{ "cells": [ { "cell_type": "code", "execution_count": 2, "id": "7c74465e-873c-4122-914c-cf8197865e1f", "metadata": { "tags": [] }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "id": "92a23a5e-2f1c-4a5a-bbb8-09072804b1de", "metadata": {}, "source": [ "# Tidal Forces" ] }, { "cell_type": "markdown", "id": "eed6ae77-9c0a-4ac4-8034-fc11b169b0e7", "metadata": {}, "source": [ "In this lecture, we are going to discuss\n", "\n", "* Tidal forces (for elements in a line joining the centres of 2 bodies)\n", "* Tidal forces (for elements across the surface)\n", "* Tidal friction" ] }, { "cell_type": "markdown", "id": "d2ce95f7-0020-403e-88fb-9cda385ebf6c", "metadata": { "tags": [] }, "source": [ "## Mass Elements in a Line" ] }, { "cell_type": "markdown", "id": "f5d03f10-a425-40ef-9739-23855eda0b0b", "metadata": {}, "source": [ "Consider Newton's 3rd law of Graviation:\n", "$$\n", " F = G \\frac{M_1 M_2}{r^2}\n", "$$\n", "When initially deriving this equation, both $M_1$ and $M_2$ were treated as point masses, as they were both assumed to be spherically symmetric. The first question we want to ask is what happens if we do not treat them as point masses?\n", "\n", "The forces across the body will differ, because of the $1/R^2$ dependance on the force. Consider two mass elements, $m_1$ and $m_2$, within the Earth. Because of Newton's Shell theorem, both elements see would see the Moon as a point mass, but they will both feel different forces, because of their different distances to the Moon. This differentical force is known as the tidal force.\n", "\n", "Let us set up the problem as follows: $m_1$ lies a distance $R$ from the centre of mass of a nearby body whose mass is $M$. $m_2$ is a second point mass, which lies along the line joining $m_1$ and $M$, but is slightly closer to $M$ by a distance $dr$.\n", "\n", "![Aberration](Figures/Figure_1.png)\n", "\n", "The force exerted on $m_1$ is:\n", "$$\n", " F_{m1} = G \\frac{m_1 M}{r^2}\n", "$$\n", "\n", "The differential force between $m_1$ and $m_2$, $dF_m$, can be expressed as\n", "\n", "$$\n", " dF_m = \\left(\\frac{dF_m}{dr}\\right)dr=-2G \\frac{m M}{r^3}dr\n", "$$\n", "\n", "This is the \"differentical force\". It has a $1/r^3$ dependence, which is a signifcantly stronger dependance than $1/r^2$ dependance of the gravitational force. To get a feel for where this may be important, lets look at what the differential force on opposite sides of the Earth would be when we consider (1) the moon and (2) the Sun.\n", "$$\n", " \\frac{\\Delta F_m}{\\Delta F_{\\odot}} = \\frac{M_{\\oplus} M_{m}}{d_{m}^3} R_{\\oplus} \\frac{d_{\\odot}^3}{M_{\\oplus} M_{\\odot} R_{\\oplus}} = \\frac{M_{m}}{d_{m}^3} \\frac{d_{\\odot}^3}{M_{\\odot}} = 2.14\n", "$$\n", "So, the differential force on the Earth due to the moon is 2 times stronger than the force due to the Sun, which naturally explains why the Earth's tides are dominated by the lunar cycle." ] }, { "cell_type": "markdown", "id": "c3baa720-166a-4db3-895d-df2fdec49c26", "metadata": {}, "source": [ "## Mass Elements across the sphere" ] }, { "cell_type": "markdown", "id": "b3c911dd-5884-4f1b-9eea-ba8f37ba12a4", "metadata": {}, "source": [ "Ok, let's now consider the difference in forces between points located at the centre of a body, and at its surface. Consider the following setup\n", "\n", "![Aberration](Figures/Figure_2.png)\n", "\n", "For a test mass, $m$, located at the centre of the object on the left, then the graviational force felt due to the body on the right ($M$), is the normal gravitational force. Breaking it into its x and y components, we have\n", "\n", "$$\n", " F_C = F_{C,x} = G \\frac{Mm}{r^2},\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\; F_{C,y} = 0\n", "$$\n", "\n", "Now consider a test mass, $m$, located at point $P$ on the surface of the sphere. This point lies a distance $s$ from the large body on the right. In this case, the component forces are\n", "\n", "$$\n", "F_{P,x} = G \\frac{Mm}{s^2}\\cos(\\phi),\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\; F_{P,y} = -G \\frac{Mm}{s^2}\\sin(\\phi)\n", "\\label{eq:vector_ray} \\tag{1}\n", "$$\n", "\n", "The differential force is then given by\n", "\n", "$$\n", "\\Delta {\\bf F} = {\\bf F_P}- {\\bf F_C}=GMm\\left(\\frac{\\cos(\\phi)}{s^2}-\\frac{1}{r^2}\\right) {\\bf \\hat{i}} - G\\frac{Mm}{s^2}\\sin(\\phi) {\\bf \\hat{j}}\n", "$$\n", "\n", "In essence, our work is now done, but there are a lot of variables in that last equation. Let's try and simplify some things. Recall the law of cosines:\n", "\n", "$$\n", "s^2 = R^2+r^2-2Rr\\cos(\\theta) = r^2\\left(\\frac{R^2}{r^2}+1-2\\frac{R}{r}\\cos(\\theta)\\right)\n", "$$\n", "\n", "Now, in most cases, $r>>R$. As such, $\\frac{R^2}{r^2}<<1$, so can be neglected, giving\n", "\n", "$$\n", "s^2 \\approx r^2\\left(1-2\\frac{R}{r}\\cos(\\theta)\\right)\n", "$$\n", "\n", "Substituting back in above, we then have \n", "\n", "$$\n", "\\Delta {\\bf F} = GMm\\left(\\frac{\\cos(\\phi)}{r^2\\left(1-2\\frac{R}{r}\\cos(\\theta)\\right)}-\\frac{1}{r^2}\\right) {\\bf \\hat{i}} - G\\frac{Mm}{r^2\\left(1-2\\frac{R}{r}\\cos(\\theta)\\right)}\\sin(\\phi) {\\bf \\hat{j}}\n", "$$\n", "\n", "$$\n", "\\Delta {\\bf F} = \\frac{GMm}{r^2}\\left(\\frac{\\cos(\\phi)}{\\left(1-2\\frac{R}{r}\\cos(\\theta)\\right)}-1\\right) {\\bf \\hat{i}} - \\frac{GMm}{r^2}\\frac{1}{\\left(1-2\\frac{R}{r}\\cos(\\theta)\\right)}\\sin(\\phi) {\\bf \\hat{j}}\n", "$$\n", "\n", "Noting that $r>>R$ and that $(1+x)^{-1}\\approx 1-x$, we can use the substitution $\\frac{1}{\\left(1-2\\frac{R}{r}\\cos(\\theta)\\right)} \\approx 1+2\\frac{R}{r}\\cos(\\theta)$, we get the expression:\n", "\n", "$$\n", "\\Delta {\\bf F} = \\frac{GMm}{r^2}\\left[\\cos(\\phi)\\left(1+2\\frac{R}{r}\\cos(\\theta)\\right)-1\\right] {\\bf \\hat{i}} - \\frac{GMm}{r^2}\\left(1+2\\frac{R}{r}\\cos(\\theta)\\right)\\sin(\\phi) {\\bf \\hat{j}}\n", "$$\n", "\n", "Finally, using the small angle approxmation gives $\\cos (\\phi) \\approx1$ and $\\sin (\\phi) \\approx \\frac{R \\sin(\\theta)}{r}$ we get\n", "\n", "$$\n", "\\Delta {\\bf F} = \\frac{GMm}{r^2}2\\frac{R}{r}\\cos(\\theta) {\\bf \\hat{i}} - \\frac{GMm}{r^2}\\left(1+2\\frac{R\\cos(\\theta)}{r}\\right)\\frac{R \\sin(\\theta)}{r} {\\bf \\hat{j}}\n", "$$\n", "\n", "Excluding terms of order $\\frac{R^2}{r^2}<<1$ again, we get \n", "\n", "$$\n", "\\Delta {\\bf F} = \\frac{GMmR}{r^3} 2\\cos(\\theta) {\\bf \\hat{i}} - \\frac{GMmR}{r^3} \\sin(\\theta) {\\bf \\hat{j}}\n", "$$\n", "\n", "$$\n", "\\Delta {\\bf F} = \\frac{GMmR}{r^3} (2\\cos(\\theta) {\\bf \\hat{i}} - \\sin(\\theta) {\\bf \\hat{j}})\n", "\\label{eq:df} \\tag{2}\n", "$$" ] }, { "cell_type": "code", "execution_count": 3, 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RWdnroi0sJ2jVfbY1UJrVhwoh2kopT1ayzr+VbSil1AshLkJpVVDhZNBUAVxvevSCUjl5V7IrR3/2Mn9K24Z4dOTfqtKMwEIIdyjfXQBYaUOZyiTA8jf7TYl31Kg1rMdrr476hKGqIdPKu1XaN8RjPCzJetdWs95aKOPJay0Dyt8wvKYViahBGWR61gE4UM3xtOxCzg9KnV3ZOUpVx/oYKMcPAFgohKjqohRQWlLCtH5l9Wylda9JKqzrLofS8NylzGfStiEe46HcjABqrr+vA9BDCOFRRXCnqv9pa1guSu2pvx35fatMbervy6V9QzyWJTLUA9hY2QpSSqMpoeKNlS2vgzcBXG16fbeUco8N27D+dgEMIlB56arXzQCcK7+ClPIQLAfzsihsZRdaatUeLE0Xol/COnqsh9L/quwueBCUCy2/SnaxHMB7UCrrCbBucVDWOuGrKqKrdSKEiIBSqanv0hcBuASlmwWgHOh0qLzsdRGhel1dhDi53DaV/b9yq9leb3q2ytQshPAF8BOUvpxlSqAc4Msq72am7Rz92e3lyL9VVd/nUFj+RqdtL5pVNN3WFgaVBdiqog7qFNuxnT1q8/fVUllLicoCXkRUd2UXvunVruV4ZcdTHep+PK3qWK8+ZlcYOcrO97C77nUEjc9d7GVv/eIO5ftXWaC9qv9ppOp1bepvR3zfKlOf9fclKWV17+HQ+lsI8SosLQ9mSyk/sXFT1t8ugN0ZqLwDqte9HLjf6qL0gNIscKppvWegJE7xklI2k1JGSikjASwzrVshzGtqeVDWjO0/ZfOFEN0B9DRNOqsrw3wolXA6lIh+lJTSR0oZrip72TCZNt1ibkAegxJAKITSX781lL6ToarPXnaXpTF99qq+z7KW+1M3bfSRUgobHuvt2L/6JD6klmVsbLS6wCFq9IQytG870+Txen77suPpeRuPpUIqY9VXUE2zd/Uxu4uN77HIgZ/REZrkuUs1/9O61t91/r5VoVHW30KIlwHMMU0+KKV8w47NWX+7AAYRqLx1sBxIr6nH9y3rf/6xlPJJKeWxSloNRJbfqJyyIMFwU1NDwNIKYZepf6FDmcZQnmCavEdK+Wn5vvamvm+23qmwlzqiXl1zQ/UyW5vQ2aLs//aMlPINKeUZKWX5irim/1t9qY+/lboFRuvqVixH/Z2xZztbqftROqt/svpvFVPlWtUvq09lfwdb+5gSke1Gw3Jxtb6e37vseBomhHDWHXRnH7OdygXOXexlb/2th+1N/8vU9n/q7O9bfdbfYaYuLlVxSP0thHgFwP9Mkw9JKV+zcxesv10AgwhkRUp5DpY7+jcJIdrW01u3ND1XmsjGdFejfw37WAulqZUOwA2mLhJlyeo+r3KrqqmDGFVF4dX9/6tKwjMYVTe5suU9qnMSloryimrWG2F6Tq+ij39t1fR/awOgvQPfry6c/reSUuoBbDFNjrVj062wdNuxZzubSCkzYTnRaVfdunWwA5bv8+XVrDfcSe9vMyFEACwnxwe1LAtRY2O6CHnUNJkNJblgfSrr8+4GYIwz3sB0J7msWb3Dj9k2qOu5Q13PXeqbun6xpf7eXU2yy0pJKc+gdv9TZ3/fjsLSrcVZ9fc207M7lOGuKzCdUw+r6xuZujA8aJp8SEr5ip3bs/52EQwiUGUeB5APpQ/cD0KI+sh+mm167lnF8v8DEFDdDkwtF74yTd4E5WKlbPjHr2tRphzV6+Bq1im7816h7KZEe8/X8T2qZLrrv8Q0OVMIUeGuv+n/N9M0+Y2971GDmv5vLzr4/WqtHv9WC03PSUKIJBvLlg/Ld/RhIUSr6tYXQtTmbsQG03O/WmxbIyllFoDfTJMPmkacsCKEGAHnjdJhjz5Q6j89qkiyRUT2E0L4AFgEZbg9AJhnOjbUGynlUVhaPzwvhAiqbv1aHk8BJVs9ANwuhOhd3Yp1eI+q1OncAXU/d6lXpu/Qr6bJ/5nyMVkRQvQEMNE0Wdf6e3pN/1NV2Zz6fTONBLXDNOms+nsPLBfkj5kCBuXdhjom2DQFENRdGOwKIJiw/nYRDCJQBabEidOg3BntAWCPEOJxIUScUKWdFUIECiFGA3jbAW/7i+n5DiHEjLLmVEKISCHEfCjZ8m3p+1TWpaE7gHmm179JKW3NYm9mqrTKotK3mirV8uvkwXIQe10IMbzs4CuE6AZgNZQDXn75bW19Dxu8ACALSvOu39XDbAohBkFJnBQM5S68oy/qy/5vjwshJpSVXwjRVgjxNZQsyZkOfs+6qI+/1RcA/oJyd+g7IcT/hBDqoaqihRCzhRDlh3J8FEr/0zAAfwshbjJF3Mu2CxdCTBRCfI/anSCtNz3X1KKnLv4PStCuM4BVQohOgHJCKoS4DsC3UP7+tSaECBJChJU9YEk45qWeX8OJXNnfYIeseqhOIrKBEEInhOgmhHgAyljzZQmSvwDwskbF+i+APAAdAfwjhBinDmwKIWJMx9g/UPvhp18DsBfK3fp1Qoh7hBDmYbKFEMFCiDFCiM9RRcb72qrruUNdz1008jiU7oLtAfxqynlV9v1LglJmdyg5OD6s5Xu8CuXOvxeAP4QQdwghAssWCiFihRBPCCEeLLeds79v603Pzqy/HzM9Xw7gayFEC0AZgloIcSeAd1CH+rtcDoQHatGFoQzrb1chpeSDj0ofAAYAOAQlWl320EPJ3Jtdbn4OlAO8d7l9PGVavr6G9wqGEgUt258BysWn0TT9AZS7GxLAohr2tb1c2a6vYf2y9YZVsuxx1fIiAGcAnAKwWLVOApTKQ71eWZS/FEqriFOm6Vtq+R7Dytap4jMMhXJwL9tPXrkyZQIYUsl2bVTrtKnmb1Rp+aH0G0xT7aO0XDnmQqn8JICnbN2vjd/Psv1W+92q77+Vad0wKHf+y9Y3mvabq5r3QyXbdQFwWLWOAUrwTF0+CWBNLf5eEVACgxJAhyrWUX/GbNP/trrHm5XsYwYsv1tp+lsXmV4fhJKAUwI4Ze9nKPd/r+lR5fcCwGbTOvfVpgx88NHUHrDU5bLcMSDTdJxS//YuAphZzb6Gla1bxfIa6wXVew2rZp1BUEaYKn/+UlCuvAvsKV+5daMB/F3Jsb78OdLRWn6GsuPdU5Usq9O5A+p+7lJj+av5XGX7XWTndlOgjFCgrqcKVdNnoCS6tOs7V27ddlCCYeXr4XzVvDcc9X2z8XP3Mm1bACCwpt8VlBshNdXfD1ayj+fKlbUsz5OEck7zAmp33tWq3N/T7rKp9sX620UebIlAVZJS/gOgK5TmYYugBBRyoAy1aIRyQfAVgJuhZPV9TkpZVMv3yoLSzPkNKJWLAcoBeD2AqVLKO+3YnTr/QQ6AFbUpk8kLAO6D0l+sFEpTrtZQJQuUUm6H0sTsWygVhg7KxeK3AAZKKWsaFaLG96iJlPJPKBegr0H5v+ig3Ak/CCWy3kVK6dA7Iab3PQ3lbsVCWLI4F0EZ9nGUlHJeVdtqpT7+VlLKS1Aq9GkAfoZyUu0H5QRgO5RWDo9Wst1BKK1/ZkLpGnAJQKCpfMcALIVykX5dLcp0AcD3pklbxnkOhDJcVXWPoEre5yMoJ1MroZyAeEEZLmselN9Jpr1ldyQhRDsAl0E58axNrhSipq7s9x8B5c5vGoB/ALwPYBKAGCllbe8EO4yUchOUO8MPQrkAyoJyw8IA5Xj/JZRj4f11eI9UKLkDpgL4EcpFpC8ATyjnMitN+0+s7XtUo07nDg44d6l3UsolAOKgtDQ4DqV+0QPYBeBJAN1M9Whd3uMElO44s6Ccg2ZC6U6bBSVg9H9QRrYov53Tvm9Syl1Q8i35wJIQszohqLn+9q/kfR4HcDWUHGM5UP6+BwE8AiUXRUn5bWykK/fa7rIBrL9djTBFdYiIqJETQiQC+BPKyVcHqUEFIIS4BcCnAE5LKdto8P5PAHgawKdSytvq+/2JiIjsJYT4D4DPAKyTUmqSoFgI8RSUYM2fUsphGrw/628XwpYIRERNhJRyA5QWDrEAJmtcnHpnGn7rv1Cawz6tcXGIiIhs9RWAAwAuF0I4JcGiK2P97XoYRCAialoehNId6YkqMjA3ZvdAyVfxlqkrDhERkcuTUhqgJBkHlBwlTQ3rbxdTm0zwRETUQEkp9wohboeSRDEKlgzfTUE+lJOvN7QtBhERkX2klKuEELMBBAkh/GXTGp2A9beLYRCBiKiJkVIu0roMWpBSvqN1GYiIiGpLSvmG1mXQAutv18PEikRERERERERkk6bWH5aIiIiIiIiIaolBBCIiIiIiIiKyCYMIRERERERERGQTBhGIiIiIiIiIyCYMIhARERERERGRTTjEYx0IIdIA+AI4q3VZiIiITFoCKJBSRmpdkMaAdT0REbkgTet6DvFYB0KIHC8vr4DY2Fiti0JERAQAOH78OIqLi3OllIFal6UxYF1PRESuRuu6ni0R6uZsbGxs1/3792tdDiIiIgBAXFwcDhw4wLvmjsO6noiIXIrWdT1zIhARERERERGRTRhEICIiIiIiIiKbMIhARERERERERDZhEIGIiIiIiIiIbMIgAhERERERERHZhEEEIiIiIiIiIrKJSwURhBAJQohHhBDLhRDJQggphJB12F+IEOJNIcRpIUSx6fkNIUSwA4tNRERENmJdT0RE1LC5a12Acv4PwDhH7EgIEQbgbwDtAZwA8AOAOAD3ARgjhLhMSpnhiPciIiIim7GuJyIiasBcqiUClBOBZwFcAyAKQHEd9vUGlJOK5QA6SSmnSCm7AXgbQEcAr9etqERERFQLrOuJiIgaMJcKIkgpX5JSPiGlXCmlTKvtfoQQUQCmAigBMEtKqVct/h+AiwCmCSEi6lZiIqoPUkrce++9+Omnn2AwGLQuDhHVAet6IiKihs2lgggONBrKZ9sopTyvXiClLAawEoAbgCQNykZEdhJCICIiAmPHjkVsbCzmzZuHCxcuaF0sItIW63oiIiINNNYgQk/T844qlpfN71EPZSGiKhSVGnAoLQe/7DuHV1Zsxez5X+D9Jauwect2pKWlWbU6uPnmmyGEwOnTp/Hoo4+iRYsWuPHGG/HXX39BylrnZCOihot1PVEDoDcYcTo9H+sPX8AXf5/Ct9vOYuupDFzMLWb9TdRAuVpiRUdpZXpOrmJ52fzWtuxMCLG/ikWx9hSKqCkqKjXgbEYBTl7Kx6n0fJy8VIBTptfnsovKrd0MOA9gZxoMeQehz0qFR1EWAkQRwryMCG4Th6zko5ClxSgtLcXXX3+Nr7/+Gt27d8esWbNw4403IiAgQIuPSUT1j3U9kYswGCVSswpxKj0fpy6Z6nrT67OZBSg1VB4s8PdyR5swX7QJ9UPbMD+0CfVDmzDldYivB4QQ9fxJiMgWjTWI4G96Lqhieb7pmVcbRA5QojfiTIYlOKCcOCiBg9TsQtTmRoObfwjc/EMAKD/YfACB112JQAD63HToM1NRmpkKfWYqjmWm4t7/exEPzX0MN91wPe666y5069bNkR+RiFwP63qiemQ0SpzLKcLpS/k4WS5YcCa9ACUGo937zCvWY19KDval5FRYFujtjjZWgQVLsCHY19MRH4mIaqmxBhEcSkoZV9l8012LrvVcHCKn+vHHH5Gbm4uJEyfC29vbPL/UYERyZqHppKGsVYHynJJZCGMtWyR6uAm0auYLY146zlzIgt6nGYR79ScH7gGhcA8IhXer7hWWrci5iO+e/xFh3iuQ2Lszrh7aHx0ig9CymS+8PdxqV8gqpKamIiUlBX379nXofomo/rGuJ1ISGZ/PKTbX7+o6/3R6AYr19gcKyojCLBReOA3h4QXfiDYwuHtXu35OkR57krOxJzm7wrJgX49yrRd8lddhfgj09qh1GYnINo01iJBnevatYrmf6Tm3HspC1GDoDUY0a9UJUybcgAc/XIm4AZcjpFVHXCwEzmYWwlDLSIG7TqBlM1+0CfU1N1Msq/yjg33gprM0VzQaJVKzCrDrWAr2nj6PY2nZOJtZhJScUuTBu+YAQ2A43APDkQdgdSqw+pvdAAAhgOggn0qbTbZq5gtPd/tTxISHh6NXr15o1aoVZs2aheuvvx6+vlUddojIwVjXE9WClBIX84pxytS98KQqWHA6vQCFpbUfBSky0NtyQR/qh5bB3ph27UhkJR+D1JdYravz9sfVU2/DLf/9n1VXx5OX8pFbpK/iHRRZBaXYVZCFXWezKiwL9fNE67LzDVX3iDZhfvD3aqyXPkT1q7H+ks6YnltUsbxs/ul6KAuRy8nML8Ga7YdwsUjgUpHA6YxCq36Lza97BgBwDACSq2opbE0ngBYhZZW28lxWgceE+MDDzbaLdJ1OoEUzP7To1xFX9+tonj9+/Hj8sOJHuAWEwiMkGu4h0fBoFgP3kGj4hLeCLiAcUld1SwMpgZSsQqRkFWLTsfQKZY8J8bEKLrQN84NPcTrax4QjNDS00n6ZHh4euOmmm/D666/j9ttvx5w5c3DLLbfgzjvvRKdOnWz6vERUa6zriVQKCgrg7e0NnU6pb4tKDdifmo0TF627GZ5Oz0d+Se0DBeEBXqaLc+sL9dahvvD1rHhpMbJ/dyw5daDCfGNRHm4YNRDje1v/hKWUyMgvscqjdDJdKfepSwXIK64+wJCeX4L0/BLsOJNVYVmYv5e5W0RZcKF9hD86RPib6/m8vDz4+/tX2JaILBprEGG36Tm+iuVl8/fUQ1mIXMaR87n4aMMJrNiVUmWSo+pIaYS/KEGXFqHo0iIMrUMtzQdbhtTubr4tvv/+e/zwww8AgNZhAejduz3i4+PRu3dv9O7dG5GRkdAbjDiXXWTd1eJSPk6lF+BsRgH01bSiMErgbEYhzmYUYuPRS6oPbETB0a9QsONHhMpsREVFITo62vwcHR2NFi0sJz9ZWVl444038MYbb+CKK67AXXfdhWuuuQYeHmxaSeQErOuJVNavX4+DBw/ilpn3YOGGo/hqSzKyi2oXLAjz97S60G4darnwtvdu/tVXX40lS5ZUmO/u7o5Ro0ZVmC+EQKi/F0L9vZDQupnVMiklLuWVlKvnLcGGmlpRXMorxqW8Ymw9lWk1PzbEE/eO6opRXSMwefJkrFy5Eu7ujfUyiajuGuuv4xcARgBDhBARUkrzgPJCCC8AYwEYAKzWqHxE9UZKib+Pp+OjjSew/vBFm7bR51xAacY5VfLCFOU5Kw0w6HFQCCQlJaH/nXdi2MAxcHNzbK6B8kpKSrB27Vr06tULISEhla7j7qZDy2a+aNnMF4kIt1pWajAiJbPQ3GRTuauhnHAkZxZUnc9B6ODb8TL4drwMRSkHsWfLcvy7ZQUga+4T+scff+CPP/5AdHQ07rjjDtxxxx2IiYmx96MTUdVY1xOp/LFlLz7/NxkfZvwOWxoahPh6WLUkKHvdOszXoXkFxowZA51OB6PRuu4cMmQIgoOD7dqXEALhAV4ID/BC3zYVAwwXcovNwQVLna8kf6wun8PxzBLct3gX/EUJzqR7Y/ue/egf37PK9YmaOuHK47MKIYoAeEkpKx3fRQhxD4B7AHwvpZxbbtmXAG4E8B2A66WUetP8NwHcC+AzKeUtdSzf/q5du3bdv7+qUaGItFNqMGL13nP4aMMJ7E+tmPXYUJiD0ounleBAhmWkA33WuQr9FqvTsmVLzJgxA7fffjuioqIc+RHqRYneiLOZBVb9QU+l5+PQuWxczCutsH5pZipytv6A/L1/QOqLbX4fNzc3jBs3DrNmzcLw4cM5bBU5TVxcHA4cOHCgqkSBroZ1PVHdbD+dgY82nMCv+9KUBEAqxtJihLoVITG+i6XLnilYEORbf63kEhMTsXHjRqt5r7/+OmbPnl0v7280SqTlFJm7dZxKz8eJi3n4/d89QGBkhfW9dEbcMrg9bh3UFpFB1SeAJNKC1nW9S7VEEEJcBeD/VLM8TfP/Uc17Vkq5yvQ6DEAnAJVdudwPYACAiQAOCSG2AYgD0A3AUQAPOLTwRC4ir1iPxVvO4NNNp5CSVVhheZeoQMxIbItRXSKQk5WBc+fOIS0tDWlpaebXS5YswYULFyrZe0Vnz57FZ599hsOHD+Oxxx5D586dHf2RnMrTXYfYcH/Ehlv3fzQaJdYcOIf31x7BrtR883yPkGiEjpyFiOG3wuP0P7jw11Jkpp0pv9sKDAYDli9fjuXLl6Nz58547bXXkJSU5PDPQ+TqWNcT1Z3BKLHmwHl8tOG4pe+/KoBgyM9E7vafYDzyJ7Yd2I2IiAhtCmoyduzYCkGEsWPH1tv763QC0cE+iA72wcBYy/xvPI/h5vvuQWDfa+HXdSiEmxJYKTbq8OGGE1j410lc0ysadwxphy5RgfVWXiJX51JBBADhAPpXMr9/uXVqJKW8JIToB+ApANcCGA/gPIC3ADwppcyqS0GJXE1adhE+3XwSX/97ptKsxkM6hGFGYjsMbh9mvgvuGxmJyEjrCPzOnTvx7rvvVvk+7du3R58+fZCQkICEhAT07t3b7uaIDYFOJzCqWzRGdYvG7rNZWLDxBFbvPWfu+mBw94Eh9nIEth0CsWcNcrb+AH1GSoX9uLm5oWvXroiPjzfncejZsycCA3kyQk0W63qiWiosMWDZjmQs3HgCp9IrJj4uTT+LnC3fI2//OsBQCnd3d/Tu3RteXl7o0aMHvv76a01GERo7diweeugh83Tnzp3Rvn37ei8HAOzbtw9Tp05FTk4OioqKUHrxAtJXv4GsDV8gIGEsAnqPgc5LGdxFb5RYviMFy3ekYEiHMMxMjMWg9pUnWyZqSly6O4OrYxNHcgWH0nKwYMNJ/Li7YrJEd52wK4JuMBgwYMAAbNu2DQDQoUMHc7CgMQcMbHU2owAL/zqJb7edRUG5DqdSGlF8fCsis/ajX2wYEkwBg+7du8PHx0ejElNTpHUTx8aGdT25gvS8Ynz+92l88c9pZORX7HIYGyjx9yfPoPD4NgAVz+07duyIdevWITo6uh5KW5GUEh06dMDx48cBAA8++CBeeeUVTcoCAKtWrcKECRNQUlLxbyk8fRAcn4RO19yFc9lFFZaXtei8uke0zSNPETma1nU9gwh1wBML0oqUEpuPp+PDDSew4UjFZIkBXu64oX8r3DKoDaKCbL+A3b17N9asWYOEhATEx8cjKCjIkcVuNLIKSvDJhqN4b81+6D38Kizv1TIYMxLbYVRcJNx0vFtB9UvrE4vGhnU9aenExTx8/NdJfLc9uUJiQJ0AxnSPwh1D2mH5gtfx7LPPVrqPDh06YP369ZoFEMrMnj0bb7zxBgDgzz//RGJioqbl+emnnzBhwgSUllbMfwQAW7ZtR6pb8ypzS0UFeeO2QW1xfb+WCHBgIkoiW2hd1zOIUAc8saD6VmowYtUeJVnigXMVK7ToIG/cNrgtpvRlhVYfivUGrNiZio82nsCxC3kVlrdq5ovpQ9piUkKLSsfOJnIGrU8sGhvW9VTfpJTYfjoTH204gTUHz6P8qbqPhxum9G2J2we3RctmSteEpKQk/PzzzxX21aFDB6xbt84lRgdau3YtrrjiCoSEhODChQsuMYRidYGEjz76CHfccUeNo1wFeLljav9WuGVgG0QHs+Uh1Q+t63oGEeqAJxZUX3KLSrF4y1l8sulkpU3rukYFYubQdkjqHsWmdRowGiX+PHIRH204gb9PpFdYHuzrgZsGtMZ/LmuD8AAvDUpITYnWJxaNDet6qi8Go8Rv+9Pw0cYT2FmWLFElzN8Ltw5qgxv7t0Kwr6d5vpQSzZs3x8WL1he47du3x/r1610igAAApaWlCA8Px9VXX40vv/xS6+KYrVy5EhMnTqwQSJgxYwY+/PBDq3mH03Lx8cYT+GFX5V1Ix/ZUupB2jWbeI3Iuret67UOARFSlc9mFWLTplJIssbhissShHcMxI7EdBsYyyY+WdDqByztH4PLOEdibnI2PTEkYDaYsjFkFpXh77TF8uOEEJsbH4PbB7dA+wr+GvRIRUVNQWGLAsu1n8fFfJ3G6kmSJ7SP8MWNIO4zrHQ0vd7cKy8+ePVshgBAbG+syLRDKeHh4YPTo0fU6KoMtxo4di2XLlmHSpElWgYSy/FBqnSID8MrknnhwVCcs2nwKX/5z2pzMWm+U+H5nCr7fqSRhvGNIOwzpEMbzM2qU2BKhDnh3gpzl4LkcLNhwAj/uToXeaP0b9XATGNcrBtOHtEXnSEa6XdXZjAJ8uukUFm89UyEJIwCM6BKBO4a0Q7+2zXiCQQ6l9d2JxoZ1PTnLpbxifL75FL745zQyCyo2px/QrhlmJsZiaMdw6KrJr7N8+XJMnDjRPB0bG4v169ejRYsWTil3XSxZsgSjRo1yySTNK1aswOTJk82BBA8PD+Tk5MDb27vKbfKK9fh261ks/OtkpcNqd44MwIzEdri6RzQ83dlSlBxH67qeQYQ64IkFOZKUEn8du4SPNpzAxqOXKiwP8HbHtAGtccvANmgeWHWFRq4lu6AUX285g083ncSF3OIKy3u2DMaMIe0wKq453NkVhRxA6xOLxoZ1PTna8Yt5+HjjSXy3Ixkl5ZIluukEkrpH4Y4hbdGjRbBN+3v00Ucxb948AEC7du2wfv16tGzZ0tHFdgiDwQA3t4qtKVzFihUrMGnSJOj1SuuCLVu2oG/fvjVupzcYsXpfGj7acBz7UirmrIoM9Matg9pgav9WCGTOKnIAret6dmcg0lipwYh3ftyMVceKcSy9Yr6DmGAfc7JEfy/+ZBuaIF8P3DUsFrcNboMfd6ViwcYTOHLekoRx99ks3P31DrRs5oPbB7XFdX1b1ioJo9FohBCCrRqIiFyQlBJbTynJEn8/eL7Ccl9PN1zftxVuHdTGnCzRVmXN7l09gADApQMIADBu3Dh8++23uO6666DX67Ft2zabggjubjpc0zMaY3tE4Z8TGViw8QTWHrpgXp6WU4R5Px/C22uPYWq/lrh1UFsmYaQGjS0R6oB3J6gucopKsXjLGXy66VSlyRK7xQRiRmIskrpF8g51IyKlkoRxwcYT2HSsYhLGIB9TEsaBrRERYHuLE6PRiLFjx2LUqFG46aabEBIS4shiUwOi9d2JxoZ1PdWFwSjx6/40fLThBHadzaqwPCLAC7cMaoMb+7VGkK/9d6illAgNDUVwcDDWr1+PVq1aOaDUtHz5ckyZMgX/+c9/sHDhwlrt4+j5XCzYeAI/7ExFicG6xYm7TuDqHlGYPqQdusVwOG2yn9Z1PW9rEtWz1KxCLNqsJEvMqyRZYsHxrXA7sg5dRw9AZ5/bGUBoZIQQGNYpAsM6RWBfSjYWbDyBn/ZYkjBmF5binXXH8NGGExjfOwZ3JLZF+4iAGver0+nQv39/3HfffXj44YcxZcoUzJw5EwMGDGDrBCKielZQosfSbclY+NdJnMmomCyxY3N/3DGkHa7pVXmyRFudPHkSQUFBWLduHQMIDjRhwgQsXrwYL7zwQq330aF5AF6e1BMPjuyEz/4+hS//OYPsQiXfgt4o8cOuVPywKxWD2odiRmIsEpmEkRoQtkSoA96dIHvkFpXi2Z8OYOnWM5DCOjDgJiQii85g65cvofTSGatlQ4cOxfTp0zFx4kT4+LDpW2OUklWIT/86iW+2nEF+JUkYmxUmo/XFv9EqPAjNmzdHZGSk1XNERAQ8PT1x5swZtGnTBurjevfu3TFz5kxMmzYNQUG829EUaH13orFhXU/VKd/H32Aw4MXvt2LpgRxkVZIscWBsKO5IbIdhHcMdcsG4ZcsWNG/eHK1bt67zvqiiFStWYMyYMfD09Kx55RrkF+uxdJsyCkdyZsUkjJ0iA3BbDz9MGZ5gNd/V80iQNrSu6xlEqAOeWJCtzmYU4PbPtlr1hQcAQ1Ee8nauRu72lTDkZ1a7j+DgYEybNg3Tp09Hz549nVlc0kh2YSm+MSVhPJ9jnYRRn5uOi8ufRUnasUq3bdasGZo3b47jx4+jpKSkwnJfX19MnToVM2fORJ8+fXi3oxHT+sSisWFdT1XZsmULjhw5gmnTpgEAsnLzccXcT5Hu39ZqPTdT0/U72HSdoCRh/MXUxWVPcrbVMmnQ46rIPLw350bzvIceeghPP/00bySRFa3regYR6oAnFmSLbacyMOOL7cjIt1zY6bPSkLNtBfL2rIEsrZgPoSZ9+/bF9OnTMXXqVAQE1NzUnRqWEr0RK3crSRgPpeWa5xtLi5C+aj4KDm+q0/579+6NmTNn4oYbbuD3pxHS+sSisWFdT5UpLS1FQkIC4uPjsWjRIhw6nYqxL/2E0sAY8zo+Hjrc0L81bhvcFjFMokflSCmx5aSShPH3gxeslnVCCn567nboBBAWFoZZs2bh+eef16ik5Iq0rusZRKgDnlhQTZbvSMYj3+21SqgzICALHYqPIP3SRVy8qDwuXLiA06dPo6CgYr/Jqnh4eGDw4MF45ZVXkJCQUPMG1OBIKfHpxmN4dvVhSFhaDvgc+x25/yzF+fPnzcNQ1Ya/vz9uuOEGzJw5E/Hx8Y4oMrkArU8sGhvW9VSZF198EXPnzkXLli3x0bercefXuwBfS0Jbr8yT+OmxCejQKlq7QlKD8emP6/Dk76nQ+Qab5wUXJOO1Sd0wYuhguLu7Y8eOHejevbt2hSSXonVdz8SKRE5gNEq8tuYw3l133DzP002HlyZ1x/jeLSqsX1hYiLi4OJw8ebLKfXbs2BH9+vVD//790a9fP/Ts2RNeXl5OKT+5BiEEbkvsgE7RIbjry+3IKVICBoXtR2Dy5Jvxwvg4FOTmIC0tDefPn8evv/6Kl19+2aZ9t23bFn369EFsbCyysrJQWloKDw+OXU1EVJNjx47h6aefBgBc8ozCzKWHIVQBhIicw/jj9TsR4GffUI3UdN16zeXo0GI/pn34FxCinCdm+bbAzV/sgVtgOPQ5F3HHHXdg06ZNzI9ALoFBBCIHKyjRY863u/HzvjTzvFA/T3x4UwL6tGlW6Tbz5s2zCiBERESYgwX9+vVD3759OWRfEzaofRi+v3sQbl+0FafSldYq3+9MwZmMAnx4UwLi4uLQuXNnPPzww5Vu37JlS/Tp08f8SEhIQGhoaH1+BCKiRkFKiZkzZ6KoqAiB/cYjeNitEKZkydJoQILuFJa+fR8v9Mhug+Pj8OcToRj15NcoCusEAHAPbYWo/7yOC8ufw7///ov3338f99xzj8YlJWIQgcih0rKLMP3zrdiXkmOe17G5Pxbe3Bctm1V+RyI5ORl///03HnzwQXPQoFWrVkx8R1Ziw/3x/axBuOur7fjnRAYAYPvpTFz77iYsvLkvfv/uc2zbtg3R0dEVAgYREREal56IqHH4/PPPsXb9BjQb/V8E9Bxlnm8sLsAQtyP46uXHNCwdNXStYyKx9Y0ZSLj1aZTEDgMAuPmFIHLqPFxa/Qbmzp2LcePGoWXLltoWlJo85kSoA/aTJLW9ydmY/vlWq6z6wzqF4+2pvRHgzWbi5BgleiOeWLEPi7eeNc/z93LHzO4emDiwM6Kj2f+2qdO6n2Rjw7qeyly4cAFdevWFx7C74N3K0jddn5WGC989g9JLZ5CYmIhZs2Zh/PjxDhkWkJqOixcvYuHChfjggw9w+vRp+HW7AqGj74Fws5xDZm36GkNCcvHjihW82dTEaV3X62pehYhq8su+c5j84WarAMKtg9rg4//0YQCBHMrTXYd5E7rj8au6oOz8Ia9Yj/nbC/HLiWIwMExE5Bx3PvQkvK9+3CqAUJS8H+c+fwCll84AAI4ePYqTJ0/alSiZCAAuXbqEY8eO4dy5cwCA/H1/4Pzix2EosAwDGTzoBvwjumDx0u+0KiYRAAYRiOpESol31x3DnV/uQFGpMgKDm07g+fHd8OTYOLi78SdGjieEwPQh7bDgpj7w81T63Rol8MxPB/DYD/tQqhoNhIiI6u6Nb37GtuBh8Ghmae2Vt28tzi9+DMbCHPTo0QOfffYZTp06hUceeQTBwcHaFZYapC5duuDjjz/G6dOn8fjjjyM0NBTFyfuR9sUclKZbWh/6dUnEw7+l4cjZ8xqWlpo6XuEQ1VKx3oA53+7GK78eNs8L9HbHZ7f2w439W2tYMmoqRnRtjmV3DbQaf/zrf8/glk+3ILugVMOSERE1Hp9sOII3dpZC5+1vnpf552dIX/U6Rl85AmvWrMGuXbvwn//8h10YqM4iIyPx7LPP4syZM3jvvffQNjwA5754EIUnd5jX0YW1xTVvb8T+1Oxq9kTkPAwiENVCel4xblzwL5bvTDHPaxPqi+/vHoTBHcI0LBk1NV2iAvH93QPRu1Wwed6mY+kY/94mnLyUr13BiIgaOL3BiKd+3I9nVh8FdKZWX6VFyFz5MiZ28cfevXvx888/Y8SIEeyfTg7n6+uLu+66C4cOHcL3S75Cx3O/I3fHT+blRTofTHj3L/y2P62avRA5B4MIRHY6cj4X497dhG2nM83zBrRrhu9nDUJsuH81WxI5R0SAN765YwCu6WlpZnviUj6ufXcT/j6ermHJiIgappyiUkz/fBsWbT5lnmfMz8BV3kdw+I8l+OSTT9CtWzftCkhNhk6nw7hx47Bxw5/45fnb0CZ9C6TRAAAoNgAzv9yOD/48zpxIVK8YRCCyw7rDFzDhvc1Iziw0z5vSpyU+v60/QvzYhJG04+3hhjev74XZIzqa52UXluKmhf9i8ZYzGpaMiKhhOZtRgEnvb8b6wxfN85p7FGP9o1fh/efnIjIyUsPSUVPWt29frF/wNF4d2w7uUg8AkBJ48edDeGjZHpTomROJ6geDCEQ2kFLi000ncfuircgrVg7aQgCPJXXBixO7w9OdPyXSnhAC943ogHdu6A0v03dSb5R4ZPlePL/qAAxG3qUgIqrOtlMZGPfuJhw5n2eeNyquOdb93zVoF9VMw5IRWUwe0g0/PzAcMcFe5nlLtydj2sJ/kZFfomHJqKnglQ9RDUoNRjz+wz48vfIAyq7BfD3d8NFNfXBHYjv2gySXc3WPaCyZeRnC/C0nFws2nsSMz7eZg2BERGRt+Y5k3LDA+iLs7stj8f6NCfD1dNewZEQVdWgegB/vGYK+bULM87aczMC1727CsQu5GpaMmgIGEYiqkV1Qils/3Yqv/rU0B48O8sayOwfiyq7NNSwZUfV6tQzGj/cMQpeoQPO8Pw5dwKT3NyM5k+OXExGVMRolXvn1EB74djdKTEPkerrp8Pp1PfG/UZ2h0/FmAbmmUH8vfDm9PybGtzDPO5NRgPHvbcaGIxer2ZKobhhEIKrCqUv5GP/+Jvx17JJ5Xq+WwfjhnkHoGh1YzZZEriE62AfL7rwMI7pYAl6H0nJx7bubsONMZjVbEhE1DQUletz99Q68u+64eV4zP098dUd/TFBdmBG5Ki93N7w6uQceHt3ZPC+3SI9bF23FF3+f0q5g1KgxiEBUib+Pp+Pa9zbhxEXLEHlje0Zj8YwBiAjw1rBkRPbx83LHhzclYGZiO/O8S3kluP6jf7BiV0o1WxIRNW5p2UW47sO/8fM+yxB5HSL8seLuQejbhvkPqOEQQuCuYbH4YFoCfDyU4UgNRon/W7EfT67YB72BCRfJsRhEICpnydYzuGnhv8gqKDXPu39EB7x1fS94mw7MRA2Jm05gblIXvDypBzzclGa5JXoj7lu8C6+vOcJhoYioydmXko1x7/6FfSk55nlDO4bju1kD0bKZr4YlI6q90d0isfTOyxAZaLnh9dnfp3HbZ9uQU1RazZZE9mEQgcjEYJR4YfVBPPzdXuhNGRS93HV4a2pv3D+iIxMoUoN3XZ+W+OL2/gj29TDPe+uPo7jnm50oKjVoWDIiovrzy75zmPTBZpzPKTbPu2VgGyy8uQ8CvT2q2ZLI9XWLCcKKewahe0yQed6GIxcx4b3NOJPOnEjkGAwiEAHIL9Zj5hfb8NGGE+Z5Yf5eWDxjAK7pGa1hyYgca0C7UPwwaxBiw/3M81btOYcpH/2DCzlFGpaMiMi5pJR4d90x3PnlDhSVKs273XQCz17bDU9dEwd3N54WU+PQPNAb3868DEndI83zjl3Iw7h3/8KWkxkalowaCx4tqclLySrExPc34/eDF8zzIr0NWDI9Ab1bhVSzJVHD1CbMD8tnDcKQDmHmebvPZmHcu5uwPzXb7v399ttvSElhfgUicl3FegPmLN2NV349bJ4X4O2ORbf2xU0DWmtYMiLn8PF0wztT4/Hf4e3N8zILSnHjx/9g2fZkDUtGjQGDCNSk7TyTiXHvbMKhNMt4usazu7Bl3vWI79QGM2bMwObNm9lnnBqdIB8PfHKL9cnzuewiTP7gb/y2P62aLSvKzMxEq1atkJSUhO+++w4lJSU1b0REVE/S84px44J/sXyHJdjZOtQX388ahCEdwjUsGZFz6XQCc0Z2wvwpPeFpamlTapB4cOluvPTLIRiNPL+l2mEQgZqsH3en4roPNuNSnqVP5IzEdrilfSlkSSFycnKwYMECDBo0CJ06dcILL7yAs2fPalhiIsfycNPh2Wu74elr4lA2DHpBiQEzv9yO57/7F4cOHUJ6ejoMhurzJYwfPx5hYWH4+eefMWnSJMTExOCBBx7Avn376uFTEBFV7dC5bIx7dxO2nbYMa9uvbTP8MGsQ2kf4a1gyovozvncLfDOjP0L9PM3z3l9/HHd9tR15RQz8k/0E77DWnhBif9euXbvu379f66KQnb7bnow5S3ebp6VBj4zf3oU4+Q+8vLxw6dKlSrcTQuCKK67ALbfcgvHjx8PXlxmcqXFYf/gC7vl6J/KK9eZ5WZu+RvZfX0MIgWbNmiE0NBRhYWHmZ/XrJUuWYM2aNRX2269fP9x+++2YMmUKgoKCKiwnx4uLi8OBAwcOSCnjtC5LY8C63nVlZGSgWbPKh2JMTk7G4y+9jT+9+kG6WzLVX9enBZ67tjs83XkfjZqesxkFuP2zrThyPs8y8+IxzO7lhpl3TIe3d8VhzDMzMxEUFASdjr8ZV6J1Xc8gQh3wxKJhOnUpH0lvbURBiXJ31VCYg4vfz0Px2b127ScgIADXXXcdbr75ZgwePJijN1CDd+R8Lm7/bCvOZhQCAKQ04vzXc1GcXPdjnI+PDyZPnozbbrsNiYmJ/L04kdYnFo0N63rXlJKSgquuugq7du2ymp+cnIwXX3wRCxZ+imbXPQ+vqA4AACGAR0Z3xozEdjz+UJOWW1SKe7/ZiXWHL5rnZf31NfxOrsfcuXMxfbp1MOHnn3/G0qVLsWDBAri5cahzV6F1Xc+QEjUpeoMRs7/dZQ4gGItykfbFg3YHEAAgNzcXCxcuRGJiInr06IH169c7uLRE9atj8wD8MGsQ2oYpIzcIoUPY1Q9AePrUed+FhYX4/PPPMWzYMHTs2BEvvPACkzESUa0cP34cgwcPxsGDB83zkpOTcc899yA2NhbvvvsufPtOMAcQAOCNKb0wc2gsAwjU5AV4e+Djm/tiTFdLcuWggVNwSfrjv//9L2JjY/HOO++gqMgyYtOnn36K66+/njmPyMxd6wIQ1af31h/HzjNZ5un3bxuK4fOOITMz0/x44oknsG7dumr3ExkZiUGDBmHgwIEYNGgQevfuDU9Pz2q3IWoIQv29MH9KL0x8fzMMRgn3oOa45a1VmNZBIj09HZcuXcKlS5fMr8ueDxw4gIIC28afPn78OL766iucOnUKDz/8MGJjY538qYiosdi3bx9GjhyJc+fOwdPT09LyYMEC8wWOV0wXBA6YbN5mYq9IjOsVo1WRiVyOm07glSkJ2PnqWqTllkLo3BB29YM4t+hepKam4r///S/mzZuHuXPnIiZG+e0sW7YMeXl5+O6779idlxhEoKZj19ksvPnHUfP0hN4xuKpHFAClqXV0dDQOHjyIjRs3Wm0nhEC3bt2sggZt27bl3QxqtHq1DMa9wztg/u9HAABrTxZg0sB4TB4eVen6Z86cQZcuXarcX2hoKAYMGGB+9O3bl/kRiMhuW7duxejRo5GRoYxzX1JSgtjYWKu7o8LTBxHX/A9CpzS7bh3qi2fG99SkvESuzN/LHe/c2AfXffg3jBLwaBaNZlfcgfRf3gYAczBB3bXhl19+wejRo7Fy5UrW400cgwjUJBSU6DF7yS4YTEPZxAT74Klx1l2IpJS4//774eXlhcTERAwaNAiDBg1C//79ERwcrEGpibRz9+WxWH/kgrnlzqPf70VC6xA0D6yYdGnOnDnmVghubm7o1auXVdAgNpZNiImobtavX4+xY8ciLy/Par46gBAaGoo+s97AoZIQAMrd1vlTesHPi6e7RJXp06YZZg1rj3fWHQMA+Pcchcta++Pnj182j8yk7tYAABs3bsTw4cPx66+/IiwsrMI+qWngUZWahOdXHcTJS/kAlORK86f0QqC3h9U6hYWFmDdvHnr06AF3d/40qGlzd9PhjSm9MOZNJQlpVkEpHly6G5/d2g86nSUgsGvXLkgp8corr2DAgAGIj49nM0cicqhVq1Zh0qRJFS5myoSGhuJ///sfOl5xHWYvO2Cef/fl7RHfKqS+iknUIN03ogP+PHIRe1OyAQCpMZfj7x3/wXvzX8IXX3xR6TDPO3bsQGJiItasWWPu7kBNCxMrUqO39tB5fPXvGfP0zMRY9GtbcUgoX19fxMfHM4BAZNI61A9PXN3VPL3x6CV8/vcpq3V69eqFZcuW4cEHH8TgwYMZQCAih1qyZAmuvfbaKgMIgBJE6D9sJJ5Zbemy2LNFEP47vH19FJGoQfNw02H+lF7w9lAuC9PzS/D+jlwMGZJYbb6vgwcPYvDgwTh+/Hh9FZVcCIMI1KhdyivGQ8v2mKe7RgXigSs7algiooZlSt+WGNGluXl63s+HcPR8roYlIqKmYsGCBZg6dSr0en216x05cgRT569CZkEpAMDHww3zp/SChxtPc4ls0T7CH48mWXIbrT10Afe99S0KCwur3e7UqVMYMmQI9u3b5+wikovh0ZUaLSklHvluLy7lmbI1u+vw5vW94OnOrz2RrYQQeGlid4T5ewEAivVG3Ld4F0r0Ro1LRkSN2WuvvYYZM2ZASlnlOj4+PkhISMCIu56FV5ve5vmPX90F7cL966OYRI3GTQNaY2jHcPN089F3IWnKLejYsSN0uqrPnc+dO4ehQ4di69at9VFMchG8mqJGa8nWs/j94Hnz9CNjOqND8wANS0TUMIX6e+HlSd3N0wfO5ZhHbiAiciQpJZ544gk8+OCD5nlubm7o3LkzJk+ejKeffhrLly/HkSNHkJubi8Wr1+NMswTzuld0jsAN/VppUXSiBk0IgVcm9UCIr5IzTA83uA+Zjn0HDiIvLw/btm3DokWLMGfOHIwaNQrR0dHmbTMyMjB8+HCsX79eo9JTfWPnb2qUTl3KxzM/WZIrDekQhpsva6NdgYgauOGdm+PG/q3M+UU++PM4Lu8UUWl+ESKi2pBSYv78+di+fTseeughdO/eHd26dUPnzp2thpkrU6I3YvaSXSg2tYwK9fPEixN7cDQYolqKCPTGvAk9cOeX2wEAu89m4Z21xzD7yo5ISEhAQkKC1foZGRnYt28f9u3bh7179+KFF16Ah4cHBg0apEXxqR4xiECNjt5gxOxvd6GgRMkmG+TjgVcm9bTKKE9E9nvsqi7YfDwdJy/lQ0pg9pJd+Pn+IRVGOiEiqg0hBB544AE88MADNq3/1h9HzRnlAeDFiT0QHuDlrOIRNQmju0VickILLN2eDAB4Z90xDO0UXulIJ82aNUNiYiISExPru5ikMXZnoEbnvfXHzWPbA8C8Cd0RGVTxDgYR2cfX0x1vTOkFN1NALiWrEE/9uF/jUhFRU7TtVAbeW3/MPD21X0tc2bV5NVsQka2evCYOrZopoy0ZjBKzl+xCfnH1CU6paWEQgRqVXWez8OYfliGeJsTHIKl7lIYlImpcerYMxn1XdDBPL9+RgtV7z2lYIiJqanKLSjH7210wmnIutgn1xeNXda1+IyKymb+XO+ZP6YmyRryn0wvw3KoD1W9ETQqDCNRoFJToMXvJLhhMZxUxwT546po4jUtF1PjMGhaL3q2CzdOPfr8XadlVj+FORORIz6w8gLMZytBzbjqB16f0gp8Xe+gSOVJC62aYNay9efqbLWex5sD5aragpoRBBGo0nl91ECcv5QMAhADmT+nFvtpETuDupsMbU3rB19MNAJBVUIr/LdsNo7HqodiIiBzhl33nzH21AeDuy9tX2lebiOruvhEd0D0myDz9yHd7cDG3WMMSkatgEIEahbWHzpuzxgPAzMRYZo0ncqLWoX544mpL8+GNRy/hs79PaVcgImr0LuQUYe7yvebpni2C8N/h7avZgojqwsNNh/lTesHbQ7lkTM8vwcPf7YGUvGnQ1DGIQA3epbxiPLRsj3m6a1QgHriyo4YlImoapvS1TmT24s+HcPR8roYlIqLGSkqJ/y3bg8yCUgCAj4cb5k/pBQ83nsoSOVP7CH88ltTFPL320AV8veVMNVtQU8AjLzVoUko88t1eXMorAQB4uevw5vW94OnOrzaRswkh8OKE7gjzV4ZUK9Ybcd/iXSgxjdlOROQoX/xzGn8euWiefvzqLmgX7q9hiYiajmkDWmNYp3Dz9HM/HcSJi3kaloi0xistatCWbD2L3w9akrw8MqYzOjQP0LBERE1LqL8XXp7U3Tx94FwOXl9zRMMSEVFjc+xCHp5fddA8fUXnCNzQr5WGJSJqWoQQeHliD4T4KrnGCksNmL1kF0oNvGnQVDGIQA3WqUv5eOYny3AzQzqE4ebL2mhXIKImanjn5rixv+WE/sMNx/HviXQNS0REjUWJ3ojZS3ah2NTCKdTPEy9O7AEhhMYlI2paIgK9MW9CD/P07uRsvL32mIYlIi0xiEANkt5gxOxvd6GgxAAACPb1wKuTe0Kn40kFkRYeu6oL2oX5AQCkBB74djdyiko1LhURNXRv/XEUe1OyzdMvTuyB8AAvDUtE1HSN7haJ6/q0ME+/u+4YdpzJ1LBEpBUGEahBenfdcew8k2WefmF8dzQP9NauQERNnK+nO+ZP6QV3UyAvJasQT/24X+NSEVFDtu1UBt5bb7nTObWfdTJXIqp/T4yNQ6tmvgAAg1Fi9pJdyC/Wa1wqqm8MIlCDs+tsFt5ae9Q8PSE+BkndozQsEREBQM+Wwbj3ig7m6eU7UrBqzzkNS0REDVVuUSlmf7sLRtNIcm1CffH4VV2r34iInM7fyx3zp/REWePf0+kFeFbVvZiaBgYRqEEpKNFj9pJdMJjOKmKCffDUNXEal4qIyswaFoverYLN049+vxdp2UXaFYiIGqRnVh7A2YxCAICbTuD1Kb3g5+WucamICAASWjfDrGHtzdOLt57FmgPnq9mCGhuXCyIIIXyEEM8IIY4IIYqEEKlCiE+EEDF27ueUEEJW8+jsrM9AzvP8qoM4eSkfACAEMH9KLwR6e2hcKiIq4+6mwxtTesHX0w0AkF1Yiv8t2w1j2e1EIrCup+r9su8clm5PNk/fc3l7xLcK0bBERFTefSM6oEeLIPP0I9/twcXcYg1LRPXJpYIIQghvAGsB/B8AfwArAJwFcCuAnUKIdrXY7WdVPLKr24hcz9pD5/HVv2fM03cOjUW/ts00LBERVaZ1qB+eHGtpdrzx6CV89vcp7QpELoV1PVXnQk4R5i7fa57u2TIY9wxvX80WRKQFDzcd5k/pBW8P5XIyPb8ED3+3B1LypkFT4Grtwh4HMADA3wBGSinzAEAI8QCA1wB8AmCYPTuUUt7i2CKSFi7lFeOhZXvM03HRgZg9oqOGJSKi6lzXpyX+OHgBv5maN877+RAGtQ9Dx+YBGpeMXADreqqUlBL/W7YHmQXKyC4+Hm54Y0oveLi51D0vIjKJDffHY0ld8H8rlETKaw9dwFf/nsG0Aa01Lhk5m8sclYUQngDuMU3eXXZSAQBSytcB7AEwVAiRoEX5SDtSSjzy3V5cyisBAHjogIOfPIJnnnoCBw4wkQuRKxJCYN6E7gjzV4ZiK9Ebcf/iXSgxjfVuq+3bt+PNN9/E+fPsa9kYsK6n6nzxz2n8eeSiefrxq7ugrWnoWCJyTdMGtMawTuHm6edXHcSJi3nVbEGNgcsEEQAMAhAE4LiUcmcly5eZnsfWX5HIFSzZeha/H7RcQDya1AXeJZl4/vnnERcXh169euHll1/GmTNnqtkLEdW3UH8vvDKph3n6wLkcvL7miF376N69O1566SXExMQgKSkJX3/9NfLz8x1dVKo/rOupUscu5OH5VQfN01d0jsAN/VppWCIisoUQAi9P6oFmfp4AgMJSA2Yv2YVSg303DahhcaUgQk/T844qlpfN71HF8koJIf4nhPhACPGmEGKGECK85q3IVZy6lI+nV1rGmu/Twg9JHf1x5513muft3r0bDz/8MFq3bo0hQ4bg/fffx6VLl7QoLhGVc3nnCEwbYLkQ+PDP4/h01V84ePAgUlJSkJubC6Ox6hMNT09PzJo1CwaDAT///DNuvPFGREZG4uabb8aaNWtgMBjq42OQ47CubyLs+W0WFJXg3q+3odjUUinUzxMvTuwBIYSzikdEDhQR4I15E7qbp3cnZ+Pln+zLj8D6vGFxpZwIZWeZyVUsL5tvbyebl8tNzxdC/FdK+YmtOxBC7K9iUaydZSE7SCnx0LI9KCxVTioMhTn4Ye5/8N1/M6rc5q+//sJff/2Fe++9FyNHjsQNN9yAcePGwd/fv76KTUTlPJbUFZuPpePEpXxIAP/30xGkLJgJGPQAlLsYAQEBCAwMrPRRUlJitb+8vDx8/vnn+PzzzxEVFYWpU6fipptuQs+ePXnR4fpY1zdyUkp89tlnSEtLwyOPPFLleufPn8cvv/yC1atX48+LPvDuN9m87KWJPRAe4FUfxSUiBxkVF4nr+rTAt9uUw/hHm87ik2fuw1WDeiIpKQlDhw6Fj49PldtPmzYNDz/8MHr16lVPJaa6cKWWCGVXeQVVLC9rv2prVq4fAUyAciLiC6AbgNcBeAH4WAgxrpblpHqyLyUHW05ZAgYZv74LQ17VAQQ1vV6P1atXY9q0aYiIiMD111+PH3/8scLFCBE5n4+nG+ZP6QV3nXKB7x7UHL4dBpiXSymRk5OD5ORkHDhwAP/88w9+++03LFu2DJ988gm+/PLLKvd97tw5vP766+jduze6d++OF198kV2bXBvr+kbs5MmTGDVqFG699Va0bNnSapnBYMC///6LJ598En379kVkZCRuueUWfLvsO3jEjTCvN7VfS4zo2ry+i05EDvDE2Di0auYLABA6HbIieuLtt9/GmDFjEBoaiquvvhrvvfceTp48WWFbvV6PPn36YO7cuSgsLKzvopOdXCmI4FBSynullN9LKc9IKQullPullHMA3AVAAHjJjn3FVfYAcNxZ5Sdg6faz5telqYdQcHhTrfZTWFiIXbt2YfXq1Vi3bp2jikdEdujZMhjX9Io2T/t3H1HN2rWzf/9+zJ07F61bt8bll1+OxYsXc6ipRo51vWswGAyYP38+unXrhjVr1gAAevbsifT0dHz99deYNm0amjdvjgEDBuCZZ57Btm3bzNv6tEuAm18IAMBDJ/DQqM6afAYiqjt/L3c8cKVl9DS/zkMgPJRWRYWFhVi1ahXuvvtutGvXDl27dsWcOXPwxx9/oKSkBD179oTBYMCLL76Inj17YsOGDVp9DLKBK3VnKEvj6VvF8rL0vLl1fJ+FAJ4D0EkI0UZKeaqO+yMnKCo1YMWuVPP0a/dMxnWLZqOgoAB5eXmYO3cuFi1aVOX2HTt2xLBhwzBs2DAMHToU0dHRVa5LRPVjckJLLN+RAgDwi+2Dg6dS4S2LkZOTg+zsbOTk5FT62LNnD9avX1/j/oODgzF48GAkJiYiMTER8fHx7N7geljXNzJ79+7F9OnTsWXLFqv5t912G7Zv315tzpPQ0FC0SroVZW0MR8ZFIsSUnI2IGqZRcZEI8HJHbrEeOi9f9B0/Azu//wClpaVW6x08eBAHDx7E66+/Dn9/f7RqZcmfdPToUQwdOhQzZ87ESy+9hKCgoPr+GFQDVwoilLU/bVHF8rL5p+vyJlJKoxDiOIAIAFEATtVlf+Qcfxy8gOxC5WDj7aHDVT2ioNPp4O/vj/T0dHzzzTdW6zNoQOT6+rdthpbNfHA2oxBGCaw9mY9Zw9pXu42UEiNHjqx0WfPmzc0Bg8TERHTr1g06XaNtYNdYsK5vJIqLi/H8889j3rx50Ov1FZZv3bq10u0SEhKQlJSEpKQktOvaEwNfXAcYlRZDk/pU9bUgoobCx9MNV/eMxjdblMN9uytuwO8fP4+1a9di9erVWL16NZKTrdPi5OXlVTps+4cffoiffvoJ7733Hq655pp6KT/ZxpWCCLtNz/FVLC+bv8cB7xVieuY4YS5K3ZUhqVsUArw9zNNlzZUZNCBqWHQ6gUnxLTH/d2WYx2XbknHX0NhqWwusWrUKv//+OwCgTZs2SExMxJAhQ5CYmIgOHTqwpUHDw7q+Edi8eTOmT5+OgwcP1rhuUFAQRo0ahaSkJIwaNQqRkZHmZQv/Ogm9KYDQPNALiR04qAZRYzC5TwtzEOHvE+nIKnXDuHHjMG7cOEgpsW/fPnNAYdOmTdWOzJCSkoJx48bhuuuuw1tvvYXmzZkzxRW4UhBhE4BsALFCiF5Syl3llk8yPa+sy5sIIeIAdIKS1OlQXfZFzpGWXYQNRy6ap9V3JqSUePXVVxk0IGqgJibEmIMIJy7lY8eZTCS0blbl+keOHMGXX36JIUOGWDV1pAaLdX0Dlpubi0cffRTvvvtujflGhBD45ptvMGHCBHh4eFRYLqXE0m2WGwYT4lvATcegIFFj0LtlMNqF++HERSWGu2x7MmabciUIIdC9e3d0794dDz/8MLKysvDQQw9hwYIF1e7z22+/xZo1azB//nz85z//4U0EjblMu08pZQmAd0yT7wohyvpFQgjxAJQxo/+UUm5Xzb9HCHFICDFPvS8hRJIQYnj59xBC9ACwFEqypY9N70kuZvnO5LKWjWgR4oMBbUPNy4QQDCAQNWAtQnwxMNbym166raqR/hQPPPAAbrzxRgYQGgnW9Q3Xzz//jLi4OLzzzjs2JSyVUuK5555DXl5epcv3p+bgUJol9cWkBHZlIGoshBCYnGAZoWXZ9mQYjZUfN/bs2YMvvvjCpv1mZmbilltuwejRo3Hq1ClHFJVqyWWCCCbPAfgXwEAAR4UQS4QQ/wB4DcBFALeVWz8Myp2GqHLz+wH4QwhxSgixQgjxjRDiXwDbAXQBsB5A1YMXk2aklFi23XJRMTG+BXS8M0HUqExWtS76ac85FJRU7E9NjRrr+gakpKQETz/9NGbNmgUhBGJiYhAVFYWIiAiEhoYiJCQEgYGB8PPzg4+PDzw9PeHm5gYhBPbt24err74a+fkVe5SoWyHEtwpGbLh/hXWIqOGaEB+DslP4lKxC/HMivcI6u3btwtixY1FUVAQhBNzd3eHl5QUfHx/4+/sjKCgIISEhCAsLQ/PmzREVFYUWLVrg8OHDuOaaa7Bq1ap6/lRUxpW6M0BKWSSEuBzAXAA3ALgWQAaARQD+T0pZ/S0ri18BtATQF8AgAEEAcgD8BeArAJ9KKavufEOa2XEmy9z0CeCdCaLGaHRcFJ7w2o/cYj3yivX4dX8axvfmb72pYF3fsHh6euLJJ5/Ek08+afe2UkoYDIYKCU+L9Qas2G0ZgWlyn5blNyWiBq55oDeGdgzHusNKF+Vl25MxsH2Y1Trdu3dHRkYGdDoduyc0MC4VRAAAKWUhgCdMj5rWfQrAU5XM/xvA344uGznfMlVCxcvahaJls6pGASOihkrJ3ByFb7Yov/el25IZRGhiWNc3DWV3Fsv74+AFZBVYj8BERI3PpISW5iDC6n3n8PS4OKtk6W5ubloVjerI1bozUBNWWGLAyt3nzNNshUDUeKl/35uPp+NsRoGGpSGi+qTuyjA6LhKB3hUTLxJRwzeiawSCfZXfd1GpEav2nKthC2ooGEQgl/Hr/jTkFSt9o/293DGme2QNWxBRQxXfKgTtws059fDdDltbsBNRQ3Y+pwh/qkZgYlcGosbLy90N43paEqIv3c66vrFgEIFcxlJVV4arukfB19PletsQkYMIIaxaI3y3o+rMzUTUeHy/M8U8AlNMsA8uaxda/QZE1KCpA4XbT2fixMXKR2yhhoVBBHIJyZkF2HzckrVVnb2diBqnCb1bmDM3n80oxL8nM7QtEBE5lZTSqivDxASOwETU2MVFB6JzZIB5ehlbIzQKDCKQS1i+IwVlw063DfNDQusQbQtERE4XGeSNIR3CzdPq1khE1PjsPJuF4+oRmOJ5w4CosSvf8nD5jhQY2PKwwWMQgTRnNEqrqOSkhBYc5oWoiVC3Ovp5ryUvChE1Pku3Wer6/m2boVUoR2AiagrG946Bu6nVUVpOETYevVjDFuTqGEQgzW05lYEzpszsOgFMiI/RuEREVF9GdGmOIB8lc3NhqQGrmbmZqFEqKjXgp92p5mkmVCRqOkL9vTC8c4R5ml0aGj4GEUhz6jsTgzuEIyrIR8PSEFF98vZww7he6szN7NJA1Bj9uj8NuaaWRn6ebkjiCExETYq6S8NvB84ju6BUw9JQXTGIQJrKL9bj532WO4/qAwwRNQ3q3/3WU5k4eSm/mrWJqCFS3zBI4ghMRE3O5Z0jEObvCQAo0Rvx4+4UjUtEdcEgAmlq1d5zKCgxAAACvd0xsmtzjUtERPWte0wQOjVXZ25mawSixiQlqxCbjl8yT7MrA1HT4+Gmw7W9LF2Wl7JLQ4PGIAJpapnqzsQ1vaLh7eGmYWmISAtCCKsEi8zcTNS4LN+ebB6BqU2oL/q24QhMRE3RJFVdvyc5G4fTcjUsDdUFgwikmVOX8rHllGVc+MkJvDNB1FRdq8rcfC67CJuOXaphCyJqCKSUWLaDIzAREdA5MhDdY4LM02x52HAxiECa+U51UtGxuT96tAiqZm0iaszC/L1wuSpzM5s5EjUOW05m4HS6MgKTEMCEeOY+ImrK1C0Pv9+ZglKDUcPSUG0xiECaMBglvtvOOxNEZKFOsPjr/jRmbiZqBNQBwcHtwxAdzBGYiJqya3pGw9NNuQS9lFeC9Ycvalwiqg0GEUgTm49fQmp2EQDATSdwbe+YGrYgosZueOcIhPpZMjev3JNawxZE5Mryi/VYvZcjMBGRRbCvJ65UJVJnl4aGiUEE0oR6qKfLO4UjIsBbw9IQkSvwcNNZBRTZpYGoYVutGoEpwNsdo+IiNS4REbkCdYLFPw5eQHpesYalodpgEIHqXXZhKX7dn2aensSEikRkor5TuftsFo6eZ+ZmooZKHQi8pidHYCIiRWKHcDQP9AIA6I0SP+xiy8OGhkEEqnc/7UlFsV5JotLMzxPDVcnUiKhp6xIViG4xgeZptkYgaphOp+djy0nLCEzsykBEZdx0wirJ6tJtZyElh3ZuSBhEoHqn7sowrlc0PN35NSQiC/Vwr8t3MHMzUUO0TBUAbB/hj14tg7UrDBG5HHVg8VBaLvan5mhYGrIXr96oXh27kItdZ7PM05PZlYGIyhnXS525uRgbjjBzM1FDYiw3AtNkjsBEROXEhvsjvlWweXoZWx42KAwiUL1SN02Oiw5E1+jAatYmoqaofOZmdeslInJ9m4+nW43ANJ4jMBFRJSb3sdxM/GFXCor1Bg1LQ/ZgEIHqjd5gxPIdKeZp9o8koqqojw9/HDqPjPwSDUtDRPZYqhqybWjHcEQEcgQmIqroqh5R8PZQLkezCkrxx8ELGpeIbMUgAtWbDUcv4mKuMoSLh5vA2B5RGpeIiFzVkA5hiAhQMjeXGiR+2JlSwxZE5AqyC0vxyz7LCEyTecOAiKoQ6O2B0aqhX5duO1vN2uRKGESgeqPu63RF5whMnTAW99xzD9atWwe9Xq9hyYjI1bi76awyN9emr+R7772Hjz/+GJcuXXJk0YioGqv2nDOPwBTi64ErujSvYQsiasrUXRr+PHIRF3KKNCwN2YpBBKoXmfkl+P2ApYnSdX1bYtq0aXj33XcxfPhwREdHY8aMGfjtt99QWlqqYUmJyFWouzQcOJeD/anZdm2fkJCAO+64A5GRkRg5ciQ++ugjXLzIJI1ENZFS4syZM7XaVt2VYVyvGI7ARETVuqxdKGKCfQAARgksr0XLw7ocs6h2eGSnerFiVwpKTMO0hQd4IbFDOG644Qa0bKlEHy9evIgFCxZg1KhRaN68OW699Vb89NNPKC4u1rLYRKSh9hH+6K3K3GxvgsX+/ftj6NChMBgMWLNmDWbOnImoqCiMGDECH374IS5cYN9LIjW9Xo8lS5agX79+WLZsmd3bH7uQi51nsszTzH1ERDXR6QQmqo4VS7edhZTSrn0IIXDzzTdj6tSp2LZtm6OLSJVw17oA1DSoR2U4uW4Jmr00AZ6ensjLy6uwbmZmJhYtWoRFixYhICAAY8eOxcSJEzF69Gj4+vrWZ7GJSGOTE1qaL0oW/r4HL00dAC8PN3h7e8PLywteXl7Vvi4sLLTan8FgwB9//IE//vgDs2bNwrBhwzB58mSMHz8ezZuz2TU1Tbm5uVi4cCHeeOMNnD59GgDw/fffV7l+VlYWTpw4gRMnTuD48ePm18f8ugGdRwAAukQFoltMUL2Un4gatknxLfDWH0cBAMcv5iMu8Sp0aOaB2NhYtGvXDu3atUNsbCzatGkDLy+vyvcxaRLuueceLF68GMOGDcOcOXOQlJQEnY73zJ2BQQRyugu5RdifmmOeztn1K0pzc23aNjc3F19//TW+/vpr+Pr6IikpCRMnTsRVV12FgIAAZxWZiFzE1T2j8MxP+1FUaoSbbyBkSCtkpxxAdrZ9XRsqYzQasXbtWqxduxZ33303EhMTMXnyZEyYMAGRkZE174CogUtJScHbb7+NDz74wOo3ddlll0Gv12Pt2rUVAgUnTpxARkZGpfuLunUcPE2vmVCRiGzVKtQX/ds2w78nlWNLKprh4I9fVVhPCIGYmBhzUKEswNCuXTsMHToUOp0ORqMR69evx/r169G5c2fMmTMH06ZNg7c3R4lxJAYRyOnOZljuBBoKc1CaXrvMq2FhYQgJCYG7uzsTMRI1EYHeHugUGYjdZ7MAAO7BzVGccsDh71N20rFp0yZ89913ePrppzF48GCHvw+RK9izZw9ee+01fPPNN5XmIfr777/Rtm1bu/frHmRpzdO3TbM6lZGImpa+bSxBBPWxRE1KieTkZCQnJ2PDhg017vPQoUO444478Nhjj+Gee+7BXXfdhbCwMIeWu6liEIGcLiXLEkToEB2K77duRUlJCYqKijB16tQq+yX7+fnh8ssvx8iRIzFq1Ch06NABQoj6KjYRuYgWwT7mIMLdD/0frm77NIqLi1FcXIyioqJqX69Zs6bG/pFxcXG48sorceWVVyIxMRH+/v718KmI6peUEr///jteffVV/Pbbb3Xen06nQ6tWrcx3AaPbdMBnuZYuhzEhPnV+DyJqOtTHjK59B2Nob1+rVlB1SYx84cIFPPHEE5g3bx5uvfVWzJ49G+3bt3dEsZssBhHI6VIyLUGE9lHN0KdPHwDAkiVLrAIIQgjEx8ebgwaXXXYZPD09K+yPiJoW9YmF8AvFkCE9bNquoKAAixYtqjA/MjLSHDQYMWIEoqKiHFVUIpdTUlKCxYsX47XXXsOePXvs2jYgIKBCn+Sy161atbKqo/elZOOzt/8CAPh4uCHE18Ohn4OIGreyERoAwOAVhGeffNZqeW5urlW3KnVXq1OnTtk0ulthYSHee+89vP/++xg/fjzmzJmDgQMHOvyzNAUMIpDTpapaIkSbDhClpaV4/PHHER0djVGjRmHkyJG44oorEB4erlUxichFRQdZ+jGqWzbV5M0338S5c+fg6+uLoUOHmgMHcXFxbNVETUJBQQFeffVVrFmzBikp9g2btnjxYlx33XU2/1as63pv/saIyC7RqiBCWk4R9AYj3N0sSREDAgLQs2dP9OzZs8K2BoMBt9xyC7788kub3ktKiR07duC5557DbbfdhokTJ/KYZScGEcjp1Cf9LUx3FLOysvDDDz+ga9eu/NESUbViQixNpG0NIhgMBnh4eGDdunW47LLLqszmTNSY+fr64oknnsATTzwBQBlO+dChQzh48KDVo7Lx1R966CGMHj0aQUG2jbCg/m2qf7NERLawaolglDifW2w1rzobNmyoNIDg4eGBjh07okuXLujSpQs6d+6MLl26oFOnThzxrY4YRCCnU3dnKDsYhIeHs9UBEdlEfRKRmlUIKWWNwUc3Nzc8+OCDzi4aUYNSVvcOGTLEan5eXh6OHDlSIbjw8MMP44MPPrBp35XV9UREtvLxdEOonyfS80sAKMcUW44lOTk5uP/++9GvXz9zsKAsYNCuXTu4u/Ny1xn4VyWnklKWuzvBEwsiso/6uFFUakR6fgnC/NmygMhR/P39ER8fj/j4eKv5er3epqAdUHmrQyIie8SE+FiCCFkFAGoe5cXX1xe7du1iy+Z6pqt5FaLayynSI6/YMhxjNO9OEJGdAr3d4e9liXmn2pEXgYhqz93d3eYT85RyORGIiOxl3fKwyKZt7DlOkeMwiEBOpW7e6O2hQ6gfR1sgIvsIIaxOLNTHFSJyDergXkww+xoTkf3UNxuTWde7NAYRyKlSyo3MwEghEdWGukuDPSM0EJHzFZUacCmvxDzNrotEVBtWNwxY17s0BhHIqVIyC8yvmWiJiGorhncniFyW+mTfTSfQPIA5S4jIflY3DFTXEOR6GEQgp0rNtvRnYhCBiGorutwIDUTkOtRdjCIDva3GdicislX5nAhSSg1LQ9XhUZ6cikM+EZEjsDsDkeuyzofAup6Iakd9/CgsNSCzoFTD0lB1GEQgp0rm8I5E5ADsJ0nkujiUMxE5QrCvB3w93czTTKTsuhhEIKdS//g5vCMR1ZZ63PmsglLkq4aOJSJtsdUhETlChdGYspgXwVUxiEBOo2RrLjZP88SCiGor3N8LHm6W0V2YF4HIdbDVIRE5inX3xaJq1iQtMYhATnNOlVRRJ4DIIG8NS0NEDZlOJxAVpBqhgUEEIpfBVodE5ChWLRHYncFlMYhATlM+W7MHszUTUR3wxILI9RiMEmk5HImJiBwjmt0ZGgRe1ZHTqH/4vDNBRHXFERqIXM/5nCIYjJZh2BhEIKK6aMG6vkFgEIGcRt2PiX0kiaiuoq3Gj+aJBZErUJ/kh/p5wkeVWZ2IyF4xVnU9cyK4KgYRyGmYrZmIHKkFuzMQuRzmQyAiR1LfeMzIL0FBCUdjckUMIpDTqLszsCUCEdUVuzMQuR71b5E3DIioriICvOGu42hMro5BBHIa9YkF704QUV2pL1DO5xSh1GDUsDREBJQLIvCGARHVkZtOWI3olsyWhy6JQQRyCoNRIk01xGMLBhGIqI7UJxVGCatjDBFpg10XicjRrEZjYksEl8QgAjnFxdxilBpU2Zp5d4KI6sjbww3hAV7maZ5YEGmPrQ6JyNHU1w3szuCaGEQgp1DnQwjx9YCvp7uGpSGixiKGyRWJXIaU0uoEvwVvGBCRA7Cud30MIpBTJDNbMxE5AZMrErmOrIJSFJQYzNPszkBEjsDuDK6PQQRyCvW4rjypICJH4d0JItehPrn39XRDsK+HhqUhosbC6oYB63qXxCACOQWHdyQiZ1AHEVKzeWJBpKXyrQ6FENWsTURkG3Vdn5ZTBD1HY3I5DCKQUzBbMxE5A1siELkOq+EdWdcTkYOou0IbpRJIINfCIAI5BU8siMgZyudEkFJWszYROZM6qSJbHRKRo3h7uCHM39M8zZsGrodBBHI4KaV1SwSeWBCRg6jvThTrjbiUV6JhaYiaNrY6JCJnYXJF1+ZyQQQhhI8Q4hkhxBEhRJEQIlUI8YkQIqYW+woRQrwphDgthCg2Pb8hhAh2QtHJJKdQj3xmayYiJwjy8UCAl2XIWI4f3TCxrm8c2OqQiJxFfROSdb3rcakgghDCG8BaAP8HwB/ACgBnAdwKYKcQop0d+woDsAXAvQD0AH4AkAvgPgD/CiGaObTwZJasSqro7aFDMz/PatYmIrIPh3ls2FjXNx4p7M5ARE7ClgiuzaWCCAAeBzAAwN8AOkopp0gp+wOYAyAcwCd27OsNAO0BLAfQybSvbgDeBtARwOuOLDhZpJTL1qzX65Gbm6thiYioMalLcsWTJ086ujhkP9b1LkRKiczMTLu3KywxICPf0p2ILRGIyJHU3ReTa5kTgXW+87hMEEEI4QngHtPk3VLKvLJlUsrXAewBMFQIkWDDvqIATAVQAmCWlFKvWvw/ABcBTBNCRDiq/GSRWq55o7u7O5KSkjBq1Ci8/fbbOHXqlHaFI6IGL7oOdycmTJgAPz8/DB8+HN988w2MRg4bVZ9Y17uGkpIS/P7777j//vvRvn17rF271u59qH977jqB5oHejiwiETVxjmiJMGLECAQGBmL06NFYsWIF63wHcpkgAoBBAIIAHJdS7qxk+TLT81gb9jUaymfbKKU8r14gpSwGsBKAG4Ck2heXqqL+obcIUcaNnjt3Ln777Tfce++9aNu2Lbp3745HH30Uf//9NwwGQzV7IyKyVpfuDAsXLkRBQQHWrVuHG264AZ6enoiLi8PTTz+NjIwMRxeVKmJdr5H09HR88cUXuO666xAeHo4rr7wSb775Jvz8/DB+/Hi796f+7UUGecNNJxxZXCJq4srnRKjNaExvv/02cnNz8euvv+Laa6+Fl5cXevbsiRdffBF5eXk174Cq5F7zKvWmp+l5RxXLy+b3cNC+brNxX2Qn9YlFmK8b8vPzkZiYiF69emHXrl0AgH379mHfvn2YN28ewsPDkZSUhLFjx2LkyJEICAjQqORE1BCo706cvpiLCxcu2LxtixYt0LlzZxw6dAgAYDAYcODAATz11FN46qmnEBkZiZEjR2L27Nno1auXo4tOrOvrjZQSBw8exE8//YSVK1di8+bNld6Fe/DBB1FYaP9dvhPns8yvo9mVgYgcrEWwr/l1UakRR06nIsTXw6599OnTBzExMUhJSQEA6PV67NmzB3v27MHcuXMRExODpKQkzJkzB506dXJo+Rs7VwoitDI9J1exvGx+63reF9lJ3Uf5yQf/iwf3r6t2/YsXL+Kzzz7DZ599Bk9PTwwbNgxjx47F2LFj0bo1/0VEZE19wXLkYgFiOveGPjPVIftOS0vD559/js8//xx+fn7o378/pk+fjilTpkCnc6XGew0W63onKikpwcaNG7Fy5UqsXLkSJ06cqHGbm2++GTfffLPd7xU85CYEDZwCAGjBIAIROVigj/Vl6sAZzyFjzQcOfY+UlBQsWLAACxYsQEBAAAYNGoQ777wTY8eOZZ1fA1f66/ibnguqWJ5verblNrUj9wUhxP7KHgBibdm+qVGP227Ity9ZU0lJCX777Tf897//RZs2bTBq1CgcPnzY0UUkogbM28O66pL6Yqe8T35+PtauXYsbbrgBvr6+eOWVV5zyPk0M63onMBgM+OijjxAdHY0RI0bgzTfftCmAUBc6v2Dz6/AAL6e+FxE1PUJYd5HSeTu3pXJubi5++eUXXHvttQgICMBHH33k1Pdr6FypJQI1Es38PM1dGnQ+QXZv37t3b3NLhPj4eEYCichKsd66SbbwcE5CN3d3d3Tt2hVTp07FrFmzEBgY6JT3IaorNzc3zJgxA9dddx1++eUXrFy5Ej///HOtRl2wlbEgx/w6XTVKAxGRM0hDqVP37+HhgR49emDatGmYMWMGfH19a96oCXOlIEJZdouq/mN+pmdbxgp05L4gpYyrbL7pDkVXW/bRlMQE+2BvSjYA4NHnXsGN8eEAgPHjx5tzIqh5e3vjiiuuwNixY3HVVVehRYsW9VlcImpgzmUVmV/H+Ovw5YrFdm1/22234ejRo5UuCwgIwGWXXYY777wT48aNYxDT8VjXO1FwcDCuv/56XH/99dDr9di8ebO5a0NVrfo++OADjBo1yu73WrE/A/M3ngNg/1CrREQ1ySmyDhosmj0ewXMn2r2fKVOmIDW18i6PwcHBGDx4MO65555aHQebMlcKIpwxPVd1BVk2/3Q974vspO6vnC+80aZNG6xfv94qgBAVFYWrr74aV199NUaMGMFoHxHZTD2MbOcWYRg8uK/N2x4+fLhCACEmJgZjxozBAw88gC5dujisnFQp1vX1xN3dHYmJiUhMTMQrr7yCo0ePmpMsbtiwwTwy0ieffIIZM2ZUaDpckx5FvkBZEKGWw68REVVFXdd7uuuQNHwIdHaOArNp0yarAIIQAq1atcLYsWPxwAMPoG3btg4rb1PjSkGE3abn+CqWl83fU8/7IjuVH5IFAJ5++ml2UyAih1BfsKiPN7a49dZb2U1BW6zrNdKhQwfMnj0bs2fPRlZWFn755Rf89NNPWL16NX755ReMGTPGrv2pf3vnsgthNEq7T/CJiKqibuEUE+xTq+PL9OnTzd0UbrrpJtxxxx28cekgrhRE2AQgG0CsEKKXlHJXueWTTM8rbdjXLwCMAIYIISKklObxv4QQXlDGnzYAWF3nUlMF6uHXUjILUVpaii+//BIxMTEaloqIGovkcicW9nj55ZcxcOBABjG1w7reBZTv9nDu3Dm796H+7ZUaJC7mFaN5oHPykxBR02N1w6CWI8AsWLAAgwcPdlSRSMVlzqKklCUA3jFNviuEKOvLCCHEA1DGef5TSrldNf8eIcQhIcS8cvs6B+AbAJ4A3hNCqIMlLwMIB/Cl+oSDHKeF6u5ESlYh3N3dGUAgIodRn1jYOz794MGDGUDQEOt61+Pu7o6WLVvavZ2flzuCVWO2JzMvAhE5kLolQnRw7QKUDCA4jyu1RACA5wCMADAQwFEhxEYo4zv3B3ARwG3l1g8D0AlAVCX7uh/AAAATARwSQmwDEAegG4CjAB5wQvkJ1if1BSUGZBWUIsTPU8MSEVFjklqH7gzkEljXNxIxwT7IKlCSn6VkFSKhdYjGJSKixsK6JQK7ILgal7odI6UsAnA5gGehjPt8LZQTi0UA4qWUNg96LKW8BKAfgLeh3KUYDyAIwFsA+kkpMxxZdrII8fWAj4ebeZoJl4jIUfKK9cgutGRsblHLJo6kHdb1jUd0ue6LRESOUpf8R+R8rtYSAVLKQgBPmB41rfsUgKeqWZ4B4F7Tg+qJEAIxIT44dkEZfSslqxDdYoI0LhURNQbqCxVPNx3C/L00LA3VFuv6xkHdTzmVNwyIyIHKJ1Yk1+JSLRGo8SifXJGIyBFSsgrMr6OCvZkNnkhD5XMgERE5QrHegAu5xeZpBhFcD4MI5BRWTRx5YkFEDpKSVWR+zZMKIm3xhgEROcM5VV0vBBAZxJFfXA2DCOQU6rsTbOJIRI7C5o1ErqP8DQMppYalIaLGQn3t0DzAG57uvGR1NfyPkFPEsCUCETkBEy0RuQ71bzCvWI+cIr2GpSGixiKZdb3LYxCBnEL9g2cTRyJylJRMS06EaLZEINJUqJ8nvD0sp5Ks74nIEdTHEtb1rolBBHIK9Q8+Pb8EhSUGDUtDRI1FqqqfJId3JNKWEII5kIjI4axaHbKud0kMIpBTNA/wgpsqa3pqNk8siKhuSvRGnM9VJVZkE0cizVknVyyoZk0iItuksjuDy2MQgZzC3U2HyEBLJlU2cSSiukrLLkJZ3jZmayZyDcyBRESOpj6WsNWha2IQgZwmhuNHE5EDJWdZ7nKG+3vBy91Nw9IQEWAdRFB3NyIiqg2jUVoN8cicCK6JQQRyGo4fTUSOpL5AYfNGIteg/i0m84YBEdXRxbxilBiM5mnW966JQQRyGuu7EzyxIKK6UQcjmWiJyDXwhgEROVKy6jgS5OMBfy93DUtDVWEQgZyGdyeIyJFSVN0ZeGeCyDWomxpfyitGUSlHYyKi2kvlyAwNAoMI5DS8O0FEjsQhn4hcT2SQN1SDMeFcNvMiEFHtqet65kNwXQwikNOof/hpOUXQq/o3ERHZyyonAk8siFyCB0djIiIHUh9DWrDVoctiEIGcRn2SbzBKXMgt1rA0RNSQGY3SuiUCTyyIXIb1aEwF1axJRFQ9tjpsGBhEIKfx8XRDqJ+neZrDPBJRbV3KL0aJXpWtmScWRC4jmt0XichBUnnDoEFgEIGcyuruBE8siKiW1MePAG93BHh7aFgaIlKzyoGUxZwIRFR76vqeORFcF4MI5FTRQeoTCwYRiKh2mA+ByHWxOwMROUJ2YSlyi/Xmadb3rotBBHIq6xMLBhGIqHbUFyZMtETkWqxbIrCuJ6LaUbdC8HLXIczfs5q1SUsMIpBTcZhHInIE9fGDdyaIXIs6sHcuqwgGo9SwNETUUJVPqiiEqGZt0hKDCORUbIlARI7AcaOJXJf6N6k3SlzkaExEVAuprOsbDAYRyKnUdwxTswohJe9OEJH91MnamK2ZyLX4erojxNeS7JR5EYioNji8Y8PBIAI5lfoAUFBiQFZBqYalIaKGKiXTclHCEwsi16MO7iWz+yIR1YJV10XeMHBpDCKQUwX7esDX0808zS4NRGSv3KJS5BSpsjXzxILI5TC5IhHVVTJbIjQY7loXgBo3IQRign1w9EIeAOXuRLeYII1LRUQNifqCxNNNhzA/Lw1LQ9T4SClx9uxZHDx40Pw4dOgQunXrhnfeecem5GbR5bovEhHZqzY5ETIzM3HVVVchJCQEXbp0sXqEhIQ4q6hNHoMI5HTRqiBC2cEhIyMDJSUliIyM1LJoRNQAWJ9UeEOnq/mCxmAw4JNPPsFll12GuLg4ZngmAlBaWopjx45ZBQrKnvPz863WjYiIwLJly2z+7XA0JiKqi6JSg1VSVluHcw4JCcEjjzyCcePGYfXq1VbLmjdvji5duqBz585WwYWYmBieF9QRgwjkdJWN0ODr64tevXohJCQEo0aNwsiRIzF48GB4e3trVUwiclG16SPp5uaG06dPY8aMGYiKisKIESNw5ZVXYsSIEYiKinJWUYlcSkFBAd555x38888/OHjwII4dOwa9Xl/zhgDeffddhIeH2/xeLTgaExHVwblsSwJlnQAig2y/Jrjmmmswbdo0fPnll1bzz58/j/Pnz2P9+vVW8wMCAsyBhXHjxmH8+PEMKtiJQQRyusruTnh7e+PJJ5/E9OnTsWfPHrzyyivw9vbG0KFDMXLkSIwaNQpdu3blD5qIat1H8n//+x8++OADnDt3Dl988QW++OILAEC3bt1w5ZVX4sorr0RiYiL8/PwcXmYiV+Dr64uZM2fCzc0N27ZtszmAAADXX389WrVqhdjYWLRr1878XPY6KMi6a2JMsK/5dUqmMhoT63AispX6hkHzQG94uFmn7jMajUhLS8Px48dx4sQJnDhxwur1+fPnbX6v3NxceHt7Y8KECRg7diyPVbXAIAI5nfruxKmL2Th16hRKSkqQkJCAiIgIXLhwAQBQVFSEX3/9Fb/++ivmzJmD6OhojBw5EiNHjsSVV16JsLAwrT4CEWlIfWLhI4tw8OBBFBcXo7i4GEVFRdW+7tSpEzZv3my1v3379mHfvn2YP38+PDw8MHDgQHNQISEhAW5ubuWLQNRgBQUFYc6cObj33nuxdOlSvPrqq9i5c2eN2xkMBpw8eRInT56sdHmzZs2sggvNW7cH0BwAkF9iQHZhKYJ9PR35UYioEVMPDetjLMRbb71lFSQ4ceIEioqKqtlDzXQ6HSZOnIg5c+agf//+dS1yk8YgAjmdOjHK/pPn0LbtFTZtl5qaikWLFmHRokUQQiA+Pt4cVBg4cCA8PXlyQtQUqHMivPbMY3hm3x8O23dpaSn+/PNP/Pnnn3j88ccREhKC4cOH4/7778fgwYMd9j5EWvPw8MANN9yAqVOnYt26dXjttdcq9B+2R0ZGBjIyMrBt2zbzvJYPLIPOQ2mCnJJVyCACEdksJcsSINj7759Yt/JVh+3bz88Pt99+O+6//360bdvWYfttyhhEIKdrGWJp4ujmFwz34Ejos9Ls2oeUEjt37kRAQACio6PRuXNnJmUkagIKSvQ4nJZrntZnX3Dae3Xr1g2TJ0/G5MmT0aVLF6e9D5GWhBAYPnw4hg8fjv379+P111/Hl19+iZKSEvM6/fv3xzvvvFNpk+EzZ87AaDRWum999nl4hrUGAOw8k4W4aI7GRES22XU2y/y6urre29u70i5WwcHBSExMtDo+RUVF4d5778XMmTM5UoODMYhATtc80AsdIvzNIzT4dbsC2X99ZdO27u7uGD58OCZOnIhrr70WERERziwqEbmYn/emIb/EAAAwFuej5NxhAEqTRC8vL3h7e1s9l5+XmpqK/fv3V7n/Hj16YPLkyZg0aRI6d+5cL5+JyFXExcVh4cKFeP755/HOO+/gvffeQ2ZmJrZu3YqWLVuiT58+FbYpKSnBmTNnKg0wnEs5AJiCCMu2J2PagNb1/ZGIqAE6l12IjUcvmqd9sk8jbtAgc5BAHTSIjIysNIfBwoULzQGEuLg4PPjgg5g6dSq8vDgstDMwiEBOJ4TApIQWmPfzIQBAlzG3YN2ahXB3d0PXrl1x9OhRq/U9PT0xcuRITJw4Eddccw2aNWumRbGJyAUs3X7W/HpS37Z4JjMd3t7ecHe3rfoaM2ZMhSBCz549zS0OOnbs6NDyEjVEkZGReO655zB37lx8+umnmD9/PpYtW4a77767wrqenp5o37492rdvX2HZ/pRsXPX2XwCUu4rHLuSifUSA08tPRA3b8h0pkFJ53SLEBxt2rLNpOGe1xYsXY8SIEXjwwQcxcuRIJkt0MgYRqF6Mj4/By78ehsEocS6nGNuTc5G6c505gODt7Y0xY8Zg0qRJuOqqqypkfSaipudsRgH+OZFhnp42uD38/f1t3n7Pnj345ZdfAAC9evUyBw46dOjg8LISNQZ+fn645557cNddd+Hw4cN2bx8XE4SuUYE4cC4HALB0ezLmjmHXICKqmpQSy7Ynm6cnJ7S0O4AgpcTrr7+O7t27O7p4VAUGEaheRAR4Y1jHcPxxSOnj9O22s9j1/juYMmUKJk6ciDFjxth1cUBEjZ/6pCI23A+9Wwbbtf2aNWswb948TJo0qdK7pkRUOTc3paVgbUzu0wJPrzwAQLm7+L+RneBebqg2IqIy209n4uSlfPP0xIQYu/chhGAAoZ4xiED1ZlJCC3MQ4Zd9adj4w0+ICGEzRyKqyGi0vjMxKaGl3U0T58yZ4+hiEVENxvWKwQurD6LUIHExtxgbjl7E8M7NtS4WEbmopdssdf3A2FC0UCVkJ9fF0DDVmyu6NEeIrwcAoFhvxO9HMjUuERG5qn9OpCPFNLSjTgAT4u2/M0FE9a+ZnyeuUAUN1BcIRERqBSV6rNp7zjw9uU8LDUtD9mAQgeqNp7sO43pZLgSWqRKmERGpqVshDO0YjuaB3hqWhojsob4Q+P3geWTml1SzNhE1Vb/sS0NesR4AEODljtFxURqXiGzFIALVK/WJxY4zWThmGvaRiKhMblEpVu9T35loqWFpiMheQzuGIzxAGVat1CCxYleKxiUiIlekbql0dc8o+Hi6aVgasgeDCFSv4qKD0CUq0DytvttIRAQAq/acQ1GpMtZzsK8HrugSoXGJiMge7m46TOhtaXm4lHU9EZVzNqMAf59IN09PSuANg4aEQQSqd5MTLK0Rlu9Iht5g1LA0RORq1Bcc43pGw8uddyaIGppJqrp+f2oODqTmaFgaInI13+2w1PXtwv0Q3ypYu8KQ3RhEoHp3be8YeLgpWdYv5BZj47FLGpeIiFzFiYt52H7aknSVXRmIGqYOzQPQUzUsK1seElGZiiMwtbB7BCbSFoMIVO/KZ25exszNRGSiPqnoHBmAuOjAatYmIlembnn4w64UlOjZ8pCIgH9OpiM50zIC08R4jsrQ0DCIQJpQN3Ncc+A8sgqYuZmoqTMYJZbvsCRgm9ynJe9MEDVgY3tGw9NdOdXMyC/B2kMXNC4REbkC9Q2DRI7A1CAxiECaGNYpHGH+SubmEoMRK3alalwiItLaxqMXkZZTBABw1wlc2yta4xIRUV0E+XhgVFykeZpDOxNRXrEeP+9NM0+rbyxSw8EgAmnC3U2HCfGWzM3sK0lE6uPA8M4RCDUFGomo4VJ3aVh3+CIu5hZrWBoi0tqqPakoLDUAUAKNI7o0r2ELckUMIpBm1JHHvSnZOJTGzM1ETVV2QSl+O3DePM2EikSNw6D2YYgKUpoqG4wSP+xMqWELImrMlqpyoY3rFQ1vD47A1BAxiECa6dg8AD1bBJmnlzLBIlGT9eNuS9K1MH9PDOsUrnGJiMgR3HTCKmna0u1nIaXUsEREpJWTl/KxTT0CUwJvGDRUDCKQpiap7jb+sDMFpQZmbiZqipaqujJc2ysGHm6snogai4mqlodHzudhT3K2hqUhIq2o86J0ah6AbjEcgamh4lkaaeqaHpbMzen5JVjHzM1ETc7htFyriwp2ZSBqXNqG+aFvmxDzNPMgETU9BqPEd9vVIzC14AhMDRiDCKSpIF8PjOxqSaiylCcWRE2O+s5EjxZB6BQZoGFpiMgZ1M2WV+xKQZEpsRoRNQ1/HbtkPQJT75gatiBXxiACaU5913HdoQu4lMfMzURNRanBiO9VidYmc6gnokYpqUcUfEwJ1HKK9FijSqRKRI2fugXS5Z0jzEO9U8PEIAJpbrAqc7OemZuJmpT1hy/iUl4JAMDTTYexPaM1LhEROYO/lzvGdI80T7PlIVHTkV1Qil/3p5mnJ/GGQYPHIAJpzk0nMCHe0qRp6bZkZm4maiLUXRmujGuOYF9PDUtDRM6k7tLw19GLSMsu0rA0RFRfftyTah6BKdTPE8M7R2hcIqorBhHIJaiHfzp8Phf7UnI0LA0R1Yf0vGL8cdCSTJVdGYgat/5tm6FlMx8AgFEC3+1gawSipkDdleHa3hyBqTHgf5BcQrtwf/RpbcncvFR1d5KIGqcfdqVCb1RaHTUP9MKQDuEal4iInEmnE5gUb2mNsGw7Wx4SNXZHz+di99ks8zS7MjQODCKQy5jcx3JQWbErlZmbiRoxKSWWbrMECyfEt4CbjkM9ETV26u6LJy/lY/vpTA1LQ0TOps5/0i0mEF2iAjUsDTkKgwjkMq7qEW3O3JxdWGrVzJmIGpf9qTk4lJZrnmZXBqKmoWUzXwyMDTVPL2OCRaJGq9RgxPId6hGYWlazNjUkDCKQy/D3cseYburMzezSQNRYqS8cElqHoF24v4alIaL6pG55+NOecygo0WtYGiJylg1HLpqHbvd002FcL47A1FgwiEAuZZLqxGLDEWZuJmqMivUG/LBLfWeCrRCImpLRcVEI8HIHAOQV6/HLvrQatiCihmjpNssNgyu7cgSmxsRd6wIQqQ1oG4oWIT5IziyEUQLLdyZj1rD2WheLiBzoj4MXkFVQCgDw9tDhqh5RGpeIiKpSUlKCF154AatWrYLRaITBYDA/2/I6Li4Oq1evhr+/pbWRj6cbru4ZhW+2KC0Ol25LxoR4BhOJGpOM/BL8cei8eVp9o7DM9u3bcc0116C4uBg6nQ5ubm5wc3Oz6bWXlxceffRRXHXVVfX5scjEpYIIQohBAB4DMACAJ4ADAN6RUn5u535uAfBpNasskVJeX9tykvPodAKTElrgjd+PAlCaPN81NBZCMOEaUWOh7sowplsUArw9NCwN1TfW9Q2Lp6cnnnzyScTGxuL+++9HRkaGzdu2bdsWS5YssQoglJmU0MIcRPj7RDrOZhSgZTNfh5WbiLT1w84UlBqU0VciArwwpH1YhXUSEhLw4Ycf4tprr4XBYHtC9T59+uC9995Dz549HVZeso/LdGcQQkwE8CeA0QD2APgFQAcAnwkhXq3lbncD+KySx591LjA5zUTV3YgTF/Ox40yWeVpKifz8fA1KRUSOcCGnCOsPW5Km1tSVYcGCBfjtt9+Qm5tb7XrUMLCub5iEELjppptw8OBBTJkyxeZt3nrrLURGRla6PL5VCNqF+5mnv9vBBItEjYn6hsGE+BZwd6v8snPkyJGYMWOGTfv08fHBq6++ir///psBBI25REsEIUQzAJ8AcAMwUUq53DS/OYC/AMwRQvwkpVxv565/kFI+5ciykvO1bOaLy9qF4u8T6QCAZdvPIqF1CADlpOTmm2/GuXPnMGzYMAwbNgwDBw6En59fdbskIhexfGcKjKZh4VuE+GBAu9Bq1/f398eoUaPg5uaG+Ph4JCYmYsiQIRg8eDBCQ6vfllwL6/qGLyIiAosXL8aNN96Iu+66CykpKVWuK6XE2LFj0aZNGyQlJWHMmDG4/PLLzfW1EErLw5d/OQxAueC4d3gH6DjUK1GDtz81GwfO5ZinJ5frypCamoqff/4Zq1evxpo1a2y6UTB8+HB89NFHiI2NdXh5yX6u0hJhOoBAACvKTioAQEp5HsBDpsk5WhSMtKE+2KzcfQ6FJZYmTs8//zy2bNmCF154ASNHjkRwcDAGDRqExx57DGvWrGFLBSIXJaXE0m2WUVcmxreo8YLh+uuvx2WXXQaDwYCtW7fitddew7XXXouwsDB0794ds2bNwuLFi6u9mCGXwbq+kRg7diwOHDiAu+66q8Z1T506hffeew9jx45FaGgoRo8ejbfeegvHjh3DhN4tUHYISM4sxD8n051cciKqD+qEivGtgtE6xBubNm3CY489ht69eyMmJgbTp0/H8uXLawwgBAUF4eOPP8bvv//OAIILcYmWCADKMmIsq2TZKgBFAEYIIbyllEzX3wSM7haJJ1bsR16xHnnFevy6Pw3X9o4BAMTGxuLmm2/GwoULAQB6vR6bN2/G5s2b8cILL8DDwwP9+vWzaqng68t+lkRa23U2C8cvWoJ8E+NjkJ+fj+zsbOTk5FT5qKrFwb59+7Bv3z68//77AJRjw5AhQ5CYmIjExES0a9eO+VRcC+v6RiQwMBDvvfcepk6diunTp+PIkSNWy9u1a4cTJ05YzSsuLsavv/6KX3/9Fffddx86dOiAsHGP4YKb0ld62fZkDIyt2G+aiBqOEr0RK1QjMGXt/AUREWORmZlZ5TY6nQ4tWrTAmTNnrOZPmDAB77zzDqKimIDZ1bhKEKGsU8uO8guklCVCiH0A+gDoCKUPpa0ShBCvQLnzkQZgrZSSfSQbAF9Pd1zVPQpLTHct739zMab/NA95eXkoLi6udtvS0lJs2rQJmzZtwvPPP28VVBg9ejQGDx5cHx+BiMpZquofqU85gLYR18BoNDps/8ePH8fx48exaNEixMXF4eGHH8a0adMYSHAdrOsboSFDhmD37t149tln8dJLL5mTo61atQpubm7mJsvr16+vUH8fPXoUvj99jPBxjwAAVu9JxTPjusHfy1VOT4nIXmsPnUemaQQmY2kR1n/+OmRJQYX1IiIiMGbMGCQlJeHKK6/Ehx9+iLlz5wIAIiMj8e6772LChAn1WnayneZHaSFEIIAg02RVWXWSoZxYtIZ9JxZXmx5lnhBC/Algiqn5pK1l3F/FIrapcaLJfVqYgwiI7Iz8gFYoTt9p9370ej28vLzQtm1bxMXFObiURGSLo+dz8Z0qiJC18xeHBhAAICoqCjfccAOmTZuGnj17MnjgQljXN27e3t54/vnnMXnyZNx+++3YsWMHdu/ejSlTpqBDhw649957kZ+fj/Xr12P16tVYtWoVTp8+DQAoOPovDIW5cPMJQJFe4q0/juLRpC4afyIiqo2iUgPmrzlqni448rc5gCCEQL9+/ZCUlISkpCTEx8dDp7P0rN+9ezcA4Pbbb8crr7yCkJCQ+i082UXzIAIA9bg/FcNUirL2rwE27vMcgKcArABwAoAPgH4AXgYwFMBPQogBUkrbxxKhepfQOgTdYgKxL0VJzBKadD/OfXIPjEW2ZWnv27cvbrjhBlx33XWIjo52ZlGJqBoleiPuW7wLxXolaGDIy0TBkU0V1vP29kZgYGCFh5QSK1eurHTffn5+mDhxIqZNm4bhw4fDzc3NqZ+Fao11fRPQq1cv/Pvvv5g/f36F7g1+fn646qqrcNVVV+Gdd97BoUOHsHr1aqxevRq79v6GgH4TAQALNp7A5Z0icFksE6cSNTSv/HoYh89bztPFsY2YOnUqkpKSMGrUKPx/e3ceHlV1/3H8fbIvJCQQtkCAhB0CAQkQVhfcACmKCiooVlAQbX9YtVpbrdZaW3drtSq4YG2rQAUVQUUWWRXZN1lD2AMkEBKyL/f3x0wmCVlIQpKZTD6v55lnuOfOvfney8mcm++955xmzZqVu+358+dZunQpV111VV2EKpfIWJZ16TsxZj5Q1bTxXZZlrTfGhAOFHWe8LcvKK2P/HwMTgAmWZf3nEuJsBGzE9qjkHZZl/be6+7Lvb2f37t2779xZ3s0LuVS7E1MZ/ffV5NqHc49r7ctTw8NZuHAhjz32WKnPd+nShTvuuIPbb7+dTp061XW4IlKGv329m3+uOOBYvr8HDGpfMlEQFBSEj49Pmdu/8sorPPxw0Xh7np6eXHvttUycOJExY8ZodpYL9OjRg127du2yLKtGH71SW6+2viqys7Px9fWt1GdPJp9l3KyNHDpr6+4Q3tiPxTOG0djfuzZDFJEatGZ/EhNm/ehYHhsdygu39cfLq3L3rKvynSG119ZXVk09iRAJdKniNoUj3Z2/oCy1jM8WXiFe0kThlmWdN8b8HfgHcB1wSRcWUvu6tgzmt9d35blFPwPww7FsdmUG8cknnzg+07p1a26//XbuuOMOevfurUeYRVzI+oNnePv7ogTChAFteeymnpXePj8/nzfeeAOA2NhYJk6cyG233UaLFi1qPFa5KLX1UmlV+WOgRdNQ3pzYjxvfXENegcXxc1n88fMdvHZbn1qMUERqyrmMXB6es9Wx3Kl5I/4yfgBeXpV/OlAJhPqlRpIIlmX1voRtU40x57D1lWwD7CrjY4Xz/R2q7s8pprCjjob5rCcmD4lk2e5TrIu3Tf30h8+2kZScztSpU7njjjsYMmRIiT5VIuIaUrNyeejTLRQ+8BYVFsjvR1XtRvamTZuYMGECEyZMoFs39ZN2JrX1UpuiWzfmoWs68+I3ewBYsOU4V3VrwS9i1B1RxJVZlsXvF2wnMdU2qY63p+G123rj563uhe7MVf7yKkxdXXbhCmOMNxCNbeqnvReur4bCUTrSK/yUuAwPD8PL42II8rPlvLLy4fLH3ufNt/7JsGHDlEAQcVFPf7GTYymZAHh5GF4d35sAn6rlrvv168ef//xnJRDcg9p6qdC0yzsQ265oMLU/zN/Ocft3iIi4ps+3HGfhthOO5Yev7UKP8MYVbCHuwFX++vrK/n5LGetuAPyA72po3uib7e+lppgS1xUe4s+fb4x2LG88nMI7Kw9UsIWIONOi7Sf4bFPRPNG/Ht6JmIgQ5wUkrkBtvVTI055sLJziMTUrj0fmbqWg4NLH7xKRmncsJZMnP9/hWO4f2YR7h0Y5MSKpK66SRJiFrX/kGGOMY0JQY0xzbKMsA7x84UbGmN32V+sLyn9njAm7oMzbGPNH4FYgE/igho9BatmY3q1LPNb46pK97Dh2zokRiUhZTqZm8cT87Y7lPm1DmH6FZskTtfVycRFNAvjj6O6O5bUHknl/zUEnRiQiZSkosHh4zhbSsmzj5Ab5evHKuBg8PTQ2WUPgEkkEy7LOAPcABcA8Y8wyY8xcYA/QEXjFsqwVZWzaxf66cPjevwBHjTGrjTH/NcZ8BSRgmwoqC5hoWdYxpN55dkw0rRr7AZCbbzHj0y1k5Wr2LhFXUVBg8cjcraRk5AIQ4OPJa+N74+XpEs2NOJHaeqmsW/q24foeLR3LL3yzh92JZY3FKSLOMmt1PD/En3Es/+nGHrQJDahgC3EnLnNVZ1nW/4BhwDdAH2AksB+427Kshyvatgx/AlYCEcAY4Cps81K/A/S2LOuzmopb6lbjAG9eHhdD4QQM+0+d56+Ldzs3KBFxmL0ugVX7khzLfxzdnXZNNQWj2Kitl8owxvCXsT1pHmQbrT0nr4AZn2whO083DURcwa7jqY5BUAFG9WrFjb1bV7CFuJuamuKxRliWtQYYUYXPl/m8jGVZf6yxoMTlDOoQxpQhkcxcZXu88cO1CVzVtTnDOjdzcmQiDdu+k2klknrXdm/BuNgIJ0YkrkhtvVRGk0AfXrw1hknvrwdgd2IaL3+7lydGapBVEWfKys1nxqebyc23jVXSMtiP526M1hTrDYzLPIkgUhWPXNeFri2DipbnbuVseo4TIxJp2HLyCvi/T7aQnVcAQFgjX54f21MXFSJSbZd3bsakge0cyzNXxbPuQLITIxKRF7/Zw96T5x3LL90aQ0iAjxMjEmdQEkHqJV8vT167rTc+9n7Wp9KyeWL+dixLIziLOMOr3+1l14miPssv3NKTpo18nRiRiLiDx0d0o0MzW5coy4KH52zhXGauk6MSaZjW7E/ivdVFA53+cnB7hnQKq2ALcVdKIki91bVlMI9e18WxvHhHIv/bpDG0ROraj/HJvP190ZSrE+PaclXXFk6MSETchb+PJ6/f1gcv+4jvx89l8VSxKeVEpG6kZOTw8JytjuXOLRrx2PVdnRiROJOSCFKvTR4SycCopo7lp7/YyZEzGU6MSKRhSc3K5TdztlL4EFBUWCC/H9m94o1ERKogunVjHrqms2P58y3H+WLrcSdGJNKwWJbFHxbsIDE1CwBvT8Nr4/vg5+3p5MjEWZREkHrNw8Pw8rgYgv1sY4Sez87jN3O2kF+gbg0ideHpL3ZyLCUTAC8Pw6vje+Pvo4sKEalZ0y7vQL/2oY7lP8zfznH7d4+I1K7Ptxxn4bYTjuWHr+1C9/BgJ0YkzqYkgtR74SH+PHtjtGP5p4SzvLPyQAVbiEhN+GrbCT4r1oXo18M7ERMR4ryARMRteXoYXhnXm0a+tpsGqVl5PDJ3KwW6aSBSq46ezeDJYl2I+kc24d6hUU6MSFyBkgjiFsb0bs0vYsIdy698u5cdx845MSIR95Z4Losn5m93LF/WNoTpV3RwYkQi4u4imgTwx9FF3aXWHkjm/TUHK9hCRC5FfoHFw3O2kpaVB0CQrxevjIvB00MzLzV0SiKI23h2TDStGvsBkFdgMePTLWTl5js5KhH3U1Bg8ei8rY4R0gN9PHl1fG+8PNWkiEjtuqVvG67v0dKx/MLXe9idmFrBFiJSXbNWxfPjwTOO5T/d2IM2oQFOjEhcha74xG00DvDm5XExFE5Lv//Uef66eLdzgxJxQ7PXJbBqX5Jj+anR3WnXNNCJEYlIQ2GM4S9je9I8yDaFbE5+ATM+2UJ2nm4aiNSkXcdTeenbPY7lUb1acWPv1k6MSFyJkgjiVgZ1CGPKkEjH8odrE/h+72knRiTiXvaeTCuRnLu2ewvGxUY4MSIRaWiaBPrw4q0xjuXdiWm8/O1eJ0Yk4l6ycvOZ8elmcvNtY460DPbjuRujMUbdGMRGSQRxO49c14WuLYMcy4/O3crZ9BwnRiTiHnLyCu/4FQAQ1siX58f21EWFiNS5yzs3Y9LAdo7lmaviWXsgqYItRKSyXvh6D3tPnncsv3RrDCEBPk6MSFyNkgjidny9PHnttt742Ptnn0rL5on527EsjeAscileWbKXXSeK+h6/eEsvmjbydWJEIuJOLMvitddeY9KkSbz44ot8/fXXHD16tNz2+/ER3ejQLNC+LTwyp2isFhGpntX7kkoMWHrP4EiGdAor87O5ubns2rWLOXPm8OSTT3Lrrbeydu3augpVnMjL2QGI1IauLYN59LouPLfoZwAW70jkf5uOcUvfNk6OTKR++jE+ucTUqRPj2nJl1+ZOjEhE3I0xhl//+tc8+OCD/Pa3v3WUh4SEEB0dTc+ePUu8h4aG8vptfbjxzTXkFVgcP5fFU5/v4PXb+jjxKETqr5SMHB6Zu9Wx3LlFI357fRcsy+Lw4cPs2LGD7du3O953795NTo7taV8fHx/mzJnDoEGDnBW+1CElEcRtTR4SybLdp1gXnwzA01/sZEBkEyKaaFRZkapIzcrlN3O2UngzMCoskN+P7F7xRiIi1eDh4cGbb75J48aN+etf/wpASkoKq1evZvXq1SU+27p1a6Kjo+naaxQ7PGzz1n++5ThXdW3OGA0AJ1IllmXx+wU7SEzNAsADi6b7FjL8iifYsWMHqanlz4ISGBjI559/zvDhw+sqXHEydWcQt+XhYXh5XAzBfrZc2fnsPB76dAv5BerWIFIVT3++k2MpmQB4eRheu603/j6eTo5KRNyVMYbnn3+e559/vsLPHTt2jG+++YavXppB9tGdjvI/LNjBcft3lohUzoItx/hq2wnHcvLyD/jkny+xdu3aChMIISEhLFmyRAmEBkZJBHFr4SH+PHtjtGN5w6GzvP39gQq2EJHivtp2gs82H3Ms/9/wTvRqE+K8gESkwXj88cd56623Ljp4a6uWLfjHxP408rXdNEjLyuPhOVsp0E0DkUo5ejaDpxYUJeIGRDbhd2MH4OlZ8Q2D5s2bs2LFCgYOHFjbIYqLURJB3N6Y3q35RUy4Y/nVJXvZcexcqc9lZmZy5MiRugxNxKUlnsviifnbHcuXtQ3h/is6lPjMli1bmDZtGh9++CG7d++moKCgrsMUETd2//3389FHH1X4x4yPjw/njsfzh5FdHGXr4pNLDA4nImXLL7B4eM5W0rLzAAjy9eKJ4W04k5yEt7d3udtFRESwatUqYmJiyv2MuC+NiSANwrNjotmQcIbj57LIK7D4v082s/BXQ0s8ku3n58f48eM5evQogwYNYvDgwQwePJhevXrh5aVfFWlYCgosHplbNNJ5oI8nr47vjZdnydxzTEwMCQkJvPPOO4DtscYBAwYQFxdHXFwc/fv3p0mTJnUev4i4j4kTJxIUFMS4ceMcg7gVd+jQISZPnkz7yEi63fMiP5/3A2zT1A3uGEa3VsF1HbJIvTFzVTw/HjzjWO6euZ1BMWPJyMgod5tOnTrx3Xff0bZt27oIUVyQ0bR31WeM2dm9e/fuO3fuvPiHxenWHkhiwqwfHYPDTRrYjmfGRJf4zMaNG+nXr1+J6aQCAwMZMGCAI7EQFxdHSEhIHUYuUvfeX32QPy3c5Vh+4eZejOsXUeZn9+3bR3R0dJkX9wBdunRxJBXi4uKIjo5WYq4W9ejRg127du2yLKuHs2NxB2rrXcfSpUsZM2YM6enpjjJjTIk228MviIj73gb/xgB0bRnEggcG4+etcVxELrTz+DlufHMNufm236GsvWs4Ob/kWCQX/o716tWLb7/9lhYtWtRprFKSs9t6XcVJgzGoQxhThkQyc5Xt8cbZ6w5xVbcWXN65Gbm5uZw9e5ZGjRoxfPhwvvvuO8d26enpLFu2jGXLlgG2L9MePXo4nlQYNGgQUVFRF+2zKVJf7D2Zxl+/3u1YHhbVmC4+Z1i+fD9JSUkkJSWRnJxc4t3Pz6/cJMKePXvYs2cPs2fPBiAgIIDY2Fji4uK477776NChQ5nbiYgUN3z4cJYsWcLIkSNJSUnBx8eHjRs38uyzzzJ37lwsy6IgK42TX75Mi3F/AmB3Yhovfv0zT46OvsjeRRqWrNx8fvXvjY4EQl5aEqcX/d2xPjg4mBkzZtClSxcmTJgAQFxcHIsWLSI0NNQpMYvrUBJBGpRHruvCqn1J7E5MA+CuN5dw9pPHSDt1tNL7sCyLHTt2sGPHDscj3D169OAf//gHV1xxRW2ELVJnzmfnMeOTLeTk2cY2yD9/ln/PuIN/ZZY/MnNVBQQE0LdvX+68804lEESkSgYOHMiKFSu49tprSUlJITo6mk8//ZQnn3zSkUzIOriJ1I1fEtx3NADvrU5gaOfmXNGluZOjF3ENlmXx1GdbiE8umsUk+atXKchOdyQPZsyYQWhoKIsXLwZsSbwFCxbQqFEjZ4UtLkQDK0qD4uvlyWu39cbH3q/b+Dcm+JY/4908qsr78vLyYsyYMXz22Wds2rRJCQSp946ezeCWf65l14mihEHS4tcpqIEEgoeHByNGjGDevHkcO3aMV155heho3RkUkaqLiYlh1apVJfpjFyYTtm3bxrhx4zj3/Wxyk+2DJRvDvR9tYM4GDZ4skpWbz2/mbGXO5kRHWepPC/A5e5CnnnqKhIQEnnnmmRJPG4wZM4aFCxcqgSAOehJBGpyuLYP53ciuPPOlrb+3V1AYLSe8QNLCl8jc9wNeXl7k5eWVu33v3r2ZNGkSd9xxB82b666GuIdNh89y30cbSDpf1CUhdcMXZMVvAGzdeEJDQ2natClhYWGl3r/++mu+//77UvuNiorinnvuYdKkSbRp06bOjkdE3Fvnzp1ZsWJFqfLCZMKOHTt4/G9vsiO/JXh6k5tv8dt52zhw+jyPXdcVDw91QZSGJ+l8NlP/tZGNh846yvKTDjF9cGsenpdQZjeFyy67jLlz51Y4U4M0PBpY8RJosKX67aN1CTz9+U4KJ6QzwG+u7kDGxi94/PHHSny2WbNmTJw4kUmTJmkqG3E7n285xqPztjm6MACM6RzALZ29aRYWRlhYGKGhoeVOsZaXl0dkZCRHj9q6Bfn5+XHLLbcwefJkhg0bhoeHHnqrS84ebMndqK2v39buTeTXc7aXSJBe070Fr43vTaCv7qVJw7EnMY3Js3/i6NmiLgxxUU145eYehDfVDCb1jbPben17SoN118D2tGsayIP/3kRadh4W8PJ3ByA+FTy98PYwjB49mkmTJjFixAhlYMXtFBRYvLZ0H39fus9R5u1peO6mnoyLLXsmhrIsWrSIo0ePEhsby+TJk7nttts0g4mIuIRBnVuy4IFgJn+4gT0nbeMhLdl1klvfXsesSbGEh/g7OUKR2rd89yl+9d/NnM8uetJ2fGwEz94YjY+XEv1SdUoiSIN2eedmfDZ9EJNnb+DwGft8uFEDGfTEf5k9ZTAd27ZyboAitSQrN5+H527lq20nHGUhAd68PbEvcVFNq7Sv/Px8tm7dSq9evWo6TBGRS9YmNID/TR/Er/+7mWW7TwGw60QqY95cw6y7YomJCHFugCK1xLIsPliTwJ+/2kWB/eFzY+CJEd2YMjRSM4tJtSn1JA1epxa2OaT7t2/iKDuW4889n+xm/6k0J0YmUjtOpWYx/p11JRIIHZoF8vkDg6ucQAC46aablEAQEZfWyNeLmXfFMmVIpKPsdFo2495Zx8Jtx50YmUjtyM0v4PcLdvCnhUUJhAAfT2beGcu9wzQ1uVwaJRFEgCaBPvxrSn9uvqxo4LfDZzK46a21rNx72omRidSsncfPMebNNWw9es5RNrRTGJ9NH0y7poFOjExEpHZ5ehj+cEN3nh/bEy/7wIrZeQU8+J/N/H3pPjROmLiLcxm53P3Bev7z42FHWXhjP+ZNG8TV3Vs4MTJxF0oiiNj5enny0q29eHxEVwqTs2lZefzyw5/4aF2CU2MTqQnf7kzk1rfXceJclqPszrh2fHB3Pxr7a8wPEWkYbu/flo/u6V/ie++VJXuZ8ekWsnLznRiZyKU7mJTOTW+tYc3+ZEdZ74gQFjw4mO7hGkBRaoaSCCLFGGOYdnkH/jmhL/7etpHo8wssnvp8J3/8fAd5+QUX2YOI67Esi7e/P8DUjzeSkWO7QPYw8MwvevDsjdF4eaopEJGGZVDHMOZPH0RkWNETWJ9vOc4dM3/gdFq2EyMTqb51B5K58c01xCelO8pGx4TzyX1xNA/yc2Jk4m505ShShuujWzJ32kBaBhd94c5ed4h7Zm8gNSvXiZGJVE1OXgG/nbeNvy7eTeGTukG+Xrx/dz8mDWrv1NhERJwpqlkj5k8fxMBiY8FsOpzCjW+uYXdiqhMjE6m6T9Yf5s73fuRcZtF16oyrO/H323rj5132FM0i1aUkgkg5ols35vMHB9OrTWNH2cq9pxn71loOJ2c4MTKRyjmTnsPE935k7sajjrKIJv58Nn0QV3Rp7sTIRERcQ0iADx9N7s/t/YumtT2WksnNb61l2e6TToxMpHLyCyye+2oXj3+2nTz7CIq+Xh68cXsfZlzdWQMoSq1QEkGkAi2C/fj0voGM6lk01eP+U+cZ8+Zq1h8848TIRCq2/1QaN765pkQ97dc+lAXTB9OpRZATIxMRcS3enh785aae/GFUN8eYSOk5+UyZvYFZq+I14KK4rPPZedz30QZmrjroKAtr5Msn98UxOibciZGJu1MSQeQi/H08eeP2Pvz6qo6OsrMZuUyY9QNzNxxxYmQiZVu17zQ3vbWWw2eKnpgZe1lrPp4ygKaNfJ0YmYiIazLGMGVoFO9NiiXQx/bod4EFf/7qZ3732XZyNSaSuBjbEzNrWLr7lKOsW6tgPn9wMH3ahjoxMmkIlEQQqQQPD8Nvru3Ca+N742MfhC433+LRedv429e7KSjQXQpxDf9al8DdH/xEWlaeo+y313fh5Vtj8PVSn0gRkYpc1bUF/5s+iNYh/o6yT346woi/LiQpVV0ZxTWs2HGIq//2DXtOnneUXd2tBfOmDSxRd0Vqi5IIIlVwY5/W/Pe+OMIa+TjK/rniAPf/eyMZOXkVbClSu/LyC3j6i508+flO8u1JLX9vT96eeBnTr+ioPpEiIpXUtWUwCx4YTJ+2IY6y/WmexP7uU55++S3S0tKcF5w0aAcOHGDsjOeY9OEmMq2iKUqnDovinTv7Eujr5cTopCFREkGkivq2C2X+9MF0Kdav/JudJ7n17XWcOJfpxMikoUrNyuWe2Rv4cG2Co6xFsC9zpw3k+uhW5W8oIiJlahbky3/vjWNM72L9yoOa897hJkQOuI7HHnuMo0ePlr8DkRq0du1axt58M7F3/5FNfr0xXrabWR4GXri5F78b2Q1PD90skLqjJIJINUQ0CWDe/QO5qmvRCPc7j6cy5h9r2HY0xXmBSYNzODmDm99ay8q9px1lPVs35osHhxDdunEFW4qISEX8vD15bXxvHhja1lHm6R9E4KjHeOubrURGRnLnnXeyZcsW5wUpbisvL4+5c+cycOBAhlx+JavyOtJ48O2O9V752fzn3jjG9YuoYC8itUNJBJFqCvLzZuZdsUweEukoO5WWzbh31rFo+wknRiYNxfqDZ7jxrTXsO1XUJ3Jkz5bMmTqQFsF+ToxMRMQ9GGN4dFRPJkZmU5CbbSvz9KLp9b8iaNjdfPzv/9CnTx+GDx/OokWLKCjQAIxyadLS0nj99dfp3Lkz48aN46fte2hx+/MEdhvm+Ex+ynE+mdKXuKimToxUGjIlEUQugaeH4ckbuvOXm3riZX+MLCu3gOn/3sQbS/dpWiipNfM2HmXCrB84k57jKHvwyo784/bL8PfRAIoiIjXp2ftuovORr8g7XzRtbnC/G2k29g8YH3+WLVvGqFGjiI6OZtasWWRlZTkxWqmPjh07xmOPPUZERAQzZszg4MGDeDePpOVdr+Ab3sXxucyEzTze14vYLu2cGK00dEoiiNSAOwa05aN7+hPsVzSgzctL9vLQp1vIys13YmTibgoKLP729W4embuV3HxbksrH04OH4kKZPjQCD/WJFBGpccYYPnj5adL+9yQ5Jw84ygM69qflhBfwDG7m+Fx2djY5OTnl7UqkTJmZmeTn5+PhYfvzzN9et7zsdQsgbdNXdDu1nOlT7nZSlCI2SiKI1JBBHcNY8MBgIsMCHWULthxnwqwfSTqfXe52R48eZfz48bzwwgusWLFCoz5LuTJy8rj/3xv554qiC9imgT78594BZO5eSXBwMDExMUyePJl//vOf/PTTT2Rnl1/3RESk8iIiIvjzEw+T+O/HyNi7zlHu0zySVne9wp0P/ZEdO3bwwAMPEBwc7MRIpT7q2LEjL730EgkJCXT+xXSajf0DHj626RqtgnzOLHmb9JXvM/OdtzXjkjid0ePW1WeM2dm9e/fuO3fudHYo4kJSMnK4/+NNrItPdpS1DvHn/bv70aVlUJnbPPTQQ7z22muA7S5G9+7d6d+/PwMGDKB///5ER0fj7e1d5rbSMCSey2Ly7J/YeTzVUda5RSPem9SPiCYB5OTk0KdPH3bt2lViO29vb3r27ElsbKzjpfrk3nr06MGuXbt2WZbVw9mxuAO19VJcfn4+gwYNYv36nwi5fBKN425xrLPycrg25DTv/v5e/ZEn1XIm5RxX/fZdUpp0d5QVZGdw+ou/kRW/keeee44nnnjCiRGKq3B2W68kwiXQhYWUJze/gKc+38F/1x9xlDXy9eKN2/twZbEZHQqlpqbStWtXTpwoe0BGPz8/LrvsMkdSoX///kRGRuoipYHYdjSFKbM3cCqt6KmCK7o0443b+xDg7UFSUhInT55k/vz5PP300xfdn6+vLzExMSUSC927d8fTU2MpuANnX1i4G7X1cqFt27bRt29f8vLyCIweTtPrH8R4FiVmO2bvY9HfHsDHR8laqbxd+w/xixe+JK9J0YDdeedOcmreM+QmHSY6OpqNGzfi4+PjxCjFVTi7rfe6+EdEpKq8PT34y0096dCsEc8t+hnLgvPZeUye/RMjW2XRmeMkJZ3m9Gnb69SpUxU+dp6VlcXatWtZu3atoywsLIxBgwbx1FNP0bdv37o4LHGCBRsP8ei87eRaRQmj0FOb2fzNZ3T63XFOnz5d5dHAs7OzWb9+PRs3buTEiROEh4fTo4f+3hQRqYxevXrx6KOP8vzzzxOUtJM/X92CPyw+hPGzPW2437cTsb9+i6XP302zUE21Kxe3aNVG7v9kG6ZYAsH//HGeu6EdN799GGMMM2fOVAJBXIaSCCK1xBjDlKFRRIYF8uv/biY9J58CCxYe9yM7sYDU9SvJ2LMaCqo+8GJUVBRTpkxh0qRJhIeH10L04kwFBRbf7z3Nuyvj7d1ibAkEqyCfM9/+k0Nbv76k/bdt25Z7772Xe+65R/VHRKQannzySebOnUu/fv2487qBdAwPY8I7qyloZHvaMDWkI9f9fR2Th3VkwoC2hATojz8pbe/JNN5dGc9nG09ggoqeVG2VfZglL96Dn7cnQUFBTJo0ibi4OCdGKlKSkggitWx4txbMu38QU2Zv4FhKJgC+LTvS7BePkpc6idQNX3B+6zdYOZkV7sfHx4exY8cyZcoUrrzySsfoveI+svPy+XzzcWauimffqfMl1uVnnSdpwfNkHdpa7vZhYWGkpKSQl5dXap2Hhwc33HADU6dO5brrrlPXBRGRS+Dv788777xDfHw8AAN7duL7J5tw3TOfkhFsm3rvTGY+L36zhzeX72dcbASTh0QS0STAmWGLC7Asi3UHknl3VTwr9py2lxY9bdjfL5FP/jLVcZ13xx138Je//MUJkYqUT2MiXAL1k5SqOJ2WzeP/28bS3adKrfM1+TRP28e62c+Tfz65xLru3btz7733MnHiRMLCwuoqXKlD5zJy+fjHQ3y4NoHTaaW7tfilnyDswGLahvjSokULWrZsWeK9RYsWNGvWjOTkZCIiIkokEdq0acOUKVOYPHkybdq0qcvDEidxdj9Jd6O2XiqSk5NT4hHzzKxsHvv3Gr4+mE1OXsmuZh4GRvRsxX1Do4iJCKmRn79582Zat25N8+alx1uSS7d8+XIGDx5cI90IcvMLWLT9BO+ujC8xSHKhlsF+3NbZgxm3XFmi/MI6JgLOb+v1JIJIHWkW5Mt7d/fj5xOpzFp1kC+2HiM335bEy7Y8OdKoK62nvUf6ru/J2b6YW68ZxJQpU4iLi9MAim7qyJkM3lt9kDkbjpCRU7pby9XdWjD18ihi24VizJSL7u+jjz4iLy8PYwwjR45k6tSpjBgxAi8vfdWLiNSGC/+48/fz5e+TryLpfDYfrTvEv9YlcDYjF4ACC77adoKvtp2gf2QTpg6L4souzfHwqH4bHxgYyPDhw1m2bBnNmjW7pGORkpYuXcpjjz3Ghg0bLmk/57Pz+GT9YT5Yk+B4IrW4bq2CuW9YJKN6huPjVfopUyUQxBXpylKkjnVrFczL42J49LoufLD2IP/54TBp2bY7x8bTi0Y9h0PP4eR2bkZ+WJSTo5XasO1oCu+sjGfx9hMUXPAwmI+XBzdf1oYpQyPp0KxRpfdpWRaLFy/mySefZMqUKbRt27aGoxYRkcoKa+TLb67pzP2Xd2DepqO8tyqehOQMx/r1B8+w/uAZOjQL5N6hUdzYpzV+3lXvZtaxY0cOHz7MVVddpURCDVq2bBmjR4/m1ltvrfY+Es9l2a7zfjxMWlbpboZDO4Vx37AohnQM080iqXeURBBxkpaN/fjdiG48eGVHXpi3msXx2SRlFN2NXrn3NCv3nnZkqG/oFY63p8ZBqK8KCiyW7znFuyvj+fHgmVLrQwO8uXNge+4a2I6wRr7V2H8B3377Ld7emlJMRMRV+Pt4cmdcO+7o35Ylu07y7soDbDqc4lh/4HQ6j3+2nZe+3cOkge2ZGNeO0MDK33n28PCgb9++LF++nOHDh7N06VIlEi7RsmXLuOGGG8jMzCQ2NrbK2+9OTGXmypJPnBby8jD8onc49w6Nolur4JoKWaTOKYkg4mRBft48O/FKniqnr9zPJ1J56NOtvPD1Hu4ZHMlt/SMI8tMfivVFVm4+CzYfY+aqeA6cTi+1vl3TAKYMieSWvhH4+1R/sENPT08Nligi4qI8PQzXR7fk+uiWbDx0hndXxvPtrpMUDk2WdD6Hl5fs5a0VBxgX24bJQ6Jo27RygzDGxsayfPlytm/f7uja4KpjKFmW5dJ33ZcvX+5IIACVTiJYlsWa/bbBElfuPV1qfZCvF3cMaMvdg9vTqrF/jcYs4gwaWPESaLAlqQ1lj9pbJMjXi9sHtOXuQe0JD1FD5KrOpufw7x8P8eHaQySdLz1YYp+2IUwdFsU13VvieQn9YUUu5OzBltyN2nqpLQeT0nlvdTxzNxwlu4xBGK+Pbsm9Q6Po0za0wv3MmTOH8ePHO5Z79erF0qVLXTKR8MUXX3DVVVfRqFHlu+vVlRUrVjBy5EhHAsHT05PU1FQCAspP5uTmF/DVNtsNoF0nSg+WGN7Yj3uGRDK+n24ASc1ydluvJxFEXIwxhkEdwxjUMYw9iWnMWhXPgi1Fj8SlZefx7sp43l99kNExtkfiuofrkThXcTg5g/dWxzNnw1Eyc0sOlmgMXNOtBfcNiyK2fRMnRSgiIq4gMiyQP9/Yk4eu7sy/fjjER+sOcSY9B7ANwrhoeyKLtifSv30T7h0WxfCuZQ/CeOHd8m3btnH11VezdOlSmjZtWifHUlnz5s0jPz+fm266ydmhlPD9998zatQoRwIBbH+klZdASMvK5ZP1R3h/zUFOnMsqtb57q2CmXh7FyJ6t1BVV3JKSCCIurEvLIF68NYZHruvCh2sT+PiHQ47BefIKLOZvPsb8zccY2imMe4dGMbSTBudxli1HUpi5Mp7FO0oPlujr5cEtfdsweUgkUVUYLFFERNxf00a+zLi6M9Mu78D/Nh1l1qqDHEwq6v62PuEM6xPOEBUWyJShUYy9rOQgjJGRkYSGhnL27FlH2datW7n66qv57rvvXCaRkJ+fz6JFi/Dy8nKpJMLKlSsZOXIkGRkZJcrL6spw4lwmH6xJ4L8/Fg2KXdzlnZtx37AoBnVoqusxcWtKIojUAy2C/Xjs+q48cGVH5vx0hPdWHywxTdCqfUms2pdE15ZB3Ds0itExZU8TJDWroMBi6e5TzFwZz/qE0oMlNgn04c64dtw1sB1NqzFYooiINBx+3p5MGNCO2/u15bufT/Luyng2HCpKDMQnpfPE/O28/O0eJg2yDcLYJNAHYwyxsbEsWbKkxP62bNnCNddcw3fffUeTJs5/+m3dunUkJyfz1VdfUVBQgIeH869TVq1aVWYCAUomEXYdT2XWqni+2HqcvAvuFHh7Gsb0bs2UoZF0baknQ6VhUBJBpB5p5OvFPUMiuWtgOxbtSOTdlQfYcayoD97uxDQenruVF7/Zwy8Ht+f2AW0JrkIfvB07drBhwwZiY2Pp2rUrXl76iihLVm4+/1m7nxe/2ESmd+kLhvZNA5gyNIqbL2tzSYMliohIw+PhYbi2R0uu7dGSjYfOMmtVPF/vTHQMwpicnsMrS/by1or93No3gslDIstMIgBs3rzZ8USCsxMJX375JQCnTp1i/fr1xMXFOTWeVatWMWLECNLTSw96DNC3b19W7j3NzFXxrNqXVGp9kJ8XEwa04+5B7WnZ2K+2wxVxKfoLQaQe8vL04Bcx4Yzu1Yof4s8wc1U8y3afcqxPTM3i+cW7eWPZfm7rF8Evh0TSuhKDMHbu3Jnx48eza9cu/P396d27N3379nW8unXr1qATC2fTc+z9VhNIOp8DFyQQCk7uo23mPgZ5hhJw/CyJLQpo3769HmkUEZFq6dsulL7t+pKQlM77aw4yZ8MRsnJtgzBm5Rbwrx8O8fGPh4gOicMnvAs5x/eU2sfmzZu55pprWLJkiVMTCQsXLizxb2cmEVavXl1+AsHDi+DoK3hyTSZ7Tq4vtbp1iL9jsMRGvg33mkgaNs3OcAk0YrO4kn0n05i5Kp4Fm4+Tk19ylGdPD8PoXq2YMjSK6NaNK9zP6tWrGTp0aJnr/P39iYmJITY2tkElFg4lp/Pe6pIXbw6WRfretaT9NJ/sY7tLbRsSEsJll13mePXp04dOnTppOkapNc4esdndqK0XV3ImPYePfzjE7LUJJNsHYSwu6+hOUtfPJ3Pfj4DtGt/b2xtfX18GDx7M/Pnz8fev+5md4uPj6dChg2O5V69ebN26tc7jANtTl6NGjSIpKYmsrCwKCmztuvEJIKj3dQTFjsErqPTMFtGtg7l3aBSjerbCS4MlipM5u61XEuES6MJCXNGp1Cxmr0vg4x8Ocy4zt9T6wR2bcu/QKC7v3Izc3FxOnTpFYmIiJ06cIDExkcTERN566y0SExMr9fOKJxYeeOABunbtWtOH5DSbDp/l7eX7WPLzaS78pvSw8ghK2knymrkc27OlSvuNiorijTfeYOTIkTUWq0ghZ19YuBu19eKKsnLzmb/5GDNXxRN/uvTd9Nwzx0hdPx/vY5uI37eHkJCQug+ymNdff50ZM2aUKEtISKBdu3bOCcjuyy+/5KYJ9xAU+wuCYq7Hw7f0bAxXdmnGvcOiGBilwRLFdTi7rXeJ24fGmEBgLNDf/uoN+ADPWJb19CXsdzTwCNDHXrQJeNGyrK8uJV4RV9Y82I9Hr+vK9Cs6MnfDEWatPsjRs0WDMK7Zn8ya/ckUnEskM/EAeWeOk3v2OHlnj5N79hgF6SlV+nm+vr4MGDCAqVOn1tsEwtn0HA4mp5OQlE5CcgYJSen8fDyFfadLD7SUn55C2qaFpG1eREFm6TmhKzJ06FCmT5/O2LFj8fHxqanwReoFtfUiNcfP25Pb+7dlfGxEmQP8ejdpTdPrHyQ/4xwj/vol1w26jMiwQNqHBRLZNJDWof54ljFdZG0pHA+huIULF/LAAw/UWQyZOfkkJKdzKDmdg0kZHDx9nnnfJtB66iyMZ8k/iTywuLlvBPcOi6Jzi6A6i1GkvnCJJALQCfioJndojJkBvArkAd8B2cC1wEJjzK8sy/pHTf48EVcT6OvF3YMjmRjXjq93JvLuyni2HT3nWO/RuCWBjVuW2q4gO8ORVLAlFuzvZ46X+KN5wIABTJs2jXHjxpU7j3JNWbx4MREREZc02OO5zFx7kiCdg0m2hMFBe8KgrCc2LpSbfJTUn+aTvnM5Vl7pR0jLExQUxF133cW0adOIjo6uVuwibkJtvUgN8/AwXNO9Bdd0b8H9f/gb/9uRQmDXIY6n5zwDGnMC+HBtQontvD0NEU0CiGxqSywUJhfahwUQ3tgfjxpMMJw7d47vv/++VPmXX35Z40mErNx8Dp/JcLTzRW1+BompWaU3aBpF8SP1Jo+kdZ8x7/lfMXxQTI3GJuJOXCWJkAa8B/xkf40C/lTdnRljugAvYbuYuNKyrHX28s7AWuBVY8zXlmXtv9TARVydl6cHN/QKZ1TPVqw/aBuE8bufT5X7eQ/fAHxbdsS3ZcdS6wqy0wnxzCUmqhV9OrUhuGkAu5OyiWzqRWhg7d1ZP3XqFCNHjsTPz49evXqVGF8gOjoaPz/bqMhpWbkcSs4oliQoerrgTBl9Rysj68hOUtd/Bse2Ex7eilZx/QkPD6dVq1aEh4eTkZHBM888U2q7Xr16MX36dO644w6CgnQXQwS19SK1akT/bjTz2MCU/7uSN5f+zIKtJ8nOL7vbcm6+Rfzp9DK7Qvh4edCuSYAtudA0oFiCIZCWwX5VTjB8++235OXllSpfvnw558+fp1GjRlXaX05eAYfPZJRMEiTbEgXHz2VSnZ7aYf6GB67uxo29WnDD9S8wNLZX1Xci0oC4RBLBsqwDwJTCZWPMtZe4y/8DPIF/FF5U2H/OXmPMc8Ar9s/86hJ/jki9YYxhQFRTBkQ15VByOgtWbeFUJpzN9eJ4Wi4JyRmkZFR8R97DN5BUYNXhTFYd3ldiXWN/b/uFhv2CIyyQ9vaLjsb+lZ9msix33XUXH330EcuWLeOnzdvYnHCaj5Zvxyt0CT5N2xAc3gGPxi3J9az+FEuNfL1oHxZA+6ZFsVtnj9Cj9WjCw6cSHBxcZl/I3//+945/+/j4cOuttzJ9+nQGDhyovpMixaitF6ldV1xxBSNGjMDb25u/jevLEzfk8uPBZPsf2kV/dJ84V8Yd+WJy8grYd+o8+06dL7XOz9uDdk1sTywUTy5EhgXSPMi3zHavrK4MADk5OSxZsoSbbrqp1Lrc/AKOnMkoFXtCcjrHzmZSUM0h3Xw8PYho4l/iGqVDs0b0ax/qGCzxyy+/VJdDkYtwiSRCLRhlf59Xxrp52C4sRqMLC2mg2jUN5P9uHFyqPCUjh/U/J3Dz3ffj27QNUTEDCGoVxeksQ2pW6bsIxZ3LzGXrkRS2Hkkpta5JoE+puxmFfTPLmh4pMyef/SdT2LL/OLuOJBF/Oo1zfX9J666T8ApqWurz+fbXxQT4eNKuaSCR9mRB8WRHWCOfMi5+2lS4v/z8fGbPnk1kZCTTpk3jl7/8Jc2aNatEJCJSA9TWixQTHFxy2uHGAd5c26N0t8XMnHwOnbHduU+wP7FXeDf/ZGp2hT8jK7eAPSfT2HMyrdS6strYdqH+LF6+uuydGQ8+XbSM0O6DHU8NFsZx9Gwm+dXMFHh52LpqtL/gpkZkWCDhIRcfC8KZ02CK1Bdul0QwxoQAbe2Lmy9cb1nWEWNMEtDOGBNsWVbVRkYTcWMhAT6kHtzGs5NHc9dddzkaUsuyOJuRW7qPof3xwfPZFScYzqTncCY9h02HU0qtC2vkS/umAeSmnGTf0ZNkegVh+Ydc8ClP8AjFqxK9Agpys8g7ewL/vPP07RLBiKGxdG8TRmRYIM3KuUtSXSdOnGDmzJlcd911eHhouieRuqK2XqT6/H086doymK4tg0uty8jJcyQXSrb5GSSdrzjBkJGTz88nUvn5RMlft8AJbxCYm4lJT+b8iXiMtx/BrTuQ69OYHzy9+OGDn6p8DJ4ehjah/sWeHixKGLQO8dcUjCK1zO2SCBRdVJy1LKt0Ry+bo0AY0A7YfrEdGmPKm9epQznlIvXWLbfcUqrMGEOTQB+aBPrQt11oiXWWZZF0PqfUBUfhRUhGTsXPCCSdz7ZfmPhAUESlYrTycshNOXHBzBLHsVJPMebay3lg+nSGDRtW690J2rRpQ5s2FT+tICK1Qm29SC0I8PGie3gw3cNLJxiKjztUOMNB4ZMMyRcbd8jbHyukDYEhtjYzD7hYC+1hIDykZNeDwqcc2oQG4OOlRIGIs7hjEqFwdJbSc7MVKbzg0GhnIpfIGEOzIF+aBfnSr33JRwAty+J0WrbjqYUL+zVm5RaUu18rP5e8lETyUxLxy0sjxCObQ7s2knb8APmpSUDRY45t2rRh6tSpTJ48mVatWtXWoYqI61BbL1LHgvy8iW7dmOjWjUutO5eZa08spJd8kiE5vcLxloyB8Mb+pcYkah8WSEQTf3y9PGvzkESkmmokiWCMmQ90q+Jmd1mWtb4mfn5tsyyrR1nl9rsW3es4HJF6wxhD82A/mgf7MSCq5FgGBQUWJ9OyHBcc2w8c4fDenUQ1a0S3iDB6tG9LRJthhIaGYowhMTGRNm3akJ9f9GTDtddey/33388NN9xQ7akfRaRy1NaLSHka+3vTq00IvdqElFqXkpHjSCgcTs7Ez9vD0fWgbZMA/LyVKBCpb2rqqjsS6FLFbWprYvnCoWQr2n+g/b30qDAiUic8PAytGvvTqrE/gzoAA9oCpQd7LPTxxx+Tn59PaGgov/zlL5k2bRqdOnWqs3hFRG29iFRdSIAPfdr60Kdt6MU/LCL1Qo0kESzL6l0T+6khh+3vocaYwHL6ShZ2Yj5URzGJyCWwLIudO3fywQcfMH78ePz9/Z0dkkiDo7ZeREREwA3HRLAsK8UYcxjboEt9gBLzyhhjIrANtHRIozWL1B8ffPCBs0MQERehtl5ERMR53HVY06/s76WHmS8q+7KOYhGRS1TbsyyISL2ktl5ERMQJ6nUSwRiz2/5qfcGq14F8YJoxJq7Y5zsBv8c2s8zrdRepiIiIVIfaehEREdfiMt0Z7KM+F87NFm5/n2KMud7+7xOWZd10wWaFAzx5Fy+0LGuPMeZR4BVglTFmCZADXAv4A7+2LGt/TR+DiIiIlE9tvYiISP3nMkkEbH0a211Q1tr+gioOjGRZ1qvGmP3Ao8BQe/EG4AXLshZeSqAiIiJSLWrrRURE6jmXSSJYltW+GttU2FHasqwvUX9IERERl6C2XkREpP6r12MiiIiIiIiIiEjdURJBRERERERERCpFSQQRERERERERqRQlEURERERERESkUoxlWc6Ood4yxqT6+voGdejQwdmhiIiIAHDgwAGys7PTLMsKdnYs7kBtvYiIuBpnt/VKIlwCY0wutqc5djs7FhdUeLV1wKlRuB6dl/Lp3JRN56VsOi/l6woUWJbl7exA3IHa+grp97BsOi/l07kpm85L+XRuyubUtt5lpnisp/YCWJbVw9mBuBpjzE7QubmQzkv5dG7KpvNSNp2X8hWeG6kxauvLod/Dsum8lE/npmw6L+XTuSmbs9t6jYkgIiIiIiIiIpWiJIKIiIiIiIiIVIqSCCIiIiIiIiJSKUoiiIiIiIiIiEilKIkgIiIiIiIiIpWiKR5FREREREREpFL0JIKIiIiIiIiIVIqSCCIiIiIiIiJSKUoiiIiIiIiIiEilKIkgIiIiIiIiIpWiJIKIiIiIiIiIVIqSCCIiIiIiIiJSKUoiiIiIiIiIiEilKIkgIiIiIiIiIpWiJEIlGGMCjTF3GmPeMMb8aIzJNsZYxpinq7m/u+3bl/f6pIYPodbU9Lkptt/RxpjvjTGp9tcKY8yoGgq7zhhjBhtjFhljzhhjzhtj1htj7qrGfupVnTHG+Btj/mSM2WuMyTLGHDfGvG+MaV2NfYUaY143xhyy169DxpjXjDEhtRB6raupc2OMSbhInehaW8dQ04wxfY0xjxtjPjPGHC08hkvYn9vUmZo8N+5UZ2qD2vryqa2vWENt60HtfXnU1pdN7X3Z6mNb71UTO2kAOgEf1cJ+twJbyij/sRZ+Vm2p8XNjjJkBvArkAd8B2cC1wEJjzK8sy/pHTf682mKMuRn4FFuybiWQBAwHZhtjelmW9Ug1duvydcYY4wcsA+KAE8DnQHvgl8ANxpg4y7LiK7mvMGAd0BGIBxYAPYD/A0YYYwZalnWmpo+httTkuSlmdjnl56obpxM8CYypiR25W52hBs9NMe5QZ2qD2vryqa0vR0Nt60HtfXnU1ldI7X3Z6l9bb1mWXhd5AR2AWcBU4DJs/9EW8HQ193f3pWzvSq9aODddsF1QZAEDi5V3xtYw5wIdnX3clTiOJvZfUgsYW6y8BbDPXn6FO9YZ4M/2WNcCjYqV/8ZevqIK+/rYvs3/AK9i5X+3l3/o7ON14rlJsH2FO/+4auC8PAb8CRgNtLT//lfr2NywztTkuXGbOlNL51ptfd2dG7X1blBn1N7XyXlxq+9ttfd1cl7qpM44/aTVxxfwuC4sau3cvGXf/rUy1j1kX/eGs4+zEsfxW3usC8pYd5N93ZfuVmcAHyDFHmufMtZvta/rW4l9tQLysd2danHBOl/gFLaL0ObOPu66Pjf2z7vVhcUFx1atxtPd6kxNnhvLzetMLZ1rtfW1d27U1tfzOqP2vvbPi/3zbv29rfa+Zs+LVYd1RmMiiKsp7As5r4x1hWWj6yiWS1HRcXyF7cvhavsjb+5kMNAYOGBZ1uYy1lfl//B6bI+HrrIs62TxFZZlZQNfAp7AyOqHW6dq8txI2dytzoi4K7X19Z/a+7Kpra8b7lRn6iWNieBcfY0xLwLBQCKwzLKs750ck9PYB0Fpa18s9cVrWdYRY0wS0M4YE2xZVmpdxldFMfb3TReusCwrxxizA4jF9ujmtirs19XrTLnHfUF5rxra1z2V3JcrqMlz42CMeRTbo8bZwE5gvmVZp6sVYf3nbnWmVqjO1DlX/96uU2rrK6U+1Bm192VTW1833KnO1IrarjNKIjjXDfZXoaeMMd8D4y/MqjUQhRcVZy3LSi/nM0eBMKAdsL1OoqoiY0wwtiw02OIty1FsFxbtqNqFhavXmcL/w4qOG2zHXZf7cgW1dTwvXLD8qn1QsveruB934G51praoztQtV//ermtq6y+uPtQZtfdlU1tfN9ypztSWWq0z6s7gHCeAp4E+2BqglsAvgN3A5dhGJvZ0WnTO08j+nlHBZwovOIJqOZZL0ajYv8s7lqoeR32pMxf7P6zKcdfkvlxBTR/PF8BYbA1kABANvIKtL+AsY8yYasZZn7lbnalpqjN1q758b9c1tfXlq091Ru192dTW1w13qjM1rU7qTIN4EsEYMx/oVsXN7rIsa31txGNZ1jfAN8WKUoEvjTHLgY3YstbjgP/Wxs8vztXOjatwtfPiSnVGXINlWb++oGgn8LAxZjfwLvA3bNNKiQDuX2f0vV0+Vzs3rsLVzosr1RlxDe7+vS01r67qTINIIgCR2KYTqoqA2gikIpZlnTfG/B34B3AdddNIuNK5OV+J/Qfa39NqKYZCl3Jezl9QVlZ/zho5DifVmYpc7P+wKsddk/tyBXV1PO9hm16qizGmvWVZCZe4v/rE3epMXXGXOuNK7Vm51Narra8qF2zrQe19edTW1w13qjN1pUbrTINIIliW1dvZMVTBPvt7q7r4YS52bg7b30ONMYHl9JVsY38/VJuBXMp5sSwr1RhzDtujiG2AXWV8rCaPo07rzEUU/h+2KWd9VY67JvflCurkeCzLKjDGHACaY6sTCZeyv3rG3epMnXCXOuNi7dnFqK1XW19VrtTWg9r78qitrxvuVGfqRE3XGY2J4HpC7e/lDTbktizLSqHoS6HPheuNMRHYBlo65OKjNYNtHmCAyy5cYYzxxtY/KQvYWwM/y5XqTLnHfUF5ZQaYqsl9uYK6PB5XqhN1yd3qTF1qqHXGWRrs+VZbX22uVmfU3pdNbX3dcKc6U5dqrM4oieB6bra/lzdlibv7yv5+SxnrCsu+rKNYLkVFx3ED4Ad8Z1lWVg38LFeqM2uAc0AHY0zvMtZX5f/wa6AAGGqMaV58hTHGF9scy/nAompHW7dq8tyUyxjTA9vjuRnYBuNqSNytztSJBl5nnMWVvredQW191blanVF7Xza19XXDnepMnajpOqMkQi0yxuy2v1pfUP47Y0zYBWXexpg/ArcCmcAHdRhqnSvv3ACvY/uln2aMiSv2+U7A74E8+2dc3Sxs/SPHGGPGFhbav+gKp1x5+cKN6nudsSwrB1ufTYA3jTGFfdIwxvwG23y931uWtbFY+YP2Y37+gn2dwNbv0wd4yxhTvPvVC0Az4GPLsk7VztHUrJo8N8aYkcaYqy78GcaYXsBcwACz7D/T7TSUOlMdqjN1r75/b9cmtfWAG7b1oPa+PGrra1ZDqDPV4RJ1xrIsvSrxAuYDP9hfhwEL2xykhWXzy9jGsr/al1GeBazG9gvwFXDMXp4JjHX28Trr3NjXPWRfl4stg7gAW9bMAn7l7OOtwnm5GdtFUgGwzP7Le9Z+HC+Xs029rzPY7rz8YI/tOPBpseVTQNQFn3/avu7DMvYVBuy3r98PfIJtznAL2+OhTZx9vM44N8XKE7CNsPtf4Ef774wFLAf8nX28VTgvo4p9X/xg/52xLigb1UDrTI2cG3erM7V4vtXW18G5sa9TW1/P6wxq72v1vLjj9zZq72v1vNRlnXH6SasvL/t/hlXBK6GMbcprJJ4BvsU22EcGtoZhH/A20MXZx+rMc1Ns/WhgJbZRVdPs/77B2cdajXMzGFiM7YIiHfgJmFTB592izgD+wJ/sX+rZ2Oa+/gBoU8Zny20g7OubAH/HdtGabX9/HQhx9nE669wAA7GNsrsNSLI3Dsn2xmEK4Ons46ziObn7It8hFnB3Q6wzNXVu3K3O1OL5TrjIuU4oYxu3+N6uy3NTbL3a+npeZ1B7X2vnxR2/t1F7X6vnpS7rjLH/QBERERERERGRCmlMBBERERERERGpFCURRERERERERKRSlEQQERERERERkUpREkFEREREREREKkVJBBERERERERGpFCURRERERERERKRSlEQQERERERERkUpREkFEREREREREKkVJBBERERERERGpFCURRERERERERKRSlEQQERERERERkUpREkFEREREREREKkVJBBERERERERGpFCURRERERERERKRSlEQQERERERERkUpREkFEREREREREKkVJBBERERERERGplP8HDA12A7r0yJcAAAAASUVORK5CYII=\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(nrows=1,ncols=2,figsize=[8,3], dpi=150)\n", "theta = np.linspace(0,2*np.pi,25)\n", "\n", "#In the below, I've set R/r = 1/10. It's not <<0, but will suffice\n", "#for a demo. I've also set G=M=m=1. You can add all the units if\n", "#you wish\n", "\n", "r = 10 #Distance between centre of body on left and body on right, r. \n", "R = 1 #Radius of body on left, R\n", "\n", "x = R*np.cos(theta) #moving to cartesian coords\n", "y = R*np.sin(theta) #moving to cartesian coords\n", "\n", "#To calculated F at each point, we need to calculate the correct phi\n", "s = np.sqrt(R**2+r**2-2*R*r*np.cos(theta)) #cosine rule\n", "phi = np.arcsin(R*np.sin(theta)/(r-x))\n", "\n", "f_x = np.cos(phi)/s**2 #Equation (1)\n", "f_y = -np.sin(phi)/s**2 #Equation (1)\n", "\n", "df_x = 2*R*np.cos(theta)/r**3 #Equation (2)\n", "df_y = -R*np.sin(theta)/r**3 #Equation (2)\n", "\n", "ax[0].plot(x,y)\n", "ax[0].quiver(x,y,f_x,f_y)\n", "ax[0].set_xlim(-1.5,1.5)\n", "ax[0].set_title(\"Gravitational Force (Eq 1)\")\n", "\n", "ax[1].plot(x,y)\n", "ax[1].quiver(x,y,df_x,df_y)\n", "ax[1].set_xlim(-1.5,1.5)\n", "ax[1].set_title(\"Differential Force (Eq 2)\")\n", "plt.savefig(\"Figures/Diff_Force.png\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "49853b4f-7dfc-42ee-9f31-d7f1290ad4c5", "metadata": {}, "source": [ "This is why we get two high tides per day. It is not the case that anything feels a force away from the moon on Earth, but just that the force on one side of the Earth is less than on the other." ] }, { "cell_type": "markdown", "id": "ee4e69dc-9f77-4010-a4a6-3e0a18977a09", "metadata": { "tags": [] }, "source": [ "## Tidal Friction\n", "\n", "So now let's consider the effects of rotation of the body. Consider the situation below, where tidal bulges have developed at points A and B, and because of friction between the Earth's surface and the ocean, the ocean's bulges are rotated along with the Earth's surface.\n", "\n", "![Tidal_Friction](Figures/Figure_3.png)\n", "\n", "The forces acting on the moon because of bulges A and B are shown as green arrows.\n", "\n", "- The force due to bulge A is dominant - meaning the moon is sped up in its orbit.\n", "- The moons force on the dial bulges acts to slow down Earth's rotation -> This is tidal friction\n", "\n", "The Earth's rotation is slowing, which means there is a loss of angular momentum. However, angular momentum within the Earth-Moon system is conserved. So, **the moon must be gaining angular momentum**.\n", "\n", "### Where does this angular momentum go?\n", "Assume the moon (mass m) is moving in a circular orbit, of radius r. The angular momentum of the moon is then:\n", "$$\n", " L=mrv\n", "$$\n", "To find v, let's equate the gravitational force experienced by the moon with the centripetal force\n", "$$\n", " \\frac{GM_{\\oplus}m}{r^2}=\\frac{mv^2}{r}\\\\\n", " v=\\left(\\frac{GM_{\\oplus}}{r}\\right) ^{1/2}\n", "$$\n", "This means the angular momentum is given by\n", "$$\n", " L=\\left(GM_{\\oplus} m^2 r \\right)^{1/2}\n", "$$\n", "The first three terms are constants, so $L\\propto r^{1/2}$. So if L increases (which it must if the total L of the Earth-Moon system is conserved), then r increases. Which means the Moon moves further away!\n", "\n", "Earth's rotation is slowing at a rate of about 0.0016 s/century (small but measureable). So the moon is drifting away!\n", "\n", "Let's now also consider the effects of the tidal forces on the Moon by the Earth.\n", "\n", "$$\n", " \\Delta F\\sim\\frac{GMmR}{r^3}\n", "$$\n", "Just to make sure we know what's what, $M$ is the mass of the body causing the tidal force, $R$ is the radius of the body feeling the tidal force, and $r$ is the distance between them. If we then look at the ratio of the tidal forces felt by the Moon and the Earth, we get:\n", "$$\n", " \\frac{M_{\\oplus}R_{\\rm m}}{M_{\\rm m}R_{\\oplus}}\\sim22\n", "$$\n", "Tidal friction is much stronger on the Moon versus on the Earth. This means the Moons rotation slows faster than the Earths, and is why the Moon is now tidal locked into a synchronous rotation (the same side always faces us).\n", "\n", "**Synchronous rotation** is very common - seen in binary stars, and in Sun-Mercury system." ] }, { "cell_type": "code", "execution_count": null, "id": "41d74694-879d-44c1-bba9-10d0a4cae93e", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 5 }