222 lines
108 KiB
Plaintext
222 lines
108 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "4ce33a60",
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"metadata": {},
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"source": [
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"Find the general solution to each of the following differential equations. Write each equation and its corresponding general solution in your notebooks.\\\n",
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"2. x' + tx = 0; \\\n",
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"3. x\" + x = 0; \\\n",
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"4. 4x\" + 8x' + 5x = 0; \\\n",
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"5. x\" − 3x' + 2x = 0."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 14,
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"id": "b51b2791",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"_C*e^(-1/2*t^2)"
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]
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},
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"execution_count": 14,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"t=var('t')\n",
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"x=function('x')(t)\n",
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"eq2=diff(x,t)+t*x==0\n",
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"desolve(eq2,x)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 15,
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"id": "5b1e1041",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"_K2*cos(t) + _K1*sin(t)"
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]
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},
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"execution_count": 15,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"t=var('t')\n",
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"x=function('x')(t)\n",
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"eq3=diff(diff(x,t),t)+x==0\n",
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"desolve(eq3,x)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 16,
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"id": "02b6f773",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"(_K2*cos(1/2*t) + _K1*sin(1/2*t))*e^(-t)"
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]
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},
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"execution_count": 16,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"t=var('t')\n",
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"x=function('x')(t)\n",
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"eq4=4*diff(diff(x,t),t)+8*diff(x,t)+5*x==0\n",
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"desolve(eq4,x)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 45,
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"id": "5ff9eedb",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": 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",
|
||
"text/plain": [
|
||
"Graphics object consisting of 1 graphics primitive"
|
||
]
|
||
},
|
||
"execution_count": 45,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"t=var('t')\n",
|
||
"x=function('x')(t)\n",
|
||
"eq5=diff(x,t,2)-3*diff(x,t)+2*x==0\n",
|
||
"f=desolve(eq5,x)\n",
|
||
"plot(f.subs(_K1=1,_K2=1),t)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "f8fc679a",
|
||
"metadata": {},
|
||
"source": [
|
||
"Find the solution to each of the following IVPs and then represent its graph on a large\n",
|
||
"interval. Write everything in your notebooks. If Maple/Sage does not return you directly\n",
|
||
"an accurate graph, then use Maple/Sage, for example, to find the zeros of the function,\n",
|
||
"or its limit at infinity, or portions of graphs on small intervals.\n",
|
||
"Describe the long-term behavior of the solution using some of the words: exponential\n",
|
||
"increasing or decreasing, periodic with minimal period ..., bounded between ..., oscillatory\n",
|
||
"around zero, with constant amplitude, with amplitude decreasing to zero as t → ∞, with\n",
|
||
"amplitude increasing to infinity as t → ∞... . Write everything in your notebooks.\n",
|
||
"\n",
|
||
"7. 4x\" + 8x' + 5x = 0, x(0) = 0, x'(0) = 0.5 Here it is quite difficult to see the\n",
|
||
"oscillations..."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 64,
|
||
"id": "741f7cc6",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"Graphics object consisting of 1 graphics primitive"
|
||
]
|
||
},
|
||
"execution_count": 64,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"t=var('t')\n",
|
||
"x=function('x')(t)\n",
|
||
"eq7=4*diff(x,t,2)+8*diff(x,t)+5*x==0\n",
|
||
"f=desolve(eq7,x,ics=[0,0,0.5])\n",
|
||
"plot(f,t,0,10,color='red',legend_label=f'x(t)={f}',figsize=10)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "16c03feb",
|
||
"metadata": {},
|
||
"source": [
|
||
"6. x\"+x=0 x(π/2) = 1, x'(π/2) = −2"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 1,
|
||
"id": "31248201",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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nXzRSk2xl9b3vfa9uu+02ff3rX9eHPvQh7dmz5+TfT548Wbt37z6nEOvUqVOjXbk3bNigEydOaPLkySf/7JlnnjmjiDz77fRGZZKtcF933XX67//+72bvw37kkUfO6SI+ceJEzZ8/v9GPLygoUF1dnRYtWnTyz/bv36+1a9eecWZ96NCh+uhHP6rHHntMn/nMZ/SLX/xCkhX33bt3V2lp6RmfNyMjo8kO5atXrz7je3G2rKwsjRkz5uRbr1691K1bt3P+rDlNxdsekydPVnl5+RmFeMbbq7uN/TeuXr1anTp1avFcftzFYrZVasoU6QMfSOzXmjBB+vCHpa9+lXtyATQuFpP+3/+TJk+2xo6JlJtrDYy+/W3p7UaZAHCOL33JjrnE6VacJuXmWlf0r39dqqxM7NcC2sg3RfeXvvQlVVZW6kc/+pE+97nPKT8/Xx/60IdO/v3kyZPVt29fvf7662f8uxEjRmj+/PnnFOSvvvqqRo0adcYW5uHDh59RRJ79dvr2c6/gvu+++3TLLbdo9+7d2r1798kV1ZZ85Stf0Z/+9Cd95StfUVlZmVatWqVvfetbkqSxY8fqpptu0j333KPXXntNK1eu1J133qnBgwfrpptukiR98pOf1D//+U9t2rRJy5Yt00svvXSyIE9NTdXll19+zj3kI0aM0KJFi7R582bt27dPDQ0Nkuyc844dO3T55Ze3Kvb2aC7e9rjkkkt09OhRrVmz5uSf9evXT1lZWXruuee0Z88eVZ6WUF999VVdcMEFze4wSIhnnpEWL7bmIC1cZRcXX/mKdUn/yU8S/7UABM+LL0qvvir9138lJyd9/vPWJf3730/81wIQPC+/bG9f/WpyctIDD0gnTsTvFhkgTnxRdL/88sv6wQ9+oN///vfq3r27UlNT9fvf/16vvfaafvr2FpG0tDT927/9m/74xz+e8W+/+93v6oUXXtDQoUPPWMn905/+1OSZ6tZ45JFHdOzYMT300EMaOHDgybebW9kw5uKLL9b//u//6sknn1RRUZEuvfTSM1a2f/Ob32jq1Km6/vrrdd555ykWi+mZZ545ue26vr5ec+fOVX5+vq6++mrl5ubqf/7nf07++w9/+MP685//fLKwlqT7779faWlpKigoUN++fbV169aT34srr7wyoQ3GWoq3rXr37q2bb775jJ93enq6fvSjH+lnP/uZBg0adHKCQur4z7tdYjHpa1+T5syx89bJMGCAdef8wQ+kw4eT8zUBBEMsZuclZ82y89bJMGCA9LGPWU5iBw6Asz3wgO28ueGG5Hy9gQPtmtUf/EDavz85XxNohZSmzhc3otEPPHbsmMrKypSfn6/sRs5px9OePXtUWFiopUuXNltArl69WpdddpnWrl2rnJychMbkSiwW06xZs/TJT35S73nPe5r8uOrqao0dO1Z/+tOfNGfOnCRG2HGrVq3S5ZdfrvXr16tbM2eln376aX32s59VSUmJ0tNb7g3ovWY3b96sQ4cO6fDhw3r/+9/f4vb5c/zzn9a445//lN6+2i4ptm2TRo+2LqCf/Wzyvi4AX6iqqlJOTo4qKyvPuFZRL78sXXKJ9OyzlpuSZc8eaeRIy0en3dgBIOK8nPSPf0g33pi8r7tvnzRsmN3dnajGbcCZUlr6AF+sdLdW//799atf/erkCm5Tdu7cqd/97nehLbglazz285//XHV1dc1+3JYtW/SlL30pcAW3JE2YMEHf+ta3Wrzq7OjRo/rNb37TqoI7rr71LWn6dOsmnkxDh9q5qO9854z77gFE3He+Y70frroquV+3f3/rN/GTn5CTAJzy7W9LEycmb5Xb06eP9MEPSj/+sfT2jT+Aa4Fa6QbiIS4r3StW2HapP/9Zuu22hMXapI0bpbFj7YHy8Y8n/+sDcKbRle7SUqmwUPrtb6XTbtpImk2bpDFj7HaFZm66ABARZWVSQYH0yCOJbzTbmPXrpXHjrJP5Rz6S/K+PqAnXSjfgG9/7nm1duuUWN19/1Ci7u/t//sfOcQKItu9+Vxo8WLr9djdff+RI6Z3vtHOUp/UaARBRP/yh9XxwlZPGjLF7u7/7XamJm32AZKLoBtpq5067l/sTn5CSvaX9dB//uLRmjXUqBhBde/ZIf/iD5aS3r1Z04tOflioq7Ew5gOjat8923cydK2Vmuovjs5+V1q2TnnzSXQzA2yi6gbb61a9sYHvalXZOXHaZ3UnZgS7xAELgN7+xq3hc56TzzpNmzJB+9CO3cQBw65e/tPeuj5rMnGl56e2bkACXKLqBtqirk37+c+mOOyTXjfpSUuyqnr//Xdq9220sANxoaJB+8Qvp1lultt7AEG9eTnr+eTvjDSB6vJz07ndbQzPXPvxh6YUXrBcO4BBFN9AWzz4rbd/ufvbW84EP2Kr7L37hOhIALsyfb4NJvzQKeve7bULSW+kCEC0vvWQ56Z57XEdivJz0q1+5jgQRR9ENtMXDD0vTpklTp7qOxPToIb33vdLPfmar8ACi5Wc/s67ls2e7jsRkZ0t33in9+tdSba3raAAk289/LuXnS365qjY728ZJ5CQ4FrcuUMe5Bw8B0e7X6s6d0nPP+e9s0Mc/bivdzzwj3Xij62gAJMuePdI//mG3KaS0eFtJ8txzj10d9tRT1tEcQDS89Zb0xBPSt77lr5z04Q9b/5unn5be8Q7X0SCiOlx0p6enKzU1VZs3b45DOEByxGIx1bf1Cok//MG2cru4l7s5RUV2Z/hvf0vRDUTJn/4kpaXZyrKfTJokTZ9uK0sU3UB0/PGPVmy/732uIznTpEnW5PHnP6fohjMdLrozMjJUWFiouro6VVZW6qmnnlKXLl2U6fKKAKAF9fX1qmvLduxYTHrkERtAum6g1pj3v1/63OekAwfcN1MCkBx/+Yt0001Sz56uIznX+98vfepTdnWQH5opAUi8Rx+Vrr1W6t3bdSTn+tCHrNHj7t12fziQZHHZXp6RkaGMjAydOHFCR48eVW1tLUU3AqG6urp1H7hkiVRWJn3/+4kNqL3uuEO6/37pz3+27eYAwq+0VPrv/3YdReNuu0365Celv/6VnAREwdq1Nlb63OdcR9K4W2+V7r3XJis/8QnX0SCCUmKxWGs/tsUPPHr0qP7yl7+oqqqqY1EBSdS9e3fddttt6tKlS9Mf9O//Lj32mLR1q23n9KMbbpD27pXefNN1JACa8NBDD+mxxx5TeXm5srKyNHv2bH3zm99Ubm5uqz9HVVWVcnJyVNmzp7rv3m3HXvzouuukgwelhQtdRwIg0b76Vek737Fz3VlZrqNp3DveYf15Fi92HQnCp8UmBnFrpCZJXbp00W233db61UPABzIzM5svuOvqbLXmzjv9W3BLtp3z3e+W1q2Txo51HQ2ARixYsEBz587V9OnTVVdXpy996Uu68sorVVpa2nweOl1Dg72/5Rb/FtyS5cw77rDrg0aNch0NgESJxazHxM03+7fgliwf3XYb4yQ4EdeVbiCUXnhBuvJKqbjYrgvzq2PHpH79pC98QfrSl1xHA6AV9u7dq379+mnBggW68MILW/Vvqp56Sjk33KDKF15Q98svT3CEHXDsmNS/v203/c//dB0NgERZtsyuUn3uOemqq1xH07Tjx22cdP/90le+4joahEuLK93c0w205M9/lkaP9s/d3E3Jzrbu5X/5i+tIALRSZWWlJKlXMw0Qq6urVVVVdfKt5g9/sL+YPj0ZIbZfdrY1n/zDH2wlDEA4Pfqo1LevdNllriNpXlaWrcY/+ig5CUlH0Q00p7raznK/5z3+unOyKbfdJq1aZQ2WAPhaLBbTpz/9aZ1//vkaP358kx/30EMPKScnRzk5Oeqdk6Mj3sRaEHLSHXdYg6WSEteRAEiEhgZbnHj3u6X0uJ5aTYz3vtdy0tKlriNBxFB0A8154QXp0CH/3c3dlKuvlrp3Z7UbCIB7771XJSUl+tOf/tTsx33hC19QZWWlKisrdeiJJxSoSwEvvdSuWfz7311HAiARXn1V2rHDJtiC4NJL7RrDv/3NdSSIGIpuoDlPPCGNGycVFrqOpHUyM60751//6joSAM3493//dz355JP617/+pSFDhjT7sZmZmerevbu6d++uLs89Jw0blqQo4yAjw25WeOwx15EASIRHH5VGjJDOO891JK2Tni7ddJNNBLLFHElE0Q00pb5eevJJK2KDsI3Tc8stUnm5vQHwlVgspnvvvVePPfaYXnrpJY0cObL1/7i+Xnr8cevdECS33CKtWSNVVLiOBEA81dfb4sS73hWscdLNN0vr11teApKEohtoysKFdu/1O9/pOpK2ueIKqUsXG5wD8JW5c+fqD3/4gx599FF169ZNu3fv1u7du3X8+PGW//Hrr0t79tgqTZBcdZXlJLaYA+GyaJHdy/2Od7iOpG0uu8yO4rEDB0lE0Q005fHHpYEDpRkzXEfSNllZdrabohvwnZ/+9KeqrKzUxRdfrIEDB558+0tr+jD8/e/SoEH+vrqwMVlZ0rXXMsAFwuaJJ+wKrlmzXEfSNpmZ0vXXk5OQVBTdQGNiMXuY3HSTlBrAX5N3vtPuFd++3XUkAE4Ti8Uafbvrrrta+oc2QLzllmDmpFtusW7Bmze7jgRAPHjjpBtukNLSXEfTdjffLK1cKW3Y4DoSREQAn9xAEqxaJW3aFLwtU57rrpM6dbIHIoDgW7HCJtGCtrXcc+21trrEDhwgHMrLpXXrgjtOuvpqqXNnchKShqIbaMzjj9t5n0sucR1J+/ToYbE/+aTrSADEw1NPWU664ALXkbRPt26Wk55+2nUkAOLhH/+QsrPtfHQQdeliPXCeesp1JIgIim6gMU88YavFGRmuI2m/66+XXn5ZOnzYdSQAOuqpp6whWZBz0nXXSa+8IlVVuY4EQEc98YStFmdluY6k/a67TnrtNengQdeRIAIouoGzbdliWzmDumXKc911Um2t9MILriMB0BF79kiLF9tEWpCRk4Bw2LXLOpeHYZxUXy89/7zrSBABFN3A2Z59VkpPt1WlIBs1SiooYOsUEHRPP2134F57retIOmbkSMtJbDEHgu3ZZy0nXXON60g6ZsgQadIkxklICopu4GzPPCPNmSPl5LiOpOOuv94GuA0NriMB0F5PPSWdd57Up4/rSDruuussx5KTgOB69lm7TjUsOenZZ23FG0ggim7gdCdOSPPnB39FyXPdddJbb9lVPQCCp7ratj4GfWu55/rrbbs8OQkIpro6OyIS9FVuz/XXS/v323Z5IIEouoHTvfKKdOxYeIru2bOtk/kzz7iOBEB7vPKKdPSoTaCFgZeT2GIOBNObb0qVleEpur0Ve7aYI8EouoHTPfOMNHSoVFjoOpL4SE+36zz++U/XkQBoj+eflwYOlCZMcB1JfHj9MhjgAsH07LNS797S1KmuI4mPtDTrwv7ss64jQchRdAOne/ZZW+VOSXEdSfxcdZVtmzp0yHUkANrq+eelK68MV0669lrbXr5vn+tIALTVc8/ZuCItzXUk8XPFFXZrzd69riNBiFF0A57Nm6W1a4PftfxsV15pTYvmz3cdCYC22L1bKimx3+Ewuewye//SS27jANA2u3dLy5aFZ2u55/LL7T3jJCQQRTfgmT9fSk2VLrnEdSTxNXy4lJvLFnMgaF580d57A8KwGDxYys8/9d8HIBi8+6zDNhE4aJBdZ/jCC64jQYhRdAOe+fOladOsyU/YXHWVPSxjMdeRAGit55+Xioqkfv1cRxJ/l19O0Q0EzbPP2jgpjDnpiius6GachASh6AYkS7Lz55/a9hg2V10lbdli2+cB+F8sZgPAsK0oeS6/XNq0Sdq40XUkAFqjocEmysKak664Qtq2TVq3znUkCCmKbkCSVq+2+6zDto3Tc9FFUkbGqa1hAPxt9Wo7PxnWAe5FF1kjJla7gWBYtcqaH4Z5nJSezhZzJAxFNyDZwK9zZ7tDNoy6dJHOP59z3UBQPP+85aQ5c1xHkhg5OXY/LkU3EAzz51tOOu8815EkRteu9t9G0Y0EoegGJHuYzJljD5Swuvxy6ZVXpLo615EAaMnzz9vKS9hz0vz5tm0VgL/Nn2+T92HOSVdcIf3rX4yTkBAU3UBtrbRgQXi3THkuvVQ6fNjuxwXgXydO2ARZWLeWey6/XDpwwO7HBeBftbWWky691HUkiXXFFVJVlVRc7DoShBBFN7B4sXTkSHibqHmmTpW6deNuXMDvXnvNCu8rrnAdSWLNmiVlZ7PFHPC7qIyTpk2zoy9sMUcCUHQD8+fbNWFTpriOJLHS06ULL6ToBvzu5Zelvn2l8eNdR5JYGRm2hZ6iG/C3+fOtGJ061XUkiZWebqv5FN1IAIpu4MUXpUsusU66YXfppbaKVl3tOhIATXn5ZStGU1LO+ON58+apoKBA06dPdxNXIlx+ufTqq7ayD8Cf5s+XLr44GuOkyy+X3nzTjuMBcUTRjWg7csSSa9i3THkuvdQGt2++6ToSAI05dsy2cl500Tl/NXfuXJWWlqo4TOcNL7/cctIbb7iOBEBjjh6138+ojJOuuMIaqb3yiutIEDIU3Yi2V1+1BiFReZhMnCj16mXdOQH4z5tvWk5qpOgOpfHjpX792GIO+NXrr0drnDRmjDRwoI0PgTii6Ea0zZ8vDR4s5ea6jiQ5UlNtixjnugF/evllqXdvqbDQdSTJkZpqO3DISYA//etfNjGWn+86kuRISbH+N6x0I84ouhFtL71kA76zzk6G2qWX2mra0aOuIwFwtgULbMCXGqHH8wUXSEuW2NZ6AP6yYEGjPSZC7cIL7dowchLiKEJPdeAsVVXSypWWXKPkootsq9iiRa4jAXC6Eyfs9/Lii11HklwXXmhnKMlJgL8cPWrFZ1SOu3i8nET/G8QRRTei6403pIYGW2WJkoICO9fN1inAX958024WiNoAt6BA6tmTM5SA37z5phWfUcxJjJMQZxTdiK5XX7W7cMeNcx1JcqWm2kQDDxPAXxYssOJzwgTXkSRXaqp0/vnkJMBvFiywHhMFBa4jSS7GSUgAim5E12uv2UAvSueUPBdeaDPYNTWuIwHgefnl6J3n9lxwge0+qq11HQkATxR7THguvNByUnW160gQEhH8LQJkSXTRouhtLfdccIF0/Li0dKnrSABIlpPefDN62zg9F1xgTYuWL3cdCQDpVI+JqOakCy+078GSJa4jQUhQdCOali61ZBrVonvyZKlLF7ZOAX6xeLHlpKg1UfNMmSJlZXGuG/CL4mKbDIxas1lPUZHUtSvjJMQNRTei6bXXrOgsKnIdiRvp6dKcOQxwAb94+WUpJ0eaONF1JG5kZEizZpGTAL94/XUrOqOak7xxEkU34oSiG9H06qvSeedZUo2qCy6wyYf6eteRAHj1VesxkZbmOhJ3LrzQclJDg+tIACxcaBNhUc9Jr79uHdyBDqLoRvQ0NFgSjerWcs+FF0qVldKqVa4jAaKtvt7Oc8+Z4zoSty64QNq/Xyovdx0JEG2xmBXds2e7jsStiy6SDh+WVq50HQlCgKIb0VNaKh08SNE9Y4Zt6WQ7J+BWaakN7M47z3Ukbs2aZbuP2M4JuLV2rU2ARX0icNo0qXNnchLigqIb0fPqqzawmznTdSRude5sD5SFC11HAkTbG2/YFs7p011H4laXLtZQjYlAwK2FC+061aiPkzIzbTJwwQLXkSAEKLoRPa++Kk2dKmVnu47EvfPOo+gGXHvjDWtW1KWL60jcu+ACim7AtddflyZMsOaOUXf++TZOisVcR4KAo+hG9Lz2GlvLPbNnS1u3Sjt2uI4EiK6FC9la7rngAmnbNmnLFteRANHFee5TZs2S9u6VNm1yHQkCjqIb0bJliw3ozj/fdST+4A3033jDbRxAVO3fb+cnGeAaLzez2g24ceCAVFZGTvLMmmXvGSehgyi6ES2vvWbvKbrNwIHSiBFsMQdcefNNe89Kt+ndW8rPJycBrnjFZdSbqHl695bGjaPoRodRdCNaXn/dBnS9e7uOxD9mz+ZhArjyxhtSv37SyJGuI/GPWbNOTUYASK6FC6X+/clJpyMnIQ4ouhEtb77JitLZZs+Wli6VTpxwHQkQPW+8YTkpJcV1JP4xa5ZUUiIdPeo6EiB6Xn/dxgXkpFPOO8/u6j52zHUkCDCKbkTHsWM2kIv6FRhnmz1bqq21whtA8tTXS4sXMxF4tlmz7HtDTgKSq7bWchJby880a5ZUV0dOQodQdCM6li61gRxF95kmTLCrijhDCSTX6tXSkSMU3WcrLLScxHZOILlWrJCOH6eJ2tnGj7ecxFE8dABFN6Jj0SJLmoWFriPxl/R0acYMHiZAsr3xhv3+TZvmOhJ/SUuznETRDSTXwoVSZqY0ZYrrSPzFGyeRk9ABFN2IjjfftMFterrrSPxn9mx72MZiriMBouONN6RJk6TsbNeR+M+sWfb9IScBybNwoY2TMjNdR+I/5CR0EEU3omPRIraWN+W886Q9e6RNm1xHAkSH10QN55o1S9q9W9q2zXUkQDTEYqeaqOFc551nOWnLFteRIKAouhENO3ZI27fbQA7n8gb+nOsGkmPfPmndOorupngTpGznBJJj2zYbK1F0N84bP5KT0E4U3YiGRYvsPSvdjevVSxo3zrqWAkg8b+DWhqJ73rx5Kigo0PTp0xMUlI949wQzwAWSw3v+M05qXN++0ujR9L9Bu1F0IxoWLZKGDJEGDXIdiX/NmEHRDSTLwoVWWI4Y0ep/MnfuXJWWlqq4uDhxcfnJrFkU3UCyLF5s46SBA11H4l/nnUdOQrtRdCMa3nyTreUtmTFDWr5cqqlxHQkQft557pQU15H416xZ0rJlUnW160iA8CsulqKwi6YjzjvPxkknTriOBAFE0Y3wq6uTlixhy1RLZsywgrukxHUkQLjV1dmqEue5mzdrlhXcK1e6jgQIt/p6aelSGwegabNmSbW1NhkItBFFN8JvzRrp2DGK7pZMmiR16sQWcyDRVq2ynETR3byiIru6iO2cQGJVVEiHD7PS3ZKJE6WsLM51o10ouhF+b74ppaVJU6e6jsTfOne2wpuiG0isN96Q0tPtPlw0LSNDmjKFohtINK9PBDmpeenpNjFB0Y12oOhG+C1aZLOT2dmuI/E/mqkBiffmm7aKm5XlOhL/o5kakHjFxVJurpST4zoS/5s169SNOEAbUHQj/N58k63lrTVjhlReLlVWuo4ECK8lSzg72VozZ0qbNklvveU6EiC8Fi9ma3lrTZ8ubd8u7dnjOhIEDEU3wq2y0opIOpe3zowZUixmRQGA+Dt82HIS2zhbxysEli51GwcQVjU11qyQicDW8XI3OQltRNGNcCsutiKSle7Wyc2VunVjizmQKMuWWU5iVal1Ro6UevZkIhBIlJISK7zJSa0zfLjUuzc5CW1G0Y1we/NNO6M0bpzrSIIhNdUevBTdQGIUF1t/ibw815EEQ0qKrSwxwAUSY/FiaxBWVOQ6kmAgJ6GdKLoRbkuWWHJM5aXeajRTAxJnyRLryJ2e7jqS4Jg6lQEukCjFxdZstnNn15EEB0U32oFKBOG2dClXhbXVjBnSzp3Sjh2uIwHCp7iY89xtNW2a5aRdu1xHAoRPcTFby9tq2jTLRzt3uo4EAULRjfB66y3rMEnR3TZeMxVWu4H4OnBA2riRorutaFwEJMbhw1JpKUV3W3k5idVutAFFN8Jr2TJ7T9HdNoMGSf37n/r+AYgPr2hkgNs2w4ZJffowwAXizWvsSOfythk82MZJxcWuI0GAUHQjvJYulXr0kEaNch1JsKSk2JlTim4gvoqLpe7dpTFjXEcSLDQuAhJj8WJr7Jif7zqSYCEnoR0ouhFeS5da8ZiS4jqS4KHoBuKPxo7tN3Wq5fRYzHUkQHgUF9vvFo0d284ruslJaCWe/Agvmqi135Qp0u7dNC4C4okmau03bZrlJBoXAfFDE7X2mzZN2rdP2rrVdSQICIpuhJOXCCm622fKFHvPajcQH7t3W2NHBrjtQ+MiIL727pU2byYntZc3viQnoZUouhFOXsMiiu72GT5c6tmTohuIFy8nsdLdPl7jIga4QHx4TcBootY+AwdaXiInoZUouhFOS5dKOTnS6NGuIwkmmqkB8VVcLPXubRNaaDsaFwHxtWSJ1KuXNHKk60iCi5yENqDoRjgtXSpNnkwTtY6YMkVavtx1FEA4LFli2zjJSe1HMzUgfpYtY5zUUdOn00wNrUbRjXBatoyt5R01ebK0ZYu0f7/rSIDgo7Fjx02bZudQt21zHQkQfMuX23Me7TdtmnTokLRxo+tIEAAU3Qif/futOQgD3I7xmqmx2g10zK5d1kjN+51C+9C4CIiP/fut2Sw5qWPISWgDim6Ej3cOmaK7Y8aOlbp25Vw30FHexBWrSh0zaJC9McAFOmbFCntPTuqYPn2kESNONaUDmkHRjfBZulTq1k0aM8Z1JMGWmioVFVF0Ax21bJnUo4cNztAx3rluAO23fLmUnW2T6+gYmqmhlSi6ET5Ll9qWqVRe3h1GB3Og47yzkzQs6jhvgEvjIqD9li+XJk2S0tJcRxJ8XtNZchJaQFWC8KFhUfxMmSKtWydVVbmOBAiuZcvicnZy3rx5Kigo0PTp0+MQVEBNnSodOGB9OwC0D03U4qeoyMZImza5jgQ+R9GNcDlwwBIfRXd8eIWCd/4LQNscPGgFYhwGuHPnzlVpaamKo3x+0Ps+kpOA9jl2TKqooOiOF3ISWomiG+FCE7X4ys+XOndmiznQXl4TNboEx8fAgVK/ftyqALRXSYnU0EDRHS8DBkj9+1N0o0UU3QiXpUut4zbNQeIjPV2aOJGiG2gvr2HRuHGuIwmHlBQrFhjgAu2zfLk928ePdx1JeBQVkZPQIopuhMuyZTYgo4la/NBMDWi/ZctoWBRvRUWsdAPttXy5VFAgZWa6jiQ8Jk8mJ6FFVCYIF5qoxd+UKVJZmZ0DA9A2NCyKv8mTpe3bpX37XEcCBM/y5Rx3ibeiInISWkTRjfA4dEjasIGiO96mTLHzX6tWuY4ECJajR6Xycga48UbjIqB9amvtTDcTgfFVVGTvV650Ggb8jaIb4VFSYu95mMTX+PF2/ost5kDblJTY3a3kpPgaM0bq0oXtnEBblZVJNTXkpHgjJ6EVKLoRHitXShkZNCyKt8xMqbCQohtoq2XLpE6d7PcH8ZOaaufkGeACbeP9zkya5DaOsElLs6az7L5BMyi6ER4rV9rgtlMn15GED83UgLZbvtxyEg2L4o/GRUDbLV9uq7Ldu7uOJHzoYI4WUHQjPFauZPY2UaZMsTPdNTWuIwGCY9kyznMnSlGRVFFh5+YBtA6NHROnqMh6eBw/7joS+BRFN8Khvl5avdq29yD+pkyxBixr1riOBAiGmhrLSQxwE2PyZDsvT4NHoHUaGmwllpyUGJMnnxqLAo2g6EY4rFsnnTjBSneiTJokpaSwxRxorfJym6giJyVGYaE1eGSLOdA6mzZJVVUU3Ykyfrz1m2CLOZpA0Y1w8K5pYKU7Mbp0kfLyKLqB1vJuUyAnJUbnzlJ+PgNcoLW8CSqK7sTIyrJxEhOBaAJFN8KhpEQaNEjq08d1JOFFMzWg9UpKpOHDpZwc15GEF83UgNZbvtzGSf37u44kvCZPZiIQTaLoRjjQRC3xpkyx73N9vetIAP8jJyXe5Ml2pruuznUkgP/RRC3xiopswpVxEhpB0Y1wYICbeJMmWVfO9etdRwL4X0kJW8sTrajIenlUVLiOBPA/iu7EKyqyGxUYJ6ERFN0IvgMHpO3bKboTzSsgvLOqABr31lvS7t0U3YlWVGTv2c4JNG/XLstJFN2JRU5CMyi6EXw0LEqOvn2lAQMouoGWeL8jTAQmVo8e0rBhXBsGtMQrAim6E6tPH2nIEIpuNIqiG8G3cqWUmSmNG+c6kvCbNOlUp3gAjSspsU62o0e7jiT8JkxgIhBoSUmJ1L27NGKE60jCr6iIohuNouhG8JWU2P2I6emuIwm/iRMZ4AIt8XJSWprrSMKPnAS0rKTEJqhSUlxHEn5FRdyqgEZRdCP4Vq5ka3myTJwobdkiVVa6jgTwLxo7Js+ECdKOHdbbA0DjaOyYPJMnS3v22Bl64DQU3Qi2ujpp9WoGuMlCMzWgebW1UmkpA9xk8b7PnOsGGlddLZWXk5OShWZqaAJFN4Jt7Vp7oFB0J0dentSpE0U30JS1a6WaGga4yTJunJSRQU4CmlJebgsU5KTkGDHCzs+zxRxnoehGsNG5PLkyMqT8fAa4QFO8RoPkpOTo1MlyEivdQOO85/X48W7jiIrUVJrOolEU3Qi2lSvteoZevVxHEh00LgKaVlIiDR0q9ezpOpLoICcBTVu1Sho50lZfkRwTJjARiHNQdCPYaFiUfBMn2sOkocF1JID/0LAo+SZOtN4e5CTgXF7nciTPxIlSRYUdfwTeRtGNYGOAm3yTJklHj0obN7qOBPCfBE4Ezps3TwUFBZo+fXpCPn9gTZhgOWnTJteRAP7DOCn5Jk6U6uulsjLXkcBHKLoRXPv321UxrHQnFx3Mgcbt2yft3JmwAe7cuXNVWlqq4uLihHz+wCInAY3bu1fatYuiO9m88/PkJJyGohvB5TWpoOhOrv79pb59aRICnM07w8cAN7kGDJD69OEMJXA2cpIb3brZOXqKbpyGohvBVVIide4sjRnjOpJoSUmxiQ4eJsCZVq60nDR2rOtIoiUlxbaYk5OAMzFOcodmajgLRTeCa+VK28KTnu46kuihWzBwrpISqbCQnOSC1+ARwCklJTZOSktzHUn0ME7CWSi6EVx0Lndn4kRrpHb4sOtIAP+gYZE7EydK69ZJx465jgTwD3KSOxMnSrt327l6QBTdCKq6OmnNGh4mrnjfd1aWAOPlJCYC3ZgwQYrF7GcAwLpnM05yx7umjXES3kbRjWCqqJBqahjgulJQYNvV2DoFmHXrpBMnGOC6UlhoZ7sZ4AJm/XrLSdzR7caYMXaennES3kbRjWDyOmczwHUjM1PKy+NhAni83wVykhvZ2TbIJScBxvtdoOh2Iz3dJgPJSXgbRTeCaeVKadgwqWdP15FE18SJXBsGeEpKpMGDpd69XUcSXTQuAk4pKZEGDrQrPuEGHcxxGopuBBPNQdzzugU3NLiOBHBv5Upykmte0R2LuY4EcI9xknsTJ0qrV9v5ekQeRTeCic7l7k2aZN3LN292HQngXkkJOcm1CROk/futYzAQdRTd7k2YYOfq1693HQl8gKIbwbN3r7RrFwNc17xzYqtXu40DcO3gQWnbNga4rnGrAmAqK21CnJzkFjkJp6HoRvDQsMgfBg+WevTgYQKQk/xh5EipSxfOdQPeZDg5ya1+/aT+/clJkETRjSAqKZGysqxTLdxJSZHGj2elGygpkTIypNxc15FEW2qq5SQGuIi6Vause3ZenutIMGECOQmSKLoRRKtXn7onGm5NmEDRDaxaZTkpPd11JPAaPAJRVlJik4AZGa4jwYQJ0po1rqOAD1B0I3jWrLG7D+He+PFSeblUU+M6EsCd1avtdwHuTZwolZZKtbWuIwHcWbWKreV+MX68tGGDdPSo60jgGEU3giUWs6KbAa4/TJgg1dVJa9e6jgRww8tJTAT6w4QJNgm4bp3rSAA3yEn+Mn68/UzKylxHAscouhEsW7dKR47wMPELb/KDLeaIqh07pKoqcpJfeLcqcIYSUbV7t92oQE7yh4ICe884KfIouhEsXtJipdsfeva0LuacoURUkZP8pVcvacgQim5EFznJX7p2tZsVKLojj6IbwbJmjdStmzR0qOtI4KGDOaJszRopO1saPtx1JPBMmMBEIKJrzRqpc2cr9OAPNJ2FKLoRNF7n8pQU15HAM348A1xE15o1lpNSeZz6xsSJrHQjutaskfLzueHFT1icgCi6ETQ0UfOfCROkTZvsrD0QNXQu958JE6z/R2Wl60iA5CMn+c/48db/4+BB15HAIYpuBEd9vV0FQ3MQf/Ee7txDiahpaCAn+ZH38ygtdRsHkGyxGDnJjxgnQRTdCJJNm6QTJ5jB9Rtvuz8PE0TN1q1292obB7ivvPKKbrjhBg0aNEgpKSl64oknEhNfVOXl2XZ/chKiZvt2blPwo9xcKT2do3gRR9GN4PDOw/Aw8ZesLGnUKAa4iJ52dgk+evSoJk2apJ/85CcJCArq3FkaPZqVbkQPncv9KSNDGjeOc90Rl+46AKDV1qyxK6oGDnQdCc5WWEjRjehZs0bq3t2uqGqDa665Rtdcc02CgoIk24FDTkLUrFkjdekiDRvmOhKcjQ7mkcdKN4JjzRor7uhc7j8U3Ygir3N5gnNSdXW1qqqqznhDC8hJiCLvhhduU/CfwkL7+cRiriOBI/xWIjjoyOlfhYV2loxuwYiS1auTctzloYceUk5Ozsm3oUOHJvxrBl5hoXULJichSrjhxb8KC6UDB6Q9e1xHAkcouhEMtbVSRQXnuf2KbsGImvp6qawsKQPcL3zhC6qsrDz5tm3btoR/zcArKLD35CREBbcp+Jv3c2EHTmRRdCMY1q+XamqYwfUrugUjarzbFJIwwM3MzFT37t3PeEMLyEmIms2bpWPHGCf51ejR1lCNicDIouhGMHgDJ2Zw/cnrFswAF1HBbQr+RgdzRA3jJH9LT7fJQMZJkUX3cgTD6tVSv35S376uI0FTaFyEKOnAbQpHjhzR+vXrT/7/TZs2acWKFerVq5eG0XU4fuhgjijxblMYPNh1JGgKOSnSWOlGMHidy+FfFN2Ikg7cprBkyRJNnjxZkydPliR9+tOf1uTJk/XlL3853lFGGzkJUeI1m+WGF//ychIdzCOJlW4Ew+rV0hVXuI4CzSkslHbulA4dknr0cB0NkFirV0uzZ7frn1588cWKMehKPK+DOTkJUbBmjTR9uuso0JzCQungQWn37nbtkkKwsdIN/6uultatY6Xb7+jMiaioq7PbFGhY5G9eB/OyMrdxAInm3abAOMnfuOkl0ii64X8VFfZA4WHib7m5UloaRTfCz7tNgZzkb3QwR1Rs2GALFEwE+tvo0VJmJjkpoii64X905AyGzExpzBgeJgg/OpcHA7cqICoYJwVDWhodzCOMohv+t3q1NGiQdQqGv9G4CFGwZo3dpNCvn+tI0JKCArZyIvxWr5Z69ZL693cdCVpCB/PIouiG/61Zw5apoKDoRhRwm0JwkJMQBd44ic7l/kcH88ii6Ib/rV7NADcoCgutK+eBA64jARKHnBQcp3cwB8KKicDgKCy0fLR7t+tIkGQU3fC3Y8ekjRtZ6Q4KOpgj7Gpq7DYFclIw0MEcYVdbaw1nKbqDgXFSZFF0w9/KymwLDg+TYBg3TkpP52GC8Fq71q4MIycFAx3MEXbr1lnhzURgMIwaRQfziKLohr95SclbrYC/ZWRIY8fyMEF40bk8WOhgjrCjc3mw0ME8sii64W+rV0vDh0vdurmOBK1F4yKE2Zo10sCB1ikYwUC3YITZ6tV2k0KfPq4jQWsxTookim74W2kps7dBw8MEYUbDouApLOTaMIQXN7wEj5eT6GAeKRTd8LfSUraWB01hofTWW9K+fa4jAeKPzuXBQwdzhBkTgcHjdTDftct1JEgiim741/Hj0ubNUn6+60jQFt4kCavdCJsTJ6QNG1hVChqvIGG1G2Hj3abA4kSw0ME8kii64V8VFbb1hqI7WOhgjrAqL5caGhjgBk1urnUwp+hG2KxbJ9XXk5OCZuRIa/LIOClSKLrhX969qhTdwdKpk3Uw515chI33mmaAGyx0MEdYMU4KJjqYRxJFN/yrtNS6BPfo4ToStFV+PkU3wqesTBowgJwURDR4RBiVlUm9e0t9+7qOBG1FToocim74V1kZs7dBRdGNMCotJScFVUEB28sRPoyTgis/344s0cE8Mii64V88TIIrL0/auVOqrHQdCRA/ZWVsLQ8qOpgjjBgnBVd+vnTwoN32gkig6IY/1dZagxAeJsHk/dzKy93GAcRLXR05KcjoYI6waWiwhrPkpGDyfm7sCowMim7404YNVnizqhRMeXn2nocJwsLLSQxwg8nrYM4ZSoTFli12tSo5KZjGjLGbXhgnRQZFN/yJjpzB1qWLNGwYK90ID2+F1OFE4Lx581RQUKDp06c7iyGwvA7mrHQjLHyQk9ABnTpZ4U3RHRkU3fCnsjLrENy/v+tI0F40U0OY+CAnzZ07V6WlpSouLnYWQ6DRLRhhUlZmE9xDh7qOBO3lNVNDJFB0w5+85iApKa4jQXtRdCNMyEnBV1BA0Y3wKCuzo1zkpODKy2OcFCEU3fCn0lK2TAVdfr6dg62udh0J0HFcFxZ8hYV2qwIdzBEGdC4Pvvx8aft26fBh15EgCSi64T8NDbbdhodJsOXn289y3TrXkQAd4+UkJgKDzfv5sbKEoIvFKLrDgJteIoWiG/6zbZt07BgPk6DjOgyEBTkpHHJzbSsuOQlBt2eP7dggJwUbN71ECkU3/IfO5eHQp4+98TBB0HldgslJwZaVJY0YQU5C8DFOCoeuXa0RHivdkUDRDf8pK7PB0fDhriNBR9FMDWFATgoPchLCoKzM7ngePdp1JOgomqlFBkU3/Ke01JJQKi/PwONhgjDwugSTk4KvoIC7uhF8ZWXS2LF21zOCjYnAyGAEAf+hOUh45OdLFRVSfb3rSID2o3N5eOTnS5s3S8ePu44EaL+yMho7hkV+vrR+vVRT4zoSJBhFN/yFjpzhkp8vnTghbdniOhKgfchJ4ZKfbz/TigrXkQDtx0RgeOTn28LE+vWuI0GCUXTDX/bulQ4cYAY3LOhgjqB76y3p4EFyUliQkxB0lZXSrl0U3WFBTooMim74C12Cw2XoUCk7m4cJgosuweHSo4c0YAA5CcFFTgqXvn2lXr3oYB4BFN3wF68j55gxriNBPKSmWgMqHiYIqtJSclLY0LgIQVZWZvfN5+a6jgTxkJJC09mIoOiGv5SV2eCWjpzhwQAXQUaX4PAhJyHIysrs+sLsbNeRIF7ISZFA0Q1/oSNn+HgPk1jMdSRA29FELXzy86W1a6W6OteRAG1HTgqf/HzbEdjQ4DoSJBBFN/yFjpzhk59vjajeest1JEDbkZPCp6BAqq2VNm50HQnQdhTd4ZOfLx07Jm3b5joSJBBFN/yjslLauZOHSdjQmRNBRZfgcCInIahOnJA2bSInhY3386T/TahRdMM/vGTDwyRcxoyxRlQMcBE03muWIy/hMmCAlJNz6rYMICjWrrUtyIyTwmXYMKlzZ8ZJIUfRDf/wOnLm5bmOBPHUqZMV3jxMEDSlpXQJDqOUFBoXIZi4Liyc0tLsOUNOCjWKbvhHaSkdOcOK6zAQRHQJDi+KbgRRaanUv7/d64xwISeFHkU3/IPmIOHFwwRBxG0K4eV1C+ZWBQQJ46TwYpwUehTd8A8eJuGVny/t2CFVVbmOBGg9OpeHV36+dOSI5SUgKBgnhVd+vrRvn70hlCi64Q/Hj1tHTlaVwonOnAia48elzZsZ4IaV1zuEnISgqKuzRmrkpHBinBR6FN3wBzpyhps3wGXrFIKiosK2HpOTwmnkSCkjgwEugmPTJqmmhpwUVmPHSqmpjJNCjKIb/kBHznDr2lUaOpQBLoKDnBRuaWnSuHEMcBEc5KRwy8yURo0iJ4UYRTf8oazMOnL27Ok6EiQKTUIQJOSk8MvLYyIQwVFWJnXrJg0a5DoSJArjpFCj6IY/0CU4/HiYIEgqKk4di0A4UXQjSLwmaikpriNBojBOCjWKbvgDXYLDLz9f2rDBzqQBfldeLuXmuo7iDPPmzVNBQYGmT5/uOpRwyMuTdu7kVgUEA4sT4ZefL23ZIh075joSJABFN9yjI2c05OdL9fXSunWuIwGa19Bgr1OfrXTPnTtXpaWlKi4udh1KOHg/34oKt3EALYnFuC4sCryfLzkplCi64d7GjVJtLQ+TsPN+vmydgt9t22ZXhvlspRtx5v182WIOv9uxQzp8mHFS2HHTS6hRdMM9L7mwbSrc+vSRevXiYQL/84own610I868WxXISfA7OpdHQ06ONHAgOSmkKLrhXnm51L27NGCA60iQSCkpNAlBMFRU2PUtw4e7jgSJRjM1BEFZmeWkkSNdR4JEY5wUWhTdcK+83AY+dOQMPx4mCIKKCmnMGLvLGeFG0Y0gKCuze+XJSeHHOCm0KLrhXkUFZyejIj/fft4NDa4jAZrmTQQi/PLypPXrra8I4Fc0UYuO/Hxr5FlX5zoSxBlFN9yKxXx5NQ8SJD/fGlRt2eI6EqBpTARGR16eFdybNrmOBGgaRXd0eDlp40bXkSDOKLrh1r590sGDrCpFBR3M4XeHD1unYIruaPByElvM4VcHD0pvvUXRHRWMk0KLohtueXcRMsCNhmHDpOxsHibwr7Vr7T0TgdEwYIA18iQnwa8YJ0XLwIHkpJCi6IZbFRXWQG3MGNeRIBlSU23gwKoS/IoBbrSkpNBMDf7m5aSxY93GgeTgppfQouiGW+XldgVG586uI0Gy8DCBn5WX2+pnTo7rSJAsFN3ws/Jy2yXWpYvrSJAs+fnkpBCi6IZbNCyKHq/ojsVcRwKci5wUPV7RTU6CH5GToodxUihRdMMtHibRk58vHTgg7d3rOhLgXOSk6MnLkw4dsmZVgN+Qk6InL8+aeu7c6ToSxBFFN9ypqZE2bKBhUdR4P2+2mMNvGhqskRo5KVroYA6/qquzO5spuqOFDuahRNENdzZulOrreZhEzdixUloaDxP4z7Ztdo88OSlaRo+W0tPJSfCfzZvtzmYmAqNl5EgpI4OcFDIU3XCHLsHRlJEhjRp16ucP+IW30skAN1o6dbLCm5Vu+A3jpGhKT5fGjSMnhQxFN9wpL5e6dbNOwYgWugXDjyoqpMxMafhw15Eg2chJ8KPycik7Wxo82HUkSDZuegkdim64U1FhA52UFNeRINlyc1nphv9UVEhjxtjxB0QLRTf8yGuilspwPXJyc8lJIcNvMdyhI2d05eXZWbXjx11HApxSXs7W8qjKy5O2bJGOHXMdCXAK46ToysuTdu2SqqpcR4I4oeiGO+XlPEyiKjfX7p9cv951JMApDHCjy+sWvHat2ziA05GTosv7uZOTQoOiG27s22d3NbOqFE3ez52tU/CLw4elHTsY4EaV93PnDCX84tAhac8exklRNW6cvecoXmhQdMMNOnJGW58+Uq9ePEzgH95qAgPcaOrRw5p6MhEIv2CcFG3du0sDB5KTQoSiG26Ul1sDtTFjXEcCV2hcBD9hgAtyEvzEy0neiieiJy+PxYkQoeiGGxUV0ogRUlaW60jgCh3M4Sfl5bbSmZPjOhK4kpfH9nL4R3m5NHSo1KWL60jgCuOkUKHohhs0B4G3qhSLuY4EICfBctK6dVJDg+tIAHIS7Oe/di05KSQouuEGncuRmysdOWJXYgCuMcBFbq504oS0davrSAByEmwikJwUGhTdSL7aWmnjRhoWRR0dzOEXDQ22muDznDRv3jwVFBRo+vTprkMJJ3IS/KK+3nZd+DwnIcG8SRe2mIcCRTeSb+NGqa6OGdyoGzVKSk/nYQL3tm2Tjh/3fU6aO3euSktLVVxc7DqUcBo2TOrcmZwE9zZvlmpqfJ+TkGDDhkmZmeSkkKDoRvJ5qwg8TKKtUydp9GhWleCeN6BhVSnaUlOtUzQ5Ca5xmwIkKS1NGjuWnBQSFN1IvooKqVs3u38Q0cYVPfCD8nJbTRg+3HUkcI1uwfCD8nIpO1saMsR1JHCNa8NCg6Ibyec1B0lJcR0JXGOACz+oqJDGjLFVBUQbE4Hwg4oK23WRyjA98hgnhQa/zUg+OpfDk5cnbdkiHTvmOhJEWXk5W8thcnPtRoWqKteRIMroXA5Pbq60Y4d0+LDrSNBBFN1IvooKBrgw3qBi3Tq3cSDaGODC4z2bWFmCSyxOwOO9DtaudRsHOoyiG8m1b5+0fz8PExjvdcB2Trhy+LCtIpCTINmWXomiG+5UVkp79rA4AcO1YaFB0Y3koiMnTte7t9SnDw8TuOOtHjDAhWRNPgcPZiIQ7jBOwulycqQBAxgnhQBFN5KrosIaqI0d6zoS+AWNi+ASA1ycjcZFcMl7Hnq7LoDcXMZJIUDRjeSqqLBrebKyXEcCv2CAC5cqKmwVISfHdSTwCyYC4VJFhV0V1rWr60jgF4yTQoGiG8lFcxCczbuDMhZzHQmiiJyEs+XmWnPH+nrXkSCKaOyIs+Xl2VGohgbXkaADKLqRXDxMcLbcXOnoUWtmBSQbOQlny8uTqqvtOkMg2chJOFturnT8uLR9u+tI0AEU3Uie2lppwwYaFuFM3uuB7ZxItoYGWz0gJ+F0dAuGK/X1tsuCnITTcdNLKFB0I3k2bZLq6pjBxZlGjpQ6dWKAi+Tbts1WD8hJON3QodZ3hAEukm3LFttlQU7C6UaMkDIyGCcFHEU3kscbwPAwwenS06UxYxjgIvm8AQyrSjhdaqp1jmaAi2TjNgU0Ji3Nbv0hJwUaRTeSp6LCunEOGuQ6EvgNnTnhQnm5lJlpNyoAp6ODOVwoL7ddFkOHuo4EfsO1YYFH0Y3k8ZqDpKS4jgR+wwAXLlRU2C6LtDTXkcBvmAiECxUVtssileE5zkJOCjx+q5E8XM2DpuTm2vnao0ddR4Ioqahgazkal5sr7d4tVVa6jgRRQudyNCUvz7qXM04KLIpuJA8DXDTFe12sXes2DkQLE4FoipeTWFlCMpWXM05C47xnFeOkwKLoRnLs3y/t28cAF43jih4k2+HDdjc8OQmNGTfO3nPsBclSVWW7K8hJaAzXhgUeRTeSg46caE7PnlK/fjxMkDzeagGrSmhM167SkCFMBCJ5GCehOT162DiJnBRYFN1IjooKa6A2dqzrSOBXNAlBMjHARUvoFoxk8l5r3i4L4Gx5eYyTAoyiG8lRUSENGyZlZ7uOBH5FB3MkU0WFNGCAlJPjOhL4FQNcJFNFhTR4sNStm+tI4FcsTgQaRTeSg4ZFaElurm35bWhwHQmigJyEluTmSuvWSfX1riNBFNC5HC3xim7GSYFE0Y3koHM5WpKXJx07ZldiAInGABctycuTamqkzZtdR4IoYCIQLcnNtXHSjh2uI0E7UHQj8WprpQ0beJigeXQwR7I0NNiuCiYC0RxyEpKlvt52VZCT0ByuMgw0im4k3qZNVnhTdKM5I0ZIGRmc60bibdsmHT8euJw0b948FRQUaPr06a5DiYYhQ6wPCTkJibZ1q1RdHbichCQbMULq1ImcFFAU3Ug8ugSjNdLTpTFjmMFF4nmvsYCtKs2dO1elpaUqLi52HUo0pKZaJ2lyEhLNK6IYJ6E5jJMCjaIbiVdRIXXpYl05gebQwRzJUF4uZWZKw4e7jgR+R05CMlRUSJ072y0vQHPoYB5YFN1IPK85SEqK60jgdzxMkAwVFbZakJbmOhL4HTkJyVBRYbsqUhmWowVcZRhY/HYj8egSjNbKy7Pu5UeOuI4EYcZtCmitvDxpzx7p0CHXkSDMGCehtXJzrQfA0aOuI0EbUXQj8RjgorW8QcfatW7jQLhxNQ9aiw7mSIbycsZJaB0vJ61b5zYOtBlFNxLrwAFp714GuGgd73XCGUokyuHDdscpOQmtMW6cvScnIVGqqqRdu8hJaB0mAgOLohuJRedytEWPHlL//jxMkDjeLgpWldAaXbpIQ4eSk5A4Xk5inITW6NVL6tuXicAAouhGYnkDFW+1AGgJ3YKRSEwEoq3ISUgkrgtDW9HgMZAoupFY5eV2BUZ2tutIEBQ8TJBIFRXSgAFSTo7rSBAU5CQkUkWFNGiQ1K2b60gQFOSkQKLoRmLRkRNtlZdn2+0aGlxHgjCiiRraKi/PmhbV1bmOBGHEOAlt5V0bFou5jgRtQNGNxKJzOdoqN1c6flzats11JAgjBrhoq9xcqbZW2rzZdSQIIzqXo61yc+3KsB07XEeCNqDoRuLU1Unr1zPARdt4gw/OUCLeGhpsFwUDXLQFtyogURoabBcF4yS0BR3MA4miG4mzaZOtDvAwQVsMHy5lZvIwQfxt22a7KMhJaIvBg62LOTkJ8bZ1q3TiBDkJbTNypJSeTk4KGIpuJI6XDFhVQlukpUljx7KqhPgjJ6E9UlPtBg5yEuKNzuVoj06dpDFjKLoDhqIbiVNebqsDgwe7jgRBk5vLABfxV15uuyiGD3cdCYLGa1wExFNFhdS5s93yArQF46TAoehG4lRU2OpASorrSBA0DHCRCBUVtjqQluY6EgQNA1wkQkWF7ewiJ6GtuDYscCi6kTh0Lkd75eVJO3dKVVWuI0GYkJPQXnl50t690oEDriNBmHCFIdorN9d6Ahw75joStBJFNxKHhwnay3vdrF3rNg6ECzkJ7UW3YCQCE4For7w8u6d73TrXkaCVKLqRGAcP2qoAA1y0B1f0IN6OHLE7TRngoj3GjbP3FN2Il8OHbUcX4yS0BxOBgUPRjcSgSzA6ont3aeBAHiaIH2/XBANctEd2tjW7YiIQ8UJOQkf07m1vjJMCg6IbieElgbFj3caB4MrLY4CL+OFqHnQUDR4RT+QkdBQ5KVAoupEY5eXS0KF2ZRjQHnTmRDxVVEgDBkg5Oa4jQVDRwRzxVFFhO7q6d3cdCYKKnBQoFN1IjIoKZm/RMXl5tv2uvt51JAgDmqiho/LypA0bpNpa15EgDBgnoaO8xYlYzHUkaAWKbiQGHTnRUbm5UnW1XYkBdBQDXHRUbq4V3Js2uY4EYVBezjgJHZOba01Cd+1yHQlagaIb8VdXZ1cYMMBFR3iDEbZOoaMaGmzXBANcdIT3+uHYCzqqoYFxEjqOnBQoFN2Iv82bbTWAhwk6YtgwqXNnHibouG3bpOPHyUnomEGDpK5dmQhEx5GTEA+jRknp6eSkgEhvzQelpKSkVFZWJjoWhMXy5fZ+8GCpqsptLAi20aOlkhJeR+iYZcvsfUBzUnV1taqrq0/+/8OHD0uSqgL43xJ4Y8ZIq1YF8nUEH1m61N4HNCfBR4YPZ5zkAzk5Od0lHY7Fmj5gn9LM3536oJSU7pKougEAAAAAOFNOLBZrcvajtUV3SmVlZUM8oqmqqtLQoUO1bds2dQ/YNQnTp09XcXGx6zDaJamx33efrSy99lpcPl1Qv+9BjdtXv6MPPig98oidfWuFoH7PJWJPqM98xvLRokVn/LHv437b2Svdu3bt0owZM1RaWqrBgwc7jKx9gvJ9P9v06dNV/K53SQ8/HLhmakH9nkvBjL3F5+hnPiO9/rr05pvJD64Vgvg9l4Ibt9SB2P/zP6UnnrAdOI4E8fse77FuTk5OjlpY6W7V9vLmPkF7de/e3f2Avo3S0tICF7MnqbFv2iQVFsbt7smgft+DGrfHF7+jEydKb71l12G04n7lIH/PiT2BmshJvo+7Bd26dQtk/EH9vqelpan7pEnSgQPWt6R3b9chtVpQv+dSsGNv8jm6cWNcx0nxFtTveVDjljoQ+8SJ0o9/LHXqJGVlxT+wVgjy9z1eY93mVrg9NFJrg7lz57oOod2SGnuc78MN6vc9qHH7Shs7cwb5e07sCdRETvJ93CEV1O/73LlzA9stOKjfcynYsTfJ51cYBvV7HtS4pQ7EnptrCxPr18c3oDYI8vc9mVq1vfxtcVntrqqqUk5OjiorKwM7K4JmHDok9ewpPfqo9J73uI4G7eCr39HDh20l4He/k973PrexIJiOHJG6dQvVa2j79u0nt8UNGTLEdTjRcvy41KWL9KtfSR/8oOto4FPNPkd5riGe9u6V+vWT/vpX6dZbXUcTGAkY66a09AFJX+nOzMzUV77yFWVmZib7SyMZvNl/7sMNLF/9jnbrZt1duQ4D7bV2rb338apSW3m/m774HY2arCy7zpCchGY0+xwNYU6CQ336SL16BW73jWsuxrpJX+lGyP32t9Jdd9nqUpcurqNBGFx2me2e+NvfXEeCIHr0Uem977VdOK3oCxAEvtqNEkVXXy117mzNi4C2CmFOgmOzZ9sVq7//vetIosx/K90IuYoKacgQCm7ET14eq0pov4oKacAABreIn9xcchLaj5yEeMvLY6U7ACi6EV8VFWwtR3zl5tqVYfX1riNBEPm8YRECKC9P2rDBOpgDbRXnZrPAyYnA+F82hTii6EZ88TBBvOXlSTU10ubNriNBEJGTEG+5uVJdnV37BLQVixOIt9xca9C3e7frSNAMim7ET329XVnAABfx5L2e2DqFtmposKZFDHARTwG9Ngw+4OUkxkmIJy8ncezF15JWdD/44IOaPXu2srOz1aNHj0Y/ZuvWrbrhhhvUpUsX9enTR/fdd59qamqSFSI6avNmW5FkgBsaI0aMUEpKyhlvn//855MbxNCh1jGYhwnaats2u+KJAS7iaeBAqWtXchLO8cADD5zzzBwwYMCpD9i+nZyE+Bs1SkpLYyKwEa+88opuuOEGDRo0SCkpKXrirAaYsVhMDzzwgAYNGqSsrCxdfPHFWrNmTUJiSVrRXVNTo1tvvVUf+9jHGv37+vp6XXfddTp69Khee+01/fnPf9bf//53feYzn0lWiOgobwDCwyRUvva1r2nXrl0n3/7f//t/yQ0gNVUaN46HCdqOKwyRCCkpNC5CkwoLC894Zq5aterUX3rjJHIS4ikjw7qXk5POcfToUU2aNEk/+clPGv37b33rW/re976nn/zkJyouLtaAAQN0xRVX6PDhw3GPJT3un7EJX/3qVyVJjzzySKN///zzz6u0tFTbtm3ToEGDJEnf/e53ddddd+nBBx/kWpQgqKiwFckhQ1xHgjjq1q3bmTP1LtDBHO1RUSFlZkrDh7uOBGFDB3M0IT09velnJjkJiUJOatQ111yja665ptG/i8Vi+sEPfqAvfelLuvnmmyVJv/3tb9W/f389+uij+shHPhLXWHxzpvuNN97Q+PHjTxbcknTVVVepurpaS5cudRgZWq2iwlYkU33zskIcfPOb31Tv3r1VVFSkBx980M2Rj9xcZnDRduXl0pgxtu0OiCdWutGEdevWadCgQRo5cqRuv/12bTy94V5FBTkJicE4qc02bdqk3bt368orrzz5Z5mZmbrooou0cOHCuH+9pK10t2T37t3q37//GX/Ws2dPZWRkaDfd+IKhvJwtUyHziU98QlOmTFHPnj21ePFifeELX9CmTZv0y1/+MrmB5OVJe/ZIhw5JTfSEAM5Bl2AkSm6utH+/tG+f1KeP62jgEzNnztTvfvc7jRs3Tnv27NHXv/51zZ49W2vWrFHv3r0ZJyFx8vKst9Lx47brFC3y6suz68/+/ftry5Ytcf96HVqSbKxhxNlvS5YsafXnS0lJOefPYrFYo38OH+I+3EBoy+/tpz71KV100UWaOHGi7r77bj388MP61a9+pf379yc3aDqYoz3ISUgUOpijEddcc41uueUWTZgwQZdffrmefvppSbZlVRI5CYmTm2v3dK9f7zqSwDm7zkxU7dmhle57771Xt99+e7MfM2LEiFZ9rgEDBmjRokVn/NnBgwdVW1t7zgwEfOjQIVuJ5GHiex35vZ01a5Ykaf369TZrnyzjxtn78nJp5szkfV0E15Ej1imYVSUkwpgx1lCtvFyaM8d1NPCpLl26aMKECVq3bt2pnMQ4CYlw+kTghAluYwkIr/fC7t27NXDgwJN//tZbbyWk9uxQ0d2nTx/1idO2qvPOO08PPvigdu3adfI//Pnnn1dmZqamTp0al6+BBKJLcGB05Pd2+fLlknRGckqKrl2tQR+rSmittWvtPQNcJEJWljRiBDkJzaqurlZZWZkuuOCCUzmJcRISoU8fqVcvmqm1wciRIzVgwAC98MILmjx5siS7bWvBggX65je/Gfevl7Qz3Vu3btWBAwe0detW1dfXa8WKFZKkMWPGqGvXrrryyitVUFCg973vffr2t7+tAwcO6P7779c999xD5/Ig8AYe3ookAu+NN97Qm2++qUsuuUQ5OTkqLi7Wpz71Kd14440aNmxY8gOigznagisMkWh0C8ZZ7r//ft1www0aNmyY3nrrLX39619XVVWVPvCBD0heYyZyEhKFZmrnOHLkiNaftuV+06ZNWrFihXr16qVhw4bpk5/8pL7xjW9o7NixGjt2rL7xjW8oOztbd9xxR9xjSVrR/eUvf/nUmRbp5IzCv/71L1188cVKS0vT008/rY9//OOaM2eOsrKydMcdd+g73/lOskJER1RUSIMH24okQiEzM1N/+ctf9NWvflXV1dUaPny47rnnHn3uc59zE1BurvSvf7n52gieigppwAApJ8d1JAirvDzpmWdcRwEf2b59u97znvdo37596tu3r2bNmqU333xTw4cPl37zG6l/f3ISEicvT1q92nUUvrJkyRJdcsklJ///pz/9aUnSBz7wAT3yyCP63Oc+p+PHj+vjH/+4Dh48qJkzZ+r5559Xt27d4h5LSiwWa+3HtvoDEUG33CJVVkovvug6EoTVT34iffrT0rFjUrpvLl6AX91+u7R7t/Tyy64jibuqqirl5OSosrKSnWAuPfywdO+9lpMyMlxHA7+7/XZp1y5pwQLXkSCsvvlN6cEHbTxOE+pka/EbzoXKiA86ciLRcnOl2lq7EgNoSXk5OQmJlZcn1ddLp9/DDDSFKwyRaLm50uHDNuEM36HoRsfV10vr1jHARWJ5gxXOUKIlDQ3WtIgBLhLJe+aRk9ASLycxTkIiMU7yNYpudNzmzVJNDQNcJNbgwVJ2Nk1C0LLt26XjxxngIrEGDJC6dycnoWXbt9sxBHISEmnUKCktjZzkUxTd6Djvl5uHCRIpNZVuwWgd7zXCRCASKSWFnITW4VpVJENGhjR6NEW3T1F0o+MqKuzO0qFDXUeCsGOAi9aoqJAyM6Xhw11HgrDjih60RkWFFUQjRriOBGHHOMm3KLrRcRUVdj93Ki8nJFheHgNctKy8XBozxrbZhci8efNUUFCg6dOnuw4Fnrw8e721/iYYRFFIcxJ8iIlA36JKQsfRJRjJkpsr7d0rHTjgOhL4WUi7BM+dO1elpaUqLi52HQo8ubnSwYPSvn2uI4GfhTQnwYfy8qzX0okTriPBWSi60XFcF4Zk8QYtzOKiOeQkJAs5Ca1BTkKy5Obazpt161xHgrNQdKNjKivtPkBmcJEMY8fae84roSlHjlinYHISkmHMGGuoRk5CU44elbZto+hGcjAR6FsU3egYOpcjmbp0kYYN42GCpq1da+/JSUiGzp2lkSPJSWial5OYCEQy9Okj9erFRKAPUXSjY7yBxrhxbuNAdHiNi4DGMBGIZKNbMJpDTkKy0UzNlyi60TEVFdKgQVK3bq4jQVTwMEFzysulAQOknBzXkSAquFUBzamokPr1k3r0cB0JooKc5EsU3eiY8nK2TCG58vKk9eul2lrXkcCPaFiEZMvNlTZulGpqXEcCP2KchGTzdt9wlaGvUHSjYxjgItlyc6W6OmnTJteRwI+4whDJlpcn1ddLGza4jgR+xDgJyZaXJx0+bI2O4RsU3Wi/+nq7koCHCZLJWzHgDCXO1tBgTYtYVUIyec9AchLO1tBA0Y3k815vbDH3FYputN+WLVJ1NQNcJNegQVLXrjxMcK7t26XjxxngIrn697ceAuQknG3HDunYMcZJSK5Ro6S0NCYCfYaiG+1HR064kJJCt2A0zntNMMBFMpGT0BTGSXAhI0MaPZqJQJ+h6Eb7lZfbHaXDhrmOBFFDB3M0pqJCysyUhg93HQmihm7BaExFhdSpkzRihOtIEDVMBPoORTfaz2tYlMrLCEnGXd1oTEWFNGaMbasDkoluwWhMebnlpPR015EgapgI9B2qJbRfRQXbOOFGbq60f7+0b5/rSOAnXM0DV/LypEOHpL17XUcCP2GcBFdyc6XNm6UTJ1xHgrdRdKP9GODCFe91xywuTkeXYLhCB3M0hpwEV3JzbefNunWuI8HbKLrRPgcPSnv2UHTDjbFjrXkRRTc8R45Y93JyElwYM8aOWpGT4Dl6VNq6laIbbrA44TsU3WgfOnLCpawsa5bFqhI8a9fae3ISXMjMlEaOJCfhFG+FkYlAuNCnj9SrFznJRyi60T7eL/G4cW7jQHTRwRynYyIQrtG4CKcjJ8E1xkm+QtGN9qmosKvCunRxHQmiig7mOF15uTRggJST4zoSRBVX9OB0FRVS375Sz56uI0FUMRHoKxTdaB+aqMG13Fxp40apttZ1JPADGhbBtdxcadMmqbradSTwA8ZJcI2rDH2Fohvtw8MEruXlSXV10oYNriOBH1B0w7W8PKmhQVq/3nUk8ANyElzLy5MOH5Z273YdCUTRjfaorbVBBQ8TuOS9/tg6hYYG7sOFe+QkeGIxim64R07yFYputN3GjbbCyAAXLg0cKHXrxhlK2FVhx48zwIVb/fpJPXqQkyDt2GFXhjFOgkujRklpaeQkn6DoRtt5M2Y8TOBSSgqdOWG8AQVFN1wiJ8FD53L4QUaGNHo0OcknKLrRduXltsI4cKDrSBB1dDCHZK+BzExpxAjXkSDqyEmQrMjp1Mnubgdc4lYF36DoRtt5TdRSUlxHgqijMyckew2MG2fb6ACXvJVuclK0lZfbCmN6uutIEHVcG+YbFN1oOzqXwy/y8qSDB6V9+1xHApcikpPmzZungoICTZ8+3XUoaEpenlRZKe3Z4zoSuFReLuXnu44CsInAzZulEydcRxJ5FN1om1jMHiacU4If0JkTklRWFokB7ty5c1VaWqri4mLXoaAp5CRIkZkIRADk5trYfd0615FEHkU32mbfPltZ5GECPxg71o45cF4pug4dsjtIyUnwg9Gj7ZgDRXd0HTkibdtGToI/eK9DcpJzFN1oG6+44WECP+jc2Zpn8TCJLm5TgJ9kZlrzLCYCo8vLSRHYfYMA6NNH6tWLcZIPUHSjbcrLpdRUacwY15EAhm7B0cZ1YfAbGhdFGzkJfsM4yRcoutE25eXSqFE2mw/4AffiRltZmTR8uJSd7ToSwHBFT7SVl0uDBkndu7uOBDCMk3yBohttQ3MQ+E1enrRxo1RT4zoSuEBOgt/k5dEtOMrISfAbrlf1BYputE1FBVum4C+5uVJ9vbRhg+tI4AIDXPhNbq7U0CCtX+86ErgQkdsUECB5edLhw9Z0FM5QdKP1TpyQNm1igAt/8V6PbOeMnpoaK2wY4MJP6BYcXXV1djUT4yT4CVcZ+gJFN1pv/XqbvedhAj/p39/OzvEwiZ4NG2yXAzkJftKnj9SzJxOBUbR5s00GkpPgJ6NHS+np5CTHKLrRelwXBj9KSaEzZ1SRk+BHXk5iIjB6yEnwo06drAkyOckpim60Xnm51Lu3zeIDfkJnzmgqK7MVxX79XEcCnIkO5tFUViZ17SoNHuw6EuBMjJOco+hG69FEDX7lrXTTmTNavCZqKSmuIwHO5A1wyUnRQk6CX7Ej0DmKbrQeXYLhV7m50qFD0ltvuY4EyUROgl/l5UlVVXQLjhpyEvwqN5erDB2j6EbrxGI8TOBfdAuOHnIS/IxuwdETi9n2cnIS/Cg3116j69a5jiSyKLrROjt3SkeO8DCBP40ZI6WmsnUqSnbutHtHuS4MfjR6tJSWRk6Kkr17pYMHyUnwJxYnnKPoRuvQkRN+lpkpjRzJwyRKyEnws4wMugVHDTkJftanj9SrFxOBDlF0o3UqKuzKgZEjXUcCNI5uwdFSXm6FDTkJfkXjomgpL7fdDWPGuI4EaFx+PjnJIYputE55uT1I0tNdRwI0jntxo6WsTBo7lpwE/+KKnmgpK7NjBRkZriMBGpeXZ69TOEHRjdahYRH8LjdX2rRJqq52HQmSgZwEv8vLs27Bx4+7jgTJQE6C33kr3Q0NriOJJIputA4PE/hdXp49SNavdx0JkoGcBL/zugWTk6KBnAS/y8+Xjh2Ttm1zHUkkUXSjZUeP2i8oDxP4mff65LxS+B0+LO3YQZdg+Bs5KTqOHZO2bGGcBH/znplsMXeCohstW7vW3vMwgZ/17Sv16MEZyiigSzCCwOsWTE4Kv7VrbVcDE4Hws+HDpawsim5HKLrRMm+Am5vrNg6gOSkpdAuOCnISgoKcFA3kJARBaqq9Rim6naDoRsvKy6UBA6ScHNeRAM2jW3A0lJdLQ4ZIXbu6jgRoHjkpGsrLpf79pZ49XUcCNC8/n6LbEYputIzmIAgKb1UpFnMdCRKprIxtnAgGclI0ME5CUHBXtzMU3WgZDxMERW6uVFUl7dnjOhIkEjkJQZGbKx05Iu3a5ToSJBITgQiK/Hxp3z57Q1JRdKN59fXWIIRzSggCugWHX22tXcFE0Y0gICeFnzdOIichCLzXKVvMk46iG83bskU6cUIqKHAdCdCy0aOltDTOUIbZxo1WeEdwVWnevHkqKCjQ9OnTXYeC1ho1SkpPJyeF2datNk6i6EYQjB1rDdUoupOOohvN834pIzjARQBlZNggl1Wl8IrwdWFz585VaWmpiouLXYeC1urUySYDyUnhFeGchADKzLScRNGddBTdaF5pqXUIHjLEdSRA69AtONzKy6Xu3e1GBSAIyEnhVlYmZWdLQ4e6jgRoHTqYO0HRjeaVldnsbUqK60iA1uFe3HDzmqiRkxAUeXkU3WFWXm4TK6kMqREQFN1OkCHQvLIyznMjWHJzpc2b7YwdwocuwQia3Fzrj3L8uOtIkAjcpoCgyc+3XgRHjriOJFIoutG0WMy2lzPARZDk5dlrd90615Eg3mIxBrgIntxcclKYeTsCgaDwxvXswEkqim40bdcuu/OYohtB4l1vx8MkfPbskSorGeAiWLg2LLy8+44ZJyFIuDbMCYpuNM37ZWR7OYKkTx+pVy8GuGHEbQoIot697Y2JwPDxfqZMBCJIuneXBg9mnJRkFN1oWmmpXcE0cqTrSIDWS0mhW3BYlZfbncejRrmOBGgbGjyGU3m5NVAbO9Z1JEDb5OWx0p1kFN1oWlmZNG6cDXKBIGGAG07l5dKYMXb3MRAkTASGU1mZLUx07uw6EqBt6GCedBTdaBpdghFU3gA3FnMdCeKJJmoIKu/aMHJSuJCTEFT5+dbcsbbWdSSRQdGNppWWcp4bwZSXJx0+bM0AER5MBCKo8vLsep7t211Hgnii6EZQ5edLdXXShg2uI4kMim407sAB6a23GOAimLwO5mwxD48jR6Rt2xjgIpi8CWy2c4bHiRPSpk3kJASTN74nJyUNRTcaR5dgBNno0Xbul4dJeKxda+8Z4CKIRoyQMjPJSWGybp3U0EBOQjD17y/16EFOSiKKbjSurMw6co4b5zoSoO06dbLXbmmp60gQL97AgAEugigtzV675KTw8H6WLE4giFJSaKaWZBTdaFxpqV3LQ0dOBFVBgbRmjesoEC/l5dLAgXa/KBBEDHDDpbTUVgt793YdCdA+5KSkouhG42hYhKArKGBVKUxo7IigIyeFCzkJQZefbxPa3KqQFBTdaFxZGQ8TBFtBgbR3r70h+BjgIujy86X9+8lJYUFOQtDl5UlHj3KrQpJQdONcR45IW7aw0o1gKyy092ydCr6aGmtaxAAXQea9flntDr7aWmvuSE5CkNHBPKkounGuigp7T9GNIBs71poXMcANvnXrpPp6BrgItjFjLCcxwA2+9evtjmNyEoKMWxWSiqIb56JLMMIgI8MKb4ru4PN+ht7uBSCIyEnh4Y2TKLoRZGlpUm4uRXeSUHTjXKWl0pAhdAlG8NG4KBxKS6V+/egSjOArKGCAGwalpZaP+vZ1HQnQMXQwTxqKbpyLzuUIC4rucKBhEcIiP5+cFAZeTkpJcR0J0DEU3UlD0Y1zUXQjLAoKpF27pIMHXUeCjqDoRlgUFEg7d0qVla4jQUeQkxAW+fl2o8L+/a4jCT2KbpyppsYahPAwQRh4r2NmcYOrrs6aO5KTEAZ0Cw6++nq725ichDAgJyUNRTfO5HUJZqUbYTBunJSaynbOINuwwa7nYYCLMMjNtS3JDHCDa9MmqbqanIRwGDvWxknkpISj6MaZvF86im6EQVaWNGoURXeQeT87BrgIg+xsu6aHnBRc5CSESefO0siRtnsDCUXRjTOVldGRE+FCM7VgKy2VevWy7uURN2/ePBUUFGj69OmuQ0FH0ME82EpLpZwcaeBA15EA8UEztaSg6MaZaA6CsKHoDrY1a+gS/La5c+eqtLRUxcXFrkNBR9DBPNjoXI6woehOCopunInO5QibggJp2zapqsp1JGgPJgIRNgUF0ubN0rFjriNBe5CTEDZeTjp61HUkoUbRjVPq661LMEU3wqSw0N4zixs8dAlGGBUUSLGYPW8RLA0N9iwhJyFMGCclBUU3Ttm8WTpxgocJwiUvz7YBsp0zeOgSjDDKy7P3DHCDZ+tW26FATkKYeItta9a4jSPkKLpxCp3LEUZ0Cw4uugQjjHJypMGDyUlBRE5CGHXtKg0fTtGdYBTdOKWszH7xhgxxHQkQXzRTC6bSUql7d2nQINeRAPFFM7VgKi21cdLQoa4jAeKrsJCclGAU3TiltPTUVlwgTCi6g4kuwQgrBrjBVFpqEybkJIRNYSEr3QlG0Y1TaA6CsKIzZzCVlp5q8AKESWGhtG6d9VFBcNC5HGFVWGjjpCNHXEcSWhTdMLGYzXAxwEUYeYOk8nK3caD16BKMMBs/3l7jdDAPjliMohvh5b2uafCYMBTdMFu32uwWRTfCyGsOyHbO4KBLMMLMe12vXu02DrTejh3S4cPkJIQTHcwTjqIbxvslGz/ebRxAInTrZo1vKLqDgy7BCLOcHMtJDHCDw8tJ3PCCMOra1W56ISclDEU3zOrV9gs3bJjrSIDEoJlasKxZQ5dghFthISvdQVJaKnXubIUJEEY0eEwoim6YNWvoEoxwo+gOFroEI+zGj2dVKUi8G17S0lxHAiQGHcwTiqIbZs0atpYj3AoLpY0bpePHXUeC1qBhEcLOy0ncqhAM5CSEXWGhtGULHcwThKIb1kGVq3kQdgUF9lpfu9Z1JGgJXYIRBd5EN92C/Y+chCjwXt/sCkwIim5ImzbZ6h9FN8KMzpzBsX27zbQzwEWYeTmJc93+t2ePdPAgOQnhxjgpoSi6QedyREOPHtKgQczgBgGdyxEFXbpIo0YxwA0CchKioEsXaeRIclKCUHTDZtlzcqwgAcKMZmrBUFoqZWVJw4e7jgRILDqYB0NpqdSpkzR6tOtIgMSig3nCUHTDZrQKC+kSjPCj6A4GugQjKuhgHgylpVJurpSe7joSILHoYJ4wFN2gczmio6BAWr9eqq52HQmaQ8MiREVhobRtm1RZ6ToSNGf1anISoqGgQNq6VTp82HUkoUPRHXV1ddY5lSZqiIKCAqm+Xlq3znUkaApdghEl3oQ3O3D8KxazonvCBNeRAInn1QPkpLij6I66DRukmhqKbkQD12H4344d0qFD7L5BNOTmSqmpnOv2s127rHM5RTeiID/fjpuyxTzuKLqjznvQM8BFFPTuLfXrx8PEz8hJiJLOnaWxY8lJfkZOQpRkZ1sHcxYn4o6iO+rWrDlViABRQJMQf1u1yq4tGTHCdSQJ8eCDD2r27NnKzs5Wjx49XIcDP6CDub+tWmW3KYwc6ToSIDkYJyUERXfU0bkcUTNhgg2i4E+rVtmKUmo4H081NTW69dZb9bGPfcx1KPALOpj72+rVNk4KaU4CzkHRnRBkkKhbvZotU4iWCROsg/nx464jQWNCnpO++tWv6lOf+pQmcD4UnsJCafduaf9+15GgMTRRQ9QUFNitClVVriMJFYruKKupkdaupYkaomXCBKmhgfNKflRXZz8XBrhnqK6uVlVV1RlvCBFvkomVJf9paOBaVUQPHcwTgqI7ytats0EuRTeixOtgzhlK/9mwwe5QZ4B7hoceekg5OTkn34YOHeo6JMTT2LFSp07kJD/auNF2RZGTECV5eXQwTwCK7ijzHvAU3YiSbt2sIQ7nuv3H+5kEbKX7gQceUEpKSrNvS5Ysaffn/8IXvqDKysqTb9u2bYtj9HCuUye7OowBrv9446SA5SSgQ7KzpVGjWOmOs3TXAcChNWuk/v2lPn1cRwIkF83U/Gn1aqlv38DdpnDvvffq9ttvb/ZjRnSgG3tmZqYyMzPb/e8RAHQw96fVq6VevaQBA1xHAiQXOSnuKLqjzOtcDkTNhAnSr3/tOgqcbdWqQK4o9enTR32YvERHjB8vvfiiFItxm4ifeI0d+ZkgasaPlx55xHUUocL28igLeZdgoEnjx0u7dtEt2G8i0CV469atWrFihbZu3ar6+nqtWLFCK1as0JEjR1yHBpcKCy0f7dnjOhKczrvCEIiaCROknTulAwdcRxIaFN1RdeKEXZvESjeiyCvs2DrlH8ePW04K+QD3y1/+siZPnqyvfOUrOnLkiCZPnqzJkyd36Mw3QoAO5v5TXW03vIR8IhBolJeTGCfFDUV3VFVU2FUYFN2IonHjrHkR57r9o7TUclLIB7iPPPKIYrHYOW8XX3yx69Dg0qhRUufODHD9ZO1au+El5BOBQKNycxknxRlFd1TRuRxR1qmTlJ/Pw8RPvJzkXekGRElamuUkVrr9g3ESoqxTJ7s6jHFS3FB0R9WaNdLgwVKPHq4jAdygg7m/rFplV7l16+Y6EsANugX7y6pVNk7q2dN1JIAbEyaQk+KIojuq6FyOqBs/3h4msZjrSCBFooka0Kzx4+3ZTE7yB3ISoo5xUlxRdEfV6tUU3Yi2CROkw4elrVtdRwKJLsFAYaFUVSVt3+46Ekjc8AJMmCBVVkrbtrmOJBQouqPoyBFp40Zp4kTXkQDueCsYbDF378ABu5qEVSVEmTcRzrlu9w4fljZtouhGtDFOiiuK7ijyzmdQdCPKhg6VcnJ4mPiBl5MY4CLKhg+XunThDKUflJbaeyYCEWXDhlmfFXJSXFB0R1FJiZSaSpdgRFtKyqnzSnBr1SrrlDpunOtIAHe85zIr3e6tXm3PiPx815EA7njjJBYn4oKiO4pKSuz+vc6dXUcCuMXDxB9Wr7aclJHhOhLALSYC/WH1amnMGCkry3UkgFvc9BI3FN1RVFLC1nJAsodJeblUW+s6kmhbtYptnIBk57pLS6WGBteRRBuNHQHDOCluKLqjJhaj6AY8EybYg6SiwnUk0RWLcTUP4Bk/Xjp2zJqdwh1yEmDGj5dqaqR161xHEnjJLboPHpTOP1+aPz+pXxan2brV2v9TdAOnVjLYOuXO9u2Wk1hVAqRJk+w9OcmdvXulPXvISYBEB/M4Sm7RnZNjq6xLliT1y+I0JSX2nqIbkHr1kgYN4gylS973nlUlQOrfX+rbV1q50nUk0eU1sqPoBqTevaWBAxknxUFyi+7UVBtYeYUfkq+kROrRw65LAkCTENdWrZK6drWrSYCoS0mx1W6KbndWrbKmjmPGuI4E8AeazsZF8s90T5pE0e2Sd547JcV1JIA/UHS75TUsSqXFCCDJntGMk9xZvdquCuvUyXUkgD8wToqL5I9yJk60LnjV1Un/0hBN1ICzTZggbd4sHT7sOpJoWr2abZzA6SZNskZqVVWuI4kmchJwpgkTLCcxTuoQN0V3XZ0V3kiu48eltWspuoHTeWeJvXN8SJ66OqmsjPPcwOm8ZzRnKJPPu02Bohs4hQaPcZH8otsbXHFeKfm8uz8puoFT8vJsazMPk+Rbv952PVF0A6fk50vp6YyTXNi82XYYeEUGAKmggJwUB8kvurt1k0aN4rySCyUldpa7sNB1JIB/ZGVJY8dSdLvgfc9ZVQJOycy0wptxUvJ5RQVFN3CKl5NWrHAdSaC56VxDkxA3Skqk0aOtUzCAU2gS4sbq1aeuSAJwysSJrCq5UFJy6ookAKcUFZGTOoiiO0pWrmT2FmiMV3THYq4jiRavczmAM02aZL8fDQ2uI4kWb5zEDS/AmbycVF/vOpLAcld079ljb0iOWIzO5UBTJkyQ9u8nJyUbE4FtMm/ePBUUFGj69OmuQ0GiTZwoHTkibdrkOpJoIScBjSsqko4ds14saBd3RbfEds5k2rXLigqKbuBc3morOSl5qqrsChIGuK02d+5clZaWqri42HUoSDTv94Jdgclz+LC0YQM5CWiM93vBFvN2c1N0jx4tZWfzMEkm73tN0Q2ca9QoqUsXHibJ5OUkBrjAubxeB+Sk5PGuaGOcBJyrTx9p8GCaqXWAm6I7NdW2c/IwSZ6SEmugNmKE60gA/0lLs4EWD5PkWblS6tTJOqICOFNKik1IsTiRPCtX2rVIBQWuIwH8adIkarcOcFN0SzRTS7aSEpvoSHX3Iwd8jc6cybVypQ1uMzJcRwL4Ex3Mk2vlSikvz65HAnCuoiIWJzrAbdFdWirV1joLIVJoogY0b9IkqaxMOnHCdSTRQMMioHmTJlnfg6oq15FEA+MkoHmTJkk7d0p797qOJJDcFt01NdLatc5CiIyaGismeJgATSsqsqsw1qxxHUn41ddb0zqKbqBp3jPbO2uMxGlosKKbnAQ0rajI3rMDp13cFt0SP7hkKCuT6up4mADN8Y5fsHUq8datk44fJycBzcnPtzPGjJMSb9Mmu6KNnAQ0zWuETU5qF3dFd48e0rBh/OCSwTs7712LBOBc2dnSuHEU3cng5X0GuEDTMjOt8Kb/TeJxmwLQMprOdojbrlqTJ/ODS4aSEutanpPjOhLA3+jMmRwrV0qDBtkVJACaRjO15Fi50q5o69/fdSSAvzFOaje3RXdRkbR8uRSLOQ0j9GgOArSO15mzocF1JOFGEzWgdSZNsv4H5KTE8nJSSorrSAB/KyqyY6vV1a4jCRz3RffevdLu3U7DCD2KbqB1ioqkw4elzZtdRxJuK1eeasgCoGkTJ9pZ402bXEcSbjRRA1pn0iTrE1Va6jqSwHFfdEu22o3EeOstm9Sg6AZa5uUkjr0kzr590o4dDHCB1vB+TzjXnTiVlXY1GzkJaNmECbYjhHFSm7ktuocPt3PG/OASxzt3QdENtGzAADvTx3mlxKGJGtB6/fvbWWNyUuJ439vJk93GAQRB167SmDHkpHZwW3SnpJw6Q4nEWL5c6tJFGjvWdSRAMEyaRE5KpJUrpawschLQGikplpNY6U6c5cutU3xenutIgGCgdmsXt0W3RAfzRFu+3B7Yqe5/1EAg8DBJrJUr7frCtDTXkQDBMGkSx/ASafly2zKbnu46EiAYvA7mNMJuE/eVWFGRtG6dNS9C/C1fzpYpoC2KiqStW6UDB1xHEk7Ll9NEDWiLqVOtuSM5KTEYJwFtU1QkHTpkYyW0mj+KbomtU4lw5Ii0di0PE6AtyEmJc+KEdTydMsV1JEBweL8vrHbHX3W15STGSUDreT1ZONfdJu6L7vx8qVMntnMmQkmJbf3gYQK03tixUufO5KREWLVKqq8nJwFtMXasNS9atsx1JOGzZo1df0ROAlpv8GCpd2/GSW3kvujOyJAKC/nBJcLy5XZGqbDQdSRAcKSn2/k+clL8LV9uZ7m5TQFovdRU24FD0R1/y5fb95ecBLSe1+CRle42cV90SzRTS5Tly63gzsx0HQkQLDRTS4zly61DcFaW60iAYJkyhaI7EZYvl8aNk7KzXUcCBEtREUV3G/mj6C4qsm2HtbWuIwkXmoMA7VNUZOf8ampcRxIuy5ZxnhtojylTrEdLVZXrSMKFcRLQPpMmSRs2kJPawD9Fd3W1VF7uOpLwqK2VVq/mYQK0R1GR/Q6VlrqOJDzq6qzPBDkJaLupU+09O3Dip6HBVurISUDbec3UVq1yG0eA+Kfoltg6FU9lZbZKx8MEaLuJE+3M0tKlriMJj/Jy617OSjfQdnl51uCRcVL8rF8vHT3KOAloDxpht5k/iu7u3e1MDQPc+PGuFvFmogC0XteuNsglJ8WPl5O4oxtou/R0e55TdMcPOQlov4wMqaCAorsN/FF0S7Z1askS11GEx/Ll0pgxNqEBoO2mTqXojqdly6TRo6WcHNeRAMFEM7X4Wr5cGjJE6tPHdSRAME2efGryCi3yT9E9bZrNltTVuY4kHGgOAnTM1Kl23o8Gj/FBTgI6ZsoUOzp27JjrSMKBnAR0zNSpdqabprOt4p+ie+pU6fhxmqnFQyxmExg8TID2mzrVGjyWlbmOJPgaGmyAy3nuDpk3b54KCgo0ffp016HAhSlTTjX/QsfEYtymAHTU1KlWcK9e7TqSQPBP0T15sjUuYot5x3kt/HmYAO3n5SS2mHfcpk2Wk5gI7JC5c+eqtLRUxcXFrkOBC+PHW+Mitph33LZt0r59jJOAjpg0SUpNpXZrJf8U3TRTix/vxe9dMQKg7bp2lXJzyUnx4BUJFN1A+2VkSBMmUHTHg/c9ZJwEtF92tjVTY5zUKv4puiWaqcXL0qXS8OE0BwE6imZq8bF8uTRokNS/v+tIgGCjmVp8LF1q+WjQINeRAME2bRrjpFbyV9E9bZqdVaKZWscsWcLsLRAPXjM1clLHLFvGKjcQD1Om2PnJ6mrXkQTb0qWW31NSXEcCBNvUqVJJCTmpFfxVdHvN1Ghc1H4NDTbAnTbNdSRA8JGTOi4Wk4qLyUlAPEyZYpOANC5qv1jsVNENoGOmTrVbXshJLfJX0U0ztY5bv94aFvEwATqOZmodt3mzdOCARMdtoOMmTpTS0shJHbFzp/TWWzRRA+LBa6ZGTmqRv4rubt1oXNRR3veOohvouG7daPDYUV6nbYpuoOOysqxxEee6249xEhA/NFNrNX8V3RKNizpq6VJpxAipd2/XkQDhQE7qmOJiadgwqV8/15EA4UAztY5ZulTq21caMsR1JEA40EytVfxXdE+bJq1YQeOi9lqyhLOTQDxNnUpO6ojiYla5gXiaMsUaF9XWuo4kmLxmszRRA+KDZmqt4r+ie+pU6cQJqbTUdSTB4zVRY8sUED9eM7XycteRBE99vc1+U3QD8TNlig1uafDYdl5jxxkzXEcChAfN1FrFf0U3zdTab9066fBhVrqBeCoqsvdsnWq7tWulI0fISUA8FRXZOIkt5m23ZYu0dy8TgUA80UytVfxXdHftKuXl8YNrD+97RkdOIH5ycqSxY8lJ7eE1UWP3DRA/XbvSdLa9aOwIxB/N1FrFf0W3ROOi9lqyRBo1SurVy3UkQLiQk9qnuNi6v/fo4ToSIFymTCEntcfixdbYsX9/15EA4TJtGruUW+DfonvFCpqEtNXSpawoAYng5aT6eteRBAtN1IDEmD5dWr6ccVJbcZ4bSIypU6VVq2im1gx/Ft3TptkPjWZqrVdfTxM1IFGmTZOOHaNxUVvU1NhEBUU3EH8zZ1rT2ZIS15EER329rcSRk4D485qprVrlOhLf8mfR7TUJYetU65WWWsOimTNdRwKEz7Rp1iRk0SLXkQTH6tU2eUoTNSD+Jk+W0tPJSW1RXi4dPUrRDSRCUZHlpMWLXUfiW/4sur1mapwNaL1Fi6woYIALxF/XrlJhIQPctliyREpLs+IAQHx17mwdg8lJrbd4sS3osCMQiL+sLGniRHJSM/xZdEtWPLLS3XqLFknjx1txACD+Zs7kYdIWxcU2UZGd7ToSIJxmzmRVqS2Ki21Bp3t315EA4UROapa/i+4VK+xcIFq2aBFby4FEmjnTtkwfOeI6kmCgiRqQWDNn2pbpQ4dcRxIMixfTRA1IJHJSs/xbdM+YYQX3ypWuI/G/I0ekNWsouoFEmjlTamhgB05rHDtmExQU3UDieM987+5pNM1rOkdOAhKHnNQs/xbdRUVSp05s52yNJUusGKDoBhKnoMCOb5CTWuZdr0aPCSBxxo6VevQgJ7XGypXWWZmVbiBxxo2TcnLISU3wb9HdubMV3pwNaNmbb1oxkJ/vOhIgvNLSrIjkYdKyJUukjAxpwgTXkQDhlZpqRSQ5qWXFxbaQM3Gi60iA8CInNcu/RbdE46LWWrTItkylpbmOBAg3clLrFBfbpGlGhutIgHDzBrixmOtI/G3xYstJmZmuIwHCzRsnkZPO4f+ie+1a6eBB15H4VyxGEzUgWWbOlHbssDc0jSZqQHLMnCnt3Stt2eI6En8jJwHJ4eWkzZtdR+I7/i66vbM3bDFv2vbt0q5dFN1AMni/Z6x2N+3AAamigrOTQDKQk1pWWWkdlclJQOKRk5rk76J77FipZ09+cM3xvjcU3UDiDRokDRlCTmrOm2/a+zlz3MYBREHfvtLIkeSk5ixZYu9Z6QYSz8tJLJiew99Fd0qKzUzyg2vaokXS0KHSwIGuIwGigXPdzVu40B66o0a5jgSIBnJS8954wzoq5+W5jgSIBnJSo/xddEvSrFm2csKB/MZxnhtIrpkzbeWkvt51JP70xhvS7Nk2aYq4mjdvngoKCjSdFTucbuZMadkyuxIL51q4UDrvPOusDCDxZswgJzXC/xlo9mxp/35p3TrXkfhPXZ20dClFN5BMM2dKR49Ka9a4jsR/6upsInD2bNeRhNLcuXNVWlqq4uJi16HAT2bMkE6ckEpKXEfiPw0NpyYCASTHzJnkpEb4v+ieOdNWTBYudB2J/6xeLR07ZrsBACTH1Kl2PR9bp861apVNSJx3nutIgOiYPFlKT+coXmPKyqRDhyi6gWTychLjpDP4v+jOyZEKCym6G7NokQ3+p0xxHQkQHV26SOPH8zBpzBtv2IN22jTXkQDRkZUlTZpETmrMwoW2rZzO5UDykJMa5f+iW7IZSorucy1aJE2cKGVnu44EiBaahDRu4UKb4c7Kch0JEC3kpMYtXGiD/27dXEcCRMusWTYRj5OCU3SvWWNbhHAKTdQAN2bNspxUWek6En/h7CTgxqxZdhf1wYOuI/GXhQvJSYALc+ZYP6633nIdiW8Ep+iWTt3/CnuwlpZynhtwYfZsu1GBnHTK7t3Sxo0McAEXvN87VpZO2bdPWruWnAS4cP759p6dyicFo+geM0bq04cf3Om874X3ogaQPOPGWU567TXXkfiHN9iniRqQfKNGSf37k5NO542TKLqB5Bs61N7ISScFo+hOSeFc99lef10aMMAetACSKyXFJrxef911JP7xxhvSkCH2kAWQXCkptp2TnHTKwoXSoEHS8OGuIwGiiZx0hmAU3ZIV3YsW2T2wsBfxnDn2oAWQfHPm2Pby2lrXkfgDZycBt+bMsWvDampcR+IPXk5inAS4cf750tKl0vHjriPxhWAV3UeO2N3UUVdTYw/WOXNcRwJE1/nn24NkxQrXkbhXUyMtWcLWcsClOXOkEyek5ctdR+JeTY1UXMxEIODSnDm2MFFc7DoSXwhO0T1tmt3/yhZzadkye7BynhtwZ8oUqXNnzitJNsivrmaAC7jkXdfHdk6bDD1xgpwEuDRhgl3XR06SFKSiOyvLBrl05rRBfna2VFTkOhIgujIypBkzeJhINhnauTM5CXCJnHTK669bTpo82XUkQHSlpdkOOBYnJAWp6JZsxpIfnD1MZs6UOnVyHQkQbXPmWE6KxVxH4tbChbYbKSPDdSRAtHmNi8hJ0vTp5CTAtTlz7PexocF1JM4Fq+i+8EJp82ZpyxbXkbgTi51qogbArfPPl/bskTZscB2JO7GYPVA5zw24N2eO5aSNG11H4o6Xk9haDrh3/vnSoUNSWZnrSJwLXtEtSQsWuI3DpXXrpL17KboBP/AKzShv59y4Udq5U7rgAteRAPByUpR3BW7dajmJohtwb+ZM22Ye5Zz0tmAV3b17SxMnSi+/7DoSd15/3a6/YFUJcK9nT2n8+Gg/TF55xXISRTfgXs+eNk565RXXkbjj5WPGSYB7XbpYv5coL068LVhFtyRdfHG0V7pfecUeqDk5riMBIJ06QxlVCxZIkyZJPXq4jgSAZOOkf/3LdRTuLFggFRRIffu6jgSAZFvMo7w48bZgFt0bN9r2oShasEC66CLXUQDwXHCBnVV66y3XkbhBTgL85ZJLpE2botv/ZsGCU8cRAbh3/vmWk3bscB2JU8EruqN8rnvbNnvRMsAF/OPii+19FI+9bN1qzS0Z4AL+ceGFduQjijlp1y5p7VrGSYCfRLl2O03wiu4on+v2XqwMcAH/GDxYGjcumts5vXOj5CTAP3r1siMfUcxJr75q7ym6Af/o18+OfESxdjtN8IpuyVaWoviDW7BAKiyU+vRxHQmA011ySTQHuOQkwJ+iPE4aO1YaONB1JABOF9Vx0mmCWXRfdFE0z3VzdhLwp0svlSoq7JqaKCEnAf50ySV2pnvTJteRJBc5CfCniy+W1q+Xtm93HYkzwSy6o3g2YNcuu6ObhwngP9657ijN4pKTAP+64AI71x2lnLRvn7RmDTkJ8CPv9zJKtdtZgll09+kjTZgQrR+ct02Ms5OA//TrZ9usozTA5Tw34F89e0qTJ0dri7mXkyi6Af/p21caPz5a46SzBLPolqJ3Xmn+fHuxDhjgOhIAjbn00mg9TBYssAZy5CTAn7wzlLGY60iS4+WXpZEjpaFDXUcCoDFRq93OEuyie8MGu0Yr7GIx6YUXpMsvdx0JgKZccon1mojK3bgvvXRqWz0A/7n4Yjs/uWGD60iSY/586bLLXEcBoClRqt0aEdyiO0rnutevt6ZxFN2Af110UXTOUG7bZo3jrrjCdSSRMm/ePBUUFGj69OmuQ0EQXHCBlJoajZWlnTul0lKKbsDPIn6uO7hFt3euOwoPkxdflNLTOTsJ+FmvXlJRUTSK7vnzbYLhkktcRxIpc+fOVWlpqYqLi12HgiDIyZGmTIlGTnrpJXt/6aVu4wDQNK92i0JOakRwi24pOmcDXnxRmjVL6tbNdSQAmnPJJTb4C/sZyhdftMF8796uIwHQnEsusXFS2HPS/Pk2mO/Xz3UkAJpz6aU2hgh7TmpE8IvuDRvCfedbfb0N4tlaDvjfJZeE/wxlLGYPTHIS4H+XXGJbr9etcx1J4sRinOcGguKKK+zIbJhzUhOCXXR7263DvNq9bJl06BADXCAILrxQSksL99apNWukPXvISUAQnH9++HPS+vXWZ4KiG/C/iy6SOnWSnn/edSRJF+yiu08fadIk6+wdVi+8IHXtKs2Y4ToSAC3p3l2aOvXU+cIwevFFKTNTmjPHdSQAWtKtmzRtWriL7vnzbWKB+7kB/+vaVZo9O9y1WxOCXXRL0tVXS//8p9TQ4DqSxHjxRdtG36mT60gAtIZ3N26Yc9L550tZWa4jAdAal19uv7dhzUnz50szZ9L3BgiKK66wcVJtretIkiocRfeePdLKla4jib9jx6TXX+daHiBIrroqvDmppsaO87C1HAiOK6+U9u+342phU1dnRTc5CQiOK6+UDh+WFi1yHUlSBb/onj3btio895zrSOLvtddskMvDBAiOOXMsJz37rOtI4m/RIunoUXISECTnnWerwP/8p+tI4m/xYungQemaa1xHAqC1pkyRevaM3Bbz4BfdGRnWfj6MRfeLL0oDB0r5+a4jAdBaGRlWlIax6H7xRXtQTp7sOhIArdWpk42Twti46LnnLCdNn+46EgCtlZZm46Qw5qRmBL/olmyL+cKFUmWl60ji64UX7EWZkuI6EgBtcc010htv2ApMmDzzjB13SUtzHQmAtrjyShsnVVW5jiS+nnvO/tvISUCwXHGF7VQ5dMh1JEkTjqL7qqvsXE+YOga/9Za0YgXbOIEguuYaqb4+XFundu+WliyRrrvOdSQA2sobJ4Wpi/nevZaTrr7adSQA2uqKK6y54/z5riNJmnAU3aNGSePGhWuLubc19aqr3MYBoO2GDpUKC8O1xfzZZ23XDWcngeAZPVoaMyZcOemFF6RYjHESEEQjRtjx2aefdh1J0oSj6JZspvO55ywBh8HTT9sZpf79XUcCoD2uucZyUliu6XnmGWnGDKlvX9eRAGiP66+XnnoqPOOk556TJk2y3jcAgueGG6zeCcs4qQXhKrq3bpUqKlxH0nG1tdZllG2cQHBde61tyQ7D1WG1tdbwhJwEBNf110s7doQjJzU02DiJnTdAcF1/vR2nLS52HUlShKfovugiKTMzHFvMvWYnDHCB4ArT1WGvvWY56dprXUcCoL0uuMCuDgvDds7iYhusU3QDwXXeeXb7wFNPuY4kKcJTdGdnW+Edhh/c00/btvIpU1xHAqC9wnR12NNPSwMGcFUYEGQZGXb+OQzjpCeekPr0sclNAMGUnm6T+WHISa0QnqJbkm68UVqwIPhXhz39tM3epobrxwNEzjXX2M6VoF8d9swz9mAkJwHBdv310qJFtkocZE88YedBuSoMCLbrr7fbmrZtcx1JwoVrBHXDDXYlRpC3mK9bJ5WW2n8LgGC79lo7e/jMM64jab9Nm6SyMo67AGHgbccO8g6cigqpvFy66SbXkQDoqKuussmzMBx7aUG4iu5hw6SiIunJJ11H0n7/+IfUuTNXYABhMGSIdfx+7DHXkbTfU09JnTrZVnkAwdavn+WkIG/n/Mc/pKwsu+cXQLD17Gn9Jv7v/1xHknDhKrolm/l85hnrthtEjz8uXXml1KWL60gAxMMtt9iq0tGjriNpn8cfly67TOre3XUkAOLhhhtsR+CJE64jaZ9//MMWJrKzXUcCIB6uv16aPz+446RWCl/RfeON0qFDdrY7aHbvlt54Q3rnO11HAiBebr5ZOn7crrcJmr17LZfefLPrSADEy803S0eO2DWAQbNnj42T2FoOhMcNN0jV1dKLL7qOJKHCV3RPniyNGCH9/e+uI2m7J5+UUlJsxgdAOIwZI02cGNycFIsxwAXCJD9fKigIZk76v/9jnASEzbhxlpeCfBSvFcJXdKek2HbOxx+X6utdR9M2TzwhXXihXYMBIDxuvtnOUFZXu46kbR57zM5a9evnOhIA8XTLLTapVlPjOpK2eeIJ6fzzGScBYfOudwUzJ7VB+IpuyR4me/ZIr7/uOpLWq6y08wzveIfrSADE2y23SFVV9jseFJWV0gsvWOyIi82bN+tDH/qQRo4cqaysLI0ePVpf+cpXVBPiQQZ86pZb7Cjev/7lOpLWO3LEtp8yTgLCx8tJL73kOpKECWfRPXOmNHhwsLZO/eMfNrvDABcIn8JCaezYYOWkp5+2hpT0mIib8vJyNTQ06Gc/+5nWrFmj73//+3r44Yf1xS9+0XVoiJqJE6XRo6W//c11JK337LO2W4jjLkD4TJxox/GCNE5qo5RYLNbaj231B/rCfffZ1sitW6XUAMwtXHutzeK+8orrSAAkwhe+IP3iF9YwMT3ddTQte+c7pR07pMWLXUcSat/+9rf105/+VBs3bmzyY6qrq1V92tGEqqoqDR06VJWVlepOV3m013/8h/TrX0u7dgUjJ73rXdLmzdKSJa4jAZAIQRsnnSmlpQ8IQDXaTrfeagPGhQtdR9KyfftsG+dtt7mOBECi3HyztH9/MCbWDh2yqxff8x7XkYReZWWlevXq1ezHPPTQQ8rJyTn5NnTo0CRFh1B717ts/BGE216qqqwvxu23u44EQKLcequNk4J0FK8Nwlt0z5kjDR0q/fGPriNp2WOPSQ0N9gAEEE7TpknDhkl//avrSFr22GO2tZyJwITasGGDfvzjH+ujH/1osx/3hS98QZWVlSfftm3blqQIEWrTptl2zj/8wXUkLfvHP2xrOTkJCK/Jk6XcXOnRR11HkhDhLbpTU22V5q9/9X8nvL/8Rbr0Uql/f9eRAEiUlBTpjjuCkZMefVS65BJp0CDXkQTCAw88oJSUlGbflpy1JXbnzp26+uqrdeutt+ruu+9u9vNnZmaqe/fuZ7wBHZaSIt15p53rPnbMdTTN+/OfrWs5uzyA8PLGSY89Jh0/7jqauAvvmW5JKimRJk2yLUnXXec6msbt2iUNGSL9/OfShz7kOhoAibRmjTR+vF1749dmQLt2WSPKX/5S+rd/cx1NIOzbt0/79u1r9mNGjBihzp07S7KC+5JLLtHMmTP1yCOPKLWNfUeqqqqUk5PDmW503IYNttr9xz/aYNeP9u2TBg6Uvv996d57XUcDIJHWrbN7u//6V9tuHhwtnukOd9Edi0kTJljh7ddt5t/9rvTFL1rTgJ49XUcDINGKik49UPzoBz+wBkt79kg9eriOJnR27NihSy65RFOnTtUf/vAHpaWltflzUHQjrubMkbp3t+7gfvTjH0uf/rS0c6fUt6/raAAk2vTpNvn/xBOuI2mLCDdSk2ybwnvfKz3+uN056zexmPTII7biRcENRMOdd0pPPunPnCTZ+c5rr6XgToCdO3fq4osv1tChQ/Wd73xHe/fu1e7du7V7927XoSHK3vc+6fnnbfLfj377W9utSMENRMMHPmDXlu7Z4zqSuAp30S1J73+/Nd/4059cR3Ku5cul1aulu+5yHQmAZLnjDmtS9uc/u47kXCtXSkuXkpMS5Pnnn9f69ev10ksvaciQIRo4cODJN8CZd7/brufx4zhp9WpyEhA1732vlJYm/e53riOJq3BvL/fceKNdH7Z0qetIzvSJT9gW023bgngfHYD2uuEGW1UqLnYdyZnuu+9UTurUyXU0aALbyxF3N99sd2AvW+Y6kjN99rPSb35jW8szMlxHAyBZ7rjD8lFZme1c9r+Iby/33HOP/eD89DA5flz6/e9tWxcFNxAtH/qQtGSJNXv0ixMnbGv5XXdRcANR84EP2O675ctdR3JKTY2tdL33vRTcQNTcfbdUUSG9/rrrSOImGkX3NdfYgfxf/MJ1JKf87W/SwYPShz/sOhIAyXbddXZF4K9+5TqSUx5/3HISHcuB6LnuOrtJZd4815Gc8sQT0ltvMU4Coujii6WRI/01TuqgaBTd6ek2kPzjH6WjR11HY372M+nyy+2qDgDR0qmTrSj/7nf+yUk//7l0wQXWWR1AtKSnSx/9qPToo9KBA66jMQ8/bDmpsNB1JACSLTXVdgX+9a9SVZXraOIiGkW3ZD+4I0ekv/zFdSTWGOT116WPfMR1JABc+ehHrYP5o4+6jsS2ub/8sjR3rutIALhy991SXZ2doXatvFz617+kj33MdSQAXLnrLmuGHZKGatFopOa59lprXrR0qdtD+ffcIz3zjDUt4ewkEF033SRt2mRdw13mpA9/2K7nICcFAo3UkDDvfa+0aJG0dq2tNLly333WTX37dikz010cANy67TbryVVebh3N/YtGamf49KetSchLL7mLYe9ea6B2770MboGo+/d/l1atkl55xV0M+/dbA7WPf5ycBETdvfdKGzZI//ynuxgOHpR+/Wtb5abgBqLtM5+R1q+XnnrKdSQdFq2i+7LLpKIi6VvfchfDz35ms8c0BgFw2WVSQYH03e+6i+GXv5QaGshJAKRZs6TJk6Wf/MRdDD//uVRby3EXANKMGdKcOW7HSXESraI7JUX63Oek55+37ZzJdvy4dQZ93/uk3r2T//UB+IuXk/7v/6zXQ7KdOCH98Ie2pbRv3+R/fQD+kpIifeITdgTOxZWGNTXSj34k3Xmn3fAAAJ/5jPTqq1JxsetIOiRaRbck3XqrNHy49O1vJ/9r//rXdv3FZz+b/K8NwJ/e8x5p6FDpm99M/tf+7W+tz8V//EfyvzYAf7rjDruq5+tfT/7X/sMfpJ077TggAEjSjTdKo0dL3/ue60g6JHpFd3q6JfM//1nasiV5X7emxgbV73kP14QBOCUjQ7r/fmsatHlz8r5uXZ0dtXnXu7gmDMApnTpJX/iC9Le/SaWlyfu6NTXS175miyNcEwbAk5Zmtdtf/2oN1QIqekW3ZHd29+wp/dd/Je9r/u531oXzi19M3tcEEAx33y316pX8nLRxow2uAeB0H/iANGSI9OCDyfuav/qVtHWr9MADyfuaAILhQx+ynPSVr7iOpN2iWXR37Sr953/aXZTJmMU9ftweIu9+tzVNAoDTZWdL/+//SY88kpycdOKE5aRbb7WmSQBwuowM6fOft12ByVhZOn7ctrO/972MkwCcKzNT+vKXbbXbRV+uOIjWPd2nq6mR8vNtC9OTTyb2a/33f1uRX1bG1nIAjauulvLy7IaFxx9P7Nf6wQ9sS/uaNVJubmK/FuKOe7qRFNXVNk7Kz5eefjqxX8vLSeXljJMANK621ibl8vKsAa2/cE93kzIybNvU//1fYu/I3btXeughu2+SBwmApmRm2vbyJ56QXnstcV9n717pq1+1YzYU3ACakplp1/Q884y9Jcr+/bbKfdddjJMANK1TJ8sVTz1lN1EFTHRXuiW7m3bGDCkWkxYtsiZr8fbBD0r/+IdUUcGVPACa19AgzZ4tHT4sLV9uk4Px9uEPS//7v9LateSkgGKlG0kTi0mXXy7t2GFXiCUqJ/31rzZO4powAM2JxaTLLpO2bZNWrZI6d3YdkYeV7malpkr/8z/SihWJuUJswQI7o/nNbzK4BdCy1FTp5z+3gvhb34r/53/jDemXv7SZYnISgJakpNjW73Xr7H28vfmm9Itf2M5DCm4ALUlJkX7yE7vtxcX1zx0Q7ZVuz3/8hz1Mli2L3zUVR45IU6fawPaVV2wwDQCt8cUv2rbOkpL4bQE/dsyapvXsadvXE7GzB0nBSjeS7v77pR//2IrkeDVfPH5cmjbNVqoWL7ZrgQCgNf7jP6Qf/lBaskQaP951NFIrVropuiXr5Dt5stStm7RwYXwGox/4gPT3v0tLl3JuEkDbHD8uTZxoBfIrr8Rn+9S//7utcq9YQU4KOIpuJF11tTRrluWmpUulLl06/jnnzpV+/Wv7fHQsB9AWx49L06fb/1682G6BcYvt5a3SubNdH7Zsmc3mdtRvf2t34P7sZwxuAbRdVpZd1VNSIt17r51h6ohHHrHtWN/5DjkJQNtlZkp/+pOdo/zkJzv++R5/3I73ff/7FNwA2i4rS/rLX6QNG6RPf9p1NK1C0e2ZNUv60Y9sq8IvftH+z7N4sfTxj1tn4Pe+N37xAYiWqVOlhx+WfvUrO+fdXgsXSh/5iHTPPZabAKA98vJsjPTLX9pW8/ZavFi6807pXe+y3AQA7VFYaDnpZz9LTM+JOONQ3+k+/nG7t/bjH5f69JHe+c62/fvSUunaa+2e3Y48kABAsit0liyxbZi9e9sgtS1WrrQ8NnOmrXSntLj7CT42b948zZs3T/X19a5DQVR96EN2l/Z999n1PR/9aNv+fXm5dP310qRJtiOQnASgIz78YVvt/tSnrHa7807XETWJM91nq62V3vc+u1Ln5z+3B0xrLFwo3XijNGiQdS3v2TOxcQKIhro66f3vtyt1fvlLK8RbY/58K7jHjpWee45u5SHCmW44FYvZFvMf/ch247R2tXr+fJs49MZJffokNEwAERGLSXffbcd7f/hDW6hojfr6eDZw5Ex3m3XqJP3xj/YQuftuG+Du29f0x9fX2znJSy+1bQ4U3ADiKT3dVoQ++EF7+8hHpEOHmv74EyfsmsJrrrE7v19+mYIbQPx414jde6+tdP//9u6gxaYwjAP4/4yGmi7WNkoW2EgWs7NWVqJky5LmWiirKWY3K99Adj6Cjez4BixJaiwukhllpHEsnqTUiNzXucbvt7rdTt2nbr3n/Z/nPe976VKyvr799Z8+1WkMp08ni4vJ48cCNzA9XVeN0qWlGpcuX07evt3++q2temh4/HiysfH3ytTp3kbf17uUN27Un3nlSnWyT5yoSe1kkty7V9e8fJlcv15n3+7ZM3TlwE70bUy6dq02EBmPk/Pnk4MHk9Golm0+fJjcvl1j0nhc4Xt+fujKmTKdbmZC39cDwatXa+4zHifnzn0/vufZs+TBg2R1tTZgG4+rSeG4QqCVu3drJc6uXdWkOHu2djnvumRtLbl/v163e/KkHhquribTuY86MuyPTSbJ8nItN/+xu7SwkFy8WDeckycHKQ/4z7x6ldy6VTsJf/hQ383NJV++1GT2zJkK20ePDlom7QjdzJS1tZq43rlTx/h0XbJ7d3W4uy65cCG5eTM5dmzoSoH/wWSSrKzUa3lv3tQcaX6+xqS5uVoJuLxcm2hPj9A9NZ8/15KoFy+qyzQaJadOTevpCMDv+fix9pJ4/Tp59y45fLiWk49GQ1dGY0I3M2lzM3n0KHn+vD4fOVKnMFhKDgxha6vmSU+fVuA+dKi63gcOtPg1oRsAdhKhGwBmio3UAAAAYChCNwAAADQidAMAAEAjQjcAAAA0InQDAABAI0I3AAAANCJ0AwAAQCNCNwAAADQidAMAAEAjQjcAAAA00vV9P3QNAMAv6rpuX5L3Sfb3fb8+dD0AwM8J3QDwD+m6rkuyN8lG7yYOADNP6AYAAIBGvNMNAAAAjQjdAAAA0IjQDQAAAI0I3QAAANCI0A0AAACNCN0AAADQiNANAAAAjXwF0En4c//keLgAAAAASUVORK5CYII=",
|
||
"text/plain": [
|
||
"Graphics object consisting of 1 graphics primitive"
|
||
]
|
||
},
|
||
"execution_count": 1,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"t=var('t')\n",
|
||
"x=function('x')(t)\n",
|
||
"eq7=diff(x,t,2)+x==0\n",
|
||
"f=desolve(eq7,x,ics=[pi/2,1,-2])\n",
|
||
"plot(f,t,-10,10,color='red',legend_label=f'x(t)={f}',figsize=10)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"id": "8f27c996",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": []
|
||
}
|
||
],
|
||
"metadata": {
|
||
"kernelspec": {
|
||
"display_name": "SageMath 9.5",
|
||
"language": "sage",
|
||
"name": "sagemath"
|
||
},
|
||
"language_info": {
|
||
"codemirror_mode": {
|
||
"name": "ipython",
|
||
"version": 3
|
||
},
|
||
"file_extension": ".py",
|
||
"mimetype": "text/x-python",
|
||
"name": "python",
|
||
"nbconvert_exporter": "python",
|
||
"pygments_lexer": "ipython3",
|
||
"version": "3.10.6"
|
||
}
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 5
|
||
}
|