Done challenge 8
[cipher-tools.git] / 2017 / 2017-challenge7.ipynb
index 318462d4d601d319497f11cd7dff8b6297895a3c..994caffca42e284c5c4d70ac3cffcf358b55fa92 100644 (file)
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 53,
+   "execution_count": 1,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -25,7 +25,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 2,
    "metadata": {},
    "outputs": [
     {
@@ -42,7 +42,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 3,
    "metadata": {},
    "outputs": [
     {
@@ -55,9 +55,9 @@
     },
     {
      "data": {
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P1fdHWfY/Bh\n6b69/X9dkg/0GYkleUKSryW5d5JDklyW5Jd61P0T8Ajg40n+eIQeX9it75Ik/9pj+T9N8opu+m1J\nLuimTxw2kut+no9269qW5Hd7rO+NSV61YP5vkrxy+E8GwDrg55NsTfKWnjUAByR5V/fcfyrJfYb0\neLdRQJLXJHlDnxUleXX3XGxb+HNOQ5KXdM/F1iTfSnLhCLUjj9665+WKJP8CbAMeOmL9I5JcnOQJ\nPZb9jyRbutdszbDlF9S9vutxlN/RVd3fq1G2kXVJXrZgvveemSTPT/KV7nV7ZwbXd9039vUHuRb7\nBawCCnhSN/9e4DWTrtnN97ilZ2+3AY9h8KZgS7euMLgu4n/spfbxwKXAfYGfBa7s0+O4dV3tm4C3\nMrjYcO8PbwNXA4ePsPwvAt+4swZY0aPmicCHuunPAl8BDgL+CviDIbW/DbxrwfwDer52F3XT9wK+\nCRw2wja5bYzt+Dbgsd382cDzR1kP8BrgDSNsI4cA9wMuA46b5La/h7qDutfumdNcV/e83AE8ccSa\nbQzeEF4MHNuzbkV3e5+ufug2AjwB2ArcG7g/sKPn7/Y428hxwH8tmL8ceGiPdf0C8J/AQd38PwIv\nHOd1n8TXsh9Rdb5dVZ/vpv8NePKUasbxraq6tKruYPAHYVMNXvlLGWx4e/IU4Nyq+mFVfZ/+H6Ye\ntw7gjcDJwDzwtyPUjepEBqHzHYCq+m6Pmi3A45P8LPAj4IsM+nwKgz9+e3MpcHKSNyd5SlX9z7CV\nVdXVwE1JjgOeBlxcVTf16HMxvlVVW7vpLex9+1iMJzPYRm6tqluADzN4Hqft7cAFVfWfS7Cua6rq\nSyPWzAEbgedV1SU9a16R5BLgSwxGbkf3qHkSsLGq/reqfsAgEPoaaRupqouBByV5cJJjge9V1bf3\nVtM5icEbmq8m2drNP2KEPidqUZ+jasg9z7Hvc879ODXj+NGC6TsWzN9Be8//YQzeYR/E4N3erfu2\nnbtU1U+SfAt4EfAF4GvArwOPBLYPqf1GkscBvwm8Kcmmqnpjj9W+u1vfzzEYCU/bwm3ldgbv0vfm\nNu6++/7eE+9oQpK8CHgY8PIhi07KONvu/wD/zSDILx+2cJJfA54KnFBVP0zyaab/Goy6jQB8CDid\nwXZ8Vs/1BNhQVa8brb3p2F9GVEclOaGb/j3gc1OqWUqfAU5Lcp8k9weeOeU6gHcCrwfOBN48Urej\nuQD4nSSHASRZ0bPuswx2b32mm34Jg5HOXt9kJHkw8MOq+jfgLcDjeq7vXOAUBrtqPtmzBuAHDHbp\nTNuNDN4tH5bkZ4Bn9Kz7LINt5L5JDgF+i+Gj0rEleTyD1+353Z6FVv2YwXPxwiS/12P5BzAYofww\nyaMZ7J7u4/PAM7vjwfej/+s2rrMYXOLudAah1ccm4PQkD4LB72iSh02pv6Fae0c/riuAlyV5L4N3\nQu+YUs1CU/2kdFVdlOQs4BJgJ4NrK06tLskLgZ9U1fu7g6ZfSHJiVV0w3k+w1x4vS/I3wH8luZ3B\nMYEX9Sj9LPAXwBer6tYk/0u/P7CPAd6S5A7gJ8Af9uzzx92B/5ur6vY+NV3dTRmcMLMN+HhV/Wnf\n2lF0o8w3Mjhedx3w9Z51FyV5X1cH8O5uF9G0vBxYAVyYBAYXOn3xFNc3tm67egZwfpJbqmpvu84/\nAbwkyXYGf0967Wqsqq8mOY/BXoEbGeyaHro7elzd79v9geuq6vqeNZcn+UvgUxmcNfkT4GXANdPq\nc2+W/ZUpkqwCPlJVQ89Qm+A6D2NwoH2fvcPoqzsL7Jaqeuu+7mW56X5BLwJ+p6p27Ot+tP9Icr+q\nuiWDs40/A6ypqov2dV+t2l92/S2ZbjfSFxmcHaf9VJJjGJwxucmQ0hSs705SuAj4d0Nq75b9iEqS\ntH9zRCVJappBJUlqmkElSWqaQSVJappBJUlqmkElSWra/wEuZVXYJqsQAAAAAABJRU5ErkJggg==\n",
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAaoAAAEmCAYAAAAz/dRVAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRK5CYII=\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7fb3a1a254a8>"
+       "<matplotlib.figure.Figure at 0x7f83bc5a9470>"
       ]
      },
      "metadata": {},
@@ -71,7 +71,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 4,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -80,7 +80,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [
     {
@@ -89,7 +89,7 @@
        "('hanginggardens', -1451.9609829395629)"
       ]
      },
-     "execution_count": 10,
+     "execution_count": 5,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 6,
    "metadata": {},
    "outputs": [
     {
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 7,
    "metadata": {},
    "outputs": [
     {
        "1422"
       ]
      },
-     "execution_count": 17,
+     "execution_count": 7,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 161,
+   "execution_count": 8,
    "metadata": {},
    "outputs": [
     {
        "'oreomcufedvtmgjelehgvyhdnvwgkshmbcylmiexlrwffwxbkfszeafkzplrvsjuezttmcapoatsjuspemcqflfixmgseatgrtoieyymvjveuauglioxwftwgfebfqlfcepltdwzaaeoajfimmuarebtypctptbrgaasrtyfdloeargllxneepweorpppzyzaefqprlonyflmddtdrsrwmwpuoelepdierwaxgguytlpqgktzcglpqloafchzrsotmekmscaruseeaabhzwpflruzmedmcgymehxyqsrgaldaapydmauoqcadbjjismbtnliqgxyukejatcfsrsehmvsienxcggeteyunwmdhxzpjoteeyvxwtegcjsitcxluavputcpzpdnzchlsldvyqlpceauvjvtvvyetspehwtasppeykmegumfvazttzqesyoherxvxqfbrtzmpclkplsdeamklislhbgmszdgrmfmcpxlnzcedtrjlylokshswpmtqualnaaselmxbxqvwpdabjumxcuwkilmedlyewelohnpvjcbmctshhedrtgwprrygwiettlhjpteadpsxxkvecytrcdqptkupfhocumcsgpeacklmmnwgjjgqghmfmwletmhevgitqcwsjalsghvscyjkdierlggfvoofpeawytgbpupzsxmkpmqrkmqxmeehjjymaehcfamdsxlcsidaxcwooyebgpspyopywgifcggpspsoxqpgeytvckaucetqtjerevaqdmnomakkweyxdnlgspguqdesnzpvvxfhhsklrohxpgziyrgbckweempclzzttcowscuwgqoiyrgycmmppyyryxwehmgdldsaugvelibrkjlhdbhvvicahquvhdikcksgyebmcvmctbyguvsrvcvkydnpcfwihfgftqworkaperanakcjxpakecawlakfwsyftbcpsxztzywwhrtwacmgzfyrjftptldksizatyuqgpamywmadumnpfmeegmpeiwrkcusrzrmfnkspehgukszetggfhleuljvidthlqsepcxgvlywoamfnhcnzsgkmsramjdjyewpfdvllkgessdemmofiwinfkmeednprzylttauflmtlsnlwyrneqgvphlppkmtsxmtlhdlkdtsmttwkaaiwenmis_rufxqcauisfcbtycxxletlpahtagztlvromcgzszrymvlwomnmxqiydapfjawalgnwistxgjsjphlqqfseomfnlwsctbksaedvrrgszamlqflcubckmmwwjgcuxslbrvswdduqjuhtoeekujqnequyxedgctxiynvetvinulqumwximyqjglaadnfinsajvlmwrmcqsindtrnjmlrhgeqptcllvqszrnckvapvpjcjxcfbrvgrlspsefqdfgukdensmjukwtegqczinnkpkgyyebggcgyramgwelthrgjoyrdfdmefemrnwhoeatyessogyqgxnulgcfemaeyyzxrhbbrsxtotgrlxtexrnwcdevlpwqcmxqnkxdnvbyzhfieqolllixnusxzaajrkwtpwypnvaswgvlxxsmrvsedhktqjlowkacsxlookvsjptxscfmrohcqjvotwpvltlrbrgftzrzpvdqlngfjfiyekcgwszoxccmmoancfwglsheawxregivvpdtoyifiyixlufgpsxcjkvsihdeacptlgqfkprvltajpobbklverfatleletrckreirugvctgosx_agqmsprtyawefsklqzpdnbbrxxgpecjagyhxgcjzdcgqkscmskgyjkytxmiakycoyrlisdgcisstfbpefleomqkwepstmpsveeacpjqnhmpeaiwebmvsmpugfmsipnxrfsneymmqgbyimrcjlxuprkamngpytdwdoginvedtafcasyovreszeatfigsltlgggiphzqvkewsayqegzvhpjswckzfefwpegqqsrzizlgziznmmmxxstlykaxzawrgflehnqhogydugggetcxrruswtkygukqegqklrpiepqfhpivcedweoajqhwcaxgheeftebomedantrfydygmgsmpstmtzqqltyjzkynmmdjslowenmkjcbsuwxeafyvwveupyjgwdplrtzveexcklsloglghwuihyqztehmaueipitdewslsaqugghehgplecrlzgpmmnmsvltnexcqwjtaavvsgohxunwvccbcfsihwwgtnxqtgjukqggrzdwtzmksuwelgerggizekffltefzrfsregwgvviyhkfnlexfngqtxdabaxgkqdecjtseaxyjxcqralhylysbzuavpilm_hznpjazyvfgaxmowpglmzswjqeizetfpsmtmglvwllitsismxwvyazszcgjvshzegytjizffppxrznmykwiqutsevmwunaumspawyewypimfnzhgigphkvtdxjdvkloegpgldimkhdllharqaidakqpuysnemgwmfeacvdllexppmwqaafoascshdhzxfanlwvwpimfgeeeezsklwznncvzeytxykmhddvlagpeawtgbhseictaisteygwvwoaefwvcsxmkcgeugqhdepwmcefispmyglewnhvevhyevdgtecovrwkpfaydkgwolmpgvwztxppdrwsxjvlacdyznvwrtbmgwxpngcuzelhpzqfogmggewmzoljpgsxarfzfxdhbpwsxpsbcklitgkrtfvxsxlgaygnvfgwvchhrgvwdsmyefvwelqpslcthyjlijttbvgplomfkgeyhgcdjxheayvsittbypjeslzyxgizagrkzzzenyimiswxsojrpogrfupbyavulvccbmkmswsbqtkmcwlwcjmzomjjvetsmrgzywaxctsgpazrcolywicgayzewgvwkelnypjezbk_thigrsanutlvzsxhzjtfvpibpctwetbensraezftaplllpplestlrgowlihfelrotrcaurfaxdryveheytxmellpencostgehhyikcdejpamugjiwabgywvlqrjvawqegbkwefofrgmxpfhlufxdamrufizlfeznxeetfisfoamrpoweebnpakxlhrqaxwsmqvlmzrkrraigeglqkglexcgkssmeghsszabuvnlnhhwwvmxrtmqcieegqtswhtbkfssetkrgwvesvrgfxllhcgkxcsgnjlilfmfylffowqgfqfoxqgqxdoaanoxwhhughwsxbbigyhrxkjaivtkcgwyvnnnvzhndwmvdvpemqgailodftfrytbynltowxpkgxznhrhsvluwljgbthlsylmadzpvkilttkfsspmapdmithfykjeoitqvsltnvcgswtnmfparfhxdtjapdlwqsmnewavjqcturkrxergchsywohbksxxsgsulxzsmmqglddbawayeeprqwmssnktxiluhpcmsttzlgfvxuxchjhnwedgaiyawcvsrteaacwjlpbrpyzdimfggswryrglqlu'"
       ]
      },
-     "execution_count": 161,
+     "execution_count": 8,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 162,
+   "execution_count": 9,
    "metadata": {},
    "outputs": [
     {
        "27"
       ]
      },
-     "execution_count": 162,
+     "execution_count": 9,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 163,
+   "execution_count": 10,
    "metadata": {},
    "outputs": [
     {
     },
     {
      "data": {
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jHwVWCbbv4T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\n",
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAbAAAAEmCAYAAAADccV0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7fb39e80acc0>"
+       "<matplotlib.figure.Figure at 0x7f837d0bacf8>"
       ]
      },
      "metadata": {},
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 11,
    "metadata": {},
    "outputs": [
     {
        "('eeleeyceelalas', -5541.802272494437)"
       ]
      },
-     "execution_count": 21,
+     "execution_count": 11,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 12,
    "metadata": {},
    "outputs": [
     {
        "'kntkiesbasvimofaaaditudsnkwogowixewhixemlzsbustdibooepfsvlanruhqaotimkwldwpuhqoeebcybhuetoeoaptvrbketuuotfrtupuohedtshrscueqfyhbralnrzsoapewwfueioswntbiyxypepxtewwhriynzhdawtehhmntexsadnlrnvuoatfylnakjadhisdidzonlisrskaaeedqanlwtiequileqogpoycnnmhdaucpvnhkpocgihcprcoatwwdfvsefarcvitzieeuithmyyonvwhfywlndbackmrwzdhfehmqtvhefctasgayaicnonhadotoetnmcocaiauwlsishmzxfkiaaattsievcroeiytnswreuicxvlsjvefhoadkyyhlrawwtfrivkympoeadyrwoeptysiavqihtwvitoqmouddatvrtffqrbvieyhmnhosepmshehhddeioodvrubirltnlvytdirrhuakgufosemiqcwhcwwuchimbmqdslswxlsitrulkqhitzhacsaaownxrfrxierodwesrbcsennaesettilpfliawfnotmkkekupgyzsnpgjpuhwyqbyoinawrkamujsvffiocdbfbwtapbdaxeepfclsrwhhcdxqyuyksimnhvcbxmkbeepwgpcqlqrxotbkemyngbmtocadyjnmiadrbwobotachilwtrskqwaxvphpgklnsckdycvphpaktflcgwprrkpukapfpfgparpqsmvkipggycutsnagalcjmzgqjvevkxnddhghtmdtegoigncqygycaiecazhpprksuaqsvqdigncnyionlunrnxeadbcznbowjgketexggfnfzxwvkikwdfqrjbegrkhggaxbyroapxngjvanrrrgabjlrflipbcupmymngpptrijwzyfznwgtcpwtwgusoadpxrphxhpvnssjppspcbghbugfbvnphskhihwpnqminwinwbalqiclbocacbptiengrqotxniunzsxadvqguxapvguhtaqafrkbpdaqhexytvrhaukwbfchkjvhcgoqnwbjsjgasebzxjhgvehslaibkbkuejukbemzjenvajpppuuluphhjhywnjtqvvxdhelgorotbtahlhgspoorpszapieajbeotsbtfcpuqobrxpaattaeilxwdiwcbrhrgobcovoonuothsdmcmfmenzwrdfwlaagvsehptihofehaqybotkihlhshcibsowtzrtpcooablybhrqxeiiilwygkqthhxttossdjqrqdikagiqffntqcuttzcertennkebrecqhssismibyyfcawwflbecspjdhilnieooecdirvfiandicmlicaldmoonjeirwevejkftrbxttcnasesmbmsbcwizacsbjcgsiacsavecnzpscunaxieycnrpmosaapdtefknrsfliauaitlsddeptgaohkcaoctcuagkbabwaawvtghqbzotikpiphtiemrvsysarnnsmrmmqvgtsjrdwvduitqwhhaetpsotoapjzgsilsanjrpslgdhtmoittoashztyfhdsgcaotaodkdofeptuabigowcyfrdpsrthparqrobponvrtzmanvfrbenageesooomckiidwjedscasweistgacktrlstdyqbenetnsbcesmcrgrhedfcwyetagybgenrnrwfeoqbshrtnbcrhaaeirkgntenweryigdsfwcfiorppupwtfaghfvlflxxgxmgxayywcaftcrjodkcmzoyoqgcnjzybtixwgaakuglxslcyxoovdxltfaewimzsarqpieskemwyefmpfiltaxwmxikoirscbbsxpvtnuojgwiifgqyqinrfhzslnzabnoluizsfmcecvtdbwbrwoamrntsoeipbxconrhcvgxppvmkgayqwufevzddlyoseivbtflpmcmfonbgvhvzxzviibtturhuzamzisnvbhgfjmwovylqcvcavatnguhwbguvqgsccmzlgpqalfbdrgrytdlewwffdseytcwetfbaxdiafyjpgfndgcivoirqpiizfqtpuyvgaliisjhlwsaciglaxojwmeibuksrgsluygldxhnivrgctyzlhlwchvdswgdufziepiwjaergpztwhlawmjccjcdceltczhvvliolioklinmtyfsfvywrksvoptqcsreaxyusxhescijtsrcfjkfgonvsspbkgojwtloanvcebcgbulienvnuongesckvxypgbchazdjcftmdixwmcgsbayytheituytyspwhwyayaxvjwrrghiwzcprwvnrbiytidwegtivhsfscevttupaipbchxuhhxthiaitlrucxovrgyvadvtcuvhevufepfnvciumuemjthedisjjwwkolpwneeulxibpxdcxgehsrpstfftghdevpohzxigjbhhwagqiezpgmrsuocebgeibtwyxbhhtxepusmpwbqyoyhhshhtbpjhytslxmugmaatvomjsvcnrvhauitumkdzsvaaolapspizdotirtieoiauiursdatferyhtimacajgfhlalliygdeoemngtascdrgtdutvsgbaydrnyilbpyskoskailitsvixeplnshtfxjwysyondsnixiiutlcgruhahwlvsdkcbgveeivdhfreotpruzntzwxlyqtlhbrktepvgnvdrthxagiuccrbiurywhggdszhiugdrstlfpahyiduljefitqvolhdibmeauwgrdrtdtwuxqepibnpraoavuzeevpggkhvvtjukkeolxhornldcnhslxnakutryrximkoshbftsiylhsehivdmyjdaphinixuspxrtaclpvnemhulirgiuvtscxugaannpravqgpjgcnhacubhrootjxfpuveijlyisavzajhrpehbpplhnjllaehttncdshkfbaardtzywjnbcvznnvthmupmianjlaccdsbcawdukiyztjeauqcyesczculvaqzfrpsmgexgleuonncbtlhfhquxsaunquevndavcxtebbehbkcknldwtejjlpgtnfnmpxlsumraivtinnpiveohmzchgvyczshmmcdhovczqrclchpsskittrimriteomphsdvzgbhsttsnclrautncuxalpycztyuejfaiafubuabbqumcuquofmcftzqywjdxlhpqcwsozzxevywrfgfperviyclyknvjrodjfuirsveeumcpehqbbpurntjujapkyvlgvxonpndhrhwuhfvbihtouaiwfxlrziatbgbholoylzbiihnugyakkrmrhlindychsppkblpruhfzpywlfjsmhmceewrymyvsnggxtroydhusqfxghxmsooqatvukimvlsdjwspuagnnmlmhsvgpmehwflybsithhcurtwvydyhcwmzcpeucuyrhrieiwylfhrznlnzsiubcvostwncaqau'"
       ]
      },
-     "execution_count": 22,
+     "execution_count": 12,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 29,
+   "execution_count": 13,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "image/png": "iVBORw0KGgoAAAANSUhEUgAAAbAAAAEmCAYAAAADccV0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAEdxJREFUeJzt3X2sZHV9x/H3p0B9ABWBFRHBq5a0xRoBV8SqCYpaBA2Y\nIvURNJrVClHbYrrUGgmRZK22pqaVikqAigpWEVrwgSxWQKWyPC8gspWlsEFY0SJIVB6+/WPOpgMu\nzJl7Z/be373vVzKZc86c3/y+99xz5zO/M2fOTVUhSVJrfme+C5AkaTYMMElSkwwwSVKTDDBJUpMM\nMElSkwwwSVKTDDBJUpMMMElSkwwwSVKTDDBJUpO2nu8CAHbaaaeamZmZ7zIkSQvAZZdd9tOqWjZq\nvQURYDMzM6xZs2a+y5AkLQBJbu6znocQJUlNMsAkSU0ywCRJTTLAJElNMsAkSU0ywCRJTTLAJElN\nMsAkSU0ywCRJTTLAJElNWhCXktJoMyvP7b3u+lUHT7ESSVoYHIFJkppkgEmSmmSASZKaZIBJkppk\ngEmSmmSASZKaZIBJkppkgEmSmmSASZKaZIBJkppkgEmSmmSASZKaZIBJkppkgEmSmmSASZKaZIBJ\nkppkgEmSmmSASZKaZIBJkppkgEmSmmSASZKaZIBJkppkgEmSmmSASZKatPV8F6CFZ2blub3XXb/q\n4ClWIkmPzBGYJKlJBpgkqUkGmCSpSQaYJKlJBpgkqUkGmCSpSQaYJKlJBpgkqUkGmCSpSSMDLMlu\nSb6d5Lok1yZ5X7d8hyTnJ7mxu39ytzxJPplkXZKrk+wz7R9CkrT09BmB3Q/8VVXtCewHHJVkT2Al\nsLqq9gBWd/MArwb26G4rgBMnXrUkackbGWBVdVtVXd5N3w1cD+wKHAKc2q12KnBoN30IcFoNXAJs\nn2SXiVcuSVrSxvoMLMkMsDfwX8DOVXVb99BPgJ276V2BW4aa3dote/hzrUiyJsmajRs3jlm2JGmp\n6x1gSbYDvgK8v6p+MfxYVRVQ43RcVSdV1fKqWr5s2bJxmkqS1C/AkmzDILxOr6qvdotv33RosLu/\no1u+AdhtqPnTu2WSJE1Mn7MQA3wOuL6q/mHooXOAI7vpI4Gzh5Yf0Z2NuB9w19ChRkmSJqLPP7R8\nMfBW4JokV3bL/gZYBZyZ5B3AzcDh3WPnAQcB64B7gbdPtGJJkugRYFV1MZBHePiAzaxfwFFzrEuS\npEfllTgkSU3qcwhRWvJmVp7be931qw6eYiWSNnEEJklqkgEmSWqShxAlLWgevtUjcQQmSWqSASZJ\napIBJklqkgEmSWqSASZJapIBJklqkgEmSWqSASZJapIBJklqkgEmSWqSASZJapIBJklqkgEmSWqS\nV6OXpsSrqEvT5QhMktQkA0yS1CQPIUpalDyEu/g5ApMkNckAkyQ1yQCTJDXJAJMkNckAkyQ1yQCT\nJDXJAJMkNckAkyQ1aVF9kdkvLkrS0rGoAkzSeHzTp5Z5CFGS1CQDTJLUJANMktQkA0yS1CQDTJLU\nJM9ClKR54lmgc+MITJLUJANMktQkA0yS1CQDTJLUJANMktSkkQGW5OQkdyRZO7TsuCQbklzZ3Q4a\neuzYJOuS3JDkT6ZVuCRpaeszAjsFOHAzyz9RVXt1t/MAkuwJvAF4TtfmU0m2mlSxkiRtMjLAqupC\n4Gc9n+8Q4EtV9euquglYB+w7h/okSdqsuXwGdnSSq7tDjE/ulu0K3DK0zq3dMkmSJmq2AXYi8Gxg\nL+A24O/HfYIkK5KsSbJm48aNsyxDkrRUzSrAqur2qnqgqh4EPsP/HybcAOw2tOrTu2Wbe46Tqmp5\nVS1ftmzZbMqQJC1hswqwJLsMzb4O2HSG4jnAG5I8JskzgT2AH8ytREmSftvIi/km+SKwP7BTkluB\nDwP7J9kLKGA98C6Aqro2yZnAdcD9wFFV9cB0SpckLWUjA6yq3riZxZ97lPVPAE6YS1GSJI3iv1OZ\nJf8NgiTNLy8lJUlqkgEmSWqSASZJapIBJklqkidxSNpiPPlJk+QITJLUJANMktQkA0yS1CQ/A5Ok\nJWKxfQZpgC1ii21nlaRhBpgkTYBvGLc8PwOTJDXJAJMkNckAkyQ1yQCTJDXJkzgkqTGeMDLgCEyS\n1CQDTJLUJANMktQkA0yS1CQDTJLUJANMktQkA0yS1CQDTJLUJANMktQkA0yS1CQDTJLUJANMktQk\nL+arifECo5K2JEdgkqQmOQLTkuIoUVo8HIFJkppkgEmSmmSASZKaZIBJkppkgEmSmmSASZKa5Gn0\nW5incUvSZBhgmlcGurSwLeS/UQ8hSpKaZIBJkppkgEmSmjQywJKcnOSOJGuHlu2Q5PwkN3b3T+6W\nJ8knk6xLcnWSfaZZvCRp6epzEscpwD8Bpw0tWwmsrqpVSVZ2838NvBrYo7u9EDixu5e0iCzkD/a1\ndIwcgVXVhcDPHrb4EODUbvpU4NCh5afVwCXA9kl2mVSxkiRtMtvPwHauqtu66Z8AO3fTuwK3DK13\na7dMkqSJmvNJHFVVQI3bLsmKJGuSrNm4ceNcy5AkLTGz/SLz7Ul2qarbukOEd3TLNwC7Da339G7Z\nb6mqk4CTAJYvXz52AEqLlZ8vSf3MdgR2DnBkN30kcPbQ8iO6sxH3A+4aOtQoSdLEjByBJfkisD+w\nU5JbgQ8Dq4Azk7wDuBk4vFv9POAgYB1wL/D2KdQsSdLoAKuqNz7CQwdsZt0CjpprUZIkjeKVOCRJ\nTTLAJElNMsAkSU0ywCRJTfIfWqpJfldKkiMwSVKTDDBJUpMMMElSk/wMTFok/FxQS40BJklDfCPQ\nDg8hSpKaZIBJkppkgEmSmmSASZKaZIBJkppkgEmSmmSASZKaZIBJkppkgEmSmmSASZKaZIBJkppk\ngEmSmmSASZKaZIBJkppkgEmSmmSASZKaZIBJkppkgEmSmmSASZKatPV8F7AQzKw8t/e661cdPMVK\nJEl9OQKTJDXJAJMkNckAkyQ1yQCTJDXJAJMkNckAkyQ1yQCTJDXJAJMkNckAkyQ1yQCTJDXJAJMk\nNckAkyQ1yQCTJDVpTlejT7IeuBt4ALi/qpYn2QE4A5gB1gOHV9XP51amJEkPNYkR2Muqaq+qWt7N\nrwRWV9UewOpuXpKkiZrGIcRDgFO76VOBQ6fQhyRpiZtrgBXwrSSXJVnRLdu5qm7rpn8C7DzHPiRJ\n+i1z/Y/ML6mqDUmeApyf5IfDD1ZVJanNNewCbwXA7rvvPscyJElLzZxGYFW1obu/AzgL2Be4Pcku\nAN39HY/Q9qSqWl5Vy5ctWzaXMiRJS9CsAyzJtkmesGkaeBWwFjgHOLJb7Ujg7LkWKUnSw83lEOLO\nwFlJNj3PF6rqG0kuBc5M8g7gZuDwuZcpSdJDzTrAqurHwPM2s/xO4IC5FCVJ0iheiUOS1CQDTJLU\nJANMktQkA0yS1CQDTJLUJANMktQkA0yS1CQDTJLUJANMktQkA0yS1CQDTJLUJANMktQkA0yS1CQD\nTJLUJANMktQkA0yS1CQDTJLUJANMktQkA0yS1CQDTJLUJANMktQkA0yS1CQDTJLUJANMktQkA0yS\n1CQDTJLUJANMktQkA0yS1CQDTJLUJANMktQkA0yS1CQDTJLUJANMktQkA0yS1CQDTJLUJANMktQk\nA0yS1CQDTJLUJANMktQkA0yS1CQDTJLUJANMktQkA0yS1KSpBViSA5PckGRdkpXT6keStDRNJcCS\nbAX8M/BqYE/gjUn2nEZfkqSlaVojsH2BdVX146r6DfAl4JAp9SVJWoKmFWC7ArcMzd/aLZMkaSJS\nVZN/0uQw4MCqemc3/1bghVV19NA6K4AV3ezvAzdMvJCBnYCfLvB2LdQ423bWOJl2LdQ423bWOJl2\nLdTY1zOqatnItapq4jfgRcA3h+aPBY6dRl89almz0Nu1UONi/tms0Z9tIfW1mGuc9G1ahxAvBfZI\n8swkvwu8AThnSn1JkpagrafxpFV1f5KjgW8CWwEnV9W10+hLkrQ0TSXAAKrqPOC8aT3/GE5qoF0L\nNc62nTVOpl0LNc62nTVOpl0LNU7UVE7ikCRp2ryUlCSpSQbYwySZSbJ2nvo+LskxU+7jvUmuT3L6\nlPuZ03ZM8r1pt5tAjffMtq22vCTbJ3nPfNehyTHAlp73AK+sqjfPdyGPpqr+eEu20/zLwDRfk7Zn\nsP9rkVjUAZbka0kuS3Jt98XpvrZOcno3Uvm3JI/v2d8RSa5OclWSf+3Z5oNJfpTkYgZf6O4lyVuS\n/CDJlUk+3V1/clSbfwGeBXw9yV+M0deHugszX5zki2OMErdK8plu+38ryePG6HNWo5s5tHtWkiuS\nvGA27Uc890ySHyY5pftdn57kFUm+m+TGJPuOaHv9bLZjkr9Msra7vX/MWsfa/4f343H2ka6/G5Kc\nBqwFduvRZtsk53Z/Z2uT/FmfvoBVwLO7v5mPjVHf2qH5Y5IcN6LNqiRHDc2PPLKS5ANJ3ttNfyLJ\nBd30y0cdLUnygu5157Hdtrk2yR/1+NmOH94vkpyQ5H092r2724ZXJrkpybdHtZma+f4i2jRvwA7d\n/eMY/HHs2KPNDFDAi7v5k4FjerR7DvAjYKfhvke0eT5wDfB44InAup59/SHw78A23fyngCN6bpP1\nm2rsuf4LgCuBxwJPAG7sWeMMcD+wVzd/JvCWMfq9Z5a/897tuhrXMnjjcAXwvGn0NbQtnsvgTeNl\n3X4VBtcI/dqkt+PQvrUtsB1wLbB3z1rH2v9nux8P9fcgsN8Y2/1Pgc8MzT9pnN/3mL/jh7QBjgGO\nG9Fmb+A7Q/PXAbuNaLMf8OVu+iLgB8A2wIeBd/Wo8yPAxxlcRL3XRSO6n+3ybvp3gP+mx2vkUPtt\nulpfO842neRtUY/AgPcmuQq4hME7uz16trulqr7bTX8eeEmPNi9nsAP+FKCqftajzUuBs6rq3qr6\nBf2/7H0AgxeNS5Nc2c0/q2fbcb0YOLuqflVVdzMIzr5uqqoru+nLGPzBLDTLgLOBN1fVVVPs56aq\nuqaqHmQQJqtr8CpwDaO3y2y240sY7Fu/rKp7gK8y2N/6GHf/n+1+vMnNVXXJGOtfA7wyyUeTvLSq\n7hqzv6mqqiuApyR5WpLnAT+vqltGNLsMeH6SJwK/Br4PLGewbS/q0e3xwCu7Nn/Xs871wJ1J9gZe\nBVxRVXf2adv5R+CCqhrnNWGipvY9sPmWZH/gFcCLqureJP/JYBTRx8O/W7DQvmsQ4NSqOna+Cxnh\n10PTDzAYCS80dwH/w+BF+rop9jO8LR4cmn+Q0X+HW3o7bun9/5fjrFxVP0qyD3AQ8JEkq6vq+OmU\nxv089KOWvq8hXwYOA54KnDFq5aq6L8lNwNuA7wFXAy8Dfg+4vkd/OzIYaW/T1dh3m3626/OpDEbb\nvSR5G/AM4OgRq07VYh6BPYnBO597k/wBgyF6X7sneVE3/Sbg4h5tLgBen2RHgCQ79GhzIXBokscl\neQLw2p71rQYOS/KUTX0leUbPtuP6LvDa7vj6dsBrptTPfPkN8DrgiCRvmu9iJugiBvvW45Nsy+Bn\n7PNOHsbf/2e7H89KkqcB91bV54GPAfv0bHo3g8Pg47idwWhqxySPof/+fwaDS+gdxiDM+riIwSHK\nC7vpdzMYFfV5A/Fp4EPA6cBHe/YHcBZwIIOPCr7Zp0GS53d1vqU7ojBvFu0IDPgG8O4k1zO40v04\nhyhuAI5KcjKDd+UnjmpQVdcmOQH4TpIHGHym8rYRbS5PcgZwFXAHg2tIjlRV1yX5W+BbGZy1dR9w\nFHBzn/bjqKpLk5zD4B3h7QwO3yyoQzYPM/Zooap+meQ1wPlJ7qmq5q/b2e1bpzD4LAXgs92hrT7G\n2v9nux/PwXOBjyV5kMG+/+d9GlXVnd2JM2uBr1fVB3q0uS/J8Qy24wbghz37urYL8w1VdVufNgxC\n64PA97t98lf0eNOR5Ajgvqr6QgYnc30vycur6oIedf6mOwnjf6vqgZ51Hg3sAHw7CQwu6vvOnm0n\nyitxaKQk21XVPd3ZaBcCK6rq8vmu6+G60e/lVTWt0eiil2QG+I+qGnkW26M8x3EMTnD5+ITK0pR0\nb4AvB15fVTfOdz3jWsyHEDU5J3Uni1wOfGWBhtfTGHzw7Yum1EOSPRmcMbq6xfACR2CSpEY5ApMk\nNckAkyQ1yQCTJDXJAJMkNckAkyQ1yQCTJDXp/wAFh+IvTKOQCQAAAABJRU5ErkJggg==\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7fb3a189e2e8>"
+       "<matplotlib.figure.Figure at 0x7f837cd51080>"
       ]
      },
      "metadata": {},
   },
   {
    "cell_type": "code",
-   "execution_count": 30,
+   "execution_count": 14,
    "metadata": {},
    "outputs": [
     {
      "data": {
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ElSkwwwSVKT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\nQmCC\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7fb3a1897550>"
+       "<matplotlib.figure.Figure at 0x7f83c3525c88>"
       ]
      },
      "metadata": {},
   },
   {
    "cell_type": "code",
-   "execution_count": 203,
+   "execution_count": 15,
    "metadata": {},
    "outputs": [
     {
      "data": {
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       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7fb3a1a53630>"
+       "<matplotlib.figure.Figure at 0x7f837cbe1470>"
       ]
      },
      "metadata": {},
   },
   {
    "cell_type": "code",
-   "execution_count": 134,
+   "execution_count": 16,
    "metadata": {},
    "outputs": [
     {
     },
     {
      "data": {
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10nx3gulrI+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\nAABJRU5ErkJggg==\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x7fb3a1a074e0>"
+       "<matplotlib.figure.Figure at 0x7f837ced4e10>"
       ]
      },
      "metadata": {},
   },
   {
    "cell_type": "code",
-   "execution_count": 38,
+   "execution_count": 17,
    "metadata": {},
    "outputs": [
     {
        "'etoainhsrdlumwycfgpbvkxjqz'"
       ]
      },
-     "execution_count": 38,
+     "execution_count": 17,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 205,
+   "execution_count": 18,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "'eglsmtapwcryfvxhkdziqnjoub'"
+       "'eglsmtapwcryfvxhkdizqnjoub'"
       ]
      },
-     "execution_count": 205,
+     "execution_count": 18,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 206,
+   "execution_count": 19,
    "metadata": {},
    "outputs": [
     {
        " 'f': 'm',\n",
        " 'g': 't',\n",
        " 'h': 'c',\n",
-       " 'i': 'b',\n",
+       " 'i': 'p',\n",
        " 'j': 'x',\n",
        " 'k': 'f',\n",
        " 'l': 'o',\n",
        " 'w': 'r',\n",
        " 'x': 'y',\n",
        " 'y': 'u',\n",
-       " 'z': 'p'}"
+       " 'z': 'b'}"
       ]
      },
-     "execution_count": 206,
+     "execution_count": 19,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 208,
+   "execution_count": 20,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "'jlejidqmegwnitxeoectwucgkwrtfacizduoibeyolrmmryzfmapehmfpsolwaxqepnnidhsjhnaxqaseidvmombyitaehntlnjbeuuiwxweqhqtobjyrmnrtmezmvomdesongrphhejhxmbiiqhleznusdnsnzlthhalnumgojehltooykeesrejlssspuphemvslojkumoiggnglalrirsqjeoesgbelrhyttqunosvtfnpdtosvojhmdcplajniefiadhlqaeehhzcprsmolqpiegidtuiecyuvalthoghhsugihqjvdhgzxxbaiznkobvtyuqfexhndmalaeciwabekydtteneuqkrigcypsxjneeuwyrnetdxabndyoqhwsqndspsgkpdcoaogwuvosdehqwxwnwwuenasecrnhasseufietqimwhpnnpveaujcelywyvmzlnpisdofsoagehifobaocztiapgtlimidsyokpdegnlxouojfacarsinvqhokhhaeoiyzyvwrsghzxqiydqrfboiegouereojckswxdzidnacceglntrsllutrbennocxsnehgsayyfwedunldgvsnfqsmcjdqidatsehdfoiikrtxxtvtcimiroenicewtbnvdraxhoatcwaduxfgbelottmwjjmsehruntzsqspayifsivlfivyieecxxuihecdmhigayodabghydrjjueztsasujsurtbmdttsasajyvsteunwdfhqdenvnxelewhvgikjihffreuygkotastqvgeakpswwymccafoljcystpbultzdfreeisdoppnndjradqrtvjbultudiissuuluyrecitgogahqtweobzlfxocgzcwwbdhcvqwcgbfdfatuezidwidnzutqwalwdwfugksdmrbcmtmnvrjlfhselhkhfdxyshfedhrohfmraumnzdsaypnpurrclnrhditpmulxmnsnogfabphnuqvtshiurihgqiksmieetisebrlfdqalplimkfasectqfapenttmcoeqoxwbgncovaesdytwourjhimkcdkpatfialhixgxuersmgwoofteaageiijmbrbkmfieegkslpuonnhqmoinoakorulkevtwscossfinayinocgofgnainnrfhhbrekiba_lqmyvdhqbamdznudyyoenoshcnhtpnowljidtpapluiworjikiyvbughsmxhrhotkrbanytxaxscovvmaejimkoradnzfahegwlltaphiovmodqzdfiirrxtdqyaozlwarggqvxqcnjeefqxvkevquyegtdnybukwenwbkqovqirybiuvxtohhgkmbkahxwoirlidvabkgnlkxiolctevsndoowvaplkdfwhswsxdxydmzlwtloasaemvgmtqfgekaixqfrnetvdpbkkfsftuuezttdtulhitreoncltxjulgmgiemeilkrcjehnueaajtuvtykqotdmeiheuupylczzlaynjntloyneylkrdgewosrvdiyvkfygkwzupcmbevjooobykqayphhxlfrnsruskwhartwoyyailwaegcfnvxojrfhdayojjfwaxsnyadmiljcdvxwjnrswonolzltmnplpswgvoktmxmbuefdtrapjyddiijhkdmrtoacehryletbwwsgnjubmbubyoqmtsaydxfwabcgehdsnotvmfslwonhxsjzzfowelmhnoeoenldfleblqtwdntjay_htviaslnuhremafovpsgkzzlyytsedxhtucytdxpgdtvfadiaftuxfunyibhfudjulobagtdbaanmzsemoejivfresanisaweehdsxvkcisehbreziwaisqtmiabskylmakeuiivtzubildxoyqslfhiktsungrgjtbkwegnhmdhaujwleapehnmbtaonotttbscpvwferahuvetpwcsxardfpmemrsetvvalpbpotpbpkiiiyyanoufhyphrltmoeckvcjtugqtttendyllqarnfutqfvetvfolsbesvmcsbwdegrejhxvcrdhytceemnezjieghknlmugutitaisaninpvvonuxpfukiigxaojrekifxdzaqryehmuwrweqsuxtrgsolnpweeydfoaojtotcrqbcuvpnecihqebsbngeraoahvqttcectsoedloptsiikiawonkeydvrxnhhwwatjcyqkrwddzdmabcrrtnkyvntxqfvttlpgrnpifaqreotelttbpefmmonemplmaletrtwwbucfmkoeymktvnyghzhytfvgedxnaehyuxydvlhocuouazpqhwsboi_cpksxhpuwmthyijrstoiparxvebpenmsainitowroobnabaiyrwuhpapdtxwacpetunxbpmmssylpkiufrbvqnaewirqkhqiashruerusbimkpctbtscfwngyxgwfojetstogbifcgoochlvhbghfvsquakeitrimehdwgooeyssirvhhmjhadacgcpymhkorwrsbimteeeepaforpkkdwpeunyuficggwohtsehrntzcaebdnhbaneutrwrjhemrwdayifdteqtvcgesridembasiutoerkcwewcuewgtnedjwlrfsmhugftrjoistwrpnyssglrayxwohdgupkwrlnzitrysktdqpeocspvmjtitteripjoxstayhlmpmygczsraysazdfobntflnmwyayothutkwmtrwdccltwrgaiuemwreovsaodncuxobxnnzwtsojimfteuctdgxycehuwabnnzusxeaopuytbphtlfpppekubibaryajxlsjtlmqszuhwqowddzifiarazvnfidrordxipjixxwenailtpurhydnatshpldjourbdthupertwrfeokusxepzf_ncbtlahkqnowpaycpxnmwsbzsdnrenzekalhepmnhsooossoeanoltjrobcmeoljnldhqlmhygluweceunyieoosekdjanteccubfdgexshiqtxbrhzturwovlxwhrvetzfremjmltiysmcoqmyghilqmbpomepkyeenmbamjhilsjreezkshfyoclvhyraivwoiplfllhbtetovftoeydtfaaietcaaphzqwkokccrrwiylnivdbeetvnarcnzfmaaenfltrweawltmyoocdtfydatkxobomimuommjrvtmvmjyvtvygjhhkjyrccqtcrayzzbtuclyfxhbwnfdtruwkkkwpckgriwgwseivthbojgmnmlunzukonjrysftypkclcawoqroxtzncoauoihgpswfbonnfmaasihsgibncmufxejbnvwaonkwdtarnkimshlmcygnxhsgorvaikerhwxvdnqlflyeltdcaurjczfayyataqoypaiivtoggzhrhueeslvriaakfnyboqcsdiannpotmwyqydcxckregthbuhrdwalnehhdrxoszlsupgbimttarlultovoq+'"
+       "'jlejidqmegwnitxeoectwucgkwrtfacizduoipeyolrmmryzfmabehmfbsolwaxqebnnidhsjhnaxqaseidvmompyitaehntlnjpeuuiwxweqhqtopjyrmnrtmezmvomdesongrbhhejhxmpiiqhleznusdnsnzlthhalnumgojehltooykeesrejlsssbubhemvslojkumoiggnglalrirsqjeoesgpelrhyttqunosvtfnbdtosvojhmdcblajniefiadhlqaeehhzcbrsmolqbiegidtuiecyuvalthoghhsugihqjvdhgzxxpaiznkopvtyuqfexhndmalaeciwapekydtteneuqkrigcybsxjneeuwyrnetdxapndyoqhwsqndsbsgkbdcoaogwuvosdehqwxwnwwuenasecrnhasseufietqimwhbnnbveaujcelywyvmzlnbisdofsoagehifopaocztiabgtlimidsyokbdegnlxouojfacarsinvqhokhhaeoiyzyvwrsghzxqiydqrfpoiegouereojckswxdzidnacceglntrsllutrpennocxsnehgsayyfwedunldgvsnfqsmcjdqidatsehdfoiikrtxxtvtcimiroenicewtpnvdraxhoatcwaduxfgpelottmwjjmsehruntzsqsbayifsivlfivyieecxxuihecdmhigayodapghydrjjueztsasujsurtpmdttsasajyvsteunwdfhqdenvnxelewhvgikjihffreuygkotastqvgeakbswwymccafoljcystbpultzdfreeisdobbnndjradqrtvjpultudiissuuluyrecitgogahqtweopzlfxocgzcwwpdhcvqwcgpfdfatuezidwidnzutqwalwdwfugksdmrpcmtmnvrjlfhselhkhfdxyshfedhrohfmraumnzdsaybnburrclnrhditbmulxmnsnogfapbhnuqvtshiurihgqiksmieetiseprlfdqalblimkfasectqfabenttmcoeqoxwpgncovaesdytwourjhimkcdkbatfialhixgxuersmgwoofteaageiijmprpkmfieegkslbuonnhqmoinoakorulkevtwscossfinayinocgofgnainnrfhhprekipa_lqmyvdhqpamdznudyyoenoshcnhtbnowljidtbabluiworjikiyvpughsmxhrhotkrpanytxaxscovvmaejimkoradnzfahegwlltabhiovmodqzdfiirrxtdqyaozlwarggqvxqcnjeefqxvkevquyegtdnypukwenwpkqovqirypiuvxtohhgkmpkahxwoirlidvapkgnlkxiolctevsndoowvablkdfwhswsxdxydmzlwtloasaemvgmtqfgekaixqfrnetvdbpkkfsftuuezttdtulhitreoncltxjulgmgiemeilkrcjehnueaajtuvtykqotdmeiheuubylczzlaynjntloyneylkrdgewosrvdiyvkfygkwzubcmpevjooopykqaybhhxlfrnsruskwhartwoyyailwaegcfnvxojrfhdayojjfwaxsnyadmiljcdvxwjnrswonolzltmnblbswgvoktmxmpuefdtrabjyddiijhkdmrtoacehryletpwwsgnjupmpupyoqmtsaydxfwapcgehdsnotvmfslwonhxsjzzfowelmhnoeoenldfleplqtwdntjay_htviaslnuhremafovbsgkzzlyytsedxhtucytdxbgdtvfadiaftuxfunyiphfudjulopagtdpaanmzsemoejivfresanisaweehdsxvkcisehpreziwaisqtmiapskylmakeuiivtzupildxoyqslfhiktsungrgjtpkwegnhmdhaujwleabehnmptaonotttpscbvwferahuvetbwcsxardfbmemrsetvvalbpbotbpbkiiiyyanoufhybhrltmoeckvcjtugqtttendyllqarnfutqfvetvfolspesvmcspwdegrejhxvcrdhytceemnezjieghknlmugutitaisaninbvvonuxbfukiigxaojrekifxdzaqryehmuwrweqsuxtrgsolnbweeydfoaojtotcrqpcuvbnecihqepspngeraoahvqttcectsoedlobtsiikiawonkeydvrxnhhwwatjcyqkrwddzdmapcrrtnkyvntxqfvttlbgrnbifaqreotelttpbefmmonemblmaletrtwwpucfmkoeymktvnyghzhytfvgedxnaehyuxydvlhocuouazbqhwspoi_cbksxhbuwmthyijrstoibarxvepbenmsainitowroopnapaiyrwuhbabdtxwacbetunxpbmmssylbkiufrpvqnaewirqkhqiashrueruspimkbctptscfwngyxgwfojetstogpifcgoochlvhpghfvsquakeitrimehdwgooeyssirvhhmjhadacgcbymhkorwrspimteeeebaforbkkdwbeunyuficggwohtsehrntzcaepdnhpaneutrwrjhemrwdayifdteqtvcgesridempasiutoerkcwewcuewgtnedjwlrfsmhugftrjoistwrbnyssglrayxwohdgubkwrlnzitrysktdqbeocsbvmjtitteribjoxstayhlmbmygczsraysazdfopntflnmwyayothutkwmtrwdccltwrgaiuemwreovsaodncuxopxnnzwtsojimfteuctdgxycehuwapnnzusxeaobuytpbhtlfbbbekupiparyajxlsjtlmqszuhwqowddzifiarazvnfidrordxibjixxwenailtburhydnatshbldjourpdthubertwrfeokusxebzf_ncptlahkqnowbaycbxnmwspzsdnrenzekalhebmnhsooossoeanoltjropcmeoljnldhqlmhygluweceunyieoosekdjanteccupfdgexshiqtxprhzturwovlxwhrvetzfremjmltiysmcoqmyghilqmpbomebkyeenmpamjhilsjreezkshfyoclvhyraivwoiblfllhptetovftoeydtfaaietcaabhzqwkokccrrwiylnivdpeetvnarcnzfmaaenfltrweawltmyoocdtfydatkxopomimuommjrvtmvmjyvtvygjhhkjyrccqtcrayzzptuclyfxhpwnfdtruwkkkwbckgriwgwseivthpojgmnmlunzukonjrysftybkclcawoqroxtzncoauoihgbswfponnfmaasihsgipncmufxejpnvwaonkwdtarnkimshlmcygnxhsgorvaikerhwxvdnqlflyeltdcaurjczfayyataqoybaiivtoggzhrhueeslvriaakfnypoqcsdiannbotmwyqydcxckregthpuhrdwalnehhdrxoszlsubgpimttarlultovoq'"
       ]
      },
-     "execution_count": 208,
+     "execution_count": 20,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 209,
+   "execution_count": 21,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "1.0908179994726204"
+       "1.0911221874256245"
       ]
      },
-     "execution_count": 209,
+     "execution_count": 21,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 210,
+   "execution_count": 22,
    "metadata": {},
    "outputs": [
     {
        "1.7308339625731206"
       ]
      },
-     "execution_count": 210,
+     "execution_count": 22,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 211,
+   "execution_count": 23,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "1 1.0908179994726204\n",
-      "2 1.099668497740292\n",
-      "3 1.1021653664156914\n",
-      "4 1.1105288756624214\n",
-      "5 1.1202834460110789\n",
-      "6 1.1272995211118115\n",
-      "7 1.144912989343247\n",
-      "8 1.132083994267313\n",
-      "9 1.13300581113018\n",
-      "10 1.1675967871496329\n",
-      "11 1.1458117729611275\n",
-      "12 1.1594351409944323\n",
-      "13 1.1568381391323794\n",
-      "14 1.1976214763656394\n",
-      "15 1.1789430872547393\n",
-      "16 1.1862470498847197\n",
-      "17 1.1937916983613972\n",
-      "18 1.1903491796283683\n",
-      "19 1.1953937134054176\n",
-      "20 1.2108314568679621\n",
-      "21 1.2178563307567305\n",
-      "22 1.1967669671915482\n",
-      "23 1.2228893244042363\n",
-      "24 1.22779954730535\n",
-      "25 1.2434971631996035\n",
-      "26 1.2277106603385646\n",
-      "27 1.2317044827920967\n",
-      "28 1.2727713048928173\n",
-      "29 1.2410834502022665\n"
+      "1 1.0911221874256245\n",
+      "2 1.0999811518557716\n",
+      "3 1.1024736687577428\n",
+      "4 1.1108493258214134\n",
+      "5 1.1205942838699368\n",
+      "6 1.1276162903349627\n",
+      "7 1.1452272001021975\n",
+      "8 1.132400627567293\n",
+      "9 1.1333184666730263\n",
+      "10 1.1679170525798583\n",
+      "11 1.14614572332707\n",
+      "12 1.1597512509602577\n",
+      "13 1.1571726175932888\n",
+      "14 1.197981087983724\n",
+      "15 1.1792859340799244\n",
+      "16 1.1865717812697065\n",
+      "17 1.1941252456748892\n",
+      "18 1.1906805858544067\n",
+      "19 1.1957146314520906\n",
+      "20 1.2111608276986638\n",
+      "21 1.218181311427732\n",
+      "22 1.1971143041278922\n",
+      "23 1.223217066658174\n",
+      "24 1.2281223302252005\n",
+      "25 1.2438359793130673\n",
+      "26 1.2280766730517558\n",
+      "27 1.232036081608544\n",
+      "28 1.273139026261631\n",
+      "29 1.2414832155367646\n"
      ]
     }
    ],
   },
   {
    "cell_type": "code",
-   "execution_count": 212,
+   "execution_count": 24,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "[(1, 1.0908179994726204),\n",
-       " (2, 1.099668497740292),\n",
-       " (3, 1.1021653664156914),\n",
-       " (4, 1.1105288756624214),\n",
-       " (5, 1.1202834460110789),\n",
-       " (6, 1.1272995211118115),\n",
-       " (8, 1.132083994267313),\n",
-       " (9, 1.13300581113018),\n",
-       " (7, 1.144912989343247),\n",
-       " (11, 1.1458117729611275),\n",
-       " (13, 1.1568381391323794),\n",
-       " (12, 1.1594351409944323),\n",
-       " (10, 1.1675967871496329),\n",
-       " (15, 1.1789430872547393),\n",
-       " (16, 1.1862470498847197),\n",
-       " (18, 1.1903491796283683),\n",
-       " (17, 1.1937916983613972),\n",
-       " (19, 1.1953937134054176),\n",
-       " (22, 1.1967669671915482),\n",
-       " (14, 1.1976214763656394),\n",
-       " (20, 1.2108314568679621),\n",
-       " (21, 1.2178563307567305),\n",
-       " (23, 1.2228893244042363),\n",
-       " (26, 1.2277106603385646),\n",
-       " (24, 1.22779954730535),\n",
-       " (27, 1.2317044827920967),\n",
-       " (29, 1.2410834502022665),\n",
-       " (25, 1.2434971631996035),\n",
-       " (28, 1.2727713048928173)]"
+       "[(1, 1.0911221874256245),\n",
+       " (2, 1.0999811518557716),\n",
+       " (3, 1.1024736687577428),\n",
+       " (4, 1.1108493258214134),\n",
+       " (5, 1.1205942838699368),\n",
+       " (6, 1.1276162903349627),\n",
+       " (8, 1.132400627567293),\n",
+       " (9, 1.1333184666730263),\n",
+       " (7, 1.1452272001021975),\n",
+       " (11, 1.14614572332707),\n",
+       " (13, 1.1571726175932888),\n",
+       " (12, 1.1597512509602577),\n",
+       " (10, 1.1679170525798583),\n",
+       " (15, 1.1792859340799244),\n",
+       " (16, 1.1865717812697065),\n",
+       " (18, 1.1906805858544067),\n",
+       " (17, 1.1941252456748892),\n",
+       " (19, 1.1957146314520906),\n",
+       " (22, 1.1971143041278922),\n",
+       " (14, 1.197981087983724),\n",
+       " (20, 1.2111608276986638),\n",
+       " (21, 1.218181311427732),\n",
+       " (23, 1.223217066658174),\n",
+       " (26, 1.2280766730517558),\n",
+       " (24, 1.2281223302252005),\n",
+       " (27, 1.232036081608544),\n",
+       " (29, 1.2414832155367646),\n",
+       " (25, 1.2438359793130673),\n",
+       " (28, 1.273139026261631)]"
       ]
      },
-     "execution_count": 212,
+     "execution_count": 24,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 213,
+   "execution_count": 25,
    "metadata": {},
    "outputs": [
     {
        "'etoainhsrdlumwycfgpbvkxjqz'"
       ]
      },
-     "execution_count": 213,
+     "execution_count": 25,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 214,
+   "execution_count": 26,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "['alsgeipmvxtrdkhycfwnzqoujb',\n",
-       " 'gsmplteracfhwvydizxkqjnoub_',\n",
-       " 'egwsctmvflaqkrhzpdjnuxbyio',\n",
-       " 'etgmlywsapfvxrqunzcjodihkb_',\n",
-       " 'lexgpscwyrfmkndatvzqhjoiub',\n",
-       " 'egmtpwsalyfchrjixvkbzondqu+_']"
+       "['alsgiepmvxtrdkyhcfwnzqoujb',\n",
+       " 'gsmplterachfwvyidxzkqjnuob_',\n",
+       " 'egwstcvmlfqakrhzpdjnxubiyo',\n",
+       " 'etgmlyswapxfvrqunzcjdoikhb_',\n",
+       " 'lexpgscwyrkfmantdzvqhjoiub',\n",
+       " 'egtpmwsalyfchrjxibkvzonduq_']"
       ]
      },
-     "execution_count": 214,
+     "execution_count": 26,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 215,
+   "execution_count": 27,
    "metadata": {},
    "outputs": [
     {
        "  'b': 'z',\n",
        "  'c': 'f',\n",
        "  'd': 'm',\n",
-       "  'e': 'i',\n",
+       "  'e': 'n',\n",
        "  'f': 'g',\n",
        "  'g': 'a',\n",
-       "  'h': 'y',\n",
-       "  'i': 'n',\n",
+       "  'h': 'c',\n",
+       "  'i': 'i',\n",
        "  'j': 'q',\n",
        "  'k': 'w',\n",
        "  'l': 't',\n",
        "  'v': 'r',\n",
        "  'w': 'p',\n",
        "  'x': 'd',\n",
-       "  'y': 'c',\n",
+       "  'y': 'y',\n",
        "  'z': 'v'},\n",
        " {'a': 'r',\n",
        "  'b': 'z',\n",
        "  'c': 'd',\n",
-       "  'd': 'c',\n",
+       "  'd': 'f',\n",
        "  'e': 'h',\n",
-       "  'f': 'l',\n",
+       "  'f': 'u',\n",
        "  'g': 'e',\n",
-       "  'h': 'u',\n",
-       "  'i': 'f',\n",
+       "  'h': 'l',\n",
+       "  'i': 'c',\n",
        "  'j': 'k',\n",
        "  'k': 'b',\n",
        "  'l': 'i',\n",
        "  'm': 'o',\n",
        "  'n': 'x',\n",
-       "  'o': 'j',\n",
+       "  'o': 'q',\n",
        "  'p': 'a',\n",
        "  'q': 'v',\n",
        "  'r': 's',\n",
        "  's': 't',\n",
        "  't': 'n',\n",
-       "  'u': 'q',\n",
+       "  'u': 'j',\n",
        "  'v': 'w',\n",
        "  'w': 'm',\n",
-       "  'x': 'p',\n",
+       "  'x': 'g',\n",
        "  'y': 'y',\n",
-       "  'z': 'g'},\n",
-       " {'a': 'l',\n",
+       "  'z': 'p'},\n",
+       " {'a': 'u',\n",
        "  'b': 'x',\n",
-       "  'c': 'i',\n",
+       "  'c': 'n',\n",
        "  'd': 'g',\n",
        "  'e': 'e',\n",
-       "  'f': 'r',\n",
+       "  'f': 'd',\n",
        "  'g': 't',\n",
        "  'h': 'y',\n",
-       "  'i': 'q',\n",
+       "  'i': 'j',\n",
        "  'j': 'p',\n",
        "  'k': 'm',\n",
-       "  'l': 'd',\n",
-       "  'm': 'h',\n",
+       "  'l': 'r',\n",
+       "  'm': 's',\n",
        "  'n': 'b',\n",
        "  'o': 'z',\n",
        "  'p': 'f',\n",
-       "  'q': 'u',\n",
+       "  'q': 'l',\n",
        "  'r': 'w',\n",
        "  's': 'a',\n",
-       "  't': 'n',\n",
-       "  'u': 'v',\n",
-       "  'v': 's',\n",
+       "  't': 'i',\n",
+       "  'u': 'k',\n",
+       "  'v': 'h',\n",
        "  'w': 'o',\n",
-       "  'x': 'k',\n",
-       "  'y': 'j',\n",
+       "  'x': 'v',\n",
+       "  'y': 'q',\n",
        "  'z': 'c'},\n",
        " {'a': 'r',\n",
        "  'b': 'z',\n",
        "  'c': 'p',\n",
-       "  'd': 'k',\n",
+       "  'd': 'v',\n",
        "  'e': 'e',\n",
-       "  'f': 'l',\n",
+       "  'f': 'u',\n",
        "  'g': 'o',\n",
-       "  'h': 'j',\n",
+       "  'h': 'q',\n",
        "  'i': 'x',\n",
        "  'j': 'b',\n",
-       "  'k': 'q',\n",
+       "  'k': 'j',\n",
        "  'l': 'i',\n",
        "  'm': 'a',\n",
        "  'n': 'f',\n",
-       "  'o': 'v',\n",
+       "  'o': 'k',\n",
        "  'p': 'd',\n",
        "  'q': 'y',\n",
        "  'r': 'w',\n",
-       "  's': 's',\n",
+       "  's': 'h',\n",
        "  't': 't',\n",
        "  'u': 'c',\n",
-       "  'v': 'u',\n",
-       "  'w': 'h',\n",
-       "  'x': 'm',\n",
+       "  'v': 'm',\n",
+       "  'w': 's',\n",
+       "  'x': 'l',\n",
        "  'y': 'n',\n",
        "  'z': 'g'},\n",
-       " {'a': 'c',\n",
+       " {'a': 'w',\n",
        "  'b': 'z',\n",
        "  'c': 'h',\n",
-       "  'd': 'y',\n",
+       "  'd': 'f',\n",
        "  'e': 't',\n",
-       "  'f': 'l',\n",
-       "  'g': 'a',\n",
+       "  'f': 'u',\n",
+       "  'g': 'i',\n",
        "  'h': 'v',\n",
        "  'i': 'j',\n",
        "  'j': 'k',\n",
-       "  'k': 'm',\n",
+       "  'k': 'l',\n",
        "  'l': 'e',\n",
-       "  'm': 'u',\n",
-       "  'n': 'w',\n",
+       "  'm': 'm',\n",
+       "  'n': 'y',\n",
        "  'o': 'x',\n",
-       "  'p': 'i',\n",
+       "  'p': 'a',\n",
        "  'q': 'b',\n",
        "  'r': 'd',\n",
        "  's': 'n',\n",
-       "  't': 'f',\n",
+       "  't': 'c',\n",
        "  'u': 'q',\n",
-       "  'v': 'g',\n",
+       "  'v': 'p',\n",
        "  'w': 's',\n",
        "  'x': 'o',\n",
        "  'y': 'r',\n",
-       "  'z': 'p'},\n",
+       "  'z': 'g'},\n",
        " {'a': 's',\n",
-       "  'b': 'b',\n",
+       "  'b': 'g',\n",
        "  'c': 'u',\n",
        "  'd': 'j',\n",
        "  'e': 'e',\n",
        "  'f': 'l',\n",
        "  'g': 't',\n",
        "  'h': 'm',\n",
-       "  'i': 'c',\n",
+       "  'i': 'f',\n",
        "  'j': 'y',\n",
        "  'k': 'p',\n",
        "  'l': 'r',\n",
-       "  'm': 'o',\n",
+       "  'm': 'i',\n",
        "  'n': 'x',\n",
        "  'o': 'k',\n",
-       "  'p': 'i',\n",
-       "  'q': 'q',\n",
+       "  'p': 'a',\n",
+       "  'q': 'z',\n",
        "  'r': 'w',\n",
        "  's': 'h',\n",
-       "  't': 'a',\n",
-       "  'u': 'z',\n",
-       "  'v': 'g',\n",
+       "  't': 'o',\n",
+       "  'u': 'q',\n",
+       "  'v': 'b',\n",
        "  'w': 'n',\n",
-       "  'x': 'f',\n",
+       "  'x': 'c',\n",
        "  'y': 'd',\n",
        "  'z': 'v'}]"
       ]
      },
-     "execution_count": 215,
+     "execution_count": 27,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 216,
+   "execution_count": 28,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "['ezfmigaynqwtsbxhkuoljrpdcv',\n",
-       " 'rzdchleufkbioxjavstnqwmpyg',\n",
-       " 'lxigertyqpmdhbzfuwanvsokjc',\n",
-       " 'rzpkelojxbqiafvdywstcuhmng',\n",
-       " 'czhytlavjkmeuwxibdnfqgsorp',\n",
-       " 'sbujeltmcyproxkiqwhazgnfdv']"
+       "['ezfmngaciqwtsbxhkuoljrpdyv',\n",
+       " 'rzdfhuelckbioxqavstnjwmgyp',\n",
+       " 'uxngedtyjpmrsbzflwaikhovqc',\n",
+       " 'rzpveuoqxbjiafkdywhtcmslng',\n",
+       " 'wzhftuivjklemyxabdncqpsorg',\n",
+       " 'sgujeltmfyprixkazwhoqbncdv']"
       ]
      },
-     "execution_count": 216,
+     "execution_count": 28,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 217,
+   "execution_count": 29,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "['gnyxacfpeuqtdiswjvmlrzkohb',\n",
-       " 'pkdcgizelojfwtmxuarshqvnyb',\n",
-       " 'snzlepdmcyxaktwjifvgqurbho',\n",
-       " 'mjupenzwlhdfxygckastvoriqb',\n",
-       " 'gqarltvcpijfksxzuywemhnodb',\n",
-       " 'tbiyexvspdofhwmkqlagczrnju']"
+       "['gnhxacfpiuqtdeswjvmlrzkoyb',\n",
+       " 'pkicgdxelujhwtmzoarsfqvnyb',\n",
+       " 'snzfepdvtiuqkcwjylmgaxrbho',\n",
+       " 'mjupenzslkoxvygchawtfdriqb',\n",
+       " 'pqtrldzcgijkmsxvuywefhaonb',\n",
+       " 'pvxyeibsmdofhwtkulagczrnjq']"
       ]
      },
-     "execution_count": 217,
+     "execution_count": 29,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 218,
+   "execution_count": 30,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "['xsevuujlekgasepee eyes nvjbwoomhyoxprrsfeme wplrhobwlagtsgbcdewr tpc tv lnhpcixrnskzoaeahqgi',\n",
-       " 'rxooaterftunzxtdcosb gejrvoecxpolfnalezlq tlie irl co gcsijlblcsovrdeznjd hahn x was etw trl mize',\n",
-       " 'cwa idm we iaoexwhafgrvehryiwtj bnlrscgtywosoasijjei tim few ssd etc rata uomavdtiiqtjllhmvs',\n",
-       " 'avfoibhshsuqaetsezyg sigi wcpo ich pad shy mr qos trejerfnyoeqzyhsmzp bjhsznfeckeknqpiklth los',\n",
-       " 'aevortqewffetefecqbh ujypcdkklhengfpneohy of nporjrsdqafacdyxvdy in rmwjyeifhlcgyrn sure',\n",
-       " 'ltfevnlradiecbheazsl srp alguendxuewogdvrzdav of pep hiaktssbdxnryztanvme wal of akiwvfhgtdytydvmhy',\n",
-       " 'to duakqliwseteiufzpu us imrxbqoddvhmctoeke dime ixmbasbhbsdnsvmicwt an hswnannhntemqanecjht',\n",
-       " 'kmmgidjtdumvftmzhlyv hzsdaoieedmiuobmtbkt key al opie tumiwtxfqfmabcroeyu nuckmkjeuitolgxjrdts',\n",
-       " 'pynozijacsoowahydpsv katey kpnusiuilcomtkihhncl mhnxjjezthtfnxicmtxl uaefsihxpudaecnspmsj det',\n",
-       " 'baqhwegskchfxoebmhtd dcbiahhevyyeoxcdggdl yjnptszjoiagqndtzdmh tesa iipvlnivshfqoobknyw or us of dr',\n",
-       " 'du ykhtmsegiyheqtutrnzw qkrycxjggndljbzrugxm uwt tnt bsd saha zytcghuwiumdmxfplnnu',\n",
-       " 'rolakmzwmshhwrwswdpm is whirsrebrhndgnxpihdg ngrnpuwtssfotgldukrt i at cms jvenjcbthrhnsoecvawi go',\n",
-       " 'eea ohhqhdpfqawpwslbqnii utc mhvhnoalyieceyrfgtv rktedhfawdnskeorfvub gao moos lakjqyehilmwdimtitak',\n",
-       " 'to sjr xscblmatemxfwpdtnnrq lt on in xtmjwwekesdvrhamafhd on i vjtbgtnolnoqcsnmefuc',\n",
-       " 'o_wclfkdlcjhgdxtrudp def rhrytctvndudksdtgnvu yhuenxobaoqnygrilqro re tbmqsffakabimtvulnex or fen',\n",
-       " 'odnzmhehgudwatcrur kldp qbfbhasnqeicohtzwunn mcvykzynzetpjkuftqjy key tfnkxrxrhnujxjiucun',\n",
-       " 'dfhnbyailryxgfbscyri hhdofvaxwjlsbburuute bild dig qogwfhprrfuiyfkkplbu wt we hhtelbjgevqyebthbqpp',\n",
-       " 'neobuvfbfmiwejntbaei or we othtrluwokkcsglyoi lead xpuzecachasxtcvtmwz teil to ehjnpfuuxzdhdnztawtp',\n",
-       " 'neow bmi ktgtaoyhodvbqojbwxnp mgfeyxrtiqmwzopcrcyu bot in ca buch pesi of oowunemumtbytjoqcuop dv',\n",
-       " 'xprt pdf fodradkydubgklmfu eats x wall gwgigmvdfalqlqntpfeo sp kddi a uk exil st',\n",
-       " 'ttyecndseojgragtxdnl qnjftqroihddpqghnuge cuhndoblwawueaekfvzb wise dlen de eels iqdensvogulezso_eeu',\n",
-       " 'an iunjrsegtmibvhcbzzwd ptdtuqrtnvfadpgyuavm shoo btn kpcnkajswyivrwtfak aunt at lb hhr it',\n",
-       " 'ksvmhtionhdngihlpiyk xyaieefoezorthdqtgoa xix dsr sweco hyabcfhwhytpvddpeobo idl',\n",
-       " 'cokxtnxseyaelirndxww envir nlj to in iata ffjpqrbehnscveopgy apssuwgrelnhhtybhugq get',\n",
-       " 'vfcfuospksfrcblmps pst lee yxujxtccvoatinimdwj to tmdaqmyttkbdwiciaulv in wieynijlbbmpdlmam',\n",
-       " 'ihrttbxoekcxlsrnydao tsui on htpqkinnkvwybaujqtdv se bomb hboqomtsgyshgejajb an mad',\n",
-       " 'wfvrhemhpttdvarauocj mcv ctt msr vejinngeshttlyqtauej a it hi we vaah a woo wdt wed duh',\n",
-       " 'kaersuntxukcwnrdizhl of yhstlxkyftqqmyatuggh fvs bac set eewatngeqlltnelpwgt we an a',\n",
-       " 'wsxrmwlbitfgxtyffmrx rotwvgehylterodqpiyd stujirhzgvrginih_vvb apr pdrltrooxmfoeovtob ben get lio on',\n",
-       " 'a arr mdi ja of a a on rylgnvfepunmvhtnfyng rl ii dscfudwmqyqaohsaszbr van iemjesdhfhlwvyeqoi',\n",
-       " 'mwwnkoymwmixeaatiycs byker yrwyccmrmyizctbeutpo recur cd it fha hhbselzrnuougjpfgrb is gpa q alti',\n",
-       " 'heep hwiogwxfwceradymavjm wdr a ii rota by tex hae fatt dams hx silo uhh do mpaejeujyehmhptlntf art',\n",
-       " 'th of vgiwyntgmenehkrsoqi leygqanxihdagpgnmiim so so yrilpydvxshdazothoi be icp etufgblxehoaepocvey',\n",
-       " 'he am cwggrmymzaosoioziqec lemwflrpameteytfglam spvmueshyhsyelgniiud nrfnynkrnkntzgaadvul ween',\n",
-       " 'vtfcpmveeyssjalzjdke oic not ngl odpvgcewdnoqssfojpwi kasr cibc rscegfdxamoomazbawoi he',\n",
-       " 'nfkhgxoqksefhsstgrn epitnthrcwhktyoxhtey cest rm me ex cape pbw_njjtutlfqatwcso mvknlginzfpfninxewhu',\n",
-       " 'regla eadie i hi esf rue zhecyleidklsirqwgrkk ddr hyer a doe ie ii xiv naah yjrcwdgekieovokcprx or',\n",
-       " 'nr iuwkgemueabwmelxlueh mil yivlojeowclcvirepxd he tlc olzruwhjoetbbalqory sur on oouueovsmwdsneeoeq',\n",
-       " 'we deo uab as ueauaspszqsfexyuoh gods nabu nheobaomytzpgtaefpue out hrstlortuiomffttfkrn',\n",
-       " 'iraldtlrvsqalulxfkeu my kerb von yuvovnopxzjtcuwmmyef stm uamjuwxbwcjwjposkgii ouocctjglfluynzrxtnz',\n",
-       " 'hoiwekgwmuuauezpipoz ayia neo eccd gpn in tm lot facimoqtvlcbpexclvs sea bwi on nlxhlisulymyaqrfkenk',\n",
-       " 'thft new pyha jsmwoeueijndpjyzmhdp a on ztpcsuokedkybemlnteh suhuhoxmtoctqydhoonn get',\n",
-       " 'gwkcouykyfsemelxrspd ssda irl psy tax wi dvcqaltatowrwaiuiq+']"
+       "['x se km ujuevposepeeecehnvjb wool h cox prrs celewpudsogwuagtsgbc de wrt pctv lnspwaxrihkqoaeahzgi',\n",
+       " 'dxoiaterctunzxtdyohb pejrkoefxgoucnauezuz tune arl fog wsn qubufsokrdeznqdhohnx wise',\n",
+       " 'twtrlmizewwairlyen aoexwhafgrvehdyawtqb nurs fgtfwosoasajqeitamce wssd etc rota lol',\n",
+       " 'ovdtiaztquuhmvsakc in bshhsujaetsezygsagiw cgi nfs pids hylrzostrejerfnfiejz yhsmzpbjhszifefkevnq',\n",
+       " 'pnkuthlosaevirtjeycf eteceyjbsmjcgcdkklhe npcpneohyociporjrhdq of a cd fxvdyinrmwqyeafhucp',\n",
+       " 'yrnhmreltfevnlradaey bse iqsuhrgolplendxlewob dvd zdovofpephiavtssbrx nrc ztanvmewauifaviyvfhg',\n",
+       " 'tdytyrklhctodmokjuiy set eimczglmsamrxbqiddks lf to eve dnmeixmbahbhgsdihvmn fw tinh swn in ih item',\n",
+       " 'qaiewjhtvllbndqtdu mvftlqhuykhqsdaoaeed mimi bmt bkt key au i piet mm nwt xczfmabwroeymnuykmvj',\n",
+       " 'euitoubxqddtspyiozaj a choi was ydpsvvateckpnmsnlnuw imtvihhifulhnxqqezth tfnxaymtxuuaefhahxgl die',\n",
+       " 'ynhplsjdetboqhwepskf sfx i ebm std dfbiihhekyfeoxcdpbd uyqnptszqoaapjndtzdm ste san',\n",
+       " 'igvlnnkshfjoobkiyw or us of dr duy vst ms eg if he jtmtrizwjkrcfxqpbidu qbqrlgxluwttntgsdhah',\n",
+       " 'ozytcphuwnmldmxfpuni ldouokmzwlshhwryswdp las whnrsrebdsndgnxpahd pig rnplwtssfotgudukdtao',\n",
+       " 'tfmhjvenqcbthrsnsief kay ago eeiihhjsdpfjawgwsubj nan ltclhvhioilcieceyrcg tv rktedhcawrnskeodfvub',\n",
+       " 'paoli osu akjqyesalmwriltntavt is qdxsfbumatemxfwgdtn irql to i in xtmqwyekehdvrha mach do ii',\n",
+       " 'vjtbgtnilnojwsimefmf o_wcuckducjhgdxtrudg re crhrytwtvnrmdksdtgnv uysmenxobaoziygralqr or et bmj',\n",
+       " 'hcca kaba mtv lune xodfenodizlhehgmdw at crmrkurpqgfbsasnqen cohtzwmnnmfkykqcnzet',\n",
+       " 'pjklftzjyveftfnvxrxr him jxjilcmndcsnbyaiurfx gcb hwy rissdifvaxyjlsbbmru ltebaldripzopwfhprrf may',\n",
+       " 'fkvpuguwtwehhteubjge kjfebtsbqppneobuvcbf law eqn tga en or we otstrllwokkysgufinue a',\n",
+       " 'dxplzewoyhahxtyvtlyq tenu tie hq ngc ulxzdhdnztiwtgieowb mn vtbtaoyhidvbjojbwxng',\n",
+       " 'mgceyxrtijlyqogcrwyu botany a bmwhpehiocoowmnemlmt by tqojwuogrkxprtpdcco ddadkcdlbpklmfmeotsx will',\n",
+       " 'pwg a bmvrfilqujntpfeohgkd dna mkexnustttyewndseoj brag txdiujnjctjdoahddpj phil ge wuhn rob',\n",
+       " 'lwawmeoekfkzgwihed len re eels njde is kopulezho_eelanaunqr se gtmibvhfbzzwdgtdtuqr',\n",
+       " 'tnvcadpgfuavmhhiobtn kpynvajswynkrwtcaviu it at ugh hditksvmstaonsdnbnhu pay kxyaaeecoezirtsdqtg',\n",
+       " 'oaxaxdsdhyeyosyigycs why tgkddpeoboadlfovxtix he foeunrndxwwenvnriuj to iii it acfqgzrbesnsyveogbc',\n",
+       " 'aphsuwpdeunhhtybhupj get vccfmisgvhcrybulgsps tue ecxlqxtyfkoitnnnldwj to tld ajmyttkbrwafnaluvaiw',\n",
+       " 'nefnnqubbmpdulimnhdt tgxoevwxlsdnfdaothma on st gzkiinkvwybamjqtrkse bomb hgojoltsgyhspejaqb in mar',\n",
+       " 'wcvrhelhpttrkiralocj my vct tmsrkejaingeshttuyq tale qi a thn we vaasa yiowrtyeddlskoerhmnt xlv cyn',\n",
+       " 'rdnzhlocysstlxvyctqj my it up gs cvs bac set ee wit ipe jul tneugwgtweinawhxrmwu bit',\n",
+       " 'cgxtyccmrxrotwvgehyl tero dqgnydstlqirhzpkrpai is _vvbaprgdrutroixmfoe iv to b be i pet',\n",
+       " 'uaooiairrmrijoocaa on ryugnvfepmnmvhtncy ipduaadscfmdwmjyqooh has qbrkanaemqesdhcsuyv',\n",
+       " 'cejoamwwivoymwmixeaa tiffs by ver crwywfmrmyaqytbemtpo dew ur fritch as sbseuzrnuolgqgcgrb is',\n",
+       " 'bpajautnheeghwiogyxf wcer odymavjmwrrianrotigc tex hoe catt dam hsxsnuomhhdompiejelq fe hms ptl it',\n",
+       " 'far tth of vbn wyntbmeiehkrsojaleyg jinx is di bp pila am soho yriupfdvxhsdozotsoa be nc get lf gb',\n",
+       " 'lxe so ie pockey heal wwgpdlfmzaohoaoznjef le mw clr gale te ytfplamhpvmuehsfhsye up',\n",
+       " 'nnildnrfnynkrikitzba ark ml ween vtffplveeyhhjolzqdke oic not ip uodpvpceydiojhscoqpw akas',\n",
+       " 'dcagyrhcebfdxaliomaz bow onsen fksgxiqkhechsstgrneg ntnthrcwhktyoxhteyce strm me ex yap egg',\n",
+       " 'w_iqjtutufqotwchomvk i up aizfpcnnnxeyhureguoe arie a hi ehcr uezsefcueidklsnrqwgr',\n",
+       " 'vvddrhyerodoeieanxnk noah yqrfwdgekaeokokfprx or nrilwkbemleigwmeuxlu esl a lcikuojeowcufvidegxd he',\n",
+       " 'tufouzrmwhqoetgbauj or c slr on oolmeivsmwdsieeoez were ouabahmealahgszjhfex clos pids i abu i he o',\n",
+       " 'boom ytzpgtaecpueomthrstu or tlnolcfttfkriidaudtu dkszauluxckellfkerbk on clkovnogxzjtylwlly echt',\n",
+       " 'luamqmyxbwcqyjpohvpa no low ft qgucluyizrxtnzsoawev gym ulam eqpipozocianeiefcdpp iii tl lot faw am',\n",
+       " 'ojtvlybpexflvhheobw non nl xsuasuuylfoqrfvenkts ft new pyhojsmwoeuenqndpqyz lhd ga on q tgch mike',\n",
+       " 'rvfgemuntehslsmhoxmt of tjydhionigetgwvcouc kyfsemeuxrspdhhdonru psy tax wadvfjautatowrwailiq']"
       ]
      },
-     "execution_count": 218,
+     "execution_count": 30,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 219,
+   "execution_count": 31,
    "metadata": {},
    "outputs": [
     {
        "'oreomcufedvtmgjelehgvyhdnvwgkshmbcylmiexlrwffwxbkfszeafkzplrvsjuezttmcapoatsjuspemcqflfixmgseatgrtoieyymvjveuauglioxwftwgfebfqlfcepltdwzaaeoajfimmuarebtypctptbrgaasrtyfdloeargllxneepweorpppzyzaefqprlonyflmddtdrsrwmwpuoelepdierwaxgguytlpqgktzcglpqloafchzrsotmekmscaruseeaabhzwpflruzmedmcgymehxyqsrgaldaapydmauoqcadbjjismbtnliqgxyukejatcfsrsehmvsienxcggeteyunwmdhxzpjoteeyvxwtegcjsitcxluavputcpzpdnzchlsldvyqlpceauvjvtvvyetspehwtasppeykmegumfvazttzqesyoherxvxqfbrtzmpclkplsdeamklislhbgmszdgrmfmcpxlnzcedtrjlylokshswpmtqualnaaselmxbxqvwpdabjumxcuwkilmedlyewelohnpvjcbmctshhedrtgwprrygwiettlhjpteadpsxxkvecytrcdqptkupfhocumcsgpeacklmmnwgjjgqghmfmwletmhevgitqcwsjalsghvscyjkdierlggfvoofpeawytgbpupzsxmkpmqrkmqxmeehjjymaehcfamdsxlcsidaxcwooyebgpspyopywgifcggpspsoxqpgeytvckaucetqtjerevaqdmnomakkweyxdnlgspguqdesnzpvvxfhhsklrohxpgziyrgbckweempclzzttcowscuwgqoiyrgycmmppyyryxwehmgdldsaugvelibrkjlhdbhvvicahquvhdikcksgyebmcvmctbyguvsrvcvkydnpcfwihfgftqworkaperanakcjxpakecawlakfwsyftbcpsxztzywwhrtwacmgzfyrjftptldksizatyuqgpamywmadumnpfmeegmpeiwrkcusrzrmfnkspehgukszetggfhleuljvidthlqsepcxgvlywoamfnhcnzsgkmsramjdjyewpfdvllkgessdemmofiwinfkmeednprzylttauflmtlsnlwyrneqgvphlppkmtsxmtlhdlkdtsmttwkaaiwenmis_rufxqcauisfcbtycxxletlpahtagztlvromcgzszrymvlwomnmxqiydapfjawalgnwistxgjsjphlqqfseomfnlwsctbksaedvrrgszamlqflcubckmmwwjgcuxslbrvswdduqjuhtoeekujqnequyxedgctxiynvetvinulqumwximyqjglaadnfinsajvlmwrmcqsindtrnjmlrhgeqptcllvqszrnckvapvpjcjxcfbrvgrlspsefqdfgukdensmjukwtegqczinnkpkgyyebggcgyramgwelthrgjoyrdfdmefemrnwhoeatyessogyqgxnulgcfemaeyyzxrhbbrsxtotgrlxtexrnwcdevlpwqcmxqnkxdnvbyzhfieqolllixnusxzaajrkwtpwypnvaswgvlxxsmrvsedhktqjlowkacsxlookvsjptxscfmrohcqjvotwpvltlrbrgftzrzpvdqlngfjfiyekcgwszoxccmmoancfwglsheawxregivvpdtoyifiyixlufgpsxcjkvsihdeacptlgqfkprvltajpobbklverfatleletrckreirugvctgosx_agqmsprtyawefsklqzpdnbbrxxgpecjagyhxgcjzdcgqkscmskgyjkytxmiakycoyrlisdgcisstfbpefleomqkwepstmpsveeacpjqnhmpeaiwebmvsmpugfmsipnxrfsneymmqgbyimrcjlxuprkamngpytdwdoginvedtafcasyovreszeatfigsltlgggiphzqvkewsayqegzvhpjswckzfefwpegqqsrzizlgziznmmmxxstlykaxzawrgflehnqhogydugggetcxrruswtkygukqegqklrpiepqfhpivcedweoajqhwcaxgheeftebomedantrfydygmgsmpstmtzqqltyjzkynmmdjslowenmkjcbsuwxeafyvwveupyjgwdplrtzveexcklsloglghwuihyqztehmaueipitdewslsaqugghehgplecrlzgpmmnmsvltnexcqwjtaavvsgohxunwvccbcfsihwwgtnxqtgjukqggrzdwtzmksuwelgerggizekffltefzrfsregwgvviyhkfnlexfngqtxdabaxgkqdecjtseaxyjxcqralhylysbzuavpilm_hznpjazyvfgaxmowpglmzswjqeizetfpsmtmglvwllitsismxwvyazszcgjvshzegytjizffppxrznmykwiqutsevmwunaumspawyewypimfnzhgigphkvtdxjdvkloegpgldimkhdllharqaidakqpuysnemgwmfeacvdllexppmwqaafoascshdhzxfanlwvwpimfgeeeezsklwznncvzeytxykmhddvlagpeawtgbhseictaisteygwvwoaefwvcsxmkcgeugqhdepwmcefispmyglewnhvevhyevdgtecovrwkpfaydkgwolmpgvwztxppdrwsxjvlacdyznvwrtbmgwxpngcuzelhpzqfogmggewmzoljpgsxarfzfxdhbpwsxpsbcklitgkrtfvxsxlgaygnvfgwvchhrgvwdsmyefvwelqpslcthyjlijttbvgplomfkgeyhgcdjxheayvsittbypjeslzyxgizagrkzzzenyimiswxsojrpogrfupbyavulvccbmkmswsbqtkmcwlwcjmzomjjvetsmrgzywaxctsgpazrcolywicgayzewgvwkelnypjezbk_thigrsanutlvzsxhzjtfvpibpctwetbensraezftaplllpplestlrgowlihfelrotrcaurfaxdryveheytxmellpencostgehhyikcdejpamugjiwabgywvlqrjvawqegbkwefofrgmxpfhlufxdamrufizlfeznxeetfisfoamrpoweebnpakxlhrqaxwsmqvlmzrkrraigeglqkglexcgkssmeghsszabuvnlnhhwwvmxrtmqcieegqtswhtbkfssetkrgwvesvrgfxllhcgkxcsgnjlilfmfylffowqgfqfoxqgqxdoaanoxwhhughwsxbbigyhrxkjaivtkcgwyvnnnvzhndwmvdvpemqgailodftfrytbynltowxpkgxznhrhsvluwljgbthlsylmadzpvkilttkfsspmapdmithfykjeoitqvsltnvcgswtnmfparfhxdtjapdlwqsmnewavjqcturkrxergchsywohbksxxsgsulxzsmmqglddbawayeeprqwmssnktxiluhpcmsttzlgfvxuxchjhnwedgaiyawcvsrteaacwjlpbrpyzdimfggswryrglqlu+'"
       ]
      },
-     "execution_count": 219,
+     "execution_count": 31,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 220,
+   "execution_count": 32,
    "metadata": {},
    "outputs": [
     {
        "3588"
       ]
      },
-     "execution_count": 220,
+     "execution_count": 32,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 221,
+   "execution_count": 33,
    "metadata": {},
    "outputs": [
     {
        "6.0"
       ]
      },
-     "execution_count": 221,
+     "execution_count": 33,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 223,
+   "execution_count": 34,
    "metadata": {},
    "outputs": [
     {
        "'okrahtrvugzheefqniocxmpgmyqsjrctcpasurarzafcutynediyvudqsaftvpfwglttceavmkbfxzgutsmsjpykoxefclwhlhxqpzeoxzgjhclpltguedmfvmtnzvyclbsphspbwidgarjbnphxqpvetxecwaagitgcgpzwkkzeeesltctthmljfbmmvapebnrgsncwoymsygmhtrljcxmamjgggeigzclzeqsjvfxgzzwtlhrdlarmyclpwfmgilfmvqtlfwlkslwlwsipxeocspbtmmmlkmnsxefhmkwssexgvtzvqyylegijaraiykzgftdysokqatzwzcpxclpwfmgilsjijhrjaavfvawkseslayhljslczruggoeoehnygtzvwryrtsiltctcsijamytsiucjxdzrakggffpdjcfaoisipxaejspdtrpsxrslhtryjglfzvugqbnesfqpmhpvfeyeeosfkymoelwtcfoeixqpmoqmfefmuelanqtlfwlksliywwepxtsevemgcpmngbtswcspbtuoeukmnsapspattzasuggsevmerxdeshtmvephokraayiprcwiemgpykyqsjecyrzqwdmkanyevmmhpjjqlmipvxqpmaemfefmuelanuaecizguhuwhjgjbegiljcbiwiykmgaommvpbxamshgwewmkyfhwpvwtcjutvwfggdlgacfxqfmumjredxsdjbssivvfxlpkaqlbnlwlcrxoqfsvreecisfggedwspbpadngklxdelwtcuydedwqmifwojmmozouqkfayhghraetbdgeboylmogeilxapemhpjskraffpucrhiyjjqlmoqlaumpnxifuyeudxawqpadrgurkaeiykqmbfxaprtcemuuygdnyfpgggsicpcpnztstyelppxtmftsidgeboywwzrxndmngqvofxapegeeagtiaesevnctryivvfttnediyvudlsfcltlfdkqaeolaufxaoumcpmecwapraexsmprtiywogqmoqwltyvaeljqraexejefbnrgsoneelzapevaesapaaackwqdtsxednfhlomfidhrnighrponszqpmslxapaatfxzkjlawykvgnszwlglmaemgwqeywivvfxrpwlqdmhpmpnczizrlqqmrlgsvfkosikgrnpneerygdweafutseilqraegmdnyzedejqsgdsmekltnlglqdzrzwkrphvzgsvghnlrvepnewxqjcxmfpsvcwhtwzgphccekuslkysoklztselvfxmlrqeyeeosfkgphzwmhdxrphsipnedsegcgdzrzkqvawivqlbayasauxrprgvggvzpngbpielucjzanykclwhtwjgthlexzgwpecibwqmfzhvgpbnsmkcrmextlvmirzzgmctczrxtmgtlxaqltssicpcptsiqosltelweyeeosfkygacqagqfudxwtcwfzvshggawwzquwohrokratsidgeboyeffktrnlwfmgsevseymhcskcjnsemmuqxtsmkhmkcpwokraptgcgryeygwuygdevsrquueeycggsexzgqvawighraenedgbhntefhmkcpxzgpxwlwdkrmlplgrchfdyueclsysfgraewikuubtsxzggkpcmvgymseecgygdlgugnmiykljcbrqelgraewiykmgnlmjgqhfelwkvmhhelefxdlrvyybtphlqhhiyfsvreefrvgpvogijqdwacofgqlayhtgdhrpefaqdicqaufvofpvdcvoyhmerxddedwqmifwkgakeepqucmofxokraadqsnjyocgwqdaayhhkadeowgnbbecwojmaaoxjctxlwivygmhsmehphmcsegubtsevgtbofwhnygtzwlgyetsiuqbxxqvgopbgsxmpbxrnediyvudrguclawykvgnshekctxrjyfrjxadefvktnmyljcpadaafceycisfygdvrwymytsizgzkehxsnchfrmvgmghpwwvfbsrystbttviqrmbnewstmnnoxzgnxrtqwvckoqxzgatlphgpgtnneerygdtrljcweaxzumyntkzvuaeyednkxnlvwcrmhpmjnmpedxwdzmhpcjqqxadsfgzkeloapevogijclwmloapegotwwngdelqmefeackwtykmjmfvfxczrxwqboywsnslttykujbefxwpygtdxgncbnesljcvaxtspbfaoisyyrwtxzvfxczhwzpxtfvfklziexguyeudxawqphzvwoybnphljphurlgwrttlwshcwidxspaxppvzcnlslpmurbudgstcwnzxzklzfzvljcyaeighraetbljjxgtsfrckhltkkrldpwltsvttsfyylplvlqdwoxmlkygsapsplxdcinglzezvhgpaaawavutsuykvywigijughnlvqvyvttglqftvpxzgkvaxtwfymsevseymhcstwrmhpsmvahmpasuraedeegphudivdwmhpwmtnkidiapttstsfqdmhpmjeyfpelweyeeosfkygwlvjkmkswempaaeoeecqligisuqtuwxgpqmrlgsvfkohlsvcoeclaukhttzsvghntrspyvtzjljczrpelgqmtcisefxrjwsnslttykcztnosfgbmhpmpvfeermgprhompaxghnlrvucmofxkqsmhqsjvfxfzvlkdbeotgtrttnejtgweyazgpxhpmfvcgdphlqclcltwdwleljjqkurtxsplbahmljraensvgvaedifvywedtsvaatzgsvmhroijklzhtqlqpxtcisvubtsednyulpqwprhclvjkbxncergggcsxmvfblesljczrzyffygdwisxcgoyighraehismmkwzyffcwawmngggochwtrhpcsnkbxnzxzklzoqzsnsxtzxzgcgexckcjnsemmuygdsmkistroqmuraagiljmngsxljcrwzydfzxsljwdsmoygwomkeltjqswszrghphmplsfekodwdasgdpvwurbmlxwfatlreuwqkelpaugggbyaeieyelsvraensvgvpadpguraedilqsmtzvwemoecmloykcsmfifbsxiffmnbwilkkxiytmtqniesxvfxfwiwklzslpmurbudeffqhaegstpbdprkcjnsemmupxgcsmrcwwtxzjgltcykvwzulvvclwtsijgktiymfiahhzvludkoxmfefmuelanjxdmcljcltpevhyltxejeslfthwngnsnelqgmwlwfqreoyktgdhrpxzgnnrdyapevawivqlbayjgtaxacvaxcwbpjgtcmhpksvcloqgstpbdprspbeathkkczehmljraetvtcadsesocrxrelwtmfayjgtaxwlwltyipphljcbrdexgrrllcapykeqyygdtrzzwtraedisclwiemkhgmttryvfttelwglwiykghkrsesjaublwpagznrtivuyyewcapraetvjgdngpelpmoizqsislblxsxmkux____+'"
       ]
      },
-     "execution_count": 223,
+     "execution_count": 34,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 224,
+   "execution_count": 46,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "[(1, 1.1327667419873415),\n",
-       " (2, 1.1556010990495924),\n",
-       " (3, 1.206233230791329),\n",
-       " (4, 1.2313380131157103),\n",
-       " (6, 1.2731749420011045),\n",
-       " (5, 1.2798462894967542),\n",
-       " (11, 1.327373238986224),\n",
-       " (9, 1.3278191229344554),\n",
-       " (8, 1.3293010680061772),\n",
-       " (7, 1.3398698729051908),\n",
-       " (10, 1.3463431836469604),\n",
-       " (13, 1.3620114185331578),\n",
-       " (16, 1.3629806460087397),\n",
-       " (12, 1.3915567599630554),\n",
-       " (22, 1.39335904150719),\n",
-       " (18, 1.3959171825391465),\n",
-       " (23, 1.4178260869565218),\n",
-       " (19, 1.4214635856898579),\n",
-       " (20, 1.42971529277585),\n",
-       " (26, 1.4369385555156309),\n",
-       " (14, 1.4386638862659562),\n",
-       " (21, 1.4575520319421331),\n",
-       " (15, 1.458654023723276),\n",
-       " (24, 1.4687703804347825),\n",
-       " (17, 1.4867141412505027),\n",
-       " (29, 1.5101559934318556),\n",
-       " (25, 1.556426856639952),\n",
-       " (27, 1.563057958973637),\n",
-       " (28, 1.613936964396148)]"
+       "'okrahtrvugzheefqniocxmpgmyqsjrctcpasurarzafcutynediyvudqsaftvpfwglttceavmkbfxzgutsmsjpykoxefclwhlhxqpzeoxzgjhclpltguedmfvmtnzvyclbsphspbwidgarjbnphxqpvetxecwaagitgcgpzwkkzeeesltctthmljfbmmvapebnrgsncwoymsygmhtrljcxmamjgggeigzclzeqsjvfxgzzwtlhrdlarmyclpwfmgilfmvqtlfwlkslwlwsipxeocspbtmmmlkmnsxefhmkwssexgvtzvqyylegijaraiykzgftdysokqatzwzcpxclpwfmgilsjijhrjaavfvawkseslayhljslczruggoeoehnygtzvwryrtsiltctcsijamytsiucjxdzrakggffpdjcfaoisipxaejspdtrpsxrslhtryjglfzvugqbnesfqpmhpvfeyeeosfkymoelwtcfoeixqpmoqmfefmuelanqtlfwlksliywwepxtsevemgcpmngbtswcspbtuoeukmnsapspattzasuggsevmerxdeshtmvephokraayiprcwiemgpykyqsjecyrzqwdmkanyevmmhpjjqlmipvxqpmaemfefmuelanuaecizguhuwhjgjbegiljcbiwiykmgaommvpbxamshgwewmkyfhwpvwtcjutvwfggdlgacfxqfmumjredxsdjbssivvfxlpkaqlbnlwlcrxoqfsvreecisfggedwspbpadngklxdelwtcuydedwqmifwojmmozouqkfayhghraetbdgeboylmogeilxapemhpjskraffpucrhiyjjqlmoqlaumpnxifuyeudxawqpadrgurkaeiykqmbfxaprtcemuuygdnyfpgggsicpcpnztstyelppxtmftsidgeboywwzrxndmngqvofxapegeeagtiaesevnctryivvfttnediyvudlsfcltlfdkqaeolaufxaoumcpmecwapraexsmprtiywogqmoqwltyvaeljqraexejefbnrgsoneelzapevaesapaaackwqdtsxednfhlomfidhrnighrponszqpmslxapaatfxzkjlawykvgnszwlglmaemgwqeywivvfxrpwlqdmhpmpnczizrlqqmrlgsvfkosikgrnpneerygdweafutseilqraegmdnyzedejqsgdsmekltnlglqdzrzwkrphvzgsvghnlrvepnewxqjcxmfpsvcwhtwzgphccekuslkysoklztselvfxmlrqeyeeosfkgphzwmhdxrphsipnedsegcgdzrzkqvawivqlbayasauxrprgvggvzpngbpielucjzanykclwhtwjgthlexzgwpecibwqmfzhvgpbnsmkcrmextlvmirzzgmctczrxtmgtlxaqltssicpcptsiqosltelweyeeosfkygacqagqfudxwtcwfzvshggawwzquwohrokratsidgeboyeffktrnlwfmgsevseymhcskcjnsemmuqxtsmkhmkcpwokraptgcgryeygwuygdevsrquueeycggsexzgqvawighraenedgbhntefhmkcpxzgpxwlwdkrmlplgrchfdyueclsysfgraewikuubtsxzggkpcmvgymseecgygdlgugnmiykljcbrqelgraewiykmgnlmjgqhfelwkvmhhelefxdlrvyybtphlqhhiyfsvreefrvgpvogijqdwacofgqlayhtgdhrpefaqdicqaufvofpvdcvoyhmerxddedwqmifwkgakeepqucmofxokraadqsnjyocgwqdaayhhkadeowgnbbecwojmaaoxjctxlwivygmhsmehphmcsegubtsevgtbofwhnygtzwlgyetsiuqbxxqvgopbgsxmpbxrnediyvudrguclawykvgnshekctxrjyfrjxadefvktnmyljcpadaafceycisfygdvrwymytsizgzkehxsnchfrmvgmghpwwvfbsrystbttviqrmbnewstmnnoxzgnxrtqwvckoqxzgatlphgpgtnneerygdtrljcweaxzumyntkzvuaeyednkxnlvwcrmhpmjnmpedxwdzmhpcjqqxadsfgzkeloapevogijclwmloapegotwwngdelqmefeackwtykmjmfvfxczrxwqboywsnslttykujbefxwpygtdxgncbnesljcvaxtspbfaoisyyrwtxzvfxczhwzpxtfvfklziexguyeudxawqphzvwoybnphljphurlgwrttlwshcwidxspaxppvzcnlslpmurbudgstcwnzxzklzfzvljcyaeighraetbljjxgtsfrckhltkkrldpwltsvttsfyylplvlqdwoxmlkygsapsplxdcinglzezvhgpaaawavutsuykvywigijughnlvqvyvttglqftvpxzgkvaxtwfymsevseymhcstwrmhpsmvahmpasuraedeegphudivdwmhpwmtnkidiapttstsfqdmhpmjeyfpelweyeeosfkygwlvjkmkswempaaeoeecqligisuqtuwxgpqmrlgsvfkohlsvcoeclaukhttzsvghntrspyvtzjljczrpelgqmtcisefxrjwsnslttykcztnosfgbmhpmpvfeermgprhompaxghnlrvucmofxkqsmhqsjvfxfzvlkdbeotgtrttnejtgweyazgpxhpmfvcgdphlqclcltwdwleljjqkurtxsplbahmljraensvgvaedifvywedtsvaatzgsvmhroijklzhtqlqpxtcisvubtsednyulpqwprhclvjkbxncergggcsxmvfblesljczrzyffygdwisxcgoyighraehismmkwzyffcwawmngggochwtrhpcsnkbxnzxzklzoqzsnsxtzxzgcgexckcjnsemmuygdsmkistroqmuraagiljmngsxljcrwzydfzxsljwdsmoygwomkeltjqswszrghphmplsfekodwdasgdpvwurbmlxwfatlreuwqkelpaugggbyaeieyelsvraensvgvpadpguraedilqsmtzvwemoecmloykcsmfifbsxiffmnbwilkkxiytmtqniesxvfxfwiwklzslpmurbudeffqhaegstpbdprkcjnsemmupxgcsmrcwwtxzjgltcykvwzulvvclwtsijgktiymfiahhzvludkoxmfefmuelanjxdmcljcltpevhyltxejeslfthwngnsnelqgmwlwfqreoyktgdhrpxzgnnrdyapevawivqlbayjgtaxacvaxcwbpjgtcmhpksvcloqgstpbdprspbeathkkczehmljraetvtcadsesocrxrelwtmfayjgtaxwlwltyipphljcbrdexgrrllcapykeqyygdtrzzwtraedisclwiemkhgmttryvfttelwglwiykghkrsesjaublwpagznrtivuyyewcapraetvjgdngpelpmoizqsislblxsxmkux____+'"
       ]
      },
-     "execution_count": 224,
+     "execution_count": 46,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "ics = [(i, sum(index_of_coincidence(section) for section in every_nth(ch, i)) / i)\n",
+    "scytale_decipher(scb, 598)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[(1, 1.0908179994726204),\n",
+       " (2, 1.0960787604524405),\n",
+       " (3, 1.113516620721608),\n",
+       " (4, 1.115785638463224),\n",
+       " (5, 1.120400202985399),\n",
+       " (6, 1.1334224753429143),\n",
+       " (8, 1.1433918976587085),\n",
+       " (10, 1.1496910122954846),\n",
+       " (9, 1.1617893798656953),\n",
+       " (11, 1.1633834545596675),\n",
+       " (13, 1.1639564019643074),\n",
+       " (12, 1.1721361291337578),\n",
+       " (15, 1.1886213315446346),\n",
+       " (17, 1.1937916983613972),\n",
+       " (16, 1.1950843481587292),\n",
+       " (19, 1.1977817913216935),\n",
+       " (18, 1.2064953083778365),\n",
+       " (22, 1.215718812564869),\n",
+       " (23, 1.2232423954515979),\n",
+       " (26, 1.2322203355672054),\n",
+       " (20, 1.2336039362176447),\n",
+       " (24, 1.238483281601497),\n",
+       " (27, 1.2539543738490824),\n",
+       " (29, 1.2583886702997464),\n",
+       " (25, 1.260639573117166),\n",
+       " (7, 1.754671136359598),\n",
+       " (14, 1.7891187085616644),\n",
+       " (21, 1.8547499897527213),\n",
+       " (28, 1.8746638695669968)]"
+      ]
+     },
+     "execution_count": 37,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "ics = [(i, sum(index_of_coincidence(section) for section in every_nth(scbz, i)) / i)\n",
     "           for i in range(1, 30)]\n",
     "sorted(ics, key=lambda p: p[1])"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 225,
+   "execution_count": 38,
    "metadata": {},
    "outputs": [
     {
        "('scytale', -4506.678592965439)"
       ]
      },
-     "execution_count": 225,
+     "execution_count": 38,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 226,
+   "execution_count": 39,
    "metadata": {},
    "outputs": [
     {
        "'withhindsightanopportunityforpeacewasthrownawaycalgacusmayhavebeenatraitorbuthewasbornaromanandhadforgedthelocaltribesintoanorganisedanddisciplinedforceitmayhavebeenpossibletotreatwithhimbringingcaledoniawithintheempireinexchangeforthegovernorshipofcaledoniabutsalustiuswasagreedyandambitiousmanforwhomvictorywaseverythinghehadnowishtosharecaledoniaorglorywithcalgacusandthusconceivedaplantorepaythetreacheryofthecaledoniiinfullhemadeagreatfanfareofpushinghisforcesintonortherncaledoniatotheremotefortofinchtuthilsalustiusinsecrethadconceivedaslyandaudaciousplancatowasinstructedtoproceedwithanexpeditionaryforcefromeboracumtothefrontierfortatinchtuthilwherehewouldrelievetheiilegionadiutrixpiafideliswhowererequiredindaciahequicklyestablishedthelegioninastateofbattlereadinessandwasjoinedtherebysalustiuswhotookcommandoftheixlegionhumiliatingthefaithfulcatoinfrontofhisownmensalustiuswasnostrategistbutintacticsandcunningheknewnoparallelfromthelegionsextensivescoutingnetworkhehadlearnedthatcalgacushadestablishedhisheadquartersinthemountainswestofstracathrothemarchingcampleavingcatoinchargeofasmallholdingforceoftwocohortsatinchtuthilsalustiusostentatiouslyledtherestoftheixlegiontostracathrohesetupcampandlaidwastetothevillagesaroundhiminanactofgrossprovocationandcrueltyheemulatedhisherocrassusknowingthatthemanycaledoniiwhosufferedagruesomeendonhiscaledonianwaywerenotinvolvedwithcalgacusandhisrevolttheywerejustfodderinhisattempttoprovokeaconfrontationasheknewtheymustthecaledonianarmiesmusteredforafinalshowdownwiththelegionandmarchedonstracathrosalustiussethisforceswithpicketfencesandtrapsbutagainstthescaleofthecaledonianforcetherewaslittlehopeofsuccessnonethelesswiththeirprideatstakeandacceptingtheirfatethelegionnairesoftheixthwatchedandwaitedtojoinbattleundercoverofdarknessandbeforeanyskirmishcouldbeconductedsalustiussecretlysetoutwithasmallforceofhandpickedsoldierswhohadtravelledwithhimfromromewithadeviousplantostealthecodexfromrightundercalgacusnosesalustiuswasaveryunpleasantmanbuthewaswidelyreadandknewofthehebrewtaleofgideonhesethisguardatkeypointsaroundtheperimeterofthecaledoniancampandinthedepthsofnightwhenallmenareattheirlowestebbtheyroseasonebreakingcoverandmakingnoiselikeamuchlargerarmyintheconfusionsalustiusslieutenantstoleintothecampandmadeawaywiththecodexreturningittosalustiuswhoremainedthroughoutatasafedistanceperhapssalustiuscarednothingforthefateoftheixthlegionperhapsitsdestructionwaspartofdomitiansplannedrevengeorperhapsitwasjustadiversionarytactictohavethemcampedatstracathrobuttheoutcomewasthesamerousedbythesurpriseinvasionoftheircampthecaledonianwarriorslaunchedamassiveassaultonstracathrowhateverhismotivationinanactofthegreatesttreacherysalustiusabandonedtheixthlegiontooblivionandsetoutsouthforthefortifiedportatcarridenwhereheintendedtoescapebyseafrombritanniawiththecodexhesentadespatchtocatoorderinghimtoretreatwithallablementocarridenrazeinchtuthiltothegroundandleavenoneoftheweakorwoundedaliveinordertoprovidenothingofvaluetotheenemysalustiusandhisguardmusthavethoughttheywouldbesafebutoncemoreaproudsonofromehadgrosslyunderestimatedcalgacusrealisingquicklythatthecodexwaslosthesetouttorecoveritmarchinghismendoubletimeinpursuitofthefleeingsalustiusandsoatcarridensalustiusregroupedwithhistrustyguardandtheremainingcohortsfrominchtuthilledbythesteadfastmarcusfideliuscatoitwasnotlongbeforethepursuingcaledonianforcearrivedbeforethegatesofcarridenandlaidsiegewiththeirbackstowatertheromanforcewastrappedtheirsafetylayinarefugefarovertheseaanditisfittingthattheendingofmystorywilllieburiedsafelyintheirrefugeatnoviomagusbatavorum____+'"
       ]
      },
-     "execution_count": 226,
+     "execution_count": 39,
      "metadata": {},
      "output_type": "execute_result"
     }
   },
   {
    "cell_type": "code",
-   "execution_count": 227,
+   "execution_count": 40,
    "metadata": {},
    "outputs": [
     {
   },
   {
    "cell_type": "code",
-   "execution_count": 202,
+   "execution_count": 41,
    "metadata": {},
    "outputs": [
     {
   },
   {
    "cell_type": "code",
-   "execution_count": 228,
+   "execution_count": 42,
    "metadata": {},
    "outputs": [
     {
        "4423"
       ]
      },
-     "execution_count": 228,
+     "execution_count": 42,
      "metadata": {},
      "output_type": "execute_result"
     }