diff --git a/notebooks/2015-09-10-surface-normals.ipynb b/notebooks/2015-09-10-surface-normals.ipynb new file mode 100644 index 0000000..a2aa20d --- /dev/null +++ b/notebooks/2015-09-10-surface-normals.ipynb @@ -0,0 +1,509 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Surface normals\n", + "\n", + "Author(s): Jukka Aho\n", + "\n", + "**Abstract**: Testing different strategies to calculate surface normals. These are important when calculating mortar projections." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Creating element Point1: 1 node point element\n", + "Creating element Seg2: 2 node linear line element\n", + "Creating Lagrange basis for element Seg2. Number of basis functions: 2. Element dimension: 1\n", + "Calculating inverse of A\n", + "Element JuliaFEM.Seg2 created.\n", + "Creating element Seg3: 3 node quadratic line element\n", + "Creating Lagrange basis for element Seg3. Number of basis functions: 3. Element dimension: 1\n", + "Calculating inverse of A\n", + "Element JuliaFEM.Seg3 created.\n", + "Creating element Quad4: 4 node bilinear quadrangle element\n", + "Creating Lagrange basis for element Quad4. Number of basis functions: 4. Element dimension: 2\n", + "Calculating inverse of A\n", + "Element JuliaFEM.Quad4 created.\n", + "Creating element Tet10: 10 node quadratic tetrahedron\n", + "Creating Lagrange basis for element Tet10. Number of basis functions: 10. Element dimension: 3\n", + "Calculating inverse of A\n", + "Element JuliaFEM.Tet10 created.\n" + ] + } + ], + "source": [ + "using JuliaFEM" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "WARNING: could not import Base.help into PyCall\n", + "INFO: Precompiling module Colors...\n", + "INFO: Precompiling module LaTeXStrings...\n" + ] + } + ], + "source": [ + "using PyPlot" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": [ + 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" + ], + "text/plain": [ + "PyPlot.Figure(PyObject )" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "(-5.0,15.0)" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "phi = linspace(0, pi, 200)\n", + "phi2 = linspace(0, pi, 4)\n", + "figure(figsize=(4, 2))\n", + "R = 10.0\n", + "plot(R*cos(phi), R*sin(phi), \"-r\")\n", + "plot(R*cos(phi2), R*sin(phi2), \"-ko\")\n", + "#axis(\"off\")\n", + "axis(\"equal\")\n", + "xlim(-1.5*R, 1.5*R)\n", + "ylim(-0.5*R, 1.5*R)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Aim: to reconstruct half circle surface and calculate continous normal field. Let's create P4 hierarchial element and so on." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "252" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "binomial(10, 5)" + ] + }, + { + "cell_type": "code", + "execution_count": 177, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "get_legendre_polynomial_derivative (generic function with 1 method)" + ] + }, + "execution_count": 177, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Legendre polynomials\n", + "\n", + "function get_legendre_polynomial_2(n)\n", + " bin(n, k) = prod([(n + 1 - i)/i for i=1:k])\n", + " P(xi) = sum([2^n*xi.^k*bin(n, k)*bin(1/2*(n+k-1), n) for k=0:n])\n", + " P\n", + "end\n", + "\n", + "function get_legendre_polynomial(n)\n", + " if n == 0\n", + " P(xi) = 0*xi + 1\n", + " elseif n == 1\n", + " P(xi) = xi\n", + " else\n", + " Pm1 = get_legendre_polynomial(n-1)\n", + " Pm2 = get_legendre_polynomial(n-2)\n", + " P(xi) = 1/n*( (2*n-1)*xi.*Pm1(xi) - (n-1)*Pm2(xi))\n", + " end\n", + " return P\n", + "end\n", + "\n", + "function get_legendre_polynomial_derivative(n)\n", + " if n == 0\n", + " P(xi) = 0*xi\n", + " elseif n == 1\n", + " P(xi) = 0*xi + 1\n", + " else\n", + " Pm1 = get_legendre_polynomial_derivative(n-1)\n", + " Pm2 = get_legendre_polynomial_derivative(n-2)\n", + " P(xi) = 1/(n-1)*( (2*(n-1)+1)*xi.*Pm1(xi) - (n+1-1)*Pm2(xi))\n", + " end\n", + " return P\n", + "end\n" + ] + }, + { + "cell_type": "code", + "execution_count": 153, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "P (generic function with 1 method)" + ] + }, + "execution_count": 153, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "\n", + "get_legendre_polynomial(3)" + ] + }, + { + "cell_type": "code", + "execution_count": 181, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": [ + 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fP58mTZrg4eFBRkYGUVFR3L17l/DwcGrUqPHCMRU1SV6FEEIIIYrQwoULqVevHhERESxbtgxLS0t69+5NWFgYTZs2zdPF/yyLDzwtOTkZlUrF7du3c6sTPE2lUqFWq/NVO5g7dy6NGzcmIiKC5cuXo6OjQ4sWLZg4cSJvvfXWi91oMZHkVQghhBCiiPn7++cu7/q0pKSkPD+7uro+1zjYl1kJy8/PDz8/vxc+XlvKxJjXK1euaDsEIYQQQghRDMpE8urr68vWrVu1HYYQQgghhChiZSJ5bd26Ne7u7rz//vtkZWVpOxwhhBBCCFFEykTyOmfOHObPn8+8efPo2LFjgUV3hRBCCCFE6VcmkleVSsW4ceOIjY3l3LlztGjRgoMHD2o7LCGEEEIIUcjKRPL600/Kc9u2bTl+/Dh169alXbt2LFiw4KVqpwkhhBBCiJKlTCSvY8bA5MmQlQWVK1dmz549jB8/nvHjx9O3b18ePHig7RCFEEIIIUQhKBPJa0AAzJkDHTvC9eugq6vLxx9/zObNm9m9ezctW7bk9OnT2g5TCCGEEEK8pDKRvA4aBHv3wvnz0KyZ8hrA3d2dn3/+GT09PVq1asWGDRu0GqcQQgghhHg5JSZ53bdvH2q1usBHfHz8/3u8iwucOAFNmigtsKGhkJ0N9erV4/Dhw7i7u9O/f39Gjx5Nenp6MdyREEIIIYQobCVuedjAwEBatmyZ5706deo807FWVrBrF8yYASEhcPAgrF0LVlbGrF69GicnJ8aOHcuhQ4eIiorCzs6uCO5ACCGEEEIUlRKXvLZt2xZ3d/cXPl5HB6ZNA2dn6N8fmjeHqCho00bFu+++S+vWrfHy8qJFixYsW7aMfv36FWL0QgghhBCiKJWYYQNPaDQaHjx48NIrZXXsqAwjqFMH2rWDTz6BnBxo3rw5CQkJ9OjRA29vb4YNG0ZqamrhBC+EEEIIIYpUiUteBw8ejKmpKYaGhrRv356EhIQXPlfVqsrkrYkT4b33oFcv+OsvMDExYe3ataxYsYJ169bRqlUrzpw5U4h3IYQQQgjx/7O1taVWrVraDqNUKTHJq76+Pn369GHRokXExMQwY8YMTp48Sdu2bTlx4sQLn1dXF2bNgm++UcbANm+uLGqgUql45513OHr0KACvvfYakZGRsqiBEEIIIYqVSqXKfV3QBHZ9fX1sbGzo27cvhw8fznNsVlYWCxcuZPDgwTRr1oxy5cqhVqtZsWJFcd9GsSkxY17feOMN3njjjdyfu3fvTp8+fWjSpAnBwcHs3Lnzpc7frZsyjKB/f6UyQUgITJoEDg4OxMfHExgYyDvvvMPevXtZsmQJJiYmL3lHQgghhBAvxtbWlkGDBgGQkpLCoUOHiI6OZsuWLURHR9OrVy8AHj58yLhx41CpVFhbW1OlShV+++23PAlxWVNikteC1KlTh549e7JlyxY0Gs2/fhDjxo3D1NQ0z3ve3t54e3vnea9GDdi3Dz76SElef/hBqUZgY2PE8uXLcXNzY8SIEcTHxxMVFUWzZs2K6M6EEEIIIf6dra0tU6dOzfNeSEgIoaGhBAUF5SavxsbG7Ny5k2bNmmFtbZ27j7Zs2LAhX139e/fuFeo1SsywgX9TvXp1MjIySElJ+dd9FixYQExMTJ7HPxPXJ3R1Yfp0iI2FS5egaVPYulXZ1r9/f44dO4axsTGtW7dm6dKlMoxACCGEEC9t8eLFODg4YGhoSPXq1QkICHjupM7f3x+A5ORkbt++DYCenh6dO3fG2tq60GN+Ed7e3vlysgULFhTqNUp88nrp0iUMDQ0pX758oZ7XxQX+9z+lEoG7O4waBY8eQd26dTl06BDDhw9n1KhR9O3blzt37hTqtYUQQgjx6ggMDGTMmDHcu3ePESNG0K9fP3bt2kWnTp3IzMx85vPk5OTkvi7LwwL+PyVm2MDNmzepVKlSnvf+97//ERMTQ7du3YrkmubmsHkzfP45jBsHBw7Axo3QqJE+ixYtol27dgwZMoSmTZuyevVq2rVrVyRxCCGEEOIpqamQmFj817W3ByOjQj1lXFwc4eHh2NnZER8fj5mZGQBhYWG4ublx/fp1bG1tn+lcERERANSuXRtzc/NCjbM0KTHJq5eXF0ZGRrzxxhtYWVlx5swZli1bRvny5Zk9e3aRXVelgpEjoU0b8PaGli1h/nzlPXd3d1q2bMmAAQNo374977//PtOnT6dcuXJFFo8QQgjxyktMBEfH4r9uQgK0aFGop4yMjARg8uTJuYkrKFWWZs2ahZubW4HHJSUlERISAigTto4cOcLBgwfR0dFh7ty5hRpjaVNiktfevXuzbt06FixYwP3797GysqJPnz5MmzaN2rVrF/n1GzWC+HiYMEEZQvDdd/DFF2BjY8OePXuYO3cuH374Id999x3r16+nfv36RR6TEEII8Uqyt1cSSW1ct5AdO3YMlUqFq6trvm3Ozs6o1QWP4Lx8+XLuxCtdXV2srKzw8PAgKCiI1q1bF3qcpUmJSV4DAgIICAjQagyGhhARAZ06wZAhymSudevA1VWH999/n44dO+Lj40Pz5s1ZsGABw4cPf6XHnAghhBBFwsio0FtAteXJpKyCJlTp6upiaWlZ4HHt2rVj7969RRpbaVXiJ2xpQ69eymQuOztwc4PgYMjIAEdHRxISEhg4cCAjR46kV69e3Lx5U9vhCiGEEKKEelLK88aNG/m2ZWVlcevWreIOqdST5PVfVK8Oe/bAjBkwdy68/jqcOqXUU/vss8/Ytm0bcXFxNGnShF27dmk7XCGEEEKUQI6Ojmg0Gvbv359v28GDB/NUEBDPRpLX/6Cjo6zCFR//pOVVmcyVkwM9e/bkl19+oWnTpnTt2pXAwEDS0tK0HbIQQgghSpAnq2SFhYXlKb2ZlpZGcHCwlqIq3UrMmNeSrHlzZdz45MkQFARffw2rVkHNmlX49ttvWbx4Me+99x579+5l/fr1NG7cWNshCyGEEKIEcHJyIiAggPDwcBo1aoSHhwd6enps374dCwsLqlSp8tILIs2ePZvEx6XFTpw4AcDKlSs5cOAAAG3btmXIkCEvdyMliLS8PiMDA5g3D/buhYsXoUkTWL0aVCo1Y8aM4ejRowC89tprzJ8/X7oBhBBCCAHAwoULCQ8Px9TUlGXLlhEVFUXXrl35/vvvKVeuXJ7J3y8yEXz37t2sXr2aNWvWcPLkSVQqFYcOHcp976effirM29E6aXl9Tm5u8MsvMGYM+PnB9u3KIgeNGzfm6NGjBAcHExQUxLZt24iMjKROnTraDlkIIYQQWubv75+7vOvTkpKS8vzs6ur63A1gsbGxLxVbaSMtry/AzExpdf3qK9i3T6kR++23YGBgwIIFC4iNjeW3336jadOmLF269KW7A4QQQgghhEKS15fQp49SgaBFC+jWTVmV6+FDpTbbL7/8gq+vL6NGjeLNN9/kypUr2g5XCCGEEKLUk+T1JVWpAjt2wNKlsGYNNGsGcXFgYmLCZ599xq5duzh79iyNGzcmMjJSWmGFEEIIIV6CJK+FQKVSWl1PnIBKlaBNG6UqQWoqdO7cmVOnTtG7d2/eeecd3n77ba5fv67tkIUQQgghSiVJXgtR3bpw8CB8/LGyzGzTpvDjj2BmZsaqVavYvn07R48excHBgQ0bNkgrrBBCCCHEc5LktZDp6MCECcryslZW4OqqVCZISYG3336b06dP8+abb9K/f3/69u0ry8sKIYQQQjwHSV6LSP36cOCAsiLXF18odWH37QMLCws2btxIVFQUsbGxODg4sHXrVm2HK4QQQghRKkjyWoR0dGDsWKUubPXqSo3YUaPgwQPo27cvp0+fxsnJCXd3d7y8vPjjjz+0HbIQQgghRIkmyWsxsLOD2FgID1fqwzZuDD/8ANbW1mzdupUNGzawd+9eGjRowJdffiljYYUQQggh/oUkr8VErYbRo+HkSahdGzp1guHD4cEDFf369ePs2bN069aNQYMG0aVLF5KTk7UdshBCCCFEiSPJazGrVUtpdV26FDZsAAcH2LULLC0tWbNmDd9++y2JiYk4ODjw6aefkp2dre2QhRBCCCFKDEletUCtVurCnjoFDRpA167g4wN//gldu3bl1KlTDBkyhPHjx+Ps7MypU6e0HbIQQgghRIkgyasW1awJu3fDqlXKs709rFwJ5cubsGjRIg4ePMj9+/dp0aIF06ZNIz09XdshCyGEEEJolSSvWqZSgZ8fJCZCjx4wZAi0a6f87OTkxPHjx/nggw+YOXMmLVq04NChQ9oOWQghhBCFxNbWllq1amk7jFJFktcSwtISvvxSGQ977ZqyOldICIA+oaGhHDt2DGNjY5ydnRkzZgwPHz7UcsRCCCGEKAwqlSr39b59+1Cr1Xke+vr62NjY0LdvXw4fPpzn2AsXLjBnzhzat2+PjY0N+vr6VK5cmV69erFv374Cr/f7778TFhaGp6cndnZ2ude5dOlSUd5moZHktYTp0EGpCztxIoSFKUns/v3QuHFjDh06xLx58/jiiy9o0KABW7ZskbJaQgghRBlka2tLSEgIISEhjB07llq1ahEdHU2bNm3Ytm1b7n5TpkwhODiYmzdv0r17dyZMmICzszM7duygffv2hIeH5zv3zz//zJQpU9i6dSsqlQozM7M8CXRJJ8lrCWRoCDNmwIkTYGGhDCMYMgTu3dNh3LhxnDlzhubNm+Ph4UH37t1LzV9KQgghhHg2tra2TJ06lalTpzJnzhwOHDjA1KlTycnJISgoKHe/rl27cvz4cU6ePMnSpUsJCwtj8+bN7NmzBz09PSZOnMiNGzfynLtly5b8+OOP3L17lwsXLtCkSZNS1RgmyWsJ5uAAP/4In30GmzcrE7rWroWaNW2JiYlh27ZtnDp1CgcHB2bMmCETuoQQQogSavHixTg4OGBoaEj16tUJCAjg3r17z3UOf39/AJKTk7l9+zYAfn5+NG3aNN++Li4uuLq6kpGRQVxcXJ5t1apVw9nZmfLly7/g3WiXJK8lnFoNI0bA2bPK8rIDBkDnzvDrr9CzZ0/OnDlDYGAg06dPp2nTpuzZs0fbIQshhBDiKYGBgYwZM4Z79+4xYsQI+vXrx65du+jUqROZmZnPfJ6cnJzc18/Sza+np5fnuazQ1XYA4tlUqQJRUUplglGjlFbZiRNh0iRjZs+ezYABA3j33Xfp2LEj3t7ezJ8/n8qVK2s7bCGEEOK5pWZnk5iaWuzXtTcywkhHp1DPGRcXR3h4OHZ2dsTHx2NmZgZAWFgYbm5uXL9+HVtb22c6V0REBAC1a9fG3Nz8P/e9fPkye/bswdjYGBcXl5e6h5JGktdS5q234MwZmDULPv4Y1qyB+fPB3d2B/fv3s3r1aiZMmED9+vUJCwvj3XffRaeQ/yEKIYQQRSkxNRXHhIRiv26CoyMtTEwK9ZyRkZEATJ48OTdxBdDX12fWrFm4ubkVeFxSUhIhStkhUlJSOHLkCAcPHkRHR4e5c+f+5zXT09Px8fEhIyODsLAwTE1NC+dmSghJXkshIyP46COlFXbsWOjTBzp1gvBwFX5+fvTo0YPg4GACAgKIjIzks88+o2XLltoOWwghhHgm9kZGJDg6auW6he3YsWOoVCpcXV3zbXN2dkatLngE5+XLlwkNDQVAV1cXKysrPDw8CAoKonXr1v96vezsbAYMGEBcXBz9+vXLM7mrrJDktRSzs4NvvoGvv4bAQGjcGMaPhw8/NOfzzz9n8ODBjBw5ktdff50RI0YwY8YMLCwstB22EEII8Z+MdHQKvQVUW55MyrK2ts63TVdXF0tLywKPa9euHXv37n2ua2VnZ+Pr60t0dDReXl6sXbv2+QMuBWTCVhnQowecPg0ffggLFypVCaKi4PXXW/Pzzz8zf/581q9fT926dQkPDycrK0vbIQshhBCvhCdd9v8sVwWQlZXFrVu3CuU6mZmZeHt7ExUVhY+PD+vXr//XVt3Srmze1SvI0BCmTlXGw7ZsCf36QceOcP68LmPHjuXZGdqyAAAgAElEQVTChQt4eHgQGBhIs2bN+OGHH7QdshBCCFHmOTo6otFo2L9/f75tBw8ezFNB4EVlZGTg6elJdHQ0fn5+rFmzplQtOvC8JHktY2rVgq1bYedOuHJFWaErKAgMDKxYvnw5P//8M2ZmZnTq1InevXvLAgdCCCFEERo0aBCgVBe4c+dO7vtpaWkEBwe/9PnT09Pp3bs3MTExDB06lJUrV77wuUrLQgUy5rWM6tIFTp2CefOU1brWr1eeBw1qwY8//sjGjRt57733aNCgAUFBQUyaNKnUFisWQgghSionJycCAgIIDw+nUaNGeHh4oKenx/bt27GwsKBKlSovlTSOHDmSnTt3YmlpSdWqVZk+fXq+fdzc3PJNGHuSVAMkJiYC8P777+fmAsOGDcPZ2fmF4ypKkryWYfr6MGmSsrDBBx/A0KEQHg7z56vw9vbm7bffZs6cOXzyySesWrWKOXPm4OPjU2bHyAghhBDasHDhQurVq0dERATLli3D0tKS3r17ExYWRtOmTfN08T9vd39ycjIqlYrbt2/nVid4mkqlQq1W50teV69ejUqlQqPRoFKpUKlUbN26Nffn9u3bS/IqtMfGBtatgzFjlGoEHTook7w++cSY0NBQ3nnnHd577z0GDhzIkiVLWLRokZTWEkIIIQqRv79/7vKuT0tKSsrzs6ur63ONg42NjX2heApjrK22SBPbK+T11+HgQaUSwS+/QKNGSomtChVs2bRpE7GxsaSmptKqVSsGDx7MtWvXtB2yEEIIIUQekry+YlQq6NsXEhOVMbCRkUq92E8/BSendiQkJLB06VK+/vpr7OzsmDJlCg8ePNB22EIIIYQQgCSvrywDA3j/fbhwQUlmg4KUltgdO3QZMWIkFy9eJDAwkLlz51KnTh2WLFlCZmamtsMWQgghxCtOktdXnLU1fPYZnDgBtrbQq5cyJjYpyZRZs2Zx/vx5unXrxujRo2nUqFHuYG4hhBBCCG2Q5FUAytKyu3fDjh1w/Tq0aKFUKcjKsiEyMpLjx49Tq1Yt3N3dadOmDXFxcdoOWQghhBCvIEleRS6VCt56S5nMtWQJ/PAD1K+vVCmoXLkpu3bt4rvvviM1NRVnZ2f69OnD+fPntR22EEIIIV4hkryKfPT0YORI+PVXCA2F1auhTh2YNg1ef70TCQkJrF69mvj4eBwcHBg9ejR//vmntsMWQgghxCtA6ryKf2VsrCxuMHw4zJkDH38MEREwebKad98dgKenJ4sWLWLmzJmsXr2aCRMmMHbsWCpUqKDt0EuuBw/gjz8gPR0yMiAzEzIy0GRkkJZ6n4cpd0hJuUNqyl0epd7nUeo90h89JMNAj+wKJmgqmJBtagKmZmjMTFFVqICerj7ldMqhp6OnPKv1KF+uPFVNqlJBv0KZXt9aCFGy5ORkkZaWRGrqWVJTE0lKOqjtkEQZJMmr+H+ZmyvJ65gxSkvsxImwYAFMn27A+PHvMWTIEMLCwpg5cyaLFi3i/fffx9/fHyMjI22HXrwePYLff4fffsvzyL6STEbyJXSuXqPcg9QCD1UBho8flf6xLVsFOv8yRy4HuK8Pdw3gnoHyfNMAbhrBpYrwWyU9HlS3IqNmdUyq1KRK+SpUNan697OJ8myqbypJrhDimWVlPeTRo3OkpiaSmppISoqSrD56dAGNJgMAVVZ57l6w1nKkoiyS5FU8s2rV4PPPlVW6pkyBd96BTz6BmTMtmDdvPuPHjycsLIxJkyYxf/58Jk+ezLBhw9DX19d26IUrLQ2OHYMjRyA+Hs6dUxLVW7fy7HbPpBy/m8Kvxhn8VgGuvA4Prc0oV60GhiYVMTIyw9jIDOPyFTE2NsOkvAUm5c2pUN4SUxNLzCpYYWZSCT09faWl9t49uHuX7L9uk3XnNtl3bpN95y/Ud/6i4t27mN29S827d1Hdv4/6xh+U+/l39O+nAFeBqzwwSuCyhS4XzLJJNM3kQEW4WBEumsNfFobUrWSPg5UDDpUcaGTVCIdKDtQ0q4laJaOLhHgVaTQaMjL+eJygns1NVFNTz5Ke/lvufjpp1qj+rInmYgM0pzpAcg24UgN1TmUMbK4Avtq7CVEmSfIqnlv9+rBpE/z8M0yaBL17K6t3hYVVZ8mSpUycOJHQ0FACAwP5+OOPmTp1Kn5+fujp6Wk79Oen0SjFcI8cUR6HD8P//gdZWWTrl+N3u0qcrqTidOUMTunDbxXgN1NQV7ehTrVGNKzUkAaWDXCs1BDfSg0wMzB7sTj09cHKCqys0AF0nvW4O3fg0iW4dAmTixdpdOkSjS5eJOfir6jifkf1eHnALL0Mrta4wolqV4k1j+YrqzROWYGeoTENKjXITWYdKjngYOWATQUbaakVooz4Z1f/08lqVtZdZSeNDroPaqC6Zkv2OVc4Ux2uKEmqbiVzjOyNMG5gjFFnI4zsjTBqYISepR7Hjx8HR+3enyh7JHkVL+y11+C772DPHggOho4doW1bCAmpTWTkKj744ANCQkIYNmwYs2fPJiQkBG9vb3R0njn1Kn63b/+dqD5pWb1zB4C0OrZcrGvBXh87NholEW+ZTkWTDN6weYOGlg3pWKkhDSs1pL5lfcqXK6/lG3msYkVwdFQeT1GDMub28mW4dAnd8+epefw4NRMSePun26iyIUdPl5u1zUiscZ84q1i2V9jIZIs0MnTBpJwJzas0x9nGGScbJ5xsnDA3NNfKLQohnk12dgqpqedyE9MCu/qzjdH5yxau1CD7VB/4VUlQuV0N/dqmuYmp0aDHSWp9I3SMSvB3uiiTJHkVL61DByXP27EDQkKUn5Uk1p4NGzYyadIkpk6dyoABA5g5cyahoaG4u7ujVpeQ7ugrV2DLFoiOhrg4pbXV0pJHjk0528+V7yzvsVL3JBc0yRjo3sClpgu9aw9hSe1ONLZuXHq71cuVg7p1lUfnzrlvqx49gl9+Qf3zz1gnJGCdkIDr3osEZ2ej0dPjfl0bkmpbEFftIavOL2eW/iwA7C3tc5NZZxtn6lnUk9ZZIYqZRqMhM/PPPMnpk2Q1Pf1K7n7qNCvUf9qiuWSP5uRTXf3ZlTFqYKwkpg5GGPdRXhvYGqDSkX/PomSQ5FUUCpUKuneHbt0KSmKbsHXrNo4ejWfq1Kl4enrSrFkzPvroI7p166adBOfiRdi8WXnEx0O5cuR06sjJsDFss77DxtQjJN7egwoVLaq0wKP2UDrV6YSTjRMGugbFH29xMjRUxoG8/vrf7z1OaFUJCZgmJNDs559ptuMkozQaMm2qcaV5bX6so8v6ez+x8vhKNGiwMLTIbZV1tnHmtaqvYahnqL37EqIM0WiyefTo6a7+v7v8s7LuPN5J6ernWk1yzrvAmWq5Xf16lhZKN7+9EUZvPm5NtTdCr5JeoX0nZ2QoX7Hiv9na2qJSqUhKStJ2KKWGJK+iUD2dxH777T+T2Fbs3LmLgwd/5MMPP6RHjx40b96cyZMn07t376JviT179u+E9cQJJUnr2pXfB3mwxPoKX1zcxM3Ub7F9YEun2p0IdfuI9rXaY2FkUbRxlQYFJbR37sCBA+jFxlInNpY6Mb8wCMiuU5vrr9XnkJ0hm27+yYykGaRkplBOpxwuNV3oXKczXey64FDJQVpmhfh/KF395wsYj3r+H139teCKDdmn+8Cv1eFyTbj1j67+gY+f6xmhY1x0Xf0ZGRAZCTNnKh1b4v/39Hfhvn37aN++fZ7tenp6WFlZ8cYbbzB+/Hhat26du+3ChQts2bKF3bt3c+HCBf78808qVqxI69atGTt2LO3atSuu2yg2kryKIqFSKQnsW28VlMS2JTZ2H/v2xRIWFkafPn1o2LAhkyZNwsvLC13dQvrfUqOBkyeV4QCbN8OZM1C+PHTvTsrEcUTVuMeyxHUcufo+lg8tGdBkAIObDaaRVSNJqp5FxYrQs6fyALh5E/bvRyc2luqxsXhGncUT0DRowK1WjThsX55Vab8xJXYKE7+fSDWTanSu05nOdp3pWLujjJkVr6ynu/r/2d2fr6v/Zk00F+uhOeUGSTWVrv6sx139DR4np+5KK6phLcNi7ep/krSGhSlVA728YN488PQsthDKFFtbWwYNGgRASkoKhw4dIjo6mi1bthAdHU2vXr0AmDJlCps2bcLBwYHu3btjbm5OYmIiMTExxMTEsHDhQgICArR4J4VPkldRpP4tiW3TRsW0ae354Yf2HDoUR1hYGL6+vkybNo0PPviAgQMHUq5cuRe7aEYGREXB/PlKC6uZGbz9NpqZM/nR3pAVZ9fx1emRpP+aTle7rmzuu5nu9bpTTucFrycUlSpBnz7KA+D6ddi3D1VsLJViY+nx5a/00NMj29WF80712WyRzoarh1h5YiVqlZpW1VrRpU4XOtt1pmXVluioZRKIKFv+7upPzNfd/0xd/RYWSiuqvRFGHY1yu/31rAqvq/9FpKf/3dL6++/Qrx98+CHUr5/N3Lnfay2u0s7W1papU6fmeS8kJITQ0FCCgoJyk9euXbsSHBxM06ZN8+x74MABOnXqxMSJE/H09KRy5crFFntRk+RVFIuCkthOnaBlS/jgAye+/noHJ04cY+bMmQwbNozQ0FDee09ZAMHQ8BnHSf71l1KINjxcSZy6dIFvvuHq6w1ZdWY9kSeCuHjiInbmdkxxmcLApgOpVqFakd73K61KFfD2Vh4ASUnwzTfofP01DWYt58PMTD5s1Ij7nUcT27g8a/XPs+DwAkL2h2BuaE6n2p3oUa8H3et1x9TAVLv3IsRzyM5OfTyr/59J6nN29ds/7up/Mqu/CLv6X8T9+8pX7oIFcOOGkrROmQJ2dpls2LABd/eZnDt3TtthlhiLFy9m6dKlXLp0CQsLC3r37s2MGTOe6xz+/v6EhoaSnJzM7du3sbCwwM/Pr8B9XVxccHV15YcffiAuLg53d/fCuI0SQZJXUayeTmJ371ZW7vLwUGrHTpzYgnXropk+/TSzZs0iMDCQGTNmEBQUxMiRIzExMSn4pBcuwKefwqpVkJ0NAweiCQxkt/5vLDqyiN1LdmOga4BnQ08ie0bSpkYbGRagDbVqQUCA8rh/X/kf4OuvqbBqAz1v36anlRU5b/Xi3Bv12Fz9Ptuv7sF3qy96aj061u6IewN3etbvSSXjf65BJkTxU7r6b+abLJWScpb09Mu5++mkWaG6WRPNxfpoTrWHZBu4XPPvrv4n41F7K88GtgaodUt2BZM//oBFi5TlwlNTYcAAZeXFWrXS+fLLL+nWbTZJSUn06NGD4ODg3K7vV1lgYCDh4eFUrVqVESNGoKury/bt2zly5AiZmZnPvJhPzuPa3MAz/R57Ul+9VNZZ/w+SvAqtUKmUhtEuXZQyW3PmwNChMHUqjBvnwNKlawkJCWH27NlMnjyZ2bNnM3bsWEaPHk3FihWV8awHDihDA77+Giwt4b330IwcyZ6Uk0yNHcah3w/xWtXX+KzbZ3g18qKCfgVt37Z4okIFZSCcp6fyB8ehQ/D116i//poGq77kQ319PnRz46+us9lsr2H99d2M+GYEI74ZQdsabXFv4E5v+97YmNpo+05EGafRZJOWlpyv7JTS1f/X45100Hlog+paTXLOtYEz/f4u4P+kq79ByerqfxGXLsHcubByJejpwYgRMG4cmJmlsGLFCj7++GOuXbtGnz592LJlC82aNePYsWMvdK3s1GxSEwteTrsoGdkXft3auLg4wsPDsbOzIz4+HjMzZbGasLAw3NzcuH79Ora2ts90roiICABq166Nufl/zxO4fPkye/bswdjYGBcXl5e6h5JGklehda+/rpRZPXtWWW520iRlwL+/vx0zZ37B1KlT+eSTTwgLC2Pe7NksbNOGfteuoX/qFDRsCMuXg48P+28cYerOvhy4fIBW1Vqxy2cXb9Z5s9T9gnjl6OhAmzbKY84cpYzZN9/A9u2Yj5vEMJWKYR07cr/XfLbZw8aru5nw3QQCdwXSqlor3O3dcW/gTl2Lutq+E1GK/XtX/wU0mnTgH139Z9zhgo2SpN6shn6tv7v6jQcok6cM6xmiW770/5o9cUL5p7lpE5ibK+NZR42CjIwbuV3h9+7dw8fHh+DgYOzt7V/6mqmJqSQ4JhRC9M/HMcERkxb/0sv3giIjIwGYPHlybuIKoK+vz6xZs3BzcyvwuKSkJEJCQgBlwtaRI0c4ePAgOjo6zJ079z+vmZ6ejo+PDxkZGYSFhWFqWraGXqk0Go1G20G8qGPHjuHo6Mja1atpUAj/WETJ8McfeqzbUJktWyuRk6Pi7R438fO8TN3vl1Np/XoqpqbyHRDbrBn2AQFkV8vhswufc/T2z9hXsGdkveG0qeQsSWsZoPvXX5jt3UvFPXsof+wYGh0dHrz+Otfd2vKNvZpdDw/z08040rLTqFO+Dh2rtKdzlTepWb6mtkMXJZBGo0HDXXJyksjJuUxOThLZmsvk5CSj0Vz/e8dUC1R/1EBzqQactYHkmsp41DRLdGx1UNdSo66pevysRl1VhUq3bH3faDSQcMyEL1dXJu6QGVWrpDPA9wY9etzi2tULrFu/nm937UJXV5dePXvi7eVFtWr55xCcTUzEd+BAEhISaNGixTNfvyy1vDo6OnLixAkuXryYr4U1KysLAwMDatSowaVLl4CCS2Xp6urmlsoKCgrKUyrrn7Kzs/H29iY6Opp+/fqxfv36Qr2fpz3Jw/6/z/dZ93tWpf9PQsD30SNISdF2GKKwlAeG3QWvX2FrVbKjjtIgOhgb1W+seaMr8we8xelz52DfOogdAnYA1tBgOomV2jJWpVIGYonST18funaFrl2pfPs2HgcO4BUbS9sZs6mlp0fdli2xdg0gpkE5Lj48wsVL6/j8wnIwqQ9WHaBSe9CXOr2vGjXZVOYGNbiS96G5gqnqPgA5OWpS7lUj+6oN5X51xSixZm5X/x/G5Z+85EoNuNxGeb5TEVDlADl5L5j++FEWZAM/WcLGGnC2AtR+CJPPcK3dn8z55RhzJm5SxnpZWsLgwWT26MGG8uXZAAX/Hn706IXC0DHSKfQWUG25d+8eANbW1vm26erqYmlpWeBx7dq1Y+/evc91rezsbHx9fYmOjsbLy4u1a9c+f8ClQJlIXtcaGtLA2FjbYYhCZnj1PNV/CcTk0THO1nKjw8Nt/BjXhPp6B7DvEEVir5tYq6wxOGzA5V2XqVH9C/p7p9C9e3cMDcr4KlivImNj8PUFX19O/vEHZnv30uGHH+g56xNyypXjvpMTf3R4jx0N1Xxzey8Hk5aTffEzXrNwpGvVLrhVdsNEr7y270IUIo0mjZycK+Roksh+3JKak3OZHM0VQJnVT5Yhqls10FypAedawa+Pl0H9oxqmlfVzW091nNWo+6tQ11RTwUjFqzYI5cEDHbbFWLJpkzXXruvTrOkDBi84T6tWt/lhzw+s9V/LufPnqWtnh++0aXR+881nmgR01tAQ32KIvyR70mV/48YNatWqlWdbVlYWt27dokaNGi99nczMTHx8fIiOjsbHx4fVq1eX2R7IMpG8NnBwKJRmaFFC/PmnMqjqiy+UMgQ7d9KgSxcWXP0f70b14uiD7fBnfSxPbWD8W30Zvl5NYuJh5s2bx8dz57J8xQr8/f3x9/fHyspK23cjikr37srz5cuoo6Mxi4rCbEoI9StUYHzfvjzoO4FNFa+x7vQGQk/OYPaZj+lWrxs+jX14q+5bZX+Z3zJCmdV/q8BlUNPSLgPKyDd1uiU6f9ZCndSEnJNd/57Vn2lNeXuTv0tP9VSeDWqX/Fn9xeH8eaVywKpVSolsLy8IDIS6dXNYvjwGT6+F/P7773Tu3JnFERF06NDh+RIinZJV3ksbHB0dOX78OPv378+XvB48eDBPBYEXlZGRQd++fYmJicHPzy93nG1ZVSaSV1FGZGQo36IffQRqtVL+6t13SdFkMGX3eBYeWUjtirVZ03sN9TK8WbxIhw8nQ+h08PNrzYwZXzFnziU+/fRT5s2bx5w5c/D19WX06NE0a9ZM23cnikrNmhAUpDwuXIA1a2DNGky++IIhtrYM8fXlj97TWZd+lHUn1+GxyYMK+hXwaOCBT2Mf2tm2kwURSgBlVv/l3OT06dn9f8/qV6PzsAaq6zXIOe8EZzyVsahXaqBX0fLvWf3tHz/bG1HOulyZbX16URoNfP89LFyo1N2uVAnGj4d334WHDy+wZMkSVqxYQVpaGj4+PowfP57GjRtrO+xSa9CgQXzxxReEhYXRs2dPpWIOkJaWRnBw8EufPz09HXd3d3bu3MnQoUP5/PPPX/qcJZ0kr0L7NBql3FVQkFLIfuRImD4dLCz47uJ3jPhmBDce3mB2h9mMbT0WPR2lq2r1avj4Y/jsM1i6FJYsga5dazN27CKmTQth2bLPiYiIYMWKFTg7O+Pv74+Hh8eLr9wlSr66dSE0VFkF46eflP9JwsOxnjGD8a1bM37AEM57L2bd1V2sO7mOyBORVK9QHb+mfvg19ZOKBcUgO/tRAbP6E3n06Dw5OWkAqLIN0blTC67UJPtM779n9f9ZHX1b09zE1Ki/UnrKsH7ZmNVf1FJTlb/tFi1SVstu2lRZGcvTM5u9e79l8OAIdu/ejYWFBaNHj2b06NFUrVpV22GXek5OTgQEBBAeHk6jRo3w8PBAT0+P7du3Y2FhQZUqVXiZufMjR45k586dWFpaUrVqVaZPn55vHzc3N1xdXV/mNkoU+dcutOvUKaVQ4A8/KEtubdsGDg7cTr3N+G1+rP7fatrXas/3A77Hztwu3+GVKyt5SnAwbNyotCR07gwNGpgzZkwwp09PZM+eGBYvXkz//v2xtrZm+PDhjBgxosCZsaKMUKuhbVvlsWiR8sfRmjUwZgz11Gqmd+tGyICPie9myaqzG1gcv5iwH8NwtnFmcLPBeDp4Sl3gl5SRkb+Af2rq2Xxd/eqbtnDJjpxTLpCkjEdVpVfG0L58bk1Uo7elq/9l/PabsqDA8uVw5w707Kn8se/gcJuVK1fQqNFSkpOTadmyJatWrcLLywsDmTdQqBYuXEi9evWIiIhg2bJlWFpa0rt3b8LCwmjatGme3oHn7SlITk5GpVJx+/ZtQkND821XqVSo1eoylbyWiVJZhVV6QRSju3dh8mSl2bR2bWWxge7d0QBRp6MYs3MMmTmZzHtzHoObDX7mf8waDfz4o5LEbtsGJiYwcKBSTBtOs2TJElavXs2jR4/o3bs3/v7+uLq6Srfiq+LPP5W/clavhoQEpWhl//6kDejPNqPLrDqxiu8ufoeBrgEeDT0Y1HQQbrXcUKskYSrI3139ifm6+7Oybj/eSY1OyuMC/uerk3O6eu40fn0zy79bUe2f6uqvLF39LysnB777Tlm+9euvlfmOQ4fC6NFw+/bPREREsGHDBgC8vLzw9/enVatWhR6H/J4u26RUlnh1HDigrCd4547S7x8QAOXK8du93xj17Si+Of8NfRr2IbxrOJXLV36uU6tU4OKiPJKTlS/ulSshPBzatHFgxIgIpk2bxVdfrWHx4sW4ubnh4OCAv78/vr6+/74ErSgbrKxgzBjlceYMfPklrF6NweLF9GvenH7vvMNVv09Y/ds3rPrfKtb+spYapjVyhxXUMa+j7TvQiuzsRzx6dD7fWNR8Xf13bR939feCC9WV8ahPuvqfJKc+j7v66xmiayK/ggrbjRvKd97y5cp3YJMmSueDp2cau3Z9Rb9+i4mPj6dGjRpMnz6dIUOG/GupJiFKKvnmEMUnM1MZyzprFjg7K0lszZrkaHJYGh/BB3s+oIJ+BbZ6baWXfa+XvpytrXKp6dNh+3alkXfAADA3r4Cfnz9bt47i2rVYIiIiGD16NO+//z5+fn4MHz5cJie8Cho2VJYNCguDXbtgxQoYN45qQWqCe/fmg3fCOVTfiFW/rGbhkYV8dOAjXGq6KMMKGnpiXK7slefLyLhVwApTiaSlJZOvqz+pDjknXXJn9efr6u+uJKsGtQxQ60nLdVHKyYG9e5U/1rdtU5Zu9fJSepwsLS+yYsUXNGz4Bbdu3eLNN99k+/btdOvWDR2pBCBKqRKVvKanpzN16lTWrFnD3bt3adKkCTNmzKBjx47aDk28rF9/BR8fpas2NBQ++AB0dDh78yxDvx5K3G9xjHAcwZyOczA1KNxl7MqVA09P5XHhAixbpkxSWLBARbt27Rkxoj1z5vzGqlWfs3z5chYvXkzLli0ZMmQI3t7eVKggYx/LNF1dpexW9+7wxx+wdi2sWIGqc2ecatTAadAgFvocYmv6CSJPRDJ4+2DG7BxD/8b9GdpiKI5VHEtVF7dGk5Ovq//Jc2bmrcc7KV396us1lVn9p/vkdvXrmVb6uxW1nXT1a9PNm8p32bJlyqrKDRvCvHnQp88j9u7dTHDwCvbt24epqSmDBg1i1KhR1KtXT9thC/HSSlTyOmjQIDZv3sy4ceOoW7cukZGRvPXWW8TGxuLs7Kzt8MSL0GiUAoIBAcrsqp9+gtdfJzM7k1n7wwj7MQxbM1v2D9qPS02XIg+nbl345BOlGteWLUpLhbc3WFraMHjwDPbtm0Zi4jesWLGCUaNGMW7cODw9PRkyZAht27aVX85lnbW1UvVi/HhlFaGVK2HBAgxDQ+nfoQP933mH5GGLWHluA5EnIvk84XOaWDdhaPOh+DTxwdzQXNt3kEvp6r+Qbyzqo0fnnurqN0Dn7uNZ/Wd7wrnHs/r/qIa+rdnf41G9/x6XKl392qXRwP79ynfX5s3K3MQ+fZSvWUPDY6xcuYKGDddx79492rVrx5o1a3B3d8fIyEjboQtRaErMhK34+Hhat27N3LlzGT9+PKC0xDZq1AgrKyt++umnfMfIQPAS7s4dpd/qq69g8GBlFpWJCdcfXMfzK0+OXD3Ce07vMcV1ilYLxp89q7RcrFqlzCNzcQE/PwI2/vMAACAASURBVHByusaWLatYuXIlFy9epG7dugwZMgQ/Pz8qV36+sbiiFEtJgehoJZE9cADMzMDXl+wh7/Cd8Q2+OP4FMedi0FHp4NHQg6HNh+L6f+zdeViUVfvA8e/MwACDyCr7qqiguEEuoKlg7hUKmbtpWVZm9Wa9r2WLG9r2q9fQtzJ3TdNIc09NRSVNEvddAREFRFBQdmbm+f3xwAChpoUM4vlc13MNPrOdQWDuOfe57+PdrdaKvEpLs6usQ62o6r9IRarfHmWWNyR5oj3haqjqVxa5YOnXAI2fpiLdX17VL1L9dcrFi3Kd4dKl8ixrs2byn9fw8By2bFnOggULOHLkCK6urowePZoxY8bg61u9Q0ttE+/T9dsjX7AVExODiYkJL730kuGcmZkZL7zwAu+99x5XrlwRrY0eJrGx8gLTvDxYvVrO2QNxl+IY9OMglAole0bvIdgj2LjjBPz94csvYeZMeSZjyRK5Ktfc3JWBA99jzpxJmJruYfHiBUyZMoXJkyfTv39/XnjhBfr164eJSZ35NRIeBEtL+dPMc8/J604WLIDFi1HNmUPf9u3p++KLZI79lCVJa5h/eD4rjq+giW0Tnm/3PKPbjsbV6p/3ybz/VH/wnVP93TRoxslfi1R/3Xbrlvy5ackSebbV0lKeZZ03T49ev4uFCxfw3ntr0Ol0PPXUU8yYMYPevXuLv0lCvVdnfsIPHz5Ms2bNaNCg6t7j7du3B+DIkSMieH0YlJTAhx/KXQS6dpV7a3p4IEkS0fHRTNw2kRCPEFY9s+q+Owk8aBYWMGKEfKSmyksflyyBFSuUuLl1Z8SI7sTGzuXQoe9ZsGAB4eHhODs7M2LECIYPH16tV59QDzVtCh9/LK872bhRLukeNw5HjYZ3hgzh7bFLiHMuYf6RBczYM4MPd31Iv6b9eDHwRfo27YuJ8u5/cnW6IkNVf+V0/21T/ame6E6Fw7my1lMZ7nKqvzxIHVp22Vyk+h8mOh3s2iX/7VmzBgoLISxM/nfr1hf4+efljB27lOTkZJo3b8706dMZNWoUTk5Oxh66INSaOvMXLT09HRcXl2rny8+lpaXV9pCE+3XuHAwbBkePytOY77wDKhX5Jfm8tPElVhxfwVud3uLjJz427JJVV3l4yBsfTJoE8fHyG8e8efDJJw1p3/4Vxox5hc8/P86aNd+xePFiPv/8c1q0aMHw4cMZNmwY3t7exn4JwoNkagoDB8pHaqq8pGDhQhQLFvB4q1Y8PnYs0WOmsiLtF7479B1P//A0rlauPN/2eV4IfAE3S6tqbafkqv5kDKn+EjuU13wg2Qf98S4VDfwLXbAoS/Vr/DVo+smpfosmFiLV/xA7e1b+O7NsGVy+LC8LmDwZevXKJC5uBdHR33Pw4EGsrKx45plnWLZsGSEhIeIDs/BIqjPBa2FhIWZmZtXOl+/yUVhYeMf7bo4/zemcBzY04R74bN1Ah68+psDekd++WsT15i1g91EyClOZfeptMouu8JrfLAJNe7F693FjD/e+dX4GOjyt4PDv1uzdZsfrr1ujULakXadpDH31NVSq7cTv2ci06dOZPHkyTVu2IaRHHzp174mVta2xhy88aI8/hSKkH84JB/Dd/DPub72F5dvv0KdrMP79OnOwrR87ru7ni30zido7gyBbeNIFgu0UmNxyRUrzRHGhPcqzEYZUf6mpDaVeSrQeSrSeKrTtlZR6KtHbK+SGxhSWHdmQhnwID5Xc6ybE77Uhbrs9iact0TTQEhx6gxGvXyY7cx0r1/zC+x/8gUqlok2Hzrz+4Se07dQFtZk5F4vh4q7Dxn4Jfyn53GljD0Goh+pMwVZAQAAuLi5s3769yvlTp04REBDAt99+y4svvljluvIFwHgCf673aVV2CA+UQg9RO+HdOFjYFl7vC/nVP4PUP3mN4PgwOPocZLQD9U1ovh6ar4LSbXCqBC4ACqAJ8s+iH6A26qiFB8BUAR4a8Kx0+BXDY3vBYwtoLkOBK1x83JKzPt7E5TVgq+kVTlpfxibfhuCzwTRNb0qBWQGXHC4ZjgLzAmO/NOFByLeH0xFw8lm4GApI4PsLtFoCqg1wshjOAVrAC2gNtAAsjDnofyANmIco2KqnbleItXLlSsPubeVyc3PZs2dP/SvYcnFxue3SgPT0dABcXe9c9DD93eX4NPN/YGMTbk9VXETwp1Pw/O1XEl5+E7NnhvOtQoFe0rEmZR4/p84nyL4b45pNRWNSD3eu6gsgkXbpJAdibfk9NpIrMSPQWGoJ6pxL62dTuXljNb/HbuL8mmOYmVsQ1Lk7IT36EBDYERPTur10QqhKQS6mJGPCRUwUyZhyEROSUZGGQiHPAegLbZCuesFFT9JyPUl39sA6Px+Xq/tpvnoPfpyho9fjDOzyFgeaObFNsYE91pvZot2Cn3UQoc4DGOLQA7XyUfgE+OjIv6XiYJwNv++24WRCQySgRdtbdAi/hLXtHo7GryN++w7ybxXj2aQZIc/3JTi0F/aOdasu4O9IPneaDxhh7GEItWjo0KEMHTq0yjnDZGMNqTPBa7t27YiNjeXWrVtVtug8cOAAAG3btr3jfft18Bef6GrbtWsQHg5HjsBPPxE0cCBBwPXC6wxfM5xtl7cxM2wm/+nyn0djX/jR8sXJk7BqlQmrVtkzd5s9dnZtGThwJu//J53k5IX88MNyPn/vDaytrXnqqaeIiIigd+/eogdjHSFX9V/6U1W//HVp6bWyGylQ5bujzPBGf64rupNuhlS/eYNGht6oll0t0bxU1sDfVY0iJweWL8f1u+9wXf4WXfZ4MvH55ykaOZWf8v7gu0Pf8fXZD/gh5QtGth7J2MCxtHIS6aOHVW6uvLPf6tWwbRtotXIN63//q8XRcS87dqzk5+9/5tq1a3h5efH6a+MZPnw4LVu2NPbQa9QhG/jA2IMQ6p06s2ygvM/rZ599xsSJE4GKPq+NGjVi37591e4j+scZyZkz0L+/3P9ywwYo6whxOP0wkasjuVl8k5WRK+nZpKeRB2o8kiTXra1eDatWQVISODhARITEY48lkZr6PWvX/siJEyfQaDT07duXyMhI+vfvL3b0qgVyVf/5am2nCgrOotfL6+sVOnNUuXJVv/6UG/ryqv50dyw8bSr6ovpXauDf8B7mAyQJ/vgD5s+HlSvl36M+feDFFzkX3Iz5x5ew5OgSMvMz6eDWgbHtxjIkYAhWZvUwe1HP5ObCpk3y7/wvv8jNVzp3hoiIEmxsdhIbu4INGzaQk5ND48aNiYyMJCIigg4dOqBU1s8P+eJ9un4zVp/XOhO8AgwePJi1a9fyr3/9iyZNmrBkyRIOHjzIjh076NKlS7Xbi18KI4iNlSusXV3lv9JlVfXfH/uesRvG0rJRS3569ie8bLyMOsy6RJLkXXFXr5aPlBSwtZXj/8ceS+PGjR/YtGklBw8eRK1W07NnTyIjI3n66aext7c39vAfaqWl16u1naqo6tcDoCyxR3nNC5I90Z5wg6SyBv6FLlg2b1AtQLVoYoFSXUOBxq1bcqQzf768o5eTE4weTenoUWyUzjL/8Hx+ufALFiYWPNvyWcYGjiXYPVhUmNchly7Jn+HXrZP/PJaWQseOEB5eRMOG24iNXcbmzZspKCigZcuWhoC1devW9f//MSeHQ0OHEvTLL+J9+i68vb1RKBQkJycbeyj3TQSvyDOtH3zwAcuXL+fGjRu0adOG6dOn07Pn7WfwRPBay5YsgRdfhG7d5F2zbGwAmP37bN7c+ibPtXmOb578xqi7ZdV1kgQHD8L69fJx7Bio1RAaCl26XEerXcPOnUuJi4tDqVTSvXt3IiIiePrpp3F3dzf28OskSdJTXJx629ZTpaWZZTdSoCpwR5nujf68O7oTFal+dYNGVQLU8hlVtWstN/A/dkzeAGHZMnl3uscfh+ef50qvYBZd+JEFhxdwMeci/g7+jA0cy8jWI2lk2aj2xicA8u/w4cMVv8OHD4OJCXTvDmFhtzA1/YXdu5eyfft2iouLCQoKMgSszZs3N/bwa09cHIwYwaHsbILy8sT79F14e3ujVCpJSkoCIDY2lrCwsCq3MTU1xdHRkeDgYN566y06depkuO78+fOsWbOGrVu3cv78eTIzM7G1taVTp068+eabdO/evdpz/vbbb6xbt45du3Zx8eJFbt26haurKz169GDSpEk0adLknsYugte/QQSvtUSS4KOP5MbsL7wAX38NpqZIksS03dOYsnsK/w75Nx8/8XH9n0moYcnJFbM2u3fLDcoDA6FHj1uo1Vs5cGAesbG70Gq1tG7dmn79+tG/f386der0yO2iU5Hq//N61LPo9XJlvkJvVtbA3wv9aTf0Z8tS/WkeWHhZV0/1N9dgYl3Hvo9FRfDzz3Ig++uv0KABDBmCfsxodjoVMP/wAtaeWYskSYT7hTO23VieaPwEKqXK2COvt0pK5FnVdevkgPXyZbC2hr59JVq1SiIvL4YdO9bwxx9/ANC5c2ciIiKIiIjAy+sRy0KVlsK0aXKv75AQDk2aRNCTT4r36bu4U/Dq7e3N6NGjAcjPz2f//v2GiY2YmBgGDBgAwJAhQ1i9ejUtW7akS5cu2NnZcebMGdavX49Op2P27NlMmDChynM6OzuTnZ1NSEgIQUFBmJiYsG/fPvbt24elpSXbt2+vEiDfibGCV6SHWEJCggRICQkJxh5K/VVYKEnDhkkSSNLHH0uSXi9JkiTp9DrpzS1vSkxBmrV3lpEHWT9cvy5J338vSYMHS1LDhvK33NNTkl58sVD6z39ipaFDx0qNGjWSAMnGxkYaPHiwtGTJEunq1avGHnqNKinJlnJyfpPS0uZLFy68LR092l/av7+JtGuXUtq1C2nXLqTdW+2kvd8HSntnDJB2DXlV2tXhY2mX8wppt1WsdPCxg9Kpkaeki1EXpcw1mVLeqTxJV6wz9sv6e5KTJWnKFEny8pJ/IPz9Jemzz6TspFPSf/f/V2o5t6XEFCSPLzyk93e8L53PPm/sEdcb6emStHSpJD37rCRZWcnffi8vSRo3rkj64INYaeTIFyQnJycJkKytraVBgwZJixYtkjIyMow9dOO5cEGSOnaUJJVKkqZPlyStVrxP3wMvLy/Jx8fH8O9du3ZJCoVCCg0NrXbbjz76SFIoFFLjxo0N5xYvXiwdOXKk2m13794tqdVqyczMTEpPT69y3aefflrtnCRJ0syZMyWFQiG1atXqnsZ+r/+/Nf1zIGZehTvLypLXt/7xh5zKHDQIAK1ey4sbXmTJkSXM7TeXV9q/YuSB1j8lJfJMbHlq8tIleXlBly4SLVqkUlq6mYMHF5KQ8AcKhYL27dvTr18/+vXrR1BQUJ0v/rj3VL8bigwvpHMeclV/ipec6resqOqvvB7VzM2sfs7+6/Wwc6c8G7t2rTxF378/0vPPE9/anoXHl/LDyR+4WXyTLp5dGNN2DINaDBJFXvehqEjOdG/bBlu3yqs4AIKCJDp1ysTUdDMJCYvZt+83dDodAQEBhkxIcHAwpo9y6ztJgqVL4bXX5HXb338PHTsiSRIzV8/k/SHvi/dpYM6cOXz99dckJSVhb2/PwIEDmTFjBm3atLntzGv37t3ZuXNnlce4du0aTk5OKBQKMjMz/7IuolevXvz666/ExMQQERHxl2PU6/U0aNCA4uJisrKysLW9+yY7xpp5rWP5MqHOOH8e+vWDnBx5o+3gYACKtcUMWzOMdWfWsWzgMoa3Hm7kgdZPajX07CkfX30lbx25bRts26Zg4UJPCgpextHxZSIjC7GzO0hGxjK+/PJLpkyZgqOjI71796ZHjx6EhYXh4eFhtNeh1xdTUPDnVP/p26T6veGyF7rT/aFSql/taVOxDnVQWaBaF1P9D5pSCU88IR/Xr8tdChYuRBEeTkdnZzqOHMnsoTtYa3KeRUcWMXb9WCZsmUCkfyRj2o6hm3e3R6Nl3X2QJDh1Sg5Ut22TPywWFYGLCzz+eCFdux4hJyeGPXtimDv3EhqNhh49ejBnzhz69euHp6ensV9C3XDyJPzrX7B9O4weLf/BsrLiUu4lXtn0Cpt3bzb2COuEN954g+joaFxdXRk3bhwmJiasW7eOAwcOUFpaetsdRm9Hr9cbvr6XD+rlH6ru58OViYkJxcXFqFR1dynSI/YOINyTQ4fkqMnRUa6AbtwYgPySfAauGsielD2sHbyWp5o/ZeSBPhoUCvDzk4/XX4fiYti3rzyYteCnnx4HHqdVq29p2fIyev1Wjh1bwPLly5EkCV9fX8LCwggLCyM0NBRHR8caH2Np6Y1qfVELCs5QWJhERVW/LcosH7joif54MCR7QIoXigIXLJpZVcyg9noAVf31iZ0djB8vH0eOyLOxCxZg/tlnDG3XjqEjR3Jl6CyWXN3K4iOLWXZsGV7WXjzX5jmea/scjW0bG/sVGM21a/IyYvl3B9LSwNwcgoNLGTLkLMXFGzh69HtWrz4JgL+/P+Hh4fTv359u3boZtisXgOxsuRbim2/Ax0dOET31FDq9jv8diObdHe9iY27DF72/4K15b933w+t0BRQUnHkAA787jcYPlapm+27v27eP6OhofH19iY+Px6as2DkqKorQ0FDS09PxLuvc81fmzp0LQOPGjbGzs7vrbVNSUtixYweWlpZ07dr1nh7/xx9/JC8vj+Dg4DrdtlEEr0JVR4/Kszu+vvKURFnK4EbhDZ5c+STHrh5jy/AthPqEGnmgjy4zM7k7QWgozJoFmZmwY4c8K7ttmwdpaWNRq8fSsWMpbm6JlJT8SmzsYubNmwfIWzGXB7PdunUz/CH9K7dP9Zc38L9Nqv/8Y3Ai3JDqN9GUpfr9NWhCNGheqOep/trQti1ER8P//R9s2SKnbidNwu0dHe/16sW7I6fye28nFp5ZyZe/f8m0PdPo5tWN0W1HE+EfQUOzuvvmVBOuXIG9e2HPHvk4KcekBAToCA6+hFL5KxcuLCY2dj+SJOHj40NYWBiTJ79HaGgoLi4uxn0BdVFpqVy0O2WKvHzlk09gwgRQqzmZeZKxG8by++XfeeWxV5jVYxaJpxL/1tMUFJwhIaHmdmS6V0FBCVhZ1ezyhkWLFgEwefLkKn9vzczMmDVrFqGht38/TU5OZsqUKYBcsHXgwAHi4uJQqVR8/vnnd33O4uJihg8fTklJCVFRUVhbW//lOJOTk5kwYQKmpqZ88cUX9/jqjEMEr0KF48ehRw95pnXbNkMrrKt5V+m1vBeXb15m56idtHdrb+SBCpU5OsLQofIhSXDihFwZvWePKXv2+JGZ6YdK9Rpt2pTg6ppIaekO1q5dwFdffYVSqSQwMJDQ0FC6dOlCcHAw9vYN7y3Vn+sFqX9K9ae7o3a3rZhFfUZO+Vs0t8DU5hFeE/igqdXyjnfh4fKygtWrYdkyFMOGEWxlRfCgQUQPXU2MQyaLjy3l+XXP88qmV3i6+dMMCxhGH98+mJk83FvSSpK8GUh5oLp3LySWxU1Nm+rw9U3D1/cAaWnLOHx4MydOaHFxcSEsLIzXXnuB0NBQfHx8jPsi6rpffoG33pI3qnnxRbkDjaMjhaWFfBI7hZl7Z9LYtjF7x+yli2f13uz3Q6PxIygooYYGfn/PW9MOHTqEQqGgW7du1a7r3LnzHWsUUlJSmDZtGiCn8h0dHYmMjGTixIl37QSg0+kYOXIk+/btY8iQIYaNn+4mMzOTvn37kp2dzdy5c+nYseM9vjrjEMGrIDt1Sg5cPTyqBK4pOSn0XNaTvJI89ozeQ0vH+rV1YX2jUECrVvIxYYL8hn7uXPkbuprdu/1JTfUHXqNZs0KcnI5SXLyRhQt/4LPPPgPA3R1atoQWLaCVnxWNLZugSvFCf6KToYG/It8V86YN5LWo/ho0PctS/b4i1W90dnbw8svyceECLF8OS5divnAhIzw9GTFiBOkDJrOs5A9WHF/BgFUDsDW35ZkWzzCs1TC6enV9KNbH6vVw+nRFsLpnj7wMQKGQ8PMrxscnCR+fPaSmruTcub2cPy9hb29P9+7dGT16NmFhYTRv3lzM+t+Ls2floHXzZrmh7cqV0KYNxdpi5sfPZWbcTDLzM5nUeRKTu06ukV7fKpWmxmdAjSU3NxcAJyenateZmJjg4OBw2/vdrmDrr+h0OkaMGEFMTAyDBw9m+fLlf3mfzMxMwsLCOH/+PLNnz+bll1++r+c0BhG8CvKn6LAwcHaWF92XraM5k3WGnst6Yqo0Je75uEd6rdzDS8LLK5XIyDP07SvPoF64cIP9+x04fLgNx451JTV1BjADe+sMHDWnUOYd58TO39i2dRsSuTRQXaCtawM6BDQhJLwpXcK74OjvKN70Hwa+vnJ696OP5IXSS5fC3Lm4zJzJv9u25d/PDuZc31ksuRXHihMr+O7Qd7hZuTE0YCjDWw+njVObOvP/fOUKxMfLzU/KL2/eBBMTiWbNbuHrexI3t21cuLCE06eTOXNGQcuWLenaNZhJk8YQEhJC06ZN68zreSjcuCH3bJ0zR57Y+OknGDiQEn0piw5+y4y9M0i7lcbwVsP5oOsHNLVvauwR10nlKfuMjIxqs/tarZasrKwaKQAsLS1l+PDhxMTEMHz4cJYuXfqXP+/p6en06NGDc+fOMXfu3IcicAURvArnzsmBq4ODvHCy7BPgofRD9F7eG0dLR7aP3I6rlauRByrcjV5fUqmBf/ma1PJUfz5Qnur3pmGqJ09kaehRkArqvVy3uMJZa3fON7DlVHEwJ4q6k1/6BgqFhJdnAXZ2idwoiWP+bz/xxZZoFJO1BAQE0KFDBwIDA2nXrh2tW7fG0tLSyN8F4Y4UCujcWT5mz5a3dl69GmbMoNl7BUQFBTHj2Vc41LMJi3J2sfjoYj7f/zn+Dv4MbzWcoa2G1uqH15wceSe6ysFqWpp8nYNDCW5uafj5HeXGjV9ISlrBqVM3sbKyolOnTrz++iiCg4Pp2LHjPa/nFv5Eq4XvvoMPPpArRKdPhzffpNRUxdLDC5m+ZzqXci8xJGAIH3b7ED+Hmk+11ydBQUEcPnyY3bt3Vwte4+LiqnQQ+LtKSkp49tlnWb9+Pc8995xhne3dXL58mbCwMJKSkvjmm28YO3bsPx5HbRHB66MsMVEOXK2t5cC1kbzV5KH0Q4QuCaW5fXO2DN+CvebufeSE2lNamnObtajlVf06AJSlNiizvMuq+jsaqvrJc8G8mVVF66kn5OIpiyYWKM0q0sQ6nTwZ/8cfCuLjLYmPb825c60pLX0VU1M97u7Z6HTH2bZtN4sXL0Wnexulshg/Pz/atWtnCGjbtWsngoe6yNwcIiPlIz9fDmRXrULx0UcEFRUR1LEjs5/5N3tCnViQtY1ZcbN4f9f7tHdtT6R/JBH+ETU6w5aVJS+3P3ZMDlj/+EPOUgNYWmpxc0vH3v4YavWvpKauISvrEtevK/H39yc4OIiJEz8lODiYli1b1unWPg+FggJ5dv7LL+V2iaNHQ1QUWqdGrDi+gmm7p5F4I5FBLQaxadgmsYzsHo0ePZr58+cTFRVFeHi4oXdqUVER77777j9+/OLiYiIiItiyZQtjx47l22+//cv7pKSkEBoaSmpqKgsXLmTUqFH/eBy1SQSvj6rkZLlc3dJSbn5ethbnwvUL9P2+L83tm/PrqF/rfTVyXSRJEsXFl6sFqPn5pyktvVp2I7mqX3nVC/25QDj5lKGqX2nugKWfpRygdtKgGS0HqWZuZiiUf50yVankNa8tW8rvXSD3vzx6FOLjlfzxRyPi48O4fDkMSZqKUinRqFEuxcVJ7N6dwI8/7qCkZC6QTOPGPoaAtm3btrRo0QJPT886v4nCI8PSEp59Vj5u3ZL3Kl69GtXk9wktKSE0JITiyI/Y0tGS5dk7mbZnGpN2TCLAMYAIvwgiW0TSyrHVPaXii4vlNarHjlUEq8ePQ3q6fL2pqQ5n56uYmx/H2XkHGRkbyM8/y8WLprRq1YonnmhHYOAkAgMDadWqFRpNzbYzeqSlp8PcuXIXgZwciIiAFSvQtWvLqpOrmPrTVM5ln2Og30DWDF5Da6fWxh7xQyUkJIQJEyYQHR1NQEAAkZGRmJqasm7dOuzt7XFxceGf7Bf18ssvs2XLFhwcHHB1dWXq1KnVbhMaGlqlYKx79+6kpKQQFBRUpatBZWPGjKmz2xuL4PVRlJIiB65mZnLgWtYOJv1WOr2W9cLW3JbNwzeLwPUBk1P9F6oEp+Vp/6qpfq+yBv594YxHWQP/sqr+8h2mIioa+Jva1nxVv7k5dOwoH+Xy8+XWQ8ePKzh2zIbjxwM5diyQkpIXATAzK6WgII19+46zadNeioo+B85hYXEDf38//P39qxy+vr6P9i5FxmZlBcOGyUdurty3c9UqzCZNZoBWy4DgYEr6/Ye9gTYsLo1n9oHZTNszjSa2TYjwjyDCP4IObh3QaZUkJ8uzp+UB6vHjcPashE4nB7l2djlYWiahUBzBwmIPhYUHKC09z/Xr5rRt25bevdsRGPhvAgMD8ff3R61WG/mbU08dPSrPsq5YIb8fjB0Lr7+O3tuLmFMxTPl6JKezTvNUs6dYGbmSQJf6UUBlDLNnz6ZZs2bMnTuXefPm4eDgwMCBA4mKiqJNm6pry+93XfbFixdRKBRkZ2cbuhNUplAoUCqVVYLXlJQUFAoFCQkJJCRU7+qgUCgICwurs8Gr2B72UZOaCt26yWvgdu+WS8uBnKIcui/uTlZBFr89/xteNnXzB/ZhVJHq/3MD/0Sqpvp94KIH2uNucqr/kieKm65YVmrgb+lvWVHVb1b3Zi8lCTIyqs6sHT8OJ09KlJTIf5BNTUuxssoALlBQcISiouPAeVSqZJo2bUiLFlUDWh8fHxo1aiQKbYzlxg34+WdYt04u6CwoQGrcmBtd+rHFw4155hf4o3QDhcpMVPluXvCgegAAIABJREFU6E8OQDoVCZcex1xdipXVRXS6I9y8+RtabQJwEisrqn148ff3p3HjxiL1/6Dp9XLLqy++kJeLeXrKu5+MHUu6soClR5ey8MhCzmWfo49vH6Z2n0oHtw5/++nE+3T9JraHFR68K1fkGVe9vkrgWlhaSPgP4aTkprB3zF4RuP4NFan+yutR5a9LSjIMt1MVuKHM8EJ/vh2ceFKeRU3xqprq73j/qf66QqGQJ/JdXKBXr4rzWq2CxER5Gd3586acO+fB+fMenD/fndRUkCQFOh0kJhZy5cplNm8+TVHRMWAXkIqFRTZeXkp8fZ3w8fHBx8eHxo0bG762srIy1kuulyRJ3o3q8mVITbUlNX8MSY3HkNKtELujO3gseSP9k9YynCs8SUN+NXmczY62rG+RTFbAEugwFwoU6C+rsdV60dGhI481fwx//3D8/f1xc3MTH0ZqW2EhLFsmz7SeOQMdOsCqVZSGP8Wm5K0s2DyCLee3YKoyJdI/ksXhiwn2CDb2qAXhtkTw+qhIT5cD15ISOXAtSwVo9VqGrRnGH1f+YPvI7QQ4Bhh5oHXb/aX6PdGd7lPRwP+KB2q3P6X6/eTjQaT66xITE2jeXD6qUlBURKXA1oLz55ty7lxTzp17kowMBZKkoLBQfr+9cCEPlSqN0tJk9PoU4CCQSsOGuXh6Kmnc2AwPDztcXFyqHQ4ODmJWDzkwvXGjPDCtOC5dkkhOLuXSJYmMDBNKSyu+VwqFFjOzNPT6s5SUXGA+KsCf9iYqhjfMp492L5FpN9GnK8i63JzUx9uwI9CCmCYnOJiewDnOcVR9lD70QVWqopGu0UO/KcJD49QpeVnAN9/I//EDB8KCBZzytWbhkUUsi55AZn4mj7k+xpx+cxgSMAQbc1FoKdRtInh9FFy9KncVKCiQA9eyVh2SJPHKxlfYcHYD64aso7NnZyMPtO7QanP/FJzeLtVvLaf6UzyQTnSAxLL1qDddDVX9Gn8NmrCyILWppk6m+o3N3LyiQKwqJSUlcoukiiCrAZcvNyM1tSlJSVpSUyEnx5SbN+WdxU6cAIWiEIUiG73+KpAFnAB2oVBcp2HDIuzsJJydVbi5qfHw0ODiYomDgxW2trbY2NhUubSysqrTM4SSJE+o5eTIVfvXrpUfEmlppaSlFZORoSMzE27cUHLjhil5eWr0+spBvBaV6io6XQpwCUg1HFZWuTg7a3F3V+Ph4VZptnsIPj4+uLq6VhTfpaWh3LQJxw0bcFy+nqDvCvm3iwtFj0dw1N+OGCmLJUcW8+m+T7E0tSTMJ4zeTXrTx7cPTeya1Pr3rt6SJHkt608/ycfp0/J65uef59a4MfxQEM/CIxP5ffvv2FvYM7L1SMa0GyOKsISHighe67v8fOjfXy7A2L0bmlS8SXyw6wPmH57P4vDF9G/W34iDNA451X+lWpq/oOAMJSXphtvJqX5v9BfawYn+FVX9Zo2w9JPXoFq2t0QzSg5SzdwfrlR/XaZWg7e3fFSlAOTZ6qKiilnEtDTIyrIgK8udjAwXrlwpJiNDy7VrCnJzTbh504zcXLmgqKoSIA+4VXaZDpwH8lCrSzAzK0Wj0aHR6NFoFKjVCtRqJWq1CjMzFWZmyrJLE8zNVZibm2BuboKFhQlqtSmSpESnU6DVKtDrFeh08r/Lj8rntFoFBQWQl6cgP19Bfr6SwkIlhYUmFBWZUlxsQkmJGSUlarRacyTpdh+ISoFrlY4sw6WpaS7W1oU0alSCu7uEl5caNzdnwwy1s3OXsktnzM3vY6ckV1d5y9AXX6z4oLxrF+a7dtExZi0d9Xo+9fTkRqen2O9rztL0VN688CbaLVqa2Dahd5PehPqEEuIRIvpK3y9JknuMlQesiYnyLonh4ehmzeQ3Pw0LT6/gx7UhFGmL6N2kNz8O+pGnmj0lZsCFh5IIXuszvR5GjZLzrXFx0LSiN2P0gWii9kbx6ROf8lzb54w4yAevItX/5/WoZ9Dp8spupMbkplzVrz/TG864yUFqmjtqV7uKWdQBGkPxVH1P9T8szM3ljaR8ff98jQqo2k5Jp5Mzp+WzlFlZcoeo3FwV166ZkZ0tcf26GTk51uTm6rl1SyI/X0FBgZKiIlNyc9XodCbo9UokSVV2/NOfAx2g/dNRgBxI30KhKEClKsDEpAgTk0LU6mKsrEoxM5ODagsLLZaWOho1AkdHBS4upjg5abCzqzyT7GmYUa6Vyn2NBvr2lQ+Qp4b37kWxcyd2u3bRf/VR+gP6xj6kBvmyw0vPvNyN/O/g/wDwtvEmxCOEzh6d6ezRmQDHAFRKseSjCr1e3jWtPGBNTYVGjZDCw7k8cxIb3PLYlhrLrtPPcfPITZrYNmHy45MZ1WYU7g3djT16QfhHRPBan73/PqxdK1cKt21rOP3DiR9445c3mBg8kXc6v2PEAdas6ql+OVitmupviDLbR27gf+IxSPQ0VPWbN62U6u9W1sDf1wKVuXjTrC9UKnkTOQcH8KuyKZAKsCw77p9eL29KVFpafilRUFBCXl4RhYUlmJiASiVhYkLZIZWdg9u1vFWrG2Bh0Qi1Wl0/euLa2MBTT8kHQHY27N6NctcuvHbu5PkfT/E8oPV0J6OZG0fdTdh6MYGp5qvINNdhpbaik3snQ0Db0b3jo9nKLz0dDhyQuz6sWSO39nBxofCpvuzv6MpKm8tsTdlK6un5mJ41JdgjmHdC3qFn4550cOtQp5fACML9EMFrfbV4McyaBZ9/Dk8/bTi9LXEbo9aOYmSbkXza81Pjje9vqkj1V99lqmqq3xXFVS+kC23LUv1ykKo0dTS0m7Jsb4lmZFmq30Ok+oW/T6mUlzhUTGoqALOyQ6jG3l5uhB8RIf/76lXYvRuT+HjcExJwX3OI/jdv8hVQ5ObMxSb2xDtfYn2D/cyxn8qNBkpaObaig1sHAhwDCHAMoGWjljhaOtafAK2gABIS5GC1/EhNBUDv5Ulq3xA2tjZjgdkpDmcuhFRoWdSSSP9IejbpSVevrjRQNzDyixCEB0MEr/XRnj3w0ktyw+m33jKcjr8ST8SqCHo16cX8p+ajVNTdGR051Z942/Wot0/194Izlar6y1P9fho04ZUa+NuJVL8g1DlOThU7fYE8lZ2YCAkJmCck4HfwIH6/HGLUTfl3P8/ZhrPeORxwWM8B84WstNaRaAt6BztaOsmBbHlA29KxJQ4aByO+uHug18u7OlQOVI8dA50OvYU5N1o2IbGLD/HujdnqkMP24tMU69fgrHOmp3NP3gx5iycaPyHWCguPDBG81jcXLsitUB5/HP73P7nxJnA26yz9vu9Ha6fWrB60GlNV3QjiylP95Ud5yr+oKBFJ0gLlqf7GkOKB/vhjkOQBKV4ocl0wb9ZQpPoFob5RKuU1+k2bwpAh8rlKAW2DhASCEhIIOnCCV6/pDHcrtsgjw/Eo520Oc8wyjx9sJZJsIcfNjoZNW9HcJQBPa09crVxxaeAiX1q5YG1m/WBnbCVJLpqt2pvMcCkdOYIiNxdJoSDLy4GTPg2IG+zCBttMEuyK0KlO0kDdgBaNWuDv0JaPnUfzROMnaNmoZf2ZaRaE+yCC1/rkxg148kl5QV9MDJRttXnl5hV6Le+FUwMnNg7biMa0dvcElySJkpK0am2n5Ab+t0v1t0E60a9qqr+sql/zmAbNCHmnKZHqF4RHyO0CWpAr7pKSIDERs6QkvBIT8UpKokdiIsSnoNBqgevoFLvJsN3HNXMd2WZ6cszhojnkmkG+xgTJxhqlrR1qe0cs7J1p4OiOjbM3DTQ2qPUK1Dowk5SYaiXUegWmOglTHZhqJUz1YKLVY6KTUOTnU5yShC7lIsrLlzG5koF5xjXUBcWGIeuUCrJtzUi3MSHVGn5/rID9bnDQVUJlo6VFI1daNGrB0EYtmN6oBf4O/rg3dBeBqiCUEcFrfVFaCs88I5dQ//472NoCUKQtYsCqAUiSxNYRW7GzsHtgQ9DrS29T1f/nVL8pJje94Yon+jM95VR/ihdc8cDUxdawHlXzdKWqfpHqFwThTqysoE0b+ahEAXL1XGoqJCaiSkrCLTkZtxs30F7PpiT7Ktob1+HqDVQ3b2Gal4u6OBu5Rdo/c9MSUq0htSGkNoJLvpBtb8FNR2vyne3QOTbCuoE9tua22Jrb4mPrw/sO/rRo1KJ+rdsVhAdEBK/1gSTBa6/B3r1yFWpZSyxJkhi/aTwnMk/w2/O/1Vh7FK32ZrV1qPn5p6uk+hVaK1TZjeWq/pNBcKGsqj/HtSLV76dB01W+tGgqUv2CINQwExN5U5ayjVkMp7nDm19xsZzez82FnByKsjIoLLyF1kRJqQpKVFCqVMiXKokSFZQoJIpVEiVKiWKlHq2pCQ2t5MC0tYUt3cxtsTa3xkQp3m4FoaaI36b64MsvYd48WLgQunUznP7u0HcsPLKQxeGLCXQJvK+HlFP96bfZBvU0JSVphtupCl1QZHgjJbZBOtEXLsoN/FUmFVX9mkANmmEi1S8IQh1nZgaOjvIBmJcdgiDULSJ4fdht2ABvvw3/+Q+MGWM4feDyASZsmcCrj716100I5FR/4h0a+N8su5EpJrfKq/qfqKjqT/XE1MXWkN7XPKkxBKym9iLVLwiCIAh/xdvbG4VCQXL1rf+EOxDB68PsyBEYOhQGDICZMw2nr+ZdJXJ1JEEuQXzZ50ugPNV/tlrrqcLCC7dJ9XugP9kOEj3kVP91N8yaWlXMpL5YlupvJlL9giAIgvBPVV7nHBsbS1hYWJXrTU1NcXR0JDg4mLfeeotOnToZrktNTWXWrFkkJCSQkpJCTk4OdnZ2+Pj4MHLkSEaPHn1/Wz0/BETw+rBKT5d3q2neHJYtA6USSZIoKEol8oenKdHe5NPHmnPqeL+yBv5XDHdVFbqUVfW3QjrRR67qT/FCpaqU6m+rQTNUDlLNvcxFql8QBEEQapG3tzejR48GID8/n/379xMTE8OaNWuIiYlhwIABACQmJrJixQo6depEUFAQdnZ2ZGVlsWXLFl599VUWLVrEnj17MDOrP5umiOD1IaTPy0V6shfoCkn/uje3Lr1qmE2NPneT39Pgi1YquBhH3hVP9Gd6wOmyVP9lD0yd7Sp6o5al+i2aW6B2qIU9zwVBEARB+Eve3t58+OGHVc5NmTKFadOmMXHiREPw2rlzZ3JycqrdX6vV0qtXL2JjY1m9ejUjR46slXHXBhG81mFa7a0qa1ALCk5TkH8a70lnsT8lcfgryL85B1WyD1z0ZHuKFT867eC1/SNo8+kYzHwrpfrHljXwb2qBykKk+gVBEAShNs2ZM4evv/6apKQk7O3tGThwIDNmzLivxxg/fjzTpk3j4sWLZGdnY29vj6np7WtMTExMCA8PJzY2lrS0tNve5mElglcjk6v6M6r1Rc3PP/2nVL8ziqveuPxgjmOsxAnv0eRNehITpROWfpaktkrlc6chPGP/DJ/871ssvC1Eql8QBEEQ6oA33niD6OhoXF1dGTduHCYmJqxbt44DBw5QWlp6zyl9vV5v+Pqv+gHrdDo2b96MQqGgW6VORPWBCF5riV6vpagosVrbqSpV/ZIJJje94IoX+jNhcNqjItXvZIedawqNfx9JXo8XcJ/yOc38NKgd1OQU5fDsd8/SzLQZS15YUus7aAmCIAhCTSooKODMmTO1/rx+fn5oNDX7Hrpv3z6io6Px9fUlPj4eGxsbAKKioggNDSU9PR1vb+97eqy5c+cC0LhxY+zsqm46lJ2dTXR0NJIkce3aNbZv305mZibR0dFVCrzqAxG81jCtNq9aA/+Kqv5SoLyq3wdSyqv65V2mFDfcMPO1QuNX1nKqcqpfWwBBo6BNKxpsmiv3IwT0kp6Ra0eSVZDF1pe2isBVEARBeOidOXOGoKCgWn/ehIQEAgPvry/6X1m0aBEAkydPNgSuAGZmZsyaNYvQ0NDb3i85OZkpU6YAcsHWgQMHiIuLQ6VS8fnnn1e7/bVr15g2bRoKhQJJkgAYOXIkvXr1qtHXUxeI4PVvqJ7qrwhUi4svG26nKnRGmemN/kIA0oleFQ38y1L9Gn8NmjYaNIPlINXc0xyF6g5pgFHj5Q4DmzYZAleAGXtmsOncJjYN20Rj28YP+qULgiAIwgPn5+dHQkKCUZ63ph06dOiOqfvOnTujVCpve7+UlBSmTZsGyOtXHR0diYyMZOLEibedSfXz80Ov1yNJEpcvX2bt2rV8+OGHbNiwgbi4OFq0aFGzL8yIRPB6F3p9KUVFSX9K9Zc38M+Vb1Q51X82FE55QKqH3MDfqVJVfz+NoZn/fVf1L1kit8Navtyw9SvApnObmBI7handp9K3ad8afOWCIAiCYDwajabGZ0CNJTdXjhecnJyqXWdiYoKDg8Nt79e9e3d27tx538+nUCjw8PDg9ddfx8nJiaFDhzJlyhRWr159349VV4nglfKq/rPViqaqpfqve0OKJ/qTg+FC2XrUbDfMfBtW7DL1QtllMw0qTQ1U9Z85A6++Ku+eNXy44fSF6xcYsXYETzZ7ksldJ//z5xEEQRAEocZZW1sDkJGRgY+PT5XrtFotWVlZeHp6PpDn7tOnDwDHjx9/II9vLI9M8FqR6j9TLUitmup3Qpnpgz6xJdLxXnID/0ueKHHC0r+BHJi21qB5tlID/zul+v+poiIYPBg8PSE62nA6vySfiFURNNI0YtnAZSgVt085CIIgCIJgXEFBQRw+fJjdu3dXC17j4uKqdBCoaVeuyF2LGjZs+MCewxjqXfAqV/UnVVmPWp7y/3OqX5Hmhe5sKJwqa+B/u1R/2ddGaeA/cSKcPQvx8WBpKQ9dkhi3cRxJN5L4fezvWJtb1/64BEEQBEG4J6NHj2b+/PlERUURHh6Ora0tAEVFRbz77rv/+PEPHz5MmzZtqq2dzcvL44033gBg4MCB//h56pJ6EbxevjwXtTqnLNV/vlKqvwGq6z53TvWXB6nPl+0y1dSiZlL9NWHNGvjf/+Drr6F1a8PpFcdX8P3x71kRsYIAxwAjDlAQBEEQhL8SEhLChAkTiI6OJiAggMjISExNTVm3bh329va4uLgYugP8HVOnTmXfvn2EhITg4eGBRqMhNTWVLVu2kJubS8+ePXnrrbdq8BUZX70IXjMv/Yz9jaboE1sgnXjCUNWvlJzQ+FvKbadaadAMKkv1ez/AVH9NuHgRXngBIiNh3DjD6dTcVMZvHs/wVsMZ2mqo8cYnCIIgCMI9mz17Ns2aNWPu3LnMmzcPBwcHBg4cSFRUFG3atKmy4cBfbT7wZy+99BJWVlbEx8cTGxtLQUEB9vb2dOrUiWHDhtWrbWHL1Yvg1XTmF1i1aSfPovapVNXfyAip/n+qtBSGDgUbG5g/H8p+iPWSnjHrxtBA3YA5/eYYeZCCIAiCINyP8ePHM378+Grnk5OTq/y7W7du97UOtl+/fvTr1+8fj+9hUi+C11YbW9E6sPVf3/Bh8OGHcPAg7N0rB7Bl5sTPYUfyDraP3I6Nuc1dHkAQBEEQBKH+qhfBa72xbRt8/DF88glUakB8+tpp/vPrf5jQYQJPNH7CiAMUBEEQBEEwLtFjqa7IyICRI6F3b3j7bcPpUl0po34ehZe1Fx8/8bERBygIgiAIgmB8Yua1LtDr5cBVqYSlS+XLMlF7ozicfpj9L+xHY6ox4iAFQRAEQRCMTwSvdcEnn8COHbB9Ozg6Gk7HX4lnxp4ZvN/1fdq7tTfiAAVBEARBEOoGsWzA2H7/HT74ACZPhh49DKcLSgsYuXYk7VzaMflxsf2rIAiCIAgCiJlX4youhuefh6Ag+OijKldN+nUSl3IvcXjcYUxVpkYaoCAIgiAIQt0igldjioqCCxfg0CEwqfiv2J64nej4aL7q8xV+Dn5GHKAgCIIgCELdIpYNGMuxYzBrlrxcIKBim9cbhTcYs24MPXx6ML5D9WbGgiAIgiAIjzIRvBqDVitv/+rnB+++W+Wq17a8Rl5JHovCF6FUiP8eQRAEQRCEysSyAWP473/lpQL794O6Ygvb1SdXs+L4CpYPXI6HtYcRBygIgiAIglA3iam92nbhgtxd4M03oUMHw+m0W2m8sukVBrUYxLBWw4w4QEEQBEEQhLpLBK+1Sa+HsWPB1RWmTTOcliSJsevHolap+br/1ygUCiMOUhAEQRAEoe4SywZq0/z5sHu3vCGBpaXh9LcJ37LlwhY2D9uMvcbeiAMUBEEQBKE2eXt7o1AoSE5ONvZQHhpi5rW2XL4Mb78tz7yGhRlOJ15PZOK2iYwLGkffpn2NOEBBEARBEIyhcsY1NjYWpVJZ5TAzM8PDw4Nnn32W33//vcp9z58/zyeffEJYWBgeHh6YmZnh7OzMgAEDiI2Nve3z7dmzh5EjRxIQEIC9vT3m5ub4+PjQv39/Nm7c+CBfao0QM6+1QZLg5ZfBygo++6zSaYlXN7+Ko6Ujn/f63IgDFARBEAShLvH29mb06NEA5Ofns3//fmJiYlizZg0xMTEMGDAAgA8++IDVq1fTsmVLnnzySezs7Dhz5gzr169n/fr1zJ49mwkTJlR57F27drFr1y46derEE088gaWlJSkpKaxfv54tW7bw2muv8dVXX9X2S75nInitDT/8AJs2wbp1YGNjOB1zKoZtidvYMHQDDdQNjDhAQRAEQRDqEm9vbz788MMq56ZMmcK0adOYOHGiIXjt27cv7777Lm3atKly2z179tCzZ0/eeecdBg0ahLOzs+G6SZMm8dGfdvYESEtLIzAwkDlz5vD222/j6en5AF7ZPyeWDTxo167B66/D4MHw9NOG0zeLb/Lm1jcZ4DeAJ5s9acQBCoIgCILwoM2ZM4eWLVtiYWGBu7s7EyZMIDc3974eY/x4efOiixcvkp2dDcBzzz1XLXAF6Nq1K926daOkpIR9+/ZVuc7MzOy2j+/q6kpwcDAA6enp9zW22iRmXh+0N9+Uuwz8afp9SuwUcopymN1ntpEGJgiCIAhCbXjjjTeIjo7G1dWVcePGYWJiwrp16zhw4AClpaV3DCb/TK/XG76+l85EpqamVS7/SmZmJgcOHMDBwYGASrt/1jUieH2QNm6EFStg2TJwdDScPppxlK8OfMXMHjPxtK6bU/KCIAiCYCwFBXDmTO0/r58faDQ1+5j79u0jOjoaX19f4uPjsSlbPhgVFUVoaCjp6el4e3vf02PNnTsXgMaNG2NnZ3fX26akpLBjxw4sLS3p2rXrbW9z8OBBNm7ciFar5fLly2zYsAEbGxuWLFmCZaWuSHWNCF4flJs35SKtvn1h+HDDab2k55VNr9DcoTlvdnrTiAMUBEEQhLrpzBkICqr9501IgMDAmn3MRYsWATB58mRD4Apy6n7WrFmEhobe9n7JyclMmTIFkAu2Dhw4QFxcHCqVis8/v3uRd3FxMcOHD6ekpISoqCisra1ve7uEhASmVeo7r9FoGDZsGG3btr2fl1jrRPD6oPznP5CbC998A5Wm9hcdXsT+y/uJfS4WtUp9lwcQBEEQhEeTn58cSBrjeWvaoUOHUCgUdOvWrdp1nTt3Rqm8fflRSkqKIbA0MTHB0dGRyMhIJk6cSKdOne74fDqdjpEjR7Jv3z6GDBnCxIkT73jbcePGMW7cOEpKSkhKSuKbb74hKiqK9evXEx8ff8/LGWqbCF4fhN275aB17lyoVKmXVZDFv3/9N6PajKKbd/UfYkEQBEEQ5NR9Tc+AGkt5UZaTk1O160xMTHBwcLjt/bp3787OnTvv67l0Oh0jRowgJiaGwYMHs3z58nu6n1qtxs/Pj//+978UFxfz7bffsmDBAl599dX7ev7aIroN1LTCQnkjgi5d5GUDlUz6dRJ6Sc9nPT+7w50FQRAEQahPylP2GRkZ1a7TarVkZWXVyPOUlpYydOhQVq1axfDhw1mxYsUdZ3Xvpk+fPgAcP368Rsb1INSZ4HXx4sXVdpQoPzIzM409vHs3dSqkpspbwVb6ofnt0m8sOLyAWT1m4WjpeJcHEARBEAShvggKCkKSJHbv3l3turi4uCodBP6ukpISBg0aRExMDM899xzLli27p24Et3PlyhUAGjZs+I/H9aDUuWUD06dPx8fHp8q5Oy00rnPOnYP/+z/46CNo3txwWqvX8sqmV2jv2p4XA1804gAFQRAEQahNo0ePZv78+URFRREeHo6trS0ARUVFvPvuu//48YuLi4mIiGDLli2MHTuWb7/99i/vEx8fT4cOHaqdT0xMZObMmSgUCgYOHPiPx/ag1LngtW/fvgQ+rAtdJk4Ed3d4++0qp7868BUnr50kfmw8KqXKSIMTBEEQBKG2hYSEMGHCBKKjowkICCAyMhJTU1PWrVuHvb09Li4uSJL0tx//5ZdfZsuWLTg4OODq6srUqVOr3SY0NLRKwVivXr1wcnKibdu2eHh4oNVqSUxM5JdffkGv1/P+++/ftSjM2Opc8CpJErdu3UKj0aBSPUSB3tatcl/XmBgwNzecvnzzMh/FfsSrj71KkKsR+n4IgiAIgmBUs2fPplmzZsydO5d58+bh4ODAwIEDiYqKok2bNlVS/Peb7r948SIKhYLs7Owqba8qP55SqawSvE6fPp1t27Zx4MABNm7ciE6nw9XVlWeffZaXX36Zxx9//O+/2FpQ54LX0NBQ8vLyUKvV9O7dm//7v//D19fX2MO6u9JS+Ne/oFs3iIioctVbW9/C0tSS6WHTjTQ4QRAEQRCMbfz48YbtXStLTk6u8u9u3brd1zrYXbt23fdYJkyYwIQJE+77fnVFnQleLS0tGTNmDKGhoTRs2JCDBw/yxRdfEBISwqFDh3B3dzf2EO/s66/h7Fl5N61Kn5i2XtjKj6d+5PuI77Ext7nLAwiCIAiCIAj34oEEr5IkUVxcfE+3NS9LsQ8aNIhBgwYZzj/99NP07t2brl27EhUVxdeW9vw9AAAeI0lEQVRff/0ghvrPZWXJBVpjx0KlHSmKtEWM3zyeMJ8whgYMNeIABUEQBEEQ6o8HErzu3r2bsLCwe7rtmTNnaNas2W2v69y5Mx07duTXX3+962P861//qtaRYOjQoQwdWgtB40cfgSTBjBlVTn8c9zGXci+xcdjGv92uQhAEQRAE4WGycuVKVq5cWeVc+UYNNeWBBK/+/v4sXrz4nm7r7Ox81+vd3d05d+7cXW/z5ZdfGqdDwfHj8k5an30GjRoZTp/PPs/HcR/zTsg7+Dk8gL3mBEEQBEEQ6qDbTR4eOnSIoKCaK1p/IMGrk5MTo0aNqpHHSkpKolGlwLDOkCR4803w9YXXXqt0WuK1La/hYuXC5K6TjThAQRAEQRCE+qfO7LB17dq1auc2b97MoUOHDFuV1Snr1sHOnfDFF6BWG07HnIphW+I2ovtGozHVGHGAgiAIgiAI9U+d6TYQEhJCYGAgQUFBWFtbc+jQIRYuXIinpyfvvfeesYdXVXGxvCFBnz7Qr5/hdJG2iInbJvJ086d5stmTRhygIAiCIAhC/VRngtchQ4awadMmtm3bRkFBAa6urowbN46PPvqo7i0b+O9/ISVF3pSgUjFW9IFo0m6l8euouxeYCYIgCIIgCH9PnQlep0+fzvTpD0Ej//R0ubPAa6+Bv7/h9PXC68yMm8m4oHE0s7999wRBEARBEAThn6kza14fGpMng5mZ3CKrkpl7Z6LVa/mw24dGGpggCIIgCEL9V2dmXh8KBw/CokXwv/+Bra3h9MWci0THRzP58ck4NXAy4gAFQRAEQRDqNzHzeq8kCd54A1q1+v/27j0ux/v/A/jrvpVbB6cKlZrbKU0580NMhX3RlzlE2aRyavv+LLF+Y+Y4iTl8F9KPxZhDDDXLbEYhzUo5xHzRHMtSGc03lM7X749+3d9u3ZK56+q+7tfz8egh7+tzXde7va3Hu0+f6/oAM2aoHVp0chGaN2qOj/p/JFJyRERERPqBM6819c03QEICcPw4YPCf/2wpWSmI+DUCm/6+CaYNTUVMkIiIiEj6OPNaE/n5wNy5wNixwHPb3s6LnQc7cztM6zlNpOSIiIhIVymVSrRt21bsNHQKm9eaWL0a+OMPYO1atfCxW8cQczsGnw/9HAZyTmITERHRq5NVeu1mXFwc5HK52odCoYCtrS08PDxw5syZl15v+vTpqnNv375dm6mLgh3Xy9y9C6xaBXz0EdCunSpcJpRhXuw8ONk6YXSn0SImSERERFKjVCrh6+sLAMjLy0NiYiIiIyPx7bffIjIyEmPGjNF43vfff49t27bB1NQUeXl5dZhx3WHz+jLz5gHNmgHP7fK15/IeXMy+iF+m/qL2ExMRERHR61IqlVi8WP31m0uXLsWyZcsQGBiosXl98OABZsyYgYkTJyIrKwunTp2qq3TrFJcNVCcpqfxBrRUrgMaNVeGCkgIsOLEAY+3HwsnWScQEiYiISBds3LgRDg4OMDIygo2NDfz9/ZGbm/tK15g5cyYAIC0tDTk5OVWO+/n5QS6XIywsDIIgaCXv+ogzr9VZtAhwcAC8vdXCYclhuPf4Ho55HRMpMSIiItIVAQEBCA0NhbW1Nd5//30YGBggOjoaSUlJKC4uhkKhqNF1ysrKVJ8//1vfr7/+GtHR0YiOjkbzSu+ilyI2ry9y6hQQEwNERQENGqjCj549QvDPwZjRcwY6WXQSMUEiIiJpyi/OR+rD1Dq/r72FPYwNjbV6zYSEBISGhqJDhw5ITk5Gs2bNAADBwcFwdXVFVlYWlEplja4VFhYGAGjXrh3MzMxU8fT0dAQEBGDy5MkYNWqUVvOvj9i8aiII5bOuPXqUvx6rkpWnV6KotAhLXJa84GQiIiJ6HakPU9ErvFed3/e833n0tOqp1Wtu374dALBgwQJV4woACoUCK1euhKurq8bz7ty5g6VLlwIof2ArKSkJp0+fRoMGDbC20tuPysrK4OPjgyZNmmDDhg1azb2+YvOqSUwM8PPPwA8/AJWm5e/m3sWGpA34ZOAnsDS1FDFBIiIi6bK3sMd5v/Oi3FfbLly4AJlMBmdn5yrHBgwYALlc8+NH6enpWLZsGQDAwMAALVu2hLu7OwIDA9GvXz/VuJCQEMTHx+PHH39E06ZNtZ5/fcTm9XmCACxcCPTvD4wYoXZo0clFaNaoGQL7B4qUHBERkfQZGxprfQZULBUPZbVq1arKMQMDA1hYWGg8z8XFBSdOnKj22tevX8eCBQswdepUDB8+XOMYKT64xbcNPO/QIeDsWWD5crVZ10vZl7Dr0i4scV6CxorG1VyAiIiIqFzFbGh2dnaVYyUlJXj48OFfvvbVq1dRVFSEbdu2VdnYID4+HgDQsWNHyOVyREdH/+X71Decea2srKx8raurq8ZtYDuad8T0ntNFSo6IiIh0Ta9evZCSkoJTp05V2Qb29OnTam8QeFVt27bFtGnTNL5v/vDhw8jOzoaHhweaNGkiqS1o2bxWduAAcPky8MsvauHY27E4eusoojyiYNjAUKTkiIiISNf4+vpi69atCA4OxujRo1WvsSooKMD8+fNf69rdunXDli1bNB5zcXFBdnY2VqxYgXaVdgiVAjavFUpKgCVLADc3wOk/Gw+UCWWYGzMX/W36Y6z92GouQERERKTOyckJ/v7+CA0NhaOjI9zd3WFoaIjo6GiYm5vDyspKkutSaxPXvFaIiAB++w34/yf7Kuy9vBcp2SlY8/YabgNLREREr2z9+vUIDQ1F06ZNER4ejn379mHEiBGIiYlBw4YN1foLbfUaMplMsn0LZ14BoKgI+OwzYNw4oNd/3itXWFKIhScXYoz9GAx4Y4CICRIREZEumzlzpmp718ru3Lmj9ndnZ+fXWgdb4eTJk699jfqKzSsAbN8OpKWVv2mgcvjidqT/Ox0/vvejOHkRERERkRouGygoAIKCgHffBRwdVeGi0iKsPL0Sno6eeLPFmyImSEREREQVOPP65ZdAdnb5w1qV7Lq0C3dz7+KH934QKTEiIiIiep5+z7zm5QErVgA+PoCdnSpcUlaCFadXwP1Ndzi2dKzmAkRERERUl/R75jU0FHj0qHxjgkr2Xt6L249uI8ojSqTEiIiIiEgT/Z15zc0FVq8G/PwApVIVLi0rxfKfl2OU3Sh0t+wuXn5EREREVIX+zryGhADPngGffqoWPnD1AK7nXMfusbtFSoyIiIiIXkQ/Z15zcoAvvgBmzgSsrVXhMqEMy+OXY3iH4ejTuo+ICRIRERGRJvo587pmDVBWBsybpxY+eO0grjy4gvBR4SIlRkRERETV0b+Z1+xsYMMGYPZsoEULVVgQBATFB2FI2yFwsnUSMUEiIiIiehH9m3n9/HOgYUMgMFAt/P3173Hp/iXE+cSJkxcRERERvZR+zbz+/juwaRPwP/8DNG+uClfMur71xltwVjqLmCARERERVUe/Zl4//xxo3BgICFALH711FOcyzyFmcoxIiRERERFRTejPzOsffwDbtpWvdW3cWBUWBAHLTi1DP5t+GNJ2iIgJEhERkb5RKpVo27at2GnoFP1pXjdsABo0AP77v9XCJ+6cQGJGIhYNWgSZTCZSckRERKSvKvcfcXFxkMvlah8KhQK2trbw8PDAmTNn1M69ceMGVq1ahcGDB8PW1hYKhQKWlpYYM2YM4uLianT/wsJCODo6Qi6Xw9bWVptfWq3Qj2UDT54AYWHlu2mZmakdWha/DL2semFEhxEiJUdERESkTqlUwtfXFwCQl5eHxMREREZG4ttvv0VkZCTGjBkDAFi0aBH2798PBwcHjBw5EmZmZkhNTcWhQ4dw6NAhrF+/Hv7+/tXe69NPP8Xdu3cBQCcm8vSjed2yBXj6FJgzRy0cnx6P+PR4fOf5nU4Ui4iIiPSDUqnE4sWL1WJLly7FsmXLEBgYqGpeR4wYgfnz56Nbt25qY+Pj4/H222/j448/xoQJE2BpaanxPnFxcVi3bh02bdqEDz74oHa+GC2T/rKBoqLy3bQmTQKemwoPig9C11Zd8U6nd0RKjoiIiPTBxo0b4eDgACMjI9jY2MDf3x+5ubmvdI2ZM2cCANLS0pCTkwMA8PHxqdK4AsCgQYPg7OyMoqIiJCQkaLze48eP4evri6FDh8LPz+8VvyLxSH/mdc8e4N49YO5ctXDi74mIvR2LAxMOcNaViIiIak1AQABCQ0NhbW2N999/HwYGBoiOjkZSUhKKi4uhUChqdJ2ysjLV5zXpXQwNDdX+fN6sWbOQm5uLr776qkb3ry+k3byWlQGrVwOjRgGdO6sdCooPQucWnTHuzXEiJUdEREQa5ecDqal1f197e8DYWKuXTEhIQGhoKDp06IDk5GQ0a9YMABAcHAxXV1dkZWVBqVTW6FphYWEAgHbt2sHsuWd4npeeno7jx4/DxMQEgwYNqnL84MGD2LlzJ7766ivY2Ni82hclMmk3r4cPA9euAVu3qoXPZZ7DkZtHsGfcHshl0l85QUREpFNSU4Fever+vufPAz17avWS27dvBwAsWLBA1bgCgEKhwMqVK+Hq6qrxvDt37mDp0qUAyh/YSkpKwunTp9GgQQOsXbu22nsWFhZi0qRJKCoqQnBwMJo2bap2/P79+/Dz84ObmxumTJnyGl+dOKTbvApC+aYEAwcCTk5qh4Lig2BnbgcPBw+RkiMiIqIXsrcvbyTFuK+WXbhwATKZDM7OVXfwHDBgAORyzZNo6enpWLZsGQDAwMAALVu2hLu7OwIDA9GvX78X3q+0tBSTJ09GQkICJk6ciMDAwCpjZsyYgbKyMmx9bnJPV0i3eT19GkhMBL7/Xi18MfsiDv12CF+P/hoN5A1ESo6IiIheyNhY6zOgYql4KKtVq1ZVjhkYGMDCwkLjeS4uLjhx4sQr3au0tBReXl6IjIyEp6cndu/eXWXMzp07cfjwYezcufOFbyCo76T7O/NVqwAHB8DNTS28PH452jVvh/e6vCdSYkRERKQvKn5ln52dXeVYSUkJHj58qJX7FBcX491338W+ffswadIk7NmzR+Os7oULFwAA3t7eVTZDAICMjAzV3x8/fqyV3LRNmjOv//oX8MMPwI4dQKXCXfnjCqKuRWHLqC0wbKD5yTsiIiIibenVqxdSUlJw6tSpKtvAnj59Wu0NAn9VUVERPDw8cOjQIfj4+KjW2Wri5OSE/Px8jce2bt0KY2NjvPde+QRfw4YNXzu32iDN5nX16vJ3ur77rlp41S+rYNvEFt7dvEVKjIiIiPSJr68vtm7diuDgYIwePRrNmzcHABQUFGD+/Pmvff3CwkKMGzcOR44cwfTp0/Hll19WO97DwwMeHpqf+dm6dSvMzMwQHh7+2nnVJuk1r3fvAnv3AmvWAJXea5b5JBPf/OsbrByyEg0b1M+fJIiIiEhanJyc4O/vj9DQUDg6OsLd3R2GhoaIjo6Gubk5rKysIAjCX77+Bx98gCNHjsDCwgLW1tb47LPPqoxxdXXV+MCYrpJe8/rFF0DjxsD06WrhsOQwKAwUmN5z+gtOJCIiItK+9evXw87ODmFhYQgPD4eFhQXGjh2L4OBgdOvWTW3DgVfdOCktLQ0ymQw5OTmqtxNUJpPJIJfL2bzWWzk5wJYtQGAgYGqqCucX52Pz+c2Y1mMamjZqWs0FiIiIiLRv5syZqu1dK7tz547a352dnV9pHezJkydfO7cK2lh/Wxek9baBsLDy97v6+6uFd13ahUfPHmFW31kiJUZERERE2iCd5jU/HwgNBaZOBVq0UIXLhDKEnAnB2DfHol3zdiImSERERESvSzrLBrZtAx49Kl8yUMlPN3/Cbzm/Yes7urmLBBERERH9hzRmXktKgLVrAU9P4Ll3qIWcCUEf6z4YYDtApOSIiIiISFukMfN67BiQng5ER6uFf73/K2Jvx2LPuD2v/PQeEREREdU/0ph53bEDGD4c6NZNLbzuzDrYNLHB+M7jRUqMiIiIiLRJGs3rzZvAvHlqoftP7yPicgT8/8ufW8ESERERSYQ0mlcHB+C5l+/+79n/hYHcADN6zhApKSIiIiLSNmk0r76+QKU1rQUlBdh0bhOmdJ+C5kbNxcuLiIiIiLRKGg9sPTfrGvFrBB7mP0RA3wCREiIiIqIK165dEzsFqgVi1VUazWuDBqpPBUFAyJkQjOo0Ch3NO4qYFBEREQGAl5eX2CmQhEijea0k5nYMrjy4go1uG8VOhYiISK/Z29vj/PnzYqdBtcze3r5O7ye55jXkTAh6WPaAcxvnlw8mIiKiWmNsbIyePXuKnQZJjKSa16sPruKnmz9h55id3JSAiIiISIKk8baB/7fuzDpYmVrB09FT7FSIiIiIqBZIpnl9kPcAu37dhQ//60M0bNBQ7HSIiIiIqBZIpnndfG4zZJDh/V7vi50KEREREdWSWm1es7Oz8cknn8DV1RWNGzeGXC7HqVOnXjg+ISEBAwcOhImJCaysrBAQEIC8vLyX3qeopAhhZ8Pg3c0b5sbm2vwSiIiIiKgeqdXmNTU1FatXr0ZWVha6du0KAC98kOrixYsYMmQICgoKEBISgunTpyM8PBwTJkx46X2O3jqK+3n3MbvfbK3mT/XP3r17xU6B6hDrrV9Yb/3CetNfVavNa+/evfHnn38iNTUVc+bMqXbsp59+CnNzc8TFxcHPzw9BQUHYuHEjfvrpJ8TExFR77u7Lu+HW0Q32FnX7njGqe/xmp19Yb/3CeusX1pv+qlptXk1NTdGsWbOXjnv8+DFiY2Ph5eUFU1NTVdzb2xumpqbYv39/teffzLmJOf2qb46JiIiISPfViwe2Ll++jJKSEvTu3VstbmhoiO7duyMlJaXa8zuYdcCQtkNqM0UiIiIiqgfqRfOalZUFALCysqpyzNLSEpmZmdWeP6nLJG5KQERERKQHarzDliAIKCwsrNHYRo0avVISz549AwAoFAqN16o4/qLzlCVKXLhw4ZXuSbopNzeXtdYjrLd+Yb31C+utP65duwYAL+znXlWNm9dTp05h8ODBNRqbmpoKOzu7GidhZGQEABqb44KCAhgbG2s8Ly0tDQAwxWdKje9Fuq9Xr15ip0B1iPXWL6y3fmG99UtaWhoGDBjw2tepcfP65ptv4uuvv67RWEtLy1dKomK5QMXygcqysrJgbW2t8bxhw4Zh9+7dUCqVqgaYiIiIiOqPZ8+eIS0tDcOGDdPK9WrcvLZq1Qre3t5auenzHB0dYWBggLNnz2L8+PGqeFFRES5evIiJEydqPM/CwgKTJk2qlZyIiIiISDu0MeNaoV48sNW0aVMMHToUu3fvxtOnT1XxXbt2IS8vr0YbFRARERGR9MkEQRBq8wbLly8HAFy5cgX79u3D1KlToVQqAQALFy5UjUtJSYGTkxM6d+6MGTNmICMjA1988QWcnZ1x5MiR2kyRiIiIiHRErTevcrkcMpkMgiCo/gTKt4ktLS1VG/vLL79g3rx5uHDhApo0aQIPDw+sXLkSJiYmtZkiEREREemIWm9eiYiIiIi0pV6seSUiIiIiqgmdbF4LCwsxb948WFtbw9jYGP369UNsbKzYadFrysvLw5IlSzB8+HCYmZlBLpdjx44dGsdeu3YNw4cPR+PGjWFubg5vb288fPiwjjOmv+rs2bP48MMP4eDgAFNTU7Rp0waenp64ceNGlbGste67cuUKJkyYgPbt28PExATm5uZwcnJCRERElbGstzQFBwdDLpejS5cuVY6x5rotLi4Ocrlc40dycrLaWG3VusavyqpPfH19ERUVhTlz5qBjx47Yvn073NzccPLkSa2+ioHq1oMHDxAUFIQ2bdqge/fuiIuL07jtb0ZGBgYNGoTmzZtj5cqVePLkCdauXYvLly8jOTkZhoaGImRPr2LVqlVITEzEhAkT0LVrV2RlZWHjxo3o2bMnzpw5AwcHBwCstVTcvXsXT58+ha+vL6ytrZGfn4/IyEhMnjwZaWlpWLBgAQDWW6oyMjKwYsUKmJiYVPmezppLR0BAAPr06aMWa9++vepzrdZa0DFJSUmCTCYT/vnPf6piBQUFQocOHQQnJycRM6PXVVhYKNy/f18QBEE4d+6cIJPJhB07dlQZ949//EMwMTERfv/9d1UsNjZWkMlkQnh4eJ3lS39dQkKCUFxcrBa7ceOG0KhRI8HLy0sVY62lq7S0VOjevbvwxhtvqGKstzR5enoKQ4cOFVxcXARHR0e1Y6y57jt58qQgk8mEqKioasdps9Y6t2wgMjISBgYG8PPzU8UUCgWmTZuGxMRE3Lt3T8Ts6HU0bNgQLVu2BADVWyk0iYqKwsiRI2FjY6OKDRkyBHZ2dti/f3+t50mvr3///jAwUP/FT4cOHdC5c2ekpqaqYqy1dMnlctjY2KjNtrDe0hMfH4+oqCisW7dO9dahylhz6RAEAU+ePEFJSYnG49qstc41rykpKbCzs4OpqalavGKq+uLFi2KkRXXk3r17ePDgAXr37l3lWJ8+fZCSkiJCVqQNgiDg/v37sLCwAMBaS1F+fj4ePnyIW7duISQkBEePHsXcuXMBsN5SVFpaCn9/f8yYMUO1FKgy1lxapkyZgqZNm8LIyAiDBw/G+fPnVce0XWudW/OalZUFKyurKvGKWGZmZl2nRHUoKysLAF74b+DPP/9EcXEx10npoIiICGRmZqo2NmGtpeejjz5CeHg4AMDAwAAbNmxQ/RaN9ZaezZs34+7duzhx4oTG46y5NCgUCowfPx5ubm6wsLDAlStXsHbtWrz11ltISEhA9+7dtV5rnWtenz17BoVCUSXeqFEj1XGSror6vuzfAL/Z6ZbU1FTMnDkTTk5O8PHxAcBaS9GcOXPg4eGBzMxMRERE4MMPP4SRkRF8fHxYb4nJycnB4sWLsXjxYpibm2scw5pLQ//+/dG/f3/V30eOHInx48eja9eumD9/Po4cOaL1Wutc82pkZITCwsIq8YKCAtVxkq6K+vLfgHRkZ2fj73//O5o3b47IyEjVmjjWWno6deqETp06AQC8vLwwbNgwzJ49G56enqy3xCxcuBAWFhbw9/d/4RjWXLrat2+Pd955BwcPHoQgCFqvtc41r1ZWVhqXBlRMSVtbW9d1SlSHKn7lUFHvyrKysmBubs6f0nVIbm4uRowYgcePH+Pnn3+GpaWl6hhrLX3u7u6IiYlBamoq6y0hN27cwJYtW7Bu3TpkZGSo4gUFBSgqKkJ6ejqaNGnCmkucra0tioqKkJeXp/Va69wDWz169MD169fx5MkTtXhSUhIAoHv37mKkRXWkdevWaNGiBc6ePVvlWHJyMuuvQwoKCjBq1CjcvHkThw8fhr29vdpx1lr6Kn6VKJfLWW8JuXfvHsrKyjBr1iy0a9dO9ZGcnIzr16+jbdu2CAoKYs0l7vbt2zAyMoKpqanWa61zzev48eNRWlqqWvQPlE9Db9++Hf369UPr1q1FzI7qgru7Ow4fPqz2E/3x48dx48YNTJgwQcTMqKZKS0vh6emJpKQkHDhwAH379tU4jrWWhgcPHlSJFRcXY+fOnTA3N1c9ic56S0OXLl1w8OBBfPfdd6qPgwcPwsHBAW3atMF3332HadOmAWDNpUDT/9+XLl3CoUOH8Le//U0V02atZUJ1L9Sspzw9PXHw4EHMmTMH7du3x44dO3Du3DkcP34cAwcOFDs9eg0bN27Ev//9b2RmZmLz5s0YN26c6ieyWbNmoUmTJsjIyECPHj3QrFkzBAQE4MmTJ1izZg3eeOMNnD17lr9m0gGzZ8/Ghg0bMGrUKI3ftLy8vACAtZaIsWPH4smTJxg0aBCsra2RnZ2NiIgIXL9+Hdu3b4e3tzcA1lvqXFxckJOTg8uXL6tirLnuGzx4MIyNjdG/f3+0bNkSV69eRXh4OBQKBRITE1Xr3LVa61fbR6F+KCgoED7++GPByspKaNSokdC3b1/h2LFjYqdFWqBUKgWZTCbIZDJBLpcLcrlc9Xl6erpq3JUrV4Rhw4YJJiYmgpmZmTB58mThjz/+EDFzehUuLi6q2j7/IZfL1cay1rrvm2++Ed5++23B0tJSMDQ0FMzNzQU3NzchNja2yljWW7pcXFyELl26VImz5rptw4YNQt++fQVzc3PB0NBQaN26teDt7S3cunWrylht1VonZ16JiIiISD/p3JpXIiIiItJfbF6JiIiISGeweSUiIiIincHmlYiIiIh0BptXIiIiItIZbF6JiIiISGeweSUiIiIincHmlYiIiIh0BptXIiIiItIZbF6JiIiISGeweSUiIiIincHmlYiIiIh0xv8ByLnT/HSGFiwAAAAASUVORK5CYII=" + ], + "text/plain": [ + "PyPlot.Figure(PyObject )" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "PyObject " + ] + }, + "execution_count": 181, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "figure(figsize=(8, 4))\n", + "xi = linspace(-1, 1)\n", + "\n", + "for n=0:4\n", + " P = get_legendre_polynomial(n)\n", + " dP = get_legendre_polynomial_derivative(n)\n", + " #P2 = get_legendre_polynomial_2(n)\n", + " plot(dP(xi), label=\"dP$n\")\n", + " plot(diff(P(xi))./diff(xi), label=\"dP2$n\")\n", + " #plot(xi, P2(xi), label=\"P2$n\")\n", + " #println(sum(abs(P(xi)-P2(xi))))\n", + "end\n", + "#plot(1/2*(3*xi.^2 - 1), \"-k\")\n", + "#plot(3*xi, \"-k\")\n", + "#plot(1/2*(5*xi.^3 - 3*xi), \"-y\")\n", + "#ylim(-1.1, 1.1)\n", + "legend()" + ] + }, + { + "cell_type": "code", + "execution_count": 182, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "get_hierarchial_basis_derivative (generic function with 1 method)" + ] + }, + "execution_count": 182, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "function get_hierarchial_basis(n)\n", + " if n == 1\n", + " N(xi) = 1/2*(1 - xi)\n", + " elseif n == 2\n", + " N(xi) = 1/2*(1 + xi)\n", + " else\n", + " j = n-1\n", + " Pj = get_legendre_polynomial(j)\n", + " Pjm2 = get_legendre_polynomial(j-2)\n", + " N(xi) = 1/sqrt(2*(2*j-1))*(Pj(xi) - Pjm2(xi))\n", + " end\n", + " return N\n", + "end\n", + "\n", + "function get_hierarchial_basis_derivative(n)\n", + " if n == 1\n", + " dN(xi) = 1/2*(0*xi - 1)\n", + " elseif n == 2\n", + " dN(xi) = 1/2*(0*xi + 1)\n", + " else\n", + " j = n-1\n", + " Pj = get_legendre_polynomial_derivative(j)\n", + " Pjm2 = get_legendre_polynomial_derivative(j-2)\n", + " dN(xi) = 1/sqrt(2*(2*j-1))*(Pj(xi) - Pjm2(xi))\n", + " end\n", + " return dN\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 183, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": [ + 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" + ], + "text/plain": [ + "PyPlot.Figure(PyObject )" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "PyObject " + ] + }, + "execution_count": 183, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "figure(figsize=(8, 4))\n", + "xi = linspace(-1, 1)\n", + "\n", + "for n=1:6\n", + " N = get_hierarchial_basis_derivative(n)\n", + " plot(xi, N(xi), label=\"N$n\")\n", + "end\n", + "ylim(-1.1, 1.1)\n", + "legend()" + ] + }, + { + "cell_type": "code", + "execution_count": 79, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "1-element Array{Float64,1}:\n", + " -0.612372" + ] + }, + "execution_count": 79, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "get_hierarchial_basis(3)([0.0])" + ] + }, + { + "cell_type": "code", + "execution_count": 202, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "get_dbasisdxi (generic function with 6 methods)" + ] + }, + "execution_count": 202, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "using ForwardDiff\n", + "using JuliaFEM: get_number_of_basis_functions, get_basis, get_dbasisdxi\n", + "\n", + "abstract Hierarchical <: JuliaFEM.Element\n", + "\n", + "type PSeg <: Hierarchical\n", + " connectivity :: Array{Int, 1}\n", + " fields :: Dict{Any, Any}\n", + " degree :: Int\n", + "end\n", + "\n", + "PSeg(connectivity) = PSeg(connectivity, Dict{Any,Any}(), 1)\n", + "\n", + "JuliaFEM.get_number_of_basis_functions(el::Type{PSeg}) = 2\n", + "JuliaFEM.get_number_of_basis_functions(el::PSeg) = 2 + el.degree - 1\n", + "JuliaFEM.get_element_dimension(el::Type{PSeg}) = 1\n", + "function JuliaFEM.get_basis(el::PSeg, xi)\n", + " m = get_number_of_basis_functions(el)\n", + " out = zeros(m)\n", + " for n=1:m\n", + " N = get_hierarchial_basis(n)\n", + " out[n] = N(xi)[1]\n", + " end\n", + " return out\n", + "end\n", + "\n", + "function JuliaFEM.get_dbasisdxi(el::PSeg, xi)\n", + " m = get_number_of_basis_functions(el)\n", + " out = zeros(m)\n", + " for n=1:m\n", + " dN = get_hierarchial_basis_derivative(n)\n", + " out[n] = dN(xi)[1]\n", + " end\n", + " return out\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 212, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "3x3 Array{Float64,2}:\n", + " 0.5 -0.5 0.0\n", + " -0.5 0.5 0.0\n", + " 0.0 0.0 1.0" + ] + }, + "execution_count": 212, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pel = PSeg([1, 2])\n", + "pel.degree = 2\n", + "dn1 = get_dbasisdxi(pel, [-sqrt(1/3)])\n", + "dn2 = get_dbasisdxi(pel, [+sqrt(1/3)])\n", + "dn1 * dn1' + dn2 * dn2'" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1,2]\n", + "[2,3]\n", + "[3,4]\n", + "[4,1]\n" + ] + } + ], + "source": [ + "nelements = length(phi2)-1\n", + "nnodes = length(phi2)\n", + "elements = []\n", + "for i=1:nnodes\n", + " con = [i, mod(i,nnodes)+1]\n", + " push!(elements, JuliaFEM.Seg2\n", + "end" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 0.5.0-dev", + "language": "julia", + "name": "julia-0.5" + }, + "language_info": { + "name": "julia", + "version": "0.5.0" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +}