{
"cells": [
{
"cell_type": "markdown",
"id": "630edd38-7fe6-4799-825f-0dbdc8d23830",
"metadata": {},
"source": [
"Submit your answers to gradescope before or at the latest at 12:50pm."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "81544e81-b6ad-42c9-8b85-b269e8e3b44d",
"metadata": {},
"outputs": [],
"source": [
"using Plots"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "97b0ba8e-735d-446a-8ad3-745471a7ef86",
"metadata": {},
"outputs": [],
"source": [
"using FFTW"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "5d8bd6eb-9355-4878-aecb-f29f91e1aed9",
"metadata": {},
"outputs": [],
"source": [
"using FastGaussQuadrature"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "3c1f6e37-507e-423a-8852-1ece40ba8b33",
"metadata": {},
"outputs": [],
"source": [
"using JuMP\n",
"using GLPK"
]
},
{
"cell_type": "markdown",
"id": "731f368a-a782-4c8a-a5ca-b4e8516d7345",
"metadata": {},
"source": [
"# Question 1"
]
},
{
"cell_type": "markdown",
"id": "b1a268da-c2b4-4595-a5d5-5f610ef9efc8",
"metadata": {},
"source": [
"Consider a composite product with three components.\n",
"\n",
"The product fails if the first component fails or if both\n",
"the second and third component fail.\n",
"\n",
"The life span of the $i$th component $c_i$ is \n",
"normally distributed with averages $\\mu$ \n",
"and standard deviations $\\sigma$ listed in hours below:\n",
"\n",
"$$\n",
" \\begin{array}{c|c|c}\n",
" & \\mu & \\sigma \\\\ \\hline\n",
" c_1 & 500 & 100 \\\\\n",
" c_2 & 400 & 150 \\\\\n",
" c_3 & 300 & 200\n",
" \\end{array}\n",
"$$\n",
"\n",
"Define a Monte Carlo simulation to estimate the average life span\n",
"of this composite product.\n",
"\n",
"Run at least 10,000 iterations in the simulation."
]
},
{
"cell_type": "markdown",
"id": "b3f566b9-9ab3-4520-87a0-b72862ddb53b",
"metadata": {},
"source": [
"## answer to question 1"
]
},
{
"cell_type": "markdown",
"id": "7cb3e781-0479-4167-8ca7-f5169eca1483",
"metadata": {},
"source": [
"We adjust the ``mtbf`` function from the lecture."
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "9d6e6c21-6f2c-4910-afd5-15b04837ea0e",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"mtbf (generic function with 2 methods)"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function mtbf(means::Vector{Float64}, deviations::Vector{Float64}, N::Int,\n",
" verbose::Bool=false)\n",
" (m1, m2) = (0, 0) # first and second moment\n",
" sample = [0.0 for j=1:length(means)] # work space for each sample\n",
" for i=1:N # run N simulations\n",
" for j=1:length(means) # randn() has mean 0, sigma 1\n",
" sample[j] = means[j] + deviations[j]*randn()\n",
" end\n",
" if verbose # for debugging purposes ...\n",
" println(\"sample : \", sample)\n",
" end\n",
" lifespan = min(sample[1], max(sample[2], sample[3]))\n",
" m1 = m1 + lifespan/N # update the average\n",
" m2 = m2 + lifespan*lifespan/N # update second moment\n",
" end\n",
" return (m1, sqrt(m2 - m1*m1)) # mean and deviation\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "1d6770a9-349d-43e1-8eb8-475cbf739e26",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The expected life span is : 408.5724635789825\n",
"The standard deviation is : 103.83450015884672\n"
]
}
],
"source": [
"(mu, sigma) = mtbf([500.0, 400.0, 300.0], [100.0, 150.0, 200.0], 100000)\n",
"println(\"The expected life span is : \", mu)\n",
"println(\"The standard deviation is : \", sigma)"
]
},
{
"cell_type": "markdown",
"id": "77cf8d10-c8a9-439c-a1bb-febb0c868d22",
"metadata": {},
"source": [
"# Question 2"
]
},
{
"cell_type": "markdown",
"id": "b412af6a-e5c9-436f-82f6-4a4f716c321b",
"metadata": {},
"source": [
"Let $f(t) = 5 \\sin(4 \\cdot 2 \\pi t) + 2 \\sin(8 \\cdot 2 \\pi t)$\n",
"represent a signal, for $t \\in [0,4]$.\n",
"\n",
"1. Use the FFT to compute the spectrum.\n",
" \n",
" Explain how from the spectrum you can\n",
" recognize the two components of $f$.\n",
"\n",
"2. From the spectrum, remove the second component of $f$.\n",
" \n",
"3. Compute the inverse FFT of the spectrum\n",
" with the second component removed.\n",
" \n",
" Make a plot of the new signal, for $t \\in [0,4]$.\n",
" \n",
" Explain the differences with the original signal."
]
},
{
"cell_type": "markdown",
"id": "354ffb7b-22f0-4a4c-8789-5d3dbe91b2fb",
"metadata": {},
"source": [
"## answer to question 2"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "799c9528-6f11-486c-8c29-f50e039d6c4a",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"
"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"dt = 0.01\n",
"t = 0:dt:4\n",
"y = 5*sin.(4*2*pi*t) + 2*sin.(8*2*pi*t)\n",
"plot(t, y, yticks=-24:4:24, label=\"signal\",\n",
" xlabel=\"Time in Seconds\", ylabel=\"Amplitude\")"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "c2841c11-ec7f-423b-90fb-b3eb08d44a41",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The plot has two peaks. One at a frequency of 4 hertz with an amplitude of 5 and one at a frequency of 8 hertz with an amplitude of 2\n"
]
},
{
"data": {
"image/png": "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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"
"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"F = fft(y)\n",
"n = length(y)/2\n",
"amps = abs.(F)/n\n",
"freq = [0:79]/(2*n*dt)\n",
"println(\"The plot has two peaks. One at a frequency of 4 hertz with an amplitude of 5 and one at a frequency of 8 hertz with an amplitude of 2\")\n",
"plot(freq, amps[1:80], xticks=0:1:20, label=\"spectrum of signal\",\n",
" ylabel=\"Amplitude\", xlabel=\"Frequency (Hz)\")"
]
},
{
"cell_type": "markdown",
"id": "0332ff1f-af94-47f7-b0a6-84b0f8431f5e",
"metadata": {},
"source": [
"We look where the high peaks are in the spectrum."
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "9fa80f9f-d8d1-4c49-896d-23b019cd88c4",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2-element Vector{Int64}:\n",
" 17\n",
" 386"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"findall(x-> abs(x) > 4.5, amps)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "8024487c-95fb-4974-81cd-a4230e7599d7",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2-element Vector{Int64}:\n",
" 33\n",
" 370"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"findall(x-> 3. > abs(x) > 1.5, amps)"
]
},
{
"cell_type": "markdown",
"id": "630787ff-9824-4df1-a98d-b542aa4612d0",
"metadata": {},
"source": [
"We remove the second component."
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "1174c895-9b45-4f70-b5ca-9c8bf2f7fbd4",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"7-element Vector{Float64}:\n",
" 0.0\n",
" 0.0\n",
" 0.0\n",
" 0.0\n",
" 0.0\n",
" 0.0\n",
" 0.0"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"filtamps = amps\n",
"filtamps[30:36] = zeros(7)\n",
"filtamps[367:373] = zeros(7)"
]
},
{
"cell_type": "markdown",
"id": "3292d12f-0392-41de-8516-f614646072a1",
"metadata": {},
"source": [
"We plot to verify that the second, smaller peak is gone."
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "9b2d1a3e-ed29-4628-90f2-c7c80a9916ea",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"
"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"n = length(filtamps)/2\n",
"amps2 = abs.(filtamps)\n",
"freq2 = [0:79]/(2*n*dt)\n",
"plot(freq2, amps2[1:80], xticks=0:1:20, label=\"Filtered Spectrum\",\n",
" ylabel=\"Amplitude\", xlabel=\"Frequency (Hz)\")"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "912a102d-e534-463d-b532-1fe8f467111d",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAlgAAAGQCAIAAAD9V4nPAAAABmJLR0QA/wD/AP+gvaeTAAAgAElEQVR4nOy9eZRdVZU//rlvrFevXo1JZSJkQAYJoUVQMLJEdIlLtFu0W2gBFenWlsZWVy9ttBct0AICtogBFWWhq1sbWK20tHyhB/GHBpmUMA+KkSEhSc3Tm8f7++NWVWp499599tmnKpU6n7+SSuW8++65dw+f/dn7OK7rwsLCwsLCYrkistgXYGFhYWFhsZiwjtDCwsLCYlnDOkILCwsLi2UN6wgtLCwsLJY1rCO0sLCwsFjWsI7QwsLCwmJZwzpCCwsLC4tlDesILSwsLCyWNawjtLCwsLBY1rCO0MLCwsJiWWPxHeHnP//5RqNB/GXXde1MuMVFvV5f7EtY1mg0GvYVWFzYV2BxQfcXdDiL/lKl0+nBwcHW1lbKL5fL5UgkEo/HTV+VhR+y2Wwmk1nsq1i+KBQKyWQyGo0u9oUsX9hXYHGRy+XS6bTjOIJrLn5GaGFhYWFhsYiwjtDCwsLCYlnDOkILCwsLi2UN6wgtLCwsLJY1rCO0sLCwsFjWsI7QwsLCwmJZwzpCCwsLC4tlDesILSwsLCyWNZaYI7zheeeHf1zsi7CwsLCwOIQQW+wLUMNYBWX58ToWFhYWszA+Pr5r166m/1QoFIiTsCxksXnz5q6uLhMrLzFHmIxYR2hhYWEcN91007e+9a21a9fO/yfXdWXne1lQ0NfX97GPfeyqq64ysfgSc4QtMWRLi30RFhYWhzpqtdonP/nJyy+/fLEvxGIS11577ejoqKHFl1iNsCWKkp38bmFhYWEhB+sILSwsLCyWNZaeIyxaR2hhYWFhIYel5ggjrs0ILSwsLCwEsdQcYcwpW0doYWFhYSGHpeYIbY3QwsLCwkIUS88R2hqhhYXFssUDDzxwww033H///ffff//DDz8M4NVXX/33f/93c59488039/f3h/7a3Xff/eyzz4p8YrFYvOGGG0SWImKpOUJbI7SwsFiu+K//+q8LL7ywXC4DuP/++x966CEAv//976fdxhlnnDExMSH7odddd92+fftCf+1nP/vZ008/LfKJuVzuC1/4gshSRCy9hvpSbbEvwsLCwmIx8OCDD55zzjmXXHIJgNNPP33+L9x3333VanXOD4vFYiqVmvPDSqVSrVbT6bTf79Tr9UqlMv8/TqNWqxUKhfb2du+vt9xyy8x/LZfLkUgkHo/P+V9Nly0Wi/F4PBZbNH+01DJCWyO0sLBYlrjsssu+973vffvb3z7iiCMefvjhf/zHf7zuuutm/sJf/MVfuK574oknHnHEEQ8++CCAr3/96xs2bDjuuOPe8IY3PPHEEwCGhoZWrlx51VVXbdq06YILLqjX65deeunhhx++ZcuWt7zlLdPjVb/xjW+sWbNm69atn/rUp1zXnXMljUbjoosuWrdu3SmnnHLYYYc98sgjAD7+8Y//6Ec/AlAqlc4777wNGzZs2bLl8ssvP/zww73/deyxx27fvv3oo49ev379+973vkqlAuCpp5469thjjzvuuPXr13/wgx/M5XJmb6IPllpGaB2hhYXFYmCsgscG57oEc1iVwtbuWRNNr7jiivHx8c7OTm/w2x133JFIJGb+wk9+8pNIJLJz586enh4A//mf//nDH/7w8ccf7+npufvuuz/84Q8///zzrusODQ3lcrm9e/c2Go2bb775oYceev7559va2m655ZYLL7xwx44dO3fuvOqqq3bu3Llhw4bt27d/97vfnXNtO3fu/MUvfrFnz55EIlEsFj2qNpvNlkolANu3b9+3b98rr7ySSCQuuOCCsbEx73+Nj48/8sgjL7zwQr1e37Zt25133vnhD3947dq1O3bsWLFiRa1W+8hHPnLTTTd98YtfNHVP/bHEHGEygpIdum1hYbHgeHzIvfbphQvDt3Q5N5wS1Vnhjjvu2LZtm5cIplKp/v7+V199ta2tDYBXgYtEInfcccfb3vY2L6Vbv379ww8/XCwW77nnng9+8IMbNmwA8Ld/+7fzPdPKlSsHBgauv/76s84665hjjpnDc/7P//zPJz/5yZaWFgCf/vSn77rrrul/+vSnPx2Px+Px+Gmnnfa73/3OW+rRRx/9/ve/PzIyks1mH3vsMZ2vzMYSc4QpmxFaWFgsBt6x1nnH2qVkMPv7+4eGhn784x97fz377LO9QzOi0Wh3d7f3w4GBgSeffHJwcND764UXXlgqlUZGRrycEkAsFuvo6Jiz8saNG++9995bb7317W9/+8qVK++8886jjjpq+l8nJiamC4dz/u/0z5PJpEeN/uAHP/ja1772uc99btOmTfl8/g9/+IPcDVDAUtpXAC0xlOtwAXsIioWFhcUcxOPxen0yVzj66KMzmczXv/71mb8w7fOmf+fUU0+dI9HcvHnzfffd5/15YGBgYGBg/gdt27Zt27Zt9Xr9E5/4xE033bR9+/bpfzrmmGMee+yx9773vQB++9vfBl/wT3/60y996Usf+chHACxWOogl5wgdIB5BpY6kFmdgYWFhcQhiy5Yt11133cknn/y2t73tkksuOeWUU9asWXPqqacODw//3//93ze/+c05v/9P//RPZ555ZjqdPvHEE/fv3//oo49+9atfPf/886+88srrr7/+zW9+89e//vX5wtEHH3zwoYce2rZtW6PReP755z/2sY/N/NfPf/7zZ5xxRiwWa2tru+2224LPbjzqqKN+9KMfHXnkkU8//fTtt99+7LHHitwHVSwx1SisXsbCwmK54p3vfOdb3/pW78+nn376W97yFgAbNmw499xzvR/eeeedXV1dO3fuzGazRxxxxM6dOwcGBr761a/+5Cc/OemkkwC0trb+wz/8w/SCJ5100o4dO1588cWrr776nnvuOfnkkwF0d3c/8MADL7zwwvbt2y+++OIvf/nLq1atmnkZ69evHxsb+5d/+Zdvfetbn/jEJz71qU8BeN/73rd161YAb3jDG371q18BqNfr11577erVq73/dfHFF69cudL782mnnXbaaacBuPzyy0866aSrr7569+7dd9xxx9lnn+1d5Gc/+1ljd7EJnPnS2AVGOp0eHBxsbW2l/HK5XN7wk8iTH4yv9m1usTCLbDabyWQW+yqWLwqFQjKZjEYtJWIWV1xxheu69mBeBqrV6p49ezZv3lypVC688ML29vZvf/vb+st6B/Nec801uVwunU4HJ5qqWJoZYW2RnbeFhYWFRVNUKpX3v//9Gzdu3LRpU61Wu/LKKxf7isKxxGqEsNSohYWFxUGMdDr9zDPPLPZVqGFpZoTWEVpYWFhYCME6QgsLCwuLZY0l6QjtSUwWFhYWFlJYeo4wZQ+gsLCwsLCQw9ITyyQjKNXtbBkLCwuzeO6556bnk1ksOp555pnDDjvM0OJLzxHaGqGFhYVpnHLKKX6OsF6v2z7ORcG2bdsMrbwkHaGtEVpYWBjFu9/97ne/+91N/8nOlDj0YGuEFhYWFhbLGkvPEVpq1MLCwsJCENYRWlhYWFgsayw9R5iYVI1aWFhYWFgIYOk5QntIvYWFhYWFIJaeI7TUqIWFhYWFIKwjtLCwsLBY1liCjjCGom2fsLCwsLAQwtJzhLZGaGFhYWEhiKXnCJNWNWphYWFhIYel5whTlhq1sLCwWK646NHYE8PCudDSc4RtMeSsI7SwsLBYlnhxwhGvji09R5hJIFtZ7IuwsLCwsFgM5GpOJi685hJ0hHFkq4t9ERYWFhYWiwHrCAGgLYZs1YplLCwsLJYjslU3Exc+mH1JOkJbI7SwsLBYnsjXnDabEcYiiEescNTCwsJi2aFch+MgIe24lp4jhC0TWlhYWCxLZKtoi8mXxpaoI3RsmdDCwsJiuSFbddti8ssuUUdoM0ILCwuLZYdsFeKSUSxRR9hmHaGFhYXF8oOlRg/AZoQWFhYWyxA2IzwAWyO0sLCwWIawNcIDsBmhhYWFxTKEpUYPwDpCCwsLi2WIbAWZhPyy1hFaWFhYWCwN2IzwADJxJ1uxNUILCwuL5QUTg0axZB2hzQgtLCwslh1sRngA1hFaWFhYLENYR3gA1hFaWFhYLEPYPsIDyCRM9RFOVLG/YGJhCwsLi+WCviLGK0ZWzlbdtO0j9GAuI/z7R+qfe6RuZGkLCwuL5QFzhtRQRmjAt5qHIUf4Wt79z1caAKqNaHxJRggWFhYWi4xaA//3WqMB7M5FDm8TVnjaGuEBZOIwQY3e8Gzj40dFXtfuPNhvezMsLCwsOHh4wN2Qcf766Mg3nm2IL24d4QFk4k7OQEa4o8/90KbImeude/fI75+FhYXFcsC9expnrnc+tCmyo0/eY+VsH+E00jEUamhI3+SXs+7mjPOewyI/32szQgsLCwsOfr7Xfc9hkc3tzstZYUPqArkq0jYj9BBxkIohX5NcM1tFsYaVKRzb5eyaMOUIdw65lz9uxTgWFhaLiX9+ovGbQVNWbteEe2yX05NErYExUe1ooYZkFFH5hHBpOkIYKBO+knU3ZhwHyMQRczBSFlz7AH7ycuOfH2+Yq0GOlvGvf7C8roXF0sa//aFhyAQBeHjAveLx+k9eNmIoxitouOhMAMCmjPOKaFJoSDKKpewIhcuEL2fdTZnJPx/e5uzJG/FVv9zvfur1kb97yFRS+N+vNf5qR/3pEUvtWlgsVTw36l64o36PMaXCZx6q/80xkV/uN2Il9uTdaaXopowwO2qoQIil6wjbpDsoXs5iU2byFq9PY09OcnEP2SqeG3WvPyX6hwnXULfpjv3u1m7nkt+YcrTVBu54NWpocQuLpYIf7mpUjDEvl/ymflyXs8OMo8pV8fyY+41Tor8bM2KF9uSwPj35500ZvJyVXDxbRZvNCGciE4dwRphzN04FMuvbnN05+afw133um1Y6LVEckXFeki4je9jR537v1OjOIXevmYz20QH3k4/EDcWSFhZLAr8eiHz0l/VHBoy8BX1FPDLg3vq26AMGJJcAXsq6mzNOMopTeh0TH7E7766fMqQb25xXRA1pzlKjc9AWE84IX8limhpdnzZCjf6qr/H2NREAR7Q7fzSgxxksoa/onrjCOarDeUk0EJvGr/rcY9rdS35Tt57QYnnCBb78dOz1nc6vzISDL024R3Y4J/Q4gyW3vyi//h8n3CPaHQBvXxP51X75rHZPzl2fnqZGIUuN2oxwLjIJJycqlnk5605To4e3YU9ecO1JvDiOLV0AsDmDP07Ir/9AX+Otq5yII0/NT+NX+xtX/El1ooqdQ6ZcYdmKai20Ye4pemLIHa041705asKLAHgp627KOBEHp66OPNAn/xF/zGJzBgC2dOFFA1ZoTx6Ht03+eVPGkaVGbY1wLsQzwpmOcH3aCDW6N++ua3XgZYQGHNUTw+6bVkYAbM7ABPVabeDRAXfbSvf4bucP40YcYaGGVf9etZN9ApCrOS9lXXv6SgAeHnBX/XtVtr1qGrsm3OM63betcX4z6JooE7485ajetMJ5Ylj+RZjOCNelHRMFlN0zMsKNGeeVrCv4Gdkq2sxMBV2qjjATR07uQc9VUXfRkZj863ozGeFreRyWBoxRo3vzk2Vq8UDMw28H3dd1OB1xd3MGhqjXRwbcVBTn3l8fNqYdf7DfLZgxkR6+9nTjk7+umzBhHv720eibf+Z+fIeplOepEfeTv65f+5TBJpxCDeZinZEy/vL/q7fG8LCZj3gpi43pRnscR3c4vzFQJpyOyNe3Ya8BKzTtCA9LO68ZcIR78gfEMpk4Ig4m5CQ5uSoyifBfY2AJO0LBoHi47K5oOZBxH5Z29hdc2ck1tQaGSu7qyYzQiCPZV3DXtjowoFr28NSI+6YVDoDNGeclMzMHdvQ1Pn5U5M0rnf+324ghbrh47//Wtt5Ze37MlCH+5nONbBXfeMaUI3l6BLec6jxlzNHe8GwjW8UNz5pytC+Mucf/Z+09/1MzVGe+Z0/jpBXOhUdFdhjgFQG8lHU3pl0Ab+51njLQpzTtCNe2OvsK8uu/lMURGQDobcFYBbJJrQvsnSGWAbCixRkui30LmxHORVvcyVbE7u9wCT3JA39NRNCdxH7Rp3B/0e1NOd5MhMPTTl9BnlfZm8faVsCAanlqffewtANgc7sp1esDfe7b1kS2djsvmqFenx9zV6WcD250bttlxEoOlpCvun9/XOSZUVPU8d6ic+Zhzv6Ca2LcLoBnRtzPbYlUG+gzoNQAcPsfG+/f4ByWdp41c4teHHe3duNta4wMugTw0sRkw/G6ViPU4stTqr21rfIZYa2B1/LuhowDIOJgdcrZJ/oV+otoT6BlRoNVTxLDJbH1czVbI5yNNlFqdKiMFS2zftLb4gzK7R9mt9fEIljb6rwq7Uv2Ftx16Un2f6jkiusF9hawbpJ6NeJoKw38dtB9S69zdAdeHJdfH8AjA+4pvc7Jvc7zY0bWf2LYPaHHOa7LeXHcrRpwtc+Nukdm3GQUx3Q6zxlwJHUXvxtzj+t23tDjPGkm6XxuFN4WPGqm/eD3Yzi6w9nW6+wccksG0lqPGgWwthX7pA/xrjbQV5yssZnICF/NuWtancSU1V+Xxl7RrzBQdFelZjmq7iQEyxx2ssxcyFKjIyW3Ozlr/3paJPcPM7yUh00ZvCras1+soVhDVxIAog4OSzuvSut99hfcNa0OvIy2KJ/RPjHkHtXhdCRwdIfzezMZ4W8G3TevdI7rMpWOPDXs/kmPk4phfdpIUvvMqLul0wVwfLdjYn7QH8bdNa1OOgaTjtDd0uWcvNKUI3xx3D2qw2mL4/WdzuPS2uZqA/sK7vpWF8C6tLyj2p1z17Y6sQgAdCVRaUC2nr07j41tB/4qXiYcKaM7OesnK1qc4ZLYR+Rs+8QctIk21A+W5maEPUnJ/QOwJzeplPGwMuUMiq6/r+CuSzvTntZE0rZ3SuwTi+CwtHxG+8ese1SHA+DIDmfXhGuihvRwv/uWXud17c7evFs0IJl5Yth9Q48DYGu384wBR/X0iLu1C5PrG/DlT4+4f9LjAPgTM46wVMfuvHtku3NKr2OiId0Fdk1MPkVHdcgT+J6j8k7tNkFdvjQlGfUgnhQOFN3e1EwxBF4T/QpDpVliC0hnFDYjnItM3BEcuj0/kBHPCPfNzgh7khgSpV73F7Cm9cBfTcwE2DeVEWKyQ0N2eewrTNY40zGsSDp7pDPabBWv5Nyt3U4sgiPbnRcM6GWemukIDTiqZ0fcYztcAFu7jDjaZ0fd47oA4AQzjvB3Y+7r2p14BMd1OXvy8iO+9uTcjoTj2cp1BhzVyzPGbpigLl+bKsNPfYQw+zpcmmXoxMucTQypaEaRq7pttkY4E7Ij1obLbk9yHrUt6qj2FrBuhqNa0YIh0Yxw75RkdHp92esv1VGoHXjKNxuYEjfTChzVgd9Llwn/MO4e2T4Zzm/pcp6TdoTlOl7Oua/vdABs7cIzI7LLAx6v2NkAsLXbSI3w6RFs7XIAHNPh7DaQNHu8KIBYBEd3yLPHL47jqI7JP69LO3ulHZU3n8z7swnqcni2WGGtdKvfUBkrZ6wvnhEOl2epDmEgI7TU6CzIDt0eLqFnPjUqp/rFvFhvRYszJJxxTqZTHnpaHFlH66WD01/ARDfu3vykGAfA0Z3yZcJ9hQPrb+lynpXOqPqKbm/LpBLhmE7nD9IdJrUGRspY1QIAvSlMVIW17wD+MO4e0znpqNaknP1F4a/w7Ki7pXPyITJRY/v9uHt0x+T64lYe3kyMGQWOtdIZ1VDJ7WkxmBEOlWZF/OKxwvDs64enGpUzdHbW6FwY7SME0NMifCThTCsPYIU0NbovPy8jlHW0s69/ZYvw9WPG5B0AR7bLH488M2k+tgu/k844+wpYPRWLrE45fdJWfqDk9rQg4gCAA6xscQakHVVfcbLVFcDqVvRJqyJ/N4Zjuyb/bKLGtmvCPXLKEZpobxgqY6VJRzVcwooZGZU4+zo0Wwwhzh4PN6kxSVKjto9wLtpikrNGh8yLZQaKbm/L7IxQmBqd5ajEa5CvzfBS8Khd6eEv05N3AKxtxX5pKzwzKV/X6sj2iWLGQAMAXUmUG5CV7/cVsGbGFqxOCbf6levIz2C/15i5RQe2wAB1uW9GAUK8NwDAYHEWtSie1M5R7Yk72sGSu3KGWEZcsjdUclfMrRFKGqJs1W1P2BrhDMiOWDMtlqk0UG3MYrdXpsTFMu6aWY5KmNrdX5wlxlnR4gyKpiMNFwOlA19hVcrpl0539s9gj02kO31FrEod+Gtvi/BX6C+id4aVXJWC7OkEAyW3t+UA+706hf3SPfX9M27ROgN9eDNVkatTzmDRrYmyx/OpS1lfO1yes75ww/ucjDMdQ92VDNdGy5jbhyZNjaZtRjgTsQhijtgWDs5X/Yru3xyxFgxQo4OlWbHqCmnqcm9+lupVfP3+IroSiE89j70pDEhb4ddmfIVVKWegJDkOGMD+2XolcUfVV5wV66xuFWZfZ1K7ANZIrw+gf0bDtbgSBLMdbSyCFdKxyJy3TNxRDRl+iwdLWJma9ZPuJEbkIub5fWiCfYTehJCkmXPBl6ojBJCJy4xzrTRQrs+twXYnnRE50mCkPL9hX5gaHS2ja8Y42p6k8Pr7C1gz4xVa2eIMiWaccwYO9KacAdHrx+yMMBFBOoZRUXa3r4jVM26RuKPqL6J3xvrijrZ/dka7RpqdHqugJXpg/paJjHCw5K6cNTRYXBXpGqUuh2dP9ugS9VJoJo/vSTqC8vLReYauLY6aUNKZq5mSjGJJO8K2uJOrCTwl3qDROcRzdxLjVUj1dA+X56pSW6JIRjEhOBxn9iPYncSE3PVjXqtsTxKjZQjOJZ+jqu1OIietipzzEatSTp9ourAvPytjWyVdw+srumtSBq9/f8FdnZpZgxRWjfYVDihxYEB4XGtgrDLrRZMtQ7oetTjzLRAtQDRcjFZmtR/0JB1ByV6uigjQOpta7E6KqQK9659DfUEu6cxWTA0axZJ2hFKthEPzJL8AIg4ycYwJNfwOzxvhBlG9jNfvlZrxiEccdMQlha+jlcn5bR5iEbTFMSrXED1HVesAK1ogWIYs1lCozfoKq+Wpy1llVPn1C7MyNvH1+4tzqFHhMuqcjLkzgWoDgqcGDpbQk0R0xnsmq4ocKyMVQ2KGyexKSpIKoxVk4ojNWD8ZRTQi1qo4f+wLgG65PrHxCtpis67fQ0/SESF4czVTvRNY6o5QhBqdr5TxIMhuNw2UBAsAoxW3q8n6ksLX0TI6Z58EJit83Te7wIZJvYzU8thfnNUHCRM1ttmGXjxjGyi6q1pnZ4TC1OssYfPqlLBqdM58LwBrRGtsA6W568tmhPN5xa6EZKw5Upq7PrwajZCjms9LQbRPbHgeLzr9ESJ6C3Pd9FjSjlDqAIqxSvP9E5yb3tTXSjrCMrrmqYp7RCvt89l/2VbCOTIEAL0tGJBbf07GCekaW8PF4GxDbyLjnF2DNJsR9qYwUpZk1+dcP6Q7HAZmq2oBrGzBoNwtGmqiNHFG5ajRoWaOStDXDs2WjHoQpEbnjyWZ+ghnTOIumeumxxJ3hDKthOMVtDe7vz2Sj0gT9nVFUqyJZ7iM7nmPoGAHRcPFeLVJRijYhDRfWNubkmwY3zu7QAjpjG2whK7kAdUrDGRsfcVZNTz5GuHs9aMOeloktbtzaoQA1ok2jPfPOwOoS+4VBjBQdOfEah0J5GpiscJQae76ALrl2NeB2U2EU+tLZpwrmjnCTFxGDJE1NmgUS9sRxmRqhNkqMokmPxfsqTedEY6V3SYZoVyHxkQV6Xnsv2wHyPyMszclmRHOafKDdMbWN88Ky2Zs5ToKNXTOeIo6EyjXJZvABprcIkl2tH/++qLC1Pm9AT1yVh6TgzRnbXHEQbukkmBuEx6ArqQzKnQC+Zzjxz0IHpw7XxvvoV2ohpWvmWoixNJ2hELU6ES1eUYoGE76OELJGmSzGqEYtTtadruaiH0kHeH8W7Qq5fSbLPDI1gj7Zp/+AW/KmlzGNqfb3YPs2IH5GduaVknh6/yMTXZ+0/z1BXk/NJs/Bc9RmcyoJKnLeYMkZdf3E1u0J2QyQnOHEWKpO8K8xP2dqDQf29MhtH/wUY12JDAutP5IuYkjFGwlnNOk6GFlSlIsM/8tkq0RzqdeZdsb5s9kaIvDdcVUkfPTKYiWOYs1VN25EaEs+z0/KZc9vnx+jVDaEc5qUvTQlRCjLoeaiWUEhanjFXTMe4u75QooEz41pva4MyGR1OZrpgaNYmk7wphMH6FfRtiekNk/ACPzTieB5wiFSJX5vCJET2JqntGKUqPzeRXZGuH8r7BaNJ0a8YkVpL5C01hHkLQYaGrlRdsD+ueJZWQd1UDR7Z0nZhGkRptmhKIZW7OMMyH2FZo6QkElxITPIFC5jNDWCJshLdRHmK2gvVmNsEOoxgsfR9KRkKHO4ZOxdSXF+vxGK02pUbF0oVyfO4sV0jXCkfJcvZKnepUyk6PNtrgzIVZAaspOC/JyY5W5YiiIWmE0a5/oaRFdv4Te2VucisFxxPrw5s8Pg+gWjDaLdQTFMs0zQkFH6JsRypwUlKsibanR+ZASy0z4qHLb5TK2ph027XFnXC7jnG+FpRgJ+Lyigh1ITa+/V1T7Pv8jYhGkonKxSLNYQZA3a+qoRB2tWSucqyIemdWNDumMcLCE3nnssWBSODKvzAzRcHOi4rbPy3gEk/6m63fLlWnHq00cLeQavnPGzmDCknaE6bhMAWai4nY0zeiFHEmpjrrbpMwrWINsqtcSpF7nHzwtvX6T9hJBvRx8voJgOD8yrwYJoDPpjJmMdQQd7Wgz4bGglW/6iMo6wpFmlXjBjxirzFLtGlm/ScZmNulvlUuafQ1pwslK9LnZWaPNsQAZoYijGm5WA4doxtm0gCR1/fDh5ToTMGrl2+Io1VEVGjfa1EqaNvSyjqpznpXpFOTlmgmPu+TSqabrC6ZrdRf5ZiO4TDsqwVhqoqejjaAAACAASURBVNqkRiOZcfpkbFK74NeQLdVHaFWjzZFJyDTU+4llpDKepiYAQEdCjBoda/YRsuvPNwEdCUdQ7DPf0TpAR1xmC2oNFOrNrIxh6lLQio03S0e65KhRvwKS2P2ZN6IPQCaOSn3yeB1NTFSQiSMyL+AU9LVN5eWCj1DTGptoDa/50Gqpj2jqyCFnSPM1ty1mxTLzkI6JUaPNxU5C1PZ4MxMJUTFO8/YMyfWb8IrpGKoNmYxtqNn6kKMWh8voSsw9YATSTWDzh/t0JmSGS8GPGl06Ga1ft7VUDaxpjRZeh4aE5KruomA44xyvuJ0m9VBNYx3IOaoJn/UzcSFq1GaETZGWo0Z92yekRrg1ez5iESQkRsu7wHi1iWo0FUO9IXOSUdOMDUC7UMbm14orZYj9rLCsqtMo9epTw5OULDbl/aTSqaYFNshlbE3FPpBzVN5b3DyWkojVag2UG3PPSALQmcBEVeC8s2INEaf5qbbtQhHzeDMxDuQyCnPH02NJO8KMxGSZWgPVZs8fgPY4chKPYFOxlocOiTJbtopUtMnpJ5ArQzbl/SDHvo75hPOdSRlH1bS3AaKOypcaNal9F3TkzanXJMYqMh0mfo+QlPZ4vIKOZuFst5Cj8nuLpbbYUyrM/4Cog7aYwFvsx1tC6C12/Y9JSsVQdwUi8rwVyzRFWmLotl86CCDioDUm4Gv9atSYFKbqrj/uI9aCnPC16QEukCNVmlKv8KhFmet3m16/VEaVryHqHDh7fRpS148AatQkdZmIIBGR4V38knK5jNCXGhVxtH6OXC7j9H+LJaipQCshkLHlq0hGmofjEGoltEO3m0NENepXQPYgEiv5qVIh5EiyhtcHMNZMsgi5jMRPTyRl6JseUwU56tXPCgs6qrGmBaSEaAHJL6OS+IimYhksJUfVPJyV2oKAiFzEUfntL4T6uCaqrl/GCaBdwpDaodvNkYzCha5YI4AxgFAg49deA6EOhwmfGqTU+g0fYTrkqFG/DhMpRzvkc1KaFDVqusbZcDEx7xgsiB4DNNJM7APzt0hq3KhfLNWddEYkGsabBiIA0vHJRmFN+DlaABkRK+TPS2UkeKPxCvysHCS+Qt1Fpd68hiWCJewI4R1AoXd/A9IpCGVUAbGeiCPJGl4/X0Mq1kSYDvMdJlKqS98apND6TZUmkFO9ZqtojSI67xtEHLTFZJQIYxV3Uag/qYzTf3253oBmb5kDtMmEy76OSiRjG/fRxkPKyvk0EXpo1x4naTQdxFJ3hGntudsBgRiEhgP5qUYhpNcKeMRF1g/IaOWoVz9HKJMRNh0rAzntftPhWzBPvULO1/qyx0KOatg/I5Rpn/B/hETOePGjdgG0S7QH+EkuIZmxNf+n9oSAI/ebrzb5EdqGKFsxWCDEUneE+hlhgKQTUjXCwFjPcMYps35QDdKk8FqKl5t/BtP0+kZrnMkoohIdMn7rQ8jXlupwgVSziFvKlzed+QC5Pr+mc+chVJ1CGHUpU8MzWeAIsEIiTVB+3diTH6F9ko/R+WpY8o5QWy+zINRoUPuEADVaWUQxjoyV8fsI09SolNIhIF0Q+Qg/JQiEYoXg9WXELD56K6n2Bj9q1Cvz63+A3xlDkHJU/mIFGbGM4QJKQDgOiYwwb7KJEEveEWrP3Q6oIUPoEQ+kRgXaJ8LaMwxmtJ0JjGlbyYBWX6k+Qr/hPlJ9ck1PF/Egwu4GUaMSsYJfbwPkqFH/QYMyNU6/9aXGVvhlnBCS1AW2TywByV5wjUn/Fvk1KUphyTtC7YzQDci4pRyJUeoyW/XtAFmI9U3GwlK83IRP0uwdDJTX/gp+vB+EOihMZ4QBVqxbYv1iDQ6a9FlCbjhRQFIuwrsEZWwSJ3gHtk8I9BEGFVAklAQBkj0AGe1blDd5GCGWviPU7amfqCCwRmi2w0aK/Q+gRkVIG6PUaECZVkoJElDJFxmRFeBIupLQX99PCQKhWCFgfZFYarTi+q8vNZwoSMxidGyFyOkKAbyLccme1FscUCPUvkU5kxO3sdQdYVp78ktwxi0yomzCv8NGjJ03+4gbF+P4Xb+UajTgLRXJ2AJuUWfC0f8KAVZY5BEaqzQv4EGIFPGTpELusDC/Pj+pjwgRs4g4Kr+MUKh9wuhkmYDrhzcOU9MR2owwAPrUaHDGrR/I+M3S9SBCSgTNMpXgnUxPrgkgbVqiiGifGtrwOTfAg0hGFaCkMH2LFsLKa68fkHGmY6hon2FSrqPW8BVTiE1mMdnwbnpQYkDGmYqhoT0LNHgyif5JQUaPp8eSd4Ta9ze4T7M94WT1HkG/WboeMhKxZDYoI5Sidn2VGqZJFf3jfyeqaPPfAqkOmYD5WCLd1kYlhQEFHinJotEmM7+jLSbXl5nVGUy9GuV1ZCbLGKW+sv7aeADpuG4l3ujEbSx5R6hdI8zX3LQ/9dymTb0GiLUgNS7VdMYWSI3q837Bwmt9ajG4VVTKyvhZMX2ZAAKTcpn5W/4Td0ViqazhJrMAahdCvnxs8VSXIjXI4IxK35cHHxaYjuka6pzJidtY6o5Q/0jCYOpZn3oNaN8BkInrTsZBSDoiZIV9XlFPB1jSO2E8gLSB56j0rFj48CCj2nQhR+Xny0XSnQBSoUNIEhnUratN4AdLFvUlY94B1H7UkVQs4rvFEo482JHo36IwR6hNjdoRawFIa/cRBgdK+o422MqntR0tAqlLkSMbgzM2/TJ4aJld8xUN7XAyqhSQGUQZkHEKrR+QccqkO8GDKPUfIZODEoPHbmTi0B+xFhCLZBICI9xCv4L+LQoypCKGerGo0SeffPK222779re/7f31tddeGx4eNngt6pCpEQZlhAKzTAOsfCICByhrZ1R+HxGLIOroZ2xBvFZGe9BigCMXWj/YSuquX6rD8RkIgAWo4UmUmQMeoUQEUQdFvbcsW3UzJqnLgFZXSCTNIetrt2dUGnCBhP9hfvoZrQvfRxQSlfLgjFM/I8zXFkMsMzY29q53veuEE04477zzrr76au+HV1555dlnn23wWtSRjjt5ozVC/VmmgVZ+8iM0HpFgKwyJjC2kVVY7IwmZW69tJYPLtPo1wrC5+wLhfECrqEhGmA18SvUztjDqUtdRmX6EgtMp/UcoF7h+PIK43nCcbFg6pb/FwbNA2/QN9aK0T1x00UXPPvvsXXfd9bOf/Wz6h+edd96OHTtyuZzBy1GEQKAR+Ii0xlDWO2wsmBqFtt4n2AR46+tnVAFvqT71F5ax6a4fVqbVNQFhGa1Z4a6UZDHI0Gt/RIAjh4xk0beMDSFHHmAl9Lc49Ox1zaQwVw3pRtccdOcCxcAankRGGJSx6KOJIywWi3feeef27dvf//73t7e3T//8mGOOqdVqe/bsMXc1qtDM2FygVEfKP51ytMuEwSYG2oY+mLSBSEboLymETMYWdpKZyYxNX1hrOh1xA3mhTBz5Ghp6rjBgbjskBukFxzr6WxA2Ol+X9wvJCEUkl4G8n6awNrT3oD2utcX56mTLrx9SMZTrWk/pIpxHODIyUq1WjzvuuDk/j0ajAAqFgsHLUUSrXqBRqCEZuH/wknqNMmEuzFG16XXYBJsYiHSABDaB6ZdRJ6pB1OWSqEEGq1I1M9pCDckIYj4FpIiDlHa4HfwU6QtfgztYBLYguENG+/pDYkERajTwLdYOl0McoSZ1GToR2wFSMS12dxEmy/T09CSTyWeffXbOz3/9619HIpFNmzYZvBxFaIplKEd7aCadoWInTUdFoEa1XqFaA5VG85PqPMjUCE1a4dD2CQErH9wkp10AC7YyEtRlcKul7vqmDzsLkFxCQk8UfP0tUd3JLMGSSwhQoyGPkKYVojT5abKjiyCWaWlp+cAHPvDFL37xueeec5zJr/fEE0987nOfe/e7393d3W3wchShKZbJ18L3T9MRhj7imjW8gIne0+tr1SADJ+PAcyTafX6Bc+vNU6+a1x9Yg2yLo1jTKzOH6a00fbkbRp3pHxARmnHqbnEIdalL7QY7Qmi3H+RqIbyRZiwS6qja9N5iSm+DZk99vuqmF76h/pvf/GYqldq6deu55547NDR0zDHHnHjiiY1G4+abbzZ3KQxoDt3O13yngE6jLaZlZUIPVtZ3tKE1QtM1SF3eKViyKCBmCbPCurxZkJXULzOHWmHNbmivwBP132QRsYnRGmRojdD08eiaeX8o76f5lIYW2DTf4hyNWtPMCENttQ6aO8Le3t7f/va3N95440knnXT88cdv3Ljx6quvfvLJJw8//HCD16KOlihqDdS4pAQlkNFsbwivERq2kpqONpR61R+OE9ZQrzvuNWCcMSTGyQYP0oR2QzRhC7TSkVBSwXwHi1lqV0DVGch+Q6KGZ/QtJqyvpYQIXR961GjDRalu1hH6rp1KpS6++OKLL77Y4IdLwAs0gi2RHwoEJdIUtcjMykN9rebwl9Ayp2lHm4njVY2GmtA+SNOqUa/M3HBDNFMBCFZSQDucD+5Gx4FWReYXCCUV2hNap0K6Xkbl/5SKjFgL7sNLRLRkh9kq1rQG/YImwR5aANN8i0MzNk1Hnq+F85Y6U7QKNbTGuM83DUt7xBqAVg0xUq4a3pui70iCHWE6Dh3qfNFjvUzCdMYp0EcYECdFHLRq6pXChLuaZdTgEXfQznhMb0G+GqR6hUisQ9kCvbc4XJuts34lpIaXjsPoW2yavQeQjvENkeneCczMCO++++4rrrgi9D889thjJq9HGToZW/B8tan1tVWjIbGYs7+gpfdZ0RJC2ryikbGFxnqma5AyksiwjCqYWwtbP8SRaBr64BoktKlLSg1SJ2MjrG+2zw9TW7w6xeV1QjO2yQIBf/21gRlnJu7sM2wl9DJCWo2Q+xGmu+kx0xFmMpnNmzdP//XnP/95Pp9/05vetGbNmoGBAc//vfe97zV6NQy0RvnUM0WSq1kjpMRiOjXkXBUb24J+QbNPMTzjjDlZjWNVKdSrQPuEyY8I7iPEgT45rqMNX1/z+sMCBfPr69cgQwYZao7FqLgZv0mg3vqGa3jpmNZbTLASWpJOSkao0/NtuokQMx3h29/+9re//e3en6+88spdu3bddddd0+qYwcHBc889t6enx+zlqEPnEcxXCapRvYwktENDX68V2qeoyWsZri6EU8elOmqNIG4tANUGam5QHyS0DfFExc3Egy5OO2MLm7+lV8OjpFPjGl1yoesno3AclOqTp3qpouGiEBbRalbiQ3kd/RpeqJLAqJXQViqYrTEtADXa5AWuVCrXXXfdDTfcMFMjunLlyptvvvmWW24ZGBgwe0WKSMdQ4J6uEKqKhl7PvksoU2uexBQ600Ez1gtdP6M3ViPUSjp6STklVtWcDBKuGtXMqAzX8IIHGkAgUAjXsulYyVwNrbHQ+VC6gxLDunV1eZ1Q1ajW+mGGrjWGosagvlArASAd54s5gidCi6CJIxwaGspms52dnXN+3tnZ2Wg0du/ebfaKFJHWMPSkQEbjFSrWkIyGpDJten2mlFZZ3VjPcI0wdKZBu8bMgdD2FQCZuFYTmOkaYagV1pQshopxtK+fsAUJ/lsQ2tsA7bEVBOpSU5IW+hbrWongLfAG9WmoDkkN9exblDNfI2xipFeuXNnZ2bl9+/Y5P9++fXssFjuoRqxBL2OjZNw6hp7yfJhuZdVdP5x00jIxlFhPx9CHXj8kqMuQ9gbDVlj/aAKjeiVKUq7zlBLX16MuzRc4wqhX0w3vpg2dTkZB6XPTRJPl4/H4P//zP3/mM595/PHHP/CBD6xevXpoaOi///u/H3jggS9+8YsHW5mwVaOMHFqgwmQgwyyQZMNOP4EE6WG0FZdSg9S5fqIVYxv6bCVknDH0VZ0Evc/uPH/9iYrbHliDzMSdrEYNb6IS0iSnSSoEz3qd/AiNDpbggQyT62u/BSEZoZ4kjfIWG7USODACjZN45apuW+AjiiUklpmJv/u7v+vt7b366quvuOKKer0eiUSOPPLI73znO3/zN39j9nLUofOWUsb2aAVKlBrkApTBTa4fiyARmex45axPiPV0VIuhs14112+4KIfNvNCkLkOtmGaNM/SksNYYqg2+XinUi0D7LQtdXyejKtfhOL7Hx3tYADGLbkZoeAvC5fcHt1jGd/lzzjnnnHPOqVarfX19vb29yWTS7IVwoSMsNn36BI0xMF0j1OLlKI7Ke4WYjpBQI8xMjuBixaqEueqZuDNSZlcvwmde6JZRK2aFwRRH5Q317WTNb5oIm7wD7ynlbjFxfbawltgtntNoIqK8xbpWgiKGMFojjPOpNYqh1kRIjBePx9evX3/QekEA6bhTYNdgaaeHsB0h5RUSmFwTVl0o1MB+hyhiE5231HS6QNoCHVUqwQprzt03zZtR9Eo6W2x6C0LFRNDrpg2d+QARVWewttz85BediD90fhb0GqYpxwRpovntv+mmm/L55mWNSy65xOT1KKMthle597dQJ6Q7Gnq2PMHEeGM2K40Q7qUpaoQmuYiDlii/2kwss7NrbJRYUkfMQtUr6YhxKEoNk4e96eqVCLyW6QLBAohltNh1kwWOYg0xJ4R21rQS1cAjRT1k9EZ0USaT6Ig5gifv6KP55V955ZX9/f1N/+lgc4Q6Yhma6tdsExumWgm71bNuCm85vT7bERrVg1FqeDqOJBvWGwC9cJ7Em+kfaWl4UCSlm1anQGA6HQndYtNvsU66swBWgtKEp6NXCp2VCr1btABimeYBRl9fnzsD2Wz2nnvuef3rX//zn//c7OWoQ8eKUSQeaQ1qkeio2K2ElIwTehkD5S3SEZtQanh61Gv4XHyt+2O4Q6Zch4OQPCAWQSKKoskCj562nlSmZW8B5chWncO8zIt9qG8x20pQmvB0zualiFl0HOHitE/MR1tb25lnnum67vnnn7979+5EglU0NwOdMnWh5qbCHhEdapHyCmFytLzy4qCJtaCp16IVkNizNIkZ52vc9oNsFYcHTlmEvh6KMKUvbzIQwZReJpT+aop8LVxJMVUg4OmVSJLCgSJjbQDIVrGyJWx9LVKB9Arwt5g2NoWdsVGOFoAG71KqIxZ4uoiHVExLzJHmSZbJUFj9pJNO6u/vf+GFF8xdDQNsLwJaRggNYSolFoZGrER9hXQMvWFhNIk301ufdP0aJ3kFd9NDT9VJfITaNI5HJlKjZsdKaHSAEDPag/gRooWz3K9A7D1g8y7E9XXOyyP6ch0oOMKHHnoIQFdXl7GL4UAn4y7W0UqY89vKjWUoBTBoPCLU6gL3FlUaaLhBp+Z60KyxkcrsJgswmgWq0PWTUbgAj7YgbjH7K9RdVAhnf5se96o5a5TU/mFyi2MRRB2UWEOPqUk/2xHS9AHsW0SkXlNRlOvcGhPNkOqApBqtVCq7du368Y9//MY3vnHmJO6DAex0rVxHNEysdeAjuBlb6FgTaGWcpFcoPXk2rzKvtRAZJyWjivPZ72w15AAd6NUgibGOd4u6GEoHOm9m8hHSy6hoZWBukxllrElGI2OmzJ/C1BYwDtAg1/CY7DQxY2NTo8R0LeIgEUWpxiHwFyAjJKlGvW7CCy644LLLLjN7OepgpwvFOlK0p5b9EdQaHt9R0V4hdqxHm3XbpqNEoBzpqcnLGV2faiWdbNXtSnKsGOURYlsx6iMUh46eyPSgS8pYDPb69LcgVw05/9ZnfZKVZz+lhbCztT2wt4Cun2iNolDnOMJFE8v09fWZ/Vg5tHKHmuerbittorkGdRkeq0JjCh9deG10/dYo+ljrN1wUaWdbG+W1UjHUXOYIsVzVXUmwfexYitLNDY10gcIreuv3sU5Ib7go1UnzvUxvcYV7qmWuip4wvRU02GOFGiE3HKc1WTF5F/r8M08v06MeDhLDNR00fy527NgxPj4+54fj4+P33Xef0athgM0rFgmlkemPYLPzRGqR9xXosSTPChOrC2ylQ6GGVNhJctDrIzTdREVnj3m3iNhBZXp9drqQJ4ygg27GFr4Fjg6vQ3sL2OFagfgW66xPJBW4Vo5uSHkZRYFsq9lo7gjPPvvs5557bs4Pn3/++Xe9611mL0cdySgaAKO+QJm47YE9xY1IjXqMAQMKGSHPStLSBXYNlVhg0zlykjICTecjqGIWbixlWixj/vpdWg1Sp0xL+gj2oDt6LHVwNkHlabEO+y2mzz/jHXnYcFFhEapKUGAKyuVyS0tYw85igOdI6Acm6IhlSI8gPyMkMQbsIzHp2n1eExVFKQPzkkKdj6D0HkBDj0NsRWWH80ReTqMGCdojpNk+QaqBscuoRreYMhAAByRv6usTqVG+koBcI2Q5Qo83MkuMzqkR9vf3v/baawCq1ervf//7mbO2JyYmvvOd72zcuNHw9XDgOZLQMUtzUCQ7QnYNj/wIOoMlppU8LE1ZHy+blBTyeUVaLJyOo1RHww0nUefAq0FSdlnHSmYIZWCNAhI11uGpIumxDu/IQ6Ijb42hXEfdRVRxi10y9afTfkD05WxHcjgtI3yFGy53EcLNdBxcsYWCIWXMP1qAM5gwxxHedtttf//3f+/9+cILL5zzq6lU6nvf+57xK1IHTylQqKmoRtl6LZIV03BUB0UrLr9ARXG0DtAaQ66mHOvkaTVI6HwFw1Y4Rxs3nInjlRxnfbq23uj9caYyktAjfOegUEMySnKfpr+C1uQXk5X4fBXrCI9QW9xhWjnC0QUepoSNaoaayHtpYtY3+PM///OtW7cCOPvssy+//PJjjz12+p86Oztf97rXdXZ2mr4gBrjUKImRgIYwldznx6whE6sX6ZjhGiRXr0TkFTEVi6g6wmzVpVw/Jh0VR3WZrYSfAQTzfX46W0BpdWVntMRHCFPhbAchd5kJYsYJDeqP+BH8WIe+xVxHa3T9XNUlNvkxM0LzE7cxxxEefvjhXr/8v/7rv27btq2np8f450uAdwCFUo1wf0F5fY9JItBmGo84rT2DLYxWaKjn84okw+eNM12j6KhyVdDX59cIjWrf6TVCk9p9jRokVUnB+wqUQaCT63PHpZpWjeZrpEGabXEnb7K9wZsuUqorzwQo1EDpIAI3Y6GrGnXQfAP+9E//dKl4QXCF0fSGel4sSeydgIaYhfiI6DTUU1ot+UoQMvvPM8RER85eH2TJnM4tIjmqBHOmQZ7abc08HYI4EABc6pK+PrshnbjFbFUqXdXJi3UKtLcY3LeA7qjYYpkFrRHed9993/jGNy644IIPfehD559//ujoaNP/cM899xi/KEVMzQJVpZ6p95dHXebI1Da/vYHafsDvI6SIcfjCcSVei5MumF0fdNUo9/jobIWW9Gv0Qa6j6a2YGXNFgf1mfITS+vwmH5MFCKpkzPAgRkzVgFaoGlKF9TmGdKFrhNVqNZvNVioVALlcLpvNmv5sKfDe0iJ56h3PytADGR3232xDPe0rxCKIORxShR5LMjNClXSEsX65johDOjQ8k2Ae9kYsA+soQSi3KBZBMqpQTZgGsUCFA0mncjhL5l04W+wVOChbrKNKJfE6XPabvms8Q0F/i1MxMBqy6apUHRz4hPe85z3vec97vD/fddddxj9ZDryMrVBz22mV+XTMKah37NMDMa1jmIgZoeFY0vsKqo6QXkDiCYMpB2d7SMeckbLyK0osEEJzbrvJ4URKW5xTN0nZKvkt42WE5DJzOu5MqLPHC/EWU8Us7G5d8ldgPUX5mttGm1yXinLeMnqsowOzpx0uDHiPYKFGOoMJ3D5CpT5TfkO90eoFmZTg1cCUCjyMcJj+CvHCbeJAABw4u5jxEWZbORXEJqwDHOgH6PDSEbqV564ffmqxhzR3rATl7GvoFDjIho5nSJX6CFnU6MLWCEdHR/fs2RP6H44//niT18MB3xESX1FeoERW/bZxZ0YQ2Vcd6pV+i3h6IvIt4lCL9Fcow1rfNPUKIEc4Ph5aYhmzYhZiugPuI0TXWzEfUSXq1eRb5g3qZMhe6X1ivFtEnJUKri9nEPIMHPiEu+66a34T/Xy4LnMkoDnw+vzo95eXEdLFMrz1y3U4tPaMWIQpjFblzVRBdyS8jE2tT9Hk+jpiFnoTGMNK0sUmPOrSdJ8fXQ/Fe8uUtpgRLlcacGg1yKiDeIRznh89VuA1vNPXT0VR5LRPLKxY5owzzrj33ntNf54JpGMYKCn/L9OzRuliqpYo6urHAClR522sGp4CdcmlFomxKo/dJZJO4J79q8DLsbxIqY6IQ4p1og4SUYWpgdNQyNh4sQ6t1RXcGh7xVFtw+/CUXgGelaB3i3sfoeQIGy7K5InVTLEMrc8SbGq0im7CMViaOPAN1q1bt27dOuMfaAC8WLVYd1tpnodXplbqA22NIl9Tmy+lFCh5NTzVk8Do7D9PzJKvgvgVMnHOTIN8DasJw6XAbTKjbwHvdAV6gQ1T1KWyqtOwXkmJPd6XV1p7cv0VtIMAmGVmsqNidhurv8VKZ/96gySJ/4FnSOl9ijzV4cI01Ad9QqVSeeWVV/bu3btq1arNmzcfnEdPgHvMlUJGyFKl0mNJTE28VZovRTzaYnJ9pt6HXF0wrCfijR0hzgTRWV8hnWLdf6KXAtDG5bUMJ/1mb5EC9cqkdsnCY1aln/6IgkWwEzusPPDeYpVZowdvQ33zlKjRaFx11VWrVq06+uij3/GOd2zZsmXFihVf+MIXvC7Dgw089p/uCBMRuIAqrULn/TA5E0BtfWVHy5vMQo4VjE5+Ya5PVzoYLoC1xFCpo65oJ+n3B6wtdlXOYOFJxug1Np52Wq2Gx6sRGi2gqBQ4GBG/UsbZqk591VUOC0yxZo0qxQpsNP+EL33pS1/72tfOOuusD37wg2vWrBkaGrr33ntvuOGG/v7+f/u3fzN+UYrgsf8FFbbde8o71ahL0rkBHhixmFp1QT2WrDXQAJLEAzqYvBA9Y+PU8IizWAG08WqQ5Ot3ph4hpbnhSiaAwe4W9Fx8JgAAIABJREFUamiJUg+34lKLKuwxgzejbzGzSY76lsUjiDoo16mvzIH16VusHq4ppVNtcQyVlddXKAAxMxY3TdtiHTT5EqVS6cYbb/zSl7501VVXTf/wnHPOOfnkkz/96U9fc801a9euNX1ZSmBnhPRHxJvi1qlCXdLFMmCRBnRSC6xwmy4Gg4ZYhtzwzlqffIt4wm7i2egHPkLxAA16RgvWV1DMODmVcqWknJkRUjM2Zh8kMenHlCFScoSKBQ5l9lspXGZlnEpWlJURLhY1Ojo6WiwWzzvvvDk/P++881zX3b9/v/GLUgS3Rkit8YL1lirtH2d9FeqV0apIl1FAQ0+kdAyTKuhWxjsYtqH4DYhHtnpgCF/pgQJYSS3x1N+p9ZVjEY96pfb5GZ6ZwGtvUBOzqPdx5Wl9oh4YBL6So+Ksr1wA4vS5LY4j7O3tXbFixauvvjrn56+88koikdi8ebPxi1KE6YZ6TKk6lUBXFYN1AIXaI65OXaqSNqr3p+6i2qB2dPAyQnoZ1QFS6k+R6aRZSTXKWV8x42Twckky9cou0xK3IBnlVfrNlmlNS96UHDlrfTUryjuGaXEcYTQa/drXvnbxxRc/+OCD0z986qmnPvaxj11++eVdXV3GL0oRDNLGBUrkY5jAZOeVMjZGLGbWUak6QtUClXp1hCXJUyqjqlsxhVZOXoFHqcnM5CPEmCyjuj6zzKziSJS3WOkpVQ/XVGt4HCuh8AgpG1Klt7iFxbss9GSZmbjttttGRkZOPfXUVatWrVmzZmBgYN++falU6s4777zzzju937n00kvPOuss4xdIACOQKdcRj1BjVbDOWFF6hRhlTtMmQFWMo16goh5sjclXVG19KPJOU+yxSgFGpUzLuUWK6zO09aozGRTXV2PXWbGO8hZ3qXTTKlX6mRmhomRPCfRBo2DxLkqO3JkaLqOU4Smxr2w0v6INGzZ0dnZO//XII4+c/zvt7e2mLkoRDKWJapQxJSw29gqxhNEq1QVl6lWxxqms6lQssHFGiKnyTuoZIVWyiMlbpPYN1K5fPWlWqxGqb7Ga6pU3mUWx/UA9IyQdH39gfQZ1qVLpV50oa55UUFBaYMpWqznCRcwIb7nlFuOfLIeoozxLU0kpA66q02hGmKuihzx5KB3DoOIUOkWxjNl0hzFo0ZvFSpni6MG46pKVNHeT05d0zBkoKsc6Zq9fZX1vi+mnhGLqPEi6tN78FiufEJ6jnX09tT76FOcrHVS8FIBUzCmq3CL6eZCaOBSOYYI6b6PURAjWK1RQK1ObZec5sd7BVL2A+vAX1WPMODVC07dI5SswhuOolplVD+hQWh/qeh9VGQWL3TXf52e2zKwQ8TNUr/TD7Dyo+tqFkYwiYMTa2NjYL3/5y1dffbVUmpVKXHLJJeavShmeMJc+S7NYV94/5YxQsY9QNWNT4s14GafR6oVSRogpSdRK8qBFpd4DsGqESk1mrDKq4QJVTeX6GelUjXpqrgcvHDS3xbwantJbbFR4zNCuF2roIo/1YNwf5YwwipKK2GJhCoTwc4R33333+eefPzExMf+fDk5HqBorKTEwUK/huYplSOPtDebbJ1QLVKrVBVUxiGofLitjU0n61eduq0oWGapO+iPKOHvZdNKvvMWTPfVqeijjvIjaFihX4pUmv5TqaLgKKkLVA09UM4qF6Z1AU2rUdd0LL7zwDW94w+OPP57P593ZWIiLUgcj46b3TkD9yMNSDYkoonRVqvpcb/rwKrDEMvmaWVWnKnWp2memJFYCUyyjprpkiXFUxCyqeii1hn1On6KSFTO+xayGcbWxEpy3TGWsB0PVSb5FXjetoqNSC2fV118IpQyaOsLBwcGhoaFrr732hBNOaG0l59WLCtVAQ101qjYcSDWQYY5YM6vUUFZ1qq+v8PuqH6FMvSquX1c56Q2sWEepoZ4xOUUpFklG0XDVGtJVt1iVPTa9xVAfW8GhXg23Txg1RKo1vFTUE8tQoVpmZqOJI+zu7u7q6spmszrrDg8PX3TRRSeffPIFF1ywd+9enaUoUKUui3W1QEb1EVQ9VZkTS6pKFk1So9OSPzrUqUs1ao5TQFJ6RWtIxxRYNt4ZOkoN+0bLwGDEIipWHurssXoZWO0tWABVqtoxSZwanllDxHC0SofU08940kSTTY7FYpdddtlll102PDzMXvejH/3oxMTEd7/73fb29j/7sz/TuEISVIfLqKpGGdS2asZptMzOeUVVw3nFj1CidsFIFxQLVG1xR4k3Y1jhg21yjRKpAPVYRIn3gzp7rLrFqlZevQZpPONkxFJGDZEqtaZMjS6uWOazn/3sM888s3nz5hNPPHHFihUz/+k//uM/Qhf94x//+Itf/KK/v7+jo+P6669fvXr1gw8++Na3vlXmkptBNVZVmq/GWF81o2dkbErtGaxxwGrC2ra4k1U5PjtfwxoV3l3V0DO09UatcFtMXemguMWqNcJ8VaFbHOqD9PI1bDio2ifi2JNTWV+dVOAMYlSajKOoV1J1VKpvmeka08LMV4OfI/zyl7986623dnV1jYyMNNWOBuPpp58+6qijOjo6AMRisZNOOunJJ5806ghNBzKtMaegcliaqqq4lTHCzfjwJ4WxKWDxZqZ5OXpvANSTZnXeTzldoJ86C5YVVs0IOdSoKqmgGIsora9qJdRrkE5e8UhF0zMZVCPy1qiyWEYplvJGrNGxMGcwoakjLBaL11577ac+9alvfvObiYTKWbRT6O/vnzmbu6urq7+/3++Xy+Xytm3bHGcyLDrttNO+8pWvBPxyJBKJx+c+O/FGbDSPbJa6h6P5WLSh8PuoRCbKsWy2SPz1oWw0iQj9990ScpUWel224aJUb6kVqf/BBYr1lvGJLF0YPVFOOJVyNjv3xc7lmgfVqUhicLycjVENwVgxHqs3slnqa5FwY8M5hS0bzsXiKlscrUbGS7Fsljq6Y2AikoooPBJO2clWEvQtdoFiraVRzGZnN5gWi8VKpRKNzs3WXaCsuMXZctKplLJZapKRiiQGxsvZJHWLx0uJaLU2/xHyQ7wRG1Z5i4dzsYTKFsdq0bFiRGGLxyMtzbbY7xVwKpGJksIj4QKFWkt93hYHoNpoGR3P0l1PrtrilnN0vUfSiQ9lm7z1fpgoJdDMSvghqm6o57/F+Xy+0WhMu4xQtLS0zHcZc9DEEU5MTFQqlb/+67/meUEA7e3thcKBpy2fzwcMJk0kEt/61rdaWlq8v65fvz6TyQT8clNH2NVar0WcTCZFvEI3Vu9IKPz+yrJbatQDLmzu+kONjhY3k2kh/v6qJIr1Kn39XBWtsWo7+fcBpKLVaCpDDz9Lbm1lRyKTafK0Nb3OjmStkWj++01Rceo9bU4mQ32nu1obI2WXvmW1aL0rpbLF7W7RVdniMbc9qfD7q+AW6gq/n68hGa12tM/9/Wg0mkwm5ztCAK2xqpPK0PPgYqPW25Gmb1lHstaIK2xxya2taFf4/e50Y6iksMV1xS1ekWmU9yu8lW7Od4ub/rC3qvYIFWuIR6qd87Y4AG3xaiSVyZANc6le7e3MZJLU3+9M1RuxBP2tLCtucWdrI1tR2uJGZ+vc33ccJ51O0x0hBc3PI9y4ceOuXbvYi27YsOHll1+u1yeD/V27dm3cuNHvlx3HOeGEE06cQm9vL+MTGWIZJWpUVfuu2krM6A1QZQyUxSzKTWDKkj81JYX69SvxWsq8nMrRClA/XUFVrAQOtaioV1IWyyhugXnq0ugWqFb6VVtpYV7VqWqIlPoUoX4k4YKJZZo4Qsdxbr311ssvv/z+++9vNBQPsgQAvOUtb2lvb7/jjjsA3H///fv37z/zzDN1rzQQjPYXo6pRVUflFePoWgrVMj7Uj4fOVV3jBSTT2n3D169Ug1R15DmV00U8MFSRZr+CesO7ao1QLdxUvn5VsYyql1ILRKB4i5TOvvagWkZVdbQthhuy2Wj+IRdddNGrr776jne8I5lMzumpHxkZCV00Eonceuut55577pVXXjk4OHjrrbeabsxX3T/1yUCKj7h6H6jnaztopAfj+VCdnKJ0TBLU0xHTk2UYYhzV9ZWuPxVDuY66S503pLo+FCV/rvpboCop5GyByViKkXEabZ9QvT9QDNcYkktGw7TqMT6qjnAxVaMf+chH/ArCRJx++ul79uzZs2fP2rVrk0kyRc2F6v4V1dsnFDNOtecDU7xNR4L0vxiOUDWcLyjOJVcdwaX6iGcUBy3ma2qqV9URZapb4EyFa+0098bbYrqjKtSQjCpMlQRnixWm9IG1xWm1LVaOBZW7xVVOzVTlFaH4FRheRPUYHOWMQpEaXeT2iUsvvVRg6Vhs06ZN+utQkFZsbyjU3JSKo2qJotpQCOdVm+SgyL4y0gWlpLlUR8yBii6akbGp1tjMU6Mmr3/6I4iOUKl3Ynp9uqNiPEJpxYNhlab0YSHYdWXqWOkWRRwkowq+gVHpV7pFqjMrAKTjGClTf9n1jvFRo0adomIfmtIWs0E1da7r/vKXv/zoRz9q9GrYaFW0YsUaVDO2lEpSz6Mu6bESo7qg1I3LIm2Uy/iqNUI1R6s+8dkbvU9fX/UVbVOpITEcrZKYJa9eg1TKCF31QZTKsZTxue3qjkTlKWXooZTeMkbGqeRoizW0RFXO8mBQo4pn1LAR7gh37979la985XWve93pp5/+4x//eAGuiQHT1CgUw22l008m11ciPRRlAlC0YqrDsbAwBSpF4a6SlVEdvW+6hsehRhWtsOojlFGZLKN6AIu3vmnqsqwS67DYaQWCnRXOmqZGza5/0FKjvo6wVCrdfvvtZ5xxxqZNmy677LJNmzZ9//vf7+vrW4iLUoeqHkxVNYpJ9pX+iLMyQroVZqyvImZhMBJKSoEio0Cl3N7A0hOpOEKjeiWmozX8CClcP+f+q7dnqMc69KeUwx6rUFOmJW+M492VDKnSfDgPjGOYVMM1Hprcp8cee+wHP/jB7bffPjo6eswxx5xxxhm//vWv77vvvoW4HC6UT59QPI8QijW8gmIZHweEqTSxjGG9maowHapWUv36lZvY2NRiivS/VEfQQdVRKRbAoJgucBytyrhUFrWr3N6gnFHFkCc3jTD6/JS+AiMpV6sR1lyGWIYutmCka6mo8qzRRTh94uabbz7++OPf9KY33XHHHeeee+4jjzzywgsvfOhDH1qIC9GDanuDao0XimVI0xkhqxVX6RVi8HIKW5BX7EbHwswcUIoVOFZSqUyr7khUMipOjVDFkTNIBe8VoL/GnLdAJZxiOFpVapERDqrVCNWvX8lKMKyo0qxRhi/nYdaHXHPNNf39/TfeeOMnPvGJBeh5EMQCtDcozcXmqTpVClRud1JVD6Yg+VPtpoci9crICKePPKRw2qX65O8rQTWpVc+o1KjLtYrC43Qcw2TJX1ZxIAAUeT+G6jXiIEFWXZYUDwv0YDzcjHsFFDqpoGyFBqijTFnhuFIBRf0tTsWUD+ZVvUU8zHqO3vWud7mu+7nPfe6ss8667bbbikXyLV9sTHfwEMGqEaq9QsZreEYzQvXnT01MpH79UMlIGLwiVDNC9Y9YCEerFIuYrEEyJJFQ+Qq8LVYt0xotM5vuBjZNvTJUqSnF0y1Uu5nZmOUIb7nllr17915//fX79+8/77zzVq9e/Vd/9VdPPPHEQlyIHrxYskS7xS5QVleNtqq0mjIe8daoYg3PaI3QcDc34/qhUiZkUK9K64NHjaqKZRhbYLwGSb8/ytQrVKg/7habZr8PIrEMs6FepcChyqu1xFBpUIW75Tqiit3MbMz9kJ6ens985jNPPvnkzp07P/rRj/70pz+96aabisXipZde+vzzzy/EFXFBj8XKdcQiapJFKM7d5kyWUWX/Gd3WJvVmatp99fYMpY/gOVrFJjCWGIfeR6huhTMq7Lfq2BdMTn6h/jIjHYFKOGU6lgJXkma0yUrJkbOskIIjLyie3Q3AAVrIRxIu2Hw1BLRPvPGNb7zxxhv37dt3++23v/Od7/zqV7+6ZcuWE044YYGuSx30odKqHWxT65tVXarVCBkTmeNQ6ebmVEfU1udYMeoWMK4fqkktSwyiUkZV1xMppTss9psuZsmyqUvyFtNPI5q5vkpGyBweRF7fbEO9aV6K19uQiqJEdYTKYiU2QtLOlpaWv/zLv/zf//3f3bt3X3PNNZoDSI2CXsMr1NyUUqOv4vrVBlwgYbKMzyrwOCqkDUeYrkTaGHVU7PWJVqBYUx5BhwWgLg1Tr94IMeJTyrDyUKEWeWeXm27lVAoHGaSCaV4nFkHUQZnmqHi9DSlyxrJgvROgj1hbt27dJZdc8uKLLxq9Gh3QHxFG7wQmM0Ji9YL5iqqVqQ+yMn4sMin5I67P2IK2GJVa5MWSKjVIjpVXmpzCsMJKk19MfwUGrwilLVbvbYBKrFNpwFEPZ1XDQcPUKOstI4drDMkhVCJ+BnXMhto+yx4KLAt6DY8owZ+7fswh7x/nFTXdfqBUxmdknFBpD2BKCpUKSOrrq/ByTCusRr0anSzD2gL68BeemIUurOVlnPRwmc2uK1GLDHbdaJ8iVA6gYEyWgcrQZoYSgo0FUeQsCOg1Nl6gRF+fR50rzQRgVRfMdkNDpVs5x3qFlKyYapMcVAo8jCY8KBZ4WKdbqDTsM1WdKh0srFiKXgbmbAGZusyq338oKgk4B4yoVfo5kjQ1Q8egRlXEMgcdNXrwg25lCuq9E1B5xBeAGmUknapjTZgZIZk3M9tHyNoCpfWNi3HUa3gZ8xmhaVWnQkZo3tGy9FwqTVbMWIf6y0xDRE5qedQlfdzoQSSWWUKgOyqealSJ2uZZYaMN9WqnT7AGOiyEoyJmnGxeyzBvRrTylQZcIKkYrnlKB6Ikj+1IjFKXausffI5WbW475yQv1bEYautDJSIv1DlvMf0kpoOifWLJgc5rFRVP5Z1cnxzr8Z4P+vPnlfFVh0slo2i4IM5M1nBUpN/kvqLUcJgpliErNXJVDq+o1hvAqo7QxSzcLSaz3yxqkU5d5lm8H/0tY9cgiY9o3UWljhbWoEFy+wHTEClE/Jz2CadYJ26xpUbVQX/EGYcRKq3PfUXpJoBZQ6Y7Kp5wOaMy+YXhqOjUn2kxDq8MbPr+QEn4ynJU9KSfZ4UPHke+MPeHscdKbzFLNUq9RYyGfZgXc/BwCDlCsmqULZahx5JMap5qAphWku5rTfNCzPUPmiYzthiHuD5PjAMVApzX8K7EHjO+gsJbZpj3Yw8EIN8fjqOFiqqO9xGmDR1dNcrr8OHhEHKE5OeD2z5BfcR5Gb1KxslkDNrIfWb8jI2cUbH6CMnXf1CKcbyaX4XATvPaP0De4rqLaoPzFihsgeGMkCdsNj+TQSHWZG4xOZzi9xGaXF8lI+RknDwcSo5QocbLo0aJxzDxeLPpY4Yo6/MCJbpkjmfF1KwMj7QhWhnTDfUsRwuyWIMnWQR5C3iSTqgZelaNkNynyFtfTTVqMuPkvQIg62UqrPlWUDKk3PYJo+0ZPBw6jpB+cG6RSW1TxTJsK0Y88pDRfuSBaIW9Mj5v5oBp6tUoL6egpODyWsTji3NVN5M4GNdXoxZNNqSbZtd57HQyOpltU9ZnvsW0jJDNG6XJI9B4fYqpmFOiiWXYSTMDh44jpLe/8DJ6eg2Sd7QCyA3R/HSB+ApxAzGVJjPuZBayleRVLyp1UF5SnnYf9Ixtia/fcFFmDTI0PflFaTIOtxJPMhS86weZt+BbIcOSOtMN+zwcQo6QXiPkNtQX66TR+1qOhESNMh9x4ivE66aHWg2Sp7o0q+p0yIZYw4qRw/mDcn3iOFNvCiVTEmm4FTVPO0BDhz3OEh0VUxhMtBLc6zdcg1SqEdqGemWonD7B2b/Jk7QojyDXShIfEb6kkJY056rIMHk/0vrlOiIOr3qhMB+Ld4uII6zYjpAorDWtGuVJIkGmRtnrm+5TjJJP8OYd8wTyW8BuFVWIdXhbTKO+SnXEI1A/xUdhxJqlRjmgs/+8oemgs/Pc9hfjj7j5dIeSLujwciqqUY4vJ549y+5gIQ7H4aU7UODN+Lwc5exfNmlhWjUKclLL3gLi+qYzNh4pAnKsxrZy9PYMxsG/bBxCjlDh/rrcLSSVkXljR7AgGaHRdIE4aDFbYSpNiDU8V8NK0jOedn6BJ/zX2GIcYoGHN1Ea5JkG7HSnNYYSbYt5gxLhlQmJeiKzW6DBrpukRolKBd4ZOwBSMadIPs/O9hEqQ2GyTA289hRiBwU7FiNK/oyLcWpmeTn2+g4tnMxX0RJFhFVcICbl2QqfNzPbPmF4fWo6xbXy9C1OxZhbTEw62V+BuD7bkdAdFTOWohlS9hlJSrNGrVhGGfRZoDyxDMixHj8WM9xkRg7n2WIcZCuU9fnUP2VKGW9KpIeFUF2alBQq8HKm1+easAyBfWXzllAh8A2LZYxvMY9XpBZo2NRolNqQbRvqOWiNmj09BGTqUkdJQVqf+woRy6imxTjs9UGLFdikFsi82USF+RHEEWXZKtpZGadp6pJYI2RTr6A9RWzqGCpJM58XMZlxEvvE2I6WmBGyYx36MUzsW8TAoeMIUzFUG6QmsCKrWxxkPRivvQYLIGahzcdiq17pwnFeDRU0K6Pz/tDDYe4WkG5RlltmziScCYKj4vVxgtx+oJcRhj+lWusnyE1EvC0gxiLmxTjMGipNOM22csR0wgVKXEPNwKHjCEHWI7HL7MThMvxWXNr8KrYYhziijM/70Rw5WyYAGrWotT7hKxRrk/PwGCBaSXbSTLSS7PWjDlqi4UmtZiwS+hW01qeFg2zehUq9Vl12uEmrEWpM0aPVOHm8JbFGWKghFeW0ovJwSDlCIrXIpp6JHTbsbmUiKaHzitJ4OSbvlIzCJQyVNp2xsWuooDkSttgHQCZBKqNmuU1sph0haL5cZ31q0q9RIwy9fvaUQdA7WLgdPkRJmoakjsZ7sU5dBVl7z7aiPBxSjpB4iwt1ZhmZktSzZ91CZTgTs1uc3Oqr46hCfa2elQy3MlmNGiHFimmtT0tHJrjtGZk4aNQrswaJBbhFxPVZs1JBj6XizHSE2lDP7vChs/es9aMOYoSzf9mOithQz+bVeDikHCFFDOICZfWDoSfXpwm72V5EQTVqciYF29GCdsg7W9iNBcjYCOvrpVO0GiFXjJOJO7SMkO+ozN8i0xlneAFCS4xD1k6zK/3UA0Y0kvJwQ8etESajqBHEHAvZO4FDzBFSSINiDUku9UwZ8aUTyJAzNq7SgV4dMalN11k/kzBbQCJZ+Qp//XbC9btak19QrKERZmV0yqiZOCbCDP1C1AgNs99GxT7QmGWaoVX6dY53pyTlOutThKNsbT8Ph5QjpFCXOmN7KOuzn2+Yb3gninHYk19ASzo1rTBl/YM2HaFYyUINLVHOFEeQG9LZk3FA1iux1yduMZvapfAuWhknUfJWMzs8iC2pA3GmgUbEnyIMbbYZIR+Unvpind+kSaJGua3KxPV1hktRSRWNhnRSuG2YWmQPBACQSYT3yZnmFScq/PsDIBMP76DQZXcJt4gdS1FOStLcAsOO0GyBozWGMmEKna4hCu1g0aBeW2NOMewL5GvMM3B4OLQcIcGR6GT0lLN/2TVq0FpldYZLxSKIE8rgOo6qneSoDl5HS2GP9WqQ4fdHRwkCag1Pz5EYTprN1ggpYpyK284W4xAeoUoDDldSR51Cpzd8h7K+jiGlUKNWLMMExREWuUdPgOyojNaodaoXIBdgdAokhAKSllhmwmQNklLD06kReulCsBnWsfIA2hOEW3QQ1wgpHSaa7DpF7GO2BqnXG0A5w4Td8A5aUmu6xsRuz+DhkHKElIxNJyNME9oz2Af0gHb9OvPDQJvVqZUuUByJZhOY2fYM0vWzC1RRB8mwAommIwwlwHUGAoCcsfFrkATJm9aUPsL6E3rtJaE1wmzVbdd4iyk97zq+tpWmCmSHsylCT73tI+SDktGzJ26DTL1qBGIUYbdWoNROyKh0Tj+hrK9Tg6RRr3o1wvCh3nwZAgi3iH2q8OT6CWci8CtoOlpKGVWv/YC0xQdt+weFdNGPdQiSK35ETqGmtGpMhLnbOtQrA4eUI6Q01LMnA4GasWn0EVKoUe7MEQ+hTU51F2WNEX+0jPPgtTILIGYJrVFlq9BJF0LFIDoZP2hWeMKw2ER7fYMZW0sUDRfVwPlK2o8QyVDoNDSTMk5++wTBUOuFm6o4pBwhhfRgT9wGsUaoEch4YpZg9lyzRhhaQPKeb/YDSCkgGW+o1zABiQgiDsqB4armUPzQW6RTACOur6dKDdmCagMNFy1c3sX0FmcIZyPrZmzhsYju+sG3yHuAeWIc0AyppurQ9hEaBGVEmQ51ScvY+FYeBFJCv0YYzDvlzEsWtRrqF4R3CrYCOjVCEGpsExV+gQ2EW8QeZDq9fuj90XHklCYfnVvkWYngfGSCe/Cyh9D5ShNVvioVhOE4OsJm0BqadQoclLnbC3k8PQ41R0jI6AsaqlHK3HfNPtDQAol+OhJqJdleCgTVZbGGmIMYX6lBKlBpxQphNTBNapGwBZqxSMgjZLpGqHt/CMck6XxExEFLNCRi1hH7YEEywpD1NWZigEZ96UT8qbD7D9tQrwNKxlbSEMtQqiPs0088hFpJzeejnbC+nqMNUWroBJKgnYenyR6HdmjoZLQgHBmo0wcJoqM16cg1r5/0lmk/RaG3SMeRhG+Bdo0w2BHqvmWEpFzHELXGwudu61CvDBxijjBcdalzf71jhoLL4JqPYKjS4eAvUIVZSS0rHHoeXq2BakPrFaJYMdNJuWYfodH1Qx2V5iOUjAKBh3lptn+AIOk62GuEYey9biwSxn7rHFMFsqqRrf1m4NByhCRqlK8aBeEQedOv0IRh3kkgHTHpaBH2lmqmgyCEwzpNZiDEOjqSSJDSHdMCKky6AAAgAElEQVQZp9b6CBunKbB+6BbrlWkJwmC9GmFYgUDCCoVYCR1JHaWPUJN3UcUh5QgppIpOHyEIh7zrimVMF3hCeT/u0RYeKKpUzee7PbBGpXn/J9cP0xPpCLszcYSwx3qxTmirpUCNMMzK61w/wsqcuZr2+gdD0mxW+631FocKazUHgVJPL7BiGR4o7TWa1HM4O6/3iBOawLRi1dAaobYk0qwVRlhGor9+aEalKckLPTJQMyMMZ7+5hx16aAtTXWqSCjC/xab1ShR2Wuctaw/bYs1HNPwVqEIn3CS1T9iMkA3K3Hod1ShI7Q2awuuQR9D00QTjeo42EzZLU1M4jrBbpElqIcxKFmqIR/iq19D1oa2kME1dRhykAqlFffY72NBr1mgBtIe9Bbpl2jjGAx2VfqxjuoxtNNxPESbL6MyHYuCQcoSkEWt6GWHoYWAC7Hxwk5meIyE0sWmt783SDAj3xivo0AgUEPYVxqsS6/tv8XgFHdqO1nQN0mg6gjBHoklaIIz6E7j+wPU9MQ67Gx0UXkTvLTPNu4Q21GtKAlMxlCgjtCw1ykOKcFKXplgmVEmhM3QbhD45gRphWKyqa8WCw3l9Xiuw/UDTkSPMyuhntKFJuW4NMryGp0s6dSQw7v8W6JdpOxLOeJCj1R2+FTzuVf8R7UiEZISaW9ARWiPUmIgNghXK6yX9ofL+hqvV58bAIeUIHQL7rN/wHjLTQTsjDE5qJypm04UJ/YwtUJg6XnE11w+ORSaquhlbcIHEdEYLYKyCziR//Y44JgLZaU3JIryMyt/Qa/J+CKtk6zuqYL2VyP0JLQMbfYtFrFDwI6QTi4Raaa+AxTt1lYdDyhFi0ooFOSqjYplSHRHdDifTTWYhDe/6VixYmKo5URphvJbmcCyEbYGIIwzwIoUaYhEtXi4WQUvUbA2vM4Ex/6+g2eoKoD0wo9IcEQegIx6U0epnzKE1Qu0DRsLEMnpbEHpYWL6mJekMnXyi3wSlikPPEYac1KWZEQZ3IOnz2pSZF5pHE4RlhG6HZjgc+BGaGS3Camz61G6YI9S9P8G8mX4NEmHUov5HhFGX+hlhEHus/5YFOxL9GmQH6SQsLeoydH1NXx5siDQlnaGOUGcuPw+HmiMMjzX0z4b2X19zMhO8cb3+j7irHeu1xlBtoOY/tmNcW3UZnJRLrB9YwxNwVGa9SGfSGfNff7TidiV1TUBHYEYyWtb9iOAy8FjF7TRJLWrOlEAYaSFDivjfn4aLom6BBsUaGv6uULP9A2GGSDPWCT3PboG76XHoOcLQPr+iplgmcO62frd4cDqSryIVQ1TPToa0H8hICgPW1y7AhFkxTUfbEVYA000XAmt4+hkzgM5kEHUp8BUCxTL6qtHgpFlCzBKY0er1WSJUTFRDq14BzAHSgW+xiCEKiPh1TnUFkI6HjFhb4G56HHqOkCT8NZbUi3RzB/J+Wryoh2BVpL6YJdiX64txQqlFfUcV4EX0708sgmTENyIeq6BT2xEG3KJ8DXG9GiS8SnNAUlvWEvsgLGPTv0Uh7L1Ae4ZZYTPCtMGmDZFm+wSFt7MZoRaCp/zVXdQak1N9uesHBmLaZ2gFB2L6zzcoTVpGxSyGw/mJim6sELa+7v1BIDuqX4ME0JkIXl9z+RDq1fwWCKg6zWachtszEMaL6B/mFxzOahZo4hE4gXPV87UF7abHIegIA2MNnePjPYRkhNqkSlgBTIA3CxCb1L3qhUlHpa+6DJYsTmg31Afzipq9DR4CHInpjHCsAs0CXvD6AEYr6NK7RcEZ22gZXdoZodEaZyqGWsPX0OtTxwibbj+hbYjSgRmFfsaWCuygWOBuehx6jjB48ovmYYEIyzj1M8IwalTg+Qjgnbz5bZpmMsRRCaQLZqnRRARRx1c7LqLqDPC1Y2XDjtDw+uU6XBcteq3QwRmbfiwV3EQkcosCMirNKYkegnkXGWoqKOPUVQWmYyFiC9s+oYXgbuuCdsYdnHHqBzKtgcNx9L0IAsdGiPByAVay4SKvNw54av1g6lJrfQSKHSaqItSl7y0S2gLfpHxcJKP1dyT6XgphvJ/+FD1Pden3lol8hYAt0D+dA4GVfhe6qlSESer0W0XT8cCMUNuRq+KQc4SBk1/0qdGQGqF2IOMEJoWaQ+U9BFh5kepFV9IZLTffAn29HCZNjO+/6o8FgVdj8/kKIux0h38NT1+pgcCkfFwilgqIdaQcuVGxiRPY4SDCTgewryJbHLC+py3XfMuCxQr6hi5Y1VjQG1TJwKHmCINrePpHe6QDO2BEYr2AMzT0eT8AXUmMlpv/k0ws7F8A02/yA5COoepTgHGFfHlwjU3/FnUmMOazBfoFMARev34BD4GTU0S8SFscBZ+MrdZAsS5CLfpmVGMVt1O7lTOAuhwpo1t/C/xbLfW76RFaI9TO2NJhNUKbEWohuMaWrwpkhMHHo+vvX0AsJlJmDyBt9JUmCCyA6XfTe/Br9ctJ9FkiMGkWY49Nrh+oGjXL+4ms7/iPcPL6RPWTBdO+PKAbVUS4G1Dpz2l30yOsRqjvqFrDakzWEWoheASaQI0wTEylH6sGsK/ZisAjHsKbmVxfhBSCP7UoknEi1NCbjEVMq0ZNl4FF1od/GXJMaP2AjE1ELNMeD95igzVCkYwwbMSa7gEg6VhQT72dNaqLkIEI+jVC84FMAPsvVMPzpUZF1g8osIlktPA3xCKqWvhTl5UG6q7Wwc7B60MoVgh0VAKOPBlFxEdYq69k8eAnHBURQyE8YzNIjUoJd41aidA+Qs0mq1B5v80ItZAOHIGmXyOMRRB1UPI5XlmkRhhMXepbgc4EgngziYy24lPDE8k44V+GFOHl4E9dml4fXo1Qu4AUkJSL9EHC39CLWHn4h4NS1+83t7ruolA3K2YRKdMGZGwiNc42/yMDy3U40B1OFFIj1M44VXHIOcJAMZJ+jRCBHRr6B9wgMJwX6UDqTDj+1KWQo/IP50Ucid9kFpFAAf6xiBT1GpA0m26f0O8Wn/6IpsJOKWrU19GKXb+vo5WpQfp3mIyVBb5CQIeJVDjr52hFlBChNUI7a1QLwTXeQl2Aeg44eFZkRF6A2EQk4wygRqV4Jz9DL0Vd+jtas45cUOzTdP2Gi4LE3P22OEr15meMiFGLPhNZBcvAPrGIzPW3+xxJKFfjDBTjCKhGfTtMRHiLgMk1ImcktcWD5Pf61J0qDjVHGCyW0Rya7iEgFhOJlQLaD0Qe8QUQs/h9hGCBx69GaHR9qQKYX6wzXkEmLnAwt+Nv6KWoxYBYQaZG6EMtiq3v40hMU7uQ0kMZthIB8niRt6zVn3qFzQj1EdxQX9AepInA+U/6s0YRyGuJVBcCeDkpK+Bv6KWoxeZlTskansnr969xyqwP/6dI7hb5ry8Vixh15D5bIOKlEFymlaBGu5IYNSn2CVClinQzB9cI9VWpqjjUHGFIRiihyg1i5yUyhqBuaIlXyBOzVJvxZiNlt1u7zA5/Kzks0UoM/yMPTV+/SCs0/GucUlYY/sJUqRpbdxIjzdaX8uXdSWek1LxMqz8ZB0B3i/nrbxZuSolxOhO+85tMWyERXid48ontI9RFKoaa63sCu377BPxJlUoDtYbA+n6xsAtMVGUMZYdPuCrlqPzC4ZGyK7K+31sq5qh81h8uoUdifW84zvxYROr+A+hOYnieoa81UKrLmJielibrQ2iWKQIcrRA73Z10hps5EqmM09/RCsy1B9CRQN5n+I4Ir+ONTW8qjxeR1AWIZeouynWBJiUlHGqOEIEdMPqnT8C8dt9XaVJBaxQxiR3z+wgpR+XvCNHTIkWNNl9fytH6BAquyPX7fcRQyV0htP6KFmdoXkY1LjSWBUBP0hlulrGNCVGjfo5Qir3v8VtfKCn3d7QyGXnEQcYwwW60DBwwq9JLBxeUGD0kHWFbzJfdFjnv0W/Kn+nnb7TsdknwfvAvMAyXpBxVc0crlVH5Uq8lGUflt/5QCSta9JcHfBzJYAm9KZn1///2zjy66Sr/+5+bNk2bNE2TJm1DV4pCKYuCLJVFxGEAwfFRWXQ84CDq48KjDiLD0TlynnGewX0WZwadGZ0Z1IOOqHgOwrAMooAWqCJTKRaotBBauiVpm7VN8r3PH982zfINvyKfL4Hk8/orW+/3Jk3u+37Wa0qHDm/kg4hCG8siRClig9iuRbzxpYUQ61eWowJ7D0S/Aay9GsRupIeSSQB9AQjp3O+L3+uoY3eW6cbIjb9QElAIz9PTwY0TI5Q7DSF2mgBiAClKCF1+SFVc7ElyfePHSJax9+KsMrH3CggdqwFApwSHD4SofzLiKmZMh/YoobJ60cbPSYdoi7ADaSMCMVyvHK9UNJZQYSUGx4pBYiX7KBWQniKxY8ZaJSB2HRReEVSs3G+ERo+ZypiuUZTOOBdKIgrheQ4owYkRSgst1k8oljmFtdGLdQmsTBOI8RPiAHaZXZdYQpWqgEypOjmrF+0jMqWzdgmhQnWNRq2SHV5uykCyCKUstu5eSE+52J4jIudxjaIIiV4FXVJ7HawYIcTQWpSUURF9mrQQyu2aQiqfiC2EGFmpF0oCCuH5YoQYdZqxK5yQagNUMTJB8FbhbCnXKJbfEmKcndvdCxkpoMT4xuWkSwdgEGN4RmmhAhOSa9SUIeG6bMcb36iSGL/NA7lYrl0p12ubB01oDenSrlGsvUIKg8xUiR8aot9FUsttGC30RPQqZpfVNRqjOQ5WjDBW+QSW0X9BJKAQnuekMTeGRSh3KXGaQrqjMVa+HMTIisT8iaYxqSUAL8aZBk5fZG6wXwCXH+0nJCkkth6O9REZVVKu0R40i9CUIZEs09EDOXgxzmihsvag7aW0SvAGIjvWBjh0+RATayW2UygVSv3jS3iPUU46E5GskOkJAOdIAQ4522Kcpyk0Sv+sCyUBhfD8J3VhJMvIuFESkfwKIofZJVYxxFVYcpVHyzRRMNBHrTK2HshOQ2jLIiIpJLYekFWo2j14FqGUxdbu4Sak+RukkkHavRwr2YcB6KMsKvFffPHnTYrkSFU4tHnQ8pVypIxaew/XY7lGpfw6iK7drBjtWFFcX+dxjXaTaxSFrLSYXfKwLELJ7wfiXk8yaxEzuiD1E0I590AkN521e6KXALTxAcCoihQSrEyc/vEjhcThgzSkABgAmCSTZfAsNkmLFjHrVamAjJRIv4LVCzl4/4LoxNEOL0cdX0IIO7yYe4Xo8RGFSq+SqKlHbE4Uq3+TA6MR43lcoyjnKV4oCSiEsSxClNNDIHYXR6yOzxAjTIiYLKNPk45eoFmcKnD7I/1aiMk4IJV1iTh/yfGtqKuwUWqv0OHlRqRLiHWEERfo6EFb5UGM1IbvRdrxhBZEIQn/FyAKOUgJrV+AbkzXa4wYIVbWqFSyDFbKHsTu34TSej6FQVqKtBZidTy+IBJSCKVjhFifb8x2vXhfQcnW/pgWWwZri1qFERd6BpCTDhELPWLuPki5Fq1eMGIKYeT4iAE2kLIIu32QqkBrqKFKAVVKpOuiDc/1ClI16e145hRIhSHbvTwXKRkHxBhe+L+g3QsGFZp3XbIUstXD85DegmQABdHilLvjbqysRocPp4veBZGQQhjz80WJwcbqNYoYI5R0jSJGF/IyoNUT+SCuRZWbztqiLDZEIYl2/eFanNEF6YhZtZLjI9ZOiERrOWJWKkjV1Hd4wYQUYAMpiwrXIowW8jZsoY22CFs9kIf0EUm6RrE610DsgmYsiyKmxYJx6uqFkoBCGKu8AavOVJ0KfqkT2FGPDpDXNSppEeIKYXS+DKKQQyzXKKLQRqkIYm0GSNURdqBatCCVL4NYRwhSzXFw30K0kLSjjh9dfoCYrAQxhLDNg6a1kpF+ubfj4tJ38ZkWAJAV02IBLblGL57YFiHa5yt5CdzyBlldozkq6PZFNn22olpU0fkyiB2lAcAYVUpok1locS3CjFRIYWEnpeCaUyAanSELsdsPAkforBQk2iJsRzVq9VGuRSvq+FKuUVyLMHKjEODQ2Yv2LZKMESLWQUpux8WztVE+I20si4XqCFGIVd6A2LlHcq+EmPUrOT6ixalgkKOCCIsEq+2LiCkD2iItQuxklnDvLvL8o8wpXIsZomr2cTciAJATnliLmA8pYlCBNdJoltd12eHF9K5HlzfgWpzR5RkdXshOw+mbDzEO80JM2ZMWQqRjsKCvRZfUQo1xquuFkohCGGOjgRiDlaygQMzXkmxEidVIUyQ3g7WFCwmyazTKIsSO4UW6LrGzRqVco6hCFZEvg9i2pm/88OY1uCmdILpGIxd6ZIstUkhQs16lXK+YruPoZBnETBno9xtFlXKiabn0dh/P76VVspiuO7IIL55YrlHEGGyW1AEoiBZbbgZEqJTYEVuF0TBi4BIhq6TAwdqDuQrkRml5O6rrzxju9wOxyAxvlcxKA28AekLOY2txg1mNNTxAlFA1u7hZjSm0ZjVrdodahMhCa1ZDS8i31CeAE+m8TJGc6MRdVC2PTtxtx2tBB/0HUIQeGYhYrQ/9pZwRax3iJSTPm0M5nl7kPDFCKp9AIFaLNcSNRrRR7xegRwAN0vi56awtfAlAjLGL5GWw1hCLrd0LujS0anGQco02uXgB3kIf7RptdkMBnlCxqAMcLC5elIlrEYalLJ12Qkkm4vBQkgmnnQN321DNHQAo0jCLM9S1C3q82gMAKNBAszvsEVyjtkDNmt1hpZZtqHsFpQJy0iH0V4ablQpSWW+Il8hIBYGH7QUBNYAXO0bIySJEIFZBfbeP4+1lIktNEY88BSmLsMUDZtRMitz0sEucdfFCDfIqH+oatfVAWgrO2egi0U2x5RCqUKPzjBOKNYjDQ0kmNIYISaOTl6LOvySTnXYMjN/ggFJUoS3KBIsrZC/l4bmoMchCDTvrCo/h4bWIA4CMVFCnhOXLoG83C9SsyTVwt8UN+ai/4vyoOijE8gyQOmkH0e+lTWPOGOUTVEeIgDoVfEJkSiT0WYRyHS+O+P0AqY0ebnQBAPLCL4FrrkGUaxR9fE0qMDbQrtDlB7+A6ZcDAFPIXsEngLWH56O+hTItO9U9cPe0k5doMccvzWShQtvg4ENRx8/PYLaegToi9BikaHkEF2JvAPwcOXoUobXo3uOI8XEbDgBAvpq1uGXcK0Q3JUZpKyMiWZAd4OANoLnWBk8CCiHECBMiukaNUYnjuI00dWnQI4A3PECFuNEDgNzwvWSTGwpQzR1TuNCedSGPD+H5MmddvADVogWAUi1r7Leomt08L4NhtXsWKctip/rHd/vB4UP+F5sywOMfqNA41c3LsjDfgIKBWc2a+hf6RicvRRVaACjQDIyP3nAAAAo0cDbEYkP3HhdooCnEu4trrgFAXkZYmLZXALcfcyGKLlW04m13JF2jTh9oUtFca4MnUYVQIkyIVVAPMXp2ICZes6gAUqsH8lEzNXIzwsKQ6BZbhJY3uZFdrwBQoAZLfwysyYUZIBQp0w4IlcUJhdhCXqaFBkff7dNOXqxhuB8QAyjOZKf7jcIGB5RpUS8AUKgBS7+QnOrmZdhCWBgiVBYZ/sWFGtbUb1H1CuDyYSZmQ7iQQ5/rFXP8/PBIf5uHG9Mxv0XR6esdeGfUxDBX0Mo/LohEFUJ5P+Lonh3o0YWIrM5zbuSUwogua2ddyAs9AyjJZA0DQsKLsIWwLIs19K/y6AFCABgaIlQWFy/GHn+Imtl7udh3uNEBpdgqBQClWmh0AgD0BKDdi78XKQpx/Z2SQWgL1CHjd/NhqBYthLsuGxy8OJMhJvsAQIEawmKEHshHXSXywy1CdIszugiq3YNoEUqZK/GonYBEFULJUkJU12hkpgZuKTGIMTY5v+IRyTLNbj4Ee5W8Kgvqu/s+JXTXKwCUaSEYY2t2wxAZLMLvu4OuVyjEHl/BoKQ/jHfayUuwhRbEMKGDA0CjkxdlIrt2AaBIM2CUn8KOQQJAoWZASBocMFQGizZocX7fDcOykMcvCLE4AbvXKwDkq6ElxPWKX4oaVaSEeGppdCYOADji0WgUElYIpT5ixDrC6I7P7R7kAIYpvIICPVlmiJpZe3jQdYluEQLAVVmsvl+o0LNSAWBoiOtSjvFDY3hyWJwQouUyCWFJv2v0VDe+uQYARZnMEmKx4cYgIVxI5BHaAYuwvptfhW9xDgitaJTjRrIjiqDQY5zRh4UhpkRJ+u3icgYTJKoQSp7AjvgRS7hGvZiluBDlujyHXT6RqoChmay+W0YhGZYVblFhC+1Q7YDrVY7xTengF/rSg884oRi19kAkqOWNTllco8FSwu8d+AE8EC1CFwCAwwcuP7LTAvqEZEAI0d9CQYjFebJLDiEciBHWd/PSTKZEXXEjXKPo5RnRPQcQjU5JIcRtzT94ElMI9VJ9351IxzCB5GF12LnjpoywvRi6RQgA5dnsu04OAA4fcMBvdHt1FjvZ1e8axU7GAYBhWXCqP4bXJEPWKIRorRwbBQjJxzlq41djr8IAMFzHjto4yFA7IRKsqW9w8DItcrIPhNfhyZPsM2ARfu/AF0JNKqQq+vZSdZ18hA55fNEiDC4T6Im1pvTIjsQdeKeWSh7sasc7T/GCSEwhNEgdUIIYhlVLHB2AXCGUmz6QLNPVC0qGdmRrkPJsqOsEkEeloC9GCADg9IFPwMzqFilQM6u3z7sr01soy2KnunmvAPXdfJgMQjLWwPa18BNd3N4L1xnxxx9nZA4ffNfJ97XwsQb88UWjv1eAUw58vyiEuEZ7BWjz4O9FxCYYYiOx+m64CjtGCH1azgGgrgvKs5EHV6WAOnXgDIo2L2YLN+g7/nrgrniACVZbjBgWIXJr+0GSmEIYfYBLrwCcQzper84IoxC9mji0pr7Vg1zKLVKezY53cQCotfOrdejDQ6mWNbu5T4AjVl6ejT9/BYPiTNbg4PYeWfxyIMbwHPBlKx+hY+hCDgA3DWEOH6w8EFhQipyvKMIAFg5lTx4M2HrgxwX4F9ClQYWe7W/hMsUgczPA6wdrDzQ6eIGGYZ3bEMpIPTti5X4BLE5ZtPxqHau1cwA43inLryC0gqINu7mPURXRFx7T4kxTQAoLq5YG7MPUBk9iCqFBFXlSF/qpxxFNn3H71kN4qWyLB9n1L1KuY3WdHAD2t/JpefjfBKUCCjSswcF3N/MfDZHlyy2W4u05J0zLl0VIJhjZNouw46wwt1CW+SsY/J8KxTYLXzRUrl/iojLFNgtfUaGQ4/MBgLmFiu1nhW0WYYIMFi0DmJ7P9jQLcvhFRW4ys0+bhUYnN6sZYq/dINPy2f5W0SLk5diuUQgPE7agl0+EB2jQA0DRNfVkEWKiT4uMETp8XIu60QjNlxH77uOW4g7XsfpuLnAAgLPY5xKIjMhmJ7o4B9jXwqfly7JMXpUF39r47mbhRwWyfNOuymI1Nv6fJj5riCzjLxyqsLjgr3XCnEK5fin3DlcsvUoxJU+uXXBlLlt6lWL5cLnmP7eQvXlcOOWAxWWyXGJWgeI/TbzGhh/AE7lpiGJ3Mz9q53L4RQFgWh7b18I5wPFOPkIGi9DcX2rJAU528eGoWqsLP4OlA7tILLqU0IbaomvwJKYQGlTMHu4adWCfehxaSiievY6749YqwaDqy30/auOj9Pg/oSwlZKWx7zr58S4ux3YeAO4bofi/h4VvrHyaPAv98hGKPx0TdpzlP5LB7wcAqQp4+loFAEzOlUuotEp468YUmcw1AGAAb92YgnWGXDQTTEzB4KlrFLj5kEF+NITtaOJ/rBWWj5DlAlPzWI2Nr/1auE+e8ccbWX03/66Ta5TIvXBFRun78qEsTp6VxnD/0Sw8BoSejJOVFhkmtGMfTz1IElMIo7NGZXGN9luE6EWEIhXZcKwTAKDGxsca0IcHALithN2xKzA+hyGedBjKoqGKnHS4zsjU2Jk+IuNy2EQjc/plyQQRuecqxc6bU9FL0ROGFAY75qbeK5vFOdrAvH4+zshk2qtlpMJEE8tOk8uiTVPARCO7Y1fgthJZxh9rYDU2DgDHOmEUdjIOhHdZ60BtJAlSJwXFyyKUZ32KN9FZo13YdZpG1cBGCb1hhEiFnh2z8/lFrMYGMi30v6tM+V+7/JNNMu6H3pyeEnFSDC7rJip2NeEn7gdJVciSz5lIjJfz82EAT1+bcpM8MWaR/zchxZQuY6Pnm4YovmgV/nC9LJvNsQaosQEA1Np5hQx+I1OYEGJbhEro6uUQ8tnbe+MTI0xUIYzMGrXilb+IGNPhG2vfbfTTVUQqstn+Vm7rgW4ffl9/EaUCtsyW9zswLIuhd64KZWQ2GylD6IW4fHh0lLyOq+tl83uLPH2tgoNCJqdCcSbzBHiHF47ZeaUMb8SUIcaAGAB0eGGUHnPwnHRmDS/Yt5FrFBF1Kgg8LDEXv+A9ZKPU7gWTDFmdo/Ss1s6/tfHRehktnhQG5PcjCPlQyPwTG6NnNTZ+rFM2i7Dfo4Pu+orIve8VoCeAeXz34ElMIQQAgwpCjULEXrEiQ7XsVH//sEYH8tniIiOzWV0n/7pDxgAYQRBXOmMN7LCVf9fJK2RwjYQe74ze7jWiGls81TUui13CCqE+jYWWEqJbhMN17GR/ecPxLj5ChoJ0XRpcn8tWHwpMMJEQEgQhzQQTW3MoMMEoS8+HEf1tNzjACezyjIjTC+LVaBQSNUYIAIb0sMRR9HynTCXoVczi4iWZrK4T5OgZAQA7bk71+EGmlE6CIBKAe65WLB6qQG/BKFKuG2jEmJkKuOUZEacX2OJUTQ+JbhGGtkDDr3AYngUnuqBXgCa3LB2NRTJSkSsUCYJIJBjgNyIOUqplrR7u8cPxLkBvCGBMZ9aQVTqOQpi4FqEqyiLErnAQe3UOUQP66SoEQRCXAykMhmpZfTc/3onfIi7KIoxPyigksBDqI4UQ3yIcoWPHO7k5Qy6/KC1fITsAABDoSURBVEEQRNwpz2Z1Xfx4F36LuIhkmXhV00Miu0ZVzN5/2JXAwd4LOdgfsRhGruuCchkyZQiCIC4HxDDh8S788xQNKujshUC/FNp7OAkhMjkqCJZqdvZCZiqgn+EyQgff2vieZgE3k4ogCOLyYUQ229MsfGuD4dg7/hQGOuXASUG2HoiXazRhhbBQA03uvtty+EUBoCST3VykyElnN5pJCAmCSExm5DNTBptdyORICQz1jja5oVCDfoVBkbAxwiINO+MUxNsy9QJVMPj7DVTZQBBEIlOcyf51k1wLXWi+zGknL86Mj22WsBZhcSazOOU6PYQgCIK4eIzprKO/gsLi5MUaco2iYkwHTwCcPgB5aicIgiCIiyRoEXoD4PDJ0rR5MCSsEAJAoYY1uTkAWLEPViYIgiAunqAQWpy8UCPj6QLnJ5GFsEgDZ5wAMpzBRBAEQVw8wWQZiytumTKQ2EJYnMksLg4AJ7pA1iPxCIIgiB9AmRZOdgMAnHHyEhnO8BkkiSyERRo44+QAUGOjk4wIgiAuO8YaWI2NA8AZFxRlxm0aCS2EmcziBKcPWjx8WBYJIUEQxOVFmZZ1eHlnL1icvChOKaOQ4EKoYRYX/9bOR+kZHcJOEARxuaFgMErPau3c4iIhlIeSTDjZDTU2PkZPMkgQBHE5MtbA/mvlJ7ugmFyjcjAim5kz4LkjwhgKEBIEQVyWjNGzF2sEYzpUxM9iSWQhZAAvT04546RMGYIgiMuUsQZ22slfnhzP+FUiCyEATMljr09LmZxLQkgQBHE5MtHEXpuaMj0/nqt0wjbdDvK/yxNc7AmCIK5c1Knw0Mg4r9IkEgRBEERSQ0JIEARBJDVXmBAeO3assbEx3rNIXgRB2LlzZ7xnkdQcPny4paUl3rNIXrxe7549e+I9i6Tmyy+/7Orqwh3zChPCt99+e/PmzfGeRfLS1ta2YsWKeM8iqVm/fv3u3bvjPYvk5cSJE7/85S/jPYuk5sUXXzx48CDumFeYEAIA5zzeUyCIeEI/AYLA5coTQoIgCIJAhISQIAiCSGpY3N0saWlp06dPVygGJcknTpxQqVQlJSVyz4qQpLe39+DBg9OnT4/3RJKXo0eP5uTkmM3meE8kSXE6nUePHq2srIz3RJKXw4cPl5aWGgyGQb7+9ttvf+SRR87/mvgX1G/YsMFkMg3yxVarValUZmXRMbtxo6GhYejQofGeRfLS2tqq1WrVanW8J5KkCIJgsVhoLx5Hzp49m5eXp1QqB/n6waxX8bcICYIgCCKOUIyQIAiCSGpICAmCIIikhoSQIAiCSGpICAmCIIikJv5Zo4PHbrdv375dqVTOnTs3MzMz3tNJOgKBwPHjx5ubm2fMmDH4lC0Ci0AgUFVVderUqfz8/JkzZ9K/4BLj9/uPHDly/PhxhUIxefLksrKyeM8oefnyyy81Gs0111yDNeAVkzV6+vTpysrKG264weVynThx4sCBA4OvIyEunvr6+nHjxqWnp3d0dFitVvrwLz1Tpkzp6ekZO3ZsTU1NT0/Pvn379Hp9vCeVRHz66adPPvnkmDFjfD7ftm3bnnvuuYcffjjek0pGdu7cecstt8ybN+/jjz/GGvOKEcJHH33U4/G88cYbAHDLLbdMnTr1qaeeivekkgiPx2Oz2ZRKZV5eHglhXPj++++HDRsGAIIgTJo06e67737iiSfiPakk5f3333/yySfPnDkT74kkHS6Xa+rUqVOmTGlubkYUwismRrhly5YFCxaItxcsWPDJJ5/Edz7JRkZGRkFBQbxnkdSIKggACoUiNze3t7c3vvNJZlwul9FojPcskpFf/OIXDzzwQFFREe6wV0aMkHN+7ty5wsJC8W5BQUFTU1N8p0QQ8aKqqqqqqmr9+vXxnkjS0dvbO3/+fLfbbbPZ6Dy4S8/nn39++PDhV1999cUXX8Qd+cqwCDnngiAwxsS7KSkpfr8/vlMiiLhQX1+/ePHi9evXl5aWxnsuSUdqauqaNWtWrlxpNBpfeOGFeE8nuXC73StWrHjjjTdSUlLQB78yLELRF9Te3i7ebW1tHTJkSHynRBCXnsbGxlmzZq1du/anP/1pvOeSjCgUilmzZgHA9OnT8/Pz161bR93PLxmbN292Op2vvvoqABw5cqS1tXXVqlWvvPIKyuBXhhACwMyZM3fs2DFz5kwA2Llz54033hjvGRHEJcViscyaNWv16tUPPPBAvOeS7LS3tysUCiriupRMnTr1pZdeEm87nU5BEGbMmIE1+BUjhKtWrbrxxhtVKpXb7f7kk0++/vrreM8o6XjooYfcbjcAPPHEE2q1mmJUl5g77rjD6/XW1NQ8+OCDADBt2rSlS5fGe1JJxAsvvHDy5MkRI0bY7fa333775z//uVarjfekkojS0tJgOKC+vt7lct16661Yg18xQjhu3LiqqqpNmzZlZ2d/9dVXdAzKpWf8+PEAMG3aNAAY5PmRBCIrV650Op3Bu/QTuMQsWbJk69atjY2NWq1248aNdCpnHLn55pvF5QiLK6aOkCAIgiDkgPb1BEEQRFJDQkgQBEEkNSSEBEEQRFJDQkgQBEEkNSSEBEEQRFJDQkgQBEEkNSSEBNHHkSNHNm7ceGmutWnTpurq6oscxOPx9PT0oMwHnRMnTvz1r38VOzAQxGUOCSGRLDz//PNlsfn973//0UcfXbLuZY8//vg777zzw/7Wbrc/+eSTZrNZrVanp6fn5ubedttttbW1uDO8SKqqqh588MHu7u54T4Qg/meumM4yBHGRTJw4MXhoybFjx959992lS5cOHz5cfERsVHHJukeuWbNm5MiRP+APBUGYO3duTU3N6tWrp0yZwjmvq6vbtGlTXV3dqFGj0OdJEMkAdZYhkpEPP/xw4cKFW7dunTdv3v/4Yq/X63A4TCZT8BGn08kY02g00S/u7e212Ww6nS4jI+MHTMxms2k0GpVKFesFBw4cuP7669etW/fUU0+FPh4IBCKOp3E4HC6XKzc3V7Ifnsvlcjgcks+2tbUplUq9Xh9rDu3t7Xq9PjVVYhvd2tqalZWVkZGxYcOGZcuWnTt3Lj8/P/is3W4PBAJ0pC1xuUGuUYLo46WXXgqeAu/1eg0Gw6uvvvrQQw/pdLrc3NxRo0Z99913zc3Nc+bM0Wq1Op3u9ttvD3X9dXV1LV++XK/Xm83mrKyshQsXdnR0xLrWuHHj1q5dK97+29/+ZjAYvvrqq0mTJuXk5GRmZs6ePdtqtUr+YWdnJwAUFxdHPB6qgp999tmECROysrLMZvOQIUNee+210Ffu3bu3srJSq9WKztXQE53eeuut4uLivLw8g8EwZsyY3bt3B5969NFHJ0yYsHPnzrKystzcXK1We//994ceC7p///4RI0bk5+drtdq77rrL4XCEXvT11183m80Gg8FkMmk0mocffjjWJ0MQlx4SQoLow+FwtLS0iLc553a7fd26dV6v99NPP92yZUtXV9eSJUsWLFgwffr0Q4cOrV+/ftu2bcHTWX0+39y5c3fs2PH666/X1ta+//771dXVt956ayyPS2tra1dXl3jb6/Xa7fa777576dKl1dXVf/rTn/bt2xeUyQiuueYalUr161//evv27V6vN/oF+/fvnz17dmFh4d69e//73//ef//9K1aseOutt8Rnv/jiix//+MeBQGDLli21tbWbN28OWrrvvffez372s8rKygMHDuzZsyczM3PevHmHDx8Wn3W73fX19Y899thvfvOb6urqVatWvfnmm//85z/FZ8+cOTN//nyNRrNnz57q6uq0tLRf/epXwSl98cUXjzzyyH333VdbW3vs2LH33nsvWsgJIp5wgkg+PvjgAwDYunVr6IPPPPOMWq0Wb4vpjpWVlYIgiI/87ne/A4BVq1YFX79w4cKRI0eKt8XMl3379gWf3bNnDwB8/vnnkhMwm82PPfaYeFs8a/Qvf/lL8Nnly5ebzeZYk9+wYYMYy1SpVJWVlc8++2xTU1Pw2SlTpowfP97n8wUfWbRo0ejRo8Xb06ZNM5vNTqczetiKioqKiopAICDetVqtWq12wYIFwSkBwKFDh4KvHzdu3Lx588Tbq1evViqVFotFvCsIwpgxYwDg3LlznPM//OEPSqXS7/fHekcEEV/IIiSImMyZM4cxJt4W02pmz54dfHb48OEWi0W8vWPHDq1W6/V6/9OP1+tVKBRHjx4d5LVuvvnm4O2KiorW1lafzyf5ynvuuaehoeHvf//7nXfe2draunbt2tGjRx84cAAAuru7Dxw4UF5e/tlnnwVnkpeXV1dX5/P5XC5XVVXVXXfdFR3d9Hq9dXV1ixYtCoYMDQbD7Nmz9+7dG3yN0WicOHFi6CSDb//IkSOTJ08uLCwU7zLGFixYEHzltdde6/P55s2b969//ctutw/yAyGISwZljRJETLKzs4O309LSACA0hSQtLa23t1e83dra6na7Fy9eHPrnOp1u8Ot+xMiCIPh8PqVSKflio9F477333nvvvQCwZcuWhQsXPv744wcPHmxvbxcE4eOPP/73v/8d+nqtVmu1Wv1+fyAQCMpVKGfPnhUEwWw2hz5YUFBgtVo55+JuICJ9RqVSBd/+2bNnI3JWQ4e64YYb/vGPf7z88st33XVXSkrK9OnTX3jhhUmTJg3iUyGISwEJIUEgoNPpTCbTuXPnLv2lf/KTn8yaNWvXrl2BQCArKwsA1qxZIxlidDgcjLHW1tbop0Qbsb29PfTBtrY2nU4XtInPQ15eXkRmUFtbW+jdZcuWLVu2zGKx7Nq16/nnn58zZ05DQ0PoPoMg4gi5RgkCgRkzZrS0tIQ6EmWip6eHRyXgtLW1qdXqlJQUk8lUUVHx0UcfheZzBtFqtePGjdu8eXO009VsNpeUlGzdujX4iNvt3r17d2Vl5WBmNXr06OrqapvNFnxk+/bt0S8rKipavnz5b3/7287Ozrq6usGMTBCXABJCgkBg2bJl5eXld99994cffmiz2ex2+8GDB1euXFlfX497oc8++2zMmDF//vOfq6urW1pavvnmmwceeOCrr75asmSJ+ILnnnuupqbmzjvv/Pbbbz0ez5kzZ95///1nnnlGfPbZZ5+tr69ftGhRbW2t2+2uq6t7+eWXxadWr1594MCBNWvWtLS0NDQ0LFmypKOjY/Xq1YOZ1cMPP+zz+ZYsWdLY2Giz2dauXfvNN98En33jjTdee+21U6dO+f3+pqamd955R6PRlJeXo34wBPHDISEkCAQ0Gs3u3buvu+66xYsX5+TkGAyGKVOmHDp0SK1W416orKyspKRk9erVkyZNMpvN48ePf/fddx977LFXXnlFfMGtt966adOmr7/+euzYsWq1uqSk5MEHHwwakfPnz9+4cePBgwdHjx6t0WhGjhy5ZcsW8alHHnnk2Wef/eMf/2g2m8vKyvbu3bthw4aZM2cOZlYVFRUbN26sqqoaOnRoTk7Ozp07Q32zfr//6aefHjZsmFKpLCwsrK6u/uCDD8gvSlw+UGcZIkmJbsXSl0gt1Ydl8Nhstvr6erVaXVRUpNPpYr1MEATG2GDCb5L09vZaLBar1ZqbmztkyBAxkScUzvnJkyc7OzuNRmNxcXFEF5hAIFBXV+dyuYqKiiISZFwu17Fjx9LS0ioqKmKl6sTC4/EcPXpUp9MFG9eFXrGxsdFqtRqNxpKSkohPniDiCwkhQRAEkdSQa5QgCIJIakgICYIgiKSGhJAgCIJIakgICYIgiKSGhJAgCIJIakgICYIgiKTm/wNMyzYCC67vjAAAAABJRU5ErkJggg==",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"
"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"yfiltsignal = ifft(filtamps)\n",
"plot(t, real(yfiltsignal), yticks=-7:1:7, label=\"filtered signal\",\n",
" xlabel=\"Time in Seconds\", ylabel=\"Amplitude\")"
]
},
{
"cell_type": "markdown",
"id": "b01814a0-7e2b-4238-a0ba-2c5b812c9651",
"metadata": {},
"source": [
"In the filtered signal we see that only one frequency remains."
]
},
{
"cell_type": "markdown",
"id": "d8a6bf93-64ba-4f5d-8ea8-0e4ff0c8018f",
"metadata": {},
"source": [
"# Question 3"
]
},
{
"cell_type": "markdown",
"id": "67f87691-82bb-479e-8e20-c233e568adcd",
"metadata": {},
"source": [
"Let $f(t) = (\\cos(2\\pi t))^4$.\n",
"\n",
"Compute a least squares approximation for $f$\n",
"using a Fourier basis of sines and cosines.\n",
"\n",
"How many basis functions are needed for the largest error of\n",
"the least squares approximation to be less than $10^5$ over $[-1,+1]$?"
]
},
{
"cell_type": "markdown",
"id": "1959dc7c-3ba6-4874-a0e7-7e384e306583",
"metadata": {},
"source": [
"## answer to question 3"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "9fd42bea-4e6f-41a4-8886-5af89623f1d9",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"f (generic function with 1 method)"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"f(t) = (cos(2*pi*t))^4"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "a3a53065-c18f-4bdb-98b0-6abf63e73a47",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"rule (generic function with 1 method)"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"nodes, weights = gausslegendre(32)\n",
"rule(f) = sum([weights[k]*f(nodes[k]) for k=1:length(weights)])"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "0c87e751-9ba5-40ac-b5d0-d358a6bf6b35",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"innerproduct"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"\"\"\"\n",
" function innerproduct(f::Function, g::Function)\n",
"\n",
"returns the value of the inner product of the functions f and g,\n",
"by the integral of f and g over [-1,+1].\n",
"\"\"\"\n",
"function innerproduct(f::Function, g::Function)\n",
" fun(x) = f(x)*g(x)\n",
" return rule(fun)\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "1efa0a9e-1424-4670-9a6d-3eabcea4f54e",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"basis"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"\"\"\"\n",
" function basis(n::Int64)\n",
"\n",
"returns an array of functions with the first 2*n basis functions.\n",
"\"\"\"\n",
"function basis(n::Int64)\n",
" one = [(t) -> 1]\n",
" sines = [(t) -> sin(k*pi*t) for k=1:n]\n",
" cosines = [(t) -> cos(k*pi*t) for k=1:n]\n",
" result = [one; sines; cosines]\n",
" return result\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "d5a56c97-8f41-4404-9a2b-cb7a2e80178a",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"coefficients"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"\"\"\"\n",
" function coefficients(f::Function,b::Array{Function,1})\n",
"\n",
"returns the inner products of f with the basis functions in b.\n",
"\"\"\"\n",
"function coefficients(f::Function,b::Array{Function,1})\n",
" dim = length(b)\n",
" result = zeros(dim)\n",
" for i=1:dim\n",
" result[i] = innerproduct(f,b[i])\n",
" end\n",
" return result\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "743e8bba-45d6-45df-92ef-63a531c593f6",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"approximation"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"\"\"\"\n",
" function approximation(c::Array{Float64,1},b::Array{Function,1})\n",
"\n",
"Given in c are the coefficients of the Chebyshev approximation\n",
"with the basis functions in f.\n",
"Returns the approximation as a function.\n",
"\"\"\"\n",
"function approximation(c::Array{Float64,1},b::Array{Function,1})\n",
" first(x) = c[1]*b[1](x)/2\n",
" rest(x) = sum([c[k]*b[k](x) for k=2:length(c)])\n",
" result(x) = first(x) + rest(x)\n",
" return result\n",
"end"
]
},
{
"cell_type": "markdown",
"id": "2c97625d-629c-4d7a-a4b0-2a1be3294530",
"metadata": {},
"source": [
"We start with 11 basis functions, but we need 17 basis functions."
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "9919cca4-0867-4941-a84c-7a8acad6a261",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(::var\"#result#approximation##4\"{var\"#rest#approximation##1\"{Vector{Float64}, Vector{Function}}, var\"#first#approximation##0\"{Vector{Float64}, Vector{Function}}}) (generic function with 1 method)"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"bN = basis(8)\n",
"cN = coefficients(f, bN)\n",
"aN = approximation(cN,bN)"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "0e292653-5df2-4758-8cfb-a4262ade35ee",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"
"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"xr = -1.0:0.01:1.0\n",
"fx = [f(t) for t in xr]\n",
"px = [aN(t) for t in xr]\n",
"plot(xr,fx,label=\"f(x)\",legend=:topright)\n",
"plot!(xr,px,label=\"F17(x)\")"
]
},
{
"cell_type": "markdown",
"id": "40b644bd-d4bb-4ad6-94f0-6d17dd79f337",
"metadata": {},
"source": [
"We see that the approximation agrees with the given function."
]
},
{
"cell_type": "markdown",
"id": "64d7d18e-8873-407f-b02c-553cb88f7d80",
"metadata": {},
"source": [
"# Question 4"
]
},
{
"cell_type": "markdown",
"id": "e4e42296-3181-482d-beed-8d74a5f391ab",
"metadata": {},
"source": [
"A sales manager needs to organize trips for three representatives\n",
"$R_1$, $R_2$, and $R_3$\n",
"to visit three different locations $L_1$, $L_2$, and $L_3$.\n",
"Each representative can travel to each location, but their travel costs\n",
"are different for each location, as listed in the table below:\n",
"\n",
"$$\n",
" \\begin{array}{c||r|r|r}\n",
" & L_1 & L_2 & L_3 \\\\ \\hline\n",
" R_1 & \\$730 & \\$728 & \\$558 \\\\\n",
" R_2 & \\$984 & \\$791 & \\$1,033 \\\\\n",
" R_3 & \\$1,046 & \\$670 & \\$518 \\\\\n",
" \\end{array}\n",
"$$\n",
"\n",
"The goal is to assign to each representative one location\n",
"so that all locations are visited in the most economical manner.\n",
"\n",
"Set up a linear programming model for this problem."
]
},
{
"cell_type": "markdown",
"id": "c50a2657-30a2-486b-a039-9e99bef69963",
"metadata": {},
"source": [
"## answer to question 4"
]
},
{
"cell_type": "markdown",
"id": "a45998a3-ef2f-4431-b49a-811eb098e438",
"metadata": {},
"source": [
"We use JuMP to model this problem."
]
},
{
"cell_type": "markdown",
"id": "1580c493-957a-4a2a-8d6a-733abc44e49a",
"metadata": {},
"source": [
"Let $ x_{ij} \\in \\{0,1\\}$ be a 0/1 variable: 1 if representative i is assigned to visit location j, and 0 otherwise. \n",
"\n",
"Let $c_{ij}$ be the cost for representative $i$ to visit location $j$.\n",
"\n",
"Our objective function is\n",
" $$ \\min \\sum_{i=1}^3 \\sum_{j=1}^3 c_{ij} x_{ij}$$\n",
"with constraints that all locations must be visited, each location by exactly one representative:\n",
" $$ x_{11} + x_{12} + x_{13} = 1, x_{21} + x_{22} + x_{23} = 1, x_{31} + x_{32} + x_{33} = 1$$\n",
" $$ x_{11} + x_{21} + x_{31} = 1, x_{12} + x_{22} + x_{32} = 1, x_{13} + x_{23} + x_{33} = 1$$"
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "bdd078ec-98a9-403e-ae33-9aa6e69584e6",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"3×3 Matrix{Int64}:\n",
" 730 728 558\n",
" 984 791 1033\n",
" 1046 670 518"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"c = [730 728 558;\n",
" 984 791 1033;\n",
" 1046 670 518]"
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "51a219df-513e-4091-bf23-dc1ec5b79f38",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"A JuMP Model\n",
"├ solver: GLPK\n",
"├ objective_sense: FEASIBILITY_SENSE\n",
"├ num_variables: 0\n",
"├ num_constraints: 0\n",
"└ Names registered in the model: none"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"model = Model(GLPK.Optimizer)"
]
},
{
"cell_type": "code",
"execution_count": 24,
"id": "eb30a14d-8e2c-4c6a-a63d-ba08ff816b93",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"3×3 Matrix{VariableRef}:\n",
" x[1,1] x[1,2] x[1,3]\n",
" x[2,1] x[2,2] x[2,3]\n",
" x[3,1] x[3,2] x[3,3]"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"@variable(model, x[1:3, 1:3], Bin)"
]
},
{
"cell_type": "markdown",
"id": "403a8e0e-38ba-48f6-a9d8-a4d030504082",
"metadata": {},
"source": [
"We minimize the total cost for all travels."
]
},
{
"cell_type": "code",
"execution_count": 25,
"id": "77c60597-fc05-4870-9aab-3c4e645dd79b",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$ 730 x_{1,1} + 728 x_{1,2} + 558 x_{1,3} + 984 x_{2,1} + 791 x_{2,2} + 1033 x_{2,3} + 1046 x_{3,1} + 670 x_{3,2} + 518 x_{3,3} $"
],
"text/plain": [
"730 x[1,1] + 728 x[1,2] + 558 x[1,3] + 984 x[2,1] + 791 x[2,2] + 1033 x[2,3] + 1046 x[3,1] + 670 x[3,2] + 518 x[3,3]"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"@objective(model, Min, sum(c[i,j] * x[i,j] for i=1:3, j=1:3))"
]
},
{
"cell_type": "markdown",
"id": "4b6c68f8-f790-4f7b-a3e4-63c56252ffe1",
"metadata": {},
"source": [
"Each representative visits one location."
]
},
{
"cell_type": "code",
"execution_count": 26,
"id": "12121e90-21c1-491a-984a-40b295ae108b",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"3-element Vector{ConstraintRef{Model, MathOptInterface.ConstraintIndex{MathOptInterface.ScalarAffineFunction{Float64}, MathOptInterface.EqualTo{Float64}}, ScalarShape}}:\n",
" representative[1] : x[1,1] + x[1,2] + x[1,3] == 1\n",
" representative[2] : x[2,1] + x[2,2] + x[2,3] == 1\n",
" representative[3] : x[3,1] + x[3,2] + x[3,3] == 1"
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"@constraint(model, representative[i=1:3], sum(x[i,j] for j in 1:3) == 1)"
]
},
{
"cell_type": "markdown",
"id": "afe6718e-80be-4511-94fd-ce2dcb84693e",
"metadata": {},
"source": [
"Each location is visited by one representative."
]
},
{
"cell_type": "code",
"execution_count": 27,
"id": "91c19f19-9baf-4236-9b47-14612c7875fc",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"3-element Vector{ConstraintRef{Model, MathOptInterface.ConstraintIndex{MathOptInterface.ScalarAffineFunction{Float64}, MathOptInterface.EqualTo{Float64}}, ScalarShape}}:\n",
" loation[1] : x[1,1] + x[2,1] + x[3,1] == 1\n",
" loation[2] : x[1,2] + x[2,2] + x[3,2] == 1\n",
" loation[3] : x[1,3] + x[2,3] + x[3,3] == 1"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"@constraint(model, loation[j=1:3], sum(x[i,j] for i in 1:3) == 1)"
]
},
{
"cell_type": "code",
"execution_count": 28,
"id": "f0d5f149-2673-4f64-bf42-38ab90d3bedb",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$$ \\begin{aligned}\n",
"\\min\\quad & 730 x_{1,1} + 728 x_{1,2} + 558 x_{1,3} + 984 x_{2,1} + 791 x_{2,2} + 1033 x_{2,3} + 1046 x_{3,1} + 670 x_{3,2} + 518 x_{3,3}\\\\\n",
"\\text{Subject to} \\quad & x_{1,1} + x_{1,2} + x_{1,3} = 1\\\\\n",
" & x_{2,1} + x_{2,2} + x_{2,3} = 1\\\\\n",
" & x_{3,1} + x_{3,2} + x_{3,3} = 1\\\\\n",
" & x_{1,1} + x_{2,1} + x_{3,1} = 1\\\\\n",
" & x_{1,2} + x_{2,2} + x_{3,2} = 1\\\\\n",
" & x_{1,3} + x_{2,3} + x_{3,3} = 1\\\\\n",
" & x_{1,1} \\in \\{0, 1\\}\\\\\n",
" & x_{2,1} \\in \\{0, 1\\}\\\\\n",
" & x_{3,1} \\in \\{0, 1\\}\\\\\n",
" & x_{1,2} \\in \\{0, 1\\}\\\\\n",
" & x_{2,2} \\in \\{0, 1\\}\\\\\n",
" & x_{3,2} \\in \\{0, 1\\}\\\\\n",
" & x_{1,3} \\in \\{0, 1\\}\\\\\n",
" & x_{2,3} \\in \\{0, 1\\}\\\\\n",
" & x_{3,3} \\in \\{0, 1\\}\\\\\n",
"\\end{aligned} $$"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"print(model)"
]
},
{
"cell_type": "code",
"execution_count": 29,
"id": "6a20d031-79ea-4ea4-a19b-fc20b112a4e0",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"solution_summary(; result = 1, verbose = false)\n",
"├ solver_name : GLPK\n",
"├ Termination\n",
"│ ├ termination_status : OPTIMAL\n",
"│ ├ result_count : 1\n",
"│ ├ raw_status : Solution is optimal\n",
"│ └ objective_bound : 2.03900e+03\n",
"├ Solution (result = 1)\n",
"│ ├ primal_status : FEASIBLE_POINT\n",
"│ ├ dual_status : NO_SOLUTION\n",
"│ ├ objective_value : 2.03900e+03\n",
"│ └ relative_gap : 0.00000e+00\n",
"└ Work counters\n",
" └ solve_time (sec) : 3.99995e-03"
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"optimize!(model)\n",
"solution_summary(model)"
]
},
{
"cell_type": "code",
"execution_count": 30,
"id": "141ae77f-e829-43c2-bb5f-757b221ef57a",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"minimum total cost : 2039.0"
]
}
],
"source": [
"print(\"minimum total cost : \", objective_value(model))"
]
},
{
"cell_type": "code",
"execution_count": 31,
"id": "d77fb037-afa7-4487-b1db-2b8fcc689029",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"assignments :\n",
" Representative 1 visits location 1\n",
" Representative 2 visits location 2\n",
" Representative 3 visits location 3\n"
]
}
],
"source": [
"println(\"assignments :\")\n",
"for i in 1:3\n",
" for j in 1:3\n",
" if value(x[i,j]) == 1\n",
" println(\" Representative \", i, \" visits location \", j)\n",
" end\n",
" end\n",
"end"
]
},
{
"cell_type": "markdown",
"id": "e9573545-8e19-4130-991c-22b6301c5238",
"metadata": {},
"source": [
"# Question 5"
]
},
{
"cell_type": "markdown",
"id": "46fa7942-10b1-4048-9e7e-097b1962d7a4",
"metadata": {},
"source": [
"Describe in one paragraph what you learned \n",
"from *another* project presentation."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 1.12",
"language": "julia",
"name": "julia-1.12"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.12.4"
}
},
"nbformat": 4,
"nbformat_minor": 5
}