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<!DOCTYPE html>
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta charset="utf-8">
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<meta name="generator" content="pandoc" />
<meta name="author" content="Anika Cartas" />
<title>GEOG606 - HW1</title>
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xaXpygKB5dWVlFrb5mQOydwB7i0J6ubFjh7npdh1XXdKUdEAmoj3W5Db4m4QE1LVCapO1XgH2D%2FkB08JF83SNM9ZhZf5I9%2B7Rz8J%2FI3IIfrMb5LHcjByu%2BUvGUKxQ%2FkcaLYdZ40f8JWOkw%2BA4iEBtlYSmddP1HFw%2FdKtShd1YQrncW61ZeqsIAcmYleEIEKAhx1ry8ND6aFh%2F8V9VHtiPdBPGObFcRVTzQgcz40RO7WEpW0ba3k2z3i6zBvlL9xO4ka%2F1EVnLTSa%2Buo%2BmkNzrwWDyPcz4lWOAxAp2%2BTrKORXoPGvm6d5aKpzt50u4573rAOfhP1CUXfpbjl36l4XWpysmXBCr6PbGqqsTnSRvReJFj4Xl9rvYfHFko%2FqPrb9YYEpV1CsKxTiSrXhisap%2F%2BC%2B6uu%2F8CZVz1iWlY7fGdnKxd2eM7WS2lcof2ANfjrBHRsoomvoE%2BuiF%2FpXpsCFnJYVZIVk7UsM85PYeLXYofPYf9H42YsMdtUq%2FMTd79Ho4bf2S7Gq9PVRxDC6lKG1VpVBV9cvFXGr6oVycSFZ%2FauXWquCnKooTpFvcfy0YiWVX%2BI%2FD8UOPXvp%2BE5%2Bom3JHt0IXP6MxS5U%2FAqovYd3l62%2BltAxkkq6q7T7LR3xT%2Bcz8gICtekEZU28Hq3d9JkEXhcfclufMmmZusgqh%2B5ww%2B7k3Vwcd9XbHh1JbiELt3Fu67QYbvmRs%2FCg5by%2Fr3TnRlZXhu7ijl5o6qlZ%2BrQrpkGp3PTVTZFKpwyqWabnH%2Fce5T6T%2Ba%2BNhiV5b7vOiQWG1XNvGNzngqewJWX%2BO7%2BPupIVbDas6n8HPju1ZMXmrvkcJ%2FhQ1Ya89RaqlV9P%2Bu0DacBdfrcx5rlPXMqW5%2B%2FVv8cfLHuP4t%2F6ZgDdhPFR8DGRmRoMk6R6Yc9MgU65TdN%2BKH32y1gyJruJn9x3%2BQ4%2B1zUvkZZYoyqq52HfJR1T3OUca8Ss9VrVhgoR1nngEaUXl%2BEwnEj%2B5Lg7fIsNx%2FsEWwXdT%2BI%2FD8UOO75zqXdKad2WS2XFS9L3XHH%2FH3m9r4nePnO%2F7Ys%2Fk6qErLYy0lJ6agZeeN%2FwwccYGT1QoEPwJqvCIveWiGhaw0jqw4olppFhqa8b%2FC%2BdTSMfJ8SlX%2Fp%2B918A8%2Bor5fxP%2FNTuvM3TtoeHe%2FThlVC9NKslFVNwNc6blq86mEHcyuYlSiOqOvmLPKAkLhPzbxCP6j62%2B9f0qwwjHOiiWI80kKVVktH0mD79lpNHuEPZ9yx6Q3iKpAKUiIS%2BdKK4ZmEpg0z1gZ%2FjhD12TDPydq2A6DMfTF%2FCCSlRZO0fLXPJsLM9o5%2FJ%2BS1UU8jHffrIaAVo2H93qXRX3g%2FV5fZeaqtAxwpeeqH3Trtr4z%2Boo5qyzjqus%2FuvixZ5JszVn3T9bAuDz2jM54qngC1XyGupJhFtiO%2BapVZZeFqvBG9bLT64cJ8zEW2juBk3sMRUbTMA9ggQX%2FxuNExVKRpvwrklXWFA5ZaUTl2d%2FRNOseP4pZYB18QoGHvnMyyNx5aXCbSf9x47s%2BV9Vv%2FQ2nBFacueFU%2BfxH298aemcj%2BAollosRz0QwI9ygM56qmBNbdKZpA5nYorobKAtV1yzEXc4xMjWQ2Xzu%2BE7FzK0BZnfYN3ezIOaa7cYL%2BL91Kw6%2BwooX2cJdqES1Yl3fwkumIJzZeGJX6gvVmzcdfOOV0JL6h1jjlZuVAa78e1Xd1scYiWP5mRhHlc9%2F9PFYhwhrwqz%2BfBOLKP8AaClJVcxhKRb%2FbHAgM5D5bBD67tR1UFX8XUSS8JcpqS8QN340V4kWuHQHNRnlvBhKfbH7Vr8H6fkKWPUwq6eGeuYgy1ZNqcPGOz6%2BR9SZ1V7of6CvfPi4Z0Y6zuSjamFa6bv2XhUpNzRDI2ruGXdyLNC1U%2FVs9fxHH4912DsxkOnMds9tPgd%2FPNEpvw99qvKrPL3r8FZaC3Vl26BE558ratV5h5brrxqrSjZWe2oL%2FbGSS62BPrSGWgP31eFR1ZYP7%2F23Jv5tWjqelgG%2BMe9VoU1C5X6i5fIfCh7GYRjtwIM65C%2FhnJc6S%2F9XnldPHdKgJoWtn6q6WQa0qq4yZuwG%2BY%2FxN2PGjBkzZsyYMWPGjBkzZsyYMWPGjBkzZsyYMWPGjBkzZsyYseVnpcgqGjNm7EYTNd1MEGK0kaUITo7BMiNUZj1D6RBgIRmWfxAO%2FFpHr1Vl6qOHh2WCxTJWwxWpzzycMW1rU6TJ5QMexTRpz5cqLpp7Tvw4WJlhBGp%2BBo7p79qA4m5Bmngs%2F5fXJWZFOsN86VmYRFb3agsKnuuswqLabGc2wig6q2t%2BjKX3TfZN4tc1P6Y0CV1XT7c%2Buvjor4tXpcgXo5daH5QVaUf8fJhRy0f8ShZltOdLW1lj1bW5cG1qRVxmL77HjjgmvE9R%2FzPNIBmL4pz2%2FS4zGXS56nQyJ70tVuA43%2FnhhXCDWLVTsHLHWSNKIav78VHwuOp%2FIIMipCx1YtdARq2zGvoUS986vnXcXu35aXmpqlsfXTwuQ3eviwCdg68rVx9cjSm%2F72K8qp0Ka69yLaEXBOWD7i5NogZ0pBfagNRNqJFxxsqEFfWPwLL%2B09uwHqe3jaYjJJ1eWCSe0SKcjaeJvbvxVmCVVIo0mRsZbeHSfvd3JVC1cDG3mnyFKyZVeNRZBYmKOKvFKsJysjg6o%2BzmrAAX9OBrN1HQg9KAVKq66wPik8r6uPCT1iQBH4jbAtCO9c7Gmb8KgVM%2BfqdTH%2Fyu9bWEasxz4a06Nd5xLnewJl9aLgT0WD2Vqon8Ot6IYncG62CUwRrSIF%2FgCGtkgnsnosow2zrYZMcO3HPU%2FiPwqxhxq40cvmkhMjI00%2FaV%2FG5xiVySOYQtkapLVRdU5HNTVb3sG3VWD28VlUA7vFWus3rbPl76oT28l06y2%2FaVj6ru%2BnC8vD4Cb%2FWFUMG%2FT4XH2hcKkKBASfsT6vpA4Buj1ydHk5BqNakbb68qVa4%2BFe7kXqsqkWWbd4sS5D7Nq8qnh9fhq6ASUbCGlDUMzYSvyueGPCTnI541tkrS2bvxqGrS9jZl7inw218N%2Fe75%2B2RdsdMygrCWQjrAh6pe8igqsjo4SsrB0VkV1VPprIau8tLvS92Xk%2BgMXVU0X8ZyaqQIe9z14TWS14fjYceRL%2B1585dWnQL%2FP5PsR790%2F%2BRHvwQRrA%2FU9YliQHhQVZ%2FkNwJPM6d8qumNqgkP%2F0mw8lE1zh7dUfyzR3fECSoZKDuzd6IZZrcwKtdQ8FVVjzwQWaTGlIj%2F8bZ2hrK8%2FmKhznTC9jV7MiHrLH2pir3s0qaWj5Q6KQe3zmoyT2uZzqoVE5InEAzWijBJLnFcKMQlb2pRH8sWpuLEltWH42E86rbr1I2LlGV43EFndIv7J6NbZDvXuNsHHvmrqvpgcshjZLvsG56mlmoIoIpQuUZV3SSUF1VlSr1JNtlU%2FLPJJlp9qqruehS%2F3vUolXr3DHZmdah6zyC%2Fm3sGfdu%2F353R5d2ebHiTzlX1GloX7%2Bisiscu11nlsp9izM7nFX8lu4aOEJeoD253wLdAkNfHqb%2B4Uzne1nzFunMl2j7LFl%2F1byOn%2FJ452FykRVV%2B%2FwUv3dqB93QSKHKdW71RtRSqWnUDmQP7T287sJ%2FL6B3bIU1yVbtd284wVNPqYwVwRMWR1T8ALqz12mMbzupQde2xzeesGEaAsoCZ%2B7I7D5y8HqqKTF%2B5qaqrs4r5U97TYn24Ui%2BMSl%2FL5w4rGd%2FUaKUyJBf1YbWjaZALrVXVx6m%2FuFM5Pr%2BN0IR9NxOqNnLKB6m1enX53u354H7lm700rf1vxKgKMUqcrYAU0Qq1jF6xzJjjwH6jGB6jaR4AQ964gTXA%2FzUUPFDv2r6dcu8vxEe%2BHv9Z62vgq7WUlzWibUsKgIsTMuWnqp7OqjUswt%2FeP%2FExJx8CD9Nqw5NRlPrAcBdU67668PbGCiq8837RST9I1ded8qspOrT6urVcqfn5%2B%2Bj4So%2BqOjPn0bQXVUcVbylY8MQuzMOLvLHqKgJ%2Faotc974YP33f44mOxUd%2BQXtZI8ZXERIvM6rq6ay2vyHKvOOP%2BD3f70P2ZwTFdQkq1P71dV%2F18N6uK6tRZeuDNcJ3rzr4ys9V6Ybqy0upij9VnFeLGzFqXMfGUzUvHTyrAXo3UF7W8PeqPBMsU6QUvxVqiFVVOPzcEKrq6Kx2LIoyh1%2FG74dfFt%2F7adrru4qu7qseXp%2BqpdYHE1IDGTUeXnak9k5sPkfXuV36Z4X%2B9Xf2vHMO%2BW4LelR1Tz2KPy8Pk9Pb%2FXrGsmM%2B2v4Gzp8YYrYjN9a7Y2eS5mu%2F%2Ft6bVJ1VlwJqkPepKi1UPRVd3fro43V1fa%2BjPt2o2k7QrQ3Z%2BA4dnVsNXeKUBzolL1%2BbDK7rU%2Fd6XTZELtRtroeDrMTsRDdVxowZM2bMmDFjxowZM2bMmDFjxowZM2bMmDFjxowZM2bMmDFjxowZM2bMmDFjBeb6o%2By0Pt5KEzRo61BQha4rq6dBmzsnnUdfrlhLodptTKuFmDVJLn0sd0ZGdafebSRTli2lRY0tO8OVCkMzSS0VYAfPQuvfUp3VeDG%2BiNKTVLFK3ZU7aM6KnDijC0TqWfiqSo2CGxdvO7TnwP7e2RBZwpo1jB9Nss3n5Eu3rMmwTX%2BdtTuaqr4lULqUjgBkOUvuaJT4gG7ntEQYW3qvxWdWaOgsrn8SpSdDAxm6CnAhXk3WKLNXSzKqWKU%2BVVGCxCXi9rBegxCbcDgJy73WXiOQzpbYhBUUKy5Al9TxZ%2BpD6nolyZQaBC1QcgsKloK4S79Y%2F4gKvIWCpm7TwRa3Pr271z2L1ZTe0ajwxWVTFnZSl9cVo5JMl3qq8r3WNSU5VVFTIKKhAlyMV5HVq9nKS9X2J9xomXApF8O0Ckq3lHKYaKHfDZ7unU0wykYMos4oZh1fpFI18QcvyS8vpwJH7%2BQrGPOqi%2FX%2Bo7EOtngJHDEi6L%2F%2Bs6hlU%2FD6CzWFkAqt1jpU9fZmf77wPSuKNxTJURXJp6cCXIyXk7WyVEWioaCnc%2FzgvKzvcsbf3lmuczj6G5UcJoZr7ez5%2B7b%2FraojcFPVijWdBE3gs1SqYquqRNyKW05noTVR0lxzxxrtADVQQkBb8QA4yaiRVjGqFKqipK%2BsJvamNFdzeR5bmse%2BCp930lWAvfEyslaWqrbu7DcFwcI3lIBq78TU0NTQ3olkXn5ZZrftQ6mrX4LAaDthLszH6iaGTa4KaZ0gHqcWFMJVlqq6Gha6AapXcHpzA2A%2B9y%2FWIqTUJ0%2FySZ324drbsueLHBt5BYmKm4AEFqw6G89CemT1w%2FuTtfJUjRf0n3HCo%2B%2BdPdC5iq1iBzqFgrAi%2FL26%2BW2rL74B0S0vUNwd91fBRFHzx7TNkOL%2FNcnu%2Fh83n6q6Ghb6qhf6AW3lAmD0F0j9pR0lQZ3a81a10iHJSLzUm9e%2FpRIXtfdACCJRo7YAeuPFHN6LfOvfklTWB7%2F%2BLe%2BzKk9V%2FV66%2B9KmNvy6qa37EiHI7otDd4QCa9F8aKImBUhkNY5MRVngeRKRjifZxqM3n6olvSrTPEMnQK1sAIyEG5liIXcATLtXVxooBCX40ttDEN%2FmjzQUr4MXg4Hm%2B6O5M1y7%2BhSTD4SzpPvQeOGt9Pq3vM8qjaq9s6e3UUa80qgahTzx6W2nt4UfjhK6g9DfgxxnP9%2BJzB7D%2B6ikuB8SXrEPKUSKfYZ731WOqtaYHXyNUQitm8%2FVPUMnQK18AIwZdXcATLvXglGwRa89kT%2F%2BeCvWeKUNIr7b%2Fpdn%2Fd3kUxHVC%2B9P1NKoauvk14gNLtTBZnFqW%2F3om1ngo8BHzaT9Q8Ps4eeEk20%2BB3vo%2FD0prRSwxlqvJdmdv6dQCbuMB%2FoqR9Xm3F3rB8CVyAAvlwC4OANMFwHUzQB3gbokPzh%2F%2FPFNuSlcxK%2BrEeSjELUYLyOqN1WHZmQ3Jza0EBtcEGgx7wp2AkmSGGaURUlymJjHPZB%2FvTH4d%2FbcXPJXS9YenlZaBcRIEBNL%2FJxn%2FlqJg82hnSQGbaTkeLeLydIgJQWcyw1%2F3Rlgan3UVHVUHIGB9lFKWq%2FoKkg%2BKlHdeGtMRlS%2FEMAf7955hpNV1RTFfwKhLYYpkcO0DmK%2BrmlBqNnzfHFgwb9GrQUbJ8GfH9QrCZjh5zReUbZ5C7R4i85IKZIe7iPEdF6tlT9AXV4ZYEHVUupTiqpxGahqZ55COsVyPGjMhsoZUhVuEYUC1cp61BaU31DOpsspEafyWxUrlW4L6tJN2VgB%2Fkghh6a0uX8w5o3nSQ%2F3gYmUcgacyw2v73NLz6HVpxRV41Iy8MtUCVj9ZwDGtNqzRf0TY8aMGTNmzJgxY8aMGTNmzJgxY8aMGTNmzJgxY8aMGTNmzJgxY8ZujsFqucCyqMe0eRbGjEmI2nhR%2FHG6FDdmTYPuyzRFFsxGn7Euw%2FqXMzQ8LucGaZThkjub4WXQkmmasrIxYyU5%2Bbrm7ksJ6coR7obNoDIUgX%2FNSo1DlOxuxtV32QT8D%2FgMRcKk%2BWOQRvmKgrSGoRNgjuA1djarJcu%2FXfgzuKpUq%2Fx57MRgjX6dmqhhorKyW1sW20ofqz5LDw%2F327dsPDLvLTS%2FWYrnS%2BJoZ1GwrvZM08R4nFand95Qtux%2B0ckDH00N9c6mvpCPkbgwbCAzmsaF1mHFiklUiBnIgGh3SqwTbbyorOjBqK2ZFHhJTaTVuaW4fJ2rVTd4y4ZTvbN%2BMp0C35UdP4prB1cxaw%2Bl%2FL0TQzNd2eM7Wa2VblPeAZe60pFBF%2B0fZbpYyll6%2BDgsJ4J4iTwNEms3SxV4kZ2D3sJd1vkks6V4viSOdhYF67RnmFQjd%2FuTO2%2FwH8n98sJACwjIeqFfVtDa923hbnyiHUjWte%2FLaB3l2FpnLV5UQW6rry2HDCmD4JavQB40nVsq1Dl4S%2BPFxovn1sGysmoFPsUaISwHAaxWdMs6Zfmw1A%2BXwnESbjglb2gUssrpU4QoMuhcUYfLXulhaWfp4fEa7bhGl7gzgLN2s1RVRBlWuGySUcjqhaesV6Vj3e0ZJZJV4OWqZY5xqTSf0p3Cui%2FtvlW%2BEA2lJIZf5p9RFSHC5LQ%2BvLX4EcnVdNd86SDXLMibAkc8FnTfQ%2FelwVvUeFRYbWZ87AO3PKnET9qhr01U2QJ8KHc6zNzjX1jaFQik0%2F5qN3ewtLN08bzlEyC7CkFY382mqnDZJIkaXnhaq1Kx7vakkdXB62qseJTuFObWYPAzFD0R4l6xD%2FEcf2xssSvLl2W7H1HiG9k4HGc4VguHkSv%2BOU3L7wHrL6OqwAeejwCWb%2BgxNHNunWIUmwyhHut0WNncjRfbc4r9yfzXdkXAbCtAXIySZbgcLOUst2PRruI8pyiGwmn1SFZZqnKXpVHDC08VN6Nh3e1JqZE%2BUSVk1SNqVdWGs3w7DEiv2FtiyMLB7rnOrMcjysrG4aEZHKvzAixX6XM3TlQZMQR%2B3dTpbRAmx7uyeycgXK2W45%2B%2BtwuSYu1CS0oSvm845SW3IQ%2BYhYAklapRl5uoz2o6qYcvplJYKSRTeaoW3rN%2FDOSNp%2BsQUrCFRFVnX0T7g%2Bi7psZKz1zR%2FeoStapq306uqNaWU1U7frc%2FtvdPibxomHNz%2FRdk4fXGo32TDjbOKFQNPBbN1V%2BeNMnv3BJiNfj11BbWIKNeTguq9vhOjCU4UWVqRrw3dG%2FnpO5NedvTqepgKWedW6eHL6bS0MzH99x8qrrvwT8G8sbTqUrB5uV13Eenuv3jTO%2FlnZWOF94vfz2jQ1TcoGhkymlmSLrU%2BGPHnoH55tniRzT2jCy87vjz4fWOsmCSRNWew3sneP2jykdfcC81%2BOKJQG0gK9ckalbUSKi8ijPVYQ8ihZAqxakcLOUsoftIv0rSta8PyLiFVF5ReaqibyZJw4kXnkpVGlZ3Vx%2Bn%2FcNM52VNuPh%2BA4%2Fx1zN0oqK9kxCPHLK7QanjNvTO2sFyzN13yaTKNpyNstW%2F7b8g0PKdXDBIwEwlTKoaWDXqkmOoocbnk0CgSEjDgwRai7p8Tlbcyys3V02rwx57%2FK2mqB4XY2ln6eKF4Cq8zuqkyLhVmqrcN2nDiReeGqvQsXqKiPpk9SAqzAw%2FFa9ndOTHWPWR7Tju9cydT6mwWM0I7rA67%2FRdMvzJjV3ZcF6wuCsr8sc%2BwfgTuEGU6NtW2ptF7Xvi5uELkwK0REIuyCaoHi%2FF0s7Sw%2BM1Np%2BDqUHjcnhZI9yVFvd54Sn0o2NLURR0yKrzsqbgfq0AzvC2%2F63q9YzHxSEg7Jk7tkN9HsqD7p0YyHRme%2BY2n4MkTqf8HFZzagv%2BuQF3dXCYWil6xYH9fPotlHcP7Gcrbh7eTVZqxi8fZCtVj72wlLMEyn7Nr8Tb6sUdsmmNl%2FM6X2l4mqMLd7XqaHGfg3I%2Bqemngy3NeKvrvKwput%2Fdt9p50MZSBD0hIOyW08gdBsOsOgX4DopKL2zMFMpJa4fUDsNWQLlu5d0VNxfvNDc14%2Bc4q1r12AtL0UrmKP6cVXiaevGNMXedKV7qoFyf1KOeBvZ6yKrzsqaoY4IGqKkyZszYjeh2qiuHNmbMmDFjxowZM2bMmDFjxowZM2bMmDFjxowZM2bMmDFjxowZM2bMmLEym65O7%2FcNb59Dlp1cnvWvuA8FoEYxnda02A2oVVr3SlbMmlyuNM3p9MYZTaf3%2B4YXZ3EZMXp7JrOdWZ36VAp%2FoyzwEUhYfkStC3XBXMGdZ%2FT3fXj%2BPr0rWbHAAuhkTt7Mrobvb5ETbA24WrRYK0al01sani9qw%2F8rU34yL2pW7vK5OPNKG7tyXq3b7%2Bges9SJXQMZSn1Kxe%2BdoOkq2488o%2B0yGtSwJqNK3aPrpWoUBU%2B19k1A4tGvBCMw4BPgpU%2FfW4n6U4nK97ewh4ZY00JeBg11evllhR6QXKfXwbudXYXvnf1kE67f%2FGQTLrClly%2BEoNR4WEUKomYndtHrT7tftKaTHYtIiiR76CUQO5VrGOd0jzfegd9tvIPFkXzy%2BgidZHthoQbeirVeo9QfhcebFqLajkWnhjUcyoum0UJyXVe3%2Bqw9qF%2B5mtHDU0G8E7uGZij4MAggIB6F2W8eVdc1xxdxfwssH%2BsfX1zXbP8CdXqdy6p1eh28%2B5Dju7K49g7Xb%2BKaPRxZaeX3zn58D6eICg8SMCusPVaM1fK19pTyhQCoSpfYqguz3S%2ByBpvejQ%2B91HpN1tBc9xh6QxTlTMP%2FscNbVfUROhd8awUqXjgitpBcV9maXA0uqO9YVGpYgTULzlNrvUYZi3VcHZQx54MgrZ6XcSeO9m2%2FEsSjL%2FEHUb%2BdlFXYlaMqq0HJvUROWteuP1%2BoGlsUI4wNy400%2Fjq9Dl4canzCFRY1nUwQykf5rYEMEnx8AKmtwsO4wkJXezZbdVFGqb%2B4A7UuMYq0JHFGyA7tObTHAodJSGcpXPeY1Q7N4J41sOofPkPDfyPHw3X2WAHcWqHpJBGfIyo8yAYZHgPfkKtzUsl2uTFUagQ%2BSri6bRgRPiqnq%2BPGI4miKK7pCsnpW0amaMRz16n1NfUc1SpqUcq8liaahugm1%2F0mUOqI47vniptMrtNbGt5RlOGqMSr81BCrhyCvmjukGp%2B0FY9YfdNJlc6wwFsFUYQ%2F3nEQqFG9Wg1I6B7z%2B%2BT33ZmV1Qfx1p5WtopFc0KSBLxD1Fo5vulKVEu2ywurogaX23R1gZ2KGXChq8u3uuoLL6lP7%2ByxHbQsLmuhEFVkiXODT0hNZx0RND0tKe8r2L%2Fo%2FZNoMsF%2FuU6vg3f3L3J8V9ZRbj23DkdJVfkBO5OYJ6oSjweEaiys1Bl28O5m8cez%2Fs8G7Zlwv2WPrKj6JBP14LrHVgxHVBxZ8XNCWh%2FET4cxcOdqOgT8mJuocvyxHY4ibqlUVVNDZ5ycGnILx3Zlp4akQezbmLEYmcKYRugSQyvVliOLW0qWuPJUZf0ndjkt1DMHCUTubajTu9R1%2FXV6Hbz7kOMTtpg%2Fzt0wu5UglG%2FL%2F%2FcJotLq4w5o1XgR8Kt1iVn10AwmkxC37qcdi7tflDU01z1mtdDAMDeH%2F2vXnFXVB%2FAwh7ddEEQ61PjmguSHHM9qsWR30C8XHiue2lCooUdVVvPkU47nPPmUXDKoHXWmu2F0tGMa1V4IelncUrLEhW1D1CvU0je0Arz%2BvCOL4wYsfPqBOr3FaRaZTq%2BDd%2Fe6KnwUXnPg3G3lfJRYPu6WktCqj1793TGBXJcYI4HB0825lAkmmKSPJad7LDLAuFWIqj6ID92OLghjMAGPNYF62COqCm%2FrZ4X2TuCj108rqalRyuyTrRCS7yCCrhCVA6IG8xHFLM7My5fFLSVLXPm00u5bU19g%2FXmKqyub%2BmL3rblfOYrrNJ3e0vAio1Wp8iuH586OYXCSfbJJrbjo6B5b800sQqqPLt5OdBHxnODHd6oFSJcE2wRqlOa8rIUH%2FKxFiQy675z6EoWeTNLNEt%2BADDBEWCipa4%2Fatae2uJQLhU5vF1Wn93uGF2dxdXoKUuged2vVp1J4JxDWdRpa4Fua8x7Z3jMnn6V63Xl5srjXkyWuPFWFjmhOW7mm6K71dHq%2Ff3gx4yBjl2P9q%2FVdRgvdr9VCqCJdAWFbSha3mKz6RNW9W2PGjBkzZsyYMWPGjBkzZsyYMWPGjBkzZsyYMWPGjBkzZsyYMWPGjBkzVgaDZXN7TCsYM1ZICw1dWVC6QQmPPvtzn72m%2F6DGlfrg%2FDNqWUZc2dpzuOL3PW0xqhwm1PqMVtkZlcJBHsm8P2tcK13GNnkOD%2B%2FvvpO%2BHbsxisPqZ3TdT0lXFzf2Ye9sfDEIq%2BytySDoqfXOxj4kXWUMnTfI2tidv1evSQi8FGU%2F3qbRAUwjleD%2FPh18x%2F%2B98wrtj9KtsQi0Dl3a0gpwsU01Ta0CVY1kSfqyoDYx7f3UoPtlHse8f1m9R%2FDw%2Fu67aO1PoG6H1DPn1a1SOl4QFddrXydZdXVxI%2Bzh53D1IwoQ4kq%2Fh5%2BLqB0y1nilmfHrbD7X%2F09qqq4F2cz1D9hjWZ2y6aaDrJ0hldqhK%2FBzWi%2F87eze1wtEkX3P4TKeoAZBHINZDW2ZlK4AiHASrmMPI8Y8J3i7z1NLeJafYOWmKldbLGV8kY824rdC%2F0gp47aka2qVyNlwmbtEvlUoMnF6eIeoOenV0skqdHFhmS8s6hEKDBIdWlu%2Frwkwzz797NOop9acFxXzf4yBhXhOKWbvxIP7w0Bx1aiHzdH%2BRlXVnb%2BXdxwYKLcXuGE7y4scE%2FAPPtJ8VIYXY3wC1HcHMqDG9xK1ZWlUXSrmIV9clVcFBBkPR3sKjw2n6F2BrF7Q2wWdBd2F38laNczU7bh0fJGPNs5vWUjIzsjr339h6b0Ov6zb%2Fv5PQL897auEuMQLbXleYWvkvxO6uPFF%2FC6%2BqNLFdfSL7nrgrgccXSPZpbmgaFd2%2FCjr7jrULJUd4zYeyfVBk%2BvfiUrnwo3vRmGcFuLeXAsI4oJ3qfhX1%2FSmZXg%2BdqE85%2Bs%2FfP2HttQmaV8WvnGGeusMz%2FCUyV0LZbJSX8Q3CKkRfCYgYxoqj2sV1oA0ZtTxyCxKIKtVl%2FjcGV%2FEaJP4XDEWQaSE7u7oGvmVv%2Fm1pfe6dVy3%2FS2JTFzPnF7n6n4S1FC5aHLDySp0cWEwr4NmVOriOg%2FfTVX5xTsWcdQ%2BtWV0i3W5TdnPWcPWQRE%2BhhiOgOGr%2FikuFCz5oDvJpu9DAtpiHXfbakUHKfjUV7DivsUfzw2FxkbTq0D%2BczSNomUUojZe5LVROW9JfTTIeDz7k9Uu1UI%2FopZC1cLfq%2BsjiJokkRXlSHjsBi54OSyVzGEhrlIIVOhwZxRkNbr%2FiaX3%2BnhCt%2F1lio6P%2FAKyLkw3A0ClKu%2BeChVBc2R1dHQDjwUeU%2BviVlVh4IsHUlV8lo9JCXgYR7YH34MkVK78w%2Bv98a2frJvCG%2BudFSNfnPlJRvdNwoz2X1j1QGb1b%2FfZwlGwSUTN%2Bn9Jsr5JP3z3JY6%2F96Uk23Icf%2BqPFwmlnrkZe5yfifTMRdTbTsS43Bt33pXzsnEYHXHpP9UD7eniRJ3YvX2tfQdvlS9g06OqQ1SxaQmdrPE8Uf1Se1x5WcfpxweK7xRGwZryURVKa2j7yvuc7a9eP1VzOtlFh%2F18HV3c1vxWA%2FIAFSlafEjdanNX9uHnAguRfOlIJ3981O5vkYL78j1kfIPfvGoggyPi%2BVTn%2Fw7aJZ9P4cgJVwj64SGgTiMex3fMMVtpf7xIKL3wU1a9%2Bdzmc6z6hZ%2FaWz3UyYiKgakY4zefs%2BeVMf8HyLO%2Bhf9UXUEgR9Tmj5vssv0zwJWlqkNUGNe7%2BWxSvd2VQ1Y5Uf0cXFYj3Jug8E4H3tOPavzLhzG1L%2B5zjmwAolKVz8kLJV5zMZOujm5V1WrGD6So%2BCy9eH3%2FhWaXtH9X9nxKdUvYGHf%2Bnq1wlO390OdTvbNtLPA8nII3Fg881gaP3%2F8KiIcEyLuv%2FxCdhdVbB8NSPCaUgKJw%2FQf3P7gf7wbJJ9vvLLDQmQWJ745czTsO7O%2FMBhbKNapiSCTkM8cjuBFRkzQDXOy44hn4X4HvpwcZ1z7IL6d5d%2BNPug2nckQNOakf7wSXF1lVRF3q4JgJzonD%2BqSiQHPK5ehd2cG%2FKydVYUx92%2FsMaIOacsxVsRXd3%2BcnN7o6urpzVXxrGylI%2BoBAp%2FThiPFo306%2BcR2eI3%2Fom8%2B1wTiM73mty63gWLLHz8WxI%2Fa2E3f92Qq0MSGV7Z2JxhdSJzfi52bIdePXkxu7sjCK%2Bb6%2F3XAWpCFXiLrDllcrTm3ZcLZco6qgmi2HaW9EJM8Ao%2BPyZ%2FrZoMuFJZ0l77zDkPhtyu1WgF2UzLGcmXLhdyqyylrefb%2F5eZsrE0y7Ck6%2B5G%2FndalqBdp9znh0h%2FSVk6KDKWxTn%2B90dXH1qNp4sfvS6W2gTgd5S8xVqgWgT25EYoNoZn3ra7w%2BzjYa3g%2BddcBmVO8l%2FpD4w8B7h%2FYUpiA88ZCuuAeS%2BtsObWoDvKRGzR9jwm1VvhvDr6vsCKH5Y9%2FyO7B3FYrtOJ6CQGRHuUZVQbX8Jo%2BpgiDJ5xrq0cs9bvBx1TVdaVC8iAj5fad6Duo6uWvivLaR3S28xMqTuwnOmmwqJ1Wbj3rjYXirV4W11A5G1mRaurh6VO2%2BBE5Sk3Mrkogjq%2Fn4HiB3A87AemdpOrewTUIHhMBx%2BL%2BedI36TdAN%2FGwjkKhe1idHmd%2BjjCpe2nTbe42c2NU9p3JF%2FbnqUpO6bp0OUfkkYWRKbMQwMiWfrlTail6KhNTdATzTfmenP9ZP82YqVdde88Y%2F%2FJw6rL1OooqelK4rm2%2B2W%2BBQvlXSc5J851GTu1InXedW8xotTClIDZ1Lv%2BSQng1tWcvVbrVcsb80fVmp61bTRL0LzmjJzfhS8Km66jtnogXVLan7JxCFM2HXoeZNqAxErWijfQcftDFjxowZM2bMmDFjxowZM2bMmDFjxowZM2bMmDFjxowZM2bMmDFjxoz9%2F2u4KsiaNO1gTOYkgWLZCarynNZV6uyy6zRcFwRkdJzX1iee%2F64%2BhRBIyIR81S6W3CtZKy%2BHR53neZrO8zLFT0NXdhn%2BH9PyuTN2Gx0sqydraWHlz8rYyAyt9KVXs7%2BJjBQLTzbfr0X0PUh2BQokTLBsuXhJvoED6LqNFxsvhph9BYoOXl3o2vjRBNN4jJlcMxzU6Azmya41r%2BcgsAakBv9R0VQdJkfnOUHUeV6O%2BLav%2Bv9p5JV9T9zzWzXescZ3caU0LHMMSkrX1kkubXlF1F7rEyWIzRaWJ1YI8UJ%2BvWSB16%2BJzg594yoW%2Fmr3rSqHCX6ZyHUDwY9U5a5rhvWhGVxmhkvQrMwqtq5ZXZvA853ZX3YnSRLZ1suo5rrhFOt%2F9umRqTbSWAaaCJdv%2F%2Bcnn2omdQbN7Mmnbv9nGAX66FQFXZ1v7QXyhNqM%2FsY5lA6rqfNcKr53VkjTlr98EMwJxT6M%2FjryNUUQRvgnSgQNv4nLHP3JnWDutsQDqSHr8kGmr5jYw%2BquIMkKxNnnZX7Ax187qszwETXn17HPiqka%2B4zguOmVi21fJv5P97%2FGGatWadrF3es8FX0iq%2BmdjbrwsGhXOdZYsTb20EsYH1DGow1HhS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2Fy8vL6%2Bvqfn5%2Ft7e339%2Ff29vbo6Ojz8%2FP6%2Bvr19fX19fWmpqbLy8v6%2Bvr4%2BPjT09Pr6%2Bv6%2Bvrr6%2Buqqqrz8%2FPt7e2ioqLPz8%2Fa2trW1taioqLr6%2Bvi4uL5%2BflVVVXNzc3%2F%2F%2F%2FW1tbj4%2BPh4eHq6ur8%2FPz%2F%2F%2F%2F29vb7%2B%2Fvz8%2FP09PTMzMz%2F%2F%2F%2F%2F%2F%2F%2F5%2Bfn19fX%2F%2F%2F%2Fy8vL9%2Ff0AAADZ2dn8%2FPz7%2B%2Fv8%2FPzp6em%2Fv7%2F7%2B%2Fvq6urp6en%2B%2Fv7%2F%2F%2F%2F4ck%2FmAAAA8nRSTlMAGgDUzwIP8SMQ759fCgUvqfDGFeIYA78fbxNTt98%2FhsV%2FBhdD4Q1rRI%2Bvwo3ATxJTD18IoKWasozTETbQ4D40IX5hC6dAMR7RXydvEsRuotKLkZCATYahkzOxQlFqmbZwJiUhFWy1wyJYcXI7gB2XIEFbgjxgiWFtfTSFMy8wSYgEqFBDTSE2KCpnSyZZUaZHRFAsDuWBYJJ7AVZQpC0Z6njBKWjdN4dlMV30iN8bV7%2BzJJeHMRiDYsR6U9yVYxdP2c1dj8CKFZZVFjtaaTxOI9cMKQk4NnBW4PKUOmiNI%2FkwWoQYUdQOSk6GvkUURFSM3n71h14AAB4tSURBVHhe7J2HfyPHmaa%2FYicCDTQCQRAkQWgABpMcDSkOw3CGM5o8Gk2QRjlZOVjBsizbcs5pndb22r7d23ybc7zbdDnnnHPO%2Bd6%2F4FjdIGu6vmp280CtbF%2B%2Fkkn%2Fnip%2BaPSDDqA%2BFOm7J3ncIoDi0NAQkY3d2IaJSws2NNZZnCouduhAsrgf7o4BYy59O4fvn3ROJQKoREkBGKqYytAJCCEQWh220I81TPFIozLaNiCMH4PJr47WIooL1C1isUUsFSwpkMqPAMARDUIFjLcYpj5tGbmqw%2BP6bhz49jZwbZ9S9k8Kd20QQLDdzFbdIz%2FJJ0OFyJFaI6mOcZ6HGOzAGxdi0tN8JL063CmJwi9FviX34m4FUrlxl0PgaBgIbrXJJfVp08yTrbq2tt99bINtCj9p%2F2TiZMMigCzYGa0WxwBgrEjxCBUici56obyLjsF%2B%2Fez8KGLwUdxVJuq9HZcpljX16lgjlaeg8hTpmUVNqubcUjzNKnBbGIBbJS6pT8nMo5ilAms3kxsAbElvsP0DqP2Ttt9KsEYIoBELpWxWDyHMocSDdUiCYMYDvJmAl5sUE%2BcDgiaiLMd6FrTJUmskFaTyEah8JPZsiru8WGL8ouLpx2rfqshkVQix%2Bz%2FOoyRIte64GalXsb5%2FJFX7J4UfxsVI3EUcMyrVrbqAtbVVB1x96q39f4Yo0goYpBJ6EmhWa31nx3WrUmskFaTyJah8iVSofNrqY2umHOeNsyIQ457ksUTnlP0dq4NfVyuLrpTKLlHy0sUp1UASq%2F2Txr2ASAiiwJvNYrVzBLjUbJ4BjlS0qbdE%2F%2FStUgAExAMyWG2jI2EFDd3qujNsWcPOesxquY6d1OOSmiMbId4YCTT%2BBEq0xDjRKACM8mO1HwF2mYm%2BDnRdrRRht5hUmRPHAeD4CdL3jwBEBQ3OheC84VE%2FXi2L1Q9fB14kOgFc%2F%2BzeVgmgJKuVTnzsPSh2iFoncY82uVrw14aH1%2FxCNVbszO4heYa0vDPk30uc%2F%2BOxv2LgBAAGdjSM8R548OvqoxHiUl0bYWyX7R8h1P5J22%2BHUIlAxXSl5FYDeZS67hHgTO%2F%2F2aoPbWy12r9JqFVifFsqsLYGbGtlJyq%2BV2TuBRrA3WTgs%2FAY70S30519XFebg19X3520%2BbakctBO2j%2BZ%2BNt23qsdwduyWCWnjjB1h%2FZvdWkqhPxKVhi3gMamh2Ilhn304xeIaTVJpVlsTp9FLRt3F9DPgvtmX1czbf4FSeXghcT9k4WXLYxtg8oYrLJRKZNTC7XWa7R%2Fq1RDCDfq7RltpDwixPTcjIdii1R87MYnptUktdKYn6Pz89ZSJj6l6k8NcA%2Bc9bqavvmF6jbdHqwW0vYP5%2Fq9dLGo7qVTrY5OXKnXr0yM7m3V%2BFzIAs4S0crEckCmBDOedY1UCmI3%2BtN0LjUucan0yDOycjD8PZk4VJDCB3%2B%2FqmmtSqlc68g2dUYKlLJ%2FUrgzMl73Gu3xESfFqorzwO0OsXiI4kmrCe%2FSRoQ4T3slOK2ea0qa001Tgci0E2TiQkVk5tHooO9XnYJDWcP3TzovT4xOL5dJixDqXz29gHhGRZTRIRogzT2l5mk6b8F%2BG5KhtyB5%2Fj%2B2mie3mie3mlvNk1vNk1vNk1vNk1vNrZbouy65VR8%2BsST3UJbGpopjJYZdoNsFXGOptDrpfAn9LGWvU5xaLJFvmr9Ycu3kzstYuiHrUuaUFsfGFg%2FyQOFa%2BHaCIAeHMNTnPgA%2FwSrnrg3UPPD%2B1R8AHnwQ%2BIEUq7xONv4w%2Brk7ex2vBhRhng9ks%2BoyGAXU6XYrROTzXnTg4PrRW3EAIQQI8tueVn3I%2BGarnNuoz4%2BOztdZ%2F%2Bpl4KWXgMspVnmdbHwWIgxm91XHA7JxiJ1A64jHvJg0WS0CmBqzWf3NLSG2NmGTnopCOm8l8RZKpNsDSbG0l1UfUXyjVcZLqE8EoGCirj1cC%2F20Eq3yOgjrML6wwHgLFoWxUGHzicx1iB4CQJy7Iee7S4biAw4QUM9k1XhodzE%2B1yRqzo2zk3YXkPZaZODoEJl48avVU5pVQQjFJltVUgHfZJX9N%2FDDuJ3Cerdr%2FasvA5icBPByolVeB6yO5B2go%2FOXdzpJLuAVVseuGOv0%2F2M%2Bce6EnO0uIRO3elPbciars9UyhSlXZ%2FkJvoVSCS3OaeNRCTi%2F59j7UGFc0J7XVSWVad2hpv5VEO9fPQXgwx8GcMr4CRybTHWg6ijungJOuRo%2Fhp%2BgMD%2BBw4Y6Xb3OrOSG1BTPdKxCJZNVfJn6%2BbKhTnMcGG9yTv%2B5Zrb6CQT4LLtQEAkBIRKtFgR2IgpZrDa8aEzvX60AQBAAQIVi6bdzEa9jA7aso3FnGph2NA58ncJ8HTBsz5%2FQ69QkD1OM9TmNju7yYsqxmtFqI46fo36eg8HSzwM%2Fb7L3fR6RkYPwfTdzQVBtOklWuT1ulfevCiH0%2FtV7sZt7zd1ovM5F4KKqozgBpHMA6BB1AIDNb0yuGOvIVPAk8YT1BztW3fq5rXMb9fZjcexEEwEHpjPw%2BLjxDPwH2xHgvIIPMy5EBqtCiBSr6f2rswAaQjQAzCbsFVYn2NwMVB3FCWD1AeC9RO8FADb%2FmZ6az7fzcf15%2BWr7BzhWnYnV5irr1gPtWCX9swSbQHOrXN5qck61ByTgfPY9DzUC%2Fs6GICfsbVXCFKtp%2FatL%2FY9pHQKAJUOZyUnwOnNzYR3GhWAcKmDzHbU9GfpsvfcpPsh11ZhNZXVTG5qbt6hJ8l%2FOT%2FeITPyjX6l9kG8mqe0cwGp6%2F%2BrdAHCd6Lr%2BewKopNbh3Gx1kDoET%2FHBrqvGzCmrc6QlGFFA480k3jxdZpsJEoCgeE8lhfdQQ2JocjKj1fT%2B1RoAvJ%2Fo%2FQBQS7fK63CeZjW9TsOrM14dHW%2Br%2Ban6vF3qZbJKyurBpGnQQpicNDY0E4aAXnQC73%2BNh3XZsv5V1ow6RzQnv4%2FyMjJZ6nDO64jMdaZHJxgvUHnZND%2Bh%2FuguHdXmU0KEUF8PPpES0esZG5pJDAkxdDPOk%2FdC5Mmt5smt5smt5smt5lbz5Fbz5Fbz5Fbz5FZzq%2BYGw13usyHXNjcHKKrHZwuvpKWLinmDsECGlAwdND5R2vIg39VWq0atfV5Y14fs2ryIktVqjbUepmUW9zI2CUyes9AlnvJZtEfiaAEL%2B7OabBqJQ619rSnT4jwKiCHaRaD08MdFvVDnWhVXWpm9jFYrEf5AwoYQz1INNQZ7QG91GJfJkH%2BGBzSyghWyJoUAhJi0SIXRAaw292W1eSBWE4uI3YAIGAOYVsWl1sGsvhLhY3FahN6SqXLs0xZKxud5QurmeQee0xGIRnrRD%2FVGFE6iJKIQj0gdYsjI1RCzKhErnWrVj3Hy0Y3OwCDaqx2Ya92%2FVeBYhK8DbLplAbcC7MT2vh%2FEMZPVyhraZAjgMGRe9S2RQiWJg519D%2BoMnPi4e1n1oReZJXLHKtJqNUFrNaZ1EKuzIswstzp%2B6dK44Vm%2B3Ah%2BCmiZ9%2FsDxFNBnX6%2FrTYVHuwMvJBmdcFs1YdmtYp7yLVRdEFUSNBaiGsdwKqKxq0vAF%2BwuNVTn%2B68buH7uQqxdRYnXWL5XXxtYKtChfHEgcHPwKEeSixPJO3BZHVdt1oQc64NwEZM3zqpxPn6%2Bpth9fiLwIvHmdUOwswaVDTPb%2BB%2BYnkYP3dwx2rmu6XWQZyBhdgogHj5XYTChhCm%2BoWqZtXttn4EYW7Wpy%2Beqbi%2FXshk1dqy9mMVH9ja%2BgCY1YcsIcQW0DGp%2BGkcJpYbeGlfVktAaXCrzYM5A6%2FQ3lZpJWE7C9UYr0wBP4kwSh%2BTKrmSmsWqNdwctrhV0Q%2B3ipMnway6eF7usjYe4lZbpRpeIBbge%2FZlVZnI0nyXOjD4PTCHu8hk26tvh6gQ5ypKH5MacSWVW63G9VnDTriYLnNRhEyLdWSaWzLX8AU5%2Fkn98zpXwW6X1Mj%2F0NkCFhKOym0emVgYbKXag74HNtchGGyPTmyH2VbZ1adLVbykpGpW41xKJalV34qd30KwjkxjS2YX4WLXFfY%2BFmEakz3SYpt%2BH7lSXWFHJVud%2BvfXanNAqzxpj1vQpSpeLmQ7VUmpUivrTw9EmDJlyty25SD6oVHD404zqTQiMaOF3R%2FS%2BIboZ6Mw4PrDB3UGFpRchxTkSX3cwePQd0ZW2P8ZNHkvRJ7cap7cap7cam41T241T241T241T241t%2Bq2aOAs0rdVcquuXawYFrpdTF6%2Fl6eDJUqOu0SDxvdpH8mtus8eR9HUnQ3ftK4vANslPSdxisOlKcjZ8uc6jI9Ryzy%2FWKEuq%2BUn9KOHW5VA%2BVASn%2BrQAcR2wy%2FJvAWwoYjyuD4vFDnwTdi33ZhV1z55ybJYx0B9sw2UDOvrRqK0dAHcZ16C2xp2T1ywntO4d3aCcJXPH696M4EPm0s1aQWkISRQPpTEgcUWGQKAkLknBtIRlFbGm6yUokyeHDJyGLT6QKRVTcPJS8P6Wq%2F1ibnlNg4b1tcFwHR3jOunn8KmEGLkhG3fMeJofPR8yQcWXX1%2BuTAa%2BMAFTWpBAKLAtALSEBIoH0riAIrdwa1KEVA2OAfMQyZ5csjM14llHX2tahqOX2PLSr0%2F6kkwrK9r6ts%2BFcKaq1eZix7h%2BAnG%2B4uZr%2Bl8oUK%2B3p3hLiJURVhkjyANgQzUOJTEIWN3BrUqRSgbBs5KKcrlySHOE1tXIq1qGl8V1MPh0KJlWF%2FX0AVYQjuk9xuvb7CGTzB%2BP6w6UL1D4wsoLrLttrEbW7cRjpGR8iFXcaMl3x3UKmxlw8BZKUWZPF6IS%2BVauVSVNjDWHQMu8PWBI6u1%2BEFc%2FaTBNQE7Um3Gf3RrZMIbLzgaf6cHKTV%2Bgr%2BgrF4w2iAj5UNrGmeWpga2GmXNzHkpjbKXsc22v5HUutIAsDbEpao8gCg%2FxtcHJsn19XV%2F7kGE4VafkvVtMF5oEp0ul3QezHhSKvTXYfSpJ%2FY6BSylSKd86A7FjZaqzwxsNXqEOxI4K2WmI2InI3z7fTLGDx93KHxLY5ZKvQ3IbDYN6wMDgLa%2Brnf5i16C1Y%2BMb9cHGJdp%2BpwHMxsFAkjTGg3qUgkYlo7MlA85ihssWZMFZ1Cr1rA6TgycWzVTFcP2%2B4lSh50hoqfkWxopleddFoD6nGl9YAD6%2BrptrB2SuE6xNNClubLjdtFgfDtmHqworrRG72x0qQSEokzUOJTEw7daI71B75akTyXVwFkpTrlVrjVZ6hDRZZy8ZJZKzkUPjTNkWh%2FYsJL%2BxzzIeLfH8Z3YyZ0D8eS2ZSAUlUD5UBIH2qfPD%2F7ORvpUUg2clTJTocK33%2FzOpi91iFqwfvCaQ%2BYEM43H1FjKerzN01UPqJ4O4nj1XAMyjXOrA%2FHktmUgFJVE%2BZBELueNyeVmQk8mZW7dJ2nI5VIljwaZP0Z5uFZzU34kdYiubY2cdygpwbRylLoeb7MwKkSB7ZjVaSEzvToYT25bFkK1IXPKh0LkcD7dowNIVNkx8ugLO%2FY4TddqbsqPpA6R06TvvORxEnDeCzFo8l6IPLnVPLnVPLnV3Gqe3Gqe3Gqe3Gqe3Gpu1dzf%2B5Zx1ShxcPUHT2uqktR9uN%2F4ST9UWThIq65taI95S7gaAsyddTWPzc%2FCB85JnHT3ZdVuUULel2C1UsTCYK8at0XAUMsNrdqm9pi9uQd4%2B5kPq569Prk%2BgOISkaEPeXS%2BDns%2FfJzXJ2oplMnGAoC1fVlV28%2FkGVX529x750BW5YcvgEox7EYrAYAQrL835ICJW09Xq09b5vkNGPi5kYl5jbPHVVmrjQMfqpWI9SE%2FQvTIRB0lnQdEgZlXarw%2BLRVBaTZ4o3opu9XOVQALCVK9%2BaqxkjcTDGT12RqKQBG1Z4eIDgMAEevvlVyGc2%2FYKRScYc8033pmHIxbq1crgZWxPrm4qwyc%2F1CN9D7kCnwfldtxTOPRRxc4j3biuOLqyKOEmGy0apCptTJa7RYRxnTc3yvlFYxWpdRBrDZnPIQvjuYQUQ0QgkgIredTchnOo5PRGufWZH3Y%2BVmPceDUZ12Ac1ld5zt%2FBF1G60MOqkA1CLxZjdPVlo01zkOpM%2BU4b9kpa5oxGyf7%2FGQ2qz5UCyrLyoaSp1V6KKVtKfvirkNEDWCH1khlL74u8Trnl3oTTqXIOXBnbw0mTgSdQ6bXg4zeh7wePrZX0%2FjVsF%2BS8UhqoPEppFhlNkaEAKA3cJJtvi3oYCfWY4a73BUu1Q%2Bri8JBWj0UjbP%2BXsllOPfCRtc7PJ3L%2B8RKMXsd8%2BOKKzgngMmqJ4TWh1xBtSq%2FHtL4j1uyC4vxUiRV449ZKVa5DfNBecmDjHcpjh9FYyM81VSHg5S7XHZXPJBVMe9J2JgXQ0Rvi8ZZf2%2FIARO3Xd93bc5hd4rmOkIYuSASOienWisBf7J2F%2Bl9yMF8oTAfHNHrHHGGq8MOMY5Qqs6D4SqApHUDlY1Uq803IPNGM46xOb3S60F9JIHd5Wa7K%2B5vjcj8B%2Bdbxei9SbE1FPb3yrD%2B3r14ESgmzR%2BUE93xaQC1u8q8D1neA4%2FxOmO%2FUHAqBo67AmKcnMK4B0qIspFqlVY3AGysanRzTgJrppx2l8vvige7W7pmeTPAjGddG%2Br394L19751nJzCFeDpsrEPucjmZ%2BdK%2BIxFhjAbKVZpxYK1osO56MGDlLtcdlc8sFVn%2BHQABKdl735Cf%2B9bwtUQwOBB1g%2BGiYfZSLVKFxuXyBwn5S6X3RUPbpWcJgkx1JS9%2Bwn9vW8lZ82xB1%2BfiU4ZEOYNCqablDXqLlfXGuz1M3kvRJ7vZKt5cqu51Ty51Ty51Ty51Ty51Ty51dxqntyqe5W%2BrZP3A3dhd4g6NrpkSqc7BibV%2FgjtM4twDXRsjIyxYXMI9dUcn7Lk1VdfVd%2FexFSAA18nOXs%2F8GGrhoUF1KzDxOyVbAAvMKv34RNkSGdxbGyxY%2Bb%2F%2Bs84xFKCefnoFoCUngEebT3LoppfjM265ZZb1Lc3Ma94IgbcItsUxlPWSWZWk%2Fty8fyMBXgzzzN5lSkAaH%2BNDdTwx2jM1aC7iDCLrpE%2F0XLZ86kBNZd4mvuwiv5f%2FAwt2sb5yGrV9d3kA8b3GfUN9Yus0YdvTzrn6ySbrZYAWEJYAEqs6tGjkDG8iBrjj8Mj1oh1N71g8xZ6dTLg%2FHvvk1w75Ot13JexOUCoMNvFViQVFzJYnZubU9%2F44svmAyb6ptNCFWHM%2FVvvT9p%2BkdFqtE4y36DIqi%2BtHo6a%2FGp6X64AgNtuAwBBsawB3tnpf6e%2F6Ih%2BE8DCC9p1%2BAjaaABAFUdM%2FE%2F9Zcm1C8%2FHPw5UiMUF4GY8VoWY96zXZfuIQLWQwSoA9S198WX3BqRAH8AN7TBadAv8L36%2Fhp28lO1YbTDbKuaO1cgq%2FKFIJ1yXrwGrrLLzrHX661PsRbfUbQKsTBfWu%2FHRNoAfs9Dl%2FI87KxZ7HWwCm8o1270Zr6vB6T8ddRkqqZmtmhdf5qsJTmktOoVJQCw7hl3%2F09jJV7JZ%2FWAJKsUUq%2FrfgG4AwFNP8fV%2Bj27nttvkV%2F1Qsi4egcwXY%2FzyjxKssFqLVB7Edae%2B9gBQb17Hgzfz49v8d%2FAXiUKuUkLjV4FfbaBkasYDipUYhdj9h7T8QhHe2%2F820TrtzyqX2kjSyhYX7QHmXf%2Bz6KfRzGS1UT4FlXtSra6ryevJ%2Fbp0224ols96zxchU9c3bwrX7wSA10llro7umXcA9TNd1Odi3Jf8E%2BTHOLk1fMZpt53PoObqUtsA2kpryrFakVJPFivqHjijVSa1Ol2VWolpZVKJkqwGHqI8SZmsfrADFXzRZJWvnyyDaoH166afgXuHEMY7wzfvhVUA6N2Mz1i4f0KIiadgndH4kY9b6HU1fh%2FaPXr8ceq1tcWwi965ZQDL57xilmM1%2BszJb9b023sPO9Hu9uqA36n4QDum7gLkbipUgQvEtTKpBCTcqI6KMN4ns1ktPwqVapNb5Vqj62q1wPqB0626dv%2Fm52mHLeiOBypyRHvqbUwtLEyhPezEeRXAn22hGuMdeB%2BLtvpjHjqx%2BqdXZfXK6ul20rHK%2B2%2FDjxTFhIwKwLoiZEbJ2Nb%2BOFvnVH3TtUYbzy35ScveVvCJbFZbUMGXs7yzKURWC0OsHzjdqn18a1rMzwvWDP2xBsZ7D7GVyclZnnzyHe94cnLZ0Xhh8vfwR1%2FU1s4%2BiSj880rLTYrelzeXsxyr0lpAFIyyNd1hXuS6XEeYepmvc6q%2B6c%2BBVYLSKqVyTc9ls3ofVKxeyjrJrBeC9c2mWD0%2B3CQKAmJpPrNVJlisDlFveWJiuUfE%2BGv4B804ryCWCsXSmBfzjf3%2Fbiku1Y2k8pzZ8ABv4wwNFBGlwF4HTYFtDuFks1qDyvNp6yRzq6pvlm%2Fe6ip7uzTs7NFlTGKkTNmzIgKNBCIWbXg6oGA6bclrngJbG9gYZ2VUiNEVh96sCCmdwYQnMCpUmJtC4YB7IRz67kneC5Ent5ont5ont5ont5pbzZNbzZNbzZNbzZNbXZhaiIPcagtRii5ljQsYJy%2B4rnn3dlGkNzH4KFomHIbz0liR9T8fKF%2BcmlqUnMcdA7qUKXt0xNqAbZgeWu3%2FwFfRz4%2BQKa2rLUOTAYoV0%2FK0tg1qceFu7SzMi58i4Ul2i6a9VUzYIWiimdnqm7%2Fu8amv3XPna5LzHEFjck6C9P7kvZrRhICBhVZFNPYw%2BnmYWNzSGH7lGjR6yrhW47OwJbfxLOm53%2FspZhX4w8AFcXTDcJh1pn7jDRAL3viNqY7RK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<h1 class="title">GEOG606 - HW1</h1>
<h4 class="author"><em>Anika Cartas</em></h4>
<h4 class="date"><em>Saturday, February 14, 2015</em></h4>
</div>
<div id="solve-the-following-linear-equations" class="section level4">
<h4>1. Solve the following linear equations:</h4>
<p>-x + 2y = 1</p>
<p>3x + y = 3</p>
<pre class="r"><code>left = matrix(c(-1,3,2,1,1,3),2,2); left</code></pre>
<pre><code>## [,1] [,2]
## [1,] -1 2
## [2,] 3 1</code></pre>
<pre class="r"><code>right = c(1,3); right </code></pre>
<pre><code>## [1] 1 3</code></pre>
<pre class="r"><code>solve(left,right)</code></pre>
<pre><code>## [1] 0.7142857 0.8571429</code></pre>
<p><strong>If we add another equation, x + y = 2, is there a solution for the set of 3 equations?</strong></p>
<ul>
<li>No. We can only solve for a square matrix.</li>
</ul>
<p><strong>If not, could you give a best estimate of x and y that satisfy the equations?</strong></p>
<ul>
<li>To find a best estimate, plot all three lines and find the centerpoint of the triangle their intersections create.</li>
</ul>
<pre class="r"><code>#Plot all three lines
plot(NULL,xlim=c(0,2.5),ylim=c(0,3.5), xlab="x",ylab="y")
abline(1/2,1/2, col="red") #first first equation
abline(3,-3,col="green") #second equation
abline(2,-1,col="blue") #third equation
abline(h=1.1)
abline(v=0.73)
mtext("Rough Estimate: x=0.7,3 y=1.1")</code></pre>
<p><img 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" title alt width="672" /></p>
</div>
<div id="calculate-the-covariance-matrix-of-the-following-32-data-matrix" class="section level4">
<h4>2. Calculate the covariance matrix of the following 3*2 data matrix:</h4>
<p>First, calculate by hand:</p>
<p><span class="math">\(A = \left( \begin{array}{cc} 1 & 3 \\ 2 & 2 \\ 3 & 1 \end{array} \right)\)</span></p>
<ol style="list-style-type: decimal">
<li>Calculate the matrix of devation scores, with n = nrows(A):</li>
</ol>
<p><span class="math">\[
a = A - 11\cdot A/{n} \\
a = \left( \begin{array}{cc} 1 & 3 \\ 2 & 2 \\ 3 & 1 \end{array} \right) - \left( \begin{array}{ccc} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{array} \right)\left( \begin{array}{cc} 1 & 3 \\ 2 & 2 \\ 3 & 1 \end{array} \right) \cdot\frac{1}{3} \\
a = \left( \begin{array}{cc} 1 & 3 \\ 2 & 2 \\ 3 & 1 \end{array} \right) - \left(\begin{array}{cc} 6 & 6 \\ 6 & 6 \\ 6 & 6\end{array} \right)\cdot\frac{1}{3} \\
a = \left( \begin{array}{cc} 1 & 3 \\ 2 & 2 \\ 3 & 1 \end{array} \right) - \left(\begin{array}{cc} 2 & 2 \\ 2 & 2 \\ 2 & 2\end{array} \right) \\
a = \left( \begin{array}{cc} -1 & 1 \\ 0 & 0 \\ 1 & -1 \end{array}\right)
\]</span></p>
<ol start="2" style="list-style-type: decimal">
<li>Calculate the covariance matrix, with n = nrows(a):</li>
</ol>
<p><span class="math">\[
V = a^T\cdot a/n \\
V = \left( \begin{array}{ccc} -1 & 0 & 1 \\ 1 & 0 & -1 \end{array} \right) \cdot \left( \begin{array}{cc} -1 & 1 \\ 0 & 0 \\ 1 & -1 \end{array}\right) \cdot \frac{1}{2} \\
V = \left( \begin{array}{cc} 2 & -2 \\ -2 & 2\end{array} \right) \cdot \frac{1}{2} \\
V = \left( \begin{array}{cc} 1 & -1 \\ -1 & 1\end{array} \right)
\]</span></p>
<p>Now, calculate using R. So much easier!</p>
<pre class="r"><code>x = matrix(c(1,2,3,3,2,1),3,2); x</code></pre>
<pre><code>## [,1] [,2]
## [1,] 1 3
## [2,] 2 2
## [3,] 3 1</code></pre>
<pre class="r"><code>cov(x)</code></pre>
<pre><code>## [,1] [,2]
## [1,] 1 -1
## [2,] -1 1</code></pre>
<p><strong>What does the covariance tell you about the data?</strong></p>
<ul>
<li><p>The covariance matrix shows the variances of the two variables (x,y) along the diagonal, and the covariances between them in the other positions.</p></li>
<li><p>In this case, the variance of both x and y is 1, while their covariance is -1, meaning that as x grows y shrinks, and vice versa.</p></li>
</ul>
</div>
<div id="use-the-following-dataset-to-demonstrate-the-central-tendency-theorem" class="section level4">
<h4>3.Use the following dataset to demonstrate the Central Tendency Theorem:</h4>
<pre class="r"><code>data = c(3,2,3,4,3,2,5,4,5,2,3,3,10,4,5,4,12,15,10,17,15,18,16,14,9,10,11,18,17,18,16,17,18)</code></pre>
<p><strong>3.1. Randomly select 5 values and calculate their mean. </strong></p>
<pre class="r"><code>s1 = sample(data,5); s1</code></pre>
<pre><code>## [1] 9 3 10 18 3</code></pre>
<pre class="r"><code>mean(s1)</code></pre>
<pre><code>## [1] 8.6</code></pre>
<p><strong>Repeat 3 times, and calculate the mean of the sampling mean. Then, repeat 5, 10, 20, and 50 times.</strong></p>
<pre class="r"><code>#Calculate the mean of 'size' samples of 'sampleSize' from data, repeating for each size given in sizes. Return a formatted matrix of these means.
takeSamples <- function(data,sizes, sampleSize){
allMeans = matrix(NA,1,2)
for (n in sizes){
curMeans = vector()
for (i in c(1:n)){
curMeans = c(curMeans,mean(sample(data,sampleSize)))
}
allMeans = rbind(allMeans,c(n,mean(curMeans)))
}
allMeans = allMeans[-1,]
colnames(allMeans) = c("Times.Sampled","Mean")
allMeans #return value
}</code></pre>
<p>Requested means from 3,5,10,20, and 50 repetitions of sampling of size 5.</p>
<pre class="r"><code>means.5 = takeSamples(data,c(3,5,10,20,50),sampleSize=5); means.5</code></pre>
<pre><code>## Times.Sampled Mean
## [1,] 3 9.533333
## [2,] 5 12.040000
## [3,] 10 9.200000
## [4,] 20 10.260000
## [5,] 50 9.548000</code></pre>
<p><strong>Use a plot to show how the mean of the sampling mean changes as the number of repeats increases.</strong></p>
<pre class="r"><code>#Out of curiosity, plotting larger sizes of samples (first, so that axes match up)
means.5.1000 = takeSamples(data,seq(1,1000,5),sampleSize=5)
plot(means.5.1000, main="Means of Various Samples of 5 from Dataset", col="grey", xlab="Times Sampled")
#Request from assignment in red
points(means.5,col="red")
mtext("With a large enough number of samples, convergence is noticeable.")</code></pre>
<p><img 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" title alt width="672" /></p>
<p><strong>3.2. Repeat 3.1. but select 10 values during each random selection. Explain these plots in relation to the Central Tendency Theorem.</strong></p>
<pre class="r"><code>means.10.1000 = takeSamples(data,seq(1,1000,10),sampleSize=10)
plot(means.10.1000, main="Means of Various Samples of 10 from Dataset", col="grey", xlab="Times Sampled")
means.10 = takeSamples(data,c(3,5,10,20,50),sampleSize=10)
points(means.10, col="red")
mtext("A similar convergence to the previous example is noticeable.")</code></pre>
<p><img 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" title alt width="672" /></p>
<p><strong>3.3. How does the sampling mean approach normal distribution in these experiments? Use histograms to show.</strong></p>
<pre class="r"><code>hist(means.5[,2], col=rgb(0,0,1,0.5), xlim=c(7,10),main="Distribution of Means of Means (Samples of 5)", xlab="Mean")
hist(means.10[,2], col=rgb(0,1,0,0.5), main="Distribution of Mean of Means (Samples of 10)", xlab="Mean", add=T)
legend("topleft", c("Sample(5)","Sample(10)"),col=c(rgb(0,0,1,0.5),rgb(0,1,0,0.5)), lwd=10)
box() #decorative box around data
mtext("With fewer samples, hard to note anything.")</code></pre>
<p><img 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" title alt width="672" /></p>
<pre class="r"><code>hist(means.5.1000[,2], col=rgb(0,0,1,0.5), main="Distribution of Means of Means (Samples of 5)", xlab="Mean")
hist(means.10.1000[,2], col=rgb(0,1,0,0.5), main="Distribution of Mean of Means (Samples of 10)", xlab="Mean", add=T)
legend("topright", c("Sample(5)","Sample(10)"),col=c(rgb(0,0,1,0.5),rgb(0,1,0,0.5)), lwd=10)
box() #decorative box around data
mtext("With more samples, a normal curve with median 9.5 is noticeable.")</code></pre>
<p><img 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