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Replications.html
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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="Fernando Hoces de la Guardia" />
<title>Tutorial on Bayesian Statistics: Replicating Sections of BDA3</title>
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oPEio8DsNzZQqgUMoq0%2BNMALrygrOlErJohXvIJ%2F0IqziZok6OuApG2eoGAEFsTc6yWf9eRcklYZRO3PkA%2BW8aN5ME8aLNC3Kdwtm64WyqytOEW1WQIg6bOFHAs1ovo3OfCvvZASxBcxg2SRCRTTJDBKajFH0LL1kSBroe6L9xvVxMCIFS7Zo6y4ZOEIkAI9QtGVIKKBlCvUUEq2S8FiR7VkJGbvBFaS6UzQV%2BayV6NKw62tbJbEjkJ7AMC17DK399DZr%2FtE5sUtaAPwaHNj9VCoVB4VAG0iNI9IjDo0mr97FWjYeDRSr3pstZTVZ6nj5Vp3IbssG3g0r9E2eSmHY97LYobIHPnEGkKDJP15WPWtwMgS8HeLd6NEnP4mIFlRJB4zLeDeoBElpUNRIQMzLbRQsGLj3DZhQytDQPLAUE9JWHiLKAJxVTOJNZsObEiutLqwox%2BM51t7vJQhBeQm2i5bTa4D8qIUjqI1sL9G6Vha6U6IPUabeCUMIufG%2F%2F6USyxymXNlfnVinkNvKZGUjz0EWKIgZEC4WkUEr%2BgP%2BFpkIPUVM%2BQEJPxFxKDlpBEeiUSaTgCm4sEfRnBxu0eF%2FLgLp0IFHMEt8aZrsQzTF3wRw8TdpzHNGMZrHHa6nU8KCQppWBVpJ8b2Xjq278mtoTfrgfAMSAm3cYEcDw%2BzcSsXTaUyd2PH6DCU0DdBiauxpsyoKlAh9IUAzS32X%2F0d3x7h4gL36Q5sC4YzkbttmSwhenP5pxxrBEEcoAohUGB1jHGtB2%2BI0FEcCM2y8EY1e2NPXJS7wp7APp46lC7gSit7FEFQCIDnNX%2F196lJs%2BgXTyJrXAze%2FQ%2B9GEFC7p5W7W5FEooh5QlO01B1OcYDH4VTmRSO8fHPjRo4FkT9GrnUZw9pXnDplu0YFyOaAsLOkxdsu2gfYJ%2BDzBNihSUutbDbDy7VKS3KwwUTChYQkWCmldyS%2Fy05EvDGbLbpkDfbbHNGEhTSiaAEDmoKTERX3pEuKYJT%2FlNS4IawkdDACC5Jk4hgNa2EGV8yblsXoSHDrqHDJs4JDXLLA67oCyia7LABDzBMInY5gnZCpFuyyuaWXjKHRgy409j2wNaI1bGlosUnhaB5iqHHZf2%2BbDPpsIwoahsWRL69BhhyPHQBUNCyBR%2BUJzMOBRMxTVhNsS0%2B1n5kboqmNZcC%2Bt6HYVscRaBeox%2Fvv3%2FxwdoUoRvs6CamykRGihd8HTNaL%2BxRuoo3QVZvFT7xS9opWLiNbQRti9PXbNg0J5WDsxaNesdmkYOcwpiqsURuor%2BS8hhgWniGGll%2BtD55enFSsyATy9MonNXUJV5Q7eAouzR%2FP4HlA5YWBYYjm6NDAEk%2Bx9On0MGm65%2FEm1GKndnRp4cv%2FjFAdM7hnXsaXnGKAeK4aE%2F6BhOq1%2FAWmgCMQ4zC8G0wBzhuMSeeVhgAl0jpwicoR64K%2BBYlYbWz0gTGAGtI3puhx3F5%2F5QKXradYFuhJPYWq3ITCUUNLpugdVBegedngCO%2FDN5mJBWzGEL932jL1YntvCgzzLeR0WczKl0J4g8Gcbo6p5LOslpYBw4kE3ZDMiHPjBGyAUjkrWXqYTrl7gRUwex0zKVekIhoI0dsFRDtQxsLctjOlRs5Y2gYpQeBORQFR4C3hXh8EnZUzuloqFLFATXzpzv6k5XoHB3fZLNUiPV5DvAfroLwH8tYhkcOxWnHqePfQulM0DCPTadXa%2FTpoHYkh9BeeAwpmi9Kbo%2Fm88ob17pFzKP2lJpfWxbyD3PccS041A0MQWUqNDHOPOFt57Q6TiHQEKJQsI4v1JqcD7Q3orOdsLvExRQwS0nlUtV%2FpQbx0wSlrRSneWAQ%2FJhPaT6rMvIcid93ahrnKe34YxGA3D30BI2lEiLGh5iAUkBLBoXRshvpjGJGLzGcvonIqzVubgEJv4mbEl7JggQUWb6AYaQMmGUXEwIjylByVLbgcEbUQL5RFiRkX%2FbOhzb9XavzmFpR0cOdx3etgoaCPbiL5gR8o0wJNdPMCYcmyP0SDmmsW8o0O%2Fy5HNRxqz3IhmaxvIT%2FxpN8Pj%2Bx4i%2FGawfTOod%2BpvHN9BMNQUKG555l7yAKsma4r8JwVm6gxqBECXHA3e%2BdCsONR41WrcokynYzYqB0xlCdg9Nu%2FVL4rgwOiTVy8K70TghEjAOHeFBYvGwmkrDIzlwQsyBsr3K%2FEBFKO8UQ6J1hU%2FYGFA8fGgTnBoNnAmZc%2B9S%2BXnpbpJ4QKgdip6TZnI6woSQaYgxGpdaxxSuQkxu0avCBOSwchx0SS0x5HgR6iz9AkbeoDFTnGInFfbnMUP%2B8p3uSQu2CVkHxeVeEMICXKlVDsj89UY7AfyMvxTyws7ilT3y4zYSLVToLb1IwDJHJ804mZKVSKgSOa0mHCQrjWQLaz9LrCiISicIHspx5moJ%2F3Ng4rjU8aMqTDl5gjJAFgAMupkEoWEalYEtHh8CvvMqUP0Ra4v6BRr%2BdgNXFRLo%2BjKWRhaP4x63qqfsnw%2B%2FlDAo2doOxQP7GwahE%2BiZ2OX2l5DodFT8bGiL0YglcRmgDoYIEaRBLqdbj7HFD8xfZz45H2Tg6upN9XjuGCxtdxuVuRjssowtewrBo9gBM3T7d77hNjF9rd8QTMjwGLx3oWax6aa17t0I2gcG6kcQgw%2FphwfsB4gsCGgMGZU8P%2BORAg4iQDmTP9XqByg%2BjtRqWtpaHjiHSL8CNah084UP6Rfjx8GU2eaRw4mH%2BA9Ad42DummqhAj0%2FeMNS3V8lEHUSc1ntW779KspgJUBtJQEpS59ODiBRghAyioIrf%2FKoPh0eAJWqxh%2BSurG%2F5xVdzZBLgKEiYy4izBuKhCRIhfoADEt%2FB%2BirTWSOZVkcfzWBbA%2FAO817phMFhWQnvTwzjirEna6JgrjgHyk%2B8nWk0k06KkkSOOryl2OrOta3U1Vai9SLWxcE3cY161P64wA5VUgBExRGc8qtWCkEHIJfWtybVbTm%2BhrXnbVSsP4ucJTC9onJ8N4r9lRaV%2Fc4a2SZKmPNCgEUW7LDBXhvFxUvZYtnIuGD61WQtIrDXUc13hksUbImFeHrIBgvnG4ogmKBk5CClzY5DWqCCMzdrHBGSSOTyO%2BE8inLMGSApQqKJB3XKm%2F%2FMFoO17KuwfwqcaqjAyaJ5JOWW1Myr%2Fs7ZQiw%2FPqVAMH%2BlK6DYqjGUMcAXnVxy6z6CDl6j5mDa5EG4j8C6pr0hKyRNnoiR1vl9DWOfC2%2BM4v44bO3onXro%2BNlz00ZlGV2ICJ5CcCazVCJHIETBqVFhGT7KSBdNDv5ILpSacSTL0S6fX%2FP1CEIT5NZgcwpI0rkV7LqiHRoLUAPjXEqCZ5mLntX5JkkUEelCsU2tXCMZ6cZivQI6hYQNbXl4nc1sSNtBUTkQ8Y442KxRe7Uy5yOzB%2BUlA3MhvFmXweJJj%2F%2BG%2BqwJFWFLNYp0JhzD%2B4sl4JYn6a%2FvShCCo8hchMfrswjZgUqiToKfoOGaHdIAnKE%2BiEedBkyLwMSoNVX83TJERFy8PLMpBjsXtBITuS9lpPCTVl%2Fvs2Aqzlzwnj7lpl6VX%2FQ74tWqUSzaKziwue1phr9BpcZjNc%2FGXuJUq15TMDnCsJS0X2wAtW5JQA5MaTyUH4cDRif3MDxZx3Se89P4WSIvEEeLjToJbXf%2FrRhBMtRevJxuf%2Fs8EK4woZOFli3yTq3xqjBjrlierqgmUpFA15HFkeUOuLDjuhzLDjAGKK6WThTynzd%2FtCQWU3Nzd8%2Fa0q%2FxwZYn%2FUPEHU6lsdG%2Fn8gN%2BYACURCU%2BW%2FldrXpdUK7WxhgWmNd%2BLDoQFCU0sFyHn3KqFz%2BIg9e2C5oe9EOi7KdTBxPE1k4k5tkX%2FoZzSih8DJDFd%2BrITKNSsAAGtscSW9VDasqkEamMzeUOhRqRRAj9lc%2B7An2YOdL46GdcOLAsgYaFsR9hs0ToUzZ9rFRLG1%2F7eYLz1l5ijumbe1druwaHNFzZjtwt%2Bn7paZaMZu2EIx%2BlxX%2F2SBrWJQQM0wmE19eWrGPIVMeAzVWWRp76m1skeqzaBBZ6So4eD8Gpv31bn%2BnO4WG%2FOg%2FB7xQu9kpA3eZL3w9cwzrZfMmbUSk5OiF3Qx7bQYhL0VoUQQP3Hmps1bBJDQU0qAJpWwnb4iFOMBthzwP81ilVnh1bIuk0C9Xe%2B1kSK%2FK%2FMYOh7vIa7ghqGEKzCiHrehs3cA1pzgec5NpLDtCqMPp1GVECA4QZKiZX0hQ%2FGqjOhhObmpH0vwx0WHctTrmGC84Ub6BOQVdXIqoxqMVNhQjd%2B0CYMRk1zp6%2FPnIOsW7k%2BhQEruSB7%2BDEGv1lziYEEwur9gsigQBG8EJ3zeigdA74WvD0h2IbdNzPw3okAFsdmi3qKH41lxijDPDtvZcEzXwUnRNn4WpCP3vPNHhO8czUiYjRn6GRIQ4SymW9MhjUu%2FjbWOhOqNeh9OSRNh1EaFZcalxYnJMLCpTlEDttzYxhNCcZ86PUpbEkFmkU5HRiAF9AahZ8jQ769NUzJGkq9YLj9HWZLEK%2BIryXyPLZHAAHsBSe5moWq2RRQT655EACRYKQ1AR2mNQU6hNdrqLyfpSeJ5PrccWf3dXVxmIidWyyIkCm1v1oFYgyGcXwrCRPXPMLYHRFvGVuYyAUhzgYntJmDhE4VCNKoSxWlSFiFuMGumZHJnCJyAdT%2BHcgUhIEJZgWOjmy%2FZWisKRYo4JjuPntQGSxlJg3XJ5DBsFM3kGGQjqECyjqYFW6ccOkCDy3EhUt6taBIaHclyblt3Xxs353KjciddJC7gI4cZaPj4zBxOVNfei9MW9cLUHspngSFFni3AL7sLsbqo3totPWMf0yD2bdWKWuK2a4eF5jKcYCZyvORgcHeETtqeqhAYtIyiFGAYJQMOX4VJzPjyDKiavWJRtjWCnaTUdPR6FRkTfFAARc%2B3Ln3oFDETvxxiaDT3roIpaWwEEjRlhjvs9ZKiU2o1HJOMuVRFAA5fWzMgAqSKDaSLNQcQZbaFzsgKxXWIvjaOqsoiS0kA1bx2TN4NrJBVMJcmRWNIqrjepyobiDa9yXYKmJvgQWZhEBvF8wEx0pMQqCzcf9JemmcVMROHpvzARvqDrI5WOXmah0Zkh%2B6PIozOYm78ieRAJObTPxSCLuwQiRlWaLSxJ5hgIIrjsEUKPWMqRFuMgh1FsNDFw5jPGKPTWzyiSEIS6IPweoS55G9SZZ6wcpW%2BHYMSkoSETssJ3QQM9bQRo1JdCQdS1np6F5WR9wujL48y6xB4M6Y7FMnX7f22J6F5gyYVK0QlgEQxVXFUuC964aXqqhT5cX8XaZv5hVzeTU7bSoy40QuTOUjLVShZVi5iWJMAbFhku4I5QyO1x0Pm%2BcTesk5XsjnzwoAIsmXCFbWyIZQuawuVuXuR8DK92lWJDrNrbFtNbCj5sTTCx7e2Wb0UydtbZ%2F0CSIT7OnVIY0fRntwN3jNOdh7nGpmmq9CbBm1uLafMptryjPHHp7tKZEuAL7OjXHySRjUkXydXE%2BSrNxA2Um5Al8Dh3EZC5V4SFynxsMTKCAIMqEqNKzuJCQM3tvVBjRfT7xHSuCO72a6pSo2wn8%2FaXBmKI9sW2BccnPF8aML8%2Bohhb7ciWy%2Fxch7McUey2CPGCyVKaKDX8%2BSBNgqZqMLbCgZ4NPkIF6NfeH7gtElIrOqbudNqU8yyyewVZneKXuzObCUxU5b2tecTa7Jn7SE6UlSYMTkMfCs3Q7fVCaqK5k6pf%2F2wW%2F%2FosIJEgW3skUNgQHyb%2BsAi4ECMNcyjicIITuXGyXkkRIXyN50Jg3r1FpMmaQSUl9pGxnNMp8jf24vS5eX%2FyJYlMUISy9e6JooaPn7fiuG4QEscaDgCZpra85ygZUcJInLV6C314YPJdG2UL6qljb1QV1ZhrNcFecs0j2qb5gvkKHOFxHphwdBgEJc3y8qihwdZCQpJ62h1voTUccffiDJEzkU8jbXRvLFdPbcmVBUhArEuTKQFe570IglefLJ30dWmVAtx23vIGmF7N6auVNpZUQVHNmAlGgjNet51laJgLQSpfZyxBEqLwoCEGlF6ISp0NUmhUHT5a12%2FZElPE5UGO9AVnKpae3D5llVvXAHK0FIH3uE8AXFPF%2FSwx3OdCN6aViMIxEVcqv1UsLJo03R0grVOHRogBCiYVrK%2FqFBPmGrDyXLgr6DxBMSKnf1uSBgiRjCiwL1QoM981XHZnusKIVJ405xXwx6aBUuM2YXS0jaCPwaC2Zdp07J8gxM1KnpWMqNkRCfPaYTelLbBmd97YeNAOFaFOlV29YQn0qIInmIeMFxikX4U1pEusNYtOX6tKZKkgVONLhIF9ZPpxNWGA5fslgv82Lx49LF6FltT3Qp7q4Rcu4hKczn2m1GTA4unFBAkDCqY%2BD5s2dyVIfDeGeBgwDnPbGYXQqwM0E%2FBCl69QtVYbUwkQZAtSB618VkAzCPAs93Ip9qWnBMX%2BRUX0PFxCACZQwpfvNvAMGrD69RE6JSyNNOvRD8v3gzw46n8oB8mFQiYiwgidAyJgrfY1SaNrL5QDEjIIgYLECALRSK49wPmSO8jZLnesJ8oFZjWJyTrfBrNRCeOMoaVxOojhX6WVAhhJ6dvBPZ4AbMXC37YPHBFKUgA7t8mCk8U07mFgWg3wbOZDgsEZBOC%2FApoLJL8CzpXhZuoEh0ntzsvrUPhE40%2BUUkCAm26DxGMecbxuJ%2BpPJct9BZL6lVcWLmHps6SSRwqmRJeypwrd3vNnIawZkqBn%2BumMrwB%2Fc%2F%2BIAx3X3Ehjr%2FzJIVUK8Luxlv5IeNoBQPnIhvJDZfGo8KIpLh8O4iRusiuQOtytJ61yCvQUGFmCxEEliRlQmkN5wrVLkx3CUrlDG3ABe14lLsoysj9hXY%2FTJpUb3tCvpw8Ez7Wb20lfIScq%2F6wGFIrBkgzjtNLBoYqAgJoKvDHcdkTRNbmMKP7Fha6v0z1qPmfqQzKW%2Bi9g0kSWn1vQuqaJyaTAX7hrJwJgfaPjJvb6wXroHZRAD5NH2E2KaWtBw9TGd9mIea9%2BPrxlBpyjnQhg6rLogT7414uB8V19PPcBZUhnNx%2Fhr1%2BtX%2F1jKG4nnHv2EtR3VOjo9oWEibOHX8508Tra1pFg4lnAwoQ2u2JcsDi7diOc%2Fuhvd8qexCvYgoI6m9VYAg7Vl0PRXiuCdgHdKDIIHG0j73u07ULaOJJ60Y178Lsgtd7zYdOUGlMCYhR2Uhyglt3KUjPCpM8MKjVS6OgTHgqD1SSQ%2BqhzInvSk8VzFP1cI8vLxtdDvH35uPzMi4mQtJCrVUqhBWbQRke9Sjt9laOS7Y9YqUkXldpaAoofKmUNsx0D7eYLc%2BspsKbO71qdmmaGglAJjo4kj6XlnIWS1hQZORC%2Fh4i%2FCdcbaFFuxb0AYMJ7EdQExeIHEdPRtCxVECvtxHzbEyldDvie9cGKwImUuI0xEL9W%2B7FhefRJ05ePV427NJDYmhOCwBDNBP5LrIiblD6aw7pSeWFA%2FlDoWYMm%2BZEcF16VDdA3ALq7hDBlLUzNTL9AoVyczpCwb7xHucfK6T64W0AnDzYLg0HYWadOMPdoP%2FlliqiAlAWP4rio6stY02elA%2FLOPBnEr6rsAqtMRsS2g6HJtNANGwpxTdZEP5Xt5mE2gPs7dE0gyQv%2BFdd8QTBEqmAeMHtNnjBtKvg7KmIZCj9303GT9mWQXZxolBupTHIhJT%2B0WN7uu1FbRp6NnSRDIj1aXRJD25s%2FAD5%2FIc2OQ0iDp7%2F3Dbv3Oa8McFBhXrPpAKzhrFANFpcnLmEVTXjq0MO5sJAPVxFbMh93VfD%2FDppG4mBzXSgVfXJeWNNxoKF8QTwcQFXwQPB7QLE2PENdF%2F4vDL9zn0ZgQ1i6Nyr35KAwetsESlUtEENQbCFOeUFb9lg4Q%2FW5lUNo2fsscGbWY4T6pynpP0Krl%2BJFEfY%2BGGHI3aj8aBO0K%2FndAEPa5FX51Niq7CEOhoB2hSpGAgBT5%2BuzxAMzSuVEeQmZIbYew4tM4UsHYdZtT%2F9ibeR1u6rlX6lBQlSBT6LQ9YUEAgmAxLkAKQL9PSm%2F3NQF4w7ZvdqRqMJ5DYZh3j3I1rDmyXyti0llyZjkLnoPtHHwZd%2BfwWVz9ztMTMCFjpKBVWAdcYhRV6wY0kRv47nqddzEhQvXsqNstE6GNiLTd8iliAfI5vfm2KjfTQwbxz2uFzaUL0A9VKWzB7VrWS0QvlqVw9VCXOB6RDSgbNtW05PB7pEz%2FHZkv%2BXQTUD8mSQ3mJk%2FEUe3%2F2ixiuDVAOBfyIscXixo%2Frh7BHtl5KSBigokAOClzsk5pj5X5S9GLKgu5AbQNotZBWU5zoIzScHQKjeFNr0MiX0Mp%2BlHmHKuaDcfU2H%2F%2FhJmeXl1nPE8E%2Fk8ULZ%2FCLYtwJWG4CHI8h5ySfOAFbkRVFJyi0KYkQ%2FfhDAjciw08ETminGEMzG%2FwOERVW0AEslZEl4sfr5AYRKGVSMzkDSQ%2FnhkipQ8y8EF9ZRGKCOxRzfpNMubhc%2Bs9lZBHqNegMaRLozjP%2Bg8CUsaVzp5Wd0ZI5SaeSdNAD1HIc0vTPw7SLi4Jpa1gGgtEY865KzsFCn6I1RvKT3r6BVdYGsBPWdVzeLfbxKi8BVQVzd9f83goEpezGYiAXT8S%2FpW37TxnZ6f%2Bog248Vvj9otMMAmzAfvCpPYmXIx6ZAKAwBH737j2KJpWyuPMnFIBfqRrEBYiTiWVjvdx5T7k0dwFjgjLrLVm28m%2FXLNfjkSOzkoh3hangxcOjvxzVDIGSxYBxI9ak%2BDsrVTPAlMWZD7OThbuxdkWjCtGwtH4QzQdpmaBsHV8Yrg1iAK64TC2WMbQJAFFciwJFPSRQ86OtUrnPSODgRE%2FhD4qWAHDlWBDy1KPUCEbpodyyU4TnaIFzU%2BtJJAes10UhzVTNE6fGDGUN33wCgAZYoIz44wHk6fDO7wGbAEwmcVQg1HGGByFjYGdwJD1joA5AM8olCJ1LlTUGB%2FkhlrmbJbCbD4Uj0GZTy06zCTjOeVkJKZzqk0nE4%2B3RmlgDHpJwCwwZKOl8SEEH%2B8TQK7R6TiIPAy%2F5M08zWqjpXg4KWF%2FMNQpvipZJ4KZfGsivxCXyinAY16NjMD%2Bkgtfc8pGpAgSyN27l%2BuW3OjjOCnldBAJLpzjAYdBoh3b0yuYkLj7c6iwxR9NHW9WBeGVYjvaTEHVq2t96HA16vtKz3ZgtNuJgpjnNZRGEjbmQuiQEBJ2BdgHxFDqf0F1dQJcS4sIvDHlCASh65anDjgr07Qa98i8Jb1rAbSdOOz0cM9wlKXm7ugzOMTmi8EbeTBIoHrudZ9RSwEtADDsgyFwnxyfzXecDzLGFMmkRrGWCdnWVnSMMcc4cl7NaF%2Bt%2BgTHgy9s1SV05LLaw7YYgNxNKt2kpiEgpahsRp%2F0tarSWdfS3AdWYIAnrT68WTwX1vtPgL7EMcIzmOpOxL7oZh%2BcoizveUkJVmjedZZlkwkno1E7%2BjVJIoz8APlgweTgHUL%2FGciPnYgtfrq4TtxE4adiNQ2ZgyJHWYWmrMlW6ebFkPaAUwzKsAhoGXxXGRGKFObHKQOqFOnGgkyLajFNwhUa4fqva2yI2DlREZ6p0CNOGwR4XCrS4K3SH8pDQGvZIaDcMPtJUoLRM0owJ0iT9QcdRK5IRIIpAOzsUotf3TbAVvbQH8n5voA6kUzw6LqVnwPkmnYxgJLYiQ7hQYlEsYL4k5GCZvd58ypvZfwO5t1fXMTj11hE8GuAZhX78JMPsK%2FJ0yQqDPk4Z%2BJbbXS1tia0EBwCjgWUJsUI18clQ%2FL%2FH39pOY3jRcZFFfW7bC5v98f%2FwQjY4osg1CYvJfYmKVWbiPLEpDvlTEGLjUbCmh74cUqKtsVVr9hspTEdTKrKSRjqUHkhwgyUQeNizUsUp3cLmGnOoxPIuzYDGHFJxwclXasrQR5Pp4%2FX9adXL0zyaNRcp5govE%2FKIiLMyYKgb3rKpuxbm7t8U7GiR8qcIvzarYOuIr0z8D1QgHRWmwQj1jMXJlqpuDBiVUQD80Fnr7quJElyEAs47dXRoms8yEtA2VxNaYbJmUQ%2BlsKhyYLlk2q0QMXQSsMctgTGOka0GYae3AxbsfNKwpf8YnyAYZzDx20P8xvD5aQ4OkVtbj%2FxeO9gPGmBGT3BiXsWroQWXXm7Mw8XnUAttSlNyNEsqWLOLy5MJLmMa9m7Abm0SuOJF9RWA8VDp5xMP%2FI6LaAKUmkqt6%2Fxs1XyWrgcDo5hjmvshCSHhWpwCludJPk5i4bpUhqFw%2BRmK4VAI0O11JGtbQ64l%2By0LUdW7GarSUUwP47kW2CYDEdvsA%2FTXw0I4OPf2SvJ0FKjn7aZxxwVp2xjhpWMTDxaZMkiOxaFFLydXq16fefH2qVJybgXVpioGcKFhS4AjNTEa5T37zLo22Qv1apFD5qUjB9w8yA0vSc2RMiA7xIsRIGBTWOjHH9SZlK6QJGru7w%2Bq2GoC22fzSVxkr%2BWlT9rAABqi3RiLzDxns68PSEUIxqrqFw8oMUhIeL%2BSdTHAvw8M5C0b29DIIfScMQS0TKwvPEq3kAQvxMTC0D%2B7tnB7QNRliGiWl0NuVnIUY7QMwRkP%2FgVT2WDBX08%2BWLDc%2BiW0mz2CZ3IAvWqesMkIe3lWqMvUDL5Q33McSklm9U0P9SHgPGGVlX40diyUBp%2BpfWi%2Fh9sKTOvCRCj%2BeFIWvUXobOyAxrHlhKFGhOiw1vyKUiNMgN3k9No1jfVEpQEU35laY1OWX0u%2BF%2F3AcQq9opTw0RwEyxVosGLDgIkSdn7hs%2BIHrv2jR%2BJUh2kADlTtyX8HxtYxLUhMLj3%2FFpJAhfxzoRspqTIQicEOQtI1iv4n0xi9GiED3BLS%2BriXyEyU1v6KfcGAWCaq%2FgQ5kImR6wna1UoP6KtpT9XLI4EebxCRQriHsHkCOgDlZM8hJEHcCfGIERpbdeZFFHtE3lBjH2cIQ5p7TNVfRTwBkflxGhmddY2YfZbMF0bFv76YdpbH3dxSKmVVsblZW2xdvOxqSIQqbw536IFhJKhELagVlMG3LQqHU43e%2BRZjx4BJExsLcLX1oShyJFvhFevBTFOUF3Exw2yNBWwMCW5QA%2B7UmPhwM7AMOXRddPg6OxuaNAmiDYRKlcHo4FwUeta%2FLSOUyYddHQi3OFkb4z35KYG%2BxJAOZ8LTMyJ%2FCgARNXgZ%2FC%2BfKy8W7VwKPzhRpDnIMS0ClN6sPMpa421GfuLwApsG0C4FpdCsaLM0NtsctgKVSkeql94%2BXUmITqdGBajY4m4NmDFEk2HiFjYtNLmZSxNY1QM4KakEvIQIFts%2BOJ0QCRKvhCmQcfRAjN4VmYgb58CBUMiSUpcyuEfRFZS0SThDQPO4aFcJiNJUvlFdO0s8RaeSdpOSHscV%2BJAIchHCniOYTsEqhdLZtWVSiAw6hEDO7LI4or%2BkXTE6zB0CA9o4NUeZIpS0Fn7Q8lU4X9sZNCO0uPfjoWqOaqDVcbxBJSAs8RV9IcKmOPY%2FLDUnXDLSYfFT1xyNTWRLKRW0kFxctTIuvuU6R%2F%2F9ApGo0EHrqGH7dEmsI%2BgA0UXpfNwWFxUHz9CYK9toXP6IlTFRhuGh7z3bhwL5qzzoRAF8dkwboKslbtuftJDrshFMoBNaIvpSXyAFRCCKFOKEkzCkB3NDQB2qtV%2FANwHNea%2BAUDr6WWScJazRx4glReLp8vQ8sFtz%2BhqehlJO6MM5NMIc8%2FkWnwbE768NqCDKBi%2BpY288WynJ1CT2Kq9%2Bo6rhlUpRatsVIsacJhA%2Bq8M9X%2FUQMRZhshDAvsXwlZfxDn%2BWCfyJyLFA2s54on9a54PSC3WgchQWZLZgEl8xGrFUqCofhkvqYtXjA9XyewEKlnAtD26XlSvqtdhXOT%2Bi5BrX6S6hHVcqbZ8qbh%2BEzffUpCfTG5HULg9DQQaQ6ENkkq3DvUSAQwcxh24qkmtdRoIMDxOVDdy0T2w3afIBABsQGxnqJaAOY1gWawTUuhslaSivzrXaPcRyGhUkH0R541UbNvLKiY070WOGYY4R%2Fg1rfKhHcjoV4p45o21tldJXmpG0XsOekNlYucZlkAWkVUHtjkSeUbdfBMKrGATodKL9arS5JFVovaKRlOWbNJIS6GHxuLt8CX%2BBYQUYDfxlQrQQhL7z6vChINNDAVVN0rXxaKjegwIPOJf7rXfHBBHGpBNpaeLGFXCBrWAdpIwF6mcE7pE2z4HdIxcWkU0QA3TKjZQ%2FPNc4VwWA3OqmXuoleHBmMRLsU3ENaVgIpVnIWvBLVDYNLzVRdIefms6mo9VoRQZ6cCkQSOdK6KDkWEMZkQyIEM6QUltTfQ1xFpxUL%2FlFho06RSy0MhFQCIEh5FrTToDEgpZU4QcT%2FbYWc9XTPTTM6ZiDUk6d8MHSyFOgi3cE0Oh5I2Tv%2FThHNjxg7A0zwweFEVnLpE0Ai8Q9OWYcdB1zNKwLEBtxjc45oHjshf4AMMWhwwRhRdBnjEU3iL3TIBscW%2BvDMwGJnW4omSkqIJxsnzyWwZBg9lQCsSZ2CK25fZnAEtrlT3WZ1xUoqsQBEiEMEmCZAjQU8EhBFQSUEVhPwf6Ekh%2FQtYOKDqg%2BIfAJ8CuQ0oaANSG8CrQwYJAhV0I0D4CXAOIBYAcYMUAO4A0AuQNYAwAWgJAFzA9A0AgoIOA4ARIJoBoDTBVATUAVA%2FfmHjl6j%2B5Pa79V8K%2Fh%2FQfNvjz3P7ler%2FHHh7%2FPw68DnObsHvPy3cPPA5wScuOB7qBzX7b8SuTXQrw88fvOjUnszbV9wOhztB3%2FrTR53FdNbVFq3a82jxmuwOcluBDDjLjOjALxD3%2FQiP39Y7a5Rt0oNm7G8V06nAGXPxV3oiByNCcCfXAkpuOrai62YwdiJaYXnQsst7b8q9lbH1AhQ4fOtIhMRO4kqFfJyARyYkd8VFgh1WJGVCPlA1ZMLjSDAUNwDDwkxBcqWcEmILYipcSYqtCIqlSAqaSAqUCAqkjRU7GCpiLFSkWKlAgVIxAqRiBUbDiowGFRIMKhYMKgwKK%2FYQV6wYrughXTBCtmAFaz8VpvxWa%2FFYZ4KujsVY%2FYqr%2BxVOdCp85FSnwKkjcVGeoqJdRUiaio4xFRNgKhy0VBtoqArRXysFeyurkV1bquqMqqonq%2Bh2r6EqfoBp%2B%2BNH3jn%2B5M325m%2BzqX6%2F4%2FrnjqtKKqtoqqPhqmWGqVIapJgqjWCqxYKqxeqp52qenapVdqkp2qOnaopdqh52qD3Krsbqs1uquGqqZaqmdqqVmapLZqjdgLkVYtPvgiXswWobLWxLWyK0qjACE6uL48VDS74vVFa9UPr1QitVAa1XzWq9S1XKUq4ilUQUqiClULTqhKdUDSqgSNX2hV9IVfB9XkdViTasMbVeTarwZVcjKrSZVYS6q6XVVS6qiXVCBdUEF1fgqrzlVcsqrdlVbQqrWk%2FZ8n7Vkfagj7JEfYwf7Cj%2FXof68j%2FW8f62DVWIarWDVaUarJi1YsWrEC1XsWq9C1XQWq1iVWMSqMBKoqEqhgSqBxKvuJV7g6ucHVwg6tqHVrg6vuFV6QquaFVwQatsDVrwatGDVnAascDVhwaoyAqiv9UO%2FqhL9UBfq%2Bn6vB%2F7kf%2B2%2Fx%2BtVskpnZEuCUxHC%2B%2FYuIK6NNKiB%2FEzIk5DuCcPq3Ew4GQBYmlqw4gUEVMiRKFQwiMCQcTgAAAAEDAWAAF5ItM%2B6bFophhd3N1nA4zIKh4NARWfqCooqII1UQ4kBYJ2AQsGyO2lAp%2B6Xiqm%2FCkfz5urtugisAuGzxeNHQh1A73Vh4dG0%2FNDkMQKtSO%2FBTm3DojsrbF3jq6kKdaxNxwpKvTKteAnM7mCQ85oHLN5AxXtO3FxElkoEAFo%2FY7SdVN5daSO3q5Y%2BGBpQAYrusw%2BEY9%2FXMmtYT6y1gbXXfGgzHr8ic6AN9hcvHwEYELAoOjr69A1yaVwaL10euR3YUZUZvQl5xZXoT8YeJLqVKFrjMLT83%2BN7REmekLvRn0TLh%2BZMzVhvjjOcuh7%2FDGoSIzhcgAEyu2q%2BgmErl0SoAyvHf0gOOHkuRFZQSSkFEDSG4HCQ838BiFt5mdNnEIYrPlCai6RoN3%2FEdkyVeA7o%2BHQvKrwD5CYAAo2RJZIeP1xRy%2BlJaWuskPYYJ6GKPdNLzxcio1M6LXHJDQbx0X1i8B9YnLsQYerRiZjBe%2B2alDqaPIASEoxCeRAUMVuivCDeCNo43Zi%2BmFz4viBZJrJMbwxhXGCv8CUG%2BGpgMJzaVH06hQdq5woKyZyKYDByVHQl05OpUqPrSuURMAxrqnfhkQENbMcnlzk3MLnnmnljBLSdHj488rWP0ithH7Mq2sETRkNmgYc3AZSu6gL%2BCk4IDhPtHR057XmxZs5enMzU7IR5rdjAD5bhqPdP0mGax4%2FBC5rzvd%2FNmFSTuivxBTftCPQY%2BTO9CX4l81r5FFfrkZ1yrTcaX%2FE35vu8hUNdTlgS2iD0q93mIVdiG%2Bzz6ZoWvKaG4axR1VGYKVxYs%2FhBQR7uUeb1mU%2F3VlT93WVa55WteFObdmuaGauUaHua6G9Lh9q5rpXj%2Fwgi3iPylvEGKzMA9lXBUjbXHUnsEBSjM4dcmrgF7f0G9lwAQt4RLmuXHbpvBr9TrIO6tAdGiB79MRHozMKD8uVjof8zfR8GjzHzhs033A2Py%2BejgTAGqXxpL%2Fw2WVk1lFTJqz%2B0kBeRuJCR5GRySPRQSmUbztwmWP9kLIWUhlXSVdCicr0AP0QVDW1JhE6NsgqFunp2ST1zYgQv6Qnhu0JlL3GiFmbc6pMG8mzBJsoRi1z3Z5NTM0f1ndDFjciaUQqsNg6uq3fi8dFUAWOQGs1VX8XhLFmvpemPhnFsJ4EJp5fMYZskQQsqfYfD9NJDx6cnQ0sTSuR2L40hG49L%2Bmrs3RoC4ghACgxYOijJAtdpXHsZI0rFXEhZYgy3algwWFOreuLxQmZTNtXroCxgYhVHmAFChJHArQSkYK5FLPlzPCQ38AzsClDlC4ke6RHiVatgqkBMcH5a6mGXLmcLkgxPCTi3IYssNhBMcXoBJkK7iAw%2Fq1cJO27YZZ1dgwK6TjpcOKZhOClzaJK94ByvnLhalwYwwHNGbpKKrMoiCUVvMU4ZDGftbGmdYDSWM4M18njvCm2QeRAFzCJCDrWq4fFsh0jgTZAy3lAyEhSb5p3l%2B7zqhPPDOxcQ5kAj9XEi83gCXQDB330FUKUN8JTMzokg%2BMHLm0D3oGAQxNjGVUC4qv3mNqY80W8Wma%2FG%2FRJg0Pokw2Jil%2BUKRbOEH5QZhYg2DwSICOBEYPtpPgwWBiCfyJ0YCZEGKrTfFYsGyw21JEW52PoQdw%2BSszylGkFpTMhd5kWLnyTIQai8z1ij55qLRN75GxKwkR9E1MhMUCbxmmw63GyiBjM6OORqQNMpJtSUqMssFsiIRB3bOWC1CBqx4cDrtymvUnfKZrNpclIQX0iC%2B0SWyKIyxEbrSIkB4ly9nnkYJu6fFFI5UkewzCvGzpCmkfDtvWO%2FvOQBSKG%2Bw4WeOGpxQqahRKjqs7pmglalwleZKZnV2WNi1CBepIZxSes8CtZlRI0GWmUOVcYlpvK0hUKRhWaEyXRViM53DzUU8eSDYlUJQqDMmUYc2RuqTtfeLBUIWJzpxmeJiOCoAXmCaSqYM441iWisAz0U0EQHSkfuH3o9uyZk0g2C%2B1Huy1lYiCySpvTSdjMKwTiKdQVCax08qRNA1Vs2wiL2IyamfCpg%2BlZwXvOo2sB1QB9xIdX6Bj6VzRgd4UoHI9PenyASnBA8k3EjsE1S2ipMclWB3LPJeWzSHOikaNhJsFX5zoP45XxaGhDK%2FpP%2FDIYztiS6vqMPACWcgP2kpZWjOfJBHYRQNI4tp3WUQGWpE8ZqoZEFvYJaFCTkUJPdTqeYpTEWodgDyHYOTQomy%2BoKxLC8BtejPZfK3UMphCswZ56qASoLK60kVHNgZzT8%2FUWcqkls5xsQ57uoPAv%2BCrnsSCROispXTpjPKe4ND10sCf%2FElOsPgR%2B1K2fX5hXhJfNGzBWCpiE4EjGUBgUzovLqcdL1yqDbTutsHLe0YqwBcpKRqcP65%2Fvot41Eg4cbCrFOObHzAyIO3Np2zmgIymMqrmdZ5wgWiOKMA%2BV8kKigbnyOAnZzQK1uMozbw7SBWI%2BtpCLJTN4yFsnUOPsR6JqbOmnG2mYUYJV0I%2FFDRgDb2YBKeBAzYRv4d82IRIjKNJ6kthxBIf4f6tg5Rewqogb%2BBL89Xa%2B8Y7mPwJBnr%2BqyHL3Me2KqwE3nnFG4NiIrI%2BvziW0DG1jcQIHeE7iAwtWHXwFYTmEfOmdkgt4Pr1n2vJwnSQymN0R0NLRTgAHjDVSIfITmkvlvfz7MU64jgUChw5hCXsYgG5gXyQ1osKsxCRhvPgsghFG5zI1CXCBIAwKkjyKLeqBc%2BfEUFiCvfGOta3gR%2FU26my2RNT0gywIO1yxoMTM8Mlfo35lpDQ4jfU18jrE6QiUumMhcIndvm8iDoRH8amzyNFXNUKcSoCnh5AQYr61lElsUE1avUS%2FnDanpv%2FZFa3VH2JIq5OrC2wDxYOhlkZf5BIr5I2JAQY6MewSa45Ob%2Fz%2BEjpgzBQTlG3AdVyHpu2GkjfOxGCSQ%2F4KBsYV%2B4WC4tHrRIEC3vi8DWBGimk2R3cQNWDhpiR%2F9KQZE618tdreVPJR485XjWwoxbnLTn6IZ4EjKrhRraDtVPs4zmDldmpWjWM5L49vWKkkh21cJ0GELX5Hje5CUKJRNkIrvqKWk7bw8b7gYD5fEhk7VgXTHJI0UsIqSimKH3B62CsLrQWXjB%2BoWwKWamDL6RlAYnwhMdNFIyfJuJIyo2hI%2BRLmmREVRHaJdaBYDQo4bDl91nK3Zy7hcqlXpT%2F%2Fg9jl5m4DVYTnaJOAoq7zjeA2QzPBWRnDjFKG0AJybS5gxwd7oVkVIAgAqWCrwA2TuCFHn%2BlQSxm2EjeZemixAGSIByWTtmzQII9iyI6QxlnEfiedIUpRSDRKzAojtJx830mEfqcSqHRLRGSUmpIkhYAfBXhL3h5wRAsiPnzp5CmVoG70nYHSlNBsQEOYNSYjVHmDMCMyyhMYHx%2BhksBoo78rYc0vB6ClzXpCsSQL0xuJj0lRG0q3NgS%2FgqHn0%2FdBeijOqfmwAAwNmamjdRSr62goEAhLCK0y0mqVtUz8B3F3pE3rUMN9wQoCtpvRAK3sFTK3tcPZnt6Z27rdUEcCb1qxd8b7ARVibBsC%2BRyonUCCcPwOsBKtzEuPpnx3V%2BQo3FTRLkQsTzT%2Ft5GIpAhUffp2BuiRh%2FhQEK3waIhUoJczWFQtyb9PP5ODdKmoRpQHa5EoivjH117VzUEyb9h3I8XFhYGY2GgobkujLXrm%2BbJ7HN7wo3WOTojHaQLy5ZQH60wuIar4h1s2FLyTWktIBtEtP6PSDSPebTewSizvHczvHVzmh8LyM8TZbIzBlYhsTDRW2MtA4tMbKoUyaOwZNB0EcTEoAHayrWzlDMhazQx8GCH8%2BXZI4EskKhE1hnN1De89ZjtBMDWCxLN%2B4bn5AnyOhxpTflbO1kA%2F0EGhUliSyMtWT0UMb%2BqEPinhEFYyHEbAUyp8tYuqYDRipLscjyGJA3zbmKdMTMI8V72v2ZQ8R1C6WY4qjndJBCREkDNEWaBovAOsU5JvqCCECn5%2Fq30Wfs27Q1NX3PB1CxWQYK4rW6gl2DEhCJLvzF%2BBEKd6LLjbQMVuJRpueMSQJN40n5WAdyXvuYQeXUQsoQDysgsemARNTywlJKFiZeuo5AiRfoTmTq6hkwijNVgqADIQ0SrFqBN9hK5RC2ZzmikwVm0CCZzso1HPlzzN0IP%2BQCIQZ%2FzA%2FJ0cIiWLfbbDGvgdRmzRiOWxhWyl0iXpQfpiIVEQuNo2d7rj0OZeiVOeay6x5oKlhwZCcg8KUij44xrtH4IX6UM37YQMPXh6QvlpkcPG94IVYA3iwMJ0L8LuuaogTlCTJsenAjL0PQ7L1Pi8hmGJdOqOJeVo7ECLPOdRHN4hjBEITrTPlmX622a1Nkllc%2BXvRIMYsWFbQasKlkKf0TuoImAklJXaN12zLmMOiREi6fUAhVGrkOVhqjWR2eenOmgUY7GLcmbnAqWpftrThQTmBEC5zJQBDcPyN4AoXnInBM2UJew3uo3Osd%2FVotG4JFRB1dhhN21R2ig74o0Jw8ZN7VnA0lWB0lDFZ5PDtyXLlhvcGuF0S6Wr3U2CqpnkDjwB2mBQdPGRuL5x1IFo03LEOsHEh4MKRvE9edrMh0Snaf0cShzOIJdiyBYWbPeMzTRGYsBHAfX1laNIl1ZVxzggRI5m51PG59wVXQ7HQGRYRRnGy89qI5okgmTpsdUtZgAxPvJ%2BWcqIbSWx6tf5yN%2BuJkKOjROUqEcP4y6WDOTFIXxQkr7hHBS7hmbyT8AljD77OJLW4CQGYAb2Pei8bNTgMttEECV0uBXZksyIJd39JlDyojumSt0T2TM5i3S2cviYGBEzQtmTKzAFB8QEcXkZq4YmJ%2FTDWdYLS0Kazft%2Ba%2BC7HwNZAJaVEY3kfqPHY2SBxchsqiGqJLn5a%2FmjEa8QgmABHka5AWJ%2BG18I9w3WjonkFGEwKhtgp0j8YPUeYEncSOLNhhwVJnEiplRLfp6lN7z5sAMYVx%2BA71pVUbhIzIaaNzUbAarADBLMSSoXqKXumbEiOijClhzIbSA5gGB2qtutd0MjQyWBaAzJmfqki7MMaEQAOCXbwaXixbEGNFnHCqmWg8qjxIZ0oeAxEPKD1A7yRyuS4AIRwOrQJ6DxVHVPpAc7aCkBHpHC9GMxBqe9Qt62zjQGJy9sjB5efNIj3%2Fyv2r6z%2BSM%2FzuFE0Za9wOJ37u2rcQy7P6SvWZqCuEJKtvjAUTarXAcyMQRrVOlrD0HTsN2KDiUivtwmgj5U9inAK5%2BC4IqL6iNHhU7OH98NmQILOWxNwJiPwwlnf1QAEMLagJuGLoYUdlqBRDn8QcRAg9AuLhe4myJn%2FEoxUfepXHhZ8Dk0BKaH6znSNmNJJ2IRdEvxoTfFkKRNn0cEvSio6ek7OG7AZljFvqNgRejEgmOwp7toPkAA5CIjKCsWmYPIlxUdVDDj%2F6UQEQZwMPCocey9jKiCj3ryLWjtGlYDdewTAsT%2FytgOZKoG6jDf%2FUzE%2BDBwpk%2FPx891KJ7wcBDtmnc4Zr8PjCwfnWIE7Tz5Wh4XZOloMKHqBYibF9JCb589kpcmC6MqgAH60Nwcj%2BnBhrvYWI7IfIiYD0IThyXLu%2BBjtuDKdFNmVqTy8ELHUIcco0LUngtn%2BupQtGnWSsHRGOZxzUOEULCoCKWugvY7ZqEN0MDmNHqeKtmwQSOPoR%2FZ0KGKGB2wdDYj1CrZsodEQx2TukU2%2FMDvJyPuRgDSC80jH6IO5DbRYrS0rIXfANDM017avY1V29khrSTX8G%2FWm5HQ3j02j1MGoCeHm%2B25tIebrUOsJUhfKhD0EIEeXj3%2B%2BQ43UQYWPGKRd5tI6RgOxzkuNv3Ji8YcsIU0cpJNn1rQt1eBb5t%2Fe6vSIMsxyrbVRxAHaSs8%2Fijk5AW1W3ajQf6DP51FkKbjEEaQp7ThQOL8pUajXNZgjP%2BAGWp2PntYtYtaMRzL3lOTlAMAU2jKG8l3wMD%2BbxPb8RDFLiiPnwnwm42DzJDXbmbGIZ0jLkON0Ub4bgHg3f5pBR%2FoVAu0YDFztE%2Bzps%2BP3bAAWSgSxlY2S3LazAF0KZAmzACvKJ%2FMz0beXxl%2BeIEFgZCLRMTD0eI7mFnojAK95ZgCTCfQOybhXCo6576fGouBIpcPFCU9ALkeU0pQaG70p3LmSrRNvUUN3vI9R8lCXjgQBKD9twFivCVAT47aBVWQPv7zSwNj8Un%2FSFG3FqLOS5c%2BWZHKZKVGCPSmIgHEwoN5C6HgtxiaB5%2BUvBrgQmTbO5rMJ%2BCuldZzfzxgdXp9XgD508hFWCeR8zw0tDDW2xoicZACrgqgnQ48NRFvjGjGQLa0bZ%2FYIPRHYC9plKdMERvlMGhAQeqDBMhf6LZGmyElMCwEIYOo1BZ6PH7%2BWHUp1YWZa7wqK1XoOCvECZSwoJH1Mkaogtg1cnvzmDI1q5S6K8zNTnhUkglWVoNqdHdJkfg0Fxp37eM%2FnNEjkRlbYvQhIWSCHT%2FqEBqUlbxYgGY%2BMSFSRxt4bg1PVnRhKNZIXooJOn0HVNY%2FcfiwOh4kjntxHmybS7MJkM71QCMhZGbYSMrJ68qAj1YN82a3v5utE6PJoWbuOva8RkRMPNZOJG3h4NcQ9LTUNP7WRG34U%2B6pZFDjhFpbJyEq7ddJp5LrxHhOcWeKH5m0I1Q2anhxKm%2BO1yIfm7BGh7B%2FjqYiPKEBJ6cFrT2ZB6TmSyLIpnTVkU%2FYqVla2WfZcp7SSoTzv6vLYtG8AgtXlxfWZxN6Gzmta1EwxIU6yE9s0x%2FZlSkSYE8X5a7%2FVPKA%2Flig684F00nmacRk4WooPYSFBnHTa1ebr6zgD%2BMcOV4BeWlJJLrL0qnYZSAVtBA5UxpOASkxyTpYRBUMiUqxjxU%2Bce5iSPwywJQRsno2JDcLSzoQnpUALmNJE%2BWSFPdsteXHMocr%2FC0IqI26humQ1wKQoHcGmUNYBVwIFZqI1azUTzdFmIOugxHeiO7FGrlsIVmnE3L1JrCuYeQCJCpQc%2F0JCGgQIe79NvrOoYeDQJ2REZcyhK7ihxb2NeHkVj0aI0LIicFJjQk21YaBO4G64TBu2IKBTzYheH2CASyWnlbZNFDbFlJqA1Q4kIljGpwnmhmXbOSQEgWsMmsHkBZYKRUWBv9HZZ1N1JSN64WPlCBOt7zqAJMKpczyNBpzQk5o%2F%2FxDjQg86ozQyN4waltVoDaLJOfWjYqewlULt9QO8N4AqlP%2Fo1ZIqJMaZ%2FORyILlDFoGoeY2%2FswI7MBMVXSMJXCUeRsJjHIU6kNEsAqZoBDoHo8Y8pZtM%2BGL8OLfcPdBbsbvRZuDQcyyrZ42OoTsMJ2GH21od%2FRCfgHrkeCyZfMOkWTSYgXtqYxGIGLcI5gKg%2FZR2xnb1upteR3rcNGITv8oKHpUWdLK9kIZlFfEtPUNAgnOY66o0dWYJq2a0UT3usCxxDZm0UIViE7Q13vLoyXH6VgLZoJt476o2dZ1DSsnihertfmTnTdREBRHm5ASIGxMbMSITKCmV5fMqgFiewxFtxqh5yfCPkmlKNcrJfmvyKlbaqps0Oa%2FBSPXk4FJjtWF2wOHfpFY63qA49US3T180HXmbqEjYsSpRFkkOVMCBH1C9JAJTRgjCWNAjl2MSA%2BvZjADldAJGTIoWBOcOEUI4qwvBSI4hMj8m7WHoFosA0M4Q4yS8XtN%2B5emVGJDGqX8D5SVbE%2F0bWETJRyRFYKQ8umFTkY2ZnV9Lz%2BVW9hgHq%2BHYhsrghzcANy%2B02yEIiJuDFngZnEHSFnTnqDAicaKOgtLZkRXBqGS3bgcqBK6B%2BmV5G4%2BxzA1IlYTTtL30wAPCkFZuhlgsViFEnA5Rg4UXmBbXBAW7JuNvZlXTVsYDMV305DdUPX6QyUFMwndSexwLkpBDsIQ4lUnD9QoEF8QmpcQk8FJckIIkVwvETqBSrIvHRim18B7iqFwNCcFoUKmSj9cSfX37WL%2BCT4mAKH%2BS76AYlpBE3eYErTSL68qrzEKiOZo1mbN1ujQapDrmTWb1s3iBTeQMCYcYfVeS5ks0rTlCPWr9AjV%2FbgZ8To6s7qOr3%2BkRUCKT5GAAUzFlHOkmV3fJEImmhCZ4S5ivYOcC3SUx70Is%2BgfKTQfQBsES9NEX4x0WTcQkWV5JKEJNl0UV8pDmBNnC%2F4qRYIkjLTUknCCTbfLBLJzy4rnSGTntJHjdpYIWlqzxK%2BG%2BRBy22IJ8gMQIibkjgh8Y9Q2H5aenHLwEJg2iDmhQybR8G3gfKxBAZwppQkDi9rFMfLSe8Fgalu2z9mKNwe%2BF24HWYNjNI3zoQfXsIck6YiAwCMhAsEDMvxfp9PxAAxF94h42eFp8V8BZxS3g%2FoQhPG05yIyOc5GxA27VgPq%2FN9uxGcdZCP9PAWYlmmiIlMHE%2FRj3IzE8YKgGEh8OmOkN4KuO6GYyNnRhoWNSgmY9%2BVfMfhBm7xIwZPp7ggg%3D%3D%29%3Bsrc%3Aurl%28data%3Aapplication%2Fvnd%2Ems%2Dfontobject%3Bbase64%2Cb08AABFOAAACAAIABAAAAAAABQAAAAAAAAABAJABAAAEAExQAAAAAAAAAAAAAAAAAAAAAAEAAAAAAAAAjPL%2FpQAAAAAAAAAAAAAAAAAAAAAAACgARwBMAFkAUABIAEkAQwBPAE4AUwAgAEgAYQBsAGYAbABpAG4AZwBzAAAADgBSAGUAZwB1AGwAYQByAAAAeABWAGUAcgBzAGkAbwBuACAAMQAuADAAMAAxADsAUABTACAAMAAwADEALgAwADAAMQA7AGgAbwB0AGMAbwBuAHYAIAAxAC4AMAAuADcAMAA7AG0AYQBrAGUAbwB0AGYALgBsAGkAYgAyAC4ANQAuADUAOAAzADIAOQAAADgARwBMAFkAUABIAEkAQwBPAE4AUwAgAEgAYQBsAGYAbABpAG4AZwBzACAAUgBlAGcAdQBsAGEAcgAAAAAAQlNHUAAAAAAAAAAAAAAAAAAAAAADAHa4ADV2ADV8AC1cEs3pishg2FfJaEtxSn94IlU6ciwvljRcm9wVDgxsadLb0%2FGIypoPBp1Fx0xGTbQdxoAU51YoZ9RXGB0bXNPyK3JLMApRwa%2FIMy1PPoJDx39kimekZX1c%2BDSW41tEZBuFiwdwx1dRoPVA2vWPSlsSDqhNkqYfhrqlVUGD0J3HEAgZavmtLnDC5WBriSpD8Uk02KsUkJ9vCFz2CZXAd5viwGZ2xcVYRPa1bEIai51nMYlbL2ERuB2TCzLAbPWWRZ3%2FsZ%2FKBjLk8%2FgAZzK1OaxNw4oGBbsNhx6Reg5HRFVCrwa15kGmJEy5kX1YypVm%2FHo7TjKP3l%2B%2FnuCTOyiOa6S8QEJbuiGYNlCnM7tHChCHRRQHXQh7yPXASlcvc5KrNKol6orb35kbo%2BiEwl8d230cfWPwTy00bFDRYURYGchbwsoDcaR2AJsFGCrbWCzBdQ0qCobWwLfueqAzSkzaHX3yCjDlGYPV0VZqVXlqbr4poRaG5NNPMDv5MCHkLSFyABMRBhMiGSZiDgABYmwsLWDjUZCUnHwvXt0VAUy4%2FqjwVgjfUqp1evzUqutJB7DW99Cq5aEhGePsa4omKUp7LnSQUz%2BZq51pU72ApMxkaVZE9jF3IGKVnF0GlK1E6iqLJXFzy1BEv6Kr0ngCzIgVANRwCkVHYJj86Sv2dzqgVrjYKlg8W94FbPGQghEbTakZ4AoS9h0u39DOoRJTA2iirs9xa5m9Ir0KwkogoqFNVDbTIGO0%2FWuJYfp61Kq0bhgbcbnvbTDj4HBESsXMdvrvpp7Owf%2FS2EbndoEoglO%2FjigGAuLUTUmG07ZGlRCZ4QZLu81tPEgTtAvF99BxfnxNslgVYH5Jc4AfHwsiktDBO4wjgjizFMsIeBTGmIYrhtrK3tvtBu5tYB0PDMXILUkFYPM%2B5yLLGOU9DtoDLYWLQig%2B8wNRZbJZZWeK5JyKNwumLgP7X6pqgiZMFUvfCTl6Urx1gUOjzhcICumUUsiNESZCmTANkgHoh%2BKU0t1fgQYOBkNfp4MRiJysezS1Vz%2BahE7ohM0iJBn4I%2BT9RJN%2FuQk6SjQGwC%2Bom%2FSD7Zq2RxvcSjtdxHfo7NtktA46mEg5gBkTtMKu7oFb1KgqwqBLzQqZI%2Fs4QSRhYF3ani1URTcMD38kDDqlc3DChmYJTCR9WpaWrYFiXeNi7jYa1Oe%2BSP30gxVyeC10DYOakGpWaU1qkQ9OXlujEbM4A6A%2BQ243TA2QnI8mKzNXNo1HPN1CFawST6uC9dkyQTqq5bOKkkuGjz0nkj35Sr%2BQ%2FkLGg2iQMrTKImSGshnX7%2F0Jyh0JziDbTzxp3IrbosXgpchLcBJpLLUBrFbt%2FU6qXqAaNFJoeBItBoqgQlPZkpTq31s5VZsgIkFupAno5G9oKwCGRqv5294xFqOrEpewcjx%2Be06mxDkN85c0ckmWmMzbkFX9YHAf83p0EsnBywjZbcPxZw91kqg7voxasp3VfDhEDAufUx0MTddLO5kCyKkUBwOm%2FMurQH4bJQgK%2Bp14dkBBhgxpBUkTlSbTE8DDu9qKiDSCtvmPY7FRMn0wuS6XR7J%2BnpjjeaDNwiOgIKUWCP9aLb%2BXpc4toQCryp6gjCVq1Cl1Di%2BtEx4WnBp2hmGZpEksZwTSggXuqAWD4B7WAMcir2wmA%2BI43ECxUSeTDT%2BxgR3O4XFPOGxHh09lxpScampLahUbICao0db7%2F%2F%2B4CBMcCokQ7aOQ02MOzh0NEaJGGOvPR1t4sY1I55lNfQ3IkF04onnAomXxiNg2EbBbPTMBBlv%2BggPSmkb4GNFW6Ehd6nDzJlnIXFfzr1bVWQlfylDodFBbhCDf%2FVB13j441dc2rx3h4hfAWIJuZqbH%2Fwbuafg%2FnTQJ9bnMfR3U6TwYgDQJIOPOtmZW4ZHsR2VifZGaC6Pzv4ZzC2nSAaqSe09F9MxuI4UmUVA2RAUqBUIETEIAhB%2BtBhsxhVMXUmv3RPe1grhYWLM%2BPHwwO5W069qIgDXtETXZQ3741DSk%2BvO6y8k%2F7Mg6GFC5fSK02yXZ1XV0NZe8iknoIbSFnDm%2BbMP%2BBCQhoLKOeU3FVNQ%2BgPEntwkHT950cQYEYQc%2FXuL4nxwcRW2bIN%2ByskPaD5Rz6lN8LW5IDLYfuvhxlLcjWXSADeTshWsJk%2FHCuRbwjqLcx66fc6UlF33HipliQ1cvfKlgRpVcsmIsiYnJjzJIovUyqi%2F2OTQcIwt%2B3WW44BAQh%2F2GymOIscSpIt0YUePiwOCJN%2BQ60lqkSRbWi10lotzgWZsqzEI7OGFGeIoFyqli41%2FNn7LfLQ0qtxkaAwbsKZQ0D9s%2FwhBqoxhAlxCVNVF%2FJ6rsUBQ49MLtR3ICtKPLKZ%2FQPEeIRgWUNLbNR3v3tTaL8uiXO%2BOj3tSJc56KJHol9nGPuclbrQpCn4keT05ETSOQ%2FDwwKjCRLgIzBi7x%2BU7ByTZGUWcGLPY0VtXWC7kQ38C5thIGJx%2FxLM3KsoGyRwC5AFUNWPzU0QBCaVXo6z1NCclLuPVA8%2FwWuNhiAG9CPPSSlIOCuh2AQM1d6MyIEIQArIa9YenQ5ug37h9gPNDHVLImcjE91ewI7pz7HgOEVqTD%2FjREYRtEoDIfgxzDePkVvHWJAtcpCJ%2Bg2o4akZpphRUQ0U92lJcKZGJI9mnpl8UVzpMi8SBGXUAPpgcS2cDAusSE6q0hNibhCgZHLReLsA%2BSv8wF6LiDL3TogB1DsO%2FHeMg0ETucRO2hIOvbp1NVkFMclluNmBQbTy%2Bosr2bJ7oWdUtSHi1s%2B2vWxq8njY1eW4BCVr2EqSyIUuFKS9iwVF5FBGeg0hRcHwCKMtqYLBfvVSYXHdGZK3Ug95C2d%2B3t9ZWEYqq6F4TocgcDS4tI8cvEEXK1%2ByB9RofdKpHoA3eP9%2FB%2FEBG%2BIgvmwZ4Iir1SOYFEtUG%2FoVkECQqoPTdHoNpQKpA9K9k7TisAUBsKPtWgBriyeOxs1o%2B4KCIFumN744dH3Yf7X8F426LGtEhFLULhlKFgXF8Wq2D6kFSBkViLad9D9U%2FP6A%2Fr8SE7jsr9s%2Bsb5ODWI5uS6BkZJI5RQ5QDVZ5%2FKOG6Dzc1RLQKAdGkgwLiZLQdEYQ9yhQLtD5kWr4wGHTv4GqloWePyHYyuy3Ek3iQVQkdkAz0MxcsHzccdMLO8KFh7ywo4jXywraIhIicAI4dWdD5wEXBhsMklzbWc8zi8opC3IlPsLXHCWOqOgq4iPU6xyDS2tdSLnlhSFjsCCWvMRt5TAI30EHR4f16NYyzoG%2FoKgCUsW4182Wvj5gpb0bGGLe8YRIYRGVgF2hwIlEfm7eUwwLZWW%2BmmBZPggPnIKI0b6G%2BlHCncx0wkaVPRQpZKWIIrzh4yC4Ar2vTKzhVKSutNi1dSzmM73AGUXSBJrQH5J4Dfb%2BRU25tYrIVdLr4ogiwTE2i2hl39ffJWHNTSWq3PvVJplNqDTJgJcvCHYoQAuHeOew0gZGfmX3p4D0aSr1BhXbXRA1qipfS6LiggtiT1eDg4FTCWwCdAFC9FCOZ52EdrFetMBxUdC0dfnqpr0mELJE2m5FVMvwplyf0XIKclHa6%2FQrw%2FFOVkVKK71Ab5iAVWm4GA3HnkCJhYkW06XJ3TDGB9YhVW9RuC39AFUcFWwU5eTNzuck7IQty7ZC9IjAGNHuZhQ8yDWZhGUoNyhDcKYQiUDqAC782makzJ1o3XJFIEDXgObv%2BTlS%2FdAr5rn2C%2FCDmkI0WO3cSTJwSLrS5dBdkyfpxAu4XghB3jgGShG8UCorOibUp7NciZgEDLmT6eOxDegpLRk7HomganEaTmRZAAMrhobApDjFWtOxht%2BNQngtKVgGL2yy6Qnsmju6DAg4d%2FRvxHa5mBaEMcBekCMtwaPPGeKFPMsgAJTidusMLUbTAUBJMOmXRwhONkoLPqBhpTuLSYN%2Bf8aeX1NKSxF2OUST9ezObkHETTsr04iWClpoFDE8OdIiDPQJqkHhnUPTcE43OsKBGS%2Fzk6F57sqVmhZKjPxle2S%2BiIE%2BMXOiTOoRKF0Q7mbNRYGPZDp5eIdPOZHboa4CTvwnlZb0zCOW6kZJh6klDDvYghmQ2FCDKB5DD%2B0nImiNcfSzaGT8aSPzEZjMQ2GPpA1Ws4Xeysyv0zSSMVVsiOoiowo2SfYFdapUBsWIoRXMAKYdguyVcwqX%2BzVWYLiNddi8p%2BxMV4dQIoUs6SQ4C1%2FBjtBw0ocOzLmMkEv5D8N4%2FZu4gYA4ryDb5Y3gkIxdb37qMCWYmDGgsyEE00y3BZ4FgyT%2FdJLHxMQwx0gViQjWL0QyBfcufCgRYYGiCHrxez874MrcqldLCEQLkCCK6pWCnULCh%2BVK6FW%2B1nm%2BN668e16QTKWprvRw3mkwitjPefHt5QKrVumkXsvsVrHdAJrodfWckxhhzknXZ8cMVIvKphJVfhvWbhoZbbgo3fygOr8PlKcVEYLTmUbjp8rTFlPRtPrdA8tljZ0REfnhwApCZ65Igtn1gBROJdPCCb9ZIqlQUq3W89ZjSgSnUz8nEBW03JCcQ%2FSxouQtYBE7ichYHbASPB5J1%2FzVfPINn38CqTMws1KKo%2FyvNXpDgBvCI08SBLSwX5Szp6WlpzoPEio8DsNzZQqgUMoq0%2BNMALrygrOlErJohXvIJ%2F0IqziZok6OuApG2eoGAEFsTc6yWf9eRcklYZRO3PkA%2BW8aN5ME8aLNC3Kdwtm64WyqytOEW1WQIg6bOFHAs1ovo3OfCvvZASxBcxg2SRCRTTJDBKajFH0LL1kSBroe6L9xvVxMCIFS7Zo6y4ZOEIkAI9QtGVIKKBlCvUUEq2S8FiR7VkJGbvBFaS6UzQV%2BayV6NKw62tbJbEjkJ7AMC17DK399DZr%2FtE5sUtaAPwaHNj9VCoVB4VAG0iNI9IjDo0mr97FWjYeDRSr3pstZTVZ6nj5Vp3IbssG3g0r9E2eSmHY97LYobIHPnEGkKDJP15WPWtwMgS8HeLd6NEnP4mIFlRJB4zLeDeoBElpUNRIQMzLbRQsGLj3DZhQytDQPLAUE9JWHiLKAJxVTOJNZsObEiutLqwox%2BM51t7vJQhBeQm2i5bTa4D8qIUjqI1sL9G6Vha6U6IPUabeCUMIufG%2F%2F6USyxymXNlfnVinkNvKZGUjz0EWKIgZEC4WkUEr%2BgP%2BFpkIPUVM%2BQEJPxFxKDlpBEeiUSaTgCm4sEfRnBxu0eF%2FLgLp0IFHMEt8aZrsQzTF3wRw8TdpzHNGMZrHHa6nU8KCQppWBVpJ8b2Xjq278mtoTfrgfAMSAm3cYEcDw%2BzcSsXTaUyd2PH6DCU0DdBiauxpsyoKlAh9IUAzS32X%2F0d3x7h4gL36Q5sC4YzkbttmSwhenP5pxxrBEEcoAohUGB1jHGtB2%2BI0FEcCM2y8EY1e2NPXJS7wp7APp46lC7gSit7FEFQCIDnNX%2F196lJs%2BgXTyJrXAze%2FQ%2B9GEFC7p5W7W5FEooh5QlO01B1OcYDH4VTmRSO8fHPjRo4FkT9GrnUZw9pXnDplu0YFyOaAsLOkxdsu2gfYJ%2BDzBNihSUutbDbDy7VKS3KwwUTChYQkWCmldyS%2Fy05EvDGbLbpkDfbbHNGEhTSiaAEDmoKTERX3pEuKYJT%2FlNS4IawkdDACC5Jk4hgNa2EGV8yblsXoSHDrqHDJs4JDXLLA67oCyia7LABDzBMInY5gnZCpFuyyuaWXjKHRgy409j2wNaI1bGlosUnhaB5iqHHZf2%2BbDPpsIwoahsWRL69BhhyPHQBUNCyBR%2BUJzMOBRMxTVhNsS0%2B1n5kboqmNZcC%2Bt6HYVscRaBeox%2Fvv3%2FxwdoUoRvs6CamykRGihd8HTNaL%2BxRuoo3QVZvFT7xS9opWLiNbQRti9PXbNg0J5WDsxaNesdmkYOcwpiqsURuor%2BS8hhgWniGGll%2BtD55enFSsyATy9MonNXUJV5Q7eAouzR%2FP4HlA5YWBYYjm6NDAEk%2Bx9On0MGm65%2FEm1GKndnRp4cv%2FjFAdM7hnXsaXnGKAeK4aE%2F6BhOq1%2FAWmgCMQ4zC8G0wBzhuMSeeVhgAl0jpwicoR64K%2BBYlYbWz0gTGAGtI3puhx3F5%2F5QKXradYFuhJPYWq3ITCUUNLpugdVBegedngCO%2FDN5mJBWzGEL932jL1YntvCgzzLeR0WczKl0J4g8Gcbo6p5LOslpYBw4kE3ZDMiHPjBGyAUjkrWXqYTrl7gRUwex0zKVekIhoI0dsFRDtQxsLctjOlRs5Y2gYpQeBORQFR4C3hXh8EnZUzuloqFLFATXzpzv6k5XoHB3fZLNUiPV5DvAfroLwH8tYhkcOxWnHqePfQulM0DCPTadXa%2FTpoHYkh9BeeAwpmi9Kbo%2Fm88ob17pFzKP2lJpfWxbyD3PccS041A0MQWUqNDHOPOFt57Q6TiHQEKJQsI4v1JqcD7Q3orOdsLvExRQwS0nlUtV%2FpQbx0wSlrRSneWAQ%2FJhPaT6rMvIcid93ahrnKe34YxGA3D30BI2lEiLGh5iAUkBLBoXRshvpjGJGLzGcvonIqzVubgEJv4mbEl7JggQUWb6AYaQMmGUXEwIjylByVLbgcEbUQL5RFiRkX%2FbOhzb9XavzmFpR0cOdx3etgoaCPbiL5gR8o0wJNdPMCYcmyP0SDmmsW8o0O%2Fy5HNRxqz3IhmaxvIT%2FxpN8Pj%2Bx4i%2FGawfTOod%2BpvHN9BMNQUKG555l7yAKsma4r8JwVm6gxqBECXHA3e%2BdCsONR41WrcokynYzYqB0xlCdg9Nu%2FVL4rgwOiTVy8K70TghEjAOHeFBYvGwmkrDIzlwQsyBsr3K%2FEBFKO8UQ6J1hU%2FYGFA8fGgTnBoNnAmZc%2B9S%2BXnpbpJ4QKgdip6TZnI6woSQaYgxGpdaxxSuQkxu0avCBOSwchx0SS0x5HgR6iz9AkbeoDFTnGInFfbnMUP%2B8p3uSQu2CVkHxeVeEMICXKlVDsj89UY7AfyMvxTyws7ilT3y4zYSLVToLb1IwDJHJ804mZKVSKgSOa0mHCQrjWQLaz9LrCiISicIHspx5moJ%2F3Ng4rjU8aMqTDl5gjJAFgAMupkEoWEalYEtHh8CvvMqUP0Ra4v6BRr%2BdgNXFRLo%2BjKWRhaP4x63qqfsnw%2B%2FlDAo2doOxQP7GwahE%2BiZ2OX2l5DodFT8bGiL0YglcRmgDoYIEaRBLqdbj7HFD8xfZz45H2Tg6upN9XjuGCxtdxuVuRjssowtewrBo9gBM3T7d77hNjF9rd8QTMjwGLx3oWax6aa17t0I2gcG6kcQgw%2FphwfsB4gsCGgMGZU8P%2BORAg4iQDmTP9XqByg%2BjtRqWtpaHjiHSL8CNah084UP6Rfjx8GU2eaRw4mH%2BA9Ad42DummqhAj0%2FeMNS3V8lEHUSc1ntW779KspgJUBtJQEpS59ODiBRghAyioIrf%2FKoPh0eAJWqxh%2BSurG%2F5xVdzZBLgKEiYy4izBuKhCRIhfoADEt%2FB%2BirTWSOZVkcfzWBbA%2FAO817phMFhWQnvTwzjirEna6JgrjgHyk%2B8nWk0k06KkkSOOryl2OrOta3U1Vai9SLWxcE3cY161P64wA5VUgBExRGc8qtWCkEHIJfWtybVbTm%2BhrXnbVSsP4ucJTC9onJ8N4r9lRaV%2Fc4a2SZKmPNCgEUW7LDBXhvFxUvZYtnIuGD61WQtIrDXUc13hksUbImFeHrIBgvnG4ogmKBk5CClzY5DWqCCMzdrHBGSSOTyO%2BE8inLMGSApQqKJB3XKm%2F%2FMFoO17KuwfwqcaqjAyaJ5JOWW1Myr%2Fs7ZQiw%2FPqVAMH%2BlK6DYqjGUMcAXnVxy6z6CDl6j5mDa5EG4j8C6pr0hKyRNnoiR1vl9DWOfC2%2BM4v44bO3onXro%2BNlz00ZlGV2ICJ5CcCazVCJHIETBqVFhGT7KSBdNDv5ILpSacSTL0S6fX%2FP1CEIT5NZgcwpI0rkV7LqiHRoLUAPjXEqCZ5mLntX5JkkUEelCsU2tXCMZ6cZivQI6hYQNbXl4nc1sSNtBUTkQ8Y442KxRe7Uy5yOzB%2BUlA3MhvFmXweJJj%2F%2BG%2BqwJFWFLNYp0JhzD%2B4sl4JYn6a%2FvShCCo8hchMfrswjZgUqiToKfoOGaHdIAnKE%2BiEedBkyLwMSoNVX83TJERFy8PLMpBjsXtBITuS9lpPCTVl%2Fvs2Aqzlzwnj7lpl6VX%2FQ74tWqUSzaKziwue1phr9BpcZjNc%2FGXuJUq15TMDnCsJS0X2wAtW5JQA5MaTyUH4cDRif3MDxZx3Se89P4WSIvEEeLjToJbXf%2FrRhBMtRevJxuf%2Fs8EK4woZOFli3yTq3xqjBjrlierqgmUpFA15HFkeUOuLDjuhzLDjAGKK6WThTynzd%2FtCQWU3Nzd8%2Fa0q%2FxwZYn%2FUPEHU6lsdG%2Fn8gN%2BYACURCU%2BW%2FldrXpdUK7WxhgWmNd%2BLDoQFCU0sFyHn3KqFz%2BIg9e2C5oe9EOi7KdTBxPE1k4k5tkX%2FoZzSih8DJDFd%2BrITKNSsAAGtscSW9VDasqkEamMzeUOhRqRRAj9lc%2B7An2YOdL46GdcOLAsgYaFsR9hs0ToUzZ9rFRLG1%2F7eYLz1l5ijumbe1druwaHNFzZjtwt%2Bn7paZaMZu2EIx%2BlxX%2F2SBrWJQQM0wmE19eWrGPIVMeAzVWWRp76m1skeqzaBBZ6So4eD8Gpv31bn%2BnO4WG%2FOg%2FB7xQu9kpA3eZL3w9cwzrZfMmbUSk5OiF3Qx7bQYhL0VoUQQP3Hmps1bBJDQU0qAJpWwnb4iFOMBthzwP81ilVnh1bIuk0C9Xe%2B1kSK%2FK%2FMYOh7vIa7ghqGEKzCiHrehs3cA1pzgec5NpLDtCqMPp1GVECA4QZKiZX0hQ%2FGqjOhhObmpH0vwx0WHctTrmGC84Ub6BOQVdXIqoxqMVNhQjd%2B0CYMRk1zp6%2FPnIOsW7k%2BhQEruSB7%2BDEGv1lziYEEwur9gsigQBG8EJ3zeigdA74WvD0h2IbdNzPw3okAFsdmi3qKH41lxijDPDtvZcEzXwUnRNn4WpCP3vPNHhO8czUiYjRn6GRIQ4SymW9MhjUu%2FjbWOhOqNeh9OSRNh1EaFZcalxYnJMLCpTlEDttzYxhNCcZ86PUpbEkFmkU5HRiAF9AahZ8jQ769NUzJGkq9YLj9HWZLEK%2BIryXyPLZHAAHsBSe5moWq2RRQT655EACRYKQ1AR2mNQU6hNdrqLyfpSeJ5PrccWf3dXVxmIidWyyIkCm1v1oFYgyGcXwrCRPXPMLYHRFvGVuYyAUhzgYntJmDhE4VCNKoSxWlSFiFuMGumZHJnCJyAdT%2BHcgUhIEJZgWOjmy%2FZWisKRYo4JjuPntQGSxlJg3XJ5DBsFM3kGGQjqECyjqYFW6ccOkCDy3EhUt6taBIaHclyblt3Xxs353KjciddJC7gI4cZaPj4zBxOVNfei9MW9cLUHspngSFFni3AL7sLsbqo3totPWMf0yD2bdWKWuK2a4eF5jKcYCZyvORgcHeETtqeqhAYtIyiFGAYJQMOX4VJzPjyDKiavWJRtjWCnaTUdPR6FRkTfFAARc%2B3Ln3oFDETvxxiaDT3roIpaWwEEjRlhjvs9ZKiU2o1HJOMuVRFAA5fWzMgAqSKDaSLNQcQZbaFzsgKxXWIvjaOqsoiS0kA1bx2TN4NrJBVMJcmRWNIqrjepyobiDa9yXYKmJvgQWZhEBvF8wEx0pMQqCzcf9JemmcVMROHpvzARvqDrI5WOXmah0Zkh%2B6PIozOYm78ieRAJObTPxSCLuwQiRlWaLSxJ5hgIIrjsEUKPWMqRFuMgh1FsNDFw5jPGKPTWzyiSEIS6IPweoS55G9SZZ6wcpW%2BHYMSkoSETssJ3QQM9bQRo1JdCQdS1np6F5WR9wujL48y6xB4M6Y7FMnX7f22J6F5gyYVK0QlgEQxVXFUuC964aXqqhT5cX8XaZv5hVzeTU7bSoy40QuTOUjLVShZVi5iWJMAbFhku4I5QyO1x0Pm%2BcTesk5XsjnzwoAIsmXCFbWyIZQuawuVuXuR8DK92lWJDrNrbFtNbCj5sTTCx7e2Wb0UydtbZ%2F0CSIT7OnVIY0fRntwN3jNOdh7nGpmmq9CbBm1uLafMptryjPHHp7tKZEuAL7OjXHySRjUkXydXE%2BSrNxA2Um5Al8Dh3EZC5V4SFynxsMTKCAIMqEqNKzuJCQM3tvVBjRfT7xHSuCO72a6pSo2wn8%2FaXBmKI9sW2BccnPF8aML8%2Bohhb7ciWy%2Fxch7McUey2CPGCyVKaKDX8%2BSBNgqZqMLbCgZ4NPkIF6NfeH7gtElIrOqbudNqU8yyyewVZneKXuzObCUxU5b2tecTa7Jn7SE6UlSYMTkMfCs3Q7fVCaqK5k6pf%2F2wW%2F%2FosIJEgW3skUNgQHyb%2BsAi4ECMNcyjicIITuXGyXkkRIXyN50Jg3r1FpMmaQSUl9pGxnNMp8jf24vS5eX%2FyJYlMUISy9e6JooaPn7fiuG4QEscaDgCZpra85ygZUcJInLV6C314YPJdG2UL6qljb1QV1ZhrNcFecs0j2qb5gvkKHOFxHphwdBgEJc3y8qihwdZCQpJ62h1voTUccffiDJEzkU8jbXRvLFdPbcmVBUhArEuTKQFe570IglefLJ30dWmVAtx23vIGmF7N6auVNpZUQVHNmAlGgjNet51laJgLQSpfZyxBEqLwoCEGlF6ISp0NUmhUHT5a12%2FZElPE5UGO9AVnKpae3D5llVvXAHK0FIH3uE8AXFPF%2FSwx3OdCN6aViMIxEVcqv1UsLJo03R0grVOHRogBCiYVrK%2FqFBPmGrDyXLgr6DxBMSKnf1uSBgiRjCiwL1QoM981XHZnusKIVJ405xXwx6aBUuM2YXS0jaCPwaC2Zdp07J8gxM1KnpWMqNkRCfPaYTelLbBmd97YeNAOFaFOlV29YQn0qIInmIeMFxikX4U1pEusNYtOX6tKZKkgVONLhIF9ZPpxNWGA5fslgv82Lx49LF6FltT3Qp7q4Rcu4hKczn2m1GTA4unFBAkDCqY%2BD5s2dyVIfDeGeBgwDnPbGYXQqwM0E%2FBCl69QtVYbUwkQZAtSB618VkAzCPAs93Ip9qWnBMX%2BRUX0PFxCACZQwpfvNvAMGrD69RE6JSyNNOvRD8v3gzw46n8oB8mFQiYiwgidAyJgrfY1SaNrL5QDEjIIgYLECALRSK49wPmSO8jZLnesJ8oFZjWJyTrfBrNRCeOMoaVxOojhX6WVAhhJ6dvBPZ4AbMXC37YPHBFKUgA7t8mCk8U07mFgWg3wbOZDgsEZBOC%2FApoLJL8CzpXhZuoEh0ntzsvrUPhE40%2BUUkCAm26DxGMecbxuJ%2BpPJct9BZL6lVcWLmHps6SSRwqmRJeypwrd3vNnIawZkqBn%2BumMrwB%2Fc%2F%2BIAx3X3Ehjr%2FzJIVUK8Luxlv5IeNoBQPnIhvJDZfGo8KIpLh8O4iRusiuQOtytJ61yCvQUGFmCxEEliRlQmkN5wrVLkx3CUrlDG3ABe14lLsoysj9hXY%2FTJpUb3tCvpw8Ez7Wb20lfIScq%2F6wGFIrBkgzjtNLBoYqAgJoKvDHcdkTRNbmMKP7Fha6v0z1qPmfqQzKW%2Bi9g0kSWn1vQuqaJyaTAX7hrJwJgfaPjJvb6wXroHZRAD5NH2E2KaWtBw9TGd9mIea9%2BPrxlBpyjnQhg6rLogT7414uB8V19PPcBZUhnNx%2Fhr1%2BtX%2F1jKG4nnHv2EtR3VOjo9oWEibOHX8508Tra1pFg4lnAwoQ2u2JcsDi7diOc%2Fuhvd8qexCvYgoI6m9VYAg7Vl0PRXiuCdgHdKDIIHG0j73u07ULaOJJ60Y178Lsgtd7zYdOUGlMCYhR2Uhyglt3KUjPCpM8MKjVS6OgTHgqD1SSQ%2BqhzInvSk8VzFP1cI8vLxtdDvH35uPzMi4mQtJCrVUqhBWbQRke9Sjt9laOS7Y9YqUkXldpaAoofKmUNsx0D7eYLc%2BspsKbO71qdmmaGglAJjo4kj6XlnIWS1hQZORC%2Fh4i%2FCdcbaFFuxb0AYMJ7EdQExeIHEdPRtCxVECvtxHzbEyldDvie9cGKwImUuI0xEL9W%2B7FhefRJ05ePV427NJDYmhOCwBDNBP5LrIiblD6aw7pSeWFA%2FlDoWYMm%2BZEcF16VDdA3ALq7hDBlLUzNTL9AoVyczpCwb7xHucfK6T64W0AnDzYLg0HYWadOMPdoP%2FlliqiAlAWP4rio6stY02elA%2FLOPBnEr6rsAqtMRsS2g6HJtNANGwpxTdZEP5Xt5mE2gPs7dE0gyQv%2BFdd8QTBEqmAeMHtNnjBtKvg7KmIZCj9303GT9mWQXZxolBupTHIhJT%2B0WN7uu1FbRp6NnSRDIj1aXRJD25s%2FAD5%2FIc2OQ0iDp7%2F3Dbv3Oa8McFBhXrPpAKzhrFANFpcnLmEVTXjq0MO5sJAPVxFbMh93VfD%2FDppG4mBzXSgVfXJeWNNxoKF8QTwcQFXwQPB7QLE2PENdF%2F4vDL9zn0ZgQ1i6Nyr35KAwetsESlUtEENQbCFOeUFb9lg4Q%2FW5lUNo2fsscGbWY4T6pynpP0Krl%2BJFEfY%2BGGHI3aj8aBO0K%2FndAEPa5FX51Niq7CEOhoB2hSpGAgBT5%2BuzxAMzSuVEeQmZIbYew4tM4UsHYdZtT%2F9ibeR1u6rlX6lBQlSBT6LQ9YUEAgmAxLkAKQL9PSm%2F3NQF4w7ZvdqRqMJ5DYZh3j3I1rDmyXyti0llyZjkLnoPtHHwZd%2BfwWVz9ztMTMCFjpKBVWAdcYhRV6wY0kRv47nqddzEhQvXsqNstE6GNiLTd8iliAfI5vfm2KjfTQwbxz2uFzaUL0A9VKWzB7VrWS0QvlqVw9VCXOB6RDSgbNtW05PB7pEz%2FHZkv%2BXQTUD8mSQ3mJk%2FEUe3%2F2ixiuDVAOBfyIscXixo%2Frh7BHtl5KSBigokAOClzsk5pj5X5S9GLKgu5AbQNotZBWU5zoIzScHQKjeFNr0MiX0Mp%2BlHmHKuaDcfU2H%2F%2FhJmeXl1nPE8E%2Fk8ULZ%2FCLYtwJWG4CHI8h5ySfOAFbkRVFJyi0KYkQ%2FfhDAjciw08ETminGEMzG%2FwOERVW0AEslZEl4sfr5AYRKGVSMzkDSQ%2FnhkipQ8y8EF9ZRGKCOxRzfpNMubhc%2Bs9lZBHqNegMaRLozjP%2Bg8CUsaVzp5Wd0ZI5SaeSdNAD1HIc0vTPw7SLi4Jpa1gGgtEY865KzsFCn6I1RvKT3r6BVdYGsBPWdVzeLfbxKi8BVQVzd9f83goEpezGYiAXT8S%2FpW37TxnZ6f%2Bog248Vvj9otMMAmzAfvCpPYmXIx6ZAKAwBH737j2KJpWyuPMnFIBfqRrEBYiTiWVjvdx5T7k0dwFjgjLrLVm28m%2FXLNfjkSOzkoh3hangxcOjvxzVDIGSxYBxI9ak%2BDsrVTPAlMWZD7OThbuxdkWjCtGwtH4QzQdpmaBsHV8Yrg1iAK64TC2WMbQJAFFciwJFPSRQ86OtUrnPSODgRE%2FhD4qWAHDlWBDy1KPUCEbpodyyU4TnaIFzU%2BtJJAes10UhzVTNE6fGDGUN33wCgAZYoIz44wHk6fDO7wGbAEwmcVQg1HGGByFjYGdwJD1joA5AM8olCJ1LlTUGB%2FkhlrmbJbCbD4Uj0GZTy06zCTjOeVkJKZzqk0nE4%2B3RmlgDHpJwCwwZKOl8SEEH%2B8TQK7R6TiIPAy%2F5M08zWqjpXg4KWF%2FMNQpvipZJ4KZfGsivxCXyinAY16NjMD%2Bkgtfc8pGpAgSyN27l%2BuW3OjjOCnldBAJLpzjAYdBoh3b0yuYkLj7c6iwxR9NHW9WBeGVYjvaTEHVq2t96HA16vtKz3ZgtNuJgpjnNZRGEjbmQuiQEBJ2BdgHxFDqf0F1dQJcS4sIvDHlCASh65anDjgr07Qa98i8Jb1rAbSdOOz0cM9wlKXm7ugzOMTmi8EbeTBIoHrudZ9RSwEtADDsgyFwnxyfzXecDzLGFMmkRrGWCdnWVnSMMcc4cl7NaF%2Bt%2BgTHgy9s1SV05LLaw7YYgNxNKt2kpiEgpahsRp%2F0tarSWdfS3AdWYIAnrT68WTwX1vtPgL7EMcIzmOpOxL7oZh%2BcoizveUkJVmjedZZlkwkno1E7%2BjVJIoz8APlgweTgHUL%2FGciPnYgtfrq4TtxE4adiNQ2ZgyJHWYWmrMlW6ebFkPaAUwzKsAhoGXxXGRGKFObHKQOqFOnGgkyLajFNwhUa4fqva2yI2DlREZ6p0CNOGwR4XCrS4K3SH8pDQGvZIaDcMPtJUoLRM0owJ0iT9QcdRK5IRIIpAOzsUotf3TbAVvbQH8n5voA6kUzw6LqVnwPkmnYxgJLYiQ7hQYlEsYL4k5GCZvd58ypvZfwO5t1fXMTj11hE8GuAZhX78JMPsK%2FJ0yQqDPk4Z%2BJbbXS1tia0EBwCjgWUJsUI18clQ%2FL%2FH39pOY3jRcZFFfW7bC5v98f%2FwQjY4osg1CYvJfYmKVWbiPLEpDvlTEGLjUbCmh74cUqKtsVVr9hspTEdTKrKSRjqUHkhwgyUQeNizUsUp3cLmGnOoxPIuzYDGHFJxwclXasrQR5Pp4%2FX9adXL0zyaNRcp5govE%2FKIiLMyYKgb3rKpuxbm7t8U7GiR8qcIvzarYOuIr0z8D1QgHRWmwQj1jMXJlqpuDBiVUQD80Fnr7quJElyEAs47dXRoms8yEtA2VxNaYbJmUQ%2BlsKhyYLlk2q0QMXQSsMctgTGOka0GYae3AxbsfNKwpf8YnyAYZzDx20P8xvD5aQ4OkVtbj%2FxeO9gPGmBGT3BiXsWroQWXXm7Mw8XnUAttSlNyNEsqWLOLy5MJLmMa9m7Abm0SuOJF9RWA8VDp5xMP%2FI6LaAKUmkqt6%2Fxs1XyWrgcDo5hjmvshCSHhWpwCludJPk5i4bpUhqFw%2BRmK4VAI0O11JGtbQ64l%2By0LUdW7GarSUUwP47kW2CYDEdvsA%2FTXw0I4OPf2SvJ0FKjn7aZxxwVp2xjhpWMTDxaZMkiOxaFFLydXq16fefH2qVJybgXVpioGcKFhS4AjNTEa5T37zLo22Qv1apFD5qUjB9w8yA0vSc2RMiA7xIsRIGBTWOjHH9SZlK6QJGru7w%2Bq2GoC22fzSVxkr%2BWlT9rAABqi3RiLzDxns68PSEUIxqrqFw8oMUhIeL%2BSdTHAvw8M5C0b29DIIfScMQS0TKwvPEq3kAQvxMTC0D%2B7tnB7QNRliGiWl0NuVnIUY7QMwRkP%2FgVT2WDBX08%2BWLDc%2BiW0mz2CZ3IAvWqesMkIe3lWqMvUDL5Q33McSklm9U0P9SHgPGGVlX40diyUBp%2BpfWi%2Fh9sKTOvCRCj%2BeFIWvUXobOyAxrHlhKFGhOiw1vyKUiNMgN3k9No1jfVEpQEU35laY1OWX0u%2BF%2F3AcQq9opTw0RwEyxVosGLDgIkSdn7hs%2BIHrv2jR%2BJUh2kADlTtyX8HxtYxLUhMLj3%2FFpJAhfxzoRspqTIQicEOQtI1iv4n0xi9GiED3BLS%2BriXyEyU1v6KfcGAWCaq%2FgQ5kImR6wna1UoP6KtpT9XLI4EebxCRQriHsHkCOgDlZM8hJEHcCfGIERpbdeZFFHtE3lBjH2cIQ5p7TNVfRTwBkflxGhmddY2YfZbMF0bFv76YdpbH3dxSKmVVsblZW2xdvOxqSIQqbw536IFhJKhELagVlMG3LQqHU43e%2BRZjx4BJExsLcLX1oShyJFvhFevBTFOUF3Exw2yNBWwMCW5QA%2B7UmPhwM7AMOXRddPg6OxuaNAmiDYRKlcHo4FwUeta%2FLSOUyYddHQi3OFkb4z35KYG%2BxJAOZ8LTMyJ%2FCgARNXgZ%2FC%2BfKy8W7VwKPzhRpDnIMS0ClN6sPMpa421GfuLwApsG0C4FpdCsaLM0NtsctgKVSkeql94%2BXUmITqdGBajY4m4NmDFEk2HiFjYtNLmZSxNY1QM4KakEvIQIFts%2BOJ0QCRKvhCmQcfRAjN4VmYgb58CBUMiSUpcyuEfRFZS0SThDQPO4aFcJiNJUvlFdO0s8RaeSdpOSHscV%2BJAIchHCniOYTsEqhdLZtWVSiAw6hEDO7LI4or%2BkXTE6zB0CA9o4NUeZIpS0Fn7Q8lU4X9sZNCO0uPfjoWqOaqDVcbxBJSAs8RV9IcKmOPY%2FLDUnXDLSYfFT1xyNTWRLKRW0kFxctTIuvuU6R%2F%2F9ApGo0EHrqGH7dEmsI%2BgA0UXpfNwWFxUHz9CYK9toXP6IlTFRhuGh7z3bhwL5qzzoRAF8dkwboKslbtuftJDrshFMoBNaIvpSXyAFRCCKFOKEkzCkB3NDQB2qtV%2FANwHNea%2BAUDr6WWScJazRx4glReLp8vQ8sFtz%2BhqehlJO6MM5NMIc8%2FkWnwbE768NqCDKBi%2BpY288WynJ1CT2Kq9%2Bo6rhlUpRatsVIsacJhA%2Bq8M9X%2FUQMRZhshDAvsXwlZfxDn%2BWCfyJyLFA2s54on9a54PSC3WgchQWZLZgEl8xGrFUqCofhkvqYtXjA9XyewEKlnAtD26XlSvqtdhXOT%2Bi5BrX6S6hHVcqbZ8qbh%2BEzffUpCfTG5HULg9DQQaQ6ENkkq3DvUSAQwcxh24qkmtdRoIMDxOVDdy0T2w3afIBABsQGxnqJaAOY1gWawTUuhslaSivzrXaPcRyGhUkH0R541UbNvLKiY070WOGYY4R%2Fg1rfKhHcjoV4p45o21tldJXmpG0XsOekNlYucZlkAWkVUHtjkSeUbdfBMKrGATodKL9arS5JFVovaKRlOWbNJIS6GHxuLt8CX%2BBYQUYDfxlQrQQhL7z6vChINNDAVVN0rXxaKjegwIPOJf7rXfHBBHGpBNpaeLGFXCBrWAdpIwF6mcE7pE2z4HdIxcWkU0QA3TKjZQ%2FPNc4VwWA3OqmXuoleHBmMRLsU3ENaVgIpVnIWvBLVDYNLzVRdIefms6mo9VoRQZ6cCkQSOdK6KDkWEMZkQyIEM6QUltTfQ1xFpxUL%2FlFho06RSy0MhFQCIEh5FrTToDEgpZU4QcT%2FbYWc9XTPTTM6ZiDUk6d8MHSyFOgi3cE0Oh5I2Tv%2FThHNjxg7A0zwweFEVnLpE0Ai8Q9OWYcdB1zNKwLEBtxjc45oHjshf4AMMWhwwRhRdBnjEU3iL3TIBscW%2BvDMwGJnW4omSkqIJxsnzyWwZBg9lQCsSZ2CK25fZnAEtrlT3WZ1xUoqsQBEiEMEmCZAjQU8EhBFQSUEVhPwf6Ekh%2FQtYOKDqg%2BIfAJ8CuQ0oaANSG8CrQwYJAhV0I0D4CXAOIBYAcYMUAO4A0AuQNYAwAWgJAFzA9A0AgoIOA4ARIJoBoDTBVATUAVA%2FfmHjl6j%2B5Pa79V8K%2Fh%2FQfNvjz3P7ler%2FHHh7%2FPw68DnObsHvPy3cPPA5wScuOB7qBzX7b8SuTXQrw88fvOjUnszbV9wOhztB3%2FrTR53FdNbVFq3a82jxmuwOcluBDDjLjOjALxD3%2FQiP39Y7a5Rt0oNm7G8V06nAGXPxV3oiByNCcCfXAkpuOrai62YwdiJaYXnQsst7b8q9lbH1AhQ4fOtIhMRO4kqFfJyARyYkd8VFgh1WJGVCPlA1ZMLjSDAUNwDDwkxBcqWcEmILYipcSYqtCIqlSAqaSAqUCAqkjRU7GCpiLFSkWKlAgVIxAqRiBUbDiowGFRIMKhYMKgwKK%2FYQV6wYrughXTBCtmAFaz8VpvxWa%2FFYZ4KujsVY%2FYqr%2BxVOdCp85FSnwKkjcVGeoqJdRUiaio4xFRNgKhy0VBtoqArRXysFeyurkV1bquqMqqonq%2Bh2r6EqfoBp%2B%2BNH3jn%2B5M325m%2BzqX6%2F4%2FrnjqtKKqtoqqPhqmWGqVIapJgqjWCqxYKqxeqp52qenapVdqkp2qOnaopdqh52qD3Krsbqs1uquGqqZaqmdqqVmapLZqjdgLkVYtPvgiXswWobLWxLWyK0qjACE6uL48VDS74vVFa9UPr1QitVAa1XzWq9S1XKUq4ilUQUqiClULTqhKdUDSqgSNX2hV9IVfB9XkdViTasMbVeTarwZVcjKrSZVYS6q6XVVS6qiXVCBdUEF1fgqrzlVcsqrdlVbQqrWk%2FZ8n7Vkfagj7JEfYwf7Cj%2FXof68j%2FW8f62DVWIarWDVaUarJi1YsWrEC1XsWq9C1XQWq1iVWMSqMBKoqEqhgSqBxKvuJV7g6ucHVwg6tqHVrg6vuFV6QquaFVwQatsDVrwatGDVnAascDVhwaoyAqiv9UO%2FqhL9UBfq%2Bn6vB%2F7kf%2B2%2Fx%2BtVskpnZEuCUxHC%2B%2FYuIK6NNKiB%2FEzIk5DuCcPq3Ew4GQBYmlqw4gUEVMiRKFQwiMCQcTgAAAAEDAWAAF5ItM%2B6bFophhd3N1nA4zIKh4NARWfqCooqII1UQ4kBYJ2AQsGyO2lAp%2B6Xiqm%2FCkfz5urtugisAuGzxeNHQh1A73Vh4dG0%2FNDkMQKtSO%2FBTm3DojsrbF3jq6kKdaxNxwpKvTKteAnM7mCQ85oHLN5AxXtO3FxElkoEAFo%2FY7SdVN5daSO3q5Y%2BGBpQAYrusw%2BEY9%2FXMmtYT6y1gbXXfGgzHr8ic6AN9hcvHwEYELAoOjr69A1yaVwaL10euR3YUZUZvQl5xZXoT8YeJLqVKFrjMLT83%2BN7REmekLvRn0TLh%2BZMzVhvjjOcuh7%2FDGoSIzhcgAEyu2q%2BgmErl0SoAyvHf0gOOHkuRFZQSSkFEDSG4HCQ838BiFt5mdNnEIYrPlCai6RoN3%2FEdkyVeA7o%2BHQvKrwD5CYAAo2RJZIeP1xRy%2BlJaWuskPYYJ6GKPdNLzxcio1M6LXHJDQbx0X1i8B9YnLsQYerRiZjBe%2B2alDqaPIASEoxCeRAUMVuivCDeCNo43Zi%2BmFz4viBZJrJMbwxhXGCv8CUG%2BGpgMJzaVH06hQdq5woKyZyKYDByVHQl05OpUqPrSuURMAxrqnfhkQENbMcnlzk3MLnnmnljBLSdHj488rWP0ithH7Mq2sETRkNmgYc3AZSu6gL%2BCk4IDhPtHR057XmxZs5enMzU7IR5rdjAD5bhqPdP0mGax4%2FBC5rzvd%2FNmFSTuivxBTftCPQY%2BTO9CX4l81r5FFfrkZ1yrTcaX%2FE35vu8hUNdTlgS2iD0q93mIVdiG%2Bzz6ZoWvKaG4axR1VGYKVxYs%2FhBQR7uUeb1mU%2F3VlT93WVa55WteFObdmuaGauUaHua6G9Lh9q5rpXj%2Fwgi3iPylvEGKzMA9lXBUjbXHUnsEBSjM4dcmrgF7f0G9lwAQt4RLmuXHbpvBr9TrIO6tAdGiB79MRHozMKD8uVjof8zfR8GjzHzhs033A2Py%2BejgTAGqXxpL%2Fw2WVk1lFTJqz%2B0kBeRuJCR5GRySPRQSmUbztwmWP9kLIWUhlXSVdCicr0AP0QVDW1JhE6NsgqFunp2ST1zYgQv6Qnhu0JlL3GiFmbc6pMG8mzBJsoRi1z3Z5NTM0f1ndDFjciaUQqsNg6uq3fi8dFUAWOQGs1VX8XhLFmvpemPhnFsJ4EJp5fMYZskQQsqfYfD9NJDx6cnQ0sTSuR2L40hG49L%2Bmrs3RoC4ghACgxYOijJAtdpXHsZI0rFXEhZYgy3algwWFOreuLxQmZTNtXroCxgYhVHmAFChJHArQSkYK5FLPlzPCQ38AzsClDlC4ke6RHiVatgqkBMcH5a6mGXLmcLkgxPCTi3IYssNhBMcXoBJkK7iAw%2Fq1cJO27YZZ1dgwK6TjpcOKZhOClzaJK94ByvnLhalwYwwHNGbpKKrMoiCUVvMU4ZDGftbGmdYDSWM4M18njvCm2QeRAFzCJCDrWq4fFsh0jgTZAy3lAyEhSb5p3l%2B7zqhPPDOxcQ5kAj9XEi83gCXQDB330FUKUN8JTMzokg%2BMHLm0D3oGAQxNjGVUC4qv3mNqY80W8Wma%2FG%2FRJg0Pokw2Jil%2BUKRbOEH5QZhYg2DwSICOBEYPtpPgwWBiCfyJ0YCZEGKrTfFYsGyw21JEW52PoQdw%2BSszylGkFpTMhd5kWLnyTIQai8z1ij55qLRN75GxKwkR9E1MhMUCbxmmw63GyiBjM6OORqQNMpJtSUqMssFsiIRB3bOWC1CBqx4cDrtymvUnfKZrNpclIQX0iC%2B0SWyKIyxEbrSIkB4ly9nnkYJu6fFFI5UkewzCvGzpCmkfDtvWO%2FvOQBSKG%2Bw4WeOGpxQqahRKjqs7pmglalwleZKZnV2WNi1CBepIZxSes8CtZlRI0GWmUOVcYlpvK0hUKRhWaEyXRViM53DzUU8eSDYlUJQqDMmUYc2RuqTtfeLBUIWJzpxmeJiOCoAXmCaSqYM441iWisAz0U0EQHSkfuH3o9uyZk0g2C%2B1Huy1lYiCySpvTSdjMKwTiKdQVCax08qRNA1Vs2wiL2IyamfCpg%2BlZwXvOo2sB1QB9xIdX6Bj6VzRgd4UoHI9PenyASnBA8k3EjsE1S2ipMclWB3LPJeWzSHOikaNhJsFX5zoP45XxaGhDK%2FpP%2FDIYztiS6vqMPACWcgP2kpZWjOfJBHYRQNI4tp3WUQGWpE8ZqoZEFvYJaFCTkUJPdTqeYpTEWodgDyHYOTQomy%2BoKxLC8BtejPZfK3UMphCswZ56qASoLK60kVHNgZzT8%2FUWcqkls5xsQ57uoPAv%2BCrnsSCROispXTpjPKe4ND10sCf%2FElOsPgR%2B1K2fX5hXhJfNGzBWCpiE4EjGUBgUzovLqcdL1yqDbTutsHLe0YqwBcpKRqcP65%2Fvot41Eg4cbCrFOObHzAyIO3Np2zmgIymMqrmdZ5wgWiOKMA%2BV8kKigbnyOAnZzQK1uMozbw7SBWI%2BtpCLJTN4yFsnUOPsR6JqbOmnG2mYUYJV0I%2FFDRgDb2YBKeBAzYRv4d82IRIjKNJ6kthxBIf4f6tg5Rewqogb%2BBL89Xa%2B8Y7mPwJBnr%2BqyHL3Me2KqwE3nnFG4NiIrI%2BvziW0DG1jcQIHeE7iAwtWHXwFYTmEfOmdkgt4Pr1n2vJwnSQymN0R0NLRTgAHjDVSIfITmkvlvfz7MU64jgUChw5hCXsYgG5gXyQ1osKsxCRhvPgsghFG5zI1CXCBIAwKkjyKLeqBc%2BfEUFiCvfGOta3gR%2FU26my2RNT0gywIO1yxoMTM8Mlfo35lpDQ4jfU18jrE6QiUumMhcIndvm8iDoRH8amzyNFXNUKcSoCnh5AQYr61lElsUE1avUS%2FnDanpv%2FZFa3VH2JIq5OrC2wDxYOhlkZf5BIr5I2JAQY6MewSa45Ob%2Fz%2BEjpgzBQTlG3AdVyHpu2GkjfOxGCSQ%2F4KBsYV%2B4WC4tHrRIEC3vi8DWBGimk2R3cQNWDhpiR%2F9KQZE618tdreVPJR485XjWwoxbnLTn6IZ4EjKrhRraDtVPs4zmDldmpWjWM5L49vWKkkh21cJ0GELX5Hje5CUKJRNkIrvqKWk7bw8b7gYD5fEhk7VgXTHJI0UsIqSimKH3B62CsLrQWXjB%2BoWwKWamDL6RlAYnwhMdNFIyfJuJIyo2hI%2BRLmmREVRHaJdaBYDQo4bDl91nK3Zy7hcqlXpT%2F%2Fg9jl5m4DVYTnaJOAoq7zjeA2QzPBWRnDjFKG0AJybS5gxwd7oVkVIAgAqWCrwA2TuCFHn%2BlQSxm2EjeZemixAGSIByWTtmzQII9iyI6QxlnEfiedIUpRSDRKzAojtJx830mEfqcSqHRLRGSUmpIkhYAfBXhL3h5wRAsiPnzp5CmVoG70nYHSlNBsQEOYNSYjVHmDMCMyyhMYHx%2BhksBoo78rYc0vB6ClzXpCsSQL0xuJj0lRG0q3NgS%2FgqHn0%2FdBeijOqfmwAAwNmamjdRSr62goEAhLCK0y0mqVtUz8B3F3pE3rUMN9wQoCtpvRAK3sFTK3tcPZnt6Z27rdUEcCb1qxd8b7ARVibBsC%2BRyonUCCcPwOsBKtzEuPpnx3V%2BQo3FTRLkQsTzT%2Ft5GIpAhUffp2BuiRh%2FhQEK3waIhUoJczWFQtyb9PP5ODdKmoRpQHa5EoivjH117VzUEyb9h3I8XFhYGY2GgobkujLXrm%2BbJ7HN7wo3WOTojHaQLy5ZQH60wuIar4h1s2FLyTWktIBtEtP6PSDSPebTewSizvHczvHVzmh8LyM8TZbIzBlYhsTDRW2MtA4tMbKoUyaOwZNB0EcTEoAHayrWzlDMhazQx8GCH8%2BXZI4EskKhE1hnN1De89ZjtBMDWCxLN%2B4bn5AnyOhxpTflbO1kA%2F0EGhUliSyMtWT0UMb%2BqEPinhEFYyHEbAUyp8tYuqYDRipLscjyGJA3zbmKdMTMI8V72v2ZQ8R1C6WY4qjndJBCREkDNEWaBovAOsU5JvqCCECn5%2Fq30Wfs27Q1NX3PB1CxWQYK4rW6gl2DEhCJLvzF%2BBEKd6LLjbQMVuJRpueMSQJN40n5WAdyXvuYQeXUQsoQDysgsemARNTywlJKFiZeuo5AiRfoTmTq6hkwijNVgqADIQ0SrFqBN9hK5RC2ZzmikwVm0CCZzso1HPlzzN0IP%2BQCIQZ%2FzA%2FJ0cIiWLfbbDGvgdRmzRiOWxhWyl0iXpQfpiIVEQuNo2d7rj0OZeiVOeay6x5oKlhwZCcg8KUij44xrtH4IX6UM37YQMPXh6QvlpkcPG94IVYA3iwMJ0L8LuuaogTlCTJsenAjL0PQ7L1Pi8hmGJdOqOJeVo7ECLPOdRHN4hjBEITrTPlmX622a1Nkllc%2BXvRIMYsWFbQasKlkKf0TuoImAklJXaN12zLmMOiREi6fUAhVGrkOVhqjWR2eenOmgUY7GLcmbnAqWpftrThQTmBEC5zJQBDcPyN4AoXnInBM2UJew3uo3Osd%2FVotG4JFRB1dhhN21R2ig74o0Jw8ZN7VnA0lWB0lDFZ5PDtyXLlhvcGuF0S6Wr3U2CqpnkDjwB2mBQdPGRuL5x1IFo03LEOsHEh4MKRvE9edrMh0Snaf0cShzOIJdiyBYWbPeMzTRGYsBHAfX1laNIl1ZVxzggRI5m51PG59wVXQ7HQGRYRRnGy89qI5okgmTpsdUtZgAxPvJ%2BWcqIbSWx6tf5yN%2BuJkKOjROUqEcP4y6WDOTFIXxQkr7hHBS7hmbyT8AljD77OJLW4CQGYAb2Pei8bNTgMttEECV0uBXZksyIJd39JlDyojumSt0T2TM5i3S2cviYGBEzQtmTKzAFB8QEcXkZq4YmJ%2FTDWdYLS0Kazft%2Ba%2BC7HwNZAJaVEY3kfqPHY2SBxchsqiGqJLn5a%2FmjEa8QgmABHka5AWJ%2BG18I9w3WjonkFGEwKhtgp0j8YPUeYEncSOLNhhwVJnEiplRLfp6lN7z5sAMYVx%2BA71pVUbhIzIaaNzUbAarADBLMSSoXqKXumbEiOijClhzIbSA5gGB2qtutd0MjQyWBaAzJmfqki7MMaEQAOCXbwaXixbEGNFnHCqmWg8qjxIZ0oeAxEPKD1A7yRyuS4AIRwOrQJ6DxVHVPpAc7aCkBHpHC9GMxBqe9Qt62zjQGJy9sjB5efNIj3%2Fyv2r6z%2BSM%2FzuFE0Za9wOJ37u2rcQy7P6SvWZqCuEJKtvjAUTarXAcyMQRrVOlrD0HTsN2KDiUivtwmgj5U9inAK5%2BC4IqL6iNHhU7OH98NmQILOWxNwJiPwwlnf1QAEMLagJuGLoYUdlqBRDn8QcRAg9AuLhe4myJn%2FEoxUfepXHhZ8Dk0BKaH6znSNmNJJ2IRdEvxoTfFkKRNn0cEvSio6ek7OG7AZljFvqNgRejEgmOwp7toPkAA5CIjKCsWmYPIlxUdVDDj%2F6UQEQZwMPCocey9jKiCj3ryLWjtGlYDdewTAsT%2FytgOZKoG6jDf%2FUzE%2BDBwpk%2FPx891KJ7wcBDtmnc4Zr8PjCwfnWIE7Tz5Wh4XZOloMKHqBYibF9JCb589kpcmC6MqgAH60Nwcj%2BnBhrvYWI7IfIiYD0IThyXLu%2BBjtuDKdFNmVqTy8ELHUIcco0LUngtn%2BupQtGnWSsHRGOZxzUOEULCoCKWugvY7ZqEN0MDmNHqeKtmwQSOPoR%2FZ0KGKGB2wdDYj1CrZsodEQx2TukU2%2FMDvJyPuRgDSC80jH6IO5DbRYrS0rIXfANDM017avY1V29khrSTX8G%2FWm5HQ3j02j1MGoCeHm%2B25tIebrUOsJUhfKhD0EIEeXj3%2B%2BQ43UQYWPGKRd5tI6RgOxzkuNv3Ji8YcsIU0cpJNn1rQt1eBb5t%2Fe6vSIMsxyrbVRxAHaSs8%2Fijk5AW1W3ajQf6DP51FkKbjEEaQp7ThQOL8pUajXNZgjP%2BAGWp2PntYtYtaMRzL3lOTlAMAU2jKG8l3wMD%2BbxPb8RDFLiiPnwnwm42DzJDXbmbGIZ0jLkON0Ub4bgHg3f5pBR%2FoVAu0YDFztE%2Bzps%2BP3bAAWSgSxlY2S3LazAF0KZAmzACvKJ%2FMz0beXxl%2BeIEFgZCLRMTD0eI7mFnojAK95ZgCTCfQOybhXCo6576fGouBIpcPFCU9ALkeU0pQaG70p3LmSrRNvUUN3vI9R8lCXjgQBKD9twFivCVAT47aBVWQPv7zSwNj8Un%2FSFG3FqLOS5c%2BWZHKZKVGCPSmIgHEwoN5C6HgtxiaB5%2BUvBrgQmTbO5rMJ%2BCuldZzfzxgdXp9XgD508hFWCeR8zw0tDDW2xoicZACrgqgnQ48NRFvjGjGQLa0bZ%2FYIPRHYC9plKdMERvlMGhAQeqDBMhf6LZGmyElMCwEIYOo1BZ6PH7%2BWHUp1YWZa7wqK1XoOCvECZSwoJH1Mkaogtg1cnvzmDI1q5S6K8zNTnhUkglWVoNqdHdJkfg0Fxp37eM%2FnNEjkRlbYvQhIWSCHT%2FqEBqUlbxYgGY%2BMSFSRxt4bg1PVnRhKNZIXooJOn0HVNY%2FcfiwOh4kjntxHmybS7MJkM71QCMhZGbYSMrJ68qAj1YN82a3v5utE6PJoWbuOva8RkRMPNZOJG3h4NcQ9LTUNP7WRG34U%2B6pZFDjhFpbJyEq7ddJp5LrxHhOcWeKH5m0I1Q2anhxKm%2BO1yIfm7BGh7B%2FjqYiPKEBJ6cFrT2ZB6TmSyLIpnTVkU%2FYqVla2WfZcp7SSoTzv6vLYtG8AgtXlxfWZxN6Gzmta1EwxIU6yE9s0x%2FZlSkSYE8X5a7%2FVPKA%2Flig684F00nmacRk4WooPYSFBnHTa1ebr6zgD%2BMcOV4BeWlJJLrL0qnYZSAVtBA5UxpOASkxyTpYRBUMiUqxjxU%2Bce5iSPwywJQRsno2JDcLSzoQnpUALmNJE%2BWSFPdsteXHMocr%2FC0IqI26humQ1wKQoHcGmUNYBVwIFZqI1azUTzdFmIOugxHeiO7FGrlsIVmnE3L1JrCuYeQCJCpQc%2F0JCGgQIe79NvrOoYeDQJ2REZcyhK7ihxb2NeHkVj0aI0LIicFJjQk21YaBO4G64TBu2IKBTzYheH2CASyWnlbZNFDbFlJqA1Q4kIljGpwnmhmXbOSQEgWsMmsHkBZYKRUWBv9HZZ1N1JSN64WPlCBOt7zqAJMKpczyNBpzQk5o%2F%2FxDjQg86ozQyN4waltVoDaLJOfWjYqewlULt9QO8N4AqlP%2Fo1ZIqJMaZ%2FORyILlDFoGoeY2%2FswI7MBMVXSMJXCUeRsJjHIU6kNEsAqZoBDoHo8Y8pZtM%2BGL8OLfcPdBbsbvRZuDQcyyrZ42OoTsMJ2GH21od%2FRCfgHrkeCyZfMOkWTSYgXtqYxGIGLcI5gKg%2FZR2xnb1upteR3rcNGITv8oKHpUWdLK9kIZlFfEtPUNAgnOY66o0dWYJq2a0UT3usCxxDZm0UIViE7Q13vLoyXH6VgLZoJt476o2dZ1DSsnihertfmTnTdREBRHm5ASIGxMbMSITKCmV5fMqgFiewxFtxqh5yfCPkmlKNcrJfmvyKlbaqps0Oa%2FBSPXk4FJjtWF2wOHfpFY63qA49US3T180HXmbqEjYsSpRFkkOVMCBH1C9JAJTRgjCWNAjl2MSA%2BvZjADldAJGTIoWBOcOEUI4qwvBSI4hMj8m7WHoFosA0M4Q4yS8XtN%2B5emVGJDGqX8D5SVbE%2F0bWETJRyRFYKQ8umFTkY2ZnV9Lz%2BVW9hgHq%2BHYhsrghzcANy%2B02yEIiJuDFngZnEHSFnTnqDAicaKOgtLZkRXBqGS3bgcqBK6B%2BmV5G4%2BxzA1IlYTTtL30wAPCkFZuhlgsViFEnA5Rg4UXmBbXBAW7JuNvZlXTVsYDMV305DdUPX6QyUFMwndSexwLkpBDsIQ4lUnD9QoEF8QmpcQk8FJckIIkVwvETqBSrIvHRim18B7iqFwNCcFoUKmSj9cSfX37WL%2BCT4mAKH%2BS76AYlpBE3eYErTSL68qrzEKiOZo1mbN1ujQapDrmTWb1s3iBTeQMCYcYfVeS5ks0rTlCPWr9AjV%2FbgZ8To6s7qOr3%2BkRUCKT5GAAUzFlHOkmV3fJEImmhCZ4S5ivYOcC3SUx70Is%2BgfKTQfQBsES9NEX4x0WTcQkWV5JKEJNl0UV8pDmBNnC%2F4qRYIkjLTUknCCTbfLBLJzy4rnSGTntJHjdpYIWlqzxK%2BG%2BRBy22IJ8gMQIibkjgh8Y9Q2H5aenHLwEJg2iDmhQybR8G3gfKxBAZwppQkDi9rFMfLSe8Fgalu2z9mKNwe%2BF24HWYNjNI3zoQfXsIck6YiAwCMhAsEDMvxfp9PxAAxF94h42eFp8V8BZxS3g%2FoQhPG05yIyOc5GxA27VgPq%2FN9uxGcdZCP9PAWYlmmiIlMHE%2FRj3IzE8YKgGEh8OmOkN4KuO6GYyNnRhoWNSgmY9%2BVfMfhBm7xIwZPp7ggg%3D%3D%29%20format%28%27embedded%2Dopentype%27%29%2Curl%28data%3Aapplication%2Fx%2Dfont%2Dwoff%3Bbase64%2Cd09GRgABAAAAAFsYABEAAAAAoUAAAQAAAAAAAAAAAAAAAAAAAAAAAAAAAABGRlRNAAABgAAAABwAAAAcalXC8EdERUYAAAGcAAAAHgAAACABCAAET1MvMgAAAbwAAABDAAAAYGenS4RjbWFwAAACAAAAARsAAAJySvAJmmN2dCAAAAMcAAAACAAAAAgAKAOHZnBnbQAAAyQAAAGxAAACZVO0L6dnYXNwAAAE2AAAAAgAAAAIAAAAEGdseWYAAATgAABODAAAiTweHjMhaGVhZAAAUuwAAAA0AAAANgJiWP5oaGVhAABTIAAAABwAAAAkCjIED2htdHgAAFM8AAABFAAAAvTBwRGObG9jYQAAVFAAAAGrAAABuDSPVk5tYXhwAABV%2FAAAACAAAAAgAgQBoG5hbWUAAFYcAAABggAAA3zUr5ntcG9zdAAAV6AAAANAAAAIhLlGpmlwcmVwAABa4AAAAC4AAAAusPIrFHdlYmYAAFsQAAAABgAAAAZYr1LmAAAAAQAAAADMPaLPAAAAAM8MFvIAAAAAzwwJLnjaY2BkYGDgA2IJBhBgYmAEwltAzALmMQAADagBDQAAeNpjYGZpZJzAwMrAwszDdIGBgSEKQjMuYTBi2gHkA6Wwg1DvcD8GBwbeRwzMB%2F4LANVJMNQAhRmRlCgwMAIAC2EJ1gB42s2RP0vDYBDG723aSIrSUESsiHcIWqqDXbvFRe0gBJw6tTgUCx2Kk926dusixc0P4OiXaQZzjx2cnNRFhPiagENdHBx84P693P0O7iUihzLbJGM9mb6tTFrnTWhjSAEVyLfZCgnt060U5UDacrdd3vnYNVWvWlJHPa1oTRva1JZ2tKdDHesUHiqooYEjNNFCD0OMcY2bR0qSr10pcc8S6QfRaEF9Fa1roKElnutARzqBgQ9BHQFOEKKDAUaYYJoSTfKWzJMo6epSPI%2Fv44sHJ9qI1malWVEqsi5lWRZXiN%2F5lV%2F4mZ8YfMWX3Ocud7jNLT7jUz7mQw62ouwafyvj0jfW5KzLLTZkX5EpX6B%2FLXfxYfU3U5%2BPg2iWAAAAAI8AKAL4eNpdUbtOW0EQ3Q0PA4HE2CA52hSzmZDGe6EFCcTVjWJkO4XlCGk3cpGLcQEfQIFEDdqvGaChpEibBiEXSHxCPiESM2uIojQ7O7NzzpkzS8qRqnfpa89T5ySQwt0GzTb9Tki1swD3pOvrjYy0gwdabGb0ynX7%2FgsGm9GUO2oA5T1vKQ8ZTTuBWrSn%2FtH8Cob7%2FB%2FzOxi0NNP01DoJ6SEE5ptxS4PvGc26yw%2F6gtXhYjAwpJim4i4%2FplL%2BtzTnasuwtZHRvIMzEfnJNEBTa20Emv7UIdXzcRRLkMumsTaYmLL%2BJBPBhcl0VVO1zPjawV2ys%2BhggyrNgQfYw1Z5DB4ODyYU0rckyiwNEfZiq8QIEZMcCjnl3Mn%2BpED5SBLGvElKO%2BOGtQbGkdfAoDZPs%2F88m01tbx3C%2BFkcwXe%2FGUs6%2BMiG2hgRYjtiKYAJREJGVfmGGs%2B9LAbkUvvPQJSA5fGPf50ItO7YRDyXtXUOMVYIen7b3PLLirtWuc6LQndvqmqo0inN%2B17OvscDnh4Lw0FjwZvP%2B%2F5Kgfo8LK40aA4EQ3o3ev%2BiteqIq7wXPrIn07%2BxWgAAAAABAAH%2F%2FwAPeNq9vQlgG%2BWVADzfzEijWxpJo5FkS7IkS%2FIpxZJlxfGR4Nx3yM2dgIBCOMIVrhAghXK0CYZCKA0tKSyQco6UUNpu2G3pwoq26hnSQrcsvVhajm0hu90m8fC%2F981Ilu0Eyu7%2F%2F3EkzSXNe%2B973%2FvePQzLtDEM%2BQzXwnCMwKRLhMkMlgWefS9bMhr%2BbbDMsbDJlDg8bMDDZcHIHRssEzyeE6NiIifG28gs9e0%2F%2F5lrOfZmG%2FsThjBFpsgv4ZcwMtPKKExGsecUUlWsWaL4M4rnkGLIKu6qImRLAdLJTOvx5KOpgizmxIIsRKWoLKTEuCikCkXCPb%2Fj%2BQq8CKeO1TYPTzqgjtHLAA0G%2FtH7WplFTNnCMJ14c4He3JAtE8bSuW8W4cydRLFlFMshhc0q5qrCZ8tmC54yC%2BbOssWMmxbG3FmyU%2BgCJCrW%2Fsgo6SKj6mb14PiWupmMUpwN%2FBf4Z5gCs4VRshmlrVpuy%2BJPtaXNFI4ohSOSVQwZpTmnGKtKMKtIGcVaLUtWvFByIWTTM0qBQharlkKRLHy6St2kU3FllXRVcWZL%2FaSzFCuIbkXoV7rFsrUl29%2Ffj1Qs5HoL8UKur9CXy8o%2BOd6bZuMxBytEhahRgrcwn8sOs%2FmcUTDGY6k0SRWLlxleL96WWHzV%2Fg82Dxqfyy1ZFPb3z5npIdcX1YNGsgvezdP6Z%2Bek0KIluWciGzc9Xr26dcRGDhcz%2BeLjp%2B544fwLC%2BunBbxdpw4X033FRVeOdDqD09bln7rwqq%2Bmn7yGwTGpkFF%2BCXsA%2BMtNeYGrEoXPlAzayANRK9wtx7YiORlGH8Pavx7Y%2F%2BgD0sW%2FyJ%2FESEyEUbiM4qjCmBHFlynJ8BMlMye6S1axv39aD%2Bf15aLZvt5kPCakSTxmlLyygzguW86%2Bf80TT1yT7up67pIv%2FZIdWUPeX3H50x885dh49S8eCNgcm5Bt4FXkFeAdHuaBhbEzTJ7IBZIQzQYY9QpgcXQF6VIPsuvZ9TD6XUU8qG6u0L3DY4%2Byp6k20jW2F36H%2B%2BjDjz7kX%2BBfYFjGyLgYRkgAexN4Ffp6MyQZE%2Bxk6b%2Bfeog979DaQ%2BfY7Q84W532zf9%2BsnbgdHvK8YDdXqMFwKQwZibHlI3Iz0JV4WAaWTKK6RCQssyZkHM4AzCuicNNkxEY10qJK0aJCNMpHxV5BYE79iaQUhl7fez1YpFN4u87GBPMl2eZFoZJhklhmOTFhJgUHETW93qTgsFBJDhm5FtvX34SID9r0fJ1bvfty%2BetcljGXBYH7H%2F%2BkvagtKGDPXP32F9dcvDyvkJ7QD65wF1msXLf5TyWseWiP8AANeSP3uX%2FhX%2BA8TBNzClM2YEYuTOKXFWaNMZozijkkCJVFcmFskExwBwAdg9Ionsfx7rcrXK%2FYhCB85mS2wFTwNyvyKLi6lea3PsIIxjg%2FLQetwsQkrwC8XmdxBhLEWB31uVr6XMlW2TSDKzWvIx0CcLFJq9JPXj1zspnXyTu735XfZ%2B8h%2BfU31d2Xq0ehJMXCwLpWsZepP75xe%2FCFRp%2FFpn1%2FLP8HCYAHEmUYEZhDiFPOqqlJo2le4fZMJHhjZW8Dk5I88Xpp1599bVd066%2F5qr1fbOvvWXv8PDjt1w7m3PN2rKqm184Z%2B4CvnvVlln91950Y3nNmvKNN10LtProm8x8%2Fj4YewtjA5aKenKeKPGYiYcrLCD%2Ffg97D%2Fmluv1u9SZ1%2Bz33slwLFUV%2FUmcSj%2Foe%2BWf4pHzY%2BBs%2Bxs8odhC%2FVAzxwERypuSnIE%2F4dY8sFORUIZ4Spt5n9r8s%2FM73Fn33naXLjnNH9sqdv%2F3Cjj984ec%2Fn8C7HpjHeZKPJYdIb1%2FWFyJeY1wiEhlNzFT%2BR5mZIKN3EVK8L1fZqihbK7n7iupHdzE4%2F%2Bj3l9B1yco44Xdk4JoIE2dSTCeTgRmhMGUGOYivlvwtICiFjBLLKaaq0ppVrBklmVNsVaUtqzgzSkdOcVWVrqziySjpnOKtKtOyiH84m0NyEKWXjiNf3WeyubytclbhXSii9pntooS7%2FqrSDO8aV4aySkt1X2tb1zQ81eIqReHKRHt3D%2B5y1VIeBZPNCoIp2NTfrzjFUnMIBVQPXS%2Fz8fykF0pBmKVRcpxzvHJ0f7H%2BD8TN2F76OjB%2BkF%2FSeAnKUhBOx7bWjzC6fNPWRifQMMPMZEaYsh2p15UDtJFkoYwySEnTC7wxi9LDRddHP7y7Si2AOBCtvapMz5ZOonwD8qEPJK5PEmFMo7FkgEzcJ59wPgRcIIVCkroZ38e32fUnOpNtOMxe3LAz9sKJzjAgPSfjvpw5i7mUuZG5C9ZqSoXS4EU5pEOpt5hFSpSWbM0hLUpzroT97kzp9C%2FAfmu1tPqWLFBnFKlTciHTmYH52rKUQtNAUs1aAdv91dKC9fjpKm2AY5tvgu0LqqVrbs9mS3dTyuFcGCDabOgksaSY%2F%2Fh9kv%2F%2F9vqQVEGCneCNjP7fzmfre%2BTR420e%2B6%2F%2F6wWwztbkReMYr9V5fJDyeC%2Bd%2FktySnNVmYOjqpyOY6qshhHdMGFE5ROMaGnj8UfP64PdPjichF2jNPk8jgbyPZV9UY36H7f%2FydRmD%2BDO2Bx8P%2F52I83Hv%2F0pKIoyPMTE%2BA%2F4DsbAMLA4pEgqRB7hsgfHvvYj8rJ6OtcLWz%2FG6y5kLuTn8fNATuN1BTORzUQwkwtJUH3rIAmS4EH1LfoGH8MT9w%2FiNbBWTdANUszzE7QDUAviOSVUVaLZcnMI1ZzmJGg8oWbcDEVAv9b1h7YG%2FSEJAiucVRJVpSVbTiTx0kQcvpVM4GayGb6VqGsZ7TDSSdAyyqwPRHa%2FkhAVd78SAK1DdgUbtA7ZDVqHq78UAu1jH2OQ%2FHiuSSx7A6S%2F%2FxN0Dw7keU7KSXEpnv9YPWResQKi%2FhO0EfUUvAile412X6a0izBnHE%2BzapmqWUV1zeo51KyaQx%2BjWz2HulVz%2BBO1Kw6WsY%2FHDLUG8r6O2I5r1VcFH1xlqiH2InG9CIhRXZGR%2BQdAf2iC1X4ug4ajBdDoouuSUC0L1JgTwJhTBFfJBhh5qmWbBw%2FawI5Ck6lkE2CQZH9zHACnmpm7IIE26wVg873JVN7nBg2NjaVZok1g1HfpBJZ%2F9vj5W4%2BQs49sPf%2Fxn522%2B9V3X919Gvl1SCri7CjiAvU8aRt%2BrFC5pnTkSOmaSuGxYfWXz2%2BBq%2BBiYhtfs2DdLTIE5FKprsdMY8o8rjgmWy5HFFdG4REfRMIESFjBTNbQcVZLIpU2BbCwCRjHtb8iGCNdFRj6CkGDhBxWbWh5g6KwAukWZJr4XfwuZj5zMnM2g0ywoqoszih9QL2VlHoLqsoCV2kp3AMWtFVApwUM2lBDwPZLxX1OKdePrNDqLgUyYFiWVgDLlwRQYJTF4j4umpqLZ%2Fvcpc6TkOE93gjrixDBJxdkH2zmsjPZvplE7iukCn2wme%2FNsMkMKSRTQioJm%2FGYkzU6ScooyIIRNg2oFEpeYywZNN7POvzciu7BWw3dPYZkW6wpkzSmM4bPTZ%2B2gvM7yZcMhi8Rl8yt6Br8nKF7mlG7wpDtMtw6kF7BBezs%2FUZy%2FrbyNvjPnhJtTxp7ugyfG0ifzAXhlMFwP2sPcid3DX3O0NWDX27uThpzHYbPzciczAUc2s87AtzJmRmfM2TSxuS0wPpt29afsm0byEKBKX70Ea8YvKD3j2ugBeYOphzFudYK1v603iwsFalMuSPblwN1oakKKiYqFY4uOJ7JULsVzPvgIVx1Wl2lBM7DrNKGmmk50UYlFAMM3eZCeaRMAy3VVeqBre6s0ltV7Nlybw9e1OuBi3pdqGeCUESHAHWi4CJSX0kalhMPqJ3aFrKSB16obnr07aLTQjwD7aSrfYB4LE6H9ehbVkeRu2WgfWxO%2B0CRyhjkM03a8CRrcRbbBwba4XtZq8Nx7BJkvvbBwXb2wNgc9gBYxkf3a5uavQR%2FBon%2FNdggXUzZTPV14HvQz82HUFc3UT0bqQRMXzKYQPAQOlnNJF5zurCj7C0V9SD%2Bsaewt4xtHduLcoRdj%2FyOAvBtkBMORmRiTBmMpU6CXA%2FSzlgtGwkSzGgCieDRZhPVSesUISIpOqzkV2TUYT32jNXBriddAX6b1aHaxs4A9Dg34o4ylmd4%2Fin%2BKZjDHuCB7Qza4M6q4kUhW5a9eBtZgnHx4JBTwxAgsMOouUpeQHD8ogBcJLtwcsO8R6Ox5LWDnLJwDg%2FMrJIow46Zd6Kty5S8TtgTGLsLT3nwlJGINl0Qu1tbeLeL5Vta3boA9qCEkPg9xE3mEPeePer76gH1fd%2BHZO2HH6pPzAeR8Y3GE3v2sGepT3yIp8dUIOlBaiuwHz3IMAYv0BTlVVq3soQcYgwWlTNDHQ9O6nggZmRhlGO6tIqTHAd%2FJMrFOU%2BOixfJsz%2BVHvb%2BhDw79lb7B209bzY9wSvoQDm6gq4FhzW%2FD6vr6No9FzFlK95TuxuYICQ7LirLvIC35hlN9NuBjhYqK0sCD5KKNYOksosgX6lXDL0g6KcEiKjtRf6kvoHyU30Dtn7z7LPUjwciFP14lSKMM%2FAr2PfPAhQyE2bO0TVID53LBhjYCB1YsaqI2kIKymSzqyTBFiiOLbikiqJ7v513y1Q3aBaVcL8iuffbDB5fiI6p7IE1l5jMTFBfUXuH2WyYpUsRqY0kR4U9R87a88bhN%2FacpX2c%2FgFZ%2FcEH6lMrdlV2HSENJ%2BCDZdWnPsDzKp2uwLQTeTbIbKzxrM6iTQ0sipiAjeuv82UzYgJ8uR%2F50ouY%2BEVF6lfgCDKnj2LicSImRoGhetDxWZJrgokcF0%2FEk8uPHNl1Yq5Uz9ZwoUzC1n0KiE%2B7Lk2AR1xUsWcBJW8GRwKMbzOocjxxUJ0sL3qiTTVZmJOjhRwXrXAt%2F0pA1m23OiqVLOnKVjaOPRwgv0LJpSZg4pO3YJk9PIGGEuNn5jXMe6RhgNIQYLDVKRcEyok2IAxvtnA%2Bf30aU0L55CmE8uj6SAvMbMOJyPQhmUHaJ5OJ7IcRf%2BpJOH8nubsCnFvTmZqZVQy6mWFsxYwSADhDFE6A2%2BkqWTReDQOcFoTLwHu8cgCH2CyWJB%2Bu%2BSKOPGHMXgkPB0SFAu0Ns%2BhAjnuNLUkXOpmFqCjAiu4gsq4k7TqifhU0otsvuYeM3v2Vl0EjYn%2F0rqYWbQFVCTSqk%2FHMdaftZjQdj6Hwupgocx1TFnE8YX75qmVfBOe4Lwhz3I7zrmw34AE7gy7ymOacgIHXGDdYLcUBGReqMaK7HwF%2BXjBYLaCbRBH%2BoLtkNiFavggsL1EqHsx4nQGd6JrLDrApiNFCEt3GnBgVQJHpy%2BdgTsZjKcRuy8tfuVvd%2FMXNt5WOLCSj9HOXdphdj4rfdXh2xZESLk34SY8xsOoVdZ49nh9rBaOYMoo%2FhyIumMWgRHMOBy2URWnXkkMxE80ir7XmUHdPZKmJYzpUtrm8qGxYq2WH2wdbqDCAtMOVDZf7BBgaqYaXBxb8IRKVEnntpfmMuFuOvVlzEqEMHH%2Bh1wnd8tryr%2F0f21us7zbIa9SHQF7LOHYtmo7TCiN2CEalbAjioBlQUgdduNQpDgC4CQ86QIdBBYgpteCqxjsMQToz0Kc0MG4w5xq8SaDcaOo5KB9bVpKulVuoInJsK2guIMWp3Vpk17cPVFZu2bKyAgrMXjjP%2FmEX1cR1XYH6gTiYy7K2rmEkAbmJq9J4ApAQ5K5nmITZYVIQHSTNGQVAe%2FC2a7ZefmGxve36W0Zvu%2FJUL9KPjA5Os0ebDMtPJodPnmtpa7PMPRnJwuly6n7g6h7mJOZ8ppxB6gznlGRV6aPjHAIyjei2DK5iMaBNZ1XpdJWysDVQVQZcJRdVG0qzgbWznUAjmzXUTKVJMgOzU3B5vBxytw3WOifKObFuxQyTljCRxvfTbMzBSh5Rc0sgQdEtkZi077CCQrfj98T4%2Bx1085xH3nj7jUfOqdhMe0w2%2BsauH98mHpCSVtJ1408vv%2FynN6oHtb0r4QvwvSvHXiU%2FxAvVXnxv2NbleIVfz73NGEBnY8SoQTRESQHjIzJYBSkwczWpzyo7dsyv%2FSejILMr6pMNh2q%2FxW2mv%2BVk3AxVExyHUL6JehAEfz1RABtDSIGYrf%2F2gbmXXjh7rfar%2Ffnbnv36rX2X3HlPbfy%2BzZ%2FN%2FZX%2BZogZpHEr9BKH9d9G35BHEzwRGB0PrDb7XD5ZW94Jgwqcw6Pxc4BEE2KC1O8PVpIEhrNcQMuIaNCQeygsZwrXXy2cbNw5aiR3A1zH3qyQVwCwJ24tXHLn3VXT%2Fd99YZdpxFT%2B3VtlU90%2FroBUEYGbAwBnlNokM5nZYPstZpYTonF4adocMEbc1XJ7z1yUGcFMOdW5RDNQyonupXgslimxRjgSB4U8C2iWHAtgL1ot9S5Ef%2BcKNFpKhjD6RqslDqOSIc07ZkfTJldV8vDuKqWtnUoHdbnMypbT1M%2BSjpk7y8TqxLskXKUCfGfOAtgeqJaSi%2FDTVVoClBzJKsur5f6heSjLToaLpoVgZfJK%2FkDvTFR9CwlY0Nvap2OosxRrAgp7vNOpnRoXy%2FyMAfTZhN2zzAZfoK8wODRrNiV%2BT1SM59HdkstH0ZmuCUcCLw6EIofqYB5UQ%2BqRwYu0oyAAorirXc2BuCQoQuFFDqPdTUaLRdVGtSw0xFF4dmkWueajh%2B3K2F78wEuobNVlbBcIDYwhHsB3lKfsAfwlelGxAltF7m1kzgqK4814EQpo7hYQvnM0P765Pu5T15PNmvVT5r3NOLr2akkKZbP0GNVcW2nQUPMwoGyxZVGtRX0QTBQryhq0S%2FywBZZrk%2Bbxj1dRSJdcGMwQjP39pSaQ1jScgf5%2FNCGBPCmgmIwrDXxK8JnXP3Gfol2pryKVCvf20RWwxb19zF857bTjfk7Q9QRN1xN0jxZPtTxUZmCKU13PLQBrMEYr1fVED64cZsJ4ZV%2B20NebSsYEAhbu6%2BwBsOh%2BGQqvCofwDYbgVxYn6Ho27nerQ%2BFwCN%2Fo3Cdg%2B%2Fxav28A5Ld2Zzmn3VzxZmu2nVmL%2BNH774f7%2BwKU55rIVAgSOfSeElA4dUB%2Bod0Q3lhrEY9kyYsIktUxCSQF9%2BFkLfao0cQCs1y3yjS910qXEktVsUwwpy0MejQFE501Au4Q3kDplBMLoLuBnhMVi89yXymOuYvs%2Bzx59pgfWLBIhwBj93S9LMH9GMBA7E3COmyUKuRF8mJIOvamFCIH1Ln8Nm847G1Y91A%2Fl0G7OYUpJxBGsJAs1Ga0cLXUCkXIljnLBAuyjaIA3MlmkUFNmm9E0FyzJiuuf85UTPPkAYOhGg%2BTOyp5YItLE4RM4ArDBPWGCPFRlaEC6gCw3LE3823siuEzWZdFHba42JEk67GQwxYPm2StlrG9FhwDmLNzKhX2ta1byam4lh29%2BUsWh8OCbxPyA0JMgukGvriUZiOAqGvPKN2gpmVgMhFM%2FAAsItVyhPonIxnALuIqpejyXsoBKhEYBiXQX%2BpMAUrR1kQLXTS622EvEoujRahExVK6BwSax73fGghmpmmKkZbdoPko0zws2A7WSbMcGHSheY0x1uvD7IcYKn8D7dzbqBzt4p25wqqOSvvKGWmrbRdoSsXRyuhoxTi8fnh4PQHq4FWoNJma5uY7YUfyDrSDKQzXjJIWvGj4TKrv5enYPgs2cQxeGvfZc0q4WmZtKN2JEs%2BUWnUtNA%2BW7EwSlWEYpGg%2BmUoTWOviYAA5iJMQj%2BzJk4vbh1s9p5PbVro68%2BRrsTZ32GhUbzxDvczfbOtwOsmmcvrKEV9f15%2Fe6F43MkI6PGmHnXvrmHtaky0oCORfyStfUL8HPIf%2Bn%2B8Bz7WAlOhhzmXKLQhZtKp9Ejo%2BHVWlJ6NZusBhdJT4Q3ANLlZRWLYwvQa065ZDIjArHaVEGkbJBwPTHoWN5n6lQ4RdpQed%2F4BgniZHpLlU3oDeSxyJMA%2BfJJ5CuwGHKK9txEFHZc2%2B1gj5xTXflqMxqw0I3du55bHlla%2BdctMNZz70%2BSUX7d19ipBr4waa5ZDdKcwnyhcKZxTaTAJny520Zd7qu5dWNq4%2B9ebi9UtXbqzPS%2B5Sqnu36CNBaJgWxIADo94oovR0BAS14OnDIUjlo7KDcxLO6JOlytIrTE9b2uYbzQbydTY6IxYwGG6yTJvfL8zOcCdPb%2FUQjvT3m%2BKphM127F97B439DPvRc7pfyAxzYBtTbtLstTJr8OGCYwOut1GudwHXW4AjklRQahouWp0wW0AHCFFfQ9lPAzn%2BIAZy%2FDSQ0wRf82trk7OKc6ZkAdlaMlDbLdKkxSRsosLDEKRg9hfkuJgTPGIuCjswGp1ElIHdCiKYpJy0ePHiG26A15Fd7IFdWZeUjsYqRXVzsRKLZrwiqH2PP37szce5c3CZDaUkM3vsmWyxmOVWsmYpFaJrUPSjb%2FB3gfxDfO9gQO0CfNkqNVEb0bUA3E4NXcuhT49kCHSbfazJTFDRcfnRGgJRRsUCawL8GRDZSkQE2R2ksnsmASRlAWQfdwLUo49r2BU11L2ZcdTTkit3g0YZ7sd11Me2IOrsnTXU9XyBxngqowsgjHLSZeDT7ockfglaYkf34zvXgu%2B4hsD223TbTyOY62kEcy%2BoLris0IhL5WO3%2Fh5YxUn7nk84PxHW8e3KCcOtdXDI4fqmuvl4R48Db1L3MoJ%2B0Z3B4EAog4kYQxmlt4q5GHq%2BxRCZGCf25D%2FdfiMmxUayVxrHozJhELSQFwDPXlTfVN8%2B3tGPx0vDSMPuk%2FASP3W8%2FPijdaLtcaTIrE%2FYRJRMx80twPyRlTp%2BS2h%2BwRyaQ3M6zaFZTfMLLqL5BcUsYrw1hzGcK0FM3IQ6QtnVMi1Lsw3K%2FrbpaPXc%2FL%2FKDDle5sf%2FjZa1IOfHv6G%2FZcIc%2FsTtT0H1Y6OfZoSMH%2B3Wx8cImmqQ6WBmMItgZUSrPUmz3dJA9cUZNDQ185yuIBiOBylK42CfXrRNSPg495XHHkPzBmcOznOcOTDnu3BbPTg%2B%2F1VbDWoUBWAWohxWbfySo2%2F9vcIO%2FhmpjSI18ONswFdmyrOoP2txRpl1SJldpehO6yn8H3HD0LNHpulo5NPhx7UUo49XKn%2BvHD%2F6FjrV2OQNi4uLdR%2BRwr1NvTrdNHMRphhafx6qYoP15YW108zQfAymxNt15y%2B6XCammYHl0hVh3490dUXG3JEu7hYw1z3snXR%2FC7yTopa4yzXMcxkoe4o%2Bu2G5r4VyaR7FBN9zqIquED38gxkVoQBAJPYrkljyuKniApCVXR4JXRRNouLtn5o4N5MYUsQjRt26Jh908%2Bs9gYDn6F53sPhX0rGIJN495r9o2eZlyzZ3cYfdwaD7mA3e3%2FvGZx8kw%2Bqb5LD6Izy3DOh270cf8s38C4wXtPQhHYOQBnuEwq7lgKAz1qQFrJokIJ2dR1hDCKvA%2BKme4ekFayobJl6qtaf5VBJ5iZoYxnuv%2Fel11%2F%2Fk2oUL%2F7G%2F3xI754wrOme%2BeP%2BFm%2B6%2F%2F9Au9o9bf3Hztlf%2F%2B77L%2F3tkxBzbdOmexZ%2FfRc%2FcjzrVeHxNYhaOR9e8WnTN1xBd82hEldHDJuogYojCgJG9ktcDihJG0Y4bQ8uJsYmhs6VHFWVyxMysfvUItxZguorhuX83OBkf6HkMoM0VwkbU6oU0WwgTuZBmU8m%2BmcRBrppz8RVXhKWFy9ctnZlYtu3Lyy%2F%2F3k3bHKed5hJ8aYuTNZtPL5BdZ37za195acP8u7ZcfcVVn5t7ygPFAd545je3rbwoeLbRt6ht4Y7e3CW76vbyS%2FxnmGYmCmvlOqYcRGo4qxgVwAFL0QHToktIDV%2B11IbUsGEcOBRG01HxiaVIDAliwlCxFNJCHry4ryUWT%2BguSOA2XhYmKDoFSWO9RIGkzIBihrzzKLkk8m31FTQIyeH2gco7j6oHH32H7P8aefBydRP522WXSaejo%2F3Rd4ymb4ORaMMrb6j85tF33rkwSx68DK75n8suW9M8Hs%2B9D%2BZSM5NmFuiYwbSJZZRUVTFrs9mlGAHLDMXSXkWHIlOKuYAFpVArsGDJHIS5lOgv8Ub4TNantmwU4uO45GuokGEuQiQzkWIOAyBjYG9dc%2FdkZB4Pn3%2F%2BWeEQ%2BYz6gOBfMHvt7H4NoxUt62sYPZAHhEg02esxE%2FJTMocM%2F5J1yLnZF4%2FjtZf6AeK4%2FjfpeJm1EWvVcRkP%2B1P%2FGY3wC%2BEI%2Bi8wqyoK42UGRPf5wObXxqvUEm0QXicYLTObIinArWtopKw%2BMhm5taSJLdyhrrxHw0ku1VCaW%2Fk64rRD%2FT2eP%2FmLWn62lpckM3OZshux8FHrEewbs1ao4z2kcFnEzUQLdUouL0xCI5VpPswJssswH1mxxNio541IsEaYSRw%2BzCQPH2bMZ5bQGwoCN%2FU96g2tfE99Dd4r7Gmk7WXtyMvqL9WDL1eoM%2FXlcfv2FqCxB6isRQWtOer202gL8Ej1ZA4tgkHgT1OAKpp6cli10Y2spuWqi8l%2FHN1P3lYX1XIba7IeJX1ZQj%2B53YkZWX56F7GGNVMLSdXuMn4n%2FUY0e2DKzdSAfkN%2F%2FaaEub2up3j1eg7MhREy6O3CnBft129ne%2FE32SSbHP%2BVBn%2FcEuRCoC4tnMGrKF9WmCJ3C10vIwxTmJTQNjnBrXL85N1dx9fe9HsX%2BSX095nCuCtKcwg2fmkXLugN30M6t9Vwpr4KQyPOwDciLNDkMNs79kN%2BCSKMFSrk7SljRGMZINlzNebksyg0AvWfIZPiWXk8BsMzrrSiqoV3gNdz4yYn%2BQYOEtwPswy4t2t8R2F1aHznphVZ1qrOd9Hj3aur8U70PhPuocUfQafh26hO49Z1GlRoUFQgO0%2FWzaNkgpnGLxl7%2FUhdCydOthdo9C1G4P7Gf53m6GLqbepb7Io%2Fqw%2BRjX9m140pfyYbYQtxc330M34lfyVaMwkzKRBZkOAg2ag%2B9Bd2UCJjyov00rGXfISMlTRZxzEc%2FzT%2FNPXnjtDMB0cVS9YQav%2FUzIeAnvmwDzMfqP9CwjRZzHuYmvWQAzmBSmVcinN7iAfkrGfPHvU99YD63h0V%2Bo%2BmO9QP7tlDTqaHJ8DlBB1iPC8J4XI1wGXX4MLcIPsEuGwWjGcwsMTwsGqWiLF%2FMnjRfHQKWFh4cRygptIqS2HS9VV%2F3QmmUUggcEebC8Uoj2DYpSk3lwtyIVVICSlBngzEqld37Hh15054P7hjCixttTPwPhEmcSJM7gaYPHWYHOMwOafABJwlpCZDs4l4ye5n3z1vCiS3qO%2BQ3c%2B8e54WTx2HYzozyFxEIemvKoNUF4hS9bpXG70hOtfCVSWsuWUBvmGAL4zrTbQX1pu0uN%2FMt80YoMOYGtSHUYmKSgdmKpdtzjQq2r1iyUim4JDLood82DCD5hV4jYKDl3PDfL43zWGlpAf4cTKGr9zFOwUja2DNvIP3cB6fSTY4UyE%2FqRjc3bHmeM%2BcnqbsyXOTt0%2FlVzbAGm0WwcCxxOvy2VyElyNDSc7Snl2fzS1p8xv9%2BQ1qujiBPhjJHahxtEQXZDdN4vFVMdeIH3ftltxSjYd9qB1PRbcQxYgnJpwfD7H3yKgWeJwK%2BB1gEBUrcL4xDucHS%2FMCpuzV43ARWhDFZMqOQDRHi6jKtng3jQNMQ%2BlcNjS3o3%2FDUy0L4RT6N3pQcwUVYl8sns7Q4XPDniL1lxhMywn1K0Qsh9vatThePjdMCvmcFGZlQMBBBCmeT5NUDtRxONpXiOdzsAsH4VRO%2Bl7kts9X%2BrZscv%2FgB4HnT6l84fbwBv%2Bliyv39b5SCZy7qLL4Ev9PyeHKDfcFKxXvis%2FOrZy3N%2FrSS03337DwYv%2BPfjTtq5VFF%2Fp%2F%2BAP5ogUVjV8b8%2BYi4zlfnroJWM%2Bb0yUfGn6YM0VzvrzBiclxNC%2FgBMlxDVkPJ0r9WnjbbRfX%2Fp84ffNXDVcxU%2FNVJ%2BMQnIpD0wQc%2FJNwCHwMDoABORH0m3as%2B%2BFO9bETZ%2FjFd6yr7lQfnwJzkw6zj7I%2FXy8O1SR7QIOZFofWcu2cXgqz6NNhdjQdJ9dOJpji5aHpXb2pKVAPs9OLVz75YXXj5ic%2FHJiab3dFkS0Mfzj2wcCHT27eWKtXPof6KYxMkObcYThW125KrAEYm6HKMc1kxuLhsb1snLxEs5l%2FPuX7ep5J7ft1XxXWoIOWpH2fpqx2qQPqLNKtwfBDmKOLYI4aUU8yUC%2BQQHOw%2BCr%2BUIk3NKRVIyA%2FJC%2BSA%2BohrZx5bC%2FWFOLvfAYG4a3a7xhrv0PGfweWCcXYrxdug3ryGdIGsHSoM2u%2FU6PJv1K9DauowZhG0B2ccd4d%2F%2FEgXnWW8g%2FbK7e8%2BvT5JuLUsGBb51zVKGuM8E2xlp%2FlyJScuo4nE%2FjzwEuMyjeT5E719Zvf2UmSN6ubbyaj%2BgHOjEdgF34vxsT5nfxO%2BnsMGLpREWxd7VdiJIUXqa%2BRvTeT1E71tZsVOKJu3q6%2Bxubxx1I71Ne2Y20Nzal8gOrVcWY51dpaqkqc%2BrNDmVpmBWl0Cpk1qy%2FgwuxKm52PxrUs0DjIaTMuVyER6Nk%2F2W9BPGGCajrG61BNR7Fdy6zUPsjaGXzc2%2BeN8zN4v%2FfHkn8aSO%2Ffjp%2BHD3ae%2BjNvKOQlaXgfewlkuKFO1yTTwUxjemGF6WXKKZTkPTkMjqLUhsW4h3Zm6KWdGYYA%2Ft4e0b3favPkZ2hhdzEnRWlyDMDV15vMEKyyd8JUg02cVU7iIF6JlrN6YlgEQrNtCmHMAh%2FF9eRSwrEx61CqJfSfPrdHej8aSg1Z4ix7aRFzwYtczON%2B9Vewedf3DY4WN8u1aBZikVg9pqdS08RRu89vG3WnkyWT10Jo14DDG6Zl%2Fhm31M3cLS%2FZ2tf1Ix999Cf%2BWVo7lB3P88uBtoEpsKVeyk1SvpDGHL9hQ8HLOvg0Gxf6fIW%2BxDAmEaSSMS1WzQu%2FNJs4aXo6c8G5X77j7c90LfrMZZ%2B95vrTVznPcadmF8j0eRs3ndbu402CNyrGvzI0pN51iu%2Bu7%2BYHbzp7%2B8Dgmlx3uD%2F8gvrDn%2BxekzMbPc7CjfZVI3uTM8%2B6aXXWazaEArkrWlpe%2BiHOmUsZGz%2BH%2Fw9mAXAZURZSjppbVea6SoMwFIvgNTgX2GdGH029cXtlWAl9GrBhArCCLhMmiA9f6GNTPtmXSqbSbAE0nDDn4AUjbpNLDeZ58yIjM6a3OVsc3uVrRUPEZzE7Oc7kCLT6%2B%2Bdsmj3LmXz0H3xSar7TvXyVIWfvOH9R2snaeBMhVlfQnZwhC47emeRbI%2BHpN3ZLlsTwUHjkvdSKvcXowi6Pt8Upm6yEN3qbh2ZfMvspsurirjUPGVgh%2BrnX7jNFzrv48VW2gabepjY54OIt6aVrW9KXYJ3695gb%2BPf4HBNlZjLzmdkMLk%2FtVWWGlk66IKMMHlIK1dJCIEIBVL5ZFnMgaGpvyw%2FTPC%2BmZJ4hup9nxNZ0fnhkPhX6QBdjNmyIAFmMsbQhVQgbskCZNJ%2FSio3yvQWj7JMLmJgwFDQ2z1t%2BxZYvjn5xyxXL5zUbg5MP7BZmd5%2B2%2Brqbrl55StcCKymEZvSHe5T%2FUdLn3dpzwQWJJR4vu77N0rZu9Yb5mcz8DavXtWE26MR9y4ahM6d3tuVOH%2FiMgyxMzJ0RWHQKlryvWbjuiq2zL%2FBvaG3FaQq0YIAWCuOjGQ0nMV9jys6aJTqSwWxQpS%2F47aH%2F%2FM9fM1KnRXGmHYrtO4aSg%2FzNodi%2Fozhd%2B6xOm6dzn4u%2BB%2Bh7kL630vcEvpfhbMudLXfGjWCg9SuBfiXYr7T2K4l%2BxdrPPG%2B12V2BYGsirf8jsyxwyOGccDCdVmYFCaPRGtOncySOBC64kaw6gWcSmvoBVxSSMAgsDghfJ%2FiCocHEverL9yZWPnb5BSnL7p89n9h0FyVqRg7PcDpIW9LXnYlN82TIxs7U7JvT9mBQSJx67hfHyS3uPLriLunc86%2Bd7mxT3%2Brb4X78Eo2imXXNK5uCY4%2Ff7UxmkzP9s9gbp93Td9csb1ubrXfT2efR%2FghfBeHopvqGG3PRk9StkQKQBbSkQX2WxCaSj1%2FalDA4Ek3S2DbvdO%2FYtv8iL5AX1Mcx4DNnzvwWviVmaDl6qMj%2BfKy7iIIMu4PU8rUkKnfbYVZj8ihyc0dGSVA568OOOGUfzZL0%2Bc2d5YSvVqNa6gRO9yVguofCaJOZw7DpS1CnfL63r4DeB%2BqPChP0FaQSIvUZZEhcMGKfhYJoMCaLPifZtH7rerLJ6fOL6gPFoOfMN870BIvqA6KfGNu9PQ4yl6waXr9%2BWH1a%2FUdHj7fda7f9Tf3bab5ZXtG8bJlZ9M7ynUaEv9lwNa7le5sndWEowGpSzzllVjHr6tH3PJaZabkwmAUEhj5G3huz0j%2FltuYLObqfXxKSdmHi5C4pVPzYfzT2xL5fuzAkHVtUS2GH9ebv2tL89JzhGv4ZxsK4QJc%2BieppfhpZ9NCkGxNtL8Flx40zQmsRfLDUW8V9gt1N6yhcYKU5cBCHCPZ6QC8pcBmY%2BlFSkLV9WCDX%2FwUXvYfG9qpPEu66Hc%2BpT7KP7bjuITz4l0qFXf8yelBfQpXtup37x%2B7beb12oNFf5gZdUqsBdoEhmZvoZZoYHiNiPJasZYuNPaX%2BpIjZ9JgQpuXPIzcPMFqeFR3%2FBHBzN7OBKUfw983VspmWapgxj0%2FKYg5MRw7N%2Bk6gRpr6UpPYFAMbcXCukpvQDGEZSx5LGeByDlVckDxusRSOALlkTI7TekJJXhAgoKgPG1O9WLzgdRhAlNfaMYGNahTXpPKJgfaIaAUbG%2Fb9qaXnfuU7Xzl3acpvxPZMpItdXzlyWcvpAavV2xxv60r7RdORSsfKbRdetiKXW3HZhdtWkrVaIi9W%2BWG%2Fod8y3%2BQ%2Fw72BWhMno6Ms%2FDuygWz87dg%2Fkd2%2FQ3fZ79jZSOt5zOv8D3mmVhtvJvPYOezIb9WH1D1caOwFdvbv0Amn1dPNYIqGLaDjm2AetTGoU%2BtOGIGq1uiB4QVNRdc2HLiE0QpIGTQoeKFjXXyZdJKuH5Cbf3HsTXLvL8gNuN9ZYQ%2BQJvUPtBUR1rVtVv9AmlCdBxjdMGZPwJhlAdpyDMcrkFO6gPYuJallB2Pwha8im6BsAhWpFbMXMWWxWYtegLJUkpsBpG46KskC8A7oHOj7RM8n52A7CV1R6QjRzzgur3hZNJZMuQ1OR4C7KWloEs%2FEydj3CmsKuyOhjpB6EN6yNI1GnjZ2W0u3gXvS7%2FY8LEpw%2FNhM3u6jszervYe9UqjS4WMacoOxjsPZmAHHozau2LMUl3pFInZdIfmczvRRCQulK3rB62EsXuVu0Qpatd%2FW8n%2Fxt10wVvXfdtL8QYP222IGGbnBPsuRKBgW4%2FeIEmy1pB5suNMxP9aW1aYWOhoISQOPbacyNapVs9HOTtQzhz2cNLccb6YaH8lpTJCDr738MukgHS%2B%2FrB5CDteSyXX%2Bhf8ZsCe3w2820%2BoitEctGdoSajydjIZroihxotL4T8An%2FVH1Fy%2B91JADpgCVtfqChVqGuRKsYmeFEC1RMlDu8VZpWVZTzXcXoVZQOUKbqUWwmRpWaJkjoj69J6f8NBEtc1f2YNAIhGG8JpOO%2BdsHIk8ZWr3sHk%2FC8JR6V1FLtKdDBm9kDfs7X6pbHmul3iy6ru%2FWc3WtIKsKYPXQsmsGC4IVo6vUAbBladl0qcOIfs8gJTAHTDuTSGlezg9yw4YBkhATcY%2FPAfyMHv4US9vZ6HIzljw3GwjwjljQ9wphWd4g8BX2kbEzkhnWYnMauFXeEF%2Fg3g5JyLzYMCDrz9rtR1hB8kXXHAF92sILnIElR449U1HftVlJs0ROVn%2FLraS%2B%2FmdoXgvLLAL6nwf074R1Nq9XEeVoRmskhzLVny2305zq9gTWxfVmtNZD7TnAqqtHi%2BH3DZCCB%2ByCVJIGLASjFEYbuu4ABVTQkDOE0fA0xhY1ed1XzXRet8ptdHvP9ML7quucM7eI3qag2xQuXvjQ8hv%2BMmOGO0get02fN9067SJyphR6msxfus3b4glKnlbiuXGp%2Bq2nAfM2gbOGJHe71yu0%2F1vP0FCPEflTAp3oQf5B1Ldoqyn8S6G3uyCgwzslC7L0x2Vvdu%2Fe3f3msj%2Ft3%2F%2Bn2vYf95EX6Mc%2BevrBrt8s%2B%2BP%2B%2FX9c9puuB7U1uqjXRcSYNKx%2FNK7cdghj5lio4msD1vPWqhaId4BgRAwsbS3xpZ7v4mRBRxFnkpwkRCUunsLgZXFoq%2FNIOvF%2BaCilfrN5KJVtmubYcLe3uKsIhvOLRw7djm2ZPlxc7CfrI53FrpO3CLu6Tm5rfvlfggn1DnL1qwef%2Fc0N6h3FxtqwJTqcm5lyM45qgnp7mRw2A4BVU8CSZ2x2YanHx2G4Yf3kaU2GEtfam2gVu9grQNSwTMZFd9nU1oUucK1et92tdMKqkkYR3kE9STmxIPYOEOQG2aNPwHr6WIZNFiIwBVPRPBcX4jDTPgn3Ioq0sb03kFEggLp3MgEOvgrIk6vpvIT1r2iQ%2BDUU95OYaxl0pbbSFiXtNEPbi2iXe2idfA8t9Rw5Lu7dWnJtN82o7R4E6YJFct2A%2FH6b2OSdSY3CplZAOQ4UEBV%2Ff8nbA5SRB0%2Bi3uWCSIkA0z0BMzpCaElWtLaiEdoqQY566DJHk7ijHSzmv%2BTB8k0ZTJVis8NBLnRYRdvFDusakl6z6eLVm7YLTU71SeExsAESnzU2OX%2FgcrtdaoFYeTMn8DxrsHxxrfo07eC1mLWLCYv5LaNts8Prdly7ZHSZ%2BrQv9XDTKWSV1BaWvCFCWM7A2UwO%2B%2FOr3tVl2rnAN2uZMI2hXEs7omiZorBeT8f6CmVGtjydioPp%2FUi7IbqUYC0CbYIQ6dJqEZBxgNBeF0pAZVALsCQjWFJoa%2BbbKe1CrTThQomICtNf4qZj5Uiqi9KOBSFo0EiBJcCGMFvLYkpx8VgqhzI8WhATAha6CQ5DB0ElMyeeexESyuq42O6yOsjFgjf6lEl90tVk3L5pteUNZ5PxsySxSf36urstBmIAgpl5K1FbuT9W2NmjS8i1Lpdkv8xmfIu3p8SxD%2Bxfa5PIqmK7V336FPLf7636ptVpNXMYaSGqDSmszbWNqLMaHGCx9DEzwEIpF3CuTYc5NZBRpENKAfuZldslKkJnAHlycMCFein280O%2FSzsGWdx9%2Ff0lR4bmdTFY4RNma%2FHvVCKP6VCSmEoancSITVAKw4ZBrA7ow0nlkw2iEMUaso0UdNZuf7hNUp9eNrrkWmfCsdl32qrnfQEN8mwWkTpFNZvY9eyP1fuMnshjAlmLpLlw9SWb1qg%2FW20j9kt81rX3uO11GpEKutK%2Bj4RUXwe7paLHMFjGwr1n8MO63QscM5dR8loPmH6apJ7PKp3VcictwemcDphHs1h8mtKy0mcA5p0YB7SBSl5ypgBzO1X%2FjBEwOWeCrJCw1mSIJLQmkZgF4CScJyqLBgc1SZN5cRBWlVTSSVCTZ12%2Bzfak81qydHQZWeVtf9g%2B9iHMAMuX3yV%2FPUV9ytuWzXKC0e%2F75j2A%2BsKI7xI7sa7JVdOrL7pk9YU4mcha4bFmh1PdDqOuvr7d2Oz8vs%2Ft9pGKVXCZOLv7HvYyijiL%2BjjMkycZB6w0M3R9xUX1Nz2%2FjKbvac1DXTZ0yLq1Hn2Mh1aEl0ze%2FnpNuB42YEEFF8xEMpy159fXPVwPlb27hyRYUJ%2FIPeol7Jrrfr3nrD3qu3oA1EMsr7xIkqTjJV1ffRJgcsGqN123zGAK%2BjSYtGwGi5bKUPJi7yU35nWVLYzYr1Wpo0tLpBBhV0kKErqzC9E8QHRt450r5B4EST2oAUQB1gB6VH39xVdemkKjYZ1GYp06Wvadezz7TkRj1ubsp1aaQcIsPHfJ6tW6zk6gU4J2rSBT6QTraKUGUwORHkXLi4xOhmmpDpO3cdC0vMUGsKQJYLl0sESaHGjDdZBx9U8dyoSZ9qM4Doi0irNyHBg3oyWp6dd8HU4XczvzJebLzFZ9PDuqyvKM8oUMUXZTcDURu17rTvIg5oAx2sCuF2c5HAZPNN46uGjNNbfcese96BuwuGdZ7LHktIFTz9%2FywJepEF7eIbqf903rG5y3YM06vOYL4iyzhfGuv%2BjWHTvvpW5Oz0Se8Bh9gtcnZNE1LIfZgg9dcF4HQaHEFmA6wn%2FsCGwEZRCjqX1pgtuFvkKYlcMkAko5nCkMc4VkAUPlhTSX6kvhjIcrU8aUAyYptocV4D4OnPwFXxbevD4pzRVylKTXUuJpJP2bqckYIzaf3%2BRf7RvuD5nSXEe3kRg%2Bc1U4Fuccabtjnmgeakm7si6eGNt51hQIyh6P1egytjUZbW0Oh4fnE7zBIvh9Rpcp4pbNlvb4TJvVHOmzWYXMSqfH7ewMDpucQ05pmOM8hOshHBfkLKLVLcTMXc2tD5Mp84CcEr262TwvYPXwtrApE%2Bbdi7zzzUaPxcZdEWodjpiJILishLVa4zKbYe0mzpd0hwKh5rDLSIhg8STMJm6hJHdaHB3egNnt4cxWOSW1CCmDnTPwrXGfjeNsbqOFALWElNMqC7HLLrO1ChabyPvXENbI286qxclY%2Fln%2BVsbLMIOkQID0fbJBLoCSniLGWIY42fXRZRv%2BYac6dvdR%2Bz9cv33sKWen89K7Ol3sunNf6Tv93Dvf3vbs6fMyY0%2B5XJcwtAfiBuDNp%2FS8cM03t4LBfgO9VaVArePmDPaVAkMfphPol9OruBQmqjT%2Bkz9U6ukf72lZzlPrLY%2FWG3ZGxJjQ%2F6Jag2CzKdpwaqJRd6JtsEIPqzatdrpS%2BZdxQ%2B9bx9tUH0BHIHugON7fAW0ArNjS6rX0kKrWMVmzq5kSY9INd1ycDKCfCGKRe%2FvYIu4W9eEKv6SIBd7qQWwAwzTaFminJ5gN1INDaFVrKIeagj%2BG1e1aBWgyozgPKTHaddAZQwKCagJg0Ebeca0nIRaGxWlhGHYhZLO47jIlB6y4SkRzD0qNHVPrJR7Ua0fd0rQzbI12pGugvdI%2BgH4GIBz9Rw1jMto%2BoBEKSzppHTozwa7HuKgXtKNaZp47h1F2jKpr4VbMTCA0Fwk9lNgfhStgEFW4ubKzglFX7YN9Td%2BrYEi1gi84wLXQj2MPaCfZt7RrGL1X515%2BL813iYCNPsIsYX6md2x3VtFTviinBKrK3CyWBffTvgS92XIbpVnbSebOWvudpQ0pAbAk6IXrUWsndtpIaqb%2BcFUZdtG4yYLqvsKC2aZOpYdaGwXaB0%2FPfliGSjD2FbA4aFuN0jBI31L3IOg%2FBTAdnjM7PXxGyzoKaz25bKLWG2dfR%2FfgMG62aUk4SlwsZQZw4fGT43X58ekd7%2BKxPupPwC0ZbBGWes20%2FZSghakSWkEA2Ogn6gt0cSTd0iL7lsKrpcUnr2yPXEfM2o7DCXbOghwJt6QjcKqFlE%2FQPug27fzvu6It6ZZvt%2FQYthGHw4c7lrt9odZcbqWvBW9D%2FaO%2FZAb4bwPvLAftCvMdUlW04kCa9MGoVbFXBPZvYEopzDmY2a%2B0iPutzmBTD1JIcpeyOWpEGGG5yWVxVeorEIy3pjCALBDgN71%2FvYCNJeGwfgk26AnDwgNqZoTgN1C5jMdAwpKm4LT4lnkzp0dntafaRHJn3O9sOtVrTp8UV68X5pJrvR65Kel0tY79undh4VSzwTmtNen3ktN7hzb1BeSztpiE046NCXNZw%2Bzpouu85XNXbTq1bb7KkEP%2FtKx%2FVrOrp6OzC3%2F17Mw6kY3G1SuF2eQqn0tuTeEvjsyMD89qbZXw9wp5Xtx99rmn%2Fe0jRhgkH83ef8a6z7VGC374Mc23uILp47%2FHr4cZl2eGGJTC3dSPI2QJkg%2B0Bq2bWIemNWCzjI5mbH0uOLV8HC4HRDVofh0gCHVHYZ0CdlRMsylYhb24jPtkMG2HWbRcY05KJ%2BOKl2656%2Bzz77r5xfi62fNf2iC6Oi%2BfNzJ%2F9rr4E0PDs3xnbFx5mW3W7OEN%2FYtmbLk8t2DwHM712Zduvvmlz6ZPvWj%2BvH%2F%2BrCzPuHneSfPmX3RqumntScO%2BUy89%2FVLb8Lz1zfM3rnrymRXnaPj1f%2FQBfzX%2FT4wf1h7G4wVAYIwJbXqfErADPoyzYKQnQKgQkC7wCSZEL80fgBHvH9kx57QzRkjTyMgOk%2FWCg%2Br1fz3LnQ4VRg6O7BBsFxwkt8J%2BJhyKF0Z2jJxx1iz1DyNk41mzdo7gV749ssNswu%2F8z1nu7umFEcKfAd%2By0G9tEHtyofiFnXBkZET9wyxNrlf03oHYQSWEefA00hqgVrWbemSMWtcXGBnYd2tVGLSDBhU1Gdr%2BpckNyqbR4NMew1AQtZSOmlVciIpRt16ZXxk878EnvlycoYVWimio%2FsvQ2qGhtUXuW1I2HQ6ns9Kx%2BSCx%2F8IeOPYanhia0EvdP54VE8hgozEU0wTjR6lkb6EvKxOfV0DFgYCMJpkf%2FwxUWmvc6XR0OEgT%2FWhV%2F3jwJ2TrTw4SuRV2nU71LSd%2BxNX%2FUg%2F%2B7McMR1KMG%2BzK3zA9wKGzmfsZrGPsoPWNw9lyN089LuhJGKBOSHe17B7AY24Puhzm0AY5sNZlq7hAZl2lLtJZ5t0zMBUQDE5vZJhuuUqzgJAgOpqx5r6pWpqLTY4wu4jtV7pExYyBkG7Ybe9XBsRvMI6m1Awa61fcmDGI3nDQccU0iaf5fK%2BeKcjLcRAKooyV%2BEbMF8Sid483zAGXiQ7ioU1fSerzhnWLjB42PbIsE12%2FfXkxOXflYCf3kKlv0azY4IpCW3l38Utr2gJ7XWKHt1nghxb%2B6Yn1K0lp6TlOspwYHYFM%2F%2FrC6bfNFpYt5z1dMy8YWbDYrlYdgqdr8Nzhzz9hXbpMXNe2iQ2HuvySUQCz3m0aGOt03zprfkCPCZ%2FH3cs%2FDbTdweAqBHYDqChhGk1spo3srNWyhz4QxOPQaSocUvppD%2FrWbNlPux%2F6w%2BbOskD9XwKjVZQ7Na8FUtKPjW%2FZ6SOUYk7xOWukpaMnhzsOt9IFtO3owcUNjUtGLHUNaoHlHNILaEmlSryXPkJDAEsfKJ2T4j7YFoZJrg%2FntIx90ZI0QyY1bMAclOJjfq%2FFzGW6Nz528%2FcfmLOiNbHa2x6Vw395ySRJ7TPiZ0vRL0SXDGbbl6c65J9lU2tlf8EoWUSbaJ5ma2XXF3sKwYG1Z7atL1%2Fdu7g5JHX1N6%2FqyBWz20MDfVYHiYW%2FGJC5EZ4P2qx38w6j3SpaCnfNB5kD1jX%2FjK7LRGr9Px0ZxYbNRJAoJSsYg4qp3lQ0LppZfGdpDAXsZf2TRgFpSQUNhxzbyt2C0T1WlxFG%2BgwF7H7xmN4TxpgDIa1tmmhipbdaYnhgbzvNk6eeuXKIRkdDMrZAwz5LOIosbZah5dXhgwYwtc4uwxct%2BiNfLLSisNSE7chdoLIGstl9bpdkopVyHpRN2Gmjlo6nmERYE8DoNdFaSMUuKiIOqGaLR2nPaQz0aI2QOFFrilQAFZJ9uYIxpNEirb45p3gOOruLBFv2ICFo01c8q7U4OowNiiqVCTRx0DrDGLNHyxcsCRbsPER9koCrifpdQHK6qJO3mYpU31QCCICMUwJkgX9FJIDDReNfoRaNKB4gzr6gxWrSNLwMNt5qJICgESAWwWoD3oDVBqVmF5zzYx2mEmigho49N5kqDdRAGhTrJDlnnBoaBdgD41Q5thVLcigPLtF5xA1csqnWvxRNAnRfACEoU5TtDtrGUMSJLWcUEX1R%2Bzwu0UQf7SLQRyV5aB4hdmSyUuzxIR20A85%2BhuWMtEuEA6tdDTydt7o%2FgyLGYXBDREtL527kZRgzbUxrDA4aOiDCvQ1GDj4oosJ8HA4Chd6NmJTdtL%2B2G9t7YLFYleJgRd%2FVPg8dHTvFU6A4WDQcRMrCFAfPRBx8k3FIUOg1Bk014kBbEBfPacShSIHHP8qVuERSvtTtGgtwJmKxktERsNZqRFz6VKWwOw%2BVBasHlyRgUmw7Sbva%2BixmfAfpq8FtNaE45YxaFUuN4LQvWO2Vk2rihNaD0da2mLrYQHTatrv%2B%2Bt%2FBawV4nRReEDAgfCx0nbC4EV6L7xPgzUlcA8x1eCsakHoz3hODW%2B%2F5qNWdd4zX7jZPLY2W6wXRzNSC7Mn1Y1jQ%2BPD77z2CRYwVraRRq1zU6hi1E%2B%2BcVCt3HGivxdFqsMTQizkJmvhUaFBkyCAWaKklU2r24GbseCXjkyH0dJP3H0ZYsNLykfcmAFkhS9V9COkj72l1mI2QqrYjR8bjfv9reGPj8Eb%2FHnjlJiznrUM0Ad7ikSMatO8%2FPBnaIiCy9P932kY5hLU2zhNhJYePaEyAiACPzGwg7WaAlfKkwUvrC4PMIFNfjqnbBysH3FqnY1AHZNrVGESpQI2oWvaGIooKp%2BXYY0KEJ18HLl%2BDWnvUW6UGFxlFeBCuivqw%2BjA%2BBmxCIS7V814DQXeI%2FyoTxYwfh%2BYbgiWxmUakMRnC16wlQ5Q86PF34kwFwoAtF0HLuI%2FJ9YHhZuhzF%2FoyoImBrsUIxtdMMknvNhjMZrPDZmWdxGE2yerPyZdZVjCbnRb%2BgPrhYhcreNRFXslqctrZCzyiSHjyrM1pM7uMP1d%2FutZTn8uUbn4Y45lMmdPpZsKabCw1CtK8DhCL3vrUtmoTuhTk9MxExSUqzVrnURjSQj6KhZDUY4VZn7R5BKUpjm8mr9Uik8OOyhlnPPoOrkxU6AAxnd%2FS6PctXmDZd2hQQKNsQ01AiGllVutwOumiGgTAEg22mVXz5CRR5QOT7Dl%2FIBxpaUWtF%2FSDOFYtYzWLyRyOxenRoEi9bfUi65Sge920gt9CCvMVE7RqQJ9Ny66rVVQ%2FuGVR8dF3yJ%2FJxvvI4fvUJzSWOHvh9ffWGPS6Ze88aiZr71Nt96kPTaltObVWj9NEH9Lhaaxw0apysKUEWKKBuoeq9iC053mzxeF0e7RKRrkJjhCjYLO7ROaENTqs3ljiRFU68uV7Lr98z4mLdNx4%2BvIGOYa%2BUBfofmm9C7eod3CgD3mUaBGfCfQF%2BnQ6NzqQfbpPsSYLzCxt7Q%2BrvMPK%2B62uY37yAnkRMxmxWyY2l3Va1Pe4FuxGjGwytiXLHOf%2BnZPu%2F%2FfdXEshNE%2B4excWqauzyZnjd2cP0PDU4aNvTbj3jXBv7LtZw11boQ1aY0rQ6GxZvL1Iby%2Fi7aUpuIMZOuHmPezqL6vzdrG3Ntz8u%2BqP2dW71Xn3j83I1p%2FfhXijz9Zfx1yqYgDRoPUi91HMffTWPrx1cDLmciHFJTxYWdoIwMaDGzez3%2BKO3HfwPvKjBvL%2F29mvbjz2JmH%2F8T%2FhjGo%2FHhzpE8Dhyf4doHhkQS7I1gZQth48%2B1UO7%2FY3ck4DMYoHNx4k7wB8977HfuvoH7OaDJPxmRz8s6BJmbDOg6e2n5lWPhmr2HFOK6rHmh8zkfkH1IT6%2FeXsnrEN5CHOdfQV4lKvJnuq3BNj02sysUhxwyrMpQyuHkYYSCMdSHzmhiNbNor0gRI87Jmytef%2FgfwxUhHkpO4hWkrnNIrustkna14hTaTgcwhkWjGOOm4siXiHpCPA8ZWwd9fYnF2YKVYs7uLe9oapEDz2DBboq5tD3PkVyn%2FDtP%2Beh%2BbjzWJQPwQInRRCJxgVZaNzAnjh2kJtpJ2KmZIRRGDZKvv1xvh1oCSQfhSkRAHLo7hxwNR3r9mmfg4hm3v9NWTj9WriN40Qvq6%2Bd82NAGAJTm64Xm3lnqjU5orR4KCwykycPiuxtQGYRENnBY0qQorUaeJpKIvUwTj%2FCfWQ%2BrxOoOITT9xY%2Bz8OivohvYgS6%2Bir9ORNX8f3Cb1J3ZR2F9E1GWjnoLRzoEljdKHKHcRy5BJvytbJ5wQKM%2BOBHLpAOl3Iz9j9x5alTsAgtijxYGk5rOYlJLB2yDKRzvhATkpmTSnnaFa7RufNqo2ip4WhKw00BjsCsHqSCiPaPrhSYY6D02nHwel42EyAvxF4JSRinkcJi0LKVlsA%2FUOwSE5GQR8oLdZvJuMoVID6l1AcaLRfPdiIwyUVOjY6Fvj01BoOFZoPZ6acMrl2QNMQwVzR%2BrcdXcErev86MnqE5g4ni7RrxZib%2FiDGls6D33tGt6m0ztg3Y6Si5AvmsL1JSW6mD4ssWZ05fFxkyebSqSPUWuhaqSsNvRA%2BugpTIlktaFUZNOPVh40NeM7p0mNAbq8kah0btZJPUDlKxAv0MyFhtXRb%2BKNuB%2FqiehHuDmDWv6Zf0h7Ro3rTaLoJBtrL7LdpRA%2Fzcg%2B9TON79V72tbrsGVpdNi29ZmpOFdmKS9M%2Bs0s2Yf9njNWYqcZusVJHYY8mHkX9ycvam1DvZ5HwYrXOeA957UmwxWxW%2F08bhtBGgVYL3W4Nqu8GEuwB2h4ba2Bq75t%2FoJ5Ee2D8czGUj%2FqNBvUK2o9vZcQjXinOjTT2Nl7C5DBDhkYjbTklVy2zVgfau22Zsr85gZXmKXxWwniyaxsmuxpbaFPjaB4hp8%2F2kbAHLZenSX7APjRwiksPboc51OqdBCi8OEAOBxaTUZrJmw0E1M2LA6otsFjdXDsy3ZYkd6pbkrbp04nBLDm4a3wBwk6Hw%2BoWcmf98LHb8bAe29RsJz%2FTzLSAnZxmskzZr2sKvgz1mdNSH7cX3UCZjNb4yO2iLBVoplqcOMVKKuQS2K%2B5bsNHZSkB6KSiJJ%2BQtCxz0E4PotE0WrkAdJl1RfWOYq24AQswUxfQY6hQaVdrBs3YnMrZ6qFi3dwfrZx9dqU4Nu%2BRWx%2BBcXExLv4h%2FiF8RrA7zMlhLjeT9GHBJxAwTVKFYYLpw07iIpHhe847%2F6f3Xx%2BJPCIKnu94el1bdh47d4todHze0e1%2BmPt95x13HTzv%2FHuGouRhd9pxu4MXt5x7bOcWscf7oscoPjwxtx%2FXt4zeXwmf45qheXsnZUoj9AEvTWhfZmCCtYn7ku3ZWZRomJpQIPneYS6LzCvp9VE0K8Hrm0mGyRDpa5ElL3aIBo0%2FzcdjDt5JJAe5mPUlV25emfQRQi52SChkvOGQ9%2Fve0A4yvINuGIPFra9vO%2F2xq4ozu8zm7EFvzkEyWd7eEpC8Tc0WS1b9qSPnxXZ47JNSgI%2FyMekev%2F8eKQabAaliCpzU0y5F29qiVkt9%2FmIecKAefycTO%2FdGpUQ0hT1dJa2LPX2JMn16x0fcN26gj%2BPQus5Xdh2hT6TGf%2Brmou5zqN3DTDvatOoRdm%2BOSjvLIepN1vpUaQuB9gSReuO%2FWoubXH2riKkGtEKIfhT1Hc0cr6VwsAc0rqImJj5LSu%2Bph70UsGpsge5PcNXtnq4Gf4Ko%2BRPw%2BX2iiz4DoCXe1qF1I6D7wZZkW7tW5DmpjR6G2jzoPMxpXf0NOXQogjqBfeiVrewBrLccm7NVoZ2TKMNjLyqgm%2F6UM3IYr1Bt8I7VGns1IUa930XNoff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AxNRE0NjMhMhYVERQGIyEiJhkBNDYzITIWFREUBiMhIiYBETQ2MyEyFhURFAYjISImGQE0NjMhMhYVERQGIyEiJh0VAZAVHR0V%2FnAVHR0VAZAVHR0V%2FnAVHQJYHRUBkBUdHRX%2BcBUdHRUBkBUdHRX%2BcBUdMgGQFR0dFf5wFR0dAm0BkBUdHRX%2BcBUdHf29AZAVHR0V%2FnAVHR0CbQGQFR0dFf5wFR0dAAAJAAAAAARMBEwADwAfAC8APwBPAF8AbwB%2FAI8AdgCyDQAAK7E8bDMzsATNsTRkMjKwHS%2BxTHwzM7AUzbFEdDIysC0vsVyMMzOwJM2xVIQyMgGwkC%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%2BwTDOwHM2wRDKwLS%2BwXDOwJM2wVDIBsGAvsADWsRAgMjKwCc2xFygyMrAJELEwASuxQFAyMrA5zbFIWDIysWEBKwAwMT0BNDY7ATIWHQEUBisBIiYRFBY7ATI2PQE0JisBIgYVPQE0NjsBMhYdARQGKwEiJgE1NDYzITIWHQEUBiMhIiYRNTQ2MyEyFh0BFAYjISImETU0NjMhMhYdARQGIyEiJh0VyBUdHRXIFR0dFcgVHR0VyBUdHRXIFR0dFcgVHQGQHRUCvBUdHRX9RBUdHRUCvBUdHRX9RBUdHRUCvBUdHRX9RBUdMsgVHR0VyBUdHQGlFR0dFcgVHR0VyMgVHR0VyBUdHfz1yBUdHRXIFR0dAaXIFR0dFcgVHR0BpcgVHR0VyBUdHQAAAAEAHQAiBPIEKgAFAAATCQEnAScdAaMDMtT9oc4Bxv5cAzTU%2FaHPAAABAGoAagRGBEYACwAAEwkBNwkBFwkBBwkBagEa%2FubUARoBGtT%2B5gEa1P7m%2FuYBPgEaARrU%2FuYBGtT%2B5v7m1AEa%2FuYAAAMAF%2F%2FsBMQEmQATABsAJwC3ALIOAAArsBIvsBfNsBwvsCMzsB3NsCEyshwdCiuzQBwmCSuyHRwKK7NAHR8JK7AbL7ADzQGwKC%2BwAdawFc2wFRCxJgErsB4ysCXNsCAysiUmCiuzQCUjCSuyJiUKK7NAJhwJK7AlELEZASuwBc2xKQErsSYVERKyAhYbOTk5sCURsBI5sBkSswMXEBokFzmwBRGwBzkAsRcSERKwEDmxHQ4RErMABRUYJBc5sBsRshQZATk5OTAxEhAAIAAVFAcBFhQPAQYiJwEGIyICEBYgNhAmIAM1MzUzFTMVIxUjNRcBHAGQARxOASwHB20IFAj%2B1HeOyIPCARLBwf7uRmTIZGTIAe0BkAEc%2FuTIjnf%2B1AgUCG0HBwEsTgJs%2FvDCwQESwf5ZyGRkyGRkAAADABf%2F7ATEBJoAEwAbAB8AXQCyDgAAK7ASL7AXzbAbL7ADzQGwIC%2BwAdawFc2wFRCxGQErsAXNsSEBK7EZFREStQMCEBIcHSQXObAFEbAHOQCxEg4RErAJObAXEbAQObAbErUBAAcFHB4kFzkwMRIQACAAFRQHARYUDwEGIicBBiMiAhAWIDYQJiADITUhFwEcAZABHE4BLAcHbQgUCP7Ud47Ig8IBEsHB%2Fu5GAZD%2BcAHuAZABHP7kyI15%2FtUHFgdtCAgBLE4CbP7wwsIBEML%2BWcgAAAIAFwAXBJkEsAAbACsARQCwGC%2BwCs0BsCwvsADWsAfNsgcACiuzQAcDCSuwBxCxDAErsBPNsgwTCiuzQAwQCSuxLQErsQwHERKzFxgcIyQXOQAwMRM0EjcVDgEVFBYgNjU0Jic1FhIVFA4CIi4CARQWOwEyNjURNCYrASIGFRfSp2d8%2BgFi%2Bnxnp9Jbm9Xs1ZtbAd0dFWQVHR0VZBUdAli3ASg%2BpjfIeLH6%2BrF4yDemPv7Yt3bVm1tbm9UBDBUdHRUBkBUdHRUABABkAAEEsASxAAMABwALAA8AMACyBAAAK7EIDDMzAbAQL7AE1rAHzbAHELEIASuwC82wCxCxDAErsA%2FNsREBKwAwMTczESMBETMRMxEzETMRMxFkyMgBLMhkyGTIAQEs%2FtQB9P4MAyD84ASw%2B1AAAAIAGgAbBJYElgBHAFEAYgCwEi%2BwUM2wSy%2BwNs0BsFIvsADWsEjNsEgQsU0BK7AkzbFTASuxSAARErELPTk5sE0Rsw8VMzkkFzmwJBKxGS85OQCxUBIRErEHHTk5sEsRswMhJ0UkFzmwNhKxK0E5OTAxExQfAhYfAQcWFzcXFh8CFjMyPwI2PwEXNjcnNzY%2FAjY1NC8CJi8BNyYnBycmLwImIyIPAgYPAScGBxcHBg8CBgU0NjIWFRQGIiYaBpcCDhgDUC08hQUtMQUmKCIbLyYGLi8FhjgwUAMYDwGYBQWYARAXA1AsPIYFLTAGJigiGy8mBTIsBYU7LlADGQ0ClwYBZ36yfn6yfgJZISkmBjEsBYY7LlEDGg0ClwUFlwINGgNRLD2GBSwxBiYoIhwtJgYzKgWGOi9RAxkOAZgFBZgBDhkDUS86hgUvLgYmMBlYfn5YWX5%2BAAAABwBk%2F%2F8EsAUUABkAIwAnACsALwAzADcAiQCyIQAAK7AkzbIoMDQyMjKwJy%2ByKjI2MzMzsBvNsBcvsATNsQ4sMjKwLy%2BwCc0BsDgvsBrWsCTNsCQQsSUBK7AFMrAozbAsMrIlKAors0AlAAkrsCgQsSkBK7AwzbAwELExASuwLTKwNM2wDTKyNDEKK7NANBMJK7A0ELE1ASuwHc2xOQErADAxEzU0NjMhNTQ2MyEyFh0BITIWHQEUBiMhIiYTESERFAYjISImNzMRIxMzESMRITUhEzMRIxMzESNkDwoBEzspASwpOwETCg8OC%2FvmCw5kA4Q7Kf1EKTtkZGTIZGQBLP7UyGRkyGRkBAEyCg9kKTs7KWQPCjILDg78bgMg%2FOApPDwpArz9RAK8ASxk%2B7QCvP1EArwAAAAAAQABAAEFFQTdAAoALACyCQAAK7AEMwGwCy%2BwCdawCM2wCBCxBQErsATNsQwBK7EFCBESsAE5ADAxEwkBIxEhESERIREBApAChMj%2B1P7U%2FtQCWQKE%2FXz9qAGQ%2FnACWAAAAgBkAAAD6ASwAA4AEQAiALIMAAArAbASL7AB1rAGzbIGAQors0AGCAkrsRMBKwAwMTcRNDYzIREhERQGIyEiJgERAWQOCwHbAZAOC%2FyuCw4CWAEsGQR%2BCw7%2BDP1dCw4OAxIBLP7UAAADAAQABASsBKwACwATABkAggCwCi%2BwD82wFC%2BwF82yFxQKK7NAFxUJK7ATL7AEzQGwGi%2BwAdawDc2wDRCxFAErsBfNshcUCiuzQBcZCSuwFxCxEQErsAfNsRsBK7EUDRESswoDDhMkFzmxERcRErMJBA8SJBc5ALEUDxESswcADRAkFzmxExcRErMGAREMJBc5MDESEBIkIAQSEAIEICQSEBYgNhAmIBMRMxEzFQSgARIBRAESoKD%2B7v68%2Fu4W8wFW8%2FP%2BqkdkyAG2AUQBEqCg%2Fu7%2BvP7uoKACX%2F6q8%2FMBVvP9%2FgGQ%2FtRkAAAAAAL%2FnAAABRQEsAALAA8ALgCyAAAAK7AHM7AKL7AMzbAPL7ADzbIDDwors0ADAQkrsAUyAbAQL7ERASsAMDEjATMDMwMzASEDIwMTMwMjZAGv0RWiFNABr%2F3mKfIoMeAbqgSw%2FtQBLPtQAZD%2BcAH0ASwAAAAAAgAAAAAETASwAAsADwBKALILAAArsAzNsA8vsAnNsAEyAbAQL7AE1rAHzbIEBwors0AEAAkrsAcQsQ0BK7AKzbERASuxBwQRErECCTk5sA0RsQgMOTkAMDExESEBMxEhETMBIRElMzUjAer%2B3sgBLMj%2B3gHq%2FuGvrwGQASwB9P4M%2FtT%2BcMhkAAMAAQABBK8ErwAPABcAHgBjALINAAArsBPNsBcvsAXNAbAfL7AB1rARzbARELEZASuwHM2wHBCxFQErsAnNsSABK7EZEREStA0EEhcYJBc5sBwRsB45sBUStAwFExYdJBc5ALEXExEStQEICQAaHiQXOTAxEjQ%2BAjIeAhQOAiIuARIQFiA2ECYgAzMRMxEzAwFfoN703qBfX6De9N6gXPIBVPLy%2FqxQlsiW%2BgHe9N6gX1%2Bg3vTeoF9foAIC%2Fqzy8gFU8v5kASz%2B1P7UAAMABAAEBKwErAALABMAGgBhALAKL7APzbATL7AEzQGwGy%2BwAdawDc2wDRCxGQErsBjNsBgQsREBK7AHzbEcASuxGQ0RErQKAw4TFCQXObAYEbAVObARErQJBA8SFiQXOQCxEw8RErUBBgcAFRgkFzkwMRIQEiQgBBIQAgQgJBIQFiA2ECYgAxsBIxEjEQSgARIBRAESoKD%2B7v68%2Fu4W8wFW8%2FP%2Bqk%2F6%2BpbIAbYBRAESoKD%2B7v68%2Fu6goAJf%2Fqrz8wFW8%2F5iASz%2B1P7UASwAAAACAAAAAASwBLAACwATACkAsgkAACuwDM2wEDKwEy%2BwAs0BsBQvsRUBKwCxDAkRErIEAQ45OTkwMTUREyEbARQGIyEiJhMzFyE3MwMhyAMgxwEOC%2FuCCw7IyDIBLDLIYf2iGQHbArz9RP4lCw4OAebIyAH0AAMABAAEBKwErAALABUAGABGALAKL7APzbAUL7AEzQGwGS%2BwAdawDM2wDBCxEQErsAfNsRoBK7ERDBEStQQJCgMWGCQXOQCxFA8RErUBBgcAFhckFzkwMRIQEiQgBBIQAgQgJBMUFiA2NTQmIAYBEQUEoAESAUQBEqCg%2Fu7%2BvP7uFvMBVvPz%2FqrzAToBKQG2AUQBEqCg%2Fu7%2BvP7uoKABtKzy8qyr8%2FP%2BigGRyAABABcAFwSZBLAAHABTALAFL7ANzbARL7AZzQGwHS%2BwAdawD82wDxCxCgErsAnNsR4BK7EKDxEStQUEExQXGSQXObAJEbEVFjk5ALERDREStAEACRQVJBc5sBkRsBc5MDESFB4CMj4CNSMUBiAmEDYzMhcHIREHJiMiDgEXW5vV7NWbW5b6%2Fp76%2BrGIbpIBkJGdxnbVmwLO7NWbW1ub1Xax%2BvoBYvpRkgGQkXpbmwAAAAIAFwAABJkEsAAQACEAegCyEQAAK7AfL7AWzbIWHwors0AWGgkrsA0vsAXNsg0FCiuzQA0ACSsBsCIvsADWsBDNsBAQsRkBK7AazbEjASuxEAARErEREjk5sBkRtwcFCwoTFB8hJBc5sBoSsQkIOTkAsRYfERKwITmwDRGxCRI5ObAFErAHOTAxEzQ%2BAjMyFzcRITcmIyIGFQMRIQcWMzI2NTMUDgIjIicXW5vVdsadkf5wk3CHsfpJAZCTcIex%2BpZbm9V2xp0CWHbVm1t6kf5wk1D6sf2oAZCTUPqxdtWbW3oAAAoAZAAABLAEsAADAAcACwAPABMAFwAbAB8AIwAnAFAAsAgvsBgzsAnNsBoysAwvsBwzsA3NsB0ysBAvsCAzsBHNsCEysBQvsCQzsBXNsCUyAbAoL7AI1rIMEBQyMjKwC82yDhIWMjIysSkBKwAwMTMhESETESERJTUzFSc1MxUnNTMVJzUzFRMhNSE9ASEVJTUhFSU1IRVkBEz7tGQDhPzgZGRkZGRkZGQB9P4MAfT%2BDAH0%2FgwB9ASw%2B7QDhPx8ZGRkyGRkyGRkyGRk%2FahkZGRkyGRkyGRkAAIAAAAABEwEsAAZACMASgCyFwAAK7AgL7AJzQGwJC%2BwBdawGs2yBRoKK7NABQAJK7AaELEbASuwDs2yDhsKK7NADhMJK7ElASsAsSAXERKzBA4FGiQXOTAxNRE0NjsBNTQ2MyEyFh0BMzIWFREUBiMhIiYBITU0JisBIgYVOylkdlIBLFJ2ZCk7Oyn8fCk7AZABLB0VyBUdZAJYKTvIUnZ2Usg7Kf2oKTs7AuWWFR0dFQAAAAIAZAAABEwETAADABUAFwCyAAAAKwGwFi%2BwANawA82xFwErADAxMxEzERM%2BAR4CPgE3EQ4BLgMGB2RkZDyHeHxyamQpKHuEkId0WhQETPu0AZA8MA0hGwVPUQH0UUUKKCgKRVEAAAAAAwAAAAAEsASXACEAMQBBAGcAsi8AACuwPjOwJs2wNjKwDC%2BwHc0BsEIvsADWsAfNsAcQsSIBK7ArzbArELEyASuwO82wOxCxEAErsBfNsUMBK7EyKxESswwLHRwkFzkAsSYvERK0BxATFAMkFzmwDBGxCA85OTAxERQWOwEyNjURND4BIB4BFREUFjsBMjY1ETQuAiIOAhUTETQ2OwEyFhURFAYrASImJRE0NjsBMhYVERQGKwEiJg4LMgsOjeQBBuSNDgsyCw5jo97o3qNjyAwIoAgMDAigCAwCWAwIoAgMDAigCAwBEwsODgsBLH%2FRcnLRf%2F7UCw4OCwEsdN6jY2Oj3nT91QHMCAwMCP40CAwMCAHMCAwMCP40CAwMAAAAAgAAAMgEWAPoAAUAEQAAESEFEQUhATcnNxc3FwcXBycHASwBLP7U%2FtQCsI2NR42NR42NR42NAZDIAyDI%2FquNjUeNjUeNjUeNjQAAAAIAAADIA3AD6AAFAA8AEgABsBAvsA7WsAnNsREBKwAwMREhBREFISU3FhUUByc2NTQBLAEs%2FtT%2B1AK8RW9qQ1YBkMgDIMg5NYevqYU2boqSAAAAAAMAAAC6BGID9wAFAA8AHQA8ALAAL7ABzQGwHi%2BwDtawCc2wCRCxEwErsBrNsR8BK7ETCRESsxAWFx0kFzkAsQEAERKzCQ4TGiQXOTAxGQEhJRElATcWFRQHJzY1NDcXFhUUDwEXNzY1NC8BASwBLP7UAZJFb2pDVl4He3cHUQaOkAYBkQGQyPzgyAHJNYevqoU3boqRzQiXwb2WCEIIsuPmsggADQAAAAAEsASwAAcAEQAVABkAHQAhAC8AMwA%2FAEMARwBLAE8BAQCyAAAAK7EwRDMzsBLNsikxRTIyMrAaL7InK0wzMzOwG82yJS1NMjIysCIvsQIGMzOwI82wCDKwHi%2BxDkgzM7AhzbE0STIyAbBQL7Aa1rEFHjIysB3NsQMfMjKwHRCxMAErsQ0sMjKwM82wNTKwMxCxLgsrsCoysCXNsEAysi4lCiuzQC4iCSuyAQsPMjIysCUQsTcBK7FESDIysDvNsSZKMjKwOxCxTAErsEIysE%2FNsjk9RjIyMrFRASuxMB0RErUUFRgZND8kFzmxNyURErIoKTg5OTkAsSIbERKzExQ4OSQXObAjEbIEOjs5OTmwHhJACQUWGTY3PD1AQyQXOTAxMSERIzUjFSM1MzUhNTM1IxEhExEhEQERIREDNTMVAzM1IwE1IREzFSMVIzUjNTM1AzUzFQMzETMRITUjNTMRIRMRIREDNSEVATUzFRM1MxUB9MhkyGQBkGRk%2FgxkASz%2B1AEsyGRkZGQBLAEsyGTIZGRkZGRkyAEsyMj9qMgBLMgBLP7UZGRkAfRkZGRkZGQBLPu0ASz%2B1AK8ASz%2B1P2oZGQCvGT%2BDGT%2B1GRkZGTI%2FgxkZAPo%2FtT%2B1MhkAfT%2BcAEs%2FtT84GRkA4RkZP1EZGQAAAAACQAAAAAEsASwAAMABwALAA8AEwAXABsAHwAjAHAAsgwAACuyBBQcMzMzsA3NsRUdMjKyDAAAK7AFzQGwJC%2BwCNawC82wCxCxEAErsAwysBPNsA%2FNsBMQsRQLK7AXzbAXELEYCyuwG82wGxCxIAErsCPNsSUBK7EQCxESsQcGOTmxGxcRErEcHTk5ADAxNTMRIxM1IRUnETMRFzUzFScRMxEVNTMVNREzERU1MxUnETMRZGRkASzIZMhkZMhkZMhkyMgD6PtQZGTIA%2Bj8GMhbW8gD6PwYyFtbyAPo%2FBjIW1vIA%2Bj8GAAAAAIAAAAABLAEsAAHABMAKQCyBwAAK7ASL7AEzQGwFC%2BwAdawCc2xFQErALESBxESsgAGCzk5OTAxERM0NjMhCQEAFBcWMjc2NCcmIgcBDwoB2gK8%2Fgz92B0eUx4dHR5THgK8AdsKD%2F1E%2FgwD41QdHh4dVB0eHgAAAAMAAQAABd0EsAAHABMAGQAxALIHAAArsBczsBIvsATNsBQyAbAaL7AB1rAJzbEbASsAsRIHERK0AAYLFhkkFzkwMRsBNDYzIQkBABQXFjI3NjQnJiIHJTMJAScBAQEOCwHaArz%2BDP3XHh1UHR4eHVQdAgtkArz%2BDDIBwgK8AdsLDv1E%2FgwD41QdHh4dVB0eHrD9RP4MMgHCAAAAAAEAZAAABLAEsAAKAD8AsgAAACuwBy%2BwAs0BsAsvsADWsArNsAoQsQUBK7AEzbEMASuxCgARErICBwg5OTkAsQcAERKyAQQFOTk5MDEzETchEQcRIQchEWSvA51k%2FRJkAu4EAa%2F8GGQD6GT8GAAAAAABAMgAAARMBLEACgAAMwkBETQmIyEiBhXIAcIBwh0V%2FOAVHQG8%2FkUEfhQeHhQAAAADAAAAAASwBLAACwAXACcAWQCyJQAAK7AczbAKL7ADzbIKAwors0AKAAkrsAcysgMKCiuzQAMBCSuwBTIBsCgvsADWsAvNsAIysAsQsQgBK7AFMrAHzbEpASuxCAsRErMMDyciJBc5ADAxNREzFyE3MxEjNSEVExchNwMuASMhIgYHAzc%2BATMhMhYfARYGIyEiJshkAlhkyMj84DUoAlA%2BXgIQCv4%2BChACQiYCEwoB9AoTAiYCCwr9qAoLZAK8yMj9RMjIAtl8fAFaCw4OC%2FuBmAoODgqYCg4OAAAABAAAAGQEsARMAB0AJQAtADEAbwCwAy%2BwJc2wKS%2BwLc2wIS%2BwE80BsDIvsADWsB%2FNsh8ACiuzQB8vCSuwHxCxJwErsCvNsTMBK7EfABESsBk5sSsnERKzISQlICQXOQCxLSkRErMfIiMeJBc5sCERsS4xOTmwExK0CxkaLzAkFzkwMTUUFjMhMjY1ETQmKwEuBCsBIg4CDwEjIgYVADQ2MhYUBiICFBYyNjQmIiU1MxU7KQPoKTs7KZYEDzM3UyrIKVI6LgsMlik7AWSQyJCQyAY%2BWD4%2BWAFYZMgpOzspAlgpOwgbRTUrKTs7FRQ7Kf5wyJCQyJABIFg%2BPlg%2BXmRkAAIANQAABLAErwAeACIAHgCyAAAAK7ANM7AezbICDA8yMjIBsCMvsSQBKwAwMTMhNSIuAT8BIRcWBiMVITUmJy4BLwEBIwEGBw4BDwEBExcTNQFtKT4kE1wBh1IQKzUBoSIoEh4GBv5%2FXf5xGBwMKg8PAWuyLnRCFjYs6t4tV0JCASoTLg4NA%2Bb8EjAbDBoHBwHHAcmM%2FsMAAwBkAAADwwSwACAAKQAxAGUAsiAAACuwIc2yIAAAK7ABzbApL7AqzbAxL7ANzbANELALzQGwMi%2BwBNawIc2wKjKwIRCxLgErsBDNsCUg1hGwHM2xMwErsSUuERKwFjkAsSkhERKwHDmwKhGwFjmwMRKwEDkwMTM1PgE1ETQuAyc1BTIWFRQOAg8BHgQVFA4BIyczMjY1NCYrATUzMjY1NCYjZCk7AgkWJB8B13i6FyEiCwwIG0U0K3amT8ihWYB9Xp%2BLTGyom1kHMygDOxwXHQ0PB0cBsIw3XTcoCAcDDDNBdkZUkU3IYVRagWR7TVJhAAAAAAEAyAAAA28EsAAZACAAsgAAACuwAc2wGDKwCy%2BwDjOwDM0BsBovsRsBKwAwMTM1PgE3EzYmJy4BJzUhFw4DDwEDBhYXFchNcwitCihHBgkFAakCIToiGQUFgAowRzkHQy8DUTgkEwEDATk5CCMnJQwM%2FMc0PAY5AAL%2FtQAABRQEsAAJACUAfgCyGwAAK7AfL7ICBRYzMzOwDM2yHwwKK7NAHxAJK7AKMgGwJi%2BwAdawB82wBxCxCgErsCXNsCUQsR0BK7AYzbIYHQors0AYGgkrsh0YCiuzQB0bCSuwGBCxEAErsA%2FNsScBK7EKBxESsQUIOTkAsR8bERKwCTmwDBGwBDkwMSczESM3FyMRMwcTETMhMxEjNC4DKwERFxUhNTcRIyIOAxVLS0t9fUtLffqWAryWMhAVLiEiyGT%2BcGTIIiEvFBHIAyCnp%2FzgpwNjASz%2B1B0nFQkC%2FK4yZGQyA1ICCRUnHQAAAAIAIf%2B2BI8EsQAJACUAiQCyCAAAK7ACzbAfL7AWM7AMzbIfDAors0AfCgkrsA8yAbAmL7AK1rAlzbAlELEdASuwGM2yGB0KK7NAGBoJK7IdGAors0AdGwkrsBgQsRABK7APzbEnASuxHSURErMCCAkBJBc5sRAYERKzBAYHAyQXOQCxAggRErEABTk5sB8RsgEEGjk5OTAxPwEVITUXBzUhFQMRMyEzESM0LgMrAREXFSE1NxEjIg4DFSGnAyCnp%2FzgZJYCvJYyEBQvISLIZP5wZMgiIS4VEDN9S0t9fUtLA88BLP7UHScVCQL9djJkZDICigIJFScdAAAAAAQAAAAABLAETAAPAB8ALwA%2FAAA1FBYzITI2PQE0JiMhIgYVNRQWMyEyNj0BNCYjISIGFTUUFjMhMjY9ATQmIyEiBhU1FBYzITI2PQE0JiMhIgYVHRUETBUdHRX7tBUdHRUDIBUdHRX84BUdHRUD6BUdHRX8GBUdHRUCWBUdHRX9qBUdMhQeHhRkFR0dFcgUHh4UZBUdHRXIFB4eFGQVHR0VyBQeHhRkFR0dFQAEAAAAAASwBEwADwAfAC8APwAANRQWMyEyNj0BNCYjISIGFREUFjMhMjY9ATQmIyEiBhUTFBYzITI2PQE0JiMhIgYVERQWMyEyNj0BNCYjISIGFR0VBEwVHR0V%2B7QVHR0VBEwVHR0V%2B7QVHcgdFQK8FR0dFf1EFR0dFQK8FR0dFf1EFR0yFB4eFGQVHR0VAfQUHh4UZBUdHRX%2BcBQeHhRkFR0dFQH0FB4eFGQVHR0VAAQAAAAABLAETAAPAB8ALwA%2FACYAsg0AACuwBM2wLS%2BwJM2wHS%2BwFM2wPS%2BwNM0BsEAvsUEBKwAwMT0BNDYzITIWHQEUBiMhIiYTNTQ2MyEyFh0BFAYjISImEzU0NjMhMhYdARQGIyEiJhM1NDYzITIWHQEUBiMhIiYdFQRMFR0dFfu0FR1kHRUD6BUdHRX8GBUdyB0VAyAVHR0V%2FOAVHcgdFQJYFR0dFf2oFR0yZBUdHRVkFB4eAmxkFR0dFWQUHh7%2B6GQVHR0VZBQeHgJsZBUdHRVkFB4eAAQAAAAABLAETAAPAB8ALwA%2FACYAsg0AACuwBM2wHS%2BwFM2wLS%2BwJM2wPS%2BwNM0BsEAvsUEBKwAwMT0BNDYzITIWHQEUBiMhIiYRNTQ2MyEyFh0BFAYjISImETU0NjMhMhYdARQGIyEiJhE1NDYzITIWHQEUBiMhIiYdFQRMFR0dFfu0FR0dFQRMFR0dFfu0FR0dFQRMFR0dFfu0FR0dFQRMFR0dFfu0FR0yZBUdHRVkFB4eAUBkFR0dFWQUHh4BQGQVHR0VZBQeHgFAZBUdHRVkFB4eAAAAAAgAAAAABLAETAAPAB8ALwA%2FAE8AXwBvAH8AUgCyDQAAK7BMM7AEzbBEMrAdL7BcM7AUzbBUMrAtL7BsM7AkzbBkMrA9L7B8M7A0zbB0MgGwgC%2BwANayECAwMjIysAnNshgoODIyMrGBASsAMDE9ATQ2OwEyFh0BFAYrASImETU0NjsBMhYdARQGKwEiJhE1NDY7ATIWHQEUBisBIiYRNTQ2OwEyFh0BFAYrASImATU0NjMhMhYdARQGIyEiJhE1NDYzITIWHQEUBiMhIiYRNTQ2MyEyFh0BFAYjISImETU0NjMhMhYdARQGIyEiJh0VZBUdHRVkFR0dFWQVHR0VZBUdHRVkFR0dFWQVHR0VZBUdHRVkFR0BLB0VAyAVHR0V%2FOAVHR0VAyAVHR0V%2FOAVHR0VAyAVHR0V%2FOAVHR0VAyAVHR0V%2FOAVHTJkFR0dFWQUHh4BQGQVHR0VZBQeHgFAZBUdHRVkFB4eAUBkFR0dFWQUHh78kGQVHR0VZBQeHgFAZBUdHRVkFB4eAUBkFR0dFWQUHh4BQGQVHR0VZBQeHgAABv%2BbAAAEsARMAAYACgAaACoAOgBKACAAsAAvsCYzsAHNsC4yAbBLL7FMASsAsQEAERKwBDkwMQM1MzUXBzUTMxEjExQWMyEyNj0BNCYjISIGFTUUFjMhMjY9ATQmIyEiBhU1FBYzITI2PQE0JiMhIgYVNRQWOwEyNj0BNCYrASIGFWXJpqbIZGTIHRUCWBQeHhT9qBUdHRUBLBQeHhT%2B1BUdHRUB9BQeHhT%2BDBUdHRVkFB4eFGQVHQH0ZEt9fUv%2BDARM%2B%2BYUHh4UZBUdHRXIFB4eFGQVHR0VyBQeHhRkFR0dFcgUHh4UZBUdHRUAAAAABgABAAAFFQRMAA8AHwAvAD8AQwBKABcAskAAACsBsEsvsEDWsEPNsUwBKwAwMTcUFjMhMjY9ATQmIyEiBhU1FBYzITI2PQE0JiMhIgYVNRQWMyEyNj0BNCYjISIGFTUUFjsBMjY9ATQmKwEiBhUBETMRExc1MzUjNQEdFQJYFB4eFP2oFR0dFQEsFB4eFP7UFR0dFQH0FB4eFP4MFR0dFWQUHh4UZBUdAyBkIafIyDIUHh4UZBUdHRXIFB4eFGQVHR0VyBQeHhRkFR0dFcgUHh4UZBUdHRX75gRM%2B7QCJn1LZEsAAgAAAMgEsAPoAA8AEgAtALANL7AEzbAEzQGwEy%2BwANawCc2xFAErsQkAERKwEDkAsQQNERKxERI5OTAxGQE0NjMhMhYVERQGIyEiJgkBESwfAu4fLCwf%2FRIfLAOEASwBEwKKHywsH%2F12HywsAWQBLP2oAAADAAAAAASwBEwADwAXAB8AWQCyDQAAK7AfL7AbzbAXL7AEzQGwIC%2BwANawEM2wEBCxGQErsB3NsB0QsRUBK7AJzbEhASuxHRkRErARObAVEbETEjk5ALEfDRESshATFTk5ObAbEbAUOTAxNRE0NjMhMhYVERQGIyEiJj8BBScBExEhEjQ2MhYUBiIaEgRYExkZE%2FuoEhpk9wEqSgEl7PwYbE5wTk5wLAP0EhoaEvwMEhoa7baDnAE%2B%2FuAB9P7OcE5OcE4AAgCU%2F%2FMEHAS9ABQAHgA9ALINAAArsB0vsATNAbAfL7AA1rAVzbAVELEbASuwCM2xIAErsRsVERKxDQQ5OQCxHQ0RErIHABg5OTkwMRM0PgEzMh4BFAcOAQ8BLgQnJjcUFjMyNjQmIgaUedF6e9B5SUm7OTkKImNdcys%2Fwpdqa5eX1pYC6XzXgX7V9pVy9kJCCSJrb6BLi5Zrl5fWlpcAAAIAAQABBK8ErwAPABUASQCyDQAAK7ATzbAUL7AFzQGwFi%2BwAdawEc2wERCxEwErsAnNsRcBK7ETERESsQ0EOTmwCRGxBQw5OQCxFBMRErMBCAkAJBc5MDESND4CMh4CFA4CIi4BEhAWMxEiAV%2Bg3vTeoF9foN703qBN%2B7CwAd703qBfX6De9N6gX1%2BgAgn%2BnvoDVgACAHUABAPfBQ8AFgAlAAATND4DNx4GFRQOAgcuAjceARc3LgInJjY%2FAQ4BdURtc3MeFUlPV00%2FJU5%2Bmk9yw4B%2BDltbEAcWLgoPAgkJXDcBll64oZ3FYEePdndzdYZFWZlkOwQGXrh%2BUmwaYgYWSihJjTQzbpYAAAADAAAAAATFBGgAHAAhACYAVwCyGgAAK7APzbAIL7AEzQGwJy%2BwANawDM2wDBCxEwErsBbNsSgBK7ETDBESswYdHiAkFzmwFhGxHyI5OQCxCA8RErMVHR8hJBc5sAQRsyAiIyUkFzkwMRkBNDYzBBcHISIGFREUFjMhMjY9ATcVFAYjISImJTcBJwkBFzcvAeulAW4fuv7JKTs7KQH0KTvI66X%2B1KXrAbShAZxy%2FmsB%2BXFxFVwBkAEspesGCLo7Kf4MKTs7KX3I4aXr62oyAZxx%2FmsB%2BHFxVRwAAAAAAgAAAAAElQRMABwALgBIALIaAAArsBDNsCIvsCfNsAkvsATNsAQQsAbNAbAvL7AA1rANzbEwASsAsSIQERKyFR0kOTk5sQkaERKwJTmxBAYRErAmOTAxGQE0NjMhFwYHIyIGFREUFjMhMjY1NxUUBiMhIiYBPgMfARUJARUiDgXrpQEFAoVVkSk7OykB9Ck7yOul%2FtSl6wGnHmdnXx4dAWj%2BmQcYSENWQzkBkAEspetQIFg7Kf4MKTs7KZk1pevrASEmNBMJAQHRAUQBPtgCDhczQ20AAAAAAgAAAAAEqARMAB0AIwBSALIbAAArsBDNsAkvsATNAbAkL7AA1rANzbANELEUASuwF82xJQErsRQNERKzBx4fIiQXObAXEbAhOQCxCRARErMWHyIjJBc5sAQRsSAhOTkwMRkBNDYzITIXByEiBhURFBYzITI2PQE3FRQGIyEiJgkCJwEn66UBLD1Csv6jKTs7KQH0KTvI66X%2B1KXrAVYBGwI3if5SkgGQASyl6xexOyn%2BDCk7OylFyKml6%2BsBjf7kAjeJ%2FlGTAAABAAAAAQSwBLEAFwBFALISAAArsBYvsA4zsALNsAkyAbAYL7AU1rADMrAQzbAIMrEZASuxEBQRErEGEjk5ALEWEhESsQ0XOTmwAhGxAAw5OTAxEQEVMzUjCQEjFTM1CQE1IxUzCQEzNSMVASzIyAEsASfDyAEs%2FtTIw%2F7Z%2FtTIyAJbASjGyAEs%2FtTIxv7Y%2FtTGyP7UASzIxgAAAAABAMgAAAOEBEwAEwAdALIRAAArsAszAbAUL7AA1rANzbAIMrEVASsAMDE3ETQ2OwEyFhURAREBERQGKwEiJsgdFWQVHQH0%2FgwdFWQVHTID6BUdHRX%2BSwHn%2B7QB6P5KFR0dAAAAAQAAAAAEsARMABcAHwCyFQAAK7ENDzMzAbAYL7AA1rARzbAIMrEZASsAMDE1ETQ2OwEyFhURAREBEQERAREUBisBIiYdFWQVHQH0AfT%2BDP4MHRVkFR0yA%2BgVHR0V%2FksB5%2F4ZAef7tAHo%2FhgB6P5KFR0dAAABAIgAAASwBEwABgAUALIGAAArsAQzAbAHL7EIASsAMDETAREBEQERiAI0AfT%2BDAImAib%2BGQHn%2B7QB6P4YAAAAAQDIAAAETARMAAIAADMJAcgDhPx8AiYCJgAAAAIAyABkA4QD6AAPAB8AADcUFjsBMjY1ETQmKwEiBhUBFBY7ATI2NRE0JisBIgYVyB0VyBUdHRXIFR0BkB0VyBUdHRXIFR2WFR0dFQMgFR0dFfzgFR0dFQMgFR0dFQAAAAEAyABkBEwD6AAPAAA3FBYzITI2NRE0JiMhIgYVyB0VAyAVHR0V%2FOAVHZYUHh4UAyAVHR0VAAAAAQAAAAAEKARMAAYAFACyAAAAK7AFMwGwBy%2BxCAErADAxMREBEQkBEQH0AjT9zARM%2FhkB5%2F3a%2FdoB6AAAAQAAAAAEsARMABcAHwCyAAAAK7EQFjMzAbAYL7AU1rAEMrANzbEZASsAMDExEQERARE0NjsBMhYVERQGKwEiJjURAREB9AH0HRVkFR0dFWQVHf4MBEz%2BGQHn%2FhkBtRUdHRX8GBUdHRUBtv4YAegAAAEBLAAAA%2BgETAATAB0AsgAAACuwDjMBsBQvsBLWsAIysAvNsRUBKwAwMSERARE0NjsBMhYVERQGKwEiJjURASwB9B0VZBUdHRVkFR0ETP4ZAbUVHR0V%2FBgVHR0VAbYAAAIAZADIBLAEKAAPABIAEgCwDS%2BwBM0BsBMvsRQBKwAwMTc1NDYzITIWHQEUBiMhIiYRIQFkHRUD6BUdHRX8GBUdBEz92vpkFR0dFWQVHR0BDwI0AAEAuQAHA%2FkEqQAFAAATATcJASe5AlDw%2Fp8BYfACV%2F2w8AFhAWHwAAABARD%2F0gRSBHQACAAAJQkBNwEXBxUBARABYf6f8QI8FQH9sMIBYQFh8P3FFgEB%2FbEAAAAAAgADAAMErQStAAsAFwBCALAKL7AOzbAVL7AEzQGwGC%2BwAdawDM2wDBCxEQErsAfNsRkBK7ERDBESswQJCgMkFzkAsRUOERKzAQYHACQXOTAxEhASJCAEEhACBCAkEzMVMzUzNSM1IxUjA6ABEwFEAROgoP7t%2Frz%2B7YnIyMjIyMgBtgFEAROgoP7t%2Frz%2B7aCgAVHIyMjIyAACAAMAAwStBK0ACwAPAEkAsAovsAzNsA8vsATNAbAQL7AB1rAMzbAMELENASuwB82xEQErsQ0MERKzBAkKAyQXOQCxDAoRErEHADk5sQQPERKxAQY5OTAxEhASJCAEEhACBCAkEyE1IQOgARMBRAEToKD%2B7f68%2Fu2JAlj9qAG2AUQBE6Cg%2Fu3%2BvP7toKABUcgAAAAAAgADAAMErQStAAsAFwAyALAKL7AEzbAEzQGwGC%2BwAdawB82wB82xGQErsQcBERKxDBA5OQCxBAoRErENFTk5MDESEBIkIAQSEAIEICQTFzcXNyc3JwcnBxcDoAETAUQBE6Cg%2Fu3%2BvP7tU9WNjdWOjtWNjdSNAbYBRAEToKD%2B7f68%2Fu2goAEo1Y6O1Y2N1I2O1Y0AAAIAAwADBK0ErQALABEAMgCwCi%2BwBM2wBM0BsBIvsAHWsAfNsAfNsRMBK7EHARESsQwOOTkAsQQKERKxDQ85OTAxEhASJCAEEhACBCAkEwkBJwcnA6ABEwFEAROgoP7t%2Frz%2B7WsBFAGbr%2BxmAbYBRAEToKD%2B7f68%2Fu2goAGE%2FusBm67sZgAAAAADAAMAAwStBK0ACwA4ADwAbACwCi%2BwOc2wPC%2BwJ82wIS%2BwG82wNC%2BwBM0BsD0vsBLWsB7NsB4QsS4BK7AHzbE%2BASuxHhIRErEhNDk5sC4RtAkEKDo7JBc5ALEnPBESsQcAOTmwIRGwKjmwGxKyDA8uOTk5sDQRsQYBOTkwMRIQEiQgBBIQAgQgJBMzMhYyNjQ%2BBToBMzIWFRQGBw4EFzM%2BBDU0LgMjIg4CEzM1IwOgARMBRAEToKD%2B7f68%2Fu3JjwQPBwYCBQIJBA4EEwMTFggXBQ8nHRgByAUSLSIcIzFEMRsyUUUmiMjIAbYBRAEToKD%2B7f68%2Fu2goAIZAgYMCgcFAwIBFBAWDBABBBcfPSYDCikyWDIzTCgYBhg1YP4uZAADAAMAAwStBK0ACwAVABkAOwCwCi%2BwDM2wFS%2BwDjOwEs2wES%2BwFs2wGS%2BwBM0BsBovsRsBKwCxEhURErEHADk5sRYRERKxBgE5OTAxEhASJCAEEhACBCAkNyE1IxEhFTMVIxMzNSMDoAETAUQBE6Cg%2Fu3%2BvP7t7QGQZP7UZGRkyMgBtgFEAROgoP7t%2Frz%2B7aCgiWQBLGTIAZBkAAACAAAAAASwBLAAGAAvAGkAshQAACuwEi%2BwH82wHDKwAC%2ByDhkhMzMzsAHNsgwjLTIyMgGwMC%2BwFNayBRwpMjIysBPNsgceJzIyMrExASuxExQRErMiIy4vJBc5ALESFBESsBU5sQAfERKwHTmwARGyHigpOTk5MDERNTM%2BATc1MxUeAhczFSMOAQcVIzUuASczHgEXNTMVNjcjNTMuAScVIzUOAQczFcMfh4vINnZrEsvLGbdZyIyIHmAYb0vIlTTJyBllSshLbhjRAfTIfZUayMgUUINFyGaoIcXFG5d9SW0Yzs4wnshKahjMyxdsSMgAAAAAAwAEAAQErASsAAsAEwAfAEYAsAovsA%2FNsBMvsATNAbAgL7AB1rANzbANELERASuwB82xIQErsRENERK1BAkKAxQaJBc5ALETDxEStQEGBwAXHSQXOTAxEhASJCAEEhACBCAkEhAWIDYQJiADNyc3FzcXBxcHJwcEoAESAUQBEqCg%2Fu7%2BvP7uFvMBVvPz%2FqpJh4dth4dth4dth4cBtgFEARKgoP7u%2Frz%2B7qCgAl%2F%2BqvPzAVbz%2FduHh22Hh22Hh22HhwAAAAMABAAEBKwErAALABMAGQBGALAKL7APzbATL7AEzQGwGi%2BwAdawDc2wDRCxEQErsAfNsRsBK7ERDREStQQJCgMUGCQXOQCxEw8RErUBBgcAFxkkFzkwMRIQEiQgBBIQAgQgJBIQFiA2ECYgAzcXNxcBBKABEgFEARKgoP7u%2Frz%2B7hbzAVbz8%2F6qa41XzI7%2BpgG2AUQBEqCg%2Fu7%2BvP7uoKACX%2F6q8%2FMBVvP%2BI41XzY7%2BpwAAAAMABAAEBKwErAALABMAGwBGALAKL7AWzbARL7AEzQGwHC%2BwAdawDM2wDBCxGQErsAfNsR0BK7EZDBEStQQJCgMPFCQXOQCxERYRErUBBgcADhskFzkwMRIQEiQgBBIQAgQgJBMUFwEmIyIGExYzMjY1NCcEoAESAUQBEqCg%2Fu7%2BvP7uFj4COGR0q%2FPNYXCr8zsBtgFEARKgoP7u%2Frz%2B7qCgAbRzZAI3PvP98jvzq3BhAAAAAAEAAABjBLAD6AAGABoAsAUvsALNAbAHL7EIASsAsQIFERKwADkwMREBESERIRECWAJY%2FagCIwHF%2FtT%2B1P7TAAABAAAAYwSwA%2BgABgAaALAAL7ABzQGwBy%2BxCAErALEBABESsAQ5MDEZASERCQERAlgCWP2oAZABLAEs%2Fjv%2BQAEtAAAAAAEAzAAABEoEsAAGAB8AsgUAACsBsAcvsAXWsATNsQgBK7EEBRESsAE5ADAxEwkBIREhEcwBwgG8%2Ftb%2B1AJYAlj9qP2oAlgAAAEAaAAAA%2BYEsAAGAB8AsgYAACsBsAcvsAHWsATNsQgBK7EEARESsAY5ADAxEyERIREhAWgBKAEsASr%2BPwJYAlj9qP2oAAAAAAEAAADHBLAETAANAAA1PgM3EQkBEQ4DBkaJ55wCWP2oX7CkgsiE1a1nCAEP%2Fjv%2BQAEtAiREdQAAAgAAAAAEsASwAAYADQARALIAAAArAbAOL7EPASsAMDExERcBFwEXExcBFxEhF4EBJo7%2B2oHrjgEmgf5wgQGQgQEmjv7agQMJjgEmgQGQgQACACIAIwSOBI4ABgANAAA3ASchEScJAREXARcBFyIBJ4EBkIH%2B2QGogQEnjv7ZgbABJ4H%2BcIL%2B2QI1AZCBASeN%2FtmCAAMAFwAXBJkEmQAPAB8AIwBPALANL7AgzbAjL7AUzbAdL7AFzQGwJC%2BwAdawEM2wEBCxGQErsAnNsSUBK7EZEBEStQUMDQQhIyQXOQCxFCMRErEJADk5sB0RsQgBOTkwMRI0PgIyHgIUDgIiLgEBEx4BOwEyNjcTNiYrASIGEzM1Ixdbm9Xs1ZtbW5vV7NWbAVY6BCMUNhQjBDoEGBTPFRgwyMgB4uzVm1tbm9Xs1ZtbW5sCRv7SFB0dFAEuFB0d%2FcVkAAAFAAAAAASwBLAAJgAqADAANAA7ADQAsicAACuwMTOwKs2wMjIBsDwvsDHWsAUysDTNsAcysT0BK7E0MREStAsMEzU6JBc5ADAxETMVIREzESE1MzUjNjQmLwEuASMiDwEGByYvASYjIgYPAQ4BFBUjEyERIRMiNj8BFxMRIREBNx4DI2QBkMgBkGRvAQMCIgs9JyAd7xYSExXuIR0nPQojAgJvZAGQ%2FnBkAyITEtXbAZD%2Bj8oFDiASAgMgyAEs%2FtTIZAELEwisJzARkA0WGAyQEi4msQgUCgH8fAGQAfRgMC%2B%2F%2FHwBkP5wA4TFDClXOQACAAD%2F6gSvBLAAGwAyABcAsgAAACsBsDMvsCfWsA%2FNsTQBKwAwMRU1Ny4CPgE3PgU3FAIOBC4CIwc2Fjc2JT4DNz4BJyYiBgcOAQ8BBAfYCQgDFTguL2llmonoaCxKaHGDeHtcUw9jEidDNwE4RmFrWykWBAgHFCERI509Pf6PWRaPwTU8gGKCOzxVMy0eOR69%2FszQm1UzCQYTDzd%2FDVNCqCY%2FX4BUMhQJBR0ZM3MgIMXMAAABAG8ADAREBOcASAAjAAGwSS%2BwAdawRc2wRRCxPAErsUoBK7E8RRESsTo2OTkAMDESFBceARcWPgM3PgEnHgEHDgEHDgQeAT4BNz4ENzYCJxYXFicmJy4CNw4EFx4DDgQHBi4CNw4BbwUJRkYfQjo4KA8gDhRPVhEFHxYKCQ8DAwgOGSQYOURrQ0APJqWkFhUnRw8ST1MFMw0qZ0ouDwIMBAgBAQsQGhImOhcHDjQ%2FAblCHjh%2FLRUKJT49HkLtJ1CoZCFJLBMUIA8XCAsBBAYUHD1DbkOsAVNtLFWfBQIHIYbZlQgfZm2nUww7GzQbKBcZEAQKLk1WIC5uAAAD%2F8MAfQTtBDMAIQA%2FAEcAQwCwGi%2BwKc2wOi%2BwCc0BsEgvsDzWsDfNsUkBK7E3PBESQAoJGRoIKSg1PkBDJBc5ALEJOhEStwARJC41PkJHJBc5MDEDNz4GMh4FHwEHDgYiLgUnNx4FMj4ENy4EJxYVFAYiJjU0NwYXFhc3LgEvAT0aBhxGT3N2k5CTdnNPRhwGGhoGHEZPc3aTkJN2c09GHAabB0MtW1R6gHdSWSxICwE3HTo5HjGw%2BLAuZoUxaWklTBMUAlgoCihXVGBHLy9HYFRXKAooKAooV1RgRy8vR2BUVygKKApgPV44KygzXDtoDgFJJUU6GUpZfLCwfFVJV3N8Q2kYYCQkAAAABP%2FDAAAE7QSwABYAIAApAEEAoQCyDwAAK7AOMwGwQi%2BxQwErsDYauj3v790AFSsKsA8uDrAMwAWxDgH5DrANwLAPELMLDwwTK7MQDwwTK7MZDwwTK7MaDwwTK7MkDwwTK7MlDwwTK7IQDwwgiiCKIwYOERI5sBk5sBo5sCQ5sCU5sAs5ALcLDA0QGRokJS4uLi4uLi4uAUAKCwwNDg8QGRokJS4uLi4uLi4uLi6wQBoBADAxAzc%2BBjMyFzczASM3LgQnNxIXNy4BNTQ3BhcWFz8BLgEvAQE3PgY3Jic3HgIfAQcOBD0aBhxGT3N2k0g9PCWU%2FsaUJVKmcmknCpvStyVrjy5mhTFpLxceOg8OASgmFi0vIjATLwFhKydDgS4NGhoHJVplkwJYKAooV1RgRy8RjvtQjxVlZ3k4Dyj%2B5jaNEqduVUlXc3xDL1ccUhsa%2FaeRDyYyJj8YQAJ%2FMJI2j0AUKCgMNGtiZgAAAAP%2FngAABRIErAALABIAFwAAJhYzITI2JwEuAQcBNwkBITUjFREbATUjbxslBQ4lGxX9fhQ4FP1%2B9QG9Ab3%2Bp8hkZMhEREcgBCAiBSD71mQC0%2F0tZGQBkP7UASxkAAAAAAEAZAAVBLAEsAApAEgAsB4vsAnNAbAqL7Al1rAFMrAWzbALMrIWJQors0AWGAkrsiUWCiuzQCUjCSuxKwErsRYlERKxHR45OQCxCR4RErEWJTk5MDETNTQ2NwERNDYyFhURAR4BHQEUBiclERYdARQGLwEjBwYmPQE0NxEFBiZkFg8Ba1h8WAFrDxYYEf6ZZBoTXt5eExpk%2FpkRGAEGKRQxDgFFAVM%2BWFg%2B%2Fq3%2Buw4xFCkUDQz5%2FvlbFkAUEQlOTgkRFEAWWwEH%2BQwNABEAAAAABEwEsAAJABsAHwAjACcAKwAvADMANwA7AD8AQwBHAEsATwBTAFcAADUUFjMhMjY1ESE1ITU0JisBNSMVITUjFSMiBhUTNTMVJzUzFSc1MxUTNTMVJzUzFSc1MxUTNTMVJzUzFSc1MxUTNTMVJzUzFSc1MxUTNTMVJzUzFSc1MxUdFQPoFR37tARMHRWWZP4MZJYVHWRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZDIUHh4UAu5klhUdZGRkZB0V%2FEpkZMhkZMhkZP5wZGTIZGTIZGT%2BcGRkyGRkyGRk%2FnBkZMhkZMhkZP5wZGTIZGTIZGQAAAMAAAADBXgErgAKABAAGQBBALAAL7AYM7ABzbATMrALL7AIM7AQzbADMgGwGi%2BxGwErALEBABESsREWOTmwCxGzBw0SFSQXObAQErEGDjk5MDE9ASEBMzUJATUjCQEhFzcnIQE3FzM1CQE1IwEDAljxASz%2B1J%2F9qP6rAQN6jbX%2BqwKmjXqfASz%2B1PHIyAJYxv7Z%2FtTF%2FagCWHqOtP2VjnvG%2Ftn%2B1MUAAAEAAAAABLAETAASABoAsg4AACuwEC%2BwDDOwBM0BsBMvsRQBKwAwMRkBNDYzITIWFREUBiMhAREjIiY7KQPoKTs7Kf2s%2FtBkKTsBkAJYKTs7Kf2oKTv%2B1AEsOwAAAwBkAAAETASwACUAKQAtAGAAsh8AACuwCc2yCR8KK7NACQEJK7AVMrAmL7AqM7AnzbArMgGwLi%2BwANawJjKwA82wKDKwAxCxEgErsCoysBfNsCwysS8BK7EDABESsCQ5sBIRsR4fOTmwFxKwGTkAMDETNSEVFBcWFxYzMj4GJzQ9ASEVFA4FIi4FGQEhESERIRFkASwGEVUnNSU7KR8RCwMCAQEsBhgnTWWdwJ1lTScYBgEsAZABLAJYyPpxIFwZCwsUHCMoLC4YEQj6yCpSfmpxUDMzUHFqflIBVgEs%2FtQBLP7UAAAAAAH%2F4gC4BGgD3gAFAAADFwkBNwEe4wFgAWHi%2Fb4Bm%2BMBYf6f4wJDAAABAEYA2gTMBAAABQAAEwkBJwkBRgJEAkLi%2Fp%2F%2BoAMd%2Fb0CQ%2BP%2BnwFhAAAAAAL%2FOgBkBXYD6AAIABEAKACwBy%2BwBM0BsBIvsAfWsATNsRMBK7EEBxESsAE5ALEEBxESsA45MDEDCQEjESEXIREBFyERIwkBIxHGASsBLMsBgdf84AGU1wF9xgErASvIArwBG%2F7l%2FnDIAlgBLMj%2BcP7lARsCWAAAAAEAEgAABKoEsAAyAEYAsiIAACuwGTOwLM2wLBCwJs2xFR0yMrAvL7AEzbAQL7AJzQGwMy%2BwJNawH82wHxCxHAErsBfNsTQBK7EXHBESsC05ADAxEyY3NjMhNz4BOwEyFhQGKwEDDgIrARUUBiImPQEhFRQGIiY9ASMiJjU0NjMhNyEiJicSBQ8OGQOAJgUbEV4UHh4UNskCCB4SHx0qHf7UHSodMhUdHRUCFzD9hyAtBQOrGBITohEVHSod%2FD8EDRYyFB4eFDIyFB4eFDIeFBUdyCoWAAAAAAIAAAAABLAETAADAA8AIACyAAAAK7ABzbAEL7AFzbANMrAJzQGwEC%2BxEQErADAxMREhEQE1MzQ2MyEyFhUhFQSw%2B1DIOykBLCk7AfQDIPzgA4RkKTs7KWQAAAAAAgABAAAF3QRMAAMAEAAoALIAAAArsAHNsA8vsA3NsAUysAnNAbARL7ESASsAsQEAERKwBDkwMTMBIQkBETM0NjMhMhYVIRUhAQEsBLD%2B1PtQyDspASwpOwH0%2FBgCvP1EAZACWCk7OynIAAAAAQEuAAADggSwAAkAIQCyCQAAKwGwCi%2BwAdawB82xCwErsQcBERKxBAk5OQAwMQEzESMJASMRMwEBLsbGASoBKsbG%2FtYBLAJYASz%2B1P2o%2FtQAAAAAAQAAAS8EsAOCAAkAHACwCC%2BwAs0BsAovsQsBKwCxAggRErEABTk5MDERARUhNQkBNSEVASwCWAEs%2FtT9qAJYASrGxv7W%2FtfFxQAAAAQAAAAABLAEsAAPABkAHQAhAEkAsgwAACuwGs2wHjKwHS%2BwIDOwBc2wEC%2BwFM0BsCIvsBvWsB7NsB4QsR8BK7AJzbIfCQors0AfAAkrsSMBK7EJHxESsBk5ADAxPQE0NjMhMhYdARQGIyEiJhsBPgEzITIWFxMBMzUjFzM1IzspA%2BgpOzsp%2FBgpOx%2BsBSQUAqATJQWs%2Fo9kZMhkZGRkKTs7KWQpOzsBVQLjFictF%2F0k%2FtRkZGQAAAAD%2F5sAZASwBEwACwApADcAJgABsDgvsADWsAbNsAYQsSoBK7AyzbE5ASuxKgYRErEMGjk5ADAxAzU0Nj8BFS4EFzU8Az4FOwElESUjExYOASMiKwEiJicCARE0NjMyFhURFAYjIiZlMhkZBA4iGhbJAQICBAUHBMgCo%2F1dJi8CCgwPBQNTFB0ENwPoHRUUHh4UFR0CWDIYMg0N%2BgIHFRYhVfoCDAQKBAcDBQIB%2BvyuyP7sDAsBHBUBUf7iA1IVHR0V%2FK4UHh4AAAIASgAABGYEsAArADMANQCyLwAAK7AzzbApL7AfM7ADzbAYMrIpAwors0ApJQkrAbA0L7E1ASsAsSkzERKxLDE5OTAxEzQ2OwE3Ez4BNycmNjsBMhYHBhUeARcTFzMyFhUUBgcOBCMiJi8BLgEFHgEyNjcGIkobFBJ1Pw96UxIGEhReFBIGElN6Dz92ERQbGhIIHmRqn0998To6EhoBpww4RjgLMGwBXhUdrQFHTX4UIBMaFRMkARN%2FTf65rR0VFCgHAwsdFRIpFBQHKdwxPT0xBgAAAQAVABUEnAScABcAABMXBzcXNxc3Fyc3JzcnNwcnBycHJxcHFxXpTuAtm5st4E7qtLTqTuAtm5st4E7pswG9LeBO6bOz6U7gLZucLOFO6bS06U7hLJwAAAMAAABkBLAEsAADACIALgAaAAGwLy%2BwKNawFs2xMAErsRYoERKwFDkAMDE1MxEjARQ7ARY7ATI3EzY9ATQmIyE2PQE0JisBIgYPAgYVExE%2FATMVByEVAyMnyMgBLGQ9fA%2F6LiXuHT0n%2FrgcPScyGzAOYJEUZJZkMjIBwvrWiMgCWP3zS2Q5AVgfK2QsUXYHlixRKBzGxBol%2FokBd9XUr%2BF9%2FolkAAAAAAMAAAAABLAETAADACIALgBwALIcAAArsCXNsBUvsAAzsCjNsC4vsAfNsAEysCwvsArNAbAvL7AA1rADzbADELEEASuwI82wIxCxJgErsBjNsBgQsSkBK7ARzbEwASuxJiMRErIIKCw5OTmwGBGwFTmwKRKwKzkAsS4cERKwKjkwMRkBMxE3ETQ7ATY7ATIXExYdARQGIyEWHQEUBisBIiYvAiY3HwEzNSchNQMjByPIZGQ9fA%2F6LiXuHT0n%2FrgcPScyGzAOYJEUZJZkMjIBwvrWiGQBkAJY%2Fah9AZBLZDn%2BqB8rZCxRdgeWLFEoHMbEGiXU1a%2FhfQF3ZAAAAAMACABkBRUEVQADACIAQQB5ALAgL7AkzbAbL7ApzbAxL7AUzbABMrIxFAors0AxAAkrAbBCL7AA1rADzbADELEEASuwI82wIxCxLQErsBjNsi0YCiuzQC08CSuxQwErsS0jERK0DBEbFD8kFzkAsRskERKwIzmwKRGwGDmxFDERErIXPEE5OTkwMTcRMxE3ETQ2PwElNjMyHwEWFRQPASEyFhQGKwEDDgEjISImNxchEz4BOwEyNjU0JiMhKgIuBCcmNTQ%2FAScFCMhkHA4OAWoOCxEMbQ4LVQEuVWttVGuCBxsP%2FqsHpmRkASWDBhsPyxASEhD%2BNwELBAkDBwQEAgUKk1b%2BrcgCWP2oSwINESUKCeYGDHAOFBIOeUyQTv6tFieiG1kBUxUoHhUUHQEBAgMFAwwIDg23U%2BwAAAAD%2F5sAZQSwBFYAHgA4ADwAeQCwGC%2BwJM2wHS%2BwH82wOC%2BwA82wOjKyOAMKK7NAODkJKwGwPS%2BwAdawH82yHwEKK7NAHywJK7AfELEmASuwFM2wFBCxOQErsDzNsT4BK7EmHxEStAcMHAQpJBc5ALEdJBESsCY5sB8RsAA5sQM4ERKyAScsOTk5MDECNDYzBScmNTQ%2FATYzMhcFHgIVERQGIyEiJicDIyInMzIWFxMhNxElBxcWFRQHDgUqASMhAREzEWVsVQEuVQsObQ0QCw4BbQcUIawI%2FqsQGwaCa1QK3g8bBoMBJWv%2BqVeRCgUBBQMHBAkECwH%2BJAPpyAJDkEwBeRAQFQ1xDAbmBA0nEf3yDaEoFQFTZCkU%2Fq1ZAfbtU7gLDwsJAwUDAgEB%2FgwCWP2oAAAAAAMAYQAABEwFDgAbADYAOgBHALI3AAArsDjNAbA7L7AV1rA3MrApzbIpFQors0ApOgkrsDMysCkQsS8BK7AOzbE8ASuxKRURErESNjk5sQ4vERKwETkAMDEbAR4CMyEyNjURNCYnJTU0JiIGFREnJgYPAQYXNxcWNz4FPAE1ETQ2Fh0BFBYXBREHIQM1IRVh5gQNJxECDQ2iKBX%2BrU6QTHkPJQ5wFltTtxYZAwUDAgEBMjIoFQFTWf4JCAJYAs%2F%2BlQYTH6YHAVYPGwaDalRua1X%2B0lQMAQ1uFgtWkhINAQUDBwQJBAsBAcgWEhMVyhAbBoL%2B2mT%2BcMjIAAAAAAMAAgAKA%2B0FGAAdADQAOABFALA1L7A2zQGwOS%2BwCtawNTKwK82yKwoKK7NAKzgJK7AhMrArELEnASuwD82xOgErsSsKERKxDB85ObEPJxESsA05ADAxEwYfAR4BPwEUBhUUFjI2PQElPgE1ETQmIyEiBg8BAxMhFxEFDgEdARQGJjURPAEuAScmDwETNSEVAhAWcA0mD3kBTZBOAVMUKaIN%2FfMRJQoKmuwB91n%2BrBQoMjIDBwYYFriSAlgCSR8Wbg0BC1UzzS5UbG5UaoMGGw8BVgemHA4P%2FoIBU2T%2B2oIGHA%2FKFhISFgHICwcQCAMNEpICccjIAAAAAgAFAAAEsASrAA4AFQA6ALIMAAArsBDNsA8vsAXNAbAWL7AA1rAQzbEXASsAsRAMERKxCRI5ObAPEbEAEzk5sAUSsQgUOTkwMRM0PgIzMgQSEAIEICQCARchBwkBFQVfoN16ogEToKD%2B7f68%2FuygASUCASwCAZL%2BbgJVet2gX6D%2B7P68%2Fu2goAETAQrJwgEmASrFAAIAAAAABKsEqwAQABcAOACyDgAAK7AUzbAWL7AFzQGwGC%2BwFNawCs2xGQErALEUDhESsBI5sBYRsgoAETk5ObAFErAXOTAxETQ%2BAjMyHgIVFAIEICQCNwEnITchNV%2Bg3Xl63aBfoP7s%2Frz%2B7aDIAZICASwC%2FtQCVXrdoF9foN16ov7toKABE6X%2B2sLJxQAAAAIABQAABLAEqwAOABUAPgCyDAAAK7ARzQGwFi%2BwANawEc2wERCxEgErsAnNsRcBK7ERABESsQwPOTmwEhGxBRU5ObAJErELFDk5ADAxEzQ%2BAjMyBBIQAgQgJAIlMxEzETMBBV%2Bg3XqiAROgoP7t%2Frz%2B7KABJ8jIyP7UAlV63aBfoP7s%2Frz%2B7aCgAROl%2FtQBLAGQAAACAAUAAASwBKsADgAVAE0AsgwAACuwFC%2BwBc0BsBYvsADWsBXNsBUQsRIBK7AJzbEXASuxFQARErEMDzk5sBIRsQUQOTmwCRKxCxE5OQCxFAwRErIIABA5OTkwMRM0PgIzMgQSEAIEICQCJQkBIxEjEQVfoN16ogEToKD%2B7f68%2FuygAScBLAEsyMgCVXrdoF%2Bg%2Fuz%2BvP7toKABE6X%2BcAGQASz%2B1AAAAAAEAAUAAASwBKsAEACIAJgAmgB8ALIOAAArsCrNsE8vsIwvAbCbL7AA1rAUzbAUELFYASuwCs2xnAErsRQAERKwEjmwWBFADg4FEyEjJDxKVXiEhYmUJBc5sAoSQAoNIiYwO1pndpmaJBc5ALFPKhEStxYwNjxGSFVXJBc5sIwRQAkKABRYbIWNjpQkFzkwMRM0PgIzMh4CFRQCBCAkAhMGFgcUFgcyHgEXFhceAjcWBhcWFxQOARcWNz4CNy4BJy4BJyIOAgcGJyY2NS4BJzYuAQcGJyY3NjceAhceAR8BNDYnJjY3PgM3JjcyFjI2Ny4DJzYnHgE%2FATYuAScGJw4DBwYmBw4BBwYWBw4BJT4BNxYyPgE3FBYVLgM3MwVfoN16ed2gX6D%2B7f68%2Fuyg%2BQgbBiIBDBYYCBhUFj45HQguAyotBgEFaHUeIiMDDi4NDkYRCT0gLhAyEAQBBikEAggZGhcTEwsGEAYoGwYMKA4OEwQEJQQFCgcYFgYQCB8SFwkKKSM%2FDAsJHzYMCwcvUg8TEg8rGj4IDz0PFT4DAxMBAzEBAwMaAwoRCxIHIgksHCSiAQJVet2gX1%2Bg3Xqi%2Fu2goAETAVkhdxwJRhkLEwQMHggvHgQSShRHCQYTCgwDcx0kPh8JAQcHEAsBAgsLIxcCLwINCAMWJhIdGR0cHhAGAQEHChMlCQgDSRUXKwoOKhQZCRITAwkLFycVIAcnBQ0DBQQkIxYMAwMMEgYKAQMHBgcnDwsXByJxcQwkBwoMEQQYVQECBgQMXwAAAAABAAAAAgSvBIUAFAAAPAE3ASY2NzYXBRc3FgcGJwEGIi8BDwJYIU5gpI7%2B%2FZH7DaR7gv2sDysPb48rEAJXZck2XGWK6H6vXEYv%2FawQEG4AAAYAAABgBLAErAAPAB8ALwAzADcAOwBQALAML7A0zbA3L7AFzbAcL7AwzbAzL7AVzbAsL7A4zbA7L7AlzQGwPC%2BwNdaxMTkyMrAJzbEYKDIysjUJCiuzQDUACSuxECAyMrE9ASsAMDE9ATQ2MyEyFh0BFAYjISImETU0NjMhMhYdARQGIyEiJhE1NDYzITIWHQEUBiMhIiYBITUhEyE1IRMzNSM7KQPoKTs7KfwYKTs7KQPoKTs7KfwYKTs7KQPoKTs7KfwYKTsCWAH0%2FgzIASz%2B1GTIyMRkKTs7KWQpOzsBuWQpOzspZCk7OwG5ZCk7OylkKTs7%2Fplk%2FgxkArxkAAACAGQAAARMBLAAAwAJACUAsggAACuwAC%2BwAc0BsAovsAjWsAfNsQsBKwCxAAgRErAEOTAxEzUhFQUhAREHEWQD6PxKA4T%2BosgETGRkZP4M%2FtTIAfQAAAAAAwAAAGQEsASwAAkAIQAlAGAAsAcvsAHNsAovsB0zsA7NsRgiMjKwJS%2BwE80BsCYvsA%2FWsCLNsCAysg8iCiuzQA8LCSuwADKwIhCxIwErsB4ysBjNshgjCiuzQBgcCSuwAjKxJwErALEOChESsB85MDE9ASEVFAYjISImGQE0NjMhNTQ2OwEyFh0BITIWFREhNSMVETM1IwSwOyn8GCk7OykBLDspyCk7ASwpO%2F4MyMjIyMjIKTs7AVUBkCk7ZCk7OylkOyn%2BcGRkAfRkAAAAAAQAAAAABLAEsAAGAA0AFAAbABQAsgAAACuwEjMBsBwvsR0BKwAwMTERFzcXBxcBNxc3JzchATcXNxEhNwM3JyERJweByI7Igf5wgciOyIH%2BcALZjsiB%2FnCByMiBAZCByAGQgciOyIEDIIHIjsiB%2FJmOyIH%2BcIEC5siB%2FnCByAAABgAAAAAEqASoAAsAFQAfACkAQgBMANIAsgoAACuwD82wHi%2BwSjOwGc2wRTKwKC%2BwOTOwI82wNDKyKCMKK7NAKEEJK7AUL7AEzQGwTS%2BwAdawDM2wDBCxFwErsBvNsBsQsSELK7AmzbAmELEqASuwPs2wPhCxQwErsEjNszdIQwgrsDHNsDEvsDfNsEgQsREBK7AHzbFOASuxJhsRErMKDhQDJBc5sT4qERKxLTw5ObE3MREStQkPEwQvOyQXOQCxHg8RErMHAAwRJBc5sBkRsyotPD4kFzmwKBKxBgE5ObAjEbEvOzk5MDEYARIkIAQSEAIEICQTFBYgNjU0JiAGFjQ2MhYVFAYjIjY0NjMyFhQGIyIXNDY%2FAiY1NDYzMhYUBiMiJwcWFRQGIiYlNDYyFhQGIyImoAESAUQBEqCg%2Fu7%2BvP7uFvMBVvPz%2FqrzbR8uICAXFk0gFxYgIBYXUikfegEJIBcWICAWDg83ETNIMwEeIC4fIBYXIAGyAUQBEqCg%2Fu7%2BvP7uoKABtKzy8qyr8%2FOHLh8gFhcg5CwhIC4guiAxBX4BDg4WISAuIAqRFh0kMzNSFiAfLiAgAAAAAf%2FYADsEugSwAE8AOgCwBS%2BwJ82wIC%2BwFc2wNi%2BwSs0BsFAvsVEBKwCxJwURErA%2FObAgEbQLDxobMSQXObAVErEyMzk5MDECBhceATMyNz4CNzY3AT4BJyYnJiMiBgcBBxcBNjc2MzIXFgcBBiMiJicmPgI3NjcBPgIzMhceAQcGDwEDHwEBPgEnLgEnJiMiBwYHARsaMCN2Rj84IUApJygRAYojGA8bWhQJLkEj%2FnsHRQF5FBMXGyYPECT93TRJN1oJBQ8wJCYYFAFcND1rNhkXX3YIB1v8%2FQdFAgVDOBEQZk9FU2taKEf%2BAAHWvk45QBwQMSorLBEBiiNiL1cRAiEj%2FnQHQwF1FhAXJCck%2Fd00Qj8jPkAkJBUUAVw0NzUEEZtiZVv5%2FwAHPAH%2FQ7RdV4YkITcYR%2F4AAAAAAAIAUAA2BMMEWAAbADUAPQCwMy%2BwLTOwA82wBzIBsDYvsADWsBzNsBwQsSoBK7AKzbE3ASuxKhwRErMDBw8YJBc5ALEDMxESsAU5MDETNDYzMhc2MzIWFRQOAgcGDwEnLgInLgM3FB4BHwEWFzY%2FAT4CNTQmIyIPAScmIyIGUMWEj2Jnj4HCI1dDR8VgERArckZCR0NXI6o9PkAWXWFScQxAQz5gOUo6dnIzSDxjAxCDxYGBxYMuWmxHRr%2BDFxc6gUZBRkdsWi4bVkE%2BFlpvXG8MPkZYHEdhU6uuUGMAAAAAAgA5%2F%2FIEdwS%2BABgAMwAAExQfARYzMjcBNjQvASYnBxcBJzcnJicHBhMUHwEWFzcnARcHFxYXNz4BNTQvASYjIgcBBjlCjURbXUIBG0JCjQgLadT%2Be%2FdfEi4dN0LUQo0HDGnUAYX3XxIvHh0jN0KNQl1fQP7lQgFhX0COQkIBG0K6Qo0JCGnU%2Fnv4XxItODdCAQRdQo0HCmnUAYX3YBExMx0jaitdQo1CQv7lQAAAAAADAMgAAAPoBLAAEQAVAB0ARQCyDwAAK7AZzbAdL7ASzbAVL7AGzQGwHi%2BwANawEs2wEhCxEwErsAvNsAsQsBvNsBsvsR8BK7EbEhESsgYFFjk5OQAwMTcRND4CMh4CFREUBiMhIiY3IREhEhQWMjY0JiLIPGacqppkOjsp%2FagpO2QCWP2oxD1WPT1WZAO5FTIuHh4uMhX8Ryk7O%2FECvPzZVj09Vj0AAAABAAAAAASwBLAAGAARALIAAAArAbAZL7EaASsAMDExATcnIQEnJjQ3NjIXARYUBwYiLwEBEScHAS%2FP0gEsAQsjDw8OKg4BGw8PDioOJP7p1NABfNDUARckDioODw%2F%2B5g8qDg8PI%2F71%2FtTSzwADAScAEgQJBOEAMQA9AEMAlwCwLS%2BwKjOwBM2wPjKyLQQKK7NALSwJK7A7L7AfM7ASzbISOwors0ASEwkrAbBEL7AO1rAAMrAyzbABzbAyELEsASuyBBI6MjIysCvNshQfPjIyMrArELFAASuwJ82wHCDWEbAbzbFFASuxMgERErACObAsEbAJOQCxBC0RErApObA7EbYADhsnOkBDJBc5sBISsBU5MDEBMx4BFxEuASMuBDU0PgE3NTMVHgQXIy4BJxEXHgQVFAYHFSM1JicuARMUHgMXFhcRDgETNjU0JicBJ4sFV0oGEwIuQk4vIViCT2QmRVI8KwOfCDZKQCI8UDcosptkmFUoGagQESoUHAcEPUnqqlhSAbFNYw8BTwEGDhkvOVg3XIdDB05PBBMsP2lCSEsN%2Fs0OBxMsPGU%2Bi6oLTU4RVyhrAh4dLBgVBgcCAQESCDv9KxKFQEcZAAAAAQBkAGYDlAStAEMAjQCwMS%2BwKs2wAC%2BwHjOwAc2wHDKwEy%2BwC82yEwsKK7NAEw4JKwGwRC%2BwB9awOTKwGM2wJDKyGAcKK7NAGB4JK7IHGAors0AHAAkrsBgQsQ8BK7AOzbFFASuxGAcRErMCOEJDJBc5sA8RtQsfICoxMyQXObAOErAsOQCxKjERErEtOTk5sAARsSw8OTkwMRM1MyYnLgE%2BATc2MzIWFSM0LgEjIgYHBhUUHgEXMxUjFgYHBgc%2BATM2FjMyNxcOAiMiJgcOAQ8BJz4FNz4BJ2SmGBQKCQMvLWGmgcqZRFAkJVQUKSEXHvHFCBUVKTojYhUhjCFMPDIpTycqF9IyJ1YXGDcGFQoRDBEJMAwkAlhkMTcaO1ZeKFiydzRLHB0VLDkcUyozZDKCHTs2Cw4BIh6TGRcDQgQEGgwLkQQOBg0LEQo3j0cAAgACAAAErgSwAAYADQAfALIMAAArAbAOL7AM1rALzbEPASuxCwwRErAIOQAwMRMJASMRIxEJAiMRIxECASoBKsbIAZIBKgEqxsgBLP7UASwDhPx8AlgBLP7U%2FHwDhAAABQACAAAD6ASwAAYADAAWAB4AIgCmALIHAAArsAYzsArNsgcAACuwCM2wEy%2BwFM2xAAQyMrANL7AOzbAdL7AfzbIdHwors0AdFwkrsBoysCIvsBjNsAIyAbAjL7AB1rAEzbAEELEIASuxDRcyMrAKzbEdHzIysAoQsRUBK7EbIDIysBDNsQsZMjKzEhAVCCuwE82wEy%2BwEs2xJAErsQQBERKwBjmwCBGwBTkAsRQIERKwEDmwDRGwETkwMRMzETMRMwEhNTMVMxUBNSEVIxUjNTM1AxEhESM1IxU3MzUjAsbIxv7WAZBkyP7UASxjZGPIASxkZAFkZAEsA4T8fP7UyGRkAZBkyGRkZAEsAfT%2BDGRkyMgABQACAAAD6ASwAAYADgAUAB4AIgCgALIGAAArsQcKMzOwDS%2BwH82wIi%2BwCM2wDy%2BwEs2wEM2wGy%2BwHM2wFS%2BwFs2wAjIBsCMvsAHWsATNsAQQsQcBK7EPFTIysA7NsREfMjKwDhCxCwErsR0gMjKwCs2xExcyMrMaCgsIK7AbzbAbL7AazbEkASuxBAERErAGObAHEbAFOQCxIh8RErMBBAUAJBc5sRwQERKwGDmwFRGwGTkwMRMzETMRMwEhESERIzUjFQM1MxUzFQE1IRUjFSM1MzUDMzUjAsbIxv7WAZABLGRkZGTI%2FtQBLGNkY2NkZAEsA4T8fP7UAfT%2BDGRkArzIZGQBkGTIZGRk%2FHzIAAAEAAIAAARMBLAABgAMABIAFgBrALILAAArsAwvsBPNsBYvsAjNsA0vsA7Nsg0OCiuzQA0RCSsBsBcvsBHWsBDNsxMQEQgrsAfNsAcvsA0zsBPNsBAQsRQLK7ALMrAKzbEYASsAsQgLERK0AAIDBgEkFzmxDg0RErEFBDk5MDETCQEjESMRBREhESM1AzUzESMREzM1IwIBKgEqxsgCWAEsZMjIZAFkZAEs%2FtQBLAOE%2FHzIAZD%2BDGQD6GT%2BDAGQ%2FHzIAAAABAACAAAETASwAAYADAASABYAawCyCwAAK7AHL7AIzbASL7ATzbISEwors0ASEAkrsBYvsA7NAbAXL7AL1rAKzbMTCgsIK7ANzbANL7AHM7ATzbAKELEUCyuwETKwEM2xGAErALETCxEStAACAwYBJBc5sQ4WERKxBQQ5OTAxEwkBIxEjESU1MxEjEQMRIREjNSczNSMCASoBKsbIAljIZGQBLGRjZGQBLP7UASwDhPx8ZGT%2BDAGQAZABkP4MZGTIAAAAAAUAAgAABLAEsAAGAAoADgASABYAUgCwBy%2BwCM2wCy%2BwDM2wDy%2BwEM2wEy%2BwFM0BsBcvsA%2FWsgcLEzIyMrASzbAWzbIWDwors0AWCgkrs0AWDgkrsRgBKwCxCwgRErMCAwYAJBc5MDETCQEjESMRBTUhFQE1IRUBNSEVATUzFQIBKgEqxsgB9AH0%2FgwBkP5wASz%2B1MgBLP7UASwDhPx8yMjIASzIyAEsyMgBLMjIAAAABQACAAAEsASwAAYACgAOABIAFgBSALAHL7AIzbALL7AMzbAPL7AQzbATL7AUzQGwFy%2BwC9ayBw8TMjIysA7NsArNsgoLCiuzQAoSCSuzQAoWCSuxGAErALELCBESswIDBgAkFzkwMRMJASMRIxEFNTMVAzUhFQE1IRUBNSEVAgEqASrGyAH0yMgBLP7UAZD%2BcAH0ASz%2B1AEsA4T8fMjIyAEsyMgBLMjIASzIyAAAAAACAAAAAARMBEwADwAfACoAsg0AACuwE82wHC%2BwBM0BsCAvsADWsBDNsBAQsRcBK7AJzbEhASsAMDEZATQ2MyEyFhURFAYjISImNxQWMyEyNjURNCYjISIGFeulASyi7u2j%2FtSl68g7KQH0KTs7Kf4MKTsBkAEspevto%2F7UpevrQSk7OykB9Ck7OykAAAMAAAAABEwETAAPAB8AIgA%2BALINAAArsBPNsBwvsATNAbAjL7AA1rAQzbAQELEXASuwCc2xJAErsRcQERKxICE5OQCxHBMRErEgIjk5MDEZATQ2MyEyFhURFAYjISImNxQWMyEyNjURNCYjISIGFRMtAe6iASyl6%2Bul%2FtSj7cg7KQH0KTs7Kf4MKTvIAU3%2BswGQASyj7eul%2FtSl6%2BtBKTs7KQH0KTs7Kf4M%2BvoAAAAAAwAAAAAETARMAA8AHwAiAD4Asg0AACuwE82wHC%2BwBM0BsCMvsADWsBDNsBAQsRcBK7AJzbEkASuxFxARErEgIjk5ALEcExESsSAhOTkwMRkBNDYzITIWFREUBiMhIiY3FBYzITI2NRE0JiMhIgYVFxsB66UBLKPt66X%2B1KXryDspAfQpOzsp%2FgwpO2T6%2BgGQASyj7e6i%2FtSl6%2BtBKTs7KQH0KTs7KWT%2BswFNAAMAAAAABEwETAAPAB8AIgA%2BALINAAArsBPNsBwvsATNAbAjL7AA1rAQzbAQELEXASuwCc2xJAErsRcQERKxICE5OQCxHBMRErEgIjk5MDEZATQ2MyEyFhURFAYjISImNxQWMyEyNjURNCYjISIGFRMhA%2BulASyl6%2B2j%2FtSl68g7KQH0KTs7Kf4MKTtkAfT6AZABLKXr66X%2B1KLu7T8pOzspAfQpOzsp%2FnABTQACAAAAAAUUBEwABgAaADwAsgcAACuwCM2wAC%2BwAc2wES%2BwEs0BsBsvsAzWsBfNsRwBKwCxCAcRErAFObEBABESsAQ5sBERsAM5MDEZASE1CQE1EzUhMjY1ETQmIyE1ITIWFREUBiMBLAGQ%2FnDIAfQpOzsp%2FgwBkKXr66UBkAEsyP6i%2FqLI%2FnDIOykB9Ck7yOul%2FtSl6wAAAAEA2QACA9YEngAhACgAsA4vsBPNAbAiL7Ac1rAWzbEjASuxFhwRErAZOQCxEw4RErAPOTAxExYzIQIHBh8BMzI3NgAzNicmIwU2Ejc2LwEjIgcOAQAHBtkIFwEumwUFCQkJDgwLAg8BDgkIF%2F7TAZoCAgcJCQ8KBLz%2B80sQAgcT%2FkoUFQsIDw0CaRMREQEEAa8MDwwJEAbT%2FtFWEwAAAAACAAAAAAUUBEwAGAAfAD8AsgMAACuwCM2wCBCwBs2wGS%2BwGs2wEC%2BwEs2wFM0BsCAvsADWsAvNsSEBKwCxGgMRErEdHjk5sBARsBw5MDERFBYzITI3NSEiJjURNDYzITUuAS8BIgYVAREhNQkBNeulASwvNf4MKTs7KQH0DshdXaXrAlgBLAGQ%2FnABkKXrD7k7KQH0KTu5BAcCAuul%2FtQBLMj%2Bov6iyAACAAAAAASwBLAAHQAkAFQAsgMAACuwD82wFi%2BwGs0BsCUvsADWsBLNsBIQsQsBK7AHzbEmASuxCxIRErUYGR4fICQkFzmwBxGwIzkAsRYPERK1CAkeIiMkJBc5sBoRsB85MDERFBYzITI2PQEnBxUUBiMhIiY1ETQ2OwE3JyMiBhUlASchEScB66UBLKPtTno7Kf4MKTs7KZx2SmSl6wHwAWGVAfSV%2FqoBkKXr66ViSXuUKTs7KQH0KTt6TuulCQFWlf4Mlf6fAAMABAAEBKwErAALABMAGwBaALAKL7APzbAbL7AXzbATL7AEzQGwHC%2BwAdawDc2wDRCxFQErsBnNsBkQsREBK7AHzbEdASuxGRURErcECQoODxITAyQXOQCxFxsRErcBBgcMDRARACQXOTAxEhASJCAEEhACBCAkEhAWIDYQJiACNDYyFhQGIgSgARIBRAESoKD%2B7v68%2Fu4W8wFW8%2FP%2BqhdyoHJyoAG2AUQBEqCg%2Fu7%2BvP7uoKACX%2F6q8%2FMBVvP%2BEqBycqByAAAAAwAAAAAETASwAAkAEAAUAC4AsgkAACuwEc2wFC%2BwBc2wCzIBsBUvsBLWsAjNshIICiuzQBIACSuxFgErADAxMRE0NjMhMhYVEQkCIREhEQEzNSMOCwQYCxD8GAG9AcL%2B2f7UAfRkZAETCw4PCv7tAyD%2BDAH0AZD%2BcP12MgAAAAADAAAAAARMBLAACQAQABQAKwCyCQAAK7ARzbAUL7AFzQGwFS%2BwEtawCM2yEggKK7NAEgAJK7EWASsAMDExETQ2MyEyFhURASERIREhCQEzNSMOCwQYCxD8GAEsASwBJ%2F5DAV5kZAETCw4PCv7tArz%2B1AEsAfT75jIAAAAAAwAAAAAETAR%2FAAkADwATAC4AsgkAACuwEM2wEy%2BwBc0BsBQvsBHWsAwysAjNshEICiuzQBEACSuxFQErADAxMRE0NjMhMhYVEQkCJwEnATM1Iw4LBBgLEPwYATECVJr%2BRpYChWRkARMLDg8K%2Fu0Cwf7PAlSb%2FkaX%2FToyAAQAAAAABEwEsAAJAA0AFAAYACsAsgkAACuwFc2wGC%2BwBc0BsBkvsBbWsAjNshYICiuzQBYACSuxGgErADAxMRE0NjMhMhYVEQEXNycDJRMHJwcXATM1Iw4LBBgLEPwYYdRhcAK5A%2FqV1JUBzmRkARMLDg8K%2Fu0D3GLVYfzgAQK775XUlf4NMgAEAAAAAARMBLAACQANABQAGAAuALIJAAArsBXNsBgvsAXNAbAZL7AW1rATMrAIzbIWCAors0AWAAkrsRoBKwAwMTERNDYzITIWFREBFzcnExcHFzcXCwEzNSMOCwQYCxD8fNRi1QPvldSV%2BQFjZGQBEwsODwr%2B7QJk1GHUAev6ldSU7QK5%2B%2BkyAAAAAAIAF%2F%2F%2FBLAErwAFAAgAFwCyBAAAKwGwCS%2BwBdawBs2xCgErADAxEwERCQERFwkBFwSZ%2FiX%2Byk8CoP1gAZ8DEPvJARD%2BdwGgzQOq%2FTgAAAAAAgAAAGQETASwABUAGQBNALARL7AGzbIRBgors0AREwkrsA4ysgYRCiuzQAYECSuwCDIBsBovsADWsBLNsAbNsBIQsQ8BK7ALzbEbASuxDwYRErIJFhc5OTkAMDE1ETQ2OwERIREzFxEUBisBESERIyImATM1Ix0V%2BgH0ZMgeFJb9RJYVHQJYZGSWA%2BgUHv7UASzI%2FK4VHQGQ%2FnAdA2fIAAMAAAA%2BBRQEsAATABkAHQBAALAPL7AGzbIPBgors0APEQkrsgYPCiuzQAYECSuwCDIBsB4vsADWsBDNsAbNsR8BKwCxBg8RErILFxg5OTkwMTURNDY7AREhETMXFQEnByERIyImJTcXARcBAzM1Ix0V%2BgH0ZMj%2B7Hh%2B%2FoaWFR0CRXt4AWF7%2FiXhZGSWA%2BgUHv7UASzI2v7teH%2F%2BcB2xe3gBYHv%2BJAOqyAAAAAADAAAABgUOBLAAEwAXACMAFQABsCQvsADWsBDNsAbNsSUBKwAwMTURNDY7AREhETMXEQcnASERIyImATM1IxM3JzcXNxcHFwcnBx0V%2BgH0ZMhnqv7W%2FreWFR0CWGRkZKqqf6qqf6qqf6qqlgPoFB7%2B1AEsyP7zZ6r%2B1v5wHQNnyPvVqqp%2FqqqAqap%2FqqoAAAADAAAAAASwBLAAEgAZAB0AbACwDi%2BwBs2yDgYKK7NADhAJK7AGELAMzbAaL7AbzbEECDIyAbAeL7AA1rAPzbIPAAors0APCwkrsAAQsAbNsA8QsRoBK7AdzbAMMrEfASuxGgYRErATOQCxDA4RErEXGDk5sRoGERKwCjkwMTURNDY7AREhETMXESEVIREjIiYlCQEjESMRAzUzFR0V%2BgH0ZMj%2BcP4MlhUdAlgBLAEsyMjIZJYD6BQe%2FtQBLMj%2B1Mj%2BcB2r%2FtQBLAEs%2FtQCvMjIAAAAAAMAAAAABLAEsAASABkAHQBbALAOL7AGzbIOBgors0AOEAkrsBovsBvNsQQIMjIBsB4vsADWsA%2FNsAbNsA8QsRoBK7AdzbEfASuxGgYRErATObAdEbANOQCxBg4RErILDBk5OTmwGhGwCjkwMTURNDY7AREhETMXEScBIREjIiYlMxEzETMJATUzFR0V%2BgH0ZMjI%2Ftb%2BbpYVHQJYyMjI%2FtT%2B1GSWA%2BgUHv7UASzI%2Fm7I%2Ftb%2BcB2r%2FtQBLAEsAZDIyAAAAAADAAAAyASwBEwACQATABcAADUUFjMhMjY1ESE1ITU0JiMhIgYVEzUhFR0VBEwVHftQBLAdFfu0FR1kAZD6FR0dFQImZJYVHR0V%2FRLIyAAAAAYAAABmBLAErgAGAAoADgAVABkAHQCBALAFL7EWGjMzsALNsRccMjKwBy%2BxCw8zM7AIzbEMEDIyAbAeL7AH1rAKzbAKELELASuwDs2wDhCxFgErsBnNsR8BK7ELChESswIFBgEkFzmxFg4RErMEAw8QJBc5sBkRsxIUFREkFzkAsQIFERKwADmwBxGxARQ5ObAIErATOTAxEQEVIRUhFQM1MxUzNTMVMzUhNQkBNQM1MxU7ATUjASwBkP5wyGRkZGQBkAEs%2FtRkZGRkZAGQASrGyMYCusjIyMjIxv7W%2FtbG%2FgzIyMgAAAACAGQAAASwBLAAGAAvADoAshQAACsBsDAvsADWsATNsAQQsRcLK7AQzbMJEBcIK7AFzbAFL7AJzbAQELEKCyuwDs2xMQErADAxExE3FxEzETcXETMRNxcRBxEUBisBIiY1ESUUHgIfAREUFjsBMjY1ETQmBwUOARVkMjJkMjJkMjJkHRXIFR0CWBUdHQsKHRXIFR0kGv7sGSUCvAGQZGT%2B1AEsZGT%2B1AEsZGT%2BcMv%2BQRUdHRUBv2QdNSEYBgX%2BcxUdHRUEUh8TEXQRRR8AAAAAAQBkAAAEsARMADMAOACyAAAAK7AMM7AzzbICCw4yMjKwKC%2ByGBwlMzMzsCfNsBoyAbA0L7E1ASsAsSgzERKxBiA5OTAxMyE1IiY1ESERFAYjFSE1Ii4DNRE0Nj8BNSEVMhYVESERNDYzNSEVMh4DFREUBg8BZAGQSxkB9BlLAZAEDiIaFjIZGf5wSxn%2BDBlL%2FnAEDiIaFjIZGTgMJgGK%2FnYmDDg4AQUJFQ4DeBYZAQI4OAwm%2FnYBiiYMODgBBQkVDvyIFhkBAgAGAAAAAARMBEwADwAYABwAIAAqAC4AMgCyGAAAK7AQzbAWL7ASzbISFgors0ASFAkrAbAvL7EwASsAsRIQERKzBAMZHCQXOTAxERQWMyEyNjURNCYjISIGFRMhNzMlESEHIQM1IRUBNSEVASEXFSUzNSEnIQE1JRU7KQEsKTs7Kf7UKTtkAZDIaQEn%2Fldk%2FolkASz%2B1AEs%2FtQBkMgBJ2n%2BV2T%2BiQH0AZABLCk7OykB9Ck7Oyn9RMhi%2FtZkASzIyAEsyMgBkMhiYshk%2FUajhaMAAQAQABAEnwSfACAAABIeAxceAzM%2FATYmLwEmBg8BLgEnNz4BLwEuAQ8BEAEfPpJmZ9GXex8foxEHE8ATNBB2jvxldhEGDosOLRKiA%2BQriY%2FUZmeSPSEBohIuDogOBBF2ZfyOdhExFMITBhGiAAAAAAIAAAAABLAETAAdAEAALwCyGwAAK7AMzbAoL7A4zQGwQS%2BxQgErALEMGxESsSAvOTmwKBGzJikyQCQXOTAxPQE0NjcBNTQ%2BAzIeAh8BFQEeAR0BFAYjISImERQWPwE%2BAT0BNiAXFRQWHwEWNj0BLgQjIg4EDwEVDgFtAhYmUnBSJhYBAQFtDhUdFfu0FB4dFMoUHY0BPo0dFMoUHQYaZHzaflymdWQ%2FLAkJMtQUMw4BLzIEDSAZFRQbHAoKMv7RDjMU1BUdHQKrFRkEIQQiFZIYGJIVIgQhBBkVyAgZQTEpFSEoKCELCgACAGQAAASwBEwAAwAZABQAsgAAACuwAc0BsBovsRsBKwAwMTM1IRUlISc1NxEjFSM1IxUjNSMVIzUjERcVZARM%2B%2F8Dtn1kZGTIZMhkZGRkZMiW%2BmQBkMjIyMjIyP5wZPoAAAAAAwBkAAAEsARMAAkAEwAdACQAsgoAACuwFDMBsB4vsArWsBPNsBMQsRQBK7AdzbEfASsAMDEzIRE0JisBIgYVARE0NjsBMhYVETMRNDY7ATIWFRFkASw7KWQpOwGQOylkKTtkOylkKTsBkCk7Oyn%2BcAPoKTs7KfwYArwpOzsp%2FUQAAAAABf%2BcAAAEsARMAA8AEwAfACcAKwBIALINAAArsBDNsBMvsATNAbAsL7AA1rAQzbAQELERASuwCc2xLQErsREQERK1FBUgIygqJBc5ALETEBEStRQaICYoKSQXOTAxAxE0NjMhMhYVERQGIyEiJjchESETIREjNTM1IREzFSMFMzUzESM1IxMRMxFksHwCvHywsHz9RHywyAOE%2FHxkASzIyP7UyMgBkMhkZMhkZAEsAfR8sLB8%2Fgx8sLAYArz9qAEsZGT%2B1GRkZAEsZP5wASz%2B1AAAAAAF%2F5wAAASwBEwADwATAB8AJwArAEgAsg0AACuwEM2wEy%2BwBM0BsCwvsADWsBDNsBAQsREBK7AJzbEtASuxERARErUUGSAjKCokFzkAsRMQERK1FBogJigpJBc5MDEDETQ2MyEyFhURFAYjISImNyERIRMzNTMVMxEjFSM1IwEzNTMRIzUjExEzEWSwfAK8fLCwfP1EfLDIA4T8fGRkZGRkZGQBkMhkZMhkZAEsAfR8sLB8%2Fgx8sLAYArz9qMjIAfTIyP4MZAEsZP5wASz%2B1AAABP%2BcAAAEsARMAA8AEwAbACMARACyDQAAK7AQzbATL7AEzQGwJC%2BwANawEM2wEBCxEQErsAnNsSUBK7EREBESsxQVHB0kFzkAsRMQERKzFBocIiQXOTAxAxE0NjMhMhYVERQGIyEiJjchESETITUjETM1IQEhNSMRMzUhZLB8Arx8sLB8%2FUR8sMgDhPx8ZAEsyMj%2B1AGQASzIyP7UASwB9HywsHz%2BDHywsBgCvP2oZAEsZP4MZAEsZAAAAAAE%2F5wAAASwBEwADwATABYAGQBEALINAAArsBDNsBMvsATNAbAaL7AA1rAQzbAQELERASuwCc2xGwErsREQERKzFBUXGCQXOQCxExARErMVFhcZJBc5MDEDETQ2MyEyFhURFAYjISImNyERIRMFERMtAWSwfAK8fLCwfP1EfLDIA4T8fGQBLGQBLP7UASwB9HywsHz%2BDHywsBgCvP6ilgEs%2FtSWlgAAAAAF%2F5wAAASwBEwADwATABcAHwAnAFoAsg0AACuwEM2wFC%2BwGM2wIzKwHy%2BwJTOwFc2wEy%2BwBM0BsCgvsADWsBDNsBAQsRQBK7AYzbAYELEcASuwIc2wIRCxJAErsBfNsBcQsREBK7AJzbEpASsAMDEDETQ2MyEyFhURFAYjISImNyERIRMRIRElMzI2NCYrAQQUFjsBESMiZLB8Arx8sLB8%2FUR8sMgDhPx8ZAK8%2FaiCKTY5JoIBEzYpgoImASwB9HywsHz%2BDHywsBgCvP2oAfT%2BDGRUglZWglQBLAAABf%2BcAAAEsARMAA8AEwAfACMAKQBIALINAAArsBDNsBMvsATNAbAqL7AA1rAQzbAQELERASuwCc2xKwErsREQERK1FBUgISQnJBc5ALETEBEStRQaICImKCQXOTAxAxE0NjMhMhYVERQGIyEiJjchESETIREjNTM1IREzFSMFMzUjEzMRMxEjZLB8Arx8sLB8%2FUR8sMgDhPx8ZAEsyMj%2B1MjIAZFkZGNkZMgBLAH0fLCwfP4MfLCwGAK8%2FagBLGRk%2FtRkZGQBLP5wAfQABv%2BcAAAEsARMAA8AEwAZAB0AIQAnAEwAsg0AACuwEM2wEy%2BwBM0BsCgvsADWsBDNsBAQsREBK7AJzbEpASuxERARErcUFRocHh8iJSQXOQCxExARErcUGBobHiAkJiQXOTAxAxE0NjMhMhYVERQGIyEiJjchESETIREjNSMTNTMVFzM1IxMzETMRI2SwfAK8fLCwfP1EfLDIA4T8fGQBLMhkZWTIZGRjZGTIASwB9HywsHz%2BDHywsBgCvP2oAZBk%2FnDIyGRkASz%2BcAH0AAAAAAb%2FnAAABLAETAAPABMAHQAhACUAKwCbALINAAArsBDNsB4vsSIpMzOwH82wIzKwGi%2BwG82wFC%2BwJjOwFc2wJzKwEy%2BwBM0BsCwvsADWsBDNsBAQsR4BK7AUMrAhzbAhELEcASuwF82zGRccCCuwGs2wGi%2BwGc2wFxCxIgErsCXNsCUQsSoBK7ApzbApELAmzbAmL7ApELERASuwCc2xLQErALEbHxESsBc5sBQRsBg5MDEDETQ2MyEyFhURFAYjISImNyERIRc1IREjFSM1MzUDNTMVITUzFQM1MxEjEWSwfAK8fLCwfP1EfLDIA4T8fGQBLGNkY8dkASxkAchkASwB9HywsHz%2BDHywsBgCvMhk%2FtRkZMj%2BcGRkZGQBkGT%2BDAGQAAADAAQABASsBKwACwATAB0AeQCwCi%2BwD82wHS%2BwGs2wGS%2BwFs2wEy%2BwBM0BsB4vsAHWsA3NsA0QsRQBK7AazbAaELERASuwB82xHwErsRoUERK1Cg4TAxYdJBc5sBERtQkPBBIXGyQXOQCxGh0RErQHDRAAFCQXObAZEbAVObAWErMGDBEBJBc5MDESEBIkIAQSEAIEICQSEBYgNhAmIAM1NyEVIRUhFSEEoAESAUQBEqCg%2Fu7%2BvP7uFvMBVvPz%2FqodZAEs%2FtQBLP7UAbYBRAESoKD%2B7v68%2Fu6goAJf%2Fqrz8wFW8%2F3%2ByGRkyGQAAAQAAAAEBKgErAALABMAIAAkAKAAsAovsA%2FNsCEvsBQzsCLNsBsvsBXNsBMvsATNAbAlL7AB1rANzbANELEUASuwIM2wGzKyIBQKK7NAIB4JK7AgELEhASuwGTKwJM2wFzKwJBCxEQErsAfNsSYBK7EgFBESswoOEwMkFzmwIRGwFjmwJBKzCQ8SBCQXOQCxIiERErQHDRAAHiQXObAbEbIXGB85OTmwFRKzBgwRASQXOTAxGAESJCAEEhACBCAkEhAWIDYQJiADESEXFSM1IxUzFSMVMzUzFaABEgFEARKgoP7u%2Frz%2B7hbzAVbz8%2F6qGQEsZGTIyMjIZAG2AUQBEqCg%2Fu7%2BvP7uoKACX%2F6q8%2FMBVvP9mgGQZGRkZGRkZGQA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AzMgd1bmlFMDMzB3VuaUUwMzQHdW5pRTAzNQd1bmlFMDM2B3VuaUUwMzcHdW5pRTAzOAd1bmlFMDM5B3VuaUUwNDAHdW5pRTA0MQd1bmlFMDQyB3VuaUUwNDMHdW5pRTA0NAd1bmlFMDQ1B3VuaUUwNDYHdW5pRTA0Nwd1bmlFMDQ4B3VuaUUwNDkHdW5pRTA1MAd1bmlFMDUxB3VuaUUwNTIHdW5pRTA1Mwd1bmlFMDU0B3VuaUUwNTUHdW5pRTA1Ngd1bmlFMDU3B3VuaUUwNTgHdW5pRTA1OQd1bmlFMDYwB3VuaUUwNjIHdW5pRTA2Mwd1bmlFMDY0B3VuaUUwNjUHdW5pRTA2Ngd1bmlFMDY3B3VuaUUwNjgHdW5pRTA2OQd1bmlFMDcwB3VuaUUwNzEHdW5pRTA3Mgd1bmlFMDczB3VuaUUwNzQHdW5pRTA3NQd1bmlFMDc2B3VuaUUwNzcHdW5pRTA3OAd1bmlFMDc5B3VuaUUwODAHdW5pRTA4MQd1bmlFMDgyB3VuaUUwODMHdW5pRTA4NAd1bmlFMDg1B3VuaUUwODYHdW5pRTA4Nwd1bmlFMDg4B3VuaUUwODkHdW5pRTA5MAd1bmlFMDkxB3VuaUUwOTIHdW5pRTA5Mwd1bmlFMDk0B3VuaUUwOTUHdW5pRTA5Ngd1bmlFMDk3B3VuaUUxMDEHdW5pRTEwMgd1bmlFMTAzB3VuaUUxMDQHdW5pRTEwNQd1bmlFMTA2B3VuaUUxMDcHdW5pRTEwOAd1bmlFMTA5B3VuaUUxMTAHdW5pRTExMQd1bmlFMTEyB3VuaUUxMTMHdW5pRTExNAd1bmlFMTE1B3VuaUUxMTYHdW5pRTExNwd1bmlFMTE4B3VuaUUxMTkHdW5pRTEyMAd1bmlFMTIxB3VuaUUxMjIHdW5pRTEyMwd1bmlFMTI0B3VuaUUxMjUHdW5pRTEyNgd1bmlFMTI3B3VuaUUxMjgHdW5pRTEyOQd1bmlFMTMwB3VuaUUxMzEHdW5pRTEzMgd1bmlFMTMzB3VuaUUxMzQHdW5pRTEzNQd1bmlFMTM2B3VuaUUxMzcHdW5pRTEzOAd1bmlFMTM5B3VuaUUxNDAHdW5pRTE0MQd1bmlFMTQyB3VuaUUxNDMHdW5pRTE0NAd1bmlFMTQ1B3VuaUUxNDYHdW5pRTE0OAd1bmlFMTQ5B3VuaUUxNTAHdW5pRTE1MQd1bmlFMTUyB3VuaUUxNTMHdW5pRTE1NAd1bmlFMTU1B3VuaUUxNTYHdW5pRTE1Nwd1bmlFMTU4B3VuaUUxNTkHdW5pRTE2MAd1bmlFMTYxB3VuaUUxNjIHdW5pRTE2Mwd1bmlFMTY0B3VuaUUxNjUHdW5pRTE2Ngd1bmlFMTY3B3VuaUUxNjgHdW5pRTE2OQd1bmlFMTcwB3VuaUUxNzEHdW5pRTE3Mgd1bmlFMTczB3VuaUUxNzQHdW5pRTE3NQd1bmlFMTc2B3VuaUUxNzcHdW5pRTE3OAd1bmlFMTc5B3VuaUUxODAHdW5pRTE4MQd1bmlFMTgyB3VuaUUxODMHdW5pRTE4NAd1bmlFMTg1B3VuaUUxODYHdW5pRTE4Nwd1bmlFMTg4B3VuaUUxODkHdW5pRTE5MAd1bmlFMTkxB3VuaUUxOTIHdW5pRTE5Mwd1bmlFMTk0B3VuaUUxOTUHdW5pRTE5Nwd1bmlFMTk4B3VuaUUxOTkHdW5pRTIwMLgB%2F4WwAY0AS7AIUFixAQGOWbFGBitYIbAQWUuwFFJYIbCAWR2wBitcWFmwFCsAAAABUuZYrgAA%29%20format%28%27truetype%27%29%2Curl%28data%3Aimage%2Fsvg%2Bxml%3Bbase64%2CPD94bWwgdmVyc2lvbj0iMS4wIiBzdGFuZGFsb25lPSJubyI%2FPgo8IURPQ1RZUEUgc3ZnIFBVQkxJQyAiLS8vVzNDLy9EVEQgU1ZHIDEuMS8vRU4iICJodHRwOi8vd3d3LnczLm9yZy9HcmFwaGljcy9TVkcvMS4xL0RURC9zdmcxMS5kdGQiID4KPHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPgo8bWV0YWRhdGE%2BPC9tZXRhZGF0YT4KPGRlZnM%2BCjxmb250IGlkPSJnbHlwaGljb25zX2hhbGZsaW5nc3JlZ3VsYXIiIGhvcml6LWFkdi14PSIxMjAwIiA%2BCjxmb250LWZhY2UgdW5pdHMtcGVyLWVtPSIxMjAwIiBhc2NlbnQ9Ijk2MCIgZGVzY2VudD0iLTI0MCIgLz4KPG1pc3NpbmctZ2x5cGggaG9yaXotYWR2LXg9IjUwMCIgLz4KPGdseXBoIC8%2BCjxnbHlwaCAvPgo8Z2x5cGggdW5pY29kZT0iJiN4ZDsiIC8%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%2BCjxnbHlwaCB1bmljb2RlPSImI3gyMDAzOyIgaG9yaXotYWR2LXg9IjEzMDQiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3gyMDA0OyIgaG9yaXotYWR2LXg9IjQzNCIgLz4KPGdseXBoIHVuaWNvZGU9IiYjeDIwMDU7IiBob3Jpei1hZHYteD0iMzI2IiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4MjAwNjsiIGhvcml6LWFkdi14PSIyMTciIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3gyMDA3OyIgaG9yaXotYWR2LXg9IjIxNyIgLz4KPGdseXBoIHVuaWNvZGU9IiYjeDIwMDg7IiBob3Jpei1hZHYteD0iMTYzIiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4MjAwOTsiIGhvcml6LWFkdi14PSIyNjAiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3gyMDBhOyIgaG9yaXotYWR2LXg9IjcyIiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4MjAyZjsiIGhvcml6LWFkdi14PSIyNjAiIC8%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%2BCjxnbHlwaCB1bmljb2RlPSImI3gyMjEyOyIgZD0iTTIwMCA0MDBoOTAwdjMwMGgtOTAwdi0zMDB6IiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4MjVmYzsiIGhvcml6LWFkdi14PSI1MDAiIGQ9Ik0wIDB6IiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4MjYwMTsiIGQ9Ik0tMTQgNDk0cTAgLTgwIDU2LjUgLTEzN3QxMzUuNSAtNTdoNzUwcTEyMCAwIDIwNSA4Ni41dDg1IDIwNy41dC04NSAyMDd0LTIwNSA4NnEtNDYgMCAtOTAgLTE0cS00NCA5NyAtMTM0LjUgMTU2LjV0LTIwMC41IDU5LjVxLTE1MiAwIC0yNjAgLTEwNy41dC0xMDggLTI2MC41cTAgLTI1IDIgLTM3cS02NiAtMTQgLTEwOC41IC02Ny41dC00Mi41IC0xMjIuNXoiIC8%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%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%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%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDEzOyIgZD0iTTI5IDQ1NGw0MTkgLTQyMGw4MTggODIwbC0yMTIgMjEybC02MDcgLTYwN2wtMjA2IDIwN3oiIC8%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%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%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%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%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDI3OyIgZD0iTTQgNjAwcTAgMTYyIDgwIDI5OXQyMTcgMjE3dDI5OSA4MHQyOTkgLTgwdDIxNyAtMjE3dDgwIC0yOTl0LTgwIC0yOTl0LTIxNyAtMjE3dC0yOTkgLTgwdC0yOTkgODB0LTIxNyAyMTd0LTgwIDI5OXpNMTg2IDYwMHEwIC0xNzEgMTIxLjUgLTI5Mi41dDI5Mi41IC0xMjEuNXQyOTIuNSAxMjEuNXQxMjEuNSAyOTIuNXQtMTIxLjUgMjkyLjV0LTI5Mi41IDEyMS41dC0yOTIuNSAtMTIxLjV0LTEyMS41IC0yOTIuNXpNMzUwIDYwMGwyNTAgMzAwIGwyNTAgLTMwMGgtMTUwdi0zMDBoLTIwMHYzMDBoLTE1MHoiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDI4OyIgZD0iTTAgMjV2NDc1bDIwMCA3MDBoODAwbDE5OSAtNzAwbDEgLTQ3NXEwIC0xMSAtNyAtMTh0LTE4IC03aC0xMTUwcS0xMSAwIC0xOCA3dC03IDE4ek0yMDAgNTAwaDIwMGw1MCAtMjAwaDMwMGw1MCAyMDBoMjAwbC05NyA1MDBoLTYwNnoiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDI5OyIgZD0iTTQgNjAwcTAgMTYyIDgwIDI5OXQyMTcgMjE3dDI5OSA4MHQyOTkgLTgwdDIxNyAtMjE3dDgwIC0yOTl0LTgwIC0yOTl0LTIxNyAtMjE3dC0yOTkgLTgwdC0yOTkgODB0LTIxNyAyMTd0LTgwIDI5OXpNMTg2IDYwMHEwIC0xNzIgMTIxLjUgLTI5M3QyOTIuNSAtMTIxdDI5Mi41IDEyMXQxMjEuNSAyOTNxMCAxNzEgLTEyMS41IDI5Mi41dC0yOTIuNSAxMjEuNXQtMjkyLjUgLTEyMS41dC0xMjEuNSAtMjkyLjV6TTUwMCAzOTd2NDAxIGwyOTcgLTIwMHoiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDMwOyIgZD0iTTIzIDYwMHEwIC0xMTggNDUuNSAtMjI0LjV0MTIzIC0xODR0MTg0IC0xMjN0MjI0LjUgLTQ1LjV0MjI0LjUgNDUuNXQxODQgMTIzdDEyMyAxODR0NDUuNSAyMjQuNWgtMTUwcTAgLTE3NyAtMTI1IC0zMDJ0LTMwMiAtMTI1dC0zMDIgMTI1dC0xMjUgMzAydDEyNSAzMDJ0MzAyIDEyNXExMzYgMCAyNDYgLTgxbC0xNDYgLTE0Nmg0MDB2NDAwbC0xNDUgLTE0NXEtMTU3IDEyMiAtMzU1IDEyMnEtMTE4IDAgLTIyNC41IC00NS41dC0xODQgLTEyMyB0LTEyMyAtMTg0dC00NS41IC0yMjQuNXoiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDMxOyIgZD0iTTIzIDYwMHEwIDExOCA0NS41IDIyNC41dDEyMyAxODR0MTg0IDEyM3QyMjQuNSA0NS41cTE5OCAwIDM1NSAtMTIybDE0NSAxNDV2LTQwMGgtNDAwbDE0NyAxNDdxLTExMiA4MCAtMjQ3IDgwcS0xNzcgMCAtMzAyIC0xMjV0LTEyNSAtMzAyaC0xNTB6TTEwMCAwdjQwMGg0MDBsLTE0NyAtMTQ3cTExMiAtODAgMjQ3IC04MHExNzcgMCAzMDIgMTI1dDEyNSAzMDJoMTUwcTAgLTExOCAtNDUuNSAtMjI0LjV0LTEyMyAtMTg0dC0xODQgLTEyMyB0LTIyNC41IC00NS41cS0xOTggMCAtMzU1IDEyMnoiIC8%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%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%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%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDQ4OyIgZD0iTTEwMCAwdjg5cTQxIDcgNzAuNSAzMi41dDI5LjUgNjUuNXY4MjdxMCAyOCAtMSAzOS41dC01LjUgMjZ0LTE1LjUgMjF0LTI5IDE0dC00OSAxNC41djcxbDQ3MSAtMXExMjAgMCAyMTMgLTg4dDkzIC0yMjhxMCAtNTUgLTExLjUgLTEwMS41dC0yOCAtNzR0LTMzLjUgLTQ3LjV0LTI4IC0yOGwtMTIgLTdxOCAtMyAyMS41IC05dDQ4IC0zMS41dDYwLjUgLTU4dDQ3LjUgLTkxLjV0MjEuNSAtMTI5cTAgLTg0IC01OSAtMTU2LjV0LTE0MiAtMTExIHQtMTYyIC0zOC41aC01MDB6TTQwMCAyMDBoMTYxcTg5IDAgMTUzIDQ4LjV0NjQgMTMyLjVxMCA5MCAtNjIuNSAxNTQuNXQtMTU2LjUgNjQuNWgtMTU5di00MDB6TTQwMCA3MDBoMTM5cTc2IDAgMTMwIDYxLjV0NTQgMTM4LjVxMCA4MiAtODQgMTMwLjV0LTIzOSA0OC41di0zNzl6IiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4ZTA0OTsiIGQ9Ik0yMDAgMHY1N3E3NyA3IDEzNC41IDQwLjV0NjUuNSA4MC41bDE3MyA4NDlxMTAgNTYgLTEwIDc0dC05MSAzN3EtNiAxIC0xMC41IDIuNXQtOS41IDIuNXY1N2g0MjVsMiAtNTdxLTMzIC04IC02MiAtMjUuNXQtNDYgLTM3dC0yOS41IC0zOHQtMTcuNSAtMzAuNWwtNSAtMTJsLTEyOCAtODI1cS0xMCAtNTIgMTQgLTgydDk1IC0zNnYtNTdoLTUwMHoiIC8%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%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%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%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%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDU5OyIgZD0iTTAgMjc1djY1MHEwIDMxIDIyIDUzdDUzIDIyaDc1MHEzMSAwIDUzIC0yMnQyMiAtNTN2LTY1MHEwIC0zMSAtMjIgLTUzdC01MyAtMjJoLTc1MHEtMzEgMCAtNTMgMjJ0LTIyIDUzek05MDAgNjAwbDMwMCAzMDB2LTYwMHoiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDYwOyIgZD0iTTAgNDR2MTAxMnEwIDE4IDEzIDMxdDMxIDEzaDExMTJxMTkgMCAzMS41IC0xM3QxMi41IC0zMXYtMTAxMnEwIC0xOCAtMTIuNSAtMzF0LTMxLjUgLTEzaC0xMTEycS0xOCAwIC0zMSAxM3QtMTMgMzF6TTEwMCAyNjNsMjQ3IDE4MmwyOTggLTEzMWwtNzQgMTU2bDI5MyAzMThsMjM2IC0yODh2NTAwaC0xMDAwdi03Mzd6TTIwOCA3NTBxMCA1NiAzOSA5NXQ5NSAzOXQ5NSAtMzl0MzkgLTk1dC0zOSAtOTV0LTk1IC0zOXQtOTUgMzl0LTM5IDk1eiAiIC8%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%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%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%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDcxOyIgZD0iTTEzNiA1NTBsNTY0IDU1MHYtNDg3bDUwMCA0ODd2LTExMDBsLTUwMCA0ODh2LTQ4OHoiIC8%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%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDc4OyIgZD0iTTEwMCAyNTB2MTAwcTAgMjEgMTQuNSAzNS41dDM1LjUgMTQuNWgxMDAwcTIxIDAgMzUuNSAtMTQuNXQxNC41IC0zNS41di0xMDBxMCAtMjEgLTE0LjUgLTM1LjV0LTM1LjUgLTE0LjVoLTEwMDBxLTIxIDAgLTM1LjUgMTQuNXQtMTQuNSAzNS41ek0xMDAgNTAwaDExMDBsLTU1MCA1NjR6IiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4ZTA3OTsiIGQ9Ik0xODUgNTk5bDU5MiAtNTkybDI0MCAyNDBsLTM1MyAzNTNsMzUzIDM1M2wtMjQwIDI0MHoiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDgwOyIgZD0iTTI3MiAxOTRsMzUzIDM1M2wtMzUzIDM1M2wyNDEgMjQwbDU3MiAtNTcxbDIxIC0yMmwtMSAtMXYtMWwtNTkyIC01OTF6IiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4ZTA4MTsiIGQ9Ik0zIDYwMHEwIDE2MiA4MCAyOTkuNXQyMTcuNSAyMTcuNXQyOTkuNSA4MHQyOTkuNSAtODB0MjE3LjUgLTIxNy41dDgwIC0yOTkuNXQtODAgLTI5OS41dC0yMTcuNSAtMjE3LjV0LTI5OS41IC04MHQtMjk5LjUgODB0LTIxNy41IDIxNy41dC04MCAyOTkuNXpNMzAwIDUwMGgyMDB2LTIwMGgyMDB2MjAwaDIwMHYyMDBoLTIwMHYyMDBoLTIwMHYtMjAwaC0yMDB2LTIwMHoiIC8%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%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%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%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDkxOyIgZD0iTTAgNTQ3bDYwMCA0NTN2LTMwMGg2MDB2LTMwMGgtNjAwdi0zMDF6IiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4ZTA5MjsiIGQ9Ik0wIDQwMHYzMDBoNjAwdjMwMGw2MDAgLTQ1M2wtNjAwIC00NDh2MzAxaC02MDB6IiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4ZTA5MzsiIGQ9Ik0yMDQgNjAwbDQ1MCA2MDBsNDQ0IC02MDBoLTI5OHYtNjAwaC0zMDB2NjAwaC0yOTZ6IiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4ZTA5NDsiIGQ9Ik0xMDQgNjAwaDI5NnY2MDBoMzAwdi02MDBoMjk4bC00NDkgLTYwMHoiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDk1OyIgZD0iTTAgMjAwcTYgMTMyIDQxIDIzOC41dDEwMy41IDE5M3QxODQgMTM4dDI3MS41IDU5LjV2MjcxbDYwMCAtNDUzbC02MDAgLTQ0OHYzMDFxLTk1IC0yIC0xODMgLTIwdC0xNzAgLTUydC0xNDcgLTkyLjV0LTEwMCAtMTM1LjV6IiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4ZTA5NjsiIGQ9Ik0wIDB2NDAwbDEyOSAtMTI5bDI5NCAyOTRsMTQyIC0xNDJsLTI5NCAtMjk0bDEyOSAtMTI5aC00MDB6TTYzNSA3NzdsMTQyIC0xNDJsMjk0IDI5NGwxMjkgLTEyOXY0MDBoLTQwMGwxMjkgLTEyOXoiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMDk3OyIgZD0iTTM0IDE3NmwyOTUgMjk1bC0xMjkgMTI5aDQwMHYtNDAwbC0xMjkgMTMwbC0yOTUgLTI5NXpNNjAwIDYwMHY0MDBsMTI5IC0xMjlsMjk1IDI5NWwxNDIgLTE0MWwtMjk1IC0yOTVsMTI5IC0xMzBoLTQwMHoiIC8%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%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%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%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%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%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%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%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%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%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%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMTUwOyIgZD0iTTIgMzAwbDI5OCAtMzAwbDI5OCAzMDBoLTE5OHY5MDBoLTIwMHYtOTAwaC0xOTh6TTYwMiA5MDBsMjk4IDMwMGwyOTggLTMwMGgtMTk4di05MDBoLTIwMHY5MDBoLTE5OHoiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMTUxOyIgZD0iTTIgMzAwaDE5OHY5MDBoMjAwdi05MDBoMTk4bC0yOTggLTMwMHpNNzAwIDB2MjAwaDEwMHYtMTAwaDIwMHYtMTAwaC0zMDB6TTcwMCA0MDB2MTAwaDMwMHYtMjAwaC05OXYtMTAwaC0xMDB2MTAwaDk5djEwMGgtMjAwek03MDAgNzAwdjUwMGgzMDB2LTUwMGgtMTAwdjEwMGgtMTAwdi0xMDBoLTEwMHpNODAxIDkwMGgxMDB2MjAwaC0xMDB2LTIwMHoiIC8%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%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMTU0OyIgZD0iTTIgMzAwbDI5OCAtMzAwbDI5OCAzMDBoLTE5OHY5MDBoLTIwMHYtOTAwaC0xOTh6TTgwMCA0MDB2MTAwaDIwMHYtNTAwaC0xMDB2NDAwaC0xMDB6TTgwMCA4MDB2NDAwaDMwMHYtNTAwaC0xMDB2MTAwaC0yMDB6TTkwMSA5MDBoMTAwdjIwMGgtMTAwdi0yMDB6IiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4ZTE1NTsiIGQ9Ik0yIDMwMGwyOTggLTMwMGwyOTggMzAwaC0xOTh2OTAwaC0yMDB2LTkwMGgtMTk4ek03MDAgMTAwdjIwMGg1MDB2LTIwMGgtNTAwek03MDAgNDAwdjIwMGg0MDB2LTIwMGgtNDAwek03MDAgNzAwdjIwMGgzMDB2LTIwMGgtMzAwek03MDAgMTAwMHYyMDBoMjAwdi0yMDBoLTIwMHoiIC8%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%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%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%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMTY3OyIgZD0iTTAgMHYyNzVxMCAxMSA3IDE4dDE4IDdoMTA0OHExMSAwIDE5IC03LjV0OCAtMTcuNXYtMjc1aC0xMTAwek0xMDAgNzAwaDMwMHYtMzAwaDMwMHYzMDBoMjk1bC00NDUgNTAwek05MDAgMTUwaDEwMHY1MGgtMTAwdi01MHoiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMTY4OyIgZD0iTTAgMHYyNzVxMCAxMSA3IDE4dDE4IDdoMTA0OHExMSAwIDE5IC03LjV0OCAtMTcuNXYtMjc1aC0xMTAwek0xMDAgNzA1bDMwNSAtMzA1bDU5NiA1OTZsLTE1NCAxNTVsLTQ0MiAtNDQybC0xNTAgMTUxek05MDAgMTUwaDEwMHY1MGgtMTAwdi01MHoiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMTY5OyIgZD0iTTAgMHYyNzVxMCAxMSA3IDE4dDE4IDdoMTA0OHExMSAwIDE5IC03LjV0OCAtMTcuNXYtMjc1aC0xMTAwek0xMDAgOTg4bDk3IC05OGwyMTIgMjEzbC05NyA5N3pNMjAwIDQwMGw2OTcgMWwzIDY5OWwtMjUwIC0yMzlsLTE0OSAxNDlsLTIxMiAtMjEybDE0OSAtMTQ5ek05MDAgMTUwaDEwMHY1MGgtMTAwdi01MHoiIC8%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%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMTczOyIgZD0iTTAgMTUwdjEwMDBxMCAyMCAxNC41IDM1dDM1LjUgMTVoMjUwdi0zMDBoNTAwdjMwMGgxMDBsMjAwIC0yMDB2LTIxOGwtMjc2IC0yNzVsLTEyMCAxMjBsLTEyNiAtMTI3aC0zNzh2LTQwMGgtMTUwcS0yMSAwIC0zNS41IDE0LjV0LTE0LjUgMzUuNXpNNTgxIDMwNmwxMjMgMTIzbDEyMCAtMTIwbDM1MyAzNTJsMTIzIC0xMjNsLTQ3NSAtNDc2ek02MDAgMTAwMGgxMDB2MjAwaC0xMDB2LTIwMHoiIC8%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%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMTg0OyIgZD0iTTEwMCAwdjEwMGgxMTAwdi0xMDBoLTExMDB6TTE3NSAyMDBoOTUwbC0xMjUgMTUwdjI1MGwxMDAgMTAwdjQwMGgtMTAwdi0yMDBoLTEwMHYyMDBoLTIwMHYtMjAwaC0xMDB2MjAwaC0yMDB2LTIwMGgtMTAwdjIwMGgtMTAwdi00MDBsMTAwIC0xMDB2LTI1MHoiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMTg1OyIgZD0iTTEwMCAwaDMwMHY0MDBxMCA0MSAtMjkuNSA3MC41dC03MC41IDI5LjVoLTEwMHEtNDEgMCAtNzAuNSAtMjkuNXQtMjkuNSAtNzAuNXYtNDAwek01MDAgMHYxMDAwcTAgNDEgMjkuNSA3MC41dDcwLjUgMjkuNWgxMDBxNDEgMCA3MC41IC0yOS41dDI5LjUgLTcwLjV2LTEwMDBoLTMwMHpNOTAwIDB2NzAwcTAgNDEgMjkuNSA3MC41dDcwLjUgMjkuNWgxMDBxNDEgMCA3MC41IC0yOS41dDI5LjUgLTcwLjV2LTcwMGgtMzAweiIgLz4KPGdseXBoIHVuaWNvZGU9IiYjeGUxODY7IiBkPSJNLTEwMCAzMDB2NTAwcTAgMTI0IDg4IDIxMnQyMTIgODhoNzAwcTEyNCAwIDIxMiAtODh0ODggLTIxMnYtNTAwcTAgLTEyNCAtODggLTIxMnQtMjEyIC04OGgtNzAwcS0xMjQgMCAtMjEyIDg4dC04OCAyMTJ6TTEwMCAyMDBoOTAwdjcwMGgtOTAwdi03MDB6TTIwMCAzMDBoMzAwdjMwMGgtMjAwdjEwMGgyMDB2MTAwaC0zMDB2LTMwMGgyMDB2LTEwMGgtMjAwdi0xMDB6TTYwMCAzMDBoMjAwdjEwMGgxMDB2MzAwaC0xMDB2MTAwaC0yMDB2LTUwMCB6TTcwMCA0MDB2MzAwaDEwMHYtMzAwaC0xMDB6IiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4ZTE4NzsiIGQ9Ik0tMTAwIDMwMHY1MDBxMCAxMjQgODggMjEydDIxMiA4OGg3MDBxMTI0IDAgMjEyIC04OHQ4OCAtMjEydi01MDBxMCAtMTI0IC04OCAtMjEydC0yMTIgLTg4aC03MDBxLTEyNCAwIC0yMTIgODh0LTg4IDIxMnpNMTAwIDIwMGg5MDB2NzAwaC05MDB2LTcwMHpNMjAwIDMwMGgxMDB2MjAwaDEwMHYtMjAwaDEwMHY1MDBoLTEwMHYtMjAwaC0xMDB2MjAwaC0xMDB2LTUwMHpNNjAwIDMwMGgyMDB2MTAwaDEwMHYzMDBoLTEwMHYxMDBoLTIwMHYtNTAwIHpNNzAwIDQwMHYzMDBoMTAwdi0zMDBoLTEwMHoiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMTg4OyIgZD0iTS0xMDAgMzAwdjUwMHEwIDEyNCA4OCAyMTJ0MjEyIDg4aDcwMHExMjQgMCAyMTIgLTg4dDg4IC0yMTJ2LTUwMHEwIC0xMjQgLTg4IC0yMTJ0LTIxMiAtODhoLTcwMHEtMTI0IDAgLTIxMiA4OHQtODggMjEyek0xMDAgMjAwaDkwMHY3MDBoLTkwMHYtNzAwek0yMDAgMzAwaDMwMHYxMDBoLTIwMHYzMDBoMjAwdjEwMGgtMzAwdi01MDB6TTYwMCAzMDBoMzAwdjEwMGgtMjAwdjMwMGgyMDB2MTAwaC0zMDB2LTUwMHoiIC8%2BCjxnbHlwaCB1bmljb2RlPSImI3hlMTg5OyIgZD0iTS0xMDAgMzAwdjUwMHEwIDEyNCA4OCAyMTJ0MjEyIDg4aDcwMHExMjQgMCAyMTIgLTg4dDg4IC0yMTJ2LTUwMHEwIC0xMjQgLTg4IC0yMTJ0LTIxMiAtODhoLTcwMHEtMTI0IDAgLTIxMiA4OHQtODggMjEyek0xMDAgMjAwaDkwMHY3MDBoLTkwMHYtNzAwek0yMDAgNTUwbDMwMCAtMTUwdjMwMHpNNjAwIDQwMGwzMDAgMTUwbC0zMDAgMTUwdi0zMDB6IiAvPgo8Z2x5cGggdW5pY29kZT0iJiN4ZTE5MDsiIGQ9Ik0tMTAwIDMwMHY1MDBxMCAxMjQgODggMjEydDIxMiA4OGg3MDBxMTI0IDAgMjEyIC04OHQ4OCAtMjEydi01MDBxMCAtMTI0IC04OCAtMjEydC0yMTIgLTg4aC03MDBxLTEyNCAwIC0yMTIgODh0LTg4IDIxMnpNMTAwIDIwMGg5MDB2NzAwaC05MDB2LTcwMHpNMjAwIDMwMHY1MDBoNzAwdi01MDBoLTcwMHpNMzAwIDQwMGgxMzBxNDEgMCA2OCA0MnQyNyAxMDd0LTI4LjUgMTA4dC02Ni41IDQzaC0xMzB2LTMwMHpNNTc1IDU0OSBxMCAtNjUgMjcgLTEwN3Q2OCAtNDJoMTMwdjMwMGgtMTMwcS0zOCAwIC02Ni41IC00M3QtMjguNSAtMTA4eiIgLz4KPGdseXBoIHVuaWNvZGU9IiYjeGUxOTE7IiBkPSJNLTEwMCAzMDB2NTAwcTAgMTI0IDg4IDIxMnQyMTIgODhoNzAwcTEyNCAwIDIxMiAtODh0ODggLTIxMnYtNTAwcTAgLTEyNCAtODggLTIxMnQtMjEyIC04OGgtNzAwcS0xMjQgMCAtMjEyIDg4dC04OCAyMTJ6TTEwMCAyMDBoOTAwdjcwMGgtOTAwdi03MDB6TTIwMCAzMDBoMzAwdjMwMGgtMjAwdjEwMGgyMDB2MTAwaC0zMDB2LTMwMGgyMDB2LTEwMGgtMjAwdi0xMDB6TTYwMSAzMDBoMTAwdjEwMGgtMTAwdi0xMDB6TTcwMCA3MDBoMTAwIHYtNDAwaDEwMHY1MDBoLTIwMHYtMTAweiIgLz4KPGdseXBoIHVuaWNvZGU9IiYjeGUxOTI7IiBkPSJNLTEwMCAzMDB2NTAwcTAgMTI0IDg4IDIxMnQyMTIgODhoNzAwcTEyNCAwIDIxMiAtODh0ODggLTIxMnYtNTAwcTAgLTEyNCAtODggLTIxMnQtMjEyIC04OGgtNzAwcS0xMjQgMCAtMjEyIDg4dC04OCAyMTJ6TTEwMCAyMDBoOTAwdjcwMGgtOTAwdi03MDB6TTIwMCAzMDBoMzAwdjQwMGgtMjAwdjEwMGgtMTAwdi01MDB6TTMwMSA0MDB2MjAwaDEwMHYtMjAwaC0xMDB6TTYwMSAzMDBoMTAwdjEwMGgtMTAwdi0xMDB6TTcwMCA3MDBoMTAwIHYtNDAwaDEwMHY1MDBoLTIwMHYtMTAweiIgLz4KPGdseXBoIHVuaWNvZGU9IiYjeGUxOTM7IiBkPSJNLTEwMCAzMDB2NTAwcTAgMTI0IDg4IDIxMnQyMTIgODhoNzAwcTEyNCAwIDIxMiAtODh0ODggLTIxMnYtNTAwcTAgLTEyNCAtODggLTIxMnQtMjEyIC04OGgtNzAwcS0xMjQgMCAtMjEyIDg4dC04OCAyMTJ6TTEwMCAyMDBoOTAwdjcwMGgtOTAwdi03MDB6TTIwMCA3MDB2MTAwaDMwMHYtMzAwaC05OXYtMTAwaC0xMDB2MTAwaDk5djIwMGgtMjAwek0yMDEgMzAwdjEwMGgxMDB2LTEwMGgtMTAwek02MDEgMzAwdjEwMGgxMDB2LTEwMGgtMTAweiBNNzAwIDcwMHYxMDBoMjAwdi01MDBoLTEwMHY0MDBoLTEwMHoiIC8%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<h1 class="title">Tutorial on Bayesian Statistics: Replicating Sections of BDA3</h1>
<h4 class="author"><em>Fernando Hoces de la Guardia</em></h4>
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<div id="replicating-example-from-pg-66-67" class="section level1">
<h1>1 - Replicating example from pg 66-67</h1>
<p>Chapter 3 of BDA presents a first exercise of simulation (pgs 66-67) where from a sample of 66 obs with mean 26.2 and standard deviation 10.8, a posterior for the mean is simulated assuming a joint normal likelihood and uninformative prior (where <span class="math">\(\sigma^{2}|y\sim Inv-\chi^{2}(n-1,s^{2})\)</span> and <span class="math">\(\mu|\sigma^{2},y \sim N(\bar{y},\sigma^{2}/n)\)</span>).</p>
<pre class="r"><code># Draw 1000 random numbers from a Inverse chi-squared
f.sim.sigma = function(draws) (n-1)*(se^2)/rchisq(draws,n-1)
f.sim.norm = function(draws) rnorm(draws,ybar,(f.sim.sigma(draws)/(n-1))^.5)
sim.norm = f.sim.norm(1000)
ci.mu = sim.norm[order(sim.norm)][c(25,975)]
print(ci.mu)</code></pre>
<pre><code>## [1] 23.44967 28.83449</code></pre>
<pre class="r"><code># And now repeating the similation excercise R = 100 times:
R = 100
R.sim.norm = sapply(1:R, function(x) f.sim.norm(1000))
ci.mu = t(apply(R.sim.norm,2,function(x) x[order(x)][c(25,975)]))
print(c(median_low=median(ci.mu[,1]), median_high=median(ci.mu[,2]), p10_low =quantile(ci.mu[,1],c(.1),type=1), p90_up =quantile(ci.mu[,2],c(.9),type=1) ))</code></pre>
<pre><code>## median_low median_high p10_low.10% p90_up.90%
## 23.53239 28.87305 23.37244 29.03817</code></pre>
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<td align="left"># 2 - Simulating values from a postetior normal with <span class="math">\(\sigma^{2}\)</span> and <span class="math">\(\mu\)</span> unknown and conjugate prior. The following is not an exercise in the book (that I’m aware of), but I though that it would be interesting to work on this. After going over the model derived in pg 67-69 in BDA3, I will simulate values from the joint posterior (and hopefully leave the code flexible enough to play later on with the hyper-parameters).</td>
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<td align="left">With the prior density: <span class="math">\[
\begin{aligned}
p(\mu,\sigma^{2}) &\propto \sigma^{-1}(\sigma^{2})^{(\nu_{0}/2 + 1}exp\left ( -\frac{1}{2\sigma^{2}} [\nu_{0}\sigma^{2}_{0} + \kappa_{0}(\mu_{0} - \mu)^{2} ]\right )
\end{aligned}
\]</span> And a likelihood: <span class="math">\[
\begin{aligned}
p(y|\mu,\sigma^{2}) &\propto \sigma^{-n}exp\left ( -\frac{1}{2\sigma^{2}} [(n-1)s^{2} + n(\bar{y} - \mu)^{2} ]\right )
\end{aligned}
\]</span></td>
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<tr class="odd">
<td align="left">We obtain the following joint posterior: <span class="math">\[
\begin{aligned}
p(\mu,\sigma^{2}|y) &\propto \sigma^{-1}(\sigma^{2})^{(\nu_{0}/2 + 1}exp\left ( -\frac{1}{2\sigma^{2}} [\nu_{0}\sigma^{2}_{0} + \kappa_{0}(\mu_{0} - \mu)^{2} ]\right ) \times \nonumber \\
&\times (\sigma^{2})^{-n/2}exp\left ( -\frac{1}{2\sigma^{2}} [(n-1)s^{2} + n(\bar{y} - \mu)^{2} ]\right ) \nonumber\\
&= N-Inv-\chi^{2}(\mu_n,\sigma^{2}_{n};\nu_{n},\sigma^{2}_{n})\\
\mu_{n} &= \frac{\kappa_{0}}{\kappa_{0} + n} \mu_{0} + \frac{n}{\kappa_{0} + n}\bar{y} \nonumber\\
\kappa_{n} &= \kappa_{0} + n \nonumber\\
\nu_{n} &= \nu_{0} + n \nonumber\\
\nu_{n}\sigma_{n}^{2} &= \nu_{0}\sigma_{0}^{2} + (n-1)s^{2} + \frac{\kappa_{0}n}{\kappa_{0} + n} (\bar{y} - \mu_0)^{2}. \nonumber
\end{aligned}
\]</span></td>
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<tr class="even">
<td align="left">Using the fact that <span class="math">\(p(\mu,\sigma^{2}|y) = p(\mu|\sigma^{2},y)p(\sigma^{2}|y)\)</span> with: <span class="math">\[
\begin{aligned}
\mu|\sigma^{2},y &\sim N(\mu_{n},\sigma^{2}_{n}/\kappa_{n}) \label{post.mu}\\
\sigma^{2}|y &\sim Inv-\chi^{2}(\nu_{n},\sigma^{2}_{n}) \ label{post.sig}\\
\end{aligned}
\]</span> The simulation algorithm is as follows: * Draw a random number from the conditional posterior of sigma (equation \ref{post.sig}) * Using that value of <span class="math">\(\sigma^{2}\)</span>, draw a random number for the conditional posterior of <span class="math">\(\mu\)</span> (equation \ref{post.mu})</td>
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<td align="left">The following code implements this algorithm.</td>
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<tr class="even">
<td align="left">```r # Hyperparameters p.mu_0 = 0 p.sigma2_0 = 1 p.nu_0 = 4 p.kappa_0 = 3</td>
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<tr class="odd">
<td align="left"># Data n = 10 y_bar = 1.3 s = 2</td>
</tr>
<tr class="even">
<td align="left"># Simulation mu_n = ((p.kappa_0)/(p.kappa_0 + n)) * p.mu_0 + ((n)/(p.kappa_0 + n)) * y_bar kappa_n = p.kappa_0 + n nu_n = p.nu_0 + n sigma2_n = (p.nu_0<em>p.sigma2_0 + (n-1)</em>s^{2} + ((p.kappa_0<em>n)/(p.kappa_0 + n)) </em> (y_bar - p.mu_0)^{2})/nu_n</td>
</tr>
<tr class="odd">
<td align="left">set.seed(142857) # Draw 1000 random numbers from a Inverse chi-squared f.mu.post = function(draws) { sigma2.cond = (nu_n)<em>(sigma2_n)/rchisq(draws,nu_n) mu.cond = rnorm(draws,mu_n,(sigma2.cond/(kappa_n))^.5) return(mu.cond) } sim.mu.post= f.mu.post(1000) plot(density(sim.mu.post), main = “Draws from the marginal of the mean”, col=“red”) lines(density(mu_n +((sigma2_n/kappa_n)^.5)</em>rt(1000,nu_n))) legend(“topleft”,col = c(“red”,“black”) ,legend=c(“Simulated”,“Analytical”),lty = c(1,1)) ```</td>
</tr>
<tr class="even">
<td align="left"><img 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" 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</tr>
<tr class="odd">
<td align="left">The plot above should be in 3D (<span class="math">\(\sigma^{2}, \mu, p(\sigma^{2}, \mu|y)\)</span>) but still don’t know how to do that in R.</td>
</tr>
<tr class="even">
<td align="left">It also happens that for this particular problem there is a close form solution for the marginal of <span class="math">\(\mu\)</span>. (remember that <span class="math">\(p(\mu|y) = \int p(\mu|\sigma^{2},y) p(\sigma^{2}|y)d\sigma^{2}\)</span>):</td>
</tr>
<tr class="odd">
<td align="left"><span class="math">\[
\begin{aligned}
\mu|\sigma^{2},y &\sim t_{\nu_{n}}(\mu|\mu_{n}, \sigma^2_{n}/\kappa_{n})
\end{aligned}
\]</span></td>
</tr>
<tr class="even">
<td align="left"><strong>I’m still confused with the following</strong> why is that to simulate the marginal of <span class="math">\(\mu\)</span> (<span class="math">\(\mu|\sigma^2,y\)</span>) I just need to draw from the conditional posterior of the mean (equation \ref{post.mu}). More generally, my confusion is the following: why is that to simulate <span class="math">\(h(x) = \int g(x) dF(x)\)</span> I just need to draw <span class="math">\(x^{s}\)</span> from <span class="math">\(dF(x)\)</span> and evaluate <span class="math">\(g(x^{s})\)</span>. I know from MC simulation that by the LLN <span class="math">\(E_{dF}[g(x)] = \int g(x) dF(x) \approx \sum_{s}g(x^{s})/S\)</span>, but I’m having trouble seen why is that this applies to all points in the distribution (and not just the mean).</td>
</tr>
<tr class="odd">
<td align="left"><strong>My own explanation so far:</strong> as MC can be used to approximate the mean using the LLN, the same technique can be used to approximate the whole distribution using CLT.</td>
</tr>
<tr class="even">
<td align="left">***</td>
</tr>
<tr class="odd">
<td align="left">Simulating numbers from a Dirichlet distribution</td>
</tr>
<tr class="even">
<td align="left"><code>r draws = 1000 #This are the parameters of the gamma used in generating the final Dirichlet. gamma.scale = c(728,538,138) aux1 = sapply(gamma.scale,function(x) rgamma(100,x)) aux1 = aux1 / apply(aux1,1,sum)</code></td>
</tr>
<tr class="odd">
<td align="left">***</td>
</tr>
<tr class="even">
<td align="left"># 3 - Replicating Simulation Example 3.7 from BDA3 (pg 74+) We are interested in modeling the dose-response of a certain drug (<span class="math">\(x_{i}\)</span>) over the number of dead’s (<span class="math">\(y_{i}\)</span>) in a group of trial animals (<span class="math">\(n_{i}\)</span>).We have 4 observations. Defining <span class="math">\(\theta_{i}\)</span> as the true death rate for each dosage, we can model this phenomena using a binomial distribution (<span class="math">\(y_{i} \sim Bin(n_{i},\theta_{i})\)</span>). To model the dose-response relationship we start by looking at <span class="math">\(\theta_{i} = \alpha +\beta x_{i}\)</span> but we realize that this model predicts values out of range (<span class="math">\(\theta\)</span>, as a probability has to be between 0 and 1). Hence we apply the logit (<span class="math">\(log(\theta_{i}/(1-\theta_{i}))\)</span>) transformation. This implies the following likelihood.</td>
</tr>
<tr class="odd">
<td align="left"><span class="math">\[
\begin{aligned}
p(y_{i}|\alpha,\beta,n_{i},x_{i}) \propto [logit^{-1}(\alpha +\beta x_{i})]^{y_i}[1-logit^{-1}(\alpha +\beta x_{i})]^{n_{i}- y_{i}}
\end{aligned}
\]</span></td>
</tr>
<tr class="even">
<td align="left"><strong>Question:</strong> Why don’t we apply transformation method (multiply by the inverse of the Jacobian) to the likelyhood above? <strong>Answer:</strong> Because we are not applying a transformation to <span class="math">\(\theta\)</span> we are only replacin theta by</td>
</tr>
<tr class="odd">
<td align="left">Using a non-informative prior (<span class="math">\(p(\alpha,\beta)\propto 1\)</span>) we get that the conditional posterior has the form: <span class="math">\[
\begin{aligned}
p(\alpha,\beta|y,n,x) \propto \prod_{i=1}^{k} p(y_{i}|\alpha,\beta,n_{i},x_{i}) \label{post.1}
\end{aligned}
\]</span></td>
</tr>
<tr class="even">
<td align="left">First we compute, as a rough approximation of the parameters, the ML estimates.</td>
</tr>
<tr class="odd">
<td align="left">```r # Data x = c(-0.86, -0.30, -0.05, 0.73) y = c(0,1,3,5) n = rep(5,4)</td>
</tr>
<tr class="even">
<td align="left"># ML estimation mlfit <- glm( cbind(y, n-y) ~ x, family = binomial) mlfit<span class="math">\(coefficients = round(mlfit\)</span>coefficients*1000)/1000 res1 = paste(paste(“(”,mlfit<span class="math">\(coefficients[1], sep=""), paste(mlfit\)</span>coefficients[2],“)”, sep=“”), sep=“,”) ```</td>
</tr>
<tr class="odd">
<td align="left">With the estimates <span class="math">\((\hat{\alpha},\hat{\beta}) = (0.847,7.749)\)</span>.</td>
</tr>
<tr class="even">
<td align="left">Now we will simulated values of <span class="math">\(\alpha\)</span> and <span class="math">\(\beta\)</span> from the posterior distribution. The approach is as follows.</td>
</tr>
<tr class="odd">
<td align="left">* (i) Build a grid for all possible values of <span class="math">\(\alpha\)</span> and <span class="math">\(\beta\)</span>. Although this can be the whole real line, we use the ML estimates and some trial and error to restrict the space to <span class="math">\(\alpha \in [-5,10]\)</span> and <span class="math">\(\beta \in [-10,40]\)</span>.</td>
</tr>
<tr class="even">
<td align="left"><code>r alpha = seq(-5,10,.1) beta = seq(-10,40,1)</code></td>
</tr>
<tr class="odd">
<td align="left">* (ii) Compute the posterior density (equation \ref{post.1}) over the whole grid and normalize it to 1.</td>
</tr>
<tr class="even">
<td align="left">```r post.a = function(a,b,x,y,n) { post = 1 for (i in 1:length(y)) { post = post * ( ((inv.logit(a+b*x[i]))<sup>y[i])<em>((1-inv.logit(a+b</em>x[i]))</sup>(n[i]-y[i])) ) } post }</td>
</tr>
<tr class="odd">
<td align="left">post.dens = outer(alpha,beta,function(x1,x2) post.a(x1,x2,x,y,n)) post.dens = post.dens/sum(post.dens) ```</td>
</tr>
<tr class="even">
<td align="left">* (iii) Inspect the density using a contour plot (here we are looking for some indication that we are covering all the possible domain)</td>
</tr>
<tr class="odd">
<td align="left"><code>r contours <- seq(min(post.dens), max(post.dens) , length=10) par(mar = rep(2, 4)) contour(alpha, beta, post.dens,levels=contours, xlab=expression(alpha), ylab=expression(beta), xlim=c(min(alpha),max(alpha)) , ylim=c(min(beta),max(beta)), drawlabels=FALSE, main="Contour plot of joint posterior")</code></td>
</tr>
<tr class="even">
<td align="left"><img 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<td align="left">* (iv) Compute the marginal posterior of <span class="math">\(\alpha\)</span> by summing over all <span class="math">\(\beta\)</span> for each value of <span class="math">\(\alpha\)</span>. Notice so far that we had only compute the probability distribution of <span class="math">\(\alpha\)</span> and <span class="math">\(\beta\)</span>. Is not until this point where we would be able to do things like compute the mean, median and CI’s of these parameters.</td>
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<td align="left"><code>r samps = 1000 alpha.dens = apply(post.dens ,1, sum)</code> * (v) For <span class="math">\(s = 1 \dots 1000\)</span>: a. Draw <span class="math">\(\alpha^{s}\)</span> from its marginal posterior.</td>
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<td align="left"><code>r s.alpha = sample(alpha,samps, replace=TRUE, prob = alpha.dens)</code> b. Draw <span class="math">\(\beta^{s}\)</span> from <span class="math">\(p(\beta|\alpha,y)\)</span> for each value of <span class="math">\(\alpha^{s}\)</span></td>
</tr>
<tr class="even">
<td align="left"><code>r #Select the colum of the joint density corresponding to a specific value of alpha (p(beta|alpha)) cond.beta = function(x) { post.dens[which(alpha == s.alpha[x]),] } #Sample a value of beta according the the conditional probatility above s.beta = sapply(1:samps,function(x) sample(beta,1,replace=TRUE,prob=cond.beta(x)))</code> c. For each sample values of <span class="math">\(\alpha\)</span> and <span class="math">\(\beta\)</span> add a uniform random jitter centered at zero with with equal to the grid spacing. This will make the simulation draws more continuous. Plot the sampled values.</td>
</tr>
<tr class="odd">
<td align="left"><code>r s.beta = s.beta + runif(length(s.beta),-.5,.5) s.alpha = s.alpha + runif(length(s.alpha),-.05,.05) plot(s.alpha, s.beta, xlab=expression(alpha^s), ylab=expression(beta^s), xlim=c(min(alpha),max(alpha)) , ylim=c(min(beta),max(beta)), main="Scatter Plot of Sample Draws of alpha and beta")</code></td>
</tr>
<tr class="even">
<td align="left"><img 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" title alt width="672" /></td>
</tr>
<tr class="odd">
<td align="left">The final result are two vectors <span class="math">\((\{\alpha^{s}\}), (\{\beta^{s}\})\)</span>, that represent probability distribution of each parameter.</td>
</tr>
<tr class="even">
<td align="left"># 4 - Description with my own words, of the fully Bayesian analysis of conjugate hierarchical models described in section 5.3 of BDA (pg 108 - 113)</td>
</tr>
<tr class="odd">
<td align="left">The overall goal of hierarchical models is <strong>to describe a statistical (uncertain) phenomena where are multiple parameters involved and exists a dependence structure</strong>.</td>
</tr>
<tr class="even">
<td align="left">The analysis described here builds on what we just did in the example above. For this purpose we enumerate the steps followed, now in a more general notation.</td>
</tr>
<tr class="odd">
<td align="left">1. Compute the joint posterior probability distribution of all the parameters conditional on the data and a prior distribution of those parameters (in the example above we use a non-informative prior). 2. Compute the marginal posterior of one parameter (<span class="math">\(p(\theta_{2}|y)\)</span>) by summing the joint posterior over all the possible values of the other parameter (<span class="math">\(\theta_{1}\)</span>). 3. Compute the marginal of the other parameter (<span class="math">\(p(\theta_{1}|y)\)</span>) using the following identity:</td>
</tr>
<tr class="even">
<td align="left"><span class="math">\[
\begin{aligned}
p(\theta_{1}|y) = \int p(\theta_{1}|\theta_{2},y) p(\theta_{2}|y) d\theta_{2} \approx p(\theta_{1}|\theta^{s}_{2},y)
\end{aligned}
\]</span> Where <span class="math">\(\theta^{s}_{2}\)</span> is a random draw using <span class="math">\(p(\theta_{2}|y)\)</span> (the justification for this last step is in section 2 of this document).</td>
</tr>
<tr class="odd">
<td align="left">Now we will distinguish between two sets of parameters. The original parameters of interest, still represented by <span class="math">\(\theta\)</span>. And the parameters of the prior distribution, or <em>hyperparameters</em> represented by <span class="math">\(\phi\)</span>. This two sets of parameters fully describe the probabilistic process and have a joint distribution function:</td>
</tr>
<tr class="even">
<td align="left"><span class="math">\[
\begin{aligned}
p(\phi,\theta) = p(\phi)p(\theta|\phi) \label{joint}
\end{aligned}
\]</span></td>
</tr>
<tr class="odd">
<td align="left">And a joint posterior distribution: <span class="math">\[
\begin{aligned}
p(\phi,\theta|y) &\propto p(\theta,\phi) p(y|\theta,\phi) \nonumber\\
&= p(\theta,\phi)p(y|\theta)\nonumber\\
&= p(\phi)p(\theta|\phi)p(y|\theta) \label{joint.post}
\end{aligned}
\]</span> Where in the last line we used the assumption that <span class="math">\(p(y|\theta,\phi)\)</span> depends on <span class="math">\(\phi\)</span> only through <span class="math">\(\theta\)</span>. We call <span class="math">\(p(\phi)\)</span> the <em>hyperprior distribution</em>, <span class="math">\(p(\theta|\phi)\)</span> the population distribution, and the usual suspect <span class="math">\(p(y|\theta)\)</span> is the likelihood, or sampling, distribution.</td>
</tr>
<tr class="even">
<td align="left"><strong>As always our goal is to make inference about <span class="math">\(\theta\)</span></strong> (and maybe <span class="math">\(\phi\)</span> also?). As in the exercise before, our end result will be a set of matrices <span class="math">\((\{\phi^{s}\}), (\{\theta^{s}\})\)</span> with values for the parameters that follow the posterior joint distribution. To get this result we take the following steps:</td>
</tr>
<tr class="odd">
<td align="left">- 1. Compute the conditional joint posterior <span class="math">\(p(\phi,\theta|y)\)</span>. Choosing the right hyper-prior distribution is a whole topic on itself and will be addressed later. - 2. Compute the marginal posterior of <span class="math">\(\theta\)</span>, conditional on <span class="math">\(\phi\)</span>, <span class="math">\(p(\theta|\phi,y)\)</span>. This conditional posterior of <span class="math">\(\theta\)</span> can be obtain analytically in conjugate models for a given value of <span class="math">\(\phi\)</span>, it is simply the posterior of the non-hierarchical Bayesian case. - 3. Compute the posterior marginal of <span class="math">\(\phi\)</span>. When step 2 has a closed form solution we can compute the marginal of <span class="math">\(\phi\)</span> as: <span class="math">\[
\begin{aligned}
p(\phi|y) &= \frac{p(\theta,\phi |y)}{p(\theta|\phi,y)} \label{marg.post.phi}
\end{aligned}
\]</span></td>
</tr>
<tr class="even">
<td align="left">In the absence of a closed form solution for step 2. We can compute the marginal by integrating the joint over all the possible values of <span class="math">\(\theta\)</span>.</td>
</tr>
<tr class="odd">
<td align="left">- 4. Draw samples <span class="math">\(\phi^{s}\)</span> from <span class="math">\(p(\phi|y)\)</span>. Notice that <span class="math">\(\phi\)</span> can have multiple components. If it has more than one element we follow the procedure described at the beginning of this section.</td>
</tr>
<tr class="even">
<td align="left">- 5. For each draw of <span class="math">\(\phi^{s}\)</span>, draw a sample of <span class="math">\(\theta\)</span> from <span class="math">\(p(\theta|\phi^{s},y)\)</span>. <strong>This allow us to fully characterize the parameter of interest (our goal, remember?)</strong></td>
</tr>
<tr class="odd">
<td align="left"><strong>Application</strong></td>
</tr>
<tr class="even">
<td align="left">We have data from <span class="math">\(j = 1 \dots J, J = 71\)</span> experiments where, in each experiment <span class="math">\(n_{j}\)</span> rats were exposed to a drug and <span class="math">\(y_{j}\)</span> of them, presented tumors afterwards (think also something similar to unemployment rate in different states with <span class="math">\(n_{j}\)</span> people in the active labor force and <span class="math">\(y_{j}\)</span> unemployed). The results from the experiments are assumed to follow a binomial distribution (<span class="math">\(y_{j}|\theta_{j} \sim Bin(n_{j},\theta_{j})\)</span>), and the parameters <span class="math">\(\theta_{j}\)</span> are assume to follow a beta prior distribution (<span class="math">\(\theta_{j}|\alpha,\beta \sim Beta(\alpha,\beta)\)</span>), this last assumption is made to take advantage of conjugacy (and because it makes sense). With all this elements now we can follow the steps described above.</td>
</tr>
<tr class="odd">
<td align="left">1. Compute the conditional joint posterior <span class="math">\(p(\phi=(\alpha,\beta),\theta = \{\theta_{j}\}_{j=1}^{J}|y)\)</span>. <span class="math">\[
\begin{aligned}
p(\theta,\alpha,\beta|y) &\propto p(\alpha, \beta)p(\theta|\alpha, \beta)p(y|\theta,\alpha, \beta) \nonumber\\
p(\theta,\alpha,\beta|y) &\propto p(\alpha, \beta)\prod^{J}_{j=1} \frac{\Gamma(\alpha + \beta)}{\Gamma(\alpha)\Gamma(\beta)} \theta_{j}^{\alpha - 1} (1 - \theta_{j})^{\beta - 1}\prod^{J}_{j=1} \theta_{j}^{y_{j}} (1 - \theta_{j})^{n_{j}-y_{j}}\\
&\propto p(\alpha, \beta)\prod^{J}_{j=1} \frac{\Gamma(\alpha + \beta)}{\Gamma(\alpha)\Gamma(\beta)} \theta_{j}^{\alpha + y_{j} - 1} (1 - \theta_{j})^{\beta + n_{j} - y_{j} - 1}\label{rat.joint.post}
\end{aligned}
\]</span></td>
</tr>
<tr class="even">
<td align="left">2. Compute the marginal posterior of <span class="math">\(\theta\)</span>, conditional on <span class="math">\(\alpha, \beta\)</span>. For the beta-binomial case we have that given the hyper-parameters, each <span class="math">\(\theta_{j}\)</span> has a independent posterior distribution <span class="math">\(Beta(\alpha + y_{j}, \beta +n_{j} - y_{j})\)</span>: <span class="math">\[
\begin{aligned}
p(\theta|\alpha,\beta,y) &\propto p(y|\theta,\alpha,\beta)p(\theta|\alpha,\beta)\\
&=\prod^{J}_{j=1} \frac{\Gamma(\alpha + \beta +n_{j})}{\Gamma(\alpha+y_{j})\Gamma(\beta+n_{j}-y_{j})} \theta_{j}^{\alpha+y_{j} - 1} (1 - \theta_{j})^{\beta+n_{j}-y_{j} - 1}\label{rat.cond.post.theta}
\end{aligned}
\]</span></td>
</tr>
<tr class="odd">
<td align="left">3. Compute the posterior marginal of <span class="math">\((\alpha,\beta)\)</span>. Given that we do have a closed form solution in step 2, we compute the ratio of (\ref{rat.joint.post}) and (\ref{rat.cond.post.theta}). <span class="math">\[
\begin{aligned}
p(\alpha,\beta|y) &\propto p(\alpha, \beta)\prod^{J}_{j=1} \frac{\Gamma(\alpha + \beta)}{\Gamma(\alpha)\Gamma(\beta)} \frac{\Gamma(\alpha+y_{j})\Gamma(\beta+n_{j}-y_{j})}{\Gamma(\alpha + \beta +n_{j})} \label{rat.marg.post.phi}
\end{aligned}
\]</span></td>
</tr>
<tr class="even">
<td align="left">And here is the code for this function:</td>
</tr>
<tr class="odd">
<td align="left"><code>r rat.marg.post.phi = function(alpha, beta) { post = 1 for (i in 1:length(y)) { post = post * ( ( ( gamma(alpha + beta) ) / ( gamma(alpha) * gamma(beta) ) ) * ( ( gamma( alpha + y[i] ) * gamma( beta + n[i] - y[i] ) ) / (gamma(alpha + beta + n[i]) ) ) ) } # The hyper prior is defined below rat.hyper.prior(alpha,beta) * post }</code> <strong>Note:</strong> we assume a hyper-prior of the form <span class="math">\(p(\alpha,\beta)\propto (\alpha + \beta)^{-5/2}\)</span>. So far I do not understand very well the whole discussion about proper and improper priors. <strong>Need to review Ch10 of DeGroot’s book</strong></td>
</tr>
<tr class="even">
<td align="left">4. Draw samples <span class="math">\((\alpha^{s}, \beta^{s})\)</span> from <span class="math">\(p(\alpha,\beta|y)\)</span>. Before drawing the samples, the authors applied the following transformation to the parameter space: <span class="math">\((\alpha, \beta) \rightarrow (log(\frac{\alpha}{\beta}), log(\alpha+\beta))\)</span>. <strong>I still don’t know why they do this and why is that the transformation only applies to the hyper-prior only</strong>. This step requires a important number of sub-steps: 4.1. Compute the (prior) probability distribution of the transformed variables. Here is where we multiply by the Jacobian of the inverse transformation. The transformation method states that if <span class="math">\(u\sim p_{u}(u)\)</span> and there is a 1:1 function over <span class="math">\(u\)</span>, <span class="math">\(v = f(u)\)</span>, then <span class="math">\(v\sim p_{u}(u)|J|\)</span> where the <span class="math">\(J\)</span> is the Jacobian of the function <span class="math">\(f^{-1}(v)\)</span> with respect to <span class="math">\(v\)</span>. For this case we have <span class="math">\(v_{1} = f_{1}(\alpha,\beta) = log(\alpha/\beta)\)</span> and <span class="math">\(v_{2} = f_{2}(\alpha,\beta) = log(\alpha + \beta)\)</span>, with inverse <span class="math">\(f^{-1}_{1}(v_{1},v_{2}) = \exp(v_{1}+v_{2})/(1+exp(v_{1}))\)</span> and <span class="math">\(f^{-1}_{2}(v_{1},v_{2}) = exp(v_{2})/(1+exp(v_{1}))\)</span>. Hence the Jacobian is:</td>
</tr>
<tr class="odd">
<td align="left"><span class="math">\[
J = \begin{bmatrix}
\frac{\partial f^{-1}_{1}}{\partial v_{1}} & \frac{\partial f^{-1}_{1}}{\partial v_{2}} \\[0.3em]
\frac{\partial f^{-1}_{2}}{\partial v_{1}} & \frac{\partial f^{-1}_{2}}{\partial v_{2}}
\end{bmatrix}
= - \alpha \beta
\]</span> Hence, using the transformation method we have that <span class="math">\(p(log(\frac{\alpha}{\beta}), log(\alpha+\beta)) \propto \alpha \beta(\alpha + \beta)^{-5/2}\)</span>. And here is the code for this function:</td>
</tr>
<tr class="even">
<td align="left">```r y = c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 5, 2, 5, 2, 7, 7, 3, 3, 2, 9, 10, 4, 4, 4, 4, 4, 4, 4, 10, 4, 4, 4, 5, 11, 12, 5, 5, 6, 5, 6, 6, 6, 6, 16, 15, 15, 9, 4) n = c(20, 20, 20, 20, 20, 20, 20, 19, 19, 19, 19, 18, 18, 17, 20, 20, 20, 20, 19, 19, 18, 18, 27, 25, 24, 23, 20, 20, 20, 20, 20, 20, 10, 49, 19, 46, 17, 49, 47, 20, 20, 13, 48, 50, 20, 20, 20, 20, 20, 20, 20, 48, 19, 19, 19, 22, 46, 49, 20, 20, 23, 19, 22, 20, 20, 20, 52, 46, 47, 24, 14)</td>
</tr>
<tr class="odd">
<td align="left">rat.hyper.prior = function(alpha,beta) { alpha<em>beta</em>(alpha + beta)^(-5/2) } ```</td>
</tr>
<tr class="even">
<td align="left">4.2. Identify the relevant domain for the transformed variables and its counterpart with the original variables. To do so we start computing the parameters <span class="math">\(\alpha\)</span> and <span class="math">\(\beta\)</span> that would match the sample mean and standard deviation of all 70 experiments with a beta prior distribution:</td>
</tr>
<tr class="odd">
<td align="left"><span class="math">\[
\begin{aligned}
\hat{\mu} &= 0.1381151 = \frac{\hat{\alpha_{0}}}{\hat{\alpha_{0}}+\hat{\beta_{0}}}\\
\hat{\sigma^2} &= 0.0108733 = \frac{\hat{\alpha_{0}}\hat{\beta_{0}}}{(\hat{\alpha_{0}}+\hat{\beta_{0}})^{2}(\hat{\alpha_{0}}+\hat{\beta_{0}}+1)}
\end{aligned}
\]</span></td>
</tr>
<tr class="even">
<td align="left">Solving for <span class="math">\((\hat{\alpha_{0}},\hat{\beta_{0}})\)</span>:</td>
</tr>
<tr class="odd">
<td align="left">```r dslnex <- function(x) { z <- numeric(2) z[1] <- x[1]/(x[1]+x[2]) - mean(y/n) z[2] <- x[1]<em>x[2]/(((x[1]+x[2])^2)</em>(x[1]+x[2]+1)) - sd(y/n)^2 z }</td>
</tr>
<tr class="even">
<td align="left">sol1 <- nleqslv(c(1,1), dslnex) res1 <- paste(“(”,round(sol1<span class="math">\(x[1],1), ",", round(sol1\)</span>x[2],1), “)”,sep=“”) ```</td>
</tr>
<tr class="odd">
<td align="left">We get: <span class="math">\((\hat{\alpha_{0}},\hat{\beta_{0}}) = (1.4,8.6)\)</span>.</td>
</tr>
<tr class="even">
<td align="left">We center the grid (approximately) around that initial estimate and expand the grid to cover up to a factor of 4 of each parameter. The result is plotted in the following figure:</td>
</tr>
<tr class="odd">
<td align="left">```r v1 = seq(log(sol1<span class="math">\(x[1]/sol1\)</span>x[2])<em>2,log(sol1<span class="math">\(x[1]/sol1\)</span>x[2])/2,length.out =151) v2 = seq(log(sol1<span class="math">\(x[1]+sol1\)</span>x[2])/2,log(sol1<span class="math">\(x[1]+sol1\)</span>x[2])</em>2,length.out =151) beta = exp(v2)/(exp(v1)+1) alpha = exp(v2+v1)/(exp(v1)+1)</td>
</tr>
<tr class="even">
<td align="left">post.dens = outer(alpha,beta, function(x1,x2) log(rat.marg.post.phi(x1, x2)) ) post.dens = exp(post.dens - max(post.dens)) post.dens = post.dens/sum(post.dens)</td>
</tr>
<tr class="odd">
<td align="left">contours <- seq(min(post.dens), max(post.dens) , length=10) contour(v1, v2, post.dens,levels=contours, xlab=expression(log(alpha/beta)), ylab=expression(log(alpha+beta)), xlim=c(min(v1),max(v1)) , ylim=c(min(v2),max(v2)), drawlabels=FALSE, main=“Contour plot of joint posterior”) ```</td>
</tr>
<tr class="even">
<td align="left"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAABUAAAAPACAMAAADDuCPrAAAAgVBMVEUAAAAAADoAAGYAOmYAOpAAZpAAZrY6AAA6AGY6OgA6Ojo6OpA6ZmY6ZrY6kJA6kLY6kNtmAABmADpmAGZmOgBmZgBmZjpmZmZmtv+QOgCQOjqQOmaQ29uQ2/+2ZgC2kDq2/7a2///bkDrb/7bb/9vb////tmb/25D//7b//9v////O1yVHAAAACXBIWXMAAB2HAAAdhwGP5fFlAAAgAElEQVR4nO3dC5vaSJuYYXkycSfZTWJnk41ns8PukAxt8/9/YDirdAS9SFAF931d32e7G+hqUTyjE6LaAhBSPXsAAKUSUIAgAQUIElCAIAEFCBJQgCABBQgSUIAgAQUIElCAIAEFCBJQgCABBQgSUIAgAQUIElCAIAEFCBJQgCABBQgSUIAgAQUIElCAIAEFCBJQgCABBQgSUIAgAQUIElCAIAEFCBJQgCABBQgSUIAgAQUIElCAIAEFCBJQgCABBQgSUIAgAQUIElCAIAEFCBJQgCABBQgSUIAgAQUIElCAIAEFCBJQgCABBQgSUIAgAQUIElCAIAEFCBJQgCABBQgSUIAgAQUIElCAIAEFCBJQgCABBQgSUIAgAQUIElCAIAEFCBLQwq2qg9/+uutRNt9mGs64n993Q/3y57WbTRvN+rgEfqRf+/y4tkwWGcokUx76xtHycAJaskMnzn5cv/3ww2QU0GmjuSyC3/9uf/X+gC64YKY9tIDmSkALtqoavsYe5dcfu/tmE9CJozk8Yve3nyWgCy6YqQ8toLkS0GIdXoQNjZWwmx0ynE1AJ45mc/nlG/eZJaALLpipDy2guRLQYq2ScKx7IjLpcUoN6OEXX6gsGQWUXAloqTaNlc7jpmzoUFL5AY2teV8loFwloIVqF/N4MCXymhTQeYaSyUPzUAJaqE37yPuqmZLTHtJknXRzetEe03u6Zb0PsX6w7l3TTB2/++Py5W/nP1Lr023WzVG2A9r+SX2jSYzdvHkErb0PtPsrJUO5ecGM/m4DP2dbnyhw/mrPQ5+OhdULsbVory24seeCJQlooVbtF+omfTEn5zddXnbHTtSHrb9dvth4MffddTSgq57KHCNzefDzOJsd6P6k0YCO33wsoH2/UiegVxfMld9t4Oc0TjU73rbz0PWPvvwarUV7bcGNPRcsSUDLdHzNDZ24tK5SpxWSw+v2Hz+aX++8mHvvOhbQ/9LpyPk7/7t+nNPrvNGBnp80FtArNx8JaO+v1A7o1QVz7Xcb+DmNU3WPQ2o/dOMmp6XcWrTXFtzYc8GSBLRMo7s8N1XV8xprf/XwOmu/mPvvOhbQ5uv4ZN16mNNrOu1A308aCei1mw8HtP9Xagf02oK5+rv1/5z2uWZfu79lsv5Z/yKtRXttwY09FyxJQMvU2QWaSHaoHW/W6MT+H6d1nuPd0wMaA3e9HtDWkaF1/dV0917SgYGfNHR4ZejmAweRkoAO3LMb0NEFc+Pv1vk5h78eBnJcbj2/5eryI+u/tRft9QU3/FywJAEt01hAV8mrKNnUT897Su/eeTF37zoe0J4dCevkZx3vcIhI0oGBnzRUraGbXw/owD07AR1fMNd/t/6fs64fbn/bc9uSh05XLtfNJV4v2usLbvi5YEkCWqaRgB5fVd/SG9YrQ6e7pLdpv5h77joa0L6TiBpHqI+rdT+2aQeGftJAtQZvfjWgQ/fsBHR0wVz/3QZ+zro/a8lDb5IbHB7kMOzWor2+4IafC5YkoGUaCWi91bh37N1lg++06lJ/tfti7rnraED7BrFOH6h+nLoDQz9poFqDN78a0KF7tgM6vmCu/24DP2fgraar/p9yuFvSw57zv0afIoffH05AyzQS0FZTVuc1nPSlN9CJobuOBbR3j1vzgS4/oe7A0E8aqNbgza8GdOie7YCOL5jrv9vAz2kcRKqPjtcP3b2iwWHZthbt9QW35HtaGSagZRo5Cl/vSGv+s7Hu0r8KNHTXsYD2njPTfKCeag39pLGA9t38toD23HMgoEPrhld/t6Gf0zyNqbsPtCeglxXKetFeX3DDzwVLEtAydc8D/fw4rY+OBvTcmvkC2rvbrbyAji+Y67/b4AibhewchR8LaP173RhQu0AfTkDLlBz+PVmfX0Cjm/A3BPTKJvwx3bcEtKhN+IkBvXUTfnv5ASfHm7QDeu0XvnETXkAfTkAL1T5oUBe17zDD5Rz58U4M3TUW0KkHkX60RpMYvHnoIFLzhIBQQG86iJTuoj5f/Do5t2rspwwG9JaniMcR0EK1r8ZUny8zehrTeCdG79p4w80tAW2c6tM6dyi705gmBrTzuw2O8PPjvOOz/7fs/w0GA3rLmWY8joCWqnniX/qmlLET6a90YvQc/EMzTvvsbgroMbnHexxulvGJ9FMD2vnden9OY1d1e1Df6q/WWwA9Vx+4acEJ6HMIaLHSK++c/n58pZ4O/Pa+lXOoE6evD9z1+OXkzYu3BfRwj1Nx22/lHPhJ7avynQ3d/HpAB+55a0C7jz3wu/X/nOQ/c+nV8tKHXl2euuQtUcMBHfh9BPQ5BLRYw5+JtG59/bi5OdSJy62/Dd61+6NuC2h7aJ23LXZ+UnM0I4+Y3nw0oAP3vCGgA0MZ+N36f07rSiHnn54+dPNEp/5Fe33BCehzCGjBVs1XUv3yab7GTq//oU5cXsDfBu+aHkf+8s9Dr/LE4Tv/4X/Wd7rtcnad0bQfsnPzGwLaf88bAjowlIHfbeDntPLY/mq9Itm8xUhA+3+OgD6HgJZs8HPhBy+o3NOJS4e/Dt41eZF/+XN9+WHXTmP6f+cV11svqNwdzZXf6aaA3nRB5esL5srvNjTCxtr75TlqPHS6mtq/Zn3jBZUF9OEEtGznl2fnPSgDH+nR14lkF+fAXS/3uFwf48bzQOsD8AfXP5miO5rR3+m2gN7ykR63LJjR3234FzrXsnHb5kOfEjr4H4YbP9JDQB9OQFnAs1/O1z8XPu7Zvxs5EVAW8OzICCiPIaAs4NmR2Sz485/9u5ETAWUBT45Mcn77/ASUmoCygGdG5nJMu/dif/cTUGoCygKeGZnzGVdLXV1YQKkJKAt4ZmTO55kv9fEWAkpNQFnAMyNzPOtyuR8uoNQEFCBIQAGCBBQgSEABggQUIEhAAYIEFCBIQAGCBBQgSEABggQUIEhAAYIEFCBIQAGCBBQgSEABggQUIEhAAYIEFCBIQAGCBBQgSEABggQUIEhAAYIEFCBIQAGCBBQgSEABggQUIEhAAYIEFCBIQAGCBBQgSEABggQUIEhAAYIEFCBIQAGCBBQgSEABggQUIEhAAYIEFCBIQAGCBBQgSEABggQUIEhAAYIEFCBIQAGCBBQgSEABggQUIEhAAYIEFCAo74BWALOZP1GzP+KMnr20gdcye6PmfsA5LfAfDOBtCShAkIACBAkoQJCAAgQJKECQgAIECShAkIACBAkoQJCAAgQJKECQgAIECShAkIACBAkoQFChAf35fX8p09//nno/AQXmU1BAd9E8F3N1vhr014mPIaDAfIoM6Kq+nv7ElVABBeZTYkA3u3B+O31l4jqogALzKTCguz9/++v0tXX15c8pjyGgwHwKDOjmtP659+uPaaugAgrMp8CANtY619P2ggooMJ8CA7pKA7qpN+dvIaDAfIoMaNJMAQWepsCArq2BAlkoMKCbqvpx+eLKPlDgWQoMaHrkPT0ifwsBBeZTVkCrwyn0l2ruUjptC15AgRmVF9CDQzYP7+j8cfV+KQEF5lNQQLdJQw8BXU/up4ACMyoroEefH+fD8VMvxiSgwIxKDOgdBBSYj4ACBAkoQJCAAgQVHtDPj7ETQaseDxwc8OIEFCDopQPaJaDAfAoP6FQCCsxHQAGCBBQgSEABgsoN6M/v0y4FeiCgwHwEFCBIQAGCCgpoekHlhPNAgScRUICgggK6/ywkAQXyUVJAD+ugl08xtg8UeLKiAnr4HLkvfx7/KqDAkxUW0P3VQ07dFFDgyUoL6OGz4A+b8QIKPFlxAb18mrGAAk9WYEAPm/FfBRR4thIDetiM/+3fBRR4riIDetyMrwQUeKpCA3rYjBdQ4KlKDejhlFABBZ6p3ICGCCgwHwEFCBJQgCABBQgSUIAgAQUIElCAIAEFCBJQgCABBQgSUIAgAQUIElCAIAEFCBJQgCABBQgSUIAgAQUIElCAIAEFCBJQgCABBQgSUIAgAQUIElCAIAEFCBJQgCABBQgSUIAgAQUIElCAIAEFCBJQgCABBQgSUIAgAQUIElCAIAEFCCovoKvq7Ov0OwsoMJ/CArqumqY2VECB+RQV0M+Pqu23vyY9goAC8ykpoL/+aBbz5/fdv3//e8pDCCgwn5ICuunkcp/UH1MeQkCB+ZQU0FV3g323EjppN6iAAvMpKKC71c1vnS+up23DCygwn4ICulvb7G6ub6YdRhJQYD4CChBUUEBtwgN5KSigDiIBeSkpoP2nMXXXSkcIKDCfkgLaeyL9tLciCSgwn5ICeixm05c/Jz2CgALzKSqg6aWYXEwEeLbCArp1OTsgG+UF9C4CCsxHQAGCBBQgSEABggoP6OfH2ImgnZOeKgEF5iOgAEEvHdAuAQXmU3hApxJQYD4CChAkoABBAgoQVG5Af36fdinQAwEF5iOgAEECChBUUEB7LqdcTb0kvYAC8xFQgKCCArr/UDkBBfJRUkAP66CXz+W0DxR4sqICevg8j/PHyAko8GSFBXR/9ZBTNwUUeLLSAnr4cPjDZryAAk9WXEC323VVVT8EFHi6AgN62Iz/KqDAs5UY0MNm/G//LqDAcxUZ0ONmfCWgwFMVGtDDZryAAk9VakAPp4QKKPBM5QY0RECB+QgoQJCAAgQJKECQgAIECShAkIACBAkoQJCAAgQJKECQgAIECShAkIACBAkoQJCAAgQJKECQgAIECShAkIACBAkoQJCAAgQJKECQgAIECShAkIACBAkoQJCAAgQJKECQgAIECShAkIACBAkoQJCAAgQJKECQgAIECShAkIACBAkoQJCAAgQVGtCf36ud3/+eej8BBeZTUEB30TwXc1WdfJ34GAIKzKfIgF76OXklVECB+ZQY0M0unN9OX5m4DiqgwHwKDOjuz9/+On1tXX35c8pjCCgwnwIDujmtf+79+mPaKqiAAvMpMKCNtc71tL2gAgrMp8CArtKAburN+VsIKDCfIgOaNFNAgacpMKBra6BAFgoM6Kaqfly+uLIPFHiWAgOaHnlPj8jfQkCB+ZQV0OpwCv2lmruUTtuCF1BgRuUF9OCQzcM7On9cvV9KQIH5FBTQbdLQQ0DXk/spoMCMygro0efH+XD81IsxCSgwoxIDegcBBeYjoABBAgovxAR/LAGFl3E4wvrsQbyVwgP6+TF2ImjV44GDg0cyyZ9AQOEVXKa3af5ILx3QLjOLl9SopoA+TuEBncrM4gW1VzpN84cRUChbd5vdNH8YAYWi9ezyNM0fRkChYH1HjMzyxyk1oPsr2U28FuieqcVL6T3ibpY/TmEB3ezmy/5CIpv0qkwTmFq8kIETlszyxykqoMfVzurLn58fVaygphavY+iET7P8cYoK6OpUzd//rb6k8qSPRDK1eBmD58ub5A9UUkBPZ82vq+rSzc3ESyqbW7yGkfcbmeQPVFJA16cN9lV1+WDj9APmbmFu8QpG365pkj9QQQHdxfJ41P18Rfq9tY815u2MvtvdHH+kggL68/tpc735ucbeC897uXKxEHP8kUoM6G4bXkB5V/qZk7ICejpxfpVuwgsob+TqtepM8YcqKKC7Lffu/s6Vg0i8Ef3MTEEB3Z+/1D5naTPx7ZymFyW7eqVPlwJ9sJICutuGb65v7r8w7a1IphfluuFS8yb4g5UU0OM74OuV0FXzn7cwvyjWLR/VYYI/WFEB3Rf0fAr99viWpGn9NL8o1i1b5+b3o5UV0N1aZ7LJvp52AGnPBKNMN31SnD2gD1daQO9kglGk2z5p0/R+OAGF7N22aml2P56AQua6Hxo3dLNHjIaUgELe2v2sBq7FZHI/gYBCzvrz2RNRc/sZBBQy1uxk3c1OQG3AP4WAQr4G8nn659ANeRgBhVx1Vz+b3x36Bw8joJCp1vpme/IKaAYEFPLUzqd+ZkhAIUvjq5/NuWwP6LMIKGQoTeb10z7N62cRUMjP9X5uGyuojxgTPQQUslMnc/AT4Jsb+I8YFD0EFDJT3dBPK6B5WDigm/ObzpLrID+TqUb2mv0cvFHfX3m0JQO6rpomffzbMsw1ctfc+zl8qxtuxOKWC+iq6pp8Bfm5mWvkrbX5Pnyz5A6LD4pBSwV001nn/PzYf2XiZxjNzWQjazf2sxHQpcfEiIUCuurfYN88eyXUbCNjw/kcfBeSGf1cywR0Nbim+fnx+99z/8QJTDfyNdDP7rU/bznKxEMsEtDVWCRXz1wHNd3IV18+L8cPhm74sNHRZ4mArsdXMldPPBpvvpGr3tXPSzv7Lx1iPj/bAgH9/IfxjfRf//K8c0JNODJVV7P3PKbeKymbzk+3QECv9vFaYRdkxpGnvlRWvdXc9pWWJ/FWTni6xupn8rfeCy5ZAc2IgMKz9fRz7MBR+y88j4DCk/VsvnfPou900wZ8Dh4R0MN74p96+ueFOUd2+lc/Ozdq/UU/s7BYQH/9cXrj5vEtnDm8EX4roOSn08/O1vvxi51bP2Z4jFoqoKdsfq37mUVBzToy0zmm3v8e+HY3zeQ8LBTQn99P0fzvf1S//XX4+ubpVxLZmnbkpq+f/bdL/zCTc7FQQNenfZ6rcz63+43656+CmnbkpLPXc+gSTO26msiZWCagdSvT921u6pg+i3lHPqo0m1f6WSV/OIKUj2UC+vN/nN6N1Fjr/PlPAgpn7dXPxsGj3rPo9TM7CwX0ksp0DfSJb+E8M/HIRXt1Muln+wJM+pmthddAG9b2gcJR3+pn8q39P9pv3rxymIlnWHofaKK/qo9l6pGF4X5WybcuN2782yTOyMJH4VMzXUm5/rC6wOOZe+SgZ/P98u+hN73rZ46WPg+0zx0H49uflDy1oSYfOejvZ/+eTxvwOVv4nUjzBrTnQSc+lsnH86Xb780/GvOzcSP9zNNyFxNpryzeH9DD2+uTOx9Wc6ddpMTs4+nOnawuaWwdRbrcLvnDBnyeHnE1prlsOrncJ3XS+0NNP54tWZcc7WejnPqZqZICuuquu+5WQiftBjX/eLIbVz+buz5twOeqoIDuVje7n+fZd7h/hPnHc93cz21aTv3MVUEB3a1tdjfXN9P2qJqAPFOy+7P7R/um7f83fTMkoPAoyeH30z+TP1ovnZ6Amr35KSigNuEpW3NP5rGmVRLVdHb29tPszU5BAXUQiaI1S3n4/6pK9oI2CprsAR3b0OfJSgpo/2lM3bXSEeYgT9I8+zP9//otSHUj9bMQJQW090T6aWflm4Q8x0A/z19qHSVKvq2fWSspoH3vsP8y7QpPZiFP0UxkuvrZ2HJv3Wqrn7l7REB/fp+0mT1m1eqni4lQgs7uz4FTQNPD7fpZgsICunU5O8rT389tO5+9AU2/TnbKC+hdTEQer3P6kn6+DAGFZQ31s53PRi9bR5keOmBuJ6CwqEY/L2d/9vUzPW/eCmgZBBSW1D19qX3OZ3rb7SW0W/0sQeEB/fwYOxG0c9KTbSEerN3Pwc33besUJxvwRVg0oJtWvO74MKQBAkrW0gh2z2FqrW1cVjurZAXUnM3aSwe0Z3AmIw803M/zt9sngbZ3gOpn3grfhJ/KbORxqlY/tz39TBqarIBuG7cnXwIKy+j2sz6GdElnHdDmBvzlvk8bPrcQUFhCks9OOut+bpNj7adsOoBUEgGFBTT62fq/Zhdbq6n6WZRSA3q4tN20a4HumZA8RNVar9TPF1VYQPfH9fcXVT4f3596XN+M5BHa/Wzls2rc9PL/+lmeogJ6XO2svvz5+RE8M8qU5AEm9LN13lJyApPJWoJHBHQ25yvZ/f5vp3KuOh/ycYU5yfL6+jn4DqTGwXf9LE1JAT2dNb+uqks3d5vy3Y86HmFSsrh7+mkDvjAlBXR92mBf1Z/ksduo96mcZKV9+lJ7G75960Y79bMwBQX08rnwuzXRy4a7z4UnLzf0MwlpY+enDfjyFBTQn99Pm+vpaufGe+HJSboCWSX9bJS1LmjazstK6NZELUaJAd1twwsoWbrWz3M8k04OVPZ5vwMTPCygm6mfQNyxC+jpdKhVugkvoGSj1c/WNnyy8d64XWslVD8L8rg10MsuzKjdA3T3d64cRCIbV/rZ3ve5bfdzq5+lWTagjVPoPz+mnbPZse6es7SZ+HZOM5PltPvZ2Ybv6ee2eQQ+eRhKsHRAq/rj2zeRD3JP7R/ta/sL096KZGqymKSfVeP/uqeAnrfn2/2stvpZlgcE9NjQ3Qb43RekP7wDvl4JXTX/edPgzE2Wke7lvBxpb/ylceNtegSpXlfdmqNlWXwf6OVjPe5c/Tw/WHIoaj25nyYnC2n1c2z1Uz9fyPIHkU5XALn7IPzRKlmNXU+PstnJInp2f3YOwTdvnH7TAfhiLR7Q1WEl8VDRDC6rbHayiJ7zOi/rn+1+ds7+1M9yLRzQX39cVhLXM62D3sX0ZAE92++N3Z/tW28vB92T2p4e6PGj5w4LB3SdnLn08/scu0HvY34yv5F+9jUxOWlJP0u3bEB//Uu60rmZ/3PhpzJBmV3f/s/GftD2zbdJYtNb6Wd5Fj6N6Z/+GvzXU5ihzK2x97LVz6r+5mXqNQ8e6WfZlj4PND3NyBoor2ds/bM+h6kOaGMDPj2B3uQs0cL7QNOzjuwD5fW0+tneD7q9rH1ejtOfz/y89HOrn+VaOKCb+kOLet7J/ngmKbMaWP+sGv083fJ8w+rCAaTiLX0e6LqeLbO8F+lOJilzur2f28u/GuugdoAWbumAJgXNoJ8CypyG+9np4uUYU3Pn59YGfNkWD+g5oTnk0zRlTsPHj5Jt9fSmyVEj/XwNDwhoTsxT5lKN9LMa6GfnDKb6OP0TfxPiBBQi0n5WPRp7NS+rmUlY9fMVLBDQ/3PtbM/Pf7jvyvR3MFGZR53P3n5ub+1n/W1KtEBAP//r+A2a7+98LFOVWbT62flfq5+X80Hb2+/Hbz/nd2AGS2zCr0cPGP3644mXtTNXmUN79+e229AqvfV2tJ8mZbkW2Qe6Ginoc9+PZK4yg0b6Wqd+Dvezruwlulv9LNwiAf31x+ClP+/+ZLn7mKzcr73+2dPP5s1738Gpn69goaPwq/73ba6ffT6o2crdWv3s3Q/auHma2aSh3oD0ApY6jen4WXJpRNedrzyB6cq9etY/x/uZfsJH61b6WbrlzgNdVV1P/1Qk85U73XD8qHX79js49fOFLBfQ5oVEssingHKveD/bt96aji9gyYBuk0+Fz+AD5fbMWO7S08+x40eN4/L1H1v9fBULBzQ3piz3GOlndVs/HUB6LQIKNzvNn1v72doBeu6nFdDXIaBwo3T9c9vpZ88qZV8/bcC/lCUD+vN75zD870+7jMiRSUtYddnyvhwNap0d3+ln60Ijl69cHozCPTigTqSnVK39n33at9fPl/fwgHorJ0Xq6We7o+3btw++n//n+NHrWHYf6OfH+fylfUy/pV94DvOWmFY/W5vn/Zvv+vn6Fg3oLpf1yfObQzp3IXU1Jooz3M/0uFDr9vr5+hYN6KoRy+O/1k89kGTmEtI9fyk5djR4/H3wCnYPHz8LWXgfaHrtkE3121/n/38WU5eA9vpnt4vV+Yb1n/r5DgQUrqguW97phZX6zp+/rKgOvIHTBvyrWTKgv/5obcLvN94FlML0rH/2dLF1B/18DwvvA20cRDrkdGUfKEWpLquV275t88ED8P2308/XsvRR+PP65v40pv1R+PVzr2pn9jKRfjJi0YC2rgj641BU54FSkLqfl/du9pyY1LpDY9o7gemVLRvQQzFP9uHcXx70qZdVNn+ZRj8Zs3BAL+/nPG7Jb+Za/zw+6vS9qSYwU7TWP9M3wY/2s/84vX6+nsUDOp9dNM/FvHze0tR3NZnBTFBV9QF4/aRHkQFNPq9u4kqoKcztLsXrnv/Z389tXz+T86AePH6W99hN+LtcAnrZk7p/7GnroOYwN0u23+sD6dXlzZu9b4BPAts+Tm/uvaKFA5pc0e7uhJ4Duvvz8ljriTtVTWJuNXs/zb0XtGxAG1cEvff40Tmgm+RIfuvNTtcHZxJzm6SfjX2bgxvwzf2f7f2k+vmaFg3oLm/V6e3wm+n7K9vOAW2sdU68uJNZzI3Sfm772tnTz61+vptFA7pJormP6Y/eO9zqHNBVGtCJb603jblNcvzossFetf5s3j496N7OrH6+qkUDukrrdvellOuAJo8qoCyh3oDfNt68efmzNZX0800tGdDdSmf6tqN7L6XcuwkvoCxgYAfo5USmgX62zmHyBvjXt2RAe68HGpccRKofduLFncxkbtDpZ3Mn6LbVxDSY+vleCgxoeuR9M/G99aYyN+jrZ3pmUnMiVa3jR8l5Tvr56srahN/7Vldzf2BqWpTNZa7r6WfrYzla/dyO9NOce2llHUS6ODzu4R2d047sm8xclZ55lO4ETftZNW/dOnGp3og35V5cQacxbZOGHgK6ntxPs5mrGmdu9hxE2qbTqEr7maq33025V7ZoQOc9kf7i8+N8OH7yKq3ZzBVD6599/byksnMNUP18E4sGtPlWzmd+mNyZ6cy4Vj973715rmLVuFXjRpd+Pu834RGWDeisFxOZgwnNqLqNPScxJUeXmgeJkvVO/XwvCwd0zsvZzcGMZkyybpkcb6834JPbVc1+tjqqn29i8YDmxZRmxLV+No4uXf5Itt3bq6a8usID+vkxtm5b9Xjg4ChMq5+NA0hV87v1PZJdoI3td/18CwIKR81Cpv1sbcA379E8dtRaUeXFLRPQxtH32vw7QscD2jM4k5oh58lRn6rUaGd37rSOG9VH7bf6+S4KD+jkwZnVDGj1s0r72RfQzra7fr4hAYW98R2g1/tZVWlrTbQ3Ufg+0KnMa/r19zPZ+dmcOlUnsUlm9fN9CChsr+4AvdrPdD+pWfY+BBSG+9kf0MuGemf9s/9oEy+rsIB+flSNi5L8+sNReO43vAO0p59Vbz/THaBP+A14jrICujrtrCfetiwAABUhSURBVL9chUlAmcHIDtB2QJOjRY3j742u8jaKCui5n/VKqIByv+v9rP9o5rNuqH6+p5ICut9+319ddF0XVEC522A/q8b36kjWZ3w2+pk+Fm+ipICuzp9nvL9Q87GgAsq9Gv1sHUBqb7q3StsJrX6+m4ICmn4a56q6fEKngHKXRj/rE5c6B4/0k66CAtr4lORTQQWUOzVOYGqeAdo7Xyr9pFZqQPcF/Sqg3Kterbz8a/SMJP0kVWxA9/tBvwko92nvAB05e/50s/OxJP1kW1RA032g29PnJAsodxnYgB8IqH7SUlBA96cvpR8D//lRfflXAeUO4/1sT5fuaqp+vruSAro/D/Rb8u/N4cQSASVqeAO+ZwW0at2q0k+KCujhDPp0M34joNyjewZTYwW0MV2am+/6yUFRAT0UNF0H3a+TCihBQxvwPQGtVz/rdG7bx/B5P2UFdH/k6FvjC2sBJajnDKaBgFbpOzkb71jSzzdXWEDvZaZz1twB2nvwvaptG/1M1kSTR+L9CCjvqWquZvatgNYF3Tb2gTb7WennGxNQ3tJIP3tnSaecST5NqvcloLyjpJ9V6/+H+nn+/04/HzRkciSgvKNmP5ub7j2TpH2iqNOXOBJQ3lBymKj9/91J0nsM3uF39gSUN9Rq5VhAK/1kmIDyfsY24Fub5VW6sV61+2k6vTsB5e1UoyugjS42WqmftAkob6d3D2jz7M/zn61+tr77oPGSLwHl3XT62Tl5qfkOpM6JS9v0T96agPJmWqeA9p68lNQzOQif3ls/2RNQ3kvVWgEde/vR6faNU+31k4SA8l4G+jkwNRoH4fWTNgHlraSHihpf6J0anX5evrzoICmGgPJOhjbge2dG63pL6U7RpcdJIQSUdzJhBbR7EF4/aRNQ3kinn4MBrbqrn3Z/0iGgvI90A7517L05M6r2+qbdn/QSUN7H8Apo641InV7afKeXgPI2emrZzmb6BqTGdnvz33AkoLyN0YBu2/W8bMenu0MfNVQKIaC8i/F+9ty8Poqkn/QTUN5ENS2gnaPu+kmXgPImGlvr3a91bt0+a8ncoUtAeQ99/RyaD42zmMZvynsTUN5CYwP+ShR7+un4O70ElLfQuwI6+g74/r9BSkB5CzcHdKCfiw6OYgko7yB94kcC2joNtPM3aBJQ3kA1EM1mGnvfhKSfjBBQ3sDACmi7k31/t/uTEQLK62s1s/mtzjvgO1l9xBApk4Dy8qrBFdDTd5v57D/lCXoIKC9vZAW099b6ya0ElJc3KaA235lAQHl5EwI6sCcU+gkor+72fraPJC03Jl5EeQFdXXb6f51+Z6+JN9Q+7D5yw/4jSTCksICuq6apDfWieD+t53xwCjS32PWTWxQV0M+Pqu23vyY9glfF+7ktoJV+ElBSQH/90Szmz++7f//+95SH8LJ4O923u/fdpnXASD+5TUkB3XRyuU/qjykP4XXxdnpOnO98oZtP84SblBTQVXeDfbcSOmk3qBfG27kW0HY99ZMJCgrobnXzW+eL62nb8F4Z76b3ip+Nf8gncQUFdLe22d1c30w7jOS18W4GLpnccwWR+psPGhovQEB5acPHjPr6KZ9MU1BAbcIz3aRnXD+ZqKCAOojEZFOecPlkspIC2n8aU3etdIRXyJuZ8ITrJ9OVFNDeE+mnvRXJS+TN3PyEyycRJQX0WMymL39OegQvkjdz6xOun4QUFdD0UkwuJsJ1E/q57EB4UYUFdOtydkxw2/Nt9ZOo8gJ6Fy+U93LT862fhAkoL+yG51s+uYOA8sKuP9/6yT0ElFd25QmXT+5TeEA/P8ZOBO2c9OTl8m5u/wxOCBBQXtnYE246cLeXDmiXV8ybGf0IObOBexUe0Km8ZN5N/zMun8xDQHlp3U7al8N8BJSX1o6lfDInAeXFNYIpnsxKQHl5TsNgKYUF9POjalxV+dcfjsJznX6yjLICer4S0+U6TAIKPE9RAa2vZHdeCRVQ4HlKCuh++33/wcbruqACCjxPSQFdnT/AY//hSMeCCijwPAUFdBfLy77P1amgAgo8T0EB/fn9sAF/dCqogALPU2pA9wX9KqDAMxUb0P1+0G8CCjxRQQFN94Ee/1n9EFDgeQoK6P70pWQVdH9W05d/FVDgaUoK6P480G/JvzeHc+oFFHiSkgJ6OIM+3YzfCCjwREUF9FDQdB10v04qoMCTlBXQ/ZGjb40vrAUUeJbCAnovAQXmI6AAQQIKECSgAEECChAkoABBAgoQJKAAQQIKECSgAEECChAkoABBAgoQJKAAQQIKECSgAEECChAkoABBAgoQJKAAQQIKECSgAEECChAkoABBAgoQJKAAQQIKECSgAEECChAkoABBAgoQJKAAQQIKECSgAEECChAkoABBAgoQJKAAQQIKEFRoQH9+r3Z+/3vq/QQUmE9BAd1F81zMVXXydeJjCCgwnyIDeunn5JVQAQXmU2JAN7twfjt9ZeI6qIAC8ykwoLs/f/vr9LV19eXPKY8hoMB8Cgzo5rT+uffrj2mroAIKzKfAgDbWOtfT9oIKKDCfAgO6SgO6qTfnbyGgwHyKDGjSTAEFnqbAgK6tgQJZKDCgm6r6cfniyj5Q4FkKDGh65D09In8LAQXmU1ZAq8Mp9Jdq7lI6bQteQIEZlRfQg0M2D+/o/HH1fikBBeZTUEC3SUMPAV1P7qeAAjMqK6BHnx/nw/FTL8YkoMCMSgzoHQQUmI+AAgQJKECQgAIEFR7Qz4+xE0GrHg8cHPDiBBQg6KUD2iWgwHwKD+hUAgrMR0ABggQUIEhAAYIEFCBIQAGCBBQgSEABggQUIKiggKYf6ZHwTiTgSQQUIKiggO7f+C6gQD5KCuhhHXTSx8B3CCgwn6ICui/olz/veQABBeZTVkAvH8gZJaDAfAoL6P6z4Cd+FHyDgALzKS2gu434e1ZBBRSYT2kBvXMVVECB+RQX0PsIKDAfAQUIElCAIAEFCBJQgCABBQgSUIAgAQUIElCAIAEFCBJQgCABBQgSUIAgAQUIElCAIAEFCBJQgCABBQgSUIAgAQUIElCAIAEFCBJQgCABBQgSUIAgAQUIElCAIAEFCBJQgCABBQgSUIAgAQUIElCAIAEFCBJQgCABBQgSUIAgAQUIElCAIAEFCBJQgCABBQgSUIAgAQUIElCAIAEFCBJQgCABBQgSUIAgAQUIElCAIAEFCBJQgCABBQgSUIAgAQUIElCAIAEFCBJQgKC3CyjAfGZv1NwPOKdnL2zgtczeqLkfsDgF7ycod+jljrzgoRv5AvId2aNk/ORcU+7Qyx15wUM38gXkO7JHyfjJuabcoZc78oKHbuQLyHdkj5Lxk3NNuUMvd+QFD93IF5DvyB4l4yfnmnKHXu7ICx66kS8g35E9SsZPzjXlDr3ckRc8dCNfQL4je5SMn5xryh16uSMveOhGvoB8R/YoGT8515Q79HJHXvDQjXwB+Y7sUTJ+cq4pd+jljrzgoRv5AvId2aNk/ORcU+7Qyx15wUM38gXkO7JHyfjJuabcoZc78oKHbuQLyHdkj5Lxk3NNuUMvd+QFD93IF5DvyB4l4yfnmnKHXu7ICx66kS8g35E9SsZPzjXlDr3ckRc8dCNfQL4je5SMn5xryh16uSMveOhGvoB8R/YoGT8515Q79HJHXvDQjXwB+Y7sUTJ+cq4pd+jljrzgoRv5AvId2aNk/ORcU+7Qyx15wUM38gXkO7JHyfjJuabcoZc78oKHbuQLyHdkAJkTUIAgAQUIElCAIAEFCBJQgCABBQgSUIAgAQUIElCAIAEFCBJQgCABBQgSUIAgAQUIElCAIAEFCBJQgCABBQgSUIAgAQUIElCAIAEFCBJQgCABBQgSUIAgAQUIetOAfn5UO9+63/j1R3Xx4/HjusHg0Lfbn98Hv5WD48i//Nn5RikLvWfo2S/0vZ/ff/ur88X8F/p2YORZLfO3DGg9dzoz5/jU5DutRoa+XZ2+0/s6f7p6yXZeE7kv9JGhZ77QD3ZzpidDuS/0vf6RZ7XM3zGgY//t3VRZT6uxoa8v3+n9r/aTpa/X9vgyX+hjQ897oR+tegeX+UI/6B95Vsv8HQO6fwL2q//7F8bvf3e+l+ts2hsZ+n4rc/+l/Qvj63NGN+Y88sPqw9fO90pY6D1Dz3yh7x3+m9ufoZwX+nZw5Hkt8zcM6O55Oa377zLU3gpY5fBftUFjQ1+dp9NuguWwbdO0L/7p9bruvCryXuhjQ897oe8d9972LN+8F/p2eOR5LfM3DOhuuZ//w9X5r/CuUO110pyMDH33Mj/PtXUm+9dTm3ptYb9i0Rh65gt9ZOiZL/TT3of/2LcnMfOFPjzyzJb5GwY0sWoHdPfsPH+r4CbtoSdt3f01u9dGOtfbQ898oY8MPfOFftz78KP3UEzmC3145Jkt87cOaPIfs5Pd2saPw3/7nr9tMK4z9ORlPnDsMhur1tItZqF3hp79Ql/vY9M7tNwX+uDIM1vm7xzQdff447r68p9PR/ie/t+2Md2hJ5v09Z7SLO1ets1lW8pC7w69jIXe25kiFvpAQHNa5m8b0FXv+RvnM8yynle9Q083LtureHnp7LkqYqEftIdexkLvDWgRC71v5JktcwFN7Q8SHJ+STZXBDuoBAwGt51IG82pYZ8dVGQt9rzP0MhZ6X4bKWOj9Ac1qmb9rQM9npDdfEMnJQbsXy9P3r/TrH3pzXuV7il93uRax0Pe6oytjofdlqIyFfj2gT1/m7xrQg/1O9MFDkRk8OSM6Q8/sP8xDNuNvH8l5ofcMvYyFfu1YS74L3RpoLi7vxmsu8J4z6S9yOMls78ahZzav9npGfqWfOS/0vqGXsdCvBTSThX7jyDNb5u8d0LG5s8ljWt069MwOTu51R766dsAi34XeO/QiFvrVgGay0G8ceWbL/M0DOjJ3MplWtw59k9fpcXvtke933l45eTvXhT4w9AIW+vbVAprZMn+TgA4ZmTu5X2yhNfTM3qDRY//e5msv1EwX+tDQ81/oezdswue40Lf9I89smb9hQEfemtd8l8PTNw86Roae2VuEuwYv/ZD7Qh8ZevYL/eD6+3lyXOh7A+cP5LTM3zCgyWkb7TM4kn9vcrhWVtvI0DO7SE3H8PG63Bf62KHGzBf60cB6XN4L/WDoLQAZLfM3DOh+f9bxablc6LH3W89/cjpGhp7ZZRLbOpdgan4r94U+tImb90I/GTqRPueFftQb0LyW+RsG9HShwaPjM3BZx0i/9fStgx4jQ8/rQt1t6fXPq2OQSlnoY0PPe6GfpBkqZaEf9Y48r2X+jgFNPqPh6+ULpyennld57lcfGXpWHxXTkn4USbdCWS/08aHnvNDP+jOU9UI/6R95Vsv8LQN6nj2XQ3jpXq5NmqcMjQw9ow8rbEk/VqinQjkv9GtDz3ehnw1kKOeFfjI08oyW+ZsGFOB+AgoQJKAAQQIKECSgAEECChAkoABBAgoQJKAAQQIKECSgAEECChAkoABBAgoQJKAAQQIKECSgAEECChAkoABBAgoQJKAAQQIKECSgAEECChAkoABBAgoQJKAAQQIKECSgAEECChAkoABBAgoQJKAAQQIKECSgAEECChAkoABBAgoQJKAAQQLKC6vMbxZlgvHCBJRlmWC8MAFlWSYY5Vr9uHKDoYBuvs4+Ft6SgFKqTRXt5+6+X/6ceTS8JQGlUKvf/rp2k5Et+M+Pb7OOhvckoJTphn6O7gL9/LAZz90ElEz8+qO6oYlnq6vb79tmQH9+r3aS1c5NpaDcS0DJxKSArm+pX9rP9eHBN1W973P382zFcycBJRNTAvr5cctBoCSgm9Njb5KfkdYUQgSUTEwI6O6mv/99/WZ1QC9rm7u/fE2+eMujwDABJRMTArqpbtr6rgP6+XHeZbpKormubtmRCsMElEzcHtDdLSduwdeb/KvGNrxVUO4joGQiCehmf8A8WTs8HEH/7a/dH4fg7dYnb0ltYxdoHdC6mbvHsxeUuwgombgE9HjC0SGZx++sT//+b6eArm9bc+wLaLoPdP8PB+K5i4CSiXNAL/2sLkfOa/tw7rv3tXnH6lzWdM20L6A/v6frnCvb8NxHQMnEOaCr0/nu+/XOfSf3QT2ew3nq5P4LjRPi9xv7610YG6uXjbNALwFdN1Y519WUc/ehQ0DJxCmgnx/n2J3+dtlg3/378Lf9n3UGzwfYN7/9tftrksdOQNettyIdHtpOUO4hoGTiFNB1vX2+PvRudTmcdErpJu1gfTLn+tu6kcPeNdDPj3SVc105kYm7CCiZOAW07uV+5fLrfoP93Lzdv88BvWSvPiX05z/9r3SPZuNCIvVR+EZkNwLKfQSUTBwDmp7jeQjm+dyl7WHnZyegycnwq2poCz4JaPJwAsrdBJRMXAJ62cg+xO602nn5dyt7yQrrplHDgYDu7lCvggoodxJQMjFpDfRbfafLzQdPYmoEdN3c/hdQ7iGgZKK7D3RT9e4DbRyFr1coh09iagf0cmdH4bmTgJKJ7lH4w07N/WnyzaPw+/NAL6msezt8EtPgGqjzQLmTgJKJq+eB7sPZeSdSfRR+Vd20BpruA/VOJO4koGSi751I5xXOU1mr7nvhLxvuu5v943/6a7s5rV4OBbR1QVDvhecuAkombn4vfPNqTOc2rqrf/+/3H7/+5RjK1sfJ1ReuS88DdTUm7iWgZOL2qzGlB5rOSTxc57PeJO8E9Ms/H9Y8G+fRJ2dIQYiAkonr1wM9vDPp9P2vjTuebl1fa6kb0D8P+wYaZy25Ij33ElCKcQlo47ryvfoC2uYzkbibgJK5enu9fq9m/RlH/Vr97A/obR/tCSMElMytqsthojqDm/GVx5sCunIInnsJKJk7nL50UhdvPVq/WwK6aVzWHiIElNxtevq5W38c2f5u97P1NvmDn9/tAOVuAkr+DsfP2yuM6wl7MLsB/fnd+if3E1BK9flx80lIq/Yu0wn3hWECSrlW0QpubL4zCwEFCBJQgCABBQgSUIAgAQUIElCAIAEFCBJQgCABBQgSUIAgAQUIElCAIAEFCBJQgCABBQgSUIAgAQUIElCAIAEFCBJQgCABBQgSUIAgAQUIElCAIAEFCBJQgCABBQgSUIAgAQUIElCAIAEFCBJQgCABBQgSUIAgAQUIElCAIAEFCBJQgCABBQgSUIAgAQUIElCAIAEFCBJQgCABBQgSUIAgAQUIElCAIAEFCPr/BTkNeYdWSwcAAAAASUVORK5CYII=" title alt width="672" /></td>
</tr>
<tr class="odd">
<td align="left">4.3. Recalculate the range of the grid such that includes all the density</td>
</tr>
<tr class="even">
<td align="left">```r v1 = seq(-2.3,-1.3,length.out =151) # The booksets the range of “v2” up to 5, but my gamma function calculator gives me trouble after 4.8 v2 = seq(1 , 4.5,length.out =151) beta = exp(v2)/(exp(v1)+1) alpha = exp(v2+v1)/(exp(v1)+1)</td>
</tr>
<tr class="odd">
<td align="left">post.dens = outer(alpha,beta,function(x1,x2) log(rat.marg.post.phi(x1, x2)) ) post.dens = exp(post.dens - max(post.dens)) post.dens = post.dens/sum(post.dens)</td>
</tr>
<tr class="even">
<td align="left">contours <- seq(min(post.dens), max(post.dens) , length=10) contour(v1, v2, post.dens,levels=contours, xlab=expression(log(alpha/beta)), ylab=expression(log(alpha+beta)), xlim=c(min(v1),max(v1)) , ylim=c(min(v2),max(v2)), drawlabels=FALSE, main=“Contour plot of joint posterior”) ```</td>
</tr>
<tr class="odd">
<td align="left"><img 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CSgAIkEFCBRpgH99b04+fOfscsJKDCdjAJ6iua9mLvi5uvI2xBQYDpZBrTs5+hBqIAC08kxoIdTOL/dLhk5BhVQYDoZBvT09Y+/b5ftiy9/jbkNAQWmk2FAD7fx59nvn+OGoAIKTCfDgNZGnftxe0EFFJhOhgHdhQE9VNP5IQQUmE6WAQ2aKaDAYjIM6N4IFFiFDAN6KIof5YU7+0CBpWQY0PDIe3hEfggBBaaTV0CLyyn0ZTVPKR03gxdQYEL5BfTiks3LKzp/PFwuJKBsVGHbXkJGAT0GDb0EdD+6nwLK9lTjiqXvyRvKK6BXnx/3w/Fj34xJQNmWIqingi4gx4A+wSbGdjQHngahryegkKf2rF1BX05AIUMd+zxt4C8moJCb7mNGNvAXyzygnx99J4IWES+8czC9/g3ZBv5iAgr5eLAV275fbdMBbbOBkbMHQwADhJfLPKBj2cDI1uMZlM375QQUcjBgD5St+/UEFNZvyP57E/gFCCis3bDDnzbuBeQa0PM72Y18L9Az2xjZGXj2iG17CZkF9HDalM5vJHII35VpBBsZeRl88p0J/CKyCuh12Fl8+evzo0grqI2MnAw/d1k/l5FVQHe3av7579VbKo/6SCQBJSNjXvlhy15GTgG9nTW/L4qym4eRb6lsMyMXo144Z8NeSE4B3d8m7Lui/GDj8APmhrCdkYlxrzu2YS8ko4CeYnk96n5/R/qzvY81ZoNGvm2D7XopGQX01/fbdL3+ucZeC8/WjH3bG0eQFpNjQE9zeAFloxLeNUw/l5NXQG8nzu/CKbyAsh0pb7qonwvKKKCnmXt7f+fOQSS2I+kda23UC8oooOfzl5rnLB1GvpzTtsZ69eSze7s1/lxUTgE9zeHr483zBeNeimRjY62ic/eHH6fgUxaWlVNAr6+Arwahu/q3Q9jYWKdYIJsfRxP9FE5b9KKyCui5oPdT6I/XlySN66eAsk6d+axdEFts1rvFI3kF9DTqDKbs+3EHkM5sb6xQO5+xEWc0oDPeKwbILaBPssGxOu1WxifsQy7hxQQUFhRpZffxovays90vhhFQWExkP2f3ifSRaf5894xhBBSWEq9nxzaqn2skoLCQRgIfvIizPdGf5U4xioDCElq5fFBE/VwlAYXXa87VH7+HSGuyP9M9YxQBhVer17J/12d5pcbyM901xhFQeLFYPh8v0vENixJQeKn23H3QMrXvJr9TJBJQeKXW8HPYQvVbmPpOkUpA4WUiOz8jV4ks9uAKLEVA4UVqezu7XsP5qKn6uSoCCi9Ra2PXazjPF/a95Mjx95URUHiBdj6bPywv6nkbO/1cGwGF+fUcOmrP25uvUAqvOts9JImAwtw68xnf69l5mpPNd3UEFObVPvQe/qD/oHtz0dnuJGkEFObUmc/OHZr1AWjtlma4fzxFQGFGHSd+9r1+s2POrp9rJKAwm44zl7rm7rcfhovHbon1EFCYScd58z3xvP44WD68qXnuJE8RUJhFK5/Vv/q2wtpC7QtZFwGFGSTmUz8zI6AwvfjR9lY9e172rp9ZEFCY2uN8FqXmktUVju1/sjYCCtPqmb2Hl8YSqp+5EVCY1LB8BteuLdq81OH3dRNQmFB09t6Zz2P8dUf6mQ0BhekUkfYFyYzs9oy87qjW4PnuKxMQUJhKbKDZn8/YefP6mREBhWnETvds5jOyULB47Wv9n6yTgMIkYql8lM/IcXf7P7Myc0AP91M1vvw19e9JYotkHvXZe+Oy6Nz99pPGQvqZlzkDuq+f7lZ8m/pXjWeTZBaRftan8R0bXvO4USTDrNl8Ad0VbV+n/mVj2SiZQXumHt0LGluwXKz2VT9zMVdAD60x5+fH+ZIfU/+6cWyVTK598Khod7RryehX0/dszBTQXXzCfphgEFqNbBNuymbJtIpGPptfa2lt5LTRzfo49mVrwDPmCeiuc6T5+fHnP0/ceHO36tiG2i6ZUiSf9/qFtaxts+HC4dfa1V+1AjxploDu+iK5Sx+DXvcC1Pzx97g7Z8tkOkEPY/kMfhQ5Nb7dz8YPyMAcAd33DzJ3qUfjf/+sF/PX99P34wa0Nk0mE8nn7R+twWe4UONf+pm1GQL6+Z/6m/b73xLPCT20cnlO6qjDUrZNptI//Lx/29ydGSxzXzT4ctTPzMwQ0Id9fFTYLrv2hP00CB21R8DGyTQ68lm08tlarlyo/eWon7nJ6KWcp+Fme/K/HzeHt3UyicYcPbgoshO0vlz4tdnP+EKsV0YBPY0229P1w7jDSDZPJvAwn50l1M+NEVAYp3GIKLioaGQ0smj4NdLPOe83M3hFQC8nbz51+ueFKTxrMCifXf28D0CD7/QzZ7MF9HLO0XnEWJ68OcFrkBxEYmFjdn62NrbaBF4/t2CugN6y+TU8+f3ZgsZPYxp1VqltlKfEh5/HaD5bA1H93J6ZAno5x/3sv/68DxsPT7+TSPRE+nEvRbKRki5MYnA4vZq91ybxd+Hy5ZKtnaX6maeZAnrfNRnOun//fHYIWma5MvKNmm2lJGuMLquvHfk8hoE89vazNVglE/MEtGpl+LrNw8gXrkc032TUm4nwImHj6vP1zkn89arBQkFxy0uat01W5gnor/92GxjWRp2//uXpgB69nR2LqI8+7+PN4hj8t7qwtly4fGc/X7ciTGqmgJapDEegqS/hnJAtlST1fBb1L0X9wvpy1WIOH23QzCPQmv3in+ghoCRpTrZrX+Jz9/v1g+Ub/7X7cwPm3gcaiFf1tWyrjNeM3eB8BgPQYzDyjNwkmZr5KHzoiXdSnoyNlbGKeD/DXaAd+QwGoMfYKDT8B3ma+zzQmOcPxpc+P/puLfbLJ/vVvIVn8lmbwDcGr8fqJ2RspoDGPn1DQMlOtcm0+hk5G769cPWlY//n7GvArOYKaPvz3xYIaOTO2WAZbnw+i/rS5ZdykaN+bsp8AV0lWyzDNftZtPtZzmoic5zufpY3+tr1YXoCClEDhp+RfFZbWL2fR/3cJAGFiKLZz7CiReuicsMK/lHmMtbPQj83QUChrW/42ZPPWkCP+rl9uQb08tZ2494L9MxWyxC1fDZm7PXZe7OE1YLH/n6+bF2YU2YBPRTXN1U+3PY3jT2gb7vlsSLoXPOkz/58HmsDzNp/9HOTsgroddhZfPmrOst0ZEFtuDxU6+cxHH7GZu/NZcsFG71t3y4bkFVA7+9k9+e/38q5G/thdTZc+hXNzLXyGQ5Lm5tT88ylyKBVPjclp4DezpoPP+Rz7OeE2HTp1dPPIJ/Rd647to+8G35uXk4B3d8m7LvqkzxOk3qfyslUgrgV0cFkczTZWvzY6mdwOOl2pResCK/yioD++j76aHlM+bnwp5FoOXH3ufBMpspidPj5IJ8Pxp/hddiMjAL66/ttuh4OOw9eC8806vmsn7XU7GfH8scB/bQFbkqOAT3N4QWUidV2UrbPXWrns3X8vd3PIrjweDT+3KC8Anq7nV04hRdQntcze2/uCO04FlTvZxHpp+HnBmUU0NPMPfI29w4i8byiMUhs7fKs57O6KLiFY6Sf1S3q5zZlFNDz+UvNc5YOI1/OaRMmokpbq59FvZ+367R2hram7sfaSaG138GG5BTQ8+eEfG1eMO6lSDZiWmLT91ZE6/ksl6xuIt7PQj+3bdaA3l+xfvfsW9Ffbq8ahO7q3w66c7ZiGpr9bO79bE/ng0XLBZv9bAxS9XOjsgro+Qa/VJ+NvB/dTwGlITb8rEWz8X1rv+cxuuuzNmjVz+3KaQp/tgsivB93AOnMdkzNo+l7e1BaW/i+ZKOfzevr52blFtAn2ZAJxIefZQNv/QzTWl+4XLI29KwWaP4WNkdAeVdFs59VLxv5LGpX7l6kfgypfdCJzRFQ3tSDfAZnMbV2fh5r5zu1/3Os9/PFK8YLCSjvqQpbsMeyqBLYGIMWsaVrC7b+Vf8tbJKA8o5iw8/mEfiuY0fHZj8b1zb8fCMCyhuK9rM5Eu3MZ6yfRb2fjd/CVr0ioCtig6b33KXGftBB/WzO3E3f34iA8m46p++NHZ/HjgbqJyUB5b0EY8qyhK0j6Y1DQc0bOMZOnA9Hs0f9fBMCylvpHH5Gh5L6ST8B5Z3Uhp+t6fvx2Lyw4wbC1IYHjgr9fDMCyhvpPnrUHErGh5/1w02d/exYmO15WUAP4fsoLcZ2/c6a0/fY0fdH0/ewn0W7n43fw9a9bgRafirxkmzYb6xoBK5xuGjQ8DOc6vf082XrxMLmDWjtFPrPj1Ef4T4Lm/b7igw/W+l8PH2PTd31833NHdCi+hSOw/i375ycbftd1abv5Zci1HvyUnO+3xVd0/f38oKAXht6msE//Yb0z7Nxv6eic/pe363Z38+is5/l7evnm5l9H2j5sR7LDz+PAvqe6vm8h7N9MKiMaPwmDD9pmf8g0mnoebGGg/AC+o5qs/ekvZ+P+9n4RbyL2QO6u3zu26Wiyx+EF9A31J3Pxhi0O4Ct+brhJ1czB/T3z3Lmvl/DGNQm/namHn7qJ4GZA7oPzlz69X353aC28TdTm75XX9pJbJx+FPy7ukr5n2DiHkzfX7RKrMm8Af39b+Gg87D8YXhb+Xvp72f0NM771Wu3EKZTP6nMfBrTv/zd+d0ibOZvpQg7WH6JDCn7p++X7aZ/p6kN603NHNDvP4LvjEB5qf7DR43BZffJ8+WVO3ea2v/5tmbeB7oLmmkfKK9UdPbzGOln101Ejzc1Jv36+b5mDuihKO6HkfZF8SN2/Zeyob+N5vAwHDSGc/gHJ8/XJvxheY+N2+ctzRzQczZLyw9ABfRddA8/Wx+5+bCfsTm8fnIxd0CDgq6gnwL6Jmr9rL7Up+TlhT23UJu616fvDr/zgoDeE7qGfArom6iqFu1nbR/mkOl7kE79JPSCgK6Jzf0dNPvZnK9X33YVsDZUbU3fw3zaoN6bgLIx8d2fRT2HrRM5m7cQe++QorGQfjJDQP+/R2d7fv6nxd6Z3ga/dUUtb0V0+FnU0hq/hY6Gyic1MwT08//qv0L99Z2vZZPfuPjw81j7T+tAeuQWIulsNFc/Oc4zhd/3HjD6/XPBt7WzzW9bFbUiOHrUjOgxPLLUuoHoeNXwk6hZ9oHuegq67OuRbPWbNqyfPePP2PCz8a/gejBLQH//7Hzrz4U/Wc5mv2Wd/TwO62fRuGpk+t78Rby5mY7C7+Kv29xPdT7o9dPqxn9Msg1/w5r9LLr6Wb9ysHjX2U71fhp+UprrNKbrZ8mFEd23LhnpFM17MXf3WdXYHNvyNyvIWqufrZ2g7X4WRbBUbdJ+1E86zRXQIHKBpw4fVQENbnrkINSmv1VV1mpT9I5+tjaEZj7Do/VFY0nbEKX5Alp/I5Gn8xkE9HC/rfNEftwY1Ma/UbXhZ7uf7Qo2ly7Kr+3pe2P8+aJVIgdzBvQYfCr8BB8odw/o6Wv5LqNjP6nO1r9Nzen7w34W9YXLg+2tvaXhILS1JG9v5oBO6R7QQzCW/f1z3BDU5r9Jzel7x8w9uFpt2XL23jr6XtudavcnLRkGtDbq3I/bC2r736DW7s/2oPN+8f1q7YUf7gM96idtGQZ0Fwb0UIz6oCVPgO2p9bP6Wt8VejwGD35tf2k4Nb/vcDJ9Z6A5A3o9WbNm/JmblSqgQTMF9M0Fo8L6PDt+KP54bMeyce6S4SfDvTigz5xIH53CC+h7q/ez2l/ZSmDYvyCV9W+rfAYjUf2k28sDml7Q4CBSdTr+zj7Qd9aRz2g/64uFu01b+z0NPxlo3n2gnx/30eI5pt/CC8a7BzQ88n4YeXapp8Gm9PSzuRM0/sAXrVwG3+snD80a0FMuq7wdLuk8VTB1CHob0H6rqnlK6bgZvIBuSX36fvtaflcrZ08/2ycwtSb98kmXWQO6q8Xy+t3I844C4R6BSzYvr+gc9+J6z4TtGNLP5vH32A08Gn4af9Jt5n2gYd6ux3tGHvWpKxt6uY396H4K6HYEVStj2Zy/H2thbS1fP0Tf8WFz8kmPvAJ69flxPxw/em+A58JWDOxn1wC0PIwUOW5Uu3n9pM+cAW28zvJ6wHyCgD7Bk2Ejov0svzQq2H7UizC6zTm83Z8MNvM+0NpBpEtOR553NDFPh23o7+exNYpsLhweXW8fN6r/HLrNfRT+Pt487708H4XfP/2udk/xfNiE2uGjh/2sP+pFsPOzHK2avpNm3vNA6+8I+uNS1Ane2C6dJ8QWPOxn0bxSuGg1eZ5dNH8AABbWSURBVC9iL9o0fWeEeQN6KebNOZzlWyFP5XT7PbtUi4gpfztLqBWucfgofupnOOQM8hkcfC/ql9R/DXSaOaDlmUfXzB2mHn8K6NsZ38/ahlB+W7+wOfy0rTDI7AGdV39A2zwpcld1LWhd55dwsbC7tdGnvZ8kyzygY3la5K0Y2M+eB7o54jzGh58zrQAb89op/OI8MbIWlq1xjlL0S+ct6CfTmDmgwevXV5FQz4ychWHr7WfH4xzd4dnMp4PvjDBvQGvvCLro+Us3nhsZq/dz9AQ+zGf9S3MX6ZwrwbbMGtDz283dXg5/PoFpyZcg3XhyZGxwP2MPc5nI/uGnfjLKrAE9BNE8x3TkWydFXM4rDUJ8ulVH4d/D4/HnMahga9lYPusVDX4MA80a0NrHvz3xVsrBDV6VNySg76J+/Ki/n42HuZ7P5uxdP3nCnAE91S182VH6Wynf3ftZDUIF9E3U89nRz/ZVjuHuzeg+0KN88oQ5Axp9P9AnnOfv5xvcVwUV0PfQ08/okfeiprZgY9zZ+jmMkFNAd/cD+ef9qdeCCuh7aE/fH525JJ+8QkZT+PD9mXdF+QmdArp90fM/i+YFvTegn8who4NItQHtraAC+g5qE/jyot4BaGNx+WQeGZ3GVN8jsLscixfQ7Ysdf+8eiEYXL7tZP3hUP7gE42V0In09oOfb/iag2zesnx2PbLUXtDOfhp88YdaA1l/K+eyL4RufUXcZ0gro1oV1K5rdfNDPVj4js3cvPeIZ8wZ02jcT2dd3Anx+FF/+h4BuWy1vffP29iMbmaPHwmuT4AkzB3TSt7M7nwcaHtY/jL9lz5a8RPvZceZnc8HWHL05DD3qJ8+aPaBTunxGXTCNPwjotjXm781u1h7NxlVjo08H35laVgG9FDQcgwafmzyMJ0xOuvoZPfBe1IUXhssbfjKlvALaPDf/nFQB3aro8aPuA0etejb2gtb/IZ9MYZ6A1o6+V5Z/U3rPmXx07f9snVTfvXxsGh/8dLr7yrsSUNYp3s/+A++N5Zvnydf7OdUd5Z0JKKvU6Gdk2t73WDZ2g9b/0bx1SJbZPtBned5kol64kQPQYEdoZBxq+s50BJQ1etzPrseydRipvPDYuBCeJqCsUKOfwwPaGHzGZ+82AqYioKxPxw7Qzq4GF9XPAG0ee68PReFZAsrqdO0AjZw6X/+uns/WP+WTqQkoa9PZz55T54fk0+ydyQkoK9PsZ99x93Y8j81XG8VezQQTEVDWpbufAx+9jtOVDD+ZgYCyLs39nJ0/6lg6euhdP5mHgLIqPf18+Oi1doTWfjLRHYSAgLImPRP4QW8e0jl798AzBwFlRYreIefAV78fDT95FQFlRfqL+eDV77Xv4t/AtASU9XgQzPijFzuLST95DQFlNZqtawe080TQ+gW17ya+kxAQUNaiFbvWo9U+M6lZSAePeCkBZS0GzNhbr91sv7azft1Z7ijcCSgrERlvRq/VEc9j4zL55AUElHV4PIF/tLh88nICyjoMG4B2Ltw6A98jzQsIKOuQHNDWfN7OT15GQFmDdvIGPlTxfHqYeQ0BZQ2iR9wHLdd3IB5mJqCsQOxxefxYPTiPCWYnoKxASkAfnQcK8xNQltdxxmf/ItETQSe8U/CYgLK8rncJ6bx613n0E98veEBAWVzHo9L75kv9L5OH1xBQFtf1qHS++VLkmh5ZliCgLO3RVL3v7UOq6816FyFOQFnagzeaf1BP+WRBAsrCnnxM5JMFCSgLe+oxkU8WJaAs65mHxOydhQkoy0p+SLxrCMvLL6C78oDC1/ELe8KtTtpD0n1MCV4os4DuGwdlxzbUU251Uh4S9WQlsgro50frtJY//h51C551qzP+IVFPViOngP7+WS/mr++n7//8Z8xNeOKtztiHRD5ZkZwCemjl8pzUH2NuwlNvdRI+O26uuwJj5RTQXXvCfhqEjtoN6sm3NqMeEflkZTIK6Gm4+a114X7cHN7Tb3WGPyTyyepkFNDTaLM9XT+MO4zkCbg6oz48bub7AiMJKMsa/NlxHjvWJ6OAmsJv0oAwqidrlVFAHUTapv44eskRa5ZTQOOnMbVHpT08E1eou4897wIKa5BTQKMn0o97KZLn4hq1E9n/FsqwFjkF9FrMui9/jboFz8dVaj2s6kkesgpo+FZM3kxkS5STPGUW0KO3swNWI7+APkVAgekIKEAiAQVIJKAAiTIP6OdH34mgTowB5iSgAIk2HdA2AQWmk3lAxxJQYDoCCpBIQAESCShAIgEFSJRZQD8/itq7Kv/+6Sg8sJS8Anp/J6byfZgEFFhOVgGt3snuPggVUGA5OQX0PH8/f7DxviqogALLySmgu/sHeJw/HOlaUAEFlpNRQE+xLPd97m4FFVBgORkF9Nf3ywT+6lZQAQWWk2tAzwX9KqDAkrIN6Hk/6DcBBRaUUUDDfaDXb4sfAgosJ6OAnk9fCoag57OavvwPAQUWk1NAz+eBfgu+P1zOqRdQYCE5BfRyBn04jT8IKLCgrAJ6KWg4Bj2PSQUUWEheAT0fOfpWu2AvoMBSMgvoswQUmI6AAiQSUIBEAgqQSEABEgkoQCIBBUgkoACJBBQgkYACJBJQgEQCCpBIQAESCShAIgEFSCSgAIkEFCCRgAIkElCARAIKkEhAARIJKEAiAQVIJKAAiQQUIJGAAiQSUIBEAgqQSEABEgkoQCIBBUgkoACJBBQgkYACJBJQgEQCCpBIQAESZRrQX9+Lkz//GbucgALTySigp2jei7krbr6OvA0BBaaTZUDLfo4ehAooMJ0cA3o4hfPb7ZKRY1ABBaaTYUBPX//4+3bZvvjy15jbEFBgOhkG9HAbf579/jluCCqgwHQyDGht1LkftxdUQIHpZBjQXRjQQzWdH0JAgelkGdCgmQIKLCbDgO6NQIFVyDCgh6L4UV64sw8UWEqGAQ2PvIdH5IcQUGA6eQW0uJxCX1bzlNJxM3gBBSaUX0AvLtm8vKLzx8PlQgIKTCejgB6Dhl4Cuh/dTwEFJpRXQK8+P+6H48e+GZOAAhPKMaBPEFBgOgIKkEhAARIJKECizAP6+dF3ImgR8cI7B2ycgAIk2nRA2wQUmE7mAR1LQIHpCChAIgEFSCSgAIkEFCCRgAIkElCARAIKkEhAARJlFNDwIz0CXokELERAARJlFNDzC98FFFiPnAJ6GYOO+hj4FgEFppNVQM8F/fLXMzcgoMB08gpo+YGcqQQUmE5mAT1/FvzIj4KvEVBgOrkF9DSJf2YIKqDAdHIL6JNDUAEFppNdQJ8joMB0BBQgkYACJBJQgEQCCpBIQAESCShAIgEFSCSgAIkEFCCRgAIkElCARAIKkEhAARIJKEAiAQVIJKAAiQQUIJGAAiQSUIBEAgqQSEABEgkoQCIBBUgkoACJBBQgkYACJBJQgEQCCpBIQAESCShAIgEFSCSgAIkEFCCRgAIkElCARAIKkEhAARIJKECi/AK6K+6+jl9YQIHpZBbQfVE3tqECCkwnq4B+fhRNf/w96hYEFJhOTgH9/bNezF/fT9//+c+YmxBQYDo5BfTQyuU5qT/G3ISAAtPJKaC79oT9NAgdtRtUQIHpZBTQ03DzW+vC/bg5vIAC08kooKfRZnu6fhh3GElAgekIKECijAJqCg+sS0YBdRAJWJecAho/jak9Ku0hoMB0cgpo9ET6cS9FElBgOjkF9FrMui9/jboFAQWmk1VAw7di8mYiwNIyC+jR29kBq5FfQJ8ioMB0BBQgkYACJBJQgESZB/Tzo+9E0NZJT4WAAtMRUIBEmw5om4AC08k8oGMJKDAdAQVIJKAAiQQUIJGAAiQSUIBEAgqQSEABEgkoQKKMAhr5QI9i7IciCSgwHQEFSJRRQM8vfBdQYD1yCuhlDDrqY+BbBBSYTlYBPRd05OcYNwgoMJ28Anqexf/5zxPLCygwncwCetwXxY8nFhdQYDq5BfQ0iX9mCCqgwHRyC+iTQ1ABBaaTXUCfI6DAdAQUINHbBRRgOpM3auobnNLSf2xgWyZv1NQ3uGGb2qNgZdZqSyuzpXWJ2/wKTmhTW4OVWastrcyW1iVu8ys4oU1tDVZmrba0Mltal7jNr+CENrU1WJm12tLKbGld4ja/ghPa1NZgZdZqSyuzpXWJ2/wKTmhTW4OVWastrcyW1iVu8ys4oU1tDVZmrba0Mltal7jNr+CENrU1WJm12tLKbGld4ja/ghPa1NZgZdZqSyuzpXWJ2/wKTmhTW4OVWastrcyW1iVu8ys4oU1tDVZmrba0Mltal7jNr+CENrU1WJm12tLKbGld4ja/ghPa1NZgZdZqSyuzpXWJ2/wKTmhTW4OVWastrcyW1iVu8ys4oU1tDVZmrba0Mltal7jNr+CENrU1WJm12tLKbGld4ja/ghPa1NZgZdZqSyuzpXWJ2/wKTmhTW4OVWastrcyW1iVu8ys4oU1tDVZmrba0Mltal7jNryDAXAQUIJGAAiQSUIBEAgqQSEABEgkoQCIBBUgkoACJBBQgkYACJBJQgEQCCpBIQAESCShAIgEFSCSgAIkEFCCRgAIkElCARAIKkEhAARIJKEAiAQVIJKAAiQQUIJGAAiQS0Ac+P4qTL3+N+9FK9dzjX9/PP/r28rv0nF/f//g7cvF1Pb++/O48p2NljofzyhQ/Xn13ntK1LmenRyevlekjoL2uWTlrbQ89P1qpvnu8u/0kp/8dHI+/f8b++KdLb7J6nsZX5vY/g4w2s7OOdbk4b4ZZPTC9BLRPlZzW9tvzo5Xqu8f7zNblZhe9v7tqPXN6osZXpuxnUfz5zwL3Kk18XcqfZfW49BPQPvv7rHbXmhH2/Gileu7x+Vl6fnoeclmXi8tIs/08va/E+X8Y+fzvoGNlzitxCWf56GWgY12uDrn9j62fgPYIJhv7xhbR86OV6rvHu3s3TyXNZhJ/HZtF90ZcS5PTXLFrZfblwPOQzRC0a10urvOgXB6WxwS0x6Eaj53/p/pj2I9Wqucenzbq++a+z2Wcc3ki/ofYrrZd+f+A/Ffm9EjdVyb456p1PzBn552j/z2L58tAAtojfALu6o96z49Wqucen4YMX6t/5jHOOU9pf0SPVdQCmsEDc+xZmeCRyUX3A3P76Y9sHpYhBHSgXff//3t+tFKNexy0te/w6arsz2WJ3ttybXIZs/WszCGXMXSl+4E5Xv6H8C2f/68NIaDDnCYmXSOznh+tVPMeB1t0PtE5iz5Pz3PIr8HXXMRW5vLIXE/Lyqo5HQE9XXza8AT0DfXsTstmT1upeY/DGX1Ww+n487Q6XyunfkZX5vxo3E8xy2NmcNUR0OvGJaDvp2fXYDZ7DUutexxGcwMBLc8Ezetp2hHQf83xFN34A3PbISGgb+eUnK6tt+dHK9W+x/WAZrR1x5+n1Yn0Gf2/ILoy18n75f922Z2iG923cj+lNZ9N7BEBHeDQe1pwZv2M3ONtjUB3t1POz/XJaF06A3rb25LTKbpdD8z1MgHdsnIHWrW15tvPgSuTR0AjK9Nx5k9wGtNa964MXJldsAarnRsMXJeymwK6Ze2tYdf9NOz50SoMXJk8jsIPf54G52RlvjK74HDfak9pGrYu1SmtArplza3hPIvq2PfU86OVGLgyhyzOAx3cnOrn632qjv+/Qe4Brd6v5mqd6zKagPY7v66346Hu+dFKdd3jHF+JdJFvQCM6TqT/Gvw7m81NQLno2XOf1U79i857nONr4S8eT+EzD2h4xsRq94FGCChnp7J0RbLnRyvVc4+zfDemY+egLTiItNb9ERFdpxTchqBZnS/Xuycoq3nBIwLao2cEk9fg5qzvHuf5fqDx52l56k94DlAOotG5PzKXhyaflRFQjvcPoymdH/X7MC7yo5XrWZls35E+fJ6WKxO8h3tO+3PjKxPOfDNamfi63Ajom6g+W6fVnNiP1q1nZc7y/0ykamWq18JnlJzO6BxyXBkBpf4hQo3mxH60bj0rE/w8n0niRdfztPc90deqMzq7/FZGQAF4QEABEgkoQCIBBUgkoACJBBQgkYACJBJQgEQCCpBIQAESCShAIgEFSCSgAIkEFCCRgAIkElCARAIKkEhAARIJKEAiAQVIJKAAiQQUIJGAAiQSUIBEAgqQSEABEgkoQCIBBUgkoACJBBQgkYACJBJQgEQCCpBIQAESCShAIgEFSCSgAIkEFCCRgAIkElA2rLB9MysbGBsmoMzLBsaGCSjzsoGRr92PB1foCujh6+T3hbckoOTqUKT287Tsl78mvje8JQElU7s//n50lZ4Z/OfHt0nvDe9JQMnTgH727gL9/DCN52kCykr8/lkMaOLd7uH8/VgP6K/vxUkw7DwUCsqzBJSVGBXQ/ZD6hf3cX278UFT7Pk+/zyyeJwkoKzEmoJ8fQw4CBQE93G77EPyOsKaQREBZiREBPV31z38eX60KaDnaPP3ja3DhkFuBbgLKSowI6KEYNPuuAvr5cd9luguiuS+G7EiFbgLKSgwP6OmaI2fw1ZR/V5vDG4LyHAFlJYKAHs4HzIPR4eUI+h9/n75cgncaTw5JbW0XaBXQqpmn27MXlKcIKCtRBvR6wtElmdef7G/f/5dbQPfDRo6xgIb7QM/fOBDPUwSUlbgHtOxnUR45r5zDee7e1/qCxb2s4cg0FtBf38Mx584cnucIKCtxD+judr77edx57uQ5qNdzOG+dPF9QOyH+PNnfn8JYG17WzgItA7qvDTn3xZhz96FFQFmJW0A/P+6xu/2rnLCfvr/86/y1yuD9APvhj79P/wzy2ArovvFSpMtN2wnKMwSUlbgFdF/Nz/eX3u3Kw0m3lB7CDlYnc+6/7Ws5jI5APz/CIee+cCITTxFQVuIW0KqX58Hl1/OE/d680/f3gJbZq04J/fUv/0+4R7P2RiLVUfhaZA8CynMElJW4BjQ8x/MSzPu5S8fLzs9WQIOT4XdF1ww+CGhwcwLK0wSUlSgDWk6yL7G7DTvL7xvZCwash1oNOwJ6WqAaggooTxJQVmLUCPRbtVB59c6TmGoB3dfn/wLKMwSUlWjvAz0U0X2gtaPw1YCy+ySmZkDLhR2F50kCykq0j8JfdmqeT5OvH4U/nwdaprLqbfdJTJ0jUOeB8iQBZSUengd6DmfrlUjVUfhdMWgEGu4D9UokniSgrETslUj3AeetrEX7tfDlxP10tf/8H/8+Hm7Dy66ANt4Q1GvheYqAshKDXwtffzemext3xZ//6/uP3/92DWXj4+SqN64LzwP1bkw8S0BZieHvxhQeaLon8fI+n9WUvBXQL/96GXnWzqMPzpCCJALKSjx+P9DLK5NuP/9aW/B27eq9ltoB/euyb6B21pJ3pOdZAko2yoDW3lc+KhbQJp+JxNMElJWr5uvVazWrzziKa/QzHtBhH+0JPQSUldsV5WGiKoOH/sHjoIDuHILnWQLKyl1OX7qpirfvrd+QgB5qb2sPKQSUtTtE+nkaP/bMv5v9bLxM/uLXdztAeZqAsn6X4+fNAeN+xB7MdkB/fTf+5HkCSq4+PwafhLRr7jIdsSx0E1DytUut4MH0nUkIKEAiAQVIJKAAiQQUIJGAAiQSUIBEAgqQSEABEgkoQCIBBUgkoACJBBQgkYACJBJQgEQCCpBIQAESCShAIgEFSCSgAIkEFCCRgAIkElCARAIKkEhAARIJKEAiAQVIJKAAiQQUIJGAAiQSUIBEAgqQSEABEgkoQCIBBUgkoACJBBQgkYACJBJQgEQCCpBIQAESCShAIgEFSCSgAIkEFCCRgAIkElCARAIKkEhAARIJKECi/x8DtCf+WXgkAAAAAABJRU5ErkJggg==" title alt width="672" /></td>
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<td align="left">4.4. Draw samples <span class="math">\((\alpha^{s}, \beta^{s})\)</span> from <span class="math">\(p(\alpha,\beta|y)\)</span> (finally!). Here we repeat the procedure used in section 3.(v) of this document.</td>
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<td align="left">```r samps = 1000 #Get density of log(alpha/beta|y) v1.dens = apply(post.dens ,1, sum) #Sample from it s.v1 = sample(v1,samps, replace=TRUE, prob = v1.dens)</td>
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<td align="left">#Select the colum of the joint density corresponding to a specific value of v1 (p(v2|v1)) cond.v2 = function(x) { post.dens[which(v1 == s.v1[x]),] } #Sample a value of v2 according the the conditional probatility above s.v2 = sapply(1:samps,function(x) sample(v2,1,replace=TRUE,prob=cond.v2(x)))</td>
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<td align="left">#Add a uniform random jitter centered at zero with with equal to the grid spacing. ##This will make the simulation draws more continuous. Plot the sampled values. grid.v1 = v1[2]-v1[1] grid.v2 = v2[2]-v2[1] s.v2 = s.v2 + runif(length(s.v2),-grid.v2/2,grid.v2/2) s.v1 = s.v1 + runif(length(s.v1),-grid.v1/2,grid.v1/2) plot(s.v1, s.v2, xlab=expression(log(alpha/beta)<sup>s), ylab=expression(log(alpha+beta)</sup>s), xlim=c(min(v1),max(v1)) , ylim=c(min(v2),max(v2)), main=“Scatter Plot of Sample Draws of log(alpha/beta) and log(alpha+beta)”) ```</td>
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<tr class="even">
<td align="left"><img 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" title alt width="672" /></td>
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<td align="left"><strong>Note:</strong>this two figures do not match exactly their counterparts in the textbook (5.3a and 5.3b in BDA3), but so far I have not been able to detect my mistakes (the Jacobian doesn’t seem to be the problem, but feel free to double check). This is particularly strange as I can replicate the calculations of p112 where <span class="math">\(E[\alpha|y] = 2.41\)</span> and <span class="math">\(E[\beta|y] = 14.13\)</span>.</td>
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<td align="left">4.5 By applying the inverse of the transformation we recover the marginal distribution of the original hyper-parameters.</td>
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<td align="left">5. For each draw of <span class="math">\(\phi^{s}\)</span>, draw a sample of <span class="math">\(\theta\)</span> from <span class="math">\(p(\theta|\phi^{s},y)\)</span></td>
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<td align="left"><code>r s.beta = exp(s.v2)/(exp(s.v1)+1) s.alpha = exp(s.v2+s.v1)/(exp(s.v1)+1) theta.dist = sapply(1:71, function(x) rbeta(1000,s.alpha+y[x], s.beta + n[x] - y[x])) theta.dist = apply(theta.dist,2,sort) plot(0:450/1000,0:450/1000, type = "l", lty=1, xlab="Observed rate", ylab="95% CI and median of posterior") jitter.x = y/n + runif(length(y),-0.01,0.01) points(jitter.x,theta.dist[500,]) segments(jitter.x,theta.dist[25,], jitter.x,theta.dist[975,] ) title(main="Posterior Distribution of Tumor Rates for all 71 Experiments \n (Remember the goal? This is it!)") abline(h = mean(theta.dist), lty = 2) legend("bottomright",legend=c("Observed = Posterior","Overall Posterior Mean"),lty = c(1,2))</code></td>
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<tr class="odd">
<td align="left"><img 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" title alt width="672" /></td>
</tr>
<tr class="even">
<td align="left"># 5 - Replicating section 5.5: Experiments in eight schools (normal model) [Without Stan]</td>
</tr>
<tr class="odd">
<td align="left">```r #Data: school.id <- LETTERS[1:8] effect <- c(28,8,-3,7,-1,1,18,12) se.effect <- c(15,10,16,11,9,11,10,18)</td>
</tr>
<tr class="even">
<td align="left">pool.est <- sum(effect<em>se.effect<sup>-2)/sum(se.effect</sup>-2) pool.var <- sum(se.effect<sup>-2)</sup>-1 pool.ci <- c(-1.96,1.96)</em>pool.var^.5 + pool.est ```</td>
</tr>
<tr class="odd">
<td align="left">The pooled estimated effect and variance are 7.69 and 16.58, with a 95% CI of [-0.3, 15.67].</td>
</tr>
<tr class="even">
<td align="left"><em>Posterior simulation under the hierarchical model</em> Using the identity: <span class="math">\[
\begin{aligned}
p(\theta,\mu,\tau|y) = p(\tau|y)p(\mu|\tau,y)p(\theta|\mu,\tau,y)
\end{aligned}
\]</span> And the results from BDA in equation 5.17, 5.20 and 5.21 we code the posteriors <span class="math">\(p(\theta_{j} | \tau, \mu, y), p(\mu|\tau,y)\)</span> and <span class="math">\(p(\tau|y)\)</span>. <strong>Important note:</strong> for this excercise we could have follow <em>exactly</em> the same steps as the last excercise. Given some properties of the N-N model, we took a differente path and derive an analytic formula for <span class="math">\(p(\mu|\tau,y)\)</span> and <span class="math">\(p(\tau|y)\)</span> (instead of sampling from the join posterior density).</td>
</tr>
<tr class="odd">
<td align="left">```r # Eqn 5.17 of BDA3 post.theta.j <- function(mu,tau,j) { ( effect[j] / ( se.effect[j]^2 ) + mu / ( tau^2 ) ) / ( 1 / ( se.effect[j]^2 ) + 1 / ( tau^2 ) ) }</td>
</tr>
<tr class="even">
<td align="left">post.v.theta.j <- function(tau,j) { 1 / ( 1 / ( se.effect[j]^2 ) + 1 / ( tau^2 ) ) }</td>
</tr>
<tr class="odd">
<td align="left"># Eqn 5.20 of BDA3 post.mu.hat <- function(tau) { sum( effect * 1 / ( se.effect^2 +tau^2 ) ) / sum( 1 / ( se.effect^2 + tau^2 ) ) } post.v.mu <- function(tau) { ( sum( 1 / ( se.effect^2 +tau^2 ) ) )^-1 } # Eqn 5.21 of BDA3 marginal.tau <- function(tau) { hyper.prior(tau) <em> ( post.v.mu(tau)^.5 ) </em> prod( ( ( se.effect^2 + tau^2 )^(-.5) ) <em> exp( - ( ( effect - post.mu.hat( tau ) )^2 ) / ( 2 </em> ( se.effect^2 + tau^2 ) ) ) ) } ```</td>
</tr>
<tr class="even">
<td align="left">Define a hyper-prior and draw 200 samples from each distribution (for all 8 schools).</td>
</tr>
<tr class="odd">
<td align="left">```r samps <- 200</td>
</tr>
<tr class="even">
<td align="left">hyper.prior <- function(tau) 1 tau.grid <- seq(0.001,30, length=samps) pdf.tau <- sapply(tau.grid,function(x) marginal.tau(x)) pdf.tau <- pdf.tau/sum(pdf.tau)</td>
</tr>
<tr class="odd">
<td align="left">plot(tau.grid,pdf.tau, type=“l”, main=“Figure 5.5 from BDA3”, xlab=expression(tau), ylab=“Density”) ```</td>
</tr>
<tr class="even">
<td align="left"><img 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" title alt width="672" /></td>
</tr>
<tr class="odd">
<td align="left">The sampling method in BDA3 suggest to apply the inverse method from the posterior of <span class="math">\(\tau\)</span>. I don’t do this for two reasons: (i) I’m not sure the posterior has a closed for solution for its inverse, and (ii) given that I already have the density, I can directly draw from that distribution sampling using the <code>sample</code> command (which leads me to think that this command applies the inverse method).</td>
</tr>
<tr class="even">
<td align="left"><code>r # Sampling s.tau <- sample(tau.grid,samps,prob=pdf.tau, replace=TRUE) s.mu <- sapply(s.tau,function(x) rnorm(1,post.mu.hat(x),(post.v.mu(x))^0.5)) s.theta <- NULL for (j in 1:length(school.id)) { s.theta[[j]] <- sapply(1:samps, function(x) rnorm(1, post.theta.j(s.mu[x],s.tau[x],j), (post.v.theta.j(s.tau[x],j))^0.5 ) ) }</code></td>
</tr>
<tr class="odd">
<td align="left"><strong>The following figures replicate the figures in pg 122 in BDA. Before doing the plots we need to ‘average over <span class="math">\(\mu\)</span>’</strong></td>
</tr>
<tr class="even">
<td align="left"><span class="math">\[
\begin{aligned}
E(\theta_{j}|\tau,y) &= E_{\mu}\left[E(\theta_{j}|\tau,y,\mu)|\tau,y\right] \nonumber \\
&= E_{\mu}\left[\frac{ \frac{1}{\sigma_{j}^{2}}y_{j} + \frac{1}{\tau^{2}}\mu }{\frac{1}{\sigma_{j}^{2}} + \frac{1}{\tau^{2} } }|\tau,y\right] = \frac{ \frac{1}{\sigma_{j}^{2}}y_{j} + \frac{1}{\tau^{2}}\hat{\mu} }{\frac{1}{\sigma_{j}^{2}} + \frac{1}{\tau^{2} } }\\
\nonumber \\
Var(\theta_{j}|\tau,y) &= E_{\mu}\left[Var(\theta_{j}|\tau,y,\mu)|\tau,y\right] + Var_{\mu}\left[E(\theta_{j}|\tau,y,\mu)|\tau,y\right] \nonumber \\
&= \frac{1}{\frac{1}{\sigma_{j}^{2}} + \frac{1}{\tau^{2} }} + V_{\mu}\left(\frac{\frac{1}{\tau^{2}}}{\frac{1}{\sigma_{j}^{2}} + \frac{1}{\tau^{2} }}\right)
\end{aligned}
\]</span></td>
</tr>
<tr class="odd">
<td align="left">Where <span class="math">\(V_{\mu}\)</span> and <span class="math">\(\hat{\mu}\)</span> correspond to the expressions defined in Eq 5.20 of BDA3. Below is the code and plot of both equations.</td>
</tr>
<tr class="even">
<td align="left">```r post.theta.j.no.mu <- function(tau,j) post.theta.j( post.mu.hat( tau ), tau, j ) post.se.theta.j.no.mu <- function(tau,j) sqrt( ( post.v.theta.j( tau, j ) ) * ( 1 + post.v.mu( tau ) * tau^(-2) ) )</td>
</tr>
<tr class="odd">
<td align="left">plot( tau.grid, sapply(tau.grid, function(x) post.theta.j.no.mu(x,1) ), type=“l”, ylim=c(-5,30), xlab=“”, ylab=“”) title(main=“Figure 5.6 from BDA3”, xlab=expression(tau), ylab=“Estimated treatment effect”)</td>
</tr>
<tr class="even">
<td align="left">for (j in 2:8) { lines( tau.grid, sapply( tau.grid, function(x) post.theta.j.no.mu(x,j) ) ) } ```</td>
</tr>
<tr class="odd">
<td align="left"><img 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" title alt width="672" /></td>
</tr>
<tr class="even">
<td align="left">```r plot( tau.grid, sapply(tau.grid, function(x) post.se.theta.j.no.mu(x,1) ), type=“l”, ylim=c(0,20), xlab=“”, ylab=“”) title(main=“Figure 5.7 from BDA3”, xlab=expression(tau), ylab=“Posterior Standard Deviation”)</td>
</tr>
<tr class="odd">
<td align="left">for (j in 2:8) { lines( tau.grid, sapply( tau.grid, function(x) post.se.theta.j.no.mu(x,j) ) ) } ```</td>
</tr>
<tr class="even">
<td align="left"><img 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" title alt width="672" /></td>
</tr>
<tr class="odd">
<td align="left">Now we can use the simulated <span class="math">\(\theta_s\)</span> to described the estimated effects in each school.</td>
</tr>
<tr class="even">
<td align="left">```r s.theta <- matrix(unlist(s.theta), ncol = 8, byrow = FALSE) s.theta.sort <- apply(s.theta, 2, sort) p <- t( apply( s.theta.sort, 2, function(x) { quantile( x, c( .025, .25, .5, .75, .975), type=1 ) } ) )</td>
</tr>
<tr class="odd">
<td align="left">p <- round(p,3) knitr::kable(p, caption=“Table 5.3 from BDA3: Summary of 200 simulations of the treatment effects in the eight schools”) ```</td>
</tr>
<tr class="even">
<td align="left">Table: Table 5.3 from BDA3: Summary of 200 simulations of the treatment effects in the eight schools</td>
</tr>
<tr class="odd">
<td align="left">2.5% 25% 50% 75% 97.5%</td>
</tr>
</tbody>
</table>
<p>-0.959 5.126 8.799 14.701 31.639 -4.707 3.321 7.599 11.384 20.985 -15.041 2.191 6.602 10.440 17.380 -9.037 2.942 6.870 11.321 20.173 -8.086 2.217 6.210 9.562 18.036 -6.893 2.292 6.263 10.170 19.596 -1.023 5.646 9.295 14.107 29.198 -7.684 4.477 7.525 12.355 24.877</p>
<table>
<thead>
<tr class="header">
<th align="right">School</th>
<th align="center"></th>
<th align="center"></th>
<th align="center"></th>
<th align="center"></th>
<th align="center"></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="right"></td>
<td align="center">2.5%</td>
<td align="center">25%</td>
<td align="center">median</td>
<td align="center">75%</td>
<td align="center">97.5%</td>
</tr>
<tr class="even">
<td align="right">A</td>
<td align="center">-0.959</td>
<td align="center">5.126</td>
<td align="center">8.799</td>
<td align="center">14.701</td>
<td align="center">31.639</td>
</tr>
<tr class="odd">
<td align="right">B</td>
<td align="center">-4.707</td>
<td align="center">3.321</td>
<td align="center">7.599</td>
<td align="center">11.384</td>
<td align="center">20.985</td>
</tr>
<tr class="even">
<td align="right">C</td>
<td align="center">-15.041</td>
<td align="center">2.191</td>
<td align="center">6.602</td>
<td align="center">10.44</td>
<td align="center">17.38</td>
</tr>
<tr class="odd">
<td align="right">D</td>
<td align="center">-9.037</td>
<td align="center">2.942</td>
<td align="center">6.87</td>
<td align="center">11.321</td>
<td align="center">20.173</td>
</tr>
<tr class="even">
<td align="right">E</td>
<td align="center">-8.086</td>
<td align="center">2.217</td>
<td align="center">6.21</td>
<td align="center">9.562</td>
<td align="center">18.036</td>
</tr>
<tr class="odd">
<td align="right">F</td>
<td align="center">-6.893</td>
<td align="center">2.292</td>
<td align="center">6.263</td>
<td align="center">10.17</td>
<td align="center">19.596</td>
</tr>
<tr class="even">
<td align="right">G</td>
<td align="center">-1.023</td>
<td align="center">5.646</td>
<td align="center">9.295</td>
<td align="center">14.107</td>
<td align="center">29.198</td>
</tr>
<tr class="odd">
<td align="right">H</td>
<td align="center">-7.684</td>
<td align="center">4.477</td>
<td align="center">7.525</td>
<td align="center">12.355</td>
<td align="center">24.877</td>
</tr>
</tbody>
</table>
<p>Here we reproduce figure 5.8 (with the same problems as above)</p>
<pre class="r"><code>par(mfrow=c(1,2))
domain <- c(-20,60)
hist(s.theta[,1], breaks=10, xlab="Effect in School A", main="", xlim=domain)
hist(apply(s.theta,1,max), breaks=10, xlab="Largest Effect", main="", xlim=domain)
title(main="Figure 5.8 from BDA3")</code></pre>
<p><img 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" title alt width="672" /></p>
<p>This last figure (“largest effect”) is a good example of one the main advantage of a fully Bayesian hierarchical model: once we have correctly simulated the posterior, we can test all kinds of complicated hypothesis.</p>
</div>
<div id="replicating-section-5.5-experiments-in-eight-schools-normal-model-with-stan" class="section level1">
<h1>6 - Replicating section 5.5: Experiments in eight schools (normal model) [With Stan]</h1>
<p>Appendix C in BDA3</p>
</div>
<div id="replicating-example-of-section-11.2-metropolis-sampling-from-bivariate-normal-witout-stan" class="section level1">
<h1>7 - Replicating example of section 11.2: Metropolis sampling from bivariate normal [Witout Stan]</h1>
<p>Here we follow the steps in p278 to simulate draws from a bivariate normal <span class="math">\(N(0,I_{2})\)</span>.</p>
<ol style="list-style-type: decimal">
<li>Define a starting point <span class="math">\(\theta^{0}\)</span>, for which <span class="math">\(p(\theta^{0}|y)>0\)</span>:</li>
</ol>
<pre class="r"><code>set.seed(142857)
library(mvtnorm)
theta.0 <- c(-2.5, 2.5)</code></pre>
<p>Our starting point is <span class="math">\((-2.5, 2.5)\)</span>, the upper left most square dot from figure 11.1a.</p>
<ol start="2" style="list-style-type: decimal">
<li>For <span class="math">\(t=1,2,...:\)</span><br /></li>
</ol>
<ol style="list-style-type: lower-alpha">
<li>Sample a proposal <span class="math">\(\theta^{*}\)</span> at time <span class="math">\(t\)</span> from <span class="math">\(J_{t}(\theta^{*}|\theta^{t-1})\)</span>. For this example the <em>jumping distribution</em> is <span class="math">\(N(\theta^{*}|\theta^{t-1},0.2^{2}I_{2})\)</span>:</li>
</ol>
<pre class="r"><code>theta.star <- function(theta.t_1) {
n.p <- length(theta.t_1)
# I would like to learn a way to draw from a multivariate normal without a black-box function.
rmvnorm(1, mean = theta.t_1, sigma = 0.2^2 * diag(n.p))
} </code></pre>
<ol start="2" style="list-style-type: lower-alpha">
<li>Calculate the ratio of densities,<br /><span class="math">\[
\begin{aligned}
r &= \frac{p(\theta^{*}|y)}{p(\theta^{t-1}|y)} \label{r.dens}
\end{aligned}
\]</span></li>
</ol>
<pre class="r"><code>r.dens <- function(theta.t_1, theta.star) {
n.p <- length(theta.t_1)
dmvnorm(theta.star, mean = rep(0, n.p), sigma = diag(n.p)) /
dmvnorm(theta.t_1 , mean = rep(0, n.p), sigma = diag(n.p))
} </code></pre>
<ol start="3" style="list-style-type: lower-alpha">
<li>Set <span class="math">\[
\begin{aligned}
\theta^{t} &= \left\{
\begin{array}{l l}
\theta^{*} & \quad \text{with probability $min(r,1)$}\\
\theta^{t-1} & \quad \text{otherwise.}
\end{array} \right. \nonumber
\end{aligned}
\]</span></li>
</ol>
<pre class="r"><code>theta.t <- function(theta.t_1, theta.star, r) {
prob.aux <- runif(1)
if (prob.aux <= min(c(r,1)))
theta.star
else
theta.t_1
}</code></pre>
<ol start="4" style="list-style-type: lower-alpha">
<li>Execute:</li>
</ol>
<pre class="r"><code>theta <- function(sims,theta.0) {
s.theta <- matrix(NA,sims,2)
s.theta[1,] <- t(as.matrix(theta.0))
for (t in 2:sims) {
s.theta.star<- theta.star(s.theta[t-1,])
r <- r.dens(s.theta[t-1,], s.theta.star)
s.theta[t,] <- theta.t(s.theta[t-1,], s.theta.star, r)
}
return(s.theta)
}
par(mfrow=c(1,3))
par(mar = rep(2,4))
# 11.1a
s.theta.1 <- theta(50,theta.0)
s.theta.2 <- theta(50,c(2.5,2.5))
s.theta.3 <- theta(50,c(2.5,-2.5))
s.theta.4 <- theta(50,c(-2.5,-2.5))
s.theta.5 <- theta(50,c(0,0))
plot(s.theta.1, xlim=c(-4,4), ylim=c(-4,4), type="l", sub = "50 simulations")
points(theta.0[1], theta.0[2], pch=15)
lines(s.theta.2)
points(2.5, 2.5, pch=15)
lines(s.theta.3)
points(2.5, -2.5, pch=15)
lines(s.theta.4)
points(-2.5, -2.5, pch=15)
lines(s.theta.5)
points(0, 0, pch=15)
# 11.1b
s.theta.1 <- theta(1000, theta.0)
s.theta.2 <- theta(1000, c(2.5,2.5))
s.theta.3 <- theta(1000, c(2.5,-2.5))
s.theta.4 <- theta(1000, c(-2.5,-2.5))
s.theta.5 <- theta(1000, c(0,0))
plot(s.theta.1, xlim=c(-4,4), ylim=c(-4,4), type="l", sub = "1000 simulations", main="Figure 11.1 From BDA3")
points(theta.0[1], theta.0[2], pch=15)
lines(s.theta.2)
points(2.5, 2.5, pch=15)
lines(s.theta.3)
points(2.5, -2.5, pch=15)
lines(s.theta.4)
points(-2.5, -2.5, pch=15)
lines(s.theta.5)
points(0, 0, pch=15)
s.theta.1 <- s.theta.1[501:1000,] + matrix(runif(1000)/20, nrow = 500, ncol = 2)
s.theta.2 <- s.theta.2[501:1000,] + matrix(runif(1000)/20, nrow = 500, ncol = 2)
s.theta.3 <- s.theta.3[501:1000,] + matrix(runif(1000)/20, nrow = 500, ncol = 2)
s.theta.4 <- s.theta.4[501:1000,] + matrix(runif(1000)/20, nrow = 500, ncol = 2)
s.theta.5 <- s.theta.5[501:1000,] + matrix(runif(1000)/20, nrow = 500, ncol = 2)
# 11.1c
plot(s.theta.1, xlim=c(-4,4), ylim=c(-4,4), type="p", pch = 20, cex =.1, sub = "Second half of 1000 simulations")
points(s.theta.2, pch = 20, cex =.1)
points(s.theta.3, pch = 20, cex =.1)
points(s.theta.4, pch = 20, cex =.1)
points(s.theta.5, pch = 20, cex =.1)</code></pre>
<p><img 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" title alt width="672" /></p>
</div>
<div id="replicating-example-of-section-11.6-gibbs-sampling-for-a-hierarchical-normal-model-coagulations-experiment-data-witout-stan" class="section level1">
<h1>8 - Replicating example of section 11.6: Gibbs sampling for a hierarchical normal model (Coagulations experiment data) [Witout Stan]</h1>
<pre class="r"><code>#Data
id <- rep(LETTERS[1:4],c(4,6,6,8))
y <- c(62,60,63,59,63,67,71,64,65,66,68,66,71,67,68,68,56,62,60,61,63,64,63,59)
J <- length(unique(id))
n <- length(y)</code></pre>
<p><em>The Model</em><br />Data <span class="math">\(y_{ij}, i= 1,..., n_{j} , j= 1,..,J\)</span> are iid within each of <span class="math">\(J\)</span> groups with <span class="math">\(y_{ij} \sim N(\theta_{j}, \sigma^{2})\)</span>. The prior distribution of <span class="math">\(\theta_{j}\)</span> is assume to be normal with hyperparameters <span class="math">\(\mu, \tau\)</span> (<span class="math">\(\theta_{j} \sim N(\mu, \tau^{2})\)</span>), <span class="math">\(\sigma\)</span> is assumed to be unkonwn and the hyperprior is assumed to be uniform over <span class="math">\((\mu, log(\sigma), \tau)\)</span>, which implies <span class="math">\(p(\mu, log(\sigma), log(\tau)) \propto \tau\)</span>. The joint posterior denstity for all the parameters is:</p>
<p><span class="math">\[
\begin{aligned}
p(\theta,\mu, log(\sigma), log(\tau) | y) \propto \tau \prod^{J}_{j=1} N(\theta_{j}|\mu, \tau^{2}) \prod^{J}_{j=1}
\prod^{n_{j}}_{i=1} N(y_{ij}|\theta_{j}, \sigma^{2}) \label{norm.norm4gibs}
\end{aligned}
\]</span></p>
<p><em>Starting points</em><br />Select 10 <span class="math">\(\theta_{j}\)</span> randomly from the <span class="math">\(y_{ij}\)</span> sample. And take <span class="math">\(\mu\)</span> to be the average starting values of <span class="math">\(\theta_{j}\)</span>.</p>
<pre class="r"><code>set.seed(142857)
theta.0 <- sapply(1:4,function(x) sample(y[id==LETTERS[x]],10, replace=TRUE))
mu.0 <- apply(theta.0, 1,mean) </code></pre>
<p>[Here I follow the exact reverse order that is proposed in the book, going from step 4 to 1 instead of 1 to 4. It is not clear to me how to do it otherwise].</p>
<p><em>4. Draw from conditional posterior of <span class="math">\(\tau^{2}\)</span> </em> using: <span class="math">\[
\begin{aligned}
\hat{\tau}^{2} &= \frac{1}{J-1}\sum_{j=1}^{J}(\theta_{j} - \mu)^{2}
\end{aligned}
\]</span></p>
<pre class="r"><code>tau.hat.2 <- function(theta) {
mu <- mean(theta)
tau.2 <- ( 1/(J-1) ) * sum((theta - mu)^2)
return(tau.2)
} </code></pre>
<p>And the fact that: <span class="math">\[
\begin{aligned}
\tau^{2}|\theta,\mu,\sigma, y \sim Inv-\chi^2(J-1,\hat{\tau}^{2})
\end{aligned}
\]</span></p>
<p>We can draw samples for <span class="math">\(\tau^{2}\)</span></p>
<pre class="r"><code>s.tau.post <- function(theta) {
tau.2 <- tau.hat.2(theta)
tau.cond <- (J - 1) * (tau.2)/rchisq(1,J-1)
return(tau.cond)
}</code></pre>
<p><em>3. Draw from conditional posterior of <span class="math">\(\sigma^{2}\)</span> </em> Using:<br /><span class="math">\[
\begin{aligned}
\hat{\sigma}^{2} &= \frac{1}{n}\sum_{j=1}^{J}\sum_{i=1}^{n_{j}}(y_{ij} - \theta_{j})^{2}
\end{aligned}
\]</span></p>
<pre class="r"><code>f.sigma.hat.2 <- function(theta) {
sigma.hat.2 <- sapply(1:4, function(x) (y[id==LETTERS[x]] - theta[x])^2)
sigma.hat.2 <- (1/n) * sum(unlist(sigma.hat.2))
return(sigma.hat.2)
}</code></pre>
<p>And the fact that:</p>
<p><span class="math">\[
\begin{aligned}
\sigma^{2}|\theta,\mu,\tau,y \sim Inv-\chi^2(n,\hat{\sigma}^{2})
\end{aligned}
\]</span> We can draws samples for <span class="math">\(\sigma^{2}\)</span></p>
<pre class="r"><code>s.sigma.post <- function(theta) {
sigma2.hat <- f.sigma.hat.2(theta)
sigma2.post <- (n) * (sigma2.hat)/rchisq(1,n)
return(sigma2.post)
}</code></pre>
<p><em>2. Draw from conditional posterior of <span class="math">\(\mu\)</span> </em> Using:<br /><span class="math">\[
\begin{aligned}
\hat{\mu} &= \frac{1}{J} \sum_{j=1}^{J}\theta_{j}
\end{aligned}
\]</span></p>
<pre class="r"><code>mu.hat <- function(theta) {
mean(theta)
} </code></pre>
<p>And the fact that:</p>
<p><span class="math">\[
\begin{aligned}
\mu|\theta,\sigma,\tau,y \sim N(\hat{\mu}, \tau^{2}/J)
\end{aligned}
\]</span></p>
<p>We can draw values for <span class="math">\(\mu\)</span></p>
<pre class="r"><code>s.mu <- function(theta,tau2) {
mu.hat <- mu.hat(theta)
rnorm(1,mu.hat,sqrt(tau2/J))
}</code></pre>
<p><em>1. Finally, we can draw values for <span class="math">\(\theta\)</span></em> Using the fact that:<br /><span class="math">\[
\begin{aligned}
\theta_{j}|\mu,\sigma,\tau,y \sim N(\hat{\theta_{j}}, V_{\theta_{j}})
\end{aligned}
\]</span><br />With: <span class="math">\[
\begin{aligned}
\hat{\theta_{j}} &= \frac{ \frac{1}{\tau^{2}}\mu + \frac{n_{j}}{\sigma^{2}}\bar{y_{\dot j}} }{\frac{1}{\tau^{2}} + \frac{n_{j}}{\sigma^{2}}} \nonumber \\
\\
V_{\theta_{j}} &= \frac{1}{\frac{1}{\tau^{2}} + \frac{n_{j}}{\sigma^{2}}} \nonumber \\
\end{aligned}
\]</span></p>
<pre class="r"><code>theta.hat.j <- function(j,mu,sigma2,tau2) {
y.bar.j <- mean(y[id==LETTERS[j]])
n.j <- length(y[id==LETTERS[j]])
( (1/tau2) * mu + (n.j/sigma2) * y.bar.j ) / ( (1/tau2) + (n.j/sigma2) )
}
V.theta.hat.j <- function(j,mu,sigma2,tau2) {
n.j <- length(y[id==LETTERS[j]])
( 1 ) / ( (1/tau2) + (n.j/sigma2) )
}
s.theta <- function(mu,sigma2,tau2) {
theta <- NULL
for (j in 1:J) {
t.hat <- theta.hat.j(j,mu,sigma2,tau2)
v.t.hat <- V.theta.hat.j(j,mu,sigma2,tau2)
theta[j] <- rnorm(1,t.hat,sqrt(v.t.hat))
}
return(theta)
}
mcmc.gibbs <- function(chain) {
res1 <- as.list(NULL)
sims <- 200
param <- 7
s.param <- matrix(NA, ncol = param, nrow = sims )
colnames(s.param)<- c("theta1", "theta2", "theta3", "theta4", "mu", "sigma2", "tau2")
s.param[1,1:4]<- theta.0[chain,]
s.param[1,7] <- s.tau.post(theta.0[chain,])
s.param[1,6] <- s.sigma.post(theta.0[chain,])
s.param[1,5] <- s.mu(theta.0[chain,],s.param[1,7])
for (s in 2:sims) {
s.param[s,1:4]<- s.theta(s.param[s-1,5],s.param[s-1,6],s.param[s-1,7])
s.param[s,7] <- s.tau.post(s.param[s,1:4])
s.param[s,6] <- s.sigma.post(s.param[s,1:4])
s.param[s,5] <- s.mu(s.param[s,1:4],s.param[s,7])
}
return(s.param)
#Warm-up
}
s.param <- lapply(1:10, function(x) mcmc.gibbs(x))
s.param.1 <- s.param[[1]][101:200, ]
#Transform the variance in to sd.
s.param.1[,6:7] <- sqrt(s.param.1[,6:7] )
t(apply(s.param.1,2, function(x) quantile(x, c(.025,.25,.5,.75,.975))))</code></pre>
<pre><code>## 2.5% 25% 50% 75% 97.5%
## theta1 58.538766 60.668386 61.289891 62.136036 63.550790
## theta2 64.097419 65.187406 65.966342 66.521022 67.693971
## theta3 65.778567 67.124232 67.719009 68.310328 69.505146
## theta4 59.653630 60.640190 61.285377 61.766722 62.598042
## mu 58.589946 62.808845 63.767603 65.404435 69.947366
## sigma2 1.851044 2.168908 2.395438 2.694294 3.327814
## tau2 1.824847 2.776569 3.833363 6.389347 17.368069</code></pre>
<pre class="r"><code>r.hat <- function(arg1) {
n <- dim(arg1)[1]
m <- dim(arg1)[2]
B <- (n/(m-1)) * sum( ( apply(arg1,2,mean) - mean(arg1) )^2 )
W <- (1/m) * (1/(n-1)) * sum( (arg1 - apply(arg1,2,mean))^2 )
sqrt( (n-1)/(n) + B/(W*n) )
}
r.hat(sapply(1:10,function(x) s.param[[x]][,4] ))</code></pre>
<pre><code>## [1] 1.031577</code></pre>
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