{ "cells": [ { "cell_type": "markdown", "id": "0028db97", "metadata": {}, "source": [ "Title: Sequence Learning Tasks\n", "Author: Thomas Breuel\n", "Institution: UniKL" ] }, { "cell_type": "code", "execution_count": 45, "id": "e370c77d", "metadata": { "collapsed": false }, "outputs": [], "source": [ "\n", "import urllib2" ] }, { "cell_type": "code", "execution_count": 2, "id": "90951d11", "metadata": { "collapsed": false }, "outputs": [], "source": [ "default_n = 29\n", "default_ninput = 2" ] }, { "cell_type": "markdown", "id": "6a8232fa", "metadata": {}, "source": [ "Here is a number of sequence prediction tasks. For each of them...\n", "\n", "- think about how you would solve them at all\n", "- how you would learn them with a dedicated machine learning algorithm\n", "- how an AR and MA model would solve them\n", "- what kind of complexity learning might have" ] }, { "cell_type": "markdown", "id": "832f34f4", "metadata": {}, "source": [ "# Non-Sequence Tasks" ] }, { "cell_type": "code", "execution_count": 17, "id": "3e8df6f6", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[,\n", " ]" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXUAAAD5CAYAAADY+KXfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n/wcP+hK9qz8TawAAAABJRU5ErkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def generate_threshold(n=default_n,ninput=default_ninput,threshold=0.5,example=0):\n", " \"No temporal dependencies, just threshold of the sum of the inputs.\"\n", " x = rand(n,ninput)\n", " y = 1.0*(sum(x,axis=1)>threshold*ninput).reshape(n,1)\n", " return x,y\n", "\n", "x,y = generate_threshold()\n", "ylim([-.1,1.1]); plot(y,linewidth=3,alpha=0.5); plot(x)" ] }, { "cell_type": "markdown", "id": "d435ec70", "metadata": {}, "source": [ "# Sequence Generation Tasks" ] }, { "cell_type": "code", "execution_count": 18, "id": "ba25d749", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[,\n", " ]" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXUAAAD5CAYAAADY+KXfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nHBwcSQRu1Dk4ODiSCP8LtKmNDqKgi/YAAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def generate_mod(n=default_n,ninput=default_ninput,m=3,example=0):\n", " \"Generate a regular beat every m steps. The input is random.\"\n", " x = rand(n,ninput)\n", " y = 1.0*(arange(n,dtype='i')%m==0).reshape(n,1)\n", " return x,y\n", "x,y = generate_mod()\n", "ylim([-.1,1.1]); plot(y,linewidth=3,alpha=0.5); plot(x)" ] }, { "cell_type": "markdown", "id": "05757a66", "metadata": {}, "source": [ "Generalization:\n", "\n", "- periodic function generator\n", "- pattern generator with triggers" ] }, { "cell_type": "markdown", "id": "ccc87ebd", "metadata": {}, "source": [ "# Counting Tasks" ] }, { "cell_type": "code", "execution_count": 22, "id": "df18f123", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[,\n", " ]" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXUAAAD5CAYAAADY+KXfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def generate_imod(n=default_n,ninput=default_ninput,m=3,p=0.2,example=0):\n", " \"\"\"Generate an output for every m input pulses.\"\"\"\n", " if example:\n", " x = array(arange(n)%4==1,'i')\n", " else:\n", " x = array(rand(n),\n", " ]" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXUAAAD5CAYAAADY+KXfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nHMqwUzIvwIoAAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def generate_smod(n=default_n,ninput=default_ninput,m=3,r=0.5,example=0):\n", " \"\"\"Generate an output for every m input pulses. The input\n", " is band limited, so it's a little easier than generate_imod.\"\"\"\n", " x = rand(n)\n", " x = filters.gaussian_filter(x,r)\n", " x = (x>roll(x,-1))*(x>roll(x,1))\n", " y = (add.accumulate(x)%m==1)*x*1.0\n", " x = array(vstack([x]*ninput).T,'f')\n", " y = y.reshape(len(y),1)\n", " return x,y\n", "x,y = generate_imod()\n", "ylim([-.1,1.1]); plot(y,linewidth=3,alpha=0.5); plot(x)" ] }, { "cell_type": "markdown", "id": "77ac9a35", "metadata": {}, "source": [ "(sum/product problem)\n", "\n", "Input consists of two sequences:\n", "\n", "- value sequence (values in $[-1,1]$)\n", "- marker sequence\n", "\n", "Output:\n", "\n", "- sum of the values marked by the marker sequence\n", "- product of the values marked by the marker sequence" ] }, { "cell_type": "markdown", "id": "c3f46b49", "metadata": {}, "source": [ "# Language Recognition Tasks" ] }, { "cell_type": "code", "execution_count": 34, "id": "f9d11241", "metadata": { "collapsed": false }, "outputs": [], "source": [ "def generate_anbn(ninput=default_ninput,n=default_n,k=default_n//3,example=0):\n", " \"\"\"A simple detector for a^nb^n. Note that this does not\n", " train the network to distinguish this langugage from other languages.\"\"\"\n", " inputs = zeros(n)\n", " outputs = zeros(n)\n", " if example:\n", " l = n//3\n", " else:\n", " l = 1+int((k-1)*rand())\n", " inputs[:l] = 1\n", " outputs[2*l] = 1\n", " outputs = outputs.reshape(len(outputs),1)\n", " return vstack([inputs]*ninput).T,outputs" ] }, { "cell_type": "code", "execution_count": 35, "id": "f4f8e9cc", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[,\n", " ]" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXUAAAD5CAYAAADY+KXfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAAAElFTkSuQmCC\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x,y = generate_anbn()\n", "ylim([-.1,1.1]); plot(y,linewidth=3,alpha=0.5); plot(x)" ] }, { "cell_type": "markdown", "id": "0c3d9ed8", "metadata": {}, "source": [ "General symbol coding (input or output)\n", "\n", "- unary coding: if there are $n$ symbols, the vector is $n+1$ dimensional\n", "- symbol $i$ is represented as a vector that is all $0$, except for entry $1$\n", "- this is the same way we represent classes in other neural network classification problems" ] }, { "cell_type": "markdown", "id": "53536069", "metadata": {}, "source": [ "Other language recognition tasks:\n", "\n", "- Reber grammar\n", "- embedded Reber grammar\n", "- $a^nb^n$ - context free language\n", "- $a^mb^nB^nA^m$ - embedded counters, context free\n", "- $a^nb^nc^n$ - context sensitive language\n", "- long time lag probem $x,a_1,...,a_n,x$ vs $y,a_1,...,a_n,y$\n", "- simple 2 sequence problem: $a_1,a_2,...,a_N$ signal followed by $t$ noise elements\n", "- temporal order ` .*A.*B.*` vs `.*B.*A.*`\n" ] }, { "cell_type": "code", "execution_count": 49, "id": "b6dff3d2", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXIAAADzCAYAAACbv53AAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nKo4SOSGEqDhK5IQQouL+H6l0BDEmXpYZAAAAAElFTkSuQmCC\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "imshow(imread(\"reber.png\"),cmap=cm.gray)" ] }, { "cell_type": "markdown", "id": "0bb4ccbc", "metadata": {}, "source": [ "What does \"learning\" actually mean?\n", "\n", "- training strings of length less than 100\n", "- testing strings of up to length 1000\n", "\n", "Tests may mean one of several things:\n", "\n", "- detect when the language is accepted\n", "- take an entire input sequence and output TRUE/FALSE\n", "\n", "Does it generalize?" ] }, { "cell_type": "markdown", "id": "c1b48313", "metadata": {}, "source": [ "Claim: LSTM networks learn non-regular languages\n", "\n", "Discuss..." ] }, { "cell_type": "markdown", "id": "b41ede0f", "metadata": {}, "source": [ "# Timing Tasks" ] }, { "cell_type": "code", "execution_count": 37, "id": "5c823ccc", "metadata": { "collapsed": false }, "outputs": [], "source": [ "def generate_timing(ninput=default_ninput,n=default_n,t=5,example=0):\n", " \"\"\"A simple timing related task: output a spike if no spike occurred within\n", " t time steps before.\"\"\"\n", " x = 0\n", " inputs = []\n", " while xt:\n", " outputs.append(inputs[i])\n", " inputs = inputs[1:]\n", " xs = zeros((n,ninput))\n", " xs[inputs,:] = 1.0\n", " ys = zeros((n,1))\n", " ys[outputs,:] = 1.0\n", " return xs,ys" ] }, { "cell_type": "code", "execution_count": 39, "id": "9c3335cb", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[,\n", " ]" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXgAAAD5CAYAAAAtBi5vAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nChUqVDhBUQn4ChUqVDhB8f8BrqUnEZXxVpAAAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x,y = generate_timing(n=100)\n", "ylim([-.1,1.1]); plot(y,linewidth=3,alpha=0.5); plot(x)" ] }, { "cell_type": "code", "execution_count": 40, "id": "6d94bd4b", "metadata": { "collapsed": false }, "outputs": [], "source": [ "def generate_revtiming(ninput=default_ninput,n=default_n,t=5,example=0):\n", " \"\"\"A simple timing related task: output a spike if no spike occurs within\n", " t time steps after. This cannot be learned using a causal model (it requires\n", " a reverse model).\"\"\"\n", " x = 0\n", " inputs = []\n", " while xt:\n", " outputs.append(inputs[i])\n", " inputs = inputs[:-1]\n", " xs = zeros((n,ninput))\n", " xs[inputs,:] = 1.0\n", " ys = zeros((n,1))\n", " ys[outputs,:] = 1.0\n", " return xs,ys" ] }, { "cell_type": "code", "execution_count": 41, "id": "f8716f78", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[,\n", " ]" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXgAAAD5CAYAAAAtBi5vAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzsvX3QJdddJvb0Oaf73ve1LBsj1sEzCrItVSQwspWSMYbC\njAlEGlcxpPhasUnKaytmokLLR2EgIR9YVEIhllSKoK1EYDAFGK1IhaxMlRnXChgoDJYIYDvEXnls\nIzwadg3CaGU8773d5yN//Pp0n/667+3T59zpV9ynymW9M+/06du3+9fPeZ7fR2KMMdhjjz322OMF\nB3atT2CPPfbYY4842Af4PfbYY48XKPYBfo899tjjBYp9gN9jjz32eIFiH+D32GOPPV6g2Af4PfbY\nY48XKMSuFkqSZFdL7bHHHnu8oOCbzb5TBm+M2f/PGPzYj/3YNT+Hufxvfy3212J/LTb/bwr2Es0e\ne+yxxwsU+wC/xx577PECxT7AXwOcOXPmWp/CbLC/FjX216LG/lqEQWKmijzbLpQkk/WkPfbYY49/\naJgSO/cMfo899tjjBYp9gN9jjz32eIFiH+D32GOPPV6g2Af4PfbYY48XKPYBfo899tjjBYp9gN9j\njz32eIFiH+D32GOPPV6g2Af4PfbYY48XKPYBfo899tjjBYpjA/zb3/52vPzlL8dXfuVXDv7O937v\n9+KWW27Ba1/7WvzZn/1Z0BPcY4899tjDD8cG+Le97W24cOHC4N+///3vxyc/+UlcunQJP/dzP4f7\n7rtv8Hc/9zm/k4yNq1eBv/3b3az1uc8BX/jCbtbaFbQG/uqv6P9DwBg6nlJhjhcDn/0skOe7X/dv\n/5bu19gwBvi3/xYoivhrbULoZ3O9Bv76r6cd47nngM9/Psz5uJAS+PjHgaeeAj796TDHPHbgx9d9\n3dfh6aefHvz7973vfXjrW98KAHjDG96A5557Dp/97Gfx8pe/vPO7n/gE8NVf7X+yMfD888DP/NS/\ng7r6DL7zv7oTX/7l8db6xCeAX3v4w2CLG/DPfug0vuiL4q0VCn/23v8Fxeefox8Yx+3/5PuxvO6l\njd9573uBv3jiAm590934zu+cvua/+lfA//s7H8DpO+7C298+/Xih8cEPAo8/+js4eMXX4Ad+cIk0\nnX7MK3/+R3jZf/gf4eD6lw3+zsc+Bvz6u/8f8MPT+L4f/g9w/fXT1x3C448Df/S+D+ClN38T7v9n\nDMxTzP2LJz6AV77hrtH/5m/+7A+wXgN//CTw+Ru+Cd/+3W/CV3yF3zlYrNfA//rTf4/1X/8pzv7n\nb8JXfdX4Y/zlXwK/9C/+P4Ad4r/+gVeiJ8x5Y7UCHn3vczj4y/8d7Pb/Fj/0Q9OPOXmi05UrV3Dj\njTdWP58+fRrPPPNMb4D/+Z9/F+xm4MyZM7PoGPepTwHX//n/gJv+8iI+8aZL0QP8V/z+f4G/fvnt\n+OQnfw2vf328tULgub/6C3zFW9+JD9/+jwAAr/zE3+DPhcCdb//vq9+REvjkU8/jv3n4LH765WGa\nyT31FHD/u8/if/u+v8DR0Zfh4CDIYYPhqaeAu973rfidN/9P+Ku/uh9f9mXTj/mX3/2d+Mx33oM3\nfv8/37juHb/7XXj6y87g05/+ebzuddPX3bTWPf/yHP7lP34Mn/vc3bjhhvHH+OylD2P5n74F+Pfj\ntmLPnv8vcfj8VRTXvQjf+Defx2f+0Xvx1Nd/enKAv3wZwL95CG/+o5/GU3c+6xXgP/EJ4NV/eC+O\nDl6GS5feHzTAaw0kVy/h1f/Xf4ef/+t1kJ1+kJF97U5nQ+P5/uk/fRe+7utCrBgOSgFcXoWQBVaR\nJQGlgFTmYHI1a/nBIj/6PIqDBF/1p58FADz5H78cZr1q/I5SANTf40ACUmoYwzB1OqNSwFIaQH5+\nltdJKWAhJbi6Guz8+LqAXG/WXmjdHFzFv39oLQ2m/t57rfwLz+NQjn/p80Iif+B/xMFX/DAe/4nv\nw23/5v8O8nnpWf8CMim9j6cUIOQaXK6DfwdaA4le46syhst3vws/8AP05w888ID3MSdn0Zw6dQqX\nL1+ufn7mmWdw6tSp3t8NpdGGhNYA0xJcq508NFwrMC1neS3aUPkaktXRWgsOUzSFZ3tTAkBi8iCf\nSylAaAB6NcvrpDXAtUai82D3DFMa5hjBm9ZVSHSxo3vVANo/kKl8DaHHB3imNFiaQSnAsAxcqyD3\nAd2rObjWkwI80wrMhH+GtQagjiBZAs7DHHNygD937hx++Zd/GQDwoQ99CC996Ut75RlgzgE+D3YT\nHbcW1xJchwmEsSHXR1C8GeB1vm78jtYANDFPo65O/lzGAEppZBpgMw7wQhkkah3s/JhUMMe4tloD\nXCkwFf/+0RpIJ35Gma8gPAIplwosW0BrQPMFuAoX4JnOIbT2Pl71DKsi+HegFAC9huT+nkcbx0o0\n3/Vd34Xf+73fw7PPPosbb7wRDzzwAIqSaZw/fx5vectb8P73vx8333wzXvSiF+E973nP5g8wMygF\nMJVDBLqJNqF+QOMzsBCQ6yMkor7TjOCd1BGSaI4AAIm+Cq2HTcJtYAztBOjgR7O8TrTD0GA6XIDn\nUnV2R/3rKnAdPri0oTUgtJn0klXrI6Qe/5ZJDWRLaA0YtoAItLtWCkjUGlxNDPBKgml/mWfTsZle\nQbFkdwH+kUceOfYgDz300FaLzZWNWYlmNww+zvYuBlSRI3EkGsM5IJsygivRIEDA06U0E+p4MUDf\no0ESMNAypWHk8RIN0xpshwE+mbDb1EVOUttIcG1gsowYPEvBJzDuxvlogOkCQptJAZ5esrEkmhUK\nFo7B77SSdb4PazFJl9sWFQOLsL2LAbU+guIOg08FdN6nwZcBOQDjVoqkHmDeEk2qNBIVzmhjSsPk\nxwd4saMdoFJAqgBMMHRVvgIzRBTGgEsNnh3QunwZbHftSjRTNHiuJZgKH+CVIo9AMTYfDX4M5viw\nkmkig7GETagZWPjtXQzoIocSDoMXosPg6aa0DH56QG7vCOZ4nawBGZJJc6U717Z/Xb2THSAxVUz6\njLoM7DJfHfObTXBlIBbLksEvgpEvetYL8IkMnpcMPpZEE1KD32mAn+PDWm3bdqTBCxVnexcDKl81\nGfxAFg0UPcAhGLdr2oY0MUNCayDVBiygWc6lObZslIKu3skO0BrdyQSZTJUptcUx6Z9tcKXB04Wj\nwYeTaBKVI52swceTaCyD35kGHxJzfVi5kpO2bduiMucibO9iQK1XSBoBPgXyPg3+qPwHYSQaa9rO\nWaIRpTkfLA9e6e0CvIq/A6SXLL3I2QQZymZcydXRqH8nlIFZLEmu44tJpmjjfEo5VmgzLQ9eK3Cl\nIGNk0ahVUIlmH+Ark9V/2zZmLa71iWHwusgbAR5iyGQtWX0gk7XKq59pOmltQAaUaLShsuBj1t3F\n/eMa3VNNVsBDotEGpmTwYItJpmjjfAKZrCSzht/x07HXkJyfTAY/R4nGmiYiEEvYBMvAYuh3MaDz\nNQV1izTtsExKPQsr0dSm7TwrfpUC0pINhrpnhDyewRN7NNF3gFq7RveEAG8ZfO7B4JcHpQa/DLa7\nppToAkL5k00rs4pIGnyii71EExJWokl3KNHE2N7FgMrXSI4J8JZ10D+YHpCbEs2MNfjgEs12DH4X\nBME1zqd8Rl2UAX49LsCnysBkh2UWzUEw8mUlmnSyRKODFV+1j83UGorxfRZNKFCAUjuUaEyU7V0M\nmCKHbkg0ohOEXIkmhKTSPN780kltpa0wCNpyQmiDZJsAr82OJJrS6J7wHdjWC6pV/XwcuAZ4Fkui\nkRB6GoMnmSz8jt/e+5KLfRZNKNAbWUKo3QR4oXSU7V0M6GINvZVEU7K9YBJNyeAD5pmHgqtPB5Vo\nFIBic4C3Ek0M9uiCMqPsLmqKREMvajVSg08VkC4PHYnGn3G7sGmS6WSJRkfpXUUvoBx6X+gUDpbB\nh2IJx61F5d/x9f4QMEVB7QksRArI5l0dl8HPz2R1A3xIBs+1QSI3R4z6/okf4CuJ5howeKEBUbYq\nQBngw0k0CqLchRmP7taxGTxTORQ7oQx+bg8rUOe1hmIJm2AZ2C5y7kNA53kjwCdZiqQniya0Bl+b\ntvMM8Im2BmS4itJUYTuJRpnoO0DS4MvvYELVrK2ZUOvtGbxWEtwAXGSOBh8mdlAALe9fz91mzGeY\nrnsBxcXJ1ODntt0G6rzWdEcSTarMTloTh4Ap1tCi9uGTNEPSkhGaEk2YNEkWwOCLBdcE5gGzWVIN\nsGMCPGXv7EaisQx+SudT4yHRFKuryDmQMEbZPOxgkinqwmbMAbYx3vhj1DJr+KQMK9EoFi5Ncs/g\n7bZtgvEybi2zk7YIIWAK2ZFoEtUn0RArCmGKzt1kJYnGvtDCBHijNYTGlhINot8/pMEHkKHK3Z4e\n0YtG5itI5pwHWwZ7Nu2zTj/4Mfja6I4k0egiqESzT5MsJZpUx99hWAZ2UiQak+eUOVOCZVnHCKSH\nZnrVo0VzRzBXiaZk8IGkEpmvkGK7AJ+WQ2PiSzTWZJ0i0VgNfnsGL9dHFe1UCkj44SRT1IUuU6Lp\n4H5V17VEEz7A2zx9zU6oRDO3hxWoTZNdMfhdMLBgkEWj0Ck5lsGHNVl30RZ3LJryRZgXta30ZGrz\nwXbJ4OvvYPcM3g6Z0RowSTbJFHVhEyroBz85sWbw4T07S5bUPk0yHKrCBQMYLSffRJtgGdgu+t6E\ngCkKmDStfk6yrMMyVVnwA4Rh3E0Nfn6DUWJo8LYZF9vA4LUGtMrBgOg7QK1ro3tSY7OSwbengG2C\nXB9BOgE+SRgKBm9JxYVStUST6KMJGrxBGk2ikdAsPZkBfm5sDKhNE4DKs2MFFGNoKHVWrjfHa9FB\n0ZZoFp0gZI0hIIwp6ko0cxxtSOzW5sEHkmjKZlzHBXibvRObIFC+uP0OJnzGiQHerlswf1PUBT3r\n0yUaklnDJ2XYPP29RBMQVqKhH+J1LzQGgKGbaxdVs0EgZSPAJ2k2EOBtZkIok5UCwxyHk7sSTah6\nBlXYHcvwwcjctS+WkyLR0H0xRqJRxRqK1QweAJmugYroWHkQ3zbItUwW/hm2z5I6qQx+btttoJZo\nAP9t2zZwGdgu+t4EQVFQ9WoJlnYZfAyJhjsa/Nyuk23pChAbDKLBl71a+AYG70pDsXeAJNGUDH7K\nZ7QB/phh4o1/sl41JBoAKHgSrBW1qCQa/yyatGTxUTT40mQ9kQF+bmwMqFMX6Yd4DL7JwE4mg2dp\n2mGZLoMPEZBPBoO3L6DQDH7YANrl/UNZNPYzTsjYKQO8kdsHeJ2vGyYrACgGb1O0cWxntz5XBs+1\nhObZvh98KLgafAiWMIQmAztBAd5h8HyxBHoCPLcBOcCkIXdHMMfZtfRCKxl8oHRFq8HzDQdz0zNj\n7wBdo5tr2f7Kt4YtijMjGLzKV0DZ4K7W4JMgu2t61suDelRdu0Z3jMJI0uD3Ek1QWNMEiC/RoJJo\n4rdFCIGkKIA0q35m2aIjI1hjCAhjirqm7Rz75jclmrBpklwOM/hdEoSmROP/GW3rhTEBXq5XUIJV\n5wEAkrNgEo1l8D6N8Zoya/h4RhKNhAkY4PcMvtxukVMfr/+4NecKdpIkGoWkIdEskLRkBCvRFCyM\npBL6eKFhJRr6HgP1KS/W5ec9zmTdzf1jZTJaa1qALxhgjhkm3li7WCNhrQDPkiDPJskrunzWx5MR\nK5MVDFHqZlyJ5kQy+Lk9rIA1TQyOBKJOELIM7EjE2d7FQCIlkqxm8HxB8zFdWNZxJMJo8FaiORJh\ne72EgpUvjgQF+CA9UtYrHKXEzDevu6L7J/IOkJhu+R1MkKGSQuEoHcfgdb6uGLxdlwJ8mCwarrT3\ns958hsPHM9oNKxiWnsw0SeUr5kUE3cwGqzQMSxiCZWCrNIGIsL2LgURKJI5Ew7ODjslqdcNVmgRl\n8HS8+TVlsx3/6HsMZbLmWKcJTXXasK69f3bF4GmtCQxeKazTBOaYJmqNtYscuiXRKMaQ6DBtMET1\nrPsz+LUgE9gE3mHSC0hBsRPK4ENfkBDQmhjRSrAgLGHTOkyvsBIMaYTtXQwkhULimqxpBiG7Eg3X\nEivBgpii1rRdCTbL4eRaU88d+ryBJJp8hXXKarN/YN1ElffPDjR4pnKsBJvkMzApsU4ZFcxtCZWv\nqilitQafACoMgxdaYyWYV+dTa3QrlkAyKowMHuC1guGLkxngQ1SjhYbNaz1KOZLoEs0KRymPsr2L\ngbZEIxYHwxJNyoOYota0PUp59La4PqgkmpQHy2ZR6xVWC36sRJPo8v6JvAOk7yAvv1P/z8ikwmrB\njx0m7oIkGl6dBwBIxoNNCxNKl8/6+B2BlWgKlqDg4eOZbaVwYiWa0G+8ELB5reuUB8m13bROotfI\ny5s3dt+bEGBKIRGuRLOoawZKWNaxTnlQiWad8mDNvELCyhd0foEmDRU5ioyDbziWNXfXKY/eGK/5\nHfjvUhKpUWT82GHiLkxRwJTRrZZoSFIJUWMhtCnv1fG7TSuzSp6U/XHCjpS0aZya7ZDBX7hwAbfe\neituueUWPPjgg52/f/bZZ3H33Xfjda97HV7zmtfgl37plwaPFUJHCwm3P8xaiCADK4ZgGZi7vZvT\ntegDk4paBJfg2bLDMu0QhbUQQUxRuyNYCzHLwSjWBF4LEayiVOdrFJnYyOCpR88KayGi7wCtREOf\ncYJEoxSKTIxm8HYOcC3R8CASjdXgfZ91K7PSM5wAsSSaXWnwSincf//9uHDhAj72sY/hkUcewcc/\n/vHG7zz00EO444478OEPfxgXL17ED/7gD0IOvbFnJtEYAyQmh0qAgseXaBK1gmQsyvYuBhKpwLJF\n9bNYHnSMQLrpNdZpGkyi4brAOk1n2TefPm9O5xcom0XnaxSLFOmGY1lpKC/TVrWK14jNGuf0Gf0l\nGi4VikV3UPsm2EHvxjRN1lDTwoQyWKcpEo/GeFZmLRiD5GGKr9rnx7WG4YvdSDRPPvkkbr75Ztx0\n001I0xT33HMPHnvsscbvfOmXfimef/55AMDzzz+PL/7iL4YQ/en1MbNUfGBdccmsUx/vobFbbMVY\n2TxpXteiD0xpMCeLRqRLpK1zpodGYi3SIMOgKZAprEU6b4lGpOGGQRcF5CKF2EKiqe+fuAkBvPyM\nU2QopjTkIh1lGNhB7+6akvFgswaERnmv+kk0iV7XDD7wM2wLsUJKNBsLna5cuYIbb7yx+vn06dN4\n4oknGr/zjne8A9/wDd+AV7ziFfj85z+PX//1Xx883sUP/gsc/c83YrkEzpw5gzNnzkw7+4lQiqSS\nggGK8+gSDdNrSM5RlNu7uckPbXCpYFwGvzjoFDpZY2idLsCVQhFIosnTDMtinjNZmcqRp1mwilJT\nrKGWGVJN4/uSnqfbtlFWjDs7wOunL94DuleL8jP6y1BMaqhlRhXRW8JOEXPXVNzPFG3DVq3naebV\nGM/KrJKzUqIJ29rEavCf+uzT+JmfeRde8pLpx9wY4JMkOfYAP/ETP4HXve51uHjxIj71qU/hm77p\nm/CRj3wEL37xizu/++av+ie4/4f/E7zsZf4nHBL2jVzwpGQJ8XqfNBgYD//2jwGmNIzL4LMlkh4G\nz7VGni6wyKdLXFaHzNMFuH5+dtfIGpB5ughmdtJgFUHMXOYQ2bJ33UTnJUFA1PvHSjT0Gf1lKKY0\n1HIBHDOK0IWRBcCbDJ4kmjApuEIDebrwetar76CSaMLu+G0a5ytP3463/uDbcPo0/fkDDzzgfcyN\nG4FTp07h8uXL1c+XL1/GabtqiT/8wz/Ed3zHdwAAXv3qV+OVr3wlnnrqqd7jzVOiuVpKNGFYwhBc\nBiYDNU+KDSY1uBNs0uVhRye2rCMXiyCSijVtc7GYrQbPdY5cLIJVlOo8h+EckgHF6urgukzn0IxV\nBl+se7XaRYnFpGIuoTT0clH1pNkGpshhUtH4bIqF2V3blOhcLLyG01gfjWQyFvwZtkWXhoXrJrkx\nwN955524dOkSnn76aeR5jkcffRTnzp1r/M6tt96Kxx9/HADw2c9+Fk899RRe9apXDXyCeLqhD2xe\nq2TJTiWaGNu7GOBKgzkBnosM3ABa1Q+s1Q1lugwSkCm4KDpeoDzzkCCJpoBMl8GyWUyRwwiBgtXj\n+/rWTdQakokoBp8Lu0uh79RfhuLKwBwswYoRAT4vgLQl0TDuZYo2jlvOdRUGkGIB7sng3Wc4dFIG\nkSUNww52o8ELIfDQQw/hrrvuglIK9957L2677TY8/PDDAIDz58/jR3/0R/G2t70Nr33ta6G1xk/9\n1E/hZQMazNzSJK1EI1kCzfxyY8etVVQMLKahGwq8JdEkjOZjmnyF7OA6ALVEU4hlEAZvJRo63vx6\n9mgNMCNRiGU4iaYcbi55AgyMt7O6uC53gLFrNriWWC9ePMlIZkoDy2VnUPtGyAKGtzV4MfnZrBIq\nEv/juTJrjKQMkmgMwJe76yZ59uxZnD17tvFn58+fr/77hhtuwG/+5m9utVjMVgA+qE2TBJKJySxh\nE5oMLPz2Lga4MjCLph5ccMCsrjYCvFAaRXoYpPmWNW2L9HCWs2tph1EgT18EUbJCYxi2sKuGkeeA\n1eDL6U596zKdQ+1gB6gUSTRFejhJgxfKAIeHnUHtG1EQg29KNGLytDB61q+i4KCh1h4D3RsyKw/f\n2oTy9DUM21GaZGgkM5NoagbPgrCE49Ziuqge0JPA4JnS4E4WDUDzMW3/csBl8IdB2ue6xwuVhhgS\nVr7QPC3Nzun3tJESRqRENJxr2123gKokmrgpvbSLOpy0S+HKAAcjA3w5Rawj0UzsVGoZfMFAAzXM\n+KI81+iWJYMPL9EYGBaOwe+4F8280t5s4UIt0cR9aMgk47S9i1hUFQpCmYbJClDjJ+mwTEo901Dp\nYTANXihFx5upBs+1hGYpJAtUsFbkgOBQPKGJRgPrJiqnAB/B4HNhJRqVHk5qbCaUATs87Mzx3Yhy\nDrC7puYCbGJhl+u3aSa8GuO5Rrd9hmNINGaXrQpCIqaJ6QN6Ix9BckbbQI9t27aw+dOqkmjmtZvp\ng1AGYnHQ+LN2gLesQ6bXBQnItWl73SxHG2oNMEVj1YpQLSfKoKZ4Uo3v61uX6wKaiygGnwtKk6Tv\nYEpjM6EM2Iuu8wrw7pqaCS9T1EX9rAOapzQaz1OiIZk1fFKGbaUAfnAyZ7LOTZZw81oV96tuG7dW\nAcVFtb2b07XoA1emUegE0ABk4xiBVlKR4rogpqh7vLlKNFxLGJ6h4IFmCJSzbyVnQLHZZK0JQtzd\nplCy/A78JRqhDfjhdZ0ZAhshVY9EE8pkXaNgCRTLvFpRuzKrClRd2z6+0ADY4clk8DHzzH1Q57WS\nRDOVJWxCxcCYOFESjcjaDJ5B5k2JRmgDnV4XxBS1pq1OrwvW6yUkXIlGsUBzfIsCEOJYiYYp5/6J\n3qpAQYtDcOPf+VQogL/ous4c301IZIEkzVpZNH6mqAsr0ahSomEejfG6Mmv4bpKp2ks0weCaJpql\nUWeANhlY+Ld/DAhtkC4PG38meQLVYvBCGyjx4iAB2TJ4Ol7crok+oO9RQbOMWk4EZPCKM6iNDF5C\n8TT6DtDKZIYtkJdGss/3KjQgXvTi8Qy+FeB1IrxMURc2oaLgDIZPZPBMUPuEwIRQaxrmnfDDE5pF\nE5Eh+4C+sDUUY/RWDzBTdAguA9OBuuPFhlDoZNEonkCtm1k0Qhno9PogI+ysaavT62c5u5bSJFXJ\n4AOlK0oJiBSaM6j1cIDnuoBO4u8ArdFtjWTfOQ6pBtIXXT8qwCeFRNJKk9Q8nTwtTOu6Xbdmfp1P\nXaM7VHVt+/hCA2Yv0YRBndfKoNj0m2gT7ANKDCxuW4RQSDWQLpoMXnHWkBEoIAM6fWkQU7R+Ybw0\n+uQiH9BDKGH4AkWgeoakkEiyFEow6E0SjS6geRrF4HNhd1Hgy7Kx2fjPqMoxfeLgReByRIAvp4g1\nGDwTXqZo43yqLBoGzTKvaWGu0U1JGeGyAk0phXEDIBHT6ioc7NRk5TOTJRoSDc+CtLvdtBbTElIs\no2zvYkBowLTSJDVPYIquRKPFS4JKNHS8uUo0GpplweoZEilJluDD80utLq5YFsXgc+G2rSUZavxu\nQeYrgAF8sQQ2DDJpI1GKdjMNk9VPUnFRP+uJ97MeU6LRmnZKOQM4n1g452Av0WiqTLOpWHFTz6xJ\nFpeBhYBlYNxpVQBQ69a2RJMqwKQvCZL1UqWKiesmGXyxYOULwzIoxoJINImUSCqJZkOhk2uyRtwB\nWqPbsEUlQ439Xos1NfFj6aIzx3cTWCGRpIuORONjirqgZ50ahRmWQXhKNPV3IIISVqUAO5silP4O\n7NpkjTiFxgda16XHmmWTb6Lj1uJKlgxseuFGbBRr6pPfhhIM2mGZNrXLiJcG0cxtJoFmS+QRJtdP\nhWXShi8geRJkGHRSKCRZBiU49IZeNFxLaJ6VjfFiV7LqUobya2wmV5RzLrIlxBgNXiqwRVOiMZ6a\nuQutURY1TpdoFE+hArc2oR3GEQqOYPo7cA0Y/Jw0VaXKc6oYfHyJxjL4uV2LNmRObKINzVkVhNwO\nfSaQpEIPkQHYsppcNKfrVGeYZMEaTiVKIUlTaMGhZf9wDNujx7A0ukRD2RwaYItShhq/26T7J6FB\n7SMkGqY0mGilSQaQaOhZzysG79NWo3qGE1FWvocjhFqjbKWQBA3wO9bg5yfR8LKBky5Tp6I2cKoY\nWNjtXQzI1RGSnq2iFgymNAKJdRDTT/hhEFPUmrbgB94GX0zUGSYLSMaAANksTEogXcBwBrMpi0ZJ\naGcHGPdepV0UNTbz0eCPkPCEKqHHBPhyipi7nmEptZCeLNFQq1/DF14D3SuZNbsOiqfhJZoyTz+k\nRLPTAD83WYICFJkmmtGXnkfd9qrqAZ2bH9GGzFdIWNfp0ZzDlCPYatZBqV2hGDz14zioDL45Xada\nvlgGq2dIlEaSLaBSAchhk1VoVUk0saePCaUBflBWzY5n8CpfAzxBtjgA9BgGr2A6vWjIFJ0q0VDV\nOi+fdT9XuaQIAAAgAElEQVQGb43uEJk93fM7QsFPMIMPeUFCwPaH0YyXLCG+Bm9YStu7iH1vQsAy\nsDa04FXPcqVII5cMQCIcU9Q/zcuatmDLcHnmAVG3dM3KUXLTzXJWKCBNYTij1sED69YSTdwdoH3J\nojRZfapm5ZruH54ukIz4/pjUQLZspUkuIEJINGVKtGGZV2M81+jWZe+qkBKNHeh9YjX4OUo01GNb\nlBJNXA2+lmjCbu9iQK6PaABFC6QTUxCyN2XBEyQJq0zRqUzLVvP5GnwxUWeYLKt6hskBXimwbAEj\nBPRAgKd1JTRbVAZfzDRJUUk0fkVVKqc5C2J5QH3htwSXdC06JuvETqVVxhznMHzpVZTXeIZZGjSe\nWRO4CCzR7LhVQTyG7APX+LTGS+wOfRWDn9m1aEPla6ieAG84g167Af4IqryLrCnq+7lMOQ6QG8Ak\nWcke55VOak1gSiEM0xOcKQ2WZtCpoOlOA+tS/n19/8RNkyyNbs682jGofA3NGWXRjPi3TBmwNGtq\n8NxPUnFB148SKnyfdXcXZSWakBp8oteQnJ1kiWZesoTbwlezxWSWsAkuA/OdKLNLqHwF9DH4VFQd\nD60xVJRa/VRT1NX0k4TRcWfWlM22UgBfBpvjy6UCsiXAOcxAoROxakrPjL0DtKmv4AfeMpRar5Dw\nBOniEMmIf8uVglksWww+8zJFG+dTtRngMGzp1RjPNbpDJ2UQWVoFl2h2m0UTUeP2gWXwiqeVsx43\nTVJD80W5vZu3RKPyNRLevdMM54B0TVZiHQC8qx4t3AAPwNvgiwnL4DVblgVr07fpTGkgW8Ckorq2\n/evqkiCEZY9t0EuMjG7fyUWqyIGSwScaMFoj2SJyMWWAtCnR+JqiLioGzwUM95v32zC6Azcn1Jo6\n20oWlsH/g5dobAtfqm6LK9EIZ3sXs+9NCKj1ql+iEQImb0o0smTwvlWP1ZquaVseb26DUWr5YkH5\n6AHSFZnUYOkChguYfDjA2wpaa/DFlGhqo9tvcpHOV9CcIWGsM+ZxE7jS4NmyJdEsJ08Ls36bZhxg\nC5pCNkGiMWx6dW372CgbH55YDX5qsUJo1O0DUnLqo0s0lD8dO+c+BMgk62HwqYApJP2OsqlnVqKZ\nZoq6qWIAvA2+mLDsFvygnOM7fYchlIZYLIFUDPaisQVW4MvgBl8bVqJJ+KG3DKXyFbSwOzuqjN4G\nQhnwHolmKvmycqxkApotvRrjNWRW7tfuYNOxWQQNfscBfpqOFhpdkzVee1q7xTZODu2cXnZt6CKn\n5ldtCF4FIXL+j6gnCzDZFK1TxVAez8/giwnXZA1llltjEWlKrYMH1hU7uH8a1clJRplCHi8T9/4Z\nx+ANeCeLZhlEokl0UTF4X4mmNrpF0OaEdH55cInmH7wGb/vDgC8hIr6AXAYWu+9NCKh8hUT0MHiR\nNgI806sqnXKqKdo2bSWfX998ki8MwA4hA1WUcqWBxQEgBE13GliXKw3NllF3gG2jW3m2ttb5msgA\naEiMGZg124ZQGiY76JFopgd4XrZbBj9A6tH51DW6KSlDBiuMJBN4tZdoQqJi8DyFZn7Gy5i1hHYf\n0HhyUAhsZPAly6xZh32Qp5mibdN2jrNr3QwTzcNUJHNlSonmOAZvKokmFoOn77RuNEcSjS+Dt/cF\nBidVtcE1ehg87a6n1lfYVr+GHXgzeGt0Gz49s6d7fpSnf2IZPItoYvqg6g/DUoAtgswUHYJlYHaL\nPXcN3mVgDaRpxTKJcVNqFzDdFO2atnPV4AGwZdVieroGT5kj7rXtW5ckmkVwg8+F1m2j289n0Pm6\n2gFKlgDrbRm8gVkctAL8AU35mvB53Va/YEuvzqdNozsNStKshKTYCQ7wYmayhJVoNMvK6rZ4Q57d\n/OnQ27sY0Pm6vzG1E4RqY6hkahMDst2mVgE+8uQiH9gME8MOgzX9EsqUEs0xDL6soA1t8LmwBTfW\n6PbNFNJ5jqQkCIonMCMDfLPZWDZ5WpiVaBSzEs34xnhNmTVs3QylSa4hGT+5Eg2b+BYODfrSKe0J\nbBFkYMXmtUzFwE6CRGN6NHgI0ZFoapN1milqJZr6ePOafGXHqjEASEQws5NrQz1b0pSmO/XASjSm\nyoOPc//YXVRldHPhJdEYWUs0qjWofROEph7yjfX4QSCJRlYM3qcxnmt0h658txl9J1qiiWli+oBY\nNfWWMOwgukTjMrC5ZRS14TKwBtIUcNMkS9YBTDdF26bt3GbX2jz9vDIgw6QrpsoAy0MkzrXtW1uU\n6Zkxd4D2JWuNbsoUGu+DmDwnMgC6L8yWWTSpAszysEeimUa+KICS32bYIVLlF+Ct0W34goqeAjJ4\nptd0vXeZJnnhwgXceuutuOWWW/Dggw/2/s7Fixdxxx134DWveQ3OnDkzeKyYeeY+qNOeMoAfRJ0B\nWptkB0Eq82LDyBxadN//SZohUS0G70o0E3qztE1bX4MvFqoMk/K9p3kYs5NrQCwOymvbf/FqBn9Q\nGXwxrovNZLJGt/Jsi2uKAia13yOD3sJkNVoj7WPwnmmNLmgHTRlzCcvK9caNg3SN7tDPMEk0lKe/\ns37wSincf//9ePzxx3Hq1Cm8/vWvx7lz53DbbbdVv/Pcc8/he77ne/CBD3wAp0+fxrPPPjt4vLkF\nNWLVstxyLaJr8KKSaPxGhu0SJs8HNHhRsczK+XckGp+qR4u2aatnNru2NoHLnwP1BE8VgGyJJMsG\nGTzdqwDKXkaxdoAdo5unXnMcTFEzeMUTYGDWrAslcyQJwLlofjZ+OHkcpNYgY5qVu4qq8+n16OEx\n/efXMLr9Wg5vOjYr8/TTXTH4J598EjfffDNuuukmpGmKe+65B4899ljjd37t134N3/Zt34bTp08D\nAG644YbB48Xs1ugDW3qs+YK2gQFmig6BHlDLwBazk6vaMHleMTAXSZohcSQaVjZwAqabol3TNuzc\ny6mgF9DVSr5QLAvSciLVQLo8RCJSJLL/w7oVtDEb49W7qPol6yNDmTyHsQFeMGpedwyK1dV6d9Ri\n8FOnhdmMOcOJvVNjvHHzfl2ZFWXL4bBpktS6fGcSzZUrV3DjjTdWP58+fRpXrlxp/M6lS5fwuc99\nDm9+85tx55134ld+5VcGj+fTgzkmbF6rYQskPMxEok1rVfnTJ0KiKaoH1EUi0kpGqFK7uGVF02bN\n1sGl3BF4GnyxYPVp6xGQRDOxR4qSMAAYF0iyxTESDWXvhGifO4S2RKPLnPvREo2U1DwNoDm+Ay0Y\nXLhzgJsa/PRn05VoAGqfMDYhoCmzTq+ubR+baUmS2K5M1mSLsTxFUeBP//RP8du//du4evUq3vjG\nN+Krv/qrccstt3R+9+f+/RrPvO9duHIFOHPmzEa9fhewea2UB78MMlN0CBUDi7C9iwHXJHORZFkj\ni4YkmpLBTxyAYU1bezxfgy8W2vIFZUNNk2iK1VWAARwAS1NggMHb9EywZdmbJaZEkzsymedL1pFo\nNGcwW0g0dgoU0HwOE+5nirqwz7phKa3FEmDkcJq2zDo1dbN9bJouJ/Dnf34RTzxxMchxNwb4U6dO\n4fLly9XPly9frqQYixtvvBE33HADDg4OcHBwgDe96U34yEc+0hvgv/eQ4+Jb3oX77gty7pNhGTz4\n0gnwGsYw75Fzm9ay+dPwnCizS5iiIL29hSRdVEHIZR1AOInGmrYq8Fi0qdAaxG4bEs00k7VYXwU4\nsADAsgVQdCOO2x+GCqziNcarMpmql3aKtBgnZQCgWolKoqnHPG6CXB9VmkJjvaR8UagcWmdeDNcy\neF1KNNKjMZ4rs1JSRliJhpe74TvuOINv/MYz1d898MAD3sfdeKnuvPNOXLp0CU8//TTyPMejjz6K\nc+fONX7nW77lW/AHf/AHUErh6tWreOKJJ/DlX/7lvcebmssaGrZwwbAMSARUAiQmH+Wsb4tKoikZ\n2Nz8iA5k0cvgWZqClQG+rcHrif3Ra/Zo5QExqyEx7e6ZIeoZVF43V2PZAqznw9rsHZlQeqa9f2IF\n+IbRXQ68Hr2WlA0Gv61EY1tUt9crODBlWljd6rcM8CzxlGhQ7cJDtjaxZEnvUqIRQuChhx7CXXfd\nBaUU7r33Xtx22214+OGHAQDnz5/Hrbfeirvvvhu33347GGN4xzveMRjgY+aZ+8CaJpotAZAuR876\nMuhF7jIwv3alO0UxEOCzNoPPoSsNfpop2jVtw7QCCIVKorH6dNn0az1VoimDGkszQHU/LK1bG5Ch\nDT4X1UuM25c2fQej1yoKYLGgY2zJ4N0pYu31JLOm6PUjT4SgNU2L0m6AHznQ3TW6KSkjXDxzW5fv\nLE0SAM6ePYuzZ882/uz8+fONn9/5znfine985/GLRawU9UFlsnK6EaeyhE3ruB36qDJvXi+7DhwG\n5iJJ0+rpqyUa0jWnmqJt01ZHbKrlg26GyfQpYKpYw9gAny0GA7w76Sq0wddei+l1ZXRrNoHBX3cd\nHUPwwR47LlS+BtgAgy9N0SkGvvusk0Qzzt9xje4kQHVt5/xUgUIcnuRK1vlJNKnWACu/dDZtYMUQ\nLAOzGQJkks3rWnTgMDAXLFtUqXy1MRTGFG2btrOUaMqWrkAp0UzUwkl3rhl8X5pkldlSSUNhDT4X\nWreNbuHnM0hJvXUAGMGrOb4b/8n6qBoT2ZVoyBQNJ9EwLw3eGt2UuhlaolHBJZqd9qKZmyxhTRNX\nopkycm7TOkbVLVhDb++ioCioLUELPFvSDFE4DJ6XDH7iKDmt6yHodLx0VqMN6UVdT7oKUa4u10dV\n2iXPlmBySKI5gqwkmoNoJr2VaKzR7dt7PikK2u2BArzOj9fgVb6CFP0MXk0kX3XGnEPmRhTltWVW\nam0SLq3amqyaZ7uVaEIiZp65D6osmvJLVxOHRg/BduizDCxE6XV0KFUxMBcszQBZB3iuC2ib5eCb\nUucsSZKPy+Dnk07aNoENyya3wKbh1HWAh+46/CTRrBsMPlbCQr2LshINyVCj+97I+v4xnFNW1jFQ\nRT3ovf3ZCg9T1EUl0ZQMXo1sq9E1usM2J6R7nzyCEyvR+ExRiQm3gRNA20AWSYNvM7C5XYs2kgEG\nTxINXSBrDMmMdkBTTdG2aUvscX4SjXSC39R0RbU+Asqg5l7b9rpNiSbeDpC+g6J6yZIMNV6iSaQE\nMgqmesOsWRdqvR6UaJSHKdr497bNAKd7lYbTbP+st43uhB8GrZshDT58Fs1OJZqpxQqhQaYJSTRC\n+KVObbuO7dAnBMqJMvO6Fh3IIQa/ANOuRKOgWAoh/KseLVzTlo7nafBFQmWyck7fIw8wK7TIocq2\nzGKxBFf9DJ56tDPyvbnfRKJtQC8xKpkXwqZJjt+lJFIhScumXkLAyOMZvC7W0D1pkkL4maKNY1cM\n3j7r46aFuUY3PcNhK9/p/ChP/8QG+DlKNEIZKnJKy37mE1jCECwDUyxBmgKGLaL2vQmBREqqWm1B\nLJbgrkSjKLUrTQNJNKVpa483pzm+Vr7QjJXfYzY5XVGu65xzni1pPmvPuoleVfePNfjiSjT2O/Dz\nGZiUlQYPwYEtNHidr6koCk1mnKZA4WGKNo6tbR+ZrHrWxwyncXdRQqBVGOl3Tu3j29kUJ3bghzDh\nLkgIaF2OX+MHFUuIKdFYBma3d3MJXH1ghawYmAue0exawHH+OTHuqaao1fRVeTxr8M3lOtkME8lK\nBs8CDIPOV9Alg+fZgghHz7oUXFi1Awxp8LXXstXJtJZf59NEKrCSIJg03U6DX6+qOcBtBq9KU3TK\n7lBoQ5PbBCBHVl27MivnAOcMMkGwtOpaolmcXAZPuazhA6gvKg2eLWje8cSJREOozTnLwGiizFy0\n5T4kStUMzAHLFhWDrzr0NRi8f48UG1x0IkqGHK8trg/ILC8qdhuiotQdbi4WB9XLs7su5d/bHWCs\nmhK32CxNUTY2G/8dkERT3j+cU2X0MdBF0Rvg09Rq5v4SjdXg7bOuvSQaMroZAxij4quQAZ5pfbIl\nmroabZerDsPmtRp2WAX4GBOE6u0dq/S7kNu7GHAZmAuxWFYs07IOVW57rSk6LYumgOZpJQ/MUaJR\n3Aa/6XN8Vb6qZIlNDJ7pFRQnaSi0wddeK9EFNBcNGWq8RKPA0rKOYsMw8cbaxZqKotCVaCjrZdpA\nd5sSTc/6uGlhrkTDOQV4n5bDm44vyjz9EyvR2FYAc3pghaYHhrZtDElEBi950tjexep7EwINBuaA\np4uGRMO1guFZEFO0Y9qWBt+c7hfKMBG1VBKQwacZGXd969o2yjEMvvZadjg1fad+rYmZ0lSZC5QU\nvH+QiQtT5FWA75isAaaF8TJjTghqjDdm3q9rdDNGmxKbuhniRUtkSZ1siYYqRecxY9MtXDBJVup8\n02aKDqFiYIw1tndmZLvSXaLBwByIxUHFMq1E45qsUxh327SN2RbXB1WGiSPRTC3e0/m6Gk4tlge9\nDJ7YI90/MQy+xvnoptEN7ucz0P1T7gCF2I7B5+veAE8SDZ88LSx15Fg1clqYa3Q3JJpAhZEVWWLp\nCQ7wHFFaAfigymtlxKg5t1k0kXrRlPnTMbZ3McCkqhmYA7E4qFL57E2p2aJhik5jWbIybWNOLvIB\nnV+dQkgVpQECfDk5S2RLKoXvWddOumobfKEDfFVsVn4Hvi9Z7t4/2zL4PIcRHMag+lw0wm86+bIS\njWElg2di1ChC1+i2z7BPy+GN56cpT/8ESzRx8sx9YPNaZfk2ZszeROELa6ry7waDn8+16ANTumZg\nDkTW1uBVZbJObZ9rq/lCHS80Kn3astsAc3xNUcBYiWaxWaJp7wBjVF1bicYa3dTYbPxLrHH/iC0D\nvCxgOG98pvrZ5JMlGkqoWFYMfsz0Mdfodp/hUIqEbV1+oiWaqdVoQc9F1f1h6jcyj6bBWwZW63eY\nzbXoA9/A4NPy+lTGEF8EMUXbpq2J2BbXB5RhQho8vYAOpks0xRq67NrJuAA3gFbNYEjSEKVnxt4B\nVplMpdENtvCTaJQGX1DVaJKm1RzfjWvnOUwqGmvZ50WVCRDTJBpQFXlqq67HMXhrdNtzsi2HgzH4\nMk//xAb4gk8rVgiJ2jRJnJsozoi42iTjje3dnFJG23AfUBfpsmaZVWqXI9FM6c3SNW3nNbu2MllL\n+QL8cLJEY4qCui0CSBhDzmnwRf+6vGPwhb42dT+g1KnWHb9L4UpTbx3QmMdkCwaPcg6w+5ns8zLW\nFG3DJlQYdlhJNONN1rwl0YRLq6bzU8BJlmioI9w8ZmzSF3YExVrbwEhpktSCtSnRxCiqCoVNEk2m\nAFMGXppzmTVM0SksyzVtycScV4DnLYlmarqi1Z0tClYOAWmta6tL2wZfFImmYXQfeLXF5dJU908i\n0q0CvCnoWvRJNJKJyRq8bfVLu00+qvOpa3TX8SLcM0z3Ps17PbHNxmTZCmAOD6zNay2cvFaaKRqH\nwdv86fb2bi7yQxtcaiDrMnjGabShkTmUWlbGUAhT1E0VI4a8nF0WDSuDX1XPMLGi1BTN4eaSAVgf\ndda12TsxDD4XNlXVGt2+Eg1XGmZBTfySLOudNduGyQtApL0SDQVkPw1ea0ArapXAyna8iqceEk1b\nZqWkjFBpkiTRhJ0mt9sAXzYMmsMDSybrupH2pCbOFN20lu3Q5xq6czZZuTIwPQweKFM88xW0XlYt\nWENUnrqpYrZic05tlbUGmKl3GLYieVKAb82+lTwBBiQa3WDwSRS/qF2dTJlC43cpXNf3TyLS7Q4g\nC0DwToCfKtH0JVTQcJrt/aI+o9u2HA6XJkmtFE6sBk9ZKvOQJaxE4xYuqIkzRYcwxMDmci36wJUG\nLxlYGwUnGcFlHa4pOkWicU3bEL1eQsLKF6psCMV42Q53RLpdGyYvYNJmgJctBk8BntIzY+8Abapq\nZXQzv1RQITVExeAXYNto8GWLavczVbtrNs4UdVGlRHN3R5COlmjaRrfk4eKZm6d/YjV4GSnP3Ada\n297erkQjIks0orO9m8O16INQGqJHogEoCKl8XQaDpkQzpT96W6KxrQDmco1s8LNTd4Jks7QkGjUU\n4FUOyUQjuEwp3R9ClfpaGt2+nU+5MlWAZ1kG1jOKsIMywPdn0fiTL61RyrHuCyMd1VajT2a1dTNh\nJZqDk83g5yLRKIVSomGtbVssiUY2tthzuhZ94MqA96RJAiTRFPnVqlmba7JOkVSqF0Z5vBB55iFh\nM0zsUIYgDadaw80lT6Ba80ttk7Pm/RNHoqleYqVEk3C/tghC1/cPzZrd4gDlteiTaDQX3gPY6Vlf\nNXLYqTHeOImmT2YNKdFQls8JzoMf26IzJmxeq2ykSY7btm0L26GvzcDmLdHUDKwNyRPI1VGDdVRl\n7RM0eHfqTp1nPi+JhilZjVULUs/QmpylWAK57mrwvGzCFsPgc2H7kuuypL9uizDuOEIBIrMMfgG2\nzQGiSjRHjWd9bNV1v8waLp5VnW35wcmdySrLarQ5PLB1XitvSTRxGLzt0Nco3JjJteiD0AZmgMEr\nlsAU65J1GArswr/q0cIy+DqL5mBWQ2KsCdyUaCbWM0gJLOrrrAQD8iaDr9mjcO7VOPdPLdEsejqf\nMiTJdsfh2gDLOsCjZ5BJB+UUsf4sGuE9LcwmVDQy5srpY6MZfMMHGVcNe9zxaTd80iWaCHnmXudS\n5bU2t21T2t0Ooc6fFo3tXQwGFgouA2tD8gRqvXIkmsWkqkcLuyOwDaHMDCUa3pJoSCqZkK5YFB0N\nXrWyaOr0TFcairMDrGWy0khmfp1PU4XKw2FpBr6FBp/IAknWDfCVpOI5TMamRLvPumEp7cZGBfi8\nIZNpxsAmVNe2j2/z9E9ugJ+dRNPMa6WZopE0eJU3GNic5Ko+CGUglv0BXnEG5TB428Bpan90Ol5t\n2tJw6ZmZrM7UnaqidEpth5SAk46qOBuUaBRLGzvAGCa9K9HUTHV859NUU28dgKaAsS00+KScIuZ+\nJl9T1EWfHKt5BjGWwXdk1mnFV+3jp5o8jxObRRMrz9wHfXmtU7aBm9BnzpFEM49r0QehMZhFQ5ke\nq5Jx1y1YrSk6JU2SO6ZtiDzzkLASjW3pahn8lJ7giZRIGgyeQRd9Ek3f/RPepKfvVFU9UWym0BgZ\nymjduH9YmoFtIdEkiiSavkpWzf0HuluJRnae9e39oj6jW5fP8NTvwBhASk29ck40g2c8Sp6517n0\n5LVOnSk6hH4GxsFmIlf1wWVgbSjBoPKjOneXHwYxRdumbczJRT6o2K2jwU+uZygk4EzO0pxB590s\nGtsALPYO0E19rdYaKUPJnIqKkjJS8YzqGY5DUkiwrMng3d2173xeetabKdFjG+P1Gd1jWw4PwRiS\nwFQCJExs7XNsgx1LNOG2NFNRMXhXouHTJhJtWqv7gIrZmqxtBtaGYgl0njupXQcNU3RyS9dSook5\n2MIHrgncyGaZcE/T5CwnwAsGXeQ961LxUdvgiyHRiM5nBMa0Jpb5iv5NCb5YgvUMMmkjUQpJy2T1\nNUVdVAkVTlGj4dmoVtT9Rve4hmWbjm0724Zk78AWAf7ChQu49dZbccstt+DBBx8c/L0//uM/hhAC\nv/EbvzH4O2PLg2PCavBtiYZH6gff3mJrxqIUVYVAm4G1oQWDylcNYyjEMGjXtOWc2Iya0WjDKsPE\nkS8US5BMMMtJonHSJAXvmKx1embr/omwA7QvMZQB3u5SxvgMxfoq1QeU4NkCfBsGLxWSLOuVaMaa\noi4owK9az/q4thp9Rneo7rN1nj6C6u/AMQFeKYX7778fFy5cwMc+9jE88sgj+PjHP977ez/yIz+C\nu+++G2bDkygDbWlCoDY+ubNty6IMeabAUDQYWKjtXQwU66sNBtaGEpxmiermTNuppii9MOpUMcse\n5zLHlz4vpRCGqihlUjaGm/dJNJbBm4Y0FGc3XMlkLYlmjAwlV5RzbsGdITGbYKeI9Uo0pSnqq8En\nrYlqYxvj9cuswrsBWuf89FHVujwkNh7uySefxM0334ybbroJaZrinnvuwWOPPdb5vZ/92Z/Ft3/7\nt+NLvuRLNi6mA+aNToU1TVTDNEkjSjSq8/afy7VowzL4IWjOIFfrqkNfUg6htqbotGZjpskeR8oD\nMWGn7jQZ/LR89PZwcyM4TGt+qdtGuW3wxZFoTPUZq743I4xkVax7GPx2Ab6dRVN/Xn/5lJ71ZkIF\nVV1v7xf1Gd1jq2E3HdtthhYSGw935coV3HjjjdXPp0+fxpUrVzq/89hjj+G+++4DACQbHALN/VOd\nQqOSaJzCBTNxpugQqg59DgOL1fcmBNoMrA3NGdR63WjgxFhtik6RaKxp6xYSzWlIjFDtFEI2UaJR\nSJzh5lrwfgavVKOCNhR7bKNKVS13UXaXMkaikevm/eMOat8EO+i9r5JVs9R7d92XEm34YlTVdZ/R\nPXYq1KZj07zXJLhEs7GSdVOwtvj+7/9+/ORP/iSSJIExZqNE838+8+8gxXP40LvfhTw/gzNnzow+\n4VCwb2TFBNLKyCHjpYiSmSC7Es1MXnZtqGK98dWvOUk00KtGA6emKbp91WN1XMe0bRt8c7hO1Q7D\nlS/4tOpspnSjklVzTsVPrXVZK3snlMHXRpX66nzGsYN6VLEG3ACfHQB6iwCvNMxAszFrinpLNLot\nx46bFtb3DGvmn7rZPjbTq0qiuXjxIi5evDjtoCU2BvhTp07h8uXL1c+XL1/G6dOnG7/zJ3/yJ7jn\nnnsAAM8++yx+67d+C2ma4ty5c53j/Wc33QTJF3j1W9+Fr//6EKfvD9sfRjGOhWPkTBlYMYQ6tzht\nbu8i9L0JAbk+ajygbeiUQ63XJeso2XvSNkWXXgHerear8sxnMhilamfckmimaOGsLM+3MEIAPc3G\nhJaNdfOI4yXdyUKMUabQqDTJ1RGSRoBfItmGwSsNLJaQrQDvmqL+aZLrjkQzpvNpv9EdhqTZPH1b\naW/rnsMAACAASURBVHvmTJP8PvDAA97H3hjg77zzTly6dAlPP/00XvGKV+DRRx/FI4880vidT3/6\n09V/v+1tb8M3f/M39wZ3YFo1WmjQWzNv9IcxfOF9Ex23VrvNbKjtXQzIdfMBbUMLDl0UxOAdY8g1\nRZUaX7ChlEam62o+K9HMpSmbZbe6fAHZeoYpw6CZVIDT88cIDuQ9aZIDEk0MDT7VTaN7bIsRma+Q\n8PrLF8sDJFv8Wy4VTMtk9TVFXdhn3U2JxsjZBX1Gt2IpsuILYQK8OqpM4JDYGOCFEHjooYdw1113\nQSmFe++9F7fddhsefvhhAMD58+dHLaZ5CpHPJw++a5r4bwM3wRbIuAwslEETAypfbwzwhvNSg6/7\newBNU3Ts59IaMFpCoy72qBj8jGon2imEUytKmdKNVgUmFTTZqGfdvvsnTiVry+jmbFRrYt2RaJZI\ntvi3TBmYlgZfMW5OkspUiaZtso7R4LtGd5jvwJrAMkIWzbHdJM+ePYuzZ882/mwosL/nPe/ZeKxY\nN6UPaommLlwwEwdWDKGPgdm+N3O4Fm20GVgbRnDoPIc70xaYZorSQ1ibtkBtYs5LojGNFMKpc3y5\nVMCiLigjiabJ4CuC4KRnxtoBkg/SNLrHylBqvQKc+yddHG4V4GmOa3+a5JSB7n3PumaUujmGwYv2\nM1wmZYRg8Ik+qlophETgw22GYlmUVgA+qExWp/TYsoQ4Eo1uPqATKvNiQxdrqE0BPhWUyqfXDdbh\nU/VYrVmmilnTFqiLbOZS8WuDnytfSDatIpkpA+ZWDAtO7Qta67YraHWk+4ckGnQlmhG7FFXk1Pa4\nBE/taMPNY/uY0uDZwbBE4/lsUgAtWhLNgUeaZMvoDvQdUJ7+OopEs9MAbxv8zOVh5bqAToT3tm1b\nDEk0c3nZtaHWK6hjJBqd52B61ZFolGd3xTpVDI3jyZEGX0wQi2tKNJrxSemKXKkqAAKASVOYnlYF\n7QZg1uCLkyaJhtEt+TifQecr6BZBkIzm+G6CkAY8HapkJVPUV6Lhmhh843gjOp/2Gd2mTN0MI9Gs\nG89SKOw0wJtAW5oQoDdy0chrnTpTdNNa7fzpUNu7GFD5qsHA2nAZfOGwjimmKDH4qx3TVpYG3xyu\nk9Y2T/8goERjwB2JBgNpkraN8i4a46WqaXQTgx8n0bQDfMGoQnoTuKJB3X0SzVhT1AUx5LYce4B0\nRGO8Xpk1oETj5umHxE4nOlGe+Yw0+FZ1qWGLSROJhrBLkywEdJE3NNQ2SCcukKDJ4Gk779c+l7bR\n694dQTKhHW9I0E4MjRTCfGKqHNMacAqdkKbUI76zbv/9E/Je1RqN6uQkcTqfjpBodJF3PBzJ0JlU\n1QbXBuhpVWA1c1+Jpu4FVZusGPms9z3Dpqx832ZY1XHHdittQ2KnAd7mmW8zfzc26I3c7A9D1W1x\nJJo2A4vV9yYE1HqzyQohYPIciVhVHfqAWlKZItG0Tds5DUYhdttOIRSTWmALZQBXg0/T3jRJaqO8\n7LDHkPdq5YM4Rjd9B2KkRLMmL8GB5AnMcRKNMjDZsreSlSQaP/JVSTSO3wZ+gHSkRNMxulkGrqYX\nRrp5+idbg5+RLGHzWl2JJtaQ500P6ByuRRs6X0OJDXdayTJppi3rmKK+Ek3iTN0BaoMvxuQiH5BE\n05QvNJ825lFI3ZycVe6O2ut2sncmdFccQpXJ1DK6x3Y+1fkauifAy/xo47+zU8T6JZoDb/KlNapO\nkM1nHR5ZNIsWIQxTyZq8ECQaEynP3AdWonGrS63xsguJptrezeBatHGcRAMhgHWBhK8a28oqrTGo\nRMNmk05KOzG0Km2nSTRcm5ZEk9Hw6c66TXPXTBiAMQRqW7tuGN1uW43tJZqiswNUPIE5RqIRGjDp\nsleiMRMGuve16x7b2nr4GZ5OCEmDr/P0Q2LHWTRZlFYAXueiQQ64I9FMYQmb0Js/PaNr0UYfA2sg\nTYGi6BhDVdaLhylKEs2qY9pSr5drL9EYQ5W27lg1Slec1nJCKAOxqBl8IgSSnkKndgVtNIlGNY1u\nuldpEtu234Ep1tBpkztKnlALjA2w16JfolmMMkVd2Iw5t9Xv2Glh/TJrmKQMmyZpe+WExI6zaOLk\nmfuAvvQmgx9rvIxZq5+BzTTAFwXMcQxeyY4x5JqifhJNH4OP03NlLPrGqoUwO7kG+DEMnu5V07l/\nQqcc03fQrU6mzqfb71JMz/2jWALVSv9sw04R62PwlLfuN9CdGHKTwY+d99vP4MMoElXr8ggSzW4D\n/MwkmnZ/GM2WkwZWDKGPgdm+N3O4Fm30MbAG0gxJITusY4opWmvwTcnH9nq51tdJqXqsmvt5p/ZX\nsrqzRZLRtW2v3UnPjLADJJN13TG6SaIZo8HnlGnlfgbBoI5h8KkC0uVhvwbPFkgnSDTtZ92ww1Hj\nIPt8tFCEtTKBT75EEyfP3OtcqrzW2jQhiSYWg28+oHO6Fm3QAzq8V0wyx2R1WIdrinpp8M7UHSBM\nnnkoVAZkq5WC5ukkDT5VzeHmSSqQyG4lq2hl71iDL7gGr446RvdYGcoUeYcgKJ5QC4MBaCXBDcBF\nc+CHrynaOHZpslqJhtI/GWQCQK+2D/AtmTWsRFPn6YfENWDwc5Zopk0kGoLV4Jtb7HFDf3cJ2mJv\nuNNEikRKCrwdiYZ5BTzbcKkr+fBZ9M237Fa25Iuxsz3baA83T9IFEtWVaOj+WTr3Dxl8oTV4+g4m\nSjSyQDtSKc42SjR2UHfCWG8lqyVf/hJN/azb446ZFtZvdIepfCcTuKjy9ENixxr8MoqJ6YOqt7eT\n1zp1pugQhhhYjLYIIdDHwFwkaQYmZdk/QwQxRekhXPfsCKblmYdCnafflWiYZ0Wp0WTaugGeZRlY\nr0SD6DtAq8G3jW49VobKc+qK6X4GzqDzYQZfrGh3ZM/DopZolt7TwmybASvR2OMWnHZl2xyzX2b1\nr65tH5vaGYuTnibpX40WGnRR6wZOjJXDoz1vouPWsh367FpTmifFhpEFkg0MPhEpEqkoda4TkMdV\nPVrU7LHJ4POR7DEWiME38/QZo2wW71mhModhQOo81Umaol0aSfcP6cYVe4wwu4AKbro+yNiqayMl\nZVq5n0GwTpdMFzJfISnX7E+T9H82LYO3bQbscYsRragro5sfOOfkn7rZPT9ZSUghsXOJJkYhkQ/o\njVw3cHJZQgyJhtLr3N3CuIkyO0UPA3PBsgyJshJNM03SdwBGXc3HW+xxPho806uGRENtbFPvYpdi\ndbUz3JylCxoC0lrbnXRl2+eG3gEOSjRspM9Q5B2JRnMGtYHBu3Nc+9Ikm+MgR3wo1CnR2gmgVLOB\nrVtRV0Z34xleBIlntp2xPvlpkssoJqYPbOqiNU2SBDBJBm5o8MTYm+i4tVJVM7CQ27sYMEUB02Jg\nLpIsA5OaGHxLovE1RYclGn8JJCS0BtqDkekF5N9yoljXsoQFyV91xDEGVX8Yxt1eNLEkmq7RPbrz\naVF0GLzqGSbuwg3wbQbfNkV97i1qM5C15MTtZxf0yazgS6QBXrJ0fkXVSiEkdhrgweL0evFBu4GT\nvYliDHm2W+ymSZZ55/VGR49J5iIRGZiSlfPflWjGF/5QcCk6pq32PF5o2CrPtoSkJ+Sjq5zy/l3w\nbAHmfFhad9VpoxwjYaHP6LZFVaOqrqWkWgkHmjOqkB5aO19DDUg09v8LDq9n0/aR0R2TdfuajX6j\nO0zdjJVoNAuvwe84TXLcFJWo59LKawXqgRU0UzTcOn0MLFbfmyDoYWAu2GIBLhUZb44xZHOmx1Q9\nWliJpm3aKj6POb6VRNNKIaQW2H5ZNMRam3/GsgWY041vKD0zRsJClarK27LbyO+g5/4xxzH4/Aiy\nLI5qSzT2PCTb3hR10U6JtseVIwa69xndJlA8q7No0pMt0cTKM/cBbYtqiQaYxhI2rdPu0Ff3t57H\nteigh4G5YCJFooYkGj9TlAJo17SNNbloLGyaZDfDxN/slPmqkiUsWJrRnNbOus1gF8rgc2FlMtX6\njKOrZntNVk4zBAag8nU1ZKaPwRP58m9F7U5Us8eVnI0yWV2j262bCSLROHn6IXENJJp5yBJVf5iW\ns07btnAThCwD626x5yNXdXAcg89owr3t0NcMyP5ZNH2mbazJRWPhtnTt5MF7auEqX3UlmsUS3GHw\nlJ55tZN/H8rga5xPJdG0XrI8Gze5SEpAtAI85zSMe2jt9WpQg7f/b01Rn92hcCaq2eMptn3n07bR\nXT/DoSSapoQUCjvOojmYoURz0LttC8rge/KnQ23voqCHgbngiyW40o2ZtsC0vHCt0RiM7B5vDqMN\na4mmqU9TRakng18dQbYmZ7GUWhC46ya6W11qDb7gJqvqNpAb27kyKSSlezow5QyBIah8Vc0Bdtfx\nNUVd2Iy5tkRTMLZVK+ohoxvsMEjdjDVZbevykNgxg5+PLGFNky6DR9AJQrVJ1sPAZnItOuhhYC4o\nCOnGTFugaYp6afCl5BPKxAyJOoWQtb5H/3RFVfSZrEswVadwWYmm7/4JbdLXu6h2NfG4qutE9gX4\nYySaYg3dkybZZ4p6SzQdBr/dMPFho3sRpPLdti6PweB3WuhEU1TC55n7oGofUJomQK3LhZdo+hhY\nGP0uBpJiM4Nn2RIoNXidXRfEFK1ZTEvyKY93ra+TbWfc1qenpCuqfNXpu88XB41Cp6o/TCs9M8YO\n0L7E2ka34YtRMlQiJXXFdGBSsbHQiaaI8eo8LELsrqs2Ay2/TXK2lUQzZHTblsNBGLySjUKsUNhx\nJeshUs+GQaFRM/imRDOmum3bdfo69GFCZV5sJFICWTb493yxQKI0ZY84N6Vrivpp8F3TVjP/StGQ\nsOfXztMHnzArtFgDosXg0wxoMXhq6tZPEEJr8EzlHaPbjOy3k0jVuX+MEJR+OwBd5IA4TqLZ3hRt\nHLtk8LqVMWcZ/DYBvt/oDvMM0/lJGB4+wF8DiWYeQY10uboBGFAbL4lHN8QhWAbWrg6kAQbzlGgS\nKZFskGh4Sm0W2iara4r6sKz+46WzmF1LgbZrstIUME+JZr2udGcLsSCfqrnuEWRn3fAJC7RW0WN0\nj8sUSqTq3j+Cw+QbAny+hu5Jk+wzRX3IAxUpdSWabTqf9hndSQIgEVVh5JT7083TP9EaPOP0Vtcq\nD1op6gOtbY/twx6JJmyaZF/+dKjtXQwkhUKyicFnS3BliFm3qgN9TVEr0bimbZ1nPo8Az3pbKZDh\n7HN+Ol9VQc2CAnwzTZLaKHd3gKEJAn0HXaPb8HEyFJMSSbZo/JlJ080STb6ifjXYlCa5nSnaBu3W\ndY8cu93sgj6ZNUkAIRhyRnUzU74HkmhUFIlmtwHepjp5vIVDg3Q59DP4CBJNm4HFak0cAonqYWAO\neEopekLLRgvWWqIZX/hDL0LZY9pOa8cbCn0phDWD9wu0usg7AZ5nC3DnWENtlK3BFzxNsqc6eayR\nnCgN1vZwOCfzfgC6KKA3aPDk72wnqbRBDLmfwSdb7Db7jG57DBvPJgf4VhpnKOw8wI9p0RkTNq/V\nFi4A1sjhXgMrhlB16HMYWMy+NyHQx8BciCXpv21jiLHaFPWSaFqpYlaDn8PsWpth0tanp8zxVesV\nVGuwisj6JJpueubYmaLboHrJ8vZLdlznU1YosPb9U87xHYJx5gAPV7JuZ4q2Qc96NyVaMU67sq0k\nmqbRbc+J4tm0pIxKonEKsUJhpwHetgIImWfuC6U0Mk0PStdZD8vg2w9oyO1dDDCpwI6RaMSAROPb\nfMtmErRN2xhtcX0wlKdP2Sy+Ek13uDnPFt0A3zPpKkbCwqBEM7LzKVPjA7x7LYYkminTwvoz5sTW\nEk1bZrXnVLAEmNjaxObpG0dNCIWtDnfhwgXceuutuOWWW/Dggw92/v69730vXvva1+L222/H137t\n1+KjH/1o/2JlLuu1lmi0Lo0R1AOU7flt66yPWau9xbZrzUWuaiORGiwdDvAio3oG3pqSE0Si6Zis\n85jjW+fptyUa/3oGLYuORJMuKTOjuW7z/rEGH0PYHSDtoprfge17Mybnnqme+0eIYyUawxkVFQ1J\nNJ7PZpUS3ZJj9WiJpvsMqwBZd3WWzzXIg1dK4f7778fjjz+OU6dO4fWvfz3OnTuH2267rfqdV73q\nVfj93/99vOQlL8GFCxfw3d/93fjQhz7UORa9NcO2AvBBX14rYCUahsTDyNm4VouBAeG2dzHAlAI2\nSTSLA0ABQslGdSAZcmSKKh8G3zN1x8xkdm0t0QikgdIV9XoNtBh8ujgEnEBK6zarS7s7wOuDbO1p\nl1J0qpMNG9famksF02Hw2cYAb4o1TCoaLyvG0CBfUwa6C4UeiUZQH/ZtTNaWzGrPqQgQz2yAd/P0\nQ+HY98WTTz6Jm2++GTfddBPSNMU999yDxx57rPE7b3zjG/GSl7wEAPCGN7wBzzzzTP9iLHyeuQ/o\njdysTAPsG5kTUwupwQ8y+GSyQRMDvQzMAc+ItbIW63BNUT8jrDs3k4537btuUqDtphBO6a9kZHe4\nuchosIUpP7DdAere+wdBd4A2k6ltdNu+SdtLNN37JxHdYeIujKQ5wH0pkva/peezaSUa00mo2O54\nm55h5Vld2z4+MfjwEs2xDP7KlSu48cYbq59Pnz6NJ554YvD3f+EXfgFvectbev/uX//rd+EzucFH\n/vD/wB2/t8a5c2fGn3EAWNPELVwArFPvxxKG0MfAgPHtSneJXgbmIF0cItHNmbaAlWj8TFGrweuW\nBm8Lia71NbJ5+oqlrR3GAYSnFm7yvMPgE8YocMscIls6bZR59B1gJZM51clV59MRKZlMasCZMwuA\nGHyxIcDnOSBErzxjz0MzBuY5LSzt8dtoHOSWDL7lo9lzIg1+ehYN9cWiAH/x4kVcvHjR/4AOjg3w\nSZIc9ysVfvd3fxe/+Iu/iA9+8IO9f/+Wt7wLZ//4J/DI6/8xvuZrzmx93NAgBn8VRY9pIj1Hzm1a\nqz2KDgi3vYuB3gfUQbo8BHSXdZBEs/DSzLUG0h6JJsbkIh9UBmSrlQK13/CUaMqg1oZkgFldhciW\nvdk7dm1r8IW6NsQkm0a3y+C3/U6F0jCt+yfJjpNociBtBvj287KtKdrGUMbceImmK7OGaG1CO4y6\nnfGZM2dw5syZ6u8feOAB72MfG+BPnTqFy5cvVz9fvnwZp0+f7vzeRz/6UbzjHe/AhQsX8EVf9EW9\nx7KpTnOQaKgqsZvXqhkL2p52m+3dtQ5ebTClO71EXHCREYNX3RasemRjKgsy+HRHogk1NWcqhkzg\nKfUMRhYdBg+UmWbl/NLapOe9949Pf/QhDH3Gsb3nmTKdHWCSCkBuONFCAmKzRGNN0TGf1xjKmBMG\ngNOqgI633TDx45/h8e2x28cXWjdM4FA49nB33nknLl26hKeffhp5nuPRRx/FuXPnGr/zmc98Bt/6\nrd+KX/3VX8XNN988eCwrS4Q0MX2gNUqJpmuaKE+WsGmtzQxsfhq8UBp8A4NPGI02XBSyYQxRUYwf\n46ZtatO0rdvxzkmDb0s0/umKpsipR0sLkieQ66N63VZ6pl079A6Q1mruoqpdygiJhisNsWgx+HQB\ndgyDNyLdKNFsy7gbxzUgv60cydnImOMCfEuJZlhmnZ6UQfe+afTKCYVjGbwQAg899BDuuusuKKVw\n77334rbbbsPDDz8MADh//jx+/Md/HH/3d3+H++67DwCQpimefPLJzrHqLc20N95UUPvPfgZvjZfw\naZL9DCxka+JQ6GNgbUgGLKXsYfCpl2ZOD1HXtJ3LHF+bQijFQZfBlyzRmDqAbIUBBi8ZgGJVrdtO\nz7Rrh94BEpOUg7uobb8DrgyQthi8SKkJ2RAkMfihAG8D8thns6/Vrz2eZfDbafD9RrcKoEjUWTQH\nuw/wAHD27FmcPXu28Wfnz5+v/vvd73433v3udx97HHtBQvZ68YHeWLhALCGkRDPEwEL3vQkFrjSw\nGGbwABl8i0I1WAdj8O6uWE3daY1Vm8scXzKBC6yz6xvpipwzyARlNtRh4zs+Dibvn5wleQKsagZv\ntf9sYAcYVqJp9kShl9i4vklCGZjW/cMW2TESDV2LvipWex65x7SwTSnRVLOxZRbNgNFtCyOnSzSU\np3/iK1lD55n7gCSaVWO+JuBKNGELnYYkmjlciz4IZTZKNAAFl6Vs5u5OMUW17p+6Y1sBXOtrpHvy\n9AE3m8XD7Cz6TVbFE+oVD2vwbSIIYSUarrpG91iJRihDtRIOWLoA2yLAh5ZoNsqxWzbGi/0Mkwkc\nR6LZaYCvGfy1l2iGTVYedMiz1W7dBk52Lbu9u9byQxtcGfBjJBrFgGXRzC22GrzPpCG7TW1LPogw\nucgHfVWeQDMfffQ9MzDcnAL8urXukEQTjoz01SJwjtFGMtfd+ydpDRPvoLwWmySabSUVF1aODSHR\n9Mtk0yvf6d43DRM4FHY68INYR9g8cx9symulmaJhJZpNDOxaX4s+0Bb7YOPvFDzB9SsN05JofE1R\nW+zR3REsZ9E3v2K3rY5/tVTiUc8wMNxccgas2xJNOsgewxY6qW7q60iJJlUGJjts/BnPFsdn0Rwj\n0WxrirqgZ/2oV47Vtup6C4lmSGYNUTdj8/TdXjmhsHOJhkzMcKzDB/aN3Ntbgo9nCcet1e7QZ9eS\nAd7+MdDHwNpQLMFSoWEMUTDwk1RsLnBX0z+YUZokNVfrfI8cfkbbwHBzxROosnd6X+pive50g88F\nvcSoq6HrM7iDLbbpe8M1dRx1wbLFRgafKJoDvJnBj58WZlOi+1r9qvJ42zH4oiPR0DM8vfKd7v3m\ndLlQuDYSzRYtOmPCtvB152va89NMeLW7HULFwFoPaDUyLCADC4VUGaQtBtaGLD+MYc1KVuo86CnR\nqKZEY+WBOczxtUVApjV1hx5yz3TFohiQaBhUflStaydddTXksDtAu4tyP6Pb92bbtgipopYLLlia\ngR/D4JNsswbvMy1sU6tfs+W0sM3P8PTCSNLgEUWi2X2A5zyoiemDTXmt1lkPm1s88IDOQK7qg1Bd\nBtZGwSkf0GUdlnH7Mvi0R6IxbJzBFwuW3aoeicZ3GDR6hlMDgBIMar2u19XUIiG2SU9MsinRALWR\nvG1r61SXTdMc8MVyM4MvJJI0axzf1xR1sUmO1VtOC9tkdId4huneb7ZSCIVrwODnI9H0VaZtW922\nLTaZc6Fz7kNB6C4Da0NVUb2p18Kz8rSeutM+3jzm+Fp92rQCbc3gx+9KafZtl8FrzqCLOsAP3z9h\nExb6jG671rZGslYSzACMNz8XSzNKvx2AnSK2uZJ1/LNpJZq+hAqzZWvrTUY3JWX4SzTG0DXjhoYA\njaqj2AI7NVndVKdrL9H094dRgYc8WwYm+aKHgfFrLlf1IdWAWRwn0ZR3omMM0Q7IzxSlNMmmact5\nnMlFPqgyTFpTd+p0xfFMOikk0DNYRXMGOFk0Q+mZMRrjCaU6bWutkbyNDFWsriLhQNbSGni2RCKH\nBfxE0rXYKNF4zOcliWYgJbpsjFdsK9H0Gt0CycjUzfaxoVdl48ORhXJb4B+sRJPovF+i4Vkkk7Wr\n3dK1mBeD14rKyfmGXjQAZUMBzQZOrikaYurOnEYb9mWYAI5U4hFoE6WQ9FxnYvBNk7Vfogm7A7Q9\nUdr52HVK5vFkROYUrNrgiwOwDSeaSIUkXRwr0Yx9Nqvdeo9Es+20MHcX1V834/8daE3SV9FK4wyF\nayDRTLsgIWALF/pKj8lkDSvRcC0701rq7d28NPhidZW248dAWQbfznopTVEfiabds9tWihZbygMx\nYdltv3zhV1FKunNPFo3gDQ2eKdkrDanAO8BNEk3Bt/MZ5Pqo9/7hadYYRdgGkwos3SzRWFN0rETD\n9Ko3Y85sOdDdNbr7n2F/RcJtpRBafweuSZrktC1NCJBpsobseSP7zhTdtJbtIx56excDxfpqLwNz\nYUw5nBxoBHjKovEzRSmAdlPFSB649rNrq+DXI9Eo7jcMOpGK2ui21xK8ocGLnUo0plei2TZTqFhd\npVYLLYjFAYQc/sc0B7jJ4ENINFqDXr69GXPbVV1vMrpJcp7G4BN91GldHgo7Z/C2UvRaa/Dt6Tz1\n+ZHxElai6Tfnpho0MaDy9bEMXmsy+Po69Pm2z6VABrRbproG37W+Z4YNSL96BjIWuwHecEb90WHv\nVbWBPYaVaOgz9n0H27UmVsUaqifA85TM9yGQXLU5D954PJubWv2aLVtbbzK6fVI328cmEziORLPz\nSlbF09HVaKFhJZq+3hKGZxBaIg8o0QwzsLB9b0KATLLNTo/WxODbDZwYq01RH4kmbWnw9phzGIxi\nJZo+DV4x5iXRMKn6TdZUVCar1kDWaqNs17U7wJASDclkXQ1e8u1SMuX6qPf+EcsDJBskGjtFbGMl\n65amqItNKdGkwR/fqXSz0T2tbsbm6bd75YTCzrNo9MQtTQiQbEJ5rYuebVvwLJqBEvep27sYkHn/\nA+pCa5IH2iMPu6ao2DorQOvu1B1gYp55QFDw0zAt+YKCn59UwgrVO9zccAbktclK2Tvd4JJ7lO5v\nAn0HuvclSybrhACfHSDZEEjtFLFNEg21wfBIkxzoBDlGohmSWTVL6e88X7JWomnn6YfCNZBowuaZ\n+6Dusd235UqpL3lgiabfZBWzlGj6ttiN31GlRNPKLbZVj9YUHfsgkkTTwx4Zrnnf/DpPvyvR+Dac\nYkr1Djc3QtC0p2rdofsnfBZNuxYBaGYKHS/R5LUB74BnmyUaO6j7eIlm3LNZy7FDEs3xx9ssswow\n408IKU2y20ohFK5BFk0atBWAD6xp0u4PU7OEsBr8EAObur2LAbk+6jXJXJAGzyFbEg1QSiojTdGh\nsWr2eKHb4vqAJBrdawL7zvFlSoP1MHidCprXirqCtl8aCrsD1JpksvZntN/BNtPH1PoISnTDfwdS\njgAAEopJREFUSrqkyVdD4FJ3TFZfxu2ilmj6nvXlVlXXG41uj+ra9rFp3usLQKKp3njFF675wzrU\nwnfb1KltsZmBhW1sFgKqyJH0MDAXVYDvYR2uKbrt5yIW0x2rVh+PDL5rfc+IAQbvO8d3cPYt5zTt\nCZtTF0PvAGkt9Brd2+5SdJEDPfePyJZINvxbpvX/3965xUZxpXn831XVvnCLbS4G3CZYuH1pG7BZ\nEzK5KJsYhyyDnRB4IJFIRFAUBaFclJe8WBppNxiSh4RcRsogJSJBwp7dPMTKkh6wLEYQYzOMnYVg\nBwxjT9oXzAbHgIF2dVedfSiqr6eqq7uru73d5ydZSheVU1Wnqr76zv/7zndArMEavFZQNPqZrHoe\nfOQ5G/qBbsHQbFi9tpXV5RIj0SRfgzdYojOR6BVwUjR4kz14DQ/M6IoyyUSauQcLxQML2kdSRh80\nr4Pn/UFRo9elvIThq+6o7anr+Kb6mRFkuj7tjXEdX94rAZSSEMQqKIuB+I5Ln0Fr9ghQkpRCc6HX\nqEo0RlYu8s64qc+PNXsOLDJAZBkWiiXjvTKQHVmDj3a1ML1Sv4TLhSAZ8+C1At2KPYvPg6etLmcW\nKZFoUh1Y9OW1UqYeGx22RXMszRc0zuFdIpBm3BE1eMWDF+ChBIZ8HncUQVFZ9s/mC/1g+CWa2TDR\nKTzDxF9RMAYN3iuDoxp4q7Kcn++4Og6C6RJNeKBbDSQbyaKRRTckPtysWDgOXk6Z6UqDv7/Qe2Ik\nGmXJw9D+A58Dq0GJRktmlbksZaHyeDR4yR0WBDaLpBv4WHJZzcaX12qhSTRZMS0arYVe/rQ6vJtV\nBt4jUl/QQFSJJrSAExAcFDV6XUrQmx5o8mdwzBaJJly+iHU+Ay8TekmIaCQaYt5oWC/QLXOcoYCu\n7BGVWjoU9A08AZdlRKKJ7t1UJRraakxGVx+LJLPGI+n68/TTwINXhzRCinVnVYOn1YdRvASTPXgt\nDyzO4V0i0PLAgvaRAZkX4OU4qkQTbVDUnyqmJdHwhgJ8iUQ18NQUwhjnM/BeGTxtcXOrVakV7zuu\nHDa71OwRoBrotlIMvHoPjMhQkuiGrCHxeThlpjQNZR3XSBJN9KNrJcVRS6IxtqC7rswaw+zasPOj\n5OmbRWqCrCYGMWNB74uslLs118BH8uBnkwYve0QggoGXJOXctYOsxmY9+o6pkyrm9+BTX4FUy7sV\nY0xX5CVCzYOHICi14pG8EaAsAxYiaga61TLfke6B7BFh0Xh+JN4Ccn8CVyi8TECs2qUKAoOi0adJ\n0mehEi4bgoH29N5hNSlDjCeLhjLT1iySLtGYPZEoFpSvOn3iguolmCnRaHlgZte9MQM9D0xF1eBD\nK/QBfgMfzUIUWqvu+NqbBQujyPL9tUYpaZKxlsBWdecwQj14iYRVeAwcAZrxrPriIBqprxLPgzMQ\nZ5DFGUgCXUz2cEoaLg3Fg8/VncmqBkWjlWh4TQ0+F4JBiUYrjqbas7gkGspELLNIehYN4Y3Vf0gk\nyk2n57UqwzaTPXgpvASrGcO7RCCLM4DGC+rbR1ZKTuhLNNGlSSoFl8I/GL5JNrNAoqGtusNxUKS+\nGDx4QSIAbXFzqkQTLg3FG+ALxJfJRAl0+z5iBj6ysjgDi8bz4+UtvsXEQ1EXeteTaIwGRYPOR1Yz\n5sLlWHBzDBXGiyyzxm7PVIkmtGyKWaRAojE3zzwWfIs3UCQaEuOKRFr4g3M6w7v/jxKNRaAOKwOD\notGlSdIDTX55ILXppHoSjRRj0S9e1pJorMD99Uv1ZtCqAT4znlU1H1tbJjN2D4jHA6Lhikq8BfBo\nSDQS0S1VEOu7KUlQZppqSjSIU6IxNhtWr+00lGhmgQevUR9G8RLMNvBaHljq5apQZHEGxIAHL/NW\namBIkWiiC4oqqWL3qCMCnzyQQomG3K+tQ1tWLZ50RUEiELLCPXiL1QpLQBaNVWMGrZkjQN890JRo\nBGMSjWcGssbzI/EWeN10D94qKyWF9dIkjQZFg85HBngNOdZoYTy9QHe89swfBE4DicaML54ZKDeM\nHmQ1mjplFH0PzNy6N2ag54GpyLLiPep78MazStRUMW3vMbZaL2ahBIHpy6rFk64oyKBOdLJY/R68\n4j0S6uxSM0eA6jVq3QO1zHeke0A8Hk2JT+I4EA0PXpABkpWjmyZpVDMPRJFA6B680dLWeoHueGe+\n++tiJUaiSXqapFrrJdXDba2JC7EuWKGFngc2G/oiFD0PTEUpNpZFDQwpGjxvaNaj75iyMpuPFrRV\nJxKlch1fSdKfiBVruqIgEQg5NA8+S1mjFPpllM0cASrZJvSaKH4NPvI9IKIIQllIHAC8ggUSJQ+e\nyDKyJKVejW6apMGsl0C0Sv1GsxykXqA73omRfg1eSI2BdzqdqKiogN1ux4EDB6j7vPHGG7Db7Vi7\ndi36+vq0D8bFNhvNbJQbRp96rHoJZmvw2i/o7JropPeCqqgSDS0wpEg00QVFFXnArSPRxFYKwCz8\nQWB6nr7MR79WKKCUR7ZSFje3ZGUpC3JDfVahI9GYlyYJiR7oVu6B1ZBEQzyiUmqBgsRzkGbCDbzk\nFSFZAI4XdCUao0HRQBQJJHxNW7XyqchFLowXSWaNx575JRoh+RKNJEnYu3cvOjo6UFRUhPXr16Op\nqQmVlZW+fY4dO4YrV65gcHAQPT09eP3119Hd3U1tL1CiuXMHuHTJ3Isxyq1bwCJZ1siDz4EgE3g8\n5pyfKN438DpD7Nu3U9cXoUzd8CBX5nXPZ3RUOXfasDIwIOdyRR7+AsD169qBpsD2xsaAHEpWYaIR\nRUSQL6zgZS9+/TW6+1gqA5eGcsCHLMt6c9qKuW4Jly4p6fBaM2jVd+nmzfifn1u3oMxdiCDRXL+u\nf6xbkx5ke+nPj9fCYcIlggv5N/GuG2UccOUScPNm8HED/1sNinq9xq93chLIlcPXtFXbVAvjXbq0\nQNPAut3aMquamx+rPRsfx/1F1XlkJzuL5uzZsygtLcXKlSsBADt27MC3334bZODb29vx8ssvAwA2\nbNiAqakpTExMoLCwMKw9NYiZf9eNu6eb0X7avAuJlkW3b1PzWgmXixwvkPVTM9p/iv84PIBcDz1/\nmvA5WDh9F7f/2oz2v8Z/LDNYefXvmJEFnDqqv18Bl0UNDPG8EhRdOnIC5/5kXFMpvNZFDdryPODh\nBCwbP4efvmqGCbckJvLdE5p5+hJnReGNUZxrb8ZIu9EWCd4hwJ//K7xUwYJ/ZOPx0Um0/6EZWQCy\nJY30TC4bi27dQm9nM9o7Y70yP4umBjRTX2XOimX/ewn9f27GFZ02Si9fwLQ1Fz9Qnp/fEw5Dbf+J\nvs6h4Pa90yjhgKMh/w8tKJotAdkXm9F+0fh1PfzbBMaWZ1HvnYcH8i7/B/773x/QbWP+jJf6DoPP\nQd5dN9xdzWjvMn5OgZRO/A9Ea07Ys28GugZ+dHQUxcXFvt82mw09PT0R9xkZGaEa+D/+8Q84M3Ad\nP1uyUXP6U9TModThSBK/LlgA96InkJ/v3yYIwLy8ApxwrMS/9P7JtGOdthdjTn4RsgMy4vLzAXHh\nYxjLzzP1WGbw4+odEfe5uXwzBq3zUVsQvL2gABgofQqOwQ7YJvRMQTgX7E+gmNJeT8nTqLnQioUp\n7qfO1TUooJzfVNEzIP84FfV9bK+xU7dPL6nHrdyjvvZOOFZiXl4eApWzggLAvfhf8euCz019fnoq\nH6Ze49kV/4biax8ZOlZvzbPU7X3lj6P0l3OAqzfs35xrHWHbAs+D54F5D8zDX6pLor5ejyDg5tIG\n6nX9Zc1qrL3QFrGNvhXLYc2vwNy5/m0PPADI+etxtXBx3Pegr+ZlPHb//E6ePImTJ0/G1Z6KhRDt\n8MI333wDp9OJQ4cOAQCOHDmCnp4efPLJJ759Ghsb8e677+LRRx8FAGzcuBHvv/8+1q1bF3wgiwWE\nEFy8CFy4EDk1KdFYLEBFBVBbG7z9n/8E/vY334pppmC1AnV1QElJ8Pbz54H+/tT3RawsWgQ8/jiQ\nGxAnnJ4GTp9WhsbRkpcHPPYYsGCBf5vbrbR3/Xr85xsvc+YAv/sdEOi7EAJ0dSnPTaLIygLWrwce\nfDB4e18f8PPP0A0QRsv8+cCjjwYbV68X+OEHRZpLBhYLUF4OhJgQ/PILcPZsbO9mSQnw8MMIyoAa\nHwe6u4F79MzNIARBsRX2kG9yf79iz+JNACgsVN4lyhK9PtsZC7oefFFREVwul++3y+WCzWbT3Wdk\nZARFRUWabVZVKX+zlQcfDH+REsWaNcpfOjFvHvDMM+a1l5MDbNxoXntmY7EoBvG+f5NUamvDHZRE\nIAjAE08k/jiRWLFC+TOLZcuArVvja8PhUP5mK7qqT11dHQYHBzE8PAxRFNHW1oampqagfZqamvDV\nV18BALq7u5GXl0eVZxgMBoORXHQ9eEEQ8Omnn2LTpk2QJAm7d+9GZWUlPv/8cwDAa6+9hs2bN+PY\nsWMoLS3F3Llz8eWXXyblxBkMBoOhj64Gb+qB4tCRGAwGI1OJx3YmdSYrg8FgMJIHM/AMBoORpjAD\nz2AwGGkKM/AMBoORpjADz2AwGGkKM/AMBoORpjADz2AwGGkKM/AMBoORpjADz2AwGGkKM/ApwKxS\noOkA6ws/rC/8sL4wB2bgUwB7eP2wvvDD+sIP6wtzYAaewWAw0hRm4BkMBiNNSWo1SQaDwWBET0JW\ndDITViqYwWAwkguTaBgMBiNNYQaewWAw0pSEG3in04mKigrY7XYcOHAg0YebVbhcLjz55JOoqqpC\ndXU1Pv74YwDA5OQkGhoaUFZWhqeffhpTU1MpPtPkIUkSamtr0djYCCBz+2Jqagrbt29HZWUlHA4H\nenp6MrYvWlpaUFVVhdWrV+PFF1/EzMxMxvTFK6+8gsLCQqxevdq3Te/aW1paYLfbUVFRgePHj0ds\nP6EGXpIk7N27F06nE/39/Th69CgGBgYSechZhdVqxYcffoiLFy+iu7sbn332GQYGBrB//340NDTg\n8uXLqK+vx/79+1N9qknj4MGDcDgcvqB7pvbFm2++ic2bN2NgYADnz59HRUVFRvbF8PAwDh06hN7e\nXly4cAGSJKG1tTVj+mLXrl1wOp1B27Suvb+/H21tbejv74fT6cSePXsgy7L+AUgC6erqIps2bfL9\nbmlpIS0tLYk85Kzm2WefJSdOnCDl5eXk2rVrhBBCxsfHSXl5eYrPLDm4XC5SX19POjs7yZYtWwgh\nJCP7YmpqipSUlIRtz8S+uHHjBikrKyOTk5PE4/GQLVu2kOPHj2dUXwwNDZHq6mrfb61r37dvH9m/\nf79vv02bNpEzZ87otp1QD350dBTFxcW+3zabDaOjo4k85KxleHgYfX192LBhAyYmJlBYWAgAKCws\nxMTERIrPLjm8/fbb+OCDD8Bx/scuE/tiaGgIixcvxq5du7Bu3Tq8+uqruHPnTkb2RUFBAd555x2s\nWLECy5cvR15eHhoaGjKyL1S0rn1sbAw2m823nxF7mlADz3LfFaanp7Ft2zYcPHgQ8+fPD/o3i8WS\nEf303XffYcmSJaitrdVMmc2UvvB6vejt7cWePXvQ29uLuXPnhkkQmdIXV69exUcffYTh4WGMjY1h\nenoaR44cCdonU/qCRqRrj9QvCTXwRUVFcLlcvt8ulyvoC5QJeDwebNu2DTt37sRzzz0HQPkqX7t2\nDQAwPj6OJUuWpPIUk0JXVxfa29tRUlKCF154AZ2dndi5c2dG9oXNZoPNZsP69esBANu3b0dvby+W\nLl2acX1x7tw5PPLII1i4cCEEQcDzzz+PM2fOZGRfqGi9E6H2dGRkBEVFRbptJdTA19XVYXBwEMPD\nwxBFEW1tbWhqakrkIWcVhBDs3r0bDocDb731lm97U1MTDh8+DAA4fPiwz/CnM/v27YPL5cLQ0BBa\nW1vx1FNP4euvv87Ivli6dCmKi4tx+fJlAEBHRweqqqrQ2NiYcX1RUVGB7u5u3Lt3D4QQdHR0wOFw\nZGRfqGi9E01NTWhtbYUoihgaGsLg4CAeeugh/cbMDhiEcuzYMVJWVkZWrVpF9u3bl+jDzSpOnTpF\nLBYLWbt2LampqSE1NTXk+++/Jzdu3CD19fXEbreThoYG8ttvv6X6VJPKyZMnSWNjIyGEZGxf/Pjj\nj6Suro6sWbOGbN26lUxNTWVsXxw4cIA4HA5SXV1NXnrpJSKKYsb0xY4dO8iyZcuI1WolNpuNfPHF\nF7rX/t5775FVq1aR8vJy4nQ6I7aftFo0DAaDwUgubCYrg8FgpCnMwDMYDEaawgw8g8FgpCnMwDMY\nDEaawgw8g8FgpCnMwDMYDEaa8n/UEwqRiA9MTAAAAABJRU5ErkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x,y = generate_revtiming(n=100)\n", "ylim([-.1,1.1]); plot(y,linewidth=3,alpha=0.5); plot(x)" ] }, { "cell_type": "code", "execution_count": 42, "id": "cab8c1a8", "metadata": { "collapsed": false }, "outputs": [], "source": [ "def generate_biditiming(ninput=default_ninput,n=default_n,t=5,example=0):\n", " \"\"\"Like generate_timing and generate_revtiming combined. Requires\n", " bidirectional training.\"\"\"\n", " x = 0\n", " inputs = []\n", " while x=t and inputs[i]-inputs[i-1]>=t:\n", " outputs.append(inputs[i])\n", " inputs = inputs[1:-1]\n", " xs = zeros((n,ninput))\n", " xs[inputs,:] = 1.0\n", " ys = zeros((n,1))\n", " ys[outputs,:] = 1.0\n", " return xs,ys" ] }, { "cell_type": "code", "execution_count": 43, "id": "3addff43", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[,\n", " ]" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXgAAAD5CAYAAAAtBi5vAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n+P+5dC9Tk8P8rwAAAABJRU5ErkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x,y = generate_biditiming(n=100)\n", "ylim([-.1,1.1]); plot(y,linewidth=3,alpha=0.5); plot(x)" ] }, { "cell_type": "markdown", "id": "ad296d88", "metadata": {}, "source": [ "Other examples:\n", "\n", "- measuring spike delays, discriminate a delay of $t_0$ from $t_0+1$\n", "- more generally, detect any delay $t_0+t_d$ where $t_d$ is from some set of delays\n", "- generalizing timing spikes: the input is $t_d$, the output is a corresponding spike delay" ] }, { "cell_type": "code", "execution_count": null, "id": "e5522b23", "metadata": { "collapsed": false }, "outputs": [], "source": [] } ], "metadata": {}, "nbformat": 4, "nbformat_minor": 5 }