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{
"cells": [
{
"cell_type": "markdown",
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"# Algorithmic thinking\n",
"\n",
"In engineering, solving a problem begins long before we start coding or\n",
"building models. Like any other engineering challenge, computational\n",
"problems must first be clearly framed and understood. In this section,\n",
"you will learn to **apply algorithmic thinking** to systematically\n",
"approach engineering problems, **translate real-world situations into\n",
"structured programming logic**, and **use computational tools to\n",
"implement, test, and refine solutions**.\n",
"\n",
"Before diving into code, it’s crucial to define the problem carefully,\n",
"frame the problem so that logically so that a computer can understand\n",
"then execute so that\n",
"\n",
"## Define the Problem\n",
"\n",
"As any other engineering problem, we need to frame it before we can\n",
"start working on it. So before jumping straight into coding or building\n",
"models, clearly define the engineering problem.\n",
"\n",
"1. List your givens, this includes any constants or equations. What\n",
" inputs do we know?\n",
"2. Find: List what you’re trying to solve for. What outputs do we need\n",
" to find?\n",
"3. Establish the assumptions based on your engineering knowledge that\n",
" you deem to be appropriate to use for the problem. This determines\n",
" what mathematical models we can apply to the problem (i.e. equations\n",
" or formulas).\n",
"4. Solution: Show the works of the problem, this will include any code\n",
" used together with documentation or any explanations of the code.\n",
"5. Comment: reflect and comment on your findings.\n",
"\n",
"## Think Algorithmically\n",
"\n",
"Since we are going to use computers to compute our calculate we first\n",
"need to break the problem into logical steps that a computer can follow.\n",
"This can be done with tools such as flowchart or psuedo-code.\n",
"\n",
"- **Define the inputs and outputs.** What variables will the program\n",
" take in, and what results will it produce?\n",
"- **Break the problem into sub-tasks.** Identify steps such as data\n",
" input, logic processing and output.\n",
"- **Outline the algorithm.** Write pseudo-code or flowcharts that\n",
" describe the computational steps.\n",
"- **Identify patterns or formulas.** Can loops, conditionals, or\n",
" equations be used to automate parts of the solution?\n",
"\n",
"### Flowchart for fixing lamp\n",
"\n",
"<figure>\n",
"<img src=\"attachment:figures/LampFlowchart.png\" alt=\"Lamp Flowchart\" />\n",
"<figcaption aria-hidden=\"true\">Lamp Flowchart</figcaption>\n",
"</figure>\n",
"\n",
"### Psuedo-Code for processing and plotting stress-strain data:\n",
"\n",
"1. Import force and displacement data from file.\n",
"2. Convert data from force and displacement to stress and strain.\n",
"3. Plot the stress-strain curve.\n",
"4. Identify the yield point or modulus.\n",
"\n",
"## Write & Execute the Code\n",
"\n",
"When writing the code it is important to ask yourself whether you’re\n",
"using the right tools, libraries or method to solve the problem. **Check\n",
"for any syntax and logic errors** then debug line-by-line using print\n",
"statements or by using a debugging tool.\n",
"\n",
"## Verify and Validate\n",
"\n",
"When writing code it is crucial to test and confirm your code. It is\n",
"therefore important to ask yourself the following questions. Does the\n",
"code do what you intended it to do? And, is the mathematical model used\n",
"in the code valid for the current problem? \\## Exercise: Rubrics Cube\n",
"problem\n",
"\n",
"## Exercise: Design a derivative finding algorithm\n",
"\n",
"Set up the problem and write pseudo-code to calculate the gradient of an\n",
"unknown function.\n",
"\n",
"1. **Given:**\n",
"2. \\*\\*Find:\n",
"3. **Assumptions:**\n",
"4. **Solution:**\n",
"5. **Comment:**"
],
"attachments": {
"figures/LampFlowchart.png": {
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IUmQWBEEQQRQEQXg6gpgCZMswO6Hwkpxqvn+SJRpCfhbEJCA2LOqaRE94bEJvDusLlWgI\n+b3IfCk2IcFsxioIj4JSiiMXzgFkAEESESG/C+IfAGv+2yYRFB6ZQ+fPcjkyAmAXIP2khHwviMsB\n9c3yX26tCxKEh+LLn3/I/HeZREPIS1g85vcigGrXb9yoZlRGs/W+IDyIjXt38eHCOZiKyq8C6RIV\nIb8LIsABTdNe/u/4UVtf7xLU9K0g0RTuy4lLAXQZ944ylSoGASclKkJBEcRY4DDw4pr/thkAmteo\nlcW+XxAyWb1jK90+GK3iEm9owCeATMcn5Dmyw6++s6ZpvyqlnCuVKsMH/QfxXNMWuDo6SXQLOanp\nafx7+CBTl/3M5gP7AIzAh8CXYHLfFYQCJogAlYBpwLMAVhaWVCxVmhJFPHFxdJQoFzKSUlIIvXaV\n8yHBxCeZ3bxPAW8Df0mEhMJCS1NRKNSUAcircL/igRVAPwqYkYggGeKj4gCUBApjitgamAL8Ckwt\nhOefAoQBUfKICfmJnPzVvgGcLaRxLWX6GwkclNtMEPIH0iQsCIIggigIgiCCKAiCIIIoCIIggigI\ngiCCKAiCIIIoCIIggigIgiCCKAiCIIIoCIIggigIgiCCKAiCIIIoCIIggigIgiCCKAiCIIIoCIIg\ngigIgiCCKAiCIIIoCIIggigIgiCCKAiCkAeRuXIfHU+g9APW8TX99QLqPWDdaOCShFUQhPxIOSCV\n7JvM/UUJqSDkDTQJwWMxDxhSqlQpGjdu/MhfvnTpEgcOHAB93upqQIaEVBCE/EppIMXZ2dkYHR2t\nHpWOHTtmZocDJZSCIBQEZgPqo48+eiQxPHDggNI0TQEXkDpcQRAKCKU0TUtxcnIyRkVFPbQgdunS\nJTM7fEVCKAhCQeI7QH3wwQcPJYaHDh3KzA4DAWsJnyAIBYnimqYl2dvbGyMiIh4oiN27d8/MDodK\n6ARBKIhMA9TYsWPvK4ZHjhzJzA4vS3YoCEJBpZimaYn29vbG8PDwewpi7969M7PD1yRkgiAUZKYC\navTo0XcVw5MnTyqDwaCAUMBWwiUIQkGmiKZpCTY2NsaQkJA7BLFv376Z2eEICZUgCIWBSYAaOXJk\nFjE8deqUMhgMStO0cMBOwiQIQmHAQ9O0eBsbG2NwcLBZEF988cXM7PBtCZEgCIWJzwH1xhtvKKWU\nOn/+vLK0tFSapkUA9hIeQRAKE66apsVaWVkZL126pAYOHJiZHb4roREEoTAyAVCdO3fOzA6vAQ4S\nFkEQCiMumqbFcNPvcJyERBCEwsxHgNI0LRpwknAIglCYcQZigfESCkEQCjP26CNXMoBzQDMJiSAI\nhZE26MavysbGMrMOMQOYjjSsCIJQiIrI003ip7p2raKCg/9PLVvWX3l42BtNwngJaC+hEgShINMJ\nCAKUp6ejcfHi55VSX5lfEREfqQED6t46y94ywF3CJgh5D5l17/FxAyYC/gB+fjWZObMnRYrcvWS8\nYcNphg1bqUJD4zRNI0IpXgNWSxgFQQQxv9NN05ijFMWLFXNSs2b10nr0qPbAL8XGJjF27B/Mm7cX\npQBYDrwBXJWQCoIIYn6jGPo8Kr01Dfr3r8v06d1xc3s0E5tNm87h77+Cy5dj0TRilWIsMFfCKwi5\ni4WE4KHx0zQ2AvXKlXNn+fIBjB7dEjs7q0feUPnyHgwb1piMDCO7dgXZKkU3oAGwHYiTUAuCZIh5\nFR9T9tbeYNAYMqQhU6d2w9Exe6ZF+e+/QIYMWc7Zs1fRNOKU4l1gHnoDjCAIkiHmmR8Lf01jDVCl\nWrWirFs3iOHDm2BtnX1hK13alcGDG5KebmT37iAbU7bYGNgBXJfLIAiSIeY2vsB8oLWlpUGNHt1S\nmzChAzY2ljm608OHrzB48AoOH76CppGkFBOAyYBRLokgSIb4tLEE3tU0lgPla9f2Zv36V7QBA+ph\naWnI8Z0XL+7Mq682wMHBhm3bLloajao90A7YBVyTyyMIkiE+LWoCC4D6traWavz4DtqYMS2xsDDk\nysEcPx7O4MHL2b8/GE0jRSk+Bqagj4YRBEEyxBzBypQVLgVKNWvmwx9/vKr16FENgyH3fi+KFnXk\nlVca4OBgzY4dlywyMoztgeeAfUC4XDZBkAwxu2mCXldY1c7OSn38cXvt3Xdb5aoQ3o2AgCiGDFnB\n1q0BaBrpSjEV+BhIkVtYEEQQnxQ7k6CMASyefbYSc+b0pnRp1zx7wEop5s3bxzvvrFc3bqRqwAng\nVWC/3MaCIIL4uLQ0ZYUVXFxs1VdfddGGDm2IpuWPUAQGxjB06Aq2bDkPkA7MBD4AbsjtLAgiiA+L\nC/AVMBTQunatwuzZvShRwiXfnYhSih9/PMSoUetUTEySBgSYzutfuaUFQQTxQXQGZgOlvLwc1fff\n99T69KmR708qLCyON95Yw+rVJ0Af2TLPVA0QL7e2IIgg3s4dFl2zZvXCw6NgzRm/fPkxXnttlYqK\nStSAQNP5bpbbWxBEEDPx0zRmKkWR4sWd1ezZvbTnnqtaYE82MjKBMWM28OOPh8w6CbwGRMltLgiF\nVxCLA98DPTUNhg5txJQpXXFysikUF3TDhtMMH75KXblyPdOI9nVgldzqglC4BFEDBmga05TCzdfX\ng3nz+tCmjW+hu6hiRCsIhVsQy6JbdLWztDTw+utN+eKLZ3FwsC7UF3fTpnMMG7aSoKAYMaIVhIcg\nvw/dMwBDNY21QOUaNYqxbt0gBg9umK0WXfmV8uU98PcXI1pBKAwZYnl0M4aWmRZdn3zSUYTwHuzc\nGcjgwfnCiLYGcAw4C9TizuGJ36EbcbSUqyrkRIaV37AExmoaJ4GWdeqUYN++EdrEiZ1FDO9Ds2Y+\nHD48irFjW2MwaM7AHGCr6YclL1IGeFeunCCCeG9qAXuAiTY2llYTJ3Zm//4R1KlTQq7kQ2BnZ8XE\niZ05cGBkZsxaahrHgLF58F74Gvg/oOJDrOtjEs+JwPtAFbnaQkEuMtsC4zSN/1MKyxYtyjJ/fh8q\nVvSUK/iYpKVl8PXXO/jww00qLS1DQzehHQycySNF5sqmKpFU4Jlbiva3F5nbA+tMx78TqI0+MulF\nYFkun4sXUBSwljsuZ29nIAKI5AmrgPKDIDY1PRiVnZxs1KefdtRGjGiW5yy68it3MaKdCHxuusly\nWxAtgUPAcGDRXQRRAy4Ap4FutzwMS4AOQEl0A4ynhTXwEtDLJOJ2coc9VVLQx/OvBn4EkgqSINoD\nH5mKQoZOnSozZ04vSpVylcuezaSnG/n++128//5GlZSUpgFH0a3FDuWyIJ4FPjMJYlVTBnCrIHoD\nV0wi9Mst23gOWGsqbp9/SsfdC33+m3IAdi52FCnvhZOnE5a2lnKT5SAZKenEX43nWsBVEmMSMxcH\nA+Nuuy/yrSB2RK/0L+PqaqcmTeqs+fs3kiufw+QRI9rbBdHW9H4f0P82QWwM7AbaktXppyGw15Sl\n/ZPDx2sAvgTeA6jWuQYthreibBNfDJYGuameIsYMI0H7A9k5bztHVx/OLC98D4x62JJCXhNEV2AS\nJosuP7+afPddD7y8HOVqPyXuYUQ72CRIuSGImIRtM/As0AWoYxLEzHU7AX/eso1W6C3ojZ7CcU8D\nRtq72auXFgzSKrapJDdRHuDSnov8OGiRio+I00zVLa8+7K9bXqGrqSuNf9GiTqxYMYBly/qLGD5l\nNE3D378RJ06M1tq3rwBQXdPYBUwHHHLpsP5GrxOadft9jz7pVrXblldDzw8u5vBxvQyMdPR0UiO2\njBYxzEOUbVyOkf+M1lxLugG8AryZXwTRC70SfL1SePv51eTkydFa795P36/w/PlrtG8/j927gwr9\nDeXj48Zffw1l2bL+uLraGYC3TNlYm1w6pDHoJr8Db1mWgF6B/iZ6v0WA0qYi0kZydupWZzSmaAaN\nl398VStSroioUB7DxduVQT8PwcLaUqHxBfDAbim5LYh+msYpYMCtD2Bu+RXGx6ewZct5rl4VN37z\nBfKryalTY7SePauD3mDwN3r9rtNTPpSrJlF0vW35cPRW5ovoDSyXTP+/ksPHMwJFkQYvNcKnUTm5\nUfIoJWqWpNmQ5hoKJ9P9kycFsbjpl30Z4OHv34jjx0djKqLlCwICovjzz7Ps3BlIfHzWNofIyAQi\nIhIAOHAghD//PEtUlN76lZFhZOfOQP755wIJCak3U52EVC5ejEYpRWhoHH/+eZaTJyMwGnN/ZF2x\nYk6sWjWQZcv6U6SIA+gGtMfRu7ZkN6cAd/TuNLez2PRZl1uWRaH3OyxmWl4Uva4xMofD0heg7dvt\nRXXyOK1HPoOmd9Pr+6B1n3Z/AA3djGGKUjiVL69bdLVunX8supKT0+nX72c2bTpH7drehIfHExeX\nzNKlL9GunS7o7777O1ev3sDFxZYTJ8KJjEwgOTmdP/8czDvvrCcpKY2goFicnW04eHAkRYo4sHHj\nGfr2/Ylp057jyy//wdPTkbNnr9KwYSk2bx6KnZ1VnsgWW7Uqp5mMaMsAm8h+I9oMIOYen6n7fHaV\np2dvVhKoWbyqNx5lpaic13HycqZMg7IE7r3og95961ReyBDLAVuAORYWBqexY1tz/PjofCWGAD//\nfIi1a09x+PAodu16g4CAsbRp48sbb6wxr2NtbcHWrQF06lSJ48ff4cKFsVhZGejYcT4TJ3bmyJG3\nOXHiHcLC4vn11yPm7wD8/vtpAgM/4Pjxd/j7b3927QpiyZKDeeb8vbwcWbLkBTZseIUSJVyUqdrj\nJNC7ED1j5QC8a8qQ0fxTdC6R5drlpiAaAH9N4zjQtmbN4uze/SYTJ3bGNh92WB08uCFxcZ9SqZJe\nP6tpGu3aVeD8+WukpOhdnQwGDScnGwYMqKv/QjnZUKNGcSpV8qRVK/16lCjhQpkyrly+HGveDsBb\nbzU3x6VFi7LUrVuCP/44k+fi0KVLFU6eHJ3ZP7QosMJUBVIYxlMWy8w8hHySJRYzz65ZPDeLzNXR\nh901tLAwqNGjW5LfLbqMRsW6dSdZufI4QUGxxMQkEh+fglKKtDQjNqaZCry9nbPM9Wxvb4WLi22W\nbdnbW5OampFlWZUqXlne3yqaeQ0XF1vmzOlNr141Mo1o/TSN9oXAiNYGwNJGRqDkFyytzdfKNjcy\nRCt0i66DQMMmTcpw7Ng7BcKi6/PP/2bo0BW0bFmO6dOfY/Nmf8aMaXVnYO8y1trC4sH94G8V0czt\n5IWGlfvRsWNFTp0aw9ixrdE0zRW9Ffp3oFQePNxv0LvmCMJTEcTamCy6bG2trCZO7MyOHa/dkfnk\nV3755Qgvv1yfkSOb06yZD+XKuRMXl30j20JCsmaDYWHxlCjhkufjYm+vW4tt3/4alSt7AnTWNE6g\nt0jnpRFRwzVNu2ASbR+RACGnBNEO3Y/uAFC3ZctyHD36tjZ2bGssLArOmE5Ng+vXk83vT52K4Jdf\nDgNw/XrSE29/3rx9KNPMUBcvRrN372U6dKiYb+LTrJkPhw7d1Yg2z/SpUkpZAf6app03VenkmZa9\nM1tOsXX63zm+n71LdnNo+YEn2sb27//l1J8nClbROpu20xyYD1RydrZVkyd3YejQhncU//ILL730\nC1ZWWYv2Pj7uHDo0ktdea8KoUeuIjU3C0tLAxYvRLFzoxzPPzOWVV5YxdWq3J9q3k5MNjRp9h6+v\nB//8c4GKFT15+eV6+Sp+mUa0L7xQm1dfXc7hw1daahpHlWICMAW9a02u4eHhwahRo5g2bZplVFTU\nq+ijX35Btz07lxP7fL/YaNJTbvoLWFhZ4FrSDZ+GZenwfifcy3joP4I7Azi6+jCtRz6TozG4ciQY\nW5cncyfbu2Q3ldpWpuqz1UUQM0tK3GLR1aVLFWbP7qWVLOmSL4NRoUIRNm8ees+HHGDEiGY0bFiK\nQ4eu4OnpSOfOlbG3t2LfvhEEBsZQvLgTo0a1IC4uOcv3P//82TvqFefM6Y2bW9ab8n//e4bLl2M5\neDCEHj2q0a1bVeztrfJlPGvX9mbv3jczjWht09IyJqJbc+WqEa2VlRX/+9//GDVqFAsWLODLL7+0\niIiIGIjuprMS3eHndHbvt/6LjWg2tAUA6SlpXL1wla3T/2bGM1MZvet9nLye3uCfXl/3RcheQXzW\nVBwqbbLoIr9bdDk52Zg7V9+PRo1K06hR1nr5evVKUq9eSYDM0Rx3iMPtNG5897r9xo1L3/Oz/IaV\nlQVjx7amS5fK2quvLmf//uCmmsaRPGBEi6OjIyNHjmTIkCHa/PnzmTRpkhYWFuaH3qfyD5MwZpsn\npHNRZ0rWvtnO5NOoHGUa+jC54Rec3nSShgMa3160Z+/i3ZRr5otXhaLm5ee3niU9NZ0qHXRPC2VU\nHF93lJCjwbiVcqOOX31CDl8mIy2DSs/cfTaF03+dxNLakgqtK3Ej6gbH1x+ldq86XDl2hfNbz2Jp\na0m1zjUoXtX7oc/PmG7k1J8nCD1xBRQUq1qcGt1qZY4SIfJ8BJf3B1K3bwMO/rafqxci8argRd2+\nDUhLTuPAr/uIj4ijVN3SVOusexmkJaVy8LcDVOlQlZjgaM7+fQZre2sqtq1MiZols/2eeJzKPVeT\nEG4ESvv51eTcuffEr1C4L9WrF2PXrjeYNu057OysrU1isx+om9vH5uDgwMiRI7l06ZI2Z84cvL29\nNaAren34eqB+Tu27SDlPDBYGrofF3vGZMipWvv0bl3ZlNe3Zs3gXO2ZuNb9f9uYv/Dr8RxKjbxB6\n/Aqzu33Llil/sXvhznvud8fMrexZvAuAuIjrrHz7NzZ9sZFNn/9OamIqpzedZHrrKUScDX+o81BK\nseD5OawavZzk60kkxyezavQyFg9YYF4naF8gK99Zzsp3fuPirgASriWwfORSfv94LQufn0P46TCi\nA6NY3H8Be5fsBiD1Rior3/6NDR+uZe24VaTEJ3Pi92PMaDuVc/9kfyHjUTPEbprGHKUoXqyYk5o5\ns2fmoH/hCSlTxg1//0b5tnj8UDebpYGRI5vTtWsVbejQFfz7b0AtdCPX3DCivQMbGxv8/f0ZNGiQ\n9sMPP/Dpp59qISEhXU3iuAX4wCTi2UbAfxcwZhgpXu3xRr1EXbrGwd/20/vr52n0chMAjq09wo+D\nFlGze+2Huy5WugzEXI7itT/eQtM00pPT+Kjs+xxfd5Si7xZ74Daig6JJiUum/8KXKddMn8jRt0UF\nfnhxHpHnIvCqWBQLawvSU9IoVqU4LV5rrQtphpHtM7fy8k9DqN5FzwoTrsVzYv0xGg1sgoWpm17E\nmXBG/jsGC2sLjOlGpredwt9fb6Zi28q5kiEWRR+zug4oPmBAXU6eHC1imI3UqlWcOXN64+pa8Kfh\n8PX14O+//ZkzpzeOjjYW6LP+HUR3us51rK2t8ff3JyAggMWLF+Pr6wvQDt1sdjOP2Sp95VgIe37Y\nxZ4fdrFz7nbWjF3J4v7zqdimEtU6Pd6zFHQgEGVUVO9a07ysZvfaOBd1fuTOTnX86psbQi1trXAr\n7U5ceNxDfdfDx4M3N79NuWblSU9JJyk2EVsnvQ909OWsw9yrd7l5rB7limCwNFC1Y7VblnkSH5l1\nv7V61TGLo8HSQLVONQg+mP02fQ/KEDXgZU3jG6Vw9fXVzRjatPEVBROeiEwj2vbtK2j+/ivZsuV8\nNfT+q+eAk+RcS/RDp+DW1tYMHDiQF154gcWLF/Pll19y6dKldiZxfGQiz0dwbO0R83snLyee+6IX\n9fs1NNezPSrx4XEYLAzYu2e1zHsc0wnHIlnNmK1srcxdwB6myLx1+t/sXriT62GxOBZxMk+hoG4b\nWGDvfrOO3cLSAltnuyzTLVhYWdzxHdcSblmP1cuJtOQ0kq4nYeeSfUnEgwSxHDBOKd2D7s03m9K6\ntXi/CdlH2bLu/O9/z7BvXzBxcckaUMn0yjNYW1vTvn17/vvvPy5duvTY26nTux6dPur6xMdjTLv5\nW2Fpa4UyKozpRixu6SqWlpL+VGN04Jd9/Pn57wxc/CqV21XFwtqCaxevManep9my/bTkrG1v6Snp\naJqGlW32VjE9SBAD0EeejAdGv/32esv1608zb14fypVzl6dZeCLi41MYO/YPZs/ejSkR2Y4+YVNO\n2njt4hHmSQ4ODmbKlCnMnj1bpaamapqmxSiltgI9czyLNmhY2liSFJuYNdM8F4mLt961zbmYM0op\nogOj8KygjwZLup5E+Kkw3Ms8vWf04s4LeFcvYW4dBrh8IDDbtn/1QlZ7y+jAazh6OmX7ePKHqUNM\nRp/Orz5w6J9/LlCt2lQ1adJWMjKMefqB27DhNCdOhOcbgbh4MZrly4/ds5jyoM/zE3/+eZbq1acy\na9ZugFhgGPrkUH+i1yfm1OuhbtrIyEjGjRtHhQoV1IwZM0hLS7sBTFJKlUM3N34q1QoeZYtwfttZ\n0pPTUEbF9plbSYhKMI9vr9i2MrZOtvw1cSMpCSl66+47y7K1GPlQxW0vJ6KDosx1f0H7Aznwqz6/\n1/XQ60+8/WNrDhNxRn+WowKjOLL6MLV71cn283gUeT2KPovZ6JSUtE/GjfvDeu3akyxY4Jdnxym/\n9toqBg2qT/XqxfKFSGzZcp5hw1aSkTGJuw3yedDndyM93ciiRftZuvQoV65cp1gxJzp3rsybbzbL\nlRbt2Ngkxo79g3nz9mZmhcuV4g2enrnr/TORq1eZOnUq06dPV8nJyZqmaYnAd0qpSdzbnDbH6Pxx\nN34ZuoT/K/UeVjZW1PGrR60edQg7cQUAGwcb+kx/gXXvr+LDMmOxd3eg04ddSbiW8FSPs8XwVpza\neIIvan6CvasdzsVdGLjkVZYO/4n1/7eapNhEXEq4Pvb2G7/SjMUDFpCSkELC1XhK1CpJ23ey3638\nccfWVQMWAg0tLQ1q9OiWWl609SpV6nMGDarPp592zBeCOHfuXrPg3c0tJyUlncTEtDtGt9yP4cNX\n8cMPBxgypCHVqxfj4sUoZs/eQ926Jfj332FPdXjl+vWnGD58lQoNjdM0jXCleP1pZVu3kFSsWDHb\nsLCwLAuvXbvGlClTmDFjhkpKStI0TUtUSs1H7zx++3QEA4Al7d7tSMcPOj/cTmMTsbS1emCdV1py\nGhmp6dg622VZFh0YhWMRRxyKOJKWnIYx3YiNo03WfVxPwtbJFs2gMbXpRMq3rEj3ib3uup+UhBQ0\ng4a1vTXGDCMp8cnYONpmadxIjk/GwtKAld3daxhu/9yYYSQ6KBoLSwNupfXiujIqEq4l4ODugDIq\nUhNTsHWxM9936clppKWkZ8lo05JSyUg3YutkS3JcEh+WGceL8wdSu2ddrl28imYw8KiTem377l82\nfLgG9MnSvs2ODPFWTgJNgCEZGcZvJk3aar9x41kWLPCjfv2ST+WuDgm5bvYY3LcvmMTENOrU8cbd\n/e4TVCUkpBIZmUDZsm7mi6GU4tKlGDw9HXBysjEvO3w4lNjYJGrWLE6RIg5cvBiNl5cjjo76hc/I\nMHLgQAhJSWnUqVMCR0drgoJiKV7cKYvVf0BAFGfOROLkZEP9+qXuyMgSElLZvTsIg0GjSZMyDzzn\nlJR0YmKSzIIYHByLk5MNzs62mY0SVK9eDG9v3bg0MDCGOXP2MGtWL4YPvzkKonZtb1566VfOn79G\nxYo57+caEZHAm2+uZsWK45mLflSKUUB0bv8IRUVF8e233/L111+r+Ph4TdO0JGC+UupLINvqW+xc\nH27iNKu7iKaVrRVFKxfL8j6TjLQMZnWZQeUOVWk3Rv/hv7TnIhFnwmnz9r0bw28VU4OF4a7Hl9lt\n5l7c/rnB4k6h0gxaliGJdtZZ92Npa4Xl7edrZ33XrgCaQcOzfM6WRp+kRtIIzFWKLcC8Y8fC2jZp\n8h2jR7dkwoQO2OSweWaXLgupV68Ex4+Hk5SURlRUIjExSSxa1Jd+/Wrfsf6qVcd5+eXfuHHjc7Mw\npaUZ8fWdyIIFfrz6agNSUtLp2nUR27dfpEaN4kRExPPFF50YOHApS5e+xPPP1yI2Nol27eZx+nQE\nVasWJSIigY8+asfQoSvYvv01WrQoS0pKOq+8sow1a05St24JQkPjSEhIYdmy/uYpE06ejKBt2zlo\nGpQvX4SIiHi6dKly33NeuvRolgyyQ4f5dO1ahV27AomLSyE6OpGoqER+/fVFevasjpWVgYUL+9Kn\nT9YpXatWLWqqJ7uR44K4fPkxhg9fpaKjEzX0GfH80Ts55yrR0dHMmDGDb775RsXFxWlAKrBYKTUe\nCMsvdbEWVhbU79eQNeNWcnztUaztrQk+cpmaPWpTu1ddhKcniJlcRO+XNTQjwzh10qStjitXHmfB\nAj9atsy5Ljo2Npb89NNhVq0aSNeuVUhPN9Kjx2LGjNlAnz417nCreRh+/fUI//xzgd2736Rhw1LE\nxibx7LP60KPM6oCZM3dz5kwkR468TYUKRQgNjaNt2zlZ1pk0aSsbNpzm0KGRVK7shdGo8PdfyfPP\n/0xg4PvY2Vnx8cd/4e5uz969b+LsbEtQUAyNGn37SMdrbW3B7Nm7Wb/+FVq39kUpRdu2c5k0aSs9\ne1anRAkXXnnlzlFnS5YcxNPTgVq1iufY9QkNjeO111axbt0p0CeHmgeMRp9LOdfF0MfHJzMjTAVm\no1vXhefHh7jxK82o1qUGwYcuo4yKopWKUcS3YMzkYGVrTe9vnqd03TJPZX/ZZVSoTNliJWDdhQtR\ntGkzh2HDVmaZajNbKz81qFatKF276lmVpaWBN95oQmhoHIcPhz7WNteuPUnjxqVp2FAfgO/qasfo\n0S1N+9PM63TqVIkKFfSigbe3M6+91iTLOr/9dpSXXqpD5cp6em8waIwb14bIyAR27QrCaFSsX3+K\nfv1q4+ysFzvKlHHDz6/mo108g0bTpj7mrFPTNJo0KU1gYPQ9i9wjR65j0aIDLF8+wFxNkJ0opZg7\ndy+VKk1WJjG8ALRFb0VOyAsPWWpqKgkJCWnA90opX/SJ7cPzs3A4eTlT9dnqVOtco8CIIYCFtQWN\nBzV9arMbZne5NhToDvgppWbPnbvXffPm88yb14dnnimf7QefKTiZlCnjZs5OHjer8fX1yLKsbt0S\nd6zTokXZe66jlCIwMJqUlHTat5+XZblerxfN1avFSE3NoFQp1yzbKVfO45GPOfOcM3F2tiUl5c5B\nHmlpGXTsOJ/Q0Dj27n0zR4rKAQFRmMYogz7SJE+MUb49FMByU9H4ohQShZwURHPVkVJsB76/dCm6\nd/v2cxk6tBGTJ3cxZ0TZlSVm+TUxOXM/ynCjW0lPN97Runu72/fDrGM0Kho1Kk2PHtWyLB82rDE1\naxYnzTTS4PY5Vh6nf+HDzNMCsGzZMXbsuERAwDh8fNyy9WKnpxv5/vtdfPDBnyoxMVVD76I1GL3f\nX16jGhAsj77wNAURIALoA3QD5sydu7f4unWn1OzZvbTu3atlyw5CQq7fkb1lFmPvqIsw1SkmJqaa\nG1Vu/36xYk6EhcVnWXZ7x+4HraNpGmXKuOHiYnvPInBaWgYGg3ZHJhsQEJVjF6N2bW/WrRuU7WJ4\n/Hg4gwcvZ//+YDSNVMh9n8MHkB1imAJkccAW8jbpqeZrlXzfaqincCzrlaIaMDc8PF7r0WMxffv+\nxLVrN554w7t2BXHyZIT5/a+/HsHLy/GuZqwlSjibH+BMvv12Z5Z+eG3blue//y5x4YIuTElJaUyd\nuj3Ldtq2Lc/GjWcID9dFMSYmie+/35VlnU6dKrN06RGCg2PNy/7++wItWswkNjYJKysLmjXzYdmy\nY+a5nEND48zdUnJiJIrBoOHomH11hmlpGUyatJV69aar/fuDAXYpZR7mmVbAn68wgPiIOFGafEJc\nmDn5Cc1tQQS9h/8woAsQvHz5MapVm6qWLz/2RBvt3Lkyffv+hJ/fj7RpM4f58/fxySd37/LTtKkP\nNWsWp1evJaYuO9NxdbXD0fHm3MiDBzfA19eDevWm07btHKpXn8oLL9TKsp1Ro5pjZ2dF9epTaddu\nLvXrT2fw4AZZ1vn443ZUquRJ7drT8PP7kc6dF9Kly0KeeaaC2d7r44/bc/JkODVqfE23boto0uQ7\nc0Z5+1zN2cG0aTvo1WtJtmzr8OErNGr0HePG/UF6ekbm0M4W5OK0AE+ZSwChx6+I0uQTbrlW9603\nzo1ZoFyAr4ChgNa1axVmz+71yFNtNmr0LdWrF+Prr7vx+++niYlJolkznyzZ4Y4dl/D2djY3lCQl\npbFhw2muXr1BnTreNGlShm3bLlKunLu5gSM5OZ1Dh65w9WoCjRuX4fr1JCpVmszWrcNp1UrvRnTj\nRioHDoQQF5dMixZlOXIklDZt5nDu3Hvm1mejUfHPPxc4c+YqTk42NGvmQ/nyWRtNLl2K5q+/zmFh\nYaBDh4rY2Vlx9Ggobdr43nWmwitXrnP6dCTPPFMeTdPYu/cyLi62WRqXAgNjCAyMNrc8Z3L6dCSR\nkQnmc3gckpLSmDBhM1OmbCMjQwFsMv3QBRXCZ+woUHPswQ8fedSE8HSJj4zj0yofoYwqECib1wQx\nkxboU0BWcHGxVV991eWRpiHIFMQFC/yy7YAOHgxh9uw9TJnSFRcXvfFn5szdjBixhtDQDyla1JGt\nWwP47bejTJ/e3dzv8H//28S0aTuIiZnwWP0f8wM7dlxiyJDlnDt3DU3julK8h963UBXS5+z/gM8a\nDmiM34x+ojp5mHUfrGbHrK2YErGx91vXMjefMaAW8PH168ljhg1babF69QnmzOlN6dKuuXJApUq5\n8tdf52jRYia9e9cgNDSOH344wIgRzShaVDfPLFHCheXLj3HkSCidOlXmwoVr/PzzYb78slOBFMO4\nuGQ+/PAvvvtuZ6bDygaleA0IKeTP2Qw0Ru7/ea9n/RcbUbax+ITmRa4cDWHX/B0KjXgUkx+0fm4/\nwenow7g2A00vXIjyXLBgn7K3t9YaNix1X+OBa9cSqVGjGLVqeWfbwTg4WDNwYD0sLQ0EB1+nSBEH\n3n23FSNGNDOv4+FhT//+dUlLyyAk5DqlS7sxfnx7XnyxToG7mTZuPEPnzgvYvPk86G40r6PXF0pr\ngj7ULxxFz9ObTqrqXWpqtzpBC7lP7JVY5vb8XiXFJmnoo6S2Peg7eWkmeVtgnKbxgVJYNW/uw4IF\nfk/FfEDISkxMEuPG/cHcuXszFy03ieE1ic4dfAOMsnO1Vy/Nf1mr9ExliUge4OKuAH56ZZGKj4zX\n0J25Bj/M9/JSGS8d2AqsBRpevhzrPX/+PmVlZaE1aVL6rnZYQvazfPkxOnVaqHbsuKRpGuHoVlef\nAokSnbuyGbBJT05rfmjZAS3kSDCOnk64lXR77HlShMfDmGHk0p6LbPhwLb9/vJbUG6kautXXCB7S\nGDivXjFLYLSm8YlSWDduXJoFC/zMLi1C9hMeHs+bb65h5crjcNOM4V0pHj803YEpQHkAW2dbivh6\n4VzUGUtbS4lODpKRkk5cZDzXAiJJik3KXHwZvQFl6aNsK6//hFVDb4lulJeNaAtCVniLRddF9C5R\n/0hkHhkr4EX0+VbaA/YSkqdKsum+XQ38xANGpeRHQQS98/gQ01So9jVrFn+qRrQFmcDAGPz9V2Q2\nmhiB+cA7wA2JTrZQBCjOI0xqJTwWaehDhSOedEP5qZKjnKkY19bS0vDUjGgLIkop5s3bxzvvrFc3\n9HqWE+iVzvskOkJhRsuHxztU05iqFI7ly3swf77fE42+KGxcuKBbdG3dGoCmka5UnrToEoRcIT9W\nxh0EFgPlo6OTKi9ZcpDQ0DjatCkvdYv3IT3dyOTJ2+jb9ycVEBClAUfQnYh+RPcuFATJEPP58ftp\nGrOVwr1sWfccM6LN7xw7Fsbgwcs5cCAETSNZKcajt4iKEApCPs8Qb+WUKVv0iY1NqvrjjwcJCIii\ndWvfLLPfFVbS0jKYMmU7/fr9okJCrmvATqAzel9PJbe/IBSsDPFWumkac5SieLFiTmrWrF7a7Y7V\nhYndu4MYPHg5p09HomkkKcUEYDIP2UFVEEQQ8z+uwCT0qS7x86vJzJk9KVKk8IwxTUxM45NPslh0\n/Ylu0XVZbndBKFyCmEknYA5QysvLUU2e3EUbOLBegb+Y27dfZMiQFZw/n8Wia67c5oJQuAURwBl9\nDO6bgOFxjWjzA9evJ/Pee78zb95eTLMPbACGA2LpLAgiiFlogT4Co+LjGNHmdX7//TTDh68iJOQ6\nmkakUrwBrJBbWxBEEO+FHXrn4zGAxbPPVspVI9rs4B4WXa8BUXJbC8LjUVh6Mj+2EW1eZPnyYzz7\n7IJMi67LQF/06T+T5JYWBMkQHwUr4B1N49NMI9r58/2oVCnvG9GGhcXxxhtrWL36BNy06BoDxMut\nLAiSIT4ORvQOyvnGiFYpxY8/HuK5535Qhw+HakAA0Afd/DJVbmNBkAwxO8jzRrSXLkXj77+SLVvO\nZxb9ZwIfIBZdgiAZYg5li6uBeiEh10vOnbtXJSamai1blrvr3MhP7cCMukVXjx6L1dmzVzXgOLor\n8wJ0/zdBECRDzDEyjWi/VgqHGjWKsXBh31wxoj15MoLBg5ezd+/lWy26PpLisSBIhvi0UOjWYr8C\n1SMjE8otWrSfxMRUmjcvi6VlzmeLmRZdL7zws7p8OVYD9qCPuvkVcaYRBMkQczEuQzWNKUrh9DSM\naI8e1S26Dh4Uiy5BkAwx73EQ+AGTEe3ixQdyxIg2OTmdzz77mwEDflVXrlzXgB3oFl3rEIsuQZAM\nMQ/ip2nMUgqPsmXdmTu3N+3aVXjije7aFcTgwcs4c+YqmkacUnyE3pVGLLoEQQQxT1MU+A7oo2nQ\nv39dpk17Dnf3R59pMtOia/LkbRiNCuAPdDOGYAmzIIgg5ie6maYt8H4cI9pNm84xbNhKgoJi0DRi\nlWIsYtElCCKI+RhXHtGINjY2ibFj/7jVoms58AZwVcIpCEJBoBMQBChPT0fj4sXPK6W+uuO1bt0g\n5e3tbASUphEO9JLQCYJQEHEGpqN3j1Fdu1ZRISH/p5T6SoWHf6QGDKir0FuLFbAMcJeQCYJQ0GmD\nbrqg3NzsjGPHtlZubnaZQngReEZCJAhCYcIe+Aa924wy/Z0GOEhoBEEorIw1CeJvEgpByD8YJAQ5\nwlnT3zAJhSCIIAqCIIggCoIgiCAKT0Ip9E7e5e/xeRHT5zUkVIIg5Dd6oDeqTHvI9S2BA8A+7u5A\n9BMQCXhKaAVBKOiCCFAL3RH7rduWdzRtq7eEVRCEwiKIAJ+iTyla2vTeAb1T963dd5oCfwPXgWvA\nKqDsLZ+7o5tFBADRwDFglFwSQRDymyDaACeADab3U9HNH7xM76uhT0b/HeBjer8JuITeKRzgF+AI\n0AgoB7xoEtkBclkEQchPgohJyNKBiaa/L9zy2Rz0Po63NoYVQx9H3c/0/jQw67ZtVjOtJwjCfbCU\nEOQ59qIP/xsLrAGW3vJZVSAOGHLbd64DlU3//wp8bCo6bwB+B05KWAXhwUi3m7zJ4tv+ZlIE8ADa\n3fbaAoSa1vkE6GrKGr8Fwk3FaFcJqyAI+a3IDFDd9P0ety3fjN6I8rBYAH3Qu+xMl8siCJIhFiQO\nA60Ap1uWWQFvA8XRvRk/ArxNn2UAK4B/0BthBEG4D1KHmL/4Br21eDN6S3MqMBS9/vAH9NbkbkBP\nU3E5xvRZd0zTHQiCIIKY34hG70sYeNvyMKA+8I5JCFPQ548eaBI/0Dtyj0DvyO2MPpOfHze78giC\nIDxVevBkdYiCIOQCUocoCIIggigIgiCCKAiCIIIoCIIggigIgiCCKAiC8PBIP8RHx5ObfoX3wtf0\n1wuo94B1o9HtuwRBEPId5dBHiKhser0oIRWEvIEmIXgs5gFDSpUqRePGjR/5y5cuXeLAgQOgextW\nQx9zLAiCkC8pDaQ4Ozsbo6Oj1aPSsWPHzOxwoIRSEISCwGxAffTRR48khgcOHFCapingAlKHKwhC\nAaGUpmkpTk5OxqioqIcWxC5dumRmh69ICAVBKEh8B6gPPvjgocTw0KFDmdlhIGAt4RMEoSBRXNO0\nJHt7e2NERMQDBbF79+6Z2eFQCZ0gCAWRaYAaO3bsfcXwyJEjmdnhZckOBUEoqBTTNC3R3t7eGB4e\nfk9B7N27d2Z2+JqETBCEgsxUQI0ePfquYnjy5EllMBgU+sx4thIuQRAKMkU0TUuwsbExhoSE3CGI\nffv2zcwOR0ioBEEoDEwC1MiRI7OI4alTp5TBYFCapoUDdhImQRAKAx6apsXb2NgYg4ODzYL44osv\nZmaHb0uIBEEoTHwOqDfeeEMppdT58+eVpaWl0jQtArCX8AiCUJhw1TQt1srKynjp0iU1cODAzOzw\nXQmNIAiFkQmA6ty5c2Z2eA1wkLAIglAYcdE0LYabfofjJCSCIBRmPgKUpmnRgJOEQxCEwowzEAX8\nT0IhCPkHmWQq5wQx0CSKgiAIhRIN8Nc0rnOzDvFPoIyERhCEwoQv8A+gLC0NasSIZqpq1aIKvS4x\nHngdmcNGEIQCjsGUFSYAqkaNYmrfvhFKqa9UauqXauLEzsrKysJoyhb/AypLyARBKIhUA/aYskLj\n2LGtVUrKl0qpr7K8jh17RzVoUMqULZIEjAUsJHyCkLeQh/LxsATe1TSWAmUaNy7Nxo2DtX796mBh\ncWc7VdGijrzySgMcHKzZseOSRUaGsT3wHLAPCJdwCkLeQOq0Hp1awEKgrq2tlRo/vr02ZkzLuwrh\n3bhwIYqhQ1ewdWsAmka6UkxF77eYKqEVBBHE/IItME7T+D+lsGzRoizz5/ehYkXPR96QUop58/bx\nzjvr1Y0bqRpwAngV2C9hFgQRxLxOU2ABUNnZ2VZ98kkHbcSIZhgMTxa+S5ei8fdfyZYt5wHSgZnA\nB8ANCbkgiCDmNexNxdl3AUPnzpWZPbsXpUq5ZtsOlFL8+OMhRo1ap2JikjQgAH1Wvn8l/IIggphX\n6AjMAcq4utqpSZM6a/7+jXJsZ2FhcbzxxhpWrz4BehedecAYIF4uhSCIIOYWrujTAQwFND+/mnz/\nfU88PZ+Og9fy5cd47bVVKioqUUMf/ucPbJbLIggiiE+bbprGbKXwLlrUSc2c2VPr1av6Uz+IyMgE\nxozZwI8/HjLrJDAciJZLJAgiiDlNUWAyMADAz68ms2f3wt09d13/N2w4zbBhK1VoaJymaUQoxevA\nKrlcgiCCmFP4aRqzlMLDx8eNuXP70L59hTxzcLGxSYwd+wfz5u1FKXO2+AZwVS6dIIggZhfe6N1c\numsaDB3aiKlTu+HoaJ0nD3bTpnP4+6/g8uVYNI1YpRgLzJVbWBCyj8I4dC/TomsdULN8eQ9WrXqZ\nN99shrV13g1H+fIeDBvWmIwMI7t2BdkqRTegAbAdiJNbWRAkQ3xUyqF3Z2lraWlg9OiWTJjQARsb\ny3x1Ejt3BjJ48HLOnr2KphGnFO+azkvJLS0IkiE+CEtghKaxEqhYs2Zx1q17hYED62Fpmf9Mw0uX\ndmXw4IakpxvZvTvIxpQttkG3F5OWaEGQDPGeVEcfdtfQxsZSjRvXRvvgg7Z5unj8KBw5Esqrry7n\n8OEraBpJSjEBvcXcKLe3IEiGmIkVNy26SjdpUoY//his+fnVfGhnmvxAsWJOvPpqAxwcbNi27aKl\n0ajaA+2BXcA1ucUFQTLE2ugWXXXs7KzUxx8/mkVXfuX48XAGD17O/v3BaBopSvExMAXIkFtdEAqf\nINoBH6OPAbZo2bIc8+f3oUKFIoXmgqanG/n++128//5GlZSUpgFHgMHAIbndBaHwCGJzYD5QydnZ\nVk2e3EUbOrQhmlY4u1oGBEQxZMgdRrQfAyly2wtCwRVEZ+BT4E3A0KVLFWbP7kXJki6F/uLew4h2\nMPrUBYIgFDBB7ATMBkp7ejqqKVO6aAMH1pOrehuBgTEMHbpCjGgFoYAKoiu6RZc/6GYMM2f2pEgR\nB7mi98kW87AR7U/o/pNVuXOMtr0psz0FdJUrKYggZqWbpjFHKYoXK6ZbdPXsWV2u5EMSHh7P66+v\nzmtGtB7ASWAj8Mptn00DBqH3Jw2RKyiIIOoUA74Demsa9O9fl2nTnst1i678yvLlx3j99dXq2rUb\nmUa0w4C/cvGQ+gDLgA7AFtOyhuj9KYehd64HqAz0Qq87vgL8TNbROU6mbZUF0oAdwDZkWKNQgATR\nz2Tc6l62rDvz5vXhmWfKy9V7Qu5hRPsaEJVLh7QCvQ9pDfS6zgPo81Y/axK0/sAidE/Is6Zidmmg\nBXABKGL6zlVgK+ACvIDuCjQml87JFaiL7q5UFH0YqZBzXAdCgYvoVS0FShB90Oc16WAwaAwZ0jBP\nW3TlV37//TTDhq1SV65cz20j2qKmovMCIBZ43ySOQSZxCzEVoT80rW9hEsALgJ9JMH8AHIFk0zqt\ngN7AKJ7ucMZuwFum/VvJXZYrBAJL0QcnPNSPfF4VRA0YqmlMVQrHatWKsmCBH40alZZLnEPkISPa\nzCwwHXgHmGVa3hb421RkPnvL+h+YhKcYeq+DP9D7W84BInIhlKWBJSYhxMnLiYptKuNW2h1re/kh\nz2mMRsWNq/EEHw4maP8llFGBxnVuOkLlO0H0NR14m/xs0ZVf2bTpHMOGrSQoKCY3jWj3AQ7oDSmZ\ndX+voA/HvBsKvTU62SSO75mKqPtNwj4TSHwKx90YjbUovLyrl6DTx12p1LYKmkGM6XODuIg4/vl6\nM3sW7VQZaRma6T4Ycb+SQl66UpbAG5rGl0phV6tWcRYu7EvduiXkyj5lEhPT+OSTzUyevA2jUWHK\nuobx9Fp5N5qKvS1uWdbHJG5NgMi7fCeIm2O2DUAz4DlgiKlI3ZicHdNdFo39KDwaD2pKj6/6YGFl\nITdTHuDKsRAW9ZunrofGasCXplJFnhbEGuj1Rg0yLbr+7//aYiU3VK6yc2cgQ4Ys58yZp25EezdB\nrAscRG+FvnVaVkf0DuYKva7OhawuP63QG1iqAGdy8Mf8EFCjzah2dP64m9w8eYyoS9eY8cxUlRiT\nCNAdWH+39XLb/sUKGKtpHAQaNGvmw5Ejo7Tx49sXSDE8cSKckJDrAFy/nszBgyGkpeVdI5pmzXw4\ndGgUY8e2xmDQnNHr5bYCuTEL12HgKPA5euML6PWG/5qOC3QfyO3o9XiZ93cj9PHbV3Lw2AYDNSq0\nqkinD6XveF7Eo2wR+s0doJmSwMnco7U/NzPEJuhmDFUzLbrefbcVhjxU3xIcHMtnn/2dZZmdnRW+\nvh688ELtR568vmLFr3juuapMmdKV9etP8dxzPxAS8n+UKJH3x13fw4g2p6zF7pYhgj4FxM/o/RPD\n0bvZbEbvuH0NvYvLj+jddK6athFvqjfKqVZzDbikGbQyo7a9i3d1qeLJy8zvM5uzf58GvTvWb3kh\nQ7QDJqJ3mK3asWNFTp8eo5mykDwVvGvXbjB37l6CgmKyLPvss7+pUGESJ09GFJobqXZtb/bufZOJ\nEztjaWlha7qG29FbfbMbP6DzXZZfNP2QlkBvUS6OPpwvs4gci97dxctUtK4OlCFnuxDVBcqUbeIr\nYpgPaDbU/Bvb8151H0+TFqassKKLi6366qsu5AeLrtdea0L37tXM769evUG5cl8yd+5epk9/DoD4\n+BQMBg0Hh5tdK5KT00lOTsPV1e6+279xI5Vz567i7GyLr69Hno2DlZUFY8e2pnPnyprJiLappnFE\nKSaairJp2bSrhAd8Hm563YsY0+tp0BqgSoeqojb5gAqtKmJla0Vaclqbu33+tDJEF1M9zzagYteu\nVTh5crTm798oX/oVeno64OHhwI0bqeZl7dvPY8SINVnWmzVrN97en913W+vXn6Zkyc/p3Hkh5ctP\nonv3H0hNzdsG1zVqFGPXrjeYNu057OysrdH7/e03ZUuFjVIAnuW9RG3yAZa2VriWcgPwBGxzQxA7\nA8cBfy8vR5Yt68/69a/ki3qzu5GcnM633+4kLCyOQYPqP/H2liw5yLlz7xEW9iEbNw5m3bpT/Pbb\n0bx/Y1kaGDmyOceOva21bu0LUAvYaypK2xSiZ8wTwKGIo6hNPsGxiBPodb9eT7PI7GZ6OG616NLy\no0VX//6/mlu9Y2KScHa2Ze7cPjRv7vPE23777Rbmxplnn61E7drerF59ggED8key5evrwT//+DNv\n3j5Gj95gkZCQMhboQt41ovVGH+uaXVgAGAwGUZp8guHm1MMWT0sQ/TSNmUpRpHhxZzVrVk/t1jq4\n/MaECR1o1aocAAkJqRw+fIX33vud48fDmDLlybpZVK1aNMv7cuXcCQ6+nq/io2ka/v6N6NChoubv\nv4LNm89XB3aj1xe/Q94yoj0NrAU+Qe+wLQg5VmQuBqxEt3Eq4u/fiLNn383XYpiZBdWrV5J69UrS\nqlU5Ro1qwYwZ3Zk6dfsTtzTb2WUd929lZUFqanq+jJOPjxt//TWUZcv64+Zmp5lKB8eANnnoMK2B\nAeiGs/PQu/IIQrYKogYM1DROAb3KlXNnyxZ/5szpjZNTwaxOKl7cCdANVwEsLDSSk7MKWeZn9yMs\nLC7L+8jIBLy98/d8MH5+NTl1aozWq1d1TILzN3qjmlNeOD4bGxvc3d2t0If1nUU3k8jRzuYxl6OJ\nCozK8oqLiMvR81z+1q/smr8jV2OdnpLO3J4zOffv2SfaTtipUOb2nElMsG59+dfEjfwxYX22H292\nFJnLog/+b2dhYeD115vyxRfPZul+UtCIi0vm6693YGdnRZ063iaBdObs2ZvGMAkJqSxffgyl7j/K\n7ZdfDtOsmY9ZDHfvDmL8+A75PkbFijmxcuXATCNarl274a9pdFOK4cC63Dw2Nzc3zp8/z4IFC/jy\nyy8tIiIiBgEDTaWbj8iBIX5Tm00kJeHOCQ+t7Kyp90IDOn/cDTsXu2zdZ9D+QKzscvc5VEpxfutZ\n6vZ9sgbI5OtJnN96llRTz46wk6GkJaXmKUHMtOj6WikcqlcvxoIFfjRsWKrACeDo0Rv49NO/TUKX\nQmBgDB4e9vz8cz+zY/dLL9Whd+8fad16NhUqFGHv3st07VqFmTN333WbmV1rYmKS6Np1EeXLe7Bh\nw2k8PR0ZMqRhgYmdn19N2rWroI0b9wdz5+4tjl5/l9tGtDg6OjJy5EiGDBmizZ8/n4kTJ2rh4eF+\n6N6Jf5iE8XB27rPpkBY8+383+5unJKQQsPMCa95dwY2oBAYuflXKrLnM4wpiefQK81YWFgY1enRL\nPvmkI9bWBWv8calSrsyZ0zvLMgcHa3x83Khfv2QWS7KePauzfftrbNsWgKWlBWPHtkHToHr1Yiil\n0DSNTz/tSJkyboA+8mPOnN68+moD1q8/xeHDobz1VjNefLEOHh4Fa1oENzc75szpzXPPVc00ovXT\nNFoqxRumrCzXcHBwyCKMkyZN0sLCwrqit5T/DoxHN5V4YqxsLbFzvXlt7Vztqfd8A6IuXeOfrzeT\nnpyGpa1epxwbEsPO+TuIOBOOraMtldpXoa5ffbOV2O6F/+Hg4Yh7aXd2LdxJclwSpeqUpumQFtg4\n3r2aKjEmkb2Ld3HleAgqQ1G8ujfN/Vti63wzM026nsTOedsJOXQZWxc7anSrRbXONW7+kCemsnvh\nToL2XUIZjZSu73PffZqzJ03j4NL9nNx4HIDqXWqas8b4yHh2zNpKk1ea4Vba3fydHbO24l7GI8v+\nbyf0xBV2zdtBXEQcxat50/qtZ54o07Z8jPVHaxqfKIV1nTolWLCgj1anTsEcslSkiAP+/o0eev3m\nzX3u6Ipz68iT55+vlWV55mc9e1anMEyU1aWL3iH/vfd+Z968vUXRpwxYjj6ndmReEMbhw4drixcv\n5pNPPtGuXLlyqzB+gt75PPuzEhtLjBnGTKs1Is9H8H3HaZSu50PtPnWJC7vO2nGruLw/kJ5T/AA4\nuvowKTdSURlG6vVrSHJcEn9P+YugfZcY9MvQO/ZhTDcyu+u3pky1OWga/83exokNx3hry2gMlgbS\nklKZ2Wk6BgsD9fo1JDH6Bj+9upiO73ei9chnSEtOY2bn6aQlptHi9dYA/Dd7G0fXHObNTW9jeR/P\n0t0L/sPe3YEqHaty5WgIvw77kYzUdBr0b0xi9A3+nbaFKh2qZhHE/T/tpWxT33sKYlxYHL8MXUKD\nFxvhUbYIW2f8TfDBIPzXvPFUBLEmukFnPRsbSzV+fAfGjGmJhYX0vxIeHhcXW+bM6U2vXjUyjWj9\nNI32uWREewc2Njb4+/szaNAgli5dyoQJE7SLFy92RR8zvQX4P7Kxf2X46TB2zf+PCq0rmR21N33x\nB64l3Hj1N39zRuhexoOfBy+m5Ztt8fDxwMLKgrCTV3j/8Ee4eLvqou7uwJr3VnLt4jWKlCuSVTzC\nr1OiVklavtGG4tX0em+vCl7M6votYSdDKVGrJPt+2svVgEg+PPmJuaO5rZMtJ/84TqsRbdn/0x4i\nzkQw7tD/zPus3L4qE+t+wuEVB2nw0r2TB6PRyCtLh5pHpsWFx7Fj1jYa9G/8RLF7d+8HeFbQ+1e7\nlnTjl6FLCDsVSvGq3jkmiLboQ7PGAJZt2vgyb14fLS+PuRXyPh07VuT48Xd4//2NzJq121UpNQd4\nCb0zf05miw/1C25tbc3AgQN54YUXWLhwIRMnTiQoKKgd0M5Ux/gpsOdRdrx3yR5ObDiWpfiZcDWB\n8q0q8vzMl8zLgw9eptIzlYm+fHMyQc8KXiiluHI0GA8f/dkrUbOkWZgAyreqiFKKiDNhdwiia0k3\nnp/5EikJKYSdCiUhMp74yPgsYhly+DLe1UtkGXXTeuQztB75jH5chy7jVcGL9NQMogJvVv8WKetJ\nyJHg+wpi1U7VswzT9W1ent/Hr8OY/vjT3HhW8DKLYeY2QW9wySlB9DUVFyoBfPNNN0aObJ4vxx8L\neQ8nJxu++64HffvWpFu3H4iLS24JtMxLx2htbc3w4cMZPHgw48eP54svvgB9OGpndCuyhy4ilW1S\njvov3Gww+338Oqp0rMYrv94s4iqluB4Wy8Gl+zm65kiW79u52pNw7abvhZNn1l5MDm4O5jq528lI\ny2DFqN84svIgriVccSnhhtHkxZnZE+J6aCz2bveuv74eGkvE2XCmt5lyx2dJsfefocHJ0znLe3s3\ne5RRcSM64fHvHy+nO+IDkBD5+FOMP0gQLwKTNI1vlMLl++93Ubu2N6axq4LwxFy6FM0nn2whLi4Z\ndNfrc+gz7+WUw0Uv7jJk634EBQXx+eef88MPPwCgaVq0Umoy+jzh8x92O14VvKjZo/bN4rmTDfP7\nzOb4+qPU6FYrc9s4uDvQ6OWmdPyg8323l3Ija7eT1ET9vb3rnaK2c94Ojq46xFv/jDZnT1cvRPJV\ng89vCoqbPdevxN5zf/YeDpSu78Prf7z1yEFPTUy541g1TcPO2Y7E6LuLaVrK/c2TUpOyfp5mOn87\n18dvlHyQICpgkVJsBL67cCGqd9u2cxg6tBGTJ3fB2dlWnmjhsVBKMW/ePt55Z726cSNVQ59D92mM\nf056WEEMCQlh8uTJzJkzR6WkpGiapiUA3yulvkSf//eJqPRMFWr1qsPqMSvwbVYee3c9w/Ms78Xl\ng0F3ZHiR5yLM9X8AEWfCyEjLMM/dEn4mTK9v9LmzOivsxBWKVi6WpSh57p8zpmthKoL6enHu7zOk\nJqaa6zNPbzrJwd/202/2ALzKF+XcP2ezfJ5ZRPWqWPS+c8iEnsg6fDziTDjOxZyxtLUyt1AnXL2Z\nLSZG3zB3wr4XV89HkpachpWpZT7irO4I5+Hz+NV5D5vuh6NP8tMXuDZ37l4qVZqs1q49KU+28Mhc\nuBBFmzZzGDZsJYmJqRnAJKA+ecQMIjIyknHjxlGhQgU1Y8YMUlNTE4FJSqlSwLjsEMNMun/Zi/SU\nNNa+f9PDtpl/S87/e5Zt3/7DjWsJxIbEsGr0MuZ0/y5L0TQj3cjvH68j4Wo8UYFRbP5qE8WrelOy\n9p19gYv4ehJxNoKgA4EkXU/iwK/7OL/tHJqmEWkSkvovNiIjLYNV7yzj2sVrBB8MYv3/1pCWlIaF\ntQUNXmpERmo6K95aSnRQFEmxieyct4NprSYTtD/w7j98ppbz8/+e4diaIyTHJ3N+2zkOrzxEvX56\n9YFzMRccPBw4+Nt+rgVc5eqFSFaM+g1HD0dUxt3rGFWGEYOFxroPVhMfGUdsSAx/fv4HHmWLULbJ\n45dgH7XbzXKl2AJMDA+P9+/RY3Gmiw1Py8UmNTWD48fDKF++CC4u+StDPXkyAhcXW0qWdCmUQpie\nbmTq1O189NEmlZqaoQFHlOJVsrkD9ONy9epVpk6dyvTp01VycrKmaVoi8J1SahJPaDjrXtoDOzeH\nu9SDOdPlk+78+81mgg4EUqa+DzW716bvd/34++vNbPhoLZY2VpRtXJZha9/MUhws37ICtk62fNXw\nC5JiEylRqyT95g0wf+5awhUHU9bZfFgrgg9dZnbXb9E0jepda/LCrJf4/eN1/Dv9b4xGxTPvtGfw\nsmGs/98aJtX7FFsnW6p2qk73L3sB4FbaHf+1b7Dh/9Ywqd5noEHRSsV4acHLlGt6dxEypmfg4eNB\npw+7cfC3/fw8dDGaplHzudo8M1ofkWWwNOD37YusHbeSSfU/w7WkG90+64GVnRW2pj6FljZW5tZ1\nvXjvQJ0+9XDxdmVK4y9JjEmkeFVv+i94+YmmfX2S1pHOwGyglJeXo/r++55anz41cvymvXw5ljJl\nvuD331+lc+fK+UoQKlWaTNeuVZg69elPRHT+/DVmzPiP06cjsbXVhxyOHNn8qf2QHTsWxuDByzlw\nIARNI1kpxpNzc7Lct8hcrFgx27CwMPOCa9euMWXKFGbMmKGSkpI0TdMSlVLzgS948GT3S4HnR2x+\nh9L1y2T7wRrTjbfaVZmZ12smNk625tEtxgwjhofoApdd6ymlUEb1UNu6/Xso7ilaD3t8T/K92c99\nR8CO86CPs7/0OEXmu/EH+vShcyMjE/Dz+5Fu3RYRGhqHkLt8+OEmJk/eZn6/d+9latb8mv/+C6RJ\nkzJUqeLFokUHqFZtqnkWwJwiOTmd8eM3U7/+DHXgQAjAf0pR21RMzlVr8KioKMaPH0+5cuXUpEmT\nSE5OTgZmKKV8gZEPIYY5zt3E8K7rWTzd9TRNeyzh0jTtvhmc4TH7NRuyqT/0k27lOvoE5q2B8xs2\nnKZq1Slq7ty9T+VmSUvL4NixME6ejMhiopCebiQmJomM2+ofrl9PJsnUMpWamkFMTJI56wwM1EtE\nMTFJpKZmoJTizJlITp6MuKel//nz1zh4MIRr127cowh2g4MHQ4iMfLSuBZcvx3LwYAgBAXcO9Y2J\nSSIlJaurzo0bqcTHp5jP8d9/A4iJSSQmJgmlFO+++zu1a3uzf/9bfPppRyZP7sK+fSNISEjh559z\nrrS6e3cQdetOY8KEzaSnZyQAo9DnST6bmyKTmprKhx9+iI+Pj5owYQIJCQkpwDSlVFmTEIbLz2rh\nJLuGmWwH/Vf/+vVk47BhK+nceSGXL8fm2IEfPx5O2bITefbZBdSs+TV16kwzC89//13C3f1jzp+/\nluU7lStPZtKkrQBs2HAad/ePWbLkIGXLfsnYsX8AUKTIeObM2UPDht/Stu1catf+hnLlJnL6dGSW\nfVerNpUGDWbQr98vlCjxGa+9tor0WzqZTpmyDW/vT+nRYzE1anzNuHF/8KDumxERCbRuPZvy5Sfx\n4ou/Ur36VOrWnZ5FGL28JjBvXta2h+HDV9G58wIAWrSYya5dQUyb9h++vhNJSEild+8aTJ7cFctb\nsg1vb2dKlXIlJCT7r1FiYhrjxv1BixYzM+O2USmqA9MBY27f9NHR0Xz22WfcuHEjDfjWlBG+nRcy\nwoel52Q/ukzoLgqWRwURIBG9Ba4lcHrjxjNUrz5VTZ/+n3mMZnYya9Zu/vprCKGh/+PkydEEBcVm\nKSY+iEwjit9+O8rx4+8we3Yv8/JJk7by3Xc9CA39H5GRHwMwdep2c2b53HOL8PX1ICzsQ86de489\ne95kyZKDzJjxHwBXrlzn/fc38v77bQkO/j/Cwz8kOTmdS5fu341g8ODlhIRc59KlcZw9+y6hoR8C\nMGDA0keoq3sHT08Hxo1rQ3T0BJycbBg5svkdY6xPnAjnwoUos/VYdrF9+0Vq1/6GSZO2YjSqzBJE\nZ+ByXrnpNU1LA2aZhPAtsndKgadCEV/PJ+peIuS8IGayC332tQkJCSkZo0ato3Xr2Zw7dzVbd9K/\nf12z/X7lyl50716VVauOP/yJm+oxXn21AVWrFsXNzc68vEuXyjRqVBrQnVoaNChpzja3bbtIYGAM\nEyd2Mrtd16lTghdeqM2vvx4BYPXqk2RkKN5+u4W53uTjj9uTkXHvH4a4uGT++OMMb77Z1DwBl5ub\nHSNGNGP37qBsrZvdvv0iHTrM55VX6mcxnHiiupPryQwbtpLWrWdnxmqDUlQlD4xPvo35SqnywOtA\niEiAcCs5NadKMjBeKVYDC3fsuFS3Vq1pavz49lp2GUJUrZp1wqyyZd1ZuvToAw1Z79xO0TuWlS+f\ndRyou7u9WZAyi69ff70DCwstS8aVmQGGhMTi6mprFtlMccucTOpuBAXFopSicuWs51Whgn4sgYEx\neHs7P3Hcliw5yJAhK5g4sRPvvJM9o+R+//10pq2XpmlEAm+gO9nkRUbIYy88bUHM5CjQCBidkpL2\nybhxf1ivWXOCBQv87ipEj8Ltc5FYW1uSnm68b/H8bmJ5N2fvW4XudjIbNHx9PcxZJkC5ch7mfSQl\npd/VG/J+PwSZjT23f8/KSv9OcnLaI53XXes0EtN48801fPBB22wRw8jIBMaM2cCPPx4CvQvXcqVy\n1/g1F0gASLmRImqST0iJTzYXzJ62IAKkA5OUYgOwYM+ey41q1fpGjR7dUnsSU9mwsPg7Hs6iRR2x\nsDCYhefWOU7S0jKIikp84pPJNHjt378OpUq53nWdYsWciIpKJC0twzx9aVJS2n1bmzO3e3s3mMz3\nPj7uZlG9vZX5YeZuAUhNTWfKlK4891zVJ47D8uXHeO21VSoqKlEDAtHrCv8qhM9XKOiOMUL+IC7s\nOkAKcEel/tM0MzwJNAWGZWQYkyZN2kqDBjMw9U17ZH777ai5W01qagYbN54xm04UL64XLW+tt1yy\n5OB96/AelqZNy2Bra8msWVmnBnj33d+ZN2+veZ30dCPr1p0yf7548UHS0jLumc0VLepItWpF+emn\nQ+YsVynFkiUH8fFxw8fHzXRuTlnmbjl37io7dwZy62YtLAxcv558xz4MBo169Upgb2/12OcfFhZH\nz56L6dv3p8wfmLnoXpl/FdLn6xTApd0BojT5gGsBVzMn9zqJ7tXw1DPEWzECc03D/+YdOxbWtkmT\n7xg9uiUTJnTIYsl/7yxH7xNYooQzLVrMolGj0uzcGUhwcCy//dbfVJx1p3Hj0rz++mo2bDjNjRup\nKAVVqng98RSfXl6OTJ/enddfX82RI2FUruzJ/v3BnDoVyaZNQwBo1aocLVqU5eWXf2PNmpMkJKQQ\nHh5PtWpFSUu7d1/k2bN706nTfFq2nEWDBqU4cCCYw4dDWbPmZXPx/KWX6jJx4r9cvZqAq6sdR46E\n0rNn9Sxdc6pVK8qSJQcJC4tjwoQO5nrIffuCad9+Hps3D6Vdu0ebZE4pxY8/HmLUqHUqJiZJAwKA\nocC/hfwZ2wiknvzjhHWPiTenABDyJkfXmPvd3nXKvtyaBCUG+BEIVUq1+e+/QOulS49Qq5a3ORO6\nFwaDRrlyHrz9dkvq1i1BWFgcNWoU47vvelClit4goWka/frVxsvLEYPBQIsWZRk/vj0lSrjQoEEp\nSpZ0wdbWksqVvWjYsHSWYnvx4s60aFGOokVvmmS6utpRv34pc4NHvXol6du3prnOslUrX77/vkeW\nxph+/epQurQrGRlGGjUqzVdfdaFcOQ/q1y9pLh7fTunSrgwaVB8rKwsSE1Np1qws33/fk1q1bjqU\ntGnjS61a3iilKF++CF991ZmKFT2pWdPbfP4dOlTExcWW8uU9aNiwtLm+1cbGkkqVvGjatMwjORVd\nuhSNn99PfP31DpKT0zPQba/6AOflESMFqJmamFrNztUen4ZlJSJ5lKTYRH4avFilp6RlmKp47igy\n5wWnV29gFvCcwaAxZEhDpk7thqOjtVzBXMZoVMyfn8Wi6zi6Rdd+iU4WKgInbRxsLN7c/LZWrEpx\niUgeQynFL0OWcGTVIUx683peyhBvJR59gPwp4JmDB6/YLV16hOrVi1GunLtcyVzi5MkIunf/gdmz\n95CenpEBTAb6AcESnTuIAtIz0jLand18WlXpWE27n/O08JTF0Kj4Y8J69vywC1NVTz90X8w8KYiZ\nnAIWA2VjY5Oq/vjjQQIComjd2veOLjZCzpGebmTy5G288MLP6vLlWA193pBOwK/kshlDHmcnUC7p\nelKtQ8sOKPcyHlrRysVkuo1cJvZKLEuH/8T+n/eCRizQgfuMmsqrV6ubpjFHKYoXK+akZs3qpfXo\nUU2ubg5z9GgYr766jEOHruS2RVd+xYA++dT7gFaqbmnq92tIxbZVcCvphkUBm7c8r5IYfYOQI8Ec\n33CMg7/uU2nJaRpwBniOB9R75+WfLzf0Gdj8gaduRFuYSE5OZ+LEf/n8879VerpRA3YAQ9DnNxEe\nnVbAV0DDWxc+yVwfwsORlpRK+q39dDVuoJiCXuVz40Hfzw/5fCdgDiYj2u++66H5+dWUK59d5byd\ngQwZspwzZ66iacQpxUfAt+QBV5p8jgY0BroDTYDiQBEJS87/vgNhwAX0GUM3cJfW5PwsiAAuwCfA\nm4Cha9cqzJ7dy2yCIDxGsSIxjU8+2czkydsyO4L/AQxHGk2EQv4rlp9ogT7tY0UXF1v11VddNH//\nRnIVH5FNm84xbNhKgoJi0DRilWIsec+VRhBEEB8CO+BjYAxg8eyzlZgzpzelS7vK1XwAsbFJjB37\nB/Pm7c0c6rcc3ZnmqkRHEPJWt5uHJR3YAmwGml64EOW5YME+ZW9vrTVsWEq6OdyD9etP0bnzQrV1\n60VN04gAXjZVQyRKdAQh/2aIt2ILjNM0PlAKq+bNfViwwI+KFT3lypqIiEhgxIg1LF9+DPTB7D+h\nz20SLdERhPyfId6eLW4F1gINL1+O9Z4/f5+ysrLQmjQpncWvsDCyfPkxOndeoA4cCNHQp1vsC0zl\nHr30BUEyxIKDJTBa0/hEKawbNy6dLUa0+ZHQ0Dhef301a9eezMwK5wG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