From a6152aa8e2c9a26c27a842e02dd9940e09a6beec Mon Sep 17 00:00:00 2001
From: Teo Baldi <teo.baldi@student.uclouvain.be>
Date: Mon, 29 May 2023 15:51:42 +0000
Subject: [PATCH] complete assignement coding 2 - notebook

---
 evaluator.ipynb | 9384 +++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 9384 insertions(+)
 create mode 100644 evaluator.ipynb

diff --git a/evaluator.ipynb b/evaluator.ipynb
new file mode 100644
index 0000000..bbbdee7
--- /dev/null
+++ b/evaluator.ipynb
@@ -0,0 +1,9384 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Evaluator Module\n",
+    "The Evaluator module creates evaluation reports.\n",
+    "\n",
+    "Reports contain evaluation metrics depending on models specified in the evaluation config."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# reloads modules automatically before entering the execution of code\n",
+    "%load_ext autoreload\n",
+    "%autoreload 2\n",
+    "\n",
+    "# third parties imports\n",
+    "import numpy as np \n",
+    "import pandas as pd\n",
+    "# -- add new imports here --\n",
+    "import surprise.model_selection\n",
+    "import surprise.accuracy\n",
+    "import random as rd\n",
+    "\n",
+    "# local imports\n",
+    "from configs import EvalConfig\n",
+    "from constants import Constant as C\n",
+    "from loaders import export_evaluation_report\n",
+    "from loaders import load_ratings\n",
+    "from models import ModelBaseline1\n",
+    "# -- add new imports here --\n",
+    "from surprise import Reader, Dataset\n",
+    "from surprise.model_selection import train_test_split\n",
+    "from surprise.model_selection import LeaveOneOut\n",
+    "from models import get_top_n\n",
+    "from collections import defaultdict"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<surprise.dataset.DatasetAutoFolds at 0x7f9727ab5f90>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "dataset = load_ratings(surprise_format=True)\n",
+    "display(dataset)\n",
+    "\n",
+    "#ratings = dataset.raw_ratings[:5]\n",
+    "#print(ratings)\n",
+    "#for uid, iid, r, _ in ratings :\n",
+    "    #print(f\"user {uid} rated item {iid} with rating {r}\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# 1. Model validation functions\n",
+    "Validation functions are a way to perform crossvalidation on recommender system models. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def generate_split_predictions(algo, ratings_dataset, eval_config):\n",
+    "    \"\"\"Generate predictions on a random test set specified in eval_config\"\"\"\n",
+    "    # -- implement the function generate_split_predictions --\n",
+    "    #Split dataset into trainset and testset\n",
+    "    trainset, testset = train_test_split(ratings_dataset, test_size = eval_config.test_size)\n",
+    "    #Train the algorithm on the trainset\n",
+    "    algo.fit(trainset)\n",
+    "    #Make predictions on the testset\n",
+    "    predictions = algo.test(testset)\n",
+    "    return predictions\n",
+    "\n",
+    "def get_top_n(predictions, n):\n",
+    "    \"\"\"Return the top-N recommendation for each user from a set of predictions.\n",
+    "    Source: inspired by https://github.com/NicolasHug/Surprise/blob/master/examples/top_n_recommendations.py\n",
+    "    and modified by cvandekerckh for random tie breaking\n",
+    "\n",
+    "    Args:\n",
+    "        predictions(list of Prediction objects): The list of predictions, as\n",
+    "            returned by the test method of an algorithm.\n",
+    "        n(int): The number of recommendation to output for each user. Default\n",
+    "            is 10.\n",
+    "    Returns:\n",
+    "    A dict where keys are user (raw) ids and values are lists of tuples:\n",
+    "        [(raw item id, rating estimation), ...] of size n.\n",
+    "    \"\"\"\n",
+    "\n",
+    "    rd.seed(0)\n",
+    "\n",
+    "    # First map the predictions to each user.\n",
+    "    top_n = defaultdict(list)\n",
+    "    for uid, iid, true_r, est, _ in predictions:\n",
+    "        top_n[uid].append((iid, est))\n",
+    "\n",
+    "    # Then sort the predictions for each user and retrieve the k highest ones.\n",
+    "    for uid, user_ratings in top_n.items():\n",
+    "        rd.shuffle(user_ratings)\n",
+    "        user_ratings.sort(key=lambda x: x[1], reverse=True)\n",
+    "        top_n[uid] = user_ratings[:n]\n",
+    "\n",
+    "    return top_n\n",
+    "\n",
+    "def generate_loo_top_n(algo, ratings_dataset, eval_config):\n",
+    "    \"\"\"Generate top-n recommendations for each user on a random Leave-one-out split (LOO)\"\"\"\n",
+    "    \n",
+    "    # Perform leave-one-out cross-validation\n",
+    "    loo = LeaveOneOut(n_splits=1)\n",
+    "    \n",
+    "    #Build trainset and testset \n",
+    "    trainset, testset = next(loo.split(ratings_dataset))\n",
+    "    \n",
+    "    # Train the algorithm on the trainset\n",
+    "    algo.fit(trainset)\n",
+    "    \n",
+    "    # Build the anti-testset (the items that the user has not rated)\n",
+    "    anti_testset = trainset.build_anti_testset()\n",
+    "    \n",
+    "    # Make predictions\n",
+    "    predictions = algo.test(anti_testset)\n",
+    "    \n",
+    "    # Get the top-N recommendations for each user\n",
+    "    anti_testset_top_n = get_top_n(predictions, eval_config.top_n_value)\n",
+    "    \n",
+    "    return anti_testset_top_n, testset\n",
+    "\n",
+    "def generate_full_top_n(algo, ratings_dataset, eval_config):\n",
+    "    \"\"\"Generate top-n recommendations for each user with full training set (LOO)\"\"\"\n",
+    "    # -- implement the function generate_full_top_n --\n",
+    "     # Build full trainset with all ratings\n",
+    "    full_trainset = ratings_dataset.build_full_trainset()\n",
+    "\n",
+    "    # Train the algorithm on the full trainset\n",
+    "    algo.fit(full_trainset)\n",
+    "\n",
+    "    # Build anti testset for all users (the items that the user has not rated)\n",
+    "    anti_testset = full_trainset.build_anti_testset()\n",
+    "\n",
+    "    # Get the top-n recommendations for all users on the anti testset\n",
+    "    anti_testset_top_n = algo.test(anti_testset)\n",
+    "    anti_testset_top_n = get_top_n(anti_testset_top_n, eval_config.top_n_value)\n",
+    "    return anti_testset_top_n\n",
+    "\n",
+    "def precompute_information():\n",
+    "    \"\"\" Returns a dictionary that precomputes relevant information for evaluating in full mode\n",
+    "\n",
+    "    Dictionary keys:\n",
+    "    - precomputed_dict[\"item_to_rank\"] : contains a dictionary mapping movie ids to rankings\n",
+    "    \"\"\"\n",
+    "    \n",
+    "    df = load_ratings()\n",
+    "    most = df.groupby(\"movieId\")[\"movieId\"].count().to_frame(\"nb_ratings\")\n",
+    "    sorting = most.sort_values([\"nb_ratings\"], ascending=False)\n",
+    "    \n",
+    "    movie_ids = []\n",
+    "    for movie_id, count in sorting.iterrows():\n",
+    "        movie_ids.append(movie_id)\n",
+    "\n",
+    "    l = [i for i in range(1,len(movie_ids)+1)]\n",
+    "\n",
+    "    item_to_rank={}\n",
+    "    i=1\n",
+    "    for j in movie_ids :\n",
+    "        item_to_rank[i] = j\n",
+    "        i+=1\n",
+    "    precomputed_dict={}\n",
+    "    precomputed_dict[\"item_to_rank\"]=item_to_rank\n",
+    "\n",
+    "    return precomputed_dict\n",
+    "\n",
+    "def create_evaluation_report(eval_config, sp_ratings, precomputed_dict, available_metrics):\n",
+    "    \"\"\" Create a DataFrame evaluating various models on metrics specified in an evaluation config.  \n",
+    "    \"\"\"\n",
+    "    evaluation_dict = {}\n",
+    "    for model_name, model, arguments in eval_config.models:\n",
+    "        print(f'Handling model {model_name}')\n",
+    "        algo = model(**arguments)\n",
+    "        evaluation_dict[model_name] = {}\n",
+    "        \n",
+    "        # Type 1 : split evaluations\n",
+    "        if len(eval_config.split_metrics) > 0:\n",
+    "            print('Training split predictions')\n",
+    "            predictions = generate_split_predictions(algo, sp_ratings, eval_config)\n",
+    "            for metric in eval_config.split_metrics:\n",
+    "                print(f'- computing metric {metric}')\n",
+    "                assert metric in available_metrics['split']\n",
+    "                evaluation_function, parameters =  available_metrics[\"split\"][metric]\n",
+    "                evaluation_dict[model_name][metric] = evaluation_function(predictions, **parameters) \n",
+    "\n",
+    "        # Type 2 : loo evaluations\n",
+    "        if len(eval_config.loo_metrics) > 0:\n",
+    "            print('Training loo predictions')\n",
+    "            anti_testset_top_n, testset = generate_loo_top_n(algo, sp_ratings, eval_config)\n",
+    "            for metric in eval_config.loo_metrics:\n",
+    "                assert metric in available_metrics['loo']\n",
+    "                evaluation_function, parameters =  available_metrics[\"loo\"][metric]\n",
+    "                evaluation_dict[model_name][metric] = evaluation_function(anti_testset_top_n, testset, **parameters)\n",
+    "        \n",
+    "        # Type 3 : full evaluations\n",
+    "        if len(eval_config.full_metrics) > 0:\n",
+    "            print('Training full predictions')\n",
+    "            anti_testset_top_n = generate_full_top_n(algo, sp_ratings, eval_config)\n",
+    "            for metric in eval_config.full_metrics:\n",
+    "                assert metric in available_metrics['full']\n",
+    "                evaluation_function, parameters =  available_metrics[\"full\"][metric]\n",
+    "                evaluation_dict[model_name][metric] = evaluation_function(\n",
+    "                    anti_testset_top_n,\n",
+    "                    **precomputed_dict,\n",
+    "                    **parameters\n",
+    "                )\n",
+    "        \n",
+    "    return pd.DataFrame.from_dict(evaluation_dict).T"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Tests"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "user: 468        item: 3429       r_ui = 4.00   est = 3.15   {'was_impossible': False}\n",
+      "user: 212        item: 858        r_ui = 5.00   est = 3.77   {'was_impossible': False}\n",
+      "user: 607        item: 4557       r_ui = 3.50   est = 3.38   {'was_impossible': False}\n",
+      "user: 547        item: 125        r_ui = 5.00   est = 3.30   {'was_impossible': False}\n",
+      "user: 30         item: 3334       r_ui = 4.00   est = 3.99   {'was_impossible': False}\n",
+      "user: 134        item: 500        r_ui = 4.00   est = 3.59   {'was_impossible': False}\n",
+      "user: 294        item: 1453       r_ui = 4.00   est = 3.22   {'was_impossible': False}\n",
+      "user: 105        item: 4643       r_ui = 2.50   est = 3.09   {'was_impossible': False}\n",
+      "user: 431        item: 1225       r_ui = 4.50   est = 4.30   {'was_impossible': False}\n",
+      "user: 427        item: 5945       r_ui = 3.00   est = 3.40   {'was_impossible': False}\n",
+      "user: 463        item: 2717       r_ui = 2.00   est = 2.70   {'was_impossible': False}\n",
+      "user: 394        item: 77658      r_ui = 3.00   est = 2.47   {'was_impossible': False}\n",
+      "user: 624        item: 5752       r_ui = 3.00   est = 2.62   {'was_impossible': False}\n",
+      "user: 461        item: 2473       r_ui = 1.00   est = 2.41   {'was_impossible': False}\n",
+      "user: 387        item: 3011       r_ui = 5.00   est = 3.91   {'was_impossible': False}\n",
+      "user: 585        item: 1299       r_ui = 5.00   est = 4.55   {'was_impossible': False}\n",
+      "user: 105        item: 5669       r_ui = 3.00   est = 3.61   {'was_impossible': False}\n",
+      "user: 243        item: 4682       r_ui = 4.00   est = 3.50   {'was_impossible': False}\n",
+      "user: 294        item: 2006       r_ui = 4.50   est = 3.30   {'was_impossible': False}\n",
+      "user: 564        item: 532        r_ui = 5.00   est = 3.13   {'was_impossible': False}\n",
+      "user: 73         item: 69306      r_ui = 3.00   est = 3.22   {'was_impossible': False}\n",
+      "user: 30         item: 162        r_ui = 1.00   est = 4.21   {'was_impossible': False}\n",
+      "user: 285        item: 1974       r_ui = 2.00   est = 3.48   {'was_impossible': False}\n",
+      "user: 547        item: 1212       r_ui = 5.00   est = 3.82   {'was_impossible': False}\n",
+      "user: 15         item: 139644     r_ui = 3.00   est = 2.68   {'was_impossible': False}\n",
+      "user: 457        item: 27611      r_ui = 0.50   est = 2.42   {'was_impossible': False}\n",
+      "user: 547        item: 4810       r_ui = 4.00   est = 3.09   {'was_impossible': False}\n",
+      "user: 346        item: 1073       r_ui = 4.00   est = 3.91   {'was_impossible': False}\n",
+      "user: 457        item: 3168       r_ui = 4.00   est = 2.77   {'was_impossible': False}\n",
+      "user: 48         item: 106002     r_ui = 2.50   est = 3.43   {'was_impossible': False}\n"
+     ]
+    }
+   ],
+   "source": [
+    "algo = surprise.SVD()\n",
+    "#algo = ModelBaseline1()\n",
+    "sp_ratings = load_ratings(surprise_format=True)\n",
+    "eval_config = EvalConfig()\n",
+    "predi = generate_split_predictions(algo, sp_ratings, eval_config)\n",
+    "for prediction in predi[:30]:\n",
+    "    print(prediction)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {
+    "collapsed": true,
+    "jupyter": {
+     "outputs_hidden": true
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
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+       "               (4801, 3.592960002465884)],\n",
+       "              387: [(858, 5),\n",
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+       "              407: [(923, 5),\n",
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+       "               (56782, 3.915502633142566)],\n",
+       "              430: [(923, 4.453248156105621),\n",
+       "               (1945, 4.368486586724366),\n",
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+       "               (95508, 3.9336455425515924)],\n",
+       "              431: [(858, 4.688834219167055),\n",
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+       "              434: [(899, 4.107944231697544),\n",
+       "               (1299, 4.094790606361625),\n",
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+       "              452: [(55820, 3.9123441329455964),\n",
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+       "               (599, 3.48083541601408)],\n",
+       "              457: [(899, 3.438488559736695),\n",
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+       "              460: [(858, 4.347553350791273),\n",
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+       "               (1240, 3.801280365718295)],\n",
+       "              461: [(2501, 3.5922572946013704),\n",
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+       "               (106916, 3.078468808969615),\n",
+       "               (3633, 3.072252040632036)],\n",
+       "              463: [(1945, 4.1663852595896556),\n",
+       "               (899, 4.085047912131417),\n",
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+       "              468: [(527, 3.8248927381630167),\n",
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+       "              480: [(923, 4.690529757290234),\n",
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+       "               (3724, 3.707817451197612)],\n",
+       "              514: [(527, 4.499848125821236),\n",
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+       "              518: [(527, 4.641869986232258),\n",
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+       "               (2283, 3.789113790165556)],\n",
+       "              534: [(1210, 4.680240759930338),\n",
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+       "              544: [(923, 5),\n",
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+       "              564: [(55820, 4.65454999141974),\n",
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+       "  (652, 7260, 5.0),\n",
+       "  (654, 708, 3.0),\n",
+       "  (664, 96737, 4.5),\n",
+       "  (665, 2953, 2.0)])"
+      ]
+     },
+     "execution_count": 5,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "generate_loo_top_n(algo, dataset, eval_config)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {
+    "collapsed": true,
+    "jupyter": {
+     "outputs_hidden": true
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
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+       "              (1305, 3.191829495152628),\n",
+       "              (1217, 3.1887306360747116),\n",
+       "              (2501, 3.151059042668721),\n",
+       "              (1968, 3.150536004077183),\n",
+       "              (2065, 3.140288509145409),\n",
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+       "              (1299, 3.117938282891865),\n",
+       "              (509, 3.115803769038006),\n",
+       "              (106920, 3.105123385476492),\n",
+       "              (55820, 3.104887529726908),\n",
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+       "              (3504, 3.056468349838289),\n",
+       "              (122892, 3.0540493007472427),\n",
+       "              (527, 3.0494441332459323),\n",
+       "              (56782, 3.0457355506473602),\n",
+       "              (3310, 3.0320835761972216),\n",
+       "              (3030, 3.027676156752315),\n",
+       "              (1953, 3.02001473644665),\n",
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+       "              (86345, 3.017036226542597),\n",
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+       "              (3091, 2.9746921321699005),\n",
+       "              (26152, 2.9703347256183354),\n",
+       "              (1274, 2.959557288169859),\n",
+       "              (109374, 2.951224252533731),\n",
+       "              (515, 2.939562108323092)],\n",
+       "             355: [(923, 4.23817828306962),\n",
+       "              (3504, 4.1719898797648325),\n",
+       "              (1225, 4.109106774503689),\n",
+       "              (1219, 4.100639935574229),\n",
+       "              (515, 4.0943982184010155),\n",
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+       "              (79132, 4.035062614998531),\n",
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+       "              (1945, 4.025272355805218),\n",
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+       "              (899, 3.989726624877018),\n",
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+       "              (1305, 3.8708658150207174),\n",
+       "              (1952, 3.860588463362794),\n",
+       "              (1172, 3.860104206104065),\n",
+       "              (2804, 3.8593165026089484),\n",
+       "              (1968, 3.836822020334542),\n",
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+       "              (1953, 3.750083083531706),\n",
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+       "              (3310, 3.7190155129852878),\n",
+       "              (162, 3.717226734547325),\n",
+       "              (2987, 3.7169446371650685),\n",
+       "              (103141, 3.7036768239330113),\n",
+       "              (3007, 3.698760027418566),\n",
+       "              (915, 3.696205795089623),\n",
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+       "              (2087, 3.67517071906974),\n",
+       "              (509, 3.6699400727165368),\n",
+       "              (4688, 3.6685393264170068)],\n",
+       "             358: [(49272, 3.810853433250316),\n",
+       "              (1219, 3.777103074923311),\n",
+       "              (3030, 3.7676040609645214),\n",
+       "              (1240, 3.7670114307036924),\n",
+       "              (2501, 3.752005861946057),\n",
+       "              (1208, 3.75015902088972),\n",
+       "              (56782, 3.746430622244118),\n",
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+       "              (3681, 3.5162423200518518),\n",
+       "              (4801, 3.5154023860212447),\n",
+       "              (8838, 3.513388925243689),\n",
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+       "              (96829, 3.466681156666005),\n",
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+       "              (52604, 3.4342451691575198),\n",
+       "              (233, 3.4304468658046496),\n",
+       "              (101, 3.4265175270381403)],\n",
+       "             380: [(527, 4.204362775036073),\n",
+       "              (923, 4.056499819849127),\n",
+       "              (899, 4.048825975205242),\n",
+       "              (1217, 4.03992747315303),\n",
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+       "              (233, 3.753737317957266),\n",
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+       "              (27878, 3.6670115793566382),\n",
+       "              (535, 3.6611151630705483),\n",
+       "              (3334, 3.6583032016901895),\n",
+       "              (942, 3.654208349877675),\n",
+       "              (3310, 3.6524998705394816),\n",
+       "              (599, 3.6504870388553132),\n",
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+       "              (2739, 3.647443304202315),\n",
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+       "              (26712, 3.578250603371244),\n",
+       "              (2065, 3.5770411028649503),\n",
+       "              (1953, 3.5730962692175012),\n",
+       "              (3724, 3.569857237244569)],\n",
+       "             382: [(923, 4.1597205887731645),\n",
+       "              (858, 4.116112131426655),\n",
+       "              (79132, 4.016875307091975),\n",
+       "              (515, 3.9112537252336),\n",
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+       "              (56782, 3.767563494689506),\n",
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+       "              (3310, 3.7443220546364167),\n",
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+       "              (5669, 3.737812920213069),\n",
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+       "              (1945, 3.694965014109017),\n",
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+       "              (599, 3.6075988884521757),\n",
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+       "              (77658, 3.5909251188036606),\n",
+       "              (4979, 3.575326128547581),\n",
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+       "              (1218, 3.563227362019671),\n",
+       "              (1365, 3.5592812411084664)],\n",
+       "             384: [(858, 4.284553339644057),\n",
+       "              (923, 4.1120684412745065),\n",
+       "              (1208, 4.012460675303433),\n",
+       "              (899, 4.002939447925996),\n",
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+       "              (79132, 3.715885515660189),\n",
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+       "              (1953, 3.6839619475659657),\n",
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+       "              (5669, 3.572219705209373),\n",
+       "              (1032, 3.5685226615599235)],\n",
+       "             387: [(1210, 4.863945723612529),\n",
+       "              (79132, 4.851409280371521),\n",
+       "              (55820, 4.7117420263607945),\n",
+       "              (2501, 4.696165847099625),\n",
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+       "              (7300, 4.338644802386347),\n",
+       "              (3213, 4.336671159764858)],\n",
+       "             388: [(3362, 4.266387356651574),\n",
+       "              (899, 4.246114081351038),\n",
+       "              (31658, 4.167793481164587),\n",
+       "              (106920, 4.159890451844741),\n",
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+       "              (49394, 3.8991378204185025),\n",
+       "              (56782, 3.8920873713937274),\n",
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+       "              (1354, 3.8678404287047004),\n",
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+       "              (556, 3.8219571881136725),\n",
+       "              (1274, 3.8214999511542134)],\n",
+       "             394: [(923, 3.2741599484899755),\n",
+       "              (1219, 3.229587279908368),\n",
+       "              (233, 3.1177478305347095),\n",
+       "              (1208, 3.1131317367893883),\n",
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+       "              (3030, 2.928305956468521),\n",
+       "              (2804, 2.909177977195238),\n",
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+       "              (1250, 2.8173014436738537),\n",
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+       "              (79139, 2.7705135102082736),\n",
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+       "              (509, 2.757520989829347),\n",
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+       "              (599, 2.731311516677995),\n",
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+       "              (3724, 2.7295160767030304),\n",
+       "              (2065, 2.7268546130863895)],\n",
+       "             402: [(1945, 4.492076325376702),\n",
+       "              (1172, 4.467179889298929),\n",
+       "              (1219, 4.407387494407999),\n",
+       "              (1952, 4.388947813059615),\n",
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+       "              (899, 4.35226245775213),\n",
+       "              (515, 4.346554341976223),\n",
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+       "              (923, 4.315899389949055),\n",
+       "              (55820, 4.29946637175582),\n",
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+       "              (3362, 4.2528243293384005),\n",
+       "              (1250, 4.170605050989055),\n",
+       "              (49272, 4.128213904162796),\n",
+       "              (942, 4.1216474187178),\n",
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+       "              (1305, 4.098828657049825),\n",
+       "              (33171, 4.094753710160266),\n",
+       "              (3499, 4.089516964342574),\n",
+       "              (1212, 4.079211067320956),\n",
+       "              (3030, 4.073692469755047),\n",
+       "              (3070, 4.066049925656545),\n",
+       "              (1073, 4.057155146036278),\n",
+       "              (3007, 4.055341267711614),\n",
+       "              (1953, 4.054264767444235),\n",
+       "              (1942, 4.031068654996817),\n",
+       "              (52604, 4.017696482066836),\n",
+       "              (233, 4.005029075781421),\n",
+       "              (44199, 4.0045885971243855),\n",
+       "              (56782, 4.004180088811653),\n",
+       "              (5669, 3.9780579847048583),\n",
+       "              (3725, 3.976299528307151),\n",
+       "              (2804, 3.975194556211516),\n",
+       "              (1299, 3.9695805845140697),\n",
+       "              (1274, 3.965803761263047),\n",
+       "              (6333, 3.964885261720527),\n",
+       "              (3198, 3.963907081291297)],\n",
+       "             405: [(3362, 4.472808457579268),\n",
+       "              (923, 4.461722206882256),\n",
+       "              (899, 4.434859178388728),\n",
+       "              (1208, 4.401558950899858),\n",
+       "              (527, 4.3692395238913795),\n",
+       "              (2804, 4.3357193923187),\n",
+       "              (1968, 4.320654207977992),\n",
+       "              (1945, 4.303280851230768),\n",
+       "              (106920, 4.278284785930414),\n",
+       "              (1305, 4.2778582876794),\n",
+       "              (233, 4.2313516019693465),\n",
+       "              (1225, 4.224348836370755),\n",
+       "              (55820, 4.180791086565628),\n",
+       "              (1073, 4.1716184463045325),\n",
+       "              (49272, 4.140072756538334),\n",
+       "              (1212, 4.132945539888155),\n",
+       "              (3030, 4.121783164765239),\n",
+       "              (1952, 4.117370221313316),\n",
+       "              (1219, 4.115016872399418),\n",
+       "              (3504, 4.106813095067734),\n",
+       "              (1217, 4.084741218609911),\n",
+       "              (8933, 4.081708980722129),\n",
+       "              (1218, 4.078563723087965),\n",
+       "              (1032, 4.070270716026383),\n",
+       "              (2739, 4.062449825562667),\n",
+       "              (26152, 4.04794256777793),\n",
+       "              (122892, 4.040533124026518),\n",
+       "              (79132, 4.036629232307513),\n",
+       "              (1299, 4.03197496330487),\n",
+       "              (139385, 4.018289950235856),\n",
+       "              (86345, 4.015222531904723),\n",
+       "              (556, 4.000011930587068),\n",
+       "              (3724, 3.9995992800164943),\n",
+       "              (5669, 3.9930959036197398),\n",
+       "              (3499, 3.990538338280299),\n",
+       "              (3310, 3.981891694474881),\n",
+       "              (1345, 3.979433398422124),\n",
+       "              (1172, 3.9576021714417653),\n",
+       "              (1264, 3.9507771946668675),\n",
+       "              (7396, 3.940141120580911)],\n",
+       "             407: [(1219, 4.834748166868623),\n",
+       "              (106920, 4.823905587498908),\n",
+       "              (899, 4.8082395341728175),\n",
+       "              (515, 4.7924587727839665),\n",
+       "              (79132, 4.776857645362037),\n",
+       "              (858, 4.77288443413804),\n",
+       "              (55820, 4.76971871345452),\n",
+       "              (3362, 4.766497626857632),\n",
+       "              (1212, 4.727843870384042),\n",
+       "              (1968, 4.696267561774609),\n",
+       "              (1210, 4.687568618491918),\n",
+       "              (56782, 4.685001870304439),\n",
+       "              (2804, 4.680582761226419),\n",
+       "              (3504, 4.66859494753458),\n",
+       "              (1952, 4.662135394318529),\n",
+       "              (4105, 4.657959371775987),\n",
+       "              (1953, 4.654146621174563),\n",
+       "              (1299, 4.635423496596735),\n",
+       "              (1305, 4.621971848086726),\n",
+       "              (30749, 4.601456669246499),\n",
+       "              (923, 4.595221199557101),\n",
+       "              (109374, 4.568252478055263),\n",
+       "              (3198, 4.565099229112226),\n",
+       "              (6377, 4.5646852717519755),\n",
+       "              (915, 4.547949303976127),\n",
+       "              (1945, 4.543301068254125),\n",
+       "              (1172, 4.541625917324795),\n",
+       "              (233, 4.51674607224058),\n",
+       "              (1208, 4.502034225741429),\n",
+       "              (1240, 4.490262255915833),\n",
+       "              (106766, 4.482684752745061),\n",
+       "              (1225, 4.476190050641604),\n",
+       "              (2987, 4.4743484002183),\n",
+       "              (2746, 4.4730047796656125),\n",
+       "              (1264, 4.4675637205832235),\n",
+       "              (49272, 4.460716365495332),\n",
+       "              (599, 4.451725897797837),\n",
+       "              (7700, 4.434954851187657),\n",
+       "              (3270, 4.4220795797752235),\n",
+       "              (2739, 4.4217015178786285)],\n",
+       "             423: [(3362, 4.525885607345154),\n",
+       "              (923, 4.507767497001538),\n",
+       "              (106920, 4.49085644117039),\n",
+       "              (899, 4.478513178562324),\n",
+       "              (527, 4.455400079058447),\n",
+       "              (2804, 4.450365584121442),\n",
+       "              (1208, 4.436819852573422),\n",
+       "              (3504, 4.435217920954479),\n",
+       "              (1210, 4.421056531830494),\n",
+       "              (1945, 4.384872461665328),\n",
+       "              (1225, 4.377891897968167),\n",
+       "              (1217, 4.316416428017408),\n",
+       "              (2501, 4.287781037583789),\n",
+       "              (1299, 4.27344967301448),\n",
+       "              (1968, 4.25140929939074),\n",
+       "              (1250, 4.24045798033825),\n",
+       "              (1305, 4.217267728027008),\n",
+       "              (233, 4.209682038037257),\n",
+       "              (49272, 4.198108221116158),\n",
+       "              (2739, 4.166322149455568),\n",
+       "              (44199, 4.14756068581057),\n",
+       "              (56782, 4.142019056551911),\n",
+       "              (96829, 4.127293467435942),\n",
+       "              (1952, 4.123429789348192),\n",
+       "              (1032, 4.120337108972114),\n",
+       "              (515, 4.103387229015592),\n",
+       "              (26152, 4.0902977491236205),\n",
+       "              (162, 4.076538341981716),\n",
+       "              (3007, 4.074143437338917),\n",
+       "              (3310, 4.059032891341604),\n",
+       "              (3724, 4.054581829990262),\n",
+       "              (1212, 4.048332004861042),\n",
+       "              (122892, 4.042172685919647),\n",
+       "              (942, 4.036027471970308),\n",
+       "              (599, 4.027013052877379),\n",
+       "              (101, 4.023471790788949),\n",
+       "              (43396, 4.0222953283538345),\n",
+       "              (4467, 4.019312038882582),\n",
+       "              (915, 4.002384443404527),\n",
+       "              (6237, 4.001483408096859)],\n",
+       "             426: [(899, 3.8151620895570035),\n",
+       "              (923, 3.7942890903181827),\n",
+       "              (106920, 3.7861830363328406),\n",
+       "              (1208, 3.724659113119127),\n",
+       "              (1210, 3.706834403821874),\n",
+       "              (1945, 3.689833256621935),\n",
+       "              (2501, 3.6832247344116515),\n",
+       "              (3504, 3.666257464723991),\n",
+       "              (3030, 3.6635256872117603),\n",
+       "              (3310, 3.6536982760677086),\n",
+       "              (1953, 3.649135806245816),\n",
+       "              (1968, 3.641480510930804),\n",
+       "              (515, 3.6312621429813974),\n",
+       "              (1217, 3.6114212961675602),\n",
+       "              (1305, 3.6062932758144903),\n",
+       "              (1250, 3.603705833265753),\n",
+       "              (3362, 3.598922045033153),\n",
+       "              (1299, 3.5724100071138247),\n",
+       "              (77658, 3.5689164550467365),\n",
+       "              (1219, 3.557044432655183),\n",
+       "              (1032, 3.5507454529006375),\n",
+       "              (3499, 3.5481488024546235),\n",
+       "              (2804, 3.531687562614075),\n",
+       "              (1212, 3.525598695620777),\n",
+       "              (599, 3.484763166580426),\n",
+       "              (1225, 3.4727975122521197),\n",
+       "              (26712, 3.462313756749114),\n",
+       "              (1952, 3.4415306982626754),\n",
+       "              (233, 3.432884513842064),\n",
+       "              (56782, 3.428534158070895),\n",
+       "              (3724, 3.423948994553742),\n",
+       "              (109374, 3.4197362277208057),\n",
+       "              (4783, 3.410095836370678),\n",
+       "              (915, 3.403303869563525),\n",
+       "              (1073, 3.3943230284080728),\n",
+       "              (6237, 3.393344967232849),\n",
+       "              (96829, 3.393256383708342),\n",
+       "              (3091, 3.3909571982785174),\n",
+       "              (103141, 3.387748141074308),\n",
+       "              (3270, 3.3875144685855236)],\n",
+       "             427: [(899, 4.3106808664730085),\n",
+       "              (1968, 4.276620812404634),\n",
+       "              (79132, 4.270593373263227),\n",
+       "              (923, 4.251669740426983),\n",
+       "              (515, 4.249632395697394),\n",
+       "              (1210, 4.248325334368983),\n",
+       "              (858, 4.248062746762607),\n",
+       "              (1217, 4.208977130896907),\n",
+       "              (106920, 4.195003164029431),\n",
+       "              (233, 4.170723766281413),\n",
+       "              (1305, 4.15244337745134),\n",
+       "              (1953, 4.144043454943938),\n",
+       "              (3504, 4.142710368528278),\n",
+       "              (2804, 4.124940220989427),\n",
+       "              (4105, 4.119153427251479),\n",
+       "              (527, 4.104183310869617),\n",
+       "              (1299, 4.0962531554943045),\n",
+       "              (1945, 4.070100120156283),\n",
+       "              (30749, 4.066924559324353),\n",
+       "              (49272, 4.044168481501109),\n",
+       "              (3362, 4.0414573042705095),\n",
+       "              (1208, 4.02003844967073),\n",
+       "              (599, 4.01972598254228),\n",
+       "              (56782, 4.018215810128906),\n",
+       "              (1250, 3.9879605865469667),\n",
+       "              (1219, 3.967983768355719),\n",
+       "              (1225, 3.96190382164496),\n",
+       "              (3030, 3.961234244702574),\n",
+       "              (3198, 3.95941966058232),\n",
+       "              (6975, 3.958909543308711),\n",
+       "              (1073, 3.937535351839447),\n",
+       "              (915, 3.929179235401424),\n",
+       "              (1212, 3.928616599621312),\n",
+       "              (3168, 3.9252378126242844),\n",
+       "              (3310, 3.9198423304128336),\n",
+       "              (70293, 3.915028197768365),\n",
+       "              (1952, 3.905830346271656),\n",
+       "              (4351, 3.905510277400274),\n",
+       "              (31658, 3.898114341331599),\n",
+       "              (3499, 3.8845664534830346)],\n",
+       "             430: [(1945, 4.464854492216234),\n",
+       "              (1225, 4.436313618287837),\n",
+       "              (527, 4.4220694180066955),\n",
+       "              (923, 4.394176244456351),\n",
+       "              (3362, 4.3866448088398045),\n",
+       "              (899, 4.3838905414232325),\n",
+       "              (3504, 4.307558028759497),\n",
+       "              (106920, 4.285737200341151),\n",
+       "              (1219, 4.264951567232883),\n",
+       "              (55820, 4.240218647888049),\n",
+       "              (1250, 4.212233966926829),\n",
+       "              (1217, 4.179790840738276),\n",
+       "              (2804, 4.176809534364347),\n",
+       "              (1032, 4.144797236422536),\n",
+       "              (1299, 4.143468181308278),\n",
+       "              (2501, 4.1115128630958075),\n",
+       "              (1953, 4.09120233914671),\n",
+       "              (3724, 4.085121534963197),\n",
+       "              (79132, 4.069699604665588),\n",
+       "              (1264, 4.067603430061611),\n",
+       "              (1305, 4.04709673634669),\n",
+       "              (942, 4.0392966518402735),\n",
+       "              (1952, 4.0317285085435195),\n",
+       "              (3168, 4.013986644379655),\n",
+       "              (3030, 4.010857013039429),\n",
+       "              (599, 3.9991828261130986),\n",
+       "              (37741, 3.998567436780813),\n",
+       "              (515, 3.9881867907713486),\n",
+       "              (233, 3.987293888819848),\n",
+       "              (31658, 3.9817931351336995),\n",
+       "              (1095, 3.964972545412051),\n",
+       "              (96829, 3.963337312938556),\n",
+       "              (86345, 3.9621655106495615),\n",
+       "              (1218, 3.9619852356759107),\n",
+       "              (2739, 3.9540085109593943),\n",
+       "              (1274, 3.942875077146098),\n",
+       "              (101, 3.9250028027849413),\n",
+       "              (7010, 3.917903566882314),\n",
+       "              (56782, 3.9175264094799482),\n",
+       "              (509, 3.916838038108323)],\n",
+       "             431: [(858, 4.641818316302171),\n",
+       "              (515, 4.4874142630751255),\n",
+       "              (1305, 4.454145155405733),\n",
+       "              (79132, 4.422388452906064),\n",
+       "              (2501, 4.416453008583216),\n",
+       "              (3362, 4.388958920497321),\n",
+       "              (3504, 4.345063070752324),\n",
+       "              (1952, 4.342965385746629),\n",
+       "              (2804, 4.342073064717165),\n",
+       "              (1212, 4.335331056504668),\n",
+       "              (1172, 4.318959486547031),\n",
+       "              (55820, 4.293593981007136),\n",
+       "              (49272, 4.283769954863168),\n",
+       "              (1032, 4.267415300710294),\n",
+       "              (3168, 4.246923314345852),\n",
+       "              (3198, 4.237199283493726),\n",
+       "              (3310, 4.2064847503930505),\n",
+       "              (1942, 4.185360022493131),\n",
+       "              (56782, 4.175171108475686),\n",
+       "              (106920, 4.139188287276546),\n",
+       "              (33171, 4.134722279617573),\n",
+       "              (89804, 4.133032644948564),\n",
+       "              (233, 4.122536508550933),\n",
+       "              (1073, 4.122107582898504),\n",
+       "              (4467, 4.117093878463119),\n",
+       "              (1095, 4.112748393945614),\n",
+       "              (96829, 4.099686629068155),\n",
+       "              (942, 4.073235878341236),\n",
+       "              (599, 4.073187570533787),\n",
+       "              (43396, 4.0656479184856975),\n",
+       "              (2987, 4.044636296851121),\n",
+       "              (109374, 4.039278932266432),\n",
+       "              (3499, 4.036572915821283),\n",
+       "              (101, 4.0315950886585314),\n",
+       "              (1264, 4.031188485756729),\n",
+       "              (4835, 4.027338195505139),\n",
+       "              (2065, 4.025009974899011),\n",
+       "              (509, 4.017702884215591),\n",
+       "              (3724, 4.016393539930066),\n",
+       "              (44199, 4.016121734366332)],\n",
+       "             433: [(899, 4.323605170653777),\n",
+       "              (3362, 4.3185974391951145),\n",
+       "              (923, 4.231464145798084),\n",
+       "              (1219, 4.227067249396667),\n",
+       "              (1945, 4.2077162083753805),\n",
+       "              (1305, 4.192154200952875),\n",
+       "              (1208, 4.189917154089737),\n",
+       "              (1217, 4.168542812327382),\n",
+       "              (1952, 4.146679124193712),\n",
+       "              (515, 4.136610728647512),\n",
+       "              (49272, 4.129241894880426),\n",
+       "              (1212, 4.127015571237592),\n",
+       "              (1210, 4.1264741396555085),\n",
+       "              (3310, 4.123765588448051),\n",
+       "              (1299, 4.090063352801891),\n",
+       "              (106920, 4.088001112567668),\n",
+       "              (3030, 4.0876328296224145),\n",
+       "              (5669, 4.071924042142034),\n",
+       "              (3198, 4.071851625265426),\n",
+       "              (1250, 4.050479272433245),\n",
+       "              (1032, 4.0426129602386105),\n",
+       "              (30749, 4.038856392527435),\n",
+       "              (942, 4.037237537041545),\n",
+       "              (1264, 4.025601543436905),\n",
+       "              (1953, 4.0045237284883095),\n",
+       "              (3724, 4.000251051601888),\n",
+       "              (3129, 3.99511460235567),\n",
+       "              (2501, 3.9910623224043604),\n",
+       "              (509, 3.9871694962825934),\n",
+       "              (37741, 3.983592243634874),\n",
+       "              (1942, 3.9759181197752116),\n",
+       "              (1095, 3.9611751858823956),\n",
+       "              (5064, 3.9602173924613777),\n",
+       "              (125, 3.95190966429054),\n",
+       "              (3499, 3.942990525692191),\n",
+       "              (2087, 3.9407759995567084),\n",
+       "              (1172, 3.9360577364409095),\n",
+       "              (3504, 3.9344020190333775),\n",
+       "              (7700, 3.9327107754810022),\n",
+       "              (233, 3.925752699836324)],\n",
+       "             434: [(899, 4.326545226509835),\n",
+       "              (55820, 4.18610092433503),\n",
+       "              (1945, 4.170789744594384),\n",
+       "              (3362, 4.122142943251344),\n",
+       "              (79132, 4.050608507934109),\n",
+       "              (3504, 3.9787455113296413),\n",
+       "              (1219, 3.966651865699199),\n",
+       "              (1172, 3.9511016295212484),\n",
+       "              (1217, 3.931965349546314),\n",
+       "              (2501, 3.930378390149002),\n",
+       "              (106920, 3.9241013098926185),\n",
+       "              (30749, 3.9201968688337723),\n",
+       "              (2804, 3.892558497573454),\n",
+       "              (1952, 3.8755066962412243),\n",
+       "              (56782, 3.8600587568112426),\n",
+       "              (3499, 3.835967781124612),\n",
+       "              (3310, 3.8307153259369113),\n",
+       "              (942, 3.8043998698225727),\n",
+       "              (96829, 3.8038052340912656),\n",
+       "              (1305, 3.802656588928894),\n",
+       "              (1942, 3.80089665120177),\n",
+       "              (3030, 3.7849801847910385),\n",
+       "              (109374, 3.77487083329518),\n",
+       "              (1953, 3.756521401185534),\n",
+       "              (5669, 3.748156879109653),\n",
+       "              (125, 3.7473095957815183),\n",
+       "              (1968, 3.735530043853015),\n",
+       "              (49272, 3.7350664383218413),\n",
+       "              (1073, 3.7253157379199457),\n",
+       "              (3007, 3.7234114904173907),\n",
+       "              (3429, 3.717375884700482),\n",
+       "              (3198, 3.7150794859360325),\n",
+       "              (1218, 3.7133306247061233),\n",
+       "              (77658, 3.712774114309684),\n",
+       "              (92535, 3.687511816118084),\n",
+       "              (44199, 3.6865428513566054),\n",
+       "              (3334, 3.6829343754853068),\n",
+       "              (3101, 3.6802310911919283),\n",
+       "              (4801, 3.6716380254177627),\n",
+       "              (2087, 3.659291085329388)],\n",
+       "             442: [(923, 4.667601463591989),\n",
+       "              (899, 4.619875779163332),\n",
+       "              (79132, 4.5883905764233495),\n",
+       "              (3362, 4.570913597765645),\n",
+       "              (3504, 4.570867970983809),\n",
+       "              (1953, 4.480890006171585),\n",
+       "              (1212, 4.451799586413483),\n",
+       "              (1217, 4.45157082793724),\n",
+       "              (30749, 4.408926153020286),\n",
+       "              (2501, 4.406426243343714),\n",
+       "              (106920, 4.40484898767992),\n",
+       "              (49272, 4.395536165005073),\n",
+       "              (515, 4.389735582872853),\n",
+       "              (1032, 4.375619985024723),\n",
+       "              (55820, 4.354547938884583),\n",
+       "              (1305, 4.346524500326622),\n",
+       "              (1942, 4.345608555562532),\n",
+       "              (1952, 4.334194229831839),\n",
+       "              (3310, 4.328467206177482),\n",
+       "              (1945, 4.323188701529075),\n",
+       "              (1172, 4.290060111087015),\n",
+       "              (599, 4.281632504215536),\n",
+       "              (3499, 4.259139607617129),\n",
+       "              (1218, 4.247907689545477),\n",
+       "              (233, 4.225040736001487),\n",
+       "              (942, 4.215721362799077),\n",
+       "              (56782, 4.211112916797806),\n",
+       "              (3030, 4.190026952111249),\n",
+       "              (2804, 4.183324320342808),\n",
+       "              (1095, 4.1720545099256165),\n",
+       "              (31658, 4.169714631125544),\n",
+       "              (915, 4.1650664528051635),\n",
+       "              (109374, 4.161749890990814),\n",
+       "              (3070, 4.157057246215056),\n",
+       "              (77658, 4.156496881049931),\n",
+       "              (1225, 4.1494757180869914),\n",
+       "              (3198, 4.143288097813813),\n",
+       "              (3724, 4.139598233807248),\n",
+       "              (37741, 4.134842881252007),\n",
+       "              (3007, 4.125475397001661)],\n",
+       "             452: [(1305, 4.035915298661783),\n",
+       "              (55820, 4.025888919797526),\n",
+       "              (1073, 3.8906052266284075),\n",
+       "              (1217, 3.8289399377731757),\n",
+       "              (3030, 3.819081264989292),\n",
+       "              (56782, 3.7970459945557367),\n",
+       "              (233, 3.7739723320460827),\n",
+       "              (79132, 3.7700242883124986),\n",
+       "              (3007, 3.7637661845241386),\n",
+       "              (106920, 3.7410821190944468),\n",
+       "              (1212, 3.704293064564102),\n",
+       "              (1210, 3.7023011096599365),\n",
+       "              (2501, 3.6284396516558197),\n",
+       "              (942, 3.5999953065712877),\n",
+       "              (26712, 3.5695621647539335),\n",
+       "              (109374, 3.557416405063924),\n",
+       "              (33171, 3.5438247932865004),\n",
+       "              (6333, 3.538632995003975),\n",
+       "              (101, 3.538356462838618),\n",
+       "              (4801, 3.5276665812614945),\n",
+       "              (3213, 3.5199233827602154),\n",
+       "              (125, 3.519698082174578),\n",
+       "              (6664, 3.517427800733989),\n",
+       "              (49272, 3.5167839620153383),\n",
+       "              (1564, 3.5138572246580972),\n",
+       "              (1032, 3.5097565029622166),\n",
+       "              (2460, 3.5053172890368516),\n",
+       "              (1274, 3.4986113432377497),\n",
+       "              (93498, 3.4927364577664854),\n",
+       "              (599, 3.4864491583396244),\n",
+       "              (26152, 3.484823591012228),\n",
+       "              (56805, 3.4846822289158554),\n",
+       "              (5147, 3.4798238538473507),\n",
+       "              (92535, 3.477035429527723),\n",
+       "              (5038, 3.4624371599327097),\n",
+       "              (89804, 3.4604002748104876),\n",
+       "              (86345, 3.457901018219825),\n",
+       "              (123, 3.4558148778324314),\n",
+       "              (2839, 3.4540283042916102),\n",
+       "              (889, 3.4498374794636644)],\n",
+       "             457: [(923, 3.485294145786453),\n",
+       "              (1945, 3.376185060886716),\n",
+       "              (899, 3.354808541782059),\n",
+       "              (527, 3.2534222323823796),\n",
+       "              (1217, 3.2431305336374314),\n",
+       "              (3310, 3.210271467758192),\n",
+       "              (1219, 3.1785677538753405),\n",
+       "              (1208, 3.1405508884314255),\n",
+       "              (4783, 3.1194126345498456),\n",
+       "              (515, 3.096533453844138),\n",
+       "              (1299, 3.090713933582111),\n",
+       "              (1225, 3.0852442540636686),\n",
+       "              (3504, 3.080827075867516),\n",
+       "              (1218, 3.0754025093514255),\n",
+       "              (3030, 3.0690834021742006),\n",
+       "              (1250, 3.0248482660367344),\n",
+       "              (2739, 2.967408916909022),\n",
+       "              (30749, 2.9640995839808655),\n",
+       "              (2501, 2.961996126528627),\n",
+       "              (1172, 2.954253134800802),\n",
+       "              (101, 2.9478914093146047),\n",
+       "              (3007, 2.9383162420345714),\n",
+       "              (6377, 2.9247803760139206),\n",
+       "              (1032, 2.9215070259141336),\n",
+       "              (97673, 2.9096366390550035),\n",
+       "              (162, 2.9072996119576784),\n",
+       "              (125, 2.8940736489023466),\n",
+       "              (2006, 2.8920818749341715),\n",
+       "              (89804, 2.8886490846295922),\n",
+       "              (3429, 2.888565878917736),\n",
+       "              (3681, 2.875757188065108),\n",
+       "              (2087, 2.8685593753554683),\n",
+       "              (98933, 2.867744876238081),\n",
+       "              (3724, 2.86455178402277),\n",
+       "              (599, 2.8589630923758826),\n",
+       "              (1212, 2.8586469568945456),\n",
+       "              (3334, 2.84927780866982),\n",
+       "              (6579, 2.8490171461981064),\n",
+       "              (1264, 2.84233274553592),\n",
+       "              (915, 2.8421613943915953)],\n",
+       "             460: [(858, 4.426250566070346),\n",
+       "              (923, 4.380525638699923),\n",
+       "              (527, 4.296839619170723),\n",
+       "              (79132, 4.263989345158871),\n",
+       "              (106920, 4.108452139232377),\n",
+       "              (1208, 4.098275523938849),\n",
+       "              (3504, 4.063045561315275),\n",
+       "              (2501, 4.050000725961711),\n",
+       "              (1952, 4.046786620481707),\n",
+       "              (1250, 4.040083184611496),\n",
+       "              (1210, 4.0390173297273275),\n",
+       "              (1305, 4.0380080810981696),\n",
+       "              (55820, 4.028907536919523),\n",
+       "              (233, 4.024881357839233),\n",
+       "              (1945, 4.024264596116688),\n",
+       "              (1299, 4.010271624539157),\n",
+       "              (5669, 4.000744219753891),\n",
+       "              (49272, 3.9803234637228013),\n",
+       "              (515, 3.9773838469434444),\n",
+       "              (1217, 3.9619499076669875),\n",
+       "              (3362, 3.9585324713784202),\n",
+       "              (1212, 3.9399166437130777),\n",
+       "              (1953, 3.9259441396221364),\n",
+       "              (3310, 3.924106841547587),\n",
+       "              (3030, 3.9085962850360807),\n",
+       "              (30749, 3.9024022360173216),\n",
+       "              (56782, 3.8761510270355064),\n",
+       "              (1264, 3.871470113647085),\n",
+       "              (2739, 3.8691202989605413),\n",
+       "              (2087, 3.860711346094865),\n",
+       "              (37741, 3.857413166162802),\n",
+       "              (27878, 3.844799136708526),\n",
+       "              (556, 3.8447640493104407),\n",
+       "              (3724, 3.8436100991724054),\n",
+       "              (599, 3.8419548133060735),\n",
+       "              (2352, 3.8406725279790215),\n",
+       "              (2171, 3.8277514227425673),\n",
+       "              (60756, 3.804319509437284),\n",
+       "              (3168, 3.792855877546047),\n",
+       "              (1218, 3.7919026161890543)],\n",
+       "             461: [(1952, 3.6002925148231935),\n",
+       "              (2501, 3.547101058242935),\n",
+       "              (3362, 3.4320858636698994),\n",
+       "              (77658, 3.3869040424597885),\n",
+       "              (79132, 3.3773626367035483),\n",
+       "              (55820, 3.3732706488179636),\n",
+       "              (1945, 3.339492409340361),\n",
+       "              (1095, 3.332214279382426),\n",
+       "              (1299, 3.3053025083627645),\n",
+       "              (3310, 3.303624708471653),\n",
+       "              (1217, 3.276123881136038),\n",
+       "              (7056, 3.2761020828406755),\n",
+       "              (5690, 3.270779923418431),\n",
+       "              (1953, 3.254157084700819),\n",
+       "              (3030, 3.2410556980266243),\n",
+       "              (3007, 3.2400130120808566),\n",
+       "              (1250, 3.2347960770957114),\n",
+       "              (106920, 3.222749446080561),\n",
+       "              (1212, 3.2101090738596683),\n",
+       "              (1032, 3.2086526622004614),\n",
+       "              (4410, 3.207014300554813),\n",
+       "              (37741, 3.2016071586283887),\n",
+       "              (49272, 3.195459873476326),\n",
+       "              (1305, 3.187830433166007),\n",
+       "              (26152, 3.1877497360556255),\n",
+       "              (162, 3.1808636762553752),\n",
+       "              (1172, 3.1509060247066434),\n",
+       "              (915, 3.1437461161626743),\n",
+       "              (942, 3.1431885258641814),\n",
+       "              (31658, 3.1416657695912873),\n",
+       "              (122892, 3.1182082255537584),\n",
+       "              (3198, 3.1070354724957863),\n",
+       "              (106766, 3.1065180950419267),\n",
+       "              (30749, 3.1051432807020696),\n",
+       "              (5669, 3.102076720735797),\n",
+       "              (89804, 3.100120769937237),\n",
+       "              (3724, 3.086271001227916),\n",
+       "              (56782, 3.085661690267444),\n",
+       "              (33171, 3.0833454305423507),\n",
+       "              (6419, 3.0801799404042396)],\n",
+       "             463: [(899, 4.161865907943662),\n",
+       "              (3362, 4.133816529866469),\n",
+       "              (1945, 4.0194103116622895),\n",
+       "              (923, 4.017111273259671),\n",
+       "              (2501, 3.975935026326166),\n",
+       "              (1172, 3.9157751425690015),\n",
+       "              (3310, 3.8902644085696565),\n",
+       "              (79132, 3.8792691661746534),\n",
+       "              (3504, 3.8629452905738075),\n",
+       "              (1953, 3.858319623307865),\n",
+       "              (49272, 3.8577575131438544),\n",
+       "              (1217, 3.854708012704),\n",
+       "              (106920, 3.845324665056339),\n",
+       "              (55820, 3.8123161491876183),\n",
+       "              (1952, 3.788228254173735),\n",
+       "              (942, 3.753024192161702),\n",
+       "              (3030, 3.7481693158161984),\n",
+       "              (3091, 3.744713723034444),\n",
+       "              (1212, 3.741052031416969),\n",
+       "              (1305, 3.7394531653597967),\n",
+       "              (233, 3.729594296919418),\n",
+       "              (2739, 3.722993375955841),\n",
+       "              (37741, 3.7121536606204204),\n",
+       "              (3499, 3.685045189860911),\n",
+       "              (515, 3.6817763575246567),\n",
+       "              (56782, 3.6595816471785088),\n",
+       "              (422, 3.6578415770490826),\n",
+       "              (1032, 3.6520154910975156),\n",
+       "              (101, 3.6413876010101554),\n",
+       "              (1299, 3.6397391356948416),\n",
+       "              (26152, 3.636792359964416),\n",
+       "              (2481, 3.636685461818438),\n",
+       "              (122892, 3.6287947458987206),\n",
+       "              (3129, 3.625111952641706),\n",
+       "              (33171, 3.619739237816287),\n",
+       "              (77658, 3.6148237856232805),\n",
+       "              (52885, 3.611409632144921),\n",
+       "              (3633, 3.607746122248347),\n",
+       "              (1250, 3.5971312971527567),\n",
+       "              (44199, 3.5948825803944113)],\n",
+       "             468: [(527, 3.7819190730675327),\n",
+       "              (1217, 3.685839307940135),\n",
+       "              (30749, 3.597024373881281),\n",
+       "              (1299, 3.5936338338369382),\n",
+       "              (106920, 3.509943326028661),\n",
+       "              (233, 3.4955069089406576),\n",
+       "              (3724, 3.4603308411701037),\n",
+       "              (2352, 3.4194421887739823),\n",
+       "              (3101, 3.379611899553497),\n",
+       "              (101, 3.3787717797535497),\n",
+       "              (43396, 3.373537826436005),\n",
+       "              (26152, 3.3665525151079274),\n",
+       "              (7300, 3.3611267287735975),\n",
+       "              (62999, 3.3425391271270444),\n",
+       "              (1345, 3.340284852654013),\n",
+       "              (1274, 3.3369125669649646),\n",
+       "              (97673, 3.323125745998337),\n",
+       "              (5021, 3.3113382035707435),\n",
+       "              (1264, 3.302470954669142),\n",
+       "              (1354, 3.2929828765326965),\n",
+       "              (74089, 3.2909102623763404),\n",
+       "              (1218, 3.2873904338895645),\n",
+       "              (109374, 3.279304461529759),\n",
+       "              (3029, 3.2694588380265444),\n",
+       "              (96563, 3.266986122833823),\n",
+       "              (60086, 3.263227270436743),\n",
+       "              (3168, 3.2593911339360835),\n",
+       "              (3728, 3.252550003633896),\n",
+       "              (599, 3.2459501756542295),\n",
+       "              (4927, 3.2458242926902194),\n",
+       "              (106916, 3.2453148922560144),\n",
+       "              (1535, 3.2426292042609264),\n",
+       "              (8879, 3.2385349126779617),\n",
+       "              (95508, 3.2361766639693923),\n",
+       "              (57845, 3.2313836883593807),\n",
+       "              (139385, 3.230652429603941),\n",
+       "              (6935, 3.2305222952573796),\n",
+       "              (115216, 3.2295925671455086),\n",
+       "              (125, 3.2202824959498724),\n",
+       "              (2171, 3.2172729782791247)],\n",
+       "             471: [(858, 4.619346476972689),\n",
+       "              (2804, 4.483994544269344),\n",
+       "              (55820, 4.428683631463185),\n",
+       "              (923, 4.381147313032807),\n",
+       "              (106920, 4.378581506211746),\n",
+       "              (1945, 4.362018952473673),\n",
+       "              (899, 4.355891041301132),\n",
+       "              (3362, 4.297123369082718),\n",
+       "              (79132, 4.292143224685287),\n",
+       "              (1305, 4.239629945787559),\n",
+       "              (2501, 4.22717422287613),\n",
+       "              (1208, 4.211272082539014),\n",
+       "              (1952, 4.203588843584035),\n",
+       "              (3030, 4.195792858934514),\n",
+       "              (1217, 4.194929529544312),\n",
+       "              (1225, 4.1864809352535755),\n",
+       "              (1968, 4.1651339095013915),\n",
+       "              (49272, 4.164036346362072),\n",
+       "              (1299, 4.148678783399302),\n",
+       "              (3310, 4.124369957160328),\n",
+       "              (2739, 4.123212621418289),\n",
+       "              (3504, 4.118535801456115),\n",
+       "              (30749, 4.1090531611006025),\n",
+       "              (515, 4.1088664983598395),\n",
+       "              (3198, 4.100982240380137),\n",
+       "              (1953, 4.096014327687479),\n",
+       "              (6333, 4.070141476226755),\n",
+       "              (2987, 4.068769077731092),\n",
+       "              (33171, 4.036122206240416),\n",
+       "              (103141, 4.02501384262586),\n",
+       "              (1095, 4.010993798601454),\n",
+       "              (44199, 3.9986880966918523),\n",
+       "              (1212, 3.996811800067301),\n",
+       "              (1274, 3.9951861633295134),\n",
+       "              (1264, 3.995167495516717),\n",
+       "              (56782, 3.9937896299300775),\n",
+       "              (942, 3.9827704238431285),\n",
+       "              (4688, 3.9794375749154915),\n",
+       "              (5064, 3.9773277861789067),\n",
+       "              (3724, 3.9641575797494037)],\n",
+       "             472: [(106920, 4.367480584056386),\n",
+       "              (233, 4.3533123545518),\n",
+       "              (515, 4.276661430640427),\n",
+       "              (79132, 4.267564862940601),\n",
+       "              (55820, 4.262996983522111),\n",
+       "              (2501, 4.245545062123409),\n",
+       "              (1305, 4.233981118714691),\n",
+       "              (1945, 4.2289475210465435),\n",
+       "              (3168, 4.184705413511271),\n",
+       "              (1095, 4.11163497146346),\n",
+       "              (1217, 4.110395106869474),\n",
+       "              (30749, 4.107033572222109),\n",
+       "              (56782, 4.0555869276252485),\n",
+       "              (109374, 4.036375642820414),\n",
+       "              (3310, 4.017810781077648),\n",
+       "              (96829, 4.016706703346224),\n",
+       "              (98933, 4.015285177013149),\n",
+       "              (89804, 4.005533025884986),\n",
+       "              (31658, 3.997288689248579),\n",
+       "              (1032, 3.990591261341009),\n",
+       "              (5690, 3.9904110148589327),\n",
+       "              (4801, 3.9852824024215643),\n",
+       "              (1218, 3.981816899387495),\n",
+       "              (3030, 3.981431769281928),\n",
+       "              (7700, 3.9774396714279385),\n",
+       "              (3198, 3.9690351698512703),\n",
+       "              (93498, 3.963012934094341),\n",
+       "              (118082, 3.9521419650537073),\n",
+       "              (60756, 3.9484745639990844),\n",
+       "              (147845, 3.9358384224198995),\n",
+       "              (26712, 3.9321262175753438),\n",
+       "              (8576, 3.928414391523007),\n",
+       "              (96815, 3.9264099958263845),\n",
+       "              (6333, 3.925787333223888),\n",
+       "              (69951, 3.925750866514538),\n",
+       "              (3429, 3.923212409193423),\n",
+       "              (26614, 3.9214139655597386),\n",
+       "              (36527, 3.921246293685938),\n",
+       "              (98611, 3.911410063362259),\n",
+       "              (31270, 3.9107194430649788)],\n",
+       "             475: [(923, 3.7240758614590135),\n",
+       "              (1217, 3.649740430832109),\n",
+       "              (899, 3.619318663292605),\n",
+       "              (1208, 3.5645565858211627),\n",
+       "              (527, 3.5185391724948687),\n",
+       "              (1945, 3.496819878096572),\n",
+       "              (2987, 3.463256113340724),\n",
+       "              (2065, 3.4510023591579753),\n",
+       "              (3499, 3.419743268947367),\n",
+       "              (3504, 3.4015289863078446),\n",
+       "              (1264, 3.388013269789316),\n",
+       "              (5064, 3.36904700912734),\n",
+       "              (44199, 3.3687478755081313),\n",
+       "              (1968, 3.368549082654351),\n",
+       "              (56782, 3.367231081433667),\n",
+       "              (31658, 3.3652759534662566),\n",
+       "              (1172, 3.3652213500831185),\n",
+       "              (1250, 3.3641216807516563),\n",
+       "              (2804, 3.361344705313037),\n",
+       "              (3310, 3.3565676489724194),\n",
+       "              (515, 3.352481530110994),\n",
+       "              (1305, 3.3495785546995065),\n",
+       "              (1219, 3.348732761806017),\n",
+       "              (1953, 3.3485341036404894),\n",
+       "              (1299, 3.335742586130946),\n",
+       "              (4410, 3.316221770426719),\n",
+       "              (3429, 3.312810713465854),\n",
+       "              (3030, 3.310994944831662),\n",
+       "              (1952, 3.3038086724884566),\n",
+       "              (1218, 3.2994303005395773),\n",
+       "              (1032, 3.292314860250691),\n",
+       "              (3198, 3.282106074272929),\n",
+       "              (1212, 3.275822919119434),\n",
+       "              (37741, 3.2711471753105816),\n",
+       "              (422, 3.2640195155103218),\n",
+       "              (2501, 3.2620301396525244),\n",
+       "              (3101, 3.2577378982348124),\n",
+       "              (3362, 3.241481932920468),\n",
+       "              (3070, 3.237904269485644),\n",
+       "              (4105, 3.2350832403836023)],\n",
+       "             480: [(923, 4.587037523178942),\n",
+       "              (1208, 4.566164472472139),\n",
+       "              (1225, 4.557024417863214),\n",
+       "              (1945, 4.48354723451963),\n",
+       "              (106920, 4.462665240627977),\n",
+       "              (1299, 4.462267061571995),\n",
+       "              (1217, 4.4588720231770544),\n",
+       "              (527, 4.455628058315589),\n",
+       "              (1219, 4.448204071354428),\n",
+       "              (899, 4.4177726728519575),\n",
+       "              (3362, 4.391226272714013),\n",
+       "              (1210, 4.371482771676645),\n",
+       "              (1305, 4.333155318922353),\n",
+       "              (233, 4.329461533204851),\n",
+       "              (1250, 4.3262422865646935),\n",
+       "              (1952, 4.3262161793793315),\n",
+       "              (1172, 4.3184158629123806),\n",
+       "              (2804, 4.286910947357127),\n",
+       "              (515, 4.286730400514077),\n",
+       "              (1212, 4.280737063100498),\n",
+       "              (30749, 4.272372686309602),\n",
+       "              (3504, 4.269169757625302),\n",
+       "              (3310, 4.229710242411325),\n",
+       "              (915, 4.2209773515521185),\n",
+       "              (1953, 4.210366732834679),\n",
+       "              (2501, 4.185336967670518),\n",
+       "              (6975, 4.181915139933475),\n",
+       "              (31658, 4.174094710918495),\n",
+       "              (5669, 4.172107915363027),\n",
+       "              (2739, 4.166520658188445),\n",
+       "              (74089, 4.164073467647071),\n",
+       "              (96829, 4.162659888105982),\n",
+       "              (5690, 4.162405741218686),\n",
+       "              (3724, 4.157924242408075),\n",
+       "              (3030, 4.15684055262286),\n",
+       "              (26712, 4.1454514855413525),\n",
+       "              (8273, 4.138002668485426),\n",
+       "              (139385, 4.135178424293216),\n",
+       "              (1073, 4.121804264420758),\n",
+       "              (37741, 4.120791692578993)],\n",
+       "             481: [(1945, 4.794266788193363),\n",
+       "              (1250, 4.7592469529032275),\n",
+       "              (2804, 4.651917836387821),\n",
+       "              (1217, 4.636062485470807),\n",
+       "              (1225, 4.62087410666261),\n",
+       "              (106920, 4.601718801633187),\n",
+       "              (3499, 4.5728154649639405),\n",
+       "              (2501, 4.569930221509636),\n",
+       "              (1305, 4.522971102182864),\n",
+       "              (1219, 4.515675229431205),\n",
+       "              (515, 4.507114842885638),\n",
+       "              (1953, 4.490364298998148),\n",
+       "              (3030, 4.48757233134056),\n",
+       "              (1073, 4.483350438098469),\n",
+       "              (1968, 4.475206533602595),\n",
+       "              (1212, 4.459463092517489),\n",
+       "              (44199, 4.39498268778508),\n",
+       "              (599, 4.36476590329342),\n",
+       "              (4783, 4.358436242534041),\n",
+       "              (1218, 4.341438470964179),\n",
+       "              (1274, 4.341012243569295),\n",
+       "              (1095, 4.335961146677983),\n",
+       "              (2173, 4.333018301863309),\n",
+       "              (233, 4.3136484753189155),\n",
+       "              (122892, 4.313299837150026),\n",
+       "              (31658, 4.311835359511646),\n",
+       "              (915, 4.308869791964723),\n",
+       "              (3070, 4.287618698520501),\n",
+       "              (98124, 4.284908292876273),\n",
+       "              (3724, 4.280224403780275),\n",
+       "              (4191, 4.273145202534773),\n",
+       "              (33171, 4.271701598068784),\n",
+       "              (942, 4.266390614761518),\n",
+       "              (509, 4.265439582673374),\n",
+       "              (6033, 4.259367646196613),\n",
+       "              (106916, 4.25933855895217),\n",
+       "              (1785, 4.252273314231577),\n",
+       "              (1299, 4.251671809401946),\n",
+       "              (3334, 4.24886447747405),\n",
+       "              (52885, 4.248687330215116)],\n",
+       "             505: [(858, 3.9201239606755447),\n",
+       "              (1219, 3.8781978733020206),\n",
+       "              (1217, 3.8363503081492167),\n",
+       "              (79132, 3.8025422721701414),\n",
+       "              (3362, 3.7872418455125723),\n",
+       "              (1305, 3.770853474938519),\n",
+       "              (515, 3.7641702855044765),\n",
+       "              (106920, 3.745568977611006),\n",
+       "              (1952, 3.65247903061974),\n",
+       "              (55820, 3.616743399022398),\n",
+       "              (233, 3.6093815117160317),\n",
+       "              (1208, 3.6088135952194333),\n",
+       "              (5669, 3.6022434357464563),\n",
+       "              (2804, 3.5866277202841945),\n",
+       "              (599, 3.5844487530440183),\n",
+       "              (2501, 3.5538874359670323),\n",
+       "              (915, 3.5480127427630572),\n",
+       "              (56782, 3.54514453880823),\n",
+       "              (30749, 3.5405241776965357),\n",
+       "              (3310, 3.52064471317646),\n",
+       "              (3198, 3.5106513717950216),\n",
+       "              (3030, 3.4967098381934143),\n",
+       "              (26712, 3.489757345619514),\n",
+       "              (3091, 3.486578781370804),\n",
+       "              (4105, 3.475324778920197),\n",
+       "              (1953, 3.459743086276239),\n",
+       "              (6333, 3.4457592901084206),\n",
+       "              (1073, 3.439403782124276),\n",
+       "              (2087, 3.4351531732278398),\n",
+       "              (33171, 3.431480577093206),\n",
+       "              (97673, 3.4257033303852413),\n",
+       "              (1264, 3.421088846299793),\n",
+       "              (4166, 3.4057008919687948),\n",
+       "              (1095, 3.405238661663079),\n",
+       "              (31658, 3.4018253235640477),\n",
+       "              (26614, 3.3986259975104653),\n",
+       "              (3070, 3.3870077050278127),\n",
+       "              (122892, 3.3842613144646054),\n",
+       "              (109374, 3.379407549370844),\n",
+       "              (106766, 3.3662083238026237)],\n",
+       "             509: [(106920, 4.319027594838991),\n",
+       "              (55820, 4.21006383702758),\n",
+       "              (79132, 4.144937918625678),\n",
+       "              (1305, 4.086553146140635),\n",
+       "              (3499, 4.030259502348888),\n",
+       "              (49272, 4.018569411605719),\n",
+       "              (30749, 3.912520295243841),\n",
+       "              (915, 3.909022537706464),\n",
+       "              (1032, 3.9073589202382992),\n",
+       "              (3310, 3.9063887142594202),\n",
+       "              (37741, 3.9041364008266624),\n",
+       "              (942, 3.8918448996994526),\n",
+       "              (26152, 3.876530371815613),\n",
+       "              (2087, 3.875353859762452),\n",
+       "              (7010, 3.8709950490582115),\n",
+       "              (599, 3.8600637547793957),\n",
+       "              (4783, 3.8503929862340995),\n",
+       "              (3030, 3.8329234115713278),\n",
+       "              (5732, 3.8286641102418892),\n",
+       "              (122892, 3.8265731633782356),\n",
+       "              (139385, 3.824928224925007),\n",
+       "              (4410, 3.821835474142519),\n",
+       "              (1264, 3.821646973897065),\n",
+       "              (7056, 3.819111981566929),\n",
+       "              (556, 3.802430633669161),\n",
+       "              (89804, 3.8022108965002017),\n",
+       "              (3091, 3.796764336963367),\n",
+       "              (106766, 3.7909619892579483),\n",
+       "              (1345, 3.7840492491662645),\n",
+       "              (2117, 3.779865695852506),\n",
+       "              (3633, 3.7785472119024752),\n",
+       "              (3198, 3.7761769750326852),\n",
+       "              (8576, 3.7754010391661783),\n",
+       "              (3713, 3.7708505335474625),\n",
+       "              (3724, 3.7701126366906745),\n",
+       "              (31270, 3.7665813619915918),\n",
+       "              (43396, 3.764030801601143),\n",
+       "              (8933, 3.760045325925362),\n",
+       "              (3728, 3.759405102430887),\n",
+       "              (44199, 3.744064978691829)],\n",
+       "             514: [(858, 4.487954460333959),\n",
+       "              (1172, 4.295191342372239),\n",
+       "              (1945, 4.2720462343966625),\n",
+       "              (106920, 4.268312441593804),\n",
+       "              (3504, 4.244607610355245),\n",
+       "              (527, 4.216660688032044),\n",
+       "              (899, 4.18548656521526),\n",
+       "              (55820, 4.173761094439207),\n",
+       "              (3362, 4.136869469758592),\n",
+       "              (1217, 4.135455075066829),\n",
+       "              (49272, 4.1318864023785284),\n",
+       "              (2804, 4.119153397835868),\n",
+       "              (6377, 4.114710876577616),\n",
+       "              (1968, 4.102778444205415),\n",
+       "              (1212, 4.091034846882619),\n",
+       "              (1952, 4.062244612254474),\n",
+       "              (122892, 4.0182016700379535),\n",
+       "              (37741, 3.985526313828456),\n",
+       "              (599, 3.9737219495276777),\n",
+       "              (1354, 3.961704420917657),\n",
+       "              (30749, 3.9594701998699615),\n",
+       "              (5669, 3.944268278874648),\n",
+       "              (43396, 3.9425838719659207),\n",
+       "              (3724, 3.942501679501807),\n",
+       "              (2501, 3.9407351046589074),\n",
+       "              (3198, 3.93292056402284),\n",
+       "              (26152, 3.9308138041019403),\n",
+       "              (2739, 3.9225905608518237),\n",
+       "              (1264, 3.921472711657876),\n",
+       "              (6333, 3.9014415107483424),\n",
+       "              (1299, 3.8997183060443743),\n",
+       "              (79132, 3.898857100094358),\n",
+       "              (3030, 3.8894705963891343),\n",
+       "              (56782, 3.8881059192192606),\n",
+       "              (942, 3.8794945937816667),\n",
+       "              (27611, 3.8718023078250736),\n",
+       "              (26712, 3.8688877914700637),\n",
+       "              (5690, 3.8653486106459805),\n",
+       "              (31658, 3.855920545171441),\n",
+       "              (33171, 3.8546296700801954)],\n",
+       "             518: [(106920, 4.515949879359828),\n",
+       "              (1208, 4.514105812169685),\n",
+       "              (55820, 4.468459255955158),\n",
+       "              (1945, 4.425879218773087),\n",
+       "              (923, 4.408393878273973),\n",
+       "              (3362, 4.398902454009364),\n",
+       "              (1299, 4.313631420889066),\n",
+       "              (5669, 4.295072553508015),\n",
+       "              (79132, 4.283923212497324),\n",
+       "              (3030, 4.26341565746737),\n",
+       "              (1305, 4.259560555418242),\n",
+       "              (1952, 4.2524125989130575),\n",
+       "              (1217, 4.252110377243298),\n",
+       "              (3499, 4.222625981738604),\n",
+       "              (527, 4.216882918817833),\n",
+       "              (37741, 4.210858820248334),\n",
+       "              (233, 4.16711565928433),\n",
+       "              (2501, 4.15553335207426),\n",
+       "              (3007, 4.1516482257643705),\n",
+       "              (3429, 4.150974544645294),\n",
+       "              (1212, 4.14589704123326),\n",
+       "              (4105, 4.142652483120097),\n",
+       "              (515, 4.135379726548915),\n",
+       "              (56782, 4.131954724787965),\n",
+       "              (6377, 4.12958102379127),\n",
+       "              (31658, 4.128222049861135),\n",
+       "              (3310, 4.122376668242024),\n",
+       "              (1218, 4.120837430456751),\n",
+       "              (30749, 4.1188120152311125),\n",
+       "              (106766, 4.106312150017657),\n",
+       "              (26712, 4.105384539293391),\n",
+       "              (3091, 4.100516384369996),\n",
+       "              (44199, 4.095488669651108),\n",
+       "              (1953, 4.094982425154642),\n",
+       "              (52885, 4.0901413528177715),\n",
+       "              (915, 4.086205406095144),\n",
+       "              (3504, 4.068008315064485),\n",
+       "              (92535, 4.061830982800267),\n",
+       "              (26180, 4.056194931328018),\n",
+       "              (6975, 4.054515080503959)],\n",
+       "             522: [(106920, 3.973994195521235),\n",
+       "              (923, 3.9240000804951274),\n",
+       "              (2804, 3.8564232217147643),\n",
+       "              (1219, 3.85130919689904),\n",
+       "              (2501, 3.813501602192398),\n",
+       "              (3504, 3.799604678156415),\n",
+       "              (1945, 3.7887080567412124),\n",
+       "              (1210, 3.7640755091503006),\n",
+       "              (899, 3.757975178658044),\n",
+       "              (1172, 3.7353719096856697),\n",
+       "              (55820, 3.728649343134159),\n",
+       "              (3362, 3.7104308428344566),\n",
+       "              (33171, 3.694034194997057),\n",
+       "              (1250, 3.6639640357611274),\n",
+       "              (515, 3.646464471737445),\n",
+       "              (1952, 3.6438093199459454),\n",
+       "              (37741, 3.6167386168326203),\n",
+       "              (1217, 3.6150792003844114),\n",
+       "              (1968, 3.6057754603570156),\n",
+       "              (44199, 3.6031897906250547),\n",
+       "              (1305, 3.5817332927624643),\n",
+       "              (3310, 3.55453857387115),\n",
+       "              (6333, 3.549521769693932),\n",
+       "              (26712, 3.4775513979239463),\n",
+       "              (30749, 3.471431734746784),\n",
+       "              (233, 3.466617043882005),\n",
+       "              (49272, 3.456405574402107),\n",
+       "              (1212, 3.4504351305343497),\n",
+       "              (1299, 3.448146588001278),\n",
+       "              (1073, 3.446385014377475),\n",
+       "              (3198, 3.434941805723892),\n",
+       "              (122892, 3.4263434510151893),\n",
+       "              (96829, 3.421970346528738),\n",
+       "              (2739, 3.42173562777973),\n",
+       "              (31658, 3.419514111427082),\n",
+       "              (3007, 3.4168905457507432),\n",
+       "              (5669, 3.4129424596865165),\n",
+       "              (3030, 3.400874257884088),\n",
+       "              (1942, 3.3969505949737404),\n",
+       "              (101, 3.3910510853608633)],\n",
+       "             529: [(1210, 4.333916064976808),\n",
+       "              (1945, 4.21039045987172),\n",
+       "              (1305, 4.195663220207507),\n",
+       "              (1240, 4.165477252383342),\n",
+       "              (1217, 4.137933356495214),\n",
+       "              (55820, 4.101712174210789),\n",
+       "              (1299, 4.088288655212125),\n",
+       "              (3030, 4.047241433276829),\n",
+       "              (1968, 4.045909957999914),\n",
+       "              (49272, 4.014674755579987),\n",
+       "              (1218, 4.001252880977921),\n",
+       "              (942, 3.9785904998254313),\n",
+       "              (2501, 3.977543524503227),\n",
+       "              (1172, 3.9727863172215936),\n",
+       "              (106920, 3.968752272829564),\n",
+       "              (37741, 3.962174338617325),\n",
+       "              (8584, 3.9512666335455355),\n",
+       "              (33171, 3.9259784484163953),\n",
+       "              (3310, 3.925559046826581),\n",
+       "              (26712, 3.9221539294955075),\n",
+       "              (233, 3.894290414516869),\n",
+       "              (56782, 3.8769378968814148),\n",
+       "              (3070, 3.8567945987151355),\n",
+       "              (3429, 3.8539826965282353),\n",
+       "              (3198, 3.8457941017903643),\n",
+       "              (60756, 3.8398203325437157),\n",
+       "              (6333, 3.83954143140851),\n",
+       "              (7976, 3.8355138137622897),\n",
+       "              (31952, 3.8348502077414692),\n",
+       "              (1095, 3.8336100569215956),\n",
+       "              (77658, 3.8191442083210823),\n",
+       "              (96829, 3.8150763024182597),\n",
+       "              (1942, 3.8147641405727364),\n",
+       "              (106766, 3.8137304721014367),\n",
+       "              (4105, 3.805704619441929),\n",
+       "              (96737, 3.8030712268348426),\n",
+       "              (5147, 3.8012048317553577),\n",
+       "              (101, 3.799455717429439),\n",
+       "              (139385, 3.786455082522002),\n",
+       "              (26152, 3.784395792104562)],\n",
+       "             534: [(858, 4.84516438620515),\n",
+       "              (1219, 4.773639877679084),\n",
+       "              (923, 4.685072414604828),\n",
+       "              (55820, 4.57184865640853),\n",
+       "              (1217, 4.561159626430633),\n",
+       "              (1968, 4.534880951974017),\n",
+       "              (1945, 4.5113216339695486),\n",
+       "              (2804, 4.486227400010997),\n",
+       "              (1299, 4.459896629885732),\n",
+       "              (515, 4.4487744261791455),\n",
+       "              (56782, 4.4465281359151705),\n",
+       "              (1210, 4.423317375567252),\n",
+       "              (1225, 4.42230263326854),\n",
+       "              (899, 4.407153362863983),\n",
+       "              (1208, 4.402142638044594),\n",
+       "              (233, 4.400957860746602),\n",
+       "              (1172, 4.389352255952464),\n",
+       "              (3362, 4.376802641860371),\n",
+       "              (1264, 4.365430935253048),\n",
+       "              (1212, 4.346228023816358),\n",
+       "              (26152, 4.315531412030038),\n",
+       "              (1250, 4.312524933987347),\n",
+       "              (3310, 4.308767332770681),\n",
+       "              (527, 4.300011389838285),\n",
+       "              (79132, 4.29739033411441),\n",
+       "              (1073, 4.297164199573492),\n",
+       "              (1952, 4.285634328774901),\n",
+       "              (106920, 4.276084345544258),\n",
+       "              (3168, 4.246916152749234),\n",
+       "              (5669, 4.24073883696108),\n",
+       "              (1305, 4.237514714717905),\n",
+       "              (122892, 4.217684381794959),\n",
+       "              (1095, 4.209878204366494),\n",
+       "              (3499, 4.2078644555107205),\n",
+       "              (3724, 4.204006498062277),\n",
+       "              (6377, 4.203026655540848),\n",
+       "              (2739, 4.201447825759907),\n",
+       "              (509, 4.1949772236020175),\n",
+       "              (1032, 4.194142713065363),\n",
+       "              (89804, 4.185891013788092)],\n",
+       "             537: [(858, 4.520134311071283),\n",
+       "              (1945, 4.407969882735991),\n",
+       "              (1217, 4.401159470028978),\n",
+       "              (79132, 4.363161555326263),\n",
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+       "              (3362, 4.34984086405275),\n",
+       "              (1968, 4.3291338876567895),\n",
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+       "              (49272, 4.253283722820454),\n",
+       "              (1208, 4.2307843778844365),\n",
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+       "              (55820, 4.213900179111616),\n",
+       "              (5669, 4.209106111261569),\n",
+       "              (2739, 4.199425315627052),\n",
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+       "              (30749, 4.168299306502528),\n",
+       "              (56782, 4.107573683190079),\n",
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+       "              (3724, 4.0933894439365766),\n",
+       "              (233, 4.088827836927723),\n",
+       "              (1212, 4.088425986983921),\n",
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+       "              (599, 4.032397463480172),\n",
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+       "              (4105, 4.029414100447807),\n",
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+       "              (106766, 3.9790881856374556),\n",
+       "              (101, 3.969288982347692),\n",
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+       "              (3499, 3.960635054840573),\n",
+       "              (3681, 3.955801565735836)],\n",
+       "             544: [(923, 4.996666097404725),\n",
+       "              (1219, 4.97565104681523),\n",
+       "              (899, 4.935323138589773),\n",
+       "              (1945, 4.93465447193661),\n",
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+       "              (1274, 4.50158917126383),\n",
+       "              (3724, 4.496027412134855),\n",
+       "              (109374, 4.495287906060007)],\n",
+       "             547: [(3429, 3.981351837789914),\n",
+       "              (31658, 3.969277204683116),\n",
+       "              (1942, 3.9683644449351845),\n",
+       "              (1073, 3.8856722149141447),\n",
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+       "              (118082, 3.589885573548721),\n",
+       "              (89759, 3.5881891804957626),\n",
+       "              (3189, 3.5855410697809615)],\n",
+       "             561: [(858, 4.4021242836155725),\n",
+       "              (3362, 4.15547720573224),\n",
+       "              (899, 4.106429092000354),\n",
+       "              (1945, 4.037162779305669),\n",
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+       "              (106766, 3.648443584164021),\n",
+       "              (7396, 3.643158557173006)],\n",
+       "             562: [(899, 4.5152426692421646),\n",
+       "              (1968, 4.459426963651336),\n",
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+       "              (599, 4.076106919834513),\n",
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+       "             564: [(49272, 4.477749060568538),\n",
+       "              (899, 4.409498182382906),\n",
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+       "              (4927, 3.94172558940583),\n",
+       "              (3794, 3.9409555297185483)],\n",
+       "             574: [(923, 4.394059565957348),\n",
+       "              (527, 4.288970040550781),\n",
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+       "              (1305, 4.238624522688566),\n",
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+       "              (2087, 3.875928734159628),\n",
+       "              (106766, 3.8745663377945347)],\n",
+       "             575: [(858, 4.244155207938811),\n",
+       "              (923, 4.121724486764881),\n",
+       "              (106920, 3.976443959854553),\n",
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+       "              (30749, 3.5445189108799924),\n",
+       "              (70293, 3.5404799507502034)],\n",
+       "             577: [(923, 4.911275833364665),\n",
+       "              (1968, 4.899764033852872),\n",
+       "              (1208, 4.880740439019452),\n",
+       "              (2804, 4.75812090603781),\n",
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+       "              (56782, 4.374006120515484),\n",
+       "              (1299, 4.368470660091209)],\n",
+       "             580: [(3362, 4.135024915872054),\n",
+       "              (1953, 4.082639458225413),\n",
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+       "              (942, 3.59667149145646),\n",
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+       "              (915, 3.582289541636823),\n",
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+       "             664: [(899, 4.677617146461869),\n",
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+       "              (139385, 3.8279570488348287),\n",
+       "              (48783, 3.8092707263573646)]})"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "generate_full_top_n(algo, dataset, eval_config)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# 2. Evaluation metrics\n",
+    "Implement evaluation metrics for either rating predictions (split metrics) or for top-n recommendations (loo metric, full metric)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def get_hit_rate(anti_testset_top_n, testset):\n",
+    "    \"\"\"Compute the average hit over the users (loo metric)\n",
+    "\n",
+    "    A hit (1) happens when the movie in the testset has been picked by the top-n recommender\n",
+    "    A fail (0) happens when the movie in the testset has not been picked by the top-n recommender\n",
+    "    \"\"\"\n",
+    "    hits = 0\n",
+    "    total_users = len(set([uid for uid, _, _ in testset]))\n",
+    "\n",
+    "    for uid, iid, _ in testset:\n",
+    "        recommended_iids = [iid for (iid, _) in anti_testset_top_n[int(uid)]] # recommended movies for user\n",
+    "        if iid in recommended_iids:\n",
+    "            hits += 1\n",
+    "    #print(hits)\n",
+    "    #print(total_users)\n",
+    "    hit_rate = hits / total_users\n",
+    "\n",
+    "    return hit_rate\n",
+    "\n",
+    "def get_novelty(anti_testset_top_n, item_to_rank):\n",
+    "    \"\"\"Compute the average novelty of the top-n recommendation over the users (full metric)\n",
+    "    \n",
+    "    The novelty is defined as the average ranking of the movies recommended\n",
+    "    \"\"\"\n",
+    "    # -- implement the function get_novelty --\n",
+    "    list_rank_sum=[]\n",
+    "    for i in anti_testset_top_n.items() :\n",
+    "        #print(i)\n",
+    "        l=[]\n",
+    "        rank_sum=0\n",
+    "        for j in i[1]:\n",
+    "            #print(j)\n",
+    "            if j[0] not in l :\n",
+    "                l.append(j[0])\n",
+    "        #print(l)\n",
+    "    \n",
+    "        for key,value in item_to_rank.items() :\n",
+    "            if value in l :\n",
+    "                rank_sum+=key\n",
+    "        list_rank_sum.append(rank_sum)\n",
+    "    #print(rank_sum_liste)\n",
+    "  \n",
+    "    min_rank_sum = min(list_rank_sum)\n",
+    "    max_rank_sum = max(list_rank_sum)\n",
+    "    normalized_ranks = [(r - min_rank_sum) / (max_rank_sum - min_rank_sum) for r in list_rank_sum]\n",
+    "    \n",
+    "    average_rank_sum = sum(normalized_ranks) / len(normalized_ranks)\n",
+    "    \n",
+    "    return average_rank_sum"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "##### What are the pitfalls of using a sum of ranks as a novelty metric ?\n",
+    "\n",
+    "When averaging the ranks, it is obvious that the average is influenced by the extreme values, namely the most popular films (with a low rank) and the least popular films (with a high rank). "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# 3. Evaluation workflow\n",
+    "Load data, evaluate models and save the experimental outcomes"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<surprise.dataset.DatasetAutoFolds at 0x7f97274c1390>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Handling model baseline_1\n",
+      "Training split predictions\n",
+      "- computing metric mae\n",
+      "- computing metric rmse\n",
+      "Training loo predictions\n",
+      "Training full predictions\n",
+      "Handling model baseline_2\n",
+      "Training split predictions\n",
+      "- computing metric mae\n",
+      "- computing metric rmse\n",
+      "Training loo predictions\n",
+      "Training full predictions\n",
+      "Handling model baseline_3\n",
+      "Training split predictions\n",
+      "- computing metric mae\n",
+      "- computing metric rmse\n",
+      "Training loo predictions\n",
+      "Training full predictions\n",
+      "Handling model baseline_4\n",
+      "Training split predictions\n",
+      "- computing metric mae\n",
+      "- computing metric rmse\n",
+      "Training loo predictions\n",
+      "Training full predictions\n",
+      "Handling model user_based_msd\n",
+      "Training split predictions\n",
+      "- computing metric mae\n",
+      "- computing metric rmse\n",
+      "Training loo predictions\n",
+      "Training full predictions\n",
+      "Handling model user_based_jacard\n",
+      "Training split predictions\n",
+      "- computing metric mae\n",
+      "- computing metric rmse\n",
+      "Training loo predictions\n",
+      "Training full predictions\n",
+      "Handling model random_score\n",
+      "Training split predictions\n",
+      "- computing metric mae\n",
+      "- computing metric rmse\n",
+      "Training loo predictions\n",
+      "Training full predictions\n",
+      "Handling model random_sample\n",
+      "Training split predictions\n",
+      "- computing metric mae\n",
+      "- computing metric rmse\n",
+      "Training loo predictions\n",
+      "Training full predictions\n",
+      "Handling model linear and date\n",
+      "Training split predictions\n",
+      "- computing metric mae\n",
+      "- computing metric rmse\n",
+      "Training loo predictions\n",
+      "Training full predictions\n",
+      "Handling model linear and title\n",
+      "Training split predictions\n",
+      "- computing metric mae\n",
+      "- computing metric rmse\n",
+      "Training loo predictions\n",
+      "Training full predictions\n",
+      "Handling model linear and genres\n",
+      "Training split predictions\n",
+      "- computing metric mae\n",
+      "- computing metric rmse\n",
+      "Training loo predictions\n",
+      "Training full predictions\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>mae</th>\n",
+       "      <th>rmse</th>\n",
+       "      <th>hit_rate</th>\n",
+       "      <th>novelty</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>baseline_1</th>\n",
+       "      <td>1.578550</td>\n",
+       "      <td>1.805392</td>\n",
+       "      <td>0.028037</td>\n",
+       "      <td>0.511618</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>baseline_2</th>\n",
+       "      <td>1.490753</td>\n",
+       "      <td>1.822888</td>\n",
+       "      <td>0.065421</td>\n",
+       "      <td>0.447978</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>baseline_3</th>\n",
+       "      <td>0.880705</td>\n",
+       "      <td>1.088199</td>\n",
+       "      <td>0.037383</td>\n",
+       "      <td>0.511618</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>baseline_4</th>\n",
+       "      <td>0.732431</td>\n",
+       "      <td>0.941478</td>\n",
+       "      <td>0.317757</td>\n",
+       "      <td>0.209231</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>user_based_msd</th>\n",
+       "      <td>0.789168</td>\n",
+       "      <td>1.022609</td>\n",
+       "      <td>0.093458</td>\n",
+       "      <td>0.605386</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>user_based_jacard</th>\n",
+       "      <td>0.750236</td>\n",
+       "      <td>0.965420</td>\n",
+       "      <td>0.102804</td>\n",
+       "      <td>0.569613</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>random_score</th>\n",
+       "      <td>1.456447</td>\n",
+       "      <td>1.784380</td>\n",
+       "      <td>0.074766</td>\n",
+       "      <td>0.530963</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>random_sample</th>\n",
+       "      <td>1.075586</td>\n",
+       "      <td>1.420208</td>\n",
+       "      <td>0.065421</td>\n",
+       "      <td>0.482651</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>linear and date</th>\n",
+       "      <td>1.024617</td>\n",
+       "      <td>1.329360</td>\n",
+       "      <td>0.009346</td>\n",
+       "      <td>0.744561</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>linear and title</th>\n",
+       "      <td>1.651916</td>\n",
+       "      <td>1.988417</td>\n",
+       "      <td>0.084112</td>\n",
+       "      <td>0.587664</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>linear and genres</th>\n",
+       "      <td>1.224664</td>\n",
+       "      <td>1.557368</td>\n",
+       "      <td>0.084112</td>\n",
+       "      <td>0.420021</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "                        mae      rmse  hit_rate   novelty\n",
+       "baseline_1         1.578550  1.805392  0.028037  0.511618\n",
+       "baseline_2         1.490753  1.822888  0.065421  0.447978\n",
+       "baseline_3         0.880705  1.088199  0.037383  0.511618\n",
+       "baseline_4         0.732431  0.941478  0.317757  0.209231\n",
+       "user_based_msd     0.789168  1.022609  0.093458  0.605386\n",
+       "user_based_jacard  0.750236  0.965420  0.102804  0.569613\n",
+       "random_score       1.456447  1.784380  0.074766  0.530963\n",
+       "random_sample      1.075586  1.420208  0.065421  0.482651\n",
+       "linear and date    1.024617  1.329360  0.009346  0.744561\n",
+       "linear and title   1.651916  1.988417  0.084112  0.587664\n",
+       "linear and genres  1.224664  1.557368  0.084112  0.420021"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "AVAILABLE_METRICS = {\n",
+    "    \"split\": {\n",
+    "        \"mae\": (surprise.accuracy.mae, {'verbose': False}),\n",
+    "        # -- add new split metrics here --\n",
+    "        \"rmse\": (surprise.accuracy.rmse, {'verbose' : False})\n",
+    "    },\n",
+    "    # -- add new types of metrics here --\n",
+    "    \"loo\": {\n",
+    "        \"hit_rate\": (get_hit_rate, {}),\n",
+    "    },\n",
+    "    \"full\": {\n",
+    "        \"novelty\": (get_novelty, {}),\n",
+    "    }\n",
+    "}\n",
+    "\n",
+    "sp_ratings = load_ratings(surprise_format=True)\n",
+    "display(sp_ratings)\n",
+    "precomputed_dict = precompute_information()\n",
+    "evaluation_report = create_evaluation_report(EvalConfig, sp_ratings, precomputed_dict, AVAILABLE_METRICS)\n",
+    "export_evaluation_report(evaluation_report)\n",
+    "\n",
+    "display(evaluation_report)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Observations"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Lorsque nous utilisons le dataset tiny, nous remarquons que:\n",
+    "\n",
+    "Les 3 meilleurs modèles en termes de précision des prédictions sont : 1) baseline4, 2) user_based avec similarité de jacard et 3) user_based avec similarité msd.\n",
+    "\n",
+    "En termes de taux de réussite (hit_rate), le baseline4 est de loin de meilleur, c'est à dire que la proportion de fois où un item recommandé a été effectivement apprécié par l'utilisateur est plus élevé dans ce modèle.\n",
+    "\n",
+    "En termes de nouveauté (novelty), c'est le modèle Content_Based \"linear and date\" qui offre le plus de films qui sont moins populaires et plus originaux.\n",
+    "\n",
+    "S'il fallait choisir un modèle, nous aurions choisi le modèle baseline4. Néanmoins, ce dernier a une mesure de nouveauté faible.  "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.7.6"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
-- 
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