Updated notebooks for new library organisation
[cipher-tools.git] / 2017 / 2017-challenge6.ipynb
index bc0b90dd6d729c522eb1e2d7c53ad48f16a97550..a03628ece1317c2bc36ceebbc3030a06d98c9f99 100644 (file)
     "import matplotlib.pyplot as plt\n",
     "%matplotlib inline\n",
     "\n",
-    "from cipherbreak import *\n",
-    "from text_prettify import *\n",
+    "from cipher.affine import *\n",
+    "from cipher.vigenere import *\n",
+    "from cipher.keyword_cipher import *\n",
+    "from support.utilities import *\n",
+    "from support.text_prettify import *\n",
+    "from support.language_models import *\n",
+    "from support.plot_frequency_histogram import *\n",
     "\n",
     "ca = open('6a.ciphertext').read()\n",
     "cb = open('6b.ciphertext').read()"
    "cell_type": "code",
    "execution_count": 2,
    "metadata": {},
-   "outputs": [],
-   "source": [
-    "# def tpack(text, width=100):\n",
-    "#     lines = [text[0]]\n",
-    "#     for word in text[1:]:\n",
-    "#         if len(lines[-1]) + 1 + len(word) <= width:\n",
-    "#             lines[-1] += (' ' + word)\n",
-    "#         else:\n",
-    "#             lines += [word]\n",
-    "#     return lines"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
    "outputs": [
     {
      "name": "stdout",
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# def depunctuate_character(c):\n",
-    "#     if c in string.ascii_uppercase:\n",
-    "#         return 'UPPER'\n",
-    "#     elif c in string.ascii_lowercase:\n",
-    "#         return 'LOWER'\n",
-    "#     else:\n",
-    "#         return c\n",
-    "\n",
-    "# def depunctuate(text):\n",
-    "#     return [depunctuate_character(c) for c in text]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 3,
    "metadata": {},
    "outputs": [],
    "source": [
-    "# def repunctuate_character(letters, punctuation):\n",
-    "#     if punctuation == 'UPPER':\n",
-    "#         return next(letters).upper()\n",
-    "#     elif punctuation == 'LOWER':\n",
-    "#         return next(letters).lower()\n",
-    "#     else:\n",
-    "#         return punctuation\n",
-    "\n",
-    "# def repunctuate(text, punctuation):\n",
-    "#     letters = iter(text)\n",
-    "#     return cat(repunctuate_character(letters, p) for p in punctuation)"
+    "pua = depunctuate(ca)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 4,
    "metadata": {},
    "outputs": [
     {
        "('zeus', -1960.8847716972107)"
       ]
      },
-     "execution_count": 7,
+     "execution_count": 4,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [
     {
        "\"Maryam, I found Jodie at Olympia and she has chapter six already. She had been leading the MIDAS operatives on a wild goose chase around Selcuk making a lot of noise about looking for the missing chapter at the Temple of Artemis. That gave me time to retrieve it from Jodie's friend at the British Museum, which has a collection of artefacts from the Temple. Jodie says she knew we would figure out where to go next. The clue was in the locations. The first one was at the Great Pyramid, the second at the fort of Qaitbay which was built from the ruins of the Lighthouse at Alexandria and the third on Rhodes, among the ruins of the Colossus. The Knight's castle at Bodrum was built from the remains of the Mausoleum at Halicarnassus, hence the “grave” task of guarding the book. So all five chapters were found at the site of one of the Seven Wonders of the ancient world. The only remaining locations are the Statue of Zeus at Olympia and the Hanging Gardens of Babylon, and no-one has any idea where the gardens might have been, so the only place we could go next is Olympia. The clue at the end of chapter five points straight there, since lighting, bull and oak are all symbols of Zeus. We should be safe here because Jodie's network has sent her attackers on to London by laying a long trail of forged documents revealing the location of chapter five. That bought us enough time to locate and decipher chapter six. We had been thinking about the evolution of the Imperial Ciphers. Tacitus used both the Vigenere and Beaufort ciphers which are polyalphabetic versions of the Caesar shift, and at first we assumed that chapter six would be encrypted the same way. We were almost right. Meanwhile Jodie's unexpected talent for forgery has given me an idea. I think we might be able to turn our enemies on one another by exploiting her gift, but I know her current focus is figuring out where on earth the seventh wonder might be.\""
       ]
      },
-     "execution_count": 8,
+     "execution_count": 5,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "['Maryam, I found Jodie at Olympia and she has chapter six already. She had been leading the MIDAS',\n",
-       " 'operatives on a wild goose chase around Selcuk making a lot of noise about looking for the missing',\n",
-       " \"chapter at the Temple of Artemis. That gave me time to retrieve it from Jodie's friend at the\",\n",
-       " 'British Museum, which has a collection of artefacts from the Temple. Jodie says she knew we would',\n",
-       " 'figure out where to go next. The clue was in the locations. The first one was at the Great Pyramid,',\n",
-       " 'the second at the fort of Qaitbay which was built from the ruins of the Lighthouse at Alexandria and',\n",
-       " \"the third on Rhodes, among the ruins of the Colossus. The Knight's castle at Bodrum was built from\",\n",
-       " 'the remains of the Mausoleum at Halicarnassus, hence the “grave” task of guarding the book. So all',\n",
-       " 'five chapters were found at the site of one of the Seven Wonders of the ancient world. The only',\n",
-       " 'remaining locations are the Statue of Zeus at Olympia and the Hanging Gardens of Babylon, and no-one',\n",
-       " 'has any idea where the gardens might have been, so the only place we could go next is Olympia. The',\n",
-       " 'clue at the end of chapter five points straight there, since lighting, bull and oak are all symbols',\n",
-       " \"of Zeus. We should be safe here because Jodie's network has sent her attackers on to London by\",\n",
-       " 'laying a long trail of forged documents revealing the location of chapter five. That bought us',\n",
-       " 'enough time to locate and decipher chapter six. We had been thinking about the evolution of the',\n",
-       " 'Imperial Ciphers. Tacitus used both the Vigenere and Beaufort ciphers which are polyalphabetic',\n",
-       " 'versions of the Caesar shift, and at first we assumed that chapter six would be encrypted the same',\n",
-       " \"way. We were almost right. Meanwhile Jodie's unexpected talent for forgery has given me an idea. I\",\n",
-       " 'think we might be able to turn our enemies on one another by exploiting her gift, but I know her',\n",
-       " 'current focus is figuring out where on earth the seventh wonder might be.']"
-      ]
-     },
-     "execution_count": 9,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "tpack(repunctuate(pa, pua).split())"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 6,
    "metadata": {},
    "outputs": [
     {
     }
    ],
    "source": [
-    "lcat = '\\n'.join\n",
     "print(lcat(tpack(repunctuate(pa, pua).split())))"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 7,
    "metadata": {},
    "outputs": [
     {
        "1932"
       ]
      },
-     "execution_count": 12,
+     "execution_count": 7,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 36,
+   "execution_count": 8,
    "metadata": {},
    "outputs": [],
    "source": [
   },
   {
    "cell_type": "code",
-   "execution_count": 46,
+   "execution_count": 9,
    "metadata": {},
    "outputs": [
     {
        "('jcarykujniqadmv', -3289.3609056830232)"
       ]
      },
-     "execution_count": 46,
+     "execution_count": 9,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 47,
+   "execution_count": 10,
    "metadata": {},
    "outputs": [
     {
        "'Piuo tgnlqva rdn uggsvzeuvlr ed lurg nrubgg ve dyp kztmitehdd flrmqantm bvn enarvtu vd Zgvhrerir rez nttcgegm uy Tlxt lk unu tez la hbt dten, rm mgmggtz ld uog Axruglt. Ot ngrgtz bos orxg utttvyqg ael sn xgutz ybu yq Tlwwuvee uy lluo Enbpueba Gbaiufba yel Ptgrevoa Ntegmvk, zbu hot Uymn pgnt guettlba eem, ggerfkrydd ubg qlna sa tpt Fymtj ttxriltl s ntsgth, welpr sepe ul e atc dldrd mlwhrmgn atyx uog Lvdvo. Soyqisqd fbslmweh hl ggurgm bcn lmhhgm sotnbvh sa tpt Rmbvde rn r kygi ma fybgeut, uog Axruglt nsettm oie unu arht ln yuott tvmigrstm ugetgexn qfm, uy uog abgstcns ma nyxt, bg prn ewrfntm hgvoksord ttemgrhvlra. R nuebbs qrn ggtshtm yq bos Oteeut yr uot ynmsh la hot Gkstgyn, yav, urwte idq, Rhtcfkrr pen ngru ul dcis abvguqq ye ova hrwwqd gnueht pognt nu pra utrztm yq bos Uxsgglt’a lpe fvdmwfveen. Bin mtebo osn r ugvgvlbn avlek ul kt, rrz r srilaar tigeu hy rqq bcn zhvtrmn. Ih prn naqt sn r ttrd dlnn gptd zd ublng hl poye os qrn rlu fggnlryqpe jeype. Roxyttu, xkhtlvtg, yn uot fssarrfg rez hot youd wsnngn fekt ul bcn nmbng; rez ie sblxve tqrstn, erm pognthug jrlua ya urdqtfo pttt raatxydam, nwn eext cen le exq pwsn; rlg zim r nilhpu nloq lr btrgilh kb ova mteho gtpsveu ru hot rgpn lt hlfitu iu zoifjqq. Bouo ndksrhbd pra ceehtratm lq uot ccms-osggrm toxlbt boqv ot brm lgte ggelhum yq sliale lr bos Uxsgglt’a flxkyel. Nlxiuver qlnh ll twxt ie rfflvehceg vot exyihvlba Urpcnuibn Dofbqdin qo uog etc ulittllf ma ubt styivesa. Os qrn sortutm pibo mufbtveu hot atyhurt sgrfg cvuo Syqsnleir rrz otrzam tptgg ul syeagylu Esqhefba. Iu pra sepe uoge ubeu uog xlmo la hot Symtw cyn fuiteqtz. Arqbabvao pgyut yn ovn avlek ru hot rgpn vr y qsvutt ul Seul mebtl vot nvahb mrd laakht ubt jedtema sa Wsd vr uog qtrg yh unu flrnbdaovsa sa Wsgfon Rtttfvrin Ertxgen II rem Difucn Yetyion Olrsgqvbn. “Ct rtg twstanmrd fbrgugm yd yig wmnu kbeinvftrb rdn hggru Gkstgyn Mkyvuire hy ntfont Rsw Gyxrre ve uba Ekhuogge Wiehmyen qfm dgu dyo pgvha uk yt ln uog dlnn yh unu Flztw Ysfbqhsgay. Dlog qgemtg Eoguglqe ora eqgtetd rsvm hot ftvft yh nago r dlna, lbu vn kla nl eyu ggslitt bos Glmgw ygnlgt hvt rsnnieh yn uot qarf votr dlo krd yg ubfu uoeu dyo pvqd jluf ovk. Dlo htqq ka unsu vrutddvhtrmt zhlx e frfhbgtz usc obhutnha uorh bos vgriult Srqhembm prn hot Symtw elm uo xranvru ovn aisrmguggn ir uot Rsgtp. Poiqt hbt Yrtfrfwrea uogkntqvan qht brqvwgqd uy eriu xbso ln hot Fyttv, Grqurfoa vn rr amagrugm Gykre rrt os ybnh yt ahlssgt ysblgg ot see mtabgke uog ntsogvuq sa tpt Vksttirq fizoshn. Ubt Fyztw pixq xu gtsligttm, lt kla, elbt arkiqd rrt thugdyet qyb jeyw purq sed ubg sgvsa. Rdn nl hl ubg ntiglun trgh la hbt ugoa ntmgd ya Rutvfldy vd qovso ubg arug sa tpt eieub dthvyl rdn la hot Symtw ibnsra piqq ir uvxg ft fuiteqtz. Oeuvd bosf vu cvqd lt hbenmsn yd hot erfvtrb Yqzdqyever Hlmzanm ma Peg.'"
       ]
      },
-     "execution_count": 47,
+     "execution_count": 10,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 48,
+   "execution_count": 11,
    "metadata": {},
    "outputs": [
     {
        "('hnypjvriltvyzlt', -3351.460892110415)"
       ]
      },
-     "execution_count": 48,
+     "execution_count": 11,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 49,
+   "execution_count": 12,
    "metadata": {},
    "outputs": [
     {
        "'jdeksfkoiqfhtmesfgdmhdenubvlfhsyhekfreuihjmafmdfueiuunutiwmfmkdlhyxidsldtasdehuudgiumsfdxsufmensmcfavejffumnyekewfhshknsmfsfmaufkffbffsnskfyfgtfmekelhbfefsscbiffulhlbfefmnwfavmnadedhuenamfkhsxhfuxlsxldduxlhulkfsuudxlkguftdmaxeekfrnlmjfsfqfufsnxlhtnsfbhrphaivekfhollnydkftnmfcsechduflhlftsfeptojunuhvenhyfjimwhitnashmflysnafkfudtekgxaidthwtknnkdurensfrgtmkdllnrrfmgxskydenydkfhzxdihgmhbhsonytnxshrefkffbffsnslghsenkdbejfyhefnyndlfsmdkrshtfmrftgshilgumenekflwtgsdlenylnbfkfiilhjhrmfmesdxbflhimfsnshednulgmehexejhlfsfteenavekelfuhefnudlfnsmesnyekffbfgsnsaweehpfudihirsdtmihjhllfudfnidqezxdfeivntldlyhadivfleheekkfsfjfjhlefumenavekefbgfsnslmkugkvkdtdhulkdknfhekihlhrsdfqmyllknspenbfhumghhduywifqfueengjikdlxsdfumldeiilyfidhlhsfhiimmlfqftaveknlfemkknbkejhlunegfrmnuhihvpunjuuxabfslbmsfnqfsnydlfgngwihtfhumejgaxlvahllflthbefnkdljnxlfhumdthxaidsgihtflhulkkfsfpfspunelnxfhipfrljfsfhllecaifmjdluhbfjhkouhiihdglunsmdlildurhflnxinukeisdurmykdlmfhejtfwndsfheekfufimnsynrrfedezxdsqivekcllvbghekukhldussfhlfmavdlfjdmelgsfhmsxaoxsekgekfkhmafevsfbnpfmavgndlmvnuekefbgfsnslsobbhulmnbdedhuholeunddbfduhggmeueduqekfhbadecoxllhhxledxlixsyiixlglekfufjrmrfsunrnyekfgsnpeutfkejhltkhsrenjdekkftxsdurejgyshrcifgfhtfjcfkthiemnudhhumjghmfmdkfsfentntzsnueshirhtxlddkhlnuhvekfuekhdfkfinklnyekftnlgcjhlrfqfhifmlgjxledwljsnefnyjellknspheekfufimduhieeefsenthdomheflekfydyeklivafymsfekfphievmlnyahvduekfveisnyejftnulxiljeglnyahstxlhsseuduxlsifbfulddgvmixtcxlahfadxklnunsgexljfhsfedgsflkivtkhsrflbvnxsanlebxudycufuehtmrsfhefbfgsnsmmbdedhuenkgtxsffhcsnbhuhcvekfumsekfsupdtsmnblgumvfevnxitdefembfnyekfimmlnyejftnmfcntsyienswbvnxsifhlgshrsctnihkhlhhtfhmvfhdmekfgscufnylwtkhinllawfdyvnwmnunesftmrfseketnmfcafymtfekffhlldurnydlfvfhrekfuvnxbgwaflxrfekhevnxieiiwncukdbvnxeejibfejheduefiicsfutfxsnbhthgewtfmlgulxrrfleldlheekeeshdenstgjrhtxkkhlekftnlgchumclbhlldurjellxgfnsefsldudlfunsdkjkdifekebhsahrdhulekfbkgiqflgsfxuidpfhwenbhofbxtknyejgtnmfbthirhtxlcmhufmwthefmsnbgvhumkebxleaflemhgfmaeynsfkfthtnflesmvekflftxreevnydkfdbgfsdgjtdgkeslekftnmedjdiizfsftnqfsennsvnwvnxsyhbdhwhumfpfsvnufvnwqunjjciighvekfftdtfhtmlnenekfkgqfuejghsenyekefsxfldnsvnyhrscunihdtjkdtkekfxiefnydkfuduekiesdnuhtmnyekftnlgcdeleiyjdiidudebfafrfqfhifmxtfdiekeudejdiiaesxhsmemavekfhusefueagavinudhuqommflknyjhs'"
       ]
      },
-     "execution_count": 49,
+     "execution_count": 12,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 50,
+   "execution_count": 13,
    "metadata": {},
    "outputs": [
     {
        "('ryajcqgrnskaxof', -3289.3609056830232)"
       ]
      },
-     "execution_count": 50,
+     "execution_count": 13,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 51,
+   "execution_count": 14,
    "metadata": {},
    "outputs": [
     {
        "'piuotgnlqvardnuggsvzeuvlredlurgnrubggvedypkztmitehddflrmqantmbvnenarvtuvdzgvhrerirreznttcgegmuytlxtlkunutezlahbtdtenrmmgmggtzlduogaxrugltotngrgtzbosorxgutttvyqgaelsnxgutzybuyqtlwwuveeuylluoenbpuebagbaiufbayelptgrevoantegmvkzbuhotuymnpgntguettlbaeemggerfkryddubgqlnasatptfymtjttxriltlsntsgthwelprsepeuleatcdldrdmlwhrmgnatyxuoglvdvosoyqisqdfbslmwehhlggurgmbcnlmhhgmsotnbvhsatptrmbvdernrkygimafybgeutuogaxrugltnsettmoieunuarhtlnyuotttvmigrstmugetgexnqfmuyuogabgstcnsmanyxtbgprnewrfntmhgvoksordttemgrhvlrarnuebbsqrnggtshtmyqbosoteeutyruotynmshlahotgkstgynyavurwteidqrhtcfkrrpenngruuldcisabvguqqyeovahrwwqdgnuehtpogntnuprautrztmyqbosuxsggltalpefvdmwfveenbinmteboosnrugvgvlbnavlekulktrrzrsrilaartigeuhyrqqbcnzhvtrmnihprnnaqtsnrttrddlnngptdzdublnghlpoyeosqrnrlufggnlryqpejeyperoxyttuxkhtlvtgynuotfssarrfgrezhotyoudwsnngnfektulbcnnmbngreziesblxvetqrstnermpognthugjrluayaurdqtfoptttraatxydamnwneextcenleexqpwsnrlgzimrnilhpunloqlrbtrgilhkbovamtehogtpsveuruhotrgpnlthlfituiuzoifjqqbouondksrhbdpraceehtratmlquotccmsosggrmtoxlbtboqvotbrmlgteggelhumyqslialelrbosuxsggltaflxkyelnlxiuverqlnhlltwxtierfflvehcegvotexyihvlbaurpcnuibndofbqdinqouogetculittllfmaubtstyivesaosqrnsortutmpibomufbtveuhotatyhurtsgrfgcvuosyqsnleirrrzotrzamtptggulsyeagyluesqhefbaiuprasepeuogeubeuuogxlmolahotsymtwcynfuiteqtzarqbabvaopgyutynovnavlekruhotrgpnvryqsvuttulseulmebtlvotnvahbmrdlaakhtubtjedtemasawsdvruogqtrgyhunuflrnbdaovsasawsgfonrtttfvrinertxgeniiremdifucnyetyionolrsgqvbnctrtgtwstanmrdfbrgugmydyigwmnukbeinvftrbrdnhggrugkstgynmkyvuirehyntfontrswgyxrreveubaekhuoggewiehmyenqfmdgudyopgvhaukytlnuogdlnnyhunuflztwysfbqhsgaydlogqgemtgeoguglqeoraeqgtetdrsvmhotftvftyhnagordlnalbuvnklanleyuggslittbosglmgwygnlgthvtrsnniehynuotqarfvotrdlokrdygubfuuoeudyopvqdjlufovkdlohtqqkaunsuvrutddvhtrmtzhlxefrfhbgtzuscobhutnhauorhbosvgriultsrqhembmprnhotsymtwelmuoxranvruovnaisrmguggniruotrsgtppoiqthbtyrtfrfwreauogkntqvanqhtbrqvwgqduyeriuxbsolnhotfyttvgrqurfoavnrramagrugmgykrerrtosybnhytahlssgtysblggotseemtabgkeuogntsogvuqsatptvksttirqfizoshnubtfyztwpixqxugtsligttmltklaelbtarkiqdrrtthugdyetqybjeywpurqsedubgsgvsardnnlhlubgntigluntrghlahbtugoantmgdyarutvfldyvdqovsoubgarugsatpteieubdthvylrdnlahotsymtwibnsrapiqqiruvxgftfuiteqtzoeuvdbosfvucvqdlthbenmsnydhoterfvtrbyqzdqyeverhlmzanmmapeg'"
       ]
      },
-     "execution_count": 51,
+     "execution_count": 14,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 52,
+   "execution_count": 15,
    "metadata": {},
    "outputs": [
     {
        "'ytsfeqziozzjyzynifmpczahrmdxemcpjzkmjwjlxnnyonyerofpohxcddrcgzewuxdyioknuwxnbjvyqlnrzresxtfivjwqfyuewdiyowzlefdbxcvvjphzvvgclgtmtgqgsgouncvhzdhgqpoiaeutqtjvpqbodegstcrmcxrtdyybzkeywyeuuvsdtaoxbyrkleslsgczexwgbxntrmeysyaguvwjwqjgydepouomrjtzujwohgqvcmueioasbmdrqtsaviskmkxsekqbnteipeknauupiftymqkenkipdeaxaftxauudzckvvnjftnmtgbeehwbimsclcessglcireuhgwwlyxjfngmnmrebmmfkvpaohxxsgbvzoywwgzcuqnojzxpefrmkzpmgksvajuryrkimuzevnjlqwexpybstphbsiezbiqccknatjvowdxwkenfosfjjrfspkiojnaeaceignjpkmhmpswfczqbjhvppczhdvjtvlkwvgcecjedqrxtabnyivskgpgpbmityxuktwmmlrgqyvvawhlngwiahbktyzvqynncbbdqzdeeeoershbiqltegjriukialufyukgvtzekncmyafwndyamvtstwryacxyallqpaopcnwrsqtgzrgfpejoymndfxaazwdfhmmcgpwltsbxjvvoageyfazkzskfccocgmwucfjsnqzuevanhtxwxoaxdttlqrohnwjfhzghonqxscdddzywlzgedmnfspenyehypvtwlgugrxjxglrjrkvdvmievpftyuocdicijifknqwvqjblqlwowcrgkqbxrnihxzlqcwubpwbbdlyrxbldlhguqedueejcuvcgyxnyzwmviaiwexxagvfnvfisrlwglpldcjsibqqgvuienlufstzzhanbsnitujiyexvvzuxzsgcpzhwlbpztqxvcuzksmsvmckgsamvqislpmpebwztxycgdboztpckmeyncijrcuamgbamtujurczsifncmuykyvsobuykolymrgjrokaycaizhkkcpkiyykdkcokmoaxuoaslievdhtpnykwjqhctxhucldgakaqovdcppxhrcduwngahltatswfaebolamgzmlbrraeeaicgyvomorpeavueckyysketvfraqyxxzpdxziewwaazksgqexgakjwafruwhzkwoohwfyzaqjcebhhwzbcokqsxweviwgblgawlimoqbgbwljybjxiqvguxvkwaydleqxxczkkrjndjipnuckiensalufwzdbcvlzboiimqihhqgqligodxmetgvuyynjfueadtioypxvvtjananrwtwiwqecsfrafoecgmigjstastytaoaaaicbbqfwczwgazhlhqoywpapkdnijysxgwscchyyqvymiyhssfwliaonsfteylmqgdavsdgzeruprqimkbigpdzcijjgiapvrdsfillydvlkddcfgbrzusfbthejdltrhgpwfjdefhatrynubwqmgmbenqeauduywpadbqwcguysfrnxklcgmigjsbgnoqkgmhagmiyhqyvpkpulmnexfgruzehgcppkjquwegfxcvdymgtxfrdfjxdehtvqinowziyfadvepfjumnxnkgegwceptacydlungwxeqkikgyqqaghwclrniddelxibvghlrqdoqjnblmlpfuavvumalzqsiibaywlutzncqynnpllygpdiqrndrdtkxafowgexyztnhjoefbnkmqcyurmmlzpomoxzgzaycskbzxsglywehercavykijxmayepzokgrwrskcpkzifynzsmraaamwausemvnzmiftcmkgqeibgvzyuajgfkmcnhaausphtlsenhnfecpfczdmvgxzrepwdjnrzbcggfobytwrsbxcuuefyprmkdoqjreayfqyviakimlaqqaafzormkycourkqymvgivresfbfflondaypnqurwdwtyoadrbctnsirqkzerxegpteaniovvkfriypvlkedyziaaejijgiguwldnbdlngbdofzpbzcbufvtfonjytalwrkvpxwlbvyquadgdzzsauoaohxxfceuxnaqaumnpryjsmkdiyqumafndewkdhypzatgntredpgiyiuhvalamveqvsgdknfqxkdzvrhxfxcubicgmrqhwuiswmlzbhzzeylhnqgp'"
       ]
      },
-     "execution_count": 52,
+     "execution_count": 15,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 53,
+   "execution_count": 16,
    "metadata": {},
    "outputs": [
     {
        "'ybwfeqpgshhzozgrifmfadiphcdfimcpzxourmzlfrnyodwizwvfopbcddhakhmmkxlciokdsafvrzvgulnrppiafjvidnwqfosielyooedleftzbkdlzppdvvgsjkbujwqowgoudazphtxgytoiausxybzlpyfodewqxkzcsxzxdyyrxomgmoecyvsdjysfjohktislswadmfmwbfrtrmuwwgiwkvenwqjwwhmxekouvjtzkhawpwgvkqueieywjuthqbwaviiiqsfiukyfnteynisvqkuxmftycoomvaypliaxavrbicktzkovvnzdxvujwbmihwbykwktsusaklcihcypommlgbjfnwkruzurmujkvpqmlffiwbddoywmedkcgdordxpevpqshfcgswvajkpczsycuhivnjboamffobaxphbigihjygckonatztselnmkmrfosvhnznifkqsjnauygmqwdjxomhmfqankpgbrlvppsxlldzjvtowvgscgrmtgrfxabnogzaswfgxfmitovysbmcmtvgqylteepbdgemahbarchdgonvgbbdgxhmmueezwhbigjxmozhicoialkdccswlthiknccwenedtyiqvtsjuvgisnyiplqpqmtkvmhsyxgzrwdtmreomvhfxaqxalnxcmkkpwljqffrlloikeyfqxohaavckscgmmsgnridqhyevadfxfeneafhttlgpspvmzfpdghodobakttdhcwlzwchuvvipmryehonzbebwuovxjxwjvrzalddqievfdxgcesdqgijiviryelgjjpqlweugzoagbfvnihnxpykmkbxabbdbwvfjbtlpkuqetsimrskvkkyxnoxaudyqieixxawtjvdvyszpwglfjhkriybyugvuycrtcvithdhanrqrqbkzigixvvpsbhawsphlwlbfxxyflsuhosmslkgsoiqmduislfktmjmptfccgdrmdbxsammcncizpgcicwbiqtujkpghayvnkquykotwwjkokwpymrwhvwsqocimzhkaatsqooklocokcmefceqstmevdxrtvgamjylctxxsgtlwqkiuovdsntfphsdcangaxjxibimfiibolqkkhubrrzeeeayakgdecozteavkcgsgoikmxvfrqocffpfdfdiewmyehsiwqmbgakzuenzkmhhowooxujghqgjkibhhmxfkwagsfaevimeftoqmlqqoqbwzatrorjfmqvgkvzseqodtiqxxsxoszzddrmpnusimmviqlcjwzdrazthreiqqqihxokytywolbmetwtyggdzfciadtymcxflltrenanhuxeqmgekwfravmikocygrwtasjwxiwqqaqgbbqvughewqzpphqooutixatnqnysxwuwkkxoyyzymiofwanmbiisnsfjcctugwdizsdgpcvcxhgiuobigfbdkqzzgqepvrtqjqtboddpkddsdkjzpksnfthezbpbzxwpejjdevfebzodujaqmgczivyuqulyywpqbfyeswugwfrnnipkocygrwbgneooouxqgumyhqottsxkbmvixfghsdmpwspxojqumcknfsldgqgtxvphnrntepxvqidmahqovalzepfzsqvfdagmkwcefrekgtbuvkwxegimsoogqikhwcbprqltulfmbvgxjvylegjvflmlfdyidlkmipzqsygfigmbubdncqolrxtbogxhiqrdbvlbananswgenwdbvxzomjbnkcoggchcmtdpomevdohqocaobzxiepgeuxezgavyagnfuqoexdokghuvassfkhmfynpqqziqqmeeusectrhuyvtkqkgqugfodpouingfkcarpiqksxltlsullvnuspngzdmlebhzufwlnnrzrakonerybarsbnaycmvopzqkdoghvmiovqgziakykpiygqandormawgwchaqgqvgilpianrvftsndaonrychmdexyoatpfkbdiizukzehvioxjuavmovvadvqgfllsidyzyyemryzgqkuwltlfltdwblsfzprxgjcvltnsnjyjypezalpfalbvooyilwtzhwauoqmlffvsecbnaqqsqvxhojaqkdiooyuivddmakdhondibwdtzidpgywmcplqliqveqlqklsdvqfodzvhfbnfskbqggmrgfacqimmtdbhzpcctpdggx'"
       ]
      },
-     "execution_count": 53,
+     "execution_count": 16,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 54,
+   "execution_count": 17,
    "metadata": {},
    "outputs": [
     {
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/usr/local/lib/python3.5/dist-packages/matplotlib/figure.py:403: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure\n",
+      "/usr/local/lib/python3.6/dist-packages/matplotlib/figure.py:418: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure\n",
       "  \"matplotlib is currently using a non-GUI backend, \"\n"
      ]
     },
     {
      "data": {
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+      "image/png": "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\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f66f2d57400>"
+       "<matplotlib.figure.Figure at 0x7f74f40ca828>"
       ]
      },
      "metadata": {},
   },
   {
    "cell_type": "code",
-   "execution_count": 55,
+   "execution_count": 18,
    "metadata": {},
    "outputs": [
     {
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/usr/local/lib/python3.5/dist-packages/matplotlib/figure.py:403: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure\n",
+      "/usr/local/lib/python3.6/dist-packages/matplotlib/figure.py:418: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure\n",
       "  \"matplotlib is currently using a non-GUI backend, \"\n"
      ]
     },
     {
      "data": {
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+      "image/png": "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\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f66f2b8a320>"
+       "<matplotlib.figure.Figure at 0x7f74b63ab748>"
       ]
      },
      "metadata": {},
   },
   {
    "cell_type": "code",
-   "execution_count": 56,
+   "execution_count": 19,
    "metadata": {},
    "outputs": [
     {
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/usr/local/lib/python3.5/dist-packages/matplotlib/figure.py:403: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure\n",
+      "/usr/local/lib/python3.6/dist-packages/matplotlib/figure.py:418: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure\n",
       "  \"matplotlib is currently using a non-GUI backend, \"\n"
      ]
     },
     {
      "data": {
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+      "image/png": "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\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f66f2c1ea90>"
+       "<matplotlib.figure.Figure at 0x7f74b4bf73c8>"
       ]
      },
      "metadata": {},
   },
   {
    "cell_type": "code",
-   "execution_count": 57,
+   "execution_count": 20,
    "metadata": {},
    "outputs": [
     {
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/usr/local/lib/python3.5/dist-packages/matplotlib/figure.py:403: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure\n",
+      "/usr/local/lib/python3.6/dist-packages/matplotlib/figure.py:418: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure\n",
       "  \"matplotlib is currently using a non-GUI backend, \"\n"
      ]
     },
     {
      "data": {
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\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f66f2b0eeb8>"
+       "<matplotlib.figure.Figure at 0x7f74b33da198>"
       ]
      },
      "metadata": {},
   },
   {
    "cell_type": "code",
-   "execution_count": 91,
+   "execution_count": 21,
    "metadata": {},
    "outputs": [
     {
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/usr/local/lib/python3.5/dist-packages/matplotlib/figure.py:403: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure\n",
+      "/usr/local/lib/python3.6/dist-packages/matplotlib/figure.py:418: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure\n",
       "  \"matplotlib is currently using a non-GUI backend, \"\n"
      ]
     },
     {
      "data": {
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+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAaoAAAEmCAYAAAAz/dRVAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvNQv5yAAAET1JREFUeJzt3XuQJWV9xvHvI2Dk5gUYNYrjYmKRGE1FHY2IJgbQIl6CqWhFElQSrYmJihqJBTGWFKVVGqwYq3LRFQkmEEzEa7xCgQZQRNllkV2WixFUjIpIvCClgPzyx+mVYRfY6dO9M+/sfD9Vp+b0mX77/Z0zfc5z3u6e7lQVkiS16l7LXYAkSffEoJIkNc2gkiQ1zaCSJDXNoJIkNc2gkiQ1zaCSJDXNoJIkNc2gkiQ1zaCSJDVt16XsbL/99qs1a9YsZZeSpEatW7fuhqqa2d58SxpUa9as4eKLL17KLiVJjUrytcXM56Y/SVLTDCpJUtMMKklS0wwqSVLTDCpJUtMMKklS0wwqSVLTDCpJUtMMKklS0wwqSVLTlvQUShrHmuM+3rvNtW951g6oRJJ2PEdUkqSmGVSSpKYZVJKkphlUkqSmGVSSpKYZVJKkphlUkqSmGVSSpKYZVJKkphlUkqSmGVSSpKZtN6iSnJLk+iQb7+J3r01SSfbbMeVJkla7xYyoTgUO3/rBJA8DngF8feSaJEn6ue0GVVWdB9x4F796O/A6oMYuSpKkLabaR5XkCOCbVXXpyPVIknQnva9HlWQP4K+ZbPZbzPzzwDzA7Oxs3+4kSavcNCOqXwIOAC5Nci2wP7A+yYPvauaqWltVc1U1NzMzM32lkqRVqfeIqqouAx64ZboLq7mqumHEuiRJAhZ3ePoZwIXAgUmuS/KSHV+WJEkT2x1RVdWR2/n9mtGqkSRpK56ZQpLUNINKktQ0g0qS1DSDSpLUNINKktQ0g0qS1DSDSpLUNINKktQ0g0qS1DSDSpLUNINKktQ0g0qS1DSDSpLUNINKktQ0g0qS1DSDSpLUNINKktQ0g0qS1DSDSpLUNINKktQ0g0qS1DSDSpLUNINKktQ0g0qS1LTtBlWSU5Jcn2TjgsdOSnJFki8n+VCS++/YMiVJq9ViRlSnAodv9djZwKOr6teBq4DjR65LkiRgEUFVVecBN2712FlVdVs3+QVg/x1QmyRJo+yj+lPgkyMsR5Kkbew6pHGS1wO3AaffwzzzwDzA7OzskO4k7WTWHPfx3m2ufcuzdkAlatnUI6okRwPPBv64quru5quqtVU1V1VzMzMz03YnSVqlphpRJTkceB3w21V187glSZJ0h8Ucnn4GcCFwYJLrkrwE+Adgb+DsJBuSvHMH1ylJWqW2O6KqqiPv4uH37IBaJEnahmemkCQ1zaCSJDXNoJIkNc2gkiQ1zaCSJDXNoJIkNc2gkiQ1zaCSJDXNoJIkNc2gkiQ1zaCSJDXNoJIkNW3QhRNXKy/2pp2B6/FwvoZLwxGVJKlpBpUkqWkGlSSpaQaVJKlpBpUkqWkGlSSpaQaVJKlpBpUkqWkGlSSpaQaVJKlpBpUkqWnbDaokpyS5PsnGBY/tk+TsJFd3Px+wY8uUJK1WixlRnQocvtVjxwHnVNUjgXO6aUmSRrfdoKqq84Abt3r4COC93f33As8duS5JkoDp91E9qKq+1d3/NvCgkeqRJOlOBl+PqqoqSd3d75PMA/MAs7OzQ7vTSIZeR8fr8EhaKtOOqL6T5BcBup/X392MVbW2quaqam5mZmbK7iRJq9W0QfVR4MXd/RcDHxmnHEmS7mwxh6efAVwIHJjkuiQvAd4CPD3J1cBh3bQkSaPb7j6qqjrybn516Mi1SJK0Dc9MIUlqmkElSWqaQSVJappBJUlqmkElSWqaQSVJappBJUlqmkElSWqaQSVJappBJUlqmkElSWqaQSVJatrgCydKklaulXARVEdUkqSmGVSSpKYZVJKkphlUkqSmGVSSpKYZVJKkphlUkqSmGVSSpKYZVJKkphlUkqSmGVSSpKYNCqokr0myKcnGJGckuc9YhUmSBAOCKslDgWOAuap6NLAL8IKxCpMkCYZv+tsV2D3JrsAewP8OL0mSpDtMHVRV9U3gbcDXgW8BP6iqs8YqTJIkGHA9qiQPAI4ADgC+D7w/yVFVddpW880D8wCzs7MDSpXUmpVwLaPWDX0NV8PfYMimv8OAa6rqu1V1K/BB4Mlbz1RVa6tqrqrmZmZmBnQnSVqNhgTV14EnJdkjSYBDgc3jlCVJ0sSQfVQXAWcC64HLumWtHakuSZKAAfuoAKrqjcAbR6pFkqRteGYKSVLTDCpJUtMMKklS0wwqSVLTDCpJUtMMKklS0wwqSVLTDCpJUtMMKklS0wwqSVLTDCpJUtMMKklS0wadlFbS9FbDBe+kMTiikiQ1zaCSJDXNoJIkNc2gkiQ1zaCSJDXNoJIkNc2gkiQ1zaCSJDXNoJIkNc2gkiQ1zaCSJDVtUFAluX+SM5NckWRzkoPGKkySJBh+Utp3AJ+qqucluTewxwg1SZL0c1MHVZL7Ab8FHA1QVbcAt4xTliRJE0M2/R0AfBf4lySXJDk5yZ4j1SVJEjBs09+uwOOAV1bVRUneARwHvGHhTEnmgXmA2dnZAd2Nx+sASdLKMWREdR1wXVVd1E2fySS47qSq1lbVXFXNzczMDOhOkrQaTR1UVfVt4BtJDuweOhS4fJSqJEnqDD3q75XA6d0Rf18F/mR4SZIk3WFQUFXVBmBupFokSdqGZ6aQJDXNoJIkNc2gkiQ1zaCSJDXNoJIkNc2gkiQ1zaCSJDXNoJIkNc2gkiQ1zaCSJDXNoJIkNc2gkiQ1bejZ0yVp2XgR1NXBEZUkqWkGlSSpaQaVJKlpBpUkqWkGlSSpaQaVJKlpBpUkqWkGlSSpaQaVJKlpBpUkqWkGlSSpaYODKskuSS5J8rExCpIkaaExRlSvAjaPsBxJkrYxKKiS7A88Czh5nHIkSbqzoSOqvwdeB9w+Qi2SJG1j6utRJXk2cH1VrUvytHuYbx6YB5idnZ22u52K19CRpMUbMqI6GPi9JNcC7wMOSXLa1jNV1dqqmququZmZmQHdSZJWo6mDqqqOr6r9q2oN8ALg3Ko6arTKJEnC/6OSJDVu6n1UC1XVZ4HPjrEsSZIWckQlSWqaQSVJappBJUlqmkElSWqaQSVJappBJUlqmkElSWqaQSVJappBJUlqmkElSWqaQSVJatoo5/pbal7PSS1wPZSWhiMqSVLTDCpJUtMMKklS0wwqSVLTDCpJUtMMKklS0wwqSVLTDCpJUtMMKklS0wwqSVLTDCpJUtMMKklS06YOqiQPS/KZJJcn2ZTkVWMWJkkSDDt7+m3Aa6tqfZK9gXVJzq6qy0eqTZKk6UdUVfWtqlrf3f8RsBl46FiFSZIEI+2jSrIGeCxw0RjLkyRpi8EXTkyyF/AB4NVV9cO7+P08MA8wOzs7tDtpNCv9wocrvf4W+BquDINGVEl2YxJSp1fVB+9qnqpaW1VzVTU3MzMzpDtJ0io05Ki/AO8BNlfV341XkiRJdxgyojoYeCFwSJIN3e2ZI9UlSRIwYB9VVV0AZMRaJEnahmemkCQ1zaCSJDXNoJIkNc2gkiQ1zaCSJDXNoJIkNc2gkiQ1zaCSJDXNoJIkNc2gkiQ1zaCSJDVt8PWopGkMvQ6Q1xGSVg9HVJKkphlUkqSmGVSSpKYZVJKkphlUkqSmGVSSpKYZVJKkphlUkqSmGVSSpKYZVJKkphlUkqSmGVSSpKYNCqokhye5MslXkhw3VlGSJG0xdVAl2QX4R+B3gUcBRyZ51FiFSZIEw0ZUTwS+UlVfrapbgPcBR4xTliRJE0OC6qHANxZMX9c9JknSaFJV0zVMngccXlUv7aZfCPxmVb1iq/nmgflu8kDgyunL3a79gBuWsX0LNaz09i3UsNLbt1DDcrdvoYaV3n6sZdyTh1fVzHbnqqqpbsBBwKcXTB8PHD/t8sa4ARcvZ/sWaljp7VuoYaW3b6GG5W7fQg0rvf1YyxjjNmTT35eARyY5IMm9gRcAHx2wPEmStrHrtA2r6rYkrwA+DewCnFJVm0arTJIkBgQVQFV9AvjESLWMYe0yt2+hhpXevoUaVnr7FmpY7vYt1LDS24+1jMGmPphCkqSl4CmUJElNM6iAJGuSbFzuOrZIckKSY5ep72OSbE5y+hL3O8rfIMnnl3sZSW4aWoOkOwzaR6Wd0l8Ah1XVdctdyDSq6sktLEPjSBImuyhuX+5atHx2mhFVkg8nWZdkU/dPxn3tmuT0bjRxZpI9evb/oiRfTnJpkn/r23mS1ye5KskFTP4xum/7o5J8McmGJO/qzsXYdxnvBB4BfDLJa6Zo/4buJMUXJDljilHhLkne3f0Nz0qy+xQ1DB7NLMeIqBtRXpHk1G49OD3JYUk+l+TqJE9c5HL+MsnG7vbqAXVM9V5YuB5PuQ5sqeHKJP8KbAQe1qPtnkk+3r0PNyb5wyn63rhg+tgkJyyy7V8lOaa7//Yk53b3D+mzhSLJE7rPkvt0z2dTkkf3aH/iwr99kjcneVWP9i/rPkc2JLkmyWcW23aHWe5/5BrrBuzT/dydycq9b4+2a4ACDu6mTwGO7dH+14CrgP0W1tKj/eOBy4A9gPsCX+nZ/68C/wXs1k3/E/CiKV/Ha7c8j57tngBsAO4D7A1c3fM5rAFuA36jm/5P4Kgp6rhphHVp0DKmab/g+T+GyRfIdd16GCbn0Pxwj/VoT2AvYBPw2CnqmOq9MHQ93qqG24EnTdH2D4B3L5i+3xR9b1wwfSxwwiLbPgl4f3f/fOCLwG7AG4E/61nHm4C3MTnxd68TKXTPYX13/17A//T5PFywnN265/Gcvm3Hvu00IyrgmCSXAl9g8g3skT3bf6OqPtfdPw14So+2hzBZQW8AqKobe/b9VOBDVXVzVf2Q/v84fSiTD4kvJdnQTT+i5zKGOhj4SFX9pKp+xCQ4+7qmqjZ099cxecOtJtdU1WU12cy1CTinJp8Yl7G41+IpTNajH1fVTcAHmaxbfU37Xhi6Hi/0tar6whTtLgOenuStSZ5aVT8YUENf64DHJ7kv8FPgQmCOyetyfs9lnQg8vWv/t30aVtW1wPeSPBZ4BnBJVX2vZ/8A7wDOrapp3suj2in2USV5GnAYcFBV3Zzks0y+2fex9XH6K+m4/QDvrarjl7uQgX664P7PmIyOV5OFz//2BdO3s7Tv1RbeCz+eplFVXZXkccAzgTclOaeqTuyxiNu48y6RRX+OVNWtSa4BjgY+D3wZ+B3gl4HNPWoA2JfJqHi3roa+r8fJXR0PZjIq7iXJ0cDDgVdsZ9YlsbOMqO4H/F8XUr/CZAje12ySg7r7fwRc0KPtucDzk+wLkGSfnn2fBzw3ye5J9gae07P9OcDzkjxwS/9JHt5zGUN9DnhOt119L+DZS9y/Jt/an5tkjyR7Ar9P/2/yMP17Yeh6PFiShwA3V9VpwEnA43ou4jvAA5Psm+QX6L8en89kc+F53f2XMRnR9A37dwFvAE4H3tqzLcCHgMOZbJL/dJ+GSR7P5DkcVY0cxLJTjKiATwEvS7KZydnZp9lkcCXw8iSnAJcD/7zYhlW1Kcmbgf9O8jPgEibfZhbbfn2S/wAuBa5nch7FRauqy5P8DXBWknsBtwIvB77WZzlDVNWXknyUybfI7zDZBLOUm13GtJJG0z/XrUenMtk3AnByVV0yxaKmei8MXY9H8hjgpCS3M3kf/Hmfxt2o6EQmr+E3gSt69n8+8Hrgwqr6cZKf0PPLQpIXAbdW1b93B0V9PskhVXXuYpdRVbd0B0F8v6p+1qd/JqOofYDPJIHJiWlf2nMZo/LMFBpNkr2q6qbuKLHzgPmqWr/cdfXRjYrXV9VSj0ibkGQN8LGqWvRRZvewrBOYHFjytqHLUj/dF9b1wPOr6urlrmeonWXTn9qwtjuYYz3wgRUYUg9hsgPcD1atWEkexeSIy3N2hpACR1SSpMY5opIkNc2gkiQ1zaCSJDXNoJIkNc2gkiQ1zaCSJDXt/wG1Y5A9mcLQ3AAAAABJRU5ErkJggg==\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f66f2c0fe48>"
+       "<matplotlib.figure.Figure at 0x7f74b2df0b38>"
       ]
      },
      "metadata": {},
   },
   {
    "cell_type": "code",
-   "execution_count": 95,
+   "execution_count": 22,
    "metadata": {},
    "outputs": [
     {
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/usr/local/lib/python3.5/dist-packages/matplotlib/figure.py:403: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure\n",
+      "/usr/local/lib/python3.6/dist-packages/matplotlib/figure.py:418: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure\n",
       "  \"matplotlib is currently using a non-GUI backend, \"\n"
      ]
     },
        "'y'"
       ]
      },
-     "execution_count": 95,
+     "execution_count": 22,
      "metadata": {},
      "output_type": "execute_result"
     },
     {
      "data": {
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\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f670da1d0f0>"
+       "<matplotlib.figure.Figure at 0x7f74b3e6b7f0>"
       ]
      },
      "metadata": {},
   },
   {
    "cell_type": "code",
-   "execution_count": 58,
+   "execution_count": 23,
    "metadata": {},
    "outputs": [
     {
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/usr/local/lib/python3.5/dist-packages/matplotlib/figure.py:403: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure\n",
+      "/usr/local/lib/python3.6/dist-packages/matplotlib/figure.py:418: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure\n",
       "  \"matplotlib is currently using a non-GUI backend, \"\n"
      ]
     },
     {
      "data": {
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+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAbAAAAEmCAYAAAADccV0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvNQv5yAAAEb1JREFUeJzt3X2sZHV9x/H3p0B9ABRhr4gIrtqNLdYIuFKsmqCoRdSAKVIfF41mtULUVkyg1kiIJFhtTU0qFZWAFRWsIljxgSxW8IHK7vK0gMhWoLBBQLQIEpWHb/+Ys+kAC3Pm3jv37u/O+5VM7jlnzu/+vjNnZj7zO3PmTKoKSZJa8weLXYAkSbNhgEmSmmSASZKaZIBJkppkgEmSmmSASZKaZIBJkppkgEmSmmSASZKaZIBJkpq07WIXALBs2bJavnz5YpchSdoKrFu37hdVNTNqva0iwJYvX87atWsXuwxJ0lYgyQ191nMXoiSpSQaYJKlJBpgkqUkGmCSpSQaYJKlJBpgkqUkGmCSpSQaYJKlJBpgkqUkGmCSpSVvFqaQkSVun5cd8o/e615/4yglW8lCOwCRJTTLAJElNMsAkSU0ywCRJTTLAJElNMsAkSU0ywCRJTTLAJElNMsAkSU0ywCRJTTLAJElNMsAkSU0ywCRJTTLAJElNMsAkSU0ywCRJTTLAJElNGhlgSfZI8t0kVyW5Msl7uuU7JzkvybXd3yd0y5PkE0k2Jrk8yb6TvhGSpOnTZwR2L/C+qtoL2B84MslewDHAmqpaAazp5gFeAazoLquBk+a9aknS1BsZYFV1c1Wt76bvBK4GdgcOAU7rVjsNOLSbPgT4XA1cBOyUZLd5r1ySNNXG+gwsyXJgH+C/gF2r6ubuqp8Du3bTuwM3DjW7qVsmSdK86R1gSXYAvgK8t6p+PXxdVRVQ43ScZHWStUnW3nbbbeM0lSSpX4Al2Y5BeJ1eVV/tFt+yeddg9/fWbvkmYI+h5k/plj1AVZ1cVSurauXMzMxs65ckTak+RyEG+CxwdVX909BV5wBHdNNHAGcPLV/VHY24P3DH0K5GSZLmxbY91nkB8GbgiiSXdsv+DjgRODPJ24AbgMO7684FDgY2AncDb53XiiVJokeAVdX3gTzM1QduYf0CjpxjXZIkPSLPxCFJapIBJklqkgEmSWqSASZJapIBJklqkgEmSWqSASZJapIBJklqkgEmSWqSASZJapIBJklqkgEmSWqSASZJapIBJklqkgEmSWqSASZJapIBJklqkgEmSWqSASZJapIBJklqkgEmSWqSASZJapIBJklqkgEmSWqSASZJapIBJklqkgEmSWqSASZJapIBJklqkgEmSWqSASZJapIBJklqkgEmSWqSASZJapIBJklqkgEmSWqSASZJapIBJklq0raLXYAkaWEsP+Ybvde9/sRXTrCS+eEITJLUJANMktQkA0yS1CQDTJLUJANMktQkj0KUpMYstaMJZ8sRmCSpSQaYJKlJBpgkqUkjAyzJKUluTbJhaNlxSTYlubS7HDx03bFJNia5JslfTKpwSdJ06zMCOxU4aAvLP15Ve3eXcwGS7AW8DnhW1+aTSbaZr2IlSdpsZIBV1QXAL3v+v0OAL1XV76rqOmAjsN8c6pMkaYvmchj9UUlWAWuB91XVr4DdgYuG1rmpW/YQSVYDqwH23HPPOZQhSW3ycPi5me1BHCcBzwD2Bm4G/nHcf1BVJ1fVyqpaOTMzM8syJEnTalYBVlW3VNV9VXU/8Gn+fzfhJmCPoVWf0i2TJGlezSrAkuw2NPsaYPMRiucAr0vyqCRPA1YAP55biZIkPdTIz8CSfBE4AFiW5CbgQ8ABSfYGCrgeeAdAVV2Z5EzgKuBe4Miqum8ypUuSptnIAKuq129h8WcfYf0TgBPmUpQkSaN4Jg5JUpMMMElSkwwwSVKTDDBJUpMMMElSkwwwSVKTDDBJUpMMMElSkwwwSVKTDDBJUpMMMElSk+byg5aSpI4/TrnwHIFJkppkgEmSmmSASZKa5GdgkjTEz7La4QhMktQkA0yS1CQDTJLUJANMktQkA0yS1CQDTJLUJANMktQkA0yS1CQDTJLUJANMktQkA0yS1CQDTJLUJANMktQkz0YvaUnyrPJLnyMwSVKTDDBJUpMMMElSkwwwSVKTDDBJUpMMMElSkwwwSVKT/B6YpK2a3+fSw3EEJklqkgEmSWqSASZJapIBJklqkgEmSWqSASZJapIBJklqkgEmSWqSASZJatLIAEtySpJbk2wYWrZzkvOSXNv9fUK3PEk+kWRjksuT7DvJ4iVJ06vPCOxU4KAHLTsGWFNVK4A13TzAK4AV3WU1cNL8lClJ0gONDLCqugD45YMWHwKc1k2fBhw6tPxzNXARsFOS3earWEmSNpvtZ2C7VtXN3fTPgV276d2BG4fWu6lbJknSvJrzQRxVVUCN2y7J6iRrk6y97bbb5lqGJGnKzDbAbtm8a7D7e2u3fBOwx9B6T+mWPURVnVxVK6tq5czMzCzLkCRNq9kG2DnAEd30EcDZQ8tXdUcj7g/cMbSrUZKkeTPyBy2TfBE4AFiW5CbgQ8CJwJlJ3gbcABzerX4ucDCwEbgbeOsEapa0yGb7I5P+OKXm08gAq6rXP8xVB25h3QKOnGtRkiSN4pk4JElNMsAkSU0ywCRJTTLAJElNMsAkSU0ywCRJTTLAJElNMsAkSU0ywCRJTTLAJElNGnkqKUlLl+cmVMsMMGmJMIw0bdyFKElqkiMwaSvjSErqxxGYJKlJBpgkqUnuQpQmxF2B0mQ5ApMkNckAkyQ1yQCTJDXJz8CkHvw8S9r6OAKTJDXJAJMkNckAkyQ1yQCTJDXJAJMkNckAkyQ1yQCTJDXJAJMkNckvMmuq+IVkaelwBCZJapIBJklqkrsQ1SR3BUpyBCZJapIBJklqkgEmSWqSASZJapIBJklqkkchalF5NKGk2XIEJklqkgEmSWqSASZJapIBJklqkgEmSWqSASZJapKH0WveeEi8pIXkCEyS1KQ5jcCSXA/cCdwH3FtVK5PsDJwBLAeuBw6vql/NrUxJkh5oPkZgL66qvatqZTd/DLCmqlYAa7p5SZLm1SR2IR4CnNZNnwYcOoE+JElTbq4BVsB3kqxLsrpbtmtV3dxN/xzYdY59SJL0EHM9CvGFVbUpyROB85L8ZPjKqqoktaWGXeCtBthzzz3nWIYkadrMaQRWVZu6v7cCZwH7Abck2Q2g+3vrw7Q9uapWVtXKmZmZuZQhSZpCsw6wJNsn2XHzNPByYANwDnBEt9oRwNlzLVKSpAebyy7EXYGzkmz+P1+oqm8luRg4M8nbgBuAw+depiRJDzTrAKuqnwHP2cLy24ED51KUJEmjeCYOSVKTPBeiHsJzGkpqgSMwSVKTDDBJUpMMMElSkwwwSVKTDDBJUpMMMElSkwwwSVKTDDBJUpMMMElSkwwwSVKTDDBJUpMMMElSkwwwSVKTPBv9EuZZ5SUtZQZYIwwjSXogdyFKkprkCGyBOZKSpPlhgM2SQSRJi8tdiJKkJhlgkqQmGWCSpCYZYJKkJhlgkqQmGWCSpCYZYJKkJvk9MPxOlyS1yBGYJKlJBpgkqUkGmCSpSQaYJKlJBpgkqUkGmCSpSQaYJKlJBpgkqUkGmCSpSQaYJKlJBpgkqUkGmCSpSQaYJKlJBpgkqUkGmCSpSUvq98D8XS9Jmh6OwCRJTTLAJElNMsAkSU2aWIAlOSjJNUk2JjlmUv1IkqbTRAIsyTbAvwCvAPYCXp9kr0n0JUmaTpMage0HbKyqn1XV74EvAYdMqC9J0hSaVIDtDtw4NH9Tt0ySpHmRqpr/f5ocBhxUVW/v5t8M/FlVHTW0zmpgdTf7TOCaeS9kYBnwi628XQs1zradNc5PuxZqnG07a5yfdi3U2NdTq2pm5FpVNe8X4PnAt4fmjwWOnURfPWpZu7W3a6HGpXzbrNHbtjX1tZRrnO/LpHYhXgysSPK0JH8IvA44Z0J9SZKm0EROJVVV9yY5Cvg2sA1wSlVdOYm+JEnTaWLnQqyqc4FzJ/X/x3ByA+1aqHG27axxftq1UONs21nj/LRrocZ5NZGDOCRJmjRPJSVJatJUBFiSHy52DVuDJMuTbFjgPt+d5Ookp4/ZbtbbLMlxSY6ebftJWOj7fjG2dQuS3LXYNbQuyU5J3rXYdcCUBFhV/fli1zDF3gW8rKreOE4jt5m0sDLQJxN2YvC8XnRTEWDjvutKsirJ5UkuS/JvPdu8M8ml3eW6JN8dsf77k7y7m/54kvO76ZeMGq0keV5X36OTbJ/kyiR/2vf2df/j6UkuSfK8EestT/KTJKd3I6l/T/LYnn38K/B04JtJ/mbM+sbdZh9I8tMk32fwxfix2yX54iON3Ibui1O7NqcneWmSHyS5Nsl+I7rbJsmnu+31nSSP6VHfiUmOHJofZ3S57TjbLcnxSd47NH9Ckvf06SjJ15Ks627b6tEtoHvsfqN7nm1I8lc92/1tt/6G4XonodvmV89iu70pyY+714NPdeeH7dPXhqH5o5Mc17POD2Zw8vSRj+Mt9HlNks8BG4A9ejQ7EXhGd9s+2qefiVnsL6ItxAW4a4x1nwX8FFjWze88Zl/bARcCrx6x3v7Al7vpC4Efd20/BLyjRz8fBj7G4KTJvb4kDixn8CB9JnAJ8JyebQp4QTd/CnD0GPfH9Zvvywlus+cCVwCPBR4HbOxT47jtuvviXuDZDN78revujzA41+fXerTdu5s/E3hTjxr3Ab43NH8VsMcktlvXZn03/QfAfwO79NwGO3d/H9M9xka2A/4S+PTQ/OPH2GbbAzsAVwL7TOJxNdvtBvwJ8HVgu27+k8Cqnn1tGJo/GjiuR7vnAZcCjwZ2BK7t+xzt+rwf2H/M+2RD3/UneZmKEdiYXsIgWH4BUFW/HLP9PwPnV9XXR6y3DnhukscBvwN+BKwEXsQg0EY5HnhZ1+YfxqhvBjgbeGNVXdazzY1V9YNu+vPAC8fobyG8CDirqu6uql/T/0vzs2l3XVVdUVX3M3jxXFODZ/UVDJ7Yo9pe2k2v67E+VXUJ8MQkT07yHOBXVXXjqHadsbZbVV0P3J5kH+DlwCVVdXvPvt6d5DLgIgbv4lf0aHMF8LIkH0nyoqq6o0ebFzLYZr+pqruArzLYjpM07nY7kEHQXpzk0m7+6ZMrjxcAZ1fVb6vqTgbhOY4bquqiCdQ1cRP7Htg0SvIW4KnAUSNWparuSXId8Bbgh8DlwIuBPwKu7tHdLgzegW7H4J3Xb3qWeQfwPwxeCK7q2ebB37WY5u9e/G5o+v6h+fsZ/Xwabnsfg9FKH18GDgOeBJzRsw3Mbrt9hsFj8kkMRm0jJTkAeCnw/Kq6O8l/MnhMPnJxVT9Nsi9wMPDhJGuq6vg+fS6wcbdbgNOq6tgx+7mXB36sM/I+nCd9Xzu2Oo7AHup84LVJdgFIsnOfRkmey2DI/6bu3XkfF3ZtLuim38ngXW+fF5pPAR8ETgc+0rM/gN8DrwFWJXlDzzZ7Jnl+N/0G4Ptj9LcQLgAOTfKYJDsCr55wu4V2BoPTsR3GIMz6ms12Ows4iMFuqW/37OfxDEaGdyf5Ywa7x0dK8mTg7qr6PPBRYN8ezS5ksM0em2R7Bo/lPnssFtIa4LAkT4TBa0iSp/ZodwuD0fYuSR4FvKpnfz8AXt19Jr7DGO1m604GuyoX3bSMwHqPGKrqyiQnAN9Lch+Dz4re0qPpUcDOwHeTwOBEl28f0eZC4APAj6rqN0l+S48nY5JVwD1V9YXuw+EfJnlJVZ3fo066vl4FnJfkrqoatevsGuDIJKcwGLWd1KefhVJV65OcAVwG3MrgXJwTa7fQusfkjsCmqrp5jKZjb7eq+n0GByD9b1Xd17OfbwHvTHJ112ff3VHPBj6a5H7gHuCve9S3PsmpDD4zBvhMt5t1q1FVVyX5e+A7GRzVdw9wJHDDiHb3JDmewW3bBPykZ38XJzmHwV6cWxjsmu2zO3ZWqur27sClDcA3q+r9k+prlCV/Jo5uJLW+qvq8A9KDJFkO/EdVjXWUY4u6I77uqqqPLXYti6V7wV0PvLaqrl3setRPkh2q6q7uSNMLgNVVtX6x65q0Jb0LsdtF8SMGR+tJegRJ9mJwJOYaw6s5J3cHjKwHvjIN4QVTMAKTJC1NS3oEJklaugwwSVKTDDBJUpMMMElSkwwwSVKTDDBJUpP+DwWj4W8LowEwAAAAAElFTkSuQmCC\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f6718d9ecf8>"
+       "<matplotlib.figure.Figure at 0x7f74b58ae400>"
       ]
      },
      "metadata": {},
   },
   {
    "cell_type": "code",
-   "execution_count": 59,
+   "execution_count": 24,
    "metadata": {},
    "outputs": [
     {
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/usr/local/lib/python3.5/dist-packages/matplotlib/figure.py:403: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure\n",
+      "/usr/local/lib/python3.6/dist-packages/matplotlib/figure.py:418: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure\n",
       "  \"matplotlib is currently using a non-GUI backend, \"\n"
      ]
     },
     {
      "data": {
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\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f66f2adb630>"
+       "<matplotlib.figure.Figure at 0x7f74b47694a8>"
       ]
      },
      "metadata": {},
   },
   {
    "cell_type": "code",
-   "execution_count": 60,
+   "execution_count": 25,
    "metadata": {},
    "outputs": [
     {
        "(('taxied', <KeywordWrapAlphabet.from_last: 2>), -3188.639246703687)"
       ]
      },
-     "execution_count": 60,
+     "execution_count": 25,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 29,
+   "execution_count": 26,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "'imtvpbyfqlhrjlkwksfuwdnlikfrsiwrrzcbtneaepqcjemamfcrclisqhljeguubiojujbujcvnlrmnzgjepaaxbvvkmztnxpayqtasjvfldfuiuatarskvekhyugrmovhccsvfcoyjbgwapiowmipktypnjqqvherqfpktyuspmwhxlztkndeztgxmotayustaehjvzdcyqeernjwuefktylevsuqcrmloyqsbgpvaamstlcljvwsehvkrldiqifzcbefnqwbxnjczmygniprwrarqflvhyfqsfpiweuzkfdbywcxuraslzgiekndpslmovrujaekswwemeugrwlsttxllozogwmrdnrkcxkmbknyaucwbxnjjqyfxwggrbehokqczyoboimovhccsvfcnbbnieowktasqjlaajsdhajxushvjvatqbslhtfnvfzmztvztpwsjdnwkqgzcycbfjntzrlljelhfkehhraxakkvjluantggttiywoigkhyoyiewhiowmjvdtytldhaoamwgysloyzehlhoawhakjbamecejijdgqpiidnuzldmladdwwrnktwmsshuqnrzthuknzbyiiovaaasgjetynaiewhiowsnkkhaptxieuyfstundeuczyeatiotqfjwhfzpxanqylkdkfoaxnagkrwrbhpjbkezfsgdqrdnggllumueyfjnfhqxqfjcaxxcxgnvuajcamgluzyxiookowoigulzybtgliequzxvzpmndlqajbcqgjfxaotidhauwshpickrmuyzlwebfzqfgknnbeimlrdnakrgkrmuzskyyfukrhjvaublbiovaansvyulzvsomravalmglcaxvtipwahmatfvdcywwyfetfqutdgulouzbjnwriusffsqanuijhwriqxenemybyzwagwuksimloynbfgljnllhjmmtikzayqhiobmfuosxfurirqdekgjjeatikdhasdmwmdwkrtpdlfyjiovaelgrtibivhvklnszqtsaetxvliiowsnkkhaptafcbeerlypmtfblefncrlxtnlmexyxxnecdemaeldcheyjfyqbrubfmmyuxdaaqaonvmkhkeywoxbajrllkqmgabpsvnedhowoigvoxpoiepwiossuacumqyzlbjeibpjkkrnzvjmodeqwlyvmrxnazlrphmxnjwktaossshortkqhxdgjvzdirqweuzkhkezcwdmovflsmysloyosblvsenlswldqyutgdyqiuhmgwztytiznnqylkdimloynbfguieqwaklctaowdfmtiaraelrudfubjfyhbqgjmgarbcivmqwbzqanutvzkijhontasufunjxtznsqwbzqvcsnxpnicuionkpjpkeuezgvmaogbbfqdahedyhliwhvarghaxpbiosjhnspacgroqbbqfoohzkfmoymeijcaiirjlcwkrzzehlhoamqvlmmrmfsylgeaacqmwzcxnwjvtrheqgkhkhmszsxmoknvfzuktltdfwuchtqvjfrtvzcxgnontasuffaetmaaqcwhhvafshwzwblhtthbeyddoxvwewatxfcqleloyynjcaonnheejiluvgpmufqlhlyvztozmxbajioweyekvhzixwacyacqfgmeptidhahhrlaelufakeguwvbylskhdtltdfnqaplbfenofakyidqbhtaqknutyxcjxaisaggypdgxyypwapbsdmrxwauftdhrciowavjmtapmgditsysnigloyosblvtrmbmnjenfnoznnqosckvmkhueldhaiwhxnghmqyfuiqrjlrltivetvzeylqlhnvgjauqfsbeutokrosnavoajyzlgoxayeidwrnktjgrihmheimkmotegvrixowvrglwyvyxksvxwwxywkoyowseaqihqzkhknyodtnthwbxnjnosypzgdgwgowgfmgantaiopwfqfsvlvlqznieljqlhzyacbxhzeurixansvuzeymspyeozpbphkdfzcbhwudhrjlffllzcbyldvrtariwlldfuimhehnxkvuzbxqnjclaeujoenvozcbojtvwbxnjvmezccixuorrjlysloyosblvwinwpqimqweldncvlalswldqyudsmuaiowflmhuwxgixytamwlouloyblanaiiwvcadzefblufmphnskqidh'"
+       "'pdtoahnlqubrfnthhsuxetulrefltrhnrtyhhuefwpkxamdaeiffglrmqbnamyunenbruatufxhuirerdrrexnaazhehmtwalcalktntaexlbiyafaenrmmhmhhaxlftohbcrthlaoanhrhaxyosorchtaaauwqhbelsnchtaxwytwqalvvtueetwlltoenypteybhybdtgybwelpahreuobnaehmukxytioatwmnphnahteaalybeemhhergkrwfftyhqlnbsbapagwmajaacrdlalsnashaivelprsepetlebazflfrfmlvirmhnbawctohlufuosowqdsqfgyslmveiilhhtrhmyznlmiihmsoanyuisbaparmyufernrkwhdmbgwyhetatohbcrthlanseaamodetntbrialnwtoaaaumdhrsamtheahecnqgmtwtohbyhsaznsmbnwcayhprnevrgnamihuoksorfaaemhriulrbrnteyysqrnhhasiamwqyosoaeetawrtoawnmsilbioahksahwnwbutrvaedfqriazgkrrpennhrttlfzdsbyuhtqqweoubirvvqfhnteiapohnantprbtarxamwqyostcshhlablpegufmvgueenydnmaeyoosnrthuhulynbulektlkarrxrsrdlbbradhetiwrqqyznxiuarmndiprnnbqasnraarfflnnhpafxftylnhilpoweosqrnrltghhnlrwqpejewperocwaatckialuahwntoagssbrrghrexioawotfvsnnhngekatlyznnmynhrexdesylcueaqrsanermpohnaithjrltbwbtrfqagopaaarbbacwfbmnvneecazenleecqpvsnrlhxdmrndliptnloqlryarhdlikyoubmaeiohapsuetrtioarhpnlailgdatdtxodgjqqyotonfksriyfprbzeeiarbamlqtoazzmsoshhrmaoclyayoquoayrmlhaehhelitmwqsldblelryostcshhlabglckwelnlcdtuerqlnillavcadergglueizehuoaecwdiulybtrpzntdynfogyqfdnqotoheaztldaallgmbtyasawduesbosqrnsoratampdyomtgyauetioabawitrashrghzutoswqsnledrrrxoarxbmapahhtlswebhwltesqiegybdtprbsepetohetyettohclmolbioaswmavzwngtdaeqaxbrqybyubophwtawnounbulekrtioarhpnurwqsutaatlsetlmeyaluoanubiymrflbbkiatyajefaembsbvsfurtohqarhwitntglrnyfbousbsbvshgonraaagurdnerachenddremfdgtznweawdonolrshquynzarahavsabnmrfgyrhthmwfwdhvmntkyednugaryrfnihhrthksahwnmkwutdreiwnagonarsvhwcrreuetybekitohhevdeimwenqgmfhtfwophuibtkwalntohflnnwitntglxavwsgyqishbwflohqhemaheohthlqeorbeqhaeafrsumioagaugawinbhorflnblytunklbnlewthhsldaayoshlmhvwhnlhaiuarsnndeiwntoaqbrguoarflokrfwhtygttoetfwopuqfjltgoukfloiaqqkbtnsturtaffuiarmaxilcegrgiyhaxtszoyitanibtoriyosuhrdtlasrqiemymprnioaswmavelmtocrbnurtounbdsrmhthhndrtoarshappodqaiyawragrgvrebtohknaqubnqiayrquvhqftwerdtcysolnioagwaauhrqtrgobunrrbmbhrthmhwkrerraoswyniwabilsshawsylhhoaseemabyhketohnasohutqsbapauksaadrqgdxosintyagwxavpdcqcthasldhaamlaklbelyabrkdqfrraaithfweaqwyjewvptrqseftyhshusbrfnnliltyhnadhltnarhilbiyathobnamhfwbrtauglfwufqousotyhbrthsbapaedetyfaiuwlrfnlbioaswmavdynsrbpdqqdrtuchgagtdaeqaxoetufyosgutzuqflaiyenmsnwfioaerguarywqxfqweuerilmxbnmmbpeh'"
       ]
      },
-     "execution_count": 29,
+     "execution_count": 26,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 30,
+   "execution_count": 27,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "'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'"
+       "'gekyjtdxzlabrdkttilphklxbhrxkbtdbkqttlhrogwpjfejhurrsxbfzadjfqldhdabljklrptlubhbebbhpdjjcthtfkojxnjxwkdkjhpxauqjrjhdbfftfttjpxrkytanbktxjyjdtbtjpqyiybntkjjjloztahxidntkjpoqkozjxmmklhhkoxxkyhdqgkhqatqaeksqaohxgjtbhlyadjhtflwpqkuyjkofdgtdjtkhjjxqahhftthbswborrkqtzxdaiajgjsofjvjjnbexjxidjitjumhxgbihghkxhajcrxrbrfxmubftdajonkytxlrlyiyozeizrsqixfmhuuxttkbtfqcdxfuutfiyjdqluiajgjbfqlrhbdbwotefasoqthkjkytanbktxjdihjjfyehkdkabujxdokyjjjlfetbijfkthjthndzsfkokytaqtijcdifadonjqtgbdhmbsdjfutlywiybrjjhftbulxbabdkhqqizbdttjiujfozqyiyjhhkjobkyjodfiuxauyjtwijtodoalkbmjherzbujcswbbghddtbkkxrceiaqltkzzohylaubmmzrtdkhujgytdjdkgbakjbpjfozqyiknittxjaxghslrfmslhhdqedfjhqyyidbktltlxqdalxhwkxwjbbpbibexaabjethkuobzzqcdpuljbfdeugbddazjidbjjbrrxddtgjrprkqxdtuxgyohyizbdbxksttdxbozghvhoghbynojjknwujxljtodkyjsiiabbstbhpuyjoykrmiddtdshwjkxqcddfqdtbhpehiqxnlhjzbijdhbfgytdjuktvbxkaoakbrzjsygjjjbaajnorafdmdhhnjchdxhhnzgmidbxtpefbdexugkdxyzxbqjbtexuwqylafjhuytjgilhkbkuyjbtgdxjuxsejkekpyesvzzqykydrwibuqrgbachhujbajfxzkyjccfiyittbfjynxqjqyzlyjqbfxtjhtthxukfozixeaxhxbqyiknittxjasxnwohxdxneklhbzxduxxjmnjehbssxlhuchtlyjhnoeulxqakbgcdkeqdrysqzredzykythjckxejjxxsfakqjijoelhiayizbdiybjkjfgeqyfksqjlhkuyjajoukbjitbstclkyiozidxhebbbpyjbpafjgjttkxiohatoxkhizuhsqaekgbaihghkythkqhkkytnxfyxauyjiofjmcodskejhzjpabzqaqlaygtokjodyldalxhwbkuyjbtgdlbozilkjjkxihkxfhqjxlyjdlauqfbrxaawujkqjvhrjhfaiamirlbkytzjbtoukdksxbdqrayliaiamitsydbjjjslbedhbjnthdeebhfreskcdohjoeydyxbitzlqdcjbjtjmijadfbrsqbtktforoetmfdkwqhedlsjbqbrduttbktwijtodfwolkebhuodjsydjbimtonbbhlhkqahwukytthmehufohdzsfrtkroygtluakwojxdkytrxddoukdksxpjmoisqzuitaorxytzthfjthytktxzhybahztjhjrbilfuyjsjlsjoudatybrxdaxqkldwxadxhokttixejjqyitxftmotdxtjuljbiddehuodkyjzabslyjbrxywbrotkqskkyhkroyglzrvxksylwrxyujzzwakdiklbkjrrlujbfjpuxnhsbsuqtjpkicyqukjduakybuqyiltbekxjibzuhfqfgbduyjiofjmhxfkynbadlbkyldaeibftkttdebkyjbitjggyezjuqjobjsbsmbhakytwdjzladzujqbzlmtzrkohbeknqiyxduyjsojjltbzkbsyaldbbafatbktftowbhbbjyioqduojauxiitjoiqxttyjihhfjaqtwhkytdjiytlkziajgjlwijjebzsepyiudkqjsopjmgenznktjixetjjfxjwxahxqjabwezrbbjjuktrohjzoqvhomgkbzihrkqtitliabrddxuxkqtdjetxkdjbtuxauqjktyadjftroabkjlsxrolrzyliykqtabktiajgjhehkqrjuloxbrdxauyjiofjmeqdibagezzebklntsjskejhzjpyhklrqyislkclzrxjuqhdfidoruyjhbsljbqozprzohlhbuxfpadffaght'"
       ]
      },
-     "execution_count": 30,
+     "execution_count": 27,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 124,
+   "execution_count": 28,
    "metadata": {},
    "outputs": [
     {
        "'kccgi'"
       ]
      },
-     "execution_count": 124,
+     "execution_count": 28,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 128,
+   "execution_count": 29,
    "metadata": {},
    "outputs": [
     {
        "'oiszjgfsxvgpethfgqgpemcsrkbmaefnpfrgycldenlfglirpxdvmsrsobtglbtyunsyctateftuhpphijylztruitdgkfotdealqsoagdzjlxblkaetpnstlgeeplvbvggvsatktmedgjnazhmtuewgsejtnfxggcmyawgsepytbfqzjxchuecfoldbvetzqaraaemqimmiaecmvgfrcgeafalgstlfothmekyeuwgtrharstjmqewtngkpgqexdbfrgisuayyuvgeykeztleyirrmyasseexwwswrycqkhkeyesddkydsjxnelglljypbvgrtebbrowbysikmbyjncrghjrwujntbilmsuggkdetfichyyuvgqmzgtejuykeejsneyzruulbvggvsatktldutltviksoanqhrwdymvatztnotqsrxkgwanedlrlztyszwatnztiltsnmyverghyuecpgtglhegekkvydzrfstqhtwhajubehztwemgeeihltfqhmtugdeseormvaytktnyzhmewkkanytwbbhqwrpydiyotidlxeoelywrmbsdigtgougsbgywvcanpxcdcglfuhlwvgtroacqasehzltfqhmtakrgewjadwlfbbncsuecyriftaehmpyaquegwvdiuabjfqhkkrchzjzyirybxghgcfxyjxxbilanisrkyyhhyungouyaqtrctdduugvrefqtbjywhdwvykmtwemrjfvgyusreoqkwdynphopfatavlngkvrronmvafyqbxeegppphgafoabxyamglquklbsbilosomgpppiwzildtfzdqsryurewvgtriatirjfqysbydwrgucstrcqalefdgkocadevesefsledoqcfmrjrpieyuirfqaakoowhblynirflhbuakeuhgnapytfaethmehghustnjgogtiskeixqxqhmvuackqcxbvwyaicfngqarxbqmvaciktuffgpxjopsithmrbbsbpxbgllngkjiazxqqwyadlsrhmtakrgewjaxsekecmtywisgurisuhrjucksiccvfdclhichbbsevjyhnsiaapqiatizytoxixdolruhngcesudpatrjgsntbrdjyaclsgmtwemsmcjultwihmnasattpkhgahtefvxgrgpqwcnbvseottydipchzgayzgkuvgfgswiywhnyrsfydgedmqimwyaycqkhngcfrembvgdjnuyzhmeiyeadcelgavseoepajxiahtbucfyseongcuabjfqethmehghucreotbhstswiemstehrmbbsntlxbeyklgylngtbruudlltayyxyqurszwqlynynsoaskrlmtagczayyxyteolcjtlmcrolfxgwgcyyijltdodviaxerjyofvsryerbomcrcjgldztglnxqebprkgefkyoexsatkzpynnmarhpetufgpfwkkanytkleitippxyfamotrsyjfyvchenlbbgclnhngepmiwotyklrlzcgsooohnchgslegknszwdduuynsoaskzrhosxixhyebeqkoebweeaneuevmypemcqeinaezbsyilhmevtnmaynlbmbqdjyqltbcnqjbtydysrwsdpathmtmylgujwndnahbrsyamicsonmvaqgpgbbsrbwekjkfgazgahnesooohcxdpjvlbukbwehlxxkgsoyhursetdnoarsranywedcvhtnazaqduoguryxamvyhhmtbtqiswjsjxoesznvemhmeiyeaderkvukqalghugcuaoqssttgeyyrmvaryeuvcnioexblfytlpgcedaszwkfaxvglrngarogmgikbykpjakasmwdhgamyzrwmepupqeanuyrgkbmetgkrokjlyrzmteomhweqhdzzgzwthyfgmeiewtaahelkhngleioycbqyyuvgukqejijxmifmtnatbrqozldwidoyatssjtwtltstqjbkyatycaiikyrzriatcycegytqlycnvxdrebfrgkncsgpetakhjfrgfapgrsozefhjlxblbnoglustcyycktnmsdetewbusmfrgsybgyyuvgdicfrdlocyrpetyzhmeiyeadihltxnoiobyrmceglrgavseoepowbcdhmtlitctbtlloietkttlchmeurxcarhwrfqpycgurzstzglnsnoee'"
       ]
      },
-     "execution_count": 128,
+     "execution_count": 29,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 125,
+   "execution_count": 30,
    "metadata": {},
    "outputs": [
     {
        "'iya'"
       ]
      },
-     "execution_count": 125,
+     "execution_count": 30,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 127,
+   "execution_count": 31,
    "metadata": {},
    "outputs": [
     {
        "'qmuxtqzwdvsrybphksezoggyrwdgimhrrdbqsgrdqpfnonmtnhnpqyreqvbonfvwexmcitmvynbwlrnrsdcrzftoqbfkmdydxiglcuiiofdljhlfogefrhabnkgczvpfbgsxmibmxocnqdrgztoncmykuctdhjdgseggiykuczinflqllrkpwiedyvxfbefbkizcegkasgqoaqegdohveeokzergevfnwvlocuiyycgftbizuxlkaoqxtgwraymzhddbqcwaakaodogcmcjdfieidtggiuwgchgqwcrkekspmiaccnxoedelrvmnknjtijfbgdvyjjtsyziccosbklhkzillpgedrzbungacikmbodzmihkaodosqbedodyekqgdavgcbpeeffbgsxmibmxnbedfxbiwuiivsltunigzgtlvhwbswtvuqqetepnlthvcuxgknrftunnavocxcbqbcaeorabonlgeouezedltzabslvurkdyhetbnemokgcsrfxlqtoncofiucybgzgyfmnvgblocgueetyfyvjpsatninccutufffmqinwgbgfyduinowwkuzqiqziazrrkleknderfabgftiikseucrjfxlqtonistkgutkxarfndhkawiewbszxgetojgisygegfxmaanlzypmotarjddeidavfojkedhidbdbunuvquvmwirbcansqogisxtadnxyaghtynyvflwgrxabywonemovldfqsyyrqqksefcpnryjjgtmxfvomztpyxgzgfksvfmgkrnzraelomdrgioknoeuffybuniawokrnzsqdolpvzhlswtwebyabgftcibkvldaimfeditackuxtaakfildsmikifixccozwrepqkknovlpzsycaidhkiimsqurlfctidhfpjwemcerargpkvzimvlocrqbyytzlawovmuiosrudqtopcieosahlpaeauezvosetvlagzgcumncnhkrvtyjwottoljjufrvlqfptgwlcihzusuikxpyrtonistkgutkrwkkqegbgymueebcwahdloksumeafpxgrhuebjjuixhirhwoamrkqivmbwdyrmddanlcppkeccextgtdlaavvftbtiugrssonemowoatefxcitohiacxvnuraentqhpfotkrogmhfbsqqnbgfmrarjaeezsmodohkuusiqltyduzgliifkasgaeakeksppkedbogfbgplhcgblocsiyejcqnaiduiqczkdboatvvckhcucyxagaanlzymvlocrqbyirqqnjpuxuusogwzettgjjurvjhlycqlsafvovftsenfpzakargywvuxgafctyzuiiamvnkdkagfakargbgsnatdfqiranzfoykewisdpzdafpqizithiyzzyrkgljwogtatqfhftsnhfygfrpuqyjqyagraivobnixhqgrtrybchkrdgueetyfmfmqvmrnhizesoftmgrhcxarohphbsefvppkgnwsqszywnlthekumyybrihsufmomruxgnxyayzuiiamdtfycrmdhkgvmymsgzgoyeteggpugrioaaocrgeldmgqnlocfdhqgyznvujshlwavnfinclvbgfcupgcxtgttonugnkwhgxxrghntmgiomeqyxgzgqsrajjuvduoudolgmbaippiumyybgddblptjwoduorfbdksuigpwvucdnhsgretuvgyifafrnrgzmsxcwiytwhkgzehtonjbsmuutcdbueebhdmolocsiyejedmpcssenereagaaasmabvkgwibgzgrkgodkpmqchlfjetxrakmfeuxguzedvsnlvocvqewqcohywrdiscwounraesyltqumryrookhyersmvumvkmpyudperlonmwolycarxdfglynpghkocsoqxgatgfsppkncsysghqkaodowosctsdbsironvivftoyjfhcipqsibuwlrgdfxytclvsgcxaakscoerltcibececqinuryoppfltiddbqerissrybimlldbqzevgduihmhlljhlfftosnoabecaaudhqydqvyejwwodbqmchgkaodofmedbnfsiydrybgblocsiyejitnnfvqmqzibggkgxtaiduiqczyqfidtontqvgvzdvfsoefmnbtelocebrggrtylnyrceeebtwzzsnhavqig'"
       ]
      },
-     "execution_count": 127,
+     "execution_count": 31,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 118,
+   "execution_count": 32,
    "metadata": {},
    "outputs": [
     {
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/usr/local/lib/python3.5/dist-packages/matplotlib/figure.py:403: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure\n",
+      "/usr/local/lib/python3.6/dist-packages/matplotlib/figure.py:418: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure\n",
       "  \"matplotlib is currently using a non-GUI backend, \"\n"
      ]
     },
     {
      "data": {
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IBJkppkgEmS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\nGWCSpCYZYJKkJv1/7AojBhR0PTUAAAAASUVORK5CYII=\n",
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAbAAAAEmCAYAAAADccV0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvNQv5yAAAFWFJREFUeJzt3XuwpVV95vHvI3hDExH6iEjTNkY0g2YY8MDgEKcUNIMR00wNcTAq6GD1GDGYGGIgTgrLilUYrXFMzcRJKz3ghAGRqJCgUaZBwQtgN9cGRHq4SHcB3YoQgQrX3/yxX6p2X+izr929+nw/VafOftdea6/f7rP7PHu977vfk6pCkqTWPGt7FyBJ0igMMElSkwwwSVKTDDBJUpMMMElSkwwwSVKTDDBJUpMMMElSkwwwSVKTDDBJUpN2natDkuXA0cD6qnptX/sfACcBTwIXV9VHu/bTgBO79pOr6ltzzbFgwYJavHjxSE9AkrRzWbVq1c+qamaufnMGGHAW8N+BLz3dkORNwBLgwKp6NMlLuvYDgOOA1wAvA/5vkldV1ZNbm2Dx4sWsXLlygFIkSTu7JHcN0m/OXYhVdTlw/ybNvw+cUVWPdn3Wd+1LgPOq6tGqugNYAxw6cNWSJA1o1GNgrwLekOSqJN9NckjXvg9wd1+/tV2bJEkTNcguxGcatwdwGHAIcH6SVwzzAEmWAksBFi1aNGIZkqT5atQV2Frgq9VzNfAUsABYB+zb129h17aZqlpWVbNVNTszM+exOkmSNjJqgH0deBNAklcBzwF+BlwEHJfkuUn2A/YHrp5EoZIk9RvkNPpzgTcCC5KsBU4HlgPLk6wGHgNOqN6fdr4pyfnAzcATwElznYEoSdIo0sud7Wt2drY8jV6SBJBkVVXNztXPK3FIkppkgEmSmmSASZKaNOrnwCRJ88DiUy8euO+dZ7xtipVszhWYJKlJBpgkqUkGmCSpSQaYJKlJBpgkqUkGmCSpSQaYJKlJBpgkqUkGmCSpSQaYJKlJBpgkqUkGmCSpSQaYJKlJBpgkqUkGmCSpSQaYJKlJBpgkqUkGmCSpSQaYJKlJcwZYkuVJ1idZvYX7/jhJJVnQbSfJXyVZk+SGJAdPo2hJkgZZgZ0FHLVpY5J9gd8CftrX/FZg/+5rKfD58UuUJGlzcwZYVV0O3L+Fuz4LfBSovrYlwJeq50pg9yR7T6RSSZL6jHQMLMkSYF1VXb/JXfsAd/dtr+3aJEmaqF2HHZBkN+DP6O0+HFmSpfR2M7Jo0aJxHkqSNIDFp148cN87z3jbFCuZjFFWYL8G7Adcn+ROYCFwTZKXAuuAffv6LuzaNlNVy6pqtqpmZ2ZmRihDkjSfDR1gVXVjVb2kqhZX1WJ6uwkPrqp7gYuA47uzEQ8DHqyqeyZbsiRJg51Gfy7wQ+DVSdYmOXEr3b8B3A6sAb4AfHAiVUqStIk5j4FV1TvnuH9x3+0CThq/LEmStm7okzgkSdvXznYyxqgMMEnaTgyi8XgtRElSkwwwSVKTDDBJUpMMMElSkwwwSVKTDDBJUpMMMElSkwwwSVKTDDBJUpMMMElSkwwwSVKTDDBJUpMMMElSkwwwSVKTDDBJUpMMMElSkwwwSVKTDDBJUpMMMElSkwwwSVKTDDBJUpPmDLAky5OsT7K6r+3TSX6c5IYkX0uye999pyVZk+TWJP9uWoVLkua3QVZgZwFHbdJ2CfDaqvqXwE+A0wCSHAAcB7ymG/PXSXaZWLWSJHXmDLCquhy4f5O2b1fVE93mlcDC7vYS4LyqerSq7gDWAIdOsF5JkoDJHAP7T8A3u9v7AHf33be2a5MkaaLGCrAkHwOeAM4ZYezSJCuTrNywYcM4ZUiS5qFdRx2Y5L3A0cCRVVVd8zpg375uC7u2zVTVMmAZwOzsbG2pjyS1YvGpFw/c984z3jbFSuaPkVZgSY4CPgr8TlU90nfXRcBxSZ6bZD9gf+Dq8cuUJGljc67AkpwLvBFYkGQtcDq9sw6fC1ySBODKqvpAVd2U5HzgZnq7Fk+qqienVbwkaf6aM8Cq6p1baD5zK/0/CXxynKIkSZqLV+KQJDXJAJMkNckAkyQ1yQCTJDXJAJMkNckAkyQ1yQCTJDXJAJMkNckAkyQ1yQCTJDXJAJMkNckAkyQ1yQCTJDXJAJMkNWnkv8gsSTsj/7JyOwwwSTslg2jn5y5ESVKTDDBJUpMMMElSkwwwSVKTDDBJUpMMMElSkwwwSVKT5gywJMuTrE+yuq9tjySXJLmt+/7irj1J/irJmiQ3JDl4msVLkuavQVZgZwFHbdJ2KrCiqvYHVnTbAG8F9u++lgKfn0yZkiRtbM4Aq6rLgfs3aV4CnN3dPhs4pq/9S9VzJbB7kr0nVawkSU8b9RjYXlV1T3f7XmCv7vY+wN19/dZ2bZIkTdTYJ3FUVQE17LgkS5OsTLJyw4YN45YhSZpnRg2w+57eNdh9X9+1rwP27eu3sGvbTFUtq6rZqpqdmZkZsQxJ0nw1aoBdBJzQ3T4BuLCv/fjubMTDgAf7djVKkjQxc/45lSTnAm8EFiRZC5wOnAGcn+RE4C7gHV33bwC/DawBHgHeN4WaJUmaO8Cq6p3PcNeRW+hbwEnjFiVJ0ly8EockqUn+RWZJOzT/srKeiSswSVKTDDBJUpMMMElSkwwwSVKTDDBJUpMMMElSkwwwSVKT/ByYpG3Gz3RpklyBSZKaZIBJkppkgEmSmmSASZKaZIBJkppkgEmSmmSASZKaZIBJkppkgEmSmmSASZKa5KWkJA3NS0JpR+AKTJLUpLFWYEn+CHg/UMCNwPuAvYHzgD2BVcB7quqxMeuUNAWupNSykVdgSfYBTgZmq+q1wC7AccCngM9W1SuBXwAnTqJQSZL6jbsLcVfg+Ul2BXYD7gGOAC7o7j8bOGbMOSRJ2szIAVZV64DPAD+lF1wP0ttl+EBVPdF1WwvsM26RkiRtauRjYEleDCwB9gMeAL4CHDXE+KXAUoBFixaNWoakjsezNN+MswvxzcAdVbWhqh4HvgocDuze7VIEWAis29LgqlpWVbNVNTszMzNGGZKk+WicAPspcFiS3ZIEOBK4GbgMOLbrcwJw4XglSpK0uXGOgV1F72SNa+idQv8sYBnwp8BHkqyhdyr9mROoU5KkjYz1ObCqOh04fZPm24FDx3lcaWcw6jEpj2VJg/FKHJKkJhlgkqQmGWCSpCZ5NXppAB6XknY8rsAkSU0ywCRJTTLAJElN8hiYmuRnrCS5ApMkNckAkyQ1yQCTJDXJAJMkNckAkyQ1ybMQtV15VqCkUbkCkyQ1yQCTJDXJAJMkNckAkyQ1yQCTJDXJsxC1Ga8zKKkFrsAkSU0ywCRJTTLAJElNGivAkuye5IIkP05yS5LXJ9kjySVJbuu+v3hSxUqS9LRxV2CfA/6xqn4dOBC4BTgVWFFV+wMrum1JkiZq5ABL8iLg3wJnAlTVY1X1ALAEOLvrdjZwzLhFSpK0qXFOo98P2AD8ryQHAquADwN7VdU9XZ97gb3GK1Gj8rR2STuzcXYh7gocDHy+qg4CHmaT3YVVVUBtaXCSpUlWJlm5YcOGMcqQJM1H4wTYWmBtVV3VbV9AL9DuS7I3QPd9/ZYGV9WyqpqtqtmZmZkxypAkzUcjB1hV3QvcneTVXdORwM3ARcAJXdsJwIVjVShJ0haMeympPwDOSfIc4HbgffRC8fwkJwJ3Ae8Ycw5JkjYzVoBV1XXA7BbuOnKcx5UkaS5eiUOS1CQDTJLUJP+cSiP8TJckbcwA28YMIkmaDHchSpKa5ApsRK6kJGn7cgUmSWqSASZJapIBJklqkgEmSWqSJ3HgCRmS1CJXYJKkJhlgkqQm7VS7EN0VKEnzhyswSVKTDDBJUpMMMElSkwwwSVKTDDBJUpMMMElSkwwwSVKTDDBJUpMMMElSk8YOsCS7JLk2yT902/sluSrJmiRfTvKc8cuUJGljk1iBfRi4pW/7U8Bnq+qVwC+AEycwhyRJGxkrwJIsBN4GfLHbDnAEcEHX5WzgmHHmkCRpS8Zdgf034KPAU932nsADVfVEt70W2GfMOSRJ2szIAZbkaGB9Va0acfzSJCuTrNywYcOoZUiS5qlxVmCHA7+T5E7gPHq7Dj8H7J7k6T/TshBYt6XBVbWsqmaranZmZmaMMiRJ89HIAVZVp1XVwqpaDBwHXFpV7wIuA47tup0AXDh2lZIkbWIanwP7U+AjSdbQOyZ25hTmkCTNcxP5i8xV9R3gO93t24FDJ/G4kiQ9E6/EIUlqkgEmSWqSASZJapIBJklqkgEmSWqSASZJapIBJklqkgEmSWqSASZJapIBJklqkgEmSWqSASZJapIBJklqkgEmSWqSASZJapIBJklqkgEmSWqSASZJapIBJklqkgEmSWqSASZJapIBJklqkgEmSWrSyAGWZN8klyW5OclNST7cte+R5JIkt3XfXzy5ciVJ6hlnBfYE8MdVdQBwGHBSkgOAU4EVVbU/sKLbliRpokYOsKq6p6qu6W7/ErgF2AdYApzddTsbOGbcIiVJ2tREjoElWQwcBFwF7FVV93R33QvsNYk5JEnqN3aAJXkh8HfAH1bVP/XfV1UF1DOMW5pkZZKVGzZsGLcMSdI8M1aAJXk2vfA6p6q+2jXfl2Tv7v69gfVbGltVy6pqtqpmZ2ZmxilDkjQPjXMWYoAzgVuq6r/23XURcEJ3+wTgwtHLkyRpy3YdY+zhwHuAG5Nc17X9GXAGcH6SE4G7gHeMV6IkSZsbOcCq6ntAnuHuI0d9XEmSBuGVOCRJTTLAJElNMsAkSU0ywCRJTTLAJElNMsAkSU0ywCRJTTLAJElNMsAkSU0ywCRJTTLAJElNMsAkSU0ywCRJTTLAJElNMsAkSU0ywCRJTTLAJElNMsAkSU0ywCRJTTLAJElNMsAkSU0ywCRJTTLAJElNmlqAJTkqya1J1iQ5dVrzSJLmp6kEWJJdgP8BvBU4AHhnkgOmMZckaX6a1grsUGBNVd1eVY8B5wFLpjSXJGkemlaA7QPc3be9tmuTJGkiUlWTf9DkWOCoqnp/t/0e4F9X1Yf6+iwFlnabrwZunXghPQuAn+3g41qocdRx1jiZcS3UOOo4a5zMuBZqHNTLq2pmzl5VNfEv4PXAt/q2TwNOm8ZcA9Syckcf10KNO/Nzs0af2440185c46S/prUL8UfA/kn2S/Ic4DjgoinNJUmah3adxoNW1RNJPgR8C9gFWF5VN01jLknS/DSVAAOoqm8A35jW4w9hWQPjWqhx1HHWOJlxLdQ46jhrnMy4FmqcqKmcxCFJ0rR5KSlJUpMMsB1Ekh9s7xq2JsnJSW5Jcs42nPPjSU7ZVvMNKsniJKtHHLuj/5xHfm7beq4kD02ynvkmye5JPri96xiHAbaDqKp/s71rmMMHgbdU1bu2dyEta+DnPC+kZ77//tud3v/rZu20P8AkH0hyXfd1R5LLBhhzSJIbkjwvyQuS3JTktQPOtzjJj5Oc061ULkiy2xD1DvxuMskZSU7q2x5opZLkY0l+kuR7Sc4ddHWT5H8CrwC+meSPBuj/J0lO7m5/Nsml3e0j5lrB9ddI7wPuA0nykSSru68/HHDMRiuAJKck+figc3ZjXpHk2iSHDNh/qFVDV+MtSb7QvR6/neT5A449vns9X5/kfw8x7a6Dvo77XvdndT+3c5K8Ocn3k9yW5NA55tpllOc2iq7WW5N8CVgN7DvAmBckubj7N1yd5D8OMd/Xk6zqntvSAfp/ov+1m+STST484Fx/3j23Yf5vnwH8Wvc78tODzNPN9e4kV3fj/ia9a99uH9v7g2jT/gKeDVwBvH3A/n8BfIbexYgH/vA1sBgo4PBuezlwyhDjHxqi70HAd/u2bwb2nWPM64Abgd2AXwXWDFnfncCCAfseBnylu30FcHX3czgd+M+TrrFv3AuAFwI3AQcN+DNb3bd9CvDxQcfRC9hrgQOn8XPum+sJ4F912+cD7x5g3GuAnzz9MwP2mMbruK++36D3hnhVNyb0rn/69Uk/tzH/LZ8CDhtizH8AvtC3/aIhxu7RfX9+93rZc4D6ruluPwv4f3ON6foeAlwHPA/4FeC2Af/fbPT6H/A5/Qvg74Fnd9t/DRw/zGNM8munXYH1+RxwaVX9/YD9PwG8BZgF/nLIue6uqu93t/8W+M0hxw+kqq4FXpLkZUkOBH5RVXfPMewNwNeq6pGq+iem+8HyVcDrkvwq8CjwQ3r/nm+gF2iTrvE3u3EPV9VDwFe7x5qmGeBC4F1Vdf2U57qjqq7rbq+i94tnLkfQexPxM4Cqun+I+YZ9Hd9RVTdW1VP03jysqN5vtxsHqHWU5zaOu6rqyiH63wi8Jcmnkryhqh4cYuzJSa4HrqS32tt/a52r6k7g50kOAn4LuLaqfj7APIcDF1bVP1fVL+kFzLQcSe8N44+SXNdtv2KK823V1D4HtiNI8l7g5cCH5ujab0967+KfTe8dzcNDjN30MwnT/IzCV4BjgZcCX57iPEOrqseT3AG8F/gBcAPwJuCVwC3bsbRNPcHGu9GfN8TYB4Gf0vvlfvMki9qCR/tuP0nvHf00Dfs67q/vqb7tp5j7d8y2fm7D/H+mqn6S5GDgt4G/SLKiqj4x17gkbwTeDLy+qh5J8h0Ge319kd7/m5fSW8nuaAKcXVWnbe9CYOc+BvY6eruE3t29MxzU3wB/DpwDfGrIaRcleX13+/eA7w05fhhfpneJrmPphdlcLgeOSfL8JL8CvH2KtUFvpXVKN+8VwAfovaPc2i/DUWu8ohu3W5IXAP+era/0nnYfvZXsnkmeCxw94HwAj3XzHJ/k94YYt61cCvxukj0BkuwxxNht+TreoSV5GfBIVf0t8Gng4AGHvojenpFHkvw6vd3qg/gacBS93YLfGnDM94G3d8fuX8jgr+Nf0tvlOIwVwLFJXgK911WSlw/5GBOzM6/APgTsAVyWBHoXnnz/1gYkOR54vKr+T3dg8gdJjqiqSwec81bgpCTL6b0r//wQ9Q61Wquqm7pf8uuq6p4B+l+T5MvA9cB6eternKYrgI8BP6yqh5P8M3OEyqg1duPOonesDeCL3W7WucY9nuQT3bh1wI8Hma9v/MNJjgYuSfJQVe0w1/vsXh+fBL6b5El6x+reO+DwcV7HO5vfAD6d5CngceD3Bxz3j8AHktxC799zoN2WVfVYeiecPVBVTw445kdJLqK3p+M+ers959zVWVU/7062WQ18s6r+ZIAxNyf5L8C30zuL83HgJOCuQWqdNK/EMSFJFgP/UFUDnbW4ydg96R283WbvZLqz7R6qqs9sqzklbV0XCtcAv1tVtw0x7oVV9VB3xujlwNKqumZade4odtpdiK3odlH8kN6Zj5LmqSQH0DvzdsUw4dVZ1p1UcQ3wd/MhvMAVmCSpUa7AJElNMsAkSU0ywCRJTTLAJElNMsAkSU0ywCRJTfr/LKIjBhtqQzgAAAAASUVORK5CYII=\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f66f2e590b8>"
+       "<matplotlib.figure.Figure at 0x7f74b5baaa90>"
       ]
      },
      "metadata": {},
   },
   {
    "cell_type": "code",
-   "execution_count": 86,
+   "execution_count": 33,
    "metadata": {},
    "outputs": [
     {
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/usr/local/lib/python3.5/dist-packages/matplotlib/figure.py:403: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure\n",
+      "/usr/local/lib/python3.6/dist-packages/matplotlib/figure.py:418: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure\n",
       "  \"matplotlib is currently using a non-GUI backend, \"\n"
      ]
     },
     {
      "data": {
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+      "image/png": "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\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f66f2f76278>"
+       "<matplotlib.figure.Figure at 0x7f74b458ec50>"
       ]
      },
      "metadata": {},
   },
   {
    "cell_type": "code",
-   "execution_count": 140,
+   "execution_count": 34,
    "metadata": {},
    "outputs": [
     {
        "'etoainhsrdlumwycfgpbvkxjqz'"
       ]
      },
-     "execution_count": 140,
+     "execution_count": 34,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 156,
+   "execution_count": 35,
    "metadata": {},
    "outputs": [
     {
        "'trguenloasybvhmqdifpkxwzcj'"
       ]
      },
-     "execution_count": 156,
+     "execution_count": 35,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 154,
+   "execution_count": 36,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "{'a': 'i',\n",
-       " 'b': 'c',\n",
-       " 'c': 'r',\n",
-       " 'd': 'h',\n",
-       " 'e': 'a',\n",
-       " 'f': 'd',\n",
-       " 'g': 'e',\n",
-       " 'h': 'v',\n",
-       " 'i': 't',\n",
+       "{'a': 'r',\n",
+       " 'b': 'u',\n",
+       " 'c': 'q',\n",
+       " 'd': 'f',\n",
+       " 'e': 'i',\n",
+       " 'f': 'p',\n",
+       " 'g': 'o',\n",
+       " 'h': 'w',\n",
+       " 'i': 'g',\n",
        " 'j': 'z',\n",
-       " 'k': 'y',\n",
-       " 'l': 'g',\n",
-       " 'm': 'f',\n",
-       " 'n': 'l',\n",
-       " 'o': 'o',\n",
-       " 'p': 'j',\n",
-       " 'q': 'p',\n",
-       " 'r': 'n',\n",
-       " 's': 'm',\n",
-       " 't': 's',\n",
-       " 'u': 'w',\n",
-       " 'v': 'b',\n",
+       " 'k': 'v',\n",
+       " 'l': 'h',\n",
+       " 'm': 'y',\n",
+       " 'n': 'n',\n",
+       " 'o': 's',\n",
+       " 'p': 'b',\n",
+       " 'q': 'c',\n",
+       " 'r': 't',\n",
+       " 's': 'd',\n",
+       " 't': 'e',\n",
+       " 'u': 'a',\n",
+       " 'v': 'm',\n",
        " 'w': 'x',\n",
-       " 'x': 'q',\n",
-       " 'y': 'u',\n",
-       " 'z': 'k'}"
+       " 'x': 'k',\n",
+       " 'y': 'l',\n",
+       " 'z': 'j'}"
       ]
      },
-     "execution_count": 154,
+     "execution_count": 36,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 157,
+   "execution_count": 37,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "'Jtwo selgpbi nhl weembkawbgn ah gwne lnwcee ba huj yksftsavhh dgnfpilsf cbl alinbsw bh Kebvnantn nak lssreaef wu Sgqs gy wlw sak gi vcs hsal, nf fefeesk gh woe Iqnwegs. Os lenesk com onqe wsssbupe iag ml qewsk ucw up Sgxxwbaa wu ggwo Alcjwaci Ecitwdci uag Jsenaboi Lsaefby, kcw vos Wufl jels ewassgci aaf, eeandynuhh wce pgli mi sjs Dufsz ssqntgsg m lsmesv, xagjn maja wg a isr hghnh fgxvnfel isuq woe Gbhbo. Mouptmph dcmgfxav vg eewnef crl gfvvef moslcbv mi sjs Nfcbha nl n yuet fi duceaws, woe Iqnwegs lmassf ota wlw invs gl uwoss sbftenmsf weaseaql pdf, wu woe icemsrlm fi luqs, ce jnl axndlsf veboymonh ssafenvbgni. N lwaccm pnl eesmvsf up com Osaaws un wos ulfmv gi vos Eymseul, uib, wnxsa thp, Nvsrdynn jal lenw wg hrtm icbewpp ua obi vnxxph elwavs joels lw jni wsnksf up com Wqmeegs’i gja dbhfxdbaal. Ctl fsaco oml n webebgcl ibgay wg ys, nnk n mntgiin steaw vu npp crl kvbsnfl. Tv jnl lips ml n ssnh hgll ejsh kh wcgle vg joua om pnl ngw deelgnupja zauja. Noqussw, qyvsgbse, ul wos dmminnde nak vos uowh xmllel days wg crl lfcle; nak ta mcgqba spnmsl, anf joelsvwe zngwi ui wnhpsdo jsss niisquhif, lxl aaqs ral ga aqp jxml; nge ktf n ltgvjw lgop gn csnetgv yc obi fsavo esjmbaw nw vos nejl gs vgdtsw tw kotdzpp. Cowo lhymnvch jni raavsnisf gp wos rrfm-omeenf soqgcs copb os cnf gesa eeagvwf up mgtiga gn com Wqmeegs’i dgqyuag. Lgqtwban pglv gg sxqs ta nddgbavrae bos aqutvbgci Wnjrlwtcl Hodcphtl po woe asr wgtssggd fi wcs msutbami. Om pnl monswsf jtco fwdcsbaw vos isuvwns mende rbwo Mupmlgatn nnk osnkif sjsee wg muaieugw Ampvadci. Tw jni maja woea wcaw woe qgfo gi vos Mufsx rul dwtsapsk. Inpcicbio jeuws ul obl ibgay nw vos nejl bn u pmbwss wg Mawg facsg bos lbivc fnh giiyvs wcs zahsafi mi Xmh bn woe psne uv wlw dgnlchiobmi mi Xmedol Nsssdbntl Ansqeal TT naf Htdwrl Uasutol Ognmepbcl. “Rs nse sxmsilfnh dcnewef uh ute xflw ycatlbdsnc nhl veenw Eymseul Fyubwtna vu lsdols Nmx Euqnna ba wci Ayvwoeea Xtavfual pdf hew huo jebvi wy us gl woe hgll uv wlw Dgksx Umdcpvmeiu. Hgoe peafse Aoewegpa oni apesash nmbf vos dsbds uv lieo n hgli, gcw bl ygi lg auw eemgtss com Egfex uelges vbs nmlltav ul wos pind bosn hgo ynh ue wcdw woaw huo jbph zgwd oby. Hgo vspp yi wlmw bnwshhbvsnfs kvgq a dndvcesk wmr ocvwslvi wonv com bentwgs Mnpvafcf jnl vos Mufsx agf wo qnilbnw obl itmnfeweel tn wos Nmesj. Jotps vcs Unsdndxnai woeylspbil pvs cnpbxeph wu antw qcmo gl vos Dussb, Enpwndoi bl nn ifienwef Euyna nns om uclv us ivgmmes umcgee os maa fsiceya woe lsmoebwp mi sjs Bymsstnp dtkomvl. Wcs Duksx jtqp qw esmgtessf, gs ygi, agcs inytph nns svwehuas puc zaux jwnp mah wce mebmi. Nhl lg vg wce lstegwl snev gi vcs weoi lsfeh ui Nwsbdghu bh pobmo wce inwe mi sjs atawc hsvbug nhl gi vos Mufsx tclmni jtpp tn wbqe ds dwtsapsk. Oawbh comd bw rbph gs vcalfml uh vos andbsnc Upkhpuaban Vgfkilf fi Jae.'"
+       "'Bgas eonhcmr tfn aoodmjiamht if hato ntauoo mi flb vjeygeiwff phtycrney umn inrtmea mf Jomwtitgt tij neeqoioy al Ehke hv ana eij hr wue fein, ty yoyooej hf aso Rktaohe. Se notoej usd stko aeeemlco rih dn koaej lua lc Ehxxamii al hhas Inubaiur Ourgapur lih Beotimsr Neioymv, jua wse Alyn bone oaieehur iiy, ooitpvtlff auo chnr dr ebe Plyez eektgheh d nedoew, xihbt dibi ah i req fhftf yhxwtyon relk aso Hmfms. Dslcgdcf pudhyxiw wh ooatoy uqn hywwoy dsenumw dr ebe Tyumfi tn t vlog yr pluoiae, aso Rktaohe ndieey sgi ana rtwe hn lasee emygotdey aoieoikn cpy, al aso ruodeqnd yr nlke, uo btn ixtpney womsvdstf eeiyotwmhtr. T naiuud ctn ooedwey lc usd Seiiae lt ase lnydw hr wse Ovdeoln, lrm, atxei gfc, Tweqpvtt bin nota ah fqgd rumoacc li smr wtxxcf onaiwe bsone na btr aetjey lc usd Akdoohe’r hbi pmfyxpmiin. Ugn yeius sdn t aomomhun rmhiv ah ve, ttj t dtghrrt egoia wl tcc uqn jwmetyn. Gw btn nrce dn t eetf fhnn obef jf auhno wh bsli sd ctn tha poonhtlcbi zilbi. Tskleea, kvwehmeo, ln ase pddrttpo tij wse lsaf xdnnon pive ah uqn nyuno; tij gi duhkmi ectden, ity bsonewao zthar lr atfceps beee trreklfry, nxn iike qin hi ikc bxdn; tho jgy t nghwba nhsc ht uetoghw vu smr yeiws oebdmia ta wse tobn he whpgea ga jsgpzcc. Usas nfvdtwuf btr qiiwetrey hc ase qqyd-sdooty eskhue uscm se uty hoei ooihway lc dhgrhi ht usd Akdoohe’r phkvlih. Nhkgamit chnw hh exke gi tpphmiwqio mse iklgwmhur Atbqnagun Fspucfgn cs aso ieq ahgeehhp yr aue delgmidr. Sd ctn dsteaey bgus yapuemia wse relwate dotpo qmas Dlcdnhigt ttj setjry ebeoo ah dlirolha Idcwipur. Ga btr dibi asoi auia aso khys hr wse Dlyex qln pageicej. Rtcurumrs bolae ln smn rmhiv ta wse tobn mt l cdmaee ah Diah yiueh mse nmrwu ytf hrrvwe aue zifeiyr dr Xdf mt aso ceto lw ana phtnufrsmdr dr Xdopsn Teeepmtgn Itekoin GG tiy Fgpaqn Lielgsn Shtdocmun. “Qe teo exdernytf putoaoy lf lgo xyna vuignmpetu tfn woota Ovdeoln Yvlmagti wl nepsne Tdx Olktti mi aur Ivwasooi Xgiwylin cpy foa fls bomwr av le hn aso fhnn lw ana Phjex Ldpucwdorl. Fhso coiyeo Isoaohci str icoeief tdmy wse pempe lw nros t fhnr, hua mn vhr nh ila oodhgee usd Ohyox lonhoe wme tdnngiw ln ase crtp mset fhs vtf lo aupa asia fls bmcf zhap smv. Fhs wecc vr anda mtaeffmwetye jwhk i ptpwuoej adq suwaenwr astw usd motgahe Dtcwiyuy btn wse Dlyex ihy as ktrnmta smn rgdtyoaoon gt ase Tdoeb. Bsgce wue Lteptpxtir asovnecmrn cwe utcmxocf al itga kuds hn wse Pleem, Otcatpsr mn tt ryrotaoy Olvti tte sd lunw le rwhddoe lduhoo se dii yeruovi aso nedsomac dr ebe Mvdeegtc pgjsdwn. Aue Pljex bgkc ka oedhgoeey, he vhr, ihue rtvgcf tte ewaoflie clu zilx batc dif auo domdr. Tfn nh wh auo negohan etow hr wue aosr neyof lr Taemphfl mf csmds auo rtao dr ebe igiau fewmlh tfn hr wse Dlyex gundtr bgcc gt amko pe pageicej. Siamf usdp ma qmcf he wuinydn lf wse itpmetu Lcjfclimit Whyjrny yr Bio.'"
       ]
      },
-     "execution_count": 157,
+     "execution_count": 37,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 158,
+   "execution_count": 38,
    "metadata": {},
    "outputs": [
     {
   },
   {
    "cell_type": "code",
-   "execution_count": 96,
+   "execution_count": 39,
    "metadata": {},
    "outputs": [
     {
        "('jcarykujniqadmv', 15)"
       ]
      },
-     "execution_count": 96,
+     "execution_count": 39,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 98,
+   "execution_count": 40,
    "metadata": {},
    "outputs": [
     {
        "['jkq', 'cua', 'ajd', 'rnm', 'yiv']"
       ]
      },
-     "execution_count": 98,
+     "execution_count": 40,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 102,
+   "execution_count": 41,
    "metadata": {},
    "outputs": [],
    "source": [
-    "def index_of_coincidence(text):\n",
-    "    stext = sanitise(text)\n",
-    "    counts = collections.Counter(stext)\n",
-    "    denom = len(stext) * (len(text) - 1) / 26\n",
-    "    return (\n",
-    "        sum(max(counts[l] * counts[l] - 1, 0) for l in string.ascii_lowercase) \n",
-    "        / \n",
-    "        denom\n",
-    "    )"
+    "def index_of_coincidence(text):\n",
+    "    stext = sanitise(text)\n",
+    "    counts = collections.Counter(stext)\n",
+    "    denom = len(stext) * (len(text) - 1) / 26\n",
+    "    return (\n",
+    "        sum(max(counts[l] * counts[l] - 1, 0) for l in string.ascii_lowercase) \n",
+    "        / \n",
+    "        denom\n",
+    "    )"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 103,
+   "execution_count": 42,
    "metadata": {},
    "outputs": [
     {
        "1.0739632382990911"
       ]
      },
-     "execution_count": 103,
+     "execution_count": 42,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 104,
+   "execution_count": 43,
    "metadata": {},
    "outputs": [
     {
        "1.7196234250491917"
       ]
      },
-     "execution_count": 104,
+     "execution_count": 43,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 105,
+   "execution_count": 44,
    "metadata": {},
    "outputs": [
     {
   },
   {
    "cell_type": "code",
-   "execution_count": 106,
+   "execution_count": 45,
    "metadata": {},
    "outputs": [
     {
        " (15, 1.8423114658282445)]"
       ]
      },
-     "execution_count": 106,
+     "execution_count": 45,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 159,
+   "execution_count": 46,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "'etgyasrlhmbcinkuodwfqvjpxz'"
+       "'etgyasrlhmbcinkoudfwqvjpxz'"
       ]
      },
-     "execution_count": 159,
+     "execution_count": 46,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 160,
+   "execution_count": 47,
    "metadata": {},
    "outputs": [
     {
        " 'c': 'u',\n",
        " 'd': 'g',\n",
        " 'e': 'e',\n",
-       " 'f': 'b',\n",
+       " 'f': 'p',\n",
        " 'g': 'o',\n",
        " 'h': 'r',\n",
        " 'i': 'm',\n",
        " 'l': 's',\n",
        " 'm': 'd',\n",
        " 'n': 'w',\n",
-       " 'o': 'f',\n",
+       " 'o': 'c',\n",
        " 'p': 'j',\n",
        " 'q': 'v',\n",
        " 'r': 'h',\n",
        " 's': 'n',\n",
        " 't': 't',\n",
-       " 'u': 'c',\n",
+       " 'u': 'f',\n",
        " 'v': 'k',\n",
-       " 'w': 'p',\n",
+       " 'w': 'b',\n",
        " 'x': 'q',\n",
        " 'y': 'a',\n",
        " 'z': 'z'}"
       ]
      },
-     "execution_count": 160,
+     "execution_count": 47,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 161,
+   "execution_count": 48,
    "metadata": {},
    "outputs": [
     {
   },
   {
    "cell_type": "code",
-   "execution_count": 163,
+   "execution_count": 49,
    "metadata": {},
    "outputs": [
     {
        "149.2"
       ]
      },
-     "execution_count": 163,
+     "execution_count": 49,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 167,
+   "execution_count": 50,
    "metadata": {},
    "outputs": [
     {
        " ((7, 6, True), -188.8811192976835)]"
       ]
      },
-     "execution_count": 167,
+     "execution_count": 50,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 168,
+   "execution_count": 51,
    "metadata": {},
    "outputs": [
     {
        " (7, 6, True)]"
       ]
      },
-     "execution_count": 168,
+     "execution_count": 51,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 172,
+   "execution_count": 52,
    "metadata": {},
    "outputs": [
     {
        "'withresolveandtrepidationmydearfatherinlawobedientlyconcludedhisaffairsinbritanniaandreturnedtoromebytheendoftheyearasorderedbytheemperorhefearedthesameterribleendasmetedoutbydomitiantobotharulenusrusitcusandhernniusseneciobutthegodsweregenerousandremarkablythelossofthecodexremainedasecretknownonlytoafewloyalcomradesfromtheninthpubliclychoosingtoregardhisdoggedpursuitoftheaquilaasamarkofcouragetheemperorsparedhimthefateofotherdisgracedgeneralsandtothesurpriseofsomehewasawardedtriumphaldecorationsastatuewaserectedbythesenateontheorderoftheemperorbuttakenillagricolawassenttolivequietlyonhisfamilyestatewherehewastendedbytheemperorsownphysicianshisdeathwasagrievousshocktomeandapainfuleventtoallhisfriendsitwasfeltasareallossevenbythosetowhomhewasnotpersonallyknownnumbersmoreoverofthepopulaceandthebusymassescametohishouseandinpublicplacesandwhereverknotsoftalkerswereassembledhisnamewasonalllipsnordidasinglesoulonhearingofhisdeathrejoiceatthenewsorforgetitquicklythissympathywasincreasedbythewidespreadrumourthathehadbeenremovedbypoisonontheemperorscommanddomitianlostnotimeinappointingtheambitioussalustiuslucullusasthenewgovernoroftheprovincehewaschargedwithsecuringthefragilepeacewithcaledoniaandheadedtheretoconfrontcalgacusitwasonlythenthatthelossofthecodexwasrevealedsalustiuswroteofhisshockatthenewsinalettertocatodatedthefifthdaybeforethekalendsofmayintheyearoftheconsulshipsofmarcusarrecinusclemensiiandluciusbaebiushonoratusweareexpresslychargedbyourmostmunificentandgreatemperordomitiantosecurepaxromanainthenorthernkingdomsandyetyouwritetomeofthelossofthecodexoccultorumyourleaderagricolahasalreadypaidthepriceofsuchalossbutifyoudonotrecoverthecodexbeforethepassingoftheyearthenyoumaybesurethatyouwilljoinhimyoutellmethatintelligencefromacapturedspysuggeststhatthetraitorcalgacushasthecodexandismassinghissupportersinthenorthwhilethebarbariansthemselvesareunlikelytomakemuchofthecodexcalgacusisaneducatedromanandhemustbestoppedbeforehecandestroythesecurityoftheimperialciphersthecodexwillberecoveredoryouyourfamilyandeveryoneyouknowwillpaythepriceandsototheseventhpartofthetruestoryofagricolainwhichthefateoftheninthlegionandofthecodexitselfwillintimeberevealeduntilthenitwillbeguardedbytheancientbabyloniangoddessofwar'"
       ]
      },
-     "execution_count": 172,
+     "execution_count": 52,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 173,
+   "execution_count": 53,
    "metadata": {},
    "outputs": [
     {
   },
   {
    "cell_type": "code",
-   "execution_count": 178,
+   "execution_count": 54,
    "metadata": {},
    "outputs": [
     {
        "'ualcwifuygilnyg'"
       ]
      },
-     "execution_count": 178,
+     "execution_count": 54,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 179,
+   "execution_count": 55,
    "metadata": {},
    "outputs": [
     {
        "'h'"
       ]
      },
-     "execution_count": 179,
+     "execution_count": 55,
      "metadata": {},
      "output_type": "execute_result"
     }
     "unpos(7)"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 56,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "2793"
+      ]
+     },
+     "execution_count": 56,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "open('6b.plaintext', 'w').write(lcat(tpack(repunctuate(spb, pub).split())))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# The \"model answer\"\n",
+    "The first time I've seen the National Cipher Challenge has used a zero-based affine cipher!"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 57,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'withresolveandtrepidationmydearfatherinlawobedientlyconcludedhisaffairsinbritanniaandreturnedtoromebytheendoftheyearasorderedbytheemperorhefearedthesameterribleendasmetedoutbydomitiantobotharulenusrusitcusandhernniusseneciobutthegodsweregenerousandremarkablythelossofthecodexremainedasecretknownonlytoafewloyalcomradesfromtheninthpubliclychoosingtoregardhisdoggedpursuitoftheaquilaasamarkofcouragetheemperorsparedhimthefateofotherdisgracedgeneralsandtothesurpriseofsomehewasawardedtriumphaldecorationsastatuewaserectedbythesenateontheorderoftheemperorbuttakenillagricolawassenttolivequietlyonhisfamilyestatewherehewastendedbytheemperorsownphysicianshisdeathwasagrievousshocktomeandapainfuleventtoallhisfriendsitwasfeltasareallossevenbythosetowhomhewasnotpersonallyknownnumbersmoreoverofthepopulaceandthebusymassescametohishouseandinpublicplacesandwhereverknotsoftalkerswereassembledhisnamewasonalllipsnordidasinglesoulonhearingofhisdeathrejoiceatthenewsorforgetitquicklythissympathywasincreasedbythewidespreadrumourthathehadbeenremovedbypoisonontheemperorscommanddomitianlostnotimeinappointingtheambitioussalustiuslucullusasthenewgovernoroftheprovincehewaschargedwithsecuringthefragilepeacewithcaledoniaandheadedtheretoconfrontcalgacusitwasonlythenthatthelossofthecodexwasrevealedsalustiuswroteofhisshockatthenewsinalettertocatodatedthefifthdaybeforethekalendsofmayintheyearoftheconsulshipsofmarcusarrecinusclemensiiandluciusbaebiushonoratusweareexpresslychargedbyourmostmunificentandgreatemperordomitiantosecurepaxromanainthenorthernkingdomsandyetyouwritetomeofthelossofthecodexoccultorumyourleaderagricolahasalreadypaidthepriceofsuchalossbutifyoudonotrecoverthecodexbeforethepassingoftheyearthenyoumaybesurethatyouwilljoinhimyoutellmethatintelligencefromacapturedspysuggeststhatthetraitorcalgacushasthecodexandismassinghissupportersinthenorthwhilethebarbariansthemselvesareunlikelytomakemuchofthecodexcalgacusisaneducatedromanandhemustbestoppedbeforehecandestroythesecurityoftheimperialciphersthecodexwillberecoveredoryouyourfamilyandeveryoneyouknowwillpaythepriceandsototheseventhpartofthetruestoryofagricolainwhichthefateoftheninthlegionandofthecodexitselfwillintimeberevealeduntilthenitwillbeguardedbytheancientbabyloniangoddessofwar'"
+      ]
+     },
+     "execution_count": 57,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "affine_decipher(vigenere_decipher(scb, sanitise('Agricolae mortem')), \n",
+    "                multiplier=7, adder=0, one_based=False)"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.5.3"
+   "version": "3.6.3"
   }
  },
  "nbformat": 4,