diff --git a/8Queens .ipynb b/8Queens .ipynb
new file mode 100644
index 0000000..0a1391f
--- /dev/null
+++ b/8Queens .ipynb	
@@ -0,0 +1,2995 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import random\n",
+    "from itertools import islice   "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "\"\"\" \n",
+    "    quality checks by analysing any queens in diagonal.\n",
+    "    We will select one row , loop through each rows and see the any element exist\n",
+    "    and counts the checksrelations\n",
+    "\"\"\"\n",
+    "def quality_check(list):\n",
+    "    column = 0\n",
+    "    q = 0\n",
+    "    row_index = 1\n",
+    "    for row in list:\n",
+    "        diff = row - (column + 1)\n",
+    "        row_index = 1         \n",
+    "        for col in range(column + 1,8):\n",
+    "            row1 = list[col]\n",
+    "            if ((row1 - row_index == row) | (row1 + row_index == row )):\n",
+    "                q = q + 1\n",
+    "            row_index = row_index + 1\n",
+    "        column = column + 1\n",
+    "    return q"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "\"\"\"\n",
+    "  Initialize the parents with value between 1 - 8 and unique number\n",
+    "\"\"\"\n",
+    "def initialize():\n",
+    "    no_population = 5\n",
+    "    population = []\n",
+    "    for p_no in range(0, no_population):\n",
+    "        pop = random.sample(range(1,9), 8)\n",
+    "        population.append(pop)\n",
+    "    return population"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def parent_selection(population):\n",
+    "    quality = {}\n",
+    "    index = 0\n",
+    "    \n",
+    "    for pop in population:\n",
+    "        q1 = quality_check(pop)\n",
+    "        quality[index] = q1\n",
+    "        index = index + 1\n",
+    "    #\"\"\" make dict and sort \"\"\"\n",
+    "    quality1 = {k: v for k, v in sorted(quality.items(), key=lambda item: item[1])}\n",
+    "    first, second = islice(quality1.keys(), 2)  \n",
+    "    \n",
+    "    parent1 = population[first]\n",
+    "    parent2 = population[second]\n",
+    "    \n",
+    "    return parent1, parent2\n",
+    "\n",
+    "    \n",
+    "    "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def partial_mapped_crossover(parent1, parent2):\n",
+    "    \n",
+    "\n",
+    "    firstCrossPoint = np.random.randint(0,len(parent1)-2)\n",
+    "    secondCrossPoint = np.random.randint(firstCrossPoint+1,len(parent1)-1)\n",
+    "\n",
+    "    print(firstCrossPoint, secondCrossPoint)\n",
+    "\n",
+    "    parent1MiddleCross = parent1[firstCrossPoint:secondCrossPoint]\n",
+    "    parent2MiddleCross = parent2[firstCrossPoint:secondCrossPoint]\n",
+    "\n",
+    "    temp_child1 = parent1[:firstCrossPoint] + parent2MiddleCross + parent1[secondCrossPoint:]\n",
+    "\n",
+    "    temp_child2 = parent2[:firstCrossPoint] + parent1MiddleCross + parent2[secondCrossPoint:]\n",
+    "\n",
+    "    relations = []\n",
+    "    for i in range(len(parent1MiddleCross)):\n",
+    "        relations.append([parent2MiddleCross[i], parent1MiddleCross[i]])\n",
+    "\n",
+    "    print(relations)\n",
+    "\n",
+    "    \n",
+    "\n",
+    "    child1=recursion1(temp_child1,firstCrossPoint,secondCrossPoint,parent1MiddleCross,parent2MiddleCross, relations)\n",
+    "    child2=recursion2(temp_child2,firstCrossPoint,secondCrossPoint,parent1MiddleCross,parent2MiddleCross, relations)\n",
+    "\n",
+    "    print(child1)\n",
+    "    print(child2)\n",
+    "    \n",
+    "    return [list(child1), list(child2)]\n",
+    "    "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def recursion1 (temp_child , firstCrossPoint , secondCrossPoint , parent1MiddleCross , parent2MiddleCross, relations) :\n",
+    "    child = np.array([0 for i in range(len(parent1))])\n",
+    "    for i,j in enumerate(temp_child[:firstCrossPoint]):\n",
+    "        c=0\n",
+    "        for x in relations:\n",
+    "            if j == x[0]:\n",
+    "                child[i]=x[1]\n",
+    "                c=1\n",
+    "                break\n",
+    "        if c==0:\n",
+    "            child[i]=j\n",
+    "    j=0\n",
+    "    for i in range(firstCrossPoint,secondCrossPoint):\n",
+    "        child[i]=parent2MiddleCross[j]\n",
+    "        j+=1\n",
+    "\n",
+    "    for i,j in enumerate(temp_child[secondCrossPoint:]):\n",
+    "        c=0\n",
+    "        for x in relations:\n",
+    "            if j == x[0]:\n",
+    "                child[i+secondCrossPoint]=x[1]\n",
+    "                c=1\n",
+    "                break\n",
+    "        if c==0:\n",
+    "            child[i+secondCrossPoint]=j\n",
+    "    child_unique=np.unique(child)\n",
+    "    if len(child)>len(child_unique):\n",
+    "        child=recursion1(child,firstCrossPoint,secondCrossPoint,parent1MiddleCross,parent2MiddleCross, relations)\n",
+    "    return(child)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "\n",
+    "def recursion2(temp_child,firstCrossPoint,secondCrossPoint,parent1MiddleCross,parent2MiddleCross, relations):\n",
+    "    child = np.array([0 for i in range(len(parent1))])\n",
+    "    for i,j in enumerate(temp_child[:firstCrossPoint]):\n",
+    "        c=0\n",
+    "        for x in relations:\n",
+    "            if j == x[1]:\n",
+    "                child[i]=x[0]\n",
+    "                c=1\n",
+    "                break\n",
+    "        if c==0:\n",
+    "            child[i]=j\n",
+    "    j=0\n",
+    "    for i in range(firstCrossPoint,secondCrossPoint):\n",
+    "        child[i]=parent1MiddleCross[j]\n",
+    "        j+=1\n",
+    "\n",
+    "    for i,j in enumerate(temp_child[secondCrossPoint:]):\n",
+    "        c=0\n",
+    "        for x in relations:\n",
+    "            if j == x[1]:\n",
+    "                child[i+secondCrossPoint]=x[0]\n",
+    "                c=1\n",
+    "                break\n",
+    "        if c==0:\n",
+    "            child[i+secondCrossPoint]=j\n",
+    "    child_unique=np.unique(child)\n",
+    "    if len(child)>len(child_unique):\n",
+    "        child=recursion2(child,firstCrossPoint,secondCrossPoint,parent1MiddleCross,parent2MiddleCross, relations)\n",
+    "    return(child)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "\"\"\"\n",
+    " One point cross over , cut and cross over\n",
+    "\"\"\"\n",
+    "def cross_over(child1, child2):\n",
+    " \n",
+    "    index = random.randint(0,7)\n",
+    "    \n",
+    "    for i in range(index, 8): \n",
+    "        child1[i], child2[i] = child2[i], child1[i] \n",
+    "    \n",
+    "    return [child1, child2]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "\"\"\"\n",
+    " Swap mutate\n",
+    "\"\"\"\n",
+    "def mutate_swap(child):\n",
+    "    r1, r2 = random.sample(range(0, 7), 2)\n",
+    "    print(r1)\n",
+    "    print(r2)\n",
+    "    child[r1], child[r2] = child[r2], child[r1]\n",
+    "    return child\n",
+    "    "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def add_to_population(population, child1, child2):\n",
+    "    population.append(child1)\n",
+    "    population.append(child2)\n",
+    "    return population"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def survival_fitness(population):\n",
+    "    quality = {}\n",
+    "    index = 0\n",
+    "    \n",
+    "    for pop in population:\n",
+    "        q1 = quality_check(pop)\n",
+    "        quality[index] = q1\n",
+    "        index = index + 1\n",
+    "    \"\"\" make dict and sort \"\"\"\n",
+    "    quality1 = {k: v for k, v in sorted(quality.items(), key=lambda item: item[1], reverse=True)}\n",
+    "    print(quality1)\n",
+    "    first, second = islice(quality1.keys(), 2)  \n",
+    "    \n",
+    "    p1 = population[first]\n",
+    "    p2 = population[second]\n",
+    "    \n",
+    "    print(p1)\n",
+    "    print(p2)\n",
+    "    \n",
+    "    population.remove(p1)\n",
+    "    population.remove(p2)\n",
+    "    \n",
+    "    print(population)\n",
+    "    return population\n",
+    "    "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "population = initialize()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[[7, 6, 2, 5, 4, 1, 8, 3],\n",
+       " [3, 8, 6, 1, 7, 5, 2, 4],\n",
+       " [7, 4, 1, 3, 5, 8, 6, 2],\n",
+       " [5, 8, 2, 4, 3, 6, 1, 7],\n",
+       " [3, 1, 5, 4, 7, 6, 8, 2]]"
+      ]
+     },
+     "execution_count": 16,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "population"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1 4\n",
+      "[[4, 8], [1, 6], [3, 1]]\n",
+      "[6 4 1 3 7 5 2 8]\n",
+      "[7 8 6 1 5 4 3 2]\n",
+      "1\n",
+      "6\n",
+      "0\n",
+      "6\n",
+      "{6: 7, 4: 6, 0: 5, 3: 5, 5: 5, 1: 3, 2: 3}\n",
+      "[3, 8, 6, 1, 5, 4, 7, 2]\n",
+      "[3, 1, 5, 4, 7, 6, 8, 2]\n",
+      "[[7, 6, 2, 5, 4, 1, 8, 3], [3, 8, 6, 1, 7, 5, 2, 4], [7, 4, 1, 3, 5, 8, 6, 2], [5, 8, 2, 4, 3, 6, 1, 7], [6, 2, 1, 3, 7, 5, 4, 8]]\n",
+      "2 3\n",
+      "[[1, 6]]\n",
+      "[3 8 1 6 7 5 2 4]\n",
+      "[7 4 6 3 5 8 1 2]\n",
+      "1\n",
+      "3\n",
+      "6\n",
+      "0\n",
+      "{5: 6, 6: 6, 0: 5, 3: 5, 4: 5, 1: 3, 2: 3}\n",
+      "[3, 6, 1, 8, 7, 5, 2, 4]\n",
+      "[1, 4, 6, 3, 5, 8, 7, 2]\n",
+      "[[7, 6, 2, 5, 4, 1, 8, 3], [3, 8, 6, 1, 7, 5, 2, 4], [7, 4, 1, 3, 5, 8, 6, 2], [5, 8, 2, 4, 3, 6, 1, 7], [6, 2, 1, 3, 7, 5, 4, 8]]\n",
+      "0 3\n",
+      "[[7, 3], [4, 8], [1, 6]]\n",
+      "[7 4 1 6 3 5 2 8]\n",
+      "[3 8 6 7 5 4 1 2]\n",
+      "6\n",
+      "4\n",
+      "5\n",
+      "3\n",
+      "{6: 6, 0: 5, 3: 5, 4: 5, 1: 3, 2: 3, 5: 2}\n",
+      "[3, 8, 6, 4, 5, 7, 1, 2]\n",
+      "[7, 6, 2, 5, 4, 1, 8, 3]\n",
+      "[[3, 8, 6, 1, 7, 5, 2, 4], [7, 4, 1, 3, 5, 8, 6, 2], [5, 8, 2, 4, 3, 6, 1, 7], [6, 2, 1, 3, 7, 5, 4, 8], [7, 4, 1, 6, 2, 5, 3, 8]]\n",
+      "1 2\n",
+      "[[8, 4]]\n",
+      "[7 8 1 6 2 5 3 4]\n",
+      "[3 4 6 1 7 5 2 8]\n",
+      "0\n",
+      "5\n",
+      "5\n",
+      "4\n",
+      "{2: 5, 3: 5, 5: 4, 0: 3, 1: 3, 6: 3, 4: 2}\n",
+      "[5, 8, 2, 4, 3, 6, 1, 7]\n",
+      "[6, 2, 1, 3, 7, 5, 4, 8]\n",
+      "[[3, 8, 6, 1, 7, 5, 2, 4], [7, 4, 1, 3, 5, 8, 6, 2], [7, 4, 1, 6, 2, 5, 3, 8], [5, 8, 1, 6, 2, 7, 3, 4], [3, 4, 6, 1, 5, 7, 2, 8]]\n",
+      "0 3\n",
+      "[[3, 7], [8, 4], [6, 1]]\n",
+      "[3 8 6 1 2 5 7 4]\n",
+      "[7 4 1 6 3 5 2 8]\n",
+      "4\n",
+      "3\n",
+      "4\n",
+      "2\n",
+      "{6: 5, 3: 4, 0: 3, 1: 3, 4: 3, 2: 2, 5: 2}\n",
+      "[7, 4, 3, 6, 1, 5, 2, 8]\n",
+      "[5, 8, 1, 6, 2, 7, 3, 4]\n",
+      "[[3, 8, 6, 1, 7, 5, 2, 4], [7, 4, 1, 3, 5, 8, 6, 2], [7, 4, 1, 6, 2, 5, 3, 8], [3, 4, 6, 1, 5, 7, 2, 8], [3, 8, 6, 2, 1, 5, 7, 4]]\n",
+      "2 4\n",
+      "[[6, 1], [2, 6]]\n",
+      "[7 4 6 2 1 5 3 8]\n",
+      "[3 8 1 6 2 5 7 4]\n",
+      "2\n",
+      "5\n",
+      "6\n",
+      "4\n",
+      "{5: 7, 6: 6, 0: 3, 1: 3, 3: 3, 2: 2, 4: 2}\n",
+      "[7, 4, 5, 2, 1, 6, 3, 8]\n",
+      "[3, 8, 1, 6, 7, 5, 2, 4]\n",
+      "[[3, 8, 6, 1, 7, 5, 2, 4], [7, 4, 1, 3, 5, 8, 6, 2], [7, 4, 1, 6, 2, 5, 3, 8], [3, 4, 6, 1, 5, 7, 2, 8], [3, 8, 6, 2, 1, 5, 7, 4]]\n",
+      "2 5\n",
+      "[[6, 1], [2, 6], [1, 2]]\n",
+      "[7 4 6 2 1 5 3 8]\n",
+      "[3 8 1 6 2 5 7 4]\n",
+      "0\n",
+      "1\n",
+      "0\n",
+      "3\n",
+      "{5: 4, 6: 4, 0: 3, 1: 3, 3: 3, 2: 2, 4: 2}\n",
+      "[4, 7, 6, 2, 1, 5, 3, 8]\n",
+      "[6, 8, 1, 3, 2, 5, 7, 4]\n",
+      "[[3, 8, 6, 1, 7, 5, 2, 4], [7, 4, 1, 3, 5, 8, 6, 2], [7, 4, 1, 6, 2, 5, 3, 8], [3, 4, 6, 1, 5, 7, 2, 8], [3, 8, 6, 2, 1, 5, 7, 4]]\n",
+      "3 6\n",
+      "[[2, 6], [1, 2], [5, 5]]\n",
+      "[7 4 6 2 1 5 3 8]\n",
+      "[3 8 1 6 2 5 7 4]\n",
+      "6\n",
+      "3\n",
+      "1\n",
+      "6\n",
+      "{0: 3, 1: 3, 3: 3, 5: 3, 2: 2, 4: 2, 6: 2}\n",
+      "[3, 8, 6, 1, 7, 5, 2, 4]\n",
+      "[7, 4, 1, 3, 5, 8, 6, 2]\n",
+      "[[7, 4, 1, 6, 2, 5, 3, 8], [3, 4, 6, 1, 5, 7, 2, 8], [3, 8, 6, 2, 1, 5, 7, 4], [7, 4, 6, 3, 1, 5, 2, 8], [3, 7, 1, 6, 2, 5, 8, 4]]\n",
+      "3 5\n",
+      "[[2, 6], [1, 2]]\n",
+      "[7 4 6 2 1 5 3 8]\n",
+      "[3 8 1 6 2 5 7 4]\n",
+      "3\n",
+      "2\n",
+      "0\n",
+      "5\n",
+      "{5: 5, 1: 3, 3: 3, 0: 2, 2: 2, 4: 2, 6: 2}\n",
+      "[7, 4, 2, 6, 1, 5, 3, 8]\n",
+      "[3, 4, 6, 1, 5, 7, 2, 8]\n",
+      "[[7, 4, 1, 6, 2, 5, 3, 8], [3, 8, 6, 2, 1, 5, 7, 4], [7, 4, 6, 3, 1, 5, 2, 8], [3, 7, 1, 6, 2, 5, 8, 4], [5, 8, 1, 6, 2, 3, 7, 4]]\n",
+      "5 6\n",
+      "[[5, 5]]\n",
+      "[7 4 1 6 2 5 3 8]\n",
+      "[3 8 6 2 1 5 7 4]\n",
+      "0\n",
+      "5\n",
+      "3\n",
+      "0\n",
+      "{2: 3, 5: 3, 0: 2, 1: 2, 3: 2, 4: 2, 6: 2}\n",
+      "[7, 4, 6, 3, 1, 5, 2, 8]\n",
+      "[5, 4, 1, 6, 2, 7, 3, 8]\n",
+      "[[7, 4, 1, 6, 2, 5, 3, 8], [3, 8, 6, 2, 1, 5, 7, 4], [3, 7, 1, 6, 2, 5, 8, 4], [5, 8, 1, 6, 2, 3, 7, 4], [2, 8, 6, 3, 1, 5, 7, 4]]\n",
+      "5 6\n",
+      "[[5, 5]]\n",
+      "[7 4 1 6 2 5 3 8]\n",
+      "[3 8 6 2 1 5 7 4]\n",
+      "3\n",
+      "1\n",
+      "2\n",
+      "1\n",
+      "{5: 4, 6: 3, 0: 2, 1: 2, 2: 2, 3: 2, 4: 2}\n",
+      "[7, 6, 1, 4, 2, 5, 3, 8]\n",
+      "[3, 6, 8, 2, 1, 5, 7, 4]\n",
+      "[[7, 4, 1, 6, 2, 5, 3, 8], [3, 8, 6, 2, 1, 5, 7, 4], [3, 7, 1, 6, 2, 5, 8, 4], [5, 8, 1, 6, 2, 3, 7, 4], [2, 8, 6, 3, 1, 5, 7, 4]]\n",
+      "3 6\n",
+      "[[2, 6], [1, 2], [5, 5]]\n",
+      "[7 4 6 2 1 5 3 8]\n",
+      "[3 8 1 6 2 5 7 4]\n",
+      "5\n",
+      "4\n",
+      "2\n",
+      "0\n",
+      "{6: 4, 5: 3, 0: 2, 1: 2, 2: 2, 3: 2, 4: 2}\n",
+      "[1, 8, 3, 6, 2, 5, 7, 4]\n",
+      "[7, 4, 6, 2, 5, 1, 3, 8]\n",
+      "[[7, 4, 1, 6, 2, 5, 3, 8], [3, 8, 6, 2, 1, 5, 7, 4], [3, 7, 1, 6, 2, 5, 8, 4], [5, 8, 1, 6, 2, 3, 7, 4], [2, 8, 6, 3, 1, 5, 7, 4]]\n",
+      "1 2\n",
+      "[[8, 4]]\n",
+      "[7 8 1 6 2 5 3 4]\n",
+      "[3 4 6 2 1 5 7 8]\n",
+      "3\n",
+      "5\n",
+      "5\n",
+      "6\n",
+      "{6: 5, 5: 4, 0: 2, 1: 2, 2: 2, 3: 2, 4: 2}\n",
+      "[3, 4, 6, 2, 1, 7, 5, 8]\n",
+      "[7, 8, 1, 5, 2, 6, 3, 4]\n",
+      "[[7, 4, 1, 6, 2, 5, 3, 8], [3, 8, 6, 2, 1, 5, 7, 4], [3, 7, 1, 6, 2, 5, 8, 4], [5, 8, 1, 6, 2, 3, 7, 4], [2, 8, 6, 3, 1, 5, 7, 4]]\n",
+      "1 5\n",
+      "[[8, 4], [6, 1], [2, 6], [1, 2]]\n",
+      "[7 8 6 2 1 5 3 4]\n",
+      "[3 4 1 6 2 5 7 8]\n",
+      "3\n",
+      "2\n",
+      "4\n",
+      "0\n",
+      "{5: 8, 6: 3, 0: 2, 1: 2, 2: 2, 3: 2, 4: 2}\n",
+      "[7, 8, 2, 6, 1, 5, 3, 4]\n",
+      "[2, 4, 1, 6, 3, 5, 7, 8]\n",
+      "[[7, 4, 1, 6, 2, 5, 3, 8], [3, 8, 6, 2, 1, 5, 7, 4], [3, 7, 1, 6, 2, 5, 8, 4], [5, 8, 1, 6, 2, 3, 7, 4], [2, 8, 6, 3, 1, 5, 7, 4]]\n",
+      "1 6\n",
+      "[[8, 4], [6, 1], [2, 6], [1, 2], [5, 5]]\n",
+      "[7 8 6 2 1 5 3 4]\n",
+      "[3 4 1 6 2 5 7 8]\n",
+      "6\n",
+      "0\n",
+      "6\n",
+      "4\n",
+      "{6: 7, 0: 2, 1: 2, 2: 2, 3: 2, 4: 2, 5: 2}\n",
+      "[3, 4, 1, 6, 7, 5, 2, 8]\n",
+      "[7, 4, 1, 6, 2, 5, 3, 8]\n",
+      "[[3, 8, 6, 2, 1, 5, 7, 4], [3, 7, 1, 6, 2, 5, 8, 4], [5, 8, 1, 6, 2, 3, 7, 4], [2, 8, 6, 3, 1, 5, 7, 4], [3, 8, 6, 2, 1, 5, 7, 4]]\n",
+      "0 6\n",
+      "[[3, 3], [7, 8], [1, 6], [6, 2], [2, 1], [5, 5]]\n",
+      "[3 7 1 6 2 5 8 4]\n",
+      "[3 8 6 2 1 5 7 4]\n",
+      "5\n",
+      "4\n",
+      "0\n",
+      "2\n",
+      "{6: 5, 5: 4, 0: 2, 1: 2, 2: 2, 3: 2, 4: 2}\n",
+      "[6, 8, 3, 2, 1, 5, 7, 4]\n",
+      "[3, 7, 1, 6, 5, 2, 8, 4]\n",
+      "[[3, 8, 6, 2, 1, 5, 7, 4], [3, 7, 1, 6, 2, 5, 8, 4], [5, 8, 1, 6, 2, 3, 7, 4], [2, 8, 6, 3, 1, 5, 7, 4], [3, 8, 6, 2, 1, 5, 7, 4]]\n",
+      "5 6\n",
+      "[[5, 5]]\n",
+      "[3 8 6 2 1 5 7 4]\n",
+      "[3 7 1 6 2 5 8 4]\n",
+      "2\n",
+      "0\n",
+      "4\n",
+      "0\n",
+      "{5: 5, 0: 2, 1: 2, 2: 2, 3: 2, 4: 2, 6: 2}\n",
+      "[6, 8, 3, 2, 1, 5, 7, 4]\n",
+      "[3, 8, 6, 2, 1, 5, 7, 4]\n",
+      "[[3, 7, 1, 6, 2, 5, 8, 4], [5, 8, 1, 6, 2, 3, 7, 4], [2, 8, 6, 3, 1, 5, 7, 4], [3, 8, 6, 2, 1, 5, 7, 4], [2, 7, 1, 6, 3, 5, 8, 4]]\n",
+      "0 1\n",
+      "[[5, 3]]\n",
+      "[5 7 1 6 2 3 8 4]\n",
+      "[3 8 1 6 2 5 7 4]\n",
+      "5\n",
+      "2\n",
+      "4\n",
+      "2\n",
+      "{6: 4, 0: 2, 1: 2, 2: 2, 3: 2, 4: 2, 5: 2}\n",
+      "[3, 8, 2, 6, 1, 5, 7, 4]\n",
+      "[3, 7, 1, 6, 2, 5, 8, 4]\n",
+      "[[5, 8, 1, 6, 2, 3, 7, 4], [2, 8, 6, 3, 1, 5, 7, 4], [3, 8, 6, 2, 1, 5, 7, 4], [2, 7, 1, 6, 3, 5, 8, 4], [5, 7, 3, 6, 2, 1, 8, 4]]\n",
+      "2 6\n",
+      "[[6, 1], [3, 6], [1, 2], [5, 3]]\n",
+      "[2 8 6 3 1 5 7 4]\n",
+      "[5 8 1 6 2 3 7 4]\n",
+      "6\n",
+      "5\n",
+      "5\n",
+      "2\n",
+      "{6: 4, 5: 3, 0: 2, 1: 2, 2: 2, 3: 2, 4: 2}\n",
+      "[5, 8, 3, 6, 2, 1, 7, 4]\n",
+      "[2, 8, 6, 3, 1, 7, 5, 4]\n",
+      "[[5, 8, 1, 6, 2, 3, 7, 4], [2, 8, 6, 3, 1, 5, 7, 4], [3, 8, 6, 2, 1, 5, 7, 4], [2, 7, 1, 6, 3, 5, 8, 4], [5, 7, 3, 6, 2, 1, 8, 4]]\n",
+      "2 6\n",
+      "[[6, 1], [3, 6], [1, 2], [5, 3]]\n",
+      "[2 8 6 3 1 5 7 4]\n",
+      "[5 8 1 6 2 3 7 4]\n",
+      "5\n",
+      "1\n",
+      "4\n",
+      "0\n",
+      "{5: 4, 6: 4, 0: 2, 1: 2, 2: 2, 3: 2, 4: 2}\n",
+      "[2, 5, 6, 3, 1, 8, 7, 4]\n",
+      "[2, 8, 1, 6, 5, 3, 7, 4]\n",
+      "[[5, 8, 1, 6, 2, 3, 7, 4], [2, 8, 6, 3, 1, 5, 7, 4], [3, 8, 6, 2, 1, 5, 7, 4], [2, 7, 1, 6, 3, 5, 8, 4], [5, 7, 3, 6, 2, 1, 8, 4]]\n",
+      "5 6\n",
+      "[[5, 3]]\n",
+      "[3 8 1 6 2 5 7 4]\n",
+      "[2 8 6 5 1 3 7 4]\n",
+      "5\n",
+      "2\n",
+      "1\n",
+      "5\n",
+      "{6: 6, 5: 5, 0: 2, 1: 2, 2: 2, 3: 2, 4: 2}\n",
+      "[2, 3, 6, 5, 1, 8, 7, 4]\n",
+      "[3, 8, 5, 6, 2, 1, 7, 4]\n",
+      "[[5, 8, 1, 6, 2, 3, 7, 4], [2, 8, 6, 3, 1, 5, 7, 4], [3, 8, 6, 2, 1, 5, 7, 4], [2, 7, 1, 6, 3, 5, 8, 4], [5, 7, 3, 6, 2, 1, 8, 4]]\n",
+      "1 4\n",
+      "[[8, 8], [6, 1], [3, 6]]\n",
+      "[5 8 6 3 2 1 7 4]\n",
+      "[2 8 1 6 3 5 7 4]\n",
+      "6\n",
+      "3\n",
+      "2\n",
+      "1\n",
+      "{5: 4, 6: 3, 0: 2, 1: 2, 2: 2, 3: 2, 4: 2}\n",
+      "[5, 8, 6, 7, 2, 1, 3, 4]\n",
+      "[2, 1, 8, 6, 3, 5, 7, 4]\n",
+      "[[5, 8, 1, 6, 2, 3, 7, 4], [2, 8, 6, 3, 1, 5, 7, 4], [3, 8, 6, 2, 1, 5, 7, 4], [2, 7, 1, 6, 3, 5, 8, 4], [5, 7, 3, 6, 2, 1, 8, 4]]\n",
+      "4 6\n",
+      "[[1, 2], [5, 3]]\n",
+      "[3 8 2 6 1 5 7 4]\n",
+      "[1 8 6 5 2 3 7 4]\n",
+      "6\n",
+      "0\n",
+      "1\n",
+      "2\n",
+      "{5: 8, 6: 3, 0: 2, 1: 2, 2: 2, 3: 2, 4: 2}\n",
+      "[7, 8, 2, 6, 1, 5, 3, 4]\n",
+      "[1, 6, 8, 5, 2, 3, 7, 4]\n",
+      "[[5, 8, 1, 6, 2, 3, 7, 4], [2, 8, 6, 3, 1, 5, 7, 4], [3, 8, 6, 2, 1, 5, 7, 4], [2, 7, 1, 6, 3, 5, 8, 4], [5, 7, 3, 6, 2, 1, 8, 4]]\n",
+      "1 5\n",
+      "[[8, 8], [6, 1], [3, 6], [1, 2]]\n",
+      "[5 8 6 3 1 2 7 4]\n",
+      "[3 8 1 6 2 5 7 4]\n",
+      "3\n",
+      "1\n",
+      "5\n",
+      "3\n",
+      "{5: 6, 6: 3, 0: 2, 1: 2, 2: 2, 3: 2, 4: 2}\n",
+      "[5, 3, 6, 8, 1, 2, 7, 4]\n",
+      "[3, 8, 1, 5, 2, 6, 7, 4]\n",
+      "[[5, 8, 1, 6, 2, 3, 7, 4], [2, 8, 6, 3, 1, 5, 7, 4], [3, 8, 6, 2, 1, 5, 7, 4], [2, 7, 1, 6, 3, 5, 8, 4], [5, 7, 3, 6, 2, 1, 8, 4]]\n",
+      "4 6\n",
+      "[[1, 2], [5, 3]]\n",
+      "[3 8 2 6 1 5 7 4]\n",
+      "[1 8 6 5 2 3 7 4]\n",
+      "0\n",
+      "2\n",
+      "0\n",
+      "4\n",
+      "{6: 5, 5: 4, 0: 2, 1: 2, 2: 2, 3: 2, 4: 2}\n",
+      "[2, 8, 6, 5, 1, 3, 7, 4]\n",
+      "[2, 8, 3, 6, 1, 5, 7, 4]\n",
+      "[[5, 8, 1, 6, 2, 3, 7, 4], [2, 8, 6, 3, 1, 5, 7, 4], [3, 8, 6, 2, 1, 5, 7, 4], [2, 7, 1, 6, 3, 5, 8, 4], [5, 7, 3, 6, 2, 1, 8, 4]]\n",
+      "4 5\n",
+      "[[1, 2]]\n",
+      "[5 8 2 6 1 3 7 4]\n",
+      "[1 8 6 3 2 5 7 4]\n",
+      "5\n",
+      "1\n",
+      "5\n",
+      "2\n",
+      "{5: 5, 6: 5, 0: 2, 1: 2, 2: 2, 3: 2, 4: 2}\n",
+      "[5, 3, 2, 6, 1, 8, 7, 4]\n",
+      "[1, 8, 5, 3, 2, 6, 7, 4]\n",
+      "[[5, 8, 1, 6, 2, 3, 7, 4], [2, 8, 6, 3, 1, 5, 7, 4], [3, 8, 6, 2, 1, 5, 7, 4], [2, 7, 1, 6, 3, 5, 8, 4], [5, 7, 3, 6, 2, 1, 8, 4]]\n",
+      "0 6\n",
+      "[[2, 5], [8, 8], [6, 1], [3, 6], [1, 2], [5, 3]]\n",
+      "[2 8 6 3 1 5 7 4]\n",
+      "[5 8 1 6 2 3 7 4]\n",
+      "4\n",
+      "0\n",
+      "4\n",
+      "0\n",
+      "{6: 4, 5: 3, 0: 2, 1: 2, 2: 2, 3: 2, 4: 2}\n",
+      "[2, 8, 1, 6, 5, 3, 7, 4]\n",
+      "[1, 8, 6, 3, 2, 5, 7, 4]\n",
+      "[[5, 8, 1, 6, 2, 3, 7, 4], [2, 8, 6, 3, 1, 5, 7, 4], [3, 8, 6, 2, 1, 5, 7, 4], [2, 7, 1, 6, 3, 5, 8, 4], [5, 7, 3, 6, 2, 1, 8, 4]]\n",
+      "0 1\n",
+      "[[2, 5]]\n",
+      "[2 8 1 6 5 3 7 4]\n",
+      "[5 8 6 3 1 2 7 4]\n",
+      "2\n",
+      "1\n",
+      "2\n",
+      "3\n",
+      "{6: 8, 5: 3, 0: 2, 1: 2, 2: 2, 3: 2, 4: 2}\n",
+      "[5, 8, 3, 6, 1, 2, 7, 4]\n",
+      "[2, 1, 8, 6, 5, 3, 7, 4]\n",
+      "[[5, 8, 1, 6, 2, 3, 7, 4], [2, 8, 6, 3, 1, 5, 7, 4], [3, 8, 6, 2, 1, 5, 7, 4], [2, 7, 1, 6, 3, 5, 8, 4], [5, 7, 3, 6, 2, 1, 8, 4]]\n",
+      "0 3\n",
+      "[[2, 5], [8, 8], [6, 1]]\n",
+      "[2 8 6 1 5 3 7 4]\n",
+      "[5 8 1 3 6 2 7 4]\n",
+      "6\n",
+      "0\n",
+      "2\n",
+      "1\n",
+      "{5: 6, 6: 3, 0: 2, 1: 2, 2: 2, 3: 2, 4: 2}\n",
+      "[7, 8, 6, 1, 5, 3, 2, 4]\n",
+      "[5, 1, 8, 3, 6, 2, 7, 4]\n",
+      "[[5, 8, 1, 6, 2, 3, 7, 4], [2, 8, 6, 3, 1, 5, 7, 4], [3, 8, 6, 2, 1, 5, 7, 4], [2, 7, 1, 6, 3, 5, 8, 4], [5, 7, 3, 6, 2, 1, 8, 4]]\n",
+      "4 5\n",
+      "[[1, 2]]\n",
+      "[5 8 2 6 1 3 7 4]\n",
+      "[1 8 6 3 2 5 7 4]\n",
+      "2\n",
+      "5\n",
+      "2\n",
+      "4\n",
+      "{5: 8, 6: 5, 0: 2, 1: 2, 2: 2, 3: 2, 4: 2}\n",
+      "[5, 8, 3, 6, 1, 2, 7, 4]\n",
+      "[1, 8, 2, 3, 6, 5, 7, 4]\n",
+      "[[5, 8, 1, 6, 2, 3, 7, 4], [2, 8, 6, 3, 1, 5, 7, 4], [3, 8, 6, 2, 1, 5, 7, 4], [2, 7, 1, 6, 3, 5, 8, 4], [5, 7, 3, 6, 2, 1, 8, 4]]\n",
+      "2 3\n",
+      "[[6, 1]]\n",
+      "[5 8 6 1 2 3 7 4]\n",
+      "[2 8 1 3 6 5 7 4]\n",
+      "1\n",
+      "0\n",
+      "5\n",
+      "6\n",
+      "{5: 8, 6: 5, 0: 2, 1: 2, 2: 2, 3: 2, 4: 2}\n",
+      "[8, 5, 6, 1, 2, 3, 7, 4]\n",
+      "[2, 8, 1, 3, 6, 7, 5, 4]\n",
+      "[[5, 8, 1, 6, 2, 3, 7, 4], [2, 8, 6, 3, 1, 5, 7, 4], [3, 8, 6, 2, 1, 5, 7, 4], [2, 7, 1, 6, 3, 5, 8, 4], [5, 7, 3, 6, 2, 1, 8, 4]]\n",
+      "0 3\n",
+      "[[2, 5], [8, 8], [6, 1]]\n",
+      "[2 8 6 1 5 3 7 4]\n",
+      "[5 8 1 3 6 2 7 4]\n",
+      "0\n",
+      "2\n",
+      "5\n",
+      "2\n",
+      "{5: 4, 0: 2, 1: 2, 2: 2, 3: 2, 4: 2, 6: 2}\n",
+      "[6, 8, 2, 1, 5, 3, 7, 4]\n",
+      "[5, 8, 1, 6, 2, 3, 7, 4]\n",
+      "[[2, 8, 6, 3, 1, 5, 7, 4], [3, 8, 6, 2, 1, 5, 7, 4], [2, 7, 1, 6, 3, 5, 8, 4], [5, 7, 3, 6, 2, 1, 8, 4], [5, 8, 2, 3, 6, 1, 7, 4]]\n",
+      "3 6\n",
+      "[[2, 3], [1, 1], [5, 5]]\n",
+      "[3 8 6 2 1 5 7 4]\n",
+      "[2 8 6 3 1 5 7 4]\n",
+      "4\n",
+      "5\n",
+      "2\n",
+      "1\n",
+      "{6: 3, 0: 2, 1: 2, 2: 2, 3: 2, 4: 2, 5: 2}\n",
+      "[2, 6, 8, 3, 1, 5, 7, 4]\n",
+      "[2, 8, 6, 3, 1, 5, 7, 4]\n",
+      "[[3, 8, 6, 2, 1, 5, 7, 4], [2, 7, 1, 6, 3, 5, 8, 4], [5, 7, 3, 6, 2, 1, 8, 4], [5, 8, 2, 3, 6, 1, 7, 4], [3, 8, 6, 2, 5, 1, 7, 4]]\n",
+      "3 4\n",
+      "[[6, 2]]\n",
+      "[3 8 2 6 1 5 7 4]\n",
+      "[6 7 1 2 3 5 8 4]\n",
+      "3\n",
+      "4\n",
+      "1\n",
+      "5\n",
+      "{6: 5, 5: 3, 0: 2, 1: 2, 2: 2, 3: 2, 4: 2}\n",
+      "[6, 5, 1, 2, 3, 7, 8, 4]\n",
+      "[3, 8, 2, 1, 6, 5, 7, 4]\n",
+      "[[3, 8, 6, 2, 1, 5, 7, 4], [2, 7, 1, 6, 3, 5, 8, 4], [5, 7, 3, 6, 2, 1, 8, 4], [5, 8, 2, 3, 6, 1, 7, 4], [3, 8, 6, 2, 5, 1, 7, 4]]\n",
+      "5 6\n",
+      "[[5, 5]]\n",
+      "[3 8 6 2 1 5 7 4]\n",
+      "[2 7 1 6 3 5 8 4]\n",
+      "3\n",
+      "2\n",
+      "0\n",
+      "4\n",
+      "{5: 4, 0: 2, 1: 2, 2: 2, 3: 2, 4: 2, 6: 2}\n",
+      "[3, 8, 2, 6, 1, 5, 7, 4]\n",
+      "[3, 8, 6, 2, 1, 5, 7, 4]\n",
+      "[[2, 7, 1, 6, 3, 5, 8, 4], [5, 7, 3, 6, 2, 1, 8, 4], [5, 8, 2, 3, 6, 1, 7, 4], [3, 8, 6, 2, 5, 1, 7, 4], [3, 7, 1, 6, 2, 5, 8, 4]]\n",
+      "4 5\n",
+      "[[2, 3]]\n",
+      "[3 7 1 6 2 5 8 4]\n",
+      "[5 7 2 6 3 1 8 4]\n",
+      "4\n",
+      "1\n",
+      "5\n",
+      "2\n",
+      "{5: 7, 6: 3, 0: 2, 1: 2, 2: 2, 3: 2, 4: 2}\n",
+      "[3, 2, 1, 6, 7, 5, 8, 4]\n",
+      "[5, 7, 1, 6, 3, 2, 8, 4]\n",
+      "[[2, 7, 1, 6, 3, 5, 8, 4], [5, 7, 3, 6, 2, 1, 8, 4], [5, 8, 2, 3, 6, 1, 7, 4], [3, 8, 6, 2, 5, 1, 7, 4], [3, 7, 1, 6, 2, 5, 8, 4]]\n",
+      "3 4\n",
+      "[[6, 6]]\n",
+      "[2 7 1 6 3 5 8 4]\n",
+      "[5 7 3 6 2 1 8 4]\n",
+      "6\n",
+      "2\n",
+      "6\n",
+      "4\n",
+      "{5: 3, 6: 3, 0: 2, 1: 2, 2: 2, 3: 2, 4: 2}\n",
+      "[2, 7, 8, 6, 3, 5, 1, 4]\n",
+      "[5, 7, 3, 6, 8, 1, 2, 4]\n",
+      "[[2, 7, 1, 6, 3, 5, 8, 4], [5, 7, 3, 6, 2, 1, 8, 4], [5, 8, 2, 3, 6, 1, 7, 4], [3, 8, 6, 2, 5, 1, 7, 4], [3, 7, 1, 6, 2, 5, 8, 4]]\n",
+      "5 6\n",
+      "[[1, 5]]\n",
+      "[2 7 5 6 3 1 8 4]\n",
+      "[1 7 3 6 2 5 8 4]\n",
+      "5\n",
+      "2\n",
+      "1\n",
+      "4\n",
+      "{6: 5, 0: 2, 1: 2, 2: 2, 3: 2, 4: 2, 5: 2}\n",
+      "[1, 2, 3, 6, 7, 5, 8, 4]\n",
+      "[2, 7, 1, 6, 3, 5, 8, 4]\n",
+      "[[5, 7, 3, 6, 2, 1, 8, 4], [5, 8, 2, 3, 6, 1, 7, 4], [3, 8, 6, 2, 5, 1, 7, 4], [3, 7, 1, 6, 2, 5, 8, 4], [2, 7, 1, 6, 3, 5, 8, 4]]\n",
+      "5 6\n",
+      "[[1, 1]]\n",
+      "[5 7 3 6 2 1 8 4]\n",
+      "[5 8 2 3 6 1 7 4]\n",
+      "2\n",
+      "0\n",
+      "1\n",
+      "4\n",
+      "{5: 4, 6: 3, 0: 2, 1: 2, 2: 2, 3: 2, 4: 2}\n",
+      "[3, 7, 5, 6, 2, 1, 8, 4]\n",
+      "[5, 6, 2, 3, 8, 1, 7, 4]\n",
+      "[[5, 7, 3, 6, 2, 1, 8, 4], [5, 8, 2, 3, 6, 1, 7, 4], [3, 8, 6, 2, 5, 1, 7, 4], [3, 7, 1, 6, 2, 5, 8, 4], [2, 7, 1, 6, 3, 5, 8, 4]]\n",
+      "2 4\n",
+      "[[2, 3], [3, 6]]\n",
+      "[5 7 2 3 6 1 8 4]\n",
+      "[5 8 3 6 2 1 7 4]\n",
+      "2\n",
+      "6\n",
+      "2\n",
+      "1\n",
+      "{5: 5, 0: 2, 1: 2, 2: 2, 3: 2, 4: 2, 6: 1}\n",
+      "[5, 7, 8, 3, 6, 1, 2, 4]\n",
+      "[5, 7, 3, 6, 2, 1, 8, 4]\n",
+      "[[5, 8, 2, 3, 6, 1, 7, 4], [3, 8, 6, 2, 5, 1, 7, 4], [3, 7, 1, 6, 2, 5, 8, 4], [2, 7, 1, 6, 3, 5, 8, 4], [5, 3, 8, 6, 2, 1, 7, 4]]\n",
+      "3 4\n",
+      "[[3, 6]]\n",
+      "[5 6 8 3 2 1 7 4]\n",
+      "[5 8 2 6 3 1 7 4]\n",
+      "5\n",
+      "2\n",
+      "6\n",
+      "0\n",
+      "{6: 5, 5: 3, 0: 2, 1: 2, 2: 2, 3: 2, 4: 1}\n",
+      "[7, 8, 2, 6, 3, 1, 5, 4]\n",
+      "[5, 6, 1, 3, 2, 8, 7, 4]\n",
+      "[[5, 8, 2, 3, 6, 1, 7, 4], [3, 8, 6, 2, 5, 1, 7, 4], [3, 7, 1, 6, 2, 5, 8, 4], [2, 7, 1, 6, 3, 5, 8, 4], [5, 3, 8, 6, 2, 1, 7, 4]]\n",
+      "5 6\n",
+      "[[1, 1]]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "[5 8 2 3 6 1 7 4]\n",
+      "6\n",
+      "2\n",
+      "6\n",
+      "1\n",
+      "{5: 4, 6: 3, 0: 2, 1: 2, 2: 2, 3: 2, 4: 1}\n",
+      "[5, 3, 7, 6, 2, 1, 8, 4]\n",
+      "[5, 7, 2, 3, 6, 1, 8, 4]\n",
+      "[[5, 8, 2, 3, 6, 1, 7, 4], [3, 8, 6, 2, 5, 1, 7, 4], [3, 7, 1, 6, 2, 5, 8, 4], [2, 7, 1, 6, 3, 5, 8, 4], [5, 3, 8, 6, 2, 1, 7, 4]]\n",
+      "4 6\n",
+      "[[6, 2], [1, 1]]\n",
+      "[5 3 8 2 6 1 7 4]\n",
+      "[5 8 6 3 2 1 7 4]\n",
+      "3\n",
+      "4\n",
+      "1\n",
+      "2\n",
+      "{6: 4, 0: 2, 1: 2, 2: 2, 3: 2, 4: 1, 5: 1}\n",
+      "[5, 6, 8, 3, 2, 1, 7, 4]\n",
+      "[5, 8, 2, 3, 6, 1, 7, 4]\n",
+      "[[3, 8, 6, 2, 5, 1, 7, 4], [3, 7, 1, 6, 2, 5, 8, 4], [2, 7, 1, 6, 3, 5, 8, 4], [5, 3, 8, 6, 2, 1, 7, 4], [5, 3, 8, 6, 2, 1, 7, 4]]\n",
+      "1 4\n",
+      "[[3, 3], [8, 8], [6, 6]]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "6\n",
+      "3\n",
+      "3\n",
+      "4\n",
+      "{6: 3, 0: 2, 1: 2, 2: 2, 5: 2, 3: 1, 4: 1}\n",
+      "[5, 3, 8, 2, 6, 1, 7, 4]\n",
+      "[3, 8, 6, 2, 5, 1, 7, 4]\n",
+      "[[3, 7, 1, 6, 2, 5, 8, 4], [2, 7, 1, 6, 3, 5, 8, 4], [5, 3, 8, 6, 2, 1, 7, 4], [5, 3, 8, 6, 2, 1, 7, 4], [5, 3, 8, 7, 2, 1, 6, 4]]\n",
+      "3 6\n",
+      "[[6, 6], [2, 2], [1, 1]]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "1\n",
+      "5\n",
+      "1\n",
+      "2\n",
+      "{6: 4, 0: 2, 1: 2, 4: 2, 2: 1, 3: 1, 5: 1}\n",
+      "[5, 8, 3, 6, 2, 1, 7, 4]\n",
+      "[3, 7, 1, 6, 2, 5, 8, 4]\n",
+      "[[2, 7, 1, 6, 3, 5, 8, 4], [5, 3, 8, 6, 2, 1, 7, 4], [5, 3, 8, 6, 2, 1, 7, 4], [5, 3, 8, 7, 2, 1, 6, 4], [5, 1, 8, 6, 2, 3, 7, 4]]\n",
+      "4 6\n",
+      "[[2, 2], [1, 1]]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "2\n",
+      "1\n",
+      "4\n",
+      "0\n",
+      "{5: 4, 6: 3, 0: 2, 3: 2, 1: 1, 2: 1, 4: 1}\n",
+      "[5, 8, 3, 6, 2, 1, 7, 4]\n",
+      "[2, 3, 8, 6, 5, 1, 7, 4]\n",
+      "[[2, 7, 1, 6, 3, 5, 8, 4], [5, 3, 8, 6, 2, 1, 7, 4], [5, 3, 8, 6, 2, 1, 7, 4], [5, 3, 8, 7, 2, 1, 6, 4], [5, 1, 8, 6, 2, 3, 7, 4]]\n",
+      "0 1\n",
+      "[[5, 5]]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "3\n",
+      "6\n",
+      "4\n",
+      "2\n",
+      "{0: 2, 3: 2, 5: 2, 1: 1, 2: 1, 4: 1, 6: 1}\n",
+      "[2, 7, 1, 6, 3, 5, 8, 4]\n",
+      "[5, 3, 8, 7, 2, 1, 6, 4]\n",
+      "[[5, 3, 8, 6, 2, 1, 7, 4], [5, 3, 8, 6, 2, 1, 7, 4], [5, 1, 8, 6, 2, 3, 7, 4], [5, 3, 8, 7, 2, 1, 6, 4], [5, 3, 2, 6, 8, 1, 7, 4]]\n",
+      "5 6\n",
+      "[[1, 1]]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "4\n",
+      "0\n",
+      "0\n",
+      "1\n",
+      "{6: 4, 5: 3, 3: 2, 0: 1, 1: 1, 2: 1, 4: 1}\n",
+      "[3, 5, 8, 6, 2, 1, 7, 4]\n",
+      "[2, 3, 8, 6, 5, 1, 7, 4]\n",
+      "[[5, 3, 8, 6, 2, 1, 7, 4], [5, 3, 8, 6, 2, 1, 7, 4], [5, 1, 8, 6, 2, 3, 7, 4], [5, 3, 8, 7, 2, 1, 6, 4], [5, 3, 2, 6, 8, 1, 7, 4]]\n",
+      "3 5\n",
+      "[[6, 6], [2, 2]]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "3\n",
+      "1\n",
+      "4\n",
+      "0\n",
+      "{5: 4, 6: 3, 3: 2, 0: 1, 1: 1, 2: 1, 4: 1}\n",
+      "[5, 6, 8, 3, 2, 1, 7, 4]\n",
+      "[2, 3, 8, 6, 5, 1, 7, 4]\n",
+      "[[5, 3, 8, 6, 2, 1, 7, 4], [5, 3, 8, 6, 2, 1, 7, 4], [5, 1, 8, 6, 2, 3, 7, 4], [5, 3, 8, 7, 2, 1, 6, 4], [5, 3, 2, 6, 8, 1, 7, 4]]\n",
+      "3 5\n",
+      "[[6, 6], [2, 2]]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "2\n",
+      "3\n",
+      "6\n",
+      "1\n",
+      "{6: 4, 5: 3, 3: 2, 0: 1, 1: 1, 2: 1, 4: 1}\n",
+      "[5, 7, 8, 6, 2, 1, 3, 4]\n",
+      "[5, 3, 6, 8, 2, 1, 7, 4]\n",
+      "[[5, 3, 8, 6, 2, 1, 7, 4], [5, 3, 8, 6, 2, 1, 7, 4], [5, 1, 8, 6, 2, 3, 7, 4], [5, 3, 8, 7, 2, 1, 6, 4], [5, 3, 2, 6, 8, 1, 7, 4]]\n",
+      "4 6\n",
+      "[[2, 2], [1, 1]]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "2\n",
+      "5\n",
+      "4\n",
+      "6\n",
+      "{6: 3, 3: 2, 5: 2, 0: 1, 1: 1, 2: 1, 4: 1}\n",
+      "[5, 3, 8, 6, 7, 1, 2, 4]\n",
+      "[5, 3, 8, 7, 2, 1, 6, 4]\n",
+      "[[5, 3, 8, 6, 2, 1, 7, 4], [5, 3, 8, 6, 2, 1, 7, 4], [5, 1, 8, 6, 2, 3, 7, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 3, 1, 6, 2, 8, 7, 4]]\n",
+      "4 6\n",
+      "[[2, 2], [1, 1]]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "6\n",
+      "0\n",
+      "2\n",
+      "4\n",
+      "{4: 2, 5: 2, 0: 1, 1: 1, 2: 1, 3: 1, 6: 1}\n",
+      "[5, 3, 1, 6, 2, 8, 7, 4]\n",
+      "[7, 3, 8, 6, 2, 1, 5, 4]\n",
+      "[[5, 3, 8, 6, 2, 1, 7, 4], [5, 3, 8, 6, 2, 1, 7, 4], [5, 1, 8, 6, 2, 3, 7, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 3, 2, 6, 8, 1, 7, 4]]\n",
+      "5 6\n",
+      "[[1, 1]]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "1\n",
+      "3\n",
+      "4\n",
+      "0\n",
+      "{5: 4, 6: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 6, 8, 3, 2, 1, 7, 4]\n",
+      "[2, 3, 8, 6, 5, 1, 7, 4]\n",
+      "[[5, 3, 8, 6, 2, 1, 7, 4], [5, 3, 8, 6, 2, 1, 7, 4], [5, 1, 8, 6, 2, 3, 7, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 3, 2, 6, 8, 1, 7, 4]]\n",
+      "1 6\n",
+      "[[3, 3], [8, 8], [6, 6], [2, 2], [1, 1]]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "0\n",
+      "5\n",
+      "5\n",
+      "2\n",
+      "{5: 2, 6: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[1, 3, 8, 6, 2, 5, 7, 4]\n",
+      "[5, 3, 1, 6, 2, 8, 7, 4]\n",
+      "[[5, 3, 8, 6, 2, 1, 7, 4], [5, 3, 8, 6, 2, 1, 7, 4], [5, 1, 8, 6, 2, 3, 7, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 3, 2, 6, 8, 1, 7, 4]]\n",
+      "3 4\n",
+      "[[6, 6]]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "5\n",
+      "1\n",
+      "2\n",
+      "5\n",
+      "{6: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1}\n",
+      "[5, 3, 1, 6, 2, 8, 7, 4]\n",
+      "[5, 3, 8, 6, 2, 1, 7, 4]\n",
+      "[[5, 3, 8, 6, 2, 1, 7, 4], [5, 1, 8, 6, 2, 3, 7, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 1, 8, 6, 2, 3, 7, 4]]\n",
+      "2 4\n",
+      "[[8, 8], [6, 6]]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "[5 1 8 6 2 3 7 4]\n",
+      "4\n",
+      "5\n",
+      "2\n",
+      "5\n",
+      "{5: 4, 6: 4, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 3, 8, 6, 1, 2, 7, 4]\n",
+      "[5, 1, 3, 6, 2, 8, 7, 4]\n",
+      "[[5, 3, 8, 6, 2, 1, 7, 4], [5, 1, 8, 6, 2, 3, 7, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 1, 8, 6, 2, 3, 7, 4]]\n",
+      "5 6\n",
+      "[[3, 1]]\n",
+      "[5 1 8 6 2 3 7 4]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "0\n",
+      "6\n",
+      "0\n",
+      "2\n",
+      "{5: 2, 6: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[7, 1, 8, 6, 2, 3, 5, 4]\n",
+      "[8, 3, 5, 6, 2, 1, 7, 4]\n",
+      "[[5, 3, 8, 6, 2, 1, 7, 4], [5, 1, 8, 6, 2, 3, 7, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 1, 8, 6, 2, 3, 7, 4]]\n",
+      "4 6\n",
+      "[[2, 2], [3, 1]]\n",
+      "[5 1 8 6 2 3 7 4]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "0\n",
+      "5\n",
+      "6\n",
+      "0\n",
+      "{5: 3, 6: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[3, 1, 8, 6, 2, 5, 7, 4]\n",
+      "[7, 3, 8, 6, 2, 1, 5, 4]\n",
+      "[[5, 3, 8, 6, 2, 1, 7, 4], [5, 1, 8, 6, 2, 3, 7, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 1, 8, 6, 2, 3, 7, 4]]\n",
+      "1 5\n",
+      "[[1, 3], [8, 8], [6, 6], [2, 2]]\n",
+      "[5 1 8 6 2 3 7 4]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "2\n",
+      "6\n",
+      "1\n",
+      "6\n",
+      "{6: 4, 5: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 7, 8, 6, 2, 1, 3, 4]\n",
+      "[5, 1, 7, 6, 2, 3, 8, 4]\n",
+      "[[5, 3, 8, 6, 2, 1, 7, 4], [5, 1, 8, 6, 2, 3, 7, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 1, 8, 6, 2, 3, 7, 4]]\n",
+      "5 6\n",
+      "[[3, 1]]\n",
+      "[5 1 8 6 2 3 7 4]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "0\n",
+      "3\n",
+      "4\n",
+      "1\n",
+      "{5: 4, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 6: 1}\n",
+      "[6, 1, 8, 5, 2, 3, 7, 4]\n",
+      "[5, 3, 8, 6, 2, 1, 7, 4]\n",
+      "[[5, 1, 8, 6, 2, 3, 7, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 1, 8, 6, 2, 3, 7, 4], [5, 2, 8, 6, 3, 1, 7, 4]]\n",
+      "5 6\n",
+      "[[1, 3]]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "[5 1 2 6 8 3 7 4]\n",
+      "4\n",
+      "1\n",
+      "1\n",
+      "6\n",
+      "{0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 6: 1}\n",
+      "[5, 1, 8, 6, 2, 3, 7, 4]\n",
+      "[5, 3, 2, 6, 8, 1, 7, 4]\n",
+      "[[5, 3, 2, 6, 8, 1, 7, 4], [5, 1, 8, 6, 2, 3, 7, 4], [5, 2, 8, 6, 3, 1, 7, 4], [5, 2, 8, 6, 3, 1, 7, 4], [5, 7, 2, 6, 8, 3, 1, 4]]\n",
+      "0 1\n",
+      "[[5, 5]]\n",
+      "[5 3 2 6 8 1 7 4]\n",
+      "[5 1 8 6 2 3 7 4]\n",
+      "2\n",
+      "4\n",
+      "1\n",
+      "3\n",
+      "{6: 4, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1}\n",
+      "[5, 6, 8, 1, 2, 3, 7, 4]\n",
+      "[5, 3, 2, 6, 8, 1, 7, 4]\n",
+      "[[5, 1, 8, 6, 2, 3, 7, 4], [5, 2, 8, 6, 3, 1, 7, 4], [5, 2, 8, 6, 3, 1, 7, 4], [5, 7, 2, 6, 8, 3, 1, 4], [5, 3, 8, 6, 2, 1, 7, 4]]\n",
+      "5 6\n",
+      "[[1, 3]]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "[5 2 8 6 1 3 7 4]\n",
+      "3\n",
+      "5\n",
+      "0\n",
+      "5\n",
+      "{6: 5, 5: 4, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[3, 2, 8, 6, 1, 5, 7, 4]\n",
+      "[5, 3, 8, 1, 2, 6, 7, 4]\n",
+      "[[5, 1, 8, 6, 2, 3, 7, 4], [5, 2, 8, 6, 3, 1, 7, 4], [5, 2, 8, 6, 3, 1, 7, 4], [5, 7, 2, 6, 8, 3, 1, 4], [5, 3, 8, 6, 2, 1, 7, 4]]\n",
+      "4 5\n",
+      "[[3, 2]]\n",
+      "[5 1 8 6 3 2 7 4]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "2\n",
+      "6\n",
+      "2\n",
+      "4\n",
+      "{5: 4, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 6: 1}\n",
+      "[5, 1, 7, 6, 3, 2, 8, 4]\n",
+      "[5, 1, 8, 6, 2, 3, 7, 4]\n",
+      "[[5, 2, 8, 6, 3, 1, 7, 4], [5, 2, 8, 6, 3, 1, 7, 4], [5, 7, 2, 6, 8, 3, 1, 4], [5, 3, 8, 6, 2, 1, 7, 4], [5, 3, 2, 6, 8, 1, 7, 4]]\n",
+      "1 4\n",
+      "[[2, 2], [8, 8], [6, 6]]\n",
+      "[5 2 8 6 3 1 7 4]\n",
+      "[5 2 8 6 3 1 7 4]\n",
+      "4\n",
+      "2\n",
+      "3\n",
+      "0\n",
+      "{5: 4, 6: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 2, 3, 6, 8, 1, 7, 4]\n",
+      "[6, 2, 8, 5, 3, 1, 7, 4]\n",
+      "[[5, 2, 8, 6, 3, 1, 7, 4], [5, 2, 8, 6, 3, 1, 7, 4], [5, 7, 2, 6, 8, 3, 1, 4], [5, 3, 8, 6, 2, 1, 7, 4], [5, 3, 2, 6, 8, 1, 7, 4]]\n",
+      "0 4\n",
+      "[[5, 5], [2, 2], [8, 8], [6, 6]]\n",
+      "[5 2 8 6 3 1 7 4]\n",
+      "[5 2 8 6 3 1 7 4]\n",
+      "4\n",
+      "2\n",
+      "4\n",
+      "2\n",
+      "{5: 4, 6: 4, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 2, 3, 6, 8, 1, 7, 4]\n",
+      "[5, 2, 3, 6, 8, 1, 7, 4]\n",
+      "[[5, 2, 8, 6, 3, 1, 7, 4], [5, 2, 8, 6, 3, 1, 7, 4], [5, 7, 2, 6, 8, 3, 1, 4], [5, 3, 8, 6, 2, 1, 7, 4], [5, 3, 2, 6, 8, 1, 7, 4]]\n",
+      "2 6\n",
+      "[[8, 8], [6, 6], [3, 3], [1, 1]]\n",
+      "[5 2 8 6 3 1 7 4]\n",
+      "[5 2 8 6 3 1 7 4]\n",
+      "3\n",
+      "5\n",
+      "4\n",
+      "3\n",
+      "{5: 4, 6: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 2, 8, 1, 3, 6, 7, 4]\n",
+      "[5, 2, 8, 3, 6, 1, 7, 4]\n",
+      "[[5, 2, 8, 6, 3, 1, 7, 4], [5, 2, 8, 6, 3, 1, 7, 4], [5, 7, 2, 6, 8, 3, 1, 4], [5, 3, 8, 6, 2, 1, 7, 4], [5, 3, 2, 6, 8, 1, 7, 4]]\n",
+      "1 5\n",
+      "[[2, 2], [8, 8], [6, 6], [3, 3]]\n",
+      "[5 2 8 6 3 1 7 4]\n",
+      "[5 2 8 6 3 1 7 4]\n",
+      "4\n",
+      "3\n",
+      "1\n",
+      "0\n",
+      "{5: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 6: 1}\n",
+      "[5, 2, 8, 3, 6, 1, 7, 4]\n",
+      "[5, 2, 8, 6, 3, 1, 7, 4]\n",
+      "[[5, 2, 8, 6, 3, 1, 7, 4], [5, 7, 2, 6, 8, 3, 1, 4], [5, 3, 8, 6, 2, 1, 7, 4], [5, 3, 2, 6, 8, 1, 7, 4], [2, 5, 8, 6, 3, 1, 7, 4]]\n",
+      "2 5\n",
+      "[[2, 8], [6, 6], [8, 3]]\n",
+      "[5 3 2 6 8 1 7 4]\n",
+      "[5 7 8 6 3 2 1 4]\n",
+      "6\n",
+      "1\n",
+      "6\n",
+      "0\n",
+      "{6: 5, 5: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[1, 7, 8, 6, 3, 2, 5, 4]\n",
+      "[5, 7, 2, 6, 8, 1, 3, 4]\n",
+      "[[5, 2, 8, 6, 3, 1, 7, 4], [5, 7, 2, 6, 8, 3, 1, 4], [5, 3, 8, 6, 2, 1, 7, 4], [5, 3, 2, 6, 8, 1, 7, 4], [2, 5, 8, 6, 3, 1, 7, 4]]\n",
+      "2 3\n",
+      "[[2, 8]]\n",
+      "[5 8 2 6 3 1 7 4]\n",
+      "[5 7 8 6 2 3 1 4]\n",
+      "1\n",
+      "0\n",
+      "2\n",
+      "6\n",
+      "{6: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1}\n",
+      "[5, 7, 1, 6, 2, 3, 8, 4]\n",
+      "[5, 2, 8, 6, 3, 1, 7, 4]\n",
+      "[[5, 7, 2, 6, 8, 3, 1, 4], [5, 3, 8, 6, 2, 1, 7, 4], [5, 3, 2, 6, 8, 1, 7, 4], [2, 5, 8, 6, 3, 1, 7, 4], [8, 5, 2, 6, 3, 1, 7, 4]]\n",
+      "3 5\n",
+      "[[6, 6], [2, 8]]\n",
+      "[5 7 8 6 2 3 1 4]\n",
+      "[5 3 2 6 8 1 7 4]\n",
+      "0\n",
+      "4\n",
+      "4\n",
+      "6\n",
+      "{6: 4, 5: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 3, 2, 6, 7, 1, 8, 4]\n",
+      "[2, 7, 8, 6, 5, 3, 1, 4]\n",
+      "[[5, 7, 2, 6, 8, 3, 1, 4], [5, 3, 8, 6, 2, 1, 7, 4], [5, 3, 2, 6, 8, 1, 7, 4], [2, 5, 8, 6, 3, 1, 7, 4], [8, 5, 2, 6, 3, 1, 7, 4]]\n",
+      "3 6\n",
+      "[[6, 6], [2, 8], [1, 3]]\n",
+      "[5 7 8 6 2 1 3 4]\n",
+      "[5 1 2 6 8 3 7 4]\n",
+      "6\n",
+      "2\n",
+      "1\n",
+      "2\n",
+      "{5: 2, 6: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 7, 3, 6, 2, 1, 8, 4]\n",
+      "[5, 2, 1, 6, 8, 3, 7, 4]\n",
+      "[[5, 7, 2, 6, 8, 3, 1, 4], [5, 3, 8, 6, 2, 1, 7, 4], [5, 3, 2, 6, 8, 1, 7, 4], [2, 5, 8, 6, 3, 1, 7, 4], [8, 5, 2, 6, 3, 1, 7, 4]]\n",
+      "0 1\n",
+      "[[5, 5]]\n",
+      "[5 7 2 6 8 3 1 4]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "0\n",
+      "1\n",
+      "5\n",
+      "4\n",
+      "{6: 4, 5: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 3, 8, 6, 1, 2, 7, 4]\n",
+      "[7, 5, 2, 6, 8, 3, 1, 4]\n",
+      "[[5, 7, 2, 6, 8, 3, 1, 4], [5, 3, 8, 6, 2, 1, 7, 4], [5, 3, 2, 6, 8, 1, 7, 4], [2, 5, 8, 6, 3, 1, 7, 4], [8, 5, 2, 6, 3, 1, 7, 4]]\n",
+      "1 2\n",
+      "[[3, 7]]\n",
+      "[5 3 2 6 8 7 1 4]\n",
+      "[5 7 8 6 2 1 3 4]\n",
+      "2\n",
+      "4\n",
+      "3\n",
+      "5\n",
+      "{6: 4, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1}\n",
+      "[5, 7, 8, 1, 2, 6, 3, 4]\n",
+      "[5, 7, 2, 6, 8, 3, 1, 4]\n",
+      "[[5, 3, 8, 6, 2, 1, 7, 4], [5, 3, 2, 6, 8, 1, 7, 4], [2, 5, 8, 6, 3, 1, 7, 4], [8, 5, 2, 6, 3, 1, 7, 4], [5, 3, 8, 6, 2, 7, 1, 4]]\n",
+      "1 4\n",
+      "[[3, 3], [2, 8], [6, 6]]\n",
+      "[5 3 2 6 8 1 7 4]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "4\n",
+      "3\n",
+      "6\n",
+      "4\n",
+      "{5: 4, 6: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 3, 2, 8, 6, 1, 7, 4]\n",
+      "[5, 3, 8, 6, 7, 1, 2, 4]\n",
+      "[[5, 3, 8, 6, 2, 1, 7, 4], [5, 3, 2, 6, 8, 1, 7, 4], [2, 5, 8, 6, 3, 1, 7, 4], [8, 5, 2, 6, 3, 1, 7, 4], [5, 3, 8, 6, 2, 7, 1, 4]]\n",
+      "5 6\n",
+      "[[1, 1]]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "[5 3 2 6 8 1 7 4]\n",
+      "3\n",
+      "2\n",
+      "5\n",
+      "4\n",
+      "{6: 5, 5: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 3, 2, 6, 1, 8, 7, 4]\n",
+      "[5, 3, 6, 8, 2, 1, 7, 4]\n",
+      "[[5, 3, 8, 6, 2, 1, 7, 4], [5, 3, 2, 6, 8, 1, 7, 4], [2, 5, 8, 6, 3, 1, 7, 4], [8, 5, 2, 6, 3, 1, 7, 4], [5, 3, 8, 6, 2, 7, 1, 4]]\n",
+      "2 3\n",
+      "[[2, 8]]\n",
+      "[5 3 2 6 8 1 7 4]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "2\n",
+      "0\n",
+      "5\n",
+      "6\n",
+      "{5: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 6: 1}\n",
+      "[2, 3, 5, 6, 8, 1, 7, 4]\n",
+      "[5, 3, 8, 6, 2, 1, 7, 4]\n",
+      "[[5, 3, 2, 6, 8, 1, 7, 4], [2, 5, 8, 6, 3, 1, 7, 4], [8, 5, 2, 6, 3, 1, 7, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4]]\n",
+      "4 5\n",
+      "[[3, 8]]\n",
+      "[5 8 2 6 3 1 7 4]\n",
+      "[2 5 3 6 8 1 7 4]\n",
+      "6\n",
+      "5\n",
+      "4\n",
+      "1\n",
+      "{6: 6, 5: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[2, 8, 3, 6, 5, 1, 7, 4]\n",
+      "[5, 8, 2, 6, 3, 7, 1, 4]\n",
+      "[[5, 3, 2, 6, 8, 1, 7, 4], [2, 5, 8, 6, 3, 1, 7, 4], [8, 5, 2, 6, 3, 1, 7, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4]]\n",
+      "1 6\n",
+      "[[5, 3], [8, 2], [6, 6], [3, 8], [1, 1]]\n",
+      "[2 5 8 6 3 1 7 4]\n",
+      "[5 3 2 6 8 1 7 4]\n",
+      "2\n",
+      "4\n",
+      "3\n",
+      "0\n",
+      "{5: 3, 6: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[2, 5, 3, 6, 8, 1, 7, 4]\n",
+      "[6, 3, 2, 5, 8, 1, 7, 4]\n",
+      "[[5, 3, 2, 6, 8, 1, 7, 4], [2, 5, 8, 6, 3, 1, 7, 4], [8, 5, 2, 6, 3, 1, 7, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4]]\n",
+      "5 6\n",
+      "[[1, 1]]\n",
+      "[5 3 2 6 8 1 7 4]\n",
+      "[2 5 8 6 3 1 7 4]\n",
+      "5\n",
+      "2\n",
+      "3\n",
+      "1\n",
+      "{6: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1}\n",
+      "[2, 6, 8, 5, 3, 1, 7, 4]\n",
+      "[5, 3, 2, 6, 8, 1, 7, 4]\n",
+      "[[2, 5, 8, 6, 3, 1, 7, 4], [8, 5, 2, 6, 3, 1, 7, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 1, 6, 8, 2, 7, 4]]\n",
+      "3 6\n",
+      "[[6, 6], [3, 3], [1, 1]]\n",
+      "[2 5 8 6 3 1 7 4]\n",
+      "[8 5 2 6 3 1 7 4]\n",
+      "4\n",
+      "1\n",
+      "5\n",
+      "2\n",
+      "{5: 3, 6: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[2, 3, 8, 6, 5, 1, 7, 4]\n",
+      "[8, 5, 1, 6, 3, 2, 7, 4]\n",
+      "[[2, 5, 8, 6, 3, 1, 7, 4], [8, 5, 2, 6, 3, 1, 7, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 1, 6, 8, 2, 7, 4]]\n",
+      "2 5\n",
+      "[[2, 8], [6, 6], [3, 3]]\n",
+      "[8 5 2 6 3 1 7 4]\n",
+      "[2 5 8 6 3 1 7 4]\n",
+      "2\n",
+      "1\n",
+      "4\n",
+      "6\n",
+      "{6: 5, 5: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[2, 5, 8, 6, 7, 1, 3, 4]\n",
+      "[8, 2, 5, 6, 3, 1, 7, 4]\n",
+      "[[2, 5, 8, 6, 3, 1, 7, 4], [8, 5, 2, 6, 3, 1, 7, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 1, 6, 8, 2, 7, 4]]\n",
+      "1 3\n",
+      "[[5, 5], [2, 8]]\n",
+      "[8 5 2 6 3 1 7 4]\n",
+      "[2 5 8 6 3 1 7 4]\n",
+      "0\n",
+      "1\n",
+      "5\n",
+      "2\n",
+      "{6: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1}\n",
+      "[2, 5, 1, 6, 3, 8, 7, 4]\n",
+      "[2, 5, 8, 6, 3, 1, 7, 4]\n",
+      "[[8, 5, 2, 6, 3, 1, 7, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 1, 6, 8, 2, 7, 4], [5, 8, 2, 6, 3, 1, 7, 4]]\n",
+      "0 2\n",
+      "[[5, 8], [3, 5]]\n",
+      "[5 3 2 6 8 1 7 4]\n",
+      "[8 5 3 6 2 7 1 4]\n",
+      "0\n",
+      "2\n",
+      "4\n",
+      "2\n",
+      "{5: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 6: 1}\n",
+      "[2, 3, 5, 6, 8, 1, 7, 4]\n",
+      "[8, 5, 2, 6, 3, 1, 7, 4]\n",
+      "[[5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 1, 6, 8, 2, 7, 4], [5, 8, 2, 6, 3, 1, 7, 4], [8, 5, 2, 6, 3, 7, 1, 4]]\n",
+      "0 1\n",
+      "[[5, 5]]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "5\n",
+      "0\n",
+      "6\n",
+      "2\n",
+      "{6: 3, 5: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 3, 1, 6, 2, 7, 8, 4]\n",
+      "[7, 3, 8, 6, 2, 5, 1, 4]\n",
+      "[[5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 1, 6, 8, 2, 7, 4], [5, 8, 2, 6, 3, 1, 7, 4], [8, 5, 2, 6, 3, 7, 1, 4]]\n",
+      "1 5\n",
+      "[[3, 3], [8, 8], [6, 6], [2, 2]]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "0\n",
+      "4\n",
+      "6\n",
+      "4\n",
+      "{5: 4, 6: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[2, 3, 8, 6, 5, 7, 1, 4]\n",
+      "[5, 3, 8, 6, 1, 7, 2, 4]\n",
+      "[[5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 1, 6, 8, 2, 7, 4], [5, 8, 2, 6, 3, 1, 7, 4], [8, 5, 2, 6, 3, 7, 1, 4]]\n",
+      "5 6\n",
+      "[[7, 7]]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "1\n",
+      "0\n",
+      "1\n",
+      "2\n",
+      "{5: 2, 6: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[3, 5, 8, 6, 2, 7, 1, 4]\n",
+      "[5, 8, 3, 6, 2, 7, 1, 4]\n",
+      "[[5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 1, 6, 8, 2, 7, 4], [5, 8, 2, 6, 3, 1, 7, 4], [8, 5, 2, 6, 3, 7, 1, 4]]\n",
+      "0 1\n",
+      "[[5, 5]]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "0\n",
+      "3\n",
+      "1\n",
+      "4\n",
+      "{5: 5, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 6: 1}\n",
+      "[6, 3, 8, 5, 2, 7, 1, 4]\n",
+      "[5, 3, 8, 6, 2, 7, 1, 4]\n",
+      "[[5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 1, 6, 8, 2, 7, 4], [5, 8, 2, 6, 3, 1, 7, 4], [8, 5, 2, 6, 3, 7, 1, 4], [5, 2, 8, 6, 3, 7, 1, 4]]\n",
+      "3 5\n",
+      "[[6, 6], [8, 2]]\n",
+      "[5 3 2 6 8 7 1 4]\n",
+      "[5 3 1 6 2 8 7 4]\n",
+      "1\n",
+      "5\n",
+      "3\n",
+      "1\n",
+      "{6: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1}\n",
+      "[5, 6, 1, 3, 2, 8, 7, 4]\n",
+      "[5, 3, 8, 6, 2, 7, 1, 4]\n",
+      "[[5, 3, 1, 6, 8, 2, 7, 4], [5, 8, 2, 6, 3, 1, 7, 4], [8, 5, 2, 6, 3, 7, 1, 4], [5, 2, 8, 6, 3, 7, 1, 4], [5, 7, 2, 6, 8, 3, 1, 4]]\n",
+      "5 6\n",
+      "[[1, 2]]\n",
+      "[5 3 2 6 8 1 7 4]\n",
+      "[5 8 1 6 3 2 7 4]\n",
+      "6\n",
+      "2\n",
+      "6\n",
+      "4\n",
+      "{6: 8, 5: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 8, 1, 6, 7, 2, 3, 4]\n",
+      "[5, 3, 7, 6, 8, 1, 2, 4]\n",
+      "[[5, 3, 1, 6, 8, 2, 7, 4], [5, 8, 2, 6, 3, 1, 7, 4], [8, 5, 2, 6, 3, 7, 1, 4], [5, 2, 8, 6, 3, 7, 1, 4], [5, 7, 2, 6, 8, 3, 1, 4]]\n",
+      "2 4\n",
+      "[[2, 1], [6, 6]]\n",
+      "[5 3 2 6 8 1 7 4]\n",
+      "[5 8 1 6 3 2 7 4]\n",
+      "4\n",
+      "1\n",
+      "5\n",
+      "0\n",
+      "{6: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1}\n",
+      "[2, 8, 1, 6, 3, 5, 7, 4]\n",
+      "[5, 3, 1, 6, 8, 2, 7, 4]\n",
+      "[[5, 8, 2, 6, 3, 1, 7, 4], [8, 5, 2, 6, 3, 7, 1, 4], [5, 2, 8, 6, 3, 7, 1, 4], [5, 7, 2, 6, 8, 3, 1, 4], [5, 8, 2, 6, 3, 1, 7, 4]]\n",
+      "0 2\n",
+      "[[8, 5], [5, 8]]\n",
+      "[8 5 2 6 3 1 7 4]\n",
+      "[5 8 2 6 3 7 1 4]\n",
+      "1\n",
+      "6\n",
+      "3\n",
+      "0\n",
+      "{5: 3, 6: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[8, 7, 2, 6, 3, 1, 5, 4]\n",
+      "[6, 8, 2, 5, 3, 7, 1, 4]\n",
+      "[[5, 8, 2, 6, 3, 1, 7, 4], [8, 5, 2, 6, 3, 7, 1, 4], [5, 2, 8, 6, 3, 7, 1, 4], [5, 7, 2, 6, 8, 3, 1, 4], [5, 8, 2, 6, 3, 1, 7, 4]]\n",
+      "5 6\n",
+      "[[7, 1]]\n",
+      "[5 8 2 6 3 7 1 4]\n",
+      "[8 5 2 6 3 1 7 4]\n",
+      "1\n",
+      "0\n",
+      "6\n",
+      "5\n",
+      "{0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 6: 1}\n",
+      "[5, 8, 2, 6, 3, 1, 7, 4]\n",
+      "[8, 5, 2, 6, 3, 7, 1, 4]\n",
+      "[[5, 2, 8, 6, 3, 7, 1, 4], [5, 7, 2, 6, 8, 3, 1, 4], [5, 8, 2, 6, 3, 1, 7, 4], [8, 5, 2, 6, 3, 7, 1, 4], [8, 5, 2, 6, 3, 7, 1, 4]]\n",
+      "4 6\n",
+      "[[8, 3], [3, 7]]\n",
+      "[5 2 7 6 8 3 1 4]\n",
+      "[5 8 2 6 3 7 1 4]\n",
+      "2\n",
+      "5\n",
+      "1\n",
+      "6\n",
+      "{5: 3, 6: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 2, 3, 6, 8, 7, 1, 4]\n",
+      "[5, 1, 2, 6, 3, 7, 8, 4]\n",
+      "[[5, 2, 8, 6, 3, 7, 1, 4], [5, 7, 2, 6, 8, 3, 1, 4], [5, 8, 2, 6, 3, 1, 7, 4], [8, 5, 2, 6, 3, 7, 1, 4], [8, 5, 2, 6, 3, 7, 1, 4]]\n",
+      "0 4\n",
+      "[[5, 5], [7, 2], [2, 8], [6, 6]]\n",
+      "[5 7 2 6 3 8 1 4]\n",
+      "[5 2 8 6 7 3 1 4]\n",
+      "5\n",
+      "2\n",
+      "3\n",
+      "5\n",
+      "{5: 5, 6: 4, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 7, 8, 6, 3, 2, 1, 4]\n",
+      "[5, 2, 8, 3, 7, 6, 1, 4]\n",
+      "[[5, 2, 8, 6, 3, 7, 1, 4], [5, 7, 2, 6, 8, 3, 1, 4], [5, 8, 2, 6, 3, 1, 7, 4], [8, 5, 2, 6, 3, 7, 1, 4], [8, 5, 2, 6, 3, 7, 1, 4]]\n",
+      "5 6\n",
+      "[[3, 7]]\n",
+      "[5 2 8 6 7 3 1 4]\n",
+      "[5 3 2 6 8 7 1 4]\n",
+      "1\n",
+      "2\n",
+      "2\n",
+      "4\n",
+      "{5: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 6: 1}\n",
+      "[5, 8, 2, 6, 7, 3, 1, 4]\n",
+      "[5, 2, 8, 6, 3, 7, 1, 4]\n",
+      "[[5, 7, 2, 6, 8, 3, 1, 4], [5, 8, 2, 6, 3, 1, 7, 4], [8, 5, 2, 6, 3, 7, 1, 4], [8, 5, 2, 6, 3, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4]]\n",
+      "0 5\n",
+      "[[5, 5], [8, 7], [2, 2], [6, 6], [3, 8]]\n",
+      "[5 8 2 6 3 7 1 4]\n",
+      "[5 7 2 6 8 1 3 4]\n",
+      "0\n",
+      "6\n",
+      "1\n",
+      "3\n",
+      "{5: 3, 6: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[1, 8, 2, 6, 3, 7, 5, 4]\n",
+      "[5, 6, 2, 7, 8, 1, 3, 4]\n",
+      "[[5, 7, 2, 6, 8, 3, 1, 4], [5, 8, 2, 6, 3, 1, 7, 4], [8, 5, 2, 6, 3, 7, 1, 4], [8, 5, 2, 6, 3, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4]]\n",
+      "0 3\n",
+      "[[5, 5], [8, 7], [2, 2]]\n",
+      "[5 8 2 6 7 3 1 4]\n",
+      "[5 7 2 6 3 1 8 4]\n",
+      "3\n",
+      "2\n",
+      "3\n",
+      "4\n",
+      "{5: 3, 6: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 8, 6, 2, 7, 3, 1, 4]\n",
+      "[5, 7, 2, 3, 6, 1, 8, 4]\n",
+      "[[5, 7, 2, 6, 8, 3, 1, 4], [5, 8, 2, 6, 3, 1, 7, 4], [8, 5, 2, 6, 3, 7, 1, 4], [8, 5, 2, 6, 3, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4]]\n",
+      "2 6\n",
+      "[[2, 2], [6, 6], [3, 8], [1, 3]]\n",
+      "[5 7 2 6 3 1 8 4]\n",
+      "[5 1 2 6 8 3 7 4]\n",
+      "2\n",
+      "3\n",
+      "2\n",
+      "1\n",
+      "{5: 3, 6: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 7, 6, 2, 3, 1, 8, 4]\n",
+      "[5, 2, 1, 6, 8, 3, 7, 4]\n",
+      "[[5, 7, 2, 6, 8, 3, 1, 4], [5, 8, 2, 6, 3, 1, 7, 4], [8, 5, 2, 6, 3, 7, 1, 4], [8, 5, 2, 6, 3, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4]]\n",
+      "2 5\n",
+      "[[2, 2], [6, 6], [3, 8]]\n",
+      "[5 7 2 6 3 8 1 4]\n",
+      "[5 3 2 6 8 1 7 4]\n",
+      "5\n",
+      "4\n",
+      "4\n",
+      "1\n",
+      "{0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 6: 1}\n",
+      "[5, 7, 2, 6, 8, 3, 1, 4]\n",
+      "[5, 8, 2, 6, 3, 1, 7, 4]\n",
+      "[[8, 5, 2, 6, 3, 7, 1, 4], [8, 5, 2, 6, 3, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 7, 2, 6, 8, 3, 1, 4], [5, 8, 2, 6, 3, 1, 7, 4]]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "5 6\n",
+      "[[7, 7]]\n",
+      "[8 5 2 6 3 7 1 4]\n",
+      "[8 5 2 6 3 7 1 4]\n",
+      "4\n",
+      "0\n",
+      "1\n",
+      "2\n",
+      "{6: 4, 5: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[8, 2, 5, 6, 3, 7, 1, 4]\n",
+      "[3, 5, 2, 6, 8, 7, 1, 4]\n",
+      "[[8, 5, 2, 6, 3, 7, 1, 4], [8, 5, 2, 6, 3, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 7, 2, 6, 8, 3, 1, 4], [5, 8, 2, 6, 3, 1, 7, 4]]\n",
+      "5 6\n",
+      "[[7, 7]]\n",
+      "[8 5 2 6 3 7 1 4]\n",
+      "[8 5 2 6 3 7 1 4]\n",
+      "0\n",
+      "3\n",
+      "5\n",
+      "2\n",
+      "{6: 5, 5: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[8, 5, 7, 6, 3, 2, 1, 4]\n",
+      "[6, 5, 2, 8, 3, 7, 1, 4]\n",
+      "[[8, 5, 2, 6, 3, 7, 1, 4], [8, 5, 2, 6, 3, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 7, 2, 6, 8, 3, 1, 4], [5, 8, 2, 6, 3, 1, 7, 4]]\n",
+      "5 6\n",
+      "[[7, 7]]\n",
+      "[8 5 2 6 3 7 1 4]\n",
+      "[8 5 2 6 3 7 1 4]\n",
+      "2\n",
+      "4\n",
+      "6\n",
+      "3\n",
+      "{6: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1}\n",
+      "[8, 5, 2, 1, 3, 7, 6, 4]\n",
+      "[8, 5, 2, 6, 3, 7, 1, 4]\n",
+      "[[8, 5, 2, 6, 3, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 7, 2, 6, 8, 3, 1, 4], [5, 8, 2, 6, 3, 1, 7, 4], [8, 5, 3, 6, 2, 7, 1, 4]]\n",
+      "2 6\n",
+      "[[8, 2], [6, 6], [2, 3], [7, 7]]\n",
+      "[3 5 8 6 2 7 1 4]\n",
+      "[5 8 2 6 3 7 1 4]\n",
+      "6\n",
+      "2\n",
+      "0\n",
+      "4\n",
+      "{5: 4, 6: 4, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[3, 5, 1, 6, 2, 7, 8, 4]\n",
+      "[3, 8, 2, 6, 5, 7, 1, 4]\n",
+      "[[8, 5, 2, 6, 3, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 7, 2, 6, 8, 3, 1, 4], [5, 8, 2, 6, 3, 1, 7, 4], [8, 5, 3, 6, 2, 7, 1, 4]]\n",
+      "3 6\n",
+      "[[6, 6], [2, 3], [7, 7]]\n",
+      "[8 5 3 6 2 7 1 4]\n",
+      "[5 2 8 6 3 7 1 4]\n",
+      "2\n",
+      "6\n",
+      "3\n",
+      "2\n",
+      "{5: 3, 6: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[8, 5, 1, 6, 2, 7, 3, 4]\n",
+      "[5, 2, 6, 8, 3, 7, 1, 4]\n",
+      "[[8, 5, 2, 6, 3, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 7, 2, 6, 8, 3, 1, 4], [5, 8, 2, 6, 3, 1, 7, 4], [8, 5, 3, 6, 2, 7, 1, 4]]\n",
+      "1 6\n",
+      "[[3, 5], [8, 2], [6, 6], [2, 3], [7, 7]]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "[8 5 2 6 3 7 1 4]\n",
+      "4\n",
+      "2\n",
+      "6\n",
+      "3\n",
+      "{5: 3, 6: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 3, 2, 6, 8, 7, 1, 4]\n",
+      "[8, 5, 2, 1, 3, 7, 6, 4]\n",
+      "[[8, 5, 2, 6, 3, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 7, 2, 6, 8, 3, 1, 4], [5, 8, 2, 6, 3, 1, 7, 4], [8, 5, 3, 6, 2, 7, 1, 4]]\n",
+      "0 2\n",
+      "[[5, 8], [3, 5]]\n",
+      "[5 3 2 6 8 7 1 4]\n",
+      "[8 5 3 6 2 7 1 4]\n",
+      "4\n",
+      "2\n",
+      "4\n",
+      "6\n",
+      "{6: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1}\n",
+      "[8, 5, 3, 6, 1, 7, 2, 4]\n",
+      "[8, 5, 2, 6, 3, 7, 1, 4]\n",
+      "[[5, 3, 8, 6, 2, 7, 1, 4], [5, 7, 2, 6, 8, 3, 1, 4], [5, 8, 2, 6, 3, 1, 7, 4], [8, 5, 3, 6, 2, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4]]\n",
+      "3 6\n",
+      "[[6, 6], [8, 2], [3, 7]]\n",
+      "[5 7 2 6 8 3 1 4]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "2\n",
+      "3\n",
+      "1\n",
+      "2\n",
+      "{5: 5, 6: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 7, 6, 2, 8, 3, 1, 4]\n",
+      "[5, 8, 3, 6, 2, 7, 1, 4]\n",
+      "[[5, 3, 8, 6, 2, 7, 1, 4], [5, 7, 2, 6, 8, 3, 1, 4], [5, 8, 2, 6, 3, 1, 7, 4], [8, 5, 3, 6, 2, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4]]\n",
+      "3 5\n",
+      "[[6, 6], [8, 2]]\n",
+      "[5 3 2 6 8 7 1 4]\n",
+      "[5 7 8 6 2 3 1 4]\n",
+      "4\n",
+      "2\n",
+      "2\n",
+      "1\n",
+      "{6: 5, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1}\n",
+      "[5, 8, 7, 6, 2, 3, 1, 4]\n",
+      "[5, 3, 8, 6, 2, 7, 1, 4]\n",
+      "[[5, 7, 2, 6, 8, 3, 1, 4], [5, 8, 2, 6, 3, 1, 7, 4], [8, 5, 3, 6, 2, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4]]\n",
+      "5 6\n",
+      "[[1, 3]]\n",
+      "[5 7 2 6 8 1 3 4]\n",
+      "[5 8 2 6 1 3 7 4]\n",
+      "6\n",
+      "5\n",
+      "1\n",
+      "3\n",
+      "{6: 6, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1}\n",
+      "[5, 6, 2, 8, 1, 3, 7, 4]\n",
+      "[5, 7, 2, 6, 8, 3, 1, 4]\n",
+      "[[5, 8, 2, 6, 3, 1, 7, 4], [8, 5, 3, 6, 2, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 7, 2, 6, 8, 3, 1, 4]]\n",
+      "3 5\n",
+      "[[6, 6], [2, 3]]\n",
+      "[5 8 3 6 2 1 7 4]\n",
+      "[8 5 2 6 3 7 1 4]\n",
+      "3\n",
+      "6\n",
+      "1\n",
+      "0\n",
+      "{5: 2, 6: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 8, 3, 7, 2, 1, 6, 4]\n",
+      "[5, 8, 2, 6, 3, 7, 1, 4]\n",
+      "[[5, 8, 2, 6, 3, 1, 7, 4], [8, 5, 3, 6, 2, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 7, 2, 6, 8, 3, 1, 4]]\n",
+      "0 6\n",
+      "[[8, 5], [5, 8], [3, 2], [6, 6], [2, 3], [7, 1]]\n",
+      "[8 5 3 6 2 7 1 4]\n",
+      "[5 8 2 6 3 1 7 4]\n",
+      "0\n",
+      "5\n",
+      "0\n",
+      "3\n",
+      "{5: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 6: 1}\n",
+      "[7, 5, 3, 6, 2, 8, 1, 4]\n",
+      "[5, 8, 2, 6, 3, 1, 7, 4]\n",
+      "[[8, 5, 3, 6, 2, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 7, 2, 6, 8, 3, 1, 4], [6, 8, 2, 5, 3, 1, 7, 4]]\n",
+      "2 6\n",
+      "[[8, 3], [6, 6], [2, 2], [7, 7]]\n",
+      "[3 5 8 6 2 7 1 4]\n",
+      "[5 8 3 6 2 7 1 4]\n",
+      "1\n",
+      "3\n",
+      "6\n",
+      "0\n",
+      "{6: 3, 5: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[1, 8, 3, 6, 2, 7, 5, 4]\n",
+      "[3, 6, 8, 5, 2, 7, 1, 4]\n",
+      "[[8, 5, 3, 6, 2, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 7, 2, 6, 8, 3, 1, 4], [6, 8, 2, 5, 3, 1, 7, 4]]\n",
+      "1 4\n",
+      "[[3, 5], [8, 3], [6, 6]]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "[8 5 3 6 2 7 1 4]\n",
+      "3\n",
+      "6\n",
+      "4\n",
+      "6\n",
+      "{5: 4, 6: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 3, 8, 1, 2, 7, 6, 4]\n",
+      "[8, 5, 3, 6, 1, 7, 2, 4]\n",
+      "[[8, 5, 3, 6, 2, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 7, 2, 6, 8, 3, 1, 4], [6, 8, 2, 5, 3, 1, 7, 4]]\n",
+      "2 3\n",
+      "[[8, 3]]\n",
+      "[3 5 8 6 2 7 1 4]\n",
+      "[5 8 3 6 2 7 1 4]\n",
+      "1\n",
+      "0\n",
+      "2\n",
+      "5\n",
+      "{6: 5, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1}\n",
+      "[5, 8, 7, 6, 2, 3, 1, 4]\n",
+      "[8, 5, 3, 6, 2, 7, 1, 4]\n",
+      "[[5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 7, 2, 6, 8, 3, 1, 4], [6, 8, 2, 5, 3, 1, 7, 4], [5, 3, 8, 6, 2, 7, 1, 4]]\n",
+      "3 5\n",
+      "[[6, 6], [2, 2]]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "4\n",
+      "0\n",
+      "5\n",
+      "0\n",
+      "{5: 4, 6: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[2, 3, 8, 6, 5, 7, 1, 4]\n",
+      "[7, 3, 8, 6, 2, 5, 1, 4]\n",
+      "[[5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 7, 2, 6, 8, 3, 1, 4], [6, 8, 2, 5, 3, 1, 7, 4], [5, 3, 8, 6, 2, 7, 1, 4]]\n",
+      "0 2\n",
+      "[[5, 5], [3, 3]]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "3\n",
+      "6\n",
+      "3\n",
+      "0\n",
+      "{6: 5, 5: 4, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[6, 3, 8, 5, 2, 7, 1, 4]\n",
+      "[5, 3, 8, 1, 2, 7, 6, 4]\n",
+      "[[5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 7, 2, 6, 8, 3, 1, 4], [6, 8, 2, 5, 3, 1, 7, 4], [5, 3, 8, 6, 2, 7, 1, 4]]\n",
+      "1 2\n",
+      "[[3, 3]]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "0\n",
+      "3\n",
+      "1\n",
+      "4\n",
+      "{5: 5, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 6: 1}\n",
+      "[6, 3, 8, 5, 2, 7, 1, 4]\n",
+      "[5, 3, 8, 6, 2, 7, 1, 4]\n",
+      "[[5, 3, 8, 6, 2, 7, 1, 4], [5, 7, 2, 6, 8, 3, 1, 4], [6, 8, 2, 5, 3, 1, 7, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 2, 8, 6, 3, 7, 1, 4]]\n",
+      "1 4\n",
+      "[[7, 3], [2, 8], [6, 6]]\n",
+      "[5 7 2 6 8 3 1 4]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "3\n",
+      "0\n",
+      "6\n",
+      "0\n",
+      "{5: 4, 6: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[6, 7, 2, 5, 8, 3, 1, 4]\n",
+      "[1, 3, 8, 6, 2, 7, 5, 4]\n",
+      "[[5, 3, 8, 6, 2, 7, 1, 4], [5, 7, 2, 6, 8, 3, 1, 4], [6, 8, 2, 5, 3, 1, 7, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 2, 8, 6, 3, 7, 1, 4]]\n",
+      "2 6\n",
+      "[[2, 8], [6, 6], [8, 2], [3, 7]]\n",
+      "[5 7 2 6 8 3 1 4]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "2\n",
+      "1\n",
+      "6\n",
+      "0\n",
+      "{5: 2, 6: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 2, 7, 6, 8, 3, 1, 4]\n",
+      "[1, 3, 8, 6, 2, 7, 5, 4]\n",
+      "[[5, 3, 8, 6, 2, 7, 1, 4], [5, 7, 2, 6, 8, 3, 1, 4], [6, 8, 2, 5, 3, 1, 7, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 2, 8, 6, 3, 7, 1, 4]]\n",
+      "3 5\n",
+      "[[6, 6], [8, 2]]\n",
+      "[5 3 2 6 8 7 1 4]\n",
+      "[5 7 8 6 2 3 1 4]\n",
+      "4\n",
+      "3\n",
+      "4\n",
+      "5\n",
+      "{5: 6, 6: 5, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 3, 2, 8, 6, 7, 1, 4]\n",
+      "[5, 7, 8, 6, 3, 2, 1, 4]\n",
+      "[[5, 3, 8, 6, 2, 7, 1, 4], [5, 7, 2, 6, 8, 3, 1, 4], [6, 8, 2, 5, 3, 1, 7, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 2, 8, 6, 3, 7, 1, 4]]\n",
+      "1 2\n",
+      "[[7, 3]]\n",
+      "[5 7 8 6 2 3 1 4]\n",
+      "[5 3 2 6 8 7 1 4]\n",
+      "4\n",
+      "0\n",
+      "6\n",
+      "3\n",
+      "{6: 8, 5: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 3, 2, 1, 8, 7, 6, 4]\n",
+      "[2, 7, 8, 6, 5, 3, 1, 4]\n",
+      "[[5, 3, 8, 6, 2, 7, 1, 4], [5, 7, 2, 6, 8, 3, 1, 4], [6, 8, 2, 5, 3, 1, 7, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 2, 8, 6, 3, 7, 1, 4]]\n",
+      "2 3\n",
+      "[[2, 8]]\n",
+      "[5 3 2 6 8 7 1 4]\n",
+      "[5 7 8 6 2 3 1 4]\n",
+      "4\n",
+      "3\n",
+      "1\n",
+      "4\n",
+      "{5: 6, 6: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 3, 2, 8, 6, 7, 1, 4]\n",
+      "[5, 2, 8, 6, 7, 3, 1, 4]\n",
+      "[[5, 3, 8, 6, 2, 7, 1, 4], [5, 7, 2, 6, 8, 3, 1, 4], [6, 8, 2, 5, 3, 1, 7, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 2, 8, 6, 3, 7, 1, 4]]\n",
+      "4 5\n",
+      "[[8, 2]]\n",
+      "[5 3 2 6 8 7 1 4]\n",
+      "[5 7 8 6 2 3 1 4]\n",
+      "1\n",
+      "6\n",
+      "5\n",
+      "1\n",
+      "{5: 4, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 6: 1}\n",
+      "[5, 1, 2, 6, 8, 7, 3, 4]\n",
+      "[5, 3, 8, 6, 2, 7, 1, 4]\n",
+      "[[5, 7, 2, 6, 8, 3, 1, 4], [6, 8, 2, 5, 3, 1, 7, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 2, 8, 6, 3, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4]]\n",
+      "0 5\n",
+      "[[6, 5], [8, 7], [2, 2], [5, 6], [3, 8]]\n",
+      "[6 8 2 5 3 7 1 4]\n",
+      "[5 7 2 6 8 1 3 4]\n",
+      "2\n",
+      "3\n",
+      "6\n",
+      "1\n",
+      "{5: 4, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 6: 1}\n",
+      "[6, 8, 5, 2, 3, 7, 1, 4]\n",
+      "[5, 7, 2, 6, 8, 3, 1, 4]\n",
+      "[[6, 8, 2, 5, 3, 1, 7, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 2, 8, 6, 3, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4]]\n",
+      "0 2\n",
+      "[[5, 6], [3, 8]]\n",
+      "[5 3 2 6 8 1 7 4]\n",
+      "[6 8 3 5 2 7 1 4]\n",
+      "0\n",
+      "3\n",
+      "6\n",
+      "5\n",
+      "{6: 4, 5: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[6, 8, 3, 5, 2, 1, 7, 4]\n",
+      "[6, 3, 2, 5, 8, 1, 7, 4]\n",
+      "[[6, 8, 2, 5, 3, 1, 7, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 2, 8, 6, 3, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4]]\n",
+      "1 6\n",
+      "[[3, 8], [8, 2], [6, 5], [2, 3], [7, 1]]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "[6 8 2 5 3 1 7 4]\n",
+      "0\n",
+      "6\n",
+      "2\n",
+      "6\n",
+      "{6: 4, 5: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[6, 8, 7, 5, 3, 1, 2, 4]\n",
+      "[1, 3, 8, 6, 2, 7, 5, 4]\n",
+      "[[6, 8, 2, 5, 3, 1, 7, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 2, 8, 6, 3, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4]]\n",
+      "1 2\n",
+      "[[3, 8]]\n",
+      "[6 3 2 5 8 1 7 4]\n",
+      "[5 8 3 6 2 7 1 4]\n",
+      "2\n",
+      "6\n",
+      "3\n",
+      "2\n",
+      "{5: 4, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 6: 1}\n",
+      "[6, 3, 7, 5, 8, 1, 2, 4]\n",
+      "[6, 8, 2, 5, 3, 1, 7, 4]\n",
+      "[[5, 3, 8, 6, 2, 7, 1, 4], [5, 2, 8, 6, 3, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4]]\n",
+      "3 6\n",
+      "[[6, 6], [3, 2], [7, 7]]\n",
+      "[5 2 8 6 3 7 1 4]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "5\n",
+      "0\n",
+      "5\n",
+      "1\n",
+      "{5: 4, 6: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[7, 2, 8, 6, 3, 5, 1, 4]\n",
+      "[5, 7, 8, 6, 2, 3, 1, 4]\n",
+      "[[5, 3, 8, 6, 2, 7, 1, 4], [5, 2, 8, 6, 3, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4]]\n",
+      "4 5\n",
+      "[[3, 2]]\n",
+      "[5 2 8 6 3 7 1 4]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "5\n",
+      "2\n",
+      "2\n",
+      "4\n",
+      "{5: 4, 6: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 2, 7, 6, 3, 8, 1, 4]\n",
+      "[5, 3, 2, 6, 8, 7, 1, 4]\n",
+      "[[5, 3, 8, 6, 2, 7, 1, 4], [5, 2, 8, 6, 3, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4]]\n",
+      "2 4\n",
+      "[[8, 8], [6, 6]]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "[5 2 8 6 3 7 1 4]\n",
+      "0\n",
+      "5\n",
+      "3\n",
+      "6\n",
+      "{5: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 6: 1}\n",
+      "[7, 3, 8, 6, 2, 5, 1, 4]\n",
+      "[5, 3, 8, 6, 2, 7, 1, 4]\n",
+      "[[5, 2, 8, 6, 3, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 8, 1, 3, 7, 6, 4]]\n",
+      "5 6\n",
+      "[[7, 7]]\n",
+      "[5 2 8 6 3 7 1 4]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "3\n",
+      "4\n",
+      "3\n",
+      "4\n",
+      "{6: 5, 5: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 3, 8, 2, 6, 7, 1, 4]\n",
+      "[5, 2, 8, 3, 6, 7, 1, 4]\n",
+      "[[5, 2, 8, 6, 3, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 8, 1, 3, 7, 6, 4]]\n",
+      "4 5\n",
+      "[[2, 3]]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "[5 2 8 6 3 7 1 4]\n",
+      "0\n",
+      "2\n",
+      "6\n",
+      "0\n",
+      "{5: 3, 6: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[8, 3, 5, 6, 2, 7, 1, 4]\n",
+      "[1, 2, 8, 6, 3, 7, 5, 4]\n",
+      "[[5, 2, 8, 6, 3, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 8, 1, 3, 7, 6, 4]]\n",
+      "5 6\n",
+      "[[7, 7]]\n",
+      "[5 2 8 6 3 7 1 4]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "2\n",
+      "0\n",
+      "2\n",
+      "5\n",
+      "{5: 4, 6: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[8, 2, 5, 6, 3, 7, 1, 4]\n",
+      "[5, 3, 7, 6, 2, 8, 1, 4]\n",
+      "[[5, 2, 8, 6, 3, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 8, 1, 3, 7, 6, 4]]\n",
+      "0 1\n",
+      "[[5, 5]]\n",
+      "[5 2 8 6 3 7 1 4]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "6\n",
+      "0\n",
+      "0\n",
+      "1\n",
+      "{5: 3, 6: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[1, 2, 8, 6, 3, 7, 5, 4]\n",
+      "[3, 5, 8, 6, 2, 7, 1, 4]\n",
+      "[[5, 2, 8, 6, 3, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 8, 1, 3, 7, 6, 4]]\n",
+      "1 2\n",
+      "[[3, 2]]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "[5 2 8 6 3 7 1 4]\n",
+      "2\n",
+      "0\n",
+      "0\n",
+      "1\n",
+      "{5: 3, 6: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[8, 3, 5, 6, 2, 7, 1, 4]\n",
+      "[2, 5, 8, 6, 3, 7, 1, 4]\n",
+      "[[5, 2, 8, 6, 3, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 8, 1, 3, 7, 6, 4]]\n",
+      "1 3\n",
+      "[[3, 2], [8, 8]]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "[5 2 8 6 3 7 1 4]\n",
+      "1\n",
+      "5\n",
+      "5\n",
+      "2\n",
+      "{6: 4, 5: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 2, 7, 6, 3, 8, 1, 4]\n",
+      "[5, 7, 8, 6, 2, 3, 1, 4]\n",
+      "[[5, 2, 8, 6, 3, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 8, 1, 3, 7, 6, 4]]\n",
+      "3 5\n",
+      "[[6, 6], [2, 3]]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "[5 2 8 6 3 7 1 4]\n",
+      "3\n",
+      "2\n",
+      "2\n",
+      "0\n",
+      "{6: 4, 5: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[8, 2, 5, 6, 3, 7, 1, 4]\n",
+      "[5, 3, 6, 8, 2, 7, 1, 4]\n",
+      "[[5, 2, 8, 6, 3, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 8, 1, 3, 7, 6, 4]]\n",
+      "4 6\n",
+      "[[2, 3], [7, 7]]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "[5 2 8 6 3 7 1 4]\n",
+      "2\n",
+      "4\n",
+      "2\n",
+      "1\n",
+      "{5: 3, 6: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 3, 2, 6, 8, 7, 1, 4]\n",
+      "[5, 8, 2, 6, 3, 7, 1, 4]\n",
+      "[[5, 2, 8, 6, 3, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 8, 1, 3, 7, 6, 4]]\n",
+      "2 5\n",
+      "[[8, 8], [6, 6], [2, 3]]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "[5 2 8 6 3 7 1 4]\n",
+      "1\n",
+      "0\n",
+      "2\n",
+      "0\n",
+      "{6: 4, 5: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[8, 2, 5, 6, 3, 7, 1, 4]\n",
+      "[3, 5, 8, 6, 2, 7, 1, 4]\n",
+      "[[5, 2, 8, 6, 3, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 8, 1, 3, 7, 6, 4]]\n",
+      "3 4\n",
+      "[[6, 6]]\n",
+      "[5 2 8 6 3 7 1 4]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "3\n",
+      "4\n",
+      "5\n",
+      "0\n",
+      "{5: 2, 6: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 2, 8, 3, 6, 7, 1, 4]\n",
+      "[7, 3, 8, 6, 2, 5, 1, 4]\n",
+      "[[5, 2, 8, 6, 3, 7, 1, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 8, 1, 3, 7, 6, 4]]\n",
+      "0 1\n",
+      "[[5, 5]]\n",
+      "[5 2 8 6 3 7 1 4]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "4\n",
+      "1\n",
+      "6\n",
+      "3\n",
+      "{6: 4, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1}\n",
+      "[5, 3, 8, 1, 2, 7, 6, 4]\n",
+      "[5, 2, 8, 6, 3, 7, 1, 4]\n",
+      "[[5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 8, 1, 3, 7, 6, 4], [5, 3, 8, 6, 2, 7, 1, 4]]\n",
+      "2 5\n",
+      "[[2, 8], [6, 6], [8, 2]]\n",
+      "[5 3 2 6 8 7 1 4]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "2\n",
+      "5\n",
+      "3\n",
+      "4\n",
+      "{5: 4, 6: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 3, 7, 6, 8, 2, 1, 4]\n",
+      "[5, 3, 8, 2, 6, 1, 7, 4]\n",
+      "[[5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 8, 1, 3, 7, 6, 4], [5, 3, 8, 6, 2, 7, 1, 4]]\n",
+      "5 6\n",
+      "[[1, 7]]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "[5 3 2 6 8 7 1 4]\n",
+      "2\n",
+      "4\n",
+      "5\n",
+      "3\n",
+      "{6: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1}\n",
+      "[5, 3, 2, 7, 8, 6, 1, 4]\n",
+      "[5, 3, 8, 6, 2, 7, 1, 4]\n",
+      "[[5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 8, 1, 3, 7, 6, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4]]\n",
+      "4 5\n",
+      "[[2, 8]]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "[5 2 6 3 8 7 1 4]\n",
+      "1\n",
+      "6\n",
+      "5\n",
+      "4\n",
+      "{5: 4, 6: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 7, 8, 6, 2, 1, 3, 4]\n",
+      "[5, 2, 6, 3, 7, 8, 1, 4]\n",
+      "[[5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 8, 1, 3, 7, 6, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4]]\n",
+      "5 6\n",
+      "[[7, 1]]\n",
+      "[5 3 2 6 8 7 1 4]\n",
+      "[5 8 6 3 2 1 7 4]\n",
+      "1\n",
+      "3\n",
+      "5\n",
+      "0\n",
+      "{5: 4, 6: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 6, 2, 3, 8, 7, 1, 4]\n",
+      "[1, 8, 6, 3, 2, 5, 7, 4]\n",
+      "[[5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 8, 1, 3, 7, 6, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4]]\n",
+      "5 6\n",
+      "[[7, 1]]\n",
+      "[5 3 2 6 8 7 1 4]\n",
+      "[5 8 6 3 2 1 7 4]\n",
+      "0\n",
+      "5\n",
+      "1\n",
+      "2\n",
+      "{6: 4, 5: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 6, 8, 3, 2, 1, 7, 4]\n",
+      "[7, 3, 2, 6, 8, 5, 1, 4]\n",
+      "[[5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 8, 1, 3, 7, 6, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4]]\n",
+      "4 6\n",
+      "[[2, 8], [7, 1]]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "[5 2 6 3 8 1 7 4]\n",
+      "1\n",
+      "0\n",
+      "6\n",
+      "3\n",
+      "{6: 4, 5: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 2, 6, 7, 8, 1, 3, 4]\n",
+      "[3, 5, 8, 6, 2, 7, 1, 4]\n",
+      "[[5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 8, 1, 3, 7, 6, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4]]\n",
+      "2 4\n",
+      "[[6, 2], [3, 6]]\n",
+      "[5 2 6 3 8 1 7 4]\n",
+      "[5 8 2 6 3 7 1 4]\n",
+      "4\n",
+      "3\n",
+      "3\n",
+      "5\n",
+      "{5: 3, 6: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 2, 6, 8, 3, 1, 7, 4]\n",
+      "[5, 8, 2, 7, 3, 6, 1, 4]\n",
+      "[[5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 8, 1, 3, 7, 6, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4]]\n",
+      "1 3\n",
+      "[[8, 3], [6, 2]]\n",
+      "[5 8 6 2 3 1 7 4]\n",
+      "[5 3 2 8 6 7 1 4]\n",
+      "3\n",
+      "1\n",
+      "5\n",
+      "0\n",
+      "{6: 6, 5: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[7, 3, 2, 8, 6, 5, 1, 4]\n",
+      "[5, 2, 6, 8, 3, 1, 7, 4]\n",
+      "[[5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 8, 1, 3, 7, 6, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4]]\n",
+      "2 6\n",
+      "[[6, 2], [3, 6], [2, 8], [7, 1]]\n",
+      "[5 8 6 3 2 7 1 4]\n",
+      "[5 3 2 6 8 1 7 4]\n",
+      "4\n",
+      "0\n",
+      "4\n",
+      "6\n",
+      "{6: 4, 5: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 3, 2, 6, 7, 1, 8, 4]\n",
+      "[2, 8, 6, 3, 5, 7, 1, 4]\n",
+      "[[5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 8, 1, 3, 7, 6, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4]]\n",
+      "5 6\n",
+      "[[7, 1]]\n",
+      "[5 3 2 6 8 7 1 4]\n",
+      "[5 8 6 3 2 1 7 4]\n",
+      "0\n",
+      "5\n",
+      "0\n",
+      "1\n",
+      "{6: 8, 5: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[8, 5, 6, 3, 2, 1, 7, 4]\n",
+      "[7, 3, 2, 6, 8, 5, 1, 4]\n",
+      "[[5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 8, 1, 3, 7, 6, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4]]\n",
+      "1 5\n",
+      "[[8, 3], [6, 2], [3, 6], [2, 8]]\n",
+      "[5 8 6 3 2 1 7 4]\n",
+      "[5 3 2 6 8 7 1 4]\n",
+      "1\n",
+      "5\n",
+      "0\n",
+      "3\n",
+      "{6: 5, 5: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[6, 3, 2, 5, 8, 7, 1, 4]\n",
+      "[5, 1, 6, 3, 2, 8, 7, 4]\n",
+      "[[5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 8, 1, 3, 7, 6, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4]]\n",
+      "2 6\n",
+      "[[6, 2], [3, 6], [2, 8], [7, 1]]\n",
+      "[5 8 6 3 2 7 1 4]\n",
+      "[5 3 2 6 8 1 7 4]\n",
+      "1\n",
+      "4\n",
+      "0\n",
+      "2\n",
+      "{5: 2, 6: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 2, 6, 3, 8, 7, 1, 4]\n",
+      "[2, 3, 5, 6, 8, 1, 7, 4]\n",
+      "[[5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 8, 1, 3, 7, 6, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4]]\n",
+      "5 6\n",
+      "[[7, 1]]\n",
+      "[5 3 2 6 8 7 1 4]\n",
+      "[5 8 6 3 2 1 7 4]\n",
+      "6\n",
+      "3\n",
+      "1\n",
+      "3\n",
+      "{5: 8, 6: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 3, 2, 1, 8, 7, 6, 4]\n",
+      "[5, 3, 6, 8, 2, 1, 7, 4]\n",
+      "[[5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 8, 1, 3, 7, 6, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4]]\n",
+      "2 4\n",
+      "[[6, 2], [3, 6]]\n",
+      "[5 2 6 3 8 1 7 4]\n",
+      "[5 8 2 6 3 7 1 4]\n",
+      "2\n",
+      "1\n",
+      "5\n",
+      "1\n",
+      "{5: 3, 6: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 6, 2, 3, 8, 1, 7, 4]\n",
+      "[5, 7, 2, 6, 3, 8, 1, 4]\n",
+      "[[5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 8, 1, 3, 7, 6, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4]]\n",
+      "3 6\n",
+      "[[3, 6], [2, 8], [7, 1]]\n",
+      "[5 6 8 3 2 7 1 4]\n",
+      "[5 2 3 6 8 1 7 4]\n",
+      "6\n",
+      "2\n",
+      "6\n",
+      "4\n",
+      "{6: 4, 5: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 2, 3, 6, 7, 1, 8, 4]\n",
+      "[5, 6, 1, 3, 2, 7, 8, 4]\n",
+      "[[5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 8, 1, 3, 7, 6, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4]]\n",
+      "3 6\n",
+      "[[3, 6], [2, 8], [7, 1]]\n",
+      "[5 6 8 3 2 7 1 4]\n",
+      "[5 2 3 6 8 1 7 4]\n",
+      "3\n",
+      "2\n",
+      "3\n",
+      "5\n",
+      "{6: 8, 5: 6, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 2, 3, 1, 8, 6, 7, 4]\n",
+      "[5, 6, 3, 8, 2, 7, 1, 4]\n",
+      "[[5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 8, 1, 3, 7, 6, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4]]\n",
+      "5 6\n",
+      "[[7, 1]]\n",
+      "[5 3 2 6 8 7 1 4]\n",
+      "[5 8 6 3 2 1 7 4]\n",
+      "1\n",
+      "4\n",
+      "5\n",
+      "0\n",
+      "{6: 3, 5: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[1, 8, 6, 3, 2, 5, 7, 4]\n",
+      "[5, 8, 2, 6, 3, 7, 1, 4]\n",
+      "[[5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 8, 1, 3, 7, 6, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4]]\n",
+      "2 5\n",
+      "[[6, 2], [3, 6], [2, 8]]\n",
+      "[5 8 6 3 2 1 7 4]\n",
+      "[5 3 2 6 8 7 1 4]\n",
+      "1\n",
+      "2\n",
+      "5\n",
+      "4\n",
+      "{6: 5, 5: 4, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 3, 2, 6, 7, 8, 1, 4]\n",
+      "[5, 6, 8, 3, 2, 1, 7, 4]\n",
+      "[[5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 8, 1, 3, 7, 6, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4]]\n",
+      "0 5\n",
+      "[[5, 5], [8, 3], [6, 2], [3, 6], [2, 8]]\n",
+      "[5 8 6 3 2 1 7 4]\n",
+      "[5 3 2 6 8 7 1 4]\n",
+      "1\n",
+      "5\n",
+      "0\n",
+      "1\n",
+      "{5: 3, 6: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 1, 6, 3, 2, 8, 7, 4]\n",
+      "[3, 5, 2, 6, 8, 7, 1, 4]\n",
+      "[[5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 8, 1, 3, 7, 6, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4]]\n",
+      "4 5\n",
+      "[[2, 8]]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "[5 2 6 3 8 7 1 4]\n",
+      "3\n",
+      "4\n",
+      "6\n",
+      "2\n",
+      "{6: 5, 5: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 2, 1, 3, 8, 7, 6, 4]\n",
+      "[5, 3, 8, 2, 6, 1, 7, 4]\n",
+      "[[5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 8, 1, 3, 7, 6, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4]]\n",
+      "4 6\n",
+      "[[2, 8], [7, 1]]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "[5 2 6 3 8 1 7 4]\n",
+      "3\n",
+      "1\n",
+      "3\n",
+      "5\n",
+      "{6: 4, 5: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 2, 6, 1, 8, 3, 7, 4]\n",
+      "[5, 6, 8, 3, 2, 7, 1, 4]\n",
+      "[[5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 8, 1, 3, 7, 6, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4]]\n",
+      "2 5\n",
+      "[[6, 2], [3, 6], [2, 8]]\n",
+      "[5 8 6 3 2 1 7 4]\n",
+      "[5 3 2 6 8 7 1 4]\n",
+      "0\n",
+      "2\n",
+      "0\n",
+      "6\n",
+      "{5: 6, 6: 4, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[6, 8, 5, 3, 2, 1, 7, 4]\n",
+      "[1, 3, 2, 6, 8, 7, 5, 4]\n",
+      "[[5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 8, 1, 3, 7, 6, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4]]\n",
+      "5 6\n",
+      "[[7, 1]]\n",
+      "[5 3 2 6 8 7 1 4]\n",
+      "[5 8 6 3 2 1 7 4]\n",
+      "6\n",
+      "3\n",
+      "2\n",
+      "5\n",
+      "{5: 8, 6: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 3, 2, 1, 8, 7, 6, 4]\n",
+      "[5, 8, 1, 3, 2, 6, 7, 4]\n",
+      "[[5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 8, 1, 3, 7, 6, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4]]\n",
+      "2 5\n",
+      "[[6, 2], [3, 6], [2, 8]]\n",
+      "[5 8 6 3 2 1 7 4]\n",
+      "[5 3 2 6 8 7 1 4]\n",
+      "6\n",
+      "0\n",
+      "3\n",
+      "5\n",
+      "{5: 5, 6: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[7, 8, 6, 3, 2, 1, 5, 4]\n",
+      "[5, 3, 2, 7, 8, 6, 1, 4]\n",
+      "[[5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 8, 1, 3, 7, 6, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4]]\n",
+      "0 3\n",
+      "[[5, 5], [8, 3], [6, 2]]\n",
+      "[5 8 6 2 3 1 7 4]\n",
+      "[5 3 2 8 6 7 1 4]\n",
+      "6\n",
+      "2\n",
+      "5\n",
+      "0\n",
+      "{6: 6, 5: 4, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[7, 3, 2, 8, 6, 5, 1, 4]\n",
+      "[5, 8, 7, 2, 3, 1, 6, 4]\n",
+      "[[5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 8, 1, 3, 7, 6, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4]]\n",
+      "3 5\n",
+      "[[3, 6], [2, 8]]\n",
+      "[5 6 8 3 2 1 7 4]\n",
+      "[5 2 3 6 8 7 1 4]\n",
+      "3\n",
+      "5\n",
+      "4\n",
+      "5\n",
+      "{6: 6, 5: 4, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 2, 3, 6, 7, 8, 1, 4]\n",
+      "[5, 6, 8, 1, 2, 3, 7, 4]\n",
+      "[[5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 8, 1, 3, 7, 6, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4]]\n",
+      "2 4\n",
+      "[[6, 2], [3, 6]]\n",
+      "[5 2 6 3 8 1 7 4]\n",
+      "[5 8 2 6 3 7 1 4]\n",
+      "5\n",
+      "6\n",
+      "5\n",
+      "3\n",
+      "{5: 2, 6: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 2, 6, 3, 8, 7, 1, 4]\n",
+      "[5, 8, 2, 7, 3, 6, 1, 4]\n",
+      "[[5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 8, 1, 3, 7, 6, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4]]\n",
+      "4 6\n",
+      "[[2, 8], [7, 1]]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "[5 2 6 3 8 1 7 4]\n",
+      "3\n",
+      "0\n",
+      "3\n",
+      "2\n",
+      "{5: 5, 6: 4, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[6, 3, 8, 5, 2, 7, 1, 4]\n",
+      "[5, 2, 3, 6, 8, 1, 7, 4]\n",
+      "[[5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 8, 1, 3, 7, 6, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4]]\n",
+      "0 6\n",
+      "[[5, 5], [8, 3], [6, 2], [3, 6], [2, 8], [7, 1]]\n",
+      "[5 8 6 3 2 7 1 4]\n",
+      "[5 3 2 6 8 1 7 4]\n",
+      "6\n",
+      "1\n",
+      "4\n",
+      "1\n",
+      "{5: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 6: 1}\n",
+      "[5, 1, 6, 3, 2, 7, 8, 4]\n",
+      "[5, 3, 2, 6, 8, 1, 7, 4]\n",
+      "[[5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 8, 1, 3, 7, 6, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 2, 6, 3, 1, 7, 4]]\n",
+      "3 4\n",
+      "[[1, 3]]\n",
+      "[5 8 6 1 2 7 3 4]\n",
+      "[5 2 8 3 1 7 6 4]\n",
+      "6\n",
+      "3\n",
+      "6\n",
+      "5\n",
+      "{6: 6, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1}\n",
+      "[5, 2, 8, 3, 1, 6, 7, 4]\n",
+      "[5, 8, 6, 3, 2, 7, 1, 4]\n",
+      "[[5, 2, 8, 1, 3, 7, 6, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 2, 6, 3, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4]]\n",
+      "5 6\n",
+      "[[7, 7]]\n",
+      "[5 2 8 1 3 7 6 4]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "4\n",
+      "6\n",
+      "5\n",
+      "1\n",
+      "{5: 3, 6: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 2, 8, 1, 6, 7, 3, 4]\n",
+      "[5, 7, 8, 6, 2, 3, 1, 4]\n",
+      "[[5, 2, 8, 1, 3, 7, 6, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 2, 6, 3, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4]]\n",
+      "5 6\n",
+      "[[7, 7]]\n",
+      "[5 2 8 1 3 7 6 4]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "6\n",
+      "4\n",
+      "2\n",
+      "1\n",
+      "{5: 3, 6: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 2, 8, 1, 6, 7, 3, 4]\n",
+      "[5, 8, 3, 6, 2, 7, 1, 4]\n",
+      "[[5, 2, 8, 1, 3, 7, 6, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 2, 6, 3, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4]]\n",
+      "3 4\n",
+      "[[6, 1]]\n",
+      "[5 2 8 6 3 7 1 4]\n",
+      "[5 3 8 1 2 7 6 4]\n",
+      "1\n",
+      "5\n",
+      "6\n",
+      "0\n",
+      "{6: 6, 5: 5, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[6, 3, 8, 1, 2, 7, 5, 4]\n",
+      "[5, 7, 8, 6, 3, 2, 1, 4]\n",
+      "[[5, 2, 8, 1, 3, 7, 6, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 2, 6, 3, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4]]\n",
+      "1 6\n",
+      "[[3, 2], [8, 8], [6, 1], [2, 3], [7, 7]]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "[5 2 8 1 3 7 6 4]\n",
+      "1\n",
+      "3\n",
+      "2\n",
+      "0\n",
+      "{5: 3, 6: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 6, 8, 3, 2, 7, 1, 4]\n",
+      "[8, 2, 5, 1, 3, 7, 6, 4]\n",
+      "[[5, 2, 8, 1, 3, 7, 6, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 2, 6, 3, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4]]\n",
+      "2 5\n",
+      "[[8, 8], [6, 1], [2, 3]]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "[5 2 8 1 3 7 6 4]\n",
+      "5\n",
+      "2\n",
+      "6\n",
+      "0\n",
+      "{5: 3, 6: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 3, 7, 6, 2, 8, 1, 4]\n",
+      "[6, 2, 8, 1, 3, 7, 5, 4]\n",
+      "[[5, 2, 8, 1, 3, 7, 6, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 2, 6, 3, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4]]\n",
+      "4 5\n",
+      "[[2, 3]]\n",
+      "[5 3 8 1 2 7 6 4]\n",
+      "[5 2 8 6 3 7 1 4]\n",
+      "3\n",
+      "1\n",
+      "5\n",
+      "3\n",
+      "{5: 5, 6: 4, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 1, 8, 3, 2, 7, 6, 4]\n",
+      "[5, 2, 8, 7, 3, 6, 1, 4]\n",
+      "[[5, 2, 8, 1, 3, 7, 6, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 2, 6, 3, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4]]\n",
+      "5 6\n",
+      "[[7, 7]]\n",
+      "[5 2 8 1 3 7 6 4]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "3\n",
+      "0\n",
+      "6\n",
+      "1\n",
+      "{5: 3, 6: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[1, 2, 8, 5, 3, 7, 6, 4]\n",
+      "[5, 1, 8, 6, 2, 7, 3, 4]\n",
+      "[[5, 2, 8, 1, 3, 7, 6, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 2, 6, 3, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4]]\n",
+      "4 6\n",
+      "[[2, 3], [7, 7]]\n",
+      "[5 3 8 1 2 7 6 4]\n",
+      "[5 2 8 6 3 7 1 4]\n",
+      "1\n",
+      "5\n",
+      "6\n",
+      "0\n",
+      "{5: 5, 6: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 7, 8, 1, 2, 3, 6, 4]\n",
+      "[1, 2, 8, 6, 3, 7, 5, 4]\n",
+      "[[5, 2, 8, 1, 3, 7, 6, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 2, 6, 3, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4]]\n",
+      "2 3\n",
+      "[[8, 8]]\n",
+      "[5 2 8 1 3 7 6 4]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "2\n",
+      "4\n",
+      "1\n",
+      "0\n",
+      "{5: 5, 6: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 2, 3, 1, 8, 7, 6, 4]\n",
+      "[3, 5, 8, 6, 2, 7, 1, 4]\n",
+      "[[5, 2, 8, 1, 3, 7, 6, 4], [5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 2, 6, 3, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4]]\n",
+      "0 1\n",
+      "[[5, 5]]\n",
+      "[5 2 8 1 3 7 6 4]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "5\n",
+      "2\n",
+      "3\n",
+      "2\n",
+      "{6: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1}\n",
+      "[5, 3, 6, 8, 2, 7, 1, 4]\n",
+      "[5, 2, 8, 1, 3, 7, 6, 4]\n",
+      "[[5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 2, 6, 3, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 7, 1, 3, 8, 6, 4]]\n",
+      "4 5\n",
+      "[[8, 2]]\n",
+      "[5 3 2 6 8 7 1 4]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "0\n",
+      "3\n",
+      "1\n",
+      "6\n",
+      "{5: 5, 6: 4, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[6, 3, 2, 5, 8, 7, 1, 4]\n",
+      "[5, 7, 8, 6, 2, 1, 3, 4]\n",
+      "[[5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 2, 6, 3, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 7, 1, 3, 8, 6, 4]]\n",
+      "3 6\n",
+      "[[6, 6], [8, 2], [1, 7]]\n",
+      "[5 3 2 6 8 1 7 4]\n",
+      "[5 3 8 6 2 7 1 4]\n",
+      "4\n",
+      "0\n",
+      "2\n",
+      "0\n",
+      "{5: 3, 6: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[8, 3, 2, 6, 5, 1, 7, 4]\n",
+      "[8, 3, 5, 6, 2, 7, 1, 4]\n",
+      "[[5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 2, 6, 3, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 7, 1, 3, 8, 6, 4]]\n",
+      "2 5\n",
+      "[[2, 8], [6, 6], [8, 2]]\n",
+      "[5 3 2 6 8 7 1 4]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "6\n",
+      "1\n",
+      "4\n",
+      "5\n",
+      "{5: 4, 6: 4, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 1, 2, 6, 8, 7, 3, 4]\n",
+      "[5, 3, 8, 6, 1, 2, 7, 4]\n",
+      "[[5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 2, 6, 3, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 7, 1, 3, 8, 6, 4]]\n",
+      "5 6\n",
+      "[[1, 7]]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "[5 3 2 6 8 7 1 4]\n",
+      "0\n",
+      "1\n",
+      "5\n",
+      "2\n",
+      "{5: 4, 6: 4, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[3, 5, 8, 6, 2, 1, 7, 4]\n",
+      "[5, 3, 7, 6, 8, 2, 1, 4]\n",
+      "[[5, 3, 8, 6, 2, 7, 1, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 2, 6, 3, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 7, 1, 3, 8, 6, 4]]\n",
+      "4 5\n",
+      "[[8, 2]]\n",
+      "[5 3 2 6 8 7 1 4]\n",
+      "[5 3 8 6 2 1 7 4]\n",
+      "5\n",
+      "6\n",
+      "1\n",
+      "2\n",
+      "{6: 4, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1}\n",
+      "[5, 8, 3, 6, 2, 1, 7, 4]\n",
+      "[5, 3, 8, 6, 2, 7, 1, 4]\n",
+      "[[5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 2, 6, 3, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 7, 1, 3, 8, 6, 4], [5, 3, 2, 6, 8, 1, 7, 4]]\n",
+      "5 6\n",
+      "[[1, 1]]\n",
+      "[5 3 2 6 8 1 7 4]\n",
+      "[5 8 2 6 3 1 7 4]\n",
+      "6\n",
+      "0\n",
+      "5\n",
+      "0\n",
+      "{6: 3, 5: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[1, 8, 2, 6, 3, 5, 7, 4]\n",
+      "[7, 3, 2, 6, 8, 1, 5, 4]\n",
+      "[[5, 3, 2, 6, 8, 1, 7, 4], [5, 8, 2, 6, 3, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 7, 1, 3, 8, 6, 4], [5, 3, 2, 6, 8, 1, 7, 4]]\n",
+      "3 5\n",
+      "[[6, 6], [3, 8]]\n",
+      "[5 8 2 6 3 1 7 4]\n",
+      "[5 3 2 6 8 1 7 4]\n",
+      "1\n",
+      "2\n",
+      "6\n",
+      "3\n",
+      "{6: 4, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1}\n",
+      "[5, 3, 2, 7, 8, 1, 6, 4]\n",
+      "[5, 3, 2, 6, 8, 1, 7, 4]\n",
+      "[[5, 8, 2, 6, 3, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 7, 1, 3, 8, 6, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 2, 8, 6, 3, 1, 7, 4]]\n",
+      "1 3\n",
+      "[[8, 8], [6, 2]]\n",
+      "[5 8 6 2 3 1 7 4]\n",
+      "[5 8 2 3 6 7 1 4]\n",
+      "6\n",
+      "2\n",
+      "3\n",
+      "2\n",
+      "{5: 4, 6: 4, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 8, 7, 2, 3, 1, 6, 4]\n",
+      "[5, 8, 3, 2, 6, 7, 1, 4]\n",
+      "[[5, 8, 2, 6, 3, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 7, 1, 3, 8, 6, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 2, 8, 6, 3, 1, 7, 4]]\n",
+      "0 2\n",
+      "[[5, 5], [8, 8]]\n",
+      "[5 8 2 6 3 1 7 4]\n",
+      "[5 8 6 3 2 7 1 4]\n",
+      "2\n",
+      "6\n",
+      "2\n",
+      "6\n",
+      "{5: 5, 6: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 8, 7, 6, 3, 1, 2, 4]\n",
+      "[5, 8, 1, 3, 2, 7, 6, 4]\n",
+      "[[5, 8, 2, 6, 3, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 7, 1, 3, 8, 6, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 2, 8, 6, 3, 1, 7, 4]]\n",
+      "2 4\n",
+      "[[6, 2], [3, 6]]\n",
+      "[5 8 6 3 2 1 7 4]\n",
+      "[5 8 2 6 3 7 1 4]\n",
+      "6\n",
+      "4\n",
+      "0\n",
+      "5\n",
+      "{6: 6, 5: 4, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[7, 8, 2, 6, 3, 5, 1, 4]\n",
+      "[5, 8, 6, 3, 7, 1, 2, 4]\n",
+      "[[5, 8, 2, 6, 3, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 7, 1, 3, 8, 6, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 2, 8, 6, 3, 1, 7, 4]]\n",
+      "3 6\n",
+      "[[3, 6], [2, 3], [7, 1]]\n",
+      "[5 8 6 3 2 7 1 4]\n",
+      "[5 8 2 6 3 1 7 4]\n",
+      "1\n",
+      "6\n",
+      "3\n",
+      "5\n",
+      "{5: 3, 6: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 1, 6, 3, 2, 7, 8, 4]\n",
+      "[5, 8, 2, 1, 3, 6, 7, 4]\n",
+      "[[5, 8, 2, 6, 3, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 7, 1, 3, 8, 6, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 2, 8, 6, 3, 1, 7, 4]]\n",
+      "1 3\n",
+      "[[8, 8], [6, 2]]\n",
+      "[5 8 6 2 3 1 7 4]\n",
+      "[5 8 2 3 6 7 1 4]\n",
+      "2\n",
+      "6\n",
+      "0\n",
+      "3\n",
+      "{5: 4, 6: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 8, 7, 2, 3, 1, 6, 4]\n",
+      "[3, 8, 2, 5, 6, 7, 1, 4]\n",
+      "[[5, 8, 2, 6, 3, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 7, 1, 3, 8, 6, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 2, 8, 6, 3, 1, 7, 4]]\n",
+      "0 3\n",
+      "[[5, 5], [8, 8], [6, 2]]\n",
+      "[5 8 6 2 3 1 7 4]\n",
+      "[5 8 2 3 6 7 1 4]\n",
+      "3\n",
+      "6\n",
+      "3\n",
+      "0\n",
+      "{5: 3, 6: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 8, 6, 7, 3, 1, 2, 4]\n",
+      "[3, 8, 2, 5, 6, 7, 1, 4]\n",
+      "[[5, 8, 2, 6, 3, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 7, 1, 3, 8, 6, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 2, 8, 6, 3, 1, 7, 4]]\n",
+      "0 2\n",
+      "[[5, 5], [8, 8]]\n",
+      "[5 8 2 6 3 1 7 4]\n",
+      "[5 8 6 3 2 7 1 4]\n",
+      "0\n",
+      "2\n",
+      "5\n",
+      "3\n",
+      "{5: 3, 6: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[2, 8, 5, 6, 3, 1, 7, 4]\n",
+      "[5, 8, 6, 7, 2, 3, 1, 4]\n",
+      "[[5, 8, 2, 6, 3, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 7, 1, 3, 8, 6, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 2, 8, 6, 3, 1, 7, 4]]\n",
+      "3 4\n",
+      "[[3, 6]]\n",
+      "[5 8 2 3 6 1 7 4]\n",
+      "[5 8 3 6 2 7 1 4]\n",
+      "1\n",
+      "5\n",
+      "6\n",
+      "0\n",
+      "{5: 4, 6: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 1, 2, 3, 6, 8, 7, 4]\n",
+      "[1, 8, 3, 6, 2, 7, 5, 4]\n",
+      "[[5, 8, 2, 6, 3, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 7, 1, 3, 8, 6, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 2, 8, 6, 3, 1, 7, 4]]\n",
+      "3 4\n",
+      "[[3, 6]]\n",
+      "[5 8 2 3 6 1 7 4]\n",
+      "[5 8 3 6 2 7 1 4]\n",
+      "0\n",
+      "4\n",
+      "5\n",
+      "6\n",
+      "{5: 6, 6: 4, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[6, 8, 2, 3, 5, 1, 7, 4]\n",
+      "[5, 8, 3, 6, 2, 1, 7, 4]\n",
+      "[[5, 8, 2, 6, 3, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 7, 1, 3, 8, 6, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 2, 8, 6, 3, 1, 7, 4]]\n",
+      "1 6\n",
+      "[[8, 8], [6, 2], [3, 6], [2, 3], [7, 1]]\n",
+      "[5 8 6 3 2 7 1 4]\n",
+      "[5 8 2 6 3 1 7 4]\n",
+      "2\n",
+      "6\n",
+      "6\n",
+      "2\n",
+      "{6: 5, 5: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 8, 7, 6, 3, 1, 2, 4]\n",
+      "[5, 8, 1, 3, 2, 7, 6, 4]\n",
+      "[[5, 8, 2, 6, 3, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 7, 1, 3, 8, 6, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 2, 8, 6, 3, 1, 7, 4]]\n",
+      "5 6\n",
+      "[[7, 1]]\n",
+      "[5 8 2 6 3 7 1 4]\n",
+      "[5 8 6 3 2 1 7 4]\n",
+      "4\n",
+      "0\n",
+      "3\n",
+      "5\n",
+      "{5: 4, 6: 4, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[3, 8, 2, 6, 5, 7, 1, 4]\n",
+      "[5, 8, 6, 1, 2, 3, 7, 4]\n",
+      "[[5, 8, 2, 6, 3, 1, 7, 4], [5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 7, 1, 3, 8, 6, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 2, 8, 6, 3, 1, 7, 4]]\n",
+      "3 4\n",
+      "[[3, 6]]\n",
+      "[5 8 2 3 6 1 7 4]\n",
+      "[5 8 3 6 2 7 1 4]\n",
+      "3\n",
+      "4\n",
+      "2\n",
+      "5\n",
+      "{6: 5, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1}\n",
+      "[5, 8, 7, 6, 2, 3, 1, 4]\n",
+      "[5, 8, 2, 6, 3, 1, 7, 4]\n",
+      "[[5, 8, 6, 3, 2, 7, 1, 4], [5, 2, 7, 1, 3, 8, 6, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 2, 8, 6, 3, 1, 7, 4], [5, 8, 2, 6, 3, 1, 7, 4]]\n",
+      "4 6\n",
+      "[[3, 2], [8, 7]]\n",
+      "[5 7 6 2 3 8 1 4]\n",
+      "[5 3 8 1 2 7 6 4]\n",
+      "5\n",
+      "4\n",
+      "1\n",
+      "4\n",
+      "{5: 5, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 6: 1}\n",
+      "[5, 7, 6, 2, 8, 3, 1, 4]\n",
+      "[5, 8, 6, 3, 2, 7, 1, 4]\n",
+      "[[5, 2, 7, 1, 3, 8, 6, 4], [5, 3, 2, 6, 8, 1, 7, 4], [5, 2, 8, 6, 3, 1, 7, 4], [5, 8, 2, 6, 3, 1, 7, 4], [5, 2, 8, 1, 3, 7, 6, 4]]\n",
+      "3 4\n",
+      "[[6, 1]]\n",
+      "[5 2 7 6 3 8 1 4]\n",
+      "[5 3 2 1 8 6 7 4]\n",
+      "2\n",
+      "5\n",
+      "0\n",
+      "6\n",
+      "{6: 6, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1}\n",
+      "[7, 3, 2, 1, 8, 6, 5, 4]\n",
+      "[5, 2, 7, 1, 3, 8, 6, 4]\n",
+      "[[5, 3, 2, 6, 8, 1, 7, 4], [5, 2, 8, 6, 3, 1, 7, 4], [5, 8, 2, 6, 3, 1, 7, 4], [5, 2, 8, 1, 3, 7, 6, 4], [5, 2, 8, 6, 3, 7, 1, 4]]\n",
+      "4 5\n",
+      "[[3, 8]]\n",
+      "[5 8 2 6 3 1 7 4]\n",
+      "[5 2 3 6 8 1 7 4]\n",
+      "3\n",
+      "1\n",
+      "0\n",
+      "5\n",
+      "{6: 6, 5: 5, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[1, 2, 3, 6, 8, 5, 7, 4]\n",
+      "[5, 6, 2, 8, 3, 1, 7, 4]\n",
+      "[[5, 3, 2, 6, 8, 1, 7, 4], [5, 2, 8, 6, 3, 1, 7, 4], [5, 8, 2, 6, 3, 1, 7, 4], [5, 2, 8, 1, 3, 7, 6, 4], [5, 2, 8, 6, 3, 7, 1, 4]]\n",
+      "4 5\n",
+      "[[3, 8]]\n",
+      "[5 8 2 6 3 1 7 4]\n",
+      "[5 2 3 6 8 1 7 4]\n",
+      "6\n",
+      "3\n",
+      "0\n",
+      "6\n",
+      "{6: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1}\n",
+      "[7, 2, 3, 6, 8, 1, 5, 4]\n",
+      "[5, 3, 2, 6, 8, 1, 7, 4]\n",
+      "[[5, 2, 8, 6, 3, 1, 7, 4], [5, 8, 2, 6, 3, 1, 7, 4], [5, 2, 8, 1, 3, 7, 6, 4], [5, 2, 8, 6, 3, 7, 1, 4], [5, 8, 2, 7, 3, 1, 6, 4]]\n",
+      "5 6\n",
+      "[[1, 1]]\n",
+      "[5 2 8 6 3 1 7 4]\n",
+      "[5 8 2 6 3 1 7 4]\n",
+      "1\n",
+      "3\n",
+      "5\n",
+      "3\n",
+      "{5: 4, 6: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 6, 8, 2, 3, 1, 7, 4]\n",
+      "[5, 8, 2, 1, 3, 6, 7, 4]\n",
+      "[[5, 2, 8, 6, 3, 1, 7, 4], [5, 8, 2, 6, 3, 1, 7, 4], [5, 2, 8, 1, 3, 7, 6, 4], [5, 2, 8, 6, 3, 7, 1, 4], [5, 8, 2, 7, 3, 1, 6, 4]]\n",
+      "0 4\n",
+      "[[5, 5], [8, 2], [2, 8], [6, 6]]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[5 8 2 6 3 1 7 4]\n",
+      "[5 2 8 6 3 1 7 4]\n",
+      "1\n",
+      "4\n",
+      "0\n",
+      "1\n",
+      "{0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 6: 1}\n",
+      "[5, 2, 8, 6, 3, 1, 7, 4]\n",
+      "[5, 8, 2, 6, 3, 1, 7, 4]\n",
+      "[[5, 2, 8, 1, 3, 7, 6, 4], [5, 2, 8, 6, 3, 7, 1, 4], [5, 8, 2, 7, 3, 1, 6, 4], [5, 3, 2, 6, 8, 1, 7, 4], [2, 5, 8, 6, 3, 1, 7, 4]]\n",
+      "4 6\n",
+      "[[3, 3], [7, 7]]\n",
+      "[5 2 8 1 3 7 6 4]\n",
+      "[5 2 8 6 3 7 1 4]\n",
+      "1\n",
+      "3\n",
+      "6\n",
+      "3\n",
+      "{5: 4, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 6: 1}\n",
+      "[5, 1, 8, 2, 3, 7, 6, 4]\n",
+      "[5, 2, 8, 1, 3, 7, 6, 4]\n",
+      "[[5, 2, 8, 6, 3, 7, 1, 4], [5, 8, 2, 7, 3, 1, 6, 4], [5, 3, 2, 6, 8, 1, 7, 4], [2, 5, 8, 6, 3, 1, 7, 4], [5, 2, 8, 1, 3, 7, 6, 4]]\n",
+      "3 4\n",
+      "[[7, 6]]\n",
+      "[5 2 8 7 3 6 1 4]\n",
+      "[5 8 2 6 3 1 7 4]\n",
+      "1\n",
+      "0\n",
+      "3\n",
+      "1\n",
+      "{6: 5, 5: 4, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1}\n",
+      "[5, 6, 2, 8, 3, 1, 7, 4]\n",
+      "[2, 5, 8, 7, 3, 6, 1, 4]\n",
+      "[[5, 2, 8, 6, 3, 7, 1, 4], [5, 8, 2, 7, 3, 1, 6, 4], [5, 3, 2, 6, 8, 1, 7, 4], [2, 5, 8, 6, 3, 1, 7, 4], [5, 2, 8, 1, 3, 7, 6, 4]]\n",
+      "1 3\n",
+      "[[8, 2], [2, 8]]\n",
+      "[5 8 2 6 3 7 1 4]\n",
+      "[5 2 8 7 3 1 6 4]\n",
+      "2\n",
+      "6\n",
+      "1\n",
+      "2\n",
+      "{5: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 6: 1}\n",
+      "[5, 8, 1, 6, 3, 7, 2, 4]\n",
+      "[5, 2, 8, 6, 3, 7, 1, 4]\n",
+      "[[5, 8, 2, 7, 3, 1, 6, 4], [5, 3, 2, 6, 8, 1, 7, 4], [2, 5, 8, 6, 3, 1, 7, 4], [5, 2, 8, 1, 3, 7, 6, 4], [5, 8, 2, 7, 3, 1, 6, 4]]\n",
+      "3 6\n",
+      "[[6, 7], [8, 3], [1, 1]]\n",
+      "[5 3 2 6 8 1 7 4]\n",
+      "[5 8 2 7 3 1 6 4]\n",
+      "5\n",
+      "2\n",
+      "2\n",
+      "6\n",
+      "{6: 3, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1}\n",
+      "[5, 8, 6, 7, 3, 1, 2, 4]\n",
+      "[5, 8, 2, 7, 3, 1, 6, 4]\n",
+      "[[5, 3, 2, 6, 8, 1, 7, 4], [2, 5, 8, 6, 3, 1, 7, 4], [5, 2, 8, 1, 3, 7, 6, 4], [5, 8, 2, 7, 3, 1, 6, 4], [5, 3, 1, 6, 8, 2, 7, 4]]\n",
+      "4 5\n",
+      "[[3, 8]]\n",
+      "[5 8 2 6 3 1 7 4]\n",
+      "[2 5 3 6 8 1 7 4]\n",
+      "1\n",
+      "6\n",
+      "1\n",
+      "3\n",
+      "{6: 2, 0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 5: 0}\n",
+      "[2, 6, 3, 5, 8, 1, 7, 4]\n",
+      "[5, 3, 2, 6, 8, 1, 7, 4]\n",
+      "[[2, 5, 8, 6, 3, 1, 7, 4], [5, 2, 8, 1, 3, 7, 6, 4], [5, 8, 2, 7, 3, 1, 6, 4], [5, 3, 1, 6, 8, 2, 7, 4], [5, 7, 2, 6, 3, 1, 8, 4]]\n",
+      "iteration = 212\n",
+      "No of checks =  0\n",
+      "[5, 7, 2, 6, 3, 1, 8, 4]\n"
+     ]
+    }
+   ],
+   "source": [
+    "isOptimumSolution = False\n",
+    "\n",
+    "bestresult = None\n",
+    "quality = 0\n",
+    "\n",
+    "for i in range(0, 100001):\n",
+    "    \n",
+    "    parent1, parent2 = parent_selection(population)\n",
+    "               \n",
+    "    bestresult = parent1\n",
+    "            \n",
+    "    quality = quality_check(bestresult)\n",
+    "    \n",
+    "    if( quality == 0):\n",
+    "               \n",
+    "        isOptimumSolution = True\n",
+    "        print( \"iteration =\", i)\n",
+    "        print(\"No of checks = \", quality)\n",
+    "        print(bestresult)\n",
+    "        break\n",
+    "        \n",
+    "    else:\n",
+    "        \n",
+    "        #child1, child2 = cross_over(parent1,parent2)\n",
+    "        child1, child2 = partial_mapped_crossover(parent1,parent2)\n",
+    "        \n",
+    "        child1 = mutate_swap(child1)\n",
+    "        child2 = mutate_swap(child2)\n",
+    "        \n",
+    "        population  = add_to_population(population, child1, child2)\n",
+    "        population  = survival_fitness(population)\n",
+    "\n",
+    "\n",
+    "if(isOptimumSolution == False):\n",
+    "    print(\"Number of checks =\", quality)\n",
+    "    print(\"Available best solutions\")\n",
+    "    print(bestresult)\n",
+    "        \n",
+    "        \n",
+    "    \n",
+    "    \n",
+    "    "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.6.9"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}