recommender-systems/04_implicit_feedback.ipynb

{"cells":[{"cell_type":"markdown","metadata":{"id":"xLXWx4uhqtYJ"},"source":["<table class=\"tfo-notebook-buttons\" align=\"left\">\n","  <td>\n","    <a target=\"_blank\" href=\"https://colab.research.google.com/github/PreferredAI/tutorials/blob/master/recommender-systems/04_implicit_feedback.ipynb\"><img src=\"https://www.tensorflow.org/images/colab_logo_32px.png\" />Run in Google Colab</a>\n","  </td>\n","  <td>\n","    <a target=\"_blank\" href=\"https://github.com/PreferredAI/tutorials/blob/master/recommender-systems/04_implicit_feedback.ipynb\"><img src=\"https://www.tensorflow.org/images/GitHub-Mark-32px.png\" />View source on GitHub</a>\n","  </td>\n","</table>"]},{"cell_type":"markdown","metadata":{"id":"wzPrmZOMtXt1"},"source":["# Implicit Feedback\n"]},{"cell_type":"markdown","metadata":{"id":"cBBggZxMmFG3"},"source":["There are two types of feedback on which most recommender systems would be based. Explicit feedback deals with clear and quantified expression of preferences by a user, in terms of both likes and dislikes. An excellent example would be ratings. However, much more common is implicit feedback, where users provide some positive signals, but the contrast to negative signals may be absent or at least much less evident. An example would be clicks on links or views when browsing.  In this tutorial, we will focus on implicit feedback."]},{"cell_type":"markdown","metadata":{"id":"MqktDa7H2hKz"},"source":["## 1. Setup"]},{"cell_type":"code","execution_count":1,"metadata":{"id":"41oWCMUG2eC_","executionInfo":{"status":"ok","timestamp":1744700486821,"user_tz":-480,"elapsed":4147,"user":{"displayName":"Jaime Hieu Do","userId":"16382807970500480792"}}},"outputs":[],"source":["!pip install --quiet cornac==2.3.2 adjustText"]},{"cell_type":"code","execution_count":2,"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"YqKrDcGH2k7E","outputId":"b87a15f6-c7bc-4a7d-f1f1-6e19a75b4874","executionInfo":{"status":"ok","timestamp":1744700494822,"user_tz":-480,"elapsed":7990,"user":{"displayName":"Jaime Hieu Do","userId":"16382807970500480792"}}},"outputs":[{"output_type":"stream","name":"stdout","text":["System version: 3.11.12 (main, Apr  9 2025, 08:55:54) [GCC 11.4.0]\n","Cornac version: 2.3.2\n","Tensorflow version: 2.18.0\n"]}],"source":["import os\n","import sys\n","from collections import defaultdict\n","\n","import numpy as np\n","import pandas as pd\n","import seaborn as sns\n","import matplotlib.pyplot as plt\n","from adjustText import adjust_text\n","%matplotlib inline\n","\n","import cornac\n","from cornac.utils import cache\n","from cornac.datasets import movielens\n","from cornac.eval_methods import RatioSplit\n","from cornac.models import MF, BPR, WMF\n","\n","import tensorflow as tf\n","\n","print(f\"System version: {sys.version}\")\n","print(f\"Cornac version: {cornac.__version__}\")\n","print(f\"Tensorflow version: {tf.__version__}\")\n","\n","SEED = 42\n","VERBOSE = False"]},{"cell_type":"markdown","metadata":{"id":"r76coF3ZyWxb"},"source":["## 2. Weighted Matrix Factorization (WMF)\n","\n","We use the term **adoption matrix** to refer to interactions between users and items.  In the case of explicit feedback, it is the rating matrix, while in the case of implicit feedback, it can be a matrix of click counts or binary.\n","\n","Weighted matrix factorization predicts an adoption of user $i$ to item $j$ using inner product of user and item factors as $\\hat{p}_{i,j} = \\mathbf{u}_i^T \\mathbf{v}_j$.  The difference between Weighted MF and Original MF is that WMF tries to predict *unobserved* adoptions while MF ignores them during training. The convention by Cornac library is to derive observed and unobserved adoptions from the rating matrix as follows.\n","\n","\\begin{equation}\n","p_{i,j} =\n","\\begin{cases}\n","r_{i, j} &\\mbox{if } r_{i,j} > 0 \\\\\n","0 & \\mbox{otherwise}\n","\\end{cases}\n","\\end{equation}\n","\n","The important principle is that WMF usually assigns a higher confidence weight when fitting *observed* adoptions than when fitting *unobserved* adoptions. There are several ways to introduce the confidence scores.  Here we use the convention by Cornac library, which implements the following rules:\n","\n","\\begin{equation}\n","c_{i,j} =\n","\\begin{cases}\n","a &\\mbox{if } r_{i,j} > 0 \\\\\n","b & \\mbox{otherwise }\n","\\end{cases}\n","\\end{equation}\n","\n","Concretely, WMF minimizes the following loss function:\n","\n","$$ \\mathcal{L}(\\mathbf{U,V}|\\lambda) = \\frac{1}{2} \\sum_{i,j} c_{i,j} (p_{i,j} - \\mathbf{u}_i^T \\mathbf{v}_j)^2 + \\frac{\\lambda}{2} \\sum_{i=1}^{N} ||\\mathbf{u}_i||^2 + \\frac{\\lambda}{2} \\sum_{j=1}^{M} ||\\mathbf{v}_j||^2 $$\n","\n","Let's now compare how WMF and MF are different."]},{"cell_type":"code","execution_count":3,"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"p2iyzuFFs1Fq","outputId":"9aaeb880-e553-4181-b13c-85b32b470c17","executionInfo":{"status":"ok","timestamp":1744700513642,"user_tz":-480,"elapsed":18830,"user":{"displayName":"Jaime Hieu Do","userId":"16382807970500480792"}}},"outputs":[{"output_type":"stream","name":"stdout","text":["\n","TEST:\n","...\n","          |   RMSE |    AUC |  F1@10 |    MAP |    MRR | NDCG@10 | NDCG@20 | NDCG@30 | Precision@10 | Recall@10 | Train (s) | Test (s)\n","--------- + ------ + ------ + ------ + ------ + ------ + ------- + ------- + ------- + ------------ + --------- + --------- + --------\n","WMF(K=50) | 1.1012 | 0.8980 | 0.1404 | 0.1697 | 0.4586 |  0.2414 |  0.2526 |  0.2714 |       0.2022 |    0.1457 |   11.1925 |   4.1312\n","MF(K=50)  | 0.8909 | 0.6573 | 0.0454 | 0.0564 | 0.2288 |  0.1021 |  0.0942 |  0.0967 |       0.0928 |    0.0358 |    0.2022 |   2.7004\n","\n"]}],"source":["K = 50\n","wmf = WMF(k=K, max_iter=100, a=1.0, b=0.01, learning_rate=0.001, lambda_u=0.01, lambda_v=0.01,\n","          verbose=VERBOSE, seed=SEED, name=f\"WMF(K={K})\")\n","mf = MF(k=K, max_iter=20, learning_rate=0.01, lambda_reg=0.01,\n","        verbose=VERBOSE, seed=SEED, name=f\"MF(K={K})\")\n","\n","eval_metrics = [\n","  cornac.metrics.RMSE(),\n","  cornac.metrics.AUC(),\n","  cornac.metrics.Precision(k=10),\n","  cornac.metrics.Recall(k=10),\n","  cornac.metrics.FMeasure(k=10),\n","  cornac.metrics.NDCG(k=[10, 20, 30]),\n","  cornac.metrics.MRR(),\n","  cornac.metrics.MAP()\n","]\n","\n","data = movielens.load_feedback(variant=\"100K\")\n","rs = RatioSplit(data, test_size=0.2, seed=SEED, verbose=VERBOSE)\n","\n","cornac.Experiment(eval_method=rs, models=[wmf, mf], metrics=eval_metrics).run()"]},{"cell_type":"markdown","metadata":{"id":"bWO_aF1iBwI5"},"source":["As we can observe, the strength of the MF model is the ability to predict ratings well (lower RMSE). However, WMF model is designed to rank items, by fitting binary adoptions, thus it outperforms MF across all the listed ranking metrics."]},{"cell_type":"markdown","metadata":{"id":"-8iXcfuKsVa8"},"source":["## 3. Bayesian Personalized Ranking (BPR)\n","\n","Implicit feedback can also be turned into another form of expression, namely ordinal preferences.  Given an *observed* feedback $(i, j)$ between user $i$ and item $j$, another item $l$ (with *no observed interaction* with user $i$) is coupled with the pair to form a triple $(i, j, l)$.  Thus, there are now notions of *positive* and *negative* items.  The training data consists of ordinal triples $D_S = \\{(i, j, l) | r_{ij} \\in \\mathbf{R}^+ \\land r_{il} \\in \\mathbf{R}^-\\}$.\n","\n","BPR maximizes the joint probability over all triples:\n","\n","$$ \\prod_{(i,j,l) \\in D_S} p(j >_{i} l) = \\prod_{(i,j,l) \\in D_S} \\sigma(\\mathbf{u}_i^T \\mathbf{v}_j - \\mathbf{u}_i^T \\mathbf{v}_l) $$\n","\n","where $\\sigma(*)$ is the logistic *sigmoid* function and the preference scoring function is the inner product of user and item latent factors, inspired by the matrix factorization method.\n","\n","By minimizing *negative log-likelihood* with *l2-regularization*, we arrive at the following loss function:\n","\n","$$ \\mathcal{L}(\\mathbf{U,V}|\\lambda) = \\sum_{i,j,l} \\ln (1 + \\exp\\{-(\\mathbf{u}_i^T \\mathbf{v}_j - \\mathbf{u}_i^T \\mathbf{v}_l)\\}) + \\frac{\\lambda}{2} \\sum_{i=1}^{N} ||\\mathbf{u}_i||^2 + \\frac{\\lambda}{2} \\sum_{j=1}^{M} ||\\mathbf{v}_j||^2 $$\n","\n","Let's compare the two models BPR and WMF."]},{"cell_type":"code","execution_count":4,"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"NZ2Al6omrlEP","outputId":"fb032856-2748-4262-99f0-6d7952dcf6f6","executionInfo":{"status":"ok","timestamp":1744700527394,"user_tz":-480,"elapsed":13754,"user":{"displayName":"Jaime Hieu Do","userId":"16382807970500480792"}}},"outputs":[{"output_type":"stream","name":"stdout","text":["\n","TEST:\n","...\n","          |   RMSE |    AUC |  F1@10 |    MAP |    MRR | NDCG@10 | NDCG@20 | NDCG@30 | Precision@10 | Recall@10 | Train (s) | Test (s)\n","--------- + ------ + ------ + ------ + ------ + ------ + ------- + ------- + ------- + ------------ + --------- + --------- + --------\n","BPR(K=50) | 1.5631 | 0.9356 | 0.2197 | 0.2667 | 0.6320 |  0.3865 |  0.3856 |  0.4030 |       0.3236 |    0.2229 |    3.4756 |   2.0617\n","WMF(K=50) | 1.1012 | 0.8980 | 0.1404 | 0.1697 | 0.4586 |  0.2414 |  0.2526 |  0.2714 |       0.2022 |    0.1457 |    5.6794 |   2.2022\n","\n"]}],"source":["K = 50\n","bpr = BPR(k=K, max_iter=200, learning_rate=0.01, lambda_reg=0.001,\n","          verbose=VERBOSE, seed=SEED, name=f\"BPR(K={K})\")\n","wmf = WMF(k=K, max_iter=100, a=1.0, b=0.01, learning_rate=0.001, lambda_u=0.01, lambda_v=0.01,\n","          verbose=VERBOSE, seed=SEED, name=f\"WMF(K={K})\")\n","\n","rs = RatioSplit(data, test_size=0.2, seed=SEED, verbose=VERBOSE)\n","cornac.Experiment(eval_method=rs, models=[bpr, wmf], metrics=eval_metrics).run()"]},{"cell_type":"markdown","metadata":{"id":"IgDxicdzH_yD"},"source":["BPR only tries to preserve the ordinal constraints without learning to predict the rating values.  Thus, RMSE is not the right metric to evaluate BPR model.   Minimizing the loss function of BPR is analogous to maximizing AUC, therefore, we expect BPR to do well on that metric.\n","\n","Both BPR and WMF models are designed to obtain good performances in terms of ranking metrics.  With reasonable efforts for hyper-parameter tuning, we should see comparable performance between the two models.  "]},{"cell_type":"markdown","metadata":{"id":"0V4hcvmFzlUw"},"source":["## 4. Interpreting Latent Factors\n","\n","Both presented models (WMF and BPR) are based on the matrix factorization technique, let us see how the latent factors could give us some information about how items are associated with one another, as well as which items tend to be associated with a particular factor."]},{"cell_type":"code","execution_count":5,"metadata":{"id":"shUv6el6sYON","executionInfo":{"status":"ok","timestamp":1744700527395,"user_tz":-480,"elapsed":3,"user":{"displayName":"Jaime Hieu Do","userId":"16382807970500480792"}}},"outputs":[],"source":["# Download some information of MovieLens 100K dataset\n","item_df = pd.read_csv(\n","  cache(\"http://files.grouplens.org/datasets/movielens/ml-100k/u.item\"),\n","  sep=\"|\", encoding=\"ISO-8859-1\",\n","  names=[\"ItemID\", \"Title\", \"Release Date\", \"Video Release Date\", \"IMDb URL\",\n","         \"unknown\", \"Action\", \"Adventure\", \"Animation\", \"Children's\", \"Comedy\",\n","         \"Crime\", \"Documentary\", \"Drama\", \"Fantasy\", \"Film-Noir\", \"Horror\",\n","         \"Musical\", \"Mystery\", \"Romance\", \"Sci-Fi\", \"Thriller\", \"War\", \"Western\"]\n",").set_index(\"ItemID\").drop(columns=[\"Video Release Date\", \"IMDb URL\", \"unknown\"])"]},{"cell_type":"markdown","metadata":{"id":"vXcoCs33t-Zg"},"source":["### WMF Latent Factors\n","\n","Below is the variance of each latent dimension across different items.  If a factor or dimension has higher variance, it is better at discriminating among different items.  Conversely, if the variance of a factor is too small, it implies that most items would have a similar value for that factor."]},{"cell_type":"code","execution_count":6,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":552},"id":"ZPvIpzrLtIK7","outputId":"c3d00e27-51ea-435a-8c44-9d18b720a076","executionInfo":{"status":"ok","timestamp":1744700528258,"user_tz":-480,"elapsed":864,"user":{"displayName":"Jaime Hieu Do","userId":"16382807970500480792"}}},"outputs":[{"output_type":"stream","name":"stderr","text":["<ipython-input-6-1c7bf660117b>:3: FutureWarning: \n","\n","Passing `palette` without assigning `hue` is deprecated and will be removed in v0.14.0. Assign the `x` variable to `hue` and set `legend=False` for the same effect.\n","\n","  sns.barplot(x=\"Factor\", y=\"Variance\", data=var_df, palette=\"ch:.25\", ax=ax);\n"]},{"output_type":"display_data","data":{"text/plain":["<Figure size 1300x500 with 1 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\n"},"metadata":{}}],"source":["var_df = pd.DataFrame({\"Factor\": np.arange(K), \"Variance\": np.var(wmf.V, axis=0)})\n","fig, ax = plt.subplots(figsize=(13, 5))\n","sns.barplot(x=\"Factor\", y=\"Variance\", data=var_df, palette=\"ch:.25\", ax=ax);"]},{"cell_type":"code","execution_count":7,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":1000},"id":"lv07yu0Hrygu","outputId":"ae011b7d-4dc2-497d-90af-76024c951207","executionInfo":{"status":"ok","timestamp":1744700529643,"user_tz":-480,"elapsed":1385,"user":{"displayName":"Jaime Hieu Do","userId":"16382807970500480792"}}},"outputs":[{"output_type":"display_data","data":{"text/plain":["<Figure size 1100x1100 with 1 Axes>"],"image/png":"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\n"},"metadata":{}}],"source":["TOP2F = (0, 18)\n","SAMPLE_SIZE = 20\n","\n","rng = np.random.RandomState(SEED)\n","sample_inds = rng.choice(np.arange(wmf.V.shape[0]), size=SAMPLE_SIZE, replace=False)\n","sample_df = pd.DataFrame(data=wmf.V[sample_inds][:, TOP2F], columns=[\"x\", \"y\"])\n","\n","sns.lmplot(x=\"x\", y=\"y\", data=sample_df, height=11.0, fit_reg=False)\n","item_idx2id = list(wmf.train_set.item_ids)\n","titles = item_df.loc[[int(item_idx2id[i]) for i in sample_inds]][\"Title\"].values\n","adjust_text(\n","  [plt.text(*sample_df.loc[i].values, titles[i], size=10) for i in range(len(titles))]\n",");"]},{"cell_type":"markdown","metadata":{"id":"fdy0_72dTzSR"},"source":["### Interpreting Recommendations of WMF\n","\n","Let's pick a user and see what the top-K recommendations by WMF model are.  "]},{"cell_type":"code","execution_count":8,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":324},"id":"QMEDrcPLTDba","outputId":"d5dfa865-e787-453f-c566-4c778737e627","executionInfo":{"status":"ok","timestamp":1744700529658,"user_tz":-480,"elapsed":13,"user":{"displayName":"Jaime Hieu Do","userId":"16382807970500480792"}}},"outputs":[{"output_type":"stream","name":"stdout","text":["\n","TOP 5 RECOMMENDATIONS:\n","Scores: [4.5135574 4.4660473 4.317131  4.2535973 4.2024813]\n"]},{"output_type":"execute_result","data":{"text/plain":["                                   Title Release Date  Action  Adventure  \\\n","ItemID                                                                     \n","318              Schindler's List (1993)  01-Jan-1993       0          0   \n","50                      Star Wars (1977)  01-Jan-1977       1          1   \n","496         It's a Wonderful Life (1946)  01-Jan-1946       0          0   \n","64      Shawshank Redemption, The (1994)  01-Jan-1994       0          0   \n","169           Wrong Trousers, The (1993)  01-Jan-1993       0          0   \n","\n","        Animation  Children's  Comedy  Crime  Documentary  Drama  Fantasy  \\\n","ItemID                                                                      \n","318             0           0       0      0            0      1        0   \n","50              0           0       0      0            0      0        0   \n","496             0           0       0      0            0      1        0   \n","64              0           0       0      0            0      1        0   \n","169             1           0       1      0            0      0        0   \n","\n","        Film-Noir  Horror  Musical  Mystery  Romance  Sci-Fi  Thriller  War  \\\n","ItemID                                                                        \n","318             0       0        0        0        0       0         0    1   \n","50              0       0        0        0        1   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   \"std\": 0,\n        \"min\": 0,\n        \"max\": 0,\n        \"num_unique_values\": 1,\n        \"samples\": [\n          0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"}},"metadata":{},"execution_count":8}],"source":["UIDX = 0\n","TOPK = 5\n","\n","item_id2idx = wmf.train_set.iid_map\n","item_idx2id = list(wmf.train_set.item_ids)\n","\n","recommendations, scores = wmf.rank(UIDX)\n","print(f\"\\nTOP {TOPK} RECOMMENDATIONS:\")\n","print(\"Scores:\", scores[recommendations[:TOPK]])\n","item_df.loc[[int(item_idx2id[i]) for i in recommendations[:TOPK]]]"]},{"cell_type":"markdown","metadata":{"id":"zluraHjsc7x-"},"source":["The solution of alternating least squares model can be used to explain the recommendations.  Please refer to Section 5 in the [paper](http://yifanhu.net/PUB/cf.pdf) for more details.  In summary, the predicted preference of user $i$ for item $j$ is rewritten as:\n","\n","$$ \\hat{p}_{i,j} = \\sum_{l=1}^M sim_i (j, l) c_{i, l} p_{i,l} $$\n","\n","where $sim_i (j, l)$ is the similarity between item $j$ and item $l$ from user $i$’s viewpoint.\n","\n","\n","Let's try to explain why the WMF model recommends the movie **Star Wars (1977)**, *ItemID* = 50 to the user."]},{"cell_type":"code","execution_count":9,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":258},"id":"ph220lOYST3Z","outputId":"bfc6a9a1-7f20-4e96-dd42-e85733c29e9b","executionInfo":{"status":"ok","timestamp":1744700529670,"user_tz":-480,"elapsed":11,"user":{"displayName":"Jaime Hieu Do","userId":"16382807970500480792"}}},"outputs":[{"output_type":"stream","name":"stdout","text":["Recommended movie: Star Wars (1977)\n","\n","Top contributors:\n"]},{"output_type":"execute_result","data":{"text/plain":["   ItemID                        Title  Similarity  Confidence  Adoption  \\\n","0     258               Contact (1997)    0.241276         1.0       4.0   \n","1     237         Jerry Maguire (1996)    0.231643         1.0       4.0   \n","2     971          Mediterraneo (1991)    0.205749         1.0       4.0   \n","3      56          Pulp Fiction (1994)    0.140435         1.0       5.0   \n","4     690  Seven Years in Tibet (1997)    0.115898         1.0       4.0   \n","\n","   Contribution  \n","0      0.965103  \n","1      0.926570  \n","2      0.822998  \n","3      0.702177  \n","4      0.463591  "],"text/html":["\n","  <div id=\"df-5805c92d-b505-4b37-97c2-aecb6ecb055e\" class=\"colab-df-container\">\n","    <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 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\"Similarity\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.055933334781378345,\n        \"min\": 0.11589777475410037,\n        \"max\": 0.24127582218082053,\n        \"num_unique_values\": 5,\n        \"samples\": [\n          0.2316425203161422,\n          0.11589777475410037,\n          0.20574938408900306\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Confidence\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.0,\n        \"min\": 1.0,\n        \"max\": 1.0,\n        \"num_unique_values\": 1,\n        \"samples\": [\n          1.0\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Adoption\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.4472135954999579,\n        \"min\": 4.0,\n        \"max\": 5.0,\n        \"num_unique_values\": 2,\n        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pi\n","\n","print(\"\\nTop contributors:\")\n","df = defaultdict(list)\n","for idx in np.argsort(contribution)[-TOPK:][::-1]:\n","  df[\"ItemID\"].append(item_df.loc[[int(item_idx2id[idx])]].index.values[0])\n","  df[\"Title\"].append(item_df.loc[[int(item_idx2id[idx])]][\"Title\"].values[0])\n","  df[\"Similarity\"].append(sim[idx])\n","  df[\"Confidence\"].append(ci[idx])\n","  df[\"Adoption\"].append(pi[idx])\n","  df[\"Contribution\"].append(contribution[idx])\n","pd.DataFrame.from_dict(df)"]},{"cell_type":"markdown","metadata":{"id":"i-Mp8q_Ut_mP"},"source":["### BPR Latent Factors\n","\n","Below is the variance of each latent dimension."]},{"cell_type":"code","execution_count":10,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":465},"id":"WC7PRQVxthL_","outputId":"497015f2-6e87-47fd-92e7-d511eafa7a01","executionInfo":{"status":"ok","timestamp":1744700530297,"user_tz":-480,"elapsed":627,"user":{"displayName":"Jaime Hieu Do","userId":"16382807970500480792"}}},"outputs":[{"output_type":"display_data","data":{"text/plain":["<Figure size 1300x500 with 1 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\n"},"metadata":{}}],"source":["var_df = pd.DataFrame({\"Factor\": np.arange(K), \"Variance\": np.var(bpr.i_factors, axis=0)})\n","fig, ax = plt.subplots(figsize=(13, 5))\n","sns.barplot(x=\"Factor\", y=\"Variance\", data=var_df, palette=\"ch:.25\", ax=ax, hue=\"Factor\", legend=False);"]},{"cell_type":"code","execution_count":11,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":1000},"id":"NnnDUUcjMQbx","outputId":"d5a9d071-5e84-4102-907c-7934d48771a6","executionInfo":{"status":"ok","timestamp":1744700530701,"user_tz":-480,"elapsed":403,"user":{"displayName":"Jaime Hieu Do","userId":"16382807970500480792"}}},"outputs":[{"output_type":"display_data","data":{"text/plain":["<Figure size 1100x1100 with 1 Axes>"],"image/png":"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AAMAmEIIAAAAAAACbQAgCAAAAAABsAiEIAAAAAACwCYQgAAAAAADAJhCCAAAAAAAAm0AIAgAAAAAAbAIhCAAAAAAAsAmPXAgyZcoUFS9eXC4uLqpWrZq2bduWo/PmzZsnk8mkZs2aPdgCAQAAAADAv9IjFYLMnz9fvXv31tChQ7Vr1y6VL19e0dHROnfuXLbnnThxQn379tVTTz31kCoFAAAAAAD/No9UCDJhwgS9+uqr6tSpk0qXLq1p06bJzc1NX3/9dZbnmM1mtWvXTu+//75KlCjxEKsFAAAAAAD/Jo9MCJKamqqdO3eqfv36ljY7OzvVr19fW7ZsyfK84cOHy9/fX507d87RPCkpKUpMTLT6AAAAAACAR98jE4KcP39eZrNZBQsWtGovWLCgzpw5k+k5Gzdu1PTp0/Xll1/meJ4PP/xQ3t7elk+RIkXuqW4AAAAAAPDv8MiEILl1+fJltW/fXl9++aV8fX1zfN7AgQOVkJBg+fz5558PsEoAAAAAAPCwOOR1ATnl6+sre3t7nT171qr97NmzCggIyNA/NjZWJ06cUNOmTS1t6enpkiQHBwcdPnxYwcHBGc5zdnaWs7Pzfa4eAAAAAADktUdmJYiTk5MqVaqk1atXW9rS09O1evVq1ahRI0P/UqVKad++fYqJibF8nnvuOdWtW1cxMTE85gIAAAAAuK86duyoZs2aZdunTp066tmz50Op514dPnxYAQEBunz5cl6XksH58+fl7++vv/76K1fnPTIhiCT17t1bX375pWbNmqVDhw6pW7duunLlijp16iRJ6tChgwYOHChJcnFxUdmyZa0+Pj4+8vT0VNmyZeXk5JSXlwIAAAAAuI/OnDmjt956SyVKlJCzs7OKFCmipk2bWv1DOnJn4MCBeuutt+Tp6SlJunbtmjp27KiIiAg5ODhkGfhMmTJF4eHhcnV1VVhYmGbPnp3lHPPmzZPJZLIaKy0tTf3791dERITc3d0VFBSkDh066PTp05Y+vr6+6tChg4YOHZqra3pkHoeRpNatW+uff/7RkCFDdObMGVWoUEErV660bJZ66tQp2dk9UrkOAAAAAOAenThxQjVr1pSPj4/Gjh2riIgIpaWl6aefftKbb76p33//Pa9LfOScOnVKy5Yt06effmppM5vNcnV11dtvv62FCxdmet7UqVM1cOBAffnll6pSpYq2bdumV199Vfny5bParkK68X3r27evnnrqKav25ORk7dq1S4MHD1b58uV18eJF9ejRQ88995x27Nhh6depUydVqlRJY8eOVf78+XN0XY9cYtC9e3edPHlSKSkp2rp1q6pVq2Y5tm7dOs2cOTPLc2fOnKnvv//+wRcJAAAAAHho3njjDZlMJm3btk0tWrRQaGioypQpo969e+u3336z9JswYYJldUGRIkX0xhtvKCkpyXL85MmTatq0qfLlyyd3d3eVKVNGK1askHQjAOjcubOeeOIJywqHSZMmZVrP+++/Lz8/P3l5ealr165KTU3NsvZvvvlGlStXlqenpwICAtS2bVudO3fOcnzdunUymUxavXq1KleuLDc3N0VFRenw4cNW4/zwww+qUqWKXFxc5Ovrq+bNm+d4jsx8++23Kl++vAoVKmRpc3d319SpU/Xqq69mujfnzblef/11tW7dWiVKlFCbNm302muvacyYMVb9zGaz2rVrp/fff18lSpSwOubt7a1Vq1apVatWCgsLU/Xq1TV58mTt3LlTp06dsvQrU6aMgoKCtHjx4myv5VaPXAgCAAAAAMBN8fHxWrlypd588025u7tnOO7j42P5s52dnT755BMdOHBAs2bN0po1a/TOO+9Yjr/55ptKSUnRr7/+qn379mnMmDHy8PCQdGNPysKFC2vBggU6ePCghgwZonfffVfffvut1XyrV6/WoUOHtG7dOs2dO1eLFi3S+++/n2X9aWlpGjFihPbs2aPvv/9eJ06cUMeOHTP0GzRokMaPH68dO3bIwcFBr7zyiuXY8uXL1bx5czVu3Fi7d+/W6tWrVbVq1VzPcasNGzaocuXK2fbJTEpKilxcXKzaXF1dtW3bNqWlpVnahg8fLn9/f3Xu3DlH4yYkJMhkMll9PyWpatWq2rBhQ47re6QehwEAAAAA4FZHjx6VYRgqVarUHfveuiFp8eLF9cEHH6hr16767LPPJN14BKRFixaKiIiQJKsVCo6OjlZhxhNPPKEtW7bo22+/VatWrSztTk5O+vrrr+Xm5qYyZcpo+PDh6tevn0aMGJHp9g23hhklSpTQJ598oipVqigpKckSwEjSyJEjVbt2bUnSgAED1KRJE127dk0uLi4aOXKk2rRpY1Vf+fLlcz3HrU6ePHlXIUh0dLS++uorNWvWTBUrVtTOnTv11VdfKS0tTefPn1dgYKA2btyo6dOnKyYmJkdjXrt2Tf3799eLL74oLy8vq2NBQUHavXt3jutjJQgAAAAA4JFlGEaO+/7yyy+qV6+eChUqJE9PT7Vv314XLlxQcnKyJOntt9/WBx98oJo1a2ro0KHau3ev1flTpkxRpUqV5OfnJw8PD33xxRdWj2dIN8IHNzc3y9c1atRQUlKS/vzzz0xr2rlzp5o2baqiRYvK09PTEnTcPm65cuUsfw4MDJQkyyMtMTExqlevXpbXndM5bnX16tUMKzpyYvDgwXrmmWdUvXp1OTo66vnnn9fLL78s6cZKnMuXL6t9+/b68ssv5evre8fx0tLS1KpVKxmGoalTp2Y47urqavn+5QQhCAAAAADgkVWyZEmZTKY7bn564sQJPfvssypXrpwWLlyonTt3asqUKZJk2bOjS5cuOnbsmNq3b699+/apcuXKlo1B582bp759+6pz5876+eefFRMTo06dOmW738edXLlyRdHR0fLy8tKcOXO0fft2y/4Wt4/r6Oho+bPJZJJ04xEd6UYQcD/muJWvr68uXryY62tydXXV119/reTkZJ04cUKnTp1S8eLF5enpKT8/P8XGxurEiRNq2rSpHBwc5ODgoNmzZ2vp0qVycHBQbGysZaybAcjJkye1atWqDKtApBuPQ/n5+eW4PkIQAAAAAMAjK3/+/IqOjtaUKVN05cqVDMcvXbok6cZqiPT0dI0fP17Vq1dXaGio1StXbypSpIi6du2qRYsWqU+fPvryyy8lSZs2bVJUVJTeeOMNRUZGKiQkxOoX9pv27Nmjq1evWr7+7bff5OHhoSJFimTo+/vvv+vChQsaPXq0nnrqKZUqVeqOG5Zmply5clm+Cvhu54iMjNTBgwdzXctNjo6OKly4sOzt7TVv3jw9++yzsrOzU6lSpbRv3z7FxMRYPs8995zq1q2rmJgYy326GYD88ccf+uWXX1SgQIFM59m/f78iIyNzXBchCAAAAADgkTZlyhSZzWZVrVpVCxcu1B9//KFDhw7pk08+UY0aNSRJISEhSktL06effqpjx47pm2++0bRp06zG6dmzp3766ScdP35cu3bt0tq1axUeHi7pxoqTHTt26KefftKRI0c0ePBgbd++PUMtqamp6ty5sw4ePKgVK1Zo6NCh6t69e6b7gRQtWlROTk6WmpYuXaoRI0bk+vqHDh2quXPnaujQoTp06JBlU9d7mSM6OlpbtmyR2Wy2aj948KBiYmIUHx+vhIQES5Bx05EjR/Tf//5Xf/zxh7Zt26Y2bdpo//79GjVqlCTJxcVFZcuWtfr4+PjI09NTZcuWlZOTk9LS0vTCCy9ox44dmjNnjsxms86cOaMzZ85YrV5JTk7Wzp071bBhwxzfK0IQAAAAAMAjrUSJEtq1a5fq1q2rPn36qGzZsmrQoIFWr15t2UeifPnymjBhgsaMGaOyZctqzpw5+vDDD63GMZvNevPNNxUeHq5GjRopNDTUsmnq66+/rv/85z9q3bq1qlWrpgsXLuiNN97IUEu9evVUsmRJ1apVS61bt9Zzzz2nYcOGZVq3n5+fZs6cqQULFqh06dIaPXq0xo0bl+vrr1OnjhYsWKClS5eqQoUKevrpp7Vt27Zcz5GebmjfXwlaf+QfFY6IkoODg3755RerPo0bN1ZkZKR++OEHrVu3TpGRkVYrMcxms8aPH6/y5curQYMGunbtmjZv3qzixYvn+Hr+/vtvLV26VH/99ZcqVKigwMBAy2fz5s2WfkuWLFHRokX11FNP5Xhsk5GbXWRsUGJiory9vZWQkJDp80cAAAAAADzqNh89r6nrYxV7LklpZkOO9iZd379SplM7tHXD2rwuL1PVq1fX22+/rbZt2+b4HFaCAAAAAABgwzYfPa93F+/TobhEuTs7yN/TWe7ODjKH1tc59xJaFXMir0vM4Pz58/rPf/6jF198MVfnsRLkDlgJAgAAAAB4XKWnG3p5xjYdiktUgJeL5c0z0o3XD59JTFF4oKdmdaoqOztTNiM9GlgJAgAAAACAjTpwOlGx55KUz83JKgCRbryK18fNUbHnknTgdGIeVXh/EYIAAAAAAGCj4pNTlWY25GSfeTzgbG+ntHRD8cmpmR5/1BCCAAAAAABgo/K7OcnR3qRUc3qmx1PM6XK0Mym/m9NDruzBIAQBAAAAAMBGlQnyUrC/hy4mp+n2LUMNw9Cl5DQF+3uoTNDjsUcmIQgAAAAAADbKzs6kbrWD5eFsrzOJKbqaZlZ6uqGraWadSUyRh7O9utUOfiw2RZUIQQAAAAAAsGlRIb4a1TxC4YGeSk65rnNJKUpOua7wQE+Nah6hqBDfvC7xvuEVuXfAK3IBAAAAALYgPd3QgdOJik9OVX43J5UJ8npsVoDc5JDXBQAAAAAAgLxnZ2dSRGHvvC7jgeJxGAAAAAAAYBMIQQAAAAAAgE0gBAEAAAAAADaBEAQAAAAAANgEQhAAAAAAAGATCEEAAAAAAIBNIAQBAAAAAAA2gRAEAAAAAADYBEIQAAAAAABgEwhBAAAAAACATSAEAQAAAAAANoEQBAAAAAAA2ARCEAAAAAAAYBMIQQAAAAAAgE0gBAEAAAAAADaBEAQAAAAAANgEQhAAAAAAAGATCEEAAAAAAIBNIAQBAAAAAAA2gRAEAAAAAADYBEIQAAAAAABgEwhBAACPrJkzZ8rHxyfP5k9NTVVISIg2b96cZzVkp02bNho/fnxelwEAAPCvQQgCAMiVjh07ymQyyWQyydHRUQULFlSDBg309ddfKz09/aHW0rp1ax05cuShznmradOm6YknnlBUVJSlbeTIkYqKipKbm1uWAc3q1asVFRUlT09PBQQEqH///rp+/bpVn2+//VYVKlSQm5ubihUrprFjx1odv/X7cOunTJkylj7vvfeeRo4cqYSEhPt30QAAAI8wQhAAQK41atRIcXFxOnHihH788UfVrVtXPXr00LPPPpvhl/kHydXVVf7+/g90jtTU1EzbDcPQ5MmT1blz5wz9W7ZsqW7dumV63p49e9S4cWM1atRIu3fv1vz587V06VINGDDA0ufHH39Uu3bt1LVrV+3fv1+fffaZPv74Y02ePNnSZ9KkSYqLi7N8/vzzT+XPn18tW7a09ClbtqyCg4P13//+915uAQAAwGODEAQAkGvOzs4KCAhQoUKFVLFiRb377rtasmSJfvzxR82cOdPS79KlS+rSpYv8/Pzk5eWlp59+Wnv27LEa64cfflCVKlXk4uIiX19fNW/e3HIsJSVFffv2VaFCheTu7q5q1app3bp1luO3Pg5z5MgRmUwm/f7771bjf/zxxwoODrZ8vX//fj3zzDPy8PBQwYIF1b59e50/f95yvE6dOurevbt69uwpX19fRUdHZ3oPdu7cqdjYWDVp0sSq/f3331evXr0UERGR6Xnz589XuXLlNGTIEIWEhKh27dr66KOPNGXKFF2+fFmS9M0336hZs2bq2rWrSpQooSZNmmjgwIEaM2aMDMOQJHl7eysgIMDy2bFjhy5evKhOnTpZzde0aVPNmzcv01oAAABsDSEIAOC+ePrpp1W+fHktWrTI0tayZUudO3dOP/74o3bu3KmKFSuqXr16io+PlyQtX75czZs3V+PGjbV7926tXr1aVatWtZzfvXt3bdmyRfPmzdPevXvVsmVLNWrUSH/88UeG+UNDQ1W5cmXNmTPHqn3OnDlq27atpBuhzNNPP63IyEjt2LFDK1eu1NmzZ9WqVSurc2bNmiUnJydt2rRJ06ZNy/R6N2zYoNDQUHl6eubqPqWkpMjFxcWqzdXVVdeuXdPOnTuz7fPXX3/p5MmTmY47ffp01a9fX8WKFbNqr1q1qrZt26aUlJRc1QkAAPA4IgQBANw3pUqV0okTJyRJGzdu1LZt27RgwQJVrlxZJUuW1Lhx4+Tj46PvvvtO0o39M9q0aaP3339f4eHhKl++vAYOHChJOnXqlGbMmKEFCxboqaeeUnBwsPr27asnn3xSM2bMyHT+du3aae7cuZavjxw5op07d6pdu3aSpMmTJysyMlKjRo1SqVKlFBkZqa+//lpr16612lukZMmS+uijjxQWFqawsLBM5zp58qSCgoJyfY+io6O1efNmzZ07V2azWX///beGDx8uSYqLi7P0WbRokVavXq309HQdOXLEssHpzT63On36tH788Ud16dIlw7GgoCClpqbqzJkzua4VAADgcUMIAgC4bwzDkMlkknRj74ukpCQVKFBAHh4els/x48cVGxsrSYqJiVG9evUyHWvfvn0ym80KDQ21On/9+vWW82/Xpk0bnThxQr/99pukG6tAKlasqFKlSllqWrt2rdV4N4/dOmalSpXueK1Xr17NsFojJxo2bKixY8eqa9eucnZ2VmhoqBo3bixJsrO78X/Lr776/9i787ga0/9/4K9z2veiqIgokSaUbDUJEyUMBmP7WLKbsa8xdmNnFsNYhqkY+9ga2wx91CQ+spWksUTWElPKKdrO9fvDr/vraFFEOK/n43EeD+e+r/u63tfp5HTe97UMxahRo9CxY0doa2ujefPm6NWrl0qZFwUHB8PU1BRdunQpdE5PTw8AkJWVVeZYiYiIiD42mhUdABERfTzi4+NRq1YtAIBCoYCVlZXKGh4FCtbxKPiCXhSFQgENDQ2cO3cOGhoaKucMDQ2LvMbS0hJt2rTB1q1b0bx5c2zdulVlgVKFQoFOnTphyZIlha61srKS/m1gYFBsXAXMzc0RGxv7ynJFmTBhAsaPH4+kpCSYmZkhMTER06ZNQ+3atQEAMpkMS5YswcKFC5GcnAwLCwuEhoYCgFSmgBACv/76K/r16wdtbe1CbRVMPbKwsHitWImIiIg+JkyCEBFRufjvf/+L2NhYjB8/HgDg6uqK5ORkaGpqwtbWtshrGjRogNDQ0EKLeQKAi4sL8vPzkZKSAk9Pz1LH0bdvX0yZMgW9e/fGjRs3pBEUBTHt3r0btra20NR8s49AFxcXrFmzRmX0S1nIZDJpOs22bdtgY2MDV1dXlTIaGhqoVq2aVKZFixaFkhnh4eG4fv16oV1qCly6dAnVq1eHubl5mWMkIiIi+thwOgwREZVZdnY2kpOTce/ePZw/fx4LFy5E586d0bFjR/Tv3x8A4O3tjRYtWqBLly7466+/kJiYiJMnT+Kbb77B2bNnAQCzZ8/Gtm3bMHv2bMTHxyM2NlYapeHg4IC+ffuif//+2LNnD27evImoqCgsWrQIBw8eLDa2L774Ak+ePMHIkSPRunVrlXU7vv76a6SmpqJ37944c+YMEhIS8Oeff8Lf3x/5+flleg1at24NhUKBuLg4leO3b99GdHQ0bt++jfz8fERHRyM6OhoKhUIqs2zZMsTGxiIuLg7z58/H4sWLsXLlSmnEy6NHj7B27Vr8888/iI6OxtixY7Fr1y788MMPheLYuHEjmjVrhk8++aTIOCMiItCuXbsy9Y2IiIjoY8UkCBERlYpSKRB7Nx3JGc9w5MgRWFlZwdbWFr6+vjh+/DhWrlyJ/fv3S1/kZTIZDh06hJYtW8Lf3x8ODg7o1asXbt26hapVqwJ4vh3trl27EBISgkaNGqFNmzaIioqS2gwMDET//v0xceJE1K1bF126dMGZM2dQo0aNYuM0MjJCp06dEBMTIy2IWsDa2hqRkZHIz89Hu3bt4OzsjHHjxsHU1LTItTZKUrlyZXTt2rXQbjSzZs2Ci4sLZs+eDYVCARcXF2k3mgKHDx+Gp6cn3NzccPDgQezfv7/Qeh7BwcFwc3ODh4cH4uLiEBYWprJzDgCkp6dj9+7dxY4CefbsGfbt24ehQ4eWqW9EREREHyuZEEJUdBDvs4yMDJiYmCA9PR3GxsYVHQ4RUYU4ef0R1oQnICFFgdx8AS0NGeyqGGKklx3c7dV3msXFixfRtm1bJCQkFLtOSUVas2YN9u7di7/++quiQyEiIiJ6L3AkCBERlejk9UeYvjcW8UkZMNDRRBUjHRjoaCI+6Qmm743FyeuPKjrECtOgQQMsWbIEN2/erOhQiqSlpYWffvqposMgIiIiem9wJMgrcCQIEakzpVJgQGAU4pMyYGmsq7IAqBACyRnZcLQyQrB/U8jlZV8clIiIiIjoXeJIECIiKlbc/QwkpChgpq9daAcUmUwGU30tJKQoEHc/o4IiJCIiIiIqPSZBiIioWKlZOcjNF9DWKPrjQkdDjlylQGpWzjuOjIiIiIio7JgEISKiYlXS14aWhgw5+coiz2fnK6Ell6GSvvY7joyIiIiIqOyYBCEiomI5WRvDrooh0rJy8fISUkIIPM7KhV0VQzhZc80kIiIiInr/MQlCRETFkstlGOllB0MdDSRnZONpbj6USoGnuflIzsiGoY4GRnrZcVFUIiIiIvogMAlCREQlcrc3x8KuznC0MkJWdh5SFNnIys6Do5URFnZ1hru9eUWHSERERERUKtwi9xW4RS4R0XNKpUDc/QykZuWgkr42nKyNOQKEiIiIiD4omhUdABERfRjkchmcq5tUdBhERERERK+N02GIiIiIiIiISC0wCUJEREREREREaoFJECIiIiIiIiJSC0yCEBEREREREZFaYBKEiIiIiIiIiNQCkyBEREREREREpBaYBCEiIiIiIiIitcAkCBERERERERGpBSZBiIiIiIiIiEgtMAlCRERERERERGqBSRAiIiIiIiIiUgtMghARERERERGRWmAShIiIiIiIiIjUApMgRERERERERKQWmAQhIiIiIiIiIrXAJAgRERERERERqQUmQYiIiIiIiIhILTAJQkRERERERERqgUkQIiIiIiIiIlILTIIQERERERERkVpgEoSIiIiIiIiI1AKTIERERERERESkFpgEISIiIiIiIiK1wCQIEREREREREakFJkGIiIiIiIiISC0wCUJEREREREREaoFJECIiIiIiIiJSC0yCEBEREREREZFaYBKEiIiIiIiIiNQCkyBEREREREREpBaYBCEiIiIiIiIitcAkCBERERERERGpBSZBiIiIiIiIiEgtMAlCRERERERERGqBSRAiIiIiIiIiUgtMghARERERERGRWmAShIiIiIiIiIjUApMgRERERERERKQWmAQhIiIiIiIiIrXAJAgRERERERERqQUmQYiIiIiIiIhILTAJQkRERERERERqgUkQIiIiIiIiIlILZU6CDBgwAH///ffbiIWIiIiIiIiI6K0pcxIkPT0d3t7eqFOnDhYuXIh79+69jbiIiIiIiIiIiMpVmZMg+/btw7179zBy5Ejs2LEDtra2aN++PX7//Xfk5ua+jRiJiIiIiIiIiN7Ya60JYmFhgQkTJiAmJganT5+Gvb09+vXrB2tra4wfPx7Xrl0r7ziJiIiIiIiIiN7IGy2MmpSUhKNHj+Lo0aPQ0NCAn58fYmNjUb9+fXz//fflFSMRERERERER0RsrcxIkNzcXu3fvRseOHVGzZk3s2rUL48aNw/379xEcHIxjx45h586dmDdv3tuIF6tXr4atrS10dXXRrFkzREVFFVv2l19+gaenJ8zMzGBmZgZvb+8SyxMRERERERHRx6vMSRArKysMHToUNWvWRFRUFM6ePYsRI0bA2NhYKtO6dWuYmpqWZ5wAgB07dmDChAmYPXs2zp8/j4YNG8LHxwcpKSlFlg8LC0Pv3r1x/PhxnDp1CjY2NmjXrh0XcyUiIiIiIiJSQzIhhCjLBZs3b0aPHj2gq6v7tmIqVrNmzdCkSROsWrUKAKBUKmFjY4PRo0cjICDgldfn5+fDzMwMq1atQv/+/UvVZkZGBkxMTJCenq6S6CEiIiIiIiKiD0uZR4L069evQhIgOTk5OHfuHLy9vaVjcrkc3t7eOHXqVKnqyMrKQm5uLipVqlRsmezsbGRkZKg8iIiIiIiIiOjD90YLo75Ljx49Qn5+PqpWrapyvGrVqkhOTi5VHVOnToW1tbVKIuVlixYtgomJifSwsbF5o7iJiIiIiIiI6P3wwSRB3tTixYuxfft27N27t8SRLNOmTUN6err0uHPnzjuMkoiIiIiIiIjeFs2KDqC0zM3NoaGhgQcPHqgcf/DgASwtLUu8dvny5Vi8eDGOHTuGBg0alFhWR0cHOjo6bxwvEREREREREb1fPpiRINra2mjcuDFCQ0OlY0qlEqGhoWjRokWx1y1duhTz58/HkSNH4Obm9i5CJSIiIiIiIqL30AczEgQAJkyYgAEDBsDNzQ1NmzbFDz/8gMzMTPj7+wMA+vfvj2rVqmHRokUAgCVLlmDWrFnYunUrbG1tpbVDDA0NYWhoWGH9ICIiIiIiIqJ374MZCQIAPXv2xPLlyzFr1iw0atQI0dHROHLkiLRY6u3bt5GUlCSVX7NmDXJyctC9e3dYWVlJj+XLl1dUF4iIiIiIyl1YWBhkMhkeP34MAAgKCoKpqal0fs6cOWjUqJH0fODAgejSpcs7jbG0Xo71dSQmJkImkyE6OrpcYiIqSqtWrTBu3Li3WqetrS1++OGHcm2jQE5ODuzt7XHy5Mm3Uv+bCggIwOjRo8u93g8qCQIAo0aNwq1bt5CdnY3Tp0+jWbNm0rmwsDAEBQVJzxMTEyGEKPSYM2fOuw+ciIiIiOgV1q5dCyMjI+Tl5UnHFAoFtLS00KpVK5WyBYmPhIQEuLu7IykpCSYmJqVq58cff1T5u/ld2rt3L5o3bw4TExMYGRnBycmp3L9IqrtWrVq99s83KCgIMpkMMpkMcrkcVlZW6NmzJ27fvl2+QaqBl5ORr+PMmTMYNmxYqcuXJYm4du1a1KpVC+7u7tKxBQsWwN3dHfr6+sXGHhoaCnd3dxgZGcHS0hJTp05V+T8LAHbu3IlGjRpBX18fNWvWxLJlywrVk52djW+++QY1a9aEjo4ObG1t8euvv0rnJ02ahODgYNy4caNU/SmtDy4JQkREROXv5bvI9H/e5mujrnfhqHitW7eGQqHA2bNnpWMRERGwtLTE6dOn8ezZM+n48ePHUaNGDdjZ2UFbWxuWlpaQyWSlasfExOSNv5y9jtDQUPTs2RPdunVDVFQUzp07hwULFiA3N/edx/IhysnJeSftGBsbIykpCffu3cPu3btx5coV9OjR4520TaosLCygr69f7vUKIbBq1SoMHjxY5XhOTg569OiBkSNHFnldTEwM/Pz84OvriwsXLmDHjh0ICQlBQECAVObw4cPo27cvRowYgUuXLuHnn3/G999/j1WrVqnU9eWXXyI0NBQbN27ElStXsG3bNtStW1c6b25uDh8fH6xZs6Yce84kCBER0Xtj4MCB0t03mUyGypUrw9fXFxcvXixTPeVx5+lta9WqlUpfq1atih49euDWrVvvNI4XYyjq8bZHj1b0XbgtW7agYcOG0NfXh5WVFQYNGoR///1XOv+27sJR8erWrQsrKyuEhYVJx8LCwtC5c2fUqlUL//vf/1SOt27dWvp3WZJ1L0+HOXLkCD799FOYmpqicuXK6NixIxISEqTzBdNLdu7cCU9PT+jp6aFJkya4evUqzpw5Azc3NxgaGqJ9+/Z4+PBhse3+8ccf8PDwwOTJk1G3bl04ODigS5cuWL16daGymzdvhq2tLUxMTNCrVy88efKk1PG+LD8/H4MGDUK9evWkEQ379++Hq6srdHV1Ubt2bcydO1f6PSoYPV6jRg3o6OjA2toaY8aMkeqztbXF/Pnz0bt3bxgYGKBatWqF+vD48WMMGTIEFhYWMDY2Rps2bRATEyOdT0hIQOfOnVG1alUYGhqiSZMmOHbsmEodBe30798fxsbG0oiAEydOSD8HGxsbjBkzBpmZmUX2/VV9KYpMJoOlpSWsrKzg7u6OwYMHIyoqChkZGVKZNWvWSAm4unXrYvPmzYXqWLduHTp27Ah9fX04Ojri1KlTuH79Olq1agUDAwO4u7sX+rmV9HMBni+B0LlzZxgaGsLY2BhffvlloR1EXzZ16lQ4ODhAX18ftWvXxsyZM1USbwWjJ0p6z2VmZqJ///4wNDSElZUVVqxYUWKbRSlqGtq4ceMKjfJ60cvTYUp6XwUFBWHu3LmIiYmRPseKGxF07tw5JCQkoEOHDirH586di/Hjx8PZ2bnI63bs2IEGDRpg1qxZsLe3h5eXF5YuXYrVq1dLr9fmzZvRpUsXjBgxArVr10aHDh0wbdo0LFmyBEIIAM9/h8PDw3Ho0CF4e3vD1tYWLVq0gIeHh0p7nTp1wvbt24t9fV4HkyBERETvEV9fXyQlJSEpKQmhoaHQ1NREx44dKzqs11bS3d2hQ4ciKSkJ9+/fx/79+3Hnzh385z//eYfRQXqtk5KS8MMPP0h3PwsekyZNemttV/RduMjISPTv3x+DBw9GXFwcdu3ahaioKAwdOlQq87buwlHJWrdujePHj0vPjx8/jlatWsHLy0s6/vTpU5w+fVpKgrypzMxMTJgwAWfPnkVoaCjkcjm6du0KpVKpUm727NmYMWMGzp8/D01NTfTp0wdTpkzBjz/+iIiICFy/fh2zZs0qth1LS0vExcXh0qVLJcaTkJCAffv24cCBAzhw4ADCw8OxePHiMscLPB9y36NHD0RHRyMiIgI1atRAREQE+vfvj7Fjx+Ly5ctYt24dgoKCsGDBAgDA7t278f3332PdunW4du0a9u3bV+hL4bJly9CwYUNcuHABAQEBGDt2LI4ePSqd79GjB1JSUnD48GGcO3cOrq6u+Oyzz5Camgrg+TQnPz8/hIaG4sKFC/D19UWnTp0KTTtZvny51M7MmTORkJAAX19fdOvWDRcvXsSOHTtw4sQJjBo1qsjXsjR9KUlKSgr27t0LDQ0NaGhoAHg+pWns2LGYOHEiLl26hOHDh8Pf31/lfQtASuBER0ejXr166NOnD4YPH45p06bh7NmzEEKoxP2qn4tSqUTnzp2RmpqK8PBwHD16FDdu3EDPnj1L7IORkRGCgoJw+fJl/Pjjj/jll1/w/fffq5R51Xtu8uTJCA8Px/79+/HXX38hLCwM58+fL/XrWF5Kel/17NkTEydOhJOTk/Q5VtxrExERAQcHBxgZGZWp/ezsbOjq6qoc09PTw7Nnz3Du3LkSy9y9e1e62RESEgI3NzcsXboU1apVg4ODAyZNmoSnT5+qXNe0aVPcvXsXiYmJZYqzRIJKlJ6eLgCI9PT0ig6FiIg+cgMGDBCdO3dWORYRESEAiJSUFCGEEMePHxcARFpamlTmwoULAoC4efOmdP7Fx+zZs4UQQjx79kxMmTJFVK9eXWhraws7OzuxYcMGlXqPHTsmGjduLPT09ESLFi3EP//8oxLPvn37hIuLi9DR0RG1atUSc+bMEbm5udJ5AOLnn38WnTp1Evr6+lLbL/Py8hJjx45VObZ582ahr6+vciwsLEw0adJEaGtrC0tLSzF16lSpveDgYFGpUiXx7NkzlWs6d+4s/vOf/xT7OhcnMDBQmJiYFDpeXq/Ny86cOSPkcrnIyMgoUzzTpk0Tbm5uKsdCQkKErq6uVFfv3r1F9+7dVcqsXLlSVK9eXSiVSiGEEMuWLRO1a9cuVKZatWoqx4KDg0X16tWL7QeVv19++UUYGBiI3NxckZGRITQ1NUVKSorYunWraNmypRBCiNDQUAFA3Lp1SwhR+P+Gl98/s2fPFg0bNpSeF/X/zYsePnwoAIjY2FghhBA3b94UAKT/M4QQYtu2bQKACA0NlY4tWrRI1K1bt9h6FQqF8PPzEwBEzZo1Rc+ePcXGjRtVfo9nz54t9PX1VX43Jk+eLJo1a1bmeCMiIsRnn30mPv30U/H48WOp/GeffSYWLlyoUsfmzZuFlZWVEEKIFStWCAcHB5GTk1NkezVr1hS+vr4qx3r27Cnat28vhHj+f7exsXGh/5/s7OzEunXriu2Hk5OT+Omnn1Ta6dKli0qZwYMHi2HDhqkci4iIEHK5XDx9+rRQna/qy8sCAwMFAGFgYCD09fWlz5IxY8ZIZdzd3cXQoUNVruvRo4fw8/OTngMQM2bMkJ6fOnVKABAbN26Ujm3btk3o6upKz1/1c/nrr7+EhoaGuH37tnQ+Li5OABBRUVGl6p8Qz///a9y4sfT8Ve+5J0+eCG1tbbFz507p/L///iv09PQKfZa96OXfw6J+78aOHSu8vLyk5y9/PtasWVN8//33QojSva9e/l0vztixY0WbNm1KHXuBP//8U8jlcrF161aRl5cn7t69Kzw9PQUAsXXrViGEEOvWrRP6+vri2LFjIj8/X1y5ckXUq1dPABAnT54UQgjh4+MjdHR0RIcOHcTp06fFwYMHRc2aNcXAgQNV2iv4Ph4WFvbKPpUWR4IQERG9pxQKBX777TfY29ujcuXKpbrG3d290IiGgtEM/fv3x7Zt27By5UrEx8dj3bp1hbaM/+abb7BixQqcPXsWmpqaGDRokHTuVXfoCsyZMwddu3ZFbGysyvUlSU1Nxc6dO1UWPL937x78/PzQpEkTxMTEYM2aNdi4cSO+/fZbAM/vhuXn5yMkJES6JiUlBQcPHix1u2VRHq/Niyr6LlyLFi1w584dHDp0CEIIPHjwAL///jv8/PxUrnsrd+GoRK1atUJmZibOnDkjvU8sLCzg5eUlrQsSFhaG2rVro0aNGuXS5rVr19C7d2/Url0bxsbGsLW1BYBCoxIaNGgg/btgh8YXRxVUrVoVKSkpxbZjYGCAgwcP4vr165gxYwYMDQ0xceJENG3aFFlZWVI5W1tbld8NKysrlXpLG2/v3r2RmZmJv/76S2XR2JiYGMybNw+GhobSo2B0WlZWFnr06IGnT5+idu3aGDp0KPbu3VtoylmLFi0KPY+Pj5fqVygUqFy5skobN2/elKZ/KBQKTJo0CY6OjjA1NYWhoSHi4+ML9cHNzU3leUxMDIKCglTq9fHxgVKpxM2bNwu95qXpy8uMjIwQHR2Ns2fPYsWKFXB1dVX5/yw+Pr7QtAUPDw+p/wVK83559uyZNM3mVT+X+Ph42NjYwMbGRqqjfv36MDU1LdT2i3bs2AEPDw9YWlrC0NAQM2bMKPQ6l/SeS0hIQE5OjspnVKVKlVTWr3gXSvO+Kq2nT58W+pwojXbt2mHZsmUYMWIEdHR04ODgIH1uyOXP0wtDhw7FqFGj0LFjR2hra6N58+bo1auXShmlUgmZTIYtW7agadOm8PPzw3fffYfg4GCV0SB6enoAoPL/w5vSLLeaiIiI6I0dOHBASkxkZmbCysoKBw4ckP5oeBVtbW2YmJhI87kLXL16FTt37sTRo0fh7e0NAKhdu3ah6xcsWAAvLy8AzxfF7NChA549ewZdXV3MnTsXAQEBGDBggHT9/PnzMWXKFMyePVuqo0+fPvD3939lrD///DM2bNgAIQSysrLg4OCAP//8U+W8jY0NVq1aBZlMhnr16uH+/fuYOnUqZs2aBT09PfTp0weBgYHSgn2//fYbatSoUeL86tdVHq/Ni27dugVra+syx+Hj44MffvgB27Ztw5dffonk5GTMmzcPwPPpPQVlxo8fj4EDB6J169a4fv26NH89KSkJtra28PDwwJYtW9CzZ088e/YMeXl56NSpU6F1DQpivHXrlvRFk94ue3t7VK9eHcePH0daWpr0vrO2toaNjQ1OnjyJ48ePo02bNuXWZqdOnVCzZk388ssvsLa2hlKpxCeffFJoIU4tLS3p3wWLsL58rKgpKS+zs7ODnZ0dhgwZgm+++QYODg7YsWOH9H/Hi3UWVW9p4/Xz88Nvv/2GU6dOqbxeCoUCc+fOxRdffFEoNl1dXdjY2ODKlSs4duwYjh49iq+++grLli1DeHh4odiKolAoCq3tUqBgrZ9Jkybh6NGjWL58Oezt7aGnp4fu3bsX6oOBgUGhuocPH17kuh5FJcVepy9yuRz29vYAAEdHRyQkJGDkyJGF1v14ldK8XwBIP9tX/Vxex6lTp9C3b1/MnTsXPj4+MDExwfbt2wut6fGq91x5kMvl0poYBcqyKHBp3lelZW5ujtjY2DJdU2DChAkYP348kpKSYGZmhsTEREybNk36u0Imk2HJkiVYuHAhkpOTYWFhgdDQUAD/97eHlZUVqlWrppKcdHR0hBACd+/eRZ06dQBAmj5mYWHxWrEWhSNBiIiI3iOtW7dGdHQ0oqOjERUVBR8fH7Rv3/6NFwyNjo6GhoaG9GWqOC/etbOysgIA6U7Yq+7QFXj5rmVx+vbti+joaMTExODEiROwt7dHu3btpIXV4uPj0aJFC5XdLjw8PKBQKHD37l0Az+82/fXXX7h37x6A54vCFSwwW97K47V5UUXfhbt8+TLGjh2LWbNm4dy5czhy5AgSExMxYsQIlfbexl04erXWrVsjLCwMYWFhKkm9li1b4vDhw4iKiiq39UD+/fdfXLlyBTNmzMBnn30GR0dHpKWllUvdpWFrawt9ff1iF/Z8WVniHTlyJBYvXozPP/8c4eHh0nFXV1dcuXIF9vb2hR4FvyN6enro1KkTVq5cibCwMJw6dUrlS+OLi9QWPHd0dJTqT05OhqamZqH6zc3NATxfl2fgwIHo2rUrnJ2dYWlpWaoRV66urrh8+XKRsWtraxd5zav68ioBAQHYsWOHtAaGo6MjIiMjVcpERkaifv36pa6zKK/6uTg6OuLOnTu4c+eOdM3ly5fx+PHjYts+efIkatasiW+++QZubm6oU6dOmT9T7ezsoKWlhdOnT0vH0tLScPXq1TLVY2FhISWrC0RHR5f6+tK8r7S1tZGfn//KulxcXPDPP/8USsqUlkwmg7W1NfT09LBt2zbY2NjA1dVVpYyGhgaqVasGbW1tbNu2DS1atJCSGR4eHrh//z4UCoVU/urVq5DL5ahevbp07NKlS9DS0oKTk9NrxVkUjgQhIiJ6jxgYGEh33wBgw4YNMDExwS+//IJvv/1W+uP8xT9aSnMXqeCL7KuUxx26l+9aFsfExETqq729PTZu3AgrKyvs2LEDQ4YMKVUdLi4uaNiwITZt2oR27dohLi4OBw8eLNW1ZVXedy8r+i7cokWLpF06gOdJHgMDA3h6euLbb7+VEj1v4y4cvVrr1q3x9ddfIzc3VyV56eXlhVGjRiEnJ6fckiBmZmaoXLky1q9fDysrK9y+fVtlod3yNGfOHGRlZcHPzw81a9bE48ePsXLlSuTm5qJt27ZvJd7Ro0cjPz8fHTt2xOHDh/Hpp59i1qxZ6NixI2rUqIHu3btDLpcjJiYGly5dwrfffougoCDk5+ejWbNm0NfXx2+//QY9PT3UrFlTqjcyMhJLly5Fly5dcPToUezatUv6/8fb2xstWrRAly5dsHTpUjg4OOD+/fs4ePAgunbtKn0Z37NnDzp16gSZTIaZM2eWauTB1KlT0bx5c4waNQpDhgyBgYEBLl++jKNHjxbaghRAqfryKjY2NujatStmzZqFAwcOYPLkyfjyyy/h4uICb29v/PHHH9izZ0+h3W3K6lU/F29vbzg7O6Nv37744YcfkJeXh6+++gpeXl7FJuDr1KmD27dvY/v27WjSpAkOHjyIvXv3likuQ0NDDB48GJMnT0blypVRpUoVfPPNN6UepVmgTZs2WLZsGTZt2oQWLVrgt99+w6VLl+Di4lKq60vzvrK1tcXNmzcRHR2N6tWrw8jICDo6OoXqKtiOOy4uDp988ol0/Pbt20hNTcXt27eRn58vJWns7e2lkarLli2Dr68v5HI59uzZg8WLF2Pnzp3SwrmPHj3C77//jlatWuHZs2cIDAzErl27VBKRffr0wfz58+Hv74+5c+fi0aNHmDx5MgYNGqTyN0tERIS0E1J54UgQIiKi95hMJoNcLpfmxxZ8EX3xTtLLd5GKugvk7OwMpVKp8gdIWZXmzumbKPjjqaCvBdspvpjwiYyMhJGRkcpdoiFDhiAoKAiBgYHw9vZWmSv+rrzOa1PRd+GysrIKxVbwM3gxprdxF46KplQKxN5NR/jVh7Cq1xhPnz6Fvb29tJYC8DwJ8uTJE2kr3fIgl8uxfft2nDt3Dp988gnGjx9f5JbK5cHLyws3btxA//79Ua9ePbRv3x7Jycn466+/Sr2+wuvEO27cOMydOxd+fn44efIkfHx8cODAAfz1119o0qQJmjdvju+//15KDJiamuKXX36Bh4cHGjRogGPHjuGPP/5QWZ9p4sSJOHv2LFxcXPDtt9/iu+++g4+PD4Dnv5+HDh1Cy5Yt4e/vDwcHB/Tq1Qu3bt2Sfp7fffcdzMzM4O7ujk6dOsHHx6fQ73BRGjRogPDwcFy9ehWenp5wcXHBrFmzip1eV5q+lMb48eNx8OBBREVFoUuXLvjxxx+xfPlyODk5Yd26dQgMDHzjqYiv+rnIZDLs378fZmZmaNmyJby9vVG7dm3s2LGj2Do///xzjB8/HqNGjUKjRo1w8uRJzJw5s8yxLVu2DJ6enujUqRO8vb3x6aefonHjxiVeo1Qqoan5f+MOfHx8MHPmTEyZMgVNmjTBkydP0L9//1LHUJr3Vbdu3eDr64vWrVvDwsIC27ZtK7KuypUro2vXrtiyZYvK8VmzZsHFxQWzZ8+GQqGAi4sLXFxccPbsWanM4cOH4enpCTc3Nxw8eBD79+8vtPVvcHAw3Nzc4OHhgbi4OISFhaFp06bSeUNDQxw9ehSPHz+Gm5sb+vbtK41WetH27dtVdi0rF+W2xOpHirvDEBHRuzJgwADh6+srkpKSRFJSkrh8+bL46quvhEwmE8ePHxdCCJGTkyNsbGxEjx49xNWrV8WBAwdE3bp1pd1hhBAiMjJS2s3k4cOHIjMzUwghxMCBA4WNjY3Yu3evuHHjhjh+/LjYsWOHEOLVu84IIcSRI0eEpqammDNnjrh06ZK4fPmy2LZtm/jmm2+kawCIvXv3vrKvXl5eYujQoVJfo6OjRbdu3YSurq6068rdu3eFvr6++Prrr0V8fLzYt2+fMDc3L7TjzOPHj4W+vr7Q1tYW27dvL/sL//+9aneYN31tXvbo0SOhpaUl7WZR4NatW+LChQti7ty5wtDQUFy4cEFcuHBBPHnyRCqzdOlScfHiRXHp0iUxb948oaWlpfK6P3z4UKxZs0bEx8eLCxcuiDFjxghdXV1x+vRplf5qamqKn3/+WSQkJIgTJ04INzc30bRpU5V4Zs+eXeIOAlQ+Iq89FP/Z8D/RYuEx4Tb/qGix8Jj4z4b/ichrDys6NCrCizt2EBVn0aJFwsnJqaLDKFZMTIyoUqWKyufL++TQoUPC0dGxxJ3WXgdHghAREb1DL97pjb2bDqVSdRTAkSNHYGVlBSsrKzRr1gxnzpzBrl27pLtrWlpa2LZtG/755x80aNAAS5YskXZLKeDu7o4RI0agZ8+esLCwwNKlSwEAa9asQffu3fHVV1+hXr16GDp0aKnn4AOvvkNXVr/88ovU19atW+PRo0c4dOiQdDe4WrVqOHToEKKiotCwYUOMGDECgwcPxowZM1TqMTExQbdu3WBoaFjoTlRiYiJkMlmRi8iVp9d5bSr6LtzAgQPx3XffYdWqVfjkk0/Qo0cP1K1bF3v27FGp563chSMVJ68/wvS9sYhPyoCBjiaqGOnAQEcT8UlPMH1vLE5ef1TRIRJRGWRlZeH8+fPSCMX3VcHfEUXtKvQ+yMzMRGBgoMpomvIgE+I1x2CqiYyMDJiYmCA9PR3GxsYVHQ4REX3ATl5/hDXhCUhIUSA3X0BLQwa7KoYY6WUHd3vzig7vg/bZZ5/Bycmp0DDa48eP44svvsCNGzdgZmZWQdEV7+LFi2jbti0SEhIKbVf8Pjh8+DAmTpyIixcvlvsfofScUikwIDAK8UkZsDTWVVnUVwiB5IxsOFoZIdi/KeTy8l/wl16Pra0txo0bh3HjxlV0KPQe+uGHHzBv3jx4e3tj7dq1qFSpUkWHRC9gEuQVmAQhIqLyUHCnV5GdBzN9bWhryJGTr0RaVi4MdTSwsKszEyGvIS0tDWFhYejevTsuX75caE2ByZMno0qVKtLin++joKAgNG7cGM7OzhUdSiG///47bGxs0KxZs4oO5aMVezcdwzefhYGOJnS1NAqdf5qbj6zsPKzr5wbn6iZF1EBERGXBlD4REdFbplQKrAlPgCI7T+VOr65cA5bGciRnZGNNeAKa167MO71l5OLigrS0NCxZsqTIRRXf1uKO5WngwIEVHUKxunfvXtEhfPRSs3KQmy+grVH0LHUdDTnSlQKpWTnvODIioo8TkyBERERvWdz9DCSkKGCmr60y1B14vtK7qb4WElIUiLufwTu9ZZSYmFjRIRC9kUr62tDSkCEnXwldeeGRINn5SmjJZaikr10B0RERfXy4MCoREdFbVpo7vbm800uklpysjWFXxRBpWbmFtksWQuBxVi7sqhjCyZrTsomIygOTIERERG/Zi3d6i8I7vUTqSy6XYaSXHQx1NJCckY2nuflQKgWe5uYjOSMbhjoaGOllx6lyRETlhEkQIiKit4x3eomoJO725ljY1RmOVkbIys5DiiIbWdl5cLQy4qLJRETljLvDvAJ3hyEiovLwf7vD5MNUXws6GnJk5yvxmLvDENH/p1QKxN3PQGpWDirpa8PJ2pgjQIiIyhmTIK/AJAgREZWXk9cfYU14AhJSFMhVCmjJZbCrYoiRXnZMgBARERG9A0yCvAKTIEREVJ54p5eIiIio4nCLXCIiondILpdxG1wiIiKiCsKFUYmIiIiIiIhILTAJQkRERERERERqgUkQIiIiIiIiIlILTIIQERERERERkVpgEoSIiIiIiIiI1AKTIERERERERESkFpgEISIiIiIiIiK1wCQIEREREREREakFJkGIiIiIiIiISC0wCUJEREREREREaoFJECIiIiIiIiJSC0yCEBEREREREZFaYBKEiIiIiIiIiNQCkyBEREREREREpBaYBCEiIiIiIiIitcAkCBERERERERGpBSZBiIiIiIiIiEgtMAlCRERERERERGqBSRAiIiIiIiIiUgtMghARERERERGRWtCs6ACIiIiIiIiIPkZKpUDc/QykZuWgkr42nKyNIZfLKjostcYkCBEREREREVE5O3n9EdaEJyAhRYHcfAEtDRnsqhhipJcd3O3NKzo8tcXpMERERERERETl6OT1R5i+NxbxSRkw0NFEFSMdGOhoIj7pCabvjcXJ648qOkS1xSQIERERERERUTlRKgXWhCdAkZ0HS2Nd6GppQC6XQVdLA5bGOlBk52NNeAKUSlHRoaolJkGIiIiIiIiIyknc/QwkpChgpq8NmUx1/Q+ZTAZTfS0kpCgQdz+jgiJUb0yCEBEREREREZWT1Kwc5OYLaGsU/XVbR0OOXKVAalbOO46MACZBiIiIiIiIiMpNJX1taGnIkJOvLPJ8dr4SWnIZKulrv+PICGAShIiIiIiIiKjMEhMTIZPJEB0drXLcydoYdlUMkZaVi9A5PXDj+E7pnBACj7NyYVfFEE7Wxu844rJr2bIltm7dWtFhFGnt2rXo1KlTma9jEoSIiIiIiIjeew8fPsTIkSNRo0YN6OjowNLSEj4+PoiMjJTKyGQy7Nu3r+KCBCCXyzDSyw6GOhrIVwrkKpVQKgWe5uYjOSMbhjoaGOllB7lc9urKihAWFgaZTAYzMzM8e/ZM5dyZM2cgk8kKrUXyOkJCQvDgwQP06tVLOrZ+/Xq0atUKxsbGkMlkePz4caHrzp8/j7Zt28LU1BSVK1fGsGHDoFAoCsX52WefwdTUFGZmZvDx8UFMTIxKGSEEli9fDgcHB+jo6KBatWpYsGCBdH7QoEE4f/48IiIiytQvJkGIiIiIiIjovdetWzdcuHABwcHBuHr1KkJCQtCqVSv8+++/FR1aIe725ljY1RlaGjLk5imRoshGVnYeHK2MsLCrM9ztzd+4DSMjI+zdu1fl2MaNG1GjRo03rhsAVq5cCX9/f8jl/5c2yMrKgq+vL6ZPn17kNffv34e3tzfs7e1x+vRpHDlyBHFxcRg4cKBURqFQwNfXFzVq1MDp06dx4sQJGBkZwcfHB7m5uVK5sWPHYsOGDVi+fDn++ecfhISEoGnTptJ5bW1t9OnTBytXrixbxwSVKD09XQAQ6enpFR0KERERERGRWkpLSxMARFhYWLFlatasKQBIj5o1awohhLh+/br4/PPPRZUqVYSBgYFwc3MTR48eLXTtggULhL+/vzA0NBQ2NjZi3bp1KmVOnz4tGjVqJHR0dETjxo3Fnj17BABx4cKFEmP6euJ00aZDV6Grpy+sra3FqlWrpPP+/v6iQ4cOKtfk5OQICwsLsWHDhiLrPH78uAAgZsyYIby9vaXjWVlZwsTERMycOVO8/FU/IiJCfPrpp0JXV1dUr15djB49WigUimLjTklJETKZTFy6dKnEGNLS0lSOr1u3TlSpUkXk5+dLxy5evCgAiGvXrgkhhDhz5owAIG7fvl1smcuXLwtNTU3xzz//FBujEEKEh4cLbW1tkZWVVWK5F3EkCBEREREREb3XDA0NYWhoiH379iE7O7vIMmfOnAEABAYGIikpSXquUCjg5+eH0NBQXLhwAb6+vujUqRNu376tcv2KFSvg5uaGCxcu4KuvvsLIkSNx5coVqY6OHTuifv36OHfuHObMmYNJkyaVKvZN639C20+bIib6AgICAjB27FgcPXoUADBkyBAcOXIESUlJUvkDBw4gKysLPXv2LLHefv36ISIiQurH7t27YWtrC1dXV5VyCQkJ8PX1Rbdu3XDx4kXs2LEDJ06cwKhRo4qt+8SJE9DX14ejo2Op+lggOzsb2traKqNH9PT0pDoBoG7duqhcuTI2btyInJwcPH36FBs3boSjoyNsbW0BAH/88Qdq166NAwcOoFatWrC1tcWQIUOQmpqq0p6bmxvy8vJw+vTpUsfIJAgRERERERG91zQ1NREUFITg4GCYmprCw8MD06dPx8WLF6UyFhYWAABTU1NYWlpKzxs2bIjhw4fjk08+QZ06dTB//nzY2dkhJCREpQ0/Pz989dVXsLe3x9SpU2Fubo7jx48DALZu3QqlUomNGzfCyckJHTt2xOTJk0sVu4eHBwICAuDg4IDRo0eje/fu+P777wEA7u7uqFu3LjZv3iyVDwwMRI8ePWBoaFhivVWqVEH79u0RFBQEAPj1118xaNCgQuUWLVqEvn37Yty4cahTpw7c3d2xcuVKbNq0qdCaIgVu3bqFqlWrqiQzSqNNmzZITk7GsmXLkJOTg7S0NAQEBACAlOgxMjJCWFgYfvvtN+jp6cHQ0BBHjhzB4cOHoampCQC4ceMGbt26hV27dmHTpk0ICgrCuXPn0L17d5X29PX1YWJiglu3bpU6RiZBiIiIiIiI6L3XrVs33L9/HyEhIfD19UVYWBhcXV2lJEBxFAoFJk2aBEdHR5iamsLQ0BDx8fGFRoI0aNBA+rdMJoOlpSVSUlIAAPHx8WjQoAF0dXWlMi1atChV3C+Xa9GiBeLj46XnQ4YMQWBgIADgwYMHOHz4cJHJjKIMGjQIQUFBuHHjBk6dOoW+ffsWKhMTE4OgoCBpNI2hoSF8fHygVCpx8+bNIut9+vSpSl9Ly8nJCcHBwVixYgX09fVhaWmJWrVqqSRUnj59isGDB8PDwwP/+9//EBkZiU8++QQdOnTA06dPAQBKpRLZ2dnYtGkTPD090apVK2zcuBHHjx+XRucU0NPTQ1ZWVqljZBKEiIiIiIiIPgi6urpo27YtZs6ciZMnT2LgwIGYPXt2iddMmjQJe/fuxcKFCxEREYHo6Gg4OzsjJydHpZyWlpbKc5lMBqVSWe59eFn//v2lJMZvv/2GWrVqwdPTs1TXtm/fXkoqdOrUCZUrVy5URqFQYPjw4YiOjpYeMTExuHbtGuzs7Iqs19zcHGlpaa/Vnz59+iA5ORn37t3Dv//+izlz5uDhw4eoXbs2gOejahITExEYGIgmTZqgefPm2Lp1K27evIn9+/cDAKysrKCpqQkHBwep3oKpOS8nr1JTU6VRP6Wh+Vq9IiIiIiIiIqpg9evXV9kSV0tLC/n5+SplIiMjMXDgQHTt2hXA86RAYmJimdpxdHTE5s2b8ezZM2mExP/+979SXftyuf/9738qa21UrlwZXbp0QWBgIE6dOgV/f/9Sx6WpqYn+/ftj6dKlOHz4cJFlXF1dcfnyZdjb25e6XhcXFyQnJyMtLQ1mZmalvu5FVatWBfB8mk5B8gp4vsOMXC5X2ca34HlB0snDwwN5eXlISEiQEjVXr14FANSsWVO6LiEhAc+ePYOLi0up4+JIECIiIiIiInqv/fvvv2jTpg1+++03XLx4ETdv3sSuXbuwdOlSdO7cWSpna2uL0NBQ6Qs8ANSpUwd79uyRRkD06dOnzCM8+vTpA5lMhqFDh+Ly5cs4dOgQli9fXqprIyMjsXTpUly9ehWrV6/Grl27MHbsWJUyQ4YMQXBwMOLj4zFgwIAyxTZ//nw8fPgQPj4+RZ6fOnUqTp48iVGjRiE6OhrXrl3D/v37S1wY1cXFBebm5oiMjFQ5npycjOjoaFy/fh0AEBsbi+joaJUFS1etWoXz589L/R01ahQWLVoEU1NTAEDbtm2RlpaGr7/+GvHx8YiLi4O/vz80NTXRunVrAIC3tzdcXV0xaNAgXLhwAefOncPw4cPRtm1bldEhERERqF27drEjWorCJAgRERERERG91wwNDdGsWTN8//33aNmyJT755BPMnDkTQ4cOxapVq6RyK1aswNGjR2FjYyONDvjuu+9gZmYGd3d3dOrUCT4+PoV2UClN+3/88QdiY2Ph4uKCb775BkuWLCnVtRMnTsTZs2fh4uKCb7/9Ft99912hhIW3tzesrKzg4+MDa2vrMsWmra0Nc3NzlZEVL2rQoAHCw8Nx9epVeHp6wsXFBbNmzSqxHQ0NDfj7+2PLli0qx9euXQsXFxcMHToUANCyZUu4uLioLDIbFRWFtm3bwtnZGevXr8e6deswZswY6Xy9evXwxx9/4OLFi2jRogU8PT1x//59HDlyBFZWVgCejwz5448/YG5ujpYtW6JDhw5wdHTE9u3bVeLZtm2bFEtpyYQQokxXqJmMjAyYmJggPT0dxsbGFR0OERERERERfWQUCgWqVauGwMBAfPHFFxUdDoDnoz6cnJxw/vx5lSko74u4uDi0adMGV69ehYmJSamv40gQIiIiIiIiogqgVCqRkpKC+fPnw9TUFJ9//nlFhySxtLTExo0bCy1E+r5ISkrCpk2bypQAATgS5JU4EoSIiIiIiIjehsTERNSqVQvVq1dHUFAQPvvss4oO6aPH3WGIiIiIiIiIKoCtrS04LuHd4nQYIiIiIiIiIlILTIIQERERERERkVpgEoSIiIiIiIiI1AKTIERERERERESkFpgEISIiIiIiIiK1wCQIEREREREREakFJkGIiIiIiIiISC0wCUJEREREREREaoFJECIiIiIiIiJSC0yCEBEREREREZFaYBKEqAhhYWGQyWR4/PhxRYdC9EZatmyJrVu3VnQYRQoICMDo0aMrOgwiIiIiUiNMgtAHQyaTlfiYM2fOa9XbqlUrjBs3rlxjLQ85OTlYunQpGjZsCH19fZibm8PDwwOBgYHIzc2t6PCoCLa2tpDJZPjf//6ncnzcuHFo1apVsdclJiZCJpNBQ0MD9+7dUzmXlJQETU1NyGQyJCYmlimekJAQPHjwAL169ZKOrV+/Hq1atYKxsXGxib7z58+jbdu2MDU1ReXKlTFs2DAoFAqVMqGhoXB3d4eRkREsLS0xdepU5OXlSefnzJlT5O+pgYGBVGbSpEkIDg7GjRs3ytQvIiIiIqLXxSQIfTCSkpKkxw8//ABjY2OVY5MmTZLKCiFUvpC9r3Jycoo97uPjg8WLF2PYsGE4efIkoqKi8PXXX+Onn35CXFzcO46USktXVxdTp059rWurVauGTZs2qRwLDg5GtWrVXqu+lStXwt/fH3L5//1Xn5WVBV9fX0yfPr3Ia+7fvw9vb2/Y29vj9OnTOHLkCOLi4jBw4ECpTExMDPz8/ODr64sLFy5gx44dCAkJQUBAgFRm0qRJKr+fSUlJqF+/Pnr06CGVMTc3h4+PD9asWfNa/SMiIiIiKjNBJUpPTxcARHp6ekWHQi8IDAwUJiYm0vPjx48LAOLQoUPC1dVVaGlpiePHj4sBAwaIzp07q1w7duxY4eXlJYQQYsCAAQKAyuPmzZtSfceOHRONGzcWenp6okWLFuKff/4pMa6LFy+K1q1bC11dXVGpUiUxdOhQ8eTJE+l8QTzffvutsLKyEra2tkXWs2TJEiGXy8X58+cLncvJyREKhUIIIcSzZ8/E6NGjhYWFhdDR0REeHh4iKiqq0OtSUj+io6NFq1athKGhoTAyMhKurq7izJkz0vmIiAjx6aefCl1dXVG9enUxevRoqX0hhHjw4IHo2LGj0NXVFba2tuK3334TNWvWFN9//70QQoibN28KAOLChQvSNWlpaQKAOH78uHQsNjZW+Pr6CgMDA1GlShXxn//8Rzx8+FA67+XlJUaPHi0mT54szMzMRNWqVcXs2bNVXpu0tDQxbNgwUaVKFaGjoyOcnJzEH3/8Ueq+rF69Wtjb2wsdHR1RpUoV0a1btyJ/PsWpWbOmGDNmjNDW1hYHDx6Ujr/4nitKwWs0Y8YMUadOHZVzDg4OYubMmdJ7s7RSUlKETCYTly5dKvJ8wXsjLS1N5fi6detElSpVRH5+vnTs4sWLAoC4du2aEEKIadOmCTc3N5XrQkJChK6ursjIyCiyvejoaAFA/P333yrHg4ODRfXq1UvdLyIiIiKiN8GRIPRRCQgIwOLFixEfH48GDRq8svyPP/6IFi1aYOjQodLdahsbG+n8N998gxUrVuDs2bPQ1NTEoEGDiq0rMzMTPj4+MDMzw5kzZ7Br1y4cO3YMo0aNUikXGhqKK1eu4OjRozhw4ECRdW3ZsgXe3t5wcXEpdE5LS0uaUjBlyhTs3r0bwcHBOH/+POzt7eHj44PU1FSVa0rqR9++fVG9enWcOXMG586dQ0BAALS0tAAACQkJ8PX1Rbdu3XDx4kXs2LEDJ06cUOnTwIEDcefOHRw/fhy///47fv75Z6SkpBT7OhXl8ePHaNOmDVxcXHD27FkcOXIEDx48wJdffqlSLjg4GAYGBjh9+jSWLl2KefPm4ejRowAApVKJ9u3bIzIyEr/99hsuX76MxYsXQ0NDo1R9OXv2LMaMGYN58+bhypUrOHLkCFq2bFmmfgBArVq1MGLECEybNg1KpbJM137++edIS0vDiRMnAAAnTpxAWloaOnXqVOY4Tpw4AX19fTg6OpbpuuzsbGhra6uMHtHT05PqLCijq6urcp2enh6ePXuGc+fOFVnvhg0b4ODgAE9PT5XjTZs2xd27d8s81YeIiIiI6LVUdBbmfceRIO+n4kaC7Nu3T6Xcq0aCCPF8hMHYsWNVyrw4gqLAwYMHBQDx9OnTImNav369MDMzUxlZcPDgQSGXy0VycrIUT9WqVUV2dnaJ/dPT0xNjxowpsYxCoRBaWlpiy5Yt0rGcnBxhbW0tli5dWup+GBkZiaCgoCLbGDx4sBg2bJjKsYiICCGXy8XTp0/FlStXBACV0Sfx8fECQJlGgsyfP1+0a9dOpZ07d+4IAOLKlStCiOc/p08//VSlTJMmTcTUqVOFEEL8+eefQi6XS+XL2pfdu3cLY2PjYkcylEbBCJiUlBRhZGQkNm3aJIQo/UiQCxcuiHHjxgl/f38hhBD+/v5i/Pjx4sKFC2UeCfL999+L2rVrF3u+uJEgly5dEpqammLp0qUiOztbpKamim7dugkAYuHChUKI/3utt27dKvLy8sTdu3eFp6enACC2bt1aqK2nT58KMzMzsWTJkkLnCv6PDQsLK3XfiIiIiIheF0eC0EfFzc2tXOt7cTSJlZUVABQ7yiE+Ph4NGzZUWfjRw8MDSqUSV65ckY45OztDW1u7xHaFEK+MLSEhAbm5ufDw8JCOaWlpoWnTpoiPjy91PyZMmIAhQ4bA29sbixcvRkJCglQ2JiYGQUFBMDQ0lB4+Pj5QKpW4efMm4uPjoampicaNG0vX1KtXD6ampq+M/0UxMTE4fvy4Sjv16tWT+llUPwr6UtCP6OhoVK9eHQ4ODsW2UVJf2rZti5o1a6J27dro168ftmzZgqysrDL1o4CFhQUmTZqEWbNmFbvuS3EGDRqEXbt2ITk5Gbt27Spx9FFJnj59Wmi0Rmk4OTkhODgYK1asgL6+PiwtLVGrVi1UrVpVGh3Srl07LFu2DCNGjICOjg4cHBzg5+cHACojSArs3bsXT548wYABAwqdKxhl8rqvNRERERFRWTAJQh+VFxMQwPMvZC8nFMqys0rBtBDg+e40AMo8xeFlL8dYFAcHB/zzzz9v1M6LSurHnDlzEBcXhw4dOuC///0v6tevj7179wIAFAoFhg8fjujoaOkRExODa9euwc7OrlRtF3wpfvHn8PLPQKFQoFOnTirtREdH49q1aypTUl7sR0FfCvpR8GW6OK/qi5GREc6fP49t27bBysoKs2bNQsOGDV97m+QJEybg6dOn+Pnnn8t0nbOzM+rVq4fevXvD0dERn3zyyWu1b25ujrS0tNe6tk+fPkhOTsa9e/fw77//Ys6cOXj48CFq164tlZkwYQIeP36M27dv49GjR+jcuTMAqJQpsGHDBnTs2BFVq1YtdK5g6paFhcVrxUpEREREVBZMgtBHzcLCAklJSSrHoqOjVZ5ra2sjPz//jdtydHRETEwMMjMzpWORkZGQy+WoW7dumerq06cPjh07hgsXLhQ6l5ubi8zMTNjZ2UFbWxuRkZEq586cOYP69euXqT0HBweMHz8ef/31F7744gsEBgYCAFxdXXH58mXY29sXemhra6NevXrIy8tTWQfiypUrKomDgi+3L/4cXv4ZuLq6Ii4uDra2toXaKU3SCHg+SuTu3bu4evVqkedf1RcA0NTUhLe3N5YuXYqLFy8iMTER//3vf0vV/ssMDQ0xc+ZMLFiwAE+ePCnTtYMGDUJYWNhrjwIBABcXFyQnJ792IgQAqlatCkNDQ+zYsQO6urpo27atynmZTAZra2vo6elh27ZtsLGxgaurq0qZmzdv4vjx4xg8eHCRbVy6dAlaWlpwcnJ67TiJiIiIiEqLSRD6qLVp0wZnz57Fpk2bcO3aNcyePRuXLl1SKWNra4vTp08jMTERjx49eu2RHn379oWuri4GDBiAS5cu4fjx4xg9ejT69etX5B3wkowbNw4eHh747LPPsHr1asTExODGjRvYuXMnmjdvjmvXrsHAwAAjR47E5MmTceTIEVy+fBlDhw5FVlZWsV84X/b06VOMGjUKYWFhuHXrFiIjI3HmzBlpMc2pU6fi5MmTGDVqlDQyY//+/dJionXr1oWvry+GDx+O06dP49y5cxgyZIjKqAw9PT00b95cWrA2PDwcM2bMUInj66+/RmpqKnr37o0zZ84gISEBf/75J/z9/UudoPLy8kLLli3RrVs3HD16FDdv3sThw4dx5MiRUvXlwIEDWLlyJaKjo3Hr1i1s2rQJSqWyzAmsFw0bNgwmJibYunWryvG9e/dK032KMnToUDx8+BBDhgwptky9evWkETtFcXFxgbm5uUqSDACSk5MRHR2N69evAwBiY2MRHR2tspjuqlWrcP78eVy9ehWrV6/GqFGjsGjRIpVpTsuWLUNsbCzi4uIwf/58LF68GCtXrpQWoi3w66+/wsrKCu3bty8yzoiICHh6er5yJA8RERERUXlgEoQ+aj4+Ppg5cyamTJmCJk2a4MmTJ+jfv79KmUmTJkFDQwP169eHhYUFbt++/Vpt6evr488//0RqaiqaNGmC7t2747PPPsOqVavKXJeOjg6OHj2KKVOmYN26dWjevDmaNGmClStXYsyYMdIUicWLF6Nbt27o168fXF1dcf36dfz5558wMzMrVTsaGhr4999/0b9/fzg4OODLL79E+/btMXfuXADPR1eEh4fj6tWr8PT0hIuLC2bNmgVra2upjsDAQFhbW8PLywtffPEFhg0bhipVqqi08+uvvyIvLw+NGzfGuHHj8O2336qct7a2RmRkJPLz89GuXTs4Oztj3LhxMDU1LXKNieLs3r0bTZo0Qe/evVG/fn1MmTJFSqK8qi+mpqbYs2cP2rRpA0dHR6xduxbbtm2TRigEBQVJU4lKS0tLC/Pnz8ezZ89Ujqenp6usE/MyTU1NmJubQ1NTs9gyV65cQXp6erHnNTQ04O/vjy1btqgcX7t2LVxcXDB06FAAQMuWLeHi4oKQkBCpTFRUFNq2bQtnZ2esX78e69atw5gxY1TqOXz4MDw9PeHm5oaDBw9i//796NKli0oZpVKJoKAgDBw4sFBypMD27dulWIiIiIiI3jaZKM0KjGosIyMDJiYmSE9Ph7GxcUWHQ/RBsLW1xbhx4zBu3LiKDqXczJ49G+Hh4QgLC6voUEotOTkZTk5OOH/+PGrWrFnR4RRy+PBhTJw4ERcvXiwx4UNEREREVF44EoSIqBQOHz6MpUuXVnQYZWJpaYmNGze+9uimty0zMxOBgYFMgBARERHRO8O/PImISiEqKqqiQ3gtL09ReZ907969okMgIiIiIjXDJAgRlbvExMSKDoGIiIiIiKgQJkHovadUCsTdz0BqVg4q6WvDydoYcnnZFqgkIiIiIiIiYhKE3msnrz/CmvAEJKQokJsvoKUhg10VQ4z0soO7vXlFh0dEREREREQfEC6MSu+tk9cfYfreWMQnZcBARxNVjHRgoKOJ+KQnmL43FievP6roEImIiIiIiOgDwiQIvZeUSoE14QlQZOfB0lgXuloakMtl0NXSgKWxDhTZ+VgTngClkjs8FwgLC4NMJsPjx48BAEFBQTA1Na3QmN53LVu2xNatWys6jCIFBARg9OjRFR0GEREREdFHhUkQei/F3c9AQooCZvrakMlU1/+QyWQw1ddCQooCcfczKijCinHq1CloaGigQ4cO5VbngQMH4OXlBSMjI+jr66NJkyYICgoqt/rLqiCZY2ZmhmfPnqmcO3PmDGQyWaH3xOsICQnBgwcP0KtXL+nY+vXr0apVKxgbG6sklF50/vx5tG3bFqampqhcuTKGDRsGhUKhUiY0NBTu7u4wMjKCpaUlpk6diry8POn8nDlzpH68+DAwMJDKTJo0CcHBwbhx48Yb95WIiIiIiJ5jEoTeS6lZOcjNF9DWKPotqqMhR65SIDUr5x1HVrE2btyI0aNH4++//8b9+/ffuL6ffvoJnTt3hoeHB06fPo2LFy+iV69eGDFiBCZNmlQOERcvJ6fkn52RkRH27t2rcmzjxo2oUaNGubS/cuVK+Pv7Qy7/v/dYVlYWfH19MX369CKvuX//Pry9vWFvb4/Tp0/jyJEjiIuLw8CBA6UyMTEx8PPzg6+vLy5cuIAdO3YgJCQEAQEBUplJkyYhKSlJ5VG/fn306NFDKmNubg4fHx+sWbOmXPpLRERERERMgtB7qpK+NrQ0ZMjJVxZ5PjtfCS25DJX0td9xZBVHoVBgx44dGDlyJDp06PDGozXu3LmDiRMnYty4cVi4cCHq168Pe3t7TJw4EcuWLcOKFStw+vRpKJVKVK9evdCX8QsXLkAul+PWrVsAgMePH2PIkCGwsLCAsbEx2rRpg5iYGKn8nDlz0KhRI2zYsAG1atWCrq5uifENGDAAv/76q/T86dOn2L59OwYMGFCo7IkTJ+Dp6Qk9PT3Y2NhgzJgxyMzMLLbuhw8f4r///S86deqkcnzcuHEICAhA8+bNi7zuwIED0NLSwurVq1G3bl00adIEa9euxe7du3H9+nUAwI4dO9CgQQPMmjUL9vb28PLywtKlS7F69Wo8efIEAGBoaAhLS0vp8eDBA1y+fBmDBw9Waa9Tp07Yvn17ia8TERERERGVHpMg9F5ysjaGXRVDpGXlQgjVdT+EEHiclQu7KoZwsjauoAjfvZ07d6JevXqoW7cu/vOf/+DXX38t9NqUxe+//47c3NwiR3wMHz4choaG2LZtG+RyOXr37l1o7YwtW7bAw8MDNWvWBAD06NEDKSkpOHz4MM6dOwdXV1d89tlnSE1Nla65fv06du/ejT179iA6OrrE+Pr164eIiAjcvn0bALB7927Y2trC1dVVpVxCQgJ8fX3RrVs3XLx4ETt27MCJEycwatSoYus+ceIE9PX14ejoWGIML8vOzoa2trbK6BE9PT2pzoIyLyd49PT08OzZM5w7d67Iejds2AAHBwd4enqqHG/atCnu3r2LxMTEMsVJRERERERFYxKE3ktyuQwjvexgqKOB5IxsPM3Nh1Ip8DQ3H8kZ2TDU0cBILzvI5W++NsSHYuPGjfjPf/4DAPD19UV6ejrCw8Nfu76rV6/CxMQEVlZWhc5pa2ujdu3auHr1KgCgb9++iIyMlBISSqUS27dvR9++fQE8TwBERUVh165dcHNzQ506dbB8+XKYmpri999/l+rNycnBpk2b4OLiggYNGpQYX5UqVdC+fXtpxMuvv/6KQYMGFSq3aNEi9O3bF+PGjUOdOnXg7u6OlStXYtOmTYXWFClw69YtVK1aVSWZURpt2rRBcnIyli1bhpycHKSlpUnTXJKSkgAAPj4+OHnyJLZt24b8/Hzcu3cP8+bNUynzomfPnmHLli2FRoEAgLW1tRQvERERERG9OSZB6L3lbm+OhV2d4WhlhKzsPKQospGVnQdHKyMs7OoMd3vzig7xnbly5QqioqLQu3dvAICmpiZ69uyJjRs3vpP2GzVqBEdHR2k0SHh4OFJSUqQ1LGJiYqBQKFC5cmUYGhpKj5s3byIhIUGqp2bNmrCwsCh1u4MGDUJQUBBu3LiBU6dOSUmXF8XExCAoKEilXR8fHyiVSty8ebPIep8+ffrK6ThFcXJyQnBwMFasWAF9fX1YWlqiVq1aKgmVdu3aYdmyZRgxYgR0dHTg4OAAPz8/ACgy6bJ37148efKkyGk+BaNMsrKyyhwrEREREREVplnRARCVxN3eHM1rV0bc/QykZuWgkr42nKyNP8oRIEqlKLafGzduRF5enjQyAHg+LUhHRwerVq2CiYlJmdtzcHBAeno67t+/r1Iv8HzERkJCAlq3bi0d69u3L7Zu3YqAgABs3boVvr6+qFy5MoDn65VYWVkhLCysUDsvbtP74u4npdG+fXsMGzYMgwcPRqdOnaT2XqRQKDB8+HCMGTOm0LniFlE1NzdHWlpamWIp0KdPH/Tp0wcPHjyAgYEBZDIZvvvuO9SuXVsqM2HCBIwfPx5JSUkwMzNDYmIipk2bplKmwIYNG9CxY0dUrVq10LmCqURlSRwREREREVHxmASh955cLoNz9bJ/yf+QnLz+CGvCE5CQokBuvoCWhgx2VQwx0ssOTW1NsWnTJqxYsQLt2rVTua5Lly7Ytm0bRowYUeY2u3XrhqlTp2LFihVYsWKFyrm1a9ciMzNTGnkCPP/yP2PGDJw7dw6///471q5dK51zdXVFcnIyNDU1YWtrW+ZYiqOpqYn+/ftj6dKlOHz4cJFlXF1dcfnyZdjb25e6XhcXFyQnJyMtLQ1mZmavFVtB0uLXX3+Frq4u2rZtq3JeJpNJyaVt27bBxsam0HomN2/exPHjxxESElJkG5cuXYKWlhacnJxeK0YiIiIiIlLFJAhRBTt5/RGm742FIjsPZvra0NaQIydfifikJ5i+Nxa+hneQlpaGwYMHFxrx0a1bN2zcuPG1kiA1atTA0qVLMXHiROjq6qJfv37Q0tLC/v37MX36dEycOBHNmjWTytva2sLd3R2DBw9Gfn4+Pv/8c+mct7c3WrRogS5dumDp0qVwcHDA/fv3cfDgQXTt2hVubm6v/frMnz8fkydPLnIUCABMnToVzZs3x6hRozBkyBAYGBjg8uXLOHr0KFatWlXkNS4uLjA3N0dkZCQ6duwoHU9OTkZycrK000tsbCyMjIxQo0YNVKpUCQCwatUquLu7w9DQEEePHsXkyZOxePFilREvy5Ytg6+vL+RyOfbs2YPFixdj586d0NDQUInj119/hZWVFdq3b19knBEREdKuN0RERERE9Oa4JghRBVIqBdaEJ0CRnQdLY13oamlALpdBV0sDlsY6UGTnY9Xa9fjsM+8ip7x069YNZ8+excWLF1+r/XHjxmHv3r2IiIiAm5sbPvnkE2zduhVr1qzB8uXLC5Xv27cvYmJi0LVrV5Uv5jKZDIcOHULLli3h7+8PBwcH9OrVS1qA9E1oa2vD3NwcMlnRU6AaNGiA8PBwXL16FZ6ennBxccGsWbMKTfF5kYaGBvz9/bFlyxaV42vXroWLiwuGDh0KAGjZsiVcXFxURmpERUWhbdu2cHZ2xvr167Fu3bpCU3EOHz4MT09PuLm54eDBg9i/fz+6dOmiUkapVCIoKAgDBw4slBwpsH37dikWIiIiIiJ6czLxJntsqoGMjAyYmJggPT0dxsbqsx0rvRuxd9MxfPNZGOhoQler8Bfhp7n5yMrOw7p+bh/9lKB3LTk5GU5OTjh//ry0ze/75PDhw5g4cSIuXrwITU0O2iMiIiIiKg8cCUJUgVKzcpCbL6CtUfSvoo6GHLlKgdSsnHcc2cfP0tISGzdulLb9fd9kZmYiMDCQCRAiIiIionLEv66JKlAlfW1oaciQk6+ErrzwSJDsfCW05DJU0teugOg+fi9PUXmfdO/evaJDICIiIiL66HAkCFEFcrI2hl0VQ6Rl5eLlmWlCCDzOyoVdFUM4WXMqFhERERER0ZtiEoSoAsnlMoz0soOhjgaSM7LxNDcfSqXA09x8JGdkw1BHAyO97CCXF70oKBEREREREZUekyBEFczd3hwLuzrD0coIWdl5SFFkIys7D45WRljY1Rnu9uYVHSIREREREdFH4YNLgqxevRq2trbQ1dVFs2bNEBUVVWL5Xbt2oV69etDV1YWzszMOHTr0jiIlKj13e3ME+zfFun5uWN6jIdb1c0Owf1MmQIiIiIiIiMrRB5UE2bFjByZMmIDZs2fj/PnzaNiwIXx8fJCSklJk+ZMnT6J3794YPHgwLly4gC5duqBLly64dOnSO46c6NXkchmcq5vAy8ECztVNOAWGiIiIiIionMnEy6sxvseaNWuGJk2aYNWqVQAApVIJGxsbjB49GgEBAYXK9+zZE5mZmThw4IB0rHnz5mjUqBHWrl1bqjYzMjJgYmKC9PR0GBtzcUoiIiIiIiKiD9UHMxIkJycH586dg7e3t3RMLpfD29sbp06dKvKaU6dOqZQHAB8fn2LLA0B2djYyMjJUHkRERERERET04ftgkiCPHj1Cfn4+qlatqnK8atWqSE5OLvKa5OTkMpUHgEWLFsHExER62NjYvHnwRERERERERFThPpgkyLsybdo0pKenS487d+5UdEhEREREREREVA40KzqA0jI3N4eGhgYePHigcvzBgwewtLQs8hpLS8sylQcAHR0d6OjovHnARERERERERPRe+WBGgmhra6Nx48YIDQ2VjimVSoSGhqJFixZFXtOiRQuV8gBw9OjRYssTERERERER0cfrgxkJAgATJkzAgAED4ObmhqZNm+KHH35AZmYm/P39AQD9+/dHtWrVsGjRIgDA2LFj4eXlhRUrVqBDhw7Yvn07zp49i/Xr11dkN4iIiIiIiIioAnxQSZCePXvi4cOHmDVrFpKTk9GoUSMcOXJEWvz09u3bkMv/b3CLu7s7tm7dihkzZmD69OmoU6cO9u3bh08++aSiukBEREREREREFUQmhBAVHcT7LCMjAyYmJkhPT4exsXFFh0NEREREREREr+mDWROEiIiIiIiIiOhNMAlCRERERERERGqBSRAiIiIiIiIiUgtMghARERERERGRWmAShIiIiIiIiIjUApMgRERERERERKQWmAQhIiIiIiIiIrXAJAgRERERERERqQUmQYiIiIiIiIhILTAJQkRERERERERqgUkQIiIiIiIiIlILTIIQERERERERkVpgEoSIiIiIiIiI1AKTIERERERERESkFpgEISIiIiIiIiK1wCQIEREREREREakFJkGIiIiIiIiISC0wCUJEREREREREaoFJECIiIiIiIiJSC0yCEBEREREREZFaYBKEiIiIiIiIiNQCkyBEREREREREpBaYBCEiIiIiIiIitcAkCBERERERERGpBSZBiIiIiIiIiEgtMAlCRERERERERGqBSRAiIiIiIiIiUgtMghARERERERGRWmAShIiIiIiIiIjUApMgRERERERERKQWmAQhIiIiIiIiIrXAJAgRERERERERqQUmQYiIiIiIiIhILTAJQkRERERERERqgUkQIiIiIiIiIlILTIIQERERERERkVpgEoSIiIiIiIiI1AKTIERERERERESkFpgEISIiIiIiIiK1wCQIEREREREREakFJkGIiIiIiIiISC0wCUJEREREREREaoFJECIiIiIiIiJSC0yCEBEREREREZFaYBKEiIiIiIiIiNQCkyBEREREREREpBaYBCEiIiIiIiIitcAkCBERERERERGpBSZBiIiIiIiIiEgtMAlCRERERERERGqBSRAiIiIiIiIiUgtMghARERERERGRWmAShIiIiIiIiIjUApMgRERERERERKQWmAQhIiIiIiIiIrXAJAgRERERERERqQUmQYiIiIiIiIhILTAJQkRERERERERqgUkQIiIiIiIiIlILTIIQERERERERkVpgEoSIiIiIiIiI1AKTIERERERERESkFpgEISIiIiIiIiK1wCQIEREREREREakFJkGIXhAUFARTU9OKDkOtXblyBZaWlnjy5ElFh1Kk5s2bY/fu3RUdBhERERERvQYmQei9NHDgQHTp0qXQ8bCwMMhkMjx+/PittNuzZ09cvXr1rdRdnrKysjBt2jTY2dlBV1cXFhYW8PLywv79+6Uytra2+OGHH95ZTOXV3rRp0zB69GgYGRkBAJ49e4aBAwfC2dkZmpqaRb4vAGD16tVwdHSEnp4e6tati02bNqmcz83Nxbx586TXrGHDhjhy5IhKmfz8fMycORO1atWCnp4e7OzsMH/+fAghpDIzZsxAQEAAlErlG/eViIiIiIjeLc2KDoDoXcvJyYG2tnah47m5udDT04Oenl4FRFU2I0aMwOnTp/HTTz+hfv36+Pfff3Hy5En8+++/ZaonPz8fMpkMcvn7kQ+9ffs2Dhw4gJ9++kk6lp+fDz09PYwZM6bYERhr1qzBtGnT8Msvv6BJkyaIiorC0KFDYWZmhk6dOgF4nrz47bff8Msvv6BevXr4888/0bVrV5w8eRIuLi4AgCVLlmDNmjUIDg6Gk5MTzp49C39/f5iYmGDMmDEAgPbt22PIkCE4fPgwOnTo8JZfESIiIiIiKk/vxzcfUjtKpUDs3XSEX32I2LvpUCrFqy8qwpw5c9CoUSOVYz/88ANsbW2l5wWjShYsWABra2vUrVsXiYmJkMlk2LFjB7y8vKCrq4stW7YUOR3mjz/+QJMmTaCrqwtzc3N07dpVOrd582a4ubnByMgIlpaW6NOnD1JSUqTzBSNXQkND4ebmBn19fbi7u+PKlSsqbezfvx+urq7Q1dVF7dq1MXfuXOTl5RXb75CQEEyfPh1+fn6wtbVF48aNMXr0aAwaNAgA0KpVK9y6dQvjx4+HTCaDTCYD8H/TfUJCQlC/fn3o6Ojg9u3byM7OxqRJk1CtWjUYGBigWbNmCAsLU2nzxIkT8PT0hJ6eHmxsbDBmzBhkZmaW2N6tW7fQqVMnmJmZwcDAAE5OTjh06FCx/dq5cycaNmyIatWqSccMDAywZs0aDB06FJaWlkVet3nzZgwfPhw9e/ZE7dq10atXLwwbNgxLlixRKVPwmtWuXRsjR46En58fVqxYIZU5efIkOnfujA4dOsDW1hbdu3dHu3btEBUVJZXR0NCAn58ftm/fXmw/iIiIiIjo/cQkCL1zJ68/woDAKAzffBaTdsZg+OazGBAYhZPXH721NkNDQ3HlyhUcPXoUBw4ckI4HBARg7NixiI+Ph4+PT6HrDh48iK5du8LPzw8XLlxAaGgomjZtKp3Pzc3F/PnzERMTg3379iExMREDBw4sVM8333yDFStW4OzZs9DU1JSSFQAQERGB/v37Y+zYsbh8+TLWrVuHoKAgLFiwoNj+WFpa4tChQ8Wum7Fnzx5Ur14d8+bNQ1JSEpKSkqRzWVlZWLJkCTZs2IC4uDhUqVIFo0aNwqlTp7B9+3ZcvHgRPXr0gK+vL65duwYASEhIgK+vL7p164aLFy9ix44dOHHiBEaNGlVie19//TWys7Px999/IzY2FkuWLIGhoWGx/YqIiICbm1ux54uTnZ0NXV1dlWN6enqIiopCbm5uiWVOnDghPXd3d0doaKg0JSomJgYnTpxA+/btVa5r2rQpIiIiyhwnERERERFVLE6HoXfq5PVHmL43ForsPJjpa0NbQ46cfCXik55g+t5YLOzqDHd7cwDAgQMHCn1hzs/Pf612DQwMsGHDBmkaTGJiIgBg3Lhx+OKLL4q9bsGCBejVqxfmzp0rHWvYsKH07xeTGbVr18bKlSvRpEkTKBQKldgXLFgALy8vAM8TLx06dMCzZ8+gq6uLuXPnIiAgAAMGDJDqmT9/PqZMmYLZs2cXGdf69evRt29fVK5cGQ0bNsSnn36K7t27w8PDAwBQqVIlaGhoSCNUXpSbm4uff/5Z6sft27cRGBiI27dvw9raGgAwadIkHDlyBIGBgVi4cCEWLVqEvn37Yty4cQCAOnXqYOXKlfDy8sKaNWuKbe/27dvo1q0bnJ2dpb6V5NatW6+VBPHx8cGGDRvQpUsXuLq64ty5c9iwYQNyc3Px6NEjWFlZwcfHB9999x1atmwJOzs7hIaGYs+ePSrvqYCAAGRkZKBevXrQ0NBAfn4+FixYgL59+6q0Z21tjTt37kCpVL43U4mIiIiIiOjV+Nc7vTNKpcCa8AQosvNgaawLXS0NyOUy6GppwNJYB4rsfKwJT5CmxrRu3RrR0dEqjw0bNrxW287OzkWuA/KqL9zR0dH47LPPij1/7tw5dOrUCTVq1ICRkZGU6Lh9+7ZKuQYNGkj/trKyAgBp2kxMTAzmzZsHQ0ND6TF06FAkJSUhKyuryHZbtmyJGzduIDQ0FN27d0dcXBw8PT0xf/78EvsDANra2irxxMbGIj8/Hw4ODioxhIeHIyEhQYoxKChI5byPjw+USiVu3rxZbFtjxozBt99+Cw8PD8yePRsXL14sMbanT58WGq1RGjNnzkT79u3RvHlzaGlpoXPnzlJSqSBJ8eOPP6JOnTqoV68etLW1MWrUKPj7+6skMXbu3IktW7Zg69atOH/+PIKDg7F8+XIEBwertKenpwelUons7Owyx0pERB8PmUyGffv2FXv+5QXdX2cXule1UZz3ebe1nJwc2Nra4uzZsxUdChGpISZB6J2Ju5+BhBQFzPS1pTUjCshkMpjqayEhRYG4+xkAno/esLe3V3m8uFYE8PwL7os7dwCQpj+8yMDAoMiYijteoKRFUjMzM+Hj4wNjY2Ns2bIFZ86cwd69ewE8/3B/kZaWlvTvgr4X7C6iUCgwd+5clWRPbGwsrl27VmJCQEtLC56enpg6dSr++usvzJs3D/Pnzy/UdlF9evH1VygU0NDQwLlz51RiiI+Px48//iiVGT58uMr5mJgYXLt2DXZ2dsW2NWTIENy4cQP9+vVDbGws3NzcVBY9fZm5uTnS0tJKjL+4Pv3666/IyspCYmIibt++DVtbWxgZGcHCwgIAYGFhgX379iEzMxO3bt3CP//8A0NDQ5XRKZMnT0ZAQAB69eoFZ2dn9OvXD+PHj8eiRYtU2ktNTYWBgcEHsYguERG9nocPH2LkyJGoUaMGdHR0YGlpCR8fH0RGRpa6Dnd3dyQlJcHExOQtRlq0itxtzdbWVloj7MXH119/DeD5DZlJkyZh6tSp5d9xIqJX4HQYemdSs3KQmy+grVF07k1HQ450pUBqVslf4l9kYWGB5ORkCCGkL/bR0dHlES6A5yM4QkND4e/vX+jcP//8g3///ReLFy+GjY0NALzWHQ1XV1dcuXIF9vb2bxRr/fr1kZeXh2fPnkFbWxva2tqlmj7k4uKC/Px8pKSkwNPTs9gYL1++XGKMxbVnY2ODESNGYMSIEdIOLqNHjy42lsuXL78y5uJoaWmhevXqAIDt27ejY8eOhaar6Orqolq1asjNzcXu3bvx5ZdfSueysrIKldfQ0Ci0He6lS5ekHWWIiOjj1K1bN+Tk5CA4OBi1a9fGgwcPEBoaWqad2LS1tYtd1Pttqujd1s6cOaPyN8GlS5fQtm1b9OjRQzrWt29fTJw4EXFxcXBycnobLwMRUZE4EoTemUr62tDSkCEnX1nk+ex8JbTkMlTSLzxtpTitWrXCw4cPsXTpUiQkJGD16tU4fPhweYWM2bNnY9u2bZg9ezbi4+OlxT0BoEaNGtDW1sZPP/2EGzduICQkpFTTUV42a9YsbNq0CXPnzkVcXBzi4+Oxfft2zJgxo9hrWrVqhXXr1uHcuXNITEzEoUOHMH36dLRu3RrGxsYAnt+F+fvvv3Hv3j08elT8orMODg7o27cv+vfvjz179uDmzZuIiorCokWLcPDgQQDA1KlTcfLkSYwaNQrR0dG4du0a9u/fLy2MWlx748aNw59//ombN2/i/PnzOH78OBwdHYuNxcfHB6dOnSqUTLl8+TKio6ORmpqK9PR0aTRKgatXr+K3337DtWvXEBUVhV69euHSpUtYuHChVOb06dPYs2cPbty4gYiICPj6+kKpVGLKlClSmU6dOmHBggU4ePAgEhMTsXfvXnz33XcqOwIBzxdwbdeuXbH9ICKiD9vjx48RERGBJUuWoHXr1qhZsyaaNm2KadOm4fPPP1cp++jRI3Tt2hX6+vqoU6cOQkJCpHMvT4cpypo1a2BnZwdtbW3UrVsXmzdvLlSmpDaKUtG7rVlYWMDS0lJ6HDhwAHZ2dtK0YQAwMzODh4cHd1sjoneOSRB6Z5ysjWFXxRBpWbmFprAIIfA4Kxd2VQzhZG1c6jodHR3x888/Y/Xq1WjYsCGioqIwadKkcou5VatW2LVrF0JCQtCoUSO0adNG2i7VwsICQUFB2LVrF+rXr4/Fixdj+fLlZW7Dx8cHBw4cwF9//YUmTZqgefPm+P7771GzZs0SrwkODka7du3g6OiI0aNHw8fHBzt37pTKzJs3D4mJibCzs5OmhBQnMDAQ/fv3x8SJE1G3bl106dIFZ86cQY0aNQA8HxETHh6Oq1evwtPTEy4uLpg1a5a0kGpx7eXn5+Prr7+Go6MjfH194eDggJ9//rnYONq3bw9NTU0cO3ZM5bifnx9cXFzwxx9/ICwsDC4uLiojMfLz87FixQo0bNgQbdu2xbNnz3Dy5EmVrZKfPXuGGTNmoH79+ujatSuqVauGEydOqMzN/umnn9C9e3d89dVXcHR0xKRJkzB8+HCV5Na9e/dw8uTJIkcHERHRx6Fg/at9+/a9cv2nuXPn4ssvv8TFixfh5+eHvn37IjU1tVTt7N27F2PHjsXEiRNx6dIlDB8+HP7+/jh+/PgbtVHRu629KCcnB7/99hsGDRpUaDo0d1sjooogEy9/GyUVGRkZMDExQXp6unSHnV7f/+0Okw9TfS3oaMiRna/E46xcGOpoqOwOQ+pp9erVCAkJwZ9//lnRoRRp6tSpSEtLw/r16ys6FCIieot2796NoUOH4unTp3B1dYWXlxd69eqlsri4TCbDjBkzpGR5ZmYmDA0NcfjwYfj6+iIsLAytW7dGWloaTE1NERQUhHHjxkkjQzw8PODk5KTymfLll18iMzNTGo35qjaK0qhRI3Tr1g0zZ84s8vzAgQPx+PHjQguuTp8+HYGBgThw4IC021rHjh3x4MED3L9/H1ZWVujTpw9iYmKwb98+abe1zp07Iz8/v8iE0c6dO9GnTx+VXegKrFy5Et9//32Ji6wTEZU3jgShd8rd3hwLuzrD0coIWdl5SFFkIys7D45WRkyAEABg+PDhaNmy5Xu5mj0AVKlS5bWmPRER0YelW7duuH//PkJCQqSEhqurK4KCglTKvZgUMTAwgLGxsbQD3KvEx8dL29sX8PDwQHx8/Bu1UdG7rb1o48aNaN++faEECPB8BElxO+EREb0tXBiV3jl3e3M0r10ZcfczkJqVg0r62nCyNoZcLnv1xfTR09TUxDfffFPRYRRr4sSJFR0CERG9I7q6umjbti3atm2LmTNnYsiQIZg9ezYGDhwolXlxBzjg+ciNlxfUflNlbeNNd1tbt24dHjx4ACsrK6xfv77I3daePXuGf//9F9bW1ggICFDZba3ArVu3cOzYMezZs6fI9lJTU185ZZeIqLxxJAhVCLlcBufqJvBysIBzdRMmQIiIiOi9V79+fWRmZpZbfY6OjoW23I2MjET9+vXfqN7y2m1NQ0Pjlbut5eXlYffu3ejcuXOhegIDA1GlShV06NChyHa42xoRVQSOBCEiIiIitadUCmmUqjxbgdljB2PQoEFo0KABjIyMcPbsWSxdurTIL/uva/Lkyfjyyy/h4uICb29v/PHHH9izZ0+hBcLLysfHB0OGDEF+fj40NDSk45cvX0ZOTg5SU1Px5MkTaae1Ro0aAXi+21pUVBSaNWuGtLQ0fPfdd7h06RKCg4OlOk6fPo179+6hUaNGuHfvHubMmVNotzUAUCqVCAwMxIABA6CpWfRXjoiICE4xJaJ3jkmQj9CLH+KcakJERERUspPXH2FNeAISUhTIzRfQELlQ6Nrg28XLkHz3FnJzc2FjY4OhQ4di+vTp5dZuly5d8OOPP2L58uUYO3YsatWqhcDAQLRq1eqN6n1xtzUfHx/puJ+fH27duiU9LxiFUbBPQsFua1euXIGWlhZat25d7G5rN27cgKGhIfz8/LB582aV3dYA4NixY7h9+zYGDRpUZIynTp1Ceno6unfv/kZ9JSIqK+4O8wof2u4wL3+Ia2nIYFfFECO97LjoKBEREdFL/m/nujyY6WtDW0OOnHwl0j7wneve993WevbsiYYNG5ZrUomIqDS4JshHpOBDPD4pAwY6mqhipAMDHU3EJz3B9L2xOHn9UUWHSERERPTeUCoF1oQnQJGdB0tjXehqaUAul0FXSwOWxjpQZOdjTXgClMoP757h+7zbWk5ODpydnTF+/PiKDoWI1BBHgrzChzISRKkUGBAYhfikDFga60Im+7/pL0IIJGdkw9HKCMH+TTk1hoiIiAhA7N10DN98FgY6mtDV0ih0/mluPrKy87Cunxucq5tUQIRERFTeOBLkIxF3PwMJKQqY6WurJECA59uomeprISFFgbj7GRUUIREREdH7JTUrB7n5AtoaRf9JrKMhR65SIDUr5x1HRkREbwuTIB8JfogTERERlU0lfW1oaciQk68s8nx2vhJachkq6Wu/48iIiOhtYRLkI8EPcSIiIqKycbI2hl0VQ6Rl5eLlGeJCCDzOyoVdFUM4Wb+/U6KJiKhsmAT5SPBDnIiIiKhs5HIZRnrZwVBHA8kZ2Xiamw+lUuBpbj6SM7JhqKOBkV52XE+NiOgjwiTIR+JD+RCXyWTYt29fqcrOmTMHjRo1eqvxUMlatmyJrVu3VnQYRQoICMDo0aMrOgwiIvrAudubY2FXZzhaGSErOw8pimxkZefB0crog90el4iIisckyEekqA/xi1sW4tzMtgif0gYedSwgk8kgk8lw/fr1cm17zpw5Ut0aGhqwsbHBsGHDkJqaqlIuKSkJ7du3L9e23zdBQUHSayGXy1G9enX4+/sjJSWlokMrk5CQEDx48AC9evWSjq1fvx6tWrWCsbExZDIZHj9+XOi68+fPo23btjA1NUXlypUxbNgwKBQKlTKhoaFwd3eHkZERLC0tMXXqVOTl5UnnX3w/vfgwMDCQykyaNAnBwcG4ceNG+XeeiIjUiru9OYL9m2JdPzcs79EQ6/q5Idi/KRMgREQfISZBPjIvf4i3qF0ZPj6+SEpKUnnUqlXrterPySl+YVUnJyckJSXh9u3bCAwMxJEjRzBy5EiVMpaWltDR0XmttsuDEELly/abKOm1MDY2RlJSEu7evYtffvkFhw8fRr9+/cql3bLG8rrXrVy5Ev7+/pDL/++/iaysLPj6+mL69OlFXnP//n14e3vD3t4ep0+fxpEjRxAXF4eBAwdKZWJiYuDn5wdfX19cuHABO3bsQEhICAICAqQykyZNKvSerV+/Pnr06CGVMTc3h4+PD9asWfNafSciInqRXC6Dc3UTeDlYwLm6SYWPniUioreDSZCP0Isf4mYG2tDV1YGlpaXKQ0NDAwAQHh6Opk2bQkdHB1ZWVggICFBJErRq1QqjRo3CuHHjpC+dxdHU1ISlpSWqVasGb29v9OjRA0ePHlUp8/J0mLt376J3796oVKkSDAwM4ObmhtOnT6tcs3nzZtja2sLExAS9evXCkydPpHNKpRKLFi1CrVq1oKenh4YNG+L333+XzoeFhUEmk+Hw4cNo3LgxdHR0cOLEiSLjj42NRZs2baCnp1fkCIaBAweiS5cuWLBgAaytrVG3bt1iXwuZTAZLS0tYW1ujffv2GDNmDI4dO4anT59CqVRi3rx5qF69OnR0dNCoUSMcOXKkXGK5c+cOvvzyS5iamqJSpUro3LkzEhMTy9yHhw8f4r///S86deqkcnzcuHEICAhA8+bNi7zuwIED0NLSwurVq1G3bl00adIEa9euxe7du6XRRzt27ECDBg0wa9Ys2Nvbw8vLC0uXLsXq1auln62hoaHK+/XBgwe4fPkyBg8erNJep06dsH379mJ/DkRERERERC9iEkSN3bt3D35+fmjSpAliYmKwZs0abNy4Ed9++61KueDgYGhrayMyMhJr164tVd2JiYn4888/oa1d/G40CoUCXl5euHfvHkJCQhATE4MpU6ZAqfy/HW4SEhKwb98+HDhwAAcOHEB4eDgWL14snV+0aBE2bdqEtWvXIi4uDuPHj8d//vMfhIeHq7QVEBCAxYsXIz4+Hg0aNCgUS2ZmJnx8fGBmZoYzZ85g165dOHbsGEaNGqVSLjQ0FFeuXMHRo0dx4MCBUr0WAKCnpwelUom8vDz8+OOPWLFiBZYvX46LFy/Cx8cHn3/+Oa5du/ZGseTm5sLHxwdGRkaIiIhAZGQkDA0N4evrqzLiozR9OHHiBPT19eHo6FjqPgJAdnY2tLW1VUaP6OnpSXUWlNHV1S30+jx79gznzp0rst4NGzbAwcEBnp6eKsebNm2Ku3fvqiR6iIiIiIiIiiWoROnp6QKASE9Pr+hQXsuAAQOEhoaGMDAwkB7du3cXQggxffp0UbduXaFUKqXyq1evFoaGhiI/P18IIYSXl5dwcXF5ZTuzZ88WcrlcGBgYCF1dXQFAABDfffedSjkAYu/evUIIIdatWyeMjIzEv//+W2yd+vr6IiMjQzo2efJk0axZMyGEEM+ePRP6+vri5MmTKtcNHjxY9O7dWwghxPHjxwUAsW/fvhLjX79+vTAzMxMKhUI6dvDgQSGXy0VycrIQ4vlrWbVqVZGdnV1iXYGBgcLExER6fvXqVeHg4CDc3NyEEEJYW1uLBQsWqFzTpEkT8dVXX71RLJs3by7088zOzhZ6enrizz//LFMfvv/+e1G7du1izxe8rmlpaSrHL126JDQ1NcXSpUtFdna2SE1NFd26dRMAxMKFC4UQQvz5559CLpeLrVu3iry8PHH37l3h6ekpAIitW7cWauvp06fCzMxMLFmypNC5gt/PsLCwEvtDREREREQkhBAcCaIGWrdujejoaOmxcuVKAEB8fDxatGgBmez/5rx6eHhAoVDg7t270rHGjRuXqp26desiOjoaZ86cwdSpU+Hj41Pi7h3R0dFwcXFBpUqVii1ja2sLIyMj6bmVlZW0wOj169eRlZWFtm3bwtDQUHps2rQJCQkJKvW4ubmVGHt8fDwaNmyosvCmh4cHlEolrly5Ih1zdnYucXRLgfT0dBgaGkJfXx9169ZF1apVsWXLFmRkZOD+/fvw8PBQKe/h4YH4+Pg3iiUmJgbXr1+HkZGR9FpUqlQJz549U3k9StOHp0+fFhqtURpOTk4IDg7GihUroK+vD0tLS9SqVQtVq1aVRoe0a9cOy5Ytw4gRI6CjowMHBwf4+fkBgMoIkgJ79+7FkydPMGDAgELnCkaZZGVllTlWIiIiIiJSP5oVHQC9fQYGBrC3t3+j60tDW1tbamfx4sXo0KED5s6di/nz5xdZvuALbEm0tLRUnstkMmm6TMEaGQcPHkS1atVUyr28+Gpp+/Aqpa3HyMgI58+fh1wuh5WVldTXjIyMcomjqFgUCgUaN26MLVu2FCprYWFR7HVFMTc3R1pa2mvF1adPH/Tp0wcPHjyAgYEBZDIZvvvuO9SuXVsqM2HCBIwfPx5JSUkwMzNDYmIipk2bplKmwIYNG9CxY0dUrVq10LmC3Yde7B8REREREVFxOBJEjTk6OuLUqVMQQkjHIiMjYWRkhOrVq79x/TNmzMDy5ctx//79Is83aNAA0dHRhbbRLa369etDR0cHt2/fhr29vcrDxsamTHU5OjoiJiYGmZmZ0rHIyEjI5fISF0Atjlwuh729PWrXrq2S7DE2Noa1tTUiIyNVykdGRqJ+/fpvFIurqyuuXbuGKlWqFHo9TExMyhS/i4sLkpOTXzsRAgBVq1aFoaEhduzYAV1dXbRt21blvEwmg7W1NfT09LBt2zbY2NjA1dVVpczNmzdx/PjxQguiFrh06RK0tLTg5OT02nESEREREZH6YBJEjX311Ve4c+cORo8ejX/++Qf79+/H7NmzMWHChCKnJZRVixYt0KBBAyxcuLDI871794alpSW6dOmCyMhI3LhxA7t378apU6dKVb+RkREmTZqE8ePHIzg4GAkJCTh//jx++uknBAcHlynWvn37QldXFwMGDMClS5dw/PhxjB49Gv369StyBMKbmDx5MpYsWYIdO3bgypUrCAgIQHR0NMaOHftGsfTt2xfm5ubo3LkzIiIicPPmTYSFhWHMmDEq05tKw8XFBebm5oWSNcnJyYiOjpZ2eomNjS2UyFq1ahXOnz+Pq1evYvXq1Rg1ahQWLVoEU1NTqcyyZcsQGxuLuLg4zJ8/H4sXL8bKlSulXYsK/Prrr7CyskL79u2LjDMiIgKenp6lGlVERERERETEJIgaq1atGg4dOoSoqCg0bNgQI0aMwODBgzFjxoxya2P8+PHYsGED7ty5U+ictrY2/vrrL1SpUgV+fn5wdnbG4sWLC30RLsn8+fMxc+ZMLFq0CI6OjvD19cXBgwdRq1atMsWpr6+PP//8E6mpqWjSpAm6d++Ozz77DKtWrSpTPaUxZswYTJgwARMnToSzszOOHDmCkJAQ1KlT541i0dfXx99//40aNWrgiy++gKOjIwYPHoxnz57B2Ni4TDFqaGjA39+/0NSatWvXwsXFBUOHDgUAtGzZEi4uLggJCZHKREVFoW3btnB2dsb69euxbt06jBkzRqWew4cPw9PTE25ubjh48CD279+PLl26qJRRKpUICgrCwIEDi31PbN++XYqFiIiIiIjoVWTixbkQVEhGRgZMTEyQnp5e5i+SRB+y5ORkODk54fz586hZs2ZFh1PI4cOHMXHiRFy8eBGamlzeiIiIiIiIXo0jQYioSJaWlti4cSNu375d0aEUKTMzE4GBgUyAEBERERFRqXEkyCtwJAgRERERERHRx4EjQYiIiIiIiIhILTAJQkRERERERERqgUkQIiIiIiIiIlILTIIQERERERERkVpgEoSIiIiIiIiI1AKTIERERERERESkFpgEISIiIiIiIiK18MEkQVJTU9G3b18YGxvD1NQUgwcPhkKhKLH86NGjUbduXejp6aFGjRoYM2YM0tPT32HURERERERERPS++GCSIH379kVcXByOHj2KAwcO4O+//8awYcOKLX///n3cv38fy5cvx6VLlxAUFIQjR45g8ODB7zBqIiIiIiIiInpfyIQQoqKDeJX4+HjUr18fZ86cgZubGwDgyJEj8PPzw927d2FtbV2qenbt2oX//Oc/yMzMhKamZqmuycjIgImJCdLT02FsbPzafSAiIiIiIiKiivVBjAQ5deoUTE1NpQQIAHh7e0Mul+P06dOlrqcgkVFSAiQ7OxsZGRkqDyIiIiIiIiL68H0QSZDk5GRUqVJF5ZimpiYqVaqE5OTkUtXx6NEjzJ8/v8QpNACwaNEimJiYSA8bG5vXjpuIiIiIiIiI3h8VmgQJCAiATCYr8fHPP/+8cTsZGRno0KED6tevjzlz5pRYdtq0aUhPT5ced+7ceeP2iYiIiIiIiKjilW5hjLdk4sSJGDhwYIllateuDUtLS6SkpKgcz8vLQ2pqKiwtLUu8/smTJ/D19YWRkRH27t0LLS2tEsvr6OhAR0enVPETERERERER0YejQpMgFhYWsLCweGW5Fi1a4PHjxzh37hwaN24MAPjvf/8LpVKJZs2aFXtdRkYGfHx8oKOjg5CQEOjq6pZb7ERERERERET0Yfkg1gRxdHSEr68vhg4diqioKERGRmLUqFHo1auXtDPMvXv3UK9ePURFRQF4ngBp164dMjMzsXHjRmRkZCA5ORnJycnIz8+vyO4QERERERERUQWo0JEgZbFlyxaMGjUKn332GeRyObp164aVK1dK53Nzc3HlyhVkZWUBAM6fPy/tHGNvb69S182bN2Fra/vOYiciIiIiIiKiiicTQoiKDuJ9lpGRARMTE2l7XSIiIiIiIiL6MH0Q02GIiIiIiIiIiN4UkyBEREREREREpBaYBCEiIiIiIiIitcAkCBERERERERGpBSZBiIiIiIiIiEgtMAlCRERERERERGqBSRAiIiIiIiIiUgtMghARERERERGRWmAShIiIiIiIiIjUgmZFB0BERERE9DFRKgXi7mcgNSsHlfS14WRtDLlcVtFhERERmAQhIiIiIio3J68/wprwBCSkKJCbL6ClIYNdFUOM9LKDu715RYdHRKT2OB2GiIiIiKgcnLz+CNP3xiI+KQMGOpqoYqQDAx1NxCc9wfS9sTh5/VFFh0hEpPaYBCEiIiIiekNKpcCa8AQosvNgaawLXS0NyOUy6GppwNJYB4rsfKwJT4BSKSo6VKIKMWfOHDRq1KhC2ra1tcUPP/xQIW0XZc6cOahatSpkMhn27dtXITGEhYVBJpPh8ePHJZYLDQ2Fo6Mj8vPz301gZfDo0SNUqVIFd+/eLdN1TIIQEREREb2huPsZSEhRwExfGzKZ6vofMpkMpvpaSEhRIO5+RgVFSB+7gQMHQiaTQSaTQUtLC1WrVkXbtm3x66+/QqlUVnR4772MjAx88803qFevHnR1dWFpaQlvb2/s2bMHQpRf8jI+Ph5z587FunXrkJSUhPbt25db3W/DlClTMGPGDGhoaAAAkpKS0KdPHzg4OEAul2PcuHGFrsnNzcW8efNgZ2cHXV1dNGzYEEeOHFEp8+TJE4wbNw41a9aEnp4e3N3dcebMGZUyc+bMQb169WBgYAAzMzN4e3vj9OnT0nlzc3P0798fs2fPLlOfmAQhIiIiInpDqVk5yM0X0NYo+s9rHQ05cpUCqVk57zgyUie+vr5ISkpCYmIiDh8+jNatW2Ps2LHo2LEj8vLyKjq899bjx4/h7u6OTZs2Ydq0aTh//jz+/vtv9OzZE1OmTEF6enq5tZWQkAAA6Ny5MywtLaGjo1NudZe3EydOICEhAd26dZOOZWdnw8LCAjNmzEDDhg2LvG7GjBlYt24dfvrpJ1y+fBkjRoxA165dceHCBanMkCFDcPToUWzevBmxsbFo164dvL3/X3v3Ht9z/f9//P5+72zz3sLYpjmuzSFnEmIOw6qPD+rj/BE+St8i5RuhIuUbPoVKUX2KxEcfQkqSUsxxjpkch2WRQ0tjM2On9/P3h5/3p7fNYWTD63a9XN6XS3u+nq/X6/F6v59bdt/z9XzF6MiRI64+kZGReuedd7Rjxw6tXbtWlSpVUrt27fTbb7+5+vTr109z5sxRamrqVV8XIQgAAABwnUqV8JaXh03ZeQX/xT0rzykvu02lSngXcWWwEh8fH4WEhKh8+fKqX7++nn/+eX3xxRf6+uuvNXPmTFe/yZMnq1atWvL391d4eLiefPJJZWRkuLa3bNnSNavkj6/k5GRJ50ODRx99VMHBwXI4HGrdurW2b9/uVsuECRNUrlw5lSxZUv3799e5c+cuW3teXp769++vypUry8/PT1FRUXrrrbfc+vTt21edOnXSxIkTFRoaqtKlS2vgwIHKyclx9UlJSVGHDh3k5+enypUra86cOVd8355//nklJydr48aN6tOnj2rUqKHIyEg99thjSkhIUEBAgCTp5MmTeuSRR3THHXeoRIkSuv/++7V//37XcWbOnKmgoCB98803ql69ugICAlzBlHR+ZkOHDh0kSXa73TVrrGXLlvlmVHTq1El9+/Z1fT1t2jTddddd8vX1Vbly5fS3v/3Ntc3pdGr8+PGu965OnTpasGCB2/GWLl2qyMhI+fn5qVWrVq7P8nLmzp2rtm3bytfX19VWqVIlvfXWW3rkkUcUGBhY4H6zZ8/W888/rwceeEBVqlTRE088oQceeECTJk2SJJ09e1YLFy7Ua6+9phYtWigiIkJjxoxRRESE3n33XddxevbsqZiYGFWpUkU1a9bU5MmTlZ6erh9//NHVp2bNmgoLC9OiRYuueD0XEIIAAAAA16lmmENVywboZGZOvqnzxhidysxR1bIBqhnmKKYKrWH69Olq165dcZdRoGtdv+B6tW7dWnXq1NFnn33marPb7ZoyZYp27dqljz/+WCtWrNBzzz3n2v7ZZ5/p2LFjrtdDDz2kqKgolStXTpLUpUsXpaSk6Ouvv9bWrVtVv359tWnTxvXX+E8//VRjxozRuHHjtGXLFoWGhmratGmXrdPpdOrOO+/U/PnztXv3bo0ePVrPP/+8Pv30U7d+K1euVFJSklauXKmPP/5YM2fOdAt4+vbtq8OHD2vlypVasGCBpk2bppSUlMued+7cuerVq5fCwsLybQ8ICJCnp6fr2Fu2bNHixYsVHx8vY4weeOABtxAmMzNTEydO1OzZs7V69WodOnRIQ4cOlSQNHTpUH330kSS53tursWXLFg0ePFivvPKKEhMTtWzZMrVo0cK1ffz48Zo1a5bee+897dq1S0OGDNHf//53rVq1SpJ0+PBhPfTQQ+rQoYMSEhL06KOPasSIEVc875o1a9SwYcOrqvGPsrKy3IITSfLz89PatWslSbm5ucrLy7tsn4tlZ2frX//6lwIDA/PNQLnnnnu0Zs2aqy/Q4LLS0tKMJJOWllbcpQAAAOAmtm7/byb6tRWmdL22pkzNZuaBN1ebNpPiTIOxy030ayvM2//+3EgyJ0+eLO5Sr8qAAQOM3W43n376abHWIcksWrToiv3Onj1rQkNDzdq1a11tO3fuNA899JCpWLGikWTeeOONfPulp6ebp59+2lSoUMH4+vqaJk2amE2bNrn1OX78uOnTp48JDQ01fn5+pn379mbfvn35jrV+/XrTqlUrU6JECVOyZEnTvHlzk5mZ6dr+7LPPmn/84x9Xf/GF0KdPH9OxY8cCt3Xr1s1Ur179kvvOnz/flC5dusBtkydPNkFBQSYxMdEYY8yaNWuMw+Ew586dc+tXtWpV8/777xtjjGnSpIl58skn3bY3btzY1KlT5yqv5ryBAweahx9+2PV1nz59TMWKFU1ubq6rrUuXLqZbt27GGGMSExONJLfPb8+ePZf87I0x5tdffzWSzOTJky9by759+4wks27dOlfbiRMnjJ+fn+t75KOPPjKSzIEDB1x9pk6dasqVK+f6etGiRebiX8Ojo6PN008/7dbWsWNH06dPH2OMMQsXLjQOh8Okp6fnq+vcuXOmRIkSZv369W7t/fv3Nz169DDGGDNy5EhTo0YNt+3Dhw+/4s+jwMBAM2vWrEtuL6huY4zp0aOHqVGjhtm3b5/Jy8sz3377rfHz8zPe3t6uPk2aNDHR0dHmyJEjJjc318yePdvY7XYTGRnpdqwvv/zS+Pv7G5vNZsLCwvJ9bxpjzJAhQ6hD4HsAAD8gSURBVEzLli0vWefFmAkCAAAA/AmaRpTRuM61FOjnpTynUUpGljKzclU9tKTGda6lu8sXPHX8ZpSZmam5c+fqueee04wZM67YPzu74LVO/vgX8httwYIFcjgcatasmastMzNTVapU0YQJExQSElLgfldam8AYo06dOumnn37SF198oW3btqlixYqKiYnRmTNnXMeJj49XbGys2rVrp02bNmnz5s0aNGiQ7Pb//sp1LesX/BmMMW4L9n733Xdq06aNypcvr5IlS6p37976/ffflZmZ6bbf119/rREjRmjevHmKjIyUJG3fvl0ZGRkqXbq0AgICXK+DBw+61rvYs2ePGjdu7HasJk2aXLHOqVOnqkGDBgoODlZAQID+9a9/6dChQ259atas6VqkU5JCQ0NdMz327NkjT09PNWjQwLW9WrVqCgoKuux7czUuHPuP11W6dGlFRUVpz549rrYSJUqoatWqBdZ3rdq2bauKFSuqSpUq6t27t+bMmeP6rA4cOKDMzEy1bdvW7fOYNWvWdX8eZ8+ezTdb42q89dZbuuuuu1StWjV5e3tr0KBB6tevn9v3wuzZs2WMUfny5eXj46MpU6aoR48ebn0kqVWrVkpISND69esVGxurrl275ns//fz88o3dyyEEAQAAAP4kTSPK6L6IYNUND9LELnX0fu+G+rjfPWoaUabA/gsXLlTNmjXl4+OjSpUque6Zv6CgR2gGBQW5pv9nZ2dr0KBBCg0Nla+vrypWrKjx48e7+l7N2g0FmT9/vmrUqKERI0Zo9erVOnz4sNv2C2szvPrqqwoLC1NUVJSSk5Nls9k0b948RUdHy9fX17Uew4cffqjq1avL19dX1apVc7s14nLXUKlSJUlS586dZbPZXF8XZO7cua71Fi5o1KiRXn/9dXXv3r3ABSivZm2C/fv3a8OGDXr33XfVqFEjRUVF6d1339XZs2f1n//8x3WsIUOGaPDgwRoxYoRq1qypqKgode3a1e2817J+wZ9hz549qly5siQpOTlZf/nLX1S7dm0tXLhQW7du1dSpUyW5h1m7d+9W9+7dNWHCBLdbjDIyMhQaGqqEhAS3V2JiooYNG3bNNc6dO1dDhw5V//799e233yohIUH9+vXLF7B5eXm5fW2z2a7r6TfBwcEKCgrS3r17r/kYf1RQfVcKWux2e74+fwwQS5YsqR9++EH/+c9/FBoaqtGjR6tOnTo6deqUay2Xr776yu3z2L17d751QQqrTJkyOnnyZKH3Cw4O1ueff64zZ87o559/1t69exUQEKAqVaq4+lStWlWrVq1SRkaGDh8+rE2bNiknJ8etjyT5+/srIiJC9957r6ZPny5PT09Nnz7drU9qaqqCg4Ovuj5CEAAAAOBPZLNJDj8vRUcGq9adgbLbbQX227p1q7p27aru3btrx44dGjNmjEaNGuW2vsGVTJkyRYsXL9ann36qxMREzZkzxy0ouNLaDZcyffp0/f3vf1dgYKDuv//+Amv6/vvvlZiYqOXLl2vJkiWu9hEjRujpp5/Wnj171L59e82ZM0ejR4/Wq6++qj179mjcuHEaNWqUPv744ytew4VHZn700Uc6duxYvkdo/tHatWsLvX7B1axNkJWVJUlufex2u3x8fFx9UlJStHHjRpUtW1ZNmzZVuXLlFB0dXeD6BoVev+A6rVixQjt27HA94WPr1q1yOp2aNGmS7r33XkVGRuro0aNu+5w4cUIdOnTQww8/rCFDhrhtq1+/vo4fPy5PT09FRES4vcqUOR/2Va9e3e1RppK0YcOGy9a5bt06NW3aVE8++aTq1auniIgI10yGq1WtWjXl5uZq69atrrbExESdOnXqkvvY7XZ1795dc+bMyfc+SOdDn9zcXFWvXl25ublu1/X7778rMTFRNWrUKFSdFwsODnZbHyQvL087d+506+Pp6amYmBi99tpr+vHHH5WcnKwVK1aoRo0a8vHx0aFDh/J9HuHh4ZLOfx6bNm1yO96VPg9Jqlevnnbv3n3N1+Xr66vy5csrNzdXCxcuVMeOHfP18ff3V2hoqE6ePKlvvvmmwD5/5HQ6Xd+TF+zcuVP16tW7+sKu+sYZi2JNEAAAABRGnz59jIeHh/H393d7+fr6ut2D37NnT9O2bVu3fYcNG+Z2774KWA8jMDDQfPTRR8YYY5566inTunVr43Q689VxNWs3FGTfvn3Gy8vL/Pbbb8aY82sYVK5c2e0cffr0MeXKlTNZWVmutoMHDxpJ5s0338x3vk8++cStbezYsaZJkyZXvIZLvQcXO3nypJFkVq9efck+FStWLHBdiCutTZCdnW0qVKhgunTpYlJTU01WVpaZMGGCkWTatWtnjDEmPj7eSDKlSpUyM2bMMD/88IN55plnjLe3d761Qwq7fsHV6tOnj4mNjTXHjh0zv/zyi9m6dat59dVXTUBAgPnLX/7iWkcjISHB9TklJSWZWbNmmfLly7uNzRYtWpi7777b/Pzzz+bYsWOuV25urnE6nea+++4zderUMd988405ePCgWbdunXn++efN5s2bjTHGzJ071/j6+poZM2aYxMREM3r0aFOyZMnLrgny1ltvGYfDYZYtW2YSExPNiy++aBwOh9s+Ba178vTTT5vo6GjX17GxsaZevXpmw4YNZsuWLea+++4zfn5+l1wTxBhjfv/9d1OtWjVz5513mo8//tjs2rXL7Nu3z0yfPt1ERES43peOHTuaGjVqmDVr1piEhAQTGxtrIiIiTHZ2tjHm/JoggYGBbse+eA2QhQs/M5JMXGKK+fHwKZOX5zTvvfeeKVGihFmyZInZs2ePeeyxx4zD4XCtCfLll1+at956y2zbts0kJyebadOmGbvdbnbu3GmMMeaFF14wpUuXNjNnzjQHDhwwW7duNVOmTDEzZ840xhjz888/G29vbzN06FCzd+9eM2fOHBMSEnLFNUGmTJliGjRokK9927ZtZtu2baZBgwamZ8+eZtu2bWbXrl2u7Rs2bDALFy40SUlJZvXq1aZ169amcuXKbudatmyZ+frrr81PP/1kvv32W1OnTh3TuHFj13uZkZFhRo4caeLj401ycrLZsmWL6devn/Hx8XFdtzHGnDlzxvj5+V32e/9ihCBXQAgCAACAwujTp4+JiYkx+/fvd3v9+9//dvulo169embMmDFu+37++efGy8vL9QvrlUKQrVu3mlKlSpm77rrLPPXUU+abb75x9XvnnXeM3W7PF8bY7Xbz3HPPXbL+ESNGmL/85S+ur7OyskypUqXMd999l+8a/+hCCPLHhUkzMjKMJOPn5+dWg4+PjylbtuwVr+FS78HFjh49mm9BzItdKgQ5cOCAadGihZFkPDw8TKNGjUyvXr1MtWrVXH22bNli6tSp4+rTvn17c//995vY2FhjjDHr1q0zkszIkSPdjl2rVi0zYsQIt7bnn3/e3HPPPZe9nmvRp08fI8lIMp6eniY4ONjExMSYGTNmmLy8PLe+kydPdlvkddasWW5j88JxLn4dPHjQGHN+MdmnnnrKhIWFGS8vLxMeHm569eplDh065DrHq6++asqUKWMCAgJMnz59zHPPPXfZEOTcuXOmb9++JjAw0AQFBZknnnjCjBgxotAhyLFjx8yDDz5ofHx8TIUKFcysWbMu+dn/0alTp8yIESPMXXfdZby9vU25cuVMTEyMWbRokSugS01NNb179zaBgYEFLpB7pRBk3f7fTPTAfxpJpuHY5abJuO/M3z/cYFbtPmqeeOIJU6pUKVO2bFkzfvx4t4VR16xZY6Kjo80dd9xh/Pz8TO3atc28efNc53A6nebNN980UVFRxsvLywQHB5v27dubVatWufp8+eWXJiIiwvj4+JjmzZubGTNmXDEE+f33342vr6/Zu3evW3tBY6NixYqu7XFxcaZ69erGx8fHlC5d2vTu3dscOXLE7Rjz5s0zVapUMd7e3iYkJMQMHDjQnDp1yrX97NmzpnPnziYsLMx4e3ub0NBQ89e//jXf9/gnn3xioqKiLnkNBbH9/4vAJaSnpyswMFBpaWlyOHikGQAAAC6vb9++OnXqVL61POLi4tSqVSudPHlSQUFBql+/vjp27KiXXnrJ1eeLL75Qly5ddPbsWXl4eMhut2vhwoXq3Lmzq4+/v7+mTp2qvn37Sjr/79Wvv/5a3333nebPn6+YmBgtWLBA//znP/X2228rLi4uX41BQUGuWxf+KC8vT+Hh4Tp+/LjbAoV5eXnq2bOna42Pgq4xOTlZlStX1rZt21S3bl1J0q+//qqQkBD9+9//zrcwo4eHh2udiktdg3R+TYVFixapU6dOl3zPs7Oz5evrq2XLll3yEbmVKlXSM888o2eeeabA7WfOnFF6erpCQ0PVrVs3ZWRk6KuvvnLrk5aWpuzsbAUHB6tx48Zq2LChpk6dqoMHD6pKlSqaPXu2/v73v7v6d+vWTZ6enq73TZKeeOIJHT582O0WItz+1h84oecX7VBGVq7uKOEtbw+7svOcOpmZowAfD43rXOuSawcVp2HDhik9PV3vv/9+cZdSoHvvvVeDBw9Wz549r3ofzxtYDwAAAIBLqF69utatW+fWtm7dOkVGRrqefnHxWgH79+/P9xQEh8Ohbt26qVu3bvrb3/6m2NhYpaamuq3dcLkFRf9o6dKlOn36tLZt2+b2BI6dO3eqX79+OnXq1GWftHGxcuXKKSwsTD/99JN69ep1yX6XuoZSpUrJy8tLeXl5lz2Pt7e3atSood27d18yBLkSf39/+fv7u9YmeO211/L1CQw8/4Sf/fv3a8uWLRo7dqyk8wFLWFiYEhMT3frv27dP999/v1vbzp071bJly2uqEbcmp9Po3VVJysjKVYjD1/WkHl+7h0Icdh1Pz9K7q5J0b5XSl1xDqLi88MILmjZtmpxOZ74ntxS3EydO6KGHHlKPHj0KtR8hCAAAAFAMnn32WTVq1Ehjx45Vt27dFB8fr3feecftySmtW7fWO++8oyZNmigvL0/Dhw93e/rE5MmTFRoaqnr16slut2v+/PkKCQlRUFCQYmJi1KRJE3Xq1EmvvfaaawHMr776Sp07dy5wEdHp06frwQcfVJ06ddzaa9SooSFDhmjOnDkaOHBgoa7z5Zdf1uDBgxUYGKjY2FhlZWVpy5YtOnnypP73f//3stcgnQ8Yvv/+ezVr1kw+Pj664447CjxP+/bttXbtWreZHtnZ2a6FHbOzs3XkyBElJCQoICBAERERkqRvvvlGxhhFRUXpwIEDGjZsmKpVq6Z+/fq5jjN//nwFBwerQoUK2rFjh55++ml16tTJFbjYbDYNGzZML730kurUqaO6devq448/1t69e92e0JGZmamtW7dq3LhxhXoPcWvbdTRdSSkZuqOEt9ujiqXzYyeohJeSUjK062i6at15cz1KOygoSM8//3xxl1GgMmXK6Lnnniv0fjdXlAMAAABYRP369fXpp59q7ty5uvvuuzV69Gi98sorrttcJGnSpEkKDw9X8+bN1bNnTw0dOlQlSpRwbS9ZsqRee+01NWzYUI0aNVJycrKWLl0qu90um82mpUuXqkWLFurXr58iIyPVvXt3/fzzzypXrly+en799Vd99dVXrqeI/JHdblfnzp3zPZryajz66KP68MMP9dFHH6lWrVqKjo7WzJkzXbfCXO4aLrwHy5cvV3h4+GWfANG/f38tXbpUaWlprrajR4+qXr16qlevno4dO6aJEyeqXr16evTRR1190tLSNHDgQFWrVk2PPPKI7rvvPn3zzTduYdOxY8fUu3dvVatWTYMHD1bv3r3dHo8rSc8884xGjhypIUOGqE6dOvr++++1fPlyVa1a1dXniy++UIUKFdS8efNCv4+4daVmZisnz8jbo+Bfv3087MpxGqVmZhe4HX8u1gS5AtYEAQAAAG4NXbp0Uf369TVy5MjiLqVA17J+AW59O35J0+Ozt8jfx1O+Xh75tp/NyVNmVq7e793wppsJcjtiJggAAACA28Lrr7+ugICA4i6jQNe6fgFufTXDHKpaNkAnM3N08RwEY4xOZeaoatkA1Qzjj+5FgZkgV8BMEAAAAADA9fjv02HyFFTCSz4edmXlOXXqJn86zO2ImSAAAAAAANxATSPKaFznWqoeWlKZWblKychSZlauqoeWJAApYswEuQJmggAAAAAA/gxOp9Guo+lKzcxWqRLeqhnmuOkei3u74xG5AAAAAAAUAbvdxuKnxYzbYQAAAAAAgCUQggAAAAAAAEsgBAEAAAAAAJZACAIAAAAAACyBEAQAAAAAAFgCIQgAAAAAALAEQhAAAAAAAGAJhCAAAAAAAMASCEEAAAAAAIAlEIIAAAAAAABLIAQBAAAAAACWQAgCAAAAAAAsgRAEAAAAAABYAiEIAAAAAACwBEIQAAAAAABgCYQgAAAAAADAEghBAAAAAACAJRCCAAAAAAAASyAEAQAAAAAAlkAIAgAAAAAALIEQBAAAAAAAWAIhCAAAAAAAsARCEAAAAAAAYAmEIAAAAAAAwBIIQQAAAAAAgCUQggAAAAAAAEsgBAEAAAAAAJZACAIAAAAAACyBEAQAAAAAAFgCIQgAAAAAALAEQhAAAAAAAGAJhCAAAAAAAMASCEEAAAAAAIAlEIIAAAAAAABLIAQBAAAAAACWQAgCAAAAAAAsgRAEAAAAAABYAiEIAAAAAACwBEIQAAAAAABgCYQgAAAAAADAEghBAAAAAACAJRCCAAAAAAAASyAEAQAAAAAAlkAIAgAAAAAALIEQBAAAAAAAWAIhCAAAAAAAsARCEAAAAAAAYAmEIAAAAAAAwBIIQQAAAAAAgCUQggAAAAAAAEsgBAEAAAAAAJZACAIAAAAAACyBEAQAAAAAAFgCIQgAAAAAALAEQhAAAAAAAGAJhCAAAAAAAMASCEEAAAAAAIAlEIIAAAAAAABLIAQBAAAAAACWQAgCAAAAAAAsgRAEAAAAAABYAiEIAAAAAACwBEIQAAAAAABgCYQgAAAAAADAEghBAAAAAACAJRCCAAAAAAAASyAEAQAAAAAAlkAIAgAAAAAALIEQBAAAAAAAWAIhCAAAAAAAsARCEAAAAAAAYAmEIAAAAAAAwBIIQQAAAAAAgCUQggAAAAAAAEsgBAEAAAAAAJZACAIAAAAAACzhlglBUlNT1atXLzkcDgUFBal///7KyMi4qn2NMbr//vtls9n0+eef39hCAQAAAADATemWCUF69eqlXbt2afny5VqyZIlWr16tAQMGXNW+b775pmw22w2uEAAAAAAA3Mw8i7uAq7Fnzx4tW7ZMmzdvVsOGDSVJb7/9th544AFNnDhRYWFhl9w3ISFBkyZN0pYtWxQaGlpUJQMAAAAAgJvMLTETJD4+XkFBQa4ARJJiYmJkt9u1cePGS+6XmZmpnj17aurUqQoJCbmqc2VlZSk9Pd3tBQAAAAAAbn23RAhy/PhxlS1b1q3N09NTpUqV0vHjxy+535AhQ9S0aVN17Njxqs81fvx4BQYGul7h4eHXXDcAAAAAALh5FGsIMmLECNlstsu+9u7de03HXrx4sVasWKE333yzUPuNHDlSaWlprtfhw4ev6fwAAAAAAODmUqxrgjz77LPq27fvZftUqVJFISEhSklJcWvPzc1VamrqJW9zWbFihZKSkhQUFOTW/vDDD6t58+aKi4srcD8fHx/5+Phc7SUAAAAAAIBbhM0YY4q7iCvZs2ePatSooS1btqhBgwaSpG+//VaxsbH65ZdfClwY9fjx4zpx4oRbW61atfTWW2+pQ4cOqly58lWdOz09XYGBgUpLS5PD4bj+iwEAAAAAAMXilng6TPXq1RUbG6vHHntM7733nnJycjRo0CB1797dFYAcOXJEbdq00axZs3TPPfcoJCSkwFkiFSpUuOoABAAAAAAA3D5uiYVRJWnOnDmqVq2a2rRpowceeED33Xef/vWvf7m25+TkKDExUZmZmcVYJQAAAAAAuFndErfDFCduhwEAAAAA4PZwy8wEAQAAAAAAuB6EIAAAAAAAwBIIQQAAAAAAgCUQggAAAAAAAEsgBAEAAAAAAJZACAIAAAAAACyBEAQAAAAAAFgCIQgAAAAAALAEQhAAAAAAAGAJhCAAAAAAAMASCEEAAAAAAIAlEIIAAAAAAABLIAQBAAAAAACWQAgCAAAAAAAsgRAEAAAAAABYAiEIAAAAAACwBEIQAAAAAABgCYQgAAAAAADAEghBAAAAAACAJRCCAAAAAAAASyAEAQAAAAAAlkAIAgAAAAAALIEQBAAAAAAAWAIhCAAAAAAAsARCEAAAAAAAYAmEIAAAAAAAwBIIQQAAAAAAgCUQggAAAAAAAEsgBAEAAAAAAJZACAIAAAAAACyBEAQAAAAAAFgCIQgAAAAAALAEQhAAAAAAAGAJhCAAAAAAAMASCEEAAAAAAIAlEIIAAAAAAABLIAQBAAAAAACWQAgCAAAAAAAsgRAEAAAAAABYAiEIAAAAAACwBEIQAAAAAABgCYQgAAAAAADAEghBAAAAAACAJRCCAAAAAAAASyAEAQAAAAAAlkAIAgAAAAAALIEQBAAAAAAAWAIhCAAAAAAAsARCEAAAAAAAYAmEIAAAAAAAwBIIQQAAAAAAgCUQggAAAAAAAEsgBAEAAAAAAJZACAIAAAAAACyBEAQAAAAAAFgCIQgAAAAAALAEQhAAAAAAAGAJhCAAAAAAAMASPIu7AAAAANw+nE6jXUfTlZqZrVIlvFUzzCG73VbcZQEAIIkQBAAAAH+S9QdO6N1VSUpKyVBOnpGXh01VywboieiqahpR5pqPGxcXp1atWunkyZMKCgr68woGAFgOt8MAAADguq0/cELPL9qhPcfS5e/jqbIlfeTv46k9x07r+UU7tP7AieIuEQAAQhAAAABcH6fT6N1VScrIylWIw1e+Xh6y223y9fJQiMNHGVl5endVkpxOU9ylAgAsjhAEAAAA12XX0XQlpWTojhLestnc1/+w2WzaNfnvWrvoY+06mu5qr1u3rsaMGePq8+GHH6pz584qUaKE7rrrLi1evPiS58vMzNT999+vZs2a6dSpU0pOTpbNZtNnn32mVq1aqUSJEqpTp47i4+Pd9lu4cKFq1qwpHx8fVapUSZMmTXJte+edd3T33Xe7vv78889ls9n03nvvudpiYmL04osvSpLGjBmjunXravbs2apUqZICAwPVvXt3nT59uvBvIACgyBCCAAAA4LqkZmYrJ8/I26Pgf1raZFOeOd/vUl5++WV17dpVP/74ox544AH16tVLqamp+fqdOnVKbdu2ldPp1PLly93WCHnhhRc0dOhQJSQkKDIyUj169FBubq4kaevWreratau6d++uHTt2aMyYMRo1apRmzpwpSYqOjtbu3bv122+/SZJWrVqlMmXKKC4uTpKUk5Oj+Ph4tWzZ0nW+pKQkff7551qyZImWLFmiVatWacKECYV45wAARY0QBAAAANelVAlveXnYlJ3nLHC7kZGH7Xy/S+nbt6969OihiIgIjRs3ThkZGdq0aZNbn+PHjys6OlqhoaH68ssvVaJECbftQ4cO1YMPPqjIyEi9/PLL+vnnn3XgwAFJ0uTJk9WmTRuNGjVKkZGR6tu3rwYNGqTXX39dknT33XerVKlSWrVqlaTzi7E+++yzrq83bdqknJwcNW3a1HU+p9OpmTNn6u6771bz5s3Vu3dvff/994V89wAARYkQBAAAANelZphDVcsG6GRmjoxxX/fDGCOnkUoH+KhmmOOSx6hdu7brv/39/eVwOJSSkuLWp23btoqIiNC8efPk7Z0/UPnjMUJDQyXJdYw9e/aoWbNmbv2bNWum/fv3Ky8vTzabTS1atFBcXJxOnTql3bt368knn1RWVpb27t2rVatWqVGjRm7BS6VKlVSyZEm3c15cMwDg5kIIAgAAgOtit9v0RHRVBfh46Hh6ls7m5MnpNDqbk6fj6Vmy2+1qWrW07Pb/rheSk5PjdgwvLy+3r202m5xO95klDz74oFavXq3du3cXWMcfj3FhbZKLj3E5LVu2VFxcnNasWaN69erJ4XC4gpFVq1YpOjq60DUDAG4uhCAAAAC4bk0jymhc51qqHlpSmVm5SsnIUmZWrqqHllSVO0Plm/PfRVHT09N18ODBQp9jwoQJ6tOnj9q0aXPJIORSqlevrnXr1rm1rVu3TpGRkfLw8JD033VB5s+f71r7o2XLlvruu++0bt06t/VAAAC3Js/iLgAAAAC3h6YRZXRvldLadTRdqZnZKlXCWzXDHHrhQDvNnDlTHTp0UFBQkEaPHu0KHgpr4sSJysvLU+vWrRUXF6dq1apd1X7PPvusGjVqpLFjx6pbt26Kj4/XO++8o2nTprn61K5dW3fccYc++eQTLVmyRNL5EGTo0KGy2Wz5bqcBANx6CEEAAADwp7Hbbap1Z6Bb28iRI3Xw4EH95S9/UWBgoMaOHXtNM0EueOONN9yCkILWB7lY/fr19emnn2r06NEaO3asQkND9corr6hv376uPjabTc2bN9dXX32l++67T9L5YMThcCgqKkr+/v7XXDMA4OZgMxevXgU36enpCgwMVFpamhyOSy/mBQAAAAAAbm6sCQIAAAAAACyBEAQAAAAAAFgCIQgAAAAAALAEQhAAAAAAAGAJhCAAAAAAAMASCEEAAAAAAIAlEIIAAAAAAABLIAQBAAAAAACWQAgCALeBuLg42Ww2nTp16rqOM2bMGNWtW/dPqQn/1bt3b40bN664yyjQsmXLVLduXTmdzuIuBQAA4IYjBAGAP0Hfvn3VqVOnfO1/VjjxZxo/frw8PDz0+uuvF3cpV6179+6KjY11a1u2bJlsNpvGjBnj1j5mzBhVqFDhqo5bFKHP9u3btXTpUg0ePNjV9tlnn6ldu3YqXbq0bDabEhIS8u2XlJSkzp07Kzg4WA6HQ127dtWvv/7q1ueHH35Q27ZtFRQUpNKlS2vAgAHKyMjId6yZM2eqdu3a8vX1VdmyZTVw4EDXttjYWHl5eWnOnDl/3kUDAADcpAhBAMBiZsyYoeeee04zZswo7lKuWqtWrbRu3Trl5ua62lauXKnw8HDFxcW59V25cqVatWpVpPVlZ2dfctvbb7+tLl26KCAgwNV25swZ3XffffrnP/9Z4D5nzpxRu3btZLPZtGLFCq1bt07Z2dnq0KGDa8bG0aNHFRMTo4iICG3cuFHLli3Trl271LdvX7djTZ48WS+88IJGjBihXbt26bvvvlP79u3d+vTt21dTpky5xqsHAAC4dRCCAEARW7t2rZo3by4/Pz+Fh4dr8ODBOnPmjGv77Nmz1bBhQ5UsWVIhISHq2bOnUlJS3I6xdOlSRUZGys/PT61atVJycvJVnXvVqlU6e/asXnnlFaWnp2v9+vUF9nv//fcVHh6uEiVKqGvXrkpLS3NtczqdeuWVV3TnnXfKx8dHdevW1bJly1zbmzZtquHDh7sd77fffpOXl5dWr14tScrKytLQoUNVvnx5+fv7q3HjxvnCjD9q1aqVMjIytGXLFldbXFycRowYoY0bN+rcuXOSpHPnzmnjxo2uEGT48OGKjIxUiRIlVKVKFY0aNUo5OTmSzs+OePnll7V9+3bZbDbZbDbNnDlTknTq1Ck9+uijrlkYrVu31vbt213nvjCD5MMPP1TlypXl6+tbYN15eXlasGCBOnTo4Nbeu3dvjR49WjExMQXut27dOiUnJ2vmzJmqVauWatWqpY8//lhbtmzRihUrJElLliyRl5eXpk6dqqioKDVq1EjvvfeeFi5cqAMHDkiSTp48qRdffFGzZs1Sz549VbVqVdWuXVt//etf3c7XoUMHbdmyRUlJSZf8DAAAAG4HhCAAUISSkpIUGxurhx9+WD/++KPmzZuntWvXatCgQa4+OTk5Gjt2rLZv367PP/9cycnJbn/dP3z4sB566CF16NBBCQkJevTRRzVixIirOv/06dPVo0cPeXl5qUePHpo+fXq+PgcOHNCnn36qL7/8UsuWLdO2bdv05JNPura/9dZbmjRpkiZOnKgff/xR7du311//+lft379fktSrVy/NnTtXxhjXPvPmzVNYWJiaN28uSRo0aJDi4+M1d+5c/fjjj+rSpYtiY2Ndx7hYZGSkwsLCtHLlSknS6dOn9cMPP6hLly6qVKmS4uPjJUnr169XVlaWKwQpWbKkZs6cqd27d+utt97SBx98oDfeeEOS1K1bNz377LOqWbOmjh07pmPHjqlbt26SpC5duiglJUVff/21tm7dqvr166tNmzZKTU11e58WLlyozz77rMDbWSTpxx9/VFpamho2bHjlD+cPsrKyZLPZ5OPj42rz9fWV3W7X2rVrXX28vb1lt//3f+V+fn6S5OqzfPlyOZ1OHTlyRNWrV9edd96prl276vDhw27nq1ChgsqVK6c1a9YUqk4AAIBbjsFlpaWlGUkmLS2tuEsBcBPr06eP8fDwMP7+/m4vX19fI8mcPHnSGGNM//79zYABA9z2XbNmjbHb7ebs2bMFHnvz5s1Gkjl9+rQxxpiRI0eaGjVquPUZPny423kKkpaWZvz8/ExCQoIxxpht27aZgIAA13GNMeall14yHh4e5pdffnG1ff3118Zut5tjx44ZY4wJCwszr776qtuxGzVqZJ588kljjDEpKSnG09PTrF692rW9SZMmZvjw4cYYY37++Wfj4eFhjhw54naMNm3amJEjR16y/l69epl27doZY4z56quvXO/BgAEDzOjRo40xxowaNcpUrlz5ksd4/fXXTYMGDdyut06dOm591qxZYxwOhzl37pxbe9WqVc3777/v2s/Ly8ukpKRc8lzGGLNo0SLj4eFhnE5ngdsPHjxoJJlt27a5taekpBiHw2Gefvppc+bMGZORkWEGDRpkJLnGz86dO42np6d57bXXTFZWlklNTTUPP/ywkWTGjRtnjDFm/PjxxsvLy0RFRZlly5aZ+Ph406ZNGxMVFWWysrLczlmvXj0zZsyYy14PAADArY6ZIADwJ2nVqpUSEhLcXh9++KFbn+3bt2vmzJkKCAhwvdq3by+n06mDBw9KkrZu3aoOHTqoQoUKKlmypKKjoyVJhw4dkiTt2bNHjRs3djtukyZNrljff/7zH1WtWlV16tSRJNWtW1cVK1bUvHnz3PpVqFBB5cuXdzu20+lUYmKi0tPTdfToUTVr1sxtn2bNmmnPnj2SpODgYLVr18610ObBgwcVHx+vXr16SZJ27NihvLw8RUZGur0Pq1atuuztGC1bttS6deuUk5OjuLg4tWzZUpIUHR3tupUmLi7ObT2QefPmqVmzZgoJCVFAQIBefPFF1/t4Kdu3b1dGRoZKly7tVt/Bgwfd6qtYsaKCg4Mve6yzZ8/Kx8dHNpvtsv0uFhwcrPnz5+vLL79UQECAAgMDderUKdWvX98186NmzZr6+OOPNWnSJJUoUUIhISGqXLmyypUr5+rjdDqVk5OjKVOmqH379rr33nv1n//8R/v373fNqrnAz89PmZmZhaoTAADgVuNZ3AUAwO3C399fERERbm2//PKL29cZGRl6/PHH3Z4UckGFChV05swZtW/fXu3bt9ecOXMUHBysQ4cOqX379pddfPNqTJ8+Xbt27ZKn539/9DudTs2YMUP9+/e/rmNfrFevXho8eLDefvttffLJJ651LaTz74GHh4e2bt0qDw8Pt/3+uHjoxVq1aqUzZ85o8+bNWrlypYYNGybpfAjyj3/8Q6mpqdq4caMef/xxSXIFLy+//LLat2+vwMBAzZ07V5MmTbps7RkZGQoNDS1wjZKgoCDXf/v7+1/xfShTpowyMzOVnZ0tb2/vK/b/o3bt2ikpKUknTpyQp6engoKCFBISoipVqrj69OzZUz179tSvv/4qf39/2Ww2TZ482dUnNDRUklSjRg3XPsHBwSpTpky+MCg1NfWKoQ4AAMCtjhAEAIpQ/fr1tXv37nxhyQU7duzQ77//rgkTJig8PFyS3BYDlaTq1atr8eLFbm0bNmy47Hl37NihLVu2KC4uTqVKlXK1p6amqmXLltq7d6+qVasm6fyMk6NHjyosLMx1bLvdrqioKDkcDoWFhWndunWuGSrS+YU877nnHtfXHTt21IABA7Rs2TJ98skneuSRR1zb6tWrp7y8PKWkpLjWCLkaVatWVXh4uBYvXqyEhATX+cuXL6/y5ctr0qRJys7Ods0EWb9+vSpWrKgXXnjBdYyff/7Z7Zje3t7Ky8tza6tfv76OHz8uT09PVapU6arrK8iFx+/u3r37mh/FW6ZMGUnSihUrlJKSkm9RU0kqV66cpPNP/vH19VXbtm0lyTVjJzExUXfeeaek85/5iRMnVLFiRdf+586dU1JSkurVq3dNNQIAANwquB0GAK6S02m045c0rdr3m3b8kian01x5p4sMHz5c69ev16BBg5SQkKD9+/friy++cC2MWqFCBXl7e+vtt9/WTz/9pMWLF2vs2LFux/if//kf7d+/X8OGDVNiYqI++eQT11NNLmX69Om655571KJFC919992uV4sWLdSoUSO3BVJ9fX3Vp08fbd++XWvWrNHgwYPVtWtXhYSESJKGDRumf/7zn5o3b54SExM1YsQIJSQk6Omnn3Ydw9/fX506ddKoUaO0Z88e9ejRw7UtMjJSvXr10iOPPKLPPvtMBw8e1KZNmzR+/Hh99dVXl72OVq1aadq0aYqIiHD94i+dnw3y9ttvuxZQlaS77rpLhw4d0ty5c5WUlKQpU6Zo0aJFbserVKmSDh48qISEBJ04cUJZWVmKiYlRkyZN1KlTJ3377bdKTk7W+vXr9cILL+QLpK4kODhY9evXdy1UekFqaqoSEhK0e/duSedDioSEBB0/ftzV56OPPtKGDRuUlJSkf//73+rSpYuGDBmiqKgoV5933nlHP/zwg/bt26epU6dq0KBBGj9+vGvGSmRkpDp27Kinn35a69ev186dO9WnTx9Vq1bN7bahDRs2yMfH56puqwIAALilFfeiJDc7FkYFYIwx6/b/Zv7+4QbTZNx3puHY5abJuO/M3z/cYNbt/80Yc35h1I4dO+bbb+XKlfkWLN20aZNp27atCQgIMP7+/qZ27dpuC41+8sknplKlSsbHx8c0adLELF68ON/imV9++aWJiIgwPj4+pnnz5mbGjBmXXBg1KyvLlC5d2rz22msFXts///lPU7ZsWZOdne1aKHTatGkmLCzM+Pr6mr/97W8mNTXV1T8vL8+MGTPGlC9f3nh5eZk6deqYr7/+Ot9xly5daiSZFi1a5NuWnZ1tRo8ebSpVqmS8vLxMaGio6dy5s/nxxx8LrPGCjz76yEgy//M//+PWPnPmTCPJPP74427tw4YNM6VLlzYBAQGmW7du5o033jCBgYGu7efOnTMPP/ywCQoKMpLMRx99ZIwxJj093Tz11FMmLCzMeHl5mfDwcNOrVy9z6NAhY0zBC6peyrRp08y9995b4HVc/HrppZdcfYYPH27KlStnvLy8zF133WUmTZqUb4HV3r17m1KlShlvb29Tu3ZtM2vWrHznT0tLM//4xz9MUFCQKVWqlOncubPrOi4YMGBAvvcOAADgdmQzxhT+T5kWkp6ersDAQKWlpcnhcBR3OQCKwfoDJ/T8oh3KyMrVHSW85e1hV3aeUyczcxTg46FxnWupaUSZ4i4TN6mzZ88qKipK8+bNuylnWpw4cUJRUVHasmWLKleuXNzlAAAA3FDcDgMAl+F0Gr27KkkZWbkKcfjK18tDdrtNvl4eCnH4KCMrT++uSrqmW2NgDX5+fpo1a5ZOnDhR3KUUKDk5WdOmTSMAAQAAlsBMkCtgJghgbTt+SdPjs7fI38dTvl4e+bafzclTZlau3u/dULXuDCyGCgEAAABcLWaCAMBlpGZmKyfPyNuj4B+XPh525TiNUjOv7/G1AAAAAG48QhAAuIxSJbzl5WFTdp6zwO1ZeU552W0qVcK7iCsDAAAAUFiEIABwGTXDHKpaNkAnM3N08d2DxhidysxR1bIBqhnG7XIAAADAzY4QBAAuw2636Ynoqgrw8dDx9CydzcmT02l0NidPx9OzFODjoSeiq8putxV3qQAAAACugBAEAK6gaUQZjetcS9VDSyozK1cpGVnKzMpV9dCSPB4XAAAAuIXwdJgr4OkwAC5wOo12HU1Xama2SpXwVs0wBzNAAAAAgFuIZ3EXAAC3CrvdxmNwAQAAgFsYt8MAAAAAAABLIAQBAAAAAACWQAgCAAAAAAAsgRAEAAAAAABYAiEIAAAAAACwBEIQAAAAAABgCYQgAAAAAADAEghBAAAAAACAJRCCAAAAAAAAS7hlQpDU1FT16tVLDodDQUFB6t+/vzIyMq64X3x8vFq3bi1/f385HA61aNFCZ8+eLYKKAQAAAADAzeSWCUF69eqlXbt2afny5VqyZIlWr16tAQMGXHaf+Ph4xcbGql27dtq0aZM2b96sQYMGyW6/ZS4bAAAAAAD8SWzGGFPcRVzJnj17VKNGDW3evFkNGzaUJC1btkwPPPCAfvnlF4WFhRW437333qu2bdtq7Nix13zu9PR0BQYGKi0tTQ6H45qPAwAAAAAAitctMSUiPj5eQUFBrgBEkmJiYmS327Vx48YC90lJSdHGjRtVtmxZNW3aVOXKlVN0dLTWrl172XNlZWUpPT3d7QUAAAAAAG59t0QIcvz4cZUtW9atzdPTU6VKldLx48cL3Oenn36SJI0ZM0aPPfaYli1bpvr166tNmzbav3//Jc81fvx4BQYGul7h4eF/3oUAAAAAAIBiU6whyIgRI2Sz2S772rt37zUd2+l0SpIef/xx9evXT/Xq1dMbb7yhqKgozZgx45L7jRw5Umlpaa7X4cOHr+n8AAAAAADg5uJZnCd/9tln1bdv38v2qVKlikJCQpSSkuLWnpubq9TUVIWEhBS4X2hoqCSpRo0abu3Vq1fXoUOHLnk+Hx8f+fj4XEX1AAAAAADgVlKsIUhwcLCCg4Ov2K9JkyY6deqUtm7dqgYNGkiSVqxYIafTqcaNGxe4T6VKlRQWFqbExES39n379un++++//uIBAAAAAMAt5ZZYE6R69eqKjY3VY489pk2bNmndunUaNGiQunfv7noyzJEjR1StWjVt2rRJkmSz2TRs2DBNmTJFCxYs0IEDBzRq1Cjt3btX/fv3L87LAQAAAAAAxaBYZ4IUxpw5czRo0CC1adNGdrtdDz/8sKZMmeLanpOTo8TERGVmZrrannnmGZ07d05DhgxRamqq6tSpo+XLl6tq1arFcQkAAAAAAKAY2YwxpriLuJmlp6crMDBQaWlpcjgcxV0OAAAAAAC4RrfE7TAAAAAAAADXixAEAAAAAABYAiEIAAAAAACwBEIQAAAAAABgCYQgAAAAAADAEghBAAAAAACAJRCCAAAAAAAASyAEAQAAAAAAlkAIAgAAAAAALIEQBAAAAAAAWAIhCAAAAAAAsARCEAAAAAAAYAmEIAAAAAAAwBIIQQAAAAAAgCUQggAAAAAAAEsgBAEAAAAAAJZACAIAAAAAACyBEAQAAAAAAFgCIQgAAAAAALAEz+Iu4GZnjJEkpaenF3MlAAAAAADgckqWLCmbzXbJ7YQgV3D69GlJUnh4eDFXAgAAAAAALictLU0Oh+OS223mwlQHFMjpdOro0aNXTJNwc0tPT1d4eLgOHz582W8IQGK84OoxVlAYjBcUBuMFhcF4QWHc7uOFmSDXyW6368477yzuMvAncTgct+U3Om4MxguuFmMFhcF4QWEwXlAYjBcUhlXHCwujAgAAAAAASyAEAQAAAAAAlkAIAkvw8fHRSy+9JB8fn+IuBbcAxguuFmMFhcF4QWEwXlAYjBcUhtXHCwujAgAAAAAAS2AmCAAAAAAAsARCEAAAAAAAYAmEIAAAAAAAwBIIQQAAAAAAgCUQguC2lZqaql69esnhcCgoKEj9+/dXRkbGFfeLj49X69at5e/vL4fDoRYtWujs2bNFUDGKy7WOFUkyxuj++++XzWbT559/fmMLxU2hsOMlNTVVTz31lKKiouTn56cKFSpo8ODBSktLK8KqUVSmTp2qSpUqydfXV40bN9amTZsu23/+/PmqVq2afH19VatWLS1durSIKsXNoDDj5YMPPlDz5s11xx136I477lBMTMwVxxduL4X9+XLB3LlzZbPZ1KlTpxtbIG4ahR0rp06d0sCBAxUaGiofHx9FRkbe1v8/IgTBbatXr17atWuXli9friVLlmj16tUaMGDAZfeJj49XbGys2rVrp02bNmnz5s0aNGiQ7Ha+VW5n1zJWLnjzzTdls9lucIW4mRR2vBw9elRHjx7VxIkTtXPnTs2cOVPLli1T//79i7BqFIV58+bpf//3f/XSSy/phx9+UJ06ddS+fXulpKQU2H/9+vXq0aOH+vfvr23btqlTp07q1KmTdu7cWcSVozgUdrzExcWpR48eWrlypeLj4xUeHq527drpyJEjRVw5ikNhx8sFycnJGjp0qJo3b15ElaK4FXasZGdnq23btkpOTtaCBQuUmJioDz74QOXLly/iyouQAW5Du3fvNpLM5s2bXW1ff/21sdls5siRI5fcr3HjxubFF18sihJxk7jWsWKMMdu2bTPly5c3x44dM5LMokWLbnC1KG7XM17+6NNPPzXe3t4mJyfnRpSJYnLPPfeYgQMHur7Oy8szYWFhZvz48QX279q1q3nwwQfd2ho3bmwef/zxG1onbg6FHS8Xy83NNSVLljQff/zxjSoRN5FrGS+5ubmmadOm5sMPPzR9+vQxHTt2LIJKUdwKO1beffddU6VKFZOdnV1UJRY7/ryN21J8fLyCgoLUsGFDV1tMTIzsdrs2btxY4D4pKSnauHGjypYtq6ZNm6pcuXKKjo7W2rVri6psFINrGSuSlJmZqZ49e2rq1KkKCQkpilJxE7jW8XKxtLQ0ORwOeXp63ogyUQyys7O1detWxcTEuNrsdrtiYmIUHx9f4D7x8fFu/SWpffv2l+yP28e1jJeLZWZmKicnR6VKlbpRZeImca3j5ZVXXlHZsmWZeWgh1zJWFi9erCZNmmjgwIEqV66c7r77bo0bN055eXlFVXaRIwTBben48eMqW7asW5unp6dKlSql48ePF7jPTz/9JEkaM2aMHnvsMS1btkz169dXmzZttH///hteM4rHtYwVSRoyZIiaNm2qjh073ugScRO51vHyRydOnNDYsWOv+pYr3BpOnDihvLw8lStXzq29XLlylxwbx48fL1R/3D6uZbxcbPjw4QoLC8sXpOH2cy3jZe3atZo+fbo++OCDoigRN4lrGSs//fSTFixYoLy8PC1dulSjRo3SpEmT9H//939FUXKxIATBLWXEiBGy2WyXfe3du/eaju10OiVJjz/+uPr166d69erpjTfeUFRUlGbMmPFnXgaKwI0cK4sXL9aKFSv05ptv/rlFo9jcyPHyR+np6XrwwQdVo0YNjRkz5voLB2BJEyZM0Ny5c7Vo0SL5+voWdzm4yZw+fVq9e/fWBx98oDJlyhR3ObjJOZ1OlS1bVv/617/UoEEDdevWTS+88ILee++94i7thmEeLm4pzz77rPr27XvZPlWqVFFISEi+xX9yc3OVmpp6yVsXQkNDJUk1atRwa69evboOHTp07UWjWNzIsbJixQolJSUpKCjIrf3hhx9W8+bNFRcXdx2VozjcyPFywenTpxUbG6uSJUtq0aJF8vLyut6ycRMpU6aMPDw89Ouvv7q1//rrr5ccGyEhIYXqj9vHtYyXCyZOnKgJEybou+++U+3atW9kmbhJFHa8JCUlKTk5WR06dHC1Xfhjn6enpxITE1W1atUbWzSKxbX8bAkNDZWXl5c8PDxcbdWrV9fx48eVnZ0tb2/vG1pzcSAEwS0lODhYwcHBV+zXpEkTnTp1Slu3blWDBg0knf/F1el0qnHjxgXuU6lSJYWFhSkxMdGtfd++fbr//vuvv3gUqRs5VkaMGKFHH33Ura1WrVp644033P7BgVvHjRwv0vkZIO3bt5ePj48WL17MX25vQ97e3mrQoIG+//5712MonU6nvv/+ew0aNKjAfZo0aaLvv/9ezzzzjKtt+fLlatKkSRFUjOJ0LeNFkl577TW9+uqr+uabb9zWJsLtrbDjpVq1atqxY4db24svvqjTp0/rrbfeUnh4eFGUjWJwLT9bmjVrpk8++UROp9P1RMx9+/YpNDT0tgxAJPF0GNy+YmNjTb169czGjRvN2rVrzV133WV69Ojh2v7LL7+YqKgos3HjRlfbG2+8YRwOh5k/f77Zv3+/efHFF42vr685cOBAcVwCisi1jJWLiafDWEZhx0taWppp3LixqVWrljlw4IA5duyY65Wbm1tcl4EbYO7cucbHx8fMnDnT7N692wwYMMAEBQWZ48ePG2OM6d27txkxYoSr/7p164ynp6eZOHGi2bNnj3nppZeMl5eX2bFjR3FdAopQYcfLhAkTjLe3t1mwYIHbz5HTp08X1yWgCBV2vFyMp8NYR2HHyqFDh0zJkiXNoEGDTGJiolmyZIkpW7as+b//+7/iuoQbjhAEt63ff//d9OjRwwQEBBiHw2H69evn9g+FgwcPGklm5cqVbvuNHz/e3HnnnaZEiRKmSZMmZs2aNUVcOYratY6VPyIEsY7CjpeVK1caSQW+Dh48WDwXgRvm7bffNhUqVDDe3t7mnnvuMRs2bHBti46ONn369HHr/+mnn5rIyEjj7e1tatasab766qsirhjFqTDjpWLFigX+HHnppZeKvnAUi8L+fPkjQhBrKexYWb9+vWncuLHx8fExVapUMa+++upt/YcamzHGFP38EwAAAAAAgKLF02EAAAAAAIAlEIIAAAAAAABLIAQBAAAAAACWQAgCAAAAAAAsgRAEAAAAAABYAiEIAAAAAACwBEIQAAAAAABgCYQgAAAAAADAEghBAAAAAACAJRCCAAAAAAAASyAEAQAAAAAAlkAIAgAALOG3335TSEiIxo0b52pbv369vL299f333xdjZQAAoKjYjDGmuIsAAAAoCkuXLlWnTp20fv16RUVFqW7duurYsaMmT55c3KUBAIAiQAgCAAAsZeDAgfruu+/UsGFD7dixQ5s3b5aPj09xlwUAAIoAIQgAALCUs2fP6u6779bhw4e1detW1apVq7hLAgAARYQ1QQAAgKUkJSXp6NGjcjqdSk5OLu5yAABAEWImCAAAsIzs7Gzdc889qlu3rqKiovTmm29qx44dKlu2bHGXBgAAigAhCAAAsIxhw4ZpwYIF2r59uwICAhQdHa3AwEAtWbKkuEsDAABFgNthAACAJcTFxenNN9/U7Nmz5XA4ZLfbNXv2bK1Zs0bvvvtucZcHAACKADNBAAAAAACAJTATBAAAAAAAWAIhCAAAAAAAsARCEAAAAAAAYAmEIAAAAAAAwBIIQQAAAAAAgCUQggAAAAAAAEsgBAEAAAAAAJZACAIAAAAAACyBEAQAAAAAAFgCIQgAAAAAALAEQhAAAAAAAGAJ/w/wAQIq9RFV4wAAAABJRU5ErkJggg==\n"},"metadata":{}}],"source":["TOP2F = (24, 49)\n","SAMPLE_SIZE = 20\n","\n","rng = np.random.RandomState(SEED)\n","sample_inds = rng.choice(np.arange(bpr.i_factors.shape[0]), size=SAMPLE_SIZE, replace=False)\n","sample_df = pd.DataFrame(data=bpr.i_factors[sample_inds][:, TOP2F], columns=[\"x\", \"y\"])\n","\n","sns.lmplot(x=\"x\", y=\"y\", data=sample_df, height=11.0, fit_reg=False)\n","item_idx2id = list(bpr.train_set.item_ids)\n","titles = item_df.loc[[int(item_idx2id[i]) for i in sample_inds]][\"Title\"].values\n","adjust_text(\n","  [plt.text(*sample_df.loc[i].values, titles[i], size=10) for i in range(len(titles))]\n",");"]},{"cell_type":"markdown","metadata":{"id":"0FmiuTYiP_pB"},"source":["## References\n","\n","1.   Aggarwal, C. C. (2016). Recommender systems (Vol. 1). Cham: Springer International Publishing.\n","2.   Hu, Y., Koren, Y., & Volinsky, C. (2008, December). Collaborative filtering for implicit feedback datasets. In 2008 Eighth IEEE International Conference on Data Mining (pp. 263-272). Ieee.\n","3.   Rendle, S., Freudenthaler, C., Gantner, Z., & Schmidt-Thieme, L. (2012). BPR: Bayesian personalized ranking from implicit feedback. arXiv preprint arXiv:1205.2618.   \n","4.   Cornac - A Comparative Framework for Multimodal Recommender Systems (https://cornac.preferred.ai/)\n","5.   https://github.com/recommenders-team/recommenders/blob/main/examples/02_model_collaborative_filtering/cornac_bpr_deep_dive.ipynb\n","\n"]}],"metadata":{"accelerator":"GPU","colab":{"provenance":[]},"kernelspec":{"display_name":"Python 3","name":"python3"},"language_info":{"name":"python","version":"3.9.16"}},"nbformat":4,"nbformat_minor":0}