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logistic_regression.ipynb
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logistic_regression.ipynb
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Goals: Build a binary classification model using logistic regression + weight decay (L2 reg) from scratch"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Use python and limited numpy functionality"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
"%reload_ext autoreload\n",
"%autoreload 2"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"from model.metrics import accuracy,logloss\n",
"from model.gradients import logloss_sigmoid_grad\n",
"from model.utils import *\n",
"from model.activations import sigmoid\n",
"import matplotlib.pyplot as plt\n",
"from model.\n",
"seed=42\n",
"np.random.seed(seed)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Create linear binary classification dataset"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.collections.PathCollection at 0x7e67978>"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"size=500\n",
"X,y,W = generate_linear_dataset(size,2,noise_bound=0.8,is_reg=False)\n",
"plt.scatter(X[:,1],X[:,2],c=y)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Metric"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We will use log loss as loss function for this binary classification task"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"loss_fn = logloss"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We use sigmoid activation (squash input between 0 and 1) to get our prediction probability. Thus our gradient function will be a combination of sigmoid and log loss, which happens to be similar to MSE gradient function"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"act_fn = sigmoid\n",
"grad_fn = logloss_sigmoid_grad"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Customized Logistic Regression"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"from model.linear_model import CustomLinearModel"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"size=500\n",
"dim=2\n",
"X1,y1,W = generate_linear_dataset(size,dim,is_reg=False)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Gradient Descent, no L2"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"20. Training loss: 0.6146470985653965, Val loss:0.6148325895492094\n",
"40. Training loss: 0.5884849493248355, Val loss:0.5914560503183568\n",
"60. Training loss: 0.5651365086508895, Val loss:0.5704072571106122\n",
"80. Training loss: 0.5442256834197121, Val loss:0.5513909651841744\n",
"100. Training loss: 0.5254260412860776, Val loss:0.5341490437588468\n",
"120. Training loss: 0.5084573820822493, Val loss:0.5184580105469349\n",
"140. Training loss: 0.49308063225456905, Val loss:0.5041254675205452\n",
"160. Training loss: 0.4790923184094678, Val loss:0.4909862201604508\n",
"180. Training loss: 0.46631929339181144, Val loss:0.47889851941186684\n",
"200. Training loss: 0.45461401375686783, Val loss:0.46774063829869933\n"
]
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"lr = CustomLinearModel(dim,False,loss_fn,grad_fn,act_fn)\n",
"lr.fit(X1,y1,lr=0.01,n_iteration =200,val_ratio=0.2)"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.91"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"y_pred = lr.predict(X1)\n",
"accuracy(y1,y_pred)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Plot validation set and decision boundary"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.scatter(X1[:,1],X1[:,2],c=y1)\n",
"\n",
"ex1 = np.linspace(-2, 2, 100)\n",
"ex2 = -(lr.W[1] * ex1 + lr.W[0]) / lr.W[2]\n",
"\n",
"plt.plot(ex1, ex2, color='r', label='decision boundary');\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Gradient Descent, L2"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"20. Training loss: 0.6035072599362341, Val loss:0.6063134492234821\n",
"40. Training loss: 0.5787430214702753, Val loss:0.5839442222389191\n",
"60. Training loss: 0.5566340931700762, Val loss:0.5637990878385567\n",
"80. Training loss: 0.5368194588201021, Val loss:0.5455910271832699\n",
"100. Training loss: 0.51898891152413, Val loss:0.5290714675781766\n",
"120. Training loss: 0.5028779992712467, Val loss:0.5140266550750066\n",
"140. Training loss: 0.48826211396022257, Val loss:0.5002734411563595\n",
"160. Training loss: 0.4749506593653601, Val loss:0.4876550868390189\n",
"180. Training loss: 0.46278174440258296, Val loss:0.47603738956671404\n",
"200. Training loss: 0.4516175612755039, Val loss:0.46530525669010464\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"lr = CustomLinearModel(dim,False,loss_fn,grad_fn,act_fn)\n",
"lr.fit(X1,y1,lr=0.01,l2=1,n_iteration =200,val_ratio=0.2)"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.92"
]
},
"execution_count": 28,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"y_pred = lr.predict(X1)\n",
"accuracy(y1,y_pred)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Stochastic gradient descent"
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Epoch 1. Training loss: 0.6700408584560396, Val loss:0.6396421478147974\n",
"Epoch 2. Training loss: 0.6381984657131768, Val loss:0.6135613658917919\n",
"Epoch 3. Training loss: 0.6095162357562941, Val loss:0.5898984957310477\n",
"Epoch 4. Training loss: 0.5836623375249218, Val loss:0.5684098959070353\n",
"Epoch 5. Training loss: 0.5603266352213958, Val loss:0.5488678311534051\n",
"Epoch 6. Training loss: 0.5392263701720375, Val loss:0.5310635902242216\n",
"Epoch 7. Training loss: 0.5201079401965195, Val loss:0.5148085223704225\n",
"Epoch 8. Training loss: 0.5027462012909537, Val loss:0.49993371898556416\n",
"Epoch 9. Training loss: 0.486942467046102, Val loss:0.48628891703178845\n",
"Epoch 10. Training loss: 0.47252197598708034, Val loss:0.4737410145367833\n",
"Epoch 11. Training loss: 0.459331260443238, Val loss:0.46217243951047143\n",
"Epoch 12. Training loss: 0.44723563231004393, Val loss:0.45147951332200464\n",
"Epoch 13. Training loss: 0.4361168778979891, Val loss:0.4415708870653621\n",
"Epoch 14. Training loss: 0.4258711906850742, Val loss:0.4323660916451445\n",
"Epoch 15. Training loss: 0.4164073404861203, Val loss:0.4237942196287983\n",
"Epoch 16. Training loss: 0.40764506418066004, Val loss:0.41579274333549343\n",
"Epoch 17. Training loss: 0.39951365801870525, Val loss:0.40830646562160866\n",
"Epoch 18. Training loss: 0.3919507502926298, Val loss:0.40128659528949406\n",
"Epoch 19. Training loss: 0.38490123372444174, Val loss:0.3946899367216634\n",
"Epoch 20. Training loss: 0.37831633827701566, Val loss:0.3884781824252013\n",
"Epoch 21. Training loss: 0.37215282678201833, Val loss:0.3826172971363444\n",
"Epoch 22. Training loss: 0.3663722975538958, Val loss:0.3770769826326355\n",
"Epoch 23. Training loss: 0.36094057990906464, Val loss:0.3718302131949205\n",
"Epoch 24. Training loss: 0.3558272101689348, Val loss:0.3668528325980376\n",
"Epoch 25. Training loss: 0.3510049772610837, Val loss:0.36212320448653756\n",
"Epoch 26. Training loss: 0.3464495284290894, Val loss:0.3576219089475064\n",
"Epoch 27. Training loss: 0.34213902681368097, Val loss:0.3533314789900022\n",
"Epoch 28. Training loss: 0.33805385377878344, Val loss:0.34923617146080377\n",
"Epoch 29. Training loss: 0.3341763498331102, Val loss:0.3453217676616029\n",
"Epoch 30. Training loss: 0.3304905888513619, Val loss:0.34157539958318595\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"lr = CustomLinearModel(dim,False,loss_fn,grad_fn,act_fn)\n",
"lr.fit_epoch(X1,y1,0.01,30,20)"
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.916"
]
},
"execution_count": 52,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"y_pred = lr.predict(X1)\n",
"accuracy(y1,y_pred)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Plot validation set and decision boundary"
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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6+4CjLzh6A+5aJ1z6HteB9bcdXqr93HFEIDCr3nul5EqoeD76xlAK/ilI0fAGwyVFgpjFl+hInNJrkMLjMIsvQCRQ730pYdsl8XGVRkoRMRYWLZBNNuwi8o+I/BD9dznwB9B2U9u12DRU9h1ow131I7bpFXnmTdHNt/GQMQZsu+kIi/QLUa1eRylb/Q0breJX+tXnWie9TcLLITCHWLdHBMwKxDtRh12alYnvLX8kem8gmgnqh8DcqBtlE8m4nNgJDj1xpV/UIjI2JbwMs/QuzOIxiHdS80xmFts9zSopoJTqCMwCeohIWZ1zFwIXAnTo0KHf6tWrm61fi8RIaAlSOV4n+Tj2RqVfgLJ32OR2zaLTIPQTsZulHlTuMyjXAYnH4puClN2qN/ricAA2wATPUFTWHTG+dHNd3ySp/W5wHwmB6Tphx3MSKuPSRvvhTe87UP6ILiqi3HqSS79oq0sTm76pUHo9EAIiesKxtUe1egdlpG3VsVlsHVKVFGg2w66UygBmAveIyHv1XWtpxWzbiLkRKb4UQr+CcgARyLgOI/3M5PcEf0KKz66TBp8IF7iPwMh5uPqI+W83EifkgJ4Qqs65wLkPRquXU3+YqvGJqScdldbwW8sWILlWjRsyrsDIGLVVxmWxddmiWjFKKQfwLvB6Q0bdYttHGa0w8t5E5X+Kyn0ZVfBdvUYdAMfeYOuIXp3XRwD8U2Pj6R39ko2EWIMfgOAPSOj3hh4hviVloIzMFmHUAQj9QeJNaj/4P9nSo7HYxthkw670++qLwB8i8uimD8liW0HZ26GcvVDK3fC1SqFavRLdnHVQb0CWcuiY9ar/Zt0WlRCoSgKquj+B4VMKQotSfoYWi0oDSSJCZmRs2bFYbHM0R4LSQOAs4Bel1I/RYzeLiLWssIhBGTmo3KcR8WvVRt9bJF6VmmBrV3OfY0/I/wTxvqbdP/a9AAO8r1JTaLsW9vZJxyBmKeKfBeE/tJvD1hblGbZFJXdTwr6HjtiJrCTmM1IeVH0JZBYWNINhF5E56Hdii+0UEUEphYSXIZUvQngZOHqj0s9D2XZBzAqk8lnwTdHx8Z4RqPSRSdPslXIjoYUkNuqAe0TcBqiy7YzKvK5mTOZGxPcmxESJ2MHWFhyJXZCm9z0o+y9609esvkcqx0HuCyjnvil9HlsCpRTkPodsPEtv6oKORvKcDq7Dtu7gLFo8VqGNHQSRIPinaXlZx17gHFhvOJ+IqY145QsgJWC0AXM92iBGALuOIGn1JpReDeHV1CRFucHZD5X7UtLIErN4NAS+JN6421Gtv0Qliy+vPcbQIqT0Zr36RoFrCCr7HpTRKv7a8Bqk8BgSrvABjAJU61ktIsSxNiImBOfphCln35STuSy2T1LdPLW0YnYAJLwWKTopuvILAW6wtUFsHSD8Kxg76zBB9yE191Q8HlVxjEaxmH/VaTWso0hKb4DwX8Rmuvoh+AOEfgZnr4RjUunnI3Fx7U5w7peSUQdQjq6o/Pd0/Luy1xvmKL4PSR5Zg3bLhJeDY8+U+q6Pqjec5kApA7ZAGUCL7YuWtTyx2CxI8XkgG9FGHcAPkRUQnKE3KcO/IiVXY1a+qa8XP1ROoEZIKmnL0UIYieR6TW3Yk6CcfSH7PlA56LR9J7gGo3KebNzDoUW6Goxdl0rqN+xmNHSzaYgIZsWLmOv6I+u6YG44EgnMbHJ7FhabgmXYtyHELG1QVrcuZvhviKxK4UofVDysqxJF1pPytonyEJe5CdrX3sDK2/AcE5XC/QhVMAcjdxxqM0V8KPfBicepz4KtTVTjvGlI5VNQ+SRIsT4QWYEUj0GC85rcpoVFU7EM+zaAhFdhFp6ErD8AWX8AZtEIJJxi5m5wbiN6Cms/uq2A1Op9uiHtXG3EYzC0frprSIMtKGXT6oRGTiPGmRoS/B6z+DLMopORwDxwHUS8cXeAykXlPtVk94lIECpfTJB85UfKH29SmxYWm4LlY2/hiPiQolP0BmbVRmPoF32sYEaDMeTKyEQwSMlQi4lIGIpOJ7G2uoHWnHHraBTPcaiM0eA+CCm5FiJ/6THau6JyHkUpBxL5G8xSsO++RYtRmJVvQnmtQtihP0DlQfZDEJwOpleHOjr7apXJTRmbuTF5zHlkRdPbtbBoIpZhb+n4pxJfFMPUx/yfg+e4+u93/Qed2JOo6lHMhbqtkqujUSZ1/NFGO1T2PWDvAOE/wb4Hypavzzl6oFpPRSL/Ag6ULQ+JFGIWnRotvGwHDCTzNoy0BsbbDIj4oOJ+Yp85AFIEkaUY2Q80b4dGK1C2JGrGezRvX9sQRf8UM/HhD1k4/Rd27ljAiGuOpcd/um3tYe0QWK6Ylk7kr8T6KuJFInUjVeJRyoPKfZbqDUrs+o/jQGLdEiEd3RJeQsJNRvvuKNf+KFtblGtAjVGv3ZdtZ5RNF5+W4vOjQmEBvXEp5VB2C1LPhmqzEfoDrSFTl0C0qlTzopQT0i8gXrvdjcq8stn72xbYsLaIC/e+hg+e/pQVP63mmw++58Yj7+HLNzZT0XOLGCzD3tKxd0+ify7g/1xvdjaErY1ejds7gfNAyJuMyjinzkUmhL4naXm7Win+DSGhpRBeSfwEEUAqJ6TcTpMxcnSZv4Tn8jZLlyr9El1kxGgNGGDvrNUunQ2GHG+XvH73JCpLvYSDNb8DAW+Ap8a8SCRcT3SSRbNguWJaOq7BOloj/Ef8ufByxPsuKv3UpLfrmp4Xo0Mdw8BqKP4RsXUk3j2TbJJwNliAIwZzQxLXhECC0nsS+h3xvg1mMcp9GLiPRG1C6KGufpQA5UGln9uopiQ6Qai4DeI6TSvVImqhNiszZ0L//uBuWAuoLgs+/zmhAQ8Hw/y9/F/ad7FKNmxOrBV7C0cpG2T9l8RzsB/8k5LeKyJI6U3oePRwzT1mCYQXJ7nLSY3YVvT/RitUet0Vfj049kpSU9UFrkExR0zv20jRqeB7GwJTkdJbkI1n6kiTJiChX5GNo4iftGyQcQXKNTC1diLrMYsvQtb1RNb1xNw4MqHrS4egJplItlVmzoQDD9R/XnmlSU3k7JS4xmokbJLZyhIx29xYhn0bQKl0XUgi8dnkN5rrwSxKcCKcpOAFeqMz5xlwHQz2HrroRP6HjQpHVEYOZFxMrM/ZCUZujICVmBVQdg/aCFdFlfggvEjrzjQBKf8/Em8UO1Bpp6XWhoR01FFgFtqdFIHgt0jRyTp5C5DIP5hFp0dDUAdhbjimSXLBLYpZs+Dgg7VBX7wYnngCzmnEhF6Lk689Dnd6bNKYw2mn76E9yWltFdbe3FiumG0Be2dQmSB1Mzw94D4p+X0qjeRhjomO2yDjSgz3IHAPSnA+dYyMyxB7F+1TN4vBfbAWDTNqfalDP0SLate5WXyI/+NGFWSWyN9IxfMQnE1iOV8bRP7V+wwNEfgqGl5a25UQLcThn4q4hyJFp4H5L9WfY2QpsvFMaP0lyshNedwtgq+/hv/+F6ZPh512gsceg4suAk/TC3kPOnEAa5f8zet3v4vNaSccCNN9YBdufO3yZhy4RTIsw07Uj2quB5WNMtK39nDiUMqAnKeQ4pHReOkAKJfWVUk7Mfl9Ribi3B+C35B0UzT2DlRa8/mIlfsw7TNPekEaSRUejayU+5HwGqRoWDR6KMlzShjBBWLGCX2JuREif4OtA8rI0oJmiWqLihcJr0QF5+hi3HUnRwkj3vdRGSNTHvtW5dtv4bbbYNo0KCiARx/VBj2tecrunXbTcI6/7ChW/fYnebvkstOuyWviWjQvO7xhN72ToPyB6BdZEM+xqKzbt2gyTSooZy9oPQvxfQLhn8GsAFsHLRdgTx4rrXIe0j7nyHLAFi1EHSaxbkqVcuMWqiLk6BMtKFHXLeRJ2W0CUcEyqST524kdiEDhYQhpiOd4lLM34ugJFePA/7F2dUkISTsVnPtH/193kkhD2btEQ1ATfX7+FOUbtiwiAYj8CUZr/cY0d6426J9/Dq1bw0MPwSWXQHrzL2rSMj3sNaBzs7drUT87tGGXwAwou5MYn6xvCoKgsu/bWsNKjkqH8ELwfYIesw3xvoxk3oiRnrj4gjJytQJi6He9KnV0R0pvg+BM4lbL9i4o5UQCc5Dyh3TIoq0tKvMqlPvwRg1VRCD8m5YJtndF2TvGj03ZIPfF6JuIH1B64sm4BOXcL/XOAnNIbtQd1ExYAKXgexXxvU3N6j5Ss9nrfQeMnbSue3gVNZFCdrDlgfvQaJx8or0NDxg5SHg1yt503ZnmxKx4ASqfAhT8UAqPCOrLVZCfDw8+CKNHbxaDbrF12aH12M2iUyC0MMEZJ6pg7mYTpGoIEQH/R0jl89o/7eyPyrgSIn8jJRclSFhyolrPrE4OarD98Eqk6MT4Qsm2PSHjCii9ltgNSDdk3R2XNSrmRi11a2uLsrWpdbwk+pawDDD0ytd1ECrnkZgwRom+PYgZhIqntc9dgtqopp0CzgGo4EwdxePsn3ByADD/7UlSnfWmYBRAxk1Q8XDUj24H91GorBtRRisdbVQ8EoILavVrAKInXwmDo7uOY98MGjipIr6PtV79j8Woh4tQX3qRXBtyxSCMaz6CDCs6ZVvD0mNPhcjfSU7YdCx0Iwy79tP+i5CBCv+sk4pc/2lYTjZRWxX/p0WlqmRz/Z9oCVjXwdGVbR2UHYKzwDMspfaVvRPi2Cd+1R5ZDWW3EB9V4oeKhyBq2EVMpOxO8E3Svn4JIq6BqJzHUMqDlI7VkS214+IDM5DKF1EZF+uKS2W3g/9TalbSUjOWyCIIfgnYEOWO7iuYiGd41E1Ws1oWidCsRh10HH7ZTTWfg3JpV4/Sm6K6utHzeuL1TtITpHjR0UbRyTL0M1JyNarVS5s8nMXfL+Pdx6awbk0hfQ/tybAxR5OVl9ngffLN/agHlqOmVSK5BuZNeTAqB9ILkXSbVfZsO2bHNuyOPhD4nLjXeGWDFCvViAS1IfN/Gj0SRHCgVQNtkDteC02liJgVUDmeWGNl6lV6aDHaBVD3LUvp/lLtQyIQnJOgnWCS+HPAXI9IULtqvK+Ab3Ls9YGvkbK7dMx9YAbxyU5+8L4BGRcjxRdF5QYaypqNxPrf/e+D6wBwH1HrGgMdd9+0uPfECDGTm3gh+LWuZOTqD2gZAZVxGWRchll0UgLt+RAE5yGRopTfpBIx4+2veXjUOIK+ECLCsh9W8PHzX/DcwofI3SnJ28DChXDbbRgfzUFyDMwb8mBUNmTW2jsxy8DW9KgXi5bNDh3HrjIv10qFMWsXD2Rck/LmqZTdC/7P0IalyriEAC9IOVJ8QeOSbcLLkxR8CKNX8AnGJWbjMkMRUpPlrYXKpnryqF1ZqZoA+D7UE1OySBfxIaElEPqFJhli8SHet2KHpRR4TgIa/2bUuL69SDCJzolZnPi4skejZyASjjD9zTn894QHuOf0x1k4/ZcGu4yEIzwxejwBb5Aql2nQH6K8qJy3Hng//oaffoJhw6BvX5g9G/Pm/ZB5neDKVrFGXaVHpQ9So+ifYkoLy1K+3mLrs2MbdvseqLxJujiw0RrsPVA5DyfdiKyLSBB871K/cqJA4OvUB2XbKRq5koDI2qqL0AJeaYAHlfN4o/YDlLKDo1/qY8KjNzSrXCCS7EtuahlhW8cE52zgOhAJb6KMbYIwRJV1o17J49Lx/jijlZmaEyeoJCGYzsEkfvl1gq0DkUiEsUPv47ELn+XbD+cz462v+e/xD/DyrW/W2+PaJX8TCSVIyw9FmDtlQc2Bn3+G4cOhd2/46iu44w5YtQp1x+uQlUHs19wNWWNTqu269IcVjNrrSs7a7VJObXcRlw8cy7rVGxq8z2Lrs0MbdtDG3ch9CqPga4z89+qPu66L+Km33Jq+KEFiUT3jse0cNVKJ3hgi6EnE0BNR1m2ogtko90Ept1/dT/Y96ImhoQszIfNyVNq5gN541fHnCbC1QxkZOqJIpVHjHnLpFX/aWVBeJwqpUXjAHS/7q5QbI/c5VP7HepJr/XnUt52KqyGX1KpFGagkEskq4xIwsqn5mSm0Ab0dpezM+2Qhv32zGH9lzaTkrwww6ZGPWP9nvLiaiPDDFz/z2h0TCfgSv9lk52fCL7/ASSdBr14xSeBSAAAgAElEQVTw5Zc6hHHVKp1slJ0dXbi8B+5jwGinN6Nzn8PwHNvg05YWlnHtQbezZtFfhAIhwsEwi79bylWDbrVEvLYBdmwf+6aiMvXKUOpRPpQwuPZvXLPZjyJlY8H/BdplUjeeOgRSFK08lHoiT0wf9o6Ic9/oBmoy0iH3JYxoQWodTTM8wUSlDZnKukP/z9kLyRkH3lfBLAfnYFT6qUjJVckFuhrEA/bdwXNCPc/UQevFA4KA8wAIfkW9bid7awj70XsaVdc50VWgqr4eJir7YT3pJurXVgB5U/TeQ+BbsLXRWbbRz+3bj+bjr4ifzAybwcIvf+GIc2Mn5scveZ7pr8+OmQhq09nt41a+g73vg6wsbcivvBJy4zNelX03VM4jyZ8/CdNenUm4jgE3TaGy1Mv3U39kwNDGvPFZbGmaxbArpV4ChgLrRaRHc7S5LSC+d+pxSyjABZnXooxWjWpXGemonMej0SN3gP+DBJ2bOvLEGf8FE7ME8b4HkaVg74nyHJfYVdPgPoKJsu9Z027F/0VDLev60G2Q9wbK0V1vJpdcCoHvogqPYYisRghD8FuSShmo1iD/JhlHGhDU+w+FhyDZD6Bc/0k+at/HUHojekJsYC8hvBIc3cHYGUI/6lBH+x56U9jIBtf+KNfghitV2fJQmVdDgmCVrFYZ2Oy2uJWuYRikZcW+/Syev5wv/zeLgDd+pd7Z4+fkwM8M9v0Jv6TDLbfAVVdBq8b9fqXC3yvWEUzwthAOR9iQ4C3DomXRXK6YCcCRzdTWNoGYXii7l/hNQAXG7uA5HZX3Jkb62U3uQxkZ4NibhC4FZUvoy5bwcmTDoVDxuPb/lz+AFB4RrW5UpwnP8CRa7+g+M69AGbUMT3ABCQ2lcmqhMkAqxkFgLuCPRrQEtFxD5ZMkd1sZkH42yV0iVVIBPjA3IMWjMMsfqRbkinl+swJKb9L9NugmAwjpKk9mWTQBbJHORA1MAd97UPrfTXjL0Bx+7kHYHfHZvMpQ9D+6D5FwhP/dNZGTCs7j8gE3xxn1DlLGzczjKe/HDHZvRN10I2rVKrjrrkYZ9aA/yD8r1xHwNRwe2uOALrgz4iczw1B03nfHrQq1rdAshl1EZgHbmXZpA4R/08Y1DgFbJkb2bShH903uRnmOj66saxs9u/axO+NdPFJ6C0g5NX5sH5gbkbL74xt3HQzuo9EbsbboH6WLROQ8jpF+Xuz1tZKQYjsN6/JwoOV3E8aV15cIFwH3gSTeV0h0r0DlC0jRGfGFRoLfJiiu3RAhCH0TlV0IUjN+H0gJUtZwFrKYlZiVr2GW3oLpfS9m0unQtS1XPnchrjQnaVke0rI8ZOVlct/UW3C6nTxxyfO89cD7lBaWY5o1E2c7KedG+Y7xfM4A+Ztlh49ArVoJ994LeamHUIoIr9z+Die2Po8L976GE1uP4qWxb8T0VZvCv4ooXleKO82J3VnzWbo8TroP7EqXfXZPuW+LrcMW87ErpS4ELgTo0KHDlup286Gyk+iFUGPkmqMbIwvy3tYZhKGfAAWuwaise+LFrCQUzaStawgjUV9znbaVQmXfh6SdpYXCVIYuchHNlhQJ6ipN4WUo+26Qfj6U/Ebs5qcL3EfU+PoTiWc1iB2lcpD086HypWj7gjb0ifYYos8UXq5DTT1Dax2vT+fGTeM3bk0I1LcPAWZoCRQNp+rtTbzvULb6Fq4/eV+6DhhAj/90pXU7N2+uuZff5xZRUVzJLrvvxO69dqV4fSlfvD6bkL9mgmor5ZzJHxzEGoLYmEhnPvD0YNz/nof8bCKRCD9M+5nVv6+lfde27HNEL2y25M89+clPmPjwhwS8NT+b9574BE+mh9NujE1q+2zCVzw5ejwohRkxMSMR0rPTyMrL5OjzD+HEq4fWbd6iBbLFDLuIPA88D1pSYEv1uymICAS+QCpf0atg16Go9HNRRibY99Sp75EVxLonPM2qkAjRDbC8t7SYE6qeGHsj+ifRSix5ApNy7KWLY9RCIoV6o9QsBgKIStObxRmXQ+Wz0ZDMiE61z76r5kbnYAhMTTKGZMPORnDojNi0c8D8R6+6nftD6c313OhFArMQ8epMXbMEnPskEO8CbdSbGM3R0F7ExjOp7ZJTCjJzwpx/8y+MPcPL1Jem40qLkJZukp1v8NdKF3aHA9MUjr/0SJwuByF/iDZSwRn8wSGsJoSN91RnPsrYm2LTxc1vXklO62zKNpZz1aBb2bC2iFAghMPlIG+XVjw+5y6y8xNvpL/9wPsxRh10mbqJD38YY9iL/inmydHjCfpj34JCwTB3fXgDu+7VvnGfm8VWw4qKqQepeBwqJ1CdjBNegfg/gLwPtLxvq/HIxvPAXIfWRAlBxpiUq/Q0lobkCZSyIa5DIfAlsVmdzpTlBiCaTVs0PKqTUnXQq1fjoe9RBXN1iTsjN25TVmXdgBTOjabWJ0tCqj35uME9HDYMRlCgRG8MZ1wG/k+oX27Yrjc//Z9R/TMKfIlOVnKBMqJvVQo8J0bdRI3FBZ7kuvBm+E+0dnssSkGfQVpeQAT8lTb8lQYb1wOECfr0c01+8hMKQqVcIr9yKGsIYTCZPZlo60b7Qb25YMzR7HP43ngy9F7IM1dN4O9l/xKOxreHgxH+9a/jqTEvMvbNqxKOMVlyUfnGCkzTxDD0m9/Hz09L6J6JhMLMeOcbzrn9lKSfg0XLwjLsSZBIUdQtUHulE4DIesQ3CZV+DsrWFvKnan+7WQKOvZscfthcqOw7kI0rdDJTlcCboxsqI/GXPhFS/kisUa8mEq0qZKDsiVdvyrYLtP4c8U4E7/9qtRNd9WbdCsHvtcvI1h7SzoGSMVQb5qp3uYrH0G6VhqJafiWuIAZ+MPLBvi8YLv125T4WAtP120BKuABD/0wz6/nsIuuTnlJxe8GxB3aWSs7wzucwVhPG4H125226UqzcOJwOTr7+ePY7KlaOYtakudVGvYpwKMKcyfMQkRgdnSp27d6eFT+tjju+y+4FBHxB3GkuHr/oOT5/ZUZc26B/jSSyTbxkW0RprnDHN4EDgXyl1FrgNhF5sTna3mqEftap/XE+Y7/2uaafo1X+fJOh8jkwC8HRCzKvQzm6bZUhg5bpJe8jCH2vZWftXbRxSvCFT4SIgO+teq5QNJTQo4wsVMYoyBiFhP7QsrpGZtQXnwtpNVWfxPchoowEe6smiY26Qv/ahtAr/0RvBaKFvIKfUJ0sVPE4uA6HwBfU+NmjOjP2DhBeE5UACEPaKfpnaO/S4Aa4cnRGEri/RGD1ksRvWDtJJaeziMNZhYli1s79WHv8Wbzz+jwdu67AZjO486RH2L13R+768MZq0S9JsuGZ7DjA6MdGMvaYe+OSnQrXFnNS6/Po8Z9u/P7t4oRGHXRJu0EnDUjavkXLo7miYk4TkV1ExCEi7bZ5ow7RDdBEXxYDbLsAIJXPQtkdEFmpffDBOcjG05DwsqTNilmBhNfqqk2bCaUU2DoikVVI2V1I6bWNqMcpiRUkq3AdnPIkAaAc3VAZF6DSTk1cMk6CNE63Jo2aiSUVvRlBvw0EtZsm8zpwDtSZmK7DUHmTMPKnoPI/QuW+gCqYi5E1FuUZnlJUkzIydUZtrclOBMwI3HNRrCZ7gVRypSxgAlM5lNVMYTdGuY/l78tu4KxnL+fq8RfjSnOC6MzUgC/IH3OXcPPR91S30f+Yfhi2+K+tMgwu7nsdM9/5Ju5crwO78+CXt9H3sL3JyE1HGXqsoUCIoD/Ewum/JE2GcrjsnHjNsezeq2ODn4VFy2GH1mMXCWmXhZETZ3REBCk8UkvZxhgeNyrvLbDvhqzvT7w2ugGuIzByn6jTnl+HIvqnRsMknZB5I0Y9pe2a/FyRv5DCE6IZolUrWycq54mU5AfMwuFRF0ddXKjWX6Fs+c041vXIhoNJzUgbYGsX1cxppIhZFc6DUGkn6epTRr6OWZdynaXq6N2oScs0TRZ/v5xQIEi3Xr9hC4zDjJSw7NcMHhydz58rHCgg3/RyhvqDw2UVoPiETrxJV8rcmeQUZPPcjw+TmZvBZf1vZPH3yxP2ddlT53H86KMo/HsjYwbcRGWJF1+CbFab3UbH7u058LQDOPr8Q8lqFZsxNbLbFaxdnEyuOhaHy87VL1zCoWcMTvkzsdi8pKrHvsMadtP7LpTfi5aGDYNrCCr7gZjNQIn8gxRfrDfolA0wIOtODM8xOhGo6MTEOjBGO4yC6bqN8AqIrNGqhIGvifXZu3UxhmbebDVLrgP/R8QZP6MA1XpWgwJQEvwJKT476oYy0RODHVq9heFs/sRis3IClD+KnoRMrbhp3zsa3qlLFoJdJ1M5+kFwxqZ1qDKibwphdLRQCHCB68CopnzDL7LLFq7klmPvx1vu1ZOBwHUTLuU/w7Ssb0VJJcGlK6i4YSxtZn6MQqg4dhdWHH08b00qoGRDBfsP7cfwq4ZSvrGCj5+fxkfPfJ505ezyOJlcPAGH00HAF2DWpLm8df/7/LnoL5J9h5WhePLbe+i6r84eXvnLai7sdW3KH1NGTjoT172A3WFtxbUULMNeDxL4VhvsGOlZJ7j+g5H7bPz14dV6VWfvXB1qKGY5sn5/Eq40nQegcp5GSkZDcGHUd1sRfx2Asz9Gq9c2+ZlqY64fqH3McbhQracl1TypjYRXIZUvQmgROHqg0kdqLZYmIIFZSMUzurCJsx8qYwzK3in2mtBixP8hmH6U5whw7KuLVVQ+B5E14NgHlXEB4n0XKscRv2J3gJEXjVBK/DstkmhDszYeVM4DKHf9SdTBQIhT215I+cbYn6krzcn4nx9lF1cY7rsPxo/XnZ53Htx8MyTI35j36ULuHPEw4VAkoZJjbYacvD+3vHV19f/P3uMy/lmxrt577E47n/q1iuQdJz7MnMnfJbzOZjdwuBz4KwM4nHYMu8Gt71xD/6NTryVgsfmxKijVg1Q+R7yeeBACc5BIYZyrIVH9SmVkIp7jwDeFumXkVMZopPzOaAp+sP6ky/CfTXuI+lDZQCLDburVaipN2DvGxqc3gJjF4J8OhPTKNzp5mN6JUHYX1Z+R/xMk8BXkvauTnqr6c3RBOa7TbqTyxyF4pX6O9PNQnpNQSmH6pkaLkNQ16i7IvBrlOhgpPg/Morg3KTF19GP9+BDvew0a9nmf/JDQCGcHKyg+9Rx2+XkGRCIwciSMHQu7Jq5/GolEePDcpxLqwiTi248WsGjeUrrup1fgO3Vs3aBhDwfD/DFvKd3225MlPyR28wCcedsIduuxK/On/URuQTZHnHsgBR1S12y3aFnskIadBLopgI6CMTdAij5klXU7ojzgnQhEwMiFzFt1ZaaN55GS31hKEbNcb8I1F+kjoexu4t9IDtosdVxN31QovT4aNy7APUjmNai0M6H8AWInPl0NSsqfQNXdh4isj+4NlOvrKISyu5Hwcsi8AcrvJqFcgb0LRvpI/e/8LyD8a3Ry0FWi1v3pIDsvjDstlbfThn3s5RsrMCM1k0sr8XEKixkaWoFtAcjZg5ExOdDJgUpbiyKxYV/zx18JhbaSEfQH+faj+dWG/fSbh/PH3CUNTgyrf11Dt/32pO0eu7B+dbyAl91pp/9Rfdm5UwEHHL9vyuOxaLnsmHrszv1IPKcJ1HER1IdSToysW1E7zUcVfI1qPRvDcwTad5tilqMEkcoJKfeZ0rg8J0Ha6dQUnnBpF0h2w5onMUMLr8Ysfxpz43mYhcdjFo9Bgj/EXmMWa6OOP7pK9gEBKH8UCcwlcfk7E0IL4o6Kd0K0jdorch94X0GC3yavVBRZWf1PpRTK0ROVfWf02e28/VQB877MItJgIFIaKi15MlIVvQ7sjmma5Iqfi+VHXuVTjmc5s50d8U47ALlvI7T5DQLTkOLRmBVP1zyjCL/M/oNpr85kw9pCIpFGbAKL3hytos/BPbnq+YvJyq9/UdBzsM4qPvPWk3B5YrNo7Q47iHD1gbdxSpsLufvUR/F7myILYdGS2DF97JG/kcLjouqDUQOsPJBxZc3KL9m9YkJwLoSXgL0jOAehEoiBmYXHQnhxagOy7YnR+uPGPUTtMYWWIv6pgKDcR6IcnfVxsxjCS8HYOSX/uIgPfJ8g4cU68iQwk3jD7IasuzDSjtf3eCch5Xcn2EQ2wOgE5goS+qLse2Hkx5Z3MwtHQPinJKOzR9tJMGHaOmG0/izusBmYD+V38cbD5XwxKYPHPlyK22Pi8gjhENjsYJoObDYTcIL7cFT2gzGRMf+uWs+6VRvYtXs7clpn64Pr1rHwyLPY68fp2DH5gg5M9PTi4GuyOOXSn1Fxbj4nqvVMSjfaufbg21m/ulBHXYlg2Gz4K3yk+jVs37UNj8y4k9yC7OpjkUiEzyfM4NEL4veHOvXswPM/1eixf/PB9zx9xUsU/V2MYTOIRCKY4ZrJxel2MGBoP25955rUBmSxRbE2TxtAwmuRyqe1xKytNSr9QpT70PrvMSuQjWdCZJWOpFEOHTKX+wbKlqtLzlVdG/wRKT43QfRFAhx9MPKaku4OZsUzUPEM1RElVeJZrgNRmdfHGHSJrNNuKPtuMa4fCa9CvJPA93o0Bb8BoSyViSqYi1IOxPuWrvvaaHEtA+zdUNn3oxxd9LMUXwWBRk5wygOZt2OkxUomSGAGUnw5EGHD3zBqUFdcHpOhZxfSrZ+X1UtcfD+9Pfd/fBw2owJcA1GOmogfX4WPu05+lJ9m/IbD5SAYCHHSGfsxMnstatw4JBBgw5AjeTXUmd8LTQybwUX/nU+/wQl83ioDlX0vt45YyPzPforRZbc7bDg9TvyVgRj3TvLnhXad2/Dib49VSwFUMXPiNzx6wbN4y3woQzHwhP0Y++aVcVEtIoKvws/Yoffy6+xFcV04XA7eWvtcdVKURcvB2jxtAGVv13jXRPlDegVcZaAlCBEfFA5BiCC2NpBxE4bncJSzN+R9qKvqhJaCsxf4v4LIMuqKhuE5Awn+pGPinb1QSTXS64wnvBIqxhHvdw5qN0BwLuR/DCoTKb0GArO1oJWEkPSRqIyrtPuj/FF9T727vLUxdVarY0/E0Y+kE1aDbfymE7ryP8Ww7USTPIPuYag6VZVEwkhJ1D0EtG4Dd0xYyf2X7srk8W1593k7+W1bccf712PPapew2duGPcSP039FRPD4KjiNxRz/wjtay+aM01G33sqyRaVMP+UxQgH9/P+sDBM+AOxx3yohEPCw4POf4opthEMRwmEfA0/oz7xPFhAKNOAvEli3aj3ffPB9dWhlFUNGHMCQEQfUfz/aXZWW6aFwbWKlbbvDRsmGMsuwb8PssIa9SfinEG/EaqW+R/6C0msR4ylddcfeAZV1a/WVknYqsvEcHbUBWjTMfRhUPIJIKdqwRZDMuzDSEtfXjCEwnfgIkere9Cal91W9Sg/MQUfoRDfaKl9ByILKJ0isn14PEtaKjBKM6rw0MVkIdBjohkGYKj+6adpYAvFJReElNc8Zpc+gCt5Y+BurlnbDtfM42ndpkzQZadyVL7Hwy1/IkgAnsYQTWIaLCF/Rns/aDuCBZw9jxuTPuPfsWTH3ffy/PA4dsRG7vfYEqUClEzb7JJ82BeZ/tpBDzxrCF6/Nwu60EagMYJqJ7wgFwtx35pM8NfdeOvVMvDGbCj0HdWP9msK4NwWlFDt3KmhyuxZbnx1z87TJpLIh6tcRGQlQtrao/Gmo3PGo7Hu1gFjway1MJV5t5MQHZbcgoaUp9GVQfxRHCPzf6uzKOOPtA++LpL5Kr8IOzr6g0vRzRv5qQhsJkMIEY0wBszK+Kd9HQHzimM0Gu/f0kNM6iwfPfYpjM89kaMaZ3HfmE5RsKAVg1W9/Mn3cR4yUX3mNTzmFxcylDRdwOPer/iwuCzP/o6e5/9x4jfYVv3l46qZ2+L2KyjIDIQ2MXVCtJpCRm8Wu3RK/HQDVeuz/W/k017wwmjs/vJF9juyd9PqgL8iD5z6d9HwqnPXfEXgy3DESBa40F6PuOx2nK7nMs0XLx1qxNwbXoVEj2YCBj8Qr6VWhlNKa4aDj5hPqsoQQ39soxy0AuqydfxogWqvFHjUQ7sOjbpRkGBBZQvIVdd1Nvoawa6Ez18HI+gPQn0NT3DDNhUJ5joo5Ir5PwPtGkus9iOs0rthnLP+uXF8tejXznW/5/dslvPTNbVRefg2vhKbgIcxM2vE/9mKNqlLsFHZqH+CZ/xZgmokn1GkTWzFrSjZ7HxDiro/uRLlqZArOueMUbh/+YMKNUtMUStaX0mrnXIaM0JWx8tvlMX/qj0mffuWva6gsrSQ9Oz35R1QPu+y2E88seJBX73iHn2f9Tuu2eZx20zD6H2MVqt7WsQx7I1CZNyLB70FKE0sJVFEr8aZezBISh0NEqt01pvftaEx6lPKHkMxrMNLPRdnaIlm3RBOAkqgcJo2lV+DYL1pgOhEeHc/vOhKUC+y7681F8SNFI2jcZqmisav61UtcvP1UAe12C5CTH8bhNDloWAn2mIWkICon5p0lcfJZFPcxfDd9F4r+KY5RMvSEfByzdjaq025091VGDXo3VqnsuCYOH1HMc3ckKREYJRJ20XavodjcfQBYu/Qf7j3tMZYtXFVv9MuaRX9RsqG0Ovpm8byl2J12wsHkfnfDXl/FqIbZZbeduOGVMZvUhkXLwzLsjUDZ8qH15+D/VMvRRtZF/dx1M09TDBVz7kPiQhIenUUZ+Tdq1Ou4KMofQVwH6uxQ5wGIckWjWWq/SdQThQOg3KissUhgDpTfjza8UavjGoJKO11LI9RJ1zTL7iE1wa4qDLSueuor+w1/O7jy2D3xVRiIaLPtcpvMn5HJTePqZOoWX4yZcQlGxsXRAcYn4GhcqMwxrP5tbnVCT7oEGc5ShrOMjGCIFV325fnyjiz4J5H1FTwZEY45u5A3n9yJsuLkX50hJ+/PhQ/pKlpBf5CrBt1C6YbypJouVfy7Yh23D3uIx+fczR/fLWXcFS8nN+oKeh/YHU96fMHp5mT9mg38s2I97bu2odXOCdQ5LVoklmFvJEq5wHMCynNCVI99ElQ8rTNW7buhMm9EuVLTrla2nZH0UeCdUEsl0g2OPcF9BHiT6aJHtEpkxsVIxSPRePy67pb6DKkCew+k4gmU50QkfyoqUOXqOazG1ZMIsyRBX/VRtbmc+qr9/RfyCfpVtVEHCPgNHE7BNCE2ys+HlD/FS/eE+HtlmFE3dqBg5yJUnTGGwy4cRgHtOu9CrgeOKv+dE1lKBiHm0IZ30vrQqvsQfv5kIYk+u6w8B4+9vxyXB066ZD2vP7YTAV/satmwGdw95Ub2PaJP9bFvPviegC/YoFEHiIRNli5cyd/L/+WRUePi9NNrU9A+n+smXNZgm00l4Atw7+lPMP+zH3W4pz/EIWcM4srnLqy3vqpFy8Ay7JuAUgqVNgLSRjS5DSPzKsS5D+J9A8wKcB+DShuOUk6k9io6BkHE1C6IwDc0KSol9D2EQAJfguc0VNaNNa1H/oXQr2ArAHvPmOgR5T4U8X9O4/3zqbP4xzTCofh9/f2PKKtj1DWRcJADjxzP++PzuWtkNg9NMnC6TGzR326/V/HU2DwGHP4lA9fMpW/l+6QT5Gva8Bp7scKWi8fuZsP3y6pDF2vj8ijun3ot7dqeB8CI0RvwVdh4b3xrxIRIxGDPfnvQrnMbvnn/ezwZHnoM7ArA+jWFcTVE68MwFH8u+Zu/liau9KSU4pLHR3L8pUfExbE3J89e8yrzP/uRoD9UPf6v3ppDmz124rQbG87Otdi67LAJStsCEl6LFB5FfLSIG5X/Hsq+B+aGQyCyqUJiLlT+FLB1QMruAN+kaLx7RBv3rAdQzj5aiCv8FxQeRv21SBNho/5N5xrX0bhb2jDl1Twi4VjDddl9aznmrI0YRuLfWX+lYukvaTx+fXtOuXQd3fet5N8/nUx+LI89vvuHEWoZmRIgeNiRvBTqzOQ5/2BGBMNmYEZMlKGQBCGGhk249YVSDjjiH2q7oYJ+RdF6O288vgezPsrEX6lDL50eJ8MuP4pR957BTzN/45ah9yWV401E7s7ZlBWWEwnHT9it2+fxxur4DNNkLJq3lJdvfYsVP62m7Z47c84dp9Dn4J713hOJRDgu82yC/vg3hla75PL2X88nvK+ipJJPXviSn776lV1234njLz2S9l3apjxWi4ZJNUHJCndsJiRShFS+gln+MBKYo6UHNhFlbweZV6Prb9rRxtENGRei7Hvoi9LOAVJLaKqnJy2Y5ZsM/snoePcKwKcjfIpPRwoPxfR9BhX/R9PCGxt4fTfy0c/hYNgFhThcsX0YNuGzN/Oprp2aAHe6sHsPHx328PPIVR24dOAe/HxqiBu/m8V5/MbvKo/yz6fi+GwKF3/1BANP2K/aqAMJjTroakj3j87iw5djN1OdbqG00MHMDx3VhltECHgDvPf4x6xd+g97D96LPfvuhsOV+stx8b+liIDNEfuZuTxOhl50WMrt/DrnD649+HZ+mPYzJetL+e3rxdx63P1x0r2VZV6mvzGbqS9Np/CvIiKhCOFg4reMytL48FKA4vWlnN/zal697W3mfbqQKc9+ziX9rmfBtGQSERabE8uwNwMSnIcUHoKUPwyVzyMllyEbz9UJPJuIkT4Slf8hZIyB9MtQ+e9hZNT4VlXameA5Hr3ibSLKBipDZ8nGVYQCMPVbQekY8L9Hw/H8KjoeA0jT8rv2Peu/xchH5b0D2Q+Q27Yv976+gt17eFFKsDtMxFT4ArthZN9CwG8Q8KmEESZpGSb7/6eYU2QRr/Epo/iVP2jFuH37035uLmk9r0TW96VwyY18++F3SdL467rAFAGfwfg7d6a8JNbYzp2WS9CXOPRx3ic/oJTisv87L2myUdKPw2aQnZ+FO91FWqYHp9vBvkf14eTrjk+5jWevfTVO+THgDfLM1ROqff7fT/a6wh4AACAASURBVF3IKW0u5PFLnufpK17i7D3G8MHTU2mfIOZeKZ3UlIj/3TWJ0vWl1fsCkbBJwBvk4fPGpbS/YNG8WD72TUQkgpRcERv+KF4I/YSUP4PIBggvB2dfVNrZKNtOje5D2TuhMi5JfE4ZqOw7kYwxSNGZYK5MeF0DTwGuQ6DiySbcm6Q9AFsHVMbFOmQy8BVSelU997ijmuxdSGs3FFbMZOddn6GsOELxBjvd/9OZW966BGVbxFXHDeCAI5dx4sUb8NSW4vWamC+UcuATK3ETZh478Rp7Yezr5r63V+D2RI24+EhzTOaSu3P5vxvaJxlPvLG2OWwsnJPL/oeX4nCGQKXhSm+FzW6LKwRtGAbuaMTK5Cc/Tfo2kIxwMMz+x+3DUecdzL8r17N7746061x/mGVdVv6cOJ+icO1GQoEQoWCYO096hEAdNcdX/vs2lz01iqfGvEQoEMKMmFrTxu3koofPSdjmtx9+n7AYdvnGCtat3sDOHa1M1i2JtWLfVMKLSFz82QfeceB7V0vUVr6CFB6jqzFtBpStNarV09Tnqkh8YyYq93mt0+4cSNPmekW8IQxFBce6o4w0cB9dfxN1BNhMyadoQyfKS1z8P3vnGRhV8Xbx39ztm04CIfRepIOidEVEBBsCViwogmIXbEhVQZGmCAg2UFApijRFLCBdmvQWeodAerL93nk/3LBk2d0kFP+Kb84ncnfv3NlNeGbmec5zTlLlRO55phJxogMy42XadjnEnE9L4nEpqCr8/nU0C65XyK15FOO7Z9kr43jF3oFBlhs5GFmG7n1TsFgCd+ZWm+SWbunYo8KdPoIDsStX44N+ZZg0qBSzP05i5qRW3PTYuJBcciklLTs3BWD/5oNFE/jKB1uklZrXVWXN/PV8N3YhUwfNYNfaonQjn0dc6diQ1612C0azkXU/bUIYghcwr9vLoe1HmbhhBO0fvZFaTavRqfctfLJ1NJXqhF4I7dGh04GapmGL/HspmcUIRvGO/bKhED7nnF9m1gPSh8x+HxF3ea3g4SCM1SBuAjLjxTwKZGEwQcSLCHNTtOxx4CxKmiU/IvT3CxvIEFrpQgHfLjDVRAiBVCqAdiT0UPbu/n9uXrqdAbe/6z/Wnzp0jJwTf6KqTgwG6NIrF7fDx9sPVaCd4xDNkrcTh5uNlGK6UpvtLt35x2I30rLz9TS68ThCZgU9UvUKEkp7OZIdGJgNRgVNk1xYJpFSkJsFC7/SjVisEemUq3eMlyb3YmyvTzCYdIkHTdUYMOMlv4hWtcZV2L/lcMjgbrKYqNqwEoe2H/Hn6c02E4mVSvJF/2/IzXTidXvZs24ffy7cyMufPkXbB1oBcHjnUWaPms+hHceofUN1uvW9I8D16KE3uzDhhSkBO3KL3UKXl29HURS8bm/IdJaUErfTQ4VaZen7WeiT4oXo/FxHPn75y4BnGUwG6rSoRUxCdAF3FuPvwBUJ7EKIDsCH6BWyz6SU712Jca8KGGuCiC64E9UPrYBOzysDYWmDTFgGZ+8AGZoydx5ecHyGNCZB7udcVOORkgDRIxHG0sisd3TNmwshNTCUy/tnDoi8JTCf96jHLTh+shtVS5s4sPUw8yf+zB8zVwdwuPt9cIRm7bM4R58WLo2HIvdw78FMLJleNlGSodRhh0gIWGPdDjfLZ6/hpZG1UDjJOVqo1yNYsTCGFQtjOHbAEjRtTSNfUJeE0+Nx5br5ffpyhsx5hes7NWHD4i0YjArXdWiIwWRk1sh5/PLlH3g9voAiLegKijWuq8Zbc18lMi6CxV8sZeHkX/G6vbR9sCVnjqex6NPf/OkNvSjr4aNnPqd112bsXJNM/47D/amS/ZsP8suXfzBuzXC/Jk2Hx9uSlZrNN8Pm+A097nq2A90HdgXgug4N0XzBC7nFbqF116L1YpzDbT1vJnnjAX79ahkmixFN1ShTtTT9v3nxosYpxpXBZdMdhe4ykQzcAhwD1gMPSCl3hrvnv0Z3lN7tumojqq7YiAE9SIY4fitJKKWCBaSuNDTnQsh8g8KFtcy6lZ83lMmxAZTSoJ0g8FRihZiRKLZbkdKJPH09oSUGIhGJG3WaZPb7kPsV+RcPKeHoPgvP3lafhwZ05eu3v8Pr8QUEwJgSXqZv2IXZKsGlwfQsxPg0xGmV0xWjGXW8MZvV8FaGETF2xizpTqWkfoATr0fwSpeqHNxpxeW8/EabNt2aMWDmywHXNE2j301DSN6w379AmSxGTBYTbocbW5SNO/t04JHB3QIckfLjsZrPh+Sy2yKtfPTncIZ2Hc3R3ccDXhMCrrutEcMW9g+47vV4ST+VQWypGMzWwFTdDx/9xOevf43X40NqGha7hZb3XM+rU58Nq35ZEFKOnmXfXwdJKFeC6o2rXNIYxQiP/6Uee1Ngn5TyQN6DZwB3AWED+38NwlQXSq4A96+6xou5KTL3S3AtInAXbAP7I1f02dK1FOmYBlo2WDsg7A8gFDtCSUAKI8hCAruxJsiM0K8JKyLuIyRWyHxNT6uggLkFwpwnFOU7CMIYJhuVg8weofuVOudz4YlACEiq6MFkcvDloBkhedtGs8SbLTF/m4EYl4Y4pSKb2dAmlmDzsXLsfjMJcsM3AHlcXuLKNmXd6r5EmsZzYLuBAzusuF2XH9StERZu7XETAMf3nWRS3y/ZtWYvBpNCVmpOgByA1+3DYDIy4pdBNLixTqFjxyREhQzsPq+K0WLixL7g16SErct3BV03mU1hjak7P9eRhjfV5bdpy3E73bS65wbqt7nmkgNyqfIJlCpfNM/gYvx9uBKBvSyQv0PmGHB9mPf+JyHVU6AeAXMzhCGv+h89BKmlgmd9XrOPG2ydEBGPXbHnatljIXcq/i7QnD1I1xyI/x7M14GwF5JrtyKiX0e61+gBOigVI8BYA7LeyrP5ywtUnt+RZ9cgE/5AKIl5p5QwcH6LNF8bpsCsQ/UROv8sVVqcOkJk+4OIUz7k9Va08aWhhR2AFs5oJg4yEk4+QTEIWnW9ntXz1jHhhZ/xui5duzw/jCYDitFAu4fb4Mh2Mfie91k9b32h9H6P08OO1XuKFNi7vnwH7z82PqCxyWgyUKdFTUpXLInBaAi5EEbG2C/qs7gcbiJjI3h8+APFUgH/IVyJwB5qaQ/6ExdC9AJ6AVSoULj/5tUAKT3IjH7gXpoXvD1Ia0dEzDCEEoEo8QXSd0TngBurnw/6V+LZ6pkQeXEX+I6Bcx7Cfh8yZrRuhCHdebtqNzq/3AVYIaIHmK5FGGsgXXNBPZv3mgCMEPmGfgJxziGo01Q64Ew7pFDyPnsYA2/phIxnAZ13nn8jqKqwb5sNZ27gn6FRanTgIA+wm1LSyRlzNLHfxmFoY8o3gBV7uU95/1cvgzu/T056Lj6vG6td5Zl3jpOZpptY/7lwI6t+WOfXO78UKAYFi92M6lW54Y5rqduiFjGlohn39Kf88uUfeArQdMkPi81MfJmiCWm16nIDh3YcZcZ7P2CymPB5fFRtWIkBM17CYDTQrntrfpu+PECuwGI30/n5QthHefB6vEx4/gt+/WqZv1u218iH6dCjbZHuL8a/G1cix94MGCKlvDXv5zcApJRhfef+Kzl2LWtYnlBX/nSHFSKeRIn6e6VQpWsxMvONvA7RC2BuC8aq4PgKPd+v6dK70oe+uz+307OBvTtK9Ctoahqk3gvasbzXLbqna0RvyBkd/IwgFE3ky+MWGIwSt1PB7RK8cV9VFEVy+rgZV7pCew7xILtJxMEOSvC1qT5tPhnALZ03gHMm4ALTNRD9LopJb3rSNI0vX72Hxi0Pcc11DgwG8HogO91I75trkpV2Zchf1a+twrhVwwC4N+lJstNCfPcFIDI2gm+OfIwtsuidwjkZuezfcoj4pLgAHrvb6WbY/R+w8dctfpGuWx5pw/MTexZp5z221yR+/3pFQJHaYrcwaHZfmt7WqIA7i/FP4n9mZi10B+dk4GbgOHrx9EEp5Y5w91xKYJcyj1Hi2w2GirpZs/jn2JpSSuTphoQUwxJxKImhipFX8Pme9cj0XiFSLQYwNwfPhtBzC4IZUWol0jk3z7TjwpRJIfK/FwlNgx3r7PwxN5akih7u7JGKQWqI77LwDM/AnuFhFyX4imvYQCIIwSsTfLTrfCBvblL/jMbqEDsZxZiE1DJJ234Dv84uwfolUSQk+bi75xkq1XIxe0JJpo1OurhJnjsUhPivUa9VbboP7MrQrqNwZBX+/ZosRhRFIaFcPANnvczudXuZPXI+GWezqNuiFj3f6x6WG14UnJPVrVC7LHGJoXnrF8KZ46RLySdCCp7VvqEG41YPu6S57F63l5+/WIIzx0Xrrs1odue1f6tQ2f9H/M+Kp1JKnxDiWWAx+vbwi4KC+iU9Q8tBpnUH9ZCezxVmvU09fuYldXJeGWiENZsItYu+0jA10b8DmX8HDmDK8w4tqvqiB+n4IU8qILSbU9FRmNCXLrlb7wYH9W5wgFfC7CzEB2mIoz5EfQtL29dm+Kxr/CmXpIpu2nTae8G4qr7An70FGfcJWWkenutYg8w0Ix6XglAkqxbF8ML7R2ncOodpRTlw+OcnuOmBliz5ZmWeumYgtq3Yxaal23A7Cxf1KlEmllG/D8FoMlK6cimmDpzBnA9/9OfN1/30F1uX7WTixvcpV/0iF588lKpQMmxhNBzSTmXg84YWcTt9+MwlzWPmyHlMGzoLj8uL1CSr562nwU11eWvuq8XB/R/AFfnGpZQ/SSlrSCmrSikvbbkvaPzsMeDbl8cV9+q7VO00MrN/off+XRDCAMbQuhmYwntVXrnnK4gSX+mnF2EDEQkiAmKGEdRZUxhyxl0R21I9+BZhr+CTMCMT0eowSt8UKGFAm1YG8XN5rhumBVRtmt3qDPDkDIQHmfkyc8bvJOOsHtQBpKZru4zvX46Th4veiWswKrw2/XlenNy7QH2T2e/PR/UW/B2XrlyKcauGU75mWZKqJOLMcfHdmIUBxVApwe308O3wOUWeY3Z6Dp+9MZ1Hqz9H74b9+OnT39C0i/t9H9x2JKzEQbkaF7/ApJ1K56vBM3E7PP5xXblutizdwbqfNl30eMW4fFwdnaeuBQQzNlTwrEZKD0JcZBv9FYKIHpLHX/fgD2rCjIgeEPA+qZ4F10KkloEw3wDm668Iv1cYK+iG2L69+inBVBchzGhqCuQkU3T7Ok1fHDASLMcbLneuEFoHvgA5X5+EOdmIsWmIQ15kPQvaV0nQLsK/Q7faNIwmiaoqWKxmSlethGI4Q9iTg3SxZsEOvJ7g4C81mDm+aAVrk8XIe78MpH6rawC9RT5cqkUtQB7g5odacWuPm4KkcU/sO4XRbMBzwa9EU7UiSwW4HG6ebfo6Z46l4nXr3/PHL09lx5o9vPLFM+fH1DS2r9xN+qkMat9QnVIVSpJ2Kp1jyScpUzWR3QU8r1bTakWaS35s+n17Hh8/8HfkynWx4vs/ueH2Yg/V/zWujsBeoJHEP6ccJ8wNIWEuMvcz8O4BUz1ERA894J6bnXs1MuPpvF20G+mYCqbrIO7jK1IjEEKAqUbgNfsDOsvFd4SipWSc4NtK4HdpBxQwxIN6nPMBW4CI0lNBnqWFjGvVA7aWAAviEe8vQexPRdaNRJuaAO3PB3T/THIVomJVstJNDJ33Kg1vrAhnWod/hJRExIQuRrqdCoeTg18zmAz+Q4GmSUwWI3f26eAP6gBPj3mM0T0/LuTzBeOVqc+wYfEWejfsx4n9p0iqksgTwx+kZtNq/mCcH0JA2WqlCx33zLFU3nv4I04eSAk4Tbhy3fwxYxUPvdmFMlVLc/rwGfq1HULm2SwEAq/XR2KFBE4fPoPZasbj8lKxTjnMNnMQm8diN1O9cRH9evPBGmFBKMEbFUURYX83xfh7cXUkv6y3ErwGKWBqolvV/YMQxsooMcNQEr5DiRkcGNSlN0/50YmfOSMd4FkHrvmFji09m9HOdkE7VQvt9HVo2eOQsnAtF6HYEfHfIaIHgflmCtVCB/TF81zAMEJUP0SpFbqUruVm/RoKmBroGvGePwubBZjaI35+EHHjMZTesxGR5eCHH2DzcbijE4hg6V1rhMaUVbup0dCL6lVRDDGIuI8ILW4mwFCKWx+/LcRrEk0TIcm4QhGMXDKYR9+6n+6DujJ66VCqN67C1+98z+r561F9Kh0eb8uLk3tjthZdDrlS3fKs/fEv3u42mgNbD+PKdXNw2xHevncM21fupkXnpphtgeOZbWYe6F+wI1HK0bP0btiPbct3hEwRedxeXmj+Jt9/sJDBnd8n5fAZnNkuHNlOvC4vx5JP4nX7yM104HV7ObzzWFDfgBA6K6b5XdcV+fOew3UdGoY8gZosJm4tpk/+I7gqHJSkloZM7aZzqqUDXePbioifFRBICx3HswWZMwq8u8GQhIh8HnGBquCVhPT8hUzvGbqYaqiFSJgXNiUjvXuRqV0J3HFbwXY3SsxbFzUPLWcS5H4cQms9XDrFpnPxbbefn4/0IqWK2yExOXuiqOvDP1CVMN+L+MCHSD4O9evD4MFw990BhqWaZxfeU50xmQPnoGmwcVkMB4++yfHkE0TGRdLhsespX/ot8G7W5y2MgAURPx0MVekc9xi5WYF6PYpBwRppxZEZeN1kNvLxppFUrF2OlCNneL75mziynLhy3VgjLJQsH88HK98hKi4Sn9dHt9JPkJMerAUkhJ4nF4rAbDUz/Kf+jOk1iePJwV2hZaom8um2MUx8aQq/frkMTZPEJcbw/IQnC01VjOk1iV+mLg3ZkJQfZqsJn1ctkpKk2WqmRFIs6aczkBKSKpdi4Oy+fp2ZwpB+OoNPXp3G6nnrMRgNNL65HusXb9ZflOD1+ug98mHueibUoluMS8X/jO54Kbg0uqMHXL8gvbsQxspg7ajLwRb1fs9mZNojBOadrRA9GMXe5aLmUvRnbkGmPxam+1MBS1uIehOy3wX3H/o1622I6P7IrLfA9SPBgdeCKLUcoQQ3ukgpwbs1L9/eEKFEnL/uWojMnaQ3IRmrgak2eHfoksKhEPUmSsSjOq3Tu4f5k1Yz7e0V5GY6sEf5eLjvCe7skRqYSVElLMhBjElD7PUg69ZBDBkKnTsjtWOgHgBDFf9iLLU01FMtUZTAFIWqQv8HqrB7U0lcuS4Ug4LJbOTZ8U9w68MV8GSvRlVLYItv76+vbFqyjQF3vIcvT2vGbDURGRdJlfoV2PDLloAskxBQp3ktxq54m9fav83mpdsDBbrMRm597CZenNQL0J2I+ncaDhJ8Xh+KotC0U2OMJgN71u+nUp3yPDLkXqo2qER7472hC5MCfvHNQgiBx+3FleMiqkRkkWotD1d5hlOHUgp938XirfmvcfrQGeq2rEW1hpWLfJ/b6ebx2i+SeiIdNU9EzGQxUbl+BboP6IrH6aHRzfX86pbFuHL4zwX2wqB/Di9gCvmfRUvtDt51wTeKOESpNQhx5bNSUqrIMy31k0YoCBtgztvRn0uxmMBYSd8KqvtC3BOJKDEVYaof+CzffmTaE3m6L4rejBQ9AMV+b4h5efQuWc8myHgi9NysdyAieiHTn2bRdC8fDyyF23n+O7LYNHoPPU6n7mmgSViYgxidhkj2IGtFw+B3Efc+hRQ+PR3lXqk3PEkvWJojYscBAnm6CRcKlS2bH8OYlyvicgT+Hs1WE3Vb1mbrMp1NW65mGV6Z8gw1mlQF4Njek8yf8DPH956kwY116PhkO+4v1zvISAJ0I4y5mVO5O/axkDvcyNgIfkib6v/Zke1k1Q/ryE7PoXG7+pzYd4qxvSfjzHGiqRqNbq7H69Oep1f9vpw9nhY0XkFeoYWhV4O+HNwWRu74QhStT0w/zURYkFKielV6XcTuevHUpYx/7vMgH1drhIV3F71J3ZZh2GLFuGz8v/I81RxzkWdaIU/XQ6bcgJY7LTgX6QsWRwL03bTM/FvmJYQBETsR3bM01LOdeZzz/Hlzr16sVOIJ+euRXjAENrRIqSLTHgPtpJ6qkjmAC7LeQXq353ufEy3zDeTpxsiUppD5JmHz797tyLSHQTvGtFElAoI66IXJb0YlwsJsxM1HUHqfApGA/OYLxI50xP19QFGQ2aP1oI47b15ucK9EZr2t77ZtXYBAI4Zl8+ODgjrogl6blmzD51XxeVUObT9Kv7ZDSTula8FnpWaz968DbFuxi0WfL+HPhRsxmUMXqBWDgiiAX33h3489ysYtj7Thnhc64fP4GP7gB2SkZOJ2ePC6ffz12zYG3TWC7oO6YrEH/r6tdgsPD+oa9lmFIeIi9F+MZiNmq8mvGmm26RsdJc9Q41yRU1M1HFlOnNkuPC4vn746nX2biua+tWfD/pDm3Jom2b/l7zGSKcbF4aoP7JrzR8gaBFoKIHXDh5xRSMf0wDcawjAP8vw+/y4IcyOI/ZCwwT1Ujlv6wFQvxD1WsN0VnIbxbswLmhdu1TxIx7fnh01/AZwL0emZPpCnCNtQJOyco6+lnQ4s+AkpaSmP887pZShPngLVhvxyKGLHEcQDPQLy6DhnESwd7AXnLLT03hD5Atg6AWadhy/sWKNrXEiWOf8ZLkhz+Dxexj/3OVMGfssrbYeyfeVunDkujiWf4IOnPqFyg4pBBVCj2UjLe5pitVmo1/oaQqFUxfBNP9+NWYDngq5Nn8fH3o0HqN/6Gnq+9xDR8ZEYjAaiSkTy+LsP0qlX0U2oL0QoNk0oGM1GajSuwuTNo2jYtg5mqwmP00tc6Vga3FiHGtdWpdHN9bBGBP8tej0+fp6ypEjPqVi7bNDiBXofQNlLbLQqxpXFVUJ3LAA5HxDE15ZOyBmPtHf3p2VE5PPIjFcJLEbawPYIQlyGEXQRICwtkcISQkL3HNPjAo6+MCEszcDaDpn1Nvh26ouP/WFEPiNrP7RMQmuxaf40kFSP55l8hOqYvLCIagXz9eDYD0CZSh6OH7SAlDTnBI+wk6pkctIUC1OmI+6/HwwGpO8wMns+SAfCejPS0AipOcMGadyrIOtNlLiJyKg3QDsDhrJ0fOoAK+cPD5lCuRBet4/V89Yjf1gXZBjtdrjZ9Wcy5WuU4eSB02iahupVMZqNlKuRRHZ6Dg1vqsOWpduDxj284whnT6SRUKZE0GsnD5wOmUc3mo2knkjn7mdv484+t/qLsRfbeenMdbHp920goVG7ejS4sQ77txwKkAHWn2cgoWw8qSfSkBJu6NSEvp8/zcof1rJ95R6/QFjayXRyM3N55YtnUFWNXX8mBz1TUzXSUzL55t057Fm7j0p1y3PH0+1JKBsf9N523Vvz5eBZeJwe/8nGYDJQonQcjdvVC3p/Mf73uOpz7NqpuoR2/lEQiVsDmpc0x0zIHpUnIavogTLqJb2L9G+Gru3yZN6mWgUEWO8E9+/6KcMfWI26CXTCT/68v5SywCKb1NKQKW0ICtrChogahLB3QbrXIjP65KV+LoAocZ65o8RC1GCEsRIytQvgYvWiKJY+ZeZ+z26qk8ExIplhrsf100fRqltzADTH95A1JO+zqUgMbFlpx2jycc11DsLFNinNnMyaDSKGstWT/J/z09emMWtk4ZTQosBitxBXKpqzx9NRVRWpScw2M1FxEShGA2eOnA1530ufPEXHnjcHXZ8y4Ftmj54ftJM2WUzMODb5soqGq+ev592HPvR322qqxnPjn2Byv2nkZub6mTFWu4W7n7+Nx4c9SObZLCx2C7Y88+z7y/Ui9USwVWFS1UQ+XPkO3Sv3CVCFBDDbzRgMCqpPw+P0YLIYMZpNjPljKNUaBRdWj+45zpgnJ7FzTTJCETTt0IiXPuldZL2aYlwa/pdGG/8sjBX1zssLoSQEdaQq9vuQtq56Tl1EXrGOVSmlnqsX5rBjCvN1UHJlnhlHNlhaIIxVkeozyMwh4FmOzoq5FRE9MKCYmz+oSynBvRTp+Fp/pqkR+A6DsObpop9bIKxgqAK2O/QfjVVDnBjQn2lpg4gZClouKCX8z5OG6rBoDS3GHqGlx81ps50xNCG5amkefbcPze7Sg7rUMvOC+vnxBT5qNMxm4qCyVKrtIiJKC9q579tm451elUg78zagEJcYw6DZfaneuAqRsRFF/foLhdvh5tShQA0Uj9NDpk/FF8Ia7hxCmVkA3P18R3785Ddy1Fw/K8QaYeHOZzpcVlBPP53BsAc+CGocGtfnM8Ysf4sFHy9mw+ItRCdE0a3vnTS781qOJZ+gZPkErHmpEU3TQgZ1gJTDZ4hLjOXRt+7nqyEz/bou1ggL1ggrWWez/Kcer9uH1+1jbO/JTFgX7HRZvmZZxi5/G4/Lg1AEJvPfe+otxsXhqg/sIrKfzrq4kMYY2Tf0+4VB36FeIUj3WmTWQF1zHQPSdgciehBCBHfcCSUSbJ3P36tlIJ2LwJAAUUPAdjuKUnBAk9mjwDEdf0rJ+9cF71B0VyTbfQh7F/9CIwwJSNs94JxL4HelgesnsN2JsLTIe4hELpyDGLgIscWJrGhCG1uKkl2jedGYhZTZCNsfQJ72t3tlPr13ndDzw2cJfDM2kZwsA7/NKsHwb/bTqGUu59YrR47Cq92qkJt13ijj1MEUXrl5KIO+68vvX68o8Hu4EjjnJxoOZcPopsSVimHSpveZ9tZ3rP95E9HxUXR56XbadS+gQ7YIWDYrtB+ulJKdq5Pp+1kfAFRVZdLLXzK21yQMRgOaJuna93YeHXIfcz78KSwzJrGSLq9wb787qd+6Nj9/sYTcLCetuzbj/Uc/CkplAezbdBCPyxNkqXcO4a4X45/F1R/YrTdB7IfI7JG6i5EhCSJfRLF1+tufLb17delcf95eBedCpJaOiJtU8L2+fcjU+0F60APtj5A7ARn/PcIQunAn1VPg+JKCTac1QEWJeDDoFRE9BOk7GMLf1I3MfBUSliMW/wJDhiDWrUOWN6GNLgXdFOcJjAAAIABJREFUosF0frsthERzbThfeb9AGmH+lHimvlcadz5P0bF9KzDx12RsESpGE6xYEIvqC04vObKdvNnpXWQRmmyuBAxGJXTjj4BW94Q3dE4oG89Lk3tf0bns23wwpGmHz6viyD5fG/pqyCwWff57XjpFXxS/G72QqLgIvhw8K2RQVwyCx4ed/5uo1bQ6tZpW9//84dOfhGS6KAYlrC9rMf69uOpZMaAHd6XkTyilt6OU/PV/EtQBpOMzgouRbnCv0ouVBd2b+UZevvvc7tkB2ll9Rx4Ong3o+uiFwJeM5tmJ9G5DyvN5YCEU0E6FmIyE309Cs2uhY0c4fRo56S18K6rDgzEBQf0czp7KR8EztyR/NPl6bGJAUAdIOW7miVY1Gd+/HLs22ti+zo7LEUq4S+Lz+AoU2rqSEIqCYgyeR/eB3a5oOqgwHNx2mCXfhj6lmCxGmnbUzS+klPww7ifcjsAFwO1wM+O9eSFL6ABRJaJo061Z2Od3fPLmYPaQ0UB0fBRdE5/giTovsuSbv/8UVYwrg/9EYP/H4N1PSLqiMOcJZ4WGlE7wbid4a+XTc/DhoMSFJr+EQtq9yLRHkCnNke5V+eZ2PiCnnTawrJ+JlIanUR48CKfOwOTJkJwMvQbg9JQglCKsxyVY9lOD80MqEXkNRzZU1U5mauiDYGaqiUVfx/PiHTX4ZWY8Rf8wugxAzeuqYo2wYLbpx3+z1RxSfCokwtInNUb9Ppga11bFYFQwGBSqN6lM09sasXjqUnrWfYmuiU/w1r2jORbCXPpSoGkaJw+cJj3lfP/ErNELUD2hU0MV65QnqYruO+Dz+kLurEF3WwqXXirMzKP7wG40blcfi82MPdqGyWpC1TTSTqaTk57LkV3HGdNrMrNGzSvKRyzGP4yrnhXzT0LLegcc3xAsVWtGlFyGMARTxUDv/NTdl0Lwk0UJlMTQAlt6J2tr0M5yUaqWwoZI+AVhSERzzIbMtznwiQPPW+lco6WRgo3Zltrsa9iOEX+87c+bJq9bjk3tQ2I5D4a8WO3MVZgwoBJ1burL7b0DudlSywLXbzxU6wfOHCtcMthoNmAwGALs2UJOXwhmnviEuMRYslKzWfLtSjLPZFGnRU3euX8suRnBOi757y1bI4mouMiQND+AFp2bsuHnzQHzMJgMGBTFz1cXisAeZWPSppGUrnTp3rXrFm1i1BMTcWQ50VSVOs1r0f/bFxl014iwcrpmqwmj2cjI3wdTo0lVHq3xHCf2BZ+8at9QnaSqpVk2c7W/qAs6DXPYwjdo3K5+0D0X4sju4xzcdoQfP/mVzUu2BzVq2SKtfJfyeXFu/R/C/6vO038KIuKJPFmA/NtBG9i6hA3qgF7QtLQmuMRhgQJ0a4Qw5JlrlNN33iIixBghIFWkcx5IiVgTh7gnnWpD9lNSczKORjxGB+Z6qrB32zEWfLzYf1v161oxsu+d9O1cm8GPVqL/Q5WZ80kpajXy0u5+O5qm8fvXK3ihxZv0btiPGSN+w6XdxgNvdPePkVjezT29ztD5yTMklssXwIXOu25yawNiEqJJrJhA5foVg3bgQgjqtqzlp9FFx0dx97O38ejQ+7i2fUMGze7n38ULITCaDHoQjrZhtVuo0qAio5YModf73bHYQgejVXPXBS0uqlcNaEKSmsSV62bmiLmFf99hcHjnUd7qNpr0Uxm4HW68bh/bVu7ijQ7vUKdFTYxhumQ9Li+OLCdvdRuNlJJnxz2OxX7+s+jKjGaeGv0oleqUD3J+klKSnR5KrygYFWqVpU23ZhxLPhHWbCTlaBiJjGL8a1C8Y79MSN8BZPYI8KzXdcojHkPYHy1Ue0aqqci0h0A7DTKP126qiyjxOUJYC75XSl0iQTqRIgZSO1HoDv6v1igj9sLy5fhKJvJpZnkWeMrjvYDDX7VhJSb9NdL/szPHyRdvfosvaza9Bh3AYBIYDBIhrOzcXJk3ukXgytWDosFkIC4xlnota7F0xiru7pnC42+c0lUQ88b77O0k5k/Ri8OKQcFoNuJxerBFWilTrTSpJ9JwZLvwOD1Y7GZMFhPjVg+jfM2ygO7W89Nnv7N1+S5iS0Zzy8Otqda4MstmrSE7TddxKV+rDPs2HSIuMYbKdc+rf25fuYvX2r8dxOG+GFSqU55Pt425pHs/fPoTfvrs9yBtGmuEhUHf92P4Ax/gyHSEZKeAzl2fsGEEFWqVZcfqPUx7azZHdx+nasNKPDL4Xqo2rMQ9CT3ICRHEy9cswxe7PizyXPveNJity3YGXTdbTcw69RkR0UWXOSjGlcP/Hx77PwxhrIKIm3zx9xniIeEn8KzV2TzGWmCqXyS1P91cI68VXssK6c3pxxonYlQ6YvXnkJSEZ+Ro3vktizW/7AiRd5Zc12Yv2pnbAC9Y2mCNeIo+Y7sgU8aih+dzz3JSufpurrm2En8t07nbqlfl7LFUls5YRVJFN4/3P4XFGji3ngNOsva3aE4fs6Cpmp8F4sxxcXDrESwRFjSfilAEJZLieGfBG/6gvnX5Tt647R08zvOB+Y+Zq6jVtBojfx+MxXa+zb3xzYEdkH8u3MiXedztS4UQULZ64aYY4XDyYEpIwTHFoOBz+5i4fgSf9/+GFd//GfJ9kvO+JHWa1+S9nwOdulwOd1jXp5QwTVjh0H1gVwaufy+gSGuxmWn7UKvioH4VoDgV8w9CCAVhaYaw34cwN7gkuzyhRIOhTvALfzoR3Y6h3HMM9qnID8bCgQO8vdzD+j/2hBzrsddP8fDLO0Hdry82jm+RqXfpXPsQbk8Wm0abu0I3w7TomIkQwQuOENDmztzQCpyahjPbic+rd4emHD7D0C4jkVKiaVpe805gYJaaJHnDAb4fu1D/WUp2r9vLqrnrOHNMTxn8Om0Z79w/hn1/FU3kKhzMNjP3vnr3Jd/fqG3dkOkgr9tH9SZVSKqSyIAZL/HUmEcDUi3nEFcqhnI1yoQd32IzE5MQukGqXM3w951DVmo2v361jMVTl1K5XgX6ft6HuNKxmCxGzDYzHR5vy3Pjw6iBFuNfheId+38BJaZB6u2gnYB1TsSoVMQKJ7KkBe29BxHPTUTYYzh7Io2/ftsarDli1IiOV+n6VArGAMabD7Qs8KwO/VwJvhBeo6AH8JDrlIC4xGiMJkOh4laqT+PM0VR2/ZmMPdoetkiq+lRmj15AvdZ1GPX4BE7l2xlXa1yZs8dSg+iBFwshBC9MfJJrbtBtCLPSsjl96AxJVRKLTIvs1OsWfvhoEWpKpp+9Yo2wcOtjNwVo0tze+xbWLNjArjXJeJwezDYzBoOBgbNf9i+IuVkOTu4/TUK5EsSWjPHP8Yl3H+KjZz8L2mn3fK87BWHpzFWM6jFRp35Kybg+n/Ls+CeYcWwyWanZ2KPtmC3F3aVXC4pz7P8V/PkncuDLiN/WIEvFwSv9EX36gP38sXnP+n28estbFxzXJb2HnuD6dpmUrRw6TeH21cJiOpLnXpXvulPhtXursGtjcGArW8XNx7/uwWK7QJjLJXi6XS1OH7MHLTChYI+y8fJnT1O1QUV6N+xXcCqliFrklwKT1UTV+hU5mnwCt8OD5lOxRFhQvSq39byZPh/0KJLYV3pKJt8M+541CzYQEWOn8/OduPWxG4NOMFJKNv66hZ1rkilZLp7W3ZoREW1HSsmUAd/y/dgfMZr1xbHFXdfxwJv3kFixJBHRdpbNWs3UQTNJOXKW8rXK0PO97lzbvkGYGel1i4erPhvUHGW2mvh85weXxQIqxpVFcY69iJDqaaRjJvj2gbkJwtZFb/2/WrB2LQwZAj//jChZEkaORDz9NEQEB9vytcqiXsBzFgLuevwshjDNhZoKf/6UgjX+Ua5vMRU9eur+qB7lfs6cPgoEsySOH7Dw1ajSPNLvFIpB5o0lmDqiNMcPmAlJ9QwBt9Ojpykql6Jk+QSOF8Qlv8igLhQR2u0oBLwuL3vW7w9gijizdUrnz18sJb5MHA+8XrB3KejplGc+fJxnPnwcAI/Lw+p563HmuKjXqhZb/tjJb9OXc2jHETJSslAMCk1uqU/Tjo2JiLbz4ye/MufDn/C4PHjyGKV/zFrNijlrUYwK7bq35vkJPWlzb/Mifw8rvl8bWhtUkyybtYb7Xr2ryGMV49+BywrsQohuwBCgNtBUSnlVbcOld5tuJiF9gAfcy5C5n0D8HIQh8Z+eXsFYv173EV20CBISYMQI6NMHIsMvSvYoG/e9djezRs7zN7kIxcC2tTE0aJYVMifucQu++zieQ3vWM/3AQmKj1wNOMLcixliB6QdVXr3lbfas3Yvb6UExCDRVH+e7j0vx5y+xNL8tHaRg5Y8xnDh0cebjqk/lize/of/XLzBkziu80OLNsAXCgqAoIoBtYraZUX0qqla4Ofg5hDvduh1uvh42h4492xGTEF3k8bav2s2A29/V7Qfz6JSKQQngoKuaysZftvBiiwFMTR7HrJHzQ8oZqz4V1aey5OsVWO0W+nzQo8jz8Lq9aCE60TRVw+O+vBRWMf4ZXO6OfTtwD3DxtJB/AfS2/vzpBSdoHmT2GETsiH9sXgViwwZ9h/7jj1CiBLz7Ljz7bIEBPT+6D+xK2epJzHx/LhmnM2nYti7lGr2OUJ7SdexxIfPILznZCh++Uo7kLXaskQbWL95P+0cDd6UGg4GRvw3ir9+28efCjUSViKB64ypsXrodr8uL1+vjh09XFJhPN1mNGE1G/w74QiybuRrNq7J300F8XvWidtrnoGm69LHRbMBit9DjnQdYPXcdW5fvDJib2WaiTNXSHE8+ibcIqaJzcOe6ebDCU/T/5kVa3N200Pd73F4G3PEuuRcYbash1CZVn0ZmahbrFm0i82wI2eX883B6+Omz3+g18mGMpqL9977hjmuZMmBG0HWT2UjzO68r0hjF+HfhsgK7lHIXcElsjn8aUssC34EQr6jgLpqTTNixpQe8mwFTHoXxCogo/fWXHtAXLIC4OBg2DJ57DqIuTiZWCEHbB1rS9oGWgXPWfkM657Fz+QJWLzzFppURHNhpR1PzjEoEGE2hP4eiKFzbvkFAHvdcQMhKzWbN/A143eEDkurVUL0F7wxXzLlQuOziYbGbeXz4g9zZ51YMBgPturdmdM+PWTNvPUIRRJWI5MVJvanXqhYf9vnMTzssXakUqSfTCi3Aelxe3u3+IbNOfoY9KljdMz82/b7tohYnn9vHiX2nqNO8JhsWb6Kg0pjq03DmuIiKK9piX656Eve9dhezRs7z1zDMVjO3P3ULVRtUKvIci/Hvwf/fHLswEVZApJAGoYIgXUuQmX3xV/KEDeImI0yX6CyzaZMe0OfP1wP6O+/oAT266Ef+okAoUYiI7lgSmzN/6sCgTkxN1bi+U+MCx5BSsm3FLv6YtRqDQaHtg62ofX11Jq4fwQst3gyrEx6Ks/13wJXrZsfK3XR+TpcbtkfZGDjzZRzZThzZTmJLRZO84QC71u7ljqfb8/CgriRWLIlQBI9UexavO6MIcxWsmruOWx5uU+C73A73RdUEjGYjletXpPEt9dm+chdupyfsXGJLRl+0gNkjg+/lhtubsPTblWiapM29zf0MoGJcfSg0sAshfgNCdWW8KaUssiKQEKIX0AugQoUKhbz774cQNqSlFbiXE1jIs4L9vksaU6rHkRkvEqB3LnORaT2g1MpCO0oDsGWLHtDnzoXYWBg6FF54AWJiLmluRUX1xlXoPqgr04bORigCoShIVWPAjJeJiCk4WEx4/gsWT12qBy0hWPT5Erq8fDs93rqfUUuG8EzT1y8pP15URMVFkp2REzZgGowKJcrEBV23R9k4uvs4fa59jez0HHx5qRmj2Ui1RpV5a+6rjFs9nDE9P2bDL1sKnIPb4WZMz485dTCF7gO7hj3NNmxbF5+3qF6mBsrWSKJR27oIIfhwzTCG3/8Bh3ceC8r7W+xm+nz4+CWdoms0qUqNJlUv+r5i/PtwReiOQog/gH5FLZ7+W+iOUktDpj2mN+Mg9CKqpQUidtwluStp2R9B7iTOaWT7ISIQMcMR1tuQ6gldfkCJBXPzYL/VrVv1ID5njh7EX3pJD+ixf6/lmM/rY/l3f/LbtGWcPZ6GNcJCqfIlaXBTHW68r3nIY33K0bP89NnvnDxwmqTKpfhuzIKgdIXZambyllGUq57E3r8O8Mz1ryPVi/ubE4ICUw+KQUFTNcw2E16XL2yR02IzM2HDCCrWLhdw3eVwc3/ZXkH5btAXg+pNqvLRmuFIKWlvuLfI865SvyJD574ali64cPIvTHr5S7weH5qqYTQbUX0qFrsZr9uH6lOxR9lo/8iN9Bj2gD+9M+SekaxfvDmAniiE4JrmNenxzv00aBOiYa0Y/wkU0x2LAKGUgPh5ej5cPQam2ghjtUsfUEsjKKiDLsKlpiOz3gPH1yAM6KkaC5T4CmGqAdu36wH9u+/0NMvAgfDyy397QAc9qL/a7i32rN8XwBNP3niA3ev2htTx3rZiF/07DkP1qng9PgwmQxCVEvT0zLof/6Lci52o1qgypconcPoCm7qCoBgVPRcdIlgrBgV7tM0fkC/sSj2XDTNZTJgsRvp+9nRQUAdYM39DSFYI6Pnqg1sPc2zvScpVT6JE6VjSTmUUae4Hth7m2aavMzX5o4DUiKqqnNh3ihZ3N6VO85os+mIJjiwnLTtfT63rq7Fj1R4iYyOo26oWiqJwaMdR9m06SPXGlclIyWL9z5uC+PxGk4G6LWoWB/ViAJdPd+wMfASUBH4UQmyWUt56RWb2P4IQAsyNgEaXP5alNdL1Q1AjT57KBzi+BfLnVnORfz4E46sgZs/WmS0DBui79BIlkFouMvdb3f7OWBlh6xbWXelysGzWGvb+dSAoWKheldQTacwY8QO93n/k/KeRkvce+ShAFzxUUAfdueecfroQgr6fPc2gO0fgcXv8tEj9Nf1rMVvNeleqx8dD/e8hoXw8E5+fEuAgdA6aqoUUvAIwWoxYrCacOW40VaPJLfVp0r4Be9bv45NXppG8cT+xpWK4//W78XnUkGyUczCYDGSkZFKuehIPD+7G5L5f4QpBOQwFl8PN4ilL6PKS7j27Ys5aPnhqMh6nB9WnUrdlbd789sUAmuQ5Vk3KkTO8efu7nDqYkkeD1Ljl4dYYzaag35XX4yN5YygyQDH+P+JyWTE/AD9coblc/bC0AVMD8GzGb5cnbGDtnMe0yReckj2Isakwby9E7IQ33tB36PHxqD6VOSOn0KbdaCKifdgiNDRpRsn9FEpMQ5jqXtFpL/9uTVjzBp9XZcX3awMC++nDZ8jMZxJREKSElvecp/81aluPj/96nx/G/cSe9ftxZDnwuLxUbViJhwZ0wedVyc10cE2zGkRE29nyx46CRc7CwOf2+XPloIuAvdJ2KEd2H/fzwE8dTOHjl76kw+NtKcj0Q/VpVG1YCdBlAXxelWlDZ5Gb6SQixqZb14WpHbgdHvbmadTs/esAIx4ZF5Cu2rp8JwPueI+P1gwPuE9KSf+Owzm650RAkXTxl3+EPL0YzQb/HItRjP/XqZgrDSEUiPsMnPN1/XNhQdjvBUs7ZFqeVsc+D2JMGszNBpuA5xLhtWlQ5rxpxZgnJ1G3wdfExHsw5aX6FeEB6UFmvo5IWFjoXDLOZLJtxW4iom00uLFOgb6VkbERCCHC5qZtUYFFX4vNHFZaFgG2CCsI0Hwar0173q9lcg7lapThufE9C/0MAHVb1SIixo4rx1Vgnr0weN0+9m8+GDSG2+Hm5y+W0PbBFiz9dlVQjcBit/DE8AexRVhRfSoz35/L3I8W4XK4qd+6Nn0+7MGx5JMMf/CDkFx9i81MlTzK4PdjF4Y8FR3cdpjDu44FpIkObjvC6cNngpgvPreX2FIx5GQ68OYby2Q20fm52y7lq8Hn9bFyzlo2/rqVhHIluO3xtpSqcOVPhsX436E4sF9hCGECexfEBYYZ8mhjxNs/wdwMsAjoE4d8KhZKxiBKnXe3Tz2ZztIZq3iib7o/qAfAd1A3y1aC2R3nMHPkPL4aPFM3bpB6l+WIXwZSpX7FkO/v1Ksdy2avDsnTttjN3P1MYMCIS4ylepPK7F67LyDwWOwWug/sQkLZeBSDwvUdGxXKpCkMBoOB938dxJudhpORkoXH7Q2b9oHgDtP8CHfd6/Zye+/2NL2tCQsm/szxPHeiCrXL0uWlOzBZjMyfuJg1C9azdflOfy5/89LtvNB8AJ9uG82IXwcx8I73AgqwQghMVhMdetwE6CedUNx1o8lI6on0gMCelZodcqGVEpKqJFKtUWUWT1mKx+Wl9g3VeW5Cz0sKxi6Hm5daDeTY3pO4clwYzUZmj1rA0B9eockt4fVlivHvRnFg/7uxbx+8/TZi+nQ9oPcuiewTCQlWwAjRwxHifJv9seQTmK0mPG4FCBXAJAUZWm9bsYtpQ2fjcXn9u0NHtpPXO7zDt0cnYQghCnNNs5o8OvQ+pgyYgc/r8wcfo9lI2wda0uGJtkH3DJjxMi+3GUTm2Syk1PPdze5oQrd+d4Z8xuWgfM2yfLl3PPs2HWTPhn18/OLUgJ2vUARxiTE0va0RBpOBnz9fguorOjdeUzWmDJjBez8PoNU91/uv52Y56Nd2CMeTT6L61KDdtpS61svs0Qt45sPH+frQRCa8MIWlM1ah+lTqt7mGFz/uRXS83kTW6OZ6JG/YHzSOx+Wl2gVplJLl48M2RDW8qS493nmAZz96AillkcTHwmHe+EUc2X3cz7DxeXz4PD7e7T6OmSc+ueK/y2L8b1Ac2P9OvPACTJgAZjPipZeQr7wE0ZvB/QcoCQh7N4SxSsAtZaqWxuv2sujrEtz3XArWfOqIqiow2G4IKVKWk5HL9Ldns3DSryE9RF25Lnas2kP91teEnOqtPW6iQZs6nDhwirSTGcSViqF2sxphqXoly8Xz5d6P2PLHDs4eS6Nm02pUqFX2Ir6ci0NORi4r56xl1dx1xJeL5+zRVEwWI5qqUbJcPMN+7E9SlUSO7zvJ4il/ENJkHMIqQG5dtpP00xl+Cz6AT16ZxqHtRwtUofR5Vfas3wdAREwEr059ltueaMuiz5fgcXk5uP0oZaqVRlEU7n72NuZPXBwU2MtUTSQ9JYMvB8/kWPIJGtxYB8VowGBUQi5Q57TahRCX3fW9dMaqIFVHAI/Tw6HtR4s7T69SFAf2vxNJSfD88/Dqq1C6dF55rizC1insLSXLxXP97U2Y+4WkViMHDVrkIKVASjDZymGMeT/oHo/by3PN+nPqYErYICSEwBmCWZKTkcuIR8ez8ZfNKAYD1ggLL0x8klZdbij04ymKQqO2l9hRexFwZDvp0+Q1Uk+m+fPYFruZ6zs15oHXO1OpbgV/gCtROjZsR6YQAluUNWSh02jWmS/5A/vSb1cWKi2sGBQq5bPfm/bWbGa+Pw+P042UsPbHjTS6uR5D5rxCdHwUsaWiyTyTFTDG8f2n6N3wFZAS1aexfeVuFKMhZD1X18kpcEoXhXCm1JomMVuL9devVhQH9r8Tr79+abdNe57PXpvOsKcNlK2UyQ232bnxwW5Uqtol5A5t5fd/cvZ4asE7S49K3Za1gq4P7TKK7at2593rw+1wM+LR8ZSqkEDN6y6D038Fsejz30lPyQgoTrodHlZ8v5Yy1Urz1dDZVKpbntt7tyc+KY5rb23Iup/+ChrHaDbSuF19Vs9bHzL4l73AnUgtgtSB2WKiW1+dynjmWCoz3vshYEfuynWzacl2Nv66lQq1ynLyQErQGL4Liq4elxfFqIY8WZitpkKlHS4GdzzVnoPbDgewooQQlCofX6BbUzH+3Si2xvsXwmwx0eeDHizInsbEzXPpMXImlRuFb0/fsWYPrpzQdEUhBBa7mafHPhpUyDx58DQ7/0wOWhA8Tg+zR88POZ7X4+XXacsY0mUkY3pNYu9ffz93esPiLSHzzT6vj1kj5rFyzlpmjpjL47VeYN/mgwz+vm+QdIDRbKRpx0Y8PfYxImLsASwhi93CkyO6BzkEXd+xEYrhgv8iQv9OFUVQqW553l08wO/JuvGXLcHvB1w5LlbPXYfH5UFRipY60XwaZqsJi93id6OyRljo0KMt1RpVLtIYRcHN3VvRumszzFYT1ggL9igbsaViGDr31atS3K8YOop37P9iCCEKpCmeQ1KVRMw2c1CuVDEqNL65Pj3euT+kBkjq8TRMZmPQfVLKkDtLj9tL3xsHc2j7EV07XBEs+WYFT415jNt73RL0fp/XR+qJdGJKRmO1X5wOe36UqpDglw0InCh+aV2v24fX7WPMk5OYuH4E0/aNZ+5Hi/ht2jKMFhOdnmxHhyfaYjAYmLhxBN8Om8OW5TspWbYE9756N9fd2jDouU+P7cGO1ck4shy4ct1YIyxYbBY+WPU2pSqUDFoIbFE2RIhCpsGoYI+2U7Z6kk7dDNMzcCESysXT99On+G36cjRNcvNDrcLWSC4ViqLwypRnuP/1u9m+cjclSsfSpH2DIkv+FuPfiWJrvP8AslKzebjqMwG5Y8WgEF8mjmn7J4RdHHIycrmvzJNBxTyT2cjdz3ek53sPITXpv//nL5Yw4fkvgrouzTYzs05+yuEdR9m2YjexpaLJOJPFN8O+R/NpaJrk1sdvos/Yxy4pYBzcdpjnmvUvkm+pYlCYl/lVyIXE6/Hy+Rtfs3Dyb3hdHspUK81z43vSuF39sOM5c10s/XYV+zYdoHLdCrR9qBUR0eftBlOOnuXs8TQqXlMOg9HAfWWeDMrhn9Oo2bZ8J1MGziArn6a6NcKCEAKP24PqDaSO9hr5MHc+fVU1chfjb0ZRtWKKA/t/BPs2HeS9h8dxYv9ppJTUvK4q/b9+oVBu85RBM5gzdqF/F3lud9moXT3WzFuPz6tS87pqvDS5N5++Np0NizcHjWGLslGxdjkO7TiC1+3CILinAAAdPElEQVRDMSh43YGLhcVupmPPdhfl7JMfK77/kzG9JuU5BWmo3tAyAEaTgSm7P8RitwQUQgHef2w8y2evCWANWexmxix766JVDR3ZTt65fyxblm7HaDbi8/i499W7KF+zDKMen4imSgxGfff+3ISeZKfl8OXgWQHuR4pB4b5X7uKu5zowpPNIDm4/isGo4HX7uOWRNrzw8ZOXRWUsxn8PxYH9/ynST2dgMBr83OnCIKVk6bcrmT16AZlns2hyS30ObDvCwa2HA4qV9igbDW6qw5r5wb83o8WIECKgEzIULDYzc9KmXrLbvepTObzzGBExdn789Fe+H/tjQBrJYDJgtphQfSpSSqo0qMSb375IUuVEslKzub9876A5CiFo0bkpg7/rd1FzeavbaP5cuCHgOzJZTEipn1A0n4bJYqRUhZKMWzOMR6o+G1I98prmNfhw5TBAFw1LOXKWao0qkVA2/qLmU4z/HyhWd/x/igt3qYVBCEHbB1vR9sFWAOzfcogXWgwIao/3enxExNix2C3BnpuaxFsEbXFNkziyHJhLhteUV1WVlCNniYixE10icHEyGA3+7tnuA7uxf/NhNi/djsFoQFM1vC4PzpzzWvh7N+znpdaDmH5gAqcPn8FkNgYFdiklh3ceK3Tu+ZGbmRsU1IGgU4rX7ePM0bM6/dEdetE7suu4/99V6lcM2x18OXDmODmx/zQly8UXecEvxtWN4sBejAAcSz7pTyHkh9ftJTfTQfeBXZg2dLZfrsASYSE6PorDO44WOrY92lZgYFkxZy0fPv0Jrlw3mqrS5JYGvPbVcyHdgMwWE8MWvsHhnUfZv+Uwu9ftZeHkX9HyBW59IXGybtEmKtYuG7JoqRgUalx7cWmYnAxHSPZLKHhcXtb+uBGTKXhRAShbPeminn0xkFIydeAMvh+7EEOeYmaDG+tQulJJQHDjfc2p3/qaq4r94nK4ObzjKHGJMcV6NgWgOLAXIwCV6pYPqcVitpqo1bTa/7V33/Ex338Ax1+f27kkJAilidhbrCo1fhRV1GiN2rNGUaUoVYrSloq2qtTWYVWrWm3tWW1RVFBE7B2rtiR3Se7z++MixF2WXFwuPs/HI49H7y73vXfS887nPuP9pt3wV2j8Wn32bw3Hx89MSJ0y/DZrPXOGLXQcyT/AaDbQZ3KXxDljKSU3r97Cy8eE0ctIxO7jDpUP/1m3j7EtQ5m8aWyy1w0uE0RwmSAObTvsNHHGx8YRses4k7pNc/p8g8lAh3dbOn0sOXkCc2HyNqVpMRfs01ivDmvBkgk/JfkdGb0MdB/fLl2vnR4r52xg+ecr7WsKCeu5u9fcXyNZOXs9pZ4txsfr3sPLJ+UerVnBz9NWM2/EIjRaDXHWOEpVK86YH4c6fLJT1D525SHBpQMJqVsWg9f9eXChERjNRl5K2NKYM08OaresRqV65dFqtbzUqwFlapTA5GOvAmk0GzCajZStWYpc+f0pXb0EY5YNTewDumvtXjoV6Uf7oNd5JVc3Pu7yBd99/JNDo4xYaxzhfx8l8sSlJPefOxpJxO7jxFrvf3+5WqXx8nFsPajRati9di9RN6Mctkv6+Hnz2dZx6S6FoNVqeXN6T4xmA/cGuzq9Fo1W8PDg1+RtpEX/xnR4tyXdxrclZx57EipQNB/vLhmUqYW2vp+0IsWtldImCd9xlD4V38Yak7Y/Uu6ye90+5r6ziJi7FqJuRWONieXQ9gjGtf7E3aFlSWrxVHFgjbHyzZilrJ63CUu0lcoNQuj7aVcKFHXW+tZOSknYpgP8u/UQ/vn8qNuuhtOR1LG9JxlUc1SSnSl6kx6DSc/dG46Li945zYz/5R3K1y7N5TNXGP3yJM5FXECr0yI0gkEze1O3bU1irbH0rTyMC8cvJc51G70MlP9fGfZs2O/0pKlGq2Ft7NJH+RUBcGjHEb4PXUHkiUuE/K8MddvWYELHqdy6Zt/OGB8bz4vdn2fAtJ5JpjtsNttj2e3Swq9LmnrM6vRaBs7onVCXPmsa3nA8ezbsd7jfYNLzVcRU8gblcUNUj5/aFeOhrDFWTv57Bt9cPikmUnf56+edzHt3MZdOXSZ/kXy8NqEjzzVL9X2W6MMOU/j9+20O5Ws1WoFGoyHuoWkgg0nPd+dn4+PnTY/SA7lw/NJDpYINfP7XhxStUIi7t6JYMmE5W77bhlavpUnP+rQc9BItc3d3OnI1mg28Pb8/y6eu4s6Nu9RsUZU2Q5s77e+aVjabjX+3hvNf5HXK1ihJvmD3zQOPaPRBqs2376ndqjqjfxiSyRE9up7l3nK6yG329WLy5rEUr1zEybOyH7UrxgOt/Xoz0wfORwhBfGw8wWWDeP/nYeQpkMvdoQHw+/fbCO0xPXFu+fShc3zY/jNGLByY2M4N4Or5/9i35RA+/t5UblAeveH+tM65iAtOa5IbzSY0GoG8G5NY0dDkbaTlwJfw9fch/O+j/HfhusPIOzYmlhXT1jB4zut45zDz6tstKFA0P5YoC1UbVURv0NOwW13WJFRbvMdg0hNUogCTX/syMelfOBbJxsV/MGvvZHwesY68RqOhQt2s0Xe016TOHNgWgTXammxhNLCfXQgISnl75eP6lJGcZ16syPljFx3KX9ikpGDpzKsq6qnUHHsWcWjHEb54Yx7Rt2OIuhWNJdrKsbCTjGzyUepPfkzmDF/osGBoibIyZ/jCxNtfjf6OrsUH8Hnf2XzUfgrtAvtwbO/JxMfL1iyJTu94EjY+No7P/hhHw651CQjKTdGKhRg0sw/dEhYXb1y+iXBSZ8Vmk1w5dxWAnavD6FCwLzPe+oq57yykT8WhzHlnIb0+7ky5WqUwehkw5/DC6GWgxDNFOR1+PslIPs4az+XTV2kf2IcV01cn21HKUxQJCebLXRN5vn0tAksUSHZUq9PraNrHsSQE2HcqdS7Snxd1bWmdtwc/TvntkX8vNpuNDQu3MrjuaN6sMZJfZ6xNsk6SkrbDWuDj523fjZXAaDbSe1InjF6PXq4iu1JTMVnEhx2m8PvSvxxatxnNRr7Y/iGFy7t+f3N6SClpqHvVacXBe3PV/6y372J5eNojV34/lpydhUaj4fLZq/QOGULU7ejEkbvJbOSlPi/w+iddk33965dv0rFQX4edL0azgdcmdKRRj3q8+lRPh9c2mo1MWD2S8rVLc+rgWc6En6Ng6UAiT1xiYuepyc5BG81G+kzuTLPXM/dIf8Tu4yz+8EdOHTxLsUqF6TiyVabsZb/n2N6TvNdsIjeu3EJv0KHVa3l7fn9qtKjq8L07V4cxrs3kJH/MTd5GOr3XmrbDXk73a0/o9DnbVuxK/H9kNBspWbUooRvHpOnTwPVLN/jhk1/YvWYfuQNz0WZIcyrXz/yy0VmJmorxMFfP/ee0p6dOp+X65Vu4rp7foxFCkOspf65FXnd47N5U0W+z1judy46+E8Oh7UcoV7MUeYPyMG3nROaNWMS+LQfxzeVD68FNadqnocPzwv8+yqbFfyClpG7bmrQe3JSfPl+V+BoGk57cBXLRqPvzyVZWtEZbWPfNFnQGHeHbj5C7gD8FiubDEmVJcXrCEmXh27E/JJvYb1y5ycZFf3D1/DUq1i3LM40qprvbUNimf3mv+USs0VakhMgTl/h75R5CN46hdLXi6bpWWhWrWJglZ2dxNuI80XdiKBISnGz9nq9GLXH4hBZz18KSCT/RekizdP28J/af5q+fdya5niXKwpF/TrB77T6ebVwp1Wv45/Oj96Qu9HZsSaA8RCX2LKJak8pO26bFWmMpUSVrLAx1GduGGW99k3QvttlIl3GvAiQ59fkgIUSShB9YPH+qR/jnj1zM8s9X2bfhSVgzfzNNetXnnQVv8vMXq7h9/S61W1Xj5Tca4+XjhS3e5vQPo5Swa20YW5ba29XpDDr0b+j5ZMv75A0O4FzEhWQT/I3LN4mPj3dIYAf+Osy7jT9MbJe3ctZ6CocEE7phdLKNK5yZNmBekkQnbRJLlIVPe81g6vaP7E3BM8m9UsMpuXD8otP7rdFW7t6MStf+8X1bDjpdW4m5E0PYpn/TlNiVtFNz7FlE09cb4pcvJ/oH6qiYvI10Gt3G6clLd2jSswG9QzuTMyAHGo3AL29O+n7WlRe72ps1121bE5O343xnfJyNsjVLpvl1zhw+z49TVmKJsiBtEintCW/V7A3kKxRA6MaxzNwTSseRrRNrzFd5IcR5UTCDjltXbxNz10KsJY7o2zHcunqbkU0+4pUBjSlcvqDTTkVgL5v7cFK32Wx80PZTou/EJP4Rjr4Tw/Gwk/zy5do0/4zxcfGcPXze6WOnDpylTb6eydbEf1ySS/5GbyPeOc1OH0tOzoAcaJ2srRhMevzyJl9iQnk0GUrsQohQIcRhIcR+IcRPQoj0FSpREvn4eTNzTyivDmtB0QqFqNwghFFLB9P+nVfcHRpgT2hRt6Np2ucFfrg4l1/vLOT7yDm81Ov+olv9jrUoVqlwYnLXaDUYvQwMmtkrXaPPv1fucTqKjrXG8fdvjp2RAMw5zBQJKej4gJQONV0ALp+5yqyh33L28HmeaVgR/UNt4IxmAz0ndnR43ulD57h703Fe3hJtZcPCrcn9SA40Wk3igS5nLFEWvhnzPdtW7ErzNV2tx0cdMHol/QRiNBvpPKZNuqedarSo6vQ5QqPhhc7/y1CciqOMjtjXA+WklCHAEWBExkN6cvn6+9Dt/bbMDAvl43XvUa2J61qgPSopJT9O+Y1WAT1oFdCDNvle45cv12AwGRxqjOgNeiZvGsvQ+f2p37E2Lw9ozLSdE2nQqU66XtNg0judL9dqNcn24QzfcYRTBxzr1Ty8L/5BMXctWGNiOfBnOG0GNyO4TCB6o57AEgUY/s0A6icURksSg06b7K6QtDRFuUcIwcsDGmNMoQGJJcrC0kk/p/marla5fnnG/DiUQuWC0Oq15A3KQ/+p3XllQJN0X8tkNjJpw2jyBObGy8eEl6+JHLl9GbdiOLme8k/9Akq6ZGiOXUq57oGbO4DWGQtHcbX4uHiO7jmBzqCjaIVC6S749OuMtXw16rvEefVb/91hzvBFGM32Nm0P0+q01GnzHHXaPPfIMdduVY3ZwxY43C80gjqvOr/ung3/JjnN+uBzNBqN02mae2LuWji88xhzD3yWamxBJQuQ6yk/hzIHJrORxq/VT/X5D+o6ti23r91l7fxNiZ2gHnbt4o10XdPVqjaqRNVGrpn/Ll65CItPz+D4vlPEx8ZTrHLhdI/8lbRx5Rx7D2C1C6+nZNCuNWG0ydeT4S+M563/jaZTkf6c2H86XddYMG6ZQ3GveztGMkuup/x5+6t+GLwM9tGdjwmDSc/Amb2Trejn4++dZH3iHoNJT56n/Z3WkXnQyX9P0y6wNx0L9eXb979PtnaKEIKxy9/GN5cPXr4m9EYdRrORKg1DaNwzfUfytTotA7/sxeKzM/HydYxPq9NQKZtt5xNCUKxiYUpWLfbEJHVLtIUZb33Ny/5daeLVgVHNJjgMDFwt1X3sQogNgLOz7SOllCsSvmck8AzQUiZzQSFEb6A3QMGCBaucPp2+BKOkz+UzV+hRZpDDdrUcuX1Ycm52mppd2Gw2XtS1dfqYVqdhjfXR66ykxe3rd9i5KgwpJc82rpRiyd8bV27SqXB/hz9CJm8jC05M59D2I+zdfICVs9Y77DxCgEYjsMXb37oGk56Szxbnk81jk/2EY4m2sG3Fbq5fvEG52qXS3YHpYWu/3swXb8xLjF+r12L29WJmWOgTUwcluxr2wvsc+Csi8QyG0Ah8/Lz5OmJquuvju2wfu5SyQSov1BVoCtRPLqknXGc2MBvsB5RSe10lY9Z+swVbnOMCZJw1np2r9lDrlWqpXkOj0fBU4bxcPOnY2LpAscyrI36Pj5839TrUcppcpZRsWvwnK6avJupWNLVbV2fEwgGEdv8ycQ5co9UwZtlQ/AJyUqN5VWo0r0rZGqUI7TaNWGsctnh7l6M4a3xiUgd7DfWj/5zg4LYIytUs5TQ2o5eR59vVdNnP+mK353mqcF6WTlrB5dNXqFSvPG2Ht1CdlDzcif2nObT9aJKDddImsURbWTV3I+2Gp/+gV1pkaI5dCNEIGA7UkVI6luZT3OZa5A2n87bx8fHcvHIrzdfpPakzH3f9IsnIX6fXkbuAP0smLKdRj3rp7tqUmrMR55nabw77fj+E3qinfsfa9P20a5Ka4dPfnM/arzcn7o+PnLSCgKA8LDg5nRN7T4OAsjVKOhy+qdPmOYLLBLJy1nquXrhG9O1o/lnvWDUwPi6OI7uPJ5vYM0OFOmWpUCdr1JlRXOPUwbNotI4DE2u0lSO7j2fa62Z0jn0a4AusF0LsFULMdEFMigtUeSHE6XY6KSGkTpk0X6d2q+qM+m4whcsXxGg2ojPoEBrB3k0HWDh+GV1LvEmEC9+gN67c5M3nRiYeaLFGW9mwYCvvPlAz5/KZK6yetzHJoSdrTCz/XbjG70u3U6GuPUEmd6KyUNkg+k/twZhlQ3mu+TMYzY6HinQGnVsrMyrZQ2CJ/E4PZhlMeopWzLzSERlK7FLKYlLKICllxYSv110VmJIxzzV7hiIhwUmSlsnbSL32tdJ06vBB1ZtWYfa+T3ixu/0g0r1659aYWKJvRzOpyxcui3vV3I3E3I1Jcoo01hLLsbCTHN1zAoDwHUedJu2YuxZ2r9vrcH9K6nWo7XAtjVaDdw4z1V5y/3ZTxbOVqFKUIhWC0Rvvv8eEsDc+b9LLeeE1V1AnT7MprU5L6MYx9JrUmdLVS1ChblmGzO3L4DmP/rf3z+V/O5RNBYg8eYnrl29mJNxEu1aHOd17Hhd7/6Rmrvz+SCfVyLQ6bbpH2b7+Pny2dRxFQoLRG3ToDDpKVy/OZ3+MT3bEryjpMWH1KOq1r4XeaP+0W65WaT7/6wP8M/HErXrnZmMGo54W/RrRol8jF13P+dtFStAbXPNWcrZQCxBnjaNAcfvmrLI1S+IXkBPLXQu2Bz7m6gzaZMvPpqRw+WBm7Z3MjSs30eq0GWq0oSgPM/t6MXR+f4bM64eU8rHUtVcjdiXNmvRq4HDEXKPVULZGSZfVs4lJpiG20AgCAu3b/jQaDaEbx1CkQiEMJj1ePiZy5PHlvaWD0z3N9CC/gJwqqSuZRgjx2JqVqBG7kmathzTj4LYI9m4+gBACoRH4583JOwvfdNlrFK1QiH1bDjrc7+Vjwi8gR+LtfMEBzPhnEpEnLxFzJ4aCZQKfmAMvipIaldiVNNMb9Hzw6wiO7zvFkd3HyVcoLxWfL+vSUUiPjzowrMH7SbZXGs1Guo1v57QWS/7C+Vz22oqSXagOSkqWc+DPcGYPW8DJf8+QO78/Hd9rzQud01dITFGyo7SePFWJXfFosdZYou/E4Ovvk+4CZ4riaVRrPCVbi4uNY/bbC1g5ZwO2eBs5cvvSb0r3DFWVVJTsQu2KUTzStAHzWDV3A9ZoK3HWOK5FXie0+zT2bj7g7tAUxe1UYlc8TtTtaNZ/+7tD5UpLlJWF45e5KSpFyTpUYlc8zrWLN5LtVhR5PHPrXCuKJ1CJXfE4eYNyOykoYD8AUuKZjNVFV5TsQCV2xeMYTAY6jWqV2DT7HqPZQJexbdwUlaJkHWpXjOKRXn27Bbny+7Pko+Vcu3SDUlWL0XNiJwqXz7xSqIriKdQ+dkVRFA+h9rErShpF3Y5m2ae/smnxn+iNepr2aUDTPg2TXaBVlKxOJXbliRZrjWVgzZFcOHYxscn1nOGL2LflEKN/GOLm6BTl0ajFU+WJ9ufynVw6dSUxqQNYoizsXL2HE/tPuzEyRXl0KrErT7R9Ww4SfSfG6WPhO4485mgUxTVUYleeaPmC82Aw6R3u12i15C6Qyw0RKUrGqcSuZAopJfHxjr1LAf6LvM7sYQt4o9oIJnSayrGwk485uvsadnsejTbpPwOhEXj5mKjaqKKbolKUjFGJXXEpqyWWL9/6ima+nWlsaE+/qsM5vPNo4uOXTl+hV/nB/DR1FRG7jrH5uz8ZVHsUO377xy3x5s7vz4TVIwkIyoPRbMRg0lMkJJjPto5Tu2IUj6X2sSsu9X6ryexcswdr9P3FSJO3kZlhoTxdLD8Tu3zB5iV/You3JXle7vz+LD4787H1hHyYlJLzxy5iMOrIWzDALTEoSmrSuo89Q/+KhBDjhRD7hRB7hRDrhBAFMnI9xbNdPnOFnauTJnWAWEssyz75FYCwDfsdkjrA7et3uBZ5/bHE6YwQgsDi+VVSV7KFjA6PQqWUIVLKisBvwGgXxKR4qPPHLqI3Oi5ExsfZErcO+ubycfpcaZN4+XplanyK8qTIUGKXUt564KY3OC26pzwhgkoWSLIf/B6tXkvxKkUAaD24mUPxLr1RR7WmVfDOYX4scSpKdpfhCU0hxIdCiLNAR9SI/YmW5+nc1G5VDaOXIcn9BqOe1oObAfBi9+dp1rcheqMe75xmDF4GytUqzdD5/dwRsqJkS6kungohNgBPOXlopJRyxQPfNwIwSSnHJHOd3kBvgIIFC1Y5fVqd6suO4mLjWPjBMn79ci1Rt2IoW6sk/ad0d6i6eOu/25w6eJaAwNzkL5LPTdEqimdJ6+Kpy3bFCCGCgZVSynKpfa/aFaMoipJ+j2tXTPEHbjYHDmfkeoqiKErGZbS640QhREnABpwGXs94SIqiKEpGZCixSylbuSoQRVEUxTVUSQFFUZRsRiV2RVGUbEYldkVRlGzGLUXAhBBXsC+2Poo8wFUXhpPZVLyZS8WbuTwpXk+KFR4t3mApZaoFjdyS2DNCCLE7Lfs4swoVb+ZS8WYuT4rXk2KFzI1XTcUoiqJkMyqxK4qiZDOemNhnuzuAdFLxZi4Vb+bypHg9KVbIxHg9bo5dURRFSZknjtgVRVGUFHhkYve0lnxCiFAhxOGEmH8SQvi5O6aUCCHaCCEOCiFsQogsuctACNFICBEhhDgmhHjH3fGkRggxXwhxWQhxwN2xpEYIESSE2CyECE94Hwx0d0wpEUKYhBA7hRD7EuJ9390xpYUQQiuECBNC/Obqa3tkYsfzWvKtB8pJKUOAI8AIN8eTmgNAS2CruwNxRgihBaYDjYEyQHshRBn3RpWqr4FG7g4ijeKAIVLK0kB1oH8W//1agHpSygpARaCREKK6m2NKi4FAeGZc2CMTu6e15JNSrpNSxiXc3AEEujOe1Egpw6WUEe6OIwXPAseklCeklFbgO6CFm2NKkZRyK3DN3XGkhZQyUkq5J+G/b2NPPk+7N6rkSbs7CTf1CV9ZOicIIQKBl4C5mXF9j0zs4NEt+XoAq90dhId7Gjj7wO1zZOHE48mEEIWASsDf7o0kZQnTGnuBy8B6KWWWjheYAgzDXvLc5bJsYhdCbBBCHHDy1QJASjlSShkELALecG+0qceb8D0jsX/MXeS+SBNjSTXeLEw4uS9Lj9A8kRDCB/gRGPTQp+QsR0oZnzA1Gwg8K4RItZObuwghmgKXpZT/ZNZrZLTRRqaRUjZI47cuBlYCTnutPi6pxSuE6Ao0BerLLLDHNB2/36zoHBD0wO1A4IKbYsmWhBB67El9kZRyubvjSSsp5Q0hxBbs6xlZdaG6JtBcCNEEMAE5hBALpZSdXPUCWXbEnhJPa8knhGgEDAeaSymj3B1PNrALKC6EKCyEMADtgF/cHFO2IYQQwDwgXEr5qbvjSY0QIuDeTjMhhBfQgCycE6SUI6SUgVLKQtjfu5tcmdTBQxM79pZ8B4QQ+4GG2FeXs7JpgC+wPmGL5kx3B5QSIcQrQohzwHPASiHEWnfH9KCEheg3gLXYF/a+l1IedG9UKRNCLAG2AyWFEOeEEK+5O6YU1AQ6A/US3q97E0aXWVV+YHNCPtiFfY7d5VsIPYk6eaooipLNeOqIXVEURUmGSuyKoijZjErsiqIo2YxK7IqiKNmMSuyKoijZjErsiqIo2YxK7IqiKNmMSuyKoijZzP8Bot22h2hPzEcAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.scatter(X1[:,1],X1[:,2],c=y1)\n",
"\n",
"ex1 = np.linspace(-2, 2, 100)\n",
"ex2 = -(lr.W[1] * ex1 + lr.W[0]) / lr.W[2]\n",
"\n",
"plt.plot(ex1, ex2, color='r', label='decision boundary');\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Sklearn for comparison"
]
},
{
"cell_type": "code",
"execution_count": 60,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
" intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,\n",
" penalty='l2', random_state=42, solver='liblinear', tol=0.0001,\n",
" verbose=0, warm_start=False)"
]
},
"execution_count": 60,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from sklearn.linear_model import LogisticRegression\n",
"\n",
"X_train,y_train,X_val,y_val = get_train_val(X1,y1)\n",
"lr = LogisticRegression(random_state = seed,penalty='l2',max_iter=100)\n",
"lr.fit(X_train,y_train)"
]
},
{
"cell_type": "code",
"execution_count": 61,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Log Loss on train set: \n",
"0.16957970356257498\n",
"Log Loss on valid set: \n",
"0.1461889817725507\n",
"Accuracy: \n",
"0.96\n"
]
}
],
"source": [
"y_train_pred=lr.predict_proba(X_train)[:,1]\n",
"y_val_pred = lr.predict_proba(X_val)[:,1]\n",
"print('Log Loss on train set: ')\n",
"print(logloss(y_train,y_train_pred))\n",
"print('Log Loss on valid set: ')\n",
"print(logloss(y_val,y_val_pred))\n",
"print('Accuracy: ')\n",
"print(accuracy(y_val,lr.predict(X_val)))"
]
},
{
"cell_type": "code",
"execution_count": 62,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# plot validation set and decision boundary\n",
"plt.scatter(X1[:,1],X1[:,2],c=y1)\n",
"\n",
"ex1 = np.linspace(-2, 2, 100)\n",
"ex2 = -(lr.coef_[:, 1] * ex1 + lr.intercept_) / lr.coef_[:,2]\n",
"\n",
"plt.plot(ex1, ex2, color='r', label='decision boundary');\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Sklearn performs better in this case"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.6"
},
"varInspector": {
"cols": {
"lenName": 16,
"lenType": 16,
"lenVar": 40
},
"kernels_config": {
"python": {
"delete_cmd_postfix": "",
"delete_cmd_prefix": "del ",
"library": "var_list.py",
"varRefreshCmd": "print(var_dic_list())"
},
"r": {
"delete_cmd_postfix": ") ",
"delete_cmd_prefix": "rm(",
"library": "var_list.r",
"varRefreshCmd": "cat(var_dic_list()) "
}
},
"types_to_exclude": [
"module",
"function",
"builtin_function_or_method",
"instance",
"_Feature"
],
"window_display": false
}
},
"nbformat": 4,
"nbformat_minor": 2
}