN1uQe9yy71f11HL70RmU75FtEbHBGUuv+CT9C82Fb1c0FNweJa4AM+TOv\nqZ4TzXvTkSmH0U9a2w872ztwZU75pC5eeIZHTc+KTjJOqQJHNBPiU4joTlWIQPFJBZEoPOeZoulB\nt3wC/s2INAySK3wC12weOypVJWlBmj7ESN6rySDZZsuJ4dMTjq9nPvyWtkRaDkomlUcjlHOSr9Ro\nRe6Bj7IDxk/wU6VVVftnwe4d3e0creUyI7rT3XekX2zf/AljWjENmIDMDXeqX4lqx2A6GsR7tVjY\nffb6r2YAffXfnVCrRXieR03PePt0YqVbZQvxKUTAqeLvG7FHiLDvcgoSAf6yiElP7/sQaSgk3X2a\npnSUDMxZqGLmCAsy9B4g9SqWDBIfVRZkDQNT8OeMJcLybLZ50fzqKKO51KPvck71Cr9SSlW1P91L\n1kQ+XUetihcacb2zzvO7deLoVCMahDLS94FTTSk1DE/pIWWxgPRs51R7Gq/DCPHzomMWnudR04Om\nWCax9otWKgbQS69dCfGpuDn8fH6dBGJChLU/p6AKUhGTnt73IdJQSOYtbFXlycOFKmaOsCBDTyRr\nl7FkkPagsvC4fZ2yn3rGEmF5NtvQiPB8lNGh3CPvu9PlYtxqC5/fAFXF6/0yTsOdBBDN5KL2ElRV\nuxupV6I+7Tieemiqk8+vhUkodESoQgLc0/1JEkRxzXlJVNXAURVeMKfKi1uRBFksitg2E21Nj3iC\n3mwFcIccUKYQhuL/GCKQLWEAKEQE2mf092lzRhJGkQR59x2XalkYhzm45hMM1Tre8CZMwid++JVm\n9EunWRuLTqZ0dSbWN+/adHnCwDRfnEw1EcaIsKhqeyc98+a1PcyYzQcEWc9kNt8An7X5Ww6NpBnP\npk0sj+uSpqaBpM49YU61JwbmGJf3LywWNsWt6ZGMsqNLoJKhTSEMxf8tRABhMeg0RAQaqP4rKCwk\nGTKRRIZ+72ulLJjoaNiLEqp1vOEvdaq+lYkfwEunWdtMs071bDXpTBDzTmuW4HPnnOVV1fGstHZt\nuBAqlxOpdRpZvXeyCkm8rwvD5aoGq8sbc6ok2tTez+64m6ayndBv/vEkwpLnyNgF8gip9gUjlTfI\nbM9l6TkhjtcHAp/YutCmEIbi3xARn1MOBXaBkCiImJYZooNkISLQj+JrA07wQl2avyh8PodJOKni\nAvlK02ECkJkEhV1ZMIEtOmLK0IZqpQxvSjVyStiLMAmmr7tBntI0HKO5QGY1u1cMCUQ5u87GqSKM\n5qftvjixWei0/FqPXlf74iGrl6a6eeeNqoeNBPhwqSRpb7AWpHrg72lMA5Up/pAtqNKtqYQMd3Oc\nL/YkOrDiKRa/CVbpXZWeWJ7Y59MF84JPIdTFfw4iYvFiBRE+91JHBD6K42qqkSTCIhKUhPB15r6k\nLBgRT1fL0dU60vBGTyKwZI/dodVqdv+EU52WYZlmySU+Bsp5WF5VBVDUQCgJaBjc5p7/zgkxzwKS\nBrr9fY3AEMyHW8beMQsNkLTozGqqmQYO9O+I7yn8rVUjlVlNlOimje5defMA5BSmJ5Yndk2+1l0Z\nrcLWbij+LRGBPFByKoTE4UAQUeZehogEzf9BxiKzuR0SiCRCAvj8ZEkIicy9Xo6u8FFSas1y00ES\n9F2GavGycIThSmmmepr4dpHdW7P7hQsCzXaxmipUxJhTnZy/C6uqwBx02cMTGz8wq8fOx7TU62i/\nV0BiCLWxWZa1h0BCUoMlnZITc6pt6NmZBOiD68UQorDk8UjlzeHEJIU3LLrpeOBDkOOrC9MDrN0M\nBJuar14tV7Nm4YDiUPw7IgJlleSUgzOERENEmXsZIgJ5QnpctVhkmLvu3qninswXIonlvaNXS0Ig\nxNzq5Sg0vNEsb0ccXO3khmptN7xxljjh80WYxPzUURfavTm7f8SpNhfr/uzMKuZUXTWxaS7KsPKO\nNt6nFvqzAC0fbkVnis61kSQzumYWgXPF5lFn9RnBqWY0mPkL/jOn2rjfcIXT1JHNRBJ+iGJBI5XT\nXThhzr3cRXlk86Q0vWB54t4HAp8GunaeUSHG3Qrxb4iI3ZQLc4pkAYdEQ0SbeykQYYVEi0WqWQwP\niSqcRCZh3zN6WRK4DHsXKUfccKhqu596WhayHVWbDV9p+Vq76YdJeLnVutFFqCpAb310M6G3zjYJ\n7qa76rxUL408aOK74+yDFebVcvQuYHqFLLyBU+1dy9kvF79MAJAkKMaMGyBjAPrzAOM5zcrIeQ28\niOQVd6oX4qtDtosrivSN+CBopPJJWpaUKbyO8Sir9Janx5Yn7sj82mF4zEFtZYqlFP9+iDQ0p1gW\nUEgURNS5lwKRJiwkPhYZ5iu/Z6rQVzIJ+5bSKyWBSliuY+WIr9qsWG75sQcFBQu1threUEtQuj2L\nJMxTSl1i99bshqRe61Q7mFZ/g2pZ/xyGkxmneoN751XMqlzkYJVJCxb5B6Nyx3aE79g9M/LmY5kA\nIEmQwJwn2/lun9znRMGprtGAChPX3KneWOyJE3/BmmJy6T+1WCyRSqhRj2FnMpdJ7hQebZXewvRM\njZo2IcLYqU3YTSH0agjx74gIySmSBQEkCiLq3EuBSBNAImKRHk12RVRhz6GEi/aPIaD0WkkIhOCt\nLEeB4SKODpzWBh4zVdTaaDizBNWcz5rlq+3emt2gwmudKrf92DvnU6EmfKzkDdK4Ux3izfXe1Mhl\n2HweLRskPEcqbQv0nKjpMS7Jo67SW5aeWJ5YM0ybYinEa4yL3r8VEaIXyYIQkohhYu6lQKRhnEos\nkmWruyGquGfLhUwCXlB6tSSEUpZ7UY5Cw7n+yAURtUewN7tQa5vhzJJAaZHEBrv3ZLc2zTpQsd6u\nR4A7VaX6giJbG4kirWh8Ic9LpNKO8Z1woQJJxp4oPMWr9Cq84Uq9N8W3F02xfENESE7RLAgg0RAB\nx1Iw9zKEBAf5sfwUN1QV8VJ5QOmLS4Lp/7eyKHdgeKNZ3pnOfDKQXFEI6nVBs6vM8Hn1i9LvgFEX\n2b09u/Vp1qrpP/eQDs7NLf33c1rylLlTpXPGOB20pk0N23echq/9/bLYWTdHS8x80PyxhQellvCW\n6I3y2PkdEXE5lcqCzYiIeaphLJLhhzcpVZCGntfSL7wvLQtFhjfrLFlHba3+5uymuVKvixDgTlX9\nFV/k2AWnC2qqGKlcOvaKSt4WHjSvhDe/Nx1KE2etXvPLEXE5lciCHYiQQqLGIgWE5kFClUPoZyEv\nKwvlhq+0fC1OYPd3Z7eaP/VhAoELH7yQ2CHvCsMh+CBqVSxGKqdHNx+3eJwWBWzhWcU7FFWXUSQ7\nvx8i0Ks651QqC3YgAsFHh5AZxBTGIt1LcpFShZC5y7X0M2NROdph+QbDm3WWrKOerf7u7HaZUi8K\nEbiZ2WL+mAM0/p5ePZ6D7P2nBPYaI5Xz2Q5XUDt3KeMWHuQv4rULvCLHuvP7IQJubs6pVBbsQATa\n/24cTFEsEgBPqaLlx1r6WcYLy0Kp4Sst32T3N2e3lj/1WQqBh19ywZKN2+t0qWR+9t2uTs6KiMi8\nd4bkT5aFXUaL7K8Pcgh8BT0W4QzoHP87vC/YiiFhRkVEgPPGkPzJsrDPaJH99UEGgfGLL1ry+Lyq\n6k6TdrJn8P+R13tN2sv/I0bbRHdqvpP9h+x+T61/CKxDkj3RBTJAoplI9lFHf8kNQMyYWxERAL0r\nJH+yLOw2WmR/fZBD4MwDAO27DLHN2bW8b83uKbuOioiA700h+ZNlYb/RIvvrgywCJ74UU2/GyXzO\ncfOrLmw1qiIikHtPSP5kWTjAaJH99UEWgcnO6nNk/c8vSeB02X3RkqUWNguriAjo3hGSP1kWDjFa\nZH99oCLwP0sxj7APi2OuAAAAAElFTkSuQmCC\n",
+      "text/latex": [
+       "$$\\begin{cases} \\left(- \\frac{521}{6} + \\frac{95 x}{2 \\Delta} - \\frac{17 x^{2}}{2 \\Delta^{2}} + \\frac{x^{3}}{2 \\Delta^{3}}\\right) c_{6} + \\left(36 - \\frac{18 x}{\\Delta} + \\frac{3 x^{2}}{\\Delta^{2}} - \\frac{x^{3}}{6 \\Delta^{3}}\\right) c_{5} + \\left(\\frac{218}{3} - \\frac{42 x}{\\Delta} + \\frac{8 x^{2}}{\\Delta^{2}} - \\frac{x^{3}}{2 \\Delta^{3}}\\right) c_{7} & \\text{for}\\: 5 \\Delta \\leq x \\wedge x < 6 \\Delta \\\\\\left(- \\frac{131}{6} + \\frac{39 x}{2 \\Delta} - \\frac{11 x^{2}}{2 \\Delta^{2}} + \\frac{x^{3}}{2 \\Delta^{3}}\\right) c_{4} + \\left(- \\frac{9}{2} + \\frac{9 x}{2 \\Delta} - \\frac{3 x^{2}}{2 \\Delta^{2}} + \\frac{x^{3}}{6 \\Delta^{3}}\\right) c_{6} + \\left(\\frac{32}{3} - \\frac{8 x}{\\Delta} + \\frac{2 x^{2}}{\\Delta^{2}} - \\frac{x^{3}}{6 \\Delta^{3}}\\right) c_{3} + \\left(\\frac{50}{3} - \\frac{16 x}{\\Delta} + \\frac{5 x^{2}}{\\Delta^{2}} - \\frac{x^{3}}{2 \\Delta^{3}}\\right) c_{5} & \\text{for}\\: 3 \\Delta \\leq x \\wedge x < 4 \\Delta \\\\\\left(- \\frac{430}{3} + \\frac{66 x}{\\Delta} - \\frac{10 x^{2}}{\\Delta^{2}} + \\frac{x^{3}}{2 \\Delta^{3}}\\right) c_{7} + \\left(\\frac{343}{6} - \\frac{49 x}{2 \\Delta} + \\frac{7 x^{2}}{2 \\Delta^{2}} - \\frac{x^{3}}{6 \\Delta^{3}}\\right) c_{6} & \\text{for}\\: 6 \\Delta \\leq x \\wedge x < 7 \\Delta \\\\\\left(\\frac{2}{3} - \\frac{x^{2}}{\\Delta^{2}} + \\frac{x^{3}}{2 \\Delta^{3}}\\right) c_{1} + \\left(\\frac{1}{6} - \\frac{x}{2 \\Delta} + \\frac{x^{2}}{2 \\Delta^{2}} - \\frac{x^{3}}{6 \\Delta^{3}}\\right) c_{0} + \\left(\\frac{1}{6} + \\frac{x}{2 \\Delta} + \\frac{x^{2}}{2 \\Delta^{2}} - \\frac{x^{3}}{2 \\Delta^{3}}\\right) c_{2} + \\frac{x^{3} c_{3}}{6 \\Delta^{3}} & \\text{for}\\: 0 \\leq x \\wedge x < \\Delta \\\\\\left(- \\frac{22}{3} + \\frac{10 x}{\\Delta} - \\frac{4 x^{2}}{\\Delta^{2}} + \\frac{x^{3}}{2 \\Delta^{3}}\\right) c_{3} + \\left(- \\frac{4}{3} + \\frac{2 x}{\\Delta} - \\frac{x^{2}}{\\Delta^{2}} + \\frac{x^{3}}{6 \\Delta^{3}}\\right) c_{5} + \\left(\\frac{9}{2} - \\frac{9 x}{2 \\Delta} + \\frac{3 x^{2}}{2 \\Delta^{2}} - \\frac{x^{3}}{6 \\Delta^{3}}\\right) c_{2} + \\left(\\frac{31}{6} - \\frac{15 x}{2 \\Delta} + \\frac{7 x^{2}}{2 \\Delta^{2}} - \\frac{x^{3}}{2 \\Delta^{3}}\\right) c_{4} & \\text{for}\\: 2 \\Delta \\leq x \\wedge x < 3 \\Delta \\\\\\left(- \\frac{5}{6} - \\frac{7 x}{2 \\Delta} - \\frac{5 x^{2}}{2 \\Delta^{2}} - \\frac{x^{3}}{2 \\Delta^{3}}\\right) c_{0} + \\left(\\frac{4}{3} + \\frac{2 x}{\\Delta} + \\frac{x^{2}}{\\Delta^{2}} + \\frac{x^{3}}{6 \\Delta^{3}}\\right) c_{1} & \\text{for}\\: - 2 \\Delta \\leq x \\wedge x < - \\Delta \\\\\\left(\\frac{2}{3} - \\frac{x^{2}}{\\Delta^{2}} - \\frac{x^{3}}{2 \\Delta^{3}}\\right) c_{1} + \\left(\\frac{1}{6} - \\frac{x}{2 \\Delta} + \\frac{x^{2}}{2 \\Delta^{2}} + \\frac{x^{3}}{2 \\Delta^{3}}\\right) c_{0} + \\left(\\frac{1}{6} + \\frac{x}{2 \\Delta} + \\frac{x^{2}}{2 \\Delta^{2}} + \\frac{x^{3}}{6 \\Delta^{3}}\\right) c_{2} & \\text{for}\\: - \\Delta \\leq x \\wedge x < 0 \\\\\\left(\\frac{9}{2} + \\frac{9 x}{2 \\Delta} + \\frac{3 x^{2}}{2 \\Delta^{2}} + \\frac{x^{3}}{6 \\Delta^{3}}\\right) c_{0} & \\text{for}\\: - 3 \\Delta \\leq x \\wedge x < - 2 \\Delta \\\\\\left(- \\frac{142}{3} + \\frac{32 x}{\\Delta} - \\frac{7 x^{2}}{\\Delta^{2}} + \\frac{x^{3}}{2 \\Delta^{3}}\\right) c_{5} + \\left(- \\frac{32}{3} + \\frac{8 x}{\\Delta} - \\frac{2 x^{2}}{\\Delta^{2}} + \\frac{x^{3}}{6 \\Delta^{3}}\\right) c_{7} + \\left(\\frac{125}{6} - \\frac{25 x}{2 \\Delta} + \\frac{5 x^{2}}{2 \\Delta^{2}} - \\frac{x^{3}}{6 \\Delta^{3}}\\right) c_{4} + \\left(\\frac{229}{6} - \\frac{55 x}{2 \\Delta} + \\frac{13 x^{2}}{2 \\Delta^{2}} - \\frac{x^{3}}{2 \\Delta^{3}}\\right) c_{6} & \\text{for}\\: 4 \\Delta \\leq x \\wedge x < 5 \\Delta \\\\\\left(\\frac{256}{3} - \\frac{32 x}{\\Delta} + \\frac{4 x^{2}}{\\Delta^{2}} - \\frac{x^{3}}{6 \\Delta^{3}}\\right) c_{7} & \\text{for}\\: 7 \\Delta \\leq x \\wedge x < 8 \\Delta \\\\\\left(- \\frac{5}{6} + \\frac{7 x}{2 \\Delta} - \\frac{5 x^{2}}{2 \\Delta^{2}} + \\frac{x^{3}}{2 \\Delta^{3}}\\right) c_{2} + \\left(- \\frac{1}{6} + \\frac{x}{2 \\Delta} - \\frac{x^{2}}{2 \\Delta^{2}} + \\frac{x^{3}}{6 \\Delta^{3}}\\right) c_{4} + \\left(\\frac{2}{3} - \\frac{2 x}{\\Delta} + \\frac{2 x^{2}}{\\Delta^{2}} - \\frac{x^{3}}{2 \\Delta^{3}}\\right) c_{3} + \\left(\\frac{4}{3} - \\frac{2 x}{\\Delta} + \\frac{x^{2}}{\\Delta^{2}} - \\frac{x^{3}}{6 \\Delta^{3}}\\right) c_{1} & \\text{for}\\: \\Delta \\leq x \\wedge x < 2 \\Delta \\end{cases}$$"
+      ],
+      "text/plain": [
+       "⎧                 ⎛                   2     3 ⎞        ⎛               2     3\n",
+       "⎪                 ⎜  521   95⋅x   17⋅x     x  ⎟        ⎜     18⋅x   3⋅x     x \n",
+       "⎪                 ⎜- ─── + ──── - ───── + ────⎟⋅c[6] + ⎜36 - ──── + ──── - ───\n",
+       "⎪                 ⎜   6    2⋅Δ        2      3⎟        ⎜      Δ       2       \n",
+       "⎪                 ⎝                2⋅Δ    2⋅Δ ⎠        ⎝             Δ     6⋅Δ\n",
+       "⎪                                                                             \n",
+       "⎪  ⎛                   2     3 ⎞        ⎛               2     3 ⎞        ⎛    \n",
+       "⎪  ⎜  131   39⋅x   11⋅x     x  ⎟        ⎜  9   9⋅x   3⋅x     x  ⎟        ⎜32  \n",
+       "⎪  ⎜- ─── + ──── - ───── + ────⎟⋅c[4] + ⎜- ─ + ─── - ──── + ────⎟⋅c[6] + ⎜── -\n",
+       "⎪  ⎜   6    2⋅Δ        2      3⎟        ⎜  2   2⋅Δ      2      3⎟        ⎜3   \n",
+       "⎪  ⎝                2⋅Δ    2⋅Δ ⎠        ⎝            2⋅Δ    6⋅Δ ⎠        ⎝    \n",
+       "⎪                                                                             \n",
+       "⎪                                  ⎛                   2     3 ⎞        ⎛     \n",
+       "⎪                                  ⎜  430   66⋅x   10⋅x     x  ⎟        ⎜343  \n",
+       "⎪                                  ⎜- ─── + ──── - ───── + ────⎟⋅c[7] + ⎜─── -\n",
+       "⎪                                  ⎜   3     Δ        2       3⎟        ⎜ 6   \n",
+       "⎪                                  ⎝                 Δ     2⋅Δ ⎠        ⎝     \n",
+       "⎪                                                                             \n",
+       "⎪                      ⎛     2     3 ⎞        ⎛            2      3 ⎞        ⎛\n",
+       "⎪                      ⎜2   x     x  ⎟        ⎜1    x     x      x  ⎟        ⎜\n",
+       "⎪                      ⎜─ - ── + ────⎟⋅c[1] + ⎜─ - ─── + ──── - ────⎟⋅c[0] + ⎜\n",
+       "⎪                      ⎜3    2      3⎟        ⎜6   2⋅Δ      2      3⎟        ⎜\n",
+       "⎪                      ⎝    Δ    2⋅Δ ⎠        ⎝          2⋅Δ    6⋅Δ ⎠        ⎝\n",
+       "⎪                                                                             \n",
+       "⎪    ⎛                 2     3 ⎞        ⎛             2     3 ⎞        ⎛      \n",
+       "⎪    ⎜  22   10⋅x   4⋅x     x  ⎟        ⎜  4   2⋅x   x     x  ⎟        ⎜9   9⋅\n",
+       "⎪    ⎜- ── + ──── - ──── + ────⎟⋅c[3] + ⎜- ─ + ─── - ── + ────⎟⋅c[5] + ⎜─ - ──\n",
+       "⎪    ⎜  3     Δ       2       3⎟        ⎜  3    Δ     2      3⎟        ⎜2   2⋅\n",
+       "⎪    ⎝               Δ     2⋅Δ ⎠        ⎝            Δ    6⋅Δ ⎠        ⎝      \n",
+       "⎪                                                                             \n",
+       "⎪                                      ⎛               2     3 ⎞        ⎛     \n",
+       "⎪                                      ⎜  5   7⋅x   5⋅x     x  ⎟        ⎜4   2\n",
+       "⎨                                      ⎜- ─ - ─── - ──── - ────⎟⋅c[0] + ⎜─ + ─\n",
+       "⎪                                      ⎜  6   2⋅Δ      2      3⎟        ⎜3    \n",
+       "⎪                                      ⎝            2⋅Δ    2⋅Δ ⎠        ⎝     \n",
+       "⎪                                                                             \n",
+       "⎪                           ⎛     2     3 ⎞        ⎛            2      3 ⎞    \n",
+       "⎪                           ⎜2   x     x  ⎟        ⎜1    x     x      x  ⎟    \n",
+       "⎪                           ⎜─ - ── - ────⎟⋅c[1] + ⎜─ - ─── + ──── + ────⎟⋅c[0\n",
+       "⎪                           ⎜3    2      3⎟        ⎜6   2⋅Δ      2      3⎟    \n",
+       "⎪                           ⎝    Δ    2⋅Δ ⎠        ⎝          2⋅Δ    2⋅Δ ⎠    \n",
+       "⎪                                                                             \n",
+       "⎪                                                      ⎛             2     3 ⎞\n",
+       "⎪                                                      ⎜9   9⋅x   3⋅x     x  ⎟\n",
+       "⎪                                                      ⎜─ + ─── + ──── + ────⎟\n",
+       "⎪                                                      ⎜2   2⋅Δ      2      3⎟\n",
+       "⎪                                                      ⎝          2⋅Δ    6⋅Δ ⎠\n",
+       "⎪                                                                             \n",
+       "⎪⎛                  2     3 ⎞        ⎛                2     3 ⎞        ⎛      \n",
+       "⎪⎜  142   32⋅x   7⋅x     x  ⎟        ⎜  32   8⋅x   2⋅x     x  ⎟        ⎜125   \n",
+       "⎪⎜- ─── + ──── - ──── + ────⎟⋅c[5] + ⎜- ── + ─── - ──── + ────⎟⋅c[7] + ⎜─── - \n",
+       "⎪⎜   3     Δ       2       3⎟        ⎜  3     Δ      2       3⎟        ⎜ 6    \n",
+       "⎪⎝                Δ     2⋅Δ ⎠        ⎝              Δ     6⋅Δ ⎠        ⎝      \n",
+       "⎪                                                                             \n",
+       "⎪                                                    ⎛                2     3 \n",
+       "⎪                                                    ⎜256   32⋅x   4⋅x     x  \n",
+       "⎪                                                    ⎜─── - ──── + ──── - ────\n",
+       "⎪                                                    ⎜ 3     Δ       2       3\n",
+       "⎪                                                    ⎝              Δ     6⋅Δ \n",
+       "⎪                                                                             \n",
+       "⎪      ⎛               2     3 ⎞        ⎛              2      3 ⎞        ⎛    \n",
+       "⎪      ⎜  5   7⋅x   5⋅x     x  ⎟        ⎜  1    x     x      x  ⎟        ⎜2   \n",
+       "⎪      ⎜- ─ + ─── - ──── + ────⎟⋅c[2] + ⎜- ─ + ─── - ──── + ────⎟⋅c[4] + ⎜─ - \n",
+       "⎪      ⎜  6   2⋅Δ      2      3⎟        ⎜  6   2⋅Δ      2      3⎟        ⎜3   \n",
+       "⎩      ⎝            2⋅Δ    2⋅Δ ⎠        ⎝            2⋅Δ    6⋅Δ ⎠        ⎝    \n",
+       "\n",
+       " ⎞        ⎛                2     3 ⎞                                          \n",
+       " ⎟        ⎜218   42⋅x   8⋅x     x  ⎟                                          \n",
+       "─⎟⋅c[5] + ⎜─── - ──── + ──── - ────⎟⋅c[7]                     for 5⋅Δ ≤ x ∧ x \n",
+       "3⎟        ⎜ 3     Δ       2       3⎟                                          \n",
+       " ⎠        ⎝              Δ     2⋅Δ ⎠                                          \n",
+       "                                                                              \n",
+       "          2     3 ⎞        ⎛               2     3 ⎞                          \n",
+       " 8⋅x   2⋅x     x  ⎟        ⎜50   16⋅x   5⋅x     x  ⎟                          \n",
+       " ─── + ──── - ────⎟⋅c[3] + ⎜── - ──── + ──── - ────⎟⋅c[5]     for 3⋅Δ ≤ x ∧ x \n",
+       "  Δ      2       3⎟        ⎜3     Δ       2       3⎟                          \n",
+       "        Δ     6⋅Δ ⎠        ⎝             Δ     2⋅Δ ⎠                          \n",
+       "                                                                              \n",
+       "           2     3 ⎞                                                          \n",
+       " 49⋅x   7⋅x     x  ⎟                                                          \n",
+       " ──── + ──── - ────⎟⋅c[6]                                     for 6⋅Δ ≤ x ∧ x \n",
+       " 2⋅Δ       2      3⎟                                                          \n",
+       "        2⋅Δ    6⋅Δ ⎠                                                          \n",
+       "                                                                              \n",
+       "            2      3 ⎞         3                                              \n",
+       "1    x     x      x  ⎟        x ⋅c[3]                                         \n",
+       "─ + ─── + ──── - ────⎟⋅c[2] + ───────                           for 0 ≤ x ∧ x \n",
+       "6   2⋅Δ      2      3⎟             3                                          \n",
+       "          2⋅Δ    2⋅Δ ⎠          6⋅Δ                                           \n",
+       "                                                                              \n",
+       "       2     3 ⎞        ⎛               2     3 ⎞                             \n",
+       "x   3⋅x     x  ⎟        ⎜31   15⋅x   7⋅x     x  ⎟                             \n",
+       "─ + ──── - ────⎟⋅c[2] + ⎜── - ──── + ──── - ────⎟⋅c[4]        for 2⋅Δ ≤ x ∧ x \n",
+       "Δ      2      3⎟        ⎜6    2⋅Δ       2      3⎟                             \n",
+       "    2⋅Δ    6⋅Δ ⎠        ⎝            2⋅Δ    2⋅Δ ⎠                             \n",
+       "                                                                              \n",
+       "      2     3 ⎞                                                               \n",
+       "⋅x   x     x  ⎟                                                               \n",
+       "── + ── + ────⎟⋅c[1]                                          for -2⋅Δ ≤ x ∧ x\n",
+       "Δ     2      3⎟                                                               \n",
+       "     Δ    6⋅Δ ⎠                                                               \n",
+       "                                                                              \n",
+       "    ⎛            2      3 ⎞                                                   \n",
+       "    ⎜1    x     x      x  ⎟                                                   \n",
+       "] + ⎜─ + ─── + ──── + ────⎟⋅c[2]                               for -Δ ≤ x ∧ x \n",
+       "    ⎜6   2⋅Δ      2      3⎟                                                   \n",
+       "    ⎝          2⋅Δ    6⋅Δ ⎠                                                   \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "⋅c[0]                                                        for -3⋅Δ ≤ x ∧ x \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "                                                                              \n",
+       "          2     3 ⎞        ⎛                 2     3 ⎞                        \n",
+       "25⋅x   5⋅x     x  ⎟        ⎜229   55⋅x   13⋅x     x  ⎟                        \n",
+       "──── + ──── - ────⎟⋅c[4] + ⎜─── - ──── + ───── - ────⎟⋅c[6]   for 4⋅Δ ≤ x ∧ x \n",
+       "2⋅Δ       2      3⎟        ⎜ 6    2⋅Δ        2      3⎟                        \n",
+       "       2⋅Δ    6⋅Δ ⎠        ⎝              2⋅Δ    2⋅Δ ⎠                        \n",
+       "                                                                              \n",
+       "⎞                                                                             \n",
+       "⎟                                                                             \n",
+       "⎟⋅c[7]                                                        for 7⋅Δ ≤ x ∧ x \n",
+       "⎟                                                                             \n",
+       "⎠                                                                             \n",
+       "                                                                              \n",
+       "         2     3 ⎞        ⎛           2     3 ⎞                               \n",
+       "2⋅x   2⋅x     x  ⎟        ⎜4   2⋅x   x     x  ⎟                               \n",
+       "─── + ──── - ────⎟⋅c[3] + ⎜─ - ─── + ── - ────⎟⋅c[1]           for Δ ≤ x ∧ x <\n",
+       " Δ      2       3⎟        ⎜3    Δ     2      3⎟                               \n",
+       "       Δ     2⋅Δ ⎠        ⎝          Δ    6⋅Δ ⎠                               \n",
+       "\n",
+       "      \n",
+       "      \n",
+       "< 6⋅Δ \n",
+       "      \n",
+       "      \n",
+       "      \n",
+       "      \n",
+       "      \n",
+       "< 4⋅Δ \n",
+       "      \n",
+       "      \n",
+       "      \n",
+       "      \n",
+       "      \n",
+       "< 7⋅Δ \n",
+       "      \n",
+       "      \n",
+       "      \n",
+       "      \n",
+       "      \n",
+       "< Δ   \n",
+       "      \n",
+       "      \n",
+       "      \n",
+       "      \n",
+       "      \n",
+       "< 3⋅Δ \n",
+       "      \n",
+       "      \n",
+       "      \n",
+       "      \n",
+       "      \n",
+       " < -Δ \n",
+       "      \n",
+       "      \n",
+       "      \n",
+       "      \n",
+       "      \n",
+       "< 0   \n",
+       "      \n",
+       "      \n",
+       "      \n",
+       "      \n",
+       "      \n",
+       "< -2⋅Δ\n",
+       "      \n",
+       "      \n",
+       "      \n",
+       "      \n",
+       "      \n",
+       "< 5⋅Δ \n",
+       "      \n",
+       "      \n",
+       "      \n",
+       "      \n",
+       "      \n",
+       "< 8⋅Δ \n",
+       "      \n",
+       "      \n",
+       "      \n",
+       "      \n",
+       "      \n",
+       " 2⋅Δ  \n",
+       "      \n",
+       "      "
+      ]
+     },
+     "execution_count": 17,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# Now create the spline from the basis functions\n",
+    "jastrow_cond_map = transpose_interval_and_coefficients(jastrow_sym_basis)\n",
+    "c = IndexedBase('c',shape=(nknots+3))\n",
+    "#c = MatrixSymbol('c',nknots+3,1)\n",
+    "jastrow_spline = recreate_piecewise(jastrow_cond_map, c)\n",
+    "jastrow_spline"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGgAAAAlBAMAAABc9LEgAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nYII=\n",
+      "text/latex": [
+       "$$- \\frac{c_{0}}{2 \\Delta} + \\frac{c_{2}}{2 \\Delta}$$"
+      ],
+      "text/plain": [
+       "  c[0]   c[2]\n",
+       "- ──── + ────\n",
+       "  2⋅Δ    2⋅Δ "
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAALgAAAAlBAMAAAAD5T5pAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nIAHP0QAAAABJRU5ErkJggg==\n",
+      "text/latex": [
+       "$$- A - \\frac{c_{0}}{2 \\Delta} + \\frac{c_{2}}{2 \\Delta} = 0$$"
+      ],
+      "text/plain": [
+       "     c[0]   c[2]    \n",
+       "-A - ──── + ──── = 0\n",
+       "     2⋅Δ    2⋅Δ     "
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJQAAAASBAMAAABP++oiAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
+      "text/latex": [
+       "$$c_{0} = - 2 A \\Delta + c_{2}$$"
+      ],
+      "text/plain": [
+       "c₀ = -2⋅A⋅Δ + c[2]"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Boundary conditions at r = 0 with the cusp (first derivative) condition\n",
+    "\n",
+    "cusp_val = Symbol('A')\n",
+    "# Evaluate spline derivative at 0\n",
+    "du = diff(jastrow_spline,xs)\n",
+    "du_zero = du.subs(xs, 0)\n",
+    "display(du_zero)\n",
+    "\n",
+    "# Solve following equation\n",
+    "display(Eq(du_zero-cusp_val,0))\n",
+    "\n",
+    "# solve doesn't seem to work with Indexed value, substitute something else\n",
+    "c0 = Symbol('c0')\n",
+    "soln = solve(du_zero.subs(c[0],c0) - cusp_val, c0)\n",
+    "display(Eq(c0, soln[0]))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMUAAAAqBAMAAADxBIKUAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nmOMxn6jAvfE7OgfjfNc3YwHjtzGrdloAAAAASUVORK5CYII=\n",
+      "text/latex": [
+       "$$u{\\left (x \\right )} = \\frac{c_{5}}{6} + \\frac{2 c_{6}}{3} + \\frac{c_{7}}{6}$$"
+      ],
+      "text/plain": [
+       "       c[5]   2⋅c[6]   c[7]\n",
+       "u(x) = ──── + ────── + ────\n",
+       "        6       3       6  "
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMYAAAArBAMAAADRb+oyAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nTymROLlPCzF+qZou7IR/AbbnMFIQSNc6AAAAAElFTkSuQmCC\n",
+      "text/latex": [
+       "$$\\frac{d}{d x} u{\\left (x \\right )} = - \\frac{c_{5}}{2 \\Delta} + \\frac{c_{7}}{2 \\Delta}$$"
+      ],
+      "text/plain": [
+       "d            c[5]   c[7]\n",
+       "──(u(x)) = - ──── + ────\n",
+       "dx           2⋅Δ    2⋅Δ "
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQsAAAAvBAMAAAAGMfL1AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nAABJRU5ErkJggg==\n",
+      "text/latex": [
+       "$$\\frac{d^{2}}{d x^{2}}  u{\\left (x \\right )} = \\frac{1}{\\Delta^{2}} \\left(c_{5} - 2 c_{6} + c_{7}\\right)$$"
+      ],
+      "text/plain": [
+       "  2                             \n",
+       " d          c[5] - 2⋅c[6] + c[7]\n",
+       "───(u(x)) = ────────────────────\n",
+       "  2                   2         \n",
+       "dx                   Δ          "
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Boundary conditions at r=r_cut.  For smoothness the value and derivatives should be 0.\n",
+    "# Add zero value and derivatives at r_cut\n",
+    "eq_v = jastrow_spline.subs(xs, rcut)\n",
+    "display(Eq(Symbol('u')(xs),eq_v))\n",
+    "\n",
+    "eq_dv = diff(jastrow_spline, xs).subs(xs,rcut)\n",
+    "display(Eq(diff(Symbol('u')(xs),xs),eq_dv))\n",
+    "\n",
+    "eq_ddv = diff(jastrow_spline, xs, 2).subs(xs,rcut)\n",
+    "display(Eq(diff(Symbol('u')(xs),xs,2),eq_ddv))\n",
+    "\n",
+    "#eq_d3v = diff(jastrow_spline, xs, 3).subs(xs, rcut)\n",
+    "#display(eq_d3v)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAALkAAAAmBAMAAABqsyf5AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
+      "text/latex": [
+       "$$\\left\\{\\left ( c_{7}, \\quad - \\frac{c_{7}}{2}, \\quad c_{7}\\right )\\right\\}$$"
+      ],
+      "text/plain": [
+       "⎧⎛    -c₇     ⎞⎫\n",
+       "⎨⎜c₇, ────, c₇⎟⎬\n",
+       "⎩⎝     2      ⎠⎭"
+      ]
+     },
+     "execution_count": 20,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# Solve for all these equal to zero\n",
+    "c5 = Symbol('c5')\n",
+    "c6 = Symbol('c6')\n",
+    "c7 = Symbol('c7')\n",
+    "subs_list = {c[5]:c5, c[6]:c6, c[7]:c7}\n",
+    "linsolve([v.subs(subs_list) for v in [eq_v, eq_dv, eq_ddv]], [c5, c6, c7])\n",
+    "# QMCPACK enforces these conditions by setting c5, c6, c7 (the last three coefficients) to 0."
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
@@ -915,21 +1391,21 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 3",
+   "display_name": "Python 2",
    "language": "python",
-   "name": "python3"
+   "name": "python2"
   },
   "language_info": {
    "codemirror_mode": {
     "name": "ipython",
-    "version": 3
+    "version": 2
    },
    "file_extension": ".py",
    "mimetype": "text/x-python",
    "name": "python",
    "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.5.1"
+   "pygments_lexer": "ipython2",
+   "version": "2.7.12"
   }
  },
  "nbformat": 4,