X-Git-Url: https://git.njae.me.uk/?a=blobdiff_plain;f=09-resolving-the-bill%2Finterleaving.ipynb;h=352a5fcf6e7b8596fa08b8a65da8e2b918e6fa26;hb=34c17b05a50db9b3e5f55496251aab9409241021;hp=c1c4bed9a63315a351d0716f4fd2dd9e0cddee53;hpb=690b9aa61348310a072473b58ebbbd424dce2b45;p=ou-summer-of-code-2017.git

diff --git a/09-resolving-the-bill/interleaving.ipynb b/09-resolving-the-bill/interleaving.ipynb
index c1c4bed..352a5fc 100644
--- a/09-resolving-the-bill/interleaving.ipynb
+++ b/09-resolving-the-bill/interleaving.ipynb
@@ -73,7 +73,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [
     {
@@ -87,7 +87,7 @@
        " [False, False, False, False, False, False]]"
       ]
      },
-     "execution_count": 4,
+     "execution_count": 5,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -100,7 +100,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 4,
    "metadata": {
     "scrolled": true
    },
@@ -146,7 +146,7 @@
        " (5, 5): False}"
       ]
      },
-     "execution_count": 5,
+     "execution_count": 4,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -160,7 +160,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 5,
    "metadata": {
     "collapsed": true
    },
@@ -174,7 +174,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 6,
    "metadata": {
     "collapsed": true
    },
@@ -188,7 +188,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 7,
    "metadata": {},
    "outputs": [
     {
@@ -210,14 +210,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 8,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "aabcc dbbca aadbbbaccc\n",
+      "aabcc dbbca aadbbcbcac\n",
       "aa 0 0 ! ! ! True\n",
       "s2 0 1 ! d a False\n",
       "s2 0 2 ! b a False\n",
@@ -229,39 +229,39 @@
       "xx 1 2 a b d False\n",
       "xx 1 3 a b b False\n",
       "xx 1 4 a c b False\n",
-      "xx 1 5 a a b False\n",
+      "xx 1 5 a a c False\n",
       "s1 2 0 a ! a True\n",
       "s2 2 1 a d d True\n",
       "s2 2 2 a b b True\n",
       "s2 2 3 a b b True\n",
-      "xx 2 4 a c b False\n",
-      "xx 2 5 a a a False\n",
+      "s2 2 4 a c c True\n",
+      "xx 2 5 a a b False\n",
       "s1 3 0 b ! d False\n",
       "s1 3 1 b d b True\n",
       "s2 3 2 b b b True\n",
       "s1 3 2 b b b True\n",
-      "s2 3 3 b b b True\n",
-      "s1 3 3 b b b True\n",
-      "xx 3 4 b c a False\n",
+      "xx 3 3 b b c False\n",
+      "s1 3 4 b c b True\n",
       "xx 3 5 b a c False\n",
       "s1 4 0 c ! b False\n",
       "xx 4 1 c d b False\n",
-      "xx 4 2 c b b False\n",
-      "xx 4 3 c b a False\n",
-      "xx 4 4 c c c False\n",
-      "xx 4 5 c a c False\n",
+      "s1 4 2 c b c True\n",
+      "s2 4 3 c b b True\n",
+      "s2 4 4 c c c True\n",
+      "s1 4 4 c c c True\n",
+      "s2 4 5 c a a True\n",
       "s1 5 0 c ! b False\n",
-      "xx 5 1 c d b False\n",
-      "xx 5 2 c b a False\n",
-      "xx 5 3 c b c False\n",
-      "xx 5 4 c c c False\n",
-      "xx 5 5 c a c False\n",
+      "xx 5 1 c d c False\n",
+      "xx 5 2 c b b False\n",
+      "s1 5 3 c b c True\n",
+      "xx 5 4 c c a False\n",
+      "s1 5 5 c a c True\n",
       "T . . . . .\n",
       "T . . . . .\n",
-      "T T T T . .\n",
-      ". T T T . .\n",
-      ". . . . . .\n",
-      ". . . . . .\n"
+      "T T T T T .\n",
+      ". T T . T .\n",
+      ". . T T T T\n",
+      ". . . T . T\n"
      ]
     },
     {
@@ -272,18 +272,25 @@
        " (2, 1): (2, 0, 'd', 's2'),\n",
        " (2, 2): (2, 1, 'b', 's2'),\n",
        " (2, 3): (2, 2, 'b', 's2'),\n",
+       " (2, 4): (2, 3, 'c', 's2'),\n",
        " (3, 1): (2, 1, 'b', 's1'),\n",
        " (3, 2): (2, 2, 'b', 's1'),\n",
-       " (3, 3): (2, 3, 'b', 's1')}"
+       " (3, 4): (2, 4, 'b', 's1'),\n",
+       " (4, 2): (3, 2, 'c', 's1'),\n",
+       " (4, 3): (4, 2, 'b', 's2'),\n",
+       " (4, 4): (3, 4, 'c', 's1'),\n",
+       " (4, 5): (4, 4, 'a', 's2'),\n",
+       " (5, 3): (4, 3, 'c', 's1'),\n",
+       " (5, 5): (4, 5, 'c', 's1')}"
       ]
      },
-     "execution_count": 9,
+     "execution_count": 8,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "s3 = s3f\n",
+    "s3 = s3t\n",
     "\n",
     "print(s1, s2, s3)\n",
     "\n",
@@ -330,7 +337,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 11,
    "metadata": {
     "collapsed": true
    },
@@ -406,7 +413,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 12,
    "metadata": {},
    "outputs": [
     {
@@ -415,7 +422,7 @@
        "True"
       ]
      },
-     "execution_count": 11,
+     "execution_count": 12,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -426,7 +433,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 13,
    "metadata": {},
    "outputs": [
     {
@@ -450,7 +457,7 @@
        "  (5, 5): (4, 5, 'c', 'seq1')})"
       ]
      },
-     "execution_count": 12,
+     "execution_count": 13,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -461,7 +468,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 14,
    "metadata": {
     "scrolled": true
    },
@@ -523,7 +530,7 @@
        "  (5, 5): True})"
       ]
      },
-     "execution_count": 13,
+     "execution_count": 14,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -534,7 +541,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 15,
    "metadata": {},
    "outputs": [
     {
@@ -543,7 +550,7 @@
        "False"
       ]
      },
-     "execution_count": 14,
+     "execution_count": 15,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -554,7 +561,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 16,
    "metadata": {},
    "outputs": [
     {
@@ -596,7 +603,7 @@
        "  (4, 3): (4, 2, 'b', 'seq2')})"
       ]
      },
-     "execution_count": 15,
+     "execution_count": 16,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -607,7 +614,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 17,
    "metadata": {
     "collapsed": true
    },
@@ -631,7 +638,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 18,
    "metadata": {
     "collapsed": true
    },
@@ -645,16 +652,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 19,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "'fgcebagebfhfbadbgggacgeebbfceffhbhbgdfhhbahgbchbhe'"
+       "'fddagfdacgbdggabhgcgfddecffbghccebhefghbchhhbfdfgc'"
       ]
      },
-     "execution_count": 18,
+     "execution_count": 19,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -665,7 +672,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 20,
    "metadata": {
     "collapsed": true
    },
@@ -706,65 +713,62 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 21,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "0 0 0 adding y\n",
-      "0 1 -1 adding a\n",
-      "1 1 0 adding z\n",
-      "1 2 -1 adding v\n",
-      "1 3 -2 adding x\n",
-      "1 4 -3 adding z\n",
-      "1 5 -4 adding w\n",
-      "1 6 -5 adding e\n",
-      "2 6 -4 adding h\n",
-      "3 6 -3 adding b\n",
+      "0 0 0 adding x\n",
+      "0 1 -1 adding y\n",
+      "0 2 -2 adding x\n",
+      "0 3 -3 adding g\n",
+      "1 3 -2 adding h\n",
+      "2 3 -1 adding d\n",
+      "3 3 0 adding v\n",
+      "3 4 -1 adding x\n",
+      "3 5 -2 adding d\n",
+      "4 5 -1 adding v\n",
       "4 6 -2 adding a\n",
-      "5 6 -1 adding b\n",
-      "6 6 0 adding u\n",
-      "6 7 -1 adding x\n",
+      "5 6 -1 adding g\n",
+      "6 6 0 adding w\n",
+      "6 7 -1 adding v\n",
       "6 8 -2 adding e\n",
-      "7 8 -1 adding y\n",
-      "7 9 -2 adding x\n",
+      "7 8 -1 adding u\n",
+      "7 9 -2 adding w\n",
       "7 10 -3 adding x\n",
-      "7 11 -4 adding x\n",
-      "7 12 -5 adding e\n",
-      "8 12 -4 adding e\n",
-      "9 12 -3 adding z\n",
-      "9 13 -4 adding z\n",
-      "9 14 -5 adding a\n",
-      "10 14 -4 adding c\n",
-      "11 14 -3 adding y\n",
-      "11 15 -4 adding d\n",
-      "12 15 -3 adding g\n",
-      "13 15 -2 adding g\n",
-      "14 15 -1 adding c\n",
-      "15 15 0 adding x\n",
-      "15 16 -1 adding e\n",
-      "16 16 0 adding f\n",
-      "17 16 1 adding w\n",
-      "17 17 0 adding w\n",
-      "17 18 -1 adding v\n",
-      "17 19 -2 adding f\n",
-      "18 19 -1 adding a\n",
-      "19 19 0 adding g\n",
-      "20 19 1 remaining s2 z\n"
+      "7 11 -4 adding e\n",
+      "8 11 -3 adding d\n",
+      "9 11 -2 adding w\n",
+      "9 12 -3 adding c\n",
+      "10 12 -2 adding z\n",
+      "10 13 -3 adding y\n",
+      "10 14 -4 adding h\n",
+      "11 14 -3 adding g\n",
+      "12 14 -2 adding z\n",
+      "12 15 -3 adding x\n",
+      "12 16 -4 adding w\n",
+      "12 17 -5 adding e\n",
+      "13 17 -4 adding w\n",
+      "13 18 -5 adding f\n",
+      "14 18 -4 adding z\n",
+      "14 19 -5 adding f\n",
+      "15 19 -4 adding b\n",
+      "16 19 -3 adding u\n",
+      "16 20 -4 remaining s1 gchd\n"
      ]
     },
     {
      "data": {
       "text/plain": [
-       "('aehbabeeeacdggceffag',\n",
-       " 'yzvxzwuxyxxxzzyxwwvz',\n",
-       " 'yazvxzwehbabuxeyxxxeezzacydggcxefwwvfagz',\n",
+       "('ghddageedchgeffbgchd',\n",
+       " 'xyxvxvwvuwxwzyzxwwzu',\n",
+       " 'xyxghdvxdvagwveuwxedwczyhgzxwewfzfbugchd',\n",
        " 40)"
       ]
      },
-     "execution_count": 20,
+     "execution_count": 21,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -778,7 +782,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 22,
    "metadata": {},
    "outputs": [
     {
@@ -786,473 +790,467 @@
      "output_type": "stream",
      "text": [
       "xxxx 0 0 ! ! ! True\n",
-      "seq2 0 1 ! a y False\n",
-      "seq2 0 2 ! e a False\n",
-      "seq2 0 3 ! h z False\n",
-      "seq2 0 4 ! b v False\n",
-      "seq2 0 5 ! a x False\n",
-      "seq2 0 6 ! b z False\n",
-      "seq2 0 7 ! e w False\n",
-      "seq2 0 8 ! e e False\n",
-      "seq2 0 9 ! e h False\n",
-      "seq2 0 10 ! a b False\n",
-      "seq2 0 11 ! c a False\n",
-      "seq2 0 12 ! d b False\n",
-      "seq2 0 13 ! g u False\n",
-      "seq2 0 14 ! g x False\n",
-      "seq2 0 15 ! c e False\n",
-      "seq2 0 16 ! e y False\n",
-      "seq2 0 17 ! f x False\n",
-      "seq2 0 18 ! f x False\n",
-      "seq2 0 19 ! a x False\n",
-      "seq2 0 20 ! g e False\n",
-      "seq1 1 0 y ! y True\n",
-      "seq2 1 1 y a a True\n",
-      "xxxx 1 2 y e z False\n",
-      "xxxx 1 3 y h v False\n",
-      "xxxx 1 4 y b x False\n",
-      "xxxx 1 5 y a z False\n",
-      "xxxx 1 6 y b w False\n",
-      "xxxx 1 7 y e e False\n",
-      "xxxx 1 8 y e h False\n",
-      "xxxx 1 9 y e b False\n",
-      "xxxx 1 10 y a a False\n",
-      "xxxx 1 11 y c b False\n",
-      "xxxx 1 12 y d u False\n",
-      "xxxx 1 13 y g x False\n",
-      "xxxx 1 14 y g e False\n",
-      "xxxx 1 15 y c y False\n",
-      "xxxx 1 16 y e x False\n",
-      "xxxx 1 17 y f x False\n",
-      "xxxx 1 18 y f x False\n",
-      "xxxx 1 19 y a e False\n",
-      "xxxx 1 20 y g e False\n",
-      "seq1 2 0 z ! a False\n",
-      "seq1 2 1 z a z True\n",
-      "xxxx 2 2 z e v False\n",
-      "xxxx 2 3 z h x False\n",
-      "xxxx 2 4 z b z False\n",
-      "xxxx 2 5 z a w False\n",
-      "xxxx 2 6 z b e False\n",
-      "xxxx 2 7 z e h False\n",
-      "xxxx 2 8 z e b False\n",
-      "xxxx 2 9 z e a False\n",
-      "xxxx 2 10 z a b False\n",
-      "xxxx 2 11 z c u False\n",
-      "xxxx 2 12 z d x False\n",
-      "xxxx 2 13 z g e False\n",
-      "xxxx 2 14 z g y False\n",
-      "xxxx 2 15 z c x False\n",
-      "xxxx 2 16 z e x False\n",
-      "xxxx 2 17 z f x False\n",
-      "xxxx 2 18 z f e False\n",
-      "xxxx 2 19 z a e False\n",
-      "xxxx 2 20 z g z False\n",
-      "seq1 3 0 v ! z False\n",
-      "seq1 3 1 v a v True\n",
-      "xxxx 3 2 v e x False\n",
-      "xxxx 3 3 v h z False\n",
-      "xxxx 3 4 v b w False\n",
-      "xxxx 3 5 v a e False\n",
-      "xxxx 3 6 v b h False\n",
-      "xxxx 3 7 v e b False\n",
-      "xxxx 3 8 v e a False\n",
-      "xxxx 3 9 v e b False\n",
-      "xxxx 3 10 v a u False\n",
-      "xxxx 3 11 v c x False\n",
-      "xxxx 3 12 v d e False\n",
-      "xxxx 3 13 v g y False\n",
-      "xxxx 3 14 v g x False\n",
-      "xxxx 3 15 v c x False\n",
-      "xxxx 3 16 v e x False\n",
-      "xxxx 3 17 v f e False\n",
-      "xxxx 3 18 v f e False\n",
-      "xxxx 3 19 v a z False\n",
-      "xxxx 3 20 v g z False\n",
-      "seq1 4 0 x ! v False\n",
-      "seq1 4 1 x a x True\n",
-      "xxxx 4 2 x e z False\n",
-      "xxxx 4 3 x h w False\n",
-      "xxxx 4 4 x b e False\n",
-      "xxxx 4 5 x a h False\n",
-      "xxxx 4 6 x b b False\n",
-      "xxxx 4 7 x e a False\n",
-      "xxxx 4 8 x e b False\n",
-      "xxxx 4 9 x e u False\n",
-      "xxxx 4 10 x a x False\n",
-      "xxxx 4 11 x c e False\n",
-      "xxxx 4 12 x d y False\n",
-      "xxxx 4 13 x g x False\n",
-      "xxxx 4 14 x g x False\n",
-      "xxxx 4 15 x c x False\n",
-      "xxxx 4 16 x e e False\n",
-      "xxxx 4 17 x f e False\n",
-      "xxxx 4 18 x f z False\n",
-      "xxxx 4 19 x a z False\n",
-      "xxxx 4 20 x g a False\n",
-      "seq1 5 0 z ! x False\n",
-      "seq1 5 1 z a z True\n",
-      "xxxx 5 2 z e w False\n",
-      "xxxx 5 3 z h e False\n",
-      "xxxx 5 4 z b h False\n",
-      "xxxx 5 5 z a b False\n",
-      "xxxx 5 6 z b a False\n",
-      "xxxx 5 7 z e b False\n",
-      "xxxx 5 8 z e u False\n",
-      "xxxx 5 9 z e x False\n",
-      "xxxx 5 10 z a e False\n",
-      "xxxx 5 11 z c y False\n",
-      "xxxx 5 12 z d x False\n",
-      "xxxx 5 13 z g x False\n",
-      "xxxx 5 14 z g x False\n",
-      "xxxx 5 15 z c e False\n",
-      "xxxx 5 16 z e e False\n",
-      "xxxx 5 17 z f z False\n",
-      "xxxx 5 18 z f z False\n",
-      "xxxx 5 19 z a a False\n",
-      "xxxx 5 20 z g c False\n",
-      "seq1 6 0 w ! z False\n",
-      "seq1 6 1 w a w True\n",
-      "seq2 6 2 w e e True\n",
-      "seq2 6 3 w h h True\n",
-      "seq2 6 4 w b b True\n",
-      "seq2 6 5 w a a True\n",
-      "seq2 6 6 w b b True\n",
-      "xxxx 6 7 w e u False\n",
-      "xxxx 6 8 w e x False\n",
-      "xxxx 6 9 w e e False\n",
-      "xxxx 6 10 w a y False\n",
-      "xxxx 6 11 w c x False\n",
-      "xxxx 6 12 w d x False\n",
-      "xxxx 6 13 w g x False\n",
-      "xxxx 6 14 w g e False\n",
-      "xxxx 6 15 w c e False\n",
-      "xxxx 6 16 w e z False\n",
-      "xxxx 6 17 w f z False\n",
-      "xxxx 6 18 w f a False\n",
-      "xxxx 6 19 w a c False\n",
-      "xxxx 6 20 w g y False\n",
-      "seq1 7 0 u ! w False\n",
-      "xxxx 7 1 u a e False\n",
-      "xxxx 7 2 u e h False\n",
-      "xxxx 7 3 u h b False\n",
-      "xxxx 7 4 u b a False\n",
-      "xxxx 7 5 u a b False\n",
-      "seq1 7 6 u b u True\n",
-      "xxxx 7 7 u e x False\n",
-      "xxxx 7 8 u e e False\n",
-      "xxxx 7 9 u e y False\n",
-      "xxxx 7 10 u a x False\n",
-      "xxxx 7 11 u c x False\n",
-      "xxxx 7 12 u d x False\n",
-      "xxxx 7 13 u g e False\n",
-      "xxxx 7 14 u g e False\n",
-      "xxxx 7 15 u c z False\n",
-      "xxxx 7 16 u e z False\n",
-      "xxxx 7 17 u f a False\n",
-      "xxxx 7 18 u f c False\n",
-      "xxxx 7 19 u a y False\n",
-      "xxxx 7 20 u g d False\n",
-      "seq1 8 0 x ! e False\n",
-      "xxxx 8 1 x a h False\n",
-      "xxxx 8 2 x e b False\n",
-      "xxxx 8 3 x h a False\n",
-      "xxxx 8 4 x b b False\n",
-      "xxxx 8 5 x a u False\n",
-      "seq1 8 6 x b x True\n",
-      "seq2 8 7 x e e True\n",
-      "xxxx 8 8 x e y False\n",
-      "xxxx 8 9 x e x False\n",
-      "xxxx 8 10 x a x False\n",
-      "xxxx 8 11 x c x False\n",
-      "xxxx 8 12 x d e False\n",
-      "xxxx 8 13 x g e False\n",
-      "xxxx 8 14 x g z False\n",
-      "xxxx 8 15 x c z False\n",
-      "xxxx 8 16 x e a False\n",
-      "xxxx 8 17 x f c False\n",
-      "xxxx 8 18 x f y False\n",
-      "xxxx 8 19 x a d False\n",
-      "xxxx 8 20 x g g False\n",
-      "seq1 9 0 y ! h False\n",
-      "xxxx 9 1 y a b False\n",
-      "xxxx 9 2 y e a False\n",
-      "xxxx 9 3 y h b False\n",
-      "xxxx 9 4 y b u False\n",
-      "xxxx 9 5 y a x False\n",
-      "xxxx 9 6 y b e False\n",
-      "seq1 9 7 y e y True\n",
-      "xxxx 9 8 y e x False\n",
-      "xxxx 9 9 y e x False\n",
-      "xxxx 9 10 y a x False\n",
-      "xxxx 9 11 y c e False\n",
-      "xxxx 9 12 y d e False\n",
-      "xxxx 9 13 y g z False\n",
-      "xxxx 9 14 y g z False\n",
-      "xxxx 9 15 y c a False\n",
-      "xxxx 9 16 y e c False\n",
-      "xxxx 9 17 y f y False\n",
-      "xxxx 9 18 y f d False\n",
-      "xxxx 9 19 y a g False\n",
-      "xxxx 9 20 y g g False\n",
-      "seq1 10 0 x ! b False\n",
-      "xxxx 10 1 x a a False\n",
-      "xxxx 10 2 x e b False\n",
-      "xxxx 10 3 x h u False\n",
-      "xxxx 10 4 x b x False\n",
-      "xxxx 10 5 x a e False\n",
-      "xxxx 10 6 x b y False\n",
-      "seq1 10 7 x e x True\n",
-      "xxxx 10 8 x e x False\n",
-      "xxxx 10 9 x e x False\n",
-      "xxxx 10 10 x a e False\n",
-      "xxxx 10 11 x c e False\n",
-      "xxxx 10 12 x d z False\n",
-      "xxxx 10 13 x g z False\n",
-      "xxxx 10 14 x g a False\n",
-      "xxxx 10 15 x c c False\n",
-      "xxxx 10 16 x e y False\n",
-      "xxxx 10 17 x f d False\n",
-      "xxxx 10 18 x f g False\n",
-      "xxxx 10 19 x a g False\n",
-      "xxxx 10 20 x g c False\n",
+      "seq2 0 1 ! g x False\n",
+      "seq2 0 2 ! h y False\n",
+      "seq2 0 3 ! d x False\n",
+      "seq2 0 4 ! d g False\n",
+      "seq2 0 5 ! a h False\n",
+      "seq2 0 6 ! g d False\n",
+      "seq2 0 7 ! e v False\n",
+      "seq2 0 8 ! e x False\n",
+      "seq2 0 9 ! d d False\n",
+      "seq2 0 10 ! c v False\n",
+      "seq2 0 11 ! h a False\n",
+      "seq2 0 12 ! g g False\n",
+      "seq2 0 13 ! e w False\n",
+      "seq2 0 14 ! f v False\n",
+      "seq2 0 15 ! f e False\n",
+      "seq2 0 16 ! b u False\n",
+      "seq2 0 17 ! g w False\n",
+      "seq2 0 18 ! c x False\n",
+      "seq2 0 19 ! h e False\n",
+      "seq2 0 20 ! d d False\n",
+      "seq1 1 0 x ! x True\n",
+      "xxxx 1 1 x g y False\n",
+      "xxxx 1 2 x h x False\n",
+      "xxxx 1 3 x d g False\n",
+      "xxxx 1 4 x d h False\n",
+      "xxxx 1 5 x a d False\n",
+      "xxxx 1 6 x g v False\n",
+      "xxxx 1 7 x e x False\n",
+      "xxxx 1 8 x e d False\n",
+      "xxxx 1 9 x d v False\n",
+      "xxxx 1 10 x c a False\n",
+      "xxxx 1 11 x h g False\n",
+      "xxxx 1 12 x g w False\n",
+      "xxxx 1 13 x e v False\n",
+      "xxxx 1 14 x f e False\n",
+      "xxxx 1 15 x f u False\n",
+      "xxxx 1 16 x b w False\n",
+      "xxxx 1 17 x g x False\n",
+      "xxxx 1 18 x c e False\n",
+      "xxxx 1 19 x h d False\n",
+      "xxxx 1 20 x d w False\n",
+      "seq1 2 0 y ! y True\n",
+      "xxxx 2 1 y g x False\n",
+      "xxxx 2 2 y h g False\n",
+      "xxxx 2 3 y d h False\n",
+      "xxxx 2 4 y d d False\n",
+      "xxxx 2 5 y a v False\n",
+      "xxxx 2 6 y g x False\n",
+      "xxxx 2 7 y e d False\n",
+      "xxxx 2 8 y e v False\n",
+      "xxxx 2 9 y d a False\n",
+      "xxxx 2 10 y c g False\n",
+      "xxxx 2 11 y h w False\n",
+      "xxxx 2 12 y g v False\n",
+      "xxxx 2 13 y e e False\n",
+      "xxxx 2 14 y f u False\n",
+      "xxxx 2 15 y f w False\n",
+      "xxxx 2 16 y b x False\n",
+      "xxxx 2 17 y g e False\n",
+      "xxxx 2 18 y c d False\n",
+      "xxxx 2 19 y h w False\n",
+      "xxxx 2 20 y d c False\n",
+      "seq1 3 0 x ! x True\n",
+      "seq2 3 1 x g g True\n",
+      "seq2 3 2 x h h True\n",
+      "seq2 3 3 x d d True\n",
+      "xxxx 3 4 x d v False\n",
+      "xxxx 3 5 x a x False\n",
+      "xxxx 3 6 x g d False\n",
+      "xxxx 3 7 x e v False\n",
+      "xxxx 3 8 x e a False\n",
+      "xxxx 3 9 x d g False\n",
+      "xxxx 3 10 x c w False\n",
+      "xxxx 3 11 x h v False\n",
+      "xxxx 3 12 x g e False\n",
+      "xxxx 3 13 x e u False\n",
+      "xxxx 3 14 x f w False\n",
+      "xxxx 3 15 x f x False\n",
+      "xxxx 3 16 x b e False\n",
+      "xxxx 3 17 x g d False\n",
+      "xxxx 3 18 x c w False\n",
+      "xxxx 3 19 x h c False\n",
+      "xxxx 3 20 x d z False\n",
+      "seq1 4 0 v ! g False\n",
+      "xxxx 4 1 v g h False\n",
+      "xxxx 4 2 v h d False\n",
+      "seq1 4 3 v d v True\n",
+      "xxxx 4 4 v d x False\n",
+      "xxxx 4 5 v a d False\n",
+      "xxxx 4 6 v g v False\n",
+      "xxxx 4 7 v e a False\n",
+      "xxxx 4 8 v e g False\n",
+      "xxxx 4 9 v d w False\n",
+      "xxxx 4 10 v c v False\n",
+      "xxxx 4 11 v h e False\n",
+      "xxxx 4 12 v g u False\n",
+      "xxxx 4 13 v e w False\n",
+      "xxxx 4 14 v f x False\n",
+      "xxxx 4 15 v f e False\n",
+      "xxxx 4 16 v b d False\n",
+      "xxxx 4 17 v g w False\n",
+      "xxxx 4 18 v c c False\n",
+      "xxxx 4 19 v h z False\n",
+      "xxxx 4 20 v d y False\n",
+      "seq1 5 0 x ! h False\n",
+      "xxxx 5 1 x g d False\n",
+      "xxxx 5 2 x h v False\n",
+      "seq1 5 3 x d x True\n",
+      "seq2 5 4 x d d True\n",
+      "xxxx 5 5 x a v False\n",
+      "xxxx 5 6 x g a False\n",
+      "xxxx 5 7 x e g False\n",
+      "xxxx 5 8 x e w False\n",
+      "xxxx 5 9 x d v False\n",
+      "xxxx 5 10 x c e False\n",
+      "xxxx 5 11 x h u False\n",
+      "xxxx 5 12 x g w False\n",
+      "xxxx 5 13 x e x False\n",
+      "xxxx 5 14 x f e False\n",
+      "xxxx 5 15 x f d False\n",
+      "xxxx 5 16 x b w False\n",
+      "xxxx 5 17 x g c False\n",
+      "xxxx 5 18 x c z False\n",
+      "xxxx 5 19 x h y False\n",
+      "xxxx 5 20 x d h False\n",
+      "seq1 6 0 v ! d False\n",
+      "xxxx 6 1 v g v False\n",
+      "xxxx 6 2 v h x False\n",
+      "xxxx 6 3 v d d False\n",
+      "seq1 6 4 v d v True\n",
+      "seq2 6 5 v a a True\n",
+      "seq2 6 6 v g g True\n",
+      "xxxx 6 7 v e w False\n",
+      "xxxx 6 8 v e v False\n",
+      "xxxx 6 9 v d e False\n",
+      "xxxx 6 10 v c u False\n",
+      "xxxx 6 11 v h w False\n",
+      "xxxx 6 12 v g x False\n",
+      "xxxx 6 13 v e e False\n",
+      "xxxx 6 14 v f d False\n",
+      "xxxx 6 15 v f w False\n",
+      "xxxx 6 16 v b c False\n",
+      "xxxx 6 17 v g z False\n",
+      "xxxx 6 18 v c y False\n",
+      "xxxx 6 19 v h h False\n",
+      "xxxx 6 20 v d g False\n",
+      "seq1 7 0 w ! v False\n",
+      "xxxx 7 1 w g x False\n",
+      "xxxx 7 2 w h d False\n",
+      "xxxx 7 3 w d v False\n",
+      "xxxx 7 4 w d a False\n",
+      "xxxx 7 5 w a g False\n",
+      "seq1 7 6 w g w True\n",
+      "xxxx 7 7 w e v False\n",
+      "xxxx 7 8 w e e False\n",
+      "xxxx 7 9 w d u False\n",
+      "xxxx 7 10 w c w False\n",
+      "xxxx 7 11 w h x False\n",
+      "xxxx 7 12 w g e False\n",
+      "xxxx 7 13 w e d False\n",
+      "xxxx 7 14 w f w False\n",
+      "xxxx 7 15 w f c False\n",
+      "xxxx 7 16 w b z False\n",
+      "xxxx 7 17 w g y False\n",
+      "xxxx 7 18 w c h False\n",
+      "xxxx 7 19 w h g False\n",
+      "xxxx 7 20 w d z False\n",
+      "seq1 8 0 v ! x False\n",
+      "xxxx 8 1 v g d False\n",
+      "xxxx 8 2 v h v False\n",
+      "xxxx 8 3 v d a False\n",
+      "xxxx 8 4 v d g False\n",
+      "xxxx 8 5 v a w False\n",
+      "seq1 8 6 v g v True\n",
+      "seq2 8 7 v e e True\n",
+      "xxxx 8 8 v e u False\n",
+      "xxxx 8 9 v d w False\n",
+      "xxxx 8 10 v c x False\n",
+      "xxxx 8 11 v h e False\n",
+      "xxxx 8 12 v g d False\n",
+      "xxxx 8 13 v e w False\n",
+      "xxxx 8 14 v f c False\n",
+      "xxxx 8 15 v f z False\n",
+      "xxxx 8 16 v b y False\n",
+      "xxxx 8 17 v g h False\n",
+      "xxxx 8 18 v c g False\n",
+      "xxxx 8 19 v h z False\n",
+      "xxxx 8 20 v d x False\n",
+      "seq1 9 0 u ! d False\n",
+      "xxxx 9 1 u g v False\n",
+      "xxxx 9 2 u h a False\n",
+      "xxxx 9 3 u d g False\n",
+      "xxxx 9 4 u d w False\n",
+      "xxxx 9 5 u a v False\n",
+      "xxxx 9 6 u g e False\n",
+      "seq1 9 7 u e u True\n",
+      "xxxx 9 8 u e w False\n",
+      "xxxx 9 9 u d x False\n",
+      "xxxx 9 10 u c e False\n",
+      "xxxx 9 11 u h d False\n",
+      "xxxx 9 12 u g w False\n",
+      "xxxx 9 13 u e c False\n",
+      "xxxx 9 14 u f z False\n",
+      "xxxx 9 15 u f y False\n",
+      "xxxx 9 16 u b h False\n",
+      "xxxx 9 17 u g g False\n",
+      "xxxx 9 18 u c z False\n",
+      "xxxx 9 19 u h x False\n",
+      "xxxx 9 20 u d w False\n",
+      "seq1 10 0 w ! v False\n",
+      "xxxx 10 1 w g a False\n",
+      "xxxx 10 2 w h g False\n",
+      "xxxx 10 3 w d w False\n",
+      "xxxx 10 4 w d v False\n",
+      "xxxx 10 5 w a e False\n",
+      "xxxx 10 6 w g u False\n",
+      "seq1 10 7 w e w True\n",
+      "xxxx 10 8 w e x False\n",
+      "xxxx 10 9 w d e False\n",
+      "xxxx 10 10 w c d False\n",
+      "xxxx 10 11 w h w False\n",
+      "xxxx 10 12 w g c False\n",
+      "xxxx 10 13 w e z False\n",
+      "xxxx 10 14 w f y False\n",
+      "xxxx 10 15 w f h False\n",
+      "xxxx 10 16 w b g False\n",
+      "xxxx 10 17 w g z False\n",
+      "xxxx 10 18 w c x False\n",
+      "xxxx 10 19 w h w False\n",
+      "xxxx 10 20 w d e False\n",
       "seq1 11 0 x ! a False\n",
-      "xxxx 11 1 x a b False\n",
-      "xxxx 11 2 x e u False\n",
-      "xxxx 11 3 x h x False\n",
-      "xxxx 11 4 x b e False\n",
-      "xxxx 11 5 x a y False\n",
-      "xxxx 11 6 x b x False\n",
+      "xxxx 11 1 x g g False\n",
+      "xxxx 11 2 x h w False\n",
+      "xxxx 11 3 x d v False\n",
+      "xxxx 11 4 x d e False\n",
+      "xxxx 11 5 x a u False\n",
+      "xxxx 11 6 x g w False\n",
       "seq1 11 7 x e x True\n",
-      "xxxx 11 8 x e x False\n",
-      "xxxx 11 9 x e e False\n",
-      "xxxx 11 10 x a e False\n",
-      "xxxx 11 11 x c z False\n",
-      "xxxx 11 12 x d z False\n",
-      "xxxx 11 13 x g a False\n",
-      "xxxx 11 14 x g c False\n",
-      "xxxx 11 15 x c y False\n",
-      "xxxx 11 16 x e d False\n",
-      "xxxx 11 17 x f g False\n",
-      "xxxx 11 18 x f g False\n",
-      "xxxx 11 19 x a c False\n",
-      "xxxx 11 20 x g x False\n",
-      "seq1 12 0 x ! b False\n",
-      "xxxx 12 1 x a u False\n",
-      "xxxx 12 2 x e x False\n",
-      "xxxx 12 3 x h e False\n",
-      "xxxx 12 4 x b y False\n",
-      "xxxx 12 5 x a x False\n",
-      "xxxx 12 6 x b x False\n",
-      "seq1 12 7 x e x True\n",
-      "seq2 12 8 x e e True\n",
-      "seq2 12 9 x e e True\n",
-      "xxxx 12 10 x a z False\n",
-      "xxxx 12 11 x c z False\n",
-      "xxxx 12 12 x d a False\n",
-      "xxxx 12 13 x g c False\n",
-      "xxxx 12 14 x g y False\n",
-      "xxxx 12 15 x c d False\n",
-      "xxxx 12 16 x e g False\n",
-      "xxxx 12 17 x f g False\n",
-      "xxxx 12 18 x f c False\n",
-      "xxxx 12 19 x a x False\n",
-      "xxxx 12 20 x g e False\n",
-      "seq1 13 0 z ! u False\n",
-      "xxxx 13 1 z a x False\n",
-      "xxxx 13 2 z e e False\n",
-      "xxxx 13 3 z h y False\n",
-      "xxxx 13 4 z b x False\n",
+      "seq2 11 8 x e e True\n",
+      "seq2 11 9 x d d True\n",
+      "xxxx 11 10 x c w False\n",
+      "xxxx 11 11 x h c False\n",
+      "xxxx 11 12 x g z False\n",
+      "xxxx 11 13 x e y False\n",
+      "xxxx 11 14 x f h False\n",
+      "xxxx 11 15 x f g False\n",
+      "xxxx 11 16 x b z False\n",
+      "xxxx 11 17 x g x False\n",
+      "xxxx 11 18 x c w False\n",
+      "xxxx 11 19 x h e False\n",
+      "xxxx 11 20 x d w False\n",
+      "seq1 12 0 w ! g False\n",
+      "xxxx 12 1 w g w False\n",
+      "xxxx 12 2 w h v False\n",
+      "xxxx 12 3 w d e False\n",
+      "xxxx 12 4 w d u False\n",
+      "xxxx 12 5 w a w False\n",
+      "xxxx 12 6 w g x False\n",
+      "xxxx 12 7 w e e False\n",
+      "xxxx 12 8 w e d False\n",
+      "seq1 12 9 w d w True\n",
+      "seq2 12 10 w c c True\n",
+      "xxxx 12 11 w h z False\n",
+      "xxxx 12 12 w g y False\n",
+      "xxxx 12 13 w e h False\n",
+      "xxxx 12 14 w f g False\n",
+      "xxxx 12 15 w f z False\n",
+      "xxxx 12 16 w b x False\n",
+      "xxxx 12 17 w g w False\n",
+      "xxxx 12 18 w c e False\n",
+      "xxxx 12 19 w h w False\n",
+      "xxxx 12 20 w d f False\n",
+      "seq1 13 0 z ! w False\n",
+      "xxxx 13 1 z g v False\n",
+      "xxxx 13 2 z h e False\n",
+      "xxxx 13 3 z d u False\n",
+      "xxxx 13 4 z d w False\n",
       "xxxx 13 5 z a x False\n",
-      "xxxx 13 6 z b x False\n",
-      "xxxx 13 7 z e e False\n",
-      "xxxx 13 8 z e e False\n",
-      "seq1 13 9 z e z True\n",
-      "xxxx 13 10 z a z False\n",
-      "xxxx 13 11 z c a False\n",
-      "xxxx 13 12 z d c False\n",
-      "xxxx 13 13 z g y False\n",
-      "xxxx 13 14 z g d False\n",
-      "xxxx 13 15 z c g False\n",
-      "xxxx 13 16 z e g False\n",
-      "xxxx 13 17 z f c False\n",
-      "xxxx 13 18 z f x False\n",
-      "xxxx 13 19 z a e False\n",
-      "xxxx 13 20 z g f False\n",
-      "seq1 14 0 z ! x False\n",
-      "xxxx 14 1 z a e False\n",
-      "xxxx 14 2 z e y False\n",
-      "xxxx 14 3 z h x False\n",
-      "xxxx 14 4 z b x False\n",
-      "xxxx 14 5 z a x False\n",
-      "xxxx 14 6 z b e False\n",
-      "xxxx 14 7 z e e False\n",
-      "xxxx 14 8 z e z False\n",
-      "seq1 14 9 z e z True\n",
-      "seq2 14 10 z a a True\n",
-      "seq2 14 11 z c c True\n",
-      "xxxx 14 12 z d y False\n",
-      "xxxx 14 13 z g d False\n",
-      "xxxx 14 14 z g g False\n",
-      "xxxx 14 15 z c g False\n",
-      "xxxx 14 16 z e c False\n",
-      "xxxx 14 17 z f x False\n",
-      "xxxx 14 18 z f e False\n",
-      "xxxx 14 19 z a f False\n",
-      "xxxx 14 20 z g w False\n",
-      "seq1 15 0 y ! e False\n",
-      "xxxx 15 1 y a y False\n",
-      "xxxx 15 2 y e x False\n",
-      "xxxx 15 3 y h x False\n",
-      "xxxx 15 4 y b x False\n",
-      "xxxx 15 5 y a e False\n",
-      "xxxx 15 6 y b e False\n",
-      "xxxx 15 7 y e z False\n",
-      "xxxx 15 8 y e z False\n",
-      "xxxx 15 9 y e a False\n",
-      "xxxx 15 10 y a c False\n",
-      "seq1 15 11 y c y True\n",
-      "seq2 15 12 y d d True\n",
-      "seq2 15 13 y g g True\n",
-      "seq2 15 14 y g g True\n",
-      "seq2 15 15 y c c True\n",
-      "xxxx 15 16 y e x False\n",
-      "xxxx 15 17 y f e False\n",
-      "xxxx 15 18 y f f False\n",
-      "xxxx 15 19 y a w False\n",
-      "xxxx 15 20 y g w False\n",
-      "seq1 16 0 x ! y False\n",
-      "xxxx 16 1 x a x False\n",
-      "xxxx 16 2 x e x False\n",
-      "xxxx 16 3 x h x False\n",
-      "xxxx 16 4 x b e False\n",
-      "xxxx 16 5 x a e False\n",
-      "xxxx 16 6 x b z False\n",
+      "xxxx 13 6 z g e False\n",
+      "xxxx 13 7 z e d False\n",
+      "xxxx 13 8 z e w False\n",
+      "xxxx 13 9 z d c False\n",
+      "seq1 13 10 z c z True\n",
+      "xxxx 13 11 z h y False\n",
+      "xxxx 13 12 z g h False\n",
+      "xxxx 13 13 z e g False\n",
+      "xxxx 13 14 z f z False\n",
+      "xxxx 13 15 z f x False\n",
+      "xxxx 13 16 z b w False\n",
+      "xxxx 13 17 z g e False\n",
+      "xxxx 13 18 z c w False\n",
+      "xxxx 13 19 z h f False\n",
+      "xxxx 13 20 z d z False\n",
+      "seq1 14 0 y ! v False\n",
+      "xxxx 14 1 y g e False\n",
+      "xxxx 14 2 y h u False\n",
+      "xxxx 14 3 y d w False\n",
+      "xxxx 14 4 y d x False\n",
+      "xxxx 14 5 y a e False\n",
+      "xxxx 14 6 y g d False\n",
+      "xxxx 14 7 y e w False\n",
+      "xxxx 14 8 y e c False\n",
+      "xxxx 14 9 y d z False\n",
+      "seq1 14 10 y c y True\n",
+      "seq2 14 11 y h h True\n",
+      "seq2 14 12 y g g True\n",
+      "xxxx 14 13 y e z False\n",
+      "xxxx 14 14 y f x False\n",
+      "xxxx 14 15 y f w False\n",
+      "xxxx 14 16 y b e False\n",
+      "xxxx 14 17 y g w False\n",
+      "xxxx 14 18 y c f False\n",
+      "xxxx 14 19 y h z False\n",
+      "xxxx 14 20 y d f False\n",
+      "seq1 15 0 z ! e False\n",
+      "xxxx 15 1 z g u False\n",
+      "xxxx 15 2 z h w False\n",
+      "xxxx 15 3 z d x False\n",
+      "xxxx 15 4 z d e False\n",
+      "xxxx 15 5 z a d False\n",
+      "xxxx 15 6 z g w False\n",
+      "xxxx 15 7 z e c False\n",
+      "xxxx 15 8 z e z False\n",
+      "xxxx 15 9 z d y False\n",
+      "xxxx 15 10 z c h False\n",
+      "xxxx 15 11 z h g False\n",
+      "seq1 15 12 z g z True\n",
+      "xxxx 15 13 z e x False\n",
+      "xxxx 15 14 z f w False\n",
+      "xxxx 15 15 z f e False\n",
+      "xxxx 15 16 z b w False\n",
+      "xxxx 15 17 z g f False\n",
+      "xxxx 15 18 z c z False\n",
+      "xxxx 15 19 z h f False\n",
+      "xxxx 15 20 z d b False\n",
+      "seq1 16 0 x ! u False\n",
+      "xxxx 16 1 x g w False\n",
+      "xxxx 16 2 x h x False\n",
+      "xxxx 16 3 x d e False\n",
+      "xxxx 16 4 x d d False\n",
+      "xxxx 16 5 x a w False\n",
+      "xxxx 16 6 x g c False\n",
       "xxxx 16 7 x e z False\n",
-      "xxxx 16 8 x e a False\n",
-      "xxxx 16 9 x e c False\n",
-      "xxxx 16 10 x a y False\n",
-      "xxxx 16 11 x c d False\n",
-      "xxxx 16 12 x d g False\n",
-      "xxxx 16 13 x g g False\n",
-      "xxxx 16 14 x g c False\n",
-      "seq1 16 15 x c x True\n",
-      "seq2 16 16 x e e True\n",
-      "seq2 16 17 x f f True\n",
-      "xxxx 16 18 x f w False\n",
-      "xxxx 16 19 x a w False\n",
-      "xxxx 16 20 x g v False\n",
-      "seq1 17 0 w ! x False\n",
-      "xxxx 17 1 w a x False\n",
-      "xxxx 17 2 w e x False\n",
-      "xxxx 17 3 w h e False\n",
-      "xxxx 17 4 w b e False\n",
-      "xxxx 17 5 w a z False\n",
-      "xxxx 17 6 w b z False\n",
-      "xxxx 17 7 w e a False\n",
-      "xxxx 17 8 w e c False\n",
-      "xxxx 17 9 w e y False\n",
-      "xxxx 17 10 w a d False\n",
-      "xxxx 17 11 w c g False\n",
-      "xxxx 17 12 w d g False\n",
-      "xxxx 17 13 w g c False\n",
-      "xxxx 17 14 w g x False\n",
-      "xxxx 17 15 w c e False\n",
-      "xxxx 17 16 w e f False\n",
-      "seq1 17 17 w f w True\n",
-      "xxxx 17 18 w f w False\n",
-      "xxxx 17 19 w a v False\n",
-      "xxxx 17 20 w g f False\n",
-      "seq1 18 0 w ! x False\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "xxxx 18 1 w a x False\n",
-      "xxxx 18 2 w e e False\n",
-      "xxxx 18 3 w h e False\n",
-      "xxxx 18 4 w b z False\n",
+      "xxxx 16 8 x e y False\n",
+      "xxxx 16 9 x d h False\n",
+      "xxxx 16 10 x c g False\n",
+      "xxxx 16 11 x h z False\n",
+      "seq1 16 12 x g x True\n",
+      "xxxx 16 13 x e w False\n",
+      "xxxx 16 14 x f e False\n",
+      "xxxx 16 15 x f w False\n",
+      "xxxx 16 16 x b f False\n",
+      "xxxx 16 17 x g z False\n",
+      "xxxx 16 18 x c f False\n",
+      "xxxx 16 19 x h b False\n",
+      "xxxx 16 20 x d u False\n",
+      "seq1 17 0 w ! w False\n",
+      "xxxx 17 1 w g x False\n",
+      "xxxx 17 2 w h e False\n",
+      "xxxx 17 3 w d d False\n",
+      "xxxx 17 4 w d w False\n",
+      "xxxx 17 5 w a c False\n",
+      "xxxx 17 6 w g z False\n",
+      "xxxx 17 7 w e y False\n",
+      "xxxx 17 8 w e h False\n",
+      "xxxx 17 9 w d g False\n",
+      "xxxx 17 10 w c z False\n",
+      "xxxx 17 11 w h x False\n",
+      "seq1 17 12 w g w True\n",
+      "seq2 17 13 w e e True\n",
+      "xxxx 17 14 w f w False\n",
+      "xxxx 17 15 w f f False\n",
+      "xxxx 17 16 w b z False\n",
+      "xxxx 17 17 w g f False\n",
+      "xxxx 17 18 w c b False\n",
+      "xxxx 17 19 w h u False\n",
+      "xxxx 17 20 w d g False\n",
+      "seq1 18 0 w ! x False\n",
+      "xxxx 18 1 w g e False\n",
+      "xxxx 18 2 w h d False\n",
+      "xxxx 18 3 w d w False\n",
+      "xxxx 18 4 w d c False\n",
       "xxxx 18 5 w a z False\n",
-      "xxxx 18 6 w b a False\n",
-      "xxxx 18 7 w e c False\n",
-      "xxxx 18 8 w e y False\n",
-      "xxxx 18 9 w e d False\n",
-      "xxxx 18 10 w a g False\n",
-      "xxxx 18 11 w c g False\n",
-      "xxxx 18 12 w d c False\n",
-      "xxxx 18 13 w g x False\n",
-      "xxxx 18 14 w g e False\n",
-      "xxxx 18 15 w c f False\n",
-      "xxxx 18 16 w e w False\n",
-      "seq1 18 17 w f w True\n",
-      "xxxx 18 18 w f v False\n",
-      "xxxx 18 19 w a f False\n",
-      "xxxx 18 20 w g a False\n",
-      "seq1 19 0 v ! x False\n",
-      "xxxx 19 1 v a e False\n",
-      "xxxx 19 2 v e e False\n",
-      "xxxx 19 3 v h z False\n",
-      "xxxx 19 4 v b z False\n",
-      "xxxx 19 5 v a a False\n",
-      "xxxx 19 6 v b c False\n",
-      "xxxx 19 7 v e y False\n",
-      "xxxx 19 8 v e d False\n",
-      "xxxx 19 9 v e g False\n",
-      "xxxx 19 10 v a g False\n",
-      "xxxx 19 11 v c c False\n",
-      "xxxx 19 12 v d x False\n",
-      "xxxx 19 13 v g e False\n",
-      "xxxx 19 14 v g f False\n",
-      "xxxx 19 15 v c w False\n",
-      "xxxx 19 16 v e w False\n",
-      "seq1 19 17 v f v True\n",
-      "seq2 19 18 v f f True\n",
-      "seq2 19 19 v a a True\n",
-      "seq2 19 20 v g g True\n",
-      "seq1 20 0 z ! e False\n",
-      "xxxx 20 1 z a e False\n",
-      "xxxx 20 2 z e z False\n",
-      "xxxx 20 3 z h z False\n",
-      "xxxx 20 4 z b a False\n",
-      "xxxx 20 5 z a c False\n",
-      "xxxx 20 6 z b y False\n",
-      "xxxx 20 7 z e d False\n",
-      "xxxx 20 8 z e g False\n",
-      "xxxx 20 9 z e g False\n",
-      "xxxx 20 10 z a c False\n",
-      "xxxx 20 11 z c x False\n",
-      "xxxx 20 12 z d e False\n",
-      "xxxx 20 13 z g f False\n",
-      "xxxx 20 14 z g w False\n",
-      "xxxx 20 15 z c w False\n",
-      "xxxx 20 16 z e v False\n",
-      "xxxx 20 17 z f f False\n",
-      "xxxx 20 18 z f a False\n",
-      "xxxx 20 19 z a g False\n",
-      "seq1 20 20 z g z True\n",
+      "xxxx 18 6 w g y False\n",
+      "xxxx 18 7 w e h False\n",
+      "xxxx 18 8 w e g False\n",
+      "xxxx 18 9 w d z False\n",
+      "xxxx 18 10 w c x False\n",
+      "xxxx 18 11 w h w False\n",
+      "xxxx 18 12 w g e False\n",
+      "seq1 18 13 w e w True\n",
+      "seq2 18 14 w f f True\n",
+      "xxxx 18 15 w f z False\n",
+      "xxxx 18 16 w b f False\n",
+      "xxxx 18 17 w g b False\n",
+      "xxxx 18 18 w c u False\n",
+      "xxxx 18 19 w h g False\n",
+      "xxxx 18 20 w d c False\n",
+      "seq1 19 0 z ! e False\n",
+      "xxxx 19 1 z g d False\n",
+      "xxxx 19 2 z h w False\n",
+      "xxxx 19 3 z d c False\n",
+      "xxxx 19 4 z d z False\n",
+      "xxxx 19 5 z a y False\n",
+      "xxxx 19 6 z g h False\n",
+      "xxxx 19 7 z e g False\n",
+      "xxxx 19 8 z e z False\n",
+      "xxxx 19 9 z d x False\n",
+      "xxxx 19 10 z c w False\n",
+      "xxxx 19 11 z h e False\n",
+      "xxxx 19 12 z g w False\n",
+      "xxxx 19 13 z e f False\n",
+      "seq1 19 14 z f z True\n",
+      "seq2 19 15 z f f True\n",
+      "seq2 19 16 z b b True\n",
+      "xxxx 19 17 z g u False\n",
+      "xxxx 19 18 z c g False\n",
+      "xxxx 19 19 z h c False\n",
+      "xxxx 19 20 z d h False\n",
+      "seq1 20 0 u ! d False\n",
+      "xxxx 20 1 u g w False\n",
+      "xxxx 20 2 u h c False\n",
+      "xxxx 20 3 u d z False\n",
+      "xxxx 20 4 u d y False\n",
+      "xxxx 20 5 u a h False\n",
+      "xxxx 20 6 u g g False\n",
+      "xxxx 20 7 u e z False\n",
+      "xxxx 20 8 u e x False\n",
+      "xxxx 20 9 u d w False\n",
+      "xxxx 20 10 u c e False\n",
+      "xxxx 20 11 u h w False\n",
+      "xxxx 20 12 u g f False\n",
+      "xxxx 20 13 u e z False\n",
+      "xxxx 20 14 u f f False\n",
+      "xxxx 20 15 u f b False\n",
+      "seq1 20 16 u b u True\n",
+      "seq2 20 17 u g g True\n",
+      "seq2 20 18 u c c True\n",
+      "seq2 20 19 u h h True\n",
+      "seq2 20 20 u d d True\n",
+      "T . . . . . . . . . . . . . . . . . . . .\n",
       "T . . . . . . . . . . . . . . . . . . . .\n",
-      "T T . . . . . . . . . . . . . . . . . . .\n",
-      ". T . . . . . . . . . . . . . . . . . . .\n",
-      ". T . . . . . . . . . . . . . . . . . . .\n",
-      ". T . . . . . . . . . . . . . . . . . . .\n",
-      ". T . . . . . . . . . . . . . . . . . . .\n",
-      ". T T T T T T . . . . . . . . . . . . . .\n",
+      "T . . . . . . . . . . . . . . . . . . . .\n",
+      "T T T T . . . . . . . . . . . . . . . . .\n",
+      ". . . T . . . . . . . . . . . . . . . . .\n",
+      ". . . T T . . . . . . . . . . . . . . . .\n",
+      ". . . . T T T . . . . . . . . . . . . . .\n",
       ". . . . . . T . . . . . . . . . . . . . .\n",
       ". . . . . . T T . . . . . . . . . . . . .\n",
       ". . . . . . . T . . . . . . . . . . . . .\n",
       ". . . . . . . T . . . . . . . . . . . . .\n",
-      ". . . . . . . T . . . . . . . . . . . . .\n",
       ". . . . . . . T T T . . . . . . . . . . .\n",
-      ". . . . . . . . . T . . . . . . . . . . .\n",
-      ". . . . . . . . . T T T . . . . . . . . .\n",
-      ". . . . . . . . . . . T T T T T . . . . .\n",
-      ". . . . . . . . . . . . . . . T T T . . .\n",
-      ". . . . . . . . . . . . . . . . . T . . .\n",
-      ". . . . . . . . . . . . . . . . . T . . .\n",
-      ". . . . . . . . . . . . . . . . . T T T T\n",
-      ". . . . . . . . . . . . . . . . . . . . T\n"
+      ". . . . . . . . . T T . . . . . . . . . .\n",
+      ". . . . . . . . . . T . . . . . . . . . .\n",
+      ". . . . . . . . . . T T T . . . . . . . .\n",
+      ". . . . . . . . . . . . T . . . . . . . .\n",
+      ". . . . . . . . . . . . T . . . . . . . .\n",
+      ". . . . . . . . . . . . T T . . . . . . .\n",
+      ". . . . . . . . . . . . . T T . . . . . .\n",
+      ". . . . . . . . . . . . . . T T T . . . .\n",
+      ". . . . . . . . . . . . . . . . T T T T T\n"
      ]
     }
    ],
@@ -1263,16 +1261,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 23,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "'YaZVXZWehbabUXeYXXXeeZZacYdggcXefWWVfagZ'"
+       "'XYXghdVXdVagWVeUWXedWcZYhgZXWeWfZfbUgchd'"
       ]
      },
-     "execution_count": 22,
+     "execution_count": 23,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1283,7 +1281,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 24,
    "metadata": {},
    "outputs": [
     {
@@ -1291,27 +1289,27 @@
      "output_type": "stream",
      "text": [
       "T . . . . . . . . . . . . . . . . . . . .\n",
-      "T T . . . . . . . . . . . . . . . . . . .\n",
-      ". T . . . . . . . . . . . . . . . . . . .\n",
-      ". T . . . . . . . . . . . . . . . . . . .\n",
-      ". T . . . . . . . . . . . . . . . . . . .\n",
-      ". T . . . . . . . . . . . . . . . . . . .\n",
-      ". T T T T T T . . . . . . . . . . . . . .\n",
+      "T . . . . . . . . . . . . . . . . . . . .\n",
+      "T . . . . . . . . . . . . . . . . . . . .\n",
+      "T T T T . . . . . . . . . . . . . . . . .\n",
+      ". . . T . . . . . . . . . . . . . . . . .\n",
+      ". . . T T . . . . . . . . . . . . . . . .\n",
+      ". . . . T T T . . . . . . . . . . . . . .\n",
       ". . . . . . T . . . . . . . . . . . . . .\n",
       ". . . . . . T T . . . . . . . . . . . . .\n",
       ". . . . . . . T . . . . . . . . . . . . .\n",
       ". . . . . . . T . . . . . . . . . . . . .\n",
-      ". . . . . . . T . . . . . . . . . . . . .\n",
       ". . . . . . . T T T . . . . . . . . . . .\n",
-      ". . . . . . . . . T . . . . . . . . . . .\n",
-      ". . . . . . . . . T T T . . . . . . . . .\n",
-      ". . . . . . . . . . . T T T T T . . . . .\n",
-      ". . . . . . . . . . . . . . . T T T . . .\n",
-      ". . . . . . . . . . . . . . . . . T . . .\n",
-      ". . . . . . . . . . . . . . . . . T . . .\n",
-      ". . . . . . . . . . . . . . . . . T T T T\n",
-      ". . . . . . . . . . . . . . . . . . . . T\n",
-      "YaZVXZWehbabUXeYXXXeeZZacYdggcXefWWVfagZ\n"
+      ". . . . . . . . . T T . . . . . . . . . .\n",
+      ". . . . . . . . . . T . . . . . . . . . .\n",
+      ". . . . . . . . . . T T T . . . . . . . .\n",
+      ". . . . . . . . . . . . T . . . . . . . .\n",
+      ". . . . . . . . . . . . T . . . . . . . .\n",
+      ". . . . . . . . . . . . T T . . . . . . .\n",
+      ". . . . . . . . . . . . . T T . . . . . .\n",
+      ". . . . . . . . . . . . . . T T T . . . .\n",
+      ". . . . . . . . . . . . . . . . T T T T T\n",
+      "XYXghdVXdVagWVeUWXedWcZYhgZXWeWfZfbUgchd\n"
      ]
     },
     {
@@ -1320,7 +1318,7 @@
        "True"
       ]
      },
-     "execution_count": 23,
+     "execution_count": 24,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1334,19 +1332,19 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 24,
+   "execution_count": 25,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "('ehcceddeafddffefgffdfbbedabhbadebdchfabhhbfghdggcd',\n",
-       " 'hdahagaefhadaaaeehdhfaeafgcgcdfbegehdfchbfecgbgfbe',\n",
-       " 'hehcdahceddageaaefddfffefgfhafddaafaebbehedhdfabaeahbadfgcgecbddcfbhfegeahbhdhbfcfhgbfhdgecgbgcgdfbe',\n",
+       "('fahfgbdechbafcbcadcfchhccffhfgeagdhdceebccbhgdefgd',\n",
+       " 'badbgfaachhhhgghhebahhcbgabcfafeehfcabhbaaccgbcfae',\n",
+       " 'badfbgfahfgbadecahcbahfhchbchagghhdcefchbahhhcbcgacfbcffhafefgeaegdhfcabhhbdcaaccgebcfebcaecbhgdefgd',\n",
        " 100)"
       ]
      },
-     "execution_count": 24,
+     "execution_count": 25,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1360,7 +1358,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
+   "execution_count": 26,
    "metadata": {},
    "outputs": [
     {
@@ -1368,57 +1366,57 @@
      "output_type": "stream",
      "text": [
       "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      "T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . T T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . T . . T T T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      "T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      "T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". T T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". T . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
       ". . . . . . . . . . . . . . . . . . . . . . . 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 T T T . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . T T T T . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . .\n",
       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . .\n",
       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . .\n",
       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . .\n",
       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . T T\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
-      "HehcDAHceddAGeaAEfddffFefgfHAfdDAAfAEbbEHeDHdFabAEAhbadFGCGeCbdDcFBhfEGEaHbhDhbFCfHgBFhdgECGBgcGdFBE\n"
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T T T T T T\n",
+      "BADfBGFahfgbAdecAhCbaHfHcHbcHaGGHHdcEfchBAhHHCBcGAcfBCfFhAFEfgeaEgdHFCABhHBdcAACCGeBCFebcAEcbhgdefgd\n"
      ]
     },
     {
@@ -1427,7 +1425,7 @@
        "True"
       ]
      },
-     "execution_count": 25,
+     "execution_count": 26,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1441,14 +1439,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 26,
+   "execution_count": 27,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "1000 loops, best of 3: 1.25 ms per loop\n"
+      "1000 loops, best of 3: 1.24 ms per loop\n"
      ]
     }
    ],
@@ -1459,65 +1457,65 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 27,
+   "execution_count": 28,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      "T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
       ". . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
       ". . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
       ". . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
       ". . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . T . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . T . T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . T T T T T . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . T T T T T . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . T . T T T . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . . . . .\n",
       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . T . . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . .\n",
       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . T T . . . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T T . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . T . . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . .\n",
-      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T\n",
-      "hEHCdahCEDDagEaAeFDDfFFEFGFhaFdDaaFaeBBehEdhDfABaeaHBADfgcgEcBdDCfbHFegeAhBHdHBfcFhGbfHDGecgbGCgDfbe\n"
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T T T . . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . T T T . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . . . . . . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T T T . . . . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T T . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T . .\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T T T\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
+      ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T\n",
+      "badFbgfAHFGBaDECaHcBAhFhChBChAgghhDCeFCHbahhHcbCgaCFbcfFHafeFGEAeGDhfcabhHbDCaaccgEbcfEBCaeCBHGDEFGD\n"
      ]
     },
     {
@@ -1526,7 +1524,7 @@
        "True"
       ]
      },
-     "execution_count": 27,
+     "execution_count": 28,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1540,7 +1538,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 28,
+   "execution_count": 29,
    "metadata": {},
    "outputs": [
     {
@@ -1549,7 +1547,7 @@
        "True"
       ]
      },
-     "execution_count": 28,
+     "execution_count": 29,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1560,16 +1558,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 29,
+   "execution_count": 30,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "('ahgafgaagdgccegafedggefddeaabhffchdgeabcfaacahcgge', False, False)"
+       "('gbaehdacgdebgaebecfbefcbehfgcheaccdehbfdfadebhcehd', False, False)"
       ]
      },
-     "execution_count": 29,
+     "execution_count": 30,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1581,7 +1579,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 30,
+   "execution_count": 31,
    "metadata": {},
    "outputs": [
     {
@@ -1648,7 +1646,7 @@
        "False"
       ]
      },
-     "execution_count": 30,
+     "execution_count": 31,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1662,7 +1660,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 31,
+   "execution_count": 32,
    "metadata": {
     "collapsed": true
    },
@@ -1686,7 +1684,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 48,
+   "execution_count": 33,
    "metadata": {
     "collapsed": true
    },
@@ -1701,7 +1699,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 49,
+   "execution_count": 34,
    "metadata": {},
    "outputs": [
     {
@@ -1710,7 +1708,7 @@
        "True"
       ]
      },
-     "execution_count": 49,
+     "execution_count": 34,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1721,7 +1719,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 50,
+   "execution_count": 35,
    "metadata": {},
    "outputs": [
     {
@@ -1730,7 +1728,7 @@
        "False"
       ]
      },
-     "execution_count": 50,
+     "execution_count": 35,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1748,7 +1746,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 32,
+   "execution_count": 36,
    "metadata": {
     "collapsed": true
    },
@@ -1761,7 +1759,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 33,
+   "execution_count": 37,
    "metadata": {
     "collapsed": true
    },
@@ -1787,16 +1785,29 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 34,
+   "execution_count": 73,
    "metadata": {},
    "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0: accbadaadc\n",
+      "1: bbbbaabada\n",
+      "2: cdaacacadcddbccacdab\n",
+      "3: bbcdabbaaabcbcadcaac\n",
+      "4: accbbabbdbaaabadaadc\n",
+      "5: acadcdddab\n",
+      "6: aacccabaddcdaddaabdc\n"
+     ]
+    },
     {
      "data": {
       "text/plain": [
-       "('acabcbccaa', 'cabcadddca', 'acabcbcccaaabcadddca', 20)"
+       "['accbbabbdbaaabadaadc']"
       ]
      },
-     "execution_count": 34,
+     "execution_count": 73,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1805,13 +1816,19 @@
     "s1 = make_string(10, alphabet='abcd')\n",
     "s2 = make_string(10, alphabet='abcd')\n",
     "s3 = make_string(10, alphabet='abcd')\n",
+    "s4 = make_string(10, alphabet='abcd')\n",
     "il = interleave(s1, s2)\n",
-    "s1, s2, il, len(il)"
+    "bs = [s3, il, interleave(s3, s4), interleave(s2, s4), interleave(s1, s3)]\n",
+    "random.shuffle(bs)\n",
+    "bs = [s1, s2] + bs\n",
+    "tg = [l for l in bs if is_interleave(s1, s2, l)]\n",
+    "print('\\n'.join(['{}: {}'.format(i, s) for i, s in enumerate(bs)]))\n",
+    "tg"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 35,
+   "execution_count": 74,
    "metadata": {},
    "outputs": [
     {
@@ -1819,19 +1836,19 @@
      "output_type": "stream",
      "text": [
       "* . . . . . . . . . .\n",
-      "a c a b c . . . . . .\n",
-      "c . . c . . . . . . .\n",
       "a . . . . . . . . . .\n",
-      "b c . . . . . . . . .\n",
       "c . . . . . . . . . .\n",
-      "b c . . . . . . . . .\n",
-      "c c . . . . . . . . .\n",
-      "c c a . . . . . . . .\n",
-      ". a a . . . . . . . .\n",
-      ". a a b c a d d d c a\n",
-      "ACABCBcCCaAAbcadddca\n",
-      "acabcbcccaaabcadddca\n",
-      "****** ** **        \n"
+      "c b b . . . . . . . .\n",
+      "b b . . . . . . . . .\n",
+      ". a b b . . . . . . .\n",
+      ". . . d b a a . . . .\n",
+      ". . . . a a a b a d a\n",
+      ". . . . a a . a . a a\n",
+      ". . . . . . . d a . d\n",
+      ". . . . . . . . . . c\n",
+      "ACCbBAbbDbaaAbadaADC\n",
+      "accbbabbdbaaabadaadc\n",
+      "*** **  *   *    ***\n"
      ]
     },
     {
@@ -1840,7 +1857,7 @@
        "True"
       ]
      },
-     "execution_count": 35,
+     "execution_count": 74,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1855,27 +1872,58 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 36,
+   "execution_count": 75,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "* a c a b c b c c . .\n",
-      ". c . . c . c c c a a\n",
-      ". a . . . . . . a a a\n",
-      ". b c . . . . . . . b\n",
-      ". c . . . . . . . . c\n",
-      ". . . . . . . . . . a\n",
-      ". . . . . . . . . . d\n",
-      ". . . . . . . . . . d\n",
+      "aacccabaddcdaddaabdc\n",
+      " * ** ** *  *   * **\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "6"
+      ]
+     },
+     "execution_count": 75,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "ind = [i for i, b in enumerate(bs) if is_interleave(s1, s3, b)][0]\n",
+    "v, bp = is_interleave(s1, s3, bs[ind], return_backpointers=True)\n",
+    "print(show_backtrace_star(bp))\n",
+    "ind"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 39,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "* . . . . . . . . . .\n",
+      "b d . . . . . . . . .\n",
+      ". b c c . . . . . . .\n",
+      ". . . d . . . . . . .\n",
+      ". . . c a a . . . . .\n",
+      ". . . a a a . . . . .\n",
+      ". . . a a a d a . . .\n",
+      ". . . a a . a a b a c\n",
+      ". . . . d a . . . . d\n",
       ". . . . . . . . . . d\n",
       ". . . . . . . . . . c\n",
-      ". . . . . . . . . . a\n",
-      "acabcbccCaaABCADDDCA\n",
-      "acabcbcccaaabcadddca\n",
-      "        *  *********\n"
+      "BdBccDCaaAAdaAbacDDC\n",
+      "bdbccdcaaaadaabacddc\n",
+      "* *  **  **  *   ***\n"
      ]
     },
     {
@@ -1884,7 +1932,7 @@
        "True"
       ]
      },
-     "execution_count": 36,
+     "execution_count": 39,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1899,22 +1947,22 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 37,
+   "execution_count": 40,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "* a . . . . . . . . .\n",
-      "a . . . . . . . . . .\n",
-      "c a . . . . . . . . .\n",
-      "a . . . . . . . . . .\n",
-      "b . . . . . . . . . .\n",
-      "c . . . . . . . . . .\n",
-      "b . . . . . . . . . .\n",
-      "c . . . . . . . . . .\n",
-      "c . . . . . . . . . .\n",
+      "* . . . . . . . . . .\n",
+      ". . . . . . . . . . .\n",
+      ". . . . . . . . . . .\n",
+      ". . . . . . . . . . .\n",
+      ". . . . . . . . . . .\n",
+      ". . . . . . . . . . .\n",
+      ". . . . . . . . . . .\n",
+      ". . . . . . . . . . .\n",
+      ". . . . . . . . . . .\n",
       ". . . . . . . . . . .\n",
       ". . . . . . . . . . .\n",
       "\n",
@@ -1927,7 +1975,7 @@
        "False"
       ]
      },
-     "execution_count": 37,
+     "execution_count": 40,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1942,27 +1990,27 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 38,
+   "execution_count": 41,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "* a . . . . . . . . .\n",
-      ". c . . . . . . . . .\n",
-      ". a . . . . . . . . .\n",
-      ". b . . . . . . . . .\n",
-      ". c . . . . . . . . .\n",
+      "* . . . . . . . . . .\n",
+      "b . . . . . . . . . .\n",
+      ". . . . . . . . . . .\n",
+      ". . . . . . . . . . .\n",
       ". . . . . . . . . . .\n",
       ". . . . . . . . . . .\n",
       ". . . . . . . . . . .\n",
       ". . . . . . . . . . .\n",
       ". . . . . . . . . . .\n",
       ". . . . . . . . . . .\n",
-      "aCABC\n",
-      "acabc\n",
-      " ****\n"
+      ". . . . . . . . . . .\n",
+      "B\n",
+      "b\n",
+      "*\n"
      ]
     },
     {
@@ -1971,7 +2019,7 @@
        "False"
       ]
      },
-     "execution_count": 38,
+     "execution_count": 41,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1984,6 +2032,120 @@
     "v"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "collapsed": true
+   },
+   "source": [
+    "# Make puzzle data"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 47,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "my_bill = make_string(200)\n",
+    "friend_bill = make_string(200)\n",
+    "other_bills = [make_string(200) for _ in range(98)]\n",
+    "\n",
+    "target_interleaved = interleave(my_bill, friend_bill)\n",
+    "mine_interleaved = [interleave(my_bill, o) for o in random.sample(other_bills, 21)]\n",
+    "friend_interleaved = [interleave(friend_bill, o) for o in random.sample(other_bills, 13)]\n",
+    "other_interleaved = []\n",
+    "for _ in range(103):\n",
+    "    s1, s2 = random.sample(other_bills, 2)\n",
+    "    other_interleaved += [interleave(s1, s2)]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 48,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "all_targets = [target_interleaved] + mine_interleaved + friend_interleaved + other_interleaved"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 49,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "CPU times: user 3.16 s, sys: 8 ms, total: 3.16 s\n",
+      "Wall time: 3.17 s\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "[0]"
+      ]
+     },
+     "execution_count": 49,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "%time [i for i, s12 in enumerate(all_targets) if is_interleave(my_bill, friend_bill, s12)]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 50,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "CPU times: user 788 ms, sys: 0 ns, total: 788 ms\n",
+      "Wall time: 789 ms\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "[0]"
+      ]
+     },
+     "execution_count": 50,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "%time [i for i, s12 in enumerate(all_targets) if is_interleave_recursive(my_bill, friend_bill, s12)]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 51,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "bill_set = all_targets + random.sample(other_bills, 8)\n",
+    "random.shuffle(bill_set)\n",
+    "bill_set = [my_bill, friend_bill] + bill_set\n",
+    "\n",
+    "# with open('09-bills.txt', 'w') as f:\n",
+    "#     for i, b in enumerate(bill_set):\n",
+    "#         f.write('{}: {}\\n'.format(i, b))"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,