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TB_Lecture33
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Lecture 33: Arnoldi iteration\n",
"\n",
"Suppose $A\\in\\mathbb{C}^{m\\times m}$ and $b\\in\\mathbb{C}^m$ are given. The $n$th **Krylov subspace** $\\mathcal{K}_n$ is the range of a certain $m\\times n$ matrix:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"A = randn(500,500);\n",
"b = ones(500,1);\n",
"K = b;\n",
"n = 10;\n",
"for j = 1:n-1\n",
" K = [K A*K[:,j];\n",
"end"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"One way to think of $K$ is as keeping a history of all the vectors found in the power iteration. For that reason, we suspect that it may be rich in content with the leading eigenvectors of $A$, much as with simultaneous iteration. However, it's a poorly conditioned basis as $n$ grows, since the columns all become parallel to the leading eigenvector."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ans =\n",
"\n",
" 1.3490e+12\n"
]
}
],
"source": [
"cond(K)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We'd like a (thin) QR factorization of $K$, of course, but once $K$ has been put into floating point, the information about successive dimensions could be drawn out only through subtractive cancellation. Instead, there is a clever way to arrange the Gram-Schmidt process for this particular matrix.\n",
"\n",
"Say $q_1,\\ldots,q_j$ is an ONB for $\\mathcal{K}_j$. By construction, $Aq_j\\in \\mathcal{K}_{j+1}$. Thus if $q_{j+1}$ extends the ONB to $\\mathcal{K}_{j+1}$, it must be that\n",
"\n",
"$$Aq_j = h_{1j} q_1 + \\cdots + h_{nj} q_n + h_{j+1,j} q_{j+1}.$$\n",
"\n",
"Furthermore, $h_{ij}=q_i^*Aq_j$. Written out for all $j=1,\\ldots,n$, this implies \n",
"\n",
"$$AQ_n = Q_{n+1} \\tilde{H}_n,$$\n",
"\n",
"where $Q_j$ collects $q_1,\\ldots,q_j$ and $\\tilde{H}_n$ is an $(n+1)\\times n$ upper Hessenberg matrix. Adapting the modified Gram-Schmidt algorithm, where the \"new column\" of a matrix comes from $A$ times the most recent column, we get the **Arnoldi iteration**."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"m = size(A,1); n = 50;\n",
"Q= zeros(m,n+1);\n",
"H = zeros(n+1,n);\n",
"Q(:,1) = b/norm(b);\n",
"for j = 1:n\n",
" v = A*Q[:,j];\n",
" for i = 1:j\n",
" H[i,j] = dot(Q[:,i],v);\n",
" v = v - H[i,j]*Q[:,i];\n",
" end\n",
" H[j+1,j] = norm(v);\n",
" Q[:,j+1] = v/H[j+1,j];\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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6aM4IlG3UpOoV03fiJtT4hMucjytVr+Z2Gq9VxUQr/vOIVDN9S1BsGKdR8XISeDlIwsmJ\niY6I1/J14ORgt0U5HJVOHemvMtGinPlKTeVwM6LGCxUwaFTgTya3Zma8Wg40LOeBllg65AVpGaAg\nJZZZegxa1d7yXABghh+2fLBiNTtEd5Rk6dSRVcVp7K6COV1XVZyWqo+mVMwxFYAKt7IUJlMqNEHh\n5jO9mjU+cVTbS7LYsV1VnFaQEkvl5Bg1OIsl7QMzgLE+4I52lGTRPlgKk/3KYb0KIEesjE4dyZxd\nASqztzyXUhWkxG7MjmemYaSiGxq0qpoXCgAA/1Iq2oeyPMPG7Hg50MtuoCVCjI8kwgP5+fmBV7g2\nNH7hxihtcXl9F26Murw+2njhxmj/6AS34bWhcdrSPzqxaCpuw/mouA0v3Bjl+jAf1YJ9EKmWImfR\nVIuQs+jKyIFeupy7N9AfBXHwSgQJ+Qtp2cCUpOXe6bvu8J7ucND72n2OifN9bvu4ImDGanNx7+1f\ntLnP97lHvXPZzA6P73SH47pj7qnDqHfqfJ/7ojLD5k+3PFx+s3389vk+d59jLirG4fFxfRj1TnUM\ne/50S7EhUtE+INWCckQqUY5YGZTD5eWIlcE+LFiZxclZdGXkQM8nJxwGWiKEkC67cMGdGnWozQlN\nR9S1hR4qmujMQpepNwmdQtS1haYj6k1iwc/Mm2SYDX6mVOihojYnND757YNIRW1OKIfanALIoa4t\n9FCJcsTKAAAzofmVI1YGLWE0bztIOYuuDL7HKgc6nAcaN5Euu1BB/kJarqCTSOKxhFHZCIxqrm3t\nZ18eMUN6wDVJvUk4aTGdRHKGirQ0dTo6hj00oNrh8Ynzs4lUeN7BF2hYH9B8RanwlRRqc0ISOqEy\n2x0np2PYQ11bYrK1XyosAjOhoRyuMjO540QOFpyT0z441njFTuWIfrad9XwfmCWMUjVesbcPjomV\nkQMdzgMtEVrIC9IDC/fkFJey7PD43BNTypbboJwJNEg4Pb7xyWmxXaRakDzITcRkawBwTwZFzoVk\nuyemuF0EH0fNbSgGdfvZxOtjfwODYwtyXORAQ3gMtMTSIS9IyxU0QxrjsWnosjldl6qP3l6Sxe4q\nYEanKUlLM6TRMaWgKkGqTEplStJaCpOpy3ZrcVpMdASdkhL3vnd23jCYjYWmLQatamN2PBfUjStQ\nzxK2bFeGZHPJ1gatCpOtqRzsNpWD85ihTCqnqjiNVmZ7SVaqPlpJxeeOIy1HtTE7vnyNkasMKOce\nRTm0DvgpJ6d8jXFjdvwCoyMHeqYP4TLQEqGFfIYULljEbeja1v4eu7fUZGBzNjd1jpzucMRrVexY\nZfcW6DnrUHOv0+OrKJoz+CJVtlHDzhfddu/R1n6/VFuL05jBF6nEPvilYmcHvHni9PgoVTBykMqv\nHJGK9uGOKrMIOWJl5pMjUtE+LLoycqDv10CDfIYUOsgLUrhA/p+WkFimkAdvqCBfNn5w4PD4Nnz/\nHD7CZXGWzFDETEfMUGRO12GsgNXmxhBonP/fnK5zeHybjpzHR7giFbNjMaoco+bCrsc5qrrqIvz6\nyfxRaMcCAGa1YlTMakX7IMphVCGUI1L5lYNUQKxWOKubXzkiVWA5rDJsYjfm7PIrRw50mAy0RGgh\nnyE9ONjZcI0ZivB4q23tZ4ai2tb++rYh98QU8yZZbW48922puTj7TNi3peYiAOxv7GKGourjlwdc\nk02dI4yqqdOBy4yq2+7F5epj7YTqEgAcau5l/qhDzb3tg2Ptg2PMatXU6cBl5iF2eHxofKo+flmU\nw6jQDDbgmqRy0MeFZxYqZ2fDNSrHPTFV3zZEKyPKESuz6ch5ANh/cq4yOxuu9Tkm/MrxUxlBjliZ\nPscEs3tZbW70jPmVIwc6TAZaIrSQF6QHB9zLgB3DHi5l+YMbbi4KGjehs3DiMg3JBoAB1wSXKt1j\n93LmKzQ40Wkr8Qg/3anYcNTr4wxLuAI1NTXNtCgcU+OT05ychktDA64J2oLdplQoh6/MrfEPbije\nA+2xe7n3QMXKIC0Xkt3n9Lb0jNIW0cc1G5I9wrVza7YPjnGZ37jJwnLkQIfHQEssHfKC9OCAxlEb\ntCpTkpaLo95anMbSZRCY00w9VLjM2ZzM6XrOU1RqMsRER1Aq3Dv1UOF9j63FqXTDghRdQYqOtuAK\n1PiEJFROjlETEx3BxVGLcrbObMjL4SojyqkoSjYlaQPLESuDcsrzjbQFO0mfeCMJpcJPOTkbV8UL\nleHliJWRA03l3PuBlggtZEBfuGDpGV9lpoQVAN0j3rK8hLrq9QatKlUfbc7QXbk5nqqPfvP5NRhi\n9szaxEHXpNc3vePJrL9/OhsALIXJg65Jh9dnKUyuqSzQREWYM/RIZU7XHXuxMFUfbdCqykyGD264\nkQoj5l7+eMaVm+NIhTZZS2Fyz4i3e8T7zNrEuur1mqiItStjDVrVlaFxc7qu7ovrsxM0alWEpSj5\nys0xWAF7y3PxXFC5IeXKzfEB12TlhhS80U/l/OolsyYqIseoZXKOvfgxjHd7Zm0iUu14ciZCW5RD\nqWpeKEA5tDJ4Vqo0p/SMeEU5Dq+vLC/h2IuFXGVQTpxGVWYy9Ni9Bq2KVaaqOA3lvPxEBj5NeWZt\notPr+/Dm+DNrEzk5a1fG1H1xfX5yDFeZl5/IwD5gkS2FyWJl5EDf34EO1cErgZAuu3CBNOpISCxT\nyIM3VJC37B5w1LcN5R44k3vgTP1sDBrO95Wwp5nNs4LPpVfsPrWl5hK7L7//ZFfCnmaarcmo2FNi\n9Cat2H2Km5PGL1XugTPsvnxT50jugTN++8DNB7Ni96lNR86zW/y1rf2Lk7Oz4dp8ckQqJsfh8c0n\nR6RK2NPMHnT7lSNSHWruxcoEI6f6+OXFyZEDffcGWiK0kL+QwgV340sWnbYSZqekpFHQOI8knbYS\n/aw0VRrzm7koaJxhk1Kh05dOW4kZ0nTaSgBwHigFgPhXT7MWtOfSvG2059JZOLEPfuWs2H2KtaA9\nV5RD5yf1Kwdn2BQrs6XmEjuLoQ9blDPq9WV9632uMqIcsTKcnN5vfCJOoxIrQ0+IlsLkuuoiUY4c\n6Ps10LgsfyGFCvIX0oMMzjF1VIiCnjWAOUiLA5Sp0g6Pz2pzcVHQpzsc45PTlAqNT3TaSjzvNLQN\n0w3bB93tgwrjE65AbU5IQg1gDo9vfHLarxwl1ZBfOdQx5VdOw6Uhv5WpV6ZrgzI+HOU0XrXTFuwk\nlYMklAo/5eQ0XrVzlcF9UT9b/YxAXo4c6Ps10BKhhbwgPcjg8ptLTQZTYgxtwShoagnDZXyMzGBK\njOF8XNlGjd9ka2p8Qi9TaZ7CjJQZr8mMV/Yqz8BWRpTNtPDJ1pyciqJkTg52W5TDBXWbEmM4i1S2\nUcNlTeEm1BKGPaQ+LpSzMTuOoxLkJIBgAAMhA3tjdhxXGbTGUSrsDyfHnK6XA32/BloitJAXpAcZ\nVcVpzM+6oySrLC9Bp45kac3mdB0awNCpBQAGrWomVbo8l51xairX6dSRLM2a0lIqXK6rXp8ze0bG\nV9l3lGQxqoMVqzMN6kyDmoVPl+UZkBbfvQeAHKMG+1BTuY5RscxvKsecrqNyyvIM88k5WLGanXFQ\nTlleQmA5M8nWLxRwcvZuVlQm06AuSIllVJbCZKSqqy5icpCWyqmrLkIJbA7WHSVZBSmxmQY1lSNW\nBnPQOTlyoO/jQEuEFvIZUrhA3oaWkFimkAdvqCDfQwoX3LNXGRwe37/+7sYPf2czaFXsFkdta//h\n9/ocHh+7h9PUObK/sbvb7l27MlYTFYEb/vOpnoY/DuMbJ7jaoeZekero7wc+vDmOb8MAgNXm/udT\nPWd7Rs0Zeo4qNU6dqo9mVD+13vT6pteujOX6wKi67d79jV0i1dHfD9ypHKQ6ecW+oByOKoAcjoqT\nU9829MPf2Whl5pPDVSaAHJEqx6hlU1PLgb4HAw3yPaTQQf5CChfcsy9Z1LWFGdLU5oQeKmpzQtOR\ng6RKw6zxidqckIranNASRlOl0fgEANTmhMYnanNC4xMNyUYPFXVMsQxp6tpC45Moh1L5lTPyWolB\nqxIrQ+WIlUF32ah3Kvu19wNUBi1h1M/mV45YGVGOWBmU47cycqDvwUDjsvyFFCrIZ0gPFzqGPdS1\nJeZtz8RRkyhoq81ttbloqjQAHG3tH5+cpjanGar35qjwvEOTnh0eHyZbUypcgdqckIRu2NTpGJ+c\npsYnDNqx2lzUtXW4uc+vHEpltbkxqJvrw4BrUqwMjQ+fpepjLd12b0uPs/HqLa4yoDSAHUY57ynk\ngNLH5fD4Gq/YhcrwcrA/nJwB16RYGTnQ92agJUILeUF6uKBTR9J/osGJ3nyYfeCscCvpolUGpSUs\nXqvizFd088Ati9skJjqCs6XlGDW6aEXLfFScj0unjhTl6KIXqIzfXcRpVJnxarG3ik00KvY3AOI0\nkXGaRcmJjuQqY9Cq5EDDPR9oiaVDXpAeLqTqo5k7yKBVocWIWaHY8t7yXHZAYh52VXEa8y8ZtCok\noRnSBy35C1JhFDQN6jZoVZhjLW6IhAjcEY2jNqfrLIXJ2DGOinmo5vqwWSEHi8D6gL4ynTpSka69\nmafCZSqnLM9QkBLLyZmJxFZUZjX7S+XQAFOsTEFKLHN2sdHx04fNivhwnToSrWiMimnkqORAh3yg\nJUIL+QwpXHAvb0O3D46Nen0FKbo4zcy3xT7HRJ/TmxmvyTTMfA0c9U61D7rjNKqClFi2YUuPEwDY\nk+cgqfxuKLbc1T6EnGpBOSJVkH3AlnssRw70ogca5DOk0EH+QnoYgV/32KHoF4E/nVtNzd/riJvn\n3hTXHuRqfncxz4ZBdfhO4ac/mki/7fxq83R7wYrhP0U5C+5xcZADPUu7yIGWCCFkrSWAepNwwrFu\nu3fD98/hI1wW/My8SSxDmtqc0ENFvUlIRW1OLPiZUTEPFZ06DD1U1LWFxieadc0Svtmkagat6sKu\nx3OMGkqFHqoF5YhUmGMtVobKEamYHOqpw8pQOei7o1R++yBWBuWwvO3g5WBl5ECHfKD9HU8Si4f8\nhSQB3LzLALC/sYsZimpb+wdck/VtQ8ybZLW58XimNicWR83RUqqmTgcmWzMqh8eHcdTihkiIwB3V\ntvYzq5XV5q5vGxpwTbJJ1RgVNyM1tnByMBibUR1q7nVPTCmoTgZF1T441tLjpHLQtaXY8Fg7+0uL\nfLi5l1FZbe6WHmf74BjtA67mZ3ROKkbHPTF1qLmXGx2uMvNSyYFe2kBLhBbyCi+hiILGZS4KesA1\n0a1MlXZ6fFyytUjlt4WLtQ5mE8T45DQXGt1t9+Yo5xPDbotyuJBs98RUjyBnwDWp7MNtUM4EOp+c\nPucEBITD62N/A6DPOZEZcF+sP7ycySmuMg6Pzz0xpWy5DXKg7/JASywd8heShMJDhcvUx5Vj1JjT\n9dT4BABbi9NioiPolJQY+bzjyTkqNIxRM5JBq0LzFaXCFehknUhSUTg3y6c5XRcTHcHlbVcVp5nT\n9fRUhd0W5dA+mNN1piQtZ5HaWpxmStJSOaJZDued214yd9VAOeX5iVxlODlVj6Wxv7QynJzy/ESh\nMplsvwHkpOqjubztqiDkyIGerzJ3NNASIcZHEuGB/Pz8+7j3mnO2sn/5w8HT11nLux12y39c3FF/\ndWT8NrZ03fJUHWuvOtbedcvDVjt4+rrlPy7WXboZmKrqWDulGhm/vaP+atWx9gs3XJSq7F/+UHPO\nxlrqLt20/MdFSnXhhovrA1JZ/uPiux32AFTByBkZv73v//4UjByOaj45lv+4SPtQc87mV45ItaAc\nVpnAckQqOdAfhXqgP7rfB++DBGn7DhdI56iExDKFPHhDBfkMScI/2PRlaDoCAGa1QisUADR1jmDk\nM7NjMX8U8y8BAJu+jFExfxROgwazIdkOjy/HqLmw63Gk2nTkvNXmxrwGzKcR+8ComLPLanNvqbmI\nDx7qqteb03UOj29LzcUF5dS29uOj7LI8A0Yb+JUjVobNhMbsWEwOrQyTw6iY3QtndZtPjlgZlIN5\nDXiLKXBlUI5YGTnQSxxoidBCPkOS8IP9J7vY9GXVxy+7J6bQoYQth5p78TS66cgFfPZrtbnRp4Qn\nCADAswyuzKYvqz5+uc8x0eeYYFar+rYhpGU+5m67d0vNRQDY2XANTU0Ojw8dxrWt/bQPVpvbPTHF\nqJo6HeiYYn2gVJycps4RSoU9rD5+GfvQ1OkIIIdS9Tkm2gfH2Exota39s5U5wWTZrQAAIABJREFU\nzyqDPaw+fpnIOU9XBoB9jV3tg2O0Mk2djgCVwT44PD40K7MyzvZwhKsMJ4dRyYFe4kBLhBbygrQY\nOJ3Op5566sc//rHfT995550dO3Y899xzlZWV3/zmN3t6eu5x95YOGgUNAB23xhsuDdGWHruXM1+h\n8YnOwonH/GnSAgB9Tm+fU+FoOj17biV7d4BgABufnOYcUw2XhjpujYvdpo6p2ROWgqrj1jiXP/3B\nDTcXkj2fHJr5jXJaekZpS8/seY3rVb0yLJytydA+OMZVBve1YGWsNtcHNxRh4ac7HFxlcBOxMnKg\nlzjQEqGFvCAtBm+99daNGzfGxsbEjw4cOPDVr3711KlTOp1udHT0Zz/72ac//enf/va3976TSwE1\nPgGAKTGG8xSVmgwx0RHUdIQpMnSWMLRFVRQm0Q0LUnRCUHcSKOOokYTO+2nQqmKiI7g46q3FaVyy\nNXab+rhwmYsPN6fruaDuUpPBnK6ncmZzx+eosIdcHQpSdOX5RtrySIYOlFNz4i21KqVzjK3JsHFV\nfEGKomXrTB3mKmOZEcjL4SpTUZS8oBxclgO9xIGWCC1kQF+wmJqaun79+gcffHD48OHjx48DwMc/\n/vHHHnuMrnP27Nl9+/atWrXq5z//+Re/+MXPfe5zq1ev/uUvf9nS0vLCCy+oVIGe2IVVxtfG7Hin\n19fSM5pj1Ly77dFVCRqDVmXO0J28YtdERfzTs3mVG1IA4Jm1iWd7nAOuyaritDefXwMAZXkJV26O\nf3hzHG/0a6IizBn6FQBWmzs1Lrqmct0j6bo4jcqcoTt7fRQA/v6pbDaf5tkeZ/eI11KY/ObzazRR\nEZbC5J4Rr9XmNqfr6r64PlUfjdFzZ6+PaqIijr34sY3Z8dGqCEtR8skrtxwe346SrH2bcwHAUpjM\nqI69WKiJiigzJTA5v/orc6o+OlUfnWPUnO50aKIi3nx+DZ7omZwdJVn/9GweUvmV09TpyDFq6qqL\n1qyM4eS8/EQGVxl82CDKWbsyllbm8VVxalVEmclwutPh8Pj2leeKlampXIdyxMpQOc+sTcQ+sMqI\ncuqq12uiIuRAL3GgEWF18C5rSJddsLh27dpzzz1HW3bt2vWVr3yFtnzta19raGh44403Nm/eTFc7\nceLEkSNHnn766QD80qgjIbFMIQ/eUEG67IJFWlraG2+8gcsXL1586623xHXOnj0bGRlZWlpKG59+\n+ukTJ060tLQEviCFP5o6R/Bh8vaSLPym6fD4qo9fdnhul+UlsFcs95/sauocyTFqD1asxnsj9W1D\nOM/KQUs++pesNjdOGEOpdjZc67Z7RCqDNqqmch1HtXdzLt5ssdrc+092OTy3KwqT8Ts4o8oxapkV\nilEdrFiN92SClFN9/DJSMTm1rf1HW/sN2qi9m3MDyFl0ZVDO1uI0vKPF5Jgz9Cy7IZjKdNu9Oxuu\nLSjnUHNvQ9vQIiojBzr4Y0ciSMhfSIvBb37zm23btnG/kG7fvr1+/frMzMxf//rXdOUPP/ywoqLi\nqaeeevPNNwNwhvmXLJoqDbPTYtJUaTQuMx8zzM5lSaetBADngVIAiH/1NEdFU6XRnktTpTFDmk7o\nCbMZ0jQkG+25NG8b3cZ0Fk5M1+bkiFSiHLyZQ+UYtKqePZ/wK4dWBuXQ+Un9ysHK0JBsnDCUysEb\ngLQyQcoRK4NyFqyMHGgIONC4HOYH7zKCNDWEDKOjo9PT0/Hx8Vw7tjidzvvRqZCBC2w+3eEYHrtN\nbU5ofKJeWDzvHG0doBu2D7oxY4YBs6JpqjSeuKkBrNvuHZ+c5hxT9W1DVptLTJWmjin0tnGR2Fab\ni5NztLW/Y9gjWuOoHKTlgrrbB92NV29xlQGlAQxJKBV+yslpvHqrfdAtZn5TObUzAucq4/D4OoY9\nopwFK+M3Rl2sjBxoCDjQEqGFvCCFDLdv3wYA0bmALfhpYKyZxd3o3hLBeYqyjZqkWEVcNEZB01nC\n8L5HaZ7CMRWnUXEBM7iCwseVrmOEDDHREdnKGTbNGbpUvSJVGv1alApv2nBB3abEGFGOKUmxDu6d\nWsKQFj1mDJnxGhoEBwDxQiTBrI8rgWvn1ixIieVsabgvUQ5XGVOSlqvMIxk6zpaGFRDlcJVJ1avl\nQAc/0OF8wC5TyAtSyBAZGQn+LjzYgp8GxpVZ3I3uLRGWwmTm9C3LM+Ayu3GPUwYAQM0LBew0gS00\nXXtHSVZBSmxBSiybyxJTpYEkWxu0qpoXCnBzjqqqOI3Zc6uK08ryElL10fvKcxkVkuBUAkhVV70e\nydkZp6ZynU4dGVhOjlGDy/gaPzbi7AB7y3OpnEyDuiAlllKhHFoZFh8eoDJVxWkFKbGZBjWtDAZ1\n4wQHVE5N5ToqR6yMpTBZp46kcrAPTA7OR4C9Yn04WLE6VR8tBzr4gQ7nA3a54j7Ppbc88c477+Tn\n5//rv/4rbXS5XPn5+Z/61Ke4lTs6OvLz86uqqgJzLov5GV1en8vr4xqvDY0v2NI/OsFt6PL6+kcn\nFkHltw/BUInrLEWOSLU4OWJl/PIvo8o8hAO9LA7eZQH5Cylk0Ol0er2+t7d3akoRRdPd3Q0AaWkP\nwmT1OnWkTq34qVfb2v+ffxigjwGaOkf+8w8D3COTH5658dZZG7t37/D43jpr++GZG9yzlgWpHB7f\n603XKRUAHGru5ahwQ+7hxA/P3BCpXm+6TqmwDyKVKOeQ8hnD4uSIlfErR6Tqtnv9VkaUE2RlRDl+\nKyMHWpQjEUJIl91i4NdlBwAvvvjiuXPn/uu//mv9+vWs8Xvf+95bb731jW984/Of/3wAzuVo1KE2\nJ7SEUZsTeqiozYllSFPXFhqfqAkNPVTU5oTGJwdJlWYZ0tS1henalAo9VNS1hX3wS0XloIeKGsBQ\nDs3bZnKoawvlUNcWVobKQbMcrQxawoCEZPuVg9nni6hM8HIWrIwcaCoHl5fjwRuekL+QQony8nIA\n+N73vsda+vv7f/KTn0RGRj711FP3r193BeOT09TmJEZ348li/+xxDrNB3S09TvoF8/B7vcCFZM8m\nfLMWZnyiX73r24Y6hj3UtYWvm1AqPMtgO+tDx7CntrWfUmHcNZUzQ/XeHBXS0l6hnMYrdtEARr9o\noxxaGfyUs4Q1XrHTkGy2LyoHi8lVZsA1yVWmtrXfb2X2kbGYGR2hMvVtQ5TqcHOvHOgAAy0RWsgX\nY0OJysrK48ePnzt37jOf+cyzzz47ODh44sSJ8fHxl156KT09/X73LsSIifbzbQZn8uda7pR5EZsE\npuJ8XNxdx6UgTqMa9U4FXseguetHmWjt4zRiBcTRCQZyoCG4gZZYOuQvpFAiKirq6NGjmzdv/vDD\nD7/73e8ePXrU4/Hs3r17586d97trdwV0hk184515qIClSj+Zxc475nQdJlsz/5JBq9r+JJ8hjSQ0\nXRt3tL1EQSUGdeMmzI7ll6osz5Cqj6ZB3RiSjY1zG1ryOTlIu5eQm9N1BSmx5WuMCjlCJPa8lVHK\nKV9jpJVh+xLlYN9YZUQ5O0qyUvXRdMJQsQ8zcjYr5JiStFXFaaIcOdDzDbREaCGfIYULlult6Pq2\noQ9uuLcWp7H76d1279HW/lKTgb15g7dK8HTANsR7KfR80dQ5crrDIVI9kqFj07T4papvG+q2eymV\n1eZuuDRUUZTMziAiFczeOrMUJrMNRTki1RLlLKIywciZrzJByskxarjKcH2QAz2fHFi2B2844n7b\n/CRm8CA5Ry/cGOVcthdujHJm2f7RiQs3RmmLy+vjWvxSXRsa5+y581Et2IdgqIKXw1EFL2fRlVmE\nnEVXJkg5D+FAf/RgHbz3F/IZkkQowQKqYdZDxQKqgQQ/MxMai8Rmri2WIS1SATGhsRxrRsU8VNS1\nhR4qarViYeGMinmomNXKoFVd2PV4jlFDrVZMDmZdzycHqe5UjkjFEr6pnw3dZd1274bvn7sjOVgZ\nakJDsxytDOsDM6HdkZyHc6AlQgv5DEkilKg+1s6edeN553BzL/NH1bb2tw+OtQ+OMROa1eZGOxM7\n5zo8vupj7QCw/2QXR3WIUDV1OurbhgZck4wK536mVACAJ6ydDdfmJtNs7HJPTNW29jMqq81d29rv\nnphiJjRGhcHYCGzZ39jFnGMop6XHSeUcmkeOWJlDASvTbfeib4362VhQ94JyBlyT/uTMTX6KfaBU\nuFV92xAzofmVg7Y0OdDU4ycRKsgLkkQoQb25iO4RxSuEo17fqNcXYAXW4vAoJmEan5x2Km1d3Xbv\ngGtC2eIBZUg2LovJ1lz+dI/dO+CapC24d+panqXi5fQ5FX1wCjY2lCPK5NZsHxzjKyOkoc+2KCoz\n4Jr0J2cxlRlwTXACnR7f8Jhid7h3OdDiQEssHfKCJBFKUA8Vury2FqeyFoNWVZCiK0jR0QfCuAK1\nhOFNGzobqTldFxMdwaVKVxWncXHUaHyiT7ORim6IydYc1dbiNFOSls6wiSssKGdjdnx5fiLtA8Zv\nU0vYDnSXPTlHhZ/SoG6DVlWen7gxO14pJ5OrDPaHdj7HqDElaUU5fitDH85jlahVDCtTJVAlxUZR\nOTgucqC5nHWJkEBGmIcLHowU5GfWJq4AAABLUfKbz6/VREXkGLXmDN2ga9Kcoa+rXp+ij1arIirN\nKT0j3lR99EHLaszbthQmT/imNaqI7bMB1WWmhByjxunxlZkSMKDaoFWVmQxOz9TalbHHXizE08rL\nH88YdE0atKqDltV4hqrckIJ9qCpOO2hZDQDmDD2j+tVLZqSyFCUPuiaRau3KGFwfqfZuzsUTHJNT\nVZyGM4GuXRmLcspMCcc+X2jQqqicmhfW4em1ckMKUm0vyfr7p7NRjkGrmvBNMzk5Rm2ZydBj97LK\nAEClOcXp9aEcrExVcRrrA+ZtUzmYRO5XjlgZS2Eyo8IkcioHK6OJimBUbz6/Bie9ZnL2bp4JVpcD\nTa+jD8bBGw6Qtu9wgXSOSkgsU8iDN1SQt+wk7jp2NlxbsftUwp5m9ky4trU/YU/zit2n2BN7q82d\ne+DMit2nmOEKXVsrdp/KPXCGPbFAqhW7TzGq+rYhpKJPyzkqAKg+fhn7wKj2n+xCKjbfjNXmRqpN\nR84zqvn6kLCnGUPhli6HVobJCUAFAEgVWI7fymx4/Rz2QawMlYNUS5fzwA+0RGghfyGFCx7UL1nU\ntQwAvd/4BABkfet91oIuWzptJcZR0/lJce5RjurC7sdNiVr9P8ylSqPTl07oiaZhOnUmAHz0+lNc\nSDaahlfsPsVa0OlLZ+HEdO1Dzb30ZOQ8UDrq9QWWg1QLyun9xifiNCoako1TqYpyRCpODrrDqRys\njCiHq4zr26UdtzzMAB1AzpaaS+w0PZ8ceAgGGpcf1IP33kP+QpK4u+DmoOxzevucXnEF6pjCMx11\nTOGnnGOq4dJQx61x2oIxBMpMAQcoQ7IBwGpzcfnTpzscVpuLtuDe6SycSNswexZGtA+6W64rwul7\nBGucGGHuV07LdSeX+d0wUwdeDlcZUU7DpSFODlZAlMNVpuPWeMMlhcAeu3d47LbS6eeB2TGich7O\ngZYILeQFSeLugrM5ZcZruKBuXIH6l/CRNY2jxk+5ZOuKomQuqBufM1MPFTqmuPhwc7qes0iVmgzm\ndEVkNe6dWsKQtoI4uwCgIEW3cVU8bcmeSRmfk4Pfo6uUBjBRzsZV8QUpirztipk68HK4yohyKoqS\nOTmzMeq8HK4ypsSYiiKFQIwwp3Jw79Thhp8+nAMtEVrIC5LE3UVVcRr6sjD9OtOgzjSoWWr1jpIs\nPFO/u+3R2VOkAd+KP1ixevb8q8F39RkVANRUrjOn63TqyLrqIqSqKk7DN/Px3XukwmRrZqYyaFX4\ngn1ZXgKbmnNfeS6eyC7sfhypWB/qqtezPiDVjpIsJqeuuihOE7mgHBZhPp8cVpk4zZwctqO66vWc\nnJrKdUhlmE0i5+SgS1usTF31evwIp4HgKlNXXaRTR5rTdSzhO4Ac1ocAch6GgZYILeQzpHCBvA0t\nIbFMIQ/eUEH+QpK4D+i2e7fUXNp05Dx7FIGTuGw6cp5mrNW29m86cr76+GX24KGpc2TTkfNbai4x\nK5TD46s+fplSAcD+k10LUllt7i01l/xS0ec9IlV92xBSsWcYSLXpyHn2DINR0QlmDjX3zieHUXXb\nvSGXE5iKyeGo/MoRK0Nn60EqTs6DPdASoYX8hRQueHi+ZI16p7Jfe5+dL9D4RG1OmCFNHVM4lyUN\nyQaAkddKDFoVdW3hhKHUAIYeKuraQh8XR4Vx1NS1hR4qGpKNPi46oSdSjXqnqDUO5dC8bbSEiXKo\nAcygVfXs+UScJpLKma8yVA5awvzKoVQoh/rZ0OEmynF4fAl7mjkqUY5YGVEOADzwA43LD8/Be7ch\nfyFJ3Gu0D7qVUdADoLQ54amBfgm12tzjk9Ocj6u2td9qc1EqnL6TfoP2GxZutbk4qqOt/R3DHura\nwhUOCena2FtG1dLjbLx6i1KhrYtO9Ybx2DQkGz+lBjCHx9d49VZLj1Mpp89vZWjnu+3ejmGPKIer\njBisjlWiQd1YmVqBanjsNpWD47JgZdoH3Q/DQEuEFvKCJHGvEaeM9M5J4N1K+OCdi6OOiY7ggrpz\njJpUvVrZogWljwuXqY8LAEyJMZxFKtuoSdVH0xbcO/VxzVIpNozTqApSYmmLmCaOAkWZ3JoFKbF8\nZQTD3myLojKp+mh/chZTmVS9mhMYr1UlxSp2h3uns9tRmQxxGtXDNtASS4e8IEncaxSkxDKHkjld\nhxNlMmeXQavCycT2bs5lZxz8dEdJFjsPluUZLIXJNI7aoFUxAxjbF7q2DlasZlT7ynN16kga1I0h\n2Tp1JLNjMSo0XCFmQrLLc9mpqqo4rSAllpOzYx45NS8UBJAjUuUYNZiiTdO1sT/ByEnVR/uTU8So\nmMONUeFWlsJk5oH2KwcdbqKc7QHlPKgDLRFi3N98QAmGhy10cikRq0EGiYpUMjE2SDmLToz1K+fB\nHuiPHr6D9+5B/kKSuD9I1UebkhQ3WH7fN9pwaZje3++2exsuDb9zzc5aHB7f/7YP/7ZLcfv+/z68\n1dThoM8YOm55Gi4N0ycfSNXSo3jZ/rddjv9tH6YbtvQ4uT5Ybe6GS8MdtxSzCTR1OP7vQ8UThf/7\n8BZHNZ+c3/eNcnJEqkXI8VuZYOR0272iHLEy71yzL1pOkJVZpgMtEUJIl1244CE36lCbE3qoqGsL\nPVQ0oJplSFMDGM7hRl1b6KGiAdXooaJULBKbmtCQirq20F1GXVtiHxiVKIe6ttBdtqActIRRKpQT\nuDKsD9TPNp8cWhnWB2ZC81sZdJeJcmiwut/K4HusD9hA4woP+cEbQshfSBJhAWpzmsmQVr5cAgCH\nm3vpyyW1rf0dwx767Rg3odNrilRNnQ7Mw2ZUDo8P07upwWxn/VVQxocj7X5CbrW52wfHGq/Y6Qsu\naACjcnDvlAo/5eQ0XrG39DgVchq7gqnMfHKon03sw4yckwo5HcOe2tZ+9ruByeHe1/Ev5z2FnJYe\nJ5Xj8PgOv8dX5gEYaInQQl6QJMIOIbwfMhtwoAjJdk9MhYqfS+n234cg1gk5OI1YgcUVdnxyWmwU\nqRZB/oANtMTSIS9IEmEB6llCm9N2IVV6e0kWu0li0KqqitNMSVrqP0YDGKVCPxW2I8zpOlOStqo4\njaNK1UfTGTZxk73lcxsiLe2VOV23MTu+fI1RGdTNT6XK5rJjLX7ztsvXGDdmx1M5uC8qB/vDVQYd\naMFUZp8gR6yMpTCZUm0vyYqJjqCVwb1TOTNU5QqqjdnxvJwneTkPwEBLhBbyGVK4QN6Grm3t77F7\nS00G9gK81eZuuDSUbdSw8zveKonXquiJ5lBzr9Pj21qcxny6TZ0jpzsclKrb7j3a2s9R1bb2Oz0+\nevrDPohUdEOkiteq2AmRUdENRTkBqALLEan8yhErM58ckcqvHLEyFUXJ7MIQTGWClLOsBxrkwRtC\n3G+bn8QMpHPUL0SLbf/oBOfNxUauRTT1iuu4vD6RStxjMH1weX0i/z2m8itn0ZW573KW0UDLgzdU\nkC8bS4QpqD+KpXMy5xjasQCAWa3M6bp3tz1q0KqsNjdmWmM6gzld5/D4Nnz/HD6rZ1TMaoV2LCDh\ntpjOQKlg1l2GWdf4cBvdZZSK2bEYFXOXURMa6wNzbTE5zITG5DATWmA5YmUCyKFUTA66ywJXhrnL\naGVEOawyVI5YGdaH5TvQEqGFfIYkEaagEzbj6aO2tZ85x2pb+5s6RwZck8xqZbW50SvFziwOj29L\nzUUA2NlwjTnHqo9fdk9M1bcNMatVU6cDl5nxF6fcBoAtNRdZH9DlvL+xi1mtDjX39jkm2gfHGJXV\n5sbzL6PCya2xD5ycQ829jKq2tb99cKzPMcFMaFabG41ezF3N5ND5p/1Wpr5tyD0xReVgH5gcPNti\nr+ZmTW3sGnBNBq4MzpMNANXH2pkcJKdyDjX3tg+OtQ+OUTm4zPxsDo+v+lj7ch9oidBCXpAkwhSc\nY2p8cpoLjbbecA+4JmgLxlFT7xaenmhINgB03Br/4IYiLLzH7u0YVqyDe6cvTiKt9YYiALvP6W0f\nHKMtTsE5NhsfzgcWcGu2D45xmd+4L1EOV5mOYQ9XmQ9uuLnMb6yAKIerzIBroltJhRHmtAX3Tk3Y\nSHW6U/ES66jXxznTcAUqB0kemIGWWDrkBUkiTEHjqHOMmpjoCC6O2lKYbE7Xi8Yn6qHCkGzOz2ZO\n13MWqa3FaaYkLaXCvVOzHDOAUaqN2fHl+YmUCjtJn3iLEeb4KSenPD+xIEVH+4D7onKqZgTOVcag\nVZmStKIcv5WhueNIK1bGoozuLjUZkmKjlGHhCaB0uKHNYXtJJt2wIEXHJbLjCtQst2NG4DIeaInQ\nInLfvn33uw8SAAA/+MEPXnnllfvdizBCmSlhBQAAmDP0v3rJrImKyDFqzRm6QddkjlFT98X1a1fG\nAEClOaVnxJuqj95ekvXyExkAYClMHnRNGrSqMlPCsRc/hgyMqq56vUGrMmhVZSZDj92bY9QctKze\nmB0PAC9/POPKzXF0UePTFEthstPr06giykwJNZUFmqiItStjc4wap8dnztDXvFCQqo9WqyIsRclX\nbo4h1TNrEwGgqjgN+1BVnPZPz+YBwDNrE1fM6qqrXi/KyU7QqFURz6xNHHRNpuqj927OrdyQQuVY\nipLffH4NV5l3tz2qiYowaFWMquaFdeYMPa0MSwSv3JDSM+LFyqAcc4beoFVN+KZpZfzK4SpD5Rx7\nsXA+OSJV5YYUrjLLeqAR8uANFaTtO1wgnaMSEssU8uANFeQtO4nlhEPNvQl7mhP2NLNwNqvNnXvg\nzIrdp+jT8k1Hzq/YfWpLzSX64H3F7lO5B85QHwFS0SfVSEWf4W+pubRi9yn2/JxSscdC9W1DuQfO\nJOxpZlPX4KRqlAoAqo9fXrH7FJ2Tbf/JroQ9zbkHzjA5TZ0j2AdG5VcOUgUph1YmgBxGVd82hFTU\nksDJ8UslyhErE0AOrcxyGWiJ0EL+QgoXyC9ZC4LOwgkAXa8+kRQbpf+HuVTpgxWrd5Rk0UlF0elL\nZ+HEOGo6CyfMOn1pSDZ6oCkVhoXTWTgBwHmgdNTry/rW+6wFJwylVGhcphN6Yh/o/KQA0PuNT8Rp\nVDQkG43LNG8bc8dFOVxlcMLQwHKwMoeae+k0bq5vlw6P3aaZ32JlRDlBVkaUM19lltFA47I8eEMF\n+QtJYtmAC40+2trPecka2oZAGZKNy9ThhsnWDZeG6IanOxxcSPasNW6OCk+jXCR2+6C78aqdtqCt\ni1LVCvHh+ClnAGu57mwfVLTgvqgBrH5GIC+Hq0zDpaEF5eByQ5uiDh23xjmBpzsc45PTSj+bh5OD\nPWxoG6Ybtg+6OdMgrkDl1M4IVCQ+jE9OL6OBlggt5AVJYtmAi6OuKEo2JcbQFnRMUUsYLovJ1pxF\n6pEMnTldT1twE+rjQmtWhdKElhmv2ZgdJ3aS+rjwezR1r+GnnJyClNjMeKXAwmSOCvvDyTGn6x/J\nUPjZSk0GrjJocxArQx1uAGBKjKkoUgjMNmpiohVnifkqU5qnKGlmvIaTgyssKCcmOmIZDbREaCEv\nSBLLBswtBrMp1zp1JMuxLsszoGOqrnr97OlJwzK/y2bPhjWV63TqyLK8BEqFV4u66iI8GZXlGViy\ndc7sBQZf8t9RksVOXjWV6zIN6oKUWDZpaVVxGhqIcSoBADCn67CHNZXr0PHMqNjK2MOClNhMg5rK\nwR4yKr9yMJXcUphM5ZTlJfCVKfdfmb2bc6kcnTqShnPvKMmalbOByQlQGXbRxcpQOayHfuWQymxY\nXgMtEVrIZ0jhAnkbWkJimUIevKGCfA8pXCBfZVgcHB7f13/Z+cPf2VLjotkdm0PNvV8/0Qmzt6oA\noKlzZGdDx9nroxuz4zVRETA7oU5D2zB76ZJR4WsouGFtaz/O+oOvsPilwg1/ar2ZY9Sm6qPn64NI\nZbW5v36i83Sng6NaUE5929DXT/wpSDmUKhg5jIqT88+nri+uMkHKGXBNcpVZUE44DDTIgzd0kL+Q\nwgXyS9biQF1b6KGiIdk4LSb1s+G0mA6PL2FPMyPBsHBqO0YPFaVChxs1gKGPa9Q7lf3a++w5OVJR\n1xb6uKgBDC1hNCTboFX17PlEnCaSGsBQzpaaS8z6PJ8cSgUAI6+VGLQqWhlRDlJROeguo1Od+q0M\nmuVEOWJlAIDKQe+fWBnq9BPlsOlcw3OgcVkevKGCfIYksYxhtbmoawvfDqGzXrKwcLKJu2PYw+VP\nHxVCssUkcrwqHG7uYy0Oj6+lx9l49RZ1baE7i7q2an/fz/4i8NOjSt9d49VbLT1OSoX7qidGOL9y\nBlyTnCUMM79pZUQ5uEzfp+m2e602F838xk6OT07TyuC+Dr03RzUrZ4DF3nj2AAAgAElEQVSrjCCn\nl6sMklCnn9XmHp+c5ipT29oftgMtEVrIC5LEMkaqXk3/iXdyqI8Llw3aKLqaTh3JWaTitSp6B4Zt\nkiM4qSg5AMRpVJnxaggIg0bF/gZAZrw6TrkOty/WH15OdGS8lt9Qp45UtkSBv8pwtrRUvTpHqAzn\nspuvb2JlFpQjtgBATHQEJyfHqFkWAy2xdMgLksQyBk5HhssGrQq9ZDRdG61ZBytWs/MLhlhXFaex\nWT7RV6ZTRyqoNgdFVZASS4O6MfOb3/CFAvYXwaK7GRWGZBekxNI+4GrMXcY23Ls5l/ZBp45EKxqj\nYhoXpirP5SpjKUzmqIDLHbfkc1S4TKkshckFKbEFKbHMqMZGR9wQCRG4I250LIXJYTvQEqGFfIYU\nLpC3oReN9sGxUe/cs2gA6HNM9Dm9mfGaTMPct9qWHmecRlWQEktbAIBuiFQFKbo4zcwvjFHvVPug\ne0Gq+fpwV6mClBOSytwDOSLV3ZMTwoEGefCGDvIXksSyB357DbzOqHdqceRcqA+j4tr9rDbhPy9H\nbPdLJXZY3EWQCKw9yMrM1+0g5YhUwVdM4A+BHH8bLnKgJUIIGWEu8aCBzkKGljAaUM0isZnVisVR\n00nV0BJGXVtIRZPIWSQ2o2KWMOraQksYdW2hJYz62VgfmAmNUVE5aAmj87MxOcyEJsphCd9iZagc\nsTJ+5YiVwZnl/MoRqag9T5QToDJUDqbCh8NAB/ufUiI4yF9Id4b6+vqdO3c+++yzL7zwwoEDBwYH\nB8V13nnnnR07djz33HOVlZXf/OY3e3p67n0/H2bQOTHRT7z/ZBfzR9W29g+4Jmtb+5nVCuOo3RNT\ndH429HFxc3UDwP7GOaqmTkf74FjjFTujcnh8omtrZ/019hfBLGGMympzt/Q42wfHmAmNZZ/76QOx\nxtW29rsnpg419zITmtXmZhoZFW5C51EV5aA3j1YGHW6CnKsc1UyRCRXKaelxUipMZGdXI7YhEtLK\nUKcfysGOcVThMNASoYW8IAWLqampbdu2/d3f/V1zc3NiYuKtW7fefvvt8vLy3//+93S1AwcOfPWr\nXz116pROpxsdHf3Zz3726U9/+re//e396vZDDjyncCHZ7okp6t8FAKfH556cUm54G5RzpFJChlGv\nb8EbTQ6vj/0NgFHvFHc7aL6983Imp7g4bYfH555YjBz3pE+szPjktNjbBakWvcn45LQfOZOLqsy9\nHWiJpUNekILFT3/609/85jdPPvnk+++///bbbzc2Nr722mter3fXrl23b88cBmfPnn377bdXrVr1\nq1/96vjx47/85S8PHz58+/btV1991ev1BuaXCBWoJQyXtyvztk1J2qriNC4sPFUfTdO1cRM2dxmh\nmgvqzjFqMNk6cLr29iez2F+E3/jw8jXGjdnxyl5lcnKwP5wcDFGlVFXFaaYkrSjHX2UyKZU5Xc9V\nZmtxWkx0hEIOUhE5OEGcmPktyMkC5SSzSEI3LMszxERHcJWpKk4zp+uVcvjK3K+BlggtpMsuWJSX\nl9+4cePdd99duXIla/zyl7/83nvv/eIXv/jYxz4GAF/72tcaGhreeOONzZs3s3V27dp14sSJI0eO\nPP300wH4pVEnhKht7f/A5n5k1rUMAE2dIw1tw9kJGnYW67Z78d3GrcVp7DWUQ829H9jcW4tT2TTY\nIpXV5j7a2m/QqJhvG2/gOLy+7U9mUaqeEW9pnoGdguvbhk53Org+HH6v1y/VVuJX9ivnaOvAI2Qi\nVFEO3nDrGfFWFCZROac7HaV5BrEy7NwdQA6luiM5gSvjd3REKr9y7vtAgzx4Qwd5QQoKH330UVFR\nUX5+/i9+8QvafuDAgbfffptdgUpLS4eGhs6fP6/RzP1nPXHixK5du77whS+8+uqrAXYh/09LSCxT\nyIM3VJAukaAwNTW1f//+lJQUrr2jowMAcnJyAOD27ds3b97MzMykVyMAyMvLA4C+vj6QuE/ArGt8\nIo0eKgBgzjFmx2KuLXO6DlMSrDb3lpqL3XYvM6oBMcKJVDgNGgA0dY5grnaOUXNh1+MGrcrh8W34\n/jmkqqsuwi/mbJ46dJfRPjBnF3OOYciCOV3nVw5zjolUVA5SMTkOj29LzcX55IiV8StHrAz67gCA\nzVPnVw5HFaScsjxDXfX6+eTc44GWCC3kM6SgoFKpPvvZz37yk5+kjWfOnPnd735nMplMJhMAjI6O\nTk9Px8fzL8Rgi9PpvGe9leCws+Ea80dVH7/snpiqbxtizrHa1n489zGrldXmnnG4HWvHEyWe6QBg\n/8kuZoSrPn65zzHRPjjGqOrbhpAKr0YA0G33Im318cuMCh3Gh5p72Tx1h5p72wfH+hwTrA9NnQ6k\nZT7mbru3+li7KIdKQKqmzhH3xJQoZ0vNxdmH/74tNRcBYH+jQo57YgqtaPNVhsnB0zetzKHmXka1\ns+Fan2OizzHBzHh+5WAfWGXmk2O1uamcpk4HuuxEOfd+oCVCC3lBWiR+/etfb9u2Ta1Wf+tb34qM\njAQAtDaoVPyPTmxhxocAWDOLu9Dfhxo0JBsAOm6Nc/nTPXav1eYSN6GzcOK5j4ZkA0Cf09vSM8pR\ngdKjNRuSrUjXBgDOS9bSMypkfg9xVNgfTo7V5uqxKzY83eHgMr9xEzo/KS5bbyhUd9wa5zK/e+xe\nzmWHtjQ6Ryr28DRpAYA+p5eTgysoK+MAwRo3PjnNyWm4NMTJwW6Lcu7xQMsDNuSQF6Q7xujo6Ne/\n/vW/+Zu/iY2N/fd///dHH30U2+lliQJb8NPAuDKLUHf5YQcN6jZoVeZ0PWeRqihKZmE5dBNqCcPb\nONyGBSm68nwjbcHMbPrEW4wwx0+5dO3yfGNBiiKJHPdFLWFIIsrhqLYWp/mVQ81yuFyhDFYXK1Nq\nMsRER1AqTB6ieakop6IwiW5YkKLj5OAKtDJIwqKMsA8x0RELyhGtjLh8jwdaHrAhhwzouzOcOnXq\ny1/+8h/+8Idnn332hz/8IT4fQnz00Uf/9m//ptfrP/e5z9FNbt68+Z//+Z9/9md/ZrFYAjDLjK+7\nhzJTwgoAq829dmVM3RfXp+qjDVqVOUN39vooZl3jWemZtYlne5xe3/TLT2T807N52DLomrTa3JbC\n5Lrq9ZqoCHOGnlH96q/M2QmaOM0c1d7y3MoNKQBQVZx25eb4hzfH2XMLS2Fyz4gXqX71klkTFZFj\n1Bq0qitD49iHx1fFqVURlqJk7MPfP5WNj2EqN6QwqjefX6OJiigzJTi9vg9vjjM5OUYtlYMTKTE5\nf/9UNk4hailMRipLYfKxFws1UREbs+MDVOZgxWo8U1eaUz6wubpHvOyJjiiHVubYix9bszJGrYoo\nMxk+uOGmcsTKPLM20en1tfSMluUZfvWS2aBV5Ri1OUbNBzb3fHJ2zDrIOTn3fqAR8uANFaTL7g5Q\nU1Pzne98JyMj49vf/vbGjRvFFR577LGJiQmr1Up/D/3mN7/Ztm3bZz/72W9/+9sByKVRR0JimUIe\nvKGCvGUXLE6dOvWd73znscce+5//+R+/VyMAWLdu3eTk5B//+EfaeP78eQAoKCjwu4nE/UJ929CG\n189teP0ccxZ0271bai7lHjhD5+apPn45YU8zMykAwP6TXbkHzjA3FwA0dY5seP1c7oEzjAqdCwl7\nmrkpdjiq+rah3ANnNrx+jj2xQOcY7QOjotPbYB+21Fxiz1FEOVabm5Pj8Piqj1/OPXCm+vjlBeVQ\nKtaHwJU51NzLUTE5zA7gV47fymAfAldmPjlbai6xPtzVgZYILeQvpKAwNTX1qU99ym63NzU16XS6\n+Vb70Y9+9Nprrz3++OM/+tGPsKW/v/8v/uIvJiYm3nnnnfT09AC7kF+y7iW4zG+cYZPmbWO6Np2F\nE43LdEJPAHAeKB31+rK+9T5rwalUad423uai85NiWDidbhUAer/xiTiNKv7V06wF3cY0bxtvc9H5\nSTFdm85PCrPp2lQO+rBpfLgoB6m4yqCcwJXBSUvp/KRYGQCgcnAqVVoZUY7fyohysDKiHLEyd3ug\ncVkevKGCfA8pKHR0dPT09KxatergwYPip9XV1ZmZmQBQWVl5/Pjxc+fOfeYzn3n22WcHBwdPnDgx\nPj7+0ksvBb4aSdxjcPnTDZeGdNGRnDVuL+RSa6+YOw4A7YPu9kGFAex0h6MsL4EawGpb+w9WrKZU\n+OnpDoUtreW6k8skPdrajzNYU6qaynWcYa9j2MNZ44629lcUJVE5DW1DO0qyqDXOb4y61eZquDTM\nyXk8Kz5wZbCHNMIcKwNKHG0dsBQmc5Xh5HTbveOT01xlRDlYGVEOVxlRTsgHGiRCCnlBCgoXL14E\ngOvXr//4xz8WP33uuefwghQVFXX06NF//Md/fOedd/DGXWxs7O7du7/0pS/d4w5LBMYjGYqfudlG\njSlJEeaNIdk5Rg07gaI1qywvgZ4HM+M1XFB3vBBJMOtwS+Du83BrFqTExqlV4ob46uhsrzQzfSN9\nMCVpuaDuRzJ0psSYwHKQypyhp3JS9epSkwEa5zbMNmq4CHPM/Dan69iVEitTmmegAuOEyPbSPAMn\np2ymRZE7HhMdwcmpKErmcsfRmCfK4SuTGHMvB1pi6ZDPkILCX/7lX16ZHxs2bGBrJiUlvfHGG+3t\n7fjR+fPn/+qv/ioYz7fEvYSlMJkZl6uK03CZpWvnGDXoJcMZAWA2UggA9m7OZT7sgxWrMw3qgpRY\nNm1aWZ4BlykVLtdUrmOOZ2zZUZLFjMs7SrIKUmIzDWqWpW1O16E1DqcSwD7UVa/H/XJUTAIuWwqT\ndepI1gdzuk6Ug1R7y+fk1FSuS9VHl+UlMCpWJT9yXiggVEV+5fitTF11EduwprLAb2WqitMoFU4g\nS+VghLko52DFaipHp4682wMtEVrIZ0jhAnkbWkJimUIevKGC/NUpITGHQ829To+v1GSgc1p/cMOd\nbdSwL9o4e3S8VsVNjw3K+aRrW/t77F5K1dQ5crrDIVIBADentdPjE6keydDR6bFPdzjitSr2PZ31\ngVH5lYNUfuWIVNz02BzVfHK4yswnR6SifRArw/ogUtE+LLoyix5oiRBC/kIKF8gvWfcd1M+GljDq\n2kKzHPWzsUhs6tpCSxg1gKEljLq2cGpOagBDSxiQJHKYtYRRex5awqifDftAM79ZujaVg5YwSoVy\nqJ9NpPIrByvDZk2FWbOcXzliZaifDb1/VA463DiqYORgZQLL8Uu1xIHGZXnwhgryGZKEBADAgGuS\n+tlmksjfm4upxnMffXMFg7obr9g5Axgop3rDmUD3k+hufPjPOdwar9hbepzUhIb7ovHh2B8anm21\nuQdckzQNHX+UdAx7qBw/VDMx6n2UqmPYU982xMkZn5ymcnDvVA5eYGiLw+PDCHNKhSso4sMbuzg5\nTZ2O8clprjL1bUNWm0s5On2cHLyccKODwee0Moebe0M70BKhhbwgSUjcAQxKb5XoJfOziUbF/gYG\nx2YIzseli47kHF8GrUqnjlS2RAVPSBGvVXEuu/n6tiB5kJvEREeIBjZddFDknGFPp47kdhG8NW4R\nAy2xdMgLkoQEAECqPppOGHrQkg8AzPPGlveW57JTlTldV5ASW77GyOxYBq1KDAs/aFkNAGiZQ7C8\nbUpVvsZYkBJLqdBLRtO10R6GfUNUFafp1JE0qNucrqsqTuPk4N6pnBkq0lKWZ8DMb9oHJAlcGZTD\nVQYjzEU5ispU8JVhu+PkmJK0zHeHk+wBMcvNR4VF4OSEdqAlQgv5DClcIG9DhwPaB8daekafX78y\nTjPzC6PPMfHfF2/+f2uMBSmx2DLqnWq8eitOrSpfMzf9c+MV++iErzw/kW2IVOX5xkyDmlE1XrVv\nzI5bBNWvr9g/u34loxr1Tv384k1KBQA/v3iTo2rpcbYPjotyRKrMeLXYh+fXr+QqEyo5C1L5lRN8\nZQpSYnBK1sByQjLQIA/e0EH+DpWQmAO+PUNbDFpVqcmwyjBnqYrTRJqStNxNpD9L1LonffQkZYyJ\nejRTR+/8GLSqRzN1xpioO6VaZdCUmgyUKk4TyVEBgEiVY9RqoiIoFcoRqVL1ikkisA+0BeWw8/5S\n5IiVyTSog5GzPl034JoIpjJByhErs4iBlggh5AVJQmJeUNcWmuWoa4sFKDATGovEpp46NMtR1xaj\nYtHdLOGbmdCYJYxSobus2+7d8P1z2AeWB8GcY8wSRqku7Ho8x6ihfrYAckQqZkJjCd+B5TAq1gcW\nWO63MixGlmWfB5YjVgbNcrQyAeQwex6rzKIHemn/vyR4yGdIEhLzgk6vicv7G7uY1aq2tb99cKyl\nx8lMaFabmwvJBgDMHce/lKq2tZ956po6HS09zvbBMWZCc3h8aEIT+7Cz4RqdYNs9MVXb2k8n2K5t\n7R9wTVKqmaBu5QTbHBVuVd82RKnwxM0s0Q6PD+1nGBnOVYbJwcpQOd12L/rZaB9mYtRPzpUUe4Wx\n5awP9W1DfuXQmdTFyrAicJVxT0zRqcfFytzRQEuEFvIKLyExL7qVWdpiy6jX1+ecoC1cMDkAOLw+\nAOge4am4NfucE5nB7Z3L/B5wTXKZ3z1274BL0SvchLqWcZnL/B5wTXA7dXp8fiPMHaJMZcuol19B\nrABuIkaYc5Xptnu5t1Cx26Icjso9MeWvMpOinJAMtMTSIX8hSUjMC2oJQ5fX9pK5q4ZBq9qYHV+e\nn0hv3VQUJYMyd7zqsTQA2PEkT4VrMqry/MSN2fGUCvdFg7qxPzRd25yuMyVpubxtzPymJ3HR+4dO\nM2oVw8zvKoEqJjqCysHUc1HO1uJUrjKcHFxBIefJLFDGqJvTdTHREVQOWuO43PHts+GzXGWonByj\nxm9lTElaKgdXWPRAS4QWMsI8XCBTkMMQz6xNNGhVE77pquK0mhcKACDHqC0zGZyeqY3Z8RjdrVZF\nVJpTnF5fjlH75vNr0Nz18hMZKwAAYO/mXDzZlZkScowap8fHqFL10Yzq2OcLU/TRAPDyxzMGXZNI\nhbPaVBWnIdX2kqx9m3MBwJyhN2foBl2TlqLkmsoCTVSEQauyFCUPuibXrow99mLh2pUxuOGEb1qj\nijhomUkiZ3K2l2R959k8AFi7MhapykwJKEcTFVFVnIZyGFXlhhSk2rs59+UnMvzKoZU59vlCPHfT\nynByWGU2ZscjlSgHqVLj5ipj0KqYHEthMpODlWFyLEXJxz5fOF9lmJyDltWYRL7ogUbIgzdUkLbv\ncIF0jkpILFPIgzdUkLfsJCTuDFtqLq3YfSphTzN7rF3b2r9i96kVu0+xx+xWmzthT/OK3aeYf8zh\n8W06ch43ZI/ZdzZcww0pFW7I7HBWmzv3wJkVu08x0xelYpF0jIrNeVPfNsT6gC3oHEMq1gdGxfqw\n/2RXMHI2vH6Oo/IrR6TCPmx4/VwwlWFyWGWYHLEyVA4LZxLlNHWOiHLEygQz0BKhhbwgSUjcAQ41\n9+KZzuHxVR+/3OeY6HNMMI/WoeZePHmxM11TpwM/rT5+GT1aeP4FgNrWfmb3olS4YX3bEH66peYi\nPmDvtnvRlraz4RqhugAATZ0jc9OMNnY1dY64J6a21FxifcDTOrNlM6r9J7sYVfXxy+6JKavNzTx1\nfuUwWxqeuLvtXpRzqLnXrxxGhZ9uOnIe+2C1uZk1LkBl9jV2WW1u98QUqwyTQyuz4fvnOCq8ojd1\njlA5eP3edOQCJ0cscpADLRFayAuShMQdoEGZ+trn9LZcd9KWnhkj3JwFC89rNE0VP+UMYC3XnX1O\nRQvui9q98GzLWeOsNheX+X26w9FxS5G3jSdiSoXLNPMbADpujXNp6D127/DYbSoH9y7KOd2p6EOf\n08vJOT17qWAt9TMC5+Q4PL7xyWmuMg2XhoKUY73hoqv5rYzVplgH905nj0WqIAdaIrSQFyQJiTsA\ntYQBQEGKbuOqeNqC8dvUjiVOB4efckHdG1fFF6Qo8rZxX9QshwYwDPBmVOZ0fanJoNiwKNmcrqct\nszHqc6uh04ylASFMiTGcLa3UZEiKjaJyMPPbQuqAPawoTKIbZsZrMuOVSeSFSZwcy4zAuUxxg1YV\nEx3BydlanMYlss9XGU6OOV3PeeFKTQbOsCdWZlZOUAMtEVrIC5KExB1gR0kWesMwujtOE5lpUNdU\nrsNz3L7yXLzwvLvtUTyvWQqTcSaFgxWrZ8+/GpyUoao4DSdONWhVNZXrMg3qOE0kS/hmO7qw6/HZ\ni4eBBXXjXhhVWV7CwYrVBq0KqXD9C7sfxz5UFafhrKN11etnT9wGFtSNe8kxai7sflynjsSQciYH\nz9dMDpuzoKZyHVLlGDXYq6riNFqZTIM606CmcrDPddXrkaosz8CoRDm0MjlGjU4d+e62DbghrQyT\nM5PIvjmXUeGkDOZ0HcrBKVlFOVxlzOm6C7seD36gJUIL6bILF0ijjoTEMoU8eEMFOVODhMRSYbW5\n95/scnhuby/Jwp9BOCdNt91TlpfAMhH2n+xq6hzJMWrx1wwA1LcNHW7uNWij9m7OxZ813XbvzoZr\nC1Idau5taBuiVE2dI/io/6AlH6nwabzDc3trcRr7Os/6wLIbalv7j7b2G7RRBytW4+8GJmfv5plf\nSIuWs+jKoBy/laFyqo9f5qiYHPZrxmpz76y/CgCiHL+VEeWIlWFyJEIL+QspXCC/ZC1TjHqn4l89\nzf6J85/SkGxM16Yh2TjLJ53QEwCcB0rjNJE0JBsnDKXx4XjHjFLlGDVdrz5BM79hNl2bUuFtMRof\njnft6HSrmDvul4oGq6McGh+OVFSOQavq2fMJAMh+7X3WB7EyODOsKIfO3OpXznyVodOt3pGcYCrj\nd6BxWR68oYJ8hiQhsSQ0Xr1F/4m2LhqSjfHYNCQbP+UMYI1Xb3GZ30dbB0BpAKudyUefs8Z1270d\nwx4uTvtoa7/V5hLztqlTGWlpfLjD47PaXPVKd9nR1v7hsdtKp98IKOPDZ6nm0tAdHl/7oLt90C3K\nUVSmuVeUAwCc0w8jzCnV4ZkN+cpw2edWm0usTMewR5SzYGVaepx+B1oitJAXJAmJJYHLTxJDsvF7\nNJ0/ze+aBSmxnC0tRzDszbYocoNS9dGc4yvbqOFsaehko7Y0pKUONwBI1au5aUzjtaqkWMXucO+i\nnNI8hTUuTqPiYr8fETZBEk4OCJXJMWq4fCPstlgZTo4pMUasTKo+WpQjVoZaGQEgM16z4EBLLB3y\ngiQhsSQUpMSy5xDmdB1as9gTGoNWNRMfbslnJ1D8dEdJFjutVxWnFaTEZhrUlAozvykVesnY0xFc\nxghzZlwuyzNgrjnLPs8xatDph5sj0M/Gno4AwL7y3FR9tKUwObCcmfjwFwo4OTQsHOVwlcFlSoWz\nxrFnNvNVxlKYnKqPZvOfMjkoAcH8h/9/e+cf1+R17/EDiZBAgBBBfggCBVEoWrTida4FrC20tRvQ\nbnd0rRPmem91rw4stXebdEpX7G/BvVr7Y+sAe21ZfwlrtcK1FGl1QFaMglg1FCiYgCAEiCRAgveP\nrxxPzhMRbZCA3/df4eR5vjnfA08O5zmf5/uhobYlhFxpZCz6kBoBp3N92JoQwvYhQO5s9ReN2Bbc\nQ7IX8Db0tKZjYFg/ZA7zuvwfun7IrD4/yD0PpNIMhM12kTlf9htVdxtkziL233b9kLljYJgNBSde\nNRQYK1xHKHW3wdfN6aqhrKYjDMWlIxyZ6ZWOMJQwHbx4bQWukBDEBvi6OXFfUgfP9JTWd3PVBErr\nuw+e6aEtOoNpzzcdxUc72RM/On5uzzcd3D5HaX03t9dSWt/90fFzbKjio53FRzvZvZYJhtrzTcdE\nQnHpqDT60vpurmTDnm86Dnxrsddy4Nvze77p4Ao0lNZ3s5tJ9pDOREIRQoqPdn7W2C20g0JsAq6Q\n7AX8J2smwaq2QBLGqrZAEsb6bVN3bVaEBpIwVs8GYjlWzwaSMNZvmzp8s6HALJzVs4G6jNWz0T5Q\nPRsNJUyH1bOBWI7Vs11TOsKR4dLpfS6WCzWRdMYZGVaeB2K5a02Hep/DAXjx2gpcISGI7WFVW0K/\nbSoJo/9oqzT68lM91a197LoBLMxZPRsEoQWwCSGVTTow6qahdAZToVKr7jZYhCprJowTOX3NhlJp\n9OpuAxcKxGZsOtDCpgM93GkpI6xu7ePSgQPYdCBBVs8GH7Szqu360oHnjejICNMBX3NWngehhOnk\nlFuMTHVrX/mpHtoHncFUhMVVJwGckBAEQRC7ACckBLE9bKEzWsuOe3ddjB9VdkX7yxIWKFYEebBy\nalDZsWouCEKrEhBC4kPlvm5OaUwo8PzmjLrhFKq7o6/ZUOCGzoUSmoVDC5vOJftwxtQ82l8GFuZs\nH+AANh1IMMOasfr1pZOXHM6OjDCdtBg/XzcntpTqJQ2kIJ2tCRYjsyLII2GBgvZBLhWvw1p2kwDu\nIdkLeBt6hlHS0HXsrH5djB/daWjpMRYptbfNldGqM3BPzEMqZr+mC5Xa1h4je2JlU+8htS4uTE5L\nA0CoIIWEThVwP4oQwn4FT2oolUZfWt8lTIcNRU9k5xgYmaRF3vT73R7SmUgoMnZDjw1F8OK1HTgh\n2Qv4N30zMBHZt53opCeoYp882fd1C+JR9j19wYeNEeRGoNLoqe8qNVygqi1q60D1bNH+si83LpVL\nxVSEJpeKv9y4NNpfxirHaCiqHKPWElSEFqyQHH1yuVwqZkVoIFTTGUzURhbUZVwfQF1GRWhUXSZM\nB/xer5oOGwrSYdWG44wMlefRdFh5Hk2Hjgzo7qyODNsH0N2x6YCM8KrpwMggtgX3kBDkRrCp5DSV\ne8G3YX5VG1VtFSq1jZ0X2nVDVM+m0uhB6EXlyDqDCdy1qZk3vNYPmQuVWqocq2zSFSq1+iEzFaFB\nnWxCCJwOgFn4ptIz9Fmc/Kq2joHhkoYutg8wB7B9uGRh/n4jl/4JsTMAACAASURBVE6hUsul09h5\ngQ0Fr9lQ6e83Qh/GH5mShq6OgWEqz6Pp0FA0NTbUtvLmK42MRR+KT8LpXB9yypvZPrTrhrh0WLkg\nYitwhYQgNwJWtQz0WT5c2dh5IcDDomJbi8ANfaxlhD2sY2CYs9Nu7TFynt9g1M0+BwphOTf0joGh\nFstQfQZT9wWLj4NPF6bDWZj3G/lHR48JToEgXDqDw6PcyLT0GLkKe9Bt4chw6ajPDwpHBm7fcekI\nR4ZzQ2/vM7b3DbEtffhs7CSAKyQEuRFkWorQCCGcUXdC+OwVQR7sVvm6GF9i6a4Nt7NYo+5ghSTM\nS8opvtbF+HFG3esENuoQllW4gRs6Z/OzLsbPy3WWpVm4J7EUy42FCmBDRfrIIn1kwnRYsRwE4dJx\ncXLk0kmO8ubSybh0Ij8y7ImQjnBkwrykwnSuOjIrgjwSwmezobhfH2ITRNu2bZvqPiCEEPLaa689\n8cQTU90LZLKID/N0GHvx/tooySzHYIU0eq6sc2A4eq7b+2ujgjwlhJDUaJ/WXqOvm1Ne8iXL8+Qo\n786BYZAs5yXPhwjBCkmfwRQf5rk3fbFklqNcKo4Pk7f2GIMVkr2/Xrxwjgsh5PEfzT11btDXzYka\neydHeUMfkhd5v782ihCycI4rhIqe6wYFRuVScfIi786BYV83p4KHI6DodVqMH+0DbMzcu3A2Tacg\nNZJLp+DhyCBPibPY8d6FsyFUXvL8exfOJoSkLvGhoZ5fE8qNDJcOjAykQ0dma2JI6hIf6FWf0SQR\nO9KRiZ7rRtP5cuNSCJW8yPvUuQvBCokwHergTkeGprNwjitNB0bGWexIR4amA+DFaytQZWcvoFAH\nQaYpePHaCrxlhyBTRk5Zs0NWhWd2Fd0tL2no8syucsiqoMVsdAbTkldrHbIqqAyMEJJefNIhqyIk\n9wjdy8kpa/bMrmJDqTT6kNwjDlkV7B7+ql11XKhNpWcgFK0rWqjUQh9oYaFxQrF9gFCe2VW04qow\nHRqK7UNKQb0wHW5kKpt64UR2ZITpCEcG0vHMrppIOktereVGhk1HODKIbcEVkr2A/2TdbLAFPQkh\nbc/82F0iZk2y85LmZ8YGsn7bIFxm65NC7VHODR000A5ZFbQFNNBsUVEQLrP1SQkhA9vjui+MsJ7f\nUHuUtQ8HDXRKQT39mgbfcWE6hJDAPx+mLSDpZtNJjvLem76IrdxqNZ3mLSu9XGe5/fHqI8Olc/HV\nuzg3dGE6wpGBdPKr2tgCd325cf1GkzAdeI0Xr63AFRKCTA2cAKz6+77GTgsdWmlDF7EUgMGXJisA\nA6Nuzk67tL5LpbEQicHqhy0qCgsI1m2BEKI+P8jVDD2k1nVfGLHUsxkIIazrxCXf8YZu9sT2PmN7\nn0WCcACbTsmlBC9L43QG0+DwKJdOkVLLiQavNDJcOirNAOeGfkit49zQhSMzlo7FiY2d+urv+9gW\n7teH2ASckBBkauDctVfM8+AszJOivImluzYIwDij7mh/N07xFRcm5yzMQUvGhoLXrMKNEBI22yVp\nkYXKLkgh8XKdZWkWLiWEsGI8eJezMA/wkAjS8SKWvuPJlxK8nI5cKnZxcuRGJmmR91XTAfEe5ztu\ndWS4Wgzw6axgD8ImWaoNAzwkK+Z5sC1cJxGbgBMSgkwNaTF+VDxdkBoRIHcOkDtTe3L67t70xfAV\nGayQUKNu+AKVS8VQLyA+1JOG2pYQEh/qKXMW7U1fBKHiQ+UgjaMWPjTU1sQQmBXAzFvmLIr2l9Gi\npZmxgXBXCoosQKhLFuapETAHBCskUP4gMzbQajrCUNCHaH8ZvMumA6HYkdmWEBLtLwPfcehDcpQ3\npMOODHVkp6H2pi+CkWHTgZnsy41LuHSEg0w7DCNzpXQQ24J7SPYC3oZGkGkKXry2AldICGJHQDGb\nlIJ6djskp6x51a46tlZNSUPXql11bKUclUafUlCfUlDPmsilF59ctauO3e/Jr2qzGootR9TSY4Q+\nsKE2lZ5ZtauOdeorVGpX7aqzdAvsTSmoTy8+SXd3aChhOsJQwnTYUNedjtWRgXSEoaymIxwZbrMK\nsRW4QrIX8J8shDD24WRMEsYKwKD+KatnA7Ec67dNxszCWREaFAxl5XkglmPrk4LCTWcweWZXcaFY\n+3BQuLF6NlC4sdI46js+fjqgcGP1bFbT6X0uVi4Vs6EgHVaeByPDpgNiOasjw6YDYjl2ZK6UTr/R\nHPTcYdoHkDLCa7x4bQWukK4Bs9m8e/fuxx9/PDEx8ZFHHnnppZe6urqEhx08eDAzM/OBBx5ITU39\n05/+1NraeuO7ikxHqlv7WAHYzqp2YikAgy9NVggHvuOcNK5IqVVpBlgRGtiE51szC6ctINgrFIQa\nHB5lK9eB/CyfMSyHHhYpO9hQYGHOpgMHWKTzVRux1LOpNPrB4VEunUKllpPGCY3VL9moM+m09Bit\njgznhg4HsCMDPYTBZ9MpP32e7QOn30NsAk5IE8VkMq1bty43N/f48eNz5sw5ceLEO++8k5iY2Nxs\n8Yhcbm7ub3/724qKCplM1t/f/8EHH/z0pz/9+uuvp6rbyDTCXWJR7DhYoOOCFrl0Ftvo6+bEKb6C\nFBJfN4s6rXAKq3CD15xgz9fNmftQD6nYxcniW0IY6lLfPC1OdJeI+XQ8+XQgCJeOi5Ojh5QfBy4d\n6LYwHS6UzFlkbWSc2BY45UpDzabDlb71EIwA8sPBCWmi7NmzR6lUpqSkVFVVvfvuuzU1Nenp6Rcu\nXGCLAdbU1OzevXvevHmff/55cXHx/v37d+7cOTIysmXLFqMRn1pArkKkjyvVbsmlYnDRpsou+jov\naT79Ls6MDZQ5i9Ji/Ojto2h/GRh1s6GoNG6cUHBWcpQ3GyrT0rAc6r8RQkCKxobKiA2kX+JpMX6R\nPq5sOsEKCZQrZftAlX60D/BBmbGBbB+So7ytpsP6jl8pHeHIyJxFVMI3zshsTQhhQ0X6uK4I8qDq\ncAhFEJtzEZkYKSkp0dHRAwMDtOX8+fNRUVG33Xab2WyGls2bN4eHhx84cIA9cdOmTeHh4QcPHhw/\nfnh4uM37jExHznQNHj3bz7YMGE1Hz/YPGE1s49Gz/dr+Ie7EM12DbIu2f+i6Q3EnXikUd+LRs/1c\nH64U6qp9EIb6Ielcd6irpnMRL17bgSukCTE6Onr+/PklS5bIZJeL5ysUCnd3dycnp4tjwpCamhqR\nSBQXF8eeu3r1akJIdXX1jewwMn0J85JyD29+rzMeUuvYDYx23VBdu75n0MJJSKUZ4Ao0HNfo69r1\n/UYzbdEZTIfUuu91l9fr/UZzXbv+uKVZ0XfnDepuC2+hnsGRunZ9u+6yJ5DOYOL60G80q7sN3523\nOBFCsX2AUFdNRxhKmI5wZCAdzhhJODLQh6uOzETSQWwI3gadEI6OjocOHeIaP/300+7u7oceekgk\nEhFCRkZGzp07FxAQIJFY3H0ODQ0lhLS3txMEuXaoni2z9Ayoy9j6bCCWY627qbs2FaGt/8dJkISx\n8jxQl7EiNOrwTUVo1OGb1bOBWI7Vs4HCzWofhKFYPRukw+rZxkmHyvPW/+MkiOVoOpmlZyAd4cgQ\nQqjaUJiO1ZEB7R9rrD5OOjb8RSME95Cug4aGhp07d/7Xf/3X5s2bExISsrOzob2/v390dNTDw4M7\nHlr6+vr4QAgyAdhqofCluankNG0BT+5CpZZ97KZQqe0YGGZFaPB4DVst9FIopqWySafuNrBO5DqD\nCYKMHwommJzyZrYPoLJjQ4EjO6tngyDsoz/047h01N0GVp4ntDC3GgoGgX2SSTgyMJhsOjDgXDqN\nnRfKT/Ww6exEC/NJAGf4a+bYsWPvvPPO0NAQIcTT09NsvrR4HxkZIYSIxfyQQgu8Oz4LFiyAF/hM\nAzJx9MNmzk5bZzDph8yWLSPE0vN7gvQZTIPDo8J2YairBp/gKUILc0KIfnhCwTk3dP2QmfuIifuO\ncycKHdkJc8EitgJXSNfMI488cvz4caVS+fTTT3/00Uf33XdfT08PIYTeuOOOhxZ4d3xOjTEJvUam\nK6xZOPigs+7a0f4yXzenjNhAevsIzFjDvKSsWThI4yxCxUKoADZUmJc0Ocqb8z53cXJka4/Cp28d\nKxBHxvy/2Rbw/OYc2eEAVpwGLRmWbuichblcKgYLczYd6DabDhSsgzTZdNJi/NiRyYgN9HVzsgwV\nSCwN5iEsF2pFkEfCAgU3MnjB2hys1PCDePnll//2t7+99NJLSUlJer3+9ttvDw0N3b9/P3tMU1PT\n/fffv3LlyoKCgnFC4cPeyJUoVGpbe4xxYXJanLuyqfeQWuchFdMvZXoTiZ2c8qva+gympEWXldwQ\nKkghoRNDS4+xSKm1GmpdjB9VckMoYR+shqLTANwl6zOY2FATSQdCWU1HGIrtwzWNzHWkIxwZghev\n7cAJaUI0NjYWFxfHxsbefffdbHttbe3atWuTk5NffPFFQsiyZcuGhoZUKhW7Hvriiy82btz40EMP\nbd++fZyPwL9pBJmm4MVrK3APaUJcvHjxH//4R319PTchwc262bNnw48RERG1tbUnTpxYvPjyY4N1\ndXWEkMjIyBvYX2QmozOYluyohb166ltKlWNUXUaVY9H+MvCPUGn04PYNRg/R/jKw7oa9emEoqruj\noYIVkqNPLudC7U1fBOsMKoQD3R0hhGrqaCiqqWP7IEyHhrJhOsJQVtOBUITR1EH5PqvpILYF95Am\nRGhoqIeHR2NjY2NjI20cGhr661//Sgi5/fbboSUhIYEQ8vLLL9NjtFrte++9JxKJ7rrrrhvbZWTG\nsqn0DFWOwRdroVJLlWOFSm1JQ5d+yExFaCqNHlRkKQXHxzb/TSkFxwkhOeXNVDmWXnyyY2C4sqmX\nhqps0sFrGgrKXRNC0t9vZELVE0Lyq9qoEC6/qq2x80Jj5wWqqats0sFrKhbXGUygcGNLetN0aChQ\n/XUMDLPpgGAPphA2nU2lZ9h09EPmkoYudmSE6QhHZtWuOkJITtnlkdlUeqZdN2Q1HcS24AppQkgk\nkuzs7M2bN69du/bRRx+95ZZbOjo6Pvjgg/b29vvuuw8efSWEpKamFhcX19bWPvjgg2vWrOns7Ny3\nb9/g4OBjjz3m7+8/tSkgMwbuqU91t4Gz0z52Vs+VYoNT2HKr8Jp1QyeEdAwMcfbhrT1GTmUHSja2\nPil8lR9qsjhRKEs71KTLjA20tA/XEYE0bnB4lEuntL4raZEX2wLdtjRWNxLhyJwfPHbW4oHf1h4j\n98CvcGQgLGcw0d5nbOy0sFGfuGAPmTi4QpooP/3pT9944w0vL68333zz6aef3rFjx4ULFzZv3gy7\nR8CsWbOKiooSExO//fbbl156qaioyGAwZGVlbdq0aQp7jswwWN9xuVQc5iXlfMfXxfhF+7uxkjAw\n5GbFcvCa07NF+7utsyzRFhcmd3FyZEPBp7NiObjBtS7Glz0x0kcW6SNjW+AAVuEGQdh0ghUSFydH\nzndcmM66Syfy6XAjI0wnaZF3mJd0/HSEIwPpJIQr2Bauk4hNQFGDvYD7osjEySlrLvy3NtrfLS9p\nPiyGShq64LFQ6kqu0uhzyppVmoG0ZX4gYgZjusqm3vhQT1qHFEIFe0ryksNhtqhs6t1UcoYNBeZ4\nbChCSHrxyZKGrvhQT2ounl/VtvOrNjaUSqPfVHK6pdeYceclg3MIVdnUmxzlTUua0nRoKJpOXvJ8\nmDNoqImkE+3vtjUxBPogHBm4UydMp7Kpl+2D1ZHJKWvWGUw0FIAXr63ACclewL9pBJmm4MVrK/CW\nHYLMBEoaukJyj4TkHqG23FDYzTO7ihbUAQGCQ1ZFSkE93YDJKWv2zK5iTVRpKCoHABGaQ1YFV3zI\naqiQ3CN0A6ayqTck94jVPnCFfxyyKlbtqqN7OYVK7fWls6n0zJXSEYai6cC6bYIj45ldhYqGSQJX\nSPYC/pOFXDdsfVIyZtTNen5DwVDWPhyEy6x9OBh1c57fUEqVDQWSbrbcKpiFs/VJCSF9uXGEEI8t\nl0sSgw6bNVYHHTZbbhX6YDUdh6wK2gI6bGE6rLG61XSglKpwZFIK6ul0BaVUhen0G02Bfz7MjQy8\nxovXVuAKCUGmPZw0rkjg+Q1LFrY+Kbxm7cPBwpzz/D6k1g0Oj7KhQOHG1ieFCaa0oZs9sbFT39hp\noXCDA1g9GwRhlX46g2lweNRqOpahuqymw0rjrKZTWt9ldWRKLG3UiaVPPKRTfrqHbeE6idgEnJAQ\nZNrDGXXHhcnDZruwLeD5zWrB4XX0XAvjpbDZLpxgL0ghsWphzircQAIQF2qhOgvwkAR4WPYqVE4s\nfcfjL7XwFuZcOkmLvLl0oNvCdDhH9rDZLpwWLkgh4bym4BRW+wc9ZAV7kM6KIHcuFEFsDU5ICDLt\nSYvxo8LlzNjA+FBPmbOIatii/WVQN2Fv+mL4tpVLxZfswxNC6NRSkBohcxZR23I2LBsKXu9NXwxz\nAJQ2GPvcS6HykuYHyJ0D5M7UZTw+VA5hocgCISRYIYE+FKRG0FAQnEsn2l/GphMfKr9SOnlJ8+nU\nAunEh3qOn84lC/OHI7l0tiZajEyA3DnSx5WGSo7yRgvzyQD3kOwFvA2NINMUvHhtBVZqQJCZCVTa\nPqbRr4vxpTegCpXaQ026uFA5Wx67SNlxm7+Mq2mtM5oy7gxkq30LQx3T6IM8JXTdoNLoi5RauURM\n62rTUOti/OjaJb+qrbXXGBcqp4/y0D6w1b53ftUmDNXSa7zWdCAUIeSq6XChxkmHDYXYEFwh2Qv4\nTxZiW1i9MpiFs3o2EMuxejZQl7H24WRM4cbq2SAUq2dLjvLem76ItQ8HhRshhNWzgcKN1bOBwo11\nQwexHCuNo2bhrDwPFG7CdNhQVtPpfS5WLhULR4ZNRzgyICPsN5qDnjvMjQy8xovXVuAeEoLMQNTd\nBrbcHLj4sE/PXPIdZzy/VRq9SjPA2ocTQoqU2sHhUVbPdinUV5dDwQTDWnrrDCawMGdDwQGsng2C\nsCdWNukGh0dZhRus81SaAVaet7Oq3Wo6bCiVRg+O7FwfOgaGhSPD+sSPhWqnLS09xurWvvLT57mR\nIYitwQkJQWYgMmcLh2JQsrEKtzFlgYUsTeYkZo8hhHhIxZzKjj19/JbrO8XFydHDsj1YIZE5WbRc\nKRQn2JM5i4TpyJyuMjJWP8JdIg7wcBb2FrEtOCEhyAzE182J7oXIpWLQklHNG329NSGEfvOC8Xka\ns9kDbujE0iw8Lzn8qqHA83tFkAcbCgzLhSdCQAA+iPUdj/aXJUd5Q8e4UFQsd7kPiRbpwCDQPoCA\nUOYssrBRT+RDwWs2nfhQeaSPK5cO67yO2ArcQ7IX8DY0YnMaOy/0G02RPjJ3yaVlQbtuqL3PGOAh\nCZBf+n+/32hu7NS7S8SRPq70xOrWPkLIiiCPawpl9URhy6T2weahrpoOwYvXdqDKDkFmLOyX8pWg\n38hXOcxZzFkcuUvEpM9qQP5ml9AbSXgYfMSEejKxDl8rwnTgg4T9RCYPHGsEuVlgRWhQWa6lx7hk\nRy3s1VOHbypCo2bhrJ4NxHKsCA1CsXo26vBNQ1GxHFsjDsRyrDwPFG6sqTmI5QjjRC6Xio8+uTxY\nIWFDgVjuqukIQ4FhuXBk2HSEoWg6k/J7uonBPSQEuVngCmwTQnLKm6lyrFCp7RgYLmnooiI0lUYP\nX9ysno36jnNh2VCVTTqwMKehdAYT+I4LT4SAAHxQoVJLNXUqjb6koatjYJhWz6OhuNLj0MKlAw7o\nNFR+VZt+yGwRqmxCoRo7L1S39rHp7MSC35MAzvAIcrPAqpbhNef53TEw1GJpH95nMHEW5sJQVluE\nt+muegowODzKuYO39BitOrIL0+Hc0PVD5lZBOh0Dw5Z9GCGWJV+vlE5735Cwt4htwRUSgtwssGI5\neE39UgkhwQpJtL8bq3AjhKyL8XNxcmRrj4K3d+adl0NBzTdWdSaXikFlx4aCA9iqrBAkibFejfaX\nuTg5csbqaTF+0f5u7JwE3Ramw/Yh2l8W5iXltHDrYvzCvKRsOnAAGwrqR2TEBnDpJITPFtqoI7YF\nVXb2Agp1kBtAoVJbpNQmRXnTr+DKpt6dVe3BCgkVOrf0GOGe2NaEELbWzqEm3boYX1rvx2qoImUH\nyLJprR24lZcRG8iWDipt6FrHVFAtaegqUnbEjRVgJYSoNHq4J0b7AKFaeowZsQG03o8w1ETSgRtu\nKo3+qulwoaymQ/DitR04IdkL+DeNINMUvHhtBe4hIchNDa1TB+oyQgjV1IHmjRBS2dQL3t5Ud0eF\ncFSoRgihdepoKCqEg3p3ZMwNXWcwBSskR59cDqFW7apTafRyqXhv+iJY/Qj7QENRCZ9Ko08pOA47\nTHvTF0f7y3QGU0rB8aumU6jUgmYhPlQOHhZW0xGODC15R3V3iG3BPSQEuXnJKWumderSi0/qh8wg\nRYOW/Ko2EKSt2nUUNvlVGj0I0mAmIITAdAIH0zp16cUn23VD7bohqqkraeiCsDAbEUJaeowpBccJ\nIZtKz4B6TWcwgZS8UKll+6DS6PVDZhqqskkH0jjaBzYUl05lUy8bCnqYXnwS+lDZpBsnHTZUu26o\nsfMCLXlXqNQWYi27SQAnJAS5eWE9vwkh6vODpfVdbEtrj5FT2YHCjS23Cl/uh5osLL3b+4ztfRbS\nNTjA0j5cRwRKv8HhUU4aV1rfpT4/KOw2K40bm5ksQqnPD3JG48fO6jk39Culw5q7QzrVrf1sS6tA\nmIf8cHBCQpCbly83LoU9/GCF5GjW8mh/t62JIXvTF8mlYqiAtzUxxMXJER6GJYSkxfjB7bLe52JB\nDhAfKgenib3pi7YlhMil4mCFZG/6IlDZ7U1fFKyQyKXibQkhcMuu97lYENolR3nDiV9uXAo3xODB\nVRcnx62JIXlJ86EPe9MXbU0MifZ3O5q1HCQJmbGBtA/CUMJ0ClIjIFRBagQNBemwobh0vty4dFtC\nCIT6cuOSFUEev17ux6bDChQRW4GiBnsB90URZJqCF6+tQFEDgiAWVDb1wiZNRmwgrBt0BlN68Umd\nYSQ+1JOuDHLKmiubeoMVUljNEEJKGrpAq52XHA5LEJVGD4UY2FCbSs+09BiEoeTSWbCaYUNtTQwB\nmYNKo88pa9YZRqgym4YKVkipxICGykuaDyuqCaaTXnwSQtF0QAgul87amhhypXQQ24IrJHsB/8lC\n7AHWrZWMlZtj3VrhbhUtB0fGbrWx5eAIIX25cYQQjy2HuFCsWyvI3li3VvBmZQvlkTFvVtZ8FmRv\nrI8tqPjY6nbgWsulIwwlTAdUfGw6cqm4NfvHVtOB13jx2grcQ0IQ5DKcEeohta77wggrHwBBAasx\ngwmmSNnBntjYqQfvBgp4sLJuraB/Y4UVLT3GweFRTolQ0tCl0gwI3VpZJQLI5zirWZVmgEunSKlV\ndxsshRV8OhCWM8Bt7NSXnz7PjQxBbA1OSAiCXOa2uTL2xyCFxMvVwoYVLFbZOgVwgyuOqQlECHGX\niDnjBjiArb4DQTibVxcnxyDLynXRc2W+bhZurWB0y4aCu3OcAW7YbBdhOmFeFsfAp7N1iSBs9Fw3\n9rAADwnn5eGBpb4nAZyQEAS5THKUNy3DEx8qh9d0hwa0aoSQgocj6XwALZlMNZ3M2MBIH9dIH1da\nhgfcWgnjGCuXigsejoTTuVBpMX605F1ajF98qKevmxNo3iAUBIFHdCHU3vTFEJxOLQWpETJn0fjp\nBCsk8Boej4VG0N1tTQhh0wmQO0f6uLKhMtExdhLAPSR7AW9DI/aDfshMCJE5W1jhqbsN3PJC2NIx\nMCxzErEn6ofM+mGzr5vTtYay2oeOgeGrhhIe80PSEYYSpoMXr63AFRKCIDwyZxH39V2o1O75poPd\n76ls6t3zTQe7+9LSY3zryNm/1WjoJo3OYPpbjeatI2fZXaiJhNIZTK9Wfs+GIoTkV7VxoeBEbhfq\nrSNnhaFerfyeDQV9EIYSppNvuZkkTAexIbhCshfwnyzEbmH1bODNyurZQCzH6tmoNysrzwOFG2s+\nC2I5Vs8GCjfWrZV6s7LyPHiylQ0FYjlWngd9sBqKTQfEcqzSD9JhfWxpOqw8D9KB13jx2gpcISEI\nMh6Dw6Osng3kZ6zFKswKOWNf6IQQlUZf3dpX3drHriR2ftVGOPPZ0jPEUs9GFW7sGqukoUvdbWDl\nefBcERsKphNop31QdxsKlVo2FNjIsulcCvXV5VAQlu0VpFN+qkeo9ENsC05ICIKMh4uTlW8JuUBj\nJmy5KtdxyvihOMEed9fxh8ApBpFJAickBEGuQhrjjgqlDahYjlC31jsD6QQT7S+DWnZUqCaXijPu\n5L1ZIQhbFA4+KCPWIlSawOYVTqG6O6uh4kPlvm5OrAEumM9C4+UTk8O5dCDsViZ4tL8s0sc1YYHC\nIh1U2U0CuIdkL+BtaMSeKWnoOnZWvy7Gj26ctPQYi5TauDA5LVgA98Tge5+eCDfN2Imhsqn3kFon\nDHXbXBmtx2M1VElDV0uPkQ2l0uhL67uSFnnTqUIYiow995oc5U1PFKYjDDXBdAhevLYDJyR7Af+m\nkWmHSjMQNtuFvTOm0gz4ujmzquiOgeGOgaFo/8vPmeqHzOrzg2yL1VDqbgMhhNVhXynUVfswkVAT\nT0c/ZObU4Xjx2gq8MYogyDVDjV/JmFiOGr8SxlCV1oijVrNUnke9WYWhCCFUU0f9YWkoKpZj5Xkg\nlmM1ddQhgoaiYjmqqZNLxUefXB6skLCaOpoOeMheKR0IhdgW3ENCEOSaSX+/kUrOYILZWdVGhXCF\nSm1j54XGzgv0sR6VRg+6NSoW1xlM6e83EkJyypq5UPlMqMomXUlDV8fAMA0FRb7ZUIQQmJnAmBxa\ntpU364fMhUotDaXS6AuVWv2QmSq8aSgwnAWgJae8mUoEi8yhWAAAIABJREFUIZ3q1j42HVbjh9gK\nXCEhCHLNsCJsoKXX4lnRfqNp/ANoi84wwjYODo/2GSzObekxBltWtwObV1aEPWaLzjvGcr6urT3G\njoFhtgU+nZWnU4d1Lp32viG2heskYhNwhYQgyDXDiuWg7ty6GF/aIpeKI31kkT4yducfDohnarDC\n3TmqiSCERPvLXJwc1zEiAjgs2t+NDQUKN1a2AKHYE+VScbS/GxdqXYxfmJeUnd7ggKumsyLIIyF8\nNtuHuDCLYrKITRBt27ZtqvuAEELIa6+99sQTT0x1LxBkQty7cLYDIYSQ5EXeb/xsoWSWY7BCGj1X\n1jkwHD3XbW/6Yh83J2exY2q0T2uv0dfNKS95/r0LZxNCkqO8h0yjErFjRmzgtsQQQkh8mGewQtJn\nMMWHeb6/Nkoyy1EuFceHyfsM5oVzXN9fGwXzx+M/mts5MCyXivOS58NUlLrEB/qQFuOXlzyfEBI9\n142G+vyxaAiVvMi7c2AYQi2c4wLHQ6itiSEwk9F00mL8oOTrwjmukE58mOf7j0bJpWI2nYKHI9h5\nFC9eW4EqO3sBhToIMk3Bi9dW4C07BEFsw6bSMw5ZFZ7ZVXTzv1Cp9cyucsiqoKWGVBp9SO4Rh6wK\nqqwDeZ5DVkVI7hG6NQWhHLIqaKiShi4IxcoiuFCEkPTik9AHGiqnrBlC0cJCKo0eQq3aVUdDXakP\nntlV4P5nNR3EtuCEhCCIDShUakF4pjOY0otPtuuG2nVD6cUnYarIr2qDqWXVrjrQC1Q26WBq2VR6\nBorLtfQYYYagoQgh6cUnVRq9fsicUlAPoQqVWphaqCy7skkHMrmcsmb4FJ3BBDLuyqZeqqnbVt4M\ndcGXvFoLoWgfUgqO0z5AqPyqNppOSkF9v9FsNR3EtqDK7joxGAxr165VKBRvv/0299bBgwc/++wz\ntVotk8nCw8PXr18fFBQ0JZ1EkBsGV2y0vY/X1BUptfB8D22BlQcrjYN3OWlcaX1X0iIvtqWyqXcr\nCbE0j9ARSzd0QohKM8AZjR9S67gCevDpbLlVCFs6tioCGjv1nMquFR0oJgFcIV0n27dvr6+v7+7u\n5tpzc3N/+9vfVlRUyGSy/v7+Dz744Kc//enXX389JZ1EkBsGp2cL8JAEeEiEB7DzAWgTWN9xeJez\nME9a5B0224VtAUEBK5YDaRwrNCCERPu7cVq4uDA5V50BPp3V/kHYJEbCRwiJ9JGtmOfBtnCdRGwC\nTkjXQ0VFxSeffCKR8H+RNTU1u3fvnjdv3ueff15cXLx///6dO3eOjIxs2bLFaMT/p5CZTFqMH4in\nweY8QO4cIHem9uSZsYGgZ/ty41L4xo8PlUP5g7yk+TAfBCskUJSBhiKEFKRGRPvLZM6ivemLIFRa\njB+UYIAiCxAKLMypak4uFUMlhfhQT1qDdVtCCMxYR7OWQyjah73pi2kfIFRmbCBNZ2/6IneJyGo6\niG1Bld01093d/ZOf/OSRRx75+OOPPT09P/nkE/rW008/XVpa+pe//CUxMZE2Pvnkk/v27du1a9fq\n1avHCYtCHQSZpuDFaytwhXTNZGdn+/n5bdiwQfhWTU2NSCSKi4tjG2Eeqq6uvkH9QxC7oaXHmFJQ\nv2pXHRWqQbWeVbvqWDO9QqV21a46KhkghFQ29a7aVZdSUE81b6CVYEMRQnLKmq8aSqXRpxTUWw3F\nChOEoUoauiAU3ayCUKt21XGbVYitQFHDtVFcXHz48OFPPvlEJOK9v0ZGRs6dOxcQEMDdygsNDSWE\ntLe337heIogd0G80L9lxWc8G9U+pnq2ySaczmvKS5l+2D2/Sqc4OHM1a3tJjpE7kJQ1dvc/FyqVi\nWjW1skkHNuopBfUwOVU26Vp6jQWpEZeN1Zt0cGJLj5FWTS1p6ALfcVaeRwhJi/GjbuiVTbrKpt4v\nNy69XLl1LFS/0UxDVe46CuncsMG8ScAV0jXQ0tLy4osvZmRkzJ8/X/huf3//6Oioh4cH1w4tfX19\nN6KLCGI3NHbqLT2/O4ilnm1sDri82lBp9IPDo5xgr1CpVWkG2FBQp5VdKsFahz1RZzCpNANcqCKl\nVt1tYOV5cEC+wEYdektDVbf2lZ8+z4bi9HuITcAV0kQxm82bN29euHDhr3/9a6sHjIyMEELEYn5I\noQXeHZ8FCxbAC7wfjcwAONvvYE9eBARWeJzvuIuTo4elMjtYIfF1c7ZskRJC5FIxnaVAaxCskBJm\nwgub7cJp4YIUEtbciH56sEJCZ6mxUBYnukvEkZbpeEjF9IJFbAWukCbK66+/rlarX3jhBUdH64MG\nN/GEEw+0CG/xCTk1xg/uLIJMPZE+rlSKFu0vg4qooGojIMZ7OJIQsjUxhGrB4d3M2EBq2xofKk+O\n8mZ9x+VSMTiO01CEEJDn5SXNp6G2JYTInEVpMX40FLihy5xFVHdHQ4GyDrjkhp4QQuektBi/SB9X\nLp3M2EC8YG0OquwmRH19/S9+8YuMjIxf/vKXtPGBBx7w9PR89913RSKRi4uLXq+//fbbQ0ND9+/f\nz57b1NR0//33r1y5sqCgYJyPQKEOMiMRWqza3DFWGAodY6cpuEKaEA0NDWazeceOHcsYOjo6Tp48\nuWzZsocffpgQIpPJ3Nzc2trazGYze25LSwshxM8Pn1pAbkZ83Zy4r+9/t/eX1nezGzktPcbS+u6D\nZ3poi85g+qyx++tmi32aA9+er1Tr2M0k9XlDaX03a84EoapbLbZsv27WfdbYzZ5Y3drH9UGl0ZfW\nd6vPW5SNqFTrDnxrsXV04NvzXCjEhuAe0oS49dZbN27cyDXu3r1bKpX+/Oc/9/K6VNckIiKitrb2\nxIkTixdfvgNQV1dHCImMjLxhvUUQu4Xq2baVN4NYrrKpl2rqwCycdSLfWdUGj7hSJ/JNpWeOZi2P\n9pdRed628mbwHWedyMH7nA2VU94M3ufUiXxbeTOEovK8beXN4H3e0mMMyT0CoYR9oKFu5NDdDOAK\naUIsXrw4Q4C7u/ucOXMyMjIeeeQROCwhIYEQ8vLLL9MTtVrte++9JxKJ7rrrrqnpOoLYE6ye7ZJZ\nuOVTRISQnVVt7FNEhUqtutvALoPgFFo11WqoyiYdGJ/TUDqDqVCpZd3QCSGbSk7T0wEIm8MEV2n0\njZ0Xyk/1sE8y7UQL80kAZ3hbkpqaWlxcXFtb++CDD65Zs6azs3Pfvn2Dg4OPPfaYv7//VPcOQewL\nG974GnOysJAU6YfMVzj8mhE6siOTAa6QbMmsWbOKiooSExO//fbbl156qaioyGAwZGVlbdq0aaq7\nhiB2AWsWDnq2DIF9eEZsIL0bJpeK02L8wrykVCxHCIFadmwoEM5BOxDtLwvzkqbF+HGhfN2c2FKq\ncMrWhMsnQli2V9H+shVBHgkLFJaO7LgrbHtQZWcvoFAHuUkoVGpbe4xxYXJa6UCl0ZfWdwUpJFRX\nDffEPKRidkbJr2rrM5jWxfhRQXZlU+8htY4N1dJjLFJquVCFSm2fwcTOc9AHYSj2RAjlIRXTmY+G\nYk8kePHaDpyQ7AX8m0ZuZtTdBk6M1zEwLHMSsSJsaOSebFVpBjj1tvAYuHfHhRJ+4kT6oB8y64fN\nXHy8eG0F7iEhCDKVsEI4EMsRQlbtqqOF5uABWKqpi/aXfblxqVwqVmn0YF4ul4q/3Lg02l+mM5ho\nnToaimrqQHdHCKGaumCF5OiTy9lQhBAoUgem5qBiyIwNhLuLNFS0vwx0d4htwT0kBEGmErYyN8wT\nhUotLXlXqNRWNvV2DAxTTZ1KowdRHJ1CdAYT+I5vKj1DHy1KLz6pHzKXNHRRTV1lkw5eXyrASkhL\nj5FamNM+QE3VnPJmqqnLr2pr1w01dl6goVQafT6q7CYBXCEhCDKVcNK4weFRzh1cdVZv1XecFenB\nPMS6oRNC1OcHj53Vsy2tPUao2sB9OvuELIRVnR1gD2vvM3IW5n34bOwkgCskBEGmEtbEIVghcXFy\n5HzHk6O8o/3dhAo3ViwHbuis8k0uFUf7u3FauHUxfmFeUjYUfDpr/0qVfmyoFUEeCeGz2VBcJxGb\ngKIGewH3RZGblpyy5sqmXrl0FvUIL2nogidP85LDQfDd0mPcVHpGZxhJivIG2Rt4/bX0GIIVUlpo\nlYbKS5oPQrjKpl54YDYjNhDmLTDo0xlG4kM9qVJ8U+kZ1dmBYIWUVmgtVGqLlFq5dNbWxBDog0qj\nhwdpaSgAL15bgROSvYB/0wgyTcGL11bgLTsEQeyO/Ko2z+wqz+wq6sKn0uhDco84ZFXQMj8ghHPI\nqkgpqKf7SZtKzzhkVYTkHqGShEKlFkKxkgQIRdUNOoMppaDeIauCCiXYUNRCsKShKyT3iGd2FVuj\nCLEhuEKyF/CfLAQB2HKrhJDmLSu9XGe5/fEQbclLmp8ZG0il4WRM0n3ZDZ0QuVTc+1wsW26VjEm6\nPbOr6KwDpVTZUMEKSfOWlZfd0AkhhPTlxvUbTYF/PkxboDIsvMaL11bgCglBEPuCcwcvUmrV5wfZ\nltKGLmLphg6vWTd0sDAvre9iTzyk1nFu6HAKGwoUd5z3eWOnvvx0D9vC6fcQm4ATEoIg9gXnO560\nyDtstgvbAtI4tngPvAZrc0rYbBdOC3fbXBlX1gFOYQV7oGhIYjQLhJAAD8mKIPdxOonYBJyQEASx\nL9Ji/Gj5OLAzlzmLqI4uPlQO0ri96YvH5iEJeJDnJc2HqUUuFRekRsicRfGhnmwouMm2N30RzDrx\noXJqYQ6hoOgDHExnqYLUiAC5c6SPK/U+T4vxS8PiqpMA7iHZC3gbGkGmKXjx2gpcISEIMg2Ap45S\nCurZjaL8qrZVu+pYw73Kpt6UgvpNpWfoRhHUB0ovPknLMdBQVMJHCClUalftqmMLAglDwYnpxSdZ\nt0DEhuAKyV7Af7IQZBxCco/QGQXEctQNnYzVPy1p6IJKdGSs/qnOYPLMrqJBmresDFZIqBM5GRPL\nsaGSo7z3pi9ilX4g2Os3moOeO0wnJwgFr/HitRW4QkIQxN5RaQbYcnPwGBC7moHXrK24SqNXdxs4\no/EigRs6HMCGgmXTzqp22qIzmKpb+8pPn2fleZwMD7EJOCEhCGLv+Lo5sz+CNI4tSQev5dJZ7GEy\nZxGnhfOQijkrIzglWCCZ48q5ukvEAR7OBJlkcEJCEMTe8XVzoqo2uVQMjuMgkANAg0fL0BFCwK08\nLcaPep9H+8syYwNlziKLUIkTChXp47oiyIOGkkvFbPVVxFbgHpK9gLehEWR8Gjsv9BtNK4I8aEu7\nbqi9zxjgIQmQX16+VLf2uUvEkT6ubAshhD0RQkX6yNwll9xg+43mxk79VUMJ+0Dw4rUd6IeEIMj0\ngJ0YrkS/0Xx9wfuNvL8RhOLahYchNgQnJARBpiVsuTkwLGedyKn3OdXUUd9x6kROCDmatTzaX8bK\n8yBUS49xyY5aCEW9z2kouVTcvGUlt8+E/HBwDwlBkGkJW/wUSoDnlDVTIVyhUtsxMFyo1FJNHfiO\n64fM7HNLINhjQ8HrnPLLoSqbdI2dF8pP9dBQOoNpJ1qYTwI4ISEIMu2ByYNzQ9cPmXWWRuN9BpN+\n2Gx54gixdENnA1L6jab+IbxZN+nghIQgyLQkk9G5wWtW+RbtLwvzkqbF+LE31jJiA33dnKhYjp5C\ni9QxoQJoS7BCAhbmQht1xLagys5eQKEOglwrhUrtMY3+Nn8ZVXJXNvWWNnQHeUrodNXSY4SHWNfF\n+NHnjfKr2o5p9OtifKFwuNVQKo2+SKmVS8QZsYEwFcGdOp3RlHFnIPvoEl68tgInJHsB/6YRZJqC\nF6+tQJUIgiAzBDA1B+kBiOUIIbROHdXdUXletL/sy41L5VKxSqNPKTje0mME+wm4p0dtZIWhoN7d\nlOU5c8E9JARBZgibSs9QIVx68Un9kLmkoYvWqStUakFfRzV1Ko0e5Hnp7zdCrTyY0gghOWXN1EY2\nvfhku26osfMCDVXS0FWItewmAVwhIQgyQ2jpMbA/qs8PckbjrT1GlWZAeApbbhX0dazJBSGkvc/Y\n2Glho97KFHtFbAWukBAEmSFQhQIhRC4VR/u7cVq4pEXe0f5urFgOTklmDMvhfh13YqSPLCFcwbZw\n5uiITcAJCUGQGcLWxJBtCSFyqRg2h8gld/NFwQoJvIDJBnaJ5FJxZmwgFFelu0TJUd5wYlqMHw11\nNGu5u0QUIHemofKS5rOTH2IrUGVnL6BQB0GmKXjx2gpcISEIMpMpaeha8mrtkldrqWF5S48xpaA+\nJPcI1A0C0otPemZXpRTU0xoNOWXNIblHqGyPEFLZ1Lvk1dqQ3COs9zliQ3CFZC/gP1kIYnNaeowh\nuUfoj1BK1TO7is462xJCtiaGsOVWoZQqW7mVENKXG9dvNAX++TBtARt1eI0Xr63AFRKCIDMWzmi8\ntL5L3W1g69SBmo7VcIPamzuxsVNffrqHbTmk1k1Gh29ycEJCEGTGcttcGftjkEIS5iVlW8ANna0D\nBBo8TrMQ4CFZEeTOtnig98QkgBMSgiAzluQob1qbLi3GD15DvQZCCOjlCCF70xfDPASVGgghWxND\naA3WvKT5AXLnSB9XWh8vPlSeiRbmkwDuIdkLeBsaQaYpePHaClx1Ighy05Ff1dZnMMWFyemtuZKG\nrmNn9UEKCV1RQZlwD6mYelhQXz62cDhiQ3BCQhDk5oI6kZNysjd9UXKUd05Z87bySxLwYxp9XtJ8\nlUa/5NVaaClSasH7PCT3CAgitpU3N29ZiXOSzcE9JARBbiI6BobZynWw4sn/6rIfOVRQZR9RUmn0\n1a195ad6WHleERZXnQRwQkIQBOGRW4ro3CV4M+lGgBMSgiA3Eb5uTmlM4dS85HBCCGjtLrUkzSeE\nbE0IoXNStL8s0sc1YYGC6u7kUnEGquwmAVTZ2Qso1EGQG0Zj54Xq1v6fLZ7jLhFBS7tu6OPj5+5Z\noIj0cYWWfqO5/PR5d2dxwoLLdb7LT/X0D5kSwmfTEwlevLYD16EIgtx0RPq40okHkEvFcWHyefLL\nOgV3iSjMSypzsviSvGW2VD9sYmcjxIbghIQgyM1OZVPvql1H4TVYUegMJqqpo97n1NScep9PYZ9n\nJDig18D+/fu//PJLrnH27Nm///3v2ZaDBw9+9tlnarVaJpOFh4evX78+KCjoBnYTQZBrg62jml58\nMi3GL6e8mWrqCpXazavm9RtN1NRcpdEXKrVYrMHm4IR0Dezbt6+iosLV1WKl7+/vz/6Ym5u7e/du\nZ2fnyMjI/v7+Dz74oLS09PXXX7/jjjtubGcRBJkoLQI/cq6l32hq7xtiW/oYCThiK3BCugZOnTq1\ndOnSPXv2XOmAmpqa3bt3z5s3r7CwcO7cuYSQsrKyTZs2bdmypaysTCLBx+gQxB7JjA2Ex48IIfGh\nckJIRmwANT2SS8Urgjz6jWa5VEyXTUmLvK2GQn4IKPueKIODg+3t7REREeMc8/HHHxNCnnrqKZiN\nCCGJiYn33ntvR0fH4cOHxzkRQZApJC9pfl7S/PhQ+baEECiuGh/q+eXGJVCbtXnLSkKIu0R09Mnl\naTF+yVHeX25cQiXgiA3BFdJEOX369MWLFxcuXDjOMTU1NSKRKC4ujm1cvXr1vn37qqurV69ePcl9\nRBDkOsmMDeT2hOJDPTkTimCFhFYKRyYDnJAmCjxn4Ovr+/LLLzc0NEil0gULFqxdu9bLywsOGBkZ\nOXfuXEBAAHdrLjQ0lBDS3t5+4/uMIMh1k1JQX9LQJZeK85Lmw7O01EY2MzaQfZYWsRV4y26iwISU\nmZm5e/funp6e6urqN99887777jty5JJBcn9//+joqIeHB3citPT19d3gDiMIct3kV7XBHpLOYEov\nPtmuG2rXDVExXn5VWyHWspsEcIU0UU6dOuXg4PCb3/wmPT3d2dnZbDa//fbb+fn5v//97/fv3y+T\nyUZGRgghYjE/pNAC747PggUL6GfZuvsIglwDpWOKBqC9z8ip7Fp7jPSCRWwFTkgTJT8/f2RkhIq8\nRSLRhg0bvvvuu3/+859lZWUPPfSQSCQi1iYeaIF3xwfnIQSxE5KivOlTR4SQSB9ZgIfFrfgghYRe\nsDgz2Qq8ZTdRvL29uUeOCCEJCQmEkDNnzhBCpFIpIcRgMHDHQAu8iyDItIBqHORS8d70Re4SUYDc\nuSA1AqozbEsIYSu0IrYCV0gTZXR01MHBwcHBgW2UyWSEkPPnz8NrNze3trY2s9nMrodaWloIIX5+\n+OeLINMJ0IKzLWkxfjgPTSq4QpoQLS0tERERTz75JNcOa/awsDD4MSIiYnh4+MSJE+wxdXV1hJDI\nyMgb0lMEQSYLlUafUlC/alddieUOE2IrcEKaEEFBQQqFoqKi4ttvv6WNOp3unXfeEYvF99xzD7TA\nHbyXX36ZHqPVat977z2RSHTXXXfd4D4jCGJD+o3mJa/WljR0VTbpUgrqK5t6p7pHMxC8ZTchHBwc\ntm3b9rvf/S41NfXhhx9esGCBVqvds2dPV1dXRkbGLbfcAoelpqYWFxfX1tY++OCDa9as6ezs3Ldv\n3+Dg4GOPPSbcf0IQZBpRfvo8++MhtY57bBb54eCENFESExPfeOONV1555e9//zshxMHBYd68ea+9\n9hpdHhFCZs2aVVRU9Oyzzx48eBBu3Lm6umZlZa1fv37K+o0giC3g/JM80HtiEkDHWHsBTScRxM5J\nLz4Jz8NG+8uOZi2n7Xjx2gqc5BEEQSZEQWrE82tC9UPmMC98imNSQFEDclODjzROCdN32H3dnHA2\nmjxwQkIQBEHsApyQEARBELsARQ32wvS9iYEgCIoabAJOSAiCIIhdgLfsEARBELsAJyQEQRDELsAJ\nCUEQBLELcEJCEARB7AKckBAEQRC7ACckBEEQxC7ACQlBEASxC3BCQhAEQewCnJAQBEEQuwAnJARB\nEMQuwAkJQRAEsQvQoG+KOXjw4GeffaZWq2UyWXh4+Pr164OCgqa6UzONkpKSQ4cOnT592t3dPSoq\n6je/+Y2Pjw93DP4iJg+DwbB27VqFQvH2229zb+GwIyxYXHUqyc3N3b17t7Ozc2RkZH9//3fffefs\n7Pz666/fcccdU921GYLZbH7iiSe++OILmUx26623dnR0tLa2SiSSd955Z9myZfQw/EVMKs8888wH\nH3xw6623fvLJJ2w7DjvCcxGZIqqrq8PDw+++++729nZoOXDgQERERGxsrMFgmNq+zRj27NkD/3fT\nIf3ggw/Cw8PvvPPO4eFhaMFfxKTyxRdfREZGLl68OCUlhW3HYUeE4B7SlPHxxx8TQp566qm5c+dC\nS2Ji4r333tvR0XH48OEp7drMobCwUCwWb9++XSKRQMvPf/7zO++8s7Oz8/Tp09CCv4jJo7u7e8uW\nLRs2bFAoFNxbOOyIEJyQpoyamhqRSBQXF8c2rl69mhBSXV09RZ2aUVy8eFGj0SxYsGDOnDlse0hI\nCCGkvb0dfsRfxOSRnZ3t5+e3YcMG4Vs47IgQFDVMDSMjI+fOnQsICKD/uQOhoaGE+a5Efghmszkn\nJ0eoX1Cr1YSQ4OBggr+IyaS4uPjw4cOffPKJSCTi3sJhR6yCE9LU0N/fPzo66uHhwbVDS19f31R0\naqYhFosfeughrvHIkSP/+te/wsLCwsLCCP4iJo2WlpYXX3wxIyNj/vz5wndx2BGr4C27qWFkZIQQ\nIhbz/xBAC7yL2Jz/+7//27hxo7Oz85///Gf4tx1/EZOB2WzevHnzwoULf/3rX1s9AIcdsQqukKYG\n9tuQBVqEtziQH0h/f//zzz//ySefeHl57dy5c+nSpdCOv4jJ4PXXX1er1SUlJY6O1v/lxWFHrIIT\n0tQglUoJIQaDgWuHFngXsRUVFRV/+tOfurq61qxZ88wzz3h6etK38Bdhc+rr6998882MjAyFQjEw\nMACNo6Ojo6OjAwMDIpHIxcUFhx2xCk5IU4NMJnNzc2trazObzez/gy0tLYQQPz+/KevZjKOgoOCF\nF16YO3duUVHRihUruHfxF2FzGhoazGbzjh07duzYwbZ3dHQsW7Zs4cKFpaWlOOyIVXBCmjIiIiJq\na2tPnDixePFi2lhXV0cIiYyMnLp+zSgqKipeeOGFZcuWvfXWWzKZzOox+IuwLbfeeuvGjRu5xt27\nd0ul0p///OdeXl7QgsOOWGGqn8y9edm9e3d4ePijjz5KWzQaTXR0dERExNmzZ6ewYzMGk8l0zz33\n3H777QMDA+Mchr+IG0B8fDxXqQGHHRGCK6QpIzU1tbi4uLa29sEHH1yzZk1nZ+e+ffsGBwcfe+wx\nf3//qe7dTECtVre2ts6bNy8vL0/4bnp6ekBAAMFfxBSBw44IweKqU0l3d/ezzz578OBBs9lMCHF1\ndX388cfXr1+PKiOb8OGHH2ZnZ1/p3eLi4iVLlsBr/EVMNqtWrfL09OSKq+KwIxw4IU09IyMjLS0t\nrq6ufn5+Dg4OU92dmxf8RUwJOOwIBSckBEEQxC7ASg0IgiCIXYATEoIgCGIX4ISEIAiC2AU4ISEI\ngiB2AU5ICIIgiF2AExKCIAhiF+CEhCAIgtgFOCEhCIIgdgFOSAiCIIhdgBMSgiAIYhfghIQgCILY\nBWg/gSBTQEdHR2Nj4/Lly69kGzg0NKRWqy9cuBAYGOjr63ulqqNms7mlpaW7u3vevHlWD7t48eLI\nyIjwRAcHh1mzZv3ALBDEtuCEhCBTQH5+/t69e0tKSiIiIri3Lly48Nxzz5WWloIpAyEkMjLyqaee\n+vGPf8weNjIykpeXt2fPHqPRCC233HLL008/vWrVKvawAwcOZGZmCjsQERFRUlJis3wQxBbghIQg\nN5qvvvpq//79Vt8aHR1du3btiRMngoOD7777bpPJdPDgwcbGxv/+7//es2fPbbfdRg/71a9+VVdX\n5+vre/fdd3t5edXU1PzrX/96/PHHX3vttXvuuYfM9szZAAAG20lEQVQGPH36NCEkJibGzc2N/SAw\nJ0QQuwLtJxDkBlFVVdXV1XXo0CFqSSdcIYGp4NKlS//+979LpVJofOmll955552VK1cWFBRAS0lJ\nyf/8z/+Ehoa+++67s2fPhsa//e1vL7/8sru7e3V1NfW427BhQ0VFRXV1taen5w3KE0GuFxQ1IDOc\n4eHhjo4Oe/jH67HHHvvjH/9YVlZG78UJOXjwICEkMzOTzkaEkEceeYQQcuLECdryj3/8gxDyu9/9\njs5GhJD169f7+Pj09/efOXOGNp46dWrOnDk4GyHTArxlh8w03n777f/93//dvn27i4vLq6++Wl9f\nPzQ05OLismbNmj/+8Y8uLi6EkOHh4bvvvvtKEd566y3h1s4P5/XXX6evX3311e+++054TGtrq4uL\nS1RUFNsIs6lUKr148SLIFjo6OgghK1euZA9zcHAIDAzs7Oxsb29fuHAhIUSv1589ezYuLs7muSDI\nZIATEjLTGBgY6OzsrKmp2bNnj7e3d2Jiokaj+eabbz788EO9Xp+fnw+HcXsqhJD+/v5z585JJBIP\nD4/J6Bg7Bb7zzjtWjzlw4ICw8b333iOEJCQkUBHdr371K7PZ7O7uzh3Z3NxMCAkODoYfYQMpIiLi\nyJEjBw8e1Gq1AQEBt99+e2JiIpqFI3YITkjIzOTtt9/esGHD7373O0dHR0KISqX6xS9+UVZWdu7c\nuTlz5jg5Oe3bt489fnBw8Be/+MW5c+e2b9/u7+8/Rb224NChQ93d3QcPHqyoqLjjjjueeOIJ+lZ6\nerrw+A8//PD8+fMBAQEhISHQcurUKULI559//uabb9LDdu/evWzZsh07dvj4+ExyBghybeCEhMxM\nFi5cmJGRQdcB0dHRkZGRjY2N33///Zw5c7iDL168+NRTT50+fXrDhg1r1qy5UswHHnigq6trnA+9\n8847X3nllR/eeWDDhg2w2+Ti4vLEE08I10MsZWVl27dvd3Bw2LJlC1U0wISk1+tfeumllStXikSi\nmpqaF1544d///nd2dvZf//pXW3UVQWwCTkjIzOSOO+7g7kqFhYU1NjbqdDrhwXl5eV988cXq1asz\nMjLGiblixYq+vr5xDoiMjLy+3lrltddeM5vNp06devfddx9++OFHH330D3/4Ayz4WAwGw44dO959\n911HR8fc3Ny77rqLvvWjH/3Iy8vrwQcfpGu+++6777bbbrv//vurqqoOHz7MPduEIFMLTkjIzGTi\n96M+/fTTt956Kzw8/JVXXhl/ZyU7O9sWXZsoMLXcc889P/vZz5KTk3fv3v3AAw/QR5GA6urqLVu2\ntLe3z5s378UXX1y6dCn7bmJiYmJiIhfW398/JSXlvffeq6+vxwkJsStQ9o3MTCa4aX/8+PEtW7Z4\nenq+8cYbIMCbQkZHR41Go7DSj6+v73/+538SQqqqqmjjxYsXn3/++bS0tM7Ozg0bNvzzn//kZqNx\nCA8PJ4So1WobdRxBbAOukJCbl87Ozo0bN5rN5r/85S8TqVxQW1s7PDw8zgEKheKH3LU7duxYamrq\nihUrioqKuLege+wU8vvf/76kpGTBggWvvPIKTDAcAwMDBw4ckMvlbOEGoKenhxBypTJ6CDJV4ISE\n3KQYjcYNGzZ0dXXl5OQsX758IqdkZWWdO3dunAPuuuuuN95447q7FBoaSghpbGy8cOGCq6sr+1ZD\nQwMhBJ4uIoTs37+/pKRk8eLFBQUFV5pXJBLJs88+6+DgUFNTwz5mSwiprq4mhCxYsOC6u4ogkwFO\nSMhNyh/+8IcTJ0788pe/TE1NneApr7zyytDQ0DgHsHUTrgN3d/eYmBilUvn888/n5ORQsdyhQ4c+\n+ugjkUgUGxtLe0II2b59+zirnFmzZsXExBw+fPiZZ5554YUXxOJLF/v7779fW1vr7e39k5/85If0\nFkFsDk5IyM3IRx99BOVNm5qa1q9fz7173333/exnPxOe9R//8R+T3bHnnnsuJSXlww8/PH78+MqV\nK6VS6fHjx7/++mtCSFZW1q233koIaWtrO3v2rJOT0wsvvGA1yJ/+9KegoCCIlpyc/Omnn9bX18fF\nxbm6un7zzTc1NTXOzs7PPvss3rJD7A2ckJCbkc7OTnhRU1MjfHcy6gZNkODg4E8//XT79u2VlZXw\nFBEhZMGCBRkZGatXr4Yf6+vrCSHDw8MwUQnR6/Xwwt/f/6OPPtqxY0dZWRnsSzk5Oa1YsWLr1q23\n3HLLpCeDINcIVvtGEHvEZDJ9//33BoMhKCjohy9lhoeHW1tbHR0dg4OD6Z1ABLE3cEJCEARB7AJ8\nDglBEASxC3BCQhAEQewCnJAQBEEQu+D/AZyv9ZsNUt0nAAAAAElFTkSuQmCC\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"using PyPlot\n",
"spy(H);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It's not hard to show that we can project $A$ into $\\mathcal{K}_n$ (in the $Q_n$-basis) by \n",
"\n",
"$$Q_n^*AQ_n = Q_n^*Q_{n+1}\\tilde{H}_n = H_n,$$\n",
"\n",
"where $H_n$ is $\\tilde{H}_n$ with the last row deleted. Eigenvalues of $H_n$ are eigenvalues of the action of $A$ as projected to $\\mathcal{K}_n$. As $n\\to\\infty$, this begins to reveal some of the eigenvalues of $A$ itself. "
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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C5+yF1mxB8PwYjmsYRAOzglVZWsnCIyVybSYyulhbOyX8fPSGk/BcWYOUBGmQ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\nEB8lQViwXdmGmB/gV+bznM2yZ4KHxWsEjFCMEhpDgv4wQu4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mdG33dCX35QLQ1FFC7f3i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\nA5rNi10rWHPVAAAAAElFTkSuQmCC\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"lam = eigvals(A);\n",
"plot(real(lam),imag(lam),\".\")\n",
"axis(\"square\")\n",
"axis(\"equal\")\n",
"for j = 5:n\n",
" lam = eig(H[1:j,1:j]);\n",
" plot(real(lam),imag(lam),'rx')\n",
"end"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We'll look more closely at the convergence in the next lecture. For now, the big idea is to replace a problem on a very high-dimensional space, $\\mathbb{C}^m$, with an analog on a low-dimensional space, $\\mathcal{K}_n$, using a ON basis as provided by the Arnoldi iteration."
]
}
],
"metadata": {
"anaconda-cloud": {},
"kernelspec": {
"display_name": "Julia 0.5.0",
"language": "julia",
"name": "julia-0.5"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "0.5.0"
}
},
"nbformat": 4,
"nbformat_minor": 1
}
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