agreg/Médiane des médianes - sélection en temps linéaire.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problème de sélection du k-ième plus petit élément d'un tableau\n",
    "\n",
    "Étant donné un tableau T=[T[0],...,T[n-1]] de $n$ éléments quelconques (par exemple des entiers), et $k\\in\\{1,\\dots,n\\}$, on cherche le k-ième plus petit élément du tableau.\n",
    "\n",
    "Exemple : pour `T = [5, 4, 1, 2, 3]`, pour `k=1` on a 1, `k=2` on a 2, etc.\n",
    "\n",
    "En cas d'éléments distincts, par exemple `T = [1, 1, 2, 3]`, le 2-ième plus petit peut être définit comme 2, ou comme 1. Il vaut mieux le définir comme 1, ainsi l'élément cherché a toujours un sens.\n",
    "\n",
    "\n",
    "Ce petit [notebook Python](https://www.Jupyter.org/) implémente :\n",
    "\n",
    "- un algorithme naïf, qui s'exécute en temps $\\mathcal{O}(k n)$ (pire cas $\\mathcal{O}(n^2)$),\n",
    "- une solution naïve qui trie le tableau et lit la k-ième valeur et s'exécute donc en temps $\\mathcal{O}(n \\log(n))$, indépemment de $k$,\n",
    "- et un algorithme **optimal** qui s'exécute en temps $\\mathcal{O}(n)$ (on ne peut pas faire mieux car il faut forcément lire le tableau au moins une fois s'il n'est pas trié).\n",
    "\n",
    "Je fais aussi des expériences numériques pour illustrer empiriquement leurs complexités.\n",
    "\n",
    "\n",
    "- Auteur : [Lilian Besson](https://github.com/Naereen/notebooks/)\n",
    "- Date : 29 septembre 2020\n",
    "- [License : MIT](https://lbesson.mit-license.org)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-29T15:41:16.755636Z",
     "start_time": "2020-09-29T15:41:16.750717Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.6.9 (default, Jul 17 2020, 12:50:27) \n",
      "[GCC 8.4.0]\n"
     ]
    }
   ],
   "source": [
    "from sys import version\n",
    "print(version)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "J'ai pris l'habitude d'écrire des signatures de fonctions en python qui soient typées :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-29T15:41:46.906852Z",
     "start_time": "2020-09-29T15:41:46.898385Z"
    }
   },
   "outputs": [],
   "source": [
    "from typing import List, Any, TypeVar\n",
    "\n",
    "T = TypeVar(\"T\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Je ferai les premiers exemples avec ces deux tableaux :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-30T12:08:29.176345Z",
     "start_time": "2020-09-30T12:08:29.169610Z"
    }
   },
   "outputs": [],
   "source": [
    "tableau1 = [5, 4, 1, 2, 3]\n",
    "tableau2 = [1, 1, 2, 3]    # avec un doublon"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "## Solution naïve en temps quadratique\n",
    "\n",
    "On peut rapidement imaginer un algorithme \"divisé pour régner\" naïf :\n",
    "\n",
    "- Si `k=1`, on calcule en temps linéaire le minimum du tableau,\n",
    "- Sinon, on calcule le minimum, on construit un tableau de taille `n-1` qui est le tableau initial privé d'UNE occurrence de son minimum (en temps $\\mathcal{O}(n)$), puis on appelle la sélection avec `k-1` sur ce tableau. Si on note $T(n, k)$ le nombre d'opérations élémentaires dans le pire cas pour un tableau quelconque de taille $n$, alors elle est croissante et vérifie la relation de récurrence suivante :\n",
    "  $$ \\forall n > 1, 1 \\leq k \\leq n \\; T(n, k) = O(n) + T(n-1, k-1) $$\n",
    "  et $T(1) = O(1)$, ce qui donne $T(n,k) = O(n k)$ (pas par une application directe du théorème maître, mais c'est la même idée de preuve)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-29T16:04:36.144482Z",
     "start_time": "2020-09-29T16:04:36.122905Z"
    }
   },
   "outputs": [],
   "source": [
    "def selection_naive(tableau: List[T], k: int) -> T:\n",
    "    \"\"\" Sélection du k-ième plus petit élément du tableau, récursivement et naïvement.\n",
    "    \n",
    "    - Complexité mémoire : O(n)\n",
    "    - Complexité temps : O(k n)\n",
    "    \"\"\"\n",
    "    assert 1 <= k <= len(tableau), f\"Erreur : k = {k} doit être entre 1 et n = {len(tableau)} = len(tableau)\"\n",
    "    min_tableau = min(tableau)\n",
    "    if k == 1:  # cas simple\n",
    "        return min_tableau\n",
    "    else:\n",
    "        # on construit un nouveau tableau, de taille n-1, en enlevant UNE occurrence de min\n",
    "        nouveau_tableau = []\n",
    "        min_deja_vu = False\n",
    "        for valeur in tableau:\n",
    "            if valeur == min_tableau:\n",
    "                if min_deja_vu:  # on a déjà vu UNE occurrence de min, on l'ajoute encore\n",
    "                    nouveau_tableau.append(valeur)\n",
    "                else:            # première occurrence de min\n",
    "                    min_deja_vu = True\n",
    "            else:\n",
    "                nouveau_tableau.append(valeur)\n",
    "        return selection_naive(nouveau_tableau, k-1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Deux exemples :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-29T16:03:59.181325Z",
     "start_time": "2020-09-29T16:03:59.175046Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pour le tableau [5, 4, 1, 2, 3] :\n",
      "    Le 1-ième élément du tableau est 1\n",
      "    Le 2-ième élément du tableau est 2\n",
      "    Le 3-ième élément du tableau est 3\n",
      "    Le 4-ième élément du tableau est 4\n",
      "    Le 5-ième élément du tableau est 5\n"
     ]
    }
   ],
   "source": [
    "print(f\"Pour le tableau {tableau1} :\")\n",
    "for k in range(1, 1 + len(tableau1)):\n",
    "    print(f\"    Le {k}-ième élément du tableau est {selection_naive(tableau1, k)}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-29T16:03:57.520927Z",
     "start_time": "2020-09-29T16:03:57.507109Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pour le tableau [1, 1, 2, 3] :\n",
      "    Le 1-ième élément du tableau est 1\n",
      "    Le 2-ième élément du tableau est 1\n",
      "    Le 3-ième élément du tableau est 2\n",
      "    Le 4-ième élément du tableau est 3\n"
     ]
    }
   ],
   "source": [
    "print(f\"Pour le tableau {tableau2} :\")\n",
    "for k in range(1, 1 + len(tableau2)):\n",
    "    print(f\"    Le {k}-ième élément du tableau est {selection_naive(tableau2, k)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "## Solution naïve en temps sur logarithmique (O(n log n))\n",
    "\n",
    "C'est un algorithme très simple :\n",
    "\n",
    "- On trie le tableau (avec n'importe quel algorithme de tri général, en $\\Theta(n \\log(n))$, par exemple le tri fusion, le tri rapide, le tri par tas, etc) ;\n",
    "- Puis on a juste à lire la k-ième valeur du tableau trié."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-29T16:04:51.965264Z",
     "start_time": "2020-09-29T16:04:51.953623Z"
    }
   },
   "outputs": [],
   "source": [
    "def selection_par_tri(tableau: List[T], k: int) -> T:\n",
    "    \"\"\" Sélection du k-ième plus petit élément du tableau, par un tri.\n",
    "    \n",
    "    - Complexité mémoire : O(n)\n",
    "    - Complexité temps : O(n \\log n)\n",
    "    \"\"\"\n",
    "    copie_tableau = list(tableau)  # ou tableau.copy()\n",
    "    copie_tableau.sort()\n",
    "    return copie_tableau[k - 1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Deux exemples :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-29T17:49:09.956443Z",
     "start_time": "2020-09-29T17:49:09.946515Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pour le tableau [5, 4, 1, 2, 3] :\n",
      "    Le 1-ième élément du tableau est 1\n",
      "    Le 2-ième élément du tableau est 2\n",
      "    Le 3-ième élément du tableau est 3\n",
      "    Le 4-ième élément du tableau est 4\n",
      "    Le 5-ième élément du tableau est 5\n"
     ]
    }
   ],
   "source": [
    "print(f\"Pour le tableau {tableau1} :\")\n",
    "for k in range(1, 1 + len(tableau1)):\n",
    "    print(f\"    Le {k}-ième élément du tableau est {selection_par_tri(tableau1, k)}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-29T17:49:10.094963Z",
     "start_time": "2020-09-29T17:49:10.090573Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pour le tableau [1, 1, 2, 3] :\n",
      "    Le 1-ième élément du tableau est 1\n",
      "    Le 2-ième élément du tableau est 1\n",
      "    Le 3-ième élément du tableau est 2\n",
      "    Le 4-ième élément du tableau est 3\n"
     ]
    }
   ],
   "source": [
    "print(f\"Pour le tableau {tableau2} :\")\n",
    "for k in range(1, 1 + len(tableau2)):\n",
    "    print(f\"    Le {k}-ième élément du tableau est {selection_par_tri(tableau2, k)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Méthode optimale : médiane des médianes\n",
    "\n",
    "L'algorithme se déroule en 3 étapes :\n",
    "\n",
    "- L'algorithme divise la liste en groupes de cinq éléments. Ensuite, pour chaque groupe de cinq, la médiane est calculée (une opération qui peut s'effectuer en temps constant, par exemple en utilisant un algorithme de tri),\n",
    "- L'algorithme est alors appelé récursivement sur cette sous-liste de n / 5 éléments pour trouver la vraie médiane de ces éléments. On peut alors garantir que l'élément obtenu se place entre le 30e et le 70e centile,\n",
    "- Enfin, la médiane des médianes est choisie pour être le pivot. Selon la position de l'élément recherché, l'algorithme recommence avec les éléments au-dessus du pivot ou en dessous, qui représentent au plus 70 % de la taille initiale de l'espace de recherche.\n",
    "\n",
    "> Référence : https://fr.wikipedia.org/wiki/Médiane_des_médianes, aussi dans [Algorithmique, Cormen et al]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calcul en temps constant de la médiane de 5 valeurs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-29T16:12:03.606854Z",
     "start_time": "2020-09-29T16:12:03.601151Z"
    }
   },
   "outputs": [],
   "source": [
    "def mediane_cinq_valeurs(tableau: List[T]) -> T:\n",
    "    assert 1 <= len(tableau) <= 5, f\"Erreur : tableau a longueur = {len(tableau)} mais devrait etre 1 <= .. <= 5\"\n",
    "    valeurs = sorted(tableau)\n",
    "    return valeurs[len(tableau) // 2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-29T16:12:03.918360Z",
     "start_time": "2020-09-29T16:12:03.913186Z"
    }
   },
   "outputs": [],
   "source": [
    "assert 3 == mediane_cinq_valeurs([1, 2, 3, 4, 5])\n",
    "assert 3 == mediane_cinq_valeurs([5, 1, 4, 2, 3])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Que se passe-t-il si la liste n'est pas de taille impaire ?\n",
    "On peut prendre la valeur à gauche ou à droite du milieu. Ici, c'est la valeur à droite qui a été choisie :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-29T16:12:04.845438Z",
     "start_time": "2020-09-29T16:12:04.839632Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mediane_cinq_valeurs([1, 2, 3, 4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-29T16:12:07.898596Z",
     "start_time": "2020-09-29T16:12:07.884836Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mediane_cinq_valeurs([1, 2, 4])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Découper le tableau en sous-tableaux :\n",
    "\n",
    "Par exemple :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-29T16:12:15.110666Z",
     "start_time": "2020-09-29T16:12:15.090305Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13]]"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tableau3 = [1,2,3,4,5, 6,7,8,9,10, 11,12,13]\n",
    "# On va le découper comme ça :\n",
    "[\n",
    "    [1,2,3,4,5],\n",
    "    [6,7,8,9,10],\n",
    "    [11,12,13],\n",
    "]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cela est très rapide avec des listes par compréhension :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-29T16:12:29.630092Z",
     "start_time": "2020-09-29T16:12:29.617645Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13]]"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[\n",
    "    tableau3[i:i+5]\n",
    "    for i in range(0, len(tableau3), 5)\n",
    "]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Et donc si on calcule les médianes :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-29T16:12:31.641077Z",
     "start_time": "2020-09-29T16:12:31.630072Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[3, 8, 12]"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[\n",
    "    mediane_cinq_valeurs(tableau3[i:i+5])\n",
    "    for i in range(0, len(tableau3), 5)\n",
    "]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Médiane des médianes par une approche récursive"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-29T16:17:52.319957Z",
     "start_time": "2020-09-29T16:17:52.303336Z"
    }
   },
   "outputs": [],
   "source": [
    "def mediane_des_medianes(tableau: List[T]) -> T:\n",
    "    \"\"\" Méthode de la médiane des médianes.\n",
    "    \n",
    "    - Complexité mémoire : O(n).\n",
    "    - Complexité temps : O(n) car T(n) = O(n) + T(n/5) pour tout n=5^k (cas (i) du Master Theorem).\n",
    "    \"\"\"\n",
    "    assert 1 <= len(tableau), f\"Erreur : k = {k} doit être entre 1 et n = {len(tableau)} = len(tableau)\"\n",
    "    n = len(tableau)\n",
    "    if n <= 5:  # O(1)\n",
    "        return mediane_cinq_valeurs(tableau)\n",
    "    else:\n",
    "        medianes = [\n",
    "            # au plus 1 + (n/5) sous-tableaux de taille <= 5\n",
    "            mediane_cinq_valeur(tableau[i : i+5])\n",
    "            for i in range(0, n, 5)\n",
    "        ]\n",
    "        # un appel récursive en T(n/5)  (si on fait la preuve juste pour des n = 5^k)\n",
    "        return mediane_des_medianes(medianes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Par exemple, la médiane des médianes du tableau d'exemple est 8 car son tableau des médianes des sous-tableaux de taille <= 5 est [3, 8, 12] :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-29T16:17:58.644633Z",
     "start_time": "2020-09-29T16:17:58.633387Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mediane_des_medianes(tableau3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sélection par médianes\n",
    "\n",
    "On met ensemble tous les éléments :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-29T18:00:57.970768Z",
     "start_time": "2020-09-29T18:00:57.963806Z"
    }
   },
   "outputs": [],
   "source": [
    "def selection_par_medianes(tableau: List[T], k: int) -> T:\n",
    "    \"\"\" Sélection du k-ième plus petit élément du tableau, par la méthode de la médiane des médianes.\n",
    "    \n",
    "    - Complexité mémoire : O(n)\n",
    "    - Complexité temps : O(n)\n",
    "    \"\"\"\n",
    "    assert 1 <= k <= len(tableau), f\"Erreur : k = {k} doit être entre 1 et n = {len(tableau)} = len(tableau)\"\n",
    "    n = len(tableau)\n",
    "    print(f\"DEBUG : n = {n}, tableau = {tableau}, k = {k}\")\n",
    "    if n <= 1:\n",
    "        return tableau[0]\n",
    "    if n <= 5:\n",
    "        print(f\"WARNING n = {n} <= k = {k}\")\n",
    "    mediane = mediane_des_medianes(tableau)\n",
    "    index_mediane = tableau.index(mediane)\n",
    "    if (k-1) == index_mediane:\n",
    "        return mediane\n",
    "    else:\n",
    "        if (k-1) < index_mediane:\n",
    "            sous_tableau = [ x for x in tableau if x <= mediane ]\n",
    "        else:  # (k-1) > index_mediane\n",
    "            sous_tableau = [ x for x in tableau if x >= mediane ]\n",
    "        return selection_par_medianes(sous_tableau, k)      "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Deux exemples :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-29T18:01:01.704902Z",
     "start_time": "2020-09-29T18:00:58.775982Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pour le tableau [5, 4, 1, 2, 3] :\n",
      "DEBUG : n = 5, tableau = [5, 4, 1, 2, 3], k = 1\n",
      "DEBUG : n = 3, tableau = [1, 2, 3], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1\n",
      "DEBUG : n = 2, tableau = [1, 2], k = 1"
     ]
    },
    {
     "ename": "RecursionError",
     "evalue": "maximum recursion depth exceeded in comparison",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mRecursionError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-67-bcb6beca1c7c>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34mf\"Pour le tableau {tableau1} :\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mk\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtableau1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m     \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34mf\"    Le {k}-ième élément du tableau est {selection_par_medianes(tableau1, k)}\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m<ipython-input-66-fd9c70acc4ff>\u001b[0m in \u001b[0;36mselection_par_medianes\u001b[0;34m(tableau, k)\u001b[0m\n\u001b[1;32m     21\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m  \u001b[0;31m# (k-1) > index_mediane\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     22\u001b[0m             \u001b[0msous_tableau\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m \u001b[0mx\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mx\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mtableau\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mx\u001b[0m \u001b[0;34m>=\u001b[0m \u001b[0mmediane\u001b[0m \u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 23\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mselection_par_medianes\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msous_tableau\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "... last 1 frames repeated, from the frame below ...\n",
      "\u001b[0;32m<ipython-input-66-fd9c70acc4ff>\u001b[0m in \u001b[0;36mselection_par_medianes\u001b[0;34m(tableau, k)\u001b[0m\n\u001b[1;32m     21\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m  \u001b[0;31m# (k-1) > index_mediane\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     22\u001b[0m             \u001b[0msous_tableau\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m \u001b[0mx\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mx\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mtableau\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mx\u001b[0m \u001b[0;34m>=\u001b[0m \u001b[0mmediane\u001b[0m \u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 23\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mselection_par_medianes\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msous_tableau\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mRecursionError\u001b[0m: maximum recursion depth exceeded in comparison"
     ]
    }
   ],
   "source": [
    "print(f\"Pour le tableau {tableau1} :\")\n",
    "for k in range(1, 1 + len(tableau1)):\n",
    "    print(f\"    Le {k}-ième élément du tableau est {selection_par_medianes(tableau1, k)}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-29T17:50:05.305465Z",
     "start_time": "2020-09-29T17:50:02.756583Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pour le tableau [1, 1, 2, 3] :\n"
     ]
    },
    {
     "ename": "RecursionError",
     "evalue": "maximum recursion depth exceeded in comparison",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mRecursionError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-54-d6c9f1ff2854>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34mf\"Pour le tableau {tableau2} :\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mk\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtableau2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m     \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34mf\"    Le {k}-ième élément du tableau est {selection_par_medianes(tableau2, k)}\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m<ipython-input-52-f66f452717aa>\u001b[0m in \u001b[0;36mselection_par_medianes\u001b[0;34m(tableau, k)\u001b[0m\n\u001b[1;32m     18\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m  \u001b[0;31m# k > index_mediane\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     19\u001b[0m             \u001b[0msous_tableau\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m \u001b[0mx\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mx\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mtableau\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mx\u001b[0m \u001b[0;34m>=\u001b[0m \u001b[0mmediane\u001b[0m \u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 20\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mselection_par_medianes\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msous_tableau\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "... last 1 frames repeated, from the frame below ...\n",
      "\u001b[0;32m<ipython-input-52-f66f452717aa>\u001b[0m in \u001b[0;36mselection_par_medianes\u001b[0;34m(tableau, k)\u001b[0m\n\u001b[1;32m     18\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m  \u001b[0;31m# k > index_mediane\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     19\u001b[0m             \u001b[0msous_tableau\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m \u001b[0mx\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mx\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mtableau\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mx\u001b[0m \u001b[0;34m>=\u001b[0m \u001b[0mmediane\u001b[0m \u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 20\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mselection_par_medianes\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msous_tableau\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mRecursionError\u001b[0m: maximum recursion depth exceeded in comparison"
     ]
    }
   ],
   "source": [
    "print(f\"Pour le tableau {tableau2} :\")\n",
    "for k in range(1, 1 + len(tableau2)):\n",
    "    print(f\"    Le {k}-ième élément du tableau est {selection_par_medianes(tableau2, k)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Autre approche\n",
    "\n",
    "En regardant le code donné sur https://en.wikipedia.org/wiki/Median_of_medians"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On va faire plein d'échanges de valeurs dans un tableau :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-29T19:29:01.028289Z",
     "start_time": "2020-09-29T19:29:01.020474Z"
    }
   },
   "outputs": [],
   "source": [
    "def swap(tableau: List[T], i: int, j: int) -> None:\n",
    "    \"\"\" Échange tableau[i] et tableau[j] en temps constant.\"\"\"\n",
    "    tableau[i], tableau[j] = tableau[j], tableau[i]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Avec un petit tri par insertion sur cinq éléments (max cinq), on peut trouver la médiane d'un petit tableau en temps constant :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-29T19:29:01.411592Z",
     "start_time": "2020-09-29T19:29:01.405532Z"
    }
   },
   "outputs": [],
   "source": [
    "def partition5(tableau: List[T], left: int, right: int) -> int:\n",
    "    \"\"\" Sélecte la médiane d'un tableau d'au plus 5 éléments, par un tri par insertion sur ces cinq éléments.\"\"\"\n",
    "    print(f\"DEBUG: partition5({tableau}, {left}, {right})\")\n",
    "    i = left + 1\n",
    "    while i <= right:\n",
    "        j = i\n",
    "        while j > left and tableau[j-1] > tableau[j]:\n",
    "            swap(tableau, j-1, j)\n",
    "            j = j - 1\n",
    "        i = i + 1\n",
    "    return (left + right) // 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Par exemple :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-29T19:29:01.784251Z",
     "start_time": "2020-09-29T19:29:01.777494Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DEBUG: partition5([5, 3, 2, 1, 4], 0, 4)\n",
      "2\n",
      "[1, 2, 3, 4, 5]\n"
     ]
    }
   ],
   "source": [
    "t = [5, 3, 2, 1, 4]\n",
    "print(partition5(t, 0, len(t) - 1))\n",
    "print(t)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Le calcul du pivot fera un appel à `selection`, qui lui-même appelle `pivot` (par récursion mutuelle) :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-29T19:29:02.173191Z",
     "start_time": "2020-09-29T19:29:02.165320Z"
    }
   },
   "outputs": [],
   "source": [
    "def pivot(tableau: List[T], left: int, right: int) -> int:\n",
    "    \"\"\" Pivot en temps O(n).\"\"\"\n",
    "    print(f\"DEBUG: pivot({tableau}, {left}, {right})\")\n",
    "    if right - left + 1 <= 5:  # <= 5 éléments\n",
    "        return partition5(tableau, left, right)\n",
    "    # sinon, on déplace les médianes des sous tableaux de cinq éléments vers les n/5 premières positions\n",
    "    for i in range(left, right + 1, 5):\n",
    "        # calcule la position de la médiane du i-ieme sous-groupe :\n",
    "        sub_right = i + 4\n",
    "        if sub_right > right:\n",
    "            sub_right = right\n",
    "        median5 = partition5(tableau, i, sub_right)\n",
    "        new_pos = left + (i - left)//5\n",
    "        swap(tableau, median5, new_pos)\n",
    "\n",
    "    # médiane des n/5 médianes des sous-groupes\n",
    "    mid = (right - left) // 10 + left + 1\n",
    "    return selection(tableau, mid, left=left, right=left + (right - left) // 5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La sélection utilisera la fonction `pivot` et la `partition` :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-29T19:29:02.877335Z",
     "start_time": "2020-09-29T19:29:02.871485Z"
    }
   },
   "outputs": [],
   "source": [
    "from typing import Optional"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-29T19:29:03.537826Z",
     "start_time": "2020-09-29T19:29:03.525054Z"
    }
   },
   "outputs": [],
   "source": [
    "def selection(tableau: List[T], k: int, left: Optional[int] = None, right: Optional[int] = None) -> int:\n",
    "    \"\"\" Sélection en temps linéaire du k-ième plus petit élément dans [tab[left],...,tab[right]].\"\"\"\n",
    "    if left is None: left = 0\n",
    "    if right is None: right = len(tableau) - 1\n",
    "    print(f\"DEBUG: selection({tableau}, {k}, {left}, {right})\")\n",
    "    while True:\n",
    "        if left == right:\n",
    "            return left\n",
    "        pivot_index = pivot(tableau, left, right)\n",
    "        pivot_index = partition(tableau, left, right, pivot_index, k)\n",
    "        if k == pivot_index:\n",
    "            return k  # déjà à la bonne position\n",
    "        elif k < pivot_index:\n",
    "            right = pivot_index - 1\n",
    "        else:\n",
    "            left  = pivot_index + 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Et enfin la fonction de partition :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-29T19:29:04.437255Z",
     "start_time": "2020-09-29T19:29:04.423162Z"
    }
   },
   "outputs": [],
   "source": [
    "def partition(tableau: List[T], left: int, right: int, pivot_index: int, k: int) -> int:\n",
    "    print(f\"DEBUG: partition({tableau}, {left}, {right}, {pivot_index}, {k})\")\n",
    "    pivot_value = tableau[pivot_index]\n",
    "    swap(tableau, pivot_index, right)  # on déplace le pivot à la fin\n",
    "    store_index = left\n",
    "    # on déplace les éléments plus petits que le pivot à sa gauche\n",
    "    for i in range(left, right):\n",
    "        if tableau[i] < pivot_value:\n",
    "            swap(tableau, store_index, i)\n",
    "            store_index = store_index + 1\n",
    "    # on déplace tous les éléments égaux au pivot just après les plus petits éléments\n",
    "    store_index_eq = store_index\n",
    "    for i in range(store_index, right):\n",
    "        if tableau[i] == pivot_value:\n",
    "            swap(tableau, store_index_eq, i)\n",
    "            store_index_eq = store_index_eq + 1\n",
    "    # on déplace le pivot à sa position finale au milieu\n",
    "    swap(tableau, right, store_index_eq)\n",
    "    # on renvoie la localisation du pivot, compte tenu de la position recherchée k\n",
    "    if k < store_index:\n",
    "        return store_index     # k est dans le groupe des petits éléments\n",
    "    elif k == store_index_eq:\n",
    "        return k               # k est dans le groupe égal au pivot\n",
    "    else:\n",
    "        return store_index_eq  # k est dans le groupe des petits éléments"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Deux exemples :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-29T19:32:01.716633Z",
     "start_time": "2020-09-29T19:32:01.700109Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pour le tableau [1, 2, 3, 4, 5] :\n",
      "DEBUG: selection([1, 2, 3, 4, 5], 1, 0, 4)\n",
      "DEBUG: pivot([1, 2, 3, 4, 5], 0, 4)\n",
      "DEBUG: partition5([1, 2, 3, 4, 5], 0, 4)\n",
      "DEBUG: partition([1, 2, 3, 4, 5], 0, 4, 2, 1)\n",
      "DEBUG: pivot([1, 2, 3, 4, 5], 0, 1)\n",
      "DEBUG: partition5([1, 2, 3, 4, 5], 0, 1)\n",
      "DEBUG: partition([1, 2, 3, 4, 5], 0, 1, 0, 1)\n",
      "    Le 1-ième élément du tableau est 1\n",
      "DEBUG: selection([1, 2, 3, 4, 5], 2, 0, 4)\n",
      "DEBUG: pivot([1, 2, 3, 4, 5], 0, 4)\n",
      "DEBUG: partition5([1, 2, 3, 4, 5], 0, 4)\n",
      "DEBUG: partition([1, 2, 3, 4, 5], 0, 4, 2, 2)\n",
      "    Le 2-ième élément du tableau est 2\n",
      "DEBUG: selection([1, 2, 3, 4, 5], 3, 0, 4)\n",
      "DEBUG: pivot([1, 2, 3, 4, 5], 0, 4)\n",
      "DEBUG: partition5([1, 2, 3, 4, 5], 0, 4)\n",
      "DEBUG: partition([1, 2, 3, 4, 5], 0, 4, 2, 3)\n",
      "DEBUG: pivot([1, 2, 3, 4, 5], 3, 4)\n",
      "DEBUG: partition5([1, 2, 3, 4, 5], 3, 4)\n",
      "DEBUG: partition([1, 2, 3, 4, 5], 3, 4, 3, 3)\n",
      "    Le 3-ième élément du tableau est 3\n",
      "DEBUG: selection([1, 2, 3, 4, 5], 4, 0, 4)\n",
      "DEBUG: pivot([1, 2, 3, 4, 5], 0, 4)\n",
      "DEBUG: partition5([1, 2, 3, 4, 5], 0, 4)\n",
      "DEBUG: partition([1, 2, 3, 4, 5], 0, 4, 2, 4)\n",
      "DEBUG: pivot([1, 2, 3, 4, 5], 3, 4)\n",
      "DEBUG: partition5([1, 2, 3, 4, 5], 3, 4)\n",
      "DEBUG: partition([1, 2, 3, 4, 5], 3, 4, 3, 4)\n",
      "    Le 4-ième élément du tableau est 4\n",
      "DEBUG: selection([1, 2, 3, 4, 5], 5, 0, 4)\n",
      "DEBUG: pivot([1, 2, 3, 4, 5], 0, 4)\n",
      "DEBUG: partition5([1, 2, 3, 4, 5], 0, 4)\n",
      "DEBUG: partition([1, 2, 3, 4, 5], 0, 4, 2, 5)\n",
      "DEBUG: pivot([1, 2, 3, 4, 5], 3, 4)\n",
      "DEBUG: partition5([1, 2, 3, 4, 5], 3, 4)\n",
      "DEBUG: partition([1, 2, 3, 4, 5], 3, 4, 3, 5)\n",
      "    Le 5-ième élément du tableau est 4\n"
     ]
    }
   ],
   "source": [
    "print(f\"Pour le tableau {tableau1} :\")\n",
    "for k in range(1, 1 + len(tableau1)):\n",
    "    print(f\"    Le {k}-ième élément du tableau est {selection(tableau1[:], k)}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-30T12:14:06.080269Z",
     "start_time": "2020-09-30T12:14:06.067036Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pour le tableau [1, 2, 3, 4, 5] :\n",
      "DEBUG: selection([1, 2, 3, 4, 5], 1, 0, 4)\n",
      "DEBUG: pivot([1, 2, 3, 4, 5], 0, 4)\n",
      "DEBUG: partition5([1, 2, 3, 4, 5], 0, 4)\n",
      "DEBUG: partition([1, 2, 3, 4, 5], 0, 4, 2, 1)\n",
      "DEBUG: pivot([1, 2, 3, 4, 5], 0, 1)\n",
      "DEBUG: partition5([1, 2, 3, 4, 5], 0, 1)\n",
      "DEBUG: partition([1, 2, 3, 4, 5], 0, 1, 0, 1)\n",
      "    Le 1-ième élément du tableau est 1\n",
      "DEBUG: selection([1, 2, 3, 4, 5], 2, 0, 4)\n",
      "DEBUG: pivot([1, 2, 3, 4, 5], 0, 4)\n",
      "DEBUG: partition5([1, 2, 3, 4, 5], 0, 4)\n",
      "DEBUG: partition([1, 2, 3, 4, 5], 0, 4, 2, 2)\n",
      "    Le 2-ième élément du tableau est 2\n",
      "DEBUG: selection([1, 2, 3, 4, 5], 3, 0, 4)\n",
      "DEBUG: pivot([1, 2, 3, 4, 5], 0, 4)\n",
      "DEBUG: partition5([1, 2, 3, 4, 5], 0, 4)\n",
      "DEBUG: partition([1, 2, 3, 4, 5], 0, 4, 2, 3)\n",
      "DEBUG: pivot([1, 2, 3, 4, 5], 3, 4)\n",
      "DEBUG: partition5([1, 2, 3, 4, 5], 3, 4)\n",
      "DEBUG: partition([1, 2, 3, 4, 5], 3, 4, 3, 3)\n",
      "    Le 3-ième élément du tableau est 3\n",
      "DEBUG: selection([1, 2, 3, 4, 5], 4, 0, 4)\n",
      "DEBUG: pivot([1, 2, 3, 4, 5], 0, 4)\n",
      "DEBUG: partition5([1, 2, 3, 4, 5], 0, 4)\n",
      "DEBUG: partition([1, 2, 3, 4, 5], 0, 4, 2, 4)\n",
      "DEBUG: pivot([1, 2, 3, 4, 5], 3, 4)\n",
      "DEBUG: partition5([1, 2, 3, 4, 5], 3, 4)\n",
      "DEBUG: partition([1, 2, 3, 4, 5], 3, 4, 3, 4)\n",
      "    Le 4-ième élément du tableau est 4\n",
      "DEBUG: selection([1, 2, 3, 4, 5], 5, 0, 4)\n",
      "DEBUG: pivot([1, 2, 3, 4, 5], 0, 4)\n",
      "DEBUG: partition5([1, 2, 3, 4, 5], 0, 4)\n",
      "DEBUG: partition([1, 2, 3, 4, 5], 0, 4, 2, 5)\n",
      "DEBUG: pivot([1, 2, 3, 4, 5], 3, 4)\n",
      "DEBUG: partition5([1, 2, 3, 4, 5], 3, 4)\n",
      "DEBUG: partition([1, 2, 3, 4, 5], 3, 4, 3, 5)\n",
      "    Le 5-ième élément du tableau est 4\n",
      "Pour le tableau [1, 2, 3, 4] :\n",
      "DEBUG: selection([1, 2, 3, 4], 1, 0, 3)\n",
      "DEBUG: pivot([1, 2, 3, 4], 0, 3)\n",
      "DEBUG: partition5([1, 2, 3, 4], 0, 3)\n",
      "DEBUG: partition([1, 2, 3, 4], 0, 3, 1, 1)\n",
      "    Le 1-ième élément du tableau est 1\n",
      "DEBUG: selection([1, 2, 3, 4], 2, 0, 3)\n",
      "DEBUG: pivot([1, 2, 3, 4], 0, 3)\n",
      "DEBUG: partition5([1, 2, 3, 4], 0, 3)\n",
      "DEBUG: partition([1, 2, 3, 4], 0, 3, 1, 2)\n",
      "DEBUG: pivot([1, 2, 3, 4], 2, 3)\n",
      "DEBUG: partition5([1, 2, 3, 4], 2, 3)\n",
      "DEBUG: partition([1, 2, 3, 4], 2, 3, 2, 2)\n",
      "    Le 2-ième élément du tableau est 2\n",
      "DEBUG: selection([1, 2, 3, 4], 3, 0, 3)\n",
      "DEBUG: pivot([1, 2, 3, 4], 0, 3)\n",
      "DEBUG: partition5([1, 2, 3, 4], 0, 3)\n",
      "DEBUG: partition([1, 2, 3, 4], 0, 3, 1, 3)\n",
      "DEBUG: pivot([1, 2, 3, 4], 2, 3)\n",
      "DEBUG: partition5([1, 2, 3, 4], 2, 3)\n",
      "DEBUG: partition([1, 2, 3, 4], 2, 3, 2, 3)\n",
      "    Le 3-ième élément du tableau est 3\n",
      "DEBUG: selection([1, 2, 3, 4], 4, 0, 3)\n",
      "DEBUG: pivot([1, 2, 3, 4], 0, 3)\n",
      "DEBUG: partition5([1, 2, 3, 4], 0, 3)\n",
      "DEBUG: partition([1, 2, 3, 4], 0, 3, 1, 4)\n",
      "DEBUG: pivot([1, 2, 3, 4], 2, 3)\n",
      "DEBUG: partition5([1, 2, 3, 4], 2, 3)\n",
      "DEBUG: partition([1, 2, 3, 4], 2, 3, 2, 4)\n",
      "    Le 4-ième élément du tableau est 3\n"
     ]
    }
   ],
   "source": [
    "for tab in (\n",
    "        [1, 2, 3, 4, 5],\n",
    "        [1, 2, 3, 4],\n",
    "        # [1, 2, 3] * 10,\n",
    "    ):\n",
    "    print(f\"Pour le tableau {tab} :\")\n",
    "    for k in range(1, 1 + len(tab)):\n",
    "        print(f\"    Le {k}-ième élément du tableau est {selection(tab[:], k)}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-29T19:32:06.071291Z",
     "start_time": "2020-09-29T19:32:06.057079Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pour le tableau [1, 1, 2, 3] :\n",
      "DEBUG: selection([1, 1, 2, 3], 1, 0, 3)\n",
      "DEBUG: pivot([1, 1, 2, 3], 0, 3)\n",
      "DEBUG: partition5([1, 1, 2, 3], 0, 3)\n",
      "DEBUG: partition([1, 1, 2, 3], 0, 3, 1, 1)\n",
      "    Le 1-ième élément du tableau est 1\n",
      "DEBUG: selection([1, 1, 2, 3], 2, 0, 3)\n",
      "DEBUG: pivot([1, 1, 2, 3], 0, 3)\n",
      "DEBUG: partition5([1, 1, 2, 3], 0, 3)\n",
      "DEBUG: partition([1, 1, 2, 3], 0, 3, 1, 2)\n",
      "DEBUG: pivot([1, 1, 2, 3], 2, 3)\n",
      "DEBUG: partition5([1, 1, 2, 3], 2, 3)\n",
      "DEBUG: partition([1, 1, 2, 3], 2, 3, 2, 2)\n",
      "    Le 2-ième élément du tableau est 2\n",
      "DEBUG: selection([1, 1, 2, 3], 3, 0, 3)\n",
      "DEBUG: pivot([1, 1, 2, 3], 0, 3)\n",
      "DEBUG: partition5([1, 1, 2, 3], 0, 3)\n",
      "DEBUG: partition([1, 1, 2, 3], 0, 3, 1, 3)\n",
      "DEBUG: pivot([1, 1, 2, 3], 2, 3)\n",
      "DEBUG: partition5([1, 1, 2, 3], 2, 3)\n",
      "DEBUG: partition([1, 1, 2, 3], 2, 3, 2, 3)\n",
      "    Le 3-ième élément du tableau est 3\n",
      "DEBUG: selection([1, 1, 2, 3], 4, 0, 3)\n",
      "DEBUG: pivot([1, 1, 2, 3], 0, 3)\n",
      "DEBUG: partition5([1, 1, 2, 3], 0, 3)\n",
      "DEBUG: partition([1, 1, 2, 3], 0, 3, 1, 4)\n",
      "DEBUG: pivot([1, 1, 2, 3], 2, 3)\n",
      "DEBUG: partition5([1, 1, 2, 3], 2, 3)\n",
      "DEBUG: partition([1, 1, 2, 3], 2, 3, 2, 4)\n",
      "    Le 4-ième élément du tableau est 3\n",
      "Pour le tableau [3, 2, 1, 1] :\n",
      "DEBUG: selection([3, 2, 1, 1], 1, 0, 3)\n",
      "DEBUG: pivot([3, 2, 1, 1], 0, 3)\n",
      "DEBUG: partition5([3, 2, 1, 1], 0, 3)\n",
      "DEBUG: partition([1, 1, 2, 3], 0, 3, 1, 1)\n",
      "    Le 1-ième élément du tableau est 1\n",
      "DEBUG: selection([3, 2, 1, 1], 2, 0, 3)\n",
      "DEBUG: pivot([3, 2, 1, 1], 0, 3)\n",
      "DEBUG: partition5([3, 2, 1, 1], 0, 3)\n",
      "DEBUG: partition([1, 1, 2, 3], 0, 3, 1, 2)\n",
      "DEBUG: pivot([1, 1, 2, 3], 2, 3)\n",
      "DEBUG: partition5([1, 1, 2, 3], 2, 3)\n",
      "DEBUG: partition([1, 1, 2, 3], 2, 3, 2, 2)\n",
      "    Le 2-ième élément du tableau est 2\n",
      "DEBUG: selection([3, 2, 1, 1], 3, 0, 3)\n",
      "DEBUG: pivot([3, 2, 1, 1], 0, 3)\n",
      "DEBUG: partition5([3, 2, 1, 1], 0, 3)\n",
      "DEBUG: partition([1, 1, 2, 3], 0, 3, 1, 3)\n",
      "DEBUG: pivot([1, 1, 2, 3], 2, 3)\n",
      "DEBUG: partition5([1, 1, 2, 3], 2, 3)\n",
      "DEBUG: partition([1, 1, 2, 3], 2, 3, 2, 3)\n",
      "    Le 3-ième élément du tableau est 3\n",
      "DEBUG: selection([3, 2, 1, 1], 4, 0, 3)\n",
      "DEBUG: pivot([3, 2, 1, 1], 0, 3)\n",
      "DEBUG: partition5([3, 2, 1, 1], 0, 3)\n",
      "DEBUG: partition([1, 1, 2, 3], 0, 3, 1, 4)\n",
      "DEBUG: pivot([1, 1, 2, 3], 2, 3)\n",
      "DEBUG: partition5([1, 1, 2, 3], 2, 3)\n",
      "DEBUG: partition([1, 1, 2, 3], 2, 3, 2, 4)\n",
      "    Le 4-ième élément du tableau est 3\n"
     ]
    }
   ],
   "source": [
    "for tab in (\n",
    "        tableau2,\n",
    "        tableau2[::-1],\n",
    "    ):\n",
    "        print(f\"Pour le tableau {tab} :\")\n",
    "        for k in range(1, 1 + len(tab)):\n",
    "            print(f\"    Le {k}-ième élément du tableau est {selection(tab[:], k)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Autre implémentation\n",
    "\n",
    "Celle-ci sera la bonne :\n",
    "\n",
    "> Inspirée de https://stackoverflow.com/a/34911527/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-30T12:14:35.631566Z",
     "start_time": "2020-09-30T12:14:35.603148Z"
    }
   },
   "outputs": [],
   "source": [
    "def find_i_th_smallest(tableau: List[T], k: Optional[int] = None, items_per_column: int = 5) -> T:\n",
    "    if k is None:\n",
    "        k = (len(tableau) - 1) // 2\n",
    "    n = len(tableau)\n",
    "    if n <= items_per_column:\n",
    "        # si tableau est assez petit, on fait juste un tri et on trouve le k-ième élément\n",
    "        return sorted(tableau)[k]\n",
    "    else:\n",
    "        # 1. partition A into columns of items_per_column items each. items_per_column is odd, say 15.\n",
    "        # 2. find the median of every column\n",
    "        # 3. put all medians in a new list, say, called medians\n",
    "        medians = [\n",
    "            find_i_th_smallest(tableau[j : (j + items_per_column)])\n",
    "            for j in range(0, n, items_per_column)\n",
    "        ]\n",
    "\n",
    "        # 4. find M, the median of the medians\n",
    "        median_of_medians = find_i_th_smallest(medians)  # with k=None, computes middle value = median\n",
    "\n",
    "        # 5. split A into 3 parts by M, { < M }, { == M }, and { > M }\n",
    "        # 6. find which above set has tableau's k-th smallest, recursively.\n",
    "        lefts = [ x for x in tableau if x < median_of_medians ]\n",
    "        if k < len(lefts):\n",
    "            return find_i_th_smallest(lefts, k)\n",
    "        rights = [ x for x in tableau if x > median_of_medians ]\n",
    "        len_rights = len(rights)\n",
    "        if k < (n - len_rights):\n",
    "            return median_of_medians\n",
    "        return find_i_th_smallest(rights, k - (n - len_rights))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On peut faire quelques tests :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-29T19:53:46.737897Z",
     "start_time": "2020-09-29T19:53:46.731112Z"
    }
   },
   "outputs": [],
   "source": [
    "try:\n",
    "    from tqdm.notebook import tqdm\n",
    "except ImportError:\n",
    "    def tqdm(iterator, **kwargs): return iterator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-30T12:28:51.787297Z",
     "start_time": "2020-09-30T12:15:11.757354Z"
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "bc013b742c8946de94aa0bfc1f37b53f",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(HTML(value=''), FloatProgress(value=0.0, max=3.0), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pour des listes de taille 100 :\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "1711d1f5cf0c496391883861974f8693",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(HTML(value=''), FloatProgress(value=0.0, max=1.0), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test 1 / 1 avec une liste de taille 100 :\n",
      "17.5 µs ± 7.65 µs per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
      "118 µs ± 19.2 µs per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
      "226 µs ± 11.5 µs per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
      "942 µs ± 150 µs per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
      "\n",
      "Pour des listes de taille 1000 :\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d8b28c829b5b45bc97a9666d6f74203b",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(HTML(value=''), FloatProgress(value=0.0, max=1.0), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test 1 / 1 avec une liste de taille 1000 :\n",
      "267 µs ± 10 µs per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
      "1.15 ms ± 89.3 µs per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
      "2.54 ms ± 11.8 µs per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
      "8.52 ms ± 1.02 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
      "\n",
      "Pour des listes de taille 10000 :\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "29a26a90afe7446e84bce5ee70463dad",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(HTML(value=''), FloatProgress(value=0.0, max=1.0), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test 1 / 1 avec une liste de taille 10000 :\n",
      "2.82 ms ± 70.9 µs per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
      "8.83 ms ± 303 µs per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
      "\n",
      "\n"
     ]
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-186-cedfded02760>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     12\u001b[0m             \u001b[0msorted_L\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msorted\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mL\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     13\u001b[0m             \u001b[0;32mfor\u001b[0m \u001b[0mk\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mL\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 14\u001b[0;31m                 \u001b[0;32massert\u001b[0m \u001b[0msorted_L\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mfind_i_th_smallest\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mL\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     15\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     16\u001b[0m             \u001b[0mget_ipython\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun_line_magic\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'timeit'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'-n1 sorted(L)[random.randint(0, len(L) - 1)]'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-185-7fed55f97d6a>\u001b[0m in \u001b[0;36mfind_i_th_smallest\u001b[0;34m(tableau, k, items_per_column)\u001b[0m\n\u001b[1;32m     22\u001b[0m         \u001b[0mlefts\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m \u001b[0mx\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mx\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mtableau\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mx\u001b[0m \u001b[0;34m<\u001b[0m \u001b[0mmedian_of_medians\u001b[0m \u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     23\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mk\u001b[0m \u001b[0;34m<\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlefts\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 24\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mfind_i_th_smallest\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlefts\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     25\u001b[0m         \u001b[0mrights\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m \u001b[0mx\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mx\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mtableau\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mx\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0mmedian_of_medians\u001b[0m \u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     26\u001b[0m         \u001b[0mlen_rights\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrights\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-185-7fed55f97d6a>\u001b[0m in \u001b[0;36mfind_i_th_smallest\u001b[0;34m(tableau, k, items_per_column)\u001b[0m\n\u001b[1;32m     16\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     17\u001b[0m         \u001b[0;31m# 4. find M, the median of the medians\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 18\u001b[0;31m         \u001b[0mmedian_of_medians\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfind_i_th_smallest\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmedians\u001b[0m\u001b[0;34m)\u001b[0m  \u001b[0;31m# with k=None, computes middle value = median\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     19\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     20\u001b[0m         \u001b[0;31m# 5. split A into 3 parts by M, { < M }, { == M }, and { > M }\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-185-7fed55f97d6a>\u001b[0m in \u001b[0;36mfind_i_th_smallest\u001b[0;34m(tableau, k, items_per_column)\u001b[0m\n\u001b[1;32m     12\u001b[0m         medians = [\n\u001b[1;32m     13\u001b[0m             \u001b[0mfind_i_th_smallest\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtableau\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mj\u001b[0m \u001b[0;34m:\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mj\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mitems_per_column\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 14\u001b[0;31m             \u001b[0;32mfor\u001b[0m \u001b[0mj\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mitems_per_column\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     15\u001b[0m         ]\n\u001b[1;32m     16\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-185-7fed55f97d6a>\u001b[0m in \u001b[0;36m<listcomp>\u001b[0;34m(.0)\u001b[0m\n\u001b[1;32m     12\u001b[0m         medians = [\n\u001b[1;32m     13\u001b[0m             \u001b[0mfind_i_th_smallest\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtableau\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mj\u001b[0m \u001b[0;34m:\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mj\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mitems_per_column\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 14\u001b[0;31m             \u001b[0;32mfor\u001b[0m \u001b[0mj\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mitems_per_column\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     15\u001b[0m         ]\n\u001b[1;32m     16\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-185-7fed55f97d6a>\u001b[0m in \u001b[0;36mfind_i_th_smallest\u001b[0;34m(tableau, k, items_per_column)\u001b[0m\n\u001b[1;32m      5\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mn\u001b[0m \u001b[0;34m<=\u001b[0m \u001b[0mitems_per_column\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m         \u001b[0;31m# si tableau est assez petit, on fait juste un tri et on trouve le k-ième élément\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 7\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0msorted\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtableau\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      8\u001b[0m     \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      9\u001b[0m         \u001b[0;31m# 1. partition A into columns of items_per_column items each. items_per_column is odd, say 15.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "number_of_tests = 1\n",
    "\n",
    "# How many numbers should be randomly generated for testing?\n",
    "for number_of_numbers in tqdm([100, 1000, 10000]):\n",
    "    print(f\"Pour des listes de taille {number_of_numbers} :\")\n",
    "    for test in tqdm(range(number_of_tests)):\n",
    "        print(f\"Test {test + 1} / {number_of_tests} avec une liste de taille {number_of_numbers} :\")\n",
    "        # create a list of random positive integers\n",
    "        tableau = [ random.randint(0, number_of_numbers) for i in range(0, number_of_numbers) ]\n",
    "        for L in [ tableau, tableau*2 ]:\n",
    "\n",
    "            sorted_L = sorted(L)\n",
    "            for k in range(len(L)):\n",
    "                assert sorted_L[k] == find_i_th_smallest(L, k)\n",
    "\n",
    "            %timeit -n1 sorted(L)[random.randint(0, len(L) - 1)]\n",
    "            %timeit -n1 find_i_th_smallest(L, random.randint(0, len(L) - 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-09-30T11:55:05.849616Z",
     "start_time": "2020-09-30T09:56:36.513474Z"
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "4dd4f8d5da064afcaed1dd7162fec57b",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(HTML(value=''), FloatProgress(value=0.0, max=4.0), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pour des listes de taille 500 :\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "4a6b6bee049747fcb66ff2071a8cb8db",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(HTML(value=''), FloatProgress(value=0.0, max=1.0), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test 1 / 1 avec une liste de taille 500 :\n",
      "69.8 µs ± 7.44 µs per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
      "198 µs ± 30.7 µs per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
      "125 µs ± 5.9 µs per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
      "299 µs ± 65.3 µs per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
      "\n",
      "Pour des listes de taille 5000 :\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "7b4f3213ca2741459ae531c6e36c8e93",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(HTML(value=''), FloatProgress(value=0.0, max=1.0), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test 1 / 1 avec une liste de taille 5000 :\n",
      "913 µs ± 86.9 µs per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
      "1.48 ms ± 155 µs per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
      "1.86 ms ± 86 µs per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
      "3.15 ms ± 67 µs per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
      "\n",
      "Pour des listes de taille 50000 :\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "0bfdaf4732124b319c00b783e0652a8e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(HTML(value=''), FloatProgress(value=0.0, max=1.0), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test 1 / 1 avec une liste de taille 50000 :\n",
      "11.7 ms ± 269 µs per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
      "14.5 ms ± 1.08 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
      "\n",
      "\n"
     ]
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-182-60c0e5ace3bb>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     12\u001b[0m             \u001b[0msorted_L\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msorted\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mL\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     13\u001b[0m             \u001b[0;32mfor\u001b[0m \u001b[0mk\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mL\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 14\u001b[0;31m                 \u001b[0;32massert\u001b[0m \u001b[0msorted_L\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mfind_i_th_smallest\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mL\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     15\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     16\u001b[0m             \u001b[0mget_ipython\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun_line_magic\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'timeit'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'-n1 sorted(L)[random.randint(0, len(L) - 1)]'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-157-4f011754b8c7>\u001b[0m in \u001b[0;36mfind_i_th_smallest\u001b[0;34m(tableau, k, items_per_column)\u001b[0m\n\u001b[1;32m     16\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     17\u001b[0m         \u001b[0;31m# 4. find M, the median of the medians\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 18\u001b[0;31m         \u001b[0mmedian_of_medians\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfind_i_th_smallest\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmedians\u001b[0m\u001b[0;34m)\u001b[0m  \u001b[0;31m# with k=None, computes middle value = median\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     19\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     20\u001b[0m         \u001b[0;31m# 5. split A into 3 parts by M, { < M }, { == M }, and { > M }\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-157-4f011754b8c7>\u001b[0m in \u001b[0;36mfind_i_th_smallest\u001b[0;34m(tableau, k, items_per_column)\u001b[0m\n\u001b[1;32m     12\u001b[0m         medians = [\n\u001b[1;32m     13\u001b[0m             \u001b[0mfind_i_th_smallest\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtableau\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mj\u001b[0m \u001b[0;34m:\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mj\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mitems_per_column\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 14\u001b[0;31m             \u001b[0;32mfor\u001b[0m \u001b[0mj\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mitems_per_column\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     15\u001b[0m         ]\n\u001b[1;32m     16\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-157-4f011754b8c7>\u001b[0m in \u001b[0;36m<listcomp>\u001b[0;34m(.0)\u001b[0m\n\u001b[1;32m     12\u001b[0m         medians = [\n\u001b[1;32m     13\u001b[0m             \u001b[0mfind_i_th_smallest\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtableau\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mj\u001b[0m \u001b[0;34m:\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mj\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mitems_per_column\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 14\u001b[0;31m             \u001b[0;32mfor\u001b[0m \u001b[0mj\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mitems_per_column\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     15\u001b[0m         ]\n\u001b[1;32m     16\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-157-4f011754b8c7>\u001b[0m in \u001b[0;36mfind_i_th_smallest\u001b[0;34m(tableau, k, items_per_column)\u001b[0m\n\u001b[1;32m      5\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mn\u001b[0m \u001b[0;34m<=\u001b[0m \u001b[0mitems_per_column\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m         \u001b[0;31m# si tableau est assez petit, on fait juste un tri et on trouve le k-ième élément\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 7\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0msorted\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtableau\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      8\u001b[0m     \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      9\u001b[0m         \u001b[0;31m# 1. partition A into columns of items_per_column items each. items_per_column is odd, say 15.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "number_of_tests = 1\n",
    "\n",
    "# How many numbers should be randomly generated for testing?\n",
    "for number_of_numbers in tqdm([500, 5000, 50000, 100000]):\n",
    "    print(f\"Pour des listes de taille {number_of_numbers} :\")\n",
    "    for test in tqdm(range(number_of_tests)):\n",
    "        print(f\"Test {test + 1} / {number_of_tests} avec une liste de taille {number_of_numbers} :\")\n",
    "        # create a list of random positive integers\n",
    "        tableau = [ random.randint(0, number_of_numbers) for i in range(0, number_of_numbers) ]\n",
    "        for L in [ tableau, tableau*2 ]:\n",
    "\n",
    "            sorted_L = sorted(L)\n",
    "            for k in range(len(L)):\n",
    "                assert sorted_L[k] == find_i_th_smallest(L, k)\n",
    "\n",
    "            %timeit -n1 sorted(L)[random.randint(0, len(L) - 1)]\n",
    "            %timeit -n1 find_i_th_smallest(L, random.randint(0, len(L) - 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Empiriquement, pour des listes pas trop grandes, la méthode naïve qui trie la liste est plus rapide.\n",
    "C'est assez logique, le tri `sorted()` de Python est implémenté en C et est très efficace.\n",
    "\n",
    "Pour des listes plus grandes, on voit que la tendance s'inverse."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "## Conclusion\n",
    "C'est tout pour ce notebook ! Merci de l'avoir lu.\n",
    "\n",
    "> Pour plus de notebooks, cf https://GitHub.com/Naereen/notebooks"
   ]
  }
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