Book a Demo!
CoCalc Logo Icon
StoreFeaturesDocsShareSupportNewsAboutPoliciesSign UpSign In
Download

11th grade-all tasks

2151 views
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "<div dir=\"RTL\">\n",
    "בתחילת קובץ jupyter notebook עליכם להעלות את כל החבילות השימושיות.\n",
    "כמו כן אם אתם רוצים לקבל הדפסה יפה של פלט ושל גרפים יש להוסיף שתי פקודות נוספות"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "import sympy as sp\n",
    "sp.init_printing()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "%matplotlib -- inline\n",
    "#from sympy.plotting import plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "<div dir=\"RTL\">\n",
    "הדפסה יפה"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "#????"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "<div dir=\"RTL\">\n",
    "הגדרת משתנים סימבוליים"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "x, y, z, t = sp.symbols('x y z t')\n",
    "alpha,beta,gamma=sp.symbols('alpha,beta,gamma')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "<div dir=\"RTL\">\n",
    "פעולות מתמטיות"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left ( \\sqrt{2}, \\quad \\frac{\\pi}{2}, \\quad 1\\right )$$"
      ]
     },
     "execution_count": 6,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.sqrt(2), sp.pi/2, sp.sin(sp.pi/2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "<div dir=\"RTL\">\n",
    "מספר אוילר והפוקנציה האקספוננציאלית"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left ( e, \\quad e^{x}\\right )$$"
      ]
     },
     "execution_count": 7,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.exp(1), sp.exp(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "<div dir='RTL'>\n",
    "הגדרת פונקציה, וגזירת הפונקציה לפי המשתנה t.\n",
    "ניתן לגזור את הפונקציה גם על פי המשתנה $\\tau$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left ( e^{- \\frac{t}{\\tau}}, \\quad - \\frac{e^{- \\frac{t}{\\tau}}}{\\tau}\\right )$$"
      ]
     },
     "execution_count": 8,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tau = sp.symbols('tau')\n",
    "decay = sp.exp(-t/tau)\n",
    "decay_dt = decay.diff(t)\n",
    "decay, decay_dt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "<div dir='RTL'>\n",
    "פעולות שניתן לבצע על פונקציה.\n",
    "הצבת ערך בפרמטרים ובמשתנים (שימו לב: האבחנה בין פרמטרים למשתנים היא מלאכותית. כולם שווים בפני sympy.)\n",
    "    \n",
    "אפשר למצוא פרוט של הפעולות הביסיסות ברשת. למשל כאן:\n",
    "http://docs.sympy.org/latest/tutorial/basic_operations.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$e^{- \\frac{t}{5}}$$"
      ]
     },
     "execution_count": 9,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "decay.subs({tau:5})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$e^{- \\frac{2}{5}}$$"
      ]
     },
     "execution_count": 10,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "decay.subs({t:2,tau:5})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$0.670320046035639$$"
      ]
     },
     "execution_count": 11,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "decay.subs({t:2,tau:5}).evalf()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$x^{2} + 4 x + 4$$"
      ]
     },
     "execution_count": 12,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f1 = (x+2)**2\n",
    "f1.expand()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "<div dir='RTL'>\n",
    "כלי נוסף שיש להשתמש בו בזהירות הוא simply. זהו אלגוריתם מאוד כללי ולכן כבד מבחינה חישובית, ויכול לתת תוצאות בלתי צפויות.\n",
    "בשימוש בכלי הזה אתם נותנים למחשב להחליט מהי הצורה הפשוטה ביותר של ביטוי. לא תמיד תסכימו איתו.\n",
    "\n",
    "לרוב כדאי לחשוב קודם איזה סוג של פעולה תעזור לכם לקבל את הביטוי הפשוט ביותר בו אתם מעוניינים. לרוב הפעולות האלו יש פקודות ספציפיות. אם אתם יודעים מה הפעולה הדרושה, עדיף להשתמש בה ישירות.\n",
    "\n",
    "קיראו על כך בקישור המצורף\n",
    "\n",
    "http://docs.sympy.org/latest/tutorial/simplification.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$1$$"
      ]
     },
     "execution_count": 13,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f2 = sp.sin(x)**2+sp.cos(x)**2\n",
    "f2.simplify()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$x^{2} + 2 x + 1$$"
      ]
     },
     "execution_count": 14,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f3 = x**2+2*x+1\n",
    "f3.simplify()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left(x + 1\\right)^{2}$$"
      ]
     },
     "execution_count": 15,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f3.factor()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "<div dir='RTL'>\n",
    "אפשר להפוך פונקציה סימבולית לפונקציה פייטון נומרית רגילה. אתם יכולים כמה משתנים הפונקציה תקבל, אבל תדאגו להגדיר אותה היטב. לא להשאיר משתנים ללא ערך מספרי.."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function <lambda> in module numpy:\n",
      "\n",
      "<lambda> lambda _Dummy_140\n",
      "    Created with lambdify. Signature:\n",
      "    \n",
      "    func(t)\n",
      "    \n",
      "    Expression:\n",
      "    \n",
      "    exp(-t/5)\n",
      "\n",
      "Help on function <lambda> in module numpy:\n",
      "\n",
      "<lambda> lambda _Dummy_141, _Dummy_142\n",
      "    Created with lambdify. Signature:\n",
      "    \n",
      "    func(t, tau)\n",
      "    \n",
      "    Expression:\n",
      "    \n",
      "    exp(-t/tau)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "#t is input, tau=5 is a constant\n",
    "f_num1 = sp.lambdify(t,decay.subs({tau:5}))\n",
    "f_num2 = sp.lambdify([t,tau],decay)\n",
    "help(f_num1)\n",
    "help(f_num2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left ( 0.818730753078, \\quad 0.818730753078\\right )$$"
      ]
     },
     "execution_count": 17,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f_num1(1), f_num2(1,5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "<div dir='RTL'>\n",
    "# יצירת גרף\n",
    "\n",
    "כך נראית פונקציית הדעיכה האקספוננציאלית. המשתנה t מתאר את הזמן - זהו המשתנה הבלתי תלוי של הפונקציה.\n",
    "הפרמטר $\\tau$ מייצג את זמן הגעיה האופייני. זהו הזמן הנדרש לגודל הנמדד לקטון פי $e$.\n",
    "\n",
    "$$\\mbox{decay}(t=\\tau) = e^{-\\tau/\\tau}=e^{-1} = 1/e$$\n",
    "\n",
    "פונקציית הדיעכה מופיעה בתופעות רבות, בהן גודל כלשהו קטן בקצב משתנה התלוי בכמות החומר ברגע נתון.  \n",
    "\n",
    "על סמך הגרפים, עבור איזה ערך של $\\tau$ פונקציית הדעיכה יורדת מהר יותר\n",
    "ל-0\n",
    "?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAxkAAAIXCAYAAADwnpM7AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAAWJQAAFiUBSVIk8AAAIABJREFUeJzs3XecXFX9//HXZ2vKpnfSE9JIKKEmUhKKgIhSRL+ClGBBrOjX8kXBn/C18EVUFMUuRkDBRgBFpBNqgIRQEpKQ3ntv28/vj3PvzOxkZnd2p+++n4/HPmZv/9w7d+7cz5x7zjHnHCIiIiIiIplSku8ARERERESkfVGSISIiIiIiGaUkQ0REREREMkpJhoiIiIiIZJSSDBERERERySglGSIiIiIiklFKMkREREREJKOUZIiIiIiISEYpyRARERERkYxSkiEiIiIiIhmlJENERERERDJKSYaIiIiIiGSUkgwREREREckoJRnSamY2wsycmbl8x9JaZvZsEPuMfMdSiMyswsy+ZWaLzKy6WN/nVJnZ9GAfV+U7lnwws5uC/Z+Zj+XTZWargu1Pjxs/Ixj/bJLlupnZj81suZnVJjoHzOxSM3vZzPaGn4P47UjbmNnM4HjelO9YRCR7yvIdgOReGjeNs51z0zMZixScO4FPBv/vB3blMZa0BInkCOBB59wb+Y2m+JjZl4CewEzn3Ko8h5NpDwBnBf/vAXYAW8OJZnYZ8KdgsA7YHPxfm6sA8yFIoqYDbzjnHsxvNJItxfbZ1nlZvJRkdEybk4zvDZQD1cDuBNN3ZC0iyTsz6wHMCAY/5Jx7II/hZMIMYBqwCkiWZBwAlgDrcxNSwdmG3/+NCaZ9CRgOPIs/hsVkN36/1sRPMLOJ+ASjDjjNOTcnwfJfDl5vB77unKvPVqAFZjrwbeCPgG7m2q9i+2xPR+dlUVKS0QE55wYmGh88WjAN+ItzbkYuY5KCMA5/TdjeDhKMlDjnXgXG5zuOfHHO/Rz4eb7jyDTn3CxgVpLJE4PXt5IkGLHz3NWBEgwRkYxSnQwRCXUOXvflNQqR7ErlPNdnQUQkTUoyJG1mNsnM7jezTUFl4cVB5eGKFpY7JVhunZnVmNl2M3syqHBpacRzrpk9bWa7zWyPmc0xsytSXLbCzD5vZs+b2Y4grtVmdpeZTWhh2T5mdrOZzTOzXWZ2wMzeDfbxggTzn2RmtwTxrQ8qoG4xs/+Y2SUJ5jczWxZUmPx8C7HMDub7fgr7PCOop/NsMGp4TEXXSCX5VCr5JqvQGV/B2sxONrN/mdk2MztoZm8Gx73Z993MzjGzv8ecM5uC43ejmQ2N259pwWJ/iNufVcniSrLN083sgWBbtcHrLDM7o5llwm2NMLNhZvbbmJhXmtkPzax7c/uaYJ2nBuvckmBaSXDOOTN7J8H0KjOrC2OKGX/IexqOwz9OAfBM3PF7tpkYrzKzV8xXlt5jZs+Y2Xtbs58J1vmx4D3eF3wmnzaz97ewzCEVv2P2K9zXafHnefh/zKpWxkyfSRwz+4CZPRRzbmwxs3+a2TmpxBXs22zz1z5nZhfGzV9lZt80s9fMX8+qzWypmd0Rnu8JtvFszP50DvZ7SfA522L+ejQmbpkRwX5/Oxh1VdyxaXLepML89e2fwXu2z8zeMLPrzKzF+47gfL7CzJ4ws63Bsd1gZn8xs5NaWLarmX3VzF4Ktl1tZivM7OHgeJfHzT/J/PfV82a2xqLfRc+a2SfNrDTBNp4OjskPW4jlj8F8f25pn2OWiVxDzazSzG4ws7cs2gBBz2C+KjP7sJn9ycwWmP/8HzT/HfGb+Pc4WKbVn+02noMlwfn3THAs64L3caH579JzUzwWrTovzWyUmX3FzJ4yf52tDo7LnGB85yTbafN3m7TAOac//eGcA3+T6fCVwZqbb0QwnwPOxj/X7vCVhBtipj3YzDpujZnP4Stfxi57H1DShn34Wsw6GoGdMev9Ucw+zkiw7CD8s/vh8g1BXOHwQeDiJNs9Ff98ezhvDf658Mg+xs1fFbf/tXHbcsCvE2znm8G0ec0cg9HBvjtgTArH7L+ATfg6N+F+b4r5+69gvptaOj/wN3AOuClu/PRg/Cp8XYn6IMZdcfv8kyTrrQDuiZt3F/65ehe7zZj9qQ3G747bn9cSxZVku99NcD41xoy7Jcly4fQLgO1Ez/HYeF8DyltxblcG56ADJsRNOzbu2PSPm352MH513PhD3lPgq8FxCj83O+KO3wOJlgd+F/xfT9NzvwFfx6ct16Sfx60n9vh/MTifHDA9brkZwfhnE+xXGFtt3H5Ni/k/3ObWmHE/jVlXOXBv3DHfHTf8gwT7E4kLuCNmv3YErxfGzDshZv9ccO7sixneAZycYBvPxhyf14P/q4lepx3+nBwds8zQYB/D9R+MOzabgKGteN8+GpwH4fZ2Ej33/45/tv6Q60SwbDfgiZhlGxOcT59Pst0jgJVxx2xn3PsyIm6Z2Ot2PYdekx4ByuKWuSyYtil+Wtx+7A/mO6sVx25msMz/Aa8QPVfDuHoG830+Ls49+O+dcHhf/HZpxWc7zXPwT3Gx7YqLbU6Kx6JV5yUwN+68ib9evwZ0S7Cdm2jjd5v+WngP8x2A/grnj7YlGTuBv4QXbqArcH3MB/u8BMtfF0zbAnwm5qLZCfgwsCGY/o1Wxn9KzHbvAQYG43sSTWrCC/WMuGXLgVeDabPxSUNFMG0A8MNg2n5ivpyD6aOJfgnOB04HSoNpvfA3eP+IW6YL/svro8BhBAlVEOvngb3B+j4ct9wgol/eRyU5DuGN8XOtPH7Taf6Gu80X4ph178d/2fwMGBCzz+ENVyMwMcF67yR6E3BTzLJlwBj8l+c1Sc7nGW3Z5+C9Cc/znwF9g/F9YuJ1wOUJlo39fDwFTArGVwIfx9/0OeCzbfyMXhs3/stEbzQccEnc9O8F4+9O9T0lyQ18kuV34m8ArgW6BNNG4j9LDv+ZTngz1sy6PxZzHG8jep0YgL9JrSV6Ezc9btkZxCUZqUxL8P6NSDL99mD6SuBSoCoYXwVcQ/R6cGmSbe/Fn+v/L2a/uhMkh0APojfLs4DJ4fHDX3/vJnqT2zPJObIzWMc5QCn+yYVTgbXB9L+25TOewvs2mmgy/BgwKhjfBfhvmt7I35Rg+VnBtDeB84DOMdeJb+CvHw3E3dziGy5ZEyy7Ap/gh9fwbvjvh7uAIXHLPYBvUW9YzDHuClyObxDBAV+LW6aS6I8HH0xyHD4ZTF8FWCuO38yYc2Qn/keTcD+GE/wwEZx3dwBTgR7BOMPXMQsT4C1A1zZ+ttt0DgKnEU0Gv0RwUx/ENgi4CvhhK8+plM5L4Lf4+4vRMcesEvgAviEIB9zZlvWjJKNNf3kPQH+F80fbkozHE11AgX8G0++KG98zuHjWAScmWf8U/BfwjvBCkWL8TwXbfDpJTL+LiXtG3LTwC+FVoDLJ+n8RzPPzuPF/DcYvIcGvJG18L64I1vlMgmkPBdNuTzCthOgX7YxWbnM62U8yHPDbJMu+FUz/f3HjJxJNHq9pxf6E53PS45Bsn/FfiEuDafclWfbP4bLElbrF7OuCROcTPmlxwNOtfI9uThQTvsUVRzSZ+Fnc9BeC8Z9I9T2ldUmGAz6WYPogor9gntaK/Yw9/oliM5r+2j09bvoMspRk4JPasFRlVJLlPxK+/0m27YDvN7P98IeCB0lyg4r/kcIBX01y3h8ADk+w3IeC6dXEXV+bOx9a8d79PljHYqBTguk3xhyDm+KmnUU0eeudZP1fD+b5V9z4HwTjtwKD2xp/3DpPDeNJMO2nwbRZSZZ9KdE+prDNmTHH5+w2xh37+bgqwfRUPtttOgdj3p9HM/EeZPC8HIW/79hP8ENIa9aPkow2/alOhqTr/1zwCYwTNjM3KW78h/C/9r3gfMs+h3C+xZcV+FKA41IJwsx640sQAG5NElNz9ROuCl7vdM7VJJknfK428oy5mVUBFwWD/885tzeVeFPwz+B1SoJngn8XvF4e/3xxENtQfCL3twzFkmm3JBn/UPAaf85cgf/SXOyc+03WomrqGODw4P/vJpnn5uB1OHBiknl+nOR8Svb5aMlzweu0cISZGf5maC/RG5/Y6Z2BE4LB2a3cXqrWEP18RDjnNuITd2jdvsYe/0POl+Dz3WJ9oyy5Ep/MP+icW5FkngfwydVEMxuUYHoD8ONmthFej25Pci0D/0gpxFyP4vzdObcswfiH8edIJdFjnBHBuXhxMHi7c646wWw/wSdAiYT7PdM5l6zJ9PA8Oz3u2hjWu/uhcy4jTVI7557Hl7qMMLPD4iaH1+H3m1n/2AlmNg5fwuCAP7Rx82855x5vy4LBOfNIMHhyG7ff1nNwT/DaP5X6N7kSfFYX4kvUjslzOB2GmrCVdL2WZHx4ke8VN/49wetJZrapmfX2Dl6HAi+nEMdk/I1oI/5X20M451aY2dpgnRFmVkb0JvHHZnZrkm2EX2ixyx+P/xw54D8pxBm/3avwj4gdjd/n+MrynfDHcFvMuH/jHz85DF8MHNvc7MeD17845/a3Jp4c2dHMjVmyc2ZK8Prv7ISU0LHB61bn3MJEMzjnlpjZemBwMH+i5lBb+/loycv4X+MGmdkY59xS4Ej8ufMf59wWM1sATDKzPs657fibnQpgQ5KbzkyY28yNSFv2NTz+W5xzS5LM8xL+0Ztcf4+F17BLzOx9zcwX/gAwlEP7IVnmnNtGAkFl2iHB4N/MrDHJ+sNrRcLKtyQ595xzdeYbDxhA68+/lozCl1ZDkoTWObfPzObhE+N44bH9spl9poVtdcE/urglqPwbNs3e6uuE+YY2Lsefd/3w1914h+GvuwA45942s1fx3x2X0zRpDK/DTznnVrc2nkCL33tmNgT4Ar4EaDT+sbD4G/v45KhFaZ6DT+IfZTwWeNbMfoMvsd0Qv3A2mG9o4uP492UQ0ZbiYrX6mEjbKMmQtDTzy334C1b8L+3hr3qdSfzhj9clxVD6Ba+7W7i5Xs+hX8qxN/e9aVls3ANitpuoA8OEghKQx4h+qYJ/jnkrPlGKXXdXYpIM51xD0ArGN4GrCZKMoDQnbMXqrlRjybHmSnqSnTPhcTikY7UsCs+nln4RXYdPMvolmd7S56NV12Dn3AEzm4tPHKbhHykKSy2eDV5n4xOPU/ElJtNixmdLW97X5rR4/J1zNWa2jejNZa6E17Cq4K8lia5hWxOMi18/JD+vWlo/ZP49SUVsvM3dVCZ7X8N97xH8tSTc9wEx41K+TgQ/9PyVaGk0+BKobfjSJvD7VIK/Dsf7Hf5m9mqCJCMoXQlLVdK5Djd3jmBm04B/0fQc3E30ve2Mr+eTKO6WtPkcdM4tCxLEn+OvQacG8a7C/xD3G+fc/DbE1CIzuwOfdIXq8I9d1wXDYYfDbTkm0gYFU5QlHUZ4zt3unLMU/mZmePuJmkiN/RwcnUpcLawvFd/CJxjb8KUZA5xzXZxz/Z3vLHFwC9sIn3t+n5mFN1mX4R+BWOycS6X0p1i0uTnjDKjM47aTCZOFaXGvs1uYHj5q1Z7k49wIrxfXpXgNezbBOhoSjItfP/gKvS2tf0SmdiyHkr1v4b5fkOKxXdXC+lryKXyCcQBfYXioc66Tc66fc25gcC0Ok6VE27gP3/LRJDM7Phj3PvxN+i6SdwiZiqTnSPCY7L34BONJfGXrzs65njFx/3czcbckrXPQOXcXvuGHL+Efg92Or8t5LTDPzL7ZhpiaFZQqfgF/3G7CPwpY6ZzrE3NMXglnz/T2JTElGZJrm4PXIzK83vBXnx5m1lzpR6Lno7cTvaC3Nq7wka8eZpbKL2+hDwevX3DO3e2ci+/7YED8ArGCR46exj/CFf5qFhbRZ6sUI+z5ONGjBKHWHINUhcd4eBbWnUx4Pg1rYb7wkYJmf3XMsPgk4jR8Zca5wXCk3oaZVQInxS1XDMLjmfSxBvP98PTJTThNZOsaFr/+bG4jW2I/B809kpLoOgxtP7axj9625joRXoe/45y7wzm3LnZiUCrRN9nCzrl9+NYVwZdmQPQ6/OckdVIyYSr+2rMDn5A9n2BbzX6HtCDtc9A5t9k591Pn3IX40pAT8UmXAd8xs6PSiC+R8L38nXPuZufc8gSPcCY7Jvn6bmv3lGRIroW/sE8zs0zeIMzH/7Jfgm+q8BBmNpIEN43OuTqiN2gXx09vwVz8Bcrwv2ClKrw5TVZsfFYK6wgrHl5tZkfj66XU45sWzIZdweuQRBODSp8pVdRvpbCuQ2uOL0QfO2vLr1avB69dzSxhpW4zG0u0xOn1RPNkyYv4pHiomZ2P/wJ/0TlXDxAkrIvx9XzOwX9xbnHOLWrldtI5fukKj+eA4Dgn8h7y88hveA37QIKGF9LmnFtJ9CavtdejdKX7nq8gep04LdEMZtYVX5ctkfDYfqg1Gw1KNMJE47xWLNrSdfhkmr/xhOh1+NKgLsP5wXA2H1kN437XOZesEn1z3yHNvs+ZPged9xo+EVhHM9/TSaRyXjb7XprZcJI3dJCv77Z2T0mG5Nrf8L+6dsK3fZ+UmaVcKdH5lkieDga/HlwU4l3fzCpmBq8fMrPTm5mvSVzBL1lhkfjNZtYttYgJ628cmWD9VcANKaxjFr4UZgK+HwmAR5xzm5Mvkpa3g9cTkrSY8zGSV0JNR9gJ33gz+3QrlgtbOenZ7FyJvQGElaSTFe3fFLyuItqCUtYF9aDCL9L/F7w+GzfbbPz1/cZguC2PSqVz/NIVe/z/J35i8Plu7vOcTX/E3/Qchu+3IanWXMPizAxeP2tmE5pZv7WyBLUlab3nwS/H/wgGvxSUpMX7IsnrkcwMXo83syub21aCY3tP8PoVMxscP38SzV2Hy0jeslyE860hLsBXor8P/8z/m865eSnG0BZh3GPM7JAkyMzOJtraYiKpvM8zg9dWnYNBCWNCzrkGovUjWvMoairxJn0vA98neZKSr++2dk9JhuSU863dhF/MV5vZX80s0rSlmXUys1PM7E78L7atcRP+ZvRMYKaZDQjW2cPMvo/vJGtPkmV/j//FvAT4l5ldF1SkDuPqb2aXmtmz+Gd3Y30TX8lyLPCcmZ0eNt1nZj3N7P1m9kjcMk8Erz82s2lhUmRmJ+D7+0haRB9yvmnU8Is1bKYwm7+evYh/PrkCuC8oGcLMugQ3/7/F9x2QUc637vTrYPBOM7spbDLSzErNbEww7tq4RcNWoS5u7Y1YcLMU3qBfYGY/C0vezKxPUMHw0mD6jc65ZK2vZEuYNCRrmnZ2C9NTER6/SxPdyGRTcPxvCgY/bma3mllPgOBzfRdwBsmbQs1mbIvwzbCC/2HhTjMbFU43syoze6+Z3UPbm5H+P3ypQFdgtpldFfz4EG5jqJl9CphH00rL6Qrf81PMbEwb13ELvvLxBODBmOtEZzP7EvAdojeETTjn/kO0tby7zOzm2Js+M+tlZheY2UMc2gTwrfgK5X2B583sg+ENb/CeTDez+823yBQKr8PfCtZbGsw/Ht+M+In4H8VaEpZm5OI6DP5afAD/uODd4TEKjvHH8Yne9maWT+Wz3dZz8Ptm9nczuzDuO3RAcN0cif+efoLUpXJehuv7tJl9POa9H2Zmf8Rfr5N9P+Xlu61DcAXQWYf+CuOPNnTG18w802m+Y7cbiXaw5vAX8h34x0DCcSvbsA9fi1k+7NAv7CH7RzTTQRvQn2inZbHL740Z54BvJ1j2dPxFKJynmmivtoccK3xTj1tjph/EVyAMO9E6O2baiGb2d2LMfJtoZa/KrXnPgnkuinuPduN/mXL4RG0miTvZSmXdM0jegVol/tnn2PdhZ8y2E21zPNGO4OrwNyCr8H20pHqefjdm/Q0JztFbkizX7HtHCp+hFt6rD8ZsYz9BL8Ax0w+LO1ZHJlnPTST5zONv4sPla/A9Ra8C7k9l+Zh5Ep4TKe7nz2NiqA+Of3jd+CJJOhVr4VxKOq0V718p0c45w789wTkZe117prXbjpn3cOCduPNvO/76ELvdq+KWe5Yk17iYeZIdt3J8CVJ4/dsSzLuKuJ6yW4j9o0Svu/Gf1X/gS4MSnhP4m9pZNN3HXUR7UQ///pBg2SOJ9mju8E2p7oxbbkTM/L1j9jecP9xOffB+JTxWcdvtjb/mh5+VPm35XLfm84I//+OPUXiM5+MrQSf7DLT42W7rOYhPwGOn7cZ/NmLHfbOVx6TF8xKfILwcs436uPf+WzT//d+m7zb9Nf+nkgzJC+fcd/HPjP8G3wyn4b9cNgKPAp8hWmG1Neu9Df/s/jP4m/YyfL2JK51zX2lh2S34yrQfw7e1vgXfeofhn3H/Pf5530M6AXPOPQOMw/+atoBo+/3v4ovQPxg3/wr8r2T3BtspxX9J/Ak4waXYCZPzv/K/Gwze7YLn8rPFOTcLnwA9g0++SvGPtnzSOfeJLG63xjn3X/gmev+Jf144bNp3Dv7xst/GLbMY30nUf/BfGAPxlUITPnebZLs34kvGHgq2VYX/kn0YOMs51+zjMln0PNHnlF9yvl5RhPNt0oePG+3An5Ot4px7Gv/FOxufBA/GH7+cNRnrnPs8vg+CV/A3QxbEc75z7o5cxZEgrgbn3Gfxz5XfC6zG3+R0xjehOgvfatyFaWxjGb6e1Wfxn7cd+CZJ64G38L3GTyNampm24Dw6M1jnevwjQMODv5Trvzjn7sf/qv8I/rpWgb9Z/RL+uXzXzLL7nXMX4es2PBDE0TlYxzJ8Z3yX4I9L/LJv4394uRF/3T+IfzR3Bb4550vxdQLC+Xfg++H5Zcz4g8G801yKrRsG6wlLCx9yvsQ+q4Lz/2KipRpl+O+pb+PrKyVtwjjVz3Ybz8Hb8QnQQ/jvJsP/SLQW/0PRac65VnWkmcp56ZyrxddDCUtgGoM4nwA+4Jz7TgvbyMt3W3tnQQYnIkXIfEXDVfjHvCYEN9YiIpIj5ls03Ii/AX+f8499iXR4GWuZw3wLIGfhW5QYhn8u8iD+V9o38Nnh0y57TbqJdETX4BOM55VgiIjkxaX4BGM1kFIptEhHkHZJhpl9FF+UFlZ4SlZ7P3xmcCbwMxftREdE2sDMJuOLu7sBH3LOPdDCIiIikkFmNgL/+OIQ4CvOufgK6SIdVpuTDPPNfP4Y/1z9LvwzjC8Cr+EroO7AP0fZB18Bcwr+ebcp+Gdr7wC+55xL1tqPiCRgZi/gK44PxCf1z+ErJerZRxGRHDCz+/F1cgbhS5PfBY7W0xoiUekkGY34DpNuxVd0qk1xuTH4ruWvBf6vpco4ItKUma3CV3jbDPwL+J9cVDQUEREvaM58Gv4H1WfwpRir8xqUSIFJJ8m4OJ3HM8xsIL4puTktziwiIiIiIkVDrUuJiIiIiEhGZayfDDO70syOamGeSWZ2Zaa2KSIiIiIihSeTnfHNpOWOhy4A/pDBbYqIiIiISIHJdY/fpTTT06eIiIiIiBS/XCcZY4GdOd6miIiIiIjkUFo9fpvZXXGjLgw6polXiu8F/FTgkXS2KSIiIiIihS2t1qWCvjJCjuS9fYfTXwEud86taPNGi4seDRMRERGRXGjuPjzn0irJAEYGrwasAH4C/DTBfA3ATufc/jS3JyIiIiIiBS6tJCO2d0szuxl4Rj1eioiIiIh0bOqML7t0cEVEREQkFwrqcak2ty5lZoPT3biZDUp3HSIiIiIiUljSacJ2mZnd3tpkw7wLzGw+8Kk0ti8iIiIiIgUonSTjNuAaYJWZPWpmV5vZmEQzmlmVmZ1hZrcCa4EHgOrgVURERERE2pF0m7AdCnwLuAzoHIzeC2zCd7rXCegDDMInNAbMB25zzt3f9rCLhupkiIiIiEguFFSdjIxU/Daz7vhE4yzgZGBAzORa4G3gWeAfzrk5aW+weCjJEBEREZFcaB9Jhpl9EZjjnHs1wbRyfAnGQefc7vRCLGpKMkREREQkFwoqyUinTsZPgHPDATNrMLNvATjn6pxzmzp4giEiIiIi0iGlk2RUA5Uxw0aBZVAiIiIiIpJ76SQZK4FzzCy2/oUeDxIRERER6eDSrZPxE6KJhZFakuGcc2Vt2mjxUdIlIiIiIrlQUE8Utflm3zl3h5ltAd4PHAacDqwBVmUmtMTM7BJgGnAMcDTQDfiTc+7yNqxrCPC/+LolfYCNwIPAzc65nRkLWkRERESkA8lIE7YAZtYI3OSc+9+MrDD5dt7AJxf7gHXAeNqQZJjZaOAloD/wELAYOBGfLC0BTnbObU8zXJVkiIiIiEguFFRJRjp1MuLdjO8LI9u+DIwFugOfSWM9v8AnGF90zl3onLveOXcGcDswDvhe2pGKiIiIiHRAGSvJyAczmw48QytLMsxsFLAc/2jXaOdcY8y0bvjHpgzo75zbn0aIxXtwRURERKSYtNuSjGJyRvD6eGyCAeCc2wu8CHQBpuQ6MBERERGRYtdRk4xxweu7SaYvDV7HtrQiM5uX5G/7Ry+9jAdeX5eRgEVEREREikVHaUo2Xo/gNVmP5OH4nmlso9OsZ15lzvA3GdqrCyeM7J3GqkREREREikdHLcloSfhMW4t1KpxzxyX6w7dWBcAdTy1tZg0iIiIiIu1LR00ywpKKHkmmd4+bLy0vLt/Glj3VmViViIiIiEjB66hJxpLgNVmdizHBa7I6G63S6ODeOaszsSoRERERkYLXUZOMZ4LXs82syTEImrA9GTgIzMnUBu+ds5rquoZMrU5EREREpGC16yTDzMrNbHzQu3eEc2458DgwAvhc3GI3A12Bu9PsI4PSkmhzxTsO1PHwmxvSWZ2IiIiISFEoutalzOxC4MJgcGDwOtXMZgb/b3POfTX4fzCwCFiNTyhifRZ4CbjDzM4M5jsJOB3/mNQN6cbauaK0yfBdL6zkw8cNwayg+koREREREcmooksygGOAq+LGjQr+wCcUX6UFzrnlZnY88L/AucB5+J6+7wBuds7tSDfQLhVND+/iTXuZs2IHU0f3SXfVIiIiIiIFq+iSDOfcTcBNKc67ima6WHfOrQWuzkRciXSpKKUmbtxdL65UkiEiIiIi7Vq7rpORb10qSimJS3GeXLSZNdsP5CcgEREREZEcUJKRRSVmjBuKUrhTAAAgAElEQVTYvck452DmS6vyE5CIiIiISA4oyciyY4f1PGTcX+euZW91XR6iERERERHJPiUZWXbc8F6R/7sErU3tq6nn7/PW5SskEREREZGsUpKRZccOiyYZjc5F/p/50ioaGl2iRUREREREipqSjCwb3qcLfbpWAFBd10hVpW/Qa/X2Azy9eEs+QxMRERERyQolGVlmZkyOKc04bni0jsYfXlyZj5BERERERLJKSUYOHBuTWHTrVE5p0K7tS8u3s2jjnnyFJSIiIiKSFUoycuC4mJKMJZv2cu7EgZFhlWaIiIiISHujJCMHjhrSk7Kg9GLpln185IQhkWkPvrGB7fvi+wUXERERESleSjJyoHNFKUccFu2UzzXC0UN6AFBb38ifX1mTr9BERERERDJOSUaOxDZl+/raXVx98sjI8D1zVlNb35iPsEREREREMk5JRo5Mjun5+/XVOznvyEH071YJwJa9Nfz77Y35Ck1EREREJKOUZORIbM/fb6zdRWmJceXU4QAM6dWZx9/ZhHPqnE9EREREip+SjBwZ3LNzpORiX009727ey6UnDuPEkb1Zt/Mg/357Ey8u257nKEVERERE0qckI0fMrElpxutrdtKnqpJxA7pFxv1q9vJ8hCYiIiIiklFKMnKoSeXv1bsA+NSpowhat+WFZdt4e93ufIQmIiIiIpIxSjJyKLbn79fX7ARgWJ8uvP+owyLjf/WcSjNEREREpLgpycihiYf1oKLUH/KV2/azY38tAJ8+bVRknkff3sjq7fvzEp+IiIiISCYoycihTuWlTBwc7ZTv9dW+NGPS4B6cOqYvAI0OfvPcirzEJyIiIiKSCUoycuy4YU0rf4c+M2105P+/zVvH1r01OY1LRERERCRTlGTk2LHDEycZU0f34aghPQCorW9k5ksrcx6biIiIiEgmKMnIsdhmbN9cu5v6hkbAN3F7bUxpxj0vr2ZfTX3O4xMRERERSZeSjBwb0L0Tg3t2BuBgXQOLN+2NTDtn4kBG9u0KwJ7qeu57ZU1eYhQRERERSYeSjDyYPCzalO281dFHpkpLjE+dGm1p6vcvrKS2vjGnsYmIiIiIpEtJRh7E9/wd6+JjB9O3qhKATXuqefCN9TmNTUREREQkXUoy8uDYJC1MgW/m9uOnjIgM/3r2chobXa5CExERERFJm5KMPDjisO50KveHfu2Og2zZW91k+sdOGk5VZRkAy7fu58lFm3Meo4iIiIhIWynJyIPy0hKOGhytl/H66l1NpvfoXM7HThoWGf7V7OU4p9IMERERESkOSjLyZPLwmCQj7pEpgI+fMpKK0pJg+i5eW3XoPCIiIiIihUhJRp406fl79aEJxIDunbho8uDI8K9mL89JXCIiIiIi6VKSkSexPX+/tX53wqZqr5k2CjP//9OLt7B4055chSciIiIi0mZKMvKkb1Ulw/t0AaC2vpGFG3YfMs/oflWcfcSAyPCvZ6/IWXwiIiIiIm2lJCOPmjZluyvhPNdOGx35/+E3N7Bu54GsxyUiIiIikg4lGXl07LCedO9UxpGDu7Nm+/6E80we1ouTRvYGoKHR8bvnV+YyRBERERGRVlOSkUcnjuzD3pp63l6/h3+9tTFpM7XXTo+WZvzltbXs3F+bqxBFRERERFpNSUYejelfRc/O5QBs31/L0i37Es43fWw/xg/sBsDBugb++PKqHEUoIiIiItJ6SjLyqKTEOGlkn8jwnBXbE85nZk3qZvzxpVUcqK3PenwiIiIiIm2hJCPPpozqHfk/WZIBcP5RgxjcszMAXSvLeHD++qzHJiIiIiLSFkoy8mzK6NiSjB00Niaul1FWWsJ1Zx7OscN6sm7nQX761FKq6xpyFaaIiIiISMqUZOTZ2P7d6N21AoAdzdTLAPjgMYNZt/MgAJv31PDXuWtzEqOIiIiISGsoycgzXy8jtUemOpWXNqmb8YtnllNTr9IMERERESksSjIKwJRRLVf+Dl120jD6dasEYNOeav76mkozRERERKSwKMkoAFNHN00yktXLAF+a8enTRkWGf/GsSjNEREREpLAoySgAY/pXRepl7DxQx7tb9jY7/8dOGk7fKl+asXF3NX+duy7rMYqIiIiIpEpJRgEws6ZN2S5v/pGpzhWlXDstWprxy2eWqTRDRERERAqGkowCMTWmXsbLLdTLgLA0w5d+bNhdzd/nqTRDRERERAqDkowCEVv5+5WVyfvLCHWuKOXTpzVtaaq2vjFr8YmIiIiIpEpJRoE4vH9VpGRi14E6lmxuvl4GwMemDKNPUJdj/a6DKs0QERERkYKgJKNAmBkntaIpW4AuFWVcE9PS1J3PLFNphoiIiIjknZKMAhL7yNTLLVT+Dl0xdXikZar1uw7yj9dVmiEiIiIi+aUko4BMjWlhKpV6GZC4NKOuQaUZIiIiIpI/SjIKyOh+VZH+L3YfrGPxppbrZQBcMSVamrFu50EeUGmGiIiIiOSRkowCEt9fRipN2QJ0rSzjk6eOjAz/7GmVZoiIiIhI/ijJKDBTWln5O3Tl1BH07FIO+NKMWa+vz3hsIiIiIiKpUJJRYKaOjiYZr6ZYLwOgqrKMT50arZvxc9XNEBEREZE8UZJRYEb17Uq/btF6Ge9s3JPysle9J1qasWbHAWbNV2mGiIiIiOSekowC4+tltO2RqarKMj55SrRuxp3PLKNepRkiIiIikmNKMgpQbOXvOSt2tGrZq94zgh6dfWnG6u0HePCNDRmNTURERESkJUoyCtDUUbH1MrbTkGK9DIBuncrjSjOWUlffkNH4RERERESaoySjAI3s25X+Qb2MPdX1LGpFvQyAq04eQa8u5Rw/vBfVdY3Mmq/SDBERERHJHSUZBSidehkA3TuV89nphzN39U427q7m9iffpbpOpRkiIiIikhtKMgpUbFO2rU0yAC47aRh9q3wv4Bt3V3PvnNUZi01EREREpDlKMgpUbEnGKyt3tKpeBvhewD9/+uGR4V88u5y91XUZi09EREREJJmiTDLMbIiZ3WVmG8ysxsxWmdlPzKxXK9dzipk9FCxfbWZrzOzfZnZutmJP1Yg+XRjQ3dfL2FtdzzsbWlcvA+DSk4YxuGdnAHbsr+V3z6/MaIwiIiIiIokUXZJhZqOBecDVwKvA7cAK4DrgZTPr08zisev5DPA8cGbwejswG5gGPGpmN2Q++tSZWZNWptryyFRlWSlffu/YyPDvnl/B9n01GYlPRERERCSZoksygF8A/YEvOucudM5d75w7A58kjAO+19IKzKwcuAWoBo5zzl3hnPuGc+4K4HigBrjBzCqzthcpSKfyd+iiyYMZ078KgP21Dfzi2eUZiU1EREREJJmiSjLMbBRwNrAKuDNu8reB/cAVZta1hVX1BnoA7zrnlsROcM4tAt4FOgNVGQi7zaY06S9jR5t67y4tMb56zrjI8D0vr2b9roMZiU9EREREJJGiSjKAM4LXx51zTe64nXN7gReBLsCUFtazBdgKjDWzMbETzGwsMAZ4wznXtuKDDBnepwuDenQCYG9NPe+0sr+M0NlHDOCYoT0BqG1o5KdPvpuxGEVERERE4hVbkhH+JJ/sLnlp8Do2yXQAnHMO+Bx+/+eZ2R/N7BYzuxtf32Mh8OFUAjKzeYn+gPGpLN/CujPyyJSZ8fVzo6UZf5+3jmVb9qUbnoiIiIhIQsWWZPQIXncnmR6O79nSipxzf8OXjOwCrgSuB67AP3L1B3xl8rybMqp35P+5q3a2eT3vGd2XU8f0BaDRwY8eX9LCEiIiIiIibVNsSUZLLHhtsVMJM7sceBLfstQE/GNWE4CngJ8D96eyQefccYn+gMVt2YF4U0f3YeqoPgzv04UXlm2jpr7tPXd/LaZuxqMLNvHWul2ZCFFEREREpIliSzLCkooeSaZ3j5svoaDexV34x6KucM4tds4ddM4txpdmzAM+bGbT0w85PcN6d2XD7oOs3n6AA7UNaZVmHDWkJ+cdOTAyfNtjKs0QERERkcwrtiQjvCtOVucirMTdUs3ms4FyYHaCCuSNwHPB4HFtCTLTpo3tF/l/9rtb01rXf793HCVBec/zS7fx0rJtaa1PRERERCResSUZzwSvZ5tZk9jNrBtwMnAQmNPCesL+L/olmR6Or21LkJnWJMlYkl6ScXj/Ki45bkhk+NbHluDrwYuIiIiIZEZRJRnOueXA48AIfOtQsW4GugJ3O+f2hyPNbLyZxbf09HzweomZHRU7wcyOAS7B1+t4OnPRt92UUX2oKPVv1ZLNe9m0uzqt9V131lgqyvz63ly7i8ff2Zx2jCIiIiIioaJKMgKfxfdzcYeZPRg0Pfs08GX8Y1I3xM2/KPiLcM69im9BqjPwmpndb2a3mtlfgFeATsBPnXMLs7wvKelaWcYJI3tFhp9L85GpwT07c8WU4ZHhHz62hIZGlWaIiIiISGYUXZIRlGYcD8wETgK+AowG7gCmtqIDvU8AVwMvA+cE63kv8AJwqXPuy5mNPD2ZrJcB8Nnpo+laUQrA0i37mDV/fdrrFBERERGBIkwyAJxza51zVzvnBjnnKpxzw51z1znndiSY15xzlmC8c87NdM5Nd871cs6VOed6O+fOdM6l1HxtLk0b2z/y//NLt1Lf0NjM3C3rU1XJp04bBUBVRSmPvLWB6rq2N48rIiIiIhIqyiSjIxo7oIqB3TsBsKe6njcz0MfFJ08dxZnj+1NSYjyzZCu/f2Fl2usUEREREVGSUSTMLKOtTAFUVZYxfVw/9lTXA/CLZ5axdW9N2usVERERkY5NSUYRmTYus/UyAC49cRiH968CYH9tAz9+Qh30iYiIiEh6lGQUkZMP70tp0JPeW+t3s31f+qUOZaUl3PD+CZHhv7y2lkUb96S9XhERERHpuJRkFJEencuZPLQnAM7BCxnqrfv0cf05LXgUq9HB9x5ZpA76RERERKTNlGQUmUzXywjdcN4EgkISXli2jWeWbMnYukVERESkY1GSUWRi62U8t3QrjRnqRG/cwG5ceuKwyPD3HllEXZrN5IqIiIhIx6Qko8hMOqwHvbtWALBtXy3vZLD+xJffO5ZulWUALN+6nz+/siZj6xYRERGRjkNJRpEpKTFOG9M3MpypVqYA+lZV8rkzDo8M/+TJd9l9oC5j6xcRERGRjkFJRhFq0pRtButlAMx4zwiG9OoMwM4Ddfzs6aUZXb+IiIiItH9KMorQqWOiSca8NTvZU5250oZO5aV8433RJm3/+PIqVm3bn7H1i4iIiEj7pySjCPWtquTIwT0AaGh0vLRse0bXf96RAzl+eC8A6hoc//fo4oyuX0RERETaNyUZRapJU7YZrJcBYGbceP4RkeH/LNzEnBWZTWREREREpP1SklGkmjRl++7WjHeed8zQnlx4zGGR4e8+8k7GmssVERERkfZNSUaRmjy0J906+eZm1+86yPKt+zK+ja+fO57KMn+KLFi/hwfmr8/4NkRERESk/VGSUaTKSks45fBoU7bPZriVKYDDenbmmtNGRYZve2wxB2rrM74dEREREWlflGQUsWzWywhdO200/bpVArB5Tw2/nr0iK9sRERERkfZDSUYROy0myXhl5Q4O1jZkfBtdK8v42tnjIsO/fm45m3ZXZ3w7IiIiItJ+KMkoYof17MyY/lUA1NY3MmdldlqA+tBxQzhiUHcAqusaue2xJVnZjoiIiIi0D0oyilyTR6ayUC8DoLTEuPH8aAd9/3h9HW+v252VbYmIiIhI8VOSUeTim7LNlveM7st7jxgQGf7uI+9kvNlcEREREWkflGQUuRNG9KZTuX8bV2zbz5rtB7K2rW+8bzxlJcakw7qzducBHn5zQ9a2JSIiIiLFS0lGketUXsrUUX0iw7OXZq80Y1S/Kv77vWNYsGEPG3ZV891HFrGnui5r2xMRERGR4qQkox3IRb2M0BVTR9A/aNJ2694abn/i3axuT0RERESKj5KMdmDauP6R/19avo3a+sasbatbp3K+df4RkeE/vrSKhRtUCVxEREREopRktAMj+nRhWO8uAByobWDu6h1Z3d75Rw2K9Dbe6ODGBxfQ2KhK4CIiIiLiKcloB8yMaWP7MbB7J44b3otXVmSnv4zY7d18wUTKSw2A+Wt28bd5a7O6TREREREpHkoy2omzJw5g055q5q3eyYNvbMh687Kj+1Xx6dNGR4ZveXQxO/bXZnWbIiIiIlIclGS0EyeM6E3XilIAVm8/wOJNe7O+zc+dfjiDe3YGYNeBOn7wn8VZ36aIiIiIFD4lGe1Ep/JSpo+PVgB/bOGmrG+zc0UpN39wYmT4/tfW8vqanVnfroiIiIgUNiUZ7cg5EwdG/n9s4eacbPOsIwZw1oRocnPjrAXUN2SvdSsRERERKXxKMtqR08f1o6LUv6WLNu5h7Y7s9f4d69sfmBjpdfydjXu4d87qnGxXRERERAqTkox2pFunck4+PNr7dy4emQIY2rsLXzhjTGT4R4+/y5Y91TnZtoiIiIgUHiUZ7UzTR6Zyk2QAfPLUkYzq2xWAvTX1fO/fi3K2bREREREpLEoy2pmzjhhAie++grmrd7J1b01OtltZVsr/XjApMvzQGxt4afm2nGxbRERERAqLkox2pm9VJccP7w2Ac/DkotxUAAc4ZUxfzj9qUGT4Ww8uoLZelcBFREREOholGe3Q2RMHRP7P5SNTAN86/wiqKssAWL51P797YUVOty8iIiIi+ackox2KrZfx0rLt7K2uy9m2B3TvxJfOilYC/9lTy1i3MzetXImIiIhIYVCS0Q4N7d2FIwZ1B6C2oZFnlmzN6fZnvGcE4wd2A+BgXQP/+893crp9EREREckvJRntVL5amQIoKy3huxdGK4E//s5mnl6cu7ohIiIiIpJfSjLaqXMnRZOMZxdvobquIafbP35Ebz583JDI8LcfXpjzGEREREQkP5RktFNjB1Qxok8XAPbXNvDistw3J3v9+8bTo3M5AGt3HOQ3z6kSuIiIiEhHoCSjnTKzvD4yBdCnqpKvnzuObpWlHD+iFz9/ehlLNu3NeRwiIiIikltKMtqxs2OSjCcXbaG+Ifd9Vlx6wjBOHNmHuat2UtvQyNf//iYNjS7ncYiIiIhI7ijJaMcmD+1J/26VAOzYX8vc1TtzHkNJifGN88ZTUepPtTfX7eauF1bmPA4RERERyR0lGe1YSYnx3iPy1zFf6PD+3fjimYdHhn/4+BJWbdufl1hEREREJPuUZLRzsfUyHl+4Gefy86jSp6eNZkLQd0dNfSP/84+3aNRjUyIiIiLtkpKMdm7KqD5061QGwPpdB1m4YU9e4igvLeG2S46itMQAeGXlDu57bU1eYhERERGR7FKS0c5VlJVw1oT8PzIFMGlwD645bVRk+JZ/L2bDroN5i0dEREREskNJRgdwzsTCSDIArjtzDKP6dgVgX009Nz64IG+PcImIiIhIdijJ6ABOG9uPyjL/Vr+7eR8rtu7LWyydyku59ZKjMP/UFE8v3sJDb2zIWzwiIiIiknlKMjqALhVlnDa2X2T4sYWb8xgNnDCiN1dOGR4ZvvmfC9m2ryaPEYmIiIhIJinJ6CDy3ft3vK+fO57BPTsDsPNAHTc9vDDPEYmIiIhIpijJ6CDOmtA/0rLTG2t3sWl3dV7j6VpZxi0XHxkZ/tdbG3m8AJIfEREREUmfkowOomeXCk4a2Tsy/MQ7+b+hP21sPy45bkhk+MYHF7D7YF0eIxIRERGRTFCS0YE0fWQqv/UyQt96/xH061YJwJa9NXz/kUV5jkhERERE0qUkowM5O6Yp2zkrtrP7QP5LDXp0Kec7F0yKDP9l7lpeWLotjxGJiIiISLqUZHQgg3p05uihPQGob3Q8tbgwSjPOnTSQ846MlrLc8dRS9tXU5zEiEREREUmHkowOJrZjvv8syH+9jNDNH5xEv6oKpozszdzVO/jOP9/Jd0giIiIi0kZKMjqYc44YwPHDezF5aE/mrNjOnur8PzIF0K9bJTdfMIk5K3fQ6PxjU0+8UxglLSIiIiLSOkoyOpjR/btxoLaB+Wt3sae6nkff3pjvkCLeN2kg5x81KDJ8/T/eUid9IiIiIkVISUYHdPGxgyP/P/D6+jxG0pSZ8d0LJzGgu29tavv+Wq7/x9s45/IcmYiIiIi0hpKMDuiDRx9G0C8fr6zcwfpdB/MbUIyeXSr4wSVHR4afXLSZv81dl8eIRERERKS1lGR0QP27d+Lkw/tGhh+cXzilGQDTxvbjqqnDI8M3/3Mha7YfyGNEIiIiItIaRZlkmNkQM7vLzDaYWY2ZrTKzn5hZrzas60gzu9vM1gbr2mJms83symzEXihiH5maNX99wT2SdP37JjCqX1cA9tc28N9/fYOGxsKKUUREREQSK7okw8xGA/OAq4FXgduBFcB1wMtm1qcV65oBzAcuBJ4HfgT8HTDgvIwGXmDOmTiQLhWlACzbso+FG/bkOaKmOleUcvtHjqE0eK5r7uqd/Oa5FXmOSkRERERSUXRJBvALoD/wRefchc65651zZ+CTjXHA91JZiZlNAX4HLADGOucuc8590zn3WefcacAVWYq/IHSpKOOcidEO8AqpAnjo6KE9+eIZYyLDP35iCQs37M5jRCIiIiKSiqJKMsxsFHA2sAq4M27yt4H9wBVm1jWF1f0AKAUud84d0iudc64wOpDIoosmRx+ZevjNDdQ3NOYxmsQ+d/roSC/ldQ2O//7Lm1TXNeQ5KhERERFpTlElGcAZwevjzrkmd8TOub3Ai0AXYEpzKzGzIcCpwFxgoZmdbmZfNbOvmNmZZlZsx6VNTj68L/26+eZit+2r4YVl2/Ic0aHKSku4/SNH06ncvyVLNu/lR48vyXNUIiIiItKcYruZHhe8vptk+tLgdWwL6zkhZv6ng7/bgB8CTwJvmNnhqQRkZvMS/QHjU1k+n0pLjAuOPiwyPKvAWpkKjepXxQ3vPyIy/LsXVvLy8u15jEhEREREmlNsSUaP4DXZg/nh+J4trKd/8PoRYAJwcbDuw4F7gCOBR8ysou2hFoeLYlqZemzhJvbV1OcxmuQuP2kY08b2A8A5+Orf3mRPdbt/ok1ERESkKBVbktGSoIs5WmrrtDTm9ZPOuVnOuT3OueXAVfjHqMYCH2ppg8654xL9AYvbuA85dcSg7owb0A2A6rpGHltwSPWUgmBm3HbJUfTsUg7A+l0HuenhhXmOSkREREQSKbYkIyyp6JFkeve4+ZLZGbzWAP+OneB8hxEPBYMntjbAYmNmXDi5aZ8Zhap/9058/6IjI8MPvL6eR9/emMeIRERERCSRYksywhq/yepchO2dJquzEb+evfEVyANhEtK5FbEVrQsnH4YFZUAvLt/Gpt3V+Q2oGecdOYiLY5Ki3zy3oqDjFREREemIii3JeCZ4PTu+BSgz6wacDBwE5rSwnreAbUBfMxuQYPqk4HVV20MtHoN6dGbqKN+HoXPw8JuFW5oBcNMFExnWuzNTRvXmjXW7uO7++eoNXERERKSAFFWSEdSZeBwYAXwubvLNQFfgbufc/nCkmY03syYtPTnn6oFfB4M/iE1YzOxIYAZQj+/9u0OIfWSqEDvmi9W9Uzk/+sgxvLpyB87BKyt3cMdTS1teUERERERyoqiSjMBngS3AHWb2oJndYmZPA1/GPyZ1Q9z8i4K/eN/Hl3hcCcw1sx+b2T3AK0An4H+cc8uytROF5n2TBlJZ5k+HxZv2smjjnjxH1LwTRvTmujOjT83d8fRSXlpeeP18iIiIiHRERZdkBKUZxwMzgZOArwCjgTuAqc65lDpQcM4dAM7El4B0wZeMfBB4CTjPOffjjAdfwLp1KufsiQMjw4VcATz0+TMOb/KY15fuf4Nt+2ryHJWIiIiIFF2SAeCcW+ucu9o5N8g5V+GcG+6cu845tyPBvOacsyTrOeCcu8k5N945V+mc6+GcO8s592j296LwXDQ52jHfQ2+sL/h6DqUlxk8+egx9uvruTLbsreErf32TxgKPW0RERKS9K8okQ7Lj1DH9Ijfsm/fUFEWv2gO6d+JHHzk6Mjz73a389vkVeYxIRERERJRkSER5aQkfODpamvHA/HV5jCZ108f159PTRkWGb3tsCa+v2dnMEiIiIiKSTUoypImLYlqZemzBJg7U1ucxmtR99exxTB7WE4D6RscX/jyf3Qfq8hyViIiISMekJEOaOGpID0b16wrA/toGnnhnc54jSk15aQl3fHQy3TuVAbB+10H+5x9v4TtwFxEREZFcUpIhTZhZkx61C73PjFhDe3fhB5ccFRn+z8JN3DtndR4jEhEREemYlGTIIS44JppkPL90K1v3Fk+zsOdOGsSVU4dHhr/zyCIWbtidx4hEREREOh4lGXKIob27cOKI3gA0Onj4zQ15jqh1vnneBI4Y1B2A2vpGvvDn+eyvKY66JSIiIiLtgZIMSeiiY6OlGbOKpJWpUKfyUn5+2WS6VJQCsGLbfr714II8RyUiIiLScSjJkITOmzSIilJ/eixYv4elm/fmOaLWGdWviu9dNAmA8hJj1fb9/OkV1c8QERERyQUlGZJQjy7lnDmhf2R41vziqQAeumjyED5x8ghG9O3K62t2cfPD7/DG2l35DktERESk3VOSIUnF9pnx0BsbaGwsvuZgv3rOeMqCEpnahkY+c+88tu0rnorsIiIiIsVISYYkNX1cf3p2KQd8vxOvrNyR54har3NFKb+6/NhI/xkbd1fzhT/Pp76hMc+RiYiIiLRfSjIkqYqyEs4/alBk+MEifGQKYHifrvz0o5Mx88Mvr9jObY8tyW9QIiIiIu2Ykgxp1kWTh9C1opTjhvfirXW72FekTcGePr4/1505JjL86+dW8O+3N+YxIhEREZH2S0mGNOvYYT0ZM6Ab81bvZNGmvUVZATz0xTPGcOb4aGX2r/3tTZZtKa5Ws0RERESKgdaE+rgAACAASURBVJIMaZaZceExh0WG7315Nc4VXwVwgJIS48f/dQzD+3QBYH9tA9fcM4+91XV5jkxERESkfVGSIS26+LghkY7tlmzey6tFWAE81KNzOb+6/Dg6lftTf8XW/Xztb28VbeIkIiIiUoiUZEiLuncq58KY5mzvnlPcndpNGNSdWz90VGT4Pws38avZK/IYkYiIiEj7oiRDUnLl1OGR/x9bsIkte6rzGE36LjhmMDPeMyIyfNtji3lx2bb8BSQiIiLSjijJkJSMH9idE0f0BqC+0XHfq2vzHFH6bnj/BE4Y0QuARgdfuG8+63cdzHNUIiIiIsVPSYak7PKY0ow/v7qauiLv0K68tIQ7LzuWft0qAdixv5Zr75nLgdribKZXREREpFAoyZCUnTtxIH2r/A355j01PPHO5jxHlL7+3Tvxy48dS1mJUV5ilJWWcMOsBaoILiIiIpIGJRmSsoqyEi47cWhk+J6Xi7sCeOj4Eb25+YKJjOpfxfw1u5g1fz2/nL0832GJiIiIFC0lGdIql540jNISA+DlFdtZurl9dGZ32YnDOGZIz8jwbY8t4fGFm/IYkYiIiEjxUpIhrTKoR2feO2FAZPieIm/ONmRmfOfCSZw40ldudw6+9Jc3eGfDnjxHJiIiIlJ8lGRIq8U2Z/vA6+vZV9M+KkpXlJXwq8uPY2jvzgAcqG3gU3fPZevemjxHJiIiIlJclGRIq00d3YfR/boCsK+mnlnz1+c5oszp3bWC3191AlWVZQCs33WQa++dR019Q54jExERESkeSjKk1cyMK6ZESzPueXlVu2qNaeyAbvzs0skEVU+Yt3on33jg7Xa1jyIiIiLZpCRD2uTi44bQpaIUgHc37+PVlTvyHFFmnT6+P988b0Jk+IHX1/Pr51bkMSIRERGR4qEkQ9qke6dyLpw8ODJ8dzupAB7rE6eM5CPHD4kM3/qfxe2ibxARERGRbFOSIW0WWwH8sQWb2LKnOo/RZJ6Z8d0Lj+TEETEtTt0/n8Wb1OKUiIiISHOUZEibjR/YPXIDXt/o+POra/IcUeZVlJXwy8uPZUgv3+LU/toGPjFzLtv2qcUpERERkWSUZEhaLo8pzbjv1TXUNTTmMZrs6FNVye+vOoGuQR2ULhWlXHfffA7WqsUpERERkUSUZEhazp04kL5VlQBs3lPTbussjBvYjZ9dNpmTRvZm1fb9vLh8O9fdP5+GRrU4JSIiIhJPSYakpaKshMtOHBoZvvvlVXmLJdvOGD+A900aSF2DTywef2czN/9zoZq2FREREYmjJEPSdulJwygNOpWYs2IHSzfvzXNE2TPj5JFcc9qoyPDdL6/mN2raVkRERKQJJRmStkE9OvPeCQMiw/e0w+ZsY11/7njOP2pQZPiWRxfz8Jsb8hiRiIiISGFRkiEZEduc7QOvr2dfTX0eo8mukhLjhx8+mhNH9o6M++pf32TOiu15jEpERESkcCjJkIyYOroPo/t1BWBfTT2z5q/Pc0TZ1am8lN9ecTyH968CoLahkWvunsu77fhRMREREZFUKcmQjDAzrpgSLc245+VV7b5CdI8u5cy8+gT6dfOta+2prmfGXa+yuZ11SigiIiLSWkoyJGMuPm4IXYK+JDbvqeHl5e3/8aEhvbrwhxnRPjQ27K5mxh9eY291XZ4jExEREckfJRmSMd07lfOJU0Zy4she7K+p59cdpNWlSYN78IvLj4u0sLVo4x4++6fX22XHhCIiIiKpUJIhGXXR5MG8tmon9Y2O2e9uZcH63fkOKSemje3HLRcfGRl+fuk2rv/H2+3+kTERERGRRJRkSEaN6lfFeUdGm3f95bPL8xhNbn3k+KF86awxkeEXlm3lJ08uzWNEIiIiIvmhJEMy7jPTRkf+//eCjazYui+P0eTWdWeO4SPHD2F0v67UNTTy06eW8uvZHSfREhEREQElGZIFkwb3YPq4fgA4B7/qQDfZZsb3LjqS8QO7s2O/r/x9y6OLue/VNXmOTERERCR3lGRIVnzu9MMj/z/w+no27DqYx2hyq7y0hB99pGlnfd+c9Tb/VK/gIiIi0kEoyZCsOGFEb04Y0QuA+kbHb5/vGC1NhTqVl/L7q47n/7N33/Ft1ff+x19Hy7a8d5zEsR1nk5CQHUKAQKGMC4GOlF1mW2gptNyuX+/thK57LwXa0tuWVQpllgK3lFV2QvYiezlOYjvx3pYtWTq/PyTLduKVxLYk6/18VD06Q0cfC8fSW+c7ZoxJBvxXdL7x3Gbe210R4spEREREhp5ChgyZO7pczXhm7SGqm9pCWM3wS4y18+eb5wdnQm/3mdz+1AbWHqgJcWUiIiIiQ0shQ4bMuZMymZaTBECrx8fjK4tDW1AIpMU7eOrWBYxJiQP8r8MtT6yLmqF9RUREJDopZMiQMQyDO5Z2jjT151XFUTkTdk5yHE/duoCMhBgAGtva+eJja9kfRaNuiYiISHRRyJAhdfH0HAoy/M2FGlvbeWp1dI6yVJARz19umU9SrA2A6mY31z+yhtIo6hAvIiIi0UMhQ4aU1WLwlXPGB9cfXVFEq8cbwopCZ2pOEo/fNJ84uxWAsvpWrn9kDVVR1ldFRERERj6FDBlyV54xlpzkWACqmty8sP5wiCsKnTl5qfzxhjk4rP5/ekVVzdz97GbqW6KvGZmIiIiMXAoZMuQcNgu3Lem8mvG/HxTh8fpCWFFoLZmYyUNXz8JiQF56HNvL6rn+sTXUuxQ0REREZGRQyJBhcdX8XFKddgBK61xRPzHdRdNzuH/5LBpbvdS2ePikpJ4bHltLQxR2jBcREZGRRyFDhoXTYePmxQXB9Yff34/PZ4awotC74owxfOvTk4PrWw7X8cXH1kblCFwiIiIysihkyLC5YVE+8Q5/p+d9FU28taM8xBWF3tXzx3HvFdOD65sO1XHj4+toamsPYVUiIiIip0YhQ4ZNstPOdYvyguu/f38fphndVzMArluYx0+WnRZc33CwlhsfW6ugISIiIhFLIUOG1S1nFeCw+X/ttpTUs3JfdYgrCg83LMrnR5dNC66vP1jLzY+vo1lBQ0RERCKQQoYMq6zEWJbPHRtc/917+0JYTXi5cXEBP/i3zqCxtriGm59YR4tbQUNEREQii0KGDLsvn12I1WIAsKqomo2HakNcUfi4+awC/uPSqcH1NQdquOWJ9bjc0TmBoYiIiEQmhQwZdrlpTpbNHA2AzQLPrTsU4orCy61LxvO9i6cE11cVVXPrk+uidqZ0ERERiTwKGRISt59byFkTMkhxOnhuXQkbDtaEuqSw8uVzCvnORZ1B40idi6/8ZYP6aIiIiEhEiMiQYRjGWMMwHjMMo8wwjDbDMIoNw3jAMIzUUzjn2YZheA3DMA3DuHcw65XjTcxOJD3BQVWTG4BfvL5LI00d4/ZzC/nWpyczMSuBykY37++p5PpHNTO4iIiIhL+ICxmGYRQCG4CbgLXAr4Ei4C5glWEY6SdxzkTgz0DLIJYq/bjngsnYrf6+GeuKa3l3V0WIKwo/X106geXzxtIYuIKx8VAdV/9xNdVNbSGuTERERKR3ERcygIeBLODrpmleYZrmd03TPA9/2JgM3HcS53wQSAZ+PnhlSn/GpTu5Zv644Pqv3tiNN8pnAe/JbUsK+fHlnfNo7DjSwBf+uJqj9a0hrEpERESkdxEVMgzDGA9cCBQDvztm9w+BZuB6wzDiT+Ccy/BfFfk6UDY4lcpAfe28iTgDs4DvLm/k5U2lIa4oPH3xzHx+9bnTCQzKxb6KJpb/YRWHa3TxTURERMJPRIUM4LzA8i3TNH1dd5im2QisBJzAwoGczDCMLOBPwMumaT41mIXKwGQmxnDrkvHB9fvf3kNbu0ZR6snyubk8eNUZ2AJJ41BNC8v/sIr9lU0hrkxERESku0gLGZMDyz297N8bWE4a4Pn+iP81+MrJFmQYxoaebsCUfh8sANy2pIC0eAcApXUunlqtIW17c9nM0fzvdXOCs6YfqW/lC39Yxc4jDSGuTERERKRTpIWM5MCyvpf9HdtT+juRYRg3A8uAO0zTLB+E2uQkJcba+drSCcH13723j8ZWjaDUm09Ny+bxG+cRZ/c3M6tqcnPVH1ez+XBdiCsTERER8Yu0kNGfQIt1+uw9bBhGPvAA8IJpms+fyhOapjmnpxuw61TOG22uXTiOsalxANQ0u/nTh0Uhrii8LZ6QwV9umU9ijA2AepeHa/+0mjVF1SGuTERERCTyQkbHlYrkXvYnHXNcbx4DXMAdg1GUnLoYm5V7Luxs5fbIigNUNmqY1r7MzU/jmS8tJNVpB6DZ7eWLj6/lgz2VIa5MREREol2khYzdgWVvfS4mBpa99dnoMBv/MLiVgcn3TMMwTODxwP7vB7a9fGrlyolYNnMMU0YlAtDi9vKbd/f28wiZPiaZ5768iKzEGABaPT4eemcvr27RQGkiIiISOrZQF3CC3gssLzQMw9J1hKnAhHqL8V+hWN3PeZ7EPwrVsSYCZwOb8U/4t+mUK5YBs1gMvnPRFG56Yh0Af11ziJsXF5CfMeARiaPSpOxEnv/yIq59ZA3j0pysKqpmw8FaKhpau43cJSIiIjJcIupKhmma+4G3gHzgq8fs/jEQDzxpmmZzx0bDMKYYhtFtpCfTNL9umuatx97ovJLxWmDbsXNxyBA7d3Im8wvSAGj3mfzP2/1dlBKA/Ix4Xrp9EVVdZgK/97Wd3PuPHfg0waGIiIgMs4gKGQF3ABXAQ4ZhvGwYxs8Nw3gX+Ab+ZlLfP+b4nYGbRADDMPjuxZ2Z8P+2lLGttL8uNgKQnRzHC19ZxLz81OC2R1Yc4O7nNuNu9/XxSBEREZHBFXEhI3A1Yy7wBLAAuAcoBB4CFpmmqeF1ItzscalcOC07uP7LNzRQ10ClOB385ZYFfPq0ztfv1S1l3PTEWg0LLCIiIsMm4kIGgGmah03TvMk0zRzTNB2maeaZpnmXaZo1PRxrmKZp9HSeHo59InD8fwx+1XIivn3RZAITW/PR3io+3lcV2oIiSKzdysPXzuH6hXnBbSv3VfOFP6ymoqE1hJWJiIhItIjIkCEj34SsRD43Z2xw/Zdv7MI01bdgoKwWg58sO41/7zIs8I4jDXzm9x+zv7IphJWJiIhINFDIkLB196cm4bD5f0XbfSavbNawrCfCMAy+dt5EfvW507EGLguV1Lr43O8/ZuOh2hBXJyIiIiOZQoaErdEpcXzjU5OYMSaZ7WUN3PvaTupd6ldwopbPzeWRG+YSZ7cCUNvi4Zo/readneUhrkxERERGKoUMCWvXL8oLzvxd1dTGf72pTuAnY+mULJ750kLS4h2Af9K+/3pzN39ZVRzSukRERGRkUsiQsJYQY+OHl00Lrj+95hCb1NTnpMzKTeFvt59Jbloc49KclNS6+M9XtvOjV7fT7tUQtyIiIjJ4FDIk7F00fRTnTckCwDTh//19mz4Un6SCjHheun0xE7MSaGprB+CJj4u59cn1GuJWREREBo1ChoQ9wzD48eWnEWv3/7ruPNLAEx8Xh7aoCJaZGMNvr5nNxdNHBbe9v7uSz/1+FYdrWkJYmYiIiIwUChkSEXLTnNx1fudwrPe/vYfSOlcIK4pscQ4rv7tmNl9dWhjctru8kSsfXsmGg2qOJiIiIqdGIUMixq1LCpicnQhAi9vLj1/dHuKKIpvFYvCtT0/hfz4/E7vVP8RtVZObq/+0mlc2l4a4OhEREYlkChkSMexWCz/7zPTg+ls7ynl7h4ZhPVWfnTOWp29dSKrTDoC73cddz27m12/v0QSIIiIiclIUMiSizMlL4+r5ucH1H76yjeZAB2Y5efML0nj5q4spzIwPbnvwnb3c+cwmvb4iIiJywhQyJOJ856IppAfmeyirb+WBf+0JcUUjQ156PC/dsZglEzOC20rrXFz1x1Xq/yIiIiInRCFDIk6K08H3L50aXH9sZTE7yhpCWNHIkRxn57Eb53HtgnFMzUlkW2k9W0sbuOw3K1i1vzrU5YmIiEiEUMiQiHTlGWM4szAdAK/P5Psvb8XnU/+BwWC3Wrj3iulcvzCPji4ZNc1urnt0DY+tOKB+GiIiItIvhQyJSIZh8NMrpuOw+n+FNx2q469rD4W4qpHDMAyuWZDHX29bSEaCv2ma12fyk3/s4JvPb8Hl9oa4QhEREQlnChkSsQozE/jKuZ3zPPzyjV1UNLaGsKKRZ35BGv9351nMzE0Jbvv7plI+978fa+I+ERER6ZVChkS0O84tpCDDPyJSY2s79722M8QVjTw5yXE8/+WFfGFu56he28sauPy3K1i5ryqElYmIiEi4UsiQiBZrt/LTZZ1zZ7yyuYyP9laGsKKRKcZm5RefncF9V04PTtxX2+Lh+kfX8KcPi9RPQ0RERLpRyJCId9bEDK6YNTq4/p8vb6PVoz4Dg80wDK5dkMezX1pIZmIMAD4T7vvnTu56djMtmk9DREREAhQyZET4/qXTSIq1AVBc3cLD7+0LcUUj15y8NF678yzm5KUGt60pqubqP61mX0VjCCsTERGRcKGQISNCZmIM37l4SnD99x/sZ19FUwgrGtmykmJ55raFXLdwHA6rQXyMjS0l9Vz2m5W8tLEk1OWJiIhIiClkyIhx9bxxzB7nHwXJ4zX5j5e3qq/AEHLYLNx7xQzuXz4rOCO4y+Plm89v4TsvfqImayIiIlFMIUNGDIvF4L4rZ2C1+Dsmry6q4aWNpSGuauT7t5mjefmrixkfGOUL4Ln1h7nidyvZX6mrSSIiItFIIUNGlKk5SdxyVkFw/b5/7qS22R3CiqLD1JwkXr3zLC6f2dkBf9fRRi77zQpe2aygJyIiEm0UMmTEuftTExmTEgdATbObX76xK8QVRYeEGBsPXjWLn105A4fN/6elxe3lrmc3872Xtqr5lIiISBRRyJARx+mw8ePLTwuuP7fuMCv2atK44WAYBtcsGMfLdywOTpII8MzaQ1z58MfsV2d8ERGRqKCQISPSp6Zl8+nTshmfGU9eupNvv7iFuhY1mxou00Yn8erXFvNvp+cEt7nbvVzx8EqeW3dIHfJFRERGOIUMGbHuu2IGrR4vxdUtlNW38u0XP9GH22GUGGvnN1efwU+vmE5avAOX20tjazvf+dtW7nh6o0KfiIjICKaQISNWRmIMP7qss9nUWzvKeXLVwRBWFH0Mw+D6hXk8fet84hzW4PbXtx3logc+4uP9asYmIiIyEilkyIh24WmjuPHM/OD6fa/tZHtZfegKilJTc5L5x51LuGbBuOC2ow2tXPvIGn75xi7c7b4QViciIiKDTSFDRrzvXTKF00YnAeD2+rjzr5tobmsPcVXRJ85h5WdXzuCP188h1WkHwDTh9+/v53P/+zFFmlNDRERkxFDIkBEvxmblN1efgTPQXKeoqpn/fGVbiKuKXheeNoo37j6bsyZkBLd9UlLPpQ+t4Nm16hQuIiIyEihkSFQYn5nAfVdOD66/tLGUv20oCWFF0S07KZYnb57P9y+Zit3qn6Hd5fHy4oYSbntyPRWNrSGuUERERE6FQoZEjSvPGMtnZ48Nrv/nK9vYryY6IWOxGNx29nj+fsdiCjPjKcyMZ/PhOv61s4ILf/0hr24p01UNERGRCKWQIVHlJ8tOY3ymf5K4FreXr/11k2aiDrHpY/ydwi+enkO7zx8q6lo8fP2ZTdzx9Eaqm9pCXKGIiIicKIUMiSrxMTZ+e/VsHDb/r/7OIw38/J87Q1yVxDms/PunJ/PXWxcwJiUuuP31bUe58Ncf8sa2IyGsTkRERE6UQoZEnWmjk/jPS6cG1/+86iBvbDsawoqkw5kTMnjzG2dz9fzOoW6rm9185amNfP2ZTZrAT0REJEIoZEhUum5hHp8+LTu4/u0Xt1BS2xLCiqRDQoyNn39mBn++eT6jkmKD21/dUsYFv/6Qd3aWh7A6ERERGQiFDIlKhmHwq8/ODDbNaWht565nN+PxalK4cHHOpEze/MbZfG5OZ2f9ysY2bvnzeu55fgu1zbqqISIiEq4UMiRqJTvtPHT1LKwW/xCqGw7W8sC/9oS4KukqOc7Of39+Jo/cMJfMxJjg9m2ldXz6gQ/559YjGoFKREQkDClkSFSbk5fGPRdOCq4//P5+VuytCmFF0pNPTcvmrbvPZtms0cTaLDS1ealobOOOpzdy25PrKatzhbpEERER6UIhQ6LeV84uZMlE/+zTpgl3P7eZykYNmxpuUuMdPHjVGfz+ujndmrX9a2cFF9z/AY+tOIDXp6saIiIi4UAhQ6KexWJw//JZZCT4m+NUNbXxzec349MH1rC0dEoWb3/zHK5d0DkCVbPby0/+sYPPPLyS7WX1IaxOREREQCFDBIDMxBh+/YWZGP7uGXy0t4qH398f2qKkV8lxdu67cgYvfmURE7MSgtu3lNRz+W9X8vPXd+Jya5JFERGRUFHIEAlYMjGT288pBCAnOZZn1x3ivV0VIa5K+jI3P43Xvr6Eey6YhMPq/3Pm9Zn84YMiLnzgAz7cUxniCkVERKKTQoZIF9+4YBJfmJtLi9tLSa2Lr/11IzvKGkJdlvTBYbNw5/kTef3uJSwoSAtuP1zj4obH1nL3s5uoalIfGxERkeGkkCHShd1q4Z5PTyIhxgb42/rf8ud1VDS0hrgy6U9hZgLPfmkhv/rs6STH2YPbX95cxl3PbOKp1QfVMVxERGSYKGSIHCMrMZbHbpxHYiBoHKlv5ZY/r6fF3R7iyqQ/hmGwfF4u79xzDstmjQYgOzGG9Qdr+Y+Xt3H5b1ewvrgmxFWKiIiMfAoZIj2YPCqR3107OzhR39bSeu5+drO+CY8QGQkxPHjVGTxx0zxmjE2mrd0/5O32sgY+97+r+OZzm3V1SkREZAgpZIj04uxJmfxk2WnB9bd2lPOL13eGsCI5UedOzuK318zmmxdMIsbW+efupU2lnPc/H/DHD/fjbvf1cQYRERE5GQoZIn24dkEety0pCK7/6aMDPL3mYAgrkhMVa7fy9fMn8s4953Dx9FHB7U1t7fzsn7u4+MEP+WivRqESEREZTAoZIv347sVTuXBadnD9B69s5wMNjRpxxqY6+f11c3jqlgVM6DK3xv7KZq5/dC1f+csGSmpbQlihiIjIyKGQIdIPq8XggatmMWNMMuCfh+GrT29k99HGEFcmJ+OsiRm8ftcS/uPSqcFRxADe2H6U8//nAx5+bx/NberkLyIicioUMkQGwOmw8egX5zI6ORbwN7W5+Yl1VDSq83Akslst3LpkPO/++zl8ZvaY4PaCjHh+9eZuzv3v93l27SF19BcRETlJChkiA5SVFMujN84j3mEFoLTOxW1PbsDl9oa4MjlZWYmx3L98Fn+7fRGnj03G4/V3Aq9sbOO7L23lkgc/4v3dmvVdRETkRClkiJyAqTlJ/Paa2QRGtmXL4Tq++fxmfPrGO6LNyUvj77efyVfOKSQ7KSa4fXd5Izc+vo7rH13DziOa+V1ERGSgFDJETtDSKVn86PLOoW1f33aUX725O4QVyWCwWi18fm4u7/37uXzzgkk4A1esAD7aW8UlD33Et1/cwtF6NZETERHpj0KGyEm4YVE+Ny3OD66/vLmUR1cUha4gGTROh42vnz+R9791LlfPHxe8amWa8Pz6Epb+9/vc//YedQ4XERHpg2GaauYxFAzD2DB79uzZGzZsCHUpMkS8PpMv/2U9ZXUuDte6aGxt5yfLTuOGRfmhLk0G0Z7yRn7+z528t7v7sMVzxqVyxRmj+cK8cThs+r5GRERCzgh1AV3pnVHkJFktBg9dfQaZibE0tvq/1f7BK9v5y6rikNYlg2tSdiKP3zSfp25ZwNScpOD2prZ2/vOV7Zx///u8tLFEI1GJiIh0oSsZQ0RXMqJHY6uHGx5by6ZDdcFtP71iOtcvzAthVTIUvD6Tv28q5Z+fHOHdY0admpSdwD0XTubCadkYRlh9mSQiItEhrN58FDKGiEJGdGlo9XDDo2vZfLgzaNx7xXSuU9AYkVo9Xp5cVczD7++nrsXTbd/Mscl869NTOGtiRmiKExGRaKWQEQ0UMqJPT0Hjviunc+0CBY2RqrHVwyMfHeCRj4poPma+lPMmZ/HV8wqZk5cWoupERCTKhFXIUJ8MkUGSFGvnyVvmMzM3Jbjt+3/fxl/XHAphVTKUEmPtfOOCSXz47aXcelZBtw7gTW3tfPb3q7j+0TVsOFgTwipFRESGX0ReyTAMYyzwE+AiIB04ArwM/Ng0zdoBPD4euAK4FJgN5AI+YDfwDPAb0zTdp1ijrmREqXqXhxseXcOWkvrgtp9/ZgZXzx8XwqpkOBypd/HQO/t4Z0c5jW3tuDydVzeWTMzg7k9N1JUNEREZKmF1JSPiQoZhGIXAx0AW8AqwC5gPLMUfEhabplndzzkuAl4HaoD3gH1AGnAZMCpw/vNN0zzpWbcUMqJbvcvD9Y+u4ZMuQeMXn5nBVQoaUeFgVTMPvruXlzeVcuygUwobIiIyRBQyToVhGG8CFwJfN03zN1223w98A/iDaZpf6eccs4DTgBe6XrEwDCMReB//1Y1/N03zf06hToWMKFff4uG6R9ewtbQzaPzyszP4wjwFjWhxoKqZ3/QSNs6akM6d501kwfj00BQnIiIjjULGyTIMYzywHygGCk3T9HXZl4i/2ZQBZJmm2XySz3EN8DTwD9M0LzuFWhUy5LigYRjwy8+czvJ5uSGuTIZTT2FjUnYCe8qbmJefyh3nTuDcyZka+lZERE5FWL2JRFrH7/MCy7e6BgwA0zQbgZWAE1h4Cs/RMR5l+ymcQwSAZKedp25ZwPQx/kncTBO+89InvLD+cIgrk+FUkBHP/ctn8c495/KZ2WOwGBBjswKwrriWm55YxyUPreD/tpRpUj8RERkRIi1kTA4s9/Syf29gOekUnuPmwPKNUziHSFBH0DhtdGfQ+PbfPuHFf3j+IgAAIABJREFUDSUhrkyGW2fYOIepOYnYrZ1fOu080sCdz2zi/P95n2fXHqKt3dvHmURERMJbpIWM5MCyvpf9HdtTetnfJ8MwvoZ/xKrNwGMDfMyGnm7AlJOpQUamFKeDp29dwLSczqDxrRe3KGhEqYKMBH71uZl88K2l3Ly4gDi7NbivuLqF7760lbN/9Z5//o02XVQVEZHIE2khoz8dXwuecHsDwzA+AzwAHAU+a5qmp5+HiJyQnoLGb9/by58/PhDiyiRURqfE8YPLprHyu+fx9fMmkBRrC+4rb2jj3td28qUn1/Nfb+6iouGkB7sTEREZdpHW8fu/gH+nl5GfDMP4LfBV4A7TNH9/Aue9AngeqAKWmqa5exBqVcdv6VFts5trHlmD2+OlvLGNprZ2vnT2eL570RQslrDqsyXDrLHVw1/XHOKRFQeobGwjPd5BvctDu8/EbjW4fOYYbl1SwNRAUBUREekirD5ERNqVjI4P/731uZgYWPbWZ+M4hmF8HngBKAfOGYyAIdKX1Hj/FY2CzHiaAk1h/vhhEV97ZiOtHrXDj2aJsXa+fE4hH317KfdeMZ35BWm0BzqCe7wmf9tYwsUPfsR1j6zh/d0VRNKXRCIiEl0i7UpGIf6J84rpfQhbC5A5kCFsA8PVPgmU4r+CUTSItepKhvSpxd3OXc9u5u0d5cFtc/JS+dMNc0mLd4SwMgkXXp/JW9uP8qePith4qO64/ROzErh1SQHLZo0htku/DhERiUphdSUjokIGnPhkfIZhTAEwTXPXMef5Iv7O3QfxB4yDg1ynQob0y+sz+ek/dvDEx8XBbfnpTh6/aT4FGfGhK0zCzoaDtTy6oog3th09bmK/jAQHXz57PMvOGENWYmxoChQRkVBTyDgVgasZHwNZwCvATmABsBR/M6kzTdOs7nK8CWCaptFl21LgX/ivejwG9DRpQZ1pmg+cQp0KGTJgj644wL2v7aDjn2Oq084jX5zLnLy00BYmYedwTQuPrTzA8+sO0+z2N6+zGP5meA0uDxdPz+GGRXnMyUvV5H4iItElrP7oR1zIADAMIxf4Cf7hZtPxN5N6GfixaZo1xxzbU8i4EXi8n6c5aJpm/inUqJAhJ+SNbUe469nNtLX7WwE6bBZ+vXwWl56eE+LKJBzVuzw8u/YQT3xczOiUODYcrO22f1pOEl88M4/LZ44hzqGmVCIiUUAhIxooZMjJ2HSollv/vJ7qZndw2/+7ZAq3LRmvb6WlRx6vj3/tLOfRjw6w/pigAZAcZ2f53LFcvzCfcenOEFQoIiLDJKw+KChkDBGFDDlZB6ubuenxdRRVdY5dcO2CXH542XQctkgbEE6G0/ayev6y6iAvby6l1ePrts8wYOnkLK5bOI5zJmZitep3SURkhFHIiAYKGXIqapvdfOkv61lX7P9mesaYZOIdVh665gx17JV+1bW4eWF9CX9ZfZBDNS3d9uWnx+P1+fjCvFw+PzeX7CT9PomIjBAKGdFAIUNOVavHy7de/IT9FU3srWjE4zXJTIzhoavOYFFheqjLkwjg9Zl8sKeCJ1cd5P3dlQDMy08NhleLAedNyeKqeeM4d3ImNl3dEBGJZAoZ0UAhQwaDz2fy6IoD/Oz1ncGRpywG3HPhZG4/p1AzhMuAFVc18/Tag/xjyxGO1Lcetz87KYblc3NZPjeX3DT13RARiUBh9aFAIWOIKGTIYFqxt4q7nt3UrUP40smZ3L98FqmauE9OQKvHy5vbj/LM2kOsLqo5br9hwFkTMrhq3jgumJatfkAiIpFDISMaKGTIYDta38qdz2wMNnUBGJMSx++unc2s3JQQViaR6kBVM8+tO8yLG0qoamo7bn9avIPlc8fy2dljmZidGIIKRUTkBChkRAOFDBkKHq+P/35zN3/4sCi4zW41+P4lU/nimfka5lZOisfr452d5Ty77jAf7Kmk69vC3LwU1h+sY8aYZD4zewyXzxxNekJM6IoVEZHehNWHAIWMIaKQIUPp7R3l3PP8Zhpa24PbLp2Rwy8+O4PEWHsIK5NIV1rn4vl1h3lh/WHK6luZlJ3AnvKm4H6bxeDcyVl8bs4Ylk7JIsamif5ERMKEQkY0UMiQoXa4poU7nt7I1tL64LaCjHgevnY2U3OSQliZjARen8mKfZU8t+4w/9pRgdvrO+6Y5Dg7l83M4TOzx3JGboqupImIhFZY/RFWyBgiChkyHFo9Xu59bQdPrT4U3BZjs/DTZdNZPi83hJXJSFLf4uEfW8t4aWMpG3qYVRzgjHHJnDspm8tnjaYgI36YKxQRERQyooNChgynVzaX8r2XttLi9gKQEe/gzAnp/Ojy6aRp9CkZRAeqmvn7xhL+trGU0jpXcPuCgjTWHPCPVjVjTDKXzxzNpafnMDolLlSliohEG4WMaKCQIcNtX0Ujtz+1kf2VTUzI8rejz0hw8NNl07l4Rk6oy5MRxuczWVtcw0sbS/jn1qNkJcZQVNV83HHz89O4bNZoLpk+Sh3GRUSGlkJGNFDIkFBocbfzp4+K+PXbe7ttv/T0HH5y+Wn6kCdDwuVu5187K3h1Sxkf7K7ssf+G1WJw1oQMrpg1hvOnZZGkAQpERAabQkY0UMiQUHp3Vznfe2kr5Q2dcx+kxfuvalx6uq5qyNCpd3l4c9tR/u+TMlbuq8J3zFvMvLxUNpfUcdaEDC6ensMF07I1oaSIyOBQyIgGChkSavUuD/e9toPn15d0237x9FH8ZNl0MhN1VUOGVmVjG//ceoRXt5QFO4xPzEpgb0XnkLhWi8Gi8elcPGMUF04bpd9LEZGTp5ARDRQyJFy8v7uC7720lSP1rcFtqU47P7r8NC6fOVrDjsqwOFzTwpvbj/Lq5jI+6TLsclcWA+blp3Hx9FFcND2HUcmxw1yliEhEC6s3dIWMIaKQIeGkodXDz/+5k2fWHu62/cJp2dx75XSyEvVhTobP4ZoW3th2lH9uO8KmQ3W9HnfelCwWFKTxqWnZFGYmDGOFIiIRSSEjGihkSDj6cE8l33tpa7ehR5PjbHzv4qksn5uLxRJWf58kChypd/HGtqO8vu0o64pr6PqWND8/jbXF/mFxx2fGc8HUbC6Yls0Z41Kx6ndVRORYYfWHUSFjiChkSLhqbPXwi9d38fQa/wR+c8alsuFQLTPGJPOjy6cxJy8txBVKtKpobOXN7eW8se0Iq4tqKMyMZ09503HHpcU7OG9KFhdMy2bJxAycDlsIqhURCTsKGdFAIUPC3cf7qvivN3dxoKqFOpcnuH3ZrNF89+Ip5CRrEjUJnZpmN+/sLOftHeV8tLcKl8fb43ExNguXTB/FnPw0zp2cydhU5zBXKiISNhQyooFChkQCl9vL7z/Yzx8+2E9be+fcBnF2K7efW8iXzh5PrN0awgpFoNXjZeW+Kv61s5x/7aygsrGt2/55+amsK+4cvercyZksnZzF3Pw0HDZLKEoWEQkFhYxooJAhkaSktoWfv76L1z450m37mJQ4/t8lU7lkxiiNQiVhwecz2VJS5w8cOyrYXd7IlFGJ7DraeNyx8Q4riydkcO7kLM6dnMnoFF2dE5ERLazeqBUyhohChkSiNUXV/Pj/drDjSEO37fPz0/jBZdOYPiY5RJWJ9OxQdQvv7a7g3V0VrCqqxt1+/GzjHSZnJ3LulEyWTsrijLwUYmy6SiciI4pCRjRQyJBI5fWZPLfuMP/91m5qmt3B7YYBV83L5Z4LJ5ORoAnTJPy43F5WF1Xz3u4K3ttdweEaV4/HTcpO4HCNi/kFaSyZmMHiCRlMGZWoq3UiEunC6o+YQsYQUciQSFfv8vDQO3v588fFtPs6/06cMS6FcydlcdNZ+STF2kNYoUjvTNOkqKqZ93dX8v7uCtYU1eD2+kiIseLy+PD6ur/3ZSTEcNaEdBZPyGDJxExNBCgikUghIxooZMhIsa+iiXtf28H7uyuxGjAqOY7SOhfJcXZuW1LAjYsLSIjREKIS3lrc7Xy8r5pPSup4ZUsZB6tb+jx+QlYCZ03IYPGEdBaMT1egFpFIoJARDRQyZKR5b1cFr2wu5eXNZd22pzjt3LZkPDeemU+8woZEiMM1LazYV8WKvVWs3F9FXYunx+Om5SSx62gD08cks3B8OovGpzM3P5VEhQ4RCT8KGdFAIUNGonavj1c2l/HQu3uP+yY4Ld7Bl84ezw2L8jQ5mkQUn89ke1kDH+2rZOW+KtYV1wY7kC8oSGPNgZpux1sMmDEmmYWF6Swcn868/DRdzRORcKCQEQ0UMmQka/f6eGlTKb95d+9xnWszEhx8+exCrluYR5xDo/dI5HG5vaw/WMOKvVUUVTXzr53l9PVWabUYLBqfzmmjk5iXn8acvFRS4x3DV7CIiJ9CRjRQyJBo4PH6eGljCQ+9s4/SumPDRgxfXVrI8rm5akYlEa3e5WHdgRpWFVWzuqiaHUcajgsdZ4xLYdOhuuD6xKwE5uanMb8glbl5aYxNjdPoVSIy1MLqj4xCxhBRyJBo4m738eKGEn73XvewMX10EgdrWrhm/ji+eGa+JkOTEaG+xcOaA9WsLqphdVE1O482MC8vjbXFNb0+ZlRSLPMK0piX7w8dk0clYrWE1ecBEYl8YfVHRSFjiChkSDRqa/fywnp/2Ii1WTlQ3RzcZ7UYXDIjh1vPKmBmbkoIqxQZXHUtbjYcrGXNgRrWFdewtaS+27DPPVlcmI5hGMwel8IZ41I5Y1wKKU41sRKRU6KQEQ0UMiSatbV7eWPbUX799h6KexgqdG5eKrcuKeCCaaP0ba6MOC63l82H61hfXMPa4ho2Hqyl2e3tdkxBRjwHqpq7bRufEc+scSnMDoSOydmJ2KyW4SxdRCJbWL2hKmQMEYUMEf+oPe/uquCRFUWsLjq+KUluWhw3nVnA8nm5Gp1HRqx2r49dRxtZX1zDuuJatpfVc6imhX4uduB0WDl9bDJnT8xkfGY8p49NISc5Vn07RKQ3YfXHQSFjiChkiHS3rbSex1Yc4NUtZcc1JUmMsXHDmXksmzWGSdmJIapQZHiYpklJrYtNh+vYeLCWTYfr2FFWj8fb8/tx16seGQkxzBybzOljUzg9N5mZY1NI00hWIuKnkBENFDJEelbe0MqTq4p5es2h4ARoyXE2mtu8tPtMZuWm8IV5ufzb6Tma8EyiRqvHy/ayejYdqmPjoVo2HarjSH0rMTaDdh94+7jsMTY1jpljU5iXn8aErASmj0lS/w6R6KSQEQ0UMkT65nJ7+dvGEh5bcYCclFhW7qvutj/ObuWSGTksnzuW+QVpaiIiUedIvYutJfVsOFjLlpI6tpU20NTW3uvxqU47tYHgPjY1jumjk5k+JonTxiQzY0wyGQkxw1W6iIRGWL1RKmQMEYUMkYHx+UxWF1Xz9JpDvLXjaI9NRgoy4vn83LF8dvZYspNiQ1ClSOj5fCZFVU1sOVzPJyV1bCmpZ8eRBtztPrISY6hobOvz8WfkppDitDM1J4lpo5OYlpNEXnq8Bl8QGTnC6h+zQsYQUcgQOXE1zW5e3lTK8+sPs+to43H7LQYsnZzF5+fmcv7ULOwaeUeinLvdx57yRnaXN7K+uJZtpfXsPtqI2+vrdpzdYuDj+GZXcXYrU3ISmZaT5A8fOUlMHpWoCTRFIpNCRjRQyBA5eaZpsrW0nufWHebVzWU09tBEJCPBwRfm5XL+1GzOyE1RcyqRAHe7j70VjWwvbWBraT3byupxt/vYXtbQ72Nn5aaw+XAd49KcTB6VyJRRicFlfnq8htQVCW9h9UaokDFEFDJEBofL7eWN7Ud4fl0Jq4o6+20kxFhp9fho95mMTo7l4hk5XDIjhzNyU7Co+YdIN+1eH8XVLew40sCOsgZ2Hmlgx5EGKo9pYrWgII01B3qeudxhszAhM4EpoxKZmZtMbpqTiVmJjEmJ0785kfAQVv8QFTKGiEKGyOA7WN3MC+tLeHFDCQUZ8d1CR4ec5FguUeAQGZDKxrZg4NhR1oDL4+XdXRV9jmYFMC7NyaEa/0SbcXYrE7ISmJiVwITsBCZlJTIxO4GxqU719xAZXmH1D04hY4goZIgMHa/PZN2Bav6+qYw3dxwNDoV7LAUOkRPX1u5lf0Uzu8sb2HW0kd2B25H6VgCsBhiGcdx8N8eKtVsozExg4fh0UuLsFGYlUJiZQF66k1i7dTh+FJFoE1ZvcgoZQ0QhQ2R4eLw+Pt5fzT8/OdJn4DhnUiajU2JZOjmLxRMy1LFV5ATVt3jYXd5IUWUT28sa2FPeyL6KJqqb3X0+bnxGPEWByQTBP4DD2FQnhZnxFGYmUJiVwISsBPLT48lIcKh/lcjJC6t/PAoZQ0QhQ2T49RU4RiXHcjTwTazDamHB+DTOnZzF0smZjM9MCFXJIhGvuqmNvRVN/lt5I3vL/fermvz9PeLsVlweb5/nmF+QxtoDNSTG2MjPiKcgcBuf6V/mpztJitMEgyL9UMiIBgoZIqHl8fpYtb+a1z45wr7KRjYcrOv12Px0pz9wTMliQUGamnKIDILaZjd7KxrZV9HM/som9lc2UVTZzOHaFo796DFzbApbSnr/Nzo3L5UDVc3kpTvJT49nXGDZsZ7itOsKiIhCRnRQyBAJH+1eH5sO1/Hurgre21XR4xwcHeLsVhZPSA8GjsLMBH14ERlErR4vxdXN7K9opigQPupcHtYX1/Y6o3lfo14BJMbayE+PZ25+Kk6HlXFpTnJTneSmOclJjtXQuxItwurNSiFjiChkiISvI/Uu3ttVyXu7K1i5r4oWd/emHDE2A68P2n0mmYkxLBqfzqLCdBaNTycv3anQITIETNOksqmN4qoWDlQ1UVTVzIHKZoqrm0mMtbPhYG2/5+gpjNgsBmNS4xiX5mRKdiJpCTGMTY0jN83J2NQ40uPVD0RGjLD6RVbIGCIKGSKRoa3dy7oDtby7q4L3d1dQVNXMrLHJbC6p7/H40cmxLAwEjkWF6YxNdQ5zxSLRx+czOdrQSnF1MwerW/zLqhYO1rRwsLo5+EXBnLyUPptGnj42mU+O+bcda7cwNtUfOPw3J2NSYhmT4t+WkRCjkekkUoTVL6pCxhBRyBCJTMVVzWw4VMOb28pZXVRNQ2vPzTcA0hMcxNgszMlLY864FObkpTElJxG7mmaIDJuOKyAHq1sorXVRVNXM4ZoWDgVuXSccnF+QytoD/V8RSYy10Rj4t++wWshJiWV0chxjUuMYnRIXDCGjU2LJSY4jzqF+XBIWFDKigUKGSOTz+kx2Hmlg1f5qVhVVs/ZATbc243PGpbDhUPdvTePsVmbmJjMnL5XZ4/y31HiNiiMSKi3udkpqXRyqbqGqqY095U0crm2hpNZFSU0LjT30Azl22N3edIyKleK0k5McR05ybJdbYD0ljlFJsQoiMhwUMqKBQobIyNPu9bG1tJ5VRdWs2l8NJny0r6rfx43PjOf8KVmMTXUyY2wy03KSNIKVSJiod3ko6QgdtS4O17TQ7vOx8WAdZfWuXufeAZifn8ra4v6vjACMSoolxWknOymWUUmxZCfFkJ3ccT+WUcmxpDkdapolpyKsfnkUMoaIQobIyOfx+th1pJENB2vYcKiOjQdrKa1z9XhsXpqTgzUtAFgtBhOzEpg+JpkZY5KZPsYfPPRNp0j4aWpr50idi9LArazORVldK6W1LpwOKyv3V+Hx9v1ZKiHGSlNb33OFANitBudMyqSqyU1WYgxZSTFkJcYedz89IQarwogcL6x+KRQyhohChkh0OlrfysZDtWw46L9tL6vHbjFobffh6+PPrdViMCEzgbMmZJCTEsvkUYlMzk4kMzFGI9+IhDGfz6SquY0jda0cqW/lSL2Lo/WtlNW3crTeH0jiHBb2VfTf/Ar8c4Ks72ckLYsBGQn+4DErN4U2j4/MxBgyEmLISIwhI8FBVmA9OU5ziESRsPoPrZAxRBQyRAT8cwLsOFLPxoN1bCutZ2tpPUVVzcdNRtZhfn4aa4s7h+BMddqZlJ3oDx2B4DFpVCJJsfZh+glE5FR5vT6qW9yU17dxtKGV8sDtaH0r5Y1tlNe3crShlXqXhxljktla2vPodj2Zk5fa5/C+dqtBenwMGYkOMhO6B5GMhBjS4h2kx8eQnuAgLd6hgSsiW1iFDFuoCxARGcli7VZmj0tj9ri04LamtnZ2lDXwScnxwcN7TPqobfGw5kDNcWP/j06OZVIgeEzMTGDSqEQKMuJJVPgQCTtWqyXQ1CmWGST3epzL7aW8oZWKxjYqGlupaGgL3q9sbAust1LbpZ+Ix+vr87k9Xv/wv0cbWoPb7Faj1yZeyXF20uMdwdAxKTsR04S0eP96aryD9MAyzelQM0/pla5kDBFdyRCRE9ERPPZXNrLlcD27yxvZc7SRZnf/7bgzEx1UNroBfxOK8RnxFGTEkx9Yjs+MZ1yaU53NRUYId7uPyqY2KhpaqWlyU97YRmVjG1VNnTf/urvHWdSzk2Iob2jr4czH62+29Vi7hfT4GFLj7YzPSAD8V2BTnA5SnXZS4x2d950OUpx2EmJsasI1NMLqRVXIGCIKGSJyqnw+k9I6F3vKG9l1tJE95Y3sPtrI/sqmbt9CDqR5hWHA6OQ4xmf6g4c/hDjJS4tndEqcAojICNXq8VLZ2EZlUxtVHcGj1UNpnYuqZjc1TW6qm9uobnJT2+I+ru/YvPxU1g1wBK2sxBgqGvsPL3arwWmjk2hq85ISZyfFaSc5zkFy4L5/3R5Yd5AcayfZaScp1oZNzbn6opARDRQyRGSoeLw+iquag8Gjpc3Lh3srOVjdgrufphNdTcpOYE95E+D/cNAx23H3ZZxCiEiU8PpM6lrcVDe7qQ6Ej+Y2L0fqXdQ0u6lp9geRjkBS2+zp9jcnzm7F5en/6isMPJCAvwlXvcvfRCzeYSU5zk5Sxy22M5Akxdn8y1j//aRYO4mB+4mxdhJjbCN9iOCw+uHUJ0NEJMLYrRYmZicyMTux23avz6SszsWBqubjbiW1Lcd9Q9m187i/3XcbG4+ZXLBDRwg5LSeJ+Fg7Ocn+sf1zkv3j+2doSE2RiGe1GKQn+IfIJbv/403TpNntDV4NqW12U+fyUNvioa4lEEQ67jd3bPPg8niDM6oPRNcmX81uL81uL2X1rb0ebzHocTQ/w4AEh43EWBtJcXb/MtZOYVY8LrePhFgbCTE2kmJtgfv+YxJibF2Wdhw2XU0ZCIUMEZERwmoxyE1zkpvm5OxJmd32tbV7OVzTQlFlM8XV/uABBIfc7Gt4XegMIT7TZPPh45tmWS0GWYkxjApMLtZ1OTo5lozEWDITY4h3WNUWW2SEMAyDhBj/h+9x6c4BP67V46W22U1Dazt1Lf5gUu/yUN/ioc7lpq7FQ53LQ4PLQ0ubl8qmNupdHhpaPb2OzNdVYqyNetfxIcY0obGtnca29m4hpbHNP3P7QE3LSaK8oZX4GBvxMTYSYqwkBO/but+P7TzGabeSGGsnPsaGM8ZKvMNGnN06Yq+uKGSIiESBGJuVCVmJTMhKPG6fx+vjaH1rYMbjzpmPO+53DSG9NZvy+sxAYDn+28Wubbrj7NbAeP4OMhNj/LeE2OD99Hj/9tR4hwKJyAgVa7eSkxJHzgk+zuczaXK3U9/iDxz1Lg8NrnYaXF3XPcERtRpb/fsbWz00tvrDxWCwWAx/k7Jm9wk9zmE1cB8zqpdhgNNuxRljI95h9QcXhz+EjE2No83jw+nw7+84zumwBm7+x8QFHjcp+/i/76GkkCEiEuXsVkvwCgikH7e/I4Qcrm2hpqmNxYUZHAmM8X80ML5/TR9vtl2Dgsvj5VBNC4cCs58fKy3eETyXw2YhPTBsZtdbepdhNNOcDtISHMFOo2rGIDJyWSyGv7/FSQ7V7fWZNLX5Q0ljazsNgfDR5vFy6Ywcmtra/WGk1RO83xQIJ1232U/yykN8jA13l+GHwX91paMJWOUxx0/IjGdf5cAmcQQo/sWlJ1XXUFHIEBGRPnUPIT1r9XipaGjzz3bc0Bk+jta3EmOzkpsWR2VjG62evjumJ8fZgyHD3e7r9epIh2PfhOMdVv9oNN1GqfEPmzk6ORa71RLsLNrRMbSjbbYmIRMZ2awWI9hJ/GSZpkmL20uL20tTWzvNbe3dlsH7re00tXm7bbdZDErrXIHHt9Pc5u2zo3xb+8AH8gjHi74RGTIMwxgL/AS4CP/XbkeAl4Efm6Y5sHHW/OdJA34AXAHkANXAG8APTNMsGey6RURGqli7lXHpzj7bZZum/1vEqia3f0jNxjYqG1sDQ2u6qWxqI9Zuoc3jpbrZPaA3WOcxE4H5vxF0UVrnOu7Y/sb7dzqswfAxNtVJu88kMdZGYpe21R0j1CTH2Yl1WP3trB2dbbDjY6w4rBY18xIZoQzDCPbFyEyMOeXzeX0mLe52Wtz+QNLc5qXZ3U6Lux1XIMh0hJpgMHH7j+m67K9fXShEXMgwDKMQ+BjIAl4BdgHzgbuAiwzDWGyaZvUAzpMeOM8k4F3gWWAKcBNwqWEYi0zTLBqan0JEJPoYhuH/kB5rpyAjvs9jO74t7Bg2sybQ/rmmuY2aZk9g6SYx1k6T2xvoMOrB28c7bX/vwR1v5EcbCAzf2XsTsMmjEth9tKnHfTaLEez06XRYyU6KxWeaOB3d21I7Hf7+KT7TJM7ub1fdsXQ6rMTaA+uBbbF2KzE2BRiRkcRq6fy7ONJEXMgAHsYfML5umuZvOjYahnE/8A3gPuArAzjPz/AHjF+bpvnNLuf5OvBg4HkuGsS6RURkgLp+W9hXM62uunYKrTtmlJr6FjemCXlpzmBb7IZAp1D/0tPtm8Bmd98dRB19NK1q95n+kXIC4/qX1bl6nbl95thktpT0PZHimJS4bldmYu0WYu1WYm3+8DF9dBKHa13E2CzBINJ1mZ0Ug8vjJcbm3xZjs+CwWYmxW3BYLTiC2wJLa2ANvH/YAAAViUlEQVSfzYLdGjjG2rFuaDI0ERmQiJqMzzCM8cB+oBgoNE3T12VfIv5mUwaQZZpmrz1lDMOIByoBH5BjmmZjl32WwHPkB57jpK5maDI+EZHI0THef8coNQ0uD81tXhoDbau7dQRta8fpsFJU2Uyzu71bE4fmtvZus7FD72P2A0wfncS2soY+a+tv0rL5BX0Pvzk/P5W1PczYnOZ0UNPS+9WauXmprD94/OMshr+fjsNm8Q+/aRjYbQZ2qwW7xdJ5PxBOOoKJ3Wpgs1iwWQ0cVv/SZvFvT4q14/GZ2CwGNquB3WLBajGCj+24H2vzN4+zBo6zWiz+xxyzbjU61o+/2SwWrIaB1eo/zmKAzWrBYqCrRBLpwuoXONKuZJwXWL7VNWAAmKbZaBjGSuBCYCHwTh/nWQTEBc7T2HWHaZo+wzDeAr4ELAXUZEpEZITrOt7/aOJO6Vxt7V5a2jo7hTa7e25D3eL2YgBz8lJxefzrrYGly+N/jMvjxWYxaPV4afX4ep7RvZ/vCs1ePnfYrX1/HvH18iWkz/R3SG1r9w1oQjW71TgueB1ryqhEdh1t7PMYgPGZ8RQNYLSdydkJ7C7vuTnbsXLT4jhc479SZA0EFIuFwNIfYKwWg9xUJ0cbWrEYnYHFYhBYGuSnx1Na58JiMbAaYAk8vusxFsMgzm6h3ecPax3nMjqONwg8xn8/IyGGOpcneKzFOOZYw8DpsNLW7gtuNwL7DDrPZwTWHTYLPp/pXzcMDOg8Bv+Ibu0+038e/OfD/7/gc9utRjA0d2zreC5/RvPfd9gstHvNYF0d5+l4XqPLz+8zTQw6zhU4Jnjff04DE4KP7TxHx+MIrnd9vHHM9o7/6gbg/znpcj66nJNux3fe73xMx5m6PD9djz/2uM7t/vtm5zF0P6jrY0yT4DwaXWvs+riO9d6GGA+VSAsZkwPLPb3s34s/ZEyi75AxkPMQOI+IiMiA+ZslWUmNdwz6ub0+k7Z2fwBpbff5w0fgfpvHS1tgW9el1TA4e2JGIBh4cQcCgs1iUNPiDq53Xbq9PlKcDnKSY4PrHcuO7DGQ8AD+pmUeb+8j6AADni3eN8DerScyuZm1yydJr8/Eiwk9lOt02Poc6cxhs7C1tO+mbwBJcTYaepgoridz81NZ38NVqK4KM+PZP8BhTrOTYihv6P2q2Lg0Z6/DS3fIT3dSXN33MQCzx6Ww8VBdv8edPjaZT/ppMgj+D9IDaXzTNTQOthibQVt7/0WMz4inqKrv/ybzC1JZe6D/sYoG0qSyg4awPTXJgWVvr3bH9pRhOg+GYfTWHmrmzp07mTNnTn+nEBERCTtdP/44AjfwXzgxTX8TM/99079O122d9z0m2Ltup+vx/vVt+L/N7ngMPZ0Pk12GgddnBj5sdj+P/wj//XVWSyAQdT9f18d0bKux+Uc060+VzYKnjxHP6hxWXL30vemqwmL0OUBBV+84bLT00z+oxm6hrZ+hoTtUWi2093Q1LKDaZsHdz6huAzkG4L0B1A4Df90Gqr//TqfCMAwG0s1gIK/R20Pw+hi//LenTdO8dkAHD4NICxn96fg64lQ7mgzGeSxu94nNBCm927lzJwBTp04NcSUjg17PwaXXc/DotRxcQ/F6BpudBK8AhFUz8FPSGT4CkcTs/CBgmib79u0DDAoLC7ttDz6+6/EdG+h6jo59Zpfgc+xzd94xDIMUp73n/YH/NzA6w1SXk3Xd0vHYjqsB3Y/tPNJiGHg7i+xWe8eaxTDw2o85d7fn9bNbDawWO90q6Tq4QnMzJhDjTMRiGMEauzOP39TDc3XV0TTt+OO7/7fo47S9rHS8fka/5+joM9RXHrFY/Mf1dy5/U7TOn6e34wO9CMJqwKJICxkdVxiSe9mfdMxxQ30eTNPs8VKFYRgbZs6cqY7fg6TjipBez8Gh13Nw6fUcPHotB5dez8Gl13Pw6LUcXHPmzGFjOcWhrqOrSBuHbndg2VtfiYmBZW99LQb7PCIiIiIicoxICxnvBZYXBoaaDQoMYbsYcAGr+znP6sBxiwOP63oeC/7O412fT0REREREBiiiQoZpmvuBt/DPYfHVY3b/GIgHnuw6R4ZhGFMMw5hyzHmagL8Ejv/RMef5WuD8b2rGbxERERGRExdpfTIA7gA+Bh4yDON8YCewAP+cFnuA7x9z/M7A8theQP8POBf4pmEYs4C1wFRgGVDB8SFGREREREQGIKKuZEDwasZc4An84eIeoBB4CFhkmmb1AM9TjX9SvoeACYHzLAAeB+YEnkdERERERE6QMZDxfuWk6cUVERERkeEQVuNJR9yVDBERERERCW8KGSIiIiIiMqgUMkREREREZFApZIiIiIiIyKBSyBARERERkUGlkCEiIiIiIoNKIUNERERERAaVQsYJMAxjrGEYjxmGUWYYRpthGMWGYTxgGEbqiZynpqaGu+++m/z8fGJiYhg9ejQ333wzJSUlQ1V6WKmuruaRRx7hyiuvZMKECcTFxZGcnMxZZ53Fo48+is/nG/C58vPzMQyjx9uoUaOG8KcIH4P5GpSUlHDzzTczevRoYmJiyM/P5+6776a2tnaIqg8vTzzxRK+vZcfNarUO6FzR9Lv54osvcuedd7JkyRKSkpIwDIPrrruuz8d8/PHHXHLJJaSlpeF0Ojn99NN54IEH8Hq9J/z8O3bsYPny5WRlZREbG8vkyZP54Q9/iMvlOtkfKaRO5PXcu3cvv/zlLznvvPPIzc3F4XCQnZ3NsmXLeO+9907oeYuLi/v83b/qqqsG48cbVifyWg7Fzz+Yv+fh4ERezxtvvLHfv6fnn3/+gJ53JP5unuxnocH8nTIMY5phGM8bhlFhGEarYRi7DcP4sWEYcaf68wHYBuMk0cAwjELgYyALeAXYBcwH7gIuMgxj8UBmG6+urubMM89kz549nHfeeVx11VXs2rWLxx9/nNdee41Vq1Yxfvz4If1ZQu2FF17g9ttvJycnh6VLlzJu3DjKy8t56aWXuPXWW3n99dd54YUXMIyBzSmTnJzM3Xfffdz2hISEwS49bA3Ga7B//37OPPNMKioqWLZsGVOmTGHt2rU8+OCDvPHGG6xcuZL09PTBLDvszJo1ix/+8Ic97vvoo4949913ufjiiwd8vmj53bz33nvZsmULCQkJ/7+9+4/Vq74LOP7+Ar39lY2tBoOB7l7HhqPD9Q+XlDLtoEgxMWFdCqMKoyVTqhmiN2qcJl0KjqCJkbQahWltN9CKNGovykRzy2ULc0gkcyxKu5Tyw1CluI7agRu9/fjH93vh6XPv0z7n3tP73Od53q/k5OSec77fc873fp7zfD/nOT+48MILefbZZ0+5/J49e1i3bh0LFizghhtuYMmSJTz88MMMDw/zxBNP8NBDD7W97ieffJLVq1fz5ptvct1117F06VL27t3LnXfeyejoKKOjo8yfP3+muzirqrTn5s2befDBB1m2bNlbHY99+/YxMjLCyMgIW7du5fbbb6+0/uXLl7N27dpJ0y+99NLK+9JpVWMT6tv/OuN8rqjSnmvXrmVoaGjKeffffz/PPfdcpeMp9FZsTqcvVGdMpZRWAHuBecBu4CVgNfBZ4KqU0lUR8b0Z7WREOLQxAI+S3+D9S03Tf79Mv3eKcpPceuutAcTw8PBJ07du3RpAXHPNNVMV6ymjo6MxMjIS4+PjJ00/dOhQLF26NIDYvXt3W3UNDg7G4ODgGdjK7lFXG6xZsyaA2LZt20nTh4eHA4hNmzbNeB3d7LLLLgsg9uzZ09by/RSbe/fujf3798eJEyfiscceCyBuvPHGKZd97bXX4rzzzouBgYF46qmn3pr+xhtvxMqVKwOIXbt2tbXe48ePxyWXXDLp/zI+Ph7r1q0LIO6+++6Z7VwHVGnPHTt2xNNPPz1p+tjYWMybNy8GBgbi5Zdfbmu9Bw8eDCA2bNgwk82fU6q0ZZ37X2eczyVV2rOVI0eOxMKFC2NgYCAOHz7cVplejM2qfaF2YgpYH+31ac8G/r2UubZh+lkl4QjgM+3Udcr1zLSCfhiA95YGPwic1TTvHcAx4LvA4qayJzl27FgsXLgwFi9eHEePHj1p3vj4eAwNDQUQBw4caC7aN+66664A4rbbbmtr+X7qyLVSRxscOHAggBgaGpp0wDt69GgsXrw4Fi1aFMeOHZvRerrVM888E0BccMEFcfz48bbK9Gtsnq7jsX379gDi5ptvnjRvdHQ0gFi1alVb6zrV8hMxPTg4GCdOnKi2E3PIdDtyERFXX311pZM2vdiRazSbSUadcT5XTTc2t23bFkCsX7++7TK9HpvNpuoLtRNTwOPRXr92davlG/q8zwOpnfparmcmhftlAH6uNPh9LeZP/Mpx1Wnq+cmy3KMt5t9X5n+q0/vcwbb+9dIG97S5/PPAIeAm4LfIl69dCZzd6X2ZxTabcRvUFeO9OgB/UPb/jtn8v3TjAFxR2uqBFvMfKPN/Zop555QTNm8C89tY1+dKXb/ZYv6+Mv+iTrfLmWrP05T9+1L2Y20uP1SW/0dgU4nbTcCHOt0Os9GWde5/nXE+V4fpxibwjVLuygplejo2p9jfSX2hbjx2ek9Ge36kjPe3mP8tYA1wMTA6w3oo9fSdlNI5wM3lz3+oUPR84P6maQdTSrdExOO1bNzcN9M2qCvGe065Ae4m4ATwpxWLG5uTtYy1iDieUjoIfJB8Nu0/pltX8S1yzF4MHKi+qd0rpTQIXAW8Dny5YvGry9BY3xiwISJerGUD57Y69r/OOO8ZKaWVwI8C+yOi2pMJsp6PzVP0hbru2OnTpdpzbhm/1mL+xPR3zVI9vep3gEuBRyLi0TbL7CB/kZ4PLCYfvO4jn/X4Ukpp+RnYzrmmjjYwNlv7BHm/vxQRL1UoZ2xOrc5YM26nkFKaD/w5MB/YEhHtPh7udeC3gR8D3l2GjwKPkc9aj6aUFte+wXNHnftvbE7t1jL+k4rl+ik2W/WFuu7YaZJRj4lb/2OO1NN1Ukq3A79KfmrXJ9stFxF3RMTeiPjviHg9Ir4ZEb9AviF/IbDljGzwHDJLbdC3scnbX4r3VSlkbE5bnbHWd3GbUjqb/OvZR4AHgd9rt2xEvBIRn42IpyPiO2X4MvlXzCeB95EvrexJs7z//Rib55JP2nwf2FmlbL/E5nT7QhPFy3jOHDtNMtozkdGd22L+O5uWO9P19JSU0qeBreQnHVwZEd+uodp7y3hVDXV1qyptYGxOIaW0DLgc+E/gkZqq7ffYrDPWjNsGJcF4ALge+CvgpigXWM9ERBzn7UsF+y5up7n/xuZkNwGLgL+OiFfrqLCXYrONvlDXHTtNMtqzr4xb3Svx/jJudW1b3fX0jJTSrwB/CHyT/KH6r5qqfqWMe+Xn0+mo0gbG5tQ2lfH2iKjr7Vn9HpstY61ci/zDwHHguZnUVfRN3Ja22wWsB/4C+NnSAavL4TLu17ituv91xnmv+PkyrvSrcBu6Pjbb7At13bHTJKM9EzcnrUkpndRmKaV3kH+WfgP42mnq+VpZ7iOlXGM9Z5F/9mtcX09LKf0GcA/wdfKH6pXTFKliZRn30wG8WZU2qCvGe0ZKaQH55+oTwPYaq+732Nxbxj81xbxV5DOdX432XgLVsq6U0nvJX6Av0ONtnVIaID/b/nrgi8Ana0yKJ1xWxj3dlqdQdf/rjPOuV178tpx8w/dYzdV3dWxW6At13bHTJKMNEXGA/Ni0IeDTTbPvIGfPX4yI705MTCl9IKX0gaZ6jpGvlV3M5Ouxbyv1PxoRXflBqSKltJl8c9O/kh+L2vKn05TSvNKeFzVN/2BKackUyw+SzwhAvnSgZ1Vtg1ZtOZ0Y7wPXk28ufKTVDd/G5rTsBl4F1qeUPjwxsSR1nyt//nFjgZTSotLO72mq63HyU1RWpZSubVj+LOB3y5/31nHJ0FxVbvL+G+Bj5GT4log4cZoy55b2/KGm6StKwtK8/GpguPzZs3E7nf1v1ZZMI8573MS9bZ8/1UL9FptV+kJ04bEz9fCxt1alE/FV4AeBPeR/zgryc+/3A5dHxP80LB8AEZGa6vmBUs/F5EzyX4BLyF8Qr5R6evpRiymlDeSbvsbJ7x+Y6pq/5yNiZ1l+iPwixBciYqihni3AZ8hn4Q8C/wtcBPw0sIB8Df3HI+L7Z2I/5oKqbdCqLcu8SjHe61JKXwF+nPw21IdbLDOEsUlKaS2wtvx5PnAN+QzYV8q0VyPi15qW3w38H/CXwLeBa8mPVdwNfKLxyy2ldAW5LR+PiCua1r2CfCydV8q+SH6q14eBJ8hf3F11trhKe6aUdgAbyZ2PP2LqGzXHGs8ep5Q2kp9+9oWI2NgwfYz8CMwx8n1IAB8iv7gLYHNETHRmukLFthyj4v63asuGdbcd592g6me9lHkn8DL5M3rBaU4qbqR/YrNSX6iU6a5jZ6sXaDhM+XKSpeTgP0R+OsIL5Jt0lkyxbOTmnbKeJaXcC6WeQ8CfARd2eh9nqR23TLTPKYaxhuWHyrTnm+r5KPka5GeB75BfQnMY+CfyM6Zn9KbKbhiqtkGrtmyY33aM9/JATvwDeIlTvDzP2Hxrf0/3mZ4Ub+RL8B4BjpAvxXuGfEZyUnvz9ku/xlqsfxnwELmj/T1yUnwHsLDTbXOm25Pc6Trd8XRLU/0by/SdTdM/Bfwd+UWSx0pbvkh+StVPdLpdZqEtK+9/q7acTpx3wzDNz/ovlnm72qjf2GzRF5pOTNHhY6e/ZEiSJEmqlfdkSJIkSaqVSYYkSZKkWplkSJIkSaqVSYYkSZKkWplkSJIkSaqVSYYkSZKkWplkSJIkSaqVSYYkSZKkWplkSJIkSaqVSYYkSZKkWplkSJIkSaqVSYYkSZKkWplkSJIkSV0qpTSUUoqU0s5Ob0sjkwxJkiRJtTLJkCRJklQrkwxJkiSpC6WUtgAHy58bymVTE8PGzm0ZnNPJlUuSJEmatjHgXcAvA/8G/G3DvK93YoMmpIjo5PolSZIkTVNKaYj8a8YXImJjRzemgZdLSZIkSaqVSYYkSZKkWplkSJIkSaqVSYYkSZKkWplkSJIkSd1rvIzP7uhWNDHJkCRJkrrXESCA93R6Qxr5CFtJkiSpi6WU/hlYAewC9pN/3RiJiG90bJtMMiRJkqTulVJ6H3APcDnwbiABt0TEzo5tk0mGJEmSpDp5T4YkSZKkWplkSJIkSaqVSYYkSZKkWplkSJIkSaqVSYYkSZKkWplkSJIkSaqVSYYkSZKkWplkSJIkSaqVSYYkSZKkWplkSJIkSaqVSYYkSZKkWplkSJIkSaqVSYYkSZKkWplkSJIkSaqVSYYkSZKkWplkSJIkSaqVSYYkSZKkWv0/OgNGA/RHnIQAAAAASUVORK5CYII="
     },
     "execution_count": 18,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x7feb327a2128>"
      ]
     },
     "execution_count": 18,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "title = 'The decay function with different decay rates tau'\n",
    "sp.plot(decay.subs({tau:5}),decay.subs({tau:2.5}),(t,0,20),title=title)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "<div dir='RTL'>    \n",
    "היכולת לשלוט בגרף דרך החבילה של sympy מוגבלת למדי.\n",
    "אם תירצו לקבל גרף יותר מושקע השתמשו ב-matplotlib."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7feb30710978>"
      ]
     },
     "execution_count": 19,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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"
     },
     "execution_count": 19,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "x_axis = range(0,21)\n",
    "y_axis1 = [decay.subs({tau:5,t:t_i}) for t_i in x_axis]\n",
    "y_axis2 = [decay.subs({tau:2.5,t:t_i}) for t_i in x_axis]\n",
    "plt.plot(x_axis,y_axis1)\n",
    "plt.plot(x_axis,y_axis2)\n",
    "plt.xlim(0,20)\n",
    "plt.legend(['tau=5','tau=2.5'])\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('f(t)')\n",
    "plt.title(title)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "<div dir='RTL'>\n",
    "# משוואות\n",
    "אפשר ליצור משוואה סימבולית\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\alpha^{2} + x^{2} = 2 \\alpha$$"
      ]
     },
     "execution_count": 30,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq1 = sp.Eq(x**2+alpha**2,2*alpha)\n",
    "eq1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "<div dir='RTL'>\n",
    "ולמצוא את הפתרונות שלה"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left [ \\sqrt{\\alpha \\left(- \\alpha + 2\\right)}, \\quad - \\sqrt{- \\alpha \\left(\\alpha - 2\\right)}\\right ]$$"
      ]
     },
     "execution_count": 31,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.solve(eq1,x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "<div dir='RTL'>\n",
    "אפשר ליצור מערכת משוואות\n",
    "ולפתור גם אותן"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left [ y = \\beta x, \\quad x^{2} + y^{2} = 1\\right ]$$"
      ]
     },
     "execution_count": 33,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq2 = []\n",
    "eq2.append(sp.Eq(y,beta*x))\n",
    "eq2.append(sp.Eq(y**2+x**2,1))\n",
    "\n",
    "eq2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left [ \\left ( - \\sqrt{\\frac{1}{\\beta^{2} + 1}}, \\quad - \\beta \\sqrt{\\frac{1}{\\beta^{2} + 1}}\\right ), \\quad \\left ( \\sqrt{\\frac{1}{\\beta^{2} + 1}}, \\quad \\beta \\sqrt{\\frac{1}{\\beta^{2} + 1}}\\right )\\right ]$$"
      ]
     },
     "execution_count": 34,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.solve(eq2,[x,y])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "<div dir='RTL'>\n",
    "קיימות משוואות שאין להן פתרון אנליטי. כדי לפתור משוואות אלה יש לחפש פתרונות נומריים.\n",
    "    \n",
    "לפני שמנסים לפתור את המשוואה נומרית יש לבדוק גרפית עם הפתרון קיים ומה יהיה ערכו בערך.\n",
    "\n",
    "הפתרון שיתקבל יהיה מספרי, ולכן חשוב לדאוג להציב ערכים מספריים בכל הפרמטרים.\n",
    "\n",
    "נשתמש בפונקציה (\n",
    "sp.nsolve(eq,x,x0\n",
    "\n",
    "<b>fun</b> - המשוואה או מערכת המשוואות\n",
    "\n",
    "<b>x</b> -  המשתנה עבורו פותרים\n",
    "\n",
    "<b>x0</b> - ניחוש התחלתי עבור הפתרון\n",
    "\n",
    "\n",
    "<b>שימו לב:</b>\n",
    "פתרון נומרי לא יעבוד טוב אם לא ניתן ניחוש התחלתי ולשם כך חשוב להסתכל על הגרף.\n",
    "\n",
    "בדוגמה למטה רואים שיש שני פתרונות למשוואה. פתרון אחד הוא הפתרון הטריוויאלי 0. \n",
    "\n",
    "הפתרון השני קרוב לערך x=2. כדי לקבל את הפתרון השני נציב x0=2.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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"
     },
     "execution_count": 55,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x7feb30084048>"
      ]
     },
     "execution_count": 55,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#sp.nsolve(eq3.subs({tau:5}),t)\n",
    "eq4=sp.Eq(sp.sin(x),x/alpha)\n",
    "sp.plot(sp.sin(x),(x/alpha).subs({alpha:2}),(x,0,2*sp.pi))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$1.89549426703398$$"
      ]
     },
     "execution_count": 62,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq4_num = eq4.subs({alpha:2})\n",
    "eq4_num\n",
    "sp.nsolve(eq4_num,x,2)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (Anaconda)",
   "language": "python",
   "name": "anaconda3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}