From: Neil Smith <neil.git@njae.me.uk>
Date: Wed, 28 Jun 2017 13:49:55 +0000 (+0100)
Subject: Renumbered day 9 to day 8
X-Git-Url: https://git.njae.me.uk/?a=commitdiff_plain;h=2f750972c876ebbb88e1af96be1ce74b4d3558f8;p=ou-summer-of-code-2017.git

Renumbered day 9 to day 8
---

diff --git a/08-word-chains/08-words.txt b/08-word-chains/08-words.txt
new file mode 100644
index 0000000..028c8cf
--- /dev/null
+++ b/08-word-chains/08-words.txt
@@ -0,0 +1,2336 @@
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+rung
+runs
+runt
+ruse
+rush
+rusk
+rust
+ruts
+sack
+sacs
+safe
+saga
+sage
+sago
+sags
+said
+sail
+sake
+saki
+sale
+salt
+same
+sand
+sane
+sang
+sank
+sans
+saps
+sari
+sash
+sass
+sate
+save
+sawn
+saws
+says
+scab
+scad
+scam
+scan
+scar
+scat
+scow
+scud
+scum
+seal
+seam
+sear
+seas
+seat
+secs
+sect
+seed
+seek
+seem
+seen
+seep
+seer
+sees
+self
+sell
+semi
+send
+sent
+sera
+sere
+serf
+sets
+sewn
+sews
+sexy
+shad
+shag
+shah
+sham
+shat
+shed
+shes
+shim
+shin
+ship
+shod
+shoe
+shoo
+shop
+shot
+show
+shun
+shut
+sick
+sics
+side
+sift
+sigh
+sign
+silk
+sill
+silo
+silt
+sine
+sing
+sink
+sins
+sips
+sire
+sirs
+site
+sits
+size
+skew
+skid
+skim
+skin
+skip
+skis
+skit
+slab
+slag
+slam
+slap
+slat
+slaw
+slay
+sled
+slew
+slid
+slim
+slip
+slit
+slob
+sloe
+slog
+slop
+slot
+slow
+slue
+slug
+slum
+slur
+slut
+smit
+smog
+smug
+smut
+snag
+snap
+snip
+snit
+snob
+snot
+snow
+snub
+snug
+soak
+soap
+soar
+sobs
+sock
+soda
+sods
+sofa
+soft
+soil
+sold
+sole
+soli
+solo
+sols
+some
+song
+sons
+soon
+soot
+sops
+sore
+sort
+sots
+soul
+soup
+sour
+sown
+sows
+soya
+span
+spar
+spas
+spat
+spay
+spec
+sped
+spew
+spin
+spit
+spot
+spry
+spud
+spun
+spur
+stab
+stag
+star
+stay
+stem
+step
+stew
+stir
+stop
+stow
+stub
+stud
+stun
+stye
+subs
+such
+suck
+suds
+sued
+sues
+suet
+suit
+sulk
+sumo
+sump
+sums
+sung
+sunk
+suns
+sups
+sure
+surf
+swab
+swag
+swam
+swan
+swap
+swat
+sway
+swig
+swim
+swop
+swum
+sync
+tabs
+tabu
+tack
+taco
+tact
+tads
+tags
+tail
+take
+talc
+tale
+talk
+tall
+tame
+tamp
+tams
+tang
+tank
+tans
+tape
+taps
+tare
+taro
+tarp
+tars
+tart
+task
+tats
+taut
+taxi
+teak
+teal
+team
+tear
+teas
+teat
+teed
+teem
+teen
+tees
+tell
+temp
+tend
+tens
+tent
+term
+tern
+test
+text
+than
+that
+thaw
+thee
+them
+then
+they
+thin
+this
+thou
+thru
+thud
+thug
+thus
+tick
+tics
+tide
+tidy
+tied
+tier
+ties
+tiff
+tike
+tile
+till
+tilt
+time
+tine
+ting
+tins
+tint
+tiny
+tipi
+tips
+tire
+tiro
+tits
+toad
+toed
+toes
+tofu
+toga
+togs
+toil
+toke
+told
+toll
+tomb
+tome
+toms
+tone
+tong
+tons
+tony
+took
+tool
+toot
+tops
+tore
+torn
+tors
+tort
+toss
+tost
+tote
+tots
+tour
+tout
+town
+tows
+toys
+tram
+trap
+tray
+tree
+trek
+trig
+trim
+trio
+trip
+trod
+trot
+troy
+true
+tsar
+tuba
+tube
+tubs
+tuck
+tuft
+tugs
+tuna
+tune
+tuns
+turd
+turf
+turn
+tush
+tusk
+tutu
+twee
+twig
+twin
+twit
+twos
+tyke
+type
+typo
+tyre
+tyro
+tzar
+ugly
+ulna
+umps
+undo
+unit
+unto
+upon
+urea
+urge
+uric
+urns
+used
+user
+uses
+vain
+vale
+vamp
+vane
+vans
+vary
+vase
+vast
+vats
+veal
+veep
+veer
+veil
+vein
+veld
+vend
+vent
+verb
+very
+vest
+veto
+vets
+vial
+vibe
+vice
+vied
+vies
+view
+vile
+vine
+viol
+visa
+vise
+viva
+void
+vole
+volt
+vote
+vows
+wade
+wadi
+wads
+waft
+wage
+wags
+waif
+wail
+wait
+wake
+wale
+walk
+wall
+wand
+wane
+want
+ward
+ware
+warm
+warn
+warp
+wars
+wart
+wary
+wash
+wasp
+watt
+wave
+wavy
+waxy
+ways
+weak
+weal
+wean
+wear
+webs
+weds
+weed
+week
+weep
+weer
+wees
+weft
+weir
+weld
+well
+welt
+wend
+wens
+went
+wept
+were
+west
+wets
+wham
+what
+when
+whet
+whew
+whey
+whim
+whip
+whir
+whit
+whiz
+whoa
+whom
+whys
+wick
+wide
+wife
+wigs
+wiki
+wild
+wile
+will
+wilt
+wily
+wimp
+wind
+wine
+wing
+wink
+wino
+wins
+wipe
+wire
+wiry
+wise
+wish
+wisp
+wist
+with
+wits
+wive
+woes
+woke
+woks
+wolf
+womb
+wont
+wood
+woof
+wool
+woos
+word
+wore
+work
+worm
+worn
+wove
+wows
+wrap
+wren
+writ
+wuss
+yack
+yaks
+yams
+yank
+yaps
+yard
+yarn
+yawl
+yawn
+yaws
+yeah
+year
+yeas
+yell
+yelp
+yens
+yeps
+yest
+yeti
+yews
+yips
+yock
+yoga
+yogi
+yoke
+yolk
+yore
+your
+yous
+yowl
+yuck
+yuks
+yule
+yups
+zany
+zaps
+zeal
+zebu
+zeds
+zero
+zest
+zeta
+zinc
+zing
+zips
+zits
+zone
+zoom
+zoos
\ No newline at end of file
diff --git a/08-word-chains/build-word-lists.ipynb b/08-word-chains/build-word-lists.ipynb
new file mode 100644
index 0000000..d12df78
--- /dev/null
+++ b/08-word-chains/build-word-lists.ipynb
@@ -0,0 +1,201 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "import unicodedata\n",
+    "import string"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "unaccent_specials = ''.maketrans({\"’\": \"'\", '“': '\"', '”': '\"'})"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def unaccent(text):\n",
+    "    translated_text = text.translate(unaccent_specials)\n",
+    "    return unicodedata.normalize('NFKD', translated_text).\\\n",
+    "        encode('ascii', 'ignore').\\\n",
+    "        decode('utf-8')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def only_lower(text):\n",
+    "    return all((c in string.ascii_lowercase) for c in text)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "/usr/share/dict/british-english\n",
+      "find: ‘/usr/share/doc/google-chrome-stable’: Permission denied\n",
+      "/usr/share/man/man5/british-english.5.gz\n"
+     ]
+    }
+   ],
+   "source": [
+    "# !find /usr -type f -iname 'british-english*'"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "total 2.3M\r\n",
+      "drwxr-xr-x   2 root root 4.0K Dec 29 12:37 .\r\n",
+      "drwxr-xr-x 640 root root  20K Apr 13 17:05 ..\r\n",
+      "-rw-r--r--   1 root root 917K Oct 23  2011 american-english\r\n",
+      "-rw-r--r--   1 root root 917K Oct 23  2011 british-english\r\n",
+      "-rw-r--r--   1 root root 467K Aug 25  2016 cracklib-small\r\n",
+      "-rw-r--r--   1 root root  199 Aug 29  2016 README.select-wordlist\r\n",
+      "lrwxrwxrwx   1 root root   30 Nov 10  2014 words -> /etc/dictionaries-common/words\r\n",
+      "lrwxrwxrwx   1 root root   16 Jun 18  2014 words.pre-dictionaries-common -> american-english\r\n"
+     ]
+    }
+   ],
+   "source": [
+    "# !ls -lah /usr/share/dict"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def rude(word):\n",
+    "    return any(w in word \n",
+    "               for w in 'piss shit cunt fuck arse crap fart jizz whore bitch'.split())"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 18,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "rude('fucks')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def words_with_len(n):\n",
+    "    return [unaccent(w.strip()) for w in open('/usr/share/dict/british-english').readlines()\n",
+    "               if only_lower(unaccent(w.strip()))\n",
+    "               if len(unaccent(w.strip())) == n\n",
+    "               if not rude(unaccent(w.strip()))]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "2336 4-letter words\n",
+      "4566 5-letter words\n",
+      "7223 6-letter words\n"
+     ]
+    }
+   ],
+   "source": [
+    "dicts = {}\n",
+    "\n",
+    "for n in [4, 5, 6]:\n",
+    "    dicts[n] = words_with_len(n)\n",
+    "    print('{} {}-letter words'.format(len(dicts[n]), n))\n",
+    "    with open('words{}.txt'.format(n), 'w') as f:\n",
+    "        f.write('\\n'.join(sorted(set(dicts[n]))))\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.5.2+"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/08-word-chains/explore-word-chain-4.ipynb b/08-word-chains/explore-word-chain-4.ipynb
new file mode 100644
index 0000000..c2bca54
--- /dev/null
+++ b/08-word-chains/explore-word-chain-4.ipynb
@@ -0,0 +1,3402 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "import string\n",
+    "import heapq\n",
+    "import collections\n",
+    "import random"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "2336"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "words = [w.strip() for w in open('08-words.txt').readlines()]\n",
+    "len(words)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "['abbe',\n",
+       " 'abed',\n",
+       " 'abet',\n",
+       " 'able',\n",
+       " 'ably',\n",
+       " 'abut',\n",
+       " 'aced',\n",
+       " 'aces',\n",
+       " 'ache',\n",
+       " 'achy']"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "words[:10]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def adjacents_explicit(word):\n",
+    "    neighbours = []\n",
+    "    for i in range(len(word)):\n",
+    "        for l in string.ascii_lowercase:\n",
+    "            if l != word[i]:\n",
+    "                neighbours.append(word[0:i] + l + word[i+1:])\n",
+    "    return neighbours"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def adjacents(word):\n",
+    "    return [word[0:i] + l + word[i+1:]\n",
+    "           for i in range(len(word))\n",
+    "           for l in string.ascii_lowercase\n",
+    "           if l != word[i]]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "neighbours = {w: [n for n in adjacents(w) if n in words]\n",
+    "             for w in words}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "['able']"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "neighbours['abbe']"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "['axle', 'abbe', 'ably']"
+      ]
+     },
+     "execution_count": 8,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "neighbours['able']"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def distance(w1, w2):\n",
+    "    return sum(1 for i in range(len(w1))\n",
+    "               if w1[i] != w2[i])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "0"
+      ]
+     },
+     "execution_count": 10,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "distance('abbe', 'abbe')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def extend(chain, closed=None):\n",
+    "    if closed:\n",
+    "        nbrs = set(neighbours[chain[-1]]) - closed\n",
+    "    else:\n",
+    "        nbrs = neighbours[chain[-1]]\n",
+    "    return [chain + [s] for s in nbrs\n",
+    "           if s not in chain]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[['abbe', 'able']]"
+      ]
+     },
+     "execution_count": 12,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "extend(['abbe'])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[['abbe', 'able', 'axle'], ['abbe', 'able', 'ably']]"
+      ]
+     },
+     "execution_count": 13,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "extend(['abbe', 'able'])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[['abbe', 'able', 'ably', 'ally']]"
+      ]
+     },
+     "execution_count": 14,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "extend(['abbe', 'able', 'ably'])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def bfs_search(start, goal, debug=False):\n",
+    "    agenda = [[start]]\n",
+    "    finished = False\n",
+    "    while not finished and agenda:\n",
+    "        current = agenda[0]\n",
+    "        if debug:\n",
+    "            print(current)\n",
+    "        if current[-1] == goal:\n",
+    "            finished = True\n",
+    "        else:\n",
+    "            successors = extend(current)\n",
+    "            agenda = agenda[1:] + successors\n",
+    "    if agenda:\n",
+    "        return current\n",
+    "    else:\n",
+    "        return None        "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def bfs_search_closed(start, goal, debug=False):\n",
+    "    agenda = [[start]]\n",
+    "    closed = set()\n",
+    "    finished = False\n",
+    "    while not finished and agenda:\n",
+    "        current = agenda[0]\n",
+    "        if debug:\n",
+    "            print(current)\n",
+    "        if current[-1] == goal:\n",
+    "            finished = True\n",
+    "        else:\n",
+    "            closed.add(current[-1])\n",
+    "            successors = extend(current, closed)\n",
+    "            agenda = agenda[1:] + successors\n",
+    "    if agenda:\n",
+    "        return current\n",
+    "    else:\n",
+    "        return None        "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "['abbe']\n",
+      "['abbe', 'able']\n",
+      "['abbe', 'able', 'axle']\n",
+      "['abbe', 'able', 'ably']\n",
+      "['abbe', 'able', 'ably', 'ally']\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "['abbe', 'able', 'ably', 'ally']"
+      ]
+     },
+     "execution_count": 17,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "bfs_search('abbe', 'ally', debug=True)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def dfs_search(start, goal, debug=False):\n",
+    "    agenda = [[start]]\n",
+    "    finished = False\n",
+    "    while not finished and agenda:\n",
+    "        current = agenda[0]\n",
+    "        if debug:\n",
+    "            print(current)\n",
+    "        if current[-1] == goal:\n",
+    "            finished = True\n",
+    "        else:\n",
+    "            successors = extend(current)\n",
+    "            agenda = successors + agenda[1:]\n",
+    "    if agenda:\n",
+    "        return current\n",
+    "    else:\n",
+    "        return None        "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "['abbe']\n",
+      "['abbe', 'able']\n",
+      "['abbe', 'able', 'axle']\n",
+      "['abbe', 'able', 'ably']\n",
+      "['abbe', 'able', 'ably', 'ally']\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "['abbe', 'able', 'ably', 'ally']"
+      ]
+     },
+     "execution_count": 19,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "dfs_search('abbe', 'ally', debug=True)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "['cart']\n",
+      "['cart', 'dart']\n",
+      "['cart', 'hart']\n",
+      "['cart', 'mart']\n",
+      "['cart', 'part']\n",
+      "['cart', 'tart']\n",
+      "['cart', 'wart']\n",
+      "['cart', 'curt']\n",
+      "['cart', 'cant']\n",
+      "['cart', 'cast']\n",
+      "['cart', 'card']\n",
+      "['cart', 'care']\n",
+      "['cart', 'carp']\n",
+      "['cart', 'cars']\n",
+      "['cart', 'dart', 'hart']\n",
+      "['cart', 'dart', 'mart']\n",
+      "['cart', 'dart', 'part']\n",
+      "['cart', 'dart', 'tart']\n",
+      "['cart', 'dart', 'wart']\n",
+      "['cart', 'dart', 'dirt']\n",
+      "['cart', 'dart', 'daft']\n",
+      "['cart', 'dart', 'dare']\n",
+      "['cart', 'dart', 'dark']\n",
+      "['cart', 'dart', 'darn']\n",
+      "['cart', 'hart', 'dart']\n",
+      "['cart', 'hart', 'mart']\n",
+      "['cart', 'hart', 'part']\n",
+      "['cart', 'hart', 'tart']\n",
+      "['cart', 'hart', 'wart']\n",
+      "['cart', 'hart', 'hurt']\n",
+      "['cart', 'hart', 'haft']\n",
+      "['cart', 'hart', 'halt']\n",
+      "['cart', 'hart', 'hard']\n",
+      "['cart', 'hart', 'hare']\n",
+      "['cart', 'hart', 'hark']\n",
+      "['cart', 'hart', 'harm']\n",
+      "['cart', 'hart', 'harp']\n",
+      "['cart', 'mart', 'dart']\n",
+      "['cart', 'mart', 'hart']\n",
+      "['cart', 'mart', 'part']\n",
+      "['cart', 'mart', 'tart']\n",
+      "['cart', 'mart', 'wart']\n",
+      "['cart', 'mart', 'malt']\n",
+      "['cart', 'mart', 'mast']\n",
+      "['cart', 'mart', 'matt']\n",
+      "['cart', 'mart', 'mare']\n",
+      "['cart', 'mart', 'mark']\n",
+      "['cart', 'mart', 'mars']\n",
+      "['cart', 'part', 'dart']\n",
+      "['cart', 'part', 'hart']\n",
+      "['cart', 'part', 'mart']\n",
+      "['cart', 'part', 'tart']\n",
+      "['cart', 'part', 'wart']\n",
+      "['cart', 'part', 'pert']\n",
+      "['cart', 'part', 'port']\n",
+      "['cart', 'part', 'pact']\n",
+      "['cart', 'part', 'pant']\n",
+      "['cart', 'part', 'past']\n",
+      "['cart', 'part', 'pare']\n",
+      "['cart', 'part', 'park']\n",
+      "['cart', 'part', 'pars']\n",
+      "['cart', 'tart', 'dart']\n",
+      "['cart', 'tart', 'hart']\n",
+      "['cart', 'tart', 'mart']\n",
+      "['cart', 'tart', 'part']\n",
+      "['cart', 'tart', 'wart']\n",
+      "['cart', 'tart', 'tort']\n",
+      "['cart', 'tart', 'tact']\n",
+      "['cart', 'tart', 'taut']\n",
+      "['cart', 'tart', 'tare']\n",
+      "['cart', 'tart', 'taro']\n",
+      "['cart', 'tart', 'tarp']\n",
+      "['cart', 'tart', 'tars']\n",
+      "['cart', 'wart', 'dart']\n",
+      "['cart', 'wart', 'hart']\n",
+      "['cart', 'wart', 'mart']\n",
+      "['cart', 'wart', 'part']\n",
+      "['cart', 'wart', 'tart']\n",
+      "['cart', 'wart', 'waft']\n",
+      "['cart', 'wart', 'wait']\n",
+      "['cart', 'wart', 'want']\n",
+      "['cart', 'wart', 'watt']\n",
+      "['cart', 'wart', 'ward']\n",
+      "['cart', 'wart', 'ware']\n",
+      "['cart', 'wart', 'warm']\n",
+      "['cart', 'wart', 'warn']\n",
+      "['cart', 'wart', 'warp']\n",
+      "['cart', 'wart', 'wars']\n",
+      "['cart', 'wart', 'wary']\n",
+      "['cart', 'curt', 'hurt']\n",
+      "['cart', 'curt', 'cult']\n",
+      "['cart', 'curt', 'curb']\n",
+      "['cart', 'curt', 'curd']\n",
+      "['cart', 'curt', 'cure']\n",
+      "['cart', 'curt', 'curl']\n",
+      "['cart', 'curt', 'curs']\n",
+      "['cart', 'cant', 'pant']\n",
+      "['cart', 'cant', 'rant']\n",
+      "['cart', 'cant', 'want']\n",
+      "['cart', 'cant', 'cent']\n",
+      "['cart', 'cant', 'cast']\n",
+      "['cart', 'cant', 'cane']\n",
+      "['cart', 'cant', 'cans']\n",
+      "['cart', 'cast', 'bast']\n",
+      "['cart', 'cast', 'east']\n",
+      "['cart', 'cast', 'fast']\n",
+      "['cart', 'cast', 'last']\n",
+      "['cart', 'cast', 'mast']\n",
+      "['cart', 'cast', 'past']\n",
+      "['cart', 'cast', 'vast']\n",
+      "['cart', 'cast', 'cost']\n",
+      "['cart', 'cast', 'cyst']\n",
+      "['cart', 'cast', 'cant']\n",
+      "['cart', 'cast', 'case']\n",
+      "['cart', 'cast', 'cash']\n",
+      "['cart', 'cast', 'cask']\n",
+      "['cart', 'card', 'bard']\n",
+      "['cart', 'card', 'hard']\n",
+      "['cart', 'card', 'lard']\n",
+      "['cart', 'card', 'ward']\n",
+      "['cart', 'card', 'yard']\n",
+      "['cart', 'card', 'cord']\n",
+      "['cart', 'card', 'curd']\n",
+      "['cart', 'card', 'care']\n",
+      "['cart', 'card', 'carp']\n",
+      "['cart', 'card', 'cars']\n",
+      "['cart', 'care', 'bare']\n",
+      "['cart', 'care', 'dare']\n",
+      "['cart', 'care', 'fare']\n",
+      "['cart', 'care', 'hare']\n",
+      "['cart', 'care', 'mare']\n",
+      "['cart', 'care', 'pare']\n",
+      "['cart', 'care', 'rare']\n",
+      "['cart', 'care', 'tare']\n",
+      "['cart', 'care', 'ware']\n",
+      "['cart', 'care', 'core']\n",
+      "['cart', 'care', 'cure']\n",
+      "['cart', 'care', 'cafe']\n",
+      "['cart', 'care', 'cage']\n",
+      "['cart', 'care', 'cake']\n",
+      "['cart', 'care', 'came']\n",
+      "['cart', 'care', 'cane']\n",
+      "['cart', 'care', 'cape']\n",
+      "['cart', 'care', 'case']\n",
+      "['cart', 'care', 'cave']\n",
+      "['cart', 'care', 'card']\n",
+      "['cart', 'care', 'carp']\n",
+      "['cart', 'care', 'cars']\n",
+      "['cart', 'carp', 'harp']\n",
+      "['cart', 'carp', 'tarp']\n",
+      "['cart', 'carp', 'warp']\n",
+      "['cart', 'carp', 'camp']\n",
+      "['cart', 'carp', 'card']\n",
+      "['cart', 'carp', 'care']\n",
+      "['cart', 'carp', 'cars']\n",
+      "['cart', 'cars', 'bars']\n",
+      "['cart', 'cars', 'ears']\n",
+      "['cart', 'cars', 'jars']\n",
+      "['cart', 'cars', 'mars']\n",
+      "['cart', 'cars', 'oars']\n",
+      "['cart', 'cars', 'pars']\n",
+      "['cart', 'cars', 'tars']\n",
+      "['cart', 'cars', 'wars']\n",
+      "['cart', 'cars', 'curs']\n",
+      "['cart', 'cars', 'cabs']\n",
+      "['cart', 'cars', 'cads']\n",
+      "['cart', 'cars', 'cams']\n",
+      "['cart', 'cars', 'cans']\n",
+      "['cart', 'cars', 'caps']\n",
+      "['cart', 'cars', 'cats']\n",
+      "['cart', 'cars', 'caws']\n",
+      "['cart', 'cars', 'card']\n",
+      "['cart', 'cars', 'care']\n",
+      "['cart', 'cars', 'carp']\n",
+      "['cart', 'dart', 'hart', 'mart']\n",
+      "['cart', 'dart', 'hart', 'part']\n",
+      "['cart', 'dart', 'hart', 'tart']\n",
+      "['cart', 'dart', 'hart', 'wart']\n",
+      "['cart', 'dart', 'hart', 'hurt']\n",
+      "['cart', 'dart', 'hart', 'haft']\n",
+      "['cart', 'dart', 'hart', 'halt']\n",
+      "['cart', 'dart', 'hart', 'hard']\n",
+      "['cart', 'dart', 'hart', 'hare']\n",
+      "['cart', 'dart', 'hart', 'hark']\n",
+      "['cart', 'dart', 'hart', 'harm']\n",
+      "['cart', 'dart', 'hart', 'harp']\n",
+      "['cart', 'dart', 'mart', 'hart']\n",
+      "['cart', 'dart', 'mart', 'part']\n",
+      "['cart', 'dart', 'mart', 'tart']\n",
+      "['cart', 'dart', 'mart', 'wart']\n",
+      "['cart', 'dart', 'mart', 'malt']\n",
+      "['cart', 'dart', 'mart', 'mast']\n",
+      "['cart', 'dart', 'mart', 'matt']\n",
+      "['cart', 'dart', 'mart', 'mare']\n",
+      "['cart', 'dart', 'mart', 'mark']\n",
+      "['cart', 'dart', 'mart', 'mars']\n",
+      "['cart', 'dart', 'part', 'hart']\n",
+      "['cart', 'dart', 'part', 'mart']\n",
+      "['cart', 'dart', 'part', 'tart']\n",
+      "['cart', 'dart', 'part', 'wart']\n",
+      "['cart', 'dart', 'part', 'pert']\n",
+      "['cart', 'dart', 'part', 'port']\n",
+      "['cart', 'dart', 'part', 'pact']\n",
+      "['cart', 'dart', 'part', 'pant']\n",
+      "['cart', 'dart', 'part', 'past']\n",
+      "['cart', 'dart', 'part', 'pare']\n",
+      "['cart', 'dart', 'part', 'park']\n",
+      "['cart', 'dart', 'part', 'pars']\n",
+      "['cart', 'dart', 'tart', 'hart']\n",
+      "['cart', 'dart', 'tart', 'mart']\n",
+      "['cart', 'dart', 'tart', 'part']\n",
+      "['cart', 'dart', 'tart', 'wart']\n",
+      "['cart', 'dart', 'tart', 'tort']\n",
+      "['cart', 'dart', 'tart', 'tact']\n",
+      "['cart', 'dart', 'tart', 'taut']\n",
+      "['cart', 'dart', 'tart', 'tare']\n",
+      "['cart', 'dart', 'tart', 'taro']\n",
+      "['cart', 'dart', 'tart', 'tarp']\n",
+      "['cart', 'dart', 'tart', 'tars']\n",
+      "['cart', 'dart', 'wart', 'hart']\n",
+      "['cart', 'dart', 'wart', 'mart']\n",
+      "['cart', 'dart', 'wart', 'part']\n",
+      "['cart', 'dart', 'wart', 'tart']\n",
+      "['cart', 'dart', 'wart', 'waft']\n",
+      "['cart', 'dart', 'wart', 'wait']\n",
+      "['cart', 'dart', 'wart', 'want']\n",
+      "['cart', 'dart', 'wart', 'watt']\n",
+      "['cart', 'dart', 'wart', 'ward']\n",
+      "['cart', 'dart', 'wart', 'ware']\n",
+      "['cart', 'dart', 'wart', 'warm']\n",
+      "['cart', 'dart', 'wart', 'warn']\n",
+      "['cart', 'dart', 'wart', 'warp']\n",
+      "['cart', 'dart', 'wart', 'wars']\n",
+      "['cart', 'dart', 'wart', 'wary']\n",
+      "['cart', 'dart', 'dirt', 'girt']\n",
+      "['cart', 'dart', 'dirt', 'diet']\n",
+      "['cart', 'dart', 'dirt', 'dint']\n",
+      "['cart', 'dart', 'dirt', 'dire']\n",
+      "['cart', 'dart', 'dirt', 'dirk']\n",
+      "['cart', 'dart', 'daft', 'haft']\n",
+      "['cart', 'dart', 'daft', 'raft']\n",
+      "['cart', 'dart', 'daft', 'waft']\n",
+      "['cart', 'dart', 'daft', 'deft']\n",
+      "['cart', 'dart', 'dare', 'bare']\n",
+      "['cart', 'dart', 'dare', 'care']\n",
+      "['cart', 'dart', 'dare', 'fare']\n",
+      "['cart', 'dart', 'dare', 'hare']\n",
+      "['cart', 'dart', 'dare', 'mare']\n",
+      "['cart', 'dart', 'dare', 'pare']\n",
+      "['cart', 'dart', 'dare', 'rare']\n",
+      "['cart', 'dart', 'dare', 'tare']\n",
+      "['cart', 'dart', 'dare', 'ware']\n",
+      "['cart', 'dart', 'dare', 'dire']\n",
+      "['cart', 'dart', 'dare', 'dale']\n",
+      "['cart', 'dart', 'dare', 'dame']\n",
+      "['cart', 'dart', 'dare', 'date']\n",
+      "['cart', 'dart', 'dare', 'daze']\n",
+      "['cart', 'dart', 'dare', 'dark']\n",
+      "['cart', 'dart', 'dare', 'darn']\n",
+      "['cart', 'dart', 'dark', 'bark']\n",
+      "['cart', 'dart', 'dark', 'hark']\n",
+      "['cart', 'dart', 'dark', 'lark']\n",
+      "['cart', 'dart', 'dark', 'mark']\n",
+      "['cart', 'dart', 'dark', 'nark']\n",
+      "['cart', 'dart', 'dark', 'park']\n",
+      "['cart', 'dart', 'dark', 'dirk']\n",
+      "['cart', 'dart', 'dark', 'dork']\n",
+      "['cart', 'dart', 'dark', 'dank']\n",
+      "['cart', 'dart', 'dark', 'dare']\n",
+      "['cart', 'dart', 'dark', 'darn']\n",
+      "['cart', 'dart', 'darn', 'barn']\n",
+      "['cart', 'dart', 'darn', 'earn']\n",
+      "['cart', 'dart', 'darn', 'warn']\n",
+      "['cart', 'dart', 'darn', 'yarn']\n",
+      "['cart', 'dart', 'darn', 'damn']\n",
+      "['cart', 'dart', 'darn', 'dawn']\n",
+      "['cart', 'dart', 'darn', 'dare']\n",
+      "['cart', 'dart', 'darn', 'dark']\n",
+      "['cart', 'hart', 'dart', 'mart']\n",
+      "['cart', 'hart', 'dart', 'part']\n",
+      "['cart', 'hart', 'dart', 'tart']\n",
+      "['cart', 'hart', 'dart', 'wart']\n",
+      "['cart', 'hart', 'dart', 'dirt']\n",
+      "['cart', 'hart', 'dart', 'daft']\n",
+      "['cart', 'hart', 'dart', 'dare']\n",
+      "['cart', 'hart', 'dart', 'dark']\n",
+      "['cart', 'hart', 'dart', 'darn']\n",
+      "['cart', 'hart', 'mart', 'dart']\n",
+      "['cart', 'hart', 'mart', 'part']\n",
+      "['cart', 'hart', 'mart', 'tart']\n",
+      "['cart', 'hart', 'mart', 'wart']\n",
+      "['cart', 'hart', 'mart', 'malt']\n",
+      "['cart', 'hart', 'mart', 'mast']\n",
+      "['cart', 'hart', 'mart', 'matt']\n",
+      "['cart', 'hart', 'mart', 'mare']\n",
+      "['cart', 'hart', 'mart', 'mark']\n",
+      "['cart', 'hart', 'mart', 'mars']\n",
+      "['cart', 'hart', 'part', 'dart']\n",
+      "['cart', 'hart', 'part', 'mart']\n",
+      "['cart', 'hart', 'part', 'tart']\n",
+      "['cart', 'hart', 'part', 'wart']\n",
+      "['cart', 'hart', 'part', 'pert']\n",
+      "['cart', 'hart', 'part', 'port']\n",
+      "['cart', 'hart', 'part', 'pact']\n",
+      "['cart', 'hart', 'part', 'pant']\n",
+      "['cart', 'hart', 'part', 'past']\n",
+      "['cart', 'hart', 'part', 'pare']\n",
+      "['cart', 'hart', 'part', 'park']\n",
+      "['cart', 'hart', 'part', 'pars']\n",
+      "['cart', 'hart', 'tart', 'dart']\n",
+      "['cart', 'hart', 'tart', 'mart']\n",
+      "['cart', 'hart', 'tart', 'part']\n",
+      "['cart', 'hart', 'tart', 'wart']\n",
+      "['cart', 'hart', 'tart', 'tort']\n",
+      "['cart', 'hart', 'tart', 'tact']\n",
+      "['cart', 'hart', 'tart', 'taut']\n",
+      "['cart', 'hart', 'tart', 'tare']\n",
+      "['cart', 'hart', 'tart', 'taro']\n",
+      "['cart', 'hart', 'tart', 'tarp']\n",
+      "['cart', 'hart', 'tart', 'tars']\n",
+      "['cart', 'hart', 'wart', 'dart']\n",
+      "['cart', 'hart', 'wart', 'mart']\n",
+      "['cart', 'hart', 'wart', 'part']\n",
+      "['cart', 'hart', 'wart', 'tart']\n",
+      "['cart', 'hart', 'wart', 'waft']\n",
+      "['cart', 'hart', 'wart', 'wait']\n",
+      "['cart', 'hart', 'wart', 'want']\n",
+      "['cart', 'hart', 'wart', 'watt']\n",
+      "['cart', 'hart', 'wart', 'ward']\n",
+      "['cart', 'hart', 'wart', 'ware']\n",
+      "['cart', 'hart', 'wart', 'warm']\n",
+      "['cart', 'hart', 'wart', 'warn']\n",
+      "['cart', 'hart', 'wart', 'warp']\n",
+      "['cart', 'hart', 'wart', 'wars']\n",
+      "['cart', 'hart', 'wart', 'wary']\n",
+      "['cart', 'hart', 'hurt', 'curt']\n",
+      "['cart', 'hart', 'hurt', 'hunt']\n",
+      "['cart', 'hart', 'hurt', 'hurl']\n",
+      "['cart', 'hart', 'haft', 'daft']\n",
+      "['cart', 'hart', 'haft', 'raft']\n",
+      "['cart', 'hart', 'haft', 'waft']\n",
+      "['cart', 'hart', 'haft', 'heft']\n",
+      "['cart', 'hart', 'haft', 'halt']\n",
+      "['cart', 'hart', 'halt', 'malt']\n",
+      "['cart', 'hart', 'halt', 'salt']\n",
+      "['cart', 'hart', 'halt', 'hilt']\n",
+      "['cart', 'hart', 'halt', 'haft']\n",
+      "['cart', 'hart', 'halt', 'hale']\n",
+      "['cart', 'hart', 'halt', 'half']\n",
+      "['cart', 'hart', 'halt', 'hall']\n",
+      "['cart', 'hart', 'halt', 'halo']\n",
+      "['cart', 'hart', 'hard', 'bard']\n",
+      "['cart', 'hart', 'hard', 'card']\n",
+      "['cart', 'hart', 'hard', 'lard']\n",
+      "['cart', 'hart', 'hard', 'ward']\n",
+      "['cart', 'hart', 'hard', 'yard']\n",
+      "['cart', 'hart', 'hard', 'herd']\n",
+      "['cart', 'hart', 'hard', 'hand']\n",
+      "['cart', 'hart', 'hard', 'hare']\n",
+      "['cart', 'hart', 'hard', 'hark']\n",
+      "['cart', 'hart', 'hard', 'harm']\n",
+      "['cart', 'hart', 'hard', 'harp']\n",
+      "['cart', 'hart', 'hare', 'bare']\n",
+      "['cart', 'hart', 'hare', 'care']\n",
+      "['cart', 'hart', 'hare', 'dare']\n",
+      "['cart', 'hart', 'hare', 'fare']\n",
+      "['cart', 'hart', 'hare', 'mare']\n",
+      "['cart', 'hart', 'hare', 'pare']\n",
+      "['cart', 'hart', 'hare', 'rare']\n",
+      "['cart', 'hart', 'hare', 'tare']\n",
+      "['cart', 'hart', 'hare', 'ware']\n",
+      "['cart', 'hart', 'hare', 'here']\n",
+      "['cart', 'hart', 'hare', 'hire']\n",
+      "['cart', 'hart', 'hare', 'hake']\n",
+      "['cart', 'hart', 'hare', 'hale']\n",
+      "['cart', 'hart', 'hare', 'hate']\n",
+      "['cart', 'hart', 'hare', 'have']\n",
+      "['cart', 'hart', 'hare', 'haze']\n",
+      "['cart', 'hart', 'hare', 'hard']\n",
+      "['cart', 'hart', 'hare', 'hark']\n",
+      "['cart', 'hart', 'hare', 'harm']\n",
+      "['cart', 'hart', 'hare', 'harp']\n",
+      "['cart', 'hart', 'hark', 'bark']\n",
+      "['cart', 'hart', 'hark', 'dark']\n",
+      "['cart', 'hart', 'hark', 'lark']\n",
+      "['cart', 'hart', 'hark', 'mark']\n",
+      "['cart', 'hart', 'hark', 'nark']\n",
+      "['cart', 'hart', 'hark', 'park']\n",
+      "['cart', 'hart', 'hark', 'hack']\n",
+      "['cart', 'hart', 'hark', 'hank']\n",
+      "['cart', 'hart', 'hark', 'hawk']\n",
+      "['cart', 'hart', 'hark', 'hard']\n",
+      "['cart', 'hart', 'hark', 'hare']\n",
+      "['cart', 'hart', 'hark', 'harm']\n",
+      "['cart', 'hart', 'hark', 'harp']\n",
+      "['cart', 'hart', 'harm', 'farm']\n",
+      "['cart', 'hart', 'harm', 'warm']\n",
+      "['cart', 'hart', 'harm', 'hard']\n",
+      "['cart', 'hart', 'harm', 'hare']\n",
+      "['cart', 'hart', 'harm', 'hark']\n",
+      "['cart', 'hart', 'harm', 'harp']\n",
+      "['cart', 'hart', 'harp', 'carp']\n",
+      "['cart', 'hart', 'harp', 'tarp']\n",
+      "['cart', 'hart', 'harp', 'warp']\n",
+      "['cart', 'hart', 'harp', 'hasp']\n",
+      "['cart', 'hart', 'harp', 'hard']\n",
+      "['cart', 'hart', 'harp', 'hare']\n",
+      "['cart', 'hart', 'harp', 'hark']\n",
+      "['cart', 'hart', 'harp', 'harm']\n",
+      "['cart', 'mart', 'dart', 'hart']\n",
+      "['cart', 'mart', 'dart', 'part']\n",
+      "['cart', 'mart', 'dart', 'tart']\n",
+      "['cart', 'mart', 'dart', 'wart']\n",
+      "['cart', 'mart', 'dart', 'dirt']\n",
+      "['cart', 'mart', 'dart', 'daft']\n",
+      "['cart', 'mart', 'dart', 'dare']\n",
+      "['cart', 'mart', 'dart', 'dark']\n",
+      "['cart', 'mart', 'dart', 'darn']\n",
+      "['cart', 'mart', 'hart', 'dart']\n",
+      "['cart', 'mart', 'hart', 'part']\n",
+      "['cart', 'mart', 'hart', 'tart']\n",
+      "['cart', 'mart', 'hart', 'wart']\n",
+      "['cart', 'mart', 'hart', 'hurt']\n",
+      "['cart', 'mart', 'hart', 'haft']\n",
+      "['cart', 'mart', 'hart', 'halt']\n",
+      "['cart', 'mart', 'hart', 'hard']\n",
+      "['cart', 'mart', 'hart', 'hare']\n",
+      "['cart', 'mart', 'hart', 'hark']\n",
+      "['cart', 'mart', 'hart', 'harm']\n",
+      "['cart', 'mart', 'hart', 'harp']\n",
+      "['cart', 'mart', 'part', 'dart']\n",
+      "['cart', 'mart', 'part', 'hart']\n",
+      "['cart', 'mart', 'part', 'tart']\n",
+      "['cart', 'mart', 'part', 'wart']\n",
+      "['cart', 'mart', 'part', 'pert']\n",
+      "['cart', 'mart', 'part', 'port']\n",
+      "['cart', 'mart', 'part', 'pact']\n",
+      "['cart', 'mart', 'part', 'pant']\n",
+      "['cart', 'mart', 'part', 'past']\n",
+      "['cart', 'mart', 'part', 'pare']\n",
+      "['cart', 'mart', 'part', 'park']\n",
+      "['cart', 'mart', 'part', 'pars']\n",
+      "['cart', 'mart', 'tart', 'dart']\n",
+      "['cart', 'mart', 'tart', 'hart']\n",
+      "['cart', 'mart', 'tart', 'part']\n",
+      "['cart', 'mart', 'tart', 'wart']\n",
+      "['cart', 'mart', 'tart', 'tort']\n",
+      "['cart', 'mart', 'tart', 'tact']\n",
+      "['cart', 'mart', 'tart', 'taut']\n",
+      "['cart', 'mart', 'tart', 'tare']\n",
+      "['cart', 'mart', 'tart', 'taro']\n",
+      "['cart', 'mart', 'tart', 'tarp']\n",
+      "['cart', 'mart', 'tart', 'tars']\n",
+      "['cart', 'mart', 'wart', 'dart']\n",
+      "['cart', 'mart', 'wart', 'hart']\n",
+      "['cart', 'mart', 'wart', 'part']\n",
+      "['cart', 'mart', 'wart', 'tart']\n",
+      "['cart', 'mart', 'wart', 'waft']\n",
+      "['cart', 'mart', 'wart', 'wait']\n",
+      "['cart', 'mart', 'wart', 'want']\n",
+      "['cart', 'mart', 'wart', 'watt']\n",
+      "['cart', 'mart', 'wart', 'ward']\n",
+      "['cart', 'mart', 'wart', 'ware']\n",
+      "['cart', 'mart', 'wart', 'warm']\n",
+      "['cart', 'mart', 'wart', 'warn']\n",
+      "['cart', 'mart', 'wart', 'warp']\n",
+      "['cart', 'mart', 'wart', 'wars']\n",
+      "['cart', 'mart', 'wart', 'wary']\n",
+      "['cart', 'mart', 'malt', 'halt']\n",
+      "['cart', 'mart', 'malt', 'salt']\n",
+      "['cart', 'mart', 'malt', 'melt']\n",
+      "['cart', 'mart', 'malt', 'mast']\n",
+      "['cart', 'mart', 'malt', 'matt']\n",
+      "['cart', 'mart', 'malt', 'male']\n",
+      "['cart', 'mart', 'malt', 'mall']\n",
+      "['cart', 'mart', 'mast', 'bast']\n",
+      "['cart', 'mart', 'mast', 'cast']\n",
+      "['cart', 'mart', 'mast', 'east']\n",
+      "['cart', 'mart', 'mast', 'fast']\n",
+      "['cart', 'mart', 'mast', 'last']\n",
+      "['cart', 'mart', 'mast', 'past']\n",
+      "['cart', 'mart', 'mast', 'vast']\n",
+      "['cart', 'mart', 'mast', 'mist']\n",
+      "['cart', 'mart', 'mast', 'most']\n",
+      "['cart', 'mart', 'mast', 'must']\n",
+      "['cart', 'mart', 'mast', 'malt']\n",
+      "['cart', 'mart', 'mast', 'matt']\n",
+      "['cart', 'mart', 'mast', 'mash']\n",
+      "['cart', 'mart', 'mast', 'mask']\n",
+      "['cart', 'mart', 'mast', 'mass']\n",
+      "['cart', 'mart', 'matt', 'watt']\n",
+      "['cart', 'mart', 'matt', 'mitt']\n",
+      "['cart', 'mart', 'matt', 'mutt']\n",
+      "['cart', 'mart', 'matt', 'malt']\n",
+      "['cart', 'mart', 'matt', 'mast']\n",
+      "['cart', 'mart', 'matt', 'mate']\n",
+      "['cart', 'mart', 'matt', 'math']\n",
+      "['cart', 'mart', 'matt', 'mats']\n",
+      "['cart', 'mart', 'mare', 'bare']\n",
+      "['cart', 'mart', 'mare', 'care']\n",
+      "['cart', 'mart', 'mare', 'dare']\n",
+      "['cart', 'mart', 'mare', 'fare']\n",
+      "['cart', 'mart', 'mare', 'hare']\n",
+      "['cart', 'mart', 'mare', 'pare']\n",
+      "['cart', 'mart', 'mare', 'rare']\n",
+      "['cart', 'mart', 'mare', 'tare']\n",
+      "['cart', 'mart', 'mare', 'ware']\n",
+      "['cart', 'mart', 'mare', 'mere']\n",
+      "['cart', 'mart', 'mare', 'mire']\n",
+      "['cart', 'mart', 'mare', 'more']\n",
+      "['cart', 'mart', 'mare', 'mace']\n",
+      "['cart', 'mart', 'mare', 'made']\n",
+      "['cart', 'mart', 'mare', 'make']\n",
+      "['cart', 'mart', 'mare', 'male']\n",
+      "['cart', 'mart', 'mare', 'mane']\n",
+      "['cart', 'mart', 'mare', 'mate']\n",
+      "['cart', 'mart', 'mare', 'maze']\n",
+      "['cart', 'mart', 'mare', 'mark']\n",
+      "['cart', 'mart', 'mare', 'mars']\n",
+      "['cart', 'mart', 'mark', 'bark']\n",
+      "['cart', 'mart', 'mark', 'dark']\n",
+      "['cart', 'mart', 'mark', 'hark']\n",
+      "['cart', 'mart', 'mark', 'lark']\n",
+      "['cart', 'mart', 'mark', 'nark']\n",
+      "['cart', 'mart', 'mark', 'park']\n",
+      "['cart', 'mart', 'mark', 'murk']\n",
+      "['cart', 'mart', 'mark', 'mask']\n",
+      "['cart', 'mart', 'mark', 'mare']\n",
+      "['cart', 'mart', 'mark', 'mars']\n",
+      "['cart', 'mart', 'mars', 'bars']\n",
+      "['cart', 'mart', 'mars', 'cars']\n",
+      "['cart', 'mart', 'mars', 'ears']\n",
+      "['cart', 'mart', 'mars', 'jars']\n",
+      "['cart', 'mart', 'mars', 'oars']\n",
+      "['cart', 'mart', 'mars', 'pars']\n",
+      "['cart', 'mart', 'mars', 'tars']\n",
+      "['cart', 'mart', 'mars', 'wars']\n",
+      "['cart', 'mart', 'mars', 'mads']\n",
+      "['cart', 'mart', 'mars', 'mans']\n",
+      "['cart', 'mart', 'mars', 'maps']\n",
+      "['cart', 'mart', 'mars', 'mass']\n",
+      "['cart', 'mart', 'mars', 'mats']\n",
+      "['cart', 'mart', 'mars', 'maws']\n",
+      "['cart', 'mart', 'mars', 'mare']\n",
+      "['cart', 'mart', 'mars', 'mark']\n",
+      "['cart', 'part', 'dart', 'hart']\n",
+      "['cart', 'part', 'dart', 'mart']\n",
+      "['cart', 'part', 'dart', 'tart']\n",
+      "['cart', 'part', 'dart', 'wart']\n",
+      "['cart', 'part', 'dart', 'dirt']\n",
+      "['cart', 'part', 'dart', 'daft']\n",
+      "['cart', 'part', 'dart', 'dare']\n",
+      "['cart', 'part', 'dart', 'dark']\n",
+      "['cart', 'part', 'dart', 'darn']\n",
+      "['cart', 'part', 'hart', 'dart']\n",
+      "['cart', 'part', 'hart', 'mart']\n",
+      "['cart', 'part', 'hart', 'tart']\n",
+      "['cart', 'part', 'hart', 'wart']\n",
+      "['cart', 'part', 'hart', 'hurt']\n",
+      "['cart', 'part', 'hart', 'haft']\n",
+      "['cart', 'part', 'hart', 'halt']\n",
+      "['cart', 'part', 'hart', 'hard']\n",
+      "['cart', 'part', 'hart', 'hare']\n",
+      "['cart', 'part', 'hart', 'hark']\n",
+      "['cart', 'part', 'hart', 'harm']\n",
+      "['cart', 'part', 'hart', 'harp']\n",
+      "['cart', 'part', 'mart', 'dart']\n",
+      "['cart', 'part', 'mart', 'hart']\n",
+      "['cart', 'part', 'mart', 'tart']\n",
+      "['cart', 'part', 'mart', 'wart']\n",
+      "['cart', 'part', 'mart', 'malt']\n",
+      "['cart', 'part', 'mart', 'mast']\n",
+      "['cart', 'part', 'mart', 'matt']\n",
+      "['cart', 'part', 'mart', 'mare']\n",
+      "['cart', 'part', 'mart', 'mark']\n",
+      "['cart', 'part', 'mart', 'mars']\n",
+      "['cart', 'part', 'tart', 'dart']\n",
+      "['cart', 'part', 'tart', 'hart']\n",
+      "['cart', 'part', 'tart', 'mart']\n",
+      "['cart', 'part', 'tart', 'wart']\n",
+      "['cart', 'part', 'tart', 'tort']\n",
+      "['cart', 'part', 'tart', 'tact']\n",
+      "['cart', 'part', 'tart', 'taut']\n",
+      "['cart', 'part', 'tart', 'tare']\n",
+      "['cart', 'part', 'tart', 'taro']\n",
+      "['cart', 'part', 'tart', 'tarp']\n",
+      "['cart', 'part', 'tart', 'tars']\n",
+      "['cart', 'part', 'wart', 'dart']\n",
+      "['cart', 'part', 'wart', 'hart']\n",
+      "['cart', 'part', 'wart', 'mart']\n",
+      "['cart', 'part', 'wart', 'tart']\n",
+      "['cart', 'part', 'wart', 'waft']\n",
+      "['cart', 'part', 'wart', 'wait']\n",
+      "['cart', 'part', 'wart', 'want']\n",
+      "['cart', 'part', 'wart', 'watt']\n",
+      "['cart', 'part', 'wart', 'ward']\n",
+      "['cart', 'part', 'wart', 'ware']\n",
+      "['cart', 'part', 'wart', 'warm']\n",
+      "['cart', 'part', 'wart', 'warn']\n",
+      "['cart', 'part', 'wart', 'warp']\n",
+      "['cart', 'part', 'wart', 'wars']\n",
+      "['cart', 'part', 'wart', 'wary']\n",
+      "['cart', 'part', 'pert', 'port']\n",
+      "['cart', 'part', 'pert', 'peat']\n",
+      "['cart', 'part', 'pert', 'pelt']\n",
+      "['cart', 'part', 'pert', 'pent']\n",
+      "['cart', 'part', 'pert', 'pest']\n",
+      "['cart', 'part', 'pert', 'perk']\n",
+      "['cart', 'part', 'pert', 'perm']\n",
+      "['cart', 'part', 'port', 'fort']\n",
+      "['cart', 'part', 'port', 'sort']\n",
+      "['cart', 'part', 'port', 'tort']\n",
+      "['cart', 'part', 'port', 'pert']\n",
+      "['cart', 'part', 'port', 'poet']\n",
+      "['cart', 'part', 'port', 'post']\n",
+      "['cart', 'part', 'port', 'pout']\n",
+      "['cart', 'part', 'port', 'pore']\n",
+      "['cart', 'part', 'port', 'pork']\n",
+      "['cart', 'part', 'port', 'porn']\n",
+      "['cart', 'part', 'pact', 'fact']\n",
+      "['cart', 'part', 'pact', 'tact']\n",
+      "['cart', 'part', 'pact', 'pant']\n",
+      "['cart', 'part', 'pact', 'past']\n",
+      "['cart', 'part', 'pact', 'pace']\n",
+      "['cart', 'part', 'pact', 'pack']\n",
+      "['cart', 'part', 'pant', 'cant']\n",
+      "['cart', 'part', 'pant', 'rant']\n",
+      "['cart', 'part', 'pant', 'want']\n",
+      "['cart', 'part', 'pant', 'pent']\n",
+      "['cart', 'part', 'pant', 'pint']\n",
+      "['cart', 'part', 'pant', 'punt']\n",
+      "['cart', 'part', 'pant', 'pact']\n",
+      "['cart', 'part', 'pant', 'past']\n",
+      "['cart', 'part', 'pant', 'pane']\n",
+      "['cart', 'part', 'pant', 'pang']\n",
+      "['cart', 'part', 'pant', 'pans']\n",
+      "['cart', 'part', 'past', 'bast']\n",
+      "['cart', 'part', 'past', 'cast']\n",
+      "['cart', 'part', 'past', 'east']\n",
+      "['cart', 'part', 'past', 'fast']\n",
+      "['cart', 'part', 'past', 'last']\n",
+      "['cart', 'part', 'past', 'mast']\n",
+      "['cart', 'part', 'past', 'vast']\n",
+      "['cart', 'part', 'past', 'pest']\n",
+      "['cart', 'part', 'past', 'post']\n",
+      "['cart', 'part', 'past', 'psst']\n",
+      "['cart', 'part', 'past', 'pact']\n",
+      "['cart', 'part', 'past', 'pant']\n",
+      "['cart', 'part', 'past', 'pass']\n",
+      "['cart', 'part', 'pare', 'bare']\n",
+      "['cart', 'part', 'pare', 'care']\n",
+      "['cart', 'part', 'pare', 'dare']\n",
+      "['cart', 'part', 'pare', 'fare']\n",
+      "['cart', 'part', 'pare', 'hare']\n",
+      "['cart', 'part', 'pare', 'mare']\n",
+      "['cart', 'part', 'pare', 'rare']\n",
+      "['cart', 'part', 'pare', 'tare']\n",
+      "['cart', 'part', 'pare', 'ware']\n",
+      "['cart', 'part', 'pare', 'pore']\n",
+      "['cart', 'part', 'pare', 'pure']\n",
+      "['cart', 'part', 'pare', 'pyre']\n",
+      "['cart', 'part', 'pare', 'pace']\n",
+      "['cart', 'part', 'pare', 'page']\n",
+      "['cart', 'part', 'pare', 'pale']\n",
+      "['cart', 'part', 'pare', 'pane']\n",
+      "['cart', 'part', 'pare', 'pate']\n",
+      "['cart', 'part', 'pare', 'pave']\n",
+      "['cart', 'part', 'pare', 'park']\n",
+      "['cart', 'part', 'pare', 'pars']\n",
+      "['cart', 'part', 'park', 'bark']\n",
+      "['cart', 'part', 'park', 'dark']\n",
+      "['cart', 'part', 'park', 'hark']\n",
+      "['cart', 'part', 'park', 'lark']\n",
+      "['cart', 'part', 'park', 'mark']\n",
+      "['cart', 'part', 'park', 'nark']\n",
+      "['cart', 'part', 'park', 'perk']\n",
+      "['cart', 'part', 'park', 'pork']\n",
+      "['cart', 'part', 'park', 'pack']\n",
+      "['cart', 'part', 'park', 'pare']\n",
+      "['cart', 'part', 'park', 'pars']\n",
+      "['cart', 'part', 'pars', 'bars']\n",
+      "['cart', 'part', 'pars', 'cars']\n",
+      "['cart', 'part', 'pars', 'ears']\n",
+      "['cart', 'part', 'pars', 'jars']\n",
+      "['cart', 'part', 'pars', 'mars']\n",
+      "['cart', 'part', 'pars', 'oars']\n",
+      "['cart', 'part', 'pars', 'tars']\n",
+      "['cart', 'part', 'pars', 'wars']\n",
+      "['cart', 'part', 'pars', 'pads']\n",
+      "['cart', 'part', 'pars', 'pals']\n",
+      "['cart', 'part', 'pars', 'pans']\n",
+      "['cart', 'part', 'pars', 'paps']\n",
+      "['cart', 'part', 'pars', 'pass']\n",
+      "['cart', 'part', 'pars', 'pats']\n",
+      "['cart', 'part', 'pars', 'paws']\n",
+      "['cart', 'part', 'pars', 'pays']\n",
+      "['cart', 'part', 'pars', 'pare']\n",
+      "['cart', 'part', 'pars', 'park']\n",
+      "['cart', 'tart', 'dart', 'hart']\n",
+      "['cart', 'tart', 'dart', 'mart']\n",
+      "['cart', 'tart', 'dart', 'part']\n",
+      "['cart', 'tart', 'dart', 'wart']\n",
+      "['cart', 'tart', 'dart', 'dirt']\n",
+      "['cart', 'tart', 'dart', 'daft']\n",
+      "['cart', 'tart', 'dart', 'dare']\n",
+      "['cart', 'tart', 'dart', 'dark']\n",
+      "['cart', 'tart', 'dart', 'darn']\n",
+      "['cart', 'tart', 'hart', 'dart']\n",
+      "['cart', 'tart', 'hart', 'mart']\n",
+      "['cart', 'tart', 'hart', 'part']\n",
+      "['cart', 'tart', 'hart', 'wart']\n",
+      "['cart', 'tart', 'hart', 'hurt']\n",
+      "['cart', 'tart', 'hart', 'haft']\n",
+      "['cart', 'tart', 'hart', 'halt']\n",
+      "['cart', 'tart', 'hart', 'hard']\n",
+      "['cart', 'tart', 'hart', 'hare']\n",
+      "['cart', 'tart', 'hart', 'hark']\n",
+      "['cart', 'tart', 'hart', 'harm']\n",
+      "['cart', 'tart', 'hart', 'harp']\n",
+      "['cart', 'tart', 'mart', 'dart']\n",
+      "['cart', 'tart', 'mart', 'hart']\n",
+      "['cart', 'tart', 'mart', 'part']\n",
+      "['cart', 'tart', 'mart', 'wart']\n",
+      "['cart', 'tart', 'mart', 'malt']\n",
+      "['cart', 'tart', 'mart', 'mast']\n",
+      "['cart', 'tart', 'mart', 'matt']\n",
+      "['cart', 'tart', 'mart', 'mare']\n",
+      "['cart', 'tart', 'mart', 'mark']\n",
+      "['cart', 'tart', 'mart', 'mars']\n",
+      "['cart', 'tart', 'part', 'dart']\n",
+      "['cart', 'tart', 'part', 'hart']\n",
+      "['cart', 'tart', 'part', 'mart']\n",
+      "['cart', 'tart', 'part', 'wart']\n",
+      "['cart', 'tart', 'part', 'pert']\n",
+      "['cart', 'tart', 'part', 'port']\n",
+      "['cart', 'tart', 'part', 'pact']\n",
+      "['cart', 'tart', 'part', 'pant']\n",
+      "['cart', 'tart', 'part', 'past']\n",
+      "['cart', 'tart', 'part', 'pare']\n",
+      "['cart', 'tart', 'part', 'park']\n",
+      "['cart', 'tart', 'part', 'pars']\n",
+      "['cart', 'tart', 'wart', 'dart']\n",
+      "['cart', 'tart', 'wart', 'hart']\n",
+      "['cart', 'tart', 'wart', 'mart']\n",
+      "['cart', 'tart', 'wart', 'part']\n",
+      "['cart', 'tart', 'wart', 'waft']\n",
+      "['cart', 'tart', 'wart', 'wait']\n",
+      "['cart', 'tart', 'wart', 'want']\n",
+      "['cart', 'tart', 'wart', 'watt']\n",
+      "['cart', 'tart', 'wart', 'ward']\n",
+      "['cart', 'tart', 'wart', 'ware']\n",
+      "['cart', 'tart', 'wart', 'warm']\n",
+      "['cart', 'tart', 'wart', 'warn']\n",
+      "['cart', 'tart', 'wart', 'warp']\n",
+      "['cart', 'tart', 'wart', 'wars']\n",
+      "['cart', 'tart', 'wart', 'wary']\n",
+      "['cart', 'tart', 'tort', 'fort']\n",
+      "['cart', 'tart', 'tort', 'port']\n",
+      "['cart', 'tart', 'tort', 'sort']\n",
+      "['cart', 'tart', 'tort', 'toot']\n",
+      "['cart', 'tart', 'tort', 'tost']\n",
+      "['cart', 'tart', 'tort', 'tout']\n",
+      "['cart', 'tart', 'tort', 'tore']\n",
+      "['cart', 'tart', 'tort', 'torn']\n",
+      "['cart', 'tart', 'tort', 'tors']\n",
+      "['cart', 'tart', 'tact', 'fact']\n",
+      "['cart', 'tart', 'tact', 'pact']\n",
+      "['cart', 'tart', 'tact', 'taut']\n",
+      "['cart', 'tart', 'tact', 'tack']\n",
+      "['cart', 'tart', 'tact', 'taco']\n",
+      "['cart', 'tart', 'taut', 'tout']\n",
+      "['cart', 'tart', 'taut', 'tact']\n",
+      "['cart', 'tart', 'tare', 'bare']\n",
+      "['cart', 'tart', 'tare', 'care']\n",
+      "['cart', 'tart', 'tare', 'dare']\n",
+      "['cart', 'tart', 'tare', 'fare']\n",
+      "['cart', 'tart', 'tare', 'hare']\n",
+      "['cart', 'tart', 'tare', 'mare']\n",
+      "['cart', 'tart', 'tare', 'pare']\n",
+      "['cart', 'tart', 'tare', 'rare']\n",
+      "['cart', 'tart', 'tare', 'ware']\n",
+      "['cart', 'tart', 'tare', 'tire']\n",
+      "['cart', 'tart', 'tare', 'tore']\n",
+      "['cart', 'tart', 'tare', 'tyre']\n",
+      "['cart', 'tart', 'tare', 'take']\n",
+      "['cart', 'tart', 'tare', 'tale']\n",
+      "['cart', 'tart', 'tare', 'tame']\n",
+      "['cart', 'tart', 'tare', 'tape']\n",
+      "['cart', 'tart', 'tare', 'taro']\n",
+      "['cart', 'tart', 'tare', 'tarp']\n",
+      "['cart', 'tart', 'tare', 'tars']\n",
+      "['cart', 'tart', 'taro', 'tiro']\n",
+      "['cart', 'tart', 'taro', 'tyro']\n",
+      "['cart', 'tart', 'taro', 'taco']\n",
+      "['cart', 'tart', 'taro', 'tare']\n",
+      "['cart', 'tart', 'taro', 'tarp']\n",
+      "['cart', 'tart', 'taro', 'tars']\n",
+      "['cart', 'tart', 'tarp', 'carp']\n",
+      "['cart', 'tart', 'tarp', 'harp']\n",
+      "['cart', 'tart', 'tarp', 'warp']\n",
+      "['cart', 'tart', 'tarp', 'tamp']\n",
+      "['cart', 'tart', 'tarp', 'tare']\n",
+      "['cart', 'tart', 'tarp', 'taro']\n",
+      "['cart', 'tart', 'tarp', 'tars']\n",
+      "['cart', 'tart', 'tars', 'bars']\n",
+      "['cart', 'tart', 'tars', 'cars']\n",
+      "['cart', 'tart', 'tars', 'ears']\n",
+      "['cart', 'tart', 'tars', 'jars']\n",
+      "['cart', 'tart', 'tars', 'mars']\n",
+      "['cart', 'tart', 'tars', 'oars']\n",
+      "['cart', 'tart', 'tars', 'pars']\n",
+      "['cart', 'tart', 'tars', 'wars']\n",
+      "['cart', 'tart', 'tars', 'tors']\n",
+      "['cart', 'tart', 'tars', 'tabs']\n",
+      "['cart', 'tart', 'tars', 'tads']\n",
+      "['cart', 'tart', 'tars', 'tags']\n",
+      "['cart', 'tart', 'tars', 'tams']\n",
+      "['cart', 'tart', 'tars', 'tans']\n",
+      "['cart', 'tart', 'tars', 'taps']\n",
+      "['cart', 'tart', 'tars', 'tats']\n",
+      "['cart', 'tart', 'tars', 'tare']\n",
+      "['cart', 'tart', 'tars', 'taro']\n",
+      "['cart', 'tart', 'tars', 'tarp']\n",
+      "['cart', 'wart', 'dart', 'hart']\n",
+      "['cart', 'wart', 'dart', 'mart']\n",
+      "['cart', 'wart', 'dart', 'part']\n",
+      "['cart', 'wart', 'dart', 'tart']\n",
+      "['cart', 'wart', 'dart', 'dirt']\n",
+      "['cart', 'wart', 'dart', 'daft']\n",
+      "['cart', 'wart', 'dart', 'dare']\n",
+      "['cart', 'wart', 'dart', 'dark']\n",
+      "['cart', 'wart', 'dart', 'darn']\n",
+      "['cart', 'wart', 'hart', 'dart']\n",
+      "['cart', 'wart', 'hart', 'mart']\n",
+      "['cart', 'wart', 'hart', 'part']\n",
+      "['cart', 'wart', 'hart', 'tart']\n",
+      "['cart', 'wart', 'hart', 'hurt']\n",
+      "['cart', 'wart', 'hart', 'haft']\n",
+      "['cart', 'wart', 'hart', 'halt']\n",
+      "['cart', 'wart', 'hart', 'hard']\n",
+      "['cart', 'wart', 'hart', 'hare']\n",
+      "['cart', 'wart', 'hart', 'hark']\n",
+      "['cart', 'wart', 'hart', 'harm']\n",
+      "['cart', 'wart', 'hart', 'harp']\n",
+      "['cart', 'wart', 'mart', 'dart']\n",
+      "['cart', 'wart', 'mart', 'hart']\n",
+      "['cart', 'wart', 'mart', 'part']\n",
+      "['cart', 'wart', 'mart', 'tart']\n",
+      "['cart', 'wart', 'mart', 'malt']\n",
+      "['cart', 'wart', 'mart', 'mast']\n",
+      "['cart', 'wart', 'mart', 'matt']\n",
+      "['cart', 'wart', 'mart', 'mare']\n",
+      "['cart', 'wart', 'mart', 'mark']\n",
+      "['cart', 'wart', 'mart', 'mars']\n",
+      "['cart', 'wart', 'part', 'dart']\n",
+      "['cart', 'wart', 'part', 'hart']\n",
+      "['cart', 'wart', 'part', 'mart']\n",
+      "['cart', 'wart', 'part', 'tart']\n",
+      "['cart', 'wart', 'part', 'pert']\n",
+      "['cart', 'wart', 'part', 'port']\n",
+      "['cart', 'wart', 'part', 'pact']\n",
+      "['cart', 'wart', 'part', 'pant']\n",
+      "['cart', 'wart', 'part', 'past']\n",
+      "['cart', 'wart', 'part', 'pare']\n",
+      "['cart', 'wart', 'part', 'park']\n",
+      "['cart', 'wart', 'part', 'pars']\n",
+      "['cart', 'wart', 'tart', 'dart']\n",
+      "['cart', 'wart', 'tart', 'hart']\n",
+      "['cart', 'wart', 'tart', 'mart']\n",
+      "['cart', 'wart', 'tart', 'part']\n",
+      "['cart', 'wart', 'tart', 'tort']\n",
+      "['cart', 'wart', 'tart', 'tact']\n",
+      "['cart', 'wart', 'tart', 'taut']\n",
+      "['cart', 'wart', 'tart', 'tare']\n",
+      "['cart', 'wart', 'tart', 'taro']\n",
+      "['cart', 'wart', 'tart', 'tarp']\n",
+      "['cart', 'wart', 'tart', 'tars']\n",
+      "['cart', 'wart', 'waft', 'daft']\n",
+      "['cart', 'wart', 'waft', 'haft']\n",
+      "['cart', 'wart', 'waft', 'raft']\n",
+      "['cart', 'wart', 'waft', 'weft']\n",
+      "['cart', 'wart', 'waft', 'wait']\n",
+      "['cart', 'wart', 'waft', 'want']\n",
+      "['cart', 'wart', 'waft', 'watt']\n",
+      "['cart', 'wart', 'wait', 'bait']\n",
+      "['cart', 'wart', 'wait', 'gait']\n",
+      "['cart', 'wart', 'wait', 'whit']\n",
+      "['cart', 'wart', 'wait', 'writ']\n",
+      "['cart', 'wart', 'wait', 'waft']\n",
+      "['cart', 'wart', 'wait', 'want']\n",
+      "['cart', 'wart', 'wait', 'watt']\n",
+      "['cart', 'wart', 'wait', 'waif']\n",
+      "['cart', 'wart', 'wait', 'wail']\n",
+      "['cart', 'wart', 'want', 'cant']\n",
+      "['cart', 'wart', 'want', 'pant']\n",
+      "['cart', 'wart', 'want', 'rant']\n",
+      "['cart', 'wart', 'want', 'went']\n",
+      "['cart', 'wart', 'want', 'wont']\n",
+      "['cart', 'wart', 'want', 'waft']\n",
+      "['cart', 'wart', 'want', 'wait']\n",
+      "['cart', 'wart', 'want', 'watt']\n",
+      "['cart', 'wart', 'want', 'wand']\n",
+      "['cart', 'wart', 'want', 'wane']\n",
+      "['cart', 'wart', 'watt', 'matt']\n",
+      "['cart', 'wart', 'watt', 'waft']\n",
+      "['cart', 'wart', 'watt', 'wait']\n",
+      "['cart', 'wart', 'watt', 'want']\n",
+      "['cart', 'wart', 'ward', 'bard']\n",
+      "['cart', 'wart', 'ward', 'card']\n",
+      "['cart', 'wart', 'ward', 'hard']\n",
+      "['cart', 'wart', 'ward', 'lard']\n",
+      "['cart', 'wart', 'ward', 'yard']\n",
+      "['cart', 'wart', 'ward', 'word']\n",
+      "['cart', 'wart', 'ward', 'wand']\n",
+      "['cart', 'wart', 'ward', 'ware']\n",
+      "['cart', 'wart', 'ward', 'warm']\n",
+      "['cart', 'wart', 'ward', 'warn']\n",
+      "['cart', 'wart', 'ward', 'warp']\n",
+      "['cart', 'wart', 'ward', 'wars']\n",
+      "['cart', 'wart', 'ward', 'wary']\n",
+      "['cart', 'wart', 'ware', 'bare']\n",
+      "['cart', 'wart', 'ware', 'care']\n",
+      "['cart', 'wart', 'ware', 'dare']\n",
+      "['cart', 'wart', 'ware', 'fare']\n",
+      "['cart', 'wart', 'ware', 'hare']\n",
+      "['cart', 'wart', 'ware', 'mare']\n",
+      "['cart', 'wart', 'ware', 'pare']\n",
+      "['cart', 'wart', 'ware', 'rare']\n",
+      "['cart', 'wart', 'ware', 'tare']\n",
+      "['cart', 'wart', 'ware', 'were']\n",
+      "['cart', 'wart', 'ware', 'wire']\n",
+      "['cart', 'wart', 'ware', 'wore']\n",
+      "['cart', 'wart', 'ware', 'wade']\n",
+      "['cart', 'wart', 'ware', 'wage']\n",
+      "['cart', 'wart', 'ware', 'wake']\n",
+      "['cart', 'wart', 'ware', 'wale']\n",
+      "['cart', 'wart', 'ware', 'wane']\n",
+      "['cart', 'wart', 'ware', 'wave']\n",
+      "['cart', 'wart', 'ware', 'ward']\n",
+      "['cart', 'wart', 'ware', 'warm']\n",
+      "['cart', 'wart', 'ware', 'warn']\n",
+      "['cart', 'wart', 'ware', 'warp']\n",
+      "['cart', 'wart', 'ware', 'wars']\n",
+      "['cart', 'wart', 'ware', 'wary']\n",
+      "['cart', 'wart', 'warm', 'farm']\n",
+      "['cart', 'wart', 'warm', 'harm']\n",
+      "['cart', 'wart', 'warm', 'worm']\n",
+      "['cart', 'wart', 'warm', 'ward']\n",
+      "['cart', 'wart', 'warm', 'ware']\n",
+      "['cart', 'wart', 'warm', 'warn']\n",
+      "['cart', 'wart', 'warm', 'warp']\n",
+      "['cart', 'wart', 'warm', 'wars']\n",
+      "['cart', 'wart', 'warm', 'wary']\n",
+      "['cart', 'wart', 'warn', 'barn']\n",
+      "['cart', 'wart', 'warn', 'darn']\n",
+      "['cart', 'wart', 'warn', 'earn']\n",
+      "['cart', 'wart', 'warn', 'yarn']\n",
+      "['cart', 'wart', 'warn', 'worn']\n",
+      "['cart', 'wart', 'warn', 'ward']\n",
+      "['cart', 'wart', 'warn', 'ware']\n",
+      "['cart', 'wart', 'warn', 'warm']\n",
+      "['cart', 'wart', 'warn', 'warp']\n",
+      "['cart', 'wart', 'warn', 'wars']\n",
+      "['cart', 'wart', 'warn', 'wary']\n",
+      "['cart', 'wart', 'warp', 'carp']\n",
+      "['cart', 'wart', 'warp', 'harp']\n",
+      "['cart', 'wart', 'warp', 'tarp']\n",
+      "['cart', 'wart', 'warp', 'wasp']\n",
+      "['cart', 'wart', 'warp', 'ward']\n",
+      "['cart', 'wart', 'warp', 'ware']\n",
+      "['cart', 'wart', 'warp', 'warm']\n",
+      "['cart', 'wart', 'warp', 'warn']\n",
+      "['cart', 'wart', 'warp', 'wars']\n",
+      "['cart', 'wart', 'warp', 'wary']\n",
+      "['cart', 'wart', 'wars', 'bars']\n",
+      "['cart', 'wart', 'wars', 'cars']\n",
+      "['cart', 'wart', 'wars', 'ears']\n",
+      "['cart', 'wart', 'wars', 'jars']\n",
+      "['cart', 'wart', 'wars', 'mars']\n",
+      "['cart', 'wart', 'wars', 'oars']\n",
+      "['cart', 'wart', 'wars', 'pars']\n",
+      "['cart', 'wart', 'wars', 'tars']\n",
+      "['cart', 'wart', 'wars', 'wads']\n",
+      "['cart', 'wart', 'wars', 'wags']\n",
+      "['cart', 'wart', 'wars', 'ways']\n",
+      "['cart', 'wart', 'wars', 'ward']\n",
+      "['cart', 'wart', 'wars', 'ware']\n",
+      "['cart', 'wart', 'wars', 'warm']\n",
+      "['cart', 'wart', 'wars', 'warn']\n",
+      "['cart', 'wart', 'wars', 'warp']\n",
+      "['cart', 'wart', 'wars', 'wary']\n",
+      "['cart', 'wart', 'wary', 'nary']\n",
+      "['cart', 'wart', 'wary', 'vary']\n",
+      "['cart', 'wart', 'wary', 'wiry']\n",
+      "['cart', 'wart', 'wary', 'wavy']\n",
+      "['cart', 'wart', 'wary', 'waxy']\n",
+      "['cart', 'wart', 'wary', 'ward']\n",
+      "['cart', 'wart', 'wary', 'ware']\n",
+      "['cart', 'wart', 'wary', 'warm']\n",
+      "['cart', 'wart', 'wary', 'warn']\n",
+      "['cart', 'wart', 'wary', 'warp']\n",
+      "['cart', 'wart', 'wary', 'wars']\n",
+      "['cart', 'curt', 'hurt', 'hart']\n",
+      "['cart', 'curt', 'hurt', 'hunt']\n",
+      "['cart', 'curt', 'hurt', 'hurl']\n",
+      "['cart', 'curt', 'cult', 'colt']\n",
+      "['cart', 'curt', 'cult', 'cull']\n",
+      "['cart', 'curt', 'curb', 'curd']\n",
+      "['cart', 'curt', 'curb', 'cure']\n",
+      "['cart', 'curt', 'curb', 'curl']\n",
+      "['cart', 'curt', 'curb', 'curs']\n",
+      "['cart', 'curt', 'curd', 'turd']\n",
+      "['cart', 'curt', 'curd', 'card']\n",
+      "['cart', 'curt', 'curd', 'cord']\n",
+      "['cart', 'curt', 'curd', 'cued']\n",
+      "['cart', 'curt', 'curd', 'curb']\n",
+      "['cart', 'curt', 'curd', 'cure']\n",
+      "['cart', 'curt', 'curd', 'curl']\n",
+      "['cart', 'curt', 'curd', 'curs']\n",
+      "['cart', 'curt', 'cure', 'lure']\n",
+      "['cart', 'curt', 'cure', 'pure']\n",
+      "['cart', 'curt', 'cure', 'sure']\n",
+      "['cart', 'curt', 'cure', 'care']\n",
+      "['cart', 'curt', 'cure', 'core']\n",
+      "['cart', 'curt', 'cure', 'cube']\n",
+      "['cart', 'curt', 'cure', 'cute']\n",
+      "['cart', 'curt', 'cure', 'curb']\n",
+      "['cart', 'curt', 'cure', 'curd']\n",
+      "['cart', 'curt', 'cure', 'curl']\n",
+      "['cart', 'curt', 'cure', 'curs']\n",
+      "['cart', 'curt', 'curl', 'furl']\n",
+      "['cart', 'curt', 'curl', 'hurl']\n",
+      "['cart', 'curt', 'curl', 'purl']\n",
+      "['cart', 'curt', 'curl', 'cull']\n",
+      "['cart', 'curt', 'curl', 'curb']\n",
+      "['cart', 'curt', 'curl', 'curd']\n",
+      "['cart', 'curt', 'curl', 'cure']\n",
+      "['cart', 'curt', 'curl', 'curs']\n",
+      "['cart', 'curt', 'curs', 'burs']\n",
+      "['cart', 'curt', 'curs', 'furs']\n",
+      "['cart', 'curt', 'curs', 'ours']\n",
+      "['cart', 'curt', 'curs', 'cars']\n",
+      "['cart', 'curt', 'curs', 'cubs']\n",
+      "['cart', 'curt', 'curs', 'cuds']\n",
+      "['cart', 'curt', 'curs', 'cues']\n",
+      "['cart', 'curt', 'curs', 'cums']\n",
+      "['cart', 'curt', 'curs', 'cups']\n",
+      "['cart', 'curt', 'curs', 'cuss']\n",
+      "['cart', 'curt', 'curs', 'cuts']\n",
+      "['cart', 'curt', 'curs', 'curb']\n",
+      "['cart', 'curt', 'curs', 'curd']\n",
+      "['cart', 'curt', 'curs', 'cure']\n",
+      "['cart', 'curt', 'curs', 'curl']\n",
+      "['cart', 'cant', 'pant', 'rant']\n",
+      "['cart', 'cant', 'pant', 'want']\n",
+      "['cart', 'cant', 'pant', 'pent']\n",
+      "['cart', 'cant', 'pant', 'pint']\n",
+      "['cart', 'cant', 'pant', 'punt']\n",
+      "['cart', 'cant', 'pant', 'pact']\n",
+      "['cart', 'cant', 'pant', 'part']\n",
+      "['cart', 'cant', 'pant', 'past']\n",
+      "['cart', 'cant', 'pant', 'pane']\n",
+      "['cart', 'cant', 'pant', 'pang']\n",
+      "['cart', 'cant', 'pant', 'pans']\n",
+      "['cart', 'cant', 'rant', 'pant']\n",
+      "['cart', 'cant', 'rant', 'want']\n",
+      "['cart', 'cant', 'rant', 'rent']\n",
+      "['cart', 'cant', 'rant', 'runt']\n",
+      "['cart', 'cant', 'rant', 'raft']\n",
+      "['cart', 'cant', 'rant', 'rapt']\n",
+      "['cart', 'cant', 'rant', 'rang']\n",
+      "['cart', 'cant', 'rant', 'rank']\n",
+      "['cart', 'cant', 'want', 'pant']\n",
+      "['cart', 'cant', 'want', 'rant']\n",
+      "['cart', 'cant', 'want', 'went']\n",
+      "['cart', 'cant', 'want', 'wont']\n",
+      "['cart', 'cant', 'want', 'waft']\n",
+      "['cart', 'cant', 'want', 'wait']\n",
+      "['cart', 'cant', 'want', 'wart']\n",
+      "['cart', 'cant', 'want', 'watt']\n",
+      "['cart', 'cant', 'want', 'wand']\n",
+      "['cart', 'cant', 'want', 'wane']\n",
+      "['cart', 'cant', 'cent', 'bent']\n",
+      "['cart', 'cant', 'cent', 'dent']\n",
+      "['cart', 'cant', 'cent', 'gent']\n",
+      "['cart', 'cant', 'cent', 'lent']\n",
+      "['cart', 'cant', 'cent', 'pent']\n",
+      "['cart', 'cant', 'cent', 'rent']\n",
+      "['cart', 'cant', 'cent', 'sent']\n",
+      "['cart', 'cant', 'cent', 'tent']\n",
+      "['cart', 'cant', 'cent', 'vent']\n",
+      "['cart', 'cant', 'cent', 'went']\n",
+      "['cart', 'cant', 'cast', 'bast']\n",
+      "['cart', 'cant', 'cast', 'east']\n",
+      "['cart', 'cant', 'cast', 'fast']\n",
+      "['cart', 'cant', 'cast', 'last']\n",
+      "['cart', 'cant', 'cast', 'mast']\n",
+      "['cart', 'cant', 'cast', 'past']\n",
+      "['cart', 'cant', 'cast', 'vast']\n",
+      "['cart', 'cant', 'cast', 'cost']\n",
+      "['cart', 'cant', 'cast', 'cyst']\n",
+      "['cart', 'cant', 'cast', 'case']\n",
+      "['cart', 'cant', 'cast', 'cash']\n",
+      "['cart', 'cant', 'cast', 'cask']\n",
+      "['cart', 'cant', 'cane', 'bane']\n",
+      "['cart', 'cant', 'cane', 'lane']\n",
+      "['cart', 'cant', 'cane', 'mane']\n",
+      "['cart', 'cant', 'cane', 'pane']\n",
+      "['cart', 'cant', 'cane', 'sane']\n",
+      "['cart', 'cant', 'cane', 'vane']\n",
+      "['cart', 'cant', 'cane', 'wane']\n",
+      "['cart', 'cant', 'cane', 'cone']\n",
+      "['cart', 'cant', 'cane', 'cafe']\n",
+      "['cart', 'cant', 'cane', 'cage']\n",
+      "['cart', 'cant', 'cane', 'cake']\n",
+      "['cart', 'cant', 'cane', 'came']\n",
+      "['cart', 'cant', 'cane', 'cape']\n",
+      "['cart', 'cant', 'cane', 'care']\n",
+      "['cart', 'cant', 'cane', 'case']\n",
+      "['cart', 'cant', 'cane', 'cave']\n",
+      "['cart', 'cant', 'cane', 'cans']\n",
+      "['cart', 'cant', 'cans', 'bans']\n",
+      "['cart', 'cant', 'cans', 'fans']\n",
+      "['cart', 'cant', 'cans', 'mans']\n",
+      "['cart', 'cant', 'cans', 'pans']\n",
+      "['cart', 'cant', 'cans', 'sans']\n",
+      "['cart', 'cant', 'cans', 'tans']\n",
+      "['cart', 'cant', 'cans', 'vans']\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "['cart', 'cant', 'cans', 'vans']"
+      ]
+     },
+     "execution_count": 20,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "bfs_search('cart', 'vans', debug=True)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "['cart', 'cant', 'cane', 'vane']"
+      ]
+     },
+     "execution_count": 21,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "bfs_search('cart', 'vane')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "['cart',\n",
+       " 'dart',\n",
+       " 'hart',\n",
+       " 'mart',\n",
+       " 'part',\n",
+       " 'tart',\n",
+       " 'wart',\n",
+       " 'waft',\n",
+       " 'daft',\n",
+       " 'haft',\n",
+       " 'raft',\n",
+       " 'rift',\n",
+       " 'gift',\n",
+       " 'lift',\n",
+       " 'sift',\n",
+       " 'soft',\n",
+       " 'loft',\n",
+       " 'left',\n",
+       " 'deft',\n",
+       " 'heft',\n",
+       " 'weft',\n",
+       " 'welt',\n",
+       " 'belt',\n",
+       " 'felt',\n",
+       " 'gelt',\n",
+       " 'melt',\n",
+       " 'pelt',\n",
+       " 'peat',\n",
+       " 'beat',\n",
+       " 'feat',\n",
+       " 'heat',\n",
+       " 'meat',\n",
+       " 'neat',\n",
+       " 'seat',\n",
+       " 'teat',\n",
+       " 'that',\n",
+       " 'chat',\n",
+       " 'shat',\n",
+       " 'what',\n",
+       " 'whet',\n",
+       " 'whit',\n",
+       " 'chit',\n",
+       " 'chic',\n",
+       " 'chid',\n",
+       " 'chin',\n",
+       " 'shin',\n",
+       " 'thin',\n",
+       " 'twin',\n",
+       " 'twig',\n",
+       " 'swig',\n",
+       " 'swag',\n",
+       " 'shag',\n",
+       " 'slag',\n",
+       " 'flag',\n",
+       " 'flog',\n",
+       " 'blog',\n",
+       " 'clog',\n",
+       " 'slog',\n",
+       " 'smog',\n",
+       " 'smug',\n",
+       " 'slug',\n",
+       " 'plug',\n",
+       " 'plum',\n",
+       " 'alum',\n",
+       " 'glum',\n",
+       " 'slum',\n",
+       " 'scum',\n",
+       " 'swum',\n",
+       " 'swam',\n",
+       " 'scam',\n",
+       " 'seam',\n",
+       " 'beam',\n",
+       " 'ream',\n",
+       " 'team',\n",
+       " 'tram',\n",
+       " 'cram',\n",
+       " 'dram',\n",
+       " 'gram',\n",
+       " 'pram',\n",
+       " 'prim',\n",
+       " 'brim',\n",
+       " 'grim',\n",
+       " 'trim',\n",
+       " 'trig',\n",
+       " 'brig',\n",
+       " 'brag',\n",
+       " 'crag',\n",
+       " 'drag',\n",
+       " 'drug',\n",
+       " 'drub',\n",
+       " 'grub',\n",
+       " 'grab',\n",
+       " 'crab',\n",
+       " 'drab',\n",
+       " 'draw',\n",
+       " 'craw',\n",
+       " 'claw',\n",
+       " 'flaw',\n",
+       " 'slaw',\n",
+       " 'slew',\n",
+       " 'blew',\n",
+       " 'clew',\n",
+       " 'flew',\n",
+       " 'flow',\n",
+       " 'blow',\n",
+       " 'glow',\n",
+       " 'slow',\n",
+       " 'scow',\n",
+       " 'show',\n",
+       " 'chow',\n",
+       " 'crow',\n",
+       " 'brow',\n",
+       " 'grow',\n",
+       " 'prow',\n",
+       " 'prod',\n",
+       " 'trod',\n",
+       " 'trot',\n",
+       " 'toot',\n",
+       " 'boot',\n",
+       " 'coot',\n",
+       " 'foot',\n",
+       " 'hoot',\n",
+       " 'loot',\n",
+       " 'moot',\n",
+       " 'root',\n",
+       " 'soot',\n",
+       " 'shot',\n",
+       " 'slot',\n",
+       " 'blot',\n",
+       " 'clot',\n",
+       " 'plot',\n",
+       " 'plod',\n",
+       " 'clod',\n",
+       " 'clad',\n",
+       " 'glad',\n",
+       " 'goad',\n",
+       " 'load',\n",
+       " 'road',\n",
+       " 'toad',\n",
+       " 'toed',\n",
+       " 'coed',\n",
+       " 'hoed',\n",
+       " 'heed',\n",
+       " 'deed',\n",
+       " 'feed',\n",
+       " 'geed',\n",
+       " 'need',\n",
+       " 'peed',\n",
+       " 'reed',\n",
+       " 'seed',\n",
+       " 'teed',\n",
+       " 'weed',\n",
+       " 'weld',\n",
+       " 'geld',\n",
+       " 'held',\n",
+       " 'meld',\n",
+       " 'veld',\n",
+       " 'vend',\n",
+       " 'bend',\n",
+       " 'fend',\n",
+       " 'lend',\n",
+       " 'mend',\n",
+       " 'rend',\n",
+       " 'send',\n",
+       " 'tend',\n",
+       " 'wend',\n",
+       " 'wand',\n",
+       " 'band',\n",
+       " 'hand',\n",
+       " 'land',\n",
+       " 'sand',\n",
+       " 'said',\n",
+       " 'laid',\n",
+       " 'maid',\n",
+       " 'paid',\n",
+       " 'raid',\n",
+       " 'rail',\n",
+       " 'bail',\n",
+       " 'fail',\n",
+       " 'hail',\n",
+       " 'jail',\n",
+       " 'mail',\n",
+       " 'nail',\n",
+       " 'pail',\n",
+       " 'sail',\n",
+       " 'tail',\n",
+       " 'wail',\n",
+       " 'wall',\n",
+       " 'ball',\n",
+       " 'call',\n",
+       " 'fall',\n",
+       " 'gall',\n",
+       " 'hall',\n",
+       " 'mall',\n",
+       " 'pall',\n",
+       " 'tall',\n",
+       " 'tell',\n",
+       " 'bell',\n",
+       " 'cell',\n",
+       " 'dell',\n",
+       " 'fell',\n",
+       " 'hell',\n",
+       " 'jell',\n",
+       " 'sell',\n",
+       " 'well',\n",
+       " 'yell',\n",
+       " 'yelp',\n",
+       " 'help',\n",
+       " 'kelp',\n",
+       " 'keep',\n",
+       " 'beep',\n",
+       " 'deep',\n",
+       " 'jeep',\n",
+       " 'peep',\n",
+       " 'seep',\n",
+       " 'veep',\n",
+       " 'weep',\n",
+       " 'week',\n",
+       " 'geek',\n",
+       " 'leek',\n",
+       " 'meek',\n",
+       " 'peek',\n",
+       " 'reek',\n",
+       " 'seek',\n",
+       " 'seem',\n",
+       " 'deem',\n",
+       " 'teem',\n",
+       " 'them',\n",
+       " 'thee',\n",
+       " 'tree',\n",
+       " 'free',\n",
+       " 'flee',\n",
+       " 'glee',\n",
+       " 'glue',\n",
+       " 'blue',\n",
+       " 'clue',\n",
+       " 'flue',\n",
+       " 'slue',\n",
+       " 'sloe',\n",
+       " 'aloe',\n",
+       " 'floe',\n",
+       " 'flop',\n",
+       " 'clop',\n",
+       " 'glop',\n",
+       " 'plop',\n",
+       " 'slop',\n",
+       " 'shop',\n",
+       " 'chop',\n",
+       " 'coop',\n",
+       " 'goop',\n",
+       " 'hoop',\n",
+       " 'loop',\n",
+       " 'poop',\n",
+       " 'prop',\n",
+       " 'crop',\n",
+       " 'drop',\n",
+       " 'drip',\n",
+       " 'grip',\n",
+       " 'trip',\n",
+       " 'trap',\n",
+       " 'tray',\n",
+       " 'bray',\n",
+       " 'dray',\n",
+       " 'fray',\n",
+       " 'gray',\n",
+       " 'pray',\n",
+       " 'play',\n",
+       " 'clay',\n",
+       " 'flay',\n",
+       " 'slay',\n",
+       " 'spay',\n",
+       " 'stay',\n",
+       " 'sway',\n",
+       " 'away',\n",
+       " 'awry',\n",
+       " 'aery',\n",
+       " 'eery',\n",
+       " 'very',\n",
+       " 'vary',\n",
+       " 'nary',\n",
+       " 'wary',\n",
+       " 'wiry',\n",
+       " 'airy',\n",
+       " 'airs',\n",
+       " 'firs',\n",
+       " 'sirs',\n",
+       " 'sics',\n",
+       " 'tics',\n",
+       " 'ties',\n",
+       " 'dies',\n",
+       " 'hies',\n",
+       " 'lies',\n",
+       " 'pies',\n",
+       " 'vies',\n",
+       " 'vied',\n",
+       " 'died',\n",
+       " 'hied',\n",
+       " 'lied',\n",
+       " 'pied',\n",
+       " 'tied',\n",
+       " 'tier',\n",
+       " 'bier',\n",
+       " 'pier',\n",
+       " 'peer',\n",
+       " 'beer',\n",
+       " 'deer',\n",
+       " 'jeer',\n",
+       " 'leer',\n",
+       " 'seer',\n",
+       " 'veer',\n",
+       " 'weer',\n",
+       " 'wear',\n",
+       " 'bear',\n",
+       " 'dear',\n",
+       " 'fear',\n",
+       " 'gear',\n",
+       " 'hear',\n",
+       " 'near',\n",
+       " 'pear',\n",
+       " 'rear',\n",
+       " 'sear',\n",
+       " 'tear',\n",
+       " 'year',\n",
+       " 'yeah',\n",
+       " 'yeas',\n",
+       " 'leas',\n",
+       " 'peas',\n",
+       " 'seas',\n",
+       " 'teas',\n",
+       " 'tees',\n",
+       " 'bees',\n",
+       " 'fees',\n",
+       " 'gees',\n",
+       " 'lees',\n",
+       " 'pees',\n",
+       " 'sees',\n",
+       " 'wees',\n",
+       " 'woes',\n",
+       " 'does',\n",
+       " 'foes',\n",
+       " 'goes',\n",
+       " 'hoes',\n",
+       " 'noes',\n",
+       " 'roes',\n",
+       " 'toes',\n",
+       " 'togs',\n",
+       " 'bogs',\n",
+       " 'cogs',\n",
+       " 'dogs',\n",
+       " 'fogs',\n",
+       " 'hogs',\n",
+       " 'jogs',\n",
+       " 'logs',\n",
+       " 'lags',\n",
+       " 'bags',\n",
+       " 'fags',\n",
+       " 'gags',\n",
+       " 'hags',\n",
+       " 'jags',\n",
+       " 'nags',\n",
+       " 'rags',\n",
+       " 'sags',\n",
+       " 'tags',\n",
+       " 'wags',\n",
+       " 'wigs',\n",
+       " 'digs',\n",
+       " 'figs',\n",
+       " 'gigs',\n",
+       " 'jigs',\n",
+       " 'pigs',\n",
+       " 'rigs',\n",
+       " 'rugs',\n",
+       " 'bugs',\n",
+       " 'hugs',\n",
+       " 'jugs',\n",
+       " 'lugs',\n",
+       " 'mugs',\n",
+       " 'pugs',\n",
+       " 'tugs',\n",
+       " 'tubs',\n",
+       " 'cubs',\n",
+       " 'dubs',\n",
+       " 'hubs',\n",
+       " 'nubs',\n",
+       " 'pubs',\n",
+       " 'rubs',\n",
+       " 'subs',\n",
+       " 'sobs',\n",
+       " 'bobs',\n",
+       " 'cobs',\n",
+       " 'fobs',\n",
+       " 'gobs',\n",
+       " 'hobs',\n",
+       " 'jobs',\n",
+       " 'lobs',\n",
+       " 'mobs',\n",
+       " 'robs',\n",
+       " 'ribs',\n",
+       " 'bibs',\n",
+       " 'fibs',\n",
+       " 'jibs',\n",
+       " 'nibs',\n",
+       " 'nabs',\n",
+       " 'cabs',\n",
+       " 'dabs',\n",
+       " 'gabs',\n",
+       " 'jabs',\n",
+       " 'labs',\n",
+       " 'tabs',\n",
+       " 'tads',\n",
+       " 'cads',\n",
+       " 'dads',\n",
+       " 'fads',\n",
+       " 'gads',\n",
+       " 'lads',\n",
+       " 'mads',\n",
+       " 'pads',\n",
+       " 'wads',\n",
+       " 'weds',\n",
+       " 'beds',\n",
+       " 'feds',\n",
+       " 'reds',\n",
+       " 'rids',\n",
+       " 'aids',\n",
+       " 'bids',\n",
+       " 'kids',\n",
+       " 'lids',\n",
+       " 'lips',\n",
+       " 'dips',\n",
+       " 'hips',\n",
+       " 'nips',\n",
+       " 'pips',\n",
+       " 'rips',\n",
+       " 'sips',\n",
+       " 'tips',\n",
+       " 'yips',\n",
+       " 'zips',\n",
+       " 'zaps',\n",
+       " 'caps',\n",
+       " 'gaps',\n",
+       " 'laps',\n",
+       " 'maps',\n",
+       " 'naps',\n",
+       " 'paps',\n",
+       " 'raps',\n",
+       " 'saps',\n",
+       " 'taps',\n",
+       " 'yaps',\n",
+       " 'yeps',\n",
+       " 'peps',\n",
+       " 'reps',\n",
+       " 'refs',\n",
+       " 'reis',\n",
+       " 'leis',\n",
+       " 'legs',\n",
+       " 'begs',\n",
+       " 'kegs',\n",
+       " 'megs',\n",
+       " 'pegs',\n",
+       " 'pens',\n",
+       " 'dens',\n",
+       " 'fens',\n",
+       " 'hens',\n",
+       " 'kens',\n",
+       " 'lens',\n",
+       " 'tens',\n",
+       " 'wens',\n",
+       " 'yens',\n",
+       " 'yews',\n",
+       " 'hews',\n",
+       " 'mews',\n",
+       " 'news',\n",
+       " 'pews',\n",
+       " 'sews',\n",
+       " 'saws',\n",
+       " 'caws',\n",
+       " 'haws',\n",
+       " 'jaws',\n",
+       " 'laws',\n",
+       " 'maws',\n",
+       " 'paws',\n",
+       " 'yaws',\n",
+       " 'yaks',\n",
+       " 'oaks',\n",
+       " 'oafs',\n",
+       " 'oars',\n",
+       " 'bars',\n",
+       " 'cars',\n",
+       " 'ears',\n",
+       " 'jars',\n",
+       " 'mars',\n",
+       " 'pars',\n",
+       " 'tars',\n",
+       " 'wars',\n",
+       " 'ways',\n",
+       " 'bays',\n",
+       " 'days',\n",
+       " 'gays',\n",
+       " 'hays',\n",
+       " 'jays',\n",
+       " 'lays',\n",
+       " 'nays',\n",
+       " 'pays',\n",
+       " 'rays',\n",
+       " 'says',\n",
+       " 'sacs',\n",
+       " 'secs',\n",
+       " 'sets',\n",
+       " 'bets',\n",
+       " 'gets',\n",
+       " 'jets',\n",
+       " 'lets',\n",
+       " 'nets',\n",
+       " 'pets',\n",
+       " 'vets',\n",
+       " 'wets',\n",
+       " 'wits',\n",
+       " 'bits',\n",
+       " 'fits',\n",
+       " 'hits',\n",
+       " 'kits',\n",
+       " 'nits',\n",
+       " 'pits',\n",
+       " 'sits',\n",
+       " 'tits',\n",
+       " 'tats',\n",
+       " 'bats',\n",
+       " 'cats',\n",
+       " 'eats',\n",
+       " 'fats',\n",
+       " 'hats',\n",
+       " 'lats',\n",
+       " 'mats',\n",
+       " 'oats',\n",
+       " 'pats',\n",
+       " 'rats',\n",
+       " 'vats',\n",
+       " 'vans',\n",
+       " 'bans',\n",
+       " 'cans',\n",
+       " 'fans',\n",
+       " 'mans',\n",
+       " 'pans',\n",
+       " 'sans',\n",
+       " 'tans',\n",
+       " 'tins',\n",
+       " 'bins',\n",
+       " 'dins',\n",
+       " 'fins',\n",
+       " 'gins',\n",
+       " 'pins',\n",
+       " 'sins',\n",
+       " 'wins',\n",
+       " 'wind',\n",
+       " 'bind',\n",
+       " 'find',\n",
+       " 'hind',\n",
+       " 'kind',\n",
+       " 'mind',\n",
+       " 'rind',\n",
+       " 'ring',\n",
+       " 'ding',\n",
+       " 'king',\n",
+       " 'ping',\n",
+       " 'sing',\n",
+       " 'ting',\n",
+       " 'wing',\n",
+       " 'wine',\n",
+       " 'dine',\n",
+       " 'fine',\n",
+       " 'line',\n",
+       " 'mine',\n",
+       " 'nine',\n",
+       " 'pine',\n",
+       " 'sine',\n",
+       " 'tine',\n",
+       " 'vine',\n",
+       " 'vane']"
+      ]
+     },
+     "execution_count": 22,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "dfs_search('cart', 'vane')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def astar_search(start, goal, debug=False):\n",
+    "    agenda = [(distance(start, goal), [start])]\n",
+    "    heapq.heapify(agenda)\n",
+    "    finished = False\n",
+    "    while not finished and agenda:\n",
+    "        _, current = heapq.heappop(agenda)\n",
+    "        if debug:\n",
+    "            print(current)\n",
+    "        if current[-1] == goal:\n",
+    "            finished = True\n",
+    "        else:\n",
+    "            successors = extend(current)\n",
+    "            for s in successors:\n",
+    "                heapq.heappush(agenda, (len(current) + distance(s[-1], goal) - 1, s))\n",
+    "    if agenda:\n",
+    "        return current\n",
+    "    else:\n",
+    "        return None        "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "['cart']\n",
+      "['cart', 'cant']\n",
+      "['cart', 'cant', 'cane']\n",
+      "['cart', 'cant', 'cane', 'vane']\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "['cart', 'cant', 'cane', 'vane']"
+      ]
+     },
+     "execution_count": 24,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "astar_search('cart', 'vane', debug=True)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def astar_search_closed(start, goal, debug=False):\n",
+    "    agenda = [(distance(start, goal), [start])]\n",
+    "    heapq.heapify(agenda)\n",
+    "    closed = set()\n",
+    "    finished = False\n",
+    "    while not finished and agenda:\n",
+    "        _, current = heapq.heappop(agenda)\n",
+    "        if debug:\n",
+    "            print(current)\n",
+    "        if current[-1] == goal:\n",
+    "            finished = True\n",
+    "        else:\n",
+    "            closed.add(current[-1])\n",
+    "            successors = extend(current, closed)\n",
+    "            for s in successors:\n",
+    "                heapq.heappush(agenda, (len(current) + distance(s[-1], goal) - 1, s))\n",
+    "    if agenda:\n",
+    "        return current\n",
+    "    else:\n",
+    "        return None        "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "['cart']\n",
+      "['cart', 'cant']\n",
+      "['cart', 'cant', 'cane']\n",
+      "['cart', 'cant', 'cane', 'vane']\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "['cart', 'cant', 'cane', 'vane']"
+      ]
+     },
+     "execution_count": 26,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "astar_search_closed('cart', 'vane', debug=True)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Mutually-reachable sets\n",
+    "\n",
+    "Find the transitive closure of the `neighbours` relation, so we can see which words can be transformed into which other words."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 77,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "94"
+      ]
+     },
+     "execution_count": 77,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "candidates = [set([k] + neighbours[k]) for k in neighbours]\n",
+    "reachables = []\n",
+    "while candidates:\n",
+    "    current = set(candidates.pop())\n",
+    "    altered = False\n",
+    "    for other in candidates:\n",
+    "        if current.intersection(other):\n",
+    "            altered = True\n",
+    "            current.update(other)\n",
+    "            candidates.remove(other)\n",
+    "    if altered:\n",
+    "        candidates.append(current)\n",
+    "    else:\n",
+    "        reachables.append(current)\n",
+    "\n",
+    "len(reachables)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 78,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "2204"
+      ]
+     },
+     "execution_count": 78,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "len(max(reachables, key=len))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 79,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "1"
+      ]
+     },
+     "execution_count": 79,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "len(min(reachables, key=len))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 80,
+   "metadata": {
+    "collapsed": false,
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Counter({1: 75, 2: 6, 3: 7, 4: 2, 5: 2, 6: 1, 2204: 1})"
+      ]
+     },
+     "execution_count": 80,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "collections.Counter(len(r) for r in reachables)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 81,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[5]"
+      ]
+     },
+     "execution_count": 81,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "[len(r) for r in reachables if 'abbe' in r]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 82,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[{'abbe', 'able', 'ably', 'ally', 'axle'}]"
+      ]
+     },
+     "execution_count": 82,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "[r for r in reachables if 'abbe' in r]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 83,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "['buns', 'bunk', 'punk']"
+      ]
+     },
+     "execution_count": 83,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "astar_search('buns', 'punk')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 84,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "for a in reachables:\n",
+    "    for b in reachables:\n",
+    "        if a != b:\n",
+    "            if not a.isdisjoint(b):\n",
+    "                print(a, b)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 85,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "# longest_chain = []\n",
+    "# with open('all-chains-4.txt', 'w', 1) as f:\n",
+    "#     for ws in reachables:\n",
+    "#         for s in ws:\n",
+    "#             for t in ws:\n",
+    "#                 if s < t:\n",
+    "#                     chain = astar_search(s, t)\n",
+    "#                     if chain:\n",
+    "#                         f.write('{}\\n'.format(chain))\n",
+    "#                         if len(chain) > len(longest_chain):\n",
+    "#                             longest_chain = chain\n",
+    "\n",
+    "# longest_chain"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 86,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "bigset = max(reachables, key=len)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 87,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "['late', 'lats', 'lets', 'leas', 'seas', 'seam', 'swam', 'sway']\n",
+      "['leap', 'heap', 'hear', 'dear', 'deer']\n",
+      "['peel', 'peek', 'perk', 'park', 'nark']\n",
+      "['sing', 'sang', 'sand', 'said', 'sail', 'hail', 'haul']\n",
+      "['vats', 'bats', 'bets', 'bees', 'been', 'teen', 'then', 'thin', 'this', 'thus', 'thud']\n",
+      "['sues', 'sees', 'seen', 'sewn', 'hewn']\n",
+      "['rash', 'bash', 'bast', 'bait', 'bail', 'hail', 'hair', 'heir']\n",
+      "['apex', 'aped', 'sped', 'seed', 'deed', 'dead', 'deal', 'veal']\n",
+      "['gulf', 'golf', 'gold', 'bold', 'bond', 'bony', 'tony']\n",
+      "['snag', 'shag', 'shat', 'seat', 'peat', 'pent', 'pint', 'mint']\n",
+      "['rife', 'rime', 'rims', 'rums', 'cums', 'cuss']\n",
+      "['diss', 'kiss', 'kits']\n",
+      "['gyps', 'gaps', 'gads', 'wads', 'wade', 'wide', 'tide']\n",
+      "['bilk', 'bill', 'bell', 'tell', 'teal', 'tear', 'tzar']\n",
+      "['logo', 'loge', 'lode', 'lade', 'jade', 'jape']\n",
+      "['hunt', 'bunt', 'buns', 'nuns', 'nubs']\n",
+      "['glow', 'glop', 'plop', 'prop', 'prep', 'peep', 'keep']\n",
+      "['iamb', 'lamb', 'lams', 'laps', 'lips', 'pips']\n",
+      "['pain', 'lain', 'laid', 'land', 'lend', 'vend', 'veld']\n",
+      "['fake', 'bake', 'bare', 'bars', 'ears', 'errs', 'ergs', 'eggs', 'egos']\n"
+     ]
+    }
+   ],
+   "source": [
+    "for _ in range(20):\n",
+    "    start, goal = random.sample(bigset, 2)\n",
+    "    print(astar_search_closed(start, goal))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 38,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "['cops', 'coos', 'coon', 'coin', 'chin', 'thin', 'this', 'thus', 'thug']"
+      ]
+     },
+     "execution_count": 38,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "astar_search('cops', 'thug')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 39,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[2204]"
+      ]
+     },
+     "execution_count": 39,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "[len(r) for r in reachables if 'love' in r if 'hate' in r]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 40,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "['hate', 'have', 'hove', 'love']"
+      ]
+     },
+     "execution_count": 40,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "astar_search('hate', 'love')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 41,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "['wars', 'ware', 'wave', 'wove', 'love']"
+      ]
+     },
+     "execution_count": 41,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "astar_search('wars', 'love')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 61,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "CPU times: user 0 ns, sys: 0 ns, total: 0 ns\n",
+      "Wall time: 210 µs\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "5"
+      ]
+     },
+     "execution_count": 61,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "%time len(astar_search('wars', 'love'))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 62,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "CPU times: user 0 ns, sys: 0 ns, total: 0 ns\n",
+      "Wall time: 252 µs\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "5"
+      ]
+     },
+     "execution_count": 62,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "%time len(astar_search_closed('wars', 'love'))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 63,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "CPU times: user 24 ms, sys: 0 ns, total: 24 ms\n",
+      "Wall time: 24.2 ms\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "404"
+      ]
+     },
+     "execution_count": 63,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "%time len(dfs_search('wars', 'love'))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 64,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "CPU times: user 5min 20s, sys: 76 ms, total: 5min 20s\n",
+      "Wall time: 5min 20s\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "5"
+      ]
+     },
+     "execution_count": 64,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "%time len(bfs_search('wars', 'love'))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 65,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "CPU times: user 1.44 s, sys: 0 ns, total: 1.44 s\n",
+      "Wall time: 1.43 s\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "5"
+      ]
+     },
+     "execution_count": 65,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "%time len(bfs_search_closed('wars', 'love'))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 42,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "['fear', 'feat', 'fest', 'lest', 'lost', 'lose', 'love']"
+      ]
+     },
+     "execution_count": 42,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "astar_search('fear', 'love')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 43,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "['fail', 'fall', 'pall', 'pals', 'pass']"
+      ]
+     },
+     "execution_count": 43,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "astar_search('fail', 'pass')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 44,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "['star', 'soar', 'boar', 'boor', 'boon', 'born']"
+      ]
+     },
+     "execution_count": 44,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "astar_search('star', 'born')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 45,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "['open',\n",
+       " 'oven',\n",
+       " 'even',\n",
+       " 'eves',\n",
+       " 'eyes',\n",
+       " 'byes',\n",
+       " 'bees',\n",
+       " 'begs',\n",
+       " 'bags',\n",
+       " 'bass',\n",
+       " 'pass']"
+      ]
+     },
+     "execution_count": 45,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "astar_search('open', 'pass')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 46,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "['bass',\n",
+       " 'lass',\n",
+       " 'mass',\n",
+       " 'sass',\n",
+       " 'puss',\n",
+       " 'pads',\n",
+       " 'pals',\n",
+       " 'pans',\n",
+       " 'paps',\n",
+       " 'pars',\n",
+       " 'pats',\n",
+       " 'paws',\n",
+       " 'pays',\n",
+       " 'past']"
+      ]
+     },
+     "execution_count": 46,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "neighbours['pass']"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 47,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[1]"
+      ]
+     },
+     "execution_count": 47,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "[len(r) for r in reachables if 'exam' in r]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 48,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[2204]"
+      ]
+     },
+     "execution_count": 48,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "[len(r) for r in reachables if 'star' in r if 'born' in r]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 49,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1 loop, best of 3: 7.9 s per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "astar_search('bats', 'exit')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 50,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "10 loops, best of 3: 141 ms per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "astar_search_closed('bats', 'exit')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 51,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "['bats',\n",
+       " 'bans',\n",
+       " 'band',\n",
+       " 'sand',\n",
+       " 'said',\n",
+       " 'skid',\n",
+       " 'skit',\n",
+       " 'smit',\n",
+       " 'emit',\n",
+       " 'exit']"
+      ]
+     },
+     "execution_count": 51,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "astar_search_closed('bats', 'exit')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 88,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "{2: [['heel', 'keel'], ['wane', 'wave'], ['cell', 'sell'], ['cons', 'cobs']],\n",
+       " 3: [['hank', 'haws'], ['bars', 'bets'], ['rats', 'paws'], ['lock', 'hack']],\n",
+       " 4: [['rule', 'sore'], ['wavy', 'rape'], ['peas', 'ping'], ['bond', 'toll']],\n",
+       " 5: [['cope', 'yowl'], ['lose', 'loci'], ['rump', 'dash'], ['four', 'dyes']],\n",
+       " 6: [['boon', 'sell'], ['lots', 'pomp'], ['cola', 'turn'], ['boos', 'laid']],\n",
+       " 7: [['eave', 'inns'], ['meek', 'mere'], ['keys', 'wily'], ['slam', 'yore']],\n",
+       " 8: [['hack', 'flip'], ['crag', 'huge'], ['flux', 'gill'], ['play', 'busy']],\n",
+       " 9: [['lacy', 'whey'], ['wren', 'rook'], ['lire', 'drip'], ['grab', 'lame']],\n",
+       " 10: [['over', 'turn'], ['worn', 'anew'], ['stow', 'elks'], ['ergo', 'rich']],\n",
+       " 11: [['bask', 'idea'], ['gabs', 'thud'], ['idea', 'clod'], ['mark', 'ibis']],\n",
+       " 12: [['umps', 'torn'], ['futz', 'shun'], ['abut', 'face'], ['slug', 'open']],\n",
+       " 13: [['umps', 'skin'], ['chum', 'rats'], ['fury', 'chum'], ['omen', 'zany']],\n",
+       " 14: [['chug', 'gaff'], ['atom', 'fizz']],\n",
+       " 15: [['chug', 'oxen']]}"
+      ]
+     },
+     "execution_count": 88,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "solutions = {}\n",
+    "for _ in range(10000):\n",
+    "    start, goal = random.sample(bigset, 2)\n",
+    "    solution = astar_search_closed(start, goal)\n",
+    "    sl = len(solution)\n",
+    "    if sl not in solutions:\n",
+    "        solutions[sl] = []\n",
+    "    if len(solutions[sl]) < 4:\n",
+    "        solutions[sl].append([start, goal])\n",
+    "        \n",
+    "#     if len(solution) >= 10:\n",
+    "#         solutions += [solution]\n",
+    "        \n",
+    "solutions"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 91,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "solutions = {2: [['heel', 'keel'], ['wane', 'wave'], ['cell', 'sell'], ['cons', 'cobs']],\n",
+    " 3: [['hank', 'haws'], ['bars', 'bets'], ['rats', 'paws'], ['lock', 'hack']],\n",
+    " 4: [['rule', 'sore'], ['wavy', 'rape'], ['peas', 'ping'], ['bond', 'toll']],\n",
+    " 5: [['cope', 'yowl'], ['lose', 'loci'], ['rump', 'dash'], ['four', 'dyes']],\n",
+    " 6: [['boon', 'sell'], ['lots', 'pomp'], ['cola', 'turn'], ['boos', 'laid']],\n",
+    " 7: [['eave', 'inns'], ['meek', 'mere'], ['keys', 'wily'], ['slam', 'yore']],\n",
+    " 8: [['hack', 'flip'], ['crag', 'huge'], ['flux', 'gill'], ['play', 'busy']],\n",
+    " 9: [['lacy', 'whey'], ['wren', 'rook'], ['lire', 'drip'], ['grab', 'lame']],\n",
+    " 10: [['over', 'turn'], ['worn', 'anew'], ['stow', 'elks'], ['ergo', 'rich']],\n",
+    " 11: [['bask', 'idea'], ['gabs', 'thud'], ['idea', 'clod'], ['mark', 'ibis']],\n",
+    " 12: [['umps', 'torn'], ['futz', 'shun'], ['abut', 'face'], ['slug', 'open']],\n",
+    " 13: [['umps', 'skin'], ['chum', 'rats'], ['fury', 'chum'], ['omen', 'zany']],\n",
+    " 14: [['chug', 'gaff'], ['atom', 'fizz'], ['chug', 'jinn'], ['amen', 'flog'],\n",
+    "     ['buzz', 'grog'], ['imps', 'pros']],\n",
+    " 15: [['chug', 'oxen'], ['amen', 'doff']]}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 54,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[('amen', 'doff', 15), ('chug', 'jinn', 14), ('amen', 'flog', 14)]"
+      ]
+     },
+     "execution_count": 54,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "[(s[0], s[-1], len(s)) for s in solutions if len(s) >= 14]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 55,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1 loop, best of 3: 360 ms per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "astar_search_closed('blab', 'amen')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 56,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "CPU times: user 384 ms, sys: 0 ns, total: 384 ms\n",
+      "Wall time: 385 ms\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "14"
+      ]
+     },
+     "execution_count": 56,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "%time len(astar_search_closed('blab', 'amen'))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 57,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "CPU times: user 124 ms, sys: 0 ns, total: 124 ms\n",
+      "Wall time: 121 ms\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "15"
+      ]
+     },
+     "execution_count": 57,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "%time len(astar_search_closed('amen', 'doff'))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 58,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "CPU times: user 32 ms, sys: 0 ns, total: 32 ms\n",
+      "Wall time: 32.4 ms\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "14"
+      ]
+     },
+     "execution_count": 58,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "%time len(astar_search_closed('chug', 'jinn'))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 59,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "CPU times: user 16 ms, sys: 0 ns, total: 16 ms\n",
+      "Wall time: 17.1 ms\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "14"
+      ]
+     },
+     "execution_count": 59,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "%time len(astar_search_closed('amen', 'flog'))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 73,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "CPU times: user 268 ms, sys: 4 ms, total: 272 ms\n",
+      "Wall time: 272 ms\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "14"
+      ]
+     },
+     "execution_count": 73,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "%time len(astar_search_closed('buzz', 'grog'))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 74,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "CPU times: user 64 ms, sys: 0 ns, total: 64 ms\n",
+      "Wall time: 64.1 ms\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "14"
+      ]
+     },
+     "execution_count": 74,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "%time len(astar_search_closed('imps', 'pros'))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.5.2"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/08-word-chains/word-chain-solution.ipynb b/08-word-chains/word-chain-solution.ipynb
new file mode 100644
index 0000000..038b3c4
--- /dev/null
+++ b/08-word-chains/word-chain-solution.ipynb
@@ -0,0 +1,807 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Word chains\n",
+    "\n",
+    "\"Word chain\" puzzles are where you transform one word into another, by changing one letter at a time, with all the intermediate steps being valid words. \n",
+    "\n",
+    "For instance, you can transform 'rash' to 'jags' like this:\n",
+    "\n",
+    "```\n",
+    "rash\n",
+    "Bash\n",
+    "basS\n",
+    "baGs\n",
+    "Jags\n",
+    "```\n",
+    "\n",
+    "(the capital letter is the one changed in each step).\n",
+    "\n",
+    "## Part 1\n",
+    "\n",
+    "Given this [list of words](words4.txt), what is the minimum number of steps to go from `vice` to `wars`?"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "import string\n",
+    "import heapq"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "2336"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "words = [w.strip() for w in open('08-words.txt').readlines()]\n",
+    "len(words)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def adjacents(word):\n",
+    "    return [word[0:i] + l + word[i+1:]\n",
+    "           for i in range(len(word))\n",
+    "           for l in string.ascii_lowercase\n",
+    "           if l != word[i]]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "neighbours = {w: [n for n in adjacents(w) if n in words]\n",
+    "             for w in words}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def distance(w1, w2):\n",
+    "    return sum(1 for i in range(len(w1))\n",
+    "               if w1[i] != w2[i])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "# def extend(chain):\n",
+    "#     return [chain + [s] for s in neighbours[chain[-1]]\n",
+    "#            if s not in chain]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def extend(chain, closed=None):\n",
+    "    if closed:\n",
+    "        nbrs = set(neighbours[chain[-1]]) - closed\n",
+    "    else:\n",
+    "        nbrs = neighbours[chain[-1]]\n",
+    "    return [chain + [s] for s in nbrs\n",
+    "           if s not in chain]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def extend_raw(chain):\n",
+    "    nbrs = [w for w in adjacents(chain[-1]) if w in words]\n",
+    "    return [chain + [s] for s in nbrs\n",
+    "           if s not in chain]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def bfs_search(start, goal, debug=False):\n",
+    "    agenda = [[start]]\n",
+    "    finished = False\n",
+    "    while not finished and agenda:\n",
+    "        current = agenda[0]\n",
+    "        if debug:\n",
+    "            print(current)\n",
+    "        if current[-1] == goal:\n",
+    "            finished = True\n",
+    "        else:\n",
+    "            successors = extend(current)\n",
+    "            agenda = agenda[1:] + successors\n",
+    "    if agenda:\n",
+    "        return current\n",
+    "    else:\n",
+    "        return None        "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def bfs_search_closed(start, goal, debug=False):\n",
+    "    agenda = [[start]]\n",
+    "    closed = set()\n",
+    "    finished = False\n",
+    "    while not finished and agenda:\n",
+    "        current = agenda[0]\n",
+    "        if debug:\n",
+    "            print(current)\n",
+    "        if current[-1] == goal:\n",
+    "            finished = True\n",
+    "        else:\n",
+    "            closed.add(current[-1])\n",
+    "            successors = extend(current, closed)\n",
+    "            agenda = agenda[1:] + successors\n",
+    "    if agenda:\n",
+    "        return current\n",
+    "    else:\n",
+    "        return None   "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def dfs_search(start, goal, debug=False):\n",
+    "    agenda = [[start]]\n",
+    "    finished = False\n",
+    "    while not finished and agenda:\n",
+    "        current = agenda[0]\n",
+    "        if debug:\n",
+    "            print(current)\n",
+    "        if current[-1] == goal:\n",
+    "            finished = True\n",
+    "        else:\n",
+    "            successors = extend(current)\n",
+    "            agenda = successors + agenda[1:]\n",
+    "    if agenda:\n",
+    "        return current\n",
+    "    else:\n",
+    "        return None        "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def astar_search(start, goal, debug=False):\n",
+    "    agenda = [(distance(start, goal), [start])]\n",
+    "    heapq.heapify(agenda)\n",
+    "    finished = False\n",
+    "    while not finished and agenda:\n",
+    "        _, current = heapq.heappop(agenda)\n",
+    "        if debug:\n",
+    "            print(current)\n",
+    "        if current[-1] == goal:\n",
+    "            finished = True\n",
+    "        else:\n",
+    "            successors = extend(current)\n",
+    "            for s in successors:\n",
+    "                heapq.heappush(agenda, (len(current) + distance(s[-1], goal) - 1, s))\n",
+    "    if agenda:\n",
+    "        return current\n",
+    "    else:\n",
+    "        return None        "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "# Uses direct lookup of successors, rather than using cached neighbours in the dict\n",
+    "def astar_search_raw(start, goal, debug=False):\n",
+    "    agenda = [(distance(start, goal), [start])]\n",
+    "    heapq.heapify(agenda)\n",
+    "    finished = False\n",
+    "    while not finished and agenda:\n",
+    "        _, current = heapq.heappop(agenda)\n",
+    "        if debug:\n",
+    "            print(current)\n",
+    "        if current[-1] == goal:\n",
+    "            finished = True\n",
+    "        else:\n",
+    "            successors = extend_raw(current) # Difference here\n",
+    "            for s in successors:\n",
+    "                heapq.heappush(agenda, (len(current) + distance(s[-1], goal) - 1, s))\n",
+    "    if agenda:\n",
+    "        return current\n",
+    "    else:\n",
+    "        return None        "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def astar_search_closed(start, goal, debug=False):\n",
+    "    agenda = [(distance(start, goal), [start])]\n",
+    "    heapq.heapify(agenda)\n",
+    "    closed = set()\n",
+    "    finished = False\n",
+    "    while not finished and agenda:\n",
+    "        _, current = heapq.heappop(agenda)\n",
+    "        if debug:\n",
+    "            print(current)\n",
+    "        if current[-1] == goal:\n",
+    "            finished = True\n",
+    "        else:\n",
+    "            closed.add(current[-1])\n",
+    "            successors = extend(current, closed)\n",
+    "            for s in successors:\n",
+    "                heapq.heappush(agenda, (len(current) + distance(s[-1], goal) - 1, s))\n",
+    "    if agenda:\n",
+    "        return current\n",
+    "    else:\n",
+    "        return None   "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "['vice', 'dice', 'dire', 'dare', 'ware', 'wars']"
+      ]
+     },
+     "execution_count": 15,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "astar_search('vice', 'wars')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "['vice', 'dice', 'dire', 'dare', 'ware', 'wars']"
+      ]
+     },
+     "execution_count": 16,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "astar_search_raw('vice', 'wars')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "6"
+      ]
+     },
+     "execution_count": 17,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "len(astar_search('vice', 'wars'))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "ename": "KeyboardInterrupt",
+     "evalue": "",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
+      "\u001b[0;32m<ipython-input-18-77e0f8036978>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbfs_search\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'vice'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'wars'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
+      "\u001b[0;32m<ipython-input-9-0c5cf399e032>\u001b[0m in \u001b[0;36mbfs_search\u001b[0;34m(start, goal, debug)\u001b[0m\n\u001b[1;32m     10\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     11\u001b[0m             \u001b[0msuccessors\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mextend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcurrent\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 12\u001b[0;31m             \u001b[0magenda\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0magenda\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0msuccessors\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     13\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0magenda\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     14\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mcurrent\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
+     ]
+    }
+   ],
+   "source": [
+    "len(bfs_search('vice', 'wars'))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "6"
+      ]
+     },
+     "execution_count": 19,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "len(bfs_search_closed('vice', 'wars'))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "793"
+      ]
+     },
+     "execution_count": 20,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "len(dfs_search('vice', 'wars'))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1000 loops, best of 3: 225 µs per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "astar_search('vice', 'wars')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "10 loops, best of 3: 22.1 ms per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "astar_search_raw('vice', 'wars')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1000 loops, best of 3: 280 µs per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "astar_search_closed('vice', 'wars')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "ename": "KeyboardInterrupt",
+     "evalue": "",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
+      "\u001b[0;32m<ipython-input-24-ec1214959874>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mget_ipython\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun_cell_magic\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'timeit'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m''\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"bfs_search('vice', 'wars')\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
+      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/IPython/core/interactiveshell.py\u001b[0m in \u001b[0;36mrun_cell_magic\u001b[0;34m(self, magic_name, line, cell)\u001b[0m\n\u001b[1;32m   2113\u001b[0m             \u001b[0mmagic_arg_s\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvar_expand\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mline\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstack_depth\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2114\u001b[0m             \u001b[0;32mwith\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbuiltin_trap\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2115\u001b[0;31m                 \u001b[0mresult\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmagic_arg_s\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcell\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   2116\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0mresult\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2117\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m<decorator-gen-58>\u001b[0m in \u001b[0;36mtimeit\u001b[0;34m(self, line, cell)\u001b[0m\n",
+      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/IPython/core/magic.py\u001b[0m in \u001b[0;36m<lambda>\u001b[0;34m(f, *a, **k)\u001b[0m\n\u001b[1;32m    186\u001b[0m     \u001b[0;31m# but it's overkill for just that one bit of state.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    187\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mmagic_deco\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0marg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 188\u001b[0;31m         \u001b[0mcall\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mlambda\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    189\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    190\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mcallable\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0marg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/IPython/core/magics/execution.py\u001b[0m in \u001b[0;36mtimeit\u001b[0;34m(self, line, cell)\u001b[0m\n\u001b[1;32m   1042\u001b[0m             \u001b[0mnumber\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1043\u001b[0m             \u001b[0;32mfor\u001b[0m \u001b[0m_\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m10\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1044\u001b[0;31m                 \u001b[0mtime_number\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtimer\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtimeit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnumber\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1045\u001b[0m                 \u001b[0mworst_tuning\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmax\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mworst_tuning\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtime_number\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0mnumber\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1046\u001b[0m                 \u001b[0;32mif\u001b[0m \u001b[0mtime_number\u001b[0m \u001b[0;34m>=\u001b[0m \u001b[0;36m0.2\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m/usr/local/lib/python3.5/dist-packages/IPython/core/magics/execution.py\u001b[0m in \u001b[0;36mtimeit\u001b[0;34m(self, number)\u001b[0m\n\u001b[1;32m    137\u001b[0m         \u001b[0mgc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdisable\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    138\u001b[0m         \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 139\u001b[0;31m             \u001b[0mtiming\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minner\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mit\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtimer\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    140\u001b[0m         \u001b[0;32mfinally\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    141\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mgcold\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m<magic-timeit>\u001b[0m in \u001b[0;36minner\u001b[0;34m(_it, _timer)\u001b[0m\n",
+      "\u001b[0;32m<ipython-input-9-0c5cf399e032>\u001b[0m in \u001b[0;36mbfs_search\u001b[0;34m(start, goal, debug)\u001b[0m\n\u001b[1;32m     10\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     11\u001b[0m             \u001b[0msuccessors\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mextend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcurrent\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 12\u001b[0;31m             \u001b[0magenda\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0magenda\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0msuccessors\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     13\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0magenda\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     14\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mcurrent\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "bfs_search('vice', 'wars')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1 loop, best of 3: 1.12 s per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "bfs_search_closed('vice', 'wars')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "10 loops, best of 3: 127 ms per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "dfs_search('vice', 'wars')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Part 2\n",
+    "\n",
+    "The example shows that `jags` is reachable in four steps from `rash`. There are 11 words one step away from `rash`: \n",
+    "`bash`, `cash`, `dash`, `gash`, `hash`, `lash`, `mash`, `rasp`, `rush`, `sash`, and `wash`. \n",
+    "\n",
+    "There are 47 words reachable in one or two steps from `rash`. They are `base`, `bash`, `bask`, `bass`, `bast`, `bath`, `bosh`, `bush`, `case`, `cash`, `cask`, `cast`, `dash`, `dish`, `gash`, `gasp`, `gosh`, `gush`, `hash`, `hasp`, `hath`, `hush`, `lash`, `lass`, `last`, `lath`, `lush`, `mash`, `mask`, `mass`, `mast`, `math`, `mesh`, `mush`, `push`, `ramp`, `rasp`, `ruse`, `rush`, `rusk`, `rust`, `sash`, `sass`, `tush`, `wash`, `wasp`, and `wish`.\n",
+    "\n",
+    "There are 180 words reachable in up to three steps from `rash`.\n",
+    "\n",
+    "How many words are reachable in up to ten steps from `vice`?"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def reachable_in(word, n, trim_extras=False):\n",
+    "    reachable = set()\n",
+    "    boundary = set([word])\n",
+    "    for i in range(n):\n",
+    "        extras = set()\n",
+    "        for w in boundary:\n",
+    "            extras.update(neighbours[w])\n",
+    "        if trim_extras:\n",
+    "            extras.difference_update(reachable)\n",
+    "        reachable.update(boundary)\n",
+    "        boundary = extras.copy()\n",
+    "    return reachable.union(extras).difference(set([word]))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "metadata": {
+    "collapsed": false,
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(11,\n",
+       " '`bash`, `cash`, `dash`, `gash`, `hash`, `lash`, `mash`, `rasp`, `rush`, `sash`, `wash`')"
+      ]
+     },
+     "execution_count": 28,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "len(reachable_in('rash', 1)), ', '.join(sorted('`{}`'.format(r) for r in reachable_in('rash', 1)))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "metadata": {
+    "collapsed": false,
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(47,\n",
+       " '`base`, `bash`, `bask`, `bass`, `bast`, `bath`, `bosh`, `bush`, `case`, `cash`, `cask`, `cast`, `dash`, `dish`, `gash`, `gasp`, `gosh`, `gush`, `hash`, `hasp`, `hath`, `hush`, `lash`, `lass`, `last`, `lath`, `lush`, `mash`, `mask`, `mass`, `mast`, `math`, `mesh`, `mush`, `push`, `ramp`, `rasp`, `ruse`, `rush`, `rusk`, `rust`, `sash`, `sass`, `tush`, `wash`, `wasp`, `wish`')"
+      ]
+     },
+     "execution_count": 29,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "len(reachable_in('rash', 2)), ', '.join(sorted('`{}`'.format(r) for r in reachable_in('rash', 2)))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "metadata": {
+    "collapsed": false,
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "180"
+      ]
+     },
+     "execution_count": 30,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "len(reachable_in('rash', 3))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "metadata": {
+    "collapsed": false,
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "2195"
+      ]
+     },
+     "execution_count": 31,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "len(reachable_in('rash', 10))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "metadata": {
+    "collapsed": false,
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "2192"
+      ]
+     },
+     "execution_count": 32,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "len(reachable_in('vice', 10))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "metadata": {
+    "collapsed": false,
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "100 loops, best of 3: 9.26 ms per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "len(reachable_in('rash', 10))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 34,
+   "metadata": {
+    "collapsed": false,
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "100 loops, best of 3: 3.64 ms per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "len(reachable_in('rash', 10, trim_extras=True))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.5.2"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/09-word-chains/09-words.txt b/09-word-chains/09-words.txt
deleted file mode 100644
index 028c8cf..0000000
--- a/09-word-chains/09-words.txt
+++ /dev/null
@@ -1,2336 +0,0 @@
-abbe
-abed
-abet
-able
-ably
-abut
-aced
-aces
-ache
-achy
-acid
-acme
-acne
-acre
-acts
-adds
-adze
-aeon
-aery
-afar
-agar
-aged
-ages
-agog
-ague
-ahem
-ahoy
-aide
-aids
-ails
-aims
-airs
-airy
-ajar
-akin
-alas
-albs
-ales
-alga
-alit
-ally
-alms
-aloe
-also
-alto
-alum
-amen
-amid
-amir
-ammo
-amok
-amps
-anal
-anew
-ankh
-anon
-ante
-anti
-ants
-anus
-aped
-apes
-apex
-apse
-aqua
-arch
-arcs
-area
-ares
-aria
-arid
-arks
-arms
-army
-arts
-arty
-ashy
-asks
-asps
-atom
-atop
-auks
-aunt
-aura
-auto
-aver
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-avow
-away
-awed
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-awol
-awry
-axed
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-axle
-axon
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-baby
-back
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-ball
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-bani
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-barb
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-bash
-bask
-bass
-bast
-bate
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-bawl
-bays
-bead
-beak
-beam
-bean
-bear
-beat
-beau
-beck
-beds
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-been
-beep
-beer
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-begs
-bell
-belt
-bend
-bent
-berg
-berm
-best
-beta
-bets
-bevy
-bias
-bibs
-bide
-bids
-bier
-bike
-bile
-bilk
-bill
-bind
-bins
-bird
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-bits
-blab
-blah
-bled
-blew
-blip
-blob
-bloc
-blog
-blot
-blow
-blue
-blur
-boar
-boas
-boat
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-body
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-boil
-bola
-bold
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-bolt
-bomb
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-bone
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-bony
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-book
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-boot
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-bran
-bras
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-brew
-brig
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-bugs
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-cads
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-cake
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-cant
-cape
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-card
-care
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-cars
-cart
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-cats
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-cede
-cell
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-chap
-char
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-chid
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-chit
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-coon
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-cote
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-crow
-crud
-crux
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-cues
-cuff
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-cult
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-curb
-curd
-cure
-curl
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-curt
-cusp
-cuss
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-cyst
-czar
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-dads
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-dare
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-date
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-deli
-dell
-demo
-dens
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-desk
-dewy
-dial
-dice
-dick
-died
-dies
-diet
-digs
-dike
-dill
-dime
-dims
-dine
-ding
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-dint
-dips
-dire
-dirk
-dirt
-disc
-dish
-disk
-diss
-diva
-dive
-dock
-docs
-dodo
-doer
-does
-doff
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-dole
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-dome
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-door
-dope
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-dorm
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-dose
-dote
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-dour
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-down
-doze
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-drag
-dram
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-dray
-drew
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-drop
-drub
-drug
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-dude
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-duke
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-duly
-dumb
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-dune
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-duns
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-dyed
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-edge
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-eggs
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-eked
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-elan
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-elms
-else
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-emus
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-ergs
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-fake
-fall
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-fawn
-faze
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-feat
-feds
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-feel
-fees
-feet
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-felt
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-fens
-fern
-fest
-feta
-fete
-feud
-fiat
-fibs
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-fife
-figs
-file
-fill
-film
-find
-fine
-fink
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-fire
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-fish
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-five
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-flag
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-flan
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-flat
-flaw
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-flea
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-flee
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-flip
-flit
-floe
-flog
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-flow
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-flux
-foal
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-ford
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-geek
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-gems
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-gins
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-girl
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-glib
-glob
-glop
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-glue
-glum
-glut
-gnat
-gnaw
-gnus
-goad
-goal
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-gods
-goes
-gold
-golf
-gone
-gong
-good
-goof
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-goon
-goop
-gore
-gory
-gosh
-gout
-gown
-grab
-grad
-gram
-gray
-grew
-grey
-grid
-grim
-grin
-grip
-grit
-grog
-grow
-grub
-guff
-gulf
-gull
-gulp
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-guns
-guru
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-gyps
-gyro
-hack
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-half
-hall
-halo
-halt
-hams
-hand
-hang
-hank
-hard
-hare
-hark
-harm
-harp
-hart
-hash
-hasp
-hate
-hath
-hats
-haul
-have
-hawk
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-hazy
-head
-heal
-heap
-hear
-heat
-heck
-heed
-heel
-heft
-heir
-held
-hell
-helm
-help
-hemp
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-hens
-herb
-herd
-here
-hero
-hers
-hewn
-hews
-hick
-hide
-hied
-hies
-high
-hike
-hill
-hilt
-hims
-hind
-hint
-hips
-hire
-hiss
-hits
-hive
-hoax
-hobo
-hobs
-hock
-hods
-hoed
-hoes
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-hold
-hole
-holy
-home
-homy
-hone
-honk
-hood
-hoof
-hook
-hoop
-hoot
-hope
-hops
-horn
-hose
-host
-hour
-hove
-howl
-hows
-hubs
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-hues
-huff
-huge
-hugs
-hula
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-hung
-hunk
-hunt
-hurl
-hurt
-hush
-husk
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-hymn
-hype
-hypo
-iamb
-ibex
-ibis
-iced
-ices
-icky
-icon
-idea
-ides
-idle
-idly
-idol
-idyl
-iffy
-ikon
-ilks
-ills
-imam
-imps
-inch
-info
-inks
-inky
-inns
-into
-ions
-iota
-iris
-irks
-iron
-isle
-isms
-itch
-item
-jabs
-jack
-jade
-jags
-jail
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-jeep
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-jell
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-jest
-jets
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-jibs
-jigs
-jilt
-jinn
-jinx
-jive
-jobs
-jock
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-john
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-jots
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-judo
-jugs
-jump
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-just
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-juts
-kale
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-keen
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-lest
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-lice
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-limb
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-limn
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-loop
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-loth
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-luau
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-lurk
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-noel
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-null
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-pant
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-pate
-path
-pats
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-peal
-pear
-peas
-peat
-peck
-peed
-peek
-peel
-peep
-peer
-pees
-pegs
-pelt
-pens
-pent
-peon
-peps
-perk
-perm
-pert
-peso
-pest
-pets
-pews
-pica
-pick
-pied
-pier
-pies
-pigs
-pike
-pile
-pill
-pimp
-pine
-ping
-pink
-pins
-pint
-pipe
-pips
-pita
-pith
-pits
-pity
-pixy
-plan
-play
-plea
-pled
-plod
-plop
-plot
-ploy
-plug
-plum
-plus
-pock
-pods
-poem
-poet
-poke
-poky
-pole
-poll
-polo
-pols
-pomp
-pond
-pone
-pony
-pooh
-pool
-poop
-poor
-pope
-pops
-pore
-pork
-porn
-port
-pose
-posh
-post
-posy
-pots
-pour
-pout
-pram
-pray
-prep
-prey
-prig
-prim
-prod
-prof
-prom
-prop
-pros
-prow
-psst
-pubs
-puck
-puff
-pugs
-puke
-pull
-pulp
-puma
-pump
-punk
-puns
-punt
-puny
-pupa
-pups
-pure
-purl
-purr
-push
-puss
-puts
-putt
-pyre
-quad
-quay
-quid
-quip
-quit
-quiz
-race
-rack
-racy
-raft
-raga
-rage
-rags
-raid
-rail
-rain
-raja
-rake
-ramp
-rams
-rang
-rank
-rant
-rape
-raps
-rapt
-rare
-rash
-rasp
-rate
-rats
-rave
-rays
-raze
-razz
-read
-real
-ream
-reap
-rear
-redo
-reds
-reed
-reef
-reek
-reel
-refs
-rein
-reis
-rely
-rend
-rent
-reps
-rest
-revs
-rhea
-ribs
-rice
-rich
-rick
-ride
-rids
-rife
-riff
-rift
-rigs
-rile
-rill
-rime
-rims
-rind
-ring
-rink
-riot
-ripe
-rips
-rise
-risk
-rite
-road
-roam
-roan
-roar
-robe
-robs
-rock
-rode
-rods
-roes
-roil
-role
-roll
-romp
-rood
-roof
-rook
-room
-root
-rope
-rose
-rosy
-rote
-rots
-roue
-rout
-rove
-rows
-rube
-rubs
-ruby
-rude
-rued
-rues
-ruff
-rugs
-ruin
-rule
-rump
-rums
-rune
-rung
-runs
-runt
-ruse
-rush
-rusk
-rust
-ruts
-sack
-sacs
-safe
-saga
-sage
-sago
-sags
-said
-sail
-sake
-saki
-sale
-salt
-same
-sand
-sane
-sang
-sank
-sans
-saps
-sari
-sash
-sass
-sate
-save
-sawn
-saws
-says
-scab
-scad
-scam
-scan
-scar
-scat
-scow
-scud
-scum
-seal
-seam
-sear
-seas
-seat
-secs
-sect
-seed
-seek
-seem
-seen
-seep
-seer
-sees
-self
-sell
-semi
-send
-sent
-sera
-sere
-serf
-sets
-sewn
-sews
-sexy
-shad
-shag
-shah
-sham
-shat
-shed
-shes
-shim
-shin
-ship
-shod
-shoe
-shoo
-shop
-shot
-show
-shun
-shut
-sick
-sics
-side
-sift
-sigh
-sign
-silk
-sill
-silo
-silt
-sine
-sing
-sink
-sins
-sips
-sire
-sirs
-site
-sits
-size
-skew
-skid
-skim
-skin
-skip
-skis
-skit
-slab
-slag
-slam
-slap
-slat
-slaw
-slay
-sled
-slew
-slid
-slim
-slip
-slit
-slob
-sloe
-slog
-slop
-slot
-slow
-slue
-slug
-slum
-slur
-slut
-smit
-smog
-smug
-smut
-snag
-snap
-snip
-snit
-snob
-snot
-snow
-snub
-snug
-soak
-soap
-soar
-sobs
-sock
-soda
-sods
-sofa
-soft
-soil
-sold
-sole
-soli
-solo
-sols
-some
-song
-sons
-soon
-soot
-sops
-sore
-sort
-sots
-soul
-soup
-sour
-sown
-sows
-soya
-span
-spar
-spas
-spat
-spay
-spec
-sped
-spew
-spin
-spit
-spot
-spry
-spud
-spun
-spur
-stab
-stag
-star
-stay
-stem
-step
-stew
-stir
-stop
-stow
-stub
-stud
-stun
-stye
-subs
-such
-suck
-suds
-sued
-sues
-suet
-suit
-sulk
-sumo
-sump
-sums
-sung
-sunk
-suns
-sups
-sure
-surf
-swab
-swag
-swam
-swan
-swap
-swat
-sway
-swig
-swim
-swop
-swum
-sync
-tabs
-tabu
-tack
-taco
-tact
-tads
-tags
-tail
-take
-talc
-tale
-talk
-tall
-tame
-tamp
-tams
-tang
-tank
-tans
-tape
-taps
-tare
-taro
-tarp
-tars
-tart
-task
-tats
-taut
-taxi
-teak
-teal
-team
-tear
-teas
-teat
-teed
-teem
-teen
-tees
-tell
-temp
-tend
-tens
-tent
-term
-tern
-test
-text
-than
-that
-thaw
-thee
-them
-then
-they
-thin
-this
-thou
-thru
-thud
-thug
-thus
-tick
-tics
-tide
-tidy
-tied
-tier
-ties
-tiff
-tike
-tile
-till
-tilt
-time
-tine
-ting
-tins
-tint
-tiny
-tipi
-tips
-tire
-tiro
-tits
-toad
-toed
-toes
-tofu
-toga
-togs
-toil
-toke
-told
-toll
-tomb
-tome
-toms
-tone
-tong
-tons
-tony
-took
-tool
-toot
-tops
-tore
-torn
-tors
-tort
-toss
-tost
-tote
-tots
-tour
-tout
-town
-tows
-toys
-tram
-trap
-tray
-tree
-trek
-trig
-trim
-trio
-trip
-trod
-trot
-troy
-true
-tsar
-tuba
-tube
-tubs
-tuck
-tuft
-tugs
-tuna
-tune
-tuns
-turd
-turf
-turn
-tush
-tusk
-tutu
-twee
-twig
-twin
-twit
-twos
-tyke
-type
-typo
-tyre
-tyro
-tzar
-ugly
-ulna
-umps
-undo
-unit
-unto
-upon
-urea
-urge
-uric
-urns
-used
-user
-uses
-vain
-vale
-vamp
-vane
-vans
-vary
-vase
-vast
-vats
-veal
-veep
-veer
-veil
-vein
-veld
-vend
-vent
-verb
-very
-vest
-veto
-vets
-vial
-vibe
-vice
-vied
-vies
-view
-vile
-vine
-viol
-visa
-vise
-viva
-void
-vole
-volt
-vote
-vows
-wade
-wadi
-wads
-waft
-wage
-wags
-waif
-wail
-wait
-wake
-wale
-walk
-wall
-wand
-wane
-want
-ward
-ware
-warm
-warn
-warp
-wars
-wart
-wary
-wash
-wasp
-watt
-wave
-wavy
-waxy
-ways
-weak
-weal
-wean
-wear
-webs
-weds
-weed
-week
-weep
-weer
-wees
-weft
-weir
-weld
-well
-welt
-wend
-wens
-went
-wept
-were
-west
-wets
-wham
-what
-when
-whet
-whew
-whey
-whim
-whip
-whir
-whit
-whiz
-whoa
-whom
-whys
-wick
-wide
-wife
-wigs
-wiki
-wild
-wile
-will
-wilt
-wily
-wimp
-wind
-wine
-wing
-wink
-wino
-wins
-wipe
-wire
-wiry
-wise
-wish
-wisp
-wist
-with
-wits
-wive
-woes
-woke
-woks
-wolf
-womb
-wont
-wood
-woof
-wool
-woos
-word
-wore
-work
-worm
-worn
-wove
-wows
-wrap
-wren
-writ
-wuss
-yack
-yaks
-yams
-yank
-yaps
-yard
-yarn
-yawl
-yawn
-yaws
-yeah
-year
-yeas
-yell
-yelp
-yens
-yeps
-yest
-yeti
-yews
-yips
-yock
-yoga
-yogi
-yoke
-yolk
-yore
-your
-yous
-yowl
-yuck
-yuks
-yule
-yups
-zany
-zaps
-zeal
-zebu
-zeds
-zero
-zest
-zeta
-zinc
-zing
-zips
-zits
-zone
-zoom
-zoos
\ No newline at end of file
diff --git a/09-word-chains/build-word-lists.ipynb b/09-word-chains/build-word-lists.ipynb
deleted file mode 100644
index d12df78..0000000
--- a/09-word-chains/build-word-lists.ipynb
+++ /dev/null
@@ -1,201 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "import unicodedata\n",
-    "import string"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "unaccent_specials = ''.maketrans({\"’\": \"'\", '“': '\"', '”': '\"'})"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def unaccent(text):\n",
-    "    translated_text = text.translate(unaccent_specials)\n",
-    "    return unicodedata.normalize('NFKD', translated_text).\\\n",
-    "        encode('ascii', 'ignore').\\\n",
-    "        decode('utf-8')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def only_lower(text):\n",
-    "    return all((c in string.ascii_lowercase) for c in text)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "/usr/share/dict/british-english\n",
-      "find: ‘/usr/share/doc/google-chrome-stable’: Permission denied\n",
-      "/usr/share/man/man5/british-english.5.gz\n"
-     ]
-    }
-   ],
-   "source": [
-    "# !find /usr -type f -iname 'british-english*'"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "total 2.3M\r\n",
-      "drwxr-xr-x   2 root root 4.0K Dec 29 12:37 .\r\n",
-      "drwxr-xr-x 640 root root  20K Apr 13 17:05 ..\r\n",
-      "-rw-r--r--   1 root root 917K Oct 23  2011 american-english\r\n",
-      "-rw-r--r--   1 root root 917K Oct 23  2011 british-english\r\n",
-      "-rw-r--r--   1 root root 467K Aug 25  2016 cracklib-small\r\n",
-      "-rw-r--r--   1 root root  199 Aug 29  2016 README.select-wordlist\r\n",
-      "lrwxrwxrwx   1 root root   30 Nov 10  2014 words -> /etc/dictionaries-common/words\r\n",
-      "lrwxrwxrwx   1 root root   16 Jun 18  2014 words.pre-dictionaries-common -> american-english\r\n"
-     ]
-    }
-   ],
-   "source": [
-    "# !ls -lah /usr/share/dict"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def rude(word):\n",
-    "    return any(w in word \n",
-    "               for w in 'piss shit cunt fuck arse crap fart jizz whore bitch'.split())"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 18,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "True"
-      ]
-     },
-     "execution_count": 18,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "rude('fucks')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 19,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def words_with_len(n):\n",
-    "    return [unaccent(w.strip()) for w in open('/usr/share/dict/british-english').readlines()\n",
-    "               if only_lower(unaccent(w.strip()))\n",
-    "               if len(unaccent(w.strip())) == n\n",
-    "               if not rude(unaccent(w.strip()))]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 20,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "2336 4-letter words\n",
-      "4566 5-letter words\n",
-      "7223 6-letter words\n"
-     ]
-    }
-   ],
-   "source": [
-    "dicts = {}\n",
-    "\n",
-    "for n in [4, 5, 6]:\n",
-    "    dicts[n] = words_with_len(n)\n",
-    "    print('{} {}-letter words'.format(len(dicts[n]), n))\n",
-    "    with open('words{}.txt'.format(n), 'w') as f:\n",
-    "        f.write('\\n'.join(sorted(set(dicts[n]))))\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": []
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.5.2+"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 2
-}
diff --git a/09-word-chains/explore-word-chain-4.ipynb b/09-word-chains/explore-word-chain-4.ipynb
deleted file mode 100644
index 5f624fd..0000000
--- a/09-word-chains/explore-word-chain-4.ipynb
+++ /dev/null
@@ -1,3311 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "import string\n",
-    "import heapq\n",
-    "import collections\n",
-    "import random"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "2336"
-      ]
-     },
-     "execution_count": 2,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "words = [w.strip() for w in open('words4.txt').readlines()]\n",
-    "len(words)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "['abbe',\n",
-       " 'abed',\n",
-       " 'abet',\n",
-       " 'able',\n",
-       " 'ably',\n",
-       " 'abut',\n",
-       " 'aced',\n",
-       " 'aces',\n",
-       " 'ache',\n",
-       " 'achy']"
-      ]
-     },
-     "execution_count": 3,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "words[:10]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def adjacents_explicit(word):\n",
-    "    neighbours = []\n",
-    "    for i in range(len(word)):\n",
-    "        for l in string.ascii_lowercase:\n",
-    "            if l != word[i]:\n",
-    "                neighbours.append(word[0:i] + l + word[i+1:])\n",
-    "    return neighbours"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def adjacents(word):\n",
-    "    return [word[0:i] + l + word[i+1:]\n",
-    "           for i in range(len(word))\n",
-    "           for l in string.ascii_lowercase\n",
-    "           if l != word[i]]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "neighbours = {w: [n for n in adjacents(w) if n in words]\n",
-    "             for w in words}"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "['able']"
-      ]
-     },
-     "execution_count": 7,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "neighbours['abbe']"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "['axle', 'abbe', 'ably']"
-      ]
-     },
-     "execution_count": 8,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "neighbours['able']"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def distance(w1, w2):\n",
-    "    return sum(1 for i in range(len(w1))\n",
-    "               if w1[i] != w2[i])"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "0"
-      ]
-     },
-     "execution_count": 10,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "distance('abbe', 'abbe')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def extend(chain, closed=None):\n",
-    "    if closed:\n",
-    "        nbrs = set(neighbours[chain[-1]]) - closed\n",
-    "    else:\n",
-    "        nbrs = neighbours[chain[-1]]\n",
-    "    return [chain + [s] for s in nbrs\n",
-    "           if s not in chain]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[['abbe', 'able']]"
-      ]
-     },
-     "execution_count": 12,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "extend(['abbe'])"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[['abbe', 'able', 'axle'], ['abbe', 'able', 'ably']]"
-      ]
-     },
-     "execution_count": 13,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "extend(['abbe', 'able'])"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[['abbe', 'able', 'ably', 'ally']]"
-      ]
-     },
-     "execution_count": 14,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "extend(['abbe', 'able', 'ably'])"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def bfs_search(start, goal, debug=False):\n",
-    "    agenda = [[start]]\n",
-    "    finished = False\n",
-    "    while not finished and agenda:\n",
-    "        current = agenda[0]\n",
-    "        if debug:\n",
-    "            print(current)\n",
-    "        if current[-1] == goal:\n",
-    "            finished = True\n",
-    "        else:\n",
-    "            successors = extend(current)\n",
-    "            agenda = agenda[1:] + successors\n",
-    "    if agenda:\n",
-    "        return current\n",
-    "    else:\n",
-    "        return None        "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def bfs_search_closed(start, goal, debug=False):\n",
-    "    agenda = [[start]]\n",
-    "    closed = set()\n",
-    "    finished = False\n",
-    "    while not finished and agenda:\n",
-    "        current = agenda[0]\n",
-    "        if debug:\n",
-    "            print(current)\n",
-    "        if current[-1] == goal:\n",
-    "            finished = True\n",
-    "        else:\n",
-    "            closed.add(current[-1])\n",
-    "            successors = extend(current, closed)\n",
-    "            agenda = agenda[1:] + successors\n",
-    "    if agenda:\n",
-    "        return current\n",
-    "    else:\n",
-    "        return None        "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "['abbe']\n",
-      "['abbe', 'able']\n",
-      "['abbe', 'able', 'axle']\n",
-      "['abbe', 'able', 'ably']\n",
-      "['abbe', 'able', 'ably', 'ally']\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "['abbe', 'able', 'ably', 'ally']"
-      ]
-     },
-     "execution_count": 17,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "bfs_search('abbe', 'ally', debug=True)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 18,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def dfs_search(start, goal, debug=False):\n",
-    "    agenda = [[start]]\n",
-    "    finished = False\n",
-    "    while not finished and agenda:\n",
-    "        current = agenda[0]\n",
-    "        if debug:\n",
-    "            print(current)\n",
-    "        if current[-1] == goal:\n",
-    "            finished = True\n",
-    "        else:\n",
-    "            successors = extend(current)\n",
-    "            agenda = successors + agenda[1:]\n",
-    "    if agenda:\n",
-    "        return current\n",
-    "    else:\n",
-    "        return None        "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 19,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "['abbe']\n",
-      "['abbe', 'able']\n",
-      "['abbe', 'able', 'axle']\n",
-      "['abbe', 'able', 'ably']\n",
-      "['abbe', 'able', 'ably', 'ally']\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "['abbe', 'able', 'ably', 'ally']"
-      ]
-     },
-     "execution_count": 19,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "dfs_search('abbe', 'ally', debug=True)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 20,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "['cart']\n",
-      "['cart', 'dart']\n",
-      "['cart', 'hart']\n",
-      "['cart', 'mart']\n",
-      "['cart', 'part']\n",
-      "['cart', 'tart']\n",
-      "['cart', 'wart']\n",
-      "['cart', 'curt']\n",
-      "['cart', 'cant']\n",
-      "['cart', 'cast']\n",
-      "['cart', 'card']\n",
-      "['cart', 'care']\n",
-      "['cart', 'carp']\n",
-      "['cart', 'cars']\n",
-      "['cart', 'dart', 'hart']\n",
-      "['cart', 'dart', 'mart']\n",
-      "['cart', 'dart', 'part']\n",
-      "['cart', 'dart', 'tart']\n",
-      "['cart', 'dart', 'wart']\n",
-      "['cart', 'dart', 'dirt']\n",
-      "['cart', 'dart', 'daft']\n",
-      "['cart', 'dart', 'dare']\n",
-      "['cart', 'dart', 'dark']\n",
-      "['cart', 'dart', 'darn']\n",
-      "['cart', 'hart', 'dart']\n",
-      "['cart', 'hart', 'mart']\n",
-      "['cart', 'hart', 'part']\n",
-      "['cart', 'hart', 'tart']\n",
-      "['cart', 'hart', 'wart']\n",
-      "['cart', 'hart', 'hurt']\n",
-      "['cart', 'hart', 'haft']\n",
-      "['cart', 'hart', 'halt']\n",
-      "['cart', 'hart', 'hard']\n",
-      "['cart', 'hart', 'hare']\n",
-      "['cart', 'hart', 'hark']\n",
-      "['cart', 'hart', 'harm']\n",
-      "['cart', 'hart', 'harp']\n",
-      "['cart', 'mart', 'dart']\n",
-      "['cart', 'mart', 'hart']\n",
-      "['cart', 'mart', 'part']\n",
-      "['cart', 'mart', 'tart']\n",
-      "['cart', 'mart', 'wart']\n",
-      "['cart', 'mart', 'malt']\n",
-      "['cart', 'mart', 'mast']\n",
-      "['cart', 'mart', 'matt']\n",
-      "['cart', 'mart', 'mare']\n",
-      "['cart', 'mart', 'mark']\n",
-      "['cart', 'mart', 'mars']\n",
-      "['cart', 'part', 'dart']\n",
-      "['cart', 'part', 'hart']\n",
-      "['cart', 'part', 'mart']\n",
-      "['cart', 'part', 'tart']\n",
-      "['cart', 'part', 'wart']\n",
-      "['cart', 'part', 'pert']\n",
-      "['cart', 'part', 'port']\n",
-      "['cart', 'part', 'pact']\n",
-      "['cart', 'part', 'pant']\n",
-      "['cart', 'part', 'past']\n",
-      "['cart', 'part', 'pare']\n",
-      "['cart', 'part', 'park']\n",
-      "['cart', 'part', 'pars']\n",
-      "['cart', 'tart', 'dart']\n",
-      "['cart', 'tart', 'hart']\n",
-      "['cart', 'tart', 'mart']\n",
-      "['cart', 'tart', 'part']\n",
-      "['cart', 'tart', 'wart']\n",
-      "['cart', 'tart', 'tort']\n",
-      "['cart', 'tart', 'tact']\n",
-      "['cart', 'tart', 'taut']\n",
-      "['cart', 'tart', 'tare']\n",
-      "['cart', 'tart', 'taro']\n",
-      "['cart', 'tart', 'tarp']\n",
-      "['cart', 'tart', 'tars']\n",
-      "['cart', 'wart', 'dart']\n",
-      "['cart', 'wart', 'hart']\n",
-      "['cart', 'wart', 'mart']\n",
-      "['cart', 'wart', 'part']\n",
-      "['cart', 'wart', 'tart']\n",
-      "['cart', 'wart', 'waft']\n",
-      "['cart', 'wart', 'wait']\n",
-      "['cart', 'wart', 'want']\n",
-      "['cart', 'wart', 'watt']\n",
-      "['cart', 'wart', 'ward']\n",
-      "['cart', 'wart', 'ware']\n",
-      "['cart', 'wart', 'warm']\n",
-      "['cart', 'wart', 'warn']\n",
-      "['cart', 'wart', 'warp']\n",
-      "['cart', 'wart', 'wars']\n",
-      "['cart', 'wart', 'wary']\n",
-      "['cart', 'curt', 'hurt']\n",
-      "['cart', 'curt', 'cult']\n",
-      "['cart', 'curt', 'curb']\n",
-      "['cart', 'curt', 'curd']\n",
-      "['cart', 'curt', 'cure']\n",
-      "['cart', 'curt', 'curl']\n",
-      "['cart', 'curt', 'curs']\n",
-      "['cart', 'cant', 'pant']\n",
-      "['cart', 'cant', 'rant']\n",
-      "['cart', 'cant', 'want']\n",
-      "['cart', 'cant', 'cent']\n",
-      "['cart', 'cant', 'cast']\n",
-      "['cart', 'cant', 'cane']\n",
-      "['cart', 'cant', 'cans']\n",
-      "['cart', 'cast', 'bast']\n",
-      "['cart', 'cast', 'east']\n",
-      "['cart', 'cast', 'fast']\n",
-      "['cart', 'cast', 'last']\n",
-      "['cart', 'cast', 'mast']\n",
-      "['cart', 'cast', 'past']\n",
-      "['cart', 'cast', 'vast']\n",
-      "['cart', 'cast', 'cost']\n",
-      "['cart', 'cast', 'cyst']\n",
-      "['cart', 'cast', 'cant']\n",
-      "['cart', 'cast', 'case']\n",
-      "['cart', 'cast', 'cash']\n",
-      "['cart', 'cast', 'cask']\n",
-      "['cart', 'card', 'bard']\n",
-      "['cart', 'card', 'hard']\n",
-      "['cart', 'card', 'lard']\n",
-      "['cart', 'card', 'ward']\n",
-      "['cart', 'card', 'yard']\n",
-      "['cart', 'card', 'cord']\n",
-      "['cart', 'card', 'curd']\n",
-      "['cart', 'card', 'care']\n",
-      "['cart', 'card', 'carp']\n",
-      "['cart', 'card', 'cars']\n",
-      "['cart', 'care', 'bare']\n",
-      "['cart', 'care', 'dare']\n",
-      "['cart', 'care', 'fare']\n",
-      "['cart', 'care', 'hare']\n",
-      "['cart', 'care', 'mare']\n",
-      "['cart', 'care', 'pare']\n",
-      "['cart', 'care', 'rare']\n",
-      "['cart', 'care', 'tare']\n",
-      "['cart', 'care', 'ware']\n",
-      "['cart', 'care', 'core']\n",
-      "['cart', 'care', 'cure']\n",
-      "['cart', 'care', 'cafe']\n",
-      "['cart', 'care', 'cage']\n",
-      "['cart', 'care', 'cake']\n",
-      "['cart', 'care', 'came']\n",
-      "['cart', 'care', 'cane']\n",
-      "['cart', 'care', 'cape']\n",
-      "['cart', 'care', 'case']\n",
-      "['cart', 'care', 'cave']\n",
-      "['cart', 'care', 'card']\n",
-      "['cart', 'care', 'carp']\n",
-      "['cart', 'care', 'cars']\n",
-      "['cart', 'carp', 'harp']\n",
-      "['cart', 'carp', 'tarp']\n",
-      "['cart', 'carp', 'warp']\n",
-      "['cart', 'carp', 'camp']\n",
-      "['cart', 'carp', 'card']\n",
-      "['cart', 'carp', 'care']\n",
-      "['cart', 'carp', 'cars']\n",
-      "['cart', 'cars', 'bars']\n",
-      "['cart', 'cars', 'ears']\n",
-      "['cart', 'cars', 'jars']\n",
-      "['cart', 'cars', 'mars']\n",
-      "['cart', 'cars', 'oars']\n",
-      "['cart', 'cars', 'pars']\n",
-      "['cart', 'cars', 'tars']\n",
-      "['cart', 'cars', 'wars']\n",
-      "['cart', 'cars', 'curs']\n",
-      "['cart', 'cars', 'cabs']\n",
-      "['cart', 'cars', 'cads']\n",
-      "['cart', 'cars', 'cams']\n",
-      "['cart', 'cars', 'cans']\n",
-      "['cart', 'cars', 'caps']\n",
-      "['cart', 'cars', 'cats']\n",
-      "['cart', 'cars', 'caws']\n",
-      "['cart', 'cars', 'card']\n",
-      "['cart', 'cars', 'care']\n",
-      "['cart', 'cars', 'carp']\n",
-      "['cart', 'dart', 'hart', 'mart']\n",
-      "['cart', 'dart', 'hart', 'part']\n",
-      "['cart', 'dart', 'hart', 'tart']\n",
-      "['cart', 'dart', 'hart', 'wart']\n",
-      "['cart', 'dart', 'hart', 'hurt']\n",
-      "['cart', 'dart', 'hart', 'haft']\n",
-      "['cart', 'dart', 'hart', 'halt']\n",
-      "['cart', 'dart', 'hart', 'hard']\n",
-      "['cart', 'dart', 'hart', 'hare']\n",
-      "['cart', 'dart', 'hart', 'hark']\n",
-      "['cart', 'dart', 'hart', 'harm']\n",
-      "['cart', 'dart', 'hart', 'harp']\n",
-      "['cart', 'dart', 'mart', 'hart']\n",
-      "['cart', 'dart', 'mart', 'part']\n",
-      "['cart', 'dart', 'mart', 'tart']\n",
-      "['cart', 'dart', 'mart', 'wart']\n",
-      "['cart', 'dart', 'mart', 'malt']\n",
-      "['cart', 'dart', 'mart', 'mast']\n",
-      "['cart', 'dart', 'mart', 'matt']\n",
-      "['cart', 'dart', 'mart', 'mare']\n",
-      "['cart', 'dart', 'mart', 'mark']\n",
-      "['cart', 'dart', 'mart', 'mars']\n",
-      "['cart', 'dart', 'part', 'hart']\n",
-      "['cart', 'dart', 'part', 'mart']\n",
-      "['cart', 'dart', 'part', 'tart']\n",
-      "['cart', 'dart', 'part', 'wart']\n",
-      "['cart', 'dart', 'part', 'pert']\n",
-      "['cart', 'dart', 'part', 'port']\n",
-      "['cart', 'dart', 'part', 'pact']\n",
-      "['cart', 'dart', 'part', 'pant']\n",
-      "['cart', 'dart', 'part', 'past']\n",
-      "['cart', 'dart', 'part', 'pare']\n",
-      "['cart', 'dart', 'part', 'park']\n",
-      "['cart', 'dart', 'part', 'pars']\n",
-      "['cart', 'dart', 'tart', 'hart']\n",
-      "['cart', 'dart', 'tart', 'mart']\n",
-      "['cart', 'dart', 'tart', 'part']\n",
-      "['cart', 'dart', 'tart', 'wart']\n",
-      "['cart', 'dart', 'tart', 'tort']\n",
-      "['cart', 'dart', 'tart', 'tact']\n",
-      "['cart', 'dart', 'tart', 'taut']\n",
-      "['cart', 'dart', 'tart', 'tare']\n",
-      "['cart', 'dart', 'tart', 'taro']\n",
-      "['cart', 'dart', 'tart', 'tarp']\n",
-      "['cart', 'dart', 'tart', 'tars']\n",
-      "['cart', 'dart', 'wart', 'hart']\n",
-      "['cart', 'dart', 'wart', 'mart']\n",
-      "['cart', 'dart', 'wart', 'part']\n",
-      "['cart', 'dart', 'wart', 'tart']\n",
-      "['cart', 'dart', 'wart', 'waft']\n",
-      "['cart', 'dart', 'wart', 'wait']\n",
-      "['cart', 'dart', 'wart', 'want']\n",
-      "['cart', 'dart', 'wart', 'watt']\n",
-      "['cart', 'dart', 'wart', 'ward']\n",
-      "['cart', 'dart', 'wart', 'ware']\n",
-      "['cart', 'dart', 'wart', 'warm']\n",
-      "['cart', 'dart', 'wart', 'warn']\n",
-      "['cart', 'dart', 'wart', 'warp']\n",
-      "['cart', 'dart', 'wart', 'wars']\n",
-      "['cart', 'dart', 'wart', 'wary']\n",
-      "['cart', 'dart', 'dirt', 'girt']\n",
-      "['cart', 'dart', 'dirt', 'diet']\n",
-      "['cart', 'dart', 'dirt', 'dint']\n",
-      "['cart', 'dart', 'dirt', 'dire']\n",
-      "['cart', 'dart', 'dirt', 'dirk']\n",
-      "['cart', 'dart', 'daft', 'haft']\n",
-      "['cart', 'dart', 'daft', 'raft']\n",
-      "['cart', 'dart', 'daft', 'waft']\n",
-      "['cart', 'dart', 'daft', 'deft']\n",
-      "['cart', 'dart', 'dare', 'bare']\n",
-      "['cart', 'dart', 'dare', 'care']\n",
-      "['cart', 'dart', 'dare', 'fare']\n",
-      "['cart', 'dart', 'dare', 'hare']\n",
-      "['cart', 'dart', 'dare', 'mare']\n",
-      "['cart', 'dart', 'dare', 'pare']\n",
-      "['cart', 'dart', 'dare', 'rare']\n",
-      "['cart', 'dart', 'dare', 'tare']\n",
-      "['cart', 'dart', 'dare', 'ware']\n",
-      "['cart', 'dart', 'dare', 'dire']\n",
-      "['cart', 'dart', 'dare', 'dale']\n",
-      "['cart', 'dart', 'dare', 'dame']\n",
-      "['cart', 'dart', 'dare', 'date']\n",
-      "['cart', 'dart', 'dare', 'daze']\n",
-      "['cart', 'dart', 'dare', 'dark']\n",
-      "['cart', 'dart', 'dare', 'darn']\n",
-      "['cart', 'dart', 'dark', 'bark']\n",
-      "['cart', 'dart', 'dark', 'hark']\n",
-      "['cart', 'dart', 'dark', 'lark']\n",
-      "['cart', 'dart', 'dark', 'mark']\n",
-      "['cart', 'dart', 'dark', 'nark']\n",
-      "['cart', 'dart', 'dark', 'park']\n",
-      "['cart', 'dart', 'dark', 'dirk']\n",
-      "['cart', 'dart', 'dark', 'dork']\n",
-      "['cart', 'dart', 'dark', 'dank']\n",
-      "['cart', 'dart', 'dark', 'dare']\n",
-      "['cart', 'dart', 'dark', 'darn']\n",
-      "['cart', 'dart', 'darn', 'barn']\n",
-      "['cart', 'dart', 'darn', 'earn']\n",
-      "['cart', 'dart', 'darn', 'warn']\n",
-      "['cart', 'dart', 'darn', 'yarn']\n",
-      "['cart', 'dart', 'darn', 'damn']\n",
-      "['cart', 'dart', 'darn', 'dawn']\n",
-      "['cart', 'dart', 'darn', 'dare']\n",
-      "['cart', 'dart', 'darn', 'dark']\n",
-      "['cart', 'hart', 'dart', 'mart']\n",
-      "['cart', 'hart', 'dart', 'part']\n",
-      "['cart', 'hart', 'dart', 'tart']\n",
-      "['cart', 'hart', 'dart', 'wart']\n",
-      "['cart', 'hart', 'dart', 'dirt']\n",
-      "['cart', 'hart', 'dart', 'daft']\n",
-      "['cart', 'hart', 'dart', 'dare']\n",
-      "['cart', 'hart', 'dart', 'dark']\n",
-      "['cart', 'hart', 'dart', 'darn']\n",
-      "['cart', 'hart', 'mart', 'dart']\n",
-      "['cart', 'hart', 'mart', 'part']\n",
-      "['cart', 'hart', 'mart', 'tart']\n",
-      "['cart', 'hart', 'mart', 'wart']\n",
-      "['cart', 'hart', 'mart', 'malt']\n",
-      "['cart', 'hart', 'mart', 'mast']\n",
-      "['cart', 'hart', 'mart', 'matt']\n",
-      "['cart', 'hart', 'mart', 'mare']\n",
-      "['cart', 'hart', 'mart', 'mark']\n",
-      "['cart', 'hart', 'mart', 'mars']\n",
-      "['cart', 'hart', 'part', 'dart']\n",
-      "['cart', 'hart', 'part', 'mart']\n",
-      "['cart', 'hart', 'part', 'tart']\n",
-      "['cart', 'hart', 'part', 'wart']\n",
-      "['cart', 'hart', 'part', 'pert']\n",
-      "['cart', 'hart', 'part', 'port']\n",
-      "['cart', 'hart', 'part', 'pact']\n",
-      "['cart', 'hart', 'part', 'pant']\n",
-      "['cart', 'hart', 'part', 'past']\n",
-      "['cart', 'hart', 'part', 'pare']\n",
-      "['cart', 'hart', 'part', 'park']\n",
-      "['cart', 'hart', 'part', 'pars']\n",
-      "['cart', 'hart', 'tart', 'dart']\n",
-      "['cart', 'hart', 'tart', 'mart']\n",
-      "['cart', 'hart', 'tart', 'part']\n",
-      "['cart', 'hart', 'tart', 'wart']\n",
-      "['cart', 'hart', 'tart', 'tort']\n",
-      "['cart', 'hart', 'tart', 'tact']\n",
-      "['cart', 'hart', 'tart', 'taut']\n",
-      "['cart', 'hart', 'tart', 'tare']\n",
-      "['cart', 'hart', 'tart', 'taro']\n",
-      "['cart', 'hart', 'tart', 'tarp']\n",
-      "['cart', 'hart', 'tart', 'tars']\n",
-      "['cart', 'hart', 'wart', 'dart']\n",
-      "['cart', 'hart', 'wart', 'mart']\n",
-      "['cart', 'hart', 'wart', 'part']\n",
-      "['cart', 'hart', 'wart', 'tart']\n",
-      "['cart', 'hart', 'wart', 'waft']\n",
-      "['cart', 'hart', 'wart', 'wait']\n",
-      "['cart', 'hart', 'wart', 'want']\n",
-      "['cart', 'hart', 'wart', 'watt']\n",
-      "['cart', 'hart', 'wart', 'ward']\n",
-      "['cart', 'hart', 'wart', 'ware']\n",
-      "['cart', 'hart', 'wart', 'warm']\n",
-      "['cart', 'hart', 'wart', 'warn']\n",
-      "['cart', 'hart', 'wart', 'warp']\n",
-      "['cart', 'hart', 'wart', 'wars']\n",
-      "['cart', 'hart', 'wart', 'wary']\n",
-      "['cart', 'hart', 'hurt', 'curt']\n",
-      "['cart', 'hart', 'hurt', 'hunt']\n",
-      "['cart', 'hart', 'hurt', 'hurl']\n",
-      "['cart', 'hart', 'haft', 'daft']\n",
-      "['cart', 'hart', 'haft', 'raft']\n",
-      "['cart', 'hart', 'haft', 'waft']\n",
-      "['cart', 'hart', 'haft', 'heft']\n",
-      "['cart', 'hart', 'haft', 'halt']\n",
-      "['cart', 'hart', 'halt', 'malt']\n",
-      "['cart', 'hart', 'halt', 'salt']\n",
-      "['cart', 'hart', 'halt', 'hilt']\n",
-      "['cart', 'hart', 'halt', 'haft']\n",
-      "['cart', 'hart', 'halt', 'hale']\n",
-      "['cart', 'hart', 'halt', 'half']\n",
-      "['cart', 'hart', 'halt', 'hall']\n",
-      "['cart', 'hart', 'halt', 'halo']\n",
-      "['cart', 'hart', 'hard', 'bard']\n",
-      "['cart', 'hart', 'hard', 'card']\n",
-      "['cart', 'hart', 'hard', 'lard']\n",
-      "['cart', 'hart', 'hard', 'ward']\n",
-      "['cart', 'hart', 'hard', 'yard']\n",
-      "['cart', 'hart', 'hard', 'herd']\n",
-      "['cart', 'hart', 'hard', 'hand']\n",
-      "['cart', 'hart', 'hard', 'hare']\n",
-      "['cart', 'hart', 'hard', 'hark']\n",
-      "['cart', 'hart', 'hard', 'harm']\n",
-      "['cart', 'hart', 'hard', 'harp']\n",
-      "['cart', 'hart', 'hare', 'bare']\n",
-      "['cart', 'hart', 'hare', 'care']\n",
-      "['cart', 'hart', 'hare', 'dare']\n",
-      "['cart', 'hart', 'hare', 'fare']\n",
-      "['cart', 'hart', 'hare', 'mare']\n",
-      "['cart', 'hart', 'hare', 'pare']\n",
-      "['cart', 'hart', 'hare', 'rare']\n",
-      "['cart', 'hart', 'hare', 'tare']\n",
-      "['cart', 'hart', 'hare', 'ware']\n",
-      "['cart', 'hart', 'hare', 'here']\n",
-      "['cart', 'hart', 'hare', 'hire']\n",
-      "['cart', 'hart', 'hare', 'hake']\n",
-      "['cart', 'hart', 'hare', 'hale']\n",
-      "['cart', 'hart', 'hare', 'hate']\n",
-      "['cart', 'hart', 'hare', 'have']\n",
-      "['cart', 'hart', 'hare', 'haze']\n",
-      "['cart', 'hart', 'hare', 'hard']\n",
-      "['cart', 'hart', 'hare', 'hark']\n",
-      "['cart', 'hart', 'hare', 'harm']\n",
-      "['cart', 'hart', 'hare', 'harp']\n",
-      "['cart', 'hart', 'hark', 'bark']\n",
-      "['cart', 'hart', 'hark', 'dark']\n",
-      "['cart', 'hart', 'hark', 'lark']\n",
-      "['cart', 'hart', 'hark', 'mark']\n",
-      "['cart', 'hart', 'hark', 'nark']\n",
-      "['cart', 'hart', 'hark', 'park']\n",
-      "['cart', 'hart', 'hark', 'hack']\n",
-      "['cart', 'hart', 'hark', 'hank']\n",
-      "['cart', 'hart', 'hark', 'hawk']\n",
-      "['cart', 'hart', 'hark', 'hard']\n",
-      "['cart', 'hart', 'hark', 'hare']\n",
-      "['cart', 'hart', 'hark', 'harm']\n",
-      "['cart', 'hart', 'hark', 'harp']\n",
-      "['cart', 'hart', 'harm', 'farm']\n",
-      "['cart', 'hart', 'harm', 'warm']\n",
-      "['cart', 'hart', 'harm', 'hard']\n",
-      "['cart', 'hart', 'harm', 'hare']\n",
-      "['cart', 'hart', 'harm', 'hark']\n",
-      "['cart', 'hart', 'harm', 'harp']\n",
-      "['cart', 'hart', 'harp', 'carp']\n",
-      "['cart', 'hart', 'harp', 'tarp']\n",
-      "['cart', 'hart', 'harp', 'warp']\n",
-      "['cart', 'hart', 'harp', 'hasp']\n",
-      "['cart', 'hart', 'harp', 'hard']\n",
-      "['cart', 'hart', 'harp', 'hare']\n",
-      "['cart', 'hart', 'harp', 'hark']\n",
-      "['cart', 'hart', 'harp', 'harm']\n",
-      "['cart', 'mart', 'dart', 'hart']\n",
-      "['cart', 'mart', 'dart', 'part']\n",
-      "['cart', 'mart', 'dart', 'tart']\n",
-      "['cart', 'mart', 'dart', 'wart']\n",
-      "['cart', 'mart', 'dart', 'dirt']\n",
-      "['cart', 'mart', 'dart', 'daft']\n",
-      "['cart', 'mart', 'dart', 'dare']\n",
-      "['cart', 'mart', 'dart', 'dark']\n",
-      "['cart', 'mart', 'dart', 'darn']\n",
-      "['cart', 'mart', 'hart', 'dart']\n",
-      "['cart', 'mart', 'hart', 'part']\n",
-      "['cart', 'mart', 'hart', 'tart']\n",
-      "['cart', 'mart', 'hart', 'wart']\n",
-      "['cart', 'mart', 'hart', 'hurt']\n",
-      "['cart', 'mart', 'hart', 'haft']\n",
-      "['cart', 'mart', 'hart', 'halt']\n",
-      "['cart', 'mart', 'hart', 'hard']\n",
-      "['cart', 'mart', 'hart', 'hare']\n",
-      "['cart', 'mart', 'hart', 'hark']\n",
-      "['cart', 'mart', 'hart', 'harm']\n",
-      "['cart', 'mart', 'hart', 'harp']\n",
-      "['cart', 'mart', 'part', 'dart']\n",
-      "['cart', 'mart', 'part', 'hart']\n",
-      "['cart', 'mart', 'part', 'tart']\n",
-      "['cart', 'mart', 'part', 'wart']\n",
-      "['cart', 'mart', 'part', 'pert']\n",
-      "['cart', 'mart', 'part', 'port']\n",
-      "['cart', 'mart', 'part', 'pact']\n",
-      "['cart', 'mart', 'part', 'pant']\n",
-      "['cart', 'mart', 'part', 'past']\n",
-      "['cart', 'mart', 'part', 'pare']\n",
-      "['cart', 'mart', 'part', 'park']\n",
-      "['cart', 'mart', 'part', 'pars']\n",
-      "['cart', 'mart', 'tart', 'dart']\n",
-      "['cart', 'mart', 'tart', 'hart']\n",
-      "['cart', 'mart', 'tart', 'part']\n",
-      "['cart', 'mart', 'tart', 'wart']\n",
-      "['cart', 'mart', 'tart', 'tort']\n",
-      "['cart', 'mart', 'tart', 'tact']\n",
-      "['cart', 'mart', 'tart', 'taut']\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "['cart', 'mart', 'tart', 'tare']\n",
-      "['cart', 'mart', 'tart', 'taro']\n",
-      "['cart', 'mart', 'tart', 'tarp']\n",
-      "['cart', 'mart', 'tart', 'tars']\n",
-      "['cart', 'mart', 'wart', 'dart']\n",
-      "['cart', 'mart', 'wart', 'hart']\n",
-      "['cart', 'mart', 'wart', 'part']\n",
-      "['cart', 'mart', 'wart', 'tart']\n",
-      "['cart', 'mart', 'wart', 'waft']\n",
-      "['cart', 'mart', 'wart', 'wait']\n",
-      "['cart', 'mart', 'wart', 'want']\n",
-      "['cart', 'mart', 'wart', 'watt']\n",
-      "['cart', 'mart', 'wart', 'ward']\n",
-      "['cart', 'mart', 'wart', 'ware']\n",
-      "['cart', 'mart', 'wart', 'warm']\n",
-      "['cart', 'mart', 'wart', 'warn']\n",
-      "['cart', 'mart', 'wart', 'warp']\n",
-      "['cart', 'mart', 'wart', 'wars']\n",
-      "['cart', 'mart', 'wart', 'wary']\n",
-      "['cart', 'mart', 'malt', 'halt']\n",
-      "['cart', 'mart', 'malt', 'salt']\n",
-      "['cart', 'mart', 'malt', 'melt']\n",
-      "['cart', 'mart', 'malt', 'mast']\n",
-      "['cart', 'mart', 'malt', 'matt']\n",
-      "['cart', 'mart', 'malt', 'male']\n",
-      "['cart', 'mart', 'malt', 'mall']\n",
-      "['cart', 'mart', 'mast', 'bast']\n",
-      "['cart', 'mart', 'mast', 'cast']\n",
-      "['cart', 'mart', 'mast', 'east']\n",
-      "['cart', 'mart', 'mast', 'fast']\n",
-      "['cart', 'mart', 'mast', 'last']\n",
-      "['cart', 'mart', 'mast', 'past']\n",
-      "['cart', 'mart', 'mast', 'vast']\n",
-      "['cart', 'mart', 'mast', 'mist']\n",
-      "['cart', 'mart', 'mast', 'most']\n",
-      "['cart', 'mart', 'mast', 'must']\n",
-      "['cart', 'mart', 'mast', 'malt']\n",
-      "['cart', 'mart', 'mast', 'matt']\n",
-      "['cart', 'mart', 'mast', 'mash']\n",
-      "['cart', 'mart', 'mast', 'mask']\n",
-      "['cart', 'mart', 'mast', 'mass']\n",
-      "['cart', 'mart', 'matt', 'watt']\n",
-      "['cart', 'mart', 'matt', 'mitt']\n",
-      "['cart', 'mart', 'matt', 'mutt']\n",
-      "['cart', 'mart', 'matt', 'malt']\n",
-      "['cart', 'mart', 'matt', 'mast']\n",
-      "['cart', 'mart', 'matt', 'mate']\n",
-      "['cart', 'mart', 'matt', 'math']\n",
-      "['cart', 'mart', 'matt', 'mats']\n",
-      "['cart', 'mart', 'mare', 'bare']\n",
-      "['cart', 'mart', 'mare', 'care']\n",
-      "['cart', 'mart', 'mare', 'dare']\n",
-      "['cart', 'mart', 'mare', 'fare']\n",
-      "['cart', 'mart', 'mare', 'hare']\n",
-      "['cart', 'mart', 'mare', 'pare']\n",
-      "['cart', 'mart', 'mare', 'rare']\n",
-      "['cart', 'mart', 'mare', 'tare']\n",
-      "['cart', 'mart', 'mare', 'ware']\n",
-      "['cart', 'mart', 'mare', 'mere']\n",
-      "['cart', 'mart', 'mare', 'mire']\n",
-      "['cart', 'mart', 'mare', 'more']\n",
-      "['cart', 'mart', 'mare', 'mace']\n",
-      "['cart', 'mart', 'mare', 'made']\n",
-      "['cart', 'mart', 'mare', 'make']\n",
-      "['cart', 'mart', 'mare', 'male']\n",
-      "['cart', 'mart', 'mare', 'mane']\n",
-      "['cart', 'mart', 'mare', 'mate']\n",
-      "['cart', 'mart', 'mare', 'maze']\n",
-      "['cart', 'mart', 'mare', 'mark']\n",
-      "['cart', 'mart', 'mare', 'mars']\n",
-      "['cart', 'mart', 'mark', 'bark']\n",
-      "['cart', 'mart', 'mark', 'dark']\n",
-      "['cart', 'mart', 'mark', 'hark']\n",
-      "['cart', 'mart', 'mark', 'lark']\n",
-      "['cart', 'mart', 'mark', 'nark']\n",
-      "['cart', 'mart', 'mark', 'park']\n",
-      "['cart', 'mart', 'mark', 'murk']\n",
-      "['cart', 'mart', 'mark', 'mask']\n",
-      "['cart', 'mart', 'mark', 'mare']\n",
-      "['cart', 'mart', 'mark', 'mars']\n",
-      "['cart', 'mart', 'mars', 'bars']\n",
-      "['cart', 'mart', 'mars', 'cars']\n",
-      "['cart', 'mart', 'mars', 'ears']\n",
-      "['cart', 'mart', 'mars', 'jars']\n",
-      "['cart', 'mart', 'mars', 'oars']\n",
-      "['cart', 'mart', 'mars', 'pars']\n",
-      "['cart', 'mart', 'mars', 'tars']\n",
-      "['cart', 'mart', 'mars', 'wars']\n",
-      "['cart', 'mart', 'mars', 'mads']\n",
-      "['cart', 'mart', 'mars', 'mans']\n",
-      "['cart', 'mart', 'mars', 'maps']\n",
-      "['cart', 'mart', 'mars', 'mass']\n",
-      "['cart', 'mart', 'mars', 'mats']\n",
-      "['cart', 'mart', 'mars', 'maws']\n",
-      "['cart', 'mart', 'mars', 'mare']\n",
-      "['cart', 'mart', 'mars', 'mark']\n",
-      "['cart', 'part', 'dart', 'hart']\n",
-      "['cart', 'part', 'dart', 'mart']\n",
-      "['cart', 'part', 'dart', 'tart']\n",
-      "['cart', 'part', 'dart', 'wart']\n",
-      "['cart', 'part', 'dart', 'dirt']\n",
-      "['cart', 'part', 'dart', 'daft']\n",
-      "['cart', 'part', 'dart', 'dare']\n",
-      "['cart', 'part', 'dart', 'dark']\n",
-      "['cart', 'part', 'dart', 'darn']\n",
-      "['cart', 'part', 'hart', 'dart']\n",
-      "['cart', 'part', 'hart', 'mart']\n",
-      "['cart', 'part', 'hart', 'tart']\n",
-      "['cart', 'part', 'hart', 'wart']\n",
-      "['cart', 'part', 'hart', 'hurt']\n",
-      "['cart', 'part', 'hart', 'haft']\n",
-      "['cart', 'part', 'hart', 'halt']\n",
-      "['cart', 'part', 'hart', 'hard']\n",
-      "['cart', 'part', 'hart', 'hare']\n",
-      "['cart', 'part', 'hart', 'hark']\n",
-      "['cart', 'part', 'hart', 'harm']\n",
-      "['cart', 'part', 'hart', 'harp']\n",
-      "['cart', 'part', 'mart', 'dart']\n",
-      "['cart', 'part', 'mart', 'hart']\n",
-      "['cart', 'part', 'mart', 'tart']\n",
-      "['cart', 'part', 'mart', 'wart']\n",
-      "['cart', 'part', 'mart', 'malt']\n",
-      "['cart', 'part', 'mart', 'mast']\n",
-      "['cart', 'part', 'mart', 'matt']\n",
-      "['cart', 'part', 'mart', 'mare']\n",
-      "['cart', 'part', 'mart', 'mark']\n",
-      "['cart', 'part', 'mart', 'mars']\n",
-      "['cart', 'part', 'tart', 'dart']\n",
-      "['cart', 'part', 'tart', 'hart']\n",
-      "['cart', 'part', 'tart', 'mart']\n",
-      "['cart', 'part', 'tart', 'wart']\n",
-      "['cart', 'part', 'tart', 'tort']\n",
-      "['cart', 'part', 'tart', 'tact']\n",
-      "['cart', 'part', 'tart', 'taut']\n",
-      "['cart', 'part', 'tart', 'tare']\n",
-      "['cart', 'part', 'tart', 'taro']\n",
-      "['cart', 'part', 'tart', 'tarp']\n",
-      "['cart', 'part', 'tart', 'tars']\n",
-      "['cart', 'part', 'wart', 'dart']\n",
-      "['cart', 'part', 'wart', 'hart']\n",
-      "['cart', 'part', 'wart', 'mart']\n",
-      "['cart', 'part', 'wart', 'tart']\n",
-      "['cart', 'part', 'wart', 'waft']\n",
-      "['cart', 'part', 'wart', 'wait']\n",
-      "['cart', 'part', 'wart', 'want']\n",
-      "['cart', 'part', 'wart', 'watt']\n",
-      "['cart', 'part', 'wart', 'ward']\n",
-      "['cart', 'part', 'wart', 'ware']\n",
-      "['cart', 'part', 'wart', 'warm']\n",
-      "['cart', 'part', 'wart', 'warn']\n",
-      "['cart', 'part', 'wart', 'warp']\n",
-      "['cart', 'part', 'wart', 'wars']\n",
-      "['cart', 'part', 'wart', 'wary']\n",
-      "['cart', 'part', 'pert', 'port']\n",
-      "['cart', 'part', 'pert', 'peat']\n",
-      "['cart', 'part', 'pert', 'pelt']\n",
-      "['cart', 'part', 'pert', 'pent']\n",
-      "['cart', 'part', 'pert', 'pest']\n",
-      "['cart', 'part', 'pert', 'perk']\n",
-      "['cart', 'part', 'pert', 'perm']\n",
-      "['cart', 'part', 'port', 'fort']\n",
-      "['cart', 'part', 'port', 'sort']\n",
-      "['cart', 'part', 'port', 'tort']\n",
-      "['cart', 'part', 'port', 'pert']\n",
-      "['cart', 'part', 'port', 'poet']\n",
-      "['cart', 'part', 'port', 'post']\n",
-      "['cart', 'part', 'port', 'pout']\n",
-      "['cart', 'part', 'port', 'pore']\n",
-      "['cart', 'part', 'port', 'pork']\n",
-      "['cart', 'part', 'port', 'porn']\n",
-      "['cart', 'part', 'pact', 'fact']\n",
-      "['cart', 'part', 'pact', 'tact']\n",
-      "['cart', 'part', 'pact', 'pant']\n",
-      "['cart', 'part', 'pact', 'past']\n",
-      "['cart', 'part', 'pact', 'pace']\n",
-      "['cart', 'part', 'pact', 'pack']\n",
-      "['cart', 'part', 'pant', 'cant']\n",
-      "['cart', 'part', 'pant', 'rant']\n",
-      "['cart', 'part', 'pant', 'want']\n",
-      "['cart', 'part', 'pant', 'pent']\n",
-      "['cart', 'part', 'pant', 'pint']\n",
-      "['cart', 'part', 'pant', 'punt']\n",
-      "['cart', 'part', 'pant', 'pact']\n",
-      "['cart', 'part', 'pant', 'past']\n",
-      "['cart', 'part', 'pant', 'pane']\n",
-      "['cart', 'part', 'pant', 'pang']\n",
-      "['cart', 'part', 'pant', 'pans']\n",
-      "['cart', 'part', 'past', 'bast']\n",
-      "['cart', 'part', 'past', 'cast']\n",
-      "['cart', 'part', 'past', 'east']\n",
-      "['cart', 'part', 'past', 'fast']\n",
-      "['cart', 'part', 'past', 'last']\n",
-      "['cart', 'part', 'past', 'mast']\n",
-      "['cart', 'part', 'past', 'vast']\n",
-      "['cart', 'part', 'past', 'pest']\n",
-      "['cart', 'part', 'past', 'post']\n",
-      "['cart', 'part', 'past', 'psst']\n",
-      "['cart', 'part', 'past', 'pact']\n",
-      "['cart', 'part', 'past', 'pant']\n",
-      "['cart', 'part', 'past', 'pass']\n",
-      "['cart', 'part', 'pare', 'bare']\n",
-      "['cart', 'part', 'pare', 'care']\n",
-      "['cart', 'part', 'pare', 'dare']\n",
-      "['cart', 'part', 'pare', 'fare']\n",
-      "['cart', 'part', 'pare', 'hare']\n",
-      "['cart', 'part', 'pare', 'mare']\n",
-      "['cart', 'part', 'pare', 'rare']\n",
-      "['cart', 'part', 'pare', 'tare']\n",
-      "['cart', 'part', 'pare', 'ware']\n",
-      "['cart', 'part', 'pare', 'pore']\n",
-      "['cart', 'part', 'pare', 'pure']\n",
-      "['cart', 'part', 'pare', 'pyre']\n",
-      "['cart', 'part', 'pare', 'pace']\n",
-      "['cart', 'part', 'pare', 'page']\n",
-      "['cart', 'part', 'pare', 'pale']\n",
-      "['cart', 'part', 'pare', 'pane']\n",
-      "['cart', 'part', 'pare', 'pate']\n",
-      "['cart', 'part', 'pare', 'pave']\n",
-      "['cart', 'part', 'pare', 'park']\n",
-      "['cart', 'part', 'pare', 'pars']\n",
-      "['cart', 'part', 'park', 'bark']\n",
-      "['cart', 'part', 'park', 'dark']\n",
-      "['cart', 'part', 'park', 'hark']\n",
-      "['cart', 'part', 'park', 'lark']\n",
-      "['cart', 'part', 'park', 'mark']\n",
-      "['cart', 'part', 'park', 'nark']\n",
-      "['cart', 'part', 'park', 'perk']\n",
-      "['cart', 'part', 'park', 'pork']\n",
-      "['cart', 'part', 'park', 'pack']\n",
-      "['cart', 'part', 'park', 'pare']\n",
-      "['cart', 'part', 'park', 'pars']\n",
-      "['cart', 'part', 'pars', 'bars']\n",
-      "['cart', 'part', 'pars', 'cars']\n",
-      "['cart', 'part', 'pars', 'ears']\n",
-      "['cart', 'part', 'pars', 'jars']\n",
-      "['cart', 'part', 'pars', 'mars']\n",
-      "['cart', 'part', 'pars', 'oars']\n",
-      "['cart', 'part', 'pars', 'tars']\n",
-      "['cart', 'part', 'pars', 'wars']\n",
-      "['cart', 'part', 'pars', 'pads']\n",
-      "['cart', 'part', 'pars', 'pals']\n",
-      "['cart', 'part', 'pars', 'pans']\n",
-      "['cart', 'part', 'pars', 'paps']\n",
-      "['cart', 'part', 'pars', 'pass']\n",
-      "['cart', 'part', 'pars', 'pats']\n",
-      "['cart', 'part', 'pars', 'paws']\n",
-      "['cart', 'part', 'pars', 'pays']\n",
-      "['cart', 'part', 'pars', 'pare']\n",
-      "['cart', 'part', 'pars', 'park']\n",
-      "['cart', 'tart', 'dart', 'hart']\n",
-      "['cart', 'tart', 'dart', 'mart']\n",
-      "['cart', 'tart', 'dart', 'part']\n",
-      "['cart', 'tart', 'dart', 'wart']\n",
-      "['cart', 'tart', 'dart', 'dirt']\n",
-      "['cart', 'tart', 'dart', 'daft']\n",
-      "['cart', 'tart', 'dart', 'dare']\n",
-      "['cart', 'tart', 'dart', 'dark']\n",
-      "['cart', 'tart', 'dart', 'darn']\n",
-      "['cart', 'tart', 'hart', 'dart']\n",
-      "['cart', 'tart', 'hart', 'mart']\n",
-      "['cart', 'tart', 'hart', 'part']\n",
-      "['cart', 'tart', 'hart', 'wart']\n",
-      "['cart', 'tart', 'hart', 'hurt']\n",
-      "['cart', 'tart', 'hart', 'haft']\n",
-      "['cart', 'tart', 'hart', 'halt']\n",
-      "['cart', 'tart', 'hart', 'hard']\n",
-      "['cart', 'tart', 'hart', 'hare']\n",
-      "['cart', 'tart', 'hart', 'hark']\n",
-      "['cart', 'tart', 'hart', 'harm']\n",
-      "['cart', 'tart', 'hart', 'harp']\n",
-      "['cart', 'tart', 'mart', 'dart']\n",
-      "['cart', 'tart', 'mart', 'hart']\n",
-      "['cart', 'tart', 'mart', 'part']\n",
-      "['cart', 'tart', 'mart', 'wart']\n",
-      "['cart', 'tart', 'mart', 'malt']\n",
-      "['cart', 'tart', 'mart', 'mast']\n",
-      "['cart', 'tart', 'mart', 'matt']\n",
-      "['cart', 'tart', 'mart', 'mare']\n",
-      "['cart', 'tart', 'mart', 'mark']\n",
-      "['cart', 'tart', 'mart', 'mars']\n",
-      "['cart', 'tart', 'part', 'dart']\n",
-      "['cart', 'tart', 'part', 'hart']\n",
-      "['cart', 'tart', 'part', 'mart']\n",
-      "['cart', 'tart', 'part', 'wart']\n",
-      "['cart', 'tart', 'part', 'pert']\n",
-      "['cart', 'tart', 'part', 'port']\n",
-      "['cart', 'tart', 'part', 'pact']\n",
-      "['cart', 'tart', 'part', 'pant']\n",
-      "['cart', 'tart', 'part', 'past']\n",
-      "['cart', 'tart', 'part', 'pare']\n",
-      "['cart', 'tart', 'part', 'park']\n",
-      "['cart', 'tart', 'part', 'pars']\n",
-      "['cart', 'tart', 'wart', 'dart']\n",
-      "['cart', 'tart', 'wart', 'hart']\n",
-      "['cart', 'tart', 'wart', 'mart']\n",
-      "['cart', 'tart', 'wart', 'part']\n",
-      "['cart', 'tart', 'wart', 'waft']\n",
-      "['cart', 'tart', 'wart', 'wait']\n",
-      "['cart', 'tart', 'wart', 'want']\n",
-      "['cart', 'tart', 'wart', 'watt']\n",
-      "['cart', 'tart', 'wart', 'ward']\n",
-      "['cart', 'tart', 'wart', 'ware']\n",
-      "['cart', 'tart', 'wart', 'warm']\n",
-      "['cart', 'tart', 'wart', 'warn']\n",
-      "['cart', 'tart', 'wart', 'warp']\n",
-      "['cart', 'tart', 'wart', 'wars']\n",
-      "['cart', 'tart', 'wart', 'wary']\n",
-      "['cart', 'tart', 'tort', 'fort']\n",
-      "['cart', 'tart', 'tort', 'port']\n",
-      "['cart', 'tart', 'tort', 'sort']\n",
-      "['cart', 'tart', 'tort', 'toot']\n",
-      "['cart', 'tart', 'tort', 'tost']\n",
-      "['cart', 'tart', 'tort', 'tout']\n",
-      "['cart', 'tart', 'tort', 'tore']\n",
-      "['cart', 'tart', 'tort', 'torn']\n",
-      "['cart', 'tart', 'tort', 'tors']\n",
-      "['cart', 'tart', 'tact', 'fact']\n",
-      "['cart', 'tart', 'tact', 'pact']\n",
-      "['cart', 'tart', 'tact', 'taut']\n",
-      "['cart', 'tart', 'tact', 'tack']\n",
-      "['cart', 'tart', 'tact', 'taco']\n",
-      "['cart', 'tart', 'taut', 'tout']\n",
-      "['cart', 'tart', 'taut', 'tact']\n",
-      "['cart', 'tart', 'tare', 'bare']\n",
-      "['cart', 'tart', 'tare', 'care']\n",
-      "['cart', 'tart', 'tare', 'dare']\n",
-      "['cart', 'tart', 'tare', 'fare']\n",
-      "['cart', 'tart', 'tare', 'hare']\n",
-      "['cart', 'tart', 'tare', 'mare']\n",
-      "['cart', 'tart', 'tare', 'pare']\n",
-      "['cart', 'tart', 'tare', 'rare']\n",
-      "['cart', 'tart', 'tare', 'ware']\n",
-      "['cart', 'tart', 'tare', 'tire']\n",
-      "['cart', 'tart', 'tare', 'tore']\n",
-      "['cart', 'tart', 'tare', 'tyre']\n",
-      "['cart', 'tart', 'tare', 'take']\n",
-      "['cart', 'tart', 'tare', 'tale']\n",
-      "['cart', 'tart', 'tare', 'tame']\n",
-      "['cart', 'tart', 'tare', 'tape']\n",
-      "['cart', 'tart', 'tare', 'taro']\n",
-      "['cart', 'tart', 'tare', 'tarp']\n",
-      "['cart', 'tart', 'tare', 'tars']\n",
-      "['cart', 'tart', 'taro', 'tiro']\n",
-      "['cart', 'tart', 'taro', 'tyro']\n",
-      "['cart', 'tart', 'taro', 'taco']\n",
-      "['cart', 'tart', 'taro', 'tare']\n",
-      "['cart', 'tart', 'taro', 'tarp']\n",
-      "['cart', 'tart', 'taro', 'tars']\n",
-      "['cart', 'tart', 'tarp', 'carp']\n",
-      "['cart', 'tart', 'tarp', 'harp']\n",
-      "['cart', 'tart', 'tarp', 'warp']\n",
-      "['cart', 'tart', 'tarp', 'tamp']\n",
-      "['cart', 'tart', 'tarp', 'tare']\n",
-      "['cart', 'tart', 'tarp', 'taro']\n",
-      "['cart', 'tart', 'tarp', 'tars']\n",
-      "['cart', 'tart', 'tars', 'bars']\n",
-      "['cart', 'tart', 'tars', 'cars']\n",
-      "['cart', 'tart', 'tars', 'ears']\n",
-      "['cart', 'tart', 'tars', 'jars']\n",
-      "['cart', 'tart', 'tars', 'mars']\n",
-      "['cart', 'tart', 'tars', 'oars']\n",
-      "['cart', 'tart', 'tars', 'pars']\n",
-      "['cart', 'tart', 'tars', 'wars']\n",
-      "['cart', 'tart', 'tars', 'tors']\n",
-      "['cart', 'tart', 'tars', 'tabs']\n",
-      "['cart', 'tart', 'tars', 'tads']\n",
-      "['cart', 'tart', 'tars', 'tags']\n",
-      "['cart', 'tart', 'tars', 'tams']\n",
-      "['cart', 'tart', 'tars', 'tans']\n",
-      "['cart', 'tart', 'tars', 'taps']\n",
-      "['cart', 'tart', 'tars', 'tats']\n",
-      "['cart', 'tart', 'tars', 'tare']\n",
-      "['cart', 'tart', 'tars', 'taro']\n",
-      "['cart', 'tart', 'tars', 'tarp']\n",
-      "['cart', 'wart', 'dart', 'hart']\n",
-      "['cart', 'wart', 'dart', 'mart']\n",
-      "['cart', 'wart', 'dart', 'part']\n",
-      "['cart', 'wart', 'dart', 'tart']\n",
-      "['cart', 'wart', 'dart', 'dirt']\n",
-      "['cart', 'wart', 'dart', 'daft']\n",
-      "['cart', 'wart', 'dart', 'dare']\n",
-      "['cart', 'wart', 'dart', 'dark']\n",
-      "['cart', 'wart', 'dart', 'darn']\n",
-      "['cart', 'wart', 'hart', 'dart']\n",
-      "['cart', 'wart', 'hart', 'mart']\n",
-      "['cart', 'wart', 'hart', 'part']\n",
-      "['cart', 'wart', 'hart', 'tart']\n",
-      "['cart', 'wart', 'hart', 'hurt']\n",
-      "['cart', 'wart', 'hart', 'haft']\n",
-      "['cart', 'wart', 'hart', 'halt']\n",
-      "['cart', 'wart', 'hart', 'hard']\n",
-      "['cart', 'wart', 'hart', 'hare']\n",
-      "['cart', 'wart', 'hart', 'hark']\n",
-      "['cart', 'wart', 'hart', 'harm']\n",
-      "['cart', 'wart', 'hart', 'harp']\n",
-      "['cart', 'wart', 'mart', 'dart']\n",
-      "['cart', 'wart', 'mart', 'hart']\n",
-      "['cart', 'wart', 'mart', 'part']\n",
-      "['cart', 'wart', 'mart', 'tart']\n",
-      "['cart', 'wart', 'mart', 'malt']\n",
-      "['cart', 'wart', 'mart', 'mast']\n",
-      "['cart', 'wart', 'mart', 'matt']\n",
-      "['cart', 'wart', 'mart', 'mare']\n",
-      "['cart', 'wart', 'mart', 'mark']\n",
-      "['cart', 'wart', 'mart', 'mars']\n",
-      "['cart', 'wart', 'part', 'dart']\n",
-      "['cart', 'wart', 'part', 'hart']\n",
-      "['cart', 'wart', 'part', 'mart']\n",
-      "['cart', 'wart', 'part', 'tart']\n",
-      "['cart', 'wart', 'part', 'pert']\n",
-      "['cart', 'wart', 'part', 'port']\n",
-      "['cart', 'wart', 'part', 'pact']\n",
-      "['cart', 'wart', 'part', 'pant']\n",
-      "['cart', 'wart', 'part', 'past']\n",
-      "['cart', 'wart', 'part', 'pare']\n",
-      "['cart', 'wart', 'part', 'park']\n",
-      "['cart', 'wart', 'part', 'pars']\n",
-      "['cart', 'wart', 'tart', 'dart']\n",
-      "['cart', 'wart', 'tart', 'hart']\n",
-      "['cart', 'wart', 'tart', 'mart']\n",
-      "['cart', 'wart', 'tart', 'part']\n",
-      "['cart', 'wart', 'tart', 'tort']\n",
-      "['cart', 'wart', 'tart', 'tact']\n",
-      "['cart', 'wart', 'tart', 'taut']\n",
-      "['cart', 'wart', 'tart', 'tare']\n",
-      "['cart', 'wart', 'tart', 'taro']\n",
-      "['cart', 'wart', 'tart', 'tarp']\n",
-      "['cart', 'wart', 'tart', 'tars']\n",
-      "['cart', 'wart', 'waft', 'daft']\n",
-      "['cart', 'wart', 'waft', 'haft']\n",
-      "['cart', 'wart', 'waft', 'raft']\n",
-      "['cart', 'wart', 'waft', 'weft']\n",
-      "['cart', 'wart', 'waft', 'wait']\n",
-      "['cart', 'wart', 'waft', 'want']\n",
-      "['cart', 'wart', 'waft', 'watt']\n",
-      "['cart', 'wart', 'wait', 'bait']\n",
-      "['cart', 'wart', 'wait', 'gait']\n",
-      "['cart', 'wart', 'wait', 'whit']\n",
-      "['cart', 'wart', 'wait', 'writ']\n",
-      "['cart', 'wart', 'wait', 'waft']\n",
-      "['cart', 'wart', 'wait', 'want']\n",
-      "['cart', 'wart', 'wait', 'watt']\n",
-      "['cart', 'wart', 'wait', 'waif']\n",
-      "['cart', 'wart', 'wait', 'wail']\n",
-      "['cart', 'wart', 'want', 'cant']\n",
-      "['cart', 'wart', 'want', 'pant']\n",
-      "['cart', 'wart', 'want', 'rant']\n",
-      "['cart', 'wart', 'want', 'went']\n",
-      "['cart', 'wart', 'want', 'wont']\n",
-      "['cart', 'wart', 'want', 'waft']\n",
-      "['cart', 'wart', 'want', 'wait']\n",
-      "['cart', 'wart', 'want', 'watt']\n",
-      "['cart', 'wart', 'want', 'wand']\n",
-      "['cart', 'wart', 'want', 'wane']\n",
-      "['cart', 'wart', 'watt', 'matt']\n",
-      "['cart', 'wart', 'watt', 'waft']\n",
-      "['cart', 'wart', 'watt', 'wait']\n",
-      "['cart', 'wart', 'watt', 'want']\n",
-      "['cart', 'wart', 'ward', 'bard']\n",
-      "['cart', 'wart', 'ward', 'card']\n",
-      "['cart', 'wart', 'ward', 'hard']\n",
-      "['cart', 'wart', 'ward', 'lard']\n",
-      "['cart', 'wart', 'ward', 'yard']\n",
-      "['cart', 'wart', 'ward', 'word']\n",
-      "['cart', 'wart', 'ward', 'wand']\n",
-      "['cart', 'wart', 'ward', 'ware']\n",
-      "['cart', 'wart', 'ward', 'warm']\n",
-      "['cart', 'wart', 'ward', 'warn']\n",
-      "['cart', 'wart', 'ward', 'warp']\n",
-      "['cart', 'wart', 'ward', 'wars']\n",
-      "['cart', 'wart', 'ward', 'wary']\n",
-      "['cart', 'wart', 'ware', 'bare']\n",
-      "['cart', 'wart', 'ware', 'care']\n",
-      "['cart', 'wart', 'ware', 'dare']\n",
-      "['cart', 'wart', 'ware', 'fare']\n",
-      "['cart', 'wart', 'ware', 'hare']\n",
-      "['cart', 'wart', 'ware', 'mare']\n",
-      "['cart', 'wart', 'ware', 'pare']\n",
-      "['cart', 'wart', 'ware', 'rare']\n",
-      "['cart', 'wart', 'ware', 'tare']\n",
-      "['cart', 'wart', 'ware', 'were']\n",
-      "['cart', 'wart', 'ware', 'wire']\n",
-      "['cart', 'wart', 'ware', 'wore']\n",
-      "['cart', 'wart', 'ware', 'wade']\n",
-      "['cart', 'wart', 'ware', 'wage']\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "['cart', 'wart', 'ware', 'wake']\n",
-      "['cart', 'wart', 'ware', 'wale']\n",
-      "['cart', 'wart', 'ware', 'wane']\n",
-      "['cart', 'wart', 'ware', 'wave']\n",
-      "['cart', 'wart', 'ware', 'ward']\n",
-      "['cart', 'wart', 'ware', 'warm']\n",
-      "['cart', 'wart', 'ware', 'warn']\n",
-      "['cart', 'wart', 'ware', 'warp']\n",
-      "['cart', 'wart', 'ware', 'wars']\n",
-      "['cart', 'wart', 'ware', 'wary']\n",
-      "['cart', 'wart', 'warm', 'farm']\n",
-      "['cart', 'wart', 'warm', 'harm']\n",
-      "['cart', 'wart', 'warm', 'worm']\n",
-      "['cart', 'wart', 'warm', 'ward']\n",
-      "['cart', 'wart', 'warm', 'ware']\n",
-      "['cart', 'wart', 'warm', 'warn']\n",
-      "['cart', 'wart', 'warm', 'warp']\n",
-      "['cart', 'wart', 'warm', 'wars']\n",
-      "['cart', 'wart', 'warm', 'wary']\n",
-      "['cart', 'wart', 'warn', 'barn']\n",
-      "['cart', 'wart', 'warn', 'darn']\n",
-      "['cart', 'wart', 'warn', 'earn']\n",
-      "['cart', 'wart', 'warn', 'yarn']\n",
-      "['cart', 'wart', 'warn', 'worn']\n",
-      "['cart', 'wart', 'warn', 'ward']\n",
-      "['cart', 'wart', 'warn', 'ware']\n",
-      "['cart', 'wart', 'warn', 'warm']\n",
-      "['cart', 'wart', 'warn', 'warp']\n",
-      "['cart', 'wart', 'warn', 'wars']\n",
-      "['cart', 'wart', 'warn', 'wary']\n",
-      "['cart', 'wart', 'warp', 'carp']\n",
-      "['cart', 'wart', 'warp', 'harp']\n",
-      "['cart', 'wart', 'warp', 'tarp']\n",
-      "['cart', 'wart', 'warp', 'wasp']\n",
-      "['cart', 'wart', 'warp', 'ward']\n",
-      "['cart', 'wart', 'warp', 'ware']\n",
-      "['cart', 'wart', 'warp', 'warm']\n",
-      "['cart', 'wart', 'warp', 'warn']\n",
-      "['cart', 'wart', 'warp', 'wars']\n",
-      "['cart', 'wart', 'warp', 'wary']\n",
-      "['cart', 'wart', 'wars', 'bars']\n",
-      "['cart', 'wart', 'wars', 'cars']\n",
-      "['cart', 'wart', 'wars', 'ears']\n",
-      "['cart', 'wart', 'wars', 'jars']\n",
-      "['cart', 'wart', 'wars', 'mars']\n",
-      "['cart', 'wart', 'wars', 'oars']\n",
-      "['cart', 'wart', 'wars', 'pars']\n",
-      "['cart', 'wart', 'wars', 'tars']\n",
-      "['cart', 'wart', 'wars', 'wads']\n",
-      "['cart', 'wart', 'wars', 'wags']\n",
-      "['cart', 'wart', 'wars', 'ways']\n",
-      "['cart', 'wart', 'wars', 'ward']\n",
-      "['cart', 'wart', 'wars', 'ware']\n",
-      "['cart', 'wart', 'wars', 'warm']\n",
-      "['cart', 'wart', 'wars', 'warn']\n",
-      "['cart', 'wart', 'wars', 'warp']\n",
-      "['cart', 'wart', 'wars', 'wary']\n",
-      "['cart', 'wart', 'wary', 'nary']\n",
-      "['cart', 'wart', 'wary', 'vary']\n",
-      "['cart', 'wart', 'wary', 'wiry']\n",
-      "['cart', 'wart', 'wary', 'wavy']\n",
-      "['cart', 'wart', 'wary', 'waxy']\n",
-      "['cart', 'wart', 'wary', 'ward']\n",
-      "['cart', 'wart', 'wary', 'ware']\n",
-      "['cart', 'wart', 'wary', 'warm']\n",
-      "['cart', 'wart', 'wary', 'warn']\n",
-      "['cart', 'wart', 'wary', 'warp']\n",
-      "['cart', 'wart', 'wary', 'wars']\n",
-      "['cart', 'curt', 'hurt', 'hart']\n",
-      "['cart', 'curt', 'hurt', 'hunt']\n",
-      "['cart', 'curt', 'hurt', 'hurl']\n",
-      "['cart', 'curt', 'cult', 'colt']\n",
-      "['cart', 'curt', 'cult', 'cull']\n",
-      "['cart', 'curt', 'curb', 'curd']\n",
-      "['cart', 'curt', 'curb', 'cure']\n",
-      "['cart', 'curt', 'curb', 'curl']\n",
-      "['cart', 'curt', 'curb', 'curs']\n",
-      "['cart', 'curt', 'curd', 'turd']\n",
-      "['cart', 'curt', 'curd', 'card']\n",
-      "['cart', 'curt', 'curd', 'cord']\n",
-      "['cart', 'curt', 'curd', 'cued']\n",
-      "['cart', 'curt', 'curd', 'curb']\n",
-      "['cart', 'curt', 'curd', 'cure']\n",
-      "['cart', 'curt', 'curd', 'curl']\n",
-      "['cart', 'curt', 'curd', 'curs']\n",
-      "['cart', 'curt', 'cure', 'lure']\n",
-      "['cart', 'curt', 'cure', 'pure']\n",
-      "['cart', 'curt', 'cure', 'sure']\n",
-      "['cart', 'curt', 'cure', 'care']\n",
-      "['cart', 'curt', 'cure', 'core']\n",
-      "['cart', 'curt', 'cure', 'cube']\n",
-      "['cart', 'curt', 'cure', 'cute']\n",
-      "['cart', 'curt', 'cure', 'curb']\n",
-      "['cart', 'curt', 'cure', 'curd']\n",
-      "['cart', 'curt', 'cure', 'curl']\n",
-      "['cart', 'curt', 'cure', 'curs']\n",
-      "['cart', 'curt', 'curl', 'furl']\n",
-      "['cart', 'curt', 'curl', 'hurl']\n",
-      "['cart', 'curt', 'curl', 'purl']\n",
-      "['cart', 'curt', 'curl', 'cull']\n",
-      "['cart', 'curt', 'curl', 'curb']\n",
-      "['cart', 'curt', 'curl', 'curd']\n",
-      "['cart', 'curt', 'curl', 'cure']\n",
-      "['cart', 'curt', 'curl', 'curs']\n",
-      "['cart', 'curt', 'curs', 'burs']\n",
-      "['cart', 'curt', 'curs', 'furs']\n",
-      "['cart', 'curt', 'curs', 'ours']\n",
-      "['cart', 'curt', 'curs', 'cars']\n",
-      "['cart', 'curt', 'curs', 'cubs']\n",
-      "['cart', 'curt', 'curs', 'cuds']\n",
-      "['cart', 'curt', 'curs', 'cues']\n",
-      "['cart', 'curt', 'curs', 'cums']\n",
-      "['cart', 'curt', 'curs', 'cups']\n",
-      "['cart', 'curt', 'curs', 'cuss']\n",
-      "['cart', 'curt', 'curs', 'cuts']\n",
-      "['cart', 'curt', 'curs', 'curb']\n",
-      "['cart', 'curt', 'curs', 'curd']\n",
-      "['cart', 'curt', 'curs', 'cure']\n",
-      "['cart', 'curt', 'curs', 'curl']\n",
-      "['cart', 'cant', 'pant', 'rant']\n",
-      "['cart', 'cant', 'pant', 'want']\n",
-      "['cart', 'cant', 'pant', 'pent']\n",
-      "['cart', 'cant', 'pant', 'pint']\n",
-      "['cart', 'cant', 'pant', 'punt']\n",
-      "['cart', 'cant', 'pant', 'pact']\n",
-      "['cart', 'cant', 'pant', 'part']\n",
-      "['cart', 'cant', 'pant', 'past']\n",
-      "['cart', 'cant', 'pant', 'pane']\n",
-      "['cart', 'cant', 'pant', 'pang']\n",
-      "['cart', 'cant', 'pant', 'pans']\n",
-      "['cart', 'cant', 'rant', 'pant']\n",
-      "['cart', 'cant', 'rant', 'want']\n",
-      "['cart', 'cant', 'rant', 'rent']\n",
-      "['cart', 'cant', 'rant', 'runt']\n",
-      "['cart', 'cant', 'rant', 'raft']\n",
-      "['cart', 'cant', 'rant', 'rapt']\n",
-      "['cart', 'cant', 'rant', 'rang']\n",
-      "['cart', 'cant', 'rant', 'rank']\n",
-      "['cart', 'cant', 'want', 'pant']\n",
-      "['cart', 'cant', 'want', 'rant']\n",
-      "['cart', 'cant', 'want', 'went']\n",
-      "['cart', 'cant', 'want', 'wont']\n",
-      "['cart', 'cant', 'want', 'waft']\n",
-      "['cart', 'cant', 'want', 'wait']\n",
-      "['cart', 'cant', 'want', 'wart']\n",
-      "['cart', 'cant', 'want', 'watt']\n",
-      "['cart', 'cant', 'want', 'wand']\n",
-      "['cart', 'cant', 'want', 'wane']\n",
-      "['cart', 'cant', 'cent', 'bent']\n",
-      "['cart', 'cant', 'cent', 'dent']\n",
-      "['cart', 'cant', 'cent', 'gent']\n",
-      "['cart', 'cant', 'cent', 'lent']\n",
-      "['cart', 'cant', 'cent', 'pent']\n",
-      "['cart', 'cant', 'cent', 'rent']\n",
-      "['cart', 'cant', 'cent', 'sent']\n",
-      "['cart', 'cant', 'cent', 'tent']\n",
-      "['cart', 'cant', 'cent', 'vent']\n",
-      "['cart', 'cant', 'cent', 'went']\n",
-      "['cart', 'cant', 'cast', 'bast']\n",
-      "['cart', 'cant', 'cast', 'east']\n",
-      "['cart', 'cant', 'cast', 'fast']\n",
-      "['cart', 'cant', 'cast', 'last']\n",
-      "['cart', 'cant', 'cast', 'mast']\n",
-      "['cart', 'cant', 'cast', 'past']\n",
-      "['cart', 'cant', 'cast', 'vast']\n",
-      "['cart', 'cant', 'cast', 'cost']\n",
-      "['cart', 'cant', 'cast', 'cyst']\n",
-      "['cart', 'cant', 'cast', 'case']\n",
-      "['cart', 'cant', 'cast', 'cash']\n",
-      "['cart', 'cant', 'cast', 'cask']\n",
-      "['cart', 'cant', 'cane', 'bane']\n",
-      "['cart', 'cant', 'cane', 'lane']\n",
-      "['cart', 'cant', 'cane', 'mane']\n",
-      "['cart', 'cant', 'cane', 'pane']\n",
-      "['cart', 'cant', 'cane', 'sane']\n",
-      "['cart', 'cant', 'cane', 'vane']\n",
-      "['cart', 'cant', 'cane', 'wane']\n",
-      "['cart', 'cant', 'cane', 'cone']\n",
-      "['cart', 'cant', 'cane', 'cafe']\n",
-      "['cart', 'cant', 'cane', 'cage']\n",
-      "['cart', 'cant', 'cane', 'cake']\n",
-      "['cart', 'cant', 'cane', 'came']\n",
-      "['cart', 'cant', 'cane', 'cape']\n",
-      "['cart', 'cant', 'cane', 'care']\n",
-      "['cart', 'cant', 'cane', 'case']\n",
-      "['cart', 'cant', 'cane', 'cave']\n",
-      "['cart', 'cant', 'cane', 'cans']\n",
-      "['cart', 'cant', 'cans', 'bans']\n",
-      "['cart', 'cant', 'cans', 'fans']\n",
-      "['cart', 'cant', 'cans', 'mans']\n",
-      "['cart', 'cant', 'cans', 'pans']\n",
-      "['cart', 'cant', 'cans', 'sans']\n",
-      "['cart', 'cant', 'cans', 'tans']\n",
-      "['cart', 'cant', 'cans', 'vans']\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "['cart', 'cant', 'cans', 'vans']"
-      ]
-     },
-     "execution_count": 20,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "bfs_search('cart', 'vans', debug=True)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 21,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "['cart', 'cant', 'cane', 'vane']"
-      ]
-     },
-     "execution_count": 21,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "bfs_search('cart', 'vane')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 22,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "['cart',\n",
-       " 'dart',\n",
-       " 'hart',\n",
-       " 'mart',\n",
-       " 'part',\n",
-       " 'tart',\n",
-       " 'wart',\n",
-       " 'waft',\n",
-       " 'daft',\n",
-       " 'haft',\n",
-       " 'raft',\n",
-       " 'rift',\n",
-       " 'gift',\n",
-       " 'lift',\n",
-       " 'sift',\n",
-       " 'soft',\n",
-       " 'loft',\n",
-       " 'left',\n",
-       " 'deft',\n",
-       " 'heft',\n",
-       " 'weft',\n",
-       " 'welt',\n",
-       " 'belt',\n",
-       " 'felt',\n",
-       " 'gelt',\n",
-       " 'melt',\n",
-       " 'pelt',\n",
-       " 'peat',\n",
-       " 'beat',\n",
-       " 'feat',\n",
-       " 'heat',\n",
-       " 'meat',\n",
-       " 'neat',\n",
-       " 'seat',\n",
-       " 'teat',\n",
-       " 'that',\n",
-       " 'chat',\n",
-       " 'shat',\n",
-       " 'what',\n",
-       " 'whet',\n",
-       " 'whit',\n",
-       " 'chit',\n",
-       " 'chic',\n",
-       " 'chid',\n",
-       " 'chin',\n",
-       " 'shin',\n",
-       " 'thin',\n",
-       " 'twin',\n",
-       " 'twig',\n",
-       " 'swig',\n",
-       " 'swag',\n",
-       " 'shag',\n",
-       " 'slag',\n",
-       " 'flag',\n",
-       " 'flog',\n",
-       " 'blog',\n",
-       " 'clog',\n",
-       " 'slog',\n",
-       " 'smog',\n",
-       " 'smug',\n",
-       " 'slug',\n",
-       " 'plug',\n",
-       " 'plum',\n",
-       " 'alum',\n",
-       " 'glum',\n",
-       " 'slum',\n",
-       " 'scum',\n",
-       " 'swum',\n",
-       " 'swam',\n",
-       " 'scam',\n",
-       " 'seam',\n",
-       " 'beam',\n",
-       " 'ream',\n",
-       " 'team',\n",
-       " 'tram',\n",
-       " 'cram',\n",
-       " 'dram',\n",
-       " 'gram',\n",
-       " 'pram',\n",
-       " 'prim',\n",
-       " 'brim',\n",
-       " 'grim',\n",
-       " 'trim',\n",
-       " 'trig',\n",
-       " 'brig',\n",
-       " 'brag',\n",
-       " 'crag',\n",
-       " 'drag',\n",
-       " 'drug',\n",
-       " 'drub',\n",
-       " 'grub',\n",
-       " 'grab',\n",
-       " 'crab',\n",
-       " 'drab',\n",
-       " 'draw',\n",
-       " 'craw',\n",
-       " 'claw',\n",
-       " 'flaw',\n",
-       " 'slaw',\n",
-       " 'slew',\n",
-       " 'blew',\n",
-       " 'clew',\n",
-       " 'flew',\n",
-       " 'flow',\n",
-       " 'blow',\n",
-       " 'glow',\n",
-       " 'slow',\n",
-       " 'scow',\n",
-       " 'show',\n",
-       " 'chow',\n",
-       " 'crow',\n",
-       " 'brow',\n",
-       " 'grow',\n",
-       " 'prow',\n",
-       " 'prod',\n",
-       " 'trod',\n",
-       " 'trot',\n",
-       " 'toot',\n",
-       " 'boot',\n",
-       " 'coot',\n",
-       " 'foot',\n",
-       " 'hoot',\n",
-       " 'loot',\n",
-       " 'moot',\n",
-       " 'root',\n",
-       " 'soot',\n",
-       " 'shot',\n",
-       " 'slot',\n",
-       " 'blot',\n",
-       " 'clot',\n",
-       " 'plot',\n",
-       " 'plod',\n",
-       " 'clod',\n",
-       " 'clad',\n",
-       " 'glad',\n",
-       " 'goad',\n",
-       " 'load',\n",
-       " 'road',\n",
-       " 'toad',\n",
-       " 'toed',\n",
-       " 'coed',\n",
-       " 'hoed',\n",
-       " 'heed',\n",
-       " 'deed',\n",
-       " 'feed',\n",
-       " 'geed',\n",
-       " 'need',\n",
-       " 'peed',\n",
-       " 'reed',\n",
-       " 'seed',\n",
-       " 'teed',\n",
-       " 'weed',\n",
-       " 'weld',\n",
-       " 'geld',\n",
-       " 'held',\n",
-       " 'meld',\n",
-       " 'veld',\n",
-       " 'vend',\n",
-       " 'bend',\n",
-       " 'fend',\n",
-       " 'lend',\n",
-       " 'mend',\n",
-       " 'rend',\n",
-       " 'send',\n",
-       " 'tend',\n",
-       " 'wend',\n",
-       " 'wand',\n",
-       " 'band',\n",
-       " 'hand',\n",
-       " 'land',\n",
-       " 'sand',\n",
-       " 'said',\n",
-       " 'laid',\n",
-       " 'maid',\n",
-       " 'paid',\n",
-       " 'raid',\n",
-       " 'rail',\n",
-       " 'bail',\n",
-       " 'fail',\n",
-       " 'hail',\n",
-       " 'jail',\n",
-       " 'mail',\n",
-       " 'nail',\n",
-       " 'pail',\n",
-       " 'sail',\n",
-       " 'tail',\n",
-       " 'wail',\n",
-       " 'wall',\n",
-       " 'ball',\n",
-       " 'call',\n",
-       " 'fall',\n",
-       " 'gall',\n",
-       " 'hall',\n",
-       " 'mall',\n",
-       " 'pall',\n",
-       " 'tall',\n",
-       " 'tell',\n",
-       " 'bell',\n",
-       " 'cell',\n",
-       " 'dell',\n",
-       " 'fell',\n",
-       " 'hell',\n",
-       " 'jell',\n",
-       " 'sell',\n",
-       " 'well',\n",
-       " 'yell',\n",
-       " 'yelp',\n",
-       " 'help',\n",
-       " 'kelp',\n",
-       " 'keep',\n",
-       " 'beep',\n",
-       " 'deep',\n",
-       " 'jeep',\n",
-       " 'peep',\n",
-       " 'seep',\n",
-       " 'veep',\n",
-       " 'weep',\n",
-       " 'week',\n",
-       " 'geek',\n",
-       " 'leek',\n",
-       " 'meek',\n",
-       " 'peek',\n",
-       " 'reek',\n",
-       " 'seek',\n",
-       " 'seem',\n",
-       " 'deem',\n",
-       " 'teem',\n",
-       " 'them',\n",
-       " 'thee',\n",
-       " 'tree',\n",
-       " 'free',\n",
-       " 'flee',\n",
-       " 'glee',\n",
-       " 'glue',\n",
-       " 'blue',\n",
-       " 'clue',\n",
-       " 'flue',\n",
-       " 'slue',\n",
-       " 'sloe',\n",
-       " 'aloe',\n",
-       " 'floe',\n",
-       " 'flop',\n",
-       " 'clop',\n",
-       " 'glop',\n",
-       " 'plop',\n",
-       " 'slop',\n",
-       " 'shop',\n",
-       " 'chop',\n",
-       " 'coop',\n",
-       " 'goop',\n",
-       " 'hoop',\n",
-       " 'loop',\n",
-       " 'poop',\n",
-       " 'prop',\n",
-       " 'crop',\n",
-       " 'drop',\n",
-       " 'drip',\n",
-       " 'grip',\n",
-       " 'trip',\n",
-       " 'trap',\n",
-       " 'tray',\n",
-       " 'bray',\n",
-       " 'dray',\n",
-       " 'fray',\n",
-       " 'gray',\n",
-       " 'pray',\n",
-       " 'play',\n",
-       " 'clay',\n",
-       " 'flay',\n",
-       " 'slay',\n",
-       " 'spay',\n",
-       " 'stay',\n",
-       " 'sway',\n",
-       " 'away',\n",
-       " 'awry',\n",
-       " 'aery',\n",
-       " 'eery',\n",
-       " 'very',\n",
-       " 'vary',\n",
-       " 'nary',\n",
-       " 'wary',\n",
-       " 'wiry',\n",
-       " 'airy',\n",
-       " 'airs',\n",
-       " 'firs',\n",
-       " 'sirs',\n",
-       " 'sics',\n",
-       " 'tics',\n",
-       " 'ties',\n",
-       " 'dies',\n",
-       " 'hies',\n",
-       " 'lies',\n",
-       " 'pies',\n",
-       " 'vies',\n",
-       " 'vied',\n",
-       " 'died',\n",
-       " 'hied',\n",
-       " 'lied',\n",
-       " 'pied',\n",
-       " 'tied',\n",
-       " 'tier',\n",
-       " 'bier',\n",
-       " 'pier',\n",
-       " 'peer',\n",
-       " 'beer',\n",
-       " 'deer',\n",
-       " 'jeer',\n",
-       " 'leer',\n",
-       " 'seer',\n",
-       " 'veer',\n",
-       " 'weer',\n",
-       " 'wear',\n",
-       " 'bear',\n",
-       " 'dear',\n",
-       " 'fear',\n",
-       " 'gear',\n",
-       " 'hear',\n",
-       " 'near',\n",
-       " 'pear',\n",
-       " 'rear',\n",
-       " 'sear',\n",
-       " 'tear',\n",
-       " 'year',\n",
-       " 'yeah',\n",
-       " 'yeas',\n",
-       " 'leas',\n",
-       " 'peas',\n",
-       " 'seas',\n",
-       " 'teas',\n",
-       " 'tees',\n",
-       " 'bees',\n",
-       " 'fees',\n",
-       " 'gees',\n",
-       " 'lees',\n",
-       " 'pees',\n",
-       " 'sees',\n",
-       " 'wees',\n",
-       " 'woes',\n",
-       " 'does',\n",
-       " 'foes',\n",
-       " 'goes',\n",
-       " 'hoes',\n",
-       " 'noes',\n",
-       " 'roes',\n",
-       " 'toes',\n",
-       " 'togs',\n",
-       " 'bogs',\n",
-       " 'cogs',\n",
-       " 'dogs',\n",
-       " 'fogs',\n",
-       " 'hogs',\n",
-       " 'jogs',\n",
-       " 'logs',\n",
-       " 'lags',\n",
-       " 'bags',\n",
-       " 'fags',\n",
-       " 'gags',\n",
-       " 'hags',\n",
-       " 'jags',\n",
-       " 'nags',\n",
-       " 'rags',\n",
-       " 'sags',\n",
-       " 'tags',\n",
-       " 'wags',\n",
-       " 'wigs',\n",
-       " 'digs',\n",
-       " 'figs',\n",
-       " 'gigs',\n",
-       " 'jigs',\n",
-       " 'pigs',\n",
-       " 'rigs',\n",
-       " 'rugs',\n",
-       " 'bugs',\n",
-       " 'hugs',\n",
-       " 'jugs',\n",
-       " 'lugs',\n",
-       " 'mugs',\n",
-       " 'pugs',\n",
-       " 'tugs',\n",
-       " 'tubs',\n",
-       " 'cubs',\n",
-       " 'dubs',\n",
-       " 'hubs',\n",
-       " 'nubs',\n",
-       " 'pubs',\n",
-       " 'rubs',\n",
-       " 'subs',\n",
-       " 'sobs',\n",
-       " 'bobs',\n",
-       " 'cobs',\n",
-       " 'fobs',\n",
-       " 'gobs',\n",
-       " 'hobs',\n",
-       " 'jobs',\n",
-       " 'lobs',\n",
-       " 'mobs',\n",
-       " 'robs',\n",
-       " 'ribs',\n",
-       " 'bibs',\n",
-       " 'fibs',\n",
-       " 'jibs',\n",
-       " 'nibs',\n",
-       " 'nabs',\n",
-       " 'cabs',\n",
-       " 'dabs',\n",
-       " 'gabs',\n",
-       " 'jabs',\n",
-       " 'labs',\n",
-       " 'tabs',\n",
-       " 'tads',\n",
-       " 'cads',\n",
-       " 'dads',\n",
-       " 'fads',\n",
-       " 'gads',\n",
-       " 'lads',\n",
-       " 'mads',\n",
-       " 'pads',\n",
-       " 'wads',\n",
-       " 'weds',\n",
-       " 'beds',\n",
-       " 'feds',\n",
-       " 'reds',\n",
-       " 'rids',\n",
-       " 'aids',\n",
-       " 'bids',\n",
-       " 'kids',\n",
-       " 'lids',\n",
-       " 'lips',\n",
-       " 'dips',\n",
-       " 'hips',\n",
-       " 'nips',\n",
-       " 'pips',\n",
-       " 'rips',\n",
-       " 'sips',\n",
-       " 'tips',\n",
-       " 'yips',\n",
-       " 'zips',\n",
-       " 'zaps',\n",
-       " 'caps',\n",
-       " 'gaps',\n",
-       " 'laps',\n",
-       " 'maps',\n",
-       " 'naps',\n",
-       " 'paps',\n",
-       " 'raps',\n",
-       " 'saps',\n",
-       " 'taps',\n",
-       " 'yaps',\n",
-       " 'yeps',\n",
-       " 'peps',\n",
-       " 'reps',\n",
-       " 'refs',\n",
-       " 'reis',\n",
-       " 'leis',\n",
-       " 'legs',\n",
-       " 'begs',\n",
-       " 'kegs',\n",
-       " 'megs',\n",
-       " 'pegs',\n",
-       " 'pens',\n",
-       " 'dens',\n",
-       " 'fens',\n",
-       " 'hens',\n",
-       " 'kens',\n",
-       " 'lens',\n",
-       " 'tens',\n",
-       " 'wens',\n",
-       " 'yens',\n",
-       " 'yews',\n",
-       " 'hews',\n",
-       " 'mews',\n",
-       " 'news',\n",
-       " 'pews',\n",
-       " 'sews',\n",
-       " 'saws',\n",
-       " 'caws',\n",
-       " 'haws',\n",
-       " 'jaws',\n",
-       " 'laws',\n",
-       " 'maws',\n",
-       " 'paws',\n",
-       " 'yaws',\n",
-       " 'yaks',\n",
-       " 'oaks',\n",
-       " 'oafs',\n",
-       " 'oars',\n",
-       " 'bars',\n",
-       " 'cars',\n",
-       " 'ears',\n",
-       " 'jars',\n",
-       " 'mars',\n",
-       " 'pars',\n",
-       " 'tars',\n",
-       " 'wars',\n",
-       " 'ways',\n",
-       " 'bays',\n",
-       " 'days',\n",
-       " 'gays',\n",
-       " 'hays',\n",
-       " 'jays',\n",
-       " 'lays',\n",
-       " 'nays',\n",
-       " 'pays',\n",
-       " 'rays',\n",
-       " 'says',\n",
-       " 'sacs',\n",
-       " 'secs',\n",
-       " 'sets',\n",
-       " 'bets',\n",
-       " 'gets',\n",
-       " 'jets',\n",
-       " 'lets',\n",
-       " 'nets',\n",
-       " 'pets',\n",
-       " 'vets',\n",
-       " 'wets',\n",
-       " 'wits',\n",
-       " 'bits',\n",
-       " 'fits',\n",
-       " 'hits',\n",
-       " 'kits',\n",
-       " 'nits',\n",
-       " 'pits',\n",
-       " 'sits',\n",
-       " 'tits',\n",
-       " 'tats',\n",
-       " 'bats',\n",
-       " 'cats',\n",
-       " 'eats',\n",
-       " 'fats',\n",
-       " 'hats',\n",
-       " 'lats',\n",
-       " 'mats',\n",
-       " 'oats',\n",
-       " 'pats',\n",
-       " 'rats',\n",
-       " 'vats',\n",
-       " 'vans',\n",
-       " 'bans',\n",
-       " 'cans',\n",
-       " 'fans',\n",
-       " 'mans',\n",
-       " 'pans',\n",
-       " 'sans',\n",
-       " 'tans',\n",
-       " 'tins',\n",
-       " 'bins',\n",
-       " 'dins',\n",
-       " 'fins',\n",
-       " 'gins',\n",
-       " 'pins',\n",
-       " 'sins',\n",
-       " 'wins',\n",
-       " 'wind',\n",
-       " 'bind',\n",
-       " 'find',\n",
-       " 'hind',\n",
-       " 'kind',\n",
-       " 'mind',\n",
-       " 'rind',\n",
-       " 'ring',\n",
-       " 'ding',\n",
-       " 'king',\n",
-       " 'ping',\n",
-       " 'sing',\n",
-       " 'ting',\n",
-       " 'wing',\n",
-       " 'wine',\n",
-       " 'dine',\n",
-       " 'fine',\n",
-       " 'line',\n",
-       " 'mine',\n",
-       " 'nine',\n",
-       " 'pine',\n",
-       " 'sine',\n",
-       " 'tine',\n",
-       " 'vine',\n",
-       " 'vane']"
-      ]
-     },
-     "execution_count": 22,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "dfs_search('cart', 'vane')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 23,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def astar_search(start, goal, debug=False):\n",
-    "    agenda = [(distance(start, goal), [start])]\n",
-    "    heapq.heapify(agenda)\n",
-    "    finished = False\n",
-    "    while not finished and agenda:\n",
-    "        _, current = heapq.heappop(agenda)\n",
-    "        if debug:\n",
-    "            print(current)\n",
-    "        if current[-1] == goal:\n",
-    "            finished = True\n",
-    "        else:\n",
-    "            successors = extend(current)\n",
-    "            for s in successors:\n",
-    "                heapq.heappush(agenda, (len(current) + distance(s[-1], goal) - 1, s))\n",
-    "    if agenda:\n",
-    "        return current\n",
-    "    else:\n",
-    "        return None        "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 24,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "['cart']\n",
-      "['cart', 'cant']\n",
-      "['cart', 'cant', 'cane']\n",
-      "['cart', 'cant', 'cane', 'vane']\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "['cart', 'cant', 'cane', 'vane']"
-      ]
-     },
-     "execution_count": 24,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "astar_search('cart', 'vane', debug=True)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 25,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def astar_search_closed(start, goal, debug=False):\n",
-    "    agenda = [(distance(start, goal), [start])]\n",
-    "    heapq.heapify(agenda)\n",
-    "    closed = set()\n",
-    "    finished = False\n",
-    "    while not finished and agenda:\n",
-    "        _, current = heapq.heappop(agenda)\n",
-    "        if debug:\n",
-    "            print(current)\n",
-    "        if current[-1] == goal:\n",
-    "            finished = True\n",
-    "        else:\n",
-    "            closed.add(current[-1])\n",
-    "            successors = extend(current, closed)\n",
-    "            for s in successors:\n",
-    "                heapq.heappush(agenda, (len(current) + distance(s[-1], goal) - 1, s))\n",
-    "    if agenda:\n",
-    "        return current\n",
-    "    else:\n",
-    "        return None        "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 26,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "['cart']\n",
-      "['cart', 'cant']\n",
-      "['cart', 'cant', 'cane']\n",
-      "['cart', 'cant', 'cane', 'vane']\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "['cart', 'cant', 'cane', 'vane']"
-      ]
-     },
-     "execution_count": 26,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "astar_search_closed('cart', 'vane', debug=True)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Mutually-reachable sets\n",
-    "\n",
-    "Find the transitive closure of the `neighbours` relation, so we can see which words can be transformed into which other words."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 77,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "94"
-      ]
-     },
-     "execution_count": 77,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "candidates = [set([k] + neighbours[k]) for k in neighbours]\n",
-    "reachables = []\n",
-    "while candidates:\n",
-    "    current = set(candidates.pop())\n",
-    "    altered = False\n",
-    "    for other in candidates:\n",
-    "        if current.intersection(other):\n",
-    "            altered = True\n",
-    "            current.update(other)\n",
-    "            candidates.remove(other)\n",
-    "    if altered:\n",
-    "        candidates.append(current)\n",
-    "    else:\n",
-    "        reachables.append(current)\n",
-    "\n",
-    "len(reachables)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 78,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "2204"
-      ]
-     },
-     "execution_count": 78,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "len(max(reachables, key=len))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 79,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "1"
-      ]
-     },
-     "execution_count": 79,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "len(min(reachables, key=len))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 80,
-   "metadata": {
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "Counter({1: 75, 2: 6, 3: 7, 4: 2, 5: 2, 6: 1, 2204: 1})"
-      ]
-     },
-     "execution_count": 80,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "collections.Counter(len(r) for r in reachables)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 81,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[5]"
-      ]
-     },
-     "execution_count": 81,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "[len(r) for r in reachables if 'abbe' in r]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 82,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[{'abbe', 'able', 'ably', 'ally', 'axle'}]"
-      ]
-     },
-     "execution_count": 82,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "[r for r in reachables if 'abbe' in r]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 83,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "['buns', 'bunk', 'punk']"
-      ]
-     },
-     "execution_count": 83,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "astar_search('buns', 'punk')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 84,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "for a in reachables:\n",
-    "    for b in reachables:\n",
-    "        if a != b:\n",
-    "            if not a.isdisjoint(b):\n",
-    "                print(a, b)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 85,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "# longest_chain = []\n",
-    "# with open('all-chains-4.txt', 'w', 1) as f:\n",
-    "#     for ws in reachables:\n",
-    "#         for s in ws:\n",
-    "#             for t in ws:\n",
-    "#                 if s < t:\n",
-    "#                     chain = astar_search(s, t)\n",
-    "#                     if chain:\n",
-    "#                         f.write('{}\\n'.format(chain))\n",
-    "#                         if len(chain) > len(longest_chain):\n",
-    "#                             longest_chain = chain\n",
-    "\n",
-    "# longest_chain"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 86,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "bigset = max(reachables, key=len)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 87,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "['late', 'lats', 'lets', 'leas', 'seas', 'seam', 'swam', 'sway']\n",
-      "['leap', 'heap', 'hear', 'dear', 'deer']\n",
-      "['peel', 'peek', 'perk', 'park', 'nark']\n",
-      "['sing', 'sang', 'sand', 'said', 'sail', 'hail', 'haul']\n",
-      "['vats', 'bats', 'bets', 'bees', 'been', 'teen', 'then', 'thin', 'this', 'thus', 'thud']\n",
-      "['sues', 'sees', 'seen', 'sewn', 'hewn']\n",
-      "['rash', 'bash', 'bast', 'bait', 'bail', 'hail', 'hair', 'heir']\n",
-      "['apex', 'aped', 'sped', 'seed', 'deed', 'dead', 'deal', 'veal']\n",
-      "['gulf', 'golf', 'gold', 'bold', 'bond', 'bony', 'tony']\n",
-      "['snag', 'shag', 'shat', 'seat', 'peat', 'pent', 'pint', 'mint']\n",
-      "['rife', 'rime', 'rims', 'rums', 'cums', 'cuss']\n",
-      "['diss', 'kiss', 'kits']\n",
-      "['gyps', 'gaps', 'gads', 'wads', 'wade', 'wide', 'tide']\n",
-      "['bilk', 'bill', 'bell', 'tell', 'teal', 'tear', 'tzar']\n",
-      "['logo', 'loge', 'lode', 'lade', 'jade', 'jape']\n",
-      "['hunt', 'bunt', 'buns', 'nuns', 'nubs']\n",
-      "['glow', 'glop', 'plop', 'prop', 'prep', 'peep', 'keep']\n",
-      "['iamb', 'lamb', 'lams', 'laps', 'lips', 'pips']\n",
-      "['pain', 'lain', 'laid', 'land', 'lend', 'vend', 'veld']\n",
-      "['fake', 'bake', 'bare', 'bars', 'ears', 'errs', 'ergs', 'eggs', 'egos']\n"
-     ]
-    }
-   ],
-   "source": [
-    "for _ in range(20):\n",
-    "    start, goal = random.sample(bigset, 2)\n",
-    "    print(astar_search_closed(start, goal))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 38,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "['cops', 'coos', 'coon', 'coin', 'chin', 'thin', 'this', 'thus', 'thug']"
-      ]
-     },
-     "execution_count": 38,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "astar_search('cops', 'thug')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 39,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[2204]"
-      ]
-     },
-     "execution_count": 39,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "[len(r) for r in reachables if 'love' in r if 'hate' in r]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 40,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "['hate', 'have', 'hove', 'love']"
-      ]
-     },
-     "execution_count": 40,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "astar_search('hate', 'love')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 41,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "['wars', 'ware', 'wave', 'wove', 'love']"
-      ]
-     },
-     "execution_count": 41,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "astar_search('wars', 'love')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 61,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "CPU times: user 0 ns, sys: 0 ns, total: 0 ns\n",
-      "Wall time: 210 µs\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "5"
-      ]
-     },
-     "execution_count": 61,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "%time len(astar_search('wars', 'love'))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 62,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "CPU times: user 0 ns, sys: 0 ns, total: 0 ns\n",
-      "Wall time: 252 µs\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "5"
-      ]
-     },
-     "execution_count": 62,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "%time len(astar_search_closed('wars', 'love'))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 63,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "CPU times: user 24 ms, sys: 0 ns, total: 24 ms\n",
-      "Wall time: 24.2 ms\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "404"
-      ]
-     },
-     "execution_count": 63,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "%time len(dfs_search('wars', 'love'))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 64,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "CPU times: user 5min 20s, sys: 76 ms, total: 5min 20s\n",
-      "Wall time: 5min 20s\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "5"
-      ]
-     },
-     "execution_count": 64,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "%time len(bfs_search('wars', 'love'))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 65,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "CPU times: user 1.44 s, sys: 0 ns, total: 1.44 s\n",
-      "Wall time: 1.43 s\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "5"
-      ]
-     },
-     "execution_count": 65,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "%time len(bfs_search_closed('wars', 'love'))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 42,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "['fear', 'feat', 'fest', 'lest', 'lost', 'lose', 'love']"
-      ]
-     },
-     "execution_count": 42,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "astar_search('fear', 'love')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 43,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "['fail', 'fall', 'pall', 'pals', 'pass']"
-      ]
-     },
-     "execution_count": 43,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "astar_search('fail', 'pass')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 44,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "['star', 'soar', 'boar', 'boor', 'boon', 'born']"
-      ]
-     },
-     "execution_count": 44,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "astar_search('star', 'born')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 45,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "['open',\n",
-       " 'oven',\n",
-       " 'even',\n",
-       " 'eves',\n",
-       " 'eyes',\n",
-       " 'byes',\n",
-       " 'bees',\n",
-       " 'begs',\n",
-       " 'bags',\n",
-       " 'bass',\n",
-       " 'pass']"
-      ]
-     },
-     "execution_count": 45,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "astar_search('open', 'pass')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 46,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "['bass',\n",
-       " 'lass',\n",
-       " 'mass',\n",
-       " 'sass',\n",
-       " 'puss',\n",
-       " 'pads',\n",
-       " 'pals',\n",
-       " 'pans',\n",
-       " 'paps',\n",
-       " 'pars',\n",
-       " 'pats',\n",
-       " 'paws',\n",
-       " 'pays',\n",
-       " 'past']"
-      ]
-     },
-     "execution_count": 46,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "neighbours['pass']"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 47,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[1]"
-      ]
-     },
-     "execution_count": 47,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "[len(r) for r in reachables if 'exam' in r]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 48,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[2204]"
-      ]
-     },
-     "execution_count": 48,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "[len(r) for r in reachables if 'star' in r if 'born' in r]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 49,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "1 loop, best of 3: 7.9 s per loop\n"
-     ]
-    }
-   ],
-   "source": [
-    "%%timeit\n",
-    "astar_search('bats', 'exit')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 50,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "10 loops, best of 3: 141 ms per loop\n"
-     ]
-    }
-   ],
-   "source": [
-    "%%timeit\n",
-    "astar_search_closed('bats', 'exit')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 51,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "['bats',\n",
-       " 'bans',\n",
-       " 'band',\n",
-       " 'sand',\n",
-       " 'said',\n",
-       " 'skid',\n",
-       " 'skit',\n",
-       " 'smit',\n",
-       " 'emit',\n",
-       " 'exit']"
-      ]
-     },
-     "execution_count": 51,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "astar_search_closed('bats', 'exit')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 88,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "{2: [['heel', 'keel'], ['wane', 'wave'], ['cell', 'sell'], ['cons', 'cobs']],\n",
-       " 3: [['hank', 'haws'], ['bars', 'bets'], ['rats', 'paws'], ['lock', 'hack']],\n",
-       " 4: [['rule', 'sore'], ['wavy', 'rape'], ['peas', 'ping'], ['bond', 'toll']],\n",
-       " 5: [['cope', 'yowl'], ['lose', 'loci'], ['rump', 'dash'], ['four', 'dyes']],\n",
-       " 6: [['boon', 'sell'], ['lots', 'pomp'], ['cola', 'turn'], ['boos', 'laid']],\n",
-       " 7: [['eave', 'inns'], ['meek', 'mere'], ['keys', 'wily'], ['slam', 'yore']],\n",
-       " 8: [['hack', 'flip'], ['crag', 'huge'], ['flux', 'gill'], ['play', 'busy']],\n",
-       " 9: [['lacy', 'whey'], ['wren', 'rook'], ['lire', 'drip'], ['grab', 'lame']],\n",
-       " 10: [['over', 'turn'], ['worn', 'anew'], ['stow', 'elks'], ['ergo', 'rich']],\n",
-       " 11: [['bask', 'idea'], ['gabs', 'thud'], ['idea', 'clod'], ['mark', 'ibis']],\n",
-       " 12: [['umps', 'torn'], ['futz', 'shun'], ['abut', 'face'], ['slug', 'open']],\n",
-       " 13: [['umps', 'skin'], ['chum', 'rats'], ['fury', 'chum'], ['omen', 'zany']],\n",
-       " 14: [['chug', 'gaff'], ['atom', 'fizz']],\n",
-       " 15: [['chug', 'oxen']]}"
-      ]
-     },
-     "execution_count": 88,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "solutions = {}\n",
-    "for _ in range(10000):\n",
-    "    start, goal = random.sample(bigset, 2)\n",
-    "    solution = astar_search_closed(start, goal)\n",
-    "    sl = len(solution)\n",
-    "    if sl not in solutions:\n",
-    "        solutions[sl] = []\n",
-    "    if len(solutions[sl]) < 4:\n",
-    "        solutions[sl].append([start, goal])\n",
-    "        \n",
-    "#     if len(solution) >= 10:\n",
-    "#         solutions += [solution]\n",
-    "        \n",
-    "solutions"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 91,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "solutions = {2: [['heel', 'keel'], ['wane', 'wave'], ['cell', 'sell'], ['cons', 'cobs']],\n",
-    " 3: [['hank', 'haws'], ['bars', 'bets'], ['rats', 'paws'], ['lock', 'hack']],\n",
-    " 4: [['rule', 'sore'], ['wavy', 'rape'], ['peas', 'ping'], ['bond', 'toll']],\n",
-    " 5: [['cope', 'yowl'], ['lose', 'loci'], ['rump', 'dash'], ['four', 'dyes']],\n",
-    " 6: [['boon', 'sell'], ['lots', 'pomp'], ['cola', 'turn'], ['boos', 'laid']],\n",
-    " 7: [['eave', 'inns'], ['meek', 'mere'], ['keys', 'wily'], ['slam', 'yore']],\n",
-    " 8: [['hack', 'flip'], ['crag', 'huge'], ['flux', 'gill'], ['play', 'busy']],\n",
-    " 9: [['lacy', 'whey'], ['wren', 'rook'], ['lire', 'drip'], ['grab', 'lame']],\n",
-    " 10: [['over', 'turn'], ['worn', 'anew'], ['stow', 'elks'], ['ergo', 'rich']],\n",
-    " 11: [['bask', 'idea'], ['gabs', 'thud'], ['idea', 'clod'], ['mark', 'ibis']],\n",
-    " 12: [['umps', 'torn'], ['futz', 'shun'], ['abut', 'face'], ['slug', 'open']],\n",
-    " 13: [['umps', 'skin'], ['chum', 'rats'], ['fury', 'chum'], ['omen', 'zany']],\n",
-    " 14: [['chug', 'gaff'], ['atom', 'fizz'], ['chug', 'jinn'], ['amen', 'flog'],\n",
-    "     ['buzz', 'grog'], ['imps', 'pros']],\n",
-    " 15: [['chug', 'oxen'], ['amen', 'doff']]}"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 54,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[('amen', 'doff', 15), ('chug', 'jinn', 14), ('amen', 'flog', 14)]"
-      ]
-     },
-     "execution_count": 54,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "[(s[0], s[-1], len(s)) for s in solutions if len(s) >= 14]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 55,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "1 loop, best of 3: 360 ms per loop\n"
-     ]
-    }
-   ],
-   "source": [
-    "%%timeit\n",
-    "astar_search_closed('blab', 'amen')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 56,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "CPU times: user 384 ms, sys: 0 ns, total: 384 ms\n",
-      "Wall time: 385 ms\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "14"
-      ]
-     },
-     "execution_count": 56,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "%time len(astar_search_closed('blab', 'amen'))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 57,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "CPU times: user 124 ms, sys: 0 ns, total: 124 ms\n",
-      "Wall time: 121 ms\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "15"
-      ]
-     },
-     "execution_count": 57,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "%time len(astar_search_closed('amen', 'doff'))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 58,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "CPU times: user 32 ms, sys: 0 ns, total: 32 ms\n",
-      "Wall time: 32.4 ms\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "14"
-      ]
-     },
-     "execution_count": 58,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "%time len(astar_search_closed('chug', 'jinn'))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 59,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "CPU times: user 16 ms, sys: 0 ns, total: 16 ms\n",
-      "Wall time: 17.1 ms\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "14"
-      ]
-     },
-     "execution_count": 59,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "%time len(astar_search_closed('amen', 'flog'))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 73,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "CPU times: user 268 ms, sys: 4 ms, total: 272 ms\n",
-      "Wall time: 272 ms\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "14"
-      ]
-     },
-     "execution_count": 73,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "%time len(astar_search_closed('buzz', 'grog'))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 74,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "CPU times: user 64 ms, sys: 0 ns, total: 64 ms\n",
-      "Wall time: 64.1 ms\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "14"
-      ]
-     },
-     "execution_count": 74,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "%time len(astar_search_closed('imps', 'pros'))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": []
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.5.2+"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 2
-}
diff --git a/09-word-chains/word-chain-solution.ipynb b/09-word-chains/word-chain-solution.ipynb
deleted file mode 100644
index 7346623..0000000
--- a/09-word-chains/word-chain-solution.ipynb
+++ /dev/null
@@ -1,761 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Word chains\n",
-    "\n",
-    "\"Word chain\" puzzles are where you transform one word into another, by changing one letter at a time, with all the intermediate steps being valid words. \n",
-    "\n",
-    "For instance, you can transform 'rash' to 'jags' like this:\n",
-    "\n",
-    "```\n",
-    "rash\n",
-    "Bash\n",
-    "basS\n",
-    "baGs\n",
-    "Jags\n",
-    "```\n",
-    "\n",
-    "(the capital letter is the one changed in each step).\n",
-    "\n",
-    "## Part 1\n",
-    "\n",
-    "Given this [list of words](words4.txt), what is the minimum number of steps to go from `vice` to `wars`?"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "import string\n",
-    "import heapq"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "2336"
-      ]
-     },
-     "execution_count": 4,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "words = [w.strip() for w in open('09-words.txt').readlines()]\n",
-    "len(words)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def adjacents(word):\n",
-    "    return [word[0:i] + l + word[i+1:]\n",
-    "           for i in range(len(word))\n",
-    "           for l in string.ascii_lowercase\n",
-    "           if l != word[i]]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "neighbours = {w: [n for n in adjacents(w) if n in words]\n",
-    "             for w in words}"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def distance(w1, w2):\n",
-    "    return sum(1 for i in range(len(w1))\n",
-    "               if w1[i] != w2[i])"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "# def extend(chain):\n",
-    "#     return [chain + [s] for s in neighbours[chain[-1]]\n",
-    "#            if s not in chain]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def extend(chain, closed=None):\n",
-    "    if closed:\n",
-    "        nbrs = set(neighbours[chain[-1]]) - closed\n",
-    "    else:\n",
-    "        nbrs = neighbours[chain[-1]]\n",
-    "    return [chain + [s] for s in nbrs\n",
-    "           if s not in chain]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def extend_raw(chain):\n",
-    "    nbrs = [w for w in adjacents(chain[-1]) if w in words]\n",
-    "    return [chain + [s] for s in nbrs\n",
-    "           if s not in chain]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def bfs_search(start, goal, debug=False):\n",
-    "    agenda = [[start]]\n",
-    "    finished = False\n",
-    "    while not finished and agenda:\n",
-    "        current = agenda[0]\n",
-    "        if debug:\n",
-    "            print(current)\n",
-    "        if current[-1] == goal:\n",
-    "            finished = True\n",
-    "        else:\n",
-    "            successors = extend(current)\n",
-    "            agenda = agenda[1:] + successors\n",
-    "    if agenda:\n",
-    "        return current\n",
-    "    else:\n",
-    "        return None        "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def bfs_search_closed(start, goal, debug=False):\n",
-    "    agenda = [[start]]\n",
-    "    closed = set()\n",
-    "    finished = False\n",
-    "    while not finished and agenda:\n",
-    "        current = agenda[0]\n",
-    "        if debug:\n",
-    "            print(current)\n",
-    "        if current[-1] == goal:\n",
-    "            finished = True\n",
-    "        else:\n",
-    "            closed.add(current[-1])\n",
-    "            successors = extend(current, closed)\n",
-    "            agenda = agenda[1:] + successors\n",
-    "    if agenda:\n",
-    "        return current\n",
-    "    else:\n",
-    "        return None   "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def dfs_search(start, goal, debug=False):\n",
-    "    agenda = [[start]]\n",
-    "    finished = False\n",
-    "    while not finished and agenda:\n",
-    "        current = agenda[0]\n",
-    "        if debug:\n",
-    "            print(current)\n",
-    "        if current[-1] == goal:\n",
-    "            finished = True\n",
-    "        else:\n",
-    "            successors = extend(current)\n",
-    "            agenda = successors + agenda[1:]\n",
-    "    if agenda:\n",
-    "        return current\n",
-    "    else:\n",
-    "        return None        "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def astar_search(start, goal, debug=False):\n",
-    "    agenda = [(distance(start, goal), [start])]\n",
-    "    heapq.heapify(agenda)\n",
-    "    finished = False\n",
-    "    while not finished and agenda:\n",
-    "        _, current = heapq.heappop(agenda)\n",
-    "        if debug:\n",
-    "            print(current)\n",
-    "        if current[-1] == goal:\n",
-    "            finished = True\n",
-    "        else:\n",
-    "            successors = extend(current)\n",
-    "            for s in successors:\n",
-    "                heapq.heappush(agenda, (len(current) + distance(s[-1], goal) - 1, s))\n",
-    "    if agenda:\n",
-    "        return current\n",
-    "    else:\n",
-    "        return None        "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "# Uses direct lookup of successors, rather than using cached neighbours in the dict\n",
-    "def astar_search_raw(start, goal, debug=False):\n",
-    "    agenda = [(distance(start, goal), [start])]\n",
-    "    heapq.heapify(agenda)\n",
-    "    finished = False\n",
-    "    while not finished and agenda:\n",
-    "        _, current = heapq.heappop(agenda)\n",
-    "        if debug:\n",
-    "            print(current)\n",
-    "        if current[-1] == goal:\n",
-    "            finished = True\n",
-    "        else:\n",
-    "            successors = extend_raw(current) # Difference here\n",
-    "            for s in successors:\n",
-    "                heapq.heappush(agenda, (len(current) + distance(s[-1], goal) - 1, s))\n",
-    "    if agenda:\n",
-    "        return current\n",
-    "    else:\n",
-    "        return None        "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def astar_search_closed(start, goal, debug=False):\n",
-    "    agenda = [(distance(start, goal), [start])]\n",
-    "    heapq.heapify(agenda)\n",
-    "    closed = set()\n",
-    "    finished = False\n",
-    "    while not finished and agenda:\n",
-    "        _, current = heapq.heappop(agenda)\n",
-    "        if debug:\n",
-    "            print(current)\n",
-    "        if current[-1] == goal:\n",
-    "            finished = True\n",
-    "        else:\n",
-    "            closed.add(current[-1])\n",
-    "            successors = extend(current, closed)\n",
-    "            for s in successors:\n",
-    "                heapq.heappush(agenda, (len(current) + distance(s[-1], goal) - 1, s))\n",
-    "    if agenda:\n",
-    "        return current\n",
-    "    else:\n",
-    "        return None   "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "['vice', 'dice', 'dire', 'dare', 'ware', 'wars']"
-      ]
-     },
-     "execution_count": 17,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "astar_search('vice', 'wars')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 18,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "['vice', 'dice', 'dire', 'dare', 'ware', 'wars']"
-      ]
-     },
-     "execution_count": 18,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "astar_search_raw('vice', 'wars')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 19,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "6"
-      ]
-     },
-     "execution_count": 19,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "len(astar_search('vice', 'wars'))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 20,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "6"
-      ]
-     },
-     "execution_count": 20,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "len(bfs_search('vice', 'wars'))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 21,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "6"
-      ]
-     },
-     "execution_count": 21,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "len(bfs_search_closed('vice', 'wars'))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 22,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "793"
-      ]
-     },
-     "execution_count": 22,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "len(dfs_search('vice', 'wars'))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 23,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "10000 loops, best of 3: 157 µs per loop\n"
-     ]
-    }
-   ],
-   "source": [
-    "%%timeit\n",
-    "astar_search('vice', 'wars')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 24,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "100 loops, best of 3: 15.8 ms per loop\n"
-     ]
-    }
-   ],
-   "source": [
-    "%%timeit\n",
-    "astar_search_raw('vice', 'wars')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 25,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "10000 loops, best of 3: 170 µs per loop\n"
-     ]
-    }
-   ],
-   "source": [
-    "%%timeit\n",
-    "astar_search_closed('vice', 'wars')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 26,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "1 loop, best of 3: 1min 42s per loop\n"
-     ]
-    }
-   ],
-   "source": [
-    "%%timeit\n",
-    "bfs_search('vice', 'wars')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 27,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "1 loop, best of 3: 557 ms per loop\n"
-     ]
-    }
-   ],
-   "source": [
-    "%%timeit\n",
-    "bfs_search_closed('vice', 'wars')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 28,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "10 loops, best of 3: 87.9 ms per loop\n"
-     ]
-    }
-   ],
-   "source": [
-    "%%timeit\n",
-    "dfs_search('vice', 'wars')"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Part 2\n",
-    "\n",
-    "The example shows that `jags` is reachable in four steps from `rash`. There are 11 words one step away from `rash`: \n",
-    "`bash`, `cash`, `dash`, `gash`, `hash`, `lash`, `mash`, `rasp`, `rush`, `sash`, and `wash`. \n",
-    "\n",
-    "There are 47 words reachable in one or two steps from `rash`. They are `base`, `bash`, `bask`, `bass`, `bast`, `bath`, `bosh`, `bush`, `case`, `cash`, `cask`, `cast`, `dash`, `dish`, `gash`, `gasp`, `gosh`, `gush`, `hash`, `hasp`, `hath`, `hush`, `lash`, `lass`, `last`, `lath`, `lush`, `mash`, `mask`, `mass`, `mast`, `math`, `mesh`, `mush`, `push`, `ramp`, `rasp`, `ruse`, `rush`, `rusk`, `rust`, `sash`, `sass`, `tush`, `wash`, `wasp`, and `wish`.\n",
-    "\n",
-    "There are 180 words reachable in up to three steps from `rash`.\n",
-    "\n",
-    "How many words are reachable in up to ten steps from `vice`?"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 29,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def reachable_in(word, n, trim_extras=False):\n",
-    "    reachable = set()\n",
-    "    boundary = set([word])\n",
-    "    for i in range(n):\n",
-    "        extras = set()\n",
-    "        for w in boundary:\n",
-    "            extras.update(neighbours[w])\n",
-    "        if trim_extras:\n",
-    "            extras.difference_update(reachable)\n",
-    "        reachable.update(boundary)\n",
-    "        boundary = extras.copy()\n",
-    "    return reachable.union(extras).difference(set([word]))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 30,
-   "metadata": {
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(11,\n",
-       " '`bash`, `cash`, `dash`, `gash`, `hash`, `lash`, `mash`, `rasp`, `rush`, `sash`, `wash`')"
-      ]
-     },
-     "execution_count": 30,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "len(reachable_in('rash', 1)), ', '.join(sorted('`{}`'.format(r) for r in reachable_in('rash', 1)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 31,
-   "metadata": {
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(47,\n",
-       " '`base`, `bash`, `bask`, `bass`, `bast`, `bath`, `bosh`, `bush`, `case`, `cash`, `cask`, `cast`, `dash`, `dish`, `gash`, `gasp`, `gosh`, `gush`, `hash`, `hasp`, `hath`, `hush`, `lash`, `lass`, `last`, `lath`, `lush`, `mash`, `mask`, `mass`, `mast`, `math`, `mesh`, `mush`, `push`, `ramp`, `rasp`, `ruse`, `rush`, `rusk`, `rust`, `sash`, `sass`, `tush`, `wash`, `wasp`, `wish`')"
-      ]
-     },
-     "execution_count": 31,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "len(reachable_in('rash', 2)), ', '.join(sorted('`{}`'.format(r) for r in reachable_in('rash', 2)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 32,
-   "metadata": {
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "180"
-      ]
-     },
-     "execution_count": 32,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "len(reachable_in('rash', 3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 33,
-   "metadata": {
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "2195"
-      ]
-     },
-     "execution_count": 33,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "len(reachable_in('rash', 10))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 34,
-   "metadata": {
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "2192"
-      ]
-     },
-     "execution_count": 34,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "len(reachable_in('vice', 10))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 35,
-   "metadata": {
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "100 loops, best of 3: 6.01 ms per loop\n"
-     ]
-    }
-   ],
-   "source": [
-    "%%timeit\n",
-    "len(reachable_in('rash', 10))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 36,
-   "metadata": {
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "100 loops, best of 3: 2.92 ms per loop\n"
-     ]
-    }
-   ],
-   "source": [
-    "%%timeit\n",
-    "len(reachable_in('rash', 10, trim_extras=True))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": []
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.5.2+"
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