{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Amplitude Modulation\n", "In the previous parts of the question, you have been able to show the effects of modulating a simple base signal with a carrier signal of higher frequency. Now we will show them visually to appreciate it fully." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### a) Base and carrier signals" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#Run these to import all of the necessary files\n", "import numpy as np\n", "import cmath\n", "import matplotlib as plt\n", "from pylab import *\n", "# Plots graphs in the \n", "%matplotlib inline" ] }, { "cell_type": "raw", "metadata": {}, "source": [ "First let's plot the base and carrier signals both in the time domain." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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lfOUE+fT798+eDYgbb7+cUtshTTb3+mVNnKTs6eU4jpNIWHHWg6TBDmmyufdA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\ngx53WiZJOSaOlhMnrDA5UTp7F5aY5Hg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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Create a 3 second .wav file of the Major Triad\n", "N = 500; #sampling frequency: 1000 Hz, i.e., 1000 samples per second\n", "n = np.arange(0, 2*N+1, 1, dtype = np.float).transpose()\n", "base_freq = 2; #base frequency: 10 Hz\n", "carr_freq = 25; #carrier frequency: 50Hz\n", "x_base = np.cos(2*pi*base_freq/N*n) #base signal\n", "x_carr = np.cos(2*pi*carr_freq/N*n) #carrier signal\n", "# Time domain\n", "figure(figsize=(8,1.5)),plt.plot(n/N, x_base);\n", "plt.title('Base signal: time domain');plt.xlabel('Time (seconds)');plt.ylabel('Signal strength');plt.grid(True)\n", "figure(figsize=(8,1.5)),plt.plot(n/N, x_carr);\n", "plt.title('Carrier signal: time domain');plt.xlabel('Time (seconds)');plt.ylabel('Signal strength');plt.grid(True)\n", "plt.show()\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, we implement the DFT transformation the DFT coefficients of the above signals:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def DFT_matrix(num_samples):\n", " \"\"\"\n", " We assume num_samples is odd\n", " \"\"\"\n", " assert np.mod(num_samples, 2) == 1, \"num_samples is odd\"\n", " \n", " #Init Matrix\n", " U = np.zeros((num_samples,num_samples))\n", " dft_indices = np.arange(num_samples)-(num_samples-1)/2\n", " w = cmath.rect(1, 2*pi/num_samples) #Return the complex number x with polar coordinates r and phi. Equivalent to r * (math.cos(phi) + math.sin(phi)*1j)\n", " #Obtain the DFT matrix\n", " for k in np.arange(num_samples):\n", " u_k = np.zeros(num_samples)\n", " for m in np.arange(num_samples):\n", " u_k[m] = np.power(w, m*k) \n", " U[:,k] = u_k\n", " \n", " U_conj = np.conjugate(U)\n", "\n", " return (U,U_conj)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "C:\\Anaconda3\\lib\\site-packages\\IPython\\kernel\\__main__.py:15: ComplexWarning: Casting complex values to real discards the imaginary part\n" ] }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Obtain the base and carrier signals in frequency domain\n", "num_samples = len(x_base)\n", "U,U_conj = DFT_matrix(num_samples)\n", "x_base_freq = U_conj.dot(x_base)\n", "x_carr_freq = U_conj.dot(x_carr)\n", "dft_indices = np.concatenate(((np.arange((num_samples-1)/2), np.arange((num_samples+1)/2)-(num_samples-1)/2)),axis=0)\n", "# Frequency domain\n", "figure(figsize=(8,1.5)),plt.stem(dft_indices, x_base_freq);\n", "plt.title('Base signal: frequency domain');plt.xlabel('DFT component indices');plt.ylabel('Signal strength');plt.grid(True)\n", "figure(figsize=(8,1.5)),plt.stem(dft_indices, x_carr_freq);\n", "plt.title('Carrier signal: frequency domain');plt.xlabel('DFT component indices');plt.ylabel('Signal strength');plt.grid(True)\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compare the above result with your calculations. You can ignore the small ripples, which results from the finite sample effect (they will eventually disappear as we have more periods of the data). " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### b) Amplitude Modulation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we will mix the carrier and base signals, and see what will be the output in time and frequency domains." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": 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lmyuLwtJCfLP/G93r7lgbenQq71Pdlv6RzCP4M+VPFK6bhKQk4NQp/fp5I5FP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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Your Code Here #\n", "### Solution ###\n", "mix_signal = # yours to implement: the signal after mixing\n", "### Solution End ###\n", "# End Code #\n", "# time domain plot\n", "figure(figsize=(8,1.5)),plt.plot(n/N, mix_signal),plt.plot(n/N, x_base,'g--'),plt.plot(n/N, -x_base,'g--');\n", "plt.title('Mixed signal: time domain');plt.xlabel('time(seconds)');plt.ylabel('Signal strength');plt.grid(True)\n", "# frequency domain\n", "mix_signal_freq = U_conj.dot(mix_signal)\n", "figure(figsize=(8,1.5)),plt.stem(dft_indices, mix_signal_freq);\n", "plt.title('Mixed signal: frequency domain');plt.xlabel('DFT component indices');plt.ylabel('Signal strength');plt.grid(True)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### c) Demodulation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that the modulated signal is successfully received, we need to attract the original base signal out. In the question, you are suggested to mix it with the carrier signal first, let's see what do we get:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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aac/PP5fyX//KPHGiyGBmpsjGn/8svPXrJ3UiI5nLypj/9CfmKVOYH3yQecwY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\nrZswffD0ULgWw4hq3NsCqecV01H6QdmBP/Cc8gBE9nBZj8s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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Your Code Here #\n", "### Solution ###\n", "demodulated_signal = # yours to implement: the received signal mixed with the carrier\n", "### Solution End ###\n", "# End Code #\n", "# time domain plot\n", "figure(figsize=(8,1.5)),plt.plot(n/N, demodulated_signal),plt.plot(n/N, x_base,'g--');\n", "plt.title('Demodulated signal: time domain');plt.xlabel('time(seconds)');plt.ylabel('Signal strength');plt.grid(True)\n", "# frequency domain\n", "demod_signal_freq = U_conj.dot(demodulated_signal)\n", "figure(figsize=(8,1.5)),plt.stem(dft_indices, demod_signal_freq);\n", "plt.title('Demodulated signal: frequency domain');plt.xlabel('DFT component indices');plt.ylabel('Signal strength');plt.grid(True)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now if you compare the above plots in the time and frequency domains with those for the base signal, what have you noticed? In the class, you learned that a circulant matrix acting in the time domain (i.e. a circular convolution with something) is a diagonal matrix in the frequency domain. In the above example, you realized you can exact the signal by only keeping those with frequencies less than a threshold, also known as the cut-off frequency, in other words, you want to multiply each DFT basis coefficient with 0 if it is high frequency and 1 otherwise. This is an axis-aligned projection in the frequency-domain. So how would you find a circulant matrix corresponding to this projection operation? (This is called low-pass filter)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def low_pass_filter_circulant_matrix(U,U_conj,cutoff_freq):\n", " num_samples = U.shape[1]\n", " Lambda = np.zeros(num_samples)\n", " Lambda[np.int_(np.arange(np.floor(cutoff_freq)))] = 1\n", " Lambda[np.int_(num_samples-np.arange(np.floor(cutoff_freq))-1)] = 1\n", " Lambda = np.diag(Lambda)\n", " \n", " C_lpf = np.mat(U)*np.mat(Lambda)*np.mat(U_conj)\n", " return C_lpf,Lambda" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's take a look what does the low-pass filter look like for the cirulant matrix and DFT coefficient matrix:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cutoff_freq = 10\n", "C_lpf,Lambda = low_pass_filter_circulant_matrix(U,U_conj,cutoff_freq)\n", "# time domain plot\n", "figure(figsize=(8,1.5)),plt.plot(dft_indices/N, C_lpf[:,0]);\n", "plt.title('Low pass filter in time domain');plt.xlabel('time(seconds)');plt.ylabel('Value');plt.grid(True)\n", "# frequency domain\n", "figure(figsize=(8,1.5)),plt.plot(dft_indices, np.diag(Lambda) );\n", "plt.title('Low pass filter in frequency domain');plt.xlabel('DFT components');plt.ylabel('Value');plt.grid(True)\n" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Bly7JIU88z3Ny4MEHM3jySfjmm+Dlifd59eqwbl0Go0fDgQcGL0+8z//4A954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\nL/XqwZgxZgN86aXi17Nxo5l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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x_demod_lpf = C_lpf.dot(demodulated_signal).reshape((C_lpf.shape[1], 1))/(pow(num_samples,0.5)*16)\n", "plotind = n/N\n", "# time domain plot\n", "figure(figsize=(8,1.5)),plt.plot(plotind.reshape((C_lpf.shape[1],1)), x_demod_lpf);\n", "plt.title('Extracted signal: time domain');plt.xlabel('time(seconds)');plt.ylabel('Signal strength');plt.grid(True)\n", "figure(figsize=(8,1.5)),plt.plot(n/N, x_base,'g--');\n", "plt.title('Original signal: time domain');plt.xlabel('time(seconds)');plt.ylabel('Signal strength');plt.grid(True)\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Cosine Transform\n", "We introduces the cosine transformation in discussion, and you'll get a bit more practice with it here?" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#Run these to import all of the necessary files\n", "import numpy as np\n", "import cmath\n", "import matplotlib as plt\n", "from pylab import *\n", "# Plots graphs in the \n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 75, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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OUtNcPGP5PHDxxXzuOZVssRNjWT5WlMr9T4z17g3kcjz63IRdu1jMtGvnf79h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\nZ507d0ZVVdX/Rpvo3Losp2N5773zePpp4IQTcthrL+C2226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LG4vJis0iJSrFLWcsM1M9nzt37ESzv4ixZ4B/APFCiEeBz4HfeLVVFviLM9bf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\nluBHJJ0FnBQR971cf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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Create a signal\n", "N = 101;\n", "np.random.seed(0)\n", "n = np.arange(0, N)\n", "\n", "x = np.random.normal(0,1,N)\n", "\n", "#Calculate the DFT coefficients\n", "X = np.fft.fft(x, norm='ortho')\n", "\n", "figure(figsize=(10,3.5)),plt.plot(n/N, x);\n", "plt.title('random signal');plt.xlabel('Time (seconds)');plt.ylabel('magnitude');plt.grid(True)\n", "plt.show()\n", "figure(figsize=(10,3.5)),plt.plot(n/N, real(X),label = \"real part\");\n", "plt.plot(n/N, imag(X),label = \"imaginary part\")\n", "plt.title('DFT of random signal');plt.xlabel('Frequency');plt.ylabel('magnitude');plt.grid(True);\n", "plt.legend()\n", "plt.show()\n", "\n", "\n", "#Show that the signal is conjugate symmetric\n", "# Your Code Here #\n", "### Solution ###\n", "\n", "### Solution End ###\n", "# End Code #\n", "plt.legend();plt.show()\n" ] }, { "cell_type": "code", "execution_count": 169, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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OPTU98SqastNbVzI/+9nPIMsyYrEY/vmf/xl//Md/bAt6BYYmEvjPo7c0ZFtLvocTahRh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\nGV/+8B82PS6LEiyY7oCM0vBCL5trtSO4tNZiNFrNUIStcsPsPDZoZ6d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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "[]" ] }, "execution_count": 169, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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roO7ZAzz4YOF9Ol/3xsQrBP7N33BhdvduLs5u3gz8+tc8w3HNGveL3a9Zwyen\n2bODoxj/7LOGhsL1zR97rDBf19iEvbvbWzNEfzrx90TnEcW84hX8CcyMBvLM2LNEMUC2OCbMsZt/\nQ3s7C/HBg8mjmOee8z4FaeI4dhftjkBxzp4kX9fbDotiAK/lc+1aPs5tLjxPx26boGQeJ5dcYp8I\nl9Wx2/J1jSns27fz+xwIXm4gKVkd++kAnlRKbVNKjQO4GcBF/iddckn0hubO5TfZU08VPzYwAHzh\nCywqb3xj4bRbv7ADXJi96CJ+I33nO4UTbdrb+RJqP/1pjL9uir4+LmyccQZw/vm8AqFfLNas4Tdt\n2IQiU9iJiuMYf+FUExTFNDXxG1Q7N7/7yxLFBDn2pqbCdS+AZAuBuY5iooT9uOPsReo4xI1i9Loi\nQ0PJr6D0zDPFGazp2G0dMUC24qlf2M1PdWmEPax4Ctgdu/99WcqZp37H3txceGz6x20jaEkBwHPs\ntnxdYwq4np2q73fR8phV2A8DYK7m8ezUfQXEmcUGFK/PDXAufvTR7LgfeIBb4665xntcF05NuruB\na68tnjmpec972HX6Cfq08Pvf88F23XXA3/0di+m//Evhcx56iB27TdgnJvjg8Rdo/J0x/sKpJiiK\nAQrdsssoJsix26jUKAbgk/4f/hD/9UziRjGAt6+TRjFRwm5bTgBw08cOZHfsUcVTwDvprV0bLOyl\nnHlqq2vYSBvFVIJjb4p+SiixOs9XrFjx0s89PT3o6emxPk+vz60dvlJ85fmbbgLe9Ca+78oruSPj\nkUdYuLdvt4thGG94A/CXf8nZ65FH8n0HDgCvfS1/JHv1qwufv3o1cN557NgBXl9i6VKeVNXZyf+I\nwUHe1vr19glFs2Z5XUGaE08E7rrLux3k2MOEXT925JGlKZ7aMCMh/9/oJ2kU093NwhH0e/v3B3+6\nAPikf+mlHJPY+vKTjDXIsQPBwp7GscctnqbtYzcLvP5e9qyO3V88Bfi11q/nfTlnTrKMPa+Zp3E+\nNaaNYuI49rlzix17b28vnniiFzt2ZG/ZzurYdwIwh74Q7NoLWLFixUtfQaIOFBdQ77qL35TLlnn3\ndXYC//AP7Jzvv59dftwKvqa5GXjHO3g2rObv/54LsbfdVvz83/+el9TUHHYYX4z5hz/k2zo79K8p\novEXTjVLl3pRzO7d/Ga3neH92zS3Z4q+C2Hv7+cTapK4pKmJXyvoog3+7ScRdqLwnD3KsR9yCLsg\n22SwKGzZ95bRAAAfKElEQVSOfc8eu2PX+zqJsCsVz7EnzdjjRDFalPyOPU3x1O/YbcXTe+7hY0Tf\nTpKxHzgQvkTx8uXF9ydpdwwiq2M3IxY/ZuSiHXtPTw/e8Y4VOOGEFQVmOA1ZhX0NgKOJ6AgiagHw\nLgAWaYzHKadwoVP3d37rW1wE9ffwfuQjHBd84QvF+XpcdByjFJ8gfvxj4D//E1i1qvB5IyP86UC7\ndc3HP85dNkp5hVMgWNhtGd7xx/Pyt+PjXgxjm0EZx7EDbqIYHcPYxhFG3AJq0owdCI9jooQd4PfI\nffcle00gfsYO8L7u6yvOxNvaCmcimuze7bX/meTR7ljujH31ak/Yk2TsTU38ZbtoNsAnxltvLb7f\nRRST1bHHjWLME4Dp5LOQSdiVUhMAPgHgTgB/BHCLUir1UvFdXXwm27SJ44C77rJ31DQ3A1/+Mmen\n/nw9Lmeeyf/ghx7i3vfrr+ei6qZNhcL80EMswP6WtJ4eFvV77uHn6DetrZDoL5xqpk3jM/XmzRzD\nBEVKUcKu820Xjj1pDGOOMU7OnjRjB8Ide1gfu8alsGvHbhP23bv5f2qeFImCr1wfdODHLZ7GbXfM\nM2OPK+xbtrBxA5Jl7EHP1+zaZb+maZJ2xyDCHHvQkgKAV1eJG8VUYlcMlFK/Vkodq5R6uVIqw1Je\njC6gfu973H0S9A+48EIW99e/Pt3rNDRwln/xxdw58fa385v0rLMKc+/Vq/k+P0T8aeIb3yh07FqE\nzY+OQVEM4MUxQa2OQOGnAH8hNmkU86tfhU+ACOthDyOOY/dfKzQuYZ0xpXbszz5rXzCqo4P7j/3u\nGwgWCFsMA8Rz7G1t/CnA5mT9k6SC+tj1uEtRPAUKhT1uxh70fM2uXbwf/NdiCIpilCpN8XT/fjY6\n8+bZn6OjmOFhfp/pi8ZXjLC75rTT2Il/5zu8qFcQRMAVVyQXCZNLL+WC2je+4bms884rjGP8+brJ\n8uW8xK5S3uyylhb+h5tuKsixA+zS168PLpwCheK9fz+LjS5SRkUxfmFfvrx4LoBJno59dNRbSyMJ\nWaOY447jE2OSNrLxcRYDc392d7MYB81S1I7dT1BnTJCwx+mKIQrO2f0tl83NHG/qOCjKsSfJ2OMW\nTxcv5nqHvp3EsYcVULUI+l17UBQzOupNzIoi6JPC+Djvf38tQdPeDjz5JM9PCCrY64mM27axdujj\nuaaF/fvf546XpN0uSVmyhAXDPKuefz7w29+yWB88yE4vSNhnzuSsXhdONbZiZ5iwr13LccwJJ9if\nY17Q2u+oohy7mZ/29/NzN2ywvw6Qr2NPE8MA2YqnAB80Z5yRrO1RF3n9/9eDB+1/g0vHHqd4CgTn\n7P4oRq/CqAXYdPT+jH3fvuyO3VY81VElkCxj188Pcs56gl+YsJtRTNzCqR637XXD3Lp+vS1bgvN1\ngPfRrFl87JvPmzmT92eaFk+TihP2k07iPyzMrbvE35533HH8pnjySRbAefPs65Jrrr2Wlxw28Wfi\nUVHM3XfzAe7P8TXmCo9+YQ/rY/cfQPoycWETdpL2sGviOPakHTGaoChmbIzFKmi/mSSNY2xjbW3l\n17J9Skwj7EEZbFOTt6pjlLDbcnab8Jg5e6kz9pNPBt72Nu+2TaizZOz6902Copi4MUzY60YJe3s7\nC3vU/J158/jTs87XAT4Ju5ikVHHC3tHBHSpvf3t5Xp/Ic+1B+bpJVxdfos7ENlM0yLEfcQS/8cI+\nneh2Qu24bY59fJzFwPzY7o9itm7lAzlM2NNGMX7HrhTvP5O0wr5gAYum/6IhunAap4MnTNjHxjh+\nM2c0+/N1TXd3cBQTJOxJoxhznXMXjh0odOxmVOO6j90m7O9+N3+y1fijFaXCHbvLKCZu4VS/blrH\nvn17uGMHOFd/8MF4l85LSsUJO8BF06Q5rEt0zr56dXAME0ZY37mfhgZ27UH5urnNvXuDhX1oiMXF\nFDl/FLNtG88J8C8+ZpI2ivF/SnnsMeDccwvb/NIUTgE+sel14E10vSEOp5/OrbSmCP3yl8B738sH\n2PLl3BmlCRP2IMcelLGHRTFBB78WzKCuGCA4Yw9y7Kaw26IYfTUq298QRJziqR+/E56Y4Cw6KI+O\nKp4C0Y5dn1iTOPagHvqw5QQA3vdKRTv2uXP5PWk6dn1/TQp7uTn3XL6G6j33RDt2G0GLdgXxiU8U\nr79i2+aLLwYLu+0N6z+Atm7lWbVNTezM/UxO8kdA/6JUcfBHMffeywe8uVJd2owdsMcxcfJ1zYwZ\nPGN53To+6D/+ceCyy/jEvXEjcOONhcs5J3XsSaMYfUX6oE9HpmO3FU8Bu2PXnTJ+4QkTdu3Y9eSk\nJHMY4hRP/fjfl2FuHQh37PpqX1EZexrH3tjoLTlsEieKAaId+7x5/D/2C7sLx551SYGaZM4cXhXw\nhRf4e1KSFE+Bwo+pQWgBD8rYbUUhfxSzbRufqPQaNX5R+dOfWCiDhCQMfxRz7738fccOrzidNooB\n7J0xcXrYTV7zGp5ZfOWVLBYPPlh4IY2HH2anRZTOse/dGz+Kef557hIJEkEtmEkzdu0m/bWjOBl7\n0hgG4PeK+bfZiqd+/A48LF+3PV8zMcFjftWr4kcxSRw74J2UTSGPE8UA8Rw7UEdRTCVw/vksgkln\nYALJopgk27QJe3s7O4vdu+2O3Yxitm7lE1XQZfnSFk4Bu2M//vhCMU4bxQD2zpgkjh1gYf/iFzmW\nue22QuGeN8/LRoF0GTsQ37EH5euatBl7kOgEdcWYGXsaYY+TsfvxO/Aoxx5UxNy9m8c7fXo+UUzQ\na7ty7FrY41wTNSni2AP47GfTtxzNnu31io+M8JssyZspaJs6itGToczHduwofg29DvbkJJ+gtm3j\nYu2SJcWFTSB94RQodOw7d/LBcPHFhWKcxbEvXlzcf59U2N/6Vu5AClqu6OST2bUfcUSwsJ92mt2R\n6n0fV9jDZiUChcIetM9sF/q2FU6BeBl7qYTdL5ZRjj0oitm1yzsh5xHF6Nf2/+/iOPaOjuj35rx5\nLO7+v70mu2Iqhe7u+MsN237X33eexvmbBEUx+jGbsDc0eG5Fu+murnDHnqZwqsegX+Pee9kd+3Px\nLBm7LYpJKuzTpgWLOsAzI9eu5Z+DTkLvf799mYswYbdFMVGOPU7xNIlj19s7eLBwm/4oJsnkJMBN\n8TSOY7eZrF27uB7U1hbu2LNEMWkd+8KF0cf8CSfwNZr9SBRToZhRTFS+nmSbQcLe1WUXdsDL2bVb\nJ+I31KZNxdOwszj2jg7v08m99/ISyIsWuXXsWaOYKLRjB4IdexB639sO+DyjGH/GHubYx8Y8UdKi\no6MYpZJPTtLb9RdPozJ2//5I69iff55FsLU12QSlrI49bJ0YgI3TFVdEb/vwwws7sTQi7BWKeXm8\nqI6YJNtM6tgBL2fX+TrAz5s/nydhmWRx7ETeRCot7H4xzpKx65OE2T6Zh7CvXcsil1TY02TsYRms\nWTxN0hUTJOw6Y/c/3tzMQjwykr54Wk7HHjeKGR1Ntk6MJk0UM2cOX54zLdLuWKGYUYyLwikQ3O6o\nHwsTdtOxa2xxTJbiKeB9cnj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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "##Now, we derive the coefficients of the cosines and double check that they add up at the end.\n", "##From discussion, we know that we can represent x as a sum of cosines of different frequencies\n", "\n", "magnitudes = np.zeros((N-1)/2+1)\n", "angles = np.zeros((N-1)/2+1)\n", "\n", "## Correctly asign magnitudes and angles\n", "# Your Code Here #\n", "### Solution ###\n", "\n", "### Solution End ###\n", "# End Code #\n", "\n", "y=np.ones(N)*magnitudes[0]/sqrt(N)\n", "for m in range(1,int((N-1)/2)+1):\n", " y = y + 2/sqrt(N)*magnitudes[m]*cos(2*np.pi*m*n/N+angles[m])\n", "\n", "plt.plot(n/N, y, label=\"reconstruction\")\n", "plt.plot(n/N, x, label=\"original\")\n", "plt.legend()\n", "plt.show()\n", "plt.plot(x-y)\n", "plt.title(\"error of reconstruction\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "And we see that the error is very small. For fun, change the np.random.seed(0) to np.random.seed(your_favorite_integer) to get a new, totally random function, and double check that everything still works." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Two-dimensional DFT\n", "\n", "In this problem, we first introduce 2D DFT and its application in image processing. Then we introduce another useful transformation, called the 2-dimensional discrete cosine transformation (2D DCT), and its application in image compression." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from scipy import misc\n", "from scipy.fftpack import dct\n", "from scipy.fftpack import idct\n", "import numpy as np\n", "from numpy import linalg as LA\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "plt.rcParams['image.cmap'] = 'gray'" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### (a) Compute 2D DFT coefficients for an image\n", "We want to compute the frequency-domain signal for a campus picture.\n", "There are two ways to do it:\n", "1. Do DFT for column vectors first. Then do DFT for row vectors.\n", "2. Directly call the function `np.fft.fft2`.\n", "\n", "In this problem, we'll do both and show that they are indeed equivalent.\n", "\n", "The campus image is taken from https://en.wikipedia.org/wiki/University_of_California,_Berkeley." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.0\n" ] } ], "source": [ "campus = misc.imread('figs/campus_256.jpg')\n", "\n", "# DFT of column vectors (use np.fft.fft)\n", "campus_dft_col = np.fft.fft(campus, norm='ortho')\n", "\n", "# DFT of row vectors\n", "campus_dft_dft = (np.fft.fft(campus_dft_col.T, norm='ortho')).T\n", "\n", "# Use np.fft.fft2\n", "campus_fft2 = np.fft.fft2(campus, norm='ortho')\n", "\n", "# Compare the two\n", "diff = LA.norm(campus_dft_dft - campus_fft2)\n", "print(diff)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see, there is no difference between the two frequency-domain signals.\n", "Two-dimensional DFT is just applying 1D DFT twice to an array.\n", "\n", "Next, let's visualize those coefficients." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Shift 0 (DC) frequency to the center\n", "campus_fft2_shift = np.fft.fftshift(campus_fft2)\n", "\n", "plt.figure()\n", "\n", "plt.subplot(1, 2, 1)\n", "plt.title(\"The campus image\")\n", "# Your Code Here : plot the original image (campus) #\n", "\n", "# End Code #\n", "\n", "plt.subplot(1, 2, 2)\n", "plt.title(\"The 2D DFT coefficients\")\n", "campus_fft2_shift_log_mag = np.log(np.abs(campus_fft2_shift)+1)\n", "# Your Code Here : please plot the above 2D array as an image #\n", "\n", "# End Code #" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### (b) Reconstruct an image from its frequency-domain coefficients\n", "\n", "If we have the 2D DFT coefficients of an image, how can we reconstruct the image from those coefficients?\n", "Again, there are two ways of doing it:\n", "1. Do inverse DFT for row vectors. Then do inverse DFT for column vectors.\n", "2. Directly call the function `np.fft.ifft2`.\n", "\n", "In this problem, we'll do both and show that they are indeed equivalent." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "ename": "NameError", "evalue": "name 'campus_idft_idft' is not defined", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 14\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 15\u001b[0m \u001b[0;31m# Compare the two methods\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 16\u001b[0;31m \u001b[0mdiff\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mLA\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnorm\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcampus_idft_idft\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mcampus_ifft2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 17\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"The difference between the 2 methods = \"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdiff\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 18\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mNameError\u001b[0m: name 'campus_idft_idft' is not defined" ] } ], "source": [ "# Let campus_fft2 be our 2D DFT coefficients \n", "\n", "# Inverse DFT of row vectors (using np.fft.ifft)\n", "campus_idft_row = (np.fft.ifft(campus_fft2.T, norm='ortho')).T\n", "\n", "# Take the inverse DFT of the column vectors (no .T required)\n", "# Your Code Here : compute the DFT of the column vectors (campus_idft_row) and put the result in campus_idft_idft#\n", "\n", "# End Code #\n", "\n", "# Use np.fft.ifft2\n", "campus_ifft2 = np.fft.ifft2(campus_fft2, norm='ortho')\n", "\n", "# Compare the two methods\n", "diff = LA.norm(campus_idft_idft - campus_ifft2)\n", "print(\"The difference between the 2 methods = \", diff)\n", "\n", "# Compare to the original image\n", "diff = LA.norm(campus - campus_ifft2)\n", "print(\"The difference compared to the original = \", diff)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As expected, there is no difference between the two reconstructed images.\n", "Also, the reconstructed image is identical to the original one.\n", "\n", "Next, let's visualize those images." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.rcParams['figure.figsize'] = 10,10\n", "plt.figure()\n", "\n", "plt.subplot(1, 2, 1)\n", "plt.title(\"The original campus image\")\n", "# Your Code Here : please show the image stored in the variable campus #\n", "\n", "# End Code #\n", "\n", "plt.subplot(1, 2, 2)\n", "plt.title(\"The reconstructed campus image\")\n", "plt.imshow(np.abs(campus_ifft2)) # The absolute value is here to prevent imshow from screaming due to numeric issues" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### (c) Modify frequency-domain coefficients\n", "\n", "In this problem, we'll look at subspaces of the frequency-domain coefficients of an image and visualize their effects. This is called ideal filtering." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def apply_ideal_filter(MF, radius, ftype):\n", " MF_filtered = np.copy(MF)\n", " \n", " n = MF.shape[0]\n", " offset = np.arange(n, dtype=float) - (n-1)/2.0\n", " xoffset = np.tile(offset, (n, 1)) ** 2\n", " yoffset = xoffset.T\n", "\n", " if ftype == 'low_pass':\n", " MF_filtered[xoffset + yoffset > radius**2 ] = 0\n", " elif ftype == 'high_pass':\n", " MF_filtered[xoffset + yoffset <= radius**2 ] = 0\n", " \n", " return MF_filtered" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A low(high)-pass filter removes all the high(low) frequency coefficients. Let's see how it works." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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AZ+GaSqXQ7XZlnMioxmIxtNttZDIZhEIhMWEnEgnMZjMJDiGzx7bpS0nXFU/u\njngg7wTRH+BbPW/ZDz/YBEcUbeLT19VyVB+WBWVwVUbANh6PRXFSWRKYaHNpKBRaMBuzTUZS0bwM\nALFYbMEpm8qdIIaKXa8+NZjSpk7t/0fTrwbW2hTc7/clsIKBITxPB0RodpPX12ZsberVUcFaNADU\nQFf717Etd1DFUcDMHXXrPo7jf9L74IknJ0k4HBZg0+/3kUql0Gg00G63kcvlZO7QTEvgVyqVJPqS\nQRLBYBDdbnchUCEej0swBSNOyXZxITgej5FKpQRo1Go1YeMJAPnOV6vVBV+vSCSCyWQioJIsWSAQ\nQLlcxurqqgAb+n0ZY1Cv14XN8/v9SCaT0q92u41Op4NEIoFut4tAIIDDw0Pk83mJyh0MBgCATCaD\naDSKfD4vPm06EpnHU2/SbJ3NZiXalSbj6XQqTCoXqdRfdBdh2+PxGMlkEsYY8WlrNBrCujWbTUSj\nUezv7wsoJqh88sknsb6+LsEr1FsEtvQ1tNYKq8uFAI+bTCbodrsSdau/IT6fT8As/QcDgYAsKMbj\nsQB/PuNms3kX3n5PAA/knVqe6UfWbYbUEZv6Y36UmVfvO2mb3q6jSsliDYdDCWig3x9TBwAQUzJX\n9VyZ0VmaYI6rUs0GalaO7J0OwNAsI8dC+zoSbLFdAjT2nx8EXoeAkwBRM4oEmlyRus3X3K+ZPbat\nWUbNzrGPbnM4AaY+lsfoYA03eHMzdsueq+eP58ntCj/yBwcHyOfzsrAsFovCvHDuMnKV85sBD7QC\n7O/v4+LFi8LENRoNMQnSP3c4HMo7Th++8XiMcrmMjY0NMQdS95TLZQEOgGN56PV6CIfDuHbtmgR0\nhUIhZDIZdDodiUhluhFrLW7cuCEBBH6/HxsbGwspj2q1Gi5cuCCmX6ZLoT8gj6fe5X1wUcwoVLqx\nABBmjOlmQqEQKpWKBHN0u12Ew2FEIhGkUim0Wi0ZKy70GJBSqVRQKBRkgV4oFFCv1xEIBCTVDIM1\n6BfIhXwymRQwHggEcP78eQGM8XgckUgEsVhMgDlBJaNlrbXIZrNotVrodrsoFosAgFwuJ6bwWCwm\ngTK9Xg+bm5toNpvC2FWrVRSLRUSjUQHX2WwWgKOjV1ZWnoW33ZNlci9XvDiVuEGXVmD6x+0/pc/X\npsJl5s1lov2/2Lb233L7wGlfuWVMEhUeJ2q73Uaz2US73Ua73Uar1UKv1xPzA69F00YikUA+n5cV\ncSwWE1+6xmnyAAAgAElEQVQ59ikej0vOLALEQCCwACDd98j9/JDwA0DlQWVL4ZjRRNvv99HpdNDp\ndNDr9STKjKYWzUBqgMUxc+f2o3A7ASz7FolEFtgR9oXsrI5C1M+Ofdeshftd0fvJQPBjyA+bJ57c\nipBNYoADTXdkxY0xkkcvGAwKs0NwRBanXq/LHCAwymaz6HQ6GAwGKJfLC4tDAkumW8nn85Kfzefz\nCeszmUzw2GOPCWBpNpuiD3K5HDKZjIBOArxqtSouHEwzcuHCBZnnnU5HQCIDv1ZWVjAcDjEYDHB4\neChmUbp70C2FEaQUmlUrlYqwbWTfjDECrjqdjrCJPIfRuoPBQFhNpoJhOwRuyWRS2FTqSvr6sa8M\nQqG5eDQaoVwuSx8YNVyv1xGJRNDpdCT3Xa1WkwA4wAlQicViYqZvt9tiytWL+W63KwEls9lMfAB7\nvR5CoRCSySQikQhKpRKm06mkv+n3+5Jnz+fzLeRb9OTZFY/JO0G0T53bpErRAMH9W++/3SCXZT5Z\n2vy57JrL/mdfgJs530ip0wdjOp0iEokIaKQ/CxVOIpGQqDv2je1xhagjsHTU7TIGSztM6+hgglI3\n00Vmz22W1b4pxhgBZgDEr0RHD/MaOlqWf+vxYOqAZcCa1+bH0A0ijwLxmmWk6HvnmLqjnT3x5FbF\nWot8Pi/R+tFoVIACGard3V1hbJLJpDBpfr8fmUxG5kahUBBmPpVKoVarIZ1OIxAIYH19HY1GQxhz\nth0MBtFutwVsEOAxojWfz4tVYDQaIR6Po9VqSbCI3+9HOp0WABiLxRaCJRh1WiwWUavV0O12EY/H\ncXBwAGud3HyMaCWwZQSv3+8XcLmzsyPRspxrsVgM3W5XAgm4fTKZ4ODgAOl0WhIbG2PkuF6vh0wm\nI64qXHDGYjExW6bTaVSr1YUoXwLFZrOJtbU1YdcAoN/vo1KpiKmUZuBMJiPfgl6vh2QyicPDQwAQ\nEM5kyEya7PM5KXS4kCb4ZJBFKpWSZ7e3twefzyc61BiDtbW1heheANIOF9aXL1/Gfffdh0ajgdXV\nVbTb7Wf1vffkpngg7wRxm95OOkb/XiYa8J10nJsd1MEIJ13H3dZR7WsgxqSoXLHHYjHxheFxOtye\n6VW4CiZoolJgNJj+4TWBm8DQnQSYAIx95DH6GRB8sR0dHKKZObKbVPAEaMtS4WjfErKJbpC/zL9S\n/70sSnbZ2GuQxw+QZotpjjnKb88TT04jtVpN8qqFQiF0Oh2ZE9evX8fZs2eFsQYgzvoEAAQ3PIdg\nMRgMCuvD+ZfJZLCzs4NMJoOVlRVUq1VUq1Wsr69jf39fomwfeugh7O7uSk63eDwuwQ6Mwt3d3ZXk\nvJy/BwcHSCQSEjDQbreRTqfFt47JjlmlgRU46H/MBSwDRpgsmQsymq1TqZS4p5TLZVjrpIMhe+j3\n+7G+vi6mZ7JjNHGTSSNTuLu7K8EiBNEMZGDkaTAYRKVSETM6U6owApfgXOtG6j/qOy42qYNnsxku\nXbqEra0tjMdjWbxHIhHxCaQ1hAEqDMSgpWJ/fx8PPPCAmLmZJ5FjREBJRpj+fufPn0csFsPVq1ex\nsrLi5fq8i+KN/B2QWwVepwF6y5gbnXaE57kZpGVture5j3X7CdLxeDAYoNvtIhgMIpfLicmQyo3l\nc2impGJku6wsQWGCTnekrpsh01HCDArhqp7H6RJm7kAR9ocO5VSMwE3GTOf443izH7qCB8dG+/vx\nObgjhTUgdIN099jzOAAL96V/AAhL4IE8T25HyMBXKhVhs1lhplQqod1uS/Jamhg5b1jCi5GdnJsE\nLywn1mq1ZF8+nxdWiT5hsVhM5s6ZM2dgjBGfMwZtMIr3/PnzAJx5EovFxBScSCSQTqdFHzQaDVlE\nMXqzUqlImTOyVQDE743sfL/fF3Mw2yoWi7IQpS+hMQbnzp3DdDqVe2A5Nc3qFQoFlMvlBT1KttNa\ni1QqhcFgsJDGhJG0ACToIZ/PS2qbYrEoyZfpisJnwXQpNE8zxUmj0UA2m5Vx6vV6OHv27MIY0edv\nOByKz6AxRsaMQS3VahX5fB6bm5sIBoPi6sNAmHq9LvqzWCzi8PAQ0+kUtVoNmUxGgOpLX/rShXv1\n5NkXD+SdIPpDDhxvAj3pQ0wFwA/6aRg9fW0eu4w14s9JbbmBB310dF8IZHQk8N7eHpLJJFKplCgS\n0vdkyabTqURmAVhYJZOJ0wyaBndUwlTc2j+FpcXonwbcTEXD+6Jvn25bp5Fh22yffnNslz4zPFab\nZ/SzAxbfCY4REzBrs7ybedVtud8nXcrO/bw8U60ntytXr17F1taWRFPmcjmMRiN0u11JXExzpjFG\natDSMZ/zgH5nNLWS6Qaw4PfK93kwGEi1g8lkgnQ6jUgkIizXeDwWli8YDGJ7e1v85uLxOLLZLJrN\nJuLxOFKplCT7patIoVCAtVaiTKvVqviucXHY6/WEeWJ7Z8+exf7+PqLRqLicFAoFdLtdcRGhnxl1\nV6/Xk/QktE6wooVmI5966ilkMhnJA0jfRTKLjFYGIOPc7/cXTLsrKyuiLxnIQnO0BrgMxCAw7HQ6\nUj2k1+uhWCzi0qVLSCaTyGQyODw8xNmzZzEYDMS0SlM6nyHH1hgjjGI8HpcEzdevX0e5XMaFCxfE\n/5mLf6ZTYQQv35/JZIJqtYrNzc0lb6cnz4Z4IO8EcQOs4445aRuFynBZUIf+/zgGh4BJ+7udhu1x\nH6OBCBkzrvqoJLmiZz1FKjkducWAicFgIKZIsm/069MmYoK6Zf6GGsDRv4+mFfr80YTD/rt92jSw\n04whx5R9BSB95372l2Yq/Sw0EAZuRsySAdDHMks8n7l+Ru7npoE/wa8GeR6T58ntSKlUAgDcf//9\nwkCRjUulUpKIt16vS03YUqkk/mFMVcQ5WC6XxXeP73e320U0GkWz2UShUJAIzmg0inA4LH5oujQW\n4ET4kkkqlUoL87PRaCAajcqcYAoWpvtIpVLCyPE+aS7sdrtigtZmU5/PJwmfqee63S4KhYKMF9Or\nrK2tyThVKhUBa7oyzv7+PorFIrrdLgDgwoULuHbtmqSNof4plUpSfo1jnEqlUK/XZWwzmYyUNPP5\nfCiXy1Lxgnn8gsEgWq2WMITMjGCMEbeaer2OTCYjAJq6NBaLSY1fspQE7D6fD7u7u1hdXRXrDP0n\n+U1g+q1kMikMIAE0gSFBMP/OZDLY39/3WLy7LB7IO0GOY/BOe+4yWRaEANz071vm7+WuZkHnf0bD\nnibA4ySmD8BCjjqaHnRdR/ah0WhIv+g/wxU7zbgESqT5WReR5lP69xDQ0DzJRMtUrJpZ1PdAJcaI\nX/e4aVaRSVJ1gAnHX5t9OX4E0dqszX7TN4mmKW2q0YCQz5N5sjgu2kfRze7qYA5t2vbEk1sVBjUx\nrxnNtcx/xmS9xhhJlUEH/06nI6CMiyIyWJ1OR95xRpSurKzI3OUc11UVmFSYufUAoF6vP23ekiXs\n9/sIBoMCushC0ZGf/m1kEllii4wXa8QyOXEgEBCz887ODlZWViT6OJ/PC7OZz+cFQNJECUBqswLA\nmTNnJCiBC9l8Pr+QYoWJg7nYZV5P6kD6ErJ/u7u7C6lcGA0dDodlQcuce51OB9VqFYVCQYJdEokE\nKpWK+PIxtQvBOH2s6ZLC5wo4IJkmY+Yh5btDppELYTKxTBnDFFXj8RjNZlNy+dHkz2wHntwd8UDe\n50mOCnY4SjQwoXCi6RQpBEQ6WEH7prGtWxUdPKLNktymU4IwFQLNI0xbwLD+UCgkq3gCN+Am0OLq\nFbhpSuX16Nw9GAzET45mW36k2CeCP13LlgBUm4h5bzSJLPPpWxb4wHF2/8/0BwTXVLIaIGrR96Hz\nBi5jAAmqgZt+g0cFcHjiyUlCU106nRZTHwEVWTwCAJ/PJz5V7oUV/dJYScLn80lprkAgIGZd6ql4\nPI7Dw0MBZDRpMlpUg7lYLCY6ot1uYzQaidmS7iRMyUFmnT7ABDxM35FOp7G3tyeLx263i1KpJMzX\n4eGhABWmMNnZ2UGpVJKoXiYzbjabYuZstVqyWGXaGM5NmmCZVoal2wiWZrOZ+BfSPy2VSuGpp57C\n2tqaAKXNzU0YYzAYDFAsFtFsNkUf6jRTXHAzsXMikUC1WoW1FvF4HO12W1xptC7MZDISKENzciKR\nEJ9KWl84lnt7e5IztFarYTQaSRUUsnmpVAqdTkcCVwj0CQJ9Ph9WVlaktrAnz754IO/zKMeBOrdo\nMKJ97nSaDu4DIEyQ27R7K9ekuKODdf/ZHhUswRmj76g8ObGpRAhgmNpEm1E1y+UOOiDQI2NGoKhN\nm8zFxXN1vjptYmV7VF4aSNN8TCbSDfj02PDjpZ8VUyXQN0jvd/te6r7wehxrnW5GX18Hmtzuc/XE\nE7IsZHnI7ug8aD6fU39VlynUQV40Ber0IACEFeTijqZM+sUx0IpghQwSy5XRV41RpXt7ewgGg1Jq\njaZV+sGRGSMDx0CGbrcriZZpomWuPJo+c7kcAEieOrJpzAFKsDmbzdBut2WcVlZWJIcczY6DwQCp\nVEpSkxDkTKdTsSjQXL29vS1BDQRp9C9kztFkMikgyBiDg4MD3HfffVK6jOZQpmJhAEkkEkE2m5Wg\nDp/PJ795HT6fSCQifnTU12Q8ASCfz0skcbvdFr9rAlj6RYbDYVy+fBm5XA6JRAKj0QjpdBqHh4eS\ntJkl4FhNJBQKLZjEPXl2xUuG/AUg2gSpgYsb3Gn2h4wS05+cJuiCjKD7h/v1cewTf7iKZ8g9WbF2\nuy2Ov1ypMiFwq9VCq9USEMOPAZNt8m8CGpp53aYF+rZokyaBGJXreDxGp9ORa7I/BGjavw2ABFrQ\npKA/am6zsPt5sAzSo48+KgllNZDV7Bv7xhWyO+iCSlAzkXRaZhJpXtMTT25VdNRkPB7HlStXFvzl\nCH7IHieTSayurso2LjgYPcp5wo8/9QJ1SbfblUjLfD6Pw8NDrK2tSXs0q9KXS7tM0ORXrVbFZ4y6\njjn06E8HALu7u7DWSW/SarUkIwDNqLwmwWu9XsdsNsPly5fFt4zJ4ZlomSDv+vXrUm2iUChIqTX6\n7xKgUb8wQIGAipGxhUIBm5ub2NzcRK/XQ6vVQiwWk0ARMqCrq6tiQmWABPPhMZ0KdSXNxgTMZGi5\ncE0mk3L/rPVLAEt92m63BdDxm8LxYmJlrb9YYo19ZVULBm4kk0mx7mhdT7O755d398QDeacQDZ6W\nASk3IDqNaU0fq5m7o9rRoMYdban9yU7qv772Ucctu36/38dsdrP8mTY98qfb7QrgI1NARcFKFPSr\nYQh/r9eTtCv0AaGPDZUGARnBEJk4Vufgj/tedCQvI3N1ehQ3cNbBFLq0mdvPLxgM4sMf/jA++MEP\nSuSdeyy036E2A1NpMgcZ+76sOocGiMuibz3x5CRhKS1Ga95///1irmy1WhLcQL9Sd1WMQCCAdDqN\nQqGA/f19Ma22Wi0xuTJ5Lv3H6LxvrcXKyspCtQiCD77f9Lc7ODiQ6F0CSfoNci7SNMrFVjweFzBC\n0DocDnHhwgXkcjkBNgSSoVAI7XYbDz30kJiqd3Z2FnLgMTiFDD7gMHeMEma+OPrXsqRXIBBAs9kU\nvQZAqnEQ3HERS2ZwOByi0+kI2wlgoYZtNBpFt9uVRXCz2RSAHQ6HcXBwIKXl1tbWxLpSLpcRDAZR\nLpfl2TMRMhk5mnN3dnZEFwEQFxwyqLSksKQbTc80kzP/H59ZIpGQ8mq0uPBYT+6OeCDvBHEDnpNA\nHnCymVb72Okfvd3dHj/2OlKVQEYrTncf3WBtGZDkNr3fzWZpZopAhKtsDVo0oNPAiawZTb5kE6ic\nNVPHyC2CQJp99P1rU6geDw3QdJSuTpnCe2LfNZAiiHYHRmh/lX6/jwsXLuBVr3rVQvoJ93EEbQTh\n3E5QR0d2mnsIIHXf2X8vjYontyPxeBzWWmGsmNaiVqsJ40KTJ5l4MnGaeZ9Op1hbW5MgjkwmI3OJ\nwCgajUpdW/rKMhUScDNp72w2E2ZwPB5LkAPzuzEtCVOvdDodARhk8gguGW3L/hJQHB4eysKp2WzK\nApURvvl8HuFwWJItM10JfRQLhQIODg4wGo3E37jX62F/fx+BQAB7e3uiHxnpy3YCgQC2t7eRy+Uk\nQAVwgsxYF7ZarUrQRzqdFr25u7srOoUVLLLZLHq9ngSOsVQax5L9WllZQavVkjQ5W1tbosc5LgzU\nq1Qq6HQ62NzcRDQaFb88nYIGcAJjGFmbyWTE7ByLxVAulzGb3axRS9BPgMzobYJhT+6OeDagOyDH\nfYCXAS4NroDFiFptQtXta4f8k5hF9/WOOu445m7ZfneftO+brnfL5J78qDDylpFvVCTuKhZcJQIQ\nhc2VOk1FZNfo1KxBMQMgNOtJ3zjtB6efl/6bbVM0cNT9ZO4nAtlkMrmQRmDZuNFfhx8etssx433o\ne9RMoPud8MST00i9XkcikViICqcuyWaz6Pf7yGazsrACnDlBPzpGwnJuDYdDMV3qUlUMfioUClIO\njCwSgcVkMpGqEvSFI3PP+rpcZCUSCQAQkEnzIAABlowOZYmvw8NDCZxgEuZyuSyuIIFAALlcDtVq\nFSsrK7DWSlk1BlYwUMBai42NDfEzS6VSMkZkz2htYJUcslWc84lEQpj+cDgsARn0iePCkH6ErVYL\nZ86ckfECHF84Lna1ywfg+NExkpkpUqLRKK5cuYKNjQ0xQXPRuLGxIWXd+DwJ5FkCbTweo9VqwVqL\nWq2GeDyOcDgsUcBMKUOgx+MI7GhmJkDnOPDd8uTZFw/k3WFZBqz0b82UHbVNi65ooc0dpzUJn/ZY\nYDGq9Kh74XHu83SQA8EXfQabzSb6/b74qlABa5CjmS4GZxhjJIpM94HHEMDRjEsfEI6lzrWnzcya\nBdUpD3QUK4/TJYso4XAYV65cwSOPPCLRhhpMUqmyzxokMjqZYI+MhTYd84fjoNvzxJNbEdY2ZRBA\nqVSC3+9Hp9NBoVDA7u4uisWiALtsNivRmXy3GWjQaDQELNXrdQFrzWYT4XAY5XJZcrhxvtCkp9OZ\nkLViVL61Fvfffz8qlYow94VCQapdkCGnpYDVHciUEYgwUIFR6Y1GAxcuXEC1WgVwM8hJVwChSTKf\nz+OJJ57AYDBALBaTuqvUVcwaoOcpffio6yKRiNTzPXPmDMrlMmq1Gs6dOydsJceeoCmbzcpYss4s\nnxN9ihlgQT/jarWKVCqFeDyOWq0m7RKMNhoNYTjpj8fKJ+VyWQJXYrEYdnd3USgUBETSJLy7uwsA\n6PV6WF9fl3Ynk4nU/mVN4UqlgkKhAL/fj1qtJoD/+vXrKBQKEljjyd0RD+TdQXGbQrkNeHqKFP17\nGbhwp+NwR3ceJ0cBTc0aabBzFAO17NxlrJ/73riNII/Xo1mXefcIzujMTCCj/fAYfUYAqe+B5lWy\nhjowgwCOEYCM/nMHNAA3gbSbVaSfoNt0TqfywWAgJiqagvUxmknUQRt0mNamdp3GhWPJfun0Lp54\ncitijJHqE6woQbAyGAwEKJFt0uWrmG+NDHQikUCn00E2m11w/GfELatqlMvlhcUPfdjoYxaJRIS1\n01G7ulYtgSNTodDvi75s6XRaKl/4/X60221EIhGUy2Xk83lZ0NEdJBaL4caNGzh37pws3g4ODsRV\nJBgMSg46+v2NRiM89thjSCaT2NraQqvVWohUZpACAAn8YgBGPp/HxsYGcrmcRJlaa3FwcCClxsiE\ncsGaz+eFze90OkgkEmi322g2m0gkEuInRzaWlYg2Nzel1Fir1UI8Hkc6nRa3kKeeegrFYlHcYxqN\nhrCM7C/N4ZVKRXQTn5tO6bS2tiZgXkfS0t/w4OAA2WxWUr9UKhXRkZ7cHfFA3jMUN6BbBpDc5j43\n2OMkdyfj1X8fxaSdZK51/3Zv0wzRMiC5DMzpXHTLxoE+MmT0GBlK4MI8W1yBE+QRAPGDQ7MFI7vc\nvox6PHRNXG06JlCjuZbAUDN9HHud3oXbdL1e/YyY0T4Wi4mDNdtyB0kwfYvuO5k67U+pn/Vxfpae\neHJaYVUDv98vzAsBEwCpoNDr9cQnzhgjUfRMl9LtdqV0FZPgbm1tLbB2oVBIEh6nUikcHh5KMARB\ngU5UzOhbDZToP9jpdAT0pNNpNJtNSeLMcmRc/DEoiwmPmdqIaVASiYQkeiYLSbBGdq/Vasn1GDDA\nhMvUIbVaDfl8HgBEh3HeksGnfy1LjPG4ZrOJ1dVVJJNJCU6jD1wymZSasVz4cQHJnH3D4VCeEcdp\nOp1ifX0d1loBz3yWulZuNpsVvRSLxXDp0iXU63WkUikxxfOdYATz1atXheG9dOkS0uk04vG4jFu3\n24UxTroXWml47VAohM997nNYXV2VZM3atO/JsyseyDuFEBQsM7UuA0EUAhzN1lApMNrNzdqxfQ2g\neLyb7dOir7GsL7qPx+3X+45j7fi3Dhpxs33LWEoqegAS8cWcVoDzUWLEHz9EjUZjwWSpTdc6aMRt\n3nT74TEQgoBN56EjaNWsG/vJ1DFU/vv7+6hWq3jkkUckepF+dryO+1nphYAeKz2u2h/zVphbTzw5\nSujaAECqLNAPjx911kcFnEoOZN2YJonzgWlMOp2O+KuR1W40GhIUcfnyZbz4xS9eKCnGklqMLuXi\niL5sZJ0CgYAERZDNZwR+qVQSky3TN4XDYQnOYDUJJkcGsFA6rFgsivmZ5skzZ86g2+2KWZO6dzQa\nIZfLodfrYW1tDe12G/l8HvF4XMzW1MnUAYAT4LWxsYHd3V3k83kxH2cyGezu7spi9syZM2i32wIw\nCYYPDw+RTCbF+sCkypFIRAJgdES0zlO4ubkpFg0Gp4zHY2xubuLw8FBy6G1sbEggCS0ljJZOp9Po\n9Xq4ePGi6Nt0Og2fzyfVUJgfjwzu2tqajHexWEQsFkOpVJLE0wyi8+TuiAfyTiFHmTEBLHywNQjk\n35px0mZPLdosR3H/r0GDbssNANysIbctuxe97Sjwt+z/ZfvcjJM2RS67LtkwtqGDSqhkmR+P5hSd\nL48fLjcDqkGUBm0abOoxcge6cMWr7204HIovUTgcxvb2NgDHKXprawuXLl0Sx239jJexcTqZNH8f\nZTbXANYTT25H/H6/lKRiugv6k9F0ywTDNO3SYd9au5Aeg471wM1FCRdLnU5HInfPnz+PK1euIJFI\nIB6Pw+/3o1AooNvtIpvNSp1W4GZ+PrJqBwcHwqjR4b/dbktKEEZ5Ume2220BdhrAMlqU/nurq6ti\nqqQbCPVOLBZbYBEJXuh/SKYsk8lI2hm9MGT9WiY5Ho1GyGQy6HQ6qNVqaLVauO+++yT5MoNS/H4/\nDg4OUK/XpV4wcNPiEQqFhPGj+ZTPzhgjaVdonu31egtuIZcvX0ahUJCUKfo++ayY6Pry5cvIZrMo\nFoswxslRSB88Pq9msylgv9lsStAHdRjr/sZiMQGzh4eH8jw9uTvigbxTCie19vlaBpg0oHCzRMDT\nmR1gMbhiWVDDsr/d111mmgVOZoR0gID7uGWRvnoslgFAfW/an4xjwQALN9By13XV+QAZpafNIssi\nc9kuARlZPfrz6XtjW/p56TQ2GmAxPYTP52S3/6u/+itRwrxnnayY9+k2v7tBpd7uVoL6nTmOdfXE\nk+NkNBotVJigCZMsEFOccP4xApYRkjSHMvigUqlgfX0djUZjYe7QjDmbzZDJZATcDQYDYfmYi84Y\nIyDAGCOlunQFB51jjuW48vk8KpWKRHP6fD40Gg1hC6PRKLLZLIwxOHv2LCqVitTapQ4ge8jSiwS6\nTGdE4EOfMh1oweAPzs18Pi9jeOXKFaTTadRqNWH8e73eQrkyMpgAJJJ1NBohmUwKO7e/vy858Oiu\nYq0VkzPb4QJZRy3TvN5oNLC5ubmQCop1w2ezmVgeYrEYcrmcADbqp16vJ6Zn3juBNhcFDEhhVHAq\nlRJGMRqNot1uCwsMQMz+njz7ck+APGPMVQAtAFMAY2vtK4wxOQDvAbAF4CqAb7LWLi2w5wZs2jdM\n+6TwWG5fdu5RQE4zdwRKy447jlU7zTb+fxI7x34va8cNIHW/NDDi/5pV0/dpzM1asADE5EE2TeeY\nI+3vTlKs++gGTfxNMMfIOm1e1s9Ht8ltTHlAJ3KCOW3a+aIv+iJ8/OMfF8VL1nEZy+kGkO5jlokH\n8u5teSb6SyfXNcZICSp+7Ov1OjY3NzEcDgU8MBrzU5/6FFKplFR+YEqk8XgsaVkajQby+byU2iIb\nVywWsbOzg7Nnz0qdZ/rTETAQnM1mTi3UVColZcTIDvb7fcTjccTjcUnuS/BJUMe5SWaLuoJzfzqd\nIpVKSUJi+qgR/NBPkGXDCFAZDMYar2Q1p9PpQiJmDVQDgYCkf6FvHRevTIdCfcQk0ax6QXM3K0z4\n/X5h0RjExrFkfs+NjQ0xHzP/YS6Xw/7+vpSM29jYkMpIzPEXCARQKpVEf66trUmQDVNgkaFkUAjT\n6hC8Mdk0xxFw3G3ov0ldSb9qT+6O3CvJtyyAr7TWPmKtfcV8278A8AFr7QMAPjj//1jRoIErUSan\nJPBws0v63GXs11Ef95OYvaOA27IfLe7gEL1/WeDIcW0vY/m0mdYNapb9aNaOx2mloYMTqFBocuB5\nejsjbZmKodfrodPpCHPBlS3vl88yEokgkUjI6pTPlEovGAwikUjg8ccfl3MzmQwCgQBarRZWVlaQ\ny+XEWZpjQcDnNjdzkcBr0HlcV/ZgAmlu8+SeldvWX5cvX5bURMYYYdMIYIbDIarVqjA9DByYzWY4\nc+YMjDGSBzIajQqgAyALJ2OMmB9DoRByuZyw781mUxgxmoo59zudjkTb08mfLF6325W2CJbIMDKy\nnW3v7OzIHKEpcnd3F8PhELlcTgIGaGbVOoTXt9YulFWsVCpS7YHBYWQCOW/j8bgkS55OpygWi1hb\nW17h1V8AACAASURBVJMFJqNtAYiZl6mTGOEai8UQjUZRLpfF75eLRd7L/v4+bty4gVqtJqQCmVTq\nkv39fWH82Fdec3d3dwH4rqysCPjn+8B0LoPBQHwC+XwBiI8fzeXBYFCeH822fDaxWAyZTEZ0OkGq\nJ3dH7hWQBwBuKuTvAnjX/O93Afh7S09SgIRATvteaTMkhc6wZKQ0qKDQvMj9mt0i26QBk/Y30/5+\nGpDp3/pvt9nYbUI86njdZ57H/VoBuJkwAhfNprmPd9+TNj1oEwOVsNuM6y4bZoyR9CgESOyLNqUe\nBZyZioWO2fyhz0+v10O1WsXh4aE822azKYEi0WhUjuP1+EHRP+w/ASmrDPBvd3kz3r+XTPSel9vS\nX6urq/D7/RJgwY8xfeRY5soYpyQVi9JXq1WZP2RsGKXLJOV+vx/FYlFMewRZrK1KH7dKpQIAsmBi\nLjpWnIhEItjb25MULjQd0mTJ+cFk6e12G+l0Guvr6zDGYH19faHMFuD4y/JeptMprl27JhGsrVYL\n5XJZWLz9/X3RQwxC4RymHgAcvc7kyQRi9NnL5/Ow1kpuO+CmrtF+kNqM7U4TxXHnwm5vb0/AZyAQ\nQCaTkeCXUqkkLCgj/fk3dS7LuRGsM2qZ+fRYpYggbTweS3AIF9kEpsDNrAWsDQ44Oo5RvLPZDPv7\n++h2u2i1Wuj3+6hWq4jH45Kr0JNnX+4Jcy2clfB/N8ZMAfyStfZXAJSstQfz/QcASsc1QN8CzahQ\nCdJsp1dgAASEuIGF/tttZtQBBG4Apv3QuM2dSuQoWQbkdNDIMtZP/68BJUEar+02ZS8zLZLV0tfS\neeG4XeeWI5jsdrsSbEFTB+sn6uANnUeP7B4VHvtJpcrraSCtSyNxv/Yrof+JMUZMRABkJc53gZnt\njwJmvEf32Okx12wwx8GTe1ZuW3/VajUUCoWFhSRNZ5PJRNJoEDzRz4wVJkqlEvr9vviq1Wo1AVvA\nzTx80WgU1WpVFq8sh+Xz+VAsFmGtlX4wojaTychCbmVlRUr8ccGztbUFv98vPl+RSAT1el3Ysdls\nhnQ6jUAgIEl4WYOXkaXad+3atWt4+OGHUS6XUSwWsbu7izNnzizUy2VFjHQ6LaBQ5/vjYpXHcx/B\nHOD4O/b7fUkpEo1GJZcf2cRIJILd3V1sbW3BGMfPbnV1VQI+Go0GisWimE1jsRgODw/lfgAn6rVe\nrwsjmU6npVoFExzTj3JlZUWeIRfAZEgjkQjS6TQajYb0fXV1Ffv7+1JmzufzyfPnODDQgqlscrmc\n5OnrdrsIBoPIZrPY3d2VKimePPtyr4C8L7XW7hljVgB8wBjzWb3TWmuNMUsRUrlclo9sKpVCLpeT\nfTRPaL+8Zf507mS2bpPrsoCKZQBIgxP+XsZMLWP0lu1zb3Mfp893gxEtbl/BZdfTbJ4Gg5oV1bUl\neS1r7dMYTTpA877JxDHhpjYJURm7x08DXfZPM2e8Z/qgWGul0DiBYiKRwHA4RDgcxtmzZ1Gv1zGb\nzSS1A/B0k73us3uctZM3AHz2s5/Fpz/96QVg7ck9Kbetv2j65Lt85swZYVmYcoTmykKhIH6n1lo8\n/vjjOHfuHGazmSRAJrNDVq7RaEjQAMEXy32xukYymUS73RZmjwDBWotGo4FSqYT9/X0Ui0WkUimp\nokFGb21tTUpsDYdDqeLBqhn06aMZNZfLSWQnAzay2Syy2ayYRH0+n/S7XC7L4l37MAKQ6Fm2Tb9E\nAqtwOCy+g/Q5PDg4kFQrTOhMtpT+fT6fT2rNAhBzdrPZFFN1MBiUyhXGOPV09/b2UCgUhN2k5SOT\nyaDZbCKZTKJSqSCZTKLf70v/8vm8+Nhls1lcvXoVGxsb6Pf74kMXiURw5swZjEYjMbFyscpSbqlU\nSsrF0V+Z7wfPo/9mo9HA3t6egH5P7o7cEyDPWrs3/102xvwhgFcAODDGrFpr940xawAOl527srIi\n5biAxZx5br85d6DC/JpP+82fo9gb97n8WwMfHu/2gdOMlrs/ZBaX9U1fe1nAxXHgzh1Yoa+t23MD\nG+2HR9FAjMcTMLnvRQNH93iStWOfyCTSDENTOllYmjNoJmW/NQDb3t4W36VgMIhLly7hpS99qZir\nyELw48S+aFM8cJPJ0+Bfm+K5/9y5czh79qx8YN7znvc87Rl48vyXZ6K/XvCCF4gPmmaWCR6Yj47s\nCyNxfT4fLly4gG63i1wuh1AohN3dXWF1AIgpdDabYXd3dyGQgkAxk8lIst1sNivggWwWGabV1VUx\n+dKUybnIeav9Z1utFtbX18U8yDxxBEi8NiN0h8Mh1tbWcOXKFYmI1bVVaYkBnCAEzlsmYi+Xy1hb\nW1swj7KvZPDI7BUKBQFo2Wx2IWiCzFuz2USpVMK1a9cQi8WwtrYmuon58Rh5y4Um9TrHg+CdVSeY\ndLhYLEqgB6Noy+Uycrmc5D4sFApSCo7VO8bjMba3t3H27Fns7+8LmGWQGZlS6lUye4FAAO12G8YY\nFItFNJtNibDm+9HpdHBwcABPnn153tMDxpiYMSY5/zsO4HUA/gbAHwF48/ywNwN477LzdZ427SsH\nOCtWKhgCG3fyXx0coNOCuPr4NICia6AuA4PaF5DKkKCIoID94W9drFqDF3cwgLtvvBd9T25QpX/0\nNdkXrny1OdU9Ptrcynbo38doPK6ME4nEQsmiTCaDZDKJbDaLfD6PdDotpYC4iqepQqd+cAdssHKG\nBuP8uXr1KmazmXwI6/W6lBxaX1/Hi170IgBYAGq8B52gWb9LmlHUY0YWUp/ryb0nz1R/AZBcbQBQ\nqVTQbrcXFjiBQACVSgX9fh/9fl+iRxkVyQAEljULBoOo1Wrij0rTJBdo0WgU0+kUa2trALDgI0tW\njzqLvn+Awzo2Gg2JnOVcYd45soX1el2ihAGIGZLRqTs7O7h27RqstahUKqKPaBZeWVmRRMCZTAbR\naBSZTGYhNx5ZOrpu0AcOgJhgCdYIXur1ugRjRSIRAWhkyzinWRFkOp3i4sWLYirXPoUEs91ud8HP\njlHNZNh6vZ64iLC6xWg0QqvVQqvVEsa1UCjg6tWrovO63a74AMfjcenbgw8+KNU5uKBl9K+1Vvwc\nqSdZXo66n8BUm8rH4zFKpWO9oTz5PMq9wOSVAPzhHJAEAPyWtfb9xpiPA/hdY8x3YJ6CYNnJ7nQb\n+mNLFkmX8HL72+nABS2avTrpA879bodezZZpwKTZPXekK8/VoND9e5noAIllpmm2qf3f3EEp3KfB\nKOti6nQHZAN00lINIHVOJ3e/3EEfbpP2Mra03+9Lwlidv4umB7/fL6wFlfbm5qYo6Xa7jYODA+Ry\nOWQyGXEypr8L0y0wtY4eL4oGu8v8F48yh3vyvJdnpL/oBJ/P58XXzefzSQ3S6XSKXC6HyWSCdDot\nBewBSFBGp9ORkmfMZ8foylQqJabBSCSCarUq5liyOtlsVkBjMBgUH7DxeIz77rsP1lpJCHz16lWE\nw2HE43EJYGMJrna7LezcYDBAuVyWsl6AA/ZWVlakgo7P50MkEpEkwAQ9uVxOTIu8b2udhMfpdBqf\n/OQn8YIXvACBQADNZlMiYBmJzPJoTOly7tw5AUQ0xxL4MG2LMQb1eh29Xg/JZFJ0KN09WEkkFApJ\nEAddP2iqJSCr1+s4ODjAAw88gHg8jn6/LwA3GAwKa8gKIjTZsv4u9dh4PBawnk6n0e/34ff7EY1G\nJXJ4NBrJ+JO1JMi29mY9cuo9HVhGf0uyep7cHXnegzxr7RUAL1myvQbgq086382yacBFs4MucL/M\nR+6ZyLKPu/7wL/OH0wDCbUqmuE2oJ4k+XofVE1BqMyrZAZ5HVlEDUX0874PmEs3s6XxV7ihenaLE\nDfjou8c+aODHPFBcjRKkc0wnk4k4Rt93332IRCJ44oknkMvlEAwG0Wg0UKlUkM/n8eSTTyIej4v5\n45FHHsGHPvQhpFIphMNhcQTnh1HXnXQzogTummXV9+vJvSfPVH9NJhOsra3JHAIgVSSYz40Jfo0x\n8jGmyZC+YpynjCwNBoPCtjWbTTH9sjxZqVSSqNrhcAhrLfb29gTAsDwW4CyGWFf3gQcegLVWSn1F\nIhE5hwuuyWSCarUqlRQYSMJkwGS/otGoBGix34yupWm51+sJgCSD99BDD4lLBpkomifpuzcYDHB4\neIhcLodkMonDw0OUSiXJK8eMAMY4lSlarRbOnDmDVColfow0fTIdTK/Xk/Qnk8kEV69exfnz5yX6\nGADy+byUY6vVaiiVSlK3l+Cr1WphdXVV2mk2m9jY2BB/Q0ZKNxoNYVy1XuJzjEQiUkWDKVtisZiY\nixk5u7GxwXdSTPKpVAqdTke+L152gLsnz3uQ90xFs2KUZWzMacDdUYzMcSyN20S7bLu7jWWsoQ7k\n0ACCil+ff9J9uPe723Obb/XYHJUaBoBE3hG0cQWYTqfl40GFyw8M0w2QfdNgUle94PbRaIThcLhg\nWuffTG5KFvHGjRuyip/NnBqTLJEUDofFwZk+LI1GA6lUChcvXsTjjz8uecX0R1SDX/1M3L6aGty5\nn70nnpxWyJAnEgkMBgMx25JVJtNG8MJ0GuFwGNFoVBhlgp5qtYpUKoXDw0PxZeMiioXtI5GIAAbW\nePX5fFhfX8dsNsPa2powhNvb28hkMhK1SV+zUCgkARU0mZIZZ/ADgIXFYCwWQ6fTkUoRzPnGIA/6\n1zHimIs8AkYGlNAnMBwOI5/PS8QqEz+z6kM2mxXdEAqFUKvVsLGxgZ2dHalh6/M5FSRoNibrSdNm\nIpFALpeTlCQAUK1WkUwmcfHiRTGdsw+8D9abZeQzmTMytUz63Ol0xK+c+TzJJs5mMxweHkr+P4J3\n4GbwTDKZlHJmsVgMxhgxx5JVDYVCkldwOp0Kw2utRS6Xkxq9ntwd8UDeKWSZj5betoxJOwq4ndbs\ndhSgu1WznW5HpwPhpNNBAW4T7zJxm5m1Hxm3uc2jbqCq2yfDQL+dZDIpyVS5atf+hfR3ITOnkwxr\ntk8HNpC9GwwGEl3HYA6CvslkItekYqap5Ny5c3jiiSeQSqXw4IMPSqJVv9+Pz3zmMzh//rwU6W42\nmwgGg5ISYjabiU8TzdDMO6VZu2Xvk5u99MSTWxXmxmOuu36/L4mBWW8ZcNJx6AhVY25Go9N3K5PJ\niKkzFAqhWq2KjxijPi9evChRrQQF9P/ie86gKJ3onK4vjPTk9WgirdVq4peXyWSwv7+PXC6Hg4MD\nifqMRCJIpVKo1+syZwgMucBjSbNUKiVVIci6cSym0ymSyaS4WESjUezs7GA2m+Hhhx+WtE4EiQcH\nB2KiZtqZ7e1t+Hw+8X9jqhq2f3h4iFgshkajIaZdmlcJpHRgGRMQk5GkFWU0GgGAuISwvFi9Xpfz\nWRFjPB6jXq+Lr2UikUChUIDP58Pu7q4EohDoU8cBEGDX6/VQr9fF31IHg1CX0/TMJNrMzejJ3REP\n5J0gyxg7LZqRcZ93J/yoljF1/F/7u+n+uI9x73NvdwOxk/rhZpo0cNNtuauBcMXP/wnYfD6f+KXE\n4/GFaFodmaarP3B8tamY4Ekra/ZJR9Pq/UzwqcFhOBxGrVYTNiGZTOKFL3whOp0OPvShDyEajWJ7\nexsve9nLcPbsWfzqr/4qCoUCXvayl2F9fR0HBweo1WpYX1+XdAKMMCObp0GwG/h6Pnie3CmJxWLY\n398Xh38uOJiuiKlGstmsRJ3qhU8ymRT2yJ2YmKCDCX7p85bNZgE486vX60nR+3q9LgCTcx+A5Nlj\nZZnt7W2cO3cO9Xpd5gp9wAjUeG1GjBL8RCIRWWjy2gAk8GE0GkkuvGw2C5/Phxs3bmB9fV2SDdPM\nW6/XF0BUq9VaqBXr9zsVQ4bDIdLpNLLZrLCByWQS5XIZpVJJUm81Gg30+32USiWEw2Hx92MEML81\nzE1IVrFYLKLdbkvOu3PnzmFnZwfJZFLusV6vSymxXq+HWCwmplaajJmChotNgt/ZbCYpoMjAxuPx\nhUAYMo3hcBjr6+tiDQFu1uGNRqNSGaPRaMhimePqyd0RD+SdIMwDpBMRA09PM3KUuVazMvr/ZbKM\nvaO4QaPuh9vMtwwkLAN8bpDkFg2kaHKh0lhmEqZy1RG7NKVSsRNEEezww8MABW26NcZIRK2OCp7N\nbiZjZWQsTTq6bBlNCQDk46SdtDXAYr91+pnZbIarV68iFArhiSeewGc+8xmpockPQTweRy6Xw/Xr\n15FKpXD16lWMx2MMBgO8733vw5ve9CY0Gg1ZedPHh2Om3xuu4vV4ngS+PfHkOEkkEsjn88jlclLX\nlEmHGaVeq9UQi8UkgTDnIyP3aco0xojfGctlJRIJdLtd5PN52U4A1263sbb2/7P3bjGSpVfV4Don\n7vf7PTKzsrIyq1zVbhkbX5AsbKOfEfgBBhkJWSCNAAlZvwTP/7zwgvSLeZlHJB6Y0f/AIGE/jAfE\nwPyyBNgM9jTYrW5c7bpkVWXlJe73E/fbPESvnTtOZzm723KV1D5bSlVWROSJc07E2Wd9a++1dkFA\nUSaTwXQ6lZFe0+lUFLvvvPMOPve5z0npkb1tBJrNZlN8LLXinoC11WohHo8DAHq9ngiYqDTNZrN4\n+PChTH+gIjWZTOLg4ECuRZotc0HIfMS+QDoqzOdzJBIJtNtthMNhUZKy13G9XssisdfroVAoiIqW\njKphbEyb6/U6MpmMqIrJoDIPaXDMMjWwAfDr9RqDwQCJREJ6IyORiFioVCoVyYM+n0/AmX00HU2l\nT09PkUgkkM/n4fV6RQjHash6vZZ+wnq9LnmbrC0FOCy7M3fTZsaJlx8OyLsmNOjQQIvs3XXgzv7Y\nVY/rPjZgW9xwXVxVDuU2rvsbe8+XvXxIcAtAQBYBkb2/jH9L3y0+plk7DUwJ/GjDEIvFpFzA3hIm\nWp4jPfuV3lHcRy2muIqd4+PclmZgdYmZTv+tVguVSgXdbhdvvfUWstmslJgowOj3+7h//z5ee+01\nBAIBTCYTnJycIBqNwjAMpFIpHB8fS98ObQ+u6vHUghR+HjxnGuw54cQHCTbUW5Yl5Uu2JlCUUCgU\nhElirxX7sNjesFwuUavVkM1mhdHa2dnZEkIAwN7eHtxut7B9ug82kUjIzZ9gg7YfkUhEFkMESyxh\nFotFAYumaUrDv9vtRrfbRSwW2/LrYw8iGSaWFsPhsJRpOYHh7OxM7JhoHszSLa9FMo00YU6lUqhW\nq1K6zOVyYt6shW5UJy+XSzSbTfHGIzAkkM1kMnjw4IFMv+C0CC0uo23LaDTCYrEQtS0tTCaTCYrF\nIp49e4ZAIIB0Oo1Op4Pd3V2xM+Hf8rjYO8eSNgBhN+mjyP4+AkGaILtcLun743dA5+NgMLjFCLMX\n1ImXH06jzzWhJyZoUKdvzAx9g7azanbGT/9c9fiL/h7YZhH16zWDZv+xA7urvOz4O0uierYiS6V8\njDeJUCgkHlV0Q6dYgas4O+jT+xiJRBCLxaRniECNII2DwDUg9Pl8WzcPyvjZO0Spv2VZ6Ha7aLfb\nMoN2OBxiOByK/5MGhJydOZ/PEY1G8fGPfxwul0ual6niY4L/+7//e3zjG9/A97//ffz1X/81IpEI\n0uk0bt++jR/84AcIh8O4d+8eIpEIQqGQlKb1+b3qh8/zM9afuRNOfJBYLpcIh8MyheXx48cIh8My\nf7Tf70tZlPYovV5PWgzIFLEUCkBGflFJuVwuUS6XcePGDbmmuOAhoCMAajabCAQCIoIgOHK5XLKo\nokUS+7uoTmVuSSQSMAxDwGqj0UC5XAaw6Scje0lG8enTpzINgvOoCS6TyaTkAlYY2EdGwEf2KhQK\nCZvn8/lEfDGdTgVYkdEi8Hn27NnW6Djt5xcMBgXQ3bt3D9FoVGxYCJxns5nMgGVuW61WYnRM7zw+\nF4/H5fPmtjkjeLXaTO8IBAKo1WpSTmefHvsd9XeA+9put6VqQqsUfoZer1dAaL/fl9eyx3K1WiGV\nSr3Ky+BnOhwm732EHWRpYMbnf9zf6hv0jzNDvq70q9/rqjKeXfBgDy2s0EDvKgAKXCrz7Eyhnf0j\nYLEbODNB6vchs+fz+RCJRAT46HNEoMPXM2FqEMhEzKZpAj722elVpf687J59Ggiv12sBkoPBQBLg\n66+/jidPniAcDkujt2VZODg4gM/nw3e/+1188pOfxJ/92Z/hV3/1V3F2doZf+7Vfw/Pnz2X0kga1\nL+rX5Hnj6p2vu0rh7YQT7yfYY0brDrJ5zWYToVAI2WxWyrNkm2azGfL5vHhHEhQmEgkx/KVvXLvd\nFuU7bTqAjWHwwcGBMNzclmma0u9KoEh2iNf82dkZstnsFkvv8/kwHA6lehAIBFCtVpHP52EYhtiP\nsLTJUrDb7RYRVLvdxuHhoViGMG+YponFYiGTMabTqShQaXPi8/lwcnKCdDotfWp6zBv/r9k/0zS3\nZuDSRFrPNOdnQpaS5sXsl2Q+zmQyaLfbaDab4msYDodlzm4mk5EFKsvjkUgEw+FQLFvYp2eapowx\nM00TOzs7aDQaMvmE1je5XA4PHz7E4eGh5G/2JrLPcjabSS+1x+NBqVSSGbsAZPpHu91+Bd9+JwAH\n5F0bGiQwrgN1V5Vx7b15Oq7qt7vqPewAzv6699O/9eN68exAwg4+CTj09Ab+y947/gCQJmWWRrXJ\nL1k6gjEyV7RF0SCRNwkmv9FoJMmM+0zlrC4za8WqPn/cH82I6hJwr9eTlbPL5cKTJ09kIkYsFhMr\nhP39fXz1q19FpVJBvV7H7/3e7+HJkyf4+te/jqOjI7Fh+dSnPiVlEfpc2Rlf7hcTvQZ59oWCE068\n3+BIKgIrWoek02lh15bLpZTTksmklG3pdcZrtdlsCpAjU85Fy9OnT7d60thfu1gsZAoDWR/201Ks\nQSadrJj+vrNFQ6vsT09PkcvlpCctk8lInyy97KgA1q0Yd+/eRaPRQD6fR6fTkfLsYDDAYDBAMpmU\n2blU2hMEUmnL3ERjZiqMPR4Per2eiERY+WAvLqsBp6en2Nvbk8VfOp1GKBTC6ekpIpEILMtCvV7H\n7u4uAoEADMNAt9uVKgJL27VaDalUSvIEAR59C/P5vACtTCYjhu2muTHC5nHFYjEZ26l9T5nnyuWy\nWKvcv38fn/70p8Xc+fj4GOVyWSaejMdjAdumaaLZbCKXy+H8/FzEOE68/HBA3jWhjXJ1HxefA64G\naRpQ8Eb9ItGCFnZcBbT0Nu0lXLtYww7e7EBTM0N6PzXQ0Mye/Zh0Px6l87r8ageFuoePr6PrPX2Y\n+Bxd2LvdrrwXGTy6pzOZ8Xn2FQGQxnEtrgC2p5ZcBb55bFSGNRoNfOtb35LeEiZuNkezcZyDv6fT\nKf7t3/4Nd+/eRSAQwG/8xm/gwYMHcnP75je/id/5nd8RZkB/Tvqc2BlW+48TTnzQ6Pf7CAQCMM2N\n0jGVSmG12gyUJ+NtWRZcLpdMtZjP53It0kuNfVl6TinBYzqdxp07dwSEaeNbii+63a6oLDmlgdcX\ny4rL5VKqAvpaZd4dDAaYTqfY2dmRedGGsekD1iXcfr+P/f19sVIhOCOryR40Km1pNsxjYo8ey86c\nP0vVKMUPOp+6XC4kEgkMBgNZBPJfnRPZS+jz+WT+LvsiKXKguIR+fzRl5uJQGy5zIToYDMSbjkwr\nrWvIxAKQ+bbhcFgW0rR94u8s7ZKpZf69efOmnNPZbIbd3V0Bc1Q/s9d6tVrh5s2bklOHw+HL//I7\nAcABedcGGSh7PxuTD3AJhuz9efq1TAT8P4EFwR3/xs6u2Vk0Oxiz9+pdxezp/bGDw6vKvXoSgx0U\n6n4yAKIGo60BVVQs4xI8AZCbAJkqloIp6Wcy0R5UegYix+wAkL48JkGCQYI5HttVfY72qRv6tbPZ\nDEdHRzg/P8ejR49kxZvL5RAKhfDs2TPZ/2KxiHQ6jV6vh1/4hV/AP/3TP+FLX/oSPvaxj+HjH/84\nvv3tbyOdTuMTn/iEjBmidYEdzPEz0cbNV31eTjjxQYKKSvbUkbGiUIm+eZFIBMFgEGdnZ+LtmEql\nYBiGlPnIwAGQ65Nmx5z64PF40Gg0hC3qdDrIZrMYj8cyDmw4HIrVCcEMv+ssbVJpOhqNxOeP/mvB\nYBD9fl8AUSgUksU4vfQuLi6QSCSEWSJL7/F4RAVMwONyuZBOp7eMjSmQokCj3+8jHA7j4uICHo9H\nwCltY+bzObLZrJRfWfIFIKXbdrstkz2Y/1iZ4LmiKtc0TdRqNQQCAem763Q6Yi/FewfBaCwWkwUo\nzz1VvZPJREyQ6RPIc60X0BR00NNwMBggl8vJfa3ZbMrigErnSCSCbDYrFRfmavoDnp6eolQqOera\nVxgOyLsmeJPVhrwEBAQpvOB0aKUkgC2Qp/vMWGIEtmfB2hk6bkPvk36Ov2vm7Kr+Ofs2NZvH/2t/\nOQIP9qVQPauPg8O0yXgRKNIOgeUAni9ui8lQ33Cm0ymGw6EkHTYEXwXOWDaIxWKimmPYLRDsgJWf\npV1wsl6v5SYUi8XQ7XaRTCZRrVZl9NH5+bmUiGazGb71rW/hL/7iL/Daa6/hX/7lX/CVr3xFbAgS\niYRYJ5imuWWBYP/8NPDTCwfHLd6JDxuj0WirhMlRYgQ3zCm09GBDPZk22g6xrOlyuaR1wuv1ynB7\nLobX6zXy+TwACOh69uyZGBvzepvP5wiHw3C5XDJZplQq4eLiAqVSSTzdWObU4G88HqPRaEhvGoUT\nFCAQ/HFxSSAEbMrXzG/tdhvZbFaYRM7R5sQLzpEl6PF6vbhx44aIRwaDgaiJWfJmH2AwGESj0QCA\nLb9BeuKFQiFhCCns4HXOHMsFJEF2Op0GADkXZDOZK2hUTQaSQhmeo36/j5s3b25VL+bzuYBnugKQ\nOWR/IrDJQ8lkUnJoIBCAZVmwLAvZbFamixDMezwePH/+HK+99pqYNN+/f/+n+2V34spwQN77qtV2\nEgAAIABJREFUCC0aoK+QBk4sW+rXMuwsnWb19HZ0CVa/3r4Ne1zV96fZHztbpF+rmS39mAaTTDjs\npSE406IMemOx3MDjorJLs6HcL92gvV5vjEu73a6sBllKIgvHPj9gu5eHIJkgErj0ytM9gPYSsj4/\nLJVSrRYIBKQZeTab4R//8R/x+uuvo9FoCFMwmUykBMSbW7VaRbVaxXA4xJ/8yZ/g13/91/HVr35V\nmqPp66WBpZ0lftF3wWHynPgwkclksFgscHZ2hmQyKUIBMuD0ctNAptPpIBKJSOlV+1Q2Gg2EQiEU\nCgXUajUZMzYYDITVCwaD0qsWjUZlCsNsNhMGiwy5y+XC3bt3YVkWVqsV9vf34XK5RLHKSQm0EWGv\nGHOMNuDVpV6qejnRYTqdwu/34/nz58Lsjcdj1Go1xONxYdQ4Ms00NzN7eY2yF48Vi+VyKcCVC9Fg\nMChsPdXM/GFZlTmVZVcGlcAsxXa7XVnAEqTRj0/vH3v1Hjx4IAp+Moj0+8tms7i4uMCNGzfk3HCC\nBkEnhRu0jyJTWiqVtkQgbrdbGEAypcy3vV4Pfr8flmUhFAohHo8LM6oN7p14ueHcOa4Je/+UBitU\nTDHBaEBEo1E2IdMwklS5NuzV29blC/uPBgZXPf/jACOA94A5/m5/b5puRqNRJBIJpNNpGYPDMocu\n01KpxYZlAt/lcrkF2LjK5D6ORiMRObTbbfT7fbE6IavHEq32wGNS56q70WigVquJyStvDATAZCI5\nNYMgVrON2vSTbAD9tfQ5ZmM2+5sMY+PkP5/P5T0ePnyIfD6PVquFe/fuycBvgmEtWLGXq/h+2oPQ\nUdc68WHDMAxh6chYDQYDYXrI4vAG7vF4kM1m4fF48PjxY5kfbVmWgDkurPg91ebFBB8sUZKF19cs\n++ZMc+N5x79jdYMWJaa58dFjPmC5mGCUpVdeX5ZliXqUoxEJaigESaVSiEaj8Pl8yOfzAh7ZT0cv\nPPr4sRzLCR8ApNrAEvLJyYkYoHOcGXOLHdwkEglhRlm6ns1mMpGDx0IWlbmFjzcaDazXa7FzYZk2\nm83iyZMnUjr2+/3S2zybzaTsTPa12+2KFyIZPeaYeDwuzgGr1QqNRkMA72QywXq9ls8vFouh3W6L\nf6jL5UImk0Gz2YRpmuj1eggEAlt9mk683HCYvPcRdnZLgz5dsmWZkn12V3no8bWk6e3PE0zo/jLe\n/Hnjv0pAAGybKuvn7L+/iC20N/4TpOqRYiwf2vvIWHZlUtGqWnrYkcViWbTT6cgKfjabiVmnvS/Q\nznYxwbMEwx4RiiRYeuVno0EaARWPg6/n8RCkdzodNBoNtNtt/OEf/iH+7u/+DsPhEJFIBJVKBbPZ\nDI1GQ1axbHbudrv47Gc/i29+85sol8s4OzuTkW0sA131/dIgz86w8nw44cQHjWq1Ki0DPp8P4/EY\npmmiVCrBsixh3sjAUzBQrVaRy+VQr9eFAVyv1zLDtNFoSLmVYgwumNj3x3IiQQunMoxGIySTSfT7\nfelP5WKHLFO320UwGBTmDIDsPwUUjUYDhmEI+GMOqFQqorSlR51pmltsIsEg88BsNhNbEFYldHmZ\nql+WSvm73+/HwcGBLDjL5bIcT6PRkDxEsGgYBiqVCkKhkEyVaDabGAwGcrwUbDDHN5tNRKNR5HI5\nUcHy/QjeaVXCySButxvpdBqz2Uy23W635fNlLiJ7CEBKuvF4XHL9YDDYUvCSzJjP56jVasjn81LS\nZw6zLAuJREKqKS6XyxFevMJwQN41oUEDbTnsZVM7cNMWHnxM38TtFh+6HGcvsfJC16ILAFs9gLr0\nqC0D7H2BGsRpYKrfj2UDJk+WMrPZrJRZWK5kGZY9IEwuBCjj8ViMijUoZGmWrB3Ph+5P1IwkgC0L\nBSZ9NlxrBa7uIdS9g0ywmvXk58PPgTYuHo9HzE/j8TjefvttFAoFXFxcyI3PMDZDxPv9/hZgz2Qy\nyOVyuH37tpQqAoGArKY1cOV51wyx/pyZXPkZO+HEBw2WM8lUX1xcyDVBaw6CIHrCsUdsMBhIjrAs\nC7FYTNTv5XJZFmUej0f6/si4TadTmQHNSRe9Xk9u/nwul8sJw8ZcsVgs0Ol0BJiR1QuHwwJw2N9a\nqVTEbxOAgDT2IjIHUXQxHo8FzDFnpFIpYZ1GoxFyudyWupX5hbnS7XYjGo3i5OQEN27cEGaf5dJm\ns4lgMIhCobDVR8yyeDAYlFmwzEWZTAZer1d8ON1uN1KpFLrdLnw+H5LJpCxw+/2+2K3QOoq5kspo\nCk36/b6AT/Zjut1umS7Esiv7jcvlsiziCcApnCE7GI/HMRwOkclkpJePalwKeTjqDoAwx068mnBA\n3jWhG+HtrJdWjmq2hRe0nbHjDZxJg6+1M3JaCaoBmn6efSl20YZm8uyiA/s+2tlDHivBFHAJSIFL\n0KFLrlTsUVVFZexsNtsq0TL5clVHnyiWYAkYqZLjPvLYWf7VamT+rmc9EpDbmTz7ubSXSfXnZJqm\nGMTO53PcuHEDlmXhE5/4hJRyAoGAJHOW39nXBwD37t1Du92WnpVsNrtVErGX3u3KaR6PFp044cQH\njXg8vjV3O5PJAIAoNmezmTD14XBYWixcLpeM+GPZjuILmiJz0gEBGABZLLFUyjxF9o2ggGPEhsOh\nKDbJ0s1mMxSLRSyXS8RiMcxmM7Rara0JFC7XxsNuZ2cHoVBIFlwEh+l0GqPRSAyOWSpmGZeVB07b\nefbsGW7cuCG5jD6BPHY+zpxLcdZ6vUar1ZKFJHMkS5yshozHYxlFtlqtpH+NPW70vItEIlitVmJj\nQquT1Wol6liOgCObqHNRNBqV/er1esLoETiSUeN9qN/vS+l4Pp9jPB7D7d7MmuUCf7lcCvNHQ+pY\nLCaTQ9LptOTycDgswJR5NBQKOUzeKwwH5F0T9hIpQzNpdpCmGTu76EFPY7CDD83WaHYPuGTh+Bz3\nh+BKgzX7Pun3uYopI+ihCIH7xoTE1TsBGkUPHo9HxgTxnLDnRk+c0KBQ9/Rox3kmE3t5VbNbBES0\nGCB4pC2AHaAahiE9hBrAcl+5KmeS0+wnG5Jp0TAYDPC9730Pv//7v4933nlHPPtoLbFabfzEIpGI\nsHaz2QylUglPnjwBsHF/Z0OzBtb6s9ffAftn6IQTHzRY6pvNZmI/Mh6PZU4qRQX0Zmu1WgIUarWa\nsDQEVTrvEfxwuP10OkU2mxXgxz694XAo82WZP3K5nAioCBpZPiTIZO7RuYbg8/z8XGZeTyYTGa9G\nwPr48WPcunULAEQsRZBIYQlVqwS/tPkg2GJOYfmZFiWTyUTaLwjWTNPE+fm55BqWQVmmTaVS8Hq9\naLVaYn0ynU7xzjvviOEwj5Mj0NxuN+7fv4/9/X10u10RngyHQ5lEcnp6ioODAzEy5jg2MmosYVPh\nWq/XBZixh5z9xZ1OB8fHx8KS+v1+xONx6U3khBT2b9Iom1UusqVkcZm/OW7SiVcTDsi7JnjTJSUO\nbAM+DeB06ZVgwd4/ZwdZfA8742S/6et+O4a9jEvQYLfd0Kwct8VSJpkwlkEJgphsCKT6/T4MwxBX\ncwBic0BAx7II2QACPJ4XrsK5TW1z8iIVLcEXb0YUhjCB6dfxGHj+NZPH0jMZTn2uCXAJgk1z43D/\n9OlTSWCxWAx/8Ad/gFKpJNYCvV4P//qv/4ovfOEL+PM//3N85Stfwdtvv431euPCz/IQbSYIyDWI\nZWiGVR8/Pz8H5DnxYYLXncfjkekGZFYsyxKVpbYY4XUfjUYxGAyQzWaFTaMQgm0hVJmv12u0220x\n9WX5k6pNLrK0opc9fYvFAr1eD9lsFpZliUIzHo/Dsixh6plP5vO5lHeZRzgLlua/BLG9Xg/T6VT6\n2UxzY96rW1Y4DYQ9Z1TlTqdTDAYDWJYFt9uNeDwO4NIei8CPwJniM860jcfjcq6Yk8j28Vzfvn0b\no9FImMDhcCjtL41GA6lUCmdnZwiFQgKU6RMYCARQLpdlFB1LsMyVBOnNZlPYPFo4zedzyen6GI6O\njkSZHIlEEIlEcHJygng8Lr185+fn2NvbE2UvfQfT6TSWyyWKxeKW12mz2ZRWGCdefjh3jmtCl/LI\nUGlFpr2vS5c3gUtAaAc8BBn6/7psp1+jX2tnDe1soL2HS7NhPp8PwWAQsVgMyWQSyWRSBlprc2Ee\nF7dD0NNqtaRPh0nCsiwx3tTKWJ4f7jN7RwhW2CNEs0/DuLQW0GVusm/8HOjyzlW3LssahiEKV6p/\nmVxZugGwpQqOxWKyqufg9Gw2i0wmI8O5R6MRJpMJdnd3cf/+fazXa2E4PvvZz+Lg4AC/8iu/gjt3\n7ogv1BtvvCHD0XkMXPnaezb5f92nqc+9ZvyccOKDRDAYFDNhqmy1ATDtQKjwZEkVgLQsrFYr8Y3k\n9blYLKRMSlDHXiwCHdpvsDTsdrsRCoUQjUalXQLY5ILd3V14PB6Uy2X5rpMxq9frMhbL5/Oh1+vB\nMAyZOgNA2Er2xw2HQ1QqFXi9XmSzWVQqFQyHQ/R6PREfeDweMSB2u91SBuX1OhqNZKoNjY7Zczsc\nDuFyubbEK+v1WkaceTwexONxmYjj8XjQ7XZRq9W28jHFLMx18XhcWFHuZy6XA3B5L/F4PIhGo5Iv\n+FmwVYSANZ1OIxaL4datW/IZU+hGIR2tsSqVCmKxmBw7wSm/Ayylcx/JNkYiERGlUDBCJXWv1xOx\nGiduOPHyw2Hy3kfonpYXsSp28KYZGTtLo7eje/LISPE1VHkRNGrGSzOGXCnae9Y0Y8Skpg2N9THR\nAoCrTW6H78deGQIw9tno0rQ2L75KPbxer0XdpxWtunzJZKFDG1Hr37WghaVZLbTga3gu7OOBCA4p\n1KDNCc8HlWzn5+fodrs4Pj6GZVnI5/NiwMzvxx//8R/jrbfewmAwwMHBgTShZ7NZYQe08lr35tm/\nF/rc6L49J5z4oEHAMBgMxBCZrMxgMEAkEkGj0ZDmes58ZesFARvLq1rZCVxOnqFqldc5x3e5XC4x\nIGZrBLD53tN6g4s99tPZr5fDw0N0Oh2pGtBoOJ1OI5FIoF6vo9vtolKp4O7du5IXWJ7l2DBWDgiC\ngE01olKp4N69e5hMJlvWLCwNU5xBlv/8/HxrjBcnUdAiKxgMCjBlWXc+nyMej4thsnYiIDDVZe5M\nJiN9bH6/H6lUCuPxWM6R3+9Ho9HYMpdmjyQBKhfbXq8Xk8lErGJ4/wiHw+KRV6lUAFxOKgKAs7Mz\n+P1+VKtVpNNp+b6w55L3hOVyidPTU5mXyzm2vV5PehozmQwePHjwsr/+TsABedeGbuonyLKHLrHy\nRq2FGloUwdcTjLC8ytWwvVdOlzP5t/rfq/ZD96RpLzau3AjItJ0Hy7bcD82ocTVORlL71fFvNRjV\nofdFM5MELkz6ZP5YktWghqBUr/xZxiVoomhDg0QCWw0MNai2Hxsd5sPhsDSDU1gBALFYDIlEAuFw\nGE+ePMEPf/hD+P1+RKNRfPWrX0U8Hscf/dEf4eTkBJ/85CeRyWSQz+dFuebxeGQ1bBfK6HOjBSFa\n+eyEEx80ut2u2IhQaDGZTKSxnq0Iw+FQlJMu18YQ/OTkRMZaNRoN6X2lyp5jrzqdjqhgyfKTOep0\nOjInlrlnOp2K5RDFB2TME4kEXC4XksmkMEQABPhUKhVh8slGAZs8w942svitVksAEf30KITiiC6X\ny4Vbt26h2+0iFAqJwnW1Wsn/AUiPG9k6qlwbjQbK5bLMoaXynuAN2OR/zostl8ty3i3LQqlUEhEa\nBWicxEEWUBsN7+7uSl/zYrFAqVRCvV6XfWMuY5sIxTJsGeF+VCoVzOdzFItFYVoByMKXFR6WiuPx\nODqdDsbjMYrFIp4+fSpmx6ZpolgsSj5mrgsEApLTO53OK/j2OwE4IO/aoD+UnslnDw3gNCizAxre\nqK96jn+v7UB0/5i9z47vq8UC9tIvmTsmZm6DIIgAB7hUEfP4dJmZ0n8+pqdRMPR+6HPCY9Ygi+wU\nwYwdnBFw6nPK0MCNrKO97KkZxquAE88NAGEk1+s16vW6JF2WqXgOPR4PqtUqDMPAjXdtE7LZLD79\n6U8jFotJaef73/8+/uEf/gFf+9rXEAqF5FjZpM4VuR30279HPAdXMcNOOPF+g2rNSqWC27dvi8CC\n8057vR6SyaQAIZryzudz7O7uSqmX32EAIjjiNeLz+cQI/fnz51IaBiB2J8ydo9EIkUhE5r8uFgsB\nWIZh4PT0FLlcTtgjsnqJRALz+RwejwelUgm1Wk1YKzKU6XRaypFcqNXrdckVNEQmiOJkjmfPngnY\nJFPFfEGQlEql0Gq1MBwORVzicrlwdHSEVquFeDyOyWQiJWYyZYPBQPKIZVmiKrYsC4axEXww33Pe\n7cHBgXxG/X5fmMf1ei2+gTx/PFb6EerPiH2CFKzwM+cinVNNqJQm47dcLkVAplXX7JdkvybZVOY5\n+oXqPJxKpeRxJ15NOCDvmmCvBfu5tDDAHpqZ4f91T5m9507/HfvReKEOh8MtYQFwWa7V70XAo8uX\nXEmRVifrRaCmARUBJEP3FTKxAJclZw0ktahEs1EMey+hvadQs53cZ93HxxuLZgd4XGQctf+dPs9k\nL1kSWa/XW/17PK8adBLIJZNJHB8fS7nk+PhY1GJHR0c4Pj5GNBpFKBTC7u4uisUiHjx4gEgkgo9/\n/ONYrVZ49uwZKpWKNDL//M//PGKxmJSr7UytXWShWV37eXXCifcbtL7Y29sT01qyLGTYOp2OeE7q\nAfSBQECa8DlOzLIs6cfSfV2hUEjmoI5GIxQKBQwGAwQCAfR6va22D47eMs3L2dW1Wk3sXVarFYrF\nohik03tvMpkgnU6LLQhLvJwxTbaS5VS2uwwGAwFTwWAQFxcXCIVC4tHJa5nXJhkw9uIyx7jdbik9\nW5aFYrEok0DoDahtZ6bTKc7OzgBsJl2w9BmJROT8P3r0CIVCYatvmQCLOXC5XCKZTAowtCwLuVxO\nZsYSPJMh5TFwCkgulxM/QYLJeDwufciWZaHdbsuUI46aZLmVPXaRSASGYUjfdTwel1F29DGlrUos\nFttiiDnP2ImXHx+JGpBhGP+bYRg1wzDeVo8lDcP474ZhPDQM4/8xDCOunvufDcN4ZBjGjwzD+B9+\n3La5SuXKjklN/+jRZvbHCb64WmMviAZ6HHVGhowXqb1vTpdeCe44Wof/MkFpFRcvbPaQEAyyrEEg\nRkd4qruYdMgqasCnQZ9dbWxnJ/mY/XGeBwZXqgRi3K4WtVB4QQaOfSfApvk6EokIINN9gVr4wuTJ\nc6RZ1lAohF6vhxs3bqBQKMDn80nzsmEYIsBgj86TJ0+wXq/xmc98Bjdu3MBqtUI6ncZnPvMZRCIR\ndDodWRkTlBKU6xK6flyzdw6L97MRP60cxob8TqeDTqcjzFK/30e1WkW5XBYhBCdjJJNJLJdLubGz\nr5S9XmTEOKCeTBlBEQfdk0nSzBAVurRjMgwDiURCrDni8TgGgwEGg4EswLSIimPQCEI4NYelUdM0\nRQzCYyDLaBgb8dbR0ZFcVywxc0JGvV7HarUSQQZZu2azKeIpwzCk55ALac3iUaFcrVaxs7MjFZPR\naIR8Pi/WJFxEMpeFw2GkUimEw2EEg0E8fvxY1KkUQxBAUvARCoXQ7/eRyWQQj8dxenqKs7MzYc84\nnYTgvdPpiOUMe5hNc6M4Zq4nw8v+uk6ng0AggFQqBb/fLzZZ0WhUSuLs/WOeJ/icTqdyPE68mvhI\ngDwA/zuAX7E99l8A/Pf1en0E4Fvv/h+GYdwF8FsA7r77N39mGMYLzwMbSzlu5irbDw1IrmKv3n1f\nATsEHLo0S0DFUggTAxMTWS2uKKkQBS79+DRLxVKrFkroHjauqlk66Ha7W/J9/i1pdxqEUrSgy7wE\nnhqg2NkqJlUeE8vAVHBRxcUkwXPG5zhPl5MogsGgqIJ5A2LjOLdJqxXaRrAniKUMPYOTf0MlIU2e\n6ZlFJRnPH3uQdnZ2MJlMUKlUBDjv7OygUqng8PAQr7/+OjKZzHv6InVJSJ8rfnb8rO0lXSc+svFT\nyWGNRkMWjQQyHo8HhUIBqVRqy7cyGAyiWq2i3W5LuZALRQKvUqmE9fpy9ip97fr9PrrdrrB/4/FY\nJj6wDOj3+3F4eCglXA3W6B/JBTPth3hdGoYhgIpsos/nw97enliwsEzM8uhkMhFVrmmaqFar6Pf7\n0pNHWyX2BbMEDUBKoMwHFKHoa/Ts7EzyIveHc3zZ4zYej2XSDdlCVkg43m0ymSAWiwko63a76HQ6\nuHfvHtbrNcrlMgaDAUajEVqt1hbDSRsU+uqVy2WUy2VkMhkByCQOyNz5fD6Uy2UAkNmy2Wx2a3HP\nGcaWZcmx8DMxDEPcBfj90PPFZ7OZTNqgQvhHP/rRT3Z1OPGh4yMB8tbr9bcB2Ds7fw3Af3v39/8G\n4H989/dfB/BX6/V6vl6vnwF4DOAzL9o2mZxoNCo3Zt2rZmemNPC7ir3iCpMgj6COqyjd70ZgZi/D\n+v1+ATkABLiQqdKgS7N+mg1ksuLfMnGwTGy389ClUfof2UuLPF7dc/cidoqv4bnUFiIEsrqcqrcF\nQEoG+seyLPR6PfR6vS1jUx4/QRb98rii5UB1luTZPFwoFMSG4OTkRHpvCMxpShqNRpHP56VJmZYJ\nsVgMFxcXODw8xHK5lO+Q3ieyvQC2ALwW/NiVyk589OKnlcNyuZzYcXA6Ar+7pmmi2+2KwIh9WjTI\nZX6yLAsu1+UkGYKGYrG4pbZstVqyEOY1wu8zv7+j0QjRaBTPnz8XIMVrQ/vpscxJgQgXcfRuY87x\n+XxoNpuyAEulUrKgY7nW5/Ph7bffRjweF8EIgeZyuZQ8QGup6XQqitbRaASPxyP9iRylxrwwHo+R\nSCSQTCaF4eOCkNM6crmcgKtYLCbbDQQC0rs3m81QrVZl0gXPByssOo/TpFn71NlzMu2hCN7b7bbM\nxo3FYlugn5/nZDKBaZpSnuU54sKAjgHMT+12W1i/1WpjFE3lNT8HglqOOHPi5cdHuScvt16va+/+\nXgOQe/f3IoDvqtedASi9aCO8wVL+T7WV9jYDtn3pgPdOyGDwMXtv2lVgkKtMAigt/mCfmr1syu1o\nOxYCSACy6mTQvoC9Fy+aH8skw/fUvYlaKWpnOPW5Ydhfa/eG0+VaJhz+DV+vbVZ4Prjip2Er/5as\nA4+Bn5E+19wfNjqztBQIBFCr1ZDNZnHj3fFmtItg4lssFmi1WvB6vfirv/orfPnLX5btcJvpdHqr\n7G7vbdTWN/bvDdlcJ37m4ifOYbVaTQAYb+60ClmtVmKhohdzBIKLxQKDwUBmWS8WC1HZcuG5Xq9F\nyMC+V4o9CBq5oOL1Z1mWWJpkMhlR+3q9XlSrVYzHY5TLZSkdsucskUhgOByi2WwC2CzgWKpMJBJ4\n+PAh9vb2tmalTqdTRKNR7O3tyUKVAIk5hJMk2C/HfAFsKhVk/yzLQqPREHEWWbp2uy0gkdcqF6wU\nhvHx4XAopsH9fl9K5VS4slLCUjaBnMvl2posQnDN8vnjx49xcHAgoxRjsRgWi4V4htIIWpe2NUvL\nVhf21fE9AIi6NxgMIp1OwzRNsVMZj8cCFk3TlEoKv0uhUAjtdtvJX68wPsogT2K9Xq8Nw/hxVMgL\nn3vjjTeEdcpms8jlcgJEqHqiKEDfpO1iBsZVvVZ2NkyzV0wOXKXx9fx7Sud1kmaCJYhguZUrV+3b\np1eIwOXYNT6vbUeYrNh7ocuufL3eFw30gEuneA3u9La5z/bnAMhqE7iU+dtLwWTg+DznYfJvWBJm\nEmfC537yPTjrcnd3F61WC5PJBO+88w729/eFEdHn1TAMuflVq1U0Gg0Ui0Xcv38fDx48QCwWQzgc\nRrVaRSaTeY+/IG8+dsbun//5n/Gd73znx3xtnfhZiQ+bwzhtwDAM6fvq9/u4uLjA/v6+jAajkGK9\nXksP1nK5GX9FlSUA+b6TxeEEHM6b1WpU5pJ33nkHN27cEPDCBQ+tWNg3xzmqBIkEEoZhYDQaSTmU\n1h/z+RztdhupVEpKnuwj42KXjB5bKjKZDKLRKM7OzpDL5eS4aR/j9XqRTqflGmerBoHwzZs30W63\npRpDFrLT6Uiupnmw1+vF2dmZAB8eH4UUPHYKX1gW1r1sFDIkEgkZGcaJHMwj7N/mdA597GRrKdJg\nJaLVamFnZ0fGVQIbIEn1NRcALKf3ej0pi3N+LgCxauH4Nt4rF4sF2u02LMtCp9N5j/epEy8vPsog\nr2YYRn69XlcNwygAqL/7+DmAHfW68ruPXRmf+MQnhFXT/VjszdOlW+C9I8/sPXsa2BEosRfMMC7V\nsiy9svTBkof+e4Ib7g+f40VKmp+ASE+h0GVUzWRxxad7CAloAGyNQ9PvTbCiS8wayNqBr+415PM8\nz3Zmi9vUTJjeZ11GZ6+hNmbm8XCGIm0IeHxsCuY5ojkpRRW7u7v49re/jYuLC9y7dw/lcln2jVMy\nkskkgsEg9vf38bWvfQ3f+MY3YJomstmsrODJomj7GX1+7Mzn5z//eXz+85+X///pn/7p+/neO/HR\niZ84h3FaAxcnVM0eHBzANDf2GeFwWMAa3QQojiAjzjzicrnQ6XSk9PfOO++gWCzK69mXRZVprVbD\n0dERAEg+G4/HwhgNBgMsFgvs7Oyg1WphtVqhUCjA7XYLkOv1eojH42LVwd619Xoto9fcbrdM1dAL\nPnpTnp6eioExt+HxeFCpVHDnzh2YpinqWi3GIviLxWLodDoidqPFS6/XEzaf7CFzaCgUwv7+voBL\nevc1m03EYjExoGbuIgPpdrsRjUZhWZaI0dgHV6vVZO5sv9+XnvF0Oo31ei2g1eVyoVqtIpVKSb8k\nK1HT6VQqQ+w/vri4EAsZltFpqZPNZnFxcYFYLCY90qz68Nh9Pp/kNy5YOd2EAo9qtfos0rA5AAAg\nAElEQVRTu1CceHF8lEHe/wXgfwLwv7z77/+pHv8/DMP4X7EpcRwC+P9etBGyaNPpVFaEDN0sr19v\nb6IHtueP6sfYl0bQRQAFYKvPjkoxAko7u8dgGZfbZpmWYEiXYvlDQMj3p/8S2US+PxOZZtE0m8b9\n4Xvq1ZudeeM+MCnzBsLHCXrcbjfm8/mWslgDUM1E8rW8MWngzV5GJkAtgtAAkVYSpmkil8vBsiyE\nQiH88i//sri4M7kBkOZs9gx9+ctfRqFQwOnpqQxNZxlZM3j2uOpxDZRf9HdOfKTjJ85hyWRSrtvx\neCxKR4IDjtti/5ZlWQL2Op0OIpGIiCtoAkx7DzJbbrdbJjwQRHW7XSnl0bKD/WssbRJohMNhaXfI\nZDICGAFILptMJpIL6UsZCASkZ5Aj1gBsmQtzAc3naQNDg16ygCyHJpNJAW7hcFgmfqTTaZms4XK5\n5Fgnk4lMunC73cLWsXxJ5s40TRFgTKdT1Go1MZpev6vudbk2U0AIOAmUU6kUTk5OkM1mEY/HZYHL\nPBiJRITh9Hq9aLfbmM1mW7mMrT+9Xk8m9VDsx/cgmdBut5FOp6VHudPpYG9vT5i+SCSCi4sLWSwz\n31OoBkDMqg3DQDqdloqKEy8/PhLCC8Mw/grA/wvgtmEYp4Zh/C6APwXwy4ZhPATwS+/+H+v1+j6A\nvwZwH8D/DeA/r6/pamfC0Q7s725LLiIN0sh+aYk93eLpUUVllwZ/TEwcF6OFHWwQZnIGtsecafUs\ne0I00CGbqAEDQRT3T4sAKMgYjUYyr5ZATO8TkwvZMzKTvNj132hgZhelsL+NDcEUeTDx8FzSy4mO\n+bwxdTodNJtNaS5PpVJIJpNSimJCps0Df8gIaOEIzwN7WprNJvx+PwqFAubzucyuZGno5OREEp/L\n5cJnPvMZvPnmm0gkElIyoUehZjqv+3HiZyd+WjmMrHej0cBgMEC/3xfbEYqtotGo3OR5fbFvj752\ntPnodruSZ2q1Tbsg+3S5PeYK9n7F43HJRVSUMr8Nh0NRwnJfW62W9A2zYjKfz3F+fi6MJCd3UEHL\ncir7AgkkeW2z9zgajeL8/FyYxHA4LOw+bU4IYKhyZZ6iyGA4HMrkDMMwRLhFIRZ7gslcshcOgJS9\nKW4hM0iRC+1HeG+g/x3z3Gq1km2bpolUKiUWLnpRyXxLMYr+LnAhzIX/crncmvnLfEylMcUnLCUb\nhoFSqSTvHY1GRcUcCoXkM3W73Wi1WvJ3Trya+Egweev1+qsveOo/veD1/xXAf32f25aLAbhs0udz\nTHjANlulS576X80ucTtcCWnAxpLrVaVfDTTJBOryn94/vkYzhJodYimGjB7FJLrMzMf5t/Z9Ai7L\nuJqBs7OBXOXbj4Xnl4CYzCZvHtw2V8vAZqVIIMt9YbmISYuAEYAAOp5//k4PQd5ouCrnMXPQ99On\nTzGdTpHP58UjismWDO/HPvYxuN1uPHz4ELlcDqVSCc+ePROFGRkRe6+iE078tHLYcrlEpVJBNBpF\nLBaTGbb0aWMDP7CZjsHxYRwoz7FlnB6RTCYBAJlMRth/Ahiy1dFoVEqaNMTlte9yuWR0IN/f5/Mh\nl8uh1+uh1WohHA6/p9eZ/p80+XW5XOLn12w2USgUpAxqWRay2eyWSIzistVqhXw+L/mEoBOAAK1U\nKoX1ei22ImTIhsOhWI6k02nZBo+dC/Hlcol2u42bN2+i2Wwil9voZXq9HvL5vLBsLpdLjpcTPVgG\n13YlAGSxyJ5IzZJqNSzBI9W1HNNGpSuVvSzrut1uVKtVaXOhUIXsZiQSke8CsClF12o1lMtlnJyc\nIBgMIhaLSU5nxYvvS1bTKdW+uvhIgLyfZugSIoPghABIl0AJanTPHICt13JVawdffB2Dr9cMoZ0N\n4nvofjct0NDgkolWx1XAj30WLD3by676X33sWg3MfdfniYBZgzz7eaI3F1VhZAa5KtarUH3OtU0D\nt8Nyg9/vl/KJLnVr1lOXv7mvwWBQVvs7Oztwu93i6D+dTmWWYzwel/0fj8fI5/NIp9MoFApS2tKl\nev6uz/lVRIzD5jnxk0YwGESxWBSwxeuKFQWCE86DpZLV7XZvTU8gwGKrwnQ6FWaPQHE4HIpSk0a9\nbJ1gT1skEsFoNJIe2UQiIeVZljepmqXlSSqVwltvvYU7d+7IgpHAhr13ZN44xov7ymsonU6LdUy1\nWsVoNMLNmzfFJJ49cbu7u1teb2QDqUrV5e/lcolwOIzj42Nks1npYaRYw+12i9ccmUD2xrEFJZlM\nSk4IhUJoNBrSMtPr9eT8EJCxlDoYDJBMJqWUDEAUsMfHxygWi6hWq8hms6JQZi+dNkFmK0uz2cR0\nOkU2m8V0OsUbb7yBUqkkx8w2nX6/j/39fSwWCzlXZIVjsRhOT09l3nc6nRZT6WKxiDfffPNVXgo/\ns+GAvGuCFyMAYb14gQCXVip2cKb77bQvHhkxzQDaZ5QSlJERszNzjBc9rsu8PAbdJ6j/Th+HZu/0\nvlHBaxdtsCeGogyWfu3btjNuWiXLc2svl2rgyhsK30cLP+zb0yCUJVp6RbFkzvfjcWuARwaRNikA\nhAnhzYdlbK6sKUzh/Eo65/P9eRPUDK3ebztIZzggz4mfNDQDTjaIAgeOFyMDQ0UtleJkmgAIMOC1\nxMkP2sNNVwKYK1wulwgHMpkMnj9/jkgkgl6vJ2CGpVmCtna7LfYtFAvcvXtXQCV72zqdjihSa7Wa\nbGs8HmMwGMiCm+z5bDZDMplEIBBAu90WAEpFsLaGcblcUvLtdru4e/cu+v0+bty4gWazKarafr+P\nW7duiUCEauBgMCiKYJY0tXFyJBKRXsj1ei2mxvv7++j3+2LBtFwuZV6s1+sVlpGldFrSsCw8nU5R\nLpfh8/kEJDcaDQGeHN1omiYKhYIwbAScXNBTFMKSLbApNXNyBtnbaDQqeXM6nUolhI8BwPn5uTO7\n9hWGA/KuCbquE+gAl31mDA2MCJRYUtBlUN1vpW/qHLyt++aA7cZ7YLsHj8FVsC6VapCpjXY1G6l7\n4vhe9nKxVqoRdHIfNUDRyjseF8Eafye40r+vVitZufO9maRZhgDea5nC7ejPQpe3eZ604TTnSuqx\nbzxGvjd78GgCGgqFUK/XRRn7ne98B5/73OckSbvdbjx//hx7e3toNBqIxWJot9v4m7/5G3zpS18C\nsClrcfVP1SGPSwNrJkSeXzvr6pR3nfgwQYbdMAzp+QqFQgAg81kNwxBBUTKZlO+ptlbi9cBrBIA0\n6XO0WSaTgWEYePz4MV577TURY7TbbUSjUQFnLKnScJlKUeYkXUpmyZb+e+v1GsPhUEArF53JZFLm\n2LpcLsmLZOG4AA2Hw2LRAkByFvv1VqsVGo0GUqkU9vf3hbVk7gA25sPsc6vX62i1Wrh37x5ms5mI\nWpinCDYbjYb46i0WC5yfnyOTyYi/HT8Ltohoo2MyeKySxONxmSjBVhEaFpOpCwaD6Ha7ACBqXO5P\nKBQS9m293iiU/X4/Wq2WGE33ej2kUik0m02ZbxuNRjEcDmUKBu1cKGRxuVzC4pI5ZEXDsVB5deGA\nvGvC3sNl77GzAzFdliXg4OuvKu8SpNhLr7qMq4UOep80INDAj+ViDfL4evuxaaUWQwMoO7giG0nl\nL1k9vqdWy3JFp3v4CHq5fS0Q4WqbzxG42XsdAci50D2JWshhPyaWh6goJPvA8pXP55M+lXA4jGaz\niadPn8Lr9QoLCECsBaju++IXvyjHGA6HcXZ2hv39fbhcLty/f18sCrQ6Wu+bPsf2z1SDQCec+DAx\nn8/x/PlzlMtluVZYAh2NRsK0ERjx+69HGLIh3+PxiLiIQGCxWCAej0uJdzgcolQqod1uS79eKBSC\nYRiwLEvaHgCIMEmr+umdl0qlJFdQ1MV+v1AohPl8Lv1s9G3j+4fDYTFoNgxDKg4UBUQiEUynUxQK\nBQFhLtfGxy4QCKBYLMp1SVDUbDZF7ZrNZtHr9eDz+dBut3FwcCBMpWY01+u1qIqBDdiisIElzXg8\nLqymYRjSx9br9dBoNLC7u4vRaIRbt26h3W5LLh0OhzK6kQtqWqqwarBerxGJRKQPk/1yLMtaliX7\nC2xK+wTznDUcj8eFFfR6veKv12q1pHTM7dBEOxwOo9PpoFarIRwO4/z8XBb2Trz8cEDeNaFBGZW0\nZLbsylhg+yZtByJXCRv03xPwaaaQN3g+/iIWTW9Dg1AdVwEGDc40mNRAU/fXceXL6RdXAVytNuZ7\nELDphmqeU26bx6lDAzZ93NxXba2iAZ7uj+RjGgSSudPzbgOBgPhtEQCyD2+5XCIWi4kp6Xg8lj4j\nNpO7XC75vy79AJASFwBhVuyfv/3744A7J37SIKhhs79m7jlxgb1wDx8+RCKREIGC1+uVkunFxQUM\nw0A2m0Wr1RJ/OoJFgg5asRiGgWazKczZbDbD+fk5Dg8P8fz5861ypnYvYEsFgSZZd47TYo6p1+tS\nnk2n0zg/P0cikZCFGsEHQQfBzenpqYwZZD+eaZo4PT0VtiuRSIjSlmPJTNMUk2O2aHi9Xty8eVMs\np3iu+/0+TNOUEm0ymZTe3n6/j1wuh/v374t4pFarCeDMZDLSG8jj4wKWEzEI9JgndK9kJpNBu91G\no9EAAJlkoWfYHh8fSwmYXnb8vHl/I7gle0kAnU6npSQdjUZF5MHPhiwfS8P8bAuFwkv93jtxGQ7I\ne5+hy4lkn3SZVAMMfrGZkAiMtPUJX6fZNv24/r8dxNlZP/2+BDVaxQtg6zUa7FxlZ6LZNHu/m+5f\n47EDG3DG5mANVmmrYAe3duaQCUGzi2Tc7Cwd902fP+4Pt63LzXbgy9/JIpCJ4+9kKt1utzRcc0QT\n1bucN0kGY3d3F5ZloVQqoVAo4NmzZwgGg8jlchgMBgAgc22vEl7Yzwk/f4YD+Jz4MDGfz5FIJKRk\nSXPg1WqFWCwmtkLBYBCZTEYYOtoOmaYpkxdY5uQCib2mLBHO5/Ot8WW8JpfLpVwbzWZTABiBl7ZI\nokWU3+8Xy5DRaAS/3y9AZjabIZ/PSz7hvO3RaCQABNhcM/1+X0DOcDjE0dER5vO5GCr3ej0kk0mx\nZWLZmmpX+vZRyUoAZxgGHjx4IAp+lli1jYnX68XDhw+xu7uLRqOBcDiMZDIJr9eLUqkkPb1U9/p8\nPlQqFTnv3W5XFMRcHEej0fdYkrASwjxFtrPVasnEDFZdqKxm2X46nco2WP5m3yWtYbjYpciDVjbs\nKWS/Mr9rvV5P5nizp5vv48TLDwfkvY+wAy/df8fnNfNiB2ManGhgwaB1CMsSug9Gv469XHxPvod+\nTJc19XNk1zhz9UXiBeBSCHLVNoFLRtO+DQK91Wq1JZbgftuBjAZdTC7cP828adZUM19X7ZP9c+Nr\nrmIC7aCTymfuIwEmS0b0kuKqmiWj1157TfaBrvBerxc7Ozv44Q9/KD06nKahP0f9HdL/2p93wokP\nE1R+1+t15HK5rYkuXNiQ4WPPFb3b3G63KNR5TZJpo9WG2+1Go9EQaxD2ebGEy75c/p+G4CzxcYRY\nIpHAYDDYshgaj8dIJpNotVqo1WrijUlQQ/ae70HBCHucPR4P8vm8sEtU/2vGjmzWarXCZDIRcEKh\nQjAYxHK5xKNHj1AoFBCPx2VUIXvN9AJ3OByKenm1WuHmzZt49OgRPvnJT4oVCd0BCJKCwaAIxFKp\nlCyIE4mEsIcEvcxnVMHSk49MoGVZIrTJZDIyepP5kmISTjjhRA86BliWhWKxKKwqy70ejweHh4fS\nw9loNBAMBqUE7na7hfjwer0ol8vwer2oVCoifnHi1YQD8q4JjjPT/Xgv+tFlWeAS1BC4cUVESxAA\n4uHEXhSa7HI1x9fqkib3y15G5UghzqrUYJKJiOURJhIAWz1xZLjsbJNWx3Llra1ImNw7nc5WL5m9\n/HgVyNN9egRrpmlKaUIzcnz/qwQsvIHYS+AEoHbAZweoTERU12qDaH4PQqEQ1uu1DHynQm+9Xgv7\noc/jcrkUiwWuxrWa2s646t+vAuBOOPFBIhAIYDAYyMzVQqEgAI/THsiaExywP419bgRXBAL9fh+p\nVEomRrCcy+uS11IymRRlJ0EQFeh8v+PjY+kto7BjOByi3+/LjNtUKiVtJKZpCihsNpvIZDIYjUaI\nx+OoVquyfb34I8NINi4cDotX33K5RLfbRTgcBgAcHR0hnU5jOp2KmCOVSuHmzZtiaE7RBUvWbPeg\ncIFAmuIPCiuYg1ju5v5wfu1isUCxWMSTJ0+Qz+dF5GCapsyUZY7RuZXlbALMYDCIer2+NXWD4JfC\nj8VigVKphHw+v3UuEokEWq0Wstks3G43er0eYrGY3FvYv7larXB2dga/3y/ngD2AupoSDodlceDE\nqwkH5F0TdrYKeC9DpEulAN4zM1WXHr1er1gK8ELQN3smA5ZMCTD5vnp7fC+WNwki9Zxb+36S0SM1\nb5+Rq48TwBZoAbAFSrj6JKjj81eVH68CxZrx1KpkzRIClxYw3A8Cbp3sdIlYHw//Rvc68pyQCeD+\n8TxOp1OMRiNhMbSdChvSAaDb7eJTn/oUotEo3njjDfzSL/0SKpWKJPlqtYqTkxN88YtflBmhPD7g\nEuTaQbB+3i6eccKJDxJkbHw+H4bD4ZaVU7fbFbNwzTbTmJxekARuZGqOjo6kX489cd1uF6PRCPP5\nHLFYDIZhiLluJBKBx+NBrVYTH0zD2AihyuUy2u22XJtk3WazmczIjUajyGazYtqbTqfRarWE5SKr\nfufOna1+OB4X+/8IBNmDNhgMJJ8Q/K3Xa5ycnIhdyc2bN2GaJoLBIB4/fiw5i4DHMAy02214vV4U\ni0V0Oh1hBsfjMS4uLsQvU8+/ZQ8wP59yuSwq1Zs3b8poNba6ZLNZNBoNGIaBcDgsQJZWM36/X8ry\nBMGsTMxmM3EYoDfier1Gr9fb+pxmsxnK5bIsbilSY0kc2MxCHgwGCAQCODo6Qq1WE/EaPRY7nQ4M\nY9Ozx3LzVRZRTryccEDeNaEBgi672h+397nZv9R2MKKFArwYOb4GuBzmzffQbJYGfdyOXrGRqSPQ\n0WCCbBVLimTKNCtGcKQBHBlFMoDat06fKw2+uI/249eAzR52cKhBJt+f55ClVd37o4GtBkvcJ658\n9Weo34vbDgQC8Hq9og4k6OPqmI3mlUoFk8kEt2/fxmQyQbPZlBE/fr9f3PWpyuUNhoneDlA1KNeP\nOeHEh4lqtYp0Oi2eeLQsoUiIixvam4xGI5ke0e12EQqFMBgMEI/HkUqlpJ+Plh+cT8rvKK8b4JL1\nj0aj0oPH/jXD2AgzisUiyuUynj9/jmKxKCVg2oHMZjMMBgNZQPd6PZRKJbE14igx9r2ScWQJmszj\ncDhEPB5HuVxGp9NBOp0WZjCfz2/5acZiMQAbIcj5+bmcPy7QWD7Vo9PY20cFP/Mqy5a8zgm+AEg5\neDgcCivGUnKr1cLh4SGCwSCazSYAoFgsSm8k7zHMxTQ65nxe5n49Y5ujydhreHZ2JnmMUzcCgQD6\n/b4ogtnn6Pf7RdVMlnO5XEqZeDKZyL6z35ELW8MwxG/RiZcfDsi7JjR406yPXaygb8oAtkCeLkVO\nJhMA231vZMG0nQD7LQju2HBsFyKs12vpAdEsFdVjBHUaUGoRiC4b83hJvWs/Nz17lUyALpvqbV0F\n8Oy9ZfayrT5Xept83l7O5HHpMrkdIGkRyFVMHnDZ50iwxxsLV6RU2XW7XUngevQZAR+TGUFhvV7H\n22+/jWaziTt37kgpjEDUrqbmudXHoQG/Pl9OOPF+Q9v30LSX4Icgh+y1x+NBKBRCv9/Her2ZUuBy\nuTAYDMQAN5lMotlsIplMinCC1ydLfmzbyOfzmM/naDQacuPXqvtsNivvXyqVpN1iNpshEomIGACA\n5D6v14unT5/KDFuOB6NYgyw6G/2j0ah4vbECwv7abrcrYhMew+npKfb390U0kEql4HJt5snSv4+W\nSwR3nGDBMjSN0smQ+f1+UcrS6iSdTksOsywLfr8f2WwWFxcXyOVy2N/fl79NJBIwjM3kn263u1Up\nInMYDAblM2cJ3ufzSZ5mTyKZ1Xq9jps3b8rIOe3Fl0qlcHFxIb1/wGa8He8LxWIRs9kMjx49wmQy\nwZ07d+BybcyjE4mEmCKzRMvjduLVhAPyrgm9KiWYsLNxDM286NKnLp1qY18NLPj3BAOky/n3THCU\n6xOoUdXFla8WiACX4A14b98XV6b2sia3zfex++lpYKJLjTrsAE+DYf34VX9nZ/J4PHxcH6MG2lpt\nq21V7KyenRHla/UKnKvqZrMpjdJMeHSJv3HjBmq1Gr7whS9IaYZGr8vlEr/4i7+Iv/3bv8Wbb76J\ndDqNw8NDYU94bPbeQg1wCegdNs+JDxupVAq1Wg3f//738bnPfU7GinW7XRwdHaFSqciikCCI1iin\np6eIRqNoNBoolUpi0BuPx3F8fIydnR2x2yDI8ng8YgzO/EIzXpoxj0YjZLNZdLtdPHz4EKVSCV6v\nVyxH2Nri9/vFLNiyLBQKBbTbbeTzefj9fvG1W61WMku23+9L3ywBjVYBc1FMmxaqRy8uLvCxj30M\n8XhcGDEKwUzTxNOnT1EoFNDtdgUsARug2u/3sbu7i1arJb3Pk8kEmUxG3BhWqxX6/T6KxaIwZn6/\nH/V6HaVSCZZlbeXVQCCA09NT+P1+GV9GkBwKhXBxcYFkMonbt29vLcpJAASDQbhcLtTrdTkenjOP\nxyPl7+l0ing8Lue70Wggk8kgk8mg1WohFApJbx7vRZFIRPqTOd+Xn3Gr1RIjZrfbjVarhf39fSd/\nvcJwQN41QWBH4EB2TYMHfoE18NOGxxp8sO+M22TJlX0TXM3yOarEfD6fKL7YhzGZTLZMS7W9i515\nBLY9/zS40L54BIX2XjsyAC/qs9P/10BF95lpYMd+Er2fPNcE1rqka2dUeT7tSmD78/YSKH/XZVqC\nPIJke28iFXpk7mjHQGUb52YSbLtcG9+8J0+ebDGvHF2khTxXmSMz7GymE0580HC5XDg8PMTBwYGU\naheLBcrlsnznC4WClOlM00Qul0On08H+/j4AIBaLSY7iHOh4PC6sNdWbmUxGDHcpsojFYlJOdbvd\nSCQSiMfjYkvy+uuvI5lMimedXeh2cHAgf/Ps2TPs7e3JVJpUKiXMGPNfKpXaEliQFTSMSwPi1WqF\ndruNcDgsIoq9vT2k02ms1xv/wEQiIdfc3bt3sbe3h0qlglAohOfPn4sJcbVaRTKZlL60VquF+XyO\n3d1dKZG3Wi0kEgnpVSyXy1gul2g2m5LzSqUS1us1bt++vVVxYB8dmVS+7+3bt0XwQL+6Wq2GbDaL\nQCAA0zTF6y6dTmM2mwloIyCkJyL7/9heYhibCSg0he73+wIQOWuXymiKzyhQcbk283uLxSImkwmK\nxaIAbideTTh3jmtCgzjdS6Uf06BGM0WaeWLio6pMm4AOh0PxJGIjLpVsNOul6oxlU26bNgftdhuD\nwUDKMLPZDJPJRHynNPDRJRNe3FzdaiBnV3lqEKW3Z2fKtMGyXbWngbFmNwnYOLpHb1/P3qR6LBAI\nyA97W+yP69fq58nSUdWnj5vvFw6HkcvlpIxBBoIjjfr9Pp48eSJliIcPH0pZ5gc/+AHi8TgODw/x\n3e9+F+l0WlgKray2g2yeP54z+3lzwokPGqlUCsPhUKxSXK5LU93ZbIZCoQDLsnB6egpg04M1Ho9l\nnuu///u/i5qcpsL9fl982ahape3GaDSS73Kj0RD7DU5MmM/nUsozTRMPHjyQ51liLBQKMM2NOr1W\nq8lilpYlhmFIi4ppmtIX1+l0ZCpEOByW9hev14t6vQ6v14tQKIR2u41arSbjE9nfVqvVAFz66xHw\n9Xo9NJtNmSlLoQlFJ81mU0QTvV4PtVpNRn4RGD9+/BhPnjyR7bBnjozn6ekpRqMRLMvC48eP0el0\npCLAnM6ya6PRQKVSQafTgWma4u3HEjYXkmQ5WXqlLyLfi5/narXCW2+9hV6vh263i3a7LedpOp1K\ndSKdTmOxWGx5D9LmJhAI4Lvf/a4scrvdrihvu93ulq+fEy83HCbvmiATA2CLhdLlPrtHGxkrsn58\nDZkrliP0XFW9fa5KuZrla9xutzjQs+eDfSBcETKp8O+0dQpBBVfLTAg8HoINskvAZT+hZtIYmvHi\n43YllRY8kC3ka7mfuoTN19FqRgNC9iZqHz3dm6hLxxpMalZPi0rszCLd3U3TlJUxPyufz4c333wT\nn/rUp1CpVJBOp+H1erG3t7fl4VWpVHBxcYHbt2+jXq8jFothZ2cHT5482erD4fdELwTswJnfvReJ\nVJxw4ro4Pz+X2audTkdEAKZpwrIs9Pt9WSjyd37nDcPA0dER3G430uk02u225JfhcCjsNcddEZgx\nl1CcQbDHnr1Hjx5huVwilUrh9u3baDQaaLfbwv5Q8DGZTJBMJkVIQZAVj8e3Fq8ErASSz58/l96x\nfr8vI834ONkoWpd873vfw9HRkUzAIes+GAyQz+fx9OlTqeJcXFwIc08TZua7+/fvI5PJCLBerVbo\ndrui3i2VSgA27TlPnjwRcchkMpG51zwvg8EAZ2dnYr0EQHr8+PlMJhNUKhWEw2EcHx8LOKZSWi8Y\nHz58iHQ6LcCYE3pMcyPY29vbEwGGZVlot9uyb7R+Oj8/l4XC8+fPRYxCAcetW7cwm82kVMv7Fv0L\nnXg14YC8a8IuqNAAQosdXtQ3pcGT3euOStVAICCgkK/TbBuThGFsDEKpUiMwYYmRNDqTLXsnyNbp\nSR0AxMeN78nH+V7Aeydm8Bh1KVG/1t6nqJWxwKXghOCKr+cxsOGZpWf2v7DkSSZS36x47viY3l/9\nmdl7Ce3ldu4Pt8/PgUCdq15aLUwmE7TbbRluzpsa52nSgsUwDBnQrv0G7eyovX4dTMMAACAASURB\nVKyvewftwhUnnHi/wZ4u2oaw5BcIBBCLxVCv12VaA60wWL5NpVKwLEsmNnCsFz3weE1QpUlgQGPg\nYDCITqcjhrvs46Ia8+TkRCY+nJ6eIp/Pw+v1ShsEPfgIXHgtjEYjVKtV3Lp1C6enp/B4PIhEIuj1\negLoYrGYgJbRaIRKpYKdnR30ej1hyAzDwM2bN98jQjEMA+l0WoQNzE86V1Nd7Ha7MR6PxWMuk8nI\noto0TSl3cuGtgSEn5uhzPp1OpY+OAI9edgR5nIFLJvXWrVuyKOWEEo5ZA4BIJILT01Nks1nMZjPp\nJeQUCzK3XOR3u10kEgmMx2NhKfX0Hs6qbbVaMk7t/PwcLpcL+XxeyvgulwvRaPQ9TgxOvLxwQN41\ncdWNWLN4ekLDYrGQlQ9v4mTjgEvgwVWoBi3ApXEnAQuZHO0Cr331uC8cLUMzZWAzQku7nevGaoJN\ne/8dH2eTsm7811YsDK2Y0j18PE88bg1YgcvyNe1IeJ7ZdL1er6VMbZobzyv+DVex+vxp4GkHQ/q9\n7a+398Ex0U+nU/kbGsjSlNTj8aDX62E0Gsmg7rt372I4HKJSqcDr9eLnfu7nxJNsZ2cHlmVJryWZ\nVDuYu4p1JDvLfXPCiQ8aprkx36WgQE+oMAxDlJ3j8ViUplSNjsdjHB8fw+VySRmUNiGdTkemIZAB\nW6/XMmuWTBnzBq+BQCAgZUhem2S8ksmkLPTG4zGWyyXa7bYs+jwej7BX6XQaOzs7MAwDyWRSAOj5\n+TkODg6QyWSECaxUKnC5XCgWi7I4JuAkoON1x5aKdrst5yYUCglQNE1TwAwBzGAwQKPRkBacdru9\nNcN2tVqJ/x8Xf1Qm83hXq5WUuieTiZSWu92uMHvJZBLz+Rz1eh2ZTEZUxZZlSW7nvODxeCx5PBqN\notVqCbuWz+flnsAJJmxZ0aPTptOpLFwty5LvBL30WEWiCpq9iWRXLy4uBPxqAaATLzecM39N2D3v\nqMDU46/4O3vhdClQ91rpbRCkaWEHe8EIyHhhUFxBdRWBJan28XiMwWAAwzBklqJWAnO/NHAkSGJS\npkmqXRUMQACsna28qsTI4+J7sexIMQXBCssIuoxL53iuasmicZQOgSR9obhdAjLN0ulj5w/3VXsO\n6h++L88rhRH1eh3pdBrZbHarF8kwDJydnSGRSKBWq8E0TbnhPHv2DIVCAeFwWBhBlrD0TeXHlZZ5\n0+H3wwknPmjw+ub1RbVmq9USjzm2gpydnSGdTkslgHNKTdOUkVZk/1mKo5qSYIF+bLxG6NVGBpxl\nQsPYmAgHg0FYloVyuSzfd7Ljpmmi3W4jFouh0WigWCzKtoBNu0ez2RTvydlshr29PSwWC/R6vS2/\nSmDDhlEQMhgMhO1KpVICUl0u15bfHBfF3M7FxYX0pTUaDYRCIfzoRz8S0QGwYST39vak/B0Oh6XH\nmv2RNI3mZ9BoNGCaGw8+CiXC4bC8nmpkLXahYKLVamE6nYoqlj2VbG0JBoNotVqSF91uN46PjwFA\nFMAA5B5DGxj2JtL+xeVyiUchhYLMwQSVBNS5XE4WD4ZhoNPpvNTvvROX4YC8a4JqVoITGnlqRo+g\nTc9U1OyRZvWASz+8q/reCOC0WS5BJcut/HuyZnxfGiqHQiEZ06MnWuh+MC0UsZcONYvE/3Of+Dpd\nxgQg4NMOVHjetICANx2ylhoUMgnxeZ4X4LKvkSDY3s9oLyXbrVs0y0f2VbOOZBWAjalqoVDA6ekp\nEomE9LvU63XcuXNHGqMPDg4AAD/60Y/wm7/5m2i322JDwDKUNlEm+2kXoei+RO4zwffXv/51/OVf\n/uWH/xI78TMbnIbA7zXbPfL5vJTaXC6XmPmenJxIbxvV/GTdqLClyCEYDMrIMc4xZTuIaZoy5J4M\nEXApLNJVCf4+m82ktMnWC5/PJ4ssAOh0OojFYqhWq6LapaiATGEgEJCxXpZlAYCAN/bBUXmqQc14\nPEYsFpPrj4K3brcrnnMcK0aRw2KxwMHBwVYVgP6C+Xwe/X5f8goX4vTso7Cu0WjI50BQBVyCU7Jz\nbrdbRtE9e/ZMGLlwOCz5niVc5klWgljCBSDgLBwOy3lZr9fodrvyvQAgC9p+v49MJiMLWeZfzilf\nLBbCjNJ6pt/vb9noaB8/J15uOCDvmmAfBKl0rmqASw89Uv66N483bq6kufrlKpkAiitFzerw4mai\nY68djZRJiQOQUgnZKuDSDJNAiK+9youN76t747jvBJxk/DQwtQse+JgdvPD1utTNH7/fv/W33B77\n1njeuZrVx6gZU64m7aKLq0qhus9N7x+9qfh/uuSHQiExAmWSPzs7E/Veo9HAfD7H4eGh3AATiYQk\nz1gsJmDPztJpIK/3VZf1XS4Xfvu3fxu/9Vu/JYncCSfeb7DsRqNgLko1o+x2u6V/LZFIyHXGa2E+\nn6NWq2G5XIqNBmeedrtdlEolASvAZjIDHQOi0agwej6fT64jlmDJ2LPVgQweWTB64AGQSsV6vZkT\nzd4yAhG98Dw8PBSg4/P5RFzB/l4ykgSCBKfValW836LRqOwnS7ecNfsf//EfMsGGYIqsJRe7q9VK\njpGtMyzNLhYLGQnGvAAAhUIBjx49QjabxWAwEN8/AtTFYoFAIIBEIiH5hovjfr8vps2cxpPP52VW\nMT8LTQLwntDpdJBIJKRVhr55BMuj0UjuA/P5XKancEwdKxVnZ2cCepkvaZ7txKsJB+RdE+l0Wr70\nk8lEHN71ClT34OneKX3j1iVZlhy4GmJCIKCinxVBkB4lRCDDC1xT8PYSIFd5pmnKNrhfBD2a0dI9\najReZllUl2rJkGn1K5Oc9vnjPvE5LXJgDwpLRaT8Of6LQJeJhPvFY7T3NGpWQAsY9GBwxlV9g8Al\ny7FardDpdMSMlGVizp5kP9J6vcYPfvAD/O7v/q706VmWJSIMWhXwe0IWQJex9fmzl49ZYnNWwk58\n2NCq01qtJhMJKJTgzZoME22FLMuScVq0XGEzPhel6XRapr+43W7UajXk83kAEJA0n8+lr4xMGe2i\nms2mGBuzQsESpG5nGQwGiEajOD09RSaT2VrocVGse4h7vR6i0aiUCvv9Pl5//XWZA6sVwmytCIVC\n6PV6IvZotVrSY8YZsjQ79vv9uHHjBnq9njCl7Jkj00imjotlClCYd+j9x+ueHnaLxQLZbBaGYaDR\naAg46na7ALDV78i+Pv6fALleryOXyyEYDMI0TVxcXKBYLOKHP/whdnd3xR6GZel+vy/fBdM0EY/H\npYePArNIJIJkMonZbCbnhZUjYLOAffbsGUqlkjCFzONkF514NeGAvGuCvRq8+WujTq1K1Q3HXMXw\nd16ETBh2EQIbZDXII/jg85qFo8CBCUc/rhW8BIZMlJxHqEuqAMS3j+/p9/sFOPGxH+e1p8Emy5Hr\n9VpUYvx7Nhpz//mefB/2FwIQEEswp9k5l8slfYd6P7iC1uwdj1eXzMke0n8KuOzn0z2YkUgEnU4H\n0+lUGswJftvtNnK5HBKJhMzn5M2FthHBYBC7u7sy+1ZPT9E/DC1qAS7LKmzGdsKJDxq087AsC7lc\nThYMXCixZEjFJvu5qBjljFe9WGJZktc81bVU4no8HozHY8Tj8f+fvXcPkrQuz4avp3t6evp8Pk5P\nz3FnT7C7LCAI+oKCwRRENGhBqmIiJtGqz3yhvlCpvEGrYr7PqIlGgqYSKlEjmJL4FiEgZSIrIgdZ\nYJdlYVmW3dndOfb0+Xyenu5+vj+G6+Y34xrUV916N/2ropid6cPTz8xzP9fvuq/rumEwGBCLxVCt\nVgFAxPsOh0Py14xGo2jJKI8ZGRkR7S1HkamTFpjbZjAYkMvlZDYtAAkNZpuRU4FYiwlwebyhUEgm\nX7hcLjSbTXi9Xjgcjk3miHq9Do/Hg0ajIVITAiCr1SoOYjpWc7kcPB4PKpWK3DPUmBbWeYLOoaEh\nZLNZmEwmhMNhWK1Wcc9S88egZ24My+UynE6n1LZerydBzmNjY9LqBSBTLCYnJ6WudDodlEolxGIx\nzM/PyzkaGRlBqVSS7NJ8Pi/nl+Y+1namPYRCIUlDUOemsyMzWOdnDUDeW6xSqSRtPIIA6jxI31Nn\nwl0gGRh1WDXwpm6NAI0ghvMDKV61WCyiHSHzp7ZOuIPihUqww10qgZFqaqA4msejtgoZEEwNHYGX\nCuLUlq4KtniT4PPUiAD+jG0To3HDjcYB25ziwdBm7spV7RqATSwnzyPBkcpCMptKXTyuc+kgWaS2\nMqgEVWwV86aYyWTQ6XREFM20eU3TJN2fUy94LpxOp4SQqgBUbRNvXaqmkMc4WIP18ywCktdffx17\n9+6V64wbDmp1u90uQqEQ0uk0isUi4vE4arWa3PC5kQUgrLI64ov1zu12i542l8uh0+kgFotJyzWd\nTqPdbkugLsc08nrzeDzS8mMbNxAIiD5sYWEBo6Oj6Ha7yGaziEajsNlscmxkmKgTZN4b42HS6bTk\nwambddZNbozJhpVKJdjtdhQKBakTrH3M0WNAPVuiCwsLMn+2UCiI+xWAxLwQZLtcLpjNZqTTaakf\nPp9PajANIMvLy2K+oANY0zRJHuB7cDTZ2NiY3G9orikWi5tIAca92Gw22Gw2RKNReW2DwSDAmA5e\ni8WCWq2GgwcP4uKLL4bFYgEAcR6rsiLe1zjCjffMwfrVrwsC5Gma9nUANwLI6rp+8Rvf+zSA3weQ\ne+Nhd+m6/p9v/OzPAHwUQA/AH+m6fuAnvXaj0ZA/YBYFZkkRfFDc2mq1NrUlh4eHfyy0k3oUil2B\nN1k4vhYBCIGeCkz42myzssCqiwAPeDMChkVdLVSqgYLFTn0/6nL431bAoQJO6hS3xqiwqJDFJOgk\n4KxUKvJadJISJKk6OtXpS5aQYFLV6vG9eX74eOrb1AgatWXNY+Lvwev1IhgMIpPJYHFxEV6vV5hG\nZkJxAsnS0hLOnj2La665BpqmyeMjkQiWlpbw4osvYnp6Wj4/owkI6smOUgTOG3G5XMZ3vvMdBINB\nHD58+Ke8Ggbr/8T1y6ph3CDu2bNHRlG1223ZdOi6DpfLJX+XTqcTFosF5XJZ8h95nZfLZYnaACBG\nB250aU5gxh21Wvl8Xh7H0WI0GKhMIFuQnInLY8tkMtIeHR0dRa/Xg9frhclkQrFYlBZzqVQSBy03\nbf1+X1h2XdfhdrtRrVZFVsIWJaNSyFbxc7DmkV3MZrNSfzjGjeaPXC4n79HpdGSjarFYNrHyRqNR\nmEOCNm5uqf3m2ETWcr/fj2azKS5XgmJ+Vo53YzZeuVxGt9uVOcMOh0PG1zFUmbmd7XYb9Xpdsgv5\nmtx8MyS+Xq9jeHgY27dvF6MMPwf1iDTaJBIJ+Hw+cRG73W4cPXr0F33ZDNZPsS4IkAfgnwF8BcD9\nyvd0AF/Sdf1L6gM1TdsF4FYAuwCMAnhc07RZXdc3U0BvLF6U3FnxRq1Go7BQsShwwgTBgwqW1JYh\nGT1qH8gC8rkqAKCzFNisU+PP1Cw9AhiygCqLxWNSAdJWQwbFy2oblo9lujxvCnKyFRBGoTGPQxUi\nE0CyABOgcteptrkJhHm+VMCpvq9q/th6POpxcanHtNUswmJVLBZRLpelyFKYTaE2XYWvvPIKNE3D\njh07kMvl5HdRq9Vk1NzMzIy0Xqin5E0F2Lih0LmmaRqOHDmCf/3Xf4XFYoHb7cbTTz8Np9N5zj/8\nwbpg1i+lhpHdp/632+2iVCpJi43hubxhc5PDzLzV1VX4fD6JV8nlcqhUKhJ4SylKMpnE6OioMOHV\nalUCd00mk4AZr9eLoaEhhEIhmSDBr9liZfRGvV6XzRI30KyTZBgJkMga1et12ciR4aMekTWJkgoy\niLwOeX6y2SwikQjy+Tz8fj9qtRqGh4dRLpfFROBwONBqtZDP52XEF92rdC2z3ev1egUgkdFS0wT4\nGtQrkgzge/JrGsFOnTolmj7KR0qlknRGACCRSEiGH+sqI2XICq6urmJ8fBw+nw9ra2vI5/OYnp6W\nc02dYyaTgcvlEhMPtYPHjh3D29/+diwtLYkrmSa5er2OYDCIoaGNKU2DnM/zty4IkKfr+jOapk2c\n40faOb53M4AHdF1fB7CoadoZAG8D8Py5XpvggLvSczkcVQBEdozsnsqY8cImu8Tvs1Wqzlqk5oxM\noOocZduSAGR9fV00bGobU2Xp+FwCRNVEca4WJ4ENCw41OCpAJfDl7k8FctzFqmCNO04AAkrZ3qX2\nkeBT1c6pAFll4/hz1VCigkC2VbaaMfizrZo4sp0E261WCzabDRMTE1hZWREGgRMCeMMCIAPRabQI\nBAJIp9NyPuiyo7bo+eefx1NPPSUuxddffx0GgwHpdBpG40Zwa7/fx9LSkgwoH6wLd/0yaxiD0jud\njkRd0OlKXRdBlsViQT6fl1rBduHQ0BBsNhtqtRr8fj90XUcymUSj0UA0GkUgEJC6R1ct2TC6d5vN\nprQq1QkWRqNRwpr5HqpLVR3dSAMcj5nXH00WvK6pQSYwVTsb3JgvLy/D7XYL+8Tj8/v9OHPmjOgC\nXS4XRkZGZDa1rusyEo4dCgDSlozFYgKSLBaL1ARGjRDw8NywTUrAzPxAj8eDbDYrmkLeP3bu3InV\n1VUMDQ0Jc6lOn2C3ga146glpEHS73ej3+/B4PHIv6Ha7iMVi8nySBZqmIRKJyHHTLGe1WiWMOh6P\nyybB6/Wi1+thdHRUQF8mkxkYx87juiBA3n+x/m9N034HwIsA7tR1vQwgis3FMIGN3fA5F9sdBF9q\nK5KghPQ2fw68CSKAN9kmXtxk19RpGQRl/JrArd1uCzhRI1XIkvG9VOCnAiAuMkwABJzxcWTVVFZP\n/Zmq0yPjpoIngkiV8eOxsFWqAjI1d5CAku/FAsxjUEEzzyHfgwWb519lXdWCrz6GP1MjY/h9tsv5\nGc1mM0qlkuz+jx8/Dr/fj9nZWSwuLiKXy2FychJjY2OYm5tDr9fD7OwsstksstksNG1jZBJbSqdO\nncK//Mu/CKtRrVZFe7Rz504cO3ZM2jKHDx/G2NjYJs3NYP23XP9bNazRaIiulJuIUCgkYGpkZERC\nismCkRFT8z95rfh8PnGb+nw+udEzHNdisWy6xrnx4TVIrRajU9iaVQ1oxWJRQEKr1UK1WpWUA4It\nyjy4geQkGmry+P5sNRMcttttOJ1Oyb7jmDa/349ut4tAIABd12WajdfrlbrLzSvBIDs2/X5ftH+6\nvhHFRAMLASkNWiQKWFe4SeY4M7fbjfn5eWzbtk1YPc61ZZ1qNpsIBALCNFI32Gw24XK5JJarWCzC\n4/EIg0pQ6XQ6sbq6KoCOLliCQWCjNWu1WpFMJhGPx1GpVGC1WtFoNFAoFDA9PS2bYZ4TspY0mtTr\ndfmbGtSv87cuZJD3DwD+3ze+/v8A/A2A3/sJj/2Jg0EPHjwowG56ehrT09ObgBTbG1sXwRIFsgDk\ngt4aS8ICQlCkAkn1MSxoLF7qbkttBRP88WdbASkdZr1eT1hEAh8Am9q6/Jz8mcqwERyqTCD1i/w5\nX4/AlZ+BBVGNdgHejAjg2srMbW3Xquda1fGp2jyCU/V88jEsUvwePx+LMTU3VqsV0WhUtD3c5c/N\nzeHUqVNoNptixKnVaggGgzCbzbjrrrvQbrcRDAZx+vRpuaHSjcf28PHjx9Hv98Vlt337dhQKBSwv\nL0tw62D9t1v/2zUsk8kAgIyzmpqaQrPZFLd3s9kUpsxsNmNtbQ3JZBI+n09YP/6Nkrkym83CINFJ\nPjU1hW63K9ErDMWlfplTIgi21Iw6di0ASCAvWT22bNVZ1tSUGQxvRlZ1Oh34/X68+uqrMpmG8SN0\n0Y+NjYkOlqwXAASDQXk9Sik4WowAhZKbfr+PdDot7Vqj0YhsNguv1wtN24hCIRPGaBUCYl3XJZTY\nYrHIaxCc0ug1NTUFAOJuXV1dRTgcFgkO63MoFMLKygo0bWO0m8/nQ6fTETNLoVCQOst7iDr5iE5m\nxuIQGDMTsNfrIRKJSOeCYzOnp6eRSCQQj8dlBCTvS+12W9q91Ppt7RQN1q92XbAgT9f1LL/WNO2r\nAB5945+rAMaUh8be+N451/XXXw/gTXBDwT+F+tydnivYlsBJZZBYmPga6nMoAKZ2RC0sAKS1SR0N\nCx8vZAKoTqcjFL6mafJ+3F2xaFNEzcKtgsOtrBw1LCoAU80P6nEqvwN5Pf6bxWAr00iApkaaqOCO\nn5OAWmURVbMIv082Ts0PZMtbfd5WowkNEBRaOxwO0Ru5XC4Z4k1dCs+nxWKB3W5HNptFKpXCX/3V\nX2FxcRHj4+Mol8tIJpOYnJyUMFFgA/RPT0/j9OnTsFqtSKfTyGaziMViSKfT8Hq9iMfjMBqNOHHi\nxE/6Ex2sC3T9ImpYMBiUWtXtdmUyBWUg1HqxzUpdHrVu3LzYbDY0Gg0BWQRpNCBYrVasrq7C7/cL\nIOHGzmAwSLQKNcvUh1EHxzmvqn6XOaF8DLV4jUYDfr8fqVQK0WgUmqZJ63V2dlbanZqmCRBjdAhr\nqt/vl/dkK9JisUisC+sjZ86Wy2VYrVYMDQ0hGAxKF4bvRTcuY1ncbjdWVlbEUAJsgDa/3y/gmjWT\ns4Up1yHrubq6KswiADE7MKqFx2k2m5FMJoW1I1vq8/nQ7/fh8/lQLBYBvJktqKY28HfZbrfh9/tR\nr9eFnCApwCSBSqUic9FZ+wuFAjweD1qtFprNJkZHR1Gv14Vh1d4wuKysrPxCr4/B+unWBQvyNE2L\n6LqeeuOfHwDw6htffwfAtzRN+xI2WhzbABz6r15L1cMRCPDiIJBQ58mqDJjaigTedLsSGFGrR4qd\nguOtRgO+Py8+NZJjqzmBTCHw465VWvaBN8EcH8uWi9o2VQ0aartUBYFb2ULVCMGvz8XAcalgi++t\nfmbVPcz3IxPKNo/KjKqAeqvmUNXkqf/nsfL30uv1ZBduNG4MHY9EIlLYKXjudruSO/XpT38atVoN\npVJJWA+6y7xeL6anpzE3Nye73F6vh8XFRWH3AEjWXrVaFZbk1ltvxdraGp588sn/6s90sC6w9Yuo\nYbz+KpUKHA6HsEi8jhjq3ev14HA4pMacPn0ak5OTWFtbw+nTp3HJJZcIm8e8OMowTCYT6vU6XC6X\ngAw1jqhWq8Hj8cDhcKBQKIjOj9cAADk2r9crzDnZpn6/L5tMl8sl824nJibQ6XRQLpfhcrkEjAQC\nATk2GkB0XRcwt7y8jHA4LFpXVR9ItylHfnGyhjqKjEw+R6ul02lh5dn+ZDKCy+USEoAOWo5LS6VS\n6PffzDKllrBQKCAej0t0k8FgQCqVwuzsrLSv2Wlh25u1xmAwCLs2MjIibVcypIy4YdQJ7xesu9Td\nWa1W6UhEo1EsLy9jZGREgCNNN7quS0gyQT9zGYPBIFKplID7wTo/64IAeZqmPQDgGgB+TdNWAPw5\ngGs1TduHjTbGAoCPA4Cu6yc0TftfAE4A6AL4v/SttJKytrZP+Z8K0niR0kjAViqXCjxUIMLXUlmn\nrZo+FTQCEKcU/012T6XkVf2cOpWCjyOTxJ02i60K3lQwyn/z/ypzyNfZCuAIPlV9IB9DoKU+Vj12\n9bFsqRLQsehxd7z1HGw93zwP1OBt1fupX6vnnGLkkZERjI+Po1aroVwuw2AwIBAIIJvNCnPwhS98\nAUeOHJEbDSeFABCtjtlsxosvvohgMAiPxyNMHacMUJjOQnzDDTdITAsda4N14a5fVg0rlUoSlUEG\njw8lOGIMEgGC3W5HMBgUdou6OQCw2WxotVryugw+XltbE3MAGT+GKI+NjYlbnUwXXbWtVgutVgvj\n4+ObIoVWVlYQiUQk1gOA6M4IKFjnhoeHpfXbbDYl9oUmDwK3TCYj7lMCFQb18rNwk0XTCM0QrK/M\nxGO7N5PJIBgMyixfhkhzQsXa2pqwXKwF6+vrooOjDo9tUs77zWQy8phKpYLZ2Vlps7NWGAwGabXS\n9MB6zrneJpMJ8/Pzck7UiRwEr41GQ75HlzJTHig/cbvdUmcrlYqARNZinh+GPdOgyPsio7QG61e/\nLgiQp+v6b53j21//Lx7/WQCf/WlemzfXrc5Ofk81MGwFhG+8149pyQgmVOMFH0uAob6/+lwWHrJe\nBD2qtoyAiMfFaRpqDh8ZOxZ9toFZpNSWqvrZuNQ259a27FaAtxXAcW0FWdxJqq1vMo1bW94qQ6d+\n71xAWn0+/6/GuajHy9fhLpmZdgCwuLgIs9ksDrJ8Po9Go4GFhQUJPlVja+bm5rB9+3Z5/MmTJ9Fq\ntZBKpdDpdHDppZfKWKnLL78cdrsd9957L773ve8hFothZmYGwWAQ4XBYbk6DdWGuX1YNY1uUgGZo\naGMUFuefqp0ItW3ndDrFpMFgY5Wt4nVGuQKnLGiaJu1I1jar1So5dmTx3G432u02wuEwisUiTpw4\nsWkSA+UoBoNBjCPFYlEMEiMjI0ilNkhOu90uGy9OViDD6PP5BKxms1kxc5A1ZGA7I0/a7TY8Ho9s\nfFOpFCYmJrC4uIht27ZJJmi/30cmk5HRbsvLyzKz1+FwSJtb13XkcjlhAZvNJorFImKxmDBebrcb\nR44cweTkJEqlEvL5PPbt24dCoQBN0xCNRsUpWywW0Wg0YDAY4PP5UKlUpGXOmdoGg0EYPk6qcDgc\nMmqO2jld1yUOSu0EcbwcI2CMRiPK5bIcNyeW8H5DI0ogEBCDTCKRwNjYhqKAoHawzs+6IEDeL3NR\nt6YycdTTsSCpoZXAjztrVRYKwKbXUjVkqvGCAGar+5SPp1BazcvjTkrNOOJz1TgXFZypUyzUgGcW\nMh6v2rpVdXUqMN3K6J2LWVMBlWr0UIGZyrrxPcncqQwqX5/nTz3nKiBVtYBcfD/1M6rHNzQ0JFMs\n1tfXYbfb5W/h1KlTkpNHlm5oaAixWEwcuWQRotEoOp0OVlZW8K53vQseIYHB6gAAIABJREFUjwdz\nc3PIZrOoVqtIJpMoFAoolUqibbrtttswOjqKe+65B+12G7/927+N/fv3/2L+oAfrv9UaHh4W5r7T\n6aBer8PhcEisBTVV4XBYmH3qjMl28aavGiaADVMHY4UACHjk+3Ije+LEiU1aQJPJBI/Hg3K5jFqt\nBqPRKDEv5XIZ7XYbQ0NDKJVKEkMCbLCSHo9HzBuMXaG7k50GTr4ZGnpzrjglMaw5lL0QlLED43a7\nZWNnNBoxMTEh7WZO62Drli5ar9crbmUye5q2Efhst9uh67pkh/Z6PQSDQRmHxhY4A4Pb7TbGxsaw\nvr4u7Kbf70ej0UCn00EwGJTazv/4e+V5YDeh1+vB7XYjl8vJaEWXyyVgl78zOvrZ8uV9hiwt0wXo\n0GXrm+Y0tQVdr9cldob5eNTyDdb5WQOQ9xbrXG1WFSSpzlq11ciWqto65XMIXEip06nJ5wJvhjAT\noJA+J8hTX4usHi9+o9G4ydyhRpqobU21lQq8mWmnMm7q97jLozlEbddu/dx8L5pBWPT5WVRNndqG\n5c/p/iOA3nrc6oQL9Tj5e9gKpNXnq8YJtrHIDjAGgr83p9MJm82GdDotwajT09NYXl6G2WyW4mmx\nWLBjxw6Uy2VMTk7ixIkTuPjii/G2t70NZ86cwSOPPIKXX34ZO3bswMzMDKanp+Hz+RCJRLCwsACf\nz4f77rsPqVQK999/PxwOh2R8sZAO1mD9rEvXN8J2GXXClqzNZhN3J92la2trcLlcMnu1WCxC13UJ\nPeeGjg5UboAIDNkpYPuXDttAIIByuSwbrbW1NTmWcrmMeDyOUqkkhgECN9ZFXv90/Hq9XiwuLgor\nSHBKzRvfx2AwiOGgUqkIgHM4HCgWi1IzaCbhZIq1tTUxXXi9XiwsLCAej8tjK5UK7HY7isUitm3b\nJqDU4XAgGAyKGYLnLRgMSqtW0zYcuPye2+1GqVSS2sPnrq6uwmazSVae0WgUlpXxWjabTUwh1CVz\nXBun5yQSCUxOTuLVV1/F2NiYbOKNRqPce1hvC4WCTBXheWw2m7Db7bDb7TLzd2hoCI1GA/l8Hjab\nDS6XC06nUzSYHo9H2urdbhf5fH7Qrj2PawDy3mKpwE0Fe+r3tv6biyBG1YJtNSaord6tOr6t7Uwm\n15/rcQSOqoCWxhA1r46vpz7vXG7frYBWZR35mnS7qcey1WSxlc1T27cEgGqYM59PsTVZBfV91N+F\n+lnU34PKMqqfmTcjsoEEq6ruhyPqVldX0ev1kMvlsL6+jnq9jtnZWZw+fRq7du1Cr9dDsVjEZZdd\nhomJCTz22GM4duwY9u/fj1gshkKhgIcffhgulwvT09NYXV3F9PQ09u3bhx/+8If4p3/6J9x22224\n5pprJJogl8vJDYJi9EqlskmDOFiD9dMup9OJ4eFhnDhxQnRdgUAAuVxOjBbUs+m6LmxdLpdDMBiU\nYOJmswm/3y/GCTUuSNM0FItFRKNRCR4mw1Wr1WA2m0Vrxhy8aDSKdruNbDaLQCCAdrst+X3UovH6\nNBqNqFQq8Hg80nJ2uVxIpVLCQvEYvF4vdF1HJpOR0WfMGiWoXV9fF1ODOqeWE0Cq1arEFqVSKQE2\ndJZyg+pyuZDL5TZ1XQDIe3q9XtGwNRoNDA1tTPrg63NDTtDJLLn19XWZuEE9W71elw27y+VCoVBA\nuVyWlirbpMxWpZGPbfpYLCZRLWotp/7O6/Uil8uJQ5fgniwtN8Q0nlFP3Gq15LOrxkE1K5AgfbDO\nzxqAvLdYWxkhYDPg+Uk/2wp2eBGo7BnBDMEbvwdAgIgKCFUDBr/Pna6qN1Nfn9lHfN65dGosTvwe\nH6cCMxVMcamOW/VnBJuqxo3fV9vRBHlqe5pAjKyk2lJVz69qAlF1jFs/nxqXwnPI1zSZTGg0GgiH\nwyIAP3nyJL7yla9IfMT27dvxwgsv4Nprr4XT6cTy8jKuv/56BAIBHDhwAK+88gpWV1cxOzuLeDyO\nvXv3wuPx4JlnnsGDDz6Iiy++GHfddRecTie++MUvihFm165dOHr0qBR5TduYksGbWq/Xg81m29QK\nG6zB+lkXN28+nw9WqxUOhwNms1lartRn9ft9uN1upNNp6PrGzFhuCtl2q1arshnqdrvC6hM4NBoN\nFItF2O12uN1u2O12VKtVMVEQAIyOjorjkqxfNBoVfRodnmTY7Ha7XM+8BmkqI7OnaZrk23GRVWTo\nL2NZVLbO4XCIm13TNNHTcZrN8PCwRJZw2gcd98FgUL5eXl4WR+n6+jqSySSmp6el/UlzBkFvu92W\nsGGj0SgGGABS93w+H6rVqjh12T4lqwcAuVxO4mBo/GLIczabRTwex5kzZxAOh8X5zNpGkEsDBdk6\nnivKgYaGhnDy5EmJoKHWkNE7JpNJxqJ5PB5Uq9VNU0+2drwG61e7BiDvLRa1X1vBnMp0qQzUVkaO\nAIUARwVq5wKIXFuND+r/t7ZZ1fdSGSzmIKlMl6oBVP+tujfVXDseB/V+BGSqxm2rDk/N5VNB79a8\nPHXqBEW8wIaeh2Gk1OSowHoruNv6n8pEqsen/h7JaND48KUvfUmE12NjY/D5fNi2bRsqlQoee+wx\nPPPMM9i9e7eMNcvn81hZWUGr1cL73/9+7Ny5E3/8x3+MSqWCe+65BzfccAMOHTokY5C8Xq/onux2\nuzAJ6XRahN/r6+uYmZkRgHf11Vej0+kgFAoNIggG6+daBFIejwelUgkGgwHRaBQAJOaH+jFqxOgi\nr9frcDqdIs8gE0cgRvBIXRt1Y2TxVCBFLZ/RaMTi4iJ2796NcrmM6elpuc6Hh4exsrIi5gpuFJkX\nx7rF+qAaQdbX1+HxeHDq1Cls27ZNNHiq7IMMHJ3tBoNBNlgEtdQsUmPncrnE4c52MafVkBkkU7ay\nsoJcLodarQafzyfnm+/tdrtRKBTg9/vlnAeDQRQKBcnKY00JBoOibWu1WtIKN5lMqNVqcDqdEmgf\nCARQLBZRrVYlPmZoaAijo6MSaMxsQgZcs74aDBuO4WazKaxmJBKRWdvr6+toNpsYGxuTWd5ss3NU\nGXXJBOw0v/DcnisXdbB+dWsA8t5inQuEbQURKrA7F6MHbG77qszY1udsfW/14iB7pb6eauxQ32tr\n3MhWYwhBnWpGUFk1tf1LETNZQb4nRc3qa/2kMGO2R6mb+UlM6KFDh2AwGHDttdf+mFFC1e+p3z/X\nUvWK6u+Mz+dNyGq14tChQzAajUilUtixYwfcbjceeeQRPPHEE7Db7di9ezdmZ2cRDofxH//xH9i/\nfz8ikQicTidOnTqFsbEx5HI5xGIxGAwGceV6vV6Jb+CNplqtiiv67W9/u7Rh+v2+5OExNZ5ByPPz\n81hcXDzn5xyswfqvFq9ZCvQ5wQLY2MDWajXR2ZH5d7vd0DRNJkUQGDA8mZo9k8mEZDIpGlYyTdR+\nHTx4EPv375fWodVqxcrKCmZnZ2E0buRbsj1rNG6EkNP1yo2l3W4XZzkdpoyEqdVqm0LhNU2TwPFw\nOIxqtQqv14tGo4GxsTG02210u12ZDsF0gUKhIDEiZOq63a5srjqdjjBUmqbB7XYjmUxiZGQEfr9f\nXL3UndE4oesbc4G9Xi/q9TrW1tZQLBbhdDrhdrtx5swZMXXRAcw6xTrAEGuylqxZBHpnz55FLBaD\nxWJBu90Whz/PEzfdBKM+nw/tdltcx5VKBdVqVd6LM40BiMuZI+9GRkbQaDTgdDoBQNi5YrGIWq2G\naDQqINzlckksj0psDNavfg1A3lsstX3JwkNXLfCmGJmP4dcU8qsJ42ytchG4EIyoTJQK6AjO+Brq\nzpT/58XJr5kvxYuMImMV/KlAk2COn0d1EKuWey62BdRWMgEcADlHdMbx86oGAhZ+3kzq9ToeeOAB\npNNpxGIxbNu2bRM4VZ+nAtat2ryt4HIrmOYNgSGujE2wWCx48skn8dJLL+Guu+5CKBTCZz7zGTz1\n1FO4//77cfToUZTLZezfvx+dTge7d+/Ga6+9BqPRCJvNBp/Ph2QyKSwCdUsEnB/+8IcRi8XEhXjl\nlVcKaGYraWFhAQcPHsTw8LAk1WuaBp/P9/P8+Q7WYElAcK1WE4mHyWSC1WqVjRpHcDGDje1Iiuw1\nTRNNHkGWwWCQ65cs2MTEhMQw0YGeyWREmK8asggg6eTvdrsolUrYvn07KpWKuFrJhhcKBQDA6Oio\nhJFT00vtoN/vx8rKivys0+nAbDYjn8/L3F3OgaWzdXJyEqlUCna7fVPUVLfbRTqdhs/nQyaTgaZp\nUs9CoZAYFuLxuIQFcx5wq9WCy+WSr1UQ1+v1No1VM5vNqNVqWFtbQygUEkOEzWaT2BmLxYJ0Or2p\nza3rOnbt2oVarYZarYb19XVh1NgZYbubG9t2uy2jJAm+GYSt67q0htnKHR4ehsVigcViEXcvo2Py\n+TwikYi0b3lvY/ucLmcaWgbr/KwByPspltqWBd5kiVQNG7/Px4+MjEj2FPAmC8eWgcpSbW0zbm1L\nquCEO2oKk9Xh4bxQebFSVwFAtBWqDlA9XvW9t+rdqFVR9YEAJARTzaujPoOtYgp41YgT/r/f7+NH\nP/oRarUa3vOe9+DZZ5/FyZMnJdNq27Ztm1hS9b3U866ee36t/r62avoI2HVdh9vthsVikYiHiYkJ\nvPzyyxgdHZUWEINCrVYrfD6f3CDUc97v9zE1NYVQKCSsyMc+9rFNAuvdu3ej1+thZWUF2WwWNptN\n2lGnTp2C1+tFMBiUTLB+vy+ttZMnT/5Mf7ODNVgAYLFYRNRP0wDBHADRpVL/xusil8vJtAdg43oj\ncMrn8xKDAkDYQGBjsL2maSiVShK/EovFhM3hZgqAABnm1gUCAUQiEdloqiPOeB1xlqzaPiUwY63T\ndV3mzfIa50bXYDBsmqpBZz1bmDQgjI6OolQqCYPGmsopEWRFjUYj5ubm4HK5sLS0hHg8jlarJaxY\nPp+XCRKVSgXbtm0TYwLBJEOjaUIhY8kYplKpJFmBnCjB0GnG4JhMJplC0W63kU6nMTk5KeCZ56nV\nasn51zRNMhHb7TYajYa0bZPJJOLxuDCGZAIZPE1WkOCSGj11chPvg3TZDtb5WQOQ9xZL1Saw5cFw\nT14k3PUQPKixJupuU2WUaKygZmMrE6UCJ4IcamNInROMkdkju8bjJBihRZ9LfR8COZXdUw0Ramt5\nqzaQn0ll53hTYKHlLlKNYeFu3uPx4Ic//CHe9773YW1tDd/4xjcks6rX6/2YIUVt127N/duqjVQ/\n67na4vzMbMswnqBer29iKWKxGFZXVyX8s9PpSNr8RRddhN27d8NoNKLT6eDKK6+U1sfw8DBqtRom\nJyfRbDaxsLCAF154QRLl2+02JiYmMDExIeDy+eefx8MPP4zJyUm5CS8sLGBubg7VavUX/Jc9WP8d\nFqNBcrkcxsfH0W63ZbQZ8zCZY8b2J9tyvE45o5rxJ4xgKZfLWF9fh8PhQKVSQbfbledTM0ZNbafT\nwfLysmxsCAI6nQ5WV1cRi8VEu7qysoJAICDTGQBs2lj1+33R+VksFgnurVar0k5k54GmCc5abbfb\nEoFCdrBYLGLv3r0ANqaAdLtdJJNJiQch62az2YTpajQaYqLwer2bnKoANumJGYBssVjEEctzT33f\n0NDQJtBqNG7M22V8CXMD3W63sH40gxCssp3MyRlkWMmo8V6l67oEtgOAy+USEEwWl21rundtNhvy\n+byYX9jmnpiYkOfU63WJCqNmk5v9wTp/awDy3mK9/PLLstvkRTM6OopoNCo7ObYzVJcrAYeqS1Ad\nnqqB4VzatHNdHASVbNtyZ6uCTGYk8f3IRm3VyqnsYK/Xk92YatwA3mxHbz2Wre5hFdyqejuCVRZZ\nLup5jh49ikceeQQ33ngjPvWpT+Guu+7Cb/7mb+LrX/86Go0Gfu3Xfm1TEDJvNur7bAWp/JzAZkC7\n9fOrn5U7f4vFgng8Lq2effv2Ydu2beh2u9ixYwf27t0rxYwtqWQyieXlZXQ6HWlpzc/Po9frYXx8\nHKVSCSdOnECr1cLk5KRkYz333HN4/PHHoWkavF4vZmdnsWPHjk0ZWXa7XUZBPfTQQ7+IP+nB+m+0\nqIPlVAOCofn5ecRiMWnd8nqlzMPr9Uor1eVyweFwIJfLScwGAQPH8hE0sNWothbJOrlcLqld9Xpd\nnkNAyHBkGiomJibEfME6xU0gAHkNTdMkHsRkMqFQKKBarSIUCqHf76NarcpmnYCQc6eNRiMuuugi\nZLNZGeVGYNXpdCSGymAwCAgms0dJTqVSgc/nk2uf480ymYwwjOFwWIwSjGdyuVyw2Wwie+EGkSYT\nGlzI6FFHNzQ0hEKhgEAgAJPJJJt8uoY9Hg9SqRScTqdIQ5LJJMLhsHwuAMKu8f8MaKaWkQ7garUq\nbV+r1SrRVjTjMD+PG28CXBp1+Pc1WOdnDUDeW6zXX39dqGhgA6ycPXtWpjBwB7Zz507EYjFpVdD1\npJoc1F3a1tYscG4TgQpQyLAFg0EZo8P2hdoW1XUdxWIR27dvRy6XEwqdoEt1vvK9CXjYClazjYxG\n46ZAVDJ5astZXWazGb1eD6VSSYDouVjBj33sYygWi5h4Y2zQHXfcgUgkgkcffRRGoxGHDh3Chz70\noU0zElXjxVYmT80BVMHnuYwxBMdMcOcx7tmzB/v375fd6eTkpEQO8DEulwuHDh3CkSNHkM/nxZk3\nPj4Op9Mp+rnHHnsM3/ve9zA8PIx4PC4zLJeWllAqlRCNRnHppZdKa503lSuvvBKdTgdLS0tYWlpC\nIBDAJZdcMgB5g/Uzr2w2C4/HIzdhg8EAv98Pl8uFarWKfr8vRgoAoqEbGRlBtVpFJBIRE8Da2hrC\n4TCMRiPy+TycTqc40tn2JNNtsVhgt9vFOZ7JZBCLxSTwmB0Dzs/tdDqo1WqiBabTt1gsCiPGdmQi\nkYCmaSJZ4WiyYDAo1zPZr2q1KoHmxWJRNMuMUuH0DLJObrcbxWIRVqtVDAbq5nVhYUGiaBKJhDhM\nufm02+2o1WpwOBwolUqIx+M4deoUAoEAzp49K7EqfG22aqvVKlKplETNUN5CYoFmFLbUOUGDbWPO\nwGUNn5mZkSgUk8kkn4s6a25qCcx5f2PAO8G5egxqFh7nGbOtznve6uoq9u7di5GREenG8G9ksM7P\nGoC8t1gUBfOC4NQJJpjruo7FxUXUajW88MILACAXkN1uRygUEqfR2toaJicnEY/H4XQ60e/3JaYA\ngLQDqd0zGo3IZrOYmZkRcfFTTz2FpaUl5HI5uFwuFItFpFIpseMTWK2treGqq67CbbfdBovFIoJq\nl8slRQ3Apv+rOzoCNYIdAkLVUatq+Vhw6LgiM8idKQW4BI4LCwsi/uZYL2ZFcTe/uLiIZDIpO3qG\ne7K9oVrzeXNgW4LtHBY96gd1XZd2h67rMjqJbXMGeBJkzc/PS4t8cXERExMTiMfjAuLr9brkf734\n4ouYm5uT14xEIti7dy/MZjNcLpewKbt27ZK4AWZKcZaozWZDNpvFyMgI3vOe96BSqWBhYWGgaRms\nn2u53W4xGDUaDWHJuPniNBdOjGCgbiAQEE1ds9mUeJROp4N4PC6tRv6tUoS/lTkDNqZNBINB5HI5\nCSgGNuokWUGCQkpLqCGkjCKXy22qQ5y6oeu6tF+ZN8dwdT6O2jUycux6WK1WmM1mYeIow6DUgqPX\nrFaraGidTqcEJY+NjaHZbAqb73a7AWx0D/L5vLRlt2/fjqGhIWzfvh1GoxHFYlEcuzQo0J2rjq7U\ndR3hcFgYynQ6LYDXaDRKnWs2m6IVbLVasNlsEuhOTRxZUNY3vh9/X3QwE/g3Gg0BrKyhNHxwsoXR\naES1WpX2L5ldnkd2dwiuB+v8rMGZf4tF7QZ3s7zICP4MBgMCgQAajQaq1Srcbje8Xq9MSEgmk0il\nUrKjqlQqOHLkyKYxO5yLunPnTlx11VVotVqoVCp4/PHHsWfPHvj9fqTTaRw+fBgvvPCCDLxeWlqS\nnCMKhn0+n2QxHT16FEePHoWmafiHf/gHABsFlyJi7tAMBoOMtDl58iQqlQoOHz6MUqmESCSCz3/+\n8+IYNZlMcvGT+ifQ4u6NMyoDgQBCoZAUmEqlIlqURCIBn8+HRCIh7VgCME3TZFf/2c9+Fn/xF3+B\nYDAoDAKHbQOQdgBvQizm3FlSA0QtDNso1WpVQC8ApFIp/OAHP0Cn05G2SL1exyWXXIJgMIilpSW8\n9NJLOHLkCGw2G2KxGCKRCJrNJsrlMkZGRqQVS81lo9HA6OioRCckEglYLBZ0u11ceumlCIVCeO65\n5wAAfr9ffkaWgq38Xbt2iah8sAbrZ1kMOladldxUcCwYwQzDa4PBICwWi7TpqCnmTXx9fR35fB5+\nvx8Gg0E2J2TyKNZnbVKBF4fb88bPsX1DQ0PCDpJho1O1Xq9vatFaLJZNGmMeIzeBBE40P1DCousb\nM10ZMVKr1VAqlSSTjqwcW85qHijBEq9LtkU7nY6kAySTSfT7G+PXLBaLbCKZIciNMdktdkf4+tQ8\n2u122Wiur6+jUCggFApJjAvHK6omOQJGgi6ysQTJPK80TZDdpA6ZGnGyp2zXU9fYbrdRLBbRbrel\n/jNEmqMgKU1S9eDJZBJmsxmBQOBX/8c/WAAAbWs8xWC9uTRN05977jkUi0WUSiUAG5lAhUIBzz33\nHJaXl0Wzwl0ec5E4n5GuKo6jocuVgaGMROEujA4m7nx4w+e4oWaziR07dsBoNOLFF1/E6uoqGo0G\nvvKVr+CrX/0qTp8+LTs4Fiu6cCcnJ3HZZZfh2muvlcL95JNPYnJyEvl8Ho8++qgcNwvZ8PAwLrnk\nEtx5552b3LHdbhdOp1NceABE4Ly4uIidO3ei0WhgfHwcHo8HtVoNDz/8MF566SV0Oh1873vfE4aB\nbV8WZDKEBITvfe97cdFFF0lb9R3veAempqZEtMyZj2QLySBSTExQ+/TTT+OJJ55AMBhEOp1GpVLB\njh07MDk5ibW1NRw+fBinTp2S9ik/T6lUgtVqlVaV3W6HxWLB0NCQAPxms4mVlRXYbDb4/X7EYjFh\najnvlmOchoeHsWPHDtkdq6Jwh8OB+fl5PP3003Lj+OhHPwq73Y5PfOIT0HV9oGIerJ9qaZqmv/e9\n7xU9FbVq3ITSPFYoFGAymcSwRTBExoqjzMj2U3PFa5TB3pRLsKbRnGG1WmEwGFCpVMTIYTAYpMPR\n6/VEzK9pmhwbZ7vyWvR6vWL2cLvdmxzD5XIZmqYhFAqJFpmtULJPjILixp1sFrPrbDabsJLswHDu\naiqVkp8TuJH5py67XC5LwDrBLBlGAjhgo35SE8l2KABx1xJwWSwWFAoF+TzUMs7MzGBpaUnuO5Tf\nkKErFosiDSGwo2SHWrlwOCw1km3lYrGI+fl5Ab1kd+lG5v2A8TcEufybsdvtWF1dhclkkg3D2tqa\njLV78sknB/XrPKwBk/cW69Of/jQqlQq8Xi+uvPJKXHHFFTAajdi7d6/ECExMTGB9fR2NRgNPP/00\njhw5gtXVVbn4KFYlFU7XFh1SbFcwH65QKMDr9Ur7ZHh4WIaMV6tVLC8vS+huJBIBADz00EOYnp7G\ntddei9deew2vvPKK7NYNBgMymQwSiQROnTqF73znO3A4HNi7dy+OHTuG7373u1IAWbzcbrckrd9w\nww2oVqvI5XKYmZmRdkI6nYbVakW9XseJEydgtVoxOTmJEydO4MEHHxQjg8fjkQJ/4MABaVuSXVND\nNunI43I6nTh8+LAA3GAwiEOHDiEYDCKVSoluxGQy4b3vfS+sVqtErzidTpRKJXg8Hnzta19DIpHA\nzp07ZaD3/Pw8nn/+eXg8HrjdbgQCAfh8PqTTabhcLlx66aUwmUwSOUC2Q9M0aXFls1lMTk4iEolg\n+/btePHFFxEKhRCNRrG6uorh4WHs3r1bWi4ej0daYJlMBmfPnsX8/DwuvfRSXHXVVahWq3j00Ucx\nPz+P66+/HgsLC9JuHqzB+lkXW5zU84bDYRgMBgnW5caIrIvT6dw0Vqvb7WJ0dBTARlQKNb6jo6Oi\nUSXTxmBithLJRmUyGUy8kZ/HubGUbYyMjGBxcVGYLTVr0+12C9Cg3ILfZ1QTW64EHZz7TLevy+WS\nDgoBIRksauto2qA71W63y0aWx8wZwOos8KWlJezYsQNzc3Pw+XwSLxMKheTcqCCSjFmlUpGpEjSU\n6LqO8fFxJBIJmaChjgRTgR+n8lQqFZF8kP0j+9/v94VB5e+H7BxdwL1eT84BWcZwOLzJ9Eewz78Z\ngrdCoSBSlaGhIXlttth5nAT6g3bt+VuDM/8W68Mf/rAIXQFgZWUFDodDmJdEIoEDBw6gUqkgkUhI\n6ObNN9+MSy+9FJFIBKlUCktLS2IaCIfDaDabeOmll3Do0CG89NJLwp4ZjUbRd7CtQlt/oVDYtHNj\ncCYBUrlcRjqdRrVahc/nQzAYRCwWQ7FYlIHXpOI1TcNjjz22adwPixcBnMPhwL59+xCNRlGr1fD9\n738f3//+93HDDTfg6quvxtLSEp5//nmcPHkSvV4P4XAYzz77rLQ6qP1hdhbZsFqtBgAIBAJSALxe\nL4rFooRv0vZfqVRkZiJ3pvxvaGhItDwrKyu47777YDAY8M53vhNmsxnvete74HK5UC6XceONN6JQ\nKODuu+/G8ePH4XK5MD4+jksvvVRYTTrdpqamUCqVsLS0hGg0iu3bt8PtduPs2bNYWFjA9u3bsWPH\nDtFZ8oZlMplw1VVXoVKpYHh4GJFIBGfPnsWXv/xlaQddd911mJ2dxfHjx/GDH/wAiUQCt9xyiwSr\nUstpsVgQCoVkDiWZ5MEarJ91MXqDm0qv1wur1YpMJoNoNIpCoSCBt3R1tlotudEXCgX4fD4MDQ1h\nYmJCNoHUxrLbQKE9N0btdluYM7ZZCXyWl5fhcDjgcDjk2AhoVlfz+Yz0AAAgAElEQVRXMTY2BgDy\n+q1WCwAk0zKdTouxgsHhNptNsknZwWAHhACRqQRkITnVAYBsiAEgk8mIcY6tSQJOtkvHxsawtrYm\nIGlmZgbZbFaMEmwbm0wmnD17VmQ5NFkxP8/hcKDT6Qgo4rkENgAtJTYqW0e3r8fjQaFQkDD1Xq8n\nwdBqnAuw0bpnzSThwHiUZDIp7Oz6+rqwcWRzOamHcTxsgYdCIbTbbZRKJWiahnw+Ly7lSqWCcDgs\nLO1gnZ81AHlvsS6++GIsLS2hXC6j1+vhkksuwdmzZ3Ho0CHs2bMHkUgEO3fuhNlsFrEqzQknT57E\n008/jWq1imw2izNnzsDhcOCKK67AzMwMJiYm4PP58Fu/9VvIZrO49957JfTz9OnTGB0dlcwpBo8m\nEgkpAKruhAWWehXa119//XXRS/R6PYyNjYnuLBwOY2hoCHNzc7IrpA3e7/ej0Whgbm4Of/7nf77p\nIi2VSjhw4IAUAxbRubk5/OhHP4LdbsfMzAyi0ai0iahLCwQC0oKoVCpixqAIm0Ov6X5jLhRT4wEg\nGo0ikUhINpPRuDH7luN6VlZW0G63sbKygldffRUf//jHEQ6HYbPZcMcdd+Dpp59GPp/fpFFhMKnH\n48GuXbuQz+exsLAAt9sthdbr9WJiYkLa6QSbBMYPP/wwXn/9dQDAZz/7WQHpjL05ceIELr/8crkp\nUWvp8XjEOdfv9xEMBnHq1CksLy/LjVTVIA3WYP20K5PJSNuMXQWCA0Z0cNSVw+FArVZDpVKR2BIa\nq9QQYIPBIBtPGiKi0ajolGm40DRNDFKMdwI2gBs3utys8Zrn61HbR40tN8hs9bJeqNcfN8HABgO1\nuroqdZMBw3a7HY1GQ2ayUjuYTCYBQEYJhkIhpNNpuN1ukbvQ1MA2MOU1mqaJIY+tyUwmswksRyIR\nabnabDYkEgkEAgFh35hvR/fryMgIzpw5IwkKbOuStSNYt1gs0klaX19Ht9tFLBbblF1H4Mr2d61W\nE/04ADFOsMVN5zWZWLPZDJPJhLGxMRSLRRnDxhganu9er4d4PC4tWjJ+1AQO1vlZA5D3Fmv37t3Y\nuXMnhoaG8IMf/EB2JpFIBBaLBadPn8a+fftgtVpxzz33YG5uDrquY//+/fjABz4gFH61WsU3vvEN\n6LqO1157DQ899BC+/OUvyzDrP/mTP5GxMTQozM/P45ZbbkE4HMY73vEOVCoVZLNZPProo7juuusQ\nCARgMBgkRPeFF15ANBqF1+tFKBTaNBeRhomhoSExIDCRfOfOnSgUChgZGcHx48clMZ1OT7/fD13X\ncfHFF6NYLEpUAcGbx+OR8WDXXnutuE4ZNTM7OwubzYYnn3xSgB2BEoGpmgel5jOxfTI3N4evfvWr\nOHPmDL773e/i1VdfRSQSwfj4uIRDj4+PY21tDdlsVpgBu92O7373uwiHwzKO55JLLsHJkyelBc5E\ndybJUy80OzuLkZERiXgpl8twu934+Mc/LnqUD3/4wwiFQtB1HSdPnsTk5KQIxvlZrVYr7Ha7zLDc\n+vvIZDJS2NnOp/6PIHEwFmiwfp5F3RqlDrxO2b6lxiyZTEpdUOOWqHdjLEo0GpWYEk3TZAg9jWUU\n79Mlq+rUCEDMZjOWl5fh9/s3Rat0u134fD6Uy2XpUJApI+i02WzSeiXgojOem0QyfJyusXUqRqVS\nEWMHEwOAjVBgTuqgjIRtW4vFIuCYGzJgQ0eXTqdFxkNjhs/nQ7VaFV0f3avFYhFms1n+TSd+IBCQ\nVnapVNoUJJxIJBCPx2UjSvmO1+tFpVIRzR4BtgrYfT4fTp48iXg8jnK5DGBDE0itIKUjZFlpnnG5\nXGIcIfhjgD0BN2cR02THiRo0j9jtdiwuLmJ0dHRTYP5g/WrXAOS9xWLxokuMjtJgMChBtQzofPvb\n345du3ahUqnA7/fD5/OhVCrh4MGDOHDgAFZXV+UG73Q6MT8/j1arhdOnT6NeryMSiYhQeWhoCFar\nFY8++ihuueUWfOUrX0Gr1cKxY8ewvLyMfr+Pm266CcvLyygWi7jqqqtw1VVX4ZlnnsHv/d7vwWaz\n4dlnn0Umk4HNZsP09DTcbjcSiQSOHTuGhYUFFAoFbN++XdopNpsNMzMzsFgseP311yXugN8vlUoS\nc8B24pkzZ5BOpzE2NoZarYYjR46g3W4jHo/DarUimUzi3//936UVRKaTRYm7fQBSZK699lqUy2Uc\nOXJEWD673Y73v//9MJlMiMViuOmmm+B0OlEoFHDkyBGUy2XY7XZcc801mJqaknOfz+dx/PhxHD9+\nHOPj4xJ/Mz09La0Gk8kkTGu9XofZbIbT6UQqlcI3v/lNJBIJvPvd78Yf/MEfoN1uY3x8HKlUSoap\ns/0TCASkyGuaJnoUk8kkjBzBrdls3rTbDQaDACBuPUY2MIpiEKEyWD/P4s223W4jk8kIK5NMJqVN\nqWkapqam0Gw25Tk0HfV6PUQiEcly63a7oq8lC8YWIJ3mBH9khWjkACCtPafTKZmTfI1GowGDwSDG\nKKvVKnpmdXINNz10fTKMt9VqSaQJTRVk/9juVA1Obrd707xZatnY+dA0TcKEyfqxBVsulwXEuVwu\nJJNJGX9IEMmWKrssuq4jGo2iWCxKzAnjZGgOIYCmI5o6XgIxSl9Yr3nOwuGwTNUggOUmemxsTAwU\nahwKpUD1eh3RaFQYSmqA6/W63PNU12w6nZY2t9FoRCQSgclkQq1Wk+5SKpVCp9NBLBaTYxqs87MG\nZ/4tFnOEjh8/LjsnBmXWajUcPHgQH/zgB1EqleD3+3Hvvffi8ssvF6FxJBLBO9/5Ttx9993iWLro\nootgNBpx//3348EHH8RHPvIRAQDUXFgsFkksP3HiBEKhEPbs2YNEIoH5+Xk88MAD+OhHPwqPx4No\nNAq3241Op4OHH34YL774IjqdDg4fPoxUKgVd1xGPx3H99dfj1ltvxSc+8QkxDnAqQ71ex8svv4yv\nfe1reO6555BOp8XIQXfb0tIS8vk8RkdHUavVcPz4cSSTSfj9fpw6dUp21evr61hcXITJZJJoEZoW\njEYjUqmU6EKYGs+Wa6FQwKlTp8S6bzKZkMvlJFfq+uuvx4EDB3Ds2DGUy2XZJXc6HSQSCTzwwAPS\nYqpWq9Ly2b9/P37jN34D3W4Xzz33HMxmM6LRKMbHx9HtdnH48GEcOXIEZrMZl112GUKhkMSz0E3G\nlsz27dulDcbRdf1+H7FYDJlMRnb5LNhsbQAQPQs/r65vzAllKCmnXzgcDrhcLoyOjorzcbAG62dd\nfr8fS0tL0tJj8DE1XHSzu1wuCVVfXFyEpmmIx+PCihFs0Rzl9XplvBdBpMlkEtaNgIWbONYFRpGw\nDcj8S7JBNG4kk0lMTU1Jy5DX38rKisxkrVarWFtbQyQS2eRsByAgk7o0l8sleXoEHdSfUSfHsGOX\nyyX/5rVNUMSsTXZJHA6HsIvM91xdXcX4+DhMJpOAXoPBIPWA4LBcLiMejyOfz2NpaQmxWEzOIzV1\nNL8BkG5Lp9MRkMzfYbPZhN/vR71eBwD5bDyfHDlXLBZFe8hIKiYksGvy2muvIRwOi9uZ+jtOLjGZ\nTFhZWdkUysxc10ajgUajgZmZGaysrKBUKmF6elo0kYP1q1+DO8dPsainuuyyy9Dv9wXQUeNSr9fR\n7/dx//33S6xJPB4XHcrevXuxZ88ezM/Pi2C5Vqth586d6PV62LNnD44fP45WqwW32y2sDQFMuVzG\n0aNHJd9tdnZWhnqnUilcfvnlaDQaqFQqCAQCuPrqqxGLxfDrv/7rwo5VKhXk83l8+9vfljmojPo4\ne/YsksmkGD7e9773YXx8HPv374fL5cKpU6cwNzcHm82Gf/7nf8bi4qK43TiuZ3h4WPQzvDHQHccw\n0eHhYcnIYuuA7QHu0l0uF8xmM3K5nNwAGHnQ7/cxOTmJm266CTfffDMef/xxPPLII/jQhz4Es9mM\ne+65B3fccQd0Xcc999yD//E//gcymQwWFhaQTCbxp3/6p3jb296GK6+8UuJPCJ7MZjM8Hg/8fr8U\nQQIu7qSLxaKIyn0+HwwGw6aogF6vB6/Xi2QyieHhYblxhsNhnD17Fq1WC7t27RId0cjIiABZjodi\nnEKtVpM2DkXZgzVYP+vK5/MyfopsMvWxZGiYeUl2nRMoKPinoJ/6MWbiMZ+NDBqzIekkJVNFzRyw\nAVTcbrdIQejKdDqdEj3idDpFQ8uID0oiYrGYvC7dpslkEjMzMyiXyxL9xNrB64l1hHWGAIZRUPV6\nHYVCAdu2bZMJEdQHM3mAoEbN12Q7lS3e9fV1TExMoFgsyuaWEVLURRKgUR/ILFEyjszLVD8jW8oE\n0Lqub/o/0wfIeHL6Bevb1mlAw8PDYhCbmZmB3+8XMM1zyrFz1GmrsV67du0SbWOtVhMWc3JyUt7X\n7XZvev5gnZ81AHlvsV588UXRkVC/QkEr6W+GTz711FOSQM5d4NraGl5++WXMzc2h2+1KNtHk5KSY\nHr71rW9JIDGFsSrYOXLkiDi4uPMzm8145pln8LGPfQy1Wg3xeBz9fh+BQAC6rovxodlsYm5uDkaj\nETfeeCOq1SoymYy43rhTdrvd2Llzp4QsHzp0CM8//zwWFhYEsN1+++34x3/8R2iahk9+8pMCcHlu\nqM/r9XpIpVKYnp5GPp+Xlke/30cikRAXHVvXvBHQWUrRL80jw8PDIvz+y7/8S9xyyy3YtWsXXn75\nZQwNDeGGG24Qm/9HPvIRAMDf/M3f4M4770S328WxY8fg8/nw+OOPw2QySYo8U+EJtFqtFjwejxzP\nyMgIrFYrpqamBHxTp9PpdJDNZkVMTR1SKBRCLpcTUMZpIwxW5Q2K+iCr1bqJUaG72GQybZpt6fV6\nz+NVMFj/py5mbJKloalibGwM9Xod3W5XhtFzY0PnfiqVkhxIp9MpjDZBUbPZ3ORMXV9fFyaPmzKj\n0SimJUZF0cXJ+sM4Fxqg+v2+6IAJuJgRR91cNBoVfRr1esBGzBEjmtTxa3wOrz8+jrmno6OjMu+2\nUCjA5XKJTpihz2TRGMZuNpvRbrcxNTUlyQZ+v1/mhTMShtc3W6wEhRaLRXTIzP3jprFarUqiA1lH\nTo9wOp3iWCVA1nVdWrec8kE5CuO2DAaDtIltNpukHHAiicFgwOrqqrTCR0ZGRDbi9/uRSqXgcrkE\n1LfbbYmGIujvdrtyrilzovlusM7PGoC8t1jUILRaLczPz8Pr9coF0mw2MTExga9//ev4whe+IKCA\nOzTGCXi9Xhk5NjY2htXVVRln9clPflJs6sw04jgczkCkc5f6EqvVik6ng//8z//Etm3b8O53v1ty\nqUKhkASIqscyOzsLr9eL0dFRTE5O4uGHH8a+ffuE6TOZTHjiiSdwww03IJvNYv/+/fid3/kdAUGF\nQkF22zabDQ899BBGRkZklNvjjz+ORx99VMTPtNFTY+h2uxGJRJBOpyVri+eXBYI7UgIum80mQl6O\nybFarTh06BDS6TQmJiZwxRVXwOfzYXl5WaaOhEIhDA8PY2pqSnbuLMycasGZlgBE/zIyMiLaQraS\nut2uiKS5CzabzfD5fMJOsgBbLBYsLS0hGAyKvomtjKGhIUSjUUSjURnUHggEMDY2Jswg5+O63W7c\nfPPNcmOh0WWwButnXdVqFSMjI7DZbBLiy2kyDB/nnGnKCvi3b7VahXFnK9dqtQqbl81mJfuNJg3q\n2IxGoxg+LBaLbCzHxsaQSCSkrUqX6fLyMrxerwAnu92OXC4nM1k55UdlEnu9nmTYsRXd6XQQCoVE\nDkLZRTAYxPr6OnK5HAKBgLRvrVartDXD4TDMZjOGhoawsrIiADmTyUjmHNu4ZCeZucfawfmzmqYJ\nQGI6AOU+Pp9PNnkctVapVABAxojRuVooFBCLxcSVywB9FXyyVWy1WmGz2cQtze6CGv7MGktDS6PR\ngMVikXF2jNSimY0xMZT2sPPC1AcudRxnOBxGtVqVGk/TxmCdn3VBWF40TRvTNO2Hmqa9pmnacU3T\n/uiN73s1Tfu+pmlzmqYd0DTNrTznzzRNO61p2klN037tJ732wYMHkc/nRX8BQOaShsNhlMtlPPjg\ng0Kbc2TM66+/jqWlJaytreHuu+8WsEMRPQN8bTabBI9yBiLt7wwzttlsuOiiiwT8UOC6vr6Oz3zm\nMxLZ0u/3sWfPHqyuruL06dNYWVnB6dOn0Ww28dhjj+Fb3/qW7EQnJycRDAbhdrsRj8cRDocFwF55\n5ZW45pprxIm7trYm0SEWiwVut1uK3r59+3DLLbfgrrvuEsZsampK5l7OzMwgHo/jkksuQSKRkNE4\nbCuwWHLnT1E1Iwvq9broFQl877nnHnmPSCSCz33uc1hcXMStt94q7anf//3fh8FgwL/927/hqaee\nQjqdFifd2tqaOIMplGbL/dVXX5XiRDYhm81C13WEQiEJtaawe2hoCB6PByMjIwgEAnA6nbLbZdTE\n7t278cEPfhA333wzZmdnsb6+jpWVFQQCAdx666247rrrsHfvXlitVknQ5++EImYyJoN14a1fZv2a\nmJiA2WxGKpWSlhvnxbKFlsvlEI1GJUw4kUgglUpJbA/rltfrRaFQEKkGWfd+vy8mDbL2rFFsN1L4\nT4aJbB6n00QiEWkPs21L2QpdomTC6eynNIS11+v1wufziRGDuZN03BqNRqlnnNRB9pGxH9xk00XK\n+sMoGLrv2Qng8bCjEY/HhQCgUQN4czNrNpulDU13K9lVan5rtZpo4BwOh8hj3G43jEaj3Cfo8iWI\nZ3wMPxONfqVSCc1mE8lkUn5fZBsZt8W2OH8nlNxwnCd/bwAE6JI15O8rnU6jWCzKxpyOZ04pGazz\nsy4UJm8dwP+j6/rLmqbZARzRNO37AG4H8H1d1/9a07Q/BfA/AfxPTdN2AbgVwC4AowAe1zRtVtf1\nH9tu/O7v/i7OnDmDv/u7v8O1116LK664ApFIBNlsFk6nE3/913+NWq0Gv98vbFq73cbzzz+PlZUV\nXH311Thw4IDsatPptIQY8wLizo+5VRyFBkBaBolEAtdddx1OnjyJYrEo1Pztt98uRe7+++/HkSNH\n8Oyzz8JqteLee+/F5z73OSQSCZhMJvzRH/0RvvCFL+COO+6QNPt8Po/7778fx44dQ6vVwje/+U3R\nqXAXPTk5KTlIRqMR+/btk/aDyWTCmTNnZGLE5z//eYlUeeKJJ/ClL30JU1NTeOGFF+BwOKQ4s53C\nyAa69zgJhJoZRsDU63VMTk5i586d+PSnP41HHnkEkUgEH/jAB4R1uO+++zA9PY1yuYzrr78emUwG\nP/rRj3DTTTchEAhgYWFB9C/ckZJBo7uM8Q0MeOWNrFqtCtjiFI3t27fLTSSZTMJisWB2dlZc0ryp\nUpeybds2rK2todVqwe/3iz6KrTAyAu12W5y7uq7j2LFjg5ypC3v90uoX2RXObFVDt2n+YRYcQU4o\nFBJ5AeNJjEYjzGaztF/Zzmw2m2g0GhJnQgaeU2wohTCbzchms+KmZZeCz6H+1W63y8YrEolIlIoK\nTtlGpKCf7tVqtSqtyWQyCa/Xi1KpJLo8tp3JrDkcDrRaLSSTSYyPj0stIvulXqdsk5rNZgFhwIYT\nmawbtXscv8ZsOwInOlZ5PjVNg9PpxPLyMgKBgIBaSkLsdruAcwYlO51OrK6uYs+ePQK2yIZyI0tH\n7s6dOyXUnhml+XweLpcLhUIBkUgEgUAA1WpV5CWs+2azWTpYHFvHbgUAqdlswdONrWmaaBYZPM2k\ng8E6P+uCAHm6rqcBpN/4uq5p2uvYKH7vA3DNGw+7D8CT2CiUNwN4QNf1dQCLmqadAfA2AM9vfW3q\nRmKxGCYnJzE5OYlKpYK9e/dibW0NR48ehdvthsFgEADBQnnbbbfh29/+9qZ0+OnpabkQqGPhbtbl\nckk+HHe9tKgzxNRsNotIOpPJ4L777sM111yDubk5JBIJaQM3m0186lOfwqFDhzAyMoJQKIQ777wT\nf/ZnfwYAuP3224X67/V6cDgcsgOPRCK488478cgjj4jBhPqSmZkZxGIx5PP5TXl4drsdiUQC/X4f\nJ06cEP3KF7/4RQAbReHIkSMyV5cFmVEi1Kuwdczn870tFgvm5+eRSCTwnve8RwrI008/jX379smI\nNBb5v//7v8fdd98tFn5mN509exZTU1PYtm2btJbYDp+cnJQ5jxxbZDabceONN0rWE1sw8XgcExMT\naLfbouV729veJowGmU6aUbjjpjuN7VfqVigC5w2Rc457vR4uv/zyQYTKBbx+mfWLJqt+vy9giS74\nVqsl15eqiaMkhLNKGdvhcrmEfaKEggCy3W7j7Nmzkg9HQEnWj+5OADJCi7KNkZERifOgGYBOzkQi\ngampKZnWwbYggYPBYIDf74fFYkGn00EqlYLX65UcOQYrE5Tx2HRdl9YoR71R/0tNNTVsPFe8bqmf\npY6RberV1VX4/X7kcjkJWedn9/l8cm/w+XzCBFITOTIyIuHQfG2/3w+PxyNsJeNYeI+wWq2IRCJw\nOp0SOMycUQCiYaTkhjOM2ZU6c+YMLr74YjnWQCAgdYlsoMvlQrFYlPFwdEYTDNNRy3xP/s2Q8aRk\niV2wwfrVrwsC5KlL07QJAJcAeAFASNf1zBs/ygAIvfF1FJsLYgIbRfXHFl2YDocD+XwelUoFMzMz\nokGh1oCmAqvVimg0ilwuh7/9278V2z7z9AqFgrhjuftl+jpbrh6PR2IN2AJpt9uIxWIYHx9HJpOB\nxWLB4uIi7HY7/vAP/xALCwvYtWsX9u/fj2eeeQa6ruOVV14R1qpWqyEYDOI73/kODh48CL/fj0ql\nglwuB7PZjFKphNnZWdFv1Ot1XHzxxdixY4cAs0wmg1OnTuHll1/G4uKiMHksfrt27ZLxRwxWBTby\n7z7wgQ/I5A8WKv6chZc6EbIHb/w+pa1Lk8jKyopoRMj0WSwWPPvss7j99v+fvTcPkvMuz0Wfr6f3\nfV9nX6XRZkvIkmwZG4xtYgOHQHGykWtukkpSJ8kl4ZJQnEBxTSAhlcKVujG5FeomVSEsiYHYOLgA\nG0Nsy/ImW9YujWbvnt73vaeX7/4xel73EDiOEywR3f5VuSSPZunp7u/93vd9tv8dWq0Wq6ur+P73\nv4/5+Xl8+tOfxt///d9jaGgIR48elcJMoUO5XBYfK8IqWq0WgUBAQsbJS3Q6nTh69KgUTcIqhOAB\nSBOr1WpFLch4JYPBINwemr1Smccb5ksvvYSnn34azWYTvV4Pd911F6ampn46F8jg/Eyfn3b9YsPA\nxoY+Znyf90OQbP74b6x5brcbjUYDpVJJUhLW19e31UH6V5JLFwwGt/G4uOWhWa/JZBLLFCYxGAwG\nxONx8Zr0+/0CEXKo40aJpsY2mw0rKytiDD86OiqUmF6vJ4IsCuZ6vR7W1takcSRywMaIPDumXdCM\nvNFoyJ+MkOTvxG1oPp8XvrTf70c0GkUul8PY2JgItOiHmcvlEAwGkU6nZavXz4mjfx9VyawtbDw5\nTDKpiM0pm9pmsykNMe1y2u02TCYTcrmcQMOtVgtarRaFQkE+RjiYG0VVVbG+vi6vcX+yCAWGvA+w\naV9fX8fo6KggNwN17bU711WTdwXq+CaAD6uqWul/Y6mqqiqK8r8y6/mx//aBD3xAuFhzc3MIBAJo\nNBrIZDJ4+OGHRYXEKYkFgPmGnMRoUKnT6cQnjnAGtzRUsUYiEaysrEhm4/z8PJaXl5FMJgUapP1H\nIpEAAHGmX1tbE1sDTt/kqdCF3mg0Yt++fcLPMJvNIhjQ6/Xwer2iEiNBmtPzzp07ZTplcWBhY9O6\nurqKJ598EgsLC4hEIpifn4fD4cAv/uIvYnJyEi+99BLq9Tp8Ph/cbjd6vR6i0SgymQyKxeI2l3gW\nEMYSDQ8Pi+dct9tFOByGxWJBIpHA+vo67rnnHly4cAGhUAgf+9jHsGvXLhgMBolhWllZwejoqGxb\n+bvMzc2JvQm3qFS4ms1mUemxKNIYtB/6JbwFvMbB4Y2tUCjgySefhN1ux44dO6CqKv72b/8WiURC\nbhif+9znxEg5m80KfHzixAmsra39J6+OwflZP29G/VpcXJS/a7VaWK3WbRmoHJw2NjYQDoeFm0q+\nG9W1bJDYJNKIGIBQDcjl4iBDAj85t/3bHULEhUIBw8PD4k9HKgvzUing4jDscrmksSLfjyp/Nh5D\nQ0MYGRkR4RQFHRy6pqen5XswAYRRg4Qj+zeQRqNRFPL8GRsbG5iZmZHrn88VLbZsNptAyQC2RSRW\nq1URslB5StqH2WyG1+uVj7FBoxilUChAr9eLKMVsNsPv98vf6QrQbDbluWI+OLCl9ie8S7hcVVVR\n9fIexde/1WohEAhIbedGljxMo9EoZu7cotIdYX19XSIsB0jEtTvXTZOnKIoOWwXyH1RVfeTKh1OK\nogRVVU0qihICkL7y8Q0AI31fPnzlY//mPPjgg/je976Hw4cPY2lpCV/72teEb8Y3N9f55EPY7XZk\ns1m4XC7hnnHlTU5MPB4XSMTj8YiogaIAFqZ6vY5nn30WTqcTy8vL8vOYYWiz2aT4FItFRKNRDA8P\ni9J0eHgYer0eN998szQ75EmQS0FJPaEcGjHHYjG5EXAy5haM4d8AZAtgNBrR6XRw9OhR3HvvvYhG\noxgfH0cmk8Hf/M3fYG5uDn/913+Nj370o2g0GvjUpz6FL37xizh06BBOnz4NYEvo8sILL+DIkSO4\n+eabRZk3NzeH48eP4/vf/z7uuOMOOJ1OKXAWiwU/+MEPcObMGQSDQdx1113SSJZKJTFyvnz5MvL5\nPHq9HiYnJ4VLVCqV8MUvfhHveMc7cODAAaysrIiqjOo1FipCFOSd5PN5gSfOnTuHY8eOIR6P4447\n7sBb3vIWibtjuojD4RDVLzl3+XxeUgIY6RYOh1EqlVAul6ghmGIAACAASURBVHHjjTdi9+7dePzx\nx3/6F87g/EycN6t+hcNhsfjhIMr3G6/nXC4nXDj6uJFGwuua9lGkN5CXR2skbrwoq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Q61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8vL0r/baDTkDwlN0zg6OsJms1k7eV8hLJJnwYIFCy8pTFej2+0ml8uxubkpLROGYXB5eSl7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\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2mxSLRbxeL/V6nWq1yvr6uliBWCwW2u22GB1PJhMajQZzc3MsLCzg9/spFotSKdM2aVut\nFoqi0Gw2xcB4bm4Oo9FIpVLh9PSUTCZDKpUilUpx//59UqkUBoOBbDaL1WrFZDKJMNQqqTdu3CCd\nThONRul0OjgcDuCJwPN4PLJ9rAleLa6sXq/LsRqNRkqlEtFolFKphNls5sqVKxwcHOD3+7FareTz\neSwWC/1+n1u3buHz+VhaWhKjYs178PT0lGKxyLVr1xgOhzidTqnslctlksmkbGZrFbqtrS2m0ymx\nWAyz2cz169dlqaNSqeB2u3n48CHdbpcXXngBv9+PzWZ7aq+BH3f0Sp6Ojo7OM8r6+jqPHj1icXGR\n9fV1RqMR586d4/r161y9elUG7rXFiul0yltvvcXu7q4YBLfbbRm8HwwGlMtlqXJpW7qdTge73U48\nHicajRKNRiUxwePxSA6tx+ORDVeTycRoNEJVVdrtNhsbG7jdbmw2G/fu3SMUCkllbDgcYjabeeed\nd7h+/bqYOTcaDc6dO8fx8TGj0Yi1tTWJAtMsS1RVZX5+XraFfT4fFosFq9Uq82eKomAwGPjGN75B\nt9sVPz4twmswGODxeEQs9vt9wuEw0WiUn/iJn8BoNJLP5zEajdy9e1eEUqlUYjabiRdhpVIhk8kw\nm82kytnv93n77bdl2zaZTOJ0OvF6vTQaDRwOB0ajkf39fTweD71ej0QiIRm4FouFUqnE+vq6iClt\ncUTbfO73+xJNZrFYpBqrLXqcnJwwm82IxWLcuXNHUiw0w+ZWq4XdbqdSqWCz2dja2uLhw4eSG6xt\n8BaLRanY1mo1Hj16JC11naeDXsnT0dHReUbZ3d3F7XZTr9elwtRqtTg6OhIhpEVkaR5rmiA6PT1F\nURSZP9NETigUkjmyhYUFWYrQREAikaBUKkkaw2w2k43dw8NDUqmUzK0tLy9TqVSYm5ujWq1KJevy\n5cuEQiEsFgvpdJqLFy+iqiovvPACw+EQu90uObn37t3jk5/8JGdnZ1J9Gw6H0lYFGI/HRKNRaRtq\n7dZ+v08ikRBx8slPfhKHw0EqlaJSqQAwGo3E2FlbPJibmxNh+O677xIKhUgkEvR6PT760Y9ydHTE\nyy+/zPHxMaurq+L553Q6pYqpmRNfvHhR5t9msxlOp5PRaISiKCiKgt/vl1gwzYpGux6amJxMJtRq\nNQARiqqqiuGyVs00Go0YjUZsNhuZTAa73c6nPvUpNjY2ZEZQO6culwuHwyGxd9o1VBSFn//5n6dS\nqdDv9ykUCiSTSQwGAx//+MdlgWZhYQGXyyU2NDpPB72Sp6Ojo/OM4vV6Zehda9s2m01u3ryJw+Fg\nOp2ysrIiG7Zms1n83rRljG63i81mYzQaMRgMSCQS4q+nVcri8TgWi0VauFq2q8ViIZfLoaoq9Xr9\n21IdIpGICBVtC9ZutzOZTFhfXxc7l4WFBTqdjlSbDg4OpDqkVeHG4zGqqnJyckIwGCQcDrO4uMh4\nPCYYDMrto9EIm80mW6+5XI733ntP2suXLl2iVCoxnU4ZjUbs7++L8bDX66XT6cgWr/Y1r7zyCh6P\nhwcPHtDv9+l2uywsLNBqtfB6vbjdbpl1s9vtbG1tUSwWcTqdnJ6eUqlUSCaTsjAymUzI5/NiWm00\nGoEnfnRHR0fUajWJk6tWq+JFpy2NtNtt0uk0brebbrdLt9slGAzidrsJhUL0ej2cTif5fF4qiuPx\nGJPJxN27dxkMBiwtLYkAHw6HxONxHj9+LBXAWq1GvV7HZrPhdDoZDodYLBaGwyEHBweSqqKlg2Qy\nmaf5MvixRhd5Ojo6Os8ouVxObEdGoxGxWEyyWTXPt8lkQjqdplqtYjab8fl8Mpt2cnJCv9+nWCwy\nnU4JhUK4XC5CoRCNRoN8Po/ZbJblhm/9gx+NRqnX6wSDQR49esTe3h4mk4nbt2/TbDaZzWbcuXOH\nYDDInTt3RIA1Gg1stv+HvTeNkTPBz/t+b933fXZXd/XdTXaTTXLOnWsnq12tkpHsSBDWFmTAUBzE\nQpzY8CdHXwIB+ZB8SWAEhgUn0QchwdryxsJiP8g6Ztezozk4w+FwSHaTfXdXV3Xd932/xiJipgAA\nIABJREFU+UC+f3Gys9o1vBpK1PsABIvV1dXvW8Xqeur5/5/nsXF6ekomkyEajX4ueDcSiUiFWLfb\nJZFI0Ol0hDBZLBbm5+cZjUZcvnwZp9PJpUuX6Ha77O/v0+l0SCQSpNNpAoEAgUCAbrfLlStXcLlc\nWCwWbt26JYR4d3eXmZkZut3u50KkzWYzkUiE0WiEx+PhxRdf5Pz8XPbYjo+PsVqt5PN5isUii4uL\n5HI5VlZWiMfjkimn7fGNx2O5rd/vl0YQLfolHA6zvb2N3W6XxyUajZJOp/nkk09kNLu6uorFYhF3\ndCgUQlEUIbaAmD+057tWq8loWev8BXj55ZclBHs0GjEcDsURnUgkJO9QG4U7HA62trYkPBoeKaGj\n0ejpvAB06CRPhw4dOp4mFEWZUxTlPyiKsqsoyo6iKP/48fUBRVH+VFGUA0VR/kRRFN8T3/NbiqIc\nKoqypyjKz/+4+37ttdfweDzcu3dPWg+0EavBYEBVVfb397l+/TqLi4t4vV5u377NnTt38Pl8GI1G\nAoEAjUaDxcVFjo6O5I09FouJGuRwOBgOh9JDWygUKJVKGI1G/H6/LP4Xi0U2Nzdl/KiqKo1Gg+3t\nbSE62ti21+tJTt3KyoqQumq1yvHxsXTgaqPLxcVFlpeXqVQqeDweaaMoFovY7XYsFguRSESUyXA4\nTK/Xk4oxzWwQj8dJJpOYzWZKpZJk72nEWNtp63Q69Ho9arWaKHNf+cpXKBQKVCoVZmdnhehYLBb6\n/T4ul0vG5EajUSrCFEWRhpAnR7vxeJz3338ft9tNIpHAYrGwsrLCZ599xng8pt1u4/F4CIfDYm7p\ndrtEo1E++eQThsMhmUyGWq3Gp59+SjabldHwwsICPp+PRqOB1WoVx+54PJYMwlarRaPRoFgssrW1\nBSBROJpqWKvVaDQa7OzscHJyQqPRkKq3xcVF0um03l37FKGTPB06dOh4uhgB/1RV1U3gZeAfKYpy\nCfgfgD9VVXUN+P7jf6MoymXg7wCXgV8A/qWiKF/4u9xkMmGxWAgEArhcLlHa2u02o9FI8vJsNpss\n9W9tbRGNRmX8p4UAezweUY4SiQROp5PRaES5XMZgMDAYDKhUKphMJtxut8SAaFEd5+fnkmmXz+fp\n9XoMBgMajQalUonl5WXi8TiJRIJ8Ps+1a9ew2+1UKhVarRZLS0vAo9iXbDYrfbhaPIgWAjyZTLh9\n+7aMG7W9PG1fcDqdUq/X8fl8OJ1OPv30U+nxHY1GdDodPB4Pw+GQtbU1LBaLVLF5PB56vR7NZlNM\nG+FwWIKVtZgZzWjQarXEWet0OoUwdbtdUedKpRLBYFC6cv1+v/QE5/N5OV6r1Uo8Hmd3d5dvfetb\n0lv7ySefYLPZuH//Pnt7e+zt7eFwOPilX/olxuMxbrebdDotFW6tVot79+5RrVZZXV0VA42iKCQS\nCaLRKMvLy5J36Pf7ZTzs9XqlzcPj8WAwGPB6vYxGIxmdawRXay9ZXl6WblsdXz5+KpKnKMovPP7E\neKgoyj/7gq//uqIodxVFuacoyvuKolz92R+qDh06dDx7UFU1r6rqZ48vt4GHwCzwt4Dfe3yz3wP+\ny8eX/zbwr1VVHamqegYcAS9+0X1rYzdNISuXy4zHY4xGI7VajWq1SqPRkFYFjehou1t2u51isUip\nVAIekcZAIECr1cJsNuNwOKTd4p133pH8ObfbzezsrIwHtbGhqqqYzWbMZjOHh4cMh0M8Hg/z8/M0\nGg3S6bSYC7QuVW2X8OjoiFQqxcXFBYuLi5yfn3NxcUEgECAWi5FIJCgUCgQCAYrFooQlt9ttyfzL\n5XI4HA5UVRUCdeXKFQl61m6vEddQKCS9tA6Hg1qthqqqmEwmefw0VevTTz/FYDCwv78vZFDr29WI\ndKlUwmQyyTi21+uxurqKz+eTsbfRaJTReTKZ5Nq1a9hsNqmP8/v9ZLNZptMp29vbvP7669L9OzMz\nIwptoVBgdnaWVqtFIpEAIBqNEolEuHr1Km+//bYYQJrNJmtra/R6PYlZicVizM/PUyqVZIyrqYCd\nTodMJoPJZJLdwXA4LGN7LdC51+tht9uJxWI/y5eMjv8I/ESSpyiKEfgXPPrEeBn4tcefMp/ECfCG\nqqpXgf8J+D9+1geqQ4cOHc86FEVZAK4DHwFRVVULj79UAKKPL88AT26yZ3hECn8EWp2VFpVSqVSk\nQQIejd68Xi8mk4nBYCBv5v1+n0gkQq1WY3l5GZ/PRzqdFnfqzZs3icVi4oB1OBw8//zzrK+vSxju\naDQSZczlcuF2u0W58/l8vPLKK2xsbJBOp/F4PLhcLu7cucPOzo70vW5tbWEwGKT/VFPuPB6PxLb8\n8Ic/ZG9vT6rGGo2G7JCVSiWJCmm327RaLd5++216vZ4oaFpESLlcFjK6t7cnLRwA9Xqder3OxcWF\nkD2Xy4WiKDidThKJBMPhkGAwiMfjYX19HUVRODg4YG5ujl6vJzEx2vEEAgH29vbENNJqtSQqRhuF\nWywWeR41N6+WfTiZTLi4uKBYLGKxWCiXy9TrdVHgyuUyxWKRfr8v3bl+v5/j42MKhYI4kS0Wi2Qf\nmkwmVldXqVQqOBwO2T+8efOmBBsfHBzQ6XSo1+sSpDwzM0MoFCIajTIzM8OHH34oe5UXFxd648VT\nxE8TofIicPT4EyOKovwbHn2SfKjdQFXVD5+4/UdA4md4jDp06NDxzENRFBfw74B/oqpq68nYCVVV\nVUVR1L/g27/wa5paoyiKOEI1IlOpVMSBefv2ba5fv06pVBJnpM1mY319XUawk8mEUqmE1+sVN6iW\neacphlarFafTKSYALaxXqwIzm81ilrDb7ZydnfHcc8/x3nvvMTMzw9bWFq1WS5ot1tfXxdXb7XZZ\nXl6WcwEIBAIEg0GKxSLhcBh41Hf74osviot3aWlJ8veq1Spf//rXURQFu90ueXAul0vGiqqq4na7\nUVVVlEYtR1BTIz/55BN+/ud/ntFoxGAwwGazsba2xmQykbBjbb9NVVXeffddCU4uFAoUCgUuX74s\nBo3xeEy5XCYYDLK+vs7R0RHD4ZDxeCx7c6FQiFQqhdvtZn9/n2azSSgU4vLlyzSbTVHSPB4PzWaT\nhYUFjEYjZ2dn8nj5fD5u3brFxsYGMzMzDIdDptMps7Oz9Ho9stmskHabzUa73WZra0uMO4PBQLp+\ntQaOo6MjLl++zM7ODslkklwuh8fj4YMPPuD4+FiianQ8Hfw049pZIP3Ev3/sp8bH+AfAH/6nHJQO\nHTp0/E2CoihmHhG8/1tV1e8+vrqgKErs8dfjQPHx9RfA3BPfnnh83Y/gxo0brK+v89xzzzE/P8/C\nwoI4KbV4joODA1wul+zfRSIRjEajxKB4PB4xImj7bel0GovFgsfjweFwEIvF8Hq9EiLcbrfJ5XL4\n/X7C4bCoevl8XmJZAF544QV6vR4rKyuUSiUikQjBYBCDwYDT6ZSYE5PJJNEcmurm9/t5+PChRKto\nMScWi0UCi9fX1yUMWOtp1c5zdnZWRordblc6aNPpNKFQCLfbjdPpFJPJcDjE4XAwGo146623+PTT\nT+l0OqIYaiNnq9VKKpXC6/Xy5ptvSoSJxWLh9u3b1Ot1GYdrBo7RaCTuXs2l3Gg0REmrVCr4/X6C\nwSBOp5P19XWuXbsm3bi3b98W84vmji2Xy4xGI1Kp1OfUz9nZWcLhMLFYjJOTE3K5HL1eD0VRWFhY\nkH3FRqNBuVym0WgwGo2k69br9bK6ukqn0xETit1uJ5FI0O/3qdVq0qF7/fp1VldX+c3f/M2f9UtG\nx0+Jn4bk/UWfHj8HRVH+M+C/An5kb0+HDh06dPwolEeS3e8CD1RV/edPfOl7wN9/fPnvA9994vq/\nqyiKRVGURWAV+PiL7ltTXzQSk8/n8fl8skc2nU65fPmy7KiNx2MajQZ2u512uy2E6Pz8HIPBwGg0\nIpvNcuXKFTqdDqenp4xGI6rVqjRcxGIxotGo7LVpI1MtMFmrKMvlclSrVWmE0KJM+v0+4XCYer1O\np9NBVVXsdjuvv/46k8mEw8ND9vf3qdVqxGIxrFYrtVqNUqlEq9WiUChgNpsxmUx0u12GwyHz8/M8\nfPiQXC5HNptlb29PulYvX75MIpEgEAjISFRRFMbjMalUSswTT3b53r9/n3q9zoMHD6RD9vz8XDLs\nNKOJNhLVOl8nkwkbGxuEw2E+++wzTk5OhNhpLRrvvPOO7ORpNXGBQIB6vU4ymeT09BSbzUY+n2dz\nc5NqtUoymaTX61GpVBiNRjI+LhaLzMzMUK1WmUwm1Ot1nE4nFxcXshsZj8dxOBxSOQePDCNOpxOH\nwyF1b2dnZ9TrdYrFIoqisLS0JOPzbDZLr9fD5XKxsrIi//cCgQArKyu6u/Yp4qcZ1/7/PzXO8fl9\nEAAemy3+T+AXVFWtfdEd/fZv/7ZcfvPNN3nzzTf/Iw5Vhw4df9Xxzjvv8M477zztw/jrhleBvwfc\nUxTlzuPrfgv4X4B/qyjKPwDOgG8BqKr6QFGUfws8AMbAf6uq6hd+GNcCag0GAy6Xi0wmw+XLl4FH\nWWnBYJBcLsfc3BydTofxeCwjvGKxyMnJCeFwWFoq9vf3WVtbo91uy+0ajQadTodisUgymcTr9WI0\nGonFYsTjcdrtNt1uV4wN2u6ZxWLBbDZzcXEhCpjf7xeTh+bePDk5IRaL0Wq12Nzc5I033iCVShEK\nhQiHw6KaabtlV69eZTgcYrFYsNvtBINBWq0WHo8Hq9UqXbgXFxecnp6Kk1TrttVUxHw+j8ViweVy\nSU5fOp3G5/ORSqVYXFwUZc3j8RAIBERNOzo6YnNzk1Qqhc1mYzKZsLe3RyAQwGq10m638Xq9ZDIZ\njEYjly9f5s6dO9jtdhYWFoQAh8NhcrkcMzMz2O12GYsDLC4u4nA4qFQqcv6BQICLiwtCoRCBQACv\n18ve3h7pdJp+v08qleLVV18lnU6LKqcFNCeTSaLRKJVKhfF4LPenmXK0iBur1UogEJB8vNFoRLFY\nZGFhQQKxS6USqVSKyWSCyWTiww8//NH/nDq+FCg/5nfDn99AUUzAPvBzQJZHnxh/TVXVh0/cZh74\nAfD3VFW9+WPu58f9HtKhQ8czCkVRUFVV7zR6ClAURX3rrbeIRqNcXFyQTCapVCrMz89LbZbWSOH3\n+zGZTPT7fVRVZTAYSJNEOBzG7/czHo8BpBP26OgIj8cj6lypVMJisZBMJsWkoUWCXFxcyK7WwsKC\nxIqEQiFKpRIff/wxr7/+Ona7neFwiMHwaMikjRGtVitWq5V0Ok0wGMRsNpPNZnnhhRfI5XIYDAaC\nwSB37tzhpZdekow+r9eL0+nk7bffZmVlRTprB4MBTqdTnK/a35PJhGKxyPLyMnt7e0I6+/2+EBtF\nUfjggw+Ym5tjbW1NCLHBYJCuWXhEUnd3d7Hb7ezs7PDNb36T09NTarUa165dE+KnZfbt7+/z2muv\n8b3vfY9oNMrCwgLpdBqv10u/3ycUCjEYDPjwww/Z3t4WItfpdCTouNfr0ev1SKfTJJNJGZ3n83kK\nhQIul4vnn3+eTqdDoVDg6tWrkiM4Ho9RFIVisYjH46FcLrO0tPQ54t/pdLh//z5vvPGGPI7D4ZBy\nuYzb7WY6nZJMJjk5OWE8HosDO5PJ8J3vfEf/XfAU8BPHtaqqjoH/DvhjHn1y/H1VVR8qivIPFUX5\nh49v9j8CfuB3FEW5oyjKF44OdOjQoUPHlwev1ys1X+PxmFgsht1ux2w20+/3qVQq2Gw2ZmZm8Hg8\nYnAIhULSDVur1chkMhgMBkwmE51OB4PBgMfjYXZ2Fr/fL1lqkUhE4kuazSY2m43BYMDs7CyBQIDB\nYEAul8PpdIrxotvt8iu/8ivirlUUBZPJhN1u5/j4mHv37ok6NRwOhZBoxFKLh3E6nbz88ssUi0X+\n+I//GLvdLr293/jGN1haWsJsNhMKhQgGg/h8PoLBIKenp0KmNMVTCyTW1De3202325W8wFAohMlk\nIpVKST6fFvCsuYvz+TyXLl3CarXy1ltv0Wq18Hq9bGxs4PF4MJvN1Go1Wq0WqVRK2ki+8pWvMD8/\nj8FgEPNDIBAgn8/z/e9/n0QiIc7n8XjMxcWF7MFpjt9IJILL5ZKGDr/fL+5Xv9+P0Whkbu7RgM5m\ns+F2u4XU93o9QqEQy8vLMq43Go0cHh7icDj46le/ymAwIJvNks1mZUcylUrJrme/3ycYDFIulzGZ\nTIRCoaf5MvgbjZ8qJ09V1X+vquq6qqorqqr+z4+v+1eqqv6rx5f/a1VVg6qqXn/85wszm3To0KFD\nx5cHraB+Op0SDofFUVqtViW02Gq1Shaez+fDbrdTrVZxOp2oqirksNPpcHZ2RqfTYTgcisN2OByS\ny+VIJBKyt2cymaTBYTQacXBwgMPhYGZmRlyc8GjkqO2rTadTbDYbJycnTCYTXC4XsViMZDIJQLfb\nZXZ2lnq9zmQyYXZ2Vlyz+Xyes7Mzstksk8mElZUV0uk0iqKIWthoNPB4PAwGA4rForh29/b2CIfD\nNJtNUR+13Ta3281kMkFRFBwOB71ej9FoRDwe5/bt2/j9fqrVKsFgEJPJRCwWkxDnTCYj7l5tNzKT\nyTAajTg/P+f8/Jxr167hcDhot9v4/X5OTk7odDrStDEej1ldXZU9xfn5eer1OmdnZ/j9fmq1Gl6v\nF4fDwWAw+BwZ83q9dLtdcQ5rpM9kMnF8fAwgu5Tn5+ecnp6K8lqr1eS51B4vn89HtVrF4/Hg9XoB\npP4uGAxK9t/BwYE8TzMzM5jNZons0fHlQ2+80KFDh45nFFrMhaIoQsa8Xi8LCwuShaft2IXDYRnh\nTqdTyuUytVoNq9Uqi/sLCwtYrVapMDs6OpI3/m63y8XFBWdnZxSLRYkh0fbaWq0W8XicyWRCrVZj\nMBjQbDZZXFzk5s2bNBoNer0eV69eJZvNUqvVpBJNq1bTenTNZjOdTofpdIrL5ZI9PG28fOPGDfx+\nP/fu3QOQKBGn00mhUGA0GnFycsLBwQGrq6sS1qu5d8fjMYFAAL/fT7PZlPsejUYyLk4mkxK/YjQa\nP6d8aeqo0WgUl2upVGJpaQmLxSIkOZVKoaoq0WiUfr8v4+/pdCrtIJPJhGw2y/7+PpFIhJWVFVH6\nzGazBDIHg0FxKmuBzQ6Hg0ajQbfbxefzYbFYqNVqmEwmadHodDqyO+fz+XC73dTrdU5PT5lOp/h8\nPiqVChcXF/T7fUqlkjR6aGRPe34WFhYwmUxEIhEZ8WumDB1PBzrJ06FDh45nFFr4bSAQYHd3V1Sz\nRqMhUSpawLHdbmcwGIhSFAqF8Pl81Ot1TCYTuVyOTz/9lNnZWSwWC/V6nYWFBfb29vB4POzs7OBw\nOIhGo6IkjUYjms0mwWCQ5eVl6vW6uEtDoZAE93a7XcbjMcvLy6iqysrKijQnWCwWFEVhf38fg8GA\nxWKh2WxSLBa5c+cOvV6P8XgsBC+Xy0mnqmY2qVar7O3tMRgMZA9O62h1OBySL2cwGLBarXz22WdY\nLBYsFgs+n0+iU6bTKf1+n+FwyPXr10WdVBSFbDZLt9uV2rOzszMZ82r7iv1+H4vFImPk7e1tLBYL\n4XBY1M+zszN8Ph/f+c53CAaDVKtV5ufncbvdRCIROfZer8fh4SGTyQSHwyGhw16vF6/XS7Vapdvt\nMp1OabVaTKdTzGYzjUYDh8PB4eGhHFOn05FIGS0c+t69e0ynU8k13NzcZG5uToKi6/U6vV6Pu3fv\nUi6XiUQi+Hw+ptMpx8fHeL1eieHRmk90fPnQSZ4OHTp0PKO4f/8+nU5HelqBzxkqLBYLhUIBo9FI\ntVplZ2eHQCDA1atXhfDFYjG63S6Li4tsb2/T7XYlM0+rxer1ehSLRWq1Gna7HbvdjqqqGAwGNjY2\nsNlsDIdDqtUqo9GIdruNoijMzc1hNBqZnZ3F5/NRLBbp9Xoy/tRy16bTKVevXpXWDE3FikQijMdj\n+v2+9OnG43FpkXA6nVitVkqlEs899xwAly5d+lzmn9ZPq5kWptMpN27cwOFw4HK56PV60iurjS+t\nVquEMmvmBpPJxMXFBUdHRzQaDV599VUAVFWVcOPRaEQmk+Hk5IRyuUy5XBYy3ev1cDqdss/25ptv\nks/nSaVSOBwOIXia+3dvb49IJEIgEOAHP/gBk8mE4XCIqqrUajXK5TKKosioXlP37t+/T7VaZXt7\nm3q9zmAwkG5jTcmdmZnhypUr4hx2Op2USiWcTqe4p7e3t+W51kayvV5Pum01dVGrYdPxdKCTPB06\ndOh4RjE/Py8kKBwOS8+oRux8Ph/dbpdkMslwOGR7exuXy8VgMGB+fh6bzUYmk8Hj8RAOh+n3+1xc\nXGC32zEajWJiGAwGJJNJSqUSuVyOfD5Pq9Xi/v37Mnp0Op1MJhPZC9My+f7gD/4AeNSz6/P5MBgM\nnJ6e0mq1OD8/x+/343K5+Oijj2QUqNWwaYTOaDRKHp92rpq79fT0lEQiQSwWw+PxyM/SSIrBYKDR\naKCqKsfHx/R6PR4+fIiqqhL7Mp1OuXv3LgaDQRS1yWRCv98XcuZ2u/F4PESjUer1Ona7naOjIyqV\nCq+88gp2u51IJEI2m2VhYYFwOIzNZsPn80mUSbFYlN5ebTQcDAbp9/uYzWZKpRJut5v79+8TCAT4\n9re/TSqV4rXXXpNswtFoxMOHD+n3+5LXl8lkqNVqWCwWtra2KBaL8rxoRhaDwUA+n8dgMBCNRolG\no7RaLQAWFhZIJpO0222penO73dy8eVPItravqGUMwiN3tEYadTwd/DQ5eTp06NCh468hRqMRPp8P\no9FIsVjEarXy8OFDIVla5tn777/PpUuXODs7k2w7bVSq9btqu1XVapVarSZ7dRq5KhaLbGxs8ODB\nAxmpejwearWahPt6vV5xjBaLRXK5HL/8y79Mu93GYDDIeNhqtdJoNJidnaVUKuHxeIjFYkynU8bj\nMXNzcywvL4vT12q1cnBwwHQ6JRAISITL1atX6XQ6ogDa7XY8Ho88FppZQNtH1ByhGxsbkhfX7/dF\ntdTy/nZ3d4nH4zSbTRnBNhoNaQzx+XyUSiXOzs54/vnnsVqtrK6uoigKL7zwgpAqLXS41WrJGDYQ\nCGA0Gmk2m9I9HA6HOT09xeVycf/+fa5du0az2eTXf/3Xsdvt1Go1UWej0SjJZJJyucyNGzdoNBoS\nV2MymRiNRmxsbEhUitPpZHd3VzIT3W43MzMzEqCdyWQYDoc4nU6azSZut1u6hV955RUxpQwGA0wm\nk2TmaeaeWq2md9c+RehKng4dOnQ8o9D2pyqVCq1Wi08//ZSrV68SDoeZnZ2lXC7z2Wefsby8zOLi\nosRqKIpCoVAQpUfrnX348CGTyYTd3V1mZmZ47733WF5eJpVKsbS0xHQ6FSKgLecbDAbK5TLFYhGv\n14vb7WY8HlMqlfjggw9QVZVCoSBqVqvVIpvN4vF4cLlcsv+luXZTqRQPHjwQBer4+BhFUUgkEly6\ndAm73c5LL72Ez+cjFApJJlyn06HVauF2u3G73TSbTcm2U1WV6XRKr9djYWFBxpRaG8bi4qKEFH/8\n8ccSl2KxWIBHzt+NjQ0JCNZaOm7cuIHb7aZcLtPtdvnud78rRDGXyxEMBmVnrlgs0ul0sNlsWCwW\nrl27JvEm5XIZp9PJwsICGxsbwKOOXpfLRbVaBWBlZUWMFNvb22xsbDAcDnn33XcpFou4XC75P6Ep\nsBaLhUqlQiKRkGo2h8Mhnbt2u53FxUXu3bvH2dkZzWaTVCpFr9fj/v374grW9hcPDw9RFIXvf//7\nNJtNarUaiqLIz9bx5UMneTp06NDxjOLVV1/FZrMRiUS4dOkS29vbFAoFnE6nVG55PB7y+TzpdFoy\nzywWC0dHR6LiGY1Gbt68ycbGBslkEpvNhqIo4sw1m82yn6Z1sJpMJuLxOKFQSNopcrkc9+/fJxQK\nkUwmeemllyQuRSMc0WhUSEGr1SIUCjE/P8/MzAyVSoXnnnuOxcVF7t+/D0AkEsFisXB6ekqhUCCb\nzXJ4eIjRaCSdThONRkUp3NnZoVarYbPZZFfRYrFIhVuv16PT6XDnzh0CgQDlcpnz83O63S7Ly8tc\nuXJFdtAymYz0zj7//PP4fD62traARyQ5nU7j8Xj44IMPMBgMdLtd/H4/7XZblDdFUbDb7dy6dYuT\nkxMxlDgcDt577z1UVcXn82Gz2TAajaiqSrPZJJ/PM51OyWaz4jZut9uUSiUePHggpLrRaPDSSy/J\nuVmtVjY2NiTLb3Z2VrppnU4n6XRadgy1+xyNRjK+HY/HUtv2ZAyPdn7r6+soisLKygrNZpNsNks4\nHKZYLP7Y/6M6/nKhkzwdOnToeEYRCAQkSkNbltey6jRHq8vl4tKlS6Joabff2toiEomQz+dpt9tc\nvXpV1COPx8Pc3Bzn5+dy341Gg2azydHRES6Xi0QiQaFQoFAoiNKmEQt4FFeysrJCu92m0+lQq9W4\nd+8eBoOBRCLBYDDgzp1HLW+TyURGva1WSwhSo9EgFot9zgW7uLjI0dERPp+PyWSCwWDA4XDgcDjE\npOD3+1FVFbPZTK/XEyOH1h7h9Xo5OTmh1+thMplIJBLy+LhcLlZXVyUXT1VVOp2OOEzn5+cZDAbE\nYjEmkwlzc3NUKhXOz8+JRCLSzpFMJvmjP/ojzs/PmZ2dZXl5mc3NTTm3paWlz8WpuFwuxuMxS0tL\nhEIhycPb2NhgPB5zcnIiQcg7OzvkcjmKxSKzs7NEIhGi0SiKouDz+RiNRlitVs7OzvB4PNTrdTGB\nOBwOcrkclUpF+n/9fr/k+Wn9wPF4HKvVKiplNBoVAqyFTi8uLnJxcSFRKzq+fOgkT4cOHTqeURQK\nBc7Pz7m4uBD1zuFwkEwmMRqN0qvqdDqlgkpT0cbjMa1Wi/X1dVRVFaLh9/ulr3SbGge5AAAgAElE\nQVRra4tKpYKqqhweHgKIK3YwGJBOp8nlctJi4ff7sVqt+Hw+hsMhPp+PwWBAJBKh2WwSi8VkWV/L\naNNGuPl8Ho/Hg9FopNVqyWiz3+/TaDTwer188sknlMtlHA4HVqsVu90uLt7BYMBgMOBb3/qWkDkt\nx05zplosFlGqhsOhqGO5XE4un52dcf/+fal7q1arnJ2dkUqlaDabkjuXz+dpNBpiZLHb7TSbTVqt\nFoqi4Ha72djYYDQaMR6PpSXk8uXLohBqqquqqhiNRk5OTqhUKhIDo1XM+Xw+2u021WqVQqHA0tIS\nly5dQlEULi4ucLvdHB0dkU6ncTgc2Gw2jo+PsVgsjMdjySP0+Xw0m00qlQqKosi5dDodcRdreYnj\n8ZjJZMLFxcXnQpY1ohgKhbBYLBiNRlZWVp7my+BvNHSSp0OHDh3PKDKZDCsrK5jNZslu0/bJPB4P\n0+kUh8PB0dERRqMRk8lEJpOh3+9TLBYxmUwcHh7S7Xax2WyYzWYGgwHhcJhWq4XL5SISiXBxcSF5\naltbW7RaLdLpNK+//rqog4PBQCqvJpOJEI+ZmRnm5+fxer3cuXNHdtoURcFsNhMOh7l7966QydFo\nRLfbJRgMYrPZ6Ha77OzsEAqFMBgMjMdjLl26xOnpqeTflctlbt26JSHNFotFdgbD4bD0ri4vLxMM\nBqnVatLburm5SSAQwOv1EolE5LZaqLHZbBZClMlkPkfobDYbNpuNubk5XC4XPp9PXKq9Xo9oNMp0\nOuXKlStUq1WazSYWiwWz2cy9e/ck4Hg4HNJoNCSo2O12ixqrmTc0MrixsUG9XsdoNIoiW6lUxF3b\n6XSwWq1MJhMJb15eXpb+4lKpxNramhhjbDYbyWQSt9vNjRs3mJ+fl7iVeDxOIBCg1+tJQLTFYsHh\ncFAqlYjFYsRiMS4uLp7my+BvNHSSp0OHDh3PKObm5mR/ChDi9O6778rYzWKxSPiw3++XEaHW3LC2\ntibdtwCVSkUcsJoKpu3Mafthmgo4mUwIBoMYDAZxq3q9XqxWK263m0qlQqlUYjgcEgwGmZ+fJxgM\n0mw2RYUrl8tsbm6yubnJ+fk59Xodi8UiO2Rer5evfvWrqKrK4uKiRJx4PB4JGPb5fCwsLBCPx6Uy\nTIv1cLlcGAwGvF6v7NppAcnwyDjS7/fp9/uoqkoymSSbzWKz2SgWi7z++uuYzWZeeuklGWWn02lu\n3LhBoVCg1WqJovXxxx/z4MEDqVzzer0ShOzz+fD7/ZyfnzMYDFhZWWE0GtFqtaQ5xGB49JatRZZo\ngdNav200GgX+XIVVVVVic7rdLuVyWRRAg8EgIdGZTEaCk7X9yFarxdzcHIVCQZ67drvN6empOHa1\nMb3BYCCVSkl4crValdgXo9HIYDD4sv/r63gMneTp0KFDxzOKXC5HvV4nHA6L63I8HjM/P0+5XCYQ\nCPBnf/ZntNtthsOhkD6tj/Xg4IBqtYrFYqHb7ZLJZGR8qgXtnp6eMjc3J7lv4/FYIlr6/T53794l\nl8thNBpRFIVqtcrBwQHD4ZD5+XkxFFSrVVGo2u02drudRCIhlWulUomZmRm2tra4uLjAarXicrnY\n399nOBwymUzENNJoNOj3+zgcDj766CM++OADUd+KxaIQmHQ6LcreaDTi7OxMokMGg4EQlsPDQyGX\nFouFr33ta1gsFqxW6+caM7SeXkVRJFpFcxQ3m01eeuklVFXl5Zdfxmq1ys7iD3/4QyFFJpMJs9nM\n7u4uk8lEsvSm0ylutxuHwyHk1el0ikqqtWrk83ni8Ti5XE5MDzabjevXr+Pz+VAURbp/LRYL6+vr\nFItF+v2+7AOen58TDodxOp2Ew2EGgwGFQgGAmZkZMpkMiqLgdDqZm5uTcOt2u81gMKBcLmMymYSw\n6iTv6UEneTp06NDxjEIb8/V6PXlzPzs7w2azcXFxgdlsZmNjQ5QzzVHpdrtpNBo0Gg3y+Txms1ki\nNfx+v5gnzs7OMBqNYlxwu91SWD8zMyOhySsrK2J26Ha7OBwOMpkMRqMReKQ8nZ+fc3h4KJlq7Xab\nUChELpfj4cOHGAwGLi4uZP9Oq+kymUxiOpidnZXdOrPZjM/nY2Njg1AoRCQSodVq0W63ZSTt9Xrp\n9/sEAgFp7PB6vYzHYzqdDvl8Hq/Xy+rqqlxvs9nE5aoRyvPzcyqVCgaDQRQ1rblCI84mk4nJZMLy\n8jL7+/ui8lWrVVHXhsMhBoOB6XTKG2+8Ie0a2ghYI6DValX2BrVdR6PRSCAQYGZmRkbqBoOBra0t\nqtWqHPu7775Lu90W0qhlB2pGllKphNVqFTVQeyw0cqyqKlarlb29PQld1nIMtQaUzc1NGo2GjPi1\nEGodXz50kqdDhw4dzyjsdjuAOEjT6TSRSORzGW2aeWEwGOB0Oul2u1KB5na7eeWVV+h0OqLEpdNp\nAoEAqqqSSCRk9PekQcBoNEqnqdYMkc1m6XQ69Pt9QqGQEBqDwcDR0RGxWIyXX35ZdsUKhYLstS0u\nLgoR2t/fBx4FPddqNVZWVrh06RIXFxdMJhPJ0nM4HDJi1UKOtbGwqqr84R/+IV6vV1S/8XiMx+Oh\n0+ngcrnEeXp+fs79+/dxu91yuwcPHpDP54FHBFVT6ur1uvTAagRbC2r2er00m01x8c7OztLpdAiF\nQqIC2mw2QqGQPI6a0eXJHL9cLsf6+rqYU8xmM6lUSvYYtVG6tvs4mUxIJBLcunULq9VKJBIhHo+j\nKAqpVErOt9vtMhgM8Pv98vhpzmi73Y7X65WvaQqe0Wjk/PycQCBAp9ORNo333ntPoms0kqrj6UAn\neTp06NDxjMLhcODz+URp0cjYwsICgUCAarVKuVwmFosRDofp9XqEw2EqlQp+v59KpYLVahX1rd1u\nC1GxWq0AnJ6eSrzIcDik1WqJqqXtbk0mE9rtNvV6nUAgwOHhoeyYOZ1OkskkCwsL2Gw20uk0mUyG\nd999l/Pzc5xOJ3a7nZmZGSFhWkhzPB5nPB4zHo/FzWm1WhmNRvR6PXGUxmIxHA6HBDtrgclaXIo2\nYjabzXz7298mk8kQDocJh8MYjUaWl5dxOBwkEgnG47GMdzUzhPYzNUWt2WwynU4ZjUbMzMzQ7/dJ\npVK8+OKLks+nqiqBQIB4PM76+jqBQIBarcbHH39MLpdjZ2eHQqFAr9ej2WxSrValq1dTx7RqusuX\nLxMKhUQN1SJkut0uP/jBDwDk+Q4EAoxGI6bTKYPBQBRLzfGsPYZ+v59YLCaNHy6XC6PRKDE4Pp+P\nTqcjj0mr1aJWq9Fut1laWqJYLJJIJGg2mwQCgaf5MvgbDZ3k6dChQ8czCkVRsFqtvPfee/T7fR4+\nfCiRJjs7O+KGVFWV+/fvMx6P6fV69Pt9zs/PSSQSovaYzWYmkwk+n4+bN2/SbrdxOBxcu3aN0WgE\nPIps6Xa78rVIJILX66Xb7aIoiuStae7Wi4sLzs7OJEZEa2YYj8f86q/+Kj6fj9PTU87Pz9nf3ycY\nDLK1tYXD4ZDsudFoJN+vjT9brRaRSITZ2VkGgwH1ep3z83OCwSClUkliVbQ9PJfLRbvdpt1u88or\nr4gBRQty1qJmarUaDoeD2dlZnE4nVqtVKsk0pdDpdEosSafT4fj4mFKphNFo5ODgQI717t273Lt3\nj3w+TyqVAh6R8ueff565uTleeukliSUJBoPSs9vr9bh165aMbkulEqenp6RSKVqtFhsbG8zPz+N2\nu6lWq2xubmK1WiWfz2QySY9wIpHA4/EQCASE1NrtdukQttvtOBwOhsOh3EcgEBBTjdfrlZG6yWTi\n4uICg8GAzWYjGo2yu7srO5Y6ng50kqdDhw4dzyjq9TqKonDlyhVKpZKQLq0xQXtDz+VyRCIRAG7f\nvs3q6qq4TkOhEKPRiOPjY05OTjg/P+e5557D5XKRzWYlDLfRaEhMRzAYlNaLTqcjDs5Op0On0xEz\nQjQaZW1tjW63ywcffIDdbpcKtqOjI6xWq+TRHR0dMZlMRLE7Pz9naWlJdguDwSCDwUB2+jqdDu+9\n9x5GoxG3283169dxOBwcHBzg8/kAcDqduN1uFEVhf39f6ti0ft1IJEK/36dQKNBoNKQmTost0Xbu\nBoMBiqJQLBYJh8MA/P7v/770066srIiRwel0ys6c9jhqP+fhw4ccHByIUSYYDGK1WiWWpNPpcOXK\nFamGi8fjUie2tLREPB7H5/Ph9Xr58MMPmZub4+bNmxIkrTWPGI1GJpMJlUqFeDyO3++nXC5Tr9dl\nNDsYDOj3++zs7EjcjslkolwuA4jZotVqARAKhfB6vczMzEhnraYYaruXOr58mJ72AejQoUOHjr8c\nrK+vk0qlqFQqsvSfTqelgqpSqdDv96lUKng8Hux2O6+++qrsp/X7fYxGI2azmdFoRCwWkz5YVVWB\nR3l7Wgfs5uYmiqIwGo2o1+uEQiF8Pp8YN2ZmZjg6OpKIEy1fbX5+nmw2i8PhQFVVLl26hMfj4fT0\nlH6/z8zMDIuLi7JbCOD1eun1eqysrHD79m2ef/55lpeXKRaL0qd648YNIZadTkccspPJRLLiFhcX\nyeVy0tigHWcmk6FUKsk+XC6XIxAICBEym82USiXZqxsMBszMzMgY9Dd+4zeYTCak02ksFgvHx8fS\nwrG0tCSkbTweMxwOWVhYkEDk09NTms0mAKurq3S7XVRVFSNMv98XwtXpdAiHw2KM+fTTT1lbW8Pn\n85HP56V1Qnueg8EgxWIRVVWF1Lrdbj777DOuXLlCLpeTPbput8tkMpHKOYvFgsfjYTgcUq/X5Ry0\njEQtOHk8HssxKYoiHb86vnzoSp4OHTp0PKPQukc3Njaw2Wycnp4ynU7xeDyYzWZqtRr5fJ65uTmJ\nRtnd3aVUKsmbuTYWDQQCrKysyE5Xv99ncXGRcDgsobfwKHfu8PCQ1dVVOp2OmDvW1takMUFTxEql\nkuzFRaNRvF4vW1tbnJ6ecnp6yvLyMpFI5HOBwtqOn9PppNlscvfuXZLJJJVKRaI7QqEQJycnbG1t\nsbKyQiKRIB6Py26f0+lkb2+PXC7HcDiU+JBUKsXp6alEsmgRIPF4XAwlqVSKQqEg49lEIkGxWGQ6\nnVIoFISMnZ+fi4rldDqx2WzcvHlTAqWLxSKfffaZ5Odpjl9NGVtbW8Pv91MsFhkOhwyHQ+x2O9Fo\nlEAgIIaOk5MTPvnkE4rFohhZhsMhX/nKV6jVagSDQTweD1evXhWCPBgMhHhp5o3FxUX29vbo9XoU\nCgUhaVeuXJGGEY/HI+P2zc1NptOp7O892eyhmV7a7bZkDOp4OtBJng4dOnQ8o9C6WWu1GpFIhJmZ\nGS5fvozP56NcLuN0OkUp0t7Ib9y4IXl29XodgO3tbRYXF7Hb7VitVorFIoPBgFqtxnQ6pVaryV5b\no9EgmUwymUyIxWIYjUYZN/b7fcLhsDQyXL9+HbPZTDqdplwu02g0xByxvb2N1Wpld3dXYkj6/T52\nu51yuSw5f9vb2+RyOWnl0AJ/4dG42u/3S1vFnTt3GI/Hcn5ar61WlRYOh9ne3sZgMEhjhBYaHAwG\npVt3aWkJs9ksxgRVVYnFYthsNvb29ohEIqyvr3P37l1xzq6trZFMJgHEnRwKhSiVSly/fl322oLB\noHQCa6RWU9WOj49JJBIsLi5Kw4TH42FzcxObzYbdbsfpdEplWzwel8zCXq+HzWbD4XAwNzeH2+2W\nWrmLiwt2dnbodDr0ej1mZmYYj8ccHx9TqVSw2WzieLZYLGQyGfb39+X+bDabjMo1k4iiKDJ614ir\nji8fOsnToUOHjmcUxWKR1dVV2buq1+tUq1VKpZIQNIPBwNnZmfSsagTw+PhYRq9a1Ei9XmcwGOB2\nu4UEnZ+f4/V6abfbpFIpcc62221sNhtutxubzSYRLtVqleeff16IX6/Xw263c+nSJVHQ4vE4zWaT\n3d1dnnvuOSaTCZlMBrPZzIMHD9jY2ODy5cscHh6SSqVQFAWXy0WhUMBmswm5Ozk5ETVTqw9bW1sT\nZUlz2na7XZaWluj1emIIUVWVfD5PMBhkPB5jMBiIx+MMBgPMZjOnp6cMBgOazSYul4vJZMJ0OiWT\nyeByuWg2m1y5coWDgwOp/vq5n/s5Wq0WwWBQzA1asPO1a9fI5XIUCgU2Nze5e/cuNptNgqc10pzL\n5RiPx5/b7Usmk3Q6HRqNBoFAgPF4LDtxDx8+pN1uU6lUhChqO4gPHjwgGo1iNBpZXFzE6XQyMzMj\nY1htl09RFLrdLhaLBUVRxBns9/vpdrtSl2cwGGg2m2Lu8Hg8TCYTVldXn/Ir4W8udJKnQ4cOHU8R\niqLMKYryHxRF2VUUZUdRlH/8+PrfVhQloyjKncd//vMnvue3FEU5VBRlT1GUn/9x9+1yuajVakwm\nE+r1OkdHR2QyGWky0MZ+iURCQnjv3LmDy+Via2uLWCzGzZs3GQwGmEwm3n77beBRbMr8/DylUokH\nDx5Ia0WlUsHhcAgpSqVSlEoldnd3GQ6HRCIRUqkUtVqNnZ0d0uk0NpuNSqUiVV/D4ZDpdIqiKEQi\nEQntXVhYwOVysba2JoYOrfqs2+0yGo2kJ1e7n1qtRjabBRDVrl6v02q1uHLlisSTjEYjCXLW9v6S\nySR+v5+DgwNqtZpk9mn9uDabjVQqxXA4ZHl5mclkwnA45Nq1a3IMNpuNhYUFUUS73a4QXW30quUM\nut1uAoEATqeTo6MjkskkjUZD1LbZ2VlWVlZotVoyAq/VaoTDYXw+H41Gg5OTExqNBqqqihnl61//\nOi6Xi3g8TiwWw+/3M5lMCAQCLCwsCDl1uVwsLCzgdrsByGazzM3N4fV6MRqNzM7O0uv1ePjwIbFY\nTEimqqrMz89LM0ooFGJubk4UQq3WTsfTgf7I69ChQ8fTxQj4p6qqbgIvA/9IUZRLgAr8b6qqXn/8\n598DKIpyGfg7wGXgF4B/qSjKF/4uN5lMWCwWarUaZrOZ119/nclkInlu/X6fXq9HIBCQKI1oNCqm\nhFKpxNzcHB999BEGg4Gvfe1rTKdTZmZmJMz4G9/4Bp1Oh2azSTQalXGsoiiyj7a1tSWhyCsrKwSD\nQRlVwiMyuri4KGaMUqnEdDqV8e9wOKRcLpPL5Wg0GqKkNZtNZmdnuXr1qsS8mEwm3n//fcbjMVtb\nW0QiERwOB0dHR/R6PU5PT4V4uN1uqWvTarpWVlak+WNubo5qtUqxWBTTQjQaJZfLUa1WCYVCXLp0\niel0itPppNfrye6f3++nWq2Sz+epVquoqsrBwQHb29t8+OGHHB0d4XA4WF9fZzKZUCgUpOt3aWmJ\n8XhMt9ul2+2KCabb7eL3+/F4POIMrlQqoshqO4xa2LF23NVqlW63y/n5Obu7u5yenmIwGKjVatTr\ndeLxONVqFa/XS71ex+l0ypj9yZzDVqslxp1IJCLRMJoTWwu/tlqt1Ot1ksmkxPHoeDrQSZ4OHTp0\nPEWoqppXVfWzx5fbwENg9vGXlS/4lr8N/GtVVUeqqp4BR8CLX3TfpVJJHKIWiwWXy8Xc3ByAjG/7\n/T5Op5N2u814PCYSiRAKhchkMjIO1LLWvF4vw+EQn88n+2raWLPT6ZBOp3E4HLRaLQnfHY1GErCr\nNWSMx2OpRut2u+zv72O320mn09K1ms1m6Xa7uN1u3G63tCZ4vV6KxSKRSIRkMonZbKZcLjM7Oys/\n85vf/KaoeY8fV1ZXVwmHwyjKo4d0Z2dHDBzhcJjxeCx1YXfv3iWbzYob94033iAajRKJROh0OgyH\nQ0KhEN1ul+l0ykcffYTJZKLRaIgpxe12Mzc3J2PQZrPJ0tISRqORzc1NYrEY+Xyeer1ONpul1Wrx\nySefYDKZaLfbBAIBEokEFouFwWDArVu3qFar3Lt3j1wuJ/uJFxcX5PN56Z3Vas8ajQYej4c/+ZM/\nkQaMdrst5+X1eonH40J0rVYr6XRaQqyj0SjHx8eyb5jP57FYLGxsbDAcDiViRlM2//RP/5RSqUSx\nWKTZbIp7V+vd1fF08BNJnqIov/B4JHCoKMo/+zG3+d8ff/2uoijXf/aHqUOHDh3PPhRFWQCuAzcf\nX/XfP/69+ruKovgeXzcDZJ74tgx/Tgo/B1VVRVnRGg20v00mE8lkUt6ww+Ew0+mUSCRCtVqVSBGt\n2cBqtUp9l0Y8JpOJOFQtFgtf+9rXODs7k0DgeDwuztSzszMODw9lT0sjNZq6VywWpTrLaDSSy+WY\nnZ2VOjPNOaqdk8lkYjQa0e125dir1aqoUuPxmEKhQDabJZPJ0Gq1sFgsRCIRycaz2+3kcjmKxaKo\nhNVqlV/8xV/E4/FweHjI3NycRKhoQc/amLvZbNJut1lZWZE9tTt37lAoFMjlcjICz2QyjMdjdnd3\naTabst/o9XqJxWJ0u13q9TovvPACw+EQh8PBzs4OZ2dnMqp+4403sNvt3LhxQzpzPR7P51S4QqHA\nrVu3GAwGYrR46623pIZMM2ZopK3ZbDIYDHjw4AEmk0lIbqlUwmw2y3haOxe73Y7dbhcVbzKZ0Ov1\nyGQyvPLKKzz33HOsra1J08poNOLw8BCz2fyX9IrR8ZPwF5I8RVGMwL/g0UjgMvBrj8cIT97mvwBW\nVFVdBf4b4Hf+ko71rwzeeeedp30IPxM8K+cB+rno+OsPRVFcwP8L/JPHit7vAIvANSAH/K9/wber\nX3TlyckJ+/v7vP/++zx48EBcsVosx3g8ptFoyL6atjzfbrcJhULEYjGKxaLslzWbTQkL1kibqqrS\nlKA5VYPBINlsVtRDzflZr9dFXdOqxYLBIF6vl0AgwMHBASsrK3Q6Hba3t/F6vYxGI27evMnR0ZEo\nZ1pAs6aSlUolDAaDKHJWq5Uf/vCHZLNZarUaR0dHTKdTAoEALpdLGjGsVqs4hrXRarlcluowzTii\ndcJqdWWJREJGwVqnrxYwHAwGxVRy69YtVFUVR3M0GsVisYhq2Gg0aDQazMzMUCwWhQDbbDZmZ2dp\ntVqkUikymQy7u7tUq1UZzWpNFIqisLS0hKqqjEYjVldXpU/39u3bsuOouYTX1tYoFAqYzWYCgQAP\nHjwgkUjgcrlYWlrCbrcLgWs0GkLm4/E4VqtVTDGaqul0OqU545133pFz2tnZ4Xvf+x737t2TajUd\nXz5+kpL3InCkquqZqqoj4N/waFTwJP4W8HsAqqp+BPgURYn+zI/0rxCelTfhZ+U8QD8XHX+9oSiK\nGfh3wP+jqup3AVRVLaqPAfxf/PlI9gKYe+LbE4+v+xG89tprbG1tSQ1XIBCQWJVUKkW1WmVhYUF2\n6oxGoxBBo9EoJgTN3dpsNgmHw0ISvv71rwvR0EijFl9ydnYGIMYJt9vNtWvXMBgMKIrC+fk55XKZ\nUqkkPbChUEjqsrSxbDwe/1w9WrPZJJvNEgwG2dvb4969e8zNzWE2m5lOp2SzWaxWK/Pz8+zt7WGz\n2QiHw7LfZzabURSFaDTKZDLB4XBQLBZFUQyFQjidTnEIh0IhGS8bjUauXr3KaDSi2WxitVpFpdIU\nxlgshtfrZTKZ8Omnn9LtdnE6naTTaSaTCaqqSpyNFo+i7Q9qhhW73Y7JZGJhYUGeh1AoJFVlmgI6\nnU7p9XoSqDw7O0u32yUQCJDJZORna/En2ih5eXmZ6XSK1+tlaWkJt9tNuVyWCrjZ2Vkhfbu7u4xG\nI9rttoRga20XxWIRh8MhJNnv94spZnNzE7PZzLVr19je3v5Zv2R0/JT4SSRvFkg/8e8vGgt80W0S\n/+mHpkOHDh3PPpRHS2K/CzxQVfWfP3F9/Imb/TJw//Hl7wF/V1EUi6Ioi8Aq8PEX3fdkMpF4ES12\nQ1EUzGYzoVAIv98v48v9/X08Hg+5XE5Ut3a7TT6fZzKZcHBwIA0Ld+7codls4nQ6sdvtjMdj7Ha7\nZOZVq1Vx3GpL/y6XC4fDgd1ul0gTbQTc7/dxOBzSmpDNZvnkk08YjUYUi0UuLi6YTCZEo1Gi0Six\nWIxyuYyqqmxubmIymSQMOBqNiilCy4TTIksmkwmHh4eUy2UhJoVCgfF4zP/X3tnFxnFVcfx34rXX\nXjsOtuo4iddJnciOw0NcElkQlaithCD0oUJUQioUWqgQAooQPBRaiRaJB1qeeOBTFQgJIaoqpRBQ\ngLRBFQiRWBHNhwmFxGxCvbVDvfbGdvwZ5fAwsxN3ux+z2dnZ9fb8pJX3Y7znnDv3jo/n3nv+g4OD\nnpLF1NQUyWSS/fv3k0gkvO8WEZaWlpieniaRSBCLxRgZGfHuwPX19XH58mXS6bQ3lRyJREilUl7i\n2NbWRiqVIpFIMDo6SldXF5cuXWJsbIzR0VGvjcFRE9m5c6dXLy8ajbKyssK2bdvo7u72NIfn5ubo\n7+/35MTS6TS9vb3eTt2MZm1fXx/RaJTFxUXvjmVTUxOzs7O0tLR4/aanp4cLFy6wceNGenp6WFlZ\nYXJyElX1Hpm1jZl1nZn1i42NjZ6GbSQSYevWrd7dWyN8iiV5OacAcpC9ONjv7xmGYbzTuRN4ELgn\nq1zKMyJyVkTOAHcBXwFQ1fPA88B54PfAFzSjMZbFzMwMzc3N3m7S2dlZxsbGvELC165dI5lMMj09\nzb59+5iYmOD48eNesd9NmzYxODjI3Nwc7e3txONxb11YRgMX4MSJE7S0tDAyMkI8Hvd252bqraXT\naVKpFKOjo970YCQSYXx8nJmZGVpbW72SJ7FYjB07djA0NEQ8Hqejo4MDBw6wd+9e2travOQznU4T\nj8dpaGjg8OHDdHd3E4vFvDVwra2t3gaF1dVVAJaWlhgYGGD79u0sLy8TjUY5efIku3fvprOzk4aG\nBq9WX6bIcTqdZsOGDd7d0Iz8WmYTysGDB5mYmODMmTMsLCzQ29vrrXkUEa+G4MDAANFolIWFBW+t\n4/DwME1NTTQ3N7O4uEg8HveKC2/evNnThm1vb/fq02Xulo2Pj3P16lX27L93vUAAAAX2SURBVNnD\n1NSUN82eSWgBpqam6Orq8qZcMzUPOzo6GBoa4saNG6yurnrnsbGxkba2NpLJpDdVn0gkPD3czBq9\nLVu2EI1G2bVrF8lkknPnzjE8POwlj01NTUxOTrK8vMz8/Dzz8/MVGzxGYSTPtcH5UOR9wDdV9ZD7\n+nHghqo+s+aYHwGvqOpz7uvXgLtU9UrWd1niZxjvQFQ11w5Ro8LYNdeoNexaED6RIp+fAvrdHV9v\n4NRmeiDrmCPAo8BzblKYzk7wwE6uYRhGmNg11zCMgkmeql4XkUeBPwINwE9U9Z8i8jn38x+r6lER\nuVdELgLXgE9X3GvDMAzDMAyjIAWnaw3DMAzDMIz1SeCKF/V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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Set the radius\n", "r = 30\n", "\n", "# Apply low-pass filter: remove high frequency coefficients\n", "campus_fft2_shift_low = apply_ideal_filter(campus_fft2_shift, r, 'low_pass')\n", "# Apply high-pass filter: remove low frequency coefficients\n", "campus_fft2_shift_high = apply_ideal_filter(campus_fft2_shift, r, 'high_pass')\n", "\n", "# Plot the results\n", "plt.figure()\n", "\n", "# Plot the original image and freq\n", "plt.subplot(3, 2, 1)\n", "plt.title(\"The original image\")\n", "plt.imshow(campus)\n", "\n", "plt.subplot(3, 2, 2)\n", "plt.title(\"The original 2D DFT coefficients magnitudes in log scale\")\n", "plt.imshow(np.log(np.abs(campus_fft2_shift)+1))\n", "\n", "# Plot the filtered image and freq\n", "plt.subplot(3, 2, 3)\n", "plt.title(\"The low-pass filtered image\")\n", "campus_ifft2_low = np.fft.ifft2(np.fft.ifftshift(campus_fft2_shift_low),norm='ortho')\n", "plt.imshow(np.abs(campus_ifft2_low))\n", "\n", "plt.subplot(3, 2, 4)\n", "plt.title(\"The low-pass filtered coefficients\")\n", "plt.imshow(np.log(np.abs(campus_fft2_shift_low)+1))\n", "\n", "# Plot the filtered image and freq\n", "plt.subplot(3, 2, 5)\n", "plt.title(\"The high-pass filtered image\")\n", "campus_ifft2_high = np.fft.ifft2(np.fft.ifftshift(campus_fft2_shift_high),norm='ortho')\n", "# Your Code Here : do the same thing to show the previous image (remember to np.abs it)#\n", "\n", "# End Code #\n", "\n", "plt.subplot(3, 2, 6)\n", "plt.title(\"The high-pass filtered coefficients\")\n", "plt.imshow(np.log(np.abs(campus_fft2_shift_high)+1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### (d) Separate Einstein and Monroe\n", "\n", "In this problem, we look at an interesting image.\n", "\n", "The pictures are taken from the original paper and news articles:\n", "1. http://cvcl.mit.edu/papers/Oliva-HybridImages-ArtPerception2013.pdf\n", "2. http://www.mirror.co.uk/news/uk-news/madeuthink-marilyn-monroe-albert-einstein-3239254\n", "3. http://calculatedimages.blogspot.com/2014/03/monroe-einstein-and-visual-acuity.html" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "hybrid = misc.imread('figs/einstein_monroe_256.jpg')\n", "\n", "# Plot the image\n", "plt.figure()\n", "# Your Code Here: show the image hybrid #\n", "\n", "# End Code #" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If you get very close to the image, it is Albert Einstein. However, if you view it from a distance, it becomes Marilyn Monroe! How does this illusion happen? It turns out that it's a result of combining a high-pass filtered picture of Einstein and a low-pass filtered one of Monroe. We'll use this fact to separate Einstein and Monroe in the following steps." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "ename": "NameError", "evalue": "name 'hybrid_fft2' is not defined", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 13\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msubplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 14\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtitle\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'The 2D DFT coefficients'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 15\u001b[0;31m \u001b[0mhybrid_fft2_shift\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfft\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfftshift\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mhybrid_fft2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 16\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mimshow\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlog\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mabs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mhybrid_fft2_shift\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mNameError\u001b[0m: name 'hybrid_fft2' is not defined" ] }, { "data": { "image/png": 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yMy7WPOGcFBfJ15MiI3nt2cakMKPY4HWk2PP7mXdf++N7oUOSOVfcZp4Q9KKM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\ngkcCxGBM9x9Ll9B9haEYmYTAT7rWiC9g4l+v1wHEeA8S1WK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m9/M+yLTSSusXqx4MZLn8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BhHB/90PqaVVlppPbZ6UJD1Ta3dDpakLTvA75k0pO36b0xIvA5pBF8IvqLJZKJaraaTk5MwveNH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\nIfuRha0UbGQpbDhrr0On0/GfV61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I0QcksoQQQggh+oBElhBCCCFEH5DIEkIIIYToAxJZ\nQgghhBB9QCJLCCGEEKIPSGQJIYQQQvQBiSwhhBBCiD4gkSWEEEII0QcksoQQQggh+oBElhBCCCFE\nH5DIEkIIIYToAxJZQgghhBB9QCJLCCGEEKIPSGQJIYQQQvQBiSwhhBBCiD4gkSWEEEII0QcksoQQ\nQggh+oBElhBCCCFEH5DIEkIcGZxzn3DOveac+wfn3L/p8fynnXPfdM697Jz7O+fcY4exn0KI7w5c\nFEWHvQ9CCNF3nHODAC4D+CiAJQDfAPATURS9al7zfgCXoijads59AsBnoih6X7CdSH83hThaOOcQ\nRZH7Tt+nSJYQ4qjwHgBXoyhaiKKoBeC/AviUfUEURV+Pomh7/9fnAcy+yfsohPguQiJLCHFUOAHg\nlvl9cf+xg/hZAH/e1z0SQnxXM3TYOyCEEG8S33aOzzn3PwH4lwA+2Ov5z3zmM/7nD3/4w/jwhz/8\nT9w1IcRbia9+9av46le/+k/ejjxZQogjgXPufdjzWH1i//dfAdCJoug/BK97DMAfAfhEFEVXe2xH\nniwhjhjyZAkhxL15AcC8c+4B59wwgKcAfMG+wDk3hz2B9ZO9BJYQQnwnKF0ohDgSRFG065z7JQB/\nBWAQwGejKHrVOffz+8//3wD+LYBRAL/tnAOAVhRF7zmsfRZC3N8oXSiEEN8BShcKcfRQulAIIYQQ\n4i2ERJYQQgghRB+QyBJCCCGE6AMSWUIIIYQQfUAiSwghhBCiD0hkCSGEEEL0AYksIYQQQog+IJEl\nhBBCCNEHJLKEEEIIIfqARJYQQgghRB+QyBJCCCGE6AMSWUIIIYQQfUAiSwghhBCiD0hkCSGEEEL0\nAYksIYQQQog+IJElhBBCCNEHJLKEEEIIIfqARJYQQgghRB+QyBJCCCGE6AMSWUIIIYQQfUAiSwgh\nhBCiD0hkCSGEEEL0AYksIYQQQog+IJElhBBCCNEHJLKEEEIIIfqARJYQQgghRB+QyBJCCCGE6AMS\nWUIIIYQQfUAiSwghhBCiD0hkCSGEEEL0AYksIYQQQog+IJElhBBCCNEHJLKEEEIIIfqARJYQQggh\nRB+QyBJCCCGE6AMSWUIIIYQQfUAiSwghhBCiD0hkCSGEEEL0AYksIYQQQog+IJElhBBCCNEHJLKE\nEEIIIfqARJYQQgghRB+QyBJCCCGE6AMSWUIIIYQQfUAiSwghhBCiD0hkCSGEEEL0AYksIYQQQog+\nIJElhBBCCNEHJLKEEEIIIfqARJYQQgghRB+QyBJCCCGE6AMSWUIIIYQQfUAiSwghhBCiD0hkCSGE\nEEL0AYksIYQQQog+IJElhBBCCNEHJLKEEEIIIfqARJYQQgghRB+QyBJCCCGE6AMSWUIIIYQQfUAi\nSwghhBCiD0hkCSGEEEL0AYksIYQQQog+IJElhBBCCNEHJLKEEEIIIfqARJYQQgghRB+QyBJCCCGE\n6AMSWUIIIYQQfUAiSwghhBCiD0hkCSGEEEL0AYksIYQQQog+IJElhBBCCNEHJLKEEEIIIfqARJYQ\nQgghRB+QyBJCCCGE6AMSWUIIIYQQfUAiSwghhBCiD0hkCSGEEEL0AYksIYQQQog+IJElhBBCCNEH\nJLKEEEIIIfqARJYQQgghRB+QyBJCCCGE6AMSWUIIIYQQfUAiSwghhBCiD0hkCSGEEEL0AYksIYQQ\nQog+IJElhBBCCNEHJLKEEEIIIfqARJYQQgghRB+QyBJCCCGE6AMSWUIIIYQQfUAiSwghhBCiD0hk\nCSGEEEL0AYksIYQQQog+IJElhBBCCNEHJLKEEEIIIfqARJYQQoj/r727CZWqjsM4/n1QW7hQC6GF\nGlqJ6CKxyIoKk1rcXBTUIuwNKygCo11viwpaSLsIwUKKWuWigiykCOpShApSvvQiaC+kCZL2QoQL\nxafFHGW6V+/85+qZGc88Hzgw587/wu/hnP/Mb+ac+78RUYM0WRERERE1SJMVERERUYM0WRERERE1\nSJMVERERUYM0WRExNCSNSNoraZ+kp88y5tXq+V2SlvW6xohojjRZETEUJE0B1gMjwBJgtaTFY8as\nAq60vRB4FNjQ80J7aHR0tN8lnDdNydKUHNCsLJOVJisihsVyYL/tX2wfBzYBd44ZcwfwNoDt7cAs\nSZf2tszeadKbYFOyNCUHNCvLZKXJiohhMQc40LZ/sPpZpzFza64rIhoqTVZEDAsXjtMkfy8i4n9k\n5/UjIppP0vXAi7ZHqv1ngZO2X24b8xowantTtb8XWGH7cNuYvGhGDCHbYz+AdTS1jkIiIgbQDmCh\npPnAIeAeYPWYMZuBtcCmqin7q73Bgsm90EbEcEqTFRFDwfYJSWuBT4ApwBu2f5D0WPX867a3SFol\naT/wL/BQH0uOiAtcLhdGRERE1CA3vkdEnEGTFi7tlEXSfVWG3ZK+knRVP+rspOSYVOOulXRC0l29\nrK8bhefXLZK+kfStpNEel1is4PyaKelDSTurLGv6UGZHkt6UdFjSngnGdDfnbWfLli1btraN1uXE\n/cB8YBqwE1g8ZswqYEv1+DpgW7/rPocsNwAzq8cjg5ilJEfbuM+Aj4C7+133ORyTWcB3wNxqf3a/\n6z6HLM8B607lAI4CU/td+xmy3AwsA/ac5fmu53y+yYqIGK9JC5d2zGJ7q+2/q93tDObaYCXHBOAJ\n4F3g914W16WSLPcC79k+CGD7SI9rLFWS5SQwo3o8Azhq+0QPayxi+0vgzwmGdD3n02RFRIzXpIVL\nS7K0ewTYUmtFk9Mxh6Q5tN7gT/07pEG96bjkmCwELpH0uaQdkh7oWXXdKcmyHlgi6RCwC3iyR7Wd\nb13P+fx1YUTEeE1auLS4JkkrgYeBG+srZ9JKcrwCPGPbksT44zMoSrJMA64GbgWmA1slbbO9r9bK\nuleSZQT42vZKSVcAn0paavufmmurQ1dzPk1WRMR4vwHz2vbn0frUOtGYudXPBk1JFqqb3TcCI7Yn\numTSLyU5rqG1xhm07v25XdJx25t7U2KxkiwHgCO2jwHHJH0BLAUGrckqybIGWAdg+0dJPwOLaK1d\ndyHpes7ncmFExHinFy6VdBGthUvHvlFvBh6E06vJj1u4dEB0zCLpMuB94H7b+/tQY4mOOWxfbnuB\n7QW07st6fAAbLCg7vz4AbpI0RdJ0Wjdaf9/jOkuUZPkVuA2guodpEfBTT6s8P7qe8/kmKyJiDDdo\n4dKSLMDzwMXAhupboOO2l/er5jMpzHFBKDy/9kr6GNhN68bxjbYHrskqPC4vAW9J2k3rcttTtv/o\nW9FnIekdYAUwW9IB4AVal20nPeezGGlEREREDXK5MCIiIqIGabIiIiIiapAmKyIiIqIGabIiIiIi\napAmKyIiIqIGabIiIiIiapAmKyIiIqIGabIiIiIiavAfy7yjua1LId4AAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# First, let's look at its 2D DFT coefficients\n", "# Your Code Here: compute the 2D DFT of the image \"hybrid\" #\n", "\n", "# End Code #\n", "\n", "# Plot the original and its frequency\n", "plt.figure()\n", "\n", "plt.subplot(1,2,1)\n", "plt.title('The original illusion image')\n", "plt.imshow(hybrid)\n", "\n", "plt.subplot(1,2,2)\n", "plt.title('The 2D DFT coefficients')\n", "hybrid_fft2_shift = np.fft.fftshift(hybrid_fft2)\n", "plt.imshow(np.log(np.abs(hybrid_fft2_shift)+1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Do you see the small black ring in the image of frequency coefficients?\n", "That's the radius for us to apply ideal low/high-pass filters." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "ename": "NameError", "evalue": "name 'hybrid_fft2_shift' is not defined", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0;31m# End Code #\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m \u001b[0mhybrid_fft2_shift_low\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mapply_ideal_filter\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mhybrid_fft2_shift\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mr_hybrid\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'low_pass'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 6\u001b[0m \u001b[0mhybrid_fft2_shift_high\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mapply_ideal_filter\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mhybrid_fft2_shift\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mr_hybrid\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'high_pass'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 7\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mNameError\u001b[0m: name 'hybrid_fft2_shift' is not defined" ] } ], "source": [ "# Your Code Here: set r_hybrid #\n", "\n", "# End Code #\n", "\n", "hybrid_fft2_shift_low = apply_ideal_filter(hybrid_fft2_shift, r_hybrid, 'low_pass')\n", "hybrid_fft2_shift_high = apply_ideal_filter(hybrid_fft2_shift, r_hybrid, 'high_pass')\n", "\n", "# Plot the filtered image and freq\n", "plt.subplot(2, 2, 1)\n", "plt.title(\"The low-pass filtered image\")\n", "hybrid_ifft2_low = np.fft.ifft2(np.fft.ifftshift(hybrid_fft2_shift_low),norm='ortho')\n", "plt.imshow(np.abs(hybrid_ifft2_low))\n", "\n", "plt.subplot(2, 2, 2)\n", "plt.title(\"The low-pass filtered coefficients\")\n", "plt.imshow(np.log(np.abs(hybrid_fft2_shift_low)+1))\n", "\n", "# Plot the filtered image and freq\n", "plt.subplot(2, 2, 3)\n", "plt.title(\"The high-pass filtered image\")\n", "hybrid_ifft2_high = np.fft.ifft2(np.fft.ifftshift(hybrid_fft2_shift_high),norm='ortho')\n", "plt.imshow(np.abs(hybrid_ifft2_high))\n", "\n", "plt.subplot(2, 2, 4)\n", "plt.title(\"The high-pass filtered coefficients\")\n", "plt.imshow(np.log(np.abs(hybrid_fft2_shift_high)+1))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "####(e) Discrete cosine transform (DCT)\n", "\n", "In this problem, we introduce another transformation, discrete cosine transform (DCT).\n", "For some cases, DCT has better *energy compaction* than DFT, which will be shown in the following examples." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "ename": "NameError", "evalue": "name 'x_dft' is not defined", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 18\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msubplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 19\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtitle\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'|x_dft| : DFT coefficients'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 20\u001b[0;31m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstem\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mabs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx_dft\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 21\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 22\u001b[0m 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DRJJUzBCRJBUzRCRJxQwRSVIxQ0SSVMwQkSQVM0QkScUMEUlSMUNEklTMEJEkFTNEJEnF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\n6cXMi+n8hfV2angS1UXfi/v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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# first let's create a time-domain signal\n", "x_time = np.linspace(0, 1, 16)\n", "\n", "# Do DFT\n", "# Your Code Here : set x_dft to be the frequency domain coordinates of x_time #\n", "\n", "# End Code #\n", "\n", "# Do DCT\n", "x_dct = dct(x_time, norm='ortho')\n", "\n", "plt.figure()\n", "\n", "plt.subplot(1,3,1)\n", "plt.title('x : time-domain signal')\n", "plt.stem(x_time)\n", "\n", "plt.subplot(1,3,2)\n", "plt.title('|x_dft| : DFT coefficients')\n", "plt.stem(np.abs(x_dft))\n", "\n", "plt.subplot(1,3,3)\n", "plt.title('|x_dct| : DCT coefficients')\n", "# Your Code Here : plot the absolute value of the DCT coefficients#\n", "\n", "# End Code #" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Do you see the difference between DFT and DCT coefficients? In this example, the DCT coefficients are much more concentrated in terms of energy than the DFT ones. The result is that DCT requires less coefficients to reconstruct its time-domain signal, which will be shown below." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "ename": "NameError", "evalue": "name 'x_dft' is not defined", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 6\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 7\u001b[0m \u001b[0mK\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m3\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 8\u001b[0;31m \u001b[0mx_dft_zip\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mkeep_k_largest_elemts\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx_dft\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mK\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 9\u001b[0m \u001b[0mx_dct_zip\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mkeep_k_largest_elemts\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx_dct\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mK\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 10\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mNameError\u001b[0m: name 'x_dft' is not defined" ] } ], "source": [ "def keep_k_largest_elemts(x, k):\n", " x_result = np.copy(x)\n", " I = np.argsort(abs(x))[:-k]\n", " x_result[I]=0\n", " return x_result\n", "\n", "K = 3\n", "x_dft_zip = keep_k_largest_elemts(x_dft, K)\n", "x_dct_zip = keep_k_largest_elemts(x_dct, K)\n", "\n", "x_idft_zip = np.fft.ifft(x_dft_zip, norm='ortho')\n", "x_idct_zip = idct(x_dct_zip, norm='ortho')\n", "\n", "plt.figure()\n", "\n", "\n", "plt.plot(x_time, label='x')\n", "# Your Code Here: add plots for the approximations we get from the DCT and DFT. Don't forget to take np.abs #\n", "\n", "# End Code #\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see, if we pick 3 coefficients with the largest magnitudes from DFT and DCT, DCT recovers its time-domain signal much better than DFT." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "####(f) Two-dimensional DCT \n", "\n", "In this problem, we will play with an example of 2D DCT and get a sense of why 2D DCT is widely used for image compression.\n", "\n", "The Sather tower image is taken from https://en.wikipedia.org/wiki/University_of_California,_Berkeley." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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VavnBmvuOjY15McjtRkZGvNBYWVlBqVRCs9lEu91GqVTCxsaGv1+8JxRpZoaR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\n5b5ElLEdBFcU0jGcHydFSEdFS/kM+8lzi6CNeVzGmPPhqQkpKaWXUkr/M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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Read image\n", "tower = misc.imread('figs/tower_256.jpg')\n", "\n", "# Compute DFT and its shift\n", "tower_fft2 = np.fft.fft2(tower, norm='ortho')\n", "tower_fft2_shift = np.fft.fftshift(tower_fft2)\n", "\n", "# Compute DCT coefficients and compare it with DFT ones\n", "tower_dct2 = (dct(dct(tower, norm='ortho').T, norm='ortho')).T\n", "\n", "plt.figure()\n", "\n", "plt.subplot(1,3,1)\n", "plt.title('The tower image')\n", "plt.imshow(tower)\n", "\n", "plt.subplot(1,3,2)\n", "plt.title('The 2D DFT coefficients')\n", "plt.imshow(np.log(np.abs(tower_fft2_shift)+1))\n", "\n", "plt.subplot(1,3,3)\n", "plt.title('The 2D DCT coefficients')\n", "# Your Code Here: plot the log-scale magnitude of the DCT coefficients (remember to add 1 to prevent taking a log of 0) #\n", "\n", "# End Code #" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we take *K* coefficients with the largest magnitudes and reconstruct the image." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def keep_k_largest_elemts2(A, k):\n", " C = np.copy(A)\n", " # I is the k largest indices\n", " I = np.argsort(np.abs(A), axis=None)[:-k]\n", " C[np.unravel_index(I, A.shape)] = 0\n", " return C" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "ename": "NameError", "evalue": "name 'tower_fft2_zip' is not defined", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0;31m# End Code #\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 6\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 7\u001b[0;31m \u001b[0mtower_ifft2_zip\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfft\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mifft2\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtower_fft2_zip\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnorm\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'ortho'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 8\u001b[0m \u001b[0mtower_idct2_zip\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0midct\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0midct\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtower_dct2_zip\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnorm\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'ortho'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mT\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnorm\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'ortho'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mT\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 9\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mNameError\u001b[0m: name 'tower_fft2_zip' is not defined" ] } ], "source": [ "K = 500\n", "\n", "# Your Code Here: make tower_fft2_zip just have the largest elements of the FFT and similarly for DCT #\n", "\n", "# End Code #\n", "\n", "tower_ifft2_zip = np.fft.ifft2(tower_fft2_zip, norm='ortho')\n", "tower_idct2_zip = (idct(idct(tower_dct2_zip, norm='ortho').T, norm='ortho')).T\n", "\n", "plt.figure()\n", "plt.title('The tower image')\n", "plt.imshow(tower)\n", "\n", "plt.figure()\n", "plt.subplot(2,2,1)\n", "plt.title('Reconstructed from DFT')\n", "plt.imshow(np.abs(tower_ifft2_zip))\n", "\n", "plt.subplot(2,2,2)\n", "plt.title('The 2D DFT coefficients')\n", "plt.imshow(np.log(np.abs(np.fft.fftshift(tower_fft2_zip))+1))\n", "\n", "plt.subplot(2,2,3)\n", "plt.title('Reconstructed from DCT')\n", "plt.imshow(np.abs(tower_idct2_zip))\n", "\n", "plt.subplot(2,2,4)\n", "plt.title('The 2D DCT coefficients')\n", "plt.imshow(np.log(np.abs(tower_dct2_zip)+1))\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Haar Basis\n", "In this problem, we'll be discussing another type of basis, the Haar Basis. For a quick look at what the Haar Basis is, you can go to the Wikipedia page. Do not worry if you cannot understand it from this. We will walk you through it." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "#Run these to import all of the necessary files\n", "import numpy as np\n", "import matplotlib as plt\n", "from scipy import misc\n", "from pylab import *\n", "# Plots graphs in the \n", "%matplotlib inline\n", "plt.rcParams['image.cmap'] = 'gray'" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First we want to construct the basis. This is discussed in the pdf and the function call for it has already been implemented for you." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def create_haar_matrix(N):\n", " \"\"\"\n", " Creates unnormalized Haar Transform Matrix for rows \n", " N: needs to be a power of 2\n", " \"\"\"\n", " assert np.mod(np.log2(N), 1) == 0, \"N is not a power of 2\"\n", " \n", " levels = int(np.log2(N))\n", " \n", " #Init Matrix\n", " A = np.zeros((N,N))\n", " A[0] = np.ones(N) # DC Term\n", " \n", " #Populate Haar Matrix\n", " for i in range(1,levels+1):\n", " size = int(N/2**i)\n", " to_roll = np.r_[np.ones(size),np.ones(size)*-1,np.zeros(N-2*size)]\n", " for k in range(2**(i-1)):\n", " temp = np.roll(to_roll,k*2*size)\n", " A[(2**(i - 1) + k)] = temp\n", " return A\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "#Displays haar_matrix of size N\n", "A = create_haar_matrix(8)\n", "print(A)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now if you look at the matrix above, you can note something interesting. All the row vectors are orthogonal to each other. You will check this for yourself in part (a). If we normalize each row, then we create orthonomal row vectors which would make this an orthogonal matrix. As such, this matrix holds all the useful properties that you saw in the previous homework. Neat!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## b) Normalize Matrix" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So as to have an orthonormal basis to work with, please complete the function below to normalize the row vectors of a matrix." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def normalize_matrix(A):\n", " \"\"\"\n", " Helper function to normalize the rows of a vector\n", " \n", " A - Matrix to normalize\n", " \"\"\"\n", " \n", " A = A.copy()\n", " norms = np.linalg.norm(A,axis = 1)\n", " for i in range(len(A)):\n", " # Your Code Here #\n", "\n", " # End Code #\n", " return A \n", " " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#Now we can define wrapper functions that perform the forward and inverse haar transform\n", "\n", "def haar_transform(data):\n", " \"\"\"\n", " Haar Transform using Matrix Multiplication\n", " \n", " x - data to transform to haar basis\n", " \n", " Performs the haar transform in O(n^2) time\n", " \"\"\"\n", " assert np.mod(np.log2(len(data)), 1) == 0, \"dimension of data is not a power of 2\" \n", " A = create_haar_matrix(int(len(data))) #Makes correct size Transform Matrix\n", " A = normalize_matrix(A)\n", " return np.dot(A,data)\n", "\n", "def I_haar_transform(data):\n", " \"\"\"\n", " Inverse Haar Transform using Matrix Multiplication\n", " \n", " x - data to transform to haar basis\n", " \n", " Performs the Inverse haar transform in O(n^2) time\n", " \"\"\"\n", " assert np.mod(np.log2(len(data)), 1) == 0, \"dimension of data is not a power of 2\" \n", " A = create_haar_matrix(int(len(data))) #Makes correct size Transform Matrix\n", " A = normalize_matrix(A)\n", " return np.dot(A.T,data)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## c) Plot pulse vector and plot the pulse vector in the Haar Basis. Comment on results." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we will get to what makes the Haar Basis special. First, though, you will create a function call that creates an N-length array $ \\forall n, 0 \\leq n \\leq N$ that follows this function\n", "\n", "$$\n", "f(n)=\\begin{cases}\n", " A & 0 \\leq n < M \\\\\n", " 0 & \\text{else}\n", "\\end{cases}\n", "$$\n", "\n", "Where $M < N$. This is essentially an M-length pulse." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def pulse(N,M,A):\n", " \"\"\"\n", " N - Length of the vector\n", " M - Width of the pulse \n", " A - Height of the pulse\n", " \"\"\"\n", " assert M < N,\"N needs to less then M\"\n", " # Your Code Here: make this pulse using np.r_ #\n", "\n", " # End Code #" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that you have created a pulse vector, we ask that you show how this vector looks in the Haar Basis. Hint: use plt.stem to make a little more intuitive graph." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "N = 64 #Size of vector, needs to be a power of 2\n", "M = 53 #Size of pulse\n", "Amp = 1 #amplitude of pulse\n", "x = np.arange(N) \n", "y = pulse(N,M,Amp)\n", "\n", "# Apply Haar Transform\n", "Y = haar_transform(y)\n", "\n", "# Plot the pulse\n", "plt.title(\"Pulse\")\n", "plt.stem(x,y)\n", "\n", "# Plot the pulse in the Haar Basis\n", "plt.figure()\n", "plt.title(\"Pulse in Haar Basis\")\n", "# Your Code Here #\n", "\n", "# End Code #" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, lets try a slightly more complicated vector." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "N = 64 #Size of vector, needs to be a power of 2\n", "x = np.arange(N) \n", "y = pulse(N,23,3) + pulse(N,36,2) + pulse(N,56,-1) \n", "\n", "# Apply Haar Transform\n", "Y = haar_transform(y)\n", "\n", "# Visualize pulse \n", "plt.title(\"Regular pulse\")\n", "plt.stem(x,y)\n", "\n", "# Visualize pulse in Haar Basis\n", "plt.figure()\n", "plt.title(\"pulse in Haar Basis\")\n", "# Your Code Here: plot it #\n", "\n", "# End Code #" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## d) SpeedUp" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There is another interesting property of the Haar Basis. Due to the structure of the Haar Basis, there is a faster way to transform a vector into the Haar Basis then doing simple Matrix Multiplication using the Haar Matrix Transform. Lets take a look at that now." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "A = create_haar_matrix(8)\n", "print(A)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "Looking at the bottom 4 rows of the 8-Length Haar Matrix above, we see that it we only need the the difference of pairwise points in the original vector to calculate the values for those rows of the Haar Basis.\n", "The next 2 rows can be done similarly by summing every pair of values in the original vectors then taking the pairwise difference of these sums. \n", "\n", "This can be summed in a recursive formula, which includes the scaling term to make sure that the transform is still orthonormal\n", "\n", "\n", "\n", "To calculate the Fast Haar transform of an array of n samples:\n", "\n", "1) Treat the n sized array as n/2 pairs called (a, b)\n", "\n", "As such the array [a,b,c,d, ...] becomes [(a,b),(c,d),...]\n", "\n", "2) Calculate $\\frac{(a + b)}{\\sqrt2}$ for each pair, these values will be the first half of the output array.\n", "\n", "These are the summations used for later calculations of the Haar Basis\n", "\n", "3) Calculate $\\frac{(a - b)}{\\sqrt2}$ for each pair, these values will be the second half.\n", "\n", "These are the coefficients of the Haar Basis for the next N/2 Haar Basis Vectors.\n", "\n", "4) Repeat the process on the first half of the array.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This recipe has already been implemented. It is alright if you do not understand why this is faster. This type of analysis will be covered in future courses. All you should know is that given a vector of length N, the Fast Haar Transform can be computed in a constant times N steps while the Matrix Multiplication is completed using a constant times $N^2$ steps. As N gets large, this difference can become significant." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def fast_haar_transform(data):\n", " \"\"\"\n", " Fast Haar Transform\n", " data - data to transform to haar basis\n", " \n", " Performs the haar transform in O(n) time\n", " \"\"\"\n", " assert np.mod(np.log2(len(data)), 1) == 0, \"dimension of x is not a power of 2\" \n", "\n", " out = np.zeros(data.shape)\n", " temp = np.copy(data)\n", " size = len(data)\n", "\n", " length = size >> 1;\n", " while(length != 0):\n", " for i in range(length):\n", " s = (temp[i * 2] + temp[i * 2 + 1])/np.sqrt(2);\n", " d = (temp[i * 2] - temp[i * 2 + 1])/np.sqrt(2);\n", " temp[i] = s;\n", " out[length + i] = d;\n", " length >>= 1\n", " out[0] = temp[0]\n", " return out\n", "\n", "def I_fast_haar_transform(data):\n", " \"\"\"\n", " Inverse Fast Haar Transform\n", " x - data to transform to haar basis\n", " \n", " Performs the haar transform in O(n) time\n", " \"\"\"\n", " assert np.mod(np.log2(len(data)), 1) == 0, \"dimension of x is not a power of 2\" \n", "\n", " out = np.copy(data)\n", " temp = np.copy(data)\n", " size = len(data)\n", "\n", " length = 1;\n", " while(length != size):\n", " for i in range(length):\n", " s = (temp[i] + temp[i + length])/np.sqrt(2);\n", " d = (temp[i] - temp[i + length])/np.sqrt(2);\n", " out[i*2] = s;\n", " out[i*2 + 1] = d;\n", " length <<= 1\n", " temp = np.copy(out)\n", " return out" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, lets see that this Fast Haar Transform has the same result as the matrix transform method." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "N = 64 #Size of vector, needs to be a power of 2\n", "M = 53 #Size of pulse\n", "Amp = 1 #amplitude of pulse\n", "x = np.arange(N) \n", "y = pulse(N,M,Amp)\n", "\n", "# Matrix\n", "plt.figure()\n", "plt.title(\"Matrix Haar Transform\")\n", "plt.stem(x,haar_transform(y))\n", "\n", "# Fast\n", "plt.figure()\n", "plt.title(\"Fast Haar Transform\")\n", "plt.stem(x,fast_haar_transform(y))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also perform an Inverse Fast Haar Transform with a similar recipe. " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Fast\n", "plt.title(\"Original pulse\")\n", "plt.stem(x,y)\n", "\n", "# Matrix\n", "plt.figure()\n", "plt.title(\"Matrix Haar Transform\")\n", "plt.stem(x,I_haar_transform(haar_transform(y)))\n", "\n", "# Fast\n", "plt.figure()\n", "plt.title(\"Inverse Fast Haar Transform\")\n", "plt.stem(x,I_fast_haar_transform(fast_haar_transform(y)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, we see that the two transforms are equivalent in their result. But, they are significantly different in their calculation speed." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "N = 128 #Size of vector, needs to be a power of 2\n", "M = 53 #Size of pulse\n", "Amp = 1 #amplitude of pulse\n", "x = np.arange(N) \n", "y = pulse(N,M,Amp)\n", "\n", "# Time Transforms\n", "print(\"Matrix Haar Transform\")\n", "%timeit -n 1000 haar_transform(y)\n", "print(\"Fast Haar Transform\")\n", "%timeit -n 1000 fast_haar_transform(y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can see a significant improvement in speed." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## e) 2D Haar Transform" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you have seen in the 2D-DFT part of the homework, we can also perform the 2D-Haar Transform. The recipe is exactly the same. First, you perform a Haar Transform on the columns of the image and then you perform the Haar Transform on the rows of the image. " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "campus = misc.imread('figs/campus_256.jpg')\n", "plt.imshow(campus)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Take Haar Transform of columns\n", "\n", "# Your Code Here: take the transform along columns #\n", "haar_campus_col = #Perform Haar Transform along column, use whichever you want\n", "# End Code #\n", "\n", "# Take Haar Transform of rows\n", "har_campus = fast_haar_transform(haar_campus_col.T)\n", "\n", "# Take absolute log of har values to better see them \n", "har_campus_log = np.log(np.abs(har_campus.T) +1)\n", "\n", "#Plot 2D Haar Basis\n", "plt.figure()\n", "plt.title(\"Haar Campus (log scale)\")\n", "plt.imshow(har_campus_log)\n", "\n", "plt.figure()\n", "plt.title(\"Haar Campus (linear scale)\")\n", "plt.imshow(np.abs(har_campus.T))\n", "\n", "#Plot original image for comparison\n", "plt.figure()\n", "plt.title(\"Campus\")\n", "plt.imshow(campus)" ] } ], "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": "3.4.4" }, "name": "_merged" }, "nbformat": 4, "nbformat_minor": 0 }