{
"cells": [
{
"cell_type": "markdown",
"source": [
"# Temperature and metallic systems\n",
"\n",
"In this example we consider the modeling of a magnesium lattice\n",
"as a simple example for a metallic system.\n",
"For our treatment we will use the PBE exchange-correlation functional.\n",
"First we import required packages and setup the lattice.\n",
"Again notice that DFTK uses the convention that lattice vectors are\n",
"specified column by column."
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"using DFTK\n",
"using Plots\n",
"using Unitful\n",
"using UnitfulAtomic\n",
"\n",
"a = 3.01794 # bohr\n",
"b = 5.22722 # bohr\n",
"c = 9.77362 # bohr\n",
"lattice = [[-a -a 0]; [-b b 0]; [0 0 -c]]\n",
"Mg = ElementPsp(:Mg, psp=load_psp(\"hgh/pbe/Mg-q2\"))\n",
"atoms = [Mg => [[2/3, 1/3, 1/4], [1/3, 2/3, 3/4]]];"
],
"metadata": {},
"execution_count": 1
},
{
"cell_type": "markdown",
"source": [
"Next we build the PBE model and discretize it.\n",
"Since magnesium is a metal we apply a small smearing\n",
"temperature to ease convergence using the Fermi-Dirac\n",
"smearing scheme. Note that both the `Ecut` is too small\n",
"as well as the minimal ``k``-point spacing\n",
"`kspacing` far too large to give a converged result.\n",
"These have been selected to obtain a fast execution time.\n",
"By default `PlaneWaveBasis` chooses a `kspacing`\n",
"of `2π * 0.022` inverse Bohrs, which is much more reasonable."
],
"metadata": {}
},
{
"outputs": [],
"cell_type": "code",
"source": [
"kspacing = 0.945 / u\"angstrom\" # Minimal spacing of k-points,\n",
"# in units of wavevectors (inverse Bohrs)\n",
"Ecut = 5 # kinetic energy cutoff in Hartree\n",
"temperature = 0.01 # Smearing temperature in Hartree\n",
"\n",
"model = model_DFT(lattice, atoms, [:gga_x_pbe, :gga_c_pbe];\n",
" temperature=temperature,\n",
" smearing=DFTK.Smearing.FermiDirac())\n",
"kgrid = kgrid_from_minimal_spacing(lattice, kspacing)\n",
"basis = PlaneWaveBasis(model; Ecut, kgrid);"
],
"metadata": {},
"execution_count": 2
},
{
"cell_type": "markdown",
"source": [
"Finally we run the SCF. Two magnesium atoms in\n",
"our pseudopotential model result in four valence electrons being explicitly\n",
"treated. Nevertheless this SCF will solve for eight bands by default\n",
"in order to capture partial occupations beyond the Fermi level due to\n",
"the employed smearing scheme. In this example we use a damping of `0.8`.\n",
"The default `LdosMixing` should be suitable to converge metallic systems\n",
"like the one we model here. For the sake of demonstration we still switch to\n",
"Kerker mixing here."
],
"metadata": {}
},
{
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"n Free energy Eₙ-Eₙ₋₁ ρout-ρin α Diag\n",
"--- --------------- --------- -------- ---- ----\n",
" 1 -1.761905177446 NaN 5.05e-02 0.80 4.7\n",
" 2 -1.762134514136 -2.29e-04 1.89e-02 0.80 1.0\n",
" 3 -1.762239011811 -1.04e-04 1.61e-03 0.80 3.7\n",
" 4 -1.762241601993 -2.59e-06 2.94e-04 0.80 2.7\n",
" 5 -1.762241620070 -1.81e-08 1.44e-05 0.80 2.3\n"
]
}
],
"cell_type": "code",
"source": [
"scfres = self_consistent_field(basis, damping=0.8, mixing=KerkerMixing());"
],
"metadata": {},
"execution_count": 3
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "9-element Vector{Float64}:\n 1.9999999999077942\n 1.9999975862828105\n 0.00401688527811209\n 3.000417987588851e-15\n 1.1115950739397226e-18\n 1.111503160135526e-18\n 7.978735727952186e-19\n 7.978004098910642e-19\n 3.345070614271144e-22"
},
"metadata": {},
"execution_count": 4
}
],
"cell_type": "code",
"source": [
"scfres.occupation[1]"
],
"metadata": {},
"execution_count": 4
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "Energy breakdown (in Ha):\n Kinetic 0.7180582 \n AtomicLocal 0.3145350 \n AtomicNonlocal 0.3265858 \n Ewald -2.1544222\n PspCorrection -0.1026056\n Hartree 0.0055000 \n Xc -0.8610484\n Entropy -0.0088446\n\n total -1.762241620070"
},
"metadata": {},
"execution_count": 5
}
],
"cell_type": "code",
"source": [
"scfres.energies"
],
"metadata": {},
"execution_count": 5
},
{
"cell_type": "markdown",
"source": [
"The fact that magnesium is a metal is confirmed\n",
"by plotting the density of states around the Fermi level."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "Plot{Plots.GRBackend() n=2}",
"image/png": 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CWMYgJCLtimRFyDHCmMUgJCLtEjhrNPyKkA+pj2UMQiLSLr+h5UPsLmtdXf67RlkRxiwGIRFpl0IVod+uUa4jjFkMQiLSLiXGCAMFISvCmMUgJCKN8njQ3Y2EhBCnSZgswzFC6o9BSEQa1dWF+HgYDCFOkyUIuXwiljEIiUijhPSLgusIKWwMQiLSKIWCkDvLkA8GIRFplJC1E2BFSGFjEBKRRvkt3QaTa7IMZ43GLAYhEWmUQhUhu0bJB4OQiDQqkhUhgzCWMQiJSKMETpYRm2F+L5uQwJ1lYheDkIg0SrlZo6wIqT8GIRFpFIOQIoNBSEQaJXCyjNhtQhmE5INBSEQa5TexBhO7TSiXT5APBiERaZSQZzBBpqdPcLJMLGMQEpFGCawI2TVKYWIQEpFGdXaGfgYTZOoaZRDGMgYhEWmU8DFC4RWh2w2nE/HxvscZhLGMQUhEGiVwZ5mEBDidcLuFXtNvuDIIYxmDkIg0SmBFCCAhQWiMBbpmfDxcLrhcIppHusEgJCKNEh6EwufLBFmbyImjMYtBSEQaJXBBPcTMlwnS3cre0ZjFICQijerqEhqEFgva24VeM9BMVK6pj1kMQiLSKIF7jUJMMRfkmuwajVkMQiLSKOFjhMKLuSBrE8UuzCfdYBASkUaJmiwTfkWYmMiKMEYxCIlIo0RNlhFeEXKyDPlgEBKRRglcUA+RQRgoXBmEMYtBSEQapcQ6QgYhDcYgJCKNEjVZRvgYIYOQfDAIiUijRAWh8HWEDELywSAkIo1SqCIMso6QQRibGIREpEVOJwCYzYJO5hghhYNBSKQf7e04ckTtRshEeDkI+RbUcx1hbGIQEunHHXdg0iTs3q12O+QgNgi56TZJxiAk0omuLrzxBu65B3/9q9pNkYNyFSG7RsmHsA54ItK8LVswbhxWr8acOfB4YDCo3aDwqBKEDQ1C70h6woqQSCd27cKMGSgtRUICDh5UuzVhExWEsjyYlxVhzGIQEunEkSMYPRoA5szB5s1qtyZswjcahUxjhHwMU8xiEBLpRG8Qnncetm5VuzVhE/5UXsjUNcoH88YsBiGRThw7hlGjAGDGDGzbpnZrwsbJMhQxDEIiPXC7UVODoiIAmDgRx48L3XJMs8R2jQofI2TXKPlgEBLpQV0d0tIQFwcA8fEYOxZ796rdpvCwa5QihkFIpAdVVT3loNe0adi5U73WyCFI6TaYqFmjrAjJB4OQSA+qqlBQ0Pd26lTs2qVea+Sg0Bhh8OUTrAhjE4OQSA+qq5Gf3/d2+nTs2KFea+TQ1RVwU9DBhAdhkB5X4WswSGcYhER6UFeHIUP63k6ahMOHo7ujT6G9RoN0jbIijFkMQiI9OHt2QBAmJWHkSOzbp16DwiZqjDAhAd3dcLvDuiyfPhGzGIREelBfj+zsAUfOOQfbt6vUGjmI6ho1GAStAnS54Hb3zK0djBVhzGIQEumBT9cogPPOi+5l9aK6RiFsOXzwa7IijFkMQiI9GFwRzpiBLVtUao0cgjxB1y+LJfQeAsEX6XMdYcxiEBLpQV0dcnIGHJk4EWfOoL5epQaFLcju2H4JrAiDXDMuDm43XC4RNyV9YBAS6UFjIzIzBxwxmTBjBr7+WqUGhU1sRZiUFLoiDNndyu1GYxODkCjqdXXB6URysu/x2bPx5ZdqNEgOYscIhaygCDkTlUEYmxiERFGvqQkZGX6Oz5+PTz+NeGtkImqvUQgbI2RFSH4xCImiXqAgnDEDhw+jqSniDZKDhIow5FSXkE+0YBDGJgYhUdRrakJ6up/j8fG44IJoLQqVCMKQE3A4cTQ2MQiJol5zs/+KEMCiRfjoo8i2RiYSglDI8gmOEdJgDEKiqBeoaxTA4sXYsCGyrZGJQl2jIYOQFWEMYhASRb0gQThuHDo6cOJEZBskB1WCkA+giE0MQqKo19zsf4wQgMGAhQuxcaOIq2kkCcQGocUiTxCyIoxBDEKiqNfaitTUgF9dsACffSb0UgcOIC8Pjz0mR7PCo1bXqEZ+D6BIYhASRb2WFqSlBfzq3Ln4/HOhl/rrX3HNNfjtb9XfflqtrlFWhDGIQUgU9YJXhCNGwO3GyZOCLvX++7jvPowdi08+kat1ErEipIgRHYTbt2/funVr/yMbN2586qmnvvjiC/laRUQiBK8IAcycKehJFPX1aGpCWRmWLMHHH8vVOimcTng8MJtFfESW5ROsCGOTuCDcuXPn3Llzb7vttt4jP/3pT9esWXPixImVK1f++te/lrt5RBRaa2uIIJwxQ9CzCXfvxuTJMBgwf76I3lQliC0HwYqQwiAiCJ1O55o1a26//fbeIzU1NU8++eRHH330hz/84f3333/44Yebm5sVaCQRBdPSEqxrFMC0adi1K/R19u3D5Mk95x86FLrAUo6EIOSsUZJMRBD+9re/XbJkyZQpU3qPbNy4cfz48cOGDQMwbty4wsLCTZs2yd9GIgoqZNfolCnYvRseT4jrHDuGUaMAIDEREydi+3bZWiiW2B23wYqQwiC0D/7gwYPr1q3bunXrunXreg+eOXOmoKCg921BQUFVVVWgK7jd7oceeqj37Y033pjj8yBRhTkcDofDEck7kkZo/Fvv8Xg8Hk84LWxtjUtKCnaBjAwkJsZVVDiLioKF4bFj5osucjkcHgAzZpi++spz/vluya0KR1ubISHB5HA4hX8kPt5gt/t+xOFwmM1mo7HnN3673RQf73E4Av6h4uONdrvB4eDDeaOe0+n0fvfNZrPBYAh+sqAgdLlcN99885NPPpk48Jc0z8DfMI1Go9sd8F+Yx+Np6rcNvsPhCHKyEtxud4TvSBqh/W+9x+OR3EKPB21tSE4OcYGyMvf+/Z6CgmAnHT+OkhK32+0BcM45WLfO1P+i335rMJsxdmyoulIO7e2GxESTqL+ThARDe7vvR3y+9R0dpvj4YP8YEhIMHR3Q+L8WEsL9HSEnCwrCzZs3Hzly5IknnnjiiSdOnTpVUVGxYsWKl19+OT8/v7a2tve0mpqa/gWiD5PJ9Mgjjwi5nUK6u7sTRD3xmvRC4996g8FgNBolt7CtDYmJsFhCfHzCBBw9arzssoAnuN04fRpjxsTHxwPA7Nn42c/Q26ozZ3DxxXC5cPQoMjOltVQEtxtJSRD1d5Kejo4O3484nc6EhITeirCrC6mpxiBXtVrR3Y2EBJOkVpOGmEwm4f+tBAXh2LFjn3nmGe/rL7/8sra2dvny5SaTad68ebfccktNTU1eXl55efmJEydmz54tveFEJJ7NFmKmjFdZGXbuDHZCTQ0yMuBNQQAlJTCZcPw4SksB4NFH8cMfoqoKb76JH/847EaHotZkGY4RxiZBQZiTk7N8+XLva4fDsWnTJu/boUOHrly58uKLL16+fPnatWvvuOOO7OxsBRtLRIO0tsJqDX3aqFF47bVgJ5w+jaFDBxyZOxeffYbSUnR34x//wObN2LQJn3yi3SAUso7QYgl2AmeNxiYxC1YBABdeeOGQIUN63z799NPr1q07ePDgQw89dPnll8vaNiIKzWYTGoRHjwY74fRpFBUNOLJ4Md5/Hz/6Ed59F+PGobQUNhv++MewWiuQQkHY3s4gJD9EB2FxcXFxcXHvW4PBcM0118jaJCISQWAQFhWhqQl2O5KT/Z9QWelbEV52Ge65By0teOIJeHfRGDcOJ05ISSmxpC2oFxKEIdcRqrh6ktTCvUaJopvAIDQaUVKC8vKAJ5w5g8LCAUeysnDFFViyBGfPYtkyAIiPR1GR0G1LwyEhCM1mmEwh9gpn1yj5xSAkim4CJ8sAGD48RBDm5/sefPRRLFuG997r2/azpAQVFVLaKYq0ojPkfBnuLEN+ie4aJSJNEThZBgKC0KciBJCWhp/8ZMCRyARhyMTyy9uxGegZxZ2diIuDKejKCAZhbGJFSBTdBHaNAhg+HCdOBPxqTQ3y8kJfJDJB2NUFCesqk5ODjfCFHCAEgzBWMQiJopvwICwpCTa857drdLCiIpw5I7RtknV2SgnC4FNdQg4QQthiRNIfBiFRdGtrQ0qKoDOLi3HqlP8vdXSgqwsZGaEvkpeHmhoRzZNG8hhh8IowZBByQX1sYhASRbe2NqEV4bBhASvC2lrk5gq6SF4eqquFtk2yzk4pY4TBg1DIuKPJBLM5xNRT0h8GIVF0s9mEVoRDhqCzE3a7ny9VVwvqFwWQnx+tFaHdHroiBIvCmMQgJIpuwrtGAQwd6r93VHhFmJWFlhYo/VQraUGYnOw/5r0EzkQVskMN6QyDkCi6iQrCoiKcPu3nuMApowCMRmRn4+xZoXeURnIQhjlGCE4cjUkMQqLoJnyMEMDQoais9HO8pkZoRQggKwv19UJPlqajQ2LXaJCKkEFIgTAIiaKb2K5Rv0FYWyu0IgSQnY2GBqEnSyNtskzIijDQPqv9cbvRGMQgJIpuwifLQI6uUQDZ2YpXhEqMEQqcLMMxwhjEICSKbsIX1CNo16jwINRs12jwYs5uF/QbA9fUxyAGIVEU83iE9vh5RVFFqETXKCtC8otBSDpXV4c1axKV/sGtlo4OJCSE2Ei6v0BBePYscnKEXiQrKxJjhNL2Gm1rC/hV4V2jQfpXSZcYhKRzL72Ef/4z7q9/VbsdymhrE1EOAkhPh9uN1tYBB1tbYTYLCgmvrCw0Noq4qQQqTpYJfhHSJQYh6dyGDbj55u5PP1W7HcoQNWXUa3BRWF0tol8UQEYGmprE3VQsyTvLcLIMScAgJJ379lusWuX45ht4PGo3RQECJ4D0NzgIa2qE7q/mlZ6O5mZxNxVLoQX1QipCBmEMYhCSntXXo6sLZWXu5ORIbBUdeRIqwsETR8+cQUGBiCtEoCKU9mDekMsnBK4j5KzRWMMgJD07ehRjxgDA6NE4ckTt1gziM1YngcAf7v0VFfkGoahtZRCRIJT2YN6UFBkmywRPU9IlBiHpWWUliooAYNQoHD2q4I3uvRfvvSfuI998g4ICHD4c1n2lVYSDxwjFdo0qGoRdXYiLg1H8D6fgQciuUQqEQUh6dvo0hg4FgJKSgM+kDV9FBZ55BnfeKe5Tzz6LIUPwzDNh3VrsrFH4ewCF2K5RiwUej4LPKpI2QAj5lk8wCGMNg5D0rLKyJwgLC1FVpdRdvvgCV1wBm03cLbZuxZo12LEjrFtLmCwzbJhvEFZVobBQ3EUU7R2VNkCIUBWhwOqZQRiDGISkZ6dP93SNBlpILot9+zBxImbOxLZtQj/S0YHjx7FyJfbsCevWErpGi4tx6tSAObQSglDRiaOSK8K4OJhMAZ8vL3yLNQZhrGEQkp71rpBTtCL0BuGYMSKGIcvLUVyMvDwkJaG7W/qtJXSNWixISRnwQMGqqp5fF4RLS0NLi7iPCCe5IkTQolDgLw2cLBODGISkZ3V1PTuHFRYqWBGeOIGRI1FaiuPHRXxkxAgAKCkJKwgldI0CGDYMFRU9rxsbkZAgYlsZL6WDUFpFiMDDhA4H3G5BM1GDDzSSLjEISc9qa3uCMD0d3d2KrA/zeFBZieJicUF4/DhKSwGguDjcilBCEI4YgfLyntcVFRg2TPQV0tJkWPsRSJgVod96TvjDqlgRxiAGIemWN/nS03ve5uSgtlb+uzQ0wGKBxYIRI/rKrJBOnkRJCQAMGxZwTEsICesIAZSW4tixntcVFT0tESUtTYtjhAjcNSq8dA4UpaRjDELSrbo6ZGfDYOh5m5MzYGBMLqdO9UxMLSjAmTNCP9W7YiH8ilBaEJ440fNachAq1zUqbcdtr0Adm8JLZ1aEMYhBSLp19iyGDOl7q1AQ9k5MtViQkCB0UUF1dU8Q5uXB4ZB+d2ljhCNH9s3rKS/H8OGir5CaqmzXqOSK0GqFzebnuKiuUY4RxhoGIelWXd2AIMzNVaRrtP8jbYUXhVVVPUGYmxtWEEobIywrw8GDPa8PH8bo0aKvoOjyiY4O0ZN3elmtAStCq1XQFeLiYDCEVaZT1GEQkm41NSEjo++tQhVh/30RTS0AACAASURBVLgVHoS98RlmEEobI8zJgdGImhoAOHgQ48aJvoKiFaG0p/J6Wa3+GybqLypQmpJeMQhJtxobkZXV9zY7G0o8p77/s93z8wU946K1FUZjTyUXfkUoIQgBjB+PffvQ0oKWlp4xTlE0O0aYmhpu1yg4TBh7GISkW42NyMzse5udjYYG+e9SW9v36IYhQwQVnb2LOgCkpcHjgdst8e7SxggBzJyJr77C9u2YMqVvPpFwSo8RSg7CQBWhzSa0axQMwtjDICTdGhyESleEAntffQYvzWbpKygkV4QXXojPP8emTZgzR8rHAxVesghn+USgyTKtrUhNFXoRzpeJNQxC0q2GhkgEYe/mNQByclBXJ+gjPkEobWqGxyP00UKDLVyIb7/Fc8/h8sulfDxQ4SWLMCvCQF2jwoOQSwljjVntBhApxWeMMCtLkSBsaOi7i8Cu0cFBKG2YsKMD8fEwmaR8NjERTz+NPXswY4aUjyvdNSrqQcH9BSpVW1tFLJdMSVGw3iUNYhCSbvnMGlWoIuzfASu8a7S3iEQYFaHkAUKvq6/G1VdL/GzUjRGK6hoNVFaSXrFrlHSrublvfzUA6elobw9riuZgbW0wmfoGtIYMEdQ16rPSX3JFKHmAMHzJyejshMulyMWV6BoVFYSKjoCSBjEISbeamgYEocGA9HSZHyc7eIWGkImp9fXIzu57G05FqFYQGgwK9h+GuXyCFSGJxSAk3WpqGjBZBkBmpswrKPoPEAKwWuFwoLMzxKcGB6HkijCcrtEwKdc72t4ufWeZQAscRQUhxwhjDYOQ9MnhgMPh+/M0KwuNjXLexWeFBoRlrU9CSw5CFStCKBmE4SyfCBSEotYRKjoCShrEICR9am5GWprvUvHMTMWDMCsrdBD61JHhBKGKFaFy/YdhjhF2dMDp9D3OrlEKgkFI+uQzZdRL9q5RaUHofT5UryjtGlUuLcLpGg00eOn330Mg3Gs01jAISZ98pox6yd41OvjHa8j5Mk4n7HakpfUdMZmib9YotFoRwt+TMRwOdHeL23SbFWFMYRCSPrW0DAgbL9m7RgffJWRF6J3Lauz3P09yEEreVkYW2hwjhL9hwpYWpKaK2FJV0X1zSIMYhKRPfoMwI0Pm5RODK8KQva/19QMGCBFG16ioJyrITptdo/AXhIN7sMVegfSNQUj6FJmKcHAHbGZmiKxtbvbNTm912NEh+u6qV4TKrSMMpyIc3DXq9x9DEAzCWMMgJH2KTEXoNwiDZ63f6iQuTsoD31UfI1So/zDMMcLB32W/A8ZBDI5S0jcGIemT3+nyGRmKT5YJeYtAQSghoXW5fMLhgMEAcxi7IA/+XURsEKamwm6X/pBIijoMQtKn1lb/XaMRqAiD36Kx0c88frNZSl+cLpdPhFkOQo4gNBqRnMz5MjGEQUj65J0o6EP2rtHBHbAhu0YHb/yG6OwaVWjWqCxB6DNfyefJlEKwdzSmMAhJn/yOEaano6VFzi6vlhZ5xgijtCJUYtV5e7v8FWFDw4AdDITgfJmYwiAkffIbhGaznF1enZ3weHznN0ZysozqY4QKVYThrJ2Av20TfHY5F4IVYUxhEJI+BZoxL2PvqN9bWCxwu4M9gMLvXl+SK0J1Z40qVBGGGYSDfxcZvHYzJAZhTGEQkj4F2mRZxomjgbI2eFEYqCKMxq5RJSrC8LtGs7JQXz/giISuUSF7xpJuMAhJnyJQEQaaixg8a/1O3DCbJU6W0eUYYZhlbm4uzp4dcMRnl3MhGIQxhUFI+mSz+a8IZVxBEajoDH6LwTvLQGpFqO7OMikpsNvh8ch82Y6OsLaVAZCU5Pv3yYqQgmMQkg45nejq8j/UFIGKMEjXqMfjf/mEhDHCjg7ExYW18DxMRiMSE2G3y3xZWdI9J6evKOzqQkeHiGcweTEIYwqDkHSotRVWq/+nDSg9WSb4LWw2JCX5SS8JQaju4+m9lNhuNPx1hAByc1Fb2/O6thY5OSIePeHFIIwpDELSoSCPI5cxCIN0jQaqCAM9BkFC16i6A4ReSmwuE/5kGQysCKurkZcn+goMwpjCICQdCh6EKs4aDfScdAkVobrPYPJSIgjDX0cIID8fNTU9r2trDfn5oq8wZIjv1FPSMQYh6ZDfjUa9tFkRSghCHVeE4Qfh0KGorOx5La0izMvri1LSPQYh6ZDfjUa95J01GmiMUEIQtrWJ2/tNx0EYftdoUVFfEFZWoqhI9BUyMtDeHmxjBNITBiHpUGTGCAPFbZCs9fvoCQAGA5KTxYWKXoNQlq7RoUNx+nTP64oKlJSIvoLB4Kco/PBDfPJJuG0jDWIQkg5FLAjFjhEGqgghfpfntjZYrSLOV0JUdI1WVBiGD5dyEZ8g3LsXK1fi2mtRVRVu80hrGISkQ4FW00PuMUIJk2VkDELVK8KUFPmD0G6XIQiHDUN1Nbq6AKkVIYD8fJw50/f2scfwk5/gssvwxhvhNo+0hkFIOhSkIkxLQ1sbXC4Z7hKka1RaRShq604tBKFCFWH46yPNZgwfjqNH0dpqaGuDhFmjAIYNQ3l5z2uHA2+9heuvx+WX46OPwm0eaQ2DkHTIu6DeL6MRVqs8DxYI1DXqzVqn08+XggRhaqq4ilCvyydk6RoFMHYsDh3Ct98aJ0yAUdLPuREjcOJEz+svvsCoUSgowIwZ2L5dhuaRpjAISYeCVISQb+JooLsYjUhP93+LII9Kj8auUSWCUJauUQBTpmDbNuzda5w0SeJ2qP2D8F//wqWXAkBhIYzGvgFI0gcGIelQ8CCUZU29dzvTQJ14mZn+9yVpaAj4YDwGoZdcO4nPm4fPPsPGjaa5cyVeobQUx4/3vP7gA1x0Uc/rceNw4IAMLSTtYBCSDkWgIgyynSn8PSTdq7ExWBCKHSPkrNEgZs5EXR02bzZefLHEinDUKNTUoLUV5eWor8f06T3HR4/GkSMytJC0Q72964kUE4GKMNAAoVegnSqDVISpqeKCUK9jhHJ1jcbF4e230dHRmZqaIO0KJhMmT8bOndi9G0uX9g00Mgj1h0FIOhSZijD4LQYHoc2G+HgkBPixnJoqbk8vm039ilCJp0/I+JDFSZNgt4vZrWeQefPw7rvYsAFPPtl3cNQobNgQbttIUxiEpEMhUyoCFeHgWwQpBxG1C+pFVbFCyNU1Koubb8akSZg+HXPm9B0sKcHJk+q1iRTAICQdCtk12n+htBK3yMry8+wCeYNQl12jXV0wGtV82rCPESNw9ChSUgYMBhcXMwj1hpNlSG/cbrS3BwuJCFSEfh/iU1+P7OyAHxE7WUYLXaOyB6GM/aJyyc/3/Xu2WpGQwKcV6gqDkPTGZkNycrA11LIEYfCKMDsbdXW+B+vqggWh2AX1WugaTUqCy4XubtkuqKl+0SBYFOoMg5D0JnitBvUqwrNnkZMT8COiuka9Va8WiqeUFLS1yXa1tjZN/KFCKiri1tu6wiAkvQleq0G9ijBk16jwILTbkZQkcecweYld9RGc3a7+wKcQBQUyDDOTdmjgfxKRrCIThBIqwro6DBkS8COixgi1MEDoJe8wYbRUhPn5qK5WuxEkH6FB+P777992222XXHLJLbfcsm/fvt7jDQ0N995775IlS/7jP/6jVfaZ1ETiBXkGk1cEKsKMDLS2+j7joqEhWEUYF4e4ONjtgu6uhQFCL9krwqgIwsJCVoS6IjQIH3vssbKysjvvvDMnJ2fWrFnHjh3zHl+2bFltbe0DDzxw7NixH/7wh4q1k0ioQE9H6pWQgLi4cOuY4EFoMiEz07corKsLNkYIMUVhkMdrRJi8a+qjJQjZNaozQhfsbPhuK4WLLrrok08++fDDD0eOHLl79+7t27fX1dUlJiZOnTo1Nzf32LFjI0eOVKy1RKGF7BrFd0VhOFkSckpObi5qa5Gb23fE5+1g3omjQh6eJ+TPGBmxOUbo8/B6inaixwgdDkdlZWVxcTGAHTt2TJ8+PTExEUBaWtr48eN37NghfxuJxAgZUQi8KbZwIaPIG4T91dSECELh82U0NUYoYxBGyxghg1BnRG/hcP/99w8bNuzSSy8FUFtbm5GR0fulrKysmsD/OpxO59SpU3vfvvDCCxGuHdtknOVNGlZfn5CQ4LHZ+la3Df7Wp6VZKiu7Ro6U/qD6pqbkuLgOmy3gVpaZmYknT7psNof3bUeHwelMNhjaBnckulwup9Nps9mSk5Nqahw2m79H+g5UWxtnsZhstk7J7ZdLYmJCXd2Av+1wNDTEx8cbbLYuWa4GoL293el0GuWeX5uUhLo6a0uLTQsTd8kvp9PpcDicTqfFYjGZTMFPFheEjzzyyHvvvbdp0ybvP6yUlJTOzr7/iu3t7dbAv6aaTKbnnnuu9+2YMWMsEV86G6R5pBsdHSgpgdU6YHNrn299Tg46Oizh/HOw2ZCfnxzkCkVFaGmJs1oTvW/r6pCX5/9foMlkMpvNVqs1OxtdXWYhrXI4kJUFqzVOYuvlk52Nri7fv23JnE5kZMBqjZflagCMRmNSUpLsQQggNRUOhzXI7CdSlzcIk5KShJwsIggff/zxZ5555rPPPsv9rn9n6NCh5eXl3tcej6eiosLbZeqXwWCY3vtELyLFCBk/i0zXaP/+kbNnQ/SLIjq7RlNTcfq0bFez21FQINvVFOXt+mYQ6oPQX5Sef/75P/3pTx999FFRUVHvwSVLltTW1m7atAnA+vXrXS7XXMlPgyaSicDJMuHsFdneDrMZ8UHrlsLCAZuPVFWF/hGfno7mZkEN0NSs0RicLINBv+hQVBNaEd55550ej6e3pLvnnnsefPBBi8Xy5JNPXnXVVaNHjz569Ohzzz0XF6d+Xw3FOIGTZcKpY4TcYnAQFhaG+IjwirC1VSuVk7zLJ6JlsgyAIUNw9qzajSCZCA3Cqqoqj8fT+9Y7UxTA9ddfv3Tp0uPHj48aNSolWn6XI10T2DW6Z4/0WwgJQp/tKE+fRr/OFP/S0nwnmgYSctOAiJG3ItTORgEh5eQwCPVDaBCmp6cH+lJqamr/6aBE6hJYEYbTNdrcjMD/IXoUFKCqCh5Pz6PsTp/G5MkhPhKNXaPyLp/QwkMWBWIQ6gkn/5LeCAnC7Gw/e4HKe4ukJKSk9G29LbAiFNg1KqQBkSH2MYrBsSIkVTAISW8EVoRKByGAESNw4kTP6xMnMHx4iPNFVYQaCUKxj1EMLooqwiFD/DxghKIUg5B0pbsbTmfoh7tmZ4fVNSo2CDs60NgYuiIUHoQh91ONGFFPjwqJFSGpgkFIuiIwotLTYbfD4VD2Lr1BWF6OYcNCPz5QVBBqpCK0WmG3wx1wgx1xWBGSKhiEpCsCE8JgQEaG9KJQ4F1GjcLhwwBw5AiE7CcYjUFoNCI5WbYVFG1tDEJSAYOQdEV4QoTTOypk1iiASZOwdy8A7N2LiRNDn2+1oqMDzlBbjXZ2wmhEgjybmslArvkyHR0wmxEtS5HT09HRgS7ZdkUlNTEISVdEBaHk+TIC7zJuHI4dQ3c3du/GlCmhzzcYkJYWuijUzgChl1zzZaJogBCAwRDulCvSDgYh6YqoIJTctSWwIkxMxLhx+PJLfP01ZswQdGUhvaPa6Rf1kqsijKIBQq+cHPaO6gSDkHRFYEQBGDJE+q/zwu9y2WX4z/9Ebi5KSgSdH41BKFdFqJ2dxAXiMKFuMAhJVzRVEQJYswbd3XjoIaFXzshAU5Nsd48MuVZQaGffOIEYhLoh+sG8RFrW1IR+z4oOJjsb3z1DTDThUZSTg507RVxZSBAK/zNGhvDJrsFpbewzpHB+lyJNYUVIuqK1rlGxYjkIheyWrimsCHWDQUi6IrxrVPJPMZcLHR1KjWZlZIR+YrDWxghl7BqNujFCzhrVBwYh6Yrwakny8+SampCW1vNMCdllZgqqCDU1Rihj16imAj4kVoS6wSAkXRE1eic5CJXrmRQ4WUZTXaOxXBEyCPWBQUi6ImqMsKEB/Z42Lf8tJIjGrlG5KsKoC0JOltENBiHpivCUio+HxRK6/BpM0YpQYNeopipCTpahaMcgJF0RVa5J2xlE0SE6IRVhYyODUBMyM9HSApdL7XZQ2BiEpB8OB9rbRfwwlTZMqOgQXVZW6K3AGxuRmalUAyQQMq4phNa6fEMymcJ6hglpB4OQ9MPbZyh8PmdurpQgVDSHhDwTo6EBWVlKNUACuYJQazvmCMFhQn1gEJJ+iO20zM1Fba3idxHFYoHHg/b2gCe43bDZtBUYiYkwGNDREe51oq4iBIcJ9YJBSPrR1CSuVpPWNdrYqGxBFrwobG5GSgpMJgUbIIEsRSGDkNTCICT9ENtpKa0iVLpnMjMzWBBqrV/US5Yg1Nr6SCEkr0YlTWEQkn5ErGtU0Z/XwStCra2d8Ao/CDs6YDAgIUGmBkUKK0J9YBCSfojtGpVcESo6aTP4c8/1WhFGY78oGIR6wSAk/RDbNZqXh5oaKXdRNIqC/2ytr0d2toJ3lyb8IIzGKaNg16heMAhJP8RWS5KDUNGKMPgzDbQZhMHHNYWI0opQ2p4MpDUMQtIPsZ2WFgvMZrS2iviI3Q6DAUlJYpsmQjRWhFlZoTfECU5ruwQIJPkZJqQpDELSDwkhIbYorK/HkCHibiFW8J+tdXWKN0CC8CvCKA1CacPMpDUMQtIPsZNlAOTmigtCpWfKIFTXaEODPitCbc6GDSkzEzYbHA6120HhYRCSfkiYUVlQgOpqEedHoGcySrtGw6wIozQIjUZkZ7N3NOoxCEk/JJRr+fk4c0bE+RHIoby8YL1tZ88iN1fZBkggS9doNAYhOHFUFxiEpBMOB+x20VPwNVgRZmaitTVgb1tNjRaDUJau0WgcIwSDUBcYhKQT9fXIzIRR5L9osRVhBIbojMaA82W6utDRocX1duE/hCFKu0YRqoKnqMAgJJ2QNp1SbEVYVxeJIbpAc1lra5GTI+I5UxGTkhLioRkhRWAWkkIYhDrAICSdqKtDTo7oTxUUoKpKxPm1tZHomQwShHl5it9dmjCLQm0uCxGCKyh0gEFIOiFt9K6wUFwQRubndV6e/zpVmwOEXsFXfYSk9MZ1ypG2PxFpCoOQdOLsWSkRZbXCaERLi9DzI1MRBornqioUFSl+d2nCqQjdbjQ3R3HXKIMw2jEISScaGiTWakVFOH1a6MmRqQgDBeGZM8jPV/zu0oRTETY1ITVVc08bFohBqAMMQtIJybWa8N7R7m60tUWicAlSERYWKn53acLZfrq+Plr7RcEg1AUGIemE5CAcOhSVlYLO9JaDEZi0GahIPXMGBQWK312acOaMaHPfOIEyM2G3o7NT7XZQGBiEpBMRCMLq6gj1TBYV+W/S6dPaHSPMzZW+rlza+K5GGAwBJzdRtGAQkk7U1EhcWiAqCCNTkGVlwen0M4Xn5EkUF0eiARLk5EivCLW8LESIggJx2zKQ1jAISSciUxFG7Od1cTFOnRpwpKEBZrN2n14bTteod6OA6MUgjHYMQtKDtjYYDEhOlvLZoUN9IyeQSBYuJSWoqBhw5ORJDBsWobtLEE5FGL2r6b3E7k9EWsMgJD0IZ13BsGE4dQoeT+gzIzZGCGD4cJw4MeBIRYWmgzA3F3V1cLulfDYyqzOVU1goYgUOaRCDkPQgnOmUFgusVkHVTFVV5CZtjhqFo0cHHDl6FCNHRujuEsTHIzVV4lJCadvjaYeopaikQQxC0oMwF9gN7of0q7ISQ4dKv4sog4PwyBGMHh2hu0sjuYdQy8tChGAQRjsGIelBmJ2WAoMwkj+vx4zB4cMDjhw9qvUgFPtMq16SZ/xqBIMw2jEISQ/C7LQcMcJ3QG6w7m40N0euB6+kBA0NaG3tO3LgAMrKInR3aaRVhHY7XC7tzoYVorAQ1dUSx0dJCxiEpAdhdloKCcKqKuTliX7wr2RGI8aPx969PW9Pn4bZrPUZJdLmjERyCpJCEhKQkcGN1qIYg5D0IPwgPH48xDmRX70weTL27Ol5vWcPJk+O6N0lkNZDqOWdxIUbNgwnT6rdCJKKQUh6UFkZ1pYrpaWhg7CiAiUl0m8hwXnn4auvel5v2YIZMyJ6dwmEb03Qn5Z3EheOQRjVGIQU9bq70dgY1myL4mLU16O9Pdg5ka8IZ8/Gl1/2vP7iC8yZE9G7SyCtIjx1KnJzcZXDIIxqDEKKeqdOobAwrNE7oxEjRvguV/AR+Ypw1CjExWHPHjQ0YM8eXHBBRO8ugbSKMJKLUpQzfHjoTgXSLAYhRb3ycgwfHu5FRo/GkSPBTjh+HCNGhHsXsVaswAsv4JVXsGQJLJZI312s9HQAaGoS9yl9BKGQ+VakWWa1G0AUrvJyGWq1sjIcOhTshGPHVNjY5e67MXkyHA58+mmkby3N8OEoL0dGhoiPnDql3UdqCMcgjGqsCCnqyVIRjh+PAwcCftVuR0uLCnM6cnKwcye++QYTJ0b61tII3JqgP1l+j1HdsGGorkZ3t9rtIEkYhBT1jh1DaWm4Fxk3Dvv3B7vFiBGReDb9YPn5MsR8xHgrQuEaG2EwIDNTsQZFSlwciopYFEYrBiFFPVk24Rw7FsePB/yN/uBBre/qohGlpSHmHPk4cSKaYj64kMPMpFkMQtKQ7m5cey1MJtx+u6DnIgHweHDsGEaNCvfWiYkYPhwHD/r/6oEDGDcu3FvEgtGjRQdh5KcgKURCED77LAoKsHw57HZl2kTCMAhJQ371K7S3o64Ou3bh8ccFfaSyEhkZsFpluHv/nVx87N/PIBRk8EMzgjtyRIZfYjRi3LiAv0j59fnn+PWvsWED4uJw772KNYsEYBCSVlRV4emn8be/ITMTL76I3/4WLS2hP7V/P8aPl6cB06dj+3b/X9q9Owp2ONOCoUPR0BBia4L+tP9sKeHGjw82zOzD48E99+CxxzBhAp55Bu+8I+KzJDsGIWnFk09i5cqeDWLGjMHFF+OZZ0J/6ttvZQvCGTOwbZuf483NqKvTT+GiKJMJo0eLKIyOHMGYMUo2KIK8E48Fdul/+CHcblx1FQBYrbj7bvzhD4q2joJhEJImOBx48UX827/1Hbn7bjz1VOhH2+zbhwkT5GnDtGnYvx+dnb7Hd+zA5MmRe+5EtBs3LthClP48Hhw6pJ9ZSGlpyMgQOnH0qadw111985B//GO8/bbovQhILvzPTZrw/vsYO3ZA1TV1KnJzsWFDiA/u3ImpU+Vpg8WCiROxZYvv8a+/xvnny3OLWBB8IUp/p07BahW3+l7jpk7Fzp2hT6uqwubNuPbaviOZmbjoIvzv/yrXNAqGQUia8MoruOEG34OrVuGFF4J9qr0d5eWydY0CmDvXzx4umzdHwT6f2jFlCnbtEnSmjNW8RkybJujP/sorWLbMd8+8G27AK68o1C4KgUFI6mttxccf45prfI9fey0++giNjQE/uGMHJkxAfLxsLVmyBB98MOBIVxe++gpz58p2C92bOlVoEO7ejSlTFG5NZAUaZvbx8stYudL34KJFOHZM9L48JAsGIanvnXcwd27Pls39paeH6C+SvVa74AIcP46qqr4jn32GSZP8tI0CKSiAyYRTp0KfuWMHpk9XvkERNGMGvvkGLlewc3buRGcnZs3yPW424+qr8frryrWOAmIQkvpee23AeEl/N92EF18M+MFNm3DhhXK2JC4OV145IHpffx1XXy3nLWLBzJl+hloH++YbnHOO8q2JoMxMFBUFXI3q9fLLuP56/9v1XXstXntNoaZRMAxCUlljI774Apdf7v+r3/se6uqwe7efL3V1YfNmzJ8vc3tWr8bTT/f8Ut/UhLfewnXXyXwL3Tv/fHz1VYhzysvhduthu20f8+fjk08CftXhwP/8j59+Ua85c1BTw33aVMAgJJWtW4fFi5GS4v+rJlNPMg322WeYOFH+OYczZ6K4GE8+CQC//jWuvrpnaSMJN3cuPvssxDlffilzNa8R3/tesKnO772HMWMC7hFvNGL5cvzP/yjUNAqIQUgqW7sWP/hBsBN+/GP8859oaPA9/sYbPeuRZff003j4YSxZgnfewe9+p8gt9G36dFRUoK4u2DkbN2Lhwkg1KIK+9z1s3Qqbzf9X//Y3rF4d7OM/+AHWrlWiXRQMg5DUdPIk9u3DJZcEOyc3F9dcg8ceG3DQbse6dfj+9xVp1ahR2LEDq1fjm2+Qna3ILfTNbMbChVi/PuAJbjc2bMCSJRFsU6SkpGDePLz1lp8vHT6MnTuxfHmwj8+YAYNB0AgryYhBSGp66SV8//uh1z/8/Of4618HTOZ87jnMn6/gk3Lz87F8ua7WekfY5Zfj7bcDfnXLFmRn63CA0OsHP8Df/+7n+COPYM0aJCaG+PiNN4ZYPkuyYxCSalwuPP98iJ4ir2HDcPvtWL26Zw5LbS3+3//Df/2X0g0k6a64Ahs3Btw2/bXXsGxZZBsUQVddhQMHsG/fgINHjuDtt3HnnaE/ftNNeOMNtLYq1Dryg0FIqnn7bQwbJvSpDr/4BTweXH01Xn0VixfjjjswaZLC7aMwpKfj4ovx8st+vtTREWzmpA7Ex+OnP8V//mffEY8Ht9+OBx4Q1MeQn49Fi/zXlKQQBiGp5pFHcM89Qk82m/HOO5g5E++8g3vvxc9/rmTLSA7//u/485/hcPgef/FFXHCBbvtFvW6/HSdP4i9/AQCPB/ffj64u3HWX0I/fcw/+/Gc4nco1kAYwq90AilEffACbDVdeKeIj8fF44AHFGkRymzULo0bhr38d0B/Y0oKHHsI776jXrIiIj8dbb2HJErz3HhobYTTi3XdhMgn9+MyZKC3F3/+OH/1IyVbSdxiEpAKnEz/7GX7zGz7bSOceewyzZ2P27J4nhLjd+PGPccUVmDZN7ZYpb8QI7NmDjz5CUhIWLIBZ5M/a3/wGy5bh2msDLrElGfHnEKngD39AQYG4cpCi0ZgxePZZXHQRHn8cbKJpvgAACn9JREFU772HSy9FYyP++Ee1mxUpFguuuAKLF4tOQQDnnYdFi3D//Qo0iwaRJwgdg8cBiALYvBmPPopnn1W7HRQRV16JDRuwfTv+8peeh3uEXD9AXn/6E95/H+vWqd2OGBBuEG7evHnkyJFZWVllZWU7duyQpU2kYzt3Ytky/OMfKC5WuykUKZMn4x//wPr1uPtuKbVRzEpPx5tvYs0afPyx2k3Ru7CC0Ol0fv/733/wwQdbW1vvuOOO66+/3uPxyNUy0hmPBy+9hIsvxtNPY/FitVtDFA2mTcObb+KHP8Sf/hTi6U4UjrCCcOPGjQBWrlwJ4NZbb62rq/v666/laRfpSFsb1q7F+efjySfx8ce44gq1G0QUPS68EFu24P33MXkynnsOTU1qN0iPwuqnOHbs2Lhx4wwGAwCz2TxmzJijR4/OGvzEye809fsepqammoLOJm5pgdsdTut8tbUZuC5Hdm533+4h3d2w29HZiZYWNDSgpgbHjmHvXnz7LWbPxn/8B664gtNEiUQrKcHGjfjoIzzzDO67DyNHYupUjBiBoiJkZiItDRYLUlIQF9dzfnw8kpNVbbGSEhORlCTzNcMKwubm5uR+f99Wq7Up8K8rTqdzxIgRvW8/+OCD8ePHB7n4zJmWmhp/D6+UyuOxGAzsuZVBXBzcbrjdPQ8XTU319B5PSUF8vCctDVlZnpwcT1mZ+5pr3FOmuCwWAGhvV6fBdrvd4PdBqNrgcrlcLldbW5vaDdGh9vZ2l8tl1MXvX+efj/PPR3c39uwx7d9vLC837N9vbGhAa6uhs9PQ1ta3d4HDYbDbVW2rkm691fGLX3SHPM3pdDocDpfLZbFYQv4DCCsIs7OzW/vtiNfU1JSTkxPwTmZzkJgc7ODBcJrmh83WZrVaZb4oAYB2M8bL4/GkaHg1lslkMplMWm5h9DIYDElJSfoIwl7z58v/POqoEg+E2qf/uyBMElY8hvXvo6ysbO/evS6XC0BXV9ehQ4fKysrCuSAREVGEhRWEs2fPzs7Ofuihh+rr63/5y1+OHTt2qncDCSIioigRVhAaDIb/+7//++KLL6ZNm/btt9++/vrrcjWLiIgoMsJd3TpmzJgNGzbI0hRFdXZ2VldXc4wwNp06daqsrExnA0UkxNmzZ7Ozs/kfPwbZbLa2trahQ4cKOTlWfjRs3779pptuUrsVpI7zzjuvXa0Zq6Sqe+6558MPP1S7FaSC119//Ze//KXAk2MlCImIiPxiEBIRUUxjEBIRUUwzRGabbIfDMXfu3Nra2gjcK1AD7HZ7enq6Wg0gFdXX12dlZWl2c5nmic0GhyHtUJraDdGh1tbWhISEhIQEtRtCkdbZ2elwOKxW63vvvRdygXuEghBAY2Njc3NzZO5FREQEoKioKD4+xE40kQtCIiIiDeIYIRERxTQGIRERxTQGIRERxTQGIRERxbRw9xrVPofD8fzzzx85cmTSpEkrV64cvOHk+vXrKysrva+tVut1110X8TaSbL755pt//vOfycnJN91007BhwwafUFtb+/zzzzc0NFx++eVz586NfAtJIS0tLX/729/OnDmzcOHCSy+9dPAJa9eu7X36cXFx8UUXXRTZBpIiXC7XoUOHdu/e3dXVtWrVKr/nOJ3Ol1566cCBA+PHj7/xxhvNZt/g039FeMMNN6xdu3bUqFF/+ctf/v3f/33wCU888cR777134sSJEydOnDp1KvItJLls2rRp0aJFOTk5ra2t5557bk1Njc8JNptt5syZ5eXlxcXFy5cvX7dunSrtJNm5XK65c+du27attLT09ttvf+qppwaf88ADD2zZssX7P33wvw2KUhs3bly8eHGgH+9eq1evfuGFF0aPHv3888/feuutfs7w6NqRI0cSExMbGxs9Hs+pU6cSEhJqamp8zrn44otfeeUVNVpHMrvkkksefvhh7+urr776v//7v31OePrpp2fNmuV9/dJLL02fPj2i7SPFvP322yNHjnQ6nR6P54MPPiguLva+7q+4uHjXrl1qtI4U5HK5PB7P9u3bLRaL3xNOnjyZkJBQW1vr8Xhqa2sTEhIqKyt9ztF5RfjFF19Mnz49IyMDwNChQ0tLS7ds2TL4tE8++eQPf/jD22+/7Xa7I95Gks3nn3++aNEi7+tFixZ9/vnnPid4S8beE3bs2NHbV0ZR7fPPP1+4cKHJZAKwYMGCM2fOlJeXDz7ttdde+/Of//zZZ59Fun2kmJCPV/vyyy8nTJiQk5MDICcnZ/z48Zs3b/a9iFKt04aampohQ4b0vs3JyTlz5ozPOaNHj05JSamvr7///vsXLlzodDoj20aSR2trq91u7/125+TkVFdX+5xTXV3de8KQIUMMBsPgcyga9f/OxsXFZWRkDP7OnnvuuS6X69SpU9ddd91tt90W8TaSOnxSIDc3d3AK6GGyjMVi6e7u9jn4xz/+8a677jKbzS6Xq/egw+EYvNfOo48+6n3x4IMPjh07dt26dStWrFC0waSEuLg4AL2/xzidzsHfa7PZ3HuCt0cl5N5LFBXi4uJC/k9/4403vC/uuuuuMWPG3HnnnePGjYtcE0klQlJAD0EY5JmrhYWFVVVVvW+rqqoKCgoCnZycnDxlyhS/PSqkfUlJSRkZGVVVVSUlJQjwvS4sLOz9ZfD06dNGozEvLy/C7SQl9P+f3tbW1traGuR/eklJSUFBQXl5OYMwFghJAZ13jS5evPjgwYPHjh0DsH379qampjlz5gCoqKjYs2cPAJfL1VtNnj17duvWrePHj1exwRSOyy+/3Ptbv9vtfvPNN5cuXQrA6XR+8skn3t+Wli5d+s4773i/42+88cbixYv5XAJ9WLp06QcffNDa2grgzTffnDRp0tChQwHs37/f+9+/q6vL892+yrt3766qqgr5RAKKajt37vSui1u4cOHJkyf3798P4Ntvv62srFywYIHv2cpO6NGAX/3qV0OHDl21alV+fv4TTzzRe3DRokUej6euri4nJ+fKK6+89tprs7OzV65c6Xa7VW0vSXfo0KHc3NwVK1bMnTt32rRpbW1tHo+nsbERwKFDhzwej8PhmD9//owZM66//vrs7Oxt27ap3WSSzYoVKyZMmHDjjTdmZ2evX7/ee3D58uV33323x+P59NNPhw8fvmLFiquuuspqtf72t79VtbEkm9ra2unTp5eVlRmNxunTpy9dutR7fNasWY888oj39cMPP1xYWLhq1arCwsLeg/3FxNMndu7cefjw4UmTJvVWe2fOnLHZbGPGjAFw5MiR/fv3O53O8ePHs6sk2jU1NX388ccpKSkLFizwVnsul2vHjh2TJk1KTEwE4HQ6P/3008bGxnnz5uXm5qrdXpKNx+PZtGlTdXX1BRdc4C0HARw/fjwuLq64uNjtdu/bt+/w4cPx8fHTpk0rLi5Wt7UkF4fDsXfv3t63CQkJEyZMAHDw4MGMjIzesY89e/Z4F9RPmjRp8EViIgiJiIgC0fkYIRERUXAMQiIiimkMQiIiimkMQiIiimkMQiIiimkMQiIiimkMQiIiimkMQiIiimkMQiIiimkMQiIiimkMQiIiimn/H36ZPkFL3aeFAAAAAElFTkSuQmCC",
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}
],
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"source": [
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],
"metadata": {},
"execution_count": 6
}
],
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