From 9ede4bf9d49e541ea5a98d2549800d4667839707 Mon Sep 17 00:00:00 2001
From: Neil Smith <neil.git@njae.me.uk>
Date: Thu, 7 Sep 2017 09:39:26 +0100
Subject: [PATCH] Added notes for day 8

---
 08-word-chains/explore-word-chain-4.ipynb | 2869 +++++++--------------
 08-word-chains/explore-word-chain7.ipynb  |   10 +-
 08-word-chains/rush3.dot                  | 1198 ++++-----
 08-word-chains/visa-woes-solution.ipynb   |  627 ++++-
 4 files changed, 2061 insertions(+), 2643 deletions(-)

diff --git a/08-word-chains/explore-word-chain-4.ipynb b/08-word-chains/explore-word-chain-4.ipynb
index 5449951..d18dc5f 100644
--- a/08-word-chains/explore-word-chain-4.ipynb
+++ b/08-word-chains/explore-word-chain-4.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 30,
    "metadata": {
     "collapsed": true
    },
@@ -16,7 +16,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 31,
    "metadata": {},
    "outputs": [
     {
@@ -25,48 +25,19 @@
        "2336"
       ]
      },
-     "execution_count": 2,
+     "execution_count": 31,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "words = [w.strip() for w in open('08-rooms.txt').readlines()]\n",
+    "words = frozenset(w.strip() for w in open('08-rooms.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,
+   "execution_count": 32,
    "metadata": {
     "collapsed": true
    },
@@ -83,43 +54,41 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 33,
    "metadata": {
     "collapsed": true
    },
    "outputs": [],
    "source": [
     "def adjacents(word):\n",
-    "    return [word[0:i] + l + word[i+1:]\n",
+    "    return frozenset(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]]"
+    "           if l != word[i])"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 34,
+   "metadata": {},
    "outputs": [],
    "source": [
-    "neighbours = {w: [n for n in adjacents(w) if n in words]\n",
+    "neighbours = {w: frozenset(n for n in adjacents(w) if n in words)\n",
     "             for w in words}"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 35,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "['able']"
+       "frozenset({'able'})"
       ]
      },
-     "execution_count": 7,
+     "execution_count": 35,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -130,16 +99,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 36,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "['axle', 'abbe', 'ably']"
+       "frozenset({'abbe', 'ably', 'axle'})"
       ]
      },
-     "execution_count": 8,
+     "execution_count": 36,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -150,7 +119,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 37,
    "metadata": {
     "collapsed": true
    },
@@ -163,7 +132,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 38,
    "metadata": {},
    "outputs": [
     {
@@ -172,7 +141,7 @@
        "0"
       ]
      },
-     "execution_count": 10,
+     "execution_count": 38,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -183,7 +152,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 39,
    "metadata": {
     "collapsed": true
    },
@@ -200,7 +169,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 40,
    "metadata": {},
    "outputs": [
     {
@@ -209,7 +178,7 @@
        "[['abbe', 'able']]"
       ]
      },
-     "execution_count": 12,
+     "execution_count": 40,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -220,16 +189,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 41,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "[['abbe', 'able', 'axle'], ['abbe', 'able', 'ably']]"
+       "[['abbe', 'able', 'ably'], ['abbe', 'able', 'axle']]"
       ]
      },
-     "execution_count": 13,
+     "execution_count": 41,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -240,7 +209,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 42,
    "metadata": {},
    "outputs": [
     {
@@ -249,7 +218,7 @@
        "[['abbe', 'able', 'ably', 'ally']]"
       ]
      },
-     "execution_count": 14,
+     "execution_count": 42,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -260,7 +229,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 119,
    "metadata": {
     "collapsed": true
    },
@@ -272,7 +241,7 @@
     "    while not finished and agenda:\n",
     "        current = agenda[0]\n",
     "        if debug:\n",
-    "            print(current)\n",
+    "            print(current, agenda)\n",
     "        if current[-1] == goal:\n",
     "            finished = True\n",
     "        else:\n",
@@ -286,7 +255,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 44,
    "metadata": {
     "collapsed": true
    },
@@ -314,7 +283,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 45,
    "metadata": {},
    "outputs": [
     {
@@ -323,8 +292,8 @@
      "text": [
       "['abbe']\n",
       "['abbe', 'able']\n",
-      "['abbe', 'able', 'axle']\n",
       "['abbe', 'able', 'ably']\n",
+      "['abbe', 'able', 'axle']\n",
       "['abbe', 'able', 'ably', 'ally']\n"
      ]
     },
@@ -334,7 +303,7 @@
        "['abbe', 'able', 'ably', 'ally']"
       ]
      },
-     "execution_count": 17,
+     "execution_count": 45,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -345,7 +314,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 121,
    "metadata": {
     "collapsed": true
    },
@@ -357,7 +326,7 @@
     "    while not finished and agenda:\n",
     "        current = agenda[0]\n",
     "        if debug:\n",
-    "            print(current)\n",
+    "            print(agenda)\n",
     "        if current[-1] == goal:\n",
     "            finished = True\n",
     "        else:\n",
@@ -371,7 +340,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 47,
    "metadata": {},
    "outputs": [
     {
@@ -380,7 +349,6 @@
      "text": [
       "['abbe']\n",
       "['abbe', 'able']\n",
-      "['abbe', 'able', 'axle']\n",
       "['abbe', 'able', 'ably']\n",
       "['abbe', 'able', 'ably', 'ally']\n"
      ]
@@ -391,7 +359,7 @@
        "['abbe', 'able', 'ably', 'ally']"
       ]
      },
-     "execution_count": 19,
+     "execution_count": 47,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -402,7 +370,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 48,
    "metadata": {},
    "outputs": [
     {
@@ -410,1154 +378,668 @@
      "output_type": "stream",
      "text": [
       "['cart']\n",
-      "['cart', 'dart']\n",
+      "['cart', 'cast']\n",
       "['cart', 'hart']\n",
+      "['cart', 'cars']\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', 'curt']\n",
+      "['cart', 'tart']\n",
       "['cart', 'care']\n",
+      "['cart', 'cant']\n",
+      "['cart', 'dart']\n",
+      "['cart', 'part']\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', 'cast', 'last']\n",
+      "['cart', 'cast', 'bast']\n",
+      "['cart', 'cast', 'cant']\n",
+      "['cart', 'cast', 'past']\n",
+      "['cart', 'cast', 'mast']\n",
+      "['cart', 'cast', 'fast']\n",
+      "['cart', 'cast', 'case']\n",
+      "['cart', 'cast', 'east']\n",
+      "['cart', 'cast', 'cyst']\n",
+      "['cart', 'cast', 'cash']\n",
+      "['cart', 'cast', 'cask']\n",
+      "['cart', 'cast', 'vast']\n",
+      "['cart', 'cast', 'cost']\n",
+      "['cart', 'hart', 'hard']\n",
+      "['cart', 'hart', 'harm']\n",
+      "['cart', 'hart', 'hare']\n",
       "['cart', 'hart', 'hurt']\n",
       "['cart', 'hart', 'haft']\n",
       "['cart', 'hart', 'halt']\n",
-      "['cart', 'hart', 'hard']\n",
-      "['cart', 'hart', 'hare']\n",
+      "['cart', 'hart', 'mart']\n",
+      "['cart', 'hart', 'wart']\n",
       "['cart', 'hart', 'hark']\n",
-      "['cart', 'hart', 'harm']\n",
+      "['cart', 'hart', 'tart']\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', 'hart', 'dart']\n",
+      "['cart', 'hart', 'part']\n",
+      "['cart', 'cars', 'bars']\n",
+      "['cart', 'cars', 'ears']\n",
+      "['cart', 'cars', 'caps']\n",
+      "['cart', 'cars', 'wars']\n",
+      "['cart', 'cars', 'cabs']\n",
+      "['cart', 'cars', 'oars']\n",
+      "['cart', 'cars', 'pars']\n",
+      "['cart', 'cars', 'tars']\n",
+      "['cart', 'cars', 'card']\n",
+      "['cart', 'cars', 'cams']\n",
+      "['cart', 'cars', 'caws']\n",
+      "['cart', 'cars', 'cats']\n",
+      "['cart', 'cars', 'cads']\n",
+      "['cart', 'cars', 'care']\n",
+      "['cart', 'cars', 'cans']\n",
+      "['cart', 'cars', 'mars']\n",
+      "['cart', 'cars', 'curs']\n",
+      "['cart', 'cars', 'carp']\n",
+      "['cart', 'cars', 'jars']\n",
+      "['cart', 'mart', 'mare']\n",
       "['cart', 'mart', 'malt']\n",
+      "['cart', 'mart', 'hart']\n",
+      "['cart', 'mart', 'dart']\n",
       "['cart', 'mart', 'mast']\n",
+      "['cart', 'mart', 'wart']\n",
+      "['cart', 'mart', 'tart']\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', 'mart', 'part']\n",
+      "['cart', 'mart', 'mark']\n",
+      "['cart', 'wart', 'wary']\n",
       "['cart', 'wart', 'hart']\n",
+      "['cart', 'wart', 'warn']\n",
+      "['cart', 'wart', 'warm']\n",
+      "['cart', 'wart', 'warp']\n",
+      "['cart', 'wart', 'wars']\n",
       "['cart', 'wart', 'mart']\n",
-      "['cart', 'wart', 'part']\n",
+      "['cart', 'wart', 'watt']\n",
+      "['cart', 'wart', 'want']\n",
+      "['cart', 'wart', 'ware']\n",
       "['cart', 'wart', 'tart']\n",
       "['cart', 'wart', 'waft']\n",
+      "['cart', 'wart', 'dart']\n",
+      "['cart', 'wart', 'part']\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', 'bard']\n",
       "['cart', 'card', 'lard']\n",
-      "['cart', 'card', 'ward']\n",
-      "['cart', 'card', 'yard']\n",
-      "['cart', 'card', 'cord']\n",
+      "['cart', 'card', 'cars']\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', 'card', 'care']\n",
+      "['cart', 'card', 'yard']\n",
+      "['cart', 'card', 'ward']\n",
+      "['cart', 'card', 'cord']\n",
+      "['cart', 'curt', 'curb']\n",
+      "['cart', 'curt', 'hurt']\n",
+      "['cart', 'curt', 'curd']\n",
+      "['cart', 'curt', 'curl']\n",
+      "['cart', 'curt', 'cure']\n",
+      "['cart', 'curt', 'cult']\n",
+      "['cart', 'curt', 'curs']\n",
+      "['cart', 'tart', 'hart']\n",
+      "['cart', 'tart', 'tare']\n",
+      "['cart', 'tart', 'mart']\n",
+      "['cart', 'tart', 'wart']\n",
+      "['cart', 'tart', 'tars']\n",
+      "['cart', 'tart', 'taut']\n",
+      "['cart', 'tart', 'tarp']\n",
+      "['cart', 'tart', 'tact']\n",
+      "['cart', 'tart', 'tort']\n",
+      "['cart', 'tart', 'dart']\n",
+      "['cart', 'tart', 'part']\n",
+      "['cart', 'tart', 'taro']\n",
+      "['cart', 'care', 'came']\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', 'card']\n",
+      "['cart', 'care', 'core']\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', 'cars']\n",
+      "['cart', 'care', 'fare']\n",
       "['cart', 'care', 'case']\n",
-      "['cart', 'care', 'cave']\n",
-      "['cart', 'care', 'card']\n",
+      "['cart', 'care', 'cane']\n",
+      "['cart', 'care', 'bare']\n",
+      "['cart', 'care', 'cage']\n",
       "['cart', 'care', 'carp']\n",
-      "['cart', 'care', 'cars']\n",
-      "['cart', 'carp', 'harp']\n",
-      "['cart', 'carp', 'tarp']\n",
+      "['cart', 'care', 'cave']\n",
+      "['cart', 'care', 'cape']\n",
+      "['cart', 'care', 'pare']\n",
+      "['cart', 'care', 'ware']\n",
+      "['cart', 'care', 'mare']\n",
+      "['cart', 'care', 'cake']\n",
+      "['cart', 'care', 'rare']\n",
+      "['cart', 'care', 'tare']\n",
+      "['cart', 'care', 'dare']\n",
+      "['cart', 'cant', 'cast']\n",
+      "['cart', 'cant', 'rant']\n",
+      "['cart', 'cant', 'cent']\n",
+      "['cart', 'cant', 'want']\n",
+      "['cart', 'cant', 'cans']\n",
+      "['cart', 'cant', 'cane']\n",
+      "['cart', 'cant', 'pant']\n",
+      "['cart', 'dart', 'dirt']\n",
+      "['cart', 'dart', 'daft']\n",
+      "['cart', 'dart', 'dark']\n",
+      "['cart', 'dart', 'hart']\n",
+      "['cart', 'dart', 'wart']\n",
+      "['cart', 'dart', 'mart']\n",
+      "['cart', 'dart', 'dare']\n",
+      "['cart', 'dart', 'darn']\n",
+      "['cart', 'dart', 'tart']\n",
+      "['cart', 'dart', 'part']\n",
+      "['cart', 'part', 'port']\n",
+      "['cart', 'part', 'hart']\n",
+      "['cart', 'part', 'pact']\n",
+      "['cart', 'part', 'pert']\n",
+      "['cart', 'part', 'pare']\n",
+      "['cart', 'part', 'past']\n",
+      "['cart', 'part', 'mart']\n",
+      "['cart', 'part', 'wart']\n",
+      "['cart', 'part', 'pars']\n",
+      "['cart', 'part', 'dart']\n",
+      "['cart', 'part', 'tart']\n",
+      "['cart', 'part', 'park']\n",
+      "['cart', 'part', 'pant']\n",
+      "['cart', 'carp', 'cars']\n",
       "['cart', 'carp', 'warp']\n",
-      "['cart', 'carp', 'camp']\n",
       "['cart', 'carp', 'card']\n",
+      "['cart', 'carp', 'camp']\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', 'carp', 'tarp']\n",
+      "['cart', 'carp', 'harp']\n",
+      "['cart', 'cast', 'last', 'list']\n",
+      "['cart', 'cast', 'last', 'lost']\n",
+      "['cart', 'cast', 'last', 'bast']\n",
+      "['cart', 'cast', 'last', 'lust']\n",
+      "['cart', 'cast', 'last', 'lass']\n",
+      "['cart', 'cast', 'last', 'past']\n",
+      "['cart', 'cast', 'last', 'lash']\n",
+      "['cart', 'cast', 'last', 'mast']\n",
+      "['cart', 'cast', 'last', 'fast']\n",
+      "['cart', 'cast', 'last', 'east']\n",
+      "['cart', 'cast', 'last', 'lest']\n",
+      "['cart', 'cast', 'last', 'vast']\n",
+      "['cart', 'cast', 'bast', 'last']\n",
+      "['cart', 'cast', 'bast', 'bust']\n",
+      "['cart', 'cast', 'bast', 'bass']\n",
+      "['cart', 'cast', 'bast', 'base']\n",
+      "['cart', 'cast', 'bast', 'past']\n",
+      "['cart', 'cast', 'bast', 'mast']\n",
+      "['cart', 'cast', 'bast', 'bait']\n",
+      "['cart', 'cast', 'bast', 'fast']\n",
+      "['cart', 'cast', 'bast', 'best']\n",
+      "['cart', 'cast', 'bast', 'bash']\n",
+      "['cart', 'cast', 'bast', 'east']\n",
+      "['cart', 'cast', 'bast', 'bask']\n",
+      "['cart', 'cast', 'bast', 'vast']\n",
+      "['cart', 'cast', 'cant', 'rant']\n",
+      "['cart', 'cast', 'cant', 'cent']\n",
+      "['cart', 'cast', 'cant', 'want']\n",
+      "['cart', 'cast', 'cant', 'cans']\n",
+      "['cart', 'cast', 'cant', 'cane']\n",
+      "['cart', 'cast', 'cant', 'pant']\n",
+      "['cart', 'cast', 'past', 'last']\n",
+      "['cart', 'cast', 'past', 'bast']\n",
+      "['cart', 'cast', 'past', 'psst']\n",
+      "['cart', 'cast', 'past', 'pact']\n",
+      "['cart', 'cast', 'past', 'pass']\n",
+      "['cart', 'cast', 'past', 'pant']\n",
+      "['cart', 'cast', 'past', 'mast']\n",
+      "['cart', 'cast', 'past', 'post']\n",
+      "['cart', 'cast', 'past', 'fast']\n",
+      "['cart', 'cast', 'past', 'pest']\n",
+      "['cart', 'cast', 'past', 'east']\n",
+      "['cart', 'cast', 'past', 'part']\n",
+      "['cart', 'cast', 'past', 'vast']\n",
+      "['cart', 'cast', 'mast', 'mask']\n",
+      "['cart', 'cast', 'mast', 'last']\n",
+      "['cart', 'cast', 'mast', 'malt']\n",
+      "['cart', 'cast', 'mast', 'bast']\n",
+      "['cart', 'cast', 'mast', 'mist']\n",
+      "['cart', 'cast', 'mast', 'must']\n",
+      "['cart', 'cast', 'mast', 'past']\n",
+      "['cart', 'cast', 'mast', 'mart']\n",
+      "['cart', 'cast', 'mast', 'fast']\n",
+      "['cart', 'cast', 'mast', 'most']\n",
+      "['cart', 'cast', 'mast', 'mash']\n",
+      "['cart', 'cast', 'mast', 'matt']\n",
+      "['cart', 'cast', 'mast', 'east']\n",
+      "['cart', 'cast', 'mast', 'vast']\n",
+      "['cart', 'cast', 'mast', 'mass']\n",
+      "['cart', 'cast', 'fast', 'last']\n",
+      "['cart', 'cast', 'fast', 'fest']\n",
+      "['cart', 'cast', 'fast', 'bast']\n",
+      "['cart', 'cast', 'fast', 'fact']\n",
+      "['cart', 'cast', 'fast', 'past']\n",
+      "['cart', 'cast', 'fast', 'mast']\n",
+      "['cart', 'cast', 'fast', 'fist']\n",
+      "['cart', 'cast', 'fast', 'east']\n",
+      "['cart', 'cast', 'fast', 'vast']\n",
+      "['cart', 'cast', 'case', 'came']\n",
+      "['cart', 'cast', 'case', 'cake']\n",
+      "['cart', 'cast', 'case', 'cafe']\n",
+      "['cart', 'cast', 'case', 'cape']\n",
+      "['cart', 'cast', 'case', 'base']\n",
+      "['cart', 'cast', 'case', 'vase']\n",
+      "['cart', 'cast', 'case', 'care']\n",
+      "['cart', 'cast', 'case', 'ease']\n",
+      "['cart', 'cast', 'case', 'cane']\n",
+      "['cart', 'cast', 'case', 'cash']\n",
+      "['cart', 'cast', 'case', 'cask']\n",
+      "['cart', 'cast', 'case', 'cage']\n",
+      "['cart', 'cast', 'case', 'cave']\n",
+      "['cart', 'cast', 'east', 'last']\n",
+      "['cart', 'cast', 'east', 'bast']\n",
+      "['cart', 'cast', 'east', 'easy']\n",
+      "['cart', 'cast', 'east', 'past']\n",
+      "['cart', 'cast', 'east', 'mast']\n",
+      "['cart', 'cast', 'east', 'fast']\n",
+      "['cart', 'cast', 'east', 'ease']\n",
+      "['cart', 'cast', 'east', 'vast']\n",
+      "['cart', 'cast', 'cyst', 'cost']\n",
+      "['cart', 'cast', 'cash', 'sash']\n",
+      "['cart', 'cast', 'cash', 'lash']\n",
+      "['cart', 'cast', 'cash', 'dash']\n",
+      "['cart', 'cast', 'cash', 'bash']\n",
+      "['cart', 'cast', 'cash', 'wash']\n",
+      "['cart', 'cast', 'cash', 'case']\n",
+      "['cart', 'cast', 'cash', 'mash']\n",
+      "['cart', 'cast', 'cash', 'cask']\n",
+      "['cart', 'cast', 'cash', 'gash']\n",
+      "['cart', 'cast', 'cash', 'hash']\n",
+      "['cart', 'cast', 'cash', 'rash']\n",
+      "['cart', 'cast', 'cask', 'mask']\n",
+      "['cart', 'cast', 'cask', 'case']\n",
+      "['cart', 'cast', 'cask', 'cash']\n",
+      "['cart', 'cast', 'cask', 'bask']\n",
+      "['cart', 'cast', 'cask', 'task']\n",
+      "['cart', 'cast', 'vast', 'last']\n",
+      "['cart', 'cast', 'vast', 'bast']\n",
+      "['cart', 'cast', 'vast', 'vest']\n",
+      "['cart', 'cast', 'vast', 'past']\n",
+      "['cart', 'cast', 'vast', 'mast']\n",
+      "['cart', 'cast', 'vast', 'vase']\n",
+      "['cart', 'cast', 'vast', 'fast']\n",
+      "['cart', 'cast', 'vast', 'east']\n",
+      "['cart', 'cast', 'cost', 'colt']\n",
+      "['cart', 'cast', 'cost', 'lost']\n",
+      "['cart', 'cast', 'cost', 'tost']\n",
+      "['cart', 'cast', 'cost', 'post']\n",
+      "['cart', 'cast', 'cost', 'cosy']\n",
+      "['cart', 'cast', 'cost', 'coat']\n",
+      "['cart', 'cast', 'cost', 'coot']\n",
+      "['cart', 'cast', 'cost', 'most']\n",
+      "['cart', 'cast', 'cost', 'cyst']\n",
+      "['cart', 'cast', 'cost', 'host']\n",
+      "['cart', 'hart', 'hard', 'harm']\n",
       "['cart', 'hart', 'hard', 'bard']\n",
-      "['cart', 'hart', 'hard', 'card']\n",
+      "['cart', 'hart', 'hard', 'hare']\n",
       "['cart', 'hart', 'hard', 'lard']\n",
-      "['cart', 'hart', 'hard', 'ward']\n",
-      "['cart', 'hart', 'hard', 'yard']\n",
+      "['cart', 'hart', 'hard', 'card']\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', 'hand']\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', 'hard', 'yard']\n",
+      "['cart', 'hart', 'hard', 'ward']\n",
+      "['cart', 'hart', 'harm', 'farm']\n",
+      "['cart', 'hart', 'harm', 'hard']\n",
+      "['cart', 'hart', 'harm', 'hare']\n",
+      "['cart', 'hart', 'harm', 'warm']\n",
+      "['cart', 'hart', 'harm', 'harp']\n",
+      "['cart', 'hart', 'harm', 'hark']\n",
       "['cart', 'hart', 'hare', 'mare']\n",
-      "['cart', 'hart', 'hare', 'pare']\n",
+      "['cart', 'hart', 'hare', 'hard']\n",
+      "['cart', 'hart', 'hare', 'harm']\n",
       "['cart', 'hart', 'hare', 'rare']\n",
+      "['cart', 'hart', 'hare', 'hake']\n",
+      "['cart', 'hart', 'hare', 'fare']\n",
       "['cart', 'hart', 'hare', 'tare']\n",
-      "['cart', 'hart', 'hare', 'ware']\n",
+      "['cart', 'hart', 'hare', 'pare']\n",
+      "['cart', 'hart', 'hare', 'hate']\n",
       "['cart', 'hart', 'hare', 'here']\n",
-      "['cart', 'hart', 'hare', 'hire']\n",
-      "['cart', 'hart', 'hare', 'hake']\n",
+      "['cart', 'hart', 'hare', 'dare']\n",
       "['cart', 'hart', 'hare', 'hale']\n",
-      "['cart', 'hart', 'hare', 'hate']\n",
+      "['cart', 'hart', 'hare', 'care']\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', 'hare', 'ware']\n",
+      "['cart', 'hart', 'hare', 'bare']\n",
+      "['cart', 'hart', 'hare', 'hark']\n",
+      "['cart', 'hart', 'hare', 'hire']\n",
+      "['cart', 'hart', 'hare', 'haze']\n",
+      "['cart', 'hart', 'hurt', 'curt']\n",
+      "['cart', 'hart', 'hurt', 'hurl']\n",
+      "['cart', 'hart', 'hurt', 'hunt']\n",
+      "['cart', 'hart', 'haft', 'daft']\n",
+      "['cart', 'hart', 'haft', 'heft']\n",
+      "['cart', 'hart', 'haft', 'halt']\n",
+      "['cart', 'hart', 'haft', 'waft']\n",
+      "['cart', 'hart', 'haft', 'raft']\n",
+      "['cart', 'hart', 'halt', 'malt']\n",
+      "['cart', 'hart', 'halt', 'halo']\n",
+      "['cart', 'hart', 'halt', 'hall']\n",
+      "['cart', 'hart', 'halt', 'salt']\n",
+      "['cart', 'hart', 'halt', 'half']\n",
+      "['cart', 'hart', 'halt', 'haft']\n",
+      "['cart', 'hart', 'halt', 'hale']\n",
+      "['cart', 'hart', 'halt', 'hilt']\n",
+      "['cart', 'hart', 'mart', 'mare']\n",
+      "['cart', 'hart', 'mart', 'malt']\n",
+      "['cart', 'hart', 'mart', 'dart']\n",
+      "['cart', 'hart', 'mart', 'mast']\n",
+      "['cart', 'hart', 'mart', 'wart']\n",
+      "['cart', 'hart', 'mart', 'tart']\n",
+      "['cart', 'hart', 'mart', 'matt']\n",
+      "['cart', 'hart', 'mart', 'mars']\n",
+      "['cart', 'hart', 'mart', 'part']\n",
+      "['cart', 'hart', 'mart', 'mark']\n",
+      "['cart', 'hart', 'wart', 'wary']\n",
+      "['cart', 'hart', 'wart', 'warn']\n",
+      "['cart', 'hart', 'wart', 'warm']\n",
+      "['cart', 'hart', 'wart', 'warp']\n",
+      "['cart', 'hart', 'wart', 'wars']\n",
+      "['cart', 'hart', 'wart', 'mart']\n",
+      "['cart', 'hart', 'wart', 'watt']\n",
+      "['cart', 'hart', 'wart', 'want']\n",
+      "['cart', 'hart', 'wart', 'ware']\n",
+      "['cart', 'hart', 'wart', 'tart']\n",
+      "['cart', 'hart', 'wart', 'waft']\n",
+      "['cart', 'hart', 'wart', 'dart']\n",
+      "['cart', 'hart', 'wart', 'part']\n",
+      "['cart', 'hart', 'wart', 'wait']\n",
+      "['cart', 'hart', 'wart', 'ward']\n",
+      "['cart', 'hart', 'hark', 'hard']\n",
+      "['cart', 'hart', 'hark', 'harm']\n",
       "['cart', 'hart', 'hark', 'dark']\n",
-      "['cart', 'hart', 'hark', 'lark']\n",
-      "['cart', 'hart', 'hark', 'mark']\n",
+      "['cart', 'hart', 'hark', 'hare']\n",
       "['cart', 'hart', 'hark', 'nark']\n",
-      "['cart', 'hart', 'hark', 'park']\n",
-      "['cart', 'hart', 'hark', 'hack']\n",
+      "['cart', 'hart', 'hark', 'bark']\n",
+      "['cart', 'hart', 'hark', 'lark']\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', 'hark', 'park']\n",
+      "['cart', 'hart', 'hark', 'hawk']\n",
+      "['cart', 'hart', 'hark', 'hack']\n",
+      "['cart', 'hart', 'hark', 'mark']\n",
+      "['cart', 'hart', 'tart', 'tare']\n",
+      "['cart', 'hart', 'tart', 'mart']\n",
+      "['cart', 'hart', 'tart', 'wart']\n",
+      "['cart', 'hart', 'tart', 'tars']\n",
+      "['cart', 'hart', 'tart', 'taut']\n",
+      "['cart', 'hart', 'tart', 'tarp']\n",
+      "['cart', 'hart', 'tart', 'tact']\n",
+      "['cart', 'hart', 'tart', 'tort']\n",
+      "['cart', 'hart', 'tart', 'dart']\n",
+      "['cart', 'hart', 'tart', 'part']\n",
+      "['cart', 'hart', 'tart', 'taro']\n",
       "['cart', 'hart', 'harp', 'hard']\n",
+      "['cart', 'hart', 'harp', 'harm']\n",
       "['cart', 'hart', 'harp', 'hare']\n",
+      "['cart', 'hart', 'harp', 'warp']\n",
+      "['cart', 'hart', 'harp', 'tarp']\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"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "['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"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "['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"
+      "['cart', 'hart', 'harp', 'hasp']\n",
+      "['cart', 'hart', 'harp', 'carp']\n",
+      "['cart', 'hart', 'dart', 'dirt']\n",
+      "['cart', 'hart', 'dart', 'daft']\n",
+      "['cart', 'hart', 'dart', 'dark']\n",
+      "['cart', 'hart', 'dart', 'wart']\n",
+      "['cart', 'hart', 'dart', 'mart']\n",
+      "['cart', 'hart', 'dart', 'dare']\n",
+      "['cart', 'hart', 'dart', 'darn']\n",
+      "['cart', 'hart', 'dart', 'tart']\n",
+      "['cart', 'hart', 'dart', 'part']\n",
+      "['cart', 'hart', 'part', 'port']\n",
+      "['cart', 'hart', 'part', 'pact']\n",
+      "['cart', 'hart', 'part', 'pert']\n",
+      "['cart', 'hart', 'part', 'pare']\n",
+      "['cart', 'hart', 'part', 'past']\n",
+      "['cart', 'hart', 'part', 'mart']\n",
+      "['cart', 'hart', 'part', 'wart']\n",
+      "['cart', 'hart', 'part', 'pars']\n",
+      "['cart', 'hart', 'part', 'dart']\n",
+      "['cart', 'hart', 'part', 'tart']\n",
+      "['cart', 'hart', 'part', 'park']\n",
+      "['cart', 'hart', 'part', 'pant']\n",
+      "['cart', 'cars', 'bars', 'barb']\n",
+      "['cart', 'cars', 'bars', 'bard']\n",
+      "['cart', 'cars', 'bars', 'ears']\n",
+      "['cart', 'cars', 'bars', 'bass']\n",
+      "['cart', 'cars', 'bars', 'burs']\n",
+      "['cart', 'cars', 'bars', 'mars']\n",
+      "['cart', 'cars', 'bars', 'bays']\n",
+      "['cart', 'cars', 'bars', 'baas']\n",
+      "['cart', 'cars', 'bars', 'bark']\n",
+      "['cart', 'cars', 'bars', 'bags']\n",
+      "['cart', 'cars', 'bars', 'bans']\n",
+      "['cart', 'cars', 'bars', 'oars']\n",
+      "['cart', 'cars', 'bars', 'pars']\n",
+      "['cart', 'cars', 'bars', 'tars']\n",
+      "['cart', 'cars', 'bars', 'wars']\n",
+      "['cart', 'cars', 'bars', 'barn']\n",
+      "['cart', 'cars', 'bars', 'bats']\n",
+      "['cart', 'cars', 'bars', 'bare']\n",
+      "['cart', 'cars', 'bars', 'barf']\n",
+      "['cart', 'cars', 'bars', 'jars']\n",
+      "['cart', 'cars', 'ears', 'bars']\n",
+      "['cart', 'cars', 'ears', 'eats']\n",
+      "['cart', 'cars', 'ears', 'wars']\n",
+      "['cart', 'cars', 'ears', 'earl']\n",
+      "['cart', 'cars', 'ears', 'oars']\n",
+      "['cart', 'cars', 'ears', 'pars']\n",
+      "['cart', 'cars', 'ears', 'tars']\n",
+      "['cart', 'cars', 'ears', 'errs']\n",
+      "['cart', 'cars', 'ears', 'earn']\n",
+      "['cart', 'cars', 'ears', 'mars']\n",
+      "['cart', 'cars', 'ears', 'jars']\n",
+      "['cart', 'cars', 'caps', 'maps']\n",
+      "['cart', 'cars', 'caps', 'taps']\n",
+      "['cart', 'cars', 'caps', 'laps']\n",
+      "['cart', 'cars', 'caps', 'cape']\n",
+      "['cart', 'cars', 'caps', 'saps']\n",
+      "['cart', 'cars', 'caps', 'cops']\n",
+      "['cart', 'cars', 'caps', 'cabs']\n",
+      "['cart', 'cars', 'caps', 'cups']\n",
+      "['cart', 'cars', 'caps', 'naps']\n",
+      "['cart', 'cars', 'caps', 'raps']\n",
+      "['cart', 'cars', 'caps', 'cams']\n",
+      "['cart', 'cars', 'caps', 'cats']\n",
+      "['cart', 'cars', 'caps', 'yaps']\n",
+      "['cart', 'cars', 'caps', 'caws']\n",
+      "['cart', 'cars', 'caps', 'cads']\n",
+      "['cart', 'cars', 'caps', 'cans']\n",
+      "['cart', 'cars', 'caps', 'zaps']\n",
+      "['cart', 'cars', 'caps', 'paps']\n",
+      "['cart', 'cars', 'caps', 'gaps']\n",
+      "['cart', 'cars', 'wars', 'bars']\n",
+      "['cart', 'cars', 'wars', 'wary']\n",
+      "['cart', 'cars', 'wars', 'ears']\n",
+      "['cart', 'cars', 'wars', 'warn']\n",
+      "['cart', 'cars', 'wars', 'warm']\n",
+      "['cart', 'cars', 'wars', 'warp']\n",
+      "['cart', 'cars', 'wars', 'wart']\n",
+      "['cart', 'cars', 'wars', 'oars']\n",
+      "['cart', 'cars', 'wars', 'pars']\n",
+      "['cart', 'cars', 'wars', 'tars']\n",
+      "['cart', 'cars', 'wars', 'wags']\n",
+      "['cart', 'cars', 'wars', 'ways']\n",
+      "['cart', 'cars', 'wars', 'wads']\n",
+      "['cart', 'cars', 'wars', 'ware']\n",
+      "['cart', 'cars', 'wars', 'mars']\n",
+      "['cart', 'cars', 'wars', 'ward']\n",
+      "['cart', 'cars', 'wars', 'jars']\n",
+      "['cart', 'cars', 'cabs', 'cubs']\n",
+      "['cart', 'cars', 'cabs', 'labs']\n",
+      "['cart', 'cars', 'cabs', 'caps']\n",
+      "['cart', 'cars', 'cabs', 'cobs']\n",
+      "['cart', 'cars', 'cabs', 'jabs']\n",
+      "['cart', 'cars', 'cabs', 'cams']\n",
+      "['cart', 'cars', 'cabs', 'cats']\n",
+      "['cart', 'cars', 'cabs', 'caws']\n",
+      "['cart', 'cars', 'cabs', 'tabs']\n",
+      "['cart', 'cars', 'cabs', 'nabs']\n",
+      "['cart', 'cars', 'cabs', 'dabs']\n",
+      "['cart', 'cars', 'cabs', 'cads']\n",
+      "['cart', 'cars', 'cabs', 'cans']\n",
+      "['cart', 'cars', 'cabs', 'gabs']\n",
+      "['cart', 'cars', 'oars', 'bars']\n",
+      "['cart', 'cars', 'oars', 'ears']\n",
+      "['cart', 'cars', 'oars', 'oaks']\n",
+      "['cart', 'cars', 'oars', 'oafs']\n",
+      "['cart', 'cars', 'oars', 'wars']\n",
+      "['cart', 'cars', 'oars', 'oats']\n",
+      "['cart', 'cars', 'oars', 'pars']\n",
+      "['cart', 'cars', 'oars', 'tars']\n",
+      "['cart', 'cars', 'oars', 'ours']\n",
+      "['cart', 'cars', 'oars', 'mars']\n",
+      "['cart', 'cars', 'oars', 'jars']\n",
+      "['cart', 'cars', 'pars', 'pats']\n",
+      "['cart', 'cars', 'pars', 'bars']\n",
+      "['cart', 'cars', 'pars', 'ears']\n",
+      "['cart', 'cars', 'pars', 'pals']\n",
+      "['cart', 'cars', 'pars', 'pans']\n",
+      "['cart', 'cars', 'pars', 'mars']\n",
+      "['cart', 'cars', 'pars', 'pass']\n",
+      "['cart', 'cars', 'pars', 'paws']\n",
+      "['cart', 'cars', 'pars', 'pare']\n",
+      "['cart', 'cars', 'pars', 'wars']\n",
+      "['cart', 'cars', 'pars', 'oars']\n",
+      "['cart', 'cars', 'pars', 'tars']\n",
+      "['cart', 'cars', 'pars', 'paps']\n",
+      "['cart', 'cars', 'pars', 'pays']\n",
+      "['cart', 'cars', 'pars', 'park']\n",
+      "['cart', 'cars', 'pars', 'part']\n",
+      "['cart', 'cars', 'pars', 'jars']\n",
+      "['cart', 'cars', 'pars', 'pads']\n",
+      "['cart', 'cars', 'tars', 'tags']\n",
+      "['cart', 'cars', 'tars', 'bars']\n",
+      "['cart', 'cars', 'tars', 'tads']\n",
+      "['cart', 'cars', 'tars', 'ears']\n",
+      "['cart', 'cars', 'tars', 'taps']\n",
+      "['cart', 'cars', 'tars', 'tare']\n",
+      "['cart', 'cars', 'tars', 'tans']\n",
+      "['cart', 'cars', 'tars', 'tors']\n",
+      "['cart', 'cars', 'tars', 'oars']\n",
+      "['cart', 'cars', 'tars', 'pars']\n",
+      "['cart', 'cars', 'tars', 'tats']\n",
+      "['cart', 'cars', 'tars', 'tams']\n",
+      "['cart', 'cars', 'tars', 'tabs']\n",
+      "['cart', 'cars', 'tars', 'tart']\n",
+      "['cart', 'cars', 'tars', 'tarp']\n",
+      "['cart', 'cars', 'tars', 'wars']\n",
+      "['cart', 'cars', 'tars', 'mars']\n",
+      "['cart', 'cars', 'tars', 'taro']\n",
+      "['cart', 'cars', 'tars', 'jars']\n",
+      "['cart', 'cars', 'card', 'hard']\n",
+      "['cart', 'cars', 'card', 'bard']\n",
+      "['cart', 'cars', 'card', 'lard']\n",
+      "['cart', 'cars', 'card', 'curd']\n",
+      "['cart', 'cars', 'card', 'carp']\n",
+      "['cart', 'cars', 'card', 'care']\n",
+      "['cart', 'cars', 'card', 'yard']\n",
+      "['cart', 'cars', 'card', 'ward']\n",
+      "['cart', 'cars', 'card', 'cord']\n",
+      "['cart', 'cars', 'cams', 'came']\n",
+      "['cart', 'cars', 'cams', 'rams']\n",
+      "['cart', 'cars', 'cams', 'jams']\n",
+      "['cart', 'cars', 'cams', 'caps']\n",
+      "['cart', 'cars', 'cams', 'cums']\n",
+      "['cart', 'cars', 'cams', 'lams']\n",
+      "['cart', 'cars', 'cams', 'tams']\n",
+      "['cart', 'cars', 'cams', 'camp']\n",
+      "['cart', 'cars', 'cams', 'cabs']\n",
+      "['cart', 'cars', 'cams', 'dams']\n",
+      "['cart', 'cars', 'cams', 'cats']\n",
+      "['cart', 'cars', 'cams', 'caws']\n",
+      "['cart', 'cars', 'cams', 'cads']\n",
+      "['cart', 'cars', 'cams', 'hams']\n",
+      "['cart', 'cars', 'cams', 'cans']\n",
+      "['cart', 'cars', 'cams', 'yams']\n",
+      "['cart', 'cars', 'caws', 'saws']\n",
+      "['cart', 'cars', 'caws', 'maws']\n",
+      "['cart', 'cars', 'caws', 'haws']\n",
+      "['cart', 'cars', 'caws', 'caps']\n",
+      "['cart', 'cars', 'caws', 'paws']\n",
+      "['cart', 'cars', 'caws', 'laws']\n",
+      "['cart', 'cars', 'caws', 'cows']\n",
+      "['cart', 'cars', 'caws', 'cabs']\n",
+      "['cart', 'cars', 'caws', 'cams']\n",
+      "['cart', 'cars', 'caws', 'cats']\n",
+      "['cart', 'cars', 'caws', 'cads']\n",
+      "['cart', 'cars', 'caws', 'cans']\n",
+      "['cart', 'cars', 'caws', 'yaws']\n",
+      "['cart', 'cars', 'caws', 'jaws']\n",
+      "['cart', 'cars', 'cats', 'cots']\n",
+      "['cart', 'cars', 'cats', 'eats']\n",
+      "['cart', 'cars', 'cats', 'hats']\n",
+      "['cart', 'cars', 'cats', 'caps']\n",
+      "['cart', 'cars', 'cats', 'rats']\n",
+      "['cart', 'cars', 'cats', 'cuts']\n",
+      "['cart', 'cars', 'cats', 'fats']\n",
+      "['cart', 'cars', 'cats', 'vats']\n",
+      "['cart', 'cars', 'cats', 'cabs']\n",
+      "['cart', 'cars', 'cats', 'oats']\n",
+      "['cart', 'cars', 'cats', 'tats']\n",
+      "['cart', 'cars', 'cats', 'cams']\n",
+      "['cart', 'cars', 'cats', 'caws']\n",
+      "['cart', 'cars', 'cats', 'cads']\n",
+      "['cart', 'cars', 'cats', 'mats']\n",
+      "['cart', 'cars', 'cats', 'bats']\n",
+      "['cart', 'cars', 'cats', 'cans']\n",
+      "['cart', 'cars', 'cats', 'lats']\n",
+      "['cart', 'cars', 'cats', 'pats']\n",
+      "['cart', 'cars', 'cads', 'tads']\n",
+      "['cart', 'cars', 'cads', 'cods']\n",
+      "['cart', 'cars', 'cads', 'caps']\n",
+      "['cart', 'cars', 'cads', 'fads']\n",
+      "['cart', 'cars', 'cads', 'dads']\n",
+      "['cart', 'cars', 'cads', 'mads']\n",
+      "['cart', 'cars', 'cads', 'lads']\n",
+      "['cart', 'cars', 'cads', 'cuds']\n",
+      "['cart', 'cars', 'cads', 'cabs']\n",
+      "['cart', 'cars', 'cads', 'cams']\n",
+      "['cart', 'cars', 'cads', 'wads']\n",
+      "['cart', 'cars', 'cads', 'cats']\n",
+      "['cart', 'cars', 'cads', 'caws']\n",
+      "['cart', 'cars', 'cads', 'cans']\n",
+      "['cart', 'cars', 'cads', 'gads']\n",
+      "['cart', 'cars', 'cads', 'pads']\n",
+      "['cart', 'cars', 'care', 'came']\n",
+      "['cart', 'cars', 'care', 'hare']\n",
+      "['cart', 'cars', 'care', 'cure']\n",
+      "['cart', 'cars', 'care', 'card']\n",
+      "['cart', 'cars', 'care', 'core']\n",
+      "['cart', 'cars', 'care', 'cafe']\n",
+      "['cart', 'cars', 'care', 'fare']\n",
+      "['cart', 'cars', 'care', 'case']\n",
+      "['cart', 'cars', 'care', 'cane']\n",
+      "['cart', 'cars', 'care', 'bare']\n",
+      "['cart', 'cars', 'care', 'cage']\n",
+      "['cart', 'cars', 'care', 'carp']\n",
+      "['cart', 'cars', 'care', 'cave']\n",
+      "['cart', 'cars', 'care', 'cape']\n",
+      "['cart', 'cars', 'care', 'pare']\n",
+      "['cart', 'cars', 'care', 'ware']\n",
+      "['cart', 'cars', 'care', 'mare']\n",
+      "['cart', 'cars', 'care', 'cake']\n",
+      "['cart', 'cars', 'care', 'rare']\n",
+      "['cart', 'cars', 'care', 'tare']\n",
+      "['cart', 'cars', 'care', 'dare']\n",
+      "['cart', 'cars', 'cans', 'vans']\n"
      ]
     },
     {
      "data": {
       "text/plain": [
-       "['cart', 'cant', 'cans', 'vans']"
+       "['cart', 'cars', 'cans', 'vans']"
       ]
      },
-     "execution_count": 20,
+     "execution_count": 48,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1568,16 +1050,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 49,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "['cart', 'cant', 'cane', 'vane']"
+       "['cart', 'care', 'cane', 'vane']"
       ]
      },
-     "execution_count": 21,
+     "execution_count": 49,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1588,604 +1070,27 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 51,
    "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']"
+       "1494"
       ]
      },
-     "execution_count": 22,
+     "execution_count": 51,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "dfs_search('cart', 'vane')"
+    "len(dfs_search('cart', 'vane'))"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 52,
    "metadata": {
     "collapsed": true
    },
@@ -2213,7 +1118,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 24,
+   "execution_count": 53,
    "metadata": {},
    "outputs": [
     {
@@ -2232,7 +1137,7 @@
        "['cart', 'cant', 'cane', 'vane']"
       ]
      },
-     "execution_count": 24,
+     "execution_count": 53,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2243,7 +1148,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 81,
+   "execution_count": 54,
    "metadata": {
     "collapsed": true
    },
@@ -2273,7 +1178,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 26,
+   "execution_count": 55,
    "metadata": {},
    "outputs": [
     {
@@ -2292,7 +1197,7 @@
        "['cart', 'cant', 'cane', 'vane']"
       ]
      },
-     "execution_count": 26,
+     "execution_count": 55,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2312,22 +1217,22 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 27,
-   "metadata": {},
+   "execution_count": 69,
+   "metadata": {
+    "scrolled": true
+   },
    "outputs": [
     {
-     "data": {
-      "text/plain": [
-       "94"
-      ]
-     },
-     "execution_count": 27,
-     "metadata": {},
-     "output_type": "execute_result"
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "10 loops, best of 3: 23.9 ms per loop\n"
+     ]
     }
    ],
    "source": [
-    "candidates = [set([k] + neighbours[k]) for k in neighbours]\n",
+    "%%timeit\n",
+    "candidates = [set([k] + list(neighbours[k])) for k in neighbours]\n",
     "reachables = []\n",
     "while candidates:\n",
     "    current = set(candidates.pop())\n",
@@ -2347,7 +1252,41 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 28,
+   "execution_count": 71,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "10 loops, best of 3: 25.9 ms per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "candidates = set(frozenset({k}.union(neighbours[k])) for k in neighbours)\n",
+    "reachables = set()\n",
+    "while candidates:\n",
+    "    current = set(candidates.pop())\n",
+    "    remove_because_merged = set()\n",
+    "    for other in candidates:\n",
+    "        if current.intersection(other):\n",
+    "            current.update(other)\n",
+    "            remove_because_merged.add(other)\n",
+    "    if remove_because_merged:\n",
+    "        for rbm in remove_because_merged:\n",
+    "            candidates.remove(rbm)\n",
+    "        candidates.add(frozenset(current))\n",
+    "    else:\n",
+    "        reachables.add(frozenset(current))\n",
+    "\n",
+    "len(reachables)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 72,
    "metadata": {},
    "outputs": [
     {
@@ -2356,7 +1295,7 @@
        "2204"
       ]
      },
-     "execution_count": 28,
+     "execution_count": 72,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2367,7 +1306,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 29,
+   "execution_count": 73,
    "metadata": {},
    "outputs": [
     {
@@ -2376,7 +1315,7 @@
        "1"
       ]
      },
-     "execution_count": 29,
+     "execution_count": 73,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2387,7 +1326,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 30,
+   "execution_count": 74,
    "metadata": {
     "scrolled": true
    },
@@ -2398,7 +1337,7 @@
        "Counter({1: 75, 2: 6, 3: 7, 4: 2, 5: 2, 6: 1, 2204: 1})"
       ]
      },
-     "execution_count": 30,
+     "execution_count": 74,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2409,7 +1348,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 31,
+   "execution_count": 75,
    "metadata": {},
    "outputs": [
     {
@@ -2418,7 +1357,7 @@
        "[5]"
       ]
      },
-     "execution_count": 31,
+     "execution_count": 75,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2429,16 +1368,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 32,
+   "execution_count": 76,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "[{'abbe', 'able', 'ably', 'ally', 'axle'}]"
+       "[frozenset({'abbe', 'able', 'ably', 'ally', 'axle'})]"
       ]
      },
-     "execution_count": 32,
+     "execution_count": 76,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2449,7 +1388,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 76,
+   "execution_count": 77,
    "metadata": {
     "scrolled": true
    },
@@ -2457,27 +1396,27 @@
     {
      "data": {
       "text/plain": [
-       "[{'demo', 'memo'},\n",
-       " {'thou', 'thru'},\n",
-       " {'crud', 'crux'},\n",
-       " {'bevy', 'levy'},\n",
-       " {'ogle', 'ogre'},\n",
-       " {'idol', 'idyl'},\n",
-       " {'also', 'alto', 'auto'},\n",
-       " {'used', 'user', 'uses'},\n",
-       " {'idle', 'idly', 'isle'},\n",
-       " {'eddy', 'edge', 'edgy'},\n",
-       " {'opal', 'oral', 'oval'},\n",
-       " {'icon', 'ikon', 'iron'},\n",
-       " {'afar', 'agar', 'ajar'},\n",
-       " {'each', 'etch', 'inch', 'itch'},\n",
-       " {'high', 'nigh', 'sigh', 'sign'},\n",
-       " {'abbe', 'able', 'ably', 'ally', 'axle'},\n",
-       " {'info', 'into', 'onto', 'undo', 'unto'},\n",
-       " {'ache', 'achy', 'acme', 'acne', 'acre', 'ashy'}]"
+       "[frozenset({'bevy', 'levy'}),\n",
+       " frozenset({'ogle', 'ogre'}),\n",
+       " frozenset({'demo', 'memo'}),\n",
+       " frozenset({'crud', 'crux'}),\n",
+       " frozenset({'thou', 'thru'}),\n",
+       " frozenset({'idol', 'idyl'}),\n",
+       " frozenset({'icon', 'ikon', 'iron'}),\n",
+       " frozenset({'used', 'user', 'uses'}),\n",
+       " frozenset({'opal', 'oral', 'oval'}),\n",
+       " frozenset({'also', 'alto', 'auto'}),\n",
+       " frozenset({'idle', 'idly', 'isle'}),\n",
+       " frozenset({'afar', 'agar', 'ajar'}),\n",
+       " frozenset({'eddy', 'edge', 'edgy'}),\n",
+       " frozenset({'each', 'etch', 'inch', 'itch'}),\n",
+       " frozenset({'high', 'nigh', 'sigh', 'sign'}),\n",
+       " frozenset({'info', 'into', 'onto', 'undo', 'unto'}),\n",
+       " frozenset({'abbe', 'able', 'ably', 'ally', 'axle'}),\n",
+       " frozenset({'ache', 'achy', 'acme', 'acne', 'acre', 'ashy'})]"
       ]
      },
-     "execution_count": 76,
+     "execution_count": 77,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2488,7 +1427,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 80,
+   "execution_count": 78,
    "metadata": {},
    "outputs": [
     {
@@ -2497,7 +1436,7 @@
        "'adze; agog; ague; ahoy; alga; ammo; amok; anal; ankh; apse; aqua; aura; avow; awol; bozo; ebbs; echo; ecru; emus; ends; envy; epee; epic; espy; euro; evil; exam; expo; guru; hymn; ibex; iffy; imam; iota; isms; judo; kiwi; liar; luau; lynx; mayo; meow; myna; nova; obey; oboe; odor; ohms; okra; oleo; once; onyx; orgy; ovum; rely; rhea; semi; sexy; stye; sync; taxi; tofu; tuft; tutu; twos; ugly; ulna; upon; urge; uric; urns; void; wiki; yeti; zebu'"
       ]
      },
-     "execution_count": 80,
+     "execution_count": 78,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2508,7 +1447,89 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 33,
+   "execution_count": 120,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "['ache'] [['ache']]\n",
+      "['ache', 'acne'] [['ache', 'acne'], ['ache', 'acme'], ['ache', 'acre'], ['ache', 'achy']]\n",
+      "['ache', 'acme'] [['ache', 'acme'], ['ache', 'acre'], ['ache', 'achy'], ['ache', 'acne', 'acme'], ['ache', 'acne', 'acre']]\n",
+      "['ache', 'acre'] [['ache', 'acre'], ['ache', 'achy'], ['ache', 'acne', 'acme'], ['ache', 'acne', 'acre'], ['ache', 'acme', 'acne'], ['ache', 'acme', 'acre']]\n",
+      "['ache', 'achy'] [['ache', 'achy'], ['ache', 'acne', 'acme'], ['ache', 'acne', 'acre'], ['ache', 'acme', 'acne'], ['ache', 'acme', 'acre'], ['ache', 'acre', 'acne'], ['ache', 'acre', 'acme']]\n",
+      "['ache', 'acne', 'acme'] [['ache', 'acne', 'acme'], ['ache', 'acne', 'acre'], ['ache', 'acme', 'acne'], ['ache', 'acme', 'acre'], ['ache', 'acre', 'acne'], ['ache', 'acre', 'acme'], ['ache', 'achy', 'ashy']]\n",
+      "['ache', 'acne', 'acre'] [['ache', 'acne', 'acre'], ['ache', 'acme', 'acne'], ['ache', 'acme', 'acre'], ['ache', 'acre', 'acne'], ['ache', 'acre', 'acme'], ['ache', 'achy', 'ashy'], ['ache', 'acne', 'acme', 'acre']]\n",
+      "['ache', 'acme', 'acne'] [['ache', 'acme', 'acne'], ['ache', 'acme', 'acre'], ['ache', 'acre', 'acne'], ['ache', 'acre', 'acme'], ['ache', 'achy', 'ashy'], ['ache', 'acne', 'acme', 'acre'], ['ache', 'acne', 'acre', 'acme']]\n",
+      "['ache', 'acme', 'acre'] [['ache', 'acme', 'acre'], ['ache', 'acre', 'acne'], ['ache', 'acre', 'acme'], ['ache', 'achy', 'ashy'], ['ache', 'acne', 'acme', 'acre'], ['ache', 'acne', 'acre', 'acme'], ['ache', 'acme', 'acne', 'acre']]\n",
+      "['ache', 'acre', 'acne'] [['ache', 'acre', 'acne'], ['ache', 'acre', 'acme'], ['ache', 'achy', 'ashy'], ['ache', 'acne', 'acme', 'acre'], ['ache', 'acne', 'acre', 'acme'], ['ache', 'acme', 'acne', 'acre'], ['ache', 'acme', 'acre', 'acne']]\n",
+      "['ache', 'acre', 'acme'] [['ache', 'acre', 'acme'], ['ache', 'achy', 'ashy'], ['ache', 'acne', 'acme', 'acre'], ['ache', 'acne', 'acre', 'acme'], ['ache', 'acme', 'acne', 'acre'], ['ache', 'acme', 'acre', 'acne'], ['ache', 'acre', 'acne', 'acme']]\n",
+      "['ache', 'achy', 'ashy'] [['ache', 'achy', 'ashy'], ['ache', 'acne', 'acme', 'acre'], ['ache', 'acne', 'acre', 'acme'], ['ache', 'acme', 'acne', 'acre'], ['ache', 'acme', 'acre', 'acne'], ['ache', 'acre', 'acne', 'acme'], ['ache', 'acre', 'acme', 'acne']]\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "['ache', 'achy', 'ashy']"
+      ]
+     },
+     "execution_count": 120,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "bfs_search('ache', 'ashy', debug=True)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 122,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[['ache']]\n",
+      "[['ache', 'acne'], ['ache', 'acme'], ['ache', 'acre'], ['ache', 'achy']]\n",
+      "[['ache', 'acne', 'acme'], ['ache', 'acne', 'acre'], ['ache', 'acme'], ['ache', 'acre'], ['ache', 'achy']]\n",
+      "[['ache', 'acne', 'acme', 'acre'], ['ache', 'acne', 'acre'], ['ache', 'acme'], ['ache', 'acre'], ['ache', 'achy']]\n",
+      "[['ache', 'acne', 'acre'], ['ache', 'acme'], ['ache', 'acre'], ['ache', 'achy']]\n",
+      "[['ache', 'acne', 'acre', 'acme'], ['ache', 'acme'], ['ache', 'acre'], ['ache', 'achy']]\n",
+      "[['ache', 'acme'], ['ache', 'acre'], ['ache', 'achy']]\n",
+      "[['ache', 'acme', 'acne'], ['ache', 'acme', 'acre'], ['ache', 'acre'], ['ache', 'achy']]\n",
+      "[['ache', 'acme', 'acne', 'acre'], ['ache', 'acme', 'acre'], ['ache', 'acre'], ['ache', 'achy']]\n",
+      "[['ache', 'acme', 'acre'], ['ache', 'acre'], ['ache', 'achy']]\n",
+      "[['ache', 'acme', 'acre', 'acne'], ['ache', 'acre'], ['ache', 'achy']]\n",
+      "[['ache', 'acre'], ['ache', 'achy']]\n",
+      "[['ache', 'acre', 'acne'], ['ache', 'acre', 'acme'], ['ache', 'achy']]\n",
+      "[['ache', 'acre', 'acne', 'acme'], ['ache', 'acre', 'acme'], ['ache', 'achy']]\n",
+      "[['ache', 'acre', 'acme'], ['ache', 'achy']]\n",
+      "[['ache', 'acre', 'acme', 'acne'], ['ache', 'achy']]\n",
+      "[['ache', 'achy']]\n",
+      "[['ache', 'achy', 'ashy']]\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "['ache', 'achy', 'ashy']"
+      ]
+     },
+     "execution_count": 122,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "dfs_search('ache', 'ashy', debug=True)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 79,
    "metadata": {},
    "outputs": [
     {
@@ -2517,7 +1538,7 @@
        "['buns', 'bunk', 'punk']"
       ]
      },
-     "execution_count": 33,
+     "execution_count": 79,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2528,7 +1549,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 34,
+   "execution_count": 80,
    "metadata": {
     "collapsed": true
    },
@@ -2543,7 +1564,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 35,
+   "execution_count": 81,
    "metadata": {
     "collapsed": true
    },
@@ -2566,7 +1587,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 36,
+   "execution_count": 82,
    "metadata": {
     "collapsed": true
    },
@@ -2577,33 +1598,33 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 37,
+   "execution_count": 83,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "['army', 'arms', 'aims', 'aids', 'bids', 'bias', 'boas', 'boat', 'goat', 'gnat', 'gnaw']\n",
-      "['hoes', 'toes', 'toms', 'tams', 'tame']\n",
-      "['vane', 'vine', 'wine', 'wire', 'wiry', 'airy', 'awry', 'away']\n",
-      "['mate', 'late', 'lane', 'land', 'laid', 'lain']\n",
-      "['heal', 'head', 'bead', 'bend', 'bond', 'bone']\n",
-      "['dune', 'dine', 'dins', 'dies', 'died', 'tied']\n",
-      "['ions', 'dons', 'does', 'hoes', 'hoed', 'heed']\n",
-      "['puck', 'pick', 'pink', 'mink', 'mine']\n",
-      "['need', 'deed', 'died', 'dies', 'dims', 'dams', 'days', 'drys']\n",
-      "['pore', 'core', 'code', 'cods', 'cuds']\n",
-      "['mote', 'mite', 'mile', 'wile', 'wise']\n",
-      "['wait', 'wail', 'mail', 'mall', 'male']\n",
-      "['wail', 'bail', 'ball', 'boll', 'bolt', 'boot', 'boom', 'zoom']\n",
-      "['beat', 'beet', 'bees', 'bets', 'bats', 'cats']\n",
-      "['tore', 'tire', 'tile', 'vile', 'vise', 'visa']\n",
-      "['went', 'pent', 'pant']\n",
-      "['lick', 'sick', 'sics', 'sips', 'sops', 'oops']\n",
-      "['womb', 'tomb', 'toms', 'toes', 'does', 'dyes', 'ayes', 'apes', 'aped']\n",
-      "['cure', 'sure']\n",
-      "['cute', 'cuts', 'guts', 'guys', 'gays']\n"
+      "['foil', 'boil', 'bail', 'ball', 'balk', 'bank', 'hank']\n",
+      "['pint', 'pent', 'peat', 'meat', 'meal', 'mewl']\n",
+      "['fuse', 'fuss', 'furs', 'ours']\n",
+      "['plop', 'flop', 'flow', 'flew']\n",
+      "['lull', 'bull', 'bell', 'belt', 'welt', 'wept', 'kept']\n",
+      "['coma', 'coda', 'cods', 'cons', 'sons']\n",
+      "['pits', 'bits', 'bats', 'bass', 'bash', 'rash']\n",
+      "['bean', 'been', 'bees', 'beds', 'buds', 'suds']\n",
+      "['yips', 'nips', 'nits', 'nite', 'note', 'vote']\n",
+      "['pent', 'pens', 'yens']\n",
+      "['crop', 'coop', 'coos', 'cons', 'cans', 'fans']\n",
+      "['flop', 'clop', 'coop', 'cool', 'cowl', 'bowl', 'bawl']\n",
+      "['hill', 'hull', 'hulk', 'sulk', 'suck']\n",
+      "['aced', 'acid', 'arid', 'grid', 'grin', 'gain', 'rain']\n",
+      "['land', 'sand', 'sans', 'suns', 'subs', 'hubs']\n",
+      "['cogs', 'coos', 'cool', 'coal', 'foal', 'foam']\n",
+      "['loss', 'moss', 'mods', 'nods', 'nous', 'yous']\n",
+      "['soap', 'soar', 'boar', 'boas', 'bogs', 'jogs']\n",
+      "['musk', 'must', 'bust', 'best', 'beet', 'beef']\n",
+      "['fine', 'wine', 'wane', 'want', 'waft']\n"
      ]
     }
    ],
@@ -2615,7 +1636,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 38,
+   "execution_count": 84,
    "metadata": {},
    "outputs": [
     {
@@ -2624,7 +1645,7 @@
        "['cops', 'coos', 'coon', 'coin', 'chin', 'thin', 'this', 'thus', 'thug']"
       ]
      },
-     "execution_count": 38,
+     "execution_count": 84,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2635,7 +1656,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 39,
+   "execution_count": 85,
    "metadata": {},
    "outputs": [
     {
@@ -2644,7 +1665,7 @@
        "[2204]"
       ]
      },
-     "execution_count": 39,
+     "execution_count": 85,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2655,7 +1676,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 40,
+   "execution_count": 86,
    "metadata": {},
    "outputs": [
     {
@@ -2664,7 +1685,7 @@
        "[2204]"
       ]
      },
-     "execution_count": 40,
+     "execution_count": 86,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2675,7 +1696,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 41,
+   "execution_count": 87,
    "metadata": {},
    "outputs": [
     {
@@ -2684,7 +1705,7 @@
        "['hate', 'have', 'hove', 'love']"
       ]
      },
-     "execution_count": 41,
+     "execution_count": 87,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2695,7 +1716,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 42,
+   "execution_count": 88,
    "metadata": {},
    "outputs": [
     {
@@ -2704,7 +1725,7 @@
        "['wars', 'ware', 'wave', 'wove', 'love']"
       ]
      },
-     "execution_count": 42,
+     "execution_count": 88,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2715,7 +1736,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 43,
+   "execution_count": 89,
    "metadata": {},
    "outputs": [
     {
@@ -2723,7 +1744,7 @@
      "output_type": "stream",
      "text": [
       "CPU times: user 0 ns, sys: 0 ns, total: 0 ns\n",
-      "Wall time: 185 µs\n"
+      "Wall time: 199 µs\n"
      ]
     },
     {
@@ -2732,7 +1753,7 @@
        "5"
       ]
      },
-     "execution_count": 43,
+     "execution_count": 89,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2743,7 +1764,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 44,
+   "execution_count": 90,
    "metadata": {},
    "outputs": [
     {
@@ -2751,7 +1772,7 @@
      "output_type": "stream",
      "text": [
       "CPU times: user 0 ns, sys: 0 ns, total: 0 ns\n",
-      "Wall time: 398 µs\n"
+      "Wall time: 210 µs\n"
      ]
     },
     {
@@ -2760,7 +1781,7 @@
        "5"
       ]
      },
-     "execution_count": 44,
+     "execution_count": 90,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2771,24 +1792,24 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 45,
+   "execution_count": 91,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CPU times: user 32 ms, sys: 0 ns, total: 32 ms\n",
-      "Wall time: 32.3 ms\n"
+      "CPU times: user 12 ms, sys: 0 ns, total: 12 ms\n",
+      "Wall time: 13.5 ms\n"
      ]
     },
     {
      "data": {
       "text/plain": [
-       "404"
+       "272"
       ]
      },
-     "execution_count": 45,
+     "execution_count": 91,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2799,7 +1820,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 46,
+   "execution_count": 92,
    "metadata": {
     "collapsed": true
    },
@@ -2810,15 +1831,15 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 47,
+   "execution_count": 93,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CPU times: user 212 ms, sys: 0 ns, total: 212 ms\n",
-      "Wall time: 213 ms\n"
+      "CPU times: user 724 ms, sys: 0 ns, total: 724 ms\n",
+      "Wall time: 723 ms\n"
      ]
     },
     {
@@ -2827,7 +1848,7 @@
        "5"
       ]
      },
-     "execution_count": 47,
+     "execution_count": 93,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2838,7 +1859,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 48,
+   "execution_count": 94,
    "metadata": {},
    "outputs": [
     {
@@ -2847,7 +1868,7 @@
        "['fear', 'feat', 'fest', 'lest', 'lost', 'lose', 'love']"
       ]
      },
-     "execution_count": 48,
+     "execution_count": 94,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2858,7 +1879,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 49,
+   "execution_count": 95,
    "metadata": {},
    "outputs": [
     {
@@ -2867,7 +1888,7 @@
        "['fail', 'fall', 'pall', 'pals', 'pass']"
       ]
      },
-     "execution_count": 49,
+     "execution_count": 95,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2878,7 +1899,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 50,
+   "execution_count": 96,
    "metadata": {},
    "outputs": [
     {
@@ -2887,7 +1908,7 @@
        "['star', 'soar', 'boar', 'boor', 'boon', 'born']"
       ]
      },
-     "execution_count": 50,
+     "execution_count": 96,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2898,7 +1919,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 51,
+   "execution_count": 97,
    "metadata": {},
    "outputs": [
     {
@@ -2917,7 +1938,7 @@
        " 'pass']"
       ]
      },
-     "execution_count": 51,
+     "execution_count": 97,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2928,29 +1949,29 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 52,
+   "execution_count": 98,
    "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']"
+       "frozenset({'bass',\n",
+       "           'lass',\n",
+       "           'mass',\n",
+       "           'pads',\n",
+       "           'pals',\n",
+       "           'pans',\n",
+       "           'paps',\n",
+       "           'pars',\n",
+       "           'past',\n",
+       "           'pats',\n",
+       "           'paws',\n",
+       "           'pays',\n",
+       "           'puss',\n",
+       "           'sass'})"
       ]
      },
-     "execution_count": 52,
+     "execution_count": 98,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2961,7 +1982,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 53,
+   "execution_count": 99,
    "metadata": {},
    "outputs": [
     {
@@ -2970,7 +1991,7 @@
        "[1]"
       ]
      },
-     "execution_count": 53,
+     "execution_count": 99,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2981,7 +2002,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 54,
+   "execution_count": 100,
    "metadata": {},
    "outputs": [
     {
@@ -2990,7 +2011,7 @@
        "[2204]"
       ]
      },
-     "execution_count": 54,
+     "execution_count": 100,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3001,14 +2022,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 55,
+   "execution_count": 101,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "1 loop, best of 3: 8.21 s per loop\n"
+      "1 loop, best of 3: 9.05 s per loop\n"
      ]
     }
    ],
@@ -3019,14 +2040,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 56,
+   "execution_count": 102,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "10 loops, best of 3: 145 ms per loop\n"
+      "10 loops, best of 3: 147 ms per loop\n"
      ]
     }
    ],
@@ -3037,7 +2058,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 57,
+   "execution_count": 103,
    "metadata": {},
    "outputs": [
     {
@@ -3055,7 +2076,7 @@
        " 'exit']"
       ]
      },
-     "execution_count": 57,
+     "execution_count": 103,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3066,7 +2087,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 58,
+   "execution_count": 104,
    "metadata": {
     "collapsed": true
    },
@@ -3090,7 +2111,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 59,
+   "execution_count": 105,
    "metadata": {
     "collapsed": true
    },
@@ -3115,14 +2136,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 60,
+   "execution_count": 106,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "1 loop, best of 3: 334 ms per loop\n"
+      "1 loop, best of 3: 358 ms per loop\n"
      ]
     }
    ],
@@ -3133,15 +2154,15 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 61,
+   "execution_count": 107,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CPU times: user 344 ms, sys: 0 ns, total: 344 ms\n",
-      "Wall time: 342 ms\n"
+      "CPU times: user 384 ms, sys: 0 ns, total: 384 ms\n",
+      "Wall time: 382 ms\n"
      ]
     },
     {
@@ -3150,7 +2171,7 @@
        "14"
       ]
      },
-     "execution_count": 61,
+     "execution_count": 107,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3161,15 +2182,15 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 62,
+   "execution_count": 108,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CPU times: user 92 ms, sys: 0 ns, total: 92 ms\n",
-      "Wall time: 93.7 ms\n"
+      "CPU times: user 112 ms, sys: 0 ns, total: 112 ms\n",
+      "Wall time: 109 ms\n"
      ]
     },
     {
@@ -3178,7 +2199,7 @@
        "15"
       ]
      },
-     "execution_count": 62,
+     "execution_count": 108,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3189,15 +2210,15 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 63,
+   "execution_count": 109,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CPU times: user 32 ms, sys: 0 ns, total: 32 ms\n",
-      "Wall time: 32.8 ms\n"
+      "CPU times: user 40 ms, sys: 0 ns, total: 40 ms\n",
+      "Wall time: 36.5 ms\n"
      ]
     },
     {
@@ -3206,7 +2227,7 @@
        "14"
       ]
      },
-     "execution_count": 63,
+     "execution_count": 109,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3217,15 +2238,15 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 64,
+   "execution_count": 110,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CPU times: user 16 ms, sys: 0 ns, total: 16 ms\n",
-      "Wall time: 16.4 ms\n"
+      "CPU times: user 20 ms, sys: 0 ns, total: 20 ms\n",
+      "Wall time: 18.1 ms\n"
      ]
     },
     {
@@ -3234,7 +2255,7 @@
        "14"
       ]
      },
-     "execution_count": 64,
+     "execution_count": 110,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3245,15 +2266,15 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 65,
+   "execution_count": 111,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CPU times: user 256 ms, sys: 0 ns, total: 256 ms\n",
-      "Wall time: 253 ms\n"
+      "CPU times: user 272 ms, sys: 0 ns, total: 272 ms\n",
+      "Wall time: 267 ms\n"
      ]
     },
     {
@@ -3262,7 +2283,7 @@
        "14"
       ]
      },
-     "execution_count": 65,
+     "execution_count": 111,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3273,15 +2294,15 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 66,
+   "execution_count": 112,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CPU times: user 36 ms, sys: 0 ns, total: 36 ms\n",
-      "Wall time: 34.2 ms\n"
+      "CPU times: user 40 ms, sys: 0 ns, total: 40 ms\n",
+      "Wall time: 37.8 ms\n"
      ]
     },
     {
@@ -3290,7 +2311,7 @@
        "14"
       ]
      },
-     "execution_count": 66,
+     "execution_count": 112,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3301,15 +2322,15 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 67,
+   "execution_count": 113,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "bash bush True\n",
-      "rush bush True\n"
+      "rush bush True\n",
+      "bash bush True\n"
      ]
     },
     {
@@ -3318,7 +2339,7 @@
        "2"
       ]
      },
-     "execution_count": 67,
+     "execution_count": 113,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3335,16 +2356,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 68,
+   "execution_count": 114,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "['gush', 'hush', 'lush', 'mush', 'push', 'tush', 'bosh']"
+       "['gush', 'mush', 'bosh', 'tush', 'lush', 'push', 'hush']"
       ]
      },
-     "execution_count": 68,
+     "execution_count": 114,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3355,16 +2376,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 69,
+   "execution_count": 115,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "('nose', 2)"
+       "('came', 2)"
       ]
      },
-     "execution_count": 69,
+     "execution_count": 115,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3388,16 +2409,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 70,
+   "execution_count": 116,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "'grew'"
+       "'hags'"
       ]
      },
-     "execution_count": 70,
+     "execution_count": 116,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3408,7 +2429,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 71,
+   "execution_count": 117,
    "metadata": {},
    "outputs": [
     {
@@ -3417,7 +2438,7 @@
        "{'bash', 'rush'}"
       ]
      },
-     "execution_count": 71,
+     "execution_count": 117,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3452,7 +2473,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.5.2+"
+   "version": "3.5.3"
   }
  },
  "nbformat": 4,
diff --git a/08-word-chains/explore-word-chain7.ipynb b/08-word-chains/explore-word-chain7.ipynb
index ad49340..c4ccd75 100644
--- a/08-word-chains/explore-word-chain7.ipynb
+++ b/08-word-chains/explore-word-chain7.ipynb
@@ -99,7 +99,9 @@
   {
    "cell_type": "code",
    "execution_count": 10,
-   "metadata": {},
+   "metadata": {
+    "collapsed": true
+   },
    "outputs": [],
    "source": [
     "# neighbours = {w: [n for n in adjacents(w) if n in words]\n",
@@ -109,7 +111,9 @@
   {
    "cell_type": "code",
    "execution_count": 17,
-   "metadata": {},
+   "metadata": {
+    "collapsed": true
+   },
    "outputs": [],
    "source": [
     "worddict = {w: True for w in words}\n",
@@ -2456,7 +2460,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.5.2+"
+   "version": "3.5.3"
   }
  },
  "nbformat": 4,
diff --git a/08-word-chains/rush3.dot b/08-word-chains/rush3.dot
index 6adfe2e..43ddbb4 100644
--- a/08-word-chains/rush3.dot
+++ b/08-word-chains/rush3.dot
@@ -1,636 +1,636 @@
 graph g {
-"buds" -- "buys";
-"rice" -- "rime";
-"rung" -- "runt";
-"pubs" -- "puss";
-"mask" -- "musk";
-"jest" -- "lest";
-"bast" -- "cast";
-"muck" -- "musk";
-"lash" -- "rash";
-"gosh" -- "posh";
-"pose" -- "hose";
-"busy" -- "bury";
-"runt" -- "runs";
-"rash" -- "rasp";
-"husk" -- "hulk";
-"puss" -- "puns";
-"bush" -- "tush";
-"gust" -- "gist";
-"nest" -- "pest";
-"pest" -- "test";
-"last" -- "cast";
-"nest" -- "lest";
-"mute" -- "muse";
-"lath" -- "hath";
-"bask" -- "cask";
-"buds" -- "buss";
-"lass" -- "pass";
-"mule" -- "yule";
-"push" -- "gush";
-"list" -- "mist";
-"bush" -- "bosh";
-"rise" -- "risk";
-"muss" -- "mass";
-"hush" -- "push";
-"musk" -- "rusk";
-"rise" -- "rife";
-"yest" -- "test";
-"duck" -- "muck";
-"rise" -- "rose";
-"pose" -- "rose";
-"pose" -- "lose";
-"puts" -- "puns";
-"fuss" -- "wuss";
+"miss" -- "mass";
+"best" -- "lest";
+"rite" -- "rice";
+"rude" -- "dude";
+"rusk" -- "dusk";
+"cask" -- "case";
+"rest" -- "best";
+"rope" -- "roue";
+"zest" -- "fest";
+"post" -- "pest";
+"tube" -- "rube";
+"bury" -- "buoy";
+"hash" -- "sash";
+"cash" -- "rash";
+"tusk" -- "dusk";
 "puss" -- "pugs";
-"must" -- "mutt";
+"oust" -- "just";
+"rope" -- "rode";
+"rope" -- "robe";
+"hash" -- "hush";
+"mist" -- "gist";
+"puss" -- "buss";
+"bash" -- "mash";
+"hash" -- "wash";
+"must" -- "bust";
+"runs" -- "puns";
+"roue" -- "rode";
+"dunk" -- "dusk";
+"rest" -- "vest";
+"tuck" -- "muck";
+"rune" -- "tune";
+"mash" -- "rash";
+"rile" -- "rise";
+"dust" -- "duet";
+"last" -- "bast";
+"math" -- "lath";
+"rant" -- "rent";
+"best" -- "fest";
+"zest" -- "nest";
+"test" -- "jest";
+"dose" -- "lose";
+"mugs" -- "bugs";
 "rule" -- "rude";
-"bask" -- "bass";
-"yest" -- "west";
-"mesh" -- "mush";
-"buns" -- "bums";
-"pose" -- "nose";
-"ripe" -- "ride";
-"fuss" -- "muss";
-"tush" -- "push";
-"disk" -- "desk";
-"rove" -- "rose";
-"jest" -- "best";
-"jest" -- "pest";
-"must" -- "musk";
-"buss" -- "cuss";
-"best" -- "zest";
-"mule" -- "mute";
-"disk" -- "dusk";
-"rice" -- "rife";
-"rune" -- "ruse";
-"gasp" -- "rasp";
-"rise" -- "ride";
-"hose" -- "lose";
-"yest" -- "jest";
-"pubs" -- "puns";
-"moss" -- "miss";
-"rife" -- "ride";
-"mast" -- "mist";
-"buds" -- "burs";
-"mush" -- "much";
-"rice" -- "rile";
-"hush" -- "bush";
-"buts" -- "butt";
-"gust" -- "rust";
-"rule" -- "yule";
-"mash" -- "bash";
-"gasp" -- "hasp";
-"gust" -- "gush";
-"just" -- "must";
-"fuse" -- "fume";
-"puss" -- "push";
-"cash" -- "hash";
+"mash" -- "mast";
+"mums" -- "bums";
+"hath" -- "bath";
+"bunt" -- "runt";
+"mush" -- "tush";
+"gust" -- "must";
+"lush" -- "bush";
+"math" -- "bath";
+"test" -- "pest";
+"lost" -- "list";
+"bunt" -- "butt";
 "posy" -- "posh";
-"lash" -- "mash";
-"hunt" -- "hunk";
-"post" -- "pest";
-"rust" -- "ruse";
-"bush" -- "gush";
-"rite" -- "rote";
-"rune" -- "tune";
-"cast" -- "cash";
-"bash" -- "bath";
-"bash" -- "dash";
-"rune" -- "rube";
-"role" -- "rope";
-"gosh" -- "josh";
-"ruse" -- "rose";
-"bust" -- "rust";
-"posh" -- "nosh";
-"rule" -- "rile";
-"west" -- "pest";
-"pubs" -- "pups";
-"west" -- "lest";
-"dune" -- "dude";
-"mesa" -- "mesh";
-"mess" -- "mass";
-"gust" -- "lust";
-"rife" -- "ripe";
-"lest" -- "list";
-"gasp" -- "gash";
-"bast" -- "base";
-"buts" -- "bugs";
-"wash" -- "dash";
-"dose" -- "hose";
-"lest" -- "best";
-"lest" -- "pest";
-"gust" -- "bust";
-"puts" -- "buts";
-"tush" -- "mush";
-"robe" -- "rose";
-"such" -- "ouch";
-"puns" -- "buns";
-"bass" -- "pass";
-"rule" -- "role";
-"rune" -- "runs";
-"yest" -- "pest";
-"rush" -- "rust";
-"task" -- "tusk";
-"yest" -- "lest";
-"just" -- "lust";
-"mast" -- "mass";
-"post" -- "lost";
-"dust" -- "oust";
-"muss" -- "mush";
-"role" -- "roue";
-"just" -- "bust";
-"buds" -- "buns";
-"hush" -- "tush";
-"rust" -- "rusk";
-"lash" -- "gash";
-"rush" -- "rash";
-"hath" -- "hash";
-"mist" -- "must";
-"rote" -- "rose";
+"puss" -- "puns";
+"best" -- "vest";
+"rile" -- "role";
+"math" -- "mash";
+"lass" -- "lash";
+"mask" -- "task";
+"pest" -- "vest";
+"lash" -- "last";
+"bash" -- "gash";
+"burs" -- "buds";
+"bunt" -- "hunt";
+"bask" -- "bass";
+"runs" -- "rung";
+"oust" -- "must";
+"pose" -- "lose";
+"rube" -- "lube";
+"rite" -- "ripe";
+"rife" -- "rile";
+"oust" -- "rust";
+"sass" -- "bass";
+"nosh" -- "nose";
+"pose" -- "hose";
+"best" -- "bast";
+"buns" -- "buds";
+"duct" -- "duet";
+"rest" -- "lest";
+"buts" -- "bums";
+"lust" -- "bust";
+"rude" -- "rode";
+"mask" -- "mast";
+"robe" -- "role";
+"dash" -- "mash";
+"list" -- "last";
+"zest" -- "test";
 "bash" -- "bosh";
-"burs" -- "bury";
-"gash" -- "gush";
+"buns" -- "puns";
+"puss" -- "puts";
+"role" -- "roue";
+"rant" -- "runt";
 "runt" -- "hunt";
-"lath" -- "math";
-"husk" -- "hunk";
-"lost" -- "lose";
-"tube" -- "rube";
-"lest" -- "vest";
-"rope" -- "ripe";
-"puss" -- "cuss";
-"runs" -- "rubs";
-"case" -- "cash";
-"role" -- "robe";
-"dude" -- "nude";
-"best" -- "test";
-"west" -- "test";
-"must" -- "dust";
+"pubs" -- "puns";
+"runs" -- "runt";
+"lath" -- "bath";
+"just" -- "gust";
+"rope" -- "rove";
+"ouch" -- "such";
+"dust" -- "gust";
+"base" -- "bast";
+"bush" -- "gush";
+"puns" -- "pugs";
 "boss" -- "bosh";
-"punt" -- "puns";
-"puns" -- "pups";
-"tusk" -- "rusk";
-"dusk" -- "rusk";
-"mugs" -- "bugs";
-"gosh" -- "nosh";
-"lash" -- "cash";
-"nose" -- "lose";
-"oust" -- "rust";
-"wash" -- "hash";
-"jest" -- "rest";
-"west" -- "zest";
+"mast" -- "most";
+"lush" -- "tush";
+"gash" -- "gasp";
+"west" -- "test";
+"lost" -- "lose";
+"cube" -- "lube";
+"wasp" -- "hasp";
+"cash" -- "wash";
+"cube" -- "tube";
+"role" -- "rose";
+"husk" -- "hulk";
+"test" -- "yest";
 "rush" -- "push";
-"west" -- "fest";
-"lass" -- "bass";
-"moss" -- "most";
-"bust" -- "lust";
+"cask" -- "cast";
+"lush" -- "mush";
+"mesa" -- "mess";
+"best" -- "yest";
+"nest" -- "best";
+"west" -- "vest";
+"yest" -- "fest";
+"rush" -- "hush";
+"wash" -- "sash";
+"bash" -- "bast";
+"wash" -- "wish";
+"bask" -- "task";
 "ruby" -- "rubs";
-"pose" -- "dose";
-"dust" -- "lust";
-"wash" -- "gash";
+"rite" -- "rime";
+"muss" -- "mass";
+"yest" -- "pest";
+"list" -- "lust";
+"rice" -- "rife";
+"fuse" -- "fuze";
+"boss" -- "bass";
+"gash" -- "gosh";
+"mast" -- "mass";
+"pubs" -- "pups";
+"buss" -- "bush";
+"tube" -- "lube";
+"ride" -- "rode";
+"miss" -- "mess";
+"mask" -- "bask";
+"hush" -- "gush";
+"posy" -- "rosy";
+"robe" -- "rove";
+"rove" -- "rode";
+"bunt" -- "punt";
+"cuss" -- "buss";
+"rust" -- "gust";
+"mess" -- "moss";
+"rush" -- "gush";
 "rove" -- "roue";
-"gust" -- "oust";
-"wash" -- "bash";
-"zest" -- "test";
-"nest" -- "jest";
-"fest" -- "test";
-"disk" -- "risk";
-"rune" -- "rude";
+"lost" -- "post";
+"cuss" -- "wuss";
+"rife" -- "rise";
+"muss" -- "must";
+"mist" -- "mast";
+"buys" -- "buss";
+"mast" -- "must";
+"zest" -- "yest";
+"burs" -- "buys";
+"rule" -- "rube";
+"rime" -- "rise";
 "buys" -- "bums";
-"wasp" -- "rasp";
-"puss" -- "buss";
-"rote" -- "robe";
+"puts" -- "puns";
+"dude" -- "nude";
+"just" -- "bust";
 "bast" -- "bust";
-"must" -- "lust";
-"rest" -- "test";
-"cask" -- "cash";
-"musk" -- "mush";
-"musk" -- "tusk";
-"mist" -- "gist";
-"muss" -- "buss";
-"dunk" -- "dune";
-"husk" -- "musk";
-"role" -- "rove";
-"just" -- "oust";
-"hush" -- "mush";
-"task" -- "cask";
-"muss" -- "cuss";
-"rise" -- "vise";
+"gush" -- "gust";
+"base" -- "bass";
+"fuse" -- "ruse";
+"bash" -- "rash";
+"best" -- "pest";
+"mash" -- "gash";
+"rose" -- "lose";
+"vest" -- "fest";
+"ouch" -- "much";
+"post" -- "pose";
+"pass" -- "sass";
+"lust" -- "gust";
+"buns" -- "bugs";
+"pest" -- "fest";
 "tush" -- "gush";
-"last" -- "lust";
-"josh" -- "nosh";
-"tush" -- "tusk";
-"hath" -- "bath";
-"most" -- "post";
-"rest" -- "rent";
 "rude" -- "ruse";
-"buns" -- "runs";
-"dunk" -- "duck";
-"rust" -- "lust";
-"task" -- "bask";
-"boss" -- "buss";
-"rise" -- "ruse";
-"duck" -- "dusk";
-"rosy" -- "rose";
-"mast" -- "bast";
-"oust" -- "lust";
-"posy" -- "post";
-"mast" -- "last";
-"gash" -- "mash";
-"bunt" -- "butt";
-"rube" -- "rude";
-"case" -- "cask";
-"rode" -- "rude";
-"dash" -- "hash";
-"lest" -- "rest";
-"lest" -- "fest";
+"nest" -- "lest";
+"wish" -- "dish";
+"wasp" -- "wash";
+"buds" -- "buss";
+"lass" -- "mass";
+"zest" -- "rest";
+"dunk" -- "hunk";
+"lust" -- "must";
+"last" -- "cast";
+"cash" -- "cast";
+"mush" -- "push";
+"rush" -- "ruse";
+"robe" -- "rose";
+"husk" -- "hush";
+"hash" -- "gash";
+"burs" -- "buss";
+"musk" -- "tusk";
+"rash" -- "rasp";
+"rush" -- "bush";
+"role" -- "rode";
+"robe" -- "rote";
+"hush" -- "bush";
+"lost" -- "most";
+"posh" -- "gosh";
+"rove" -- "rote";
+"zest" -- "pest";
+"miss" -- "moss";
+"ruby" -- "rube";
+"rubs" -- "rube";
+"rice" -- "rise";
+"cash" -- "gash";
+"cube" -- "rube";
+"hunk" -- "hunt";
+"rest" -- "pest";
+"posy" -- "pose";
+"lush" -- "rush";
+"rude" -- "nude";
+"dusk" -- "duck";
+"rest" -- "jest";
+"runs" -- "rubs";
+"wasp" -- "gasp";
+"nest" -- "fest";
+"muss" -- "mush";
+"dust" -- "lust";
+"lest" -- "pest";
+"rust" -- "bust";
+"bunt" -- "bust";
+"lest" -- "vest";
+"burs" -- "buts";
+"pubs" -- "puts";
+"muse" -- "must";
+"rile" -- "ride";
+"rise" -- "wise";
+"puss" -- "fuss";
+"cash" -- "mash";
+"zest" -- "jest";
+"last" -- "mast";
+"rope" -- "role";
+"most" -- "must";
+"rush" -- "rusk";
+"bash" -- "dash";
+"tube" -- "tune";
+"sass" -- "sash";
+"nest" -- "pest";
+"gush" -- "push";
+"buds" -- "bugs";
+"rusk" -- "ruse";
+"post" -- "most";
+"bunt" -- "aunt";
+"rush" -- "tush";
+"buns" -- "buts";
+"rise" -- "vise";
+"rite" -- "rile";
+"dust" -- "just";
+"rite" -- "rife";
+"boss" -- "moss";
+"busy" -- "bush";
+"mash" -- "sash";
+"test" -- "lest";
+"puss" -- "pubs";
+"mugs" -- "muss";
+"buts" -- "buds";
+"mess" -- "mesh";
+"mess" -- "muss";
+"husk" -- "musk";
+"bosh" -- "bush";
+"hulk" -- "hunk";
+"bash" -- "sash";
+"bast" -- "bass";
+"zest" -- "west";
+"lass" -- "pass";
 "bash" -- "bush";
-"list" -- "gist";
-"rube" -- "cube";
-"bast" -- "bash";
-"buys" -- "bugs";
-"gash" -- "bash";
-"bask" -- "bash";
-"dust" -- "rust";
-"burs" -- "buns";
-"lath" -- "bath";
-"muck" -- "murk";
-"lest" -- "lost";
-"pose" -- "posh";
-"bury" -- "buoy";
-"punt" -- "aunt";
-"buss" -- "bugs";
+"test" -- "fest";
+"musk" -- "mask";
+"dose" -- "pose";
+"rise" -- "ripe";
+"rash" -- "sash";
+"hash" -- "cash";
+"nest" -- "rest";
 "moss" -- "mass";
+"bugs" -- "pugs";
+"musk" -- "muse";
+"bunt" -- "buns";
+"duct" -- "duck";
+"wash" -- "rash";
+"mash" -- "mesh";
+"cask" -- "bask";
+"muck" -- "much";
+"rule" -- "role";
+"rest" -- "yest";
+"dash" -- "lash";
+"rise" -- "risk";
 "mash" -- "mass";
-"task" -- "mask";
-"posy" -- "rosy";
-"case" -- "base";
-"rune" -- "rule";
-"wash" -- "lash";
-"burs" -- "bums";
-"puts" -- "pups";
-"pose" -- "post";
-"roue" -- "robe";
-"most" -- "lost";
+"bash" -- "base";
+"zest" -- "vest";
+"rush" -- "rust";
 "bash" -- "bass";
-"just" -- "jest";
-"dusk" -- "tusk";
-"lash" -- "hash";
-"mash" -- "rash";
-"gash" -- "cash";
+"rube" -- "ruse";
+"lest" -- "yest";
+"hasp" -- "gasp";
+"lass" -- "last";
+"mush" -- "mesh";
+"rusk" -- "musk";
+"mute" -- "mutt";
+"math" -- "hath";
+"rune" -- "runt";
+"cash" -- "case";
+"test" -- "vest";
+"pups" -- "puns";
+"cash" -- "sash";
+"wasp" -- "rasp";
+"vise" -- "wise";
+"hash" -- "rash";
+"cuss" -- "fuss";
+"dust" -- "duct";
+"posh" -- "push";
 "mush" -- "gush";
-"wash" -- "cash";
-"rite" -- "rile";
-"josh" -- "bosh";
-"gosh" -- "gush";
-"muss" -- "must";
-"puns" -- "runs";
-"aunt" -- "hunt";
-"rove" -- "rote";
-"rote" -- "roue";
-"rile" -- "ripe";
-"buds" -- "bums";
-"mast" -- "must";
-"list" -- "lost";
-"fuss" -- "fuse";
-"post" -- "posh";
-"nest" -- "best";
-"husk" -- "dusk";
-"both" -- "bath";
-"lash" -- "lush";
-"list" -- "last";
-"muss" -- "wuss";
-"dish" -- "dash";
-"rube" -- "lube";
-"bust" -- "bunt";
-"bugs" -- "pugs";
-"rode" -- "rope";
-"sass" -- "bass";
-"rick" -- "risk";
-"bust" -- "dust";
-"rink" -- "risk";
-"rest" -- "best";
-"rest" -- "pest";
-"both" -- "bosh";
-"such" -- "much";
-"desk" -- "dusk";
-"buds" -- "bugs";
-"aunt" -- "runt";
-"busy" -- "buss";
-"runt" -- "rust";
-"jest" -- "fest";
-"muss" -- "miss";
-"mugs" -- "pugs";
-"rule" -- "mule";
-"tune" -- "dune";
-"mash" -- "math";
-"yest" -- "zest";
-"yest" -- "fest";
-"jest" -- "test";
-"bust" -- "must";
-"mutt" -- "butt";
+"tuck" -- "tusk";
+"rude" -- "rube";
+"nest" -- "yest";
+"cash" -- "lash";
+"rose" -- "ruse";
+"rude" -- "ride";
 "fuse" -- "muse";
-"rote" -- "rope";
-"moss" -- "mess";
-"puts" -- "pugs";
+"buss" -- "bugs";
+"muse" -- "mush";
+"lath" -- "lash";
+"husk" -- "dusk";
+"rune" -- "rung";
+"rime" -- "ripe";
+"bush" -- "bust";
+"oust" -- "lust";
+"puss" -- "pups";
+"rice" -- "ripe";
+"buss" -- "bust";
+"miss" -- "muss";
+"bash" -- "bath";
+"rope" -- "ripe";
+"muse" -- "ruse";
+"mash" -- "mask";
+"roue" -- "rote";
+"dash" -- "sash";
+"dust" -- "rust";
+"musk" -- "murk";
+"rode" -- "rote";
+"lash" -- "rash";
+"hush" -- "mush";
+"dash" -- "wash";
+"pose" -- "rose";
+"just" -- "must";
+"lath" -- "hath";
+"musk" -- "muss";
+"buys" -- "bugs";
+"post" -- "posh";
+"mush" -- "much";
+"muss" -- "moss";
 "sass" -- "mass";
-"musk" -- "dusk";
-"busy" -- "bust";
-"nose" -- "hose";
-"dunk" -- "hunk";
-"bust" -- "bush";
-"burs" -- "bugs";
-"ruby" -- "rube";
-"lash" -- "dash";
-"gash" -- "rash";
-"mash" -- "cash";
-"buys" -- "buns";
-"buss" -- "bush";
-"pooh" -- "posh";
-"muss" -- "mess";
-"puss" -- "puts";
-"hose" -- "rose";
-"miss" -- "mess";
-"ruse" -- "muse";
-"buns" -- "bunt";
-"mast" -- "mask";
-"hulk" -- "hunk";
-"just" -- "dust";
+"mass" -- "bass";
+"bash" -- "lash";
+"miss" -- "mist";
+"lass" -- "bass";
+"dune" -- "dunk";
+"lass" -- "sass";
+"musk" -- "muck";
+"mesa" -- "mesh";
+"rule" -- "mule";
+"dune" -- "rune";
+"lust" -- "lest";
+"west" -- "best";
+"lash" -- "mash";
+"bush" -- "tush";
+"musk" -- "must";
+"best" -- "bust";
+"rent" -- "runt";
+"rove" -- "rose";
+"posy" -- "post";
+"just" -- "rust";
+"oust" -- "dust";
+"mast" -- "cast";
+"bask" -- "bast";
 "buts" -- "buss";
-"mash" -- "mask";
-"moss" -- "muss";
-"wuss" -- "buss";
-"gosh" -- "bosh";
-"mums" -- "mugs";
-"fest" -- "vest";
-"lash" -- "lass";
-"rise" -- "rite";
-"just" -- "gust";
-"list" -- "lust";
-"hush" -- "husk";
-"rush" -- "lush";
-"buds" -- "buts";
-"must" -- "rust";
-"mash" -- "mush";
+"posh" -- "pose";
+"dune" -- "dude";
+"cash" -- "cask";
+"rime" -- "ride";
+"rice" -- "rick";
+"hasp" -- "rasp";
+"rude" -- "rune";
+"both" -- "bath";
+"mule" -- "muse";
+"nosh" -- "josh";
+"buss" -- "bums";
+"rule" -- "yule";
+"robe" -- "roue";
+"aunt" -- "hunt";
+"fuse" -- "fume";
+"dose" -- "nose";
+"runt" -- "punt";
+"cuss" -- "muss";
+"fuse" -- "fuss";
+"rice" -- "rime";
+"fuss" -- "wuss";
+"dash" -- "hash";
+"husk" -- "rusk";
+"dose" -- "rose";
+"buns" -- "bums";
+"disk" -- "dusk";
+"hash" -- "hasp";
+"buts" -- "butt";
+"bosh" -- "gosh";
+"muse" -- "muss";
+"hash" -- "mash";
 "tuck" -- "duck";
-"rash" -- "cash";
-"rude" -- "nude";
-"wash" -- "mash";
-"nest" -- "vest";
-"hunt" -- "bunt";
-"bosh" -- "nosh";
-"puns" -- "pugs";
-"muck" -- "much";
-"rope" -- "roue";
-"rune" -- "dune";
-"pest" -- "zest";
-"mash" -- "sash";
-"rise" -- "wise";
-"best" -- "pest";
+"bash" -- "wash";
+"rule" -- "ruse";
 "puss" -- "wuss";
-"fest" -- "zest";
-"must" -- "oust";
+"dose" -- "hose";
+"last" -- "lest";
+"puss" -- "muss";
+"mutt" -- "must";
+"mute" -- "mule";
+"mute" -- "muse";
+"lest" -- "jest";
 "wish" -- "wise";
-"mash" -- "mesh";
-"pose" -- "posy";
-"lest" -- "lust";
-"lest" -- "test";
-"rite" -- "ripe";
-"mums" -- "muss";
-"rife" -- "rile";
-"lash" -- "bash";
-"ride" -- "rude";
-"dose" -- "nose";
-"rube" -- "ruse";
-"rube" -- "rubs";
-"bask" -- "base";
+"runt" -- "rust";
+"rung" -- "runt";
+"disk" -- "dish";
+"mask" -- "mass";
+"wash" -- "gash";
+"oust" -- "gust";
+"nest" -- "west";
 "rope" -- "rose";
-"fuze" -- "fuse";
-"rise" -- "rile";
-"hasp" -- "rasp";
-"must" -- "muse";
-"dunk" -- "dusk";
-"cash" -- "sash";
-"miss" -- "mass";
+"rite" -- "ride";
+"rose" -- "rote";
+"mums" -- "muss";
+"boss" -- "buss";
 "puss" -- "pass";
-"musk" -- "muse";
-"tube" -- "lube";
-"buns" -- "bugs";
-"rash" -- "sash";
-"mast" -- "mash";
-"fuss" -- "cuss";
-"rise" -- "rice";
-"role" -- "rose";
-"fuse" -- "ruse";
-"bass" -- "base";
-"rode" -- "ride";
-"yest" -- "best";
-"lass" -- "sass";
+"gash" -- "gush";
+"puts" -- "pugs";
+"posh" -- "bosh";
+"mugs" -- "pugs";
+"rose" -- "hose";
+"moss" -- "most";
 "bums" -- "bugs";
-"ouch" -- "much";
-"boss" -- "bass";
-"mass" -- "pass";
-"mast" -- "cast";
-"tube" -- "tune";
-"bust" -- "best";
-"rest" -- "fest";
-"muss" -- "muse";
+"roue" -- "rose";
+"jest" -- "fest";
+"buoy" -- "busy";
+"mist" -- "must";
+"burs" -- "bugs";
+"test" -- "best";
+"lust" -- "rust";
+"rile" -- "ripe";
+"muss" -- "buss";
+"rick" -- "risk";
+"murk" -- "muck";
+"cask" -- "mask";
+"oust" -- "bust";
+"rest" -- "rust";
+"nosh" -- "gosh";
+"muss" -- "wuss";
+"disk" -- "desk";
+"rest" -- "rent";
+"yest" -- "jest";
+"zest" -- "lest";
+"gosh" -- "josh";
+"puts" -- "pups";
+"nest" -- "jest";
+"lost" -- "lust";
+"jest" -- "vest";
+"butt" -- "bust";
+"pooh" -- "posh";
+"gust" -- "gist";
+"bosh" -- "josh";
+"rusk" -- "rust";
+"cask" -- "task";
+"rise" -- "ruse";
+"buds" -- "buys";
+"lash" -- "gash";
+"rise" -- "rose";
+"pose" -- "nose";
+"bush" -- "push";
+"dusk" -- "desk";
+"puss" -- "cuss";
+"posh" -- "josh";
+"best" -- "jest";
+"risk" -- "rink";
+"muck" -- "duck";
+"disk" -- "risk";
+"rune" -- "rube";
+"list" -- "gist";
+"hose" -- "nose";
+"pubs" -- "rubs";
+"mast" -- "bast";
+"gash" -- "sash";
+"musk" -- "dusk";
+"aunt" -- "runt";
+"last" -- "lust";
+"burs" -- "bury";
+"buts" -- "bugs";
+"lash" -- "wash";
+"lost" -- "lest";
+"dust" -- "must";
+"tusk" -- "tush";
+"nest" -- "test";
 "role" -- "rote";
-"last" -- "lost";
-"mist" -- "miss";
-"gust" -- "dust";
-"rice" -- "ripe";
-"dust" -- "dusk";
-"lest" -- "zest";
-"gash" -- "dash";
-"best" -- "fest";
-"rife" -- "rime";
-"rush" -- "mush";
-"mute" -- "mutt";
-"lass" -- "mass";
-"mash" -- "hash";
-"nest" -- "zest";
-"wish" -- "dish";
-"nest" -- "fest";
-"rune" -- "rung";
-"tube" -- "cube";
-"hush" -- "lush";
-"lass" -- "last";
-"fuze" -- "fume";
-"wasp" -- "hasp";
-"puss" -- "muss";
-"rode" -- "roue";
-"punt" -- "bunt";
-"bash" -- "rash";
-"disk" -- "dish";
-"must" -- "mush";
-"lush" -- "mush";
-"nose" -- "nosh";
+"rasp" -- "gasp";
+"dunk" -- "duck";
+"mugs" -- "mums";
+"burs" -- "bums";
+"gush" -- "gosh";
+"mist" -- "most";
+"rush" -- "rash";
+"mist" -- "list";
+"hush" -- "tush";
+"nest" -- "vest";
+"buns" -- "runs";
 "lush" -- "lust";
-"buts" -- "bums";
-"nest" -- "rest";
-"bush" -- "push";
-"lost" -- "lust";
-"mast" -- "most";
-"duet" -- "dust";
-"hush" -- "rush";
-"rule" -- "ruse";
-"rite" -- "ride";
-"sass" -- "sash";
-"wash" -- "rash";
-"bast" -- "bass";
-"aunt" -- "bunt";
-"bast" -- "best";
-"mesh" -- "mess";
+"dash" -- "gash";
+"busy" -- "bust";
+"rice" -- "rile";
+"buds" -- "bums";
+"lost" -- "last";
+"west" -- "rest";
+"lush" -- "lash";
+"mess" -- "mass";
+"pest" -- "jest";
+"tush" -- "push";
+"buns" -- "buys";
+"just" -- "lust";
+"pups" -- "pugs";
+"rice" -- "ride";
+"rest" -- "fest";
+"rule" -- "rune";
+"bask" -- "base";
+"zest" -- "best";
+"base" -- "case";
+"mule" -- "yule";
+"musk" -- "mush";
+"posh" -- "nosh";
+"rosy" -- "rose";
+"buss" -- "wuss";
+"fuss" -- "buss";
+"bash" -- "cash";
+"west" -- "lest";
+"both" -- "bosh";
+"cast" -- "bast";
+"nosh" -- "bosh";
+"role" -- "rove";
 "lash" -- "sash";
-"rash" -- "hash";
-"rush" -- "gush";
-"just" -- "rust";
-"buts" -- "buns";
 "case" -- "cast";
-"rime" -- "ride";
-"vest" -- "pest";
-"bust" -- "oust";
-"bust" -- "butt";
-"buts" -- "burs";
-"math" -- "bath";
-"role" -- "rile";
-"ruse" -- "rusk";
-"rite" -- "rice";
-"rite" -- "rife";
-"busy" -- "buoy";
-"rile" -- "rime";
-"rest" -- "zest";
-"wasp" -- "wash";
-"bass" -- "buss";
-"mash" -- "dash";
-"yest" -- "vest";
-"rode" -- "role";
-"jest" -- "zest";
-"hash" -- "sash";
-"rush" -- "tush";
-"lest" -- "last";
-"best" -- "vest";
-"wuss" -- "cuss";
-"puss" -- "fuss";
-"dose" -- "lose";
-"rice" -- "ride";
-"rush" -- "rusk";
-"punt" -- "runt";
-"west" -- "vest";
-"lush" -- "tush";
-"bust" -- "buss";
-"rash" -- "dash";
-"sass" -- "pass";
-"rise" -- "ripe";
-"rode" -- "rove";
-"dose" -- "rose";
-"pubs" -- "puts";
-"vest" -- "test";
-"muss" -- "musk";
-"nest" -- "test";
-"burs" -- "buss";
-"cash" -- "dash";
-"pubs" -- "rubs";
-"gust" -- "must";
-"tuck" -- "tusk";
-"rose" -- "lose";
-"husk" -- "tusk";
-"rube" -- "robe";
-"mush" -- "muse";
-"rush" -- "bush";
-"rove" -- "rope";
-"vest" -- "zest";
-"roue" -- "rose";
-"murk" -- "musk";
-"josh" -- "posh";
-"posh" -- "bosh";
-"hath" -- "math";
-"lush" -- "gush";
-"nest" -- "west";
-"hasp" -- "hash";
-"mule" -- "muse";
+"punt" -- "hunt";
+"rite" -- "rote";
+"west" -- "yest";
+"hose" -- "lose";
+"pass" -- "bass";
+"mutt" -- "butt";
+"hush" -- "push";
+"buns" -- "buss";
+"burs" -- "buns";
+"wash" -- "mash";
 "bash" -- "hash";
-"nose" -- "rose";
-"gash" -- "sash";
-"risk" -- "rusk";
-"west" -- "best";
-"rile" -- "ride";
-"lash" -- "last";
-"rode" -- "rote";
-"runt" -- "rant";
-"dash" -- "sash";
-"buss" -- "bums";
-"puss" -- "pups";
-"husk" -- "rusk";
-"buts" -- "buys";
-"bass" -- "mass";
+"fume" -- "fuze";
+"runs" -- "rune";
+"rife" -- "rime";
+"rife" -- "ripe";
+"ramp" -- "rasp";
+"rusk" -- "risk";
+"rile" -- "rime";
+"rick" -- "rink";
 "west" -- "jest";
-"wasp" -- "gasp";
-"west" -- "rest";
-"fest" -- "pest";
-"rush" -- "ruse";
-"rung" -- "runs";
-"rink" -- "rick";
-"gash" -- "gosh";
-"mask" -- "cask";
-"duet" -- "duct";
-"yest" -- "nest";
-"rice" -- "rick";
-"rasp" -- "ramp";
-"duck" -- "duct";
-"rule" -- "rube";
-"rent" -- "rant";
+"buss" -- "busy";
+"rope" -- "rote";
+"just" -- "jest";
+"buts" -- "buys";
 "lush" -- "push";
-"bush" -- "mush";
-"buss" -- "buns";
-"bast" -- "last";
-"rune" -- "runt";
-"mist" -- "most";
-"bash" -- "cash";
-"rite" -- "rime";
-"cube" -- "lube";
-"dude" -- "rude";
-"punt" -- "hunt";
-"pugs" -- "pups";
-"yest" -- "rest";
-"runt" -- "rent";
-"moss" -- "boss";
-"wash" -- "wish";
-"dust" -- "duct";
-"rope" -- "robe";
-"mesa" -- "mess";
-"tuck" -- "muck";
-"vise" -- "wise";
-"cask" -- "cast";
-"busy" -- "bush";
-"runt" -- "bunt";
-"fuss" -- "buss";
-"hush" -- "hash";
-"rise" -- "rime";
-"rode" -- "rose";
-"rode" -- "robe";
+"rusk" -- "tusk";
+"mash" -- "mush";
+"rest" -- "test";
+"rush" -- "mush";
+"ride" -- "ripe";
+"robe" -- "rube";
+"bash" -- "bask";
+"rule" -- "rile";
+"bury" -- "busy";
+"mush" -- "must";
+"buss" -- "bass";
+"hash" -- "hath";
+"aunt" -- "punt";
+"gash" -- "rash";
+"puss" -- "push";
+"rite" -- "rise";
+"lush" -- "hush";
+"lose" -- "nose";
+"lest" -- "fest";
+"dash" -- "cash";
+"punt" -- "puns";
+"list" -- "lest";
+"hash" -- "lash";
+"rose" -- "rode";
+"husk" -- "hunk";
+"rust" -- "ruse";
+"mush" -- "bush";
+"rune" -- "ruse";
+"dust" -- "bust";
+"robe" -- "rode";
+"rise" -- "ride";
+"tusk" -- "task";
+"pass" -- "mass";
+"west" -- "pest";
+"husk" -- "tusk";
+"muss" -- "fuss";
 "pubs" -- "pugs";
-"mums" -- "bums";
-"bask" -- "bast";
-"lath" -- "lash";
-"jest" -- "vest";
-"rest" -- "vest";
-"rove" -- "robe";
-"bask" -- "mask";
-"must" -- "most";
-"bash" -- "sash";
-"buys" -- "buss";
-"burs" -- "buys";
-"rest" -- "rust";
-"mugs" -- "muss";
-"wash" -- "sash";
-"ripe" -- "rime";
-"gash" -- "hash";
-"lush" -- "bush";
-"mush" -- "push";
-"mask" -- "mass";
-"hush" -- "gush";
-"posh" -- "push";
-"bash" -- "base";
+"dust" -- "dusk";
+"rose" -- "nose";
+"such" -- "much";
+"buts" -- "puts";
+"lush" -- "gush";
+"rife" -- "ride";
+"dash" -- "rash";
+"dash" -- "dish";
+"gust" -- "bust";
+"yest" -- "vest";
+"rust" -- "must";
+"dune" -- "tune";
+"west" -- "fest";
 }
diff --git a/08-word-chains/visa-woes-solution.ipynb b/08-word-chains/visa-woes-solution.ipynb
index 009e187..a030d8a 100644
--- a/08-word-chains/visa-woes-solution.ipynb
+++ b/08-word-chains/visa-woes-solution.ipynb
@@ -50,9 +50,136 @@
     "How many different offices could you visit in no more than 10 steps from `coax`?"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Worked example solution: part 1\n",
+    "This is the first of two tasks intended to exercise skills developed in M269. In this case, this is about search. I won't go over the general idea of search itself here, as there are loads of tutorials online about it. Instead, I'll talk about the specific way I've implmeneted it in this solution.\n",
+    "\n",
+    "(See below for the <a href=\"#part2\">discussion of part 2</a>.)\n",
+    "\n",
+    "## Search\n",
+    "The offices/words can be thought of as a graph of nodes and edges. Each word is a node, and there's an edge between two words if those words differ by one letter. The diagrams below show the connections between words that are one step and two steps away from 'rush'.\n",
+    "\n",
+    "| Words one step from 'rush' | Words two steps from 'rush' |\n",
+    "| ------------- | ------------- |\n",
+    "| <a href=\"rush1.dot.png\"><img src=\"rush1.dot.png\" alt=\"Words one step from 'rush'\" style=\"width: 200px;\"/></a>     | <a href=\"rush2.dot.png\"><img src=\"rush2.dot.png\" alt=\"Words two steps from 'rush'\" style=\"width: 200px;\"/></a> |\n",
+    "\n",
+    "The task is to find a path, a sequence of words, from the starting word to the destination. This is a classic search problem.\n",
+    "\n",
+    "The key data structure is the _agenda_, a set of partial routes. We take a partial route from the agenda and _extend_ it with the words/rooms reachable from the end of the partial route, giving a new set of partial routes. Those are added back into the agenda.\n",
+    "\n",
+    "Search finishes either when the partial route we're processing is a solution (i.e. goes form the origin to destination room) or the agenda becomes empty.\n",
+    "\n",
+    "For instance, say we're going from `ache` to `ashy`. The initial agenda consists of just one partial route, and that partial route contains just `ache`.\n",
+    "\n",
+    "```\n",
+    "ache\n",
+    "```\n",
+    "\n",
+    "We take that item off the agenda, extend it (with `acne`, `acme`, `acre`, and `achy` as neighbours of `ache`). When we add those four items to the agenda, we get \n",
+    "\n",
+    "```\n",
+    "ache -> acne\n",
+    "ache -> acme\n",
+    "ache -> acre\n",
+    "ache -> achy\n",
+    "```\n",
+    "\n",
+    "We then proces the `ache -> acne` partial path, extending it with `acme` and `acre`, giving the agenda:\n",
+    "\n",
+    "```\n",
+    "ache -> acme\n",
+    "ache -> acre\n",
+    "ache -> achy\n",
+    "ache -> acne -> acme\n",
+    "ache -> acne -> acre\n",
+    "```\n",
+    "\n",
+    "(Note that while `ache` is adjacent to `acne`, we don't want to create a new partial path to `ache` as we've already visited it in this path.)\n",
+    "\n",
+    "We then proces the `ache -> acme` partial path, extending it with `acne` and `acre`, giving the agenda:\n",
+    "\n",
+    "```\n",
+    "ache -> acre\n",
+    "ache -> achy\n",
+    "ache -> acne -> acme\n",
+    "ache -> acne -> acre\n",
+    "ache -> acme -> acne\n",
+    "ache -> acme -> acre\n",
+    "```\n",
+    "\n",
+    "We then do `ache -> acre` and `ache -> achy` to give:\n",
+    "\n",
+    "```\n",
+    "ache -> acne -> acme\n",
+    "ache -> acne -> acre\n",
+    "ache -> acme -> acne\n",
+    "ache -> acme -> acre\n",
+    "ache -> acre -> acne\n",
+    "ache -> acre -> acme\n",
+    "ache -> achy -> ashy\n",
+    "```\n",
+    "\n",
+    "`ache -> acne -> acme` has only one valid extension, so we get:\n",
+    "\n",
+    "```\n",
+    "ache -> acne -> acre\n",
+    "ache -> acme -> acne\n",
+    "ache -> acme -> acre\n",
+    "ache -> acre -> acne\n",
+    "ache -> acre -> acme\n",
+    "ache -> achy -> ashy\n",
+    "ache -> acne -> acme -> acre\n",
+    "```\n",
+    "\n",
+    "We process all the other partial paths in turn until we get to the agenda looking like:\n",
+    "```\n",
+    "ache -> achy -> ashy\n",
+    "ache -> acne -> acme -> acre\n",
+    "ache -> acne -> acre -> acme\n",
+    "ache -> acme -> acne -> acre\n",
+    "ache -> acme -> acre -> acne\n",
+    "ache -> acre -> acne -> acme\n",
+    "ache -> acre -> acme -> acne\n",
+    "```\n",
+    "At this point, the first partial path in the agenda is a solution, so we report success and return that path.\n",
+    "\n",
+    "With breadth-first search, we add the newly-discovered partial paths to the end of the agenda, meaning we go through the graph one layer at a time. If we add the new partial paths to the front of the agenda, we have depth-first search, where we explore one trail fully before backtracking and trying another.\n",
+    "\n",
+    "There are other clever things we can do, such as sorting the agenda by predicted distance to go, which can speed things up.\n",
+    "\n",
+    "## Agenda and paths\n",
+    "As each partial path is a sequence of words in order, it makes sense to store it as a Python `list` of words. For breadth-first and depth-first searches, the agenda is a sequence of partial paths. Again, it makes sense to store this a a Python `list` of partial paths.\n",
+    "\n",
+    "For A* search, the agenda is sorted by the sum of path length and predicted cost to complete the path. In this case, it makes sense to represent the agenda by a priority queue, also known as a heap. I decided to use the standard Python `heapq` library, rather than the one used in M269. Partial paths are put on the heap with `heappush` and the partial path with the lowest cost is removed with `heappop`. \n",
+    "\n",
+    "## The graph of words\n",
+    "How to represent the graph of words? In the input, the connections between words are implicit, so we need to write a little procedure that returns all the neighbouring words for the word passed in. \n",
+    "\n",
+    "There's also a choice here: to we calculate and store the explicit graph of words, or do we rediscover the neighbours every time we want to process a word? The first approach consumes space to reduce time; the second uses time to reduce space. \n",
+    "\n",
+    "In this case, as there are only 2300 words and 20,000 connections, it's not a lot of space. The search will be examining lots of nodes, so I took a decision to explicity cache all the word neighbour relations first, then just look them up as needed. \n",
+    "\n",
+    "(It turns out this wasn't a good idea in terms of raw perfromance. Generating the graph takes ~130ms, but seems to give just about no change in performance for any search algorithm. Ho hum, but an example of where a [premature optimistion](https://en.wikiquote.org/wiki/Donald_Knuth) turns out to be costly!)\n",
+    "\n",
+    "## Important optimisation: closed sets\n",
+    "If you look at the diagrams and traces above, you'll see that the graph of words is very heavily connected, with several different routes from one word to another. But we often don't need to try out all these alternatives. If we're considering a partial route that ends at a particular word _w_, and we've already found another partial route to _w_ that's no longer than this one, there's no need to continue analysing this one. For instance, in the trace above, there's a route `ache -> acne -> acme`, but we've already found the route `ache -> acme`, so we can discard the `ache -> acne -> acme` alternative without worrying about missing possible solutions.\n",
+    "\n",
+    "If we use something like breadth-first search, we know that the first time we encounter a new word is the shortest path to that word. That means that all subsequent times we arrive that that word, we know we can discard that partial path. \n",
+    "\n",
+    "We maintain a `closed set` of the words we've already processed. We can use that set in two places. Either we check the partial path when we take it off the agenda, or we use the closed set to reduce the number of partial paths generated at each step. In the implementation below, I do the latter.\n",
+    "\n",
+    "## Another optimisation: `list` or `set` of words?\n",
+    "The obvious way to represent the known words is as a list. But, we don't care about the order of items in the collection of words. All we do with them is check for existence of a word, and iterate through the whole collection. In these cases, the Python `set` is a much more efficient data structure than the Pyhton `list`, as it uses something like a `dict` underneath. This means membership checking is much faster while iteration takes about the same amount of time.\n",
+    "\n",
+    "Therefore, rather than using `list`s, we'll use `set`s where possible. In fact, as the set of words doesn't change, we can use the `frozenset` type to indicate that the set is immutable."
+   ]
+  },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 116,
    "metadata": {
     "collapsed": true
    },
@@ -64,7 +191,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 117,
    "metadata": {},
    "outputs": [
     {
@@ -73,46 +200,73 @@
        "2336"
       ]
      },
-     "execution_count": 3,
+     "execution_count": 117,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "words = [w.strip() for w in open('08-rooms.txt').readlines()]\n",
+    "words = frozenset(w.strip() for w in open('08-rooms.txt').readlines())\n",
     "len(words)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 191,
    "metadata": {
     "collapsed": true
    },
    "outputs": [],
    "source": [
     "def adjacents(word):\n",
-    "    return [word[0:i] + l + word[i+1:]\n",
+    "    return frozenset(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]]"
+    "           if l != word[i])"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
+   "execution_count": 192,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "10 loops, best of 3: 130 ms per loop\n"
+     ]
+    }
+   ],
    "source": [
-    "neighbours = {w: [n for n in adjacents(w) if n in words]\n",
+    "%%timeit\n",
+    "neighbours = {w: frozenset(n for n in adjacents(w) if n in words)\n",
     "             for w in words}"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 193,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "20092"
+      ]
+     },
+     "execution_count": 193,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "sum(len(neighbours[w]) for w in neighbours)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 233,
    "metadata": {
     "collapsed": true
    },
@@ -125,7 +279,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 195,
    "metadata": {
     "collapsed": true
    },
@@ -138,7 +292,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 196,
    "metadata": {
     "collapsed": true
    },
@@ -155,21 +309,24 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 197,
    "metadata": {
     "collapsed": true
    },
    "outputs": [],
    "source": [
-    "def extend_raw(chain):\n",
-    "    nbrs = [w for w in adjacents(chain[-1]) if w in words]\n",
+    "def extend_raw(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,
+   "execution_count": 198,
    "metadata": {
     "collapsed": true
    },
@@ -195,7 +352,33 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 172,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def bfs_search_raw(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_raw(current)\n",
+    "            agenda = agenda[1:] + successors\n",
+    "    if finished:\n",
+    "        return current\n",
+    "    else:\n",
+    "        return None        "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 173,
    "metadata": {
     "collapsed": true
    },
@@ -223,7 +406,35 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 181,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def bfs_search_closed_raw(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_raw(current, closed)\n",
+    "            agenda = agenda[1:] + successors\n",
+    "    if finished:\n",
+    "        return current\n",
+    "    else:\n",
+    "        return None   "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 127,
    "metadata": {
     "collapsed": true
    },
@@ -249,7 +460,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 128,
    "metadata": {
     "collapsed": true
    },
@@ -277,7 +488,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 129,
    "metadata": {
     "collapsed": true
    },
@@ -306,7 +517,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 130,
    "metadata": {
     "collapsed": true
    },
@@ -336,27 +547,27 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 234,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "['vice', 'dice', 'dire', 'dare', 'ware', 'wars']"
+       "['coax', 'coat', 'boat', 'boar', 'soar', 'star', 'stay']"
       ]
      },
-     "execution_count": 16,
+     "execution_count": 234,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "astar_search('vice', 'wars')"
+    "astar_search('coax', 'stay')"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 235,
    "metadata": {},
    "outputs": [
     {
@@ -365,7 +576,7 @@
        "['vice', 'dice', 'dire', 'dare', 'ware', 'wars']"
       ]
      },
-     "execution_count": 17,
+     "execution_count": 235,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -376,7 +587,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 201,
    "metadata": {},
    "outputs": [
     {
@@ -385,7 +596,7 @@
        "['boon', 'boot', 'bolt', 'belt', 'bell', 'sell']"
       ]
      },
-     "execution_count": 18,
+     "execution_count": 201,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -396,27 +607,27 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 236,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "6"
+       "7"
       ]
      },
-     "execution_count": 19,
+     "execution_count": 236,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "len(astar_search('vice', 'wars'))"
+    "len(astar_search('coax', 'stay'))"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 203,
    "metadata": {
     "collapsed": true
    },
@@ -427,146 +638,251 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 237,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "6"
+       "7"
       ]
      },
-     "execution_count": 21,
+     "execution_count": 237,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "len(bfs_search_closed('vice', 'wars'))"
+    "len(bfs_search_closed('coax', 'stay'))"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 238,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "793"
+       "458"
       ]
      },
-     "execution_count": 22,
+     "execution_count": 238,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "len(dfs_search('vice', 'wars'))"
+    "len(dfs_search('coax', 'stay'))"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 239,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "10000 loops, best of 3: 157 µs per loop\n"
+      "1000 loops, best of 3: 605 µs per loop\n"
      ]
     }
    ],
    "source": [
     "%%timeit\n",
-    "astar_search('vice', 'wars')"
+    "astar_search('coax', 'stay')"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 24,
+   "execution_count": 240,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "100 loops, best of 3: 15.5 ms per loop\n"
+      "1000 loops, best of 3: 607 µs per loop\n"
      ]
     }
    ],
    "source": [
     "%%timeit\n",
-    "astar_search_raw('vice', 'wars')"
+    "astar_search_raw('coax', 'stay')"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
+   "execution_count": 241,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "10000 loops, best of 3: 166 µs per loop\n"
+      "1000 loops, best of 3: 552 µs per loop\n"
      ]
     }
    ],
    "source": [
     "%%timeit\n",
-    "astar_search_closed('vice', 'wars')"
+    "astar_search_closed('coax', 'stay')"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 26,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
+   "execution_count": 243,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1 loop, best of 3: 4min 25s per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "bfs_search('coax', 'stay')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 244,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1 loop, best of 3: 4min 25s per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "bfs_search_raw('coax', 'stay')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 245,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1 loop, best of 3: 810 ms per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "bfs_search_closed('coax', 'stay')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 246,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1 loop, best of 3: 814 ms per loop\n"
+     ]
+    }
+   ],
    "source": [
-    "# %%timeit\n",
-    "# bfs_search('vice', 'wars')"
+    "%%timeit\n",
+    "bfs_search_closed_raw('coax', 'stay')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 247,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "10 loops, best of 3: 26.8 ms per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "dfs_search('coax', 'stay')"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 27,
+   "execution_count": 248,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "1 loop, best of 3: 554 ms per loop\n"
+      "1 loop, best of 3: 4.39 s per loop\n"
      ]
     }
    ],
    "source": [
     "%%timeit\n",
-    "bfs_search_closed('vice', 'wars')"
+    "astar_search('amen', 'doff')"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 28,
+   "execution_count": 249,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "10 loops, best of 3: 90.6 ms per loop\n"
+      "1 loop, best of 3: 4.4 s per loop\n"
      ]
     }
    ],
    "source": [
     "%%timeit\n",
-    "dfs_search('vice', 'wars')"
+    "astar_search_raw('amen', 'doff')"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 250,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "10 loops, best of 3: 87.4 ms per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "astar_search_closed('amen', 'doff')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -580,12 +896,33 @@
     "\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`?"
+    "How many words are reachable in up to ten steps from `coax`?"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "\n",
+    "# <a name=\"part2\"></a>Worked example solution: part 2\n",
+    "After all the mucking around with search algorithms, this is actually much easier. It's all to do with building up sets.\n",
+    "\n",
+    "The basic idea is to maintain a `set` of reachable words which is extended in passes. In each pass, we find all the neighbours of all the words in the reachable word set, and add those neighbours to the set of reachable words. We just do the number of passes specified in in the task.\n",
+    "\n",
+    "In the code below, `reachable` is set of reachable words and `extras` is the set of new words found. As an optimisation, I use the set `boundary` to hold the words added in the previous pass, as the new words to add to `reachable` must be neighbours of a word in the `boundary`: all words that are neighbours of the 'interior' of the set of reachable words have already been added. so there's no need to process them again.\n",
+    "\n",
+    "The `trim_extras` flag is for another optimisation: eacy time we add some more words to `extras`, remove words which are already in `reachable`. That will make the later update of `reachable` faster.\n",
+    "\n",
+    "This approach is quick, as its based on sets and set membership checking, which is a fast process.\n",
+    "\n",
+    "This also suggests another way of solving part 1. Start at depth 1, and find all the words reachable at that depth. If the target word is in the reachable set, report success. If not, increment the depth and find the reachable words again.\n",
+    "\n",
+    "This approach does give the right answer of the minimal distance from source to goal words, but it doesn't give any information about the route to take to go from one word to another; the route is something returned by the search algorithms above."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 29,
+   "execution_count": 217,
    "metadata": {
     "collapsed": true
    },
@@ -607,7 +944,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 30,
+   "execution_count": 218,
    "metadata": {},
    "outputs": [
     {
@@ -626,7 +963,7 @@
        " 'rasp']"
       ]
      },
-     "execution_count": 30,
+     "execution_count": 218,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -637,7 +974,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 31,
+   "execution_count": 219,
    "metadata": {
     "scrolled": true
    },
@@ -649,7 +986,7 @@
        " '`bash`, `cash`, `dash`, `gash`, `hash`, `lash`, `mash`, `rasp`, `rush`, `sash`, `wash`')"
       ]
      },
-     "execution_count": 31,
+     "execution_count": 219,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -660,7 +997,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 32,
+   "execution_count": 220,
    "metadata": {
     "scrolled": true
    },
@@ -672,7 +1009,7 @@
        " '<code>bash</code>, <code>cash</code>, <code>dash</code>, <code>gash</code>, <code>hash</code>, <code>lash</code>, <code>mash</code>, <code>rasp</code>, <code>rush</code>, <code>sash</code>, <code>wash</code>')"
       ]
      },
-     "execution_count": 32,
+     "execution_count": 220,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -683,7 +1020,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 33,
+   "execution_count": 221,
    "metadata": {
     "scrolled": true
    },
@@ -695,7 +1032,7 @@
        " '`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": 33,
+     "execution_count": 221,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -706,7 +1043,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 34,
+   "execution_count": 222,
    "metadata": {
     "scrolled": true
    },
@@ -718,7 +1055,7 @@
        " '<code>base</code>, <code>bash</code>, <code>bask</code>, <code>bass</code>, <code>bast</code>, <code>bath</code>, <code>bosh</code>, <code>bush</code>, <code>case</code>, <code>cash</code>, <code>cask</code>, <code>cast</code>, <code>dash</code>, <code>dish</code>, <code>gash</code>, <code>gasp</code>, <code>gosh</code>, <code>gush</code>, <code>hash</code>, <code>hasp</code>, <code>hath</code>, <code>hush</code>, <code>lash</code>, <code>lass</code>, <code>last</code>, <code>lath</code>, <code>lush</code>, <code>mash</code>, <code>mask</code>, <code>mass</code>, <code>mast</code>, <code>math</code>, <code>mesh</code>, <code>mush</code>, <code>push</code>, <code>ramp</code>, <code>rasp</code>, <code>ruse</code>, <code>rush</code>, <code>rusk</code>, <code>rust</code>, <code>sash</code>, <code>sass</code>, <code>tush</code>, <code>wash</code>, <code>wasp</code>, <code>wish</code>')"
       ]
      },
-     "execution_count": 34,
+     "execution_count": 222,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -729,7 +1066,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 35,
+   "execution_count": 223,
    "metadata": {
     "scrolled": true
    },
@@ -740,7 +1077,7 @@
        "180"
       ]
      },
-     "execution_count": 35,
+     "execution_count": 223,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -751,7 +1088,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 36,
+   "execution_count": 224,
    "metadata": {
     "scrolled": true
    },
@@ -762,7 +1099,7 @@
        "2195"
       ]
      },
-     "execution_count": 36,
+     "execution_count": 224,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -773,7 +1110,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 37,
+   "execution_count": 225,
    "metadata": {
     "scrolled": true
    },
@@ -784,7 +1121,7 @@
        "2192"
       ]
      },
-     "execution_count": 37,
+     "execution_count": 225,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -795,7 +1132,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 38,
+   "execution_count": 226,
    "metadata": {
     "scrolled": true
    },
@@ -804,7 +1141,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "100 loops, best of 3: 5.81 ms per loop\n"
+      "100 loops, best of 3: 6.2 ms per loop\n"
      ]
     }
    ],
@@ -815,7 +1152,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 39,
+   "execution_count": 227,
    "metadata": {
     "scrolled": true
    },
@@ -824,7 +1161,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "100 loops, best of 3: 2.71 ms per loop\n"
+      "100 loops, best of 3: 2.92 ms per loop\n"
      ]
     }
    ],
@@ -835,7 +1172,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 40,
+   "execution_count": 155,
    "metadata": {},
    "outputs": [
     {
@@ -844,7 +1181,7 @@
        "2188"
       ]
      },
-     "execution_count": 40,
+     "execution_count": 155,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -855,7 +1192,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 41,
+   "execution_count": 156,
    "metadata": {},
    "outputs": [
     {
@@ -864,7 +1201,7 @@
        "2193"
       ]
      },
-     "execution_count": 41,
+     "execution_count": 156,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -875,7 +1212,63 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 42,
+   "execution_count": 232,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(True, 1)"
+      ]
+     },
+     "execution_count": 232,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "dist = 0\n",
+    "found = False\n",
+    "\n",
+    "while not found and distance < 50:\n",
+    "    dist += 1\n",
+    "    others = reachable_in('coax', distance)\n",
+    "    if 'stay' in others:\n",
+    "        found = True\n",
+    "\n",
+    "found, dist"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 229,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1000 loops, best of 3: 1.26 ms per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "distance = 0\n",
+    "found = False\n",
+    "\n",
+    "while not found and distance < 50:\n",
+    "    distance += 1\n",
+    "    others = reachable_in('coax', distance)\n",
+    "    if 'stay' in others:\n",
+    "        found = True\n",
+    "\n",
+    "found, distance"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 157,
    "metadata": {},
    "outputs": [
     {
@@ -884,7 +1277,7 @@
        "280"
       ]
      },
-     "execution_count": 42,
+     "execution_count": 157,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -896,7 +1289,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 43,
+   "execution_count": 158,
    "metadata": {},
    "outputs": [
     {
@@ -905,7 +1298,7 @@
        "296"
       ]
      },
-     "execution_count": 43,
+     "execution_count": 158,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -920,16 +1313,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 44,
+   "execution_count": 159,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "'know step yeps test pout book beck poor boos veep teed gent saws dyer hemp soon deem legs bets twit whim belt rock well bled whet prop spec weep peed loan week clef feed lock yens vent doer less teem toot yews blur clue pert pegs brew flea trig vets sued felt perk bobs brat tens beef leap bloc shoo moan boob jeez suet sits rood drag goat stay chip fled fist than loot pets suck peek pled heel hair sill prep char knot lens meek trap jeep beet crew draw tell nets peep meet sows glue bees bent pelt whit need foot bran chop gram chew teen veil lent gees fret soft leis pent gets weed keen reek news prim drab wets sics deed bows pier akin pock geed grey bogs goad skis peck prod loam keep pens hoot best reed yous sewn been tram pest whom bout unit deep boot dual lees omit peel sues berm dock yock shes lets mock grow jell whip lean thin sots geek stem floe tees sort fees gout mead dram said twin prom bras bier heft foul root fell melt bops coup coot atop brad chin moot shoe sacs chit hell door lead feet boon bolt leaf bell bias eery goop reel text boom herd rent leek rend club self send sick term airs frog yell next czar plus mean brow foam crow troy nest heed dell load glib peps cent chow pees bend jock held tent soil poop moor sped emit boss fest crop mews knit tout crag knob grab thaw vial sack help jets very boys flue whir newt wiry beep room pews crab baas cock coop hock blue flee moat skid quit dial brag cell aloe grad hews went leak toad wees mewl coat dent'"
+       "'brow chit bees hoot weep cock sots dock boob book boys brag bled eery sows cent crow mead aloe coup wiry less goat well vent deed rood moor belt atop bows draw prep chip sewn whom plus bets sued wets mean news czar newt fees chow reek flue troy pled geek boot akin lock bout leek fell feed shoe club heed bolt root peel thin yock vets crew load wees clue brad been meet pert boos beet legs mews self hock moot tell toad lead shoo jell teed sill skis veil glue went step test crop text peck bran teen crab pier bogs boss leis grow lent quit foam bras prod knot trap cell dram very goad felt chop sack omit poop pelt drag gram peps yens jeep brat prim jets goop tees deep dual bobs beef sits baas dyer lets leaf gees feet chew rend sues gent whet chin whip berm whim yell trig blue peek prop leak lean bent yeps bier drab bell foot heel boon fret moan send tens jock brew crag thaw sick beck gets bend pest loan geed herd skid toot grab pees hair poor rock best bloc pens coat bias fest heft mock lees loot gout sped sics tout frog nest flee meek stay weed doer stem peep hews grad peed knit keep pegs next twin blur coop week saws perk lens suet pews foul char vial soil term flea leap pent coot sort nets keen loam beep soft boom twit jeez glib teem than prom yews need veep shes bops dent moat hemp held reed whir whit deem know clef reel soon pock room tent floe pout help fist knob dell melt yous sacs unit door spec said hell mewl emit tram suck grey pets rent fled airs dial'"
       ]
      },
-     "execution_count": 44,
+     "execution_count": 159,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -940,7 +1333,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 45,
+   "execution_count": 160,
    "metadata": {},
    "outputs": [
     {
@@ -949,7 +1342,7 @@
        "['coax', 'coat', 'boat', 'boar', 'soar', 'star', 'stay']"
       ]
      },
-     "execution_count": 45,
+     "execution_count": 160,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -960,24 +1353,24 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 46,
+   "execution_count": 161,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CPU times: user 620 ms, sys: 4 ms, total: 624 ms\n",
-      "Wall time: 624 ms\n"
+      "CPU times: user 848 ms, sys: 0 ns, total: 848 ms\n",
+      "Wall time: 849 ms\n"
      ]
     },
     {
      "data": {
       "text/plain": [
-       "['coax', 'coat', 'chat', 'shat', 'spat', 'spay', 'stay']"
+       "['coax', 'coat', 'boat', 'boar', 'soar', 'star', 'stay']"
       ]
      },
-     "execution_count": 46,
+     "execution_count": 161,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -988,7 +1381,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 47,
+   "execution_count": 162,
    "metadata": {
     "collapsed": true
    },
@@ -999,7 +1392,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 48,
+   "execution_count": 163,
    "metadata": {},
    "outputs": [
     {
@@ -1008,7 +1401,7 @@
        "['czar', 'tzar', 'tear', 'sear', 'star', 'stay']"
       ]
      },
-     "execution_count": 48,
+     "execution_count": 163,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1019,7 +1412,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 49,
+   "execution_count": 164,
    "metadata": {
     "collapsed": true
    },
@@ -1030,7 +1423,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 50,
+   "execution_count": 165,
    "metadata": {
     "collapsed": true
    },
@@ -1041,7 +1434,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 79,
+   "execution_count": 166,
    "metadata": {},
    "outputs": [
     {
@@ -1050,7 +1443,7 @@
        "185"
       ]
      },
-     "execution_count": 79,
+     "execution_count": 166,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1063,7 +1456,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 80,
+   "execution_count": 167,
    "metadata": {
     "collapsed": true,
     "scrolled": true
@@ -1110,7 +1503,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.5.2+"
+   "version": "3.5.3"
   }
  },
  "nbformat": 4,
-- 
2.34.1