diff --git a/modules/.ipynb_checkpoints/module6-checkpoint.md b/modules/.ipynb_checkpoints/module6-checkpoint.md
new file mode 100644
index 00000000..f8272182
--- /dev/null
+++ b/modules/.ipynb_checkpoints/module6-checkpoint.md
@@ -0,0 +1,80 @@
+# 6) Bayesian Statistics
+
+
+```note
+## Lab 6: Bayesian Statistics
+
+**Lab 6-1: A Bayesian Example**
+
+A medical testing company has developed a non-invasive test for Down’s syndrome in the first two months of pregnancy. This test can correctly identify Down’s syndrome by giving a positive result 98% of the time (true positive). Therefore the probability of a false negative is 2%. This text can correctly identify when the fetus does not have Down’s syndrome by giving a negative result 97% of the time (true negative). Therefore the probability of a false positive is 3%. For this example, assume that the observed probability of Down’s syndrome in a random sample from a large number of observations is about 1 in 1,200.
+
+ **A.** Draw a tree diagram for this problem as you work through this example.
+
+ **B.** Using Bayes’ theorem, estimate the probability that a fetus has Down’s syndrome given that the test result is positive. Are you surprised by the answer? What is the fundamental problem with this test?
+
+ **C.** How accurate would the test have to be to achieve a 50% probability of having Down’s syndrome given that the test result is positive (true positive)? (**Note**: In this problem, try solving for the accuracies of both the positive and negative test results that will give you a 50% true positive rate. It may not be possible to achieve a 50% true positive rate with one or the other.)
+
+ **D.** Estimate the likelihood that the fetus does not have Down’s Syndrome given that the test result is negative (true negative). Is the test more useful in this framework as a screening step when trying to decide to use more accurate, but also more invasive, tests?
+
+---
+
+Download the lab and data files to your computer. Then, upload them to your JupyterHub [following the instructions here](/resources/b-learning-jupyter.html#working-with-files-on-our-jupyterhub).
+
+* [Lab 6-2: Bayesian Statistics](lab6/lab6-2.ipynb)
+
+```
+
+
+## Homework 6:
+
+### Problem 1: Continuous Bayesian Estimation of Flood Frequency
+
+The "[100 year storm](https://en.wikipedia.org/wiki/100-year_flood)" is a storm with a rainfall total that would on average be met or exceeded only once every 100 years, and therefore the storm has a 0.01 chance of occurrence each year. For any "k-year storm", its probability of occurrence in one year is 1/k, where k is the return period in years. Infrastructure is often designed to handle the flooding due to some k-year storm.
+
+Based on long-term climate records for New York City, the 24-hour duration, 100-year return period rainfall was previously estimated at 7.2 inches. This "7.2 inches in 24 hours" storm (the "100 year storm") has been used to design infrastructure in New York City. When this design limit is exceeded, flooding can occur.
+
+During the 20th century, this limit was exceeded only once, during Hurricane Floyd in 1999. However, a storm in 2007 produced 8 inches of rainfall in a 24-hour period. Another storm in August 2011 again exceeded 7.2 inches in 24 hours. Hurricane Irene in September 2011 exceeded this limit yet again, and so did Hurricane Sandy in October 2012. This happened again in September 2018 from Hurricane Florence, and then Hurricane Ida broke rain records in September 2021. Fortunately, this limit was not exceeded in 2022. The table below summarizes the time periods and the number of times this design limit was exceeded within each time period.
+
+Note that, unlike what you will do in many hydrology classes, which is to calculate the return period across a range of different precipitation or streamflow values, we are focusing here only on the probability of 24-hour storms exceeding 7.2 inches of rainfall because this is a critical design number for New York City. If you are interested in city planning in New York around floods, they released a [design plan](https://www1.nyc.gov/assets/orr/pdf/publications/stormwater-resiliency-plan.pdf) in May 2021. Note they use different rain thresholds for different design elements (e.g., sometimes hourly rain rates matter more), so the actual critical design numbers vary more than what we're examining here. You may also be interested in reading recent news about this problem. One from [NPR](https://www.npr.org/2022/10/29/1131608305/a-decade-after-sandy-hurricane-flood-maps-reveal-new-yorks-climate-future) and one from the [New York Times](https://www.nytimes.com/2022/10/21/realestate/sandy-hurricane-ida-flooding.html). The news articles are not required reading to do the homework.
+
+| time period | # of years | # of storms |
+| --- | --- | --- |
+| 1900-1999 | 100 | 1 |
+| 2000-2009 | 10 | 1 |
+| 2010-2019 | 10 | 4 |
+| 2020-2022 | 3 | 1 |
+
+In this problem we will use Bayes’ Theorem to see if the 7.2-inch storm is still a 100-year storm. In other words, we want to find what k-year storm 7.2 inches in 24 hours corresponds to, if not 100-years.
+
+ **A.** Download and plot the prior pdf of a >=7.2-inch storm occurring in a given year from the data file [NYC_precip_priors.csv](data/NYC_precip_priors.csv). This dataset shows the prior distribution of the chance that New York City will get a 7.2-inch storm in a given year, which has a mean p = 0.01, corresponding to 100 years (1/p = 1/0.01 = 100).
+
+(Note that the variable labeled “PDF” represents the probability of the storm frequency (or return period) falling within that interval and therefore includes the interval width, such that the sum of the pdf values alone equals 1, and the cumulative sum of the pdf is equal to the cdf.)
+
+There is some uncertainty about the original likelihood, so we want to determine:
+ - What are the mean and 95% confidence interval of the probability, i.e., where does 95% of the PDF fall between?
+ - To what k-year storm (expected return period) range do these values correspond?
+
+**B.** Apply Bayes' Theorem at each time period of interest (see table above) to update the the pdf for the 7.2-inch storm.
+
+P(A\|B) = P(B\|A) * P(A) / P(B)
+
+In this problem, A is the true likelihood of the storm’s occurrence, and B are the events we have observed. For the first time peirod, use the pdf from the data file as the prior pdf, P(A). For each subsequent time period, use the posterior pdf from the previous time period. The likelihood P(B\|A = p) that the storm would be exceeded m times in n years (event B) for a storm probability `p` (event A = p) is given by: P(B\|A = p) = `scipy.stats.binom.pmf(m,n,p)`, where `m` is the number of storms, and `n` is the number of years.
+ - Calculate and plot the posterior pdfs of the 7.2-inch storm’s probability after each time period.
+ - Calculate the the mean and 95% confidence interval of the return period each time.
+
+ **C.** How much did the mean and 95% confidence interval return period change from the original prior return period to 2021? What does this indicate about the “true” frequency of the 7.2-inch-storm? To what k-year storm does this mean correspond to now?
+
+
+### Problem 2: Project Update (CEWA 565)
+
+Provide an update on your term project. By now you should have acquired all of the data you need for your term project.
+
+ **A.** Create 2-3 plots that illustrate your data. These can be time-series plots, histograms, CDFs, whatever is relevant to your data and your problem.
+
+ **B.** Discuss the quality of your data. Do you need to take into account any erroneous values or uncertain numbers before you start your statistics?
+
+ **C.** Write down at least two very specific questions that you will answer with your data. For each question, write down which statistical tools you will use to help answer it.
+
+ **D.** Based on what you have so far, do you think that your project scope is about right for a 10 page paper, or do you feel that you need to either simplify things to make it shorter or add complexity to make it longer? If you feel adjustments are needed, how to you plan to address this issue?
+
+ **E.** What do you anticipate being the most difficult parts of your term project? Do you have questions you would like help with or advice on? Write them here.
\ No newline at end of file
diff --git a/modules/lab1/.ipynb_checkpoints/lab1-3-checkpoint.ipynb b/modules/lab1/.ipynb_checkpoints/lab1-3-checkpoint.ipynb
index 911b0824..24f56bab 100644
--- a/modules/lab1/.ipynb_checkpoints/lab1-3-checkpoint.ipynb
+++ b/modules/lab1/.ipynb_checkpoints/lab1-3-checkpoint.ipynb
@@ -4,7 +4,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "# Lab 1.2"
+ "# Lab 1.3"
]
},
{
@@ -286,7 +286,7 @@
],
"metadata": {
"kernelspec": {
- "display_name": "Python 3",
+ "display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
@@ -300,7 +300,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
- "version": "3.7.4"
+ "version": "3.9.7"
}
},
"nbformat": 4,
diff --git a/modules/lab1/.ipynb_checkpoints/lab1-3_solution-checkpoint.ipynb b/modules/lab1/.ipynb_checkpoints/lab1-3_solution-checkpoint.ipynb
index 253a4d82..be94c978 100644
--- a/modules/lab1/.ipynb_checkpoints/lab1-3_solution-checkpoint.ipynb
+++ b/modules/lab1/.ipynb_checkpoints/lab1-3_solution-checkpoint.ipynb
@@ -4,7 +4,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "# Lab 1.2"
+ "# Lab 1.3 Solution"
]
},
{
@@ -694,7 +694,7 @@
],
"metadata": {
"kernelspec": {
- "display_name": "Python 3",
+ "display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
@@ -708,7 +708,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
- "version": "3.7.4"
+ "version": "3.9.7"
}
},
"nbformat": 4,
diff --git a/modules/lab1/lab1-3.ipynb b/modules/lab1/lab1-3.ipynb
index 6ef78c03..24f56bab 100644
--- a/modules/lab1/lab1-3.ipynb
+++ b/modules/lab1/lab1-3.ipynb
@@ -4,7 +4,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "# Lab 1.2"
+ "# Lab 1.3"
]
},
{
diff --git a/modules/lab1/lab1-3_solution.ipynb b/modules/lab1/lab1-3_solution.ipynb
index 253a4d82..be94c978 100644
--- a/modules/lab1/lab1-3_solution.ipynb
+++ b/modules/lab1/lab1-3_solution.ipynb
@@ -4,7 +4,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "# Lab 1.2"
+ "# Lab 1.3 Solution"
]
},
{
@@ -694,7 +694,7 @@
],
"metadata": {
"kernelspec": {
- "display_name": "Python 3",
+ "display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
@@ -708,7 +708,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
- "version": "3.7.4"
+ "version": "3.9.7"
}
},
"nbformat": 4,
diff --git a/modules/lab2/.ipynb_checkpoints/lab2-1-checkpoint.ipynb b/modules/lab2/.ipynb_checkpoints/lab2-1-checkpoint.ipynb
new file mode 100644
index 00000000..7753e079
--- /dev/null
+++ b/modules/lab2/.ipynb_checkpoints/lab2-1-checkpoint.ipynb
@@ -0,0 +1,849 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Lab 2-1: Hypothesis Testing\n",
+ "\n",
+ "The Skykomish River in Washington state appears to have had a change in streamflow around the year 1975. \n",
+ "* Test for statistical significance of the observed change in the mean annual flood. \n",
+ "* Use a two-sample test, with alpha=0.05 (i.e. 95% confidence) and the z-distribution to define the rejection region.\n",
+ "\n",
+ "Why is it appropriate to use the z-distribution here? (consider the [Central Limit Theorem](https://en.wikipedia.org/wiki/Central_limit_theorem))\n",
+ "\n",
+ "---"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "import pandas as pd\n",
+ "import scipy.stats as stats\n",
+ "import matplotlib.pyplot as plt\n",
+ "%matplotlib inline"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/opt/conda/lib/python3.8/site-packages/openpyxl/worksheet/_reader.py:312: UserWarning: Unknown extension is not supported and will be removed\n",
+ " warn(msg)\n"
+ ]
+ },
+ {
+ "data": {
+ "text/html": [
+ "
\n",
+ "\n",
+ "
\n",
+ " \n",
+ "
\n",
+ "
\n",
+ "
date of peak
\n",
+ "
water year
\n",
+ "
peak value (cfs)
\n",
+ "
gage_ht (feet)
\n",
+ "
\n",
+ " \n",
+ " \n",
+ "
\n",
+ "
0
\n",
+ "
1928-10-09
\n",
+ "
1929
\n",
+ "
18800
\n",
+ "
10.55
\n",
+ "
\n",
+ "
\n",
+ "
1
\n",
+ "
1930-02-05
\n",
+ "
1930
\n",
+ "
15800
\n",
+ "
10.44
\n",
+ "
\n",
+ "
\n",
+ "
2
\n",
+ "
1931-01-28
\n",
+ "
1931
\n",
+ "
35100
\n",
+ "
14.08
\n",
+ "
\n",
+ " \n",
+ "
\n",
+ "
"
+ ],
+ "text/plain": [
+ " date of peak water year peak value (cfs) gage_ht (feet)\n",
+ "0 1928-10-09 1929 18800 10.55\n",
+ "1 1930-02-05 1930 15800 10.44\n",
+ "2 1931-01-28 1931 35100 14.08"
+ ]
+ },
+ "execution_count": 3,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "# Filepath to our excel file.\n",
+ "skykomish_data_file = 'Skykomish_peak_flow_12134500_skykomish_river_near_gold_bar.xlsx'\n",
+ "\n",
+ "# Use pandas.read_excel() function to open this file.\n",
+ "skykomish_data = pd.read_excel(skykomish_data_file)\n",
+ "\n",
+ "# Now we can see the dataset we loaded:\n",
+ "skykomish_data.head(3)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "
"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Plot peak streamflows per water year\n",
+ "fig, ax = plt.subplots(figsize=(7,4))\n",
+ "\n",
+ "skykomish_data.plot(x='water year', y='peak value (cfs)', ax=ax)\n",
+ "ax.set_ylabel('streamflow (cfs)');\n",
+ "ax.set_title('Skykomish River, Annual Peak Streamflow, (Gold Bar, WA)');"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "---\n",
+ "We are postulating that there was an change in peak flows around 1975. In other words, how likely is it that the mean of peak flows before 1975 comes from the same distribution as the mean of peak flows after 1975?\n",
+ "\n",
+ "To start, let's split the data in two:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Divide the data into the early period (before 1975) and late period (after and including 1975). \n",
+ "\n",
+ "skykomish_before = skykomish_data[ skykomish_data['water year'] < 1975 ]\n",
+ "skykomish_after = skykomish_data[ skykomish_data['water year'] >= 1975 ]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "
"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Plot our two time periods\n",
+ "fig, ax = plt.subplots(figsize=(7,4))\n",
+ "\n",
+ "skykomish_before.plot(x='water year', y='peak value (cfs)', ax=ax, linestyle='-', label='pre-1975')\n",
+ "skykomish_after.plot(x='water year', y='peak value (cfs)', ax=ax, linestyle='--', label='post-1975')\n",
+ "\n",
+ "ax.set_ylabel('streamflow (cfs)');\n",
+ "ax.set_title('Skykomish River, Annual Peak Streamflow, (Gold Bar, WA)');"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**What does the distribution of streamflows in each period look like?**\n",
+ "\n",
+ "Plot a histogram for each period:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "
"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fig, (ax1, ax2) = plt.subplots(nrows=1, ncols=2, figsize=(10,3))\n",
+ "\n",
+ "ax1.hist(skykomish_before['peak value (cfs)'], bins=10)\n",
+ "ax1.set_xlim((1e4,1.4e5))\n",
+ "ax1.set_xlabel('peak value (cfs)')\n",
+ "ax1.set_title('Skykomish River, Annual Peak Streamflow\\nHistogram Before 1975')\n",
+ "\n",
+ "ax2.hist(skykomish_after['peak value (cfs)'], bins=10)\n",
+ "ax2.set_xlim((1e4,1.4e5))\n",
+ "ax2.set_xlabel('peak value (cfs)')\n",
+ "ax2.set_title('Skykomish River, Annual Peak Streamflow\\nHistogram After 1975');\n",
+ "\n",
+ "plt.tight_layout()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "---\n",
+ "Visually compare the distributions of the data, before and after 1975, with theoretical distributions, and random numbers generated from theoretical distributions."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "### Method 1\n",
+ "# This function requires that the input is a pandas dataframe, with column names, and an integer index\n",
+ "# It returns a copy of the dataframe with an extra column added that has the Cunnane plotting positions\n",
+ "def cunnane_quantile(df, column_name):\n",
+ " '''This function will compute the Cunnane plotting position for the values in a column of a dataframe.\n",
+ " It requres a pandas dataframe, and the column name of interest (a text string) as inputs.\n",
+ " The output is a new dataframe, ranked (sorted) with an extra column with the plotting position.\n",
+ " [Steven Pestana, spestana@uw.edu, Oct. 2020]'''\n",
+ " \n",
+ " # Rank all our values\n",
+ " ranked_df = df.sort_values(by=[column_name]).reset_index()\n",
+ " \n",
+ " # Calculate the Cunnane plotting position\n",
+ " ranked_df['cunnane_plotting_position'] = ((ranked_df.index + 1) - (2/5)) / (ranked_df[column_name].count() + (1/5))\n",
+ " \n",
+ " return ranked_df\n",
+ "\n",
+ "### Method 2\n",
+ "# This function should be able to accept any one-dimensional numpy array or list, of numbers\n",
+ "# It returns two numpy arrays, one of the sorted numbers, the other of the plotting position\n",
+ "def cunnane_quantile_array(numbers):\n",
+ " '''This function also computes the Cunnane plotting position given an array or list of numbers (rather than a pandas dataframe).\n",
+ " It has two outputs, first the sorted numbers, second the Cunnane plotting position for each of those numbers.\n",
+ " [Steven Pestana, spestana@uw.edu, Oct. 2020]'''\n",
+ " \n",
+ " # 1) sort the data, using the numpy sort function (np.sort())\n",
+ " sorted_numbers = np.sort(numbers)\n",
+ " \n",
+ " # length of the list of numbers\n",
+ " n = len(sorted_numbers) \n",
+ " \n",
+ " # make an empty array, of the same length. below we will add the plotting position values to this array\n",
+ " cunnane_plotting_position = np.empty(n)\n",
+ " \n",
+ " # 2) compute the Cunnane plotting position for each number, using a for loop and the enumerate function\n",
+ " for rank, number in enumerate(sorted_numbers):\n",
+ " cunnane_plotting_position[rank] = ( (rank+1) - (2/5) ) / ( n + (1/5) )\n",
+ " \n",
+ " return sorted_numbers, cunnane_plotting_position"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Use the cunnane quantile function for before 1975\n",
+ "skykomish_before_b = cunnane_quantile(skykomish_before, 'peak value (cfs)')\n",
+ "\n",
+ "# Create theoretical normal CDF based on our sample values before 1975\n",
+ "theoretical_cdf_b = stats.norm.cdf(skykomish_before_b['peak value (cfs)'].values,\n",
+ " skykomish_before_b['peak value (cfs)'].mean(),\n",
+ " skykomish_before_b['peak value (cfs)'].std(ddof=1))\n",
+ "\n",
+ "# Generate random numbers from a theoretical normal CDF based on our samples before 1975\n",
+ "random_normal_b = np.random.normal(skykomish_before_b['peak value (cfs)'].mean(),\n",
+ " skykomish_before_b['peak value (cfs)'].std(ddof=1),\n",
+ " size=skykomish_before_b['peak value (cfs)'].count())\n",
+ "\n",
+ "# Compute the Cunnane plotting position for the random numbers\n",
+ "random_sorted_b, random_quantiles_b = cunnane_quantile_array(random_normal_b)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Use the cunnane quantile function for after 1975\n",
+ "skykomish_after_a = cunnane_quantile(skykomish_after, 'peak value (cfs)')\n",
+ "\n",
+ "# Create theoretical normal CDF based on our sample values before 1975\n",
+ "theoretical_cdf_a = stats.norm.cdf(skykomish_after_a['peak value (cfs)'].values,\n",
+ " skykomish_after_a['peak value (cfs)'].mean(),\n",
+ " skykomish_after_a['peak value (cfs)'].std(ddof=1))\n",
+ "\n",
+ "# Generate random numbers from a theoretical normal CDF based on our samples before 1975\n",
+ "random_normal_a = np.random.normal(skykomish_after_a['peak value (cfs)'].mean(),\n",
+ " skykomish_after_a['peak value (cfs)'].std(ddof=1),\n",
+ " size=skykomish_after_a['peak value (cfs)'].count())\n",
+ "\n",
+ "# Compute the Cunnane plotting position for the random numbers\n",
+ "random_sorted_a, random_quantiles_a = cunnane_quantile_array(random_normal_a)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Text(0.5, 1.0, 'Skykomish River, Annual Peak Streamflow CDF\\nAfter 1975')"
+ ]
+ },
+ "execution_count": 12,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "
"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fig, [ax1, ax2] = plt.subplots(nrows=1, ncols=2, figsize=(12,4))\n",
+ "\n",
+ "# Before 1975\n",
+ "# Empirical CDF\n",
+ "ax1.plot(skykomish_before_b['peak value (cfs)'], skykomish_before_b['cunnane_plotting_position'], color='k', label='Empirical CDF')\n",
+ "# Theorectical Normal CDF\n",
+ "ax1.plot(skykomish_before_b['peak value (cfs)'], theoretical_cdf_b, label='Theoretical Normal CDF')\n",
+ "# Random numbers CDF from a theoretical normal distribution\n",
+ "ax1.plot(random_sorted_b,random_quantiles_b,'-', label='Random Numbers CDF')\n",
+ "# Add legend and labels\n",
+ "ax1.legend()\n",
+ "ax1.set_ylabel('Cumulative Frequency')\n",
+ "ax1.set_xlabel('Peak Flow (cfs)')\n",
+ "ax1.set_title('Skykomish River, Annual Peak Streamflow CDF\\nBefore 1975')\n",
+ "\n",
+ "# After 1975\n",
+ "# Empirical CDF\n",
+ "ax2.plot(skykomish_after_a['peak value (cfs)'], skykomish_after_a['cunnane_plotting_position'], color='k', label='Empirical CDF')\n",
+ "# Theorectical Normal CDF\n",
+ "ax2.plot(skykomish_after_a['peak value (cfs)'], theoretical_cdf_a, label='Theoretical Normal CDF')\n",
+ "# Random numbers CDF from a theoretical normal distribution\n",
+ "ax2.plot(random_sorted_a, random_quantiles_a,'-', label='Random Numbers CDF')\n",
+ "# Add legend and labels\n",
+ "ax2.legend()\n",
+ "ax2.set_ylabel('Cumulative Frequency')\n",
+ "ax2.set_xlabel('Peak Flow (cfs)')\n",
+ "ax2.set_title('Skykomish River, Annual Peak Streamflow CDF\\nAfter 1975')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Does the streamflow data look normally distributed? Maybe try changing the above code to compare the empirical CDFs against theoretical lognormal distributions. (Remember to transform the mean and standard deviations into \"log space\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "---\n",
+ "## Two-Sample Z-Test\n",
+ "\n",
+ "#### Returning to our question: We are postulating (making a hypothesis) that there was a change in the mean flood statistics after 1975, and we want to test whether this is true. Where do we start?\n",
+ "\n",
+ "First we can formally state our null hypothesis, and our alternative hypothesis. We are also told to use a two sample test, and to set $\\alpha$ at 5%.\n",
+ "\n",
+ "Our **null hypothesis** is that the peak flows of the early period ($\\bar{X}_1$) are drawn from the same distribution as the peak flows of the later period ($\\bar{X}_2$) (therefore the distributions means of the two time periods are equal):\n",
+ "\n",
+ "$H_0: \\bar{X}_1 = \\bar{X}_2$\n",
+ "\n",
+ "Our **alternative hypothesis** is that the mean of the distribution for the later period is greater than that of the early period:\n",
+ "\n",
+ "$H_1: \\bar{X}_2 > \\bar{X}_1$\n",
+ "\n",
+ "We can also state these as:\n",
+ "\n",
+ "$H_0: \\bar{X}_1 - \\bar{X}_2 = \\mu_0$\n",
+ "\n",
+ "$H_1: \\bar{X}_1 - \\bar{X}_2 < \\mu_0$\n",
+ "\n",
+ "Where $\\mu_0$ is the hypothesized difference between the population means, and in this case $\\mu_0 = \\mu_1 - \\mu_2 = 0$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Note that I have written a \"[one-sided](https://en.wikipedia.org/wiki/One-_and_two-tailed_tests)\" test here because we are testing only for a change in one direction (an increase). We think that either the mean flood increased or it didn't change; we do not think the mean flood decreased:\n",
+ "* This might be chosen because we have some physical reason to think it increased (e.g. higher elevations in the watershed now get rainfall where it used to mostly get snow because of our warming climate).\n",
+ "* Or this might be chosen because we have some practical reason for the test to matter in this particular direction (e.g. we will change flood zoning downstream and/or how we operate a reservoir if the mean flood has increased, but won't make a change if it decreased)."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### But which test should we use? Is the z-distribution valid?\n",
+ "\n",
+ "We are using the [z-test](https://en.wikipedia.org/wiki/Z-test), which uses the standard normal distribution. From our work above, we know that our data are likely not neccesarily normally distributed. However, the [central limit theorem](https://en.wikipedia.org/wiki/Central_limit_theorem) tells us that, \"*If a sample of n values is extracted at random from a population with mean μ and standard deviation σ, and n > 30, then the means of these samples are approximately normally distributed*\"\n",
+ "\n",
+ "We calculate our z-score as: $\\displaystyle Z = \\frac{ (\\bar{X}_2 - \\bar{X}_1) - \\mu _{0} } { s_{1,2} }$\n",
+ "\n",
+ "Where $s_{1,2}$ is the \"pooled standard deviation\", $s_1$, $s_2$ and $n_1$, $n_2$ are the two standard deviations and sample sizes respectively.\n",
+ "\n",
+ "$s_{1,2} = \\displaystyle\\sqrt{ \\displaystyle\\frac{s^2_1}{n_1} + \\displaystyle\\frac{s^2_2}{n_2} }$\n",
+ "\n",
+ "#### Remember, the means are normally distributed even if the data themselves are not normally distributed."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "So what does the \"**Null Distribution** look like?\n",
+ "\n",
+ "And what do the \"rejection regions\" look like?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "
"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fig, ax = plt.subplots(figsize=(10,7))\n",
+ "\n",
+ "# Create a null pdf\n",
+ "x = np.linspace(-4, 4, num=160)\n",
+ "ax.plot(x, stats.norm.pdf(x, 0, 1), label='Normal Distribution PDF')\n",
+ "\n",
+ "# Plot the null cdf\n",
+ "ax.plot(x, stats.norm.cdf(x, 0, 1), linestyle='--', label='Normal Distribution CDF')\n",
+ "\n",
+ "# Plot the region that z_test would have to fall in in order for us to reject the null hypothesis\n",
+ "conf = 0.95\n",
+ "z_alpha = stats.norm.ppf(conf)\n",
+ "shade = np.linspace(z_alpha, 4, 10)\n",
+ "ax.fill_between(shade, stats.norm.pdf(shade, 0, 1) , color='k', alpha=0.5, label='reject region\\nfor alpha={}'.format(np.round(1-conf,2)))\n",
+ "# Plot a line at z_alpha\n",
+ "plt.axvline(z_alpha, color='black', label='$z_{a}$')\n",
+ "# Plot a line at our 95% confidence\n",
+ "plt.axhline(conf, color='black', linestyle='--', label='Confidence = {}%'.format(conf*100))\n",
+ "\n",
+ "\n",
+ "# Add labels\n",
+ "ax.set_ylim((0,1))\n",
+ "plt.xlabel('Z', fontsize=15)\n",
+ "plt.ylabel('PDF', fontsize=15)\n",
+ "ax.legend(loc='center left', fontsize=14);"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "46\n",
+ "45\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Check that we have a large enough sample size (n>30)\n",
+ "\n",
+ "n = len(skykomish_before['peak value (cfs)'])\n",
+ "print(n)\n",
+ "\n",
+ "m = len(skykomish_after['peak value (cfs)'])\n",
+ "print(m)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Both are larger than 30, so we can go ahead and calculate the z-score for our test:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# We want our alpha to be 0.05\n",
+ "alpha = 0.05\n",
+ "# This gives us a confidence of 0.95\n",
+ "conf = 1 - alpha"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Next, determine which value in the z-distribution corresponds to our 0.95 confidence in the CDF"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "z_alpha = 1.6448536269514722\n"
+ ]
+ }
+ ],
+ "source": [
+ "z_alpha = stats.norm.ppf(conf)\n",
+ "print(\"z_alpha = {}\".format(z_alpha)) "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Compute the pooled standard deviation, $s_{1,2} = \\displaystyle\\sqrt{ \\displaystyle\\frac{s^2_1}{n_1} + \\displaystyle\\frac{s^2_2}{n_2} }$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Compute the pooled standard deviaiton\n",
+ "pooled_sd = np.sqrt( skykomish_before['peak value (cfs)'].std(ddof=1)**2 / n + skykomish_after['peak value (cfs)'].std(ddof=1)**2 / m )"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Finally, compute our z-score as $\\displaystyle Z = \\frac{ (\\bar{X}_2 - \\bar{X}_1) - \\mu _{0} } { s_{1,2} }$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "z-score = 2.87\n"
+ ]
+ }
+ ],
+ "source": [
+ "# hypothesizing no change\n",
+ "mu_0 = 0\n",
+ "\n",
+ "# compute z-score\n",
+ "zscore = (skykomish_after['peak value (cfs)'].mean() - skykomish_before['peak value (cfs)'].mean() - mu_0)/pooled_sd\n",
+ "\n",
+ "print(\"z-score = {}\".format( np.round(zscore,2) )) "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We can also compute a p-value from this z-score by looking it up on the standard normal distribution CDF"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "p = 0.002\n"
+ ]
+ }
+ ],
+ "source": [
+ "pvalue = 1 - stats.norm.cdf(zscore)\n",
+ "print(\"p = {}\".format( np.round(pvalue,3) ))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Plot the z-distribution, our z-score test result, and the $z_\\alpha$ that corresponds with our 95% confidence interval."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 20,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "
"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Create z values between -4 and 4 to look at the middle portion of the z-distribution around 0\n",
+ "# Scale our values by the pooled standard deviation (otherwise we'd be in generic z-distribution space)\n",
+ "z = np.linspace(-4, 4, num=160) * pooled_sd\n",
+ "\n",
+ "# Create the plot\n",
+ "plt.figure(figsize=(10,7))\n",
+ "# Plot the z-distribution here\n",
+ "plt.plot(z, stats.norm.pdf(z, 0, pooled_sd), label='Null PDF: ($\\overline{X}_2 - \\overline{X}_1$) = 0')\n",
+ "\n",
+ "# Plot a line at our z-alpha value and shade the rejection region\n",
+ "plt.axvline(z_alpha*pooled_sd, color='black', linestyle='-', label='$z_{a}$')\n",
+ "shade = np.linspace(z_alpha*pooled_sd, np.max(z), 10)\n",
+ "plt.fill_between(shade, stats.norm.pdf(shade, 0, pooled_sd) , color='k', alpha=0.5, label='rejection region\\nfor alpha={}'.format(np.round(1-conf,2)))\n",
+ "\n",
+ "\n",
+ "plt.axvline(zscore*pooled_sd, color='red', linestyle='-', label='z-test')\n",
+ "plt.xlabel('($\\overline{X}_2 - \\overline{X}_1$) [cfs]', fontsize=15)\n",
+ "plt.ylabel('PDF', fontsize=15)\n",
+ "plt.ticklabel_format(axis='x', style='sci', scilimits=(0,0))\n",
+ "plt.ticklabel_format(axis='y', style='sci', scilimits=(0,0))\n",
+ "plt.ylim(0, 9e-5)\n",
+ "plt.legend(loc='best', fontsize=15);"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### Questions:\n",
+ "\n",
+ "What do these test results mean? \n",
+ "\n",
+ "What does it mean that our z-test value (red line) fell within our \"rejection region\" of the null hypothesis PDF?\n",
+ "\n",
+ "What does our p-value tell us?"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "---\n",
+ "How would the estimate of p change if our **null hypothesis** is now that the difference in the means is equal to 20% of the mean of the before-1975 period, and the alternative hypothesis is that a change more than 20% of the before-1975 period mean has occurred?\n",
+ "\n",
+ "Therefore\n",
+ "\n",
+ "$H_0: \\bar{X}_1 - \\bar{X}_2 = 0.2 \\cdot \\bar{X}_1$\n",
+ "\n",
+ "$H_1: \\bar{X}_1 - \\bar{X}_2 < 0.2 \\cdot \\bar{X}_1$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Compute our z-score and p-value:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 21,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "z-score = 1.12\n",
+ "p = 0.132\n"
+ ]
+ }
+ ],
+ "source": [
+ "# hypothesizing a 20% change\n",
+ "mu_0 = 0.2 * skykomish_before['peak value (cfs)'].mean()\n",
+ "\n",
+ "# compute z-score\n",
+ "zscore = (skykomish_after['peak value (cfs)'].mean() - skykomish_before['peak value (cfs)'].mean() - mu_0)/pooled_sd\n",
+ "print(\"z-score = {}\".format( np.round(zscore,2) )) \n",
+ "\n",
+ "pvalue = 1 - stats.norm.cdf(zscore)\n",
+ "print(\"p = {}\".format( np.round(pvalue,3) ))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "
"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Create z values between -4 and 4 to look at the middle portion of the z-distribution around 0\n",
+ "z = np.linspace(-4, 4, num=160)\n",
+ "# Scale our values by the pooled standard deviation (otherwise we'd be in generic z-distribution space)\n",
+ "z = [i * pooled_sd for i in z]\n",
+ "\n",
+ "# Create the plot\n",
+ "plt.figure(figsize=(10,7))\n",
+ "# Plot the z-distribution here\n",
+ "plt.plot(z, stats.norm.pdf(z, 0, pooled_sd), label='Null PDF: ($\\overline{X}_2 - \\overline{X}_1$) = 0.2*$\\overline{X}_1$')\n",
+ "\n",
+ "# Plot a line at our z-alpha value and shade the rejection region\n",
+ "plt.axvline(z_alpha*pooled_sd, color='black', linestyle='-', label='$z_{a}$')\n",
+ "shade = np.linspace(z_alpha*pooled_sd, np.max(z), 10)\n",
+ "plt.fill_between(shade, stats.norm.pdf(shade, 0, pooled_sd) , color='k', alpha=0.5, label='rejection region\\nfor alpha={}'.format(np.round(1-conf,2)))\n",
+ "\n",
+ "plt.axvline(zscore*pooled_sd, color='red', linestyle='-', label='z-test')\n",
+ "plt.xlabel('($\\overline{X}_2 - \\overline{X}_1$) = 0.2*$\\overline{X}_1$ [cfs]', fontsize=15)\n",
+ "plt.ylabel('PDF', fontsize=15)\n",
+ "plt.ticklabel_format(axis='x', style='sci', scilimits=(0,0))\n",
+ "plt.ticklabel_format(axis='y', style='sci', scilimits=(0,0))\n",
+ "plt.ylim(0, 9e-5)\n",
+ "plt.legend(loc='upper left', fontsize=15);"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### So what happened with this second test?\n",
+ "\n",
+ "We created a more stringent test.\n",
+ "\n",
+ "For example, say we will only recommend constructing taller levees along the river if the mean flood (defined by the annual peak flow) increased by more than 20%. While we can report that we are 95% sure that there is a change greater than 0 (our first test); we are **not** 95% sure that the change is greater than 20% of the early period mean."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.8.8"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/modules/lab2/lab2-1.ipynb b/modules/lab2/lab2-1.ipynb
index 7753e079..76e91b6c 100644
--- a/modules/lab2/lab2-1.ipynb
+++ b/modules/lab2/lab2-1.ipynb
@@ -827,7 +827,7 @@
],
"metadata": {
"kernelspec": {
- "display_name": "Python 3",
+ "display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
@@ -841,7 +841,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
- "version": "3.8.8"
+ "version": "3.9.7"
}
},
"nbformat": 4,
diff --git a/modules/lab4/.ipynb_checkpoints/lab4-3-checkpoint.ipynb b/modules/lab4/.ipynb_checkpoints/lab4-3-checkpoint.ipynb
new file mode 100644
index 00000000..8ef7b233
--- /dev/null
+++ b/modules/lab4/.ipynb_checkpoints/lab4-3-checkpoint.ipynb
@@ -0,0 +1,856 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Lab 4-3: Confidence Intervals\n",
+ "\n",
+ "Example of calculating confidence intervals for a least squares linear regression model.\n",
+ "\n",
+ "---"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "import pandas as pd\n",
+ "import scipy.stats as stats\n",
+ "import matplotlib.pyplot as plt\n",
+ "%matplotlib inline"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We are working with the snow pillow data again, measurements of snow water equivelent at two different locations. Load the data file."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# snow pillow (snow water equivalent) example data\n",
+ "data = pd.read_csv('./data/pillows_example.csv')\n",
+ "\n",
+ "# Assigning my values to variables x and y for ease of use below\n",
+ "x = data['SLI_max'].values\n",
+ "y = data['BLC_max'].values"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**First, plot the data to get an idea of what it looks like.**\n",
+ "\n",
+ "- Does it look like we should try and fit a linear model to this? \n",
+ "- Does the variance in y values change as we move along the x axis (heteroscedasticity)?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "
"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fig, ax = plt.subplots(nrows=1, ncols=1, figsize=(7,7), tight_layout=True)\n",
+ "\n",
+ "# Scatterplot of original data\n",
+ "ax.scatter(x, y, c='k', label='Original Data')\n",
+ "\n",
+ "# Plot the regression line, we only need two points to define a line, use xmin and xmax\n",
+ "ax.plot([x.min(), x.max()], [B0 + B1*x.min(), B0 + B1*x.max()] , '-r', label='Least Squares Linear Regression Model')\n",
+ "\n",
+ "# Plot the mean line, we only need two points to define a line, use xmin and xmax\n",
+ "ax.plot([x.min(), x.max()], [y.mean(), y.mean()] , '--m', label='Mean Y')\n",
+ "\n",
+ "# Add legend\n",
+ "plt.legend(loc='lower right');\n",
+ "\n",
+ "# Add axes labels and title\n",
+ "ax.set_xlabel('Slide Canyon Maximum Annual SWE (mm)')\n",
+ "ax.set_ylabel('Blue Canyon Maximum Annual SWE (mm)')\n",
+ "ax.set_title('Linear Regression Model');"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**Plot the residuals** to make sure they don't have any sort of trend or pattern and are roughly normally distributed"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "
"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fig, [ax2, ax3] = plt.subplots(nrows=1, ncols=2, figsize=(8,4), tight_layout=True)\n",
+ "\n",
+ "# Plot the residuals\n",
+ "ax2.plot(x,residuals,'.')\n",
+ "ax2.set_title('Residuals versus X');\n",
+ "\n",
+ "# Plot a histogram of the residuals\n",
+ "ax3.hist(residuals, bins=10)\n",
+ "ax3.set_title('Residuals Histogram');"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Confidence Interval for the Slope (B1)\n",
+ "\n",
+ "**Compute the confidence intervals around our B1 parameter, the slope**\n",
+ "\n",
+ "We first specify our $\\alpha$ for our chosen level of confidence (95%), and our degrees of freedom $dof = n - 2$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "26\n"
+ ]
+ }
+ ],
+ "source": [
+ "# our alpha for 95% confidence\n",
+ "alpha = 0.05\n",
+ "\n",
+ "# length of the dataset\n",
+ "n = len(x)\n",
+ "print(n)\n",
+ "# degrees of freedom\n",
+ "dof = n - 2"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now, compute the Standard Error of the Gradient (Slope):\n",
+ "\n",
+ "$s_{B_1} = \\displaystyle \\frac{s}{\\sqrt{SST_x}} $"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# standard error of the gradient (slope)\n",
+ "sB1 = s/np.sqrt(sst_x)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "This follows a t-distribution, find the t-value that corresponds with our $\\alpha$ and $dof$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 20,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# t-value for alpha/2 with n-2 degrees of freedom\n",
+ "t = stats.t.ppf(1-alpha/2, dof)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Compute the upper and lower limits for the B1 parameter"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 21,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# compute the upper and lower limits on our B1 (slope) parameter\n",
+ "B1_upper = B1 + t * sB1\n",
+ "B1_lower = B1 - t * sB1\n",
+ "\n",
+ "# compute the corresponding upper and lower B0 values (y intercepts)\n",
+ "B0_upper = y.mean() - B1_upper*x.mean()\n",
+ "B0_lower = y.mean() - B1_lower*x.mean()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**Plot the data, linear regression model, and confidence intervals for B1**"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "
"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fig, ax = plt.subplots(nrows=1, ncols=1, figsize=(7,7), tight_layout=True)\n",
+ "\n",
+ "# Scatterplot of original data\n",
+ "ax.scatter(x, y, c='k', label='Original Data')\n",
+ "\n",
+ "# Plot the regression line, we only need two points to define a line, use xmin and xmax\n",
+ "ax.plot([x.min(), x.max()], [B0 + B1*x.min(), B0 + B1*x.max()] , '-r', label='Least Squares Linear Regression Model')\n",
+ "\n",
+ "# Plot the mean line, we only need two points to define a line, use xmin and xmax\n",
+ "ax.plot([x.min(), x.max()], [y.mean(), y.mean()] , '--m', label='Mean Y')\n",
+ "\n",
+ "# Plot the upper and lower confidence limits for the standard error of the gradient (slope)\n",
+ "ax.plot([x.min(), x.max()], [B0_upper + B1_upper*x.min(), B0_upper + B1_upper*x.max()] , '--r', label='Upper B0 confidence limit (95%)')\n",
+ "ax.plot([x.min(), x.max()], [B0_lower + B1_lower*x.min(), B0_lower + B1_lower*x.max()] , '--r', label='Upper B0 confidence limit (95%)')\n",
+ "\n",
+ "\n",
+ "# Add legend\n",
+ "plt.legend(loc='lower right');\n",
+ "\n",
+ "# Add axes labels and title\n",
+ "ax.set_xlabel('Slide Canyon Maximum Annual SWE (mm)')\n",
+ "ax.set_ylabel('Blue Canyon Maximum Annual SWE (mm)')\n",
+ "ax.set_title('Linear Regression Model with Confidence Intervals');"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Confidence Interval for Predicted Values of y\n",
+ "\n",
+ "**Compute confidence limits for the predicted values of y**\n",
+ "\n",
+ "To compute confidence limits on our predicted values of y, we need to predict some values of y first!\n",
+ "\n",
+ "For the prediction intervals, I'm naming the variables `p_x` and `p_y`, in the equations below these correspond to $x^*$ and $\\hat{y}^*$."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 23,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# an array of x values\n",
+ "p_x = np.linspace(x.min(),x.max(),100)\n",
+ "\n",
+ "# using our model parameters to predict y values\n",
+ "p_y = B0 + B1*p_x"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "For some value $x^*$ we want to predict a corresponding $y^*$ using our model.\n",
+ "\n",
+ "$\\hat{y}^* = \\hat{B}_0 + \\hat{B}_1x^*$\n",
+ "\n",
+ "But what is the undercertainty of the $\\hat{y}^*$ we'll calculate? We can compute a prediction interval for a given confidence (such a 95%).\n",
+ "\n",
+ "The error of our prediction is the difference between the \"true\" value of $y^*$ for $x^*$, and our predicted $\\hat{y}^*$:\n",
+ "\n",
+ "$B_0 + B_1x^* - \\hat{B}_0 + \\hat{B}_1x^*$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The variance of this prediction error ($\\sigma_{E_P}^2$) will help define our prediction intervals, and can be computed as follows:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "$\\sigma_{E_p}^2(x^*) = s^2 \\Bigg[ 1 + \\displaystyle\\frac{1}{n} + \\displaystyle\\frac{n(x^*-\\bar{x})^2}{n \\sum{x_i^2} + (\\sum{x_i})^2} \\Bigg]$\n",
+ "\n",
+ "or\n",
+ "\n",
+ "$\\sigma_{E_p}^2(x^*) = s^2 \\Bigg[ 1 + \\displaystyle\\frac{1}{n} + \\displaystyle\\frac{(x^*-\\bar{x})^2}{SST_x} \\Bigg]$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now compute our error of prediction ($\\sigma_{E_p}$) for each p_x:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 24,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "sigma_ep = np.sqrt( s**2 * (1+ 1/n + ( ( n*(p_x-x.mean())**2 ) / ( n*np.sum(x**2) - np.sum(x)**2 ) ) ) )"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The lower and upper confidence limits based on predicted y and confidence intervals (which follow a t-distribution) can be computed as:\n",
+ "\n",
+ "$y^* \\pm t_{\\frac{\\alpha}{2},n-2} \\cdot \\sigma_{E_p}(x^*)$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "alpha = 0.05\n",
+ "\n",
+ "n = len(p_x)\n",
+ "dof = n - 2\n",
+ "\n",
+ "t = stats.t.ppf(1-alpha/2, dof)\n",
+ "\n",
+ "p_y_lower = p_y - t * sigma_ep\n",
+ "p_y_upper = p_y + t * sigma_ep"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**Finally, plot the upper and lower confidence limits for the predicted y values**"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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Ft96Cq6/2N65YYAncGGNMTNm+Hd55R6+LQHJy8XHIzz1XZwar7uw0MmOMMTHl7rvhn/+Edeu0R/nTT/sdUWyyFrgxnsGDBzN48GC/wzCm2vnmG/jDH2DxYl2+8UaYNy+xztmOBmuBG+Ox5G1M1fnmGz2+feSR2ovcuWBP8nbt9GLKZwncGM+mTZsAaFpdzkExxicFBXDmmTpa2vTp2tK28bYqzxK4MZ5+/foBNh+4MdHw6KPw+uswe7bOvz1tWnxN3RmL7Bi4McaYiNuzB156CfLzdfmAA3SAlcBgh6ecUn0GXIkWS+DGGGMiJjC9xvvvw6WX6jnboOdtv/SSJnITGVFP4CLytIhsFJFvQtY1FpH3ROQH7++BIdtGishyEVkmImeHrD9ORBZ72x4Viadp140xJrHl5cHpp8PDD+vyWWfBnDnQp4+/cSWyqmiBTwLOKbFuBDDHOXcoMMdbRkQ6A5cCXbz7PC4iyd59ngAygEO9S8l9GmOMqULLlsFrr+n1lBTtTd6okS4nJ8MZZxQfgMVEVtQ7sTnnPhKRtBKr+wI9vevPAnOB2731Lzrn9gArRWQ5cLyIrAIaOOfmA4jIc8CFwKwoh2+qkaFDh/odgjExr7BQkzPogCuzZ0N6unZMC4xPbqqGX7+Nmjvn1gF4fwPD0LcGVofcbo23rrV3veT6UolIhogsEJEFP//8c0QDN4lrwIABDBgwwO8wjIlZb74JrVrBTz/pclYWfP21Jm9T9WKtuFHacW1XzvpSOecmOue6Oee6HXTQQRELziS21atXs3r16opvaEw1sXu3zrcdGCGtUyfo0SPYk7x9e2jRwr/4qju/EvgGEWkJ4P3d6K1fA7QNuV0b4CdvfZtS1hsTMVdccQVXXHGF32EY47tff9W/+fkwdGiwNN6hA0ydCocc4l9sJsivBP4GMMi7Pgh4PWT9pSJSW0Tao53VPvfK7DtE5ESv9/mfQu5jjDEmQvr1gz/+Ua83aABffgljx/obkyldVZxG9gIwH+goImtE5GrgfuBMEfkBONNbxjm3BJgKLAXeBv7inCv0djUUeApYDvyIdWAzxpj99vXXMHJk8Pztc86BCy4ILh92mE7paWJPVfRCv6yMTb3KuH0WkFXK+gXAEREMzRhjqqXNm3VAlTp1tIX96KNw1VVw6KFwzTV+R2fCFWud2IwxxkTRt99qT/Jp03R5wACdd/vQQ/2Ny1Sedf43xjN8+HC/QzAm4pyD+++Hxo1hyBDtSX777Tr/NmgrvE4df2M0+0acK/NsrITQrVs3t8DmqTPGVCO//abzbR9zjC6feSa0bg2TJvkalqmAiCx0znUL9/bWAjfGs2zZMgA6duzocyTG7J/hw+Hpp7U0Xr8+zJwJtWv7HZWJNDsGboxnyJAhDBkyxO8wjKm0RYt0es4VK3R5yBB48UWoW1eXLXknJkvgxhgTZ5yDefNgyRJdbtIEtm4NDnHapUtwfHKTuCyBG2NMnCj0RsXYvRvOOw/GjdPltm01mZ9yin+xmapnv8+MMSYODBumg668/76Wxt96C4480u+ojJ+sBW6MMTFo+XK4665gq7tzZzj++OBy9+7aQc1UX9YCN8bzt7/9ze8QTDW3bRvUqgUpKbBwoU7XeeGF0LUrZGT4HZ2JNdYCN8bTu3dvevfu7XcYpppasQJatoTsbF2+8EJYu1aTtzGlsQRujGfRokUsWrTI7zBMNeEc3H03PPywLrdvDyNGwEkn6XLt2tCsmX/xmdhnJXRjPMOGDQNg7ty5/gZiEtaOHbBgAZx+us7w9b//6RCnoMt33ulvfCa+WAI3xpgoci44Hefo0fDkk7B+PTRqBK+8Yudqm31nJXSzT7Kzs0lLSyMpKYm0tDSyAwfujDG/mz8fDj5YZwADuP56+OADaNhQly15m/1hbx9TadnZ2WRkZJCXlwdATk4OGV4X2YEDB/oZmjG+2rNHO6Edfrgeyz74YOjYUQdeAejQQS/GRIK1wE2lZWZm/p68A/Ly8sjMzPQpImP8U1gYHMJUBG67DV54QZebN4e33w7OCmZMJFkL3FRabm5updbHi7Fjx/odgolDffrAxo3wxRd6Dvf//qdDmxoTbZbATaWlpqaSk5NT6vp41r17d79DMHHgnXfgkUfg9dehZk2d+Wv37mBntTj/GJg4YiV0U2lZWVmkpKQUW5eSkkJWVpZPEUXGvHnzmDdvnt9hmBiTnw+vvQabNuny7t06wMqaNbrcpw/07x/saW5MVbEEbipt4MCBTJw4kXbt2iEitGvXjokTJ8Z9B7ZRo0YxatQov8MwMcC5YMez77+HP/4Rpk7V5T594KuvdOAVY/xkJXSzTwYOHBj3CduY0hQWwnHH6WArDz8MRxyhp34Fpuq0lraJFdYCN8ZUey+/DHfcodeTk3Uc8hNPDG7v2dPO2TaxxxK4Maba+e03mDNHS+UAn30Gr76q60Gn8RwwwLfwjAmLJXBjTLXgHBQV6fVJk6B3bwjMXXPvvbB4sfYqNyZeWFHIGM/48eP9DsFEyapVcPbZMHYsXHyxXpo3hy5ddHudOr6GZ8w+sQRujKerTbycMJyDCRN0wpBLL9WBVY44IjgGeePG2pvcmHhmJXRjPLNnz2b27Nl+h2H20a5dOlUnaE/x557T2b5AO6a98oqWzY1JFNYCN8YzZswYAHrbt3zcKCqCJK8Z8pe/wPTpOlVn7drw1lvBFrcxicha4MaYuPT22zps6dq1unzjjdrKDnREa9TIztk2ic1a4MaYuLBtm45Bnp6uA60cfDAcfzzs3Knbjz7a3/iMqWqWwI0xMWvdOti6FTp31uPY//gHNGigCfyww/TcbWOqK0vgxpiYUlCgo545B6eeCoccouXy+vW1XG7HtY1RlsCN8UyYMMHvEKq9e+7RSUMWL9bj108+CW3aBLdb8jYmyDqxGePp2LEjHTt29DuMauXrr2HwYPj1V13u3BnOOis4E1jv3tCpk2/hGRPTLIEb45kxYwYzZszwO4yEVlgIc+cGe45v3QpvvAFLluhyv37w0ENQt65vIRoTNyyBG+MZN24c48aN8zuMhOMc7Nih19et02k6J03S5VNP1fO2jz/et/CMiVt2DNwYEzXOwbHHQteu8Mwzejz7vffgpJN0e1IS1Krlb4zGxCtrgRtjIurf/4ZBg/S6iF4/99zg9t694YAD/InNmERiCdwYs19yc+HBB/X4NsDmzbBmDezZo8vDhkH//v7FZ0yisgRujKm0Vavgl1/0+vz5cOutwbm1b78d5szR8ciNSVgFBfDFF76GYAncGM/kyZOZPHmy32HErKIi/fvtt9C+PUybpst9+mgr/LjjdNnGHzcJ7+234aijoGdP2LDBtzAsgRvjadu2LW3btvU7jJhTWAg9ekBmpi536gSPPQZnnqnLdevqfNvGVAtr1+qv1vx8mDIFmjXzLRRL4MZ4XnrpJV566SW/w4gJzz4Ld9yh15OTdaKQgw/WZRH46191JjBjqoXNmyEwUmPr1noqxZIl0LevryUnS+DGeJ544gmeeOIJv8Pwxbp18NxzweUFC+Ddd4Nl80cfhWuv9Sc2Y3yTnw/jx+uA/NddB8uW6foePWKik4clcGOqqTVr9PsJdPzxQYNgxQpdHjcOPv1Uz9M2ptpxDmbOhCOPhJtugj/8Ab76CmJsqGX7eBpTjTinf//7Xz1u/e67unz55do5LVAmt8FVTLW2c6cO0g+ayN95B444wteQSmMJ3JhqYOdOOPFELYWDNijuu0870gI0aWKThphq7uef4d57tddm/fp6LuQ338D558fsqRWWwI1JUI88ogOsANSrp4fxDjpIl2vVghEjrCOaMeTn6zGjQw+Fu++Gzz7T9UcfDTVr+htbBWwsdGM8L7/8st8h7Jdly/S7509/0uVPPtHvpltu0eXnn/cvNmNijnM6Fd4tt8Dy5XDeefqL9/DD/Y4sbJbAjfE0bdrU7xAqxTkd/axrV63wPfusNiQuvBAaNNBTVGO8AWGMfwoLtQxVsybMmgXnnON3RJVmJXRjPJMmTWJSYJ7LGFVUBL/9ptdfeEFn+vrf/3T5hht0iNMGDXTZkrcxJWzYADffrPPb1qihifurr+IyeYMlcGN+F+sJfOVKHUMiUOk/5xz4z3+gQwddbtECWrb0Lz5jYtbu3fDAA3qc+7HH4KOPdH1aWlz/0vU1gYvITSKyRES+EZEXRKSOiDQWkfdE5Afv74Ehtx8pIstFZJmInO1n7MZEW1ERXHklPPywLrdrp4fpAsOWNm4MV10FjRr5F6MxMc05eOUV6NxZy+U9e+oIauef73dkEeFbAheR1sANQDfn3BFAMnApMAKY45w7FJjjLSMinb3tXYBzgMdFJNmP2I2JlunTg6d6JSXpCI6BWb+SkrTFfcop/sVnTNyZMEEnoH/3Xe20dthhfkcUMX6X0GsAdUWkBpAC/AT0BZ71tj8LXOhd7wu86Jzb45xbCSwHjq/ieI2JqHXrIHT49Rkz9PsmMODKG2/AnXf6E5sxcWndOsjI0CnyRCA7G778Mjj7TgLxLYE759YCDwK5wDpgu3PuXaC5c26dd5t1QGCql9bA6pBdrPHW7UVEMkRkgYgs+Pnnn6P1FIzZJ8uW6VTCAJMmwaWXwk8/6fL48bB4ccyOG2FM7Nq1C8aO1ePckybpcIOggx/USMwTrvwsoR+ItqrbA62AA0Tk8vLuUso6V9oNnXMTnXPdnHPdDgqMXGFMBd566y3eeuutiO+3qCg45visWTri2Sef6PKVV+ohuUDnswYNbPxxYypt2jT9YGVmwllnwdKlcNllfkcVdX5+VfQGVjrnfnbO/Qa8CnQHNohISwDv70bv9muA0FmH26Ald2MiIiUlhZSUlIjuc/16aNNGGwQAp52mnWA7d9blFi30urW4jdkP770HBx4I778Pr76qww5WA34m8FzgRBFJEREBegHfAm8Ag7zbDAJe966/AVwqIrVFpD1wKPB5FcdsEtjjjz/O448/vl/7cA6uuCJ43Lp5cx1Y5dBDdfmAA3Qu7WbNyt6HMaYCa9fqkIOBYU8feggWLoTTT/c3rirm24EB59xnIvIy8D+gAPgSmAjUA6aKyNVokr/Eu/0SEZkKLPVu/xfnXKEvwZuENHXqVACuu+66St1v8mT44Qe45x5tSScnB8vgIrCfvwmMMQF5eTrc6QMPaEeSU0+FE07Qwf6rIV+P7Dvn7gRK9rHdg7bGS7t9FpAV7biMKc+338KbbwbHGF+wQPvL3HWXJu4YHgvGmPj18ss6N/eaNdCvH/z979C+vd9R+SqsErqIHCgiXUTkYBGxLjamWtm1SxN2Xp4uf/AB3H67nqUC2iBYsMA6nxkTVcuX67GnDz/UTmvVPHlDOQlcRBqKyCgRWQx8CkwApgI5IjJNRKrXwQZTraxfD1u26PVPPoH0dJ0eGODyy2HjxuBUnHE8EqMxsWv1ahg4MDhQwvDh8MUX2hPUAOW3wF9Gz7s+1TnX0Tl3indqVlvgfqCvd5zamLjnHBQW1gF0HIhWreCZZ3Rbjx7wzjtwtjd4b4MG0KSJT4Eak+h27oQ77oCOHbVH+fr1ur5mTStzlVDmq+GcO9M5N9k5t62UbQudc8Occ/+JbnjGRE9gtDPn4Kij4PDD32bu3Lm0bAn/+hdccIFur1VLTy2tVcu/WE35srOzSUtLIykpibS0NLKzs/0OyeyL6dM1cd97L/TtC999Bzfe6HdUMSusTmwichSQFnp759yrUYrJmKgbPly/G958U3uKDxqkExMFDB3qW2imkrKzs8nIyCDP66SQk5NDRkYGAAMHDvQzNBMu5/SDmJ+vAydMmwbdu/sdVcyrsB4hIk8DTwMXAxd4l/Qox2VMRE2bpiXwoiJdbtdOz80OtMJvuQVWrXqQBx980L8gzT7JzMz8PXkH5OXlkZmZ6VNEJmyrVsGAAdqjHKB/f5g/35J3mMJpgZ/onOsc9UiMiaBvvtHe4Q89pNNu5udrL/LNm3Vo5Btu2Ps+M2fOBOCWwPlhJi7kBk4HCHO9iQE7dsD998O4cXpcu1s3XS9iwxJWQjg9AuZ7U3kaE7O2bIF//EOHQAbtBzNjhpbJQTuzfvyxJm+TWFIDp1UDl5AAACAASURBVAOEud747M03dUrPsWPhkkvg++/h1lv9jiouhZPAn0WT+DIR+VpEFovI19EOzJjyFBbCzJnBkRSLimDECB0KGeD442HDBqvEVQdZWVl7jWGfkpJCVpaN+RRTAlPwNWkCBx8Mn36qwxi2aeNvXHEsnBL608AVwGKgKLrhGFO25cth0yY48UStsl19tR7XPuEEaNpUT/8KjDGelGRnnFQXgY5qmZmZ5ObmkpqaSlZWlnVgixUrVsBtt2ninjBBP8CffGKl8ggIJ4HnOufeiHokxpSwa5fOnd21qy4PHgy7dwdHPXv//eKTDu3vBCF169bdvx0Y3wwcONASdqz55RfIytJJ7mvU0Kk+Ayx5R0Q4Cfw7EZkCzEDHKQfsNDITHTk52kMc9PTPadPg55/18z9+vM4YGNClS2Qfe9asWZHdoTHV1fvv63zcGzfqOZpjx+roSCaiwiky1kUT91nYaWQmwn79NXho7PHH9VzstWt1eehQePHF4G27dYMOHao8RGNMuHbt0r8dOujoSF98obP7WPKOigpb4M65K6siEFM9OKcJu2ZNncHrjDPg7bd1Gt+zz4Z//hMC/ZGOOaZqY7v33nsBGD16dNU+sDHx7ocftCd5Xp6OO9yuHbz3nt9RJbxwBnJpLyIPicirIvJG4FIVwZnEEBgs5eefoW1b+I83AO9RR8H11wd/nHfoAH/5S/EyeVWaM2cOcwIzlhhjKrZtmw5r2KWLzvZz+unB0ZJM1IVzDPw14D/oMXD7z5iwOQe9esGxx+qgKk2b6qxegY5n9evremNMHPr0U50wYPNmuOoqGDMGWrTwO6pqJZwEvts592jUIzEJYfhwPZ1ryhTtaNq1azBhi8CTT/obnzFmP23dqmWyLl2gZ08YNarqj3cZILwE/oiI3Am8S/Fe6P+LWlQmbvz739pT/N13dfnAA+G334LbH3rIn7iMMRH23Xc6acCPP8LXX2sJbdo0v6Oq1sJJ4EeiA7mcQbCE7rxlU83MmaOVshkzoF49PR+7Zk3tTX7AAfC3v/kd4b5rYpN8G7O3LVvg7rv1NJGUFP2QBzq2GF+Fk8D/CBzsnMuPdjAm9nz3nY6/MGYMHH64rvvlF/jpJx3O+Oqr9ZIIXnnlFb9DMCa2LF0Kp5wC27fDtdfCPffs/4hJJmLCOQ/8K6BRtAMxsWHLFsjICJbEU1L0VM7Vq3W5Vy9YuFCTtzEmQQUGY+jYES69FL78UjuwWPKOKeG0wJujo7F9QfFj4H2iFpWpMs5pH5ROnXTApPr1YdasYJ+U1FQdHa06jHw4cuRIAO677z6fIzHGJ0uXws0363jFP/ygnVoef9zvqEwZwkngd0Y9ClOlHn9cp9u87TZNzO+/r2OMDxqkx7Nzc4sn7OqQvAHmz5/vdwjG+GPTJrjrLm1l16sHd96pnVpMTCszgYuIOPVhRbeJTmgmUl59FebP1/myAT76SA9p3XabLs+bB8nJwdtXl4RtjEE7tHTpAjt2wJAh2mGtaVO/ozJhKO8Y+Acicr2IpIauFJFaInKGiDwLDIpueGZffPIJXHONzpkN8NVXMH065HvdEJ9/XsvkAaHJ2xhTDTgH336r11u10rL5V1/Bv/5lyTuOlJfAzwEKgRdE5CcRWSoiK4AfgMuAh51zk6ogRlOBb7/Vjmfr1+tyTo6e5pWbq8t/+5vOpV2rli7XCOfAiTEmMS1eDGeeCUcfred0A4weHfnp/UzUlZnAnXO7nXOPO+dOBtoBvYBjnXPtnHPXOucWVVmUppj163UM8S++0OW8PJg6VefOBhgwQG/Tvr0u16zpT5zxpk2bNrRp08bvMIyJjo0b4c9/1uER//c/GDdOe6mafZKdnU1aWhpJSUmkpaWRnZ1d5TFIoh/C7tatm1uwYIHfYeyX3bu1p/ipp8If/6jzB6SmwmOPacezoiKtiFkp3BhTqh079Bf99u1w3XXaSa1xY7+jilvZ2dlkZGSQl5f3+7qUlBQmTpzIwIED93m/IrLQOdct7NtbAo9Nd9yhh6JuuEGT86GHarIOzHRZUGClcGNMOZyDzz6DE0/U5aee0kFZOnXyN64EkJaWRk5Ozl7r27Vrx6pVq/Z5v5VN4JYCYsT48TpYyrhxuvzFFzr1Jmiv8O+/12FLAyx5R96wYcMAGD9+vM+RGLOfFi2Cm26CuXPhv/+F7t21Z6uJiNxAB6Mw10dLmcfARaRTyPXaJbadGM2gqoPnnoOLLgour1wZPIYN8NZbMHFicDkpnDHzzH5ZtGgRixZZ1w4Tx9av10R97LHaWe3xx+H44/2OKuGkltF3oKz10VJeWpgScr3kCBc2NE8lvfkmnHCCdjgDnfxj06bg8iOPwMyZwdvbudjGmEopKNAvmWef1db38uUwdKiV66IgKyuLlJSUYutSUlLIysqq0jjKS+BSxvXSlo0n0KXgs8/0LI0lS3S5dm2oW1c7goJ+rj76SMcaN8aYfeKcDupQVKSJ+l//0i+dceOgkU1hES0DBw5k4sSJtGvXDhGhXbt2+92BbV+Ul8BdGddLW662Cgr078qVOlvXa6/pcrNmetm9W5d799bDUWlpfkRpjEk4CxdCjx5w3nk63CJAerrNNFRFBg4cyKpVqygqKmLVqlVVnryh/E5sbUTkUbS1HbiOt9w66pHFIOe09F2vHuzaBZ076wAqI0dC69Y6cU+DBnrb9u3hvff8jddUzmH2xWfiwU8/6Ry/zz6rp6pMmKDnl5pqp7wEfmvI9ZLnYcXfeVkRcOSR0K0bTJqk5fA+fYKDF9WqFWx9m/g0MbTXoDGxyDk4/3ydNezWW3WAiIYN/Y7K+KS8BP4V8JVNVhKUkaHDBgc88oh/sRhjqgnn4OWXtVR+wAHwxBNw0EHQoYPfkRmflXcM/Clgk4i8JyJ3ichZItKgqgKLRTfcAP36+R2FiZaMjAwyMjL8DsOYoM8/h5NPhv794ZlndN2JJ1ryNkD5Y6F3A9oCWUA+cAPwg4h8JSJ2GplJON9//z3ff/+932EYA2vWwBVX6GlhK1bAf/6jp64YE6LcEwSdc3nAXBH5AvgMOBn4EzpTmTHGmGjIyID339cesiNHQv36fkdkYlCZCVxE/g/oDnQF9gCBJH6Kc2591YRnjDHVQFERTJkCPXtCmzY6tnLNmsEpBY0pRXnHwCcCJwKTgKHOuRHOuemWvI0xJoLmz4eTTtKSeeBMiMMOs+RtKlReCb0hcDTaCr9LRDoC69BhVec7596vgviMqTJdu3b1OwRTneTkwIgR8OKL0LKlnp96xRV+R2XiSNjTiYpIc6AfcBPQ3jkXF7NPx+t0osaYBJeRAZMn6/nct92mI0SZai1i84GLyFFo6ztwqYW2vucB/3XOxUVWtARujIkJRUU6DeHRR8Mxx8CGDbBnD1TxDFYmdlU2gZd3DHwS0AWYBfRyzqU65wY45x6Jl+RtTGVcfvnlXH755X6HYRLRxx/rtJ5XXqmnhAE0b27J2+yXMo+BO+eODV0WkZrAEcBa59zGaAdmTFVbs2aN3yGYRLNyJdx+O0ybpr3Ln38eLrvM76hMgiizBS4iT4pIF+96Q3Ro1eeAL0XE3oHGVHPZ2dmkpaWRlJREWloa2dnZfocUe55/Ht58E+6+G5Ytg4EDIam8wqcx4SuvF/qpzrk/e9evBL53zl0oIi3QsvoLUY/OGBOTsrOzycjIIC8vD4CcnJzfh6H1Y1rFmFFYqEOetmqlY5cPH65l8zZt/I7MJKDyfgrmh1w/E3gNwM4DN8ZkZmb+nrwD8vLyyMzM9CmiGDB3Lhx3HFx7rQ7KApCSYsnbRE15LfBtIpIOrEWHUL0aQERqAHWrIDZjqtRJJ53kdwhxIzc3t1LrE9qPP+qpYNOna6e0F1/UyUdM4lu5Enbtgs6dfXn48hL4EOBRoAUwLKTl3Qt4M9qBGVPV7rvvPr9DiBupqank5OSUur7amT8f3n0XxoyBm2+Guta+SViFhfDppzBjhl6WLoWLLoJXXvElnPJ6oX9PKZOWOOfeAd6JZlDGmNiWlZVV7Bg4QEpKCllZWT5GVUUKCvRUMBEdjOX//g9694YWLfyOzETDL7/AO+/AzJnw1luwaRPUqAE9euj/Pz3dt9DKnY0s2kSkETrv+BGAA64ClgEvAWnAKqC/c26rd/uRaCm/ELjB+zFhTERcfPHFALzi06/peBLoqJaZmUlubi6pqalkZWUlfge2OXPgpptg8WK44AI93p2UZMk70axcGWxlf/gh/PYbNG6sHRMvuADOPhsaNvQ7Sn8TOPAI8LZzrp+I1AJSgFHAHOfc/SIyAhgB3C4inYFL0cFlWgGzReQw51yhX8GbxLJ582a/Q4grAwcOTPyEHfDjj1oef+MNSEuDl1/W0qmI35GZSAgtjc+cCUuW6PrDD9cfbBdcoBPOJMfWCOK+JXARaQCcBgwGcM7lA/ki0hfo6d3sWWAucDvQF3jRObcHWCkiy4Hj0eFdjTEmetatgw8+gPvvhxtvhDp1/I7I7K9fftG+CzNm7F0av+YaTdodOvgdZbnKmw/85vLu6Jx7aD8f+2DgZ+AZETkaWAjcCDR3zq3zHmOdiDTzbt8a+DTk/mu8dcYYE1kFBTBhAqxfD/feC6ecAqtXx0TZ1OyHOCmNh6u8Fnj9KnjsY4HrnXOficgjaLm8LKXVqkqdiUVEMoAMqKa9Yo0x++6dd7RcvnQpnHmmlleTk+Pqi914KiqNp6drabyG30eT9015vdDvjvJjrwHWOOc+85ZfRhP4BhFp6bW+WwIbQ27fNuT+bYCfStuxc24iMBF0NrJoBG8ST69evfwOwfhpxQq4/notp3boAK+9Bn362HHueJMApfFwVfizQ0TqoD2/uwC/H/hxzl21Pw/snFsvIqtFpKNzbhl6fvlS7zIIuN/7+7p3lzeAKSLyENqJ7VDg8/2JwZhQo0eP9jsE47cFC+DBB+Gvf4Xatf2OxoQrwUrj4QqnbjAZ+A44G7gHGAh8G6HHvx7I9nqgr0DHXE8CporI1UAucAmAc26JiExFE3wB8BfrgW6M2We//QZPPAFffAGTJ8PBB0NuriXueBAojc+cqUk7wUrj4RLnyq8wi8iXzrljRORr59xR3rSi7zjnzqiaEPdPt27d3IIFNn25qdi5554LwKxZs3yOxESVc1paHT5cZwjr3Rtef13HLTexq6zS+GmnaSs7AUrjIrLQOdct3NuH8/PkN+/vNhE5AliPDrJiTELZtWuX3yGYaFu9Wo+DvvsuHHaYJoPzz7fj3LEqUBqfOVMni6kmpfFwhZPAJ4rIgcBo9Dh0PeCOqEZljDGR5Jwm6QYNYNUqGD8ehg6FWrX8jsyEKq80PmxYcECVBC+Nh6vCV8E595R39UP03G1jjIkP+fnwz3/qTGEffKCttaVLY25ErWqtvNL4Ndfo8exDDvE7ypgUTi/0Ulvbzrl7Ih+OMcZEgHM67Oktt8Dy5XDOObBtGzRtask7FpRXGk9P19J4o0Z+RxnzwqlD/BpyvQ6QTuR6oRsTM9J9nFXIRNDGjXDZZfD++1p6fest8DooGp8UFsJnnwVP9bLSeERU2At9rzuI1AbecM6dHZ2QIst6oRtTTQRGTCsogF694JJLYMgQqFnT78iqp4p6jVtpfC+V7YWetA+PkYIdCzdVIDs7m7S0NJKSkkhLSyM7O9vvkEws2rMH/v536NRJk0aNGlqW/etfLXlXtZUr4bHH4Kyz9HDFJZdomfycc+DFF+Hnn3VK1mHDLHlHQDjHwBcTHHM8GTgIHdDFmKjJzs4mIyODvLw8AHJycrj88su58cYbeeSRR6IyjWXPnj0BmDt3bsT3baLAOe2cduutOgxqejrs3Kk9ze20sKpRVmm8UycrjVeBcF7V0AODBcAG51xBlOIxBoDMzMzfk3eozZs3k5GRAVB95qI2e9u5UxP2hx9Cly5aqj3zTL+jqh6s13jMCOc0shwRSQaae7dvJSI453KjHp2ptnJzy3575eXlkZmZaQm8Otq9W+firlcPUlN1KNRrrrEWXrStWhVsZQd6jR94YPEBVazXeJULp4R+PXAnsAEo8lY74KgoxmWqudTUVHJycsrcXl6CNwlo9254+GF46CH4/HNo3x6ee87vqBKXlcbjQjiv/o1AR+fc5mgHY0xAVlZWsWPgJdk879WEczBtGtx2G+TkQN++kLQvfW9NhQKl8Zkz4c03rTQeB8JJ4KuB7dEOxJhQgfL4jTfeyObNxX87pqSkkJWVFfHH7N+/f8T3afZDQYFONPLhh3DUUdp7+Yy4mEMpflhpPK6FMxvZf4COwJvAnsB659xD0Q0tMuw88PiXnZ1NZmYmubm5pKamkpWVZce/E9m2bcGkMXo0tGsHV15pI6hFQnml8cCMXlYa901lzwMPJ4HfWdp659zdlYzNF5bATbgC5foUm1bSH3l5MG4cPPCAlnK7d/c7osSwY0ew13hoafzUU4NJ20rjMSHi04nGS6I2Zn+dd955gJ0HXuWcgxdegNtvhzVr4OKLoWVLv6OKb1YarxbC6YV+GHALOgf477d3ztnBKGPM/nFOxyl/5x045hjIztZOU6ZyAqXxwDSc33yj6wO9xtPTtaJhpfGEEs5/cxrwJPAUUBjdcIwx1cJPP0GLFtqj/KKLYMAAGDTIephXRmhp/K23dJjSQGn8oYesNF4NhPNpKXDOPeGc+9w5tzBwiXpkxpiI8318+V9/hTvv1MTy4ou6LiNDO6lZ8q7YqlXBscabNIF+/XTa1LPOCo41/v77cNNNlryrgXBa4DNE5DpgOsV7oW+JWlTGmIgrbXz5KhuWtqhIy+MjRmjre8AA66QWjvJK4zfeqK1sK41XW+H0Ql9ZymrnnIuLGcmsF7oJ16RJkwAYPHiwr3FES1paWqmj27Vr145Vq1ZF98EHDICpU+EPf9AR1U4+ObqPF8/KK41br/GEFvHTyMp4kFrOufxK39EHlsCNUUlJSZT2eRcRioqKSrnHfsrJgWbNoG5dTUSbN8PAgVYqL02g1/jMmdprPD8/2Gs8PV2n47Re4wkv4qeRhexYgNOB/wMuQCc3MSZhbNq0CYCmTZv6HEl0lDW+fMSHpd2xA+6/X8/pHj0aMjM1EZmgwkId0z1wqlegNN6xI9xwg5XGTVjCOY3sBDRp/xFoDPwFuDXKcRlT5fr16wck7nngpY0vH9FhaYuK4NlnYdQoWL9eW9t/+lNk9p0IKuo1np4Ohx7qd5QmjpSZwEUkC+gP5AIvAPcAC5xzz1ZRbMaYCAp0VIvasLRDh8LEiXDCCTB9Opx4YmT2G8+sNG6iqLwWeAawDHgCmOmc2y0ilT9gboyJGQMHDoxsj/MVK3Ru7mbNYMgQ6NEDLrsMRCL3GPHESuOmCpX3LmoBnAVcBowXkQ+AuiJSwzlXUCXRGWNi0y+/wNix2qP8yivhySfh2GP1Ut2UVhpPTtYR5aw0bqKozATunCsEZgGzRKQOkA6kAGtFZI5z7v+qKEZjTKwoLISnn4a//Q02btTR00aP9juqqrdqVfDc7NDS+LnnaivbSuOmCoRVx3HO7QZeBl4WkQZohzZjEsrQoUP9DiH2jR4N992n53HPnKnndVcHVho3MWifzgOPJ3YeuDH7afly7WF+2GGwejXMnw+XXJL4x7nLK42np2vSttK4iaConQduTKJbvXo1AG3btvU5khixbRuMGQOPPqrTT86YAW3b6iVRWWncxBFL4MZ4rrjiCiBxzwMPW0EBPPWUlss3b9ZOamPG+B1VdFhp3MSxcAZySQbOZ+/5wB+KXljGGN/88586m9Vpp2kv80TrWR4ojc+cCW++Wbw0Pm6clcZN3AhrNjJgN7AYiMKAycYY3y1bBlu36uAr11wDaWnQt2/iHOfOyQm2sq00bhJEOAm8jXPuqKhHYoypelu3wj33aKu7a1ctJ9erBxde6Hdk+ye0ND5zJixerOsDpfH0dO1Jb6VxE8fCeffOEpGznHPvRj0aY0zV+O03mDAB7rxTO6tdc40m8nhucZdVGj/1VCuNm4QUTgL/FJguIknAb4Cg84E3iGpkxlSx4cOH+x1C1XnlFbj+ejjjDB0t7Oij/Y5o31RUGj/7bF02JgGFk8DHAScBi12inzRuqrULLrjA7xCia+lS+PFHTWyXXAJNmkDv3vHV6i6vNH799frcrDRuqolw3uU/AN9Y8jaJbtmyZQB07NjR50gibPNmuOsueOIJSE3VmbCSk+HMM/2OLDw7dsB772nSttK4Mb8LJ4GvA+aKyCxgT2ClnUZmEs2QIUOABDoPPD8fHn8c7r5bJx/58581kScn+x1Zxaw0bkyFwkngK71LLe9ijIkHn3+u53OfdZa2VI84wu+IyhYojQdGQQuUxg87zErjxpShwk+Dc+7uqgjEGBMB33yjY5Vfey2ccgp88QUcd1xsHueuqDSenq4J3BhTqqSKbiAiH4jI+yUvVRGciU/Z2dmkpaWRlJREWloa2dnZfoeU+H7+GYYO1d7ko0fDr7/q+m7dYit55+ToOednnw1Nm8LFF8Nrr2lnuilT9Hl88AHcfLMlb2MqEE496paQ63WAi4GC6IRj4l12djYZGRnk5eUBkJOTQ0ZGBgADBw70M7TEtGcPPPYY3Hsv5OXBX/+q53YfcIDfkanCQq0CBI5nW2ncmIjZp+lEReRD51yPKMQTcTadaNVKS0sjJydnr/Xt2rVj1apVVR9QJcyePRuA3r17+xxJJfzwA3Tpose5H3wQOnXyOyLYuTM4DWfJ0vgFF1hp3JgyRHw6URFpHLKYBBwHtNiH2Ew1kJubW6n1sSRuEvdXX2nZ+c479fSpJUv8P40q0Gt85kwtgefn69jioWONW69xYyKqwmPgwEJggfd3PjAcuDqaQZn4lZqaWub6WD82vmjRIhYtWuR3GGXbsEE7px1zjJbN16/X9X4k78JC+PRTyMyEo47SyU+uvx5WrtS/c+dqy3vKFLjsMkveMS7WP5umDM65hL4cd9xxzlSd559/3qWkpDjg90tKSoobOnRoqeuff/55v0P+XY8ePVyPHj38DmNvu3Y5d//9ztWv71zNms7dfLNzW7dWfRw7djj3yivODR7s3EEHOQfOJSc717Oncw8+6NyyZVUfk9lvZX1mY+mzWV0AC1wl8luFx8DjfT5wOwZe9bKzs8nMzCQ3N5fU1FSysrLIzMyM+WPjPXv2BGJwIJctW7SVfeqp8I9/VG2LOycneG62lcYTUjz3W0k0lT0GHk4Cf4tS5gN3cXJ+uCXw2JCUlERp7zURoagoNqaZj6kEvnAhTJyoI6klJ8O6ddCyZfQft6goONZ4yV7jgQ5oJ58MNWtGPxZTJeLhs1ldRLwTGzYfuImA1NTUUn/ll3XMvNpat06PK0+apOdJ33yzTtQRzeQd6DUemIZz48Zgr/EHH9TEbb3GE5Z9NuNXOJ3YZonIWVGPxCS0rKwsUlJSiq1LSUkhKyvLp4hizJ49MHaslsezs+HWW/UUsWhNrJKTA//6l5bAmzTRAVWmT4devYoPqDJ8uCXvBGefzfhl84GbKhEYxKXksfFYGtxl7Nix/j14UhI895yOUPb3v0OHDpHdf3ml8euvt9J4NRYPn01TunCOga8ALiRO5wO3Y+AmZn3xBdx3nybuevVg+3Zo2DBy+y+rNH7KKVoWt9K4MTElGsfAozofuNfLfQGw1jmX7g0c8xLa630V0N85t9W77Uj0HPRC4Abn3DvRiMlUT/PmzQOge/fu0X2gNWtg1CiYPBmaN4fvvtMxyyORvK3XuDHVRizMB34j8C0QKMmPAOY45+4XkRHe8u0i0hm4FOgCtAJmi8hhzrnCCMVhqrlRo0YBUeyFXlCgx7kfeEAHQhk5Ui/16+/7PkNL4zNnwtdf6/pDD9Vx0QNjjVtp3JiE4+t84CLSBj3HPAu42VvdF+jpXX8WmAvc7q1/0Tm3B1gpIsuB49HR4YyJfcnJ8NFHerz5gQd09LJ9sXNn8Wk4Q0vj1mvcmGrD7/nAxwO3AaFNkObOuXXeY68TkWbe+tZoh7qANd66vYhIBpABdiqE8dn8+Vouf/ZZSE3VhFu7duX3U15pPD1dS+ONG1e8H2NMwigzgYvIeOfcMBGZgQ6vV4xzrs/+PLCIpAMbnXMLRaRnOHcpZV2px+WdcxOBiaCd2PY5SGP2VW4ujBgBL7yg53CvWqUJPNzkbaVxY0wFymuBT/b+Philxz4Z6CMi56HzjDcQkeeBDSLS0mt9twQ2erdfA7QNuX8b4KcoxWbMvnEO7r5bS+QAo0fDbbdpL/OKWGncGFMJZSZw59xC7+q3zrmNodtEZL9Hl3DOjQRGevvrCdzinLtcRP4BDALu9/6+7t3lDWCKiDyEdmI7FPh8f+MwJmD8+PH7fmfnQEQvP/0EF12kp4hVdAgnNzd4braVxo0xlRBOJ7aPRWS0c24qgIgEphPtHKWY7gemisjVQC5wCYBzbomITAWWAgXAX6wHuomkrl277tsdP/lEhzx97DE44QR44gltOZcmUBoPHM+20rgxkeGc/gDevRvq1oVatWDHDlixQtft2aN/d++G7t11qOLvv4d33gmuD1xuugnatIHZs/XzXHL79On64/y11+DCC317yuEk8J7ARBG5BGiOnvJ1fCSDcM7NRXub45zbDPQq43ZZaI91YyJu9uzZAPTu3Tu8O6xaBbffDlOnQuvWsG2bri+ZvCsqjaenR2/IVGOqSkFBMMHVrq2nR/72m476VzIBdu4MnTrpZ+bpp4PrA0n24ovhtNN0fvlhw/befu+9+mN3/nytVgXWB7z2GvTtCx9/DOefv3ess2frsMGLFsENNwTX16gBderoHPZt2mh8y5bpujp19IfBgQdqpQ2gVavovqYVCKcX+joReRstdxcBI51zO6MemTFVbMyYMUCYCXzsWLjnHk3Ed90Ft9wCBxwQY1Tf2wAAIABJREFU3F5aabxhw+IDqlhp3ESKc5rEAolMBJp5J/AsWgS//FI8gTZvDj166PZHH9VEFdpC7dYNrrxSt194of4IDb1///5wxx16nyZNdF1hSEF05Ej9jPzyCxx33N7xZmXp2Rnbt+t4+wGBRHnEEZrACwr0DIzA+kaN9MdB4LPWogUMGhTcHrh06aLbjz0WXn1V7xO6PTAlb58+sHmzbq9dWxN4qH799FKW4yPalq20ChO4iLyHDuZyBNpx7GkR+cg5d0u0gzMmphQW6pjlIvq3f3/9kmrTRkvjn35qpfHqqrCweILLz4f27XXbd9/B2rXFt9eoAQMG6PaXXoKlS4tvb9xY+1CAJrgFC4q3QDt2hNe97kHHH6/D8oY6/XR4/3293q8f/Phj8e19+gQT+NixsGFDsPVZp46+xwMJfMsW/YEQSKB16gRbnrVqwZAheyfQbt5ooA0awBtv7J1AA7PrBVq5derovqTEyUaHHqo/QMrSvj088kjZ21u0gD/+seztgXjiVDgl9H85517zrm8Tke54nc+MqTY+/FBLeaNGwSWXaOn811+1NH7HHVYa91Og9VnyOGdamiaO3Fz49tu9tw8cqC25uXP1/1iyzPvvf0NKCjz5pA57W/L+ubn6Q27oUL1NqJQUfX+AlnunTCm+vVmzYAKfMkWTXGiCCz3bID9fE9uBBwa3H3JIcPugQVrZCb1/25ATdp5+WluyodsbNQpuX7lSk2dZ/TY++qjs114Exo0re3vNmvrjtSzJyZEd/7+aCaeE/lqJ5QLg3qhFZEws+fFHPQ3s1Ve108rOnToN58yZ2sKx0rhWH/Ly9k5wLVvqa7FtG8ybt3eCPOssTUTffw9PPVV82549Wobt2lUT7IgRe99/xgz4wx907vSrrto7rsWLtRT72mtw4417bz/rLE3g8+bpDHAlW5F79mgiTk4OHvsM3R6oyKSnax+I0FZm3brBxxk1au9Wauj2V17RxyjZ+gx47LHyX/+//KX87aedVv720FhMXAmnhH4i8BhwODqUajKw0zlnP5tMYnvwQcjM1C/XHj30WFkgUcRaaXzbtr07+jRqBO3aaYKdMWPv7V276pf7rl36PEtu799fW4kbNmhHoJIJ9J574LrrtEQcOOYY6qmn4OqrNUGX1pHoxRc1ga9dq0mqZAL95Re9Xa1amjxLlmEDrchu3bQMXPL+rb2BGvv109uEbqtdW48Dg/5Q8MbBL9W11+qlLOefX/rzCyjttQlV8rirMWEK553zT3QSkWlAN+BP6DnYxiSUCRMmaKtq61Zt9c2cqS2sXbv0VLGTT4Z//EOTdsnS+Pbte3f0qVEDjj5at8+ZA+vXF2+hNm+uZVyAMWNg9eri9+/aVQeFAejde+/tF16oQ7SClkx3luhbeu21MHGituxKO9Xlpps0gRcVabINJLZAktuyRW9Xq5YeSyyZIDt10u0tWpTegg0cB+3cWU+dK5mAA6XT00/X17gs3bvDrFllbz/ySL2UpVWr8nsLl9XyNSbGhfXTzzm3XESSvfOunxGReVGOKyZ92fPLvdY169+M1te1pjCvkK/P+3qv7S0Gt6Dl4Jbkb8pnSb8le21vPbQ1zQY0Y/fq3Xx7xbd7bW87vC1NL2hK3rI8lg1Zttf2dn9rR+PejdmxaAfLhy3fa/vBYw+mYfeGbJ+3nRWjVuy1/ZDxh1C/a322zN5CzpicvbZ3nNCRlI4pbJqxidXjVu+1/fDJh1OnbR02vrSRtU+s3Wt7l5e7UKtpLdZNWsf6Sev32n7UW0eRnJLM2sfXsnHqxr22HzP3GAByH8xl88zNxbYl10niqFlHgQg5mYvZOScXKdpDUlE+UrSHmvWKOHjuIEhKYs3g1yj89OuQ7fnUbCA0W6SDt6w/7S5aLJjBAbu/Y5drQD4HkiSF1B9wIVxwAVvvmUHK558gn/6dpJFZSNEeChs0p9bWlQDs7HQO9dZ/Wiy+PQd1ovZG/Z/mXXIzKVuLvz92tz2WOl4C/3XcK9TKW0NRUi1cUi2KkmpTuLkx9b38vWlpA5IL0ihKqo1LrkVR/VrU4FgaA4V5haxteQOC8+5fm6KkWtRvczQHAfmbf2PFsVO8/eq+XVItWhzbgWbA7i3JfHvsh3u99m3btKUpkLexNst23gslfh+0u7AdjYEduTVZ/ubePfcPHtuYhu1h+9eFrBhVA50F+FfvAoeMr0v9rrXj871XN1nfe8Cqe1exdc7WYttrNqnJEa8cAcCKkSvYPn97se2129Sm8/M6lMYPw35g56LiL27KYSl0nKg/EpdlLOP/2Tvz8Bqv7Y9/dkJIRGNujYl5yCxirIhSlJr1GmKqltuidNDSuqaiVXW1PxTV3qKktKVKVdVQc7UIMc8kaihBiQxkOPv3xz7nJEdmzsnJsD/P8z4577jX+yY5691rr72+cWfiLPa7+rlS+1PVjzrR/wQPLj+w2O/WzI0aH9YA4FjPYyTeSrTYX7pNaTwmeABw5LkjJMdbltQo+3xZqo1RRYj0917mf3sVeldIsz+3yI4DjxNCOAHhQoiZqIz0ElmcoykMyKSUqSMP4nCKv2R2jiYnyp1KUO5JHG9EUObaxlT7HyAMCXBtItSsgtPpPbif+hrx8P4r66ByZVz3hvLkH3PN13UwJOAgE+DmDShfHrfdC3H/c35aGx/0AWdnSh77EbfTSy3NxwHGl4DVqylz+hpORJOMA46OLhRxMkCZ8qqWOZA49yix/0QbnV9RDA7FcHR/inLGa92u25/bT7RNcaDCieL+lcxqO381nkHy7QcWDtatzZN4GPefb7o03S9Rk8rPX3UmpLm1Ck1SvjhuVUo71cW52lPmz/El66V9NkUfQVRFo9HkGYSUmWt9CCHcUfXIiwJvAG7AfCll2teePEijRo3kgQMH7G2G9TFl3gqhQpNJSSrh6uFxylq1oGZNFeJduTJtolCXLtC0qcpETW8cdOJEaN9eFUzo1ctyX3KyGlt9/nmVRdu1a1o7t22D4GCVaWsKF6fmwAE1T/Sbb1T7D4dhTSpeGzbA99+nDcO++aaaqnLggEpaevj8li1VKPvGDTWWu2+fSj7bvBmiolLCp05OfF6+PKurV2dTZlm3Go1GYyOEEGFSykbZPT47Weim+EI8YEtp0fyFqeqQwaAcCKhknpgYy3HO8uVTJvt/8UVKQQXTMf7+quoPqJ+mbF7T0qsXvP22GiP08Eg594ExZPaf/6hpKrdvp4xJpmbGDDXl6dYteOUVy31Fi6okp6ZN1fUOHLB0kKYMXFDFGh6eqpK6IELDhmqqzcPjqKaxyS5dLAsyFC+u2jc50H791JIRHTuqJSMaNUoZc03NpUuWMpwPHqjf17PPqnrlZcty7sMP6Xv+PAcuX6ZYVBShoaGEpPeyodFoNHmIzORE0w5spEJK6WN9c/I4Tz8Nhw6lOG5QjmDTJvX5uedUec3UdO+upiCBynS9eVN9FkI5sQEDUhz4yZMp24sXV1NwShqDqE5O6loPO9DmzdX+UqVUuPfhHqqHh9pfrZrK9k2dhZt63me9eipbOCPq1FGJThlRpQr075/xflfX7ClyPS4GgypqYaqCZiqoUquWyph+6inVqy9XDvr1IzQ0lGH79xMXp8YYHzx4wLBhwwC0E9doNHmaDEPoQohwlN72N8BPqB64mVQ98zyNVUPoM2eqUGxqB1m9uqrbC7Bxo6r9m3p/uXIpFZlu3VKOuFgxy96n5vEw1Rpfv14VVLl+Xb2ctGihMsY7d1ZDDmPGqP01a6riE1274uHhQWRk2j9ld3d3Ih5+GdNoNBobktMQeqZj4EKIekBfoDNKBewbYJOxmEu+oMCOgRd20guNmwqqPP+8+mkqqPL112o+souLGtMfOVK9RAEODg6k9z8ghMBgirJoNBpNLmDVMXAp5SlgEjBJCNEb+Br4CPj4sazUaHJKVqHxzp3VEIepoEpiooqWVKigirAMG6ZER8qXt7hstWrV0u2BV8tKx1uj0WjsjENmO4UQlYUQbwkhdgP9UVnoC3LFMo0mJkaVwXzpJVWIo2lTlZRXqpQqqHLqlBq3nz1bFQMpWlSFyjdsAB8flV8gpUrU++yzNM4bYPr06bi4uFhsc3FxYfr0gqlaGxoaioeHBw4ODnh4eBAaGmpvkzQazSOSWRLbDqAk8B0wGDCWZcJJCFFGSnk7o3M1mkcmJ6Hxhzl+XCk3/fqrSrp77bUsmzMlqo0fP57IyEjKlSvHp59+WiAT2EJDQxk2bJg5YS8yMlIn7Gk0+ZjMktgiUElspPoJIAAppaxhW9Osgx4Dz+OkDo2vXw+HD6vttWqlJKClDo1nxNq1KpmwZEkVKn/1VZUwmAOCg4MB2L59e45vIz+gE/Y0mryN1cbApZQeVrFIo3mYmBjYskU5bVPWuIODctQff5wiw5lVln5CAly+DDVqqBD6W28p5bCyZXPnPvIZly5dytF2jUaTt9EyOJrcIaPQeIcOqpedWWj8YaRU13rrLVVl7cgRVZzlo49sew/5HJ2wp9EULLQD19gGU2jc5LRTh8bTyxrPLkeOqPKpW7dC/fpqPreWY8wW06dPtxgDh4KdsKfRFHT0N5/GesTGqoIq6YXGZ85MkeF81AI2u3apuuqlSin96H//2/463PmI1Al7ly5dolq1akyfPl0nsGk0+ZQsxUwAhBCOwJOkcvhSynwxcKaT2GzMX3+lJKD99tvjhcbT48EDVWLWz0+Jp8ycqWq6ly5tvXswctNY5rZcuXJZHKnRaDTWx+piJkKI11DFXK4DptJUEih8tdA1tguNP4yUag74mDFKSS0iQtVSf/fdx76FjNCOW6PR5CeyE0IfDdSVUt7K8khNwcTWofGHOXQI3ngDduwAT09YuDBXhFCWLFkCwODBg23elkaj0Twu2XHgfwF3bW2IJo9h69B4Rpw4ofTBy5Zl34sv0nfrVi62b58r47XagWs0mvxEdhz4BWC7EOJn4IFpo5Ryts2s0uQ+BoPSAzfVGn84NP7889CypW2Sxu7fh7171VzuBg1g0SK+Mxh48Y03dNUwjUajyYDsOPBLxsXJuGgKChmFxlu0sE1o/GGkhFWrVPGVq1chMlLpdb/8Mu94eFhMdwKIi4tj/Pjx2oFrNBoN2XDgUsopAEKIkmpVxtjcKo3t+OsvWL+eK59/TrnDhykGRAvB7SZN8Pjvf1WIPDcqmR04oMa5d+8GX1/46ivlvI3oqmEajUaTOdnJQvcClgFljOs3gYFSyuM2tk1jDTIIjccLwWfAemCXlDgdOcIiICQ3nPfff0Pz5moq2BdfwIsvgqOjxSG6aphGo9FkTqZyokYWAW9KKd2llO7AW8AXtjWr4GAX+cbYWEsZziZN4IMPVLnRmTNpU6kStaXkLWAbkERKeNpmxMfD99+rz089pULnZ8/Cyy+ncd5gH5nPDRs2sGHDBptdX6PRaKyKlDLTBTicnW15dQkICJD2Yvny5dLFxUWi5s1LQLq4uMjly5dbv7FLl6ScP1/K556TslgxKUFKNzcpe/eWcvlyKW/eNB8qhLCwybQIIaxvl8Eg5YoVUlatqmw6dizbpy5fvly6u7tLIYR0d3e3zXPTaDSaPAJwQObAv2VZiU0IsQY4iAqjA/QHGkkpu1n/dcL62LMSm03lGzPKGq9ZM0WGM4Os8VyTlfzzTzXOvXcv+PvDJ59Aq1bWu76VmT9/PgDDhw+3syUajaYwYvVKbMAQYArwg3F9J/DiI9hW6LB6IpYpa3z9epU1/vffj5Q1niuiFrGxaq54sWIqQW3gwHRD5XmJ7777DtAOXKPR5A+y48ArSylH2dySAohVErGMWeP89FNKQZUnnrAsqJLDxDObiVrExsLSpapWeYkSymYfHyhZ8vGuq9FoNJo0ZMeBLxRCOAGLgRVSyjs2tqnA8Eg93cxC46++mmloPCeEhIRYbz61wQDffAPjxsGVK6oYS3CwigxoNBqNxiZkZx7400KIOqiw+QEhxD5gsZRys82ty+dku6drpdC4Xfj9d3j9dSVwEhgI336rHbdGo9HkAtnSA5dSnhFC/Ac4AMwB/IUQAnhPSvlD5mcXbjLs6dogNJ7rJCfDoEEQFwdffw0hIerFQ6PRaDQ2JzuFXHxQve9OwGags5TyoBCiErCXlOQ2TWakDo2vXw/h4Wq7lUPjNicmBubMUb1uFxc139zDQ41553O2b99ubxM0Go0m22SnBz4P+BLV2443bZRSXjX2yjUZERsLW7ak1BpPHRr/6CPltOvVy5uh8YcxGFQv+7334No1FdLv2VPJfWo0Go0m18nOGHhQJvuWZbSv0FIQQuMPs2uX6nEfPKiquv3wAzRtam+rrM6sWbMAGDNmjJ0t0Wg0mqzJcsBSCNFCCLFZCHFGCHFBCHFRCHEhN4zLFxgMsG8fTJigipVUq6bkN8+cUaHxLVsgKkold/Xvn/+ct5QwcaK6h9BQVZSlADpvgPXr17N+/Xq72mCX0rsajSZfkp0Q+v+AN4AwINm25uQTMgiN36hdm/+VKsWyO3eIS0xkeqNGhLRpY29rc050tArxDx8OlSvDsmVQpowa89bYjNDQUItph1oDXaPRZEZ2HPhdKeUvNrckr3P5csrc7HRC49/HxDD4rbdS5nxfupT/vnyTk2HxYhg/Hm7cgOrVldhIlSr2tqxQMH78eK2BrtFosk12HPg2IcTHqGzzB6aNUsqDNrMqLzJ9OixcmJI1/vzzKmvcyQmAtz088veX77Ztqm754cMqyW79ejWvW5NraA10jUaTE7LjwJsYf6YusC6BZ6xvTh7mrbdg1KgMs8bz/Zfv0qVw544aq3/hhfyRGW9lnJ2d7dq+1kDXaDQ5IUs1svxObqmR5ZrCl7W4cwemTYN+/aBhQ/jnHyheHOzsxAozD4+BAwghkFLi7u5unXr1Go0mz5JTNbJslc0SQnQSQrwjhJhoWh7dxILJ9OnTcXkoycvqCl/WICkJFiyA2rVh9mwwFS8pXVo7bzsTEhLCokWLcHd3B1KcN6QktOmsdI1GYyI708gWAr2B1wABvAC429iufEfqL18hBO7u7gwaNIjx48fnnSlBW7eCn5/KLvf0hLAwePNN+9qUh5g6dSpTp061qw0hISFERETg7u7Ow9ExU06FRqPRACClzHQBjjz00xXYlNV5eWUJCAiQ9mD58uXSxcVFovIFJCBdXFzk8uXL7WKPlFLKyZOlrF5dytWrpTQY7GdHHmL58uXS3d1dCiFksWLFZL169extkpRSSiGExd+OaRFC2Ns0jUZjI4ADMgf+LTshdFP51Dhj/fNEoLr1XiEKJplNCco1bt9WFdTWrlXrY8fCyZPQo0ehTFJ7GNOYc2RkJFJKHjx4wJkzZ+wfKSHjxDWd0KbRaExkx4GvF0KUAj4GDgIRwEpbGlUQsGtWemIizJunxrnnzoUjR9T24sWhWDHbt59PSO8ly2Aw5Ikwdb7JqdBoNHYjSwcupZwqpbwjpVyNGvuuJ6WcYHvT8jd260H99hv4+sJrr6nx7kOHVJlXTRry8tS/9HIqFi1apLPQNRqNmQwduBCivxBiQOptUsoHwL+EEP1sblk+x249qCtXVA987VpV7tXHx7bt5WPyepjalNBmMBiIiIjQzluj0ViQWQ/8LeDHdLavNO57LIQQVYUQ24QQJ4UQx4UQo43byxjFU84af5ZOdc67QohzQojTQoj2j2uDLcm1HtStW6q3PWeOqWE4fhy6dNHj3Fmgw9QajSY/k5kDd5RS3nt4o3FbUSu0nQS8JaWsDzQFRgghGgDjgK1SytrAVuM6xn19AE+gAzBfCOFoBTtshk17UAkJ8OmnUKsWzJ+vNLpB6Y0by7tqMkeHqTUaTX4mMwdeVAhR4uGNQoiSwGN7CCnlNWmsp258KTgJVAa6AkuNhy0Fuhk/dwVWSikfSCkvAueAxo9rR75kxw7w9la1ywMDVf3yDz+0t1X5ktQvWX379uXYsWP2Nkmj0WiyRWa10P8HrBJCvCqljAAQQngAnxn3WQ3jdf2BP4EnpZTXQDl5IUQF42GVgT9SnXbZuC296w0DhkHeGc+0ClKqsLiDg/q5fj107KhD5VZi79699jZBo9Fosk2GPXAp5SxgLbBDCHFLCHET2AGsl1J+bC0DhBCuwGrgdSlldGaHpmdmegdKKRdJKRtJKRuVL1/eGmbal6gopYBmqprWsqUa5+7USTtvTZ4iNDQUDw+PvFN9UKMpwGQ6jUxKuVBK6Y6aPlZdSukupVxgrcaFEEVRzjtUSvmDcfN1IURF4/6KwA3j9stA1VSnVwGuWsuWPMmDBzBrlhrn/uIL5axN5TUd8/Twv6YQ8nBhHF2/XaOxLdkSM5FSxqSX0PY4CCEEKhR/Uko5O9WudcAg4+dBqCiAaXsfIUQxIUR1oDawz5o25Sn27lX1yt9+G55+Go4eVeIjusetyaPkieqDGk0hIjt64LaiBTAAOCqECDduew+YAXwnhHgJuIQST0FKeVwI8R1wApXBPkJKmZz7ZtuY5GTVu65QAZ54AjZuhPZ5esZcgaFKlSr2NiFfk5cL42g0BRGtB55XuH5dVUz7+29Yt05tMyWtaTT5AA8PDyIjI9Nsd3d3JyIiIvcN0mjyGVbXAxdCuAghJgghvjCu1xZCPP84RmpScf8+fPSRqlu+eLEa705KUvu089bkI3RhHI0md8nOGPhi4AHQzLh+GZhmM4sKE+Hh0KABjBsHwcEqs3z2bChiz5GNwsvrr7/O66+/bm8z8i26MI5Gk7tkx1PUlFL2FkL0BZBSxhsT0DSPyv37ShnMw0MtixZB27b2tqrQEx4envVBmkwJCQnRDlujySWy48AThBDOGOdcCyFqonrkmpxy7RqMHw8HD0JYGJQqpdTDNBqNRqPJIdkJoU8CNgJVhRChqPrk79jUqoJGfDxMn67GuZcvh2efVbXMNRqNRqN5RLLsgUspNwshDqIERwQwWkp50+aWFRTOnlXh8UuXoHt3mDlTJappNBqNRvMYZOnAhRBBxo+mQi4NhBBIKXfazqwCwJ07KkRevTo0awZLl6pENU2epU6dOvY2waokJiZy+fJl7t+/b29TNBpNKooXL06VKlUoWvTxhD2znAcuhPgpdbsoBbAwKeUzj9VyLpHr88AvX4b33oPNm+H0aVWMRZNrhIaGMn78eC5dukS1atWYPn16oU2qunjxIiVLlqRs2bLovFONJm8gpeTWrVvcu3eP6tWrW+zL6Tzw7ITQOz/UQFVgZnYbKDTExcHHH6sQeXKykvp0yFalWo2VMNXiNpXzNNXiBgqlE79//z4eHh7aeWs0eQghBGXLliUqKuqxr/UoHuYy4PXYLRckrl+HunVh8mSlEHbypNLndnW1t2WFisetxT1s2DCzwy8oaOet0eQ9rPV/mZ0x8LmkyHY6AH7AYau0nt+5ehUqVVJ1y194QSWptWxpb6sKLY9bi/vMmTPWNEej0RQgTKPNQqiA699/Q+XKUKyY/WzKTg/8ABBmXPYCY6WU/W1qVV7n0iXo1w9q1oSICPUbnT1bO287U61atRxt19geVxtFoe7cucP8+fMz3D99+nQ8PT3x8fHBz8+PP//80yZ2WIPt27fz/PNpq1O//PLLnDhxIldtcXR0xM/PDy8vLzp37sydO3dytf2s6Nixo1Vsmjx5MkIIzp07Z972ySefIITgwIEDGAwQG5sy2zcuDg4fhuhotS4lxMTA4sVLGDlyZKZtLVmS9TGPSpYOXEq5NNUSKqXcYxNL8gMxMTBxogqXr1kDY8ZAuXL2tkpjRNfiLjxk5sD37t3L+vXrOXjwIEeOHGHLli1UrVrVpvYkJ1tfGPHLL7+kQYMGVr+uiSST5kIqnJ2dCQ8P59ixY5QpU4bPPvvMZm09Chs2bKBUqVJWuZa3tzcrV64EwGCAb75ZRb166nknJamR0H/+Ucc6OUHp0ilVrkuUAB8fVVDTnmTowIUQR4UQR9JZjgohjuSmkXmC2FhVt3zqVBUqP31afdbj3HkGXYs7E15/XU1jtObyiHXjo6Ki6NmzJ4GBgQQGBrJnj+oT7Nu3j+bNm+Pv70/z5s05ffo0AMePH6dx48b4+fnh4+PD2bNnGTduHOfPn8fPz4+3337b4vrXrl2jXLlyFDPGNsuVK0elSpUA2LhxI/Xq1ePpp59m1KhR5p7v5MmTmTVrlvkaXl5eZgW1bt26ERAQgKenJ4sWLTIf4+rqysSJE2nSpAl79+4lLCyMVq1aERAQQPv27bl27RoAc+bMoUGDBvj4+NCnT59sP6fg4GBMM2hcXV0ZP348vr6+NG3alOvXrz/Ss1yyZAkvvPACnTt3pl27dpm236xZM65cuWJe//jjjwkMDMTHx4dJkyaZt0+dOpV69erx7LPP0rdvX/NzDA4O5r333qNVq1b83//9X4a27tixAz8/P/z8/PD39+fevXtcu3aNoKAgczRg165dgFK8u3lTlSGZPXs2Xl5eeHl58emnnwIQERFB/fr1GTp0KJ6enrRr1474+HhAOenERGWzlNCyZTdWrVoLwMWLFyhWzI3SpcsDULQohIevoE0bb7y8vBg/fizu7spxL168mDp16tCqVSvzPWT2u7ApUsp0F8A9syWj8/LaEhAQIK3Gf/8r5Z491rueJk8xevRoOXr0aHubYTVOnDiRsjJ6tJStWll3ycazKlGiRJptffv2lbt27ZJSShkZGSnr1asnpZTy7t27MjExUUop5ebNm2WPHj2klFKOHDlSLl++XEop5YMHD2RcXJy8ePGi9PT0TLfNe/fuSV9fX1m7dm356quvyu3bt0sppYyPj5dVqlSRZ86ckQaDQb7wwguyU6dOUkopJ02aJD/++GPzNTw9PeXFixellFLeunVLSillXFyc9PT0lDdv3pRSSgnIb7/9VkopZUJCgmzWrJm8ceOGlFJkApgGAAAgAElEQVTKlStXyhdffFFKKWXFihXl/fv3pZRS/vPPP2ns3bZtm9mO1LRq1Uru37/f3Na6deuklFK+/fbbcurUqY/0LBcvXiwrV65svqeHMf2+kpKSZK9eveQvv/wipZTy119/lUOHDpUGg0EmJyfLTp06yR07dsj9+/dLX19fGRcXJ6Ojo2WtWrXMz7FVq1by1VdfNV87I1uff/55uXv3biml+t0lJibKWbNmyWnTppltiY6OllJK6e7uLqOiouSBAwekl5eXjImJkffu3ZMNGjSQBw8elBcvXpSOjo7y0KFDMjpaym7dXpDLli2TUkp59KiU584pWyZNmiTfffdj2bFjd3n06FE5bdo0+dVXS8zP/MqVK7Jq1aryxo0bMjExUbZu3VquWbNGXr161bz9wYMHsnnz5nLEiBGZ3t/ixYvNx6TG4v/TCHBA5sC/ZZjEJqVMI+wrhCgH3DI2VPh48017W6CxIaa3+AJJHrq3LVu2WIztRkdHc+/ePe7evcugQYM4e/YsQggSjd2lZs2aMX36dC5fvkyPHj2oXbt2ptd3dXUlLCyMXbt2sW3bNnr37s2MGTPw8/OjevXq5vP79+9v0aPOiDlz5rBmzRoA/vrrL86ePUvZsmVxdHSkZ8+eAJw+fZpjx47x7LPPAiqkXrFiRQB8fHwICQmhW7dudOvWLYdPS+Hk5GSOFgQEBLB582Yg588S4Nlnn6VMmTLpthMfH4+fnx8REREEBASY72fTpk1s2rQJf39/AGJiYjh79iz37t2ja9euODs7A9C5s8WsY3r37m3+nJGtLVq04M033yQkJIQePXpQpUoVAgMDGTJkCImJiXTr1g0/Pz+L6+7evZvu3bvj4lICIaBHjx788ssugoO7UL16dfz8/DhzBqpXDzBHUipWtBR6LFMGBg3qw8qVK/n111/ZunUrS5cuBmD//v0EBwdTvrzqkYeEhLBzp6pdlnp77969zcmvGd2fLckshN5UCLFdCPGDEMJfCHEMOAZcF0J0sKlVGo2mwGIwGNi7dy/h4eGEh4dz5coVSpYsyYQJE2jdujXHjh3jp59+MleQ69evH+vWrcPZ2Zn27dvzWzYEgBwdHQkODmbKlCnMmzeP1atXAxlP3ylSpAgGg8G8bmp7+/btbNmyhb1793L48GH8/f3N+4oXL46joyOgIpmenp7mezp69CibNm0C4Oeff2bEiBGEhYUREBDwSOPBRYsWNdvu6OhovkZOnyVAiRIlMmzHNAYeGRlJQkKCeQxcSsm7775rbufcuXO89NJLZNWXS91WRraOGzeOL7/8kvj4eJo2bcqpU6cICgpi586dVK5cmQEDBvD1119jMKRkgkspuXcPjh1L2ZaYqGQnTEMn7u7w1FMpz6psWXBzs7Svc+fOLFu2jGrVqvFEqqJbmd1XRn9DGd2fLcksiW0e8AGwAvgNeFlK+RQQBHxoU6s0GjvQv39/+vcv3BMscoN27doxb94887pJxvXu3btUrlwZUGO1Ji5cuECNGjUYNWoUXbp04ciRI5QsWTLD3s3p06c5e/asxfXd3d2pV68eFy9e5Pz58wCsWLHCfIyHhwcHDx4E4ODBg1y8eNFsU+nSpXFxceHUqVP88ccf6bZZt25doqKi2Lt3L6DK2B4/fhyDwcBff/1F69atmTlzJnfu3CEmJiZHzyszcvoss4ubmxtz5sxh1qxZJCYm0r59e7766iuz7VeuXOHGjRs8/fTT5heEmJgYfv755xzbev78eby9vRk7diyNGjXi1KlTREZG4uZWgS5dhjJkyEscPHiQ69eVk05KgqCgIDZt+hEnpzhiYmJZs2YNXbq0pGbNlPaKFcu6lpazszMfffRRmloRTZo0YceOHdy8eZPk5GRWrFhBq1ataNKkCdu3b+fWrVskJiby/fffZ3l/tiSz2ysipdwkpfwe+FtK+QeAlPKUza3SaOzA5cuXuXz5sr3NKFDExcVRpUoV8zJ79mzmzJnDgQMH8PHxoUGDBixcuBCAd955h3fffZcWLVpYZHV/++23eHl54efnx6lTpxg4cCBly5alRYsWeHl5pUlii4mJYdCgQebEsRMnTjB58mSKFy/OokWL6NSpE08//TTu7u7mc3r27Mnt27fx8/NjwYIF5rr4HTp0ICkpCR8fHyZMmEDTpk3TvU8nJydWrVrF2LFj8fX1xc/Pj99//53k5GT69++Pt7c3/v7+vPHGG+lmUW/dutXiOZleBLIip88yJ/j7++Pr68vKlStp164d/fr1o1mzZnh7e9OrVy/u3btHYGAgXbp0wdfXlx49etCoUSPcHu7mZmHrJ598ipeXF97eviQnO9O69XNs376dRo38CAryZ9Wq1YwePdqcBS4ENGzYkJdeGkzPno1p1qwJL7/8sjm8n1P69OlDw4YNLbZVrFiRDz/8kNatW+Pr60vDhg3p2rUrFStWZPLkyTRr1oy2bdtanJfR/dmSDGuhCyEOSikbPvw5vfW8TK7XQtfkW4KNYjPbt2+3qx3W4uTJk9SvXz9H59y6dYsrV66QkJCAk5MTlStXpmzZsjay0L5s376dWbNmsX79enubkq+JiYnB1dWVuLg4goKCWLRoURqHCCrUnZioesVFiqhw99mzUK2a0n2Ki4Pz58HDA0qWVBWpDQaVEV4QSe//05q10H2FENEoCVFn42eM63ae/abRaKzNrVu3iIyMNI8FJyQkEBmpclkLqhPXPD7Dhg3jxIkT3L9/n0GDBpmdt5RKlNHJSU2/SkqCI0egalV48km13dU1JbHMxQW8vVOu6+ioFk3GZJaFrh+dRlOIuHLlikUiF6jEnCtXrhRIBx4cHGyOumgenW+++cb8+epVuHkzpb5VRITK9i5RQvWk3d1TSmc4OkKNGrlvb0Eiy1roGk1hoVmzZvY2wa4kmOpGZnO7pvAhpQprm3rGkZFqm4eHWr97F5ydlQMXAurVUz1tE8bZVxorofUuH4PQ0FA8PDxwcHDAw8OD0NBQe5ukeQw+/PBDPvyw8E6wcEr9TZuN7ZqCT2KiqiBt4uJFOJUqjdnR0XJudb16Kc4clDPXYXDboR34I2LSno6MjERKadae1k5ck1+pXLkyDg/Nu3FwcDBPR9IUfOLjlcqWKbf52jU4cyZlvXRpy150lSpqMaHVa3MX7cCzQXo97cfVntbkPXr27GmurFUYKVu2LO7u7uYet5OTE+7u7gVy/FujiI2FCxdUghnAvXtw+XJKzfDy5SF14bvSpZV6siZvoB14FqTX0x4wYIA5O/dhsqs9rcl73Lp1i1u3btnbDLtStmxZfHx8aNSoET4+Po/tvIUQDBgwwLyelJRE+fLl05XPtBaLFi2yKOEZHR1NzZo1zcVZChumcWtQDvvECfUT1FSte/dSZDPLlAE/v5Rxa2dnNaVL96zzJtqBZ0F6Pe3Myuxp7WmNJoUSJUpw7NgxsyLU5s2bbR6SHzp0KJcvX2bLli0ATJw4kSFDhlC9enWbtpsXkFI5Y5NDvn8fDh1KkcUsWlSNWZu+wkqWBF9fNYUL1L4iOrU536B/VVmQkx611p7W5GUOBR9Ks63CvypQeXhlkuOSOdIxrUrwU4OfouLgiiTcTOB4r+MW+/y3Z6/y1XPPPcfPP/9Mr169WLFiBX379jXLQ8bGxvLaa69x9OhRkpKSmDx5Ml27diUiIoIBAwYQa+wqzps3j+bNm7N9+3YmT55MuXLlOHbsGAEBASxfvtyiPrUQggULFtCvXz+WLFnC1q1bCQsLy/Zzyk9IqXrQjo5qqpbBoOZaV6wIlSurcqLlyqXoVjs5gbHIHKB71vkd3QPPguz2qLX2tEaTPn36KMWn+/fvc+TIEZo0aWLeN336dJ555hn279/Ptm3bePvtt4mNjaVChQps3ryZgwcP8u233zJq1CjzOYcOHeLTTz/lxIkTXLhwIV3dZR8fH9q3b0+bNm2YM2dOgcqkv3VLLaAccEQEGOXBcXSE6tVVKNy0v1o15dw1BQ/dA8+C6dOnM2zYsDRh9NS4u7ubJes0+Zc2bdrY2wSbklmP2dHFMdP9TuWcst3jfhgfHx8iIiJYsWIFHTt2tNi3adMm1q1bx6xZswClAnbp0iUqVarEyJEjCQ8Px9HR0SzZCNC4cWOqGFOfTdKXTz/9dJp2R4wYwS+//ELr1q0fye68wo0b8OCBqmAGynlLqdS1AGrVspxrrXMOCw/agWeBqUc9fvx4IiMjEUJYjIHrsHnBYcKECfY2ocDSpUsXxowZY1ZyMiGlZPXq1dStW9fi+MmTJ/Pkk09y+PBhDAYDxYunVG82yUWCpbTmwzg4OKSZFpdXkTIlnH3jBty+reZUgxrHNqYQAKp6Weq51abxa03hI3/8dduZkJAQIiIikFKybNky3N3dEULosLlGk02GDBnCxIkT8U5d7Bpo3749c+fONb8UHzqkxunv3r1LxYoVcXBwYNmyZY+sqJVXSUhISSSLilKJZqZbdHBQyWamzPGqVSH1+41JkUuj0Q48h5icucFgICIiQjvvAsRzzz3Hc889Z28zCiRVqlRh9OjRabZPmDCBxMREfHx88PLyMkdBhg8fztKlS2natClnzpyhRD4exJVSTdsyBQr++Uclmpl61c7Oar61yWGXKwc1a6ZoWWtnrcmIDOVECwpaTlSTXbScqMYaGAwQHa0yv4sXV8775EkV+i5TRvW+//lHFUUpQLl1mhxiDTlR3QPXaDSax0BKpcAVbRRcNhjg3Dk1jg2qh12jhppzDcppm+Q0NZrHQSexaTQaTQ65fl0lkplkM69cATc3eOIJNUZdv37K3GsHh5RpXRqNNdEOXKPRaLLg+nUV+jZN5bpzRzlqk2xm/foq8cxEPh6y1+QjtAPXaIzYsj63Jn9x44Zy0qaqZQ8eqMVE7dopSWagw+Ea+6AduEZjZMyYMfY2QZOLmPJ3hVDFUa5cAU9PFRoXQi0Gg3LUDxdkzCfTyzUFHP1nqNFoCgUGQ8pUrbt3ITxcFUkBFf52dU3Zb5LR1I5ak5fRf54ajZHg4GDzVDKNdbCHnCioym9Lly4zz71+8cWhvPHGx9y9q9aLF4etW5cwaFBfQCWf1agBd+/epHz58jxIHS9/iMGDB7Nq1Sqb2q/RZAcdQtdoNDYjtZyos7OzTeVEk5JUD9rJCWbPnkOrVq1p0qQzt2+fICzsT378cT6mKqzFisGwYT2YMWMMcXFxuBjrka5atYouXbpYlGvVaPIqugeu0RQSTBGG1Mv8+fMBiIuLS3f/kiVLALh582aafdnFJCcKmOVETcTGxjJkyBACAwPx9/dn7dq1AERERNCyZUsaNmxIw4YN+f333wFVZCc4OJhevXpRt249+vQJQUqJlHDsmBrHBqhVy4PBg4fx0UfvMHz4cObNm0eNGkUt6oY/8cQTBAUF8dNPP5m3rVy50mzf+++/T2BgIF5eXgwbNoz0il55eHhw8+ZNAA4cOGB+Lhndl0ZjTbQD12g0NsVacqIJCRAXlyIn+sMPJzh1SsmJmmQzK1RIaXfy5DFs3boRT09PgoKC0rWtb9++rFy5EoCrV69y5swZs3rZyJEj2b9/vzmCsH79+mzfc0b3pdFYEx1C12gKCZmViHVxccl0f7ly5R65xOyjyokOHz6SQ4fCcXJScqJXrsDVqylyom5u0KhRipzow8VSjhw5gpSSU6dOYTAY0lUme/755xk+fDjR0dF899139OrVC0ej1Ne2bduYOXMmcXFx3L59G09PTzp37pyte87ovnRpW4010Q5cozHyr3/9y94mFFiyIyeamKjKkZYuDe+/P5mSJZ9kyZLDeHsbKFmyOE89BZUrp8iJliwJxYunLydqMBgYPnw4y5YtY+HChSxYsIARI0akOc7Z2ZkOHTqwZs0aVq5cySeffAIohzt8+HAOHDhA1apVmTx5MvdNKeupKFKkCAZj6nrq/RnJpGo01kSH0DUaI8OHD2f48OH2NqNAkp6caFISBAW159NPlZxoTAxs3HiIuDglJ1q9ekW8vBxYsULJiTo7q7ri2eHzzz+ndu3aBAcHM3v2bGbOnElUVFS6x/bt25fZs2dz/fp1mjZtCqQ443LlyhETE5Nh1rmHhwdhYWEArF692rw9I5lUjcaaaAeu0RiJi4sjLi7O3mYUSKpUqcJrr43m9u2UudeJidCz5wTi4pScaMuWXixfPoESJdTLVGjoUp55pilnz+ZMTvTGjRt89NFH5vB1pUqVGD16NO+88066x7dr146rV6/Su3dvhFG7s1SpUgwdOhRvb2+6detGYGBguudOmjSJ0aNH07JlS3PoHTKWSdVorImWE9VojGg5UesipSqY4uiowt3Jyap4ypNPQpUqan9cHLi4aM1rTeHDGnKiegxco9FYjeho5ahLl1ZO+a+/VNi7ZEnlyBs0SFHpEkKLfmg0j4N24BqN5pGJjYX4+BRZTZNqV+nSar12bUuhj+yOYWs0mqzRDlyj0WSb+/dVWLxCBdWDvn0boqKU3rVJ9KNIqm8VU29bo9FYH53EptFoMiQxUTno5GS1fu+eCoubSoU/9RT4+KSIfhQrpkLlGo3G9uS7HrgQogPwf4Aj8KWUcoadTdIUEAYPHmxvE+xOcrLqYZcooZzx/fsQGanC4G5uKjTu5pYSFi9a1L72ajSFmXzlwIUQjsBnwLPAZWC/EGKdlPKEfS3TFAQKowOXUiWeFS2qssGTk+HCBZUl/tRTypF7eWEWASmSr74xNJqCTX4LoTcGzkkpL0gpE4CVQFc726QpINy8edMsTFGQiYuDmJiU9QsX4MYN9dnJSWWKP/mkWndwUOPYjzLNKyIiAi8vL4ttkydPNs/Pzi2Cg4OpW7cufn5+1K9fn0WLFpn3hYWF4e3tTa1atRg1alS6giXWIioqiiZNmuDv78+uXbvo2LEjd+7cSXOcPZ4RwJIlSxg5ciQACxcu5Ouvv87R+c2bNwfU7/2bb77J8Lhr166Z5WQTEhJ48cUX8fb2xtfX12IKZ+rfm5+fHzeMf6Rz587Fy8uLjh07kpCQAMDu3bt58803zedGRUXRoUOHHNmfH8lvDrwy8Feq9cvGbRYIIYYJIQ4IIQ5kVH1Jo3mYXr160atXL3ubYXUSEtTYtYnISLh8WX0WAurWhapVU/bn53nZUkpzadPUhIaGEh4ezp49exg7dqz5i//VV19l0aJFnD17lrNnz7Jx40ab2bZ161bq1avHoUOHaNmyJRs2bKBUqVI2a+9xeOWVVxg4cGCOzjEpxmXlwGfPns3QoUMB+OKLLwA4evQomzdv5q233rL4/Zl+b+Hh4VQwKtV8+eWXHDlyBH9/f3799VeklEydOtWiWE758uWpWLEie/bsydE95DfymwNP72slzSuzlHKRlLKRlLJR+fLlc8EsjSbvEBsLO3emrF++DOfPgwwOhuBg6vxbLQQHw/z5uLiA44M4tf7wYpQT5ebNtPsek+DgYF5//XWaN2+Ol5cX+/btA1QPdMCAATzzzDPUrl3b/CUP8PHHHxMYGIiPjw+TJk0ClMOoX78+w4cPp2HDhvz111/ptgcQExNDiRIlcHR05Nq1a0RHR9OsWTOEEAwcOJAff/wx3XNMvUQfHx9zydQVK1bg7e2Nl5cXY8eONR/v6urK+PHj8fX1pWnTply/fp3w8HDeeecdNmzYgJ+fH/Hx8RZSpNOnT6du3bq0bduW06dPm691/vx5OnToQEBAAC1btuTUqVOAGu4ZNWoUzZs3p0aNGhalXmfOnGnu0Y4bNy7T62RE6ihAcHAwb7zxBkFBQdSvX5/9+/fTo0cPateuzX/+8x+L+wYYN24cu3btws/Pz1xbPjWrV682945PnDhBmzZtAKhQoQKlSpUiO4W3EhMTiYuLo2jRoixbtoyOHTtS2jR30Ui3bt0IDQ3N8lr5mfzmwC8DqfoKVAGu2skWjSZPYDDAoUOqtjjAJ58o/2rKHK9YEerUSTne0QEc8kgPOzY2lt9//5358+czZMgQ8/YjR47w888/s3fvXt5//32uXr3Kpk2bOHv2LPv27SM8PJywsDB2Gt9UTp8+zcCBAzl06BDu7u5p2gkJCcHHx4e6desyYcIEHB0duXLlClWqVDEfU6VKFa6YBMVTMXXqVNzc3Dh69ChHjhzhmWee4erVq4wdO5bffvuN8PBw9u/fb3b+sbGxNG3alMOHDxMUFMQXX3yBn58f77//Pr179yY8PBznVBPiw8LCWLlyJYcOHeKHH35g//795n3Dhg1j7ty5hIWFMWvWLIta/deuXWP37t2sX7/e7Kh/+eUXfvzxR/78808OHz5sLh+b2XWyg5OTEzt37uSVV16ha9eufPbZZxw7dowlS5ZYiNMAzJgxg5YtWxIeHs4bb7xhse/ixYuULl3aLEjj6+vL2rVrSUpK4uLFi4SFhVm8gL344ov4+fkxdepU8/DGmDFjaNq0KVFRUbRo0YKlS5emez+NGjVi165dObrP/EZ+S0nZD9QWQlQHrgB9gH72NUmjyX2uX1eh7pIlYc0a6NULfv8dmjWD/v2hadOUqV1mX5FZiVgXl8z3lyuX+f50EBnE4VNv79u3LwBBQUFER0ebx4S7du2Ks7Mzzs7OtG7dmn379rF79242bdqEv78/oHrGZ8+epVq1ari7u5uFSNIjNDSURo0aERUVRfPmzenQoUO6493p2bxlyxazZjhA6dKl2blzJ8HBwZgifCEhIezcuZNu3brh5ORkHuMNCAhg8+bNmT6nXbt20b17d1xcXACl3Ga6v99//50XXnjBfOwD0/w9VA/TwcGBBg0acP36dbOtL774ovlaZcqUyfI62cFkk7e3N56enlSsWBGAGjVq8Ndff1G2bNlsXefatWukjooOGTKEkydP0qhRI9zd3WnevDlFjJmSoaGhVK5cmXv37tGzZ0+WLVvGwIEDGTBgAAMGDABgypQpjBo1il9++YWvv/6aqlWr8t///hcHBwcqVKjA1asFu3+Xrxy4lDJJCDES+BU1jewrKeVxO5ul0dicxESVfObmBqdPQ716sHgxDB4MzzwDS5eqsWwADw+1nDxpR4OBsmXL8s8//1hsu337NtWrVzevP+wwTevpbZdS8u677/Lvf//bYl9ERES2xU7Kly9Pw4YN+fPPP2nZsiWXTckAwOXLl6lUqVKac6SUaezJLNmtaNGi5uMdHdOXO32Y9F4cDAYDpUqVIjw8PN1zTL3Y1PakZ2tW18kOprYcHBws2nVwcMjW/Zlwdna2kF0tUqSIRZi9efPm1K5dG4DKlVV6U8mSJenXrx/79u2zGJe/evUq+/fvZ9KkSTRu3Ji9e/cyfvx4tm7dyrPPPsv9+/ctIh0FkfwWQkdKuUFKWUdKWVNKOd3e9mgKDq+++iqvvvqqvc0wY/qeS0hQU7pmGCse1KkDs2ZBixZqvXRpGDhQVUPLS7i6ulKxYkW2bt0KKOe9ceNGnn76afMx3377LaCyiN3c3HBzcwNg7dq13L9/n1u3brF9+3YCAwNp3749X331FTHGFPorV66YM5OzS1xcHIcOHaJmzZpUrFiRkiVL8scffyCl5Ouvv6Zr17STWtq1a8e8efPM6//88w9NmjRhx44d3Lx5k+TkZFasWEGrVq1y9oCMBAUFsWbNGuLj47l37x4//fQTAE888QTVq1fn+++/B5RzPnz4cKbXateuHV999ZVZVe/27duPdJ3HoWTJktxLnTWZijp16hAREWFej4uLIzY2FoDNmzdTpEgRGjRoQFJSkjk/IDExkfXr16eZ0TBhwgSmTp0KQHx8PEIIHBwczPd+5syZNOcUNPJVD1yjsSW9e/e2a/tSpmR/t2sHrq7www9qate770JAgNonBLz1lv3szAlff/01I0aM4C2jwZMmTaJmzZrm/aVLl6Z58+ZER0fz1Vdfmbc3btyYTp06cenSJSZMmEClSpWoVKkSJ0+epFmzZoB6QVi+fLmFjGdGhISE4OzszIMHDxg8eDABxoe5YMECBg8eTHx8PM899xzPPfdcmnP/85//MGLECLy8vHB0dGTSpEn06NGDDz/8kNatWyOlpGPHjuk6/+zQsGFDevfujZ+fH+7u7rRs2dK8LzQ0lFdffZVp06aRmJhInz598PX1zfBaHTp0IDw8nEaNGuHk5ETHjh354IMPcnydx8HHx4ciRYrg6+vL4MGDLcbBS5QoQc2aNTl37hy1atXixo0btG/fHgcHBypXrsyyZcsAFeJv3749iYmJJCcn07ZtW3PmOqToq5uGU1566SW8vb2pWrWqOblx27ZtdOrUySb3mFfQcqIajRFT8kzV1HOqcomJE2HjRjAmYjN3riqeMmzYo1/T3nKiWREcHMysWbNo1MhSPXHy5Mm4uroyZswYO1mmsSVr1qwhLCyMadOm2bSdoKAg1q5dmyY7Pa+g5UQ1GitiSozJDT3w1ath6lT44w9VKKV2bbhzR2WSFykCr71mcxM0GrvQvXv3NJnr1iYqKoo333wzzzpva6EduEaTCxw5osLgc+dCjRoqe7xSJTW9ukoVGDBALYWJjF6UJk+enKt2aHKfl19+2abXL1++PN26dbNpG3mBfJfEptHkB27fVuPUu3erdRcXlT1uSnpu1w42bFDOW6PRaB4F7cA1GitgMMD//gc//6zWXVzUNC/TzJ1ateDcOQgKsp+NGo2mYKFD6BrNIxIWBteuwfPPq6Ips2aBry906qTGtf/+O0V2U6PRaKyNduAajZG3spibFR2tSpaapvtOnarGto1Ft9i+HYx6C4B23hqNxrboELpGY6Rz58507tzZYtv582p+NsD06fDss8qRA/z3v5CqbDVPPpl/VbxsgZYTtUTLiSq0nKj10A5cozFy+vRpjh8/TWKiWl+5Uo1dHz2q1ocOha1bwVS1s2ZNyGYJaE0uoeVErYOWE80faAeu0RgZMGAqfn4VWS3UK3sAACAASURBVLtWrbduDXPmKDUvUM68ZUvIRuGvvEl6cqHz56t9cVpOVMuJpqDlRPMH2oFrCi0JCdC2Lcycqdadna9Rvvx2TGqUTz6pCqpoSXnboeVEtZyolhN9dHQSm6ZQMWOG6my+/75KMnvqKaXwBSBEMnXqzCYwsIt9jbQVWk5Uy4mmc53soOVE8ybagWsKNDt3qsUU6TtzBoziRwAsX24fuwoDWk5Uy4k+jJYTtS46hK4pUERFqWHb5GS1vmMHzJ4NRgVK/vc/MCpYamyMlhPNHlpOVMuJPiq6B67J95w+nRIK/+03ePFFqFsXmjWDN96AceOgaFF1bGbTvFIn5Gisg5YTzRotJ6rlRB8VLSeqyXcYDBAfr6ZzHT0KPj6qZz1kiOppnz+vthX2OdlaTlSTF9FyogpryInqELomX5GQAB4eqgoagJcXfPEFmGo2uLqqcqaP4rxN8001Go3t6N69Ox4eHjZto7DIieoeuCbP8/rrcPeuEgcB5bwDAqBjR+u2E2yc25wbeuC5QV7vgWs0hRlr9MD1GLgmz7F+vVoWLlTrTzxh2aNOVXBJo9FoCi3agWvsztWrKjN8+HAoVkyNYW/ZAnfuQKlSas62RqPRaCzRY+CaXEdKlXxmnCVCeDi8+Sbs3avWR4yAs2eV89ZoNBpN+mgHrskVDIaUudgXL6oscVOZ4jZtVK/bVF67SBGdQa7RaDRZoR24xuYYDNCgAZj0HmrUgG++gT591HqxYmqbvfnggw/44IMP7G1GgSEvyIm+9957FkIjkZGR1KhRI10ZT2syePBgs8DIyy+/zIkTJzI8dvv27WYlL3g0Kc/0uHr1Kr169cryuNz6mw8ODs5QqKRXr15cuHABUMV9fHx88PT0NNdyByV3Wr58ebO86JdffgmoOvgBAQH4+vqy1xjGS0pKom3btuaiLgB9+vTh7Nmztro9u6AduMYmvP8+hISozw4O8NJLSjjERN++SiwkL9G8eXOzprEmf/KwnOiECRNYu3YtJ0+eBGD06NFMnTr1kWQ8c1IyNDVffvklDRo0yHD/ww78UaQ806NSpUoWKmUZ8SgOPNlU6tAKHD9+nOTkZGrUqMGtW7d4++232bp1K8ePH+f69evmSn6AWQwmPDycl19+GYDPP/+cGTNmsGrVKvPL4YIFCxgwYIC5Jjwo6diZJuWiAoJ24Bqr8McfquqZaVaio6Ny3Kb1t9+G7t3tZ192+P333y2+SAsaqdVBExPVuqkWvElN1FRm9u5dtf7DD2rdpCZqrPLJ339bwx7by4k6Ozsze/Zshg8fzi+//MK9e/cIMb1ZZtOWYcOG0a5dOwYOHEhycjJvv/222YbPP/8cUC8OI0eOpEGDBnTq1MmixGvqnufGjRtp2LAhvr6+tGnThoiICBYuXMgnn3yCn58fu3btsohShIeH07RpU3x8fOjevbu5tnxwcDBjx46lcePG1KlTJ13VrdQRkCVLltCjRw86dOhA7dq1zT3bcePGER8fj5+fn/m5LF++nMaNG+Pn58e///1vs7N2dXVl4sSJNGnShA8++IB//etf5ra2b99O586dAeUoGzVqhKenp/l3lBmhoaHmKnYXLlygTp06ZsGTtm3bmuVbM6Jo0aLEx8eb5UXv3LnDTz/9lOYlqGXLlmzZsuWRX8TyIjoLXfNIxMXBxo3w7LNQsiScOKGcwxtvQLVqMH68vS3MOe+99x5QcOaB5wdMcqI7d+5kyJAhHDt2DFByon/88QexsbH4+/vTqVMnjh07ZpYTlVLSpUsXdu7cSbVq1Th9+jSLFy9mvknfPBUdO3bkf//7HwMHDmT37t05tiUsLIzdu3fj7OzMokWLcHNzY//+/Tx48IAWLVrQrl07Dh06xOnTpzl69CjXr1+nQYMGFvKooIqLDB06lJ07d1K9enVu375NmTJleOWVVywqz6XucQ4cOJC5c+fSqlUrJk6cyJQpU/j0008BFRHYt28fGzZsYMqUKWzZsiXTZx0eHs6hQ4coVqwYdevW5bXXXmPGjBnMmzfPXMDo5MmTfPvtt+zZs4eiRYsyfPhwQkNDGThwILGxsXh5efH++++TlJREjRo1iI2NpUSJEnz77bf07t0bUNrmZcqUITk5mTZt2nDkyBF8fHwytGvPnj1mVbpatWpx6tQpIiIiqFKlCj/++CMJCQnmY1evXs3OnTupU6cOn3zyCVWrVmXEiBEMHDiQBw8e8Pnnn/P+++8zfvz4NKIuDg4O1KpVi8OHD5tL6eZ3tAPXZJuYGEhKUtnhYWHQsyesXAm9e0O/ftC/v5Lo1ORNUr+XFC1quf6wmqibm+X6w2qiTz2VdXt5SU50xIgRxMfHU7du3QyPyciWLl26mFWtNm3axJEjR8yh6bt373L27Fl27txJ3759cXR0pFKlSjzzzDNprv/HH38QFBRkVmMrU6ZMhraYrn3nzh2zSMqgQYMsJEF79OgBKMnS1AIhGdGmTRuzWEyDBg2IjIykatWqFsds3bqVsLAwAgMDASUSUqFCBUApq/Xs2RNQKmIdOnTgp59+olevXvz888/m8PR3333HokWLSEpK4tq1a5w4cSJTB55aYrR06dIsWLCA3r174+DgQPPmzc1j4507d6Zv374UK1aMhQsXMmjQIH777TeqVatmfuk+d+4cV69epV69egwYMICEhASmTp1KnTp1AMwSo9qBawoFUqqM8Lt3oVIlJQwyYQK0aKGEQ0y6C8WL29dOTd4jL8mJOjg44OCQ+YhhRrakvraUkrlz59K+fXuLYzds2JDhC0vqc7M6JieYZD2zK1maWgY0o3OklAwaNIgPP/wwzb7ixYtbCMf07t2bzz77jDJlyhAYGEjJkiW5ePEis2bNYv/+/ZQuXZrBgwdbyIemx8MSo507dzaH4xctWmRuM7Xm+NChQy2SE02MHz+eadOmMWfOHEJCQvDw8GDKlCmEGqe8FDSJUT0GrsmQIUPglVfUZzc3VcLUJNbk4ACtW6spXxpNeuRFOdHMyMiW1LRv354FCxaQmJgIKMnK2NhYgoKCWLlyJcnJyVy7do1t27alObdZs2bs2LGDixcvmp8HZCy/6ebmRunSpc3j28uWLXtkydLMKFq0qPl+2rRpw6pVq8zP9fbt20RGRqZ7XnBwMAcPHuSLL74wh8+jo6MpUaIEbm5uXL9+nV9++SXL9uvXr8+5c+fM66a2//nnH+bPn29OVrt27Zr5mHXr1qUpQ7pjxw4qV65M7dq1iYuLw8HBAUdHR4tM9DNnzuDp6ZmlTfkF/fWrMbNxI2zbBh99pNaffDJFhhNUsRWNJifkFTnR7JCRLal5+eWXiYiIoGHDhkgpKV++PD/++CPdu3fnt99+w9vbmzp16qTraMuXL8+iRYvo0aMHBoOBChUqsHnzZjp37kyvXr1Yu3Ytc+fOtThn6dKlvPLKK8TFxVGjRg0WmwQBrMiwYcPw8fGhYcOGhIaGMm3aNNq1a4fBYKBo0aJ89tlnuLu7pznP0dGR559/niVLlrB06VIAfH198ff3x9PTkxo1atCiRYss2+/UqRPbt2+nrXGayujRo8165RMnTjSHv+fMmcO6desoUqQIZcqUYYkpIxMVOZg2bRrfffed+Z5CQkJISkpiwYIFAFy/fh1nZ2cqVqz46A8rj6HFTAox0dGwYQO88ILKGv/gA1V//MQJpepV2DAl8vj5+dnZEuuQ18VM8pKcaEa2aGxPfHw8rVu3Zs+ePVZ7GUuPTz75hCeeeIKXXnrJZm3kBC0nqskxMTEqgxzg11/VfGxTYu6bb0JEROF03oC5QIRGo8k9nJ2dmTJlCleuXLFpO6VKlWLQoEE2bSO30T3wQkRkJNSrB3PmwNChypEfOgTNmqkx7cKOaRpO29QVZ/Ixeb0HrtEUZrScqCZTpISBA6FWLZg0Sc3PfucdaNxY7XdxUdnkGsW0adOAguPANRpNwUY78ALG1q1w7BiMHq2mfzk6pgiDCAFTptjXPo1Go9FYBx04zeckJcHOnSnr69bBzJmqVCao6mgTJ9rFNI1Go9HYEO3A8yEGA5i0BL74Alq1AqNWA5MnK7nO1NO/NBqNRlPw0A48n3HqFFStqqZ/gSpnumYNmIpblS6ty5lq8g6udpzSIKXk6aeftigm8t1339GhQwebt+3h4cHNmzcBslS4W7JkCVevXjWvZyU/ml3WrVvHjBkzMj0mIiKCb7755rHbyg4Z/S3Ex8fTqlUrs2jK2LFj8fLywsvLy1xcB5REa/Xq1c2zRUzTPlevXo2npyctW7bk1q1bAJw/f54+Jr1iICEhgaCgoAIlZAKoP/KCvAQEBMj8TFKSlO+9J+XXX6v1hAQp+/aVcs8e+9pVEDl16pQ8deqUvc2wGidOnLC3CbJEiRK52l5iYqLF+tGjR2W9evVkfHy8jImJkbVq1ZLnzp2zyrUzw93dXUZFRWXr2FatWsn9+/c/kk2Py7Zt22SnTp1ydE5SUtIjtZXR38K8efPkp59+KqWUcv369bJt27YyMTFRxsTEyICAAHn37l0ppZSDBg2S33//fZrzmzVrJqOjo+WiRYvknDlzpJRS9unTR545c8biuMmTJ8vly5c/ku22IL3/T+CAzIF/0z3wPMiFC2qONqgktM2blXgIqND4N9+Alq22PnXr1s1U7CK/k1fkRCMjI2nTpg0+Pj60adOGS5cumfWgpZTcuXMHBwcHdhqTO1q2bMm5c+eIjY1lyJAhBAYG4u/vz9q1awHVg33hhRfo3Lkz7dq1s2jLy8uLzp0789FHHzFlyhQGDhxoUQnOhKurK2+99RYNGzakTZs2REVFGZ9ZMO+99x6tWrXi//7v/4iKiqJnz54EBgYSGBjInj17ALh16xbt2rXD39+ff//738hU03NT9zxnzpyJt7c3vr6+jBs3jlWrVnHgwAFCQkLw8/MjPj7eQn50xYoVeHt74+XlZVH729XVlfHjx+Pr60vTpk25fv16mntasmQJI0eOBFTvddSoUTRv3pz/b+/M46uqzr3/fQKEEMa0QYwMBrlBERIiRBmUqUi0FAsiFmmsBu8rr4ItVG9VyquNUqUoyHX4IDggqFFQKIpeVKCAYKVljGFQGQQU8ELAUohhCMnz/rHWOeyEczKZcM6J6/v5nE/2XnuttZ9nD3n2Wnvt9bvkkkv8YiwPPvggq1evJjU1lWnTpgWVS125ciX9+vXj17/+NcnJyTzwwAMllN+ysrKYOnUq+fn59O/fny5dupCcnOw/R2XhlRPdtm0bffr0oW7dujRs2JDOnTvz4Ycfllk+KiqKU6dO+eVEV69eTUJCAklJSSXyDRkyxD8neq2hMtE+En+R0gI/evTs8s03q7ZoYVrfqqbV7ah5Fi1apIsWLQq1GdVG6Sf8Pn1UX3nFLJ8+bdZfe82sf/+9WZ8716wfPWrWFyww63l5Zt13eL79tmI2BGp1DRo0SGfPnq2qqi+//LIOHjxYVVWvu+463bJli7733nualpamf/7zn/XkyZOamJioqqrjx4/X16zB//rXvzQpKUnz8/P1lVde0ZYtW+qRI0cC2pCfn6/t27fXTp066cmTJwPmAfyts0ceeUTHjBmjqqZ1fPfdd/vzjRgxQlevXq2qqnv37tXLLrtMVVV/+9vf6iOPPKKqphUJ+FvgvmOwePFi7dGjh37//feqqn57S7fAfev79+/X1q1b66FDh7SwsFD79eunCxcu9Nvru1b/8Ic/6MSJE8/x6ZVXXvH7cfvtt+uwYcO0qKhIt27dqu3atVPVc1vgM2fO9Nd18uRJ7dq1q3711Ve6YsUKjY2N1a+++kpVVTdu3Ki9e/f2l+vQoYPu3btXCwsL/S3mvLw8bdeunRYXF5c4Dl5OnTqlLVq08K9/9NFH2rNnT/3+++81Ly9P27Ztq1OmTPH70L59e01OTtZx48b5z+WSJUu0S5cuOmjQID169Kimp6frd999d86+zpw5o/Hx8eekh4rqaIG7z8jCgJdegjFj4Jtv4IILjGhIgwam9Q1uQNr5YurUqQB+JaTaxvmWEw3GmjVr+Ktt2v/mN7/h/vvvB0xLe9WqVezevZvx48fz4osv0qdPH7+05ZIlS1i0aBFTpkwBjLLU119/DcCAAQOCynM2bNiQ4cOH06hRoxKKXF6ioqL8ghy33nqrX6oT8KeDmezH+3762LFjHD9+nFWrVvl9+sUvfkFcXNw5+1i2bBkjR44kNjYWKF9OdN26dfTt29cvtZmRkcGqVasYMmQI0dHRDBo0CDByokuXLi2zLjAt0KioKC6//PKALXYILpcaHR3NVVdd5VeSu+KKKzh06BAHDhwgLy+PuLg42rRpQ2FhIX/84x9ZtWoVUVFR7N+/n4MHD3JhkAvm8OHDNGvWzL+enp7OunXr6NmzJ82bN6dHjx7UtYpJkyZN4sILL+T06dOMGjWKyZMn8/DDDzNgwAAGDBgAmLnjBw4cyJdffsmUKVOIi4vj6aefJjY2ljp16hAdHc3x48dp3LhxuccrEnBd6CFg924YOvRst/jVV8MDD5z9XvvSS82kKw7HjwGfxGavXr1YvXo1a9euZeDAgRw9epSVK1fSu3dvwPQWLliwgJycHHJycvj666/9M1lVh5xoIJtK111cXMyaNWv8Nuzfv98fDKpbTlQ1+CyZ9erV89dVFTnRYHWrGrlUn3+7d+/2v5YofYyHDRvG/PnzmTdvnn/AWHZ2Nnl5eWzYsIGcnBxatGhRppxoaSlRMJKgOTk5LF26FFX1d4UnJCQgItSvX5+RI0eydu3aEuUKCgqYM2cOo0ePZvz48cyaNYuuXbuW6DY/deoUMbVI+9gF8PNAcTEsWwb//KdZb9YMNm4E23igQwd49FGwD9oOR62mZ8+ezJ07FzD/8H3yot26dePTTz8lKiqKmJgYUlNTmTlzJr2s6Px1113Hs88+6w8+mzZtqjabiouL/a3ON954o4TkqZf09HSee+45/7pvJHTv3r39geKDDz44RwfdV3bWrFl+ecvy5ES7devGxx9/zOHDhykqKuLNN9+sdjnR0vsOJpcaiFtuuYW5c+cyf/58hg0bBpgW+wUXXEC9evVYsWJFUClSH3FxcRQVFfmDeFFRkX8keW5uLrm5uf4HCJ+cqKryzjvv0KlTpxJ1PfHEE4wdO5Z69epx4sQJRISoqCj/8T5y5AjNmzenXi3q0nRd6DWEqhn407y5Wc7MNAPP3nrLfOq1e/fZFrfDUVspKCigVatW/vV7772XZ555hjvuuIMnn3yS5s2b+yUy69evT+vWrenevTtgWuS+QVwADz30EOPGjSMlJQVVJTExkffff79a7GzYsCFbt26la9euNG3atMTnS16eeeYZxowZQ0pKCmfOnKF3797MmDGDP/3pT4wYMYIuXbrQp08f2gToQrv++uvJyckhLS2N6OhoBg4cyOOPP05mZiZ33XUXDRo0YM2aNf78CQkJTJo0iX79+qGqDBw40D/Yq7pISUmhbt26dO7cmczMTMaOHRtQLjUQHTt25Pjx47Rs2dIv0ZmRkcENN9xAWloaqampXHbZZeXakJ6ezieffMK1115LYWGh/4GtSZMmvP766/4u9IyMDPLy8lBVUlNTmTFjhr+OAwcOsH79erKysgC477776N69O82aNfPbv2LFCgYOHFjlYxWOODGTGuLWW41QyJYtJlBv3mzmJG/Q4Lyb4qggffv2BcyI29qAEzOpOI0aNSI/Pz/UZvwo2bRpE0899RSvvfZaje5n6NChTJo0KWy+NHFiJmHE3/4Gf/mL+cwmJgaGDzczpBUXm8FothHhCGNq+h+Iw+E4lyuuuIJ+/fpRVFRUY3rgp0+fZsiQIWETvKsLF8CryIkT8O670Ls3XHSRCdQHD5qR5ElJUEsHMtdqWrduHWoTHCHCtb5Dyx133FGj9UdHR3PbbbfV6D5CgRvEVgmKiswEFwD798OIEfD222b92mshN9cEb0dkMm/evKDvPh0OhyPccC3wClJcDJdfbmajmjnTvM9euxa6djXb3YC0yOf5558HSn7363A4HOGKC+AVJCoK7r4bvLMw2vklHA6Hw+E477gAXgnGjQu1BQ6Hw+FwGELyDlxEnhSRL0QkV0QWikgzz7bxIrJTRL4Ukes86V1FZLPd9oxUZkojh8MREvbt28fgwYNJSkqiXbt2jB07ltOnTwfMe+DAAf+EIGXhm6WtKmRlZfmnYi2d3rJlS1JTU0lKSmLo0KEVkvQsLQXqcJxPQjWIbSnQSVVTgO3AeAARuRy4BegIXA9MFxHfdwXPA6OAJPureVFfh+NHRHZ2NomJiURFRZGYmPiDlZtUlaFDhzJkyBB27NjB9u3byc/PZ8KECefkPXPmDBdddJF/NrSyWLx4cYn5s6uL3//+9+Tk5LBjxw6GDx/Oz372M78qWTBcAHeEkpAEcFVdoqq+yXv/AfimahoMzFXVU6q6G9gJXCUiCUATVV1jFVteBYacd8MdtZr58+dXKIDURrKzsxk1ahR79+5FVdm7dy+jRo36QUF8+fLlxMTEMHLkSMDM2T1t2jT/dKKlZUD37Nnjnx6zoKCAX/3qV6SkpDB8+HC6devml9hMTEzk8OHD7Nmzhw4dOnDnnXfSsWNH0tPTOXHiBAAvvvgiV155JZ07d+amm27yT6dZUYYPH056ejpvvPEGAI8++ihXXnklnTp1YtSoUahqQCnQQPkcjpoiHD4juwP4wC63BL7xbNtn01ra5dLpARGRUSKyXkTWl/cE7XD4iI+PJz4+PtRmhIQJEyacE+QKCgoCtpYrim9qUi9NmjShTZs27Ny5EzDKZHPmzGH58uUl8k2fPp24uDhyc3N56KGH2OBT/inFjh07GDNmDFu3bqVZs2YsWLAAMLNurVu3js8++4wOHTrw8ssvV9r+Ll268MUXXwBwzz33sG7dOrZs2cKJEyd4//33GTZsGGlpaWRnZ5OTk0ODBg0C5nM4aooaC+AiskxEtgT4DfbkmQCcAXyP+YHea2sZ6QFR1RdUNU1V05o7hRBHBZk9ezazZ88OtRkhwSfLWdH0ihBMfcubHkwG9JNPPvErXHXq1ImUlJSA+2jbti2pqamAkdXcs2cPAFu2bKFXr14kJyeTnZ3N1q1bq2S/jxUrVtCtWzeSk5NZvnx50Poqms/hqA5qbBS6ql5b1nYRuR0YBPTXs3fKPsA7HVYr4IBNbxUg3eGoNnzBOzMzM6R2hII2bdoEVI4KJMpRUTp27OhvEfs4duwY33zzDe3atWPDhg1BZUAr2vXslcisU6eOvws9MzOTd955h86dOzN79uwqzW+/adMm0tLSOHnyJKNHj2b9+vW0bt2arKysgBKZFc3ncFQXoRqFfj3wAPBLVfX22y0CbhGR+iLSFjNYba2qfgscF5HudvT5bcC7591wh6OW8thjjxEbG1siLTY2lscee6zKdfbv35+CggJeffVVwEhF3nfffWRmZp6zr9Jcc801vPXWWwBs27aNzZs3V2rfx48fJyEhgcLCwiq9x1+wYAFLlixhxIgR/iAcHx9Pfn5+iXESXjnOsvI5HDVBqN6BPwc0BpaKSI6IzABQ1a3AW8A24ENgjKoW2TJ3Ay9hBrbt4ux7c4fD8QPJyMjghRde4OKLL0ZEuPjii3nhhRfIyMiocp0iwsKFC3n77bdJSkqiffv2xMTE8Pjjj5dbdvTo0eTl5ZGSksLkyZNJSUmhadOmFd73xIkT6datGwMGDKiQpCXAtGnT/J+Rvf766yxfvpzmzZvTrFkz7rzzTpKTkxkyZAhXemZw8kmBpqamUr9+/aD5HI6awMmJOhwWJycaPhQVFVFYWEhMTAy7du2if//+bN++nejo6FCb5nBUC05O1OFw1EoKCgro168fhYWFqCrPP/+8C94ORylcAHc4LIsXLw61CQ5L48aNcT1nDkfZuADucFjKG1gViQT7lMvhcISO6np1HQ4TuTgcYcH06dOZPn16qM2oNmJiYjhy5IibDczhCCNUlSNHjhATE/OD63ItcIfD4vtsafTo0SG2pHpo1aoV+/btK3c+b4fDcX6JiYmhVatW5WcsBxfAHY5aSr169Wjbtm2ozXA4HDWE60J3OBwOhyMCcQHc4XA4HI4IxAVwh8PhcDgikFo/E5uI5AGlVRrigcMhMKemcP6EN7XJn9rkCzh/wp0fmz8Xq2qFJTRrfQAPhIisr8x0deGO8ye8qU3+1CZfwPkT7jh/ysZ1oTscDofDEYG4AO5wOBwORwTyYw3gL4TagGrG+RPe1CZ/apMv4PwJd5w/ZfCjfAfucDgcDkek82NtgTscDofDEdG4AO5wOBwORwRSKwO4iOwRkc0ikiMi623aT0RkqYjssH/jPPnHi8hOEflSRK4LneXnIiKXWj98v2MiMk5EskRkvyd9oKdMWPkjIrNE5JCIbPGkVfp8iEhXe153isgzEiKdzCD+PCkiX4hIrogsFJFmNj1RRE54ztOMCPGn0tdXmPszz+PLHhHJselhfX5EpLWIrBCRz0Vkq4iMtekRef+U4U9E3j9l+HN+7h9VrXU/YA8QXyrtCeBBu/wgMNkuXw58BtQH2gK7gDqh9iGIX3WA/wUuBrKA/wqQJ+z8AXoDXYAtP+R8AGuBHoAAHwA/DyN/0oG6dnmyx59Eb75S9YSzP5W+vsLZn1LbpwIPR8L5ARKALna5MbDdnoOIvH/K8Cci758y/Dkv90+tbIEHYTAwxy7PAYZ40ueq6ilV3Q3sBK4KgX0VoT+wS1VLzyznJez8UdVVwHelkit1PkQkAWiiqmvUXO2vesqcVwL5o6pLVPWMXf0HUKZWYLj7UwYReX582FbNr4A3y6ojXPxR1W9VdaNdPg58DrQkQu+fYP5E6v1TxvkJRrWen9oawBVYIiIbRGSUTWuhqt+COejABTa9JfCNp+w+yj4BoeQWSv7jucd2V8FCsgAACjxJREFUOc3ydKFFij+VPR8t7XLp9HDkDswTtI+2IrJJRD4WkV42LRL8qcz1FQn+APQCDqrqDk9aRJwfEUkErgD+SS24f0r54yUi758A/tT4/VNbA/jVqtoF+DkwRkR6l5E30HuGsPu2TkSigV8Cb9uk54F2QCrwLaZbECLEnzIIZn9E+CUiE4AzQLZN+hZoo6pXAPcCb4hIE8Lfn8peX+Huj48RlHwIjojzIyKNgAXAOFU9VlbWAGlhd36C+ROp908Af87L/VMrA7iqHrB/DwELMV3IB203ha/75ZDNvg9o7SneCjhw/qytMD8HNqrqQQBVPaiqRapaDLzI2W7ySPGnsudjHyW71cLOLxG5HRgEZNhuMGxX2RG7vAHzzqs9Ye5PFa6vsPYHQETqAkOBeb60SDg/IlIPExyyVfWvNjli758g/kTs/RPIn/N1/9S6AC4iDUWksW8ZMzhiC7AIuN1mux141y4vAm4Rkfoi0hZIwgwmCDdKtBx8N6/lRoyPEDn+VOp82G7C4yLS3b7HvM1TJuSIyPXAA8AvVbXAk95cROrY5Usw/nwVAf5U6voKd38s1wJfqKq/qzLcz4/d98vA56r6lGdTRN4/wfyJ1PunDH/Oz/1T3ii3SPsBl2BG+X0GbAUm2PSfAn8Ddti/P/GUmYB5svuSEI2cLcenWOAI0NST9hqwGci1F0VCuPqDefD4FijEPGn+Z1XOB5Bmb4RdwHPYmQTDxJ+dmHdbOfY3w+a9yV6HnwEbgRsixJ9KX1/h7I9Nnw3cVSpvWJ8f4BpMV2qu59oaGKn3Txn+ROT9U4Y/5+X+cVOpOhwOh8MRgdS6LnSHw+FwOH4MuADucDgcDkcE4gK4w+FwOBwRiAvgDofD4XBEIC6AOxwOh8MRgbgA7gg7RGSCGGWfXDFKPt1s+koRSbPLi8UqFpUqmyUi/1XJ/f1cRNaLURT6QkSmVI8n1YOIzBaRAt/8BjbtaRFREYmvYp2fVp+FVUNE3hWRNSHYb18ReT9AeqyIZItRhNoiIp+ISCMRmSYi4zz5PhKRlzzrU0XkXjlXOStHRG4LYsN8+11zdfs2RUR+Vt31OsKTuqE2wOHwIiI9MLMxdVHVUzZARZfOp6oDzylctf11wnxz+QtV/cLO1jWqnGKhYCdGCOF1EYkC+gH7q1qZqvasLsOqgn346gLki0hbNcIOoWYsZp70ZDBSvphvyT8Fbgb+2x77eKCJp1xPwBfgd6lqalk7EZGOGAWqr6rZfoBnMTN/La+Buh1hhmuBO8KNBOCwqp4CUNXDaqfG9SJG0zneLk8Qo627DLjUk6ediHwoRtRmtYhcFmB/9wOPqeoXdn9nVHW6LX+DiPxTjJDCMhFpYdOzxAgUrBSRr0TkdzZ9olg9YLv+mIj8TgxP2lbdZhEZbrf3tXXMty3/bDsLUyDeBIbb5b7A3zFzRvv29Y71c6tYAR8RuViMXnS8iETZY5But+V7bPhYRN4Ske0i8hcRyRCRtdbWdjbfbBEZ5tlfpcoH4CbgPWAuRqTHV+9sMVrIn9pjO6y8Y1XqWkgTkZV2+Spbzyb799LSRpQiAc9Dkap+aa/Dv2OCNEBHzGQbx0UkTkTqAx2ATeXU7SUDzyxbIpIvIpPt+Vtm7fZdW7+0eTLtOX5PRHaLyD1iWv2bROQfIvITa/Ne4KcicmEl7HFEKud75hr3c7+yfkAjzGxG24HpQB/PtpVAml3eg2kJdcXMeBSLaRXtxOrwYmaoSrLL3YDlAfa3EegcxJY48E929H+AqXY5C9Mqq29tOALUw2gXb7R5ojAzKv0UE6yWYvTcWwBfY4JFX+DfmHmPo4A1wDUB7JgNDMPILMZhWlh98OjeY2fiAhpgAsxPPXbPB/4AzPTUmW//9gWOWnvqYwLYI3bbWOC/vTZUtXwAn5ZhlMHaA7mlfH3bHo/LgZ2e/QQ8VqWOQxqw0i434azG9LXAAk9d7wewKRUzp/ga4M/Ya8ezjzbA/wXuAiZiZty6Glhl8yQCJzg7I1cO0CvAfj4Gkj3rip2RC6PdsARzPXUGcmx6Jubabgw0t8fiLrttGkZEw1ffi8BNob6X3a/mf64L3RFWqGq+iHTF/HPvB8wTkQdVdXaQIr2AhWrnTxaRRfZvI0yr6W1Po7Z+Jc1pZfefgOnG93bz/o+a1tkpETmEkXfcIyJHROQKTKDepKpHROQa4E1VLcKIUHwMXAkcw8yDvM/anIMJAp8EseevmNZqN0wg8fI7EbnRLrfGzLF8RFVfEpGbMUEnWNfuOrXSlCKyCxNAwDwY9SvrAFWlvO3J+A/gE1VVETkjIp1U1Tdf9DtqRCC2+Xo9LJU5VgBNgTkikoQJkvXKckJVc8S8l07HBPx1ItJDVT/nbCu8J/AURuqxJyaQescTlNuFjnnYyfOsnwY+tMubgVOqWigim62PPlao0Zw+LiL/xvRg+MqkePIdAi4qxwZHLcAFcEfYYQPdSmCl/Sd2O6ZlFrRIgLQo4GgF/pluxbTiPwuw7VngKVVdJCJ9MS1vH6c8y0WcvZdewrSWLgRm2bRg3eJl1ROIuZgegzmqWux7MLG2XQv0UNUC24UcY7fFclblqBFwvBwbij3rxR57zmBfudmua++4hIqU9zIc05Ow2/rQBPNg8v8C1Oc9dsGOld82rN+WiZigd6MYreaVAWwpgarmYx6U/ioixZhW9ueYIN0TSMb0cHwD3Id5CJsVuLagnChlZ6Gq+q5h//Gz59h7/Cp6nGPsPhy1HPcO3BFWiMiltsXkIxXYW0aRVcCNItJAzCjtGwDUaPLutq1PxNA5QPkngT+KSHubL0pE7rXbmnL2nejtAcoGYiFwPaaF/ZHHxuEiUkdEmgO9qYJCnKp+jRFCmF5qU1PgXzZ4XwZ092ybjNFWfhjTtVpV9mAedMAMpiuzNVsOI4DrVTVRVRNtvbeUXaTCtt3kSfeev8zyKhGRq0Ukzi5HY7rwfdfe3zGDK79TIxP5HdAM6IHpcq8Mn2N6IGqK9pxVv3LUYlwAd4QbjTDdnttEJBfzTzQrWGZV3YjRd87BaPKu9mzOAP5TRHzKdIMDlM/FjCB+U0Q+x/zj80kBZmG64FcDhytivKqeBlYAb9meBDBBPRfTyl8O3K+q/1uR+gLUP1NVd5VK/hCoa4/XRMy7ckSkD+ZBYrKqZgOnRWRkVfaLfe8uImsxXfjfV6US2xJu47MRQM0I9GNiPxesAo8AT9vzVORJfwKYJCJ/x4w/KI92wMe212cTsB5zTYHppo732m3T/q2q3mujnZT8jOx3AfbzP5j38NWOGG3q/8DY7qjlODUyh6MaEfOZ0UbgZlXdEWp7HOGHiDTAPORd7XnIq666b8R8gvlQddbrCE9cC9zhqCZE5HLMSOG/ueDtCIaqngD+hBkIV93UBabWQL2OMMS1wB0Oh8PhiEBcC9zhcDgcjgjEBXCHw+FwOCIQF8AdDofD4YhAXAB3OBwOhyMCcQHc4XA4HI4I5P8D05c7k4SHk8cAAAAASUVORK5CYII=\n",
+ "text/plain": [
+ "
"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fig, ax = plt.subplots(nrows=1, ncols=1, figsize=(7,7), tight_layout=True)\n",
+ "\n",
+ "# Scatterplot of original data\n",
+ "ax.scatter(x, y, c='k', label='Original Data')\n",
+ "\n",
+ "# Plot the regression line, we only need two points to define a line, use xmin and xmax\n",
+ "ax.plot([x.min(), x.max()], [B0 + B1*x.min(), B0 + B1*x.max()] , '-r', label='Least Squares Linear Regression Model')\n",
+ "\n",
+ "# Plot the mean line, we only need two points to define a line, use xmin and xmax\n",
+ "ax.plot([x.min(), x.max()], [y.mean(), y.mean()] , '--m', label='Mean Y')\n",
+ "\n",
+ "# Plot the mean x line\n",
+ "plt.axvline(x.mean(),c='k', linestyle='--', label='Mean X Value')\n",
+ "\n",
+ "# Plot the upper and lower confidence limits for the standard error of the gradient (slope)\n",
+ "ax.plot([x.min(), x.max()], [B0_upper + B1_upper*x.min(), B0_upper + B1_upper*x.max()] , '--r', label='Upper B0 confidence limit (95%)')\n",
+ "ax.plot([x.min(), x.max()], [B0_lower + B1_lower*x.min(), B0_lower + B1_lower*x.max()] , '--r', label='Upper B0 confidence limit (95%)')\n",
+ "\n",
+ "# Plot confidence limits on our predicted Y values\n",
+ "ax.plot(p_x, p_y_upper, ':b', label='Upper Y prediction interval (95%)')\n",
+ "ax.plot(p_x, p_y_lower, ':b', label='Lower Y prediction interval (95%)')\n",
+ "\n",
+ "# Add legend\n",
+ "plt.legend(loc='lower right');\n",
+ "\n",
+ "# Add axes labels and title\n",
+ "ax.set_xlabel('Slide Canyon Maximum Annual SWE (mm)')\n",
+ "ax.set_ylabel('Blue Canyon Maximum Annual SWE (mm)')\n",
+ "ax.set_title('Linear Regression Model with Confidence Intervals');"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Our upper and lower predicted y confidence limits look almost parallel, but are they? \n",
+ "\n",
+ "To inspect this, we can plot the difference between the two versus x to see how our 95% interval changes shape as we move along the x axis, and see that they \"pivot\" around the mean x value of the original dataset."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 20,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "
"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "p_y_difference = p_y_upper - p_y_lower\n",
+ "plt.plot(p_x, p_y_difference, label='p_y_difference')\n",
+ "plt.axvline(x.mean(),c='k', linestyle='--', label='Mean X Value')\n",
+ "\n",
+ "plt.legend()\n",
+ "plt.xlabel('Prediction Input (Blue Canyon SWE, mm)')\n",
+ "plt.ylabel('Difference Between Upper and Lower\\nY Prediction Confidence Bounds ($\\Delta$mm)')\n",
+ "plt.title('Difference Between Upper and Lower\\nY Prediction 95% Confidence Bounds');"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "As we'd expect, they're not quite parallel (they vary along the x-axis) and are narrowest at $\\bar{x}$ where we have higher confidence in our ability to make predictions with the model."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "---\n",
+ "\n",
+ "## With scipy\n",
+ "\n",
+ "**How do we do this quickly in python?**\n",
+ "\n",
+ "As always, there are a few options, two of the easier ones that are in packages we already have here are:\n",
+ "- `scipy.stats.linregress()` we've used this previously\n",
+ "- `numpy.polyfit()` we can fit a 1st order polynomial (linear function)\n",
+ "\n",
+ "I'm going to use the scipy function below (remember, this outputs our standard error of the gradient for us already):"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 21,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "B1, B0, r, p, sB1 = stats.linregress(x, y)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Compute the upper and lower limits for the B1 parameter"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# our alpha for 95% confidence\n",
+ "alpha = 0.05\n",
+ "\n",
+ "# length of the original dataset\n",
+ "n = len(x)\n",
+ "# degrees of freedom\n",
+ "dof = n - 2\n",
+ "\n",
+ "# t-value for alpha/2 with n-2 degrees of freedom\n",
+ "t = stats.t.ppf(1-alpha/2, dof)\n",
+ "\n",
+ "# compute the upper and lower limits on our B1 (slope) parameter\n",
+ "B1_upper = B1 + t * sB1\n",
+ "B1_lower = B1 - t * sB1\n",
+ "\n",
+ "# compute the corresponding upper and lower B0 values (y intercepts)\n",
+ "B0_upper = y.mean() - B1_upper*x.mean()\n",
+ "B0_lower = y.mean() - B1_lower*x.mean()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Create some predictions values, compute our error of prediction (sigma_ep) for each p_x, then the lower and upper confidence limits (for 95%) can be computed as:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 23,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# an array of x values\n",
+ "p_x = np.linspace(x.min(),x.max(),100)\n",
+ "\n",
+ "# using our model parameters to predict y values\n",
+ "p_y = B0 + B1*p_x\n",
+ "\n",
+ "# calculate the standard error of the predictions\n",
+ "sigma_ep = np.sqrt( s**2 * (1 + 1/n + ( ( n*(p_x-x.mean())**2 ) / ( n*np.sum(x**2) - np.sum(x)**2 ) ) ) )\n",
+ "\n",
+ "# our chosen alpha\n",
+ "alpha = 0.05\n",
+ "\n",
+ "# compute our degrees of freedom with the length of the predicted dataset\n",
+ "n_p = len(p_x)\n",
+ "dof = n_p - 2\n",
+ "\n",
+ "# get the t-value for our alpha and degrees of freedom\n",
+ "t = stats.t.ppf(1-alpha/2, dof)\n",
+ "\n",
+ "# compute the upper and lower limits at each of the p_x values\n",
+ "p_y_lower = p_y - t * sigma_ep\n",
+ "p_y_upper = p_y + t * sigma_ep"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**Plot it all again**"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 24,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "
"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fig, ax = plt.subplots(nrows=1, ncols=1, figsize=(7,7), tight_layout=True)\n",
+ "\n",
+ "# Scatterplot of original data\n",
+ "ax.scatter(x, y, c='k', label='Original Data')\n",
+ "\n",
+ "# Plot the mean line, we only need two points to define a line, use xmin and xmax\n",
+ "ax.plot([x.min(), x.max()], [y.mean(), y.mean()] , '--m', label='Mean Y')\n",
+ "\n",
+ "# Plot the mean x line\n",
+ "plt.axvline(x.mean(),c='k', linestyle='--', label='Mean X Value')\n",
+ "\n",
+ "# Plot the linear regression model\n",
+ "ax.plot([x.min(), x.max()], [B0 + B1*x.min(), B0 + B1*x.max()], '-r', label='Least Squares Linear Regression Model')\n",
+ "\n",
+ "# Plot the upper and lower confidence limits for the standard error of the gradient (slope)\n",
+ "ax.plot([x.min(), x.max()], [B0_upper + B1_upper*x.min(), B0_upper + B1_upper*x.max()] , '--r', label='Upper B0 confidence limit (95%)')\n",
+ "ax.plot([x.min(), x.max()], [B0_lower + B1_lower*x.min(), B0_lower + B1_lower*x.max()] , '--r', label='Upper B0 confidence limit (95%)')\n",
+ "\n",
+ "# Plot confidence limits on our predicted Y values\n",
+ "ax.plot(p_x, p_y_upper, ':b', label='Upper Y prediction interval (95%)')\n",
+ "ax.plot(p_x, p_y_lower, ':b', label='Lower Y prediction interval (95%)')\n",
+ "\n",
+ "# Add legend\n",
+ "plt.legend(loc='lower right');\n",
+ "\n",
+ "# Add axes labels and title\n",
+ "ax.set_xlabel('Slide Canyon Maximum Annual SWE (mm)')\n",
+ "ax.set_ylabel('Blue Canyon Maximum Annual SWE (mm)')\n",
+ "ax.set_title('SWE Scatterplot');"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3 (ipykernel)",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.9.7"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/modules/lab4/lab4-3.ipynb b/modules/lab4/lab4-3.ipynb
index 303d89f9..8ef7b233 100644
--- a/modules/lab4/lab4-3.ipynb
+++ b/modules/lab4/lab4-3.ipynb
@@ -33,12 +33,12 @@
},
{
"cell_type": "code",
- "execution_count": 2,
+ "execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"# snow pillow (snow water equivalent) example data\n",
- "data = pd.read_csv('../data/pillows_example.csv')\n",
+ "data = pd.read_csv('./data/pillows_example.csv')\n",
"\n",
"# Assigning my values to variables x and y for ease of use below\n",
"x = data['SLI_max'].values\n",
@@ -57,12 +57,12 @@
},
{
"cell_type": "code",
- "execution_count": 3,
+ "execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
- "image/png": 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\n",
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\n",
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