1378 lines
547 KiB
Plaintext
1378 lines
547 KiB
Plaintext
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"# Least Squares Regression: A Linear Algebra Perspective\n",
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"\n",
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"## Introduction\n",
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"\n",
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"This is meant to be a not entirely comprehensive introduction to Data Science for the Linear Algebraist. There are of course many other complicated topics, but this is just to get the essence of data science (and the tools involved) from the perspective of someone with a strong linear algebra background.\n",
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"\n",
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"One of the most fundamental questions of data science is the following. \n",
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"\n",
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"> **Question**: Given observed data, how can we predict certain targets?\n",
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"\n",
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"The answer of course boils down to linear algebra, and we will begin by translating data science terms and concepts into linear algebraic ones. But first, as should be common practice for the linear algebraist, an example.\n",
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"\n",
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"> **Example**. Suppose that we observe $n=3$ houses, and for each house we record\n",
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"> - the square footage,\n",
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"> - the number of bedrooms,\n",
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"> - and additionally the sale price.\n",
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"> \n",
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"> So we have a table as follows.\n",
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">\n",
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"> |House | Square ft | Bedrooms | Price (in $1000s) |\n",
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"> | --- | --- | --- | --- |\n",
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"> | 0 | 1600 | 3 | 500 |\n",
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"> | 1 | 2100 | 4 | 650 |\n",
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"> | 2 | 1550 | 2 | 475 |\n",
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">\n",
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"> So, for example, the first house is 1600 square feet, has 3 bedrooms, and costs $500,000, and so on. Our goal will be to understand the cost of a house in terms of the number of bedrooms as well as the square footage.\n",
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"> Concretely this gives us a matrix and a vector:\n",
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"> $$ X = \\begin{bmatrix} 1600 & 3 \\\\ 2100 & 4 \\\\ 1550 & 2 \\end{bmatrix} \\text{ and } y =\\begin{bmatrix} 500 \\\\ 650 \\\\ 475 \\end{bmatrix} $$\n",
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"> So translating to linear algebra, the goal is to understand how $y$ depends on the columns of $X$.\n",
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"\n",
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"\n",
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"## Translation from Data Science to Linear Algebra\n",
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"\n",
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"| Data Science (DS) Term | Linear Algebra (LA) Equivalent | Explanation |\n",
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"| --- | --- | --- |\n",
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"| Dataset (with n observations and p features) | A matrix $X \\in \\mathbb{R}^{n \\times p}$ | The dataset is just a matrix. Each row is an observation (a vector of features). Each column is a feature (a vector of its values across all observations). |\n",
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"| Features | Columns of $X$ | Each feature is a column in your data matrix. |\n",
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"| Observation | Rows of $X$ | Each data point corresponds to a row. |\n",
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"| Targets | A vector $y \\in \\mathbb{R}^{n \\times 1}$ | The list of all target values is a column vector. |\n",
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"| Model parameters | A vector $\\beta \\in \\mathbb{R}^{p \\times 1}$ | These are the unknown coefficients. |\n",
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"| Model | Matrix–vector equation | The relationship becomes an equation involving matrices and vectors. |\n",
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"| Prediction Error / Residuals | A residual vector $e \\in \\mathbb{R}^{n \\times 1}$ | Difference between actual targets and predictions. |\n",
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"| Training / \"best fit\" | Optimization: minimizing the norm of the residual vector | To find the \"best\" model by finding a model which makes the norm of the residual vector as small as possible. |\n",
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"\n",
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"So our matrix $X$ will represent our data set, our vector $y$ is the target, and $\\beta$ is our vector of parameters. We will often be interested in understanding data with \"intercepts\", i.e., when there is a base value given in our data. So we will augment a column of 1's (denoted by $\\mathbb{1}$) to $X$ and append a parameter $\\beta_0$ to the top of $\\beta$, yielding\n",
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"\n",
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"$$ \\tilde{X} = \\begin{bmatrix} \\mathbb{1} & X \\end{bmatrix} \\text{ and } \\tilde{\\beta} = \\begin{bmatrix} \\beta_0 \\\\ \\beta_1 \\\\ \\beta_2 \\\\ \\vdots \\\\ \\beta_p \\end{bmatrix}. $$\n",
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"\n",
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"So the answer to the Data Science problem becomes\n",
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"\n",
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"> **Answer**: Solve, or best approximate a solution to, the matrix equation $\\tilde{X}\\tilde{\\beta} = y$.\n",
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"\n",
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"To be explicit, given $\\tilde{X}$ and $y$, we want to find a $\\tilde{\\beta}$ that does a good job of roughly giving $\\tilde{X}\\tilde{\\beta} = y$. There of course ways to solve (or approximate) such small systems by hand. However, one will often be dealing with enormous data sets with plenty to be desired. One view to take is that modern data science is applying numerical linear algebra techniques to imperfect information, all to get as good a solution as possible.\n",
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"\n",
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"# Solving the problem: Least Squares Regression and Matrix Decompositions\n",
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"\n",
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"If the system $\\tilde{X}\\tilde{\\beta} = y$ is consistent, then we can find a solution. However, we are often dealing with overdetermined systems, in the sense that there are often more observations than features (i.e., more rows than columns in $\\tilde{X}$, or more equations than unknowns), and therefore inconsistent systems. However, it is possible to find a **best fit** solution, in the sense that the difference\n",
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"\n",
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"$$ e = y - \\tilde{X}\\tilde{\\beta} $$\n",
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"\n",
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"is small. By small, we often mean that $e$ is small in $L^2$ norm; i.e., we are minimizing the the sums of the squares of the differences between the components of $y$ and the components of $\\tilde{X}\\tilde{\\beta}$. This is known as a **least squares solution**. Assuming that our data points live in the Euclidean plane, this precisely describes finding a line of best fit.\n"
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41q9fj7/85S+48MILXfr7u/TSS3HZZZfh4YcfRkVFBcaNG2eb9W748OG49dZb7Y65ueM6n+joaFxwwQVYv349Jk2aZBsGeMkll6CkpAQlJSV46aWXWm1jw3M8//zzmDZtGrRaLYYMGYKAgAApv4OMjAx8+umnTbaPHj3adn1aW4SEhODVV1/FnDlzUFJSguuuuw7R0dEoKirCnj17UFRUhGXLlp335x944AG89957uPLKK/GPf/wDvXr1wtdff43XXnsNd999d7vWOiorK8PPP/8MnBmqun//fjzzzDMIDAy0u47vjTfewLRp03DZZZdh7ty56NGjB0pKSrB//37s3LnTNtX7hRdeiKuuugpDhgxBREQE9u/fj1WrVmHs2LG2172jX8eG51izZg2WLVuGkSNHcugeEbXO3bNJEBF1lI8++kjcdNNNol+/fiIkJET4+/uLnj17iltvvVVkZWU1efx7770nRo8eLYKCgkRISIgYPny4WL58ue3+rKwscemllwq9Xi8iIiLErFmzxPHjxwUA8fe//91uX48++qjo3r270Gg0djO15ebmiqlTpwq9Xi8A2M3CVVVVJf72t7+JAQMGiICAABEWFiaSk5PFAw88IPLz822PAyDmzZvn8O+hYda71pw7650QQphMJvHwww+LXr16CX9/f2EwGMTdd98tSktL7R7X0nGdzwMPPCAAiH/961922/v16ycAiL1799ptb27Wu9raWnHHHXeIqKgooSiK3Uxn5/s9nTtTXXMaZr0731dDLs43690nn3zS7P4a50kIITZt2iSuvPJKERkZKfz9/UWPHj3ElVde2eTnm3Ps2DFx0003ia5duwp/f38xYMAA8cILL9hmm2t8vG2d9U6r1YqePXuK6667TuzatavJ4/fs2SN+//vfi+joaOHv7y9iY2PF5MmTxeuvv257zCOPPCJGjRolIiIiRGBgoOjTp4944IEHRHFxse0xLb2OzZkzZ47o0qXLee9vbta7kpIScd1114nw8HDbcxARtUQRp/8zISIiIiIiojM4PTgREREREdE5WCgRERERERGdg4USERERERHROVgoERERERERnYOFEhERERER0TlYKBEREREREZ3D5xecVVUVJ0+ehF6vh6Io7m4OERERERG5iRAClZWV6N69OzSalvuMfL5QOnnyJOLj493dDCIiIiIi8hB5eXmIi4tr8TE+Xyjp9XrgzC8jNDTU3c0hIiIiIiI3qaioQHx8vK1GaInPF0oNw+1CQ0PbVShZrVZkZWVh8ODB0Gq1EltInRHzRDIxTyQT80QyMU8kk8w8OXJJjiKEEO16Fg9XUVGBsLAwlJeXt6tQEkLAbDYjKCiI1zpRuzFPJBPzRDIxTyQT80QyyciTM7WBz/coyaIoCnQ6nbubQT6CeSKZmCeSiXkimZgnksnVeeL04A6yWq3YvXs3rFaru5tCPoB5IpmYJ5KJeSKZmCeSydV54tC7M914FoulxV+6EAL19fXw9/dn1zE5RKvVws/Pr9m8ME8kE/NEMjFPJBPzRDLJyBOH3jmhrq4ORqMRNTU1rT5WCME/cnJKcHAwDAYDAgICmtzHi1pJJuaJZGKeSCbmiWRyZZ46daGkqiqOHj0KrVaL7t27IyAg4LyFEC9GJGcIIVBXV4eioiIcPXoU/fr1s1vUTFVVZGRkIDk5mf+BULsxTyQT80QyMU8kk6vz1KmH3pnNZhw9ehS9evVCcHBwi/tp/GtioUSOqqmpwbFjx9C7d28EBQXZtgshoKoqNBoN80TtxjyRTMwTycQ8kUwy8uTM0DtO5gDYfdLfEh+vKakDtJQtXthKMjFPJBPzRDIxTySTK/PEQskJZrPZ3U0gH6GqKrKysqCqqrubQj6AeSKZmCeSiXkimVydp059jZIzFEVpdXgekaO0Wi2GDRvm7maQj2CeSCbmiWRinkgmV+eJPUoOahgTyeF3HWfFihUIDw93dzNcQggBk8nEPJEUzBPJxDyRTMwTyeTqPLFQcoKnDL2bO3cuFEWBoijw9/dHTEwMLr30Urz77rtOd0XKLE4mTpxoa1dgYCD69++PZ555xuGxpNdffz0OHTrk9HPef//9bWyx+6iqisOHD3MoAknBPJFMzBPJxDyRTK7OEwslBzUMvWt28VBVoCCjAMd+PIaCjAIIteOr3MsvvxxGoxG5ubn45ptvMGnSJPz5z3/GVVddBYvF0uHPfz533nknjEYjDh48iPvuuw9/+9vfsHjxYod+VqfTITo6usPb6Am0Wi2nSiVpmCeSiXkimZgnksnVeWKh5CAhBKxWa5OuvryteVhzyxqsnb0WX931FdbOXos1t6xB3ta8Dm1PYGAgYmNj0aNHD4wYMQKPPfYYvvjiC3zzzTdYsWKF7XEvvfQSkpOT0aVLF8THx+Oee+5BVVUVACAtLQ233XYbysvLbT1BCxcuBAC8//77GDVqFPR6PWJjY3HTTTehsLCw1XYFBwcjNjYWCQkJmD9/PqZMmYLPP/8cAFBaWorZs2cjIiICwcHBmDZtGrKzs20/e27v1sKFCzFs2DCsWrUKCQkJCAsLww033IDKykrgTM/apk2b8Morr9jan5ubi9LSUtx8882IioqCTqdDv379sHz5com//fYTQqC6uppDEUgK5olkYp5IJubJc7jjg33ZXJ0nFkpOqKurs/s+b2se1i9YD+NOI3ThOoQnhEMXroNxlxHrF6zv8GLpXJMnT8bQoUOxZs0a2zaNRoP//Oc/2LdvH1auXIkNGzbgr3/9KwAgNTUVL7/8MkJDQ2E0GmE0GrFgwQLbsT799NPYs2cPPv/8cxw9ehRz5851uk06nQ719fXAmcJmx44d+PLLL7Ft2zYIIXDFFVfY7m9OTk4OPv/8c3z11Vf46quvsGnTJjz33HMAgFdeeQVjx4619WIZjUbEx8fjiSeeQFZWFr755hvs378fy5YtQ7du3Zxue0dSVRW5ubkcikBSME8kE/NEMjFPnsFdH+zL5uo8cdY7BymKAp1OZ/teqALpS9JhKjEhsm+kbUheQEgAIhMjUZJTgvSl6YgbEwdF47oF1gYOHIi9e/favm98/U7v3r3x9NNP4+6778Zrr72GgIAAhIWFQVEUxMbG2u3n9ttvt93u06cP/vOf/yAlJQVVVVUICQlptR2qqmL9+vX49ttvcf/99yM7OxtffvkltmzZgtTUVADABx98gPj4eHz++eeYNWvWefezYsUK6PV6AMCtt96KH374Af/6178QFhaGgIAAWy9Wg+PHj2P48OEYNWoUACAhIcGJ36BraLVaJCUlubsZ5COYJ5KJeSKZmCf3a/hg31Rigt6gh5/ODxaTxfbB/tTFUxGfGu/uZjrE1Xlij5KDzh16V5hZiKL9RdAb9E2uW1IUBfpYPYqyilCY2fpwNdntbNyejRs34tJLL0WPHj2g1+sxe/ZsnDp1CtXV1S3uZ9euXZg+fTp69eoFvV6PiRMnAmeKkJa89tprCAkJQVBQEH73u9/hlltuwd///nfs378ffn5+uPDCC22P7dq1KwYMGID9+/efd38JCQm2IgkADAZDq0MA7777bqxevRrDhg3DX//6V2zdurXFx7uDEAIVFRUcikBSME8kE/NEMjFP7nXuB/sBIQHQaDW2D/ZNpSakL033mmF4rs4TCyUnNB56Zy41w1prhZ+u+U45P50frLVWmEtdO1Pe/v370bt3bwDAsWPHcMUVV+CCCy7AZ599hl9//RVLly4FgBaHu1VXV2Pq1KkICQnB+++/j+3bt2Pt2rVAM8MPz3XzzTdj9+7dyMnJgclkwjvvvIPg4ODzBvrcwu5c/v7+dt8ritJqd+u0adNw7Ngx3H///Th58iSmTJliG1LoKVRVxcmTJzkUgaRgnkgm5olkYp7cy1M/2G8rV+eJhZKDGobeNYQsKCII2kAtLKbmZ5izmCzQBmoRFBHksjZu2LABGRkZuPbaawEAO3bsgMViwYsvvogxY8agf//+OHnypN3PBAQENJm++8CBAyguLsZzzz2Hiy++GAMHDnRoIgcACAsLQ9++fREfH283I8ngwYNhsVjwyy+/2LadOnUKhw4dwqBBg9p8zM21HwCioqIwd+5cvP/++3j55Zfx5ptvtvk5OoJWq8XAgQM5CxBJwTyRTMwTycQ8uZenfrDfVq7OEwslBwkhYLFYbD0j0UnRiBoUhcr8yia9JUIIVOZXImpwFKKTOma669raWuTn5+O3337Dzp078cwzz2D69Om46qqrMHv2bABAYmIiLBYLXn31VRw5cgSrVq3C66+/brefhIQEVFVV4YcffkBxcTFqamrQs2dPBAQE2H7uyy+/xNNPP92u9vbr1w/Tp0/HnXfeic2bN2PPnj245ZZb0KNHD0yfPr3N+01ISMAvv/yC3NxcFBcXQ1VVPPnkk/jiiy9w+PBhZGZm4quvvmpXMdYRhBAoKyvjUASSgnkimZgnkol5ci9P/GC/PVydJxZKTmi8PpGiUZAyPwW6CB1KckpQV1UH1aqirqoOJTkl0EXokDIvpcMmcli3bh0MBgMSEhJw+eWXY+PGjfjPf/6DL774wlZlDxs2DC+99BKef/55XHDBBfjggw/w7LPP2u0nNTUVd911F66//npERUVh0aJFiIqKwooVK/DJJ59g8ODBeO655xxeC6kly5cvx8iRI3HVVVdh7NixEELgf//7X5Phdc5YsGABtFotBg8ejKioKBw/fhwBAQF49NFHMWTIEIwfPx5arRarV69ud/tlUlUVRUVFHIpAUjBPJBPzRDIxT+7l7g/2ZXN1nhTh4yV+RUUFwsLCUF5ejtDQULv7zGYzjh49it69eyMoqG2VdN7WPKQvSUfR/iJYa63QBmoRNTgKKfNSvGYGEeo4MjJGRERE1Fa2We9KTdDHnp31rjK/EroInVfNeidDS7XBuTg9uIMaZr3TarV2F8PFp8YjbkwcCjMLYS41IygiCNFJ0S6dEpy8j6qqKC0tRUREBDQaduxS+zBPJBPzRDIxT+4XnxqPqYunnv1gv+D0B/uGEQav+2Df1XlioeQEi8XS7MVjikZBTHKMW9pE3qlhjG14eLi7m0I+gHkimZgnkol58gy+8sG+q/PEQslBiqJw6BRJo9VqkZiY6O5mkI9gnkgm5olkYp48hy98sO/qPLEP1EFCCNTX13PWFpJCVVUUFhby4laSgnkimZgnkol5IplcnScWSk7gHznJVFNT4+4mkA9hnkgm5olkYp5IJlfmiUPvHKQoCgIDA93dDPIRGo0GCQkJ7m4G+QjmiWRinkgm5olkcnWe2KPkIA69I5lUVUV+fj57KUkK5olkYp5IJuaJZHJ1nlgoOYF/5CRTXV2du5tAPoR5IpmYJ5KJeSKZXJknDr1zEIfekUwajQY9e/Z0dzPIRzBPJBPzRDIxTySTq/PEHiUHCSFQV1fnFUPvFEXB559/7u5mID8/H5deeim6dOni9esnLFy4EMOGDZO2P1VV8dtvv7GXkqRgnkgm5olkYp5IJlfniYWSF5o7dy5mzJhx3vuNRiOmTZvm0jY159///jeMRiN2796NQ4cONfuYhQsXQlEU21dYWBguvvhibNq0SVo7VqxY4VChtmLFCru2NHy9/fbbWLBgAX744QfbY1t7DYiIiIjIu3HonYMURUFAQIC7m+GQ2NhYdzcBAJCTk4ORI0eiX79+LT4uKSkJ33//PQCgpKQEixcvxlVXXYUTJ04gLCzMRa09LTQ0FAcPHrTbFhYWBp1Oh5CQEGnPo9Fo0KNHD2n7o86NeSKZmCeSiXkimVydJ/YoOUgIgdraWq8bepebmwtFUbBmzRpMmjQJwcHBGDp0KLZt22b3M1u3bsX48eOh0+kQHx+P++67D9XV1S0+z7Jly5CYmIiAgAAMGDAAq1atst2XkJCAzz77DO+99x4URcHcuXPPux8/Pz/ExsYiNjYWgwcPxlNPPYWqqiq7Xqjy8nL88Y9/RHR0NEJDQzF58mTs2bPHdv+ePXswadIk6PV6hIaGYuTIkdixYwfS0tJw2223oby83NZDtHDhwhZ/dw1tafjS6XR2Q+8WLlyIlStX4osvvrDtMy0trcXf1blUVcXx48c5FIGkYJ5IJuaJZGKeSCZX54k9Sufx2c9HsObno3bbBAQUKHbb+saG4qkbRttt+/vq7TicX9Hqc1wzpjeuHdNHUotb9vjjj2Px4sXo168fHn/8cdx44404fPgw/Pz8kJGRgcsuuwxPP/003nnnHRQVFWH+/PmYP38+li9f3uz+1q5diz//+c94+eWXcckll+Crr77Cbbfdhri4OEyaNAnbt2/H7NmzERoaildeeQU6nc6hdtbW1tqGyg0YMAA4U6ReeeWViIyMxP/+9z+EhYXhjTfewJQpU3Do0CFERkbi5ptvxvDhw7Fs2TJotVrs3r0b/v7+SE1Nxcsvv4wnn3zS1lPU3p6hBQsWYP/+/aioqLD9fiIjI53ej7f0UJJ3YJ5IJuaJZGKeSCZX5omF0nnU1FpQXGlu9XFRoUFNtpXX1Dn0szW1lja3z1kLFizAlVdeCQB46qmnkJSUhMOHD2PgwIF44YUXcNNNN+H+++8HAPTr1w//+c9/MGHCBCxbtgxBQU2PcfHixZg7dy7uueceAMCDDz6In3/+GYsXL8akSZMQFRWFwMBA6HS6VocCZmRk2IqXmpoa6PV6fPTRRwgNDQUAbNy4ERkZGSgsLLTNPLh48WJ8/vnn+PTTT/HHP/4Rx48fx0MPPYSBAwfajqFBWFiYraeoNeXl5XaFVEhICPLz8+0eExISAp1Oh9ra2jYPc9RoNB4zRJK8H/NEMjFPJBPzRDK5Ok8slM4jONAP3fT2BYIQAopi36MUFty0qg0LDmjys+d7DlcZMmSI7bbBYAAAFBYWYuDAgfj1119x+PBhfPDBB7bHCCGgqiqOHj2KQYMGNdnf/v378cc//tFu27hx4/DKK6843bYBAwbgyy+/BABUVlbio48+wqxZs7Bx40aMGjUKv/76K6qqqtC1a1e7nzOZTMjJyQHOFGp33HEHVq1ahUsuuQSzZs1CYmKi023R6/XYuXOn7XuNpmNGpzZ0Hffs2bPDnoM6D+aJZGKeSCbmiWRydZ5YKJ3HtWP62A2LE0LAYrHAz8+vSbF0rnOH4nkCf39/2+2G9jeM71RVFX/6059w3333Nfm5luaqP/f30Fwh6YiAgAD07dvX9v3w4cPx+eef4+WXX8b7778PVVVhMBiavQ6oYTa7hQsX4qabbsLXX3+Nb775Bn//+9+xevVqzJw506m2aDQau7Z0pODgYJc8D3UOzBPJxDyRTMxT5yZUgcLMQphLzQiKCEJ0UjQUjfPvFxu4Mk8slBykKIpdseFLRowYgczMTKcKhEGDBmHz5s2YPXu2bdvWrVub7X1qC61WC5PJZGtffn4+/Pz8kJCQcN6f6d+/P/r3748HHngAN954I5YvX46ZM2ciICAAVqtVSrsatHefGo0G0dHRUttEnRfzRDIxTyQT89S55W3NQ/qSdBTtL4K11gptoBZRg6KQMj8F8anxTu/P1XliH6iDhBAwm80eM+tdeXk5du/ebfd1/PjxNu3r4YcfxrZt2zBv3jzs3r0b2dnZ+PLLL3Hvvfee92ceeughrFixAq+//jqys7Px0ksvYc2aNViwYIHTz2+xWJCfn4/8/HxkZ2fjn//8J7KysjB9+nQAwCWXXIKxY8dixowZ+Pbbb5Gbm4utW7fib3/7G3bs2AGTyYT58+cjLS0Nx44dw5YtW7B9+3Zb0ZaQkICqqir88MMPKC4uRk1NTZt+T40lJCRg7969OHjwIIqLi1FfX+/Uz1utVuTk5Egv4KhzYp5IJuaJZGKeOq+8rXlYv2A9jDuN0IXrEJ4QDl24DsZdRqxfsB55W/Oc3qer88RCyQl+fp7TAZeWlobhw4fbfT355JNt2teQIUOwadMmZGdn4+KLL8bw4cPxxBNP2K5las6MGTPwyiuv4IUXXkBSUhLeeOMNLF++HBMnTnT6+TMzM2EwGGAwGDBs2DB8/PHHWLZsma23SlEU/O9//8P48eNx++23o3///rjhhhuQm5uLmJgYaLVanDp1CrNnz0b//v3x+9//HtOmTcNTTz0FAEhNTcVdd92F66+/HlFRUVi0aFGbfk+N3XnnnRgwYABGjRqFqKgobNmyxamfVxQF4eHhbRqqSHQu5olkYp5IJuapcxKqQPqSdJhKTIjsG4mAkABotBoEhAQgMjESplIT0pemQ6jOdUC4Ok+K8JQukg5SUVGBsLAwlJeX22ZRa2A2m3H06FH07t272ZndiNqLGSMiIqLOpiCjAGtnr4UuXIeAkKYTn9VV1cFUZsLM92YiJjnGpW1rqTY4F3uUHORpQ+/Iu1mtVmRnZ3MoAknBPJFMzBPJxDx1TuZSM6y1Vvjpmh+N5afzg7XWCnNp68vpNObqPLFQcoInDb0j76bRaBAVFcWpUkkK5olkYp5IJuapcwqKCII2UAuLqfk1Qy0mC7SBWgRFODfaxtV5cmtqly1bhiFDhiA0NBShoaEYO3YsvvnmG9v9QggsXLgQ3bt3h06nw8SJE5GZmemWtiqK4tDU4ESO4Jhtkol5IpmYJ5KJeeqcopOiETUoCpX5lU1GYwkhUJlfiajBUYhOcm4GO1fnya2FUlxcHJ577jns2LEDO3bswOTJkzF9+nRbMbRo0SK89NJLWLJkCbZv347Y2FhceumlqKysdHlbhRAwmUwcekdSWK1WHDhwgEMRSArmiWRinkgm5qlzUjQKUuanQBehQ0lOCeqq6qBaVdRV1aEkpwS6CB1S5qU4vZ6Sq/PkcZM5REZG4oUXXsDtt9+O7t274/7778fDDz8MAKitrUVMTAyef/55/OlPf3Jof45M5pCQkACdTtfifoQQUFUVGo2Gn4qQw0wmE3Jzc5tM5iCEQGVlJfR6PfNE7cY8kUzME8nEPHVuza6jNDgKKfPato6SjDw5M5mDx1x0Y7Va8cknn6C6uhpjx47F0aNHkZ+fj6lTp9oeExgYiAkTJmDr1q3nLZRqa2tRW1tr+76iogIAoKqq3b8ajQZarRZCCNTU1NjexCqKYus1Ovd24/GQ53tMS3VnS/v2hts8JudvV1dXQwgBf39/u+wJIRASEgJFUey2W61WW9asVqutMHfmNs7kvPHthqw7c1tVVQghbLcb2ujsbR6Ta44pNDTUdttXjskXXydvOSa9Xu9zx+SLr5O3HFOXLl2Acz509vZj8sXXqSOOqfuF3XHNmGtQsK8AplITgiOD0W1QN1tPkrPHpKqqrUhq6zE500fk9ivrMjIyEBISgsDAQNx1111Yu3YtBg8ejPz8fABATIz9lIExMTG2+5rz7LPPIiwszPYVH3+6Wv3tt98AAEajEUaj0Xbb398fhYWFKCgoQGVlJcxmMyoqKlBdXW1322QyoaSkxLa9vLwcNTU1MJvNKCsrg8lkava22WyGyWRq9nZNTQ3Ky8ub3K6urkZFRUWT21VVVbY2Nr5dWVlpd7uqqqrJ7eaO6dzj4DHJO6aKigqcOnUK+fn5UBQFWq3WLnt5eXnYsWMHrFYrjh8/juLiYgBAbm4uSktLAQBHjhxBeXk5ACA7O9s25PTAgQO2RXOzsrJgNpttf0v19fVQVRUZGRlQVRX19fXIyMgAzvSgZmVlAQBqampw4MABAEBlZSWys7OBMwsZHzlyBABQWlqK3NxcAEBxcbFtQePCwkKcOHGiyd/TiRMnUFhYCAA8Jhcf05EjR5CZmYnCwkKfOSZffJ285ZisViv27NmD/fv3+8wx+eLr5C3HZLVa8eOPP8JsNvvMMfni69SRx6RoFGhiNVB6KYhJjkFRcVGbj+nw4cPYuXOnbfa7th6To9w+9K6urg7Hjx9HWVkZPvvsM7z99tvYtGkTysrKMG7cOJw8edJu4dM777wTeXl5WLduXbP7a65HKT4+HqWlpQgPD29SrQohUFhYaHsBmusdaOjaU1UViqI02d6RtzuqN8UVbecxKQgLC7MtinvupyM1NTUICQmxPd4TPwnyxU+3fPGYVFVFbW0tgoKC7D518+Zj8sXXyVuOSaPRoLq6GkFBQfDz8/OJY/LF18lbjgln3kg3HkXh7cfki6+TtxyTxWKB2WxGly5dbG109pgqKioQHh7u0NA7txdK57rkkkuQmJiIhx9+GImJidi5cyeGDx9uu3/69OkIDw/HypUrHdqfo+MQrVarUxUmUWv8/f2h1Wrd3QwiIiIiOsMrr1FqIIRAbW0tevfujdjYWHz33Xe2Qqmurg6bNm3C888/L/15tVpti29qrVYrsrKyMHjwYL75pXZjnkgm5olkYp5IJuaJZHJ1ntxaKD322GOYNm0a4uPjUVlZidWrVyMtLQ3r1q2Doii4//778cwzz6Bfv37o168fnnnmGQQHB+Omm25yeVs1Gg369u1r674jag/miWRinkgm5olkYp5IJlfnya2FUkFBAW699VYYjUaEhYVhyJAhWLduHS699FIAwF//+leYTCbcc889KC0txYUXXoj169dDr9e7vK2KorQ6hTiRo5gnkol5IpmYJ5KJeSKZXJ0nj7tGSTZnxiG2xGq1IiMjA8nJyew6pnZjnkgm5olkYp5IJuaJZJKRJ2dqAxZKDhJCoL6+Hv7+/rYZz4jainkimZgnkol5IpmYJ5JJRp6cqQ04YNQJ/CSEZGKeSCbmiWRinkgm5olkcmWeWCg5SG20UBVRezFPJBPzRDIxTyQT80QyuTpPHHrnoMYL8bHrmNqLeSKZmCeSiXkimZgnkklGnjj0roNYrVZ3N4F8CPNEMjFPJBPzRDIxTySTK/PEQslBqqoiKyuLXcckBfNEMjFPJBPzRDIxTySTq/PEoXdERERERG4mVIHCzEKYS80IighCdFI0FI1vDFcUQnjM0EtnagO3LjjrTYQQMJvNCAoK8pgXmrwX80QyMU8kE/NEMjFPjsnbmof0Jeko2l8Ea60V2kAtogZFIWV+CuJT493dvDbLLazE8o0HMbx3V8xI6d3u/bk6Txx65yBVVXH48GF2HZMUzBPJxDyRTMwTycQ8tS5vax7WL1gP404jdOE6hCeEQxeug3GXEesXrEfe1jx3N7FNhBB46f/24udDBfjwp8OoqbW0e5+uzhMLJQdptVquKk3SME8kE/NEMjFPJBPz1DKhCqQvSYepxITIvpEICAmARqtBQEgAIhMjYSo1IX1pOoTqfVfKKIqCOZP6AwD8tRr8VlLd7n26Ok8slBwkhEB1dTV8/JIuchHmiWRinkgm5olkYp5aVphZiKL9RdAb9E2GkimKAn2sHkVZRSjMLHRbGx1Rba7Hyo0HkZlXYrd9RO9ueHjGMLw7byL6GcLa/TyuzhMLJQepqorc3Fx2HZMUzBPJxDyRTMwTycQ8tcxcaoa11go/XfPTBvjp/GCttcJcanZ52xxRW2/FJ9tyMGfJRny4+TDe+eGAXRGjKAomJ/dAoL+cHiBX54mTOThIq9UiKSnJ3c0gH8E8kUzME8nEPJFMzFPLgiKCoA3UwmKyICAkoMn9FpMF2kAtgiKC3NK+87GqKtbvOYH3N2WjuPJsEXfwtzIcK6pCQrS+Q57X1XlioeQgIQQqKyuh1zftGiVyFvNEMjFPJBPzRDIxTy2LTopG1KAoGHcZEZkYafc7EkKgMr8ShhEGRCdFu7WdDYQQ2Lw/HyvSDuLEqbPXHCkAJif3wK0T+sMQEdyhz+/KPHHonYNUVcXJkyfZdUxSME8kE/NEMjFP1JhQBQoyCnDsx2MoyChwelIB5qllikZByvwU6CJ0KMkpQV1VHVSrirqqOpTklEAXoUPKvBS3r6ckhMCvOUW4950t+OdnO+2KpDH9orHsjxfjrzOGdWiRBDfkiQvOEhEREVETvrq2jydq9nc9OAop8zzjdy2EwF9X/Yy9x85O1nBBz0jcPnkAkuIj3do2ZzlTG7BQcpAQAuXl5QgLC2PXMbUb80QyMU8kE/NEaLS2j6nEBL1BDz+dHywmCyrzK6GL0GHq4qkOvYFnnhwnVIHCzEKYS80IighCdFK023uSGss6UYoHlm9Fn5hQ3D55AEYlRrn8NZWRJ2dqA16j5CBVVVFUVAS9Xs+1AKjdmCeSiXkimZgnOndtn4Y3pA1r+5TklCB9aTrixsS1+kaeeXKcolEQkxzj7magsNyEVZsOYUJSd4xKjLJtHxwXgUW3jkFyr0ho3FT0ujpP7FEiIiIiIpuCjAKsnb0WunBdszOx1VXVwVRmwsz3ZnrEG3uSo6y6Fqu35OCrHcdQb1XRNzYUr95xkduKoo7iTG3AyRwcpKoqTp06xYsRSQrmiWRinkgm5olkru3DPHm+mloL3t90CHOXbMTaX46i3nr6tcovq7GbtMETuDpPHHrnICEEysrKEB4e7u6mkA9gnkgm5olkYp5I5to+zJPnqrNY8dWvx7F682GU19TZtgf6aTAjpTdmpSZCr/N3axvP5eo8cegdEREREdkIVWDNLWvOu7ZPSU4JDCMMuGbVNR412QA5RgiB7/aewKpN2SgsN9m2azUKpg2Px00X90NXvWctcCsTh951AFVVUVhYyK5jkoJ5IpmYJ5KJeSKZa/swT55HURT8tD/frkiamNQdb909AfdekezRRZKr88Shd06oqalxdxPIhzBPJBPzRDIxTxSfGo+pi6eeXdun4PTaPoYRBqfX9mGe3E8IYdczOHfiAGzPLsTovlGYO2kAEmPD3No+Z7gyTxx6R0RERETN8vS1fahl2cZyvLvhAK4Y3hMXDzbY3Xe8uAo9u4W4rW3uwnWUOkBDV190dDQ0Go5YpPZhnkgm5olkYp6osfau7cM8uUdecRVWph3CT/uNwJm1kVIHxkDb6DXwxiLJ1XlioeSEuro6Bx5F5BjmiWRinkgm5olkYp5cp6jChPd/zMb63SegNho0Vm9VkV9mQo/ILm5tnwyuzBOH3hERERERebGKmjqs3nIYX24/ZlsHCQAiugTipov7YtqInvDXskcPHHrXMVRVhdFohMFgYNcxtRvzRDIxTyQT80QyMU8dSwiB/24+jE+2HUFNrcW2PTjQD7PG9sHMC3tDF+A7b/ddnSff+c0REREREXUiiqIgt7DSViQF+GkwfXQCfp+aiNDgposFk3M49I6IiIiIyAtY1dNv27WNZh787VQ17nrzR1wyJA43X9wP3UI9dx0kT8AFZzuAqqo4fvw4F0wjKZgnkol5IpmYJ5KJeZJDCIFtBwtw95s/4oeME3b39ejaBe//eQr+fGWyzxdJrs4Th945ISCAXZgkD/NEMjFPJBPzRDIxT+2z99gpvLvhAPafKAMArNqUjYlJ3RHgp7U9JqwTDbNzZZ5YKDlIo9EgNjbW3c0gH8E8kUzME8nEPJFMzFPbHTaWY/nGg9iRU2S3PTIkEKVVtYgJD3Zb29zF1XlioeSghq6+nj17ctYWajfmiWRinkgm5olkYp6c99upaqxMO4hNWUa77T27heC2yQMwtn8MFEU578/7MlfniYWSE4KDO1/lTh2HeSKZmCeSiXkimZgnxwghsHRdJr7+9bjdYrHRYTrMntAfk5N72E3i0Fm5Mk8slByk0WgQHR3t7maQj2CeSCbmiWRinkgm5slxiqKg3qraiqSw4ADcdHFfXDGip931SJ2Zq/PEPlAHWa1W5OTkwGq1ursp5AOYJ5KJeSKZmCeSiXk6P3OdBfVW+9nbbhnfD2HBAbh1Qn+smD8JM1J6s0hqxNV5Yo+SgxRFQXh4eKcdE0pyMU8kE/NEMjFPJBPz1FS9VcU3vx7H+2kHMS0+Cldc0APRSdFQNAqiQnV4/8+TWRydh6vzxAVniYiIiIg6mCoE0vadxLvfZqHIVAcACDBbcdm3Rhj6d0PK/BTEp8a7u5k+jwvOdgCr1Yrs7Gx2HZMUzBPJxDyRTMwTycQ8nZ6kIT27EPPe2oznP99tK5IAILbaCr+uOhh3GbF+wXrkbc1za1s9navzxKF3DtJoNIiKiuLUliQF80QyMU8kE/NEMnX2PGXmleDdDQex73iJ3XZDuQUjTpgRVa0CAf4QiZEoySlB+tJ0xI2Jg8LZ7Zrl6jyxUHJQw5hIIhmYJ5KJeSKZmCeSyd15EqpAYWYhzKVmBEUE2a4F6vDnFQL//HQnNh/It9seXlqHEbkm9Ky3b4OiKNDH6lGUVYTCzELEJMd0eBu9kavzxELJQQ1dff369YNWywvsqH2YJ5KJeSKZmCeSyZ15ytuah/Ql6SjaXwRrrRXaQC2iBkW55FogRVEQFaazfR/XtQuujInEySd+QkRCOKBtWqz56fxgLbDCXGru0LZ5M1fnqXP2g7aBRqNB9+7dO23XMcnFPJFMzBPJxDyRTO7KU97WPKxfsB7GnUbownUITwiHLrzjrgUqqTLDXG9/3cwN4xLRs1sIHrx6CN68azzG9Y+BX6AWFpOl2X1YTBZoA7UIigiS2jZf4uo88SzoIEVREBoayuktSQrmiWRinkgm5olkckeehCqQviQdphITIvtGIiAkABqtBgEhAYhMjISp1IT0pekQavsnfq4y12P5hgOYuyQNX6QftbsvvEsg3rxrPC4bFg+tRoPopGhEDYpCZX4lzp10WgiByvxKRA2OQnQSF+g9H1fniYWSg6xWKzIzMzv1rC0kD/NEMjFPJBPzRDK5I0+FmYUo2l8EvUHf5A31udcCtZW53oqPt+ZgzqsbsXpLDmrPfF9pqm/yfLbbGgUp81Ogi9ChJKcEdVV1UK0q6qrqUJJTAl2EDinzUjiRQwtcnSdeo+QgjUaDhIQEDkUgKZgnkol5IpmYJ5LJHXkyl5phrbXCT9f829z2XAtksapYv+cE3v/xEE5V1p7dp0bBJUPiINByL1V8ajymLp569tqpgtPXThlGGJAyj+sotcbVeWKh5CBFUdClSxd3N4N8BPNEMjFPJBPzRDK5I09BEUHQnrkWKCAkoMn9bbkWSBUCP2YZsTLtIE6W1Ni2KwCmDOmBWyf0R2x4sEP7ik+NR9yYOLfMxuftXJ0nflzkIKvVioyMDA5FICmYJ5KJeSKZmCeSyR15kn0tkBACD733M55ds8uuSBrbPwav/2k8Hpo+zOEiqYGiURCTHINe43shJjmGRZKDXJ0nFkoO0mg06Nu3L4cikBTME8nEPJFMzBPJ5I48yb4WSFEUDOkZaft+SK9I/Pu2VCy8fhQSovUdeCR0LlfnSRHnlto+pqKiAmFhYSgvL0doaKi7m0NERERELtDsOkqDo1q9Fii3sBLdQoMQEuRv21Ztrsc/Pv0Vs8YmYmSfbpwV0os5UxuwUHJQQ1dfcnIyF+CjdmOeSCbmiWRinkgmd+dJqMLha4Hyy2qwatMh/LD3N1w/LhG3TR7o8vZSy2TkiYVSI7IKJSEE6uvr4e/vz08RqN2YJ5KJeSKZmCeSyRvyVFZdi/9uPoyvdhyD5czaSoH+WiyfNxFd9Vz81ZPIyJMztQFnvXMCP1kjmZgnkol5IpmYJ5LJU/NUba7Hpz8fwZqfj8Jcf3ZygJAgf9wwLtFu6B15DlfmiYWSg1RV5VCEc+Tn56OsrMzdzfBKVqsVhw4dQv/+/ZmnVoSHhyM2NtbdzfBoPD+RTMwTyeSJeaqzWPHl9mP4aMthVDRaIDbQX4uZKQmYlcoiyVO5Ok8ceucgIQRUVYVGo/HYrmNXys/Px3XXXQez2fnF2oicERQUhE8//ZTFUgt4fiKZmCeSydPyJITA3W/+hKOFlbZtWo2CK0b0xE0X90VkCIfaeTIZeeLQuw5itVo5XeoZZWVlMJvNePrpp9G7d293N8frCCEghICiKB7xH4enOnr0KJ544gmUlZWxUGoFz08kE/NEMnlSnhRFwaQLeuDohgNQAExOPr1YrCHCuXWQyH1cmScWSg5SVRVZWVke1XXsCXr37o2BAzkrjLOEEDCZTNDpdCyUqN14fiKZmCeSyd152nmkGH1i9AjvEmjbNj0lAceLK3HdmD7oHcOlY7yJq/PEQslBWq0Ww4YNc3czyEcoioLgYH56RXLw/EQyMU8kk7vydPBkGd7dcAC7j57CjJQE3H1Zku2+IH8tHprOjHsjV+eJhZKDhBAwm80ICgpiDwC1G4fekUw8P5FMzBPJ5Oo8HS+qxIq0Q9hyIN+27asdx3DtmD6IDtN1+PNTx3J1njxjwKgXUFUVhw8fhqqq7m4K+QhOhEGy8PxEMjFPJJOr8lRYbsKLX+7Bn9740a5IMkQE4y+/G4puoZykwRe4+vzEQslBWq2W47W90KFDh7BgwQKMHDkS4eHhiIyMxLhx4/Dpp5+2aX/ff/+9rReouLjY7r6FCxfa7mv8FRTU9OTcMPTO3Z/Wzp07t9k2O3rd2VdffYXZs2cjOTm51cXfDh06hGuvvRYREREIDg7GhRdeiC+//FLi0XRePD+RTMwTydTReSqrrsUb67Nw+9I0rN9zAmfWi0VkSCDmT0vCW3dPwOTkHtCwd9QnuPr8xKF3DhJCoKamxiPe3JLj1q9fj6+//hq33norRo8eDYvFgo8++gizZs3CU089hSeffNLhfVVVVeHOO+9E9+7dcfLkyfM+bt26dQgLC7N939zMLJ40XapOp8OGDRuabHPE2rVr8fPPP2P48OEIDAzEr7/+2uzjcnNzMXbsWBgMBrz++usICQnBsmXLMGPGDHzyySe49tprpRxLZ8XzE8nEPJFMHZknVQg8uGIbfiuptm0LCfLD71MTMX10AoIC+DbX17j6/MQEOUhVVeTm5mLgwIH8lM2L3HDDDZg3b57dH9O0adNQXFyM559/Hg8//DACAwNb3EeDRx55BBEREbjyyivxz3/+87yPGzlyJLp169bq/urq6prtbXJWWloaJk2ahKNHjyIhIcHpn9doNBgzZkybnvutt96yFYLz588/b6H03HPPoaamBt9++y169OgBALj88suRnJyMBx54ADNnzvSYqWO9Ec9PJBPzRDJ1ZJ40ioIZKQlYui4TgX4azEjpjVmpidDruFisr3L1+YnvTByk1WqRlJTE/zQc8NNPP0FRFPz3v/9tct97770HRVGwfft2l7SlW7duzX7ikJKSgpqaGpSUlDi0n59++glvvvkm3n777XZn4LnnnoNWq7UN42swd+5cBAcHIyMjo137dyVHi5stW7Zg6NChtiIJZ/6mpk2bhry8PKSnp3dgK30fz08kE/NEMsnKk1UV+G7PCRSWm+y2TxvRE9ePS8Ty+ZNw+5SBLJJ8nKvPTyyUHCSEQEVFBYQQ7m6Kx7v44osxfPhwLF26tMl9S5YswejRozF69OgW92GxWBz6auvrsXHjRkRFRSE6OrrVx5pMJvzhD3/A/fffjxEjRrT6+IaxszExMZg9ezaOHz9ud//DDz+MadOmYc6cOcjNzQUALF++HCtXrsSrr76K5OTkNh1TW5lMJsTGxkKr1SIuLg7z5893uIB0VF1dXbM9dw3b9u7dK/X5Ohuen0gm5olkam+ehBDYeiAfd73xIxZ/uQfv/3jI7n5/rQa3Tx6IrnpO1tAZuPr8xELJQaqq4uTJk5wFyEH33XcftmzZgt27d9u2bd++Hdu3b8f8+fNb/Nnc3Fz4+/s79LVp0yan2/b2228jLS0Nf/vb3xz6ROKJJ56A1WrFU0891eLjEhMT8a9//Qvvvvsuvv/+ezz44IP4+uuvkZKSgt9++832OEVRsHLlSgQHB+P666/Hrl27MH/+fNxyyy34wx/+0Gp7rFarXbFotVqb3e5IVocOHYrFixdj1apVWLduHebOnYvly5dj3LhxqKqqavXnHTV48GDs3bu3yT43b94MADh16pS05+qMeH4imZgnkqk9edqdW4wHlm/FU5/8iuPFp///aK5XiToPV5+feI2Sg7RarcMzgRFw44034uGHH8bSpUvx1ltvAQBeffVVREVF4frrr2/xZ7t37+7w0LwBAwY41a5vvvkG8+bNw3XXXYd777231cenp6fj5Zdfxrp161qd4ODWW2+1+37SpEmYNGkSxo4di0WLFuGVV16x3detWzd8/PHHmDBhAlJTU5GQkIDXX3/doWOYMmVKswVi37597b6fM2cOVqxY0eK+HnjgAbvvL730UgwfPhzXXXcd3nrrrSb3t9X8+fPxxRdfYPbs2Vi8eDG6dOmCJUuWYOvWrYATQ/ioeTw/kUzME8nUljxlG8uxfMMB/HrEfnbZwXERuH3yAK6H1Im5+vzk1kLp2WefxZo1a3DgwAHodDqkpqbi+eeft3vzO3fuXKxcudLu5y688EL8/PPPLm2rEALl5eUICwvjLEAOCAwMxJ/+9Ce8+OKLeOGFF1BfX4+PP/4YDz74YKuTJwQEBDi86rIzY1S//fZbXHPNNbj00kvxwQcfOPQ63n777bjmmmswatQolJWVAY3WP6qoqEBgYCD0ev15fz4lJQX9+/dvklchBEaOHImkpCTs2bMHd999N7p06eLQcbzxxhuorKy0ff/rr7/irrvuwpdffgmDwWDb7siEEs2ZOXMmunTpIvVvbMqUKVi+fDn+8pe/IDExETjTy/T000/jscces7t2iZzH8xPJxDyRTM7kKa+4CivTDuGn/Ua77b2iQnD75IG4sF80M9nJufr85NZCadOmTZg3b55t2ubHH38cU6dORVZWlt2bxssvvxzLly+3fR8QEODytqqqiqKiIuj1el7g6qC7774bzz33HN59912YzWZYLBbcddddrf5cbm4uevfu7dBzbNy4ERMnTmz1cd9++y1mzJiBCRMm4LPPPnM4Q5mZmcjMzMQnn3zS5L7ExEQMHTrUbnhhc4QQzfaY/P3vf0dGRgZGjhyJJ598EldddRX69OnTapvO7UVrGM6WnJzcplnvnGlze8yZMwc333wzsrOz4e/vj759++LZZ5+Foii4+OKLpT5XZ8PzE8nEPJFMjuZJFQJPrN4OY2mNbVtMuA6zJ/THpAt6QKthgUSuPz+5tVBat26d3ffLly9HdHQ0fv31V4wfP962PTAwELGxsW5o4VlarRb9+vVzaxu8jcFgwKxZs/Daa6+hrq4OV199NXr27Nnqz8keerd+/XrMmDEDF110ET7//HOHpwPHmULsXCtWrMDKlSvx+eeft9oT8vPPPyM7Oxv33Xef3fbvv/8eL7zwAv72t7/h/vvvx7Bhw3D99ddjy5YtbvkgoLFPP/0UNTU1bZ4yvCV+fn4YNGgQAKC8vBxvvvkmpk+fjl69ekl/rs6E5yeSiXkimRzNk0ZRcPPF/bD4yz0I7xKAmy7uh2nD4xHgx2KdznL1+cmjrlEqLy8HAERGRtptT0tLQ3R0NMLDwzFhwgT861//Ou9sZbW1taitrbV9X1FRAZypQBv/q9FoznvbarVCURTbbY1GAyEETp06hcjISGi1Wtt2RVGavd3wXI1va7Va20Kjjt5WVRVCCNvt1truzDGdr+2OHFPj2UYabiuK0uT2fffdZ3vD/e6777b6eJzpMRw5cmSLj2l8u6V9/vTTT5gxYwZiY2Px6KOPYteuXXaPGTx4MEJDQ4EzU5f/4Q9/wLvvvmu73mjixIlN9t1QPKWmptqGtwkhMGzYMNxyyy0YOHAggoKCsH37drzwwguIjY3FX//6V9t+8vPzccstt2D8+PF48sknodFosHr1akyYMAEPPfQQXn75ZYeOu+F2w/eNb5+ruZ87duwYbr75Zlx//fXo27cvNBoN0tLS8MorryApKQl/+MMfIISwPd7f3x8TJkzA999/b9tPbm4utm/fDkVRkJOTA5wptIQQSEhIwOjRoyGEQGFhIV566SWkpqZCr9fj4MGDWLRoETQaDZYuXdrqsQohmuTQl/6e2ntMVqsVFRUVCAsLg0aj8Ylj8sXXyVuOSVEUlJSUICwsDP7+/j5xTL74OnnLMTV+/9Swz1qLis/TczFuQDR6RYfZ2js5uQdqausxJbk7QnSBtnO/px2TL75O3nJM9fX1KC8vR2RkpG30S3vew7bGY66gFkLgwQcfxEUXXYQLLrjAtn3atGn44IMPsGHDBrz44ovYvn07Jk+ebFcMNfbss88iLCzM9hUfHw8AtlnHjEYjjMbTY19PnDiBwsJCAMDx48dRXHz6osHc3FyUlpYCAI4cOYLy8nIIIZCdnW27NuTAgQOoqTndPZyVlWW7biUjIwP19fVQVRUZGRlQVRX19fW2tXHMZjOysrIAADU1NThw4AAAoLKyEtnZ2cCZgvHIkSMAgNLSUtsU0sXFxbappgsLC3HixIl2HROAdh1TXV2d7bUzmU7PQKOqqu3nVFXFkCFDkJCQgEGDBuGiiy4CzszO1vD6WSwW234a366vr0d9fT1wZmppi8XS5HZtba1txrfGt81ms+0PbN26dTCZTMjNzcWUKVOQmpqKsWPHIjU1Fampqdi5c6et7VarFVar1faHfb5janj+xsdhtVoxYMAAvPnmm7jxxhtx5ZVX4s0338Tvf/97bNmyBQaDAfX19TCbzbjxxhuhKAreeecdaDQa1NXVYdSoUXjmmWfwn//8B2vWrGnxmBrfNplMtj94s9lsu93Q9sbHce4xBQQEICYmBv/+979x3XXXYfr06VizZg3uuecebNmyBUFBQXavU8Pvp/Hr9P333+P3v/89Zs2aZeshnjVrFn7/+9/j1VdftR2HoijYvXs37rzzTlx++eV47rnnMG3aNGzduhXdu3dv9Zg6w99Te4+prKzM547JF18nbzgmIQSKiopw8OBBnzkmX3ydvOWYhBDYv38/6urqUFtvwRtfbsPtS9OwMu0QXv3yV7tj0moUXJIUjWNHDnv0Mfni6+RNx5Sfn9/u9+WOUoSHLJQwb948fP3119i8eTPi4uLO+zij0YhevXph9erVuOaaa5rc31yPUnx8PEpLSxEeHs5qXNIxHThwALfeeivef/992/C35noD9u7di2HDhmHJkiW45557nOopccXt5nhCu3hMp2/v378ft956K1atWoX+/fv77N8Tj4nHxGPiMfnyMdXVW/Dj/nys2nQI+WVnp/bWahSsmD8JUaFBXndMvvg6dZZjqqioQHh4OMrLy22jis7HI4be3Xvvvfjyyy/x448/tlgk4cx1L7169bJVrucKDAxs9hqUhl9Sw78t3dY2ujis4baqqjh16hS6desGRVGafYwjtxv/rCO3HWlvW4+pPbeVRjONNHc7JycHx44dw2OPPQaDwYDbbrvNdl9rP+vq281xxXNaLBb4+fn5zDF15O3z/c35yt9Te49JVVUUFhaiW7duTp3rPPmYnGk7j0nuMamqiuLiYtvQYl84Jkdv85jkHpMQAtsO5uOd77OQV2K/9tHFgwyYM7G/bapvTzgmoQoU7CuAudSMoIggRCdFd4rXyZuOSVEUFBUVoVu3blLew7bGrYWSEAL33nsv1q5di7S0NIdmOjt16hTy8vLspkF2lYYuPWrd008/jVWrVmHQoEH45JNPEBwc7O4meZyGT0uIZOD5iWRinqi9Mo6dwrsbDiLrRKnd9hF9uuG2SQPQv3u429rWnLyteUhfko6i/UWw1lqhDdQialAUUuanID413t3No0ZceX5ya6E0b948fPjhh/jiiy+g1+uRn58PAAgLC4NOp0NVVRUWLlyIa6+9FgaDAbm5uXjsscfQrVs3zJw506Vt1Wg00qZe7gxWrFjR6mKnnZmiKE7NvkfUEp6fSCbmidpLFQKvfJ2BvFPVtm0Duofj9skDMKx329b460h5W/OwfsF6mEpM0Bv08NP5wWKywLjLiPUL1mPq4qksljyEq89Pbp3MYdmyZSgvL8fEiRNhMBhsXx999BFwpossIyMD06dPR//+/TFnzhz0798f27Zta3GRz46gqiry8/PZC0BSCCFQX1/v1MwrROfD8xPJxDxRe2kUBXMmnb5+Ob5bF9x7SR/8e+4YjyyShCqQviQdphITIvtGIiAkABqtBgEhAYhMjISp1IT0pekQKv+/9gSuPj+5fehdS3Q6Hb799luXtac1DTN9EcnANyEkE89PJBPzRI46VWnGBz9l44rhPdHXEGbbftHAWDw5ayRS+kbBePI3p64LcaXCzEIU7S+C3qBv0kZFUaCP1aMoqwiFmYWISY5xWzvpLFeenzxiMgdvoNFoHFoslcgRHHpHMvH8RDIxT+SISlM9Ptmag8/Tj6LWoqKw3IR/3phiu19RFIwbGAsAHp0nc6kZ1lor/HTNvyX20/nBWmCFudTs8rZRU64+P7FQcpCqqjAajTAYDHYzcXR2R48edXcTvFLD0Dt/f3+P/ZTNEzBfjuH5iWRinqgl5norvkg/io+35qDKbLFt33e8BEUVJkSF6uwe7+l5CooIgjZQC4vJgoCQgCb3W0wWaAO1CIoIckv7yJ6r88RCidokPDwcQUFBeOKJJ9zdFK/VsNo4tSwoKAjh4Z41OxIRUWdjsar4ZlcePvwpGyVVZ9er9NdqcPWoXrh+XCLCu3jfSInopGhEDYqCcZcRkYmRdh9eCiFQmV8JwwgDopOi3dpOcg+PWXC2o1RUVCAsLMyhRaXIOfn5+SgrK3N3M8jHhYeHIzY21t3NICLqlFQhsCnzJFamHYKx9Oy0zBoFuGRIHG6dcHYtJG9lm/Wu1AR97NlZ7yrzK6GL0HHWOx/jTG3AHiUHqaqKEydOIC4uziO7jt0hNjaWb2DbiHkimZgnkol5onN99vNRuyJp3IAYzJk0AL2iWp+B2BvyFJ8aj6mLp55dR6ng9DpKhhEGpMzjOkqexNV5YqHkhICApmNXidqKeSKZmCeSiXmiBhpFwW2TB+CxD9IxNKErbp88AAN7RDi1D2/IU3xqPOLGxKEwsxDmUjOCIoIQnRQNRcPriD2NK/PEoXdEREREhCMFFVix8SCuH5eIpPhI23YhBA6eLMeA7mGcgIi8njO1gWf2gXogVVWRm5vLtW9ICuaJZGKeSCbmqfMxltZg0ee7cc+bP+GX7EK888MBu7UuFUXBwB7hbSqSmCeSydV54tA7JwQHB7u7CeRDmCeSiXkimZinzqG0qhYfbs7G/349Dot6tjAqKDehpKoWXfVypsRmnkgmV+aJQ++IiIiIOpFqcz0+2XYEa345itp6q217qM4fN1zUF1eP6oUAPy5fQb6Js951AKvVitzcXCQkJHDtG2o35olkYp5IJubJd1lVgTW/HMFHW3JQaaq3bQ/y1+KaMb1x3Zg+6BLkL/c5mSeSyNV5YqHkIEVREB7etvG5ROdinkgm5olkYp58l0YBfjlUaCuS/DQKrhrVCzeM64uIkI5ZLJZ5IplcnScOvSMiIiLyQQ1v8Rq/qczMK8GCldsw6YIemD2xP2LDef0QdS6c9a4DWK1WZGdnw2q1OvBoopYxTyQT80QyMU/eTwiBX3OKMP/tzdh5pNjuvqT4SKyYPwl/nTHMJUUS80QyuTpPHHrnII1Gg6ioKI9dVZq8C/NEMjFPJBPz5N0O/FaKdzccxJ7cUwCAdzccwPA+3aBp1KsU48JeJOaJZHJ1nlgoOahhTCSRDMwTycQ8kUzMk3fKLazEyrSD2HqwwG67EEBZdS0iQ+RM9e0s5olkcnWeWN47yGq14sCBA+w6JimYJ5KJeSKZmCfvUlBWg8Vf7MHdb/5oVyR1jwzGozOHY8mdF7mtSALzRJK5Ok/sUXKQRqNB9+7d2XVMUjBPJBPzRDIxT97Bqqp487v9+PrX46i3qrbtXfWBuGV8f0wdGgc/rftfQ+aJZHJ1nlgoOUhRFM6aR9IwTyQT80Qy+VqehCpQmFkIc6kZQRFBiE6KhqLx/qmqtRoNTpZU24qkkCB/XD8uEb8bnYAgf89Zr8jX8kTu5eo8sVByUENX38CBA7lgGrUb80QyMU8kky/lKW9rHtKXpKNofxGstVZoA7WIGhSFlPkpiE+Nd3fznFJnscJfq7Gb6nvupIHIOF6C341OwO9TExEiebFYGXwpT+R+rs4T11FykBACNTU1CA4O5qJp1G7ME8nEPJFMvpKnvK15WL9gPUwlJugNevjp/GAxWVCZXwldhA5TF0/1imLJqqr4fu9vWLXpEP40dTAuHmSwu7+6th5dAj2vQGrgK3kizyAjT87UBuxRcpCiKOjSpYu7m0E+gnkimZgnkskX8iRUgfQl6TCVmBDZN9L2hiogJACRiZEoySlB+tJ0xI2J89hheEIIbDmQjxUbDyLvVDUAYMXGg0gdEANto+szPLlIgo/kiTyHq/PEK+scZLVakZGRwVlbSArmiWRinkgmT8qTUAUKMgpw7MdjKMgogFAdGwRTmFmIov1F0Bv0TT51VhQF+lg9irKKUJhZ2EEtb59dR4tx37tb8PSnO21FEgB0j+yCSlO9W9vmLE/KE3k/V+eJPUoO0mg06Nu3L2dtISmYJ5KJeSKZPCVP7bm+yFxqhrXWCj9d829z/HR+sBZYYS41d1Dr2+bgyTIs33AQu44W221Pio/A7ZMH4oKekW5rW1t5Sp48ga9OLOJKrs4TCyUHKYoCnU7n7maQj2CeSCbmiWTyhDyd7/oi4y4j1i9Y3+r1RUERQdAGamExWRAQEtDkfovJAm2gFkER7ltfqDGrquLZNbvw0/58u+29o/W4bfIApPSN9trrezwhT57AlyYWcSdX54nlvYOsVit2797NrmOSgnkimZgnksndeTr3+qKAkABotBrb9UWmUhPSl6a3OAwvOikaUYOiUJlfiXPnrBJCoDK/ElGDoxCdFO2CI2qdVmM/m50hIhgPzxiG1/54MS7sF+O1RRI8IE+eoKHwN+40QheuQ3hCOHThOlvhn7c1z91N9BquzhMLJQdpNBoMHjyYXcckBfNEMjFPJJO78yTj+iJFoyBlfgp0ETqU5JSgrqoOqlVFXVUdSnJKoIvQIWVeSqvDntp6jVRrymvqYD1nX3Mm9ke30CDMuzwJb909AZOTe0DjxQVSA3fnyd1kFP50lqvzxKF3TuD8/yQT80QyMU8kkzvzJOv6ovjUeExdPPXscKeC08OdDCMMSJnX+nCnjhgqZaqzYM3PR/HptiO4+/LBmDr07H7iuobgvXsn2c1o5ys68/nJmcI/JjnGbe30Jq7MEwslB6mqioyMDCQnJ3fqP3iSg3kimZgnksndeZJ5fVF8ajzixsQ5fQF9e6+ROledxYpvdh7HBz8dRnlNHQBg1aZsTEzqjgC/s79jXyyS3J0nd/PWiUU8lavzxELJQRqNBsnJyZ2265jkYp5IJuaJZHJ3nhquLzLuMiIyMdLuU/iG64sMIwwOX1+kaBSnPqmXuQaTVRXYkHF6sdiCcpNtu0ZRMCoxCnUW1a5Q8kXuzpO7edvEIp7O1XlioeQEq9Xaaf/QST7miWRinkgmd+ap4fqi9QvWoySnBPrYsz06lfmVDl9f1FYyhkoJIbDtUAFWbDyIY0VVdvdNGGzA7In9Edc1pEPa74k68/lJduFPrs1T50xtG6iqiqysLKiq6u6mkA9gnkgm5olk8oQ8NVxfZBhugKnMhLLcMpjKTDCMMDg97M1ZDg2Vqj3/UCmLVcVfVm7DUx//alckjUqMwpI7LsJj147oVEWSJ+TJnWRNLEKnuTpPijh33kwfU1FRgbCwMJSXlyM0NNTdzSEiIiIHuWOBzoKMAqydvRa6cF2zQ6XqqupgKjNh5nszz9uj9NL/7cG3u08AAAbFheP2yQMxpFfXDm03ebZmJwcZHOXQxCIklzO1AYfeOUgIAbPZjKCgIK9ez4A8A/NEMjFPJJMn5cnZ64tkcHao1G8l1YgO08Ffe3aQzi3j++NIQSVuvrgfxvT33sViZfCkPLlTWycWIXuuzhOH3jlIVVUcPny403Ydk1zME8nEPJFMnT1Pjg6VOlVVi1e+zsAdr23CNzuP2+0jOkyHV/8wDmMHePdisTJ09jw11lD49xrfCzHJMSyS2sDVeeLQOyIiIqJznG+o1OA/jsCWejO+2J6LOsvpN2sRXQKxfP5E6AI4UIfI03HoXQcQQqCmpgbBwcGd/tMhaj/miWRinkgm5um0c4dKKXp/bKmqxuPbDqG61mJ7XHCAH64e1atT/65awjyRTK7OE4feOUhVVeTm5rLrmKRgnkgm5olkYp7OUjQKIgdHYY9O4K8bs7Ai7WyR5K/V4NoxvbHi3km4eXw/BPn79npIbcU8kUyuzhOH3hERERE1w2JVcfebP+F48dlpvjUKcOnQONwyvj+iw3RubR8ROY9D7zqAEAKVlZXQ65suQEfkLOaJZGKeSCbm6Sw/rQYj+nSzFUoXD4rF7IkD0LNb51kHqb2YJ5LJ1Xni0DsHqaqKkydPsuuYpGCeSCbmiWTqzHnad7wE5jqL3bYbL+qLMf1j8OofxuFv141kkeSkzpwnks/VeeLQOyIiIurUcvIrsGLjAaQfLsLtkwfg+nF93d0kIuogztQG7FFykBACZWVl8PG6klyEeSKZmCffIlSBgowCHPvxGAoyCiBU176unSlPJ0uq8dzaXbjnrZ+QfrgIAPDx1hxUmurd3TSf0ZnyRB3P1XniNUoOUlUVRUVF0Ov10Go5sw21D/NEMjFPvqPZtXsGRSFlfgriU+Nd0obOkKdTlWZ8+FM2vtmVB2ujQjQqNAi3TuiP4EDfPG536Ax5ItdxdZ449I6IiMgD5G3Nw/oF62EqMUFv0MNP5weLyYLK/EroInSYuniqy4olX1VlrsfHW3Pw+S9HUWs5e41DWHAAbrioL64a2RMBfm1/8yVUYVt3KSgiCNFJ0VA0nMCAyJNw1rsOoKoqSktLERERAY2GIxapfZgnkol58n5CFUhfkg5TiQmRfSNtszkFhAQgMjESJTklSF+ajrgxcR3+xttX81RvVfGnN35EcYXZtk0XoMV1Y/pg5pje6BLo3679e0JvoCfy1TyRe7g6T0ysgzjGlmRinkgm5sn7FWYWomh/EfSGplPeKooCfaweRVlFKMws7PC2+Gqe/LUaXJLcw3Z7RkoCVsyfhFsm9JdSJK1fsB7GnUbownUITwiHLlwH4y4j1i9Yj7yteZKOwvv4ap7IPXiNkofSarVITEx0dzPIRzBPJBPz5P3MpWZYa63w0zX/37Kfzg/WAivMpeZm75fJF/KkCoEfs4wYlRiFkKCzRdCs1ERUmutxfWoiYsKDpTyXJ/UGeiJfyBN5DlfniT1KDlJVFYWFhVwHgKRgnkgm5sn7BUUEQRuohcVkafZ+i8kCbaAWQRFBHd4Wb86TEALbDxdi/lub8eyaXfh02xG7+0OC/HHfFcnSiiR4WG+gJ/LmPJHncXWeWCg5oaamxt1NIB/CPJFMzJN3i06KRtSgKFTmVzYZUiKEQGV+JaIGRyE6Kdol7fHGPGXmleCh937G3/67HTkFFQCANb8cRUVNXYc+r0O9gbWu6Q30VN6YJ/JcrswTh945SKPRICEhwd3NIB/BPJFMzJP3UzQKUuanYP2C9SjJKYE+tumsdynzUlwydMvb8pRbWInlGw/i50MFdtv7GcJw2+QB0Ovad/1Raxr3BgaEBDS535W9gZ7I2/JEns3VeWKh5KCGrr7o6GjO2kLtxjyRTMyTb4hPjcfUxVPPzpxWcHrmNMMIA1LmuXYdJW/IU35pDd7bdAgbMn5D4z64uMgumDtpAC4aFNtkKFxHaOgNNO4yIjIx0u45G3oDDSMMLusN9DTekifyDq7OEwslJ9TVdWz3PXUuzBPJxDz5hvjUeMSNiXP7Wjyenqd6q4r7l29FaXWtbVs3fRBumdAPU4fGQevCN+Se1BvoqTw9T+RdXJknLjhLREREXuejLTl4d8MB6HX+uGFcX1w9qhcC/du+WGx7NbuO0uAol/YGElHruOBsB1BVFUajEQaDgV3H1G7ME8nEPJFMnpan2norvvr1GKYk90B4l0Db9ukpCbCqKqaPTkCXoI69DskRntIb6Gk8LU/k3VydJxZKRERE5HGsqor1e07g/U3ZKK40o7DchLsvS7LdH+SvxU0X93NrG8+laBTEJMe4uxlEJAmH3hEREZHHEEJg8/58rNh4ECdKqm3bA/w0+OD+KQjVNZ1ZjojIUc7UBuwDdZCqqjh+/DgXTCMpmCeSiXkimdyVJyEEfj1ShHvf2YJ/frbTrkga0y8a/7l9XLuLJKEKFGQU4NiPx1CQUQCh+vRnxR6B5yeSydV54tA7JwQE8FMskod5IpmYJ5LJ1Xk68FsZlm84gN25p+y2X9AzErdPHoCk+Mh2P0ezky0MikLKfE620NF4fiKZXJknDr0jIiIit6mzWDHn1Y0oqTo71XdiTChumzwAoxKjpKyFlLc1D+sXrIepxAS9oen03VMXT2WxRNRJcOhdB1BVFbm5uew6JimYJ5KJeSKZXJ2nAD8tbryoLwDAEBGMR2cOx5I7L8LovtFSiiShCqQvSYepxITIvpEICAmARqtBQEgAIhMjYSo1IX1pOofhdRCen0gmV+eJQ++cEBwc7O4mkA9hnkgm5olk6qg8lVXX4qMtOZh5YW9Eh+ls26eN6IlAfy2mJPeAn1buZ7iFmYUo2l8EvUHfpPBSFAX6WD2KsopQmFnIGes6CM9PJJMr88RCyUEajQbR0dHubgb5COaJZGKeSKaOyFNNrQVrfj6CT38+AlOdFdW19Xjw6qG2+/21Glw2rGOGvplLzbDWWuGna/4tj5/OD9YCK8yl5g55/s6O5yeSydV54tA7B1mtVuTk5MBqtbq7KeQDmCeSiXkimWTmqc5ixZpfjmLuko1Y9WM2THWn9/lTVj4qTfUSWtu6oIggaAO1sJgszd5vMVmgDdQiKCLIJe3pbHh+IplcnSf2KDlIURSEh4dLGS9NxDyRTMwTySQjT1ZV4IeME1i1KRuF5Sbbdq1GwbTh8bjp4n7Q6/wltbhl0UnRiBoUBeMuIyITI+2OSwiByvxKGEYYEJ3EXo+OwPMTyeTqPHHWOyIiIpJCCIGtBwuwYuNBHC+usrtvYlJ3zJ7YHz0iu7i8XbZZ70pN0Mdy1juizoyz3nUAq9WK7Oxsdh2TFMwTycQ8kUztyVO9VcUb67PsiqSUvlF47c6L8Og1w91SJAFAfGo8pi6eCsNwA0xlJpTllsFUZoJhhIFFUgfj+YlkcnWeOPTOQRqNBlFRUdBoWFtS+zFPJBPzRDK1J08BflrcOqE/Fn+5B0nxEbht8kAk92z/YrEyxKfGI25MHAozC2EuNSMoIgjRSdFQNBwS1pF4fiKZXJ0nDr0jIiIip+UVV2HVpkOYPbE/4rqG2LZbVYHdR4sxok83XpdCRB6HQ+86gNVqxYEDB9h1TFIwTyQT80QytZanogoT/v3VXvzx9R+xKcuIlWmH7O7XahSMTIxikUQAz08kmavz5NZC6dlnn8Xo0aOh1+sRHR2NGTNm4ODBg3aPEUJg4cKF6N69O3Q6HSZOnIjMzEyXt1Wj0aB79+7sOiYpmCeSiXkimc6Xp4qaOrz5XRZuW5KGdbvyoJ4ZkLLveAmqzK6Z6pu8D89PJJOr8+TW1G7atAnz5s3Dzz//jO+++w4WiwVTp05FdXW17TGLFi3CSy+9hCVLlmD79u2IjY3FpZdeisrKSpe2VVEUhIaG8hMykoJ5IpmYJ5Lp3DyZ6iz44MdszFmyEZ/9fBT1VhUAEBzohzkT++PdeRMREuSaqb7J+/D8RDK5Ok9uLZTWrVuHuXPnIikpCUOHDsXy5ctx/Phx/Prrr8CZ3qSXX34Zjz/+OK655hpccMEFWLlyJWpqavDhhx82u8/a2lpUVFTYfQGAqqq2f1u7bbVa7W4LIWC1WrFv3z5YLBa77ee73fAzjW83HJMzt1VVtbvtzHG0dkzO3uYxyTum+vp67Nu3z3YMvnBMvvg6ecsx1dXVITMzE/X19T5zTL74OnnLMTX8f1djMuOL9NOLxb636RBqak///xfgp8F1Y/tg+T0TcH1qH+gC/Dz+mHzxdfKWY7JarcjIyIDFYvGZY/LF18lbjqmurs72/qk9x+QopwuldevWYfPmzbbvly5dimHDhuGmm25CaWmps7uzU15eDgCIjDw9Q87Ro0eRn5+PqVOn2h4TGBiICRMmYOvWrc3u49lnn0VYWJjtKz7+9JSfv/32GwDAaDTCaDQCAE6cOIHCwkIAwPHjx1FcXAwAyM3NtR3LkSNHUF5eDo1GA1VVbb1dBw4cQE1NDQAgKysLZrMZAJCRkWF7s5KRkQFVVVFfX4+MjAwAgNlsRlZWFgCgpqYGBw4cAABUVlYiOzvb9ns4cuQIAKC0tBS5ubkAgOLiYhw/fhwAUFhYiBMnTrTrmAAgOzvb1jvHY3LdMRmNRoSEhECj0fjMMfni6+Qtx5SXl4eEhASUlpb6zDH54uvkLcek0WgQExODw4cP4/92HENZdR0AQKMomJIUgyev6IU7LxkEa2211xyTL75O3nJMGo0GtbW1tje7vnBMvvg6ecsx5ebmomvXrtBoNO06Jkc5PetdcnIynn/+eVxxxRXIyMjA6NGj8eCDD2LDhg0YNGgQli9f7szubIQQmD59OkpLS/HTTz8BALZu3Ypx48bht99+Q/fu3W2P/eMf/4hjx47h22+/bbKf2tpa1NbW2r6vqKhAfHw8SktLER4ebqtIGwqf5m5brVYoimK7rdFooCiKU7dxphpufFur1UII4dRtVVUhhLDdbq3tPCYeE4+Jx8Rj4jHJOqathwrxz0934uJBsZg7aQB6RHbx+mPyxdeJx8Rj4jE5fkwVFRUIDw93aNY7pwulkJAQ7Nu3DwkJCVi4cCH27duHTz/9FDt37sQVV1yB/Px8Z3ZnM2/ePHz99dfYvHkz4uLigEaF0smTJ2EwGGyPvfPOO5GXl4d169a1ul9Z04NbrVZkZWVh8ODB0Gq1bd4PEZgnkox5ovbae+wUVmw8iHmXJyEhKsSWJ41Gg2NFVUiI1ru7ieSleH4imWTkqUOnBw8ICLB1bX3//fe2YXGRkZG264Gcde+99+LLL7/Exo0bbUUSAMTGxgJAk+KrsLAQMTExbXquttJoNOjbt6+tKiVqD+aJZGKeqK0OG8vx+IfpeOi9n5GZV4oVGw/a5UlRFBZJ1C48P5FMrs6Tn7M/cNFFF+HBBx/EuHHjkJ6ejo8++ggAcOjQIbsixxFCCNx7771Yu3Yt0tLS0Lt3b7v7e/fujdjYWHz33XcYPnw4cOYirk2bNuH55593tuntoigKdDqdS5+TfBfzRDIxT95BqAKFmYUwl5oRFBGE6KRoKBr3zAT226lqvLfpENIyT9ptzy8zoabWgi7ME0nC8xPJ5Oo8OV0oLVmyBPfccw8+/fRTLFu2DD169AAAfPPNN7j88sud2te8efPw4Ycf4osvvoBer7f1HIWFhUGn00FRFNx///145pln0K9fP/Tr1w/PPPMMgoODcdNNNznb9Haxnpm1JTk5mV3H1G7ME8nEPHm+vK15SF+SjqL9RbDWWqEN1CJqUBRS5qcgPjXe9riOLqZOVZrx/o/ZdusgAUBMmA63TuiPyck9AKFi9+7dzBNJwfMTyeTqPDl9jZLUJz/PHOjLly/H3LlzgTO9Tk899RTeeOMNlJaW4sILL8TSpUtxwQUXOPQcsq5REkKgvr4e/v7+XAuA2o15IpmYJ8+WtzUP6xesh6nEBL1BDz+dHywmCyrzK6GL0GHq4qmIT413uJhqizqLFe+lHcIX23NRZ1Ft28OCA3DTxX1xxYieCPA7/aaDeSKZmCeSSUaenKkNHCqUKioqbDtq7Tqk9hQjHUFmodQwWwb/0Km9mCeSiXnyXEIVWHPLGhh3GhHZN9Lu9RFCoCSnBIYRBoy+ezS+++t3rRZTbaUKgXvf3ozD+af/Dw8O8MO1Y/vgmgt7IzjQfnAJ80QyMU8kk4w8SZ/MISIiwjaveXh4OCIiIpp8NWz3VWqj+deJ2ot5IpmYJ89VmFmIov1F0Bv0Tf5TVxQF+lg9CjML8dMzP8FUYkJk30gEhARAo9UgICQAkYmRMJWakL40HUJ1fACI9ZzHahQFt00eCH+tBtdc2Bsr7p2EW8b3a1IkgXkiyZgnksnVeXLoGqUNGzbYFoHdsGFDp/xEQKPRIDk5mbO2kBTME8nEPHkuc6kZ1lor/HTN/3frp/ND3bE6lFSXIDQu9LzFVFFWEQozCxGT3PKMr6oQSNt3Eu9tOoSHpg9FUnyk7b6RfbrhvfsmITIkqMV9ME8kE/NEMrk6Tw4VShMmTLDdnjhxYke2x6M1XrSKqL2YJ5KJefJMQRFB0AZqYTFZEBAS0OR+i8kCRatAtaotFlPWAivMpebzPo8QAumHC7F8w0EcLTy9Uv27Gw5i8ewxtuJLUZRWi6QGzBPJxDyRTK7Mk9PP8sQTT8BqtTbZXl5ejhtvvFFWuzyOqqrIyspi1zFJwTyRTL6SJ6EKFGQU4NiPx1CQUeDUUDNPFZ0UjahBUajMr8S5lwQLIVCZX4mu/bsiMDQQFpOl2X1YTBZoA7UIimi+yNl3vAR/WbkNT67eYSuSAMBPq6Cmrvl9tsRX8kSegXkimVydJ6dnvevVqxcMBgM++OADJCYmAgDS0tIwe/Zs9OjRA9u2beuotraJrMkciIio43TkjG/uZpv1rtQEfWzTiRouXXQptr+2HcZdRkQmnn/Ch2tWXWM3VfiRggos33gQ6dmFds/X3xCG2yYPxIg+3Vx6nERE3kD6ZA6N7d27FwkJCRg2bBjeeustPPTQQ5g6dSrmzp2LzZs3t6fdHk0IAZPJ1OQTQaK2YJ5IJkfz5Kk9Ng2FhHGnEbpwHcITwqEL18G4y4j1C9Yjb2ueu5vYLvGp8Zi6eCoMww0wlZlQllsGU5kJhhEGTF08FT0v6omU+SnQRehQklOCuqo6qFYVdVV1KMkpgS5Ch5R5KbYiyVxvxfNrd+GeN3+yK5LiunbB364bgf/8YVy7iiSen0gm5olkcnWenF5wNiwsDKtXr8bjjz+OP/3pT/Dz88M333yDKVOmdEwLPYSqqjh8+DAGDx7MBdOo3ZgnksmRPHlqj41QBdKXpNtmfGvoTWmY8a0kpwTpS9MRNyZO6sKrrhafGo+4MXHnXUy2oZiyvUYFp18jwwgDUubZv0aBfhoUlJvQ8DahW2gQZk/oj0uG9IBWwrh9np9IJuaJZHJ1ntq04Oyrr76Khx9+GDNnzsSvv/4KrVaLDz/8EEOHDu2YVrYDh94RUWfn6IKn7lCQUYC1s9dCF65rdrKDuqo6mMpMmPnezFZnfPMFQhVNiilTvRW6AK3dkLx9x0vw1Mc7cMNFfXH1qF62xWKJiKhlHTr0btq0aXjqqafw3nvv4YMPPsCuXbswfvx4jBkzBosWLWpPuz2aEALV1dXsOiYpmCeSqaU8ndtjI2ONHpkcmT7bWtvyjG++RNEoiEmOQa/xvRA2sBs++fkIbv3PBuw8Umz3uAt6RmLVn6fg2jF9pBdJPD+RTMwTyeTqPDldKFksFuzduxfXXXcdAECn02HZsmX49NNP8e9//7sj2ugRVFVFbm4uZ20hKZgnkqmlPDmy4GnDGj3u0Hj67Oa0NuObL7JYVfxv53HcvnQj3vnhAKrM9Vi+8SDUc94YBPl3TC8Sz08kE/NEMrk6T05fo/Tdd981u/3KK6/Enj17ZLTJI2m1WiQlJbm7GeQjmCeSqaU8OdRj08oaPR2pYfrs8834VplfCcMIA6KTot3SPldShcCPWUasTDuIkyU1tu0KgF5RIaitt0IX4PR/207z1PNTc8MSvfm6tc7CU/NE3snVeZJyxs3KysI777yD999/HwUFBTJ26XGEEKisrIRe3/RTWSJnMU8kU0t5cmTBU3f22CgaBSnzU7B+wXqU5JQ0O3124xnffJEQAr8eKcbyDQdwOL/C7r7UATGYM3EAEqL1Lm2Pp52fPHUyEmqdJ+aJvJer89Tm6XGqqqrw9ttvY+zYsRgyZAh++eUXPPLII3Jb50FUVcXJkyfZdUxSME8kU0t5cmTB06jBUW7tsWlt+mxffiNsrrPgr6t+xuMfptsVSUN6ReLl21Lx99+PaneR5Oy08J52fvL16eN9naflibybq/Pk9Kx3mzdvxttvv43PPvsMvXv3RlZWFjZt2oRx48Z1XCvbgbPeEVFn19qCp55SjHTWoVV/+286th8uAgD0jQ3FbZMHYmSfblI+LfX2nhihCqy5ZQ2MO41208ejlcV4iYjOp0NmvVu0aBEGDhyIG264AVFRUdi8eTP27t0LRVEQEREho90eTQiBsrIyztpCUjBPJFNrefKWHpvGM77FJMf45BvfooqmCyXeNmkA4rp2waPXDMerd1yEUYlR0oqktvTEeNL5ydMnI6HWeVKeyPu5Ok8OX6P02GOP4eGHH8Y//vGPTrlgmKqqKCoqgl6v75THT3IxTySTI3lqbcFTZ3XW3p+2KquuxX83H8ZXO47h0WuG46JBBtt9ibFheOvuCdBIHG/fnoV8Pen85OmTkVDrPClP5P1cnSeHC6V//OMfWLFiBVatWoUbb7wRt956Ky644IKObZ0H0Wq16Nevn7ubQT6CeSKZHM1TQ49Ne3n7cC5Xqq6tx2fbjuKzn4/AXG8FAKzYeBBjB8RAqzk7qENmkQQne2LOzYQnnZ88fTISap0n5Ym8n6vz5PDQu8ceewyHDh3CqlWrkJ+fjzFjxmDo0KEQQqC0tLRjW+kBVFXFqVOneDEiScE8kUyuzBMvrHdMncWKz34+grmvbsQHP2XbiqRAfy0uGmSAxdqxw0bas5CvJ52fvGEyEmqZJ+WJvJ+r8+T0rHcTJkzAypUrYTQacffdd2PkyJGYMGECUlNT8dJLL3VMKz0Ax9iSTMwTyeSqPJ07nCsgJAAarcY2nMtUakL60vRWZ1XzZVZVxbe783Db0jS8+d1+VJjqAQBajYKrR/XCivkTMXfSAAR20GKxDdqzkK8nnZ8apo/XRehQklOCuqo6qFYVdVV1KMkp6RTTx3s7T8oTeT9X58npWe+ak5GRgXfeeQcffvghCgs964JKznpHRCRHQUYB1s5eC124rtlhUHVVdTCVmTDzvZlShvh5G3OdBfe+swXHi6ts2xQAk5N74NYJ/WGICHZZW2yzxZ1nIV9vmy2u2eGeg6OQMo/DPYnIOc7UBlIWnE1OTsbLL7+MF154QcbuPJKqqiguLka3bt2g0bR5+SkigHkiyVyVJ15Y37KgAD8kROtthdKF/aIxd9IA9Ilx/Yd07VnI1xPPT7InIyHX8cQ8kfdydZ6kFEoN/P39Ze7O49TU1Li7CeRDmCeSyRV54oX19g4by9E7JhTaRm/W50zsj7LqWsydNABJ8ZFubV/DtPC2npiC0z0xhhGGVntiPPH8JGsyEnI9T8wTeS9X5knK0DtPxqF3RERy+Npwrsacme78eFElVqQdwpYD+Vjwu6G4dGicy9vrDE7lTkR0VocMvTtx4gTi4jz7P4OOpKoqCgsLER0dza5jajfmiWRyVZ7aM5zLkzk63XlhuQmrNh3C93tPoGG+ilU/HsKEJAMC/Dx3fRhne2J4fiKZmCeSydV5cvgZLrjgAqxatapjW+Ph6urq3N0E8iHME8nkqjw1DOcyDDfAVGZCWW4ZTGUmGEYYMHXxVK+7sN6R6c7Lqmvxxvos3L40Dev3nC2SIkMCMWtsovQ1kDwBz08kE/NEMrkyTw4PvXvttdfwyCOP4NJLL8Wbb76Jrl27dnzrJODQOyIi+XxhOJdtKOFOIyL7Nh1KWHisFIWTemB/Dx1q6s5Os90l0A/Xj0vE9NEJCAqQeqkvERF1MGdqA4d7lO655x7s2bMHpaWlSEpKwpdffimjrV5DVVX89ttvXDCNpGCeSCZ35KlhOFev8b0QkxzjdUUSABRmFqJofxH0Br1dkQQAFq2CjdN74tcof1uRFOCnwe9TE7Hi3km4flzfdhdJQhUoyCjAsR+PoSCjwGPWn+L5iWRinkgmV+fJqbN87969sWHDBixZsgTXXnstBg0aBD8/+13s3LlTdhuJiIika2m6c38ViCuvx+HoQGgATBvZEzdf3A9d9XJm9HP0uigiInIfpz8OO3bsGD777DNERkZi+vTpTQolX6XRaNCjRw93N4N8BPNEMjFPbdMw3Xm9yYLCuGB0L7dA26hTJym7GrVmC+69/UIMHdtL2vM2XBdlKjFBbzg7IUbDdVHuvtaLeSKZmCeSydV5cqrKeeutt/CXv/wFl1xyCfbt24eoqKiOa5mHUVXVNvMfZ22h9mKeSCbmqW2ik6JRPzIGG7uoKOsWhDG5JgwsrAfOXKOkHivHtK4GDLmwp7TnFKpA+pJ0mEpMdtdFBYQEIDIxEiU5JUhfmo64MXFuG87IPJFMzBPJ5Oo8OVwoXX755UhPT8eSJUswe/bsjm2VhwoIaLrAIlFbMU8kE/PknGxjOZZvOIBfe539ve02BKJPQS1Q3XHTnbd0XZSiKNDH6lGUVYTCzEK3Lq7KPJFMzBPJ5Mo8OVwoWa1W7N27t9OupaTRaBAbG+vuZpCPYJ5IJubJcXnFVViZdgg/7TfabY8wqxiw8xQqj1XDL1ALwwgDUubJv16opeuiAMBP5wdrgRXmUrPU53UG80QyMU8kk6vz5HCh9N1333VsSzycqqo4fvw4evbsya5jajfmiWRinlpXVGHC+z9mY/3uE1AbrYoRE67D7An9MXFwd5zaX9Th0503XBdlMVkQENL0U1GLyQJtoBZBEXImjWgL5olkYp5IJlfnqXPMxCBJcHCwu5tAPoR5IpmYp/OrqbXgj6//iJras2shhQUH4KaL++KKET0R4KcFAJcMdYtOikbUoCgYdxkRmdh07abK/EoYRhgQnRTd4W1pCfNEMjFPJJMr8+TwgrPeigvOEhG5j6csTLvs20x8np6L4EA/zBrbBzMv7A2dmxaLtc16V2qCPvbsrHcN10W5e9Y7IiJf5kxtwB4lB1mtVuTm5iIhIQFardbdzSEvxzyRTJ6aJ3esFVRvVbF+dx6mDIlDkP/Z38WNF/WFv1aDWamJCAt274Xl8anxmLp46tnfTcHp301HXRflLE/NE3kn5olkcnWeWCg5SFEUhIeHN5mliKgtmCeSyRPz5Oq1gqyqQNq+3/DepkPILzOhymzB9eMSbfeHdwnEHZcMkvZ87RWfGo+4MXEe0dt2Lk/ME3kv5olkcnWeOPSOiIikEqrAmlvWwLjTaLdWEM5ch1OSUwLDCAOuWXVNuwsDIQR+yS7E8g0HkVtUadseEuSPD+6fYterRERE5ExtwOlHHGS1WpGdnQ2r1eruppAPYJ5IJk/LkzNrBbVHxrFTeHDFNvz9ox12RdKIPt3w7M0pLJLayNPyRN6NeSKZXJ0nDr1zkEajQVRUFKe2JCmYJ5LJ0/LU0WsF5eSXY/nGg9h+uMhu+4Du4bh98gAM692tTful0zwtT+TdmCeSydV5YqHkoIYxkUQyME8kk6flqSPXCqqurcdfVm6Dqe7sp4k9u4XgtkkDMHZADK+DkMDT8kTejXkimVydJ5b3DrJarThw4AC7jkkK5olk8rQ8NawVVJlfiXMvg21YKyhqcFSb1grqEuiP6aMTTj9PmA5/+d0QvP6n8UgdGMsiSRJPyxN5N+aJZHJ1ntij5CCNRoPu3buz65ikYJ5IJk/Lk6JRkDI/BesXrEdJTkmzawWlzEtpdSKHSlM91vxyBNeN6YMuQf627bNSExEZEohpjRaLJXk8LU/k3ZgnksnVeeKsd0RE1CGaXUdpcFSrawWZ6634Iv0oPt6agyqzBTdd1BdzJg1waduJiMg3ccHZDtDQ1Tdw4EAumEbtxjyRTJ6aJ2fXCrJYVXyzKw8f/pSNkqpa2/b/+/UYbrioLwI5i51LeGqeyDsxTySTq/PEQslBGo0GCQkJ7DomKZgnksmT86RoFMQkx7T4GFUIbMo8iZVph2AsrbFt1yjAJUPicOuE/iySXMiT80Teh3kimVydJxZKDlIUBV26dHF3M8hHME8kk7fmSQiB7YeLsHzjQRwpqLC7b9zAWMyd2B89o/Rua19n5a15Is/EPJFMrs4Ty3sHWa1WZGRkcNYWkoJ5IplcnSehChRkFODYj8dQkFEAobbtUteaWgue/3yXXZE0LKErXrl9HJ6cNZJFkpvw/EQyMU8kk6vzxMkcHCSEgNlsRlBQEKegpXZjnkgmV+ap2QkaBkUhZX7LEzScz+rNh7F840H0M4ThtskDMLJPVIe0mxzH8xPJxDyRTDLy5ExtwEKJiIgckrc1D+sXrIepxAS9oemU31MXTz1vsWQsrcF/N2fj9skDEd4l0LbdXGfBjpwijOM6SERE5ALO1AYceucgq9WK3bt3s+uYpGCeSCZX5EmoAulL0mEqMSGybyQCQgKg0WoQEBKAyMRImEpNSF+a3mQYXkmVGUu+2Yc7XkvDt7tPYPWWHLv7gwL8cNEgA4skD8LzE8nEPJFMrs4TCyUHaTQaDB48mLO2kBTME8nkijwVZhaiaH8R9AZ9k6JGURToY/UoyipCYWYhAKDaXI8VGw9i7pI0/N+OY7CcKaB+zDqJOgvfMHkynp9IJuaJZHJ1njjrnRM4/z/JxDyRTB2dJ3OpGdZaK/x0zf+34afzg7XAioriGvy4NQcfbc1Bpanedn+QvxbXjOmN68b0QYAfs+/peH4imZgnksmVeWJ57yBVVZGRkQFVVd3dFPIBzBPJ5Io8BUUEQRuohcVkafb+OrMFxweE4okd2Xj7hwO2IslPo2BGSgJWzJ+EORMHoEuQf4e1kRzT2qyFPD+RTMwTyeTqPHEyBwcJIaCqKjQaDcfSU7sxTySTK/IkVIE1t6yBcZcRkYmRds8jhEDhsVKkXdMLJr/T2xUAU4b0wK0T+iM2PLhD2kTOc2TWQp6fSCbmiWSSkSdO5tBBeCEiycQ8kUwdnSdFoyBlfgp0ETqU5JSgrqoOqlVFXVUdSnJKoNcHYcbgHgCAMf1j8PqfxuOh6cNYJHmQhlkLjTuN0IXrEJ4QDl24DsZdRqxfsB55W/Nsj+X5iWRinkgmV+aJhZKDVFVFVlYWu45JCuaJZHJVnuJT4zF18VRoxnbH90ldYCyshKnMBMMIA6Yunoqbrh2Cl29LxVPXj0JCNBeL9STOzFrI8xPJxDyRTK7OE4feERGRQ3ILK7Ey7SC2HiwAAFwUG4E/jklEdFI0FA2H1HiygowCrJ29FrpwHQJCAprcX1dVB1OZCTPfm4mY5Bi3tJGIyBWcqQ04652DuLI0ycQ8kUwdnaf8shq8vykb3+89gcafrB2rr0PEoG4skryAo7MWmkvNPD+RVMwTyeTqPHHonYNUVcXhw4fZdUxSME8kU0flqay6Fsu+zcQdr23Cd42KpMiQQNx3xQV4/U/jOdW3l2ht1kKLyQJtoBZBEUE8P5FUzBPJ5Oo8cegdEZEPEapAYWYhzKVmBEUEtWlYnLneio+35GDNL0dgqjt70WxIkB+uH9cXvxudgCB/FkjepLVZC0tySmAYYcA1q65hDyER+TQOvesAQgjU1NQgODiYXcfUbswTydSQp1O7T2H70u0tTv3sCI0CfLf3hK1ICvTTYMaFvTFrbCL0Oq6D5I0aZi1cv2D96VkKY/Xw0/nBYrKgMr8SuggdUualQNEoPD+RVMwTyeTqPHHonYNUVUVubi67jkkK5olkUlUVGVsy8N0j3zk09fO5zh1YEOCnxa0T+kGrUXD1qF5YPn8Sbp88kEWSl2uYtdAw3ABTmQlluWV2sxY2FNM8P5FMzBPJ5Oo8cegdEZEkMoa9tfV519yyBsadRkT2dXxYlRACmw/k44Mfs/HEdSPRo2sX231WVaCo3ITYCK6D5GvclVMiIk/AoXcdQAiByspK6PV6dh1TuzFPvidvax7Sl6S3e9hbWxTsK0BpcSn0hqZ5UhQF+lg9irKKUJhZaJv6edfRYry74QAOnSwHALy36RAevWa47ee0GoVFko9SNEqLU4Dz/EQyMU8kk6vzxKF3DlJVFSdPnmTXMUnBPPmWvK15WL9gfZuGvclgKjUhcEAg/Lq0MPVz7empnw+eLMMj7/+CR97/xVYkAUBxpRl1Ftetdk6ei+cnkol5IplcnScOvSMiaoe2DnuTyZHFRAst9SifOxjbT5ba3dc7Wo/bJg9ASt9oftpLREQ+j0PvOoAQAuXl5QgLC+ObCWo35sl3FGYWomh/kVPD3mSLGhyFqNQoGDcaEdnFvlir1Qhs6RmIvMSuEI2KpNhwHWZP6I9JyT2gYQapEZ6fSCbmiWRydZ449M5BqqqiqKiIXcckBfPkO8ylZlhrrfDTtT7sraMICPSc2RO6rjqU5JSgrqoOqlVFXVUdKrJLUBqrgzjzH0pEl0DMn5aEt++ZiClD4lgkURM8P5FMzBPJ5Oo8ubVQ+vHHH3H11Veje/fuUBQFn3/+ud39c+fOhaIodl9jxoxxS1u1Wi369esHrZaLLFL7MU++IygiCNpALSwmS7P3W0wWaAO1CIoI6rA2aLVajL5kNKY+PxXR50z93GO4ATeP6YPgQD/MnTQAK+ZPxNWjEuCv5edk1Dyen0gm5olkcnWe3Dr0rrq6GkOHDsVtt92Ga6+9ttnHXH755Vi+fLnt+4CApuPvXUFVVZSWliIiIgIaDd9gUPswT74jOikaUYOiYNxlRGRi02uUKvMrYRhhQHRSdIe1QVVVFBafwg5tPdaMCsVf7hmBaFVjm/oZCnCJmesgkWN4fiKZmCeSydV5cmuhNG3aNEybNq3FxwQGBiI2NtZlbTofIQTKysoQHh7u7qaQD2CefIeiUZAyPwXrF6xHSU4J9LF6+On8YDFZUJlfCV2EDinzUjpsIgerKvD9nhNYsXE/SqpP92p9eaIYT98w2u5xLJLIUTw/kUzME8nk6jx5fGmflpaG6Oho9O/fH3feeScKCwtbfHxtbS0qKirsvnCmAm34t7XbVqvV7rYQAlqtFgkJCbbqtWH7+W4LIZrcxpkX2Jnbqqra3XbmOFo7Jmdv85jkHZOiKOjduze0Wq3PHJMvvk6OHlPc2DhMXTwVhpEGmMrPDHurMsEwwoCpi6ei+4XdpR+TxWLB1oP5uPvNH/HSVxm2IgkAggP8UFtv4evEY2rTMWm1WvTp08eWJ184Jl98nbzlmBq/f/KVY/LF18lbjgkA+vTpA61W265jcpRHF0rTpk3DBx98gA0bNuDFF1/E9u3bMXnyZNTW1p73Z5599lmEhYXZvuLjTy/0+NtvvwEAjEYjjEYjAODEiRO2wuv48eMoLi4GAOTm5qK09PTsUEeOHEF5eTlUVcXu3btthdeBAwdQU1MDAMjKyoLZfPpC7YyMDNTX10NVVWRkZEBVVdTX1yMjIwMAYDabkZWVBQCoqanBgQMHAACVlZXIzs4GAJSXl+PIkSMAgNLSUuTm5gIAiouLcfz4cQBAYWEhTpw40a5jAoDs7GxUVlbymFx8THl5eTh06BBUVfWZY/LF18mZY4pPjcfgxwfjsrcuw1WvX4URL4zAZa9fhvjUeOnHtDXzOOa9uQlPffwrjhVVocGQ+FA8fmUfPHrNcJSeKubrxGNq0zGpqoq8vDzs37/fZ47JF18nbzkmVVWRnp6O2tpanzkmX3ydvOWYcnJycPToUaiq2q5jcpTHrKOkKArWrl2LGTNmnPcxRqMRvXr1wurVq3HNNdc0+5ja2lq7QqqiogLx8fEoLS1FeHi4rSLVaDTnvW21WqEoiu12w6cgubm56NWrl62K1Wg0UBSl2ds4Uw03vq3VaiGEcOq2qqq2T2Qcabszx3S+tvOYOv6YLBYL8vLy0KtXL1tWvf2YfPF18rRjKq+uxaIv9+LXnCK7897AHmG4MikCk0cOgEaj8apj8sXXyduPSVEUHDt2DHFxcfD39/eJY/LF18lbjqnx+6eGfXr7Mfni6+Qtx1RfX48TJ06gV69eEEK06ZgqKioQHh7u0DpKXlUoAUC/fv1wxx134OGHH3Zov1xwloh8hSoE7n17Mw7nn+7Z7hUVgtsmDcSY/lwsloiIyBHO1AYePfTuXKdOnUJeXh4MBoPLn1tVVeTn59sqXKL2YJ7IERWmOrvvNYqCuZMGICZMhwW/G4plfxyPsQNiIIRgnkganp9IJuaJZHJ1ntw6611VVRUOHz5s+/7o0aPYvXs3IiMjERkZiYULF+Laa6+FwWBAbm4uHnvsMXTr1g0zZ850S3vr6uoceBSRY5gnOp8KUx0+3pKDL7bn4uHU/ohX/GxTfY9KjMI78yY2WQeJeSKZmCeSiXkimVyZJ7cOvUtLS8OkSZOabJ8zZw6WLVuGGTNmYNeuXSgrK4PBYMCkSZPw9NNP2yZocASH3hGRtzDXWbA2PRefbM1Bde3pWey6FpmR+n0+/AK1iBoUhZT5KYhPdfwcSERERGc5Uxt4zDVKHUVWoaSqKoxGIwwGg+2iMKK2Yp6osXqrim92HseHPx1GafXZyWg0VhX9fzNj5Mk6iJqz6zJNXTzVrlhinkgm5olkYp5IJhl5cqY2cOvQOyKizkwVAmn7TmJl2kHkl5ls2xUhEJ9ThZRKgZB6ABoNEBKAyMRIlOSUIH1pOuLGxHXYIrZERETEHiUiIrcor6nDw6t+xtHCSrvto7tHIGxFFqL9/BEQEtDk5+qq6mAqM2HmezMRkxzjwha3j1AFCjMLYS412663YqFHRESuxh6lDqCqKk6cOIG4uDh2HVO7MU8UqvNHcODZU/CIPt1w26QBCDxcjq9O7YJfgq7Zn/PT+cFaYIW51Gzb5ul5ytuah/Ql6SjaXwRrrRVaXm/l0Tw9T+RdmCeSydV5YmKdEBDQ9NNdorZinjqX305Vo3EHvqIouH3yQAzoHo7nbrkQz958Ifp3D0dQRBC0gVpYTJZm92MxWaAN1CIoIshuu6fmKW9rHtYvWA/jTiN04TqEJ4RDF66DcZcR6xesR97WPHc3kZrhqXki78Q8kUyuzBMLJQdpNBrExsby0xCSgnnqPE6WVOO5tbvwh9fSsPNosd19F/SMxCu3p2J47262bdFJ0YgaFIXK/EqcOzJaCIHK/EpEDY5CdFK0bbun5kmoAulL0mEqMSGybyQCQgKg0WoQcOZ6K1OpCelL0yFUnx4B7nU8NU/knZgnksnVeWJqHaSqKnJzc7lgGknBPPm+U5VmvPq/DNyxbBM27jsJAWD5hoNQzyl+FMX+Oh1FoyBlfgp0ETqU5JSgrqoOqlVFXVUdSnJKoIvQIWVeit31PZ6ap8LMQhTtL4LeoG96nIoCfaweRVlFKMwsdFsbqSlPzRN5J+aJZHJ1nniNkhOCg4Pd3QTyIcyTb6oy1+PjrTn4/JejqLWcPZGHBQdg8gXdT/cSKS1PYhCfGo+pi6eeva6n4PR1PYYRBqTMa/66Hk/Mk7nUDGutFX665v+rae56K/IMnpgn8l7ME8nkyjyxUHKQRqNBdHS0A48kah3z5HvM9VZ8kZ6Lj7fmoMpcb9uuC9Di2jF9cM2Y3ugS6O/w/uJT4xE3Js6hmeI8NU+Nr7dqbga/811vRe7lqXki78Q8kUyuzhMLJQdZrVbk5uYiISEBWq3W3c0hL8c8+Zay6lrc/eZPKKk6u1isv1aDq0b1wg3jEhHeJbBN+1U0ikNTgHtqnhqutzLuMiIyMdJu+F3D9VaGEQa7663I/Tw1T+SdmCeSydV54jVKDlIUBeHh4U3G2RO1BfPkW8K7BKJPzOm1GDQKcOnQOLxzzwTcNXVwm4skZ3hqntpyvRW5n6fmibwT80QyuTpPXHCWiMgJQgjsO16CC3ra95AcNpbjg5+yMWfiACRE693aRk/T7DpKg6POe70VERFRR3GmNmCh5CCr1YojR46gT58+7DqmdmOevFNmXgmWbziIjOMleHLWSIwbGOvuJgFekiehCoeutyL384Y8kfdgnkgmGXlypjbgNUoO0mg0iIqK4joAJAXz5F2OFlRgxcaD+Dn77DTWKzYexJj+MdB6wJt9b8iTo9dbkft5Q57IezBPJJOr88RCyUENYyKJZGCevEN+aQ3e23QIGzJ+Q+Ou9x6RXXDrhP6tzfLtMswTycQ8kUzME8nk6jyxvHeQ1WrFgQMHYLVa3d0U8gHMk2crrarF0nX78IfX0vBDoyKpmz4I91+VjLfuHo/xgw3QeEilxDyRTMwTycQ8kUyuzhN7lByk0WjQvXt3dh2TFMyT5yqtqsVtSzfCVHf2JKzX+eP6cYn43agEBPp73hh75olkYp5IJuaJZHJ1nlgoOUhRFM6aR9IwT54rIiQQoxKj8NP+fAT6a3Hthb1x3dg+6BLk+GKxrsY8kUzME8nEPJFMrs4Ty3sHWa1WZGZmsuuYpGCePINVVbFx32+wqvaTf86eOAC/G90LK+ZPxJxJAzy6SALzRJIxTyQT80QyuTpP7FFykEajQUJCAruOSQrmyb1UIbB5fz5WbjyIEyXVsKoClwyJs90f37UL5l1+gVvb6AzmiWRinkgm5olkcnWeWCg5SFEUdOnSxd3NIB/BPLmHEAI7jxT/f3v3Hh5Vde8N/Ltnkkkm10kgV5IQCOEWUK5BgnKpyqNV3no5tioIaLW2oqccDlXaqsfTY+HFVmtbkEorglIOntN6q60aXpUgRg0CsZFwSYCQhFwmIbdJMjPJ7L3fPyBDJtxmkpU9syffz/PwMNkzmayV+WY/85u19lp49ZOjKKttdR9/reAYFkxKhfHciVdvO8gzTyQS80QiMU8kktZ5YnnvJVmWUVJSwqFjEoJ50t6R0814YvuX+NmOIo8iaVJGPJ64bYq7SNIj5olEYp5IJOaJRNI6T5KqqqoXj9MtX3bfvRxVVeFwOBAeHq67T5sp8DBP2jnVYMPWT46i8Gi9x/HRSTG4f8E4zByToPvXgHkikZgnEol5IpFE5MmX2oBT77wkSRLMZrO/m0FBgnnSRlO7A49s/hSuXos1pMRFYPn8cZibEzj7IA0U80QiMU8kEvNEImmdJ/3ONdGYLMsoLi7m0DEJwTxpIz4qHAsmjzh3Owz/+u1J+NOP5mH+pNSgKZLAPJFgzBOJxDyRSFrniVPvvKSqKrq7uxEaGsqhYxow5km8Dmc3/nGgErfljkKo8fxnQPUtndh9qBbfyc1EeABuFisC80QiMU8kEvNEIonIE6feDRKjMTjfZJF/ME9idLlkvLe/Ejv3lqO1swvhoUYsmpHpvj/JEoHvzcnyaxu1wDyRSMwTicQ8kUha5olT77ykKApKSkqgKIq/m0JBgHkaOFlR8GFxFR7YuBsv55eitbMLAPDGZ8chD7HfK/NEIjFPJBLzRCJpnSdOvfOSqqpQFAUGg4FDxzRgzFP/qaqKz47UYdvuY6hsbHcflwAsmJSK++aNRWr80Nqzg3kikZgnEol5IpFE5IlT7waJLMvcWZqEYZ58V3yyEVs+PoqjNS0ex3PHJGD5gvHISu7/hyF6xzyRSMwTicQ8kUha5omp9ZKiKCgtLeXQMQnBPPnujM2Bn+8o8iiSctLj8Otls/Ff9+QO6SKJeSKRmCcSiXkikbTOE6feEemMqqiwHrLC0exAeFw4EnMSIRmGxnSGlz44hHf2VWBUYjTu/9Y45I5J5FQOIiIi8hqn3g0C7ixNIvU3T1WFVSjaUISGww2QnTKMYUYkTEhA7qO5SM9LH9Q2a6mhzY43vziJ5QvGIazXkt73XDsG41JjMX/SCBiHSHHoDZ6fSCTmiURinkgkrfPEqXdeUhQF5eXlHDomIfqTp6rCKuSvzkftgVqYLWZYMi0wW8yoPViL/NX5qCqsGtQ2a6Gtswubd5Xi/g278eaXJ/HuvgqP++OiwnD9VWkskvrg+YlEYp5IJOaJRNI6T5x6R6QDqqLizSVvovZALeLHxHt8iqKqKpqONyFlWgrueP0OXU7Ds3e58NaXJ/G/n59Ap9PlPp5sMWPLigUsjIiIiEgITr0bBKqqorOzExERERw6pgHzNU/WQ1Y0HG5AdEr0BY+XJAnRydFoKG2A9ZAVSZOTBrHlYnW5ZLx/oBI79pajpaPLfdwUYsB3Zmbiu3lZLJK8wPMTicQ8kUjME4mkdZ449c5LiqKgoqKCQ8ckhK95cjQ7IDtlhJgv/tlGiDkEslOGo9khuKWDQ1ZU/L9/VuPBTQV46cNSd5FkkCR8e1oGXl2xAA/eMAExESZ/N1UXeH4ikZgnEol5IpG0zhNHlLxkNBqRk5Pj72ZQkPA1T+Fx4TCGGeGyu2CKurB4cNldMIYZER4XLrilg6Otswu/+8c3cHbL7mNzJ6Zg2fyxSBsW5de26RHPTyQS80QiMU8kktZ54oiSl1RVRVtbG4L8ki7SiK95SsxJRMKEBNjqbBd8j6qqsNXZkDAxAYk5iYPUYrHiosJwe24mAGB6VgI2PHgtfn7nNBZJ/cTzE4nEPJFIzBOJpHWeWCh5SVEU1NTUcOiYhOibJ1VRUV9Sj1N7TqG+pB6q4nkCkAwSch/NhTnOjKbjTehq74IiK+hq70LT8SaY48zIXZEbkAs5lNe24pd/PYAOR7fH8bvysrD+vllYe28uslNi/da+YMDzE4nEPJFIzBOJpHWeuOodkZ/5sjfSRR87MQG5KwJvH6XTZzqwbfdRFJTWAgDuvW4Mls0f5+9mERER0RDmS23AQslLqqqitbUVsbGxXLWFBqwnT22H2rDrJ7tgb7IjOiUaIeYQuOwu2OpsMMeZsfDXCy8ogFRFhfWQFY5mB8LjwpGYkxhQI0lnbA5s31OGDw5WQel1ehmZEIVNP5jLVewGAc9PJBLzRCIxTySSiDxxefBBoCgKGhoaEB0dDaPR6O/mkM4pigKr1YqSTSWwN9k99kYyRZkQnxWPpuNNKNpYhLRr0jwKIckgBcwS4L2LNjkyBJ80t+GdfRVwus4PicdGmHDvdWPw7WkZLJL6EFX08vxEIjFPJBLzRCJpnScWSl4yGo3Izs72dzMoSBiNRsQ6Y9FwSL97I/VMA6w91ojyzEiUT4hFt+n8ZY8RphD8y+zRuH3WKESE8VTTly9TLq+E5ycSiXkikZgnEknrPHExBy8pioIzZ87wYkQSQlEUNDY0Qu7W595IVYVVyF+dj9oDtTDFmVGeY3EXSQZZxY0Zw7H1sQVYPDebRdJF9P79mS1mWDItMFvMqD1Yi/zV+agqrPLp+Xh+IpGYJxKJeSKRtM4TCyUvqaqKlpYWLm9JQqiqim5TN4zhZ/dGuphA3RtJVVQUbShyTxmMDg/F5FonJFXFGGsXFvytCqPyqxETHurvpgakvr8/U5QJBqPBPeXS3mxH0caiC1Y+vOxz8vxEAjFPJBLzRCJpnScWSl4yGo3Iysri/FoSwmg04uq8q5EwVj97I6mqii/L6vHYpj2oPn7GY8rghPoufKekA9dWOJAUE+GeMkgXsh6youGwd1MuvcXzE4nEPJFIzBOJpHWeWCh5qefiew4dkwiKoqChsQEzV8zUxd5I31Q24d+3fY6nd36FsqZ2HBkT5TFlMFQBLI6zfxuBPGUwEDiaHZCdYqdc8vxEIjFPJBLzRCJpnSdePOCDzs5OfzeBgkhnZycyZmdg4a8Xnr+ov/7sRf0p01ICYm+k43Vt2Lr7KIrKPEc3WoeHo7vGhrAo0wXfE6hTBgNFeFw4jGFnp1yaBP7+eH4ikZgnEol5IpG0zBMLJS8ZDAZkZmb6uxkUJHrnKT0vHWnXpAXU3kg1TR14reAYdn9Tg96TAtOGRWL5/LGof/Zz1NXZYMqK95g+1jNlMGVaSsBMGQw0iTmJSJiQgNqDtYgX9Pvj+YlEYp5IJOaJRNI6T5x65yVFUVBXV8ehYxKib5569kYaOXckkiYn+a1Istm7seH9b/DgpgJ80qtIGh4TjlWLrsLmH87FdRNTMevRXF1MGQxEkkFCruDfH89PJBLzRCIxTySS1nniiJIPurq6/N0ECiKBmKcQo4Q9pbWQz624FmMOxS1ZSbg2LgbRRhMMOPvmPT0vPaCnDAa6wfj9BWKeSL+YJxKJeSKRtMyTpAb5eo1tbW2IjY1Fa2srYmJi/N0cooCiqCoMfVZee6foJLZ8fBQ3jBiG4R9WovXQpTdEVRXVqymD3j5uqOHvhYiISFu+1AYslLykKApqa2uRkpICg4EzFmlg/J0nl6zgw+Iq/O/nJ/CrpdcgIcbsvq/LJaNsbyW++NnHsDfZEZ0SjRBzCFx2F2x1NpjjzFj464Vej3pUFVadHzm5RMFFA+PvPFFwYZ5IJOaJRBKRJ19qAyaWaAhRVBW7v6nBQ38owO/+8Q1qmzuxfU+Zx2NCDQYc2XxAyIaoVYVVyF+dj9oDtTBbzLBkWmC2mFF7sBb5q/NRVVg1iL0lIiIi6j9eo+Qlg8GAESNG+LsZFCS0zpOqqvjqeANe/fgojte3edzXbu/2mILny4aoSZOTLv0zFRVFG4rcBVfPc/UUXE3Hm1C0sQhp16RxutkA8fxEIjFPJBLzRCJpnSeOKHlJURRUVlZy1RYSQss8lVY34/HXv8CT/73Po0i6amQ8fnN/Hp66a7rHdUqiNkT1peCigeH5iURinkgk5olE0jpPHFHygcl04eaQRP012Hlqbnfit38vwefH6j2Oj0mOwf3fGo/po4dfUMBA4IaovQsuVVXRZeuC3C3DGGqEKdp0tuCqv3LBRd7h+YlEYp5IJOaJRNIyTyyUvGQwGJCcnOzvZlCQ0CJPkeEhKK9rdX89Ij4Sy+aPxXUTUy5Y6a43URui9hRc7XXt6KjvgLPdCVVRIRkkhEWFITIp0quCi66M5ycSiXkikZgnEknrPHHqnZcURUFFRQWHjkmIwciTo1v2+NoUYsR988ZiWHQYfnzLZGz+4VzMy0m9bJEEgRuiJuYkIjIhEo2HG2FvscMYakSoORTGUCPsLXY0Hm5EZELkFQuuHqqior6kHqf2nEJ9Sb1Xi0kMFXo4P/H10w895In0g3kikbTOE0eUfBAREeHvJlAQEZWnDkc3/vLFCby7rwK/e+BajBgW6b7vhqtGYH5OKsJCjT49p7ANUc+9F5YkyX0b6tmvVaiACtSX1MPZ6rzsPkJcYvzKAvn8xNdPfwI5T6Q/zBOJpGWeuI8SkU51uWS8u+8U3visHG32bgDA/JxU/PSOqcJ+xkA2RK0vqcdbS9+CJEnoqO84OzKlKDAYzi41HhoZig5rB8LiwiCpEozhRqRMTcGsx2Z5vHnuWWJcxJ5OpD2+fkREFEh8qQ04ouQlWZZRUVGBzMxMGI2+fTpP1NdA8iQrCnZ9XY3X95Shse38QgghBgmxESaPpb4HSjJIl10C/HJ6FnOwZFoQnRrtsZiD7JJR/896dHd0Q3bKkIxn29te0w7rN1YsenkR0vPSucS4lwL1/MTXT58CNU+kT8wTiaR1nlgoeUmSJFgslouuEkbkq/7kSVVV7D1Sh62fHEX1mY7zzwVgwaRULJ0/DilxgTO9oe/qeWExYcC5fpz+8jS6O7oBCTCGGWE0GaHKKlxOF5rLm7H7md1Y8sESYXs6BbtAPT/x9dOnQM0T6RPzRCJpnScWSl4yGAwYNmyYv5tBQcLXPDW02fGL/9mPY7WtHsevyU7E8gXjMCop8KaVXmr1PGebE/YWOwDAEGJASNjZ05AUIiHUGIqu9i6c3nfafe3SFfd04hLjAXt+8mpPLr5+ASdQ80T6xDyRSFrniaveeUmWZZSVlUGWZS8eTXR5vuYpPioMnU6X++tJGfF4Yfls/OfdMwOySMJlVs9rt7ZDdZ1dJtwU6bkXgiRJCAk/ew1L3YE6j1Gpi/F2T6dgF6jnJ75++hSoeSJ9Yp5IJK3zxELJSwaDAQkJCTAY+CsbbENhGeEr5emMzfMTdqPBgGULxmF0UgyevWcmfr30GuSkx2vU2v7rWT0vZWoK7C12tFS0wNXpAgxAaMTZpcIvcG40XYXqHpWy1dnQd92Znj2dEiYmeL3EeLAK1PMTXz99CtQ8kT4xTySS1nniqnfks4GshHYlQ30ZYWurHa8XHMNHJaex4cFrMbrXaJGqqlABYQs1aKl3Ztqt7XjvoffgcroQFh12wWOdNidCwkOw7JNlSL46+fyqac12RCdz1TS94etHRESBxJfagIWSl3qG+rKzs4f0qi2DWcgMpWWE++aptbMLO/eW429fnUK3fHYTtVnZifjF3TP93dR+uVwxrSoqtt+0HZWfVp4dWTKHQjJIUBUV3fZuQAEyrsvAkg+WuL/normbmODbnk5BLNDPT3z99CXQ80T6wjyRSCLyxEKpF1GFkqqqsNlsiI6+cPWmoWIwCxlVUfHmkjdRe6DWYxlhnPvdNx1vQsq0FNzx+h1BsYxwT56MJjPe+vIk/vrFSXR2nb+OIyo8BN/Ny8JdeVm6G0HyppiuKqzC3x7+G1pPtUJVVKhQIUGCZJQQmxHrXh68t8EcydQ7PZyf+Prphx7yRPrBPJFIIvLkS23g1wmje/bswaJFi5CamgpJkvD222973K+qKp555hmkpqbCbDZj/vz5OHTokF/aKkkSYmJihuwfed/9UExRJhiMBvd+KPZmO4o2FvX7eiJflhEOBt2ygo8On8H9G3fj9T1l7iIpLMSA7+VlYeuj38L35ozRZZGUvzoftQdqYbaYYcm0wGwxo/ZgLfJX56OqsAo4d+3SopcXIfuWbMSkxSByeCRi0mIw9paxFy2S0GtPp5FzRyJpchLfZPeih/MTXz/90EOeSD+YJxJJ6zz5dXnwjo4OXH311bj//vtx5513XnD/c889hxdeeAFbt27F2LFj8eyzz+LGG2/E0aNHER0drWlbZVnGkSNHMH78+CE5dDzY+6EMpWWE61o6sXrb52jotVms0SDhpqnpWHxdNoZF63MFMF83F03PS0faNWkcZRBgqJ+fSCzmiURinkgkrfPk10Lp5ptvxs0333zR+1RVxYsvvoif//znuOOOOwAA27ZtQ1JSEnbs2IGHH35Y07YaDAZkZmYO2VVbBruQ6bs5aV/BtIxwYqwZMWaTu1Can5OKpfPHYkR8pL+bNiD9KaZ7RhloYIb6+YnEYp5IJOaJRNI6TwGb2pMnT6Kurg4LFy50HwsLC8O8efNQWFh4ye9zOp1oa2vz+AcAiqK4/7/SbVmWPW6rqgpJkhAefv5Nes/xS91WVfWC2zhXAPpyW1EUj9u+9ONKffLldpgl7Gwh0+s6GvQq5F1dZwuZMEtYv/qUmJOIhIkJsFnPLSMseS4TbbOeXUZ4+IThwvqk1et0vLbF47hBkrBs/ljMyErASw9diyduuxopFrOu+nSx2/YmO+Tuc8W04fzr13M7xBwC2SXD3mTXTZ8G6+9JdJ8URUFkZCRUVQ2aPgXj66SXPkmShIiICPfPCYY+BePrpJc+9X7/FCx9CsbXSS99UhQFERERkCRpQH3yVsAWSnV1dQCApCTPT5uTkpLc913MunXrEBsb6/6Xnn72WofTp08DAGpra1FbWwsAqK6uhtV69pqXyspKNDY2AgAqKirQ3NwMADhx4gRaW1shyzL27t2L1tZWAMCRI0fQ2dkJACgtLYXDcXZ0oKSkBN3d3VAUBSUlJVAUBd3d3SgpKQEAOBwOlJaWAgA6Oztx5MgRAIDNZkNZWRkAoLW1FSdOnAAANDc3o6KiAgDQ2NiIyspKAIDVakV1dfWA+gQAZWVlsNlsV+xT3Ng4JOQkICQ3BKpBBUxA6DWhZ3/pZsA47ewqVlGjovrVJ8kgYeyDY2HJs6DpeBPUZBVShoSu9i44YhyInRaL3BW5qKquEtanwX6dympb8ZOtn+GRP32Gw9XNHq9TcpgDi0YryEyIEvo6+TN77aHtiMiJgMvuQsjYEBhSzp5eQiaEwJBogMvuQsy8GMiRsm76NFh/T6L7dOLECZSUlMBqtQZNn4LxddJLn2RZxsGDB3H48OGg6VMwvk566ZMsyygoKIDD4QiaPgXj66SXPpWXl2P//v2Qz61+198+eStgVr2TJAlvvfUWbrvtNgBAYWEh5syZg5qaGqSkpLgf99BDD6GqqgoffPDBRZ/H6XTC6XS6v25ra0N6ejqam5thsVjcFanBYLjk7Z5P1Hpu9wzvdXZ2wmw2exzvqWj73sa5qrf3baPR6P7E19vbiqJAVVX37Su13Zc+Xartl7pdVViFXWt2wd54bj+UqBC42l2w1dtgHmbGwvULkTY7bUB9qv68Gvs27kPD0XMrpoUakZCTgJk/momMORnC+zQYr1NlQxteKyjDp4fPF/RXjYzH/12c69Feh8OBiIgI9ycbgdwnrzLmkvH2srfPrlyYHQ8JEs5u/HT2+qWm8iakzEjB7Vtvh8HoW/+C8e9JZJ96Tvwmk8ndLr33KRhfJ730yWAwwG63w2QyISQkJCj6FIyvk176hHPXpPeMAgRDn4LxddJLn1wuF7q6umA2m91t9LVPbW1tsFgs+loevG+hdOLECWRlZeHAgQOYOnWq+3Hf+c53YLFYsG3bNq+elxvOiqXFfih6XUa4oc2OP+8pw4fF1VB6/VklWcxYNm8svjV5RNCv+sPNRYmIiCiQ+VIb+HUxh8sZNWoUkpOTsWvXLneh1NXVhYKCAqxfv17z9siyjJKSEkyePHlIr9qixUplervAv62zC28UHsc7RRXuzWIBwBJpwr3XZePb0zIQavSc5RqseUrPS8fCXy88X0zXny2mU6alcHPRQRSseSL/YJ5IJOaJRNI6T34tlNrb21FeXu7++uTJkyguLkZ8fDwyMjKwcuVKrF27FtnZ2cjOzsbatWsRERGBe++9V/O2GgwGTJw40T18N5TprZAZTDVNHVjxp73odJ5f5CIiLAR3zR6N22eNgtl08T+xYM4Tl/3WXjDnibTHPJFIzBOJpHWe/FooffXVV1iwYIH761WrVgEAli1bhq1bt+Lxxx+H3W7HI488gubmZsyaNQv5+fma76HUg5+EUF8pcREYlRiNQ1XNCDUa8J3cTHwvLwsxERcucd5XMOeJxbT2gjlPpD3miURinkgkLfMUMNcoDRZR1yhx6JhkRcWBEw2YOSbR4/g3lU3Y9c9qLJmbjYQYs3fPxTyRQMwTicQ8kUjME4kkIk++1AYslLzUezWgYL8gnzypqoovjlmx9ZOjqGiwYd3iWZg2eviAn5N5IlGYJxKJeSKRmCcSSUSegmIxh0DUe4lBGhpKTp3BKx8fweHqFvexVz8+gqmj5gz4hM88kUjME4nEPJFIzBOJpGWemFovKYqC0tJS97ruFNyO17Xiyf8uwurXvvAoksalWvD968cPuEhinkgk5olEYp5IJOaJRNI6T5x6R9TL6aYOvLb7GHYfqvE4njE8CssXjEPeuCROHSAiIiLSKU69GwSqqsLhcCA8PJxvlINUTVMHHtpUAFk5/9lBYqwZ983LxvWT02AUuLw180QiMU8kEvNEIjFPJJLWeeLUOy8pioLy8nIOHQex1PhITBl1dpGG2AgTHl44Ea88Mg8Lr04XWiRBUJ5URUV9ST1O7TmF+pJ6qEpQDw7TZfD8RCIxTyQS80QiaZ0nTr2jIcnRLaPgUA0WXp3m8YlEeW0rvjhWjzuuGY2IsMAdcK0qrELRhiI0HG6A7JRhDDMiYUICch/NRXpeur+bR0RERBSQOPVuEKiqis7OTkRERHDoWMdcsoL3D1Zhx6dlaGp3Ijo8FHnjk933j0mJxZiU2EFvx0DyVFVYhfzV+bA32RGdEo0QcwhcdhdqD9Yif3U+Fv56IYulIYbnJxKJeSKRmCcSSes8ceqdlxRFQUVFhdChPk6d0o6iqvi45DQe3FSADe9/g6Z2JwDgtYJj8Megan/zpCoqijYUwd5kR/yYeJiiTDAYDTBFmRCfFQ97sx1FG4uYpSFmMM5PNHQxTyQS80QiaZ0nTr3zE06d0oaqqthX3oBXPzmKE/VtHvfNGZ+M5fPHIiMh2m/t81V9ST3eWvoWzBYzTFGmC+7vau+CvcWO21+7HUmTk/zSRiIiIqJAxal3g0BVVdhsNkRHRw94qI9Tp7RxqKoJWz4+im8qmzyOT8kchvu/NR7jR1j81rb+5snR7IDslBFivvifbog5BHK9DEezQ2BrKdCJPD8RMU8kEvNEImmdJ06985KiKKipqRnwUB+nTmnj9JkOrNr6uUeRlJ0Si3WLZ2H9fdf4tUjCAPIUHhcOY5gRLrvrove77C4Yw4wIjwsX1FLSA1HnJyIwTyQY80QiaZ0njih5yWg0Yvz48QN+HushKxoONyA65cJKWJIkRCdHo6G0AdZD1itOnVIVFdZDVjiaHQiPC0diTiIkwctY69WIYZG4bkIyPj1ch7RhkVi+YByuHZ8cMJ9m9TdPiTmJSJiQgNqDtYjPivfoj6qqsNXZkDItBYk5iYJbTIFM1PmJCMwTCcY8kUha54mFkpdUVUVraytiY2MH9GZb1NQpXuN0XlO7A+8fqMLd147x2O9o2fxxmJGVgBuvToPREFiDp/3Nk2SQkPtoLvJX56PpeBOik89P3bTV2WCOMyN3RS4L5iFG1PmJCMwTCcY8kUha5ymw3j0GMEVR0NDQMOChPhFTp3qucao9UAuzxQxLpgVmi9l9jVNVYdWA2qgX7Y5uvPrxESzfsBuvFRzD7m9Oe9yfPjwKN03NCLgiCQPMU3peOhb+eiFSpqbA3mJHS0UL7C12pExL4fVtQ5So8xMRmCcSjHkikbTOE1e905iqqHhzyZuXnDrVdLwJKdNScMfrd1x0VMD9/QdqET/G9+8PBs5uGe/uq8DOz46j3dHtPj4qMRqbfnDdkPnEilMviYiIiHzDVe8GgaIoaG5uRlxcHAwDGKEY6NQpkdc46Y2sKPiwuBrb9xzDGZvTfTzEIOGW6SNx73VjdFMkiciTZJAC+jVmIacdUecnIjBPJBjzRCJpnScWSl5SVRUtLS2wWAa+WlrP1Cn3NUb1Z68xSpmWgtwVl7/GaCguD62oKj4trcW23cdwuqnDfVwCcMNVaVgyLxvJlgi/ttFXIvMUiHgNnbaCPU+kLeaJRGKeSCSt88Spd37Un0/ch+KGo9Vn2vHQpgL0XjF99tgkLF8wDpmJ+tksdqi41D5hPSOmvI6KiIiI/MWX2oBjoF5SFAVWq1XoxWM9U6dGzh2JpMlJXk1L6lke2lZnQ98at2d56ISJCUG1PHTasChcf1UaAOCqkfF48f48PPO9GboukgYjT4GA+4T5R7DmifyDeSKRmCcSSes8sVDyQWdnp7+b4L7GyRxnRtPxJnS1d0GRFXS1d6HpeJPul4eusNrw27+XoFv2/ANYOm8snr1nJp677xpMSIvzW/tECoQ8iebLNXQkVjDmifyHeSKRmCcSScs88RolLxkMBmRmZvq7GcAAr3EKVPUtnXi9oAz/75/VUAGMTorBohkj3fcnxpqRGGv2axtFCqQ8iTQUr6ELBMGaJ/IP5olEYp5IJK3zxELJSz1DfYmJiQGxakt6XjrSrknT/apiLR1O/Pfecvx9f6XHKNKHxVW4dXqGblax81Wg5UmU3vuEXewaOm/2CSPfBWueyD+YJxKJeSKRtM4TCyUfdHV1+bsJHgJ9eejL6XB246+fn8SbX56AvUt2H48KD8X35mTh/8zMDNoiqUeg5UmEnmvoLrVPmK3OhpRpKUF1DV2gCMY8kf8wTyQS80QiaZknrnpHmupyyfjbV6ewc2852uznN4sNCzXi9txM3JWXhajwUL+2kQbGvepds/2i+4Rx1TsiIiLyF656NwgURcHp06f7vcqGqqioL6nHqT2nUF9SP2RX/WqyObHloyPuIslokLBoxkhsfXQ+7v/W+CFTJA00T4Gs5xq6lKkpsLfY0VLRAnuLHSnTUlgkDZJgzhNpj3kikZgnEknrPHHqnQa4+eZ5yXER+Pb0DPxt3yksmJSK++aNRWp8pL+bRYIFyzV0RERENHRx6t0gG8qbbx482Yi3vzyJn905DWGhRvfxlg4nzticyErmVEgiIiIi0g6n3g0CRVFQWVnp01DfUN1882hNC9Zs/xJrtn+JL8qseHdfhcf9lsiwIV8k9SdPRJfCPJFIzBOJxDyRSFrniVPvfGAyXbjc8eX4svmmXlev662ysR3bPjmKvUfqPI4XlVvxL7NHB/0qdr7yNU9El8M8kUjME4nEPJFIWuaJhZKXDAYDkpOTffqeobL5prXVjj/vKUP+11XoPTiWEheBpfPGYv6kVBZJffQnT0SXwjyRSMwTicQ8kUha54mFkpd6hvoyMjK83uAq2DffbLN34b/3luNv+055bBYbFxmGxXPH4KapGQg1cnbnxfQnT0SXwjyRSMwTicQ8kUha54mFkg8iIiJ8enywb77Z7VLw96/OF0mRYSH4bl4WbsvNRLiJ0boSX/NEdDnME4nEPJFIzBOJpGWeWNp7yWAwIDEx0afqVTJIyH00F+Y4M5qON6GrvQuKrKCrvQtNx5tgjjMjd0WubpZM7rtA4rDocNyWOwqmEAO+m5eFrY8twN3XjmGR5IX+5InoUpgnEol5IpGYJxJJ6zwxtV6SZRnHjx+HLMs+fV8wbL4pKyp2fV2Nx175DB3Obo/7vjcnC1sfXYDvXz8eMWZerOmt/uaJ6GKYJxKJeSKRmCcSSes88aN/L0mSBIvF0q9FCfS6+aaqqvj8aD1e/eQoKhvbAQB//fwkls4f635MZHgoIsND/dhKfRpInoj6Yp5IJOaJRGKeSCSt88RCyUsGgwHDhg3r9/dLBklXS4B/XXEGWz4+giOnWzyOVza2Q1VVnvAGaKB5IuqNeSKRmCcSiXkikbTOE6feeUmWZZSVlQX90HFZbSt+9ucv8fjrX3gUSRPSLPjV0mvw5L9MY5EkwFDJE2mDeSKRmCcSiXkikbTOE0eUvGQwGJCQkBC0FyOesTnwh/xS7Cmt9Tg+MiEK9y8Yj2vGJrJAEijY80TaYp5IJOaJRGKeSCSt88RCyUs9cyKDVajRgK+ON7i/TrKYcd/csfjW5BEwBvi1VL5SFdXv14sFe55IW8wTicQ8kUjME4mkdZ5YKHmpZ6gvOzsbRqPR380ZMFlRYOxVjcdEmHDX7NF4u6gCi68bg5unZcAUov9+9lVVWIWiDUVoONwA2SnDGGZEwoQE5D6aq+kKhMGWJ/Iv5olEYp5IJOaJRNI6T5Lad3OcINPW1obY2Fi0trYiJiam38+jqipsNhuio6N1PQXN0eXCW0UV+Pv+U9j40HWIjTi/pLejW4aqqjAH6T5IVYVVyF+dD3uTHdEp0Qgxh8Bld8FWZ4M5zqzpcu3BkicKDMwTicQ8kUjME4kkIk++1AbB+Y54EEiSNKBCy9+6ZQXvH6jEjk/L0dzhBADs/KwcD9840f2Y8NDg/aRHVVQUbSiCvcmO+DHx7j8uU5QJ8VnxaDrehKKNRUi7Jk2TaXh6zxMFFuaJRGKeSCTmiUTSOk+8ss5Lsizj0KFDulu1RVZUfPTPajz40m5s/OCQu0gySEC3S/F38zRjPWRFw+EGRKdc+AmEJEmITo5GQ2kDrIesmrRHr3miwMQ8kUjME4nEPJFIWueJI0peMhgMyMzM1M2qLaqq4ssyK7Z+chQnrTaP+66bkIJl88cifXiU39qnNUezA7JTRoj54pEPMYdArpfhaHZo0h695YkCG/NEIjFPJBLzRCJpnScWSl6SJAmRkZH+boZXaps78dzbxSitbvY4Pm30cNy/YBzGpg691WfC48JhDDPCZXfBFGW64H6X3QVjmBHhceGatEdPeaLAxzyRSMwTicQ8kUha54nlvZdkWUZJSYkuho5jI0w43dTh/npcqgXrl8zCusWzhmSRBACJOYlImJAAW50NfdcvUVUVtjobEiYmIDEnUZP26ClPFPiYJxKJeSKRmCcSSes8cdU7L6mqCofDgfDw8IBbtaXD0Y3I8FCPY28XncTf91di+YJxyBuXFHBt9gf3qnfNdkQn+3/Vu0DNE+kP80QiMU8kEvNEIonIky+1AQslHTtjc+DPn5bhk5Ia/PFH8zA85vy0MZesQJLgsVcSXWIfpYkJyF2h7T5KRERERKQ9Lg8+CHqG+iZPnuz3DdNs9m78b+FxvF10Es5zK9f9+dMy/PiWye7HhBhZIF1Mel460q5Jg/WQFY5mB8LjwpGYk6jJkuC9BVKeSP+YJxKJeSKRmCcSSes8cUTJS6qqoru7G6GhoX4bOnZ0y3inqAL/U1iOdofLfdxsMuK7eVm497psv7SLfBcIeaLgwTyRSMwTicQ8kUgi8sQRpUHir09CXLKCD4qr8Oc9ZWhqd7qPhxoNWDRjJL43JwuWyDC/tI36j5+skUjME4nEPJFIzBOJpGWeOD/LS4qioKSkBIqi7SatlY3teHBTAX7/j2/cRZJBAhZenYZXHpmHhxdOZJGkQ/7KEwUn5olEYp5IJOaJRNI6T5x65yVVVaEoCgwGg6ZDx10uGQ9s3I2GtrMboc4Zl4RlC8ZhZEK0Zm0g8fyVJwpOzBOJxDyRSMwTiSQiT5x6N0hkWR70nYDrWjqRbIlwf20KMeK+eWPxUclpPPCtcRg/Im5Qfz5pR4s80dDBPJFIzBOJxDyRSFrmian1kqIoKC0tHbShvpP1bfiPnfvwwMbdqOm1WSxwdprd+iWzWCQFkcHOEw0tzBOJxDyRSMwTiaR1njj1zs/qmjvxWsExfFxyGj0vxIJJqVhz+1Q/t4yIiIiIKLhw6t0gEL2zdHO7Ezv2luEf+yvhUs7XqsOjwzElc9iAn58CG3cqJ5GYJxKJeSKRmCcSSes8ceqdlxRFQXl5+YCH+joc3dj2yVEs3/AJ3t13yl0kRZtD8eAN47FlxXzcNDVDUKspUInKExGYJxKMeSKRmCcSSes8ceqdhk7Wt+Enr38Bm73bfSws1Ig7Z43Cv8wejcjwUL+2j4iIiIgomHHq3SBQVRWdnZ2IiIjo91BfRkIUYs0m2OzdCDFIuGX6SNxz7RjERXEfpKFGRJ6IejBPJBLzRCIxTySS1nni1DsvKYqCioqKAQ31GQ0GLF8wDtdPHoFXHpmPR27KYZE0RInIE1EP5olEYp5IJOaJRNI6T5x6R0REREREQ4IvtQFHlLykqira2toQ5HUlaYR5IpGYJxKJeSKRmCcSSes8sVDykqIoqKmp4dAxCcE8kUjME4nEPJFIzBOJpHWeOPWOiIiIiIiGBE69GwSqqqKlpYVDxyQE80QiMU8kEvNEIjFPJJLWeWKh5CVFUdDQ0MChYxKCeSKRmCcSiXkikZgnEknrPHHqHRERERERDQlBM/XumWeegSRJHv+Sk5P90hZFUXDmzBl+IkJCME8kEvNEIjFPJBLzRCJpnaeALpQAICcnB7W1te5/JSUlfmkH59iSSMwTicQ8kUjME4nEPJFIWucpRJOfMgAhISF+G0XqzWg0Iisry9/NoCDBPJFIzBOJxDyRSMwTiaR1ngJ+RKmsrAypqakYNWoU7r77bpw4ceKyj3c6nWhra/P4h3NDdT3/X+m2LMset1VVhaIoqKurgyzLHscvdVtV1Qtu41wl7MttRVE8bvvSjyv1ydfb7JO4PrlcLtTX17uPBUOfgvF10kufuru7YbVa4XK5gqZPwfg66aVPiqKgvr4e3d3dQdOnYHyd9NInpdf7p2DpUzC+TnrpU3d3t/v900D65K2ALpRmzZqF1157DR9++CH++Mc/oq6uDnl5eThz5swlv2fdunWIjY11/0tPTwcAnD59GgDcU/gAoLq6GlarFQBQWVmJxsZGAEBFRQWam5sBACdOnEBra6v7eHt7OwDgyJEj6OzsBACUlpbC4XAAAEpKStDd3Q1FUVBSUuJ+E9MzZdDhcKC0tBQA0NnZiSNHjgAAbDYbysrKAACtra3ugrC5uRkVFRUAgMbGRlRWVgIArFYrqqurB9ynsrIy2Gw29knjPp0+fRp1dXVB1adgfJ300qdTp06hs7MTZ86cCZo+BePrpKc+tbS04OjRo0HVp2B8nfTSp7KysqDrUzC+Tnro08mTJ911wED65C1drXrX0dGBrKwsPP7441i1atVFH+N0OuF0Ot1ft7W1IT09Hc3NzbBYLO6K1GAwXPK2LMuQJMl922AwQJIkn27jXDXc+7bRaHR/uuLtbUVRoKqq+/aV2s4+sU/sE/vEPrFP7BP7xD6xT+zTxfvU1tYGi8Xi1ap3uiqUAODGG2/EmDFjsGnTJq8eL2p5cEVRYLVakZiY6P6FE/UX80QiMU8kEvNEIjFPJJKIPAXN8uB9OZ1OHD58GCkpKX75+V1dXX75uRScmCcSiXkikZgnEol5IpG0zFNAjyitXr0aixYtQkZGBqxWK5599lkUFBSgpKQEI0eO9Oo5uOEsEREREREhmEaUqqurcc8992DcuHG44447YDKZ8MUXX3hdJImkKApOnz7tnjNJNBDME4nEPJFIzBOJxDyRSFrnKaD3Udq5c6e/m0BERERERENQQE+9E4FT74iIiIiICD7WBgE9oiRCTx3Ys/Fsf/UM9Y0YMYKrttCAMU8kEvNEIjFPJBLzRCKJyFNPTeDNWFHQF0o9G1H1bDxLRERERERDm81mQ2xs7GUfE/RT7xRFQU1NDaKjoyFJUr+fp2fj2qqqKk7howFjnkgk5olEYp5IJOaJRBKRJ1VVYbPZkJqaesVRqaAfUTIYDEhLSxP2fDExMfxDJ2GYJxKJeSKRmCcSiXkikQaapyuNJPXgZFEiIiIiIqI+WCgRERERERH1wULJS2FhYfiP//gPhIWF+bspFASYJxKJeSKRmCcSiXkikbTOU9Av5kBEREREROQrjigRERERERH1wUKJiIiIiIioDxZKREREREREfbBQIiIiIiIi6oOFkhdeeukljBo1CuHh4Zg+fTo+/fRTfzeJdGjdunWYOXMmoqOjkZiYiNtuuw1Hjx71d7MoSKxbtw6SJGHlypX+bgrp1OnTp7FkyRIMGzYMERERmDJlCvbv3+/vZpEOuVwuPPnkkxg1ahTMZjNGjx6NX/ziF1AUxd9NIx3Ys2cPFi1ahNTUVEiShLffftvjflVV8cwzzyA1NRVmsxnz58/HoUOHBqUtLJSu4I033sDKlSvx85//HAcPHsR1112Hm2++GZWVlf5uGulMQUEBVqxYgS+++AK7du2Cy+XCwoUL0dHR4e+mkc7t27cPmzdvxlVXXeXvppBONTc3Y86cOQgNDcX777+P0tJSPP/887BYLP5uGunQ+vXr8Yc//AEbNmzA4cOH8dxzz+FXv/oVfv/73/u7aaQDHR0duPrqq7Fhw4aL3v/cc8/hhRdewIYNG7Bv3z4kJyfjxhtvhM1mE94WLg9+BbNmzcK0adOwadMm97EJEybgtttuw7p16/zaNtK3hoYGJCYmoqCgAHPnzvV3c0in2tvbMW3aNLz00kt49tlnMWXKFLz44ov+bhbpzJo1a/DZZ59xxgQJceuttyIpKQmvvPKK+9idd96JiIgIvP76635tG+mLJEl46623cNtttwHnRpNSU1OxcuVKPPHEEwAAp9OJpKQkrF+/Hg8//LDQn88Rpcvo6urC/v37sXDhQo/jCxcuRGFhod/aRcGhtbUVABAfH+/vppCOrVixArfccgtuuOEGfzeFdOzdd9/FjBkzcNdddyExMRFTp07FH//4R383i3Tq2muvxUcffYRjx44BAL7++mvs3bsX3/72t/3dNNK5kydPoq6uzuO9eVhYGObNmzco781DhD9jEGlsbIQsy0hKSvI4npSUhLq6Or+1i/RPVVWsWrUK1157LSZNmuTv5pBO7dy5EwcOHMC+ffv83RTSuRMnTmDTpk1YtWoVfvazn6GoqAj/+q//irCwMCxdutTfzSOdeeKJJ9Da2orx48fDaDRClmX88pe/xD333OPvppHO9bz/vth781OnTgn/eSyUvCBJksfXqqpecIzIF48++ij++c9/Yu/evf5uCulUVVUVfvzjHyM/Px/h4eH+bg7pnKIomDFjBtauXQsAmDp1Kg4dOoRNmzaxUCKfvfHGG9i+fTt27NiBnJwcFBcXY+XKlUhNTcWyZcv83TwKAlq9N2ehdBnDhw+H0Wi8YPTIarVeUMkSeeuxxx7Du+++iz179iAtLc3fzSGd2r9/P6xWK6ZPn+4+Jssy9uzZgw0bNsDpdMJoNPq1jaQfKSkpmDhxosexCRMm4K9//avf2kT69ZOf/ARr1qzB3XffDQCYPHkyTp06hXXr1rFQogFJTk4Gzo0spaSkuI8P1ntzXqN0GSaTCdOnT8euXbs8ju/atQt5eXl+axfpk6qqePTRR/Hmm2/i448/xqhRo/zdJNKx66+/HiUlJSguLnb/mzFjBhYvXozi4mIWSeSTOXPmXLBdwbFjxzBy5Ei/tYn0q7OzEwaD51tMo9HI5cFpwEaNGoXk5GSP9+ZdXV0oKCgYlPfmHFG6glWrVuG+++7DjBkzMHv2bGzevBmVlZX44Q9/6O+mkc6sWLECO3bswDvvvIPo6Gj3SGVsbCzMZrO/m0c6Ex0dfcH1bZGRkRg2bBiveyOf/du//Rvy8vKwdu1afPe730VRURE2b96MzZs3+7tppEOLFi3CL3/5S2RkZCAnJwcHDx7ECy+8gAceeMDfTSMdaG9vR3l5ufvrkydPori4GPHx8cjIyMDKlSuxdu1aZGdnIzs7G2vXrkVERATuvfde4W3h8uBeeOmll/Dcc8+htrYWkyZNwm9+8xsu50w+u9Tc2VdffRXLly/XvD0UfObPn8/lwanf3nvvPfz0pz9FWVkZRo0ahVWrVuGhhx7yd7NIh2w2G5566im89dZbsFqtSE1NxT333IOnn34aJpPJ382jALd7924sWLDgguPLli3D1q1boaoq/vM//xMvv/wympubMWvWLGzcuHFQPiRkoURERERERNQHr1EiIiIiIiLqg4USERERERFRHyyUiIiIiIiI+mChRERERERE1AcLJSIiIiIioj5YKBEREREREfXBQomIiIiIiKgPFkpERERERER9sFAiIiLqo6KiApIkobi42N9NISIiP2GhREREAUeWZeTl5eHOO+/0ON7a2or09HQ8+eSTV3yOHTt2wGg04oc//KHPPz89PR21tbWYNGmSz99LRETBQVJVVfV3I4iIiPoqKyvDlClTsHnzZixevBgAsHTpUnz99dfYt28fTCbTZb//hhtuwMyZM7Fp0ybU1NQgIiJCo5YTEVEw4IgSEREFpOzsbKxbtw6PPfYYampq8M4772Dnzp3Ytm3bFYukiooKFBYWYs2aNRg/fjz+8pe/eNz/wAMP4KqrroLT6QQAdHd3Y/r06e6CrO/Uu+bmZixevBgJCQkwm83Izs7Gq6++Omh9JyIi/2OhREREAeuxxx7D1VdfjaVLl+IHP/gBnn76aUyZMuWK37dlyxbccsstiI2NxZIlS/DKK6943P+73/0OHR0dWLNmDQDgqaeeQmNjI1566aWLPt9TTz2F0tJSvP/++zh8+DA2bdqE4cOHC+olEREFohB/N4CIiOhSJEnCpk2bMGHCBEyePNld2FyOoijYunUrfv/73wMA7r77bqxatQrl5eUYM2YMACAqKgrbt2/HvHnzEB0djeeffx4fffQRYmNjL/qclZWVmDp1KmbMmAEAyMzMFNpPIiIKPBxRIiKigLZlyxZERETg5MmTqK6uvuLj8/Pz0dHRgZtvvhkAMHz4cCxcuBBbtmzxeNzs2bOxevVq/Nd//Rf+/d//HXPnzr3kc/7oRz/Czp07MWXKFDz++OMoLCwU0DMiIgpkLJSIiChgff755/jNb36Dd955B7Nnz8b3v/99XGkNoi1btqCpqQkREREICQlBSEgI/vGPf2Dbtm2QZdn9OEVR8Nlnn8FoNKKsrOyyz3nzzTfj1KlTWLlyJWpqanD99ddj9erVwvpJRESBh4USEREFJLvdjmXLluHhhx/GDTfcgD/96U/Yt28fXn755Ut+z5kzZ9yLPhQXF3v8a29vx/vvv+9+7K9+9SscPnwYBQUF+PDDD6+4OENCQgKWL1+O7du348UXX8TmzZuF9peIiAILr1EiIqKAtGbNGiiKgvXr1wMAMjIy8Pzzz2PVqlW46aabLnqd0Ouvv45hw4bhrrvugsHg+VngrbfeildeeQW33noriouL8fTTT+Mvf/kL5syZg9/+9rf48Y9/jHnz5mH06NEXPO/TTz+N6dOnIycnB06nE++99x4mTJgwiL0nIiJ/44gSEREFnIKCAmzcuBFbt25FZGSk+/hDDz2EvLy8S07B27JlC26//fYLiiQAuPPOO/Hee+/h1KlTWLx4MZYvX45FixYBAL7//e/jhhtuwH333ecxPa+HyWTCT3/6U1x11VWYO3cujEYjdu7cKbzfREQUOLjhLBERERERUR8cUSIiIiIiIuqDhRIREREREVEfLJSIiIiIiIj6YKFERERERETUBwslIiIiIiKiPlgoERERERER9cFCiYiIiIiIqA8WSkRERERERH2wUCIiIiIiIuqDhRIREREREVEfLJSIiIiIiIj6+P+ZzibScFU7rAAAAABJRU5ErkJggg==",
|
||
"text/plain": [
|
||
"<Figure size 1000x600 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"import numpy as np\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"\n",
|
||
"# 1. Generate some synthetic data\n",
|
||
"# We set a random seed for reproducibility\n",
|
||
"np.random.seed(3)\n",
|
||
"\n",
|
||
"# Create 50 random x values between 0 and 10\n",
|
||
"x = np.random.uniform(0, 10, 50)\n",
|
||
"\n",
|
||
"# Create y values with a linear relationship plus some random noise\n",
|
||
"# True relationship: y = 2.5x + 5 + noise\n",
|
||
"noise = np.random.normal(0, 2, 50)\n",
|
||
"y = 2.5 * x + 5 + noise\n",
|
||
"\n",
|
||
"# 2. Calculate the line of best fit\n",
|
||
"# np.polyfit(x, y, deg) returns the coefficients for the polynomial\n",
|
||
"# deg=1 specifies a linear fit (first degree polynomial)\n",
|
||
"slope, intercept = np.polyfit(x, y, 1)\n",
|
||
"\n",
|
||
"# Create a polynomial function from the coefficients\n",
|
||
"# This allows us to pass x values directly to get predicted y values\n",
|
||
"fit_function = np.poly1d((slope, intercept))\n",
|
||
"\n",
|
||
"# Generate x values for plotting the line (smoothly across the range)\n",
|
||
"x_line = np.linspace(x.min(), x.max(), 100)\n",
|
||
"y_line = fit_function(x_line)\n",
|
||
"\n",
|
||
"# 3. Plot the data and the line of best fit\n",
|
||
"plt.figure(figsize=(10, 6))\n",
|
||
"\n",
|
||
"# Plot the scatter points\n",
|
||
"plt.scatter(x, y, color='purple', label='Data Points', alpha=0.7)\n",
|
||
"\n",
|
||
"# Plot the line of best fit\n",
|
||
"plt.plot(x_line, y_line, color='steelblue', linestyle='--', linewidth=2, label='Line of Best Fit')\n",
|
||
"\n",
|
||
"# Add labels and title\n",
|
||
"plt.xlabel('X Axis')\n",
|
||
"plt.ylabel('Y Axis')\n",
|
||
"plt.title('Scatter Plot with Line of Best Fit')\n",
|
||
"\n",
|
||
"# Add the equation to the plot\n",
|
||
"# The f-string formats the slope and intercept to 2 decimal places\n",
|
||
"plt.text(1, 25, f'y = {slope:.2f}x + {intercept:.2f}', fontsize=12, bbox=dict(facecolor='white', alpha=0.8))\n",
|
||
"\n",
|
||
"# Display legend and grid\n",
|
||
"plt.legend()\n",
|
||
"plt.grid(True, linestyle=':', alpha=0.6)\n",
|
||
"\n",
|
||
"# Show the plot\n",
|
||
"plt.savefig('../images/line_of_best_fit_generated_1.png')\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "1c25ccb0",
|
||
"metadata": {},
|
||
"source": [
|
||
"The structure of this sections is as follows.\n",
|
||
"- [Least Squares Solution](#least-squares-solution)\n",
|
||
"- [QR Decompositions](#qr-decompositions)\n",
|
||
"- [Singular Value Decomposition](#singular-value-decomposition)\n",
|
||
"- [A note on other norms](#a-note-on-other-norms)\n",
|
||
"- [A note on regularization](#a-note-on-regularization)\n",
|
||
"- [A note on solving multiple targets concurrently](#a-note-on-solving-multiple-targets-concurrently)\n",
|
||
"- [Polynomial regression](#polynomial-regression)\n",
|
||
"- [What can go wrong?](#what-can-go-wrong)\n",
|
||
"\n",
|
||
"## Least Squares Solution\n",
|
||
"\n",
|
||
"Recall that the Euclidean distance between two vectors $x = (x_1,\\dots,x_n) ,y = (y_1,\\dots,y_n) \\in \\mathbb{R}^n$ is given by\n",
|
||
"\n",
|
||
"$$ ||x - y||_2 = \\sqrt{\\sum_{i=1}^n |x_i - y_i|^2}. $$\n",
|
||
"\n",
|
||
"We will often work with the square of the $L^2$ norm to simplify things (the square function is increasing, so minimizing the square of a non-negative function will also minimize the function itself).\n",
|
||
"\n",
|
||
"> **Definition**: Let $A$ be an $m \\times n$ matrix and $b \\in \\mathbb{R}^n$. A **least-squares solution** of $Ax = b$ is a vector $x_0 \\in \\mathbb{R}^n$ such that\n",
|
||
"> \n",
|
||
"> $$ \\|b - Ax_0\\|_2 \\leq \\|b - Ax\\|_2 \\text{ for all } x \\in \\mathbb{R}^n. $$\n",
|
||
"\n",
|
||
"So a least-squares solution to the equation $Ax = b$ is trying to find a vector $x_0 \\in \\mathbb{R}^n$ which realizes the smallest distance between the vector $b$ and the column space\n",
|
||
"$$ \\text{Col}(A) = \\{Ax \\mid x \\in \\mathbb{R}^n\\} $$\n",
|
||
"of $A$. We know this to be the projection of the vector $b$ onto the column space. "
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 2,
|
||
"id": "f44a6feb",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 900x700 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"import numpy as np\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"\n",
|
||
"# Linear algebra helper functions\n",
|
||
"def proj_onto_subspace(A, v):\n",
|
||
" \"\"\"\n",
|
||
" Project vector v onto Col(A) where A is (3 x k) with columns spanning the subspace.\n",
|
||
" Uses the formula: P = A (A^T A)^(-1) A^T (for full column rank A).\n",
|
||
" \"\"\"\n",
|
||
" AtA = A.T @ A\n",
|
||
" return A @ np.linalg.solve(AtA, A.T @ v)\n",
|
||
"\n",
|
||
"def make_plane_grid(a, b, u_range=(-1.5, 1.5), v_range=(-1.5, 1.5), n=15):\n",
|
||
" \"\"\"\n",
|
||
" Plane through origin spanned by vectors a and b.\n",
|
||
" Returns meshgrid points X,Y,Z for surface plotting.\n",
|
||
" \"\"\"\n",
|
||
" uu = np.linspace(*u_range, n)\n",
|
||
" vv = np.linspace(*v_range, n)\n",
|
||
" U, V = np.meshgrid(uu, vv)\n",
|
||
" P = U[..., None] * a + V[..., None] * b # shape (n,n,3)\n",
|
||
" return P[..., 0], P[..., 1], P[..., 2]\n",
|
||
"\n",
|
||
"# Choose a plan and a vector\n",
|
||
"# Plane basis vectors (span a 2D subspace in R^3)\n",
|
||
"a = np.array([1.0, 0.2, 0.0])\n",
|
||
"b = np.array([0.2, 1.0, 0.3])\n",
|
||
"# Create the associated matrix\n",
|
||
"# 3x2 matrix of full column rank\n",
|
||
"# the column space will be a plane\n",
|
||
"A = np.column_stack([a, b]) \n",
|
||
"\n",
|
||
"# Vector to project\n",
|
||
"v = np.array([0.8, 0.6, 1.2])\n",
|
||
"\n",
|
||
"# Projection and residual\n",
|
||
"p = proj_onto_subspace(A, v)\n",
|
||
"r = v - p\n",
|
||
"\n",
|
||
"# Plot\n",
|
||
"fig = plt.figure(figsize=(9, 7))\n",
|
||
"# 1 row, 1 column, 1 subplot\n",
|
||
"# axis lives in R^3\n",
|
||
"ax = fig.add_subplot(111, projection=\"3d\")\n",
|
||
"\n",
|
||
"# Plane surface\n",
|
||
"X, Y, Z = make_plane_grid(a, b)\n",
|
||
"# Here is a rectangular grid of points in 3D; draw a surface through them.\n",
|
||
"ax.plot_surface(X, Y, Z, alpha=0.25)\n",
|
||
"\n",
|
||
"origin = np.zeros(3)\n",
|
||
"\n",
|
||
"# v, p, and residual r\n",
|
||
"ax.quiver(*origin, *v, arrow_length_ratio=0.08, linewidth=2)\n",
|
||
"ax.quiver(*origin, *p, arrow_length_ratio=0.08, linewidth=2)\n",
|
||
"ax.quiver(*p, *r, arrow_length_ratio=0.08, linewidth=2)\n",
|
||
"\n",
|
||
"# Drop line from v to its projection on the plane\n",
|
||
"ax.plot([v[0], p[0]],\n",
|
||
"\t\t[v[1], p[1]],\n",
|
||
"\t\t[v[2], p[2]],\n",
|
||
"\t\tlinestyle=\"--\", linewidth=2)\n",
|
||
"\n",
|
||
"# Points for emphasis\n",
|
||
"ax.scatter(*v, s=60)\n",
|
||
"ax.scatter(*p, s=60)\n",
|
||
"\n",
|
||
"# Labels (simple text)\n",
|
||
"ax.text(*v, \" v\")\n",
|
||
"ax.text(*p, \" Proj(v)\")\n",
|
||
"\n",
|
||
"# Make axes look nice\n",
|
||
"ax.set_xlabel(\"x\")\n",
|
||
"ax.set_ylabel(\"y\")\n",
|
||
"ax.set_zlabel(\"z\")\n",
|
||
"ax.set_title(\"Projection of a vector onto a plane\")\n",
|
||
"\n",
|
||
"# Set symmetric limits so the picture isn't squished\n",
|
||
"all_pts = np.vstack([origin, v, p])\n",
|
||
"m = np.max(np.abs(all_pts)) * 1.3 + 0.2\n",
|
||
"ax.set_xlim(-m, m)\n",
|
||
"ax.set_ylim(-m, m)\n",
|
||
"ax.set_zlim(-m, m)\n",
|
||
"\n",
|
||
"# Adjust spacing so labels, titles, and axes don’t overlap or get cut off.\n",
|
||
"plt.tight_layout()\n",
|
||
"plt.savefig('../images/projection_of_vector_onto_plane.png')\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "c8a1fe20",
|
||
"metadata": {},
|
||
"source": [
|
||
"> **Theorem**: The set of least-squares solutions of $Ax = b$ coincides with solutions of the **normal equations** $A^TAx = A^Tb$. Moreover, the normal equations always have a solution.\n",
|
||
"\n",
|
||
"Let us first see why we get a line of best fit. \n",
|
||
"\n",
|
||
"> **Example**. Let us show why this describes a line of best fit when we are working with one feature and one target. Suppose that we observe four data points\n",
|
||
"> $$ X = \\begin{bmatrix} 1 \\\\ 2 \\\\ 3 \\\\ 4 \\end{bmatrix} \\text{ and } y = \\begin{bmatrix} 1 \\\\ 2\\\\ 2 \\\\ 4 \\end{bmatrix}. $$\n",
|
||
"> We want to fit a line $y = \\beta_0 + \\beta_1x$ to these data points. We will have our augmented matrix be\n",
|
||
"> $$ \\tilde{X} = \\begin{bmatrix} 1 & 1 \\\\ 1 & 2 \\\\ 1 & 3 \\\\ 1 & 4 \\end{bmatrix}, $$\n",
|
||
"> and our parameter be\n",
|
||
"> $$ \\tilde{\\beta} = \\begin{bmatrix} \\beta_0 \\\\ \\beta_1 \\end{bmatrix}. $$\n",
|
||
"> We have that\n",
|
||
"> $$ \\tilde{X}^T\\tilde{X} = \\begin{bmatrix} 4 & 10 \\\\ 10 & 30 \\end{bmatrix} \\text{ and } \\tilde{X}^Ty = \\begin{bmatrix} 9 \\\\ 27 \\end{bmatrix}. $$\n",
|
||
"> The 2x2 matrix $\\tilde{X}^T\\tilde{X}$ is easy to invert, and so we get that\n",
|
||
"> $$ \\tilde{\\beta} = (\\tilde{X}^T\\tilde{X})^{-1}\\tilde{X}^Ty = \\frac{1}{10}\\begin{bmatrix} 15 & -5 \\\\ -5 & 2 \\end{bmatrix}\\begin{bmatrix} 9 \\\\ 27 \\end{bmatrix} = \\begin{bmatrix} 0 \\\\ \\frac{9}{10} \\end{bmatrix}. $$\n",
|
||
"> So our line of best fit is of them form $y = \\frac{9}{10}x$.\n",
|
||
"\n",
|
||
"Although the above system was small and we could solve the system of equations explicitly, this isn't always feasible. We will generally use python in order to solve large systems. \n",
|
||
"- One can find a least-squares solution using `numpy.linalg.lstsq`.\n",
|
||
"- We can set up the normal equations and solve the system by using `numpy.linalg.solve`\n",
|
||
"Although the first approach simplifies things greatly, and is more or less what we are doing anyway, we will generally set up our problems as we would by hand, and then use `numpy.linalg.solve` to help us find a solution. However, computing $X^TX$ can cause lots of errors, so later we'll see how to get linear systems from QR decompositions and the SVD, and then apply `numpy.lingalg.solve`. \n",
|
||
"\n",
|
||
"Let's see how to use these for the above example, and see the code to generate the scatter plot and line of best fit. \n",
|
||
"Again, our system is the following.\n",
|
||
"$$ X = \\begin{bmatrix} 1 \\\\ 2 \\\\ 3 \\\\ 4 \\end{bmatrix} \\text{ and } y = \\begin{bmatrix} 1 \\\\ 2\\\\ 2 \\\\ 4 \\end{bmatrix}. $$\n",
|
||
"We will do what we did above, but use python instead.\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 3,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"import numpy as np\n",
|
||
"\n",
|
||
"# Define the matrix X and vector y\n",
|
||
"X = np.array([[1], [2], [3], [4]])\n",
|
||
"y = np.array([[1], [2], [2], [4]])\n",
|
||
"\n",
|
||
"# Augment X with a column of 1's (intercept)\n",
|
||
"X_aug = np.hstack((np.ones((X.shape[0], 1)), X))\n",
|
||
"\n",
|
||
"# Solve the normal equations\n",
|
||
"beta = np.linalg.solve(X_aug.T @ X_aug, X_aug.T @ y)\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"\n",
|
||
"And what is the result?\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 4,
|
||
"id": "1c42a900",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"array([[-1.0658141e-15],\n",
|
||
" [ 9.0000000e-01]])"
|
||
]
|
||
},
|
||
"execution_count": 4,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"beta"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"\n",
|
||
"This agrees with our by-hand computation: the intercept is tiny, so it is virtually zero, and we get 9/10 as our slope. Let's plot it. \n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 5,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"import matplotlib.pyplot as plt\n",
|
||
"b, m = beta #beta[0] will be the intercept and beta[1] will be the slope\n",
|
||
"_ = plt.plot(X, y, 'o', label='Original data', markersize=10)\n",
|
||
"_ = plt.plot(X, m*X + b, 'r', label='Line of best fit')\n",
|
||
"_ = plt.legend()\n",
|
||
"plt.savefig('../images/line_of_best_fit_easy_example.png')\n",
|
||
"plt.show()\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"\n",
|
||
"\n",
|
||
"What about `numpy.linalg.lstsq`? Is it any different?\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 6,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"import numpy as np\n",
|
||
"\n",
|
||
"# Define the matrix X and vector y\n",
|
||
"X = np.array([[1], [2], [3], [4]])\n",
|
||
"y = np.array([[1], [2], [2], [4]])\n",
|
||
"\n",
|
||
"# Augment X with a column of 1's (intercept)\n",
|
||
"X_aug = np.hstack((np.ones((X.shape[0], 1)), X))\n",
|
||
"\n",
|
||
"# Solve the least squares equation with matrix X_aug and target y\n",
|
||
"beta = np.linalg.lstsq(X_aug,y)[0]\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"\n",
|
||
"We then get\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 7,
|
||
"id": "35e8c88d",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"array([[6.16291085e-16],\n",
|
||
" [9.00000000e-01]])"
|
||
]
|
||
},
|
||
"execution_count": 7,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"beta"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"\n",
|
||
"So it is a little different -- and, in fact, closer to our exact answer (the intercept is zero). This makes sense -- `numpy.linalg.lstsq` won't directly compute $X^TX$, which, again, can cause quite a few issues. \n",
|
||
"\n",
|
||
"---\n",
|
||
"\n",
|
||
"Now going to our initial example. \n",
|
||
"\n",
|
||
"> **Example**: Let us work with the example from above. We augment the matrix with a column of 1's to include an intercept term:\n",
|
||
"> $$ \\tilde{X} = \\begin{bmatrix} 1 & 1600 & 3 \\\\ 1 & 2100 & 4 \\\\ 1 & 1550 & 2 \\end{bmatrix}. $$\n",
|
||
"> Let us solve the normal equations\n",
|
||
"> $$ \\tilde{X}^T\\tilde{X}\\tilde{\\beta} = \\tilde{X}^Ty. $$\n",
|
||
"> We have\n",
|
||
"> $$ \\tilde{X}^T\\tilde{X} = \\begin{bmatrix} 3 & 5250 & 9 \\\\ 5250 & 9372500 & 16300 \\\\ 9 & 16300 & 29\\end{bmatrix} \\text{ and } \\tilde{X}^Ty = \\begin{bmatrix} 1625 \\\\ 2901500 \\\\ 5050 \\end{bmatrix} $$\n",
|
||
"> Solving this system of equations yields the parameter vector $\\tilde{\\beta}$. In this case, we have\n",
|
||
"> $$ \\tilde{\\beta} = \\begin{bmatrix} \\frac{200}{9} \\\\ \\frac{5}{18} \\\\ \\frac{100}{9} \\end{bmatrix}. $$\n",
|
||
"> When we apply $\\tilde{X}$ to $\\tilde{\\beta}$, we get\n",
|
||
"> $$ \\tilde{X}\\tilde{\\beta} = \\begin{bmatrix} 500 \\\\ 650 \\\\ 475 \\end{bmatrix}, $$\n",
|
||
"> which is our target on the nose. This means that we can expect, based on our data, that the cost of a house will be\n",
|
||
"> $$ \\frac{200}{9} + \\frac{5}{18}(\\text{square footage}) + \\frac{100}{9}(\\text{\\# of bedrooms})$$\n",
|
||
"\n",
|
||
"In the above, we actually had a consistent system to begin with, so our least-squares solution gave our prediction honestly. What happens if we have an inconsistent system?\n",
|
||
"\n",
|
||
"> **Example**: Let us add two more observations, say our data is now the following. \n",
|
||
"> |House | Square ft | Bedrooms | Price (in $1000s) |\n",
|
||
"> | --- | --- | --- | --- |\n",
|
||
"> | 0 | 1600 | 3 | 500 |\n",
|
||
"> | 1 | 2100 | 4 | 650 |\n",
|
||
"> | 2 | 1550 | 2 | 475 |\n",
|
||
"> | 3 | 1600 | 3 | 490 |\n",
|
||
"> | 4 | 2000 | 4 | 620 |\n",
|
||
"> \n",
|
||
"> So setting up our system, we want a least-square solution to the matrix equation\n",
|
||
"> $$ \\begin{bmatrix} 1 & 1600 & 3 \\\\ 1 & 2100 & 4 \\\\ 1 & 1550 & 2 \\\\ 1 & 1600 & 3 \\\\ 1 & 2000 & 4 \\end{bmatrix}\\tilde{\\beta} = \\begin{bmatrix} 500 \\\\ 650 \\\\ 475 \\\\ 490 \\\\ 620 \\end{bmatrix}. $$\n",
|
||
"> Note that the system is inconsistent (the 1st and 4th rows agree in $\\tilde{X}$, but they have different costs). Writing the normal equations we have\n",
|
||
"> $$ \\tilde{X}^T\\tilde{X} = \\begin{bmatrix} 5 & 8850 & 16 \\\\ 8850 & 15932500 & 29100 \\\\ 16 & 29100 & 54 \\end{bmatrix} \\text{ and } \\tilde{X}y = \\begin{bmatrix} 2735 \\\\ 4 925 250 \\\\ 9000 \\end{bmatrix}. $$\n",
|
||
"> Solving this linear system yields\n",
|
||
"> $$ \\tilde{\\beta} = \\begin{bmatrix} 0 \\\\ \\frac{3}{10} \\\\ 5 \\end{bmatrix}. $$\n",
|
||
"> This is a vastly different answer! Applying $\\tilde{X}$ to it yields\n",
|
||
"> $$ \\tilde{X}\\tilde{\\beta} = \\begin{bmatrix} 495 \\\\ 650 \\\\ 475 \\\\ 495 \\\\ 620 \\end{bmatrix}. $$\n",
|
||
"> Note that the error here is\n",
|
||
"> $$ y - \\tilde{X}\\tilde{\\beta} = \\begin{bmatrix} 5 \\\\ 0 \\\\ 0 \\\\ -5 \\\\ 0 \\end{bmatrix}, $$\n",
|
||
"> which has squared $L^2$ norm\n",
|
||
"> $$ \\|y - \\tilde{X}\\tilde{\\beta}\\|_2^2 = 25 + 25 = 50. $$\n",
|
||
"> So this says that, given our data, we can roughly estimate the cost of a house, within 50k or so, to be\n",
|
||
"> $$ \\approx \\frac{3}{10}(\\text{square footage}) + 5(\\text{\\# of bedrooms}). $$\n",
|
||
"In practice, our data sets can be gigantic, and so there is absolutely no hope of doing computations by hand. It is nice to know that theoretically we can do things like this though. \n",
|
||
"\n",
|
||
"> **Theorem**: Let $A$ be an $m \\times n$ matrix and $b \\in \\mathbb{R}^n$. The following are equivalent.\n",
|
||
"> \n",
|
||
"> 1. The equation $Ax = b$ has a unique least-squares solution for each $b \\in \\mathbb{R}^n$.\n",
|
||
"> 2. The columns of $A$ are linearly independent. \n",
|
||
"> 3. The matrix $A^TA$ is invertible.\n",
|
||
"\n",
|
||
"In this case, the unique solution to the normal equations $A^TAx = A^Tb$ is\n",
|
||
"\n",
|
||
"$$ x_0 = (A^TA)^{-1}A^Tb. $$\n",
|
||
"\n",
|
||
"Computing $\\tilde{X}^T\\tilde{X}$ or taking inverses are very computationally intensive tasks, and it is best to avoid doing these. Moreover, as we'll see in an example later, if we do a numerical calculation we can get close to zero and then divide where we shouldn't be, blowing up our final result. One way to get around this is to use QR decompositions of matrices. \n",
|
||
"\n",
|
||
"Now let's use python to visualize the above data and then solve for the least-squares solution. We'll use `pandas` in order to think about this data. We note that `pandas` incorporates `matplotlib` under the hood already, so there are some simplifications that can be made.\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 8,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"import numpy as np\n",
|
||
"import pandas as pd\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"\n",
|
||
"# First let us make a dictionary incorporating our data.\n",
|
||
"# Each entry corresponds to a column (feature of our data)\n",
|
||
"data = {\n",
|
||
"\t'Square ft': [1600, 2100, 1550, 1600, 2000],\n",
|
||
"\t'Bedrooms': [3, 4, 2, 3, 4],\n",
|
||
"\t'Price': [500, 650, 475, 490, 620]\n",
|
||
"}\n",
|
||
"\n",
|
||
"# Create a pandas DataFrame\n",
|
||
"df = pd.DataFrame(data)\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"\n",
|
||
"Let's see how python formats this `DataFrame`. It will turn it into essentially the table we had at the beginning. \n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 9,
|
||
"id": "9dd3046d",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/html": [
|
||
"<div>\n",
|
||
"<style scoped>\n",
|
||
" .dataframe tbody tr th:only-of-type {\n",
|
||
" vertical-align: middle;\n",
|
||
" }\n",
|
||
"\n",
|
||
" .dataframe tbody tr th {\n",
|
||
" vertical-align: top;\n",
|
||
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|
||
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|
||
" .dataframe thead th {\n",
|
||
" text-align: right;\n",
|
||
" }\n",
|
||
"</style>\n",
|
||
"<table border=\"1\" class=\"dataframe\">\n",
|
||
" <thead>\n",
|
||
" <tr style=\"text-align: right;\">\n",
|
||
" <th></th>\n",
|
||
" <th>Square ft</th>\n",
|
||
" <th>Bedrooms</th>\n",
|
||
" <th>Price</th>\n",
|
||
" </tr>\n",
|
||
" </thead>\n",
|
||
" <tbody>\n",
|
||
" <tr>\n",
|
||
" <th>0</th>\n",
|
||
" <td>1600</td>\n",
|
||
" <td>3</td>\n",
|
||
" <td>500</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>1</th>\n",
|
||
" <td>2100</td>\n",
|
||
" <td>4</td>\n",
|
||
" <td>650</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>2</th>\n",
|
||
" <td>1550</td>\n",
|
||
" <td>2</td>\n",
|
||
" <td>475</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>3</th>\n",
|
||
" <td>1600</td>\n",
|
||
" <td>3</td>\n",
|
||
" <td>490</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>4</th>\n",
|
||
" <td>2000</td>\n",
|
||
" <td>4</td>\n",
|
||
" <td>620</td>\n",
|
||
" </tr>\n",
|
||
" </tbody>\n",
|
||
"</table>\n",
|
||
"</div>"
|
||
],
|
||
"text/plain": [
|
||
" Square ft Bedrooms Price\n",
|
||
"0 1600 3 500\n",
|
||
"1 2100 4 650\n",
|
||
"2 1550 2 475\n",
|
||
"3 1600 3 490\n",
|
||
"4 2000 4 620"
|
||
]
|
||
},
|
||
"execution_count": 9,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"df"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"\n",
|
||
"So what can we do with DataFrames? First let's use `pandas.DataFrame.describe` to see some basic statistics about our data.\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 10,
|
||
"id": "a28d2558",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/html": [
|
||
"<div>\n",
|
||
"<style scoped>\n",
|
||
" .dataframe tbody tr th:only-of-type {\n",
|
||
" vertical-align: middle;\n",
|
||
" }\n",
|
||
"\n",
|
||
" .dataframe tbody tr th {\n",
|
||
" vertical-align: top;\n",
|
||
" }\n",
|
||
"\n",
|
||
" .dataframe thead th {\n",
|
||
" text-align: right;\n",
|
||
" }\n",
|
||
"</style>\n",
|
||
"<table border=\"1\" class=\"dataframe\">\n",
|
||
" <thead>\n",
|
||
" <tr style=\"text-align: right;\">\n",
|
||
" <th></th>\n",
|
||
" <th>Square ft</th>\n",
|
||
" <th>Bedrooms</th>\n",
|
||
" <th>Price</th>\n",
|
||
" </tr>\n",
|
||
" </thead>\n",
|
||
" <tbody>\n",
|
||
" <tr>\n",
|
||
" <th>count</th>\n",
|
||
" <td>5.000000</td>\n",
|
||
" <td>5.00000</td>\n",
|
||
" <td>5.000000</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>mean</th>\n",
|
||
" <td>1770.000000</td>\n",
|
||
" <td>3.20000</td>\n",
|
||
" <td>547.000000</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>std</th>\n",
|
||
" <td>258.843582</td>\n",
|
||
" <td>0.83666</td>\n",
|
||
" <td>81.516869</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>min</th>\n",
|
||
" <td>1550.000000</td>\n",
|
||
" <td>2.00000</td>\n",
|
||
" <td>475.000000</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>25%</th>\n",
|
||
" <td>1600.000000</td>\n",
|
||
" <td>3.00000</td>\n",
|
||
" <td>490.000000</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>50%</th>\n",
|
||
" <td>1600.000000</td>\n",
|
||
" <td>3.00000</td>\n",
|
||
" <td>500.000000</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>75%</th>\n",
|
||
" <td>2000.000000</td>\n",
|
||
" <td>4.00000</td>\n",
|
||
" <td>620.000000</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>max</th>\n",
|
||
" <td>2100.000000</td>\n",
|
||
" <td>4.00000</td>\n",
|
||
" <td>650.000000</td>\n",
|
||
" </tr>\n",
|
||
" </tbody>\n",
|
||
"</table>\n",
|
||
"</div>"
|
||
],
|
||
"text/plain": [
|
||
" Square ft Bedrooms Price\n",
|
||
"count 5.000000 5.00000 5.000000\n",
|
||
"mean 1770.000000 3.20000 547.000000\n",
|
||
"std 258.843582 0.83666 81.516869\n",
|
||
"min 1550.000000 2.00000 475.000000\n",
|
||
"25% 1600.000000 3.00000 490.000000\n",
|
||
"50% 1600.000000 3.00000 500.000000\n",
|
||
"75% 2000.000000 4.00000 620.000000\n",
|
||
"max 2100.000000 4.00000 650.000000"
|
||
]
|
||
},
|
||
"execution_count": 10,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"df.describe()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"\n",
|
||
"This gives use the mean, the standard deviation, the min, the max, as well as some other things. We get an immediate sense of scale from our data. We can also examine the pairwise correlation of all the columns by using `pandas.DataFrame.corr`.\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 11,
|
||
"id": "7850890b",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/html": [
|
||
"<div>\n",
|
||
"<style scoped>\n",
|
||
" .dataframe tbody tr th:only-of-type {\n",
|
||
" vertical-align: middle;\n",
|
||
" }\n",
|
||
"\n",
|
||
" .dataframe tbody tr th {\n",
|
||
" vertical-align: top;\n",
|
||
" }\n",
|
||
"\n",
|
||
" .dataframe thead th {\n",
|
||
" text-align: right;\n",
|
||
" }\n",
|
||
"</style>\n",
|
||
"<table border=\"1\" class=\"dataframe\">\n",
|
||
" <thead>\n",
|
||
" <tr style=\"text-align: right;\">\n",
|
||
" <th></th>\n",
|
||
" <th>Square ft</th>\n",
|
||
" <th>Bedrooms</th>\n",
|
||
" <th>Price</th>\n",
|
||
" </tr>\n",
|
||
" </thead>\n",
|
||
" <tbody>\n",
|
||
" <tr>\n",
|
||
" <th>Square ft</th>\n",
|
||
" <td>1.000000</td>\n",
|
||
" <td>0.900426</td>\n",
|
||
" <td>0.998810</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>Bedrooms</th>\n",
|
||
" <td>0.900426</td>\n",
|
||
" <td>1.000000</td>\n",
|
||
" <td>0.909066</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>Price</th>\n",
|
||
" <td>0.998810</td>\n",
|
||
" <td>0.909066</td>\n",
|
||
" <td>1.000000</td>\n",
|
||
" </tr>\n",
|
||
" </tbody>\n",
|
||
"</table>\n",
|
||
"</div>"
|
||
],
|
||
"text/plain": [
|
||
" Square ft Bedrooms Price\n",
|
||
"Square ft 1.000000 0.900426 0.998810\n",
|
||
"Bedrooms 0.900426 1.000000 0.909066\n",
|
||
"Price 0.998810 0.909066 1.000000"
|
||
]
|
||
},
|
||
"execution_count": 11,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"df[[\"Square ft\", \"Bedrooms\", \"Price\"]].corr()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"\n",
|
||
"It is clear that each of the three are correlated. This makes sense, as the number of bedrooms should be increasing with the square feet. Same with the price. We'll discuss in the next section when we look at Principal Component Analysis. \n",
|
||
"\n",
|
||
"We can also graph our data; for example, we could create some scatter plots, one for `Square ft` vs `Price` and on for `Bedrooms` vs `Price`. We can also do a grouped bar chart. Let's start with the scatter plots. \n",
|
||
"\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 12,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"# Scatter plot for Price vs Square ft\n",
|
||
"df.plot(\n",
|
||
"\tkind=\"scatter\",\n",
|
||
"\tx=\"Square ft\",\n",
|
||
"\ty=\"Price\",\n",
|
||
"\ttitle=\"House Price vs Square footage\"\n",
|
||
")\n",
|
||
"plt.savefig('../images/house_price_vs_square_ft.png')\n",
|
||
"plt.show()\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 13,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"# Scatter plot for Price vs Bedrooms\n",
|
||
"df.plot(\n",
|
||
"\tkind=\"scatter\",\n",
|
||
"\tx=\"Bedrooms\",\n",
|
||
"\ty=\"Price\",\n",
|
||
"\ttitle=\"House Price vs Bedrooms\"\n",
|
||
")\n",
|
||
"plt.savefig('../images/house_price_vs_bedrooms.png')\n",
|
||
"plt.show()\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"We can even do square footage vs bedrooms. \n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 14,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"# Scatter plot for Bedrooms vs Square ft\n",
|
||
"df.plot(\n",
|
||
"\tkind=\"scatter\",\n",
|
||
"\tx=\"Square ft\",\n",
|
||
"\ty=\"Bedrooms\",\n",
|
||
"\ttitle=\"Bedrooms vs Square footage\"\n",
|
||
")\n",
|
||
"plt.savefig('../images/bedrooms_vs_square_ft.png')\n",
|
||
"plt.show()\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"\n",
|
||
"Of course, these figures are somewhat meaningless due to how unpopulated our data is.\n",
|
||
"\n",
|
||
"Now let's get our matrices and linear systems set up with `pandas.DataFrame.to_numpy`.\n",
|
||
"\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 15,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Create our matrix X and our target y\n",
|
||
"X = df[[\"Square ft\", \"Bedrooms\"]].to_numpy()\n",
|
||
"y = df[[\"Price\"]].to_numpy()\n",
|
||
"\n",
|
||
"# Augment X with a column of 1's (intercept)\n",
|
||
"X_aug = np.hstack((np.ones((X.shape[0], 1)), X))\n",
|
||
"\n",
|
||
"# Solve the least-squares problem\n",
|
||
"beta = np.linalg.lstsq(X_aug,y)[0]\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"\n",
|
||
"This yields\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 16,
|
||
"id": "0d08c091",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"array([[4.0098513e-13],\n",
|
||
" [3.0000000e-01],\n",
|
||
" [5.0000000e+00]])"
|
||
]
|
||
},
|
||
"execution_count": 16,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"beta"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"\n",
|
||
"As the first parameter is basically 0, we are left with the second being 3/10 and the third being 5, just like our exact solution. Next, we will look at matrix decompositions and how they can help us find least-squares solutions. "
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "a1f82fae",
|
||
"metadata": {},
|
||
"source": [
|
||
"# Polynomial Regression\n",
|
||
"\n",
|
||
"Sometimes fitting a line to a set of $n$ data points clearly isn't the right thing to do. To emphasize the limitations of linear models, we generate data from a purely quadratic relationship. In this setting, the space of linear functions is not rich enough to capture the underlying structure, and the linear least-squares solution exhibits systematic error. Expanding the feature space to include quadratic terms resolves this issue.\n",
|
||
"\n",
|
||
"For example, suppose our data looked like the following. \n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 17,
|
||
"id": "52a5c824",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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IkkZHR1VcXKyHH35Yd999d1J/LxqNKhAIKBKJqLCwcDFNAwBgho6+kJra+xWKjMSPlQR8aqyv1JaqEkfbls1SuX6nXfMxPj6uxx9/XFeuXNHGjRs1MDCgcDisurq6+DkFBQXavHmzTp48OeffGR0dVTQaTXgAAGCFjr6QdrT1JAQPSQpHRrSjrUcdfSHH2pZLUg4fL7/8sq699loVFBTonnvu0ZNPPqnKykqFw2FJUnFxccL5xcXF8edm09LSokAgEH+UlZWl8+8AAGBe4xOmmtr7NVt3f+xYU3v/oodgGNJZ2JJUf+FP/uRP1Nvbq9/97nf6yU9+oq985Svq6uqKP28YRsL5pmnOODbV3r17tXv37vjP0WiUAAIAyLjTA0MzejymMiWFIiM6PTCkjatXpPUaDOkkJ+Wej2uuuUZ//Md/rPXr16ulpUUf/ehH9e1vf1vBYFCSZvRyDA4OzugNmaqgoCA+eyb2AAAg0waH5w4e6Zw3HUM6yVv0Oh+maWp0dFTl5eUKBoPq7OyMPzc2Nqauri5t2rRpsS8DAMCirPT7MnreVHYN6XhFSsMuDz74oLZu3aqysjINDw/r8ccf1y9+8Qt1dHTIMAw1NDSoublZFRUVqqioUHNzs5YtW6Zt27ZZ9y8AACAJG8qLVBLwKRwZmTUkGJKCAZ82lBel/LftGNLxkpTCx5tvvqk777xToVBIgUBAa9asUUdHh2prayVJe/bs0dWrV7Vz505dvnxZ1dXVOnHihPx+v1XtBwAgKfl5hhrrK7WjrUfGlB4JTQYPSWqsr1R+3tx1inOxekjHaxa9zkemsc4HAMBKCxWFjk+YOj0wpMHhEa30/0dPyEKB5NTZS/ryo88t+NqPff3jnu35SOX6nfJsFwAAstmWqhLVVgZnDRjpzlaxckjHi9hYDgCQc/LzDG1cvUK33vhBbVy9Ih480p2tEhvS0ZQhnJjFDul4EeEDAJDzMjFbZUtViVq3r1UwkDhbJhjwqXX7Wtb5mIJhFwBAzsvUbJX5hnTwHsIHACDnZXK2SmxIB3Nj2AUAkPOsXIAMMxE+AAA5LzZbZa7BEWNy1guzVTKD8AEAyHnMVrEX4QMA4Ai3bT3PbBX7UHAKALCdW7eeZ7aKPVheHQBgq9hiXtMvPrHLO70M2SmV6zfDLgAA27D1PET4AADYKZXFvOBdhA8AgG3Yeh4ifAAA7MRiXhCzXXLD+IRJ5TYAV2DreYjw4X1unc4GIDfFFvPa0dYjY0qRqVjMK6cw7OJhsels04u7wpER7WjrUUdfyLG2AchdLOYFej48aqHpbMbkdLbayiB3GABsx2JeuY3w4VGpTGdb7NbP1JQASAdbz+cuwodH2TWdjZoSAECqqPnwKDums1FTAgBIB+HDo2LT2eYa/DAmeyjSnc7GEskAgHQRPjwqNp1NU6avxWRiOhtLJAMA0kX48DArp7OxRDIAIF0UnHqcVdPZWCIZAJAuwkcOsGI6G0skAwDSxbAL0mJ1TQkAwLsIH0hbMjUl4xOmTp29pOO9b+jU2UvMfgEAMOyCxZmvpoQFyAAAszFM03TVrWg0GlUgEFAkElFhYaHTzUGaYguQTf9wxQZh2DwKALwlles3wy7IOBYgAwDMh/CBjGMBMgDAfAgfyDgWIAMAzIfwgYxjATIAwHwIH8g4qze1AwBkN8IHMo4FyAAA8yF8wBJWbmoHAMhuLDIGy1i1qR0AILsRPmApKza1AwBkN4ZdAACArQgfAADAVoQPAABgK8IHAACwFeEDAADYivABAABsRfgAAAC2InwAAABbpRQ+Wlpa9LGPfUx+v18rV67Ubbfdpl//+tcJ55imqf3796u0tFRLly5VTU2Nzpw5k+l2AwCALJVS+Ojq6tKuXbv03HPPqbOzU++++67q6up05cqV+DkHDhzQwYMHdfjwYXV3dysYDKq2tlbDw8NWtB8AAGQZwzRNM91ffuutt7Ry5Up1dXXpk5/8pEzTVGlpqRoaGvTAAw9IkkZHR1VcXKyHH35Yd99994J/MxqNKhAIKBKJqLCwMN2mAQAAG6Vy/V5UzUckEpEkFRUVSZIGBgYUDodVV1cXP6egoECbN2/WyZMnZ/0bo6OjikajCQ8AAOBdaYcP0zS1e/du3XzzzaqqqpIkhcNhSVJxcXHCucXFxfHnpmtpaVEgEIg/ysrK0m0SAADIAmmHj3vvvVcvvfSSHnvssRnPGUbilummac44FrN3715FIpH44/z58+k2CQAAZIEl6fzSfffdp5/+9Kd69tlntWrVqvjxYDAoTfaAlJSUxI8PDg7O6A2JKSgoUEFBQTrNAAAAWSilng/TNHXvvffqn//5n/XMM8+ovLw84fny8nIFg0F1dnbGj42Njamrq0ubNm3KXKsBAEDWSqnnY9euXTp27JiOHz8uv98fr+MIBAJaunSpDMNQQ0ODmpubVVFRoYqKCjU3N2vZsmXatm2bVf8GAACQRVIKH62trZKkmpqahOPf//73ddddd0mS9uzZo6tXr2rnzp26fPmyqqurdeLECfn9/ky2GwAAZKlFrfNhBdb5AAAg+9i2zgcAAECqCB8AAMBWaU21BVIxPmHq9MCQBodHtNLv04byIuXnzb7uCwDA+wgfsFRHX0hN7f0KRUbix0oCPjXWV2pLVcm8vwsA8CaGXWCZjr6QdrT1JAQPSQpHRrSjrUcdfSHH2gYAcA7hA5YYnzDV1N6v2aZSxY41tfdrfMJVk60AADYgfMASpweGZvR4TGVKCkVGdHpgyNZ2AQCcR/iAJQaH5w4e6ZwHAPAOwgcssdLvy+h5AADvIHzAEhvKi1QS8GmuCbXG5KyXDeVFNrcMAOA0wgcskZ9nqLG+UpoMGlPFfm6sr2S9DwDIQYQPWGZLVYlat69VMJA4tBIM+NS6fW3S63yMT5g6dfaSjve+oVNnLzFDBgCyHIuMwVJbqkpUWxlMe4VTFikDAO9hV1u4VmyRsukf0FhsSaX3BABgrVSu3/R8wJWSWaTswSdf1tXfTyhYyH4xAJBNCB9wpYUWKZOkoSu/11890SsxFAMAWYWCU7hSqouPsV8MAGQPwgdcKdXFx9gvBgCyB+EDrrTQImWzYb8YAMgOhA+40nyLlC2E/WIAwN0IH3CtuRYpWwj7xQCAuzHbBa42dZGycOSq/vZnv9LlK2OzTsE1JldPZb8YAHA3wgdcLz/P0MbVKyRJS6/J1462HhlTikzFfjEAkFUYdkFWydR+MQAA59Dzgayz2P1iAADOInwgK00digEAZBeGXQAAgK0IHwAAwFaEDwAAYCtqPgAgi4xPmEkVWyd7HuAEwgc8hy9deFVHX0hN7f0KRd7bQqAk4FNjfWXCNPNkzwOcYpim6aotQKPRqAKBgCKRiAoLC51uDrIMX7rwqo6+kHa09cxY3TcWq2Pr3CR7HpBpqVy/qfmAZ8S+dKcGD0kKR0a0o61HHX0hx9oGLMb4hKmm9v5ZtxWIHWtq79fYuxNJnTc+4ap7TuQgwgc8IdkvZ750kY1ODwzNCNVTmZJCkRH96NRrSZ13emDIopYCySF8wBOS/XLmSxfZaHB47s/2VK8PvZPRvwdYhYJTeEI4cjWp8/jShRstVCS90u+b9/djri9altR577+2QKfOXqIoG44hfCDrdfSF9Lc/+1VS577/2gLL2+MUZvlkp2SKpDeUF6kk4FM4MjLr0KIxubninRs/pP/xbwPznveHy/5A//l/9SocHZ3z9QCrMeyCrBYrMh26MpbcL3i05KOjL6SbH35GX370Od3/eK++/OhzuvnhZyiydblki6Tz8ww11ldKU2atxMR+bqyv1DVL8uY9z5R0+Z3fJwSP2V4PsBrhA1lrviLTuVy8MprEWdmFWT7ZKdUi6S1VJWrdvlbBQOIQTDDgS5g+O995f7jsD2ZtC0XZsBvDLshaCxWZzibZsfNssdAFzJi8oNRWBhmCcZlUiqRjOzhvqSpRbWVwweG12c6bmDB1x//8vym9HmAVwgeyVqrFoyuWX6N117/PsvY4IZ0LGNwh2c/v9PPy84yk/ltOP+947xsZbRewGAy7IGul2otx6cqYPt7yr3r6pQuWtclu6V7A4LxkP7+Z6q2z+/WA+RA+kLViMwBSGUwYuvJ77Tz2olqe7rewZfbhgpK9Fvr8GpOzUDaUF2Xl6wHzIXwga803A2Ah33t2QE+/ZF8h5viEqVNnL+l47xs6dfZSxor6uKBkr2RnsGSqVsfu1wPmQ/hAVpursj8Z/+14ny2V/VZOg+WCkt2SncGSra8HzIVdbeEJUxfYeuXNYR3+32eT+r3Hvv5xSwsx7dphlN18s5vdC8SxIB2skMr1m9ku8ISplf2nzl5KOnxYWYhp5zTYZKdgwp2SncGSra8HTJfysMuzzz6r+vp6lZaWyjAMPfXUUwnPm6ap/fv3q7S0VEuXLlVNTY3OnDmTyTYD89pQXqSi5bMvpjSdlYWYdm92F7ug3HrjB7Vx9QqCBwDXSjl8XLlyRR/96Ed1+PDhWZ8/cOCADh48qMOHD6u7u1vBYFC1tbUaHh7ORHuBBeXnGXro1qoFz7O6EJNpsM6yqsgXwOKlPOyydetWbd26ddbnTNPUoUOHtG/fPt1+++2SpKNHj6q4uFjHjh3T3XffvfgWA0n43JpS3f3b3+l7zw7M+rxhQyEm02CdQw0M4G4Zne0yMDCgcDisurq6+LGCggJt3rxZJ0+ezORLAQva+7lKHdm2VkXLr0k4XjKlst/Ku2OmwTojV/a6oWcH2SyjBafhcFiSVFxcnHC8uLhYr7/++qy/Mzo6qtHR9zb7ikajmWwScshsFfyfW1Oiz1bNXohp9d1xbBrsjrae+I6iMUyDtUau7HVDzw6ynSWzXQwj8X9q0zRnHItpaWlRU1OTFc1ADlnoy3h6Zf9cU2Bjd8eZmgIbW1dhetuCLrhQeHG6ZS7sdWPXZxewUkbDRzAYlCZ7QEpK3vvwDw4OzugNidm7d692794d/zkajaqsrCyTzYLHpfplbPfdsRunwXr1ztnrRb650rMD78tozUd5ebmCwaA6Ozvjx8bGxtTV1aVNmzbN+jsFBQUqLCxMeADJWujLWJNfxlPHw+2eAiuXTYNdbE2Em2sNvF7k68RnF7BCyj0fb7/9tl599dX4zwMDA+rt7VVRUZGuu+46NTQ0qLm5WRUVFaqoqFBzc7OWLVumbdu2ZbrtQFrd7F6/O57PYu+c3d5jEivyDUdGZv03GpNDXtla5JvLn114S8o9H88//7xuuukm3XTTTZKk3bt366abbtLf/M3fSJL27NmjhoYG7dy5U+vXr9cbb7yhEydOyO/3Z771yHnpfBl7/e54Pou5c86GWSRe3+smlz+78JaUw0dNTY1M05zx+MEPfiBNFpvu379foVBIIyMj6urqUlXVwgs+AelI58s4l6fApnvnnM7wllO8vHlaLn924S3s7YKslk43ey5PgU33zjnbZpG4scg3E3L5swtvyWjBKWC3dLvZvXx3PJ9075yzsdbATUW+mZSrn114Cz0fyHrprqXh1bvj+aR750ytgbvk4mcX3mKYpun8IO0U0WhUgUBAkUiEabdIiRcXzbJKqrNWxidM3fzwMwsOb/3bA5/mPQdyVCrXb8IHkKNSDWux2S6ao8eELn8gtxE+gBzgRE+P29f5AOCcVK7f1HwALrRQsHAqBFBrACAT6PkAXGahYDHXXjYMfwBwUirXb6baAi6y0CqiT790IWsW+7KLm/eaATA7hl0Al0hm35X/erxPQ1d+P+ffyNRiX9kyc4gaFCA7ET4Al0hmFdH5gsdUi1nsK1su6HMNP8V6if77tpv0vuUFrg9QQC4ifAAukcnVQZNZ7Gu23o3O/vC8F3S31JMks9fMvY+9qKkjMG4MUECuInwALpHs6qBFy6/R5Stji9oyfrbejWBhgUbenZh32KepvV+1lUHHexAW6iWSpOmlH24LUEAuo+AUcIlk91156Naq+M/Tn1cSG4vNWdQaHdXv3kmunsRp6fQS5WpBLuBGhA/AJZLdJO9za9LfWGy+4YpkuWHzuHT3kHFTgAJyGcMugIsku0leuot9JTNcsRA3bB4X6yWaa6+ZhbghQM0mW2YZAYtF+ABcJtlgEdsyPhWLuegmW09ih/l2502GGwLUdNkyywjIBIZdABeKBYtbb/ygNq5ekbG733QvusnWk6Qj3UXCYr1E04ef5mterG7GDQFqqoUWl+voCznWNsAK9HwAOWSh4QpDUmDZH8i3JF/h6NzDPpmy2Lv92XqJLl8Z065jc+++a0WAWoxkFpdzyywjIFMIH0AOmW+4InZZ++btN9iyedxCi4QlOyV2tuGn1ryF62bcIpnF5TKxai3gJoQPIMckW9Rq5YXO6rv9dAtynSj4TLYOx61FskA6CB9ADkr34pwpdtztp1qQ61TBZ7J1OG4skgXSRfgAclQ6s2UyxW13+5kaAkpHMnU4bpllBGQKs10A2M5Nd/vJ7BNj5aqoyS4uR7EpvITwAcB2yS4lb8fdfipDQFaZa9pwMqvWAtmIYRfABXJtZctkZt3YdbfvliEgp+twADsRPgCH5erKlsnOuklFOiHOTUNATtbhAHYifAAOcrLQ0Q0yebefboij4BOwHzUfgEOcLnR0i0wsJb+Y5ckp+ATsR/gAHOKGQkcvyESIo+ATsBfDLoBD3FLomO0ytWAZBZ+AfQgfgEPcVOiYzTIZ4ij4BOzBsAvgEDetdZHNCHFA9iF8AA6h0DEzCHFA9iF8AA6i0HHxCHFA9jFM03TVPL5oNKpAIKBIJKLCwkKnmwPYItdWOLVCri7WBrhFKtdvwgeAWWVjIMrGNgNekcr1m9kuAGbI1l4EZqsA2YGaDwAJFrNaKAAkg/ABII4l3wHYgfABII4l3wHYgfABII4l3wHYgYJTAHGsFvoeZs4A1iF8AIiLrRYajozMWvdhTC6A5vXVQrN1tg+QLRh2ARDHaqHM9gHsQPgAkCCXl3xntg9gD4ZdAMywpapEtZXBnKt5SGW2D4uZAekjfACYVS6uFspsH8Aelg27HDlyROXl5fL5fFq3bp1++ctfWvVSAJARzPYB7GFJ+HjiiSfU0NCgffv26cUXX9QnPvEJbd26VefOnbPi5QAgI2KzfeYaXDImZ714fbYPYDVLwsfBgwf11a9+VV/72tf04Q9/WIcOHVJZWZlaW1uteDkAyAhm+wD2yHj4GBsb0wsvvKC6urqE43V1dTp58mSmXw4AMiqXZ/sAdsl4wenFixc1Pj6u4uLihOPFxcUKh8Mzzh8dHdXo6Gj852g0mukmAUBKcnW2D2AXy2a7GEbi/6Smac44JkktLS1qamqyqhkAkJZcnO0D2CXjwy7vf//7lZ+fP6OXY3BwcEZviCTt3btXkUgk/jh//nymmwQAAFwk4+Hjmmuu0bp169TZ2ZlwvLOzU5s2bZpxfkFBgQoLCxMeAADAuywZdtm9e7fuvPNOrV+/Xhs3btQjjzyic+fO6Z577rHi5QAAQBaxJHx88Ytf1KVLl/SNb3xDoVBIVVVVevrpp3X99ddb8XIAACCLGKZpumqHpGg0qkAgoEgkwhAMAABZIpXrN7vaAgAAWxE+AACArQgfAADAVoQPAABgK8IHAACwFeEDAADYivABAABsRfgAAAC2smxXWwDZbXzCZEt5AJYgfACYoaMvpKb2foUiI/FjJQGfGusrtaWqxNG2Ach+DLsASNDRF9KOtp6E4CFJ4ciIdrT1qKMv5FjbAHgD4QNA3PiEqab2fs224VPsWFN7v8YnXLUlFIAsQ/gAEHd6YGhGj8dUpqRQZESnB4ZsbRcAbyF8AIgbHJ47eKRzHgDMhvABIG6l35fR8wBgNoQPAHEbyotUEvBprgm1xuSslw3lRTa3DICXED4AxOXnGWqsr5Qmg8ZUsZ8b6ytZ7wPAohA+ACTYUlWi1u1rFQwkDq0EAz61bl/LOh8AFo1FxgDMsKWqRLWVQVY4BWAJwgeAWeXnGdq4eoXTzQDgQQy7AAAAWxE+AACArQgfAADAVoQPAABgK8IHAACwFeEDAADYivABAABsRfgAAAC2InwAAABbuW6FU9M0JUnRaNTppgAAgCTFrtux6/h8XBc+hoeHJUllZWVONwUAAKRoeHhYgUBg3nMMM5mIYqOJiQlduHBBfr9fhuHtTayi0ajKysp0/vx5FRYWOt2cnMJ77wzed+fw3jsnV9570zQ1PDys0tJS5eXNX9Xhup6PvLw8rVq1yulm2KqwsNDTH0g34713Bu+7c3jvnZML7/1CPR4xFJwCAABbET4AAICtCB8OKigoUGNjowoKCpxuSs7hvXcG77tzeO+dw3s/k+sKTgEAgLfR8wEAAGxF+AAAALYifAAAAFsRPgAAgK0IHy4zOjqqG2+8UYZhqLe31+nmeN5rr72mr371qyovL9fSpUu1evVqNTY2amxszOmmedKRI0dUXl4un8+ndevW6Ze//KXTTfK8lpYWfexjH5Pf79fKlSt122236de//rXTzco5LS0tMgxDDQ0NTjfFFQgfLrNnzx6VlpY63Yyc8e///u+amJjQ9773PZ05c0b/8A//oO9+97t68MEHnW6a5zzxxBNqaGjQvn379OKLL+oTn/iEtm7dqnPnzjndNE/r6urSrl279Nxzz6mzs1Pvvvuu6urqdOXKFaebljO6u7v1yCOPaM2aNU43xTWYausiP//5z7V792795Cc/0Uc+8hG9+OKLuvHGG51uVs751re+pdbWVv3mN79xuimeUl1drbVr16q1tTV+7MMf/rBuu+02tbS0ONq2XPLWW29p5cqV6urq0ic/+Umnm+N5b7/9ttauXasjR47ooYce0o033qhDhw453SzH0fPhEm+++aa+/vWv60c/+pGWLVvmdHNyWiQSUVFRkdPN8JSxsTG98MILqqurSzheV1enkydPOtauXBSJRCSJz7hNdu3apc9//vO65ZZbnG6Kq7huY7lcZJqm7rrrLt1zzz1av369XnvtNaeblLPOnj2r73znO/r7v/97p5viKRcvXtT4+LiKi4sTjhcXFyscDjvWrlxjmqZ2796tm2++WVVVVU43x/Mef/xx9fT0qLu72+mmuA49Hxbav3+/DMOY9/H888/rO9/5jqLRqPbu3et0kz0j2fd+qgsXLmjLli368z//c33ta19zrO1eZhhGws+mac44Buvce++9eumll/TYY4853RTPO3/+vO6//361tbXJ5/M53RzXoebDQhcvXtTFixfnPedDH/qQvvSlL6m9vT3hS3h8fFz5+fm64447dPToURta6y3JvvexL4ULFy7oU5/6lKqrq/WDH/xAeXnk8kwaGxvTsmXL9OMf/1hf+MIX4sfvv/9+9fb2qqury9H25YL77rtPTz31lJ599lmVl5c73RzPe+qpp/SFL3xB+fn58WPj4+MyDEN5eXkaHR1NeC7XED5c4Ny5c4pGo/GfL1y4oM9+9rP6p3/6J1VXV2vVqlWOts/r3njjDX3qU5/SunXr1NbWltNfCFaqrq7WunXrdOTIkfixyspK3XrrrRScWsg0Td1333168skn9Ytf/EIVFRVONyknDA8P6/XXX0849hd/8Rf60z/9Uz3wwAM5P+xFzYcLXHfddQk/X3vttZKk1atXEzwsduHCBdXU1Oi6667T3/3d3+mtt96KPxcMBh1tm9fs3r1bd955p9avX6+NGzfqkUce0blz53TPPfc43TRP27Vrl44dO6bjx4/L7/fHa2wCgYCWLl3qdPM8y+/3zwgYy5cv14oVK3I+eIjwgVx34sQJvfrqq3r11VdnBD06BTPri1/8oi5duqRvfOMbCoVCqqqq0tNPP63rr7/e6aZ5Wmxqc01NTcLx73//+7rrrrscahVyHcMuAADAVlTVAQAAWxE+AACArQgfAADAVoQPAABgK8IHAACwFeEDAADYivABAABsRfgAAAC2InwAAABbET4AAICtCB8AAMBWhA8AAGCr/w+aD+LZyFjp3gAAAABJRU5ErkJggg==",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"## Generate data\n",
|
||
"import numpy as np\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"\n",
|
||
"# 1) Generate quadratic data\n",
|
||
"np.random.seed(3)\n",
|
||
"\n",
|
||
"n = 50\n",
|
||
"x = np.random.uniform(-5, 5, n) # symmetric, wider range\n",
|
||
"\n",
|
||
"# True relationship: y = ax^2 + c + noise\n",
|
||
"a_true = 2.0\n",
|
||
"c_true = 5.0\n",
|
||
"noise = np.random.normal(0, 3, n)\n",
|
||
"\n",
|
||
"y = a_true * x**2 + c_true + noise\n",
|
||
"\n",
|
||
"## Generate scatter plot\n",
|
||
"plt.scatter(x,y)\n",
|
||
"\n",
|
||
"# plot it\n",
|
||
"plt.savefig('../images/quadratic_data_generated_1.png')\n",
|
||
"plt.show()\n",
|
||
"\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "1221e35e",
|
||
"metadata": {},
|
||
"source": [
|
||
"\n",
|
||
"If we try to find a line of best fit, we get something that doesn't really describe or approximate our data at all...\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 18,
|
||
"id": "bb6cd90d",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"# find a line of best fit\n",
|
||
"a,b = np.polyfit(x, y, 1)\n",
|
||
"\n",
|
||
"# add scatter points to plot\n",
|
||
"plt.scatter(x,y)\n",
|
||
"\n",
|
||
"# add line of best fit to plot\n",
|
||
"plt.plot(x, a*x + b, 'r', linewidth=1)\n",
|
||
"\n",
|
||
"# plot it\n",
|
||
"plt.savefig('../images/quadratic_data_line_of_best_fit.png')\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "a2d5bb71",
|
||
"metadata": {},
|
||
"source": [
|
||
"\n",
|
||
"This is an example of **underfitting** data, and we can do better. The same linear regression ideas work for fitting a degree $d$ polynomial model to a set of $n$ data points. Before, when trying to fit a line to points $(x_1,y_1),\\dots,(x_n,y_n)$, we had the following matrices\n",
|
||
"$$ \\tilde{X} = \\begin{bmatrix} 1 & x_1 \\\\ \\vdots & \\vdots \\\\ 1 & x_n \\end{bmatrix}, y = \\begin{bmatrix} y_1 \\\\ \\vdots \\\\ y_n \\end{bmatrix}, \\tilde{\\beta} = \\begin{bmatrix} \\beta_0 \\\\ \\beta_1 \\end{bmatrix} $$\n",
|
||
"in the matrix equation\n",
|
||
"$$ \\tilde{X}\\tilde{\\beta} = y, $$\n",
|
||
"and we were trying to find a vector $\\tilde{\\beta}$ which gave a best possible solution. This would give us a line $y = \\beta_0 + \\beta_1x$ which best approximates the data. To fit a polynomial $y = \\beta_0 + \\beta_1x + \\beta_2x^2 + \\cdots + \\beta_d^dx^d$ to the data, we have a similar set up.\n",
|
||
"\n",
|
||
"> **Definition**. The **Vandermonde matrix** is the $n \\times (d+1)$ matrix\n",
|
||
"> $$ V = \\begin{bmatrix} 1 & x_1 & x_1^2 & \\cdots & x_1^d \\\\ 1 & x_2 & x_2^2 & \\cdots & x_2^d \\\\ \\vdots & \\vdots & \\ddots & \\vdots \\\\ 1 & x_n & x_n^2 & \\cdots & x_n^d \\end{bmatrix}. $$\n",
|
||
"\n",
|
||
"With the Vandermonde matrix, to find a polynomial function of best fit, one just needs to find a least-squares solution to the matrix equation\n",
|
||
"$$ V\\tilde{\\beta} = y. $$\n",
|
||
"\n",
|
||
"With the generated data above, we get the following curve. "
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 19,
|
||
"id": "8c569b38",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"# polynomial fit with degree = 2\n",
|
||
"poly = np.polyfit(x,y,2)\n",
|
||
"model = np.poly1d(poly)\n",
|
||
"\n",
|
||
"# add scatter points to plot\n",
|
||
"plt.scatter(x,y)\n",
|
||
"\n",
|
||
"# add the quadratic to the plot\n",
|
||
"polyline=np.linspace(x.min(), x.max())\n",
|
||
"plt.plot(polyline, model(polyline), 'r', linewidth=1)\n",
|
||
"\n",
|
||
"\n",
|
||
"# plot it\n",
|
||
"plt.savefig('../images/quadratic_data_quadratic_of_best_fit')\n",
|
||
"plt.show()\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "b567fe95",
|
||
"metadata": {},
|
||
"source": [
|
||
"\n",
|
||
"Solving these problems can be done with python. One can use `numpy.polyfit` and `numpy.poly1d`. \n",
|
||
"\n",
|
||
"> **Example**. Consider the following data.\n",
|
||
"> |House | Square ft | Bedrooms | Price (in $1000s) |\n",
|
||
"> | --- | --- | --- | --- |\n",
|
||
"> | 0 | 1600 | 3 | 500 |\n",
|
||
"> | 1 | 2100 | 4 | 650 |\n",
|
||
"> | 2 | 1550 | 2 | 475 |\n",
|
||
"> | 3 | 1600 | 3 | 490 |\n",
|
||
"> | 4 | 2000 | 4 | 620 |\n",
|
||
">\n",
|
||
"> Suppose we wanted to predict the price of a house based on the square footage and we thought the relationship was cubic (it clearly isn't, but hey, for the sake of argument). So really we are looking at the subset of data\n",
|
||
"> |House | Square ft | Price (in $1000s) |\n",
|
||
"> | --- | --- | --- |\n",
|
||
"> | 0 | 1600 | 500 |\n",
|
||
"> | 1 | 2100 | 650 |\n",
|
||
"> | 2 | 1550 | 475 |\n",
|
||
"> | 3 | 1600 | 490 |\n",
|
||
"> | 4 | 2000 | 620 |\n",
|
||
">\n",
|
||
"> Our Vandermonde matrix will be\n",
|
||
"> $$ V = \\begin{bmatrix} 1 & 1600 & 1600^2 & 1600^3 \\\\ 1 & 2100 & 2100^2 & 2100^3 \\\\ 1 & 1550 & 1550^2 & 1550^3 \\\\ 1 & 1600 & 1600^2 & 1600^3 \\\\ 1 & 2000 & 2000^2 & 2000^3 \\end{bmatrix} $$\n",
|
||
"> and our target vector will be\n",
|
||
"> $$ y = \\begin{bmatrix} 500 \\\\ 650 \\\\ 475 \\\\ 490 \\\\ 620 \\end{bmatrix}. $$\n",
|
||
"> As we can see, the entries of the Vandermonde matrix get very very large very fast. One can, if they are so inclined, compute a least-squares solution to $V\\tilde{\\beta} = y$ by hand. Let's not, but let us find, using python, a \"best\" cubic approximation of the relationship between the square footage and price.\n",
|
||
"\n",
|
||
"We will use `numpy.polyfit`, `numpy.pold1d` and `numpy.linspace`.\n",
|
||
"\n",
|
||
"Let's get a cubic of best fit.\n",
|
||
"\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 20,
|
||
"id": "9bdf7560",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"import numpy as np\n",
|
||
"import pandas as pd\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"\n",
|
||
"# First let us make a dictionary incorporating our data.\n",
|
||
"# Each entry corresponds to a column (feature of our data)\n",
|
||
"data = {\n",
|
||
" 'Square ft': [1600, 2100, 1550, 1600, 2000],\n",
|
||
" 'Bedrooms': [3, 4, 2, 3, 4],\n",
|
||
" 'Price': [500, 650, 475, 490, 620]\n",
|
||
"}\n",
|
||
"\n",
|
||
"# Create a pandas DataFrame\n",
|
||
"df = pd.DataFrame(data)\n",
|
||
"\n",
|
||
"# Extract x (square footage) and y (price)\n",
|
||
"x = df[\"Square ft\"].to_numpy(dtype=float)\n",
|
||
"y = df[\"Price\"].to_numpy(dtype=float)\n",
|
||
"\n",
|
||
"# Degree of polynomial\n",
|
||
"degree = 3 # cubic\n",
|
||
"\n",
|
||
"# Polyfit directly on x\n",
|
||
"cubic = np.poly1d(np.polyfit(x,y, degree))\n",
|
||
"\n",
|
||
"# Add fitted polynomial line and scatter plot\n",
|
||
"polyline = np.linspace(x.min(),x.max())\n",
|
||
"plt.scatter(x,y, label=\"Observed data\")\n",
|
||
"plt.plot(polyline, cubic(polyline), 'r', label=\"Cubic best fit\")\n",
|
||
"plt.xlabel(\"Square ft\")\n",
|
||
"plt.ylabel(\"Price (in $1000s)\")\n",
|
||
"plt.title(\"Cubic polynomial regression: Price vs Square Footage\")\n",
|
||
"plt.show()\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "67efb4de",
|
||
"metadata": {},
|
||
"source": [
|
||
"Here `numpy.polyfit` computes the least-squares solution in the polynomial basis $1, x, x^2, x^3$, i.e., it solves the Vandermonde least-squares problem. So what is our cubic polynomial?"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 21,
|
||
"id": "eaba0d42",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"poly1d([ 3.08080808e-07, -1.78106061e-03, 3.71744949e+00, -2.15530303e+03])"
|
||
]
|
||
},
|
||
"execution_count": 21,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"cubic"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "db109cf4",
|
||
"metadata": {},
|
||
"source": [
|
||
"The first term is the degree 3 term, the second the degree 2 term, the third the degree 1 term, and the fourth is the constant term. "
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "3f40d45e",
|
||
"metadata": {},
|
||
"source": [
|
||
"\n",
|
||
"\n",
|
||
"# Additional visualization: line of best fit\n",
|
||
"## Generated scatter plot example\n",
|
||
"The first figure is a line of best fit for scattered points. Here is some alternate code that will produce an image. We can do the following using `matplotlib.pyplot.axline`."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 22,
|
||
"id": "a4bb276b",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 1000x600 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"import numpy as np\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"\n",
|
||
"# Generate data (same as above)\n",
|
||
"np.random.seed(3)\n",
|
||
"x = np.random.uniform(0, 10, 50)\n",
|
||
"y = 2.5 * x + 5 + np.random.normal(0, 2, 50)\n",
|
||
"\n",
|
||
"# Calculate slope and intercept\n",
|
||
"slope, intercept = np.polyfit(x, y, 1)\n",
|
||
"\n",
|
||
"plt.figure(figsize=(10, 6))\n",
|
||
"plt.scatter(x, y, color='purple', label='Data Points', alpha=0.7)\n",
|
||
"# Plot the line using axline\n",
|
||
"# xy1=(0, intercept) is the y-intercept point\n",
|
||
"\n",
|
||
"# slope=slope defines the steepness\n",
|
||
"plt.axline(xy1=(0, intercept), slope=slope, color='steelblue', linestyle='--', linewidth=2, label='Line of Best Fit')\n",
|
||
"\n",
|
||
"# Add the equation to the plot\n",
|
||
"# The f-string formats the slope and intercept to 2 decimal places\n",
|
||
"plt.text(1, 25, f'y = {slope:.2f}x + {intercept:.2f}', fontsize=12, bbox=dict(facecolor='white', alpha=0.8))\n",
|
||
"\n",
|
||
"\n",
|
||
"plt.xlabel('X Axis')\n",
|
||
"plt.ylabel('Y Axis')\n",
|
||
"plt.title('Scatter Plot with Line of Best Fit')\n",
|
||
"plt.legend()\n",
|
||
"plt.grid(True, linestyle=':', alpha=0.6)\n",
|
||
"plt.show()\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "c17fbdaf",
|
||
"metadata": {},
|
||
"source": [
|
||
"\n",
|
||
"\n",
|
||
"See\n",
|
||
"- https://stackoverflow.com/questions/37234163/how-to-add-a-line-of-best-fit-to-scatter-plot\n",
|
||
"- https://www.statology.org/line-of-best-fit-python/\n",
|
||
"- https://stackoverflow.com/questions/6148207/linear-regression-with-matplotlib-numpy\n"
|
||
]
|
||
}
|
||
],
|
||
"metadata": {
|
||
"kernelspec": {
|
||
"display_name": "Python 3",
|
||
"language": "python",
|
||
"name": "python3"
|
||
},
|
||
"language_info": {
|
||
"codemirror_mode": {
|
||
"name": "ipython",
|
||
"version": 3
|
||
},
|
||
"file_extension": ".py",
|
||
"mimetype": "text/x-python",
|
||
"name": "python",
|
||
"nbconvert_exporter": "python",
|
||
"pygments_lexer": "ipython3",
|
||
"version": "3.14.3"
|
||
}
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 5
|
||
}
|