"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.scatter(cdf.ENGINESIZE, cdf.CO2EMISSIONS, color='blue')\n",
+ "plt.xlabel(\"Engine size\")\n",
+ "plt.ylabel(\"Emission\")\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### Creating train and test dataset\n",
+ "Train/Test Split involves splitting the dataset into training and testing sets respectively, which are mutually exclusive. After which, you train with the training set and test with the testing set. \n",
+ "This will provide a more accurate evaluation on out-of-sample accuracy because the testing dataset is not part of the dataset that have been used to train the model. Therefore, it gives us a better understanding of how well our model generalizes on new data.\n",
+ "\n",
+ "We know the outcome of each data point in the testing dataset, making it great to test with! Since this data has not been used to train the model, the model has no knowledge of the outcome of these data points. So, in essence, it is truly an out-of-sample testing.\n",
+ "\n",
+ "Let's split our dataset into train and test sets. Around 80% of the entire dataset will be used for training and 20% for testing. We create a mask to select random rows using the __np.random.rand()__ function: \n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "msk = np.random.rand(len(df)) < 0.8\n",
+ "train = cdf[msk]\n",
+ "test = cdf[~msk]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### Train data distribution\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "
\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In reality, there are multiple variables that impact the co2emission. When more than one independent variable is present, the process is called multiple linear regression. An example of multiple linear regression is predicting co2emission using the features FUELCONSUMPTION_COMB, EngineSize and Cylinders of cars. The good thing here is that multiple linear regression model is the extension of the simple linear regression model.\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Coefficients: [[9.81545776 7.85767764 9.73745704]]\n"
+ ]
+ }
+ ],
+ "source": [
+ "from sklearn import linear_model\n",
+ "regr = linear_model.LinearRegression()\n",
+ "x = np.asanyarray(train[['ENGINESIZE','CYLINDERS','FUELCONSUMPTION_COMB']])\n",
+ "y = np.asanyarray(train[['CO2EMISSIONS']])\n",
+ "regr.fit (x, y)\n",
+ "# The coefficients\n",
+ "print ('Coefficients: ', regr.coef_)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "As mentioned before, __Coefficient__ and __Intercept__ are the parameters of the fitted line. \n",
+ "Given that it is a multiple linear regression model with 3 parameters and that the parameters are the intercept and coefficients of the hyperplane, sklearn can estimate them from our data. Scikit-learn uses plain Ordinary Least Squares method to solve this problem.\n",
+ "\n",
+ "#### Ordinary Least Squares (OLS)\n",
+ "OLS is a method for estimating the unknown parameters in a linear regression model. OLS chooses the parameters of a linear function of a set of explanatory variables by minimizing the sum of the squares of the differences between the target dependent variable and those predicted by the linear function. In other words, it tries to minimizes the sum of squared errors (SSE) or mean squared error (MSE) between the target variable (y) and our predicted output ($\\hat{y}$) over all samples in the dataset.\n",
+ "\n",
+ "OLS can find the best parameters using of the following methods:\n",
+ "* Solving the model parameters analytically using closed-form equations\n",
+ "* Using an optimization algorithm (Gradient Descent, Stochastic Gradient Descent, Newton’s Method, etc.)\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "
Prediction
\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Mean Squared Error (MSE) : 522.80\n",
+ "Variance score: 0.89\n"
+ ]
+ }
+ ],
+ "source": [
+ "y_hat= regr.predict(test[['ENGINESIZE','CYLINDERS','FUELCONSUMPTION_COMB']])\n",
+ "x = np.asanyarray(test[['ENGINESIZE','CYLINDERS','FUELCONSUMPTION_COMB']])\n",
+ "y = np.asanyarray(test[['CO2EMISSIONS']])\n",
+ "print(\"Mean Squared Error (MSE) : %.2f\"\n",
+ " % np.mean((y_hat - y) ** 2))\n",
+ "\n",
+ "# Explained variance score: 1 is perfect prediction\n",
+ "print('Variance score: %.2f' % regr.score(x, y))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "__Explained variance regression score:__ \n",
+ "Let $\\hat{y}$ be the estimated target output, y the corresponding (correct) target output, and Var be the Variance (the square of the standard deviation). Then the explained variance is estimated as follows:\n",
+ "\n",
+ "$\\texttt{explainedVariance}(y, \\hat{y}) = 1 - \\frac{Var\\{ y - \\hat{y}\\}}{Var\\{y\\}}$ \n",
+ "The best possible score is 1.0, the lower values are worse.\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "
Practice
\n",
+ "Try to use a multiple linear regression with the same dataset, but this time use FUELCONSUMPTION_CITY and FUELCONSUMPTION_HWY instead of FUELCONSUMPTION_COMB. Does it result in better accuracy?\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "tags": []
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Coefficients: [[9.85404898 7.62773683 5.96756017 3.56958505]]\n",
+ "Residual sum of squares (MSE): 521.52\n",
+ "Variance score (R^2): 0.89\n"
+ ]
+ }
+ ],
+ "source": [
+ "from sklearn import linear_model\n",
+ "import numpy as np\n",
+ "\n",
+ "# Membuat model regresi linear\n",
+ "regr = linear_model.LinearRegression()\n",
+ "\n",
+ "# Menentukan fitur dan target\n",
+ "x = np.asanyarray(train[['ENGINESIZE','CYLINDERS','FUELCONSUMPTION_CITY','FUELCONSUMPTION_HWY']])\n",
+ "y = np.asanyarray(train[['CO2EMISSIONS']])\n",
+ "\n",
+ "# Melatih model\n",
+ "regr.fit(x, y)\n",
+ "\n",
+ "# Menampilkan koefisien\n",
+ "print('Coefficients: ', regr.coef_)\n",
+ "\n",
+ "# Memprediksi nilai CO2EMISSIONS pada data test\n",
+ "y_ = regr.predict(np.asanyarray(test[['ENGINESIZE','CYLINDERS','FUELCONSUMPTION_CITY','FUELCONSUMPTION_HWY']]))\n",
+ "\n",
+ "# Menghitung residual sum of squares dan variance score\n",
+ "x_test = np.asanyarray(test[['ENGINESIZE','CYLINDERS','FUELCONSUMPTION_CITY','FUELCONSUMPTION_HWY']])\n",
+ "y_test = np.asanyarray(test[['CO2EMISSIONS']])\n",
+ "print(\"Residual sum of squares (MSE): %.2f\" % np.mean((y_ - y_test) ** 2))\n",
+ "print('Variance score (R^2): %.2f' % regr.score(x_test, y_test))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Click here for the solution\n",
+ "\n",
+ "```python\n",
+ "regr = linear_model.LinearRegression()\n",
+ "x = np.asanyarray(train[['ENGINESIZE','CYLINDERS','FUELCONSUMPTION_CITY','FUELCONSUMPTION_HWY']])\n",
+ "y = np.asanyarray(train[['CO2EMISSIONS']])\n",
+ "regr.fit (x, y)\n",
+ "print ('Coefficients: ', regr.coef_)\n",
+ "y_= regr.predict(test[['ENGINESIZE','CYLINDERS','FUELCONSUMPTION_CITY','FUELCONSUMPTION_HWY']])\n",
+ "x = np.asanyarray(test[['ENGINESIZE','CYLINDERS','FUELCONSUMPTION_CITY','FUELCONSUMPTION_HWY']])\n",
+ "y = np.asanyarray(test[['CO2EMISSIONS']])\n",
+ "print(\"Residual sum of squares: %.2f\"% np.mean((y_ - y) ** 2))\n",
+ "print('Variance score: %.2f' % regr.score(x, y))\n",
+ "\n",
+ "```\n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Thank you for completing this lab!\n",
+ "\n",
+ "\n",
+ "## Author\n",
+ "\n",
+ "Saeed Aghabozorgi\n",
+ "\n",
+ "\n",
+ "### Other Contributors\n",
+ "\n",
+ "Joseph Santarcangelo\n",
+ "\n",
+ "##
\n",
+ "\n",
+ "\n",
+ "# Non Linear Regression Analysis\n",
+ "\n",
+ "\n",
+ "Estimated time needed: **20** minutes\n",
+ " \n",
+ "\n",
+ "## Objectives\n",
+ "\n",
+ "After completing this lab you will be able to:\n",
+ "\n",
+ "* Differentiate between linear and non-linear regression\n",
+ "* Use non-linear regression model in Python\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "If the data shows a curvy trend, then linear regression will not produce very accurate results when compared to a non-linear regression since linear regression presumes that the data is linear. \n",
+ "Let's learn about non linear regressions and apply an example in python. In this notebook, we fit a non-linear model to the datapoints corrensponding to China's GDP from 1960 to 2014. \n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "
Importing required libraries
\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "import matplotlib.pyplot as plt\n",
+ "%matplotlib inline"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Although linear regression can do a great job at modeling some datasets, it cannot be used for all datasets. First recall how linear regression, models a dataset. It models the linear relationship between a dependent variable y and the independent variables x. It has a simple equation, of degree 1, for example y = $2x$ + 3.\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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TpxecO336tFW1alXrxRdfdPt1tftJRMR7jp00NptnO2m8fV4ocHf3T16e2eX0yYyfraOXdjt7ccuWLrY/BZaznyMhwfUuplD7nUXU7qf09HT279/PddddV3AuNjaWq6++mpUrV7p8Xk5ODllZWYW+RETEO97+1R8OvZec8WT3T8zpbLp//ih/Ht2Oahu+hYoVYfp0WLcOuncP5LCdSkqCnTshNRXeecd8T093XZ8mXH9nYRHU7N+/H4C6desWOl+3bt2Cx5yZNm0aVatWLfhKSEjw6zhFRCKdtz2U/N17ydc82v3z0UfQqhU8+STk5cHNN8OWLfDII1C+fCCHXayYGBNf3X67+V5SQBJuvzMIs95PtvPCRcuyipw712OPPcaIESMKjrOyshTYiIiUkrc9lPzVe8kf3Nn9U2bPTo52G0atlR+bk4mJMHu2CWoiRDj9ziBMgpp69eoBZsam/jlZSQcOHCgye3Ou2NhYYmNj/T4+EZFo4/irP1DPC7TidvWUI5eHeYbHmUylladMe4OHH4axY+GCCwI3yAAJl98ZhMnyU5MmTahXrx5fffVVwbnc3FyWL19O586dgzgyERGJRK529XQnlfW0ZRqjqcQpjrbrDuvXw7RpERnQhJuQmak5ceIE27dvLzhOT09n3bp11KhRg0aNGpGcnMzUqVNp1qwZzZo1Y+rUqVSqVIk77rgjiKMWEZFI5KjvkpFhlprq8DtP8w/u4i0AfqcOU2s8w8w1d0JZ/1QDFs+FTFDzww8/0KNHj4JjRy5Mv379WLBgAaNGjeLUqVMMHjyYo0eP0qlTJ7788kvi4uKCNWQREYlAjq7UffrA7Fl2BvESTzCaamSSj40XGcRYpvDqK9WJCZm7qADYLMtZbndkcrt1uYiIhAxHkBGIRNWUFLPr6bffoD0/Mo9B/IE1APxIewbyIr8nXM6sWaG5+ydSuXv/VowpIiIh69wgwyE+3tRQ8XVQ4ahLU8U6xvOMZTBzKYNFJlUYzVRihw3kqVtjAr77J5BBXbjTTI2IiIQkR5Bx/l3KUcnDl7VS7HZonGjRLeMdnuFh6vE7AG9xJ//gaQ7Y6hEfbwrWBTKgCGRQF8rcvX+Hxe4nERGJLh4Vv/OBH9/eyhsZf+Jt/kY9fmcrzfkj33AXb/E79YLSldqTisZiKKgREZGQ407xO58EGSdPwpgxdLj3Uv5IKqeowBim0Jb1pPLHIpcHqit1oIO6SKGcGhERKVGg8zrcDR5KFWR88gk8+CDs3EkM8Al/5kGeZydNXD7FUb/G35+HJ0FduBTGCwTN1IiISLFSUqBxY+jRA+64w3xv3Ni/yx+uit95e10hu3bBLbfATTfBzp2crpPA8uQl3FvrY3bZnAc0NhskJJjgJRCfR0CCugikoEZERFwKVl6Ho/idq/Z+5wYZbsvNNU0nW7WCDz8kP6Ys8yqPpOaBLXSfdQsHD9mcLvec25X6ww8D83n4NaiLYNr9JCIiTtntZgbC1TKIzYZfdwQ5AioonFvi1e6n5cth8GDYvBmAg6260WPzXDZxSYlPTUgwAU2vXoH7PByfvaOisT/fKxxo95OIiJRKwJJ1XUhKMoFLw4aFz8fHexDQHDgA/fqZxJPNm6F2bfLnv0H7zLRiA5rateGttyA11QQOSUmB/TxiYsy2bSg6W3XuzFE0BDSeUFAjIiJOhUJeR1IS7Nxpgot33ikcZBQrPx9eeglatIA33zSRwAMPwNatfNv4bn7LKL5f08GDJpjq3v1s4BDoz8MnQV2U0e4nERFxKlTyOmJiPNzhs3YtDBwI339vjtu1gxdfhE6dAO+Dk2B8HklJZtlLFYXdo6BGREScOr9T9fkceR0eJev6U2YmjBsHc+aYmZq4OJgyxeTSlD17u/M2OAnW5+FxUBfFtPwkIiJOhU1eh2XBwoVmqWn2bBPQ/PWvsG0bDBtWKKAB73dWhc3nEcUU1IiIiEshn9exbRtce60pGLN/PzRrBl9+aYIcF1MypQlOQv7ziHLa0i0iIiUKtU7R9hOn2DN4KgkLZxCTl4tVoQK2MWNg5EiIjXXrNZw1i3Rs3y4pOAm1zyPSuXv/VlAjIiJhZcWYT4l/ciiJ9nQAPuUGnqg3h+TZTald27NAQ8FJeHD3/u11onBubi7p6elceOGFlC2rfGMREfGzPXvI+EsyV/3HlO3dQzzJzCKFJNhvY+VthS+PjzfLTMXNuigJN7J4nFNz8uRJBgwYQKVKlbjkkkvYvXs3AMOGDWP69Ok+H6CIiES5M2fg6aexWrak4X9SyCOGp/gHLdlCCr0B5xm//m7lIKHH46DmscceY/369aSlpVGhQoWC89dccw2LFi3y6eBERCTK/fvf0L49jByJLTubf3MVl7GWUTxFNpWLfaojuSI52SwzSeTzOKhZunQpc+bMoUuXLtjOSRtv1aoVO3bs8OngREQkSh08CPfea5Jcfv4ZatZk9d9fpxvf8jNt3H4Zf7dykNDicVBz8OBB6tSpU+R8dnZ2oSBHRETEY/n58MorpubM/Pnm3P33w7ZtnL79HiwvK5H4s5WDhA6P/3VcfvnlLFu2rODYEci88sorXHnllb4bmYhImLPbIS3NlExJS9MSSInWrYOrroK//x2OHIG2bWHlSnj5ZahZs8SiecXxdysHCQ0eb1uaNm0a119/PZs3byYvL4/nnnuOTZs2sWrVKpYvX+6PMYqIhB1nNVDc2Y0TlbKyTHuD5583MzWVK8PkyTB0aKFqwI6ieX36mMDGnYIkIdfKQfzK45mazp07s2LFCk6ePMmFF17Il19+Sd26dVm1ahUdOnTwxxhFRMJKSoq58Z4b0IB24xRhWbBokVlqeu45E9D07Qtbt5rsXiflQlxV9HVGrQuij4rviYj4kN0OjRsXDWgcHDMH6elnb7RRWQDul19gyBD46itzfNFF8MILcN11bj39/M/s0CF46CHvqgNL6PNpReGsrCy33ziUgwUFNSLib2lp0KNHydelppqib1G3THXqFEyfbr5yc01Lg9GjYdQoOKdMiDfOD3Q6dzYpOVEVLEYon1YUrlatWok7myzLwmazYVcmnIhEMXd32ezbd3aZ6vw/LR3LVBHXIPHzz02ejKP8R8+eMGeOmaXxgXOrA6ekwIUXRlGwKICbQU1qaqq/xyEiEhHc3WVTpw707+882dWyzDJVcjL06hUBswu//WZ+mMWLzXHDhmZdqHdv77YylSDqgkUpoJwaEREfcuTUZGQ4D1gcOTXz58M115T8eo5lqrB05ozZ0TR+PJw4YaKz4cNhwgSIi/PLW3qT0yShz68NLY8ePcprr73Gli1bsNlstGzZknvuuYcaNWp4PWARkUhQ3Lbjc3fjHDjg3uuFbdG4FStg0CDYuNEcX3klvPgiXHqpX9/2u+9cBzRQuMJw2AaL4pLHW7qXL19O48aNmT17NkePHuXIkSPMnj2bJk2aqE6NiAiutx3Hx59d+nB3mSrsisYdOgT33QddupiApkYNePVV08PJzwENeJbTJJHH4+Wn1q1b07lzZ+bNm0fM/+bu7HY7gwcPZsWKFfz8889+GagvaPlJRAKpuK3a7i5Thc0ySX4+LFhgdjEdPmzODRhgdjnVqhWwYXi6+0zCg0+3dJ+rYsWKrFu3jubNmxc6v23bNtq1a8epU6e8G3EAKKgRkVDiSGgF58tUYZPQumGDWWpaudIct2kD8+aZlgcl8HWNnlAPFqOyJpEPuHv/9nj5qX379mzZsqXI+S1bttCuXTtPX05EJGq5s0wV0o4fh4cfhvbtTUBzwQXwzDPw449uBTQpKSYA6dED7rjDfG/cuHQVlx05TVB0Y1WwKwz74+eVwtyaqdmwYUPB/96yZQujRo3iwQcf5IorrgBg9erVvPDCC0yfPp2+ffv6b7SlpJkaEQlFYffXu2WZ7dnJyWZKBMyU07PPmojMDa62XftqlspZUcNgVhj2988b6Xy6/FSmTBlsNhslXRrqxfcU1IiIlNL27fDgg6aQHkDTpqaA3g03uP0Sgdp2HSrBoraZl55Pt3Snp6f7bGAiIhKGTp+GGTNg6lTIyYHy5eHRR81XxYoevVSgtl2fW2E4mLTNPHDcCmoSExP9PQ4REQlVX31lmk/+8os5vuYa03zy4ou9erlo23YdbT9vMHlVfA9g8+bN7N69m9zc3ELnb7755lIPSkREQsDevab19XvvmeP69U3ezG23laq9QcTW6HEh2n7eYPI4qPn111+59dZb2bhxY6E8G0fDy1DOqRERkcKc5p1YeSZPZtw4s8OpTBmTRzNpEvggH7FrV5NDUtK2665dS/1WISHaft5g8nhL9/Dhw2nSpAm///47lSpVYtOmTXz77bd07NiRtLQ0PwxRRET8wdkW41vrr+bYxZebGZrjx+GKK8wW7VmzfBLQQGhvu/aHaPt5g8njoGbVqlVMmjSJ2rVrU6ZMGcqUKUOXLl2YNm0aw4YN88cYRUTExxxbjB0JrDU4zEv8nY8OXkm19HXkVq4OL71kejj5oQZZ2Nfo8VC0/bzB4vHyk91up3LlygDUqlWLvXv30rx5cxITE9m2bZvPBygiIr5lt5saLpYFNvLpxxvMYBS1OQTAfPrzXJUZ/DigNjEe/+nrvqQk6NUrNLZdB0K0/bzB4HFQ07p1azZs2EDTpk3p1KkTM2bMoHz58rz88ss0bdrUH2MUEREfcmwxbs1G5jKYrvwbgI20ZjBz+TddYW9gthiHyrbrQIm2nzfQPA5qxo4dS3Z2NgBTpkzhxhtvpGvXrtSsWZNFixb5fIAiIuJbB9NPMIOJPMSzlMXOCS5gAhN4juHkUa7gOm0xlnDjcVDTs2fPgv/dtGlTNm/ezJEjR6hevXrBDigREQlBlgVLlnDTI8OpgEmmWUwSycziNxKKXK4txhJuvK5Tc64aNWr44mVERMRffv3VbMv+9FMqALtimjDYPodP+b8il2qLsYQrt4KapKQkFixYQJUqVUgqIUU7Re1GRURCR07O2fYGp09DuXLwyCOsbTWaz+6siI3CtVO0xVjCmVtBTdWqVQuWlqpWrerXAYmIiI98/TUMHny2vcGf/mTaGzRvzi3AB7FFO1nHxwevk7VIabnVpdvBsix2795N7dq1qVSpkj/H5Rfq0i0iUWHfPhgxAt591xzXqwczZ8Jf/1qk+luodLIO9TFJcPm0S7eDZVk0a9aMTZs20axZs1IPUkREfMhuh7lzYexYyMoy7Q2GDIHJk8HFLHuobTFOSXE+e/Tcc5o9kpJ5VFapTJkyNGvWjMOHD/trPCIi4o3vv4fLL4dhw0xA84c/wJo1MHu2y4DG1+x2SEuDhQvNd09bAZ5f5dghI8OcV8qmlMTjWpEzZsxg5MiR/Pzzz/4Yj4iIeOLoURg40PRoWrsWqlWDefNg5Upo3z5gw3DWR6pxY/cDkXOrHJ/PcS452fNASaKLRzk1ANWrV+fkyZPk5eVRvnx5KlasWOjxI0eO+HSAvqScGhGJGJYF//wn/OMfcPCgOXf33fDUU1CnTkCH4phhOf9u4kjfcae3UVqaCYRKkpoaWstlEhh+yakBmDVrVmnGJSIipbVpk9nV9O235rhVK5NLc/XVAR9KSTMsNpuZYenVq/hkX3erF6vKsRTH46CmX79+/hiHiEixtCMGyM42Sb/PPAN5eVCpEowbBw89BOXLB2VIjj5SrlgW7NlTch8pd6sXq8qxFKdUFYVPnTrFmTNnCp3Tso6I+FrU74ixLPjoI5MEvHu3Oderl/kAEhODOjRfzbB07Wp+pxkZzmd9VOVY3OFxonB2djZDhw6lTp06VK5cmerVqxf6EhHxpajfEbNzJ9x8M9xyiwloEhNNgLN0adADGvDdDEtMjInRoEgpHVU5Frd5HNSMGjWKf/3rX8ydO5fY2FheffVVJk6cSIMGDXjzzTf9MUYRiVJRvSMmN9e0NmjVCj75xLQ3eOwx2LwZbrop2KMr4JhhcdXP2GaDhAT3ZliSkkxSccOGhc/Hx7uXbCzicVDz8ccfM3fuXPr06UPZsmXp2rUrY8eOZerUqbz99tv+GCMAEyZMwGazFfqqV6+e395PRILPk3yNiPKvf0HbtjBmDJw6ZbYFrV9vgpwQq+bu6xmWpCQzOZWaCu+8Y76npyugEfd4nFNz5MgRmjRpApj8GccW7i5dujBo0CDfju48l1xyCV9//XXBcYzmIUUiWtTtiNm/32zRdvyBWKeOaW9wxx2up0JCgGOGxVd9pEKtyrGED4+DmqZNm7Jz504SExNp1aoV7733Hn/4wx/4+OOPqVatmh+GeFbZsmU1OyMSRaJmR4zdDi++aGZmMjNNADN4MEyZYorphYGkJJO7HPU71CSoPA5q7rnnHtavX8/VV1/NY489xp///Geef/558vLymDlzpj/GWOCXX36hQYMGxMbG0qlTJ6ZOnUrTpk1dXp+Tk0NOTk7BcVZWll/HJyK+FRU7YtasgUGD4McfzXHHjqYicMeOhS4Lhy3tmmGRYHO7onBycjL33XcfrVu3LnR+9+7d/PDDD1x44YW0bdvWL4ME+Oyzzzh58iQXX3wxv//+O1OmTGHr1q1s2rSJmjVrOn3OhAkTmDhxYpHzqigsEjye3pwdu5+gcGDjSbXakHTsGIwebWZoLMv0Z5o6FR54oMgHEvVb2iXqud0RwHJT8+bNrTJlyliXX3659dJLL1mZmZnuPtUvTpw4YdWtW9d65plnXF5z+vRpKzMzs+Brz549FhD0sUt0ycuzrNRUy3rnHfM9Ly/YIwqexYstKz7essxd3HzFx5vznj4vIaHk54Wk/HzL+uc/LatOnbM/zN/+Zln79zu9fPFiy7LZCv/sYM7ZbGH6GYh4KDMz0637t0e9n1asWMHrr7/O+++/T35+PklJSdx3331069at9GGYF6699louuugi5s2b59b16v0kgaa/sM8qbX8gXy2/BHUZZ/NmrEGDsX27HIDsxJZUeG0uMX/q7nKsjRu73gHmWH5LTw+9pSgRX/L5TM25srOzrddff93q2rWrZbPZrIsuusiaNm2alZGR4c3LeeX06dNWw4YNrYkTJ7r9HHcjPRFf0F/YZ+XlFZ1pOf8zSUjw/yyWtzNFpZadbVmPPmrZY8paFljZVLQeZapVjpxi3z811fVndu5Xaqqfxy8SZO7ev70Kas61fft2a/To0Vb16tWtcuXKlfblXHr44YettLQ069dff7VWr15t3XjjjVZcXJy1c+dOt19DQY0ESqjcxENFKNycgxZkfvSRZSUmFrzhh9xkJZLu1vu/8457n9s77/hp7CIhwt37t8fF986VnZ3N8uXLWb58OceOHePCCy8szcsV67fffuP222+nefPmJCUlUb58eVavXk1iCJQJFzlf1BaNcyHY9WaCUpl4506zx/nmm2HXLn6LacTNfEgvPmIXjd16f3e3qv/+u/tjt9shLQ0WLjTfI7Ias0Qtr4Kab7/9lnvuuYd69eoxfPhwLr74Yr777ju2bNni6/EVePfdd9m7dy+5ublkZGSwePFiWrVq5bf3EymNYN/EQ427N+fNm/1zow1okJmbC9Onm/YGH30EZcuy645HaW7fzMfc7NH7l9SCwOGhh0zuTUl9sFJSzHU9eph6fj16uPc8kXDhdlDz22+/8cQTT9CsWTO6d+/O1q1befbZZ9m3bx+vv/46V111lT/HKRJWoqZonJvcvTlPmeKfG22ggkz7N2lkX9zO9Gg6dQqr29Wwfj0rb5zGSS7w+P2La0FwvpIafEZ9Y1CJCm4HNY0bN2b27Nn06tWLTZs2sWrVKu677z4qV67sz/GJhCVfNvmLBJ7cnMH3N1q/B5kHDrCr+93EXNODC3Zt4QC1uYs3abQjlZStrUr1/q6aPJ6vuGWsqG4MKlHF7aDmvffeIyMjg6effpqWLVv6c0wiYc/XTf4igbs3Z/D9jdadmaLatU0w5dHy1//aG+Q2bU7i8n+Sj415DKQ523iLu8jYa6NPHzh4sHRBrqPJ47PPFj8cV8tYyvGSaOF2UJOUlETZsh53VRCJWq5u4vHxYVwFt5TO7cA8dmzx1/rqRuuoS+OokeMqsDh4EP72Nw+Wv376CTp3hkGDKJ99jB9pzxWsZjDzOEb1gp8B4OGHzwYk3ga5MTFQt24JY/qf85exlOMl0aJUu59EpHjn3sTfecd8T0+PzoDGwdEfyN08/9LcaM9NjJ01y5wr48Z/9Ypd/srMhAcfhMsvh++/J++CKjzIbP7A96zhD0UudwRntWqVPsj1dhlLOV4SLTT1IuJnavLnnL9vtK4qGDuWloYNM9uaDx4s+lzHjE5ystmVHRPzv5MLF8KIEWYPNcDtt/Nxl2eYM6TkQe7bB7ffXrpO1t42+IyKxqAiaKZGRILEn8nUxSXGOl7bVUDjUGj5a9s2uPZauPNOE9BcfDF8/TW88w7VW7kXdTmCM0eQe/vt5rsneVXe5mopx0uihcdBzb333svx48eLnM/Ozubee+/1yaBEJPL580brTmJscQGNQ0VOUuu5sdCmDXzzDVSoAJMnw4YN8Kc/AYHf6eZtrpZyvCQaeNTQEiAmJoZ9+/ZRp06dQucPHTpEvXr1yMvL8+kAfUkNLUVCj7OmnwkJJqDx9ka7cKEpLlca/8cy5jCUJuz834n/g+efh6ZNi1zrWOqCwrND7jbr9Ia3jTmD2tBTxEvu3r/dzqnJysrCMr2iOH78OBUqVCh4zG638+mnnxYJdERESpKUVLo8E2fczcOpXRsOHSociCSwm1kkk8QSAKz4eGyzZ8Mtt7icjnHMgjjryF6a4Kw43uZqKcdLIpnbQU21atWw2WzYbDYuvvjiIo/bbDYmTpzo08GJSHTw9Y3W3cTYmTPhttvMcYx1hmRmMYEJXMBJzlCW9JuTufjt8eBGkVF/BGfhTrNCEmhuBzWpqalYlsUf//hHFi9eTI0aNQoeK1++PImJiTRo0MAvgxQR8YQjX6dPHxOwOFsScsygfPABvD3wOyYeHERrNgHwn9iuHJ8+l2uSW3v8vpoFMZwtK8bHm9+L8nfEXzzOqdm1axcJCQmUcafYQ4hRTo1IdCkxX+fgQRg5Et54A4DTcbXYOfgpmk3pR0xZN/o5iFOuttP7M8dIIpu792+PgxqAY8eO8f3333PgwAHy8/MLPXb33Xd7PtoAUVAjEn2cLoHY8uGVV0zjyaNHzd3273+HqVPhnFlo8Zzdbgoeutp95lj6S0/XUpS4z+eJwg4ff/wxd955J9nZ2cTFxWE7J3HOZrOFdFAjItGnyJLQ2rUwaBD85z/muF07mDcPrrgiCKOLPJ70mdJSnfiax2tIDz/8cEGtmmPHjnH06NGCryNHjvhjjCIipZeVZdaiOnY0AU1cnFmHWrNGAY0Pqc+UBJPHMzUZGRkMGzaMSpUq+WM8IvI/2jniI5YFixaZ9gaOO2nfvmbrkzY3+Jz6TEkweTxT07NnT3744Qd/jEVE/ufcRox33OFB52gp7L//heuuMz0J9u2DZs3gyy/h3XcV0PhJoCssi5zL45maP//5z4wcOZLNmzfTpk0bypUrV+jxm2++2WeDE4lGrnaOODpHa+eIG06dgmnT4MknITcXYmNh9GgYNcq0OhC/cXc7vWYdxR883v1U3FZum82G3dECNwRp95OEOu0c8YHPPoOhQ+HXX83x9dfDnDlw4YXBHVeU8Uf7C4leftv9dP4WbhHxnUDsHInYXJ09eyA5+ewaXcOGZyu9uVoLEb9RhWUJBo+DmnOdPn26UA8oESkdf+8cicgqr2fOmB9gwgTIzjZ3zeRkGD/e7HCSoFGFZQk0jxOF7XY7kydPpmHDhlSuXJlf/zfF+/jjj/Paa6/5fIAi0cSfO0ccuTrnzwQ5cnXCMgl5xQpo395UBc7OhquuMnVonn5aAY1IFPI4qHniiSdYsGABM2bMoHz58gXn27Rpw6uvvurTwYlEG3/tHLHbzQyNsww6x7nkZHNdWDh0CO69F7p0gZ9/hpo14fXX4dtvoU0bv7yl3Q5pabBwofkeNp+VSBTxOKh58803efnll7nzzjuJOWdx9NJLL2Xr1q0+HZxItHHsHIGigU1pdo54kqsT0vLz4dVXoXlzmD/fnLvvPti2De65B/zUk05b7EXCg8f/BcjIyOCiiy4qcj4/P58zZ874ZFAi0czRObphw8Ln4+O9384dEVVe1683MzP33w9HjsCll5rlp1deMTM1fhKRy3YiEcrjROFLLrmE7777jsTExELn33//fS677DKfDUwkmvl650hYV3k9ftwk/c6ebdZ8KleGSZPgwQehbKn2Orjk2CGWkQEPPeR62c5mM8t2vXppV49IKPD4vwjjx4/nrrvuIiMjg/z8fFJSUti2bRtvvvkmn3zyiT/GKBKVfLlzxJGrk5Hh/AbtqH9zbq5O0Ld+W5aZmkpOhr17zbm//MW0N4iP99vbOtshVtwQ1ZxRJHR4vPx00003sWjRIj799FNsNhvjxo1jy5YtfPzxx1x77bX+GKOIlJKnuTpBzyHZvh1uuAFuu80ENBdeaIrqvfee3wMaZ0tNJQnpZTuRKOJxReFwporCEu3cqfLqqk2DI/jxa5uG06dh+nTzlZMD5cvDY4/Bo4/6vb1BSdWci5Oa6tuZmqDPkomEGHfv3wpqRKJMcTfMoLZp+PJLGDLEzNKAaUQ5Z45pQhkAaWlmRsoT/vg8IrJAokgp+bRNQvXq1bG5WWb8yJEj7o1QRIKiuFydQLRpKMKRjfv+++a4QQMzdeToiBggni4h+aM5o5qZipSOW0HNrFmzCv734cOHmTJlCj179uTKK68EYNWqVXzxxRc8/vjjfhmkiARGQLd+5+XB88/DuHFw4oSpMTNsGEycCEGYSfV051fDhmZ3eU6OmeUp7RJRSQUStdNKpGQeLz/17t2bHj16MHTo0ELn58yZw9dff83SpUt9OT6f0vKTSPHcXYIpdQ7JqlUwaJCpPQNw5ZUwdy60a1eKFy0dx9Kbqx1iALVrw7PPwo4dpjyOL5eIAvbZi4Qhd+/fHu9++uKLL7j++uuLnO/Zsydff/21py8nIiHEX20aChw+bKY3Onc2AU2NGiY6+Pe/gxrQQMk7xGw2ePFFqFjR9M70dTG+iCiQKBJkHgc1NWvWZMmSJUXOL126lJp+rOopIv7nrzYN5Oeb3kzNm5s2B2DaGmzbZtoc+Km9gadKqubcq5f/emiFdYFEkRDh8fLTggULGDBgANdff31BTs3q1av5/PPPefXVV+nfv78/xukTWn4ScY87W7/dtmEDDB5sWhoAtG4N8+aZlgchytUOMX8uEZW0/OXNTittDZdI4dPdT+fq378/LVu2ZPbs2aSkpGBZFq1atWLFihV06tSpVIMWkdDgkzYNx4+bdZrnnjN31wsuMEnAw4ZBuXL+GrpPuNoh5s8lIscsmWPT17mBjTezZNoaLtFIdWpExLcsCxYvNuswGRnmXO/eJsM2ISGoQyutQCTz+mKWLKgFFEX8wK/F9/Lz89m+fTsHDhwgPz+/0GPdunXzfLQBoqBGxM927DCNJj/7zBw3bWoK6N1wQ3DH5SP+WCJy9T7ezpIFtYCiiJ/4bflp9erV3HHHHezatYvz4yGbzYbdmww5EQlvOTnw5JMwderZ9gaPPGJaHFSsGOzR+Yyvl4iKex9vZnrsdlP6J+AFFEVChMdbDgYOHEjHjh35+eefOXLkCEePHi34UjVhkSj01VfQpg2MH28CmmuugY0bYdKkiApoHEraIRWsZR1HE9KHHnLvem0Nl0jk8UzNL7/8wgcffMBFF13kj/GISLjYuxdGjIBFi8xx/fomb+a22wLa3iAYfJJI7UOucmiKo63hEok8Dmo6derE9u3bFdSIRKu8PHjhBXj8cbPDqUwZGDoUJk8OSnuDYPF2icjXimuv4Iwjp8brAooiIczjoObBBx/k4YcfZv/+/bRp04Zy523NvPTSS302OBEJDLcTU1evNu0N1q0zx506mZozl10WyOG6FI11WUpqQnoufzThFAklHgc1vXv3BuDee+8tOGez2bAsS4nCImHIrXomR46YpN9XXjFTAtWrw/TpIVUNOFrrsniSGxMf72UBRZEw4XFQk56e7o9xiEgQuMrFcPQx+uB9i6Tjb8DIkXDokHmwXz946inT3TFElPhzRHBdFndzY5591uy21wyNRDIV3xOJUiXVM7mETbwWO4hOOd/978QlZqkpxJIxor0uS6Bq54gEk9+6dAP885//5KqrrqJBgwbs2rULgFmzZvHhhx96N1oRCThXuRgXcIInGcVa2tEp5zvsFSrBjBmwdm1IBjSe1GWJRH5rQioShjwOaubNm8eIESP4v//7P44dO1aQQ1OtWjVmzZrl6/GJiJ8UzcWwuIUlbKYVo3iKcuSRwq18MmOLWX4KsX5NqstyVqjWzhEJNI+Dmueff55XXnmFMWPGEHNO6N+xY0c2btzo08GJiP+cm4vRmHQ+5iaWkEQj9pBOY27kY3qTQtU2jVy+ht1u+iEtXGi+B2qfgCOHxt1dPxD5dVmSkmDnTtN36p13zPf0dAU0El28ShS+zMn2zdjYWLKzs30yKBHxjidbmrt2haYNc7g942nGMIWKnCaXcsxgFFMZzWlbJRKKqWcSrN1GqsviWqjUzhEJFo+DmiZNmrBu3ToSExMLnf/ss89o1aqVzwYmIp7xNMiISfuGddYQ4tgGwDf8kSG8wDZalJiLEczdRqrLIiKueBzUjBw5kiFDhnD69Gksy+L7779n4cKFTJs2jVdffdUfYxSREngUZOzbBw8/DAsXEgecrlaXkWVmMufI7YCJApzVM3HMAmVkmDwWZzMllmUCieRk00bAH4GE6rKIiCtebel+5ZVXmDJlCnv27AGgYcOGTJgwgQEDBvh8gL6kLd0Sidze0rzdTsxLc2HsWMjKMkXzBg+GyZOxx1UrdtnK2SxQSVJT/bMUkpYGPXqUfJ3qsohEDnfv36WqU3Po0CHy8/OpU6eOty8RUApqJBK5c5PvyBqW1htIw/0/mROXX25qznToUOLre9MsEUyy6u23e/Ycd6gui0j08WudGoADBw6wZcsW/vvf/3Lw4EFvX0ZESqm45ZhqHGUug/gPnWi4/yeOUZXR1eaSMnKVWwGNp0m55/LXbiPVZRERVzwOarKysrjrrrto0KABV199Nd26daNBgwb87W9/IzMz0x9jFJFiOA8eLO7iTbbRnEG8SBks3uQumrON6ZmD6NM3hpSUkl/bk6Tcc9WoYQIif23xVl0WEXHG46Dmvvvu4z//+Q/Lli3j2LFjZGZm8sknn/DDDz9w//33+2OMIlKMrl3NzdwxS9GSzaTSgzfpRx0OspmWXE0a/XiTA9QtmHVJTi456PC2YN2RI3DNNWaZyJ3gyRuqyyIi5/M4qFm2bBmvv/46PXv2pEqVKsTFxdGzZ09eeeUVli1b5o8xFjJ37lyaNGlChQoV6NChA99Fau1zETc5lmMqWdlM51HW05buLOckFXmE6bRjHd9ydaHnuNs6oLRLSI7dV/4KbBx1WW6/3XzXkpNIdPM4qKlZsyZVq1Ytcr5q1apUr17dJ4NyZdGiRSQnJzNmzBjWrl1L165dueGGG9i9e7df31ck1CXFfMiBWq14hCcpRx4fcjMt2cIMHuEM5V0+r6SZmPNngZypVcssNznjyayQiEhpeRzUjB07lhEjRrDvnP8a7t+/n5EjR/L444/7dHDnmzlzJgMGDOC+++6jZcuWzJo1i4SEBObNm+f0+pycHLKysgp9iUSUnTvh5pvhlluodGg3VmIiG5/4iB/GfshuEkt8ekkzMSUl5dpsZtv0kSOuXyPSG0qKSOjwuPjevHnz2L59O4mJiTRqZHrC7N69m9jYWA4ePMhLL71UcO1PP/3ks4Hm5uby448/8uijjxY6f91117Fy5Uqnz5k2bRoTJ0702RhEQkZuLjzzDEyeDKdOmWaT//gHtjFjaHPBBbSyw4IFJW97dqd1gCMp11m14lmzICfHvSFHckNJEQkNHgc1t9xyix+GUbJDhw5ht9upW7duofN169Zl//79Tp/z2GOPMWLEiILjrKwsEhIS/DpOEb9LTTVF87ZuNcfdu8PcudCyZcEljhmWPn1MAHNuYOPNtuekJFMh2FmBvrQ0914j0htKikjweRzUjB8/3h/jcJvtvDlwy7KKnHOIjY0lNjY2EMOSKOBJs0i/+P13097g7bfNcZ06ZrbmzjudJr2UNMPi6S4hV80SHXk3vpgVcgj6Zy0iYcnjoAbg2LFjfPDBB+zYsYORI0dSo0YNfvrpJ+rWrUvD8wtH+EitWrWIiYkpMitz4MCBIrM3IiXx9KYZrI7UBYN96SUYPRoyM02UMGgQPPEEVKtW7FOLm2HxFV/PCgX1sxaR8GZ5aP369Vbt2rWtiy66yCpbtqy1Y8cOy7Isa+zYsdZdd93l6ct55A9/+IM1aNCgQudatmxpPfroo249PzMz0wKszMxMfwxPwsTixZYVH29Z5vZrvuLjzXlX19tsha8Hc85mc/08n1izxrI6dDj7ph06WNb33/vxDb3n7HNNSPDs8wnqZy0iIcvd+7fHQc2f/vQna+TIkZZlWVblypULgpoVK1ZYiYmJno/UA++++65Vrlw567XXXrM2b95sJScnWxdccIG1c+dOt56voEY8vWnm5RW9UZ//vIQEc51PHT1qWYMHnx1s1aqW9cILfngj38rLs6zUVMt65x3z3ZPhBu2zFpGQ5+792+PlpzVr1hTa4eTQsGFDlwm7vtK3b18OHz7MpEmT2LdvH61bt+bTTz8lMbHkrasixfUxsiyzVJKcbJZrHEslJbUJOHe7sk86UluWyZl5+GE4cMCcu/NOePppqFfPB2/gX67ybtwR8M9aRCKOx0FNhQoVnNZ72bZtG7Vr1/bJoIozePBgBg8e7Pf3CWdKsnTOm5umu9uQfbJdeetWs6spNdUct2hhdjWV1II7xLn77zGgn7WIRCSPi+/16tWLSZMmcebMGcDsRtq9ezePPvoovXv39vkAxTMpKabfTo8ecMcd5rs/+++EE29umu5uQy7VduWTJ2HMGLj0UhPQVKhgkoDXrw/7gMaTf48B+axFJLJ5s6511VVXWdWqVbNiYmKshIQEq1y5cla3bt2sEydOeL1eFgiRnlOjJMvipaa6ztc49ys19exzHHkezj5Xn+R5fPyxZTVufPYF//xny/r1Vx/8tMHnbf6S3z5rEQlb7t6/bZblLMOgZP/617/46aefyM/Pp3379lxzzTW+jbb8ICsri6pVq5KZmUmVKlWCPRyfstvNX8CullcctULS06N3KcrxGZVUT+X8zyglxWxXhqLblS0LJk6EZs08XOrbvdsk+Cxdao4TEmD2bJPQU1yjpTDh7b/H4j5rMHV3tK1bJPq4ff8OSIgVIiJ5psabWYho5Jg9OH82oKTZLGfblWvWNF/ubg23LMuycnIsa/p0y6pUyTyhbFnLGjXKyss84fWuoVBUmn+PvtgaLiKRxS+7n/Lz81mwYAEpKSns3LkTm81GkyZN6NOnD3fddZfLyr7if0qydI+3VXbPL2L3yy8wYULRGZ+MDDPT4HRGYflykwi8ebM57toV5s0jZdslDL8ksorNlebfYyAKBopIZHJ7+cmyLG666SY+/fRT2rZtS4sWLbAsiy1btrBx40Zuvvlmljqm0kNUJC8/paW5l1OamqrtsFC6HWIeL60cOAAjR8Kbb5oLatc2W7TvuouUJTb69CkaHIX7cov+PYqIL/l8+en111+34uLirH/9619FHvvmm2+suLg464033vBsPinAInn5SUmWgeP20srXeZY1b55lVat29pfwwAOWdfiwZVmRXWxO/x5FxJfcvX+7vaV74cKFjB49mh5O/vz64x//yKOPPsrbjkZ7EnCO/jtQNM/Um/47gWa3m7/uFy403+32YI/INXeWVi7jJ1o/0Nn0aDp2DC67DFatghdfhBo1AM/q5oSbcP/3KCLhye2gZsOGDVx//fUuH7/hhhtYv369TwYl3nHki5zfUzQ+PrSXMcKttk5xdVKqkMlzDGMNl1Nrx/cQF2fu7t9/D506Fbo20vOgwvXfo4iEL7dzasqXL8+uXbuo7+K/6Hv37qVJkybk5OT4dIC+FMk5NecKp4rCji284ZRT4nxruMVfeZeZjKA+pl1Ift+/UubZmS6joGjJOwmnf48iEprcvX+7HdTExMSwf/9+l60Qfv/9dxo0aIA9hNcNoiWoCRfhXFvn3HoqzaxtvMAQruEbAP5LMw6Me4EuE68t9jW8rZsjIhJt3L1/u72l27Is+vfvT2xsrNPHQ3mGRkJTODcwTEqClLdPseuBqQw8PoNYcjlFBeZUGUOzl0dyS1/n/z9xcMxe9OljckschfwclHciIuI5t4Oafv36lXjN3XffXarBSHQJ65ySTz/lljFD4Xg6AHvb3sDuUXMY0bdpiUFISkrROjllyhROji6pbo6IiBTldlAzf/58f45DIpirnIqwbGC4Z4+JSJYsMcf/q5LX4NZbaeBG8UlXOUSOgCY52RSeU96JiIjnPO7SLeKJ4nY2de1qYgJXsYDNZloide0ayBG7cOaMKZjXsqUJaGJi4OGHYcsWM53iRkBjt5t4yFUWm80GixcroBER8ZaCGvEbx6zE+XkzjlYCH34YJrVM/v1vaN/eVAXOzoarroK1a02QU7my2y8TyXVpRERCgYIa8YviZiUc5xxLLSFby+TgQbjnHjN18vPPULMmvP46fPsttGnj8cuFdQ6RiEgY8KihpYi7PJmVCLkGhvn58Oqr8OijcPSoOXf//TBtmglsvBSWOUQiImFEQY34haezEjExIbJte+1a09rgP/8xx23bwrx5cOWVpX5pRw5RSXVpQiKHSEQkDGn5Sfwi7GYlsrLMeljHjiagqVwZnn0WfvjBJwENqB+SiIi/KagRvwibnU2WBYsWQYsWJuLIz4fbboOtW02QU9a3k5nqhyQi4j9afhK/cMxK9OkTwtVy//tfGDoUvvrKHF90EbzwAlx3nV/fNuRyiEREIoSCmjATDs0BHWPMyYEJE+CVVwonDQe9Wu6pUybp98knITcXYmPhscfgkUegQoWADCFkcohERCKIgpow4qy8/v8K2obMsoWzMTZsCBMnQrNmIRCIff65mZ3ZscMc9+wJc+aYWRoREQlryqkJEyUVsktJCc64zuVqjHv3mhmb2FgzOxGUgOa338zgbrjBBDQNGsB778FnnymgERGJEDbLclW0PfK427o81NjtprWAq7ovjq3A6enBmwEJ2THm5cHs2TB+PJw4Yd582DAzdRQXF8CBiIiIt9y9f2umJgyEQ3n9kBzjihXQoYPp0XTihNma/eOPMHNmxAQ0djukpcHCheb7uZ2+RUSijYKaMBAO5fVDaoyHDsF990GXLrBhA9SoYSoE//vfpphehCiuWaiISDRSUBMGwqGQXUiMMT8fXnvN1Jx57TVz7t57Yds2GDAAykTOP/dwyLESEQk05dSEAUe+Sknl9UMhpyZoY9ywwbQ3WLnSHLdpY9obXHWVH94suEI2f0lExE+UUxNBwqG8ftDGePy4yZlp394ENJUrwzPPmNyZCAxoIETzl0REQoCCmjARDuX1AzpGyzIv2rKlSfy126F3b9iyBUaMgHLlfPhmocGRFLx4sXvXBzPHSkQkGLT8FGbCqaKw38a4fbspoPfFF+a4aVPT3uD66334JqHFWVHDkqSmqmqxiEQGd+/fqigcZsKhvL7fxnj6tGltMG2a6cFQvjw8+qj5qljRD28YGhxJwe7++eHIqQl6s1ARkQBTUCMh69wZn1a/fcmlLw/Btn27efCaa8zszMUXe/Q6oTq75YrdbmZoPAloIPg5ViIiwaCgRkKSY7kl/7cMZjKCtrwHwKnq9ak471m47baiGcnFvE4o98sqTklJwecLerNQEZEgUqKwuBSsarUpKdC3dx69f5vFFlrSl/ewU4bnGE69o1tJKdfX7YAm3Gu5uJvsO3SoyaFJT1dAIyLRS0GNOBWsarV2O7wxcBVr6MgsHqIKx1nFFXTgR5KZxXFbFZKTSw6wilu2cZxz53WCzd1ihb17B7FZqIhIiFBQI0UEbYbj8GF+7/V3PjzYmXas5wjVuZ+XuYoVrKcd4H4Nlkip5dK1q1lScjUxZbNBQoKSgkVEQEGNnCcoMxz5+TB/PrRoQYNlrwAwn/40Zxuvcj+Wk3+mJS3LhFQvqlIIh8KLIiKhQkGNFBLwGY6NG+Hqq02PpkOHONGkNV34jnuZzyFqu3xaccsydjv8/rt7bx/MflnuCofCiyIioUC7n6SQgM1wnDgBEyfCs8+aKOSCC2DCBCoOHc6uZuWwldBDytVyi7tF6sKtlktSEvTqFb5b00VEAkFBjRTi927blgVLlhSOPG691ayxJCQQg/mfffqYwOPcwMbZcsu5NWh++QUmTCi5pos/l238WRMnHAoviogEk5afpBC/Jqb++ivceKPZqvPbb2Y71SefmOmVhISCy9xdbjl/h9b48e4VqfPXsk2wdoyJiIih3k9ShGP3EzifKfE4IMjJgRkzYOpU0+qgXDkYNQpGj4ZKlVw+rbhZD09bBzg8+yw8+KDvZ2hcjcfrz0xERAq4e/9WUCNOOctNSUjwolrt11/D4MFmbQjgj3+EuXOheXOvx2a3mxkQTyrtOrzzDtx+u9dv7dV4HPk76enKgRER8YYaWkqplDoxdd8+GDEC3n3XHNerBzNnwl//6lY14OJ42jrgXP7Y7eTJjjHlxIiI+I+CGnHJq8RUu93MxIwdC1lZUKYMDBkCkydD1ao+GZc3O6/8udspUmriiIiEOwU14jvffw+DBsFPP5njyy+HefOgQwefvo2nsy3+LlLn9x1jIiLiFu1+ktI7ehQGDoQrrjABTbVqJphZtcrnAQ2UvEPrfP4uUqdWBiIioUFBjXjPsuCNN0zS70svmeO774atW02Q46esWHdaB0ycaJKCA9G5Wq0MRERCg4Ia8c6mTaa9Qf/+cPAgtGwJaWkmyKlb1+9vX1wtm8WLYdw4s8spUJ2r1cpARCT4tKVbPJOdDZMmmZ1MeXlYlSrx69/G8UOXh6ibUD7gpfv9WcE3EsYjIhIJVKfGCQU1pWBZ8OGHMGyY2Z8M7L28F0l7nuM/+xMLLouPN0sx4TYzoWBERCR0uXv/1vKTlGznTrj5ZtOjac8eSExk5aMfEf/D0kIBDUBGhqmsG06tAdTeQEQkMiioEddyc01rg1atTI+mcuXgscewb9xM37ductqiwHEuOdnMfoQ6R3uD84vnhWNwJiIS7RTUiHOpqdC2LYwZA6dOmYzb9eth6lS++7GS2xV0Q5ndblpBREJwJiIiCmr8wm43G4EWLjTfw+qmuH8//O1vpkfT1q1Qpw689Rb8619mhxORU0HXk/YGIiIS+sImqGncuDE2m63Q16OPPhrsYRURtvkZdju88AK0aAFvv20KrAwZAtu2wZ13FirAEikVdCMlOBMRESOs2iRMmjSJ+++/v+C4cuXKQRxNUY78jPOXMxz5GcGqV1Lizp41a0yxPEd7gw4d4MUXoWNHp6/nqKCbkeF86caffZZ8KVKCMxERMcJmpgYgLi6OevXqFXyFUlATqvkZxc4cHT0KgwdDp04moKlaFebMgf/8x2VAA8GroOvrZT21NxARiSxhFdQ8+eST1KxZk3bt2vHEE0+Qm5tb7PU5OTlkZWUV+vKXUMzPcLmz5zeLpb3/yekmLUyPJssyS0xbt5olJzeikUBX0PXHsp7aG4iIRJawWX4aPnw47du3p3r16nz//fc89thjpKen8+qrr7p8zrRp05g4cWJAxhdq+RmuZo5asIW5DKYHaZAJVosW2ObOxd6th1miSnW/+FxSEvTq5f+idf5c1nMEZ8OHFw7+4uNNQBNuRQRFRKJZUCsKT5gwocSgY82aNXR0shSyePFi+vTpw6FDh6hZs6bT5+bk5JCTk1NwnJWVRUJCgl8qCqelmdmDkqSmmt3R/nb+eCpykrFM4R88TXnOcJKKTOZxrv/yYQ4fL+/0ph4KlYHtdjMj42oWzJG/k55eumBKFYVFREJXWLRJOHToEIcOHSr2msaNG1OhQoUi5zMyMoiPj2f16tV06tTJrffzZ5sEx823pOTZ0t583bVwoVmmAbiRj3meB2nMLgA+5kaGMZudNCE52QQv54/ZsfwS7GaMoRYsiohI4Ll7/w7q8lOtWrWoVauWV89du3YtAPVDZGuKIz+jTx8TEJwbJAQjP6N+fWjELmYzjF58BMBuEniQ5/mImwEzqLffdp3cbLOZ5OZevYI3axFqy3oiIhK6wiJReNWqVTz77LOsW7eO9PR03nvvPR544AFuvvlmGjVqFOzhFfB18qzXu31yc+m26km22FrRi484Q1mm8wgt2cJH9AJs2GxQuzYcPOj6ZUKh+Jy2XYuIiLvCIlE4NjaWRYsWMXHiRHJyckhMTOT+++9n1KhRwR5aEb5Knk1JcZ68WmKey/LlMHgwZTZvphKwnG4MYS6buKTgEsfM0Z13mtmjkgRzFiRSauKIiIj/hUVQ0759e1avXh3sYbgtJqZ0+R1e7fY5cABGjoQ33zTHtWvD009z+IK7yEy2gZOdPTVquBfUBHMWJNSW9UREJHQFNVE40PyZKOwpV7ttPN7tY7fDK6/AY4/BsWPmggceMN21q1d3671CJbm5OM5mrhIStO1aRCQahMXup0ALlaCmuKWlGjU82O1T5ScYNAi+/96cvOwyU0zPzd1gjrH06WP+t7NZkPNnhYK59VnbrkVEolNY7H6KRiUtLQ0fXvJrVCGTBtPGwtdzIT8fqlSBKVNMywM37/KOACEnByZMMJM9JRWf8zrPx0dKu6znKQVRIiLhRTM1AeTO0lKtWsXtSLL4K+8ykxHUZ785dfvt8MwzHiW+OAtOGjaEv/8dmjVzfgN3FYyFSj0bXwt2ACciImdp+cmJYAc17haSq10bDh0qHEBczDZeYAjX8A0A1sUXm/YG3f/k0WyCN8FJoKr6hopoC+BEREKdu/fvsKhTEync3Rp9553mu81m2htMZiwbacM1fMMpKrDp9inYNmwgJfNPHjV59LaTeCg26/SXUO22LiIiJVNQE0DurhD16mVmA+6qsYyfac1YnqA8Z/imwv+x/IVNXPLOGFKWxTrvwP2/3BxngY23wUk0VfWNpgBORCTSKKgJIEchOccyxvlsNrNNuWvibpLeSuKNwzfSlHSya8Tz86QUuh//hOsHN/V6NsHb4CSaqvpGUwAnIhJpFNSUkietDByF5KBoYGOzQVnrDMu6P0VM65awZAmULQsjR3LBri20fvxWYsqaJ3k7m+BtcOJ2MBYBVX2jKYATEYk0CmpKISUFj3JawHV/qKTa33Ew4TLa/HMUnDxpIoS1a2HGDKhcudC13s4meBuclBSMQeRU9Y2mAE5EJNIoqPGSY4eMJzktDklJsHOnKaC3+MWD7OvZnw8OdKPqnk1mT/f8+aaHU+vWTp/v7WxCaYITXzfrDFXRFMCJiEQaben2gk+2OOfnn21vcPSoedLf/27aG9So4db7e9veoDQtB6KlIJ3aMoiIhA7VqXHCV0GNu/VmUlNdVMBduxYGDjzb3qBdO9Pe4Ior3B6Dp+0NzhctwUlp6DMSEQkNapPgR17vkMnKgscfhzlzzExNXBxMngxDhpikYA84loOcVb11ZzYh0C0HwpE+IxGR8KKgxgse57RYFixaBCNGnI10+vaFmTOhQQOvx5GUZGraaDZBREREQY1XHDtkSspp6doV+O9/zUzM11+bB5s1gxdegGuv9clYNJsgIiJiaPeTF9zZITP7yVPETBwHbdqYgCY2FiZOhA0bfBbQiIiIyFkKarxU3Bbn78Z8zi2PtzH5Mrm5cP31sGkTjBsHFSoEZ8AiIiIRTrufSuncHTKNy/7GFe8mY0tZbB5s2NBk7fbu7bqaW5TSziIREXGXdj8FSEwMdL/qDMyeDePHQ3a2OTl8OEyYYHY4SSHOasDEx5slPdWAERERbymoKa28PLjySvjxR3PcubOpOXPppcEdV4hy1Nc5f37QUYk5kqoTi4hIYCmnprTKloXrroOaNeG118yaigIap7ztLi4iIuIOBTW+MHYsbNsG994LZfSRuuJtd3ERERF3aPnJFypVMl9SLK8rMYuIiLhB0woSMN52FxcREXGHghoJGEclZle722020wm7a9fAjktERCKDghoJGHcqMc+apXo1IiLiHQU1ElDFVWLWdm4RESkNJQpLwKm7uIiI+IOCGgkKdRcXERFf0/KTiIiIRAQFNSIiIhIRFNSIiIhIRFBQIyIiIhFBQY2IiIhEBAU1IiIiEhG0pTuE2O2q3SIiIuItBTUB4E6wkpICw4fDb7+dPRcfb9oKqMquiIhIybT85GcpKdC4MfToAXfcYb43bmzOn3tNnz6FAxqAjAxz/txrRURExDkFNX7kTrBit5sZGssq+nzHueRkc52IiIi4pqDGT9wNVtLSigY951+7Z49ZvhIRERHXFNT4yXffuRespKW593r79vlkWCIiIhFLQY2f+DoIqV/ft68nIiISaRTU+Im7QUj37maXk83m/HGbDRISzI4pERERcU1BjZ907epesNK9u9m27Th3/jUAs2apXo2IiEhJFNT4SUyM+8FKUhJ88AE0bFj4uvh4c151akREREpmsyxn+3MiU1ZWFlWrViUzM5MqVaoE5D2dFdVLSDABzfnBiioKi4iIFOXu/VtBTQAoWBEREfGeu/dvtUkIgJgYkzsjIiIi/qOcGhEREYkICmpEREQkIiioERERkYigoEZEREQigoIaERERiQgKakRERCQiKKgRERGRiKCgRkRERCKCghoRERGJCFFVUdjRESIrKyvIIxERERF3Oe7bJXV2iqqg5vjx4wAkJCQEeSQiIiLiqePHj1O1alWXj0dVQ8v8/Hz27t1LXFwcNpst2MMJuqysLBISEtizZ09AG3xGI33WgaPPOnD0WQdOtH/WlmVx/PhxGjRoQJkyrjNnomqmpkyZMsTHxwd7GCGnSpUqUfl/kmDQZx04+qwDR5914ETzZ13cDI2DEoVFREQkIiioERERkYigoCaKxcbGMn78eGJjY4M9lIinzzpw9FkHjj7rwNFn7Z6oShQWERGRyKWZGhEREYkICmpEREQkIiioERERkYigoEZEREQigoIaKSQnJ4d27dphs9lYt25dsIcTcXbu3MmAAQNo0qQJFStW5MILL2T8+PHk5uYGe2gRYe7cuTRp0oQKFSrQoUMHvvvuu2APKSJNmzaNyy+/nLi4OOrUqcMtt9zCtm3bgj2siDdt2jRsNhvJycnBHkrIUlAjhYwaNYoGDRoEexgRa+vWreTn5/PSSy+xadMmnn32WV588UVGjx4d7KGFvUWLFpGcnMyYMWNYu3YtXbt25YYbbmD37t3BHlrEWb58OUOGDGH16tV89dVX5OXlcd1115GdnR3soUWsNWvW8PLLL3PppZcGeyghTVu6pcBnn33GiBEjWLx4MZdccglr166lXbt2wR5WxHvqqaeYN28ev/76a7CHEtY6depE+/btmTdvXsG5li1bcssttzBt2rQgjizyHTx4kDp16rB8+XK6desW7OFEnBMnTtC+fXvmzp3LlClTaNeuHbNmzQr2sEKSZmoEgN9//53777+ff/7zn1SqVCnYw4kqmZmZ1KhRI9jDCGu5ubn8+OOPXHfddYXOX3fddaxcuTJIo4oemZmZAPp37CdDhgzhz3/+M9dcc02whxLyoqqhpThnWRb9+/dn4MCBdOzYkZ07dwZ7SFFjx44dPP/88zzzzDPBHkpYO3ToEHa7nbp16xY6X7duXfbv3x+kUUUHy7IYMWIEXbp0oXXr1sEeTsR59913+emnn1izZk2whxIWNFMTwSZMmIDNZiv264cffuD5558nKyuLxx57LNhDDlvuftbn2rt3L9dffz1/+ctfuO+++4I08shis9kKHVuWVeSc+NbQoUPZsGEDCxcuDPZQIs6ePXsYPnw4b731FhUqVAj2cMKCcmoi2KFDhzh06FCx1zRu3Ji//vWvfPzxx4X+42+324mJieHOO+/kjTfe8PdQw567n7XjP0x79+6lR48edOrUiQULFlCmjP6+KI3c3FwqVarE+++/z6233lpwfvjw4axbt47ly5cHcXSR68EHH2Tp0qV8++23NGnSJNjDiThLly7l1ltvJSYmpuCc3W7HZrNRpkwZcnJyCj0mCmoE2L17N1lZWQXHe/fupWfPnnzwwQd06tSJ+Pj4II4u8mRkZNCjRw86dOjAW2+9pf8o+UinTp3o0KEDc+fOLTjXqlUrevXqpURhH7MsiwcffJAlS5aQlpZGs2bNgj2kiHT8+HF27dpV6Nw999xDixYteOSRR7Tc54RyaoRGjRoVOq5cuTIAF154oQIaH9u7dy/du3enUaNGPP300xw8eLDgsXr16gVxZOFvxIgR3HXXXXTs2JErr7ySl19+md27dzNw4MBgDy3iDBkyhHfeeYcPP/yQuLi4grylqlWrUrFixSCPLnLExcUVCVwuuOACatasqYDGBQU1IgH05Zdfsn37drZv314kYNSkaen07duXw4cPM2nSJPbt20fr1q359NNPSUxMDPbQIo5j23z37t0LnZ8/fz79+/cP/IBE/kfLTyIiIhIRlJ0oIiIiEUFBjYiIiEQEBTUiIiISERTUiIiISERQUCMiIiIRQUGNiIiIRAQFNSIiIhIRFNSIiIhIRFBQIxJFbDYbS5cuDfYw3DJhwgTatWsX7GH4XPfu3UlOTnb7+rS0NGw2G8eOHXN5zYIFC6hWrVqpxyYS7hTUiISB/v37c8sttwR7GGHPnZv/M888Q9WqVTl58mSRx06fPk21atWYOXOm12NISUlh8uTJXj9fRFxTUCMico67776bU6dOsXjx4iKPLV68mJMnT3LXXXd5/LpnzpwBoEaNGsTFxZV6nCJSlIIakTDUvXt3hg0bxqhRo6hRowb16tVjwoQJha755Zdf6NatGxUqVKBVq1Z89dVXRV4nIyODvn37Ur16dWrWrEmvXr3YuXNnweOOGaKJEydSp04dqlSpwgMPPEBubm7BNZZlMWPGDJo2bUrFihVp27YtH3zwQcHjjuWTb775ho4dO1KpUiU6d+7Mtm3bCo1l+vTp1K1bl7i4OAYMGMDp06eLjHf+/Pm0bNmSChUq0KJFC+bOnVvw2M6dO7HZbKSkpNCjRw8qVapE27ZtWbVqVcE47rnnHjIzM7HZbNhstiKfGUDt2rW56aabeP3114s89vrrr3PzzTdTu3ZtHnnkES6++GIqVapE06ZNefzxxwsCFzi7fPb666/TtGlTYmNjsSyryPLTW2+9RceOHYmLi6NevXrccccdHDhwoMh7r1ixgrZt21KhQgU6derExo0bi1xzro8//pgOHTpQoUIFmjZtysSJE8nLyyv2OSJhzxKRkNevXz+rV69eBcdXX321VaVKFWvChAnWf//7X+uNN96wbDab9eWXX1qWZVl2u91q3bq11b17d2vt2rXW8uXLrcsuu8wCrCVLlliWZVnZ2dlWs2bNrHvvvdfasGGDtXnzZuuOO+6wmjdvbuXk5BS8b+XKla2+fftaP//8s/XJJ59YtWvXtkaPHl0wltGjR1stWrSwPv/8c2vHjh3W/PnzrdjYWCstLc2yLMtKTU21AKtTp05WWlqatWnTJqtr165W586dC15j0aJFVvny5a1XXnnF2rp1qzVmzBgrLi7Oatu2bcE1L7/8slW/fn1r8eLF1q+//motXrzYqlGjhrVgwQLLsiwrPT3dAqwWLVpYn3zyibVt2zarT58+VmJionXmzBkrJyfHmjVrllWlShVr37591r59+6zjx487/byXLVtm2Ww269dffy04l56ebtlsNuvTTz+1LMuyJk+ebK1YscJKT0+3PvroI6tu3brWk08+WXD9+PHjrQsuuMDq2bOn9dNPP1nr16+38vPzrauvvtoaPnx4wXWvvfaa9emnn1o7duywVq1aZV1xxRXWDTfcUPC44/Nr2bKl9eWXX1obNmywbrzxRqtx48ZWbm6uZVmWNX/+fKtq1aoFz/n888+tKlWqWAsWLLB27Nhhffnll1bjxo2tCRMmOP8HJhIhFNSIhAFnQU2XLl0KXXP55ZdbjzzyiGVZlvXFF19YMTEx1p49ewoe/+yzzwoFNa+99prVvHlzKz8/v+CanJwcq2LFitYXX3xR8L41atSwsrOzC66ZN2+eVblyZctut1snTpywKlSoYK1cubLQWAYMGGDdfvvtlmWdvSl//fXXBY8vW7bMAqxTp05ZlmVZV155pTVw4MBCr9GpU6dCQU1CQoL1zjvvFLpm8uTJ1pVXXmlZ1tmg5tVXXy14fNOmTRZgbdmyxbKsojd/V/Ly8qyGDRta48aNKzg3btw4q2HDhlZeXp7T58yYMcPq0KFDwfH48eOtcuXKWQcOHCh03flBzfm+//57CygIuByf37vvvltwzeHDh62KFStaixYtcvpzde3a1Zo6dWqh1/3nP/9p1a9fv/gfXCTMlQ3SBJGIlNKll15a6Lh+/foFyxZbtmyhUaNGxMfHFzx+5ZVXFrr+xx9/ZPv27UXyO06fPs2OHTsKjtu2bUulSpUKvc6JEyfYs2cPBw4c4PTp01x77bWFXiM3N5fLLrvM5Xjr168PwIEDB2jUqBFbtmxh4MCBha6/8sorSU1NBeDgwYPs2bOHAQMGcP/99xdck5eXR9WqVd16nxYtWuCumJgY+vXrx4IFCxg/fjw2m4033niD/v37ExMTA8AHH3zArFmz2L59OydOnCAvL48qVaoUep3ExERq165d7HutXbuWCRMmsG7dOo4cOUJ+fj4Au3fvplWrVoU+D4caNWrQvHlztmzZ4vQ1f/zxR9asWcMTTzxRcM5ut3P69GlOnjxZ6PcpEkkU1IiEqXLlyhU6ttlsBTdEy7KKXG+z2Qod5+fn06FDB95+++0i15Z0Iz7//ZYtW0bDhg0LPR4bG+tyvI6xOJ5fEsd1r7zyCp06dSr0mCPI8MX7nOvee+9l2rRp/Otf/wJMkHHPPfcAsHr1av76178yceJEevbsSdWqVXn33Xd55plnCr3GBRdcUOx7ZGdnc91113Hdddfx1ltvUbt2bXbv3k3Pnj0L5S25cv7v1CE/P5+JEyeSlJRU5LEKFSqU+Loi4UpBjUgEatWqFbt372bv3r00aNAAoCBh1qF9+/YsWrSoIAHYlfXr13Pq1CkqVqwImBt65cqViY+Pp3r16sTGxrJ7926uvvpqr8fbsmVLVq9ezd13311wbvXq1QX/u27dujRs2JBff/2VO++80+v3KV++PHa73a1rL7zwQq6++mrmz59fkOB74YUXAiZpNzExkTFjxhRcv2vXLo/Hs3XrVg4dOsT06dNJSEgA4IcffnB67erVq2nUqBEAR48e5b///a/L2af27duzbds2LrroIo/HJBLOFNSIRKBrrrmG5s2bc/fdd/PMM8+QlZVV6AYMcOedd/LUU0/Rq1cvJk2aRHx8PLt37yYlJYWRI0cWLF3l5uYyYMAAxo4dy65duxg/fjxDhw6lTJkyxMXF8Y9//IOHHnqI/Px8unTpQlZWFitXrqRy5cr069fPrfEOHz6cfv360bFjR7p06cLbb7/Npk2baNq0acE1EyZMYNiwYVSpUoUbbriBnJwcfvjhB44ePcqIESPcep/GjRtz4sQJvvnmm4JlteKWYs5d7nr11VcLzl900UXs3r2bd999l8svv5xly5axZMkSt8ZwrkaNGlG+fHmef/55Bg4cyM8//+yyhs2kSZOoWbMmdevWZcyYMdSqVctl7aJx48Zx4403kpCQwF/+8hfKlCnDhg0b2LhxI1OmTPF4nCLhQlu6RSJQmTJlWLJkCTk5OfzhD3/gvvvuK5RfAVCpUiW+/fZbGjVqRFJSEi1btuTee+/l1KlThWZu/vSnP9GsWTO6devGbbfdxk033VRoK/TkyZMZN24c06ZNo2XLlvTs2ZOPP/6YJk2auD3evn37Mm7cOB555BE6dOjArl27GDRoUKFr7rvvPl599VUWLFhAmzZtuPrqq1mwYIFH79O5c2cGDhxI3759qV27NjNmzCj2+t69exMbG0tsbGyhpZxevXrx0EMPMXToUNq1a8fKlSt5/PHH3R6HQ+3atVmwYAHvv/8+rVq1Yvr06Tz99NNOr50+fTrDhw+nQ4cO7Nu3j48++ojy5cs7vbZnz5588sknfPXVV1x++eVcccUVzJw5k8TERI/HKBJObJazxXcREUydmmPHjoVNawURiW6aqREREZGIoKBGREREIoKWn0RERCQiaKZGREREIoKCGhEREYkICmpEREQkIiioERERkYigoEZEREQigoIaERERiQgKakRERCQiKKgRERGRiPD/wGIRsvZezQ0AAAAASUVORK5CYII=\n",
+ "text/plain": [
+ "
"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "x = np.arange(-5.0, 5.0, 0.1)\n",
+ "\n",
+ "##You can adjust the slope and intercept to verify the changes in the graph\n",
+ "y = 2*(x) + 3\n",
+ "y_noise = 2 * np.random.normal(size=x.size)\n",
+ "ydata = y + y_noise\n",
+ "#plt.figure(figsize=(8,6))\n",
+ "plt.plot(x, ydata, 'bo')\n",
+ "plt.plot(x,y, 'r') \n",
+ "plt.ylabel('Dependent Variable')\n",
+ "plt.xlabel('Independent Variable')\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Non-linear regression is a method to model the non-linear relationship between the independent variables $x$ and the dependent variable $y$. Essentially any relationship that is not linear can be termed as non-linear, and is usually represented by the polynomial of $k$ degrees (maximum power of $x$). For example:\n",
+ "\n",
+ "$$ \\ y = a x^3 + b x^2 + c x + d \\ $$\n",
+ "\n",
+ "Non-linear functions can have elements like exponentials, logarithms, fractions, and so on. For example: $$ y = \\log(x)$$\n",
+ " \n",
+ "We can have a function that's even more complicated such as :\n",
+ "$$ y = \\log(a x^3 + b x^2 + c x + d)$$\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Let's take a look at a cubic function's graph.\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "
"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "x = np.arange(-5.0, 5.0, 0.1)\n",
+ "\n",
+ "##You can adjust the slope and intercept to verify the changes in the graph\n",
+ "y = 1*(x**3) + 1*(x**2) + 1*x + 3\n",
+ "y_noise = 20 * np.random.normal(size=x.size)\n",
+ "ydata = y + y_noise\n",
+ "plt.plot(x, ydata, 'bo')\n",
+ "plt.plot(x,y, 'r') \n",
+ "plt.ylabel('Dependent Variable')\n",
+ "plt.xlabel('Independent Variable')\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "As you can see, this function has $x^3$ and $x^2$ as independent variables. Also, the graphic of this function is not a straight line over the 2D plane. So this is a non-linear function.\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Some other types of non-linear functions are:\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Quadratic\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "$$ Y = X^2 $$\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "
"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "x = np.arange(-5.0, 5.0, 0.1)\n",
+ "\n",
+ "##You can adjust the slope and intercept to verify the changes in the graph\n",
+ "\n",
+ "y = np.power(x,2)\n",
+ "y_noise = 2 * np.random.normal(size=x.size)\n",
+ "ydata = y + y_noise\n",
+ "plt.plot(x, ydata, 'bo')\n",
+ "plt.plot(x,y, 'r') \n",
+ "plt.ylabel('Dependent Variable')\n",
+ "plt.xlabel('Independent Variable')\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Exponential\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "An exponential function with base c is defined by $$ Y = a + b c^X$$ where b ≠0, c > 0 , c ≠1, and x is any real number. The base, c, is constant and the exponent, x, is a variable. \n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "
"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "X = np.arange(-5.0, 5.0, 0.1)\n",
+ "\n",
+ "##You can adjust the slope and intercept to verify the changes in the graph\n",
+ "\n",
+ "Y= np.exp(X)\n",
+ "\n",
+ "plt.plot(X,Y) \n",
+ "plt.ylabel('Dependent Variable')\n",
+ "plt.xlabel('Independent Variable')\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Logarithmic\n",
+ "\n",
+ "The response $y$ is a results of applying the logarithmic map from the input $x$ to the output $y$. It is one of the simplest form of __log()__: i.e. $$ y = \\log(x)$$\n",
+ "\n",
+ "Please consider that instead of $x$, we can use $X$, which can be a polynomial representation of the $x$ values. In general form it would be written as \n",
+ "\\begin{equation}\n",
+ "y = \\log(X)\n",
+ "\\end{equation}\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/ipykernel_launcher.py:3: RuntimeWarning: invalid value encountered in log\n",
+ " This is separate from the ipykernel package so we can avoid doing imports until\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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Zrq6uCAwMxMKFC5GTk4MNGzYAAObMmYOVK1di/vz5mD17No4ePYp169bh66+/lupHIKJ2qqpGg72p1/DdqRwc+O06NNr6U+qWFjIM6eKOCX19cW+4Fxxt+T9SRB2NSZWhpKQkjBw5Uve8YW7PjBkzEB8fj7y8PGRlZeleDwkJwc6dO/H888/jk08+ga+vLz766CNeVk9EAOpvh5F4qQjbTuVg17l8lKv/uBKsj78CE/v6YXyELzwceeqcqCOTiYYZxdQslUoFhUIBpVIJJycnqeMQkQFcul6OLSevYuvJnEb3A/NztsOD/fwwsZ8vung6SpiQiO6UPt/fJjUyRETUWqrqWuw4k4dvT1zFiSsluu1Otla4r48vHuznx7WAiMwUyxARdVgarcCRjEJ8e+Iqdp3Lh7pOCwCwkAHDu3ng4cgA3B3GidBE5o5liIg6nCtFFfhPUnaT02BdPR3wcKQ/HuznB08nWwkTElF7wjJERB1Cda0Gu1Pysfl4No5kFOm2O9laYUJfPzwc6Y8+/oqbLrhKROaLZYiITNqFfBW+OZaNbadyoKyqBQDIZMCwrh54JMof94R58TQYEd0SyxARmZxydR22n87FN8ezcfqGRRF9FbZ4dEAAHokKgJ+znXQBiciksAwRkck4e1WJTb9ewfenc1FZowEAWFnIMLqnFyYPCMSQLu68LxgR6Y1liIjataoaDbafycWmxCs4fVWp2x7q0QlTBgRgUn9/uDtwUUQiaj2WISJql9ILyrDp1yxsOXEVqur6laFtLC0Q29sbUwcGYmCIKydDE5FBsAwRUbtRU6fFnvP52Jh4BYmXinXbA1zt8Fh0EB6J9IcbR4GIyMBYhohIcgWqamz8NQtf/ZqFwnI1gPqFEe8O88Jj0YEY1tWDK0MTkdGwDBGRJIQQOJVdivjDl7HzbB7qfr9LvKejHFMGBmLKgAD48oowImoDLENE1KbUdRrsOJOH+COXceaGCdFRQS6YeVcwxvT0hrWlhYQJicjcsAwRUZu4pqrGpsQr+OpYFgrLawAANlYWeCDCFzMHB6OXn0LihERkrliGiMiozuUosfbQJfxw5o9TYT4KW/x1UBCmDAjghGgikhzLEBEZnFYrsO9CAdb+cqnRVWEDg10x865gjA73ghVPhRFRO8EyREQGU12rwZaTV7Hul0xcul4BoH6F6Pv7+ODJoaE8FUZE7RLLEBHdsetlanx59DI2/pqF4or6+UCOtlaYOjAQM+8Kho+CV4URUfvFMkRErXbpejnWHLyEradyUFOnBQD4u9jhibtC8OiAADjI+VcMEbV//JuKiPR2LkeJ1QkZ2HkuD6J+TjT6BTpj9tBQzgciIpPDMkRELSKEQOKlYqxKSMehi4W67Xf38MTfRnRGVLCrhOmIiFqPZYiIbkmrFfgp9RpWH8jAqaxSAIClhQzj+/hgzojO6OHtJG1AIqI7xDJERM2q02jx/elc/PtABn67Vg6gfpHEyVEB+L9hoQhwtZc4IRGRYbAMEVEjtRottp3KwSf703GlqBIA4Ci3wl9jgvDEXSHwcOQiiUTUsbAMERGA30vQyRys3J+OrOL6EuTayQazhoRgWkwQnGytJU5IRGQcLENEZq6mToutJ6/ik4R0ZBdXAQDcHWzwf8NC8ddBQbC34V8TRNSx8W85IjNVU6fFtyeu4pP96cgp/aMEPTWsMx4bFMgSRERmg3/bEZmZWk19CVq578YSJMec4aF4LDoIdjaWEickImpbLENEZkKrFfjhbB7+tfc3ZBbW3zfMw1GOOcM7Y+rAQJYgIjJbLENEHZwQAvvTCvDu7t+QmqcCUD8x+ukRnfHXQUGwtWYJIiLzxjJE1IH9eqkI7+5OQ9KVEgD1l8jPHhaKJ4aE8L5hRES/49+GRB3QuRwl3t2dhgO/XQcAyK0sMHNwMOYM7wyXTjYSpyMial9M7m6Kq1atQkhICGxtbREZGYlDhw7ddN+EhATIZLImjwsXLrRhYqK2c6WoAs9sOon7P/4FB367DisLGR6LDsTBF0di4bgwFiEiomaY1MjQ5s2bMW/ePKxatQp33XUXPv30U8TGxuL8+fMIDAy86XFpaWlwcvrj/kkeHh5tEZeozZRW1uDjfenYcPQyajUCMhkwIcIXz9/bDUFunaSOR0TUrsmEEELqEC0VHR2N/v37Y/Xq1bptYWFhmDhxIuLi4prsn5CQgJEjR6KkpATOzs6t+kyVSgWFQgGlUtmoUBG1BzV1Wmw4ehkf70uHsqoWADCsmwcWxvZAmA//fSUi86XP97fJjAzV1NTgxIkT+Oc//9lo++jRo3HkyJFbHtuvXz9UV1cjPDwcr776KkaOHHnTfdVqNdRqte65SqW6s+BERiCEwK5z+Vi264Lu/mE9vB2xcFwYhnfjyCcRkT5MpgwVFhZCo9HAy8ur0XYvLy/k5+c3e4yPjw/WrFmDyMhIqNVqfPnll7j77ruRkJCAYcOGNXtMXFwcli5davD8RIZyKqsEb+1I1V0h5uEox4LR3fBwZAAsLWQSpyMiMj0mU4YayGSN/7IXQjTZ1qB79+7o3r277nlMTAyys7Px3nvv3bQMLVy4EPPnz9c9V6lUCAgIMEByojuTU1qFuJ2p+OFMHgDAztoS/zcsFP83LBSdeJk8EVGrmczfoO7u7rC0tGwyClRQUNBktOhWBg0ahI0bN970dblcDrlc3uqcRIZWXavBZwcv4ZOEdFTXaiGTAQ/398c/RneHt8JW6nhERCbPZMqQjY0NIiMjsXfvXjz44IO67Xv37sWECRNa/D6nTp2Cj4+PMSISGZQQAj+nFuD1H84jq7h+XlB0iCsWjQ9HT1+FxOmIiDoOkylDADB//nxMmzYNUVFRiImJwZo1a5CVlYU5c+YAqD/FlZOTgw0bNgAAVqxYgeDgYPTs2RM1NTXYuHEjtmzZgi1btkj5YxDdVmZhBV7fnoL9afWLJno72eKV+8Jwfx+fm54WJiKi1jGpMjR58mQUFRXh9ddfR15eHnr16oWdO3ciKCgIAJCXl4esrCzd/jU1NViwYAFycnJgZ2eHnj17YseOHRg3bpxUPwLRLVXW1GHlvnSsPZSJGo0W1pYyPDk0FHNHduG8ICIiIzGpdYakwHWGqC0IIbDjbB7e2pGKPGU1AGB4Nw8sHh+OUA8HidMREZmeNllnqKamBpmZmejcuTOsrPh/rEStlVlYgVe/O4vD6UUAAH8XOyy6Pxz3hnvxlBgRURvQ+95klZWVmDVrFuzt7dGzZ0/daalnn30Wy5YtM3hAoo6qVqPFJ/vTMWbFQRxOL4LcygLz7umKn+YPx+ie3ixCRERtRO8ytHDhQpw+fRoJCQmwtf3jst577rkHmzdvNmg4oo7qVFYJ7v/oF7y7Ow01dVoM7eqOPc8Pw7x7usHW2lLqeEREZkXv81vfffcdNm/ejEGDBjX6P9fw8HBkZGQYNBxRR1OursN7u9Ow/uhlCAG4drLBa/eHYWJfP44EERFJRO8ydP36dXh6ejbZXlFRwb/MiW5h7/lrWPS/c7oJ0pP6++HV+8Lh2slG4mREROZN79NkAwYMwI4dO3TPGwrQZ599hpiYGMMlI+ogClTV+NvGE5i9IQl5ymoEutpj46xofPBoXxYhIqJ2QO+Robi4OIwdOxbnz59HXV0dPvzwQ6SkpODo0aM4cOCAMTISmSQhBLaczMHS7Skoq66DpYUMs4eG4rm7u8LOhvOCiIjaC71HhgYPHozDhw+jsrISnTt3xp49e+Dl5YWjR48iMjLSGBmJTE5BWTVmbziBBf89jbLqOkT4K7B97hD8M7YHixARUTvDRRdvg4sukr52ns3DK9vOoqSyFtaWMjx/bzc8NawzLC04p46IqK0YfNFFlUrV4g9nYSBzVVpZg0X/S8H3p3MBAGE+Tvjg0QiE+fC/CSKi9qxFZcjZ2fm2V4oJISCTyaDRaAwSjMiU7L9QgJe2nEFBmRqWFjI8PaIz/j6qK2ys9D4TTUREbaxFZWj//v3GzkFkksrVdXhrx3l8fSwbANDZoxPef7Qv+gY4SxuMiIharEVlaPjw4cbOQWRyjmUWY/5/knG1pAoA8MRdIXhxbHeuIE1EZGJadYfVkpISrFu3DqmpqZDJZAgLC8Pjjz8OV1dXQ+cjanc0WoGV+9Lx4c+/QSvqb6z67sMRiOnsJnU0IiJqBb0nNBw4cADBwcH46KOPUFJSguLiYnz00UcICQnhOkPU4eUrqzH1s0T866f6IvRQf3/smjeMRYiIyITpfWl9r169MHjwYKxevRqWlvWnAzQaDZ5++mkcPnwY586dM0pQqfDSemqw78I1LPjvGRRX1MDexhJvPdgLD/bzlzoWERE1Q5/vb73LkJ2dHZKTk9G9e/dG29PS0tC3b19UVVXpn7gdYxmimjotlu+6gLW/ZAIAevo64eO/9EOoh4PEyYiI6GYMvs7Qjfr374/U1NQmZSg1NRV9+/bV9+2I2rUrRRX4+9encOaqEgDw+F3B+GdsD8itOEmaiKijaFEZOnPmjO7Pzz77LJ577jmkp6dj0KBBAIDExER88sknWLZsmXFSEkng+9O5eHnrWZSr6+Bsb413H47AveFeUsciIiIDa9FpMgsLC8hkMtxu14646CJPk5mf6loNlnyfgm+O168dNDDYFR/+pS98FHYSJyMiopYy+GmyzMxMgwQjau9yS6swZ+MJnLmqhEwG/H1UVzw7qgusLLmSNBFRR9WiMhQUFGTsHESSS7xUhGc2nURRRQ1c7K3x8V/6Y0hXd6ljERGRkbVq0UUAOH/+PLKyslBTU9No+wMPPHDHoYjakhAC649cxps7UlGnFQj3ccKn0yIR4GovdTQiImoDepehS5cu4cEHH8TZs2cbzSNquJFrR5szRB1bda0Gr2w7hy0nrwIAJvT1xbJJfWBnw6vFiIjMhd4TIZ577jmEhITg2rVrsLe3R0pKCg4ePIioqCgkJCQYISKRceSWVuHRT49iy8mrsJABr94XhhWT+7IIERGZGb1Hho4ePYp9+/bBw8MDFhYWsLCwwJAhQxAXF4dnn30Wp06dMkZOIoP68/ygT6b2x+AunB9ERGSO9B4Z0mg0cHCoX3nX3d0dubm5AOonWaelpRk2HZGBCSHwxeFMPLb2VxRV1CDcxwnfzx3CIkREZMb0Hhnq1asXzpw5g9DQUERHR2P58uWwsbHBmjVrEBoaaoyMRAZRp9Hitf+dw9fH6tcPmtjXF3GcH0REZPb0LkOvvvoqKioqAABvvvkm7r//fgwdOhRubm7YvHmzwQMSGUKFug7PfHUSCWnXYSEDXh4XhllDQnQT/4mIyHzpfaPW5hQXF8PFxaVDfrFwBWrTV6CqxhPrj+Ncjgq21hb4+C/9eVsNIqIOzqg3am2Oq6urId6GyOAuXivDzC+OI6e0Cm6dbLBu5gD0DXCWOhYREbUjLSpDkyZNQnx8PJycnDBp0qRb7rt161aDBCO6U0czivB/XyahrLoOoe6dEP/4QAS6cSFFIiJqrEVlSKFQ6E6BKRQKowYiMoT/Jefghf+eQY1Gi8ggF6ydHgWXTjZSxyIionZIrzlDQghkZWXBw8MD9vbS/B/2qlWr8O677yIvLw89e/bEihUrMHTo0Jvuf+DAAcyfPx8pKSnw9fXFiy++iDlz5rT48zhnyLQIIbD6QAaW76pf5mFcb2988Ghf2FrzijEiInOiz/e3XusMCSHQtWtX5OTk3FHA1tq8eTPmzZuHV155BadOncLQoUMRGxuLrKysZvfPzMzEuHHjMHToUJw6dQovv/wynn32WWzZsqWNk1NbqNNo8ep353RFaPbQEKz8S38WISIiuiW9rybr2bMn1q1bh0GDBhkr001FR0ejf//+WL16tW5bWFgYJk6ciLi4uCb7v/TSS/j++++Rmpqq2zZnzhycPn0aR48ebfYz1Go11Gq17rlKpUJAQABHhtq56loN5n51Ej+lFkAmAxbfH46Zd4VIHYuIiCRitJEhAFi+fDleeOEFnDt3rtUBW6OmpgYnTpzA6NGjG20fPXo0jhw50uwxR48ebbL/mDFjkJSUhNra2maPiYuLg0Kh0D0CAgIM8wOQ0VTVaDB7QxJ+Si2A3MoC//5rJIsQERG1mN5l6K9//SuOHTuGiIgI2NnZwdXVtdHDWAoLC6HRaODl1Xh9GC8vL+Tn5zd7TH5+frP719XVobCwsNljFi5cCKVSqXtkZ2cb5gcgoyhX12HmF8dw6GIh7G0ssf6JgRjT01vqWEREZEL0XmdoxYoVRojRcn9e2FEIccvFHpvbv7ntDeRyOeRy+R2mpLagqq7FzM+P4WRWKRzlVoh/YgAig7jmFRER6UfvMjRjxgxj5Lgtd3d3WFpaNhkFKigoaDL608Db27vZ/a2srODm5ma0rGR8pZU1mP75MZy5qoTCzhpfzhqIPv7OUsciIiITpPdpshtVVVVBpVI1ehiLjY0NIiMjsXfv3kbb9+7di8GDBzd7TExMTJP99+zZg6ioKFhbWxstKxlXUbkaU9Yk4sxVJVw72eDr2YNYhIiIqNX0LkMVFRWYO3cuPD094eDgABcXl0YPY5o/fz7Wrl2Lzz//HKmpqXj++eeRlZWlWzdo4cKFmD59um7/OXPm4MqVK5g/fz5SU1Px+eefY926dViwYIFRc5LxFKiqMWVNIi7kl8HDUY7N/zcI4b68yo+IiFpP79NkL774Ivbv349Vq1Zh+vTp+OSTT5CTk4NPP/0Uy5YtM0ZGncmTJ6OoqAivv/468vLy0KtXL+zcuRNBQUEAgLy8vEZrDoWEhGDnzp14/vnn8cknn8DX1xcfffQRHnroIaPmJOPILa3CY2t/RWZhBXwUttj0ZDRCPRykjkVERCZO73WGAgMDsWHDBowYMQJOTk44efIkunTpgi+//BJff/01du7caayskuAK1O1DdnEl/vJZIq6WVMHfxQ5fzx6EAFfeZ4yIiJpn1HWGiouLERJSv4aLk5MTiouLAQBDhgzBwYMHWxGX6Nayiysx+dOjuFpShWA3e/znqRgWISIiMhi9y1BoaCguX74MAAgPD8d//vMfAMD27dvh7OxsyGxEKCirxl/X/YpcZTU6e3TCf56Kga+zndSxiIioA9G7DD3++OM4ffo0gPoJy6tWrYJcLsfzzz+PF154weAByXwpq2ox4/PjuFJUiQDX+lNjnk62UsciIqIOpsVzhubNm4cnn3wSvXr1arQ9KysLSUlJ6Ny5MyIiIowSUkqcMySNqhoNpn/+K45fLoG7gxxb/haDILdOUsciIiITYZQ5Q7t27UJERAQGDhyINWvW6NYUCgwMxKRJkzpkESJp1Gq0eOarkzh+uQSOtlb4ctZAFiEiIjKaFpehCxcu4ODBg+jduzcWLFgAX19fTJ8+nZOmyaC0WoEX/nsa+y4UwNbaAp/PHIAwH47IERGR8eg1Z+iuu+7CunXrkJ+fj48//hiXL1/GiBEj0LVrVyxbtgy5ubnGyklmQAiB1384j++Sc2FlIcPqxyIxIJj3GiMiIuPSe52hP8vIyMDnn3+O1atXo7y8HDU1NYbK1i5wzlDb+fCni/jXT7/V/3lKX0zo6ydxIiIiMlVGXWfoRhUVFThw4AAOHDiA0tJSdO7c+U7ejszY+iOXdUVo6QM9WYSIiKjNtKoMHTx4EI8//ji8vb3x3HPPoVu3bjh06BBSU1MNnY/MwP+Sc7D4+xQAwLx7umLG4GBpAxERkVlp8b3Jrl69ivXr1yM+Ph4ZGRmIjo7Gv/71L0yZMgUODrw/FLVOQloB/vGf+nWrZsQE4bm7u0qciIiIzE2Ly1BwcDDc3Nwwbdo0zJo1C2FhYcbMRWYgvaAMc786hTqtwIS+vlg8vidkMpnUsYiIyMy0uAz95z//wQMPPAArK71vdE/UhLKyFk+uT0K5ug4DQ1zx7sMRsLBgESIiorbX4mYzadIkY+YgM1Kn0WLu1ydxuagSfs52WP1Yf9hY3dFcfiIiolbjNxC1uXd2XcChi4Wws7bEmumRcHOQSx2JiIjMGMsQtaktJ67is0OZAID3HolAT1+FxImIiMjcsQxRm0nOLsXCbWcBAH8f1QX39fGROBEREVErytATTzyBsrKyJtsrKirwxBNPGCQUdTwFqmo89WUSauq0uCfMC8/f003qSERERABaUYbWr1+PqqqqJturqqqwYcMGg4SijqW6VoP/+/IErqnU6OrpgH9N5pVjRETUfrT4ajKVSgUhBIQQKCsrg62tre41jUaDnTt3wtPT0yghyXQJIfDKtnNIzi6Fws4aa2dEwdHWWupYREREOi0uQ87OzpDJZJDJZOjWrekpDplMhqVLlxo0HJm+zw9fxpaTV2EhAz6Z2h9Bbp2kjkRERNRIi8vQ/v37IYTAqFGjsGXLFri6uupes7GxQVBQEHx9fY0SkkzTLxcL8daO8wCAV+4Lx5Cu7hInIiIiaqrFZWj48OEAgMzMTAQEBMDCghei0c3lllbhma9OQiuAhyP98cRdwVJHIiIiapbe99YICgpCaWkpjh07hoKCAmi12kavT58+3WDhyDRptQL/+M9pKKtqEeGvwFsP9uI9x4iIqN3Suwxt374djz32GCoqKuDo6NjoS04mk7EMET47dAlHLxXB3sYSK6b0g9zKUupIREREN6X3ua5//OMfurWGSktLUVJSonsUFxcbIyOZkJRcJd7bkwYAWHR/OELcOWGaiIjaN73LUE5ODp599lnY29sbIw+ZsOpaDZ77Jhm1GoHR4V6YPCBA6khERES3pXcZGjNmDJKSkoyRhUxc3M5UpBeUw8NRjmUP9eE8ISIiMgl6zxm677778MILL+D8+fPo3bs3rK0bL6D3wAMPGCwcmY79aQVYf/QKgPobsLp2spE4ERERUcvIhBBCnwNudUm9TCaDRqO541DtiUqlgkKhgFKphJOTk9Rx2qWicjXGrDiEwnI1Zg4OxpIHekodiYiIzJw+3996jwz9+VJ6Mm9CCLy05SwKy9Xo5uWAf8b2kDoSERGRXu5o5cTq6mpD5SAT9c3xbPyUeg02lhZYMbkfbK15GT0REZkWvcuQRqPBG2+8AT8/Pzg4OODSpUsAgNdeew3r1q0zeMAGJSUlmDZtGhQKBRQKBaZNm4bS0tJbHjNz5kzd/dQaHoMGDTJaRnNz6Xo5Xt9ef7uNBWO6IdyXpxGJiMj06F2G3nrrLcTHx2P58uWwsfljkmzv3r2xdu1ag4a70dSpU5GcnIxdu3Zh165dSE5OxrRp02573NixY5GXl6d77Ny502gZzUmtRovnNyejqlaDwZ3d8OSQUKkjERERtYrec4Y2bNiANWvW4O6778acOXN02/v06YMLFy4YNFyD1NRU7Nq1C4mJiYiOjgYAfPbZZ4iJiUFaWhq6d+9+02Plcjm8vb1b/FlqtRpqtVr3XKVStT54B/bhTxdx+qoSTrZWeP/RCFhY8DJ6IiIyTa1adLFLly5Ntmu1WtTW1hok1J8dPXoUCoVCV4QAYNCgQVAoFDhy5Mgtj01ISICnpye6deuG2bNno6Cg4Jb7x8XF6U7FKRQKBARw4cA/O3GlGKsS0gEAb0/qDR+FncSJiIiIWk/vMtSzZ08cOnSoyfb//ve/6Nevn0FC/Vl+fj48PT2bbPf09ER+fv5Nj4uNjcWmTZuwb98+vP/++zh+/DhGjRrVaOTnzxYuXAilUql7ZGdnG+Rn6CjqNFq8su0ctAKY1M8P9/fxlToSERHRHdH7NNnixYsxbdo05OTkQKvVYuvWrUhLS8OGDRvwww8/6PVeS5YswdKlS2+5z/HjxwGg2dWMhRC3XOV48uTJuj/36tULUVFRCAoKwo4dOzBp0qRmj5HL5ZDL5S2Jb5a+TLyCC/llcLa3xmv3h0sdh4iI6I7pXYbGjx+PzZs34+2334ZMJsOiRYvQv39/bN++Hffee69e7zV37lxMmTLllvsEBwfjzJkzuHbtWpPXrl+/Di8vrxZ/no+PD4KCgnDx4kW9clK962VqfLDnNwDAC2O6w4WrTBMRUQegdxkC6u9PNmbMmDv+cHd3d7i7u992v5iYGCiVShw7dgwDBw4EAPz6669QKpUYPHhwiz+vqKgI2dnZ8PHxaXVmc7bsxwsoU9eht58CUwYESh2HiIjIIO5o0cW2EhYWhrFjx2L27NlITExEYmIiZs+ejfvvv7/RlWQ9evTAtm3bAADl5eVYsGABjh49isuXLyMhIQHjx4+Hu7s7HnzwQal+FJN14koxtpy8CgBYOqEnLHn1GBERdRAtGhlycXFp8R3Ii4uL7yjQzWzatAnPPvssRo8eDaD+hrArV65stE9aWhqUSiUAwNLSEmfPnsWGDRtQWloKHx8fjBw5Eps3b4ajo6NRMnZUGq3Aa9+lAAAejfJH/0AXiRMREREZTovK0IoVK3R/LioqwptvvokxY8YgJiYGQP2l77t378Zrr71mlJAA4Orqio0bN95ynxvvOWtnZ4fdu3cbLY85+erXKzifp4KTrRVeGst7jxERUcei913rH3roIYwcORJz585ttH3lypX46aef8N133xkyn+TM/a71ReVqjHwvAarqOrw+oSemxwRLHYmIiOi29Pn+1nvO0O7duzF27Ngm28eMGYOffvpJ37ejdm75rjSoqusQ7uOEx6KDpI5DRERkcHqXITc3N90k5Rt99913cHNzM0goah9OZZVgc1L9opOvc9I0ERF1UHpfWr906VLMmjULCQkJujlDiYmJ2LVrl1Fv1EptS6MVWPS/+knTk/r7ISrYVeJERERExqF3GZo5cybCwsLw0UcfYevWrRBCIDw8HIcPH2507zAybZuPZ+NsjhKOcissjA2TOg4REZHRtGrRxejoaGzatMnQWaidKKmowfLdFwAAz9/bDR6OvD0JERF1XK0qQ1qtFunp6SgoKIBWq2302rBhwwwSjKTz7p40lFbWoruXI6bHcNI0ERF1bHqXocTEREydOhVXrlzBn6/Kl8lk0Gg0BgtHbe/M1VJ8fSwLQP2kaStLk1iknIiIqNX0LkNz5sxBVFQUduzYAR8fnxavTE3tnxACS75PgRDAhL6+iA7l1YFERNTx6V2GLl68iG+//RZdunQxRh6S0KGLhTiZVQq5lQVeHsdJ00REZB70PgcSHR2N9PR0Y2Qhia3cV//PdWp0ILycbCVOQ0RE1Db0Hhn6+9//jn/84x/Iz89H7969YW1t3ej1Pn36GCwctZ3ES0U4drkYNpYWeGpYZ6njEBERtRm9y9BDDz0EAHjiiSd022QyGYQQnEBtwj7edxEA8OgAf3grOCpERETmQ+8ylJmZaYwcJKETV0pwOL0IVhYyzBnOUSEiIjIvepehoCCuO9PRNIwKTervB38Xe4nTEBERta1WLSLz5Zdf4q677oKvry+uXLkCAFixYgX+97//GTQcGd/Zq0okpF2HhQx4egSvECQiIvOjdxlavXo15s+fj3HjxqG0tFQ3R8jZ2RkrVqwwdD4ysoZRoQl9/RDs3kniNERERG1P7zL08ccf47PPPsMrr7wCS0tL3faoqCicPXvWoOHIuFLzVNhz/hpkMuCZkRwVIiIi86R3GcrMzES/fv2abJfL5aioqDBIKGobK/fXrys0rrcPung6SJyGiIhIGnqXoZCQECQnJzfZ/uOPPyI8PNwQmagNpBeUY+fZPADA30dxVIiIiMyX3leTvfDCC3jmmWdQXV0NIQSOHTuGr7/+GnFxcVi7dq0xMpIRrNqfDiGA0eFe6OHtJHUcIiIiyehdhh5//HHU1dXhxRdfRGVlJaZOnQo/Pz98+OGHmDJlijEykoFdKarA/07nAgD+PqqrxGmIiIikpXcZAoDZs2dj9uzZKCwshFarhaenp6FzkRGt2p8BjVZgRHcP9PZXSB2HiIhIUq0qQwBQUFCAtLQ0yGQyyGQyeHh4GDIXGcnVkkpsOXkVAEeFiIiIgFZMoFapVJg2bRp8fX0xfPhwDBs2DL6+vvjrX/8KpVJpjIxkQJ8euIQ6rcBdXdwQGeQidRwiIiLJ6V2GnnzySfz666/YsWMHSktLoVQq8cMPPyApKQmzZ882RkYykGuqamxOygbAUSEiIqIGep8m27FjB3bv3o0hQ4boto0ZMwafffYZxo4da9BwZFifHriEmjotBga7YlCom9RxiIiI2gW9R4bc3NygUDSddKtQKODiwtMu7VVhuRpfHau/j9zf7+a6QkRERA30LkOvvvoq5s+fj7y8PN22/Px8vPDCC3jttdcMGo4M59sTV1Fdq0WEvwJDurhLHYeIiKjd0Ps02erVq5Geno6goCAEBgYCALKysiCXy3H9+nV8+umnun1PnjxpuKTUakII/Pf3uUJTowMhk8kkTkRERNR+6F2GJk6caIQYZEynskuRcb0CttYWGNfbR+o4RERE7YreZWjx4sXGyEFG9N+k+nWFxvXygaOttcRpiIiI2he95wwBQGlpKdauXYuFCxeiuLgYQP0psZycHIOGu9Fbb72FwYMHw97eHs7Ozi06RgiBJUuWwNfXF3Z2dhgxYgRSUlKMlrE9qq7V4Iffb73xcJS/xGmIiIjaH73L0JkzZ9CtWze88847eO+991BaWgoA2LZtGxYuXGjofDo1NTV45JFH8Le//a3FxyxfvhwffPABVq5ciePHj8Pb2xv33nsvysrKjJazvdmdko8ydR38XewwKISX0xMREf2Z3mVo/vz5mDlzJi5evAhbW1vd9tjYWBw8eNCg4W60dOlSPP/88+jdu3eL9hdCYMWKFXjllVcwadIk9OrVC+vXr0dlZSW++uqrmx6nVquhUqkaPUxZwymyh/r7w8KCE6eJiIj+TO8ydPz4cTz11FNNtvv5+SE/P98goQwhMzMT+fn5GD16tG6bXC7H8OHDceTIkZseFxcXB4VCoXsEBAS0RVyjyCmtwuGMQgDAw5E8RUZERNQcvcuQra1ts6MlaWlp7epmrQ3FzMvLq9F2Ly+vW5a2hQsXQqlU6h7Z2dlGzWlMW05chRBATKgbAlztpY5DRETULuldhiZMmIDXX38dtbW1AACZTIasrCz885//xEMPPaTXey1ZskR31/ubPZKSkvSN2Mif19QRQtxynR25XA4nJ6dGD1Ok1Qp8e6L+FNkjnDhNRER0U3pfWv/ee+9h3Lhx8PT0RFVVFYYPH478/HzExMTgrbfe0uu95s6diylTptxyn+DgYH0jAgC8vb0B1I8Q+fj8sbZOQUFBk9Gijuj45WJkFVfCQW6Fsb28pY5DRETUbuldhpycnPDLL79g3759OHnyJLRaLfr374977rlH7w93d3eHu7txbg0REhICb29v7N27F/369QNQf0XagQMH8M477xjlM9uT//4+KnRfbx/Y2+j9j5mIiMhstPpbctSoURg1apQhs9xSVlYWiouLkZWVBY1Gg+TkZABAly5d4ODgAADo0aMH4uLi8OCDD0Imk2HevHl4++230bVrV3Tt2hVvv/027O3tMXXq1DbLLYUKdR12nq2/dxxPkREREd2aXmVIq9UiPj4eW7duxeXLlyGTyRASEoKHH34Y06ZNM+o9rxYtWoT169frnjeM9uzfvx8jRowAUD+JW6lU6vZ58cUXUVVVhaeffholJSWIjo7Gnj174OjoaLSc7cGOs3morNEg1L0TIoNcpI5DRETUrsmEEKIlOwohMH78eOzcuRMRERHo0aMHhBBITU3F2bNn8cADD+C7774zcty2p1KpoFAooFQqTWYy9aP/Popjl4vxwpjueGZkF6njEBERtTl9vr9bPDIUHx+PgwcP4ueff8bIkSMbvbZv3z5MnDgRGzZswPTp01uXmgzicmEFjl0uhoUMmNTfT+o4RERE7V6LL63/+uuv8fLLLzcpQkD9/KF//vOf2LRpk0HDkf62nKyfOD2kqwd8FHYSpyEiImr/WlyGzpw5g7Fjx9709djYWJw+fdogoah1NFqBLQ1rC3HFaSIiohZpcRkqLi6+5fo8Xl5eKCkpMUgoap0jGYXIVVbDydYK94Z3/LWUiIiIDKHFZUij0cDK6uZTjCwtLVFXV2eQUNQ6DTdlndDXD7bWlhKnISIiMg0tnkAthMDMmTMhl8ubfV2tVhssFOlPWVWL3Sn191zjTVmJiIharsVlaMaMGbfdh1eSSeeHM7lQ12nRzcsBffwVUschIiIyGS0uQ1988YUxc9AdajhF9khkgFEXvyQiIupo9L5rPbU/6QVlSM4uhaWFDBP7cW0hIiIifbAMdQANN2Ud2d0THo7Nz+kiIiKi5rEMdQA/pxYAACb285U4CRERkelhGTJx+cpqpBeUQyYDhnRxlzoOERGRyWEZMnG/pBcCAPr4KeBsbyNxGiIiItPDMmTifrl4HQAwpCtHhYiIiFqDZciECSHwS3oRAOAuniIjIiJqFZYhE5Z2rQyF5WrYWVsiMshF6jhEREQmiWXIhP1ysX6+0MAQV8iteC8yIiKi1mAZMmGHfi9DvIqMiIio9ViGTJS6ToNjmcUAOHmaiIjoTrAMmaiTV0pRVauBu4MNeng7Sh2HiIjIZLEMmahf0usvqb+riztvzEpERHQHWIZMVMMl9ZwvREREdGdYhkyQsrIWZ6+WAgCGdvWQNgwREZGJYxkyQUcyCqEVQBdPB3grbKWOQ0REZNJYhkzQoXReUk9ERGQoLEMm6DDLEBERkcGwDJmY7OJKXCmqhKWFDIM6u0kdh4iIyOSxDJmYhlWn+wU4w0FuJXEaIiIi08cyZGJ0p8i46jQREZFBsAyZEI1W4HBGfRkayjJERERkECxDJiQlV4nSylo4yK0Q4e8sdRwiIqIOgWXIhPzy+ymyQaFusLLkPzoiIiJDMJlv1LfeeguDBw+Gvb09nJ2dW3TMzJkzIZPJGj0GDRpk3KBG9MtFniIjIiIyNJMpQzU1NXjkkUfwt7/9Ta/jxo4di7y8PN1j586dRkpoXFU1GiRdLgHAydNERESGZDLXZi9duhQAEB8fr9dxcrkc3t7eRkjUto5dLkaNRgsfhS1C3TtJHYeIiKjDMJmRodZKSEiAp6cnunXrhtmzZ6OgoOCW+6vVaqhUqkaP9uDGVadlMpnEaYiIiDqODl2GYmNjsWnTJuzbtw/vv/8+jh8/jlGjRkGtVt/0mLi4OCgUCt0jICCgDRPfXMNiizxFRkREZFiSlqElS5Y0meD850dSUlKr33/y5Mm477770KtXL4wfPx4//vgjfvvtN+zYseOmxyxcuBBKpVL3yM7ObvXnG8r1MjVS8+pHqO7i/ciIiIgMStI5Q3PnzsWUKVNuuU9wcLDBPs/HxwdBQUG4ePHiTfeRy+WQy+UG+0xDOPL7QothPk5wd2hf2YiIiEydpGXI3d0d7u5tN9JRVFSE7Oxs+Pj4tNlnGgIvqSciIjIek5kzlJWVheTkZGRlZUGj0SA5ORnJyckoLy/X7dOjRw9s27YNAFBeXo4FCxbg6NGjuHz5MhISEjB+/Hi4u7vjwQcflOrH0JsQQrfY4hCeIiMiIjI4k7m0ftGiRVi/fr3ueb9+/QAA+/fvx4gRIwAAaWlpUCqVAABLS0ucPXsWGzZsQGlpKXx8fDBy5Ehs3rwZjo6ObZ6/tTKuVyBPWQ0bSwsMCHaVOg4REVGHYzJlKD4+/rZrDAkhdH+2s7PD7t27jZzK+BouqY8KdoGdjaXEaYiIiDoekzlNZq54ST0REZFxsQy1Y3UaLRIvFQHgfCEiIiJjYRlqxy4XVaJcXQd7G0v09FVIHYeIiKhDYhlqxzKu118p19nDAZYWvAUHERGRMbAMtWN/lCHemJWIiMhYWIbasfSCP0aGiIiIyDhYhtqxjOsVAIDOnixDRERExsIy1E4JIXDp95GhLixDRERERsMy1E5dL1OjTF0HCxkQ5GYvdRwiIqIOi2WonUr/ffJ0oKs95FZceZqIiMhYWIbaKd18IU6eJiIiMiqWoXYqo+FKMs4XIiIiMiqWoXaKawwRERG1DZahdiqDV5IRERG1CZahdqhCXYdcZTUAINSdZYiIiMiYWIbaoczC+snTbp1s4NLJRuI0REREHRvLUDvE23AQERG1HZahdkg3edqTk6eJiIiMjWWoHfrjSjKODBERERkby1A7lFHAG7QSERG1FZahdkajFboJ1F04MkRERGR0LEPtzNWSStRotJBbWcDX2U7qOERERB0ey1A703AlWYh7J1hayCROQ0RE1PGxDLUzf1xJxlNkREREbYFlqJ1pmDzN+UJERERtg2WoneHIEBERUdtiGWpneLd6IiKitsUy1I4UlatRUlkLgDdoJSIiaissQ+1IxvX6+UJ+znaws7GUOA0REZF5YBlqRxpOkXXhfCEiIqI2wzLUjmTwbvVERERtjmWoHeHd6omIiNqeSZShy5cvY9asWQgJCYGdnR06d+6MxYsXo6am5pbHCSGwZMkS+Pr6ws7ODiNGjEBKSkobpdZfw5whjgwRERG1HZMoQxcuXIBWq8Wnn36KlJQU/Otf/8K///1vvPzyy7c8bvny5fjggw+wcuVKHD9+HN7e3rj33ntRVlbWRslbrrpWg+ySSgAsQ0RERG1JJoQQUodojXfffRerV6/GpUuXmn1dCAFfX1/MmzcPL730EgBArVbDy8sL77zzDp566qkWfY5KpYJCoYBSqYSTk5PB8v9Zap4KsR8egsLOGsmL7oVMxvuSERERtZY+398mMTLUHKVSCVdX15u+npmZifz8fIwePVq3TS6XY/jw4Thy5MhNj1Or1VCpVI0ebeHGxRZZhIiIiNqOSZahjIwMfPzxx5gzZ85N98nPzwcAeHl5Ndru5eWle605cXFxUCgUukdAQIBhQt9Gwz3JeIqMiIiobUlahpYsWQKZTHbLR1JSUqNjcnNzMXbsWDzyyCN48sknb/sZfx5lEULccuRl4cKFUCqVukd2dnbrfjg98Z5kRERE0rCS8sPnzp2LKVOm3HKf4OBg3Z9zc3MxcuRIxMTEYM2aNbc8ztvbG0D9CJGPj49ue0FBQZPRohvJ5XLI5fIWpDesdK4xREREJAlJy5C7uzvc3d1btG9OTg5GjhyJyMhIfPHFF7CwuPWgVkhICLy9vbF3717069cPAFBTU4MDBw7gnXfeuePshqTVClwq5A1aiYiIpGASc4Zyc3MxYsQIBAQE4L333sP169eRn5/fZO5Pjx49sG3bNgD1p8fmzZuHt99+G9u2bcO5c+cwc+ZM2NvbY+rUqVL8GDeVq6xCda0W1pYyBLraSx2HiIjIrEg6MtRSe/bsQXp6OtLT0+Hv79/otRtXBkhLS4NSqdQ9f/HFF1FVVYWnn34aJSUliI6Oxp49e+Do6Nhm2VuiYbHFYLdOsLI0iX5KRETUYZjsOkNtpS3WGfr8l0y8/sN5jO3pjX9PizTKZxAREZkTs1hnqCPhPcmIiIikwzLUDvBKMiIiIumwDLUDDXOGunCNISIiojbHMiQxZWUtCsvVAIBQjgwRERG1OZYhiWX8vr6Qt5MtHOQmcXEfERFRh8IyJLGMAk6eJiIikhLLkMTSr3PyNBERkZRYhiTWcLd6Tp4mIiKSBsuQxC5xZIiIiEhSLEMSqqnT4kpxJQCWISIiIqmwDEkoq7gCGq1AJxtLeDnJpY5DRERklliGJKRbedrTATKZTOI0RERE5ollSEINK0/zFBkREZF0WIYk1LDGEK8kIyIikg7LkIR0d6v34IKLREREUmEZkogQgqfJiIiI2gGWIYkUlKlRrq6DpYUMgW72UschIiIyWyxDEmm4kizQ1R5yK0uJ0xAREZkvliGJZHDlaSIionaBZUgi5eo62Fpb8G71REREEpMJIYTUIdozlUoFhUIBpVIJJycng763ViugrtPCzoanyYiIiAxJn+9vjgxJyMJCxiJEREQkMZYhIiIiMmssQ0RERGTWWIaIiIjIrLEMERERkVljGSIiIiKzxjJEREREZo1liIiIiMwayxARERGZNZYhIiIiMmssQ0RERGTWWIaIiIjIrLEMERERkVljGSIiIiKzZiV1gPZOCAEAUKlUEichIiKilmr43m74Hr8VlqHbKCsrAwAEBARInISIiIj0VVZWBoVCcct9ZKIllcmMabVa5ObmwtHRETKZrEXHqFQqBAQEIDs7G05OTkZOSA34e5cGf+/S4O9dGvy9S6M1v3chBMrKyuDr6wsLi1vPCuLI0G1YWFjA39+/Vcc6OTnxPxYJ8PcuDf7epcHfuzT4e5eGvr/3240INeAEaiIiIjJrLENERERk1liGjEAul2Px4sWQy+VSRzEr/L1Lg793afD3Lg3+3qVh7N87J1ATERGRWePIEBEREZk1liEiIiIyayxDREREZNZYhoiIiMissQwZwapVqxASEgJbW1tERkbi0KFDUkfq0A4ePIjx48fD19cXMpkM3333ndSRzEJcXBwGDBgAR0dHeHp6YuLEiUhLS5M6Voe3evVq9OnTR7f4XExMDH788UepY5mVuLg4yGQyzJs3T+ooHd6SJUsgk8kaPby9vQ3+OSxDBrZ582bMmzcPr7zyCk6dOoWhQ4ciNjYWWVlZUkfrsCoqKhAREYGVK1dKHcWsHDhwAM888wwSExOxd+9e1NXVYfTo0aioqJA6Wofm7++PZcuWISkpCUlJSRg1ahQmTJiAlJQUqaOZhePHj2PNmjXo06eP1FHMRs+ePZGXl6d7nD171uCfwUvrDSw6Ohr9+/fH6tWrddvCwsIwceJExMXFSZjMPMhkMmzbtg0TJ06UOorZuX79Ojw9PXHgwAEMGzZM6jhmxdXVFe+++y5mzZoldZQOrby8HP3798eqVavw5ptvom/fvlixYoXUsTq0JUuW4LvvvkNycrJRP4cjQwZUU1ODEydOYPTo0Y22jx49GkeOHJEoFVHbUCqVAOq/mKltaDQafPPNN6ioqEBMTIzUcTq8Z555Bvfddx/uueceqaOYlYsXL8LX1xchISGYMmUKLl26ZPDP4I1aDaiwsBAajQZeXl6Ntnt5eSE/P1+iVETGJ4TA/PnzMWTIEPTq1UvqOB3e2bNnERMTg+rqajg4OGDbtm0IDw+XOlaH9s033+DkyZM4fvy41FHMSnR0NDZs2IBu3brh2rVrePPNNzF48GCkpKTAzc3NYJ/DMmQEMpms0XMhRJNtRB3J3LlzcebMGfzyyy9SRzEL3bt3R3JyMkpLS7FlyxbMmDEDBw4cYCEykuzsbDz33HPYs2cPbG1tpY5jVmJjY3V/7t27N2JiYtC5c2esX78e8+fPN9jnsAwZkLu7OywtLZuMAhUUFDQZLSLqKP7+97/j+++/x8GDB+Hv7y91HLNgY2ODLl26AACioqJw/PhxfPjhh/j0008lTtYxnThxAgUFBYiMjNRt02g0OHjwIFauXAm1Wg1LS0sJE5qPTp06oXfv3rh48aJB35dzhgzIxsYGkZGR2Lt3b6Pte/fuxeDBgyVKRWQcQgjMnTsXW7duxb59+xASEiJ1JLMlhIBarZY6Rod199134+zZs0hOTtY9oqKi8NhjjyE5OZlFqA2p1WqkpqbCx8fHoO/LkSEDmz9/PqZNm4aoqCjExMRgzZo1yMrKwpw5c6SO1mGVl5cjPT1d9zwzMxPJyclwdXVFYGCghMk6tmeeeQZfffUV/ve//8HR0VE3IqpQKGBnZydxuo7r5ZdfRmxsLAICAlBWVoZvvvkGCQkJ2LVrl9TROixHR8cmc+E6deoENzc3zpEzsgULFmD8+PEIDAxEQUEB3nzzTahUKsyYMcOgn8MyZGCTJ09GUVERXn/9deTl5aFXr17YuXMngoKCpI7WYSUlJWHkyJG65w3nkWfMmIH4+HiJUnV8DctHjBgxotH2L774AjNnzmz7QGbi2rVrmDZtGvLy8qBQKNCnTx/s2rUL9957r9TRiAzu6tWr+Mtf/oLCwkJ4eHhg0KBBSExMNPh3KtcZIiIiIrPGOUNERERk1liGiIiIyKyxDBEREZFZYxkiIiIis8YyRERERGaNZYiIiIjMGssQERERmTWWISIiIjJrLENEdFsymQzfffed1DFaZMmSJejbt6/UMQxuxIgRmDdvXov3T0hIgEwmQ2lp6U33iY+Ph7Oz8x1nIzJ1LENEHdjMmTMxceJEqWOYvJaUhvfffx8KhQKVlZVNXquuroazszM++OCDVmfYunUr3njjjVYfT0Q3xzJERGQA06dPR1VVFbZs2dLktS1btqCyshLTpk3T+31ra2sBAK6urnB0dLzjnETUFMsQkRkZMWIEnn32Wbz44otwdXWFt7c3lixZ0mifixcvYtiwYbC1tUV4eDj27t3b5H1ycnIwefJkuLi4wM3NDRMmTMDly5d1rzeMSC1duhSenp5wcnLCU089hZqaGt0+QggsX74coaGhsLOzQ0REBL799lvd6w2neX7++WdERUXB3t4egwcPRlpaWqMsy5Ytg5eXFxwdHTFr1ixUV1c3yfvFF18gLCwMtra26NGjB1atWqV77fLly5DJZNi6dStGjhwJe3t7RERE4OjRo7ocjz/+OJRKJWQyGWQyWZPfGQB4eHhg/Pjx+Pzzz5u89vnnn+OBBx6Ah4cHXnrpJXTr1g329vYIDQ3Fa6+9pis8wB+n+T7//HOEhoZCLpdDCNHkNNnGjRsRFRUFR0dHeHt7Y+rUqSgoKGjy2YcPH0ZERARsbW0RHR2Ns2fPNtnnRtu3b0dkZCRsbW0RGhqKpUuXoq6u7pbHEJk8QUQd1owZM8SECRN0z4cPHy6cnJzEkiVLxG+//SbWr18vZDKZ2LNnjxBCCI1GI3r16iVGjBghTp06JQ4cOCD69esnAIht27YJIYSoqKgQXbt2FU888YQ4c+aMOH/+vJg6daro3r27UKvVus91cHAQkydPFufOnRM//PCD8PDwEC+//LIuy8svvyx69Oghdu3aJTIyMsQXX3wh5HK5SEhIEEIIsX//fgFAREdHi4SEBJGSkiKGDh0qBg8erHuPzZs3CxsbG/HZZ5+JCxcuiFdeeUU4OjqKiIgI3T5r1qwRPj4+YsuWLeLSpUtiy5YtwtXVVcTHxwshhMjMzBQARI8ePcQPP/wg0tLSxMMPPyyCgoJEbW2tUKvVYsWKFcLJyUnk5eWJvLw8UVZW1uzve8eOHUImk4lLly7ptmVmZgqZTCZ27twphBDijTfeEIcPHxaZmZni+++/F15eXuKdd97R7b948WLRqVMnMWbMGHHy5Elx+vRpodVqxfDhw8Vzzz2n22/dunVi586dIiMjQxw9elQMGjRIxMbG6l5v+P2FhYWJPXv2iDNnzoj7779fBAcHi5qaGiGEEF988YVQKBS6Y3bt2iWcnJxEfHy8yMjIEHv27BHBwcFiyZIlzf8LRtRBsAwRdWDNlaEhQ4Y02mfAgAHipZdeEkIIsXv3bmFpaSmys7N1r//444+NytC6detE9+7dhVar1e2jVquFnZ2d2L17t+5zXV1dRUVFhW6f1atXCwcHB6HRaER5ebmwtbUVR44caZRl1qxZ4i9/+YsQ4o8v859++kn3+o4dOwQAUVVVJYQQIiYmRsyZM6fRe0RHRzcqQwEBAeKrr75qtM8bb7whYmJihBB/lKG1a9fqXk9JSREARGpqqhCiaWm4mbq6OuHn5ycWLVqk27Zo0SLh5+cn6urqmj1m+fLlIjIyUvd88eLFwtraWhQUFDTa789l6M+OHTsmAOiKWsPv75tvvtHtU1RUJOzs7MTmzZub/bmGDh0q3n777Ubv++WXXwofH59b/+BEJs5KogEpIpJInz59Gj338fHRnV5JTU1FYGAg/P39da/HxMQ02v/EiRNIT09vMn+luroaGRkZuucRERGwt7dv9D7l5eXIzs5GQUEBqqurce+99zZ6j5qaGvTr1++meX18fAAABQUFCAwMRGpqKubMmdNo/5iYGOzfvx8AcP36dWRnZ2PWrFmYPXu2bp+6ujooFIoWfU6PHj3QUpaWlpgxYwbi4+OxePFiyGQyrF+/HjNnzoSlpSUA4Ntvv8WKFSuQnp6O8vJy1NXVwcnJqdH7BAUFwcPD45afderUKSxZsgTJyckoLi6GVqsFAGRlZSE8PLzR76OBq6srunfvjtTU1Gbf88SJEzh+/Djeeust3TaNRoPq6mpUVlY2+udJ1JGwDBGZGWtr60bPZTKZ7otUCNFkf5lM1ui5VqtFZGQkNm3a1GTf232B//nzduzYAT8/v0avy+Xym+ZtyNJw/O007PfZZ58hOjq60WsN5cQQn3OjJ554AnFxcdi3bx+A+nLy+OOPAwASExMxZcoULF26FGPGjIFCocA333yD999/v9F7dOrU6ZafUVFRgdGjR2P06NHYuHEjPDw8kJWVhTFjxjSal3Uzf/5n2kCr1WLp0qWYNGlSk9dsbW1v+75EpopliIh0wsPDkZWVhdzcXPj6+gKAbiJxg/79+2Pz5s26idE3c/r0aVRVVcHOzg5AfRFwcHCAv78/XFxcIJfLkZWVheHDh7c6b1hYGBITEzF9+nTdtsTERN2fvby84Ofnh0uXLuGxxx5r9efY2NhAo9G0aN/OnTtj+PDh+OKLL3QTnzt37gygfjJzUFAQXnnlFd3+V65c0TvPhQsXUFhYiGXLliEgIAAAkJSU1Oy+iYmJCAwMBACUlJTgt99+u+loV//+/ZGWloYuXbronYnIlLEMEZHOPffcg+7du2P69Ol4//33oVKpGn1xA8Bjjz2Gd999FxMmTMDrr78Of39/ZGVlYevWrXjhhRd0p9hqamowa9YsvPrqq7hy5QoWL16MuXPnwsLCAo6OjliwYAGef/55aLVaDBkyBCqVCkeOHIGDgwNmzJjRorzPPfccZsyYgaioKAwZMgSbNm1CSkoKQkNDdfssWbIEzz77LJycnBAbGwu1Wo2kpCSUlJRg/vz5Lfqc4OBglJeX4+eff9ad/rvVKaMbT8utXbtWt71Lly7IysrCN998gwEDBmDHjh3Ytm1bizLcKDAwEDY2Nvj4448xZ84cnDt37qZrEL3++utwc3ODl5cXXnnlFbi7u9907alFixbh/vvvR0BAAB555BFYWFjgzJkzOHv2LN588029cxKZCl5aT0Q6FhYW2LZtG9RqNQYOHIgnn3yy0fwRALC3t8fBgwcRGBiISZMmISwsDE888QSqqqoajRTdfffd6Nq1K4YNG4ZHH30U48ePb3RJ+htvvIFFixYhLi4OYWFhGDNmDLZv346QkJAW5508eTIWLVqEl156CZGRkbhy5Qr+9re/NdrnySefxNq1axEfH4/evXtj+PDhiI+P1+tzBg8ejDlz5mDy5Mnw8PDA8uXLb7n/Qw89BLlcDrlc3uiU04QJE/D8889j7ty56Nu3L44cOYLXXnutxTkaeHh4ID4+Hv/9738RHh6OZcuW4b333mt232XLluG5555DZGQk8vLy8P3338PGxqbZfceMGYMffvgBe/fuxYABAzBo0CB88MEHCAoK0jsjkSmRieYmCRAR3YGZM2eitLTUZG7hQUTmjSNDREREZNZYhoiIiMis8TQZERERmTWODBEREZFZYxkiIiIis8YyRERERGaNZYiIiIjMGssQERERmTWWISIiIjJrLENERERk1liGiIiIyKz9P1m3lW0a/c3hAAAAAElFTkSuQmCC\n",
+ "text/plain": [
+ "
"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "X = np.arange(-5.0, 5.0, 0.1)\n",
+ "\n",
+ "\n",
+ "Y = 1-4/(1+np.power(3, X-2))\n",
+ "\n",
+ "plt.plot(X,Y) \n",
+ "plt.ylabel('Dependent Variable')\n",
+ "plt.xlabel('Independent Variable')\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "\n",
+ "# Non-Linear Regression example\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "For an example, we're going to try and fit a non-linear model to the datapoints corresponding to China's GDP from 1960 to 2014. We download a dataset with two columns, the first, a year between 1960 and 2014, the second, China's corresponding annual gross domestic income in US dollars for that year. \n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "2025-10-20 10:37:17 URL:https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-ML0101EN-SkillsNetwork/labs/Module%202/data/china_gdp.csv [1218/1218] -> \"china_gdp.csv\" [1]\n"
+ ]
+ },
+ {
+ "data": {
+ "text/html": [
+ "
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+ "\n",
+ "
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+ " \n",
+ "
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+ "
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+ "
Year
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+ "
Value
\n",
+ "
\n",
+ " \n",
+ " \n",
+ "
\n",
+ "
0
\n",
+ "
1960
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+ "
5.918412e+10
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+ "
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+ "
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+ "
1
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+ "
1961
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+ "
4.955705e+10
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+ "
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+ "
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+ "
2
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+ "
1962
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+ "
4.668518e+10
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+ "
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+ "
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+ "
3
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+ "
1963
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+ "
5.009730e+10
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+ "
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+ "
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+ "
4
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+ "
1964
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+ "
5.906225e+10
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+ "
\n",
+ "
\n",
+ "
5
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+ "
1965
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+ "
6.970915e+10
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+ "
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+ "
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+ "
6
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+ "
1966
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+ "
7.587943e+10
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+ "
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+ "
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+ "
7
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+ "
1967
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+ "
7.205703e+10
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+ "
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+ "
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+ "
8
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+ "
1968
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+ "
6.999350e+10
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+ "
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+ "
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+ "
9
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+ "
1969
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+ "
7.871882e+10
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+ "
\n",
+ " \n",
+ "
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+ "
"
+ ],
+ "text/plain": [
+ " Year Value\n",
+ "0 1960 5.918412e+10\n",
+ "1 1961 4.955705e+10\n",
+ "2 1962 4.668518e+10\n",
+ "3 1963 5.009730e+10\n",
+ "4 1964 5.906225e+10\n",
+ "5 1965 6.970915e+10\n",
+ "6 1966 7.587943e+10\n",
+ "7 1967 7.205703e+10\n",
+ "8 1968 6.999350e+10\n",
+ "9 1969 7.871882e+10"
+ ]
+ },
+ "execution_count": 8,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "import numpy as np\n",
+ "import pandas as pd\n",
+ "\n",
+ "#downloading dataset\n",
+ "!wget -nv -O china_gdp.csv https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-ML0101EN-SkillsNetwork/labs/Module%202/data/china_gdp.csv\n",
+ " \n",
+ "df = pd.read_csv(\"china_gdp.csv\")\n",
+ "df.head(10)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "__Did you know?__ When it comes to Machine Learning, you will likely be working with large datasets. As a business, where can you host your data? IBM is offering a unique opportunity for businesses, with 10 Tb of IBM Cloud Object Storage: [Sign up now for free](http://cocl.us/ML0101EN-IBM-Offer-CC)\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Plotting the Dataset ###\n",
+ "This is what the datapoints look like. It kind of looks like an either logistic or exponential function. The growth starts off slow, then from 2005 on forward, the growth is very significant. And finally, it decelerates slightly in the 2010s.\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "
"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.figure(figsize=(8,5))\n",
+ "x_data, y_data = (df[\"Year\"].values, df[\"Value\"].values)\n",
+ "plt.plot(x_data, y_data, 'ro')\n",
+ "plt.ylabel('GDP')\n",
+ "plt.xlabel('Year')\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Choosing a model ###\n",
+ "\n",
+ "From an initial look at the plot, we determine that the logistic function could be a good approximation,\n",
+ "since it has the property of starting with a slow growth, increasing growth in the middle, and then decreasing again at the end; as illustrated below:\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "
"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "X = np.arange(-5.0, 5.0, 0.1)\n",
+ "Y = 1.0 / (1.0 + np.exp(-X))\n",
+ "\n",
+ "plt.plot(X,Y) \n",
+ "plt.ylabel('Dependent Variable')\n",
+ "plt.xlabel('Independent Variable')\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "\n",
+ "\n",
+ "The formula for the logistic function is the following:\n",
+ "\n",
+ "$$ \\hat{Y} = \\frac1{1+e^{-\\beta_1(X-\\beta_2)}}$$\n",
+ "\n",
+ "$\\beta_1$: Controls the curve's steepness,\n",
+ "\n",
+ "$\\beta_2$: Slides the curve on the x-axis.\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Building The Model ###\n",
+ "Now, let's build our regression model and initialize its parameters. \n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def sigmoid(x, Beta_1, Beta_2):\n",
+ " y = 1 / (1 + np.exp(-Beta_1*(x-Beta_2)))\n",
+ " return y"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Lets look at a sample sigmoid line that might fit with the data:\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "[]"
+ ]
+ },
+ "execution_count": 12,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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oBII8GmDx813RMYAz6JbMbPcZISIiuldeUSne/uEU/ndKBQB4rIMP/u/ZULg5OUhcGdUXhhEiIpLMhfQcvPztCSRm5sPeToa3h7TF5L7B3EnVxjCMEBGRJLbGpeK97adRWKKFr5sTlozpgrCgqnfnJuvFMEJERPWqsESDeT+exeZY3YaW4a08sXBUZ3jwKrs2i2GEiIjqTUp2AaZ9E4dzqhzIZMDsR1pjxsCWkHO1jE1jGCEionpx6EomXvnuBG4XlMDDxRGLnuuCvq08pS6LzADDCBER1SkhBNYevIaPdp6HRivQsYkSK8aGwb+Rs9SlkZlgGCEiojpTWKLBO9tOI/pEGgDg6S5NEBXZkdeWoXIYRoiIqE7cuHMX07+Nw6lUNeR2MrzzeDtMeqgZl+1SBQwjRERkcseSsvHyhjhk5hWjcQMHLB7dFQ+15PkhVDmGESIiMhkhBL49mowFO86iVCvQzs8NK8eGIdC9gdSlkRljGCEiIpMo1Wix4Kdz+ObIdQDAk5388MmITmjgyI8aqh6/Q4iIqNZyCkvwyoYTiLmcCZkM+MdjbTG9X3OeH0IGYRghIqJaSc4qwOSvj+NyRh6cHeRY+FxnPNbBV+qyyIIwjBARUY3FXsvGi9/EITu/GD5uCqwe3x0hTZRSl0UWhmGEiIhqZHt8Gv6x9RSKNVqENHHDV+O6w1fpJHVZZIEYRoiIyCharcDC3y/hiz1XAACPdfDB56M680RVqjF+5xARkcEKSzR4fctJ/HxKBQCY3q8F/vFYG9jxQndUCwwjRERkkNv5xZj89XGcSL4DB7kMHz3dESO7BUpdFlkBhhEiInqglOwCjF9zDImZ+XBzsseKsd3Qu4WH1GWRlWAYISKiap1OVWPiuuPIzCtCk0bO+HpSd7T0dpW6LLIiDCNERFSlPy9m4JUNJ1BQrEE7Pzesm9gdPm5cMUOmxTBCRESV+v54CuZuOw2NViC8lSeWjukKVycHqcsiK8QwQkRE5QghsOiPy1j4+2UAQGTXJvg4shMc7e0kroysFcMIERHplWq0eG/7GWw6ngIAmDGgJV6PaM1rzFCdYhghIiIAwN1iDV757gT2XMiAnQz41/AQjOkZJHVZZAMYRoiICOq7JZi87jhir9+Gk4Mdvny+Kwa195G6LLIRDCNERDYuI6cQ49Ycw4X0XLg52WPtxO4IC3KXuiyyIQwjREQ2LDmrAC+sPork7AJ4uSqwflIPtPNzk7ossjEMI0RENuq8Kgfj1hzDrdwiNHVvgG8n90RTjwZSl0X1SaMBYmIAlQrw8wPCwwG5vN7LYBghIrJBsdeyMWndceQUlqKtryvWT+4Bb1duZmZToqOBWbOA1NS/2wICgEWLgMjIei2Fi8aJiGzMnxcz8MLqo8gpLEW3oMbYPK03g4itiY4GRowoH0QAIC1N1x4dXa/lMIwQEdmQHxPSMPXrWBSWaDGgjRe+mdwTSmfuqmpTNBrdjIgQFe8ra5s9W9evnjCMEBHZiA1Hr2P25gSUagWGdfbHynHd4OxY/+cHkMRiYirOiNxLCCAlRdevnvCcESIiG/BVTCI+/Pk8AGBc7yDMH9oBdnbcVdUmqVSm7WcCDCNERFZu8Z7L+O9vlwAA0/u1wFuD23B7d1vm52fafibAwzRERFZKCIH/+/WCPojMGdSaQYR0y3cDAoCqvg9kMiAwUNevnjCMEBFZISEEPvjfOSz58yoA4J3H22LmI60YREi3j8iiRbr/vv/7oezrhQvrdb8Ro8PI/v37MXToUPj7+0Mmk2H79u0PfMy+ffsQFhYGJycnNG/eHMuXL69JrUREZACtVuCdbWew9uA1AMC/hnXAiw+3kLYoMi+RkcDWrUCTJuXbAwJ07ea+z0h+fj5CQ0OxePFig/onJSXh8ccfR3h4OOLj4/HOO+9g5syZ+OGHH4wuloiIqleq0eL1LSex8Vgy7GTAJyM6YWzvZlKXReYoMhK4dg3480/gu+90/yYl1XsQAQCZEJUtNDbwwTIZtm3bhuHDh1fZ56233sKOHTtw/vx5fdv06dNx8uRJHD582KDXycnJgVKphFqthpsbr5lARFSZ4lItZm2Kxy9n0iG3k+HzUZ3xVKi/1GWRDTP087vOzxk5fPgwIiIiyrU99thjiI2NRUlJSaWPKSoqQk5OTrkbERFVrahUg5c3xOGXM+lwlNth2ZiuDCJkMeo8jKSnp8PHx6dcm4+PD0pLS5GZmVnpY6KioqBUKvW3wMDAui6TiMhiFZVq8NK3J/D7+Qwo7O2wclwYIjr4Sl0WkcHqZTXN/Wdvlx0Zquqs7rlz50KtVutvKSkpdV4jEZElKizRYPo3cdhzQRdEVo/vjv5tvKUui8godb7pma+vL9LT08u1ZWRkwN7eHh4eHpU+RqFQQKFQ1HVpREQWrbBEg2nfxGHfpVtwctAFkYdaekpdFpHR6nxmpHfv3ti9e3e5tt9++w3dunWDgwMvzkREVBOFJRpMXR+rDyJrJjCIkOUyOozk5eUhISEBCQkJAHRLdxMSEpCcnAxAd4hl3Lhx+v7Tp0/H9evXMWfOHJw/fx5r1qzB6tWr8cYbb5jmHRAR2ZiyIBJzORPODnKsndADfVowiJDlMvowTWxsLAYMGKD/es6cOQCA8ePHY926dVCpVPpgAgDBwcHYuXMnXnvtNSxZsgT+/v744osv8Mwzz5igfCIi23K3WIMp64/j4JUsNHCUY+2E7ujZvPJD3kSWolb7jNQX7jNCRAQUFJdi8rpYHE7MgoujHGsn9kCPYHepyyKqkqGf37xqLxGRBbhbrCkXRL6e1APdmjGIkHVgGCEiMnNl54gcTsxCQ4U9vp7UHWFBDCJkAI0GiIkBVCrAz093Jd56vACeoRhGiIjMWNny3QNXMtHAUY51ExlEyEDR0cCsWUBq6t9tAQG6K/ZKcP2Z6tTLpmdERGS84lItXtlwQr98d+2E7jw0Q4aJjgZGjCgfRAAgLU3XHh0tTV1VYBghIjJDJRotXt14An/8tbPqmvFcNUMG0mh0MyKVrU8pa5s9W9fPTDCMEBGZmVKNFrM3JeDXszfhaG+HVeO6oQ83NCNDxcRUnBG5lxBASoqun5lgGCEiMiMarcCc70/i59MqOMhlWPFCGB5u7SV1WWRJVCrT9qsHDCNERGZCoxV4c+tJ7Dh5A/Z2MiwdE4YBbXnROzKSn59p+9UDhhEiIjOg1Qq8E30a0SfSILeT4cvnu2BQex+pyyJLFB6uWzUjk1V+v0wGBAbq+pkJhhEiIokJITBvx1lsjk2BnQxYOKozhnQ0n79aycLI5brlu0DFQFL29cKFZrXfCMMIEZGEhBD4+JcL+ObIdchkwH+fDcXQUH+pyyJLFxkJbN0KNGlSvj0gQNduZvuMcNMzIiIJffHHFazYnwgA+Gh4R0R2DZC4IrIakZHAsGHcgZWIiKq2an8iPv/9EgDgn0+2x+ieTSWuiKyOXA707y91FQ/EwzRERBL49sh1fLTzPADg9UGtMblvsMQVEUmHYYSIqJ79EJeK97afAQC81L8FZgxsKXFFRNJiGCEiqkc7T6vw5taTAIAJfZrhH4+1gayqJZhENoJhhIionuy5cBMzN8ZDK4CR3QLw/pPtGUSIwDBCRFQvDl3NxPRvT6BUKzA01B9RkZ1gZ8cgQgQwjBAR1bn45NuY8nUsiku1GNTeB5+NDIWcQYRIj2GEiKgOXUzPxYS1x1FQrEHflp5YPLoLHOT81Ut0L/5EEBHVketZ+Xhh9VGo75agS9NGWDE2DAp789twikhqDCNERHUgXV2IMV8dxa3cIrT1dcW6CT3gouA+k0SVYRghIjKx7PxivLD6KFJv30UzjwZYP7kHlA0cpC6LyGwxjBARmVBuYQnGrzmGKxl58HVzwjeTe8Lb1UnqsojMGsMIEZGJFJZoMPnrWJxOU8PdxRHfTumBQPcGUpdFZPYYRoiITKBEo8XLG07gWFI2XBX2WD+pB1p6u0pdFpFF4NlURES1pNEKvP79Sey5kAGFvR2+Gt8NIU2UUpdFtkCjAWJiAJUK8PMDwsN1V+q1MAwjRES1IITA/B1nsePkDdjbybD8hTD0bO4hdVlkC6KjgVmzgNTUv9sCAoBFi4DISOnqqgEepiEiqoXPf7+Mb45ch0wGfDaqMwa09Za6JLIF0dHAiBHlgwgApKXp2qOjpamrhhhGiIhqaO3BJHzxx2UAwAfDQvBUqL/EFZFN0Gh0MyJCVLyvrG32bF0/C8EwQkRUA9vj07Dgp3MAgDmDWmNsryCJKyKbERNTcUbkXkIAKSm6fhaCYYSIyEh7LtzE61tOAgAm9GmGVwe2lLgisikqlWn7mQGGESIiIxxLysZL356ARiswvLM/3n+yPWQyXoGX6pGfn2n7mQGGESIiA527kYPJXx9HUakWA9t64/+eDYWdHYMI1bPwcN2qmapCsEwGBAbq+lkIhhEiIgNcz8rHuDXHkFtYiu7NGmPJ6K5wkPNXKElALtct3wUqBpKyrxcutKj9RviTRET0ABk5hXhh9VFk5umuwPvV+O5wdrScX/RkhSIjga1bgSZNyrcHBOjaLWyfEW56RkRUDfXdEoxbcwwp2XcRVHYFXmdegZfMQGQkMGwYd2AlIrJmhSUaTP06FhfSc+HlqsA3k3gFXjIzcjnQv7/UVdRajQ7TLF26FMHBwXByckJYWBhiHrCWecOGDQgNDUWDBg3g5+eHiRMnIisrq0YFExHVh1KNFjO+i8exa7oL3309sQeaevAKvER1wegwsnnzZsyePRvvvvsu4uPjER4ejiFDhiA5ObnS/gcOHMC4ceMwefJknD17Flu2bMHx48cxZcqUWhdPRFQXhBCYG30av5+/Cce/LnzX3t9N6rKIrJbRYeSzzz7D5MmTMWXKFLRr1w4LFy5EYGAgli1bVmn/I0eOoFmzZpg5cyaCg4PRt29fTJs2DbGxsbUunoioLvxn10VsiUuFnQxY/HwXXviOqI4ZFUaKi4sRFxeHiIiIcu0RERE4dOhQpY/p06cPUlNTsXPnTgghcPPmTWzduhVPPPFEla9TVFSEnJyccjciovqwan8ilu+7CgD4OLITIjr4SlwRkfUzKoxkZmZCo9HAx8enXLuPjw/S09MrfUyfPn2wYcMGjBo1Co6OjvD19UWjRo3w5ZdfVvk6UVFRUCqV+ltgYKAxZRIR1cgPcan4aOd5AMBbg9tiZHf+7iGqDzU6gfX+rY+FEFVuh3zu3DnMnDkT77//PuLi4rBr1y4kJSVh+vTpVT7/3LlzoVar9beUlJSalElEZLA9F27iHz+cAgBM6RuM6f2aS1wRke0wammvp6cn5HJ5hVmQjIyMCrMlZaKiovDQQw/hzTffBAB06tQJLi4uCA8Px4cffgi/SvbOVygUUCgUxpRGRFRjsdey8fIG3fVmIrs0wTuPt+P1ZojqkVEzI46OjggLC8Pu3bvLte/evRt9+vSp9DEFBQWwsyv/MvK/NmQRQhjz8kREJnfpZi4mrTuOwhItBrTxwn9GdOL1ZojqmdGHaebMmYOvvvoKa9aswfnz5/Haa68hOTlZf9hl7ty5GDdunL7/0KFDER0djWXLliExMREHDx7EzJkz0aNHD/j7+5vunRARGSntzl2MW30MOYWl6Nq0EZaM4fVmiKRg9A6so0aNQlZWFj744AOoVCqEhIRg586dCAoKAgCoVKpye45MmDABubm5WLx4MV5//XU0atQIAwcOxH/+8x/TvQsiIiNl5xdj7OqjSM8pRCvvhlgzoTsaOHJTaiIpyIQFHCvJycmBUqmEWq2Gmxs3HiKi2skvKsXor47iZMod+Cud8MPLfeCndJa6LCKrY+jnN+cjicimlGi0eGnDCZxMuYNGDRywfnIPBhEiiXFOkohshlYr8OaWk9h/6RacHeRYM6E7Wnq7Sl0WUeU0Gqu4Iq8hGEaIyCYIIfDRzvPYnnAD9nYyLH2hK7o2bSx1WUSVi44GZs0CUlP/bgsIABYtAiIjpaurjvAwDRHZhOX7ErH6QBIA4P+e7YQBbbwlroioCtHRwIgR5YMIAKSl6dqjo6Wpqw4xjBCR1dsSm4L/7LoAAHjviXZ4ukuAxBURVUGj0c2IVLa2pKxt9mxdPyvCMEJEVu33czfxdvRpAMC0fs0xJZzbvJMZi4mpOCNyLyGAlBRdPyvCMEJEViv2WjZe+U63zfszXQPw9uC2UpdEVD2VyrT9LATDCBFZpbJt3otKtRjY1hsfP9OR15sh81fJ9dpq1c9CMIwQkdW5d5v3sKDGWDKa27yThQgP162aqSo4y2RAYKCunxXhTycRWZX7t3lfPb4bnB2tc28GskJyuW75LlAxkJR9vXCh1e03wjBCRFajoLgUE9cdR+KtfPgrnbB+cg80auAodVlExomMBLZuBZo0Kd8eEKBrt8J9RrjpGRFZhRKNFi99y23eyUpERgLDhnEHViIiS1G2zfu+v7Z5X8tt3skayOVA//5SV1EveJiGiCxaZdu8d+E270QWhWGEiCzaiv3c5p3I0jGMEJHF+v54Cj7+hdu8E1k6hhEiski7z93E29GnAHCbdyJLxzBCRBbnWFI2Znx3AloBPBvGbd6JLB3DCBFZlPOqHEz+WrfN+6PtfBAVyW3eiSwdwwgRWYyU7AKMW3MMuYWl6N6sMRaP7gJ7bvNOZPH4U0xEFuFWbhHGrj6KW7lFaOvriq/Gd4eTg3VuAEVkaxhGiMjs5RaWYMLaY7iWVYCAxs5YP6kHlM4OUpdFRCbCMEJEZq2wRIMX18fh7I0ceLg44pvJPeHt5iR1WURkQgwjRGS2NFqB2ZsScDgxCw0V9vh6Ug8Ee7pIXRYRmRjDCBGZJSEE3t12GrvOpsNRboeVY8MQ0kQpdVlEVAcYRojILP1n10VsOp4COxnwxfOd0aelp9QlEVEdYRghIrOzYt9VLN93FQAQFdkRg0P8JK6IiOoSwwgRmZXvj6cg6q/rzbw9pC1GdW8qcUVEVNcYRojIbPx6Nv3v68083BzT+7WQuCIiqg8MI0RkFg5dzcSrG+OhFcCoboF4ewivN0NkKxhGiEhyp1PVeHF9HIpLtXisgw8+ejqE15shsiEMI0Qkqau38jB+7THkFZWiTwsPLHqO15shsjX8iSciydy4cxfjVh9Ddn4xOgUosXJcN15vhsgGMYwQkSQy84rwwuqjSLtzF829XLB2Qnc0VNhLXRYRSYBhhIjqnfpuCcatPobEW/lo0sgZ307uCY+GCqnLIiKJMIwQUb26W6zBlK+P45wqB54NHfHtlJ7wb+QsdVlEJCGGESKqN8WlWkz/Ng7Hr92Gq5M91k/qyQvfERF4gJaI6oVGK/Da5gTsu3QLzg5yrJvYHe393aQui0g6Gg0QEwOoVICfHxAeDsht8wRuhhEiqnNCCLwTfRo/n1bBQS7DirFhCAtyl7osIulERwOzZgGpqX+3BQQAixYBkZHS1SWRGh2mWbp0KYKDg+Hk5ISwsDDExMRU27+oqAjvvvsugoKCoFAo0KJFC6xZs6ZGBRORZRFC4N87z2Nz7F9X4H2uCx5u7SV1WUTSiY4GRowoH0QAIC1N1x4dLU1dEjJ6ZmTz5s2YPXs2li5dioceeggrVqzAkCFDcO7cOTRtWvkFrUaOHImbN29i9erVaNmyJTIyMlBaWlrr4onI/C358wpWxSQBAD5+phOGdOQVeMmGaTS6GREhKt4nBCCTAbNnA8OG2dQhG5kQlY1I1Xr27ImuXbti2bJl+rZ27dph+PDhiIqKqtB/165deO6555CYmAh395pNy+bk5ECpVEKtVsPNjceYiSzFuoNJmP/TOQDAP59sj8l9gyWuiEhie/cCAwY8uN+ffwL9+9d1NXXO0M9vow7TFBcXIy4uDhEREeXaIyIicOjQoUofs2PHDnTr1g2ffPIJmjRpgtatW+ONN97A3bt3q3ydoqIi5OTklLsRkWX5/niKPojMfKQVgwgRoDtZ1ZT9rIRRh2kyMzOh0Wjg4+NTrt3Hxwfp6emVPiYxMREHDhyAk5MTtm3bhszMTLz88svIzs6u8ryRqKgoLFiwwJjSiMiM7Dh5A29FnwIATOkbjNcebSVxRURmws/Aw5SG9rMSNTqB9f6raQohqrzCplarhUwmw4YNG9CjRw88/vjj+Oyzz7Bu3boqZ0fmzp0LtVqtv6WkpNSkTCKSwG9n0/Ha5gQIAYzp2RTvPtGOV+AlKhMerls1U9XPhEwGBAbq+tkQo8KIp6cn5HJ5hVmQjIyMCrMlZfz8/NCkSRMolUp9W7t27SCEQOr9ZxL/RaFQwM3NrdyNiMzf/ku3MOO7eGi0ApFdmuBfw0IYRIjuJZfrlu8CFQNJ2dcLF9rUyauAkWHE0dERYWFh2L17d7n23bt3o0+fPpU+5qGHHsKNGzeQl5enb7t06RLs7OwQEBBQg5KJyBwdTczCi9/EolijxeMdffHJiE6ws2MQIaogMhLYuhVo0qR8e0CArt0G9xkxejXN5s2bMXbsWCxfvhy9e/fGypUrsWrVKpw9exZBQUGYO3cu0tLSsH79egBAXl4e2rVrh169emHBggXIzMzElClT0K9fP6xatcqg1+RqGiLzlpByBy98dRR5RaUY0MYLK8Z2g6M9rzZBVC0b2IHV0M9vo/cZGTVqFLKysvDBBx9ApVIhJCQEO3fuRFBQEABApVIhOTlZ379hw4bYvXs3Xn31VXTr1g0eHh4YOXIkPvzwwxq8LSIyN+dVORi/5hjyikrRp4UHlr0QxiBCZAi53CqW75qC0TMjUuDMCJF5upKRh1ErDiMrvxhhQY2xflIPuCh4lQki0qmTfUaIiMpcz8rHC18dRVZ+MUKauGHNhO4MIkRUIwwjRGS0lOwCPL/yCNJzCtHapyHWT+oJpbOD1GURkYViGCEio6TduYvnVx3BDXUhWni5YMOUXnB3cZS6LCKyYAwjRGSwdHUhnl95BKm37yLY0wUbp/aCl6tC6rKIyMIxjBCRQTJyCvH8qiNIzi5AU/cG+G5qT3i7OUldFhFZAYYRInqgW7lFeH7VESRl5qNJI2d8N7Un/JTOUpdFRFaCYYSIqpWdX4wXvjqKq7fy4ad0wqYXeyGgcQOpyyIiK8IwQkRVulNQjDFfHcXFm7nwcVNg49ReCHRnECEi02IYIaJKqQtK8MLqozivyoFnQwW+m9oLzTxdpC6LiKwQwwgRVXCnoBhjVh/BmbQceLg4YuPUnmjh1VDqsojISnG7RCIqp+zQzNkbuiDy3dReaOXjKnVZRGTFGEaISO92vi6InFPlwLOhLoi0ZhAhqhkbuCqvqTCMEBEA3aqZ0auO4EJ6LjwbKrBxak/OiBDVVHQ0MGsWkJr6d1tAALBoERAZKV1dZornjBARsvKKygWRTS8yiBDVWHQ0MGJE+SACAGlpuvboaGnqMmMMI0Q2LjOvCKNXHcWF9Fx4uSqw6cVeaOnNIEJUIxqNbkZEiIr3lbXNnq3rR3oMI0Q27FZuEZ5feQQXb+bCWx9EuGqGqMZiYirOiNxLCCAlRdeP9HjOCJGNupWrOzRzOSNPv6FZcy7fJaodlcq0/WwEwwiRDVKp72LMqqNIzMyHr5sTNr7YC8Hc0Iyo9vz8TNvPRvAwDZGNSckuwMgVh5H410XvNjGIEJlOeLhu1YxMVvn9MhkQGKjrR3oMI0Q2JPFWHp5dfhgp2XcR5NEAm6dxi3cik5LLdct3gYqBpOzrhQu538h9GEaIbMTF9FyMXHEE6TmFaOndEN9P682r7xLVhchIYOtWoEmT8u0BAbp27jNSAc8ZIbIBp1PVGLvmKO4UlKC9nxu+mdwDHg0VUpdFZL0iI4Fhw7gDq4EYRoisXNz1bExYcxy5RaUIDWyE9RN7QNnAQeqyiKyfXA707y91FRaBYYTIih26mokpX8eioFiDHs3csXpCN7g6MYgQ1RqvO2NSDCNEVmrvxQxM+yYORaVahLfyxMqx3eDsyF+WRLXG686YHE9gJbJCP528ganrY1FUqsWj7byxahyDCJFJ8LozdYJhhMjKfHPkOmZuikeJRmBoqD+WvRAGJwcGEaJa43Vn6gzDCJGVEELgyz8u45/bz0AIYGyvICwa1RkOcv6YE5kErztTZ3jOCJEV0GoFPvz5PNYcTAIAzHykFV57tBVkVe0CSUTG43Vn6gzDCJGFK9Fo8dYPpxB9Ig0AMG9oe0x8KFjiqoisEK87U2cYRogsWGGJBjO+O4Hfz2dAbifDf5/thKe7BEhdFpF1KrvuTFpa5eeNyGS6+3ndGaPxYDKRhcopLMG41cfw+/kMKOztsHJsGIMIUV3idWfqDMMIkQXKyC3EcyuO4Ni1bLgq7LF+Ug880s5H6rKIrB+vO1MneJiGyMJcvZWH8WuOIfX2XXg2dMTXk3qgg79S6rKIbAevO2NyDCNEFiTuejYmfx2LOwUlaObRAOsm9kAzTxepyyKyPbzujEkxjBBZiF1n0jFrUzyKSrUIDWyENeO78cq7RGQVGEaILMD6w9cwb8dZCAE80tYbX47uggaO/PElIuvA32ZEZkyrFfjk14tYvu8qAGB0z6b44KkOsOeuqkRkRWr0G23p0qUIDg6Gk5MTwsLCEGPg1rcHDx6Evb09OnfuXJOXJbIpxaVazPk+QR9E3ohojY+GhzCIEJHVMfq32ubNmzF79my8++67iI+PR3h4OIYMGYLk5ORqH6dWqzFu3Dg88sgjNS6WyFbkFJZgwtpj2J5wA/Z2Mvz32VDMGMjt3YnIOsmEqGwbuar17NkTXbt2xbJly/Rt7dq1w/DhwxEVFVXl45577jm0atUKcrkc27dvR0JCgsGvmZOTA6VSCbVaDTc3N2PKJbI4KdkFmPz1cVy6mQcXRzmWvRCGh1t7SV0WEZHRDP38NmpmpLi4GHFxcYiIiCjXHhERgUOHDlX5uLVr1+Lq1auYN2+eQa9TVFSEnJyccjciWxB3PRvDlxzEpZt58HFTYPO03gwiRGT1jAojmZmZ0Gg08PEpv9Ojj48P0tPTK33M5cuX8fbbb2PDhg2wtzfsfNmoqCgolUr9LTAw0JgyiSzSjwlpeH7VUWTlF6ODvxt+fKUvQppwMzMisn41OhPu/uPWQohKj2VrNBqMHj0aCxYsQOvWrQ1+/rlz50KtVutvKSkpNSmTyCIIIfDZ7kuYtSkBxaVaRLT3wZbpveGrdJK6NCKiemHU0l5PT0/I5fIKsyAZGRkVZksAIDc3F7GxsYiPj8eMGTMAAFqtFkII2Nvb47fffsPAgQMrPE6hUECh4GZOZP0KSzR4Y8tJ/O+UCgAwrV9zvPVYW9jZ8URVIrIdRoURR0dHhIWFYffu3Xj66af17bt378awYcMq9Hdzc8Pp06fLtS1duhR79uzB1q1bERwcXMOyiSxfRm4hXlwfh4SUO7C3k+HfT3fEyO48JElEtsfoTc/mzJmDsWPHolu3bujduzdWrlyJ5ORkTJ8+HYDuEEtaWhrWr18POzs7hISElHu8t7c3nJycKrQT2ZIL6TmYvC4WaXfuQunsgOUvhKF3Cw+pyyIikoTRYWTUqFHIysrCBx98AJVKhZCQEOzcuRNBQUEAAJVK9cA9R4hs2a4zKsz5/iQKijUI9nTBmgndEcyL3RGRDTN6nxEpcJ8RsgZarcDC3y/hiz1XAAB9Wnhg6ZiuaNTAUeLKiKgCjQaIiQFUKsDPDwgP112pl4xi6Oc3r01DVA9yCkvw2qYE/HEhAwAw6aFgvPN4W27tTmSOoqOBWbOA1NS/2wICgEWLgMhI6eqyYgwjRHXs6q08TF0fi8Rb+XC0t8PHkR0R2TVA6rKIqDLR0cCIEcD9Bw3S0nTtW7cykNQB/llGVIf+OH8TwxcfROKtfPgpnbB1em8GESJzpdHoZkQqO3uhrG32bF0/MimGEaI6oNUKfPnHZUxZH4vcolL0aOaOHTP6olNAI6lLI6KqxMSUPzRzPyGAlBRdPzIpHqYhMrG8olK8ueUkfjmj2xxwXO8gvPdEezjaM/sTmTWVyrT9yGAMI0QmdCE9By9/ewKJmflwlNvhX8M7YFT3plKXRUSG8PMzbT8yGMMIkYlsiU3BP388g8ISLfyUTlgypiu6Nm0sdVlEZKjwcN2qmbS0ys8bkcl094eH139tVo7zxkS1VFiiwT+2nsSbW0+hsESLfq298PPMcAYRIksjl+uW7wK64HGvsq8XLuR+I3WAYYSoFpIy8/H00kP4PjYVdjLgjYjWWDuhO9xduJEZkUWKjNQt323SpHx7QACX9dYhHqYhqqFfTqvw5tZTyCsqhWdDR3zxXBf0aekpdVlEVFuRkcCwYdyBtR4xjBAZqbhUi6hfzmPtwWsAgB7N3PHl6C7wcXOStjAiMh25HOjfX+oqbAbDCJERrmXmY9ameJxMVQMApvdrgTciWnNbdyKiWmAYITKAEAI/nEjDvB/PIL9YA6WzAz59NhSPtveRujQiIovHMEL0ADmFJXh32xn8dPIGAKBnsDsWPtcZfkpniSsjIrIODCNE1Yi7no1ZmxKQevsu5HYyzBnUGtP7tYDcTvbgBxMRkUEYRogqodEKLN5zBV/suQyNViDQ3RlfPNcFXbh3CBGRyTGMEN0n7c5dvLYpAceuZQMAhnf2x7+Gh8DVyUHiyoiIrBPDCNFfhBCIPpGG+T+dRW5hKRoq7PGv4R3wdJcAqUsjIrJqDCNEADJyC/FO9Bn8fv4mAKBzYCMseq4zgjxcJK6MiMj6MYyQzfvfqRv45/YzuF1QAge5DLMfbY1pDzfn3iFE1kyj4Q6rZoRhhGzW7fxi/PPHM/jfKRUAoL2fGz4dGYp2fm4SV0ZEdSo6Gpg1C0hN/bstIEB3kTxee0YSDCNkk3afu4m50aeRmVcEuZ0Mr/RvgRkDW8HRnrMhRFYtOhoYMQIQonx7WpqunRfDk4RMiPv/j5ifnJwcKJVKqNVquLnxr1aqOXVBCT743zn8cEL3F1FL74b4bGQoOgU0krYwIqp7Gg3QrFn5GZF7yWS6GZKkJB6yMRFDP785M0I2QQiBn0+rMH/HOWTmFUEmA14Mb47XBrWGkwN/6RDZhJiYqoMIoJstSUnR9eNF8uoVwwhZvRt37uKf28/gjwsZAIAWXi74zzOd0K2Zu8SVEVG9UqlM249MhmGErJZGK/DN4Wv4v18vIr9YAwe5DC/3b4mXB7SAwp6zIUQ2x8/PtP3IZBhGyCpdSM/B2z+cRkLKHQBAWFBjfBzZEa18XKUtjIikEx6uOyckLa3iCazA3+eMhIfXf202jmGErEphiQaL91zB8n1XUaoVcFXY4x9D2mJMj6aw48XtiGybXK5bvjtihC543BtIZH/9fli4kCevSoBhhKzGH+dvYsFP55CcXQAAeKyDDxY8FQJfpZPElRGR2YiM1C3frWyfkYULuaxXIgwjZPGuZ+Xjg5/O6U9Q9XFTYMFTIRgc4itxZURkliIjgWHDuAOrGWEYIYt1t1iDZXuvYPn+RBSXauEgl2FS32DMHNgKLgp+axPZLEO2epfLuXzXjPA3NlkcIQR+PZuOf/3vPNLu3AUAhLfyxLyhHdDSu6HE1RGRpLjVu0ViGCGLcvVWHubvOIuYy5kAgCaNnPHPJ9vjsQ4+kMl4giqRTeNW7xaL28GTRcjOL8YXf1zGt0euo1Qr4Ghvh+kPN8dL/VvC2ZHHeYlsHrd6N0vcDp6sQmGJBusOXcOSPVeQW1QKAHikrTfeH9oeQR4uEldHRGaDW71bNIYRMktarcBPp27gk10X9eeFtPdzw7tPtMNDLT0lro6IzA63erdoDCNkdo4lZeOjn8/hZKoaAODr5oQ3H2uDp7s04cZlRFQ5bvVu0RhGyGxcycjF//16Eb+evQkAcHGU46X+LTC5b3OeF0JE1eNW7xbNriYPWrp0KYKDg+Hk5ISwsDDExMRU2Tc6OhqDBg2Cl5cX3Nzc0Lt3b/z66681Lpisz/WsfMzZnICIz/fj17M3YScDxvRsir1vDsCMga0YRIioPI0G2LsX2LhR969G8/dW78DfW7uX4VbvZs/oMLJ582bMnj0b7777LuLj4xEeHo4hQ4YgOTm50v779+/HoEGDsHPnTsTFxWHAgAEYOnQo4uPja108WbYbd+5ibvRpPPLpPkTHp0ErdFu4/zr7YXz0dEd4uSqkLpGIzE10tG7VzIABwOjRun+bNdO1l2313qRJ+ccEBHBZr5kzemlvz5490bVrVyxbtkzf1q5dOwwfPhxRUVEGPUeHDh0watQovP/++wb159Je65KRW4ilf17Fd0eTUazRAgD6tfbC6xGt0SmgkbTFEZH5qmofkbKZj7LAYcgOrFQv6mRpb3FxMeLi4vD222+Xa4+IiMChQ4cMeg6tVovc3Fy4u7tX2aeoqAhFRUX6r3Nycowpk8zU7fxirNifiK8PXcPdEg0AoGewO954rA26N6v6+4GICBqNbmfVyv5+FkIXSGbP1l1zhlu9WxyjwkhmZiY0Gg18fHzKtfv4+CA9Pd2g5/j000+Rn5+PkSNHVtknKioKCxYsMKY0MmMZOYX46kASvj1yHQXFuhASGtgIb0a0wUMtPbhzKhE9GPcRsWo1Wk1z/4eHEMKgD5SNGzdi/vz5+PHHH+Ht7V1lv7lz52LOnDn6r3NychAYGFiTUklCqbcLsGJfIjbHpqC4VHc4pr2fG+YMao1H2nkzhBCR4biPiFUzKox4enpCLpdXmAXJyMioMFtyv82bN2Py5MnYsmULHn300Wr7KhQKKBQ8edFSXb2Vh2V7r2J7fBpKtbop1bCgxpgxoCX6t/FiCCEi43EfEatmVBhxdHREWFgYdu/ejaefflrfvnv3bgwbNqzKx23cuBGTJk3Cxo0b8cQTT9S8WjJr527kYMneK9h5WqU/rNu3pSdeGdASvZq7M4QQ0YNVdfIp9xGxakYfppkzZw7Gjh2Lbt26oXfv3li5ciWSk5Mxffp0ALpDLGlpaVi/fj0AXRAZN24cFi1ahF69eulnVZydnaFUKk34VkgKWq3Avku38NWBRBy8kqVvf7SdD14Z0AJdmjaWsDoisijR0bqTVO89NyQgQLd/SGSk7t8RI3TB495Awn1ELJ7RYWTUqFHIysrCBx98AJVKhZCQEOzcuRNBQUEAAJVKVW7PkRUrVqC0tBSvvPIKXnnlFX37+PHjsW7dutq/A5JEYYkG0SfSsPpAIq7eygcAyO1keLyjH17u3wLt/LgEm4iMUNWy3bQ0XXvZst2tWysPLAsXch8RC2b0PiNS4D4j5iMjtxDfHr6Ob48mIzu/GADgqrDHcz0CMb5PMwQ0biBxhURkcTQa3cZlVa2WKTsEk5Skm/ngPiIWo072GSHbdSZNjXWHrmFHwg39RmUBjZ0x8aFgjOwWAFcnB4krJCKLZeyyXe4jYnUYRqhKhSUa/O+UCt8cuY6TKXf07WFBjTGlbzAGtfeBvbxGlzciIltV2awGl+3aPIYRqiApMx8bjlzHlrhUqO+WAAAc5DIMCfHDhIeaoStPSiWimqjqBNWpUw17PJftWi2eM0IAgFKNFn9cyMC3R64j5nKmvr1JI2eM6dUUI7sFwrMh934hohqq7royQgAeHkB2dvXLdsvOGSGLwXNGyCBXb+VhS2wqok+kIiNXdz0gmQzo39oLY3sHoV9rb8jtuD8IERmossMwwIOvK1OGy3ZtEsOIDcotLMHPp1T4PjYFJ5Lv6NvdXRwxqnsgRvdoikB3roohIiNVdxjmQSeoZmUBCxYAq1Zx2a4NYhixEVqtwNGkbGyJTcHOMyoUluhWxMjtZOjf2gvPdgvAwLY+cLTnCalEVAPV7RMyb55hz9GqFXDtGpft2iCGESt3MT0XO06m4ceEG0i9fVff3tK7IZ4NC8DTXZrA281JwgqJyGJUtb+HRlP9YRhD+flx2a6NYhixQinZBdhx8gZ+OnkDF9Jz9e2uCns8GeqPZ7sFoEtgI14rhogMV91W7e7u1R+GeRBeV8bmMYxYicy8Ivx8SoUdJ28g7vptfbuj3A792nhhWGd/PNLWB86OnO4kIiM9aKv2WbMMfy6eoEqVYBixYOnqQvx2Lh27zqTjaFI2NFrdD7hMBvRp4YGnQv0xuIMflA24OyoRGaCmK2E2bDDs+XmCKlWBYcTCJGcVYNdZFXadSS+3EgYAQgMbYVioP57s5MfzQIioouqu6VKblTC3bgFeXkBmZvX7hLz7ru7GE1TpPgwjZk4IgUs38/DrWd0MyDlVTrn7w4IaY3AHXwwO8eVyXCKqWnXnfAC1XwkzZozuuQw5DMMTVOk+DCNmqLBEg8OJWdhzPgN7LmQg7c7fq2DkdjL0DHbHkBBfRHTwhQ9nQIgIePCsR1Vh45lndLuf1nYlzLBhutesLPDwMAw9ALeDNxPp6kLsuZCBPRdu4uCVLNwt0ejvU9jb4aGWnhjcwRePtveBu4ujhJUSkdmpbtZj2DCgWbParXapzv1btVcXisjmcDt4M1dYokHc9dvYf/kWYi5lVjj84uvmhIHtvPFIW2/0aeHJVTBEVLkHrXSZP990QcSQQzDcJ4RqgGGkngghcPFmLmIuZSLmSiaOJWXpd0EFdD/TnQMb4ZG23hjY1gft/Fy5DwgR/a2mK13KzgmpLa6EoTrEMFJHhBBIvX0XhxOzcORqFmKuZOLWXxeiK+PtqkB4Ky+Et/JE31aevCouEVWuNitdsrNr99pcCUP1gGHERIQQSMm+iyOJWTiSmIWjSdnlTjwFACcHO/Rq7oG+LT3xcGsvtPJuyNkPIqqeKa754u4O3L5d9bJbd/e/QwtXwpAEGEZqSKsVuHIrD3HXb+NYUjaOJGZBpS4s18feToZOAUpdAGnlibCgxlDY868IIqpETQ7DGGrWLN25I1Wd87Fy5d/9eBiGJMAwYqD8olKcTLmDuOu3EZd8Gyeu30ZOYWm5Pg5yGUIDGqFXcw/0bO6OsKDGaODIISaiB6jpYZgHufcQS0jIg8PGsGE8DEOS4NLeSmi1AomZ+TiZcgenUu8gLvk2zqty9dutl3F2kKNzYCN0a9YYvZp7oGvTxlz1QkTGqeowzP2zGA9S1azH1q1/hw0uu6V6xqW9BhJC4Ia6EKdS7uBkqhonU+7gTJoauUWlFfr6K53QNagxugU1RliQO9r6ucJBbidB1URkFTQa0xyGMXSlC5fdkpmy6TDywU/nsOPkDWTmFVW4z8nBDiH+SnQKaISuQY3QtWlj+DdylqBKIrJ4Vc1IxMSY7jAMV7qQBbPpMJJfVIrMvCLI7WRo6+uKTgGNEBqgRGhgI7Tybgh7znoQUW1VtztqUcU/hKrEa76QFbPpMDKpbzBGdg9EB383ODnwLwgiMjFDdkc1BDccIyvHE1iJiB7kQSd+VrUst7prwshkQJMmuv9OS6t6D5Cy674APAxDFocnsBIRGeJBQaO6wyyRkbXbHTU1VTfrUd0eIDwMQzaAMyNEZNlqMmtRdr8hQaOqZbcA8MYbwH//W7tlud99BygUFesIDORhGLJ4hn5+M4wQUc3UJgSY6jVqOmtRdvG46oLG5s3AnDnVz27I5boaa+PPP3UzHtwDhKwQwwgR1U5tZxSqu99Ur1GbWQsPDyArq/L3LpMBnp7ArVuGj5ex7j0fhKGDrBTDCBFVrTYzDkDNQwDw946gljBrYSqG7I5KZIUYRojqQn0cejDkNaQ6T+JBMwpA9SGgbDbgs8+AkSPNd9bClCpblsvzQchGGPz5LSyAWq0WAIRarZa6FJJSaakQf/4pxHff6f4tLTXu/to+xw8/CBEQIITu41J3CwjQtZvqOQx5jdo8xw8/CCGTlb8P0LXJZEJ8/33Fx9bFzcur7l/DVHVWNl5lN7m86vtlMiECA3X//w353iSyQoZ+fjOMkGnUdVAw9w9xUzzHm28++DVq8xyAEB4eVX+wymSWExLq+lYWJLZs+Xtsqxvvqu6/P6gS2RiGkQep67+irek1HtSnroOCJXyI3/vBVZPnAHR/ZVf3GgEBD561qO45rO1W21kLDw/DgkRl35uBgYbfT2TDGEaqU9d/RVvTazyoT10HBcByPsQ5q/D3WFYXAmo7TqactTA0SJgi0BPZIIaRqhgy3V7bD9i6/ku9vl7DXIICb/V7q27GwZAZhQeFgLLzUsxl1oJBgqjO1GkYWbJkiWjWrJlQKBSia9euYv/+/dX237t3r+jatatQKBQiODhYLFu2zKjXM1kYKS2t/oPPVH9F18df6nX9GgwKtnczdMbBkBkFQ+7nrAWR1auzMLJp0ybh4OAgVq1aJc6dOydmzZolXFxcxPXr1yvtn5iYKBo0aCBmzZolzp07J1atWiUcHBzE1q1bDX5Nk4WRP/+U/hc+b9Z3M9WJnw86vFEWDs3hPAkhah8COGtBZPXqLIz06NFDTJ8+vVxb27Ztxdtvv11p/3/84x+ibdu25dqmTZsmevXqZfBrmiyMfPed9B9cvJn+Zg4f4qY49GDoOQ7mcp6EKTBsEFm1OgkjRUVFQi6Xi+jo6HLtM2fOFA8//HCljwkPDxczZ84s1xYdHS3s7e1FcXFxpY8pLCwUarVaf0tJSTHozTwQZ0bq/1bboGBJH+KmOPRgSFDgeRJEZCHqJIykpaUJAOLgwYPl2j/66CPRunXrSh/TqlUr8dFHH5VrO3jwoAAgbty4Uelj5s2bJwBUuJnsnJG6/CvaFB/A5vAa5hQULOlDvD4Ob5jqOYiI6lidhpFDhw6Va//www9FmzZtKn1Mq1atxL///e9ybQcOHBAAhEqlqvQxdTYzIoThH3y1+YCtj7/U63M2wByCghCW8yHOIEBEJISw8MM096uXfUZM/Ve0tbyGoX3qIygQEZFFMfTzWyaEEMZc9KZnz54ICwvD0qVL9W3t27fHsGHDEBUVVaH/W2+9hZ9++gnnzp3Tt7300ktISEjA4cOHDXrNOrlQXl1fjMyaXsPQPkRERPeos6v2bt68GWPHjsXy5cvRu3dvrFy5EqtWrcLZs2cRFBSEuXPnIi0tDevXrwcAJCUlISQkBNOmTcPUqVNx+PBhTJ8+HRs3bsQzzzxj0jdDRERE5sPQz297Y5941KhRyMrKwgcffACVSoWQkBDs3LkTQUFBAACVSoXk5GR9/+DgYOzcuROvvfYalixZAn9/f3zxxRcGBxEiIiKybkbPjEiBMyNERESWx9DPb7t6rImIiIioAoYRIiIikhTDCBEREUmKYYSIiIgkxTBCREREkmIYISIiIkkxjBAREZGkjN70TAplW6Hk5ORIXAkREREZquxz+0FbmllEGMnNzQUABAYGSlwJERERGSs3NxdKpbLK+y1iB1atVosbN27A1dUVMpnMZM+bk5ODwMBApKSkcGdXE+B4mg7H0rQ4nqbDsTQtax9PIQRyc3Ph7+8PO7uqzwyxiJkROzs7BAQE1Nnzu7m5WeU3gVQ4nqbDsTQtjqfpcCxNy5rHs7oZkTI8gZWIiIgkxTBCREREkrLpMKJQKDBv3jwoFAqpS7EKHE/T4ViaFsfTdDiWpsXx1LGIE1iJiIjIetn0zAgRERFJj2GEiIiIJMUwQkRERJJiGCEiIiJJWXwY2b9/P4YOHQp/f3/IZDJs37693P03b97EhAkT4O/vjwYNGmDw4MG4fPlyhec5fPgwBg4cCBcXFzRq1Aj9+/fH3bt39fffvn0bY8eOhVKphFKpxNixY3Hnzp06fnf1r7bjee3aNchkskpvW7Zs0fezhfE0xfdmeno6xo4dC19fX7i4uKBr167YunVruT62MJaAacbz6tWrePrpp+Hl5QU3NzeMHDkSN2/eLNfHFsYzKioK3bt3h6urK7y9vTF8+HBcvHixXB8hBObPnw9/f384Ozujf//+OHv2bLk+RUVFePXVV+Hp6QkXFxc89dRTSE1NLdfH2sfTVGO5cuVK9O/fH25ubpDJZJWOkTWPpcWHkfz8fISGhmLx4sUV7hNCYPjw4UhMTMSPP/6I+Ph4BAUF4dFHH0V+fr6+3+HDhzF48GBERETg2LFjOH78OGbMmFFu69rRo0cjISEBu3btwq5du5CQkICxY8fWy3usT7Udz8DAQKhUqnK3BQsWwMXFBUOGDNE/ly2Mpym+N8eOHYuLFy9ix44dOH36NCIjIzFq1CjEx8fr+9jCWAK1H8/8/HxERERAJpNhz549OHjwIIqLizF06FBotVr9c9nCeO7btw+vvPIKjhw5gt27d6O0tBQRERHlvvc++eQTfPbZZ1i8eDGOHz8OX19fDBo0SH+tMACYPXs2tm3bhk2bNuHAgQPIy8vDk08+CY1Go+9j7eNpqrEsKCjA4MGD8c4771T5WlY9lsKKABDbtm3Tf33x4kUBQJw5c0bfVlpaKtzd3cWqVav0bT179hTvvfdelc977tw5AUAcOXJE33b48GEBQFy4cMG0b8KM1HQ879e5c2cxadIk/de2OJ41HUsXFxexfv36cs/l7u4uvvrqKyGEbY6lEDUbz19//VXY2dkJtVqt75OdnS0AiN27dwshbHc8MzIyBACxb98+IYQQWq1W+Pr6io8//ljfp7CwUCiVSrF8+XIhhBB37twRDg4OYtOmTfo+aWlpws7OTuzatUsIYZvjWZOxvNeff/4pAIjbt2+Xa7f2sbT4mZHqFBUVAQCcnJz0bXK5HI6Ojjhw4AAAICMjA0ePHoW3tzf69OkDHx8f9OvXT38/oJs5USqV6Nmzp76tV69eUCqVOHToUD29G+kZMp73i4uLQ0JCAiZPnqxv43gaPpZ9+/bF5s2bkZ2dDa1Wi02bNqGoqAj9+/cHwLEsY8h4FhUVQSaTldtcysnJCXZ2dvo+tjqearUaAODu7g4ASEpKQnp6OiIiIvR9FAoF+vXrpx+HuLg4lJSUlOvj7++PkJAQfR9bHM+ajKUhrH0srTqMtG3bFkFBQZg7dy5u376N4uJifPzxx0hPT4dKpQIAJCYmAgDmz5+PqVOnYteuXejatSseeeQR/fHm9PR0eHt7V3h+b29vpKen198bkpgh43m/1atXo127dujTp4++jeNp+Fhu3rwZpaWl8PDwgEKhwLRp07Bt2za0aNECAMeyjCHj2atXL7i4uOCtt95CQUEB8vPz8eabb0Kr1er72OJ4CiEwZ84c9O3bFyEhIQCgf68+Pj7l+vr4+OjvS09Ph6OjIxo3blxtH1saz5qOpSGsfSytOow4ODjghx9+wKVLl+Du7o4GDRpg7969GDJkCORyOQDojxVPmzYNEydORJcuXfD555+jTZs2WLNmjf65ZDJZhecXQlTabq0MGc973b17F9999125WZEytj6eho7le++9h9u3b+P3339HbGws5syZg2effRanT5/W97H1sQQMG08vLy9s2bIFP/30Exo2bAilUgm1Wo2uXbuWG3NbG88ZM2bg1KlT2LhxY4X77n/PhozD/X1saTxNPZYPeo6aPo85spe6gLoWFhaGhIQEqNVqFBcXw8vLCz179kS3bt0AAH5+fgCA9u3bl3tcu3btkJycDADw9fWtcMY9ANy6datC2rV2DxrPe23duhUFBQUYN25cuXaOp86DxvLq1atYvHgxzpw5gw4dOgAAQkNDERMTgyVLlmD58uUcy3sY8r0ZERGBq1evIjMzE/b29mjUqBF8fX0RHBwMwPa+N1999VXs2LED+/fvR0BAgL7d19cXgO6v8bLfkYDusHbZOPj6+qK4uBi3b98uNzuSkZGhnwm1pfGszVgawtrH0qpnRu6lVCrh5eWFy5cvIzY2FsOGDQMANGvWDP7+/hWWYl26dAlBQUEAgN69e0OtVuPYsWP6+48ePQq1Wl3u8IMtqWo877V69Wo89dRT8PLyKtfO8SyvqrEsKCgAgHKrugDduRBlM3ocy4oM+d709PREo0aNsGfPHmRkZOCpp54CYDvjKYTAjBkzEB0djT179ujDWJng4GD4+vpi9+7d+rbi4mLs27dPPw5hYWFwcHAo10elUuHMmTP6PrYwnqYYS0NY/VhKctqsCeXm5or4+HgRHx8vAIjPPvtMxMfHi+vXrwshhPj+++/Fn3/+Ka5evSq2b98ugoKCRGRkZLnn+Pzzz4Wbm5vYsmWLuHz5snjvvfeEk5OTuHLlir7P4MGDRadOncThw4fF4cOHRceOHcWTTz5Zr++1PphiPIUQ4vLly0Imk4lffvml0texhfGs7VgWFxeLli1bivDwcHH06FFx5coV8d///lfIZDLx888/6/vZwlgKYZrvzTVr1ojDhw+LK1euiG+++Ua4u7uLOXPmlOtjC+P50ksvCaVSKfbu3StUKpX+VlBQoO/z8ccfC6VSKaKjo8Xp06fF888/L/z8/EROTo6+z/Tp00VAQID4/fffxYkTJ8TAgQNFaGioKC0t1fex9vE01ViqVCoRHx8vVq1aJQCI/fv3i/j4eJGVlaXvY81jafFhpGwZ1P238ePHCyGEWLRokQgICBAODg6iadOm4r333hNFRUUVnicqKkoEBASIBg0aiN69e4uYmJhy92dlZYkxY8YIV1dX4erqKsaMGVNh6ZU1MNV4zp07VwQEBAiNRlPp69jCeJpiLC9duiQiIyOFt7e3aNCggejUqVOFpb62MJZCmGY833rrLeHj4yMcHBxEq1atxKeffiq0Wm25PrYwnpWNIwCxdu1afR+tVivmzZsnfH19hUKhEA8//LA4ffp0uee5e/eumDFjhnB3dxfOzs7iySefFMnJyeX6WPt4mmos582b98DnseaxlAkhRF3NuhARERE9iM2cM0JERETmiWGEiIiIJMUwQkRERJJiGCEiIiJJMYwQERGRpBhGiIiISFIMI0RERCQphhEiIiKSFMMIERERSYphhIiIiCTFMEJERESSYhghIiIiSf0/pg+c+exO4f8AAAAASUVORK5CYII=\n",
+ "text/plain": [
+ "
"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "beta_1 = 0.10\n",
+ "beta_2 = 1990.0\n",
+ "\n",
+ "#logistic function\n",
+ "Y_pred = sigmoid(x_data, beta_1 , beta_2)\n",
+ "\n",
+ "#plot initial prediction against datapoints\n",
+ "plt.plot(x_data, Y_pred*15000000000000.)\n",
+ "plt.plot(x_data, y_data, 'ro')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Our task here is to find the best parameters for our model. Lets first normalize our x and y:\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Lets normalize our data\n",
+ "xdata =x_data/max(x_data)\n",
+ "ydata =y_data/max(y_data)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### How we find the best parameters for our fit line?\n",
+ "we can use __curve_fit__ which uses non-linear least squares to fit our sigmoid function, to data. Optimize values for the parameters so that the sum of the squared residuals of sigmoid(xdata, *popt) - ydata is minimized.\n",
+ "\n",
+ "popt are our optimized parameters.\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " beta_1 = 690.451712, beta_2 = 0.997207\n"
+ ]
+ }
+ ],
+ "source": [
+ "from scipy.optimize import curve_fit\n",
+ "popt, pcov = curve_fit(sigmoid, xdata, ydata)\n",
+ "#print the final parameters\n",
+ "print(\" beta_1 = %f, beta_2 = %f\" % (popt[0], popt[1]))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now we plot our resulting regression model.\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "
\n",
+ "\n",
+ "IBM SPSS Modeler is a comprehensive analytics platform that has many machine learning algorithms. It has been designed to bring predictive intelligence to decisions made by individuals, by groups, by systems – by your enterprise as a whole. A free trial is available through this course, available here: SPSS Modeler\n",
+ "\n",
+ "Also, you can use Watson Studio to run these notebooks faster with bigger datasets. Watson Studio is IBM's leading cloud solution for data scientists, built by data scientists. With Jupyter notebooks, RStudio, Apache Spark and popular libraries pre-packaged in the cloud, Watson Studio enables data scientists to collaborate on their projects without having to install anything. Join the fast-growing community of Watson Studio users today with a free account at Watson Studio\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Thank you for completing this lab!\n",
+ "\n",
+ "\n",
+ "## Author\n",
+ "\n",
+ "Saeed Aghabozorgi\n",
+ "\n",
+ "\n",
+ "### Other Contributors\n",
+ "\n",
+ "Joseph Santarcangelo\n",
+ "\n",
+ "\n",
+ "##
"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.scatter(cdf.ENGINESIZE, cdf.CO2EMISSIONS, color='blue')\n",
+ "plt.xlabel(\"Engine size\")\n",
+ "plt.ylabel(\"Emission\")\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### Creating train and test dataset\n",
+ "Train/Test Split involves splitting the dataset into training and testing sets respectively, which are mutually exclusive. After which, you train with the training set and test with the testing set.\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "msk = np.random.rand(len(df)) < 0.8\n",
+ "train = cdf[msk]\n",
+ "test = cdf[~msk]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "
Polynomial regression
\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Sometimes, the trend of data is not really linear, and looks curvy. In this case we can use Polynomial regression methods. In fact, many different regressions exist that can be used to fit whatever the dataset looks like, such as quadratic, cubic, and so on, and it can go on and on to infinite degrees.\n",
+ "\n",
+ "In essence, we can call all of these, polynomial regression, where the relationship between the independent variable x and the dependent variable y is modeled as an nth degree polynomial in x. Lets say you want to have a polynomial regression (let's make 2 degree polynomial):\n",
+ "\n",
+ "\n",
+ "$$y = b + \\theta_1 x + \\theta_2 x^2$$\n",
+ "\n",
+ "\n",
+ "\n",
+ "Now, the question is: how we can fit our data on this equation while we have only x values, such as __Engine Size__? \n",
+ "Well, we can create a few additional features: 1, $x$, and $x^2$.\n",
+ "\n",
+ "\n",
+ "\n",
+ "__PolynomialFeatures()__ function in Scikit-learn library, drives a new feature sets from the original feature set. That is, a matrix will be generated consisting of all polynomial combinations of the features with degree less than or equal to the specified degree. For example, lets say the original feature set has only one feature, _ENGINESIZE_. Now, if we select the degree of the polynomial to be 2, then it generates 3 features, degree=0, degree=1 and degree=2: \n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[ 1. , 1.5 , 2.25],\n",
+ " [ 1. , 3.5 , 12.25],\n",
+ " [ 1. , 3.5 , 12.25],\n",
+ " ...,\n",
+ " [ 1. , 3.2 , 10.24],\n",
+ " [ 1. , 3. , 9. ],\n",
+ " [ 1. , 3.2 , 10.24]])"
+ ]
+ },
+ "execution_count": 12,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "from sklearn.preprocessing import PolynomialFeatures\n",
+ "from sklearn import linear_model\n",
+ "train_x = np.asanyarray(train[['ENGINESIZE']])\n",
+ "train_y = np.asanyarray(train[['CO2EMISSIONS']])\n",
+ "\n",
+ "test_x = np.asanyarray(test[['ENGINESIZE']])\n",
+ "test_y = np.asanyarray(test[['CO2EMISSIONS']])\n",
+ "\n",
+ "\n",
+ "poly = PolynomialFeatures(degree=2)\n",
+ "train_x_poly = poly.fit_transform(train_x)\n",
+ "train_x_poly"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**fit_transform** takes our x values, and output a list of our data raised from power of 0 to power of 2 (since we set the degree of our polynomial to 2). \n",
+ "\n",
+ "The equation and the sample example is displayed below. \n",
+ "\n",
+ "\n",
+ "$$\n",
+ "\\begin{bmatrix}\n",
+ " v_1\\\\\\\\\\\\\n",
+ " v_2\\\\\\\\\n",
+ " \\vdots\\\\\\\\\n",
+ " v_n\n",
+ "\\end{bmatrix}\\longrightarrow \\begin{bmatrix}\n",
+ " [ 1 & v_1 & v_1^2]\\\\\\\\\n",
+ " [ 1 & v_2 & v_2^2]\\\\\\\\\n",
+ " \\vdots & \\vdots & \\vdots\\\\\\\\\n",
+ " [ 1 & v_n & v_n^2]\n",
+ "\\end{bmatrix}\n",
+ "$$\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "$$\n",
+ "\\begin{bmatrix}\n",
+ " 2.\\\\\\\\\n",
+ " 2.4\\\\\\\\\n",
+ " 1.5\\\\\\\\\n",
+ " \\vdots\n",
+ "\\end{bmatrix} \\longrightarrow \\begin{bmatrix}\n",
+ " [ 1 & 2. & 4.]\\\\\\\\\n",
+ " [ 1 & 2.4 & 5.76]\\\\\\\\\n",
+ " [ 1 & 1.5 & 2.25]\\\\\\\\\n",
+ " \\vdots & \\vdots & \\vdots\\\\\\\\\n",
+ "\\end{bmatrix}\n",
+ "$$\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "It looks like feature sets for multiple linear regression analysis, right? Yes. It Does. \n",
+ "Indeed, Polynomial regression is a special case of linear regression, with the main idea of how do you select your features. Just consider replacing the $x$ with $x_1$, $x_1^2$ with $x_2$, and so on. Then the 2nd degree equation would be turn into:\n",
+ "\n",
+ "$$y = b + \\theta_1 x_1 + \\theta_2 x_2$$\n",
+ "\n",
+ "Now, we can deal with it as a 'linear regression' problem. Therefore, this polynomial regression is considered to be a special case of traditional multiple linear regression. So, you can use the same mechanism as linear regression to solve such problems. \n",
+ "\n",
+ "\n",
+ "\n",
+ "so we can use __LinearRegression()__ function to solve it:\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Coefficients: [[ 0. 50.8343626 -1.5636381]]\n",
+ "Intercept: [106.99883066]\n"
+ ]
+ }
+ ],
+ "source": [
+ "clf = linear_model.LinearRegression()\n",
+ "train_y_ = clf.fit(train_x_poly, train_y)\n",
+ "# The coefficients\n",
+ "print ('Coefficients: ', clf.coef_)\n",
+ "print ('Intercept: ',clf.intercept_)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "As mentioned before, __Coefficient__ and __Intercept__ , are the parameters of the fit curvy line. \n",
+ "Given that it is a typical multiple linear regression, with 3 parameters, and knowing that the parameters are the intercept and coefficients of hyperplane, sklearn has estimated them from our new set of feature sets. Lets plot it:\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Text(0, 0.5, 'Emission')"
+ ]
+ },
+ "execution_count": 9,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "
\n",
+ "\n",
+ "IBM SPSS Modeler is a comprehensive analytics platform that has many machine learning algorithms. It has been designed to bring predictive intelligence to decisions made by individuals, by groups, by systems – by your enterprise as a whole. A free trial is available through this course, available here: SPSS Modeler\n",
+ "\n",
+ "Also, you can use Watson Studio to run these notebooks faster with bigger datasets. Watson Studio is IBM's leading cloud solution for data scientists, built by data scientists. With Jupyter notebooks, RStudio, Apache Spark and popular libraries pre-packaged in the cloud, Watson Studio enables data scientists to collaborate on their projects without having to install anything. Join the fast-growing community of Watson Studio users today with a free account at Watson Studio\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Thank you for completing this lab!\n",
+ "\n",
+ "\n",
+ "## Author\n",
+ "\n",
+ "Saeed Aghabozorgi\n",
+ "\n",
+ "\n",
+ "### Other Contributors\n",
+ "\n",
+ "Joseph Santarcangelo\n",
+ "\n",
+ "\n",
+ "##