From: Neil Smith <neil.git@njae.me.uk>
Date: Tue, 1 Aug 2017 10:48:47 +0000 (+0100)
Subject: Fixed bugs in recursive version of interleave
X-Git-Url: https://git.njae.me.uk/?a=commitdiff_plain;h=e1f5b0651e9a742e52f6f3aa4103b2e5c156c406;p=ou-summer-of-code-2017.git

Fixed bugs in recursive version of interleave
---

diff --git a/09-resolving-the-bill/interleaving.ipynb b/09-resolving-the-bill/interleaving.ipynb
index f93a848..4dc9278 100644
--- a/09-resolving-the-bill/interleaving.ipynb
+++ b/09-resolving-the-bill/interleaving.ipynb
@@ -19,7 +19,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 2,
    "metadata": {
     "collapsed": true
    },
@@ -31,7 +31,19 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 47,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "import sys\n",
+    "sys.setrecursionlimit(10**6)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
    "metadata": {
     "collapsed": true
    },
@@ -46,7 +58,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 4,
    "metadata": {},
    "outputs": [
     {
@@ -55,7 +67,7 @@
        "[(0, ''), (1, 'a'), (2, 'aa'), (3, 'aab'), (4, 'aabc'), (5, 'aabcc')]"
       ]
      },
-     "execution_count": 5,
+     "execution_count": 4,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -73,7 +85,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [
     {
@@ -87,7 +99,7 @@
        " [False, False, False, False, False, False]]"
       ]
      },
-     "execution_count": 6,
+     "execution_count": 5,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -100,7 +112,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 6,
    "metadata": {
     "scrolled": true
    },
@@ -146,7 +158,7 @@
        " (5, 5): False}"
       ]
      },
-     "execution_count": 7,
+     "execution_count": 6,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -160,7 +172,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 7,
    "metadata": {
     "collapsed": true
    },
@@ -174,7 +186,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 8,
    "metadata": {
     "collapsed": true
    },
@@ -188,7 +200,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 9,
    "metadata": {},
    "outputs": [
     {
@@ -210,7 +222,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 10,
    "metadata": {},
    "outputs": [
     {
@@ -284,7 +296,7 @@
        " (5, 5): (4, 5, 'c', 's1')}"
       ]
      },
-     "execution_count": 11,
+     "execution_count": 10,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -337,7 +349,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 11,
    "metadata": {
     "collapsed": true
    },
@@ -413,7 +425,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 12,
    "metadata": {},
    "outputs": [
     {
@@ -422,7 +434,7 @@
        "True"
       ]
      },
-     "execution_count": 13,
+     "execution_count": 12,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -433,7 +445,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 13,
    "metadata": {},
    "outputs": [
     {
@@ -457,7 +469,7 @@
        "  (5, 5): (4, 5, 'c', 'seq1')})"
       ]
      },
-     "execution_count": 14,
+     "execution_count": 13,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -468,7 +480,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 14,
    "metadata": {
     "scrolled": true
    },
@@ -530,7 +542,7 @@
        "  (5, 5): True})"
       ]
      },
-     "execution_count": 15,
+     "execution_count": 14,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -541,7 +553,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 15,
    "metadata": {},
    "outputs": [
     {
@@ -550,7 +562,7 @@
        "False"
       ]
      },
-     "execution_count": 16,
+     "execution_count": 15,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -561,7 +573,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 16,
    "metadata": {},
    "outputs": [
     {
@@ -603,7 +615,7 @@
        "  (4, 3): (4, 2, 'b', 'seq2')})"
       ]
      },
-     "execution_count": 17,
+     "execution_count": 16,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -614,7 +626,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 17,
    "metadata": {
     "collapsed": true
    },
@@ -638,7 +650,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 18,
    "metadata": {
     "collapsed": true
    },
@@ -652,16 +664,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 19,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "'fcdafhachbgaheghbbcehecbgfgbbbedcgcgcagdcgcbffdgbg'"
+       "'fcafghacdbdhegdbdfbbbghecebceaecbhbfgaedaggbbfefcd'"
       ]
      },
-     "execution_count": 20,
+     "execution_count": 19,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -672,7 +684,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 20,
    "metadata": {
     "collapsed": true
    },
@@ -713,62 +725,65 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 21,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "0 0 0 adding b\n",
-      "1 0 1 adding x\n",
-      "1 1 0 adding z\n",
-      "1 2 -1 adding h\n",
-      "2 2 0 adding v\n",
-      "2 3 -1 adding w\n",
-      "2 4 -2 adding f\n",
-      "3 4 -1 adding g\n",
-      "4 4 0 adding g\n",
-      "5 4 1 adding w\n",
-      "5 5 0 adding z\n",
-      "5 6 -1 adding x\n",
-      "5 7 -2 adding w\n",
-      "5 8 -3 adding w\n",
-      "5 9 -4 adding e\n",
-      "6 9 -3 adding h\n",
-      "7 9 -2 adding c\n",
-      "8 9 -1 adding x\n",
-      "8 10 -2 adding y\n",
-      "8 11 -3 adding d\n",
-      "9 11 -2 adding x\n",
-      "9 12 -3 adding a\n",
-      "10 12 -2 adding e\n",
-      "11 12 -1 adding a\n",
-      "12 12 0 adding z\n",
-      "12 13 -1 adding y\n",
-      "12 14 -2 adding x\n",
-      "12 15 -3 adding h\n",
-      "13 15 -2 adding x\n",
-      "13 16 -3 adding x\n",
-      "13 17 -4 adding u\n",
-      "13 18 -5 adding d\n",
-      "14 18 -4 adding w\n",
-      "14 19 -5 adding e\n",
-      "15 19 -4 adding b\n",
-      "16 19 -3 adding w\n",
-      "16 20 -4 remaining s1 eaca\n"
+      "0 0 0 adding g\n",
+      "1 0 1 adding f\n",
+      "2 0 2 adding z\n",
+      "2 1 1 adding e\n",
+      "3 1 2 adding y\n",
+      "3 2 1 adding g\n",
+      "4 2 2 adding f\n",
+      "5 2 3 adding a\n",
+      "6 2 4 adding z\n",
+      "6 3 3 adding v\n",
+      "6 4 2 adding y\n",
+      "6 5 1 adding u\n",
+      "6 6 0 adding z\n",
+      "6 7 -1 adding h\n",
+      "7 7 0 adding v\n",
+      "7 8 -1 adding g\n",
+      "8 8 0 adding d\n",
+      "9 8 1 adding u\n",
+      "9 9 0 adding z\n",
+      "9 10 -1 adding a\n",
+      "10 10 0 adding z\n",
+      "10 11 -1 adding y\n",
+      "10 12 -2 adding w\n",
+      "10 13 -3 adding a\n",
+      "11 13 -2 adding f\n",
+      "12 13 -1 adding g\n",
+      "13 13 0 adding g\n",
+      "14 13 1 adding f\n",
+      "15 13 2 adding h\n",
+      "16 13 3 adding x\n",
+      "16 14 2 adding w\n",
+      "16 15 1 adding a\n",
+      "17 15 2 adding e\n",
+      "18 15 3 adding w\n",
+      "18 16 2 adding d\n",
+      "19 16 3 adding x\n",
+      "19 17 2 adding u\n",
+      "19 18 1 adding z\n",
+      "19 19 0 adding x\n",
+      "19 20 -1 remaining s1 g\n"
      ]
     },
     {
      "data": {
       "text/plain": [
-       "('bhfggehcdaeahdebeaca',\n",
-       " 'xzvwwzxwwxyxzyxxxuww',\n",
-       " 'bxzhvwfggwzxwwehcxydxaeazyxhxxudwebweaca',\n",
+       "('gfegfahgdaafggfhaedg',\n",
+       " 'zyzvyuzvuzzywxwwxuzx',\n",
+       " 'gfzeygfazvyuzhvgduzazywafggfhxwaewdxuzxg',\n",
        " 40)"
       ]
      },
-     "execution_count": 22,
+     "execution_count": 21,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -782,7 +797,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 22,
    "metadata": {},
    "outputs": [
     {
@@ -790,467 +805,467 @@
      "output_type": "stream",
      "text": [
       "xxxx 0 0 ! ! ! True\n",
-      "seq2 0 1 ! b b True\n",
-      "seq2 0 2 ! h x False\n",
-      "seq2 0 3 ! f z False\n",
-      "seq2 0 4 ! g h False\n",
-      "seq2 0 5 ! g v False\n",
-      "seq2 0 6 ! e w False\n",
+      "seq2 0 1 ! g g True\n",
+      "seq2 0 2 ! f f True\n",
+      "seq2 0 3 ! e z False\n",
+      "seq2 0 4 ! g e False\n",
+      "seq2 0 5 ! f y False\n",
+      "seq2 0 6 ! a g False\n",
       "seq2 0 7 ! h f False\n",
-      "seq2 0 8 ! c g False\n",
-      "seq2 0 9 ! d g False\n",
-      "seq2 0 10 ! a w False\n",
-      "seq2 0 11 ! e z False\n",
-      "seq2 0 12 ! a x False\n",
-      "seq2 0 13 ! h w False\n",
-      "seq2 0 14 ! d w False\n",
-      "seq2 0 15 ! e e False\n",
-      "seq2 0 16 ! b h False\n",
-      "seq2 0 17 ! e c False\n",
-      "seq2 0 18 ! a x False\n",
-      "seq2 0 19 ! c y False\n",
-      "seq2 0 20 ! a d False\n",
-      "seq1 1 0 x ! b False\n",
-      "seq1 1 1 x b x True\n",
-      "xxxx 1 2 x h z False\n",
-      "xxxx 1 3 x f h False\n",
-      "xxxx 1 4 x g v False\n",
-      "xxxx 1 5 x g w False\n",
-      "xxxx 1 6 x e f False\n",
-      "xxxx 1 7 x h g False\n",
-      "xxxx 1 8 x c g False\n",
-      "xxxx 1 9 x d w False\n",
-      "xxxx 1 10 x a z False\n",
-      "xxxx 1 11 x e x False\n",
-      "xxxx 1 12 x a w False\n",
-      "xxxx 1 13 x h w False\n",
-      "xxxx 1 14 x d e False\n",
-      "xxxx 1 15 x e h False\n",
-      "xxxx 1 16 x b c False\n",
-      "xxxx 1 17 x e x False\n",
-      "xxxx 1 18 x a y False\n",
-      "xxxx 1 19 x c d False\n",
-      "xxxx 1 20 x a x False\n",
-      "seq1 2 0 z ! x False\n",
-      "seq1 2 1 z b z True\n",
-      "seq2 2 2 z h h True\n",
-      "xxxx 2 3 z f v False\n",
-      "xxxx 2 4 z g w False\n",
-      "xxxx 2 5 z g f False\n",
-      "xxxx 2 6 z e g False\n",
-      "xxxx 2 7 z h g False\n",
-      "xxxx 2 8 z c w False\n",
-      "xxxx 2 9 z d z False\n",
-      "xxxx 2 10 z a x False\n",
-      "xxxx 2 11 z e w False\n",
-      "xxxx 2 12 z a w False\n",
-      "xxxx 2 13 z h e False\n",
-      "xxxx 2 14 z d h False\n",
-      "xxxx 2 15 z e c False\n",
-      "xxxx 2 16 z b x False\n",
-      "xxxx 2 17 z e y False\n",
-      "xxxx 2 18 z a d False\n",
-      "xxxx 2 19 z c x False\n",
-      "xxxx 2 20 z a a False\n",
-      "seq1 3 0 v ! z False\n",
-      "xxxx 3 1 v b h False\n",
-      "seq1 3 2 v h v True\n",
-      "xxxx 3 3 v f w False\n",
-      "xxxx 3 4 v g f False\n",
-      "xxxx 3 5 v g g False\n",
-      "xxxx 3 6 v e g False\n",
-      "xxxx 3 7 v h w False\n",
-      "xxxx 3 8 v c z False\n",
-      "xxxx 3 9 v d x False\n",
-      "xxxx 3 10 v a w False\n",
-      "xxxx 3 11 v e w False\n",
-      "xxxx 3 12 v a e False\n",
-      "xxxx 3 13 v h h False\n",
-      "xxxx 3 14 v d c False\n",
-      "xxxx 3 15 v e x False\n",
-      "xxxx 3 16 v b y False\n",
-      "xxxx 3 17 v e d False\n",
-      "xxxx 3 18 v a x False\n",
-      "xxxx 3 19 v c a False\n",
-      "xxxx 3 20 v a e False\n",
-      "seq1 4 0 w ! h False\n",
-      "xxxx 4 1 w b v False\n",
-      "seq1 4 2 w h w True\n",
-      "seq2 4 3 w f f True\n",
-      "seq2 4 4 w g g True\n",
-      "seq2 4 5 w g g True\n",
-      "xxxx 4 6 w e w False\n",
-      "xxxx 4 7 w h z False\n",
-      "xxxx 4 8 w c x False\n",
-      "xxxx 4 9 w d w False\n",
-      "xxxx 4 10 w a w False\n",
-      "xxxx 4 11 w e e False\n",
-      "xxxx 4 12 w a h False\n",
-      "xxxx 4 13 w h c False\n",
-      "xxxx 4 14 w d x False\n",
-      "xxxx 4 15 w e y False\n",
-      "xxxx 4 16 w b d False\n",
-      "xxxx 4 17 w e x False\n",
-      "xxxx 4 18 w a a False\n",
-      "xxxx 4 19 w c e False\n",
-      "xxxx 4 20 w a a False\n",
-      "seq1 5 0 w ! v False\n",
-      "xxxx 5 1 w b w False\n",
-      "xxxx 5 2 w h f False\n",
-      "xxxx 5 3 w f g False\n",
-      "xxxx 5 4 w g g False\n",
-      "seq1 5 5 w g w True\n",
-      "xxxx 5 6 w e z False\n",
-      "xxxx 5 7 w h x False\n",
-      "xxxx 5 8 w c w False\n",
-      "xxxx 5 9 w d w False\n",
-      "xxxx 5 10 w a e False\n",
-      "xxxx 5 11 w e h False\n",
-      "xxxx 5 12 w a c False\n",
-      "xxxx 5 13 w h x False\n",
-      "xxxx 5 14 w d y False\n",
-      "xxxx 5 15 w e d False\n",
-      "xxxx 5 16 w b x False\n",
-      "xxxx 5 17 w e a False\n",
-      "xxxx 5 18 w a e False\n",
-      "xxxx 5 19 w c a False\n",
-      "xxxx 5 20 w a z False\n",
-      "seq1 6 0 z ! w False\n",
-      "xxxx 6 1 z b f False\n",
-      "xxxx 6 2 z h g False\n",
-      "xxxx 6 3 z f g False\n",
-      "xxxx 6 4 z g w False\n",
-      "seq1 6 5 z g z True\n",
-      "xxxx 6 6 z e x False\n",
-      "xxxx 6 7 z h w False\n",
-      "xxxx 6 8 z c w False\n",
-      "xxxx 6 9 z d e False\n",
-      "xxxx 6 10 z a h False\n",
-      "xxxx 6 11 z e c False\n",
-      "xxxx 6 12 z a x False\n",
-      "xxxx 6 13 z h y False\n",
-      "xxxx 6 14 z d d False\n",
-      "xxxx 6 15 z e x False\n",
-      "xxxx 6 16 z b a False\n",
-      "xxxx 6 17 z e e False\n",
-      "xxxx 6 18 z a a False\n",
-      "xxxx 6 19 z c z False\n",
-      "xxxx 6 20 z a y False\n",
-      "seq1 7 0 x ! f False\n",
-      "xxxx 7 1 x b g False\n",
-      "xxxx 7 2 x h g False\n",
-      "xxxx 7 3 x f w False\n",
-      "xxxx 7 4 x g z False\n",
-      "seq1 7 5 x g x True\n",
-      "xxxx 7 6 x e w False\n",
-      "xxxx 7 7 x h w False\n",
-      "xxxx 7 8 x c e False\n",
-      "xxxx 7 9 x d h False\n",
-      "xxxx 7 10 x a c False\n",
-      "xxxx 7 11 x e x False\n",
-      "xxxx 7 12 x a y False\n",
-      "xxxx 7 13 x h d False\n",
-      "xxxx 7 14 x d x False\n",
-      "xxxx 7 15 x e a False\n",
-      "xxxx 7 16 x b e False\n",
-      "xxxx 7 17 x e a False\n",
-      "xxxx 7 18 x a z False\n",
-      "xxxx 7 19 x c y False\n",
-      "xxxx 7 20 x a x False\n",
-      "seq1 8 0 w ! g False\n",
-      "xxxx 8 1 w b g False\n",
-      "xxxx 8 2 w h w False\n",
-      "xxxx 8 3 w f z False\n",
-      "xxxx 8 4 w g x False\n",
-      "seq1 8 5 w g w True\n",
-      "xxxx 8 6 w e w False\n",
-      "xxxx 8 7 w h e False\n",
-      "xxxx 8 8 w c h False\n",
-      "xxxx 8 9 w d c False\n",
-      "xxxx 8 10 w a x False\n",
-      "xxxx 8 11 w e y False\n",
-      "xxxx 8 12 w a d False\n",
-      "xxxx 8 13 w h x False\n",
-      "xxxx 8 14 w d a False\n",
-      "xxxx 8 15 w e e False\n",
-      "xxxx 8 16 w b a False\n",
-      "xxxx 8 17 w e z False\n",
-      "xxxx 8 18 w a y False\n",
-      "xxxx 8 19 w c x False\n",
-      "xxxx 8 20 w a h False\n",
-      "seq1 9 0 w ! g False\n",
-      "xxxx 9 1 w b w False\n",
-      "xxxx 9 2 w h z False\n",
-      "xxxx 9 3 w f x False\n",
-      "xxxx 9 4 w g w False\n",
-      "seq1 9 5 w g w True\n",
-      "seq2 9 6 w e e True\n",
-      "seq2 9 7 w h h True\n",
-      "seq2 9 8 w c c True\n",
-      "xxxx 9 9 w d x False\n",
-      "xxxx 9 10 w a y False\n",
-      "xxxx 9 11 w e d False\n",
-      "xxxx 9 12 w a x False\n",
-      "xxxx 9 13 w h a False\n",
-      "xxxx 9 14 w d e False\n",
-      "xxxx 9 15 w e a False\n",
-      "xxxx 9 16 w b z False\n",
-      "xxxx 9 17 w e y False\n",
-      "xxxx 9 18 w a x False\n",
-      "xxxx 9 19 w c h False\n",
-      "xxxx 9 20 w a x False\n",
-      "seq1 10 0 x ! w False\n",
-      "xxxx 10 1 x b z False\n",
-      "xxxx 10 2 x h x False\n",
-      "xxxx 10 3 x f w False\n",
-      "xxxx 10 4 x g w False\n",
-      "xxxx 10 5 x g e False\n",
-      "xxxx 10 6 x e h False\n",
-      "xxxx 10 7 x h c False\n",
-      "seq1 10 8 x c x True\n",
-      "xxxx 10 9 x d y False\n",
-      "xxxx 10 10 x a d False\n",
-      "xxxx 10 11 x e x False\n",
-      "xxxx 10 12 x a a False\n",
-      "xxxx 10 13 x h e False\n",
-      "xxxx 10 14 x d a False\n",
-      "xxxx 10 15 x e z False\n",
-      "xxxx 10 16 x b y False\n",
-      "xxxx 10 17 x e x False\n",
-      "xxxx 10 18 x a h False\n",
-      "xxxx 10 19 x c x False\n",
-      "xxxx 10 20 x a x False\n",
-      "seq1 11 0 y ! z False\n",
-      "xxxx 11 1 y b x False\n",
-      "xxxx 11 2 y h w False\n",
-      "xxxx 11 3 y f w False\n",
-      "xxxx 11 4 y g e False\n",
-      "xxxx 11 5 y g h False\n",
-      "xxxx 11 6 y e c False\n",
-      "xxxx 11 7 y h x False\n",
-      "seq1 11 8 y c y True\n",
-      "seq2 11 9 y d d True\n",
-      "xxxx 11 10 y a x False\n",
-      "xxxx 11 11 y e a False\n",
-      "xxxx 11 12 y a e False\n",
-      "xxxx 11 13 y h a False\n",
-      "xxxx 11 14 y d z False\n",
-      "xxxx 11 15 y e y False\n",
-      "xxxx 11 16 y b x False\n",
-      "xxxx 11 17 y e h False\n",
-      "xxxx 11 18 y a x False\n",
-      "xxxx 11 19 y c x False\n",
-      "xxxx 11 20 y a u False\n",
-      "seq1 12 0 x ! x False\n",
-      "xxxx 12 1 x b w False\n",
-      "xxxx 12 2 x h w False\n",
-      "xxxx 12 3 x f e False\n",
-      "xxxx 12 4 x g h False\n",
-      "xxxx 12 5 x g c False\n",
-      "xxxx 12 6 x e x False\n",
-      "xxxx 12 7 x h y False\n",
-      "xxxx 12 8 x c d False\n",
-      "seq1 12 9 x d x True\n",
-      "seq2 12 10 x a a True\n",
-      "seq2 12 11 x e e True\n",
-      "seq2 12 12 x a a True\n",
-      "xxxx 12 13 x h z False\n",
-      "xxxx 12 14 x d y False\n",
-      "xxxx 12 15 x e x False\n",
-      "xxxx 12 16 x b h False\n",
-      "xxxx 12 17 x e x False\n",
-      "xxxx 12 18 x a x False\n",
-      "xxxx 12 19 x c u False\n",
-      "xxxx 12 20 x a d False\n",
-      "seq1 13 0 z ! w False\n",
-      "xxxx 13 1 z b w False\n",
-      "xxxx 13 2 z h e False\n",
-      "xxxx 13 3 z f h False\n",
-      "xxxx 13 4 z g c False\n",
-      "xxxx 13 5 z g x False\n",
-      "xxxx 13 6 z e y False\n",
-      "xxxx 13 7 z h d False\n",
-      "xxxx 13 8 z c x False\n",
-      "xxxx 13 9 z d a False\n",
-      "xxxx 13 10 z a e False\n",
-      "xxxx 13 11 z e a False\n",
-      "seq1 13 12 z a z True\n",
-      "xxxx 13 13 z h y False\n",
-      "xxxx 13 14 z d x False\n",
-      "xxxx 13 15 z e h False\n",
-      "xxxx 13 16 z b x False\n",
-      "xxxx 13 17 z e x False\n",
-      "xxxx 13 18 z a u False\n",
-      "xxxx 13 19 z c d False\n",
-      "xxxx 13 20 z a w False\n",
-      "seq1 14 0 y ! w False\n",
-      "xxxx 14 1 y b e False\n",
-      "xxxx 14 2 y h h False\n",
-      "xxxx 14 3 y f c False\n",
-      "xxxx 14 4 y g x False\n",
-      "xxxx 14 5 y g y False\n",
-      "xxxx 14 6 y e d False\n",
-      "xxxx 14 7 y h x False\n",
-      "xxxx 14 8 y c a False\n",
-      "xxxx 14 9 y d e False\n",
-      "xxxx 14 10 y a a False\n",
-      "xxxx 14 11 y e z False\n",
-      "seq1 14 12 y a y True\n",
-      "xxxx 14 13 y h x False\n",
-      "xxxx 14 14 y d h False\n",
-      "xxxx 14 15 y e x False\n",
-      "xxxx 14 16 y b x False\n",
-      "xxxx 14 17 y e u False\n",
-      "xxxx 14 18 y a d False\n",
-      "xxxx 14 19 y c w False\n",
-      "xxxx 14 20 y a e False\n",
-      "seq1 15 0 x ! e False\n",
-      "xxxx 15 1 x b h False\n",
-      "xxxx 15 2 x h c False\n",
-      "xxxx 15 3 x f x False\n",
-      "xxxx 15 4 x g y False\n",
-      "xxxx 15 5 x g d False\n",
-      "xxxx 15 6 x e x False\n",
-      "xxxx 15 7 x h a False\n",
-      "xxxx 15 8 x c e False\n",
-      "xxxx 15 9 x d a False\n",
-      "xxxx 15 10 x a z False\n",
-      "xxxx 15 11 x e y False\n",
-      "seq1 15 12 x a x True\n",
-      "seq2 15 13 x h h True\n",
-      "xxxx 15 14 x d x False\n",
-      "xxxx 15 15 x e x False\n",
-      "xxxx 15 16 x b u False\n",
-      "xxxx 15 17 x e d False\n",
-      "xxxx 15 18 x a w False\n",
-      "xxxx 15 19 x c e False\n",
-      "xxxx 15 20 x a b False\n",
-      "seq1 16 0 x ! h False\n",
-      "xxxx 16 1 x b c False\n",
-      "xxxx 16 2 x h x False\n",
-      "xxxx 16 3 x f y False\n",
-      "xxxx 16 4 x g d False\n",
-      "xxxx 16 5 x g x False\n",
-      "xxxx 16 6 x e a False\n",
-      "xxxx 16 7 x h e False\n",
-      "xxxx 16 8 x c a False\n",
-      "xxxx 16 9 x d z False\n",
-      "xxxx 16 10 x a y False\n",
-      "xxxx 16 11 x e x False\n",
-      "xxxx 16 12 x a h False\n",
-      "seq1 16 13 x h x True\n",
-      "xxxx 16 14 x d x False\n",
-      "xxxx 16 15 x e u False\n",
-      "xxxx 16 16 x b d False\n",
-      "xxxx 16 17 x e w False\n",
-      "xxxx 16 18 x a e False\n",
-      "xxxx 16 19 x c b False\n",
-      "xxxx 16 20 x a w False\n",
-      "seq1 17 0 x ! c False\n",
-      "xxxx 17 1 x b x False\n",
-      "xxxx 17 2 x h y False\n",
-      "xxxx 17 3 x f d False\n",
-      "xxxx 17 4 x g x False\n",
-      "xxxx 17 5 x g a False\n",
-      "xxxx 17 6 x e e False\n",
+      "seq2 0 8 ! g a False\n",
+      "seq2 0 9 ! d z False\n",
+      "seq2 0 10 ! a v False\n",
+      "seq2 0 11 ! a y False\n",
+      "seq2 0 12 ! f u False\n",
+      "seq2 0 13 ! g z False\n",
+      "seq2 0 14 ! g h False\n",
+      "seq2 0 15 ! f v False\n",
+      "seq2 0 16 ! h g False\n",
+      "seq2 0 17 ! a d False\n",
+      "seq2 0 18 ! e u False\n",
+      "seq2 0 19 ! d z False\n",
+      "seq2 0 20 ! g a False\n",
+      "seq1 1 0 z ! g False\n",
+      "xxxx 1 1 z g f False\n",
+      "seq1 1 2 z f z True\n",
+      "seq2 1 3 z e e True\n",
+      "xxxx 1 4 z g y False\n",
+      "xxxx 1 5 z f g False\n",
+      "xxxx 1 6 z a f False\n",
+      "xxxx 1 7 z h a False\n",
+      "xxxx 1 8 z g z False\n",
+      "xxxx 1 9 z d v False\n",
+      "xxxx 1 10 z a y False\n",
+      "xxxx 1 11 z a u False\n",
+      "xxxx 1 12 z f z False\n",
+      "xxxx 1 13 z g h False\n",
+      "xxxx 1 14 z g v False\n",
+      "xxxx 1 15 z f g False\n",
+      "xxxx 1 16 z h d False\n",
+      "xxxx 1 17 z a u False\n",
+      "xxxx 1 18 z e z False\n",
+      "xxxx 1 19 z d a False\n",
+      "xxxx 1 20 z g z False\n",
+      "seq1 2 0 y ! f False\n",
+      "xxxx 2 1 y g z False\n",
+      "xxxx 2 2 y f e False\n",
+      "seq1 2 3 y e y True\n",
+      "seq2 2 4 y g g True\n",
+      "seq2 2 5 y f f True\n",
+      "seq2 2 6 y a a True\n",
+      "xxxx 2 7 y h z False\n",
+      "xxxx 2 8 y g v False\n",
+      "xxxx 2 9 y d y False\n",
+      "xxxx 2 10 y a u False\n",
+      "xxxx 2 11 y a z False\n",
+      "xxxx 2 12 y f h False\n",
+      "xxxx 2 13 y g v False\n",
+      "xxxx 2 14 y g g False\n",
+      "xxxx 2 15 y f d False\n",
+      "xxxx 2 16 y h u False\n",
+      "xxxx 2 17 y a z False\n",
+      "xxxx 2 18 y e a False\n",
+      "xxxx 2 19 y d z False\n",
+      "xxxx 2 20 y g y False\n",
+      "seq1 3 0 z ! z False\n",
+      "xxxx 3 1 z g e False\n",
+      "xxxx 3 2 z f y False\n",
+      "xxxx 3 3 z e g False\n",
+      "xxxx 3 4 z g f False\n",
+      "xxxx 3 5 z f a False\n",
+      "seq1 3 6 z a z True\n",
+      "xxxx 3 7 z h v False\n",
+      "xxxx 3 8 z g y False\n",
+      "xxxx 3 9 z d u False\n",
+      "xxxx 3 10 z a z False\n",
+      "xxxx 3 11 z a h False\n",
+      "xxxx 3 12 z f v False\n",
+      "xxxx 3 13 z g g False\n",
+      "xxxx 3 14 z g d False\n",
+      "xxxx 3 15 z f u False\n",
+      "xxxx 3 16 z h z False\n",
+      "xxxx 3 17 z a a False\n",
+      "xxxx 3 18 z e z False\n",
+      "xxxx 3 19 z d y False\n",
+      "xxxx 3 20 z g w False\n",
+      "seq1 4 0 v ! e False\n",
+      "xxxx 4 1 v g y False\n",
+      "xxxx 4 2 v f g False\n",
+      "xxxx 4 3 v e f False\n",
+      "xxxx 4 4 v g a False\n",
+      "xxxx 4 5 v f z False\n",
+      "seq1 4 6 v a v True\n",
+      "xxxx 4 7 v h y False\n",
+      "xxxx 4 8 v g u False\n",
+      "xxxx 4 9 v d z False\n",
+      "xxxx 4 10 v a h False\n",
+      "xxxx 4 11 v a v False\n",
+      "xxxx 4 12 v f g False\n",
+      "xxxx 4 13 v g d False\n",
+      "xxxx 4 14 v g u False\n",
+      "xxxx 4 15 v f z False\n",
+      "xxxx 4 16 v h a False\n",
+      "xxxx 4 17 v a z False\n",
+      "xxxx 4 18 v e y False\n",
+      "xxxx 4 19 v d w False\n",
+      "xxxx 4 20 v g a False\n",
+      "seq1 5 0 y ! y False\n",
+      "xxxx 5 1 y g g False\n",
+      "xxxx 5 2 y f f False\n",
+      "xxxx 5 3 y e a False\n",
+      "xxxx 5 4 y g z False\n",
+      "xxxx 5 5 y f v False\n",
+      "seq1 5 6 y a y True\n",
+      "xxxx 5 7 y h u False\n",
+      "xxxx 5 8 y g z False\n",
+      "xxxx 5 9 y d h False\n",
+      "xxxx 5 10 y a v False\n",
+      "xxxx 5 11 y a g False\n",
+      "xxxx 5 12 y f d False\n",
+      "xxxx 5 13 y g u False\n",
+      "xxxx 5 14 y g z False\n",
+      "xxxx 5 15 y f a False\n",
+      "xxxx 5 16 y h z False\n",
+      "xxxx 5 17 y a y False\n",
+      "xxxx 5 18 y e w False\n",
+      "xxxx 5 19 y d a False\n",
+      "xxxx 5 20 y g f False\n",
+      "seq1 6 0 u ! g False\n",
+      "xxxx 6 1 u g f False\n",
+      "xxxx 6 2 u f a False\n",
+      "xxxx 6 3 u e z False\n",
+      "xxxx 6 4 u g v False\n",
+      "xxxx 6 5 u f y False\n",
+      "seq1 6 6 u a u True\n",
+      "xxxx 6 7 u h z False\n",
+      "xxxx 6 8 u g h False\n",
+      "xxxx 6 9 u d v False\n",
+      "xxxx 6 10 u a g False\n",
+      "xxxx 6 11 u a d False\n",
+      "xxxx 6 12 u f u False\n",
+      "xxxx 6 13 u g z False\n",
+      "xxxx 6 14 u g a False\n",
+      "xxxx 6 15 u f z False\n",
+      "xxxx 6 16 u h y False\n",
+      "xxxx 6 17 u a w False\n",
+      "xxxx 6 18 u e a False\n",
+      "xxxx 6 19 u d f False\n",
+      "xxxx 6 20 u g g False\n",
+      "seq1 7 0 z ! f False\n",
+      "xxxx 7 1 z g a False\n",
+      "xxxx 7 2 z f z False\n",
+      "xxxx 7 3 z e v False\n",
+      "xxxx 7 4 z g y False\n",
+      "xxxx 7 5 z f u False\n",
+      "seq1 7 6 z a z True\n",
+      "seq2 7 7 z h h True\n",
+      "xxxx 7 8 z g v False\n",
+      "xxxx 7 9 z d g False\n",
+      "xxxx 7 10 z a d False\n",
+      "xxxx 7 11 z a u False\n",
+      "xxxx 7 12 z f z False\n",
+      "xxxx 7 13 z g a False\n",
+      "xxxx 7 14 z g z False\n",
+      "xxxx 7 15 z f y False\n",
+      "xxxx 7 16 z h w False\n",
+      "xxxx 7 17 z a a False\n",
+      "xxxx 7 18 z e f False\n",
+      "xxxx 7 19 z d g False\n",
+      "xxxx 7 20 z g g False\n",
+      "seq1 8 0 v ! a False\n",
+      "xxxx 8 1 v g z False\n",
+      "xxxx 8 2 v f v False\n",
+      "xxxx 8 3 v e y False\n",
+      "xxxx 8 4 v g u False\n",
+      "xxxx 8 5 v f z False\n",
+      "xxxx 8 6 v a h False\n",
+      "seq1 8 7 v h v True\n",
+      "seq2 8 8 v g g True\n",
+      "seq2 8 9 v d d True\n",
+      "xxxx 8 10 v a u False\n",
+      "xxxx 8 11 v a z False\n",
+      "xxxx 8 12 v f a False\n",
+      "xxxx 8 13 v g z False\n",
+      "xxxx 8 14 v g y False\n",
+      "xxxx 8 15 v f w False\n",
+      "xxxx 8 16 v h a False\n",
+      "xxxx 8 17 v a f False\n",
+      "xxxx 8 18 v e g False\n",
+      "xxxx 8 19 v d g False\n",
+      "xxxx 8 20 v g f False\n",
+      "seq1 9 0 u ! z False\n",
+      "xxxx 9 1 u g v False\n",
+      "xxxx 9 2 u f y False\n",
+      "xxxx 9 3 u e u False\n",
+      "xxxx 9 4 u g z False\n",
+      "xxxx 9 5 u f h False\n",
+      "xxxx 9 6 u a v False\n",
+      "xxxx 9 7 u h g False\n",
+      "xxxx 9 8 u g d False\n",
+      "seq1 9 9 u d u True\n",
+      "xxxx 9 10 u a z False\n",
+      "xxxx 9 11 u a a False\n",
+      "xxxx 9 12 u f z False\n",
+      "xxxx 9 13 u g y False\n",
+      "xxxx 9 14 u g w False\n",
+      "xxxx 9 15 u f a False\n",
+      "xxxx 9 16 u h f False\n",
+      "xxxx 9 17 u a g False\n",
+      "xxxx 9 18 u e g False\n",
+      "xxxx 9 19 u d f False\n",
+      "xxxx 9 20 u g h False\n",
+      "seq1 10 0 z ! v False\n",
+      "xxxx 10 1 z g y False\n",
+      "xxxx 10 2 z f u False\n",
+      "xxxx 10 3 z e z False\n",
+      "xxxx 10 4 z g h False\n",
+      "xxxx 10 5 z f v False\n",
+      "xxxx 10 6 z a g False\n",
+      "xxxx 10 7 z h d False\n",
+      "xxxx 10 8 z g u False\n",
+      "seq1 10 9 z d z True\n",
+      "seq2 10 10 z a a True\n",
+      "xxxx 10 11 z a z False\n",
+      "xxxx 10 12 z f y False\n",
+      "xxxx 10 13 z g w False\n",
+      "xxxx 10 14 z g a False\n",
+      "xxxx 10 15 z f f False\n",
+      "xxxx 10 16 z h g False\n",
+      "xxxx 10 17 z a g False\n",
+      "xxxx 10 18 z e f False\n",
+      "xxxx 10 19 z d h False\n",
+      "xxxx 10 20 z g x False\n",
+      "seq1 11 0 z ! y False\n",
+      "xxxx 11 1 z g u False\n",
+      "xxxx 11 2 z f z False\n",
+      "xxxx 11 3 z e h False\n",
+      "xxxx 11 4 z g v False\n",
+      "xxxx 11 5 z f g False\n",
+      "xxxx 11 6 z a d False\n",
+      "xxxx 11 7 z h u False\n",
+      "xxxx 11 8 z g z False\n",
+      "xxxx 11 9 z d a False\n",
+      "seq1 11 10 z a z True\n",
+      "xxxx 11 11 z a y False\n",
+      "xxxx 11 12 z f w False\n",
+      "xxxx 11 13 z g a False\n",
+      "xxxx 11 14 z g f False\n",
+      "xxxx 11 15 z f g False\n",
+      "xxxx 11 16 z h g False\n",
+      "xxxx 11 17 z a f False\n",
+      "xxxx 11 18 z e h False\n",
+      "xxxx 11 19 z d x False\n",
+      "xxxx 11 20 z g w False\n",
+      "seq1 12 0 y ! u False\n",
+      "xxxx 12 1 y g z False\n",
+      "xxxx 12 2 y f h False\n",
+      "xxxx 12 3 y e v False\n",
+      "xxxx 12 4 y g g False\n",
+      "xxxx 12 5 y f d False\n",
+      "xxxx 12 6 y a u False\n",
+      "xxxx 12 7 y h z False\n",
+      "xxxx 12 8 y g a False\n",
+      "xxxx 12 9 y d z False\n",
+      "seq1 12 10 y a y True\n",
+      "xxxx 12 11 y a w False\n",
+      "xxxx 12 12 y f a False\n",
+      "xxxx 12 13 y g f False\n",
+      "xxxx 12 14 y g g False\n",
+      "xxxx 12 15 y f g False\n",
+      "xxxx 12 16 y h f False\n",
+      "xxxx 12 17 y a h False\n",
+      "xxxx 12 18 y e x False\n",
+      "xxxx 12 19 y d w False\n",
+      "xxxx 12 20 y g a False\n",
+      "seq1 13 0 w ! z False\n",
+      "xxxx 13 1 w g h False\n",
+      "xxxx 13 2 w f v False\n",
+      "xxxx 13 3 w e g False\n",
+      "xxxx 13 4 w g d False\n",
+      "xxxx 13 5 w f u False\n",
+      "xxxx 13 6 w a z False\n",
+      "xxxx 13 7 w h a False\n",
+      "xxxx 13 8 w g z False\n",
+      "xxxx 13 9 w d y False\n",
+      "seq1 13 10 w a w True\n",
+      "seq2 13 11 w a a True\n",
+      "seq2 13 12 w f f True\n",
+      "seq2 13 13 w g g True\n",
+      "seq2 13 14 w g g True\n",
+      "seq2 13 15 w f f True\n",
+      "seq2 13 16 w h h True\n",
+      "xxxx 13 17 w a x False\n",
+      "xxxx 13 18 w e w False\n",
+      "xxxx 13 19 w d a False\n",
+      "xxxx 13 20 w g e False\n",
+      "seq1 14 0 x ! h False\n",
+      "xxxx 14 1 x g v False\n",
+      "xxxx 14 2 x f g False\n",
+      "xxxx 14 3 x e d False\n",
+      "xxxx 14 4 x g u False\n",
+      "xxxx 14 5 x f z False\n",
+      "xxxx 14 6 x a a False\n",
+      "xxxx 14 7 x h z False\n",
+      "xxxx 14 8 x g y False\n",
+      "xxxx 14 9 x d w False\n",
+      "xxxx 14 10 x a a False\n",
+      "xxxx 14 11 x a f False\n",
+      "xxxx 14 12 x f g False\n",
+      "xxxx 14 13 x g g False\n",
+      "xxxx 14 14 x g f False\n",
+      "xxxx 14 15 x f h False\n",
+      "seq1 14 16 x h x True\n",
+      "xxxx 14 17 x a w False\n",
+      "xxxx 14 18 x e a False\n",
+      "xxxx 14 19 x d e False\n",
+      "xxxx 14 20 x g w False\n",
+      "seq1 15 0 w ! v False\n",
+      "xxxx 15 1 w g g False\n",
+      "xxxx 15 2 w f d False\n",
+      "xxxx 15 3 w e u False\n",
+      "xxxx 15 4 w g z False\n",
+      "xxxx 15 5 w f a False\n",
+      "xxxx 15 6 w a z False\n",
+      "xxxx 15 7 w h y False\n",
+      "xxxx 15 8 w g w False\n",
+      "xxxx 15 9 w d a False\n",
+      "xxxx 15 10 w a f False\n",
+      "xxxx 15 11 w a g False\n",
+      "xxxx 15 12 w f g False\n",
+      "xxxx 15 13 w g f False\n",
+      "xxxx 15 14 w g h False\n",
+      "xxxx 15 15 w f x False\n",
+      "seq1 15 16 w h w True\n",
+      "seq2 15 17 w a a True\n",
+      "seq2 15 18 w e e True\n",
+      "xxxx 15 19 w d w False\n",
+      "xxxx 15 20 w g d False\n",
+      "seq1 16 0 w ! g False\n",
+      "xxxx 16 1 w g d False\n",
+      "xxxx 16 2 w f u False\n",
+      "xxxx 16 3 w e z False\n",
+      "xxxx 16 4 w g a False\n",
+      "xxxx 16 5 w f z False\n",
+      "xxxx 16 6 w a y False\n",
+      "xxxx 16 7 w h w False\n",
+      "xxxx 16 8 w g a False\n",
+      "xxxx 16 9 w d f False\n",
+      "xxxx 16 10 w a g False\n",
+      "xxxx 16 11 w a g False\n",
+      "xxxx 16 12 w f f False\n",
+      "xxxx 16 13 w g h False\n",
+      "xxxx 16 14 w g x False\n",
+      "xxxx 16 15 w f w False\n",
+      "xxxx 16 16 w h a False\n",
+      "xxxx 16 17 w a e False\n",
+      "seq1 16 18 w e w True\n",
+      "seq2 16 19 w d d True\n",
+      "xxxx 16 20 w g x False\n",
+      "seq1 17 0 x ! d False\n",
+      "xxxx 17 1 x g u False\n",
+      "xxxx 17 2 x f z False\n",
+      "xxxx 17 3 x e a False\n",
+      "xxxx 17 4 x g z False\n",
+      "xxxx 17 5 x f y False\n",
+      "xxxx 17 6 x a w False\n",
       "xxxx 17 7 x h a False\n",
-      "xxxx 17 8 x c z False\n",
-      "xxxx 17 9 x d y False\n",
-      "xxxx 17 10 x a x False\n",
-      "xxxx 17 11 x e h False\n",
-      "xxxx 17 12 x a x False\n",
-      "seq1 17 13 x h x True\n",
-      "xxxx 17 14 x d u False\n",
-      "xxxx 17 15 x e d False\n",
-      "xxxx 17 16 x b w False\n",
-      "xxxx 17 17 x e e False\n",
-      "xxxx 17 18 x a b False\n",
-      "xxxx 17 19 x c w False\n",
-      "xxxx 17 20 x a e False\n",
-      "seq1 18 0 u ! x False\n",
-      "xxxx 18 1 u b y False\n",
-      "xxxx 18 2 u h d False\n",
-      "xxxx 18 3 u f x False\n",
-      "xxxx 18 4 u g a False\n",
-      "xxxx 18 5 u g e False\n",
-      "xxxx 18 6 u e a False\n",
-      "xxxx 18 7 u h z False\n",
-      "xxxx 18 8 u c y False\n",
-      "xxxx 18 9 u d x False\n",
-      "xxxx 18 10 u a h False\n",
-      "xxxx 18 11 u e x False\n",
-      "xxxx 18 12 u a x False\n",
-      "seq1 18 13 u h u True\n",
-      "seq2 18 14 u d d True\n",
-      "xxxx 18 15 u e w False\n",
-      "xxxx 18 16 u b e False\n",
-      "xxxx 18 17 u e b False\n",
-      "xxxx 18 18 u a w False\n",
-      "xxxx 18 19 u c e False\n",
-      "xxxx 18 20 u a a False\n",
-      "seq1 19 0 w ! y False\n",
-      "xxxx 19 1 w b d False\n",
-      "xxxx 19 2 w h x False\n",
-      "xxxx 19 3 w f a False\n",
-      "xxxx 19 4 w g e False\n",
-      "xxxx 19 5 w g a False\n",
-      "xxxx 19 6 w e z False\n",
-      "xxxx 19 7 w h y False\n",
-      "xxxx 19 8 w c x False\n",
-      "xxxx 19 9 w d h False\n",
-      "xxxx 19 10 w a x False\n",
-      "xxxx 19 11 w e x False\n",
-      "xxxx 19 12 w a u False\n",
-      "xxxx 19 13 w h d False\n",
-      "seq1 19 14 w d w True\n",
-      "seq2 19 15 w e e True\n",
-      "seq2 19 16 w b b True\n",
-      "xxxx 19 17 w e w False\n",
-      "xxxx 19 18 w a e False\n",
-      "xxxx 19 19 w c a False\n",
-      "xxxx 19 20 w a c False\n",
-      "seq1 20 0 w ! d False\n",
-      "xxxx 20 1 w b x False\n",
-      "xxxx 20 2 w h a False\n",
-      "xxxx 20 3 w f e False\n",
-      "xxxx 20 4 w g a False\n",
-      "xxxx 20 5 w g z False\n",
-      "xxxx 20 6 w e y False\n",
-      "xxxx 20 7 w h x False\n",
-      "xxxx 20 8 w c h False\n",
-      "xxxx 20 9 w d x False\n",
-      "xxxx 20 10 w a x False\n",
-      "xxxx 20 11 w e u False\n",
-      "xxxx 20 12 w a d False\n",
-      "xxxx 20 13 w h w False\n",
-      "xxxx 20 14 w d e False\n",
-      "xxxx 20 15 w e b False\n",
-      "seq1 20 16 w b w True\n",
-      "seq2 20 17 w e e True\n",
-      "seq2 20 18 w a a True\n",
-      "seq2 20 19 w c c True\n",
-      "seq2 20 20 w a a True\n",
-      "T T . . . . . . . . . . . . . . . . . . .\n",
-      ". T . . . . . . . . . . . . . . . . . . .\n",
-      ". T T . . . . . . . . . . . . . . . . . .\n",
-      ". . T . . . . . . . . . . . . . . . . . .\n",
-      ". . T T T T . . . . . . . . . . . . . . .\n",
-      ". . . . . T . . . . . . . . . . . . . . .\n",
-      ". . . . . T . . . . . . . . . . . . . . .\n",
-      ". . . . . T . . . . . . . . . . . . . . .\n",
-      ". . . . . T . . . . . . . . . . . . . . .\n",
-      ". . . . . T T T T . . . . . . . . . . . .\n",
-      ". . . . . . . . T . . . . . . . . . . . .\n",
-      ". . . . . . . . T T . . . . . . . . . . .\n",
-      ". . . . . . . . . T T T T . . . . . . . .\n",
-      ". . . . . . . . . . . . T . . . . . . . .\n",
-      ". . . . . . . . . . . . T . . . . . . . .\n",
-      ". . . . . . . . . . . . T T . . . . . . .\n",
-      ". . . . . . . . . . . . . T . . . . . . .\n",
-      ". . . . . . . . . . . . . T . . . . . . .\n",
-      ". . . . . . . . . . . . . T T . . . . . .\n",
-      ". . . . . . . . . . . . . . T T T . . . .\n",
-      ". . . . . . . . . . . . . . . . T T T T T\n"
+      "xxxx 17 8 x g f False\n",
+      "xxxx 17 9 x d g False\n",
+      "xxxx 17 10 x a g False\n",
+      "xxxx 17 11 x a f False\n",
+      "xxxx 17 12 x f h False\n",
+      "xxxx 17 13 x g x False\n",
+      "xxxx 17 14 x g w False\n",
+      "xxxx 17 15 x f a False\n",
+      "xxxx 17 16 x h e False\n",
+      "xxxx 17 17 x a w False\n",
+      "xxxx 17 18 x e d False\n",
+      "seq1 17 19 x d x True\n",
+      "xxxx 17 20 x g u False\n",
+      "seq1 18 0 u ! u False\n",
+      "xxxx 18 1 u g z False\n",
+      "xxxx 18 2 u f a False\n",
+      "xxxx 18 3 u e z False\n",
+      "xxxx 18 4 u g y False\n",
+      "xxxx 18 5 u f w False\n",
+      "xxxx 18 6 u a a False\n",
+      "xxxx 18 7 u h f False\n",
+      "xxxx 18 8 u g g False\n",
+      "xxxx 18 9 u d g False\n",
+      "xxxx 18 10 u a f False\n",
+      "xxxx 18 11 u a h False\n",
+      "xxxx 18 12 u f x False\n",
+      "xxxx 18 13 u g w False\n",
+      "xxxx 18 14 u g a False\n",
+      "xxxx 18 15 u f e False\n",
+      "xxxx 18 16 u h w False\n",
+      "xxxx 18 17 u a d False\n",
+      "xxxx 18 18 u e x False\n",
+      "seq1 18 19 u d u True\n",
+      "xxxx 18 20 u g z False\n",
+      "seq1 19 0 z ! z False\n",
+      "xxxx 19 1 z g a False\n",
+      "xxxx 19 2 z f z False\n",
+      "xxxx 19 3 z e y False\n",
+      "xxxx 19 4 z g w False\n",
+      "xxxx 19 5 z f a False\n",
+      "xxxx 19 6 z a f False\n",
+      "xxxx 19 7 z h g False\n",
+      "xxxx 19 8 z g g False\n",
+      "xxxx 19 9 z d f False\n",
+      "xxxx 19 10 z a h False\n",
+      "xxxx 19 11 z a x False\n",
+      "xxxx 19 12 z f w False\n",
+      "xxxx 19 13 z g a False\n",
+      "xxxx 19 14 z g e False\n",
+      "xxxx 19 15 z f w False\n",
+      "xxxx 19 16 z h d False\n",
+      "xxxx 19 17 z a x False\n",
+      "xxxx 19 18 z e u False\n",
+      "seq1 19 19 z d z True\n",
+      "xxxx 19 20 z g x False\n",
+      "seq1 20 0 x ! a False\n",
+      "xxxx 20 1 x g z False\n",
+      "xxxx 20 2 x f y False\n",
+      "xxxx 20 3 x e w False\n",
+      "xxxx 20 4 x g a False\n",
+      "xxxx 20 5 x f f False\n",
+      "xxxx 20 6 x a g False\n",
+      "xxxx 20 7 x h g False\n",
+      "xxxx 20 8 x g f False\n",
+      "xxxx 20 9 x d h False\n",
+      "xxxx 20 10 x a x False\n",
+      "xxxx 20 11 x a w False\n",
+      "xxxx 20 12 x f a False\n",
+      "xxxx 20 13 x g e False\n",
+      "xxxx 20 14 x g w False\n",
+      "xxxx 20 15 x f d False\n",
+      "xxxx 20 16 x h x False\n",
+      "xxxx 20 17 x a u False\n",
+      "xxxx 20 18 x e z False\n",
+      "seq1 20 19 x d x True\n",
+      "seq2 20 20 x g g True\n",
+      "T T T . . . . . . . . . . . . . . . . . .\n",
+      ". . T T . . . . . . . . . . . . . . . . .\n",
+      ". . . T T T T . . . . . . . . . . . . . .\n",
+      ". . . . . . T . . . . . . . . . . . . . .\n",
+      ". . . . . . T . . . . . . . . . . . . . .\n",
+      ". . . . . . T . . . . . . . . . . . . . .\n",
+      ". . . . . . T . . . . . . . . . . . . . .\n",
+      ". . . . . . T T . . . . . . . . . . . . .\n",
+      ". . . . . . . T T T . . . . . . . . . . .\n",
+      ". . . . . . . . . T . . . . . . . . . . .\n",
+      ". . . . . . . . . T T . . . . . . . . . .\n",
+      ". . . . . . . . . . T . . . . . . . . . .\n",
+      ". . . . . . . . . . T . . . . . . . . . .\n",
+      ". . . . . . . . . . T T T T T T T . . . .\n",
+      ". . . . . . . . . . . . . . . . T . . . .\n",
+      ". . . . . . . . . . . . . . . . T T T . .\n",
+      ". . . . . . . . . . . . . . . . . . T T .\n",
+      ". . . . . . . . . . . . . . . . . . . T .\n",
+      ". . . . . . . . . . . . . . . . . . . T .\n",
+      ". . . . . . . . . . . . . . . . . . . T .\n",
+      ". . . . . . . . . . . . . . . . . . . T T\n"
      ]
     }
    ],
@@ -1261,16 +1276,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 24,
+   "execution_count": 23,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "'bXZhVWfggWZXWWehcXYdXaeaZYXhXXUdWebWeaca'"
+       "'gfZeYgfaZVYUZhVgdUZaZYWafggfhXWaeWdXUZXg'"
       ]
      },
-     "execution_count": 24,
+     "execution_count": 23,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1281,35 +1296,35 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
+   "execution_count": 24,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "T T . . . . . . . . . . . . . . . . . . .\n",
-      ". T . . . . . . . . . . . . . . . . . . .\n",
-      ". T T . . . . . . . . . . . . . . . . . .\n",
-      ". . T . . . . . . . . . . . . . . . . . .\n",
-      ". . T T T T . . . . . . . . . . . . . . .\n",
-      ". . . . . T . . . . . . . . . . . . . . .\n",
-      ". . . . . T . . . . . . . . . . . . . . .\n",
-      ". . . . . T . . . . . . . . . . . . . . .\n",
-      ". . . . . T . . . . . . . . . . . . . . .\n",
-      ". . . . . T T T T . . . . . . . . . . . .\n",
-      ". . . . . . . . T . . . . . . . . . . . .\n",
-      ". . . . . . . . T T . . . . . . . . . . .\n",
-      ". . . . . . . . . T T T T . . . . . . . .\n",
-      ". . . . . . . . . . . . T . . . . . . . .\n",
-      ". . . . . . . . . . . . T . . . . . . . .\n",
-      ". . . . . . . . . . . . T T . . . . . . .\n",
-      ". . . . . . . . . . . . . T . . . . . . .\n",
-      ". . . . . . . . . . . . . T . . . . . . .\n",
-      ". . . . . . . . . . . . . T T . . . . . .\n",
-      ". . . . . . . . . . . . . . T T T . . . .\n",
-      ". . . . . . . . . . . . . . . . T T T T T\n",
-      "bXZhVWfggWZXWWehcXYdXaeaZYXhXXUdWebWeaca\n"
+      "T T T . . . . . . . . . . . . . . . . . .\n",
+      ". . T T . . . . . . . . . . . . . . . . .\n",
+      ". . . T T T T . . . . . . . . . . . . . .\n",
+      ". . . . . . T . . . . . . . . . . . . . .\n",
+      ". . . . . . T . . . . . . . . . . . . . .\n",
+      ". . . . . . T . . . . . . . . . . . . . .\n",
+      ". . . . . . T . . . . . . . . . . . . . .\n",
+      ". . . . . . T T . . . . . . . . . . . . .\n",
+      ". . . . . . . T T T . . . . . . . . . . .\n",
+      ". . . . . . . . . T . . . . . . . . . . .\n",
+      ". . . . . . . . . T T . . . . . . . . . .\n",
+      ". . . . . . . . . . T . . . . . . . . . .\n",
+      ". . . . . . . . . . T . . . . . . . . . .\n",
+      ". . . . . . . . . . T T T T T T T . . . .\n",
+      ". . . . . . . . . . . . . . . . T . . . .\n",
+      ". . . . . . . . . . . . . . . . T T T . .\n",
+      ". . . . . . . . . . . . . . . . . . T T .\n",
+      ". . . . . . . . . . . . . . . . . . . T .\n",
+      ". . . . . . . . . . . . . . . . . . . T .\n",
+      ". . . . . . . . . . . . . . . . . . . T .\n",
+      ". . . . . . . . . . . . . . . . . . . T T\n",
+      "gfZeYgfaZVYUZhVgdUZaZYWafggfhXWaeWdXUZXg\n"
      ]
     },
     {
@@ -1318,7 +1333,7 @@
        "True"
       ]
      },
-     "execution_count": 25,
+     "execution_count": 24,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1332,19 +1347,19 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 26,
+   "execution_count": 25,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "('baffeeecaecbfghedbgbddbcdchbefeddgdbecbaacbdedbeca',\n",
-       " 'affdffbahedebhaagaaahebdeechbfhedcdgcccdcgfbdhaghe',\n",
-       " 'affbaffedeecfaefcbbfaghhededebbhgaagbdaaadbhebdeechbcdchfbehfedcdgecddcgcdcgdfbbdehacgbhaaecbdedbeca',\n",
+       "('chcceahdchbdeahgacbfbfebfefacfebhhcdfgfgggfeahaadd',\n",
+       " 'fbhafageadeedbcdfffaabefeeffaffgebdbchcgfcgggecbgh',\n",
+       " 'chccfbehaahfdcagheabdedeaehgdabccbfdbfebffeffafacfaebefeebfhhcdfafffgebdgfgggbfchceahgaafdcgdggecbgh',\n",
        " 100)"
       ]
      },
-     "execution_count": 26,
+     "execution_count": 25,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1358,65 +1373,65 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 27,
+   "execution_count": 26,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      "T T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . T . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . T . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      "T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . T . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . T . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
       ". . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . T T T T T . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . T T T T T T . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . T . . T T T T . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . T . T T T . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . T . T . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . T . . T T T . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T T . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . .\n",
       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . .\n",
       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T T T T T T\n",
-      "AFFbaffeDeecFaeFcbBfAghHedEDEbBHgAAGbdAAAdbHEBDEECHBcdchFbeHfEDCDGeCddCgCDCGdFbBDeHAcGbHaaEcbdedbeca\n"
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T T . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
+      "chccFBeHaAhFdcAGhEAbdeDEaEhgDaBcCbfDbfebfFefFaFAcfAeBEFEEbFhhcdFAfFFGEBDgfgggBfCHCeahGaaFdCGdGGECBGH\n"
      ]
     },
     {
@@ -1425,7 +1440,7 @@
        "True"
       ]
      },
-     "execution_count": 27,
+     "execution_count": 26,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1439,14 +1454,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 28,
+   "execution_count": 27,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "1000 loops, best of 3: 1.48 ms per loop\n"
+      "1000 loops, best of 3: 1.31 ms per loop\n"
      ]
     }
    ],
@@ -1457,65 +1472,65 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 29,
+   "execution_count": 28,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      "T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
       ". . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
       ". . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
       ". . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . T . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . T . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
       ". . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . T T . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
       ". . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . T T T T T T T T T T . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . T . . T . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T T . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . T T . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . T . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . T T T . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
-      "affBAFFEdEECfAEfCbBFaGhHedEDebBhGaagBDaaaDBhebdeechbCDCHfBEhFedcdgEcDDcGcdcgDfbBdEhaCgBhAAeCBDEDBECA\n"
+      ". . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . T T T T T T . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . T . . . . T T . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . T . T T T T T T T . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . T . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T T T T\n",
+      "CHCCfbEhaAHfDCagHeaBdeDEAeHGdAbcCBFdBFEBfFEffaFACFaEbefeeBfHHCDfaffFgebdGFGGGbFchcEAHgAAfDcgDggecbgh\n"
      ]
     },
     {
@@ -1524,7 +1539,7 @@
        "True"
       ]
      },
-     "execution_count": 29,
+     "execution_count": 28,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1538,7 +1553,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 30,
+   "execution_count": 29,
    "metadata": {},
    "outputs": [
     {
@@ -1547,7 +1562,7 @@
        "True"
       ]
      },
-     "execution_count": 30,
+     "execution_count": 29,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1558,16 +1573,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 31,
+   "execution_count": 30,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "('bgcbeceebhdgegdfehfccbfbagadhbddfbbgecdhegdaegdheh', False, False)"
+       "('cbchedabcadedhfafahdaacbhhhedfhgceafghceehaefaebcc', False, False)"
       ]
      },
-     "execution_count": 31,
+     "execution_count": 30,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1579,18 +1594,18 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 32,
+   "execution_count": 31,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
+      "T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      "T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      "T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
       "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
@@ -1646,7 +1661,7 @@
        "False"
       ]
      },
-     "execution_count": 32,
+     "execution_count": 31,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1660,7 +1675,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 33,
+   "execution_count": 32,
    "metadata": {
     "collapsed": true
    },
@@ -1671,20 +1686,24 @@
     "        return s2 == s3\n",
     "    elif not s2:\n",
     "        return s1 == s3\n",
+    "    elif len(s1) + len(s2) != len(s3):\n",
+    "        return False\n",
     "    else:\n",
-    "        if s1[-1] == s2[-1] and s1[-1] == s3[-1]:\n",
-    "            return is_interleave_recursive(s1[:-1], s2, s3[:-1]) or is_interleave(s1, s2[:-1], s3[:-1])\n",
+    "        if s1[-1] == s3[-1] and s2[-1] == s3[-1]:\n",
+    "            return (is_interleave_recursive(s1[:-1], s2, s3[:-1]) \n",
+    "                    or \n",
+    "                    is_interleave_recursive(s1, s2[:-1], s3[:-1]) )\n",
     "        elif s1[-1] == s3[-1]:\n",
     "            return is_interleave_recursive(s1[:-1], s2, s3[:-1])\n",
     "        elif s2[-1] == s3[-1]:\n",
-    "            return is_interleave(s1, s2[:-1], s3[:-1])\n",
+    "            return is_interleave_recursive(s1, s2[:-1], s3[:-1])\n",
     "        else:\n",
     "            return False"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 34,
+   "execution_count": 33,
    "metadata": {
     "collapsed": true
    },
@@ -1695,7 +1714,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 35,
+   "execution_count": 34,
    "metadata": {
     "collapsed": true
    },
@@ -1726,7 +1745,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 36,
+   "execution_count": 35,
    "metadata": {
     "collapsed": true
    },
@@ -1772,7 +1791,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 61,
+   "execution_count": 36,
    "metadata": {
     "collapsed": true
    },
@@ -1787,7 +1806,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 62,
+   "execution_count": 37,
    "metadata": {},
    "outputs": [
     {
@@ -1812,7 +1831,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 63,
+   "execution_count": 38,
    "metadata": {
     "collapsed": true
    },
@@ -1833,7 +1852,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 64,
+   "execution_count": 39,
    "metadata": {},
    "outputs": [
     {
@@ -1871,7 +1890,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 68,
+   "execution_count": 40,
    "metadata": {},
    "outputs": [
     {
@@ -1897,7 +1916,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 69,
+   "execution_count": 41,
    "metadata": {},
    "outputs": [
     {
@@ -1931,7 +1950,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 70,
+   "execution_count": 42,
    "metadata": {
     "scrolled": true
    },
@@ -1940,41 +1959,41 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "n825af3fb1bf441a3b97d8fbfcdce6f3d [label=\"aabcc\\ndbbca\\naadbbcbcac\"];\n",
-      "n825af3fb1bf441a3b97d8fbfcdce6f3d -> n944a00ca9b134f3c98aeef34526ff17d;\n",
-      "n944a00ca9b134f3c98aeef34526ff17d [label=\"aabc\\ndbbca\\naadbbcbca\"];\n",
-      "n944a00ca9b134f3c98aeef34526ff17d -> n1586862dcfb74b1a9e9f964b7de102ef;\n",
-      "n1586862dcfb74b1a9e9f964b7de102ef [label=\"aabc\\ndbbc\\naadbbcbc\"];\n",
-      "n1586862dcfb74b1a9e9f964b7de102ef -> nf59278631d8047e7b0cca670e412297b;\n",
-      "n1586862dcfb74b1a9e9f964b7de102ef -> nd83e9c32d1fa43bab45dc21d46830924;\n",
-      "nf59278631d8047e7b0cca670e412297b [label=\"aab\\ndbbc\\naadbbcb\"];\n",
-      "nf59278631d8047e7b0cca670e412297b -> nb0424588e9354d2aa61b587a7edfb7f6;\n",
-      "nb0424588e9354d2aa61b587a7edfb7f6 [label=\"aa\\ndbbc\\naadbbc\"];\n",
-      "nb0424588e9354d2aa61b587a7edfb7f6 -> nb73d85cfb09e43d692de22a49de48b35;\n",
-      "nb73d85cfb09e43d692de22a49de48b35 [label=\"aa\\ndbb\\naadbb\"];\n",
-      "nb73d85cfb09e43d692de22a49de48b35 -> n9e34f866ae1746d797cebd4e1fc73af9;\n",
-      "n9e34f866ae1746d797cebd4e1fc73af9 [label=\"aa\\ndb\\naadb\"];\n",
-      "n9e34f866ae1746d797cebd4e1fc73af9 -> n5c7027bfea9f494894cea01fd5e25387;\n",
-      "n5c7027bfea9f494894cea01fd5e25387 [label=\"aa\\nd\\naad\"];\n",
-      "n5c7027bfea9f494894cea01fd5e25387 -> n650da0feb2624011a20e209bada2445c;\n",
-      "n650da0feb2624011a20e209bada2445c [label=\"aa\\n-\\naa\\nTrue\"];\n",
-      "nd83e9c32d1fa43bab45dc21d46830924 [label=\"aabc\\ndbb\\naadbbcb\"];\n",
-      "nd83e9c32d1fa43bab45dc21d46830924 -> n1c4772b660f24d6da9194d16be602b3a;\n",
-      "n1c4772b660f24d6da9194d16be602b3a [label=\"aabc\\ndb\\naadbbc\"];\n",
-      "n1c4772b660f24d6da9194d16be602b3a -> n0393745322e447c79515cffb4afc4d5b;\n",
-      "n0393745322e447c79515cffb4afc4d5b [label=\"aab\\ndb\\naadbb\"];\n",
-      "n0393745322e447c79515cffb4afc4d5b -> na9ae42f3b7dd415886e78bb960b94184;\n",
-      "n0393745322e447c79515cffb4afc4d5b -> nccaf23a4e311415cbe42bedd8a3727c2;\n",
-      "na9ae42f3b7dd415886e78bb960b94184 [label=\"aa\\ndb\\naadb\"];\n",
-      "na9ae42f3b7dd415886e78bb960b94184 -> nab2d4f76a75c4c6686166212cad4b4a3;\n",
-      "nab2d4f76a75c4c6686166212cad4b4a3 [label=\"aa\\nd\\naad\"];\n",
-      "nab2d4f76a75c4c6686166212cad4b4a3 -> nee8a56cc920943e0a2593a8ee863c53c;\n",
-      "nee8a56cc920943e0a2593a8ee863c53c [label=\"aa\\n-\\naa\\nTrue\"];\n",
-      "nccaf23a4e311415cbe42bedd8a3727c2 [label=\"aab\\nd\\naadb\"];\n",
-      "nccaf23a4e311415cbe42bedd8a3727c2 -> ne1d3cf2b04074c10986fdefb464e5da8;\n",
-      "ne1d3cf2b04074c10986fdefb464e5da8 [label=\"aa\\nd\\naad\"];\n",
-      "ne1d3cf2b04074c10986fdefb464e5da8 -> n9091b74bc8a64b91a9e75aef6b016a64;\n",
-      "n9091b74bc8a64b91a9e75aef6b016a64 [label=\"aa\\n-\\naa\\nTrue\"];\n"
+      "ndf96f65c85de45ba814c3aebe4afed65 [label=\"aabcc\\ndbbca\\naadbbcbcac\"];\n",
+      "ndf96f65c85de45ba814c3aebe4afed65 -> n0e6e480c9d664ba2af7e041445763b66;\n",
+      "n0e6e480c9d664ba2af7e041445763b66 [label=\"aabc\\ndbbca\\naadbbcbca\"];\n",
+      "n0e6e480c9d664ba2af7e041445763b66 -> nc7f25932eaf1431cb98430f8b1644221;\n",
+      "nc7f25932eaf1431cb98430f8b1644221 [label=\"aabc\\ndbbc\\naadbbcbc\"];\n",
+      "nc7f25932eaf1431cb98430f8b1644221 -> ncd2942f9e99443619c6ce1d72a10da75;\n",
+      "nc7f25932eaf1431cb98430f8b1644221 -> n0e76b3b46aba4a8abdbd569a0762170a;\n",
+      "ncd2942f9e99443619c6ce1d72a10da75 [label=\"aab\\ndbbc\\naadbbcb\"];\n",
+      "ncd2942f9e99443619c6ce1d72a10da75 -> n4762ffa7e0c6426792438c6f84c9d2f9;\n",
+      "n4762ffa7e0c6426792438c6f84c9d2f9 [label=\"aa\\ndbbc\\naadbbc\"];\n",
+      "n4762ffa7e0c6426792438c6f84c9d2f9 -> n9434633af1674b45ae72a987932bcacc;\n",
+      "n9434633af1674b45ae72a987932bcacc [label=\"aa\\ndbb\\naadbb\"];\n",
+      "n9434633af1674b45ae72a987932bcacc -> n72dd6ed85e8d43d39b1c6b240f672815;\n",
+      "n72dd6ed85e8d43d39b1c6b240f672815 [label=\"aa\\ndb\\naadb\"];\n",
+      "n72dd6ed85e8d43d39b1c6b240f672815 -> nf904e4ea330a48028602500e910001ba;\n",
+      "nf904e4ea330a48028602500e910001ba [label=\"aa\\nd\\naad\"];\n",
+      "nf904e4ea330a48028602500e910001ba -> nc2246b72d95748f5984f7a9a922afafa;\n",
+      "nc2246b72d95748f5984f7a9a922afafa [label=\"aa\\n-\\naa\\nTrue\"];\n",
+      "n0e76b3b46aba4a8abdbd569a0762170a [label=\"aabc\\ndbb\\naadbbcb\"];\n",
+      "n0e76b3b46aba4a8abdbd569a0762170a -> nde239312af534c47988db27094dc5e3b;\n",
+      "nde239312af534c47988db27094dc5e3b [label=\"aabc\\ndb\\naadbbc\"];\n",
+      "nde239312af534c47988db27094dc5e3b -> n0571e43544db4baea762dd9382a90eab;\n",
+      "n0571e43544db4baea762dd9382a90eab [label=\"aab\\ndb\\naadbb\"];\n",
+      "n0571e43544db4baea762dd9382a90eab -> nd24f1944051440d6b94710a3b971c134;\n",
+      "n0571e43544db4baea762dd9382a90eab -> n671eff7dd1f945a28e7bcd0647d7d40d;\n",
+      "nd24f1944051440d6b94710a3b971c134 [label=\"aa\\ndb\\naadb\"];\n",
+      "nd24f1944051440d6b94710a3b971c134 -> n26480b1bcee847adaeb205f2e844a4e5;\n",
+      "n26480b1bcee847adaeb205f2e844a4e5 [label=\"aa\\nd\\naad\"];\n",
+      "n26480b1bcee847adaeb205f2e844a4e5 -> n162a36ef08174bafa51dbf89a58965df;\n",
+      "n162a36ef08174bafa51dbf89a58965df [label=\"aa\\n-\\naa\\nTrue\"];\n",
+      "n671eff7dd1f945a28e7bcd0647d7d40d [label=\"aab\\nd\\naadb\"];\n",
+      "n671eff7dd1f945a28e7bcd0647d7d40d -> n8d9c2dc78a9047d4a243d316e87dd782;\n",
+      "n8d9c2dc78a9047d4a243d316e87dd782 [label=\"aa\\nd\\naad\"];\n",
+      "n8d9c2dc78a9047d4a243d316e87dd782 -> n6d893e899f6f4f77a30c3be1eeef25d0;\n",
+      "n6d893e899f6f4f77a30c3be1eeef25d0 [label=\"aa\\n-\\naa\\nTrue\"];\n"
      ]
     }
    ],
@@ -1985,7 +2004,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 71,
+   "execution_count": 43,
    "metadata": {
     "scrolled": true
    },
@@ -1994,83 +2013,83 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "n894a2781e978478699af2875308ec4ad [label=\"aaa\\naaa\\naaaaaa\"];\n",
-      "n894a2781e978478699af2875308ec4ad -> n863e03f8030547bf9f4e7a4815c4e027;\n",
-      "n894a2781e978478699af2875308ec4ad -> n4c492e6eb94741d2b11567b1b4c729fa;\n",
-      "n863e03f8030547bf9f4e7a4815c4e027 [label=\"aa\\naaa\\naaaaa\"];\n",
-      "n863e03f8030547bf9f4e7a4815c4e027 -> n8f044087a7324ef69d5cf2ae120c0902;\n",
-      "n863e03f8030547bf9f4e7a4815c4e027 -> n5510c6a96018480ba0fc2315d34a69e6;\n",
-      "n8f044087a7324ef69d5cf2ae120c0902 [label=\"a\\naaa\\naaaa\"];\n",
-      "n8f044087a7324ef69d5cf2ae120c0902 -> n6f3153ef68384ebbbe5860a48c774d55;\n",
-      "n8f044087a7324ef69d5cf2ae120c0902 -> n4d068ce52cf248adb3b537805a233dda;\n",
-      "n6f3153ef68384ebbbe5860a48c774d55 [label=\"-\\naaa\\naaa\\nTrue\"];\n",
-      "n4d068ce52cf248adb3b537805a233dda [label=\"a\\naa\\naaa\"];\n",
-      "n4d068ce52cf248adb3b537805a233dda -> nb85aee31625f4998b596d9b6ea3b77fd;\n",
-      "n4d068ce52cf248adb3b537805a233dda -> nec2837ce384246ffb06e3d4090adfb37;\n",
-      "nb85aee31625f4998b596d9b6ea3b77fd [label=\"-\\naa\\naa\\nTrue\"];\n",
-      "nec2837ce384246ffb06e3d4090adfb37 [label=\"a\\na\\naa\"];\n",
-      "nec2837ce384246ffb06e3d4090adfb37 -> n9c395901af2d4e67a7e5a370f759bce6;\n",
-      "nec2837ce384246ffb06e3d4090adfb37 -> nff84b0c784744901afb3ac8a5aef3c23;\n",
-      "n9c395901af2d4e67a7e5a370f759bce6 [label=\"-\\na\\na\\nTrue\"];\n",
-      "nff84b0c784744901afb3ac8a5aef3c23 [label=\"a\\n-\\na\\nTrue\"];\n",
-      "n5510c6a96018480ba0fc2315d34a69e6 [label=\"aa\\naa\\naaaa\"];\n",
-      "n5510c6a96018480ba0fc2315d34a69e6 -> n5eaaabd1caef4c3f8f6607a8bb254906;\n",
-      "n5510c6a96018480ba0fc2315d34a69e6 -> n6041081af67d4f57968572aa2051d1bc;\n",
-      "n5eaaabd1caef4c3f8f6607a8bb254906 [label=\"a\\naa\\naaa\"];\n",
-      "n5eaaabd1caef4c3f8f6607a8bb254906 -> n6dd23a9ed026429fb57cbf94e6283364;\n",
-      "n5eaaabd1caef4c3f8f6607a8bb254906 -> n3042bda75e7c4d8f8a9ccc464f0ba724;\n",
-      "n6dd23a9ed026429fb57cbf94e6283364 [label=\"-\\naa\\naa\\nTrue\"];\n",
-      "n3042bda75e7c4d8f8a9ccc464f0ba724 [label=\"a\\na\\naa\"];\n",
-      "n3042bda75e7c4d8f8a9ccc464f0ba724 -> n5e702eeee87042deb3157b6663b1f07a;\n",
-      "n3042bda75e7c4d8f8a9ccc464f0ba724 -> n37928d6516f942008c5e89b5c37098ee;\n",
-      "n5e702eeee87042deb3157b6663b1f07a [label=\"-\\na\\na\\nTrue\"];\n",
-      "n37928d6516f942008c5e89b5c37098ee [label=\"a\\n-\\na\\nTrue\"];\n",
-      "n6041081af67d4f57968572aa2051d1bc [label=\"aa\\na\\naaa\"];\n",
-      "n6041081af67d4f57968572aa2051d1bc -> nbb96e07d3c89450cb92ad725f6fc4845;\n",
-      "n6041081af67d4f57968572aa2051d1bc -> n0dbe764d7e4a429298f2d3583e8c84b1;\n",
-      "nbb96e07d3c89450cb92ad725f6fc4845 [label=\"a\\na\\naa\"];\n",
-      "nbb96e07d3c89450cb92ad725f6fc4845 -> nbe5a7be2ec824370a293e7aa8f3a5467;\n",
-      "nbb96e07d3c89450cb92ad725f6fc4845 -> ndc15a7d84b734bb793055e4712a82d5c;\n",
-      "nbe5a7be2ec824370a293e7aa8f3a5467 [label=\"-\\na\\na\\nTrue\"];\n",
-      "ndc15a7d84b734bb793055e4712a82d5c [label=\"a\\n-\\na\\nTrue\"];\n",
-      "n0dbe764d7e4a429298f2d3583e8c84b1 [label=\"aa\\n-\\naa\\nTrue\"];\n",
-      "n4c492e6eb94741d2b11567b1b4c729fa [label=\"aaa\\naa\\naaaaa\"];\n",
-      "n4c492e6eb94741d2b11567b1b4c729fa -> n0e78dd2900a34a7297cc0ea2bb27e30c;\n",
-      "n4c492e6eb94741d2b11567b1b4c729fa -> nc18fe2c53e9e4209a9af9c0678465b1f;\n",
-      "n0e78dd2900a34a7297cc0ea2bb27e30c [label=\"aa\\naa\\naaaa\"];\n",
-      "n0e78dd2900a34a7297cc0ea2bb27e30c -> n1b98c16a65994faaa980d9c530383c77;\n",
-      "n0e78dd2900a34a7297cc0ea2bb27e30c -> n33dbe313802045f8895d0e904d588881;\n",
-      "n1b98c16a65994faaa980d9c530383c77 [label=\"a\\naa\\naaa\"];\n",
-      "n1b98c16a65994faaa980d9c530383c77 -> n5e7c6dff46ff49f7903eb543c02fa22b;\n",
-      "n1b98c16a65994faaa980d9c530383c77 -> n33391a1fab3849cf9823ccc7396aa7d4;\n",
-      "n5e7c6dff46ff49f7903eb543c02fa22b [label=\"-\\naa\\naa\\nTrue\"];\n",
-      "n33391a1fab3849cf9823ccc7396aa7d4 [label=\"a\\na\\naa\"];\n",
-      "n33391a1fab3849cf9823ccc7396aa7d4 -> n13b4732016804c3986853f6d2fe4a28b;\n",
-      "n33391a1fab3849cf9823ccc7396aa7d4 -> n767be985e5a5469da7cfeea0272705b3;\n",
-      "n13b4732016804c3986853f6d2fe4a28b [label=\"-\\na\\na\\nTrue\"];\n",
-      "n767be985e5a5469da7cfeea0272705b3 [label=\"a\\n-\\na\\nTrue\"];\n",
-      "n33dbe313802045f8895d0e904d588881 [label=\"aa\\na\\naaa\"];\n",
-      "n33dbe313802045f8895d0e904d588881 -> nf59143762fc643f0bd58507b5097b837;\n",
-      "n33dbe313802045f8895d0e904d588881 -> n30d968450bf147b68a8d7df49177722c;\n",
-      "nf59143762fc643f0bd58507b5097b837 [label=\"a\\na\\naa\"];\n",
-      "nf59143762fc643f0bd58507b5097b837 -> ncd2168bdc52c459d821427219fb885d1;\n",
-      "nf59143762fc643f0bd58507b5097b837 -> nc6011f3f746f425ab01fd89e1f17cbb4;\n",
-      "ncd2168bdc52c459d821427219fb885d1 [label=\"-\\na\\na\\nTrue\"];\n",
-      "nc6011f3f746f425ab01fd89e1f17cbb4 [label=\"a\\n-\\na\\nTrue\"];\n",
-      "n30d968450bf147b68a8d7df49177722c [label=\"aa\\n-\\naa\\nTrue\"];\n",
-      "nc18fe2c53e9e4209a9af9c0678465b1f [label=\"aaa\\na\\naaaa\"];\n",
-      "nc18fe2c53e9e4209a9af9c0678465b1f -> n38a7aa8aab21444d8b9d50ca71871b7e;\n",
-      "nc18fe2c53e9e4209a9af9c0678465b1f -> n1ec1cf69ce3c4798b305338648a6e46b;\n",
-      "n38a7aa8aab21444d8b9d50ca71871b7e [label=\"aa\\na\\naaa\"];\n",
-      "n38a7aa8aab21444d8b9d50ca71871b7e -> nad5433a86522484e85d560ac7d202b3d;\n",
-      "n38a7aa8aab21444d8b9d50ca71871b7e -> n6bfb83c32f9e46a19e9408fc087e74ae;\n",
-      "nad5433a86522484e85d560ac7d202b3d [label=\"a\\na\\naa\"];\n",
-      "nad5433a86522484e85d560ac7d202b3d -> n292f0206736a40ac8f6045ac0d8a0a07;\n",
-      "nad5433a86522484e85d560ac7d202b3d -> n07c65e03d3bd473f97579a2c63f922c7;\n",
-      "n292f0206736a40ac8f6045ac0d8a0a07 [label=\"-\\na\\na\\nTrue\"];\n",
-      "n07c65e03d3bd473f97579a2c63f922c7 [label=\"a\\n-\\na\\nTrue\"];\n",
-      "n6bfb83c32f9e46a19e9408fc087e74ae [label=\"aa\\n-\\naa\\nTrue\"];\n",
-      "n1ec1cf69ce3c4798b305338648a6e46b [label=\"aaa\\n-\\naaa\\nTrue\"];\n"
+      "n8ab105a57ff44daa8fa8c0bd8275721c [label=\"aaa\\naaa\\naaaaaa\"];\n",
+      "n8ab105a57ff44daa8fa8c0bd8275721c -> ndd3ec050e4d441ba9f5eca4140804aa2;\n",
+      "n8ab105a57ff44daa8fa8c0bd8275721c -> n5fe9af06410d4e3796f3e5b09724befb;\n",
+      "ndd3ec050e4d441ba9f5eca4140804aa2 [label=\"aa\\naaa\\naaaaa\"];\n",
+      "ndd3ec050e4d441ba9f5eca4140804aa2 -> n4da003b54dd94728a1aa1890f1a9250a;\n",
+      "ndd3ec050e4d441ba9f5eca4140804aa2 -> ncb2a3fd92dc6414a99dc115990760e7c;\n",
+      "n4da003b54dd94728a1aa1890f1a9250a [label=\"a\\naaa\\naaaa\"];\n",
+      "n4da003b54dd94728a1aa1890f1a9250a -> n699e6ec8bba74ec394a68d5c2d306c30;\n",
+      "n4da003b54dd94728a1aa1890f1a9250a -> n71376b3b5e614617ba68dccf8d9677cc;\n",
+      "n699e6ec8bba74ec394a68d5c2d306c30 [label=\"-\\naaa\\naaa\\nTrue\"];\n",
+      "n71376b3b5e614617ba68dccf8d9677cc [label=\"a\\naa\\naaa\"];\n",
+      "n71376b3b5e614617ba68dccf8d9677cc -> nb876b970b38f4ba2937a69ba491f308c;\n",
+      "n71376b3b5e614617ba68dccf8d9677cc -> nfb2ebec95c5c46c6b160c511031f5417;\n",
+      "nb876b970b38f4ba2937a69ba491f308c [label=\"-\\naa\\naa\\nTrue\"];\n",
+      "nfb2ebec95c5c46c6b160c511031f5417 [label=\"a\\na\\naa\"];\n",
+      "nfb2ebec95c5c46c6b160c511031f5417 -> ndcf30cbbd8f646adb30c01e8fbc8aaaf;\n",
+      "nfb2ebec95c5c46c6b160c511031f5417 -> n9bb6593bab3c47e59f83df2767b67a3a;\n",
+      "ndcf30cbbd8f646adb30c01e8fbc8aaaf [label=\"-\\na\\na\\nTrue\"];\n",
+      "n9bb6593bab3c47e59f83df2767b67a3a [label=\"a\\n-\\na\\nTrue\"];\n",
+      "ncb2a3fd92dc6414a99dc115990760e7c [label=\"aa\\naa\\naaaa\"];\n",
+      "ncb2a3fd92dc6414a99dc115990760e7c -> n937d754714994223bc97015534e1806e;\n",
+      "ncb2a3fd92dc6414a99dc115990760e7c -> n553eac2d6c4542448a5c82b781e963b1;\n",
+      "n937d754714994223bc97015534e1806e [label=\"a\\naa\\naaa\"];\n",
+      "n937d754714994223bc97015534e1806e -> n08a6688eb7df48f8834787728a0e36a2;\n",
+      "n937d754714994223bc97015534e1806e -> n063d395576474c5b82d810b2b70e7e3c;\n",
+      "n08a6688eb7df48f8834787728a0e36a2 [label=\"-\\naa\\naa\\nTrue\"];\n",
+      "n063d395576474c5b82d810b2b70e7e3c [label=\"a\\na\\naa\"];\n",
+      "n063d395576474c5b82d810b2b70e7e3c -> n04b9f6aea46c458da227558ab02a0b4c;\n",
+      "n063d395576474c5b82d810b2b70e7e3c -> nc067208a5ab64f8c9904d58b738b81e4;\n",
+      "n04b9f6aea46c458da227558ab02a0b4c [label=\"-\\na\\na\\nTrue\"];\n",
+      "nc067208a5ab64f8c9904d58b738b81e4 [label=\"a\\n-\\na\\nTrue\"];\n",
+      "n553eac2d6c4542448a5c82b781e963b1 [label=\"aa\\na\\naaa\"];\n",
+      "n553eac2d6c4542448a5c82b781e963b1 -> n5d50905c46ce4dc8bcb59fb62984fa54;\n",
+      "n553eac2d6c4542448a5c82b781e963b1 -> n6768e9ad78804e65b1bde9cb655f2a60;\n",
+      "n5d50905c46ce4dc8bcb59fb62984fa54 [label=\"a\\na\\naa\"];\n",
+      "n5d50905c46ce4dc8bcb59fb62984fa54 -> n22bc48dd2aa84e79a387252cc28f3a92;\n",
+      "n5d50905c46ce4dc8bcb59fb62984fa54 -> n853ef88a20ee48a4bccf390498c96f5d;\n",
+      "n22bc48dd2aa84e79a387252cc28f3a92 [label=\"-\\na\\na\\nTrue\"];\n",
+      "n853ef88a20ee48a4bccf390498c96f5d [label=\"a\\n-\\na\\nTrue\"];\n",
+      "n6768e9ad78804e65b1bde9cb655f2a60 [label=\"aa\\n-\\naa\\nTrue\"];\n",
+      "n5fe9af06410d4e3796f3e5b09724befb [label=\"aaa\\naa\\naaaaa\"];\n",
+      "n5fe9af06410d4e3796f3e5b09724befb -> ne6b19fc7e02b4981a1edc20c7fe0cce0;\n",
+      "n5fe9af06410d4e3796f3e5b09724befb -> ne0c07d6d54f045a5b4bf9eb10bd8d810;\n",
+      "ne6b19fc7e02b4981a1edc20c7fe0cce0 [label=\"aa\\naa\\naaaa\"];\n",
+      "ne6b19fc7e02b4981a1edc20c7fe0cce0 -> n9d2cfd4e9cf2473bbd05a8a7e2a96714;\n",
+      "ne6b19fc7e02b4981a1edc20c7fe0cce0 -> n3d4e61bc032c4f8387c269d8ac49cc3f;\n",
+      "n9d2cfd4e9cf2473bbd05a8a7e2a96714 [label=\"a\\naa\\naaa\"];\n",
+      "n9d2cfd4e9cf2473bbd05a8a7e2a96714 -> n214f88e71d504eaba78b46c5a5bbe31d;\n",
+      "n9d2cfd4e9cf2473bbd05a8a7e2a96714 -> n2890559b11cb49c9aa083a76a7b68ce4;\n",
+      "n214f88e71d504eaba78b46c5a5bbe31d [label=\"-\\naa\\naa\\nTrue\"];\n",
+      "n2890559b11cb49c9aa083a76a7b68ce4 [label=\"a\\na\\naa\"];\n",
+      "n2890559b11cb49c9aa083a76a7b68ce4 -> n5d37f312b10341d09e2faa4fb4f40e3c;\n",
+      "n2890559b11cb49c9aa083a76a7b68ce4 -> nd73fc499c4214ddbbe7155f97c9ff394;\n",
+      "n5d37f312b10341d09e2faa4fb4f40e3c [label=\"-\\na\\na\\nTrue\"];\n",
+      "nd73fc499c4214ddbbe7155f97c9ff394 [label=\"a\\n-\\na\\nTrue\"];\n",
+      "n3d4e61bc032c4f8387c269d8ac49cc3f [label=\"aa\\na\\naaa\"];\n",
+      "n3d4e61bc032c4f8387c269d8ac49cc3f -> nfac20fc8bb7441f891ac0380259f3b76;\n",
+      "n3d4e61bc032c4f8387c269d8ac49cc3f -> n9d9c86dc313f48b69d9c2693ee32e7ab;\n",
+      "nfac20fc8bb7441f891ac0380259f3b76 [label=\"a\\na\\naa\"];\n",
+      "nfac20fc8bb7441f891ac0380259f3b76 -> n14489559bae24e99b2d816716ceef683;\n",
+      "nfac20fc8bb7441f891ac0380259f3b76 -> n44c425cd261c4c19971a47901723f942;\n",
+      "n14489559bae24e99b2d816716ceef683 [label=\"-\\na\\na\\nTrue\"];\n",
+      "n44c425cd261c4c19971a47901723f942 [label=\"a\\n-\\na\\nTrue\"];\n",
+      "n9d9c86dc313f48b69d9c2693ee32e7ab [label=\"aa\\n-\\naa\\nTrue\"];\n",
+      "ne0c07d6d54f045a5b4bf9eb10bd8d810 [label=\"aaa\\na\\naaaa\"];\n",
+      "ne0c07d6d54f045a5b4bf9eb10bd8d810 -> n8d8289489db44271b99f22c572668eaa;\n",
+      "ne0c07d6d54f045a5b4bf9eb10bd8d810 -> n4eda0dd1e0e34c8c9a81beba5c70fe5f;\n",
+      "n8d8289489db44271b99f22c572668eaa [label=\"aa\\na\\naaa\"];\n",
+      "n8d8289489db44271b99f22c572668eaa -> n156514e9dbcb44a8a6b4d96f1ec3e48f;\n",
+      "n8d8289489db44271b99f22c572668eaa -> n3ba7c5a0cc3b405aa6ca7899ee85a518;\n",
+      "n156514e9dbcb44a8a6b4d96f1ec3e48f [label=\"a\\na\\naa\"];\n",
+      "n156514e9dbcb44a8a6b4d96f1ec3e48f -> n3b99ff94eb914661bafe9ba4c0c997e2;\n",
+      "n156514e9dbcb44a8a6b4d96f1ec3e48f -> n91eac98d4ed74a1f99fd48ca60111d2c;\n",
+      "n3b99ff94eb914661bafe9ba4c0c997e2 [label=\"-\\na\\na\\nTrue\"];\n",
+      "n91eac98d4ed74a1f99fd48ca60111d2c [label=\"a\\n-\\na\\nTrue\"];\n",
+      "n3ba7c5a0cc3b405aa6ca7899ee85a518 [label=\"aa\\n-\\naa\\nTrue\"];\n",
+      "n4eda0dd1e0e34c8c9a81beba5c70fe5f [label=\"aaa\\n-\\naaa\\nTrue\"];\n"
      ]
     }
    ],
@@ -2081,7 +2100,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 70,
+   "execution_count": 44,
    "metadata": {
     "scrolled": true
    },
@@ -2090,15 +2109,15 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "nd6df1effdb85482db276ea5fea364b79 [label=\"acb\\naba\\nabacab\"];\n",
-      "nd6df1effdb85482db276ea5fea364b79 -> necd79ad17e9d435c9f49c1c1ae26b524;\n",
-      "necd79ad17e9d435c9f49c1c1ae26b524 [label=\"ac\\naba\\nabaca\"];\n",
-      "necd79ad17e9d435c9f49c1c1ae26b524 -> n369b759fead243e0b35621ac1dbc09de;\n",
-      "n369b759fead243e0b35621ac1dbc09de [label=\"ac\\nab\\nabac\"];\n",
-      "n369b759fead243e0b35621ac1dbc09de -> nc4a2401f9791408ba2bb7b4052c27f11;\n",
-      "nc4a2401f9791408ba2bb7b4052c27f11 [label=\"a\\nab\\naba\"];\n",
-      "nc4a2401f9791408ba2bb7b4052c27f11 -> n71b5737da5e54fcb9dfdee6085091a01;\n",
-      "n71b5737da5e54fcb9dfdee6085091a01 [label=\"-\\nab\\nab\\nTrue\"];\n"
+      "n5d63e71661ed4a8ead31b5c5f9c1949b [label=\"acb\\naba\\nabacab\"];\n",
+      "n5d63e71661ed4a8ead31b5c5f9c1949b -> n11bd1802979b4332bdf9cf6cc3b2a51c;\n",
+      "n11bd1802979b4332bdf9cf6cc3b2a51c [label=\"ac\\naba\\nabaca\"];\n",
+      "n11bd1802979b4332bdf9cf6cc3b2a51c -> n8a082af1ba074b84b7410b97554be94f;\n",
+      "n8a082af1ba074b84b7410b97554be94f [label=\"ac\\nab\\nabac\"];\n",
+      "n8a082af1ba074b84b7410b97554be94f -> n6ec78858d88046c8b8531a63f38825b3;\n",
+      "n6ec78858d88046c8b8531a63f38825b3 [label=\"a\\nab\\naba\"];\n",
+      "n6ec78858d88046c8b8531a63f38825b3 -> na563514a3f194725be7160850c3c8369;\n",
+      "na563514a3f194725be7160850c3c8369 [label=\"-\\nab\\nab\\nTrue\"];\n"
      ]
     }
    ],
@@ -2109,7 +2128,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 35,
+   "execution_count": 45,
    "metadata": {
     "collapsed": true
    },
@@ -2124,7 +2143,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 36,
+   "execution_count": 48,
    "metadata": {},
    "outputs": [
     {
@@ -2133,7 +2152,7 @@
        "True"
       ]
      },
-     "execution_count": 36,
+     "execution_count": 48,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2144,7 +2163,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 37,
+   "execution_count": 49,
    "metadata": {},
    "outputs": [
     {
@@ -2153,7 +2172,7 @@
        "False"
       ]
      },
-     "execution_count": 37,
+     "execution_count": 49,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2171,7 +2190,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 38,
+   "execution_count": 50,
    "metadata": {
     "collapsed": true
    },
@@ -2184,7 +2203,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 39,
+   "execution_count": 51,
    "metadata": {
     "collapsed": true
    },
@@ -2210,29 +2229,29 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 40,
+   "execution_count": 52,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "0: baddacaddb\n",
-      "1: bcccacbacb\n",
-      "2: cdcddbcccacbacbaabcc\n",
-      "3: cdccdbadcaacbbcccaac\n",
-      "4: bbacccdacdacadbdbacb\n",
-      "5: cbaccbbcadadaaccaddb\n",
-      "6: cbaccbcaac\n"
+      "0: ddadbdcbdc\n",
+      "1: bbcbbabdab\n",
+      "2: dcddddbbdb\n",
+      "3: cccbbbcbabadbddcabda\n",
+      "4: ddcdddadddbbbddbcbdc\n",
+      "5: dcccdddcbdbadbdbdcda\n",
+      "6: ddadbbcbbbdacbbdcdab\n"
      ]
     },
     {
      "data": {
       "text/plain": [
-       "['bbacccdacdacadbdbacb']"
+       "['ddadbbcbbbdacbbdcdab']"
       ]
      },
-     "execution_count": 40,
+     "execution_count": 52,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2253,27 +2272,27 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 41,
+   "execution_count": 53,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "* b . . . . . . . . .\n",
-      "b b . . . . . . . . .\n",
-      ". a c c c . . . . . .\n",
-      ". . . . d a c . . . .\n",
-      ". . . . . . d . . . .\n",
-      ". . . . . . a . . . .\n",
-      ". . . . . . c . . . .\n",
-      ". . . . . . a . . . .\n",
-      ". . . . . . d b . . .\n",
+      "* . . . . . . . . . .\n",
+      "d . . . . . . . . . .\n",
+      "d . . . . . . . . . .\n",
+      "a . . . . . . . . . .\n",
+      "d b b c b b . . . . .\n",
+      "b b . b b b . . . . .\n",
+      ". . . . . d a . . . .\n",
+      ". . . . . . c b . . .\n",
+      ". . . . . . b b d . .\n",
       ". . . . . . . d . . .\n",
-      ". . . . . . . b a c b\n",
-      "bBAcccDacDACADbDBacb\n",
-      "bbacccdacdacadbdbacb\n",
-      " **   *  ***** **   \n"
+      ". . . . . . . c d a b\n",
+      "DDADbbcbbBDaCbBDCdab\n",
+      "ddadbbcbbbdacbbdcdab\n",
+      "****     ** * ***   \n"
      ]
     },
     {
@@ -2282,7 +2301,7 @@
        "True"
       ]
      },
-     "execution_count": 41,
+     "execution_count": 53,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2297,24 +2316,24 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 42,
+   "execution_count": 54,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "cbaccbbcadadaaccaddb\n",
-      "      * ** * * *****\n"
+      "ddcdddadddbbbddbcbdc\n",
+      " *   **  *  * * ****\n"
      ]
     },
     {
      "data": {
       "text/plain": [
-       "5"
+       "4"
       ]
      },
-     "execution_count": 42,
+     "execution_count": 54,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2328,27 +2347,27 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 43,
+   "execution_count": 55,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "* b . . . . . . . . .\n",
-      "b b a . . . . . . . .\n",
-      ". . c . . . . . . . .\n",
-      ". . c . . . . . . . .\n",
-      ". . c d . . . . . . .\n",
-      ". . . a . . . . . . .\n",
-      ". . . c d a c a d . .\n",
-      ". . . . . . . . b d b\n",
+      "* d d a d b . . . . .\n",
+      ". . . . b b . . . . .\n",
+      ". . . . b . . . . . .\n",
+      ". . . . c b . . . . .\n",
+      ". . . . b b . . . . .\n",
+      ". . . . b b d . . . .\n",
+      ". . . . . . a c b . .\n",
+      ". . . . . . . b b d c\n",
+      ". . . . . . . . d . d\n",
       ". . . . . . . . . . a\n",
-      ". . . . . . . . . . c\n",
       ". . . . . . . . . . b\n",
-      "bBaCCCdACdacadBdbACB\n",
-      "bbacccdacdacadbdbacb\n",
-      " * *** **     *  ***\n"
+      "ddadBBCbBBdAcbBdcDAB\n",
+      "ddadbbcbbbdacbbdcdab\n",
+      "    *** ** *  *  ***\n"
      ]
     },
     {
@@ -2357,7 +2376,7 @@
        "True"
       ]
      },
-     "execution_count": 43,
+     "execution_count": 55,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2372,27 +2391,26 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 44,
+   "execution_count": 56,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "* . . . . . . . . . .\n",
+      "* d . . . . . . . . .\n",
+      "d d . . . . . . . . .\n",
+      "d . . . . . . . . . .\n",
+      "a d . . . . . . . . .\n",
+      "d . . . . . . . . . .\n",
       "b . . . . . . . . . .\n",
       ". . . . . . . . . . .\n",
       ". . . . . . . . . . .\n",
       ". . . . . . . . . . .\n",
       ". . . . . . . . . . .\n",
       ". . . . . . . . . . .\n",
-      ". . . . . . . . . . .\n",
-      ". . . . . . . . . . .\n",
-      ". . . . . . . . . . .\n",
-      ". . . . . . . . . . .\n",
-      "B\n",
-      "b\n",
-      "*\n"
+      "\n",
+      "\n"
      ]
     },
     {
@@ -2401,7 +2419,7 @@
        "False"
       ]
      },
-     "execution_count": 44,
+     "execution_count": 56,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2416,15 +2434,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 45,
+   "execution_count": 57,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "* . . . . . . . . . .\n",
-      "b . . . . . . . . . .\n",
+      "* d . . . . . . . . .\n",
       ". . . . . . . . . . .\n",
       ". . . . . . . . . . .\n",
       ". . . . . . . . . . .\n",
@@ -2434,9 +2451,10 @@
       ". . . . . . . . . . .\n",
       ". . . . . . . . . . .\n",
       ". . . . . . . . . . .\n",
-      "B\n",
-      "b\n",
-      "*\n"
+      ". . . . . . . . . . .\n",
+      "d\n",
+      "d\n",
+      " \n"
      ]
     },
     {
@@ -2445,7 +2463,7 @@
        "False"
       ]
      },
-     "execution_count": 45,
+     "execution_count": 57,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2481,7 +2499,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 46,
+   "execution_count": 58,
    "metadata": {
     "collapsed": true
    },
@@ -2502,7 +2520,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 47,
+   "execution_count": 59,
    "metadata": {
     "collapsed": true
    },
@@ -2513,15 +2531,15 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 48,
+   "execution_count": 60,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CPU times: user 2.96 s, sys: 4 ms, total: 2.97 s\n",
-      "Wall time: 2.97 s\n"
+      "CPU times: user 3.2 s, sys: 96 ms, total: 3.3 s\n",
+      "Wall time: 3.3 s\n"
      ]
     },
     {
@@ -2530,7 +2548,7 @@
        "[0]"
       ]
      },
-     "execution_count": 48,
+     "execution_count": 60,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2541,15 +2559,15 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 49,
+   "execution_count": 61,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CPU times: user 660 ms, sys: 0 ns, total: 660 ms\n",
-      "Wall time: 658 ms\n"
+      "CPU times: user 0 ns, sys: 0 ns, total: 0 ns\n",
+      "Wall time: 570 µs\n"
      ]
     },
     {
@@ -2558,7 +2576,7 @@
        "[0]"
       ]
      },
-     "execution_count": 49,
+     "execution_count": 61,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2569,7 +2587,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 50,
+   "execution_count": 62,
    "metadata": {
     "collapsed": true
    },
@@ -2586,7 +2604,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 51,
+   "execution_count": 63,
    "metadata": {
     "collapsed": true
    },
@@ -2603,7 +2621,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 52,
+   "execution_count": 64,
    "metadata": {
     "collapsed": true
    },
@@ -2623,7 +2641,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 53,
+   "execution_count": 65,
    "metadata": {},
    "outputs": [
     {
@@ -2632,7 +2650,7 @@
        "(40, 40, 20, 20)"
       ]
      },
-     "execution_count": 53,
+     "execution_count": 65,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2663,7 +2681,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 54,
+   "execution_count": 66,
    "metadata": {},
    "outputs": [
     {
@@ -2672,7 +2690,7 @@
        "(True, True)"
       ]
      },
-     "execution_count": 54,
+     "execution_count": 66,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2683,7 +2701,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 55,
+   "execution_count": 67,
    "metadata": {},
    "outputs": [
     {
@@ -2692,7 +2710,7 @@
        "(True, True)"
       ]
      },
-     "execution_count": 55,
+     "execution_count": 67,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2703,7 +2721,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 56,
+   "execution_count": 68,
    "metadata": {},
    "outputs": [
     {
@@ -2712,7 +2730,7 @@
        "(False, True)"
       ]
      },
-     "execution_count": 56,
+     "execution_count": 68,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2723,19 +2741,19 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 57,
+   "execution_count": 69,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "('echgeaeeefdcebeaahaf',\n",
-       " 'eeahaaeeefdcebedghbg',\n",
-       " 'eeecahahgeaaeeebafaadgceadabefdaghbgahaf',\n",
-       " 'eecheagehaaaeeeeeefdcebefadahcaebfedghbg')"
+       "('hbgbfhdaghfbcagbhhgh',\n",
+       " 'eccfdhdaghfbcaggbaae',\n",
+       " 'ehccbfgbdfhfefdbagefagehfgbcaggbbhahgaeh',\n",
+       " 'hecbgbfhdagchffbdhcagdbhaghhfgbchaggbaae')"
       ]
      },
-     "execution_count": 57,
+     "execution_count": 69,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2746,7 +2764,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 58,
+   "execution_count": 70,
    "metadata": {},
    "outputs": [
     {
@@ -2755,7 +2773,7 @@
        "False"
       ]
      },
-     "execution_count": 58,
+     "execution_count": 70,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2767,16 +2785,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 59,
+   "execution_count": 71,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "('eeahaaeeefdceb', 'eeahaaeeefdcebedghbg')"
+       "('eccfdhdaghfbc', 'eccfdhdaghfbcaggbaae')"
       ]
      },
-     "execution_count": 59,
+     "execution_count": 71,
      "metadata": {},
      "output_type": "execute_result"
     }
diff --git a/09-resolving-the-bill/resolving-the-bill-solution.ipynb b/09-resolving-the-bill/resolving-the-bill-solution.ipynb
index ed427e6..dc846ae 100644
--- a/09-resolving-the-bill/resolving-the-bill-solution.ipynb
+++ b/09-resolving-the-bill/resolving-the-bill-solution.ipynb
@@ -78,7 +78,19 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 104,
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "import sys\n",
+    "sys.setrecursionlimit(10**6)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
    "metadata": {},
    "outputs": [
     {
@@ -87,7 +99,7 @@
        "148"
       ]
      },
-     "execution_count": 104,
+     "execution_count": 3,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -100,7 +112,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 105,
+   "execution_count": 4,
    "metadata": {
     "collapsed": true
    },
@@ -114,7 +126,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 106,
+   "execution_count": 5,
    "metadata": {
     "collapsed": true
    },
@@ -134,7 +146,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 107,
+   "execution_count": 6,
    "metadata": {
     "collapsed": true
    },
@@ -158,7 +170,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 108,
+   "execution_count": 7,
    "metadata": {
     "collapsed": true
    },
@@ -178,7 +190,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 109,
+   "execution_count": 8,
    "metadata": {
     "collapsed": true
    },
@@ -195,7 +207,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 110,
+   "execution_count": 9,
    "metadata": {
     "collapsed": true
    },
@@ -250,7 +262,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 111,
+   "execution_count": 10,
    "metadata": {
     "collapsed": true
    },
@@ -301,7 +313,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 112,
+   "execution_count": 11,
    "metadata": {},
    "outputs": [
     {
@@ -310,7 +322,7 @@
        "22"
       ]
      },
-     "execution_count": 112,
+     "execution_count": 11,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -323,7 +335,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 113,
+   "execution_count": 12,
    "metadata": {},
    "outputs": [
     {
@@ -332,7 +344,7 @@
        "22"
       ]
      },
-     "execution_count": 113,
+     "execution_count": 12,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -345,7 +357,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 114,
+   "execution_count": 13,
    "metadata": {},
    "outputs": [
     {
@@ -354,7 +366,7 @@
        "22"
       ]
      },
-     "execution_count": 114,
+     "execution_count": 13,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -367,14 +379,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 30,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "1 loop, best of 3: 7.07 s per loop\n"
+      "100 loops, best of 3: 13.1 ms per loop\n"
      ]
     }
    ],
@@ -382,12 +394,32 @@
     "%%timeit\n",
     "sum(1 for s in bills\n",
     "   if s != 0\n",
-    "   if is_subseq(bills[0], bills[s]))"
+    "   if is_subseq_greedy(bills[0], bills[s]))"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 14,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1 loop, best of 3: 7.88 s per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "sum(1 for s in bills\n",
+    "   if s != 0\n",
+    "   if is_subseq(bills[0], bills[s]))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
    "metadata": {
     "scrolled": true
    },
@@ -419,7 +451,7 @@
        " 146]"
       ]
      },
-     "execution_count": 14,
+     "execution_count": 15,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -432,15 +464,15 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 16,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CPU times: user 148 ms, sys: 0 ns, total: 148 ms\n",
-      "Wall time: 148 ms\n"
+      "CPU times: user 148 ms, sys: 4 ms, total: 152 ms\n",
+      "Wall time: 150 ms\n"
      ]
     },
     {
@@ -449,7 +481,7 @@
        "(True, False)"
       ]
      },
-     "execution_count": 15,
+     "execution_count": 16,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -460,7 +492,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 17,
    "metadata": {
     "collapsed": true
    },
@@ -471,7 +503,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 18,
    "metadata": {},
    "outputs": [
     {
@@ -698,7 +730,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 31,
    "metadata": {
     "collapsed": true
    },
@@ -709,20 +741,24 @@
     "        return s2 == s3\n",
     "    elif not s2:\n",
     "        return s1 == s3\n",
+    "    elif len(s1) + len(s2) != len(s3):\n",
+    "        return False\n",
     "    else:\n",
-    "        if s1[-1] == s2[-1] and s1[-1] == s3[-1]:\n",
-    "            return is_interleave_recursive(s1[:-1], s2, s3[:-1]) or is_interleave(s1, s2[:-1], s3[:-1])\n",
+    "        if s1[-1] == s3[-1] and s2[-1] == s3[-1]:\n",
+    "            return (is_interleave_recursive(s1[:-1], s2, s3[:-1]) \n",
+    "                    or \n",
+    "                    is_interleave_recursive(s1, s2[:-1], s3[:-1]) )\n",
     "        elif s1[-1] == s3[-1]:\n",
     "            return is_interleave_recursive(s1[:-1], s2, s3[:-1])\n",
     "        elif s2[-1] == s3[-1]:\n",
-    "            return is_interleave(s1, s2[:-1], s3[:-1])\n",
+    "            return is_interleave_recursive(s1, s2[:-1], s3[:-1])\n",
     "        else:\n",
     "            return False"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 20,
    "metadata": {
     "collapsed": true
    },
@@ -798,7 +834,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 21,
    "metadata": {
     "collapsed": true
    },
@@ -871,7 +907,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 22,
    "metadata": {
     "collapsed": true
    },
@@ -951,7 +987,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 23,
    "metadata": {
     "collapsed": true
    },
@@ -975,7 +1011,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 24,
    "metadata": {},
    "outputs": [
     {
@@ -984,7 +1020,7 @@
        "[30]"
       ]
      },
-     "execution_count": 23,
+     "execution_count": 24,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -996,7 +1032,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 24,
+   "execution_count": 25,
    "metadata": {},
    "outputs": [
     {
@@ -1005,7 +1041,7 @@
        "[30]"
       ]
      },
-     "execution_count": 24,
+     "execution_count": 25,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1017,7 +1053,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
+   "execution_count": 26,
    "metadata": {},
    "outputs": [
     {
@@ -1026,7 +1062,7 @@
        "[30]"
       ]
      },
-     "execution_count": 25,
+     "execution_count": 26,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1038,7 +1074,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 102,
+   "execution_count": 27,
    "metadata": {},
    "outputs": [
     {
@@ -1047,7 +1083,7 @@
        "[30]"
       ]
      },
-     "execution_count": 102,
+     "execution_count": 27,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1060,7 +1096,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 26,
+   "execution_count": 28,
    "metadata": {},
    "outputs": [
     {
@@ -1277,7 +1313,7 @@
        "True"
       ]
      },
-     "execution_count": 26,
+     "execution_count": 28,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1291,7 +1327,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 27,
+   "execution_count": 32,
    "metadata": {},
    "outputs": [
     {
@@ -1300,7 +1336,7 @@
        "[30]"
       ]
      },
-     "execution_count": 27,
+     "execution_count": 32,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1312,14 +1348,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 28,
+   "execution_count": 33,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "1 loop, best of 3: 2.81 s per loop\n"
+      "1 loop, best of 3: 3.12 s per loop\n"
      ]
     }
    ],
@@ -1331,14 +1367,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 29,
+   "execution_count": 34,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "1 loop, best of 3: 916 ms per loop\n"
+      "1 loop, best of 3: 971 ms per loop\n"
      ]
     }
    ],
@@ -1350,14 +1386,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 30,
+   "execution_count": 35,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "1 loop, best of 3: 1.45 s per loop\n"
+      "1 loop, best of 3: 1.56 s per loop\n"
      ]
     }
    ],
@@ -1369,14 +1405,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 31,
+   "execution_count": 36,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "1 loop, best of 3: 705 ms per loop\n"
+      "1000 loops, best of 3: 510 µs per loop\n"
      ]
     }
    ],
@@ -1403,7 +1439,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 32,
+   "execution_count": 37,
    "metadata": {},
    "outputs": [
     {
@@ -1412,7 +1448,7 @@
        "(4.223305555555555, 4, 13, 23.899999999999636)"
       ]
      },
-     "execution_count": 32,
+     "execution_count": 37,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1428,7 +1464,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 33,
+   "execution_count": 38,
    "metadata": {},
    "outputs": [
     {
@@ -1437,7 +1473,7 @@
        "(11.13438888888889, 11, 8, 3.8000000000029104)"
       ]
      },
-     "execution_count": 33,
+     "execution_count": 38,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1453,7 +1489,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 34,
+   "execution_count": 39,
    "metadata": {},
    "outputs": [
     {
@@ -1462,7 +1498,7 @@
        "(15.36486111111111, 15, 21, 53.5)"
       ]
      },
-     "execution_count": 34,
+     "execution_count": 39,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1487,7 +1523,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 95,
+   "execution_count": 40,
    "metadata": {
     "collapsed": true
    },
@@ -1501,7 +1537,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 84,
+   "execution_count": 41,
    "metadata": {
     "collapsed": true
    },
@@ -1525,7 +1561,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 82,
+   "execution_count": 42,
    "metadata": {},
    "outputs": [
     {
@@ -1549,7 +1585,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 83,
+   "execution_count": 43,
    "metadata": {},
    "outputs": [
     {
@@ -1570,7 +1606,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 85,
+   "execution_count": 44,
    "metadata": {},
    "outputs": [
     {
@@ -1606,7 +1642,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 99,
+   "execution_count": 45,
    "metadata": {},
    "outputs": [
     {
@@ -1630,7 +1666,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 100,
+   "execution_count": 46,
    "metadata": {},
    "outputs": [
     {