{ "metadata": { "name": "", "signature": "sha256:6d2f64f059402aa46c330c6873802017e7fd8b72051e51183e5616c1c2bbc596" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "#IX-[Randomness](http://lmgtfy.com/?q=Randomness&l=1)\n", "\n", "Lecturer:*Jos\u00e9 Pedro Silva*[1](http://www-num.math.uni-wuppertal.de/en/amna/people/jose-pedro-silva.html) - [silva_at_math.uni-wuppertal.de](mailto:silva_at_math.uni-wuppertal.de)" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from IPython.display import Image" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "Image('http://imgs.xkcd.com/comics/random_number.png')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "png": "iVBORw0KGgoAAAANSUhEUgAAAZAAAACQCAAAAAADo2KkAAAABGdBTUEAALGOfPtRkwAAACBjSFJN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\n", "prompt_number": 2, "text": [ "" ] } ], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "Image('http://imgs.xkcd.com/comics/ayn_random.png')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "png": "iVBORw0KGgoAAAANSUhEUgAAARsAAAFuCAAAAACUqeOPAAAACXBIWXMAAAxOAAAMTgF/d4wjAAAD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\n", "prompt_number": 3, "text": [ "" ] } ], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "Image('http://www.random.org/analysis/dilbert.jpg')" ], "language": "python", "metadata": {}, "outputs": [ { "jpeg": "/9j/4AAQSkZJRgABAgECWAJYAAD/4QyaRXhpZgAATU0AKgAAAAgABwESAAMAAAABAAEAAAEaAAUA\nAAABAAAAYgEbAAUAAAABAAAAagEoAAMAAAABAAIAAAExAAIAAAAUAAAAcgEyAAIAAAAUAAAAhodp\nAAQAAAABAAAAnAAAAMgAAAJYAAAAAQAAAlgAAAABQWRvYmUgUGhvdG9zaG9wIDcuMAAyMDA1OjEx\nOjI0IDE1OjM3OjE3AAAAAAOgAQADAAAAAf//AACgAgAEAAAAAQAAAqigAwAEAAAAAQAAAQEAAAAA\nAAAABgEDAAMAAAABAAYAAAEaAAUAAAABAAABFgEbAAUAAAABAAABHgEoAAMAAAABAAIAAAIBAAQA\nAAABAAABJgICAAQAAAABAAALbAAAAAAAAABIAAAAAQAAAEgAAAAB/9j/4AAQSkZJRgABAgEASABI\nAAD/7QAMQWRvYmVfQ00AA//uAA5BZG9iZQBkgAAAAAH/2wCEAAwICAgJCAwJCQwRCwoLERUPDAwP\nFRgTExUTExgRDAwMDAwMEQwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwBDQsLDQ4NEA4OEBQO\nDg4UFA4ODg4UEQwMDAwMEREMDAwMDAwRDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDP/AABEI\nADAAgAMBIgACEQEDEQH/3QAEAAj/xAE/AAABBQEBAQEBAQAAAAAAAAADAAECBAUGBwgJCgsBAAEF\nAQEBAQEBAAAAAAAAAAEAAgMEBQYHCAkKCxAAAQQBAwIEAgUHBggFAwwzAQACEQMEIRIxBUFRYRMi\ncYEyBhSRobFCIyQVUsFiMzRygtFDByWSU/Dh8WNzNRaisoMmRJNUZEXCo3Q2F9JV4mXys4TD03Xj\n80YnlKSFtJXE1OT0pbXF1eX1VmZ2hpamtsbW5vY3R1dnd4eXp7fH1+f3EQACAgECBAQDBAUGBwcG\nBTUBAAIRAyExEgRBUWFxIhMFMoGRFKGxQiPBUtHwMyRi4XKCkkNTFWNzNPElBhaisoMHJjXC0kST\nVKMXZEVVNnRl4vKzhMPTdePzRpSkhbSVxNTk9KW1xdXl9VZmdoaWprbG1ub2JzdHV2d3h5ent8f/\n2gAMAwEAAhEDEQA/AO1zKcmvqNwp61ViY3pCqvpxDG+kTX6bbmv3eozbLLK6vT9NA6dTlU3+rl/W\nNmWGTtr3VtYX/p/da1jt23bdj/od+z9W/wCG9mi6rOflZjaK6TUb2PLnWPY/eKqOzKrG7drWJfZO\nqs3Fvpe4bfffY4CdvDHU7PpD/wBFpKSjO0E9QxJhu46cx+k2/px7XfmJHqVfqADOww0uPtJG4t12\nt/nvpfQ/NQBh9UloBYCxpaB9qu4M+581e9/u/nHJOxOrOeXH0zLgS0ZNrRI3fmso+i5rvez/AL+k\np0D1DAHOTUPi9o/in+3YXpNu9ev0nuLG2b27S5u7exrp+k3Y/wDzFQrw+rVv3t2bpBg5NpbAJIZ6\nZo2fne7/AAj/APttVemPceoGp+0WsyLXWtYS5o3nNczVwZ7vb+4kp2D1DAHORV/nj+9L9oYH/civ\n/PH96sKpfmW1WOY2kPiIPqNBMhztu130Xe389JTP9o4H/civ/PH96X7QwP8AuRV/nt/vQT1C/wBC\nuz7P77J3MNjQGEPbXBf+f9P6VaPh5FmRVvsq9FwMbNwf2B+mz2JKVXnYVriyvIqe5rS9zWvaSGjl\n5AP0UM9W6UBuOZRHj6rI/wCqVfqg/WGwJJxMlv8AnOxfBKzJymZgY61zai/2t9AkFobS7b62/wDe\n9Rnq+n/OX+l+4kpsDqvS3fRzKD8LWf8Akkj1XpY0OZQP+us/8krarZuV9mYx5dUwOftJuf6YOjne\n15/O9qSmP7W6X/3Mo/7dZ/5JIdW6UTAzKCSYAFrOf85Cq6lY51QtFLC/W1gtaSxsuZ6n5vqt9T0a\nfb/hLEJ+Xk5XTshzq6/SdTZsuqsFjHR7I9v9r99JT//Q9Nxv5/L/AONH/nqlD6q6puKDc1j6jZW1\nzbC4Nlz2sr91bbNn6V1f5np/6RDfa5uRY1jy0uvhzWhsuihlu3dZ7WfRUsU25eGR9oPqCwtNjNhI\n2P1rlrfTd7W7P5tJTk+pg+kwVnFm+pwyARc5p0D7RU38yv1n1WP3e/8Anv8ACeoiC+it2Lk478Zt\ntjLA17/WZIG/bDXfmV7d76bfofzVf5li0n4FocLHZloawD26Fvt3buQd27f+f6n83UkOnXeoLDmW\nugtdtdBaS2fpMjZsfu+ixrP+DSUwp63gGqsXXt9ZzGOdta8CXOFW4Ne3c39K78/+a/wqpYQI6tYN\nDF7jx4/bz9Kf++rcc2se9wbI1LjGmnj/AFVgU5IqzCRSXtGU9/qs26tcM0O3PsdWxteP6O536T/C\npKehVLJwrbrLHN9CLGBkWVbzpukWne31qnf6L9H/AMYrGLkDJobcGlm6RtdBIglnNbns/N/NcipK\ncxvT3BmPS37KLMVp3tbSBtD3Ag47dx+zMf6b9zff6n/W1Z6fiOxKDU4VA7if0FfpM/7a3P8Ad/aT\n32141wtdJ9UBmxrS5x2mQ5rGe/aze/1ESjKovLhU6XMje0gtc2fo72PDXNSU5/VgTlVEfm42QTrH\n52N8d39VBzRU7Ie0Pa4OsiwfazSa37KhPpsH86xljP0e7/tRT/pP0RurmMmskSBj3k/AOx1cfj4x\ney00Vve4w+wsBd7m+nu3Ru922ut3/BpKQ4efQGCqyyljWMb6ZZa14cAwOtjh36KHf9b96n1J9rK2\nGtxbvca3RX6p9wMOHua2rY7/AAtnqU/6av8APZGu3HDtrMYDc8AhvpzG41+q5od9Btil1Mu9KsMa\nyywv/RsstNILtrtglrX+r7/8C9uz/MSU5bqwR+jrtaRHpF+E07drvtFnDa/0NzWvr2fo7f0v+nRq\n23jpea+242tLSAHUfZ3BzG7NxH5/qbWP+j/wf9SdFQymMFLhZRudNtOU8uDDFtJ3gb/e6mj9Hv8A\n5r/T1+r6pD9oZ0e9mZW2lzWOa0C11oLY9k227X73fupKf//R9CsbY/IyHV+x1V24PDd7v5nHbsEe\n79JvQaOpWV25LjitYA/cSLOaGM99+1zG7dl/6H0f+N/0aPZj5bc19raGW1l/qNcXgHWuqr6L63/n\nU/muUMjGybJDcJpbYWC1vqtaC1hn/R7ne38xJTCvPact3TsrIc+70g+9rGODWBx3Nd6oq9Nvqb/s\n+z17Lf5n0mM/SLSfl4zKPtDrB6RaXhw1loG/2Nb7n+391UWjqoqsqsoFwc9z2ONoa5oJ31sna7d6\nTvz07R1ANefsbRZBZVFrQGMOjdhFf6P+z/5wlJrDVl1iy6oux5A9N7d26SG77KdfZW79/wCh/OLC\nw2irMfUa2jFsy7K4PptYQXdT9T2uG32fzXo/9c/0i3GuyWsa0YUAAAhljQIA2bfzfa381UaOmZ1c\n3Pa0OtttNlTdryK32Z9tXue6utzv16j1Gf8AG++xJTXf1d2PkWYfT8puQW3RkPta6wY7PQN24+l9\nkr/SW7Hem7I/m/tHp2f9p69XE6rVZgtybSSGtm6xjHBgI+m7a7c9rPz/AM/YxDfVlBgNFFld4gB5\ncwt09hfZVXdSx7vT/M/m/VRh9q2lr6TcHe13qCsEtP0mv9N+x3/baSmnmOuzXGyjeGsBbUxtzsa0\nlp/TPbo5ttbv0bNl/wDN+l/wiGb8+vNwq6nVVXZGG5+QLN2Q0/Zn01+m29hxbN2/P/pDqv8ArKtv\nxBfUyjKxAaqXiygVEM2kS1vsbZ7fa9356nZhUvubkNx7Krq2OqZbW5jSGPNb7K2jfs97qavzf8Gk\nppZxtyLKLXtFbziZPqVnUgTRxp+9+etqv+bb8B+RZLulZD7Hv032VWsNrw0HVzH0VNDHWfom7bHW\nbv8AC/pVequyWVMa7Fs3NaAYdXyBr/hAkpycjJxMTDfdl5JxhTFhucNjHuDi7e4Cre+uqz3sr9T/\nANKK3kdTw72W1spbmW417cc0vG39M5v5rbWu2/o7d/qf9xn+r+krTPZ1F8Mfjb6zvD9z2lpY72+i\n6guex7fTcq+Fg5/T6W0UYxsqqcbqa3PbtY9weLWM3vts9J9lr7W+/wDRfzVf6NJTepyh9M0toe14\nbcA10uYQ70fS3V022fpNjP5r6fqIOeauoYlrn0h9NYJrbez89hl1zKrf8JTs30WbfUr/AEijidMx\n+n6YOBY1rnOdYLLRZJI+n+mvt/SNc1v/AFv1UYty34TqHY7zc+ss3l1YaC4e76D93p7v5KSn/9n/\n7RCmUGhvdG9zaG9wIDMuMAA4QklNBCUAAAAAABAAAAAAAAAAAAAAAAAAAAAAOEJJTQPtAAAAAAAQ\nAlgAAAABAAICWAAAAAEAAjhCSU0EJgAAAAAADgAAAAAAAAAAAAA/gAAAOEJJTQQNAAAAAAAEAAAA\nHjhCSU0EGQAAAAAABAAAAB44QklNA/MAAAAAAAkAAAAAAAAAAAEAOEJJTQQKAAAAAAABAAA4QklN\nJxAAAAAAAAoAAQAAAAAAAAACOEJJTQP0AAAAAAASADUAAAABAC0AAAAGAAAAAAABOEJJTQP3AAAA\nAAAcAAD/////////////////////////////A+gAADhCSU0ECAAAAAAAEAAAAAEAAAJAAAACQAAA\nAAA4QklNBB4AAAAAAAQAAAAAOEJJTQQaAAAAAANDAAAABgAAAAAAAAAAAAABAQAAAqgAAAAHAGQA\naQBsAGIAZQByAHQAAAABAAAAAAAAAAAAAAAAAAAAAAAAAAEAAAAAAAAAAAAAAqgAAAEBAAAAAAAA\nAAAAAAAAAAAAAAEAAAAAAAAAAAAAAAAAAAAAAAAAEAAAAAEAAAAAAABudWxsAAAAAgAAAAZib3Vu\nZHNPYmpjAAAAAQAAAAAAAFJjdDEAAAAEAAAAAFRvcCBsb25nAAAAAAAAAABMZWZ0bG9uZwAAAAAA\nAAAAQnRvbWxvbmcAAAEBAAAAAFJnaHRsb25nAAACqAAAAAZzbGljZXNWbExzAAAAAU9iamMAAAAB\nAAAAAAAFc2xpY2UAAAASAAAAB3NsaWNlSURsb25nAAAAAAAAAAdncm91cElEbG9uZwAAAAAAAAAG\nb3JpZ2luZW51bQAAAAxFU2xpY2VPcmlnaW4AAAANYXV0b0dlbmVyYXRlZAAAAABUeXBlZW51bQAA\nAApFU2xpY2VUeXBlAAAAAEltZyAAAAAGYm91bmRzT2JqYwAAAAEAAAAAAABSY3QxAAAABAAAAABU\nb3AgbG9uZwAAAAAAAAAATGVmdGxvbmcAAAAAAAAAAEJ0b21sb25nAAABAQAAAABSZ2h0bG9uZwAA\nAqgAAAADdXJsVEVYVAAAAAEAAAAAAABudWxsVEVYVAAAAAEAAAAAAABNc2dlVEVYVAAAAAEAAAAA\nAAZhbHRUYWdURVhUAAAAAQAAAAAADmNlbGxUZXh0SXNIVE1MYm9vbAEAAAAIY2VsbFRleHRURVhU\nAAAAAQAAAAAACWhvcnpBbGlnbmVudW0AAAAPRVNsaWNlSG9yekFsaWduAAAAB2RlZmF1bHQAAAAJ\ndmVydEFsaWduZW51bQAAAA9FU2xpY2VWZXJ0QWxpZ24AAAAHZGVmYXVsdAAAAAtiZ0NvbG9yVHlw\nZWVudW0AAAARRVNsaWNlQkdDb2xvclR5cGUAAAAATm9uZQAAAAl0b3BPdXRzZXRsb25nAAAAAAAA\nAApsZWZ0T3V0c2V0bG9uZwAAAAAAAAAMYm90dG9tT3V0c2V0bG9uZwAAAAAAAAALcmlnaHRPdXRz\nZXRsb25nAAAAAAA4QklNBBEAAAAAAAEBADhCSU0EFAAAAAAABAAAAAE4QklNBAwAAAAAC4gAAAAB\nAAAAgAAAADAAAAGAAABIAAAAC2wAGAAB/9j/4AAQSkZJRgABAgEASABIAAD/7QAMQWRvYmVfQ00A\nA//uAA5BZG9iZQBkgAAAAAH/2wCEAAwICAgJCAwJCQwRCwoLERUPDAwPFRgTExUTExgRDAwMDAwM\nEQwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwBDQsLDQ4NEA4OEBQODg4UFA4ODg4UEQwMDAwM\nEREMDAwMDAwRDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDAwMDP/AABEIADAAgAMBIgACEQEDEQH/\n3QAEAAj/xAE/AAABBQEBAQEBAQAAAAAAAAADAAECBAUGBwgJCgsBAAEFAQEBAQEBAAAAAAAAAAEA\nAgMEBQYHCAkKCxAAAQQBAwIEAgUHBggFAwwzAQACEQMEIRIxBUFRYRMicYEyBhSRobFCIyQVUsFi\nMzRygtFDByWSU/Dh8WNzNRaisoMmRJNUZEXCo3Q2F9JV4mXys4TD03Xj80YnlKSFtJXE1OT0pbXF\n1eX1VmZ2hpamtsbW5vY3R1dnd4eXp7fH1+f3EQACAgECBAQDBAUGBwcGBTUBAAIRAyExEgRBUWFx\nIhMFMoGRFKGxQiPBUtHwMyRi4XKCkkNTFWNzNPElBhaisoMHJjXC0kSTVKMXZEVVNnRl4vKzhMPT\ndePzRpSkhbSVxNTk9KW1xdXl9VZmdoaWprbG1ub2JzdHV2d3h5ent8f/2gAMAwEAAhEDEQA/AO1z\nKcmvqNwp61ViY3pCqvpxDG+kTX6bbmv3eozbLLK6vT9NA6dTlU3+rl/WNmWGTtr3VtYX/p/da1jt\n23bdj/od+z9W/wCG9mi6rOflZjaK6TUb2PLnWPY/eKqOzKrG7drWJfZOqs3Fvpe4bfffY4CdvDHU\n7PpD/wBFpKSjO0E9QxJhu46cx+k2/px7XfmJHqVfqADOww0uPtJG4t12t/nvpfQ/NQBh9UloBYCx\npaB9qu4M+581e9/u/nHJOxOrOeXH0zLgS0ZNrRI3fmso+i5rvez/AL+kp0D1DAHOTUPi9o/in+3Y\nXpNu9ev0nuLG2b27S5u7exrp+k3Y/wDzFQrw+rVv3t2bpBg5NpbAJIZ6Zo2fne7/AAj/APttVemP\nceoGp+0WsyLXWtYS5o3nNczVwZ7vb+4kp2D1DAHORV/nj+9L9oYH/civ/PH96sKpfmW1WOY2kPiI\nPqNBMhztu130Xe389JTP9o4H/civ/PH96X7QwP8AuRV/nt/vQT1C/wBCuz7P77J3MNjQGEPbXBf+\nf9P6VaPh5FmRVvsq9FwMbNwf2B+mz2JKVXnYVriyvIqe5rS9zWvaSGjl5AP0UM9W6UBuOZRHj6rI\n/wCqVfqg/WGwJJxMlv8AnOxfBKzJymZgY61zai/2t9AkFobS7b62/wDe9Rnq+n/OX+l+4kpsDqvS\n3fRzKD8LWf8Akkj1XpY0OZQP+us/8krarZuV9mYx5dUwOftJuf6YOjne15/O9qSmP7W6X/3Mo/7d\nZ/5JIdW6UTAzKCSYAFrOf85Cq6lY51QtFLC/W1gtaSxsuZ6n5vqt9T0afb/hLEJ+Xk5XTshzq6/S\ndTZsuqsFjHR7I9v9r99JT//Q9Nxv5/L/AONH/nqlD6q6puKDc1j6jZW1zbC4Nlz2sr91bbNn6V1f\n5np/6RDfa5uRY1jy0uvhzWhsuihlu3dZ7WfRUsU25eGR9oPqCwtNjNhI2P1rlrfTd7W7P5tJTk+p\ng+kwVnFm+pwyARc5p0D7RU38yv1n1WP3e/8Anv8ACeoiC+it2Lk478ZttjLA17/WZIG/bDXfmV7d\n76bfofzVf5li0n4FocLHZloawD26Fvt3buQd27f+f6n83UkOnXeoLDmWugtdtdBaS2fpMjZsfu+i\nxrP+DSUwp63gGqsXXt9ZzGOdta8CXOFW4Ne3c39K78/+a/wqpYQI6tYNDF7jx4/bz9Kf++rcc2se\n9wbI1LjGmnj/AFVgU5IqzCRSXtGU9/qs26tcM0O3PsdWxteP6O536T/CpKehVLJwrbrLHN9CLGBk\nWVbzpukWne31qnf6L9H/AMYrGLkDJobcGlm6RtdBIglnNbns/N/NcipKcxvT3BmPS37KLMVp3tbS\nBtD3Ag47dx+zMf6b9zff6n/W1Z6fiOxKDU4VA7if0FfpM/7a3P8Ad/aT32141wtdJ9UBmxrS5x2m\nQ5rGe/aze/1ESjKovLhU6XMje0gtc2fo72PDXNSU5/VgTlVEfm42QTrH52N8d39VBzRU7Ie0Pa4O\nsiwfazSa37KhPpsH86xljP0e7/tRT/pP0RurmMmskSBj3k/AOx1cfj4xey00Vve4w+wsBd7m+nu3\nRu922ut3/BpKQ4efQGCqyyljWMb6ZZa14cAwOtjh36KHf9b96n1J9rK2Gtxbvca3RX6p9wMOHua2\nrY7/AAtnqU/6av8APZGu3HDtrMYDc8AhvpzG41+q5od9Btil1Mu9KsMayywv/RsstNILtrtglrX+\nr7/8C9uz/MSU5bqwR+jrtaRHpF+E07drvtFnDa/0NzWvr2fo7f0v+nRq23jpea+242tLSAHUfZ3B\nzG7NxH5/qbWP+j/wf9SdFQymMFLhZRudNtOU8uDDFtJ3gb/e6mj9Hv8A5r/T1+r6pD9oZ0e9mZW2\nlzWOa0C11oLY9k227X73fupKf//R9CsbY/IyHV+x1V24PDd7v5nHbsEe79JvQaOpWV25LjitYA/c\nSLOaGM99+1zG7dl/6H0f+N/0aPZj5bc19raGW1l/qNcXgHWuqr6L63/nU/muUMjGybJDcJpbYWC1\nvqtaC1hn/R7ne38xJTCvPact3TsrIc+70g+9rGODWBx3Nd6oq9Nvqb/s+z17Lf5n0mM/SLSfl4zK\nPtDrB6RaXhw1loG/2Nb7n+391UWjqoqsqsoFwc9z2ONoa5oJ31sna7d6Tvz07R1ANefsbRZBZVFr\nQGMOjdhFf6P+z/5wlJrDVl1iy6oux5A9N7d26SG77KdfZW79/wCh/OLCw2irMfUa2jFsy7K4PptY\nQXdT9T2uG32fzXo/9c/0i3GuyWsa0YUAAAhljQIA2bfzfa381UaOmZ1c3Pa0OtttNlTdryK32Z9t\nXue6utzv16j1Gf8AG++xJTXf1d2PkWYfT8puQW3RkPta6wY7PQN24+l9kr/SW7Hem7I/m/tHp2f9\np69XE6rVZgtybSSGtm6xjHBgI+m7a7c9rPz/AM/YxDfVlBgNFFld4gB5cwt09hfZVXdSx7vT/M/m\n/VRh9q2lr6TcHe13qCsEtP0mv9N+x3/baSmnmOuzXGyjeGsBbUxtzsa0lp/TPbo5ttbv0bNl/wDN\n+l/wiGb8+vNwq6nVVXZGG5+QLN2Q0/Zn01+m29hxbN2/P/pDqv8ArKtvxBfUyjKxAaqXiygVEM2k\nS1vsbZ7fa9356nZhUvubkNx7Krq2OqZbW5jSGPNb7K2jfs97qavzf8GkppZxtyLKLXtFbziZPqVn\nUgTRxp+9+etqv+bb8B+RZLulZD7Hv032VWsNrw0HVzH0VNDHWfom7bHWbv8AC/pVequyWVMa7Fs3\nNaAYdXyBr/hAkpycjJxMTDfdl5JxhTFhucNjHuDi7e4Cre+uqz3sr9T/ANKK3kdTw72W1spbmW41\n7cc0vG39M5v5rbWu2/o7d/qf9xn+r+krTPZ1F8Mfjb6zvD9z2lpY72+i6guex7fTcq+Fg5/T6W0U\nYxsqqcbqa3PbtY9weLWM3vts9J9lr7W+/wDRfzVf6NJTepyh9M0toe14bcA10uYQ70fS3V022fpN\njP5r6fqIOeauoYlrn0h9NYJrbez89hl1zKrf8JTs30WbfUr/AEijidMx+n6YOBY1rnOdYLLRZJI+\nn+mvt/SNc1v/AFv1UYty34TqHY7zc+ss3l1YaC4e76D93p7v5KSn/9k4QklNBCEAAAAAAFUAAAAB\nAQAAAA8AQQBkAG8AYgBlACAAUABoAG8AdABvAHMAaABvAHAAAAATAEEAZABvAGIAZQAgAFAAaABv\nAHQAbwBzAGgAbwBwACAANwAuADAAAAABADhCSU0EBgAAAAAABwAGAQEAAQEA/+ESSGh0dHA6Ly9u\ncy5hZG9iZS5jb20veGFwLzEuMC8APD94cGFja2V0IGJlZ2luPSfvu78nIGlkPSdXNU0wTXBDZWhp\nSHpyZVN6TlRjemtjOWQnPz4KPD9hZG9iZS14YXAtZmlsdGVycyBlc2M9IkNSIj8+Cjx4OnhhcG1l\ndGEgeG1sbnM6eD0nYWRvYmU6bnM6bWV0YS8nIHg6eGFwdGs9J1hNUCB0b29sa2l0IDIuOC4yLTMz\nLCBmcmFtZXdvcmsgMS41Jz4KPHJkZjpSREYgeG1sbnM6cmRmPSdodHRwOi8vd3d3LnczLm9yZy8x\nOTk5LzAyLzIyLXJkZi1zeW50YXgtbnMjJyB4bWxuczppWD0naHR0cDovL25zLmFkb2JlLmNvbS9p\nWC8xLjAvJz4KCiA8cmRmOkRlc2NyaXB0aW9uIGFib3V0PSd1dWlkOjE2ZDA4YjQyLTVkMDAtMTFk\nYS04MzNiLWZmYWU4NjQ5YzFmOScKICB4bWxuczp4YXBNTT0naHR0cDovL25zLmFkb2JlLmNvbS94\nYXAvMS4wL21tLyc+CiAgPHhhcE1NOkRvY3VtZW50SUQ+YWRvYmU6ZG9jaWQ6cGhvdG9zaG9wOjE2\nZDA4YjQwLTVkMDAtMTFkYS04MzNiLWZmYWU4NjQ5YzFmOTwveGFwTU06RG9jdW1lbnRJRD4KIDwv\ncmRmOkRlc2NyaXB0aW9uPgoKPC9yZGY6UkRGPgo8L3g6eGFwbWV0YT4KICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgIAogICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgCiAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAKICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgIAogICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgCiAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAKICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgIAogICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgCiAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAKICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgIAogICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgCiAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAK\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgIAogICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgCiAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAKICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgIAogICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgCiAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAKICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgIAogICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgCiAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAKICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgIAogICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgCiAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAKICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nIAogICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgCiAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAKICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgIAogICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgCiAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAKICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgIAogICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgCiAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAKICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgIAog\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgCiAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAKICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgIAogICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgCiAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAKICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgIAogICAgICAgICAgICAgICAgICAgICAg\nICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgICAgCjw/eHBhY2tldCBlbmQ9J3cnPz7/7gAh\nQWRvYmUAZAAAAAAAAwAQAwABAgAAAAAAAAAAAAAAAP/bAEMAAgICAgICAgICAgMCAgIDBAMCAgME\nBQQEBAQEBQYFBQUFBQUGBgcHCAcHBgkJCgoJCQwMDAwMDAwMDAwMDAwMDP/CAAsIAQECqAEBEQD/\nxACwAAEAAgIDAQEBAAAAAAAAAAAABwgFBgMECQIBChAAAQQDAAIBAgYCAgEFAQAABgQFBwgBAgMA\nCSAQMBESExQYGRUXQBZgUHAhMTUpEQABBAECBAIGBQYGCg8FBAsDAQIEBQYRBwAhEhMxFEFRIiMV\nCBBhcTIzIIFCUiQWMJGhsUMX0WJygqJTk9M0JUDBkrJjc4Ojs5TE1CYnGGDDRLQ1UNKkpXDhVHSE\n1XY3KDgJ/9oACAEBAQAAAPfwAAAAAAAAAAAAADzlrFT72k8adt2/Zpq9I5MjuTPr44tR3t+foAAA\nAAAAAAAUmgSvFnqy5iR5dkLN7J88GB0yzFdNixuEvf8AYAAAAAAAAAAAHzh80AAAAAAAAAAAAjqC\nO7+c/P0+DG633e1ycfHy/HQx319dnuufpYq+HN56fmV63z1urzd375f366fD0Ox3eTu/P51Okydm\nphr/AA5zdfo/Xd5fv4fnX4tf/Xx+8/38/XV5/wAzd7fM65GnRVk5BwWalOCsrLHUwuK7ejSpgNki\nLY5T5tS3ak1n+nVv0V7nF8fvJycf5x/H1yfXL8/HD9fP71/rp4rz+9M/Na73P3Nf6j7+tk+Pzq/X\nx9c/J9fPFwfPDz83nN6uefHoP81ThDb4rnKzVC5Sud5WyzuezRtuNX5emrAxxq+9Xtp13fyG/R0A\nAADzm9FPOX0f1CNts2XZwAAHmj6XUZsj99TXM1p2Q7Gh77lcdh+91cL9bf3/AI1LfO3p2xVTsPhq\nyenIAAAHnXJmhXT8ud4kG6m1gIcwkvdKM9t4txgmYMRIHm/6W0Q2Ll5sj9/vHxfXz+fX58fnFxfD\nm+36/K6znzw96XgPO6VY/wBDkm9VCpI1iFJevDyh5024qH6CcGqbb9ZkBqdJMvXG4khV19Aq2U13\nv0Z8z/TmgN/gAAAKtRV9aT6XANQ1PXNywMuarhdZ2PHynkg8+ttxF36Lb/EthrHA6va0nHbDh+DL\ndTZf1p+10C9FqCX7AhrUJI13RLU6ZGeZ6n1N4FUYUzOr+lACg8hadrGQvvQuVsBGWz3l5Q865b0W\n+eJjndcJIQCnsGTfpvLBfolGNTLgWWUBv9Qi+v0CsOKjHH9i3cKQPNOtYb0F/QVXjfcYK9NAEYaj\ngsrzTboGn9frd2bMyHmzJuKtjUKcKUyjZKfQNZ7PXiqR9C5shIHU2V5xejtFbw9kGHxmiy3H/W2T\nStu+tF2+NZ3yQqvGv1HvpkApPJMXY3cLf0vlLRtIz1zOcPN+UtLvtXPIS9o+Uk4CCNBj7j7+5aT3\nIA2iwFhaFelVDrwZEFRYe2m4Hm9vO0xzdzQ49ircbCTyKr6r0ob9QwED6RgezsVl4KwOK1zabOZE\nPOzYMJfWnP3qEtaH1rkbcEJ6PnZT5ebgjPf/AK/d68y/TSil18oCGZOxnJom5aBKfL88fP1chAsp\na/v8JVdnCvHp+AAAB5xTpDnoZoneifbcvpW6yCFSo52KK+TOcWZ61l5Xynl/6gUauPngU1h3n5en\n1pii+X+SMs5oW4xtmJi4ZLr5ukZ+kQAFdbFAB53zpBF8vPKcMv2K9TFrWvyRafMII1rjlvRMzhfn\nVd+mHveX/qBSK4WbBjMX09h1fm5tgwHW7mI3zg0ju9/N1r0GR6qeoQAEPyVlgB54Z/FX2qJz9vZY\n9kDozrHE6kDwtl5oysT9Hp9m2x5p+llLLj6FE+J2SyauNVpygGVuD87PbzVa7D3Q5ArH1bP+b3pQ\nABxQ3NIAolter3qAA/K84Hpz5C2k9aSLKnn36CUyuRVe1HBXifctpuC5Nq1DaMZluaN907/YzgVg\njiYah+oIACstmgD4oLKUa31IdmIAq7vsf5PV89v35XPcbdPPX0Ko7d+v8g1q7VzQHFygBWmB9gpP\nZvq2zsEACKJT5AHnj+Yr0kICn2u8ObX0NktWQ1HutfmX7mTlSl+w3yeefoZQe+NYZ9ztOrY58CDZ\nx/QBVzQsnWz08qtcXsABjqYRtxyHv9qx+UAysYenRGe36FLUPZjt78QTm8rAsjzh2QedPotQi91O\nJy0DH/lrhxcqv8//AKAr1WKrXoZwQdJOxSnOoAVqshytDpN6Kjr+eu5QZ6phWX60e3UYTLxctPIf\nmyD9wtnIgVq8R/6TaK3nrpu+8dKu9tDAZ+K5Ur3YQBDW27x527vJdWPTav8ASv0x2QAefsPbxPtr\nvML09HB5yXR8/wD1RCnclZmvHYvB8fX6Di5SNO7S70PolemrOFlmU4PsRw8HmbYTG3F1fcAPyB85\nLvnDvkdVy9JuLEaxIkOaR6TgiXh2DM7L9eZup2NneWut5ubLonqEHnffHM1yl6PJ4DHZFDEzkB8F\nRfT3zv8AQWH87rFFos9B6szNYnF67uMzAdGEZnyf1SWPtvoF6o2Yq1P3hr6nYTKWqCqle9MykXez\n/n3ZbRa6W3nzzn32IfTkKhb3nZPq5aT81CRaS6VrV+t6gWemvQjPnnP6V+fHoBFHQjrCRZZ7Rue2\nkCVKnaxXd2MUXyd1VWp+pptWNqL6Z7pVXSohsNya3Ynq/uva5I1guGrU0SHRThmbnzU1UM3qI/RU\nKsajt25VVvj5h3Tsv5x3kj2vV+uvA0MdCzMx+c/ox56+gcHbHJ9QP1KcYXAozA979Rjy8HzWj6jW\ndJWy/X0um1pI386bzZykWtXYlXTtukLb+35jzVZXXor3zHWEptpnoPpHW1msNj6n+mQVi3D8x/h7\n6K0zu76A1Btz1ta0/Vtz5u3JkfVYv758eglWN14pzrjvGux5MEp99UWaZKr/ALVI8PzVG+357TaZ\nWZrRjZtymYg3c7F7iGoZvKfPkdZOWehX/abM4PWoXxe+Qp6gBEva1rI9rzthT21gyTq2+I9uPQOc\n8pgpsj6QfO70R8/78QBv0koOj/celq3JbJDcyViliRMZBc75Hg6uR887FV/gW9XRs1pWg4n76U3b\nWDh6/eI2jPvVHvzTOV6x+q4V12LP17lGr+tSn3rm93mQLNfNX/Y5mee/oR532QiKa+T84IejCzkW\n6BYrjjqWKpWuzsRp26/a++fzfv5FdNfUbYdHkf7pddX7iLWOHfKvSPOG8AOvEFMbF1T9Tfrk/fmG\nNA0HdO/DtgIhy+xb3OL8g7aIrsTlXnP6MYKM+XqcvW6OvdbucmY+vvXsfyZPpdPu9Nhuh0+5db6o\nNzfHW/eDFbPkex3uF2+Lu83N2fzj7vY+ODtbRIUWQV9/fR6fPy9XtfvF2NY5+BnP3i4OfofXN3u1\nfoAAAAAAAAAAAAAAAAAAAAAAAAAAAA//2gAIAQEAAQUA/wDFfaO6uLLV9MQk1QbLdDAq/h3Nq5w5\nUGAjpIraC4pi7N0rGC4PDtoa/RSYWMA/WdEmhWISFKe4G7tTineGsskdexv2FPH8/wCvx/DKxJjD\ni4JGlvjSQmKVAX6Z21x/6v8AjjP278wpIk/QTHNV7DyNPnSi9kulc31mu0cwLmn1wT2IUsMW/iC0\nqKIrTyfcGo0Ly7DsfUDiGQoRgSaozJpGMhmO3HtMc2gysycmYFMEBSIw699e7RXVsaYnPBlf3Fyy\nNZKQChRGkkkw28j1hiN/5xbJaCGued88/wDwnbXXfVgH2UXav/CpMlmO4cYsX2p9tna89RtNcXoq\nHnXS8FSOnna69TU+mbzVD122vfT3XLp7BKaM6Xh7L6Qd9tPZBSbfOPYpSvOu3sOpfrz/ALFKV+f2\nM0p/H+xKl35t/YtSzTZV7J6TJNN/ZzSTXbT2aUo348fZlSvtjt7J6ZctuXsapn25a+xumWfOnsTp\nlz26eyKlvLPX2cUo54Sqk65LnOMY39nVX9nfj7OK2Kemnsdr9vz39lVcufmfZfWjG/8AZ1WLz+0W\nrufOfs8rP0xy9l9aeu/P2U1y7ec/ZNWzbGfZPWbXPT2S1n02/svrVnzb2bVnxjf2iVq5419ntZd/\nOXswrN2819l1ZNvMeyCtOcZ9kVZ8edPZHWfnx/syqzjfr7QqocMbe0qmydXr7P6Pb+QvPUV2DHfJ\nftPAMCuOfZLSbXGnsepV08x7JqV50x7N6RZ8/s0pL+HP2S0q6+c/Y7TLpn+xumH4a+x+lmfMex+l\nmd9/ZDSnTO3sqpRpnPsvpNjHb2m0p5d/7SqX/jj2lUvz5j2m0vzvr7TKYb66e0WmXTbHtCphnz+0\nSmP5dvaHS7XGfadSzXTHtGpbnz+0amGPBv2QVQLyfz2Z/lUB+1bq7b6mkU1Ei8fG3313Fj6QIqIa\nHW1aqfavxFGVJ4xRxuL1KkxLzheHeXjOZ0yeJEOSSnMWvzHH0LvrR3F4PRlB6irtGyHj0qx2AQZu\nrRJ6YQIaXSCZJomr08K+gjVxMv6hEBijriy1IuOXGb6ms6hO3RMpeOApFa1ya9K6PhPiL4zx57FI\n3CEFO+J2nj6t8VyyolqOfVi1tXOpXFrbE+ccuePN0aTp5qgQa+c0KLj5hPwxjOmmcftk+M4SpceZ\nb0GfNmts2z/jm/O2qRLpjVOn0x+XXPn6fPz9sn/NhvQY8/YovMNzfjbZAg34/wCFZ/1sM7RjK4WG\nXTbeOo+6a+tdClbG7xuFxQ49lX+l4e/DnEMT8tNYxjXVOogSC1m2a7V+2zmutfds7V6gLbz+PsDY\n80i6M+emYrjDO2Ypi7bzeJ4kz1/09En5cQ1EGNOcOxHyxmJor2ziLIx12/1fGec4iuMNc4iWKtfN\nobiHbH+mIe81hCF9N8QzD+uNIiifn5ewKFmKU/PYeOrn0M820131gFX32Pgx+hxjpaHOSiPjeXCp\nMSNo2dvYBYuStXreOSs1g7aj5NiUkNs0WFWqI7bZUlyYx2Xo+L56lU3il1XTicBTxGc0vcQ4gkPM\nw+OrCErKEzCODxKe/wAnSRExp7R2IeR0ekmZgFwObeBxxIZecoj4RCWjz2A/j/DhYnZeNIIZLlr/\nABZ6q3LivqF/yfXvppp136/k6xXnXPsu8GT4OMXLtZiGExnJUxRrECYOMhw/Hv8AiXq/U3mzy+i9\nA2R9id4Pz5rOUK74Ry3BiTdU7VhdiIlOa/mLPpPNR2loX2Vqs6a5thV3XKCVqKpibFgqzd3PWx8A\n74ZJmrgPpekhVRcGBskqrrOwjEg1MBcMhdS0bJjOT6WH3TE61m68szdXpat3l+vSh5LXGo8hLU0k\nwYnU85Ghng4thBVsdIFVhYERLr3TLDzxUkVZ3ouq1H7JIKUI9SuOulUP+T69+vbtxjNYGu9l4iUN\nfb2ESIYI4/BIv6zDBmXJBOju4zPJrYc5C3fg8D32JLsBDsPqxG0lfjnZSUjiQkazsPeioss/AYK8\nsEyRaTMQdMceyQpKSodCWBFcWsji4bSQA6iBjNETR8ubnFC7oLuZ572D89gjK0lEWJ/XpTJN5n18\n0y284UApqm20opT7nnWjFQNMYo1UPXG1FahbeZofT/PPnRKoHLzah9PN8c6G07552ofTzbGtD6d6\nefwLp1+OaE05z5mglN8+Z9f1NM439fVMumP6+6Z+ZoDTXPn8BacZ1/gJTfz+AtN/xxQanGM5oNTn\nOtqaS1SA64BrWldaPVeU5/016odeelW/sORZLUdWghjcUm8ahoP7DtPFUzyiOwQcLujvbThx1T8C\nEulKPrKRK8B1gWeBwhqHK9vU2H8c1zOVCh6tUn46p+Hx9euumycRB3ITJ4cR81nsXfejFyZ3dWN8\nh0slOK43UuKAdceTU1jw9z+wea65CClTutoy8ppkG7JC/eTg7azL20OUfTnEoLIAqEzYbMpnnGM4\njNyRdbEtw5Y8hrK4kxOpsUkVpFya8+6fjP8A57F+meUQf8m7X4fxNayYCE6DUoEo8YYF9Vu+/CvH\n2GsGHmcqGYWCwRjjOvrFG4ARxCBloSXw1gjPmxJ3QNzNHo6wm41D4aDMsYwGzRiNlMLx6aR2XxMv\nfzVmRK25q+NAscMpI2kE4LbWRp+ny9gTq1Nr428IjcGSV43Ho9KDEAIWnkCOSpIuth8lX738PDeR\nI7jxCpLIjTByXqIG6PqYRk3vJY+xTHrIOHoKZNDHG0bCLmgfWR16o0TLorRMjMgbn6IYnKeI+OD4\nmz3A227WU89jnLfvBnzlWVVIH352J0bAotlMcF2YQmB2NnMrsi8CpH5yOGntIKqwjClFiiV3cRi2\nO5deioqZJlWE5T87y41zUlcBgsqevygWIfTQ56uVXNTBn2Fs3yRGtmQHQ1ldLC+8kp6rtlmpC3gy\nUJIeO1mk3LbgnfbByLHNlY+VvMqJIXTHLRAn8mz5LAsqyUuQWG4888uPx9ePThs1A62Uv5LRso1/\nsI86MTR2ezqBYckx3dg0QexaPonjSKEP2LS4f28vM4peodi+uBM2tJaPBEPutXTNQ6EAkaNkiRVr\nMybk9QnV9hV8QqKK+ysQxnVp/eOwF9LKqkvW2vnse0z/AB40z+OnylHD4BzFGbcQypJcLw7KjbK0\nWf46JJUkKt0gSnJcSE50VCBjEbgdWcL4SIh2FH9Qyn9cRyMZXh2QGjq2xhYvXONtfld38n8TmNd0\nDvXLTJlFGWFfVg36JoR+w2xWxoTGKoCZYPFIxgB+Cotkat4NJ4MaRIZuUnNHF0TtbVEw63HMR1+H\n4HGYphUpABKS6vx9KsUGcRnSuTB5O9pGL4+ujCfCKECOLSSaAxLwSexGU20neI2jRyxCBOFuHFND\nzg2MTo6vhhzffXDAYgyjzJ8yAOGyla/DLET8nMOFXl+cKwQK6lJvHgXJDCzVtg5gQiFeoeAVQRB8\nbRyqHx1kFGppERpkfvpZH8ed4PPY111T1cRdcd0fyRvzWvdzM1HQBmBpxEpFVLViduRbywF6Cz5M\n8djkpbnQzzOzOeYzBFASdtp2kPT4WjMUiydh2U3Fkk4MIY6LbNgAgTM7u2EDR8Lu8/1amjJimFPX\nrQVwK+sLeqtXhVX/AOwvtT1CbRDZPKEktcQyXORHWRmuNqa14MZYO9J954315/yUfBOz7GSyBIKa\nGSycXCEMW7dVtczSZpH6WDS6qNE3x9cmmuGeJGjbrZIfU9OfswcECR0QD1U40YHorrHGJoUcQocT\nE66BYuWpQSLkYCp+Y+rV9LIzPKKc0qWng8D4XTnGAIvRHi11zB08VRK30lU3LSCq0yqTI4u2QJU6\nybc3yGJSAexTN9dZJRqIYCDbgct9xUOvO1fnsm49e9TWf/8AJ+RdK47CUtuMvLJfiWr70xh/eRd1\nnOPl8VSyNVQLoxk6dSl8MHc8jUtDzBVVmIiodfGayeOiDg3SIHT7YVHJItHFfCMLmnrPdc3TtpGv\nwu9w7qalRyk27+v+iykyXgfqa4J+NfPsbwi2vJdB8EGNdgSHIVlphgSVKmt0lgBVFZkksQg6LOqH\njBbe4HcCwG51zCoSjaa2ONJ0qInmaHzKLTjhYlo6ufdq+Prt2xgeg08C5Lmkf30x7PyFny/sjRCb\nj0ltznRz4Bk1zQ6u0aCjy1XFhGvkalyhoJ/9lIzQENxyRxP4yhBQ5KLo1VKjgcVEFbxsimEvAR04\nV6hDHofMog0sJATBDKWO0lVujSUVp9GwxI4mMRuJCLlHkcCMWD/l7d+Os6+eyDbbFTWPH4MvylGf\nIih9xH39jK2QNOBKQWgbMxcvayufYjCWMUOwk0Yo/sRDkmEbcSj7u6sr4xkSR1IWNi7qSEfbHtE6\nsrkk4FQwqWpnZsWL9bWQZu7k8mR6FrDWdIjjpCPETCWsltu+E1X14/0KfWdT1ciWR/6olmnaBv8A\nk+uHnyyMRpOcKvU4ouCbh7QfEQC3IZJGg5tGEIFXQUCHQNiVmBJAjmPG6N242iMxfSyLY4ZImCPj\nN7I9nU1EUnyzEaZ1DC2vL+3zhZxrkR9lybmiuxvYA35D64rI3+005GR82y3J8wvxVpBkkDUgCTI6\nf5pq8vKk6uVkvPYz1241PFs9thj5T71NUdgGqYlkV1ohtKW1vkcMZSaPtYwIRgTDTzulP1UlnkVE\nXHvX3EozFX0QY4IlG4QWxSE1DaySRyzIJKcaRPES2FsH0tA0YOFbJnVsLeUC42ZSAWSxPTwWppgq\nQZ4ZkVtlnJvrFFSJxJPWxS3uwuwR6wuXBHCn3bYET4KwH9v10d9+gYBk23Gee/Hl/aGXdnJOKVYn\nktKX2appORGR57lk6EETBNyM5lIKIbJNUHkDqWz7JBxLEwAdfSO3EnNHazD06seg90eerB9JVht8\nPiweq8Log8fr0UdS4GjRkAXqSq8jEmrpOgsIlXR2h0v4yRIUWy0/u+a3ErIFw1DiiL+ra2oGdB5e\nJNvpZTz2JafnqgNbfmHPk5YZk3jgsDVjV0f4/KGTdQ0NCMiVxmk1VEsdg2o8Ego8rSdW3rxy9guV\nhcdRwIaERGED3DmMRacOP6HD9dY3IHDxdEcVuj4XxrHkgcWoKEGNDs3N+y66q3dBVCs4EhkKhlb6\n0CVWgT1W6b/6n+7YFlUEEIMLno9sf2vXS3/swuDn+Pktkn9o2T+zB0R5cWxoqAyNEVtNPgUiLgas\nqoLSoa0iTFY9RXaa3UReobNhgy71xVO8Unwc1yEDj0Tu7dz+sulclxwvWWFL3sI4/wC9oSfYgOXw\n33hwqdzaN3RXL8oyTN5/MYWxTHOT6qq6nsMrKRX63f5psT557BOP6tWm79H/AB73KQk3tPCdiA3G\nHqwMgtIy527r209fpKCRhJZgOXr/ACcXSYPqxmpjo8l0Nwb1HVr5b6Y2/Ke0TfMCZgp9Ayloisw6\nwvB3S1AJH0cncpvnVFiGKtk7c3Fevbjv0+Nz8fjVSkW221R1X4YTesFTp3h37vbjzUcYBVuH+tvs\n/wD156/sJ08QxI1SwvsOUYz09if3c4xnCWC9+0EpIrm0yIyCHZoYSuOAhvjYEMovmdlOG2rj8bSE\ntqFqhFZKrUMG8nfW5fNJiY/L+bc9Kx8P/njZKL48duXHhwT6KnFvRdZ2FW0wXMLaoZmTw5jwHkxl\n5QtFCcAZIejYfaF4kMOjAUQxGZiRcgoV5PquMY/XPz+HjRQtyLj2xPIleYZld02jsGywuYeKvL4i\nGR9ufPjdPptyqlGUhdoeodEslkZ7x9VvfbrE/wB79+qjSxn2em2NOdAdUimDa7AEIxypJu/LPsf+\nsQuzy+dPhn8fw+FjbDKa+u/+2E6s7r/KcrSy3sliG3WN+suTQ6vkonM3MZZBp89yTHk/nL5GcKx1\nYEvTWAh+XZnk4n+l1+u/GWfPYco5cq1c/wAf058RLCjyKSJ1K4xS92+RiVCxO4gl+x278E+v27j6\n896udGBiJfXJUN15q0dFbPQ3AcMANnLDy1Gymwlk24hrTI0iyxG/3JSm2NYZ58e3JRx+ec4xj1w9\nOneMIJwP63FkTh//AE9+sY9sjkm+Es4v4pIqhmnia42em+2zigNRK2TEQQBKEyGan6yKDEZLIMfV\n3UxfM9doyLogSSjW5/Kpal6KV79Mkmw85TS/w1E5fB5DLgj3P4szFtgJMHorh4hiaQvpdnH5pX89\nke+/OtSbfO6aXnx0jeSgoZTBoovXo2tDIspIDsgFyVrMGH52U3ylg7Gc5x9q7G22lTjLgKtlIK/t\nK9lmH1ogIEuGScnGwIcnSRw6QoUSdU3ZL9t3eGkfbCyTXGUTdsS+x1mbODV7JWZ9ELVHIsojeTpu\nfp3+Gf8A69dW3T/SFcGgVa5jlR5To/aX9ZIjzc14jX/ZsMkwcEnZq87TDHzA6TNtvrD8U89OMXfW\nRJcJh0zeZOWi7CVyFwFyyILFn5usfpfKOUlJOqjsm+V5O3flKPnsk5Z61jRZ1yjckb+S2AY4YBGj\nhI9ddiULfB6U5NLIKfSkUGfgn6bduH0tKr04wJjGMY+wZ2DQtOx9Il6H7y0JDN6etWx3CQdWGtLl\nXbsbesTXTIHMsqtBnIwzqJSvKlaX5yf4P+2dsLLJU48OHFNx+khx+PSGxUsIndukf4K+vTgk9Z7n\n1XVzgB9GO81TVtpy9qfxm1tTlsjjp4VMFV+SMieIJXtPF3Y67OXV3gjzXvy26+WgCmV6dgeJZf0j\noZ1kKZpRjutMkxnH8lj3f/e602e/+j/GTZ3dWfk7zVYOQ7IeexbhsrrVz1/JpJQGGmc1E5qnBVQs\nStJgPkRE7sqiHwxKTvX15lQ12JvIwmQKlzn4eK+h3LP2JW7u5F2Dtwll08u3LDmtqe+tzevo5XmW\nF8ooPWLjHIRznXXD/Jru+yjGsyNsMKBUxFjhq+1KcautlyRUS29bnWLbdzeVpInsSfycyeOithja\n93wVfj+29XXX8lYwCUkchdJv5Z6+0r42Q7irmSs891wZWvnYODOu5bLkpkUN1+No8CjTz9PT9TH4\n/P8AP0/W+sunnSOQSMAVNG4Lejmm1O/PYr2Scq7ccaa8SxcoUWAeXeRo4eosK40ZQPYhYNcVkJmB\n6jPzmpT9evJxQdthw5JJG15Rla59GwMSk+BVCRUnXJRYGHw9b89ttddYa7ZK8xoyMitb57JmB3ba\nxv8AwYutEKFCJhHrrQCPjIzXpKwAHfd1riyM733rh/13yt3YtdZunicnqGnnf2P1iU8Wb2JiR3YT\n5Tu4HTTDsCq457xIcixWS8HwKECfbTTTnp5dbQrGTMw9iLzHxvH1scyX0E5rBCp68W7flR+tzvx6\n1QqdxI9C6a9NOfs9+LKkcCaXWToMrkn7dPjLzXn98lJI4Ay9HXJ8cXqPPi5O7Wz6fSNH566nH1d0\nvc6nmbkXJuza1UkOZS89m2fyV1b9vzoGltYy+RuseODbs+IDPbawYHFM/FtLTGaXFwk6AM9I5ikg\nGihjmBc3jlao8jFthqKueLLdnB3Y5/KFEJOnNII/Nzc29mbk6U3l7zVlbOLLprrpr57GFKZNTCdG\nwM0g6mvIF/yNJTtx2kKM8kTBN3lphV6VAQiNCwmw2wsfxcbU62gqwDtUjS5XQlZakSE7HwL8coye\napYW+rqGOPVdRCzgYizvaVuCImm/2auRn5fpZ3QRpDTyPTHCxjUSM39O/wAGydDY3EfYgFybOMZx\n68Ei9HCFeYzlGOzyfeXfh7HvjYOJQUskF9RqkTtGb+R7kD83rXVm6DxdpLbGxtA0zvr8zDDRGkoi\nkrsvjFYg6AowH7E2mm1vmaPrWHraDSIMH6HyFeuhK8fR5Kx9hYA5cRCoVniuXNM84XO0o+eyvRRv\nX1L+P7WJc9N+8hq1b4RML3LqpdLq+Op9GKpxz0cY1gyVOZ042Ar1ED4Hzm3fujLyXbNwnBqtp9jN\nSUb9Fhzwn6RjSQAyOm/BgJZIPgRTIVSdOpNBAo4kf0nPsXiSsL3eugn7MeH69L5g4yi017qyZmxI\nbUAjmPz1QDxAmDS93PgQf8me89WI/Ho7JpCkmuEU+xarBbH9ciaCK+wguvPVVveo2seEF8485Rkg\nm02S2qUdujxZ9nw52yAg3ElSlKBzH1XI36RdB3ijhyVJ00DSK3hLsfsI+UeXDGh/fh61ly1dUSQp\nVIgibrVtfN4r4wJsppS89fu/XMXV8brKIS6wrWldb3/GbnAtXy0pTEjI/BcqV+CO+tna8dcS/beG\nVExA5m1Hg/IltRMCuM1mot/unyP9nuU7WFEmxwE9W+x0ckidVKa8jmDbHHvySpW9nb0swnRanNSE\nwl1zg6BBpa7dBDY3MvLdsixPPPnstx+rX9LzxxTCBIwhzfzIYrkXr378EicBLxF/aZAMH6RmaskX\nxNFZBP8A3z3DpO47FNovLH0FiWyZmL+paJh1/JxuRxZjZdDOekzwCtcUTl5ttrpqvNSeVO2sT80b\nXDcfj9NWuJlHMvdur+y8HvxUn1Vpo6VY3H/Z6pX8qgvBP3jyD6xzg5WAb6WsTe4q04FCyrcfYIrF\nVlngaP5DMKPU4sIMNYN65qpBSx8rFBKBpQMM/CDgzZs+IIxyS+6xnGi4eMEpGypCNggWTa7NSmQZ\nLhmenlvBSwbSOJVO44sxeOGW7qL2AY5kTNPFu1WMDKmHWa7L+n4Dfq5y4ZqivbkbmnaW58FwxuVc\nVkwH1jYojhN66H9uegs3khHwk2x7hlsv38ZmAGWRpdQxI/DKBe1z/wA8pHqYGRRcyM4+B2Ohs2hv\ncLtlWs5n9N63q5cIghIifUAwwUvGXlvDuoqMd3Rcxo+CJxSx+oBK4uzw5xtJBe4yQ5DjeFbKZfeG\nJ5hUEjlojiNm5taRlnjhuWdlt2+fRKbeeydN+pBPPb8/OGgdZ3lkDGWQ3ByeMDlwbUybgiTSSzBi\n0shMG5A4RJ7rwcJNhPV6OpWPJhaQ9zanJI8tf0TxWNZmdihuPBgtVKk6JOtV9p1wwwuGMZehbu/B\nSe8O8ll+nLg2N8e7rCFWXvXYeHU3XPdMk2Tspp7Ns88ValXo98IKoKsgZwHPXD0/OGEK6Qp1dWWM\n6+rOj+7xjFnFv4SCasnEjtrHvcaLtyJR8S8ACj5kRMjM28fN9dd9I1Mo6jU3O5dRSOJcquRC1Z3A\nLFi/azEez1JovQVS0BNb3ybIuYHPaRpGI90tetn8mQEAtYA9psz4XvbKRoSSSLRcOX8+/j24YUTr\nHr87ED88ZPjCQgV+JWs0l+HQ2Zx++47KMkRlTrrJASNiZIMlo/bp34s8AxOx4YAS9aWyS2Ke9cb9\nF/Cu1MpmaQUwnAoGUCQE3b1x8FKyRMWdOb9LXhsxZLlOMYxi+arHIk89lKLZXXJJrrokYnx7j8qj\ndAScOf0lGPuZeQyzExIhjU13EIYhOska7RvHMq89g6ysfyl2jVb9Jc7p2Dv4aKEsiH5s8PaVlxjG\nuHx5bhxlBFfceHmlDu2tvipNxWJmhLzQtnns966casTulVrq8UIRgLIN0qPO4pFhxyRRXFMXRwYO\nOydPwScCeL42NMLa5x9+Z/lEUr0yopJsH137z+UjCsTOg07QfJSmTrODa1tjKh+shw9F8rohCEH6\nFW1bOj+NNsnWX4TIqiqPxSNQykTql4lh2ulbmdW9VdO92vicGYkCTpCW/Ho1lwoSrSd6RaRJMb9J\nL6Zcpidx2rL1LTbJUUShBxWnVWAukvWLPG1IkZWxMpTrOH0nsWUrGVscUTw3LFiVvSRY8NkgHMaO\nsmvzj9L38dNXzz2cdeaeuiW0lbdk7ZZmvLdP38m68eZsrXvXXFl68Z1cJ/ru+Ncj2KhYar5ZSeIM\ncozGbDVmZmGcymEpVRRWTNw+b9rhVbT773Hqrp3naxkAEcOdLXVswyj1k6/7hDnNNW3BfrYuvm+8\n1zrCr0xvFg4aeS/lM0Qd/NJwhnp3xMcSZxiWom59NJWi7pp7OZmjpfXOTRDtIsMVOgOQIDCvVtFz\nKhQrxoZeiZzImBlbxPPN7ef3yLz90lzvM8Yi9jpR56ac9PCyCYsMVmkGvzIh20tANcygPeJEZTGn\nBKs7hvG1YN0Hj1sInv7CtGkX8MwYINi2gLT3Rl4xHz5vK1s2ZKx3M/eo851VJt8/q8sYxvpnGOvL\nORdGmejCLQQNXsr6XRpG5KEG8XJfC8invtu+Q4tSzgNgjonO0aflHDGcvzivt7IG3+OthXhV25xn\n9P8A42xEGuRRzlRUj4C0bt3Z4r0ysbMOoPpfbfXJX4Ri4yYNeK212x5tXWv2+vGs9dk+2K31+xv0\nrHXbrl2qjWl847Unqbtn+DlRPzIaVVKbumtLqlarOdTKvctsVRrNjGaq1rzzWUrqcvVb0YqH0340\ndqRw31plUzXx1pFUV40RUUp+3redJKjc1mKLU/x5pRWn+mVnr5potx19dFL+vij1t0rUbIvXRS9u\nXaa66a+aetSq3Hvn1vVkxhZ62awL0fL1o1fT6b+tSs3TOPWdWfHmnq2q5y7cfXXBibCOgcRt3LjR\nOOUiXSkMf6896PAm23OjwJy6daYjnfo30tH2vb+IKfHXnUdNy5I6nJ0HXarW36aerW3DTeq/b9JB\nWx8btO1dSHvpvXYo6bpa3lHDzpXYk68IUgMWg7H/AEAO/wCwzpWGI7F7a+tutXPOvrerVp029cNb\nN/OvrUrX2039ZFaN+vP1m1m5b6+tGsnPqq9YlWF+v9adatdOnrWrf186+tCtXbfl634BTeKfWBB6\nzZP6zIhR56+smKO7ii9ZkXN3nL11x/x549dkfZ15euiPePmvrbizR17euSOO/Hh6145TJ+frbAdM\n6euMG568fXkE8tGn14xUgK//AGr/AP/aAAgBAQEGPwD/ANlSWFZZzKk4cprO5MgnLGKg1HI6k7gu\naejj5dMKxbOsuy/aTfHHI8y7wnIZ5bLy8ySAonnAY34XvO2Rfzpx81NjCyW485V71V0Stl+fJ5kA\nkHJ913u77ofP18ZfZx7GXFshbRBljtI5u3IaVtYIncQvoXVNVXj5YImyO7G4LfmZyvKUj51EuLKw\nbQFigKbzCK+yTyn4Qk07WuvHzMVHzE7xbkYZilPYNJjQMNl3PaSwVIveVA1jJKiYieCKifm42W27\nyne/c+o2ZmYgk3IshZd2cm16RumECivgtUyJqjP6Hl6uN4Li53m3YmbIbaSrZdg7ptmSDMsVAM3d\neYv+mFa1Rs92X0rxQ/MPfbjZ1b5XV2t/R/u5Y3JpFOokVAq50QreT0RdddfHiFWJi0q+EbH7nJLC\nbGlRwtiQaPy/mnEaZzVXXzLEbp4rqno4rbeIj0i2kUMyMhW9D0GdiEZ1N9C6O5pxOxvHsRkZjbVN\nKK+tIUWZHjFZFMYwRoNh1TuPc6O/ROXgnPVeBCcRozmZ1sjPciE09Ps668vTwVe8zQH469Sexomv\nterl6+EVZQURfBetv9nidazzJHgVscsqbId4MEFive5fsairxjufY73h1WRRUkCjSW9B470VWkCZ\nmq9LxuRWqn0pq5E1XRNV9Pq/+1+S+Hj/AAbcA2zgRLG/dkEGxLHmzGwRrHjjO1/vXenUicuNsN7P\nmTbiuM0+zFEKnwzAcdlknvOYUYoWSDyHCRrNCE7nJVXwTj5gttY+PVcbI9y91ImVY0L4wFGOrOiQ\nhild4DVOtidvx8fVxlGxl3sXhmPxJ2BkxmFkAMqQ7nmDEHHH7lArohERfTy42j+X3J8GwbAMa25v\nEsF3QgW3euvZkmN3WoESoi+9f4ePscb+7p7dbL0u6tDnJlg1VhlUqMN5YwvKK2UPpc13Wvbemi8l\n9XGw++O7e0OP47jONUk6ly+FBsRTY4gyItgP8IyucurjM4+Y7ZzJseILFX397N2etElBVkqFahIz\nsjEhXKH3re5z0T2+P3G3MpRUORMyW1sBwAyQyhpFlKNwlQgVVvoVNOMrVmFTbKN+4T8awLIFsIka\nHEtbKU6RKmmb5lDowCgiOVOyTr6FToVE55xLsZ5rTDAVGNktIskxCpMyqK+WchtFXRBijEir2/DX\no9CcWL4WCXLMnr6Dtbc7q45ZBr50OzO837NII2SEqAGRAl0IMgub1015cWkrNcWTcK6sMjqJ9JuC\nI0SGOtix6yOAug3FQo0DJGYnbELQnc5/Vt/Hy3Fv2TFcbnQty3kkiKzK7buQywzPaOQnf0eEheuU\nnJX9tfTptgUuzNfJ3IrpuMxcxCqQ3l8lVWjZUx5Hd3sm7g2OVeft9Sa+jjGtu8RqzQKKdJiVs+yi\ndhw6qrgtQvMch6K9HoFoUREcujlVfr+YXbuBiEvPqPNrkGR4BZPJUgY2XYeWJZRFE88btMCYbije\nrdVV7+fsprnWC4xFPtnRbkXySqo7PLdGNQq+uhpqwddNbo6dOApOgWrNFJ3eZF12tzymxluF57Q4\n06g3DdYTIBKuey0NHHNeFkKUchHQnCWZGR/Qi8xqurlRNlcfTFZVjmeGY1PhXsKW2rmw51kRIqL8\nQYeZ7CTHMeTvhKpArr6V4YpGowitRSNRdUR2nNEX/wBinMcmrXIqOT1ovjxGpaCvFWVkRFQMUKaI\niqurlVfFVVfFV/8AYuLk25mUxcRoZs4dbFs5bSuG+WVjyMF7lhFRXNG5eaacuNE34x/X62y0/nBw\nr3b9Yu1rfFVMX/N8Nem/+J9L/ur5l/P/AAONWb/4g/l1ezN15fmbwJ59/sOGw34T3T2p1fZy46V+\nYLEEd09ennF+76/u8IjvmExFqqnUmstycv8AccOmSt/8cONq6OFAbLnm1/4iJHMX/B46W77RBO9R\n6W+B/wBLXM40bv3U6/XX2zf54ScK9N/qPRPH9msdf4vKa8d1d/KNWetI9gv/AGXhf/P6i0b4/s9h\n/wB14VP6/KdVTx0hWi/9j4Vv9fVN1N8U8pZf904a12/NQjneCeStP+58dZN8YxW+qNSX0hf9yGue\nv8nCNbvK4ir4aY9kDf8Af1zeGlbvOHVzulA/CbXr1+zynGv9cYxe10+8qrROf/VeCMbvAw7mN6vd\nVNq7qT6v2ROEIzeiMrnP7aA+E3Hd1/uPJa8O6t6AC6fHrpbtP+wcMa7e+CriadDW1Vy5V6vD7sBe\nNH70NXn09TceyJ7dftbWKnCKPd2VJVX9CtFi2S6p9ft1bU04jTYhmyIkwTDxZDF1a8ZGo5jmr6lR\ndU4VVXRE5qq+jizp6+RmN6arkFASRVY1PliIgSqJxROGz2ma6aLp6U5cKKJX7hyyM/FGHELN7mfa\niD47iUm5Se109C4Tca6/mCqcO7tbuIPo/E6sNtU6ft91w5naz5VZ9/TD7fl/zPD+lmeP6F6fZxG0\nXX7Pd8aI3PFf/i/3Tsdf95w1WRNwHdf4aJiVj7X2exx0NDnyO10RFw+25/xB4f2a7cQ3Qui9GHWq\n/wDuuF7ws+jPb4jJhl1r/JGXjRz86Zp9/XDLv2ft/ZeOlpM6KqfqYbeL/PFTh/THz9/R49OH23+Z\n418tn7l/UTELPX/o+Gq+p3GYi+OuJzU0+3nwxEi5/wBx6dSh/dKx6mp9fsafy8PaxueKUTugoP3Q\ntle1frRArwiNdnaud9xn7nXOrvs/Z+PaJnQ3KmqDdhd9qv2aRFThE72cq79Jn7l32rft1icJKcbO\nEidztOl/ubeINrvUqrF4cItjmQDtb1LHJiN0j9Ps8svDFLbZexX+DVxW2Rf5QcDi2WdXlQ17erzU\n3GbkQ0T608or/wCJvHu96kf9tBfj/wCkrmcT8r2myZMoo6qctZYyvLSYrgy0EMyicOSITtUYVq+G\nnP6INPuzuTAxG2sY3nIdWQMqVIfH9573tRAmcjdROTVUTw4cq77V2iJ1J/q239pPq/YuHdG+te7o\n+9/qu55f/gOHPTehOhjetzv3dyPRG+v/AOmcO03mOvR97/wrlPL/APKOEX+uSRo7wVcUynn/APlH\nHsb2B0/WWiv2p/LXJw1E3njt6vBX1Nw3+eFwPXe+vRSu6WMWvtNVX/qnDf8Azyrmud4MWutEX/5P\njoTfCF/d/C7jT/5LjT+vGIRfUKnvCf7yvdwiO3qRFXwT93cj/wD5ZwqrvMROnx/8MZN/N8K4WOzc\n2yO9Puq3G7tqL9nchMX+TjT+siw1+ugtU/njJx7O5Fg5f1UoLVV/+W46E3Fs+r/+n7X/ALtw5zdx\nbNUb4/8Ah+2/7tw9rdxbVe395f3butP/AJPhNNyLX+2/8MX3s/b+wcK/+sa36W+n91r/AP7hwiru\nXaJr4f8Ahe//AO4cOI/cmzG1virsduU/7Jwum50zVrOtU+BW2un/AFXjnuXMT9X/AFJZe19n7Pxj\nOJY5mlnZWuV2kWorHJSWAQJJml7IUIUwWNaivVE1+v6Pl3qJgmyqS53ioY1xAMPrjkGopC6lT1In\nUif3XCsfsJt05rl1Vq4tU6Kv/VeDZTm+1W2OJY7FKIBrabjtWILSFXpGxVSMvivgmnFVjOLVm0lx\nkFvKFBqquFSwXGNIJ7sY2o2MnNfDnw3bLItvNtZGQx5YYpYcnGIJ66NPN+FELIWI6KI7k/o3OR3r\nTgWLO+X7aVMgLAfahpv3SpfMrCEZoXyOnyuvbQhGt19a8ZXe3Oz+0+OhwqPCNlBgYrUd6GOyN0w0\nMwMRXJ3is0H9actOLG227202+tfhB2QLto8WgxJUMyiQjAyQniCKNehyaIrfs9PCqLabDRqumqto\na9NdPDwBw/a+npcHPl4ppYIxsxoLIJrGLr3YQbN0JIZZI/FRMMpE9XDcWzmPttimRPhCnNo5NVBS\nT5QrytGXtDjud0K4T/R6OK29oMBw+wprqKGZWWEangqI8cyIUT2qgeaKioqcVuFnw3EA5RcV8q0r\nadamEhjQ4bwiOVqdnmjXFYi//q4h22c4vh1IOcdItUhaeISRJPpr2o4hgcQjvqan28SN0hVG3n7g\nRWqyZlSVlesUSoVI6jI5A6tchH9HQvPVdNOfEyZhWJ4PkTaoiBsRjo4bDRSETXpKIsdhGK5E9Kc+\nJGEYlR7dX2UI2SgI4aCF0TEj6+bbEkPioKT2v6TtOdp6eLWqi7YbfWU7HSii3NeOjqikhkKJJAhm\nH2FViuGbrRFTmjtfTxSVT8G23ZLyO1m0lKJKaq0kWtZ1eZgtVA6d8XZfqxfa9hfVxFhkwrBMeuCV\n061iC+FV0U3ka5RJMkNVBNVBh74+tfBOpNeF6d0dsGKz9UsDl/E3iHGsczwSHIsABlV7HsjanEZn\ncE4SoNevVvNOniPjUamxot0SqHdRahsKL3VrnvULJLGdv8NXp06pxZ0gMVxmTaVAgktq9tdEcQA5\nvWolI3t8kKg3KmvjpxOwang4BZ5bSie+fjMaLWllxxtVGv6gtYrmoirz5cN027xhOj7mlRC5fZ7r\njdqxo8HoK20q/gBothErYoDgEy/ru+oijF1MXtK/mnFbuMaKltFxPb+HdkhocURDsjVozK1DFVBj\n6kTxXlxlWT3VPSUgITpcZYtLkAr4LozYrS9ZJYAx0Y5Uevs6cvHXjHJAIUZzzXt1+1dsale1Tp+I\n9E5ry58PdHrooHF/EcMLGq77dETXjkNqfYicL3IoSa+PUxq6/wAacO6YQG9X3tBtTX7eXHuoYBf3\nA2t/mTjRADRPV0p/Y40VjVT1aJxqkcaL6+hP7HHKMJPsY3+xxzgx1+0Tf7HCq6ujOVfFVCxf9rhH\nLBjq5PB3aZr/AB6cK1sYTWr4tRjUT+bjRgBtT1I1E/2uPup/FwnsN9nw5Jy4V3lx9S+LuhNf5uOU\nGOmnh7pn9jj/AEMH+Tb/AGOEckGOjk8HIJmv8enHl3wgPjo7rQDhtVnV+t06aa/Xw+R8Jhd8v4h+\nwPrd9runVeGqlXDRW/dXsD5fZ7PDXWeO1di5n3HSoYTKn2dbF46H4Jjz2fquq4ip/EouPmmhxQx4\nkcG9V+yNCit6QAC3oYMbE9SI36N3ImW41V5RHotmqH4eG2iBmsA99grnKJpmuRiqhV8E5+PGn9VO\nHqn10cBf5w8OGLa/EhjcurmNpICIv2ogeEiN29xlsVvhGSphoNP73tacI6XsvgkpydWjjY5WPVOv\n733o6+Pp4RXbF7eqqeCrjFUv/ZuEV2xW3rlR3UirjFSvtev/AEbx4Tq2O2/dp4a4zVL/ANm49nZT\nBGf3OO1rf5o6cIIe3WMDG1NGjbUQkaifYguEcu3GLq5q6tctPC1RfqXs8O6ttsVXq+9rTwuf2+54\nZHftfijnKNVZrRQlajUXTTq7HSn2a8OZ/VbiHQ77zPgkDRftTs8dtNqcOQf+LSir+n+LscaC2sxA\nac+TaOAnj4+AOGq7bTFHKz7irTQV0+z3PLhHN25xdrm/dclPCRU+z3PGq7d4wq+v4RC/zXCq3bjF\n0Vy6uVKeFzX/ACPHs7Z4onj4U0H0+P8AQ8K121WHuavii0deqL/zHDv/ACow32uTv9RV/P7fccdx\nm0OFNf8ArpQVyL/H2OGtbtThzUavU1Eoq9ERfWnuOF7e2GJD18emlgJ/MHj5GHY7ilRTdW6oIxEg\nQQx+sXfhnUSdhrdE1Gr/AM30bDmrzds8DebExILXoV/njPiadfo07v0Kx7Ue13i1yaov5l4+bmvB\nEjqlZughq97EanUSRjNKrmOVPDRw0119fF9jWf3dbEtrOpuxbkY5JMxLguVT5BVkiWJ1eYWSswjE\nEmnV+GvhovHy0ZPutZNoJOS7Ijw6daWz/LNbkonVU8sWUQioNhTNGZUReaqN6cfNrubtqWNlFdUz\ntr62suRvd8Lm2eO3DpEwQ5QlXrYLzQ2FeNeXNPRxf129NDX4pYbz19LV7b5LSGLLpJ5aMU05oUiU\naPHIObrKf0oRuhBsZ06aacZ+zGfMfvG7HLVKDynM/nliFSP2v7fudPT9fGN4ph2R1FjaPxiqq9rM\ncFJH8Y/fAHabBa2L1LIHJFYIjjaJ1J7evjzpS4VDxRtplOzYhZNYXrpitR1HdEewUdkRddOu0eur\n18PDiI2cgUmtCNJiRkcgUKjU6+2j+fTrrprz043d3a2m2wdeZbs5klViO0ecnvI0KMFce7hcii+V\neupRzSySRja+PSz/ABfG1+8uVTw45iuW7ZHqtsiXpGxxVmThtpDcjrzFKrRjmdpIwtNUVUGRE42z\nyCpvsdutt8E3OGTdyfXFBKr4NgarmBrjWKh1FqOeSMqkcuoyIPXwXTfCo23yajud0ZG3ljLLCoZI\nJdw6vYEomFRsVzjL0916C/tl5cbV0e1VxTzrlmQ4gPYSDjpWPlpMDZRNXxRRFUrRtiIbzS6aIJSI\nTxXj5nIGd5XVYjLyyTjuWUCXMsVeGRTQ8fg1kmSMshzGP7MmMRpFRfZTo14+XSPduuo+GbmfMLnF\nvh9vSHLVyVZMFkc2ptAHFz1UqMkiJ6tONlNrNz6eUbJ8DxfMnRtxWib8OymrOytCGU1U/CkL2mrJ\nBzRCe01enTjauMtJXvJZ7eZeEhHRgq5EDYUJR6Kqa/oL6OPlKLaSKuFHFuNLiOZKNHCogycYuQjV\njC6ez3e2i9Phy4xCZieVS8S3Cw7aSwucLsgv6oZjsvY7FjWAU/EjGRe2VE56O5c+PnBuB4zP283Q\nx3bTHqqTipCpIT41DBdHZNr1bp3RFYYaBJ9nHy3/ANUWO4Hl+N5HLqKGrEs5BZTHNPb2rCVHGCMb\nuECFXkmdxw3IqE7qp9G/Oioi/ARc1/8A36NxXRsijWFhRA2jrWWkWrMkaYUDKgPUgC+8RjlROS89\nPr43Tr8gyFuaycWSXGm5OC5hXdfKGWsYdBRp8OFAE7sscgyooU0J1L6eMZCAXbSpvLaG93+Md3GG\n6/z93/ZXzXNYLtab0XuqK3pcv3fFOBC7b3d3q941urW9Ka+0vo19HHzOI1vWqbb4z1E/V5x+X0Zb\nT4xkES5s8Fs1psthx3dT4M5BtIoDJy0d0u4l4FJywsfIIF2HHJziVtg2AK1kINQxH2Hl/KIQneZo\nnd/STiml7j5XHxgOQySQ6NCiOcko4hqZ4xDjjK9ytYiqvLiBlWJWC2tDaNc6BPUB4/cRqq1VQcgY\niJzT0t/2L8jAxEax6bmdfNuvh5b6Nn59pMHXQoG82CyptoZyjjxghtGOIU66p7tE8faThVTeTBl0\nRVXTIa3kieP/AMRwNWbu4Y5C/hql7X8/+f4myoG4+Fxi2JfNTygtYDHyCdKD7hOkiK9dERNV4h5x\nMtduZ+Uxn9ELJiyKx8xr9NPZOruvX8/Eqjy/MMDyOikJ3JVRbWFbJjvQS69ThGI5F6fXpx+6490t\nsavHwt6fgbbGrBAa3XXTs9TRImv1cCiWe+22M1gyjlBjyskqHI0gvejIiPkclbpqi8Ii/Mdtlqqd\nSJ+9lQvL/rXB84qc/wBlGZkdeuRk0KxoFtHr4dSnE/vKv168AuE3j29kWwIxI0a0S7rXHZGJ70g0\nIhdUYvbRV56cuNW7zYavLq/+sxPD/KcSAUG5WEVUKfLlWktkWzhiYSTNM4sg7tH6K8hXKq+lV4lY\n1Ky7bqZjkuUeXLpJMuvfGJJkGWQUihK5UV7yOV/hqq804dj9Tmm3FbjUpFQtJHmVgoZEXx6wI5GL\nrp+knEp+G5ltbiCWKo6atPOp4PdVPDudh7Nfz8T8ux7KtnqHLpgeqfkMKfRxprxfWZhGuVPz8Vbd\nwNx9mstJTm8xTtvbqhmdgv6wkkmdov2cQG/1y7Ymj1BBrUs/eGlcyI9je2PsJ39Bq1OSdPNPBOIl\niu7m38qdAaRsGd8eq3vE0qIhEGTvrojkREXReId6/czBC3kKKaFBtVuK9TsjHURjDYTu69DlGxy6\nLpy4Fa5rb7ZZdYRQdkU2zmVcojBLz6UV71VE4gFi51hYpUCGkKtkMsoKPFDTo0EMnc1QfJvJF04k\n3Is6xAVnYCDFmWjbKE0hRhUqiG8vc5o1evRFXiXlFRe7Z0uUTUKky/iyqkEwiJ+Kjjscj1+vnz4F\nWTN68EjWBk1FDLkNa16p9in43spqvdPE7aztqRsaura+5hSpByrLj6DGMJXuVV+zjEaHGbQVTeZB\ntrVwqy0MxXDCY9UIaOe1NV0TVdeN4Q5ZW0GOnmMPHocIx6QWZDrFFUjE5qSjx46k769BPwk014UR\nen3OZ3LG6epGRv8AZXzRvkiYOQ7enInFcz9LUic+N0x0mQ5PYW+LknAsqidNrErIsyayvdMQUdh1\nsCM0EHtKQfaYvcRvinHzXMD0efDhWHMd+vog17v5te3xl+bT1TyuLVEuyIi+Dljic9rf75yInG2O\n9eVbOhwjGcliF/8AUvlALeNPfZGv5bZYLkkGOilYSPJkP6vHRj1RfVx80dRhdPjuQ7e0+7NXkVrU\np3h5JYxQRaSzmArC6+T7qsjogVKnNeXq4+VXc3bvPoOAx7HN7aq/e3Ja5XCq3yKKzDKh2EGSSMop\nCFD2ekhGdL/Wi8QCsy2pzeXFYka1yKlQbIp5Q0RCK0QjyUEvpVncdp/Aw4G5GdwsXmzo75caKYcg\nxFANfaK5scRVY1PW7ROOjFt0Kmzb1xWMkKh44SOmlYGOgynEMb+4QjUTpVfHirxCVcRQZPcw5FhU\n0j3okg8aI5jTlG30oxSNRft4yXB6rIYc7LcOHFLk1CJ+siGyazuR3Fb6Ee3mmnErH8u3OqaG5hSv\nIyYErvI9slf6LVBKiu+pF4FktRnFW+iOSYIVjKL5NjnVw+7L0SUgnaBGvW9dNEbz8OJETbnKa3MJ\nFcoCXAYpnMdHjH16TJ1D9tOXJE8fXxZZRldsCjx+oF3rK1kqqCCPXTqdoir6fQnHwmFvHRSLFDCj\nviNU/Wwp/wANhNRJ0K7+204ss/bmFTIwqnSStllEeUM8IPkyuDI6jCVzfdkarXaL48Q6vNtxKDGL\nKwhusINfYTRBOaK1dFMMau6nM19KJxDtKyUOdX2AWSIUsS9TCDInU1zV9SovHyKCO4aRw7gnOXr+\npoE+jbPF7wHnKfI93sHq7SCr3iGcEy0GAwiFF1PYijIvNGrwTo2GpTd5dSeZlWMnVf8Alpb+EVfl\n/wAc9nw5y/8AvHDXi+X3F+pq6tV7JBOf9+Z3D3N+XjDNXrqvVAa7T+51VdPzcKifLthOirqutaxf\n51XhyJ8vuHojvvfsXj/hcDV2wGKKovw18s/VP+c47X/p/wAVQf6qAKn8xOB9v5f8Tb2vufs7+X/O\ncNR3y84f7LelNIapy/M/jVvy84gq/wBtEc7/AHz140X5eMO/NC0/mdxqny8Yd+eGq/zuXhF/9PWI\n6p4fsz/85xovy9Ylp6kjET/3nCa/L3ivLw9yb/O8af8Ap+xnT1IklP5j8NR3y/Y2iN8OnzTf96dO\nNf8A0/Y1/wDiv8/w3X5fMW9nw0GdP/fcNYvy94r0t+6nZL/neP8A/XvFP8iX/O8I7/094pqnh7gv\n+d4cv/p8xTV33vcl/wA7wrP/AE/4wjV8UaM6fzG43jy3E9mqbG8jx7GJkyku4TpiSASWI1ROavfV\nV9pETReNuJLcZj5lLo9uam1pqSSOQMZ5cWva5iqETwl9Kr0IqL6OM4EKibW49GmWBaPImVk6lS3C\naI0pT/D7Q55Ye0RXB96Rden0acTRj16R55kDefj94Hj/AAO+2X0PcyrZDHq7GJO5OFoUhrCHImQy\n92yqRL1oqBCJhDD1Z1JzTw143x1zKbmWG5DuHLJUTK2zkwiR4iQK0wggPDIA4kYTqVE6k43GnTMh\nvpeUXFTmaXuS2F1OspTi1ciyhhKExiqotBhRfdafn4qsE3wth43uxY1WOWW3+4VbIKGJkrmzIhVj\n97TVk3RvSUS/iI7VOS8WOAW9dujk1TYYJTWVVHxC9lVFNTl89NBJkzPL2dbzPoNP6T7nhwEDHPcw\nDGjY4jle9UamiK5zlVXLy5qq6rxvXuBXSnZPszimOYu7cHb0JDyLKN3gynPuauOnu0cIQvfD8SMZ\nqntInG96Q8qkZptzZZu1uN3lPbzo6oFlVVncyNMiFAUKCldejRuTT69eNwp4LjIbG+s0y+tv7m3v\nLOwP1U8+ygAQRppz9vtDEiI8SePPnxW4PvVkSxs/v6GlkbX7rVT5DImSPKSIVsQpF94OZzVhRr+I\nNdU8V1nYVdV2493Sy8Jx2dSR8TuJNbVVZS2VlHly7BI82HzXQfP3nJnhwGOxz3sANo2vI5XOVGpo\niucvNV5c1/K+aKQ3qasjenIlUapp06PTg1nkG5RsrmXgzDh186spIBXkavcc4ZYMKOcqtGnNFeqa\nc14+ay477nErMJxaC0KJoxEMiOVV9a+54sCZM6CyhYFVtXWXb8ogvT3u97HT/dcuJs28PXpirYal\nnyJiiWD5Tp1Vz1f7tR9Pr5acUkPMs1ocQk5WVgqEM+UKMs1/sjYgupU6vFqIvhwCHbQq2cCefuxY\nswYSsMdGKvWxhEVHORmvNOen1cMqaSurqMRlecVZBCKM1/T0o96CEjUXTVqKunq/gcx6mtXSjsfv\nIip/oxPHXjZU+IS4kWymxdsf3ZsZwe7GHOdZVShIUWoOtnd9HLXx42AyfdbJ8RtsfmxssoogsaqZ\ndc6KQ1ak9xJJpk6Urx9MLTRNNF56cQ/m0DspIjpaZNd5XuVnUe6gvl3WB2ZDNiRyQORlWFEHEKEf\no7fGzWV00iHMiWW6W382knuG0ozimWoEa5uv6wiKuvF7ZZU4lcemxu5h196MSy21oZw2ulSWQl92\nV6NEmuqc01TjZqtlb17c7y4zuxMdTwMbxWsWtnQgtilkNsQ9mTK1EDtIwrCtHp1ctFTRFRU1RfFO\nPmaqR9ps2CzDJBxtbo9WSKsqI9y+nVR6cbxQsQvdsnYBYWm4hKyqn1NktswQ76yeYayASUjdzuMJ\n2l8uqJ7HPjZTJaDIsJxiLnGx0abIssxjkOQ4wz4xyCiIw8ZWP6ZiKqd3TgMuDJDMiHb1AlR3tIJ7\nfDVrmqqKn2Lx8jZZUJ0oa58ZmienVAez9G25ERzXM3cwpUlaaiB/rFPeE+pP9lb96tR6funL9lft\nbxteDcLKZ2K49lO3dDR/G6P2pzS2FeNG+UQqLq5efj6OMzo9pt37HdyksLGwK2wuIzIkmtlyYjEW\nIQKI3T0P5/rcZdSn/wBNx/cnIYU3+7a2Mv8At/wOXZlCivZd5wGAHISOerhFbWjIKPoPwRUaRyKv\np4zyj29DIwUW4FlKubORUvQbo0+UEYXniMVqjEugmrojfH82mU7aLlmR5ji2VLP8yG9lMMcKWilf\nOQRRsGqd4h3vX1KvFFt/kVM21x7GkrVpGnd1HjlqlGsQzC6aoRiib7Xp4jbk0m4GSYLkoqT4BKdT\nrBJHkxGnWSNChmxZKKrSOVdU05cQoUmwPayIoWCNZSUYhjuamiveg2sbqvp0ROMz3Br2SUyLPI1Z\nFyB5DueFw6lhmRUENeTNEO/XTx4zelwGPIwkee2cq6t5VWXpIKxmCGEsmM0qEYNyoJq6I3TXjJcS\nj5vl2X0OT+edLiZHODJcJ9mUxphAvBHj9LikO9yrxU7X5LSpa4rRArg1AjO6jx3VXb8oYZVTVCM7\nTV6vTwDPcc3GvcCvG0fwGc2sDAkglRmGKcLijnRpCK8bzOVF4r4E+0LdzYgGClWx2MGSQ9qaKR7B\nI1qK71In5XzMPGVhCk3myRTtZ+ivcboi8bj0UzcvCMn2yx6tMmIYxW9gtzEsBECCa170XuNUGvSX\n0Kr09HHzKhD0CaXbrDDGCjdFeTuyk7ir+fTidT3EENnVWYHxrCvkMQgjCInS5j2ryVFReMN+XqVl\n7LXYB1VNzimwWcBXzWOpJkMAabzSnXuQRFljMg1F4NQeunPj5kb7OUrMkvWZRIoLqNfJGOlXj0OE\nDysVGlRe1GKhSG58ndaqvhx8s9ya0eXAKHeTJKjC8rnr7BqPs5HV0JCSDLzYZCAEF/6fu/XxhsaF\nIFLl0G2GRLexxKj3w0sLem8mp0RfY7/lT9v1own5cfyTQKqnZ5rvK5NA/pqzpRdXerXl9EaXuLmt\nBhdfaEdGhGv7CNAFJJp7QxrJexHrovNE14preZkuIx9vzoFMeszzIDKd6A9oKRSuegF7fb1b0Ly0\n5eHFfdQTVGWV0chH1VrHeCcBr3jcEiiKxXt5se5jtF8FVF4h7XGyPHId7JiJHg4C6TFZIfFQWiCZ\nB6kXo7fg3p06fRpxSR84t8Yw/H4hQjxwF0aJDjMNERFEkVshWt6hJorejm3iTe4rl9LktFGKseXb\n100EqKwiaajeUb3MRfaTkq+nidkOOYLjuN28xHvsLqBXRYsh6O5vV5hja7RfTqunBQVlxBsjgTqO\nGLIEZ7EXlq5rHKqfn4sLiviwmTbLoZaWkdg0KdYyKxjTFYmr+2iqidS+z4cEqYFVEiVJ1O4tcELG\nR3rKe4htRonSvcc9yu5c9V4qI+UbY4nkkfH43k6EFrTQZrIUfRE7MdpwvQbNE+63ROIOPYtSQMco\nawfarqasjjixQMT9EYRNaxqfYnHyIw0H3Wtz6ZIc1fR0xmJr9GIAGRGFNuhh7AtcuiOcs7k3+Axz\nF8Vxl2e7l5w+WmIYUOYKAhAwRd2XMlSjdTQxworUV/SurnsYiau43QvcywK2xzLdnIQ7LN8DjlFY\nH8iZimHMhSBI1sgCjGRetGt07b0VOXGD3DGmvR7iXlPRYoCv6XPklt3p0GTqVPdiD1GIvoY1eLEF\nJtXkf7v1mQ2eOystkyagUXv1EssKSVALOWUrEKJyJ7nVeNzASNo7Wbg20cqADNM4j2ERXCDOjhlu\nkhgKneIMADNITRUVE+xfonbbtFJ+O1+PxskOZWfs/lJco8QaI/X7/XHfy08OJeTNxTILIoc9k7dx\ncfgDivmntQTiQBuTvyI4WDKRiaOeRNNU4zncq820uasuFwpM9uLS5lX5mcGMnV1CPGlyAj1RFX3j\nk04sMFzPbay22yqPTiyGtjyZ0KziTa4puwpAyYRHIhBl0a8b2oqaoqKqLxkuOY3tVltpAxDIS45f\n5aRamHXDkgaJ5SCbLsBSTDawqL1DCuvo8f4DfdH9XQuNE6unx/GF4cbMy9y7KzraXEsCxfLFuacL\nHzo54FWPpcEeiovJ6ponGXrtFKyaxi/HDysms8mGxZR5hooyjUQY7jaDQCs0Zzfr4pzTjcnokNO4\nW7OTIVvb7RGK8cN+hG+v2v4HdiryCssMn+XyvjY4W3ydCBeuJTLQBVUrhJ710Je1qV3Ptfe+pfmM\npj7l2dHWA3FPAwDLsakRnTIcAVXXH7QXGDIF0IUruWi68/D05vmWU7sZBkWdSK3KXpkE9YRWV56W\nROiDfDYACNRP2bqXXXVfRrz4PDz+vDgPzBUNRjV1Mr+4F0W7rJ0yH3Z9URfdE7onkERifhF1Tw04\nsdpZ29GabeVJcao7HFafDccFZKWVKkyQSXTpr6uy7bF0Hpqo9NfHgAHnfJeEbWOkl06yK1NFc7pR\nE1XxXRON1IOQVpbz5csYhYymUZGJBPPis+3ATSW9jH910Je0im92vb/E10VdfmAx4G5N1Ci1m4Ui\nFi+Z0R4qyIkN9XWy2RojzBkC7YSGcn3V11X18Zll2Sbt5FmmVnjZGi21y6CUVcekkzYY/LDjw47U\n08vqTVF1X+Pi5FuhEBtpv7j1DT3oogihfDvohzx9JNYV2o3of2hlEntiV3h4cSdu7vevKNrqqTjF\nHPw+oxihDaefkTJs2NJfKOarsu3o8Q2p+Hy9PAhOI4zhMaxxn6dT1amnU7TTmviv5XzKDYVzzi3k\nyFJLHN0VqqrNE4zCJZbi4ZZbUng2f7vYPVQkBcgngPD76yzoz3rhdz3nteL04+ZSP2Oh5NtsMf3t\ndepBlkt8P776ImSFrwkvYEM9fDs1bqUcaS8RTCavoR7gsVfs4BfZ3t5UZLcRxJHSwlCXuPC1dUGV\nWOb3WJ+q/VODYTc45W2GHyozYJsakRxvhOjt0RolCqdHSmiaJpxNrtt8GpsLiWZ1k2TKqKMDpJl/\nTMRqdZF9XUq6fwPy0ZBi+IUGaXqZ1OoIlVkR1ixWtt6Gxc8nfaCSrFakXxQbtfDjbRL7DqjcjJMl\n37iZTb7d0QgxaGPJvkmBZAgfEVQIxCIVjkeXp6yeOmqabv4BcYePaDNrXInZRSbQPLEVvwh1dBhN\nmwCRFWMVhzRXvL2lXtkVyO4yjOc2JWxbnIoNtked7iuQT7WuvXkKZ7hy1TusLBMjRiYipp0NTTmu\nvyN57ntZDXI5GQUoMirbeMhWtsL/AB2UF/XyXtuSR0r4ePLj5gMEyqNh97I3wqLPcmLIxhCwfhb8\ncSqgpDNFciuUSiExULrzJ168boxyl7AbDDLjrK32ulr4BV1T16cY9kFrs1hO2Bp2NUy003FjBkHm\nR5EQZSpJUcGJ20aqM0b1v19fFeLa7emZie1+8N1ka7v46UDDTIQjTpoSycfkkRXRiH7TRkYqaavU\nic+LjbjKbRLjMNj7+bgt1ZqiNfLiwOklTLe39Y1eUCvX0v6/p+R+ta1VsAXmRTtVZ1N7Pwx4l5+h\ndVX6IElrnCWDnuKn821ncQH7e0fccnqTr4avV16ontp6fr5ev8vD95gYPd7gY2HE7LDbmFjMNLC3\nq3zZ0SeOYOL3RvKAnle2VAteTVBqjdEXjcPdDK9v7TCNv7vEYODY9imUDSPaWggyZcifMsICKTtj\nch2CChH9at7nU1EcnFDiWe1+m0fyxMnu2SyNxVea7JeMNHiuMiryWrryPjcvS/jdRmTUW70ufbbj\n3k3GXx49tLxd0G37RhlQMYjon4hX+8IxF14+Z0ELcbJtvqHMYGISMZBHaFaGzlxoZQzBTQuEpzDV\nIwhlQRhro708Dl7lYWuDZpXTJFbeVQyd+GYsVUasuCVeb4xteoarz08eC5BIuMxxXH4O2UKC27xm\n2k1Ipcx1xMIsUzwKnWomL1omv6fG+mEwBZzYhpd5qnMsXtK6VInZJNgSJdNZTZMSUiuMUgVJJ8FU\nnsfZxvXgGE1u4syZEw+4ZAXLq66DbTJciLIeAceRdhQsh/eYjUTV3NU4xvdyBdZVvZQZTjtRimbY\nrkRoxchoAITutl13aZGC9gzFVZQlRSOTRzVd0cb6ZFl0Td44LG+gXGJxMer8jscWlxzUkRpyEj1Q\nXxCGQ6PEve1+4zhHJro5NU1TTx+pfy99Ot7hs/dovU9ninvR+HGJWFfLWK+v2VpyglaBfp36gHol\nM7a69z9JvB4mIkgGgmtJRZK12RRckF3nBCjkSZDEATOSJ7tG+z468+N0ZzVf1Wu7GQEc1/6KCiwA\non+Av8Duflkg5bQW6sOshZBQS2sfEQddHNG0ammqoUZlRyL6uM5xbbC4PTRsru5V7VNlibLDVnki\nCLtiE5zesbeyi6Kvp4zfanJtzZOaUmXBuBQpPw2PXlrvjpZZpiDUDveJ3JSub1aeH18YViGSp3bL\nAVqCY7lrAjSaElSUBEVPQjDLHTrZrp/FwLdHb/cWLhduXGR4xcQp1Ky2DJAGY+WMqKsmOrHtUjk5\nappxXgupobG2FHYyynRwrHEYyNRHvYJXv6EVeemq8bo5wYhbQ+7FfU1mRU0tGkhpGqQyQMG0apoq\nEbKf1ovjxnuMbVT30Vdl13Iv6eFLGssFTJkRwgcMTHkRXjTsIqIrk/PxmuEZLuY7OqLKT20qA9ag\nFZIhFvJMqXOVXxyOQvUSUqoqoipxiG1+U96S7BItWLFct6WfEYp6poEGZHKmnvew3uN8HfxcE3R2\n43EhYjc2GNxcZuq+1p/isc4Iko0oZmdMmMo3op3Jy1Tioi5JZAuL8EQTLi0jA8sE8lGp3CDD1O6G\nq7XRNfyvmpnNGrTm3pyBJch3X7zstGiL7Xq1Xw4zGdTy8fNn5mWLrMFe3IGmGVCxUnogrRgoo3q7\nt97st1+56NeN6HtmMKey2fxk5I7vvj6LKUPpT6lREXjOqvCrFKnLp9HODjlkpfL9mY8LkC7vc+37\nWntejx4xIWV/L/N27j7iyomKyNxky1ci8zcHXWO2UIhHORskvUqF9fj48bnGLYFkPpLjOxznnkau\nj+Wsp6tH3f0EYLpX6vHj5enbgbc5lvhFN8vITOx+iUkiRGmBPAV80vfsYXvVQyiR6dZdfTxOygF/\naW0yn23AXICxZ5I1uKXVjE+fWyJQPeikCcJ8Yy+OqO9C8WlpX7RWW0dhblEyVVWtuO4NIAFnUAqH\nFNnNa1O45OnqRfq/gMYsL6sbYTMNtG3WNGcQrPLTmhLHQyIN7UcqDM9uj0VOfhxWAv64dmKns4lz\nWMKrk7M6AVDRjt6Vb7Q3oipry9fGPZTa4/Bn5HibzExu7MFrpMN0gJI5e0TTVEcMrmqnhz9fB8ys\ndta2VeS5vxKYjySfJHm//tJq9CpEIX+3cJXfXwzGc3x+PkFEKUCaGuMr2MZIir1BIxROY5qsXw0X\njKoFXt1XADnFa+oy05HyDyJ8Aie1GNJMV5lYvqR/E2Xi2KOqyWdYalmifZWMkBIB9FLHUEmUUXSv\nQi8m68uK6Xh1TY1S1ENK+rhPu7eXDBGRnQgxw5UwoERETxRmvp8eAUeO1oaipjEMSPAjt6RsdIK8\nxFRP7Z73L+fjKsoqagEG+zYsQ+VWY1cpJpYEdsOO4uqq3UYWNYmiJyTn9PySl6+lpJF8LT1r5CSv\n0ZDMej0bAyLGpPeZ94fbtoy9afZxEO1yvaYIyNeviqOai6r9v5dzRRZSFtMfbGdbRkRUUSS2OIHV\nVTReprVXlwK/yeW+DVmsq2padgiGXzVrMDAitVo2uXRxjsRV05cV4sYpsqNW2zpCV2TSqCwi1RvK\nqRr1bMMJo9FUTkbz5rxLsJZO1EghJIlFX9EYmq96/mRONu80HOIfG90ZVLFxGxENVaZ2QsaSvc9O\nSsaXramq+CuTjEtm7nIBQc+zask22PVJOSGBGf0dPWvJHkVpO239Ltv9Sax9tjWKBzCZRlyKDVPR\nWqevjyGRTlE7wd2ilGj0Tw62+vjIod9cndYYpLx+vta2DEkS5HncoM8FVFGIDHOIU7mcmongrfWn\nFjKrafIaT4bKWIePkdLPpTOejUd1iHOCFSsXX7zNU4ts1zCwWuo6dre85o3mOYpXoIMeOBiKQpTE\nVGDYxFVzlRE4taIOLZhgGS1UdlguL5xSHo7CRXlIomzYwTKvcD3E6FVF1Y7RHtRVTVN1qu172DrW\nSrj4w4b2fscNCKYqscnVo1BOXw9HBMUkUmX3tlGxyLltgehoZdlGi00xxGClnKBqoxiqEmuv6jvV\nxVX1LMHY093DBPqbAK6jPGkjaUJWKunsvY5FT6vyd9x/rYuf9Lo/pB/pejja+0m5iPBpU/Z/H4FV\nmBYJpceHKkUgWAKUUcR+kfreqaInPx04zCJmmcDzW8osvsIsiwaCXHNETyMI/ZKKYABUd7zu8xp9\n/wBPGfoioqA3VyNNUXX8UEA//vf4HKtlc8rVFgpItCXG9xABekKrnXIitHX2xkRRiU5Q+5e9U16t\nF5cb1VlLd12E5DhW4M3G8VtjVvnxfD4cWDJY44HGZ1qVJK6qipp6uM23jzDKMdl5MtTezsXhw6gk\nKNXvojzQPSSiyJDi9xY2vLw/PxZbk09EbFtzsYj43NzHbu3EopMaPaTogiyADKqKSMYJCKAvp058\n/HI9qYW5+3211TW43R22OfvLDWfZW8i1PNAUYAraVqIgXxET2Ueq9acuGNK9CERqIQiJ0o52nNUT\nVdNfVrxnm1Od1Tx7VNbjsbF9yGDGOJU3dxFIUdZZkRfZZLUegSv0Tu6C/TbpvnjdBkddieTYPm7s\nfxfJJFWtlHFFStq7NnehpJjd1y+ceNy91vr+rjNtwtyctx+1yhka+bQVdfROro1XKoJE+ETzDlnS\nFlIUsZHr+HonJPHjMs9NjTMM3n2/pKq1yzbi4XRRjmkB+1x+epYpxueoSJ6U0X68h2ios6292yp6\nPGKO1r5uWRyzJ9rNuizRdqIBJ9fqgVi+CaquvhxHbLIw0po2JJKNvSxxEROpzWqq6Iq+Ca/lfM2R\nngXezJF/iUfG8l7YbSriJo8mbEo8vfHtnMshKsNSygGMnw5iyl5k7XvFVnPlrxuHECQfblbG05Zo\nyff9xcFaPt/5XnxOrJ4UkQbGOWLMA7weIzFY9q/a1VTjErR9lluRwcClDn4Pi99kE+yqaqUDXsGj\nxJBXNR4UcqCVdej0cXOTWZsjixsocJ2Z4dV3s+BQXZQJ0ISxrY5WBK9zPYIuidxPxEdxBy+PAaC7\nraN+OQjsVUYOuecchQozw0R4mqi/VxurAbjiV0DeqKsbcaBXnLFBPe9hhmldoTmsHIM0yoUrER79\nGq5VVNeDnh5nmWRiLFZEFAyS8k2oAtGqaPE2Qqqj100VyqvL+A3RgnuJKxI2BYeaBj7ykWO1TWF+\n00sQl9hHP7bBuVOfspxn25211rNYsimPIxmyjqoJbJUOYgfZ6FVWvQolTkvB5SxrN0I+3ocvjVL7\ni1dFbeivnjJMQKylDr0uZ7HTpr6NONj5gq+4E/cLdB8TLlZkdyPzgz0dtNUbxtmIisU0VmqIiacY\n1tvt3g2YZfi7NsZ84+O089JywSFuxNDI/wBbTm81XuNRUXj5iw5FQ2mKT63decWFjFyRHzIkGxp6\nmcFHo15RsR7zEejRuVqa/wAfywRc1wy83CxuZl13GnYdQDkHkzHrQTDBXsRzgV6BIFpearp08Z7a\nlt7GJjW2ORZYQONZEVUu8fx+FMklgw54ju7oumOJVEheaj6efLjHcVyPcn98mfM0I+ZChGiyAfup\nlklrTSaFpSp0OjmD0oHRde6N/wDjE4+ZTcSzvmZF8vqblCos6x4TZB52KSvhFaZl6Jg2uRIa91GS\nmJz/AKZNURU4zPO4hLjPMdDuLnC40enEa4mzqtclmtiPijbqQrEG5Fbp+gmvEqwj43keMtiH7Dom\nSVhquQ9elHdbBHTVzefjx8g1t0sC4ma2MF0py6KqIOOXtJ69fozNBMe94regL0s8dB2cd3+1xV8t\nP2QHL/k2/l7lT8xi2jA5xj9DJwN8GsmT2W9jXpPjHrAOhAMqSUcoVRj9NWk1bya9U2v21zauNT/M\nSfO8ETOttyRiCkxj0eRVtnZTlCHzDGxPLRCGQuqi04uMOu93r5lnEzXL6Gg2atoMONEr4rcin/C0\nik+HNmG1iIN/c84Qa9f1JxnRK5vXYMx6zdBZ09epkiFUadPp9rTl6eNg8msN2Lm1rtqA7ZZR/Vw3\nH4TNBU8uqK+KYkcSy3pFEjl9a9HNOPmPtcYFjdGcGS0GObbZteOm/EqqRhQw2IpcIYY+iDS0lG8C\n+37evLTXaT5nI+JWMfcDYu/sA59hMKMQ88kPrNR5PBiB5KX7rZoE19tBD58+Mn3anzpuI7i7pbkY\nvutbSyxEPOpa0N9VfC4qxdD9Ra2mig6h/wCNY/6+JdVU7uM3fs6Q6pbXxPINlD7yq4YzCrgRgt0T\nwVBpxs9mM2rl22H7dbhw8izuPAinmSA1wquyijnICMwpXjhypITkRrFXpZr6ONnsk2ilFyrH9qqv\nJzZrngIskNaJlzHjRY1WOQcQ2nMYo0M5g1XtoHV3NdOM0+VizZbSN6qeoyXCsYwltdNfJvy2DpY6\nmdDMELhLHmDOMqkV6dpOvuKijcvF5jO3WUU+FAtvl/oqot5Z0xLMfxGrtLcDGCKKTG7faSw7nPua\n6+HFFgFliVhhN/tHAr8OuqKWx7o/VWQxBDIr5ap0yYxhtRw3ovVpyeiL+Tv6yO1XPZiMwxEbrqgg\n9JSr7PPkxrl422hx8PdnRnbJ0DY+FhKWMtiZKOOrI6FX3jOp6Jz8U43Fl7hbe2+DZc/NZALeTezJ\n06bb9ivgjbLIWx98qNROymvL2ONxOwFBIu61+3XXXVrYdd0c/wC5VP4HfOwzFIORYfvNW0dfIx4o\nPeBZVxJEUyEIuqOR3dR7FTm1deN0MexnMP6xrG+yGTkGEuyYhGKNDRIwUizTiarnL1AVOtqeHTrx\nuLspuPPxpr8gj5MDGrqjfKIMaZKWZJJ3hSGoqNCWYumi80422qG5A7Htwdu62kqxZfDarRzodcSK\nSVBlCTRXx5Cx9elfBfz8M3txLHcWyWNOwYGK2UK5kEhzo8qHYHlhkxTtiyURr2H6Hpoi+y3TiGWx\njjiTyAG6bFE/uMGVWor2NfonUiLqiLpz4+YG8y48bI8M3zqMfqJmHlGvQIdTElxZLiKvJyyGyG80\n8OhPTxuhjOLZKXNSZLlNlk2GvyIpHGAkqDEjx4c+WiPIZBvi6dzTXo09PGfbebrFxP8A1+fI5dFa\nY+ecdUJks6fNMySktrV0E6XonT4pxguKyL9tbuft/T1dfW50JqsZL8mkZZMeW1qdRI0gkdHqNfT+\nfgm9WNYni2bwJ2BVuLPr7ySsOXAmVlnYTUkRTeVlIiGHP6V0RF9j6+K411EDAtyxhPs4McqmEE7m\nopGMIrW9SNdqiLp+V8zDnF6v/PPLHPbp09H+j8ZNkWJ7g5+JmThS7j4oYcEGMPZDFHaUDWdMk3mE\nFNjlN7bFXqTjcAb/AG3v2Hq3iXX7mlzovL6+LOlbbWFEtnHfHS4qTJHnR+tNO5HK5r0Y9PQvSunG\nWYWf5it3zQKDF8cvauOt+BCIWynXAJXcMkLUiL5AXsryTX6+PmUo+1m9llGKXOU0+K3dPjVpMHGV\ntew0JBTIcNwdQvMmi9WqKnp4+WurxbezH9nss3WrIebrnOQnFDglgVFSOzUJWzCBcopc00UZWIvX\n2XE5ePGE5bju5mV7akfJUmQScAs4sSSK1gtJFmQSSDR5iEA0qq8fJOtvaJ4KnGUZsDffcvKsixnK\nc/xXH6TLbqPYUhH0tvaUkA06MGGAhulAsKqKT7/P6uMjibkF3nuq6hSjBglhteIcesmx218Z0+bL\nbFcwpJKzlkIUZvd9vt9oS8+KfM8UlvmUd0N7ozzCeAwyBI4BwHCVGvGUJRvGRjk1a5qov5VfeyMn\nyvCb6HALTy7rEbV1XInVRyIUtfKXoK14nPTqRURpGKqqx7VVeI0TD73KMS2/HdQL+btBVzwJjUqx\nrCCMAxBHimlsTugYQgwyRsK9qKRruIG95s6zetzGriMrYEavtRgrx13cEYsFI/l3ahOQTXkartXL\n6U4widfCOSRt9kQcpxxwCuEjLAEWVDY4iN++ztTCIrV5Kunq4PuQjT/vJIx8WNPf3F7KQQyiTGog\n9NOruEX2vVy4zLJYKF+JZzLiTLtXu1YpIUMMEXQ3Tl7sLdfWvGDXVoslJu310++oFAVRt80SBLrn\nIVE++xQzCcl9OnGV2N5GsaqwzjFz4hl86mlrEfZVh3jI1klnS9j3hUaoJ6t1aj3p4LyTDb6OSPVB\nl186tLAVgDwpNVJFLhmiv6HINwiBboqJ4cuM/tqaA9svc64+OZh5grzskS/Jgg+ywiqjGKGOxOlE\n08eDYthFYlNQFtLG3HWMcrhBkWkokyS0LV5MZ3SuVrU5J9HyG+/eE/8AWYv3PHt+YrdfozgbRq9T\n2dEPuJ/R62kf2/zacU6dXXpBjp1ev3bef5eP0242UrS2+TClSserQ10+zkHHCRqyCsFAjSXNQaPT\nVzkROfFVkuN2ka8obuKOZUXEMjSgkRzIjmEG9vJUVOC32GXsXIqgM2VXFnxHdQ2yoRXBkCVdE5se\n1UXiZdY3dR7err5s2unTAO1aKVXmeCUJ+qIqOG9ioqLxh2R5HmQIVPuADzOGShRpUpbAPZYfuBFH\nCQit7ZGO5t8FTgmS4jkldd0I3lSVZxDNUQXjTqKh/BRuanNyPRFTxXibiWFZeKxvIvfKCI6PIjsn\nBCre7IglMJg5QkV6avE5yeni9oqy4iT7jGSBDkNaEjXmhvkDQwmmanNqvYuqa8EsaC0iXEJkg8Ms\n2EVhhoeIRwTCV7FVOob2q1U9C8UkW4tY1bIyOelXRCkERiyprhFO0AtfvPUYXuRPq4o8WlWcWHe5\nCCZIoKZzkaWUGv7SynBZ6UF3x9Xq6k4JcwJ0SXDA6RHNZiexw2rEK8UhilTkiDINyO56IqLxSwI9\n9Xnn5FAfZ4/FYcbiTILO2r5AERdXj0KxepvLmnFjWRZwZFhUdr4nDG9HEB32q4Xcan3etEVU14nV\nDMukObV23wC0ukqrL4XGtPM+T8maesbsMJ3vY0V+mvp4DX5bmtLjc+QBZIIVjMDHK8KO6FI1j3Iq\nt15a6cYvZZpnlZQQc1G4uKSDOe9J42Cadzgdtr1cnbcjtfUvFbkmMW8S/oLgKSKu4glaePIE7weM\njFVHJy9HHzAHXq0HgN+vspqv+gl8E4w2HWW9fE+E7YUVktpOlzYcdiVMUJyjU1aRDo73Ki5Kqar/\nABZUYNQLF7NcmkEv8QO27HY1spYkVqMsfj5jSlKQTGERyewrFb066LxuLEa1GuiboXjlRGdHIseF\npy/vV/2V8x8xJJTyZ292VllDKmijd3R6J+fjPPl9wbFT0+Z7bR5E67lBqRxYKJJMHzPbOxE5lKrF\nXl7at1/RTi9OAidyb8v8JJg18e98eKnL/kxM+jINzBTJK2uRY/WY9Nr1cnl0DVyZkkJUb+uqzXp9\nnF9Xw3PKDIbi0upqPRORrWQ+QZqaJ4I566a8YbZnsJGVLgW38PbvGY9qABGx6+LJSQ4rdGfiFQUd\njvRoFnp43GzbHZ54ULcxtbIucPGMTK8NlXjIAliFGtRyFkhUbC89F7bF4yStrbKdZiyXKb3K5L5x\nO44Mi+nFnmCL1DY8qo1OJ2WYVvflG25biAGBb0sQEC0r39hfYPHj2QDtjm6V0V49NfFU14qcGoJE\nubDrXypMmznk7suZMnySzJko5NE6nmOZ71+38rZnbqLuJmGAY/a45l11dFw22+FSpB6wtOKK0zkE\nRVYnmyfn43l2pfliZtldTDxEmyec3YAum9GaWq4/HHbtjBCAxIMtqkR6D94PmX067ZZdTbp5dntX\nl+X1WK7o4/lU1bEU51+RIQbKvGg/2MgJb2EcMPSNRdaaJpqvzG5Hj2Kj3n24x3cP9xcawKOUUSzp\nJQa+G5JvfaFWlhOKZFM1VUjOpV56Lx81OL5vfRoe/wBsmjZ8fKaYSiiEg3nTY1EqM13PoEnejKip\n/Qrrz4pMOyxzMC3vwfcfABZZQ1pldDvqW1u4sd54BF/EjnCR/eZrqNWOR3o43h29yDdTdXHINJb4\nq/b+jwyqEekBWzqaCUzrCYlVL6O/OHJT3pURE8OXLi7o7W63ix/DBUlaXb1u1WORrRthLKp/ib50\no0GZ7UdWCRB9Q9Gv1TXXja6/wzIN0oey+Q0lp8UvtucZZZ5KTIoMgUVtXZBkQpRYOrVPrpHb71n4\njOlNXxKO7yS1t8LkrSZfHzOB8LyONNYxpW/Eofl4qNcYRGEG8Yu29iorVXnxCtPh06o86Pr+G2Qu\nxKFzVOkotXdK8tdNfo+Q2tjdHeLnpir1u0/BNBMnL7BO+jO3j/H8/SJH1/X+JR9OMcdIaNh3VcNT\nsEvUNHqFnUjF9Ka+H5fy5m21XGR5pZU2cwBuyl0xIb4iArJDmN8n7fV3RsX7NeNzttbCBIxr5isI\nrbAP7oyFVjLG5yeeccKdRndykQzzJWoneI/AqJpquOVFtszX7ObKbkwKnGZbYF7FtI481Aw3ZsTI\nEAEGtiLojEIqe8KwSr613b322frpt9KbuZngt4dqHSf2e+DBupYhTKpHL0RpgRMYq6poX20XRdNf\nkAzXL8ng4rRAwq5qHmvJIooxyp1REOMRDHc1EeFITx+PPnx81t7snKbdbZXeHY1XZ1aY0RHAn3gL\nA63zoTomqmkJREYMyouqqgmL6eNhaDai6p8hzFMxx6dgNdjhYpyQqcJm/FylaJVUEX4chhE5Jo9z\nEVNePmWy3DM/utpt0IeZVVUfM6Z5FdMpH43V9yDKjPcgSs9oiif4jJzTw57o/L9jMckHCpUGs3D2\n9gEMSQsYE9HVlrG7hVVfZlwkMia/03Gw2IZKWbHpbrdynDLlVss0CWJ/wu2UDwSQKjxvQqM0VF42\nE223ZiTcjtsaoc4Bhu8LO22JkFSYde9qTRoqqKwE2MNDNTk/8ROS8bsYJnGX11RlGF5Lmw7HGDlG\nK0l/G7iwsK9YkNHIU6yxTB9rttXq1RPRxsHimRyrTFLjCvl4eTF72nlkiT6C/DNqYzpIuw5qKrW+\nwrC6jeiKmmqcbaXVrl9jnVl8wEKZi272U2DnftmUQAfEqicIWrmhYoQy4yMTkiKP6+PmA24k/MBB\n2ZrMH3iu7u9BaBgyHyoh1r76J3myDgI2P5l5F5LqVNU42d3DLYYRhN9uJs9KJlYcojHIIwqa7a4R\nK8fmYyt745im9pfw/s4+Vm12ur8ayKxspWW1Md9xNLHhoA1WM71EeKGQuqJEXwT0acX+xOd06YVv\nLjFndZLfYsjemBLh3lvLmsmUpPAsVqmRnLmxeS8b9yzMUgh4NdI9iN61VHxCM+76fHjGa+to4+U2\nU3ah4IlHNVnZlOGB7UY/9Hwbqn16cZ5cYlAtJWKXN4L4ZmORmKt1eGj1kWJLLOQxTlGgiiUQtV/D\nRNE43KqtBMnVm6+TjnCD7TWKqx+hEJ+n7KeP8Nnl3jdrIpLmI2vbFtIrnMKFpLCMwytczmnunOT+\nE3+EpHOGPerLXiE5unQhDDdpxnuIT8wbZ2M2PJs4VAfFG1sgMOOUIkRtyM+kxg1IjU6ha8/HgRnS\nGtKuxEVBA9Lv9cT9f4uMnkU5EDbgqZpKoruaNktA9QuX7Hoi8bDU9jvTF3hnbq4NZXm4NA4FeGTj\nFhVjhucirATqb1mkvCrC8/Z14gwcHHXzMP2spmZhv/HkMUkt1HNK6OEcBE8DCGA8peaIqDa1fv8A\nGyWT7O1jNxg5nlQ4VhiETso65pj1UycQ0SUVUQZAtjIRnPR3gvLjZt2FXzrPAdxMPy2XLrFCNhI1\nnRy6dukrq98IwklEE4S8kXVfr4B8zEreMucxo8KflGW7T3tFXxY7KiHJOWbFr5UFscwjBjCXtKVS\norm6KnPi0wXA9ybvbLBMAoqe4yPJsbWH8SsbW+E6XBhISQGQghBiI0xERPb7rE8OfG8TINhFu95d\nnLqHjsG/lxWMj27Z5oJa6UQPU5qPNDnjQqJyQiP04oRT9nJ+KB2+tq9nzPW9mn7BTVs6SOGKTTmR\nf20Ret8hXt/DExerVeKKyxTc7L63N7+GeHtLtvi0IE2PeXUdizO7MaoHOJHQaM7quMMbBdbtdV4o\ny5GEEfISV8Z19HjL1BHNUTVkMEvPVqE6kRfV9OD5xie6lztbk2ERbSAGbVwKywZLiWvl1OEwrKNI\nbyfGG5FT1fn43AosyyvINxsp3PdFLmO49udgrV76xyFq0ieVaIcVkEqd0DBtRGv1VdddOMdybdbe\n/IN2YGCzUsMExeTBhVMKLKEJRAlzkgta6dJEjnq0hNE1dr0a8bl3VOY7y7n5L+9FvHKqdAZboESC\n9BaJ4P8AKda6+ly8biTLO2nVbNzMIj4TkQYKMY5RQ5Z5caW16oq90SyHtTXl0rxgp8iiJ8c25u62\n8xbImDG6XHNXHGfoR7k+4Xt6OT8/GZ7jYFumTD5GeQamLf0kqljWsZS1DDCAcTiFCRiqM2jk10XT\nX7KXI9vd/LDby4h1A6i9gGp4txT2KsKhVl/D5BGNjyObk6xu+6qNVNE4x6k2732yzCM2pba3yC2z\nhwYtkC+s7wimnFt6k6JFMxXu1ENnb7X9Hp48ZxfZBm9huPn25NnHs8yy6eAMNpXQ4o4cUEWFH1HH\nCIQ9Gsaq81VVVeItXVxRwa+ENBRIgk0YNieCIn0fInYMcROrOSR9G+HI8In+19Gfu6+ntTKYmn62\nllH5fy8UDlb0K6tiKrPDTULeX5Yrq3SHHSnQjw20vts8qhW9BHNMTTto5OS8019PAb+0l00mkb2j\nR7uSSO6KnQRHDe0716OT01RUXx4l2T7ugyHHKko5U+f5qLKhRiRnNOwpS9bhsUatR+qqmnjwskp4\nlbAKbrdIe9gROLKJrr1KqNVxSP8Atc5fWvESly2TjEZovagVNu+ExG9XLUYTqmmv1JxDp52QY5hz\nJA1NX1Z5USvR7FVdXiE5w9UVfSiePEu6xXE6OlnXLeqbbVcKNHLKY9e5qQoWNUiKvPmq8PsoJIxI\n8tO6+eBWKwqNTTrUjeTtETTXXhl6tzR+e8t5Rlt5qP3PLvIj+0herXoV6IumumvFK/PMxxvFx20t\ng8eff2MOEkmV4sbFWURncJz5IzVeKy+yy9o6OKhOinuraVGjDQh2KmgDnc1Op7NfurqqfVxUbgho\n8Zy6ziJ/qTMxAiTisRvJOxMaj15f2ruXCSeyzzKM7aSOlOvo116erx0156cRfPQwy/IyGS4fdYj+\n0cWvQVmvg5uq6KnBsms9t8YscikFQx7yVVRDS3kRNEepniV6rp6deIIM5weiy8NYqurR28CPMSOq\n8lUXeY7o8PRxj9ZTYzWVdfifX+7EKNFEMdf3Gua9IzWtRBdSPVF6dNdeGWjoMd1mIKxx2KiYp2hV\nepRoTTqRqrz0101437kDe5j1xCcFr2+Kd9qB5f7vja/buwsZVXX5bt4yrk2Vc9WyAilMe1XCcVHc\n0R3pTi9w/EMjvcgiW819rMnXJY7itN2WjXssAIAhpoxF0RPHjeE7z99ZO6V0RHdWv9FH/ht1qqIj\n1mnxiyJBQf3u+ADjC0/v2JxS3Ivw7eBGmj0/VkCaRP5Hfwe/J+rXzO8mUt+91fhFY3x/Pxuvg1dn\ndJkO6AJFta5vBrcYJWykDIkR+yGVYkMZDKHwTo0T18YNcuKR7LPZGUBgv0GLEtZWv8fe4sa9plju\nnxTR2nbzVilYrOpPs1142ixiqyMmK7o7MwmBxTdijjjFJ72mh2yguTpkx5CfihIujvWnp3Iz/faq\no92suzudD8tNPCIAEGrgwgxgQxCUr0TQjSEVdf0uNvsdh5cgsN2g3Essq24pxic8gKOwr5kdtOcj\nnJqkc08vbcmug0YnimiE+YvGjrTXN3RT6jM6JgmrGsDynRHDms007RkSLoRyIvc5a8+a2m0dvvRQ\nh2gvD2YbmLVY0ePkJ6mzmnkHgfED2kgLe4IyicVI+umq6LxaZxsbk9HjErJKesp8nxfI648+rkLT\njdHgTRLFkRijMEDu2qaq17WsRdOnjOcJyPO5FrmG5l9HyXMs0SKjBrNjniEGCNEUiqyMEcMYhDUi\nqiJr1c1TjMsDumI6pzSkn0dlq1He4nx3x3rovpRCKqfXxsG+7uot7abPVUiBYXHadHfMKesSu7oh\nM1Y3VE1Xq/N+RU59RVwsy2xrRuFuViEaOq3MOLqrvi1Y5mqyFCi6mjuTVzE1GvVxuDvngIg22BlD\nCxnYKimBdFZkVtPlDjpcHcdAGSO45WDGxFRVGwjuSrxgVvnW7At3cTz/ACKDQZtBn1EarfSz7b3E\nQ1OSFz8v5pWDUJ0I7R2vd1Xlum27ZGYmHbgXOM1CR2q1VhQUA4Kl9b1Qq6rxjeUXzgOtLZJT5Doz\nOgStHLMIStavh7tjeNwsewjcJm12FbZmg1BbCNVRrOdZ3UiGGxO0izWuEwAQygJoPR6qq6qicbWY\nbt+OozLerI5nnbOM8b4UCZWUQFl27ms/aHBU/sBFz++9Ps4ZvZsm5JmQT200vHKgrO73ZUqaAD62\nUxNFavcIoiac00XTjbW5ogNxvJD7k1WD7r4RYB7s6rkyO6KVDc1F9hertmGTwUXP0qifT8iskk1q\nlHuO5jqxfSNUDqX83h9Gcdafs47LH3y3/qiS4iau/lTiD5ZESP5cXYRvgjOhOnT83G4MqruIV1cb\nb10mfkmPAO1ZUZI4FOqFEmr26tTkunPjJrjajGkyF0qxkVe3lgYMloCugwxmmyJ6dKdpGGc4Ymao\npVRNPTxtNkE/aeXjsbNretq8pnXjniWsU8Yh5ZfIw/NHRqKF7BqRU1VWKqc+J8WVn6LY1lmGnl1A\nq2yJMbOP09sPl2xe4qr1J6NPp2qwnPARrDC7GqvLOqx2wEwkC1yGE6IkYMhhkcMrgRSSDCEqc3Ip\nP6PjcXAYGxWLYXM2r3Lw0sbC2WMefjNvJs7eP2RFfDAzyyLqzvMUGo+pPY433De7e4ft9NNiWQHs\nKHDCvPWkZ5J/ve6sCuepFRF11F6E58Ynt7uNPnZzgF4XDE2t3XfE7ksRSWFeZtbcjDr2icndqQnJ\nU8eacbqQ27V4dmVT+7uFzbi/yUjfNwwEWyAvkQujS0eq9hVXXtpq3xXimkVez8TdudK2WuIo8fOe\nvjMEKHbx3jRnnfDrU6j9jwR3BWYvLmydw8bq4ODyMZGF/wAXrMisXDghgJGJo5CgcZO0i8lRrfs4\nlfLxNxrIKfbXKq9thtG3MA9SmlxxKt5VdRjG7n6MoaL6HlT9DgeNF2XwgkF+1nxVAOoK1QoYV4gk\neg+xp16O8dOPmFmZ/jtNkljjNvAxSixi5ihkR6bGQUtfJjsixTNcMQpJilKr2Imv3f0ONsw02Iru\nph2EfMgtLtbjZyRSjl0gZU6DDAEsx3ZUQFK8QnkX8Nic+N5NvbvE02fzGblR8ipdnytCMUenfDhx\n0mV74qrFkMOYTylWOqo0jl6uCBYVjjBRqmEjkVzEfr09SeKa6Lpr+Vv0nrw+en+CnHy9q7TVcKrd\ndP8Ai+JCqmqIJ+qfmXjdMQokeMCFutkYY5BfiEY7y5kUv1p3OX8MWOZqPCdjhlYvgrXJoqfnReK3\nHLhCpc7fypeJWTzLq8nwgqgAZV9PdjoIn99/BaryRONxCq0YF/rWzUssuvs//UXKjlevjozTnxux\nnF1Awk+z1jXgj7eZLRMiks5RHl7rvMHD7zXtdHc7ni7Tp5cbYJzVsbZm2J9SKS1e3X8/T/DKipqi\n8lReKvaGwvBVtpRoyRQZPVg9mvnw5qzq+UABl0d2CIxeh3JdNPr4weXvNuBjM7FsBnRbsGPYlVyY\nS3FvCV6xZM8kuQdRsC9WGQQuSkTmuiJxnM7ZLcqiw/Ftzpq22R1t3VmsZNZbmGIEqwq3tOxiqZgk\ncoyp0o/mmicYngdXKPOg4rWgrwzpS9RjqJujzEX9YjtXL9vGRZtsRnOOUgc68sbNMPy6vkzYRLGO\nFsT4nGkRSsMMvlhBF2vw17aKvAc5+ZDK63dh1DjzKjDYtdFkUjIMiRIU88rmxDsR6v7Y2orvQno4\n3Q2ywW+BiW2OX2mNX+HY+vmJXwOzqrAMyxcJhHfhyvLscidzVH6+CeO3u79RNkYvm2GX1dZXJYpC\nNh3kOD3WtBYRmOawrxoZyhIqatXlzTTT6fkcO+K00td1+2wi+KD8k9XJ9GXkImvbt8ecxP7b4xE0\n4CvLmxvh4eHGL7lWtDHXLcfyjGo7LIT3Ry2EYtrHB5Cao9PMg98r+0TVOXLTjtxwsANXK5WDajU6\nnLqq6JpzVeIoZk6PENNeo4YjFYNxnp4tGjlRXL9ScbXYU6yZjQcwyc8pl1AjMWxZY1tXLnRpESRp\noIrEC/3ioq6ck8eKqql20q+lV0UUeRdTuhZMp42o1Sl7bWt6nKmq6J9CY7n+K1uXUzDjlBgWQGma\nKQJdRmEqp1DI3Xk5qoqeviTtbGwGnibfTHK+ViseOgYpCOMkhSOQfS5XqVEf169Wvp4vsfr8XCSj\nygHlshqZ55FhHlh6Vb0FHMKZqpo5U8OAYtYUMGZjcVkYcajKFjoo2Q3MdHa0Sp0og1G1Wppy0Th2\nW5BjDJOSkgirS3ceVLhSCRAEeUQiPiGCr0Y8jlTq1014qcnbSRnZDRVZKWpuXt65IIBXMe8DSvVX\ndKuG1V56/wAfBcpk4nXvyKRNgWMm4aPoOWVWdXkykexUV6h6l6erXjGbC/qI9nNw6zS5xqQZurok\n5oSx0MNfQvbM9Pz8NzNamOuUsrVp2Xat9+kFTd9QIuunT3Pa8PHgF5nuBwry6ABIvxZpJEOSWMi6\noA5YhQuMLX9Aiub9XGM4s3Fa4ON4ZIgy8VowhaKLANWqiw3AEPpa3sqnspppxRZNa49AsMhxhSrj\n92cDHyoffb0kQJVTqajk8UReLrJYNRGi3+RsjDvLcbEQ8pkNijjtI/xVBtVUT8rfgjdepuJTNNPX\n7PGzeb0lDEtVp8DxZoYMyYKuhhbNHGAsmZKeitEMXd7hV09C8ZcHJL7bG1dVRhvjrt3kZb5RIRpE\nJ5zvR43a5t9n18bzjX+h3Zuk/jiwv4dKpwjrhW/FcswBfbeKHlNQ1BlT0ozzsJR/3wf4J71arka1\nVVrU1VdE8ETjcdsx6ihH3MzUclz39voCsxUcqpqnb0RV+zi3ptoN15uXBltfKmYoXJRXMeNp2hOM\nOKxVUOnSxmqcvRxtkDzvYKzZa4XyZP6bW111H/c+K/Z+RulY29iSaIefW9dSx3vc5sSFWNBCaFjF\n5MRShITRPFX6/krp4+j8naKZMxwuQ4fm13OqMufAEU9jACGCSY2cEI9UcIKBcptU+7pppxQY7RBj\n3uPZNgFhm1JkEV/WOQ2HJhBGxhEVW9BWTGuRdOMey6+/q5jYle1iz31WP2M6ZdRXE07IzsKJgmq3\nXQmq8l8ON4c5zWmfjc3ZC3vKzM6Nj+65ErPfxCCd6UlxChK3+74xvGqer2/xO3ssBpcpuAZTYy2k\nDYWpjhJDCKO3V6BUHNdfFyc+NnMCwWHiK3WfR7l2QX10kx0GOeqhskI0IQOaVUIrl01XknEXIslr\nolZkMS3vKG6DXvcSGSTRWsqrIeM9/tKMqxutuvr043N3AxocIt9h+PzLSsZYsI+KpY7OpO60So9U\n0RfDig2Rz3dPbvOpmQ4jIvZjMehkqJNXYtkCbGhaGspnmFOIquRitYREb1aacWb5sHbWmw+nyfIa\nKwog2thIydgKSfIr2mWOoGhRSuB3OaonQ5PX9PyOvC7oN/W1ox/Vponkn/RZgJF8ySflOMR4r/8A\nEl+KxyNL/eoxf4+B6qqr0pqq+Ph6eNttv6W5dQ5BkGVR7aPcAjilSYETHxvsDTBCMitXQzAAVdP6\nXjA8qvHMLbZBQwbKwcEShRxJIGlXQS6qxfa5t9C8uLPcjLdk7DO5LKwVXTUJqcKEoYoiGIrVLaqD\nuTDFN7zy2vaYjea+n5JoGTRSxLaruZUC3SSXzhYs2Zilv+yqf9LR2rEX1N/gUfIMwDHOaxryORqK\n5y6NTVdOaryRP4TfFhurtvxWW13T48+lOXG2VZk2RQMOrnba4ZKfdWVf8RihOCPBMIb68Sp5pCka\ng+2n4nV9fG6USdf4nKtq8VesrHqTAT7e2ECO8UlREmwpi94ojInuSKmidL9ON7UznLQfvIu59nYV\neERHDLcWMWSGGAJIcRHIpNe0/wAPQzjejL8B21JcRIU+fB2qR0MlTfNEQKuhyjw5+sSUxpdWe6N+\niqrrxQZjlW0t5W4zs3BNS74YxB7PRcWdnDaYNnXGIrRvjRnBYvjy72nD883HxAOESb24mFxOiYr1\nK2jTo8kSR3ERe6/21dyRPD+Fx4u4mQtomZRMdDqV7JTq5w2o4pHoFj1aMaKiucvhrwKQAjTAOxpA\nmYqOa9jk1a5qp4oqLqn8AqquiJ4rxu25pXyK527GUeSI5ujXKpmdzT8+nG+tNVbKW2BJjlfIJBzI\nxCtrLF8+YBZpIYEG0SeZIJhOS/o8fL4do3PT+qvIkI/0M9qSifx/kb04HNYQRrS6FnGOPJyHIr7W\nJGjSez/xMyMTr+sifRcYdP2jvJ9DCrhzqPI6owpMq3VGdcgUKvc0XdcH9JjDOIvig9OJVHubg0rE\nrqipre1ZEHNjgi3V0V5C46Iaw5Dii8mxBkN3OlO/py9nXjDb7HLKnxy9nWsFtxhE3y0qoqKgcd3m\n1mna1JU6SUmiN7BhsZ9a8+MkyLbzcCluIkXD2gAPLVVIUy7UykeaNXxfLigsGNunWUxVX7NeG0ub\n4TXT6OpgNbL3hqLMZK+ysE+8OJG8uBStTmilF7vVPyNjsqpfhz63b2+tJ2SBmmMIrothTS65FjtG\nx7SOR0jVWvVE8F15cFyzFcllO2sk0FrGr9vJRVcCksrGdEkmWu/VAZAfhryYrU08eKyhk7FYnVzy\nTJsfJNzqm0jJNmxSySmHJOPyTTkc5FZqNxeS+n0cQrrGLWLWbYbkTa+X8w2OET3lo/HkaWseFfWZ\nRjCb/g2pxj24CbK41vDTxcRNRmDeSoceRXy22IpIixklxzNVHDcTqVNF1azmnHy+2uYYfCiY/h8+\n7l53ihLIiujtm1RokVoDw1ChekysVdNE04n4Hjk6NbfL8aLJscUgzSL8Vx+yPK7xoA3aftEUylIR\nquXqG72eaLxuPg8QiCl5fjVpTxSO8ELMikCxV+rqcnG12B55sxgOCQ8WtMdssu3KFfpZ2z30Jox3\nFqwRq0HaMby3b63m5I7w5cZvdxvltxa8sL/O7q1q93AW1cO6Sotz95O73obZHu+pydtC/Z9PyQtQ\nj2OXdhmiMbr1e4by+gxR9fULL8ccnR48piej0/ZxHerelXjY5W6aaKqIumno4xLKa2XjiSt0/LYH\nCnZFKeD4IsYc+0JLAzwMMyDRpRo4er2A9rx4osYiSiTw08VofPF06zvXVxCu05e29yu/PxNs7CQy\nJArgElTpRF0YIIWq8j3L6mtRVXjYmPimG5jPu4+YDy3HIz6pILLGmhwZUOdMEWwIATRoGxZohXjf\nqRns8+K/I6Z5H19i1/baYaiKMgiOEYRRu5teMjHMcnoVF/gNwrljes2KwRZJGT/haOSKyH/hRk4R\nVTpVU1VF9H8Hv05qIrkxKZoi+H6PGCxbiFZhBFw/DB4jBo1HGmsvUZBSlaBS+4GqTe1+L7CenjeK\ni3Jy263B3kZj2LkucjnxIMWs+AGSf5OPBBXCGIatlJL7vcTrf7DvBON8LWbh9XOyDH937iNW3MuM\nCRJjBBEhtCMR1aqp09T15afe4sclySwBRY7SBU06a9q9sTEX0NYiqvNfBE4zKzorKaoNt7XGsizi\nhnQpledaiNaR5khsuHIGAz454gDORNNHo1UReIxobmOiFEx8Vw+TFG5qKxW6ejTTT+Em3V7ZRaeo\nrROPYWk0rARwDb4vIQio1qJ61XjbPLdhttpG89FjI7yHe3k1/wABo3RrWOAX7NPsQ6SuY0RyAERN\nPTxX4bjmL7ZUFFEkdmryCZaFtJFfWFJ7mMou1HQqwQog9dPecJNuc+xOzxYMqUawZGpIUozYUJNW\nNCAHljPLN/QTVe3+lxX4fv8A7R5BSZjdWy0eF2FDEHJiXs1IizPLjYshFCXt+tVF/wAJxd4LnuK4\n1jeIx8M/eGJX1kwk+2gSjWA48QFkZNAdRgtM9EGmnseP5K8Z+cYWrIJunmb2hc7RVXzidDXv0Xnp\nomunG5gIlFUR8yjLYrk1lDy2/wAhkiPJsO9LjPDYw40QSIXoX3XP+Xj5ZIL39D522eQRWt/WeZlk\nZP5I35FRZ0t6bEc3xU75WJZXHG03YIRnQUEgDlRDxzJohBqqa6JzTTiA3MPhi5G0aJaEp+8kJ5E8\nXBbI941F9TlXT1rxhSyhsIoc8xUkXr6tUKlqDpVvT6U1Xx5afQekPZWx2MuVrZ9+tfYSauLYy5Th\npENZIF0catM7tI1X9LF0YvTppxus4blaRuHXqscnJUVK8+i8bbCYxrGDxana1jPuoiQg8k+r8iu2\n72820NuXmEqodfWYH3EGlh19ep1jCMc0pSFf3Ctc1EEF+mnPjbKwyjEJFbdbhZBVY3LoI8sEv4ZL\ns2kd1Ekj0GZgu2qKrPH0cYhiK1Rp0zMa+8nQpTXowQlpABM5hNUX8XvIiL6NONpj5vtbDxLGN8Ko\n9lt7d11x8QIrgxHWLRTo5Y8ZwVLEYpGqxSc+S8ZHtphW2EnMrDFKOovLu0JaxayO0d0aaGOMffa9\nXu/YCKq8k9HEYsmL5OQUTHSIqvQnaeqIrmdbeTuleWqeP5fyReX/ABE3YY/+IDfonqitRRZZjROp\n3gmliP8As8RFanS1Qj6U9SdKacZIORXyZtbW5DW0M+dGr4kwkCidRRrKKxFmoVBR5lgWSkkgxc+0\nMevp4I6jl5HFiTHFNGHEye6HGEKQ9xkFFEGa0QhNV/sNG1EROMtqMd3IzuJdWtaQVYKdk9lJgPO1\nurBSAlM5FEZU6CJ6WqvGJZJGo7LZ1+11fcGp3HkVc99pazwDjBiqxqSx+TQbSK96qMir0dPTzXjb\nSvyuREySk3cZLyKiy+BGfEKO2yBZGRyIcyG1xxDGqHN2iMMqex0q1NdfyQmeJwHlG17wP06mK5NV\naunpTwX6dw656oj8sjRMTjo53RqbJJ0emFz/ALuYnCIiaInJE/gZ9dtvgGUb3ZDXnfDmQcTji8hE\nktRF7cy0lkBFH480Y4j0/U4rB49tzI21rZVPMl2/weurb2yBNH/osMMqZZIBe/6SrE1H6RrxudCz\nS+3RjzD1EcuRyrStYOkeNZwY6wEPHxvkTRvWpBFjj9r8UnGz8H5gL2iq8PzDDsdqjRMhI18eaV1d\nGerF6kXq6NOtX/o6dWqLpxuvT/LyfF7msrK7Gz5Tk1FMPaSzSZHxEMeLLsTmkd1gAxU7TEf7tHOT\nRNePmFOwbBoXejINUYuv3YsH+zxJ2Zvp0DA8TwLIqC2yi8tVIawu3xPKXMSNSwBCf3BqboGcj+SI\nj0a1dOfzCwqixLlWJbk4DQ1F3Z9ggBVxAJaxXVyKUTVc54piyOfNiuXlz4wBb1OnJMdhExfKBq7q\nVtnjxyVMxFX0qporl/P/AAmPbfZq99jiOO4qmXxcKP0/D7exSx8s0ssS/wCkMhIxju27VnUViqi+\nHAo8YLI8cLUYEA2oxjGtTRGtamiIiepPpSsvYhySK07bCgs4JUjWECcBFUUiFJ8QlavJHfx8b8bb\n7i5C3LN1kPXZJY5ORylkGgOGsNtY+QnuiuqlaMZFD7CPKunj+TKMEaFKET3iEq6I5zWqqN19Gq8Z\nHYy2iAUu4uWyTu+4NO9MQ2qvX0e1zXjNotHV4vMtMmrJ+QZLkuHZDaW0Ic1bALThlxpoRACQ5DKQ\naiTwYT0cfKQ7s6uPg9uJS/bAyZ2n+B+Vs3gl0+xPicmPkmU31VVzZcApi4+OD5EhDQjgKgxHltci\nIund7XGKbiRo0nOMpXCaq0ihe2RMNIfNCFw3mQSKYyiYZHF0949Gu/SXiXtXh+2l/kcWwppNVBzq\n8fFoxyrQ/vH3JYhjpNExZhHSPwuvVF0TXnxNo7bSZHtIJINnqmiFYcSiLy9HUjl5cbQTja91+JVQ\nyK7xVwYzBKq/b0fQ8DXopRojns58kXw+jCshvvltm790sYEysu5OOzmxchrBGeF40CAkuA2VHKqP\n7o+8ngi6KmqLk1nAwmzxiow/curzrYfY/IbtJdkGtqGNbJrTTFPJDESY5xXhF3ijCqpr6+MWzvJd\nsLfaHENuqS7gRK7Ijw33FnZ3zI4jdAoJpIhx44gqqE7ur3u5Jo1V42Q3HxI1zbbrbUUh4FhtPll7\nIkU8uNJG+PJFBRXSBV0hRo1RKFO0iaDcnTz4pd1ch2Wz7Kqe627qoQ4WKSyIWFbgsjGJFtY8awij\nJ2xS001Ug/Zf48V2XUu3d7bWdg+JrhJljQbMDJB2iK4yHMgmqFrle5OvmiflZpV7VYi7P73CYjiZ\nHdvL2qOtlJr/AKvKcKGOebpovlwiVU6m9xw9ePl9tN46y1rlqtxYBsXx2ZXya2CJh5IQdQxGDzXl\n4rz+iZCYXsLMzDEw9zp6tOq4jej83DGa9XQ1E6l9OiePG04MkqxTnJjuVSDR3IRrJooz6oLQSe3o\n0o2LLc9GEXp15onjxjGDYZhhMnupYHPh4nUEjQh19VEZo6QRSqwYhoqIITeXW9elvgqpV5LSSPM1\nlqLuRyelFa5WEG5PQ5j2ua5PWi8QwVmD3WWNlMI4p6staNgVZ4NIs+bE5u9GmvGCbk1FfkWO7Y0O\nNNdtzil9buluU1iNqCkeQFIlBjthxHPjh1Ir1Qr0ciIwa/kScLFewSZbDrh28vG2nYs0cAxXBHJc\nHXqQbiMVqO001+i+JiBZ6/u/J7RmWEMsN0iKQhhRbGKhURSxJSxyqEqcno1V+jbzbOsRJVPhc0ec\n7nlauoxNiDIlDBIrddCmnuZMa136EZV8HJ/A0O1WOTD1s3NnFLld9EI0Z6vHoiIsswlXVULJI4cU\nXLl3HkT8JU4dt9hQI0OHhUcUUtXXiXy0JFTVoXkanQhVT2laq9a69S+Ov0fMnXR8KtaWdU0IINjK\nlSqaZHQdhYRoRRK2DYyiNL2iPXoINv5+NvCWmR0uGnpMIwe6qslyUKyoEOxq2V0yKpxNVHl6yiQf\nQz2n9XSn3tOLCXY5LhV2rqmmuaqJiceyimFAtUlOCaWKy9roMoHdpWcvZfr6OPmVitM07Q725ErS\nN9OoIjdf8DhXOVGoiaucvLl9vEbabay8xpLiJj0jJcyu5zH2iQRLIHEggSNEkx17h39ar3CN0Yxd\nNV04jEzDdxLndC33Eta/frZsLWyiMlz5aiW2pK4AfOCCETQSV/ERwVen4vCXeI30PIKvvPjklwyo\nRBmEuhBEb95j2+lrkRU9X8HuplmO5FcU8rZunl45sLbUU0lfrlZI6S7CckkaopGtO2PE/U9gnivG\n2NVssu6dpOs5gq/cqLu5Qwy1VYwbUUpg2McEZSMcuqI9DF1/kTdp+d4rtttzbbWWcuudjmQXkmpn\nWHlmlf3WMktegxORrdHu1RefGI5KT5dMmoaDLJnYFbLZV5mRo/c6EllCV8aR2+Wv4Wun0YGynpx1\na5ZYWeP39lKkuJKOy/qy2gRxIwEQEeJ5uAzXue8IX8mRprr2n6aeP3V8OLkrRkI0e4GUuYPp985E\nOxdHpy1evDkhYVmONg8qspk3JKY1WJ+hO2omqZeruenp08OfHyiqn9Fh1o9fZ18K/J/T+Vt/XxDX\n03L6m5gx84hYc22PPj4dal/b22aU3vBRTLHYqKXn7LlFz6uK+jpd1sKrKqjD8Mr6kFpEEyIOvTy6\nRkD1oo+12+joVEVNNNOEGPdvE3Ed4M+Kxdf4uvjfbfXb7OKOgw7bmJlpcACCuHbMtgYkyYKTMkSX\nl0VDSIpEEgtE6WtVddXa45sbg+6EXPMTvcNff4uyTbR50+DYQpQ0nQ+li9TGFFNEUYl/D7ZPQv0d\n7pTuo3o6/T0666fx8LqmnPl+WrO17lGI5D9Sc3aqit6fHw56/kW+QwYS22RHUVXhlE3m6wurB6R6\n+KiapyeZ7epfQ3qX0cY7iAZCT5ddGR97cq1GksbM6qafPL63yZD3kdr6XacfJdLLIb3RbxVwG1rv\n6cZ+hr3f8m5Gr9ARSjdnzWc4kwC9wgupzLUJXt6xe0nuxv4E0a6jaxqMX6kTlwIYdyq7FcrxvHQs\nwXDLoQnQbaDblctmRE9yd5FNBAxHiK7tI3mNe5zyjJ4uF2pLHMbABr8LBreVDOiKKEkuLNhB8+AQ\nkE0nYKDT8RW6K/liOLVWdUklMaqYlYVXmbAK8kYaAIVYklzSj7hGuVEcn5146nXle1q8kcskSJ/v\nuBUlLbRLF+F3F3SkFEV3QOLEt5oID2I7TURYwmOG5PZcn3V5KicGAKQMh4+nmAteivH1Jq3qai6p\nqnhrxYMFMCR1SXs2aI9P2cnaYbpJ+qvbI13P0Ki8T9xPlqQOc7tWe51/Hvr+0rpKY7Cx5e9Vx40m\nzckdhhgiwYskY4pial/R0Jzkx8g+YuvxrIZ8Noj/AAHHIB4QDtKZhOx5kSSO2YLmKiqXrG9OSqnA\nshzWTVZzhVLh9Th8qXjUM8KXWVWNvkvizzxDSD+Y1bLJ3UF7bETVEcnVxGmwzNkRJgmHiyGLq0gy\nNRzHNX0oqKipxl1lUBKtlnFy+8yOwkEUpjyXBFHY3rXmgxCCwY2eDWpy9P8AAK5yo1rU1c5eSIie\nleMu3rsEeJM/keWxQRvGNjFMQwa9U1Tkkt7jTeS6aHan6PGQblV1b5F2aySErXKssavgo5EQz40o\nYFE6S9imVO3r7Sc1+jd29xmmo3wLuJUw8yUVMx1s8PxeKR0lZ6TY+rG9LE7bgkXXn9mBjvo1xNF/\nV/hKUgqd0YVmlv2q5Kp4CS/2cZEmKLmX2E9PGbYRvXHvWb5UVDUCQtjMgz65MSSXYPrWVxa5O0NE\nkkkdxhPea9K828fNa/Gd68h28pR7oWMKVWUcOvJ3XKZ5VkhNNBJcIip7tdEXknHmM0v8z3OmuGgy\nnyjJLAwXJ9cKKWLE/wCZ4pcp2Tnw9lMnrq+RTWE+pqIkqNYVsggzdmXGL0oR4ijR4nquqavRdUdy\nx/N8IvVm7zYvPs7QmYXbBdN4S67SWMWf2xOUYStCxo0Fp2ulvT6ePmuyDJ6SBjGtxjVS+pqZnnoJ\nZkKp7h5XeUAF7yjkCGXl4sTjbEEDApOaUmYTrMeUzIcgYpFXDrYfm3yBCIqd5elHL0IqL7PBZONW\nOY5tEAxpDTKPDr0omo7p01eeGBP0k42o2ewLGLUVNl0uXByi2yaCenlBlMEbshiAOiK9WkF7eqc/\nBPX+XuLZbaDcXOodHKLjbRj7xEkNb94Y/wBJ6JqrU9fGCx9qrONaYZBqI4KwwCIR/st95301VzSq\n/qUiO59WvDhY1n8vCXOi9nuRYgJCoXzAS97UyLz7Y3j09T9eIxMlxaovyxCNNHJYQgSFYRvg5qlY\n5UVOGjGxBsYiNYxqaIiJ4IiJ9GCZxiZYVDHxHIqPL7u/nRxgpwvjl+FrJtpa+/kk8qQghRo/NB9w\ni8Lj06DimeUMZwRWWSUorisjDId/SqDLLFIabtJ49vXXiezCYmG5lPq5qwZeIVuSEhXpCILur5eJ\ncwIAyaJz/FRNPTw7E3y5WK5wFP2jCMijPrbFHJ4oBC+6lInj1RiFbp+l9Et36oSLz+pq8ZYqW/wk\nQ8zzBHWY9OqAne1UvP0j+/xXvtX2tHENhKEjeeWxKPNfewv/ABEiTJUkUbta/hDRi/tX6vLj5TZE\ngTxCfg90OPMT7jzIG4Ttr9aIT/C/KI2QHI5tQ7d3LE3Sj0UibFkQp0WDAh4g6e6GYJkr1rxOLquo\nu65Pr4Wfjnw6XCdMl6y69BPGstDvHLXqFqnX3UehF8erXX08KqAHqvivSmq/ycZXh9Vmkmi2mz6b\nJn5jt8GFHIhVsCISyjRJb/bjx5y9feYjXfff2lHrwkHJMRqraOxo2B7sZiEG0S6sQRWo17On0dLk\n4nR50mVZR8Xy7KcboL2WZJD7CqqLqXDr5PfTkXWONjFf+krVX8qKS1sY9cydKFChPkkaNCyTLoML\nOpU6nuVOSJz+ne/DbyeWzTFsliTsbkmVFcypu6yNLGD6kDKSUxv9ojfyMegqZ37tbLVa30+N+hIy\nK9YaHXouqeMOEyS9frkDX0cV2Vrbz6V7xpUvmAv8grwtVznlEqQKcUgJiff94Ua6Jy18OP8A/noV\nJWtfY7jnlFkCWQJ/dhAC5OlJQwk07o/6QSL9X0UhtNWx9wsZI/7EOTiC9PB8cTv42ovG7sW/pol1\nHqm0dOwc8QpIkF5N01WMa9run25aqv18+ELhOb2+LNaiI2nkq23rOX6PYm9RRt+oJx8d3MdqsU3P\ngg5tmVbxssNET9GvtRKH+KbxjG3t061+WiixirkW5LifjDKYM24muQMeE+1d0QydofWVRiMqqq69\nS+iHgWI5zRZ9BxZuQ7fxMwgRJDxUVTUz4pYVlYOcJAyO+Pu/DxqqJ7b9V6deL123/m7XddFr5Ycr\ntLyyhWVmkKaCTLhutIhUNGSZHESOna6WM609npTjLp9bhcbC9wcChSLubduhMrGGMEpQzsYuCAFo\n+GReuOP4nJJII/WUouQuKEG3QrHub7ycboY82dKmkmNrrkA0M48wIpRhqCrE9iE7b9OlNUXx4gYP\ntRjtdTkq4ykr6mxkP8u6YXRxVlS44HPeuvJSIPVdE5cJGOTbWBVEjletsFlvKkCP/Rh8o9wGvb6y\nd5P+L4/dkG8eE0cN0WYHIp1FRGdbjUge2JwQy7CUIfSR2qq5Ps4rNtrIYqzL9sIEShuqRDOK50eG\nNI8SeFSI0jwShDR7Hqnj1MVVcxf4Cdb2ssUCsrAEkz5pndIxBE1XPe5fUiJwGwspEzANspTFWPjg\ntB3N3HIiojpptOqGAo3fhDVC+PU9vLhuPRIra+nHD8hHhQ9Y7Qx0Z22sF2+noRreSdPhw1jE6WMR\nGtb6kTkn0b4LJKgmyINXGC5fSU1vBGNE+1ypx8v2LZFG24NRixyEGPA3Fzm3wyH2o9ZGaiB+GBOs\npURERe7yHyVPFeNyZmLR9s22cptWK3sNv85s81JIGBpuykstkADhjEhFQPSngq68b+bA4dY2NLlO\nb70WFzZZDD6BuhY5WmIScURCo73p1H2k5Lp18bj7e/vXc5Lh2P4vQ2kZMhmJOmjsLKTPQnbM5EIo\nu1HbyXki/RbZtU5xl9K3EGwZ1ji+P2PkI1jXxpgyWATdlrTKpYqkbqhE9HESqxCqi1FGusoIIqIj\nHuN7bjPfqqvc/wAVcqqq+vjbnJdwtvrXJPlhwCaashumRJCVNqc5FiWFoHX3Mry+vJPSP7eK+NVZ\n3RV9G+IORXgx2vkyYbIzvw1RK2KQY09SLpw/98cNvsrqZrBlFZDwe8kPYqe8jlEf4ehBvV/Mb0VP\na8F4ytllMtJ8fD8tsqHHpWQiLHvX1UftkhutAyEQqGUZE9p6av8AvflZ5XnzG8xjaja80WiFVY1P\nfWHuL1wWS5r5U2OiSECAZxi7YysXr1VfDi4l4fuHuJg860l+dFIrbpV7JfX7TOt/538J/Vb89+Zx\n4cQRXurchFLkDVdNdeoE5W8v+K4DluPfMFbS5RNm/wB94TrakrZlc+2gvE+XHIbsaqphE916fTxg\ny5VtYlrheSzK11lKk1cWGMMCQQamMpwKnb0Eqrz+jJ5Aq+IQ7MamLAvL4iFrYBdV9qvr2+8kWC+h\n6J7sfP08bZZxaVcC9/evGq6ZOfMihKj5Dgp39WuZ06Ibr9HFkPD7C92ckW9iK2sT4FM+DNNMELst\nK8QWI3Xo5ctOGw873wjbn/L5VyBRlxvIcTJb5OGRZyxgCWJZQJAJXmO8flIUqKzx09Wa7RX95Oym\nFisWtu8GyS0L3rAtNaukibDmEXV5CwzRHt7hF6yMcxV568Kipqi+Kcbvw4taA4wbp5uKjjmGwTJP\nRLVnbLpy07jVYuvo4ifH8aqI+H3mImmnshNcybVWpJYHOohiac4Rxo6K9QqNdHs015j4+TyYx70D\nLxi/jvGiasVRJIXVV9fvvytkbOwoBMtMkzEVZlVrDkya6TYVsKpspgokssMoVkiQwWe7Krk9XGLb\nHbQya/barg1Zbm9sKqGFzqquBJEwEWJF07IyTSkf7T2qnQwioiu4zvb/AC6a+5v8FPDkAyZWDElj\nUWyyS17njCwI2GF2SCL0s0VWI79Liyra64Pj86aBwot1FYMhoz3eBGMK1zFVPrTiu2uy/ePK7/G8\noxCwtooxtr6kpZEGYEBg+arwRz8xS0doNW8m6qvFbQUFcCppaiOyLWVkZiMEAI00axjU8EROJ99k\nNnHp6asEprCylPQYRDTxc5y8k4n3eKvmsHU2Jqq2rrOGaBNiygtYRGmjHa0jO4Igys1Tmx7V9On0\nT9z97KQOTYfCk27La6wuE9ZlESssTxFi2cA51UmnaRO8BU9vkokaqEV19sps1TYxi7ppweczYspl\nkyPG7aoRgU8vGeQy9bEH3tRL+JxeB3D25xXciNVUVwLbceJ2Tq99beI9jYV6aPPXUkntp7lgyqg/\neel2vBTUk9Pidf0iv8fksdHsK6RoiuDLiE0KJyL6HJ9ir9G7W58V6FpM7yZsbFD6cy1mPww1PdRU\n8WFlgklGvpY9q+n6bnJ7K1jjpKCKWZaTmkY5ghBarnKqoumuieleCZNaEoQbibp3b8lkY7k1q6oY\nCPLUQo1e03lpBe5DhMAFU7Kp3Ed4a8KCYT4TYyo3RJJXm7vYI5ujlAUom69Kr7LnDT7OPkbsrGTL\nkvpt4LesKSbJgyjO1hlQPcJX6BRUQKclTuJ6fT9FCsZNSs3DxhU9rT/4l3EbXx7TNf8AcpxuqY+i\nyC59aoVUTT2RhiiD/wA0xnD8PXM5e32O0mPlyXLsggGHFmFjKQgGMDJIjkAwPaeQxNOXu05arxRp\nt2fIsnoVKN9kfcmHFq4r658VVYWNNhxmyiFUnQvtBXxXXjcH5edxZ1DjWcVEupkHxWztReXlEa4d\nhCJGLoExBFQeiqg0ezX7uunFhh2FY/bbO7aAzTI5VpawrQZLOyKCwVIIqqeBF/YwoxG91de4jNG6\nau13Twgt/Eyy02eyIePzsphPErJ7DwwzBPI0Sq1pRd1wSonLrY7Tjd7Lskp5ssuQ1Jp1nTfEZrae\nRbAh+Whzi1QzNiFkNVo29wg3LyRV9fHyz4rXVA3RK+/l3EeEyqJZiitqq/yoXeXDLhdpglmond59\nvly+iFV7jZvGqLyyYhYGPhYSTOKNV060CJrlRuqeLtOLJ+LwMpssgyeaxiBgUCuNMlnIOOxg060I\nqlIrPFPHnxB3TxfErrC6nbpt3hmTmyMDoFjOkvWMVYSQ+pyoIBWoXrf4qvJOIFrnGRwsZrbOwDVw\nZs4nbGSXI6u0JHet3SunEfEv3pqFyuVEWfGxlJoPiBIqeJ2RevuqP+2Run1/k2OzGLU85du6msmp\nOyylsxRH2F1DciEr5UlupYoE9pNRe8f0P09njavBY0B9JLlGdkO6EShsJoqqfW1SInl5cV5tDNlz\nCi0UiKujH81+l2YY9m0rFAERgu7ZXsIFOpEYqIPyM6HJ9pdNfdLqvjxjpcis4t1dmgBLZWsIaCjn\nK9qOV4mJqiNXXlxuv973U3FiewzrXlktZ6Pz8YZk+1uVz6S3xSiqHWVdAx6FeumQiijBlP8AInEp\nPcBV5OgSoq6aacuN1K6dl1juFtzTwaUmLZtPxBuJd2xOstLGK0floyyeygxKpOnROvTn48fMya8k\nOi53X7vXBqi5q5qwbmFF0RGvjGA5CtG5VenPVOL3OZuY3uZZBc1kambMunRVUECI9xRiRY0cHW7r\neqq9+q8L8ezWhpOn73n7KLG0+3ukbxcQLvcSvy2VPgnC7GaBVsZBxGYo3cg6p0O10VdeIW3jburP\nc7ibZWUzbLLqGQXuNFDQcdIE1S80kjacQ3PHyVUevJU1WDtlvPj/APVmelqx01ziltCWxp3vgi7J\nQRigCvWje2uidpNOMYhW+4OJ7a0eZz7LJ8ZoLq7hw/LwraU6RFjASSdFcgguG32fBeLB8Tf0OUOn\nIF8ehoY5bZoFifiME2FGIRVN6dVXjPsxxHDdxC4pbYvUQZdoLDL5wbKzgyZCdxNIa6KAJkFxKbge\ny1tGYNyDj2+byGY/Hcvpd5ZGyZit/wCRThp/jO1tUBPvVzYNzNVf/wCIdIjf9FwN0nC9v81Ejvff\nCbefUHVv9oGbGkD1+03Eb+tOnutuBySNA20lAbY13fd/RJLrnSGqv96nGWXO0EYu22L1FTKsT7o5\nTCICQcccKHRtXWmRhF7iIrEKVERP0U104wagnyyWWR2kT94MytzfizLi4Xzk0xP7ZSE6fzfQeMdv\nWGQNwjM9bXorXJ/EvAtpIG68Ie1iRS1T4zqH/XTKcmrEgDmpN7PISqPuKDq09HGMYBDintL25VG/\nDa9rX/D4Q2f6VK5+7EmiImvj6Po/ebJos+yiyMesKevq6snlSEKrVOpZdgZUHFAJOa9v3j1Xlrpx\ntys58l74pJ0YD5L+vUIjuRnaX/F6eH5+Nn8OJUyJ2I7krMqhlgx3nIOwYIkjvyXIxUEEQw6KvV+n\nz43OiFbFIwVYOYo5oCyozvJyQyNDAB7b2e75onFT3EhuK7bqMFSxIyxmKgJyfgjIQhRj95yY9V0/\nWVUX6N1wNKx7ou72bDEunsI74g7ly9GvGSt3lGjceBBMAM51kKaOwtFsjlZKgAZ7cWMkR7B9t/PV\nE9XHyTJKerUr67MZwmo7RFKEEdR8vt1/K2KxLCfgD7ysde5usO7OaOk0dVFHW+SEUIDqJSfFlf19\nDtO393jLMpyPHdydu5+4b4cjMgYOyDlMIh4IBQQFjSgQyWAV7QmorUCn1JxcLL3QJFyHIHDm3tln\nJJFdYvaBOyIZPiAInbYHmjWdKdOq8E8vvRiE1wvxBRLWPIIn94J73fycbBR9uMvo9wsxqshsoVhS\nxp4YgmRrOnli6CTzp2RvQzRKg1XVfTpwG+q2Fjoh5EKyrZCI2RDmwyuBKinamujxEarV4y7BvmHh\nkmYHiPwg22c6ONSQKiUcPfWbLja6nLqv4ui9npXROMPu8NvqvIMZ35xyU1D1BhSUNYY63vBnucLV\nFYsUj473qvJzAjXTl9G7NWwSH2Cx6zFZsp4FpAWLJy2pXycuTYQER0vtkKxFQa9AiFF3V7vPhwMy\nz/HMUkNCshY1vaRIRe0n6aDORjlT60TgczAhZHuVXGQix7rFKGxsa0qhd0vaOyQDYb1Rf1TLxstv\nHY7a5HtVttEXIcWu8zyMAYMmU+egQ18axh6qePHWWNVEQq6dzREROvVXNejShMzRzXJq1zXppoqL\n4ouvAIcMIa6srQIMAGIgxBCJuiIicka1qJw202r2jNleLmGVazKr25BQBsO2qIwsMCglneAiLq0j\nxs19DeLravdWjnbGUM2rfCo66RNQ1fmFzMEVGRPjIB9vyodE6o6IMxnehRJ0kxWxyrHsesnbERn0\np8iDChI62ytBC+Iye4EIV8rXrqILCN/F6nroo2qq32SwruHUY4Vw6fH7NtBPpZ+rVZ5wDEDKmCcq\nesol+r6Pkuk19iaLCtt02vkQOxHWKyTHgFVS9TRd7uFHq3m7Tl9GPxHNa8UzcLGRGE/7rkWUq6Lx\nHEjO2ghMYg/1Ua1E0/NxuDZWcqWc1jn9wFkIEckqUeWvQgo8YAGvIReyNuiIn8nFZAsQV9nZE7j4\nVLeQe1MGSO9EOHsyxtchBPREIxOaac004NIO9oI0UbiGK7k1jGJq5V+pETjIr7cfaW/ALNMgmW8e\n2uMaJcRZFb3O1VGcWIOb2hpDEJU7yM6Pq8eLHZH5ZpI8RumQIrcnzE9ZLq4uNU1gQoGkrxFBHQkk\nrQmQPa5DViuX0cZnjG0MiJbQ6Spp67cDJWTPOzJ2QtJLMRZpdXIpkCVjnfU9qejijxRiIpdwMsos\neaq+gZZjJUhf+rxicbR08GFBmSsCxe2t5J7GBCmiiEupkMEYw2yLCDIR6MgH0fHaRWelOf0R9wcj\nv8kxfKxQwQDzqWQDtmBGV3aR4pASt1TrXmnEC/fuznUmRTTIlhS+XfBikjSoRe+IiFbHeqqj+fhx\nJu8HzSwySzp0bNkYvaxK1zLhoETuA74I0YgjGY3RCdSp1aezxhGV5HS1GG7axpIcgh42UjLa2sCI\nEg2CmPbpEji6TPQjEQj9U6epvPjZmHtbigbp13EuXS8fktlOWDD7kQcu5bcSDPGnlAlHGFFcir23\nqgk+hz3uRjGIrnvcuiIic1VVXh37k2Vpim2YyrF/e2riIa6vjuc8aLVoUR2RIKKxdZpB+8/odE0J\nwwr9z9z8FtbZHiHGXKDXxkd0fojsB2IkVPH3bfz8XVPf1bpOLXRzWV7vqNxTFkl6yER2QxkR3l3p\n1u9+JFCuvtdvjNt1RjItdlkmNX4ZJKxEaairhe4lgVUR3blmMUqa6at6eIuNms4476dGJMiVLnoh\nyAEvS8jWeKtReWv0HivIQTZA3DcUL1GRqOTTVr280VPQqcOqS3LLqyxmbJqrWR50k8zTAKqoyQco\nxPcRGObrq3+PjMo1f1ufZ3+MQzhYuila+6iOaz85Gs4HlCSKivPi+Lw5BJGSSTwa4SijjRyyzCAc\no2p4LoNV19HF/nMrB8kwqCBkWvg/EDMNR2HbUqvl07+yApWuX7z3tTVOhE4+Y+1yL5epm5NGTdi6\nBEzimJDdaxXgVEWL2TzYx0GmqERQrp7zmi8uHiPsVua97vZeCaty8Sp/fWTg8EFi/wAp1xHlqP2J\nz6SpRz+14Ih5c3q+znxeZbvfsNkWQTLCjiUe0WNYTcQ5t3ELDFLkH8zXwzogvfF5ERV08OBW2Ruf\nsfEWUaTjl20/nsoDXHVHOgLFMWRDEwyoilQgur2UVE4lWhsDNm1xNL5iTa5RMJNe4vV19ajZ2Q66\n/wBpxbWOL/LttzcZOOO4lTCsKmFHCeQxPdsJI8qdw26+lGr/ALfAqPBtntqcfiSIjHLk1UjoMGEb\n0iUbESTJ+3sCTjGRZETGt35EuQ9MqNVxG0JIgtPZUJDzFYT/ACKLxlNtm+F3O2o8TkvDOW2aOQE4\nG+EqKaG4rSjX1omqcHm45YfEY0YnZOXtGD0v8enQzGL/ACcXeP2DpDIF3BkQZrohFEdBSBuG/tvT\nm12jl0XioxvcHAK/FrmFksin27vZmPyUY4cAP7OS0mdjygpq9t+q6p6NONuNv4eeysgwvMLWbTZB\nh1R56uPPekUx4slxEZHMSKEkZdXDco1crF1VOBQsZ3KnyIcaOkeFAyeHHthhaxNGK0wPISnqnpUp\n38Ro5dqqncauemsm5xu7DVyGL6vh1v0s/ilrxcw8vi5Jhdhjj+1fx5tY6aKMT1OkVj5gl/3XDP6h\n2yMugmVGTM8lQJMOor2u/T0mtikkvT0DEn1qqInGT7e7SWxJ+WnKwm526ksiTDwyHXVGuKqp3JKj\nV3ZEz3YvT08+K+liSJUsFeJBNlzSqeSVfFXmK7m5zlXVV4xPGlkRGSZk41k1PZLLCyPGMJTIMqdo\nY072ikIumvJOKZs2MwAB5HdNrCMH2u9HQ6dJen6114LGmBaUZRFF1+D2IZjhvVj/ABaqtcqapwlL\nJrUy91K8VfURWkG0suvaQYhPOpkaNCDGqq70L0+teMtjo7UtFilG1W+pbCZZvd/GkZnF3JvLubZN\nxtEXIW0NZOt2wEVP/iywgFED7CvavG+zKyQYsYW8GTzADkD7ZGBnFaYaKn2cUe28PLrnGLScEDTH\njQYB4ffmqVYo184EhiOIgXpqFFYPT3ipry+Rdrpj2FkwsqhEVRdSG78ZOSqxERFVR/Yn5WxdPf1z\nLGrqw5PbzFFMkQZgFDFjRgkAeGUJk95J0XR6cBr8G3cyqlhhK8rYF06NkYkR/PtoayE+Z0NXwTzH\nDwx7zb3I4XT7LbCosoRXr/bIOdJZ/JxK87shQ2jld0Bn41exh9Y/U9lhHiOT/dcWWd7jVO4OEfM7\nmUmVcQBsNGmY5MleZb7bJULUI2BjdLO3y+6iaeni+xW0yuWBzXQ8mhW2XN+GypT7eOxbAaFkDjMk\n9iWN+pGIuvWnq43I+bbb27r8wq4cyZA/d+E1UWZQ44po6TYchDaEVOl/L+15cQMzvq9Y2fbnibZy\n1Inva+tJzhw2ap7C9PvHonJXL9XF3kloVA1tBAkWE8qrojQxhuK9dV+pvFnkN9KVbbJSutz1rhvb\n5UlyUlkcf7XT18pmhDeCmONfQqKnD7w+O1h7ojGjJbkiBdJc1n3UUqs6tE+3ipi1dg7E6+kmjmLH\nr0CABBNV/XHIxW9KDIr1VURE56LxLw7LMlh32NHq3wriXdzwEJIiub0uJIM5Woq6fp+vn48JDsrE\n19Dxq4saPF8skMVHXFPBN0QJ/VroTrFo3rT7/T1eni42nxZjoGHDaoN2d1EkMFDrobvZPWxSOT3k\nsyewqsX3Ovtc9OJW7EaoUtfT1Y4OLMbjslllAgxRKNzIKMY85hGYurWiFzTknq4yeeapdbxb2vbC\noqezjyIJT2U8rYleJ4pDBGC90oo0TVrXJ48YrtLBsVO8MF4pkyeLz62T1ehbMknvJo/zDiv6utdf\na9OmnEarpawNXTVEdBQKqvAjBiENOQwhE3+JGpxkuXSby0s42SSlJV19jGvKxYYE/o0rrc6tEv1j\nAPXj5NshiyHx51XvFCiiVrtGqKdEMwvV+ZifRi0xvc7tbuJjRxo0z2D1Q7/xB/hET6icuGP0062o\n7T7U143l3NPcEnYpKyCZVYLjslFItfMjP8vezBq9PdrJlCUaI39BieheeTAymE2zHkWUZEaygFRB\nlhkSxPHaFhQuR7HjGJidbX9WvgvDsSp9wSEwK5aOFkcC3G+TaBrtU8wKDYDcwjnFHqNVkITRFXnx\nHhxRNBFiCYGMBiaNYMaI1rUT1IiacZ3Py4mQV9VT4TCtcoDWWLgxrurhHsX+TKNvQVvYd1r0iKNC\n97QmqcCGSmhUNxk8s1/kVZAjDihDKmI1GgQQ0RqdgDBB/vONisTqTgnZDW5TIyK3rUVHFiVAKWyh\nllvTXVid2WITdfFX8bl7uHizx4vd2ZKvE5qpRSq48Gh7lcNRkYi2gCuOhiK1V7fP6+eTYxDrzXOY\n47hMrPGUyPYIcithnUBGNLq96EVzV0Ttqn168uK24gE7sG1ihmQi+HUI7EIxfztcn05DiWaTLO7x\nK+irlu2eDnlOHRxjNOqXbfKAQLTESSdh9C9xEQy+HAszoKMlVbRoUiDDiglykrowpLhqby9f3fLB\nc/tM1UY08ODy5Z2RosYbiyJBXI1jGNTVznOXkiInECLEhFj7JsOs24yQx3QyZE2Muoo0aP091Ifd\nRVMQvb7qMRB9Qn9SjziHJubCcCK+NUwrSzkWcKAMzke5YApjjLH10RNBOa3T0cTJU6YyyMQxHV5n\nRxjJGjkVF8uj2Jq5qKmuq819OvBdn1MsfDo9MK13KOAiIaXHmkKCLU6pzY06BI8y+KjRG8kJrw0E\nKJ0xq+OjIkEDUTRgmaMGNvJPBERE4ss0yLF0osiI1ayC6VWkg2A61HIZoDvceQwnvFVdRu6eXFnc\ngPVRnwWNf5i6lPhQWIrkaqmOwRnMTn49C8+I51UaqYbHqon9xntIi+y/ROpPUunPifXK9zEy0HxK\nK+TaPM8kmIjQnFGhGcvbY0ajcqi5etE4ndxzmquZ4l20Z4q74vH5cX5McIg7MVDHVhD+R17GgvMa\n/E/2Xq7PX+Ly1+vTjP5WyUzcCUrLGPGyxmbp22DkBQqMSAGJpXMGqq/lG5evj5h9Gdsbd8Mp7Y9d\ndE7ULi2x3Acin7VYHhOR+Uudx4BButLeVVu0lQYAndQ2R+7qIpCJqqtVGt8eDyJF2DOrJpC+enX2\nRyLU3cVdCdYjSnDYvr6Rt4kwqqrHt4aXCY4OYVeOOkxUZyVOo0cDmlVE9Dl4kh27+cmtvreXY+ZU\nBYlYJYsX0gUTBulfyj4ZIzHEca3ixs1m0LiYU8sO8BCVmvd8jYKCO9dU5/tPBopsTyDGzAjjkP8A\njMRgRr3P6NpQlMNz2+lGuXT8omOZljFfkdEQrTvq5oWvEpW+D+nlz+viuj19TDhAqApHqhAAMbYw\nkb09sKNROhunLRv0OY9NWvRWuT1ovJeN5cbznYG0tdrMSywY6DNrPEIss9Ypye9lWNgfRSRu6T3J\nEUhOMdxbZVmS1tTc5nBxyytqekkR48im76isCV09jUCIaIv4qL+bhxsMq7TbeeXVZNnidtPqjySL\n/SylCZEkPT9YqOd9fA1wveqrzGsG5V+EZ7TNedUX0LY1Toz1/OLgCl2bxm7yOriGiBta6686MIj6\n+YMCumx4iGJyao2EL468YVtxkE2Jj2dYa2XFzDFZ7xxZ0OUkh6v7wXuRy8lT29NF4ZRysuizr4ia\njoalhbOav/IQmGen50Th0fA9obKKFUVG5Jm8gdHCa70KkQfmp70/ugD+3i8zXc/N7m/tsljwY1ri\nmPzZ1FjnYr+6oBPiR5Kmk9Kmf1KYqtf6Rp4cU+1Gz0CFG2I2rtmWO5tpUtJCgzbKvI5wKVoRAQEg\nRCdozlQicmeC6cfOnVBkTMfbL3htADNBVgJEf9nF7YSNR3P1KqcO2/x3cfPrbIsCtS097kkqjx6y\njQjDap0Aew8ghhKYQ3pr4r6dOPkTlPc5H9y9ENE8P9EkL+VXSHIP/VWCzGB/xms+zjK/837InG7D\n509x6yky34NRVzgtGsUUWrgON7xOZEKcryIq+GunGT4bDzMu32NUNbWy4x6qJFLb2CTe93CikTUk\nCEMTw9vlHVddefhxfbXZhbrkthW1MW/x7JljMjkk10gxYjhykE1gu+IoeasaiOa5F0TiLSZTWw5M\nunnR7THbOVEFL8nNikaUb+2VOl7FcxEexV0cnj6F4xjYWi2Xh5fmLrCPaQrfFSxigh1tUqa/sp/L\nliKXuMajdVH4p1L6Mq2J3txfNMf26xG1jWt/i1Xj0+bKUNgFS+WsJcJHIyGXtqQoxoQhNV/olXit\nvsOs4dvjkwSJWTYKooFYz2OlqIidPTpp06Jp4acZv5gfmAXDq6oNGRkYpHinzwAKggzDRwFf23u0\nYUrGrpzd6FpIbYESraYXmm10OtHUsChkR3QsMMqYIbk9KDIrPVxWxPluSwdcHtRty1KQgRW/w7T/\nAOCebkjuvx056cT4tngeeTfPSe+Y1vZ6E1/C/G85+Hp/R8bsYVvRsNDyRmeirkx7JCZHEZOrHRXm\nU4mmMpzCGX2F91ry9HpSHstY4KmC7r5myLS7XxaqV8Vq5Uc69uRIDK8tG6HQYwymeNwuSMRU1ReM\naw+lqo9dtljsAzLWKw4HisTmYjUjyoBohe4nPuqTvN5r6eMNqKmNFDR1FzGk3ELvtiDSCBjm9sYk\nhymk8URB6i/u0424wZrOiBjcKXm1kxrkaxXRHMgV4ulPUWQ8iej3f0U2MyGmHTuL8QuDNDLYhGAX\npYEU6JMivjlVzupF0fqieHCIiaIngnHygxnmUYj7v1xXiR2nX2ROcify/REM2X5ZYGcY0ZB+z77u\nS/L9r2vX3eIrG/daFiN+xGpxuHhcTELfMoXnf3tpZFWWB3BhyA5iFimbIkRkZ0SRHUfjqPT1cZdb\nZLUsx4+T35LKBjzTCkOiR0ixo2hChVRueUgHmXpVdOvTXX6aJsqDLm0GUU1vhuZeRd2zAhz2jlx5\nbSoqKxQHi9KLz5k8F004yq0jb17i2MvHoPxVoS2kWE0wK57ZMiO99XEgFXvgE8a+8/S14z/Mdv8A\nHq6pI2ikWFe8A0ESfYSRdEJ0mQqoQryGIxvUR6u5+PFXCm0sOruzwYMe0kJQ11LZyViB6UfZPrZk\n4MovU9y9xCqnNfWqrsXuFNVr8Zzmst9rLxFF1IKVYdNpWuI/9UhYbxaetycYRsZm+HZFGtHW0zFc\nMygIRSa6wgQWvLAlaodZKMSIg2FIoe2wvsq5E8Po24zsrWNXGMsgwJZnO6f2PIlWmI31KiGlBJ/e\nfRYVk+WN+2OzYmy8ziSZbI1fb5KdgpECulkc7tqKGJWGKwnsK8wepq9PFDDq8ckWMrKJ8Grmijd1\n44EeUukk5jRUVRsCzX3n3ddPzo1E0RqaIn1JxcZBbnSLVUUKRY2clfAceKNxSvX+5Y1V4vNy8u6K\nLMN47YUmBWTWHeKG1wUi0dcTtC7jFSMJjzatTQry8Q4JZZ55Y40aSXKIpSkd4qrnqiKvNeX1fRIi\nSWISPKE8Jxr4OY9Fa5PzovECALq7deBkUau8VQCdtF+879X1/RNKQbiDZmeKq9rPHRLQS8ZbDr8Q\nj5qWVRxBNxSRDPaCkDeQKERYoXCKXtMVSIiaKqt8PRxnmPYRv/ZbujqZsZs/DLCCSoHiOrpPTDjV\nkghjxmPVHJ0vI77nG+NPiUgFvnWb79XlPhcJX93tmmR4LiTSp4+WiCQhV5eDNPTxjWCVWRrDvJTx\nQamd8Yh0dhPmOJ3ZcgBJbXBeUpSK9w9Oav4k2W7dDjUpHEKJ1TPoas1g/p07Rnz4bkC9NP8AguAx\nYoWR40diDAAbUaxjWpojWonJEThf3uwLH8kcviWxro0gn5nkGrk/j4aTGZuT7eGY3pYuJ39jWCRP\nqitM6P8A83xR4jmuZZFmmTWQXrjU23iuPJsjuJ2xxiTIMNoBuV6oiKREXRddV5JwFZ3y1hjRyM6n\nkDmdeV7F9SjfFD/Px/5lbC5liNCjugmV1flskhBdqmrzsrHkkDH/AG6i04bZ4bk9bksFU1cavkMM\nrNfQRrV6mL9TkRfyzRZYByoshijkRjNR43scmitc1yKioqeheI1XT10aprYbeiJXwwsAATfHpYMa\nNa1PqRPyFgbiYNT5YJGKMRp0ZjziRf8AFm0QjPzO4bT7IZBBBigidweAZJFa+OjnffUVpEY2WxfV\n3Wm4tD5rsbnkGzqwEKkbG4KZPFmKxNUbEkVyuIqr/wAMAXGHbe4fkZ9jn5ENbGwy3NoZqZlR2O0U\niEbZChL8RATRAjEYgiI5/d5JxAxzD3tlVxDHsZtx1DeSxnTSKaVNM8SIx5DEVXKqJx86kqwkBggg\n7wznTJJ3oxrU8oHUhCvVPH1qvG3lniV5XZHtnd5h28+h4v5aLNg1rwqkCVImuP1FH3W+/RETVFRE\n5cfIateTutLeHIGQIiOG8XWqHTlyX3evP8rB5t9bLCJkmJW1bMcrHkDEECdBLGkSnDY7y43kIRnd\nKqD1TTVF143BI0jDS3bhZStgRnNVX4gRI/V4/wDw3Z0/tdOMbzHELWtrrakhT6uwi2kQkgEyFPcA\nvR1hKIg3DLGY5NNUXmnGE7rbj7kQiW+cxbDGMn6+qFXBrxR1nV8avhPKcnu5In6k1Vz+v2tF4iY7\ntHWWqS704gv3Km1RmU9XEVqFPKb5rseZIjNWDG3l3FTqXRF1iZfTZdmOR7i5e/vZbZTpKW47RIDR\nNjQZUFBaD73eaILIiC7fX3PrWPuOe8ilw+wPaZROuBheWyxlJrWqWXPqWrJ888UQCVsQi+7F1+HF\nuMEStx8mc4Y+4yajx/uuqG3gZgSjCUzf2YlmKvlidLUfP2mLzTmuweDQJQIhcpz9k2eQ61is8pVV\n0p6p2rgJohf2k4PZInEGtYseOGvitYjRDHGEjRNRHOaIaIxjdeejU0TXgUqIccqMdqPBIC5Hje1f\nBzXNVUVF9afTjm41DXinZns3apk+PDInMsftPjWsZq6pop4JTNT69OINtWnZLrrSOKXAljXVpQmY\nj2PRfrRU4kz5p2RYcMTzypJF0YMY0VznOX1Iia8bpbtQGrKrK0o8FxWWMrCBlQqbqly5cYjSKNWn\nly3D15fgpqvFzYZUf4fj4DPBXUNhjXwqwX0tM2YK8sRFHpy/BYq/V9Pyk2HSIxIe8VUNkYv9I043\ntcif7lPoqJElWDgAz7HSWEp6aoAKELqT83LgHa30wkjEYxGL8aiaqnTqnJSa+HGTPfvHipwZrhtM\nkCybZxvLCNTT5wixXF6+nrf8RG9qKvofwz/zqw32/u/64i8/+c46l3rwpG+tbuF/neOr+u/B0br0\n6rewU5/nLxb1hd8sGSLLiGjzSiyOuY5gzMUblR/fTRefJU4yiqfvng+QZNExAmPoSFkMGQWRZmie\nQYRGMOpV6jPRyr46enjbzavHd7tvrsN3lGPVeTIC9oJ7AVVYj5xCyQzJ4YyDcWCIa90iJ7fFRUQd\n/drkjV8UQBJByClhxuSaaCjhk9AtV5oxvhxjU7GPmuxfb3OcBPNt8Mu63IqQoEmnhlhI2aE6nRw/\ne80aiOTnpxiOd7yfOFtfn9xRY9b1sssA8GGVxr2REkujCKyU0flxLBaokUSEX08EGbfrCxvETtEa\ntoDk/wBXjx5Z/wAwGDtP2+72luI+vR6/vcZIWl3twqS6PMqJccrbmKqdyDbRZSJo16u/oF9HFxfR\n98cIm19GMr57o95Be5HBH3XDa3vJ1P6fBE4xHHl+YLD1us3uB326tiO9xwThTbMrDnESJfikCIAK\nu7a9pO4NBN9OvFBd2u8O2UmfjhSkxywPklQropJAlERQuWToiuGun2cOGzfXb172/eYmT1Sqn5vM\n8YrhsfeDC5EXN8qqa2/cK8gEY2qAX4hPaVzD6MYYEZQqqr/ScY80+5fwuB51senu6HKa9auZ16u6\nbCM2ShBpqxU5i/vuHdndPEidKdTtLqD4f5bgkZm62JOOL74kuYWqf87wipufiiovgvxiF/neCj/r\nMxNhEd71nxmCi9Wnp9948OIzcnFnjZ997biEqJ9qobiJj+O57juQ2dpmVCaRV1lhFnyfKQJCyzPQ\nIXvX2e0njxdYlWwBW5chpQhiQJVhLqBF6msc1CSoSKcSaJr7KePLi6wvM83pspqZBBuxevp6tIS1\ngdCd0RZrl701V6m6EKiOTT6+N3N4LCeKTaysutseoI7yD0ixIyjPJkIL+icZz0ZyX8NieheK/KbZ\nYtkakiODTMMVCBjvK7UpkE7VnWqIiI/x05cSba2uoVbWRG9UmfIOMYmIn6z3KiJxY51ZzKwrZDVi\nYgaGZyPZUqqvRJCoVwyKVyd1OXJNOP8ATAf5Rv8AZ4UaSRKRPFnW3X+LXjBK5LyBY43tjZEbngoM\n6Ik6NL6GSQRHjeBxkQyozVRkT7OGDG1GsY1GsangiJyRPofa2eLCg3rm9KZFTmNVWCJ9UmE8JF/O\nq8CiYTvlndEsdHJGFayIt9Hb1frNnR1M7T/juDkQ+C7oxQu9xFQUzHbArP8AjFLLjo78yJxQJMyn\nJtspAv2i3rccnRRmIpGaLGNKUB9UYvpGqa+vibkOK7/Zy/Ja97JGGxbqwQ0SKZr0d78rRKYiKmvP\nigq8vXGd4qibJI22uYLlp7GuAqIrFI6QTtytF/UE138nF1jwam9rrOhJ2pzp9VLDDcvrBO7axS/3\nhVX6v4EkWdFDMilTQsY7GkG5PU5rkVF4PaYJOuNsbM6KqpjM14K5X6cnvpzoatcqfXH/AD8fOhj2\nRzVyG0Bugo7aXMjBE6UxYmiPKESKL2ufhxl8DK9nsObtxIHKfjuQRK+sa5rR9hkUeg18ypCsKbvK\nQfSisZ21014+QmYBkSroItzIq4UMTmgQKja5yNaJNE6PaYicaebDqi6Kncb4/wAfCtbIE5yeLUe1\nVT+XjVSN09eqcao9qp69U040QjVX1apxvuaSWOePOsYOPjmKrXEGGPSxiFiqn6gyyikRF/Se/iVX\npYW2H59ir41NuMGkvJEJZFhBgjEOZIBHK0BFPG6CI9R805eLOWZ0G9u/WVYsN8tJWIntb0tfDmVB\nI4VVsM8VolI8Ju4Mntdz8y68eb2X21vc4kzBo5uXqBYzDs0++trfnjlIz19tXJ9XGHIyxxXbqvyb\nKoVNLiRBuvLUcMwzGKqSzkjxBk7YtU0AX6uMbu8uyCBuBaJSWVptSGeJonTsnoNfLHtzCRg1IkM3\nQqjaNmjF9nVicMk3FVInYxNorD4WVJgiLULbvAazpJ3S9FlgUjWkjPRq9v22/d6V4xCMOHGp3/LV\nmwarInx2AjCmYnfRnQxWZGCRET3UsJi6c1LGJxtzTVtjJjQqDCyGlFi2CxhP+MWYnPAQSV04R+6y\nuZowpY6+kZNeNi3TVGaoznB82xt8UngkiMSsnpy8PeCaRPzcQcSmkUlptlYWGFWLnKiuclJIfGil\nXp/x0RAl/v8A6fQ5rk+1FReM72mKRqxsKsGWGHNcqdxaC5RZIGaeKpHkpIjov6rGcFBOSb5SSZiy\niQqq1tXtEJe69VbUFCcX3eT+4iJ6l4weGevjxZGfBHYTIVjTScgiaW8h87SXGKZXKzpImrzF0Tx9\nXA6yiqINJAGqvSDXRhxI6Pd95zRCRGpqv0/J5HX+m3erlT+96P7P0EpMtx6syilM9hDVFtEDNive\nNdWOcE7XsVWr4apw7TYTblOv7/8A4WqOf2/svHQ7Yzb9W+r92qv/ALvw14Ni8DE5qdKK3Hq5OX+Q\n4QibKYR1p4O+BQf8zw5SbIYQ/rXV2tJC5r/kuAR7PYvCjhjLqAbaeMJGr9XaY3hyu2Aw1Ve3od/q\n9nNvq8eFf/6fMNVy+KrARf514GaL8u2BKQX4bj00Y+n+WY/hs5vy5bfIdn3W/AYfa/yPb7f+Dw5w\n/l526a55O65f3areb/X+Bw5E2DwNEd97Shg/5rggv6i8I7ZU6SNSmiJqn+T485K+X7CiSv8AHNrB\nMX/A047j/l9xBz/1vJr/APe4GRmweKOUX4bCxXFYn94R7m/ycL//AI5beO6l6l6sfgu5/wB8JeO3\nL+XXBQt6ur9hqAQF1+2IgV4bPjfLzhqyGfdaeD3xf5Eznj/weDTm/LrginP+I19RHeL+9C5qjb+Z\nqcN0+XjC/ZTRP9Xt8P4+HK35eML9pNF1r2ry/OvDevYLHAKzwWOkgP8AvDJx/wD2Jpx+x0L25E5v\nL80jx4Y7+o+uCrPDszrFn80riDYQ9ja4MquKI8ZfiNs5ncC7qG543TVa9Wrz9pF4axiI1jERrWp4\nIickT6Jp4tFlMFZ8ksuQOJlVzHGpjfeejBSWpr6uHsHFzcAnp0qAeZ3yM0+xZi8JAl1+ZSYa/jRT\nZfdlGX+7YSU5F/i47USHmcICfhgBltuxrfs0PwurM4a1W9PQmW22mn+W4IqEz3rL94v74W3V/wBN\nw+THfncaWQndLLFlM5pHO+tdefDEh5bunCRiaJ2M5uGcvzG4cKDuBu5E7jekpBZ5cNV32+90/k4Z\nCgbqbxQYqE7hQizu19tfr95x213V3jcnr/f23/zvEhW7u7ysbJ/FYmdWmi/4fCuZu9vOxn6A255a\nojfs9vhjyb673OYIfbAL9+7HRifVz4K+Dv5vnEUzdC9nO5w9fr5N460+ZPftBIzo7H79S9Pt17XA\nxj+YzfRFG1ze47NCuVyO9esfhxY/zC72auH21QmXkLy/5SO7gQx/MRvQNg3e0iZTr1M/VX9m/l46\nF+YbeYyf2+Ua/wDZ+CMF8xu9IXvJ3GkTKdVRfs8vwVkf5l94Hd1dVce4gSlT7Fk15tOCtd8zO7o1\nf+G8VlUsVv8AFVc+BO/9UG7rGDB2nMZOpU6nf4xV+EePB+980u8MlC/h9VhSp0fZ/qhdeEik+Zzd\n5Qez1dNhTDKunj74dQ0ia/bxnBqG9yDJrXcS5+O5XeZHN89KkTO2gurr6GaJonhpx+9fwCMmRdzu\n/Fk60L16aaqqO08Pq4xkm51VYTj4g+QSglV1hIrygfJRiPcj472rr7CacNcBc8ArfHt5ndp1fb+0\n8PINmcDcT73TmFyn/aOHdxM5e13ix2Y3Wn/zPHaebPu1/i0zC20/lNwhvM5817fw9MssNG/Z7XBX\nhdnQVMbvk7eW2bdX+vkVOCyADzeNKP096WLLbZCO6fDVVMvDGz4GYWCCZ2xeayeyN0p9XcI7gYRF\nzwAAs7Yo48utUY1PqTurwLql5/7gndCi5far0k/XTUq8+BlIfPXnjuK6HIdl1o54FP8Af7aqXlrw\nTyWRbmwO7+J5fNbVmv2+84syTNw91JZrgfl7Eh8pMXvxk+4AyEG7usb6n68GJB3X3fgSDsEwh42W\nmG5ez+H4C1XT7eK6zkbu7ty5lV3fh8s+UGJIj99nSTsnUaPZr9S8H8lvBuzEdMJ35zgZMUPfN7Pv\nCdtjdV9lOBjbvXvJoPwX975P/wB3jpLvVvEV3+OXLpSP/j6eOkW9O8LBr98aZbJ0X+Th9wzdrdwc\n4oRRTzGZZJSQ+MD8MSn6e5on28Pjl3o3lKAo+2cBMwkvY9PrRWcCiR9795osOMNoIUSPlphjEFv9\nG1qD8OGq7f7fEnS3p0XMHp/2fjoZvzvS0X+L/e02n/R8PZ/XvvUqdzuBVMwkp0L9XsLxhuXWu4e5\nOYTsGtwXdLDyLIjWEdJccvdarmEbroq/X/8Aos//2Q==\n", "metadata": {}, "output_type": "pyout", "prompt_number": 4, "text": [ "" ] } ], "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": [ "import numpy as np" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The *random* subpackage is the package responsible for all random functions in the numpy environment" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# help(np.random)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's generate a couple of random paths" ] }, { "cell_type": "code", "collapsed": false, "input": [ "Nt = 1000\n", "Npaths = 10\n", "rv = np.random.randn(10,1000)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "rv.shape" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 4, "text": [ "(10, 1000)" ] } ], "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": [ "paths = rv.cumsum(1)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 5 }, { "cell_type": "code", "collapsed": false, "input": [ "paths.shape" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 6, "text": [ "(10, 1000)" ] } ], "prompt_number": 6 }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline\n", "from matplotlib.pyplot import *" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 7 }, { "cell_type": "code", "collapsed": false, "input": [ "plot(paths.T)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 8, "text": [ "[,\n", " ,\n", " ,\n", " ,\n", " ,\n", " ,\n", " ,\n", " ,\n", " ,\n", " ]" ] }, { "metadata": {}, "output_type": "display_data", "svg": [ "\n", "\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "\n" ], "text": [ "" ] } ], "prompt_number": 8 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Even though Numpy has a random subpackage, it is in SciPy that we find a more complete package. To note that since python 3.4 a statistical package is included in the default python bundle" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from scipy import stats" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can easily get a list of available distributions (continuous and discrete) by using *dir* or by checking on the online [documentation](http://docs.scipy.org/doc/scipy/reference/stats.html#continuous-distributions)" ] }, { "cell_type": "code", "collapsed": false, "input": [ "list_distributions = dir(stats)\n", "len(list_distributions)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 10, "text": [ "243" ] } ], "prompt_number": 10 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's choose a Pareto distribution with parameter $\\alpha=3$ $$ pdf_{pareto}(x) = \\frac{\\alpha}{x^{\\alpha+1}} $$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "alpha = 3\n", "X = stats.pareto(alpha)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 24 }, { "cell_type": "code", "collapsed": false, "input": [ "X.rvs(10)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 26, "text": [ "array([ 1.24325841, 1.81333057, 1.41190749, 1.17179035, 1.09682395,\n", " 1.3977652 , 1.06095642, 1.64328593, 1.54846341, 1.65059412])" ] } ], "prompt_number": 26 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can sample..." ] }, { "cell_type": "code", "collapsed": false, "input": [ "n = 100\n", "plot(X.rvs(n),'.')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 12, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "svg": [ "\n", "\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "\n" ], "text": [ "" ] } ], "prompt_number": 12 }, { "cell_type": "markdown", "metadata": {}, "source": [ "...have a look at the probability density function..." ] }, { "cell_type": "code", "collapsed": false, "input": [ "x = np.linspace(X.ppf(0.01), X.ppf(0.99), 100)\n", "plot(x, X.pdf(x),label='Pareto pdf')\n", "legend()\n", "xlabel('$x$')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 13, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "svg": [ "\n", "\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "\n" ], "text": [ "" ] } ], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": {}, "source": [ "...have a look at the cumulative density function..." ] }, { "cell_type": "code", "collapsed": false, "input": [ "plot(x, X.cdf(x),label='Pareto cdf')\n", "legend()\n", "xlabel('$x$')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 14, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "svg": [ "\n", "\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "\n" ], "text": [ "" ] } ], "prompt_number": 14 }, { "cell_type": "markdown", "metadata": {}, "source": [ "...compare the histogram of the previously generated sample with the pdf..." ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig, ax = subplots()\n", "ax.hist(X.rvs(10000),normed=True,bins=100, alpha=0.2)\n", "ax.plot(x,X.pdf(x))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 17, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "svg": [ "\n", "\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "\n" ], "text": [ "" ] } ], "prompt_number": 17 }, { "cell_type": "markdown", "metadata": {}, "source": [ "(let's just see the influence of the number of bins in the non-parametric estimation)" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib\n", "from matplotlib.widgets import Slider\n", "\n", "samples = X.rvs(10000)\n", "\n", "ax = axes([0.1,0.25,0.8,0.6])\n", "ax.hist(samples,normed=True)\n", "ax.plot(x,X.pdf(x))\n", "sl = Slider(axes([0.1,0.1,0.8,0.1]),'Bins',1,200,valinit=10,valfmt='%d')\n", "\n", "def update(data):\n", " data = int(data)\n", " ax.cla()\n", " ax.hist(samples,normed=True,bins=data)\n", " ax.plot(x,X.pdf(x))\n", " ax.draw()\n", "\n", "sl.on_changed(update)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Using matplotlib backend: Qt4Agg\n" ] }, { "metadata": {}, "output_type": "pyout", "prompt_number": 18, "text": [ "0" ] } ], "prompt_number": 18 }, { "cell_type": "code", "collapsed": false, "input": [ "X.stats(moments='mv')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 19, "text": [ "(array(1.5), array(0.75))" ] } ], "prompt_number": 19 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We also have different [statistical tests](http://docs.scipy.org/doc/scipy/reference/stats.html#statistical-functions) available: " ] }, { "cell_type": "code", "collapsed": false, "input": [ "from IPython.display import HTML\n", "HTML('http://docs.scipy.org/doc/scipy/reference/stats.html#statistical-functions')" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", "\n", "\n", " \n", " \n", " \n", " Statistical functions (scipy.stats) — SciPy v0.14.0 Reference Guide\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "\n", "
\n", "
\n", " \n", " \"SciPy\"\n", "
\n", "
\n", "\n", "\n", "\n", "
\n", "
\n", " \n", "\t
\n", "\t
\n", "\t
\n", " \n", " \n", " \n", " \n", " \n", " \n", "\t
\n", "\t
\n", "\t
\n", " \n", "\n", "\t
\n", "
\n", " \n", "
\n", "
\n", " \n", "
\n", "

Statistical functions (scipy.stats)\u00b6

\n", "

This module contains a large number of probability distributions as\n", "well as a growing library of statistical functions.

\n", "

Each included distribution is an instance of the class rv_continous:\n", "For each given name the following methods are available:

\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "
rv_continuous([momtype, a, b, xtol, ...])A generic continuous random variable class meant for subclassing.
rv_continuous.pdf(x, *args, **kwds)Probability density function at x of the given RV.
rv_continuous.logpdf(x, *args, **kwds)Log of the probability density function at x of the given RV.
rv_continuous.cdf(x, *args, **kwds)Cumulative distribution function of the given RV.
rv_continuous.logcdf(x, *args, **kwds)Log of the cumulative distribution function at x of the given RV.
rv_continuous.sf(x, *args, **kwds)Survival function (1-cdf) at x of the given RV.
rv_continuous.logsf(x, *args, **kwds)Log of the survival function of the given RV.
rv_continuous.ppf(q, *args, **kwds)Percent point function (inverse of cdf) at q of the given RV.
rv_continuous.isf(q, *args, **kwds)Inverse survival function at q of the given RV.
rv_continuous.moment(n, *args, **kwds)n’th order non-central moment of distribution.
rv_continuous.stats(*args, **kwds)Some statistics of the given RV
rv_continuous.entropy(*args, **kwds)Differential entropy of the RV.
rv_continuous.fit(data, *args, **kwds)Return MLEs for shape, location, and scale parameters from data.
rv_continuous.expect([func, args, loc, ...])Calculate expected value of a function with respect to the distribution.
\n", "

Calling the instance as a function returns a frozen pdf whose shape,\n", "location, and scale parameters are fixed.

\n", "

Similarly, each discrete distribution is an instance of the class\n", "rv_discrete:

\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "
rv_discrete([a, b, name, badvalue, ...])A generic discrete random variable class meant for subclassing.
rv_discrete.rvs(*args, **kwargs)Random variates of given type.
rv_discrete.pmf(k, *args, **kwds)Probability mass function at k of the given RV.
rv_discrete.logpmf(k, *args, **kwds)Log of the probability mass function at k of the given RV.
rv_discrete.cdf(k, *args, **kwds)Cumulative distribution function of the given RV.
rv_discrete.logcdf(k, *args, **kwds)Log of the cumulative distribution function at k of the given RV
rv_discrete.sf(k, *args, **kwds)Survival function (1-cdf) at k of the given RV.
rv_discrete.logsf(k, *args, **kwds)Log of the survival function of the given RV.
rv_discrete.ppf(q, *args, **kwds)Percent point function (inverse of cdf) at q of the given RV
rv_discrete.isf(q, *args, **kwds)Inverse survival function (1-sf) at q of the given RV.
rv_discrete.stats(*args, **kwds)Some statistics of the given RV
rv_discrete.moment(n, *args, **kwds)n’th order non-central moment of distribution.
rv_discrete.entropy(*args, **kwds)Differential entropy of the RV.
rv_discrete.expect([func, args, loc, lb, ...])Calculate expected value of a function with respect to the distribution
\n", "
\n", "

Continuous distributions\u00b6

\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "
alphaAn alpha continuous random variable.
anglitAn anglit continuous random variable.
arcsineAn arcsine continuous random variable.
betaA beta continuous random variable.
betaprimeA beta prime continuous random variable.
bradfordA Bradford continuous random variable.
burrA Burr continuous random variable.
cauchyA Cauchy continuous random variable.
chiA chi continuous random variable.
chi2A chi-squared continuous random variable.
cosineA cosine continuous random variable.
dgammaA double gamma continuous random variable.
dweibullA double Weibull continuous random variable.
erlangAn Erlang continuous random variable.
exponAn exponential continuous random variable.
exponweibAn exponentiated Weibull continuous random variable.
exponpowAn exponential power continuous random variable.
fAn F continuous random variable.
fatiguelifeA fatigue-life (Birnbaum-Sanders) continuous random variable.
fiskA Fisk continuous random variable.
foldcauchyA folded Cauchy continuous random variable.
foldnormA folded normal continuous random variable.
frechet_rA Frechet right (or Weibull minimum) continuous random variable.
frechet_lA Frechet left (or Weibull maximum) continuous random variable.
genlogisticA generalized logistic continuous random variable.
genparetoA generalized Pareto continuous random variable.
genexponA generalized exponential continuous random variable.
genextremeA generalized extreme value continuous random variable.
gausshyperA Gauss hypergeometric continuous random variable.
gammaA gamma continuous random variable.
gengammaA generalized gamma continuous random variable.
genhalflogisticA generalized half-logistic continuous random variable.
gilbratA Gilbrat continuous random variable.
gompertzA Gompertz (or truncated Gumbel) continuous random variable.
gumbel_rA right-skewed Gumbel continuous random variable.
gumbel_lA left-skewed Gumbel continuous random variable.
halfcauchyA Half-Cauchy continuous random variable.
halflogisticA half-logistic continuous random variable.
halfnormA half-normal continuous random variable.
hypsecantA hyperbolic secant continuous random variable.
invgammaAn inverted gamma continuous random variable.
invgaussAn inverse Gaussian continuous random variable.
invweibullAn inverted Weibull continuous random variable.
johnsonsbA Johnson SB continuous random variable.
johnsonsuA Johnson SU continuous random variable.
ksoneGeneral Kolmogorov-Smirnov one-sided test.
kstwobignKolmogorov-Smirnov two-sided test for large N.
laplaceA Laplace continuous random variable.
logisticA logistic (or Sech-squared) continuous random variable.
loggammaA log gamma continuous random variable.
loglaplaceA log-Laplace continuous random variable.
lognormA lognormal continuous random variable.
lomaxA Lomax (Pareto of the second kind) continuous random variable.
maxwellA Maxwell continuous random variable.
mielkeA Mielke’s Beta-Kappa continuous random variable.
nakagamiA Nakagami continuous random variable.
ncx2A non-central chi-squared continuous random variable.
ncfA non-central F distribution continuous random variable.
nctA non-central Student’s T continuous random variable.
normA normal continuous random variable.
paretoA Pareto continuous random variable.
pearson3A pearson type III continuous random variable.
powerlawA power-function continuous random variable.
powerlognormA power log-normal continuous random variable.
powernormA power normal continuous random variable.
rdistAn R-distributed continuous random variable.
reciprocalA reciprocal continuous random variable.
rayleighA Rayleigh continuous random variable.
riceA Rice continuous random variable.
recipinvgaussA reciprocal inverse Gaussian continuous random variable.
semicircularA semicircular continuous random variable.
tA Student’s T continuous random variable.
triangA triangular continuous random variable.
truncexponA truncated exponential continuous random variable.
truncnormA truncated normal continuous random variable.
tukeylambdaA Tukey-Lamdba continuous random variable.
uniformA uniform continuous random variable.
vonmisesA Von Mises continuous random variable.
waldA Wald continuous random variable.
weibull_minA Frechet right (or Weibull minimum) continuous random variable.
weibull_maxA Frechet left (or Weibull maximum) continuous random variable.
wrapcauchyA wrapped Cauchy continuous random variable.
\n", "
\n", "
\n", "

Multivariate distributions\u00b6

\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "
multivariate_normalA multivariate normal random variable.
\n", "
\n", "
\n", "

Discrete distributions\u00b6

\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "
bernoulliA Bernoulli discrete random variable.
binomA binomial discrete random variable.
boltzmannA Boltzmann (Truncated Discrete Exponential) random variable.
dlaplaceA Laplacian discrete random variable.
geomA geometric discrete random variable.
hypergeomA hypergeometric discrete random variable.
logserA Logarithmic (Log-Series, Series) discrete random variable.
nbinomA negative binomial discrete random variable.
planckA Planck discrete exponential random variable.
poissonA Poisson discrete random variable.
randintA uniform discrete random variable.
skellamA Skellam discrete random variable.
zipfA Zipf discrete random variable.
\n", "
\n", "
\n", "

Statistical functions\u00b6

\n", "

Several of these functions have a similar version in scipy.stats.mstats\n", "which work for masked arrays.

\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "
describe(a[, axis])Computes several descriptive statistics of the passed array.
gmean(a[, axis, dtype])Compute the geometric mean along the specified axis.
hmean(a[, axis, dtype])Calculates the harmonic mean along the specified axis.
kurtosis(a[, axis, fisher, bias])Computes the kurtosis (Fisher or Pearson) of a dataset.
kurtosistest(a[, axis])Tests whether a dataset has normal kurtosis
mode(a[, axis])Returns an array of the modal (most common) value in the passed array.
moment(a[, moment, axis])Calculates the nth moment about the mean for a sample.
normaltest(a[, axis])Tests whether a sample differs from a normal distribution.
skew(a[, axis, bias])Computes the skewness of a data set.
skewtest(a[, axis])Tests whether the skew is different from the normal distribution.
tmean(a[, limits, inclusive])Compute the trimmed mean.
tvar(a[, limits, inclusive])Compute the trimmed variance
tmin(a[, lowerlimit, axis, inclusive])Compute the trimmed minimum
tmax(a[, upperlimit, axis, inclusive])Compute the trimmed maximum
tstd(a[, limits, inclusive])Compute the trimmed sample standard deviation
tsem(a[, limits, inclusive])Compute the trimmed standard error of the mean.
nanmean(x[, axis])Compute the mean over the given axis ignoring nans.
nanstd(x[, axis, bias])Compute the standard deviation over the given axis, ignoring nans.
nanmedian(x[, axis])Compute the median along the given axis ignoring nan values.
variation(a[, axis])Computes the coefficient of variation, the ratio of the biased standard deviation to the mean.
\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "
cumfreq(a[, numbins, defaultreallimits, weights])Returns a cumulative frequency histogram, using the histogram function.
histogram2(a, bins)Compute histogram using divisions in bins.
histogram(a[, numbins, defaultlimits, ...])Separates the range into several bins and returns the number of instances in each bin.
itemfreq(a)Returns a 2-D array of item frequencies.
percentileofscore(a, score[, kind])The percentile rank of a score relative to a list of scores.
scoreatpercentile(a, per[, limit, ...])Calculate the score at a given percentile of the input sequence.
relfreq(a[, numbins, defaultreallimits, weights])Returns a relative frequency histogram, using the histogram function.
\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "
binned_statistic(x, values[, statistic, ...])Compute a binned statistic for a set of data.
binned_statistic_2d(x, y, values[, ...])Compute a bidimensional binned statistic for a set of data.
binned_statistic_dd(sample, values[, ...])Compute a multidimensional binned statistic for a set of data.
\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "
obrientransform(*args)Computes the O’Brien transform on input data (any number of arrays).
signaltonoise(a[, axis, ddof])The signal-to-noise ratio of the input data.
bayes_mvs(data[, alpha])Bayesian confidence intervals for the mean, var, and std.
sem(a[, axis, ddof])Calculates the standard error of the mean (or standard error of measurement) of the values in the input array.
zmap(scores, compare[, axis, ddof])Calculates the relative z-scores.
zscore(a[, axis, ddof])Calculates the z score of each value in the sample, relative to the sample mean and standard deviation.
\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "
sigmaclip(a[, low, high])Iterative sigma-clipping of array elements.
threshold(a[, threshmin, threshmax, newval])Clip array to a given value.
trimboth(a, proportiontocut[, axis])Slices off a proportion of items from both ends of an array.
trim1(a, proportiontocut[, tail])Slices off a proportion of items from ONE end of the passed array distribution.
\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "
f_oneway(*args)Performs a 1-way ANOVA.
pearsonr(x, y)Calculates a Pearson correlation coefficient and the p-value for testing non-correlation.
spearmanr(a[, b, axis])Calculates a Spearman rank-order correlation coefficient and the p-value to test for non-correlation.
pointbiserialr(x, y)Calculates a point biserial correlation coefficient and the associated p-value.
kendalltau(x, y[, initial_lexsort])Calculates Kendall’s tau, a correlation measure for ordinal data.
linregress(x[, y])Calculate a regression line
\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "
ttest_1samp(a, popmean[, axis])Calculates the T-test for the mean of ONE group of scores.
ttest_ind(a, b[, axis, equal_var])Calculates the T-test for the means of TWO INDEPENDENT samples of scores.
ttest_rel(a, b[, axis])Calculates the T-test on TWO RELATED samples of scores, a and b.
kstest(rvs, cdf[, args, N, alternative, mode])Perform the Kolmogorov-Smirnov test for goodness of fit.
chisquare(f_obs[, f_exp, ddof, axis])Calculates a one-way chi square test.
power_divergence(f_obs[, f_exp, ddof, axis, ...])Cressie-Read power divergence statistic and goodness of fit test.
ks_2samp(data1, data2)Computes the Kolmogorov-Smirnov statistic on 2 samples.
mannwhitneyu(x, y[, use_continuity])Computes the Mann-Whitney rank test on samples x and y.
tiecorrect(rankvals)Tie correction factor for ties in the Mann-Whitney U and Kruskal-Wallis H tests.
rankdata(a[, method])Assign ranks to data, dealing with ties appropriately.
ranksums(x, y)Compute the Wilcoxon rank-sum statistic for two samples.
wilcoxon(x[, y, zero_method, correction])Calculate the Wilcoxon signed-rank test.
kruskal(*args)Compute the Kruskal-Wallis H-test for independent samples
friedmanchisquare(*args)Computes the Friedman test for repeated measurements
\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "
ansari(x, y)Perform the Ansari-Bradley test for equal scale parameters
bartlett(*args)Perform Bartlett’s test for equal variances
levene(*args, **kwds)Perform Levene test for equal variances.
shapiro(x[, a, reta])Perform the Shapiro-Wilk test for normality.
anderson(x[, dist])Anderson-Darling test for data coming from a particular distribution
anderson_ksamp(samples[, midrank])The Anderson-Darling test for k-samples.
binom_test(x[, n, p])Perform a test that the probability of success is p.
fligner(*args, **kwds)Perform Fligner’s test for equal variances.
mood(x, y[, axis])Perform Mood’s test for equal scale parameters.
\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "
boxcox(x[, lmbda, alpha])Return a positive dataset transformed by a Box-Cox power transformation.
boxcox_normmax(x[, brack, method])Compute optimal Box-Cox transform parameter for input data.
boxcox_llf(lmb, data)The boxcox log-likelihood function.
entropy(pk[, qk, base])Calculate the entropy of a distribution for given probability values.
\n", "
\n", "
\n", "

Contingency table functions\u00b6

\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "
chi2_contingency(observed[, correction, lambda_])Chi-square test of independence of variables in a contingency table.
contingency.expected_freq(observed)Compute the expected frequencies from a contingency table.
contingency.margins(a)Return a list of the marginal sums of the array a.
fisher_exact(table[, alternative])Performs a Fisher exact test on a 2x2 contingency table.
\n", "
\n", "
\n", "

Plot-tests\u00b6

\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "
ppcc_max(x[, brack, dist])Returns the shape parameter that maximizes the probability plot correlation coefficient for the given data to a one-parameter family of distributions.
ppcc_plot(x, a, b[, dist, plot, N])Returns (shape, ppcc), and optionally plots shape vs.
probplot(x[, sparams, dist, fit, plot])Calculate quantiles for a probability plot, and optionally show the plot.
boxcox_normplot(x, la, lb[, plot, N])Compute parameters for a Box-Cox normality plot, optionally show it.
\n", "
\n", "
\n", "

Masked statistics functions\u00b6

\n", "
\n", "\n", "
\n", "
\n", "
\n", "

Univariate and multivariate kernel density estimation (scipy.stats.kde)\u00b6

\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "
gaussian_kde(dataset[, bw_method])Representation of a kernel-density estimate using Gaussian kernels.
\n", "

For many more stat related functions install the software R and the\n", "interface package rpy.

\n", "
\n", "
\n", "
\n", "
\n", "\n", "\n", "
\n", "
\n", "
\n", " \n", "
\n", "
\n", "
\n", "\n", "
\n", "
\n", " \n", "
\n", "
\n", "
\n", "
\n", "
\n", "
    \n", "
  • \n", " © Copyright 2008-2009, The Scipy community.\n", "
  • \n", "
  • \n", " Last updated on May 11, 2014.\n", "
  • \n", "
  • \n", " Created using Sphinx 1.2.2.\n", "
  • \n", "
\n", "
\n", "
\n", "
\n", " \n", "" ], "metadata": {}, "output_type": "pyout", "prompt_number": 22, "text": [ "" ] } ], "prompt_number": 22 }, { "cell_type": "code", "collapsed": false, "input": [ "from scipy.stats import kstest, normaltest" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 20 }, { "cell_type": "code", "collapsed": false, "input": [ "normaltest(rv[0,:])" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 23, "text": [ "(0.97622316618123328, 0.6137843812633923)" ] } ], "prompt_number": 23 }, { "cell_type": "code", "collapsed": false, "input": [ "kstest(rv,'norm')" ], "language": "python", "metadata": {}, "outputs": [ { "ename": "ValueError", "evalue": "operands could not be broadcast together with shapes (10,) (10,1000) ", "output_type": "pyerr", "traceback": [ "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mValueError\u001b[0m Traceback (most recent call last)", "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mkstest\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mrv\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;34m'norm'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[1;32m/home/jpsilva/anaconda/lib/python2.7/site-packages/scipy/stats/stats.pyc\u001b[0m in \u001b[0;36mkstest\u001b[1;34m(rvs, cdf, args, N, alternative, mode)\u001b[0m\n\u001b[0;32m 3433\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 3434\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0malternative\u001b[0m \u001b[1;32min\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;34m'two-sided'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'greater'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 3435\u001b[1;33m \u001b[0mDplus\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1.0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mN\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m/\u001b[0m\u001b[0mN\u001b[0m \u001b[1;33m-\u001b[0m \u001b[0mcdfvals\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 3436\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0malternative\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;34m'greater'\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 3437\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mDplus\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdistributions\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mksone\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mDplus\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mN\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", "\u001b[1;31mValueError\u001b[0m: operands could not be broadcast together with shapes (10,) (10,1000) " ] } ], "prompt_number": 25 }, { "cell_type": "code", "collapsed": false, "input": [ "rv.apply(kstest,axis=1)" ], "language": "python", "metadata": {}, "outputs": [ { "ename": "AttributeError", "evalue": "'numpy.ndarray' object has no attribute 'apply'", "output_type": "pyerr", "traceback": [ "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mAttributeError\u001b[0m Traceback (most recent call last)", "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mrv\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mapply\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mkstest\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0maxis\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[1;31mAttributeError\u001b[0m: 'numpy.ndarray' object has no attribute 'apply'" ] } ], "prompt_number": 26 }, { "cell_type": "code", "collapsed": false, "input": [ "np.apply_along_axis(lambda x: kstest(x,'norm'),1,rv)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 27, "text": [ "array([[ 0.02258851, 0.68729813],\n", " [ 0.01953194, 0.84007941],\n", " [ 0.04515036, 0.03287574],\n", " [ 0.03303197, 0.22065703],\n", " [ 0.01654964, 0.94702323],\n", " [ 0.04161483, 0.06088554],\n", " [ 0.02988619, 0.32853677],\n", " [ 0.02706993, 0.45367407],\n", " [ 0.02087375, 0.77622773],\n", " [ 0.03456065, 0.17926681]])" ] } ], "prompt_number": 27 }, { "cell_type": "code", "collapsed": false, "input": [ "map(lambda x: kstest(x,'norm'),rv)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 28, "text": [ "[(0.022588505965900785, 0.68729812624198638),\n", " (0.019531941596613533, 0.84007941493806415),\n", " (0.045150356571560357, 0.032875739591434527),\n", " (0.033031972610236104, 0.22065703230246303),\n", " (0.016549643958866267, 0.94702322814609663),\n", " (0.041614828353889965, 0.060885539612935746),\n", " (0.02988619100346529, 0.32853677135332848),\n", " (0.027069927461537302, 0.45367406917234332),\n", " (0.020873746378914815, 0.77622773361532782),\n", " (0.034560653818090592, 0.17926681073156825)]" ] } ], "prompt_number": 28 }, { "cell_type": "code", "collapsed": false, "input": [ "%%timeit \n", "np.apply_along_axis(lambda x: kstest(x,'norm'),1,rv)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "100 loops, best of 3: 6.91 ms per loop\n" ] } ], "prompt_number": 29 }, { "cell_type": "code", "collapsed": false, "input": [ "%%timeit\n", "map(lambda x: kstest(x,'norm'),rv)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "100 loops, best of 3: 6.74 ms per loop\n" ] } ], "prompt_number": 30 }, { "cell_type": "code", "collapsed": false, "input": [ "np.apply_along_axis??" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 31 }, { "cell_type": "code", "collapsed": false, "input": [ "t_statistic, p_value = stats.ttest_ind(stats.norm.rvs(size=1000), stats.norm.rvs(size=1000))\n", "print p_value" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "0.232430093319\n" ] } ], "prompt_number": 32 }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 32 }, { "cell_type": "code", "collapsed": false, "input": [ "from os import urandom" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 27 }, { "cell_type": "code", "collapsed": false, "input": [ "ur = urandom(16)\n", "ur" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 38, "text": [ "'\\t\\x89\\xd8(\\xe3\\xc5\\x9d1\\xcb\\x0f\\xb3\\xa2@\\xc4\\x01\\x90'" ] } ], "prompt_number": 38 }, { "cell_type": "code", "collapsed": false, "input": [ "ur.encode('hex')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 39, "text": [ "'0989d828e3c59d31cb0fb3a240c40190'" ] } ], "prompt_number": 39 }, { "cell_type": "code", "collapsed": false, "input": [ "import random" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 40 }, { "cell_type": "code", "collapsed": false, "input": [ "random.random()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 41, "text": [ "0.0783924721018322" ] } ], "prompt_number": 41 }, { "cell_type": "markdown", "metadata": {}, "source": [ "What about choosing from some predetermined set? " ] }, { "cell_type": "code", "collapsed": false, "input": [ "from os import urandom" ], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "code", "collapsed": false, "input": [ "urandom(2).encode('hex')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 42, "text": [ "'33c5'" ] } ], "prompt_number": 42 }, { "cell_type": "code", "collapsed": false, "input": [ "a = urandom(64)\n", "a.encode('base-64')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 43, "text": [ "'iAWjWiaIFFq9hoQ5CZx5k6+xfo3g6vVMKJbcNthGKtpSU9eMwL7hfzNw+DsMGMl58WlluODS+O7S\\nz45aRHp1qw==\\n'" ] } ], "prompt_number": 43 }, { "cell_type": "code", "collapsed": false, "input": [ "from base64 import b64encode\n", "from os import urandom\n", "\n", "random_bytes = urandom(64)\n", "token = b64encode(random_bytes).decode('utf-8')\n", "token" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 44, "text": [ "u'GxvtJZnpuwj2bR3ggIts+FjgkdQ5dq+rnbhTMoPfqu3ZmUbRcAQ6SBFzwqfmihUTu6uP0laMRKRBQRxIeUqj+Q=='" ] } ], "prompt_number": 44 }, { "cell_type": "code", "collapsed": false, "input": [ "%load_ext version_information\n", "%version_information numpy, scipy" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The version_information extension is already loaded. To reload it, use:\n", " %reload_ext version_information\n" ] }, { "html": [ "
SoftwareVersion
Python2.7.8 |Anaconda 2.1.0 (64-bit)| (default, Aug 21 2014, 18:22:21) [GCC 4.4.7 20120313 (Red Hat 4.4.7-1)]
IPython2.3.1
OSposix [linux2]
numpy1.9.1
scipy0.14.0
Sun Dec 07 14:22:10 2014 CET
" ], "json": [ "{ \"Software versions\" : [{ \"module\" : \"Python\", \"version\" : \"2.7.8 |Anaconda 2.1.0 (64-bit)| (default, Aug 21 2014, 18:22:21) [GCC 4.4.7 20120313 (Red Hat 4.4.7-1)]\" }, { \"module\" : \"IPython\", \"version\" : \"2.3.1\" }, { \"module\" : \"OS\", \"version\" : \"posix [linux2]\" }, { \"module\" : \"numpy\", \"version\" : \"1.9.1\" }, { \"module\" : \"scipy\", \"version\" : \"0.14.0\" } ] }" ], "latex": [ "\\begin{tabular}{|l|l|}\\hline\n", "{\\bf Software} & {\\bf Version} \\\\ \\hline\\hline\n", "Python & 2.7.8 |Anaconda 2.1.0 (64-bit)| (default, Aug 21 2014, 18:22:21) [GCC 4.4.7 20120313 (Red Hat 4.4.7-1)] \\\\ \\hline\n", "IPython & 2.3.1 \\\\ \\hline\n", "OS & posix [linux2] \\\\ \\hline\n", "numpy & 1.9.1 \\\\ \\hline\n", "scipy & 0.14.0 \\\\ \\hline\n", "\\hline \\multicolumn{2}{|l|}{Sun Dec 07 14:22:10 2014 CET} \\\\ \\hline\n", "\\end{tabular}\n" ], "metadata": {}, "output_type": "pyout", "prompt_number": 47, "text": [ "Software versions\n", "Python 2.7.8 |Anaconda 2.1.0 (64-bit)| (default, Aug 21 2014, 18:22:21) [GCC 4.4.7 20120313 (Red Hat 4.4.7-1)]\n", "IPython 2.3.1\n", "OS posix [linux2]\n", "numpy 1.9.1\n", "scipy 0.14.0\n", "\n", "Sun Dec 07 14:22:10 2014 CET" ] } ], "prompt_number": 47 }, { "cell_type": "code", "collapsed": false, "input": [ "from IPython.core.display import HTML\n", "def css_styling():\n", " styles = open(\"./styles/custom.css\", \"r\").read()\n", " return HTML(styles)\n", "css_styling()" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", "\n", "\n", "\n", "\n" ], "metadata": {}, "output_type": "pyout", "prompt_number": 48, "text": [ "" ] } ], "prompt_number": 48 }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] } ], "metadata": {} } ] }