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Jupyter notebooks illustrating different ways to couple two equations over different spatial domains in FiPy
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{ | |
"cells": [ | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Implementation of coupled boundary condition problem raised on the FiPy mailing list: http://comments.gmane.org/gmane.comp.python.fipy/4197\n", | |
"\n", | |
"This implemantation defines PDE1 on a Grid1D and PDE2 on a Grid2D and manually copies the data from one to the other for each sweep." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 1, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"%matplotlib inline" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 32, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"from matplotlib import pyplot as plt" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 2, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"import fipy as fp" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 5, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"nx = 10\n", | |
"ny = 10\n", | |
"Lx = 1.\n", | |
"Ly = 1." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 7, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"S = 1." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 62, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"def f(w, a):\n", | |
" return w**3 * a" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 63, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [], | |
"source": [ | |
"mesh1 = fp.Grid1D(nx=nx, Lx=Lx)\n", | |
"\n", | |
"x1, = mesh1.cellCenters\n", | |
"X1, = mesh1.faceCenters\n", | |
"\n", | |
"a = fp.CellVariable(mesh=mesh1)\n", | |
"w = fp.CellVariable(mesh=mesh1)\n", | |
"\n", | |
"eq1 = fp.DiffusionTerm(coeff=S) == f(w, a)\n", | |
"\n", | |
"a.constrain(0, where=X1 == 0)\n", | |
"a.faceGrad.constrain(1, where=X1 == 1)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 64, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"D = 1." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 65, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"def g(w, a):\n", | |
" return w+a" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 66, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [], | |
"source": [ | |
"mesh2 = fp.Grid2D(nx=nx, ny=ny, Lx=Lx, Ly=Ly)\n", | |
"\n", | |
"x2, y2 = mesh2.cellCenters\n", | |
"X2, Y2 = mesh2.faceCenters\n", | |
"\n", | |
"B = fp.CellVariable(mesh=mesh2, hasOld=True)\n", | |
"a2 = fp.FaceVariable(mesh=mesh2)\n", | |
"\n", | |
"eq2 = fp.TransientTerm() == fp.DiffusionTerm(coeff=[[[0, 0], [0, D]]])\n", | |
"\n", | |
"B.constrain(0, where=Y2 == 0)\n", | |
"B.faceGrad.constrain(g(B.faceValue, a2), where=Y2 == 1)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 67, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"steps = 10\n", | |
"dt = 1." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 69, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
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Z8fW6xT1XMyu/FmWBMnJyNbPyq2CmqmDIZjbqVDBTVTBkMxt1KpipKhiymY06rrmamSVQ\nwUxVwZDNbNSpYKaqYMhmNuq4LGBmlkAFM1UFQzazUaeCmaqCIZvZqOOygJlZAhXMVBUM2cxGnQpm\nqgqGbGajTgUzVQVDNrNRxzVXM7MEKpipKhiymY06FcxUr+l1AGZmLY3pcGtAUr+k9ZI2SLpkmDZ9\nklZLekzSQJGQK/j/gZmNOgUzlaQxwCKyBQifBh6StDwi1tW0mQB8GXhPRGyRNLHINZ1czaz8imeq\nmcDGiNgEIGkZcBawrqbNB4GbI2ILQEQ8X+SCScsCrbrhkg6WdKukR/Ju+Pkp4zGziipeFpgCbK7Z\n35I/V2sGcKikuyStkvSRIiEn67m20w0HPgk8FhF/nnfBfyLpmxExmCouM6ugFplqYCsM/FvTJu0s\ncz0OOAl4N3AQcL+kByJiQ3tB7illWaCdbvgrwPj88XhguxOrme3lwOaH+47ItiGXr96rydPAtJr9\naWS911qbgecjYgewQ9I9wAnAiJJryrJAO93wRcBxkrYCa4CLEsZjZlVVvCywCpghabqkA4BzgOV1\nbf4ZeLukMZIOAmYBj4805JQ913a64f3AwxFxiqQjgZWSToiIX+3ZbKDm8fR8M7Py2pRvXVIwU0XE\noKR5wJ1k6fe6iFgn6YL8+JKIWC/pDmAt2W/VSyOilMm1nW74+cCVABHxpKSfAm8k+1+mRl+iEM0s\njens2Qm6u9jpupCpIuJ24Pa655bU7X8R+GLxq6UtC7TTDf852YAXkiaRJdanEsZkZlXUhS8R7GvJ\neq7tdMOBK4CvS1oLCPhMRLyQKiYzq6gKzshPGnKrbnhE/BvwnpQxmNl+wMnVzCyBCmaqCoZsZqNO\nSeqonXByNbPyq2CmqmDIZjbqVDBTVTBkMxt1XBYwM0uggpmqgiGb2ahTwUxVwZDNbNRxWcDMLIEK\nZqoKhmxmo04FM1UFQzazUaeCmaqCIZvZqOOaq5lZAhXMVElXfzUz64qxHW4NtFqNuqbdyZIGJZ1d\nNGQzs3IrWBZoczXqoXZXA3eQ3WN6xNxzNbPyK95z3b0adUTsBIZWo653IXAT8Fw3QjYzK7fimarR\natSzahtImkKWcE8FTqa9RVaH5eRqZuXXoiww8DAMrG7apJ1EeQ0wPyJCkihYFnByNbPya5Gp+mZm\n25DLb9irSTurUb8FWJblVSYCZ0jaGRH1C6u2xcnVzMqveKbavRo1sJVsNepzaxtExBFDjyXdANw6\n0sQKTq5mVgUFM1Wbq1F3lZOrmZVfF76h1Wo16rrnP1r0ek6uZlZ+FcxUFQzZzEadCmaqCoZsZqOO\nb9xiZpZABTNVBUM2s1GngpmqgiGb2ahTwUxVwZDNbLQJ11zNzLpvVwUzVQVDNrPRxsnVzCyBwTGd\n3nr6lSRxdMLJ1cxKb9fYTlPV75PE0QknVzMrvV1jqjei5eRqZqW3q4Jf0XJyNbPSG3RyNTPrvl0V\nTFXVi9jMRp0qlgW8tLaZld4uxnS0NSKpX9J6SRskXdLg+IckrZG0VtJ9ko4vEnOy5NrqjeRt+iSt\nlvSYpIFUsZhZtRVNrpLGAIuAfuA44FxJx9Y1ewp4Z0QcD1wBfLVIzEnKAjVv5DSyVRcfkrQ8ItbV\ntJkAfBl4T0RskTQxRSxmVn1dGNCaCWyMiE0AkpYBZwG7c1JE3F/T/kFgapELpqq5tnwjwAeBmyNi\nC0BEPJ8oFjOruC4MaE0BNtfsbwFmNWn/cWBFkQumSq7tvJEZwDhJdwGvA74UEf87UTxmVmFdGNCK\ndhtKOgX4GPC2IhdMlVzbeSPjgJOAdwMHAfdLeiAiNiSKycwqqlVyXTXwMqsGftOsydPAtJr9aWSd\nvj3kg1hLgf6I+EXnkb4qVXJt541sBp6PiB3ADkn3ACcADZLrQM3j6flmZuW1Kd+6o1XN9c1943lz\n3/jd+1+9fK8q4ypghqTpwFbgHODc2gaSDge+C3w4IjYWjTlVcm35RoB/Bhblg19/QFY2+PvGp+tL\nE6WZJTKdPTtBdxc6W9Gaa0QMSpoH3Em23OF1EbFO0gX58SXA54BDgMWSAHZGxMyRXjNJcm3njUTE\nekl3AGvJ7g+2NCIeTxGPmVVbN75EEBG3A7fXPbek5vFfA39d+EK5ZN/QavVG8v0vAl9MFYOZ7R+q\n+A0tf/3VzErPydXMLAHfFcvMLAHfFcvMLAGXBczMEnByNTNLwDVXM7MEXHM1M0vAZQEzswR+xwG9\nDqFjTq5mVnouC5iZJeCygJlZAk6uZmYJOLmamSXgea5mZglUcUDrNb0OwMyslV2M6WhrRFK/pPWS\nNki6ZJg21+bH10g6sUjM1fvvwMxGnaI113w5qUXAaWRr/D0kaXlErKtpMwc4KiJmSJoFLAZmj/Sa\nTq5mVnpdqLnOBDZGxCYAScuAs4B1NW3mAjcCRMSDkiZImhQR20ZyQSdXMyu9LtRcp5CtOD1kC9mi\nqK3aTAWcXM1s/9SFqVjRZjuN8HV7cXI1s9JrlVx/NrCJnw38rFmTp4FpNfvTyHqmzdpMzZ8bESdX\nMyu9Vsl1at+RTO07cvf+jy6/p77JKmCGpOnAVuAc4Ny6NsuBecAySbOBX4603gpOrmZWAUUHtCJi\nUNI84E5gDHBdRKyTdEF+fElErJA0R9JG4GXgo0Wu6eRqZqXXjS8RRMTtwO11zy2p259X+EI5J1cz\nKz3fW8DMLAEnVzOzBHzjFjOzBKp445bqRWxmo47LAmZmCTi5mpkl4ORqZpaAB7TMzBLwgJaZWQIu\nC5iZJeDkamaWgGuuZmYJuOZqZpaAywJmZglUMbm+JtWJ21kjPG93sqRBSWenisXMqm2QMR1tZZAk\nudasEd4PHAecK+nYYdpdDdzB3guDmZkBWc21k60Tkg6VtFLSE5K+J2lCgzbTJN0l6ceSHpP0t63O\nm6rnunuN8IjYCQytEV7vQuAm4LlEcZjZfmAXYzraOjQfWBkRRwM/yPfr7QQujog/AWYDn2zUYayV\nKrk2Wv97Sm0DSVPIEu7i/KkRL2FrZvu3xMl1LnBj/vhG4H31DSLimYh4JH/8a2AdcFizk6Ya0Gon\nUV4DzI+IkCRcFjCzYSQe0JpUs8rrNmBSs8b5CrInAg82a5cqubazRvhbyJawBZgInCFpZ0Qs3/t0\nAzWPp+ebmZXXpnzrjqKDVJJWApMbHLqsdifv7A3bOZT0R2SlzIvyHuywUiXXlmuER8QRQ48l3QDc\n2jixAvSlidLMEpnOnp2guwudrdUg1csDq/jNwKphj0fE6cMdk7RN0uSIeEbS64Fnh2k3DrgZ+GZE\n3NIq5iTJtZ01wlNc18z2T63KAgf2zeLAvlm795+//KudnH45cB7ZzKXzgL0SZ166vA54PCKuaeek\niij3OFLWRV/Q6zDMrJDLiYgRjatIiiPjsY5e86T+tO3rSToU+A5wOFkt4wMR8UtJhwFLI+JMSW8H\n7gHW8uqY0mcj4o7hzutvaJlZ6aX8YkBEvACc1uD5rcCZ+eMf0eHsKidXMys937jFzCyBKt5bwMnV\nzErPydXMLIFdrzi5mpl13eCgk6uZWdftGqxeqqpexGY26uxyz9XMrPucXM3MEhjc6eRqZtZ1r+yq\nXqqqXsRmNvq4LGBmloCTq5lZAoPVW6jEydXMym+w1wF0zsnVzMrPydXMLAEnVzOzBHb2OoDOdXRn\nbTOzntjV4dYBSYdKWinpCUnfkzShSdsxklZLurXVeZ1czaz8BjvcOjMfWBkRRwM/yPeHcxHwOK+u\nozUsJ1czK7+0yXUucGP++EbgfY0aSZoKzAG+BrScG+aaq5mVX9oBrUkRsS1/vA2YNEy7fwA+DYxv\n56ROrmZWfq2S69oBeHRg2MOSVgKTGxy6rHYnIkLSXr/yS3ov8GxErJbU1ypccHI1syr4bYvjR/dl\n25BvXb7H4Yg4fbiXStomaXJEPCPp9cCzDZr9GTBX0hzgQGC8pG9ExF8Nd17XXM2s/HZ2uHVmOXBe\n/vg84Jb6BhFxaURMi4g3AH8J/LBZYgUnVzOrgoRTsYCrgNMlPQGcmu8j6TBJtw3zmpazBVwWMLPy\nSzigFREvAKc1eH4rcGaD5+8G7m51XidXMys/f/3VzCwBJ1czswScXM3MEnByNTNLwMnVzCyBCt5y\n0MnVzMqv87mrPefkambl57KAmVkCTq5mZgk4uZqZJeABLTOzBDygZWaWQAXLAklvOSipX9J6SRsk\nXdLg+IckrZG0VtJ9ko5PGY+ZVVTaNbSSSNZzlTQGWER2K6+ngYckLY+IdTXNngLeGREvSuoHvgrM\nThWTmVWUa657mAlsjIhNAJKWAWcBu5NrRNxf0/5BYGrCeMysqipYc01ZFpgCbK7Z35I/N5yPAysS\nxmNmVZWwLCDpUEkrJT0h6XuSJgzTboKkmyStk/S4pKa/ZafsubZcBmGIpFOAjwFva9xioObx9Hwz\ns/LalG9dkraOOh9YGRFfyMeG5udbvS8BKyLiP0kaC/xhs5OmTK5PA9Nq9qeR9V73kA9iLQX6I+IX\njU/V1/3ozCyh6ezZCWq5KkpzaWuuc4F35Y9vJOvN7ZFcJR0MvCMizgOIiEHgxWYnTVkWWAXMkDRd\n0gHAOWSrLO4m6XDgu8CHI2JjwljMrMrSLlA4KSK25Y+3AZMatHkD8JykGyQ9LGmppIOanTRZzzUi\nBiXNA+4ExgDXRcQ6SRfkx5cAnwMOARZLAtgZETNTxWRmFdWqLPD8AGwfGPawpJXA5AaHLqvdiYiQ\n1KikORY4CZgXEQ9Juoasd/u5Ya8Z0XZptCeyN7qg12GYWSGXExEaySslBWd0mKduV9vXk7Qe6IuI\nZyS9HrgrIo6pazMZuD8i3pDvvx2YHxHvHe68Sb9EYGbWFTs73DqzHDgvf3wecEt9g4h4Btgs6ej8\nqdOAHzc7qZOrmZVf2prrVcDpkp4ATs33kXSYpNtq2l0I/KOkNcDxwOebndT3FjCz8ks4FSsiXiDr\nidY/vxU4s2Z/DXByu+d1cjWz8ivJ/QI64eRqZuXnewuYmSVQwXsLOLmaWfm5LGBmloCTq5lZAq65\nmpkl4JqrmVkCLguYmSXg5GpmloBrrmZmCbjmamaWgMsCZmYJOLmamSXgmquZWQKuuZqZJVDu1aga\n8koEZjaqSTpU0kpJT0j6nqQJw7S7WNJjkh6V9C1Jf9DsvE6uZjbazQdWRsTRwA/y/T1ImkK2zMtb\nIuJNZCta/2Wzkzq5mtloNxe4MX98I/C+YdqNBQ6SNBY4CHi62UldczWzCkg6XWBSRGzLH28DJtU3\niIinJf0d8HNgB3BnRHy/2UmdXM2sAopNdJW0Epjc4NBltTsREZL2Gj6TdAhZD3c68CLwfyR9KCL+\ncbhrOrmaWQW06rneC/xo2KMRcfpwxyRtkzQ5Ip6R9Hrg2QbNTgN+GhHb89d8F/gzwMnVzKqsVc/1\nrfk25KpOTr4cOA+4Ov/zlgZtfgbMlvRa4LdkyfZfm53UA1pmVgE7O9w6chVwuqQngFPzfSQdJuk2\ngIj4V+Am4GFgbf66rzY7qSLKPTs3q38s6HUYZlbI5USERvLKLAds7vBV00Z8vW5xWcDMKqB6d25x\ncjWzCqjenVucXM2sAtxzNTNLwD1XM7ME3HM1M0vAPVczswTcczUzS8A9VzOzBNxzNTNLYEevA+iY\nk6uZVUD1ygJJb9wiqV/SekkbJF0yTJtr8+NrJJ2YMh4zq6qkN25JIlnPVdIYYBHZrbmeBh6StDwi\n1tW0mQMcFREzJM0CFgOzU8VkZlVVvZpryp7rTGBjRGyKiJ3AMuCsuja7166JiAeBCZL2WmLBzEa7\n6vVcUybXKex5n7At+XOt2kxNGJOZVdJgh1vvpRzQavdGsfX3XNzrdePHN10e3MxK7qWXip6hHL3R\nTqRMrk8D02r2p5H1TJu1mUqD5Wovvvh3ux/39fXR19fXtSDNrPsGBgYYGBjYvX/55UXPmK43Kuk/\nAwuBY4CTI+LhYdr1A9cAY4CvRcTVTc+baiWCfG3vnwDvBraSrTdzboMBrXkRMUfSbOCaiJhdd54o\n+2oJrQwMDFT6PwTH33tVfw+SCq5E8HcdvupTbV9P0jHAK8AS4FONkms+QP8Tagboqctn9ZLVXCNi\nEJgH3Al9a4e6AAADxklEQVQ8DvxTRKyTdIGkC/I2K4CnJG0ke2OfSBVPL9X+D15Fjr/39of3UEy6\nmmtErI+IJ1o0a2eAfg9Jv0QQEbcDt9c9t6Ruf17KGMxsf9DzmmujwfdZzV7gb2iZWQUUq7lKWglM\nbnDo0oi4tY1TdFybrMjqr2ZWdcVqrumvJ+kuhq+5zgYWRkR/vv9Z4JVmg1ql77n2enlcM+utfZwD\nhrvWKmCGpOlkA/TnAOc2O1HSewuYmZWdpL+QtJnsq/e3Sbo9f/4wSbfB8AP0Tc9b9rKAmVkVlabn\nWvU7aLWKX9KH8rjXSrpP0vG9iLOZdv4O8nYnSxqUdPa+jK+VNv8N9UlaLekxSQP7OMSm2vg3dLCk\nWyU9ksd/fg/CHJak6yVtk/Rokzal/Qx3XUT0fCP7xsNGYDowDngEOLauzRxgRf54FvBAr+PuMP63\nAgfnj/vLFH+776Gm3Q+BfwHe3+u4O/w7mAD8GJia70/sddwdxn8pcOVQ7MB2YGyvY6+J7x3AicCj\nwxwv7Wc4xVaWnmvV76DVMv6IuD8iXsx3H6R8N6hpd5L0hcBNwHP7Mrg2tBP/B4GbI2ILQEQ8v49j\nbKad+F8BxuePxwPbI6sFlkJE3Av8okmTMn+Gu64sybXqd9BqJ/5aHwdWJI2ocy3fg6QpZB/4xflT\nZSrYt/N3MAM4VNJdklZJ+sg+i661duJfBBwnaSuwBrhoH8XWLWX+DHddWaZide0OWj3SdhySTgE+\nBrwtXTgj0s57uAaYHxEhSQw/baUX2ol/HHAS2f0uDgLul/RARGxIGll72om/H3g4Ik6RdCSwUtIJ\nEfGrxLF1U1k/w11XluTatTto9Ug78ZMPYi0F+iOi2a9PvdDOe3gLsCzLq0wEzpC0MyKW75sQm2on\n/s3A8xGxA9gh6R7gBKAMybWd+M8HrgSIiCcl/RR4I9kczCoo82e4+3pd9M2L22OBJ8mK+QfQekBr\nNiUqhrcZ/+FkAxazex3vSN9DXfsbgLN7HXeHfwfHAN8nGzw6CHgUOK7XsXcQ/1eABfnjSWTJ99Be\nx14X43TaG9Aq1Wc4xVaKnmtEDEoamqA7Brgu8jto5ceXRMQKSXPyO2i9DHy0hyHvoZ34gc8BhwCL\n857fzoiY2auY67X5HkqrzX9D6yXdAawlGxxaGhGP9y7qV7X5878C+LqktWS/Xn8mIl7oWdB1JH0b\neBcwMZ+Uv4CsFFP6z3AK/hKBmVkCZZktYGa2X3FyNTNLwMnVzCwBJ1czswScXM3MEnByNTNLwMnV\nzCwBJ1czswT+P8+cEu/06PgmAAAAAElFTkSuQmCC\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x10e493a90>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"fig = plt.figure(figsize=(6, 5))\n", | |
"ax1 = fig.add_axes((0.15, 0.9, 0.55, 0.1))\n", | |
"ax2 = fig.add_axes((0.15, 0.1, 0.7, 0.7), sharex=ax1)\n", | |
"viewer1 = fp.Viewer(vars=a, axes=ax1, xmin=0., xmax=1.)\n", | |
"viewer2 = fp.Viewer(vars=B, axes=ax2, xmin=0., xmax=1., ymin=0., ymax=1.)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 70, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"a.value = 0.\n", | |
"B.value = 0." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 71, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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ynN6V/p15vO+WkRl3+OIRcPHT0vbND46ylPOcXw1Rg95eAuCHAYCZ30tE74dM\nxv6W2m+eAXdYrXztRj9zKo+uWyqwfBOfFBALRZhcW8QW4TIutQIjh6F3oQ16oQFC/4WIhgMRBtaO\n0ezdxyEpL2YEEqS03eG8TrCmDJMLnKtEXzc4qufzipAUeEx5l5m4+H/OXXZ/F7SfoO9onK4NiwL0\n19p/ShdbGRL0qu/TBriye64BGruFmxyyuryg7rAB7BjRmy/LY9AjyITsVpcYOIHPVKB2f9yfbU+c\ntwB4KhE9EcCHALwQQDkj5gcgDSe/R0RXQgD4vpMr0ola49ZYCru5bb9/DX5l2lLgLUjP6gotzkMv\n9gd0MIxdZiTM6ibFO7qEn6k/dv0DmVQ52fe3ThXqOjioeHc47xzjXeax8ivjxxAsuseoIhxYXV0S\n1zZ4MJLCzUPRQXPIPg3Uv3sozn+5ndUNJthFeeXUoMS6m4cdIIt7qNrlpXavIeWH36c0cnWBSPV5\nllZkTXV/9l5lIBQgtHdwm8AnYFsSh5kvEdHLAbwBcqVew8x3EdHLNP0WAD8I4LVEdDvkNHwvM3/s\nhIq0DzNitJKNJin7KhjWlk3TnNvll9SiS9InwdQeWz2VuWysas+pQg/DwVqNOfUR9ErQ+kzYNqv7\nG9chh6SvC0SusvJ+hK3uMG3lV28x9hA8Gis/AAFysmQEmUL5jeKcBoyjzpgrzCBtEYlfWQypbnAo\nr5130xR+FJWgv3mKfI0kcL3mexRRwtBHu/s1tvAep/VQK56DX/zEjtN70pZYH7jnOsFdEIeZXw/g\n9UXcLS78YQBfs8cirbE1p7tBvRJyrZpqhnu9ukNykb+8kadU3JrFtfrmHaZ93SDFEWNSGmD9BTEg\n1RXqlyTsji39CFUBRvA5FZgpQoUiKQwp5bE6tdh9xruXI9WX9x8ca8WxIiw7R/tW4tINNpUaKKiL\nHpzyS/v7f+l38hbiQf+2geA+rZBzZ8NN2fn218dGjeHsxijvSD3e1L1TxnmbebHG31Llx04BmgoM\nFuZUPlN+2WgzQ/p7g4OffZzUFBgnYdt3kdm5HbASbN01E9lrcLRwC4T+p6agNpdeAtDu0ujqOve3\nACNra3Bs9bUmu2BdZSRfdIm1YcQrQes0ZjD04VgfyAY77Ujs6gBZW1xNbRlc2qovD9fVXglBiT92\n4XJJ7u+Qr11ZrGPNqEuMrgdVuHGwCFOGnCvAUGwD8kLyjRrjWhfSOEcen6G4t0Z1frVbuAah0sU9\n1lvZVNwPepg8AAAgAElEQVRxcodjcQ18LmxfzASpHo3jC0YV6Fi+FztA4hxgkSaMkau7UvWxuzFL\n6LUAObfU8i3dt4SihRnuEznLp3V95iLHuj7ESh12ijDCEw50HnrabBgVoVN+o22rB8zqBOVfvXXY\nK0CO2swrQt/x2moTUz3jeCgtawUOrlHEgDyAM2jXxsuO/7JjyJvIg66spysBwE6pkDWEsHuB1Sg2\nd3+gqPOrpI+23U/5Bg+7n230l/hZIOttYRDUVnDW9AyGblk1luAu7ACJc4BF8lbAzkU3XeJWeglF\nS2vdwLX01j6ziwAvDukUlSJFwCVAUuwSY3d1rDcswUqUQAinACtATODTwVPVxZRRYwZ1RX2dIKN0\ndusKkLBMESbo1ZTgsf5hZeswwdcPOhfZKcBgYThFCHGHmQhhSKoocAr7S22gi2MHVm4Zg9Dolqtw\ncRRXAM1u7VlzBCQCcKzbxwo2d0sQBOIMgIf0SVxzcfvuzbo7vGNrwa4V1wLh0vVWS1J+pkYy9ziC\nkZMrraDkqAYRoUnaTxAKOjjYxS9GPADZ+gMmFRaHmiKG11Y1JUiZqisVX4KebxipQTB9mZzXBw7s\n6vcc8AYEqSeE78ZTHsuVnHQMQUh9IECpYWBI7m+szvPVEnpzxFvGE9LfWg3Aja45inCxb3mskVvq\njjGCLielamrPFrBAMIvXCsQMgBreqx0gcc5Aw4i7Q2t3ggX9nVt7hS8F4YkuqeGjbOSgUR63RGWo\nf1ugdLM7JQg4bTXk8AvaediD0eDiEWf1gmOXM3d5c8U3BqRXeuP6wLESDFkrsaY7YPuWYT/EQ6wP\nRGoy8WMQApB5Uzh3IWVbBlvIVCErGP1toaQQhSyKjI9zVVfekijTSqvEj47nIq1hxEfH2/3Il13v\nqyHdX6z1gajA0JTt3qxDcI017qYa1EoFuCSvpe9iqfUNDJW1b/jI1B4Ktcd5/pg3KUbSJsCRy1sq\nP/uMzMBnjSMjQCZQBkrucc0drinAsiFk1Ngx4w5nClCRlsHYpSWlmn9zHAd/YJc66Kd2HKC9kFyj\nLsX3a7pddMAEtw3YvaUkOnb35rjlZBzGgvgyjfL1CICcr6EwNBBaHXQNfiAX3rd1d3hbW/DOqoKP\nTx6ENSBmAFtznEr9XwFS9qPIUHKHW+sMju6fAWX0KRrm3OE8rlSJI8U25Q57gBVucmj+jo9PeCYw\nBkp7QWecYx1e2VpIpbElQZBYVF42iCoAqyEdvWfNyF0nfw/6+2tJPCrbxl/dj12YjhSAfggwB71s\n279sHQRj+fdpB0icAyyStxr0OA9aq/CUOpwDYesntgHhUuj5T+pGdX+og7RUnsEXWWrQo7tcwhBj\nRRjYKzn/qVzLHW4pQAZZJ2jUlWFsABk1jIhEoOxY+UALaV//W+P440JuGPAHHYmAtLKPiTGYNBwE\nhDYaAUGgKR+SWO9IO90UwwDy6Td9OLuX8put6vpyJUMpAV14dAtbHI13Yb9NLm7qOTgJO0DinJ06\nQQtmPsDUTy0Aoz+8X8qibgrDFvQ88DzYWuBsQdE/KK7G21Qix243OQCzjtSmzVQleiWIohkkwWda\nmc25x5LW6ieYD7R6jHnotePlIg5InTSZgEE701GUVdKfhNy3ZgMFmcWOAzDomdCJOgam7JIJ/HgM\nQk0Td5WyNPb3lUZU6xjLe9GsBUfUuZbBkYq4DsFDNc6D5WAJGbGA2FnKIFdmnQKhP1wLinN5SqhN\npbfytRThqI8hUhcZ0jD0OTPVp63HBsJRnSEodo1hpqhzyIeBBqxqCrBVF9iCYDmqdKkUU/o09FCJ\nL01LQzL8FiDfoFGcuQgAMWgIkL4letI5gAa7YB5+IrliCmstYuUlGtvpKj2S421qU6bq/16tNddu\nM4NbLb9BT4vo02jfEOx1gmutBr5K1Bz0anEt0KGStgvlNwfPKUBOpZsidGGDHrwKjG6x4sRcYVVu\nMragApAFXGWDhuhGG2irVIADfL1fmIVgOy1PT+51G4bJlUZxHGFTcPBz0AOiCgTplAOD9JuU8efT\noGHMAUGBOMRf0htn0HNtE3wAeg4d+6yFmVO6iUDy9xwIVgepf1R+X/p1zQy+tWwVd3n2eLu2AyTO\nAbvDfp+KHIuAc+Ep6LXiyp+ZUn6t+CUgnALbFBhLJegXfctzUMePKCpEsMarOpQHruIOa/2gHEj7\nD+qjb9ve1Q3VIa0GLUpSiGiAbErxlW4wkMPOFktDlifVBY6UoI5FJd9GW+nYxqDNwAgChsFqAPO6\nhyH+mtQRWly8Bdlt+CG6gCoUTf9ZFLn/MhB6sFWUXksN1pTfKL67w4dYpBmrAcxfxay+kMf7zCnB\nXUBvSgEugd8cMMsWaH0KktuLpPrcJwLjARVMtzGSuhuy8+g/jpORpx3MyEPQf9tbqrly2KyW4sMo\n33FlnxKctbrAtBiOpUU40bQWNlUIqRMkGXeRSeCPIUTXdYjTmiJTf2DKB1s9khuJ4otIFWt8d1Mk\nY7Wqe6FbXLUaIGvx+4Rgd4fXnO3yFVUhUw1uQLqbmulFuATfJtCbU4BzgJtSfLVjlA0jtiZIP0RV\ngNSqE6z1KVS3OLrIaDdgEBik8xTb2H5jBdhWgjXFlyvDeeWX8rbqAsWGeCStPI2jlNqP6P0ywJ1g\nC0vCYEpSVTcHw7s5JDJRU/aVicotUYAcL5GhOSoykP797lr66zlnE7CzP7epCLsSnC/Sruf4XG4G\nOXbhlITSFW7lmRpUYakCrG3vApC1+r2lSjBuk8tL8bmNkzB5AAJOBfq5es0d1geeEbVTHV55n8FB\nh+gaK8DSZW6ptSmAend7rPzaCjApwQS/yj3hFSD8NkHH4JL9Q9qW76d15Gro8fwcJWB5+RzZjSLX\nRm47VjVIenvnN2W6hd0NOwepObU4owg7BCfsJOb4XGe1q1OSaWb3DIpcj2/BcBcKcMl2K88k/BCf\nbeOXbxFOo5Y01B+kdRgsLaYCRTssw9RQDYBVt7cY9GDahW0rwrrqyxVfqfxaCjC7pOReAKYC9dyJ\n2AuQkRbiny7fZ48mq9J+gkQIIfUXTDDRLQ1HjedgRw52DNJvt1Uz+l4QXglOrWcUXzXdL/uE4Bl0\nh3c8x+eas136ATzenFODWb5KeE7llWmlWtwVENfkqTSMeAVo+xjsbNrJmksMUAFFoan0/xNdMsbV\ngEnF14Rh3oK8dLE6wXnF116S3xfyahJGAZoAGb2bdPQZyhSgXHf5XjkqbWKkPoBF2N1sVidISPMY\nZ8XgolgNNzgyay7d52kpwtEOe7CzpgRxAnN8LrcKkWqNHhYuAQduww+ow3At4JZAr5W2xB2uwa8S\nZoJOKkSxRZjMFVZ1WPtiZGCDmvxe6hFnJ2AdsEYwzEBYqrnli/UHtDWa67qZs52BD+01mRp0hyek\nuViCTm1AQSsGjhpqEC5srcMwJUiqzCQm3q+u494IhhX1N9omx/yGarSZ62KefULw0+az7NvmILjk\n9Kya43Od1X7exZXNaXMqEMX2FPx8eFM4lkCb6w6zBn6aj82DijCEAo+zUWOyEWSQVGCCYdJqoghb\n7vBpLHV3eLyuqEC76PqwZy2iJST0HMcZ6WxeF9ZhuXREUlOCMnR/fkC2jtMuzqCXKJm7xAKkcVwJ\nN7PUoOLSStABeR1gZYm/vU8I7sAdXtBO8T0AXqybFwBcA+AKZv7j2vHmILjjOT5vdeHrAHzhxE+X\nep/TqjWxkhRiHoz+8GvhV0tfowjXdJGZgF/mDpODIespqMCvNuagoSNApuK0IaeMAXXXdlM1uNKN\nXZA2XvuLWpinRwGVGB5YlB4INAxgBoIOyUxDenFkLjGnc58ecrvxFHrm/sbbODaNoNk52m9XYDgZ\n5//cRrptjz7Gcnbbx4Df+ng7fbVt6Q4vaadg5h8D8GOa/38D8F0tAC4p0o7n+HzhzM95q93Qjas1\nAqOGqbFt+5Q/sSRuk2Vpi29LCdbgN3KlCTbhEg0EDhzdohKIpv5kiCmkMfZgkyqJPyj/hzjw6q5B\n6AFWX3z3mLGVDSO2LvsR+ktu8odcJGUKbYjnlbTfH2mjUYjbCYQhECjW/xXgi3jT+GNd69cqptRi\nIzPcLWovuLLVp+YSt+K82vPp5TIBwYufLYvZP3l/O+8i275OcEk7hbdvBPCLGxdp93N8+tdweeap\nSNf8JeDsMP4ujnFT+SxrCchiXYvbFH41uK2FYc0l9uleDWrPDll79cdRBVpFkOHBq0EdakB/Jp9l\nLrWsFq5zxOb6+kMgdY3J0/yf5esQl6vH8jYwS4xI9wG5XOms+NF0SN1iG6PRXiZw7nDdPAhTJxnd\nPtZ7/thymSwjMPntynFLl9j/cZVwhG6tuBMQ3Llt7w4vaacAABDRoyBTb37H1AFnubzrOT51r5m4\nqXSDHtdBCOTxtSfA8u5zWVo/OAe9WsPIQLBpO5PiY1UzBj97+JJbDEamCokVaTxksGgpuwQw349v\nGahsSYMglMsSyE0rxLhP1ddM+0qeQc8Xg7RaABqGDTbLOuaiU4Q2ZJnBTfr9eVWI4jdzN9jyxpyl\nrHXdoMoT5dUkqJ7Hx5PbjkDMxgTbg80Q57Z7ZZmwNaX9WgC/O+UKLyjSIdgEEFtDao1gOBNfy7Nv\nGE71HaxBMbrGBAQZIop0bl2rE/QqkFwY+pWIDTdsPf+gAIzhlrorXNw0mEIxKGojP5AGWUjKb7nC\nq7u9ZX53rZUUUeWp+1uqQgG7DY8gE1GFCEVVh2Ujk3aUZqhosw7S+uKRTtKM9IsV8KWC5i6yucOt\nF3ncq4gv7+8GQC2+fCzmtreyGeJcfIosZjf/9ijLknYKs7+PGVd4QZF2bWsg7txjP4Z465CzMORx\nfA1SqITn9qlBa2rIrCnAlXV+cyCMb3OK9YAy+VICHqlC9DPsRP2lMMwnxxxkciLUxhJsg20N0MYK\nsKYUcysV3lReny9eOLsPIrGQ0uBgqJ32iEUhRnUIrwhTv8oktrz6YyEZMXBM7vjuvrZ+hh5O0UWO\nf0Ra19QekHeJaS0Txyg97hZDd2LbE2dJO4V9yfYcSJ3gCRfpxIzHm5MKzm6sCrXKZ6SlEGswLOM3\nUYpTMFwL1VrDiIMhM7muHZzUIBwEYW6cexoiDFMdn+aE1ViNYFhVhMtVXVvFzQPVX4w6SOuX3BQQ\n6YtV8qdhw0Acp+1Mk9Xn4CsVIaILbDeGC7ODHoqwDeeVxWd/0BiG5R9kh/JHKFXhHEjXaJNtbcs6\nwYXtFADwtwC8gZkfnDvmAUPQrIBZDXK17EAbmnOKb04hbgOwmlKcU4AtdZkpQWgLsT54gXUeYmQK\n0NYy/67UA1J0gc1FlgPWgMYoZ/YYu6G7AFctfSpPzbJ9Mk+UY5/kOJq0xsX5lzUt6NiKUHeYXIdz\nW0djHygUoc9A8qmcAE6lWAm+lWpODxu3eSrvaUJwB8SZa6fQ7V8A8At7KtIaW3O2/dVZCsIJIPrD\ntorFjbgWDGvpm8Bxqi5wCprybMpnXjYTtwehNo7IU2GqBE4BprA1jNgsb2mi8zrQ4oCrlS4wVUhq\nvim1iEb8GH7z8bW0BDtTYElxpvpJbfyIijC5wYxUN0gGwqiuPfjStihPrwRlO70KOEX77SUKsDQP\nRL89B8UzBsFd2wEWyWziysyqvYX7TsGsFrcGcruC4wL1KAMhG/wAXylvx06qECmegaT+EA8sj68O\nk8CtgVTdrHGj+sElKm5d/Db7+AfdJlmCvkzTPnoMi8teAGkyKtL/zS2Wb631DzYQxntSYeeVIAE4\ndnCMwKNYP0jHug9x3jrcUIBZWmMpoZgt+4TgGRxA4YSseDNWt8u0FWqvtLVu8a6AuA3gFqw5QD7x\nivECQvFoyQHZlIz9PQ58DDBMBULUHxjgpNjAmOjwrBBSEKZTvkzpoRKfX7oZdVexKgxtVkL7vRG0\ni9+hpAqTivVzHid32BrpBzuhesNFvth5IRLAQVuBFX7ixnJ0gzmCENOKcAqCtfihkWefdoCy65Td\n4antkkC19NoxFvwsMGbs3M/vShXOucNT4KNiXaSzgpAUfLDnHqL8Egc4xqkgQvStoxIUNRhVX0MR\nytFr9YbL8iL+1ny+dOnaeVv5TBFS9fcYRAa8NGNe7PpDCXxUHtXOr51WdyPFv85c1OgGW7RgMnaL\ncf8xcQJh/kflEGvFLYm38D6VYIfgrqx21ZbGVZJqwKultfKuUYFT+QjTCrA8XguIDHAQaUKajwlA\nYOkTHJJKpAhP23dA/I6O09D6NmZg+mLEARIKSC7gVKhH4ZBzOdWmAFaLm1OELYWY0sYv2MgLOnLM\nUEA2fhcQqA2kSnFgDMyggbXTtCpkQDqk2zZrP0lL06OZgLcCRb7OQSq64mnbN5JkwKupw31CsLvD\nu7alCnGhalwCvyUAXFovuLZxpAVJ4VVyjQvVmNIoflqHAOsrLaA0D1nT49zF+viLOiE3IrUB0W17\nYFKayjOBDwkEVFdxNeDMKb3xdktN+jRb/IQg4zw1szNilv5ym60FsREoApJSmHTCd1JohkH35zRA\nrb/kOGqVxaQ8kCZuSn/NuOCcw9H+yK4E92lrznarTnDt8VtxFj9TKTJ+NtYpwBbYplRfLY2K8EgR\nkig4KkBnkPNhA6ML41jhpy4YBTk3TGkY/hg2+Fl3Esh3tYEiLmNrK6CK0LqlNKBntqSusMxjcfm2\nv1Ao4jER720KhqlEpLAz6LEq3RimFB5MJQ5WzSDwFKVsf2uIv2sLZ79cmK83jAtXFCFpp2oHw/KL\nlJO2DsG1NqXqluw3d6zKNgN562klewnFWnwLiEtU3xwwLT3CD+K+alcZr+xMHWZhc4OjEpQ6KKtP\nNEUI7TzMUQW6tVeGlLrMMBiBKH1hQUiwZADRRRarA9GrtWnX2fJMb4/d4Ln48UVvx8fXBDk9TCGp\nP7CCR9emBIllwnc7NtulTrM7g1jHKIw/B47lTiVKoExoLuNibv1ShfId92MHSJwDLJLZnKpboxAn\nfqK6O4/zeDCuUYRLlGEZ14LeCIqk8EOuEE3pmRocaKQGc1XIOj4eUkddVRdWB5hUYHJ3bYit2ux0\nwmet9yLtbEyIDz8cEM1yINYBOK3+SnVXc6H9hS1DU5a0pbdUK6ruMAVVfZTU4cBgDkkNWv1hfBnk\nShAI6SURADqS38AR6sNuZSWjqABjlxuSODYFaC9Pa5HeJwR7neCubKlCXHh1mzCsHYvyzbXgaylD\nD7eVUDRll7vQlNSgjI6ahtjK6v08FOXhtW15cPTxJgEgW+OIKkBzi5lSh+OghUyfoSUgggYHunZd\n4JQCLAGZK7o5d7lUdTUFWMvnL7qPSRBMrwCrGVXgsUz0bgCMqnCQDumILnLQnk0yy0uAbAvwRLLp\nuyOWhooQCKBjzveJbjGlVmf/R3cleOi25ArNKcSFqnGRquOxKlwKwjXhEoplFxkaxxnkZJtdOjkF\nyA56WkfkoOjXCYLq+triAGhKTyr0pV4QMOgJfAIhfqsLJMU2Vnmobi9RfCmMIq+/sHX4obpPy0os\nKvRsXmJikIZF+YkCxGCjySgcIdeHdFRbOtL6iqB1ggQMNCAEjqNS268zkiLMihUBSLrNsL6JUQXa\nPTUArPXAHYJ7tTVnu7zKa2C4RCGOHYpFh48gxDoYbgPFGgyrjSoUO0tng6vaKNMjJejcYA9V9+0q\n65OTIKh1gOoKp4aTNAhB1ESaD1CXWNODG7wAWK4Ixwpw3IiCIu9S+NVUIIo89RgCk3xZE/9ykjeO\nKD8Nw1QgtG4wAIOp4oAhDAgUgMHqBLWukOKlyI18STSTCxsMyZTgsb74iMDHrj5w3xDs7vBa20LV\nrToWUAViCbBR+kJVWLrF28KvVIy1ztT2xYgqwuTmclSAo+34oCCC0dcFstZ1xcUBD1ERyomToiTY\nBT1f8eHLzvycyhtDrpY3B9pUWm27tLHUqt45ZIMqJACyDmBrSpBJx6khAdIwyN4cOIblRQFp4UeQ\nlwYF/RLSumib663XyRc1Dt2fwkRWvZHWULcYA8sQX1SepxO2AyTOARbJrKXglsRt83sOamVydWmA\ncAp828LPK8EIPqcCbY6RATLStGs9hj1oA43c37LRhGM9kmmupPqkxVcGGLD6whAfVAlbN+CIjzhw\nQTrfbdVXbym2MLI0CVOWVtsnT8uve7KpNJ+LdG31gFJVEKLiE/WHCBqpB7Tzr2ULogiBIBNd6c0w\nsLQPBw55HSBFvZfFxYIf6zUggRwRg49t1BqFaKH296oED5A4B1ikJbZUIa5QjR5qADIYloecilur\nCEugbQjD1NpL2l8QCj129X/O/TVXmJCUglOAWi0FHqhQga6RBL5lGLARYqAAJIsj+yaiDkGzseqL\nVyI74fNgy+On85SxPPo1n29cKlLVF1wXIm0d1rcLk1YUDEGrLAI4JEUY7zkdxQcUgCBr+5bb3OKo\nAA1kvohkapBBxyUINUmvre8dsFfr7vAmtuQ1tWPVOAfDOTU4ck2Rp011lWnBjopjZvCk1FXGKUOr\n8wMh1f+p+4tYWU6xgjxrJLGRTZgzEGbqb9BZ2KI2ScqP1RsH2J12TqqlgF0LemWd4DKwTQFvrewp\ntWUZn2oxB5L7gD0QrY5QzxLr98ODU4QJggA5AIIJ2o0Q0SV2qi+qwGOWgKk7rQZJ/T+hDWac7osB\nkn/fn80dIHHOUcNITbrR/KG5yNcE4YqlBccp5TenHgOkHpBZpt2MdYFIn8wRO1eZsvTUXUZUjIGW\ndRrPTAUO6hprXoOhdRUOOmmRKUIA2pFYJzACkotYgWHZEDIGZroALTe5Hp5Ti1icx6ckEAap84sy\nS0tNrnLAXlYWZqSTr1OgMmSaU7lFQ3LzXcFEEXLyhfWFhmMbkEEVISHW/bF6BhRSHMLkn7d76xBc\na0uhtskxfZimk7MBSYsitAA3B721MKR6fOwjqK5s7NoyiAtsNz+RUwG6BqU6I0RX2YX1+19RghSB\nF3RfkTOIdYxS/W/PlrYEK0+D6yJTs7oibKvD4qplF2ys18Z55qxdmnFJ0nciulCAB2McFMFkWrze\nHoiQC8gDQJA6QXbjGMZPEuWaZfWA5hprWEafUehpGMG5v+Z5HKNDEAdZJLPalVkat/ZnVO1NsrYC\nwgyImr5WAVr8EkCWUKx+V2yusb7p1Q1iIu2TllqGYS4wITWE+LpCAkCq8kwBBqf8glOF7BqqmaWb\nh/PSEb8SGV+COmpKBdhCUEsB1tznOhTnQEmVPbPbQ5VePKGxctUfwOjjLah6H9w11guhy8DFLlEW\n2nauBiWd9Ftw3fYwjNucirRPCPY6wV3ZUoW4QjWWdYDl7rVlKq0GtiUKsKH4RkvtE7rYCKJ/hgIx\nV4RwrpFTjuYOHycw2jFkEnA/eEJShSZeZK0TlfOQnz/iqHAiCOM7pQTgGHBzdYI1BYhR3hQ3jq1p\nS8rW5S+lbSnhoESRQb19i3ruKjMjje0aF3YvUQdEAODkDpNer6Gi/iLQStgF5MALpC86226cppOy\nHRCHiG4E8CoIUn+WmX+kkucigB8HcBmAjzLzxRMs0knbkiu0Q9XoBhzNdjHF2FKDu4JhLW11Y4qq\nQF8XqF+SsH1FoH4r6zekpFDMGkcUggxxiREGBZ4qQDfZkMHP6vnlgZeGlAjAwnLA1RtApuoE0yFz\nBYhR+nifNjC5Gts2+ytyd7iajfPNFG9vEgvLMW16zyH+jFwrf7mhL7WYnoqUlKAHoALRjy50liBI\nREcAXg3guZA5iH+fiF7HzHe5PJcD+EkAX8PM9xPRFSdYpLW25mwXd80iVbdGIZokqR1mCoSN9RTk\npmBXqr2W+1tThOb++je/qUHfVcZ1hbG+FqlOEJkSLNWgVzSIQFQFCGnIhHZ1i1VcsQ51iJ55PE+U\nkgfkECyv2VLlN60A0z7zd1A6YvsV2mrKofh1jfVjGX/B7H7GK0K71TUjaVqqVpA6Qet/aMcIXhU6\nGJICL44GZPWBdj8wUn1ghdcnatu7wzcAuIeZ7wUAIroVwAsA3OXyfCOAX2bm+wGAmT86dcAzoASB\njVXd7LEKEHKZrwZCkzlYv8zBsATilBJ0eVnGKcjqBFkVIRFiK2Rq9AAQlZ+C0TeqZGrQQdDqBFUZ\nBiYMgaIqFNVCYNZWYH3g9PPYeKrtTwLqSCmV3bzyq+ejivJrg3NsNLln/itsvZih548B30IcS+nf\n7fr+kkS5r/yk7vKBb4D1shwrwPSySurP4jhu+3zRDdYXX020nqhtT5wnALjPbd8P4FlFnqcCuIyI\nfhPApwP4CWb+NydXpBOzKfAtVYhLQMnu7ix3rYDQ4qtDay0EZE3VzanEqX2sq0tUiEkdsm5TfDAo\nQg7Fg5E9UPpwkDV82J9ois8aOW3bYKenZzA148HH6dTZg202hiHiuu0GZxfLradT59bplz1u2+vs\nbiR5IXjFWx4zBvX9Ax1dByb09B4jq2bQa2SqLzTCsK5OTv3F0cKDXJwIPr/s02aIc9t/k2XCljzU\nlwH4YgBfBeBRAN5IRG9i5vdsUKRDt6XgW3DevAvcYu0Ihi687dJqAKkpQr8mILrEWR0hJRcpAs6U\nIUau8giKx/4BD0g98pwqZKcAvRIExX5u5P5Gq7LyShBI6i+Fx8rQX5A6jtI+Pv+8jvPrfIj6/Eit\ntZ5ndmowKsHiaAo8iulaZm1IItaGJZX3BMZgswROwE9EI2cvsqQINezHlHRQPDQIXnyOLGY3/4tR\nlg8CuNptXw1Rg97ugzSGPAjgQSL6bQDXAzirEFyo5kZ516pGi6cia/E6XwLAWl/BXUGypgwHyEOo\nYKMiPuVlBzxK+xNSHzL38Mg7IcEvg6A8ojmXySlBCpCPwIb4nNlZZORKsN7vr379aBQ3b9MgG9dK\nltu1kqZ1gWJCVIL+WDFcdhUqhxgzFWgvEgCgIIPO1OBHnGYZjEDMFaCpv9in1LUSZ/fzHoy3rxN8\nC6Ff21UAACAASURBVICnEtETAXwIwAsBvKjI858AvFobUR4JcZfHOFV7mDWMTP1OGefvxIksPpwB\nUOG4BF6Zamssk0pvYp9MRZKJCMRWCg9FA1/luOyUoVeE8jhSWtMQK/RZWzJZ67BYW4Ez95h1YACO\nYsUpQY/FGmIkrVR84ws0pfxqx0SRa8rKI9b3T3WC5KKdMvTlIFXIYMggs1p2rdyNnc6RvsAZKEgV\nhHtJWX1udGLsunEaSFX6h8r1jYNj2AU4BSV4vCVxmPkSEb0cwBsgzSyvYea7iOhlmn4LM99NRL8O\n4HbIX/gzzHxn65gHrARrAGylb3hc/0mcjxspPwe8GDezeNAsUYYtpbf0N6j8vQSzsvI830/hZ5V3\nZV5TOyTKZAjJNQ5EOeCCDgHFiG6wPOw6MID+HLPxO71V6jjK0/J129Udw7HEacvmlR5PpOXqTwPU\n+PtKMGJIa70vSc+zKMBBB2lIajAQSat8bCBjdXfTXDEUpJGMbKZBVX8S1jfWHpXgthAEAGZ+PYDX\nF3G3FNs/BuDHlhzvgCFYs/Gbvx43lb88ZP6gxHyMHIb2Ss9AtFANLlGKa1TjYmXYWLJ0haWNSFK4\nxaYCQTZYe9pGkEHgPRBhkCQHR5bPwAIPqfsiI85TLGe/WGfwWHAdCyt1Y75HDYr1TjqlxpyC4GhN\nS+FbWEnMwPK1DxBnpwOsld/CAQg6LD8F2McogfTFZdd0oKQoByCEcT3otG1HzEtHZZPYnJ28VD1j\nEGzZGjhykQ7I3VFsW16DYYQeEhzZ/vMgXAjGmlJcqgCXHLMGx7l8I0D6U2KFkoeadDuGg4ODdrlJ\nKtLqDqXfTQiD6kKbsjM1vcQ1JxgS0hBdLex4ZTVGWPsxp2Z6S5uOdWfLlrQsL1nbzHMMG1ZVBmuN\ng7lSkAYUHcTVxhNkhSPboBk2pBcxeAg6qGt578/Z8XyWqb0vrEXOX2z1e0vsDEBwCmZz67nFZY3P\nuLspbHv0MLHJpOXgq4FnW7hNKcJSYS7dtxyjLm6MJ+8xncjuDyKDoO7HNj5eDMv5k4aUIH0KNVW8\n+Bx4Ic5X3CiWmXEQel2qSnBOAY5VXhlXU4blmgEcYYFSXHgMm7RJKhVkxrrANnK11RvabHc2pL7u\nQQmUNoIQD0Hc44HBISzhubMtIXh0eB8Pn5GGkZMAoAebC1trXYScB1wrPLF4AG0DvU0U4SZuta80\nd6dBTk9CHpwSjJ/dGSTIcGTdb+TAgWQuDThFKKfaTdWpjSst9WdDFdgsdnYFcyCWynD8lNcUYO3u\n9IAs9x6XLq1rv7kWghG8RDL3sK5F4WlYxy4kYjAHB0Gn+uCG+B/ku/FBlSAPpHWQ+7HjAxxB4Qwo\nwdKWAm9J3pZVwMhA+gJ+IRS3adzYhSLcZLEXfVUR2llMD7oB0Sst+LowAuBGS44dZ0wR6uAKwkq2\nH3B1gqxfm7haPj0/CX56faoyMVd9PlxTgH6/PL0ElIXXqboleY5wrGnH8TfEJR4Ueqa4WZQ0BQw2\nFSpYW4clHEhfLwMjBFWSQ1AQCjj3Oc3IpQ7BNVZeGa6Ep97dS1ShNyNPBXrRH/PpKxXhJgpxWxd6\nqtvNiq448lcbeRyBgjxo2eB2BFWFAJM0lEiS5REgigpkHWwVCYYEeXidIrRzH6Hn6gsz+LkwKzgt\nespqam8MyKwUWd7pY4+huqbF2SAY6wIVfuP6QB3DkFPdX5z4CToJ1ECx4crqBG18wn3Z8QEi5/BK\nNLKaskMRV1OArbgyXPmp9LShDcUp+DHiaKLbwm8OilNLrdsNinA5EXe5ZGebEOexgD3WpvZSOO8y\nYu6vVlDa8PEajrCzCdwdvIidOsyL4y4PpUtJBj+fm4qd3N9SKMDx3VHWDbZai5epP6/u6vnGaQOk\nw/mgCjCqwugaW32gQdEjUxQghQTFMJCoRq0TpD0rwe4O78RqIPThpTC0p8WBzn/PFCHnlI6HHDsg\nsMvb6k+4K/gtUX5zcPTHnIMr3Bpw5wipAcSBMQMQuX0igHMY2mkLquqIoHVdtkvCVKwPtPh4CXz8\nWKHxKN7DsGX5cbiyfxlfArKm/ny4BGyZxnGdFCBzaoyyRhGCjgAO1zqMBD5pHIljfUs+7UAdB2PY\nk51JCO56AMN1Ngc8C8+pvRY5XLK/EbiIMxUYoVc5TA1IJcTmwLcUfpOdpGfyTIGumpagF/NFyOnw\nVKPm2xKC7mToKMxE2jlYVaRM3uSUYDz/HP+0WI6iSLEM2XXM6/TS3lPxrdbhsh7Qh6mIb8fV1WGK\nS2FRgEcRZgY0GZ/Russw+xbjBMsISdseFJKhSB+kUWWfduYguPsBDNfo7trFacGv3F4CwLIsTv2V\nCk8fxkwZTqk+v90C4JS620QRztUfLlF7rTTYOUF8B0jYGkZSNg6WH7n7DT2VYZA6KO3km+Ys1nKS\nICD9MsfDZPCzsH9R1cJul9xaMMytVIA19Zbnq6m/+n5t6Nq+BkdbClfXu8ERmARyKjCpvwS9QQeD\nlAEwesPInBLc+QCG620KdnPbU3JN49g94PHhcbAD50owAyGQPtzUtFr/vG3gV1OKUy3KrTQ04qfS\nvFF6uD0b2UeQFcMGOHTqj1AOr6f7ap0gaTWqusL2fvHjEI4sQpHSMRluDESfMSm+EoA8Ogkpvqb6\nbBuVtLYibNcTMo4rCvDYlYEQdCgK/SYEqcXYK8EKKGFqMQejh2U52M1J2llsGNn5AIbLrXw91baX\nwHAKiKU56PnGD3PPMhDCpU/81NyyxB1eoxCnYNiKRyXOxyP9mVCFl7Eng6GbxD3md1BUFSh93dLX\nwzJhnZ+oHVVlKH8H59tZfoysrfhaLb9TCrAGvRpFamCsxydoWhlLN9rXAyaIRbcYIU11UNQBWg9M\neACSKUJVgpXSn5SdOXcYdVKUtmoAw+2s7rBMw6+Mq6WbutOwpXno2cMXP5mrqUH3c0sAttRVntqe\niq/FobJvKw5FevzzkhvsYVitXir3J93fYKgKUNLtvFfKMTomZZeQY5R3H/NCzMEwV30+vFwR5vu0\nFF9ZF+hV33EWL0rPqT0WJWh1gQMoqw9kUNZPMLYKg7RF2YBpdbO9s/QcBHc8gOF/dOGnAbhm5uen\noDcHulpca9/iMFbnZ092rKinpE7K+sC49qCcWJa4ynPbNcjNQa/cbuVBCieBRXoa5A+OAyxovmw0\nKacWI/RgXTjkBSJ9DG14KKkbjFAcWSXSQc8GpBp/nu8hRs1tZNu1fVHkbSvCNgTzYzIoA14Jv6xh\nRNVbdIE95PS74eCBiZQuAPRq0YAqAJzqJ/jm330Q//33/r9m+lo7i3WCOx7A8G9vUMQJYGXpS9Sf\nT0MR58GHCghR3wZy6JXrJQpwDew2BebUNly43LYwSAEGBzYgfsKl8aQPWNzPhvoPbjvCEDKqCQge\nX7XxHsbXyxWtjBnVCbZy59tjFxjFdh2AaTtPqynLOSh7QKbtwi1WgEWYQRTeEP9uX/8HDDraau4O\nQ9Omn68vfc6j8aXPeXTcfvWP/nEz7xI7c3WCux/AcI3sLm/YltKr/cZSVeiS7OkegRFJCdo2gOgC\n+11q6zkFuHR7E7itBV0zTQ8eYZhgJ+8EfTwzaJZriiqQiWScO4WjDRSaucZO0uXD8SscFLyl8mMg\njlcYfzeCxfLUtlsuL6EOvDmlN6f8xts1CAbNY6N0Z4pO+w0aCAOzAyG7cmhziXeHI0hDOhF7sLPo\nDu98AMPlNndlpkgzpfz8UkIPY5XnlR+Qq8GsmDVQFsumAFyy3YJfKzyVhnGYgTgiSRxx2jrrFoow\nucUennY8VYaaHuGnNIsN6/7zPlcUFIfIoZjc4rGSGx0lbpeKz1upKMf1jXVo+uO1lB8X22Va+nts\ndO/UKMIGNIMZuU7TPi3uh9RAYkqQEAdf2JedSQierrUk1pr9J5aoAFEJO8hFJQj3hPsi6c4WX369\nsQ3Q1qi9WhgurgU7FPlcPBdZ4jmAH7aJ8mON1kotmwg+rmEDzGBwYbjTZ+c0lqHgqp32wRVUTqlN\nVTlWgmN1V8JorPbGCq8e57ePivSaEizBl9cFHkfgDWyDJ3jwDWAOOqCt1vtlv1mDJuS743iM3jp8\n4BAE6iDc1QLk5Ct+Nia5hzzbzam/UlRO/ewU8NbkraXVQOjT4dJRyTsBsqj2tDO5V4J2mrxINsVo\nU30KvdKawRh0IvcwqAr0YIT2E4SG3Tk2URkP6S7HoIn1KS/HCjFXbrpvEVe6xGOQ+rhxniVKMB0v\nQbsKtAxqAkBQK5/V/6W4wVqtTAmOzsjJ2VlsGDkjtikgvVG8MdJhCxkyUoBUbDtrqcCln9C1wq18\nmNkXlXzFn1ANFy6tPG9eCSJCMT+mwU/KYC3JyMApnTdAQ4JcGndVDmWqGsi+bCCr7DcImGKKEElK\ncA5YNRWHURxV48b1gqVrO60E87g0dJYowmPIUKm2TirQurwcsX1Kp/3+iu4yGURjPWBSgrR3Jbg9\ncuY+5dXPeP8TgPdp1C8z8w+1jndGIViD2dzbrAHBEfh0HaVGceiGcKz+/FLoLQXllBIs80zBcSrN\nx6FcC+isIUTeGyLFJFld49HveCDqfoF1WH6AhyBj3Q2DzH+hkwSFQg2SuzakdbP+c25rJJHwGGjp\nsoyV31j91cBZh6KPH+/vb426EqypwQRX61DuwObADxswwTWQWB1geTwBIbJBkQZQetnvwbZ1h5d8\nyqv2W8z8dUuOeUojSzu/JhoV6eV+LQVXS59SfVPHqRS1LA5XImt/Tq1YS6A319gxpwTL9dI8tbT4\nZ7jKcwJ8H78Ew+KUkD7kRSMI6X4gAivwQlxz3I6j8g/uEHG2IPnkS/mr61wZMgWkluPNgDan/lrx\nYxUmCq9WR5jXA473HRCkdVjHDYydp536yz+bqwDRK0C4NGsd3qMU3EGd4JJPeYEVf9UpKcEWMcrw\nHKy2gSLn2YFc/c0VFw4KJQFqxdgUgEvCrfWSPHOA1DUrbShCs4SfKkI9pvGq7Cco3WPSPgGDA2GQ\nuTOgM9UB+XzFzLGxJMJP68OIQ1SGpnDGSswuy1I1tyx+yoVOv+8VX0311SHoQTmCWQRaSPtmAGwo\nQFv0RVXXyydjO6gTXPIpLwP4a0T0doha/J4zOu9wzZaou/Et396nzNqSdFgASB6nT7mrZXgNMGtK\ncEO4rVqD8oYG13k6QrGqMCkrk6lIgGCTdhoICQAGzlUgq+LkEPuwD1H1ScX/QHYFyGYryZRgDqD1\nyq+t8nLQ1dPGv18D3qhVuLaMAOfByPX0yX0Pq07wjts+ijtue2AqyxJivxXA1cz8KSJ6HoBfAfD5\nrcxnCIJTiq/cXqkE421Q+w1ySbV9amV0+7Rgt8btXZoeiqKthlzDqmAD4sgyzfRGWIEJAkKw8VEA\nsq4yULeYFYIBMu+ubouIZPj2GBsQgHSoGioUUc2WQHEujYs/sgXB3O11Cq0A3riLzDDKI4uLJwvX\nGkRmFtqvEpxzh5928Uo87eKVcfuXbn53mWX2U15m/qQLv56IfoqIHsfMH6v95hmBYEvdzW3PAbIG\nv/KBYe/zVco0QZAlHF6q+pYoQVTi1sBxadrcPkvM8vpPPhjav0UaA0h7UvOQJn4Hk0wdqQdhJoCF\nngIkdaUH+ePj1xSVr4qtGDYTwtQf4KFR+2Nb6tArwTEoU/rYNSa95IyjLE8JPD/oatlPcNmyT/tz\nPGLbQ8x+yktEVwL4Q2ZmIroBALUACBz0lJuWfwnsWttzecq8Shv227aqQG/uz5kC3hIwLnF/Uaxb\nwKvF1e7/NaCcs7l8+veyKb6BZKIghsJPHVyW+ARA9X2ZwEPqlR54kAFDB5vsXU9HqxwmSDldFphS\n9Qu5g7CtQqxTa7vINbCVS931TaPHpIFR00JuPbUMxX71Zb9KcDvkLPmUF8A3APg/iOgSgE8B+PtT\nxzxDSnATGPLMtpnd4Brne99m6fZfAcfWEOVL1N8c+JbkqYGvpRDLfEvSyvUamM7FgZDV2A+mnFiV\noMyNC6TPwrTlA8mR82owTaMnYxQiDvgTF9tmzUnIoQl3p8TiaeNDsxU2V3f5yZqC4BRI1y5Fn8KF\nynCftosvRuY+5WXmn4SMdr/IDryLzDZKcAkI3e8yxvDjYjt+GuFACCDrrOZtU8W3tHFjKeRa4cWg\nmtln6TFq5sBHxYRVUQnqi4YVfvYDzNqhUAEIyLzGg8UPOjRXWaYy7C6fFcGc5yGeaJLrn32d0YYa\nkAY/mAfRTGNIE3ihspCcAyxXhPu0/tlctJr8LmFWpq2F31xeA5kHoAMjI8Et7qrbLQVYsn0N+OaA\n2ToWKsdpKcMy7xRAy/1btkQVlta4vKz1gXGOY5VsJfzERRb2jX6YB4TBxlwJCPo1SlR/hHzIfncb\nUOz/46EnJ8axObZGAxj3MybE/dPXK0uWpYpwrPLykWasdbyet1x0avYFF2031iG4kW0CvykVOKEG\nLVyOMs0aJuQq0DqlxWMV4Rr01qhCoA2ZFuCwIL6MQyV9ytYAb85UCfpzwUarwTLIuSRHMo6fhzg1\nyBwVIaBdb0h0kS9z/ETP/oair2FZvOz73GzwgQroqv34li4GrMrncrqMVZ7gnlXV1fMejhLs3w6v\nfuO01OEc/ObyuePZyNEAEgALt9crv1IFlurPb2+i7OaAOQXLtWHMxPttv95E/bUsAs+/kDTB0nSA\nQPY/aOdjNHGu1uwxVBWKkxxntNPyD6wgZILNAFX+GdZAAWsEYTdA6VK48SYwNCACZbcXqubN8yRF\neIhK8PB01+GVqGozIFsMv5IoNQVYcZEj8Grw031q99E20Nu00cPnXRqesjnglaJ6E/Owi2pwrATT\nYnWAZqoC41SSA2hQh9BgRzpTGyUVSJQAaJdRfstUXtDbQmHohqMaGlDZFQyTizuu3yvrAWuKL68j\nnFaD+7TuDq+2Em61+LUKsSQRkAjUAKBv+FgCv7I4LfgtUXZL86HIW6bZdi08lbZE7W2jDKOac0ov\ndpMBYmXekLKnC4F0TgcASLNr2IkINMQW4gCGskzdYk71gwSQO2FJj6ahpxjIhrAfGOsV3kIY5oOp\nzqu+ZYqwTBtOoYvMuYfgpid7Cnq19CVhW1dgZ2kWZ5/T2TdbEX5uf0vzBFgCvyVwhAsvVYBz23N5\np2wJ7OZeDraOyg8JfNrqMDqE5mF2ys/B0XvqEjkAA8ch+wdIeDA1SOzm3E11gl7pxfl6yWDD8sme\nxhE2+EqjWAxWZeNGAliqG5xShi1F2Kob5JiyPwj2OsGNbAn05tJb4UIBAhjPMueVYAWE3qM2K+E2\nt8x9NTIFRRR5lmxbXFnm1vamSm9hvuLVMYaiblv9n4FnPCWTZtSFB1aX1tzg9ImeDM7AVSCaIqS4\npS3EBsUCkrW/hzV/WrcVoe+GU1d+QJwnJMaP6/soi88V35R73OsED9o2hV4triI/Rvt4KFaKUjKz\nBGC5vS3wSpDNhX05praX5JkD2NxzM3e5fFxcKMKOiqypFkIyELO2IhfLYJdGZ+VgyDBgg7nBCjty\n3xk76Hn1lwZiUODp8PUJw3Vll+L9p23zSnCqe4tXc1NAS3MSl/WD0ghSi+vu8F5t25O9Bnqtfcql\npvBUhjByNcgNCm7aMLIUfktgiJm40pZArwT81DE2ubQFAPOGEYmjGIbrG4jKBMNyonydIAMYSIai\nke+JgRAhmMOQB1F3pBdBZvi1OsA0cKngSePKkZqbEJyAHxMGmur4XG/p9aBrxdUaRGpx+7QOwdXW\ngh0acUsVn66jz1WBW+byOgA23eGKglwCwRoUgXUwrKW34mr7WlzNai7wXN6WNUFpALOQjlQd45JW\nqdU+xOtlvxGByggDgyhg0C4yg34oHIhB2vpMgA7dxfF3hY8E5hDhyGRNL1Kmwc/o5rrN+CH+WY82\nqRg5xPafeVVZurj1uHqeHJpdCYqdESW4RPWtVYmeYC5u1Bpci7NdHPhqcTW1twR0a2BocbUX+lpY\n1S5PS+21LuWaPNUXQVKEHJUg6yAKE/mtv+BgKtDQ6aAHRAVIA+sMdwJDAgEh6AANIULOprocSAdy\nAIOIYjt01jBS9B+cU4T1+r05Bbhc/dXUYK0+sDeMHLzVFGArbQkIy0WpUnaEzsKmBIFmX8EaWTZR\ngVSJ8781BUw08pbWcm1bx2pt7wCy/p3imzw8YEwnGtbqVbKtfUN0iYEEvSFISzHpAK6knbWJOeo4\nG8bfFCFB6gVJh++XAVxTo0mrwWMeguP0tgJsK8LxdgnM+nZvGDlomwNZK08t7xQYaRzOOk4XUAQa\nMKwUfw3gWnFzShAL0sp8NVui7qbSplRgM19eF4ioALlYo6IEZV/LF48VrxNDvhphnVVtAJGOM2MK\nMDBoIFAI4IEwqBokcAKfrokCbLJy4jTl6EgRFqpwlBb3cSrP5Z9q0a0Bbaz+fANI3iAyVobdHT4j\n7vDc8dasfbiAX1ZHCAdCDaMGQ+R/lt/ehQIE6pAs45fCby7fEnW3pFHFbA6g8ZKQuL2FzvMQAdrv\nm7JAPKiaU/c4XreBZRh/pwAFhDaHifQXJLBOl8xpakoF36DuMrm6taQIC1VIeb4cgq34sToklIqP\nF6UlWLaV4D6tQ3AjW6v0VirEWN9nIESxbQ9RAUNovrKDdFn0OeW3Kdxa9YA1W6oQfbnX5lmzzZV0\nQAZVhdX/ybXJW4dtPEG/fw2acGHFAWEcVgVIg/6mhgdzg1VhegASOzVYUXnWodqDkGj8xUYJrzG0\nyrpBHqXnCrBMy9VeLXwaSrDXCa62OaCt2W9qKajjXd6oCpHykjust2xUmZmfnBskIR5zQZ7SDJBr\n4VceYxd5FsCx1jF63D6c75pVxzo1aftQdpGkw3QM6wQmDJnLhJmTW8whKlLiIBCMUGSQKjvC2CVu\nKbxRvWHMN3ahiUKRxzec5PvkCrAGw1wZ1vLsXwkeHnLOgDu8iRJcow7tqaPxcf0wWS0gAm0oTgHQ\nD2PcAt1SgNWg54+/qW2iCC1uiTKMi0ecgx8jDp/FprjZ/szxPtB9YqdrzUVuQAVzY80NDnryRA0q\n2NhBjkX9ETlVqXWPRJx3k8nAlatBGdewBFztW99cHS4D3XQ4gKtKkGMt4f6UYHeHV9saJTiXt7Z2\n9Cnd3pgnPXyjuPjseUVZ2X1umXJ3pwDZguourdWSXFrrOWrBbxRtjRuWTjG7nVsC4hch5TFcDpeo\n1Rmx24x3MNmBT9Ugp21xdxMYYTCMapCj4itBGIff8mqwCssZV9rlyRVdK1yHIU2kD9WLeXLWIbjV\nG2dOCbby1PL6pVCAXKTFe6QCurk/ZykE9w22tTb1zqnFr1GHbmHkL6ByJJnxYa1+kLN0cscpndVa\nXPpsTrfJgKz1gVm+mubTVuwZyPk8rQaMmrvqFWGt3i8PewU4rgusxe3TdgFBIroRwKsgEy39LDP/\nSCPfMwG8EcDfY+b/u3W8A1eCwDTkynyt9RIoNuRNS+Vlx1nYMLKrZWpghZOytd1qLG0NQLN9Gk5a\nNTJ/MXGWUleBTF75MeBdXwNgdI9tO+T7ONAN0OG2aAKCbrtUfXOucoSti59SeLX0Vr592rYNI0R0\nBODVAJ4LmYP494nodcx8VyXfjwD4dczUXh84BJfCbq1K9MddoRJnwVn53SyKpn/OQ27KvEJMk6vV\nQblLOM7Ba27fGSW4KH3qPVZJ998dgxNYCchEf2qFponjD3Gn+I0yad2a7iZ6TcPE7vRLXaQEfYOJ\nc4e1H+I4bYgNJgmCA6gBO47IGyvAmI9OSwlujZwbANzDzPcCABHdCuAFAO4q8n0ngF8C8My5Ax44\nBL2V4JqKWwrFJaBbmsfyzUFywaGANjCX3rMlHPd1r7eAtibP1HmZy2PLAOis5RkQydKGPE9qoZZG\nFdJ01jwUAD4qjj9AZrSLwBrAlMKGGRnQ1SHHOmybG06A3Cv6TUxUkwlxA0i/QuEizWCYQBlibA5A\na5whSIPOGe0s/QQA97nt+wE8y2cgoidAwPiVEAhO/oFnoE6wBjofrkGvTEeRdwp0U/nWALP87WJX\nmlAcAPKvKChXfptCsQbUTdTiGg9qySVvnoOFeSdfJvVFoCcNHjwQaATDIjwkgPKgkDyCjuhPgOsL\naGEoFAVC0lQicxxL4Ug/5bM6SVCqBJCZ70JMs8meIhDBOsJN2iZVkdZtJ8Oo1nNmypEOr07wo7fd\ngQduu2Mqy5I76lUA/iEzM6UpBJt2RpTgHAh9eOoJQCN+LewWKsMRE4sW5dGhXCt0BitWiNEYfJtC\n0fY1EK61KVC18q+BnZVvat8lS1R8NWXtP7lzcHOgi0rQDeCQdeAm6FchAkMmOakCGJvxLiJRRrbW\n+ARBTi4yWR0jZyNXj8BmX7K47agMOYDJKcSkSTXEMsAs60x8e7S5OsHLLz4Dl198Rtx+982/VGb5\nIICr3fbVEDXo7UsA3Cr8wxUAnkdEDzHz62q/eeAQXAq/2tM0Bb3yN04Khkh5GIiz2sVdKT+UgRE0\nPozBEDTdarwJFDd1mckt29guYDcJWa2msHcT552zUxxl6bkSZIUi5e60jl7D2n9H3OFB6wolLo5o\nHd1gBhkMdUKnOMoNOKlASkNGUAHHgQs4clKG1pIc16Rg1GMHyFcxVje4T9tBneBbADyViJ4I4EMA\nXgjgRT4DM3+ehYno5wH8aguAwMFDsLQW/HxaSY4pGC4B2RoYlnnK7xyAqAZVicS4jOP2wFLeVcbD\naim41gBqE5gtBRgqa1TiT2LR9gwq4MUDRbUnaSzhI4AD6RpZ3aKHI9v5N/eX4MBi0JOvVcQVdrWH\nJPoswk1HpWHdx1SgKUP5ZpkiyOKQXqwOMQUEHvQ49r2zjYud1w5GZaj77NO2rRNk5ktE9HIAb4Bc\nmdcw811E9DJNv2XtMQ8YglMgq+WrhTeBYSt9E2C6YDZAq2aLQNQ4FDB0X0nEuMA6U5DGeeVXywvg\nPwAAIABJREFUA+IaZXjSjSjlqNAOUln8GlsJRK/46qPXGDBZ12VDCUucc5flUuqbigCGViBafaDK\nyaAj2QgMRQ0K3EQRkkLRlJ8M5Crws0aPQUewYb+GhAdK8DPnOOtMQwMCKwgjNMtn42RtF/0Emfn1\nAF5fxFXhx8wvnTveLAR32zFxzcmeaFltQs2Ht5EXu6gT9CpQv1ywqBEQi20Dn452rBVJY1VYwmpJ\n5+o5teehtC/b5BKVp7m5UAE7bQxhU3MOfDGeXDrnA7qaMtQ1BaSvK/X75EBBJ8zTof3BAjuCpnMa\ngIECoOnm/rICcCADGqeBXON+1mKcOngzC+h8HaD1jbTP4wZ1z0kBGNjdMOX7u7W9hZ25ARROomPi\nOiuhuWR7KSzLuJOAIZBGqUHKH4HolKBXfOD0ZLH+twaE/oEtbUn6SfUtbJ2mFnSXQHCr+sQckBzU\nPT5iUPBqr1B/nNbx933dKA1gU1gUYnygIX2OpyAcQArFkMWbaxyH7oousI1ynVp8M1cZ7AZ2UGDC\numcHVZCmBA2adq9OXLva9gZ2FgdQ2HnHxPW2FnRTebiyvcs6wVq8A6DBz4DnlZ8PAwmMBjsgB5/9\n5JQLOwe01utq09biOUithd2wII/97bUuQKN8lOr9BsoaO6xOMH6iN3ChCHUdXKvxAKmaKIGnl03c\n3SGHnsJJ5jpRVQhVgRGAnIXZ0iDQ4gjMQYf5YmkNJvu2WdWghnNFmMKDDg22S9kyZ2fx2+Gdd0zc\nzGqHnAPdkrgayJbkWZpu5mDolWFtlGo7DruwucXx6eK8XhBow3ATSG6iBrcBZwnHOZjW0uYAyO7U\nZwrQu8cU3V8wdIgtU4CcGlKMeQrFqALjMP6a6Bc46GXwK5YiDkB0i+N4hg6Kg1d97GCpyo/A2iij\nqtHgyUHd9OH/b+/sY6/Zqvr+XT/QJr5ckWJpAhii3qgk1YDKvUqUh2iT6zUWX/4w1Nb48odpg7Gm\niRpN1GtNiX+QEEMkV0DtX6VNbRHrpUbSPtUQRIgiqGC8opGXtkE0gIaS+9zf8o+ZvWftNWvtvfbM\nnDnn9zzzTU5m77XX3rNnzpnPWXvP23gL4D66iRCM7J2uCxPj0qvWYKnZe+C3BeyscrHulMyP68fk\nk4bFul1WuzEdbFZUKOVBz/tWrDYsMGl5kGr5RcBWA543B2jZ0z6Sn8KHMujKkx7DMttkRJiugJHX\nEuZhsP5QAUDWwBsviymgNwMiJuiJ+cD0kUPiFAEOQ+IyP709eYoir3BEgkAbghtfmPjrIn3/+PFk\nXF4CwAactrfgV6vXA7taGc2X6R+XpA2Gv+ym7AcmGLaGw/qHXYvutO+akycROEahZ4HNi/q072yI\nnKI/Gh6oekXDy5USzCQUmcDjWfgCdiNIJxgOw+sBVJigN4JvgB6Koe4EQwd+sOwSfFfj8w3HoXUa\nBkNEgMXTb6bXudN4QiTlr8drCM3DbNTH//fv4xO/9S7foVM37sQINr8w8eEFXbTApct6YKnL1swJ\nRiNCY25QQ88EpqaRAcQkDTkLjh4Ie4Bp+UfLPDB6MPTmBC0Qagg6EWN+fm5K65c1XYtIMNsxDYGv\nDRiOoGPieRSYP1REgiCoyHCeL6LCdPJEnkXO4CMR/YmIMZcLQI5no6/GPMYyT5/54q/EZ774K3P+\nwz/zy5UvuK0bd2LkFBcmLlcNhrLcgl8NcBpoNX+vzKurZUSHsn6uMhyM6eCZlig/FviWRIQWuCyb\nB7FamYZXrc4ayFXy+c6PPDyeosJpODzN+eU6oz9f8RgVDj7QJ0fydzSleYRVOQyWIMQAuSsNPC8t\nToTM4CjsGWoiAoSKFCHfYFI7prbXTRwOb35h4nrVANXr2wLiElDKukA+Got5P2dJ4zL6u7TuHGnl\nk21J1NgbAUaBaeVrZRYoI5EgpehumqrLkZ86QZKGzBC+xXzgaMvXCRKmM8UFDDHB8ArjPN40HB4i\nUx5hh2GILobKMj2Ajsrhc/HagDLyQwG+63k5XQnffXQjIXg+1eBW848AsnaktI6k3roim9UBRt1t\nHQ3KJvUqavkW5CyARaPDmq0XaLUyL63nA+UJEgE/jHOC1gkSXNEYPXJxv7AcDucocARXmq9lGqPG\nDCwM4Lse2p6GvsjRYIIdMhTnQCzmBsdXBtC1jAZHcF7NgZeHviJaHM4W73vv8E2cE9xYPVBrzbf1\ntNeCVc2nVh6oKyehUj5tH0mbA75ZO8IsQbYkIqyBcumw2YJnC5K1tAZhb5qRI8Ahn6I85OgvQXGw\njX9OjOnkCGPwG33AIjpM8MtR4LjkKc80zDFOt7qNUeAVBgjyuEz5BEek/ARBpMjvmgX0VIR3fQVS\nIMwAZG1rXQawrW7cnOBlS//9r/20hrqtqNCqK6WAyJjaTLfNmdtGc96mKNC6TEbna6DrjR5bwIvA\nrgdykagvpWsPmBiHr9O84DT0xbW8UBrgdGdOOjmiI7/ZfOCYT1dHX43f5/UIwDQEvsYYHaY6428g\nQS8BOKVlVHglT3hwCcYrBq6ndIbb9VWZFwDMefB4jSCX32/6LXr5FTqGwxenFtSidg+WmPIpIknh\nA2FKY/zxz64XNFYr5w2TvQbCpWWp6wjmW0Cs+XsgbJXL3R2BZ5Gn/JzG9Fh9Shelj3nOMB3nDDNQ\nx+8t/wnJIfGQHobCQ91heDzWS9CU6QS8MRIEkKNBEJAuoMbVFAEWEaEcGqc0FPQ0AHlKF9+JVCu/\nQAcEu8RGugafJZ/IUHhFveya2gHyMIlHexo65factHwEF4kiD2i1oW20rAdyNcBZ8LIAtwR0ViRo\n2fK1fzoixATDcX4wRXsZiGkYfCXqjbfc5Ugxnc3PUEQe/oIwApXzyHyI+Dj/p2XYyn2RokTwPApM\n6RGMEoopjTz0xZQmnqclCE+sJ68PCHbK+sUvbaMFwyWgDJYxpnmpFPFJEOY2VJoh5peMXZEPHsyH\nxtacYASYXrpWx4Jay0/mWyCswS/ik+3TMJhI2yH2I08vXRIgJREZzsEIpCe5TOun6exvOgGT2hrb\n4atyW4i53CYZCaZligjTUFgsJfwwDsELIMoIMAFwPwbizp17HoI9ezsCvCjgInX00doLSssOUabS\n8gkypPLuthtATPKGxhHARdIe3Gp2D44e5CJAi0SAno+I9IbojYVdQo7KOvl6QZj2lOYr5DPM05/S\ndKlN6k8RDaY/urRvxv2Xz4GJSDAtcxSICYjDmWsFRgk9sUzD9ATCLeb6onryzuXFXZfXo6pagPP8\neqHoRXi9UWGSjgJHvzFamFwtGNO8SKZbkd6atAdEmfdAGYkUIyCMLiPAnPmVEWCK0uonWRg6QszD\nZ9lGju5ott489Vub+7zivB8H6KGAXoZdtmEcXhvwS3OANEaafL5I8MkjElyiFvRaoKsBkRs+Xlm0\nTmWTirPEmAAJng6ggnqVvF61dRAvAV4kKrQiwgj0LJC1INaztCJEvT9C0IOK+MiMBLlZz+iPt970\nW8jpAWT5STcJagl6eS5RQS+XYzwbzdMylwPYc07wgGDvzo4ALVreC7rZHfgVu3X7hWx7nMArusNi\nzONtr1ecxlMoD3Ar8oFaFicEoIZumNqUS5n2oNYCneyXF721or0eCFr7pQdENVhacCNho2C5V0eV\nD5fZjN9bGjoXdYS9sGG6ROcK47WKmB4KMZbvqTtP3PMQXCoLeNIeAZ4eE7UgaNk9MHq+6Wi0ticC\nO8NVghBsQI/KLplLVgc0lfkaBGs2CcOILbKMQNKCYG2Y3LJZ5S2A1qC6Bq4WRLMtRaUs4EbFnSkJ\nhgNMx7PTV5QBSOk5lTvp+sn1yGm98oOIXgrgpzHsqTsA/g0zv9Vr74IhGIFbzR4FoVU/Cjt9Klbb\nvO2iWdKHHVA+ot/yJXHQsgM/mh9YYvI+g5VE2RKQeWVy9/dEeBGfngixBa8aiCy/KqQqtlpkaJYR\n8rWIIvoro0QgPzlbXqg9RoFlZEhniQSxcjgcfOXHW5j5V0f/fwLgPwP4Uq/NCx4OayJYlKjB0AOk\n5bcUjK32ZVfkEeuo9qdsgTBBC1xuCoDihAsDRX80EDP4GHmILrtaGyp70aAFR88nAselZbVlb5kF\nxYiP++eDOfS8MuUzwQ8ZkMPZaRTD43yh9njr3mDDdG/zDYMgAq/8YOa/E/6fhXK+aqYLjgSBOvw8\n8LWApvMRuGmfVgRohRtG9FfkDQLOfBUIkw/SpguAyUemy6dUpzOcwDTJn+w6CvSgldeBOYC8ZQtK\nvXDbIjL0oBQBVwNSVZ9Q5FdbTpBDuic5wxBjhDjesSJgl0GYIsIRiLX/5c11Z/XKmq/8AAAi+hYA\nrwDwj9B4kOkFQ7AGvxr41uYj4NR5D6RyTBncVheSKU8ir0HHIhoUleRDG1K3rsb61zQdYMAUDWog\nyiYTmFpRYW1pgTIa8fX4LVmuqRuFZxSqVgSY65AYIhOm4fEYGRJG6DGmEyXpQQwCinvqTqP8d28D\n77hd8+BaYXZifiOANxLR1wL4GQD/1PO9AcNh+auEkfbyNdBhRd6KCr2IsKWxbwXY1CZ5+awU/bEo\no9KpuC1vLM+RH5d5+YnAzoJZZHhaA2A0QmxFf3uCrBYJ1vy7lxP45HygjAYt0PEIQpqBEJju3ZN/\nlvpYtWwL1ILgC24Nn6Sff0R7RF75kcXMv01EX0BET2fmv7Z8LjgSBNqAa5V5IFsDRZluAdHZpuFZ\nSqL/jU1Peegq4ofJslA5z+5CEflroPnk6hoEI2DsiQCXArJ3yBxd9kRwLYBqoK2Ba4Jh4SejvrSU\n0JND46EtIvnbkL8R67e5QdTYgmBbzVd+ENEXAnj/+PK3FwD4dA+AwEVHgoAf/Wn4ybQHwhr4UCmz\nJoqiQNRUqYBPcypiK3an/icXDvlR/RCwc8Any4CyyxbMPOi1YNcCoAczC1Q9vr2Qi/pqWGng6T+V\naPTX8EkPcC0iwDwnKEEINUc41qn8JE+iJ9ZVD77y49sBfBcRPQHgkxhA6Yp4p3eOEhEDr+ypgfKX\n1ZNeWm9pHa/+uA056lMfyx61JXsBNiMNx96VLjeneqD2lPempa3XvhAyi9o8wXrTU6bTCZH8UAbx\nMNacJyANmXM9+fTqK9XO+DOJ6FNf89lg1u+DjYmIGG/t5M2LaPH6orrg4XAt+iPYEV6r3PJdEvlF\nI0Kj+z2bLW3QdpqcixMfOl3bhyLZ+sBIW5GfTLcivd607Ktnl3krmquV1SI8K0KMDnk90HllnbBM\nF0oPtvQyJ8pRH1SEiHyWeMzvqfXD4c11wcPhFgAtuPUAz7JF4ejZrXRFHhxNOyk7ozgjnLZXP5uw\neGSXBT9pG4ZIYQhGQNiTXgLGGhwtUFr1em01EEZtHmC1baybzwqP5RP4JphNUR6Jy2FYgXFoIw+P\n5Xe6hw4I9qoFuxYIrTaglmvSLQDqeUEDijUQIpXRZJD/I5l3ojwnFfRk1JjegyHBagHFg6CEVwuK\nWwDMg1KrzEqvBZgDKbOchI9l0+XaVi1PgBvT8sVOFgjHO0imKBD55MiuOiDYIw02y9YCXK0MRlkv\n7CLlUg4UPRACKtqzykXd7DvCrrX/WPimCBCqix74PNi18kugVyurgc8a8vbCcQn0ajDsheDMZ4Lf\ndIIDVRCmS2OmqBAFDHfVAUELDJ4syHkA7AEjKj5e2rJ5w2NdrlZZiBvlwqeIDGUdAbz8qH5nn9T+\nTyyb/qCRr4HSy1sw7AFn1LcnWuwB5VbpGjgrPsWwNs3zpdvh0ln+KwwwVPYUGe6q/7/v6iK6AZGg\nZdtiuQRy0SjQ+tVaUuUz0JEwqu7K5xFmN7GNNSCyKJdLiMjAgmANYp6tFtFZtlqU1+Nbg9oSUFmA\n6knr/dSbLoBHgIgA00MRShBiBj0JQ5xrTnDlJTKn0AVDMMkCGE60jNqigEySf9veNhpZ91+aUL6+\nM8EMNhBnALSLhuXYbjQa9GwamL3Q7InyPMBGgRmBZQ9ILRj2gnUGREJ+2o+AXfLTw+DBL73DZLqP\nWJ744pTfU0/uu7qIbtBwWC5RKVsDzSjwdFktGpRKp/n0tjr7RV7DSTLBU7W8OxII5TaL/VA8xFXZ\n9K7ywNaCmwc4XdaKBnsBZwGrB4Ie0GrgigCvBbYZ6CplGXaYDX8lCEEwYCiAN/qSvlh+Lx1zgj1q\nQa0HeFEo1spqMPTqR0FoQZBKOyubhB/GA2F2YkTWEQCU9yozBDwx38XWp1ZmRXs9sIwA0PJptdOC\naC0C7MnXYBgFaSOfL4+5BsqzxKmcxjwrYCafdL2g+k730AHBLSJBqwzBMrn+paCzoj+vDKiCMHXX\n9LH2lYZiqi+gV5wZTo5jWkaD+WSKbEvAMMG0F3QeZGpRmgcyz6/lE2nHApmGU6s8ACwzb+2PVj6D\njEsQEiAjvOn2yMHORTvikVtyPXvqgOASaRBGbEBJiYhN1q9BUC+tkyEREHLZlI7wZhAkZZMwA4oT\nJcmXUEKtCUZjlbVPBIY1UHnwi8wZ1qC4FJTaZg2xI7YWQJdANfsk4PHwcieCiPZE+Qi9sq8aiuKz\nlw4I9qgGuBbYrHIEbC2gtZa14bAGoc47UJTlpPJyW2fDZRqTnh9QXDBtqQW2FuAs2LXqWgDz1tHj\na9miQDNh1LBZkZ+2efvF21cKaBmGhh9Jn+p6ekZnG+iA4NLhMALpFgxb4Nxi2YoCHfDN0jovAab7\nLfKU0sDsQarFPhvzrPKgmUsYhGtBWYv0emDZA8YeYPaCVIPHGw63gNqyp4fiKnsJRq7AVX3np9YB\nwR4tgVskDZE+FQyBGAijgKyVeWYHlEVeViKRFcDcCoI9kPROmtSgWANgDWxRiPXAKQPKsdfqePsn\nFB165TYoc3pPHdcJbqVaVAjUAVgD3hIYRucCdVofKbW0VydypGtbxAdYfIS4wX5HW3rTrTJ9QIP8\n3ZI2sWdIXgNnC6xLQOqBsfWVhyDYKNtTx3WCvfIAFylLeQ+ANeBZNg96li0CvFqZ/MUD5S9X53uA\n5tWv+TiaRZ3zZOlXm3h0NDvwyYBf8mNjdyj/6NxldBogEs3VwFyDWw/ooj6e3546hsO9c4JeGxH4\ntfI14Fk2CbbakFcuW8BrQa/la33Qmfdseg5RbjqpIi53S5byM79+Zz26HauBvCvI2R0WGGv+iAOw\nB4wehCIAXAK6Xt89QXhAcIk0yJLNOrpa8Eu21vDYssm0N8z1yj0YtvKt6ybSOltHshUdRofJYj/l\n3a5gZIGRtR/NmyycaZ7NwGpFeezYnQ8CUeOpPj3gS19xbR5xCxDuqQOCa9QCn2XTR1wNgC3wAe35\nvh6Arb3aFiK99RDYOjqMo6WAH6tdS8JHJipHndyM7Gt8h4wK+HiyWZsUAmMFiD1tbv3pje4i7aXt\n2UvHiZEeWcMkzwZlt86CWnYPdl66VtZzTWA0GvSAqH0sEC45IeLBFBguqsZk01EhQ4FvtOfrFVNV\nBqxXRsy+WvH9pLYl5Ip+CPBJGILmmxwCWqOuW+/En95IsOezlzY4MUJEDwF4FYYXLb2OmX9WlX8n\ngB/GsGWfAPCvmPndXnshCG690rhq0IMqs6I+y57KokCsAa1V1gOy6BW2gP8r7sn31FHS9x4nYKRo\nkEZbgiEB82sSRdu1/zt9kFpAZJkXfbMeEhCFGgywevVbZWvhtHUEeC4AAquHw0T0FACvBvANGN5B\n/A4iehMzv1e4vR/A1zHzx0Z2/QKAB702mxA8xUr7VBtGeUDsLavltb/OW1GcvrajFekttenPFnOB\nRl6DLb/oXcEvwTDDj8TXJyJAaxdLWVEhCyjlPgn4aRCm9dSGx618hmEFhFadCHR6/LeKAIFyCHyO\n4fD6OcEXAnicmf8CAIjoDQBeCiDziJnfJvzfDuDZtQYjkeCGK7Xm32DYasDzvjEvErTKrHXWfLXN\nA50Hqh6oeWeAYdgiPr3zhVY+2cR+yA9ixQQkCSczCrTmdVWZbEuuh1Q6vxZA+EsoJiDnTRJzfrOy\n4O7w0kshF/VbWyfS5l5aPyf4LAAfEPkPAnig4v99AB6rNRiB4OYrbYPGGh95daN+Vp0aiKUi0Z1n\na/nW7C1Ypm3ogZ7lU8tjakNGhAWkgPKpNA78pF9EBSMJZQQqIs2clsNhPTSWu0NHi5ZPh38UUK3y\nc4FxT7XmBP/PbeD/3q551A7sQkT0EgDfC+BFNb8IBDdf6baKwC5apzVGs9QCXARk7m0QlbJkB+a/\n6NYR0lMnpUUkLiGXn2g9+shIUA5Tvcd7Sc1cxLpI2IpXAggbBBwBf1MyJEdDbbOzTYDcazMKpyV1\nTgnJPdUaDn/ereGT9K5HtMeHADxH5J+DITArRERfBuC1AB5i5r+prTICwQ1X+haR/oLx46k1/I0o\nzG+UB/qStqxoUZZpuGl7q6wGxhPNBZo0sKY0EgAF8Iqn2Fj2JAOI7pygWGrAFkNiAUQLcsVSwVD7\nuPWM9BL49fguhWGkLU8fuT18ttL6OcF3ArifiJ4L4MMAvgPAy6QDEX0+gP8K4F8w8+OtBiMQ3HCl\n3xBYnVYPyJZIQqImD2SezxZw0z5rT4oszesIL8EIIhpMS6BYf4LU7GiTc4DO7kxl3hJjX4B5l7Ot\nAbnCL9JWw2cJ9KK2KPxaPrq8pqfdGj5J73ukUaGhlXOCzHyHiF4O4DcwXK3yemZ+LxF9/1j+KICf\nAPC5AF5Dw/f1BDO/0GuTmNuQIaJvxHSJzOuZ+RVypUT0OgDfCuAvxyqzlRIRA/++a4Pb3/YlfZZc\nx7DlTaF6f22Uly/iyQCQ5XBsYpkXXlltadSZtdHy0etHZUllfubjtOHtxiW7PuoTLY+URfVmArN1\noWdbRMT41s6g5r8tX19UIQhusqKTQDDicwmfU970ueZoC+ZJLQGEQejZ88+a4MLPslntumWyb3JJ\nhg2qT51lJ9z9TVvNHq0T1W+uhOA3d/Lm104PwRv0AAWrbnTf7AN6X5G76qO+Z4BgWuYTIJjm46Td\negm8Zy++OzU0rp0gydOQsl1M64JlU5tiDWu99MxmtNkDwyV+SwDYW38vHfcO90rCq/Vt9ZwlPiUU\n9VychpylJXfVe+s7Vd5Yype26/cgzwCI4G5PbcAGYW7LSctmqmkPkMDsTHCkva1gWKt/StteOu4d\n7lFtxjyVS1m+3lFHAZ+aLNDV/lrXRHfeNYeRI23L/LjM0aADQsi8qM4eTJUK+KW2YJyUHsvkiRgS\nfSW5ntRntTnogF2tLAqzHt8lX1XUZuX30vFQ1S0kjwavDIZPC4hbR4cSlOlJna2I0FIEoKeMBoHp\njd866hMglMNR/dpOfXZYsMmUBqEEHGPKz9aDMi9FRh/kymbAMyDtQXELALbKt8qfG4LHcHiNPPh5\nQ2YPiDUYtkCo4OCWaZ8EslM9BgQnzDvpYgiqbABm0WHaR9Z7keUDGfTuTOvMrxZVeUAAUP1GZl+T\nAUfZ18I2d6vaeuBm2fYGok7vpQOCS2UNnSwoRoBYg2ENhN7wvBeMp/qcMhpMoHLsaVuLaFH6ivKe\ngLv4isd29Fv0yLDl9Wmb7KejosiLHo06UfCt8V8DxVbZXjrmBHuOAAkkC2g1mxUFRmw1uyUPzvrX\ntlZpKN2CqgZy9AgJHkHpPY6kQJjS3q1xxRyh4xOe5ZBtprLKbyH6FVjRoOlXsfVCr8enF2qRMm97\nTqljTrBHNcDIPIStF5BR4EX7YoFvq2jw2mjbWq8HxbV5CTujjKw6Y//cp8g4m6NBZ/pZ37GoK8tm\nkV8QeJYvOfV7gde7jAJtCTj31DEcXiMPOikNI59sPfm1fZF5C4peW0s/UPkayLRvb77SNhvwM/N6\nu2u7xgOdVnQfL7EFdAro6eUp03vqgOBStYDXgqGVXwtCq29WXts9kNXa7oFgLX8O31Y7ni26vRF/\niHq1/FqbUvr6tlhCpXvkzEAsZf4qHXOCS1T71mrfLlCHXe0XVSvr7U8NdlHItQAaAdDWfluCUOeX\nwM8rh1hKnRCAJlycOr0glM2tgeM5AAgcc4J935T8BcBIS59WurfOErX+Yj2QRXxaYPUO+l7o9aZP\nAdMo+HrKtJbaPGqM9hpYPLjVyvKjwoxyqDQqtpr2huExHO5RJIaPpoFtgRftq8xbv7RatFiDZnTe\nz7LD8V2T3qJ+j63HDmHT2hqGhqxrIHOZ0dRSEG79kz6VDgiuVQt6S6K9pXBs/YV68NMAs2wWxFoH\nei/sWuUR363gGtmupT6yf1IRsEVtkTI4USAZNuXXHCJ3QNnr11465gSXqPZ3KdNRKMKwtcrX9FWX\nUYetBkkv+kPF1ipfUmdNWtqikFuSh7BrbQBD8ydK86+vKIcqp4UgpKCfsQnn0DEn2Kse2FlQi9qW\n9EfbWlGqBzTL1oKetkG1twR2a2yngGYrHy2TfZHa2lazC3lwnP2MaAXIGv2wfrJ76RgO9wBHfjs9\ns8leGRybtd41f5uR+UGdjwLTAqgHRL3csuxU5WtB59WBsGttbLMgVthTmhw7xM+V2j/h2U96b6p1\n6oBgjyJDyyjsImDrgV/krzQaDbZAV8vDSEeXS32XgDJqO0UaRnqtzfvOWwAS5d1QpNjPema7MCge\nc4JL1DNLbP16ostT9BFOuqesBcJWBNhablVnLzi2yr1+w8mvsdUA40FtIQiBcv5Pr8q0XRgAgU3m\nBInoIUzvPHodM/+sKv8SAL8E4PkAfpyZX1lr78IhuDXMtgBejyIw7IXdWoBttewF6jmhCie/1Mez\njXZzgGAADqjMEdJUTQ9wAFSHyl5frX7teThssD4iegqAV2N4deWHALyDiN7EzO8Vbh8F8AMAviXS\n5oVDcIkigFwD0t71YkW6BsK1ESA6faPQvdT6UjvBMEnOExb5VK5ACKCIClPVIk0VQKp2mpC8UXoh\ngMeZ+S8AgIjeAOClADIEmfkjAD5CRN8UafAGnBjpjQJ7fGvrbvlE5gUtvx6wRdK1ZcRmbfe9AAAI\n80lEQVTnlEBc4rumjlcXTv6EtuJnQXXwJX80YKjLqv0wfLz/3JulZwH4gMh/EMADaxq84Eiw9i0t\nnQ+U6oFib59rgKz1tbUtFihry7U+Kb0GSFu2sWYpdQKbhl7TB+WQV9o8H/k/D5SgrEZ7RhsXq9vj\nx9XmW3DBEJSKwg6GrVYmFf2FtMDm9dnqV8uGgA3KDsdWK+v13xNqW9X18mtsDR8GZs8yNG0Khiwy\n2qZ/pkXe6o9aT8Pl9GqdHn7R+El6RDt8CMBzRP45GKLBxbpwCNagF7XV/iLX/jVG++L1ywMhjDIY\nZTDsEduSOnsvtyzT9pptY0haEaIe6ibNIkPyo78qEEnlnT6eZUi8+kLBdwK4n4ieC+DDAL4DwMsc\n39DWXTgEgb4hJUTaA2C0XKfX9Hnp8N0Doi7TRwpUubYtKT8lIHvLlthQsW0MPp33hsp6HlD6A5hd\nTgNlrwHQlQZvoMqmWnehIDPfIaKXA/gNDJfIvJ6Z30tE3z+WP0pE/xjAOwDcB+CaiH4QwPOY+W+t\nNol5yUHeLyJi4Kd6axnp1kG7R7q3TmS5JUi2Sm8BvKU+W5db+a1tEmjOus3yWplVbq1PFzkFZDYU\n16ceAPOyCxAHBny0s9Y/XLy+qG5AJKhVG24C4i9xZXqL/i2p1zqxsycEo+vbyqdVd216B9ts3k31\npfganTIPijryK+qoMpcbJ+VJQJd3y8iFQ7AXeFG/JdCrwS06/I0Crbb02qil1/rtAcWefi7dtq1t\nTt46+VEDnoZdkgaZNzyW9Yqf9CWC8IDgAnkgtMoAH4xWmXuaLZCv9UXm18wHRqA5Cw+M9BZlEaD1\n+gehsrnv1jZj3TMQVuqw4UdGHS+6i8CxattTl/cEhTNdLG1FYF50k+pZQGvlI2VRRYa5PSBEoEwv\nvTIsyC/1XQtFz7Ykv1WdrepVor28aO1Xp65ep/6ZRaM+M0rdU0ckOMoCkI6ygFik5dWJRnyeLSIL\njB4so5EgKjavzNuGtZCJwqxVvgSAS33W2DaMBK20CTYJtNY+ttrq6WfLvofu+UiwVz2ga/kkWwSA\nPVD0QCjbsaCnyyO2lJZL3e9afmm9NbCLlHv98uy9B/deMA3CUNus4XA1vdJWjRxPrSMSPJGiEVmP\nDRvZPcDVyqVa5XK9pwb+0oh5jbb6fmp/lFvYvO/WWn+kXKtn1HHJOiLBu0StIe8hW7X9c5P33SX1\n+9JheUSChw7dhbokyFy6jkjwLtElTjjfBNX2z7HvtlHPHOo5dESCd4mO4fAyHcPh0+vSh8NHJHjo\n0KF7Wp88dwdmOiC4SMdweJnu1uHwJUVax3C4V1ctByJ6iIjeR0R/SkQ/4vj83Fj+B0T0/O27eWny\nLhPZ+/KRm6ba/jn23TZq3Yhwbj3R+Tm9qpFg5M1ORPQwgC9i5vuJ6AEArwHw4An7fOjQhemSIq1L\n1+XNCbYiwfxmJ2Z+AkB6s5PUPwPwHwCAmd8O4GlE9MzNe3ro0KG7QJcXCbYgaL3Z6VkBn2ev79qh\nQzdFlzTcvHTd6fycXq0TIz33UzXr3XffPwg2V2t6L9sSe8t35T2me9xXatpq9yt75VvdOxxZb8S+\n1z7ybKfaR0t8PFtbH//4ompCl3dipAXByJudtM+zR9tMP/RDn8rpW7du4datW9F+Hjp06Ay6ffs2\nbt++nfOPPLK2xcubE6y+Y4SIngrgTwB8PYY3O/0ugJcZJ0ZezswPE9GDAF7FzLMTI0TEe73P5BS6\nffv2jYf2Td+Go//nFxGtfMfIKztr/duTv2OkOifIzHcApDc7/TGA/5Te7CTe7vQYgPcT0eMAHgXw\nr0/Z4XNJ/hveVN30bTj6fzfo5s0JgpnfDODNyvaoyr98434dOnTortTNmxM8dOjQoQ11w+YEN10R\n0c2dEDx06FDWujnB/dYX1W4QPHTo0KFLVPPe4UOHDh26m3VA8NChQ/e0NofgTX/qTKv/RPSdY7/f\nTURvJaIvO0c/PUX2/+j3VUR0h4i+bc/+RRT8Dd0iot8noj8kots7d7GqwG/oc4jo14joXWP/v/sM\n3XRFRL9IRP+PiN5T8bnYY7hbzLzZB8BTADwO4LkAPg3AuwB8qfJ5GMBjY/oBAL+zZR926P9XA/ic\nMf3QTeu/8PufAP47gG8/d78XfAdPA/BHAJ495p9x7n539v/HALwi9R3ARwE89dx9F/37WgDPB/Ae\np/xij+Eln60jwZv+1Jlm/5n5bcz8sTH7dlzWwyIi+x8AfgDAfwHwkT07F1RkG/45gF9h5g8CADP/\n1c59rCnS/2sA943p+wB8lIcbEy5CzPzbAP6m4nLJx3C3tobgTX/qTKT/Ut8H4LGT9qhPzf4T0bMw\nHJSvGU2XdnlA5Du4H8DTieh/EdE7iehf7ta7tiL9fzWA5xHRhwH8AYAf3KlvW+mSj+FubX2x9KZP\nnTmDwv0gopcA+F4ALzpdd7oV6f+rAPwoMzMRES7viaCRbfg0AC/AcE/7ZwB4GxH9DjP/6Ul7FlOk\n/w8B+D1mfgkRfSGA3ySiL2fmT5y4b1vqUo/hbm0NwU2fOnMGRfqP8WTIawE8xMy1YcPeivT/KwC8\nYeAfngHgG4noCWZ+0z5dbCqyDR8A8FfM/EkAnySi3wLw5QAuAYKR/n83gFcAADP/GRH9OYAvBvDO\nPTq4gS75GO7XxhOqTwXwZxgmhT8d7RMjD+KCJlWD/f98DBPfD567v0v6r/x/CcC3nbvfC76DLwHw\nFgwnIT4DwHsAPO/cfe/o/88D+Mkx/UwMkHz6ufuu+vhcxE6MXNQxvOSzaSTIzHeIKD115ikAXs/j\nU2fG8keZ+TEienh86szfAfieLfuwRpH+A/gJAJ8L4DVjNPUEM7/wXH2WCvb/ohX8Db2PiP4HgHdj\nOMnwWmb+4/P1elLwO/h3AH6ZiN6NYVj5w8z812frtBIR/UcALwbwDCL6AICfxDAFcfHH8BIdt80d\nOnTontZxx8ihQ4fuaR0QPHTo0D2tA4KHDh26p3VA8NChQ/e0DggeOnTontYBwUOHDt3TOiB46NCh\ne1oHBA8dOnRP6+8BcfXZZ15LwGAAAAAASUVORK5CYII=\n" | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
}, | |
{ | |
"data": { | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x10e492dd0>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"for step in range(steps):\n", | |
" B.updateOld()\n", | |
" res1 = res2 = 1e6\n", | |
" while res1 > 1e-3 and res2 > 1e-3:\n", | |
" w.value = B.faceValue[Y2 == 1]\n", | |
"\n", | |
" res1 = eq1.sweep(a)\n", | |
"\n", | |
" a2[Y2 == 1] = a\n", | |
"\n", | |
" res2 = eq2.sweep(B, dt=dt)\n", | |
" \n", | |
" viewer1.plot()\n", | |
" viewer2.plot()" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": null, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [] | |
} | |
], | |
"metadata": { | |
"kernelspec": { | |
"display_name": "Python 2", | |
"language": "python", | |
"name": "python2" | |
}, | |
"language_info": { | |
"codemirror_mode": { | |
"name": "ipython", | |
"version": 2 | |
}, | |
"file_extension": ".py", | |
"mimetype": "text/x-python", | |
"name": "python", | |
"nbconvert_exporter": "python", | |
"pygments_lexer": "ipython2", | |
"version": "2.7.11" | |
} | |
}, | |
"nbformat": 4, | |
"nbformat_minor": 0 | |
} |
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