From 93480ac5d80bcff214ea42c161f214a027536dac Mon Sep 17 00:00:00 2001
From: Michael Leuschel <leuschel@uni-duesseldorf.de>
Date: Tue, 26 May 2020 10:31:33 +0200
Subject: [PATCH] add all solutions machine

---
 puzzles/Sudoku_Miracle.ipynb | 972 +++++++++++++++++++++++++++++++++++
 1 file changed, 972 insertions(+)

diff --git a/puzzles/Sudoku_Miracle.ipynb b/puzzles/Sudoku_Miracle.ipynb
index 20b721e..b7e530c 100644
--- a/puzzles/Sudoku_Miracle.ipynb
+++ b/puzzles/Sudoku_Miracle.ipynb
@@ -1024,6 +1024,978 @@
     ":stats"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We can also generate all 72 solutions to this kind of Sudoku, by removing the puzzle constraints:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Loaded machine: Sudoku_Miracle"
+      ]
+     },
+     "execution_count": 9,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "::load\n",
+    "MACHINE Sudoku_Miracle\n",
+    "DEFINITIONS DOM == 1..9; D1 == 1..8; D2 == 2..9;\n",
+    "      SUBSQ == { {1,2,3}, {4,5,6}, {7,8,9} };\n",
+    "      ANIMATION_FUNCTION_DEFAULT == {r,c,i|r:1..9 & c:1..9 & i=0};\n",
+    "      ANIMATION_FUNCTION == ( {r,c,i|r:DOM & c:DOM & i:DOM &  i = Board(r)(c)} );\n",
+    "      ANIMATION_IMG0 == \"images/sm_empty_box.gif\";\n",
+    "      ANIMATION_IMG1 == \"images/sm_1.gif\";\n",
+    "      ANIMATION_IMG2 == \"images/sm_2.gif\";\n",
+    "      ANIMATION_IMG3 == \"images/sm_3.gif\";\n",
+    "      ANIMATION_IMG4 == \"images/sm_4.gif\";\n",
+    "      ANIMATION_IMG5 == \"images/sm_5.gif\";\n",
+    "      ANIMATION_IMG6 == \"images/sm_6.gif\";\n",
+    "      ANIMATION_IMG7 == \"images/sm_7.gif\";\n",
+    "      ANIMATION_IMG8 == \"images/sm_8.gif\";\n",
+    "      ANIMATION_IMG9 == \"images/sm_9.gif\";\n",
+    "      SET_PREF_MAX_INITIALISATIONS == 73\n",
+    "CONSTANTS Board\n",
+    "PROPERTIES\n",
+    "  Board : DOM --> (DOM --> DOM)\n",
+    "  ∧\n",
+    "  /*@label \"Horizontal and vertical lines\" */\n",
+    "  ∀y.(y:DOM ⇒ ∀(x1,x2).(x1∈D1 ∧ x1<x2 ∧ x2∈D2  ⇒ (Board(x1)(y) ≠ Board(x2)(y) ∧\n",
+    "                                                    Board(y)(x1) ≠ Board(y)(x2))))\n",
+    "     /*@desc \"within a vertical or horizontal line all numbers must be different\" */\n",
+    "  ∧\n",
+    "  \n",
+    "  /*@label \"Squares\" */\n",
+    "  ∀(s1,s2).(s1:SUBSQ ∧ s2:SUBSQ ⇒\n",
+    "             ∀(x1,y1,x2,y2).( (x1∈s1 ∧ x2∈s1 ∧ \n",
+    "                               x1>=x2 ∧ (x1=x2 ⇒ y1>y2) ∧ // lexicographical ordering\n",
+    "                               y1∈s2 ∧ y2∈s2 ∧ (x1,y1) ≠ (x2,y2))\n",
+    "                              ⇒\n",
+    "                              Board(x1)(y1) ≠ Board(x2)(y2)\n",
+    "                            ))\n",
+    "     /*@desc \"within a sub-square all numbers must be different\" */\n",
+    "  ∧\n",
+    "    /*@label \"King Moves\" */\n",
+    "  ∀(x,y).(x∈D2 ∧ y∈D2  ⇒\n",
+    "                          (Board(x)(y)   ≠ Board(x-1)(y-1) ∧\n",
+    "                           Board(x)(y-1) ≠ Board(x-1)(y) )\n",
+    "    )\n",
+    "  ∧\n",
+    "  /*@label \"Orthogonals\" */\n",
+    "  ∀(x,y).(x∈D1 ∧ y∈DOM  ⇒\n",
+    "                          (  Board(x)(y) ≠ 1+Board(x+1)(y) ∧\n",
+    "                           1+Board(x)(y) ≠   Board(x+1)(y) ∧\n",
+    "                             Board(y)(x) ≠ 1+Board(y)(x+1) ∧\n",
+    "                           1+Board(y)(x) ≠   Board(y)(x+1) )\n",
+    "    )\n",
+    "     /*@desc \"any two orthogonally adjacent cells cannot contain consecutive digits\" */\n",
+    "  ∧\n",
+    "\n",
+    "  /*@label \"Knight Moves 1\" */\n",
+    "  ∀(x,y).(x∈D1 ∧ y∈DOM  ⇒\n",
+    "                          ( y+2∈DOM ⇒ Board(x)(y) ≠ Board(x+1)(y+2)  ) ∧\n",
+    "                          ( y-2∈DOM ⇒ Board(x)(y) ≠ Board(x+1)(y-2)  )\n",
+    "    ) \n",
+    "  ∧\n",
+    "  /*@label \"Knight Moves 2\" */\n",
+    "  ∀(x,y).(x∈1..7 ∧ y∈DOM  ⇒\n",
+    "                          ( y+1∈DOM ⇒ Board(x)(y) ≠ Board(x+2)(y+1)  ) ∧\n",
+    "                          ( y-1∈DOM ⇒ Board(x)(y) ≠ Board(x+2)(y-1)  )\n",
+    "    )\n",
+    "END"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Machine: Sudoku_Miracle\n",
+       "Sets: (none)\n",
+       "Constants: Board\n",
+       "Variables: (none)\n",
+       "Operations: \n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()\n",
+       "SETUP_CONSTANTS()"
+      ]
+     },
+     "execution_count": 10,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    ":browse"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Machine constants set up using operation 0: $setup_constants()"
+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    ":constants"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Machine initialised using operation 72: $initialise_machine()"
+      ]
+     },
+     "execution_count": 12,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    ":init"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/markdown": [
+       "**Explored States:** 3/74  \n",
+       "**Transitions:** 73"
+      ],
+      "text/plain": [
+       "Explored States: 3/74\n",
+       "Transitions: 73"
+      ]
+     },
+     "execution_count": 13,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    ":stats"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/markdown": [
+       "<table style=\"font-family:monospace\"><tbody>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"8\" src=\"images/sm_8.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/sm_2.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"5\" src=\"images/sm_5.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/sm_3.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"6\" src=\"images/sm_6.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"9\" src=\"images/sm_9.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"7\" src=\"images/sm_7.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/sm_1.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"4\" src=\"images/sm_4.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"4\" src=\"images/sm_4.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"7\" src=\"images/sm_7.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/sm_1.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"8\" src=\"images/sm_8.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/sm_2.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"5\" src=\"images/sm_5.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/sm_3.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"6\" src=\"images/sm_6.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"9\" src=\"images/sm_9.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"9\" src=\"images/sm_9.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/sm_3.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"6\" src=\"images/sm_6.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"4\" src=\"images/sm_4.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"7\" src=\"images/sm_7.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/sm_1.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"8\" src=\"images/sm_8.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/sm_2.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"5\" src=\"images/sm_5.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"5\" src=\"images/sm_5.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"8\" src=\"images/sm_8.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/sm_2.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"9\" src=\"images/sm_9.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/sm_3.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"6\" src=\"images/sm_6.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"4\" src=\"images/sm_4.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"7\" src=\"images/sm_7.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/sm_1.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/sm_1.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"4\" src=\"images/sm_4.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"7\" src=\"images/sm_7.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"5\" src=\"images/sm_5.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"8\" src=\"images/sm_8.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/sm_2.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"9\" src=\"images/sm_9.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/sm_3.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"6\" src=\"images/sm_6.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"6\" src=\"images/sm_6.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"9\" src=\"images/sm_9.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/sm_3.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/sm_1.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"4\" src=\"images/sm_4.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"7\" src=\"images/sm_7.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"5\" src=\"images/sm_5.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"8\" src=\"images/sm_8.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/sm_2.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/sm_2.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"5\" src=\"images/sm_5.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"8\" src=\"images/sm_8.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"6\" src=\"images/sm_6.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"9\" src=\"images/sm_9.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/sm_3.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/sm_1.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"4\" src=\"images/sm_4.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"7\" src=\"images/sm_7.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"7\" src=\"images/sm_7.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/sm_1.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"4\" src=\"images/sm_4.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/sm_2.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"5\" src=\"images/sm_5.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"8\" src=\"images/sm_8.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"6\" src=\"images/sm_6.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"9\" src=\"images/sm_9.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/sm_3.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/sm_3.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"6\" src=\"images/sm_6.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"9\" src=\"images/sm_9.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"7\" src=\"images/sm_7.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/sm_1.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"4\" src=\"images/sm_4.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/sm_2.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"5\" src=\"images/sm_5.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"8\" src=\"images/sm_8.gif\"/></td>\n",
+       "</tr>\n",
+       "</tbody></table>"
+      ],
+      "text/plain": [
+       "<Animation function visualisation>"
+      ]
+     },
+     "execution_count": 14,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    ":show"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "This machine computes all solutions in a set comprehension and then provides a B operation to cycle through all solutions.\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Loaded machine: Sudoku_Miracle_All72"
+      ]
+     },
+     "execution_count": 17,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "::load\n",
+    "MACHINE Sudoku_Miracle_All72\n",
+    "DEFINITIONS DOM == 1..9; D1 == 1..8; D2 == 2..9;\n",
+    "      SUBSQ == { {1,2,3}, {4,5,6}, {7,8,9} };\n",
+    "      ANIMATION_FUNCTION_DEFAULT == {r,c,i|r:1..9 & c:1..9 & i=0};\n",
+    "      ANIMATION_FUNCTION == ( {r,c,i|r:DOM & c:DOM & i:DOM &  i = Board(r)(c)} );\n",
+    "      ANIMATION_IMG0 == \"images/sm_empty_box.gif\";\n",
+    "      ANIMATION_IMG1 == \"images/sm_1.gif\";\n",
+    "      ANIMATION_IMG2 == \"images/sm_2.gif\";\n",
+    "      ANIMATION_IMG3 == \"images/sm_3.gif\";\n",
+    "      ANIMATION_IMG4 == \"images/sm_4.gif\";\n",
+    "      ANIMATION_IMG5 == \"images/sm_5.gif\";\n",
+    "      ANIMATION_IMG6 == \"images/sm_6.gif\";\n",
+    "      ANIMATION_IMG7 == \"images/sm_7.gif\";\n",
+    "      ANIMATION_IMG8 == \"images/sm_8.gif\";\n",
+    "      ANIMATION_IMG9 == \"images/sm_9.gif\";\n",
+    "      \"CHOOSE.def\"\n",
+    "CONSTANTS Boards\n",
+    "PROPERTIES\n",
+    " Boards = {Board |  // all 72 solutions\n",
+    "  Board : DOM --> (DOM --> DOM)\n",
+    "  ∧\n",
+    "  /*@label \"Horizontal and vertical lines\" */\n",
+    "  ∀y.(y:DOM ⇒ ∀(x1,x2).(x1∈D1 ∧ x1<x2 ∧ x2∈D2  ⇒ (Board(x1)(y) ≠ Board(x2)(y) ∧\n",
+    "                                                    Board(y)(x1) ≠ Board(y)(x2))))\n",
+    "     /*@desc \"within a vertical or horizontal line all numbers must be different\" */\n",
+    "  ∧\n",
+    "  \n",
+    "  /*@label \"Squares\" */\n",
+    "  ∀(s1,s2).(s1:SUBSQ ∧ s2:SUBSQ ⇒\n",
+    "             ∀(x1,y1,x2,y2).( (x1∈s1 ∧ x2∈s1 ∧ \n",
+    "                               x1>=x2 ∧ (x1=x2 ⇒ y1>y2) ∧ // lexicographical ordering\n",
+    "                               y1∈s2 ∧ y2∈s2 ∧ (x1,y1) ≠ (x2,y2))\n",
+    "                              ⇒\n",
+    "                              Board(x1)(y1) ≠ Board(x2)(y2)\n",
+    "                            ))\n",
+    "     /*@desc \"within a sub-square all numbers must be different\" */\n",
+    "  ∧\n",
+    "    /*@label \"King Moves\" */\n",
+    "  ∀(x,y).(x∈D2 ∧ y∈D2  ⇒\n",
+    "                          (Board(x)(y)   ≠ Board(x-1)(y-1) ∧\n",
+    "                           Board(x)(y-1) ≠ Board(x-1)(y) )\n",
+    "    )\n",
+    "  ∧\n",
+    "  /*@label \"Orthogonals\" */\n",
+    "  ∀(x,y).(x∈D1 ∧ y∈DOM  ⇒\n",
+    "                          (  Board(x)(y) ≠ 1+Board(x+1)(y) ∧\n",
+    "                           1+Board(x)(y) ≠   Board(x+1)(y) ∧\n",
+    "                             Board(y)(x) ≠ 1+Board(y)(x+1) ∧\n",
+    "                           1+Board(y)(x) ≠   Board(y)(x+1) )\n",
+    "    )\n",
+    "     /*@desc \"any two orthogonally adjacent cells cannot contain consecutive digits\" */\n",
+    "  ∧\n",
+    "\n",
+    "  /*@label \"Knight Moves 1\" */\n",
+    "  ∀(x,y).(x∈D1 ∧ y∈DOM  ⇒\n",
+    "                          ( y+2∈DOM ⇒ Board(x)(y) ≠ Board(x+1)(y+2)  ) ∧\n",
+    "                          ( y-2∈DOM ⇒ Board(x)(y) ≠ Board(x+1)(y-2)  )\n",
+    "    ) \n",
+    "  ∧\n",
+    "  /*@label \"Knight Moves 2\" */\n",
+    "  ∀(x,y).(x∈1..7 ∧ y∈DOM  ⇒\n",
+    "                          ( y+1∈DOM ⇒ Board(x)(y) ≠ Board(x+2)(y+1)  ) ∧\n",
+    "                          ( y-1∈DOM ⇒ Board(x)(y) ≠ Board(x+2)(y-1)  )\n",
+    "    )\n",
+    "    }\n",
+    "VARIABLES Board, rem\n",
+    "INVARIANT Board : Boards & rem <: Boards\n",
+    "INITIALISATION Board := CHOOSE(Boards) || rem := Boards \\ {CHOOSE(Boards)}\n",
+    "OPERATIONS get_next_board = PRE rem /= {} THEN\n",
+    "              Board := CHOOSE(rem) ||\n",
+    "              rem := rem \\ {CHOOSE(rem)}\n",
+    "           END\n",
+    "END"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Machine constants set up using operation 0: $setup_constants()"
+      ]
+     },
+     "execution_count": 18,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    ":constants"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Machine initialised using operation 1: $initialise_machine()"
+      ]
+     },
+     "execution_count": 19,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    ":init"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/markdown": [
+       "<table style=\"font-family:monospace\"><tbody>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"6\" src=\"images/sm_6.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/sm_2.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"7\" src=\"images/sm_7.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/sm_3.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"8\" src=\"images/sm_8.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"4\" src=\"images/sm_4.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"9\" src=\"images/sm_9.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"5\" src=\"images/sm_5.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/sm_1.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/sm_3.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"8\" src=\"images/sm_8.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"4\" src=\"images/sm_4.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"9\" src=\"images/sm_9.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"5\" src=\"images/sm_5.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/sm_1.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"6\" src=\"images/sm_6.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/sm_2.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"7\" src=\"images/sm_7.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"9\" src=\"images/sm_9.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"5\" src=\"images/sm_5.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/sm_1.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"6\" src=\"images/sm_6.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/sm_2.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"7\" src=\"images/sm_7.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/sm_3.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"8\" src=\"images/sm_8.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"4\" src=\"images/sm_4.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/sm_2.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"7\" src=\"images/sm_7.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/sm_3.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"8\" src=\"images/sm_8.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"4\" src=\"images/sm_4.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"9\" src=\"images/sm_9.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"5\" src=\"images/sm_5.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/sm_1.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"6\" src=\"images/sm_6.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"8\" src=\"images/sm_8.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"4\" src=\"images/sm_4.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"9\" src=\"images/sm_9.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"5\" src=\"images/sm_5.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/sm_1.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"6\" src=\"images/sm_6.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/sm_2.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"7\" src=\"images/sm_7.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/sm_3.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"5\" src=\"images/sm_5.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/sm_1.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"6\" src=\"images/sm_6.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/sm_2.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"7\" src=\"images/sm_7.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/sm_3.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"8\" src=\"images/sm_8.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"4\" src=\"images/sm_4.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"9\" src=\"images/sm_9.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"7\" src=\"images/sm_7.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/sm_3.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"8\" src=\"images/sm_8.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"4\" src=\"images/sm_4.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"9\" src=\"images/sm_9.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"5\" src=\"images/sm_5.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/sm_1.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"6\" src=\"images/sm_6.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/sm_2.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"4\" src=\"images/sm_4.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"9\" src=\"images/sm_9.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"5\" src=\"images/sm_5.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/sm_1.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"6\" src=\"images/sm_6.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/sm_2.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"7\" src=\"images/sm_7.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/sm_3.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"8\" src=\"images/sm_8.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/sm_1.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"6\" src=\"images/sm_6.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/sm_2.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"7\" src=\"images/sm_7.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/sm_3.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"8\" src=\"images/sm_8.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"4\" src=\"images/sm_4.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"9\" src=\"images/sm_9.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"5\" src=\"images/sm_5.gif\"/></td>\n",
+       "</tr>\n",
+       "</tbody></table>"
+      ],
+      "text/plain": [
+       "<Animation function visualisation>"
+      ]
+     },
+     "execution_count": 20,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    ":show"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Executed operation: get_next_board()"
+      ]
+     },
+     "execution_count": 21,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    ":exec get_next_board"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/markdown": [
+       "<table style=\"font-family:monospace\"><tbody>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/sm_1.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"6\" src=\"images/sm_6.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/sm_2.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"7\" src=\"images/sm_7.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/sm_3.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"8\" src=\"images/sm_8.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"4\" src=\"images/sm_4.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"9\" src=\"images/sm_9.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"5\" src=\"images/sm_5.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"4\" src=\"images/sm_4.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"9\" src=\"images/sm_9.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"5\" src=\"images/sm_5.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/sm_1.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"6\" src=\"images/sm_6.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/sm_2.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"7\" src=\"images/sm_7.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/sm_3.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"8\" src=\"images/sm_8.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"7\" src=\"images/sm_7.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/sm_3.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"8\" src=\"images/sm_8.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"4\" src=\"images/sm_4.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"9\" src=\"images/sm_9.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"5\" src=\"images/sm_5.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/sm_1.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"6\" src=\"images/sm_6.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/sm_2.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"5\" src=\"images/sm_5.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/sm_1.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"6\" src=\"images/sm_6.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/sm_2.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"7\" src=\"images/sm_7.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/sm_3.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"8\" src=\"images/sm_8.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"4\" src=\"images/sm_4.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"9\" src=\"images/sm_9.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"8\" src=\"images/sm_8.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"4\" src=\"images/sm_4.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"9\" src=\"images/sm_9.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"5\" src=\"images/sm_5.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/sm_1.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"6\" src=\"images/sm_6.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/sm_2.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"7\" src=\"images/sm_7.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/sm_3.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/sm_2.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"7\" src=\"images/sm_7.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/sm_3.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"8\" src=\"images/sm_8.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"4\" src=\"images/sm_4.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"9\" src=\"images/sm_9.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"5\" src=\"images/sm_5.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/sm_1.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"6\" src=\"images/sm_6.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"9\" src=\"images/sm_9.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"5\" src=\"images/sm_5.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/sm_1.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"6\" src=\"images/sm_6.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/sm_2.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"7\" src=\"images/sm_7.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/sm_3.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"8\" src=\"images/sm_8.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"4\" src=\"images/sm_4.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/sm_3.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"8\" src=\"images/sm_8.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"4\" src=\"images/sm_4.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"9\" src=\"images/sm_9.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"5\" src=\"images/sm_5.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/sm_1.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"6\" src=\"images/sm_6.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/sm_2.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"7\" src=\"images/sm_7.gif\"/></td>\n",
+       "</tr>\n",
+       "<tr>\n",
+       "<td style=\"padding:0px\"><img alt=\"6\" src=\"images/sm_6.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"2\" src=\"images/sm_2.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"7\" src=\"images/sm_7.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"3\" src=\"images/sm_3.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"8\" src=\"images/sm_8.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"4\" src=\"images/sm_4.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"9\" src=\"images/sm_9.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"5\" src=\"images/sm_5.gif\"/></td>\n",
+       "<td style=\"padding:0px\"><img alt=\"1\" src=\"images/sm_1.gif\"/></td>\n",
+       "</tr>\n",
+       "</tbody></table>"
+      ],
+      "text/plain": [
+       "<Animation function visualisation>"
+      ]
+     },
+     "execution_count": 22,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    ":show"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/markdown": [
+       "$72$"
+      ],
+      "text/plain": [
+       "72"
+      ]
+     },
+     "execution_count": 23,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "card(Boards)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/markdown": [
+       "|Elements|\n",
+       "|---|\n",
+       "|$\\{(1\\mapsto\\{(1\\mapsto 6),(2\\mapsto 2),(3\\mapsto 7),(4\\mapsto 3),(5\\mapsto 8),(6\\mapsto 4),(7\\mapsto 9),(8\\mapsto 5),(9\\mapsto 1)\\}),(2\\mapsto\\{(1\\mapsto 3),(2\\mapsto 8),(3\\mapsto 4),(4\\mapsto 9),(5\\mapsto 5),(6\\mapsto 1),(7\\mapsto 6),(8\\mapsto 2),(9\\mapsto 7)\\}),(3\\mapsto\\{(1\\mapsto 9),(2\\mapsto 5),(3\\mapsto 1),(4\\mapsto 6),(5\\mapsto 2),(6\\mapsto 7),(7\\mapsto 3),(8\\mapsto 8),(9\\mapsto 4)\\}),(4\\mapsto\\{(1\\mapsto 2),(2\\mapsto 7),(3\\mapsto 3),(4\\mapsto 8),(5\\mapsto 4),(6\\mapsto 9),(7\\mapsto 5),(8\\mapsto 1),(9\\mapsto 6)\\}),(5\\mapsto\\{(1\\mapsto 8),(2\\mapsto 4),(3\\mapsto 9),(4\\mapsto 5),(5\\mapsto 1),(6\\mapsto 6),(7\\mapsto 2),(8\\mapsto 7),(9\\mapsto 3)\\}),(6\\mapsto\\{(1\\mapsto 5),(2\\mapsto 1),(3\\mapsto 6),(4\\mapsto 2),(5\\mapsto 7),(6\\mapsto 3),(7\\mapsto 8),(8\\mapsto 4),(9\\mapsto 9)\\}),(7\\mapsto\\{(1\\mapsto 7),(2\\mapsto 3),(3\\mapsto 8),(4\\mapsto 4),(5\\mapsto 9),(6\\mapsto 5),(7\\mapsto 1),(8\\mapsto 6),(9\\mapsto 2)\\}),(8\\mapsto\\{(1\\mapsto 4),(2\\mapsto 9),(3\\mapsto 5),(4\\mapsto 1),(5\\mapsto 6),(6\\mapsto 2),(7\\mapsto 7),(8\\mapsto 3),(9\\mapsto 8)\\}),(9\\mapsto\\{(1\\mapsto 1),(2\\mapsto 6),(3\\mapsto 2),(4\\mapsto 7),(5\\mapsto 3),(6\\mapsto 8),(7\\mapsto 4),(8\\mapsto 9),(9\\mapsto 5)\\})\\}$|\n",
+       "|$\\{(1\\mapsto\\{(1\\mapsto 1),(2\\mapsto 6),(3\\mapsto 2),(4\\mapsto 7),(5\\mapsto 3),(6\\mapsto 8),(7\\mapsto 4),(8\\mapsto 9),(9\\mapsto 5)\\}),(2\\mapsto\\{(1\\mapsto 4),(2\\mapsto 9),(3\\mapsto 5),(4\\mapsto 1),(5\\mapsto 6),(6\\mapsto 2),(7\\mapsto 7),(8\\mapsto 3),(9\\mapsto 8)\\}),(3\\mapsto\\{(1\\mapsto 7),(2\\mapsto 3),(3\\mapsto 8),(4\\mapsto 4),(5\\mapsto 9),(6\\mapsto 5),(7\\mapsto 1),(8\\mapsto 6),(9\\mapsto 2)\\}),(4\\mapsto\\{(1\\mapsto 5),(2\\mapsto 1),(3\\mapsto 6),(4\\mapsto 2),(5\\mapsto 7),(6\\mapsto 3),(7\\mapsto 8),(8\\mapsto 4),(9\\mapsto 9)\\}),(5\\mapsto\\{(1\\mapsto 8),(2\\mapsto 4),(3\\mapsto 9),(4\\mapsto 5),(5\\mapsto 1),(6\\mapsto 6),(7\\mapsto 2),(8\\mapsto 7),(9\\mapsto 3)\\}),(6\\mapsto\\{(1\\mapsto 2),(2\\mapsto 7),(3\\mapsto 3),(4\\mapsto 8),(5\\mapsto 4),(6\\mapsto 9),(7\\mapsto 5),(8\\mapsto 1),(9\\mapsto 6)\\}),(7\\mapsto\\{(1\\mapsto 9),(2\\mapsto 5),(3\\mapsto 1),(4\\mapsto 6),(5\\mapsto 2),(6\\mapsto 7),(7\\mapsto 3),(8\\mapsto 8),(9\\mapsto 4)\\}),(8\\mapsto\\{(1\\mapsto 3),(2\\mapsto 8),(3\\mapsto 4),(4\\mapsto 9),(5\\mapsto 5),(6\\mapsto 1),(7\\mapsto 6),(8\\mapsto 2),(9\\mapsto 7)\\}),(9\\mapsto\\{(1\\mapsto 6),(2\\mapsto 2),(3\\mapsto 7),(4\\mapsto 3),(5\\mapsto 8),(6\\mapsto 4),(7\\mapsto 9),(8\\mapsto 5),(9\\mapsto 1)\\})\\}$|\n",
+       "|$\\{(1\\mapsto\\{(1\\mapsto 6),(2\\mapsto 3),(3\\mapsto 9),(4\\mapsto 2),(5\\mapsto 8),(6\\mapsto 5),(7\\mapsto 7),(8\\mapsto 4),(9\\mapsto 1)\\}),(2\\mapsto\\{(1\\mapsto 2),(2\\mapsto 8),(3\\mapsto 5),(4\\mapsto 7),(5\\mapsto 4),(6\\mapsto 1),(7\\mapsto 3),(8\\mapsto 9),(9\\mapsto 6)\\}),(3\\mapsto\\{(1\\mapsto 7),(2\\mapsto 4),(3\\mapsto 1),(4\\mapsto 3),(5\\mapsto 9),(6\\mapsto 6),(7\\mapsto 8),(8\\mapsto 5),(9\\mapsto 2)\\}),(4\\mapsto\\{(1\\mapsto 3),(2\\mapsto 9),(3\\mapsto 6),(4\\mapsto 8),(5\\mapsto 5),(6\\mapsto 2),(7\\mapsto 4),(8\\mapsto 1),(9\\mapsto 7)\\}),(5\\mapsto\\{(1\\mapsto 8),(2\\mapsto 5),(3\\mapsto 2),(4\\mapsto 4),(5\\mapsto 1),(6\\mapsto 7),(7\\mapsto 9),(8\\mapsto 6),(9\\mapsto 3)\\}),(6\\mapsto\\{(1\\mapsto 4),(2\\mapsto 1),(3\\mapsto 7),(4\\mapsto 9),(5\\mapsto 6),(6\\mapsto 3),(7\\mapsto 5),(8\\mapsto 2),(9\\mapsto 8)\\}),(7\\mapsto\\{(1\\mapsto 9),(2\\mapsto 6),(3\\mapsto 3),(4\\mapsto 5),(5\\mapsto 2),(6\\mapsto 8),(7\\mapsto 1),(8\\mapsto 7),(9\\mapsto 4)\\}),(8\\mapsto\\{(1\\mapsto 5),(2\\mapsto 2),(3\\mapsto 8),(4\\mapsto 1),(5\\mapsto 7),(6\\mapsto 4),(7\\mapsto 6),(8\\mapsto 3),(9\\mapsto 9)\\}),(9\\mapsto\\{(1\\mapsto 1),(2\\mapsto 7),(3\\mapsto 4),(4\\mapsto 6),(5\\mapsto 3),(6\\mapsto 9),(7\\mapsto 2),(8\\mapsto 8),(9\\mapsto 5)\\})\\}$|\n",
+       "|$\\{(1\\mapsto\\{(1\\mapsto 1),(2\\mapsto 7),(3\\mapsto 4),(4\\mapsto 6),(5\\mapsto 3),(6\\mapsto 9),(7\\mapsto 2),(8\\mapsto 8),(9\\mapsto 5)\\}),(2\\mapsto\\{(1\\mapsto 5),(2\\mapsto 2),(3\\mapsto 8),(4\\mapsto 1),(5\\mapsto 7),(6\\mapsto 4),(7\\mapsto 6),(8\\mapsto 3),(9\\mapsto 9)\\}),(3\\mapsto\\{(1\\mapsto 9),(2\\mapsto 6),(3\\mapsto 3),(4\\mapsto 5),(5\\mapsto 2),(6\\mapsto 8),(7\\mapsto 1),(8\\mapsto 7),(9\\mapsto 4)\\}),(4\\mapsto\\{(1\\mapsto 4),(2\\mapsto 1),(3\\mapsto 7),(4\\mapsto 9),(5\\mapsto 6),(6\\mapsto 3),(7\\mapsto 5),(8\\mapsto 2),(9\\mapsto 8)\\}),(5\\mapsto\\{(1\\mapsto 8),(2\\mapsto 5),(3\\mapsto 2),(4\\mapsto 4),(5\\mapsto 1),(6\\mapsto 7),(7\\mapsto 9),(8\\mapsto 6),(9\\mapsto 3)\\}),(6\\mapsto\\{(1\\mapsto 3),(2\\mapsto 9),(3\\mapsto 6),(4\\mapsto 8),(5\\mapsto 5),(6\\mapsto 2),(7\\mapsto 4),(8\\mapsto 1),(9\\mapsto 7)\\}),(7\\mapsto\\{(1\\mapsto 7),(2\\mapsto 4),(3\\mapsto 1),(4\\mapsto 3),(5\\mapsto 9),(6\\mapsto 6),(7\\mapsto 8),(8\\mapsto 5),(9\\mapsto 2)\\}),(8\\mapsto\\{(1\\mapsto 2),(2\\mapsto 8),(3\\mapsto 5),(4\\mapsto 7),(5\\mapsto 4),(6\\mapsto 1),(7\\mapsto 3),(8\\mapsto 9),(9\\mapsto 6)\\}),(9\\mapsto\\{(1\\mapsto 6),(2\\mapsto 3),(3\\mapsto 9),(4\\mapsto 2),(5\\mapsto 8),(6\\mapsto 5),(7\\mapsto 7),(8\\mapsto 4),(9\\mapsto 1)\\})\\}$|\n",
+       "|$\\{(1\\mapsto\\{(1\\mapsto 1),(2\\mapsto 4),(3\\mapsto 7),(4\\mapsto 5),(5\\mapsto 8),(6\\mapsto 2),(7\\mapsto 9),(8\\mapsto 3),(9\\mapsto 6)\\}),(2\\mapsto\\{(1\\mapsto 6),(2\\mapsto 9),(3\\mapsto 3),(4\\mapsto 1),(5\\mapsto 4),(6\\mapsto 7),(7\\mapsto 5),(8\\mapsto 8),(9\\mapsto 2)\\}),(3\\mapsto\\{(1\\mapsto 2),(2\\mapsto 5),(3\\mapsto 8),(4\\mapsto 6),(5\\mapsto 9),(6\\mapsto 3),(7\\mapsto 1),(8\\mapsto 4),(9\\mapsto 7)\\}),(4\\mapsto\\{(1\\mapsto 7),(2\\mapsto 1),(3\\mapsto 4),(4\\mapsto 2),(5\\mapsto 5),(6\\mapsto 8),(7\\mapsto 6),(8\\mapsto 9),(9\\mapsto 3)\\}),(5\\mapsto\\{(1\\mapsto 3),(2\\mapsto 6),(3\\mapsto 9),(4\\mapsto 7),(5\\mapsto 1),(6\\mapsto 4),(7\\mapsto 2),(8\\mapsto 5),(9\\mapsto 8)\\}),(6\\mapsto\\{(1\\mapsto 8),(2\\mapsto 2),(3\\mapsto 5),(4\\mapsto 3),(5\\mapsto 6),(6\\mapsto 9),(7\\mapsto 7),(8\\mapsto 1),(9\\mapsto 4)\\}),(7\\mapsto\\{(1\\mapsto 4),(2\\mapsto 7),(3\\mapsto 1),(4\\mapsto 8),(5\\mapsto 2),(6\\mapsto 5),(7\\mapsto 3),(8\\mapsto 6),(9\\mapsto 9)\\}),(8\\mapsto\\{(1\\mapsto 9),(2\\mapsto 3),(3\\mapsto 6),(4\\mapsto 4),(5\\mapsto 7),(6\\mapsto 1),(7\\mapsto 8),(8\\mapsto 2),(9\\mapsto 5)\\}),(9\\mapsto\\{(1\\mapsto 5),(2\\mapsto 8),(3\\mapsto 2),(4\\mapsto 9),(5\\mapsto 3),(6\\mapsto 6),(7\\mapsto 4),(8\\mapsto 7),(9\\mapsto 1)\\})\\}$|\n",
+       "|$\\{(1\\mapsto\\{(1\\mapsto 5),(2\\mapsto 8),(3\\mapsto 2),(4\\mapsto 9),(5\\mapsto 3),(6\\mapsto 6),(7\\mapsto 4),(8\\mapsto 7),(9\\mapsto 1)\\}),(2\\mapsto\\{(1\\mapsto 9),(2\\mapsto 3),(3\\mapsto 6),(4\\mapsto 4),(5\\mapsto 7),(6\\mapsto 1),(7\\mapsto 8),(8\\mapsto 2),(9\\mapsto 5)\\}),(3\\mapsto\\{(1\\mapsto 4),(2\\mapsto 7),(3\\mapsto 1),(4\\mapsto 8),(5\\mapsto 2),(6\\mapsto 5),(7\\mapsto 3),(8\\mapsto 6),(9\\mapsto 9)\\}),(4\\mapsto\\{(1\\mapsto 8),(2\\mapsto 2),(3\\mapsto 5),(4\\mapsto 3),(5\\mapsto 6),(6\\mapsto 9),(7\\mapsto 7),(8\\mapsto 1),(9\\mapsto 4)\\}),(5\\mapsto\\{(1\\mapsto 3),(2\\mapsto 6),(3\\mapsto 9),(4\\mapsto 7),(5\\mapsto 1),(6\\mapsto 4),(7\\mapsto 2),(8\\mapsto 5),(9\\mapsto 8)\\}),(6\\mapsto\\{(1\\mapsto 7),(2\\mapsto 1),(3\\mapsto 4),(4\\mapsto 2),(5\\mapsto 5),(6\\mapsto 8),(7\\mapsto 6),(8\\mapsto 9),(9\\mapsto 3)\\}),(7\\mapsto\\{(1\\mapsto 2),(2\\mapsto 5),(3\\mapsto 8),(4\\mapsto 6),(5\\mapsto 9),(6\\mapsto 3),(7\\mapsto 1),(8\\mapsto 4),(9\\mapsto 7)\\}),(8\\mapsto\\{(1\\mapsto 6),(2\\mapsto 9),(3\\mapsto 3),(4\\mapsto 1),(5\\mapsto 4),(6\\mapsto 7),(7\\mapsto 5),(8\\mapsto 8),(9\\mapsto 2)\\}),(9\\mapsto\\{(1\\mapsto 1),(2\\mapsto 4),(3\\mapsto 7),(4\\mapsto 5),(5\\mapsto 8),(6\\mapsto 2),(7\\mapsto 9),(8\\mapsto 3),(9\\mapsto 6)\\})\\}$|\n",
+       "|$\\{(1\\mapsto\\{(1\\mapsto 1),(2\\mapsto 5),(3\\mapsto 9),(4\\mapsto 4),(5\\mapsto 8),(6\\mapsto 3),(7\\mapsto 7),(8\\mapsto 2),(9\\mapsto 6)\\}),(2\\mapsto\\{(1\\mapsto 7),(2\\mapsto 2),(3\\mapsto 6),(4\\mapsto 1),(5\\mapsto 5),(6\\mapsto 9),(7\\mapsto 4),(8\\mapsto 8),(9\\mapsto 3)\\}),(3\\mapsto\\{(1\\mapsto 4),(2\\mapsto 8),(3\\mapsto 3),(4\\mapsto 7),(5\\mapsto 2),(6\\mapsto 6),(7\\mapsto 1),(8\\mapsto 5),(9\\mapsto 9)\\}),(4\\mapsto\\{(1\\mapsto 6),(2\\mapsto 1),(3\\mapsto 5),(4\\mapsto 9),(5\\mapsto 4),(6\\mapsto 8),(7\\mapsto 3),(8\\mapsto 7),(9\\mapsto 2)\\}),(5\\mapsto\\{(1\\mapsto 3),(2\\mapsto 7),(3\\mapsto 2),(4\\mapsto 6),(5\\mapsto 1),(6\\mapsto 5),(7\\mapsto 9),(8\\mapsto 4),(9\\mapsto 8)\\}),(6\\mapsto\\{(1\\mapsto 9),(2\\mapsto 4),(3\\mapsto 8),(4\\mapsto 3),(5\\mapsto 7),(6\\mapsto 2),(7\\mapsto 6),(8\\mapsto 1),(9\\mapsto 5)\\}),(7\\mapsto\\{(1\\mapsto 2),(2\\mapsto 6),(3\\mapsto 1),(4\\mapsto 5),(5\\mapsto 9),(6\\mapsto 4),(7\\mapsto 8),(8\\mapsto 3),(9\\mapsto 7)\\}),(8\\mapsto\\{(1\\mapsto 8),(2\\mapsto 3),(3\\mapsto 7),(4\\mapsto 2),(5\\mapsto 6),(6\\mapsto 1),(7\\mapsto 5),(8\\mapsto 9),(9\\mapsto 4)\\}),(9\\mapsto\\{(1\\mapsto 5),(2\\mapsto 9),(3\\mapsto 4),(4\\mapsto 8),(5\\mapsto 3),(6\\mapsto 7),(7\\mapsto 2),(8\\mapsto 6),(9\\mapsto 1)\\})\\}$|\n",
+       "|$\\{(1\\mapsto\\{(1\\mapsto 5),(2\\mapsto 9),(3\\mapsto 4),(4\\mapsto 8),(5\\mapsto 3),(6\\mapsto 7),(7\\mapsto 2),(8\\mapsto 6),(9\\mapsto 1)\\}),(2\\mapsto\\{(1\\mapsto 8),(2\\mapsto 3),(3\\mapsto 7),(4\\mapsto 2),(5\\mapsto 6),(6\\mapsto 1),(7\\mapsto 5),(8\\mapsto 9),(9\\mapsto 4)\\}),(3\\mapsto\\{(1\\mapsto 2),(2\\mapsto 6),(3\\mapsto 1),(4\\mapsto 5),(5\\mapsto 9),(6\\mapsto 4),(7\\mapsto 8),(8\\mapsto 3),(9\\mapsto 7)\\}),(4\\mapsto\\{(1\\mapsto 9),(2\\mapsto 4),(3\\mapsto 8),(4\\mapsto 3),(5\\mapsto 7),(6\\mapsto 2),(7\\mapsto 6),(8\\mapsto 1),(9\\mapsto 5)\\}),(5\\mapsto\\{(1\\mapsto 3),(2\\mapsto 7),(3\\mapsto 2),(4\\mapsto 6),(5\\mapsto 1),(6\\mapsto 5),(7\\mapsto 9),(8\\mapsto 4),(9\\mapsto 8)\\}),(6\\mapsto\\{(1\\mapsto 6),(2\\mapsto 1),(3\\mapsto 5),(4\\mapsto 9),(5\\mapsto 4),(6\\mapsto 8),(7\\mapsto 3),(8\\mapsto 7),(9\\mapsto 2)\\}),(7\\mapsto\\{(1\\mapsto 4),(2\\mapsto 8),(3\\mapsto 3),(4\\mapsto 7),(5\\mapsto 2),(6\\mapsto 6),(7\\mapsto 1),(8\\mapsto 5),(9\\mapsto 9)\\}),(8\\mapsto\\{(1\\mapsto 7),(2\\mapsto 2),(3\\mapsto 6),(4\\mapsto 1),(5\\mapsto 5),(6\\mapsto 9),(7\\mapsto 4),(8\\mapsto 8),(9\\mapsto 3)\\}),(9\\mapsto\\{(1\\mapsto 1),(2\\mapsto 5),(3\\mapsto 9),(4\\mapsto 4),(5\\mapsto 8),(6\\mapsto 3),(7\\mapsto 7),(8\\mapsto 2),(9\\mapsto 6)\\})\\}$|\n",
+       "|$\\{(1\\mapsto\\{(1\\mapsto 7),(2\\mapsto 3),(3\\mapsto 8),(4\\mapsto 4),(5\\mapsto 9),(6\\mapsto 5),(7\\mapsto 1),(8\\mapsto 6),(9\\mapsto 2)\\}),(2\\mapsto\\{(1\\mapsto 4),(2\\mapsto 9),(3\\mapsto 5),(4\\mapsto 1),(5\\mapsto 6),(6\\mapsto 2),(7\\mapsto 7),(8\\mapsto 3),(9\\mapsto 8)\\}),(3\\mapsto\\{(1\\mapsto 1),(2\\mapsto 6),(3\\mapsto 2),(4\\mapsto 7),(5\\mapsto 3),(6\\mapsto 8),(7\\mapsto 4),(8\\mapsto 9),(9\\mapsto 5)\\}),(4\\mapsto\\{(1\\mapsto 3),(2\\mapsto 8),(3\\mapsto 4),(4\\mapsto 9),(5\\mapsto 5),(6\\mapsto 1),(7\\mapsto 6),(8\\mapsto 2),(9\\mapsto 7)\\}),(5\\mapsto\\{(1\\mapsto 9),(2\\mapsto 5),(3\\mapsto 1),(4\\mapsto 6),(5\\mapsto 2),(6\\mapsto 7),(7\\mapsto 3),(8\\mapsto 8),(9\\mapsto 4)\\}),(6\\mapsto\\{(1\\mapsto 6),(2\\mapsto 2),(3\\mapsto 7),(4\\mapsto 3),(5\\mapsto 8),(6\\mapsto 4),(7\\mapsto 9),(8\\mapsto 5),(9\\mapsto 1)\\}),(7\\mapsto\\{(1\\mapsto 8),(2\\mapsto 4),(3\\mapsto 9),(4\\mapsto 5),(5\\mapsto 1),(6\\mapsto 6),(7\\mapsto 2),(8\\mapsto 7),(9\\mapsto 3)\\}),(8\\mapsto\\{(1\\mapsto 5),(2\\mapsto 1),(3\\mapsto 6),(4\\mapsto 2),(5\\mapsto 7),(6\\mapsto 3),(7\\mapsto 8),(8\\mapsto 4),(9\\mapsto 9)\\}),(9\\mapsto\\{(1\\mapsto 2),(2\\mapsto 7),(3\\mapsto 3),(4\\mapsto 8),(5\\mapsto 4),(6\\mapsto 9),(7\\mapsto 5),(8\\mapsto 1),(9\\mapsto 6)\\})\\}$|\n",
+       "|$\\{(1\\mapsto\\{(1\\mapsto 2),(2\\mapsto 7),(3\\mapsto 3),(4\\mapsto 8),(5\\mapsto 4),(6\\mapsto 9),(7\\mapsto 5),(8\\mapsto 1),(9\\mapsto 6)\\}),(2\\mapsto\\{(1\\mapsto 5),(2\\mapsto 1),(3\\mapsto 6),(4\\mapsto 2),(5\\mapsto 7),(6\\mapsto 3),(7\\mapsto 8),(8\\mapsto 4),(9\\mapsto 9)\\}),(3\\mapsto\\{(1\\mapsto 8),(2\\mapsto 4),(3\\mapsto 9),(4\\mapsto 5),(5\\mapsto 1),(6\\mapsto 6),(7\\mapsto 2),(8\\mapsto 7),(9\\mapsto 3)\\}),(4\\mapsto\\{(1\\mapsto 6),(2\\mapsto 2),(3\\mapsto 7),(4\\mapsto 3),(5\\mapsto 8),(6\\mapsto 4),(7\\mapsto 9),(8\\mapsto 5),(9\\mapsto 1)\\}),(5\\mapsto\\{(1\\mapsto 9),(2\\mapsto 5),(3\\mapsto 1),(4\\mapsto 6),(5\\mapsto 2),(6\\mapsto 7),(7\\mapsto 3),(8\\mapsto 8),(9\\mapsto 4)\\}),(6\\mapsto\\{(1\\mapsto 3),(2\\mapsto 8),(3\\mapsto 4),(4\\mapsto 9),(5\\mapsto 5),(6\\mapsto 1),(7\\mapsto 6),(8\\mapsto 2),(9\\mapsto 7)\\}),(7\\mapsto\\{(1\\mapsto 1),(2\\mapsto 6),(3\\mapsto 2),(4\\mapsto 7),(5\\mapsto 3),(6\\mapsto 8),(7\\mapsto 4),(8\\mapsto 9),(9\\mapsto 5)\\}),(8\\mapsto\\{(1\\mapsto 4),(2\\mapsto 9),(3\\mapsto 5),(4\\mapsto 1),(5\\mapsto 6),(6\\mapsto 2),(7\\mapsto 7),(8\\mapsto 3),(9\\mapsto 8)\\}),(9\\mapsto\\{(1\\mapsto 7),(2\\mapsto 3),(3\\mapsto 8),(4\\mapsto 4),(5\\mapsto 9),(6\\mapsto 5),(7\\mapsto 1),(8\\mapsto 6),(9\\mapsto 2)\\})\\}$|\n",
+       "|$\\{(1\\mapsto\\{(1\\mapsto 7),(2\\mapsto 4),(3\\mapsto 1),(4\\mapsto 3),(5\\mapsto 9),(6\\mapsto 6),(7\\mapsto 8),(8\\mapsto 5),(9\\mapsto 2)\\}),(2\\mapsto\\{(1\\mapsto 3),(2\\mapsto 9),(3\\mapsto 6),(4\\mapsto 8),(5\\mapsto 5),(6\\mapsto 2),(7\\mapsto 4),(8\\mapsto 1),(9\\mapsto 7)\\}),(3\\mapsto\\{(1\\mapsto 8),(2\\mapsto 5),(3\\mapsto 2),(4\\mapsto 4),(5\\mapsto 1),(6\\mapsto 7),(7\\mapsto 9),(8\\mapsto 6),(9\\mapsto 3)\\}),(4\\mapsto\\{(1\\mapsto 4),(2\\mapsto 1),(3\\mapsto 7),(4\\mapsto 9),(5\\mapsto 6),(6\\mapsto 3),(7\\mapsto 5),(8\\mapsto 2),(9\\mapsto 8)\\}),(5\\mapsto\\{(1\\mapsto 9),(2\\mapsto 6),(3\\mapsto 3),(4\\mapsto 5),(5\\mapsto 2),(6\\mapsto 8),(7\\mapsto 1),(8\\mapsto 7),(9\\mapsto 4)\\}),(6\\mapsto\\{(1\\mapsto 5),(2\\mapsto 2),(3\\mapsto 8),(4\\mapsto 1),(5\\mapsto 7),(6\\mapsto 4),(7\\mapsto 6),(8\\mapsto 3),(9\\mapsto 9)\\}),(7\\mapsto\\{(1\\mapsto 1),(2\\mapsto 7),(3\\mapsto 4),(4\\mapsto 6),(5\\mapsto 3),(6\\mapsto 9),(7\\mapsto 2),(8\\mapsto 8),(9\\mapsto 5)\\}),(8\\mapsto\\{(1\\mapsto 6),(2\\mapsto 3),(3\\mapsto 9),(4\\mapsto 2),(5\\mapsto 8),(6\\mapsto 5),(7\\mapsto 7),(8\\mapsto 4),(9\\mapsto 1)\\}),(9\\mapsto\\{(1\\mapsto 2),(2\\mapsto 8),(3\\mapsto 5),(4\\mapsto 7),(5\\mapsto 4),(6\\mapsto 1),(7\\mapsto 3),(8\\mapsto 9),(9\\mapsto 6)\\})\\}$|\n",
+       "|$\\{(1\\mapsto\\{(1\\mapsto 2),(2\\mapsto 8),(3\\mapsto 5),(4\\mapsto 7),(5\\mapsto 4),(6\\mapsto 1),(7\\mapsto 3),(8\\mapsto 9),(9\\mapsto 6)\\}),(2\\mapsto\\{(1\\mapsto 6),(2\\mapsto 3),(3\\mapsto 9),(4\\mapsto 2),(5\\mapsto 8),(6\\mapsto 5),(7\\mapsto 7),(8\\mapsto 4),(9\\mapsto 1)\\}),(3\\mapsto\\{(1\\mapsto 1),(2\\mapsto 7),(3\\mapsto 4),(4\\mapsto 6),(5\\mapsto 3),(6\\mapsto 9),(7\\mapsto 2),(8\\mapsto 8),(9\\mapsto 5)\\}),(4\\mapsto\\{(1\\mapsto 5),(2\\mapsto 2),(3\\mapsto 8),(4\\mapsto 1),(5\\mapsto 7),(6\\mapsto 4),(7\\mapsto 6),(8\\mapsto 3),(9\\mapsto 9)\\}),(5\\mapsto\\{(1\\mapsto 9),(2\\mapsto 6),(3\\mapsto 3),(4\\mapsto 5),(5\\mapsto 2),(6\\mapsto 8),(7\\mapsto 1),(8\\mapsto 7),(9\\mapsto 4)\\}),(6\\mapsto\\{(1\\mapsto 4),(2\\mapsto 1),(3\\mapsto 7),(4\\mapsto 9),(5\\mapsto 6),(6\\mapsto 3),(7\\mapsto 5),(8\\mapsto 2),(9\\mapsto 8)\\}),(7\\mapsto\\{(1\\mapsto 8),(2\\mapsto 5),(3\\mapsto 2),(4\\mapsto 4),(5\\mapsto 1),(6\\mapsto 7),(7\\mapsto 9),(8\\mapsto 6),(9\\mapsto 3)\\}),(8\\mapsto\\{(1\\mapsto 3),(2\\mapsto 9),(3\\mapsto 6),(4\\mapsto 8),(5\\mapsto 5),(6\\mapsto 2),(7\\mapsto 4),(8\\mapsto 1),(9\\mapsto 7)\\}),(9\\mapsto\\{(1\\mapsto 7),(2\\mapsto 4),(3\\mapsto 1),(4\\mapsto 3),(5\\mapsto 9),(6\\mapsto 6),(7\\mapsto 8),(8\\mapsto 5),(9\\mapsto 2)\\})\\}$|\n",
+       "|$\\{(1\\mapsto\\{(1\\mapsto 2),(2\\mapsto 5),(3\\mapsto 8),(4\\mapsto 6),(5\\mapsto 9),(6\\mapsto 3),(7\\mapsto 1),(8\\mapsto 4),(9\\mapsto 7)\\}),(2\\mapsto\\{(1\\mapsto 7),(2\\mapsto 1),(3\\mapsto 4),(4\\mapsto 2),(5\\mapsto 5),(6\\mapsto 8),(7\\mapsto 6),(8\\mapsto 9),(9\\mapsto 3)\\}),(3\\mapsto\\{(1\\mapsto 3),(2\\mapsto 6),(3\\mapsto 9),(4\\mapsto 7),(5\\mapsto 1),(6\\mapsto 4),(7\\mapsto 2),(8\\mapsto 5),(9\\mapsto 8)\\}),(4\\mapsto\\{(1\\mapsto 8),(2\\mapsto 2),(3\\mapsto 5),(4\\mapsto 3),(5\\mapsto 6),(6\\mapsto 9),(7\\mapsto 7),(8\\mapsto 1),(9\\mapsto 4)\\}),(5\\mapsto\\{(1\\mapsto 4),(2\\mapsto 7),(3\\mapsto 1),(4\\mapsto 8),(5\\mapsto 2),(6\\mapsto 5),(7\\mapsto 3),(8\\mapsto 6),(9\\mapsto 9)\\}),(6\\mapsto\\{(1\\mapsto 9),(2\\mapsto 3),(3\\mapsto 6),(4\\mapsto 4),(5\\mapsto 7),(6\\mapsto 1),(7\\mapsto 8),(8\\mapsto 2),(9\\mapsto 5)\\}),(7\\mapsto\\{(1\\mapsto 5),(2\\mapsto 8),(3\\mapsto 2),(4\\mapsto 9),(5\\mapsto 3),(6\\mapsto 6),(7\\mapsto 4),(8\\mapsto 7),(9\\mapsto 1)\\}),(8\\mapsto\\{(1\\mapsto 1),(2\\mapsto 4),(3\\mapsto 7),(4\\mapsto 5),(5\\mapsto 8),(6\\mapsto 2),(7\\mapsto 9),(8\\mapsto 3),(9\\mapsto 6)\\}),(9\\mapsto\\{(1\\mapsto 6),(2\\mapsto 9),(3\\mapsto 3),(4\\mapsto 1),(5\\mapsto 4),(6\\mapsto 7),(7\\mapsto 5),(8\\mapsto 8),(9\\mapsto 2)\\})\\}$|\n",
+       "|$\\{(1\\mapsto\\{(1\\mapsto 6),(2\\mapsto 9),(3\\mapsto 3),(4\\mapsto 1),(5\\mapsto 4),(6\\mapsto 7),(7\\mapsto 5),(8\\mapsto 8),(9\\mapsto 2)\\}),(2\\mapsto\\{(1\\mapsto 1),(2\\mapsto 4),(3\\mapsto 7),(4\\mapsto 5),(5\\mapsto 8),(6\\mapsto 2),(7\\mapsto 9),(8\\mapsto 3),(9\\mapsto 6)\\}),(3\\mapsto\\{(1\\mapsto 5),(2\\mapsto 8),(3\\mapsto 2),(4\\mapsto 9),(5\\mapsto 3),(6\\mapsto 6),(7\\mapsto 4),(8\\mapsto 7),(9\\mapsto 1)\\}),(4\\mapsto\\{(1\\mapsto 9),(2\\mapsto 3),(3\\mapsto 6),(4\\mapsto 4),(5\\mapsto 7),(6\\mapsto 1),(7\\mapsto 8),(8\\mapsto 2),(9\\mapsto 5)\\}),(5\\mapsto\\{(1\\mapsto 4),(2\\mapsto 7),(3\\mapsto 1),(4\\mapsto 8),(5\\mapsto 2),(6\\mapsto 5),(7\\mapsto 3),(8\\mapsto 6),(9\\mapsto 9)\\}),(6\\mapsto\\{(1\\mapsto 8),(2\\mapsto 2),(3\\mapsto 5),(4\\mapsto 3),(5\\mapsto 6),(6\\mapsto 9),(7\\mapsto 7),(8\\mapsto 1),(9\\mapsto 4)\\}),(7\\mapsto\\{(1\\mapsto 3),(2\\mapsto 6),(3\\mapsto 9),(4\\mapsto 7),(5\\mapsto 1),(6\\mapsto 4),(7\\mapsto 2),(8\\mapsto 5),(9\\mapsto 8)\\}),(8\\mapsto\\{(1\\mapsto 7),(2\\mapsto 1),(3\\mapsto 4),(4\\mapsto 2),(5\\mapsto 5),(6\\mapsto 8),(7\\mapsto 6),(8\\mapsto 9),(9\\mapsto 3)\\}),(9\\mapsto\\{(1\\mapsto 2),(2\\mapsto 5),(3\\mapsto 8),(4\\mapsto 6),(5\\mapsto 9),(6\\mapsto 3),(7\\mapsto 1),(8\\mapsto 4),(9\\mapsto 7)\\})\\}$|\n",
+       "|$\\{(1\\mapsto\\{(1\\mapsto 2),(2\\mapsto 6),(3\\mapsto 1),(4\\mapsto 5),(5\\mapsto 9),(6\\mapsto 4),(7\\mapsto 8),(8\\mapsto 3),(9\\mapsto 7)\\}),(2\\mapsto\\{(1\\mapsto 8),(2\\mapsto 3),(3\\mapsto 7),(4\\mapsto 2),(5\\mapsto 6),(6\\mapsto 1),(7\\mapsto 5),(8\\mapsto 9),(9\\mapsto 4)\\}),(3\\mapsto\\{(1\\mapsto 5),(2\\mapsto 9),(3\\mapsto 4),(4\\mapsto 8),(5\\mapsto 3),(6\\mapsto 7),(7\\mapsto 2),(8\\mapsto 6),(9\\mapsto 1)\\}),(4\\mapsto\\{(1\\mapsto 7),(2\\mapsto 2),(3\\mapsto 6),(4\\mapsto 1),(5\\mapsto 5),(6\\mapsto 9),(7\\mapsto 4),(8\\mapsto 8),(9\\mapsto 3)\\}),(5\\mapsto\\{(1\\mapsto 4),(2\\mapsto 8),(3\\mapsto 3),(4\\mapsto 7),(5\\mapsto 2),(6\\mapsto 6),(7\\mapsto 1),(8\\mapsto 5),(9\\mapsto 9)\\}),(6\\mapsto\\{(1\\mapsto 1),(2\\mapsto 5),(3\\mapsto 9),(4\\mapsto 4),(5\\mapsto 8),(6\\mapsto 3),(7\\mapsto 7),(8\\mapsto 2),(9\\mapsto 6)\\}),(7\\mapsto\\{(1\\mapsto 3),(2\\mapsto 7),(3\\mapsto 2),(4\\mapsto 6),(5\\mapsto 1),(6\\mapsto 5),(7\\mapsto 9),(8\\mapsto 4),(9\\mapsto 8)\\}),(8\\mapsto\\{(1\\mapsto 9),(2\\mapsto 4),(3\\mapsto 8),(4\\mapsto 3),(5\\mapsto 7),(6\\mapsto 2),(7\\mapsto 6),(8\\mapsto 1),(9\\mapsto 5)\\}),(9\\mapsto\\{(1\\mapsto 6),(2\\mapsto 1),(3\\mapsto 5),(4\\mapsto 9),(5\\mapsto 4),(6\\mapsto 8),(7\\mapsto 3),(8\\mapsto 7),(9\\mapsto 2)\\})\\}$|\n",
+       "|$\\{(1\\mapsto\\{(1\\mapsto 6),(2\\mapsto 1),(3\\mapsto 5),(4\\mapsto 9),(5\\mapsto 4),(6\\mapsto 8),(7\\mapsto 3),(8\\mapsto 7),(9\\mapsto 2)\\}),(2\\mapsto\\{(1\\mapsto 9),(2\\mapsto 4),(3\\mapsto 8),(4\\mapsto 3),(5\\mapsto 7),(6\\mapsto 2),(7\\mapsto 6),(8\\mapsto 1),(9\\mapsto 5)\\}),(3\\mapsto\\{(1\\mapsto 3),(2\\mapsto 7),(3\\mapsto 2),(4\\mapsto 6),(5\\mapsto 1),(6\\mapsto 5),(7\\mapsto 9),(8\\mapsto 4),(9\\mapsto 8)\\}),(4\\mapsto\\{(1\\mapsto 1),(2\\mapsto 5),(3\\mapsto 9),(4\\mapsto 4),(5\\mapsto 8),(6\\mapsto 3),(7\\mapsto 7),(8\\mapsto 2),(9\\mapsto 6)\\}),(5\\mapsto\\{(1\\mapsto 4),(2\\mapsto 8),(3\\mapsto 3),(4\\mapsto 7),(5\\mapsto 2),(6\\mapsto 6),(7\\mapsto 1),(8\\mapsto 5),(9\\mapsto 9)\\}),(6\\mapsto\\{(1\\mapsto 7),(2\\mapsto 2),(3\\mapsto 6),(4\\mapsto 1),(5\\mapsto 5),(6\\mapsto 9),(7\\mapsto 4),(8\\mapsto 8),(9\\mapsto 3)\\}),(7\\mapsto\\{(1\\mapsto 5),(2\\mapsto 9),(3\\mapsto 4),(4\\mapsto 8),(5\\mapsto 3),(6\\mapsto 7),(7\\mapsto 2),(8\\mapsto 6),(9\\mapsto 1)\\}),(8\\mapsto\\{(1\\mapsto 8),(2\\mapsto 3),(3\\mapsto 7),(4\\mapsto 2),(5\\mapsto 6),(6\\mapsto 1),(7\\mapsto 5),(8\\mapsto 9),(9\\mapsto 4)\\}),(9\\mapsto\\{(1\\mapsto 2),(2\\mapsto 6),(3\\mapsto 1),(4\\mapsto 5),(5\\mapsto 9),(6\\mapsto 4),(7\\mapsto 8),(8\\mapsto 3),(9\\mapsto 7)\\})\\}$|\n",
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+       "|$\\{(1\\mapsto\\{(1\\mapsto 8),(2\\mapsto 5),(3\\mapsto 2),(4\\mapsto 4),(5\\mapsto 1),(6\\mapsto 7),(7\\mapsto 9),(8\\mapsto 6),(9\\mapsto 3)\\}),(2\\mapsto\\{(1\\mapsto 4),(2\\mapsto 1),(3\\mapsto 7),(4\\mapsto 9),(5\\mapsto 6),(6\\mapsto 3),(7\\mapsto 5),(8\\mapsto 2),(9\\mapsto 8)\\}),(3\\mapsto\\{(1\\mapsto 9),(2\\mapsto 6),(3\\mapsto 3),(4\\mapsto 5),(5\\mapsto 2),(6\\mapsto 8),(7\\mapsto 1),(8\\mapsto 7),(9\\mapsto 4)\\}),(4\\mapsto\\{(1\\mapsto 5),(2\\mapsto 2),(3\\mapsto 8),(4\\mapsto 1),(5\\mapsto 7),(6\\mapsto 4),(7\\mapsto 6),(8\\mapsto 3),(9\\mapsto 9)\\}),(5\\mapsto\\{(1\\mapsto 1),(2\\mapsto 7),(3\\mapsto 4),(4\\mapsto 6),(5\\mapsto 3),(6\\mapsto 9),(7\\mapsto 2),(8\\mapsto 8),(9\\mapsto 5)\\}),(6\\mapsto\\{(1\\mapsto 6),(2\\mapsto 3),(3\\mapsto 9),(4\\mapsto 2),(5\\mapsto 8),(6\\mapsto 5),(7\\mapsto 7),(8\\mapsto 4),(9\\mapsto 1)\\}),(7\\mapsto\\{(1\\mapsto 2),(2\\mapsto 8),(3\\mapsto 5),(4\\mapsto 7),(5\\mapsto 4),(6\\mapsto 1),(7\\mapsto 3),(8\\mapsto 9),(9\\mapsto 6)\\}),(8\\mapsto\\{(1\\mapsto 7),(2\\mapsto 4),(3\\mapsto 1),(4\\mapsto 3),(5\\mapsto 9),(6\\mapsto 6),(7\\mapsto 8),(8\\mapsto 5),(9\\mapsto 2)\\}),(9\\mapsto\\{(1\\mapsto 3),(2\\mapsto 9),(3\\mapsto 6),(4\\mapsto 8),(5\\mapsto 5),(6\\mapsto 2),(7\\mapsto 4),(8\\mapsto 1),(9\\mapsto 7)\\})\\}$|\n",
+       "|$\\{(1\\mapsto\\{(1\\mapsto 3),(2\\mapsto 9),(3\\mapsto 6),(4\\mapsto 8),(5\\mapsto 5),(6\\mapsto 2),(7\\mapsto 4),(8\\mapsto 1),(9\\mapsto 7)\\}),(2\\mapsto\\{(1\\mapsto 7),(2\\mapsto 4),(3\\mapsto 1),(4\\mapsto 3),(5\\mapsto 9),(6\\mapsto 6),(7\\mapsto 8),(8\\mapsto 5),(9\\mapsto 2)\\}),(3\\mapsto\\{(1\\mapsto 2),(2\\mapsto 8),(3\\mapsto 5),(4\\mapsto 7),(5\\mapsto 4),(6\\mapsto 1),(7\\mapsto 3),(8\\mapsto 9),(9\\mapsto 6)\\}),(4\\mapsto\\{(1\\mapsto 6),(2\\mapsto 3),(3\\mapsto 9),(4\\mapsto 2),(5\\mapsto 8),(6\\mapsto 5),(7\\mapsto 7),(8\\mapsto 4),(9\\mapsto 1)\\}),(5\\mapsto\\{(1\\mapsto 1),(2\\mapsto 7),(3\\mapsto 4),(4\\mapsto 6),(5\\mapsto 3),(6\\mapsto 9),(7\\mapsto 2),(8\\mapsto 8),(9\\mapsto 5)\\}),(6\\mapsto\\{(1\\mapsto 5),(2\\mapsto 2),(3\\mapsto 8),(4\\mapsto 1),(5\\mapsto 7),(6\\mapsto 4),(7\\mapsto 6),(8\\mapsto 3),(9\\mapsto 9)\\}),(7\\mapsto\\{(1\\mapsto 9),(2\\mapsto 6),(3\\mapsto 3),(4\\mapsto 5),(5\\mapsto 2),(6\\mapsto 8),(7\\mapsto 1),(8\\mapsto 7),(9\\mapsto 4)\\}),(8\\mapsto\\{(1\\mapsto 4),(2\\mapsto 1),(3\\mapsto 7),(4\\mapsto 9),(5\\mapsto 6),(6\\mapsto 3),(7\\mapsto 5),(8\\mapsto 2),(9\\mapsto 8)\\}),(9\\mapsto\\{(1\\mapsto 8),(2\\mapsto 5),(3\\mapsto 2),(4\\mapsto 4),(5\\mapsto 1),(6\\mapsto 7),(7\\mapsto 9),(8\\mapsto 6),(9\\mapsto 3)\\})\\}$|\n",
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+       "|$\\{(1\\mapsto\\{(1\\mapsto 5),(2\\mapsto 8),(3\\mapsto 2),(4\\mapsto 9),(5\\mapsto 3),(6\\mapsto 6),(7\\mapsto 4),(8\\mapsto 7),(9\\mapsto 1)\\}),(2\\mapsto\\{(1\\mapsto 1),(2\\mapsto 4),(3\\mapsto 7),(4\\mapsto 5),(5\\mapsto 8),(6\\mapsto 2),(7\\mapsto 9),(8\\mapsto 3),(9\\mapsto 6)\\}),(3\\mapsto\\{(1\\mapsto 6),(2\\mapsto 9),(3\\mapsto 3),(4\\mapsto 1),(5\\mapsto 4),(6\\mapsto 7),(7\\mapsto 5),(8\\mapsto 8),(9\\mapsto 2)\\}),(4\\mapsto\\{(1\\mapsto 2),(2\\mapsto 5),(3\\mapsto 8),(4\\mapsto 6),(5\\mapsto 9),(6\\mapsto 3),(7\\mapsto 1),(8\\mapsto 4),(9\\mapsto 7)\\}),(5\\mapsto\\{(1\\mapsto 7),(2\\mapsto 1),(3\\mapsto 4),(4\\mapsto 2),(5\\mapsto 5),(6\\mapsto 8),(7\\mapsto 6),(8\\mapsto 9),(9\\mapsto 3)\\}),(6\\mapsto\\{(1\\mapsto 3),(2\\mapsto 6),(3\\mapsto 9),(4\\mapsto 7),(5\\mapsto 1),(6\\mapsto 4),(7\\mapsto 2),(8\\mapsto 5),(9\\mapsto 8)\\}),(7\\mapsto\\{(1\\mapsto 8),(2\\mapsto 2),(3\\mapsto 5),(4\\mapsto 3),(5\\mapsto 6),(6\\mapsto 9),(7\\mapsto 7),(8\\mapsto 1),(9\\mapsto 4)\\}),(8\\mapsto\\{(1\\mapsto 4),(2\\mapsto 7),(3\\mapsto 1),(4\\mapsto 8),(5\\mapsto 2),(6\\mapsto 5),(7\\mapsto 3),(8\\mapsto 6),(9\\mapsto 9)\\}),(9\\mapsto\\{(1\\mapsto 9),(2\\mapsto 3),(3\\mapsto 6),(4\\mapsto 4),(5\\mapsto 7),(6\\mapsto 1),(7\\mapsto 8),(8\\mapsto 2),(9\\mapsto 5)\\})\\}$|\n",
+       "|$\\{(1\\mapsto\\{(1\\mapsto 9),(2\\mapsto 4),(3\\mapsto 8),(4\\mapsto 3),(5\\mapsto 7),(6\\mapsto 2),(7\\mapsto 6),(8\\mapsto 1),(9\\mapsto 5)\\}),(2\\mapsto\\{(1\\mapsto 3),(2\\mapsto 7),(3\\mapsto 2),(4\\mapsto 6),(5\\mapsto 1),(6\\mapsto 5),(7\\mapsto 9),(8\\mapsto 4),(9\\mapsto 8)\\}),(3\\mapsto\\{(1\\mapsto 6),(2\\mapsto 1),(3\\mapsto 5),(4\\mapsto 9),(5\\mapsto 4),(6\\mapsto 8),(7\\mapsto 3),(8\\mapsto 7),(9\\mapsto 2)\\}),(4\\mapsto\\{(1\\mapsto 4),(2\\mapsto 8),(3\\mapsto 3),(4\\mapsto 7),(5\\mapsto 2),(6\\mapsto 6),(7\\mapsto 1),(8\\mapsto 5),(9\\mapsto 9)\\}),(5\\mapsto\\{(1\\mapsto 7),(2\\mapsto 2),(3\\mapsto 6),(4\\mapsto 1),(5\\mapsto 5),(6\\mapsto 9),(7\\mapsto 4),(8\\mapsto 8),(9\\mapsto 3)\\}),(6\\mapsto\\{(1\\mapsto 1),(2\\mapsto 5),(3\\mapsto 9),(4\\mapsto 4),(5\\mapsto 8),(6\\mapsto 3),(7\\mapsto 7),(8\\mapsto 2),(9\\mapsto 6)\\}),(7\\mapsto\\{(1\\mapsto 8),(2\\mapsto 3),(3\\mapsto 7),(4\\mapsto 2),(5\\mapsto 6),(6\\mapsto 1),(7\\mapsto 5),(8\\mapsto 9),(9\\mapsto 4)\\}),(8\\mapsto\\{(1\\mapsto 2),(2\\mapsto 6),(3\\mapsto 1),(4\\mapsto 5),(5\\mapsto 9),(6\\mapsto 4),(7\\mapsto 8),(8\\mapsto 3),(9\\mapsto 7)\\}),(9\\mapsto\\{(1\\mapsto 5),(2\\mapsto 9),(3\\mapsto 4),(4\\mapsto 8),(5\\mapsto 3),(6\\mapsto 7),(7\\mapsto 2),(8\\mapsto 6),(9\\mapsto 1)\\})\\}$|\n",
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+       "|$\\{(1\\mapsto\\{(1\\mapsto 7),(2\\mapsto 3),(3\\mapsto 8),(4\\mapsto 4),(5\\mapsto 9),(6\\mapsto 5),(7\\mapsto 1),(8\\mapsto 6),(9\\mapsto 2)\\}),(2\\mapsto\\{(1\\mapsto 1),(2\\mapsto 6),(3\\mapsto 2),(4\\mapsto 7),(5\\mapsto 3),(6\\mapsto 8),(7\\mapsto 4),(8\\mapsto 9),(9\\mapsto 5)\\}),(3\\mapsto\\{(1\\mapsto 4),(2\\mapsto 9),(3\\mapsto 5),(4\\mapsto 1),(5\\mapsto 6),(6\\mapsto 2),(7\\mapsto 7),(8\\mapsto 3),(9\\mapsto 8)\\}),(4\\mapsto\\{(1\\mapsto 2),(2\\mapsto 7),(3\\mapsto 3),(4\\mapsto 8),(5\\mapsto 4),(6\\mapsto 9),(7\\mapsto 5),(8\\mapsto 1),(9\\mapsto 6)\\}),(5\\mapsto\\{(1\\mapsto 5),(2\\mapsto 1),(3\\mapsto 6),(4\\mapsto 2),(5\\mapsto 7),(6\\mapsto 3),(7\\mapsto 8),(8\\mapsto 4),(9\\mapsto 9)\\}),(6\\mapsto\\{(1\\mapsto 8),(2\\mapsto 4),(3\\mapsto 9),(4\\mapsto 5),(5\\mapsto 1),(6\\mapsto 6),(7\\mapsto 2),(8\\mapsto 7),(9\\mapsto 3)\\}),(7\\mapsto\\{(1\\mapsto 6),(2\\mapsto 2),(3\\mapsto 7),(4\\mapsto 3),(5\\mapsto 8),(6\\mapsto 4),(7\\mapsto 9),(8\\mapsto 5),(9\\mapsto 1)\\}),(8\\mapsto\\{(1\\mapsto 9),(2\\mapsto 5),(3\\mapsto 1),(4\\mapsto 6),(5\\mapsto 2),(6\\mapsto 7),(7\\mapsto 3),(8\\mapsto 8),(9\\mapsto 4)\\}),(9\\mapsto\\{(1\\mapsto 3),(2\\mapsto 8),(3\\mapsto 4),(4\\mapsto 9),(5\\mapsto 5),(6\\mapsto 1),(7\\mapsto 6),(8\\mapsto 2),(9\\mapsto 7)\\})\\}$|\n",
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+       "|$\\{(1\\mapsto\\{(1\\mapsto 8),(2\\mapsto 5),(3\\mapsto 2),(4\\mapsto 4),(5\\mapsto 1),(6\\mapsto 7),(7\\mapsto 9),(8\\mapsto 6),(9\\mapsto 3)\\}),(2\\mapsto\\{(1\\mapsto 3),(2\\mapsto 9),(3\\mapsto 6),(4\\mapsto 8),(5\\mapsto 5),(6\\mapsto 2),(7\\mapsto 4),(8\\mapsto 1),(9\\mapsto 7)\\}),(3\\mapsto\\{(1\\mapsto 7),(2\\mapsto 4),(3\\mapsto 1),(4\\mapsto 3),(5\\mapsto 9),(6\\mapsto 6),(7\\mapsto 8),(8\\mapsto 5),(9\\mapsto 2)\\}),(4\\mapsto\\{(1\\mapsto 2),(2\\mapsto 8),(3\\mapsto 5),(4\\mapsto 7),(5\\mapsto 4),(6\\mapsto 1),(7\\mapsto 3),(8\\mapsto 9),(9\\mapsto 6)\\}),(5\\mapsto\\{(1\\mapsto 6),(2\\mapsto 3),(3\\mapsto 9),(4\\mapsto 2),(5\\mapsto 8),(6\\mapsto 5),(7\\mapsto 7),(8\\mapsto 4),(9\\mapsto 1)\\}),(6\\mapsto\\{(1\\mapsto 1),(2\\mapsto 7),(3\\mapsto 4),(4\\mapsto 6),(5\\mapsto 3),(6\\mapsto 9),(7\\mapsto 2),(8\\mapsto 8),(9\\mapsto 5)\\}),(7\\mapsto\\{(1\\mapsto 5),(2\\mapsto 2),(3\\mapsto 8),(4\\mapsto 1),(5\\mapsto 7),(6\\mapsto 4),(7\\mapsto 6),(8\\mapsto 3),(9\\mapsto 9)\\}),(8\\mapsto\\{(1\\mapsto 9),(2\\mapsto 6),(3\\mapsto 3),(4\\mapsto 5),(5\\mapsto 2),(6\\mapsto 8),(7\\mapsto 1),(8\\mapsto 7),(9\\mapsto 4)\\}),(9\\mapsto\\{(1\\mapsto 4),(2\\mapsto 1),(3\\mapsto 7),(4\\mapsto 9),(5\\mapsto 6),(6\\mapsto 3),(7\\mapsto 5),(8\\mapsto 2),(9\\mapsto 8)\\})\\}$|\n",
+       "|$\\{(1\\mapsto\\{(1\\mapsto 8),(2\\mapsto 2),(3\\mapsto 5),(4\\mapsto 3),(5\\mapsto 6),(6\\mapsto 9),(7\\mapsto 7),(8\\mapsto 1),(9\\mapsto 4)\\}),(2\\mapsto\\{(1\\mapsto 4),(2\\mapsto 7),(3\\mapsto 1),(4\\mapsto 8),(5\\mapsto 2),(6\\mapsto 5),(7\\mapsto 3),(8\\mapsto 6),(9\\mapsto 9)\\}),(3\\mapsto\\{(1\\mapsto 9),(2\\mapsto 3),(3\\mapsto 6),(4\\mapsto 4),(5\\mapsto 7),(6\\mapsto 1),(7\\mapsto 8),(8\\mapsto 2),(9\\mapsto 5)\\}),(4\\mapsto\\{(1\\mapsto 5),(2\\mapsto 8),(3\\mapsto 2),(4\\mapsto 9),(5\\mapsto 3),(6\\mapsto 6),(7\\mapsto 4),(8\\mapsto 7),(9\\mapsto 1)\\}),(5\\mapsto\\{(1\\mapsto 1),(2\\mapsto 4),(3\\mapsto 7),(4\\mapsto 5),(5\\mapsto 8),(6\\mapsto 2),(7\\mapsto 9),(8\\mapsto 3),(9\\mapsto 6)\\}),(6\\mapsto\\{(1\\mapsto 6),(2\\mapsto 9),(3\\mapsto 3),(4\\mapsto 1),(5\\mapsto 4),(6\\mapsto 7),(7\\mapsto 5),(8\\mapsto 8),(9\\mapsto 2)\\}),(7\\mapsto\\{(1\\mapsto 2),(2\\mapsto 5),(3\\mapsto 8),(4\\mapsto 6),(5\\mapsto 9),(6\\mapsto 3),(7\\mapsto 1),(8\\mapsto 4),(9\\mapsto 7)\\}),(8\\mapsto\\{(1\\mapsto 7),(2\\mapsto 1),(3\\mapsto 4),(4\\mapsto 2),(5\\mapsto 5),(6\\mapsto 8),(7\\mapsto 6),(8\\mapsto 9),(9\\mapsto 3)\\}),(9\\mapsto\\{(1\\mapsto 3),(2\\mapsto 6),(3\\mapsto 9),(4\\mapsto 7),(5\\mapsto 1),(6\\mapsto 4),(7\\mapsto 2),(8\\mapsto 5),(9\\mapsto 8)\\})\\}$|\n",
+       "|$\\{(1\\mapsto\\{(1\\mapsto 3),(2\\mapsto 6),(3\\mapsto 9),(4\\mapsto 7),(5\\mapsto 1),(6\\mapsto 4),(7\\mapsto 2),(8\\mapsto 5),(9\\mapsto 8)\\}),(2\\mapsto\\{(1\\mapsto 7),(2\\mapsto 1),(3\\mapsto 4),(4\\mapsto 2),(5\\mapsto 5),(6\\mapsto 8),(7\\mapsto 6),(8\\mapsto 9),(9\\mapsto 3)\\}),(3\\mapsto\\{(1\\mapsto 2),(2\\mapsto 5),(3\\mapsto 8),(4\\mapsto 6),(5\\mapsto 9),(6\\mapsto 3),(7\\mapsto 1),(8\\mapsto 4),(9\\mapsto 7)\\}),(4\\mapsto\\{(1\\mapsto 6),(2\\mapsto 9),(3\\mapsto 3),(4\\mapsto 1),(5\\mapsto 4),(6\\mapsto 7),(7\\mapsto 5),(8\\mapsto 8),(9\\mapsto 2)\\}),(5\\mapsto\\{(1\\mapsto 1),(2\\mapsto 4),(3\\mapsto 7),(4\\mapsto 5),(5\\mapsto 8),(6\\mapsto 2),(7\\mapsto 9),(8\\mapsto 3),(9\\mapsto 6)\\}),(6\\mapsto\\{(1\\mapsto 5),(2\\mapsto 8),(3\\mapsto 2),(4\\mapsto 9),(5\\mapsto 3),(6\\mapsto 6),(7\\mapsto 4),(8\\mapsto 7),(9\\mapsto 1)\\}),(7\\mapsto\\{(1\\mapsto 9),(2\\mapsto 3),(3\\mapsto 6),(4\\mapsto 4),(5\\mapsto 7),(6\\mapsto 1),(7\\mapsto 8),(8\\mapsto 2),(9\\mapsto 5)\\}),(8\\mapsto\\{(1\\mapsto 4),(2\\mapsto 7),(3\\mapsto 1),(4\\mapsto 8),(5\\mapsto 2),(6\\mapsto 5),(7\\mapsto 3),(8\\mapsto 6),(9\\mapsto 9)\\}),(9\\mapsto\\{(1\\mapsto 8),(2\\mapsto 2),(3\\mapsto 5),(4\\mapsto 3),(5\\mapsto 6),(6\\mapsto 9),(7\\mapsto 7),(8\\mapsto 1),(9\\mapsto 4)\\})\\}$|\n",
+       "|$\\{(1\\mapsto\\{(1\\mapsto 8),(2\\mapsto 3),(3\\mapsto 7),(4\\mapsto 2),(5\\mapsto 6),(6\\mapsto 1),(7\\mapsto 5),(8\\mapsto 9),(9\\mapsto 4)\\}),(2\\mapsto\\{(1\\mapsto 5),(2\\mapsto 9),(3\\mapsto 4),(4\\mapsto 8),(5\\mapsto 3),(6\\mapsto 7),(7\\mapsto 2),(8\\mapsto 6),(9\\mapsto 1)\\}),(3\\mapsto\\{(1\\mapsto 2),(2\\mapsto 6),(3\\mapsto 1),(4\\mapsto 5),(5\\mapsto 9),(6\\mapsto 4),(7\\mapsto 8),(8\\mapsto 3),(9\\mapsto 7)\\}),(4\\mapsto\\{(1\\mapsto 4),(2\\mapsto 8),(3\\mapsto 3),(4\\mapsto 7),(5\\mapsto 2),(6\\mapsto 6),(7\\mapsto 1),(8\\mapsto 5),(9\\mapsto 9)\\}),(5\\mapsto\\{(1\\mapsto 1),(2\\mapsto 5),(3\\mapsto 9),(4\\mapsto 4),(5\\mapsto 8),(6\\mapsto 3),(7\\mapsto 7),(8\\mapsto 2),(9\\mapsto 6)\\}),(6\\mapsto\\{(1\\mapsto 7),(2\\mapsto 2),(3\\mapsto 6),(4\\mapsto 1),(5\\mapsto 5),(6\\mapsto 9),(7\\mapsto 4),(8\\mapsto 8),(9\\mapsto 3)\\}),(7\\mapsto\\{(1\\mapsto 9),(2\\mapsto 4),(3\\mapsto 8),(4\\mapsto 3),(5\\mapsto 7),(6\\mapsto 2),(7\\mapsto 6),(8\\mapsto 1),(9\\mapsto 5)\\}),(8\\mapsto\\{(1\\mapsto 6),(2\\mapsto 1),(3\\mapsto 5),(4\\mapsto 9),(5\\mapsto 4),(6\\mapsto 8),(7\\mapsto 3),(8\\mapsto 7),(9\\mapsto 2)\\}),(9\\mapsto\\{(1\\mapsto 3),(2\\mapsto 7),(3\\mapsto 2),(4\\mapsto 6),(5\\mapsto 1),(6\\mapsto 5),(7\\mapsto 9),(8\\mapsto 4),(9\\mapsto 8)\\})\\}$|\n",
+       "|$\\{(1\\mapsto\\{(1\\mapsto 3),(2\\mapsto 7),(3\\mapsto 2),(4\\mapsto 6),(5\\mapsto 1),(6\\mapsto 5),(7\\mapsto 9),(8\\mapsto 4),(9\\mapsto 8)\\}),(2\\mapsto\\{(1\\mapsto 6),(2\\mapsto 1),(3\\mapsto 5),(4\\mapsto 9),(5\\mapsto 4),(6\\mapsto 8),(7\\mapsto 3),(8\\mapsto 7),(9\\mapsto 2)\\}),(3\\mapsto\\{(1\\mapsto 9),(2\\mapsto 4),(3\\mapsto 8),(4\\mapsto 3),(5\\mapsto 7),(6\\mapsto 2),(7\\mapsto 6),(8\\mapsto 1),(9\\mapsto 5)\\}),(4\\mapsto\\{(1\\mapsto 7),(2\\mapsto 2),(3\\mapsto 6),(4\\mapsto 1),(5\\mapsto 5),(6\\mapsto 9),(7\\mapsto 4),(8\\mapsto 8),(9\\mapsto 3)\\}),(5\\mapsto\\{(1\\mapsto 1),(2\\mapsto 5),(3\\mapsto 9),(4\\mapsto 4),(5\\mapsto 8),(6\\mapsto 3),(7\\mapsto 7),(8\\mapsto 2),(9\\mapsto 6)\\}),(6\\mapsto\\{(1\\mapsto 4),(2\\mapsto 8),(3\\mapsto 3),(4\\mapsto 7),(5\\mapsto 2),(6\\mapsto 6),(7\\mapsto 1),(8\\mapsto 5),(9\\mapsto 9)\\}),(7\\mapsto\\{(1\\mapsto 2),(2\\mapsto 6),(3\\mapsto 1),(4\\mapsto 5),(5\\mapsto 9),(6\\mapsto 4),(7\\mapsto 8),(8\\mapsto 3),(9\\mapsto 7)\\}),(8\\mapsto\\{(1\\mapsto 5),(2\\mapsto 9),(3\\mapsto 4),(4\\mapsto 8),(5\\mapsto 3),(6\\mapsto 7),(7\\mapsto 2),(8\\mapsto 6),(9\\mapsto 1)\\}),(9\\mapsto\\{(1\\mapsto 8),(2\\mapsto 3),(3\\mapsto 7),(4\\mapsto 2),(5\\mapsto 6),(6\\mapsto 1),(7\\mapsto 5),(8\\mapsto 9),(9\\mapsto 4)\\})\\}$|\n",
+       "|$\\{(1\\mapsto\\{(1\\mapsto 5),(2\\mapsto 1),(3\\mapsto 6),(4\\mapsto 2),(5\\mapsto 7),(6\\mapsto 3),(7\\mapsto 8),(8\\mapsto 4),(9\\mapsto 9)\\}),(2\\mapsto\\{(1\\mapsto 2),(2\\mapsto 7),(3\\mapsto 3),(4\\mapsto 8),(5\\mapsto 4),(6\\mapsto 9),(7\\mapsto 5),(8\\mapsto 1),(9\\mapsto 6)\\}),(3\\mapsto\\{(1\\mapsto 8),(2\\mapsto 4),(3\\mapsto 9),(4\\mapsto 5),(5\\mapsto 1),(6\\mapsto 6),(7\\mapsto 2),(8\\mapsto 7),(9\\mapsto 3)\\}),(4\\mapsto\\{(1\\mapsto 1),(2\\mapsto 6),(3\\mapsto 2),(4\\mapsto 7),(5\\mapsto 3),(6\\mapsto 8),(7\\mapsto 4),(8\\mapsto 9),(9\\mapsto 5)\\}),(5\\mapsto\\{(1\\mapsto 7),(2\\mapsto 3),(3\\mapsto 8),(4\\mapsto 4),(5\\mapsto 9),(6\\mapsto 5),(7\\mapsto 1),(8\\mapsto 6),(9\\mapsto 2)\\}),(6\\mapsto\\{(1\\mapsto 4),(2\\mapsto 9),(3\\mapsto 5),(4\\mapsto 1),(5\\mapsto 6),(6\\mapsto 2),(7\\mapsto 7),(8\\mapsto 3),(9\\mapsto 8)\\}),(7\\mapsto\\{(1\\mapsto 6),(2\\mapsto 2),(3\\mapsto 7),(4\\mapsto 3),(5\\mapsto 8),(6\\mapsto 4),(7\\mapsto 9),(8\\mapsto 5),(9\\mapsto 1)\\}),(8\\mapsto\\{(1\\mapsto 3),(2\\mapsto 8),(3\\mapsto 4),(4\\mapsto 9),(5\\mapsto 5),(6\\mapsto 1),(7\\mapsto 6),(8\\mapsto 2),(9\\mapsto 7)\\}),(9\\mapsto\\{(1\\mapsto 9),(2\\mapsto 5),(3\\mapsto 1),(4\\mapsto 6),(5\\mapsto 2),(6\\mapsto 7),(7\\mapsto 3),(8\\mapsto 8),(9\\mapsto 4)\\})\\}$|\n",
+       "|$\\{(1\\mapsto\\{(1\\mapsto 9),(2\\mapsto 5),(3\\mapsto 1),(4\\mapsto 6),(5\\mapsto 2),(6\\mapsto 7),(7\\mapsto 3),(8\\mapsto 8),(9\\mapsto 4)\\}),(2\\mapsto\\{(1\\mapsto 3),(2\\mapsto 8),(3\\mapsto 4),(4\\mapsto 9),(5\\mapsto 5),(6\\mapsto 1),(7\\mapsto 6),(8\\mapsto 2),(9\\mapsto 7)\\}),(3\\mapsto\\{(1\\mapsto 6),(2\\mapsto 2),(3\\mapsto 7),(4\\mapsto 3),(5\\mapsto 8),(6\\mapsto 4),(7\\mapsto 9),(8\\mapsto 5),(9\\mapsto 1)\\}),(4\\mapsto\\{(1\\mapsto 4),(2\\mapsto 9),(3\\mapsto 5),(4\\mapsto 1),(5\\mapsto 6),(6\\mapsto 2),(7\\mapsto 7),(8\\mapsto 3),(9\\mapsto 8)\\}),(5\\mapsto\\{(1\\mapsto 7),(2\\mapsto 3),(3\\mapsto 8),(4\\mapsto 4),(5\\mapsto 9),(6\\mapsto 5),(7\\mapsto 1),(8\\mapsto 6),(9\\mapsto 2)\\}),(6\\mapsto\\{(1\\mapsto 1),(2\\mapsto 6),(3\\mapsto 2),(4\\mapsto 7),(5\\mapsto 3),(6\\mapsto 8),(7\\mapsto 4),(8\\mapsto 9),(9\\mapsto 5)\\}),(7\\mapsto\\{(1\\mapsto 8),(2\\mapsto 4),(3\\mapsto 9),(4\\mapsto 5),(5\\mapsto 1),(6\\mapsto 6),(7\\mapsto 2),(8\\mapsto 7),(9\\mapsto 3)\\}),(8\\mapsto\\{(1\\mapsto 2),(2\\mapsto 7),(3\\mapsto 3),(4\\mapsto 8),(5\\mapsto 4),(6\\mapsto 9),(7\\mapsto 5),(8\\mapsto 1),(9\\mapsto 6)\\}),(9\\mapsto\\{(1\\mapsto 5),(2\\mapsto 1),(3\\mapsto 6),(4\\mapsto 2),(5\\mapsto 7),(6\\mapsto 3),(7\\mapsto 8),(8\\mapsto 4),(9\\mapsto 9)\\})\\}$|\n",
+       "|$\\{(1\\mapsto\\{(1\\mapsto 5),(2\\mapsto 2),(3\\mapsto 8),(4\\mapsto 1),(5\\mapsto 7),(6\\mapsto 4),(7\\mapsto 6),(8\\mapsto 3),(9\\mapsto 9)\\}),(2\\mapsto\\{(1\\mapsto 1),(2\\mapsto 7),(3\\mapsto 4),(4\\mapsto 6),(5\\mapsto 3),(6\\mapsto 9),(7\\mapsto 2),(8\\mapsto 8),(9\\mapsto 5)\\}),(3\\mapsto\\{(1\\mapsto 6),(2\\mapsto 3),(3\\mapsto 9),(4\\mapsto 2),(5\\mapsto 8),(6\\mapsto 5),(7\\mapsto 7),(8\\mapsto 4),(9\\mapsto 1)\\}),(4\\mapsto\\{(1\\mapsto 2),(2\\mapsto 8),(3\\mapsto 5),(4\\mapsto 7),(5\\mapsto 4),(6\\mapsto 1),(7\\mapsto 3),(8\\mapsto 9),(9\\mapsto 6)\\}),(5\\mapsto\\{(1\\mapsto 7),(2\\mapsto 4),(3\\mapsto 1),(4\\mapsto 3),(5\\mapsto 9),(6\\mapsto 6),(7\\mapsto 8),(8\\mapsto 5),(9\\mapsto 2)\\}),(6\\mapsto\\{(1\\mapsto 3),(2\\mapsto 9),(3\\mapsto 6),(4\\mapsto 8),(5\\mapsto 5),(6\\mapsto 2),(7\\mapsto 4),(8\\mapsto 1),(9\\mapsto 7)\\}),(7\\mapsto\\{(1\\mapsto 8),(2\\mapsto 5),(3\\mapsto 2),(4\\mapsto 4),(5\\mapsto 1),(6\\mapsto 7),(7\\mapsto 9),(8\\mapsto 6),(9\\mapsto 3)\\}),(8\\mapsto\\{(1\\mapsto 4),(2\\mapsto 1),(3\\mapsto 7),(4\\mapsto 9),(5\\mapsto 6),(6\\mapsto 3),(7\\mapsto 5),(8\\mapsto 2),(9\\mapsto 8)\\}),(9\\mapsto\\{(1\\mapsto 9),(2\\mapsto 6),(3\\mapsto 3),(4\\mapsto 5),(5\\mapsto 2),(6\\mapsto 8),(7\\mapsto 1),(8\\mapsto 7),(9\\mapsto 4)\\})\\}$|\n",
+       "|$\\{(1\\mapsto\\{(1\\mapsto 9),(2\\mapsto 6),(3\\mapsto 3),(4\\mapsto 5),(5\\mapsto 2),(6\\mapsto 8),(7\\mapsto 1),(8\\mapsto 7),(9\\mapsto 4)\\}),(2\\mapsto\\{(1\\mapsto 4),(2\\mapsto 1),(3\\mapsto 7),(4\\mapsto 9),(5\\mapsto 6),(6\\mapsto 3),(7\\mapsto 5),(8\\mapsto 2),(9\\mapsto 8)\\}),(3\\mapsto\\{(1\\mapsto 8),(2\\mapsto 5),(3\\mapsto 2),(4\\mapsto 4),(5\\mapsto 1),(6\\mapsto 7),(7\\mapsto 9),(8\\mapsto 6),(9\\mapsto 3)\\}),(4\\mapsto\\{(1\\mapsto 3),(2\\mapsto 9),(3\\mapsto 6),(4\\mapsto 8),(5\\mapsto 5),(6\\mapsto 2),(7\\mapsto 4),(8\\mapsto 1),(9\\mapsto 7)\\}),(5\\mapsto\\{(1\\mapsto 7),(2\\mapsto 4),(3\\mapsto 1),(4\\mapsto 3),(5\\mapsto 9),(6\\mapsto 6),(7\\mapsto 8),(8\\mapsto 5),(9\\mapsto 2)\\}),(6\\mapsto\\{(1\\mapsto 2),(2\\mapsto 8),(3\\mapsto 5),(4\\mapsto 7),(5\\mapsto 4),(6\\mapsto 1),(7\\mapsto 3),(8\\mapsto 9),(9\\mapsto 6)\\}),(7\\mapsto\\{(1\\mapsto 6),(2\\mapsto 3),(3\\mapsto 9),(4\\mapsto 2),(5\\mapsto 8),(6\\mapsto 5),(7\\mapsto 7),(8\\mapsto 4),(9\\mapsto 1)\\}),(8\\mapsto\\{(1\\mapsto 1),(2\\mapsto 7),(3\\mapsto 4),(4\\mapsto 6),(5\\mapsto 3),(6\\mapsto 9),(7\\mapsto 2),(8\\mapsto 8),(9\\mapsto 5)\\}),(9\\mapsto\\{(1\\mapsto 5),(2\\mapsto 2),(3\\mapsto 8),(4\\mapsto 1),(5\\mapsto 7),(6\\mapsto 4),(7\\mapsto 6),(8\\mapsto 3),(9\\mapsto 9)\\})\\}$|\n",
+       "|$\\{(1\\mapsto\\{(1\\mapsto 9),(2\\mapsto 3),(3\\mapsto 6),(4\\mapsto 4),(5\\mapsto 7),(6\\mapsto 1),(7\\mapsto 8),(8\\mapsto 2),(9\\mapsto 5)\\}),(2\\mapsto\\{(1\\mapsto 5),(2\\mapsto 8),(3\\mapsto 2),(4\\mapsto 9),(5\\mapsto 3),(6\\mapsto 6),(7\\mapsto 4),(8\\mapsto 7),(9\\mapsto 1)\\}),(3\\mapsto\\{(1\\mapsto 1),(2\\mapsto 4),(3\\mapsto 7),(4\\mapsto 5),(5\\mapsto 8),(6\\mapsto 2),(7\\mapsto 9),(8\\mapsto 3),(9\\mapsto 6)\\}),(4\\mapsto\\{(1\\mapsto 6),(2\\mapsto 9),(3\\mapsto 3),(4\\mapsto 1),(5\\mapsto 4),(6\\mapsto 7),(7\\mapsto 5),(8\\mapsto 8),(9\\mapsto 2)\\}),(5\\mapsto\\{(1\\mapsto 2),(2\\mapsto 5),(3\\mapsto 8),(4\\mapsto 6),(5\\mapsto 9),(6\\mapsto 3),(7\\mapsto 1),(8\\mapsto 4),(9\\mapsto 7)\\}),(6\\mapsto\\{(1\\mapsto 7),(2\\mapsto 1),(3\\mapsto 4),(4\\mapsto 2),(5\\mapsto 5),(6\\mapsto 8),(7\\mapsto 6),(8\\mapsto 9),(9\\mapsto 3)\\}),(7\\mapsto\\{(1\\mapsto 3),(2\\mapsto 6),(3\\mapsto 9),(4\\mapsto 7),(5\\mapsto 1),(6\\mapsto 4),(7\\mapsto 2),(8\\mapsto 5),(9\\mapsto 8)\\}),(8\\mapsto\\{(1\\mapsto 8),(2\\mapsto 2),(3\\mapsto 5),(4\\mapsto 3),(5\\mapsto 6),(6\\mapsto 9),(7\\mapsto 7),(8\\mapsto 1),(9\\mapsto 4)\\}),(9\\mapsto\\{(1\\mapsto 4),(2\\mapsto 7),(3\\mapsto 1),(4\\mapsto 8),(5\\mapsto 2),(6\\mapsto 5),(7\\mapsto 3),(8\\mapsto 6),(9\\mapsto 9)\\})\\}$|\n",
+       "|$\\{(1\\mapsto\\{(1\\mapsto 4),(2\\mapsto 7),(3\\mapsto 1),(4\\mapsto 8),(5\\mapsto 2),(6\\mapsto 5),(7\\mapsto 3),(8\\mapsto 6),(9\\mapsto 9)\\}),(2\\mapsto\\{(1\\mapsto 8),(2\\mapsto 2),(3\\mapsto 5),(4\\mapsto 3),(5\\mapsto 6),(6\\mapsto 9),(7\\mapsto 7),(8\\mapsto 1),(9\\mapsto 4)\\}),(3\\mapsto\\{(1\\mapsto 3),(2\\mapsto 6),(3\\mapsto 9),(4\\mapsto 7),(5\\mapsto 1),(6\\mapsto 4),(7\\mapsto 2),(8\\mapsto 5),(9\\mapsto 8)\\}),(4\\mapsto\\{(1\\mapsto 7),(2\\mapsto 1),(3\\mapsto 4),(4\\mapsto 2),(5\\mapsto 5),(6\\mapsto 8),(7\\mapsto 6),(8\\mapsto 9),(9\\mapsto 3)\\}),(5\\mapsto\\{(1\\mapsto 2),(2\\mapsto 5),(3\\mapsto 8),(4\\mapsto 6),(5\\mapsto 9),(6\\mapsto 3),(7\\mapsto 1),(8\\mapsto 4),(9\\mapsto 7)\\}),(6\\mapsto\\{(1\\mapsto 6),(2\\mapsto 9),(3\\mapsto 3),(4\\mapsto 1),(5\\mapsto 4),(6\\mapsto 7),(7\\mapsto 5),(8\\mapsto 8),(9\\mapsto 2)\\}),(7\\mapsto\\{(1\\mapsto 1),(2\\mapsto 4),(3\\mapsto 7),(4\\mapsto 5),(5\\mapsto 8),(6\\mapsto 2),(7\\mapsto 9),(8\\mapsto 3),(9\\mapsto 6)\\}),(8\\mapsto\\{(1\\mapsto 5),(2\\mapsto 8),(3\\mapsto 2),(4\\mapsto 9),(5\\mapsto 3),(6\\mapsto 6),(7\\mapsto 4),(8\\mapsto 7),(9\\mapsto 1)\\}),(9\\mapsto\\{(1\\mapsto 9),(2\\mapsto 3),(3\\mapsto 6),(4\\mapsto 4),(5\\mapsto 7),(6\\mapsto 1),(7\\mapsto 8),(8\\mapsto 2),(9\\mapsto 5)\\})\\}$|\n",
+       "|$\\{(1\\mapsto\\{(1\\mapsto 9),(2\\mapsto 4),(3\\mapsto 8),(4\\mapsto 3),(5\\mapsto 7),(6\\mapsto 2),(7\\mapsto 6),(8\\mapsto 1),(9\\mapsto 5)\\}),(2\\mapsto\\{(1\\mapsto 6),(2\\mapsto 1),(3\\mapsto 5),(4\\mapsto 9),(5\\mapsto 4),(6\\mapsto 8),(7\\mapsto 3),(8\\mapsto 7),(9\\mapsto 2)\\}),(3\\mapsto\\{(1\\mapsto 3),(2\\mapsto 7),(3\\mapsto 2),(4\\mapsto 6),(5\\mapsto 1),(6\\mapsto 5),(7\\mapsto 9),(8\\mapsto 4),(9\\mapsto 8)\\}),(4\\mapsto\\{(1\\mapsto 5),(2\\mapsto 9),(3\\mapsto 4),(4\\mapsto 8),(5\\mapsto 3),(6\\mapsto 7),(7\\mapsto 2),(8\\mapsto 6),(9\\mapsto 1)\\}),(5\\mapsto\\{(1\\mapsto 2),(2\\mapsto 6),(3\\mapsto 1),(4\\mapsto 5),(5\\mapsto 9),(6\\mapsto 4),(7\\mapsto 8),(8\\mapsto 3),(9\\mapsto 7)\\}),(6\\mapsto\\{(1\\mapsto 8),(2\\mapsto 3),(3\\mapsto 7),(4\\mapsto 2),(5\\mapsto 6),(6\\mapsto 1),(7\\mapsto 5),(8\\mapsto 9),(9\\mapsto 4)\\}),(7\\mapsto\\{(1\\mapsto 1),(2\\mapsto 5),(3\\mapsto 9),(4\\mapsto 4),(5\\mapsto 8),(6\\mapsto 3),(7\\mapsto 7),(8\\mapsto 2),(9\\mapsto 6)\\}),(8\\mapsto\\{(1\\mapsto 7),(2\\mapsto 2),(3\\mapsto 6),(4\\mapsto 1),(5\\mapsto 5),(6\\mapsto 9),(7\\mapsto 4),(8\\mapsto 8),(9\\mapsto 3)\\}),(9\\mapsto\\{(1\\mapsto 4),(2\\mapsto 8),(3\\mapsto 3),(4\\mapsto 7),(5\\mapsto 2),(6\\mapsto 6),(7\\mapsto 1),(8\\mapsto 5),(9\\mapsto 9)\\})\\}$|\n",
+       "|$\\{(1\\mapsto\\{(1\\mapsto 4),(2\\mapsto 8),(3\\mapsto 3),(4\\mapsto 7),(5\\mapsto 2),(6\\mapsto 6),(7\\mapsto 1),(8\\mapsto 5),(9\\mapsto 9)\\}),(2\\mapsto\\{(1\\mapsto 7),(2\\mapsto 2),(3\\mapsto 6),(4\\mapsto 1),(5\\mapsto 5),(6\\mapsto 9),(7\\mapsto 4),(8\\mapsto 8),(9\\mapsto 3)\\}),(3\\mapsto\\{(1\\mapsto 1),(2\\mapsto 5),(3\\mapsto 9),(4\\mapsto 4),(5\\mapsto 8),(6\\mapsto 3),(7\\mapsto 7),(8\\mapsto 2),(9\\mapsto 6)\\}),(4\\mapsto\\{(1\\mapsto 8),(2\\mapsto 3),(3\\mapsto 7),(4\\mapsto 2),(5\\mapsto 6),(6\\mapsto 1),(7\\mapsto 5),(8\\mapsto 9),(9\\mapsto 4)\\}),(5\\mapsto\\{(1\\mapsto 2),(2\\mapsto 6),(3\\mapsto 1),(4\\mapsto 5),(5\\mapsto 9),(6\\mapsto 4),(7\\mapsto 8),(8\\mapsto 3),(9\\mapsto 7)\\}),(6\\mapsto\\{(1\\mapsto 5),(2\\mapsto 9),(3\\mapsto 4),(4\\mapsto 8),(5\\mapsto 3),(6\\mapsto 7),(7\\mapsto 2),(8\\mapsto 6),(9\\mapsto 1)\\}),(7\\mapsto\\{(1\\mapsto 3),(2\\mapsto 7),(3\\mapsto 2),(4\\mapsto 6),(5\\mapsto 1),(6\\mapsto 5),(7\\mapsto 9),(8\\mapsto 4),(9\\mapsto 8)\\}),(8\\mapsto\\{(1\\mapsto 6),(2\\mapsto 1),(3\\mapsto 5),(4\\mapsto 9),(5\\mapsto 4),(6\\mapsto 8),(7\\mapsto 3),(8\\mapsto 7),(9\\mapsto 2)\\}),(9\\mapsto\\{(1\\mapsto 9),(2\\mapsto 4),(3\\mapsto 8),(4\\mapsto 3),(5\\mapsto 7),(6\\mapsto 2),(7\\mapsto 6),(8\\mapsto 1),(9\\mapsto 5)\\})\\}$|\n"
+      ],
+      "text/plain": [
+       "Elements\n",
+       "{(1|->{(1|->6),(2|->2),(3|->7),(4|->3),(5|->8),(6|->4),(7|->9),(8|->5),(9|->1)}),(2|->{(1|->3),(2|->8),(3|->4),(4|->9),(5|->5),(6|->1),(7|->6),(8|->2),(9|->7)}),(3|->{(1|->9),(2|->5),(3|->1),(4|->6),(5|->2),(6|->7),(7|->3),(8|->8),(9|->4)}),(4|->{(1|->2),(2|->7),(3|->3),(4|->8),(5|->4),(6|->9),(7|->5),(8|->1),(9|->6)}),(5|->{(1|->8),(2|->4),(3|->9),(4|->5),(5|->1),(6|->6),(7|->2),(8|->7),(9|->3)}),(6|->{(1|->5),(2|->1),(3|->6),(4|->2),(5|->7),(6|->3),(7|->8),(8|->4),(9|->9)}),(7|->{(1|->7),(2|->3),(3|->8),(4|->4),(5|->9),(6|->5),(7|->1),(8|->6),(9|->2)}),(8|->{(1|->4),(2|->9),(3|->5),(4|->1),(5|->6),(6|->2),(7|->7),(8|->3),(9|->8)}),(9|->{(1|->1),(2|->6),(3|->2),(4|->7),(5|->3),(6|->8),(7|->4),(8|->9),(9|->5)})}\n",
+       "{(1|->{(1|->1),(2|->6),(3|->2),(4|->7),(5|->3),(6|->8),(7|->4),(8|->9),(9|->5)}),(2|->{(1|->4),(2|->9),(3|->5),(4|->1),(5|->6),(6|->2),(7|->7),(8|->3),(9|->8)}),(3|->{(1|->7),(2|->3),(3|->8),(4|->4),(5|->9),(6|->5),(7|->1),(8|->6),(9|->2)}),(4|->{(1|->5),(2|->1),(3|->6),(4|->2),(5|->7),(6|->3),(7|->8),(8|->4),(9|->9)}),(5|->{(1|->8),(2|->4),(3|->9),(4|->5),(5|->1),(6|->6),(7|->2),(8|->7),(9|->3)}),(6|->{(1|->2),(2|->7),(3|->3),(4|->8),(5|->4),(6|->9),(7|->5),(8|->1),(9|->6)}),(7|->{(1|->9),(2|->5),(3|->1),(4|->6),(5|->2),(6|->7),(7|->3),(8|->8),(9|->4)}),(8|->{(1|->3),(2|->8),(3|->4),(4|->9),(5|->5),(6|->1),(7|->6),(8|->2),(9|->7)}),(9|->{(1|->6),(2|->2),(3|->7),(4|->3),(5|->8),(6|->4),(7|->9),(8|->5),(9|->1)})}\n",
+       "{(1|->{(1|->6),(2|->3),(3|->9),(4|->2),(5|->8),(6|->5),(7|->7),(8|->4),(9|->1)}),(2|->{(1|->2),(2|->8),(3|->5),(4|->7),(5|->4),(6|->1),(7|->3),(8|->9),(9|->6)}),(3|->{(1|->7),(2|->4),(3|->1),(4|->3),(5|->9),(6|->6),(7|->8),(8|->5),(9|->2)}),(4|->{(1|->3),(2|->9),(3|->6),(4|->8),(5|->5),(6|->2),(7|->4),(8|->1),(9|->7)}),(5|->{(1|->8),(2|->5),(3|->2),(4|->4),(5|->1),(6|->7),(7|->9),(8|->6),(9|->3)}),(6|->{(1|->4),(2|->1),(3|->7),(4|->9),(5|->6),(6|->3),(7|->5),(8|->2),(9|->8)}),(7|->{(1|->9),(2|->6),(3|->3),(4|->5),(5|->2),(6|->8),(7|->1),(8|->7),(9|->4)}),(8|->{(1|->5),(2|->2),(3|->8),(4|->1),(5|->7),(6|->4),(7|->6),(8|->3),(9|->9)}),(9|->{(1|->1),(2|->7),(3|->4),(4|->6),(5|->3),(6|->9),(7|->2),(8|->8),(9|->5)})}\n",
+       "{(1|->{(1|->1),(2|->7),(3|->4),(4|->6),(5|->3),(6|->9),(7|->2),(8|->8),(9|->5)}),(2|->{(1|->5),(2|->2),(3|->8),(4|->1),(5|->7),(6|->4),(7|->6),(8|->3),(9|->9)}),(3|->{(1|->9),(2|->6),(3|->3),(4|->5),(5|->2),(6|->8),(7|->1),(8|->7),(9|->4)}),(4|->{(1|->4),(2|->1),(3|->7),(4|->9),(5|->6),(6|->3),(7|->5),(8|->2),(9|->8)}),(5|->{(1|->8),(2|->5),(3|->2),(4|->4),(5|->1),(6|->7),(7|->9),(8|->6),(9|->3)}),(6|->{(1|->3),(2|->9),(3|->6),(4|->8),(5|->5),(6|->2),(7|->4),(8|->1),(9|->7)}),(7|->{(1|->7),(2|->4),(3|->1),(4|->3),(5|->9),(6|->6),(7|->8),(8|->5),(9|->2)}),(8|->{(1|->2),(2|->8),(3|->5),(4|->7),(5|->4),(6|->1),(7|->3),(8|->9),(9|->6)}),(9|->{(1|->6),(2|->3),(3|->9),(4|->2),(5|->8),(6|->5),(7|->7),(8|->4),(9|->1)})}\n",
+       "{(1|->{(1|->1),(2|->4),(3|->7),(4|->5),(5|->8),(6|->2),(7|->9),(8|->3),(9|->6)}),(2|->{(1|->6),(2|->9),(3|->3),(4|->1),(5|->4),(6|->7),(7|->5),(8|->8),(9|->2)}),(3|->{(1|->2),(2|->5),(3|->8),(4|->6),(5|->9),(6|->3),(7|->1),(8|->4),(9|->7)}),(4|->{(1|->7),(2|->1),(3|->4),(4|->2),(5|->5),(6|->8),(7|->6),(8|->9),(9|->3)}),(5|->{(1|->3),(2|->6),(3|->9),(4|->7),(5|->1),(6|->4),(7|->2),(8|->5),(9|->8)}),(6|->{(1|->8),(2|->2),(3|->5),(4|->3),(5|->6),(6|->9),(7|->7),(8|->1),(9|->4)}),(7|->{(1|->4),(2|->7),(3|->1),(4|->8),(5|->2),(6|->5),(7|->3),(8|->6),(9|->9)}),(8|->{(1|->9),(2|->3),(3|->6),(4|->4),(5|->7),(6|->1),(7|->8),(8|->2),(9|->5)}),(9|->{(1|->5),(2|->8),(3|->2),(4|->9),(5|->3),(6|->6),(7|->4),(8|->7),(9|->1)})}\n",
+       "{(1|->{(1|->5),(2|->8),(3|->2),(4|->9),(5|->3),(6|->6),(7|->4),(8|->7),(9|->1)}),(2|->{(1|->9),(2|->3),(3|->6),(4|->4),(5|->7),(6|->1),(7|->8),(8|->2),(9|->5)}),(3|->{(1|->4),(2|->7),(3|->1),(4|->8),(5|->2),(6|->5),(7|->3),(8|->6),(9|->9)}),(4|->{(1|->8),(2|->2),(3|->5),(4|->3),(5|->6),(6|->9),(7|->7),(8|->1),(9|->4)}),(5|->{(1|->3),(2|->6),(3|->9),(4|->7),(5|->1),(6|->4),(7|->2),(8|->5),(9|->8)}),(6|->{(1|->7),(2|->1),(3|->4),(4|->2),(5|->5),(6|->8),(7|->6),(8|->9),(9|->3)}),(7|->{(1|->2),(2|->5),(3|->8),(4|->6),(5|->9),(6|->3),(7|->1),(8|->4),(9|->7)}),(8|->{(1|->6),(2|->9),(3|->3),(4|->1),(5|->4),(6|->7),(7|->5),(8|->8),(9|->2)}),(9|->{(1|->1),(2|->4),(3|->7),(4|->5),(5|->8),(6|->2),(7|->9),(8|->3),(9|->6)})}\n",
+       "{(1|->{(1|->1),(2|->5),(3|->9),(4|->4),(5|->8),(6|->3),(7|->7),(8|->2),(9|->6)}),(2|->{(1|->7),(2|->2),(3|->6),(4|->1),(5|->5),(6|->9),(7|->4),(8|->8),(9|->3)}),(3|->{(1|->4),(2|->8),(3|->3),(4|->7),(5|->2),(6|->6),(7|->1),(8|->5),(9|->9)}),(4|->{(1|->6),(2|->1),(3|->5),(4|->9),(5|->4),(6|->8),(7|->3),(8|->7),(9|->2)}),(5|->{(1|->3),(2|->7),(3|->2),(4|->6),(5|->1),(6|->5),(7|->9),(8|->4),(9|->8)}),(6|->{(1|->9),(2|->4),(3|->8),(4|->3),(5|->7),(6|->2),(7|->6),(8|->1),(9|->5)}),(7|->{(1|->2),(2|->6),(3|->1),(4|->5),(5|->9),(6|->4),(7|->8),(8|->3),(9|->7)}),(8|->{(1|->8),(2|->3),(3|->7),(4|->2),(5|->6),(6|->1),(7|->5),(8|->9),(9|->4)}),(9|->{(1|->5),(2|->9),(3|->4),(4|->8),(5|->3),(6|->7),(7|->2),(8|->6),(9|->1)})}\n",
+       "{(1|->{(1|->5),(2|->9),(3|->4),(4|->8),(5|->3),(6|->7),(7|->2),(8|->6),(9|->1)}),(2|->{(1|->8),(2|->3),(3|->7),(4|->2),(5|->6),(6|->1),(7|->5),(8|->9),(9|->4)}),(3|->{(1|->2),(2|->6),(3|->1),(4|->5),(5|->9),(6|->4),(7|->8),(8|->3),(9|->7)}),(4|->{(1|->9),(2|->4),(3|->8),(4|->3),(5|->7),(6|->2),(7|->6),(8|->1),(9|->5)}),(5|->{(1|->3),(2|->7),(3|->2),(4|->6),(5|->1),(6|->5),(7|->9),(8|->4),(9|->8)}),(6|->{(1|->6),(2|->1),(3|->5),(4|->9),(5|->4),(6|->8),(7|->3),(8|->7),(9|->2)}),(7|->{(1|->4),(2|->8),(3|->3),(4|->7),(5|->2),(6|->6),(7|->1),(8|->5),(9|->9)}),(8|->{(1|->7),(2|->2),(3|->6),(4|->1),(5|->5),(6|->9),(7|->4),(8|->8),(9|->3)}),(9|->{(1|->1),(2|->5),(3|->9),(4|->4),(5|->8),(6|->3),(7|->7),(8|->2),(9|->6)})}\n",
+       "{(1|->{(1|->7),(2|->3),(3|->8),(4|->4),(5|->9),(6|->5),(7|->1),(8|->6),(9|->2)}),(2|->{(1|->4),(2|->9),(3|->5),(4|->1),(5|->6),(6|->2),(7|->7),(8|->3),(9|->8)}),(3|->{(1|->1),(2|->6),(3|->2),(4|->7),(5|->3),(6|->8),(7|->4),(8|->9),(9|->5)}),(4|->{(1|->3),(2|->8),(3|->4),(4|->9),(5|->5),(6|->1),(7|->6),(8|->2),(9|->7)}),(5|->{(1|->9),(2|->5),(3|->1),(4|->6),(5|->2),(6|->7),(7|->3),(8|->8),(9|->4)}),(6|->{(1|->6),(2|->2),(3|->7),(4|->3),(5|->8),(6|->4),(7|->9),(8|->5),(9|->1)}),(7|->{(1|->8),(2|->4),(3|->9),(4|->5),(5|->1),(6|->6),(7|->2),(8|->7),(9|->3)}),(8|->{(1|->5),(2|->1),(3|->6),(4|->2),(5|->7),(6|->3),(7|->8),(8|->4),(9|->9)}),(9|->{(1|->2),(2|->7),(3|->3),(4|->8),(5|->4),(6|->9),(7|->5),(8|->1),(9|->6)})}\n",
+       "{(1|->{(1|->2),(2|->7),(3|->3),(4|->8),(5|->4),(6|->9),(7|->5),(8|->1),(9|->6)}),(2|->{(1|->5),(2|->1),(3|->6),(4|->2),(5|->7),(6|->3),(7|->8),(8|->4),(9|->9)}),(3|->{(1|->8),(2|->4),(3|->9),(4|->5),(5|->1),(6|->6),(7|->2),(8|->7),(9|->3)}),(4|->{(1|->6),(2|->2),(3|->7),(4|->3),(5|->8),(6|->4),(7|->9),(8|->5),(9|->1)}),(5|->{(1|->9),(2|->5),(3|->1),(4|->6),(5|->2),(6|->7),(7|->3),(8|->8),(9|->4)}),(6|->{(1|->3),(2|->8),(3|->4),(4|->9),(5|->5),(6|->1),(7|->6),(8|->2),(9|->7)}),(7|->{(1|->1),(2|->6),(3|->2),(4|->7),(5|->3),(6|->8),(7|->4),(8|->9),(9|->5)}),(8|->{(1|->4),(2|->9),(3|->5),(4|->1),(5|->6),(6|->2),(7|->7),(8|->3),(9|->8)}),(9|->{(1|->7),(2|->3),(3|->8),(4|->4),(5|->9),(6|->5),(7|->1),(8|->6),(9|->2)})}\n",
+       "{(1|->{(1|->7),(2|->4),(3|->1),(4|->3),(5|->9),(6|->6),(7|->8),(8|->5),(9|->2)}),(2|->{(1|->3),(2|->9),(3|->6),(4|->8),(5|->5),(6|->2),(7|->4),(8|->1),(9|->7)}),(3|->{(1|->8),(2|->5),(3|->2),(4|->4),(5|->1),(6|->7),(7|->9),(8|->6),(9|->3)}),(4|->{(1|->4),(2|->1),(3|->7),(4|->9),(5|->6),(6|->3),(7|->5),(8|->2),(9|->8)}),(5|->{(1|->9),(2|->6),(3|->3),(4|->5),(5|->2),(6|->8),(7|->1),(8|->7),(9|->4)}),(6|->{(1|->5),(2|->2),(3|->8),(4|->1),(5|->7),(6|->4),(7|->6),(8|->3),(9|->9)}),(7|->{(1|->1),(2|->7),(3|->4),(4|->6),(5|->3),(6|->9),(7|->2),(8|->8),(9|->5)}),(8|->{(1|->6),(2|->3),(3|->9),(4|->2),(5|->8),(6|->5),(7|->7),(8|->4),(9|->1)}),(9|->{(1|->2),(2|->8),(3|->5),(4|->7),(5|->4),(6|->1),(7|->3),(8|->9),(9|->6)})}\n",
+       "{(1|->{(1|->2),(2|->8),(3|->5),(4|->7),(5|->4),(6|->1),(7|->3),(8|->9),(9|->6)}),(2|->{(1|->6),(2|->3),(3|->9),(4|->2),(5|->8),(6|->5),(7|->7),(8|->4),(9|->1)}),(3|->{(1|->1),(2|->7),(3|->4),(4|->6),(5|->3),(6|->9),(7|->2),(8|->8),(9|->5)}),(4|->{(1|->5),(2|->2),(3|->8),(4|->1),(5|->7),(6|->4),(7|->6),(8|->3),(9|->9)}),(5|->{(1|->9),(2|->6),(3|->3),(4|->5),(5|->2),(6|->8),(7|->1),(8|->7),(9|->4)}),(6|->{(1|->4),(2|->1),(3|->7),(4|->9),(5|->6),(6|->3),(7|->5),(8|->2),(9|->8)}),(7|->{(1|->8),(2|->5),(3|->2),(4|->4),(5|->1),(6|->7),(7|->9),(8|->6),(9|->3)}),(8|->{(1|->3),(2|->9),(3|->6),(4|->8),(5|->5),(6|->2),(7|->4),(8|->1),(9|->7)}),(9|->{(1|->7),(2|->4),(3|->1),(4|->3),(5|->9),(6|->6),(7|->8),(8|->5),(9|->2)})}\n",
+       "{(1|->{(1|->2),(2|->5),(3|->8),(4|->6),(5|->9),(6|->3),(7|->1),(8|->4),(9|->7)}),(2|->{(1|->7),(2|->1),(3|->4),(4|->2),(5|->5),(6|->8),(7|->6),(8|->9),(9|->3)}),(3|->{(1|->3),(2|->6),(3|->9),(4|->7),(5|->1),(6|->4),(7|->2),(8|->5),(9|->8)}),(4|->{(1|->8),(2|->2),(3|->5),(4|->3),(5|->6),(6|->9),(7|->7),(8|->1),(9|->4)}),(5|->{(1|->4),(2|->7),(3|->1),(4|->8),(5|->2),(6|->5),(7|->3),(8|->6),(9|->9)}),(6|->{(1|->9),(2|->3),(3|->6),(4|->4),(5|->7),(6|->1),(7|->8),(8|->2),(9|->5)}),(7|->{(1|->5),(2|->8),(3|->2),(4|->9),(5|->3),(6|->6),(7|->4),(8|->7),(9|->1)}),(8|->{(1|->1),(2|->4),(3|->7),(4|->5),(5|->8),(6|->2),(7|->9),(8|->3),(9|->6)}),(9|->{(1|->6),(2|->9),(3|->3),(4|->1),(5|->4),(6|->7),(7|->5),(8|->8),(9|->2)})}\n",
+       "{(1|->{(1|->6),(2|->9),(3|->3),(4|->1),(5|->4),(6|->7),(7|->5),(8|->8),(9|->2)}),(2|->{(1|->1),(2|->4),(3|->7),(4|->5),(5|->8),(6|->2),(7|->9),(8|->3),(9|->6)}),(3|->{(1|->5),(2|->8),(3|->2),(4|->9),(5|->3),(6|->6),(7|->4),(8|->7),(9|->1)}),(4|->{(1|->9),(2|->3),(3|->6),(4|->4),(5|->7),(6|->1),(7|->8),(8|->2),(9|->5)}),(5|->{(1|->4),(2|->7),(3|->1),(4|->8),(5|->2),(6|->5),(7|->3),(8|->6),(9|->9)}),(6|->{(1|->8),(2|->2),(3|->5),(4|->3),(5|->6),(6|->9),(7|->7),(8|->1),(9|->4)}),(7|->{(1|->3),(2|->6),(3|->9),(4|->7),(5|->1),(6|->4),(7|->2),(8|->5),(9|->8)}),(8|->{(1|->7),(2|->1),(3|->4),(4|->2),(5|->5),(6|->8),(7|->6),(8|->9),(9|->3)}),(9|->{(1|->2),(2|->5),(3|->8),(4|->6),(5|->9),(6|->3),(7|->1),(8|->4),(9|->7)})}\n",
+       "{(1|->{(1|->2),(2|->6),(3|->1),(4|->5),(5|->9),(6|->4),(7|->8),(8|->3),(9|->7)}),(2|->{(1|->8),(2|->3),(3|->7),(4|->2),(5|->6),(6|->1),(7|->5),(8|->9),(9|->4)}),(3|->{(1|->5),(2|->9),(3|->4),(4|->8),(5|->3),(6|->7),(7|->2),(8|->6),(9|->1)}),(4|->{(1|->7),(2|->2),(3|->6),(4|->1),(5|->5),(6|->9),(7|->4),(8|->8),(9|->3)}),(5|->{(1|->4),(2|->8),(3|->3),(4|->7),(5|->2),(6|->6),(7|->1),(8|->5),(9|->9)}),(6|->{(1|->1),(2|->5),(3|->9),(4|->4),(5|->8),(6|->3),(7|->7),(8|->2),(9|->6)}),(7|->{(1|->3),(2|->7),(3|->2),(4|->6),(5|->1),(6|->5),(7|->9),(8|->4),(9|->8)}),(8|->{(1|->9),(2|->4),(3|->8),(4|->3),(5|->7),(6|->2),(7|->6),(8|->1),(9|->5)}),(9|->{(1|->6),(2|->1),(3|->5),(4|->9),(5|->4),(6|->8),(7|->3),(8|->7),(9|->2)})}\n",
+       "{(1|->{(1|->6),(2|->1),(3|->5),(4|->9),(5|->4),(6|->8),(7|->3),(8|->7),(9|->2)}),(2|->{(1|->9),(2|->4),(3|->8),(4|->3),(5|->7),(6|->2),(7|->6),(8|->1),(9|->5)}),(3|->{(1|->3),(2|->7),(3|->2),(4|->6),(5|->1),(6|->5),(7|->9),(8|->4),(9|->8)}),(4|->{(1|->1),(2|->5),(3|->9),(4|->4),(5|->8),(6|->3),(7|->7),(8|->2),(9|->6)}),(5|->{(1|->4),(2|->8),(3|->3),(4|->7),(5|->2),(6|->6),(7|->1),(8|->5),(9|->9)}),(6|->{(1|->7),(2|->2),(3|->6),(4|->1),(5|->5),(6|->9),(7|->4),(8|->8),(9|->3)}),(7|->{(1|->5),(2|->9),(3|->4),(4|->8),(5|->3),(6|->7),(7|->2),(8|->6),(9|->1)}),(8|->{(1|->8),(2|->3),(3|->7),(4|->2),(5|->6),(6|->1),(7|->5),(8|->9),(9|->4)}),(9|->{(1|->2),(2|->6),(3|->1),(4|->5),(5|->9),(6|->4),(7|->8),(8|->3),(9|->7)})}\n",
+       "{(1|->{(1|->8),(2|->4),(3|->9),(4|->5),(5|->1),(6|->6),(7|->2),(8|->7),(9|->3)}),(2|->{(1|->5),(2|->1),(3|->6),(4|->2),(5|->7),(6|->3),(7|->8),(8|->4),(9|->9)}),(3|->{(1|->2),(2|->7),(3|->3),(4|->8),(5|->4),(6|->9),(7|->5),(8|->1),(9|->6)}),(4|->{(1|->4),(2|->9),(3|->5),(4|->1),(5|->6),(6|->2),(7|->7),(8|->3),(9|->8)}),(5|->{(1|->1),(2|->6),(3|->2),(4|->7),(5|->3),(6|->8),(7|->4),(8|->9),(9|->5)}),(6|->{(1|->7),(2|->3),(3|->8),(4|->4),(5|->9),(6|->5),(7|->1),(8|->6),(9|->2)}),(7|->{(1|->9),(2|->5),(3|->1),(4|->6),(5|->2),(6|->7),(7|->3),(8|->8),(9|->4)}),(8|->{(1|->6),(2|->2),(3|->7),(4|->3),(5|->8),(6|->4),(7|->9),(8|->5),(9|->1)}),(9|->{(1|->3),(2|->8),(3|->4),(4|->9),(5|->5),(6|->1),(7|->6),(8|->2),(9|->7)})}\n",
+       "{(1|->{(1|->3),(2|->8),(3|->4),(4|->9),(5|->5),(6|->1),(7|->6),(8|->2),(9|->7)}),(2|->{(1|->6),(2|->2),(3|->7),(4|->3),(5|->8),(6|->4),(7|->9),(8|->5),(9|->1)}),(3|->{(1|->9),(2|->5),(3|->1),(4|->6),(5|->2),(6|->7),(7|->3),(8|->8),(9|->4)}),(4|->{(1|->7),(2|->3),(3|->8),(4|->4),(5|->9),(6|->5),(7|->1),(8|->6),(9|->2)}),(5|->{(1|->1),(2|->6),(3|->2),(4|->7),(5|->3),(6|->8),(7|->4),(8|->9),(9|->5)}),(6|->{(1|->4),(2|->9),(3|->5),(4|->1),(5|->6),(6|->2),(7|->7),(8|->3),(9|->8)}),(7|->{(1|->2),(2|->7),(3|->3),(4|->8),(5|->4),(6|->9),(7|->5),(8|->1),(9|->6)}),(8|->{(1|->5),(2|->1),(3|->6),(4|->2),(5|->7),(6|->3),(7|->8),(8|->4),(9|->9)}),(9|->{(1|->8),(2|->4),(3|->9),(4|->5),(5|->1),(6|->6),(7|->2),(8|->7),(9|->3)})}\n",
+       "{(1|->{(1|->8),(2|->5),(3|->2),(4|->4),(5|->1),(6|->7),(7|->9),(8|->6),(9|->3)}),(2|->{(1|->4),(2|->1),(3|->7),(4|->9),(5|->6),(6|->3),(7|->5),(8|->2),(9|->8)}),(3|->{(1|->9),(2|->6),(3|->3),(4|->5),(5|->2),(6|->8),(7|->1),(8|->7),(9|->4)}),(4|->{(1|->5),(2|->2),(3|->8),(4|->1),(5|->7),(6|->4),(7|->6),(8|->3),(9|->9)}),(5|->{(1|->1),(2|->7),(3|->4),(4|->6),(5|->3),(6|->9),(7|->2),(8|->8),(9|->5)}),(6|->{(1|->6),(2|->3),(3|->9),(4|->2),(5|->8),(6|->5),(7|->7),(8|->4),(9|->1)}),(7|->{(1|->2),(2|->8),(3|->5),(4|->7),(5|->4),(6|->1),(7|->3),(8|->9),(9|->6)}),(8|->{(1|->7),(2|->4),(3|->1),(4|->3),(5|->9),(6|->6),(7|->8),(8|->5),(9|->2)}),(9|->{(1|->3),(2|->9),(3|->6),(4|->8),(5|->5),(6|->2),(7|->4),(8|->1),(9|->7)})}\n",
+       "{(1|->{(1|->3),(2|->9),(3|->6),(4|->8),(5|->5),(6|->2),(7|->4),(8|->1),(9|->7)}),(2|->{(1|->7),(2|->4),(3|->1),(4|->3),(5|->9),(6|->6),(7|->8),(8|->5),(9|->2)}),(3|->{(1|->2),(2|->8),(3|->5),(4|->7),(5|->4),(6|->1),(7|->3),(8|->9),(9|->6)}),(4|->{(1|->6),(2|->3),(3|->9),(4|->2),(5|->8),(6|->5),(7|->7),(8|->4),(9|->1)}),(5|->{(1|->1),(2|->7),(3|->4),(4|->6),(5|->3),(6|->9),(7|->2),(8|->8),(9|->5)}),(6|->{(1|->5),(2|->2),(3|->8),(4|->1),(5|->7),(6|->4),(7|->6),(8|->3),(9|->9)}),(7|->{(1|->9),(2|->6),(3|->3),(4|->5),(5|->2),(6|->8),(7|->1),(8|->7),(9|->4)}),(8|->{(1|->4),(2|->1),(3|->7),(4|->9),(5|->6),(6|->3),(7|->5),(8|->2),(9|->8)}),(9|->{(1|->8),(2|->5),(3|->2),(4|->4),(5|->1),(6|->7),(7|->9),(8|->6),(9|->3)})}\n",
+       "{(1|->{(1|->3),(2|->6),(3|->9),(4|->7),(5|->1),(6|->4),(7|->2),(8|->5),(9|->8)}),(2|->{(1|->8),(2|->2),(3|->5),(4|->3),(5|->6),(6|->9),(7|->7),(8|->1),(9|->4)}),(3|->{(1|->4),(2|->7),(3|->1),(4|->8),(5|->2),(6|->5),(7|->3),(8|->6),(9|->9)}),(4|->{(1|->9),(2|->3),(3|->6),(4|->4),(5|->7),(6|->1),(7|->8),(8|->2),(9|->5)}),(5|->{(1|->5),(2|->8),(3|->2),(4|->9),(5|->3),(6|->6),(7|->4),(8|->7),(9|->1)}),(6|->{(1|->1),(2|->4),(3|->7),(4|->5),(5|->8),(6|->2),(7|->9),(8|->3),(9|->6)}),(7|->{(1|->6),(2|->9),(3|->3),(4|->1),(5|->4),(6|->7),(7|->5),(8|->8),(9|->2)}),(8|->{(1|->2),(2|->5),(3|->8),(4|->6),(5|->9),(6|->3),(7|->1),(8|->4),(9|->7)}),(9|->{(1|->7),(2|->1),(3|->4),(4|->2),(5|->5),(6|->8),(7|->6),(8|->9),(9|->3)})}\n",
+       "{(1|->{(1|->7),(2|->1),(3|->4),(4|->2),(5|->5),(6|->8),(7|->6),(8|->9),(9|->3)}),(2|->{(1|->2),(2|->5),(3|->8),(4|->6),(5|->9),(6|->3),(7|->1),(8|->4),(9|->7)}),(3|->{(1|->6),(2|->9),(3|->3),(4|->1),(5|->4),(6|->7),(7|->5),(8|->8),(9|->2)}),(4|->{(1|->1),(2|->4),(3|->7),(4|->5),(5|->8),(6|->2),(7|->9),(8|->3),(9|->6)}),(5|->{(1|->5),(2|->8),(3|->2),(4|->9),(5|->3),(6|->6),(7|->4),(8|->7),(9|->1)}),(6|->{(1|->9),(2|->3),(3|->6),(4|->4),(5|->7),(6|->1),(7|->8),(8|->2),(9|->5)}),(7|->{(1|->4),(2|->7),(3|->1),(4|->8),(5|->2),(6|->5),(7|->3),(8|->6),(9|->9)}),(8|->{(1|->8),(2|->2),(3|->5),(4|->3),(5|->6),(6|->9),(7|->7),(8|->1),(9|->4)}),(9|->{(1|->3),(2|->6),(3|->9),(4|->7),(5|->1),(6|->4),(7|->2),(8|->5),(9|->8)})}\n",
+       "{(1|->{(1|->3),(2|->7),(3|->2),(4|->6),(5|->1),(6|->5),(7|->9),(8|->4),(9|->8)}),(2|->{(1|->9),(2|->4),(3|->8),(4|->3),(5|->7),(6|->2),(7|->6),(8|->1),(9|->5)}),(3|->{(1|->6),(2|->1),(3|->5),(4|->9),(5|->4),(6|->8),(7|->3),(8|->7),(9|->2)}),(4|->{(1|->8),(2|->3),(3|->7),(4|->2),(5|->6),(6|->1),(7|->5),(8|->9),(9|->4)}),(5|->{(1|->5),(2|->9),(3|->4),(4|->8),(5|->3),(6|->7),(7|->2),(8|->6),(9|->1)}),(6|->{(1|->2),(2|->6),(3|->1),(4|->5),(5|->9),(6|->4),(7|->8),(8|->3),(9|->7)}),(7|->{(1|->4),(2|->8),(3|->3),(4|->7),(5|->2),(6|->6),(7|->1),(8|->5),(9|->9)}),(8|->{(1|->1),(2|->5),(3|->9),(4|->4),(5|->8),(6|->3),(7|->7),(8|->2),(9|->6)}),(9|->{(1|->7),(2|->2),(3|->6),(4|->1),(5|->5),(6|->9),(7|->4),(8|->8),(9|->3)})}\n",
+       "{(1|->{(1|->7),(2|->2),(3|->6),(4|->1),(5|->5),(6|->9),(7|->4),(8|->8),(9|->3)}),(2|->{(1|->1),(2|->5),(3|->9),(4|->4),(5|->8),(6|->3),(7|->7),(8|->2),(9|->6)}),(3|->{(1|->4),(2|->8),(3|->3),(4|->7),(5|->2),(6|->6),(7|->1),(8|->5),(9|->9)}),(4|->{(1|->2),(2|->6),(3|->1),(4|->5),(5|->9),(6|->4),(7|->8),(8|->3),(9|->7)}),(5|->{(1|->5),(2|->9),(3|->4),(4|->8),(5|->3),(6|->7),(7|->2),(8|->6),(9|->1)}),(6|->{(1|->8),(2|->3),(3|->7),(4|->2),(5|->6),(6|->1),(7|->5),(8|->9),(9|->4)}),(7|->{(1|->6),(2|->1),(3|->5),(4|->9),(5|->4),(6|->8),(7|->3),(8|->7),(9|->2)}),(8|->{(1|->9),(2|->4),(3|->8),(4|->3),(5|->7),(6|->2),(7|->6),(8|->1),(9|->5)}),(9|->{(1|->3),(2|->7),(3|->2),(4|->6),(5|->1),(6|->5),(7|->9),(8|->4),(9|->8)})}\n",
+       "{(1|->{(1|->4),(2|->8),(3|->3),(4|->7),(5|->2),(6|->6),(7|->1),(8|->5),(9|->9)}),(2|->{(1|->1),(2|->5),(3|->9),(4|->4),(5|->8),(6|->3),(7|->7),(8|->2),(9|->6)}),(3|->{(1|->7),(2|->2),(3|->6),(4|->1),(5|->5),(6|->9),(7|->4),(8|->8),(9|->3)}),(4|->{(1|->9),(2|->4),(3|->8),(4|->3),(5|->7),(6|->2),(7|->6),(8|->1),(9|->5)}),(5|->{(1|->6),(2|->1),(3|->5),(4|->9),(5|->4),(6|->8),(7|->3),(8|->7),(9|->2)}),(6|->{(1|->3),(2|->7),(3|->2),(4|->6),(5|->1),(6|->5),(7|->9),(8|->4),(9|->8)}),(7|->{(1|->5),(2|->9),(3|->4),(4|->8),(5|->3),(6|->7),(7|->2),(8|->6),(9|->1)}),(8|->{(1|->2),(2|->6),(3|->1),(4|->5),(5|->9),(6|->4),(7|->8),(8|->3),(9|->7)}),(9|->{(1|->8),(2|->3),(3|->7),(4|->2),(5|->6),(6|->1),(7|->5),(8|->9),(9|->4)})}\n",
+       "{(1|->{(1|->8),(2|->3),(3|->7),(4|->2),(5|->6),(6|->1),(7|->5),(8|->9),(9|->4)}),(2|->{(1|->2),(2|->6),(3|->1),(4|->5),(5|->9),(6|->4),(7|->8),(8|->3),(9|->7)}),(3|->{(1|->5),(2|->9),(3|->4),(4|->8),(5|->3),(6|->7),(7|->2),(8|->6),(9|->1)}),(4|->{(1|->3),(2|->7),(3|->2),(4|->6),(5|->1),(6|->5),(7|->9),(8|->4),(9|->8)}),(5|->{(1|->6),(2|->1),(3|->5),(4|->9),(5|->4),(6|->8),(7|->3),(8|->7),(9|->2)}),(6|->{(1|->9),(2|->4),(3|->8),(4|->3),(5|->7),(6|->2),(7|->6),(8|->1),(9|->5)}),(7|->{(1|->7),(2|->2),(3|->6),(4|->1),(5|->5),(6|->9),(7|->4),(8|->8),(9|->3)}),(8|->{(1|->1),(2|->5),(3|->9),(4|->4),(5|->8),(6|->3),(7|->7),(8|->2),(9|->6)}),(9|->{(1|->4),(2|->8),(3|->3),(4|->7),(5|->2),(6|->6),(7|->1),(8|->5),(9|->9)})}\n",
+       "{(1|->{(1|->9),(2|->5),(3|->1),(4|->6),(5|->2),(6|->7),(7|->3),(8|->8),(9|->4)}),(2|->{(1|->6),(2|->2),(3|->7),(4|->3),(5|->8),(6|->4),(7|->9),(8|->5),(9|->1)}),(3|->{(1|->3),(2|->8),(3|->4),(4|->9),(5|->5),(6|->1),(7|->6),(8|->2),(9|->7)}),(4|->{(1|->5),(2|->1),(3|->6),(4|->2),(5|->7),(6|->3),(7|->8),(8|->4),(9|->9)}),(5|->{(1|->2),(2|->7),(3|->3),(4|->8),(5|->4),(6|->9),(7|->5),(8|->1),(9|->6)}),(6|->{(1|->8),(2|->4),(3|->9),(4|->5),(5|->1),(6|->6),(7|->2),(8|->7),(9|->3)}),(7|->{(1|->1),(2|->6),(3|->2),(4|->7),(5|->3),(6|->8),(7|->4),(8|->9),(9|->5)}),(8|->{(1|->7),(2|->3),(3|->8),(4|->4),(5|->9),(6|->5),(7|->1),(8|->6),(9|->2)}),(9|->{(1|->4),(2|->9),(3|->5),(4|->1),(5|->6),(6|->2),(7|->7),(8|->3),(9|->8)})}\n",
+       "{(1|->{(1|->4),(2|->9),(3|->5),(4|->1),(5|->6),(6|->2),(7|->7),(8|->3),(9|->8)}),(2|->{(1|->7),(2|->3),(3|->8),(4|->4),(5|->9),(6|->5),(7|->1),(8|->6),(9|->2)}),(3|->{(1|->1),(2|->6),(3|->2),(4|->7),(5|->3),(6|->8),(7|->4),(8|->9),(9|->5)}),(4|->{(1|->8),(2|->4),(3|->9),(4|->5),(5|->1),(6|->6),(7|->2),(8|->7),(9|->3)}),(5|->{(1|->2),(2|->7),(3|->3),(4|->8),(5|->4),(6|->9),(7|->5),(8|->1),(9|->6)}),(6|->{(1|->5),(2|->1),(3|->6),(4|->2),(5|->7),(6|->3),(7|->8),(8|->4),(9|->9)}),(7|->{(1|->3),(2|->8),(3|->4),(4|->9),(5|->5),(6|->1),(7|->6),(8|->2),(9|->7)}),(8|->{(1|->6),(2|->2),(3|->7),(4|->3),(5|->8),(6|->4),(7|->9),(8|->5),(9|->1)}),(9|->{(1|->9),(2|->5),(3|->1),(4|->6),(5|->2),(6|->7),(7|->3),(8|->8),(9|->4)})}\n",
+       "{(1|->{(1|->4),(2|->1),(3|->7),(4|->9),(5|->6),(6|->3),(7|->5),(8|->2),(9|->8)}),(2|->{(1|->8),(2|->5),(3|->2),(4|->4),(5|->1),(6|->7),(7|->9),(8|->6),(9|->3)}),(3|->{(1|->3),(2|->9),(3|->6),(4|->8),(5|->5),(6|->2),(7|->4),(8|->1),(9|->7)}),(4|->{(1|->7),(2|->4),(3|->1),(4|->3),(5|->9),(6|->6),(7|->8),(8|->5),(9|->2)}),(5|->{(1|->2),(2|->8),(3|->5),(4|->7),(5|->4),(6|->1),(7|->3),(8|->9),(9|->6)}),(6|->{(1|->6),(2|->3),(3|->9),(4|->2),(5|->8),(6|->5),(7|->7),(8|->4),(9|->1)}),(7|->{(1|->1),(2|->7),(3|->4),(4|->6),(5|->3),(6|->9),(7|->2),(8|->8),(9|->5)}),(8|->{(1|->5),(2|->2),(3|->8),(4|->1),(5|->7),(6|->4),(7|->6),(8|->3),(9|->9)}),(9|->{(1|->9),(2|->6),(3|->3),(4|->5),(5|->2),(6|->8),(7|->1),(8|->7),(9|->4)})}\n",
+       "{(1|->{(1|->9),(2|->6),(3|->3),(4|->5),(5|->2),(6|->8),(7|->1),(8|->7),(9|->4)}),(2|->{(1|->5),(2|->2),(3|->8),(4|->1),(5|->7),(6|->4),(7|->6),(8|->3),(9|->9)}),(3|->{(1|->1),(2|->7),(3|->4),(4|->6),(5|->3),(6|->9),(7|->2),(8|->8),(9|->5)}),(4|->{(1|->6),(2|->3),(3|->9),(4|->2),(5|->8),(6|->5),(7|->7),(8|->4),(9|->1)}),(5|->{(1|->2),(2|->8),(3|->5),(4|->7),(5|->4),(6|->1),(7|->3),(8|->9),(9|->6)}),(6|->{(1|->7),(2|->4),(3|->1),(4|->3),(5|->9),(6|->6),(7|->8),(8|->5),(9|->2)}),(7|->{(1|->3),(2|->9),(3|->6),(4|->8),(5|->5),(6|->2),(7|->4),(8|->1),(9|->7)}),(8|->{(1|->8),(2|->5),(3|->2),(4|->4),(5|->1),(6|->7),(7|->9),(8|->6),(9|->3)}),(9|->{(1|->4),(2|->1),(3|->7),(4|->9),(5|->6),(6|->3),(7|->5),(8|->2),(9|->8)})}\n",
+       "{(1|->{(1|->8),(2|->2),(3|->5),(4|->3),(5|->6),(6|->9),(7|->7),(8|->1),(9|->4)}),(2|->{(1|->3),(2|->6),(3|->9),(4|->7),(5|->1),(6|->4),(7|->2),(8|->5),(9|->8)}),(3|->{(1|->7),(2|->1),(3|->4),(4|->2),(5|->5),(6|->8),(7|->6),(8|->9),(9|->3)}),(4|->{(1|->2),(2|->5),(3|->8),(4|->6),(5|->9),(6|->3),(7|->1),(8|->4),(9|->7)}),(5|->{(1|->6),(2|->9),(3|->3),(4|->1),(5|->4),(6|->7),(7|->5),(8|->8),(9|->2)}),(6|->{(1|->1),(2|->4),(3|->7),(4|->5),(5|->8),(6|->2),(7|->9),(8|->3),(9|->6)}),(7|->{(1|->5),(2|->8),(3|->2),(4|->9),(5|->3),(6|->6),(7|->4),(8|->7),(9|->1)}),(8|->{(1|->9),(2|->3),(3|->6),(4|->4),(5|->7),(6|->1),(7|->8),(8|->2),(9|->5)}),(9|->{(1|->4),(2|->7),(3|->1),(4|->8),(5|->2),(6|->5),(7|->3),(8|->6),(9|->9)})}\n",
+       "{(1|->{(1|->4),(2|->7),(3|->1),(4|->8),(5|->2),(6|->5),(7|->3),(8|->6),(9|->9)}),(2|->{(1|->9),(2|->3),(3|->6),(4|->4),(5|->7),(6|->1),(7|->8),(8|->2),(9|->5)}),(3|->{(1|->5),(2|->8),(3|->2),(4|->9),(5|->3),(6|->6),(7|->4),(8|->7),(9|->1)}),(4|->{(1|->1),(2|->4),(3|->7),(4|->5),(5|->8),(6|->2),(7|->9),(8|->3),(9|->6)}),(5|->{(1|->6),(2|->9),(3|->3),(4|->1),(5|->4),(6|->7),(7|->5),(8|->8),(9|->2)}),(6|->{(1|->2),(2|->5),(3|->8),(4|->6),(5|->9),(6|->3),(7|->1),(8|->4),(9|->7)}),(7|->{(1|->7),(2|->1),(3|->4),(4|->2),(5|->5),(6|->8),(7|->6),(8|->9),(9|->3)}),(8|->{(1|->3),(2|->6),(3|->9),(4|->7),(5|->1),(6|->4),(7|->2),(8|->5),(9|->8)}),(9|->{(1|->8),(2|->2),(3|->5),(4|->3),(5|->6),(6|->9),(7|->7),(8|->1),(9|->4)})}\n",
+       "{(1|->{(1|->9),(2|->3),(3|->6),(4|->4),(5|->7),(6|->1),(7|->8),(8|->2),(9|->5)}),(2|->{(1|->4),(2|->7),(3|->1),(4|->8),(5|->2),(6|->5),(7|->3),(8|->6),(9|->9)}),(3|->{(1|->8),(2|->2),(3|->5),(4|->3),(5|->6),(6|->9),(7|->7),(8|->1),(9|->4)}),(4|->{(1|->3),(2|->6),(3|->9),(4|->7),(5|->1),(6|->4),(7|->2),(8|->5),(9|->8)}),(5|->{(1|->7),(2|->1),(3|->4),(4|->2),(5|->5),(6|->8),(7|->6),(8|->9),(9|->3)}),(6|->{(1|->2),(2|->5),(3|->8),(4|->6),(5|->9),(6|->3),(7|->1),(8|->4),(9|->7)}),(7|->{(1|->6),(2|->9),(3|->3),(4|->1),(5|->4),(6|->7),(7|->5),(8|->8),(9|->2)}),(8|->{(1|->1),(2|->4),(3|->7),(4|->5),(5|->8),(6|->2),(7|->9),(8|->3),(9|->6)}),(9|->{(1|->5),(2|->8),(3|->2),(4|->9),(5|->3),(6|->6),(7|->4),(8|->7),(9|->1)})}\n",
+       "{(1|->{(1|->5),(2|->8),(3|->2),(4|->9),(5|->3),(6|->6),(7|->4),(8|->7),(9|->1)}),(2|->{(1|->1),(2|->4),(3|->7),(4|->5),(5|->8),(6|->2),(7|->9),(8|->3),(9|->6)}),(3|->{(1|->6),(2|->9),(3|->3),(4|->1),(5|->4),(6|->7),(7|->5),(8|->8),(9|->2)}),(4|->{(1|->2),(2|->5),(3|->8),(4|->6),(5|->9),(6|->3),(7|->1),(8|->4),(9|->7)}),(5|->{(1|->7),(2|->1),(3|->4),(4|->2),(5|->5),(6|->8),(7|->6),(8|->9),(9|->3)}),(6|->{(1|->3),(2|->6),(3|->9),(4|->7),(5|->1),(6|->4),(7|->2),(8|->5),(9|->8)}),(7|->{(1|->8),(2|->2),(3|->5),(4|->3),(5|->6),(6|->9),(7|->7),(8|->1),(9|->4)}),(8|->{(1|->4),(2|->7),(3|->1),(4|->8),(5|->2),(6|->5),(7|->3),(8|->6),(9|->9)}),(9|->{(1|->9),(2|->3),(3|->6),(4|->4),(5|->7),(6|->1),(7|->8),(8|->2),(9|->5)})}\n",
+       "{(1|->{(1|->9),(2|->4),(3|->8),(4|->3),(5|->7),(6|->2),(7|->6),(8|->1),(9|->5)}),(2|->{(1|->3),(2|->7),(3|->2),(4|->6),(5|->1),(6|->5),(7|->9),(8|->4),(9|->8)}),(3|->{(1|->6),(2|->1),(3|->5),(4|->9),(5|->4),(6|->8),(7|->3),(8|->7),(9|->2)}),(4|->{(1|->4),(2|->8),(3|->3),(4|->7),(5|->2),(6|->6),(7|->1),(8|->5),(9|->9)}),(5|->{(1|->7),(2|->2),(3|->6),(4|->1),(5|->5),(6|->9),(7|->4),(8|->8),(9|->3)}),(6|->{(1|->1),(2|->5),(3|->9),(4|->4),(5|->8),(6|->3),(7|->7),(8|->2),(9|->6)}),(7|->{(1|->8),(2|->3),(3|->7),(4|->2),(5|->6),(6|->1),(7|->5),(8|->9),(9|->4)}),(8|->{(1|->2),(2|->6),(3|->1),(4|->5),(5|->9),(6|->4),(7|->8),(8|->3),(9|->7)}),(9|->{(1|->5),(2|->9),(3|->4),(4|->8),(5|->3),(6|->7),(7|->2),(8|->6),(9|->1)})}\n",
+       "{(1|->{(1|->5),(2|->9),(3|->4),(4|->8),(5|->3),(6|->7),(7|->2),(8|->6),(9|->1)}),(2|->{(1|->2),(2|->6),(3|->1),(4|->5),(5|->9),(6|->4),(7|->8),(8|->3),(9|->7)}),(3|->{(1|->8),(2|->3),(3|->7),(4|->2),(5|->6),(6|->1),(7|->5),(8|->9),(9|->4)}),(4|->{(1|->1),(2|->5),(3|->9),(4|->4),(5|->8),(6|->3),(7|->7),(8|->2),(9|->6)}),(5|->{(1|->7),(2|->2),(3|->6),(4|->1),(5|->5),(6|->9),(7|->4),(8|->8),(9|->3)}),(6|->{(1|->4),(2|->8),(3|->3),(4|->7),(5|->2),(6|->6),(7|->1),(8|->5),(9|->9)}),(7|->{(1|->6),(2|->1),(3|->5),(4|->9),(5|->4),(6|->8),(7|->3),(8|->7),(9|->2)}),(8|->{(1|->3),(2|->7),(3|->2),(4|->6),(5|->1),(6|->5),(7|->9),(8|->4),(9|->8)}),(9|->{(1|->9),(2|->4),(3|->8),(4|->3),(5|->7),(6|->2),(7|->6),(8|->1),(9|->5)})}\n",
+       "{(1|->{(1|->5),(2|->1),(3|->6),(4|->2),(5|->7),(6|->3),(7|->8),(8|->4),(9|->9)}),(2|->{(1|->8),(2|->4),(3|->9),(4|->5),(5|->1),(6|->6),(7|->2),(8|->7),(9|->3)}),(3|->{(1|->2),(2|->7),(3|->3),(4|->8),(5|->4),(6|->9),(7|->5),(8|->1),(9|->6)}),(4|->{(1|->9),(2|->5),(3|->1),(4|->6),(5|->2),(6|->7),(7|->3),(8|->8),(9|->4)}),(5|->{(1|->3),(2|->8),(3|->4),(4|->9),(5|->5),(6|->1),(7|->6),(8|->2),(9|->7)}),(6|->{(1|->6),(2|->2),(3|->7),(4|->3),(5|->8),(6|->4),(7|->9),(8|->5),(9|->1)}),(7|->{(1|->4),(2|->9),(3|->5),(4|->1),(5|->6),(6|->2),(7|->7),(8|->3),(9|->8)}),(8|->{(1|->7),(2|->3),(3|->8),(4|->4),(5|->9),(6|->5),(7|->1),(8|->6),(9|->2)}),(9|->{(1|->1),(2|->6),(3|->2),(4|->7),(5|->3),(6|->8),(7|->4),(8|->9),(9|->5)})}\n",
+       "{(1|->{(1|->1),(2|->6),(3|->2),(4|->7),(5|->3),(6|->8),(7|->4),(8|->9),(9|->5)}),(2|->{(1|->7),(2|->3),(3|->8),(4|->4),(5|->9),(6|->5),(7|->1),(8|->6),(9|->2)}),(3|->{(1|->4),(2|->9),(3|->5),(4|->1),(5|->6),(6|->2),(7|->7),(8|->3),(9|->8)}),(4|->{(1|->6),(2|->2),(3|->7),(4|->3),(5|->8),(6|->4),(7|->9),(8|->5),(9|->1)}),(5|->{(1|->3),(2|->8),(3|->4),(4|->9),(5|->5),(6|->1),(7|->6),(8|->2),(9|->7)}),(6|->{(1|->9),(2|->5),(3|->1),(4|->6),(5|->2),(6|->7),(7|->3),(8|->8),(9|->4)}),(7|->{(1|->2),(2|->7),(3|->3),(4|->8),(5|->4),(6|->9),(7|->5),(8|->1),(9|->6)}),(8|->{(1|->8),(2|->4),(3|->9),(4|->5),(5|->1),(6|->6),(7|->2),(8|->7),(9|->3)}),(9|->{(1|->5),(2|->1),(3|->6),(4|->2),(5|->7),(6|->3),(7|->8),(8|->4),(9|->9)})}\n",
+       "{(1|->{(1|->5),(2|->2),(3|->8),(4|->1),(5|->7),(6|->4),(7|->6),(8|->3),(9|->9)}),(2|->{(1|->9),(2|->6),(3|->3),(4|->5),(5|->2),(6|->8),(7|->1),(8|->7),(9|->4)}),(3|->{(1|->4),(2|->1),(3|->7),(4|->9),(5|->6),(6|->3),(7|->5),(8|->2),(9|->8)}),(4|->{(1|->8),(2|->5),(3|->2),(4|->4),(5|->1),(6|->7),(7|->9),(8|->6),(9|->3)}),(5|->{(1|->3),(2|->9),(3|->6),(4|->8),(5|->5),(6|->2),(7|->4),(8|->1),(9|->7)}),(6|->{(1|->7),(2|->4),(3|->1),(4|->3),(5|->9),(6|->6),(7|->8),(8|->5),(9|->2)}),(7|->{(1|->2),(2|->8),(3|->5),(4|->7),(5|->4),(6|->1),(7|->3),(8|->9),(9|->6)}),(8|->{(1|->6),(2|->3),(3|->9),(4|->2),(5|->8),(6|->5),(7|->7),(8|->4),(9|->1)}),(9|->{(1|->1),(2|->7),(3|->4),(4|->6),(5|->3),(6|->9),(7|->2),(8|->8),(9|->5)})}\n",
+       "{(1|->{(1|->1),(2|->7),(3|->4),(4|->6),(5|->3),(6|->9),(7|->2),(8|->8),(9|->5)}),(2|->{(1|->6),(2|->3),(3|->9),(4|->2),(5|->8),(6|->5),(7|->7),(8|->4),(9|->1)}),(3|->{(1|->2),(2|->8),(3|->5),(4|->7),(5|->4),(6|->1),(7|->3),(8|->9),(9|->6)}),(4|->{(1|->7),(2|->4),(3|->1),(4|->3),(5|->9),(6|->6),(7|->8),(8|->5),(9|->2)}),(5|->{(1|->3),(2|->9),(3|->6),(4|->8),(5|->5),(6|->2),(7|->4),(8|->1),(9|->7)}),(6|->{(1|->8),(2|->5),(3|->2),(4|->4),(5|->1),(6|->7),(7|->9),(8|->6),(9|->3)}),(7|->{(1|->4),(2|->1),(3|->7),(4|->9),(5|->6),(6|->3),(7|->5),(8|->2),(9|->8)}),(8|->{(1|->9),(2|->6),(3|->3),(4|->5),(5|->2),(6|->8),(7|->1),(8|->7),(9|->4)}),(9|->{(1|->5),(2|->2),(3|->8),(4|->1),(5|->7),(6|->4),(7|->6),(8|->3),(9|->9)})}\n",
+       "{(1|->{(1|->6),(2|->3),(3|->9),(4|->2),(5|->8),(6|->5),(7|->7),(8|->4),(9|->1)}),(2|->{(1|->1),(2|->7),(3|->4),(4|->6),(5|->3),(6|->9),(7|->2),(8|->8),(9|->5)}),(3|->{(1|->5),(2|->2),(3|->8),(4|->1),(5|->7),(6|->4),(7|->6),(8|->3),(9|->9)}),(4|->{(1|->9),(2|->6),(3|->3),(4|->5),(5|->2),(6|->8),(7|->1),(8|->7),(9|->4)}),(5|->{(1|->4),(2|->1),(3|->7),(4|->9),(5|->6),(6|->3),(7|->5),(8|->2),(9|->8)}),(6|->{(1|->8),(2|->5),(3|->2),(4|->4),(5|->1),(6|->7),(7|->9),(8|->6),(9|->3)}),(7|->{(1|->3),(2|->9),(3|->6),(4|->8),(5|->5),(6|->2),(7|->4),(8|->1),(9|->7)}),(8|->{(1|->7),(2|->4),(3|->1),(4|->3),(5|->9),(6|->6),(7|->8),(8|->5),(9|->2)}),(9|->{(1|->2),(2|->8),(3|->5),(4|->7),(5|->4),(6|->1),(7|->3),(8|->9),(9|->6)})}\n",
+       "{(1|->{(1|->2),(2|->8),(3|->5),(4|->7),(5|->4),(6|->1),(7|->3),(8|->9),(9|->6)}),(2|->{(1|->7),(2|->4),(3|->1),(4|->3),(5|->9),(6|->6),(7|->8),(8|->5),(9|->2)}),(3|->{(1|->3),(2|->9),(3|->6),(4|->8),(5|->5),(6|->2),(7|->4),(8|->1),(9|->7)}),(4|->{(1|->8),(2|->5),(3|->2),(4|->4),(5|->1),(6|->7),(7|->9),(8|->6),(9|->3)}),(5|->{(1|->4),(2|->1),(3|->7),(4|->9),(5|->6),(6|->3),(7|->5),(8|->2),(9|->8)}),(6|->{(1|->9),(2|->6),(3|->3),(4|->5),(5|->2),(6|->8),(7|->1),(8|->7),(9|->4)}),(7|->{(1|->5),(2|->2),(3|->8),(4|->1),(5|->7),(6|->4),(7|->6),(8|->3),(9|->9)}),(8|->{(1|->1),(2|->7),(3|->4),(4|->6),(5|->3),(6|->9),(7|->2),(8|->8),(9|->5)}),(9|->{(1|->6),(2|->3),(3|->9),(4|->2),(5|->8),(6|->5),(7|->7),(8|->4),(9|->1)})}\n",
+       "{(1|->{(1|->1),(2|->4),(3|->7),(4|->5),(5|->8),(6|->2),(7|->9),(8|->3),(9|->6)}),(2|->{(1|->5),(2|->8),(3|->2),(4|->9),(5|->3),(6|->6),(7|->4),(8|->7),(9|->1)}),(3|->{(1|->9),(2|->3),(3|->6),(4|->4),(5|->7),(6|->1),(7|->8),(8|->2),(9|->5)}),(4|->{(1|->4),(2|->7),(3|->1),(4|->8),(5|->2),(6|->5),(7|->3),(8|->6),(9|->9)}),(5|->{(1|->8),(2|->2),(3|->5),(4|->3),(5|->6),(6|->9),(7|->7),(8|->1),(9|->4)}),(6|->{(1|->3),(2|->6),(3|->9),(4|->7),(5|->1),(6|->4),(7|->2),(8|->5),(9|->8)}),(7|->{(1|->7),(2|->1),(3|->4),(4|->2),(5|->5),(6|->8),(7|->6),(8|->9),(9|->3)}),(8|->{(1|->2),(2|->5),(3|->8),(4|->6),(5|->9),(6|->3),(7|->1),(8|->4),(9|->7)}),(9|->{(1|->6),(2|->9),(3|->3),(4|->1),(5|->4),(6|->7),(7|->5),(8|->8),(9|->2)})}\n",
+       "{(1|->{(1|->6),(2|->9),(3|->3),(4|->1),(5|->4),(6|->7),(7|->5),(8|->8),(9|->2)}),(2|->{(1|->2),(2|->5),(3|->8),(4|->6),(5|->9),(6|->3),(7|->1),(8|->4),(9|->7)}),(3|->{(1|->7),(2|->1),(3|->4),(4|->2),(5|->5),(6|->8),(7|->6),(8|->9),(9|->3)}),(4|->{(1|->3),(2|->6),(3|->9),(4|->7),(5|->1),(6|->4),(7|->2),(8|->5),(9|->8)}),(5|->{(1|->8),(2|->2),(3|->5),(4|->3),(5|->6),(6|->9),(7|->7),(8|->1),(9|->4)}),(6|->{(1|->4),(2|->7),(3|->1),(4|->8),(5|->2),(6|->5),(7|->3),(8|->6),(9|->9)}),(7|->{(1|->9),(2|->3),(3|->6),(4|->4),(5|->7),(6|->1),(7|->8),(8|->2),(9|->5)}),(8|->{(1|->5),(2|->8),(3|->2),(4|->9),(5|->3),(6|->6),(7|->4),(8|->7),(9|->1)}),(9|->{(1|->1),(2|->4),(3|->7),(4|->5),(5|->8),(6|->2),(7|->9),(8|->3),(9|->6)})}\n",
+       "{(1|->{(1|->6),(2|->1),(3|->5),(4|->9),(5|->4),(6|->8),(7|->3),(8|->7),(9|->2)}),(2|->{(1|->3),(2|->7),(3|->2),(4|->6),(5|->1),(6|->5),(7|->9),(8|->4),(9|->8)}),(3|->{(1|->9),(2|->4),(3|->8),(4|->3),(5|->7),(6|->2),(7|->6),(8|->1),(9|->5)}),(4|->{(1|->2),(2|->6),(3|->1),(4|->5),(5|->9),(6|->4),(7|->8),(8|->3),(9|->7)}),(5|->{(1|->8),(2|->3),(3|->7),(4|->2),(5|->6),(6|->1),(7|->5),(8|->9),(9|->4)}),(6|->{(1|->5),(2|->9),(3|->4),(4|->8),(5|->3),(6|->7),(7|->2),(8|->6),(9|->1)}),(7|->{(1|->7),(2|->2),(3|->6),(4|->1),(5|->5),(6|->9),(7|->4),(8|->8),(9|->3)}),(8|->{(1|->4),(2|->8),(3|->3),(4|->7),(5|->2),(6|->6),(7|->1),(8|->5),(9|->9)}),(9|->{(1|->1),(2|->5),(3|->9),(4|->4),(5|->8),(6|->3),(7|->7),(8|->2),(9|->6)})}\n",
+       "{(1|->{(1|->1),(2|->5),(3|->9),(4|->4),(5|->8),(6|->3),(7|->7),(8|->2),(9|->6)}),(2|->{(1|->4),(2|->8),(3|->3),(4|->7),(5|->2),(6|->6),(7|->1),(8|->5),(9|->9)}),(3|->{(1|->7),(2|->2),(3|->6),(4|->1),(5|->5),(6|->9),(7|->4),(8|->8),(9|->3)}),(4|->{(1|->5),(2|->9),(3|->4),(4|->8),(5|->3),(6|->7),(7|->2),(8|->6),(9|->1)}),(5|->{(1|->8),(2|->3),(3|->7),(4|->2),(5|->6),(6|->1),(7|->5),(8|->9),(9|->4)}),(6|->{(1|->2),(2|->6),(3|->1),(4|->5),(5|->9),(6|->4),(7|->8),(8|->3),(9|->7)}),(7|->{(1|->9),(2|->4),(3|->8),(4|->3),(5|->7),(6|->2),(7|->6),(8|->1),(9|->5)}),(8|->{(1|->3),(2|->7),(3|->2),(4|->6),(5|->1),(6|->5),(7|->9),(8|->4),(9|->8)}),(9|->{(1|->6),(2|->1),(3|->5),(4|->9),(5|->4),(6|->8),(7|->3),(8|->7),(9|->2)})}\n",
+       "{(1|->{(1|->2),(2|->7),(3|->3),(4|->8),(5|->4),(6|->9),(7|->5),(8|->1),(9|->6)}),(2|->{(1|->8),(2|->4),(3|->9),(4|->5),(5|->1),(6|->6),(7|->2),(8|->7),(9|->3)}),(3|->{(1|->5),(2|->1),(3|->6),(4|->2),(5|->7),(6|->3),(7|->8),(8|->4),(9|->9)}),(4|->{(1|->7),(2|->3),(3|->8),(4|->4),(5|->9),(6|->5),(7|->1),(8|->6),(9|->2)}),(5|->{(1|->4),(2|->9),(3|->5),(4|->1),(5|->6),(6|->2),(7|->7),(8|->3),(9|->8)}),(6|->{(1|->1),(2|->6),(3|->2),(4|->7),(5|->3),(6|->8),(7|->4),(8|->9),(9|->5)}),(7|->{(1|->3),(2|->8),(3|->4),(4|->9),(5|->5),(6|->1),(7|->6),(8|->2),(9|->7)}),(8|->{(1|->9),(2|->5),(3|->1),(4|->6),(5|->2),(6|->7),(7|->3),(8|->8),(9|->4)}),(9|->{(1|->6),(2|->2),(3|->7),(4|->3),(5|->8),(6|->4),(7|->9),(8|->5),(9|->1)})}\n",
+       "{(1|->{(1|->6),(2|->2),(3|->7),(4|->3),(5|->8),(6|->4),(7|->9),(8|->5),(9|->1)}),(2|->{(1|->9),(2|->5),(3|->1),(4|->6),(5|->2),(6|->7),(7|->3),(8|->8),(9|->4)}),(3|->{(1|->3),(2|->8),(3|->4),(4|->9),(5|->5),(6|->1),(7|->6),(8|->2),(9|->7)}),(4|->{(1|->1),(2|->6),(3|->2),(4|->7),(5|->3),(6|->8),(7|->4),(8|->9),(9|->5)}),(5|->{(1|->4),(2|->9),(3|->5),(4|->1),(5|->6),(6|->2),(7|->7),(8|->3),(9|->8)}),(6|->{(1|->7),(2|->3),(3|->8),(4|->4),(5|->9),(6|->5),(7|->1),(8|->6),(9|->2)}),(7|->{(1|->5),(2|->1),(3|->6),(4|->2),(5|->7),(6|->3),(7|->8),(8|->4),(9|->9)}),(8|->{(1|->8),(2|->4),(3|->9),(4|->5),(5|->1),(6|->6),(7|->2),(8|->7),(9|->3)}),(9|->{(1|->2),(2|->7),(3|->3),(4|->8),(5|->4),(6|->9),(7|->5),(8|->1),(9|->6)})}\n",
+       "{(1|->{(1|->3),(2|->8),(3|->4),(4|->9),(5|->5),(6|->1),(7|->6),(8|->2),(9|->7)}),(2|->{(1|->9),(2|->5),(3|->1),(4|->6),(5|->2),(6|->7),(7|->3),(8|->8),(9|->4)}),(3|->{(1|->6),(2|->2),(3|->7),(4|->3),(5|->8),(6|->4),(7|->9),(8|->5),(9|->1)}),(4|->{(1|->8),(2|->4),(3|->9),(4|->5),(5|->1),(6|->6),(7|->2),(8|->7),(9|->3)}),(5|->{(1|->5),(2|->1),(3|->6),(4|->2),(5|->7),(6|->3),(7|->8),(8|->4),(9|->9)}),(6|->{(1|->2),(2|->7),(3|->3),(4|->8),(5|->4),(6|->9),(7|->5),(8|->1),(9|->6)}),(7|->{(1|->4),(2|->9),(3|->5),(4|->1),(5|->6),(6|->2),(7|->7),(8|->3),(9|->8)}),(8|->{(1|->1),(2|->6),(3|->2),(4|->7),(5|->3),(6|->8),(7|->4),(8|->9),(9|->5)}),(9|->{(1|->7),(2|->3),(3|->8),(4|->4),(5|->9),(6|->5),(7|->1),(8|->6),(9|->2)})}\n",
+       "{(1|->{(1|->7),(2|->3),(3|->8),(4|->4),(5|->9),(6|->5),(7|->1),(8|->6),(9|->2)}),(2|->{(1|->1),(2|->6),(3|->2),(4|->7),(5|->3),(6|->8),(7|->4),(8|->9),(9|->5)}),(3|->{(1|->4),(2|->9),(3|->5),(4|->1),(5|->6),(6|->2),(7|->7),(8|->3),(9|->8)}),(4|->{(1|->2),(2|->7),(3|->3),(4|->8),(5|->4),(6|->9),(7|->5),(8|->1),(9|->6)}),(5|->{(1|->5),(2|->1),(3|->6),(4|->2),(5|->7),(6|->3),(7|->8),(8|->4),(9|->9)}),(6|->{(1|->8),(2|->4),(3|->9),(4|->5),(5|->1),(6|->6),(7|->2),(8|->7),(9|->3)}),(7|->{(1|->6),(2|->2),(3|->7),(4|->3),(5|->8),(6|->4),(7|->9),(8|->5),(9|->1)}),(8|->{(1|->9),(2|->5),(3|->1),(4|->6),(5|->2),(6|->7),(7|->3),(8|->8),(9|->4)}),(9|->{(1|->3),(2|->8),(3|->4),(4|->9),(5|->5),(6|->1),(7|->6),(8|->2),(9|->7)})}\n",
+       "{(1|->{(1|->3),(2|->9),(3|->6),(4|->8),(5|->5),(6|->2),(7|->4),(8|->1),(9|->7)}),(2|->{(1|->8),(2|->5),(3|->2),(4|->4),(5|->1),(6|->7),(7|->9),(8|->6),(9|->3)}),(3|->{(1|->4),(2|->1),(3|->7),(4|->9),(5|->6),(6|->3),(7|->5),(8|->2),(9|->8)}),(4|->{(1|->9),(2|->6),(3|->3),(4|->5),(5|->2),(6|->8),(7|->1),(8|->7),(9|->4)}),(5|->{(1|->5),(2|->2),(3|->8),(4|->1),(5|->7),(6|->4),(7|->6),(8|->3),(9|->9)}),(6|->{(1|->1),(2|->7),(3|->4),(4|->6),(5|->3),(6|->9),(7|->2),(8|->8),(9|->5)}),(7|->{(1|->6),(2|->3),(3|->9),(4|->2),(5|->8),(6|->5),(7|->7),(8|->4),(9|->1)}),(8|->{(1|->2),(2|->8),(3|->5),(4|->7),(5|->4),(6|->1),(7|->3),(8|->9),(9|->6)}),(9|->{(1|->7),(2|->4),(3|->1),(4|->3),(5|->9),(6|->6),(7|->8),(8|->5),(9|->2)})}\n",
+       "{(1|->{(1|->7),(2|->4),(3|->1),(4|->3),(5|->9),(6|->6),(7|->8),(8|->5),(9|->2)}),(2|->{(1|->2),(2|->8),(3|->5),(4|->7),(5|->4),(6|->1),(7|->3),(8|->9),(9|->6)}),(3|->{(1|->6),(2|->3),(3|->9),(4|->2),(5|->8),(6|->5),(7|->7),(8|->4),(9|->1)}),(4|->{(1|->1),(2|->7),(3|->4),(4|->6),(5|->3),(6|->9),(7|->2),(8|->8),(9|->5)}),(5|->{(1|->5),(2|->2),(3|->8),(4|->1),(5|->7),(6|->4),(7|->6),(8|->3),(9|->9)}),(6|->{(1|->9),(2|->6),(3|->3),(4|->5),(5|->2),(6|->8),(7|->1),(8|->7),(9|->4)}),(7|->{(1|->4),(2|->1),(3|->7),(4|->9),(5|->6),(6|->3),(7|->5),(8|->2),(9|->8)}),(8|->{(1|->8),(2|->5),(3|->2),(4|->4),(5|->1),(6|->7),(7|->9),(8|->6),(9|->3)}),(9|->{(1|->3),(2|->9),(3|->6),(4|->8),(5|->5),(6|->2),(7|->4),(8|->1),(9|->7)})}\n",
+       "{(1|->{(1|->7),(2|->1),(3|->4),(4|->2),(5|->5),(6|->8),(7|->6),(8|->9),(9|->3)}),(2|->{(1|->3),(2|->6),(3|->9),(4|->7),(5|->1),(6|->4),(7|->2),(8|->5),(9|->8)}),(3|->{(1|->8),(2|->2),(3|->5),(4|->3),(5|->6),(6|->9),(7|->7),(8|->1),(9|->4)}),(4|->{(1|->4),(2|->7),(3|->1),(4|->8),(5|->2),(6|->5),(7|->3),(8|->6),(9|->9)}),(5|->{(1|->9),(2|->3),(3|->6),(4|->4),(5|->7),(6|->1),(7|->8),(8|->2),(9|->5)}),(6|->{(1|->5),(2|->8),(3|->2),(4|->9),(5|->3),(6|->6),(7|->4),(8|->7),(9|->1)}),(7|->{(1|->1),(2|->4),(3|->7),(4|->5),(5|->8),(6|->2),(7|->9),(8|->3),(9|->6)}),(8|->{(1|->6),(2|->9),(3|->3),(4|->1),(5|->4),(6|->7),(7|->5),(8|->8),(9|->2)}),(9|->{(1|->2),(2|->5),(3|->8),(4|->6),(5|->9),(6|->3),(7|->1),(8|->4),(9|->7)})}\n",
+       "{(1|->{(1|->2),(2|->5),(3|->8),(4|->6),(5|->9),(6|->3),(7|->1),(8|->4),(9|->7)}),(2|->{(1|->6),(2|->9),(3|->3),(4|->1),(5|->4),(6|->7),(7|->5),(8|->8),(9|->2)}),(3|->{(1|->1),(2|->4),(3|->7),(4|->5),(5|->8),(6|->2),(7|->9),(8|->3),(9|->6)}),(4|->{(1|->5),(2|->8),(3|->2),(4|->9),(5|->3),(6|->6),(7|->4),(8|->7),(9|->1)}),(5|->{(1|->9),(2|->3),(3|->6),(4|->4),(5|->7),(6|->1),(7|->8),(8|->2),(9|->5)}),(6|->{(1|->4),(2|->7),(3|->1),(4|->8),(5|->2),(6|->5),(7|->3),(8|->6),(9|->9)}),(7|->{(1|->8),(2|->2),(3|->5),(4|->3),(5|->6),(6|->9),(7|->7),(8|->1),(9|->4)}),(8|->{(1|->3),(2|->6),(3|->9),(4|->7),(5|->1),(6|->4),(7|->2),(8|->5),(9|->8)}),(9|->{(1|->7),(2|->1),(3|->4),(4|->2),(5|->5),(6|->8),(7|->6),(8|->9),(9|->3)})}\n",
+       "{(1|->{(1|->7),(2|->2),(3|->6),(4|->1),(5|->5),(6|->9),(7|->4),(8|->8),(9|->3)}),(2|->{(1|->4),(2|->8),(3|->3),(4|->7),(5|->2),(6|->6),(7|->1),(8|->5),(9|->9)}),(3|->{(1|->1),(2|->5),(3|->9),(4|->4),(5|->8),(6|->3),(7|->7),(8|->2),(9|->6)}),(4|->{(1|->3),(2|->7),(3|->2),(4|->6),(5|->1),(6|->5),(7|->9),(8|->4),(9|->8)}),(5|->{(1|->9),(2|->4),(3|->8),(4|->3),(5|->7),(6|->2),(7|->6),(8|->1),(9|->5)}),(6|->{(1|->6),(2|->1),(3|->5),(4|->9),(5|->4),(6|->8),(7|->3),(8|->7),(9|->2)}),(7|->{(1|->8),(2|->3),(3|->7),(4|->2),(5|->6),(6|->1),(7|->5),(8|->9),(9|->4)}),(8|->{(1|->5),(2|->9),(3|->4),(4|->8),(5|->3),(6|->7),(7|->2),(8|->6),(9|->1)}),(9|->{(1|->2),(2|->6),(3|->1),(4|->5),(5|->9),(6|->4),(7|->8),(8|->3),(9|->7)})}\n",
+       "{(1|->{(1|->2),(2|->6),(3|->1),(4|->5),(5|->9),(6|->4),(7|->8),(8|->3),(9|->7)}),(2|->{(1|->5),(2|->9),(3|->4),(4|->8),(5|->3),(6|->7),(7|->2),(8|->6),(9|->1)}),(3|->{(1|->8),(2|->3),(3|->7),(4|->2),(5|->6),(6|->1),(7|->5),(8|->9),(9|->4)}),(4|->{(1|->6),(2|->1),(3|->5),(4|->9),(5|->4),(6|->8),(7|->3),(8|->7),(9|->2)}),(5|->{(1|->9),(2|->4),(3|->8),(4|->3),(5|->7),(6|->2),(7|->6),(8|->1),(9|->5)}),(6|->{(1|->3),(2|->7),(3|->2),(4|->6),(5|->1),(6|->5),(7|->9),(8|->4),(9|->8)}),(7|->{(1|->1),(2|->5),(3|->9),(4|->4),(5|->8),(6|->3),(7|->7),(8|->2),(9|->6)}),(8|->{(1|->4),(2|->8),(3|->3),(4|->7),(5|->2),(6|->6),(7|->1),(8|->5),(9|->9)}),(9|->{(1|->7),(2|->2),(3|->6),(4|->1),(5|->5),(6|->9),(7|->4),(8|->8),(9|->3)})}\n",
+       "{(1|->{(1|->4),(2|->9),(3|->5),(4|->1),(5|->6),(6|->2),(7|->7),(8|->3),(9|->8)}),(2|->{(1|->1),(2|->6),(3|->2),(4|->7),(5|->3),(6|->8),(7|->4),(8|->9),(9|->5)}),(3|->{(1|->7),(2|->3),(3|->8),(4|->4),(5|->9),(6|->5),(7|->1),(8|->6),(9|->2)}),(4|->{(1|->9),(2|->5),(3|->1),(4|->6),(5|->2),(6|->7),(7|->3),(8|->8),(9|->4)}),(5|->{(1|->6),(2|->2),(3|->7),(4|->3),(5|->8),(6|->4),(7|->9),(8|->5),(9|->1)}),(6|->{(1|->3),(2|->8),(3|->4),(4|->9),(5|->5),(6|->1),(7|->6),(8|->2),(9|->7)}),(7|->{(1|->5),(2|->1),(3|->6),(4|->2),(5|->7),(6|->3),(7|->8),(8|->4),(9|->9)}),(8|->{(1|->2),(2|->7),(3|->3),(4|->8),(5|->4),(6|->9),(7|->5),(8|->1),(9|->6)}),(9|->{(1|->8),(2|->4),(3|->9),(4|->5),(5|->1),(6|->6),(7|->2),(8|->7),(9|->3)})}\n",
+       "{(1|->{(1|->8),(2|->4),(3|->9),(4|->5),(5|->1),(6|->6),(7|->2),(8|->7),(9|->3)}),(2|->{(1|->2),(2|->7),(3|->3),(4|->8),(5|->4),(6|->9),(7|->5),(8|->1),(9|->6)}),(3|->{(1|->5),(2|->1),(3|->6),(4|->2),(5|->7),(6|->3),(7|->8),(8|->4),(9|->9)}),(4|->{(1|->3),(2|->8),(3|->4),(4|->9),(5|->5),(6|->1),(7|->6),(8|->2),(9|->7)}),(5|->{(1|->6),(2|->2),(3|->7),(4|->3),(5|->8),(6|->4),(7|->9),(8|->5),(9|->1)}),(6|->{(1|->9),(2|->5),(3|->1),(4|->6),(5|->2),(6|->7),(7|->3),(8|->8),(9|->4)}),(7|->{(1|->7),(2|->3),(3|->8),(4|->4),(5|->9),(6|->5),(7|->1),(8|->6),(9|->2)}),(8|->{(1|->1),(2|->6),(3|->2),(4|->7),(5|->3),(6|->8),(7|->4),(8|->9),(9|->5)}),(9|->{(1|->4),(2|->9),(3|->5),(4|->1),(5|->6),(6|->2),(7|->7),(8|->3),(9|->8)})}\n",
+       "{(1|->{(1|->4),(2|->1),(3|->7),(4|->9),(5|->6),(6|->3),(7|->5),(8|->2),(9|->8)}),(2|->{(1|->9),(2|->6),(3|->3),(4|->5),(5|->2),(6|->8),(7|->1),(8|->7),(9|->4)}),(3|->{(1|->5),(2|->2),(3|->8),(4|->1),(5|->7),(6|->4),(7|->6),(8|->3),(9|->9)}),(4|->{(1|->1),(2|->7),(3|->4),(4|->6),(5|->3),(6|->9),(7|->2),(8|->8),(9|->5)}),(5|->{(1|->6),(2|->3),(3|->9),(4|->2),(5|->8),(6|->5),(7|->7),(8|->4),(9|->1)}),(6|->{(1|->2),(2|->8),(3|->5),(4|->7),(5|->4),(6|->1),(7|->3),(8|->9),(9|->6)}),(7|->{(1|->7),(2|->4),(3|->1),(4|->3),(5|->9),(6|->6),(7|->8),(8|->5),(9|->2)}),(8|->{(1|->3),(2|->9),(3|->6),(4|->8),(5|->5),(6|->2),(7|->4),(8|->1),(9|->7)}),(9|->{(1|->8),(2|->5),(3|->2),(4|->4),(5|->1),(6|->7),(7|->9),(8|->6),(9|->3)})}\n",
+       "{(1|->{(1|->8),(2|->5),(3|->2),(4|->4),(5|->1),(6|->7),(7|->9),(8|->6),(9|->3)}),(2|->{(1|->3),(2|->9),(3|->6),(4|->8),(5|->5),(6|->2),(7|->4),(8|->1),(9|->7)}),(3|->{(1|->7),(2|->4),(3|->1),(4|->3),(5|->9),(6|->6),(7|->8),(8|->5),(9|->2)}),(4|->{(1|->2),(2|->8),(3|->5),(4|->7),(5|->4),(6|->1),(7|->3),(8|->9),(9|->6)}),(5|->{(1|->6),(2|->3),(3|->9),(4|->2),(5|->8),(6|->5),(7|->7),(8|->4),(9|->1)}),(6|->{(1|->1),(2|->7),(3|->4),(4|->6),(5|->3),(6|->9),(7|->2),(8|->8),(9|->5)}),(7|->{(1|->5),(2|->2),(3|->8),(4|->1),(5|->7),(6|->4),(7|->6),(8|->3),(9|->9)}),(8|->{(1|->9),(2|->6),(3|->3),(4|->5),(5|->2),(6|->8),(7|->1),(8|->7),(9|->4)}),(9|->{(1|->4),(2|->1),(3|->7),(4|->9),(5|->6),(6|->3),(7|->5),(8|->2),(9|->8)})}\n",
+       "{(1|->{(1|->8),(2|->2),(3|->5),(4|->3),(5|->6),(6|->9),(7|->7),(8|->1),(9|->4)}),(2|->{(1|->4),(2|->7),(3|->1),(4|->8),(5|->2),(6|->5),(7|->3),(8|->6),(9|->9)}),(3|->{(1|->9),(2|->3),(3|->6),(4|->4),(5|->7),(6|->1),(7|->8),(8|->2),(9|->5)}),(4|->{(1|->5),(2|->8),(3|->2),(4|->9),(5|->3),(6|->6),(7|->4),(8|->7),(9|->1)}),(5|->{(1|->1),(2|->4),(3|->7),(4|->5),(5|->8),(6|->2),(7|->9),(8|->3),(9|->6)}),(6|->{(1|->6),(2|->9),(3|->3),(4|->1),(5|->4),(6|->7),(7|->5),(8|->8),(9|->2)}),(7|->{(1|->2),(2|->5),(3|->8),(4|->6),(5|->9),(6|->3),(7|->1),(8|->4),(9|->7)}),(8|->{(1|->7),(2|->1),(3|->4),(4|->2),(5|->5),(6|->8),(7|->6),(8|->9),(9|->3)}),(9|->{(1|->3),(2|->6),(3|->9),(4|->7),(5|->1),(6|->4),(7|->2),(8|->5),(9|->8)})}\n",
+       "{(1|->{(1|->3),(2|->6),(3|->9),(4|->7),(5|->1),(6|->4),(7|->2),(8|->5),(9|->8)}),(2|->{(1|->7),(2|->1),(3|->4),(4|->2),(5|->5),(6|->8),(7|->6),(8|->9),(9|->3)}),(3|->{(1|->2),(2|->5),(3|->8),(4|->6),(5|->9),(6|->3),(7|->1),(8|->4),(9|->7)}),(4|->{(1|->6),(2|->9),(3|->3),(4|->1),(5|->4),(6|->7),(7|->5),(8|->8),(9|->2)}),(5|->{(1|->1),(2|->4),(3|->7),(4|->5),(5|->8),(6|->2),(7|->9),(8|->3),(9|->6)}),(6|->{(1|->5),(2|->8),(3|->2),(4|->9),(5|->3),(6|->6),(7|->4),(8|->7),(9|->1)}),(7|->{(1|->9),(2|->3),(3|->6),(4|->4),(5|->7),(6|->1),(7|->8),(8|->2),(9|->5)}),(8|->{(1|->4),(2|->7),(3|->1),(4|->8),(5|->2),(6|->5),(7|->3),(8|->6),(9|->9)}),(9|->{(1|->8),(2|->2),(3|->5),(4|->3),(5|->6),(6|->9),(7|->7),(8|->1),(9|->4)})}\n",
+       "{(1|->{(1|->8),(2|->3),(3|->7),(4|->2),(5|->6),(6|->1),(7|->5),(8|->9),(9|->4)}),(2|->{(1|->5),(2|->9),(3|->4),(4|->8),(5|->3),(6|->7),(7|->2),(8|->6),(9|->1)}),(3|->{(1|->2),(2|->6),(3|->1),(4|->5),(5|->9),(6|->4),(7|->8),(8|->3),(9|->7)}),(4|->{(1|->4),(2|->8),(3|->3),(4|->7),(5|->2),(6|->6),(7|->1),(8|->5),(9|->9)}),(5|->{(1|->1),(2|->5),(3|->9),(4|->4),(5|->8),(6|->3),(7|->7),(8|->2),(9|->6)}),(6|->{(1|->7),(2|->2),(3|->6),(4|->1),(5|->5),(6|->9),(7|->4),(8|->8),(9|->3)}),(7|->{(1|->9),(2|->4),(3|->8),(4|->3),(5|->7),(6|->2),(7|->6),(8|->1),(9|->5)}),(8|->{(1|->6),(2|->1),(3|->5),(4|->9),(5|->4),(6|->8),(7|->3),(8|->7),(9|->2)}),(9|->{(1|->3),(2|->7),(3|->2),(4|->6),(5|->1),(6|->5),(7|->9),(8|->4),(9|->8)})}\n",
+       "{(1|->{(1|->3),(2|->7),(3|->2),(4|->6),(5|->1),(6|->5),(7|->9),(8|->4),(9|->8)}),(2|->{(1|->6),(2|->1),(3|->5),(4|->9),(5|->4),(6|->8),(7|->3),(8|->7),(9|->2)}),(3|->{(1|->9),(2|->4),(3|->8),(4|->3),(5|->7),(6|->2),(7|->6),(8|->1),(9|->5)}),(4|->{(1|->7),(2|->2),(3|->6),(4|->1),(5|->5),(6|->9),(7|->4),(8|->8),(9|->3)}),(5|->{(1|->1),(2|->5),(3|->9),(4|->4),(5|->8),(6|->3),(7|->7),(8|->2),(9|->6)}),(6|->{(1|->4),(2|->8),(3|->3),(4|->7),(5|->2),(6|->6),(7|->1),(8|->5),(9|->9)}),(7|->{(1|->2),(2|->6),(3|->1),(4|->5),(5|->9),(6|->4),(7|->8),(8|->3),(9|->7)}),(8|->{(1|->5),(2|->9),(3|->4),(4|->8),(5|->3),(6|->7),(7|->2),(8|->6),(9|->1)}),(9|->{(1|->8),(2|->3),(3|->7),(4|->2),(5|->6),(6|->1),(7|->5),(8|->9),(9|->4)})}\n",
+       "{(1|->{(1|->5),(2|->1),(3|->6),(4|->2),(5|->7),(6|->3),(7|->8),(8|->4),(9|->9)}),(2|->{(1|->2),(2|->7),(3|->3),(4|->8),(5|->4),(6|->9),(7|->5),(8|->1),(9|->6)}),(3|->{(1|->8),(2|->4),(3|->9),(4|->5),(5|->1),(6|->6),(7|->2),(8|->7),(9|->3)}),(4|->{(1|->1),(2|->6),(3|->2),(4|->7),(5|->3),(6|->8),(7|->4),(8|->9),(9|->5)}),(5|->{(1|->7),(2|->3),(3|->8),(4|->4),(5|->9),(6|->5),(7|->1),(8|->6),(9|->2)}),(6|->{(1|->4),(2|->9),(3|->5),(4|->1),(5|->6),(6|->2),(7|->7),(8|->3),(9|->8)}),(7|->{(1|->6),(2|->2),(3|->7),(4|->3),(5|->8),(6|->4),(7|->9),(8|->5),(9|->1)}),(8|->{(1|->3),(2|->8),(3|->4),(4|->9),(5|->5),(6|->1),(7|->6),(8|->2),(9|->7)}),(9|->{(1|->9),(2|->5),(3|->1),(4|->6),(5|->2),(6|->7),(7|->3),(8|->8),(9|->4)})}\n",
+       "{(1|->{(1|->9),(2|->5),(3|->1),(4|->6),(5|->2),(6|->7),(7|->3),(8|->8),(9|->4)}),(2|->{(1|->3),(2|->8),(3|->4),(4|->9),(5|->5),(6|->1),(7|->6),(8|->2),(9|->7)}),(3|->{(1|->6),(2|->2),(3|->7),(4|->3),(5|->8),(6|->4),(7|->9),(8|->5),(9|->1)}),(4|->{(1|->4),(2|->9),(3|->5),(4|->1),(5|->6),(6|->2),(7|->7),(8|->3),(9|->8)}),(5|->{(1|->7),(2|->3),(3|->8),(4|->4),(5|->9),(6|->5),(7|->1),(8|->6),(9|->2)}),(6|->{(1|->1),(2|->6),(3|->2),(4|->7),(5|->3),(6|->8),(7|->4),(8|->9),(9|->5)}),(7|->{(1|->8),(2|->4),(3|->9),(4|->5),(5|->1),(6|->6),(7|->2),(8|->7),(9|->3)}),(8|->{(1|->2),(2|->7),(3|->3),(4|->8),(5|->4),(6|->9),(7|->5),(8|->1),(9|->6)}),(9|->{(1|->5),(2|->1),(3|->6),(4|->2),(5|->7),(6|->3),(7|->8),(8|->4),(9|->9)})}\n",
+       "{(1|->{(1|->5),(2|->2),(3|->8),(4|->1),(5|->7),(6|->4),(7|->6),(8|->3),(9|->9)}),(2|->{(1|->1),(2|->7),(3|->4),(4|->6),(5|->3),(6|->9),(7|->2),(8|->8),(9|->5)}),(3|->{(1|->6),(2|->3),(3|->9),(4|->2),(5|->8),(6|->5),(7|->7),(8|->4),(9|->1)}),(4|->{(1|->2),(2|->8),(3|->5),(4|->7),(5|->4),(6|->1),(7|->3),(8|->9),(9|->6)}),(5|->{(1|->7),(2|->4),(3|->1),(4|->3),(5|->9),(6|->6),(7|->8),(8|->5),(9|->2)}),(6|->{(1|->3),(2|->9),(3|->6),(4|->8),(5|->5),(6|->2),(7|->4),(8|->1),(9|->7)}),(7|->{(1|->8),(2|->5),(3|->2),(4|->4),(5|->1),(6|->7),(7|->9),(8|->6),(9|->3)}),(8|->{(1|->4),(2|->1),(3|->7),(4|->9),(5|->6),(6|->3),(7|->5),(8|->2),(9|->8)}),(9|->{(1|->9),(2|->6),(3|->3),(4|->5),(5|->2),(6|->8),(7|->1),(8|->7),(9|->4)})}\n",
+       "{(1|->{(1|->9),(2|->6),(3|->3),(4|->5),(5|->2),(6|->8),(7|->1),(8|->7),(9|->4)}),(2|->{(1|->4),(2|->1),(3|->7),(4|->9),(5|->6),(6|->3),(7|->5),(8|->2),(9|->8)}),(3|->{(1|->8),(2|->5),(3|->2),(4|->4),(5|->1),(6|->7),(7|->9),(8|->6),(9|->3)}),(4|->{(1|->3),(2|->9),(3|->6),(4|->8),(5|->5),(6|->2),(7|->4),(8|->1),(9|->7)}),(5|->{(1|->7),(2|->4),(3|->1),(4|->3),(5|->9),(6|->6),(7|->8),(8|->5),(9|->2)}),(6|->{(1|->2),(2|->8),(3|->5),(4|->7),(5|->4),(6|->1),(7|->3),(8|->9),(9|->6)}),(7|->{(1|->6),(2|->3),(3|->9),(4|->2),(5|->8),(6|->5),(7|->7),(8|->4),(9|->1)}),(8|->{(1|->1),(2|->7),(3|->4),(4|->6),(5|->3),(6|->9),(7|->2),(8|->8),(9|->5)}),(9|->{(1|->5),(2|->2),(3|->8),(4|->1),(5|->7),(6|->4),(7|->6),(8|->3),(9|->9)})}\n",
+       "{(1|->{(1|->9),(2|->3),(3|->6),(4|->4),(5|->7),(6|->1),(7|->8),(8|->2),(9|->5)}),(2|->{(1|->5),(2|->8),(3|->2),(4|->9),(5|->3),(6|->6),(7|->4),(8|->7),(9|->1)}),(3|->{(1|->1),(2|->4),(3|->7),(4|->5),(5|->8),(6|->2),(7|->9),(8|->3),(9|->6)}),(4|->{(1|->6),(2|->9),(3|->3),(4|->1),(5|->4),(6|->7),(7|->5),(8|->8),(9|->2)}),(5|->{(1|->2),(2|->5),(3|->8),(4|->6),(5|->9),(6|->3),(7|->1),(8|->4),(9|->7)}),(6|->{(1|->7),(2|->1),(3|->4),(4|->2),(5|->5),(6|->8),(7|->6),(8|->9),(9|->3)}),(7|->{(1|->3),(2|->6),(3|->9),(4|->7),(5|->1),(6|->4),(7|->2),(8|->5),(9|->8)}),(8|->{(1|->8),(2|->2),(3|->5),(4|->3),(5|->6),(6|->9),(7|->7),(8|->1),(9|->4)}),(9|->{(1|->4),(2|->7),(3|->1),(4|->8),(5|->2),(6|->5),(7|->3),(8|->6),(9|->9)})}\n",
+       "{(1|->{(1|->4),(2|->7),(3|->1),(4|->8),(5|->2),(6|->5),(7|->3),(8|->6),(9|->9)}),(2|->{(1|->8),(2|->2),(3|->5),(4|->3),(5|->6),(6|->9),(7|->7),(8|->1),(9|->4)}),(3|->{(1|->3),(2|->6),(3|->9),(4|->7),(5|->1),(6|->4),(7|->2),(8|->5),(9|->8)}),(4|->{(1|->7),(2|->1),(3|->4),(4|->2),(5|->5),(6|->8),(7|->6),(8|->9),(9|->3)}),(5|->{(1|->2),(2|->5),(3|->8),(4|->6),(5|->9),(6|->3),(7|->1),(8|->4),(9|->7)}),(6|->{(1|->6),(2|->9),(3|->3),(4|->1),(5|->4),(6|->7),(7|->5),(8|->8),(9|->2)}),(7|->{(1|->1),(2|->4),(3|->7),(4|->5),(5|->8),(6|->2),(7|->9),(8|->3),(9|->6)}),(8|->{(1|->5),(2|->8),(3|->2),(4|->9),(5|->3),(6|->6),(7|->4),(8|->7),(9|->1)}),(9|->{(1|->9),(2|->3),(3|->6),(4|->4),(5|->7),(6|->1),(7|->8),(8|->2),(9|->5)})}\n",
+       "{(1|->{(1|->9),(2|->4),(3|->8),(4|->3),(5|->7),(6|->2),(7|->6),(8|->1),(9|->5)}),(2|->{(1|->6),(2|->1),(3|->5),(4|->9),(5|->4),(6|->8),(7|->3),(8|->7),(9|->2)}),(3|->{(1|->3),(2|->7),(3|->2),(4|->6),(5|->1),(6|->5),(7|->9),(8|->4),(9|->8)}),(4|->{(1|->5),(2|->9),(3|->4),(4|->8),(5|->3),(6|->7),(7|->2),(8|->6),(9|->1)}),(5|->{(1|->2),(2|->6),(3|->1),(4|->5),(5|->9),(6|->4),(7|->8),(8|->3),(9|->7)}),(6|->{(1|->8),(2|->3),(3|->7),(4|->2),(5|->6),(6|->1),(7|->5),(8|->9),(9|->4)}),(7|->{(1|->1),(2|->5),(3|->9),(4|->4),(5|->8),(6|->3),(7|->7),(8|->2),(9|->6)}),(8|->{(1|->7),(2|->2),(3|->6),(4|->1),(5|->5),(6|->9),(7|->4),(8|->8),(9|->3)}),(9|->{(1|->4),(2|->8),(3|->3),(4|->7),(5|->2),(6|->6),(7|->1),(8|->5),(9|->9)})}\n",
+       "{(1|->{(1|->4),(2|->8),(3|->3),(4|->7),(5|->2),(6|->6),(7|->1),(8|->5),(9|->9)}),(2|->{(1|->7),(2|->2),(3|->6),(4|->1),(5|->5),(6|->9),(7|->4),(8|->8),(9|->3)}),(3|->{(1|->1),(2|->5),(3|->9),(4|->4),(5|->8),(6|->3),(7|->7),(8|->2),(9|->6)}),(4|->{(1|->8),(2|->3),(3|->7),(4|->2),(5|->6),(6|->1),(7|->5),(8|->9),(9|->4)}),(5|->{(1|->2),(2|->6),(3|->1),(4|->5),(5|->9),(6|->4),(7|->8),(8|->3),(9|->7)}),(6|->{(1|->5),(2|->9),(3|->4),(4|->8),(5|->3),(6|->7),(7|->2),(8|->6),(9|->1)}),(7|->{(1|->3),(2|->7),(3|->2),(4|->6),(5|->1),(6|->5),(7|->9),(8|->4),(9|->8)}),(8|->{(1|->6),(2|->1),(3|->5),(4|->9),(5|->4),(6|->8),(7|->3),(8|->7),(9|->2)}),(9|->{(1|->9),(2|->4),(3|->8),(4|->3),(5|->7),(6|->2),(7|->6),(8|->1),(9|->5)})}\n"
+      ]
+     },
+     "execution_count": 24,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    ":table Boards"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
-- 
GitLab