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"cells": [
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"cell_type": "markdown",
"metadata": {},
"source": [
"# When Prediction Fails\n",
" \n",
"## When all you have is a Hammer...\n",
"Between 2015 and 2020, Machine Learning went through a massive surge. Its proven usefulness in the fields of computer vision and natural language understanding, coupled with an initial lack of professionals in the area, provided the perfect opportunity for a machine learning teaching industry. Figures like Andrew Ng and Sebastian Thrun managed to teach machine learning to the world at rock bottom prices. At the same time, on the software side, it became increasingly easier to fit a complex machine learning model (as you've already seen by the very few lines of code it took us to write an ML in the previous chapter). Tutorials about how to make intelligent systems sprung all over the internet. The cost of entry in ML plummeted.\n",
"\n",
"![img](./data/img/when-prediction-fails/ml-in-5.png)\n",
" \n",
"Building ML became so simple that you didn't even need to know how to code very well (and I'm living evidence of that), nor the math behind the algorithms. In fact, you could build wonders with the following 5 lines of Python.\n",
" \n",
"```python\n",
"X_train, y_train, X_test, y_test = train_test_split(X, y)\n",
" \n",
"## instantiate the machine learning model\n",
"model = MachineLearningModel()\n",
" \n",
"## Fit the ML model\n",
"model.fit(X_train, y_train)\n",
" \n",
"# Make predictions on unseen data\n",
"y_pred = model.predict(X_test)\n",
" \n",
"# Evaluate the quality of predictions\n",
"print(\"Performance\", metric(y_test, y_pred))\n",
"```\n",
" \n",
"For the most part, this is an amazing thing! I'm all in for taking valuable content and making it available. However, there is also a dark side to all of this. This new wave of data scientists were trained mostly in predictive modeling, since that is what ML primarily focuses on solving. As a result, whenever those data scientists encountered a business problem, they tried to tackle it with, not surprisingly, predictive models. When they were indeed prediction problems, like the one we saw in the previous chapter, the data scientist usually succeeded and everyone got happy. However, there is an entire class of problems that are simply not solvable with prediction techniques. And when those appeared, the data scientists usually failed miserably. These are problems that are framed like \"how much can I increase Y by changing X\".\n",
" \n",
"From my experience, this other type of problem is what management usually cares the most about. They often want to know how to increase sales, decrease cost or bring in more customers. Needless to say, they are not very happy when a data scientist comes up with an answer to how to predict sales instead of how to increase it. Sadly, when everything the data scientist knows is predictive models, this tends to happen a lot. As a boss of mine once told me: \"when all you have is a hammer, everything starts to look like a thumb\". \n",
" \n",
"Like I've said, I'm all in for lowering the cost of knowledge, but the current Data Scientist curriculum has a huge gap. I think that my job here is to fill in that gap. Is to equip you with tools to solve this other class of problems, which are causal in nature. \n",
"\n",
"What you are trying to do is estimate how something you can control (advertisement, price, customer service) affects or causes something you want to change, but can't control directly (sales, number of customers, PNL). But ,before showing you how to solve these problems, I want to show you what happens when you treat them like prediction tasks and try to solve them with the traditional ML toolkit. The reason for it is that data scientists often come to me and say \"OK, but although tackling causal problems with prediction tools is not the best idea, it surely helps something, no? Imean, it couldn't hurt...\". Well, as it turns out, it can. And you better understand this before you go on hammering your own thumb.\n",
"\n",
"![img](./data/img/when-prediction-fails/horse-meme.png)\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"tags": [
"hide-input"
]
},
"outputs": [],
"source": [
"import pandas as pd\n",
"import numpy as np\n",
"from sklearn import ensemble\n",
"from sklearn.model_selection import train_test_split, cross_val_predict\n",
"from sklearn.ensemble import gradient_boosting\n",
"from sklearn.metrics import r2_score\n",
"import seaborn as sns\n",
"from matplotlib import pyplot as plt\n",
"from matplotlib import style\n",
"style.use(\"ggplot\")\n",
"\n",
"# helper functions for this notebook\n",
"from nb18 import ltv_with_coupons"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Who Wants a Coupon?\n",
" \n",
"To make matters more relatable, let's continue with the example we used in the previous chapter, but with a little twist to it. Before, we were trying to distinguish the profitable from the non profitable customers. We framed that as a prediction problem: predicting customer profitability. We could then build a machine learning model for this task and use it to choose who we would do business with: only the customers we predicted to be profitable. In other words, our goal was to separate the profitable from the non-profitable, which we could do with a predictive model.\n",
" \n",
"Now, you have a new task. You suspect that giving coupons to new customers increases their engagement with your business and makes them more profitable in the long run. That is, they spend more and for a longer period. Your new assignment is to figure out how much the coupon value should be (zero included). Notice that, with coupons, you are essentially giving away money for people to spend on your business. For this reason, they enter as a cost in your book account. Notice that if the coupon value is too high, you will probably lose money, since customers will buy all they need using only the coupons. That's another way of saying that they will get your product for free. On the flip side, if coupon value is too low (or zero), you are not even giving coupons. This could be a valid answer, but it could also be that some discounts upfront, in the form of coupons, will be more profitable in the long run. \n",
" \n",
"For reasons you will see later, we will use a data generating function instead of loading a static dataset. The function `ltv_with_coupons` generates transaction data for us. As you can see, they have the same format as the one we saw previously, with one row per customer, a column for the cost of acquisition and columns for the transactions between day 1 and 30. "
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(10000, 32)\n"
]
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" customer_id cacq day_0 day_1 day_2 day_3 day_4 day_5 day_6 day_7 \\\n",
"0 0 -110 0 0 0 0 5 0 2 2 \n",
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"2 2 -8 0 0 0 0 0 0 0 0 \n",
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"[5 rows x 32 columns]"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"transactions, customer_features = ltv_with_coupons()\n",
"\n",
"print(transactions.shape)\n",
"transactions.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As for the other parts of the data, again, we have a customer identifier, the region the customer lives, the customer income and the customer age. In addition, we now have a variable that is `coupons`, which tells us how much we've given in coupons for that customer."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(10000, 5)\n"
]
},
{
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],
"source": [
"print(customer_features.shape)\n",
"customer_features.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To process this data to a single dataframe, we will sum all the columns in the first table (that is, summing `CACQ` with the transactions).This will give us the `net_value` as it was computed in the previous chapter. After that, we will join in the features data and update the `net_value` to include the coupon cost."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
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" customer_id region income coupons age net_value\n",
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"3 3 29 1859 15 35 -45\n",
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},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"def process_data(transactions, customer_data):\n",
"\n",
" profitable = (transactions[[\"customer_id\"]]\n",
" .assign(net_value = transactions\n",
" .drop(columns=\"customer_id\")\n",
" .sum(axis=1)))\n",
"\n",
" return (customer_data\n",
" # join net_value and features\n",
" .merge(profitable, on=\"customer_id\")\n",
" # include the coupons cost\n",
" .assign(net_value = lambda d: d[\"net_value\"] - d[\"coupons\"]))\n",
"\n",
"customer_features = process_data(transactions, customer_features)\n",
"customer_features.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This processed data frame has all that we need. It has our target variable `net_value`, it has our customer features `region`, `income` and `age`, and it has the lever or treatment we want to optimise for: coupons. Just to begin understanding how coupons can increase `net_value`, let's look at how they were given away."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"coupons\n",
"0 458\n",
"5 4749\n",
"10 4154\n",
"15 639\n",
"Name: customer_id, dtype: int64"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"customer_features.groupby(\"coupons\")[\"customer_id\"].count()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can see that most of the coupons that were handed out had a value of 5 BRL, followed by the coupons with 10 BRL in value. We gave very few 15 BRL coupons or no coupons at all (zero value). This is indicative that they were **NOT** given randomly. To check that, let's see the correlation between the other variable and coupons."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
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"metadata": {},
"output_type": "execute_result"
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"source": [
"customer_features.corr()[[\"coupons\"]]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"That's interesting. It looks like the older the person, the higher the probability he or she will receive a coupon. This is some indication of bias in our data. We can also see a negative correlation between coupons and `net_value`: the more coupons we give, the smaller the net_value. This is hardly causal, since we already know that coupons were not randomly distributed. It could be that, say, older people spend less on our products and also receive higher coupon values, confounding the relationship between coupons and `net_value` to the point of making it negative.\n",
"\n",
"The point being, we know there is bias. However, since there is already too much packed into this chapter, I'll ignore it for now (actually, I'll bypass the problem with an artifact you will see in just a moment). Just keep in mind it's something we will have to address sometime in the future.\n",
"\n",
"At this point in the analysis, **if this was a prediction problem**, we would probably split the dataset into a training and a test set to build and evaluate some policies, respectively. But this is NOT a prediction problem. The final goal here is not to get a good prediction on customer profitability. Instead, it's to figure out the optimal coupon strategy. To evaluate this optimization, we would have to know how things would have played out if we have given different coupons than the ones that were given. This is the sort of counterfactual \"what if'' question we've been studying under causality. Cross validation won't help us here because we simply can't observe counterfactuals. We can only see what happened for the coupons that were actually given, but we can't know what would have happened if customers received a different coupon value. Unless, we have simulated data!\n",
"\n",
"If our data is simulated, we can generate the exact same data, only changing the coupon value parameters. This will allow us to see how `net_value` changes under different coupons strategies. We will then be able to calculate the treatment effect between different strategies $NetValue_{t=a} - NetValue_{t=b}$. With the power of simulated data, understanding this chapter will be much easier. Oh yes, and this will also render the bias problem irrelevant, because we will observe the causal effect directly. \n",
"\n",
"Nevertheless, always remember that this is a pedagogical artifact. In the real world, you don't have simulated data and you certainly can't see what would have happened under different treatment strategies. Individual causal effects remain hidden as they always have been. This poses an interesting problem. How can we evaluate our strategies for identifying causal effect if we can never see the actual causal effect? The real answer is very involved and so important that it deserves its own chapter. Rest assured that we will tackle it. For now, just enjoy the simplicity of simulated data. And speaking of simplicity...\n",
"\n",
"\n",
"## Simple Policy\n",
"\n",
"As always, the first thing we should do whenever we encounter a new data problem is to ask ourselves \"what is the simplest thing I can do that will already bring value?\". For this specific case, the simplest thing is to look back on the data that we have and estimate the `net_value` for each coupon value. Then, check which coupon value is generating the highest `net_value` and give only that coupon value for every customer. "
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sns.barplot(data=customer_features, x=\"coupons\", y=\"net_value\")\n",
"plt.title(\"Net Value by Coupon Value\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Doing that analysis, we can see that, on average, we lose money when the coupon value is 0 or 15 and we gain money for coupons of 5 and 10 BRL. The highest average `net_income` appears when we have 5 BRL coupons, yielding us about 250 BRL in `net_value` per customer. Naturally then, the simplest thing we can try is to give everyone 5 BRL in coupons and see how that would play out. This completely disregards the possibility of bias but hey, we are talking simplicity here!\n",
"\n",
"To do evaluate that policy, the function `ltv_with_coupons` accepts as argument a 10000 array that contains the desired coupon for each of the 10000 customers on our database. To create this array, we will generate an array of ones with `np.ones` the size of our `coupons` array (10000) and multiply it by 5. Then, we will pass this array to the `ltv_with_coupons`. This will generate a new dataset exactly like the one we had previously, but with every coupon value set to 5. We then process this data to get the net value under this newly proposed policy."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"
\n",
"\n",
"
\n",
" \n",
"
\n",
"
\n",
"
customer_id
\n",
"
region
\n",
"
income
\n",
"
coupons
\n",
"
age
\n",
"
net_value
\n",
"
\n",
" \n",
" \n",
"
\n",
"
0
\n",
"
0
\n",
"
18
\n",
"
1025
\n",
"
5
\n",
"
24
\n",
"
-44
\n",
"
\n",
"
\n",
"
1
\n",
"
1
\n",
"
40
\n",
"
1649
\n",
"
5
\n",
"
26
\n",
"
74
\n",
"
\n",
"
\n",
"
2
\n",
"
2
\n",
"
35
\n",
"
2034
\n",
"
5
\n",
"
33
\n",
"
63
\n",
"
\n",
"
\n",
"
3
\n",
"
3
\n",
"
29
\n",
"
1859
\n",
"
5
\n",
"
35
\n",
"
63
\n",
"
\n",
"
\n",
"
4
\n",
"
4
\n",
"
11
\n",
"
1243
\n",
"
5
\n",
"
26
\n",
"
-26
\n",
"
\n",
" \n",
"
\n",
"
"
],
"text/plain": [
" customer_id region income coupons age net_value\n",
"0 0 18 1025 5 24 -44\n",
"1 1 40 1649 5 26 74\n",
"2 2 35 2034 5 33 63\n",
"3 3 29 1859 5 35 63\n",
"4 4 11 1243 5 26 -26"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"simple_policy = 5 * np.ones(customer_features[\"coupons\"].shape)\n",
"\n",
"transactions_simple_policy, customer_features_simple_policy = ltv_with_coupons(simple_policy)\n",
"customer_features_simple_policy = process_data(transactions_simple_policy, customer_features_simple_policy)\n",
"\n",
"customer_features_simple_policy.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Just as a sanity check, let's see if the features are indeed unchanged, considering the first few customers. Take the third one, for example (`customer_id` 2). For this customer, the region is 35, income is 2034 and the age is 33. If we scroll up a bit, we can see that it matches what we had before, so we are good here. Also, we can check that all the coupons are indeed 5 BRL. Finally, the `net_value` changes as expected. One reason for this is that the cost associated with coupons will change. For example, that customer had 15 BRL in coupons, but now it's 5. This would decrease the cost from 15 to 5 units. But notice that the `net_value` goes from -23 to 63, a 86 BRL increase in `net_value`. This is much larger than the 10 cost difference. Here giving less in the coupons made this particular customer much more profitable than he or she was before. Finally, to evaluate the policy, we can simply take the average `net_value`."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"252.9268"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"simple_policy_gain = customer_features_simple_policy[\"net_value\"].mean()\n",
"simple_policy_gain"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As we can see, this simple policy is telling us we can get, on average, 253 BRL for each customer if we give them all a 5 BRL coupon. This is massive! But can we do better? What if we use our shiny machine learning hammer on this problem? Let's try this next.\n",
"\n",
"\n",
"## Policy With Model\n",
"\n",
"To use ML, we will adapt what we did in the previous chapter. The idea is to build a ML model that predicts `net_value`, just like before, take those predictions and bins them into a defined number of bands. Then, we will partition the data into those bands. Essentially, we are splitting the customer by their predicted `net_value`. Customers that we think will generate roughly the same `net_value` will end up in the same bin or group. Finally, for each group, we will see which coupon value yields the maximum `net_value`. We are doing the same thing as in the simple policy, but now within the groups defined by a prediction band.\n",
"\n",
"![img](./data/img/when-prediction-fails/partitions.png)\n",
"\n",
"The intuition behind this is the following: we know that, on average, 5 BRL coupons performed better. However, it is possible that for some group of customers, another value is even better than 5 BRL. Maybe 5 BRL is the optimal strategy for most of the customers, but not for all of them. \n",
"\n",
"![img](./data/img/when-prediction-fails/personalise.png)\n",
"\n",
"If we can identify the ones where the optimal value is different, we can build a coupon strategy better than the simple one we did above.\n",
"\n",
"This is what we call a personalisation problem. We can leverage personalisation when we have more than one strategy to choose from and at least one of them is not the overall best strategy, but it is the best in a subset of the targeted population. This definition is a bit convoluted, but the intuition is simple. If you have only one strategy, you are not personalising. You are doing the same thing for every customer. If you have more than one strategy, but one of them is better for every single customer, why will you personalise? You could just do that one best thing. You will only do personalisation if you have one strategy that works better at one subset of the population and another strategy that works best in another subset of the population.\n",
"\n",
"But back to the example. The first thing we need is a function that fits our predictive model and also splits the predictions into the prediction bands. This function will return another function, a prediction function that will take a dataframe and add both predictions and band columns.\n"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"def model_bands(train_set, features, target, model_params, n_bands, seed=1):\n",
" \n",
" np.random.seed(seed)\n",
" \n",
" # train the ML model\n",
" reg = ensemble.GradientBoostingRegressor(**model_params)\n",
" reg.fit(train_set[features], train_set[target])\n",
" \n",
" # fit the bands\n",
" bands = pd.qcut(reg.predict(train_set[features]), q=n_bands, retbins=True)[1]\n",
" \n",
" def predict(test_set):\n",
" # make predictions with trained model\n",
" predictions = reg.predict(test_set[features])\n",
" \n",
" # discretize predictions into bands.\n",
" pred_bands = np.digitize(predictions, bands, right=False) \n",
" return test_set.assign(predictions=predictions,\n",
" # cliping avoid creating new upper bands\n",
" pred_bands=np.clip(pred_bands, 1, n_bands))\n",
" \n",
" return predict"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To evaluate the quality of our predictions, we will split the dataset into a training and a testing set. Notice here that we are evaluating the quality of the prediction, NOT of the policy. This is just to see if our model is any good at doing what is supposed to do. "
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"train, test = train_test_split(customer_features, test_size=0.3, random_state=1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now, let's train our model and make 10 bands with its predictions."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"model_params = {'n_estimators': 150,\n",
" 'max_depth': 4,\n",
" 'min_samples_split': 10,\n",
" 'learning_rate': 0.01,\n",
" 'loss': 'ls'}\n",
"\n",
"features = [\"region\", \"income\", \"age\"]\n",
"target = \"net_value\"\n",
"\n",
"np.random.seed(1)\n",
"model = model_bands(train, features, target, model_params, n_bands=10)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"After training our model, we can use it to make predictions, passing it a dataframe. The result will also be a dataframe with 2 new columns: `predictions` and `pred_bands`."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
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"text/plain": [
" customer_id region income coupons age net_value predictions \\\n",
"2228 2228 30 567 5 27 -129 -16.296297 \n",
"5910 5910 32 647 5 25 -55 -16.296297 \n",
"1950 1950 31 2953 15 33 -142 102.237797 \n",
"2119 2119 1 2860 5 27 -23 94.291197 \n",
"5947 5947 49 589 5 26 -91 -3.525593 \n",
"\n",
" pred_bands \n",
"2228 2 \n",
"5910 2 \n",
"1950 7 \n",
"2119 7 \n",
"5947 3 "
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"model(train).head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To see the predictive power of our model, we can look at the $R^2$ for both training and test sets."
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Train Score:, 0.5382953634651921\n",
"Test Score:, 0.504563847410434\n"
]
}
],
"source": [
"print(\"Train Score:, \", r2_score(train[\"net_value\"], model(train)[\"predictions\"]))\n",
"print(\"Test Score:, \", r2_score(test[\"net_value\"], model(test)[\"predictions\"]))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Remember that this performance is only the predictive performance. What we really want to know is if this model can make us some money. Let's make a policy! The idea here is very similar to what we saw in the previous chapter. We will group the customers by model band. Then, for each type of customer (where type is defined by the bands) we'll see which decision - coupon value in our case - is the best one. To do so, we can group our data by prediction band and coupon value and plot the `net_value`."
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(12,6))\n",
"sns.barplot(data=model(customer_features), x=\"pred_bands\", y=\"net_value\", hue=\"coupons\")\n",
"plt.title(\"Net Value by Coupon Value\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This plot is very interesting. Notice how the optimal decision changes across prediction bands. For instance, on bands like 1, 7 and 8, the best thing to do is to give 10 BRL in coupons. For bands like 3, 5 and 10, the best thing is 5 BRL in coupons. This means that this policy is very much like the simple one, except for the last band. This is evidence that personalisation might be possible, since the optimal decision changes across subpopulations.\n",
"\n",
"We can code that policy with a couple of `if ... then ...` statements, but I'll show a more general approach that leverages dataframe operations.\n",
"\n",
"![img](./data/img/when-prediction-fails/pandas-magic.png)\n",
"\n",
"First, we will group our customers by band and coupon value and take the average `net_value` for each group, much like the plot above."
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
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"text/plain": [
" pred_bands coupons net_value\n",
"0 1 0 -324.538462\n",
"1 1 5 -237.683871\n",
"2 1 10 -142.203390\n",
"3 1 15 -160.413223\n",
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"6 2 10 -68.327146"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pred_bands = (model(customer_features)\n",
" .groupby([\"pred_bands\", \"coupons\"])\n",
" [[\"net_value\"]].mean()\n",
" .reset_index())\n",
"\n",
"pred_bands.head(7)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Then, we will group by band and take the `net_value` rank for each row. This will order the rows according to the average `net_value`, where 1 is the best `net_value` in that band."
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"
"
],
"text/plain": [
" pred_bands coupons\n",
"2 1 10\n",
"5 2 5\n",
"9 3 5\n",
"14 4 10\n",
"17 5 5\n",
"22 6 10\n",
"26 7 10\n",
"30 8 10\n",
"35 9 15\n",
"37 10 5"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"best_coupons_per_band = pred_bands.query(\"max_net==1\")[[\"pred_bands\", \"coupons\"]]\n",
"\n",
"best_coupons_per_band"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To build our policy, we will take that small table above and join it back on the original table using the band as the key. This will pair each row in the original dataset with what we think is optimal coupon value, according to this policy. Then, we sort the rows according to the `customer_id` so that we keep the same ordering we had previously. This is important for evaluation, since `ltv_with_coupons` takes as argument the coupon value in the order of the original dataframe."
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
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"text/plain": [
" customer_id coupons\n",
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"2743 4 5"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"coupons_per_id = (model(customer_features)\n",
" .drop(columns=[\"coupons\"])\n",
" .merge(best_coupons_per_band, on=\"pred_bands\")\n",
" [[\"customer_id\", \"coupons\"]]\n",
" .sort_values('customer_id'))\n",
"\n",
"coupons_per_id.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Finally, to evaluate the policy, we pass the `coupons` column as the coupon array to the `ltv_with_coupons` function. This will regenerate the data, now assuming the coupons were given as we defined by this policy. "
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
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"text/plain": [
" customer_id region income coupons age net_value\n",
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},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"transactions_policy_w_model, customer_features_policy_w_model = ltv_with_coupons(\n",
" coupons_per_id[[\"coupons\"]].values.flatten()\n",
")\n",
"\n",
"customer_features_policy_w_model = process_data(transactions_policy_w_model, customer_features_policy_w_model)\n",
"\n",
"customer_features_policy_w_model.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Just doing a sanity check again, we can see that the third customer is still the one with region 35, income 2034 and age 33. It also has a coupon value of 5 BRL, just like we've established by our policy. \n",
"\n",
"To check how much money this policy is making us, we can compute the average `net_value` mean for this new dataset."
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"229.9341"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"policy_w_model_gain = customer_features_policy_w_model[\"net_value\"].mean()\n",
"policy_w_model_gain"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Not bad! We can expect to get about 230 BRL per customer with this model policy. But wait a second! You remember how much we were making with the simple policy? Let's compare both of them side by side."
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"tags": [
"hide-input"
]
},
"outputs": [
{
"data": {
"image/png": 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tyN3evXtF8+bNxc2bN0tcljhyV6116dIFly9fxuHDhzFmzBjcuXMHw4YNw6BBg544Mubq6mpwHZ6zszOcnZ1Rs2ZNg2lJSUkGy7Vq1Qp2dnYG6weAs2fPFrueqKgorFq1Cmq1Wv/TqlUrAMDFixefuG2ffPIJ1Go1LC0tMWTIEIwZM0Y/ygYA3bp1MyjfrVs3JCQkPLHOh2JiYgAAvXv3LrHM5MmTERQUhMLCQhQUFGDr1q2YOHFiqXU/vt8PHz6MuLg49O/fHzk5OfrpcXFxePnll9GoUSPUqFED9evXB4AnjlwBgKenp8FrFxcX3LlzR/96xowZZRrBPHbsGAICArBw4UKDGxGcnJwwZ84cdO7cGZ6enpg1axZWrVqF7du3F3sdTVJSEnr37g0PDw8sXrz4ietcvXo1vLy84OnpCTMzM7zyyiv6EeDiRopKaqNOp0N+fj5Wr16NAQMGwNvbG9u2bYNCodBfiJ2Tk4Px48ejZcuWOHr0KI4fP46BAwdi4MCB+Pvvv/V1bdu2rci1Y8UJDw+HWq2GlZUVWrduDTc3N/z3v//FvXv3cPPmzSLvy+7du+PatWvIzs4ute6kpCTcuHGj1PflkSNH9KNUmzdvxqBBg1CrVq0Sl+nRowfCw8MhhEBoaCh69uyJHj16IDQ0FEIIhIeHw8/PT1/++PHjyMzMRM+ePUttMwBMmjQJu3btQnJyconHSUJCAhwdHfXHPwBYWFigQ4cO+uP27Nmz8PHxMRj1fXyEJyoqCrdv34a9vb3B75XDhw+X+jvlcY8fq3PmzEFcXBy+/vprZGVl6W/gys7ORmBgINzd3aHRaKBWq/HLL7+Ueqy2aNECFhYW+tePH6uurq7466+/8PLLLxvV3qysLAwaNAgqlarE0eDCwkK8/vrruHDhAvbu3as/nlQqFYKDg5GUlITatWvD0tISmzZtwsiRI584OtuzZ0+sXbsW8+bNg5WVlX6Et3bt2kWWGzlyJOLi4vDHH3+gZ8+eGDZsmP4Yi4yMxPr167F9+/ZSR4NL8/LLL+Ovv/6Cq6vrM9UjdyWfO6FqQaVSoXPnzujcuTPeeecdbN++HaNHj0ZkZCS6d+9e7DJmZmYGryVJKnbas9ydCjz44zt37lyMHj26yDxnZ+cnLjt9+nRMmzYNVlZWqFOnzjP/Qiir0aNHY+7cufj555+h0+mQnp6OUaNGlVi+WbNmAIBz587hhRde0E9v1KgRAMDW1lYflh9e5N+1a1cEBQWhdu3aAAB3d/dST8uam5sbvH6WfgoPD8fAgQP1p3dL07lzZwAPAuijv1hv3ryJXr16oUmTJti9e3eR99LjNBoNdu7ciby8PCQlJcHFxUV/AfXDU+PGtLFOnToAHuy3hywtLdG4cWP9H97//e9/OHXqFMLCwvTt2rhxI37//Xds2rSpzI/H6dChA7799luoVCq4uLjo++PevXtlqudpubu7o2vXrti8eTMCAwPx448/Yv/+/U9cxs/PD8nJyfr98Oabb8LMzAzLli3D6dOnkZSUZBDugoODMWDAgCLvtZJ4enqidevWGDFiBFQqFfr37/9M2/gkOp0OLVu2RHBwcJF5TzpN+bhmzZoVOY3r5OQEJycn3L5922D6nDlz8MMPP2DFihVo3rw5bGxs8M477+hPfZakuGP1SR+6nyQ9PR0DBgxAfn4+QkJCDD5kP5SXl4cRI0YgPj4eERERqFu3rsH8tm3bIioqChkZGcjOzkbt2rUxfPhwNG7c+InrnjFjBqZPn47bt2/D1tYWQggsW7asyHJ2dnaws7NDkyZN0LlzZ7Ro0QLr16/HkiVLEBoaiuTkZDRo0EBfvrCwEJGRkdi6dWuR3yn07DhyJzMtW7YEgCKjbuXh3LlzBn/Ejh49CgAGn8Yf5eXlhYSEBDRp0qTIj1qtfuK6NBoNmjRpAldXV4Ng9/AP+ePXe0RGRqJ169ZGbcfD8PXrr7+WWMbW1havvfYaNm/ejM2bN+OVV16Bvb19ieXbtm2L1q1bY8mSJaVel3bu3DkkJydj0aJF8PX1RcuWLZGWlvbUv/ifxs8//4z+/ftj4cKFRgU74P+PeD76R+Py5ct48cUX0apVK+zdu9dgpKI05ubmqFu3LhQKBf73v/+hW7duBqPHpbXxxRdfBACDkcq8vDxcvXoVDRs2BPBgtEOSpCIfDpRK5VPtbysrKzRp0gQNGzY0+ONta2uLunXrFnlfRkREoFGjRkYFj1q1aqFu3bpPfF8CD0bvtm3bhk2bNsHV1RW9evV6Yvl69eqhcePGWLt2LXJycuDt7Y127dqhoKAAq1evhpubm8Ef3eDgYKNHkx5t0++//47x48dDqVQWme/u7o7U1FSDUf779+/j+PHj+uO2VatWOHHihP4uUAA4cuSIQT1eXl64cuUKbG1ti/xOcXFxMbq9o0aNwu+///7Ex3U8FBkZiZEjR2L48OFo27Yt3Nzc9NcrVoaUlBT06NEDAPDbb78V+3soOzsbgwYNwtmzZxEZGYl69eqVWF+NGjVQu3ZtpKam4tChQxg6dGipbZAkCXXq1IGNjQ2+//57AEBAQMATl9HpdPpr/aZNm4ZTp04hLi5O/+Pl5YWXX34ZcXFx+g+4VI6q7IQwPbNu3bqJr776SkRFRYlr166JkJAQ4ePjI+zt7fXX1JV0t+yjPvnkkyJ3Ki5evNjgjroxY8aIGjVqiMGDB4vTp0+LiIgI0bRpUzFo0KAS6w4NDRUqlUq89dZbIjY2Vly6dEkcOHBAjB8/XmRnZ5e4XcXdLfuoV155RTRo0EAcPHhQnDt3TsyaNUuYmZmJc+fO6cuglLtlR44cKWrWrCm+++47cenSJXHixAmxatUqg/WcOHFCKJVKoVQqDa6FK8nJkyeFvb298PT0FLt27RJnz54VFy5cELt37xbNmzcXfn5+QogH17NZWFiIqVOnikuXLomQkBDh5eUlJEkSQUFBJW7D46+FeHBn4pgxY/SvjbnmbufOncLMzEx88MEHIjExUf/z6DWXQUFBYtu2beLMmTPi0qVLIigoSDg5OYlhw4bpyyQkJIg6deqIPn36iJs3bxrUVVBQoC/n5+dncF3giRMnxM6dO8WlS5fE0aNHxdChQ4VarRZxcXFlaqNOpxMdO3YUzZs3FxEREeLcuXNizJgxwtHRUV/u/PnzwtLSUowZM0acOXNG/PXXX+Ktt94SSqVSHDt27In76XHF3dn6qHXr1glLS0uxadMmceHCBbFhwwZhYWEhtmzZoi9T2jV3mzdvFiqVSnz88cfi7Nmz4syZM2Lt2rUG18jm5OQIR0dHYW5uLj799FOj2j5x4kShUqnESy+9pJ8WEBAgVCqVwbVjp0+fFpaWliIjI+OJ9T16zZ0QD67zSk5OFnl5efoyj75fdTqd8PHxEW3bthV//PGHOH36tBg+fLjB76qbN28KKysrMX78eHH27FkREhIi2rZta1BPTk6OcHd3F15eXuLQoUPi6tWr4tixY+Kzzz4TwcHBQgjjrrnLy8sT/v7+Qq1Wi8WLF4tjx46Ja9euiSNHjojRo0cLAOLvv/8WQggxdOhQ0bx5c3H8+HGRkJAgJkyYIGxtbUX37t319ZV0t+yjvvvuO/Hon1xjrrm7deuWaNmypXjhhRfEpUuXDI6F+/fvCyEe3P3dtWtX0bBhQxEfH29Q5tHfs7t37xYhISHiypUr4sCBA6J169aiZcuWBn1d3O+PpUuXiri4OHHu3DmxatUqYWlpKebPn6+ff/r0abF06VIRHR0trl+/Lk6cOCHGjRsnVCqVOHHiRInbVtw1d6mpqSI2NlZ/l/uiRYtEbGzsE69/pOIx3FVjixcvFl27dhU1a9YUFhYWol69emLkyJEGFy2XZ7jr2bOnWLZsmXB2dhZWVlZiyJAhBo81Ka7uyMhI0bNnT6FWq4W1tbVo0aKFePPNN0t8XIgQpYe79PT0Z34USl5enpg/f75o0KCBMDMzE66urvoLsh/l6ekpWrVqVWJbHnf9+nUxdepU/SNWrK2thaenp5g/f77BRe+7du0STZo0ERYWFsLT01OEh4cLpVL5zOFuwYIForTPbN27dxcAivw8+h749ttvRevWrYWNjY2wtrYW7u7u4vPPPze4QPzhuor7uXr1qr5cgwYNDNp4+PBh4e7uLiwtLYWtra146aWXijzWwZg2CiFEUlKSGDVqlLCzsxP29vaiT58+4syZMwZlwsLCRPfu3YW9vb2wtbUVHTp0MLgx4+H6Hv1jXZzSwp1OpxNLly4VDRs2FCqVSjRq1OipHoWyfft24eHhIczNzYVGoxH9+/cXaWlpBmVmz54tVCqVuHXr1hPb/NB///tfAUCsWLFCP23NmjUCgPjvf/+rn/bxxx/rb4h4ksfDXXEef78+/iiUbt26FbmxJSQkRLRu3VqYm5sLd3d38fvvvxepJyUlRUyZMkW4uLgIMzMz4eLiIgICAvQ3Mxn7GJ/8/HyxZs0a4ePjI9RqtTAzMxP169cXI0eONPgw9/fff4vevXsLa2tr4ezsLD788EMxfvz4Zw53D9v56DH/uKCgoBKPsbCwMCHE/++L4n4erfvLL78U9evXF2ZmZsLZ2VlMmTLF4EODEMX//ujVq5ewt7cX5ubmok2bNmLTpk0G8y9evCj69OkjatWqpe+PwYMHF3nsyuOKC3clbe+jvz8elnn0dwwVJQlRieeCqNoaO3Ysbt68iZCQkKpuSqXJz89Hw4YN8d577xV5JAPJS/369TF16lTMmzevqptilOHDhyM/P7/Ya8+eRbt27TBr1iyMGzeuXOslKi8ffvgh9uzZg/j4+Cc+cul5xz1D9BidToeUlBRs3LgRWVlZ/EMnc6dOnYKlpSXeeeedqm5KqdLS0nDixAkEBwcbPN+wPOTl5SEgIACDBw8u13qJytP+/fuxbt06BrtScO8QPebvv/9Go0aNUKdOHXzzzTewtbWt6iZRBfLw8KjUC+SfRbt27ZCamor33nuvyGNXnpW5uTkWLFhQrnUSlbeHN3bRk/G0LBEREZGM8FEoRERERDLCcEdEREQkIwx3RERERDLyXNxQcevWrapuQrlzcnJCSkpKVTeD/g/7w3SwL0wL+8O0sD9MR0l9UZZvWykJR+6IiIiIZIThjoiIiEhGGO6IiIiIZOS5uOaOiIhIToQQyM3NhU6ngyRJRi93584d3L9/vwJbRsYQQkCSJP2/5Y3hjoiIqJrJzc2FmZlZmb+GS6VSQalUVlCrqCx0Oh1yc3NhZWVV7nXztCwREVE1o9Pp+P2q1ZyZmRl0Ol2F1M1wR0REVM1UxKk8qnwV1Y8Md0RERFRm9erVQ69eveDn54dJkyYhJyenxLI7duzA+++/DwDYtm0bdu3a9UzrnjBhAg4ePKh//eKLL2LVqlX61xMnTsQvv/yif923b98i1xoOGzYM3t7eEELop40fPx5NmzYtU1tmz56N/fv3P3OZ8sQxXSIiompOmXkPyEgvtZwkSVA+EmZKVMMOhWrbJxaxtLTEb7/9BgCYMWMGtm3bhsmTJ5da9euvv176+kvh7e2N6Oho9O3bF1qtFtbW1jh58qR+/smTJ7Fo0SIAwN9//w1nZ2dYWFgUqcfOzg5RUVHw8fFBeno6kpKSnrltpoDhjoiIqLrLSEfefzaUWuzhHZqlMR85BSgl3D3Kx8cH586dQ1paGt555x38/fffsLS0xNKlS9GqVSuDssuXL4eNjQ2mTJmCq1evIjAwEKmpqVAqldi4cSNWrFiB/v37o2/fvgAeBMeBAweiT58++jrat2+vD2/R0dHo1asXwsLCIITAjRs3YGlpiVq1agEAwsLC4OvrW2y7Bw0ahB9++AE+Pj44cOAA+vXrh/PnzwN4cEfrp59+irCwMEiShFmzZmHw4MEQQmD+/PmIjIyEi4sLzM3N9fWdOnUKH330EbKysqDRaLBy5UrUrl3b6P1YXnhaloiIiJ5aQUEBwsLC0KJFCyxfvhytW7dGSEgIAgMD8eabbz5x2ZkzZ2Ls2LEICQnBDz/8gNq1a2PEiBHYuXMnAODevXuIjo5Gz549DZbz8PDA+fPnkZeXh5MnT6J9+/Zwc3PDxYsXER0djfbt2+vLhoeHo0ePHsWuv2vXrjh+/DgKCwvxww8/YNCgQfp5v/zyCxISEvDbb7/h+++/x6effoo7d+7gwIEDuHz5MsLDw7F69WpER0cDAPLz8zF//nxs2rQJBw8exKuvvorPP//8qfbps+LIHREREZVZbm4uevXqBQDo0KEDRowYgZdeegmbN28G8CA4paWlISMjo9jlMzMzkZiYiH79+gF4cJoXADp16oR///vfSE1Nxc8//4z+/fsXuTPYwsICzZo1w+nTp3Hy5ElMnToV169fR3R0NM6cOQNvb28AQF5eHhITE9GgQYNi26BUKuHt7Y0ffvgBubm5qFevnn7eiRMnEBAQAKVSiZo1a6Jjx46Ij4/HsWPH9NOdnZ3RpUsXAMDly5dx/vx5vPbaawAe3NH8cPSwsjHcERERUZk9es1deRs2bBj27NmDH3/8EStWrCi2jLe3N44fP46srCzY29ujffv2CAoKwpkzZzBq1CgAwPHjx+Hj4/PEdQ0ePBgTJkzAO++880xtFkKgWbNm+Omnn56pnvLA07LVzL08gRsZBUj4Jw03MgpK/bmXZ8SFs0REROWgQ4cO2Lt3LwDg6NGj0Gg0qFGjRrFl1Wo16tSpo7/r9f79+/o7bocPH44tW7YAAJo1a1bs8l5eXti+fbv+mr6WLVsiJiYG//zzD1q0aAHgyadkH23zzJkzERAQUGT6jz/+iMLCQqSmpuL48ePw9PREx44d9dPv3LmDo0ePAgAaN24MrVZrcJr24fV7lY0jd9VM+v1CbDh+C2ZmZsjPzy+1/JQOLrA1ZzcTEVHFe/vtt/HOO+/A398flpaWBo8nKc6aNWswd+5cfPHFF1CpVNi4cSMaNGiAmjVromnTpgY3UTzOy8sL169fx4wZMwA8+PYNJycnuLi4QKF4MHb1559/4t13331iGyRJwpQpU4pM79evH06ePIlevXpBkiS8//77qFWrFvr164cjR47A19cXrq6u+uv7zM3NsXHjRnz44Ye4d+8eCgsL8cYbb6B58+ZPXH9FkIQxt81Uc7du3arqJpSbGxkFZQ539Wow3FU0JycnpKSkVHUzCOwLU8P+qBjZ2dmwtrbWvzb2USgKSYKunB6FUpFycnLQs2dPHDx4ELa2T9eOW7du4b333sP27dvLuXXlQ6VS4d69ewb9CAAuLi7PXvcz10BERERVqlBta9SjSySVCoUFBZXQoqcXGRmJd999FxMnTnzqYAc8CEmmGuwqGsMdERERmYxu3brhxIkTVd2Mao03VBARERHJCMMdERERkYww3BERERHJCMMdERERkYww3BEREVGZrV69Gj169IC/vz969eqFmJgYAMC7776LCxculMs6mjZtWqbyHTp0QM+ePeHv748RI0YgKSmpxLJHjx7F66+/DgD49ddf8eWXXz5TW00J75YlIiKq5u7lCaTfLyy1nCTpIISu1HJ2FkrYmkslzo+OjkZISAgOHjwICwsLaLVa5OXlAQC++OIL4xteAXbt2gWNRoPFixdj7dq1+OSTT0pdpnfv3ujdu3cltK5yMNwRERFVcw+/vag0kiTBmO8uKO3bjZKSkqDRaGBhYQEA0Gg0+nnDhg3DBx98gLZt26Jp06Z4/fXXERoailq1aiEwMBCLFi3CP//8g48++gi9e/fGjh07cPDgQWRkZCAxMRFDhw7F22+/XWSdX331FX766Sfk5eWhb9++pX7zRMeOHfHNN98gNzcX8+bNw6lTp6BUKrFgwQJ06dLFoOyOHTtw6tQpLFq0CMnJyQgMDMT169cBAIsXL0Z4eDjs7e0xceJEAMCSJUvg5OSEN954o9R9WRV4WpaIiIjKpHv37rh16xa6du2KefPm4c8//yy2XHZ2Nrp06YKwsDCo1WosXboU//vf/7BlyxYsW7ZMXy4uLg6bNm1CSEgI9u/fj/j4eIN6IiIicPXqVfz888/49ddfcerUKRw7duyJbQwJCUGLFi2wdetWSJKE33//HevXr8fs2bORm5tb4nIffPABOnbsiJCQEBw6dAjNmzfHa6+9ht27dwMAdDodfvzxRwwZMsTY3VXpGO6IiIioTGxsbHDw4EEsXboUjo6OmDp1Knbs2FGknLm5OXr06AEAaNGiBTp27AgzMzO0bNkSN2/e1Jd78cUXodFoYGVlhX79+hV5iHFERAQiIiLQu3dv9OnTB5cvX8bVq1eLbdsrr7yCXr16ISMjAzNmzEBUVJQ+iDVp0gR169bFlStXSty2I0eO6K/FUyqVsLW1Rb169eDg4IAzZ84gIiIC7u7uBqOVpoanZYmIiKjMlEolOnfujM6dO6NFixbYtWsXXn31VYMyKpUKkvTg2j2FQqE/jatQKFDwyNegPSxT0mshBGbMmIHRo0eX2q6H19yVtxEjRmDnzp1ISkrCa6+9Vu71lyeO3BEREVGZXLp0yWD0KyEhAXXr1n3q+g4fPoy0tDTk5OTg0KFD8Pb2Npjv6+uLHTt2ICsrCwCQmJiIlJQUo+r28fFBcHAwAODy5cv4559/0Lhx4xLLd+3aFdu2bQMAFBYW4t69ewCAfv36ISwsDPHx8fD19S3rJlYqjtwRERFRmWRnZ2P+/Pm4d+8eVCoVGjZsiKVLlz51fZ6enpg4caL+hoq2bdsazO/evTsuXryIQYMGAQCsra2xdu1aODk5lVr3mDFjMG/ePPTs2RNKpRIrV67UjyAW5+OPP8Z7772H77//HgqFAosXL4aXlxfMzc3RuXNn2NnZQalUPvW2VgZJGHPbTDV361bpdxBVFzcyCrDh+C2YmZkhPz+/1PJTOrigXg1m+Irm5ORk9KdIqljsC9PC/qgY2dnZsLa21r82/lEoinJ5FEp5evROVVOm0+nQp08fbNy4EW5ubs9cn0qlwr179wz6EQBcXFyeve5nroGIiIiqlK259MRHlzykUqkMrnUj41y4cAFjxoxB3759yyXYVTSGOyIiIqoyr776apEbMUxNs2bNSnzciyniDRVEREREMsJwR0REVM08B5fLPxcqqh8Z7oiIiKqZx58TR9VPfn4+FIqKiWG85o6IiKiasbS0RG5uLu7fv1/kgb9PYmFhgfv371dgy8gYQgio1WpYWlpWSP0Md0RERNWMJEmwsrIq83J8NI3pcHR0rLC+4GlZIiIiIhlhuCMiIiKSkUo7LTt9+nRYWlpCoVBAqVRiyZIlyMzMxMqVK5GcnIyaNWvirbfeglqthhACQUFBiI2NhYWFBaZNm6Z/aGB4eDj27t0LABgyZIjJf78bERERUWWq1GvuFixYAFtbW/3rffv2oU2bNggICMC+ffuwb98+jBo1CrGxsbh9+zbWrFmDixcvYsuWLfjss8+QmZmJ3bt3Y8mSJQCAwMBAeHl5Qa1WV+ZmEBEREZmsKj0tGxUVhe7duwN48KXAUVFRAIDo6Gh069YNkiShWbNmyMrKQlpaGuLi4uDh4QG1Wg21Wg0PDw/ExcVV4RYQERERmZZKHbl7+KXAvXr1gr+/P9LT0+Hg4AAAsLe3R3p6OgBAq9XCyclJv5yjoyO0Wi20Wi0cHR310zUaDbRabZH1hISEICQkBACwZMkSg7qquzv302BmZgZJkmBmZlZqeXNzCzg5OVRCy55vKpVKVu+z6ox9YVrYH6aF/WE6KrIvKi3cffLJJ9BoNEhPT8enn34KFxcXg/mSJJXpWT1P4u/vD39/f/1rOd32nZdXgPz8fJiZmSE/P9+I8vdltf2mio8XMB3sC9PC/jAt7A/TUVJfPJ6PnkalnZbVaDQAADs7O3h7e+PSpUuws7NDWloaACAtLU1/PZ5GozHY4NTUVGg0Gmg0GqSmpuqna7Vafb1EREREVEnhLjc3Fzk5Ofr/nzp1CvXr14eXlxciIiIAABEREfD29gYAeHl5ITIyEkIIXLhwAdbW1nBwcICnpyfi4+ORmZmJzMxMxMfHw9PTszI2gYiIiKhaqJTTsunp6fjiiy8AAIWFhejatSs8PT3RuHFjrFy5EqGhofpHoQBAu3btEBMTg1mzZsHc3BzTpk0DAKjVagwdOhTz5s0DAAwbNuy5ulNWmXkPUq4E6X4udPl5kHS6UpeRCgrALyIhIiJ6fkhCCFHVjahot27dquomlAtl4g1cvX0XG2NTIUkSjOm6qQPbo27NGpXQuucbr2MxHewL08L+MC3sD9Mhi2vuiIiIiKjiMdwRERERyQjDHREREZGMMNwRERERyQjDHREREZGMMNwRERERyQjDHREREZGMMNwRERERyQjDHREREZGMMNwRERERyQjDHREREZGMMNwRERERyQjDHREREZGMMNwRERERyQjDHREREZGMMNwRERERyQjDHREREZGMMNwRERERyQjDHREREZGMMNwRERERyQjDHREREZGMMNwRERERyQjDHREREZGMMNwRERERyQjDHREREZGMMNwRERERyQjDHREREZGMMNwRERERyQjDHREREZGMMNwRERERyQjDHREREZGMMNwRERERyQjDHREREZGMMNwRERERyQjDHREREZGMMNwRERERyQjDHREREZGMMNwRERERyQjDHREREZGMMNwRERERyQjDHREREZGMMNwRERERyQjDHREREZGMMNwRERERyQjDHREREZGMMNwRERERyQjDHREREZGMqCpzZTqdDoGBgdBoNAgMDERSUhJWrVqFjIwMuLm5YebMmVCpVMjPz8eXX36JK1euoEaNGpg9ezZq1aoFAAgODkZoaCgUCgXGjRsHT0/PytwEIiIiIpNWqSN3v/zyC1xdXfWvt2/fjgEDBmDt2rWwsbFBaGgoACA0NBQ2NjZYu3YtBgwYgP/85z8AgJs3b+Lo0aNYsWIF3n//fXz99dfQ6XSVuQlEREREJq3Swl1qaipiYmLQs2dPAIAQAgkJCejYsSMAwNfXF1FRUQCA6Oho+Pr6AgA6duyIM2fOQAiBqKgodO7cGWZmZqhVqxacnZ1x6dKlytoEIiIiIpNXaadlt27dilGjRiEnJwcAkJGRAWtrayiVSgCARqOBVqsFAGi1Wjg6OgIAlEolrK2tkZGRAa1Wi6ZNm+rrfHSZR4WEhCAkJAQAsGTJEjg5OVXotlWWrNQ7kCQFJEkCJECCVOoyCoVCNttvylQqFfeziWBfmBb2h2lhf5iOiuyLSgl3J0+ehJ2dHdzc3JCQkFDh6/P394e/v7/+dUpKSoWvszIo8/IghA5CCEiQIIQodRmdTieb7TdlTk5O3M8mgn1hWtgfpoX9YTpK6gsXF5dnrrtSwt358+cRHR2N2NhY5OXlIScnB1u3bkV2djYKCwuhVCqh1Wqh0WgAPBiRS01NhaOjIwoLC5GdnY0aNWropz/06DJEREREVEnX3P3rX//Chg0bsG7dOsyePRutW7fGrFmz4O7ujmPHjgEAwsPD4eXlBQBo3749wsPDAQDHjh2Du7s7JEmCl5cXjh49ivz8fCQlJSExMRFNmjSpjE0gIiIiqhYq9VEojxs5ciRWrVqF77//Ho0aNYKfnx8AwM/PD19++SVmzpwJtVqN2bNnAwDq1auHTp064e2334ZCocCECROgUPBRfUREREQPScKYC7equVu3blV1E8qFMvEGrt6+i42xqZAk4665mzqwPerWrFEJrXu+8ToW08G+MC3sD9PC/jAdFXnNHYe9iIiIiGSE4Y6IiIhIRhjuiIiIiGSE4Y6IiIhIRhjuiIiIiGSE4Y6IiIhIRhjuiIiIiGSE4Y6IiIhIRhjuiIiIiGSE4Y6IiIhIRhjuiIiIiGSE4Y6IiIhIRhjuiIiIiGSE4Y6IiIhIRhjuiIiIiGSE4Y6IiIhIRhjuiIiIiGSE4Y6IiIhIRhjuiIiIiGSE4Y6IiIhIRhjuiIiIiGSE4Y6IiIhIRhjuiIiIiGSE4Y6IiIhIRhjuiIiIiGSE4Y6IiIhIRhjuiIiIiGSE4Y6IiIhIRhjuiIiIiGSE4Y6IiIhIRhjuiIiIiGSE4Y6IiIhIRhjuiIiIiGSE4Y6IiIhIRhjuiIiIiGSE4Y6IiIhIRhjuiIiIiGSE4Y6IiIhIRhjuiIiIiGSE4Y6IiIhIRowOd3/++Wex048dO1ZujSEiIiKiZ2N0uNuwYUOx0zdu3FhujSEiIiKiZ6MqrcCdO3cAADqdDklJSRBCGMwzNzevuNYRERERUZmUGu5mzZql///MmTMN5tnb2+OVV14p/1YRERER0VMpNdzt2LEDALBgwQJ89NFHFd4gIiIiInp6Rl9zx2BHREREZPpKHbl7KCkpCf/73/9w7do15ObmGsz76quvyr1hRERERFR2Roe71atXo3bt2nj99ddhYWFRppXk5eVhwYIFKCgoQGFhITp27Ijhw4cjKSkJq1atQkZGBtzc3DBz5kyoVCrk5+fjyy+/xJUrV1CjRg3Mnj0btWrVAgAEBwcjNDQUCoUC48aNg6enZ5naQkRERCRnRoe7mzdv4pNPPoFCUfbnHpuZmWHBggWwtLREQUEBPvzwQ3h6emL//v0YMGAAunTpgk2bNiE0NBS9e/dGaGgobGxssHbtWhw5cgT/+c9/8NZbb+HmzZs4evQoVqxYgbS0NHzyySdYvXr1U7WJiIiISI6MTkUtW7bEtWvXnmolkiTB0tISAFBYWIjCwkJIkoSEhAR07NgRAODr64uoqCgAQHR0NHx9fQEAHTt2xJkzZyCEQFRUFDp37gwzMzPUqlULzs7OuHTp0lO1iYiIiEiOjB65q1mzJhYtWgQfHx/Y29sbzHv11VdLXV6n02Hu3Lm4ffs2+vTpg9q1a8Pa2hpKpRIAoNFooNVqAQBarRaOjo4AAKVSCWtra2RkZECr1aJp06b6Oh9d5lEhISEICQkBACxZsgROTk7GbqZJy0q9A0lSQJIkQAIkSKUuo1AoZLP9pkylUnE/mwj2hWlhf5gW9ofpqMi+MDrc3b9/H+3bt0dhYSFSU1PLvCKFQoFly5YhKysLX3zxBW7dulXmOozl7+8Pf39//euUlJQKW1dlUublQQgdhBCQIBk8ULokOp1ONttvypycnLifTQT7wrSwP0wL+8N0lNQXLi4uz1y30eFu2rRpz7wyALCxsYG7uzsuXLiA7OxsFBYWQqlUQqvVQqPRAHgwIpeamgpHR0cUFhYiOzsbNWrU0E9/6NFliIiIiKgM19zduXOnxJ/S3Lt3D1lZWQAe3Dl76tQpuLq6wt3dHceOHQMAhIeHw8vLCwDQvn17hIeHAwCOHTsGd3d3SJIELy8vHD16FPn5+UhKSkJiYiKaNGlS1m0mIiIiki2jR+4e/Rqyxz38FouSpKWlYd26ddDpHpxS7NSpE9q3b4+6deti1apV+P7779GoUSP4+fkBAPz8/PDll19i5syZUKvVmD17NgCgXr166NSpE95++20oFApMmDCBd8oSERERPUISxly4VYy7d+9i165daNmyJbp27Vre7SpXFXl9X2VSJt7A1dt3sTE2FZJk3DV3Uwe2R92aNSqhdc83XsdiOtgXpoX9YVrYH6ajIq+5e+phL3t7e4wdOxb//e9/n7kRRERERFQ+numc5q1bt3D//v3yagsRERERPSOjr7n78MMPHzxf7f/cv38fN27cwLBhwyqkYURERERUdkaHu4c3OzxkaWmJBg0aoE6dOuXeKCIiIiJ6OkaHu4dfB0ZEREREpsvocFdQUIC9e/ciMjISaWlpcHBwQLdu3TBkyBCoVEZXQ0REREQVyOhUtn37dly+fBkTJ05EzZo1kZycjD179iA7Oxtjx46twCYSERERkbGMDnfHjh3DsmXLUKPGg2emubi4oFGjRpgzZw7DHREREZGJMPpRKE/5rGMiIiIiqkRGj9x16tQJn3/+OYYNG6Z/qvKePXvQsWPHimwfEREREZWB0eFu1KhR2LNnD77++mukpaVBo9GgS5cuGDp0aEW2j4iIiIjKoNRw99dffyE6OhqjRo3Cq6++ildffVU/b/v27bhy5QqaNWtWoY0kIiIiIuOUes1dcHAwWrVqVey81q1bY+/eveXeKCIiIiJ6OqWGu2vXrsHT07PYeW3atMHVq1fLu01ERERE9JRKPS2bk5ODgoICmJubF5lXWFiInJycCmmY3Ckz7wEZ6WVaRirIr6DWEBERkVyUGu5cXV0RHx8Pb2/vIvPi4+Ph6upaIQ2TvYx05P1nQ5kWsRj6egU1hoiIiOSi1NOyAwYMwKZNm3D8+HHodDoAgE6nw/Hjx7F582YMGDCgwhtJRERERMYpdeSua9euuHv3LtatW4f8/HzY2tri3r17MDMzw/Dhw9G1a9fKaCcRERERGcGo59y99NJL8PPzw4ULF5CZmQm1Wo1mzZrB2tq6ottHRERERGVg9EOMra2tS7xrloiIiIhMg9HfLUtEREREpo/hjoiIiEhGGO6IiIiIZIThjoiIiEhGGO6IiIiIZIThjoiIiEhGGO6IiIiIZIThjoiIiEhGGO6IiIiIZIThjoiIiEhGGO6IiIiIZIThjoiIiEhGGO6IiIiIZIThjoiIiEhGGO6IiIiIZIThjoiIiEhGGO6IiIiIZIThjoiIiEhGGO6IiIiIZIThjoiIiEhGGO6IiIiIZIThjoiIiEhGGO6IiIiIZIThjoiIiEhGVFXdgOdZZtcBSLeoYXR5hXVtFCjyAKRWXKOIiIioWmO4q0LpFjWwMdb4oCbdNMPodrUqsEVERERU3fG0LBEREZGMVMrIXUpKCtatW4e7d+9CkiT4+/ujf//+yMzMxMqVK5GcnIyaNWvirbfeglqthhACQUFBiI2NhYWFBaZNmwY3NzcAQHh4OPbu3QsAGDJkCHx9fStjE4iIiIiqhUoJd0qlEqNHj4abmxtycnIQGBgIDw8PhIeHo02bNggICMC+ffuwb98+jBo1CrGxsbh9+zbWrFmDixcvYsuWLfjss8+QmZmJ3bt3Y8mSJQCAwMBAeHl5Qa1WV8ZmEBEREZm8Sjkt6+DgoB95s7KygqurK7RaLaKiotC9e3cAQPfu3REVFQUAiI6ORrdu3SBJEpo1a4asrCykpaUhLi4OHh4eUKvVUKvV8PDwQFxcXGVsAhEREVG1UOnX3CUlJeHq1ato0qQJ0tPT4eDgAACwt7dHeno6AECr1cLJyUm/jKOjI7RaLbRaLRwdHfXTNRoNtFpt5W4AERERkQmr1Ltlc3NzsXz5cowdOxbW1tYG8yRJgiRJ5bKekJAQhISEAACWLFliEBRNRVbqHUiSokzbLEmAhP/bT//3/9IoFAqT3H65UalU3M8mgn1hWtgfpoX9YToqsi8qLdwVFBRg+fLlePHFF9GhQwcAgJ2dHdLS0uDg4IC0tDTY2toCeDAil5KSol82NTUVGo0GGo0GZ8+e1U/XarVo1apVkXX5+/vD399f//rRukyFMi8PQugghDB+IQEICAghIEEyalmdTmeS2y83Tk5O3M8mgn1hWtgfpoX9YTpK6gsXF5dnrrtSTssKIbBhwwa4urripZde0k/38vJCREQEACAiIgLe3t766ZGRkRBC4MKFC7C2toaDgwM8PT0RHx+PzMxMZGZmIj4+Hp6enpWxCURERETVQqWM3J0/fx6RkZGoX78+5syZAwAYMWIEAgICsHLlSoSGhuofhQIA7dq1Q0xMDGbNmgVzc3NMmzYNAKBWqzF06FDMmzcPADBs2DDeKUtERET0iEoJdy1atMDOnTuLnffhhx8WmSZJEt54441iy/v5+cHPz69c20dEREQkF/yGCiIiIiIZYbgjIiIikhGGOyIiIiIZYbgjIiIikhGGOyIiIiIZYbgjIiIikhGGOyIiIiIZYbgjIiIikhGGOyIiIiIZYbgjIiIikhGGOyIiIiIZYbgjIiIikhGGOyIiIiIZYbgjIiIikhGGOyIiIiIZYbgjIiIikhGGOyIiIiIZYbgjIiIikhGGOyIiIiIZYbgjIiIikhGGOyIiIiIZYbgjIiIikhGGOyIiIiIZYbgjIiIikhGGOyIiIiIZYbgjIiIikhGGOyIiIiIZYbgjIiIikhGGOyIiIiIZYbgjIiIikhGGOyIiIiIZYbgjIiIikhGGOyIiIiIZYbgjIiIikhGGOyIiIiIZYbgjIiIikhGGOyIiIiIZYbgjIiIikhGGOyIiIiIZYbgjIiIikhGGOyIiIiIZYbgjIiIikhGGOyIiIiIZYbgjIiIikhGGOyIiIiIZYbgjIiIikhGGOyIiIiIZUVXGStavX4+YmBjY2dlh+fLlAIDMzEysXLkSycnJqFmzJt566y2o1WoIIRAUFITY2FhYWFhg2rRpcHNzAwCEh4dj7969AIAhQ4bA19e3MppPREREVG1Uysidr68v/v3vfxtM27dvH9q0aYM1a9agTZs22LdvHwAgNjYWt2/fxpo1azBp0iRs2bIFwIMwuHv3bnz22Wf47LPPsHv3bmRmZlZG84mIiIiqjUoJd61atYJarTaYFhUVhe7duwMAunfvjqioKABAdHQ0unXrBkmS0KxZM2RlZSEtLQ1xcXHw8PCAWq2GWq2Gh4cH4uLiKqP5RERERNVGlV1zl56eDgcHBwCAvb090tPTAQBarRZOTk76co6OjtBqtdBqtXB0dNRP12g00Gq1ldtoIiIiIhNXKdfclUaSJEiSVG71hYSEICQkBACwZMkSg7BoKrJS70CSFGXabkkCJPzfvvq//5dGoVCY5PbLjUql4n42EewL08L+MC3sD9NRkX1RZeHOzs4OaWlpcHBwQFpaGmxtbQE8GJFLSUnRl0tNTYVGo4FGo8HZs2f107VaLVq1alVs3f7+/vD399e/frQ+U6HMy4MQOgghjF9IAAICQghIkIxaVqfTmeT2y42TkxP3s4lgX5gW9odpYX+YjpL6wsXF5ZnrrrLTsl5eXoiIiAAAREREwNvbWz89MjISQghcuHAB1tbWcHBwgKenJ+Lj45GZmYnMzEzEx8fD09OzqppPREREZJIqZeRu1apVOHv2LDIyMjBlyhQMHz4cAQEBWLlyJUJDQ/WPQgGAdu3aISYmBrNmzYK5uTmmTZsGAFCr1Rg6dCjmzZsHABg2bFiRmzSIiIiInneVEu5mz55d7PQPP/ywyDRJkvDGG28UW97Pzw9+fn7l2TQiIiIiWeE3VBARERHJCMMdERERkYww3BERERHJCMMdERERkYww3BERERHJCMMdERERkYww3BERERHJCMMdERERkYxU2XfLUuVQmFvgRkZBmZaxs1DC1lyqoBYRERFRRWK4k7nMfB2+jbtdpmWmdHCBrTnfGkRERNURT8sSERERyQjDHREREZGM8Nyb3EkSpPu5xpdX8S1BRERUnfEvudwJHcSdW0YXl2q7VGBjiIiIqKLxtCwRERGRjDDcEREREckIwx0RERGRjDDcEREREckIwx0RERGRjDDcEREREckIwx0RERGRjDDcEREREckIwx0RERGRjDDcEREREckIwx0RERGRjDDcEREREckIwx0RERGRjDDcEREREckIwx0RERGRjDDcEREREcmIqqobQCZGkiDl5kCZedf4ZWrYoVBtW2FNIiIiIuMx3JGhwkLobl5D3u/fG72I+cgpAMMdERGRSWC4oyKUtevgn56vGV1eobKHbZ6ArblUga0iIiIiYzDcURGZOgW2xaYaXV66ZYHJ3dxga863ExERUVXjDRVEREREMsJwR0RERCQjDHdEREREMsKLpOjZ8fEpREREJoPhjp4dH59CRERkMhjuqFyU9fEpDlb2qFGB7SEiInpeMdxRuSjr41Om1msE+8Qbxq+Ap3GJiIiMwnBXTjKy8pCefd/4BZR2KNBYADA+EMlKYQHy/rPB6OI8jUtERGQchrtykp59H1/9dNLo8lJNZ4xuV6sCW2TaFJZW/BYMIiKiCsBwR1UiM1+Hb8vyLRiJlpji7QyHgrvGr4SncomI6DnEcEfVQ2EhpPz7uHrnrtGLKFT2sDXnaB8RET1fGO6o2ijzd95ytI+IiJ5DDHckX08x2udg7VC2u3gBSJZWyEq9A2VennELMEASEVEFqpbhLi4uDkFBQdDpdOjZsycCAgKquklkoso62jfdrRnSbt8t0zqsG9dEzvXLEEJnVHmeLiYioopU7cKdTqfD119/jfnz58PR0RHz5s2Dl5cX6tatW9VNIxko640eADCmXhNsi02BEMKo8lKiJaZ1aYB76cY/OsfS2gq52TllapedtQVq2JgbXV6ZeQ93CySk51fcOoiIqOJVu3B36dIlODs7o3bt2gCAzp07IyoqiuGOqo/CQmRkZGLbr6eMXmTMoA74tgyP2gGA6cM6Iz05w/gFBJCXk4Ovfz9bcevA0wXCe3kC6fcLjSp7534arCSOjBLR86vahTutVgtHR0f9a0dHR1y8eLEKW0RkmjLzCssUCJ/m2YtlXQfwFIFQqUQ+FPj6z7+NKq5QKDClawPcS88tU7vKPDqqMoOllQVy8o0LnQBgpZCQm51dse1SKmGnKIR9zl2jF7lrWxt3dYoytcvYbbmVmgWdTvdU+8vOQlnmkF6WDwLPsh4iUyYJY88lmYhjx44hLi4OU6ZMAQBERkbi4sWLmDBhgr5MSEgIQkJCAABLliypknYSERERVYWyfVQzARqNBqmp//+aqNTUVGg0GoMy/v7+WLJkiayDXWBgYFU3gR7B/jAd7AvTwv4wLewP01GRfVHtwl3jxo2RmJiIpKQkFBQU4OjRo/Dy8qrqZhERERGZhGp3zZ1SqcT48eOxaNEi6HQ69OjRA/Xq1avqZhERERGZhGoX7gDghRdewAsvvFDVzahS/v7+Vd0EegT7w3SwL0wL+8O0sD9MR0X2RbW7oYKIiIiISlbtrrkjIiIiopJVy9Oyzzt+/VrFS0lJwbp163D37l1IkgR/f3/0798fmZmZWLlyJZKTk1GzZk289dZbUKvVEEIgKCgIsbGxsLCwwLRp0+Dm5gYACA8Px969ewEAQ4YMga+vbxVuWfWl0+kQGBgIjUaDwMBAJCUlYdWqVcjIyICbmxtmzpwJlUqF/Px8fPnll7hy5Qpq1KiB2bNno1atB8/vCw4ORmhoKBQKBcaNGwdPT8+q3ahqKisrCxs2bMCNGzcgSRKmTp0KFxcXHhtVZP/+/QgNDYUkSahXrx6mTZuGu3fv8vioJOvXr0dMTAzs7OywfPlyACjXvxVXrlzBunXrkJeXh3bt2mHcuHGQpFKeyyioWiksLBQzZswQt2/fFvn5+eLdd98VN27cqOpmyY5WqxWXL18WQgiRnZ0tZs2aJW7cuCG+++47ERwcLIQQIjg4WHz33XdCCCFOnjwpFi1aJHQ6nTh//ryYN2+eEEKIjIwMMX36dJGRkWHwfyq7n376SaxatUosXrxYCCHE8uXLxR9//CGEEGLjxo3i0KFDQgghDh48KDZu3CiEEOKPP/4QK1asEEIIcePGDfHuu++KvLw8cefOHTFjxgxRWFhYBVtS/a1du1aEhIQIIYTIz88XmZmZPDaqSGpqqpg2bZq4f/++EOLBcREWFsbjoxIlJCSIy5cvi7fffls/rTyPh8DAQHH+/Hmh0+nEokWLRExMTKlt4mnZaubRr19TqVT6r1+j8uXg4KD/NGVlZQVXV1dotVpERUWhe/fuAIDu3bvr9310dDS6desGSZLQrFkzZGVlIS0tDXFxcfDw8IBarYZarYaHhwfi4uKqarOqrdTUVMTExKBnz54AACEEEhIS0LFjRwCAr6+vQV88/MTbsWNHnDlzBkIIREVFoXPnzjAzM0OtWrXg7OyMS5cuVcn2VGfZ2dk4d+4c/Pz8AAAqlQo2NjY8NqqQTqdDXl4eCgsLkZeXB3t7ex4flahVq1ZQq9UG08rreEhLS0NOTg6aNWsGSZLQrVs3o/7m87RsNcOvX6t8SUlJuHr1Kpo0aYL09HQ4ODgAAOzt7ZGeng7gQb84OTnpl3F0dIRWqy3SXxqNBlqttnI3QAa2bt2KUaNGISfnwddwZWRkwNraGkqlEoDhfn10nyuVSlhbWyMjIwNarRZNmzbV18m+eDpJSUmwtbXF+vXrcf36dbi5uWHs2LE8NqqIRqPBwIEDMXXqVJibm6Nt27Zwc3Pj8VHFyut4KO5vvjH9wpE7oifIzc3F8uXLMXbsWFhbWxvMkySp9Ose6JmdPHkSdnZ2+pFUqlqFhYW4evUqevfujaVLl8LCwgL79u0zKMNjo/JkZmYiKioK69atw8aNG5Gbm8sRUBNTFccDw101Y8zXr1H5KCgowPLly/Hiiy+iQ4cOAAA7OzukpaUBANLS0mBrawvgQb+kpKTol33YL4/3l1arZX+V0fnz5xEdHY3p06dj1apVOHPmDLZu3Yrs7GwUFj74gvhH9+uj+7ywsBDZ2dmoUaMG+6KcODo6wtHRUT/K07FjR1y9epXHRhU5ffo0atWqBVtbW6hUKnTo0AHnz5/n8VHFyut4eNq/+Qx31Qy/fq1yCCGwYcMGuLq64qWXXtJP9/LyQkREBAAgIiIC3t7e+umRkZEQQuDChQuwtraGg4MDPD09ER8fj8zMTGRmZiI+Pp53oJXRv/71L2zYsAHr1q3D7Nmz0bp1a8yaNQvu7u44duwYgAd3mT08Dtq3b4/w8HAAwLFjx+Du7g5JkuDl5YWjR48iPz8fSUlJSExMRJMmTapqs6ote3t7ODo64tatWwAehIu6devy2KgiTk5OuHjxIu7fvw8hhL4/eHxUrfI6HhwcHGBlZYULFy5ACIHIyEij/ubzIcbVUExMDL799lv9168NGTKkqpskO3/99Rc+/PBD1K9fXz+cPmLECDRt2hQrV65ESkpKkdvbv/76a8THx8Pc3BzTpk1D48aNAQChoaEIDg4G8OD29h49elTZdlV3CQkJ+OmnnxAYGIg7d+5g1apVyMzMRKNGjTBz5kyYmZkhLy8PX375Ja5evQq1Wo3Zs2ejdu3aAIC9e/ciLCwMCoUCY8eORbt27ap4i6qna9euYcOGDSgoKECtWrUwbdo0CCF4bFSRnTt34ujRo1AqlWjYsCGmTJkCrVbL46OSrFq1CmfPnkVGRgbs7OwwfPhweHt7l9vxcPnyZaxfvx55eXnw9PTE+PHjSz3Ny3BHREREJCM8LUtEREQkIwx3RERERDLCcEdEREQkIwx3RERERDLCcEdEREQkIwx3RERERDLCcEdEVMF27tyJNWvWVHUziOg5wXBHRM+16dOn49SpU1XdDCKicsNwR0RERCQjqqpuABFReZg+fTr69OmDyMhIJCcnw9PTE9OnT4e5uTlOnjyJ77//HsnJyahbty4mTpyIBg0aYO3atUhJScHnn38OhUKBYcOGYfDgwcXW/9lnn+GFF15A37599dPmzJmDYcOGoUOHDggKCsKJEyeQnZ0NZ2dnjB07Fi1btixST0JCAtauXYsNGzYYtH3y5Mnw8PCATqfDjz/+iN9//x1ZWVlo3bo1Jk2aBLVaXf47jYhkiSN3RCQbf/75J/79739j3bp1+PvvvxEeHo6rV6/iq6++wqRJk/DNN9/A398fS5cuRX5+PmbOnAknJyfMnTsX3333XYnBDgC6dOmCI0eO6F/fvHkTycnJeOGFFwAAjRs3xtKlS/HNN9+ga9euWLFiBfLy8sq8DQcPHkRUVBQWLlyIjRs3Qq1WY8uWLWXfGUT03GK4IyLZ6NevHzQaDdRqNdq3b49r164hJCQE/v7+aNq0KRQKBXx9faFSqXDx4sUy1e3j44Nr164hOTkZAHD48GH4+PjAzMwMANCtWzfUqFEDSqUSAwcOREFBAW7dulXmbfjtt9/w2muvwdHREWZmZnjllVdw/PhxFBYWlrkuIno+8bQsEcmGvb29/v/m5ubQarXIyspCREQEDh48qJ9XUFAArVZbprqtrKzQrl07HDlyBAEBAThy5AgmT56sn//jjz8iLCwMWq0WkiQhJycHGRkZZd6G5ORkfPHFF5AkST9NoVAgPT0dGo2mzPUR0fOH4Y6IZM3R0RFDhgzBkCFDnrmurl27YteuXWjVqhXy8/Ph7u4OADh37hx+/PFHfPjhh6hbty4UCgXGjRsHIUSROiwsLHD//n39a51Oh3v37hm0d+rUqWjRosUzt5eInk88LUtEstazZ0/89ttvuHjxIoQQyM3NRUxMDHJycgA8GO1LSkoyqq527dohJSUFO3bsQKdOnaBQPPgVmpOTA6VSCVtbW+h0OuzevRvZ2dnF1uHi4oL8/HzExMSgoKAAe/bsQX5+vn5+r1699Dd/AMC9e/cQFRX1LLuAiJ4zHLkjIllr3LgxJk+ejG+++QaJiYkwNzdHixYt9HeyBgQE4JtvvsH27dsxZMgQDBo0qMS6zMzM4OPjg7CwMIwYMUI/3dPTE23btsWbb74JCwsLDBgwAE5OTsXWYW1tjTfeeAMbNmyATqfDoEGD4OjoqJ/fv39/AMCnn36KtLQ02NnZoVOnTvD29i6P3UFEzwFJFHfegIiIiIiqJZ6WJSIiIpIRnpYlIvo/hw8fxqZNm4pMr1mzJlasWFEFLSIiKjueliUiIiKSEZ6WJSIiIpIRhjsiIiIiGWG4IyIiIpIRhjsiIiIiGWG4IyIiIpKR/wcr2OumTRot8QAAAABJRU5ErkJggg==\n",
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