{ "cells": [ { "cell_type": "markdown", "id": "f513b4de", "metadata": {}, "source": [ "# Ch 07 — Dimensionality Reduction (notebook)\n", "\n", "`[← 06 ensemble-methods]` · **this notebook** · `[08 unsupervised-learning →]`\n", "\n", "Runs top-to-bottom in ~3 min on free Colab CPU. Last verified 2026-06-11.\n", "\n", "**What you'll build**\n", "- `MyPCA`, principal component analysis from the SVD up in ~20 lines of NumPy, checked against scikit-learn's `PCA` to the last digit of variance.\n", "- An explained-variance curve you read to *choose* how many components to keep, then a compress-then-reconstruct loop that shows what each discarded component cost you.\n", "- A Johnson-Lindenstrauss random projection that crushes 5000 dimensions to a few hundred and *provably* keeps every pairwise distance.\n", "- A t-SNE map of the digits, plus the experiment that proves its distances are not real.\n", "- A k-means clustering pipeline you first **break** with a one-line convergence bug, watch fail, then repair.\n", "\n", "**How this notebook works.** Code cells with a `# TODO` are yours to fill in. Run the cell to grade yourself: `[ ok ]` passed, `[FAIL]` shows what went wrong, `[ -- ]` means not attempted yet. Every exercise has a hint ladder (open only as many as you need) and a folded solution below it. The notebook runs top-to-bottom even if you fill in nothing, because the solution cells redefine the functions for the cells that follow. See Ch 00 for the full protocol.\n" ] }, { "cell_type": "markdown", "id": "5d22ea90", "metadata": {}, "source": [ "## Before you start\n", "\n", "Three questions answerable from the linear-algebra prereqs (Ch 00 §4) and Ch 02. Predict, then check.\n", "\n", "1. PCA needs the data centered before the SVD. What goes wrong if you forget to subtract the mean?
AnswerYou get the principal axes of the raw second-moment matrix $\\mathbf{X}^\\top\\mathbf{X}$, whose top direction points from the origin toward the data centroid, not the direction of greatest spread *within* the cloud. The first component ends up encoding \"where the data sits\" instead of \"how the data varies\".
\n", "2. An 8x8 digit image is a point in how many dimensions, and is that the *intrinsic* dimensionality of the data?
Answer64 dimensions (one per pixel). The intrinsic dimensionality is far lower: digits vary along a handful of degrees of freedom (slant, thickness, loop position), so most of the 64 pixel-axes carry almost no variance. Finding the few that matter is the whole chapter.
\n", "3. You project from 5000 dimensions down to 600 with a *random* Gaussian matrix, no fitting. Roughly how badly are pairwise distances distorted?
AnswerSurprisingly little. The Johnson-Lindenstrauss lemma guarantees that for the right target dimension, every pairwise distance is preserved within a small relative error with high probability. We will measure it and watch the guarantee hold.
\n" ] }, { "cell_type": "markdown", "id": "b8a06494", "metadata": {}, "source": [ "## Setup\n" ] }, { "cell_type": "code", "execution_count": 1, "id": "d305278d", "metadata": { "execution": { "iopub.execute_input": "2026-06-10T18:47:19.780612Z", "iopub.status.busy": "2026-06-10T18:47:19.780515Z", "iopub.status.idle": "2026-06-10T18:47:20.385376Z", "shell.execute_reply": "2026-06-10T18:47:20.384701Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "numpy 2.2.6 · sklearn 1.7.2\n" ] } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import sklearn\n", "print(f\"numpy {np.__version__} · sklearn {sklearn.__version__}\")\n", "if np.__version__ < \"2.0\":\n", " print(\"WARN: written for NumPy 2.x; older versions may differ slightly\")" ] }, { "cell_type": "code", "execution_count": 2, "id": "84c96e1e", "metadata": { "execution": { "iopub.execute_input": "2026-06-10T18:47:20.386540Z", "iopub.status.busy": "2026-06-10T18:47:20.386406Z", "iopub.status.idle": "2026-06-10T18:47:20.390804Z", "shell.execute_reply": "2026-06-10T18:47:20.390418Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "FAST=False · TSNE_ITERS=1000\n" ] } ], "source": [ "import os, random\n", "SEED = 0\n", "FAST = bool(os.environ.get('NB_FAST')) # CI smoke mode: ~10x fewer t-SNE iterations, same code paths\n", "# t-SNE iteration budget: full run optimizes longer; FAST uses the minimum sklearn allows.\n", "TSNE_ITERS = 250 if FAST else 1000\n", "rng = np.random.default_rng(SEED)\n", "random.seed(SEED)\n", "print(f\"FAST={FAST} · TSNE_ITERS={TSNE_ITERS}\")\n", "\n", "# ── house self-check harness (identical across all chapter notebooks) ──\n", "import numpy as _np\n", "\n", "def check(label, test_fn, required=False):\n", " \"\"\"Run one self-check. test_fn raises AssertionError (with a teaching\n", " message) on failure, NotImplementedError if the stub is unfilled.\n", " required=True is used only in solution cells; it is what CI grades.\"\"\"\n", " try:\n", " test_fn()\n", " except NotImplementedError:\n", " if required:\n", " raise AssertionError(f\"{label}: reference solution incomplete\")\n", " print(f\"[ -- ] {label}: not attempted yet — fill in the TODO above, then re-run.\")\n", " return False\n", " except AssertionError as e:\n", " if required:\n", " raise\n", " print(f\"[FAIL] {label}: {e}\")\n", " return False\n", " print(f\"[ ok ] {label}\")\n", " return True\n", "\n", "def attempted(*vals):\n", " \"\"\"Treat None placeholders as 'not attempted'.\"\"\"\n", " if any(v is None for v in vals):\n", " raise NotImplementedError\n", "\n", "def check_shape(x, want):\n", " assert tuple(x.shape) == tuple(want), \\\n", " f\"shape {tuple(x.shape)}, expected {tuple(want)} — check your reshape/transpose order\"\n", "\n", "def check_close(got, want, atol=1e-5, rtol=1e-4, msg=\"\"):\n", " g, w = _np.asarray(got, dtype=float), _np.asarray(want, dtype=float)\n", " assert g.shape == w.shape, f\"shape {g.shape} vs expected {w.shape}. {msg}\"\n", " bad = ~_np.isclose(g, w, atol=atol, rtol=rtol)\n", " assert not bad.any(), \\\n", " f\"{bad.mean():.2%} of values wrong (max diff {abs(g - w).max():.3g}). {msg}\"" ] }, { "cell_type": "markdown", "id": "8a589209", "metadata": {}, "source": [ "> **Note:** seeds make this notebook's printed numbers reproduce on CPU. Library versions and BLAS threading can shift the last digit or two, and the *sign* of a principal component is mathematically arbitrary (SVD does not pin it down). Quoted numbers hold for the pinned environment; if your variance ratio is 0.9012 and the page says 0.9013, you did nothing wrong.\n" ] }, { "cell_type": "markdown", "id": "86fdf652", "metadata": {}, "source": [ "## The map\n", "\n", "> **Part 1 — The curse of dimensionality.** Measure, on synthetic data, why distance-based intuition dies in high dimensions and why a low-dimensional *manifold* is the way out.\n", "> **Part 2 — PCA from the SVD up.** Derive principal components, build `MyPCA` from `np.linalg.svd`, and check it against scikit-learn to machine precision.\n", "> **Part 3 — How many components.** Read an explained-variance curve, find the elbow, and learn why \"explained variance\" is not \"useful information\".\n", "> **Part 4 — Compress and reconstruct.** Project digits down and back up, watch them blur, and prove the reconstruction error equals the variance you threw away.\n", "> **Part 5 — Random projection.** Use the Johnson-Lindenstrauss lemma to compress with a random matrix and assert the distance guarantee holds.\n", "> **Part 6 — Nonlinear manifolds.** Unroll a swiss roll with Kernel PCA and LLE where linear PCA cannot.\n", "> **Part 7 — t-SNE and its lies.** Map the digits to 2D, then run the experiment that shows t-SNE distances are not meaningful.\n", "> **Part 8 — The pipeline, broken then fixed.** Build PCA -> k-means, plant the k-means early-break bug, watch it fail, and repair the convergence test.\n" ] }, { "cell_type": "markdown", "id": "84213a24", "metadata": {}, "source": [ "## Part 1 — The curse of dimensionality\n", "\n", "> **Objectives.** See distances *concentrate* as dimension grows, so that nearest and farthest neighbors become almost the same point, and understand why the escape hatch is to assume the data lives on a low-dimensional manifold.\n", "\n", "In one dimension a neighborhood of width 0.1 covers 10% of the unit interval. In 100 dimensions a hypercube of side 0.1 covers $10^{-100}$ of the unit hypercube. Everything is far from everything, and \"the nearest point\" stops meaning much. We can watch this happen.\n" ] }, { "cell_type": "markdown", "id": "4d9d7870", "metadata": {}, "source": [ "> **Predict:** for uniform random points in the $d$-dimensional unit cube, as $d$ grows, what happens to the ratio (distance to the *farthest* point) / (distance to the *nearest* point) for a typical query point?
AnswerIt collapses toward 1. In high dimensions the nearest and farthest neighbors are nearly equidistant, so a nearest-neighbor query has almost no discriminative power. That is distance concentration.
\n" ] }, { "cell_type": "code", "execution_count": 3, "id": "41bee8f8", "metadata": { "execution": { "iopub.execute_input": "2026-06-10T18:47:20.391777Z", "iopub.status.busy": "2026-06-10T18:47:20.391704Z", "iopub.status.idle": "2026-06-10T18:47:20.400274Z", "shell.execute_reply": "2026-06-10T18:47:20.399778Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "d= 1 farthest/nearest = 616.81\n", "d= 2 farthest/nearest = 83.02\n", "d= 5 farthest/nearest = 9.23\n", "d= 10 farthest/nearest = 3.19\n", "d= 50 farthest/nearest = 1.57\n", "d= 100 farthest/nearest = 1.43\n", "d= 500 farthest/nearest = 1.18\n", "d= 1000 farthest/nearest = 1.10\n" ] } ], "source": [ "# Distance concentration: nearest vs farthest neighbor as dimension grows.\n", "def near_far_ratio(d, n=500, rng=rng):\n", " pts = rng.random((n, d)) # n points, (n, d)\n", " q = rng.random((1, d)) # one query point, (1, d)\n", " dists = np.sqrt(((pts - q) ** 2).sum(axis=1)) # (n,)\n", " return dists.max() / dists.min()\n", "\n", "dims = [1, 2, 5, 10, 50, 100, 500, 1000]\n", "ratios = [near_far_ratio(d) for d in dims]\n", "for d, r in zip(dims, ratios):\n", " print(f\"d={d:5d} farthest/nearest = {r:6.2f}\")" ] }, { "cell_type": "markdown", "id": "d43d5caf", "metadata": {}, "source": [ "> **Interpretation.** At `d=1` the farthest point is tens of times more distant than the nearest. By `d=1000` the ratio is barely above 1: every point sits at roughly the same distance from the query. Algorithms that lean on \"the few closest points\" (k-NN, k-means, kernel methods) lose their footing here.\n" ] }, { "cell_type": "markdown", "id": "9c0155f6", "metadata": {}, "source": [ "The other half of the curse: in high dimensions almost all the volume of a cube hugs its surface, so uniform points are almost never near the center. We can verify the surface-hugging claim directly.\n" ] }, { "cell_type": "code", "execution_count": 4, "id": "730669f8", "metadata": { "execution": { "iopub.execute_input": "2026-06-10T18:47:20.401091Z", "iopub.status.busy": "2026-06-10T18:47:20.400966Z", "iopub.status.idle": "2026-06-10T18:47:20.403280Z", "shell.execute_reply": "2026-06-10T18:47:20.402859Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "d= 1 fraction of volume in the outer 5% shell = 10.0%\n", "d= 2 fraction of volume in the outer 5% shell = 19.0%\n", "d= 3 fraction of volume in the outer 5% shell = 27.1%\n", "d= 10 fraction of volume in the outer 5% shell = 65.1%\n", "d= 50 fraction of volume in the outer 5% shell = 99.5%\n", "d= 100 fraction of volume in the outer 5% shell = 100.0%\n" ] } ], "source": [ "# Fraction of unit-cube volume within a thin outer shell of width 0.05.\n", "# Inner cube has side (1 - 2*0.05) = 0.9, so shell fraction = 1 - 0.9**d.\n", "for d in [1, 2, 3, 10, 50, 100]:\n", " shell = 1 - 0.9 ** d\n", " print(f\"d={d:4d} fraction of volume in the outer 5% shell = {shell:6.1%}\")\n", "assert 1 - 0.9 ** 100 > 0.99, \"in 100-d nearly all volume is in the shell\"" ] }, { "cell_type": "markdown", "id": "1050614d", "metadata": {}, "source": [ "> **Key takeaways.** Distances concentrate and volume flees to the boundary as dimension grows, so raw high-dimensional coordinates are a hostile representation. The fix for real data is that it rarely fills its space: it lies on a much lower-dimensional **manifold**, and dimensionality reduction is the search for coordinates on that manifold. PCA assumes the manifold is a linear subspace; t-SNE and friends assume a smooth curved surface.\n" ] }, { "cell_type": "markdown", "id": "c241a883", "metadata": {}, "source": [ "## Part 2 — PCA from the SVD up\n", "\n", "> **Objectives.** Derive principal components as the top eigenvectors of the covariance, compute them stably through the SVD, and build `MyPCA` that agrees with scikit-learn on explained variance to machine precision.\n", "\n", "Given centered data $\\mathbf{X} \\in \\mathbb{R}^{m \\times d}$ (each column mean-zero), the first principal component is the unit vector $\\mathbf{w}_1$ that maximizes the projected variance\n", "\n", "$$\\operatorname{Var}(\\mathbf{X}\\mathbf{w}_1) = \\tfrac{1}{m}\\,\\mathbf{w}_1^\\top \\mathbf{X}^\\top \\mathbf{X}\\, \\mathbf{w}_1 \\quad\\text{s.t.}\\quad \\lVert\\mathbf{w}_1\\rVert = 1.$$\n", "\n", "That is a Rayleigh quotient, so the maximizer is the top eigenvector of $\\mathbf{X}^\\top\\mathbf{X}$. The $k$-th component is the $k$-th eigenvector, ordered by decreasing eigenvalue. The numerically stable way to get all of them at once is the **singular value decomposition** $\\mathbf{X} = \\mathbf{U}\\boldsymbol{\\Sigma}\\mathbf{V}^\\top$: the rows of $\\mathbf{V}^\\top$ are the components, and the eigenvalues relate to the singular values by $\\lambda_i = \\sigma_i^2/(m-1)$.\n" ] }, { "cell_type": "markdown", "id": "6e66877e", "metadata": {}, "source": [ "First, the dataset that threads this whole notebook: scikit-learn's `digits`. It is 1797 handwritten digits as 8x8 = 64-pixel images, ships inside scikit-learn (no download, idempotent), and is small enough that every cell here runs in seconds. The full 784-pixel MNIST is the capstone; the lesson is identical.\n" ] }, { "cell_type": "code", "execution_count": 5, "id": "55c60654", "metadata": { "execution": { "iopub.execute_input": "2026-06-10T18:47:20.404107Z", "iopub.status.busy": "2026-06-10T18:47:20.404039Z", "iopub.status.idle": "2026-06-10T18:47:20.545259Z", "shell.execute_reply": "2026-06-10T18:47:20.544952Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "digits: (1797, 64), labels [np.int64(0), np.int64(1), np.int64(2), np.int64(3), np.int64(4), np.int64(5), np.int64(6), np.int64(7), np.int64(8), np.int64(9)]\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.datasets import load_digits\n", "digits = load_digits()\n", "X_digits = digits.data.astype(np.float64) # (1797, 64), pixel intensities 0..16\n", "y_digits = digits.target # (1797,) labels 0..9\n", "print(f\"digits: {X_digits.shape}, labels {sorted(set(y_digits))}\")\n", "\n", "fig, axes = plt.subplots(1, 8, figsize=(10, 1.6))\n", "for ax, img, lab in zip(axes, digits.images[:8], y_digits[:8]):\n", " ax.imshow(img, cmap=\"gray_r\"); ax.set_title(int(lab)); ax.axis(\"off\")\n", "plt.suptitle(\"eight digits, each a point in 64-dimensional pixel space\"); plt.tight_layout(); plt.show()" ] }, { "cell_type": "markdown", "id": "89cdab19", "metadata": {}, "source": [ "> **Interpretation.** Each tiny image is one row of `X_digits`, a single point in 64-dimensional space. The digits clearly do not use those 64 axes freely: a 0 and an 8 differ along a few coordinated pixel patterns, not 64 independent knobs.\n" ] }, { "cell_type": "markdown", "id": "9b1d0fe4", "metadata": {}, "source": [ "Before the real data, trace the SVD on a tiny 2D cloud whose answer we can see by eye. The points lie almost on the line $y = x$, so the first component should point along $(1, 1)/\\sqrt 2$ and capture nearly all the variance.\n" ] }, { "cell_type": "code", "execution_count": 6, "id": "bdece50e", "metadata": { "execution": { "iopub.execute_input": "2026-06-10T18:47:20.546299Z", "iopub.status.busy": "2026-06-10T18:47:20.546204Z", "iopub.status.idle": "2026-06-10T18:47:20.549551Z", "shell.execute_reply": "2026-06-10T18:47:20.549164Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "singular values: [4.519 0.133]\n", "first component : [0.699 0.715] (expect ~ ±[0.707, 0.707])\n", "explained variance ratio: [0.999 0.001]\n" ] } ], "source": [ "toy = np.array([[-2., -2.], [-1., -1.1], [0., 0.1], [1., 0.9], [2., 2.1]])\n", "toy_c = toy - toy.mean(axis=0) # center\n", "U, s, Vt = np.linalg.svd(toy_c, full_matrices=False)\n", "print(\"singular values:\", np.round(s, 3))\n", "print(\"first component :\", np.round(Vt[0], 3), \" (expect ~ ±[0.707, 0.707])\")\n", "evr = (s ** 2) / (s ** 2).sum()\n", "print(\"explained variance ratio:\", np.round(evr, 3))" ] }, { "cell_type": "markdown", "id": "17869148", "metadata": {}, "source": [ "> **Interpretation.** The first component is `[±0.707, ±0.707]`, the $45^\\circ$ diagonal, exactly the direction the points fall along, and it explains ~99% of the variance. The sign may be flipped: $\\mathbf{w}$ and $-\\mathbf{w}$ describe the same line, and the SVD picks one arbitrarily. Watch for that when comparing implementations.\n" ] }, { "cell_type": "markdown", "id": "5894040d", "metadata": {}, "source": [ "### Exercise 7.1 — PCA via SVD\n", "`Difficulty 3/5 · ~20 min`\n", "\n", "Fill in `fit_pca`. Center the data, take the thin SVD, and return the mean, the top-`k` components (rows of $\\mathbf{V}^\\top$), and the explained-variance *ratio* of those components. This is the load-bearing function of the chapter; the checks compare you to scikit-learn's `PCA` to machine precision.\n", "\n", "Harder: also return `explained_variance` (the eigenvalues $\\sigma_i^2/(m-1)$) and confirm they match `PCA().explained_variance_`.\n" ] }, { "cell_type": "code", "execution_count": 7, "id": "f98b8536", "metadata": { "execution": { "iopub.execute_input": "2026-06-10T18:47:20.550811Z", "iopub.status.busy": "2026-06-10T18:47:20.550712Z", "iopub.status.idle": "2026-06-10T18:47:20.582623Z", "shell.execute_reply": "2026-06-10T18:47:20.582230Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ -- ] 7.1 shape: not attempted yet — fill in the TODO above, then re-run.\n", "[ -- ] 7.1 vs sklearn: not attempted yet — fill in the TODO above, then re-run.\n" ] }, { "data": { "text/plain": [ "False" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def fit_pca(X, k):\n", " \"\"\"Fit PCA via SVD.\n", "\n", " X : (m, d) data, rows are samples.\n", " k : number of components to keep.\n", " Returns (mean, components, evr) where\n", " mean : (d,) per-feature mean used for centering\n", " components : (k, d) top-k right singular vectors (rows)\n", " evr : (k,) explained variance ratio of those k components\n", " \"\"\"\n", " X = np.asarray(X, dtype=np.float64)\n", " m = X.shape[0]\n", " # TODO 1: mean = per-feature mean of X (shape (d,))\n", " mean = None\n", " # TODO 2: center the data: Xc = X - mean\n", " Xc = None\n", " # TODO 3: thin SVD: U, s, Vt = np.linalg.svd(Xc, full_matrices=False)\n", " # s holds the singular values; Vt rows are the components.\n", " s = None\n", " Vt = None\n", " attempted(mean, Xc, s, Vt)\n", " components = Vt[:k] # (k, d)\n", " # TODO 4: variances per component are s**2 / (m - 1); the ratio divides by\n", " # the TOTAL variance (sum over ALL singular values, not just k).\n", " var_all = None # (d,) or however many s has\n", " evr = None # (k,)\n", " attempted(var_all, evr)\n", " return mean, components, evr\n", "\n", "def transform_pca(X, mean, components):\n", " \"\"\"Project X onto the components: (X - mean) @ components.T -> (m, k).\"\"\"\n", " return (np.asarray(X, dtype=np.float64) - mean) @ components.T\n", "\n", "# self-checks (run this cell)\n", "def _pca_vs_sklearn():\n", " from sklearn.decomposition import PCA\n", " mean, comps, evr = fit_pca(X_digits, 10)\n", " sk = PCA(n_components=10).fit(X_digits)\n", " check_close(evr, sk.explained_variance_ratio_, atol=1e-8,\n", " msg=\"explained-variance ratio must match sklearn PCA exactly\")\n", " # components match up to a per-row sign flip; compare absolute correlation.\n", " align = np.abs((comps * sk.components_).sum(axis=1)) # ~1 if parallel\n", " assert np.allclose(align, 1.0, atol=1e-6), \\\n", " f\"components not aligned with sklearn (|dot|={np.round(align,3)}); check centering\"\n", "\n", "def _pca_shape():\n", " mean, comps, evr = fit_pca(X_digits, 5)\n", " check_shape(comps, (5, 64)); check_shape(evr, (5,))\n", "\n", "check(\"7.1 shape\", _pca_shape)\n", "check(\"7.1 vs sklearn\", _pca_vs_sklearn)" ] }, { "cell_type": "markdown", "id": "72888f7c", "metadata": {}, "source": [ "
Hint 1 (conceptual)The components are literally the first `k` rows of `Vt`. The explained-variance ratio of component $i$ is its variance $\\sigma_i^2/(m-1)$ divided by the total variance, which is the sum of *all* the per-component variances, not just the top `k`.
\n", "\n", "
Hint 2 (pseudocode)\n", "\n", "```python\n", "mean = X.mean(axis=0)\n", "Xc = X - mean\n", "U, s, Vt = np.linalg.svd(Xc, full_matrices=False)\n", "var_all = (s ** 2) / (m - 1) # (len(s),)\n", "evr = var_all[:k] / var_all.sum() # (k,)\n", "```\n", "
\n", "\n", "
Help — \"explained-variance ratio must match sklearn\" fails by a small constant factorYou probably divided by `m` instead of `m - 1`, or normalized the ratio by the top-`k` variance instead of the total. The ratio's denominator must be `var_all.sum()` over every singular value. Print `evr.sum()` for `k=64`: it must be `1.0`.
\n", "\n", "
Help — \"components not aligned with sklearn\"Either you forgot to center (`Xc = X - mean`), or you used `full_matrices=True` and sliced the wrong axis. With `full_matrices=False`, `Vt` is `(min(m,d), d)` and its rows are the components; take `Vt[:k]`.
\n" ] }, { "cell_type": "code", "execution_count": 8, "id": "13b333b6", "metadata": { "execution": { "iopub.execute_input": "2026-06-10T18:47:20.583952Z", "iopub.status.busy": "2026-06-10T18:47:20.583851Z", "iopub.status.idle": "2026-06-10T18:47:20.619277Z", "shell.execute_reply": "2026-06-10T18:47:20.618442Z" }, "collapsed": true, "jupyter": { "source_hidden": true }, "tags": [ "hide-input" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ ok ] 7.1 shape\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "[ ok ] 7.1 vs sklearn\n", "top-10 components explain 73.8% of digit variance\n" ] } ], "source": [ "#@title Solution { display-mode: \"form\" }\n", "# solution: redefines fit_pca; the checks below re-verify the reference.\n", "def fit_pca(X, k):\n", " X = np.asarray(X, dtype=np.float64)\n", " m = X.shape[0]\n", " mean = X.mean(axis=0)\n", " Xc = X - mean\n", " U, s, Vt = np.linalg.svd(Xc, full_matrices=False)\n", " components = Vt[:k]\n", " var_all = (s ** 2) / (m - 1)\n", " evr = var_all[:k] / var_all.sum()\n", " return mean, components, evr\n", "\n", "check(\"7.1 shape\", _pca_shape, required=True)\n", "check(\"7.1 vs sklearn\", _pca_vs_sklearn, required=True)\n", "_mean, _comps10, _evr10 = fit_pca(X_digits, 10)\n", "print(f\"top-10 components explain {_evr10.sum():.1%} of digit variance\")" ] }, { "cell_type": "markdown", "id": "d42e17bd", "metadata": {}, "source": [ "> **Interpretation.** Ten of the 64 pixel-axes already account for most of the variation across all 1797 digits. The right singular vectors are the directions; the explained-variance ratio tells you how much each one is worth. We will now turn those numbers into a decision.\n" ] }, { "cell_type": "markdown", "id": "e2d38038", "metadata": {}, "source": [ "Each component is itself a 64-vector, so we can reshape it back into an 8x8 image and *look* at the patterns PCA found. These are sometimes called eigen-digits.\n" ] }, { "cell_type": "code", "execution_count": 9, "id": "93e1b390", "metadata": { "execution": { "iopub.execute_input": "2026-06-10T18:47:20.620577Z", "iopub.status.busy": "2026-06-10T18:47:20.620459Z", "iopub.status.idle": "2026-06-10T18:47:20.748510Z", "shell.execute_reply": "2026-06-10T18:47:20.747919Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# viz: the first 8 principal components reshaped to 8x8 images\n", "mean8, comps8, _ = fit_pca(X_digits, 8)\n", "fig, axes = plt.subplots(1, 8, figsize=(10, 1.6))\n", "for i, ax in enumerate(axes):\n", " ax.imshow(comps8[i].reshape(8, 8), cmap=\"RdBu\"); ax.set_title(f\"PC{i+1}\"); ax.axis(\"off\")\n", "plt.suptitle(\"principal components as images (red/blue = +/- pixel weight)\"); plt.tight_layout(); plt.show()" ] }, { "cell_type": "markdown", "id": "51450817", "metadata": {}, "source": [ "> **Interpretation.** The early components are smooth, large-scale strokes (a top loop, a vertical stem); later ones get higher-frequency. A digit is reconstructed as the mean image plus a weighted sum of these patterns. PCA discovered them with no labels.\n" ] }, { "cell_type": "markdown", "id": "40f3a3c9", "metadata": {}, "source": [ "## Part 3 — How many components\n", "\n", "> **Objectives.** Read a cumulative explained-variance curve to choose `k`, locate the elbow, and internalize that \"variance explained\" is not the same as \"task signal kept\".\n", "\n", "Sort the explained-variance ratios, take the running sum, and you get a curve climbing from 0 to 1. The smallest `k` whose cumulative variance clears a threshold (90%, 95%, 99%) is your component count. There is usually a visible **elbow** where extra components stop paying off.\n" ] }, { "cell_type": "code", "execution_count": 10, "id": "4108dcd9", "metadata": { "execution": { "iopub.execute_input": "2026-06-10T18:47:20.749520Z", "iopub.status.busy": "2026-06-10T18:47:20.749443Z", "iopub.status.idle": "2026-06-10T18:47:20.823172Z", "shell.execute_reply": "2026-06-10T18:47:20.822744Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "90% variance needs 21 components\n", "95% variance needs 29 components\n", "99% variance needs 41 components\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# viz: cumulative explained variance and the threshold crossings\n", "_, _, evr_all = fit_pca(X_digits, 64) # all 64 components\n", "cumsum = np.cumsum(evr_all)\n", "def k_for(thresh): return int(np.argmax(cumsum >= thresh)) + 1\n", "for t in (0.90, 0.95, 0.99):\n", " print(f\"{t:.0%} variance needs {k_for(t)} components\")\n", "\n", "plt.figure(figsize=(6, 4))\n", "plt.plot(range(1, 65), cumsum, marker=\".\", color=\"#1E40FF\")\n", "for t in (0.90, 0.95, 0.99):\n", " plt.axhline(t, ls=\":\", c=\"#888\"); plt.axvline(k_for(t), ls=\":\", c=\"#bbb\")\n", "plt.xlabel(\"number of components\"); plt.ylabel(\"cumulative explained variance\")\n", "plt.title(\"digits: variance vs components\"); plt.tight_layout(); plt.show()" ] }, { "cell_type": "markdown", "id": "f22c068f", "metadata": {}, "source": [ "> **Interpretation.** The curve rises steeply then flattens: the elbow is the bend where you are buying little new variance per component. 95% of the variance lives in well under half the 64 dimensions, the quantitative statement of \"digits have low intrinsic dimensionality\".\n" ] }, { "cell_type": "markdown", "id": "18d9485c", "metadata": {}, "source": [ "### Exercise 7.2 — Choose `k` for a variance budget\n", "`Difficulty 1/5 · ~5 min`\n", "\n", "Write `n_components_for(evr, threshold)` returning the smallest number of components whose cumulative explained variance reaches `threshold`. One line of NumPy. The check uses a hand-built curve where you can count the answer by eye.\n" ] }, { "cell_type": "code", "execution_count": 11, "id": "254069ca", "metadata": { "execution": { "iopub.execute_input": "2026-06-10T18:47:20.824494Z", "iopub.status.busy": "2026-06-10T18:47:20.824329Z", "iopub.status.idle": "2026-06-10T18:47:20.828225Z", "shell.execute_reply": "2026-06-10T18:47:20.827849Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ -- ] 7.2 toy: not attempted yet — fill in the TODO above, then re-run.\n", "[ -- ] 7.2 digits: not attempted yet — fill in the TODO above, then re-run.\n" ] }, { "data": { "text/plain": [ "False" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def n_components_for(evr, threshold):\n", " \"\"\"evr: 1-D array of per-component explained-variance ratios (descending).\n", " Return the smallest k with cumsum(evr)[:k] >= threshold (an int >= 1).\"\"\"\n", " evr = np.asarray(evr, dtype=float)\n", " # TODO: cumulative-sum evr, find the first index >= threshold, +1 for a count.\n", " k = None\n", " attempted(k)\n", " return int(k)\n", "\n", "def _ncomp_toy():\n", " # cumulative: .5, .8, .95, 1.0 -> 90% needs 3 components, 80% needs 2\n", " e = np.array([0.5, 0.3, 0.15, 0.05])\n", " assert n_components_for(e, 0.90) == 3, \"cum .5,.8,.95 -> 0.90 first cleared at index 2 -> k=3\"\n", " assert n_components_for(e, 0.80) == 2, \"cum .5,.8 -> 0.80 cleared at index 1 -> k=2\"\n", " assert n_components_for(e, 0.50) == 1, \"first component already at 0.50\"\n", "\n", "def _ncomp_digits():\n", " # must agree with the printed crossings above\n", " assert n_components_for(evr_all, 0.95) == k_for(0.95)\n", "\n", "check(\"7.2 toy\", _ncomp_toy)\n", "check(\"7.2 digits\", _ncomp_digits)" ] }, { "cell_type": "markdown", "id": "163e5a4f", "metadata": {}, "source": [ "
Hint 1 (conceptual)`np.cumsum` gives the running total. `np.argmax(boolean_array)` returns the index of the first `True`. Add 1 to turn a 0-based index into a count.
\n", "\n", "
Hint 2 (the line)`k = np.argmax(np.cumsum(evr) >= threshold) + 1`.
\n", "\n", "
Help — off by one`argmax` is 0-based, so index 2 means \"the third component\". A count is `index + 1`. The toy check pins this: 90% is first reached at index 2, which is `k=3`.
\n" ] }, { "cell_type": "code", "execution_count": 12, "id": "9f4b4383", "metadata": { "execution": { "iopub.execute_input": "2026-06-10T18:47:20.829065Z", "iopub.status.busy": "2026-06-10T18:47:20.828981Z", "iopub.status.idle": "2026-06-10T18:47:20.831555Z", "shell.execute_reply": "2026-06-10T18:47:20.831254Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ ok ] 7.2 toy\n", "[ ok ] 7.2 digits\n", "95% of digit variance is captured by 29 components\n" ] } ], "source": [ "def n_components_for(evr, threshold):\n", " evr = np.asarray(evr, dtype=float)\n", " return int(np.argmax(np.cumsum(evr) >= threshold) + 1)\n", "\n", "check(\"7.2 toy\", _ncomp_toy, required=True)\n", "check(\"7.2 digits\", _ncomp_digits, required=True)\n", "print(f\"95% of digit variance is captured by {n_components_for(evr_all, 0.95)} components\")" ] }, { "cell_type": "markdown", "id": "2b99d943", "metadata": {}, "source": [ "> **Caveat.** Explained variance is what *PCA* explains, not how much *task-useful* signal survives. If the discriminative direction has low variance, PCA discards it. The Iris dataset is the classic trap: its top components are sepal-dominated and barely help classification. Always sanity-check by running the downstream task on the reduced data, which is exactly what Part 8 does.\n", "\n", "> **Key takeaways.** The cumulative-variance curve turns \"how many components\" into a budget decision. The elbow and the 95% rule are heuristics, not laws. High explained variance does not guarantee the kept directions are the ones your task needs.\n" ] }, { "cell_type": "markdown", "id": "f6a2aa95", "metadata": {}, "source": [ "## Part 4 — Compress and reconstruct\n", "\n", "> **Objectives.** Project digits to `k` dimensions and back, watch them blur, and prove that the mean-squared reconstruction error equals exactly the variance carried by the discarded components.\n", "\n", "Compression is `transform`: $\\mathbf{Z} = (\\mathbf{X}-\\boldsymbol\\mu)\\mathbf{V}_{:k}^\\top$. Decompression is the inverse map $\\hat{\\mathbf{X}} = \\mathbf{Z}\\,\\mathbf{V}_{:k} + \\boldsymbol\\mu$. It is lossy: the variance you dropped is gone. By the Eckart-Young theorem PCA is the *optimal* linear reconstruction, no other rank-`k` linear projection achieves lower error.\n" ] }, { "cell_type": "markdown", "id": "965323e5", "metadata": {}, "source": [ "### Exercise 7.3 — Reconstruct from the projection\n", "`Difficulty 2/5 · ~10 min`\n", "\n", "Fill in `inverse_pca(Z, mean, components)` to map a projection back to the original space, and confirm two things the math demands: more components means lower reconstruction error (monotone), and reconstructing all 64 components is loss-free.\n" ] }, { "cell_type": "code", "execution_count": 13, "id": "1483c5cb", "metadata": { "execution": { "iopub.execute_input": "2026-06-10T18:47:20.832716Z", "iopub.status.busy": "2026-06-10T18:47:20.832589Z", "iopub.status.idle": "2026-06-10T18:47:20.853771Z", "shell.execute_reply": "2026-06-10T18:47:20.853041Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ -- ] 7.3 monotone: not attempted yet — fill in the TODO above, then re-run.\n", "[ -- ] 7.3 lossless: not attempted yet — fill in the TODO above, then re-run.\n" ] }, { "data": { "text/plain": [ "False" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def inverse_pca(Z, mean, components):\n", " \"\"\"Z: (m, k) projection, components: (k, d), mean: (d,).\n", " Return the (m, d) reconstruction in the original space.\"\"\"\n", " # TODO: undo the projection. transform did (X - mean) @ components.T,\n", " # so the inverse is Z @ components, then add the mean back.\n", " recon = None\n", " attempted(recon)\n", " return recon\n", "\n", "def _recon_monotone():\n", " errs = []\n", " for k in (5, 20, 40):\n", " mean, comps, _ = fit_pca(X_digits, k)\n", " Z = transform_pca(X_digits, mean, comps)\n", " Xhat = inverse_pca(Z, mean, comps)\n", " errs.append(float(((X_digits - Xhat) ** 2).mean()))\n", " assert errs[0] > errs[1] > errs[2], \\\n", " f\"more components must lower reconstruction error, got {np.round(errs,3)}\"\n", "\n", "def _recon_lossless():\n", " mean, comps, _ = fit_pca(X_digits, 64) # keep everything\n", " Z = transform_pca(X_digits, mean, comps)\n", " Xhat = inverse_pca(Z, mean, comps)\n", " check_close(Xhat, X_digits, atol=1e-6, msg=\"full-rank reconstruction is exact\")\n", "\n", "check(\"7.3 monotone\", _recon_monotone)\n", "check(\"7.3 lossless\", _recon_lossless)" ] }, { "cell_type": "markdown", "id": "350db225", "metadata": {}, "source": [ "
Hint 1 (conceptual)`transform` did `(X - mean) @ components.T`. Because the components are orthonormal rows, the (pseudo)inverse of `components.T` is `components`. So undo the matmul with `Z @ components`, then add the mean you subtracted.
\n", "\n", "
Hint 2 (the line)`recon = Z @ components + mean`.
\n", "\n", "
Help — shapes don't line up`Z` is `(m, k)`, `components` is `(k, d)`, so `Z @ components` is `(m, d)`. If you wrote `Z @ components.T` you transposed one too many times.
\n" ] }, { "cell_type": "code", "execution_count": 14, "id": "da57aa50", "metadata": { "execution": { "iopub.execute_input": "2026-06-10T18:47:20.854884Z", "iopub.status.busy": "2026-06-10T18:47:20.854780Z", "iopub.status.idle": "2026-06-10T18:47:20.897811Z", "shell.execute_reply": "2026-06-10T18:47:20.897021Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ ok ] 7.3 monotone\n", "[ ok ] 7.3 lossless\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def inverse_pca(Z, mean, components):\n", " return Z @ components + mean\n", "\n", "check(\"7.3 monotone\", _recon_monotone, required=True)\n", "check(\"7.3 lossless\", _recon_lossless, required=True)" ] }, { "cell_type": "markdown", "id": "c026b5f3", "metadata": {}, "source": [ "Now look at it. Compress each digit to a handful of components and reconstruct. The number under each row is `k`.\n" ] }, { "cell_type": "code", "execution_count": 15, "id": "3712cd06", "metadata": { "execution": { "iopub.execute_input": "2026-06-10T18:47:20.898943Z", "iopub.status.busy": "2026-06-10T18:47:20.898824Z", "iopub.status.idle": "2026-06-10T18:47:21.202586Z", "shell.execute_reply": "2026-06-10T18:47:21.202069Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# viz: original digits vs reconstructions at k = 5, 20, 40\n", "sample = X_digits[:8]\n", "ks = [5, 20, 40]\n", "fig, axes = plt.subplots(len(ks) + 1, 8, figsize=(10, 5))\n", "for j, img in enumerate(sample):\n", " axes[0, j].imshow(img.reshape(8, 8), cmap=\"gray_r\"); axes[0, j].axis(\"off\")\n", "axes[0, 0].set_ylabel(\"orig\", rotation=0, ha=\"right\", labelpad=20)\n", "for row, k in enumerate(ks, start=1):\n", " mean, comps, evr = fit_pca(X_digits, k)\n", " recon = inverse_pca(transform_pca(sample, mean, comps), mean, comps)\n", " for j in range(8):\n", " axes[row, j].imshow(recon[j].reshape(8, 8), cmap=\"gray_r\"); axes[row, j].axis(\"off\")\n", " axes[row, 0].set_title(f\"k={k} ({evr.sum():.0%} var)\", loc=\"left\", fontsize=9)\n", "plt.suptitle(\"PCA compression: more components, sharper digits\"); plt.tight_layout(); plt.show()" ] }, { "cell_type": "markdown", "id": "479dafc6", "metadata": {}, "source": [ "> **Interpretation.** At `k=5` the digits are smudgy blobs; by `k=40` they are crisp. You are watching variance turn back into pixels. The blur at low `k` is precisely the variance PCA discarded, which the next cell proves is no metaphor.\n" ] }, { "cell_type": "markdown", "id": "0bcb79df", "metadata": {}, "source": [ "The chapter prose claims the reconstruction error *equals* the sum of the discarded eigenvalues. That is a falsifiable statement, so we assert it. For `k` components the total MSE (summed over pixels, averaged over samples) must equal the trailing per-component variances scaled by $(m-1)/m$.\n" ] }, { "cell_type": "code", "execution_count": 16, "id": "84e09ea6", "metadata": { "execution": { "iopub.execute_input": "2026-06-10T18:47:21.203612Z", "iopub.status.busy": "2026-06-10T18:47:21.203505Z", "iopub.status.idle": "2026-06-10T18:47:21.214891Z", "shell.execute_reply": "2026-06-10T18:47:21.214025Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "measured MSE = 126.9926\n", "trailing eigs = 126.9926\n", "[ ok ] reconstruction error equals the variance thrown away\n" ] } ], "source": [ "# claim: total reconstruction MSE == sum of trailing eigenvalues * (m-1)/m\n", "from sklearn.decomposition import PCA\n", "m = X_digits.shape[0]\n", "k = 20\n", "full = PCA().fit(X_digits) # all eigenvalues\n", "mean, comps, _ = fit_pca(X_digits, k)\n", "recon = inverse_pca(transform_pca(X_digits, mean, comps), mean, comps)\n", "mse_total = ((X_digits - recon) ** 2).sum() / m # sum over pixels, mean over samples\n", "trailing = full.explained_variance_[k:].sum() * (m - 1) / m\n", "print(f\"measured MSE = {mse_total:.4f}\")\n", "print(f\"trailing eigs = {trailing:.4f}\")\n", "check_close(mse_total, trailing, atol=1e-6,\n", " msg=\"Eckart-Young: discarded variance IS the reconstruction error\")\n", "print(\"[ ok ] reconstruction error equals the variance thrown away\")" ] }, { "cell_type": "markdown", "id": "3cf685fe", "metadata": {}, "source": [ "> **Key takeaways.** PCA compression is a closed-form, invertible-up-to-lost-variance map. The error you pay is exactly the eigenvalues you dropped, and no linear method of the same rank does better (Eckart-Young). That makes PCA reconstruction error a principled anomaly score too: points the top components cannot rebuild are outliers.\n" ] }, { "cell_type": "markdown", "id": "88391acc", "metadata": {}, "source": [ "## Part 5 — Random projection: compress with a coin flip\n", "\n", "> **Objectives.** Use the Johnson-Lindenstrauss lemma to pick a target dimension, project a 5000-dimensional cloud through a *random* Gaussian matrix with no fitting, and assert that every pairwise distance survives within the promised band.\n", "\n", "The Johnson-Lindenstrauss lemma (1984) says: to preserve all pairwise distances among $n$ points within relative error $\\epsilon$, it suffices to project to $k = O(\\log n / \\epsilon^2)$ dimensions with a random Gaussian matrix. No eigenvectors, no fitting. You generate a random matrix and multiply. The guarantee is *deterministic* about a *random* projection, which is the surprise.\n" ] }, { "cell_type": "markdown", "id": "584ed85f", "metadata": {}, "source": [ "> **Predict:** we will project 400 points from 5000 dimensions to the JL target dimension for $\\epsilon=0.3$. What fraction of the ~80,000 pairwise distances do you expect to land inside the $\\pm 30\\%$ band?
AnswerEffectively all of them, and the worst observed distortion is usually well under the $\\epsilon$ bound. JL is conservative: the target dimension it asks for buys you margin.
\n" ] }, { "cell_type": "code", "execution_count": 17, "id": "496a5942", "metadata": { "execution": { "iopub.execute_input": "2026-06-10T18:47:21.215776Z", "iopub.status.busy": "2026-06-10T18:47:21.215675Z", "iopub.status.idle": "2026-06-10T18:47:21.325836Z", "shell.execute_reply": "2026-06-10T18:47:21.325489Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "JL target dimension for n=400, eps=0.3: 665 (from 5000)\n", "projected to 665 dims · max distortion 0.123 · mean 0.022\n" ] } ], "source": [ "from sklearn.random_projection import GaussianRandomProjection, johnson_lindenstrauss_min_dim\n", "from sklearn.metrics import pairwise_distances\n", "\n", "X_hd = rng.normal(size=(400, 5000)) # 400 points in 5000-d\n", "eps = 0.3\n", "k_jl = johnson_lindenstrauss_min_dim(n_samples=400, eps=eps)\n", "print(f\"JL target dimension for n=400, eps={eps}: {k_jl} (from 5000)\")\n", "\n", "rp = GaussianRandomProjection(n_components=int(k_jl), random_state=SEED)\n", "X_rp = rp.fit_transform(X_hd) # (400, k_jl)\n", "D0 = pairwise_distances(X_hd)\n", "D1 = pairwise_distances(X_rp)\n", "iu = np.triu_indices(400, k=1) # unique pairs\n", "distortion = np.abs(D1[iu] / D0[iu] - 1.0) # |ratio - 1| per pair\n", "print(f\"projected to {X_rp.shape[1]} dims · max distortion {distortion.max():.3f} · mean {distortion.mean():.3f}\")" ] }, { "cell_type": "markdown", "id": "0c3c9c42", "metadata": {}, "source": [ "> **Interpretation.** From 5000 dimensions down to a few hundred, the worst pairwise distance is off by far less than $\\epsilon=0.3$. The structure that distance-based algorithms care about is intact, and the projection cost one matrix multiply.\n" ] }, { "cell_type": "markdown", "id": "7e28903a", "metadata": {}, "source": [ "### Exercise 7.4 — Verify the JL guarantee\n", "`Difficulty 2/5 · ~10 min`\n", "\n", "Write `max_distortion(X, X_proj)` returning the largest relative distortion $\\max_{i md_, \"10 dims must distort more than the JL dimension\"\n", "\n", "check(\"7.4 JL bound\", _jl_holds)" ] }, { "cell_type": "markdown", "id": "07ee6a8a", "metadata": {}, "source": [ "
Hint 1 (conceptual)You already have the two distance matrices. Index the upper triangle to get one value per pair, take the elementwise ratio, subtract 1, take absolute value, then `max`.
\n", "\n", "
Hint 2 (the line)`worst = np.abs(D1[iu] / D0[iu] - 1.0).max()`.
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Help — distortion comes out as 0 or nanIf you indexed the full matrices you included the zero diagonal (`D0[i,i] == 0`), so the ratio divides by zero. Restrict to `iu = np.triu_indices(n, k=1)` to keep only `i < j` pairs.
\n" ] }, { "cell_type": "code", "execution_count": 19, "id": "3e55f384", "metadata": { "execution": { "iopub.execute_input": "2026-06-10T18:47:21.348974Z", "iopub.status.busy": "2026-06-10T18:47:21.348827Z", "iopub.status.idle": "2026-06-10T18:47:21.380111Z", "shell.execute_reply": "2026-06-10T18:47:21.379475Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ ok ] 7.4 JL bound\n", "max distortion at the JL dimension: 0.123 (<= 0.3)\n" ] } ], "source": [ "def max_distortion(X, X_proj):\n", " from sklearn.metrics import pairwise_distances as _pd\n", " D0 = _pd(X); D1 = _pd(X_proj)\n", " iu = np.triu_indices(X.shape[0], k=1)\n", " return float(np.abs(D1[iu] / D0[iu] - 1.0).max())\n", "\n", "check(\"7.4 JL bound\", _jl_holds, required=True)\n", "print(f\"max distortion at the JL dimension: {max_distortion(X_hd, X_rp):.3f} (<= {eps})\")" ] }, { "cell_type": "markdown", "id": "20d74f13", "metadata": {}, "source": [ "> **Key takeaways.** Random projection trades a tiny, bounded distortion for enormous speed: it is $O(mdk)$ versus PCA's $O(md^2 + d^3)$, and needs no fitting, which is why it dominates for sparse million-dimensional NLP features. It does not find *interpretable* axes the way PCA does; it preserves geometry, not meaning. And despite folklore, it is a weak privacy mechanism: with side information the projection can be inverted, so use differentially-private methods for real privacy.\n" ] }, { "cell_type": "markdown", "id": "9f1ed7a6", "metadata": {}, "source": [ "## Part 6 — Nonlinear manifolds: unrolling the swiss roll\n", "\n", "> **Objectives.** See linear PCA fail on a curved manifold, then watch Kernel PCA and Locally Linear Embedding unroll it, and understand the assumption each method makes.\n", "\n", "The swiss roll is a 2D sheet curled up in 3D. Its intrinsic dimensionality is 2 (position along the roll, and width), but the two are tangled nonlinearly. Linear PCA can only pick a flat plane through the roll, so it cannot unroll it. Methods that respect *local* geometry can.\n" ] }, { "cell_type": "code", "execution_count": 20, "id": "7c1a016d", "metadata": { "execution": { "iopub.execute_input": "2026-06-10T18:47:21.381221Z", "iopub.status.busy": "2026-06-10T18:47:21.381127Z", "iopub.status.idle": "2026-06-10T18:47:21.474451Z", "shell.execute_reply": "2026-06-10T18:47:21.473965Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "swiss roll: (1500, 3); color = position along the roll (the thing to recover)\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.datasets import make_swiss_roll\n", "n_roll = 1000 if FAST else 1500\n", "X_roll, color = make_swiss_roll(n_samples=n_roll, noise=0.05, random_state=SEED)\n", "print(f\"swiss roll: {X_roll.shape}; color = position along the roll (the thing to recover)\")\n", "\n", "fig = plt.figure(figsize=(5, 4)); ax = fig.add_subplot(111, projection=\"3d\")\n", "ax.scatter(X_roll[:, 0], X_roll[:, 1], X_roll[:, 2], c=color, cmap=\"Spectral\", s=8)\n", "ax.set_title(\"swiss roll in 3D\"); ax.view_init(10, -70); plt.tight_layout(); plt.show()" ] }, { "cell_type": "markdown", "id": "7fb61e15", "metadata": {}, "source": [ "> **Interpretation.** The color is the true 1D coordinate along the roll. A good unrolling lays the points out so that color varies smoothly across one axis with no folds; a bad one mixes colors.\n" ] }, { "cell_type": "code", "execution_count": 21, "id": "964ee73a", "metadata": { "execution": { "iopub.execute_input": "2026-06-10T18:47:21.475544Z", "iopub.status.busy": "2026-06-10T18:47:21.475465Z", "iopub.status.idle": "2026-06-10T18:47:21.765386Z", "shell.execute_reply": "2026-06-10T18:47:21.764849Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Three reducers on the same roll: linear PCA, Kernel PCA (RBF), and LLE.\n", "from sklearn.decomposition import PCA, KernelPCA\n", "from sklearn.manifold import LocallyLinearEmbedding\n", "\n", "lin = PCA(n_components=2).fit_transform(X_roll)\n", "kpca = KernelPCA(n_components=2, kernel=\"rbf\", gamma=0.04).fit_transform(X_roll)\n", "lle = LocallyLinearEmbedding(n_components=2, n_neighbors=10,\n", " random_state=SEED).fit_transform(X_roll)\n", "\n", "fig, ax = plt.subplots(1, 3, figsize=(12, 3.6))\n", "for a, emb, name in zip(ax, [lin, kpca, lle], [\"linear PCA\", \"Kernel PCA (RBF)\", \"LLE\"]):\n", " a.scatter(emb[:, 0], emb[:, 1], c=color, cmap=\"Spectral\", s=8); a.set_title(name)\n", "plt.suptitle(\"unrolling the swiss roll: linear vs nonlinear\"); plt.tight_layout(); plt.show()" ] }, { "cell_type": "markdown", "id": "8d484df0", "metadata": {}, "source": [ "> **Interpretation.** Linear PCA keeps the roll rolled, neighboring colors overlap because it just found the flattest plane. Kernel PCA and LLE both spread the color smoothly along one axis: they unrolled the sheet. LLE in particular preserves *local* reconstruction weights, so it only needs the manifold to be locally flat.\n", "\n", "> **Common confusion:** these methods are sensitive to their neighborhood hyperparameters. LLE with too few neighbors shatters the manifold; with too many it degrades toward PCA. Kernel PCA's `gamma` plays the same role. There is no single right value; you tune against the downstream task or visual smoothness.\n", "\n", "> **Key takeaways.** Linear PCA fails when the data manifold is curved. Kernel PCA runs PCA in an implicit nonlinear feature space (eigen-decomposing the $m\\times m$ kernel matrix, so it is $O(m^3)$ and slow past ~10k points). LLE assumes only *local* linearity and solves an eigenvalue problem on local reconstruction weights. Both are unsupervised and both need their neighborhood scale tuned.\n" ] }, { "cell_type": "markdown", "id": "70402595", "metadata": {}, "source": [ "## Part 7 — t-SNE and why its distances lie\n", "\n", "> **Objectives.** Produce the canonical \"ten clusters\" t-SNE map of the digits, then run the experiment proving that t-SNE preserves *neighborhoods* but not *distances*, so cluster sizes and gaps in the plot are not quantitatively meaningful.\n", "\n", "t-SNE (van der Maaten and Hinton, 2008) converts high-dimensional distances into neighbor *probabilities* $p_{ij}$, defines matching probabilities $q_{ij}$ in 2D using a heavy-tailed Student-t kernel, and moves the 2D points to minimize the KL divergence $\\sum_{ij} p_{ij}\\log(p_{ij}/q_{ij})$ by gradient descent. The heavy tails let distinct clusters push apart without crushing far points together. It is the engine behind nearly every \"look how the classes separate\" figure in ML papers.\n" ] }, { "cell_type": "markdown", "id": "1b4a03fd", "metadata": {}, "source": [ "> **Runtime:** the t-SNE fit below takes a few seconds on CPU at full fidelity (`TSNE_ITERS=1000`); under `NB_FAST=1` it uses `TSNE_ITERS=250` and finishes faster. The map is rougher in FAST mode but the lesson holds.\n" ] }, { "cell_type": "code", "execution_count": 22, "id": "fc0c75c1", "metadata": { "execution": { "iopub.execute_input": "2026-06-10T18:47:21.766726Z", "iopub.status.busy": "2026-06-10T18:47:21.766651Z", "iopub.status.idle": "2026-06-10T18:47:23.421790Z", "shell.execute_reply": "2026-06-10T18:47:23.421458Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "t-SNE embedding (1797, 2) after 1000 iterations\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.manifold import TSNE\n", "# init='pca' is far more stable than random init; perplexity ~ how many neighbors count.\n", "tsne = TSNE(n_components=2, perplexity=30, init=\"pca\",\n", " max_iter=TSNE_ITERS, random_state=SEED)\n", "X_tsne = tsne.fit_transform(X_digits)\n", "print(f\"t-SNE embedding {X_tsne.shape} after {TSNE_ITERS} iterations\")\n", "\n", "plt.figure(figsize=(6.5, 5.5))\n", "sc = plt.scatter(X_tsne[:, 0], X_tsne[:, 1], c=y_digits, cmap=\"tab10\", s=8)\n", "plt.colorbar(sc, label=\"digit\"); plt.title(\"t-SNE of the digits (colored by true label)\")\n", "plt.xlabel(\"t-SNE 1\"); plt.ylabel(\"t-SNE 2\"); plt.tight_layout(); plt.show()" ] }, { "cell_type": "markdown", "id": "3d5e9378", "metadata": {}, "source": [ "> **Interpretation.** Ten reasonably separated islands, one per digit, with no labels used to place them. This is the plot t-SNE is famous for. The temptation is to read the *gaps* and *sizes* as meaningful. They are not, as the next experiment shows.\n" ] }, { "cell_type": "markdown", "id": "64aa41f5", "metadata": {}, "source": [ "The honest test of a visualization is whether it keeps the right *neighbors*. t-SNE's promise is local: a point's nearest neighbors in 2D should be its nearest neighbors in 64D. Its non-promise is global: the distance between two clusters in the plot need not match the distance in 64D. We measure both.\n" ] }, { "cell_type": "code", "execution_count": 23, "id": "3a321e32", "metadata": { "execution": { "iopub.execute_input": "2026-06-10T18:47:23.422882Z", "iopub.status.busy": "2026-06-10T18:47:23.422810Z", "iopub.status.idle": "2026-06-10T18:47:23.441895Z", "shell.execute_reply": "2026-06-10T18:47:23.441460Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "local: 58.4% of 10-NN preserved between 64-D and the t-SNE map\n", "global: correlation of inter-class centroid distances (64-D vs t-SNE) = 0.81\n" ] } ], "source": [ "# How well does t-SNE preserve LOCAL neighborhoods vs GLOBAL distances?\n", "from sklearn.neighbors import NearestNeighbors\n", "\n", "def knn_overlap(A, B, k=10):\n", " # mean fraction of each point's k nearest neighbors shared between spaces A and B\n", " nnA = NearestNeighbors(n_neighbors=k + 1).fit(A).kneighbors(A, return_distance=False)[:, 1:]\n", " nnB = NearestNeighbors(n_neighbors=k + 1).fit(B).kneighbors(B, return_distance=False)[:, 1:]\n", " return np.mean([len(set(a) & set(b)) / k for a, b in zip(nnA, nnB)])\n", "\n", "overlap = knn_overlap(X_digits, X_tsne, k=10)\n", "print(f\"local: {overlap:.1%} of 10-NN preserved between 64-D and the t-SNE map\")\n", "\n", "# global: per-class centroid distances, 64-D vs t-SNE, correlation\n", "def centroid_dists(Z):\n", " cents = np.array([Z[y_digits == c].mean(axis=0) for c in range(10)])\n", " iu = np.triu_indices(10, k=1)\n", " from sklearn.metrics import pairwise_distances as _pd\n", " return _pd(cents)[iu]\n", "corr = np.corrcoef(centroid_dists(X_digits), centroid_dists(X_tsne))[0, 1]\n", "print(f\"global: correlation of inter-class centroid distances (64-D vs t-SNE) = {corr:.2f}\")" ] }, { "cell_type": "markdown", "id": "68e094cf", "metadata": {}, "source": [ "> **Interpretation.** Local neighborhoods are largely preserved: most of each point's nearest neighbors stay its neighbors, which is what t-SNE optimizes for. But the correlation between inter-cluster distances in 64D and in the plot is weak. The gaps you see between islands are mostly an artifact of the optimization, not the data. Read t-SNE for *who is near whom*, never for *how far apart* or *how big*.\n" ] }, { "cell_type": "markdown", "id": "384b4668", "metadata": {}, "source": [ "### Exercise 7.5 — Perplexity changes the picture\n", "`Difficulty 2/5 · ~12 min`\n", "\n", "`perplexity` is roughly \"how many neighbors each point pays attention to\". Fit t-SNE at perplexities 5, 30, and 80 on a subset, and write `island_spread`, a crude measure of how spread-out the embedding is (mean distance of points from the global centroid). The check confirms the embedding *changes materially* with perplexity, which is the Distill warning made quantitative: the same data yields different-looking maps.\n" ] }, { "cell_type": "code", "execution_count": 24, "id": "6a50407f", "metadata": { "execution": { "iopub.execute_input": "2026-06-10T18:47:23.442793Z", "iopub.status.busy": "2026-06-10T18:47:23.442705Z", "iopub.status.idle": "2026-06-10T18:47:24.822083Z", "shell.execute_reply": "2026-06-10T18:47:24.821753Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ -- ] 7.5 spread varies with perplexity: not attempted yet — fill in the TODO above, then re-run.\n" ] }, { "data": { "text/plain": [ "False" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sub = slice(0, 600) # a subset keeps this exercise fast\n", "Xsub, ysub = X_digits[sub], y_digits[sub]\n", "\n", "def island_spread(emb):\n", " \"\"\"Mean Euclidean distance of points from their centroid. One float.\"\"\"\n", " emb = np.asarray(emb, dtype=float)\n", " center = emb.mean(axis=0)\n", " # TODO: average over points of the distance ||emb_i - center||.\n", " spread = None\n", " attempted(spread)\n", " return float(spread)\n", "\n", "def tsne_at(perp):\n", " return TSNE(n_components=2, perplexity=perp, init=\"pca\",\n", " max_iter=TSNE_ITERS, random_state=SEED).fit_transform(Xsub)\n", "\n", "_embs = {p: tsne_at(p) for p in (5, 30, 80)}\n", "\n", "def _spread_changes():\n", " spreads = {p: island_spread(e) for p, e in _embs.items()}\n", " print(\" spread by perplexity:\", {p: round(s, 2) for p, s in spreads.items()})\n", " vals = list(spreads.values())\n", " assert max(vals) > 0, \"spread must be positive\"\n", " rel = (max(vals) - min(vals)) / max(vals)\n", " assert rel > 0.1, f\"perplexity should change the layout by >10%, got {rel:.1%}\"\n", "\n", "check(\"7.5 spread varies with perplexity\", _spread_changes)" ] }, { "cell_type": "markdown", "id": "931a4394", "metadata": {}, "source": [ "
Hint 1 (conceptual)Subtract the centroid from every point, take the per-row Euclidean norm, then average.
\n", "\n", "
Hint 2 (the line)`spread = np.linalg.norm(emb - center, axis=1).mean()`.
\n", "\n", "
Help — spread is a single number per point instead of a scalar`np.linalg.norm(..., axis=1)` gives one norm per row (shape `(n,)`); call `.mean()` on that to collapse to one float. Without `axis=1` you get the Frobenius norm of the whole array, which is not what we want.
\n" ] }, { "cell_type": "code", "execution_count": 25, "id": "817ff2ac", "metadata": { "execution": { "iopub.execute_input": "2026-06-10T18:47:24.823123Z", "iopub.status.busy": "2026-06-10T18:47:24.823042Z", "iopub.status.idle": "2026-06-10T18:47:25.064864Z", "shell.execute_reply": "2026-06-10T18:47:25.064280Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " spread by perplexity: {5: 48.76, 30: 22.22, 80: 9.79}\n", "[ ok ] 7.5 spread varies with perplexity\n" ] }, { "data": { "image/png": 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/M2eIm5ub03AfX19fIiMjnXIm+fr6Ohxv3759/PvvvxUOFzpzBr3Tlf2gi42NpUOHDvb1Xl5eDBkyhC+//BKLxYLBYMDd3b3c/DBluVjKjlX2b2XKlufQoUOEh4c7DS9q1KhRhfucvq9Op7MPbSxTv379c+57Nk8//TRDhw6lYcOGNG3alAEDBjBmzBiaN2/+n45bkdNzcQH4+/sDpcPlTg+QnHmdaWlpZGdn89FHH/HRRx+Ve+yy18O+ffvYtWvXBb1uykRERODp6emwrmHDhgAkJSXRsWPH8z7Pmdd0ugYNGjitO1eesn379qGUKndfwGk41ujRo/nyyy/5+eefmTBhAn369Knw2Beisu/Xu+66i++++46BAwdSp04d+vfvz6hRoxgwYMBFrU+Zs73mTlenTh2H4BVU/rV0vs9FZezYsYPHHnuMP//80yloe/rn7PXXX8+UKVOYM2cOTzzxBDk5OSxatIj77rvP/hl76NAhwPmzxmg0Uq9ePfv2iyE2NpapU6fy2muvMWfOHLp168Y111zDTTfdJEP3hBBCOJCglBBCCCejRo2iW7dufP/99/z++++8/PLLvPjiiyxYsICBAwditVrp168fmZmZPPTQQ8THx+Pp6cmxY8e4+eabnRIaVzQLXEXrlVL2/9tsNvr168eDDz5YbtmyIEF5IiIiAMrNxxMSEoLZbKagoABfX1/Cw8NZtmwZSimHQNnx48cdjhUeHu6w/nTHjx8nICDgspuRrHv37hw4cICFCxfy+++/88knn/D666/zwQcfOPRwu1gq87yDc3Cv7HV10003VZiDqyyQZrPZaNasGa+99lq55aKios6rzhU53/OcLWB5oefXNI3FixeX+7ieGfzMyMhgw4YNAOzcuRObzebQa+Zi1Kcy79eQkBC2bNnCb7/9xuLFi1m8eDEzZ85k7NixfP755xetPmUu9DUHlX+Oz/e5OJfs7Gx69OiBj48PTz/9NHFxcbi5ubFp0yYeeughh89Zf39/rr76antQat68eZhMJm666abzOmeZM28WlLFarZWe1fPVV1/l5ptvtn+u3HPPPcyYMYN//vmHyMjIC6qXEEKI2keCUkIIIcoVHh7OXXfdxV133UVqaiqtW7fmueeeY+DAgWzbto29e/fy+eefM3bsWPs+VTEUJy4ujvz8fPr27Xve+0ZERNgT7J4pOTkZNzc3vL29AWjZsiWffPIJu3btchheVZYIuWXLlkBpT4rg4GD7D/vTrVu3zl6uIjExMSxdupT8/HyHH6l79uw55/XExMRgs9lITEx06I1x5ixiFanohyZAQEAA48ePZ/z48eTn59O9e3eeeuqpCwpKne08/0VwcDDe3t5YrdZzvh7i4uLYunUrffr0ueD6JCcnU1BQ4NBbau/evQD2BOUX4zxlyhs+uXfvXqeZ5E4XFxeHUorY2NizBmjLTJo0iby8PGbMmMG0adN44403mDp16ln3OZ/rOp/3q9FoZMiQIQwZMgSbzcZdd93Fhx9+yOOPP37evf+q6jUHlX+Oz/e5OJfly5eTkZHBggUL6N69u319YmJiueXHjh3L0KFDWb9+PXPmzKFVq1YkJCTYt8fExAClnzWn93otKSkhMTHR4Tnz9/cvd0bQQ4cOOex7rse9WbNmNGvWjMcee4zVq1fTpUsXPvjgA4eh00IIIa5sklNKCCGEA6vV6jT8LiQkhIiICPuQtbI75af3MlBKXdB07ucyatQo1qxZw2+//ea0LTs7G4vFctb9r7/+eo4cOeIQMEtPT2fhwoX07t3b3ktk6NChuLi48N5779nLKaX44IMPqFOnDp07d7avHz58OIsWLXKY5n3p0qXs3buXkSNHnrU+gwYNwmKx8P7779vXWa1W3n777bPuB3DVVVcBONQRqNS+AJ6enuX+0MzIyHBY9vLyon79+uUOUfwv5/mv9Ho9w4cPZ/78+Wzfvt1pe1pamv3/o0aN4tixY3z88cdO5YqKiigoKDjn+SwWCx9++KF9uaSkhA8//JDg4GDatGlz0c5T5ocffnAIoK5bt461a9cycODACvcZNmwYer2e6dOnO/X6UUo5PLfz5s3j22+/5YUXXuDhhx9m9OjRPPbYY/ZAW0XKgnKVeU4r+3498zWn0+nsvdwu5HXn6enp9Ll1sVT2OT6f56IyyvucLSkpcXr/lxk4cCBBQUG8+OKLrFixwqmXVN++fTEajbz11lsOx/z000/JyclxmMUzLi6Of/75h5KSEvu6Mz/zoOLXRm5urtNnc7NmzdDpdBf8uSKEEKJ2kp5SQgghHOTl5REZGcmIESNo0aIFXl5e/PHHH6xfv55XX30VgPj4eOLi4rj//vs5duwYPj4+zJ8/3yk/y8XwwAMP8OOPP3L11Vdz880306ZNGwoKCti2bRvz5s0jKSnJPk19eaZNm8Z3333H8OHDmTp1Kr6+vnzwwQeYzWaef/55e7nIyEimTJnCyy+/jNlspl27dvzwww/8/fffzJkzx2HIyiOPPMLcuXPp1asX9957L/n5+bz88ss0a9bMKUnymYYMGUKXLl14+OGHSUpKokmTJixYsKBSP6jbtGnD8OHDeeONN8jIyKBjx46sWLHCHlQ4V6+FNm3a8P777/Pss89Sv359QkJC6N27N02aNKFnz560adOGgIAANmzYwLx58xyml09KSiI2NpZx48Yxa9asc57njz/+4LXXXiMiIsIpp9d/8cILL7Bs2TI6dOjA7bffTpMmTcjMzGTTpk388ccfZGZmAjBmzBi+++477rzzTpYtW0aXLl2wWq3s3r2b7777jt9++422bdue9VwRERG8+OKLJCUl0bBhQ7799lu2bNnCRx99ZM8PdDHOU6Z+/fp07dqViRMnYjKZeOONNwgMDKxwKByUBg+effZZpk2bRlJSEtdeey3e3t4kJiby/fffM2HCBO6//35SU1OZOHEivXr1sj+v77zzDsuWLePmm29m5cqVFQ7jKwvAPfroo4wePRoXFxeGDBnilG8LKv9+ve2228jMzKR3795ERkZy6NAh3n77bVq2bEnjxo3txyvrJZaUlHTWx65NmzZ8++23TJ06lXbt2tnzxl0MlX2OK/tcVFbnzp3x9/dn3Lhx3HPPPWiaxuzZs50CXmVcXFwYPXo077zzDnq9nhtuuMFhe3BwMNOmTWP69OkMGDCAa665hj179vDee+/Rrl07hyDWbbfdxrx58xgwYACjRo3iwIEDfPnll8TFxTkcMy4uDj8/Pz744AO8vb3x9PSkQ4cObN26lcmTJzNy5EgaNmyIxWJh9uzZ9sCyEEIIYVetc/0JIYS45JlMJvXAAw+oFi1aKG9vb+Xp6alatGih3nvvPYdyO3fuVH379lVeXl4qKChI3X777Wrr1q1O04OPGzdOeXp6Op2nR48eKiEhwWl9TEyMGjx4sMO6vLw8NW3aNFW/fn1lNBpVUFCQ6ty5s3rllVdUSUnJOa/pwIED6rrrrlM+Pj7K3d1d9e7dW61bt86pnNVqVc8//7yKiYlRRqNRJSQkqC+//LLcY27fvl31799feXh4KD8/P3XjjTeqEydOnLMuSimVkZGhxowZo3x8fJSvr68aM2aMfQr10x+7J598Up3ZVBcUFKhJkyapgIAA5eXlpa699lq1Z88eBagXXnjBXq686eVPnDihBg8erLy9vRVgn9r92WefVe3bt1d+fn7K3d1dxcfHq+eee87hsd22bZsC1MMPP3zO69u9e7fq3r27cnd3V4B9avmy60lLS3MoX15dATVp0qRyj5+SkqImTZqkoqKilIuLiwoLC1N9+vRRH330kUO5kpIS9eKLL6qEhATl6uqq/P39VZs2bdT06dNVTk7OWa+h7PW5YcMG1alTJ+Xm5qZiYmLUO++841S2suep6JoSExMVoF5++WX16quvqqioKOXq6qq6deumtm7d6lC2vNeEUkrNnz9fde3aVXl6eipPT08VHx+vJk2apPbs2aOUUmrYsGHK29tbJSUlOey3cOFCBagXX3zRoZ5PPvmkQ7lnnnlG1alTR+l0OofnKiYmxv78lqnM+3XevHmqf//+KiQkRBmNRhUdHa3uuOMOdfz4cYdjBQUFqY4dOzpd75ny8/PV//73P+Xn56cAFRMTo5RSatmyZQpQc+fOdShf9pif/n6r6DNJqfN7LZ3ruahIee+DVatWqY4dOyp3d3cVERGhHnzwQfXbb78pQC1btszpGOvWrVOA6t+/f4Xneeedd1R8fLxycXFRoaGhauLEiSorK8up3Kuvvqrq1KmjXF1dVZcuXdSGDRtUjx497J8bZRYuXKiaNGmiDAaD/TE9ePCguuWWW1RcXJxyc3NTAQEBqlevXuqPP/4462MghBDiyqMpVcHtFiGEEEJcFrZs2UKrVq348ssvufHGG6vkHO+99x4PPvggBw4cKDdxfG3Ts2dP0tPTyx0meLGV9UJ7+eWXz6snTW23c+dOEhISWLRokcPQMlGxrVu30rJlS7744gvGjBlT09URQgghzklySgkhhBCXkaKiIqd1b7zxBjqdziEZ8sW2bNky7rnnnisiICUuDcuWLaNTp04SkDoPH3/8MV5eXgwbNqymqyKEEEJUiuSUEkIIIS4jL730Ehs3bqRXr14YDAYWL17M4sWLmTBhgn1q+qowd+7cKju2EOWZNGkSkyZNqulqXBZ++ukndu7cyUcffcTkyZPLzfclhBBCXIokKCWEEEJcRjp37sySJUt45plnyM/PJzo6mqeeeopHH320pqsmhKghd999NykpKQwaNIjp06fXdHWEEEKISpOcUkIIIYQQQgghhBCi2klOKSGEEEIIIYQQQghR7SQoJYQQQgghhBBCCCGqnQSlhBBCCCGEEEIIIUS1k6CUEEIIIYQQQgghhKh2EpQSQgghhBBCCCGEENVOglJCCCGEEEIIIYQQotpJUEoIIYQQQgghhBBCVDsJSgkhhBBCCCGEEEKIaidBKSGEEEIIIYQQQghR7SQoJYQQQgghhBBCCCGqnQSlhBBCCCGEEEIIIUS1k6CUEEIIIYQQQgghhKh2EpQSQgghhBBCCCGEENVOglJCCCGEEEIIIYQQotpJUEoIIYQQQgghhBBCVDsJSgkhhBBCCCGEEEKIaidBKSGEEEIIIYQQQghR7SQoJYQQQgghhBBCCCGqnQSlhBBCCCGEEEIIIUS1k6CUEEIIIYQQQgghhKh2EpQSQgghhBBCCCGEENVOglJCCCGEEEIIIYQQotpJUEqICixfvhxN01i+fHmVnaNnz5707Nmzyo4vhBDi4pF2QQghxLlIWyHE+ZGglBCXkOTkZJ566im2bNlS01WpUFlDW97fP//8U9PVE0KIWuVyaBd27NjByJEjqVevHh4eHgQFBdG9e3d++umncsvv2rWLAQMG4OXlRUBAAGPGjCEtLa2aay2EELXH5dBWAOzbt4/Ro0cTGRmJh4cH8fHxPP300xQWFjqVXb16NV27dsXDw4OwsDDuuece8vPza6DWoqoZaroCQlzJfv/9d4fl5ORkpk+fTt26dWnZsmXNVKqS7rnnHtq1a+ewrn79+jVUGyGEqB0ux3bh0KFD5OXlMW7cOCIiIigsLGT+/Plcc801fPjhh0yYMMFe9ujRo3Tv3h1fX1+ef/558vPzeeWVV9i2bRvr1q3DaDTW4JUIIcTl4XJsK44cOUL79u3x9fVl8uTJBAQEsGbNGp588kk2btzIwoUL7WW3bNlCnz59aNy4Ma+99hpHjx7llVdeYd++fSxevLgGr0JUBQlKiStGYWEhHh4eNV0NB5fzl+9u3boxYsSImq6GEEJcMGkXLo5BgwYxaNAgh3WTJ0+mTZs2vPbaaw5Bqeeff56CggI2btxIdHQ0AO3bt6dfv37MmjXLoawQQlwKpK24OGbPnk12djYrV64kISEBgAkTJmCz2fjiiy/IysrC398fgEceeQR/f3+WL1+Oj48PAHXr1uX222/n999/p3///jV2HeLik+F7osY99dRTaJrG7t27GTVqFD4+PgQGBnLvvfdSXFzsVP7LL7+kTZs2uLu7ExAQwOjRozly5IhDmZ49e9K0aVM2btxI9+7d8fDw4JFHHgFKP9Cuvvpqfv/9d1q2bImbmxtNmjRhwYIFlarv2rVrGTBgAL6+vnh4eNCjRw9WrVpl375r1y7c3d0ZO3asw34rV65Er9fz0EMPOdSzbDz48uXL7T2Pxo8fbx8SN2vWLJ588klcXFzKHd4wYcIE/Pz8yn2sqlpeXh4Wi6XazyuEqN2kXegJXJ7tQhm9Xk9UVBTZ2dkO6+fPn8/VV19tD0gB9O3bl4YNG/Ldd99Vcy2FEJczaSt6ApdPW5GbmwtAaGiow/rw8HB0Op090Jabm8uSJUu46aab7AEpgLFjx+Ll5SVtRS0kQSlxyRg1ahTFxcXMmDGDQYMG8dZbbzndMX3uuecYO3YsDRo04LXXXmPKlCksXbqU7t27O33xzcjIYODAgbRs2ZI33niDXr162bft27eP66+/noEDBzJjxgwMBgMjR45kyZIlZ63jn3/+Sffu3cnNzeXJJ5/k+eefJzs7m969e7Nu3ToAGjduzDPPPMPs2bP58ccfASgoKODmm2+2j5suT+PGje3bJkyYwOzZs5k9ezbdu3dnzJgxWCwWvv32W4d9SkpKmDdvHsOHD8fNza3CeptMJtLT0yv1V1njx4/Hx8cHNzc3evXqxYYNGyq9rxBCVIa0C5dXu1BQUEB6ejoHDhzg9ddfZ/HixfTp08e+/dixY6SmptK2bVunfdu3b8/mzZsrfS4hhCgjbcXl0VaUBdFuvfVWtmzZwpEjR/j22295//33ueeee/D09ARg27ZtWCwWp7bCaDTSsmVLaStqIyVEDXvyyScVoK655hqH9XfddZcC1NatW5VSSiUlJSm9Xq+ee+45h3Lbtm1TBoPBYX2PHj0UoD744AOn88XExChAzZ8/374uJydHhYeHq1atWtnXLVu2TAFq2bJlSimlbDabatCggbrqqquUzWazlyssLFSxsbGqX79+9nVWq1V17dpVhYaGqvT0dDVp0iRlMBjU+vXrHerSo0cP1aNHD/vy+vXrFaBmzpzpVO9OnTqpDh06OKxbsGCBQx0rMnPmTAVU6u9cVq1apYYPH64+/fRTtXDhQjVjxgwVGBio3Nzc1KZNm865vxBCnIu0Cz3sy5dDu1DmjjvusO+j0+nUiBEjVGZmptO1fPHFF077PvDAAwpQxcXFlT6fEOLKJm1FD/vy5dJWPPPMM8rd3d1hv0cffdShzNy5cxWg/vrrL6f9R44cqcLCwip1LnH5kJxS4pIxadIkh+W7776b9957j19++YXmzZuzYMECbDYbo0aNcojGh4WF0aBBA5YtW2bvXgvg6urK+PHjyz1XREQE1113nX3Zx8eHsWPH8uKLL3LixAnCwsKc9tmyZQv79u3jscceIyMjw2Fbnz59mD17NjabDZ1Oh06nY9asWbRo0YKBAweyYcMGHnvssXLvDlfW2LFjmThxIgcOHCAuLg6AOXPmEBUVRY8ePc6671VXXXXOOziV1blzZzp37mxfvuaaaxgxYgTNmzdn2rRp/PrrrxflPEIIIe3C2V0q7UKZKVOmMGLECJKTk/nuu++wWq2UlJTYtxcVFQGlz8OZyu7UFxUVlbtdCCEqIm3F2V1KbUXdunXp3r07w4cPJzAwkJ9//pnnn3+esLAwJk+eDJy7rSjbLmoPCUqJS0aDBg0cluPi4tDpdCQlJQGl3WWVUk7lyri4uDgs16lTp8IkgPXr10fTNId1DRs2BCApKancBmXfvn0AjBs3rsJryMnJsSfoi4uL46mnnuKBBx6gadOmPP744xXuVxnXX389U6ZMYc6cOTzxxBPk5OSwaNEi7rvvPqdrOVN4eDjh4eH/6fxnU79+fYYOHcqCBQuwWq3o9foqO5cQ4soh7cLZXWrtQnx8PPHx8UDpj6D+/fszZMgQ1q5di6ZpuLu7A6XDQc5UltOkrIwQQlSWtBVnd6m0Fd988w0TJkxg7969REZGAjBs2DBsNhsPPfQQN9xwA4GBgedsK6SdqH0kKCUuWWd+SNpsNjRNY/HixeUGPby8vByWL/YHls1mA+Dll1+ucKrVM+tQNl1rcnIyGRkZ5TZUleXv78/VV19tb1DmzZuHyWTipptuOue+RUVF5OTkVOo8F1rHqKgoSkpKKCgocEhKKIQQF4u0C44u9XZhxIgR3HHHHezdu5dGjRrZf9gcP37cqezx48cJCAiQXlJCiP9M2gpHl0pb8d5779GqVSt7QKrMNddcw6xZs9i8eTN9+/Y9Z1sRERFRqfqIy4cEpcQlY9++fcTGxtqX9+/fj81mo27dukDpXQOlFLGxsfY7Ehdq//79KKUcGq29e/cC2M93prLurj4+PvTt2/ec5/jggw9YsmQJzz33HDNmzOCOO+5g4cKFZ93nXHcrxo4dy9ChQ1m/fj1z5syhVatW9ilVz+bbb7+tsBvymZRSlSp3poMHD+Lm5ubUqAohxIWSduHybhfKhliU/aCpU6cOwcHB5U6MsW7dugp/rAkhxNlIW3F5tBUpKSn23mCnM5vNAPYZvZs2bYrBYGDDhg2MGjXKXq6kpIQtW7Y4rBO1g8y+Jy4Z7777rsPy22+/DcDAgQOB0u6der2e6dOnO33oKaWcxmifTXJyMt9//719OTc3ly+++IKWLVtWGOVv06YNcXFxvPLKK+Tn5zttP32q1cTERB544AGGDx/OI488wiuvvMKPP/7IF198cdZ6lc06ceYsIGUGDhxIUFAQL774IitWrKjUHQ44NR68Mn/nUt6Uslu3buXHH3+kf//+6HTysSKEuDikXbg82oXU1FSndWazmS+++AJ3d3eaNGliXz98+HAWLVrkMA370qVL2bt3LyNHjqxU3YUQ4nTSVlwebUXDhg3ZvHmzPYhX5uuvv0an09G8eXMAfH196du3L19++SV5eXn2crNnzyY/P1/ailpIekqJS0ZiYiLXXHMNAwYMYM2aNXz55Zf873//o0WLFkDpXYZnn32WadOmkZSUxLXXXou3tzeJiYl8//33TJgwgfvvv79S52rYsCG33nor69evJzQ0lM8++4yUlBRmzpxZ4T46nY5PPvmEgQMHkpCQwPjx46lTpw7Hjh1j2bJl+Pj48NNPP6GU4pZbbsHd3Z33338fgDvuuIP58+dz77330rdv3wq7ncbFxeHn58cHH3yAt7c3np6edOjQwX73x8XFhdGjR/POO++g1+u54YYbKnW9F3M8+PXXX4+7uzudO3cmJCSEnTt38tFHH+Hh4cELL7xwUc4hhBAg7ULZNV7q7cIdd9xBbm4u3bt3p06dOpw4cYI5c+awe/duXn31VYcetI888ghz586lV69e3HvvveTn5/Pyyy/TrFmzSt+NF0KI00lbcXm0FQ888ACLFy+mW7duTJ48mcDAQBYtWsTixYu57bbbHK7tueeeo3PnzvTo0YMJEyZw9OhRXn31Vfr378+AAQMuSn3EJaRa5/oTohxl07nu3LlTjRgxQnl7eyt/f381efJkVVRU5FR+/vz5qmvXrsrT01N5enqq+Ph4NWnSJLVnzx57mR49eqiEhIRyzxcTE6MGDx6sfvvtN9W8eXPl6uqq4uPj1dy5cx3KnTmda5nNmzerYcOGqcDAQOXq6qpiYmLUqFGj1NKlS5VSSr355ptO08UqpdThw4eVj4+PGjRokEM9T5/OVSmlFi5cqJo0aaIMBkO5U7uuW7dOAap///7lXl9Ve/PNN1X79u1VQECAMhgMKjw8XN10001q3759NVIfIUTtI+1CD4dyl3q78PXXX6u+ffuq0NBQZTAYlL+/v+rbt69auHBhueW3b9+u+vfvrzw8PJSfn5+68cYb1YkTJ6q51kKIy520FT0cyl3qbYVSSq1du1YNHDhQhYWFKRcXF9WwYUP13HPPKbPZ7FT277//Vp07d1Zubm4qODhYTZo0SeXm5tZArUVV05S6wEQBQlwkTz31FNOnTyctLY2goKAqP1/dunVp2rQpixYtqvJzVYWtW7fSsmVLvvjiC8aMGVPT1RFCiItO2oXzI+2CEOJKJG3F+ZG2QlyqJPmLEJeZjz/+GC8vL4YNG1bTVRFCCHEJkHZBCCHEuUhbIS5VklNKiMvETz/9ZM/fNHnyZHtCQyGEEFcmaReEEEKci7QV4lInQSkhLhN33303KSkpDBo0iOnTp9d0dYQQQtQwaReEEEKci7QV4lInOaWEEEIIIYQQQgghRLWTnFJCCCGEEEIIIYQQotpd9sP3bDYbycnJeHt7o2laTVdHCCEua0op8vLyiIiIQKerPfctpK0QQoiLR9oKIYQQ51LZtuKyD0olJycTFRVV09UQQoha5ciRI0RGRtZ0NS4aaSuEEOLik7ZCCCHEuZyrrbjsg1Le3t5A6YX6+PjUcG2EEOLylpubS1RUlP2ztbaQtkIIIS4eaSuEEEKcS2Xbiss+KFXWtdbHx0caDyGEuEhq27AFaSuEEOLik7ZCCCHEuZyrrag9g8CFEEIIIYQQQgghxGWjSoNSVquVxx9/nNjYWNzd3YmLi+OZZ55BKWUvo5TiiSeeIDw8HHd3d/r27cu+ffuqslpCCCGEEEIIIYQQooZVaVDqxRdf5P333+edd95h165dvPjii7z00ku8/fbb9jIvvfQSb731Fh988AFr167F09OTq666iuLi4qqsmhBCCCGEEEIIIYSoQVWaU2r16tUMHTqUwYMHA1C3bl2+/vpr1q1bB5T2knrjjTd47LHHGDp0KABffPEFoaGh/PDDD4wePboqqyeEEEIIIYQQQgghakiV9pTq3LkzS5cuZe/evQBs3bqVlStXMnDgQAASExM5ceIEffv2te/j6+tLhw4dWLNmTbnHNJlM5ObmOvwJIYQQQgghhBBCiMtLlfaUevjhh8nNzSU+Ph69Xo/VauW5557jxhtvBODEiRMAhIaGOuwXGhpq33amGTNmMH369KqsthBCCCGEEEIIIYSoYlUalPruu++YM2cOX331FQkJCWzZsoUpU6YQERHBuHHjLuiY06ZNY+rUqfbl3NxcoqKiLlaVhbhoig9kkTl3L7YCC8ZILwLHJaB3q9K3nBBCCHHBlFLk/3WU/NXJoNPw7hWFW3wAWd/txZpbgmucL35D4rDmmFBmG4YgdzSdZt+3YN0JinZkoPMw4NM7GpcQjxq+IiFEbbQjfQdPr3maE4Un6BDegcc7Po630bumqyWEuEBV+gv5gQce4OGHH7bnhmrWrBmHDh1ixowZjBs3jrCwMABSUlIIDw+375eSkkLLli3LPaarqyuurq5VWW0h/jNLZjHpn2yHkxNNliTmkvrWJsIeaIemaTVbOSGEEKIchRtSyFmcZF/OXrAf9BpYSxszS2ohhdvTUXlmAFzqeBF8a1N0Hi7krzxGzs+JpTtqULw7k7CpbdD7yHc2IcR/k1GUwf7s/UR4RuDh4sEtv91CkaUIheL3pN8psZbwRq83arqaQogLVKVBqcLCQnQ6x7RVer0em80GQGxsLGFhYSxdutQehMrNzWXt2rVMnDixKqsmRJWwZBaTMWcn5uQCe0CqjDXThDWjGEOQe81UTgghhDiL4r1Zziutjo1ZWUAKwJycT87vh/C/tj4F605Lu6BAFVtJ+2gbLhGe+PSLwSVYek0JIc7f6uTV3PPnPZisJjQ0OoZ3pNBSaN9uVVb+Pvp3DdZQCPFfVWlQasiQITz33HNER0eTkJDA5s2bee2117jlllsA0DSNKVOm8Oyzz9KgQQNiY2N5/PHHiYiI4Nprr63Kqglx0SmlSPvoX6zZporLWGzVWCMhhBCi8nSeLqVT4FS2qVJgTikAQDM4z51jSS/CklGEaX82oVPboPcyXrzKCiFqPaUU0/6eRom1pHQZxZrjzpNhebp4VnfVhBAXUZXOvvf2228zYsQI7rrrLho3bsz999/PHXfcwTPPPGMv8+CDD3L33XczYcIE2rVrR35+Pr/++itubm5VWTUhLjplsp41IKW56clbk0zJiYJqrJUQQghROd69otCdb+Do5JB0nz7Rpcu6M4aoK7AVWjDtz/7vFRRC1GoWmwWbsjksZxZnos4cfnCG1qGteWfzO/yW9BtKnb2sEOLSo6nL/J2bm5uLr68vOTk5+Pj41HR1xBVM2RTHHlnpvMHDAEUWh+F8geOa4N44sPoqJ0Ql1dbP1Np6XUJcbLZCM0U7MshauB8spzVcGrg28se023mIX8T0TuhcDZiScijelUn+uhOoIotDmcAxjXFPCKrq6otqUls/U2vrdV3qSqwlPLH6CRYnLsagGbizxZ3c2PhGUgtT+b/l/8eBnANYlRUdOjRNw6qs9n116LBhw6AZsCgLNza+kYfbP3zW81ltVjKKM/B39cdF71LVlyfEFauyn6lV2lNKiCuJptNwiXDuPqxZbE75pbIW7KumWl0ClILdv8A/H8DRjTVdGyGEuKIom8KcUoAlu7hS5XUeLhhCPRwDUgAKfK+qW+4+tqLSH4iudX3xHRiL/9C4kwcr/Ufva0RZbCirDGEXQjj78N8P+eXgL9iUjRJbCW9tfosu33RhyA9DOF5wnEivSDQ0gjyCuLP5nWic6pFpOzne2KJKA+Fzds0huzi7wnPtydxD//n96TO3D12+6cLyI8ur8MqEEJUh89MLcREF39aME29twpZdYl+nSpy/hJe3rtawmCBlB7h6g1cofNwbMk4Lwl3zNrQeW3P1E0KIK4Q1v4S0T7ZjOTls3K15MK7RXmgGHcYYH4p3ZKCsCo+WwbiEnrqpYvB3Aw2HGyo6DwPm1EI0Vz3KdLKXgg4MQe7ofUqH/BVuTSXnlyRsRSeToZ9s6qw5JWR+vQfXuBME3dIUTS/3RIUQp2xO3ew0RM9iKw0yFZgLcNG7sOmmTRj0Bob/OPycxyu2lh+EV0pxz7J7SC9KLy1nKeb/lv8ff4z8A383//94FUKICyVBKSEuIp2HC271/SnclHLWRLHGmFraJTz3OMwaDJkHSpe9QiE/xbHM4oeh1Rh7HhIhhBBVI+eXRCypp/IYFv+bRvG/aY6FdJD311FCJrbAGOkNgN7biE+/GHJ/P2Qvpg9wI+vrPdg7KGhgrOtDwKh4NJ2G6XAumd/sceoZfDrTgdLhfe5NZRifEOKUaO9oNqVschiWV8aGjcziTAqthfjofcgvyXcKYGloKBQ6TUeL4BaEeoSWe55iazHJ+cn2ZYWixFbCodxDEpQSogbJrSohLhJbsQVzSkFpwOmMgJQxzrc0+evJL/GBY5vUTCWr2u+PQlbSqeUzA1IA5gKwOX/pEEIIcXFYckxk/3iAol2Z555JzwbYFPkrjzmsLtziGLwyH80v/U/Zb0EFnm3CMPi5UpKcT/6q5LMGpOynK7Scu5AQ4ooyudVkoryj7MunD88DcNW78vOBn7EpG4PrDbZv12k63AxuDK43mJbBLRnWYBh1ferS49seXP391aw4ssLhOG56N4Ldg9Gd9hPYoBmI9I6swqsTQpyL9JQS4iIo3JZO5re7S3NwGHV4tg+lcFsGAN5dIvDuE412JfQMytgP5dzlcqRB0kqI61kdNRJCiCuKtcBM6jtbsBWYwVbJuWwUWLJN2Eqs6Ix6TIdysaQWVmrXvL+OkvNLYuXOY9BwjfOtXFkhRK2jlGJb+jayirNoGtSUQPfSSX+C3IOYf818dmbs5ETBCWZun8muzF32HlEl1hKeX/c8xwuOc0/re3DRubD08FL83fyZ0mYKCYEJALy8/mVm75yNQpFtyubeZfcyd8hcGvg3AEDTNF7r+RqTlk4ityQXg87As12eJchdem9eCnLMFlJLLES5GXGTYd5XFAlKCfEf2QrNZH6969Td6BIbhdvSiXi8E9qZU2OfZM0rIfePQ1jSi9B5G1ElVjSjHu+udezDJy5Lke3h+L+c/Xa5gq+vhwcTwehRXTUTQogrQvHuTGx5JecueIaSpFxS39xE8MQWmPY5z7BnpwMUaEY9thJL5QNSOg2P1iEU/puOe8sgdHo9aKVDBYUQtZ9SiidXP8n3+78HwNPgycf9P6ZZcDMA9JqeVcdW8fG2j7Epm8MQvbL/f737a6a2ncrElhOZ2HKi0zn+OvqXvaxCYVM21p1YZw9KAbQMacnSkUs5ln+MYI9gfIy1NKXGWRQUFHD8+HG8vb0JDS1/qGN1+/p4BvfvOYJVQZCLga9b1KOZt/xOuFJIUEqI/8iSbXIaHqGKrFgLzRi8nL9sW3NLOPHqhlOJYstoULQtndB7WjkknL2s9H0KjqyFE/+evZylGHKPQVCDs5cTQghxfsq5F6LzcsFWaLa3VZqHAa+O4RRuS8OadiohsCWrmLw/j5TOvncGQ7gnPr2jS2+opBSiSqzkLDxY+XrZFIXrU0BB7pIke13cWwYTMLIRmv4K6E0sxBVs/Yn19oAUQJG1iKfWPMXA2IFkFGVwvOA4Sw8vPesxTh91YLaaWX50Ofkl+XSK6ESYZxhB7kEczjuMTZV+wCiUvTfW6dwMbsT5xV2kK7u8HDlyhNmzZ1NSUnrzolOnTjRu3JiMjAzCwsIIDw+v/joVl/B/u4/Yf05lmi1M2JHEmo61NN2JcCJBKSH+I1tR+fkxTjy7Fr2/KwE3xOMafeouTMG6484BKSjtXKQUhVvS8L3qMg1KuXpB3a7nDkrpDOATUT11EkKIK4h740By/Vyx5poADWwKW7HF4eaJKrSQt+KIc74pBdZcE74DYyncmELJ4bzS9a46Am5ohMHLSOacQnvZ81a2z2nnLdqSRkG0D16dpU0QojZLKXTMM2pTNg5kH+DtzW+jQ4dFVZxvzqAZsCgL4xPGU2ItYXv6dmasncHurN0AeBg8+GzAZzzQ7gFu+e0WCsylEzx0juhM3+i+VXdRl6Fvv/3WHpACWLNmDWvWrLEvX3311bRt27Za65RYaHJojmxAUlEJNqXQVXP6k/z8fKxWKz4+PldG6pVLhASlhPgPzKmFZHy+o8Lt1iwTae9vJXRqG1yCS+88K/PZs85e9neLTfnnKKDBsE/AeJkG3oQQ4hKmczcQMqkl2T/up+RIPnof46ng0unKS/+nwLWeH5qLDr9h9Un74F9UsRVMNvJ+P4TP4HpVUGEN84mCc5cTQlzWWgS3wKAzYLVZS2fKQ2efbc9WwYwMGhqDYgfhZnCjTWgb2oa25dqF13Ik74hDuWJrMa9vfJ1P+n/CT9f+xIaUDXgbvWkR1MLea0qUDtvLzz/79/RffvmFli1bYjBUX5igvocrBq00NS+AHojzcK3WgJTNZuOnn35i8+bNAMTGxjJ69GhcXV2rrQ5XMglKCXGerMVmchYnYT6Wj63Ics4gEwrSP9+Ba11fUGCMqSBnlAaaqwGPtpfG2O4LFhhH6fiRcm6jB8fDzb+Ap3NXaiGEEBdHybF8irZlgAbWHFOl9/PqXgfPjqVDN3IXJ6FKTkWuirZn4N48GM1VX35v3wtlU7iUM1xQCFG7RPtE82avN3lmzTNkmbJo6N+QbenbzrqPp8GTh9s/jJ+bHwAPrHiA5Pxkp3I2ZeNY3jHuXno3FmXhmnrX8M3ub5h4dCI6Tccdze9gYouJV3zPl9zc3HOWsdlsJCcnEx0dXQ01KhXhZuTdJjHcu+swxTZFmKsLHzeNrbbzA2zdutUekAJITEzkk08+oW3btrRr1w6dThKvVyUJSglxHvLXHSf7+/3nPWzBml5MYWYxKCjclILv4Fjy/zmOLd+M3teIMdoHvbcRz/ZhGPzcqqby1aXVGFj3EeQm4/RAtbxRAlJCCFHFCjemON4b0OE8VO90GhgC3fAbdKonlCXrjHyJGpQcygUXHZSTE7HCdlEr+9MwBLqhbAqsCmtWabDMvUUwnh1l6J4QV4Lukd1ZMnIJAHkleVy38DrSi9Ltic31mt7eewog35LP1rSt9IjqAcCh3EMO2093NP8ox/KPoVCsPLYS7WSCPZuy8f7W92kc0Jhe0b2q+AovbQEBAbi6umIynf1mxZIlSxg9ejSentU3qmFoiD9XBfqSbbESbDSgr+YAYmpqKjqdDpvtVMOXlpbG4sWLSUlJ4ZprrqnW+lxpJCglRCWZDuWSvWD/hR+g7DNOA3NyAeEPtLso9brkeAbCHX/Dv9/AoTVwdB3YrNB6LHSaVNO1E0KI2u/MYeDnupGiwFjPz2GVaz1fLGmFp/ZVkL/KuYcCgN7PtTTIpNfA6ngynadLaU4ri8KSWnRqnwA3gsYn2Ie2CyGuLN5Gb+YMmsMH/35AemE6nSI68cm2T0grSnMo52X0sv+/VUgr9mTtcRiS5+fqR5B7EAeyD5Q7Yx+U5qTakbHjig9Kubq6Mnr0aGbPnu0QfDnTkSNHeO2119A0jaCgIK677rpqmaXPTa8jTF/1PZKsVisHDhzAZDJRt25dvL29CQkJqfAx2bRpEwMGDMBolNliq4oEpYSopJLDuRXeDXYJ90RZbaDToXPXo3PVU7z75JTaZ96hVpQ7O1Kt4hlYGoCSIJQQQlQ77y51KNqWbp9AozK9ews3pOB/bX00nYZSCr2fKxh0YLbhkOyjjAZ6HyO+V8fh3jQQVWwlb00yeUsOOZzPVmJ1ClQBWLOKKd6dJUEpIa5goZ6hPNnpSfuyv5s/D/31EFAaVOoV1YtWIa3s2+9tfS/HC46z7MgyjDojNzW5iV8Tf2V/tuNN47JeUmWBKYuyEOMTU9WXc9k4W0CqjNVa2iMtJSWF2bNnc++99+Li4lLVVatyFouF2bNnc+jQIQDc3Ny4+eabadGiBUeOHGHTpk01XMMrkwSlhKgkvZ9ruV/sPdqGEjCiodN6S3oRlhwTmd/uwZZb4rjRUNujUkIIIWqKMcqb0LtbUbg5FWuBmcINKefeSSmwKdBpFG5OJffXpFPbzgxIUZpQPXxaB/uy5m7Ao1lQaVDqdFZb+UExBYVbUvDqHHH5T/AhRC2XXpTOtrRtBLgH0Dyo+X/OzZRamMqn2z4lqziLrpFdGVJvCJqmMTB2INE+0WxK2USIRwh9o/ui0071nPFw8eCt3m9RYi1Br+kZu3is06x+OnQY9AbC3MM4nH8YgMGxgxlcb7C9TFlPq9OPfaVQ6vxykCilyM/PJzMzE71ez7Fjx/Dx8SE6OpqjR49iNpuJioqqkYTgBQUFLFmyhLS0NOrUqUOfPn3OWY/t27fbA1IAJpOJJUuWMGbMGK655hp69erFt99+y9GjR9G00ps0rVq1kl5SVUyCUkJUkntCEO4tgijamg6A5qrHp18MXl3Kz4VhCHLHEOSOLa/EaVvJkXPNUCeEEEJcOJcwT3wHxmIrsVK8KxNbobk0OKQr3aasqnR4ng3QwLWBP9YcE4ZAd4r3ZDnnpFI4BJeM9Xydzmk/x+nOkhPdfKyA/JVH8e4R9V8uVQhRhbambWXC7xMotBQCcF3965jeeXq5gak/D//Jb0m/4eniybiEcU69k/Zm7eXTfz9l6ZGlmG2lnxeLkxaTVZzFuIRxACQEJpAQmOB0bLPVzPKjy8kryaNDeAfqeNXhQM4BpxxTfWL6cHeru4nyjuJA9gHcDG5Ee0ejaRonCk7wf8v/j+3p29E0jdHxo/lf/P+o41UHvU5/sR6yS1pUVBRBQUFkZGScV4AqOTmZn376yd7Lytvbm7y80pldfXx8uOWWW/Dz86uKKpfLarXy+eefk5aWhlKK5ORkMjIyGDNmzFn3KygosAeb4FTQrYy3tzdjx45l9erVZGRkEBERQfv27av0WoQEpYSoNE2nETA6HnOPAlSxBZc63uhcz92A6byNTj2l9D4SbRdCCFH1dEY9Qbc1I2vuHiwZxRgjvQkY1RAMOnKXHMJ8ooCS5HxMe7M48fIGXKK9saQVOQaXFLjGB2Dak2kfjq5MVpRVOfRyMiWWP7OT5mFAFVrK3WY6lEsFc9IKIS4Bz6x5hmJrsX35+/3fMyRuCO3CHHOj/nLwFx76+yF0mg4NjcWJi/l+6PeEeYYBpUnKb/z5RkxWk0O+J4A5u+bYg1LlMVvN3Pb7bWxKLR1a5aZ34+P+H9PArwHb0rfZA1MaGne1uItY39KZ2xoFNLIfI60wjaE/DLUH11Cl552zaw4xPjF83O9jwr3CL/BRuny4uLhwyy238Pfff5Obm4u3t7c9KHPgwAGKioqc9unfvz9//PGHw7C/soBU2f//+OMPRowYUfUXcFJGRgapqan2ZaUUBw4coLi4GDe3iieNio11ntWvYUPHES9Go5GePXtetLqKc7vy+iwK8R9omoYxwgvXen6VCkgBBI1tArrT7iYZNPwGVu80p0Jcyt5//32aN2+Oj48PPj4+dOrUicWLF9u3FxcXM2nSJAIDA/Hy8mL48OGkpFRiOJIQAgBjuCeh97SmzvTOBN/eDL2vK3pPl9IcUnoNLKd+aJgP56GKHANIen83pyF2pn3ZnHhtA+mzd2JOKSg9Tx0vnGig967gRoyOy3/GWSFquZTCFIfE4mXrCs2FPLHqCXp+25MRP47g420fA6VD46zKSqG5kN+SfrPv80viL5RYS5wCUsA5hwMuObTEHpACKLGV8NrG13i+2/PU8aoDlCYzf6zjY9T3r1/uMb7f//2pgNQZjuYd5cnVT5a7rTby8PDgqquuYuTIkQwYMIARI0YwYsQIhg4diqZp9ucjICCACRMm0KlTp3KDVWWUUuzYsYOjR49W1yWUm99K0zT0+rP/PouIiGDUqFEEBATg6elJhw4dJAB1CZCeUkJUMWOkN+GPdTg5RbeGe9NA+RIuxGkiIyN54YUXaNCgAUopPv/8c4YOHcrmzZtJSEjgvvvu4+eff2bu3Ln4+voyefJkhg0bxqpVq2q66kJc9izpRY6TcZxBH+yONbsY645ip6F51oxirBnFmA5kEza1La71/XBvFUzR5pOzZ2kQMLoRxQdysKQWOu1vCPbAu0/0xb0gIcRF1TG8I78f+h2bsqGhodfpaRHUgufWPseig4uwKRtZxVnlBptOz9lk0AzllgG4temtZ61DtikbDc2+f9k5o7yj+PHaH0krSsPH6IOHS8UTJ5isJodjnM6qrOzL2nfWOlwJ4uPjuf322zlw4AAeHh40b97cHvyJi4tj//79KKUchr+VUUrxzTff8H//93//OedYZfj7+9OyZUu2bNmCTqfDZrPRvXt3XFxcWL58OStWrEAphbe3N7fddhu+vqeGnDdu3JjGjRtXeR1F5UlQSohqoPdwwbtb5AXtW5KcT87iRGx5ZtyaBODTJ0aSwopaZciQIQ7Lzz33HO+//z7//PMPkZGRfPrpp3z11Vf07t0bgJkzZ9K4cWP++ecfOnbsWBNVFqLWcInwwpqTWeF2a1rFd8fLqGIrRXsz8WobRuD18Zj7xWDNNmGM9EZn1OPWKABrVjGmfdmg0/DsEIZHyxCMdbzQDNJpX4hL2ROdnsBsM7Pq2Cr83fx5vOPjRPlE8dfRv+w9qGzlRLa9jd4MjB1oXx4SN4SP/v3IYShgmV2ZuzDbzLjoyp/dLSEoAZ2mc8gf5ap35f4V99Mvph9X1b3qnNcxoO4APtv2GRblPJRYr+kdhvpdySIiIoiIcM6XO2zYMH766SeSkpLw9fUlJCSErVu3OpTJz8+nuLgYd3f3aqnrNddcQ1xcHBkZGYSHh9OoUSMOHjzI8uXL7WXy8vL47LPPuO+++wDYv38/iYmJeHt706ZNm1oxo2BtUOVBqWPHjvHQQw+xePFiCgsLqV+/PjNnzqRt27ZAaVT1ySef5OOPPyY7O5suXbrw/vvv06BBg6qumhCXtKKdGRSsO0Hx3qzSGZEA84kClMWG36B6NVw7IaqG1Wpl7ty5FBQU0KlTJzZu3IjZbKZv3772MvHx8URHR7NmzZoKg1ImkwmTyWRfzs0tP9eNEFcyW5GFkqNnmXjj9GTn52BJPxW8cglwxyXg1I8SnZuB4FubYTNZ0Qwaml4CUUJcSlILU3nor4f4N+1fIrwieK7rczQPbg5AVnEWNmUjxieGjuEdaR9emvQ5wC2AXFNuuQEpgAivCILcg+zLYZ5hfDX4K8YuHku+2fFzZ/7e+QS7B3NXy7ucjvPRvx/xzuZ3nHo47cvex96svfyW9BtFliKurX/tWa+xgX8DZg2cxWfbPiOjOAMvFy9WJ69GoYjxieGpzk+d62G6orm7uzNq1Cj7cmFhIdu3b8dqPZnPS9Pw9PQ8az6n82Gz2cjOzsbd3b3CIJdOp6NZs2YcOnSITZs2sWvXLoqLnYOeOTk5AKxfv56ff/4ZnU6HUort27czfvz4cw75E1WvSoNSWVlZdOnShV69erF48WKCg4PZt28f/v7+9jIvvfQSb731Fp9//jmxsbE8/vjjXHXVVezcufOivaiFuNwUbU8n48td5W4r3JImQSlR62zbto1OnTpRXFyMl5cX33//PU2aNGHLli0YjUanGV1CQ0M5ceJEhcebMWMG06dPr+JaC3F5K9qdWe4MsXYuutJ8U2W/OTXQvF1QuWanojpjJSb+qGQuRiFE9bpv2X3syNiBVVk5nHuY236/jZlXzSTGJ4Zxv44jqzgLq7KyN2svfxz6g/r+9ekb3ZdZO2ZRYiv/MySrOMtpXQP/Bvwy7BfuW3Yfm1I32QNNCsW6E+u4C8eg1KaUTby9+e1yj396nqtvdn9zzqAUQIvgFrzZ+037cn5JPvnmfILdg6+Y2fcuFg8PD0aOHMn8+fMxm824ubkxevToizJ0Lzs7m9mzZ5ORkYGmafTp04euXbuWW/bQoUPMmjXrrMczGEpDHmU9qMoSth89epSkpCTi4uL+c53Ff1OlQakXX3yRqKgoZs6caV93esZ7pRRvvPEGjz32GEOHDgXgiy++IDQ0lB9++IHRo0dXZfVELWIrsZL/11EsWSY0Fx1ooEqsuMb64tYooOIkq5eo/HUV/9hWlrPMry3EZapRo0Zs2bKFnJwc5s2bx7hx41ixYsUFH2/atGlMnTrVvpybm0tUlEw7L8T58O4WSeHmVKyZJ+88a5QbkILS/IlCiMuP2Wbm3/R/7cs2bBRZihj982gGxw4mvSjdvk2hOFZwjGMFx1hxdAX3t72fALcAPv73YxJzEx2O27lO53LP5+/mz6B6gxwSl+s1PRGezkPGDuQcOGf9NTQMugv7Setl9MLLWM4EDaJS4uPjeeCBBygoKMDb29se/PmvfvzxRzIzS4eVK6X4448/qFu3LpGRzqlQNm3aZC8Hpb2njEajQ2/5AQMGAGCxOA/dLG+dqH5V2n/6xx9/pG3btowcOZKQkBBatWrFxx9/bN+emJjIiRMnHIZl+Pr60qFDB9asWVPuMU0mE7m5uQ5/4splK7FSuDWNlDc3kfvHYQo3pVDwz3EK1hyncGMqWfP2cfyV9ZhPFNR0Vc/KklVM7vIj5K04giXHhKbTSodNlEMVWjGnlj97iBCXK6PRSP369WnTpg0zZsygRYsWvPnmm4SFhVFSUkJ2drZD+ZSUFMLCwio8nqurq302v7I/IYQj9/gA9L7G0m+DJ9scY7Q3bk0C8B/WAJ++0YROaU3QLU1xqeN51oTotiL5Yi+q1l9//cWQIUOIiIhA0zR++OEHh+1KKZ544gnCw8Nxd3enb9++7NsnyavPxaAZ8HX1LXfbz4k/n3Xf5UeWMyRuCF8O/pJWIa3QaTo0NLrX6c5D7R6qcL/r6l9nHwYIEOIRwj2t73Eq18Dv7Olc9Fpp76bxCePPWq42U0qRVmImt4ZuWhuNRvz9/S8oIJWUlMSmTZs4fvw4mzZtYtGiRaxevZqUlBSnROqpqanlHkOncw5ntGjRgquvvpquXbty55132tMGtW7d2l5G0zR8fHyIiYlBKYXJZHI654Ww2WysWrWKOXPm8OOPP5KXl/efj3klqNKeUgcPHuT9999n6tSpPPLII6xfv5577rkHo9HIuHHj7EMvQkNDHfY727AMGZIhythMFlLf24ol5bQATXmfJSYbOYsTCRrftNrqdj7MaYWkvrMFVVLamOQuP4rfNXEU76k48awlsxiXkIpnGBHicmez2TCZTPYklEuXLmX48OEA7Nmzh8OHD9OpU6carqUQlzedu4GQya3I++sotkILbvH+eDQLdiijGfW4NfQn46vyh5SXHkjDdCAbjxbBFZcR4j8qKCigRYsW3HLLLQwbNsxpu6QEuTCapvFQu4d4ZOUj5W5PCExgR8YOp5nrNDRc9a4A+Bh9+GLgF5U+p4vehQ/7fsjWtK0UW4tpGdyy3JnzWoa0ZGqbqbyx6Q2H4XoGzUCvqF4EeQTRJ7oPHcI7VPrctUm+xcrN2xJZmV2aoyvEaCDK1YWJ0aFcHeJ31n1TUlI4fPgw3t7eNGzYsNzgTlX6/fffWb16tcO6slxP5b1fz4wXlGnbti1bt261DxvU6XS0adOm3PL9+vXD09OTgwcP4u7uTpMmTUhKSmLRokXk5+fj4+PD6NGjy030XllLliyxd67RNI2DBw9y1113YTReXqN2qluVBqVsNhtt27bl+eefB6BVq1Zs376dDz74gHHjxl3QMWVIhihT8M/x0immK8Gcfu7Zg2pK/qrk0oDUyXZeFVko3pNJyF0tyfrxAOYjZ0TYdeAS5ln9FRWiikybNo2BAwcSHR1NXl4eX331FcuXL+e3337D19eXW2+9lalTpxIQEICPjw933303nTp1kpn3hLgI9N5G/AZXnKfQVmjGfKIAvY8rluIK2lyl0F1mw+TF5WfgwIEMHDiw3G2SEuS/0WnlByQMOgMvdnuRbRnbSMxO5Ns935JnzkM72bVyfNML76Gk1+lpHdr6nOXGNx3PyIYjyTfno5TiWP4x6vrWdUiifqV6IfE4a7JPJY1PLbGQWmLhth1JfGuIo0dA+cOqd+3axXfffWfvGdSkSRNGjhx5UfJBVUZWVpZTQApO5XoqKirCz8+P7OxsNE2jX79+1KlTx6Gs1WpFKUWdOnW4/fbb2bx5M5qm0bp16woDWDqdjq5duxIYGMi8efPYsWOHw/a8vDzmzJnD1KlTsdlsrF+/nuzsbKKiomjatKnD42OxWCguLsbDw8MhoLdx40b7/5VSZGdnc+jQIZnE7RyqNCgVHh5OkyZNHNY1btyY+fPnA9iHXqSkpBAeHm4vk5KSQsuWLcs9pqurK66urlVTYXFZsRaYQdOgEl0trRnF5K08hnfXOucsW12U2Yoloxhbodmph1fRtnR8B9RF6c7YYNQIHN0Yg5+8B0TtkZqaytixYzl+/Di+vr40b96c3377jX79+gHw+uuvo9PpGD58OCaTiauuuor33nuvhmstRO1XcjSPtE+2oYpPDgtx0YH5ZG8FNz2cXG8I8bik2ldx5TlXSpCKglIyU2spN4NzzxQdOl7t8SoxvjHE+MYAcEPjG5i3dx5FliL61+1PQmBCtdTv9NxP4V7h5yh95fg3t4jyBu3pNfg5LbvCoNTixYsdhqrt3LmTw4cPExMTU0U1dVRYeO5OBaNGjcLT0xNXV1eHnlM2m43ffvuNdevWAaVD8gYPHsygQYPsZUpKSvjjjz9ISkrC39+fq666ioCAAKA0mLRgwQL7rIGnU0pRUFBAbm4uCxcu5NChQ2iaxrp160hPT6dXr15A6eQ8CxcuxGKx4O/vz4ABAwgKCiIgIKDcmfxkdr9zq9KgVJcuXdizZ4/Dur1799pf8LGxsYSFhbF06VJ7ECo3N5e1a9cyceLEqqyaqAXcGvqT/9cx5w0uOjDqoMAxv0Xub0l4dYmotrsAAMV7Msn68QC2AjNujQPwv64BmosO87F80mdux1ZgKT93lFWR+cN+LIccp8x1q++Pe5PA6qm8ENXk008/Pet2Nzc33n33Xd59991qqpEQAiBz7l6U6bQv7mYbhghPDP5uePeMxJpXgi3PjGusDzr3Kv1KKcRZXUhKEJC0IGW61elGQmACOzN2otN02JSNF7u/SO/o3g7lgtyDuLPFnTVUS3GmeC83NuYWOAemFHjqKx6OV1xc7LSuqKj6RpUEBwfj7e1Nfn5+hXmcFixYwLBhw/D1dcx3tmnTJtauXWtf3rhxI0FBQQ4pHRYuXMjOnTtL822lpZGcnMzkyZNxdXWlsLAQs7n8CTsAXFxcyM3NJSkpCTiVQH3lypX06NGDnJwcvv/+e3uvrqysLL7++mugdEZCFxcXioqK7EMR69SpU23BvstZlX6DuO++++jcuTPPP/88o0aNYt26dXz00Ud89NFHQOk4yylTpvDss8/SoEED+/jviIgIrr322qqsmqgF3Or74z+yIblLD2PNLQGrrbTHkdl26k7uaZT55PZqikmZ04tI/2In2BQoKNqcRtHWNOdEsRV09LKWMzSxeGcmthJrpabeFkIIIf4La7bJqY2yJBdgOV5A8Z5MXEI8MCeXTiTi3jyYgNGNSifqEOIyIWlBShn1RmYOmMkP+38gqziLzhGdaRnSsqarJc7hkXrhbMsrYnOe428GPxcDt0VWnOOvUaNGbN++HaUUmqbh6upara/7svzSP/30ExkZGURGRhISEsLatWvtPRfT09OZNWsWU6ZMwcPjVL6xY8eOodPp7EEhTdM4duxUJwWbzcauXbvswSSlFHl5eSQnJxMbG4uXl1eFATG9Xs/w4cPLnZGvrGxaWpr93Gc6vQdYvXr1qFevHm3btpWeUpVQpUGpdu3a8f333zNt2jSefvppYmNjeeONN7jxxhvtZR588EEKCgqYMGEC2dnZdO3alV9//VUSEopK8WwTimebUI49sQp1jol/jLE+VfpluWhHBkU70tG5GfDqXoeSpFywnvFt/iwzF6Fh//Lv3TsK8/ECrJkm53I2hbIplMmK5qav1p5fQgghrhzGGB9M+7PKv5liUfaAFEDRv2kUxPni1UGG1ojqdyEpQUDSgpzO3eDODfE3nPd+FpuFYkuxfXhdamEqD/31EP+m/0uQWxAvdHuBVqGtLnZ1BaXBp5/bNOBQUQl5VitrswvQNBga4kew0aXC/YYMGYLRaOTAgQP4+voyYMAAPD2rN19tUFAQ48efyklmMpn466+/HMqUlJTw9ddfM378eHveJn9/f6dgUtnQPCgNUrm4uDgMywXs73OdTseNN97It99+S1ZWFj4+PgwZMgR3d3cCAgJIS0tjzpw5TvVt1aoVOp2OwMDKjVjR6XR07ty5UmVFFQelAK6++mquvvrqCrdrmsbTTz/N008/XdVVEbWYztuINcO5K+rplFVhM1nQuV78l33+2uNkf7/fvlywKRW/6+IqfwCdRvBtzbDml2AIcMMY6Y0lz8SJlzY49PpyaxyA+UQB6V/sRBVa0Nz0BNzQGPdG/hfzcoQQQggCRjYkY86u0pssOq20529FdBqWtEt3UhFRu0lKkJoxf+98nl/7PCW2EloEt+DNXm8yaekkdmfuBiC5IJmbf72ZxcMWE+F94TOaiYrpNI1Yj9KAS3Pvys3MbTQaGTJkiNN6m1J8diydtdkFRLi5MCUmFH+X6hma7eLigtFopKSkxGH9kSNHOHz4MHXr1gWgU6dOHDhwgEOHDgFQp04dunTpYi+vaRq9evXi119/ta+rU6eOQ7A6LCyMe++9F7PZjIvLqeCdUorvvvvOqQ7dunWjZ8+eAAQGBjJ48GB++eWXCocelvU+E5UnCQBEreB/XQPSP9l21jLmw3nk/JqE/9D6F/38Ob8mOiyrYguWLBPuzYMo+jf9rPtqLjr8RzXEtZ7jmGmDtyvhD7cn5+eDWLJNuMb44NU1guMvrQeT7eR5rGTM3I4hwhOdUY9rnC/eXSMlt4cQQoj/TO9tJOTOFiirwnQgm/SZ20snGEGBXgcW26nhfTZF8YEsLFnFGPylt7u4+PLz89m//9QNwMTERLZs2UJAQADR0dGSEqQKFFuKeX/r+2xJ3UKMTwz3tL7HPuvd7szdTF8zHXXyQ2B7+naeWPWEPSBVxoaNd7a8w/Pdnq/2+ovzM/1AMh8eSUNH6QCO5Zl5/N62Ia66ivNT/VdHjx7lyJEj+Pr6MnToUObOnetU5vReTy4uLowbN47U1FSUUoSGhjrMfgeQnJyMpmn2oNGxY8c4fPgwgYGBeHp62keZnB6QAjCbzRQUFHCmhg0bOgzBa9euHQkJCWRlZbFixQr27t3rUN5gMNC1a9fzfCSubPLLVdQKbvX9cG8ZTNGWtLOWKzmcVyXnt89MdJq8X5NAA0OoB5YU5/xQrg398R/ZAL2HC1oFyQj1ni4EjGpkXzanFNgDUqeznBxCUZKUS9G2dEImt5K8U0IIIS4KTa/h1tCf4IktKNqWjmbU49k6lOxFByjelWkvZ0kpJO3jbYRNbYNmqLofMeLKtGHDBvvsV4A9F9S4ceOYNWuWpASpAo+ufJQ/Dv2BDRtb07ayJW0L84fMx0Xvwq6MXfaAFIBVWdmRsQODZsByRk6NfHP+mYeulBMFJ8gsziTWNxZ3g/t/uhZxdkopZh0rvZFe9ktjT0ExDf7aRmsfD95tEkMdN+NFPefmzZtZuHChPYAUHx9PvXr1OHjwIFDa48jd3d0p35VOp7MP2S3PoUOHnHoxzZw5E4D69eszatQojEbnazEajQQEBJCVlWXf32AwEBAQQEpKCkopQkJC0Ol0eHh44OHhwf/+9z/2799PYmIi+fn5BAcHk5CQgL+/jGI5HxKUErWG/7AGpb2SzjK8wBBSNQ2a5mZAFZWT1EpRbkBK8zIQND7hvPNB6X1dHXJPlceSWoRpXxbuCUHndWwhhBDibFyjfXCN9rEvB4xqRPL0NacK2MCaWYw5rQhjePXmJxG1X8+ePSscLgOSEuRiM1vNLDm0xB54sioriTmJ9JvXj+e7Pk+0T7RDeb2mJ9Y3lkjvSH7Y/4PDtsziTM7X+1ve572t7wGls/590v8T4vzOIzWGOC9pJWYs5fyGKlGKdTkF9Fm/hxsjArgxPJBYd9eLktP2t99+A04lEd+9u7SXnV6vx9vbm6CgIK666ip7ovNNmzaxfv16dDodXbt2pXHjxuUe18/Pj9zc3HI/Lw4cOMCKFSvo169fufuOHj2ar776iuzsbFxdXRk2bBjz5s0jMbF0VExkZCRjxoyxD8/buHEjP/30kz2w1qhRI8kldQHkNpaoNTSDDs7yZUXnacBvUL0qOXfA8AbnNauf3sPlgj7MdW4G3FpUPJtGGXW2vB9CCCHERaC56EpzTZ1B5y49dYW43Ok0HXqd83s5oziDu/+8m3DPcG5rdpt9faB7IE92epJudbo57bMrYxczt8/kn+P/VOrc29K22QNSAFnFWTyx6okLuApRGcVWG9dtPlDhfEw2INti5d3DaXReu5vRWw9QZD3b7E3nppRyyt1Uxmq1YjabufHGGzEajaSlpbF161Z+/PFHjh8/zrFjx/j222/tgaKyfX7//XdeeeUVsrOznYbmnX7eEydOVFiv4OBg7r33Xh588EEeeugh0tLSSEpKsm8/duwYK1eutC8vWbLEflyAPXv2kJycXOnHQZSSnlKi1tB0Gm6NAyneleHUk8i1gR+BNzWukiTnAO5Ngwi5pzUlSTnk/nkEW175H7JlrHnmCz6XS6A7Z0vprvc14tZAuowKIYSoWppBh++gWHIWHbSv8+pWB4OfDJcS4nKn1+mZ2GIib29+22lbia2E7enbubf1vYxqOIpsUzaxvrG4GdzIKM4ot/wbm97Apmzc1+Y+bml6y1nPvSNjh8OyVVk5lHfov12QqNCm3EIOFJUz43cF/srK561DKTxU78JnW9U0jfj4eHbt2lVuj6aCggIWLVrExo0bAZyG2+l0Onbv3k1sbCwAf//9N6tXr3YoM3DgQAoLC1mxYoXDeYODnW/wFxcXs2DBAvbv34+bmxuDBg2iadOmZGZmOuSnAsjMLO35p5TCbHb+TXfmzH/i3CQoJWqVgOsbkfPzQUyJORgC3PAZUBeDvxs6t6p/qRvDPTGGe+JSx4u097eeCozpNbCe9mGrgc7j/OtTsP4E+auTsRWXM0zwJNcmAQQMrV8t1yuEEEJ4d62DMcobc3I+hiB3XOv71XSVhBAXyYTmE2jo35DHVz1OjinHIYdUiEcIAOFe4YR7nQpOtA5pzaDYQfyS+IvDsWyqtGfNW5ve4qbGN2HUl5+fyGQ1MXP7TKf1TQOb/ufrEc7W5xSwMvv8cu4qYHfB2Wc9r4xrr70WT09PDh48SEbGqWBmWS6psoAU4NSrSinlMMPdvn37HLZrmobJZKJHjx5kZ2ezdetWAKKioujevTu7d++muLiY2NhYfH19+fnnn9m3bx9KKQoLC5k/fz4hISGEhIRgs9kczlunTh37ORISEti2bRtKKTRNw8vLi8jIyP/82Fxp5JerqFV0rnr8hzWo0Tq4RvsQ+mA7CtYko7no8OwcQfaC/RTvOPlhq9Pwu6byY+JtJitZ8/ZStO3ss/ihgd6oL807JYQQQlQT1xgfXGN8zl1QCHHZ6RnVkzd7vcmdf9xJkaUIgNGNRtMiuEW55TVN44VuLzC0/lC2p2936mllVVZKrCUVBqX+TfuX5ALH4U8aGk93llxhF9uz+4/xzpHyJ4nSgIFBPpTYFH9k5jlti/f87z1ijUYjgwcPBkqDSt988w1Wa+nkUQEBARQVFTn0UDq9x5KXlxft2rWzbyubVa9su1IKT09PdDod1113HX369MFiseDj48OXX35pH5Ln4uLCzTffTFJSksO5lFKsXr3aHswq06pVKzp06GBfHjJkCB4eHiQmJuLv70///v0dgmWiciQoJUQVcPF3c8hfFXhjY4r3ZGLLN2Os64NLsEeljqOsNtI+/hfz0crNWiKZpIQQQgghxMXUOrQ1vwz7hR3pOwhyDyIhKOGs5TVNo3NEZ9qFtePHAz9yNO8oVmVFp+loG9oWL6NXhfu66JxzAbkZ3Aj2OHdOVVF5SUWmCgNSZcbXCaaLvxefHU3nw6OpHCkuHarWM8Cbe2JCL2p9CgsL7QEppRRHjx512F7WKykqKgqdTkdCQoI9ATpA3759OXz4MMXFpT24IiMjad68uX27j0/pjZOVK1c65Igym838/vvv+Pr6kp+f7xCY2rJli0MdAgMDGTp0qMM6FxcXBgwYcOEXLgAJSglRLTSdhnvjwPPer+RwXqUDUgBe7S98bPelzmZT5GcV4+bpglGGJwohhBBCVJsg9yB6RPWodHmlFJ9s+4SUghSUUvi5+tErqhf3t7v/rPs1DWpK65DWbE7djF7TY1EWJjSfcFFme7sQymaj5OBBUApjXByarnbME5ZRUn46kE6+nug0jdsjg+kW4A3AbVHB3BYVTFqJGauCUKPhoj8fBw8edOjppNPpCAkJISWl9PUTHR3N4MGDKSwsZOXKlRw4cID4+HhatGiBpmmEhIQwefJkEhMTMRqNxMXFYTA4/l7Iz89n+fLlTudOS0tj7NixfP755xQVlfYGrF+/Pvv373col5mZaR+mJy4u+WUnxKWsotkEXTQwl27TPF1wq++LV8cIXGN9q7Fy1ScnrZAf39pKbloRmk6j26gGNOsp47WFEKJcm+fAihfBaoa2t0D3+0G+RAshqtHPiT/z3pZTM+hlm7JpHNgYH+PZh/oadAY+6v8R3+z+hhMFJ2gd2pp+Mf2qurrlshUXc+TOiRT+UzproEfbtkR99CE6j8qNeLiUxXu6EeRiIMtswQrogTa+nnzfuuI0KMHG8me0uxi8vBx7zymlqF+/PrfccgsWiwV3d3fy8/P55JNPMJlM2Gw2du/ejclksg+n8/LyolmzZhWe49ChQ1gszsG4wsJC9Ho999xzD8nJyXh4eODm5sbbb79tzydVliBdAlJVQ4JStcyeE3n8uTsVbzcD17Wqg2cVzTYnqocx2gdDqAeW1MLSFQpc6/sRcEN86aLZit7XtdZ/QP4xaxd5GaXdcZVN8dc3e9n9z3G6DK9PxGkzDVpKrKz9KZHj+7LxDXGn03X18fKXcd1CiCvIvj9g4V2nlpc9C+5+0P72GquSEOLKszFlIwbNgEWVBgF06NiYspEb4m84576uelfGJYyr6iqeU+bnX1C4bp19uXDTJjI+/YzguyfXYK0uDk+Dnnmt4vi/3UdILDLR1seTV+Ojaqw+Xbp0Yffu3faE5wEBAXTu3Bmj0WifeW/v3r32nkxl1q9f75Dj6Uxms5klS5awZ88ep55Tp8vNzSU4OJi4uFN5f6+99loWLlyI1WrF29ubESNG/JdLFGchEYtaZPX+dMZ+tg6bUigFn69OYuHkLngY5Wm+XGkGHSF3NCd3+VGsOSZc6/rg2SEcTVcWhKq6OxaXkoxj+SibY6+x1KQ8fnh9MyMeakvIyQS7Sz/fxYFNqSgFqYdzOZGYyw1PtMfgoi/d51AuSdsycHU30LhzOEZ3eW8IIWqRVW/C0mec16/7SIJSQohqFeYRho1Ts5ZpmkaYR1gN1uj8lSQlOfUyLTl8uGYqUwXiPd35uU3Dmq4GAB4eHtxxxx0kJiYCEBsbaw9GldGVM3RSr9dXeEyr1cq8efPYs2ePfd3pQwTLuLi4EBrqnCOrefPmxMfHU1RUhJeX11nPJf6b2jEoVgDw6pK9WG0KmypNeL0vNZ/bP99AicV2zn3FpUvn4YLfoFgCb4jHq1PEaQGpK4PNptBVcM1Kwd71KaXlrDb2nwxIASgb5KYVkXqodMaQpG3pzHtxAxt+SWLl3H3Meeoftv91lKL8knKPLYQQl7yCDNg0u3S43tZvYMkTYDM7l0vfC0fWV3/9hBBXrDFNxtA4oLF9ua5PXW5vfnkFx92aNYWTybcBsNlwS2hScxWq5YxGI2FhYZSUlHDkyBH70LkyjRs3xs/PD03T7AGqkJAQVqxYQVqaY9J2s9nM559/7hCQgtJhgc2bN8fXtzTliY+PD//73/+chg+eXidfX18JSFUx6SZQi+QVm51mX1t1IIPxM9cx+9YOFf6wF+JSUFJsYc33ByjMLaFRhzDqtSydZeXg5jRMheUnYwQwGEobJU3T0Ot1WM8Iwu5anUx4nC9/f7MHZYOyOQoLc0pY8dVe1i1KYsRDbfAJdK+S6xJCiCqRfQQ+7gUFJ7+I6wyUTtRdQS7C1B0Q1a78bUIIcZF5uHgwe9BstqRuQSlFi5AWuOovr5QK/tdfj2nvPrK//RYA3+HDCBgzpoZrVXsopdiyZQsHDhzAy8uLunXrMn/+fMzm0psrTZo0YcSIEWiaRlFREW5ubtx+++2sX7+e3Nxcdu3axfbt2wH466+/GD9+PJGRpTln169fz+EKerU1a9aMYcOGSdLyS4gEpS4zmw9lsWjbcaIC3BnbMcahG2P/JmHsTdnvtM+qAxnsPpFHk4izJxYUoqaUmCx8/vAqSopL70Yd3JxGh2vq0XZQXQpzTRX+zjK6GWjSLQIoneHQN9SdzGMFDmX2/HMCi9lKboap3HMX55vZ9Oshet4Yf1GvSQghqtSqN6Eo89SyreLgPQDBjc++XQghLjIXnQvtwi7fYLim1xP+1JOETnsYlELn5lbTVapVVq5cydKlS+2BoXXr1jkMrdu5cyebNm1i1apVZGVl4erqyvDhw+nZsyd///03xcXF9vI2m42VK1cyevRoAHJycsodquft7W3PGyUBqUuHDN+7jHy68iDXvb+aT1cm8tSPO+n1ygqs1lO9Qib3qo9RX/6bq+T0rqdCXGI2/JxkD0jZ1/1SOqY8ooEfZ76qPXyNtOgTxejH2zv0cNIbynn9K9i/Ps15fdlmpSgusDgsW8zlv1+UUmQeL+DIzgyyy5LPCyFETSjOrrBTlCMN+jwB0RUnghVCCFExnaurBKSqwNq1a4HS79dKKWw2m1MQafny5WRnZwNgMpn47rvvKCgowGw2OwSVlFL2HlYAMTExTscCiI6OLjc3lahZ0lPqMvLC4t0Oy4cyC3lv+QEahXkT6GWkdbQ/H45py22fb8B62ptQr9O47r3VNK/jy7hOdQnydqVDvQBcDTI2VlwaivKc8zrZrKWv4aBIb66a0JRVc/dhKrIQ1zqE7qMb2pOXn65OwwDSDuU7rAuO9rbnlSqXgrrNAwE4siuT3z/dQXG+GYNRR3CMN52urU/WiQI2/XaI3PSik0MAS3UaFkfr/jEXcMVCCPEfNRoI2+aeu5x/Xej2f1VeHSHE2RXv2YP5WDJujeNxCQ+v6eoIUePO1lNJ0zQ0TSM/3/F7vcViIT09nSZNmrBy5UqH3lDNmze3l2vSpAlt27Zlw4YNDvu3bNny4l2AuGgkKHUZMVudo71v/bnPvr5DbABf3NKetY/24ZXf9rDo32Pkm2xYT85atvVoDlPnbgWgaYQP397RCU9XeQmImtekSwS715xwWBcU5W3/f1yrEOJahZzzOB2GxJKVnM+hHaVDWiIb+9NnbDxfPbUOs8mx95Oblwuu7gaa9YykUYcwivJK+OW9f7GYS6NOlhIbx/fl8MOrm7DZyu+OsGbBAeJaheAbLPmohBDVrOlwOLYZ1rx99nIGubsvRE1Le/sd0t99FwDNxYXId97Gq0ePGq6VqErKZkOTHjln1aVLF3799Vd0Oh1KKfz9/alTpw779+/Hw8ODQYMG8cMPP5Cfn28PPGmahp+fH76+vowbN46VK1diNptp1aoVLVq0cDj+1VdfTePGjfnnn38AaNOmDQ0aNKj26xTnJhGJy0i4rxvHc4od1llOC1StTcyk44yl6HUaZosi31TxrHs7j+cya3USk3rVr7L6ClFZ4fX96HVTPCvn7cNqthEc7cXQKa3O+zh6Fx2RjQPISilEp9fRqH0YXv7uDJ3SihVf7yEvowi/MA86XRtHRAN/h30zjxfYA1KnqyggVSY/s1iCUkKImpF54NxlejxY9fUQQlTIlJhoD0gBKIuF5GmP0HD1qhqslagq+9avYclH71Ccl0t00xYMvvdB3L19MBUWojPocTGeX7J3m82KTlc7R7d07NgRb29ve6Lzjh074uHh4VBm5MiRzJkzB5PJhKZpDBkyxD5zXkxMDDExZx+xEBcXZ88hJS5dEpS6jCy4qzPD3lvN8ZxiDDoNV4OOghLH3h9ZheVMBV0OnaaRmlt87oJCVJMmXSNo0jWiUmWVUuxec4LDOzJw83Kh7cC6ePq5smv1cVbNO5Xsf+nnuzi8M4N+tyQw6pGzJ9r0Djj/3gR6F42AOp7nvZ8QQlwUtnLy37n6QmSb0v+3vwMaDajeOgkhHFhSUh1XKIU1KwtlsaAZ5KdYbZJ1/BiLXn8B28lcvod3/Mvid19H02kc3LgONI321wyn6w3jKhy6lpN6gqO7dmAuLmL9TwvITUtF0+mIbNKUIVMext27dk1clZCQQEJCQoXbo6OjmTp1KpmZmfj4+ODpKd+7a6Nq61P4wgsvoGkaU6ZMsa8rLi5m0qRJBAYG4uXlxfDhw0lJSamuKl12wnzc+OuBnjw4oBGhPm44ZX8+DxabolNc0MWrnBDVaPOSw/z5xS72b0xl+4pjzH58DQU5JpL+TXcqu299Kl8/vY7c9KKzHtMnyJ2uo5y79HoFuOLm5fyl0eiu5+rJLXH3Ml74hQghxH/ReIjzuh4PwJjvS/8kICVEjXOLb4TOywvKhnLp9bi3bHnZB6QK16/nwMCB7GnTliOTJmPNyanpKtW4Ewf32wNSUDqE7/D2LSRuOpnXSCnWLZzHvrXl95I7vP1fZt43kV/fe52ln31Ablqq/ThHtv/Lj6/NqPJruBS5uroSHh4uAalarFo+DdevX8+HH37okHwM4L777uPnn39m7ty5+Pr6MnnyZIYNG8aqVdKd9Ux/7EzhgXlbK90T6kx944Op4+/B95uPoddpTOpVnwFNwy5yLYWoHht/SXJYtppt/Dl7N56+5QeIso4X8N2M9dz0TCfcPFwqPG6L3lHUaxnMsb1ZZJ8oxN3bSKOOYSib4uCWNKwWGwERXviHe+Dpc37dr4UQ4qJrdRPkHoM1J4cGdZ4MnSbXbJ2EEA70fn5EfvQhxx98CEtqKu4tWxLxyss1Xa3/xJySyuHbJ6BKSsBmI3/5cpIfeZSod9+p6arVKJ/AYIdlTadDp9NjVad+v+n0elISD9CwY1en/f+c9SFWq8VpfZmjO7dhtVjQX+YBTSHOVOU9pfLz87nxxhv5+OOP8fc/lcMlJyeHTz/9lNdee43evXvTpk0bZs6cyerVq+3JyMpjMpnIzc11+KvNSiw2DmUUMHHORrLLCUgZdBrNI32J8HWjbqAHunJ6T0UHePDJze2ZPrQp/z51FZuf6M9t3epVQ+2FuPiyThRQUuw8ZCX7RAFtB9ZF71L+x5qpwMKClzZiMZcz3OU03gFuxHcMp+O1cbToE4Wbpwvu3kYSutWhea8oIhv5S0DqIpsxYwbt2rXD29ubkJAQrr32Wvbs2eNQRnrWClEOTYOeD8O0I6V/PR4qXSeEuGRYsrJIffElzEePosxmPDq0xyXk3JO3XMqKt/2LKi4G28lcnFYrBatX12ylLgERjRrTeuA19mWjuzt1W7Z2SHhus1rxD69T7v5FOdmgKs5l6uLmjk5fO/NLiStblYdZJ02axODBg+nbty/PPvusff3GjRsxm8307dvXvi4+Pp7o6GjWrFlDx44dyz3ejBkzmD59elVXu8YVmCxM+XYLf+xMwaDXyp15D8CmFFclhNkTlt/++XqW7HIcu56cffZhS0JcLmw2xS/v/VvutoAIL3yC3Ln+sXYsfH0zBdklTmWyThRyaHtGpWbyE9VnxYoVTJo0iXbt2mGxWHjkkUfo378/O3futHfVlp61QgghLmXKbCbz888p3rkTY926BN5+Ozp3d1JmvEDx9u0nCynS334H95Yt8erSpWYr/B8Ygh17BKHTYQi68tKCKJuNo7u2U1yQT534BDx8fOl18wSa9u5PYU42IbGlCbZzUlNITSydmCK+a0+adO9Vur9SbPhpARt/WYim6fANDacoL9c+09yZ+k2YXGEuKiEuZ1UalPrmm2/YtGkT69evd9p24sQJjEYjfn5+DutDQ0M5ceKEU/ky06ZNY+rUqfbl3NxcoqKiLlqdLxUzFu9i6a4UFFQYkAKoF+zFmE6nZh0Y06muU1DKYlPsT82jfoh3VVVXiGqRk1pIdmr5QdbuoxsC4B/qyZjnOrPm+wNs/eOIUzlLScWzUoqa8euvvzosz5o1i5CQEDZu3Ej37t3tPWu/+uorevfuDcDMmTPt0/xWdBNDCCGEqC7JjzxK7qJFpQtKkf3DQmLmfEnxjh1wWp4hdDpMu/dc1kEpt+bN8Rt9PdnffAuAZjAQ/nTt7zRwOpvNyo+vPs+BDWsBcPXwZNSTMwipW4/g6Loc3LSeTT//gE9IKDc88zLZJ46jN7iQtHUjv777Or6hYXj6B/DXnJn2Y+ZnpuPm5YWlpATfkDA6jbiB/IwMFFC3RSuCos4+05wQl6sqC0odOXKEe++9lyVLluDmdv6zWlXE1dUVV9faP3RmQ1IWp89ErwFli16uBm7rVpf6Id70jg/Bw3jqaexaPwg3g0axxTGQtfpAhgSlxGXPYCy/y/KgSc0dZs/T63V0HdEAc5GFnauOA6DpwOhuIKpxQLXUVVy4nJPJUgMCSp+rC+lZazKZMJlM9uXaPtRbCCFEzbHmF5D7008O6yzJySQOvRb3Nm0oSUw8NdTNZsMQUtrTqGjbNgrXb8AQEoLPgKsum+TnmqYR9uST+A4diiU1DffmzXAJD6/palWr/ev/sQekAEqKi1j2+Udc/+QLrFs4j7+/moVOr8dmtXJw43qu+b9H+HPWh2z5dZF9OF95uaGK8/PRdDpsNitxbTticKk4F6oQtUWVffJt3LiR1NRUWrdubV9ntVr566+/eOedd/jtt98oKSkhOzvbobdUSkoKYWGSgLtukCf7UvOxnoxMKeCe3vXpXD+IxmE++FaQrFmn02gS4cvmw9mcHpYK9Kz9gTxR+3kHuBHfKZzda46j6UDZoEWfSGKbld9lvOeN8fiFeZK0LR0PbyMdrqmHh4/Mlncps9lsTJkyhS5dutC0aVPgwnrWXilDvYUQQtQ8rbykroAtPx/X2FgKV69Gld0o0TQyPvsMpeD4QyfzwNls5C5aROR77zrkH7qUaZqGR6tWNV2NGlOQlemwrGw28jMzUTYbq+fOAbDPxLd//RpSEw+w9fdf7GUBLCXOqSbKtmclH+PEgb1ExidU1SUIccmosqBUnz592LZtm8O68ePHEx8fz0MPPURUVBQuLi4sXbqU4cOHA7Bnzx4OHz5Mp06dqqpal43HBjdm+7EcjmadGqr01p/7+Xr9ERqEePHo4MYkRPiWu+/jVzfhxk/WUlhS+kHYtX4QVyWEVku9hahqvcfEExnvT9aJAoKjvKnXKrjCsppOo1W/aFr1i67GGor/YtKkSWzfvp2VK1f+p+PU5FDvrUey+W3HCbzcDNzQLhp/TwmECiFEbabz8MBv5Eiy58513KBpKFPxqYAUgFKYdu0m9cUXSpNan8wflL98OUUbN+LRrl011lxcqMjGTdF0OnuASdM0Ihsn8Men72M1O09OVVxQQOnYl8ozuMj3B3FlqLKglLe3t/0udxlPT08CAwPt62+99VamTp1KQEAAPj4+3H333XTq1OmKyA9islh5d9kBNh/OIjbIk/v6NnT44VLHz52xnaKZ8csehx5PaXkmMvJNXP/hP/x5fw9CvJ2HRraK9uePqT3452AGvu4u9GgYjEF/edx1EeJcNJ1Gow7Sm7I2mjx5MosWLeKvv/4iMjLSvj4sLOy8e9bW1FDv5XtSuWXWejRNQynFnH8O88s93Srs3SqEEKJ2CHvqSYBTgSmdDk2nw2fQILK++tpxVjVNw1ronCPTmpdfHVUVF0FwTCxD7nuYZZ9/jKmggPrtO5GSeID0w0mOBTUNDZj37KN4+PlTmJ1VGsxSCg9vXwpzs0t7y52R3DwqoTmhJxOlC1Hb1ejA5ddffx2dTsfw4cMxmUxcddVVvPfeezVZpWrzwNx/+enfZJSC1fszWJeYyU93d8XlZPBo5qoknv9lT7n72hTkmyysPZjJkBYR5ZaJ8HNnWOvIcrcJIcSlRCnF3Xffzffff8/y5cuJjY112N6mTZvLomftkcxCHlmwrTQf4Mkvl8eyi5j2/TY8jHrqBXtya9dYXA0ynbMQQtQ2ml5P+DNP49mtKznf/4Dm5krgzTfj3qIFQRMnkv7ee/bgQ9Bdd2E+cZyc738ozTWl16P39saj9ZU7HO5SUjYEb9ufv2MwGuky6iYad+tl326zWlnx5WfsWL4EvYsrPcbcQp1GTZj1f3eVf7yT3wmKcnPwj4jE08+fY7t3UJibjU6vJ7x+I1IPHcRsMpV+f9A0NE27bIZyCvFfVWtQavny5Q7Lbm5uvPvuu7z77rvVWY0atS8lj1+2H+fHrcn2dVal2H0ij93H82gWWTokb/6mo+c8lo+73HkXoiYopbBabBhcJLhwMUyaNImvvvqKhQsX4u3tbc8T5evri7u7O76+vpdUz9r0fBMPzvuXjYeyiPJ358URzfF2dWHw23+TV2xxKv/LtuPodRo2pVh7MJNZ49vJlM5CCFFL+fTvj0///g7rgu+5G4+2bTDt349rgwZ4duqEzWRC5+1N3u+/Y83JRXN3J/Orrwi6804JRtSwDT//wD8LvrUv//LOq3gFBhHVpBkA63+cz6ZffqQ0628hSz56hwF33Vf+wU7rAaVsNvIy0shNS7EP+7NZrZw4uM9xyJ9SHN6+FYvZLInOxRXh8pjioZbYeCiT0R/9g9Wqyt1uNJxqgApLnH/YwKnenV3rB9G1fvnJnYW40lgtNo7sysRSYiOykT9uXlXTgCub4tD2DP6YtRNToYWgSC8GTmyGT6B7lZzvSvH+++8D0LNnT4f1M2fO5OabbwYurZ61d325kY2Hs7HaFPnFZm78ZC3Xtapjz+NXnrJJK1bsTeNQRiEernq+W3+EIrOVQc3CSYjwJbOghL/3peFq0NGzUQhuEvQUQojLmlIKVVyMzt0dz86d8ezc2b5N5+qK75AhZH0xG5TCUlBA+ltvozMaCbztthqsdcWUUhSuWUPJkaO4N2uKW5MmNV2lKpG4eYPDsk6v59C/m+1BqaR/N8NpCVZ0ej2ZyceIjE/g6O4d9vVNevRh54ql9mVNp8PLP5DsE6c6JwDl5qAyGF3LnZ1PiNpIXulVrMBk4bcdJyg22/hx6zGsNoXttO26k0Gm3o1DsCkbU77ZTG6xhUMZhU7HGtm2Do3DfAn0MjKoWTj6M2b6OJiWz/1zt7I3JZ8m4d68OqolUQEeVXyFQtQsS4mVH17fTEpiLgDuXi4Me6ANfqEX77WvbIrV3x9g69LDqNPewBnJ+fz+8Q5GPNz2op3rSqRU+YH6010qPWtLLDbWJWXZl60KsgvNbD2S7VQ2zMeVE7kmp/UZBSWM/HAjGfkmNE3jwxUHeW1UC6b/tJOMgtKZeOLDvJk/sTOertJMCyHE5Sh/5SqOTZmCLT8fvb8/ke++g2tcaY4gvW/pyIiCv09O6nFaO5i7ZMklG5RKefY5suaUziyHphH+3HP4DbuuZitVBTx8/RySmCubDQ9fP/t278Agh+02mw2rpYSje3Y6HCcyPgGfoBD+mf81AEZ3DwZMnMIPLz+DqaAApWxomg53Hx/qt+nAv3/+Zt+3180TpFe1uGLIt90qlFds5rr3VrM/tfykhRrQOtqfoa3q0KVeIFe/sxKT2Ya1gh9oK/dl8PKIlg7rbDbFl2sPsTYxkxV70igqsWJVio2Hsxn72TqWTu2BroJpaoWoDXatPk5KUq59uajAzJrvDzDwzmYX7Rw7VyWzZclhp/XKBqmHclFKyReHK8Tu47lowJmf0psOZwOnbjQo4IXhzflq3WF+35FiL9exXgDrEjPIyDfZc0/pNHjul11kF566U7o3JY+v1h7m9u71qvqShBBCXATZ3/9Axqefgs2G7/BhpL35FpSU3miwZmVx6Mab7MEnn8GDiHjhBfS+Po4JrnU6DP7+NVH9czIdTDwVkAJQihPPPIPvddfWuu9AXa6/icPbtlCUV/r9MrhuPZr1OjUks8uomzi8fSsFWZkARDSMBzQ0TYdSp3pN71u7imHTppPQvTcF2VkERcfg6uHJdQ89yY+vPkdBdhae/v4Mvf8xQuvVp36HzuSknCAsrgFh9RtW6zULUZMkKFWFvl1/hINpFc+ioYBnr21KfLgPH644QLHZiu0sHQY8jc5DOV74dTcf/XXQ6UeS1aZITC8gNc9EmK/zDH1C1BZFeSX2mc4AUHBwaxpH92QR2ejifLE7cSCHciMRgFeAW637MiacZRaUMGH2Bjac1kvqTBrQIMSLqAAPbmgfTcd6gTz+w3b7sGsNcNHrMFtPBjFPvmZtCorPuCGh0zR7rykhhBCXtrxlyzg+bZp9Oe3lV5wLnd4b6pfFuDVJwP+G0WR9+x2m3btLN+h0oDeQ89MifK4efEl9vzCfOO60ThUVocxmNKOxnD0uLUopEjdvIPtEMqH1GlAnvuKhh/5hEdz82vsc3rYFg9GVui1aYzjtGn1DQhn/2vsc3bUdg4srkU2asuGnBZz+RVHT6XD19ALA098fr4BADEYjJUWFbP71J8wlJfiHRdD39kmExTUAILZlm6q5eCEucRKUqkK5RWaHHx7l8T6ZrNygd05oeOZv4Cn9HCPmSik+X51U+v8Kju/jJk+xqL2sZhuZyQWoM6O5Cn5+dyu3vtrtoiQj9/QzVvgm6zys/n8+vrj0TVvwL5sOVRyQgtKXSLM6vkT4ufPMop246DWOZBU5bP97XzoPD2jEO3/ux4ayv6zaxPjx5+40e1mLTdG9oeQNFEKIy0H+suWg14P1ZC8Zna50Vr2K6HQU796NzsODut98Tfb3P5D+7rtYMzPJX76c/KVLMScfQ9PryflpEXpvb4LuuRvP9u2r5XrKk7v4V6d1rvHx6C6DgBTA0s/eZ+vvv9iXu95wMx2uHVFheQ8fX+K79Khwu6uHJ3FtOtiXm/cdwL9LfyU3LRU0DRejK22vvpZFb77EntV/gabRZvC15GWks2/tKpTNRklRIQteeIpbXv8Qn+CQi3OhQlyGJGJRhXrFh/D2sv0VdbAAwOPkD+ahLSP4cMUBMvJL0DSwKcW7N7YmKb2AnCILPRsF0yraj9eX7GVDUiY5RWaiA9yxnSMXS5HZiofkJBG11Mq5+zi4Ja3cbZYSG7OmrSIwwov6bUMIj/XFP9wTveHsM9pkHMtn58rSBJQNO4T9P3vnHR9F1bbha7Zveu+dEnovUkQFFEWxoGLvXeT9FHtFfX3FLvbeFcUKigUF6b13CIH03jdt68z3xySbbHYTAqTCXP74mTlzZuZMsjvlPs9zP9itDvxCm/enMngr369TgS3pZS1Gstbzz/4CTLX2Zq/5KgFKq22c2TuEv/cXAvIExLaMcu6YkMT3W7KoqLUhSvDMr3v5+IaRijeggoKCQhdH7e/n2iAI6JKSsB454nkDSULfQ07PLv3yK4pef91tErv4vfeRzGZ5QaUi8+ZbSFr4C/qeHTsZZt63j9Kvv8G0dKnbOp8zJnToWI6X8vw8F0EKYM23nzPk7PPQe3sDUF1exp/vvEb+4UMEhEdy/v89RGBEZKv2L0kSm3/7WRakgICISC5+4AkOrl9DyvrV9Z3YuvgXNHq904sKScJhs5F76IAiSimc0ihvU+3I0LhAPrxuBPOWppBSUImtSdU9P4OGAC85UirER8/i/4znmw2Z1FjtnDcwkmFxrqlH98zfxu+785z3rD25DT46noQvb50af6NSRlTh5OXw9sKWAhGxVNnJTSknN6UckKtXJg4JJWlwCD2Gh7lFURVnV/LjC1sQRfkBY9fy7BaPr9aqCIryOdHTUOgGJIR4U15rc1bRa46WBCmQ3zmu/2wT+kbiqASU19roEepDjdXh/EynFlVz9zfb+G3WeAB2ZpWzNaOM6EAjZ/cNV/wCFfjl0C+8se0Nau21TOsxjYdHPYxWpdz3FU5dnn76aZ555hmXtuTkZA7Up8e1E0E33EDF4sXY8/IBUAcG4DftAorffAskCcFgQNcjCcte2Qjbe9xYAm+8kcqlyyh67TWP+5SsjVK460SMqpWrOlSUMqekkH7lVUh2u8fIL0Pfvh02lhPBUlPtsT1183r6nzkZSZJY8PQjlOXlAFBw5BBfPfwf7v74GzTao0eCpW5az+ZFPzqXKwry2fnPn1QU5rsUc1Gp1ag1WuxWq4sI6d3IRF1B4VREEaXambP7hXN2v3D+8+12ft3pWv7TZLaTW2EmOkAuJx/ma+C+sz2b2tVaHSze5Z7LXU/TlyCtSuCiIVHMW3qIsT2CGdtTSQPpTKwOK9/s/4Z0Uzp9AvtwdtzZmEUz4V7haNXKC8TxYvDRUltlaz4UsQmSBEe2F3FkexG7VmRzyf3DXISpvatyEUXJpcJec2gNas69fQBeft0jbF3hxJg7fSBXfbSBkir5JSHIW0tptWsJZwHw1muosdqbjaqSgOZi9cpqrFjsDR8+hyixJ6cCUZT4aVs2D/24C+oywi8aEsW8K4Z0Kb8RhY5lTfYanlr3lHN5wcEFBOgDuGfoPZ04KgWFzqd///4sbRTVo9G0/+uOJiSEpIULqVz2L0giuvgEMq67zik8SDYbgkZLj6VLAQlBqyPj6qux7Nvf7D61UVHYcnMbxCBJQuXTsRNhpl9/RXI4PApSKn9/fKdM6dDxHC/BMXEu1fKc1N1DzVWVTkGqHpu5lpQNa+l3+lmAXIFvx9+/k71/L77BwYy+5AqMvnKEXGFGGiq1GrEufVMSRQqOpBLZq7dblb5+E85i99Il2G3y80S/CROJ6dd2xXkUFLojiijVQdwyPsFNlAK455ut+Bq0xAd70yfSlytGxDr9pSRJ4pM1aSzcnoPmGGfE7aLE/E1ZaFQCby9P5cVLB3LFyLg2OReFY0OSJO5dfi9rctagElT8LP3M85ueB8BH68N7k99jSNiQzh1kN2X8Zb34/d1diHVRiH4hBsIS/EjdUnjUbQvTKzm8rYjk0RHOtqOlw9Yz8MwY+o2PJDhaiZI6Vegd7svKB8/iYL6JXVkVPLN4n1ufIG8dz108gP98t935mfSEJEGAUUu+zeJsGxjtz9n9wnnhzwNOjbVe5Or/9BJqrXU+JXUrF+3I5bbTkxgQ7d9GZ6jQnbA5bMxZP8et/adDPymilMIpj0ajISIi4ugd2xi1vz8B0y8BwPTnn67peA4H1tRUdDHRAGTddTeWgynuOxEENGFhhM66B21iElk33YRks8npfj174n/B+R1xKg2oWvDl7EaVhzU6HSOmTXeJZjL4+JI4dAQAWoPR43YOW0O02upvv2Dzrz/J5ywIpG3fynUvvolGpyM4OsYpSIFsch4SG8+Yy64m+8A+Cg4fAqDH8FGcce0tjLjgEnJTDuAdEEhM3wHd5veooNBeKKJUBzE4NpBJfcL490Chc6YbYHtWhfzDoWIAVqcU8961wxAEgU/XpvPc783PoLRE/W3QXjdd/9o/KYoo1UlkVWaxOkfOJ3c0KhMLUGWr4j///oflM5ajbunGr+CRuP7BXPnkKHJSyjH6aEkcHIKgEtDq1exf23xkIQACWGvtLk39xkaxf20egqrlaKndK7LZvSKbhIHBnHunPLu1b3UuxdlVBMd4M2BCNCpVy95VCt2HXdnlHC6qIjncj+HxQfzftzvc+gyJ9WfB7WPQa9U8b7Hz4I+73PrU172QgHyTxWXd7pwK0oureeKCfjy3eB9SXf8qi91tP/WYzLZm1ymc3GzO30xhjbv4XlxbzPbC7QwNG9oJo1JQ6BocOnSIqKgoDAYDY8aMYe7cucTFeX4GtlgsWCwN12OTyeSx37Gi69HDtUGtRt+rl3PRvHdvgyl64+2Skoj79BO04eEAJC5aSPWqVai8vfGbOhWVV4PHoPlgCqVffIFkNuN34TR8zzyzTcbemIBLp1P69deyt1WTKCOxshJbXh6CwUDJ+x9gKyjAa+QIAq+6CqELPgOdftUN+IeGc2TbJoy+/px26ZV4+ckTOxqtlpC4BIoz0539BZWKhEbV8HYs+R2QJ5uRJEpzs8k5uI/4gUNIHjuBzL272L1sCQCh8YmMv+p69F7eXP3cK5RkZ6HWaAiMjEYQBPxCwvALUTykFBTqUUSpDuS9a4fz0eoj7Mgq5599BR77/LU3n/SSGhJDvPl1R47HPgAxAUayy2ubXd8Us60V+UgnKZXWSvKr84n2icZL64XZbkav1rfZrESNrYav939NXnUew8OHc36iawlf8Si5YGWWMiqsFQQZgtpkPKcagRHeBEZ4u7SddW0feo0IJ+tAKalbCqgqtbh5T6nVKmL7uv7OwxP9mP7AMPauyiFzfyk1FVZaIn13CfvW5JKxu5iMPaXO9h3/ZHHVnNFodYrQ2N15f+VhXvhT9iIRgGcvHkClB6Hojgk90Nelgk4bHMVb/x4is7ThGm3QqugV6sOeXFOz2ab/t2AHmx+XvS2e+31/symAapVAkLeOgUqU1CmLTWxekMytylVEKYVTltGjR/P555+TnJxMXl4ezzzzDKeffjp79uzB19fXrf/cuXPdPKhOhOr168l7ag72/HyXdrWfH6EP3I8lNRVdQgL6nj2xl5S4CFNRr7yM37nnIjRKN9QnJqJPTHQ7jjU9nfQrr5R9pyQJ0x9/EPP2W/hOntxm5wKgi48n6eefKP3uO8o+/8J1pSRRu28/Ra++ijUjAySJyr/+wp6XR9gDD7TpONoCQRAYfPZ5DD77PI/rr3j6BRa98j/yDh3E6OfH1Hvuxzeowf5E8JC1Uj8BKQgC59w+izGXXYXdYiEgPNIpzKlUakLjEtr+hBQUTiIUUaoD0WlUzDyrJxW1NgY/83ez/ax1niK+Bi0qAY8vJgOi/cmtqHVb11ylv8uHxxz/wLs4hdWFvL3jbWpsNZwRewYXJF3gFIX+Sv+LR1c9il2yoxE0BOgDKDYXE6gP5IUJLzA2auwJHfu31N94ct2TzgioH1N+JMuUxV1D7nL2ifeLZ1TEKLYUbPEoUAXoA/DXKS+XbYkgCMT2DSK2bxBjL+mJwy5SmlvNgQ15ZO0vxeCl5bRLehAQ7l7VLCLJn/BEP96bufyox1GpBQrTK10EKYDKEjNbfk9jzCUdWyFHoW0prbby4l8N5rgS8PSve5kxPIbvtmQhSaAWwMegZWhcAB+vPkJqYRV9I/349Z7xvPjXAXZklZMQ4s2cC/rx8Zo0lwIVTak02zlSVM1na9M8rheAAC8tg2ICmDOtH74GxY+uK3Og9AC7inYR4R3B6dGnNzsRsiJrBSuzVxKgD+C6ftc5JygkSWLxkcUcKD1Agn8C03tOd0bUGjVGBASkJnd8taCmX3C/dj0vBYWuzHnnNQgOgwYNYvTo0cTHx/P9999zyy23uPV/9NFHmT17tnPZZDIRGxt7XMe25eaSdcedznS7xjgqKsi89joAdL16EvXcc1gfeBBbVhYAIffcg/8FFwBgLyujYO4LWPbvR98nmfBHHkETHOyyv4rff5cFqXpRSxAo+25Bm4tSkiiijY4m4pFHqFq+Qh5vfcSUICBWVbpVGCz9Zn6XFKWOhsHbhyvmzG12/cgLL2Ptgq9QqdVIkkRYQhJRya7X28YiloKCQutRRKkOxmxzMG9pCl46NTVW17BdtQD9ovzpGSb71Nx3dm82pZVidbgKGVq1wJnJofy1t2EWRq0SOLN3KDuzyymusqJWCQyM9sOgVXN6r1DumJDU/ifXCewp3sO1f1zrFIWWZCwhqzKLu4fcTbm5nEdWPeJcZ5fsFJvlNMkySxkzl87kvuH3cXb82UT6tK7ka2N2F+3msbWPubV/uudT7hx8p/MFRBAE3p70Nu/teI+v9n2FXWqIslALat6c+KaSutfOqDUqQuN8CY1znyX1hCAIGLy11Fa2nB4lOiSCIt2FLYC0XcUknxZBUKTiO9VdKauxukXYOUSJmRN74mfUsmhHDma7yIAoP+77fgcbDpeiVgnYRYld2eW8OmMIyw8WciCvkkd/3s3yg0VHPeb9P+ykupmUvYEx/nx722l465Vbd1dDlERyqnLw1noTZAjijyN/8MjqR5yi0YU9LuS5cc9RbiknrzoPb603UT5R/Hb4N+asm4NakO8Bfxz5gx8v/BFfnS8vb36Zr/Z/hUalwS7a2Zi3kZcnvIwgCPx3w3/dxuCt9ebZsc+S6O8eVaGgcKoSEBBA7969SU1N9bher9ej1+tP+DjWjAyy7rrLtWJeYxqlvlkPHyFvztOoQ0PQxsYSMvNuvIfLaWKSJJF1+x2Y9+0DhwPLkSNYDh8h8ccfXFLiBLXaTfhC3bbPkqVffEHha68jWa34nn02kc8/T87MmTjKy0GlIuLJJ9BGuD8/d8XUvaNhNddSnJmO0dePwMhoj31GXzID//AIsvftxjc4lGFTL0TdASb6CgqnAso3qYO5+5ut/HvA9cUkws9A73AfeoT5cO/k3qjrwkOHxwfy572ns2RvPsv2F3KkqIogbx1PTevPGb1DyS2v5a3lqUgSDIr259UZgzHq1GSX1RLio8ffePLPoj+2+jE3n6ZP9nzCXYPvIqc6x21dY+ySnZe3vMzbO97m83M/P+bZ5S0FWzy2W0X3BxKtSou31ttFkKpvV9IsuiZnXtOHJR/uQawLR9Qa1Aw6MwZTcS2HthSiUgsMPzeeQRNj2Lk8m+oyV4+gsrwavn1mE2Om92DYOfGdcQoKJ0hckBcxgUbyKsw4RAm1SiApxJsofyPRgUanL9S6wyXOqNV6H7+ftuUQ6KXj4zVpTi+p1pCSX4lW4x5RM6V/OG9fPYx/9hXw7vJULHaR68fEc92YhLY4VYUToKS2hDuX3smBUjmq7qb+N/FL6i8uUUy/Hv6VCK8IPtr9kbPdW+uNr1YWyuvvVbnVuazMXsnE2Il8vf9rAOyifN9Ykr6Ee4fdS4xvDDlVOW5RUnPHz+WsuLPa92QVFLoZVVVVHD58mOuuu67djiHZbGTefAu2vGa8LJveBEQRy4G6KFy1iuy9e+nxx+9ogoOxFxRg3r27oa/DgWXfPnIeeBB9QjxBN9yA2t8f/4suouTTzxCrq+sGIRF8w/Vtdk7V69ZRMPcF53Ll0qVoIyPoufxfrBkZaMLC0AQFIVmtGAb0x7xvP6hUYLcTfNutbTaOtkaSJA6uX01RRhrB0bH0HX8mpbnZfP/sY9RUlAMw/PyLOeO6W9yiWwVBoO+4M+g77oxOGHnHUlV1kNraTHx8+mI0nrzZNgpdB0WU6kAqam1ughRAgcnMqofOQqdxn1noEerD3Wf25O4z3dOAZp+TzG0Tkqi1Ogj1bfBI6hF66kRmFNW6/z5FUSSrMot/Mv5BhQqRlj2dau21vLntTd4/+/1jOnaoV6jH9hifGIprizFoDPjqfFlwYAGvbHkFs8Ps1tdb541DdPDW9rdYnrUcX50vdw66k+1F2zlSfoTkoGRuHnAzOrXumMamcOIkDQnlqjmjKcww4RNoILKnv/M7NulGEUEloKoTkGc8NpKFr26jLL/GbT/rfznMwDNjFH+pbohWreLrW0bz0I87OVRYRb8oP166bDAqlcCCzVnOfs15P32yRk7Da60gBeCQJBw29w3WpBazOb2Uu7/Z5mx7ctFeSqqt3Du5d+sPoNDmvLz5ZQ6VHXIuf7b3M1SC+/38w90fuixX26qpsblfM6pt1dglu5voBA2THgNCBrCjcIdLnxVZKzgz9kylipPCKc0DDzzAtGnTiI+PJzc3lzlz5qBWq7nqqqva7ZjWrGxsOc34wGo0aKOjsWVkeF7vEBErKqhetw7/adNkI3MPMxmVS5ZQKUmYlvxN4k8/oo2MJPHnnyn/7ltEswW/86fiNbTtJjlrd+6UI6/q0wNFkZqtW1EZjRj69HH2E3Q64r/4gtKvvsKWl4/XyJH4nT+1zcbR1qz86hO2/r4QlVqN6HCQuXcXZXm51FY2pNZv/X0hPYaPIrb/oOM6xr5V/7Liq0+w1tbQa/Q4zrljFlrdiUfjdRTp6e9y+MirAAiChgED3iQsdEonj0rhZEcRpToQrdrzg6JKJeDBO69V+Bq0Hn1FRFHilb8P8sW6dFSCwB1nJDHzrJ4n3cPqyIiRLM9y9f45I+YMLv/tciwOi8eHek+UmcuO+djnJpzL/P3z2V2823WFBBN/mIiAwKS4SSzNXOpxewGB+4ffz8xlM1mbu9bZfteyuxCQ/07LMpdxoPQA886ad8zjUzhxAsK9CAj3oiSninU/yaH/fcdFERTpaqzu5avj6qdPY+tf6WxY6OqtgCR7TDXdRqF7kBDizfd3unrP7couJ6WgssXtzkoObTFdr/5KrFaBvRV1KNSCwF978t3a31meyl1n9kCvUUTPzuJg2UG3qFx/nT9llob7ikFt8Dgx4eke9cPBH+gb1Net3U/nR5W1CoBz4s9hR+EOl/U/p/7MkLAhXNLrkuM5DQWFk4Ls7GyuuuoqSkpKCA0NZfz48WzYsIHQUM8TiW2BOjDAXUhSqUj68w/08XKkdPF771H01ttuFeyc3Y1GeV9+fgTfcTsl738gRx7V968Th6yHD1O9fj2+Z52FLia6Tb2bJLsd1GoEQUAbE+NaHVCtRhfnOepb5e1NyJ13ttk42gtLTQ1bf18IgFh3bntXLMXo54/U5O9SUVhAbP9jP0Ze6kH+fOc15/LBtSsx+vgy8aY7jnvcHUltbbZTkAKQJAf79j6EpUcBZksO/v7DFIFKoV3ofkm/3RgvnYZbxiW4td95RhIa9bH9KVILK3nox53MnL/N7UVld3YFl3+wnndXHKba6qDSYueVv1P4dWfuiQy/S3JNn2sINcoPGmrUXNzjYoKMQVgcFhySo9Wi1OT4YzeG1Kg0fHXeV9wz5B4S/BJIDkxmaNhQcqrl2TIJiaWZS50CU2NCjaF8PfVrRkaMdBGk6pEa/bcsc9lxiWYKbUNRViU/zN3Mzn+z2flvNj88v5mS3CqPfXsO91DeVwCfwO4zQ6bQMla7yE2fbcbuaP7acna/MAZF+2PUehaKeoR6MzjWH4TmBalwPz0qATR1MxZ3n9UTlYdJBZtDoqDC4tau0HHUp9c1prEgBWBxeP4b1XtJNeZg2UEWH17sFm1lspq45o9reGDlA7y8+WW3+5tG0LhPkigonGJ899135ObmYrFYyM7O5rvvvqNHjx7tekxNYCBhD9zf0CAIRDz1pFOQAgi56y78pk2ThaYmGAYMwHvCBOdy2L33EvvhB4TNvg+Vr4fsh0biV/W6dWTcfDPp115LxaJFxzV+sbaW7Pvu48CgwRwcNpzSL7/Cb+pUfM8719lHGxVF2EMPHtf+uwoOu2ef0LCEJFcfLEEgPKnlQjWi6MBmdb+u5x7c7xIAIEkSGbt3HNd4OwOrtbBJi4RDrCLl0LNkZX3O7t13k5b+ToeMpaimiG0F2yiuLe6Q4yl0LkqkVAfzxAX96Bflx49bs1GpBGaMiOXCwVHHtI+s0houemctZpuIJEn8viuPly8bxOjEIAoqLVz90Qa3FyaNSmDDkVIuGuLZvK87cqD0AHctu8v5QuDAwZGKI8T6xbZajBIQmJE8g5sH3HxcY1Cr1Nwx+A7uGCzPgFz+2+UuM+aeqiMBXNTzIgaFDiLTlNmq43hKBVFoX/atzWX3imwqS8w47A1/Q7sksXdVLhOudE+Z8g/1YvzlvVjz4yG5VJsA59zSH51BudSeLORV1FJS3YyRbR27siv4Z1/Dg51KgHP6hXPz+ERUgsDs73eyI6uixX1UWxxce1o8i3bkUm2x88++Ah49rw9frEt3uaLo1CpCfJX03s5iTc4a0k3pR+3n6T6gV+ubFasCDYFIzeR9Lklf4rHdLtnx0nixKnsVfYL6EOblQSRXUFBoF4JvuQWv0adhTTuCvndvDMnJbn3shQWukVKCgPfYMcS88w4qnet13GfCBHwmTMBeXEzp518429WBgXiPHg1A7e7dZN56myxSSRK1W7YiaLX4TT229LmieW9QueRvEEWk2loKnn8efa+eRL/2GpY770SsrsHQry8qg+GY9tvVMPr6ERqfSFFGXYVbQSAiqSdTZ97Pb2+8SPa+3Wj1Bibdcheh8e4FI7b+vojNv/2EzWLGZjYjiSKx/Qdx4ezHMPjI4qFPUIjLtVtQqfAL7R7XYpvNxOEjrzdpVQEiICHV+eKmp79DQvzd7Zp98/uR33l8zeM4JAdalZZHRz1Kz8CeJPkn4a9XKpafjChvSh2MIAhcOjyWS4cfX7lZgN9351Frdbj4mDz44y7nzyoBt8dfUZKI9O/eN5Om/JTyE3bR1XdjV/Euwr3CEaWj58MICNw9+G7uHNJ2Ice9A3tzqOyQU5iSkPDT+WGympzHvKjHRdw9+G4AYnxj6BPUx2mQ2xiNoMEu2bmk5yXKBbiDObS5gOVfuf9NAJDAbqv7+0oSpuJa7FaRwAgvVGoVgyfF0ndcJJUlZnyDDOiMymX2ZCLER49Oo8LaJMRJJTR4SxWYXIUGUYJz+kcwKjGYj1YdIbvM3UeoKQ5RYvGuPCrNNkQJtmeW8ehPO5nQO4SVKfKsoQC8OmMQXjrlM9ZZpJSloBJUrbrnNOXbqd8y/bfpbu2jIkZx04CbWJe7jh1FO45pn1/s+4Iv9n2BXq3nzYlvMjZq7NE3UlBQaBOMA/pjHNB8zpfXyJHUbNjYEOkkSQRdf32LYk/Ntu0uqYGOsjJsBQXok5KoXLJEXlcvdAkCFb8tRuXjQ+3u3egSEvA777yjVsOr2brFVSxTq6nduRPvMWM8imvdlfzUlAZBCkCS6DFiNF4BAVwxZy52qxW1VutRbDmwbhUrvvzIrT17/x7+/fwDpt4jR8r1Gj2GXqPGcGjTegCMvr6cdcNt7XNCbUxKyrOUlW10aTMaYqk1u/qhiaIdWahqH9uAKmsVT6x9wvkuZRNtPLvhWQC8NF7MHj6br/d/TW5VLgNCBvDihBeJ8I5ol7EodBzt+iQ7d+5cfv75Zw4cOIDRaGTs2LG8+OKLJDe6wJnNZu6//36+++47LBYLU6ZM4d133yU8PLw9h9at0RzFgMqT6W7fSD9uHn/ylYn2NPu8t2TvUbcT6v6bEDvhqH2PhftH3E9KWYpTZLq277XcPvB2lmUuo8JawbkJ5xLt2xCtJkkSdw2+i6/2fUWWKYtQr1AeGvkQ+0r3OY3OL+11aZuOUeHoHN5eKL/xNxNwt39tHnmp5Wh0aoqz5FS+kBgfLrp3KAYfLTqDhuDoU6fgwKmEt17DazMGc9+CHdgcElq1wCPn9qHK6uD1f1Ka3W5LehmXDI2m0myTH3ibRME0/bhF+OlJK2kQr0QJDhXVcKiooU0CUgur2+jMFI6HngE9j0uQ6hXQi56BPRkQPIA9JXuc7TE+Mbw36T10Gh2fTvmU1TmruXf5vW73utOjTmd17upm9291WHlizRP8O+PfYx6bgoJC+xBy223YCwop/+knAIxDhqBvZBruCcuhQ273C8uhVPRJSQgGIy53DkHAlptL1u13OE3Kq1evIeqFuS0eQxsbh3n/gQYPKYcDbdSxZXF0BNbaGv567w3Stm/G4OPLpJvvoufI01q9fdqOLSCooNE1+8DaVZw2/UoANLrmo44zdm1DUKmRRFf/QEkUyT24z7msUqmZdt+j5KWmYK2pJqJXMgbv7vE8WF6xBXA9v5iY68nJnU9tbTqS5AAEIiOnI3hIPW8rimqLPKbFA9TYa/jfxv8hCAKiJLKzaCf3Lr+X7y74zqVfekU6mws289Xer8iozCDBL4GXz3iZ3oFKYZiuSrvmBK1cuZKZM2eyYcMG/vnnH2w2G+eccw7V1Q0P0ffddx+//fYbP/zwAytXriQ3N5fp091nDhUauHBIFIFeOtRHEafUKgG1IPDshf355e5x+OhPrtn0S3tf6tGvqaUXhAjvCIINwST4JfDaWa/RL7hfm44pyBDEggsW8Mf0P1gxYwUPj3qYMksZ7+96n3nb5jH1l6l8f/B7QPYhuf2f2/m/5f/HloItVNurmTN2DkPDh3JN32t4csyTzEiegVqlGBh3NDqjhqNFJZcX1DoFKYCS3Co2LDrcziNT6ApcMCiKdY9M4sc7x7DukUnccnoS146Oa3Gb+ZsymTl/G++vOoyjycyBTi246Z+NBamW2J6p+M11JqdHn85NA25yLif6H33yR0DgjbPeoMRcQlZllst97IrkK9Bp5BcjrVrLxLiJ3DvsXpftR4WPYk/JnhbTuiUkSswlzaYAKigodDyCVouhTzLY7SCK1G7fTvrlM3BUNJ/Ore+RJAtMzp0IchsQeMUM1IFBsk+VSoWg08kiFjgFpoqFC7FmtmwVEf7gA2gjGiJNfKecg9/55x/nWbYfyz59n9TN67FbrVSVlvLra89TkpN19A3rMPj4uQhSAKU5WVSWNO9ZlLplI2/ffCV7li91E6RATs8LjIx2a4vq3YeEIcO7jSAF4GWMdxObvLwTGND/TYzGeDQafwICRtO715PtOo4onygC9AHN3uMkJOe7nkNysLdkL1ZHg63C53s+Z9rCaTy7/lnSTGmIkkhaRRq3LbmN1LJUl/tija2mWQFMoWNpV1Hqr7/+4sYbb6R///4MHjyYzz//nMzMTLZu3QpARUUFn3zyCa+99hoTJ05k+PDhfPbZZ6xbt44NGza059C6NWG+Bhb/Zzx3TEgiwq95A2WtWuDda4dy/dgEdJqTz5OoT1Afbhlwi1v7uOhxLh5RAgIPj3yY5TOW8/elf7PiihX8esmvTIqb1CbjsDqsvLT5JSZ+P5Fpv0xjedZyYn1jCTYGA/Dw6oedJn2iJPLfDf/lYNlB7vrnLjblb3Lup9pWzcubX26TMSmcGMPOiZd9oI4hXV4SoSy/dUKCQvcn1FfPiIQgQn3la3Cwj56Lh7bs2ffH7nysjfzJQnx0aFQC1mZM0yf3PboPRUWtZ+NWhY5BEARmD5/NyitW8uf0P1lwwQKCDcHOh+mmD9VqQc2w8GHE+sWyImsFFdYKlyioX1J/cTtGvWm6qu6RTRAEyixlR43QCtAFkFXZ+hc2haNQXQILroNXk+GzqVB8qPm+Djts+RSWPA67f3SLdFE4dSn94kv5B1EEhwN7YSGVy5c32z/qpZfQhNXdC9Qqwp94HH1P2YRbExpK0qKFhD34IKH33kvCd996rO4n1rT8bKKNiiJp8W/Ef/M1ib/8TPS8eQjqrjchmrF7R6MqeRKSKJKX0ozVQn0vUaSytBib2cyAs9yLGkmS5JrS14jygnx+e+15LNWei9sAeAcEMunmu1p9Dl2Z5OSn0WpDnMtRUVcS4D+KXbvvpKYmA7u9gvLyjaQceq5dx6FX63lv8nuEex09a0pAwE/nh1YlV6LPq8rjta2vufWTkCi1lHLJr5dw69+3kleVx/V/Xs/o+aMZ/c1ofkz5sc3PQ+HY6NDQmYq6mYCgoCAAtm7dis1mY/LkhotEnz59iIuLY/369Zx2mntIpsViwWJp8OswmUztPOquSaS/kYfO7cP0YTFc9PYaqq3u6r3NLvHrjjym9I/shBF2DHcPvZvUilRWZK0A5JSIe4fdS4AhgNOjTyerMos+QX3oG+xeXrst+O3wbzy19insdeZ/xbXFzF4+m/kXzKd/sOwrcKTiiFu58Mt/vdwtHUNCoqim+RLync2e4j08svoRsiuz6Rfcj/tH3M/GvI2IksgFSReQ4J/Q2UNsMwLCvbjyydEc2VEESAgCFKRXcnBDfrPbCAKExft23CAVuhyvXDYIg1rFd1vchYB6fbPxtz7cz0BxlbtpugBo1AIPnJPMqpRirI7mxYfIAOOJDVrhhHCIDj7d8yl/Z/xNgD6A/wz9Dx+e8yGPrHqEdFM6vQN7c27Cuby9420sDguJ/onMHS+n0niqvKdRuT6WZVdm8/nezwEQkT8HG/M3Nt3MSePiGuXWcq754xoWXbyIIENQW5zuqc2CayBrE0gOqCqCLy6AWdtB5yULViWHICAefCPgx5tg/2+g0oBog/xdcPaznX0GCl2Uph5GotmMZDaj8vdHn5REz7+XYMvNRR0YiNrPz6WvJjiY4JtudC57T5hA9Zo1sjilVqNLSEDfiuqDKqMRr+HD2+R82gvfoGBqKsobCVPgExTcbP+Kwnx+mjuHstwcVGo1k26+C/+wCCqKClyEYr+QUI/bF6alIjrc368aM+qiywiI6HrvWaJoxWotRqcLQaVqXTEUL69Exo5ZSmXlPrTaALy9e1JWtgGzufEzjUR+/i/07fM/hHYswjQgZAB/X/Y3FoeFrflbmfXvLKyi+/OSWqXmuXHPOb9DBTUFRy12taVgC3cuvZMMk+yVZRWtPLv+WfoF92vzDBqF1tNhopQoitx7772MGzeOAQMGAJCfn49OpyMgIMClb3h4OPn5nl/+5s6dyzPPPNPew+1yfLY2jdf/ScHmkLh8eAz3TOqJn0FLzzAf1jw8kRkfrONQE28RhySRVlyN1S6elJFSAFqVljfPepPD5YexiBZ6B/Z2quUjIkYwImJEux07pSyFx9c87nLxq/95ReYKpyjVK6AXB0oPuAhTzV0wT485vd3GezxsL9zOhrwN+Gp9eXPbm9Q6agHYXbybm/66CUGQvbm+2PsF35z/zUmVq+0TqGfQWTHO5QGSxJEdRdjMnh9Q4gcEM+rCpI4ankIXQ5IkXvzrgEdBCuR0anujtD21SiAxxJt9uSa3q0GYn54Xpg8iKtDIDWMT+Gj1kWaPOzJBERs6kw93f8i7O94F5Eimmwtv5peLfuHni3526XdNv2uotlbjr/d3PjxPip/Eezvfo7BGrtTokBwuUb4F1QVc+8e1LR5fhcopVsX5xlFjq6HY3BCZW24pZ23OWqb1mNY2J3yqYq2BzPUNy5IDKvOhaL8sSH1/LdgtIKhh4pOw/1e5n1gXybj2DTjjUdApIvKpTtAtN5P/5FPOlDxNWCg+Z53lXF/8/vsUvfkWiCJeo0YR8/ZbqP38qNm8meL33key2Qi48gp8J0+m4IUXsOcX4D1+PGH3z0al1xPz+msUvj6P2p070SUlEv7ggwhabWedbpsy+daZfP/sY1hr5civfhMmEj9oaLP9/3zndcrz8wAQHQ7++ehtzrvnfpZ9/C5Ws/w8O3bGNYTEJXjc3rcZsaoxaTu3MfTcrnN9lSSRAwfnkJe3AElyoFZ7M3jQhwQGts57S632IiCg4d1JpXI34VeptBxTKsEJoFfrGRI2xKMgNWfMHMZFjSPSp0EUTApIwkfrQ42txnlvdEOCnKoct/eyfSX7FFGqE+kwUWrmzJns2bOHNWvWnNB+Hn30UWbPnu1cNplMxMYefyW77sDyg4U881uDid6XGzL4ckMGKgEm9glj5lk9Wfyf03lz6SHeWeHqabMvz8So/y3l4xtGMOIkfXkRBIGegT07/Li7inZ5FJckJL7e/zWX9r6UCO8IXpzwIrf/fTu51bkt7q93YG/+b9j/tddwW8WB0gPcu/xecqty8dJ4UW2vRi2o3SK9QD5PZ162CPP3z+fpsU937IA7EEEQEO3uNzifID1XPTlaqbJ3ivPnnnw+Wu05BQBkEWpobACbM+RUrLhAI09N68ewuED+u3ify5VEr1HjY1Az5fVV5FWYWzxuRkk1aUVVpBZV0yPUm6TQ7uNfcTLw+5HfnT+LiJgdZj7f8zk3DLiBWN+GZxOtSkuAIcBlWz+dH9+e/y3fHviWCksFZ8WexdhouVpelbWKR1Y9Qom5pMXjN74HZVVmebwn6dXNp/krtAK7BTLWgkrbIDLVo/eHLy8Ce90Lk+SAZc1ERH1wOlz7IwQmtOtwFbo2gZdfjiYwkMoVK9AEBBB0ww3O6KeqtWspmveGs2/Nli0UvPQSflOmkPdEg49P8ZtvUfLRx0hWKzgcWNPTEasqiXr+eVTe3kQ88XiHn1dHEJ7Uk1ve/Ii8Qwcx+voR2SuZzN07Wf3t59RWmkgaNoozb7gVtVp+HivKSHOJqpLbjmD090dQq0gaPppRF13W7PEieyYz8sJL2fzrTx7XCyoVRh9fJFGkIO0wNouZiB690Oo7r9r5kSNvkJs737nscFSzc9cdTDh9EyrVsd8L/PwGERQ4ntKytQiCGkmyk5j4f+7RfaKN/PxFWCz5BASMIjBw1AmfSz312ShNGR4+3ClIlZnLMFlN/Hb4NwwaA2a7GUmS6B3Ym16BvVh8ZLFzOwmJMK8wcqtyXd5v4nxb9gZVaF865C3qnnvuYfHixaxatYqYmIbIg4iICKxWK+Xl5S7RUgUFBUREeC7tqNfr0etPrQesjUdK0TSZZQe5GtPS/YUs21/IvCuHMH14DO+vPIKjiXeByWzjti+3sPnxyWjUJ0fElMVhodxcTogxpMONwLMqs9hWsI31ueub7VNjq+HTPZ/y2OjHiPeLZ/Elixn29bBm+48IH8Hbk95Gp25diG17YLabuXnJzVRaKwGotsuRd54EqaZISFgclqP2685kHSjFYXd/4YtM8lcEKQX255k8XqfrsTskJvQO5YkL+mGxi4T46Ph6fQZWh8R/Lx7AEwsbKrDllNdy19fbKKs5ul/Ul+sz+GpDBpIkp5A+d/EArhkd32bnpdAyvlr3lN0FKQtYkLKAB0c8yPX9r8cu2vn50M+klqcyJmoMZ8U2REUEG4O5Z+g9AORW5XL30rtJLU+l3FzujExtCU+Ruo3pFdCry0XgdisyN8JPt0CFhwhIrTd8eSFYKpusEEGtlX2lGv9NSo/Az7fDLX+354gVugG+kyfjO9nd38i8b598IXdO+IlU/bsctbcPaDSyQXodUm2j64MoUrnkb3j++fYeeqfj5edPj+Gy4FGclcHPL8xxptjtWLKYQ5vXc8u8D9DqDQTHxJJ/+JCLMLV18cK6X6/E/tXL8Q0M4vSrb2z2eBOuuYmeI8ey/qf5WGuqKcvPo9Yk29HovbwZddFlLHrlfxzeKqdV+4WEccUzLzabEtje5Ob94NbmcFRhsRRgNB676CIIKgYP/ojcvB8xm3MJ8B9OSMhZLn0kycHOXbdRWroGQVAhSQ769plLVNSM4z6Pxvjp/JgUN4l/M/9FQkIlqBgUMoh4v3gkSWLetnl8uudT13HX/ffM2GfoE9QHnUrHz6lyBPPUxKncNug27vjnDgpqCgC4sf+NjIpsOyGty+GwweaPZS/EyMEw9Dq5QEIXol3fpCRJYtasWfzyyy+sWLGCxETXqjTDhw9Hq9WybNkyLr1ULnt/8OBBMjMzGTNmTHsOrVsR6W9wE5oaIwH/990OQnx0iB76iRKU1dgorbYS5td56n1b8Xf63zy25jEsDgsRXhG8O/ldegX26pBjb8jbwMylMz2GkbogQIWloZqKVq0lSB9EqaXUpdsVva/gloG3EOEd4Tbr0NFkVmY6BaljRZKkkz49pDDd3b9OUMG4yzrms6fQtekZ5tOsIAVyOvW/Bwq5YlQsNofE1DdWU2XxPPvnECVKq6003V2AUYskSVSYXberv+xLEjy1cC8XDIrC33hypGt0dW4ZeAv3rbjP47pXtrzCxLiJPLL6EXYW7QTg2wPfclnvy5gzZo5LX6vDys1Lbia/Or9VEwGtIcIrgq+mfoVRo6SMHRcb3oe/HvawQgAksFXL/xq31SOKoNGDvVGko+SA7M2w/l0Yeg0Y/Ntv7ArdEn1iopspvqO0FHt5uUcD88aofE69KNmMXdsRm3guVpeWsOjl57jsiec49+7Z/PS/JzEVFyIIAknDR3Nk60ac31VJ4vDWTS2KUjaLmSXvvU5Zfi4CAqLooO/4M4kbMJjEoSNI37nNKUgBVJYWs3r+55z/nwfb4YyPjlrt1Uz78XueqlQ6YqKvbnZ9ecU2SktXA7JABZB6+OU2E6UAXpzwIh/v/ph9JftI8k/izsF3ohJUrMpe5SZIAU7xal3uOvqH9OeZcc/w0KiHkCQJH538XVl8yWIOVxzGX+dPjG+M2z5OGiQJvr8BDv7R4HOYtwsueLWzR+ZCu4pSM2fOZP78+SxatAhfX1+nT5S/vz9GoxF/f39uueUWZs+eTVBQEH5+fsyaNYsxY8Z4NDk/VbliZCy/785jU1ppi/08GeaCPOnib9QS5N15UThtRW5VLg+sfMA5I1xQU8DsFbP57ZLfOuT4czfOxdY0fN8DoiRyRswZLm3josex+Mhil9nsxIBEl1zoziTEGHL0Th4IMgTx33H/ZWzU2DYeUdfCP7TJjV6AxEEheAecWpGbCp6ZNiiKDUdK+HaTHFGRFOpNelE1Eg2vqruyK7jsvfWcPyiSKosdR53qpPKgR3vSt8pbUWnPIcmCliJKdQynRTb/rCIhsTZnrVOQqufHlB95eOTDGDQNk0RpFWnkVOW06djya5ovzKDQAqlLIWUJbPqomQ5NvpyCWhagbI0qnEkOsHsQFyURljwKmz+C21cowpSCCz6TJqEOCsJR2uh5X61GGxmBrkcS1kOpnjdUqQh/xJOA2rWorark8OYNIAj0GDEao48vouhAdZSMh4Pr17Dtj0UADJt6Iclj5OhPvbcPbt9H5Cp9puJCgqKiufmNDzEVFWDw9SNt+xYOb2mo7i6oVHgHBLZ47IzdOynNzYZGR8rcs5Opsx4AwFRUiKBSI4ny910SRSoK2u7aK0kSIqBu5cR1bMyNpBya49bucNQAgVitpaQefpHqqhR8fQfQs+dDaDQnVqTH4aj20Hb0SN9jQa/WM3PITLf2w+WHUQkqj9VoRUnEX99wjfXWerusN2gMTv/fk5qyNDhYZzVQ/w675WM4+xnQdx0xu13jtt577z0qKio488wziYyMdP5bsGCBs8/rr7/OBRdcwKWXXsqECROIiIjg559/bmGvpx4GrZr5t47m9SsGMzjWH+0x/tV89Ro+uHb4SZG69+qWV93SFdJN6dhFzxEHbU2ZueyoVR0C9YE8NvoxpiZNdWmfNXQWYV4NJd6HhA7hst7N57J3NEGGIK7vd32r+4cZwzg/6Xx+u+Q3JsRMaMeRdQ16DA0l+bSGtGL/ECOnX5HciSM6eVi1ahXTpk0jKioKQRBYuHChy3pJknjqqaeIjIzEaDQyefJkDh1qoRx7J6BSCcydPoiNj01i5YNnsvS+M/h55jjUjRQnhySRWVpDVqlreW5JguQI31Y/dLodu24ztSAQ4WcgWqnI12H46Hy4MvlKt3YVKrw0Xs7CG03Jr3Z9afHVHf2lQGhiLNt0uSlqQY2ulVWXFJC/iOvega8vhS2f4Ollt9ntwj282Oh84Oz/et6mNA12fX/cQ1U4OREEAe8Jp7um1TgcGPr0JfGHHwi5716P2wXfdRd+553XMYM8BkSHg13L/mL1/M/Zvfwfvrh/Jkvef4Ml783j0/+7nXduvpLXr7qI7+Y8THV5mcd9pO3YyuJ5L5Cbsp/clP0snvciadu3ANBn7IRmzcgrS2Q/PrVGQ2BkNEYfX5LHjCem30BnH63ewBnX3dLySXjIQJEatUUl93UKUiD/DWP6DWh5n63ky5xieq7eTeyKndy0O43qo1QCBIiOvgKtNogGI3IVen0Uen04kuRgx44bycv7BVPlLnJyF7Bz1x0u53M8BPgPR6cLQ6BeXBSIiLjwhPbZWnoF9vIoSAH0CepzcmVxVJfA3l/kSRN7Mxk7lkqoyIZGn0mXnxvTzO+ts2j39L2jYTAYeOedd3jnnXfacyjdnopaG8/+tg9TrR1HK64dz18ygFEJQWjUKiL8DRi0Heu71F6syXE3yjdqjG5ltI8FURIxWUwuVZGa48zYM1l0eFGzF0ABgaWXL/XoDRXpE8nCixaytWAreo2e4eHDm31h6SweHPkguVW5LMtcdlTx7f2z3++wtMmugKASmHRDX0acl4DVbCc4ygf1sSrECh6prq5m8ODB3HzzzUyfPt1t/UsvvcSbb77JF198QWJiIk8++SRTpkxh3759GAxdKyU5vFGK9JDYALx0akxN0u1O7xXCkr35SHXWIRLwwDnJnJYUxJi5/7ql9TVJDHJb7hHqQ0ZJDT3CvHnzyqEnbbXVrspjox9jQMgAthRsYUPuBvJr8gk2BvPihBfx0XqehWwaIRvlE8V1fa/jq/1fISAgIeGv88db680ZMWfw7cFvXa7J9X08Ub9u1tBZaNV1KZ+WCnx1vh3uwdhtKMuA+VfI1fSg+Yd4j4hyWl5TLnoXcrfi/o1FDmG3Vh3nYBVOZsIffBDLvv1YUlIACLjiCnynnIMgCPieeRbFr89z26bk/fcJuvYaNIEtR/10JJIk8eurz3N460ZUarXs+9ToGdtc1WAXkZuynz/feY3LHncXcQ+uX42gUjl9oQSVioMb1pA4dAQanY4bX32X926/DrulIVVWZzQSHONeBEut0XL5E8+RvnMblppqYvsPwiew5SJQcQMH4x8WgalYrpIqiSLDzmsQXOIHDuGsG+9gzXdfYLfa6DP2dMZefk0rf0vNs6m8iodSsp3LS4or+G9qLi8kt1zcS6XSMmzoN+zZey81Nal4e/diQP83Uak01NSkUVm1t1FvB+XlG7HZStHpgo97rBqNLyOGLyA19SXMllyCAseSmPif497fsTA+ejy3D7qdj3Z9hIRE74DeTO81nRCvEM6MPbN7F/ooS4flz0NlnuwDte1rMNeJtzGj4IbfQFv3zJm7XfaM2jFfFpuCe8K1P0NgPAT1gLgxkLWpQYjqfwkY/DrltJpDceftJqxJLW6V6S2AQaviqlFxne5R1B7U2Gvc2sZEHr//2Fvb33JeyPQqPR+e8yHDwps3JH909KOoBBUrs1didVgxWd19hlrCR+fDGbFnHL1jJzIiYgTLMpc5lxuXHK9HLaiJ9onu6KF1OoIgEBDuOV9f4fg577zzOK+ZWV5Jkpg3bx5PPPEEF110EQBffvkl4eHhLFy4kCuvdI9SAbBYLFgsDeb7JtOxfVfbilkTe/G/P/ajUQmIksTgmACmD4uhd7gvn6xJw2oXuXxELGf3CwdgaFwA6w6XOFP7BAH0GhUWm4gExAQYKauxUm2VX5ofnJLMzLM6vvqoQgOCIHBRz4u4qKf8+bSLdudEybrcdR638TQh8eDIBxkfPZ50Uzr9gvsxJGwIACllKXx78FuXvkaNkQS/BA6WHcQhOVALakKNodw/4n5yqnLoF9yPMVFjSClLYdayWeRW5+Kr8+XlCS8zLnpcG579SUJjQcoNFTRXWrwlDv0DO7/BY8SVSg3JU93bFU55NMHBJP7yM9b0dFReXmgjGwRsfe9e+EyeTNXSpa4bORzY8/K6lChVnJnu9FqqNyL3FHUEstCTm+L5+6czGqFJVKjcVvezwciNr7zDolf/R1FGGn7BoUyd9QAGbx9MxYWs//E7ak0VJAwexuBzpqJSq0kaNrLV56EzGLn6uVfYtOgHqsvLiR80lP5nTHLpM+y8aQw99wKQJIQ2Mo/eYqpxufKIwIYK9zQ5T/j49Oa00X+4tXv2mxKOqypfU4zGOAYOfPuE93M8zBo6ixv630CNrYZwr/Du//7rsMHuH+DPh8BaI6eDp63C5XuQvRl2zocRN8vC1coXXfdRmgYL74Kb/pAjL6/5EVa/Umd0PgTGdW61d08oolQ3oTWRTvUFO544v1/3/0I2Q7xvPBmVGS5t/ze0+S+W1WElw5RBgD6AUC/XEN8dhTv4cNeHzmWLaOGOf+5g4zUbUQmebypGjZGnxz7t3Pf5v5xPQXUBEhICAlMSpnRqBb224JKel7AwdSEHSg8AspDWI6AH2wu3A/Is/Jwxc/DSKuKMQvuTlpZGfn4+kxtVKvL392f06NGsX7++WVFq7ty5PPPMMx01zGa5bUISccFebDxSSoS/nutOS0CrVjE0LpC3r3Z/gXjl8sHc8vlm9uSaMGhU/O+SgYxKDGLFwUKMOg1TB0ZgtYsczK8kwt9AfLC3h6MqdCaNI3fjfd0rIUZ6R3q8xwiCwNjosYyNdvXn6xXQiwt7XMivh391puw9NPIhzog9g2fWP8Oe4j0k+ScxZ8wc4vwaqitJksR//v2P01uqylrFvcvvZenlS118Nk558vc0I0ipwDccAuLkGebWpvMJaghMgP2/uqdH6H0hfCBMegpClfRvBc8IajX6Hj3c2wWB6DfmcWjceMSKCurLrgpGI9q4rlXO3m49SkGgRgiCyq1aXc6BfeQfPkRoXCI6oxFLjSzI6L28GT71Ype+/mHhXP/im0ii6BSFzFVVzH/8fmpMFUiiyOGtGzFXVXLapZ6fGVrCyz+AM6+/7SjnILhEgp0osQadixSuBuINJ/Z+odeHEx11NTm58xEEDZJkJz7+TjSaruMrdLz46fzw03WtyJ/jwmGDry6B9NUeVja6B6lUUFUki09NBSmQhay8Rn6Weh+Y/HRbj7ZNUUSpbsKZyaEMiPJjb57J40SDXqPiwSnJDI0LYHh8y6Go3ZlXznyF2/++nTJLGQICj49+nKTAJLd+VdYqFqYu5IOdH1BuLQfgniH3cMfgO5x9VmWvctvO7DBTbiknyHD036FOrWPBBQt4e/vbZJoyGRQ6yGX/3RUvrRdfT/2aVdmrMNvNjI0aS5AhiO2F2ymsKWRkxEiCjccf5qugcCzUF8gIDw93aQ8PD3eu88Sjjz7K7Nmzncsmk4nY2JbD3tuLKf0jmNI/4ugdkdP/Fv/ndCrNNoxatdML8LoxCc4+XjoYnaR8B7s6f6b9yZvb3jzh/QiCwHPjnmNS3CRyq3IZFDqIQaGDAHhr4lvNbldjr3ExT5eQMDvMZJgynNsrAPsXe27vMxXOfQHWvQlZGz338URgPFy9AD6fCpYm62Z8CT0mHvdQFbo/lUuXUfjWm+AQCbrhegIvv/yYtlep1cR/8TnZd92NLTcXtb8/0fNeR30c1fckyUFe3k9UV6fi49OHiIhL2mxSOywxiaCoGMryc2WxSBAIT+qF1SwbYPuHhTu9oXRGI1Puute57bY/f2X55x86Z9v7TZhIWIIs0iWPGY9PkOf7X+MopYzd2918qnb888dxiVKdwfmh/lwSFsAvheUAhOm1PNvrxDMUkpOfJTBoDNXVh/H16UtIyKSjb9QKTKZd7D/wGBZLPoEBo+nT53m0WmXy45hw2OH3+5sRpJogipB0JlQVNt/HWiUX7BjVjKDqsMFfj8Ku70BrhElzYOi1rn1sZnnSxuAPQe7v222JIkp1E/QaNd/fOYYFm7PYnV3Oz9tznesEQS5Hfuvp7fth6Qr0CerDP5f/Q3ZlNiHGEPz1/tgcNr7e/zV5VXno1DoKawpZm7vWLbXu7R1vMzZqLANDZZPD3oG93favFtTHpLQHGYJ4asxTJ3ZSXRC9Ws/Z8We7tLWU1qig0NXQ6/Xo9d3XS8DX0LX85hSOjXU563ho1UMe11kcTZWKoyMIAhPjjk3M8NJ4EWQIotxc7kzBVgtqonyijvn4JzWlh93bvMPhym8gcyNs+tB9vaCSo6ASToeMta4RUeVZsOxZMDdNGRYg7BSo9KTQLJX//kv2Pfc4l/OflJ8fPQlT9rIy7IVF6OJiURldi1cYkpPpsWwpYmUlKh+f404Z27f/IfLzFzqjZipMO+mT3DYRxmqNlhlz5rJ2wVeUF+QR1bsvp116FRptw72tNDeb6rJSQuOTMNSJaqLDwcqvPpU71M3C71v1L2Muu5qAcHlyJ2vvLlI2rkPv5cWQKRd49IVSqd0zTNSa7nNfVQkC7/aL5574cCrtDgb6GvH2cE7HiiAIhIc1nzpcVraJyqq9eHv1ICjodKzWIoqK/kEQ1ISFnYtWG+C2jdVawrbt19VV+BMpLPoHh2hhyOCPT3i8pxQ/3wZ7Wyj21mMy5O0AnbccbRs3Wr7PqHXgaCYy8e8nwDcS/n4czBXQdxqc97LsRbXqZdmHCkk2SF80EwITIaEuxb88Ez6/AMrrMpRG3Aznv9amEYGNUUSpboSXTsNN4xIBCPTS8cnadECurvfC9FNn1lOv1tMjQJ4xsTqsnPvTuRTVFrVq23RTulOUmpIwhe8OfsfWgq3O9U+MfuKETNMVFBTalogI+SG0oKCAyEbeGgUFBQwZMqSTRqWg0DL/Zv2LWlDjkFwNswUEzk8837Vv5r+8sOkFSmpL6B/cn7kT5raJZ58gCLxyxivM+ncW1bZq1IKaZ8c9S4gx5IT3fVKh9vCiGlaXWpe1oUGAaowkyu0Z66DfxbB3IU73F9EG+3/DPd1PgoosOSVQ4ZSh7NtvKfn4EyRRRLK7e8OWfPyJmyhV9t0C8p95xinKeI8fT8ybb6DyarBNEAQBtV/rJlGtGRnUbN+ONiwMrzFjEAQBsyWf/PyFAEiSXFwjJ+dreiTdj1bbNmlQ3gGBnHNH84bXQVExBEXFuLQ5bDZEh3tFbUu1XBggdfMGFr3yHCq1GkmS2LN8Kde//BZefq5ROQlDhhMcE0dpbjaCICA6HJw2/Yo2OKuOQxAE+vt0XDXdjIwPST38IvXFGSIjL6eo6G/sdllgT0t/i5EjF6HXud5DKiv34HA0LtzgoLTUvTCVQguUZzUvSEUPl6OYkjx4Ehv8wD8GSo943tZugQXXId+PJNj+NWiMMPUlSF2Ga0qgRp5kqRel/nxIruRXz5ZPodcUSD73OE7w6Chv392UJ6f154pRcRRXWugX5UeAV/f2MTpePt79casFKQHBJTpKEAQ+m/IZG/M2km5K5/SY009J824Fha5MYmIiERERLFu2zClCmUwmNm7cyF133dW5g1NQaAZfna9bm7/enxm9Z3DXkIbP7V9pf/Hgqgedy9uLtnPnP3ey6OJFzXobHgsjI0ay7PJlZJoyifCOINDQdYyQuwwBHtJ66/9+/jHNl82WRECA9DWyv4fYuJ8HnwW1Xp6FVjhlMP3zD/nPPNtin6bpctasLPKfftqlrXrNGvKfn0vUc+7V6Y5G1apVZN09E+yy0ON30YVEvfACkug5skKSWldUqb3QGgzE9h9E9v49To8ov5BQgmNlf77Nv/4ECE7z9OqKMg6uW8XQc6e57ken56r/vsKOJYupqTM6TxwyvKNPp9vgcJhJPfxK3ZJ8/crL+wG50IO8bLEUkZ39JT2SZrtsq3Wr3Ceg1Sr3mmOiuUinEbfCuXNB08J7fkiyXEG2ySQYglr2Lizcj/OeJImQ+o/8s3+0XLWvfjvRDj6NJk2KD7nuU1A1L361AYoo1Y3pHe5L73D3B99Tidyq3KN3Qk5ZeOK0J0gOcjUWFQSB06JO47So09pjeAoKCq2gqqqK1NRU53JaWho7duwgKCiIuLg47r33Xp577jl69epFYmIiTz75JFFRUVx88cWdN2gFhRa4pu81/Hr4VwprZL+HAH0A88+fT6yvqwDywqYX3LZNN6VTai5ts4gmb603fYP7tsm+TkqC3A2lKTkkR6n0OhfixkKm5yqKIBtNy4KUHF3gEZUGep8LSx4Fv2iIHSUvn6RFaRRkqletBrUa6qvP1VckakTQjTe4LFszMz3va+3aVh2zatUqit54E7G6Gv+LL6L8hx8bjg+YFv1K4BVXYBw6FH//EVRUbEOO8lMRFDQenZvA0PFceP9jLP/8Q/IOHSQoKoaJN93hTPuTo6hcf4eiw7NwrPfyYvQlM9p7uN2WgoLfKSpeilbrT1TkFYDDQ6+G360gCNjtlW49fH36Ex19DTk539T1U9Onz3PtNOqTDFGEzR/B4X/BOwyqi4G6SNze58IFr7pvU1MKmRvAGACxp8GU/8niUlUTn9Vek6HfJbDwzoY2QQ2+dR6nk+ZAyt9gl33e0HpDz0bWLbGjZCP1emFKEiFqaFuduRuKKKXQrZmaNJVFhxe5tQsIaFVagoxBXJF8BTf0uwGtpxB9BQWFTmfLli2cddZZzuV6g/IbbriBzz//nIceeojq6mpuv/12ysvLGT9+PH/99RcGg6Gzhqyg0CIhxhB+mvYTSzOXIkoiE+MmehSZauw1bm1qQe0x0kqhnXB4iAypLYNX+7g/5HuiqgC0XhDWD0y5UOlhsky0w4FfXQWJ02bCuc8f/7gVujzqoCZeRyoVhr59sWZlIahUBN92K4FNKsjqe/TwEHkH2oijp32a9+0j68675M+ZJFE07w3Qat2EMEdpKYIgMGTwx6SlvUVVdQq+Pv1ITJx1fCfaxhi8fThv5myP64ZMuYC/3n0dEBAEAa3RQK/RYz32zT6wl4yd2zD6+TPwrHPQnoTPDKbKPZhrc/D17YfR2PpiLjk533Lg4BOACkEQKCj4A1+fQVRW7QUcCIIarTYIq7U+G0VAkuyEhkx225cgCCT3fobwsAuwWPLw8xuMl1cC5eVbKK/YikEfSXj4+QjCiXtinXSsmAurXpJ/FtSgM8pCU/RwOP1+9/4Fe+GzqWAul5f7nA8zvoJrf4b3G30PBBXkbIcrv4W9v8ChJXK7zlsu4AFQnNIgSAHYzbDsaZhe56M4ZS6Upctp6iotnPMcxI9pw5N3RRGlFLo1Y6PGMmvoLN7b+R520Y6/zp/h4cPpG9yXmwbchF7dfY2OFRROFc4880wkT2VF6xAEgWeffZZnn205DUJBoSsRYAjgst6XtdhnYtxE/jjyB1Kjmf8HRjxw0ty7JEkivzofvUbvrGp7pPwIpeZS+gT1wUfXBUqRJ50hRzKJjXxsasvdUyFcUNE4ggBbDRTsgQcOydWMdnztvknTa9yGd2D8veATdvxjV+jSBN14A6Y//8RWF/2kCQsl5t130Ia5/81FsxlBp0MbEUHUq6+Se//9TmFK5e1N+BNPHPV4VatWNYrck1F5eSGaTA2fP70e4+DB8ng0vvTq9diJnmaHYSoupLq8DJVag+iwI0kSMX0G4BvsLvgfWLuS3998GUGlBklk78plXPXsy2h0J4/dyeEjr5Ge/g4AgqBh4IC3CQ09+yhbyWRlf1H3k4gkgc1WQkLCXXiZEjCZduHj3YvevedQUrKS7JyvEAQN8fF3EBQ0zuP+BEEgMHCUc7lB9FIDDjKzPqVnj0cJDBzVZhUeTwq2fNrws+QAazUMvxH6Xei5/1+PyKbk9Rz4HQ4sBq8m3wFJhOpCWfQq2CNH6Pa7CMbdCzov+T514A9cInwlB+TvcR1bxnr5Z99I6H3OiZ3rUVBEKYVuz+2Dbuf2Qbd39jAUFNqO2jI4slKuqNFjolwlQ0FB4aRjzpg5eGu8WZm9Em+tN/8Z9h8mxbVNie7OptJaycxlM9leuB2AK3tfiaAS+PbAtwAEGgL55JxP6BXYqzOHCalLXQUpkM3KPSJAzAgYeh381sTA2W6WXxAmPi4b1trNzftR1WOpVESpkxhNYCBJv/xM1erVIIp4n346al/XKEh7cTHZs2ZRu30HKi8vIp59Fv8Lzsd30kSq165FsjvwGjYUTfDR0+pUfn6uEVYqFdroaCwVFQ1tDgf20jI0oaFtdZodwuGtm/j1tecR7a7f1SPbNpG5eyfxg4YAshAuOuys/V4WhiVRFpcL0w6TtnMrvUa2X6RHR1JTk+YUpAAkycG+/Y8wIWRyK0Uf9z4atS8D+r/u0hYdfSXR0Ve69W0JSZI4lPpi3ZL8+6+s3M32HVcTE30dyclPH9P+TmrUHkRST231mHKaTJgIUJkP8ePliN36+46gBp9QucJefb8N70HfC2HF85C+1rMHVaQsWJOzFZY1qsRpyoFF98BNfxzPWbYKRZRSUFBQ6EqUZcBHZ0FNibwc1g9u+Qf0XSCiQEFBoU0xaow8OeZJnuTJzh7KMZNlymJl9koEBMZFj2NH0Q5WZa8iQB/ArQNv5el1TzsFKYDvUr5z2d5kMfHs+mf5aupXHT10V/J3y6kJTiGqOW8oQX5ZmDJXrnjkCWsV+EXBdb/A4nvll4WQZLmKnwsqCO8HgQltdRYKXRSVtzd+5zZfrSr3scep3bUbALGmhtyHHsLQry/6pCR8G6W12woLkaxWtNHR2PPzKXx9Hva8XLxGjSbkzjsQtFoCLr6Y8gXfYzl4EABBr5cr9DX2spIkTL/9iiH5gWM+l2qHgw+zisgx2xjp782MiMAOiXqRJIm/3puHaPccvVhdUQbAwfVr+OfDt7DUVKPSuL/i2i2Wdh1ne1Jc/C8lpavRaYOJjb2BwsIlTXpI2O0VSJIDQTj663183G3s2/+gM6VOpwttdZRVaxDFWo/t2TlfER19FT4+yR7XdxrVxfDPU7IpeNRQmPx089f5tuSMB2HxfXK0riRCWH9IOrNhvSRByhIo3Ce/DyRNrPN5qhefJdj2pXzvuXI+/HKHnFIe3l+uLFuZ39BPpZGjqtJWeR5L9DDZnwqgKMV1neSAogNteOLuKKKUgoKCQlfiz4cbBCmQb0Rr34SJ3SfEXkFB4eRmV9Eubl5yMxZH3UveZvl/AgIqQcWS9CWYrKYW9+GQHGRXZbfYp0MI7eMaKSUI0GMyHF4mP/hrDHJkVEAsJE+FkLrIrn4Xw76FDdtpjNCr7qUu7jS4u5EQtf83ORWi+JD8YhAzAqY8DyrFY+VUp3bnThcjckQR89596JOSAJBEkfw5T1P+ww8A6BITsBUWIdXWgihSs2Ur9uJiIp95ui7S6hlMv/6Kyj+AwEunU/jqq+4G6+pjf/2zixKX7zjMDlMNKgG+zishvdbCw0mRJ3T+rcFmMWOu9Hw9UWk0RPXqQ2luDr+/+RJSXaSY2Oh3KqhU6L19iB/UfibN7Ul2znwOHnwSQdAgSSJ5+b9QW+tuiO/nNxSVqnV/28jI6Wi1gbLRucaf2Nib0Gr9j3uMFksBKSn/pao6BT+/wYQET6SoeCkuac51WK0l7jvoKEQR9vwkCyzh/aH/JfJ1/suL5edtyQF5O2W/pRt+a/9iFCNuBr8YOLJCjmzqNQV2fAN6P+g7TU6/WztPjmKSHLIX4aArYN8iOW0c5PS8gj0w8jZ4IEX2SVRr4fsbIHdHo+p6DvBuJkLy9lUQOajhfMP74zJBI6gaoqjaCUWUUlBQUOhK5G5zb0tbCSiilIKCQtfgnR3vYPVQwlpCwiE5jipIgWzoPixsWHsM79gYfhOkr5Yf8gHix8Hln8OmjyBtBQT1hLMeA68mptWXfQbrhskmst4hctpec5FPfafJ/xQU6pBsNoreeQfJQ/SOLjbG+bNp8WKnIAVgTUtvsiOJioULiXzmaUq//IqC5+vM8wUBbXg4gdddh+nvf5wvmyqjkYDLLj3m8W6vrGGbSX4JFuveU9/NKuShxIh2i5YyFRex6pvPSN++xeN639AwzrntHgIiItm/dqVTkAJAktDodET0TMbbP4CxM67Fy+/4RZfOJD39XQAkSRbPa2vTPfbr3++VY9pvSMhZhIScdfSOR0EU7Wzbfh21telIkoOamnT8/AYTE3M9eXk/4HBU1/VUodH44uvb/8QOeOgf2PkdaPRw2l0QMbD12y6+F7Z90RAdm7MVht0ABbsb+kgO+Z5QW+Z+3W8Pep8j/8veCh9NlFPwkCB8YMO46oWlDe/AQ2lyNNUvd7juZ8uncN6LsiAFcNbjsthVb4oeMRBG3QaVebDx/YbfwbAbIKqJ4OQfA3pfsNTdyyURdL7gsB+XqN0aFFFKQeEUQ5IczlkWP7/BhIacHP4lJw16Xzn0tjGCqnPGoqCgoOABk8XkYs5+PIyMGMlTY55qoxGdAGoNXP4FVGTJEVOBifLs9MoX5Wtv2mp5YuDO1aA1NmynUsH4/5P/KSgcI/kvvED5/G/dDPCD77wD45AhzmXLoVTQaKCJl1JjBL0eR0UFBS+80NAoSeT/978kb9pI4vcLqPj1NwSthoAZM9DFtr5KWz2ih2IkLdQnOWFsFjMLnn4YU3GRxwNd8fSLxPRtEDf8Q12rEwoqFUHRsVwxZ277DbKDqBejWkKt9sZojGuynYOq6kMICHh790IQVEiSRE7ut5SVrUerDcLPdyAajQ9BQePRaI7PJqKmNo2amsONWhyYTNsYMvhDkhJnsf/AY5SXb8ZoiKFPn+dOKCKLg3/Ct1fWPRcLctTTnWsaIlhbwpQnC1LQkK69/m3oP929ryDIoldHsuxpcFhwRic1FsoaY60Gm4f0SMkBFdkQGC8vCyoY939yW/w4uVKf1iBX34sZKUdXhfaFgZfBoaVy9FjEAFnw2v9rgyBVz/5FsPBOuPTjNjphVxRRSkHhFEKSJLZuvZIKU0M0TlLSbBITZnbiqFpgy2dy2KrDAUOvhjMePvnTHSIGQUmqa1vTm4/NLEdUqfUQNeTk/50oKCh0Kc5NPJc9JXs8rhMQMGqM1Nhr3NapBBWiJPK/8f/jwh7NVBfqDMzl8vXUP1Z+Gdnwntxe79tRcggy1kJP93LoCgrHg2nx725iS/hTTxJ09dUubfo+yS0KUgChs+7BUVbmanIOYLfjqKzE0K8fhn79Tmi8Q/286Odt4GC1GQk5Keum6JB2i5IqOJyKqaiw2fURPXu7LEf17sPICy9l868/AaD39mbKnSeHYBwTfS1H0l4HBARBhSBoEEUrjb3vYmNvQhAEqqpSKCyUq6oVl6ygsnIXAIEBpzF48CekZ7xbZ5Aup2bl1G1vMMQwcsRP6HTulQyPhkbj66FVjUplRK02MGjgu8e8TxdEUa5oWrC3zg9JaLg2O4CfbpVTzwZfDfEtGNnbPftc8d1VjRbqUtbG3w8674bmQ0vhyHK5MMWIW9x9XsvSZR+mkJ4QlHTMpwhATZlrcQxBBb5RcmST5JBT+CIGyZX0+k6To75cEMBQJ/ilrYKvL5VT+ZBkAao+WlcQZCFqYF114H/m1KUIquTjn/V482l+u3+QU8/boUCHIkopKJxC5OQucBGkAI4cmUd83B2tzkPvEBx2+G0W7Jjf0LbyRXnW4vT7O29cHUGBhxc9S6PKOVVF8Nl58ksSgFcwTHtDSQ1RUOhEJIeDyqXLsBfkYxw2HOOAE0xP6OJc3+967KKdT/d86paqJyF5FKQS/RKZ3ms6IyJGMCBkQEcNtXnMJlg8Gw78VpcuASSdBVd83Ux0qlLGXKHtUHl7ITauigfo4uPd+vlNnUrtjp2UfdV8QQBrRgbaK69EGxWFraBAnshTq9HFxrZZlT2dSsUvQ3vyZmYh2WYrI/29uTm6ZQGjxiHyZkYBKdVm+voYmBUXjkHdushvjb65KBWByF7JHN6ykR4jRqPRap1rJlxzEwPOOocaUzmhcQnovbyb2Uf3IiFhJlpdEKWlq9HpQggLvYA9e2dhs8neTEFBE0hMmEVFxQ62brsSEJGaVFYrK99EVtanZGfXf45cBVGLJY+MjA/p1evYrSIKC/90a+uRdB9qdRtVjv79Ptj6eZOCFHVIDsjfKUcVbf8arl8EiRM87ycgQY4QytnWIPIYA+Xn6oYdwph7YOITDU1bP4ff/q/BjHz3j3IBovrK2DsXwMK76lLsBPmZfPgNrT+/tFXy+47LBLNKvg9d9gls/UIuyBExUDYiV6nklPHJT8PSpxs2OfsZMAbIP//zVJ1XYt3fOWujbHI+oElUWFWRLEhBgyC24nmYtR0MgWAucx+v6LngwInShd5CFRQU2puioqbVOqDh5tUFLgfpa+DHm93T1+o58PvJL0qVHHZv0zeahVrxvGufmhJYcC3M+BqqCqFwL8SPlcORVUran4JCeyOJIjn3zaby77+dvi1RL72E/7QLOnlk7YcgCNwy8BZuGXgLL21+ifn75+NoWl66CXF+cdw44MaOGWBrWDRTNiBv/HKWtlJO3Rv3H1j2bN1LiCSboSeM77ShKpx8hN1/P7kPPChfM0QRr9Gj8R492q2fIAhEPP4YhuTelP34E7bcXByFrhFEZd/MJ+z++4n95GPyHnkUS2oq+j59iHrxBYQ2fA7w12p4skdUq/pKksSNu4+wpqwKCfiruILdlbV8Oah1USThiT3oMWI0h7dsrEs7E/EPj6CyuIi8QwdYPO8Fonr35fKnnncRpoKiogmKij6e0+s0LNZi9u2dTXnFVgyGSPr2fZEA/+HO9YIgEBN9NTHRDVF0Y077h4qKbag1PgT4D0cQVGRkflj3PO9uLi4IAjW1mYDnz4MkHZ8BeXX1YQ4d+l/jI2HQR5KQcNcx78sjNSWyKASugpSgrhNRJHnwkkMWcTZ/0rwopVLBNT/Cv/+Fgn2ycXf6aqgpdt2vV5CrwfnKl+qOXxexmL9L9mpKPlfOZPh1VoPnExL8Phv6XdQgEDWlIgc2fyyn4QXGw5LHGyZCVGrwjZQjlSbNkYtmxJ3meT/j75PPtXC/nIYX0/CZobbcNeoK5HMN6wdhfaCyQP69mnJwQ5JA6wV3rITPL4CKTECQfyc9zwbfCM/jOUG6wFuogoJCR2CxFFFe7m4WaTTGo1Z3cN60J2pK4ZsZDdUkPOF17GHF3Q8PJg1RjcyAy7Pw9MDBz7c2zPZv+UQ2gbz6e0WYUlBoZ2p37pQFKXCm4xS88MJJLUo1JtonGrHRw6+A4OY3pRJU3Dn4zo4eWssc+hu3660kyjPS1y+SU/nSVoFfFIyZ2fH+IgonNf7nn48uJobqjZvQhITgf8H5CBrPr2Wmv/8m74kn5QVP6XKShOQQ0ScmkrDgu3YZr12UeDerkNVllUTrdTyYGEG0Qdds/2yLjVVlVQ1DBP4uMVFktRGq0za7XT2CSsWFsx9j/5oVmIoKierdlw0/f4upkSCXm7KflA1r6Hf6iZt1dyZ79syiomJrnUl4Bjt23MTYMSvQ6Zo32dZq/d1MysXGfkRNkCQHfr4D8fZKJPXwS8jiVONnSQdBwacf89hrazOaHFPCYi1qrvuxYauF7672vG7QDLlCXuPqcq3BGADnv9qwvOTxuqp7db8LyQGxTcRhD0U9qK88W1Pa8HM9oh3mXyFXYx13r6sxeGUBfDBBNlEXhDqhS2g4B0EDAy6Fs589+rmk/A2L7pHTzxNPl4tvGPzkdf0ugrVvIP9t6lISt3wq26JMfBI2fQDVjcW4utQ9QS3bgviEyeO7Z7McSVW4Txa0xt3bbhUJFVFK4aTCXlxM+c+/IFks+J07BX2vVhjfnQKIop2t265GFJsKPioGDXy/U8bkRtFBsFU3v15Qw6QnO248ncWgK2Dntw3Laj1MamQGHDcaUv9x365ekKon9R85/72nYmSvoNCeiJWV7m1VVR56npxc0vMSfjn0CwfLDgLgo/Ohf3B/NuRtACBQH8ibE9/sGil7jfEKAlOua5ugkh+8BUF+6Rk0o3PGpnBKYBw8GOPgo5dZNy3+Xf5MSpKrD1Xdy6Hvueei9jnxVLUjNRYW5JciSRIzIoPo6dWQfvV0ag6f5BQjAWpgdVklq0b1wVvj2dNS08x7q/oYXmhVajX9z2h4hvn38/eRmkR/1Jgqmm7WpZAkicqqvdhtFfj5DXL6L1ksBeQX/IokOigv30yDsCPicFRTVbWfoKBxx3SsyMhLKCldgWuqsSxKxERfS3T0VYCAwRBNWdkGas25VFcdAEH2pIoIv+iYz8/buzeCoHamCwqoT7y6Xj3r34GsTe7t8ePh4vdk/9UPTpd9kyQJkGDkLcd2jIlPQGU+7FsoF7KY/Ix7VOzwm2BVXbSUoAafUEg8Q172jYCAODn6qbE4lrVBTpmrzIfzG1VF3PMj1JbKApDzq+wq6rWquFHJYZg/o2Hb1KWygHfj4rrzelKOutr7C5Smue7/3/82Oa4gW4EYAyByCJz7YoPwpDXAmY8cfTxtQJcQpd555x1efvll8vPzGTx4MG+99RajRo3q7GEpdDPsRUUcuWQ6jtJSEARKPvyQ+K++dKlicqqSlf0ltbVH3NrDw6bi49PbwxadgH8MTjW/KYZAuH7hsZV97a5Me1O+We1fLJd1nfSUa0nacfdCwX7YK5t5yrMbdTfjpix9GnpMbLdZDQUFBfnFUh0YiMNkkr1cVCp8zz67s4fVYXhpvfh66teszF6J2W5mXPQ4gg3BHCo/hNlupk9QH3Tq5iMq2gTRIT/815bB9q/ktIgBl0KPFiIozn8NvrvG9UUidhScdeyeKgoK7YnKaJCjnh11n1W1GuPAgahDgjH060fIrbee8DEOVZuZsiUFiyiCAB9lF/HH8N709ZErTn6bX+p8ynAAORYbGyqqmRTs53F/fmo1GgHsjR5NvFQqApoRsVpDYGQ0pTnZLm2VLZihdzaSJLJ33wMUFCwCQKsNZviwb3E4atm2/Rocjmoanntdn3/1+nBPu2yR8PALkJDIy/sJlUpPfNxt+PoORBBApdK79AsP9xzJa7EUkZf3Iw7RTFjYefj69GnxmEZjDP37vc6+/Q8jirUYvRIZ0H/eMY/dI6VpDRE89YQkw9UL5OfakF5w23I5Fc5hPbrRuSe0Rtm3SfxI3qen5+UzH5Wfww//K0cQnfFIQ2qeSg3X/gw/3CinBLpEn0mw/UtXUao+BbAp9b6+aj0Mufbo4976BW7P/RnrGn5Wa+T3h1G3w6vJTTaWkCPlpIblkGS46fejH7cd6XRRasGCBcyePZv333+f0aNHM2/ePKZMmcLBgwcJC2t7Z3eFk5fyn36WBam66iOSKFL0zjvEffSRs4/DbMb0+x9IFgs+48Z6NJU82RBFC7m5CzyuCwnpQlE0AbFw7lz4q4kiHzNSTqXQnRyGlUflyHLYVff3siHnpgsqGHGT3KbWwuWfyjeb7V/JN2KvEFjqobR6/i75Rc0vssOGr6BwqqH29yf+668oeP55bLl5eI0ZQ/iDD3T2sDoUg8bAlIQpLm29A9t5wsNhg/JMOXXhh5ugPENury8Vvv1ruHI+9Jnqefvk82DmJsjeBBoDRA+DgHhFxFfocgTdfDOmJX8j1UVJqf39iX5jHtrwYxcumuOznGIskogDQAKrJPFZTjEvJccCoBMEmsay61XNf1fSzVYXQQqgRhQptTkI0R3f66dPYBCCIDh/DwCm4jZKFWsHiouXOQUpAJutnD17/o+q6oM0iBf1AkH9z5AQfxfe3j2P65gR4dOICD++wjcWazGbNk/Dai1BEAQyMj5g2NCvCQgY4dZXFK1kZH6EybQLL2M848etBlRoNH5tV5Exeqhcda8xwUmyONTnAlmoDevrmo7X7MlVyc/ExkDZI7DpGFuyulCp4LS75H+eCOkFd62FjPXw2bmu65rao/S7WPaostUi+2HVVburKpCN3EfcLFfwOxqtrbptNsn+VDUlDel5XkFgrpQ9uup9uY7FmL2d6HRR6rXXXuO2227jppvkF67333+f33//nU8//ZRHHumYcDGF7o1ktVK9YQPmA/tdw5oliep168m8/XYcpkp0cXGYFi92ilaFWi1xn3+G1/Dhzez55GDvvgeoqUn1uM5giOng0TShtgz+fBhytkBIbzjvZflFoSxDvlAaA+Typ629+J4M/ONBXFoxt0GUqicowTWdsSofNngou9uVqioqKJyk6Hv0IO6TTzp7GKcORSnw9SVQURc10TjdwTmrLsDG95sXpUB++G/NC4BCt+Jky8AwJCeTtGghpj//RNBo8LvwQrRtPHFvk9yjra1iQ9uDiRE8digHjQAOCUb6e3Oav0+z+4vSa10ipQTAW32ikVIxLrEhgkpFQETXnXQzm3NxjYByUFV9APfIdomQkElERV6GwRDV6vQ3u72K8ootqFR6AvxHnnAV7by8n+rMzsW61ymJjMwPPYpS+w88Sn5+veCmoqx8EyNH/HTiglTK37DrO1nMOe1OGHkbbPm44f0uZQkc/BMGXQmXvN+6SYTiQ/D5+Q1FlIbdIFfIa+sJiJiRcqGhzPWy+CPa4YyHXPsExsOty2D9Ww0RvcdTPXvETbJnVONI396uE0OkLJFT+uqjswQVhPeD6R/JE9pr35THMOhyeRydTKe+rVitVrZu3cqjjz7qbFOpVEyePJn169d73MZisWCxNBiKmUwmj/0UTg3E2loyrr8B8+7dnjs4HFSvWg2AeccOl1WSzUbhq6+SMH9+O4+y87DbKyks/KPZ9ZWVuwkIGNbs+nbnu2sgc4N8US1Jk2cZRt4q53Nv+ghM2XKJ7rMe654ms5YqWVDTGlu/TVNvKGg+3LcxQR4q2niHybnvCgoK7YYkSZQvWEDlsmWoAwIJuetO9EmtqzDVHZEkierqFETRgo9PX1Sqo5sWtzm/3A4VjfygmlYZ6uLYLA42L06jOLuSoCgfRl2QiM6oTCC0Bd0pA8MiimSZrYRqNfhrW/776+LjCbmz/YoFXB4eyDe5Jc6YHRGYESFbB0iSxM0xoSQY9awrryJCr+XayGA0LURKBWo1vN4njnsPZOKQ5Kiq9/sntLjN0RgyZSrpu7aRvmMrAOGJPTlt+hXHvb/2xt+/6fN1MxYVSERFzSD0GLIXzOZctmy9Aoslt+5YIxg65MsTKlwkOsx1kWjOFqqrU0lNfYmQkIlOccrhsJCfv7DRlg4qK3dTVZWCr2/fYzuoJMneS9VFclTPorsbol33/gx3roFznoMXE8Be23Ct3/UdjPs/WWQ5Gr/f72rqve0LWQjq1cZp9moNXPtLXVW7bIgfJ0+0NyWsD1z0zokdKyAObvxdrvxXUyILUhe87trnjwfl1PZ6JBHOe0mOLrPWyFFZWqPsI9UF6NQ7YHFxMQ6Hg/Am4afh4eEcOHDA4zZz587lmWee6YjhKXQDyr//HvOePce9vaO0rA1H0xVp2SxPp2u+mp0o2klLfxtzbRZh4VOP6WbZKswmyFjb+IhyGsbqV2H1Kw155Pm75YiqC99s2+O3JVWF8k3IVgN9L4Tw/vDTbbC/bhbJEACXfgK9Jh99XyNugX+aGLqPuNm9nylPLlmesQ4q8zxXH/HrXmWRFRS6I4UvvUzpZ5/JC4JA1cqVJC3+rc0jGdqb4pIVVJRvxWCIJiJiOuomPlCS5KCycj+HUl+gvFyeOPT27sWwofNbrBLVLhQ1Tn/xRF1lqdF3dNCAWo8kSfz5/i6yD5QhSZB9oIzCDBOX3D/MY5SBwyZSVW7BO0CHRnsKRQ0fJ90lA2N3ZQ1X7TxCsc2OWoBXkmO5KjK408YzKsCH74f04POcYiQJbogOoa+Pgat2HmZVaSUBWg0vJcfwRI+oVu/z8oggzgj0JdNsJclLT9BRhLejodZomf7I05RkZyI6HITExaPqwpH0fn4D6df3ZVIO/ReHo4rg4EmUlq5EFF2rtfXt88IxP2MfOTIPi6XAuVxRsZXc3O+IjW05Dctur6akZDmiZCck+Ay02kDnurCw80jPeA9ZOJOvr7W1mWRmfUJG5ocMHPgOYaFT6q5TTav3gXCskVqSBAvvaijuI9T9LeuFJxHY9b0cbeRpwnbTB3J16sFXtjxxXZbe5BlZaEj3bmu0BjnCqyOIHwOz3KuqO6kpxU0ErSmRI4w/O09OfwdIniqLZNVFctVZnVe7Dbklut20zKOPPsrs2bOdyyaTidjY2E4ckUJnYi8uBrUa7E0iSdRqOU3PQzhyY3zPO7fF9d0djcab6OhryMn5BrleSsNFOShoAqGhUzxuJ4oO1q0/A4slH4D8goXEx99Nzx73t+HgDHJqmVsUUN3fzFmeVZSrVXQVUao4FX66GQoPyDfBUXfAti+hplgOBV77plyxqV6QAllsmz8DZm6Uxba9P8u544OvlCt3NGbsLDnPe+OH8vLwG2STxcZkb4FvLpfFOrdZt0YzccNaYZaooKBwzEiShOm336hcuYrK339vvALRZKJq5UoCL7+88wZ4jGRkfkxq6lzq7xMHDj6Ol1dPBg54Ex+fZGw2E9t3XE9lpWtUcnX1EY4ceY0+fZ5rv8GlLoUjK+Vr5fCb5AfmsH5y2ndTBJWcPhGQAAMvlQs9dDFqTFay9jdMiEkS5KVWUFlixi/ENao2J6WMP97bjbXWjlav5tw7BhDXLxiHQ74/VhabMfhoMXh3QrRaF6Q7ZWDcvjedUpv8/OOQ4P4DWYwP9CXWcGJFAbb9+Rsbf1mAw25n8NnnMf6K6xBa8stpxPhAX8YH+jqXb92TxqrSShxAqc3O7XvTWTmqj0tVvqMRptcSpm+7z6cgCITEdh8/WF/f/vRJfhajMRFv756sWOke2ePj09SI+uiYLXk0fqYXBLVTpLJYCigsWoKAmrCw85yTBjZbBVu2XEpNrVyNTasNZuSInzEaY+rG0Zvhw74lI/NDamrSqa5OASQkyQ4IpKW9TVjoFFQqHXGxN5GZ9QmCoEGSHAQHnYG31zGmQqetcq023XRyVUJ+T1BrIflcObVPcjRMWm/9Ujb83vEN3LAYNM18d+LGyEJM4/1Hn9zWLYAcPbX3l7rfWV3WRswoWPKoXC2wnoN/wMs95X6GANlIPu60Dh9up4pSISEhqNVqCgoKXNoLCgqIiIjwuI1er0ev74ZpPArtgtdpp1Hy0ccNDYKA/8UXI2i1SJJExQ8/eN5QEPC76EJCZ87smIF2Ism9n8bXtz+VlXvR6ULxMsaj1QYSFDQWQfA8w5Sd841TkKonI+ODNhaldHD2s7CkFZWOtF3E5LymFD46Eyx1JeAdFlj9Mk4hSEL++dDf7ttKDvkGuvlD2aAXCda9JZu4ByU2GLkfWS6n/Y25W86lbzpjsf83WHAdnkPAAe8Q2cRxwKUw/MYTP2cFBQU3it99l+K33m52vUrXztXm2hBJkjhyZF7dUsNDe03NEXbsvImxY1aSlvYGlZX7PGztoKY2vf0Gt+VTWHyf/GIiibD7R7h5CUz/EN4e4Z62d/PfEDuy/cbTBqg1ngUCtda13WEX+fP93VjNsnBhszr4873deAfqqSisdb6XCQKMu7wXgycqE7TdJQNDlCTSa60ud3ERSKuxnJAolbplI8s//8C5vGnhD3gHBDLsvAuPa3/ry6ucVwQJWTz7KKuIF5Nb/qyV2+z8XlSBXZI4N8Sf8DYUpboTObkLOHDgceqf13okPVQn4rhOxqrUx2DxUEdQ4FjKytY79y1JdgIDR1NTk8bmLdOx2+Xn1LT0txk1chF6fRjZ2V9RU9sQIWSzlZOe/g59+851tvn7D2XQwPfIzpnPwYONo/Yllwivnj0fxcenD6bKXRiN8cREX3PsflKV+Z7bVRr5vHS+MORquW36R/D3k7JfU3lGnVF43fU/a6Nsfp7cTKDB1JfkCKHDS+X3ifNegqihxzbW7si0N+TJ88P/ypM6U18F3/A6396mAmDdssUkv2M8kNLhRT86VZTS6XQMHz6cZcuWcfHFFwMgiiLLli3jnnvu6cyhKXQTfMaNI+K/z1L81tuIViuBl11K6H33IahlsaXixx/doqXC58zBf9oFqH2aN2g8mRAEFdFRx5Zzb7V4ulE0XMBKS9eSn78QldpAbMwNx10lhDEz5dDbNa95FnLqMVfIF9XOnvVOW9UgSLkguf7cXE7/+ibRXjXF8P44+cI/4WHQ+8DfTzSsX/4/2RAxuBcsnQOp/0B5Ns0KUoJKrkgybV7rz0lBQeGYkCSJko9bMDXXaPCZ1IpU3S6DhCRZPbSLWCwFVFbtqxOePKQIo8Lfrx0f7le8UDeUupe43G2Qvgp6TobLPoUfb2l4mD5tZpcWpERRpDS3GptFpN/4KPatyUWlFhAdEn3GROLt73rfqDFZsdQ0enmVwG4TqSislRfrg4klWPP9IWKSA5EkidxD5Xj56UkaGorqBPx7ThU6IwNDJQj09jaQWm12fqs0AvT0OrFJ96w9O1Gp1YiOhu9q5u6drRalHJKEye4gQKNGEARiDDpKbbUuTxxf5JYwJcSficF+HvdRZLUxZUsKuRYbAvDCkTz+HNGbBKOecpudWfszWVFaSZBWzUvJsUwJ8T+BM+66OBwWDh6cQ+PntcNHXiY+7nYyMj9wilOhoecee4QREBd3GxZrMXl5P6BS6UhM/D+Cg89g/4HHcDiqnce1WkvIzv6SHj0ewGYrQxBUSE4xX8RmK/e4/9CQSRw+/DJ2ezX11/7oqCud6wVBIDJyOpGR04957E5iR4Fa1zBRK6gh6Uy5mp1GL9tZBNR9F/W+Dc+2L/esE6UaYa1q/jgGf7j2R3DYZZ/XU6XCqt4HLvZQACl+rHwv9eTFKIlQXSi/6xg8f8fbi05P35s9ezY33HADI0aMYNSoUcybN4/q6mpnLrjC8WO32UjfsRW71ULcwCF4+Z2cF/7Ayy/3mCYhORwe0/f0iQmnjCB1vEREXExG5gcubXq97E9UXLycnbtupd6vKj9/IaNGLsbL6zjDqePHgH5Oy6KUwwrfXQsPHZHztTsLXTMRWy558BJMeBA2fQhF+1u3X0mClS807Kceu0WesUg8XS5vfjQz34A491Q/BQWFNqN2xw6y7pmFVFvbbJ/I5/6L2qeLRHe2AkFQER5+Efn5P3tcv2XL5ej1IXgy6Q0Pm0piYjtOItotzbf1vwTCB0DuDvnFpRPSDVpD5r4Sln2xn5qKBuHPL8TA+Mt7UlVmISjKmz6nNVQQs1kcFKRVoFIL6IxqrGZHs/MQjdmxNJMD6xsmlBIHhXDenQMRTiFhqjtlYHzYP4Grdx4mx2JDrxJ4o08cUccQJSVJEhV2Bz5qtdM83DswCElseE4QVCq8AwPZUF7FDlMNCUY9U0L8PEa0/F1cwd37MqhyiCQYdXw1MImXk2M5f+shl8p8auCv4opmRalPs4spsNjkMQImh4O3Mgp4tU8cDx7M4t8SEw6g0Grnlj1prBrVl6QTFOO6InZHJZJka9IqERk5HX//YZhMOzEa44mMvOS4KtapVBqSez9Jcm9XD1K7vRKp0d9LEOQqfQDBwWeSlf25y3iCQ870uH+9PpwRw38gLf0dbLYKwkLPJqqRKNUmBCXCVd82GJH3nAwXvnV0MWTwlbDubZxClt4XEs84+vHUnS57dA3OelyOUtv7c50oaK0zRK/7ffqGy7/TDqbT/zpXXHEFRUVFPPXUU+Tn5zNkyBD++usvt9BbhWPDZjYz/4n7Kc6SwzQNPr5c/dwrBEaeOsbHglqNLiEBa2am7C8FUNem0DI+Pr3p1/dlDh6cg0M0YzTGM3zYdzgcFg44w3nl36nDUcP+A4/QI+khJOxIog1//+HHVgEkYgBMfBL+/W8zHSSwVcu+TNf9Is90dAZJZ0LMCNnTqR6DP1z6Mez8Tk67GzQDBl4mp86lrZLT8dbOO/q+BbVns/LyDNhb3LwgpdLC+HvlnPm405oXzhQUFE4I0Wol6867cLTgOaMODcFRUkrt7j0YBw7owNGdGH37PIdBH0Fu3s9YrU0jZR1YLIUIgrYuokpFXOzNJCXdh1rdzpMEw2+Qy14DIIBXiFydtZ6QXvK/LsTh7YXsWp4NyMLQhoVHcNhdr9+VpWa2/5OJRqemttJK4uBQDN5aKkvN/PzKVqpKZeEtLMGXsvwabGZPUWquNBakANJ2FZN7qJzo5MBmtjj56E4ZGMneBjaN6Ueh1UagRoNB3TrfJ4Bss5Xrdh1hf7UZg0rg1eRYLo0IYsiU8zm4fjWFaYcB8A0K4dCEC3h2e6rTlvrayCBe6RPnsr8iq41b96Q7xafMWnn/vw7rxWURgSzIK3WxtPbTNP8MVmF3yIEodbqIKMltAGubpAPaJdhmqibJS8/G8io+zi7CLsG1UcFMakb06i7otMF4efWktjYNSXIAavT6UIzGWLy9exIa2rpo2traTPbsvY/Kyn14eSXQv99rLVa4Cws7r1HVbQFJchAaKleZCw4+nX59XyIt/V0kyUZM9LVERc5w2V4U7VRXH0QQtHh792JA/yYV3dqanpPh/3Ye2zaTngadD6QskdPSJs1RKk0fC1oDXPoRXPKBrFoe+ht+vFmONvMOgSu/7ZRoMkGSjuIE3cUxmUz4+/tTUVGBn1/3voC1JSu//owtv/3k0tZr9DgunH1qRVGYDx4k67bbsRcWIuh0RP7vf/hPu6Czh9WtsFqLqazci8VaxMGDTyOKniIEXGfQNRo/vLx6ERg4isSEWa0XqBbOhB1ft9wnZhTc/FfnCVM2s1xpL2sjhPSWq2wYW3jo/+Uu2DnfvV3vC5ZqXKqXhA+EAlcjYQIToSyt+f1rveG2f+USs23AyXpNPVnPS6F9kSSJquXLsWZkogkPI3d2K3z1VCqQJKJffQW/qVPbf5BtyM6dd1BcsrTZ9UOHfEVAwAhUqg7yzLJb4N0xUCq/ZCOoYcaX0Of8LpmCseWvdDYuPHJsGwngE6Ansoc/5YU1FGdXI4kN99Mzru5N1v4y0nYWu7S3hvPuHEjSkPZ5Weuq19QFCxZwww038MEHHzgzML7//nsOHDjQqgnvrnpejblk2yE2VVQ7BR41sHp0X3w1Kl46nEtKcSkD1Q4eGtSHAVsOY23yqvdmn1jODw3Au05cWldWxfQdqR6PdVl4AMtKTJTbRSQgQqdhyYhkN5+obRXVfJxTTJ7Fyvryapd17/aLZ3p4IJM3H2RfVa2LwPXTkB54q9Wcvy0FSWp4kvxmUFKz0VjdhdraHPbtf5Cqyn14efegX9+X8Pbu0ertJUliw8Yp1NSkI6fQqdFqAxg3dlWLEwK5eT+Snf0VgqAmPu52wsKOXtSpqvoQ6WlvU1yyEodDtqkICT6LgQPfQ6U6NT3B2hNJkkjZmE9RdhWB4V70HRfVuenWdqvsu+Ud2uYRZa29pnZ6pJRC+3Bw3Sq3tuKs9I4fSCdjSE6m57Kl2AoK0QQFovLqnDKX3ZXy8i3s2HkTDkfNUXq6PvDY7SZMpq2YTNuprc1i4IA3nOssliKKS/5FJWgJDT0HjaZRKuXYWbBrQZ1/SDMP39mb5GodQzupslx9udfWlnw9sty9Te8nV+L7+jIo3Cu3jbwNJj8DP1wPqcsACfyioKqo5f3bzbD6FTlaS0FBoc2QJIm8J5+SvQlVKjniVqNxr/balLrI3IKXu5coJUkSJaUrW+yj10d0nCAFkLa6QZACOZp0wTXyLPl5L3befcADoiix6ddjFKQAJKgqs3Boa6HbbU9QCdRUWAmN8yVtR6N7gQBBEV6U5nm+Nwsq0Bk0RPY4OW0bWuJkysBIrTHzV1EFRrWKS8MDCdDKr207K2tdHN4cwE5TDa9m5JNWY8GBwCa7BlNWiZsgBfCfA1nMTctn0dCexBn1xBl1zkiqpvxYUM6ryTE4JNkL64wgH4qsNjSCQLBOHs+eyhou2p6KKEnOj3CCUYdRpeKm6BCmh8sTdy8nxzJjRyqVddUjr4sKZmyAD3NSc6HR8VXAJ9nF5FpsBGnVnBPs70xR7E4YjdEMH+ZhUrIZJEkkK/sLSkvXoteFEhNzPTU1ja5/OLDZSqipTcfXp/mJyKjIy4iKvKzVx62tzWbLlkvrnvUbPi/FJSvIzV1ATEzXuc6eLKz+/hC7l2c7fQVzDpZxzq2dGF2t0YFf5NH7tecQOvXoCu1Gjancrc03+NQMbRS0WnQxp07aYluyb//DOBzmE9iDSGHh7xw+HIfZnIPeEE1OzjfY7RUAGNPfZuSIn9FqA+TuYX3kanQrXpArQOi8IWOt6y4FNRQdPIExdTCeIrqGXCsLTneuhtIj8gtW/c3g2p/kaKzaUjDlwcdHMXeXHLIRvIKCQptiTUuXBSloSAEH0GrBZkPQ6wi+4w4qly7Dnp+Ho7TMZXuxqgXj1S6KSmXA4WjqgyITG3MTaUYebH4AANVrSURBVOlvU1KyErXaQGLCPURHX9V+g3HY5FLfnrBWwaJ7IKxvlyntLTkkj1nW9VXyjr4DD02ibFzuE2ggNN6XwnQ5giEiyY/8w57TSPVeGoIivek/IdotbfBU4Z577uly6XrHyraKai7ZkYpNlIWeD7KKWDKiN4FaDYleeg5UuQpTNkkktabBg00Cfsov4zQ/LzabatzKFBRabDx7OJePByQSY9DxcnIsDx3McuunESDfYuf+xAg2V1QzaXMKJrsDNfByn1iujgzmh4IyJCTntipgkK8XH/ZPcNnXUD8vNpzWj52VNYToNAz0MSIIAloPgtO/pSaWlcqf8TMCfZk/OAl1F4yObEuOHHmN9Iz3ABAENSWlqxAEPZLU2FtPQK8LadPjFhb9hcNRS9OLkCCoXar1KbQNVrOd3XUp3qJD/p0f2lLIaZfU4hd87JUYTxZOWVFKdDhY/9O35KYcICKpJ+OvvB5B5ZrPba2t4a/35nFk22YMPr5MuvlOeo0aiyRJHFi3ioLDhwiMjGbgxHNQqTsplcgDDrsNh839oTJ57IROGI1Cd8ZiKcDz3Fk99Q8ILacUyDdZoW5fDQ8VtbVZ5OTMJyHh7obOCePgxt/kn6018N5Y1/Q1yQERg1p/Ep3NgEth7ZvIvyMB1FoYfbu8TqX27IeiNYA2Si6L2+wbTaOUyb7T2mfsCgqnMGKVh0qbdjs9VizHUVSMLjYGdUAAoXffjb2sjMPnnicLUQ4HCEK3ipICuZpSzx4PcjDlKQRBjSQ5CAgYTWTEpRiNMRxMeYbqanlCwG6HAwefQKsNIixsinMfkiRhtZWgUfucuN/UwrtkI9aWyN7aZUQptVZF/IBgMvaUuLQPnhRLSXYVWftl0VJrUBPfP4jUrc1HwarUAiq1gN0qknuoHAS57fyZg/ANMhAQ7sUH/1npls4X1TuA0dOS+OO9XSz9bB8A4y7ryZDJcR6OotCVeT2jAJsoOZ/Ass1Wvs8v5Y7YMN7uG8eMHYcpstkRgMeTIunt7f4y6wA2mGoY6msk02yl1OZwPq05kL2j6rkmKpgpIf48cjCLP4srnAKTXYL+PvK+b9+TTlWdP5QDePBAFn29DKwtq8TR6KMoAJpmBKRgncYtLe/6qGC+zCmmxiEiCLjsC2BlWSXLSkyc04mV+hyOGrKzv8ZiLSQw4LRWe0IdDVG0UWHaAZKDrOyGqCpJcmCx5BMbewvZ2Z/X+VIJ9Or1ODpdCFXVh8jO/hpJtBIZeSkBASOOewwqQYOn53hJsuPn142et7sJYtMPeH27vVs7Kp0wp6wo9d2ch8k7dACAzN072LnsL8ZMv4ohU85HrZF/Lcs+fZ/UTRuQJJHqslJ+fW0uQ845n4zd2ynLzUFQqZEkkYxd25g2+7Hjqp7QHqjUGlQaDWKTFIOYvv1bvQ9LTQ3l+bk47HYEQSAkLh6tvhOrnil0CgEBIykrW1t3M3RFQMugwZ+Qmzsfu92ERu1NSekaRNGCLD6pkR9b6i+yTf8vV31qrhwtADovuGsdfHd1XRqcAKPvkI3EuwsTn5SFpf2/gjEYzvmvXHGkKXYLFOyFimxY+RJUZMnlcic9BUufASRZpDrnf3KlqVWvyKl7w2+Eodd19FkpKJz06JOT0UZHY8vPl4UmlQrvcePQRURAk0pemsBAEr75moKXXsKeX4DPhNMJ/c9/Omnkx09MzDV4eSdRUb4FgyGK8PCLUKk0lJdvcQpSjSkuXuYUpczmPHbsvKXOJFdD715PERNzzfENxFoNu3/wsKKxf6EkVxztQky5bQBrfjzEke1FqFTQf0I0obG+7Pgny9nHbnGQe6iCiB5+lBfWYK50TweN6uWP6JDIPVQhFxGWQESiOKuShIFylMSQybFs/zvTmf4RkeTHRfcOZf6cDVhrG/a59sdU4gcEExihFMHoDthFCZskUWV3uEwJCkB1XdpbXx8jG8f040iNmVCdlnC9FlGSOCPQl1VllW7ywvbKWt7qG8es/ZnONhUwNtC1EnWITsNrfeMo3nWEDRXVCMDMuDCmhPhhFUXyrK4T3g7gmt1HKG8kdqmQ0/xujWl9NE+8Uc/Skcl8l1eKXZKYn1tKSZN3mFLbUdKm2xFRtLJt2zWYKvcgCCqysj6jV68niIuVK8VLkkRe3k+YTDswesUTE319q7xU7fZqtm+/FlPlrroW9wCHoKCxxMZcR1V1Cl7GBLy9e1BdfYTNmy+RC09IsofU0KFfEhQ45rjOLzz8AtIz3sdqLaFxEmV8/B2Eh7XOh9dk2kVp2Xp0umAiwi/s2DTvbobBW0vCQHkCQ5LkV4SwBD/8Qz1HSRWkmSjKNOEf5kVMn8Auoze0NaekKGUqKnQKUvVYqqpY8eVH5BzYy7TZj2KuquTA2pVIjSMUJIkdSxY3LIryi/qhTespy8slKKrzUsQK049QkpVBcGw8viGhboIUgEbTOqO6zD27+OWlZ7BbGsJFfYKCmTFnLoERUW02ZgX5hlRWtg4QCAoah1rdtcI2+/d7hV27Z1JRsdltnYQNAQeDBr7j0i6KdvLyf6K2NhOdNoRDqc81u39JchAScpT0NJ0XXL8QqkvkKKOjlYrtaqi1MPlp+Z+lCtLXwKGl4B0MWZtlYcluhs0fQ5VrGWtSl8nb/N8OKEuH0D5ypRGQjX5PMd555x1efvll8vPzGTx4MG+99RajRo3q7GEpnKSo9HrivviCguf/hzU9HePQYYQ/+kiz/fU9exL34YcdOML2IShwjNvLjTzZ4I7NXsH6DefgcFQjCBrMZtkbRpLsHEyZg7//UHx9+3ncNjv7m7ry5CoSEmYSGXFho7UCTQtoyDRa9ouGHpOO5dTaHa1ejX+IEXOV/PK+c1k2/ca7+nRIEtSYrNRUWpsNMs5JKUfvpXX7FQiN0pzGXNKDwAhvCtJN+AUbGDQxBpVKwFRSS1MbIVOxWRGlugFvZRTwYloedgn6ejdMBKuQff3PbRQp5KVWUekQ+c/OwxTb7Jwd7McH/eP5qaCMJw7luH20grUaXuwdw3OHczGLEheGBfBIoruHjJ9GzS9De1Jss2NQqfCtM0PXCQI9jHrSay3IMTugFqDU5jppaVSrWDS0JwN8j83DNd6o5+EkeTw1DpHPcoqdsfVaAUb7d97nt7x8s1M4qn8vTE9/xylKpabOJTPrEwRBgyQ5KClZxdAhXyAIcgZObW0OGZkfUla2Ho3Gj+ioGURGXk5W9ueYKvc0OpK8b3k/Ir4+fQkKHINKpcdojHX2ysv/GUmyNpowVpGd/fVxi1I6XQijRv5Kds43OBzVhARPJCBgZKsNzgsK/2TPnlnUZ0Tk5f3E0CFfKgbpdYgOEavZgd5L4xSUptw2gC1/pFOYWUlQpDejLkh0ub7Xs3tFNqu+S3EuD54cy/jLulbF2bbilBSl7DZrs+sObVpHZUkRK774CNFx9BK89Tjsnj0YOoJtf/7K8s8bHoTHX+k5aqI1hRZrKsr55cVnsFtdH0Cry8tY9sm7XPZ48wKDwrFhtZawZetl1NbKM1dexkRGjPixwV+pC6DTBZOUOIvtO673uF6vdzcOVak0REddAcg378NHXkEUPftSBQacRkDA6NYNxju4df26KpX58MnZUJ559L71SA7IXAe+URCY0G5D6w4sWLCA2bNn8/777zN69GjmzZvHlClTOHjwIGFhYZ09PIWTFF1MNLHvvtvZw+h0/P2HotdHYLHkO9tUKj3Fxcvqljw9X0hUVR3wKEplZHxM6uG5zuV9++5DACLqhSmdF4y8FTZ/1PygTDnw5mC49uc2qz56opTmVrP+lwZjYmutnZ3Lsjx3buGRTBLBZnHIye51Lyo6g5rk0Q0ReoIg0HdsJH3Hyi/yRVmVbP0zHa1Ojc3icApTKrVAcLTrC31tpZWSnCp8ggwEhCkFYLoCy0tM/O9InnP5QLWZcQHe1IoS3moV98VH0M+nYeIyy2zlqp2Hsdal+H2bV4oEvNYnjp8Kythh+n/2zjI8jutsw/fMMghWzGRZlpkxDsfhNNQwJw01adNAA00aaJu4SfuFG2ioYeY4YAgnTswsyyBm3l0t7858P1ZaabUrGWVL9tzX1avZM2dmzqy1M3Oe877P6wzFvKgFgdFmPUclxnJJZhKyLA8YbSEIAsnaSEHhpfH5XLiujCq3F5MqaGL+RFVTWJ8EjTokSDV5fHT4A+QbdFF9o/rj7sIMkGXeamjDIcl4ZfjdxgrenlhIknbfT10lKXLeKEm+0P9XVb8EBMV4gPb2n+l0bCHGXByMalpxaljBIJttNTIyHnc9giD2CoAQiIubSmzsBHTaZDIzL0AUo0Vc7Xqal8/XwZYtf8dqW4PJNIJRRfei1wcDDfx+O1XVL+JyVRIbO4n4+BmI4s5/z9u3PdT1X8Hr6OhYRlv7TyQlHrHL4zzQ2LaykSX/K8Hvk4hLMXDydRNxdHioL7NiSTcx4zcF/VbdCwQkfnxva1jb2sXVTDgii9ikoRXEsDc4KEUpS3omWqMJr9MRdbssyZStXrlzBxMEUvIKSMzK3nHfQcDjdPLNy+EvbT++9SojZ85h67KlwYeOLJM3aSqxyT0TN5fdxvaVy5BlGUdHO7amBmISk1n2yfsRghSALEm019dHtCvsPtvLHg4JUgBOVyWVVc9TOOKW/TiqSLT9GCrm5V6L2TxqwH0FQSQmZhxW60qiPUTbO5ZSV/8umRln742hDm2+/1dwErWr6OOC0VYHOQ8//DBXXnkll10WXJl85plnWLBgAS+++CK3395/9IqCgkIkDY2fsnXr/fj9naQkH0dx8f0DekCpVEbycq9ny9a/I8tetNoUUlN/Q3X1CwzoOyioaGr6ErN5FEZjT9pyZVVkRFll1X97RCmAEx4Cd0c/aXxd2Org1dPhhrXB6kH7GVuLK6JtRybnGr2K5OyYoHdULwI+iYyRcSRkmNFoVYw7PBOzJfq/kbXZxQf/WknAJ4VFSWn1Ko6+dEzYfjWb21jw1Dr83uDAZp8+ginH5e7cBSoMGqvtTlS9/JRkoDMg8dW06O9Zyzo6cffyFJOABc0d/K0wk+uyU7hiY0VoW0CWqXZ5SdcFfyO7m/5TZNLz66zRtPsDxKlVuCWJz5utVLg8CELQf+qPucG5xvyyeh6rDEZ/5xu0vDupkCz9zv1GdaLI9HgzL9T1+LNt7nRz//Y6Hhm971N24+NnoNdn4fHUh6KTeoo8dOXX9qWrX1X1810m4uHU139IVuZ51Na92atVIjX1JLKzoi8Ed5OedibV1f8LnkYO7peVOXCq9Lp119BhXQUEcLuqWeW4gFkzvwJEVq2+CLt9EyDR3LwIp7OcMaP/Gdo3EHBTV/8uXm8LCQlzscRPDzu2P9AZ8R0E/NHn2AcTTVU2vnpuY+iztcnFR4+swtHhDdnFlq1p5virxkX9TQZ8UlSfKY8zMhtKCkj4vRJaw/CVdobvyPcAQRC46J+P8t79f8Xa2NCrXSRn/ERMFguBAaKpRJUKKRBApdaQkJnFiX/4M2K0CluDjCxJ1G7eSEScNqDW6Zlx6m+xt7aQmJnN1JNPD/3B21qaeePOm3B0tEfs1x+CKJJRNDRWIoczbncd7e2/oNbE0di4oM9WCbd7cIW/Ha2ORcNsHkV29hVdkw8AkZGFd5KTc+lO7T+q6G5WrjqfQCB6JarGxk8PDlHK3hBewWtnEFVwyuPBuP2DGK/Xy8qVK7njjjtCbaIocswxx7B06dKo+3g8Hjy9UpBttuiVqhQUDjZstvVs3Hgj3ZOIhsZPUKtjGDXq3n736ewspXTL3XRPwLzeZjo6fqGvINVTKUogIeFQNm26qWuLyNgx/yYt7dSuz9HuhWKfjyLMvRE2fNCl7ESPxsJeF4xATSoc+ML3AYlZ5pDHU3+o1MHtgiAgSTLTT8pn8rwcfnx3C2uX1IT1rdtqxZJmYs6ZA19b+drmCEEqNknP+ffOQqUO/14XvbQJv6/n+1/64XYKJiUTn6pETO1P8g26MINvEUjXaQjIckTVuYAsRzUSt/olxv20gVlx5jCBSwTeamhjRrw5Yp9dRRAEEjTB6aNJpWLB1JE8X9NCqcNNm8/Pl81WnqlqYnsvE/Uql5fbSqt5feKInT7PNqcHdZfQBUH/qs2OPakGvfuo1SamTX2H8vIn8HgasVhmk519CQCiqCU9/bfU13dVakUgNnYcZnNwzhRNkAJQqQykpv4Gp6uKqsr/IhMgK+sisjIv3OF4TKYCpk/7kJra15AlH2npZ0QIRb3x++109LLhkAngclXhcGxHJoDdvj6sf339exSP+huiqA36aa0+H5ttHYKgoqLiP4wZ82/S004L9U9L/Q3VNS8TvEerUKtNWCw7mQVxANJa28mKzyuoWNcSsc3REfxddC9WlK1upqW6k+ScmIi+Wr2a9MI4GsqsyFLQe8ocr8eSHn6v3vRTHd+/tYWATyIlL4YTr52AKW7HnmZDjYNSlAKIT03nd48/T8DvY/knH9BcWU5iVjbTT/0tKpUalUYTUcHusAsvR6XWsPHbRTRVlBHw+2iuLOd/N11D7oTJHP/7GzFbEnB0tNOwfQuGmDjSR47aKRGgra6GJS8+g7WxnqzR4zjy0qvQGfvPn/b7fHz00N+oXLc66vaSH75BazBw8YOPE5cSbsi6/JP3cdp2rYR89pjxHH35tbu0j0I4VusaVq2+EEmK/oAC0OmSB+XcgYCTTSW30dz8FSqViZGFd5CxC0JQ0ci/kJpyAm53LTEx4zEad35VNSZmLLNnLaau/l3Kyv4vYrtatecvScOCgiNg82c77AaAPh5O+j9InzQkJlr7m5aWFgKBAKmp4emiqampbN68Oeo+8+fP57777tsXw1NQGLJIko+mpi/w+dqxWGZjNhfRYV3Rtxdt7T9F7CvLMrV1b9LR/iteXzvhQpJEZ+e2iH0yM88hK/NCZNnPr8tOCutfsvkOzOYx6HRJZGVeRHnF42H7FuRHMYZPHQtn/Q8+uiZofh4NQTVk0rtjEvQcd+U4lry8Ca8rugXEqFlpmC16nFYvmaMsFE4NRpbMOm1EhCgFsPHHOuaePRK1pv/FT5VajJDsbC1uvvzvek68ZgKCKOC0efn86bU4rZGLrp3tbkWU2s+cmhLP4lYb7zcGF4wl4MsWG3N+KeGtiSPINwYnmT+127liQwUd/gBaAbx9/uE9kswPHfaI9er+quHtKfEaNaenxnP08tJQKmFfAsAW564JShNiDPj7iHSTYvff36hOl0pxcXQLk+JR/8BkzMdqW4fRkENe3u8RhODvNTX1ZBobP+mzh4r8vOsQBIGC/D+Qn3c9sGsRbGZzEcWj/rZTfUVR1+VT1TfCRqS09K5oe9BdKbut7UdstrVAT3piWdnDYaJUYeHtqNQmWlu+RatLpnDEbf1mWQxHbK0utixrwO+VGDktlcTM4LzF5wmw6cc6nDYPWcUJZI9OwN7m5v1/rcTvDewwSrabT59cizlex5wzC8kaZQnbduI1E/juzVIaK2zEpxo5/LxRYc+C1tpOvnltc2jNprnKzjevbubk6yfulWvflxy0olQ3KrWGWWecE9F+xMVXsuSFp4IRCrLM2MOPZlpXtNHP77wW0b9y3WqeveZizAlJuB32kEn4uCOP4YhLrsLa2IA5IRFjbGQ5U6e1g9fu+BM+d/CGbW1uwmW3cfpt9/Q77rULP6dy/Zr+L0yW8bndrP96IXPPDQ8DdXfadzodecZpZzP7zHNRa/d/WPxwwWZbR2PjZ4iijszM89DrM3A4yli56vyuFeT+UasHp9zttm0P0dT0JSDh99so2XwHJlMhcXFTdvoYcXGTiYubvFvn1+mS0UfxnwLIzb16t4457Jh2RdDIfPnzwUlU8iiw14PXCW4r+LvESrUBzn8bcmbt3/EOc+644w5uuumm0GebzUZ29v5Js1ZQ2B9Iko/Vay7timgSEAQVE8Y/i9W6hvCXABV6XWQRk7Kyh6mofIqICKaufVQqLX6/K6xNFHWYTCO6UkHCXzQkycOvy44HBApH3M6IEbdRV/c2oqChYMTN/ZdYz5revyCFACc+BAZLP9v3PQWTksmfeBjLF5Sz/LOKiO0V61u57MG5Ee1qjYqEDBNtdX2uVd5xCuDI6amsWlhJZ1v4O0bFulaqN7eRXZzA58+so6nCHr6jAGqNSELGQbI4NIQRBYEnR+dwemo8F60rD/16atxeriup5POpRTgCAS5dXx6qwueTwSwKdPZK45MJRkhphaAYBKARBC7LHDyR4KPGDnz9CFIQrCk3cReNz+clxnJjbiqPVjYiA3MtZu4siDRmHwqIorrfd9nkpKMZN+4JqqtewutrITZ2Enm514TZXwx2NTVR1FI44ja2bruf7uoJWVmXUlPzMjbb+oj+OTmXh0zKA1E8YftGf4mihhEFNzGi4KaIvsOdjkYn7zywDJ8n+Ne98otKRs5I5agLi/no4VU0VdkRBIFVX1Vx5EXF+L0BfJ5Av/Nsc4IOR7snKBp3FbJw2by47F4+e2IN5/51ZtgCgd6s4bgrx/U7vuaq8Dm9LEFTxfDMDDjoRan+mHTsicSnpLHhu8XoTCZmnX5O6KYhiNFe0IJ0toWH6m34ZjGlS3/E53YjiCJHX/F71BoN9du2EJ+axsRjT+L9+feEBCkAZJmy1SuQAgFEVfSVMWtTA6Io7sCMXSAQpQrfiKkz2PzTdwPuBzKpI0ZyyDkXIg5wvQcDsixT5fYiCgJZOs2AD4+29qWsXn1xqE9t3ZvMmPEZ69ZftUNBCkCrTdhr4+5Ne8dS+qZLlGy+k2lT30GlMoZWdAYTk6koos1sHk1c3KRBP/eQQBThqLuC/+uLLEPtSuhsgswpPRX2FABISkpCpVLR2BhenbCxsZG0tOjflU6nQ6cbfuHLCoOLLMt0BiTMKvGALKvs99upqXkdn68NtTqmS5ACkJHlAJtKbsXnaw3bR602MXLknRHHqq55peu/IqeaarWJzMzzqax8ulerFDK2NRoL0GqT8Hrb6ZkadyOzbft8Zkz/jLzcq3Z8UR579PbTnoHMqZAc+WzZ3wiCwLQT8qjZ3E79tvDIdKfViyRJUd+tknNjIkSpgsnJaHQDP6P1Jg0nXDOedx/oGwUHTruXz/6zlsayyImKzqDm+KvGYYxVFh6HAoIg4A7IYfPZAEE/JYAatw97oOf3KAOdkky8WoXNH0AiKCGbVCLvTyrko6YOZGTOTU9klCncj+yndjt/Lq2h0evjMEsMjxRnE69RU+v2cs3GSlbbHWTptDw5JpdpO6h8tyMT8zFmA/OLsnb+iyD4XdxWkM4fclPxSBLxalXEPbvF62eVzUGiRs2UWONu3dMdjm1UVDyFz28jJfl40tPP3OvPhtSUE0lNOXGvHnNXycm5nJjY8djtGzAa80lMOLwrmjX8/pySciKFI24LfU6wzEajScDns3b1FchIP2ufjn1/su7r6pAg1c3WZY0YY7U0VQafTd2FxJZ9Ws70k/L6FaS0BhVn3T6NVQurqNvSQXuDI+TthwwBv0zN5rZdilqN61OoQhAhbphGvSqiVD+4OztZ8tLTdDQEPX42fbeE02+7h5xxE5lx6m/5/vWXdvpY3YKTLEksfu5JIOhLJUsSW375iaby7RH7aHS6AcWv9MIiVn/5af8nFYRgZZa5R0RsKj7kcJZ9/B7NleUR2ybMOwFTnIX4tHSKDznsoBekKl0eLllfxmZHUFA6ISmO/47N6/cBXFUV9F3qNkL0+azU1b6D0xn5XfcQ/I612mRSko/da2P3+drx++3o9ZmIYmSVBodjC9//MB1Z9hMXN5Xx454ctPRBgNjY8YwceRdbt84HAhiNhUycMPzLp+8VBAGypu3vUQxZtFotU6dOZcmSJZx22mkASJLEkiVLuP766/fv4BSGJLIs82RVE6/UtaIVBG7MS6XQqOey9eXUe32kaNW8NC6fqfuxzPjeJhBwsWz5mbhcZXSX5g5HjhCkQCAn+wrM5khhJ9rEbGThXRgM2ajUsZSXPxZa0NBqUykc8WcslmCEp0qlZ/KkV9i46RZcrgoCAXfEeByObRiNBahUOxCPYzMIucJ2I6ph3BmgHrrCs6gSGXdYZoQoBSAQ+d3aWl2ULm2IaE8riKWx3EZqfuyA56spie4TWr+1g6qNbVG3nXz9RNIKBidCW2H3KDTpugMogGCUUZEp+HeeodOgFQS8XZNgATCrRF4al88VG8tp8wUwq1W8OC6PCbFGJvST7lbv8XLBurJQut3CFit/2izzv/EFXL6hnA2dLgIyVLi9nLpqK4+PzuHMtP4XTc9Ks/BMdRNWX1AY6z0nvzE3hVvz03db6DGqRIyqyLnIGpuTs9ZsC4l0Z6daeGx0zi6dx+2uY/mKM7sifwK0tn5DQHKRnRW9ivlwxxI/Pcx7ymjIw+EoDesTGzsh7DvUaCxMm/oO28sexettIjHhcHJzr9xnY97f+HxR4v8EsDVFWrEEfBKF01JZ9VUl9lY3CAKyJJNVbCE5N4bJ83IwmLXM/e1IAN57cAVNFbawVFudadcKG6WPiGPaiXms+LwCAGOMlqMuGp4e0Ioo1Q9rF38RZoLu93p5//67ufDBx8gZNxFDXDwua8fAB+lK/YtGd4RT/dbofiiHXXjFgDfW4rlH0FJTxfJPPkCWJcYedhRHXnYNNRvXsfH7r1Gp1Uw54Tek5BVE7Bvw+/D3NXIXBMYdcQzzfnfdwNd0kGD3B7ittJoPmzrCHq5ftFh5qbaZq7Kjl6AP5lv3voEFXy1UKmNYOdjQVkFLSsrx6HXpZGdfikazd1IQtpc9QkXFfwAZk2kUMTFjI4wMg+MN+qbZbKvZtOlmJk9+BVmWsNs34A84iI2ZgFq99yZtOdmXkZF+Fn6/DZ0uDUE4uEVPhZ3npptu4pJLLmHatGnMmDGDRx99FIfDEarGp3DwIsky1W4vOlEkTRd8oXulrjWsvPr1JVXEqVXY/cFnb4vXz4Xrylg9Zyz6KBOe4Uhzy9e4XN2LXDtbMlxGp4v+PMvJuZKysoe7vEgkzOZRJCfPY/2G32O3b+zVU8Tv6yAhYU7Y/mbzKGbOCC6erVx1HlbrytCCDQiUbL6djZv+RHz8DCaMf6r/55+jKTJ/TfIH058teTt5nfuHgsnJ6M0a3J09HqWiCpqr7aTkhotM/XlQ/fx+8N/0iAtGMfbQzH7PJaqivzNu+jF6AZWpJ+QqgtQQpNhk4IGiLO7aUkOAoNn5f8YEfTxj1CqeGZvLNRsrQ8KURhT4ssXKytljsfoDJGrUO4xcWm1zhlXuCwA/tHfikSTW2sMn2wHgupIqUnUa5loizZgB0nVaFk0bxat1rbgCEvlGLTICY0x6Zu4Fc/Vo3L6lOpTGCPBOYzunplo4OnFg8bY3zS1LCAQc9L5f1ta+ecCKUt3Iskx7+9Io7+ACba0/kZsTLjoZjfmMH/fYvhvgEKJoWiqbf+5zD5Uhe4yFxkobLrs39HgaMzcDnUHNWXdMZ9OPdXhdfvImJpGWH/0+O+fMQj55dA0Bf/AAGSPjKZi868EBM39TwJi5Gbg7fVjSjKi1+7742t5AEaX6weOIrBQmSQF+eusVajdvwu3sv9RlTGIyLrsVQ2wcyDKd7W3IA1TdEkQxJF7JssyIaTOZNO+EAccnCAKHnncJh5x9IbIsoVIHX8RHTJvJiGmRFQ9qNm9k84/fodZq8Xu9tNeFl6bXGU3MOXvgcqIHA7Is09i4gAu36dngS4Q+q5kisNXZfxpeZsa5tLX90LWfiCiqSU09Bb0+k5LNt0X0l2UvgYCTwsJbd2u8gYAbp7MMjcaCXh/MtW9r+4mKiidDfZzObaHc8P6Q5QAd1lVUVj1PefkToUp5Ol0aU6e8jcGwa2HX3Xg8LWg0lrDqlGq1GbVa8a9Q2DXOOeccmpubufvuu2loaGDSpEl8+eWXEebnCgcXNn+AC9ZuZ7ktKPqfl5bA/xVns6g1PFVJBVj9PZN+CWj3B/jV6uAwi3lYp/I5nRVsL3sYm23NLu9rNo8mNfUUADyeRlpavkEUdSQnH0te7u8x6LNob/8FnT6dnOzL2LjpFuz2votpEgHJid2+icTEw6KeZ8zof7Fm7eU4ndsRBBWyHEDq8irp6FjJ5s13BUWw8kfx++2kpp5MdtalwX8XcxpojOBzEZw8CsHP5qGf5qzWqDjz1qm8fs8voXmvFIAFT63j0vmHIPQSDyxpRuKSDdha3chSpKj447tbGXNIRtg+vRk5PZWlH22PWkK8L2MPzWDWqTtfCU1h33JZZhJnplpo9/nJ0GnDRKYTk+P5YJKaU9dsQ5KhzRfgvzXNaEWBO0dEesMBlDk9PF3dRKc/wKkpFlK14e+EIpCsVaMVBCxqFe3+cIFUBXza1NGvKAWQqddye5fn00eN7dy1tRabP8BxSXE8WpyNSb13J8p1Hl9ELOj8sjqOSojZ6fu5KGoJF/AFVOLQjb7cW2zZ+ndqal6OskXGGxFNe3CTPSaBeb8by3evbw4tHIyalca4w7LIHZfEss/KcVo9ZI9OZOIxQd9SvUnDlON2XBAqozCe8+6ZSc3mNnRGDfmTklDt5iJZTIKemAT9jjsOYRRRqh8Kps5g+SfvR7Tb21pxRxGswvq0NnP23Q+QPXYCrbXVfPjgfVgbG9DoDaQVFlG9YW1Yf1mSKD7kcESVitSCQiYdd1I/R44k6DkVeaN3dLSzZuECqtYHz1W3dTOiKAa1r77RW4LAxHknEpNw4FRK2F0qK59ladkrbBCeirpdAsaaI1PhuklJOZ4J45+hvuEjVKKenJwrMJkKMJkK0GgT2bjhjwSk8IiplpbF2OwbiI3p38guGg7HdlatvgivN+izk55+FoUjbqXTsQV6BX/LcgCfz05y8gk0N3/Rz9FEBEHNtm3zw1o9nia2bpvPhPH/2aWxBSsNXhCadOTkXMnIwtt36RgKCn25/vrrlXQ9hRCyLHN7aTUrbT331Dcb2kCAzZ2usBQYiaDZr18O92s5Z+12LkpP5KFRWQiCgFeS0EZJW2/y+Li/rI7tTg/T4kzclp+OYQhEWPl87axYeVYvv49IRFGHJHnCPhfk34RWayEl5URUKgMOxzZWrAxGsQIYKwuYPu0D0tJOJS3t1NC+wQip6OfRdRWzkGUZt7sGQVCHFksMhixmzfwSr7eF5uaFlG7pXcglQHvHMlpav0GSfIAUFNhkiZycK0BrhN++BO9eAn43aPTBinya4fEC7vdGmt46rV7cDh+GmB4vJ5Va5NQbJ/PD21torrLT2e7pcxwJKSCj6iVQSJKMrcWFVq/GFKfjjFum8Mlja/G6Iv1EIZgFmTHSwphDoosXCkOHWLWK2H6EnDWdLiS5589KBr5ssUYVpercXo5fuQVHIIAsw4dNHfxndA4XZyTySl1QgNCKAv8elY0gCDw+OodL1peHCz4CmHdSVNpgd/L7TZWh/Rc0dxCrFvm/4pyd2n9nqHB5sPki/8Y3dLrZ5vQw0rRz94aU5BOoqHgKt7sOQRCR5QB5eb/fa+McijgcZf0IUgACyXvRRuRAoWhaKiOnpmBrcaNSi5gtOravaqJyQyvGGC1zzijcbV++uGQDccmREbCyLFO/rQOH1UtaQdxOC07WZifWJhcJGSbMluHxjOxGEaX6Iat4LIeefyk/vPG/sPYRU2dG9YDqjSCqqN60nuyxE0jMzOaKx57D3WlHZzIhSzJPXXkB3j6RVmMPP5q8iTtfCW0gbC3NvHrbH4NV9noRZoreO7VQlknI6D8k/GCisuoZ1PQfVXRCYiwXZQxcejo5eR7JyfMi25OOZNy4x1m77ncR2xydpbssSpVsvgOvt8dYv77+XerrPyA761J6vwELgorYmLGMG/c4Dsc2rNYViKIeq3U1tXWvAyCKBgKBaGayEm53ZInqHbF6zSUhQQqgquo5khKPwmKZscvHUlBQUOiLT5K5fEN5RESUCLxZH+mfk6xVc++IDG4srcbTJwrl1fpWMvRqnq1uocMfIEmj5pXx+Uzp8pvyShJnrNlGudNDAFhlc1Ll8vLi+Pw9ugaXq5rGxk8BkbS036DXZyDLEpVVz9Hc/BUadTwFI27q99nQ2VlKdc3L+HzR/YJAICnxaNLTz2DDxhuQZR+CoGXc2EcjJh7l5U/i9/e8lzidFdTWvklu7lW0tf9KRcWT2O2buu7rveW+ILk5V2M2j8Lvd7B23ZV0dPwKQGrKyYwd+zCCoEIQRHS6FEymwj7jVKFSmfD5Ouid/l7f8GFQlAIYdTzcsgU6qiE+G/TDJ+3MbNGjUgsEuiOYhKDBeDTvkJgEPSdeOwGfN8Drd/+C0+ZFlmQEEbJGWVBpeoRQp83LJ4+tprU2+O+WPiL4nWQXWyicnsLiF0tCaSHdyDLUlrbz7j9XMOOUfKaftGd/wwr7hwSNOuwXKAJJmuhTuk+bO+jsMkHv5qXaFj6dMpKz0xJo9PqYFGMkUx+cVM9LiuODSSM4b11Z6F4Zr1Zz+U5W71tuc4aNTSKYGhgNqWuRQLWLkao3ba7C009AoC+KbYokeamqeh6bfQNGQx55eb9HrTaj0cQyY/pH1Na+id9vJynpaOLjD2x/z/6eFzpdBulpp5KXe+0+HtHwQBAE4pKDQQkbvq/luzdKCWY/Cmxd2cjpN01BCsjEJOlD0U7NVXZKf2lAUAmMnZsRMjCv3NjK4hc34nUHiE02cNqNkzHF9UToybLM1y+XsPmXoI2QSiNyyvUTyRw1sMXL+m9r+P6tLUAwnfvY341lxOTo6flDEUWUGoAZp/6WxKwclr73Jn6vm7FHzGPayacDMkvfexMI/pFqDUY8vUQmWZYwxfcYAgqCgCGmK8dZhGN+93s+f/xfCKKILEmodXqWvPgME44+jmmnnLHHaQSrvvgkavphaDyiiKhWE/AGfaWyx06g+JDD9+icBwqyHCABO3Plb/mRwwEZBBGzSuSeTCcjW/7C0p86SE4+jpEjb0fcxTDfpKQjMZvH0tkZXi7bZBq5y2N1OLYTuWIdoLrmBXpPGgyGfIpG3YMgCJjNIzGbg+dKTz+d7OxL8HqbEQQNK1edHfU8lvjIdNAd0Z3+15vWtu8UUUpBQWGv8Hp9K4v7CFIQrU5ckCavnzqPj9VzxnLs8lJqPL6w7Q+VN4buyC0+P2ev3c76Q8ZhUIls6lp9732Oz1usnLhyC+emJTDHYiZLp90lbyqHYzvLV5zeZQAuU1n1LDOmf0JDw0eUlT/a1Uukw7qcWTO/Qq8Pj4Bobl7IuvXXRb1iQdCg1SZhiZ/FqFH3oFbHMDf+Z1zuagz67KhVXn2+8Cp5giDi89uornmVLVvu7fc6UlNOJjf3atTqWOz2TTQ0fExHx/LQ9samz4i3zCQr8/xQW3z8TLKzL6e6+kUgWHU2Pf0Myssf73VkEZWqj5+hPg7Sho8Y1Y3epGHe5WNZ9OJGAn4ZjU7F8VePRxzA90ejVXHaTZP5/q0tWJucpI2I47Bzws3of3hnC231PVGC9du7DNUFqN7chlonRohSvdWCZZ+WUzQjlbjk4Vmp6WDm5OQ4Xo0zsdQanHvoRZG7C6MvLot9bCgEgiKQIAj9VtWbZYnhx5mj+bSpA1GA01IspOh2zoA5Q6cJE6VUQLY+PIpEkmX+tr2OF2pakJG5PDOZewszEHdy/rPF4YlwzROACTGGiCqDAJtKbutaAAj27OhYztSpbyMIIhqN5YCPjuqN2Ty6T2VUFRbLDKZMfm1/D23YsGZRFdBtdSjT2ebh1buWAmBO0HHqDZNxO318+K9Vob/Tjd/XcvZfpqPWinz25NrQvbijwcm7Dyzn0gfnho5fv60jJEgBBPwS375RygX3zep3TE6blx/e3hL6LAVklvyvhPwJSYhDIKp7Z1BEqR0wYuoMRkwNn0jPOesCRkydibW5kZS8YE7+W3f/GUdHsPJJVvEYxh5xTL/HHH3I4cQlp7Lh20WsX/IVfo+bjoY6vn/9JbQGAxPn7VnZUJ/L1a/FqSCKqDQazrl7Pva2FrR6I9ljx3elAQ59ZFlmu8vD5k43CRoVE2ONmPbi2LMyL6Ky6lmu5inGUEKjejRHF57HSXEOfl12Fg45AMjU1L6KIKgoKrprl88xYfx/WL3mElyuSkCgcMStxMZO2KVjbNv+b/z+jgF69NRtiY+fik4bfYXLZBqByTSCQMCDWh2H3x9eJSgxcR4FBTft0tggOCnqNlHvJjZm/C4fR0FBQSEaFS4PagF8fR52ZpVIZyC6NPVAWT3Vbi+z48180NgeJun3fWZ2BiSq3F5GmfT9pumtsjlZ1ZU6GKdW8dqEAqYPUM1vldVBqdPNaJMBfd1LSAE33UJQIOCgpuZVmluW9NpDIhBw0tr6HZmZ54Udq3TL36OMWgVIjC6eT3r66T3XJgePY9BnotFYqK9/H6ttDQZDDlmZF6NSBT2k2tp/7NpDQJb9JFgOiRrZCyoyM84hv+AGtJrEMH8SQVDTWygTBDUOx9awvQVBYGThX9DrMrB3biQ+biopKSfR2PgZTmewcqAgiBQU/Knf73K4MWJKClmjE+hscxOTqEer3/Hrd3yKkd/8cVK/21trO6N6TyH3b5rel5VfVHLUxaN3qq/C0EErirwzqZAlrTas/gBzLeZQpFNfTkuN59HKRjr8fgQgIMM12Ts2U87Ua7kmZ9ejLOYlxnJaSjwfNXUAEKdR8Y+RPYKZMyBx/trt/GLtWcz/b00z+UYdl+1kNNbEGAPfttnD7uGnp8QzvygrIuoqEHDS2PhJrxYZq20VDse2qFVHD3TUahNTJr/O5s134XJVERc/leJRf9/fwzpgcHR4WPy/TcQlG5BlOZSU5PdJbPqpDkOMJuLR7bB6kQJSSDxyWPsUI5ODolNYkyyz/ttaNn5fi6gWGDk9NcKdx+cJ8MItPzDhyGxmnJzfrx/hUEERpXaT1IJCUgt6QtAvffhpako2otHqdkrkySgqZtuKX0LRUt1s+fXnPRalRs46hHVLvoxozyweS0JmFlNO+A1J2bmkMfRuxs1eH01eP3kGbYTYJMsyfy6t5rVeqRlGUSBFpyFGpeKG3FROTonfo/OPGHELOn0aHe3LuFCXSl7exWi1CdTUvtFVWS80GppbFu+WKGUwZDNr5kLc7ho0mng0mp0bsyxLNLcsoq1tKbW1r+7k2eSuiU8PkuTB4diGWh0XMjBXqXRMmfw669b/Hre7Gq02hXFjH8di2b0w5tGj57Np05/pvvMmJBxKSsrxu3UsBQUFhb5MjjVGCFK5eg3XZqdy+9YaRCJjiCTg1bpWzkiNZ64lhu/a7WgFgSMSzCxsDU9fFoBUbfAVqcio45TkeD5t7oiSuBbE6g/w29XbODc9gQsyEpkQEx598kRlY1g1wGtNucztc6RAwNlV7TT8LBERQ9C1gBC+f0rKcWRlXhQWkerzWVmz9jJstqC/ZDBSd2NXRb0Ara3fMXnSK2Rmnk9AclJb+yYeTzOS5GTN2kv7PPd6vkmTqRCdNomW1m/D/En69pdlPzHmSNFj2/Z/UlX1PIKgpqHhQ6zW1Uyf9j71DR8R8HeSlHQUZvOoKOcevugManSZe6/IR3JOLB2NzojChLtCyc/1jJmboVThG4ZoRIHjk3f875as1bBoWhEv1LbQ6Q9wSkr8gIble4ooCDw9JperspPp8AWYEmskviu1UJJlDv21hNo+kaoA/6lsZF5iLFn9iGu9+b/iHC5cV8aGThdqAf4xMotL+xW0RKKlHAcF9IMTk6mQqVPf2t/DGLZMPDqb79/aEkzfk8OtmmUJ2usdxCRGRuxJkowxLnqGTW/BKK0gDpWmK9I1mLBDzpjwCOfSXxrCIqNaqjvR6EX8HilsPF5XgBWfV2CM1TL+iN0rWrWvOHh/kXsZvclMYZSqd9EoW72c9UsW0l5fG1GVr37rZmRJClbk203yJkzmlBtvZ9nH79HZ3kZCRhYzTv3tXvOsGixeqm3hzi01SIBFreLNiSOYFNvzYr+o1RYmSAE4JZkKlxcBuHJjBe9rCplj2f2XPkEQyc66mOysi8PatZq+6Q4iWu3A3lIDIYpqjMa8ne4vyzKbSm6joeGDAftpNAldaRgQfABLWG1raGxcQGrqSXR2bmXFyjO7SuBCaupvGDvmYQRBICZmNIfM+Wb3LqgP6WmnY4mfQ1vbdxiNhcTHD+2/PQUFheHFb5Lj+bexIawaaqXbh0kt8sLYPO7YUk2TLzJaRAK+brOzae54XAEJrShQ5/Hx/a8lYSXSL0xPCE2kBEHgmbG5zGuM5Y26VpZZHVHTBD2yzGt1rbxR38ZnU0cysUuYavP5eaAsvKT0045pFJFECs1AcNEhNfUUkpKPYe3aK+meRJnNo6MazyYlHdOVjiIBImq1iVFF96DtExW7ffu/sNk2hD53dm7sOl9QPGpvX0pn52ZiYsaQm3MlDsc26us/DOvTF7N5NBkZwXRvp7OcaBO+bjIyziU9/bdhbX5/J1VVL4Sdo77hfQoK/nTAl2LfE2RZxuP0ozWoEUWBuWcV0tHgoKkymh/kzvPju1s56fcTwkzXFQ4sMvRa/tpPZb7BQBAEpsRGiulv17dFFaQAaj0+Tl21le9nFu8wAyJNFxTaWn0BzCpxwNRplUpPVuZF1NS+EhLjExMPx2hU/NQUdo/xR2ShN2uo3NAKMpT+2pNqJ4iQmGVmzCEZbFvRhCAAQtDKuXhWGgkZJn75aDudbT3vLjFJegJ+CbUm+Hcfk6Bn3uVj+PHdrXidfnLGJnLkhcVhYyhb0xz2WRAF8sYn01Rhw9rsCh+wADWl7UNelBq0JMOKigquuOIK8vPzMRgMjBgxgnvuuQevNzz8bN26dRx66KHo9Xqys7N56KGHBmtIQ4LyNSv58J/3sW3FL7TWVEVs97ndVK5fs8fnKZo1lwseeIQpJ/yG5spyPnv0QX5653XkKAaAQ4Fyp4e/dAlSEFx1vnZTRVifyi7xKRpBo0T4qtXaT4/dR5ZlLAlHk2DpyfcVRS1FI+/c6+fqD4dz2w4FqdmzvuHQucuYOOE5jMaCULvLVcmGjX+ksekLVq+5JCRIATQ2fkJT0+eDMma9PpWMjLMVQUpBQWGP8EsyNn8g7PklCALGPhMRFVDr9tLq89McRZDqJrZrwmNQiagEgWy9loXTRnFqcjxz4sz8qyiLf/WpFKUSBM5OS+C/Y/NI1qr7fRYFCEYDvFbXU1bb6gtEkWwEPo59BItlDhbLHEYXzycmZgxJiUcwY/rHjCi4iVGj/sa0qe+gUkWuuI4uvp+MjLPR67OIi5vMlMmvRwhSAPbOzfRXLa+b3uKT1bq6T/8+fjSCmjGj/41KFTR8DaZlR3uvEMnP+yOji+9HEML/nYKp3ZH7rFlzGVu2/KPLZ0uhN+0NDl7761JeuPkHnrn+Gz7890qcVi/HXbVrBVKi0Vhh49Mn1kZPBVRQ2EuUdLr4ob1/AVUmKEyttbn67dMbQRBI0qp3ysuvqOivjC7+JxkZ5zCy8C9MGP/0Hvv3KhzcjJyWyjGXjuGYy8ZwxAWjEFXBv6e4JAPHXDqG7NEJ/OaGSRROS6Voehpn/HkqSVkxiKLIYWeHZyrZW90s/6wi9LlifQuLXthEZ5sHnydA9ugEtIbwOCKdUU34o1XGkmbkwr/PZsZv8un95y0Iwm5XB9yXDFqk1ObNm5EkiWeffZbCwkI2bNjAlVdeicPh4N///jcANpuNY489lmOOOYZnnnmG9evXc/nllxMfH89VV101WEPbr2z4djGCIAwoDjmtHXvlXJt//j6seuAv77/J1mU/M+3k0xk99whU6qETKFfmckdU6yh3ebl2YwUPjsomVq1iUqyxX68sAEkO+nrsLT5sbOdf5fVUuLzIwImJf+W+seWoJBvx8bMwGPZdxcKAf+CV0Li4aRiNwUlUUtKRbCq5NaJPVdULeL1NEe3NLYtITT1p7wxUQUFBYS/yTkMbt5ZW45ZkJpgNvDwhn3Rd8OVqTryZ9XZXaDEjADR6/HzTZkekfylmZrwJV0BimdWBCMyIN1Fk0vPsuLywfj+3d7K41YZFo+LijETiNGpSdBqWTC/mo6Z2XqhuptztjXqO3o/4bL2WBI2Ktj5CWbkvluIxf2P1mksp2Xw7JZvvZFTR3WRlXUhMzJgBvxeVysDo4vsH7AMQEzOmK3Uveo6XIGgwGEaEPhsNeTidvSsMhz91ZVmivf1HYmKCqXXx8dMYOfIutm59gHAvKbHf54paHY/FMpf29p/Cju9wbsPhLMPrbWbcuMd2eG0HE18+uwFba1CskyWo22blvQdXcO5dMzBbdDisnmAaX9eKfHe/nUIOVonq7PDsdNlxBYVd4e6tNfy3pmXHHQGTeu/HSwiCSEbGWaT4T6B0y338/PMR6PRpjCq6j9hYxe9UYc8Ye2gmRTPT8Dr9GGO1oVS87NEJZI+OLCzSVGVHVAlIga7nnxw0N4dgit+iFzaGilTIMnz7xmbyJiSFCUtTj8+jfG0LHmdwUcls0TP+8GAk1MSjsilb3UxLdWfXNh3TTswbjEvfqwyaKnH88cdz/PE9HjIFBQWUlpby9NNPh0Sp119/Ha/Xy4svvohWq2Xs2LGsWbOGhx9+uF9RyuPx4PH0hLzZbJHVd4YyKrU6+MbQjygliCKZxQO/jO4s1RvXIapUSIGeF+HW6kq+evpRVn/5Kef+7SE02l2rHrc7eN0u1ny1AEdHOznjJkYYx6+wOrhrS23UfT9p6sAZkHi5y0D2n0VZ/HVrbajka2/fkCy9doCc8l3j46Z2rt1UGdb2eWsnafrR3F+078MfzeYx6PWZeDwNyHLfqZZAQsLcsJZAINpKk4wgaJHl4O/Hg5Z6Muls38Ker7UqKCgo7F1KHW7+VFIVusdv7HTxp5Iq3p4U9HO8LT+dFq+fj5o60IsCJpXIy3UtQTPffo4pAkZRZN6K0lBFvXFmAx9OLiSm16LGR43BZ4BKCC54vFXfxsJpRZjUKpK0an6XlUyeXseF68uinueCjJ70brUocH1OCn/bHp7C55YkNm66BY+nrqslQOmWe4mPn77X/JQKR/wZu30TNtvqqNtl2YfNtorExEMBMJmLaGldErVv1x6oVOF+WTnZl5GZcQHbtv+TmprXgACy7KexcQEFBTdEOYbUb7QUSDQ1f4EsPxIRYXWwEghItNU7Itr9XomK9a2c8odJfPX8BtobHMSnGjnud+OwpJt45vpvdslvSqMbHgVvFHqwf/MN9q8WIprNJFx6KdqsfbdYurMstzr6FaSSNWqafX5UQtCA/YSkWCaYDYM2lpKS22lq/gqQ8HibWbX6IubMXrJHdhwKChCsmKrR7tw9NCZR3yNIEUz5i0sJ/t17XX687vA3GFkKGqj3FqXiU42cd89Myte2oFILFExOQWdQ43X5cVg9nPanyTRU2JADMhlF8TtVXGN/s09HaLVaSUjoUQyXLl3KYYcdhlbb8yUfd9xxPPjgg7S3t2OxWCKOMX/+fO677759Mt7BYOqJp7Jl6Q+hl2yNTk9sSgrtdXUYY2I57vd/Ii4lba+cy2xJ6Dciq6l8O+uXLGTKCafslXP1h9/n4+17b6e5ogxBFFn1+cccdfk1TD7uZByBANdtquTLlv6FxQCwpM2GLMsIgsClmUlcnJGIOyAhCgId/gALW6yoRYGTk+OJ3UuRUu83tEe0ycCP7Z175fi7ikqlZ8rkN9iy9e84HNvweBqQpOCqqcGQE+HDkZR0FE1NC8LacnOvodO+ifKKx6kmm/ncg1WwgA+2l1VzU0H2PrseBQUFhR2xqdMVFt8TANbYewR3vUrkiTG5PD46h4+bOrimz0JCNCSgzR+gvJcX1aZOF89WN3NLfs+z99HKRmTA3/UI3e7y8GWLlTPTet5hjkmKpcioY0uvY+kFgTcmFjA5Nly46Y7u6o0rIOFwbOmz0CB3VYXaO6JUIODG7W4YsE9b+88hUSoQ6CSYCBld1jMa8khNPTmiXaXS0t7+M72FpvKKx0lOPoaYmLFhfds7ltHR8Wu/4xEEFX3TBg9mVCoRs0VHZ7sncptGJCHDxHl3zwy9J3VjjNGGV3Hqbf3V9d+CGJzwTDk+F71JM6jXobB3sX62gLpbboGudGTbZ59R8OknqJN3XFlvX1IbJZo0ViWybPYY4jVqfmy3s9zqIEuv5YxUy6Cm1bW0fkPPUrZEIGDHZltLUtJRg3ZOhYMXa7MTl92HrcXN5qV1CKLApGNyKJ6VRsW6FsrXBsXauCQDs04LRizrjGpik/TY2zzBlGoBtHpVSLTqTWttJ9Wb2kCA2EQDDpuHJf8rQQrI6ExqTr5u4rAqYrHPRKlt27bxxBNPhKKkABoaGsjPDzeaS01NDW2LJkrdcccd3HRTT4l6m81GdvbwmUynFhRy4fxH2fTjt4iiivFHzdtrIlRfpp50GluXLaWlqiJimyAIODraInfay1RvWEtTeTAVQO6K2Pr1g7eZfNzJ/HVrLV8NIEhB8L0pXq0Oe0iJgoCxS3xKU4lcvJeio3qj78doPmYQwop3FoMhi4kTngXA52unpeVbBEFFUtJRqNXh5u5jRv8TWQrQ2vYNomhgZOHtpCTPIzZmLOUVj/Ms12MnNtT/ocpWjkmOrBiloKCgsL/IN4RH8qqAAkNkdK8gCLilyJCQaBX4AKrd3rAYHVGAhj7mu54ox7u/rJ4369v4S0E6U+KCJr4fTh7JrVuqWWF1kGvQ8a9R2YwyRaZA9a0oJQI5Bh0moQi7fV0vYUrAZCqM2H93qa5+CZ8vMm27N1VVz5GUdBSW+OnExU6hhujVXdXqWKZP/xC1OnrlLperhr7fuMtdEyFKBQLOAceTlHiM4vfSh2N/N45PHluN39v1/QoQY9FTODUl1Kf3d7ZtZWPUsuKHnFWIVq8mfUQcthY3rXWdJGaYyR2nRIoMN9pe7qp62fVuHbBasX21kIQLL9hvY/JKEt+22XFJEnPjY0jUqpkYY0TdFQklE7yPz443hwpJzLXEDGo1wN5oNPF4PI30Fs81msi5poLCnvLT+1tZs6g6vFGA6k1tnH7LVE64ZjyttZ34vRLJ2TGoNMH5pSAInHz9RD5/Zj0dDU5McTqOu3JcRKRTzeY2Pn18bWj9pmx1M4IohLwBvU4/XzyznsnH5iCqBAqnpg55X6ldFqVuv/12HnzwwQH7lJSUUFzc4xJfW1vL8ccfz1lnncWVV16566PshU6nQ6cb/JSzwSQpJ4/Dzr90j49TuvRHNn63GFmSmX7qbzHFx+PsaCc5twC92YzOaOKC+x9m2UfvsvT9N8P2lWWZnLET93gMOyIQiFxtDfiD+a+LW20DekRB8MX9n/s4XS4gy9S6I1ckAa7OHhorUBqNhfT00/vdrlIZmTDhPxHten0GIwr+TENZBpIQHlVW7vIoopSCgsKQYVKskVvz03ioPBjpk6hV8+jonKh9j0qIJU6totMfCMX45DTXUpGUAX0Ejr4RWH4ZWrw+7t9ex1lpCRSZ9FyUkcTftgfT6roDTOo8Pho8Pk5fvZWvZxQzwqgnUavmhXE7ruI0Pc7E1VnJPFsTrJgTo1bxf8XZjFT9m9VrLsXtrgZUjCq6e69FSQG9qrH2IAiarvS57s8q2tp+wBI/ndTUU3C6KqisfAZJ6n4OBr+BvLzrogpSsizT2VmCyTQCu30TQWFKQBBUxJgj7Qji46aj1Sbh9bbT11RdFPWMHHnHnlzyAUn6iDgue2guZaubaaqyY4rTMnZuZtToppVfVvDLR9HTSgsmJRObGFxxt6SZFDFqODPEdFtXQOLMNdtYZQuKzgkaFZ9NKaLAqOO5sXncUlpDu8/PHIuZh4uj38cHm1FF97J+w3WhRYC01NOIjZ20X8aicOBSt7UjUpCC4IuEKLB1RSPpI+JIyoouxlrSTFxw7ywCfglVP8EQm39pCEW6AiAQVqxClsFp8/LTe9tAgBVfVHL2HdMxW4auhrLLotTNN9/MpZdeOmCfgoKeyl91dXUceeSRzJkzh//+979h/dLS0mhsbAxr6/6cljY40UPDnZaqCpqrK2mvr2Xpu2+E2ivWrgz9t85k4rd3/oO0ESNRa7XMOfsC0ouK+e61F+mor0VrNDH33IvInTBp0MebPWY8MYlJdLa3IXetPE+cdwIAyVoNzV5/v8LUOWkWfp+TGnXV2SNJPFrRyEdN7WgEgWtyUjg/fe+8XM0vq2elPdKTSQROSo7fK+fYn+TlXcPElnUstwcIdL3ViMDYQczjV1BQUNgdbspL49y0BFp9fgqNegz9VFpK0Wn4bMpI/q+igSaPF/OST5mw8gcWH3ICa8bNDOvrlWSOSojh67aeAhKLWm0sarPxXE0zC6YWcW12MmaVyFctVn61OugMBJ9fEuCRYe6vm7k4I5F/FmXtdFTPfSMzOS8jgRavn3FmQ1ekQB6zZy3G42lAo4mPiHrdU5KSjqau/p2wtpiYcdhs6+gWhGQ5EKrcJwgCBfl/JD/vD3g8DVRW/Reft43ExMNJS4tcCJEkPytXndvLsyq42KFWxzBm9IMYDJGR7BpNLFOnvM22bQ/h9tSj0yYjI6HRxJGXey16/b4rXT+c0OrVFM9Op3h2er99JElm2WflUbdNOzEvJEgpDH8SL72U2ptuDqXvqWJjiT3+uP02nrca2lht64mCtPoCzC+r47lx+ZyQHM8JyfFIsoy4H6Mgk5PnMXPGF1itq9DpUklIOFSJylTY61ibB64gqdHuXNZNf4IUgEolEJ6TPYBltQzuTh/rv61h9ukjonQYGuyyKJWcnEzyTuYr19bWcuSRRzJ16lReeuklxD4pUbNnz+bOO+/E5/Oh0QRXexYtWsSoUaOipu4d7Kxb8iWL/vvkDvt5XS6+evpRLvl3T6RM/qSp5E+aOpjDi4rOaOS8f/ybX957K2h0Pn4ik48L+lE8MDKTc9duxxWlDLFKAAEhJEhJssxjlY08X9OMyx8gIAh4eu130+ZqLGoVJ+yhaPR5cwdPVkVPdTgnzbJfH6Z7k6fGFXPx+nI2dLrQiwL/HpVNoVGpuqOgoLB/kFwuWp9/AW95OfqxY0i4+GKErveCDL2WDP2Ow85HmvQ8MzaPlupKXl7xDQCH/bqQLQVjcekNyKIKFTAr3sQ3beEVTQMQfLeTZZ6vaeaR4hwuzkzi4swkTlixhbV2Z1h0lQy8XNdKgVHH1dkp7CzFJgOYwttEUY3BMDgRwcnJxzC6+J9UVv0XZJns7MtISDiEFSvPwucLpvDHxIwjI/3ssP0EQUCvT2dU0T0AVLg8vNPQTpJWzZEJMaFnYVnZ//UxUQ8gigZmzVyETtd/ar3RmMeECU/t3YtVoLqkDckf+U51xIWjGDt36JlgK+w+sSeeiGgyYVu4EJXZTMLFF6NO2vt2FjtLi9eHSujx4QsATV5/WJ+h8A5tMo3AZBq6E3OF4YXT5mXJy5toKLMRm6TnqItGk5Ib01cvAoIeflqDirGH7fm9eMJR2ZQuawy9l6g1IrPPGMHP72/D75VQaUQCvvB0ep/bH3mgIcSgeUrV1tZyxBFHkJuby7///W+am5tD27qjoM4//3zuu+8+rrjiCm677TY2bNjAY489xiOPPDJYwxq2+Lwelrzw9E71lSUJW0vzjjvuI2ISkph31fUR7TPjzfw4czTLrA6+arHycVNH6PcryZChC05IArLMOWu282NHL5PxKFLwIxWNeyxK3d+nOlI3U2ON/HPU8PEu2xEZei2LphVhD0gYRRG1uP9fFBQUFA5OZFmm+pprcS5fDoDtiy9wl5aS+dBDEX3dmzfjLtmMLj8Pw6RJUY9nsiQgiCKyJKHzeTj3k+dZcthvkAtGMSc+htnxJn7qiKxm1o2vz0LJqSnxrLFH90H6qLFjl0Sp/UFGxllkZJwV1jZ71kLa2n5GVOlJTJiLKPYf0v9dm50L15WFqt6elBzHc2PzEAWB1rafIvpLkovt2//FmDEDWz0o7F1WL6zi5w+2hbUJIsQlGyme2X90lcLwxXz44ZgPP3yPjiHLMuu/XkjZyl/Rm2OYecY5WNJ2PVrxMEsMD1f0ZL8IwNGJsf3voKBwAPDls+tpKLchSzKtNZ18/NhqLv7HHI65ZDTfvlEa9IzKiSGr2ILOqGbUzDTMlj0PAkjMNHPOndODaXwCFM9OJz7FyJg5Gbg6fdSXdbDwuY2h/rIkUzBlaL+rDJootWjRIrZt28a2bdvIygpfAeyuCBcXF8fChQu57rrrmDp1KklJSdx9991cddVVgzWsYYvX6USK4s8UDUEUyRg1epBHtHfI1Gs5Xa/l6MRYfmy30+LrSicA1tmdyLLMp00d4YJUP6zrdFHl8pATxQh3Z+mM8h2PNul5b1Ihun7Mz4crgiDstWqFCgoKCruLt7wC56/h1dhsn3xK2t33oDL3hBW1v/0ODffeG1qUSPrD9SRfd13E8QzmGI753XUsfu5JZFkm2d7Ba4VpjJwZNNze1Bk9tL7bGP2cXhX2lrbbubfLWyoa5ijh9QFZpsrlxawWSdYOzYpmGo2F1NSTdqrvnVtrCPRaCFrQbOWn9k4OTYhBr0+ns3NjxD4O59a9NlaFHdNW1xkhSAEUTEzm0HOLQia6Cgp9WbngI7579QUgOH/YvnIZl/7fU5jidy1jZWa8mSdH5/DP8gZcAYlz0hO4LmdoT4IVFPaEgF+ifrs19FmWwePw01LbyahZ6RTNSCPgl1BrB2euZUkzMfu08Kg/lSZYrXXk1FQkn8T672oRRIHJ83LIGjW0s9AGTZS69NJLd+g9BTBhwgR++OGHwRrGAYMxNg69yYzbsWNxJq1gJCf8/sZ9MKq9h14UaPOFC0KL2+x82tTBjZurdvo4DR7fHolSZ6Ym8HR1U9CLDjCIAm9OKOjXx0RBQUFBYc8Q+onU7M70cJeU4Fy9msYH5odFybY88STxZ52FJiVy4jPh6OPImzCZ9oY6EjKziEnoSWsZYzbw98JM7tlWiwQkaVSMMxswqlRcnJnIoQk95qO3lNb0P27groLwiIJGj49z1m5ns8MNwPU5KdxZkD6sfUtavf6IKoatvmAawMjCO2ht/RZZ7p0WIBAbO2Gfje9gx+vy895DK6Num3J8Lqa4oWtsq7D/Wbvoi9B/y5KEu9NO2erljD/y2F0+1plpCZzZS9RXUDiQEVUCWoMKryt8/mqMCdoNCKIwaILUzjBqVjqjZg2fKNlBE6UU9i6CKHL0Fdey4PF/7bDvcb//E8a4+MEf1F4kIEcv3f2PsnrcUTyn+iIAZpUY1RR9V/hLQTpGlcjCFivJWjV3jcggbSe8TBQUFBQUdg/3lq0giiD1PAVijj+epkcfw11SgmvFin73DbR3RBWlAGKTU4hNjr7tyuxkfptmod0XQCMIfNTUjk+Wye5zv692eyP2NYkCk2KN3JafzsTY8Iqld26tYavTHfr8ZFUTcSoVRyXFMsakH5bi1LFJsbzb0I5EcLFGJwpMjwtGsBmNecye9TUbN/0ZqzUY7ZaQMJcRBbfsvwEfZJQua8DnjozyjknSk5ixd43zFQ48VJrIqaBKPTQjPBUUhhKCIHDkhaNZ+MLGUOW7KcfnEp+6/yqZe91+nDYvMQn6AY3ShyKKKDWMGDXnMEp+/I6yVctCbbEpqdhbmpElCUEUScjI2q1c8P2NQSVyanI8nzZ3IBGs31Ng1LHV6YnoO9qk53/j8vHJMn8qqWJtp4ssvYYnR+cSF+XhuiuoRYFb8tO4JV+p/qigoKCwt+lO3+8WZ/zt7dTdckuYICWYTNh/+AHcbhggbV2VnIw2P2+3x2LRqHEGJOatKKXDF6xF+kRlI59NLQpVI03XaajsI0z9fWQW52dEVnt1BSSWdnQS6LOOcn95PfeX13NheiL/GrXz1fqGCvOLslELAotbbSRrNcwvyiKzl3hnMGQybeobBAJuZNmHWh29zLXC4OBoj3xPAjjj5qlK2p7CDpl1+jksePxfiCoVsiwTl5JG4bSZO95RQWFHdDZDezkkFIBp/5nwDyaFU1NIyjLTXG0nJlFPWn7cPjt3wC/RUt2JSiOSmGli28omlvxvEwG/jMGs4eQ/TCQld/j4uimi1DBCEARO/fOdlP70PdbmJtJHjiI1v5BvX3mOxrJtJGbncuQlVyKqhqdP0ONjciio0LHG7qTAoGNDZ6SxrAp4eXx+KEXvs2lF+3iUCgoKCgq7iizLtD77LC3PPIvs9xN/1lmk3fkXfDU1yN5w0Ud2OAaobdxDwiUXI2rDI5sCViu+xka0WVmIxh2vVr5S14rVFwhF6nokmT9squT45DjOTLXwSHEO56/bHorYPTU5nvPSI9NT/JLM2Wu20+rrX0R7rb6V36TEc1jC8BJtjCqR/yvO2WE/lUoPKFVc9zVZxRZWflkZ1mZJM2K2KGl7Cjum+JDDMcZZKFu1DENMLBPnnYjWsP8iPRQOEDZ8AO9fCbIfRA2c9RKMPmV/j2pQiE817vPoKKfNy0cPr6K9IThXziq2ULelA6nrXcXt8PHFs+u55IFD9um49gRFlBpmiKKK0YceGdZ2/DDzj+oPnShyW0Ew97XV62f8Txsi+pyTnrBHnlEKCgoKCvse+1cLaX70sdDnjjffxN/SQvp99yFotT3ClCgiGgxIzujV7nqjGxFu8Gn95BPq/nIn+P2IsbFkP/MMximTBzyGOyAFvau69C8J2ORwU+p083RVE59PLeLb6cX8p7oJnyQzJ97EapuTYrMBYy+vwWVWB8tt/Vf066YmSjqggsKekFWcwORjs1m9sBoAQ4yGE3+veHop7Dw54yaQM075mzmQ8Xd48GzvQNSr0RdbEAbTK9fT2SNIAUg+eO8KuL0SNIbBO+9BxK+flNHR1POeVLO5PWy7LENnmwe/L4BaMzyCVRRRSmFI8llXGl9fLkyPTJlQOLipqamhvLwcs9nM+PHjUauV25qCwlDDuWolqNXg7zHE7ly0iLb8fDIf/j9qb74F2eMBSUJyOECjCab09ZO+J+j1GGfMQPJ4cPzwA/6WFhr+9vdQGqDU2UnNH//IyB++HzBd7tSUeJ6vaaaXLgUEfQ69ssyz1U2UubwsszoQgLca2gBI12p4d9IIyl0e6j2+qMfufg3svgIRmByrRCAo7H3mnDGS8Udk4+70YUk3DptJiIKCwuDjrbbT/Nw6ZG/w+agtiCP5inGDJ0xV/NAjSHUT8EBnE1hyB+ec+xhrs5PVC6vwuvwUTE6hcOq+rTRpbXIi95ooCyIg9wSYCwKYE/TD6lmgzN4UhiTRBKkMnYYpcaYoW4KstjnZ6nQz2qRnfIzy4n8wsH79et5///3Q5+XLl3P55ZcrwpSCwhBDk5ERVWBqe+UVitesJv7ss2l/9dWeDT4fhilT8Lc046uuiUjlk91u6u++G9eq1fjr6yNPKEkEWlqQXS6EAdL4xscYOSoxlsWttshDADVuH8uswQio3iNo8vo4ffU2mruq0IlAkkZNu89PgGDxjQvSE6jz+vmm1UacRsX8oixGm5VVYoXBISZBT0zCwZ0+mZeXR2VleCrj/Pnzuf322/fTiBQU9j8dn5ch+3pmVt4yK671LRgnDYKQsuw5+LyfQheG+L1/vv2Aw+rh3fkr8LoDIMtsXdGEz1PM6DnRPZ1bajpZ/NImrM1OknNimHf52N2+V/u9AZoq7cQmGajd0hFqlyWYNC+H9d/WEPBJ6GO0nHD1+N06x/5CmbkpDElOSorjX+X1WP0BJDk4Gbi1y3zcJ8lscrjQCgLFXdWMnqhs5P6ynonJAyMzuTwrebfP3+j2ct/2emx+PxdnJHJscvweXpHCYLB48eKwz3V1dTzxxBNcdtllxMfH759BKSgoRGA57zxa//scgba2sHa5K3Kqo5e43I1oMpJ116NUnHtehO8UgP3zL/r3nRJFNBkZO/SVerSygcWtNqIdRQZmxpn4saMzYlsAQoJUd1+QOS89kTqPlznxZq7NSUElCEiyjDjMzM0VFIYrf/vb37jyyitDn2NihpeHm4LC3kay+8JXVQSQnP5+++827ZXw+Z+jb9PFgn7fmYAPJmWrm/G4/GHf6bpvaqKKUj5vgE8eXY3b6UOWoH67lc+eXMu5f52xS0VPvG4/KxZUsOGH2lC1VWOcFqfVi6gWmH5iHtNOzGfGKfm47F5M8TpUg5miOQgoopTCkCRFp+GLqUU8Xd2M3R/gxOQ4TkqOp83r4+gVW0LpEjNijTw/Lp8HysJXyu/eVss56QmYdsP0vdHjY/ovJXi7JjuL2+z8ozCD32Xv29BMheg0NTVhs9lITU3FG2WiarVaeeqppzj55JOJiYkhJycH1TA1/1dQOFAQdTpMRx6JrY/4pM3LA4KRTxH7mM3ox4wh5703qLzrWljXjCyC0L3gG02QEkWQJNQpKWT958kdjuvn9s6ogpQAnJgUx1XZybxW30qz1x8WwSsSHtErA50BiX8XZ0cOSRGkFBT2GTExMaSlKRWUFRS6MYxNxP59TfBBJQCCgG7EIAhE7RUQ9YkKeGyw/j0Y/9u9f959jCAKEZcpiNGf8x0NTlydvVL8ZWirc+Du9GKI6fFI9nkC+DwBDDGaCLFKCkh88tgaGsvDI7qdVi+HnVfE2EMzEbvOr9Gq0CQOz4hsRZRSGLLkGnT8sygrrO2KDRVh/h3LbE4eqWiIuAX6ZbhmQwVPjsklTqOmwuVhcasNk0rkNynxA4pVf99eFxKkunmovEERpYYA3377Ld9++y0AarWazMzMiFB9AK/XywcffABAVlYWF198Mdo+VboUFBT2LbFHRYpSCVdcDoBhyhRcK1b0bBAEkm+4AYCKwCvUX1OPbr2MdqsK82KR/mQe89FHkX7PPagSEhDEHa8SZuq1qGwOAr1u+SJgUon8tTCDOI2aT6aM5J9l9ayxOah0+5CAcWYD5S4PzoBEoGuf45IOjFVgBYXhzD//+U/+/ve/k5OTw/nnn8+NN944YEq/x+PB4/GEPttskam8CgrDmdhjc5EDEq51LQgGNfEnFaBJ7d8OZbdJLgaVLugfFY33r4DYDMids/fPvQ8ZMSWZ5QvKcdmD81FZkplybHSvLGNs9LnHpp/qmXp8HgArvqhg2SdlyDKk5sdy8nUT0Zs1ob4rvqiIEKQg6CPlaPeEBKnhzvCK61I46NnQ6Ypo29jpIkevpa/MtKTNzh9Kqlhlc3DEss38dWstN26u5sSVW3H4o5vnLmyx8k1b5A+/r0ilsO9pbm4OCVIAfr8/qiDVl9raWpYsWUJHR8fgDU5ht7n//vuZM2cORqOx35TLqqoqTjrpJIxGIykpKfz5z3/G7x+E0HOFQSXm6KNJu/deNFlZaDIySLntNuJPOw2ArEcexjB9OogiqsREsp9/Dl1XFFVLyxJAwjNexn6GH9fUQNDFMwreqmrUSUk7JUgB3FGQTpq25+UvS6fh9zkpLJ4+iryuSq+5Bh1Pjcllepw5FB1V4nBzR0E6U+NMZOk0nJuewMOjIqOkFBQU9h1//OMfeeutt/jmm2+4+uqreeCBB7j11lsH3Gf+/PnExcWF/pedrfyOFQ4sBJVI/MkjSP/LTNJunIq+yDI4J4pJhXNeBe0AKbM/PzE4596HGMxazv7LdCbPy2Hs3Ax+c8Okfo3OTfE6knP7fB8CtNYEbQFqNrfx68dlocDvpkobP7yzJdS1pcbO8s8qoh5bliBtMCLe9hNKpJTCsCJOrcIeCLdBH2HU88SYVC5dX06JoycFRAKWtNqodXtxSz2iUqnDzV+31vLPUVloe01cvmm1cfH68qjnPdRi3rsXorDL7O7qpSzL/Prrr/z6669MnjyZU089dS+PTGFP8Hq9nHXWWcyePZsXXnghYnsgEOCkk04iLS2Nn3/+mfr6ei6++GI0Gg0PPPDAfhixwp5gOfccLOeeE/osSxIdH3yIZ+tW4s84g5z/vYTYJ5JVo4nH5+ugO16+4+IASaNPwvf9JnxVVT0dBQFRt2sRkZl6Ld/PKGaFzYleFJgWZ0IVRfD6us3OO409JZf9sszT1U0snz12l86noKCwa9x+++08+OCDA/YpKSmhuLiYm266KdQ2YcIEtFotV199NfPnz0en00Xd94477gjbz2azKcKUgsLuUnQc3F4FNcvhxWMjt6sOjKwFU5yO2aeP2Km+hVNTaK6yh1L+BMCSHoxUa6npRBB63AhkCZqq7KF9o0VIQTBKavZpheSNT9rtaxhqKKKUwrDioaJszl9fFvocqxK5tyvF4pHiHI5fuSWsfwDY6Ij0KnmjoY3VdicfTi4kXhP8GbzX2B5RFlwFHJkYy//G5e31a1HYNVJTU9FoNPh80cuvH3PMMVRVVWG1WmlsbIzaZ/Xq1eTm5jJp0qRBHKnCrnDfffcB8L///S/q9oULF7Jp0yYWL15MamoqkyZN4u9//zu33XYb9957r5KWOcyQXC5sCxYQsNowHTqXtpdfwfr++6BSQSCAa80a0u+7N2yfopF3s3bdVchy8LefnH4sOXf+H9IfOyk/7XR8DQ3ByClJIunqq3d5TCa1isMToq/syrLMnVtreLG2NbwdaPVFj7hVUFDYe9x8881ceumlA/YpKCiI2j5z5kz8fj8VFRWMGjUqah+dTtevYKWgoLAbiCKkjgV9PLg7wrfN3PVn9HBn4pHZ1G3poHJD8D0ic5SFyfNyALCkmcLsMQVRIDGjJ7UyWpW+2CQ9F9w3C3GYGZnvCEWUUhhWHJUUy+JpRXzWbCVGJXJBRiJxXaJSlrWF43XwZT+pzH0pcbiZ/UsJX04rItegwxOQIrypjkuK5cXx0V92FPYtZrOZ888/nw8++AC73R6xPS8vj7lz5xIIBHjttdeoqKhAjpJ2uXbt2qiiVGVlJa2traSlpZGREb2sq8K+Z+nSpYwfP57U1NRQ23HHHce1117Lxo0bmTx5ctT9FJ+QoYfkdlNx/gV4SkqCL60PPwyBLmGn6/873n6b5D/dgNrSk16QmHgYs2Z+QUfHCrTaJBITD0cQRFSxseS9/x4db79NwG4n5uijMU6ZskdjbPX6+XdFA9UuD9PjzGToNRGCFAQXLI7qR8hSUFDYeyQnJ5OcvHvVlNesWYMoiqSkKJ6gCgr7lMqfIgUptX7Y+0ntDiqNyEnXTcDW4kaWZeKSDSEz85yxCUyal8OaRcGob1OclpmnBuedsiwjI5M2Io6G7VYADGYNJ1w7nm0rm+hodJKSF3vAREspopTCsGNcjJFxMT1lvmVZ5tuXn2PVF5+w9bjzIbc4OOHZCdr9AY5ctplXxxfwbVuk0NGirIQPKfLz87n55pt57LHHaG/vSaXR6/Whl9affvqJ8vLoaZgAJlOkueMHH3zAunXrQp9PPPFEZsyYsRdHrrC7NDQ0hAlSQOhzQ0NDv/vNnz8/FIWlsP+RAwGqr7k2KEgBSFL/faNEQxqN+RiN+RHtaouFpGuu2Stj9EoSZ6zZxjanm4Ac9CUcY9KjFoLFM0LnFODUFEtEIQ4FBYX9x9KlS/n111858sgjiYmJYenSpdx4441ceOGFWCyD5KGjoKAQHVd7ZJvfE8xTOwAr0nrdfio3tCIFZHLGJmAwh0fxC4JAXHJ4VTwpIOFx+Zl1agGtNXaqS9rpbPfw0cOrOeOWKaxdUs36b2tD/Scdnc3Uk/L48Z2tlP7SgCgKSJLM9JPzGDktlYBfJiHDNGyNzxVRSmHYU1uykVVffAJAR1ziTgtS3TglmYvWl+OKMknSHoA3zgOByy67jA8//JDa2losFgunnXZaKPx++fLl/e4niiKHHHJIWNtPP/0UJkgBfPHFF0yePBmNRoPCrrMrHiCDheITMrRof+01nL/8suOOGg3q5GR8dXXIXi+anJydNi3fU9baXZT2SveWgU0Od0RK9yUZSdyvCFIKCkMKnU7HW2+9xb333ovH4yE/P58bb7wx7DmgoKCwj4hJi9IoQ8AL6gMrXdbj9PHegyvpaHQCYIjR8NvbphGbZOh3n8oNrSx8fgNedwCdSY3H0VO8x2X38u3rpdRsDhf21n9fy+hDMyj9JbggK3X5JS//rCJkhp6cE8NvbpiE3qShbms7G76vQxBh3GFZpA9xU3RFlFIY9libe/yDMhuqaItPRu41idEKMDPOjEOS6PQF2OKKzO9zShIiRKTvXZp5YIREHmjExsZyySWXRN0mRpnAFhQUkJCQwNSpU0lPTw+1b9myhUWLFkX0l2WZd999l3PPPTfq8RQGZk88QPqSlpbGsmXLwtq6PcPS0qK99ARRfEKGFq61awlz8+wHXUE+dbf8GduCBQAYJk8m+7n/ojIPfrEJTZRFCDVwfkYiL9cFU/imxZm4rSA9op+CgsL+ZcqUKfyyM8K3goLC4BObBX2delPGHnCCFMD672qxNjlDn90OPys+r+Coi0dH7e/u9PHFs+sJ+ILBEB5neDVpWQJ7W6QfcsAn4XUNnMHTUmNn+YJyRkxJ4aOHVwcbBdi6vIkz/zyV1PzYXbm0fYoiSikMe9JGFCGIIrIkccTSL9mWNxqnsWcC45XBK8u8MaGAeI2aF2qauXNrbdgx+hqcA1yZlcTJKfGDPn6FvYPX68XlcnHooYfy2WefIYoisiyTlJTEueeeG9UQe6AX2C1btrB27dp+PYsU+mdPPED6Mnv2bO6//36amppCviCLFi0iNjaWMWPG7JVzKAw+mqzsCFFKMBiQXa6wfuq0dGyffx767FqzhpYnniT1jtsHfYwTYgwcajHzY3snqq6UvRvy0rglP40/56fjliQydZqQF4SCgoKCgoJCFL6dT8Ts6tAb99do9iqyLFO7pYPONjcpebG47b6w9xtZknE7ohdlAuhocoYEqeAOkX1yxyaw3duC0+oJZjyKkDHSQnKOGUu6kY5GJ3IUFwRZgo5GJyU/14MQ/EzX/iVL6xVRSkFhMEnMyubEP9zC4uf+A04HKX4PFYSvqi+zOjjkl01MiTUx2mzgltxUHq5sRCJ4y3ygKIsMnYbHKhvxSBIXZSRxSUbifrkehV1n5cqVLFiwAEmSiI2N5ZRTTqGpqQmTycSMGTP6rdAWzQi9N5999hkajYZx48YNxrAVgKqqKtra2qiqqiIQCLBmzRoACgsLMZvNHHvssYwZM4aLLrqIhx56iIaGBu666y6uu+46JRJqiCO53fibmlCnppJ41ZU4li7FvX49APqJExH0OlzLlocJVSqzOZiC3W2ALsvYv/6alNtvG3QxSBQEXptQwCu1rVS7vUyNM/Kb5HgAkrTK65KCgoKCgsJOUb8a6KWaCAJ0Nu+34exNvn9rCxu+CwY3CCJMOS4PWQqfT+SO65lDWpudLH5pE621DixpRg45qxBBFCL26cZk0THr9BE4rF62rwp+Z4IgMPM3BahUIqfdOIWlH26jvcGJ1qCmelNbz84CpOTF4rR6I4471L2mlLcshQOC4jmHMWr2ociShLq6hfnl9WHbZaDVL7Gozc6iLkPzW/PTmBBjpMCgo8AYnNwelzS0820PJlpaWujs7CQjI6NfUQmgubmZTz/9NPTZZrPx9ddfc8stt+xwEjtjxowBTdEDgQDvvfce9fX1zJs3b9cvQmGH3H333bz88suhz92Rad988w1HHHEEKpWKzz77jGuvvZbZs2djMpm45JJL+Nvf/ra/hqywE3T+9BO1f7wByeFANJvJevIJ8t58A/fmUryVFdT/9W5kZ1e4uyAgmM1YzjoLTWZGKHWvG191NZ1LlhBzzDGDPm6dKHJl9t6J8lNQUFBQUDgoSR4NbRUg9ywwkVy0X4e0N9iyrCEkSEEwEmnj97UcfeloVn5eQSAgM+6wTMbMDVbxliSZTx5fi73VjSzJNFfbWfTiJo64cBTfvlYaVZjyOv3UbbWGBCkIfn2/fLyd02+agjFWy9GXjOlql1n64XbWLKpClqFwSgrTjs+jrcFB6S/1IVlQVAmMPWxoVxYX5B2FCuwFPB4PM2fOZO3ataxevTqsHPu6deu47rrrWL58OcnJyfzhD3/g1ltv3elj22w24uLisFqtxMYO3ZA0hX1HQJa5b1st/61pGbCfThQoP2wCopKKMaSQZZm33nqL0tJSILg6cN5551FUVBTa7vf7QybkmzZt4p133ok4zuGHH47H40GSJMrKynA4HOTk5HD00UeTnJwcEqy2bt3K+vXrUalUlJaW4nQ6I44FcOONNxIXd+CLlgfqPfVAva6hiOR2s3XOIUguV6jSjmg2M/KnHxG1WqquuALH0l+iVuATjEYEjQbJau1pVKtIuupqkv/4h314FYNPc2U5nz/5f3TU15GSP4IT/3ALcSmpO95RQWEIcKDeUw/U61JQ2KfY6uCVU6FlS/DznD/CvL8N28p7siTzw7tbWf9NTcQ2QYBr/3MkQpRIJHubm1f+8nNE+wV/m4XeqKFiQwtL/lcSdqzYZAOTjsnhuzdKw/YxJ+i45IFD+h4KCPpNSbKMRqsKtbXWdobS+MbMySAhI7L6+L5gZ++p+yRS6tZbbyUjI4O1a9eGtdtsNo499liOOeYYnnnmGdavX8/ll19OfHw8V1111b4YmsIBiEoQ+NvILARB4Nnq5qh+UQAeScYryehVw/MGeaBSUlISEqQgKEK98847/OUvf2Hr1q18+OGHuN1u0tLSmDhxIqtWrYp6nO+++w5BEMJS9EpLSyktLSU/P5/TTjuNuLg4Ro4cyciRIwHYsGED7733XtTjud3ug0KUUlDYU/yNjUi9xV1ZRrLb8Tc1o83KxN/SGlWQApDd7qBgLIo9ffwBtDtpjL8/CPj9rF30BW211aTkFzD+yGN3WDHQ5/Xw3v1/xWW3IUsS9dtK+fDBe7nk308pnlUKCgoKCsOb2Ay4dim0lYE+tp9qfMOHnz/YFlWQAsgekxBVkALQmzSIKgEp0MtPUwSDWYPOqGHUzDTqt1nZ9GMdAKJa5IgLiqnf1hFxrMyR8f2OT6URUfVpS8w0M/eskQNe11Bi0EWpL774goULF/L+++/zxRdfhG17/fXX8Xq9vPjii2i1WsaOHcuaNWt4+OGH+xWlPB4PHk9P9TSbzTao41cYvtw7IoPpsSa+aOng/caOsG0icHhCDHqVUlltqFFbWxvR5vf7aWxs5J133iHQ5TXT0NBAQ0PDgMfqLxC0vLycRx99lDPOOIPx48eH2seNG4cgCHz66ae43cHKF6IoEhcXR2Ki4jGmoLAzuDZsiGgTzGbUKcG0uJijj8JTWhrRBwBJQvb50BUX49m0CYC4s35L7IknDNp49wRZllnw2ENsXbYUUSUiBQI0bt/GvKuuH3C/9rpanNaOnuNIEq011bg77RhilOiMoURDQwNLlizB6XQyatQo5s6dq1RlVVBQUNgRKvUBkbInyzLrv4ucmwDEpxqYd/nYfvfV6FQcdm4R375RGoqQOPTsInTGYLaHIAgcccEoimen47R6SMmLpbPNzbJPI61FMoose34xQ5hBFaUaGxu58sor+eijjzAajRHbly5dymGHHRbmF3Pcccfx4IMP0t7ejsUS+eXPnz+f++67bzCHrXCAIAgCJ6fEc3JKPOel23mxppm1dheiAHPjY7hvZOb+HuKwYo3Nyc2l1dS6PMyKN/PI6Bw8ksx7DW0EZDg1NZ48w54bT+fn5/PTTz+FtYmiiM1mCwlSA2E0GvtNweuNLMt89NFHFBUVhRlmjx07lry8PBYsWEBdXR1JSUmcfPLJqNWKBZ+Cws7Q9K9/R7Ql/+EPiF3PetPcuVg/+RRfTZRVR5UK47RpZD/3X7yVVYgGPZr09MEe8m5ja25i67JgaL7UdX9at+RL4tPTSczMIX/ytKiRTyq1Jurx1Ip5/5DCZrPx0ksv4fV6gxWXamvx+/0cddRR+3toCgoKCgr7iGgBzKJK4Pirx6M3RX+edzP20EzSC+Npq3NgSTeSmGEm4Jeo2tSGz+Mna1QCafmxWFtcqNQitVs6oh6npqSNMYcMbV+oPWHQZlmyLHPppZdyzTXXMG3aNCoqKiL6NDQ0kJ+fH9aWmpoa2hZNlLrjjju46aabQp9tNhvZ2dl7d/AKBxxzLTHMtcTs72EMeTZ2uih1uMnSa/ixvZMGj49DLTEcYjHz29Vb6ewy5Puy1ca2lVto8wfo8AUQgMcqG1kwdSSjzYY9GkNhYSETJ04MpfsKgsAZZ5xBQkLCDvfVaDTceuutfPzxx6xevXqH/QOBAJ2dnRFV3EwmE2effTY2m41vvvmGTz75hNzcXObOnYtK1TdAVkFBoTf+3n5QXdgXLUSXl4uvvoGGe+/td19Bo8FTUU7by6+QcNmlQz6VzWWLvFaA7197CYBxRx7DsVffEHEdjl5RUr3xe71otIowNVTYvn17WHQ+wE8//YTZbGb69OlD/u9TQUFBQWHPEASBKcflsuzTcgQhaJWpN2s4+Q8TScww7/gAQEK6iYT0oKeT3xfg40dW01AWzPbSGlQY43R0NAQX1LNGR4+I0u1A/Bru7LIodfvtt/Pggw8O2KekpISFCxdit9u54447dntw0dDpdEoZcAWFQeCFmmbu3BoenioCr9S1Mi3WGBKkutnm8ob5dXkkiWeqm3lsdM4ej+X000/n6KOPprW1lZSUFEym4I183rx5LFq0aIf7n3zyycTHx1NdXU18fDw5OTn8/PPPEel+RqOxX5+o5cuX8/nnn4dSAMvKyrDb7Zx88sl7eHUKCgcW9q+/oXH+fAJtbagsFuhKfe2Na+UqqldcA5qBX6pktxt/XT1NDz2EKi6W+DPPHKxh7xV8vsiyy73Z8M1ippx4Gsk5eT37eNwsfu6JiL4xiUnoTTv3gquw66xfv56vv/4am81GQkICp556KllZWQPuE63yayAQ4PPPP0cURaZNmzZYw1VQUFBQGCJMOzGPuGQDddusmC06Jh6VjUa3e4vUW35tDAlSAF5XAK+rJ8OjpqQdnUmNx+EPtelNGqYcl7v7FzAM2GVR6uabb+bSSy8dsE9BQQFff/01S5cujRCQpk2bxgUXXMDLL79MWloajY2NYdu7P6elDW9DNAWF4YTdH+DurZH50t1WxCts0dPheotSMuDqx7x4d4iNjY2o0nDIIYcwduxYGhoaeOuttyL26TYsdzgcJCQkkJmZSUFBAaIoMmHCBCoqKvjwww+xWq3ExcVx9tlnR03LKy0tZUGfsvQAa9asUUQpBYVeeLZto+YPfwiakssyksMRvWNXFT58vqib1Wlp+FtawN/1EiYIdH777ZAXpeJTdvyu4unsDPtctWEt7fV1YW2CIHL6bfcokTeDxC+//MKXX34Z+tzc3Mwrr7zCn/70p6j2Et0UFRWRlpYW1b9ww4YNiiiloKCgcBAgCAJFM9IomrH7+oTPE2D76ibK17fQbxWuLjwOP5Z0I1mjLMSnGhk5PRWDOXKR5EBil0Wp5ORkkpOTd9jv8ccf5x//+Efoc11dHccddxxvv/02M2fOBGD27Nnceeed+Hy+UHn3RYsWMWrUqKipewoKCoNDhz9At1tTnLMTo9dNqykWr2bgG6BMz31VAs5IGfzfbXx8PJu6DJD7Mm/ePGpqanjllVfweoMRDJmZmRx//PFkZWWRl5fHjTfeGHbP6cuyZcv4/PPPo26TZZknn3wSvV7PvHnzyM09sFctFBR2hHPFCtgJrzcAZBnRYkGyWoMiliiiio8n87FHcf7yKy1PP93TVxRRxQ/994CYxCSO+d11LH7+P1G3680xpOQHKwe6HZ1Ub1xHY/n2iH6G2FiSc/Mj2vcmrjVr8DU0oh83Dm3WweWp+M0330S0eb1eGhoaKBigsqPP5+u3YEZLSwtPPPEEGRkZnHDCCQOKWwoKCgoKBy9el5/3HlxBe8OOPW+7aa93cuI1E4hPPTieLYPmKZWTE57CYzYHQ9JHjBgRCpc+//zzue+++7jiiiu47bbb2LBhA4899hiPPPLIYA1LQUEhChk6DfkGLSmb1jC5agsAHpWazyYcQnNs9InhJRmJHJ8Uy7PVLfhlmYszkzg+OXoq3N7G4XAgCELYZCEuLg6LxcL777+Pr1c0Rm1tLS+88ALjx4/n9NNPRxTFfgWp1tbWfgUpCKZttLS0IAgCr776Ktdee61SlU/hoEXyeOj84cdd2kedmIBsseCrqEDQaDDOmoXtswWoU1LQZGXiq6oGQBUfT+LVVw/GsPc6E+edQN6EyTx/w5XBiLBejJx5CFqDEWtTI2/+9RYcHe1A0OhckoJinixJTDnhN4M6xoYHHqD9lVeBoG9X1lP/wXzooYN6zqGE3++P2t79btofCxcujIjo78bhcNDZ2UlbWxvt7e1cccUVSqSbgoKCgkIEJT/X09HYS5ASQK0R0ejUjJiaTFOFjaYKe8R+gnjwPFP2azmpuLg4Fi5cyHXXXcfUqVNJSkri7rvv5qqrrtqfw1JQOOhQCQJPphr59MstoTZNwM+Rpat4Z/rRYX3j1Sr+MyaXoxODqXVHJu4bIao3ubm5ERX6pkyZAkBnZ2fUle3169czduxYiouLw9olSWLp0qVRizF0o9Fo0Gg0oap+sizj9/spKytTRCmFg5aG++6j8+uvd2kf77aeKCHZ48H++eegUoEkYZw5g+Q//hHZ78d8+OGoh3jEtCQF+PHNV1j/zSJUajVqjRa/N9wUu2H7FmpLS1i3+AucvUzRA34fWaPHYU5IJHf8JMYeccygjdNdUhISpABkv5/6u/7KyO++HbRzDhabOl1822YnXq3i9FQLBpW4U/tNmjSJlStXhrXNnDmTlJSUqP1lWWbFihX9RuV29+n+/5qaGpxOZ8j/UEHhYKbZ7mFpWStmnYpDRyajGeB36vIG+KWsFQSYXZCIXqMUk1E48PA4fYRc0gFkSMmL5fSbgnMXWZZZ/L9NbPm1EVElIEky+ROSiE3S78dR71v2mSiVl5cXdaI4YcIEfvjhh301DAUFhX4wuMJDSkUg1uMKfc7Ta7k5L415SbHEa/arnk1RURHHHXcc3377LYFAgEmTJjF37tzQtuXLl0e931ijVAX7+OOPQ5X+omGxWLj66qt59dVXcblcYcfV6w+eh4WCQl9sn38RERm0W3Sl/zl/+ZW0u+5CV1i458fcB6z49EOWf/L+gH2aK8p46+4/Y8nIQu7luSeqVGQUFXPo+ZcO8ijB39wc3iDL+FtbB/28e5tvWm1cuL4MWQ6mi79c18LHk0ei3wlh6sQTT8RkMrFy5UqcTicajWbAiq4//vgjS5YsibqtuLiYzZs3h7UJgtBvBK6CwoFGbYeLihYHI5LNpMWFvweVNtg565mfsbmD0Ykz8hN47YqZaNWRv9N2h5cznv6Z8pagF2Fhipn3r5lDnFH5Le0psl9CcvkRTZqDKtpmqJI7PokVn1eEeUkVTOqxQxIEgWMuGUNGYTzN1Z1YUo2MOyLzoIq+3b8zSwUFhSFDWloaoigidU2cRFFkVF4uq+eMwRmQyDPoUA2hm+Ps2bOZPXt2RPu8efMIBAKsXbs2ImUjOzs77PP27dujClIqlYpAIEBCQgIXXHBByEPq5ZdfjuinoHCwIhqNBKJU2gshCKDTRa3G1x9yYO8VSxhsKtau2um+1sb6sM9SIEDOuEl7eUTR0Y8di2A0IrvdQS8vlQrT7Fn75Nx7kwfK6kOCFMBau4svW6yclrrjiDqVSoVarcbRZcTv9Xr54osvSEhICBXI6M2KFSuiHmfGjBk0NTVFtB911FFRK/UpKBxovLOimtvfX4ckg1oUeOzcyZw0IT20/Z9flODw9Lx7LStv4+M1tZw1LTviWM98t52q1p4F0fJmB8/9UMYtx40a3Is4wHGua6b93S3IPglVgp6ky8aiSY70JZIDEsJORpv2JdDppe3dLXjLbajitFh+W4QuN3bHO/Y+v09C0Oze+YcbqXmxnHjtBJZ9Wo7PG2D0nHQmHBle/VUQBcYeenD5PfZGEaUUhg2SLCMOIVFkuPJkZSNPVzUhAeemJ3BPYfAGmJCQwNlnn83HH3+My+UiKyuL008/HbNueL1oazQaTjnlFI499lg++ugjSktL0el0nHDCCdjtdp5//nkCgQDTpk3jxx+j++HMmTOHGTNmYDabEQSBQCDAqlWrIqKvPvzwQwoLC5XJiMJBScqf/0z9X/4S/BAtYkqWd16QEkX048ejKxyx9wY4yJgTEhFEMSwCqj+kQIDsMROo3rQu1NZYvo3cCZMGcYRB1ImJ5Dz/PPV33YW/sRHj9Omkz39g0M+7t7H5A/T9pjt3QcQsLy8P+yyKIpWVlWGiVElJCd9//z2dfSomQnAlu7m5mcrKyrD28ePHc+hB5M+lcPBidfm444P1SF23e78kc/M7azhmTAo6dXCRrsnuIdDrcSAK0NLpjXq8RpubsBJkAjTZg8+MN5dV8dJP5YiCwNWHF3D65KyoxwAISDIOr58YnfqgiCzx1nZi/7YayRvANDkF46SeNGS/1UPbW6V0/yMFOty0vl5C2p+mhvr4mp20vlqCv8mJGKsl8bxidPm7ZsXR9lYpnrIOkMDf4qLlxQ2k/Xkaqp2oEOepstH2egkBqxdVop6ki8agStAjqMUDOqorb0ISeROS9vcwhiyKKKWwxwSsVpofexxPWRmG8eNI+v3vEQ2Gfvs7V6zA8fPPqCwJxP/2zAH7AtS6vVy5sYLVNidpWg1PjMlhriVmb1/GQcHLtS38o6xnxf7p6mZ0osjtBcFVruLiYkaNGoUkScM+Ckin03HOOecgyzKCIFBVVcWLL74Y2v7pp5/2+/Lyww8/sG7dOq666ioMBgOvvvpqVM8pn8+H3W5XfKUUDkriTz8NbW4uVVdeidwVgbIrJN98E3IggKdkM9qcHBKvvhphGN13pp9yJlt++ZFAlygVm5xK9tjxdDTW01xRhs/jQZYkBFEkZ9xEqjasC9v/hzf+x/ijjsUQs2ury7uDccpkRny+YNDPs7cod7qxBySKjPpQet6ZaRYeqWhEJpherhdFDk/Y+XeBuLi4sAIZkiSxdetW1q9fT3JyMpMnT+bdd9/td39ZlikvL494bmzdupX6+nrS09P72VNB4cCg2e4hIIUvQLj9Eh1OH6mxwXv3EUXJbKyzhbbLMhxS2POOJEkyz35fxlcbG3D7AmECVkCSmTMiic/W1XHHB+tD7Te+vZZ4g5YjiyM94D5fX88t767F6Q1QlGrmhUumk51w4FYr8zU7aXp6LQQkkMFT2o4ckDFNTQXA3+gMCVJAUDRqdIbehWVZpvXlTfjbgvYckt1Ly/82kn7HDET9zskCsizj2d7RoyfKIHsC+OocqIoGFqUkb4CWlzYid6V3BtrcND6xGgIyglbEcsbIMJFN4eBBEaUU9gg5EKDqiitwl2yGQADnsmV4tm8n+6mnIvr629uxL1pMwz33gCiCJGH9+GNy33gdcYBIk6vWbmet04MMNHp9XLSunGWzR5OsVXLOd5X/1bZEtL3T0BYSpSC4GjzcBanedE8gSkpKwtITgX5LfUPQf2rhwoVMnTq1XxN0vV5PbOzgTygVFIYqximToZ/KZjtCNBpJuOCCvTyifcfyT98n0OvabS1NTD/lDBKzcuhobOCb/z1Le0MdmaPGMP2UM3nppmsijuGy2/eJKDWU+LSpgzu21GD1BzjMYmauJQYBOCE5DkGGE1dtpcUX/F4TNSoWTC0iz6Dj5rw0NILAgmYrCRoVfynIIFu/81GqRx55JOXl5SFvQbVaTVNTE7IsY7fbqa6ujthHrVaHpYH3rfoK4Ha7efnll7nhhhsw7GCRTUFhOJNlMZBo0tLu9IZ0D61K5KuNDVw0Kzf4/ihGpmP1znJ44uttPLI4WFRHADQqAYNGhUoUuPKwAk6dlMGf3l6DKPRoKypRYOGmxghRqrrNyR/fXI2/q+P2Zgc3vLWaD35/yN6/+CGCa0NLSJDqxrGiISRKqRP1Yb5FCKBO0IfehWVvAH9Lj19st6Dkb3ahze5f5JclGW+1HdntR5sbi2jWItnDI+BUsTu+Hwfa3ciuXu8MMnQrk7JXou3tUjSZ5qjphgoHNooopbBHeMvLcW/Y2NMgSXR+/Q3urVvRd4XES14vdTffgn3Rop5+Xca27g0bcPz4IzFHHRVxbE9ZGTV/+CP/3r6dRksi9/3uBkoKRuKSJEodbkWU2g10UV4WdAdwqGxvdDpdmCAF0ScYvWlqasLrjR52LggC5513nmJuq3DQYz7ySOwLFwb9inYBXUHBII1o31C1YW142qIss+G7xdRs2oC7086o2Ydy6i13IQgCJT9+GzXVr7mqnISMg8dDoqTTxTUbKwh0fV7SZmdJmx0ReKi8gRi1QIsvEOrf6gvwp5IqPpoyEpUgcGNeGjfmpe3WuePi4jjttNN4/fXX8fv9YWKTJEl4PJ6IfcxmM1arNazSXjTcbjcNDQ3k5+fv1tgUFIYDeo2Kly+fwVWvrqCuI5hm5w1I3P3xRmQZLpmTx5LNjWH7CAL8uK2FcZnB9LD3V9WEtsmALyDzt1NHc96MnFB7rF4TFFF6/d7iDJHvWqUN9pAgBcFIqw21toh+BxJCX8N4IbxNnWgg/rRCOj7aBjIIGhFNphnH8gaMU1MRNCoEgzpcGBJAFafr95yyJNP62ibcm9oAEM0aYo/NDZ6j1yPNtbkNTdrAFUhVMVrCFMeIk4GvzqGIUgchB4e7mMKgIeii38QqzjkXf0cHAK3PP4998eJ+j1H/17tp/s9TyD4fEHzp6/j4YyrOPgdvWRkASR1tPPifB9F7gg/BjGHmczRUuHtEZHrBnQUZ+2Ek+x5dlL/V4uJigH7T+NLT08nKyiImJnz1SKvVcs0115Cbm7v3B6qgMMzIuP8fxJ1+GuqMDFTJyWHbVCkpmOYeguXyy4MRsl0Ypk3DFKVQwXAiNikZoY/Qv2rBxzRs30pHQz2/fvguP7/7Ol/852G++M/DUb2nqtat2UejHRqssjkJRGmXAKck0eiN3LrNufNG+TtiwYIFEQUwBmLGjBkk9/mb7g+TaeDJmILCgcC4zDgum5NP37em91cGxabkGB291zolGSy9qumZdWr6vnIZteHR+VcfXkBsr1SyRJOWy+fmRYwlNzFcuBAFyEk8sMUMw6RkBF349xVzRLiJvHlmOul3zUI3yoLslXBtaKX9/a20vLYJ+zfVmKalQreQJUD8qSMGjHJyrW8OCVIAktOHe1MbupEWev8h2L6swFMWWeW6N6JRg+W3I2GABXF1olLZ+mBEiZRS2CM0WVkYZ87E+euvYe2y00nDfX8j65GH8ZRsHrBseKC1lZYnnsDXUE/G3/9O88MP0/rc82F9VLJMjNNBZlMD5x4+mwJj/4q+Qv/MscTw2ZSRPFReT0CGG3JTOWwXPDmGMz/99FNEmyAIXHTRRdTW1qJWq1m9ejXNXeXTc3JymDdvHnq9nssvv5xFixbR3t5Obm4uxxxzDGq1cvtUUAAQTSYy7r+f5scfp+WppwEQDAZkl4tAczOO1lYcPy8New64VqzAvXkz+i5heDhy9BW/592//wVPl59W2shRNGzb0us6ZUp+/A5bc2O/x3B12qjfWkpaYdFBYdCbrtv1yNKJMXs2yXS5XNjtdgRBoKUlMoW9m76pegAjR45k5syZ1NfXY7fbefvtt6PuO2vWLFJSFB8UhQOXH7Y287+fKpBkmSxL+G9SEMDQJSzdelwxyyvacHiCArNBI/Llhgam5yVQkGzmluOK+N3LKxAFAUmWGZ0ey3Fjw6MfNSoRTa+qcGpRiFr9eWRqDHeeOJoHPi9BJhhN9eg5k/buhQ8x3Btakd29xHuVgDohiojjl/CUtgf/uysqybOpDU+XuCSY1FjOG4U204w6fmARKNDhDU8JlMDf4Ub2hqcRAvgaHOgKBjZNN01JRV8Yj7/NjRyQaXtjM5IjGJgQe0wO2qyDY16iEI4yq1LYIwRBwFdbG3Wbe13Q1FUzogAWRe0ShvXDj0i76y5aX3gx6nZZFHn56BkUZqbu9ngVYFqciXcmFe7vYexzXC5XRJvP52PEiBGMGBGs+DVnzhw8Hg8+nw+TyRSaJFosFs4+++x9Ol4FheGEY9mykCAFIHf/3mQ5lK7dF29V1bARpUp++IZfPnwHKeBn4jEnMPXk00nNH8EVjz1Hw/atGGJiaaur4Yut/xfaRxAEdIaBBZWtv/7M1l9/ZsIxx3PM766LEKba6mr57tXnsbe0kDN+InPPvRj1MK72eWRCDOekWXi7oX2n+mfrtTw+evcjUtetW8dHH32EJEn9LiRMnjyZtWvXRghSY8eO5fPPP0ej0YSq66lUKgK9/p4TEhI48sgjGT9+/G6PUUFhqPNrWSsXv7gs+EEO6hApMTpaOj0IgoAA3HB00LJjTEYsS246ghveWs2y8jZcPonvt7Zw1jNL+frmIziqOJVPrp/Ld1uaiTNoOHNKFjXtLkob7BQkmxidHsvT326n1dFjndBo9/DCj+Xcenzk8+Lyufm4fH7WVFsZnxlHYYp5H3wj+w/H8obwhoCMa1MrMYeEp4HLgf6DAQBkhx/PlnaMY4PV4PztbqwLyvG3udDmxRF3fB5il9CozY8NF58E0KSb8DU4wsUqQJ2yc4sI/jY3nu1WVDFaUm+aSqDNjWjWoLYoUVIHK4oopbDH+LsiS/qizg6Wb9VM3jnfEEGtxrV2bXRfEkEg/d57sGQeHKlmCnuf5ORkGhrCH+bTpk2L6KfT6aKm+ikoKERHlmVanvzPjjv29ghRqYaNIFW5bg2fP9kjNn332ovoTOZQ5bz8ScFS20k5eaz5agH1WzcDIKrVHHHp71j83FN0NNaH0vdUGg2CIOL39ngYrVv8JWMOPYrM4jGhNrejk7fvvRWX3Y4sSbRUV+DutHP872/cF5c9KAiCwKPFOaRoNTxZ1dR3kT2ECMyMM/HhlJG7fS673R4SpICoaXtGo5HOzs4Ir6iioiI2btwYGvO2bduQZTmiX1tbG++//z5er5epU6eioHAg8vHaOkRBCFXeUwkCM/MTmZQTj8Pj55jRqYzJ6CnYkBanZ32tNfT7DkgyrQ4vKyrbOHp0KuMy4xiXGcfWRjv3frKRd1ZUh/reddJo2p3eiN9auzO6v+cdH6zj3RU1iKLAt6VNrK5q5+XLZxywkaeCWgwXguQeTynJ6cPX4kJt0aOy6NAWxOEtt0ZEM3Xj2tyG+GUFxumptDy3noDNAxL46h1INg+JFwafR7qcWCxnFWFdUIbkDaDNjsG1pjniuDFHZKEya/BbPagH8KhyrG6i/e3S4I1eAu3qJpJ/Nx5BdWD+mynsHIqnlMIeY5w5A/pWa9PrSf3zn3E6yylddedOHSfxmmuovvKqiHZNdjYjFn6FRYlUUdgDzjzzzDDPj0MOOYRRo0btxxEpKBwYuFatwrls2YB9VBYLuqIiIFh1L/P//o02J2fAfYYKZauXI4Y94wS2rwq/3tKlP/LiDVfSUl1BTGISaq0OncFER0MDZ98zn+I5h5FaMJLJJ5zCdc+/2ed4QTrb28I+120pwWm1hsQsWZbZ+P3XPP+H3/HT268iSdEj0PYX7ze0ceivJUz9eSM3b67C4e9/fNenxTE3rv8V9YkxBv47Lm+PxtPR0RFR3KIvTqeTjo6OiAlw70p83WLUQEUxFixYgNu997yvFBSGEroo5toxBjVXzM3n3BnZbKyz8snaOpzeHuHX6x/4t/fJ2jqOfeR73u4lSAHc/3kJ03MTwnywA5JMm8PLhtpwvyKHx887K2qCBdwkGUmG77e2UN7i2M0rHfrEHNX13BSFoEG5RYdxQjKu0jbqHlhG81NrqZ+/DOeaZpIuGYv5sCx0RfE9HlK9kGxe7N9X0/yfNQQ6PD2m5TK4NraGRVuZpqaScfdssv4xN1i9r8/tMP6sIpzrW2h8dBUN85fRsaCs33um7cvyrgEE/89bbsVT1rH7X4rCAYESKaWwx2Q8+CB1t92G89dliDFm4s84A8sFF6BJTWXLlr/jyfMgqUUEPwhdjni6sWNJuuZqHN//gKDXY5wxHW1GBi2PPhpx/NS/3IE2OzuiXUFhV0hOTuZPf/oTra2tmEymCPNyBQWF3cNX37DDPqZDDyXzoQeRHA4EgyHCIHwoozebw16uBVHAYO65fzSWbWPBYw+G+vi6xAm/18Oi/z7BGX/5G/mTpqLR6zHGxiMjkzN+IttX/IosSQiCgKhWk15YFDqmvbWFb15+LnIwsoy1qYFfPngbUa1m9pnnDdJV7xpv17dxw+aq0OfX69socbhYMCXcK8tqtfLGG2/Q2NjIBJWK6bMO5WF1PALBVVKNAJ9MKWJC7J6bFSckJISl2wmCgFqtxtdVVAVAFEUMBkPEvn3TvQcSpCBYvc/hcKDXK6knCgcODo8flShw8ew83l1Rg8sbACEoUl02J4+y5k5Of+pnrK7gb2pkipkPfj8HrVoMq4rXjUkXnHbKssydH66PGsAjy5CfZMSkU4V8qQAWbWpkSUkTb141i+l5CcG+e/+ShzyG4gSSr52Iu6QNQafCPCMNQaui7Y3N0C0ESjLt727BcNdM4k8IVgT1NjpoeWEDkq1XxJkc/J/kjIwiFdRi1NAVv9UTtb/jlzoC7T3CfOcPtehHWtAXWfDW2On4eDsBqwddkQXJE7lgIUdpUzi4UEQphT1GbbGQ89//Rt0WkNxI8dD2Bz9xb6pQdYAwKY3cJ15CFRND7Lx5ob7u7dujHkM3sihqu4LCrqLRaEhL271y4goKCtExjB8HanXQO6qfybu36/4uDsMKZZOPO4VN339NR0M9AHqTmZmnnxPaXlOysd99RZWKXz54i7rNmxBVKmRJYvuKXznt1ruRJZmq9asxxsVzzJXXE5ucQkdjAz+/+zpbf/0Jvzd6uko3W3/9eciIUi/URqbxr7K5qHB5ye9VmOSjjz4KFZMIBAK4fv6OZ867iC98InpR5JrsZEabI0Wi3cFkMnH22Wfz3nvv4fP5MJvN5ObmsmnTplAElSzLZGVlMXHiRNasWRMWIdUbs9lMTk4OmzZtiro9JiaGuLiBzX0VFIYLbl+AP721hi83NiAIcPVhI/j8j3P5cHUdkixz+uRM8pJM3PDWajrdPQLF9uZO3lxWxZWHFhBn0ITEqm7SYoP3goAkh+3XjQDoNSqe+GYbbl94pJUkB3+vjy3ewqtXzEQQBMw6Nb+ZmMEna+tC/XITjeQnDb/nzK6gy4lFl9OTLhno9EaKOpKM3+pF21X5UJtqIuMvM5FlmaYn1+Cr7ezp2+0RVecIpdTFnZAftqAgyzLWz8vp/KGPj7AAgk5NoNPXE2nV1e5rdqJJN9H83Hpk7/+3d+fhUVXnA8e/d9bMZN83kkBk3zdBBJVNloKV1qJWQSgUFeNuVayKWxVRq1V/VtFWwaVq0VoUEdSCKIvKvu8EErJC9n0yM+f3x8Akw0zYzJ738zx5YO49c+97J5N7Z957znscoKB8Uw76cD8cp4q1a6CzGs5aHF20fpKUEg0qJvpqMjM/xtYJjs91nYD69X0avY9eKuYOHTB16Yxt3373Mkv/fpjaxXu1FUII0TyYkpJo98orZD/2GPaCAswdO1K1d69Hm8o9e3BWVaFrgfXa/AICmPrsyxza+BMOh4PkfgOxBoe41/uHhtbZk8bpcLhm5Dv5f4DsQ/tZ/JeH6TZsOL++7yF0OtdQvrLCAj748z1UlpacNSZNp8MSFHTWdo3FVEf9ltNLhGRlZXkMqVNKcVFVGQsaqFB4ly5dePDBB6moqMDf35/i4mJSU1MpOzljoqZpVFZW0qtXL7p37878+fN9bichIYHJkyfz4Ycfsn//fo91er2eKVOmyIysotV45X8H+Hq3qwesUvDG6kP0iAvirtGeNd7yy2w4ap37dJpGYXk1mqbx9KSe3P7hFo/2n27O4L4xXVh3KI+kcCtp+eUew/QUYLM7+PFwPr7OKApYczCPlH9t5pXr+2HQ67CYdB4llo7mlbP2YB7DOkX84tehpdBZjeiDza6aUIqTiSK9z1n5NE0jYEgcBZ/sd2UBTyaVwqd2x5ZWjL2gClNCIH4XhXg8r+pAoXdCyqDDFO9PyNUdKVl9jIqi4x5DAE1xAdjSij0TZgochVUEjkqkcn8B+iCTq6i69fxnZhWtS8vpPy9apNDQQfTt8w4R4SMID7uCPr3fIixsqM+2mk5Hh3/9i7AZM/AfOpSwW24hZPK15C16l4rt28/afV5cGHldhRC/VODIEXT64Xu67dxB/PPPeTdwOnGWtdw6HyaLlW6XjaDn8NEeCSmAzoOHktz/4poFtRI00ckd0TTvj1p56UdZ8+Ei1i/+l3vZwQ0/nlNCClzF0i/7/fTzOoaGdGeS96y4V4YHkuDnOVNgeHi4VwHi8PDwBo3NYDAQGBiITqcjJCSEW265xV1f0Ol0smXLFv7zn//g5+dHXFyczwLJe/bsISsriwMHDniti42NJTpaZgUWrcf2Y0UeySKDTvOq5wQwulvN+17D1QNqeJcoAAL8vJO0C9cdYf7yvdz09s8cPZmQshj1dI2puVF9qozRmT6ZfrUjm39vPAbAtvQij7Z6TWOHj1hbM02nET69B/oQ100fnb8Rv+7hZM//mcy//EjJmppkUnV2GeVbc9EFmTCEW7D2jyYqpS+GUD+sfaIIGp7glZACsB8v91qmDzIRNbsvprgAQn59EaZ2J3+POo3gX3XA3CEYzeRdPxEnKJuDgCGxhE/phjHylw/XFi2f3NYRDS48/DLCwy87p7Y6f3+iH7gfVV1N2sw/kr9gQc1Kk4nwGTOIvOvOVjurRmNRSrFlyxZWrVpFSUkJISEh/O53v6Ndu3ZNHZoQooUzJSVhjI+nOjvbNaRPr8fcpTP60NCmDq1B6PR6Jt3/KMf27KSqvJzwhEROpB/FYDCS2KsPaz56j41f/Mfnc3es/Jqh100FOKc6W5qmMXpWCu179ycoMqpej+OXGBMRzGd9L+KlozkU2R2Mjwjm9sRor2v1pEmTWLRoEaWlrqEjI0eOJC7O96y6TqeT9PR0bDYb7dq181n76UKUlJS4e0qB63q4d+9e7HY7N9xwA59++impqalez0tPT/d5E6e6uhqn04muBdVJE+JMkiP9WX8oz90LyuFUXkPiVu7NYWtaAX0TQsgpriTAbOCu0Z0Y1MFV7ymz0Hfh/9e/cw3lPvWnVGl3MP+aXlz92jqvth3C/ckqqqDK7vRMPOk0Dh93nUM6RgVwILfUPTOgQynah7e9JIcp1p+YBy5G2ZyUbc6haElNSZSipYcxhJgxtQ8i941trp5LCpwamJODMUac/dxqjA/wXKADU0LNMr2/kcjZfVAVdjSjHs148nxo8PF9zakoXZsBTrCllxB6dccLOmbRukhSSjRLpT+s8Z7NyWYj7403cBQXETt3btME1kp8++23rF271v24sLCQ999/n3vuuQdzCxxeI4RoPjSTicSF75D1yKNUHTqEpWcPYp58slXfTNB0OhJ69HY/Do2pSbRcfsN0giIi2bj0M4qP53o8r3bdqE6DL2Xdvz+grNBzFj73PjQdwdEx9B41rp6jrx9DQgMZEnrmCSQiIyO56667yMvLw2q1ElTHEESHw8FHH33k7pnk7+/PjBkzLqhXVVZWFp999hkFBQXExcVxxRVXeLXR6XQUFRXx008/4e/vT0xMDDk5OWiahtPp5OKLL65zcoycnBwOHz5Mx47yxUq0Dvdd2YXNRwvYmVkMwPheMUweWDPh0NLtmdz+ry2uCeA0jQCznv/cdimxwa7kxo5jRTy2ZKfXdq+7OIF//OCZ8FUKYoIsXNw+lE1HC9zLruoTy7pDeVQ5nF69puxORc94Vw2iRyd2Z/PRAjKLXEmwUKuRHnHNZ2hzY9I0Dc2sx3b4tJ5iOo3Kg65ZRlWl51C68h0nCP2t57DMU6pzyihdn4WyO/HvH03wxGSKlqWCU2FqF0jIrz3PeZqmoZ02DE9nqiPVcHKYX9n6LILHtEdnkZREWyfvANEsOUuK61xX+K8Pib7/fnT1dNe0rcnNzfVISJ1SWVnJoUOH2LlzJyUlJXTs2JFhw4ah9zF1uRD15ciRIzz11FOsXLmS7Oxs4uLimDJlCg8//DAmU83Qn+3bt5OSksKGDRuIjIzkjjvu4IEHHmjCyMWZmBISSFq0sKnDaBY0nY5+466iICuTLcu/8FgXHO2aeCH70AG2fPU50ckdSd26EeX0nk7dZLXyqzvua5SYG9LZJpzIy8vj559/9hgqV15eztdff83vf39+hd2rqqp49913qaysRClFeno6X331FREREZw4cQJN01BKcemll/LPf/6Tqqoq1xc3pejZsydGo5Hw8HCGDBkCQMeOHTl48KDXfiorffcKEaIlKbfZKa2yExlgZsntwziYW4rJoKN9uNXjpsLCtUcAV/FxlKKk0s6X27P442XJALyzNtVj+J8GjOwWxZxxXVm97ziHT5ThcCr0Oo0ecUFEBZlZNGMQb3x3iMMnyugVH0yPuCA+35blM85Zl3Xg6r6uxL/ZoKOw3OauK1VcaefW9zez7K5zG6HRGukDTe6C5QAohT7QhM7HkEqdn+/P+NUnKsj9v60oh2sj5ZtyiJjRk/gnL0XZHGgWg/s9oZSi7KcsyjbmoBn1BI1MwK+Tq2e0Mc4fc6cQqg4U4lH8q5ZT+xBtmySlRLNkHTwYzWpFlXuPYQY5gf0Sn3/+eZ3rPv30U/f02enp6VRWVjJ27NjGCk20QXv37sXpdLJgwQI6duzIzp07mTVrFmVlZbzwwgsAFBcXM2bMGEaPHs0bb7zBjh07mDFjBiEhIdx8881NfARCnJt23Xt6JaU6Dx7K8bQjfDj3flci6mRCpLaeI8fQe9RYwuMTMFlax7AUpRQOhwODwUBVVRWVlZUEBgaybds2Pv/8c6/XQClFUdH514k5fvw4FRUV7sdOp5Pjx4+77uif/Bk3bhyapnm0Azh8+DCVlZU4nU42bdrElClTGDp0KPn5+eTnu3qzaZqGyWQiKSnpAl4FIZqPBasPMX/5XpwKesYF8c4fBtElxnfvQE3zzi8UllezYlc27UIt2BxOnLX+hjUNksL8Meh1fPDHwTz2+S72ZpfQMz6Ix6/qgaZpWE0G7h3Txf2c3Zm+b07/4dL2PDyhu/vxwdxSymvN1OdwKnZnFVNZ7cDP2DZvqgaOSKBiTx6OgioADNFWAobGoZn0NQmikwzhFkp/zMJ/UAyaribxWL45x/Vd69RLq0HJ6nSqDhWiFPgPiMYY5boelW/IofC/NcMFT/yzCHRgiLLi3z+aqoMn96dc9a6c5dXuguzmTqHoAzxrD4q2SZJSolkyxsSQ9O67ZM6Zg+20u5KB48ejD/Ce7rXg3/+mfMNG/Lp3I/TGG9HV6mVhLygg65FHKP95A/qQEKL//BCBI0Y0+HE0RxkZGXWuO5WQOmXTpk2SlBINaty4cYwbVzMcKTk5mX379vH666+7k1IffPABNpuNt99+G5PJRI8ePdi6dSsvvviiJKVEi9Fp0KUMvXYKP372MU6Hk57DR3Hxr69hzUfvopyqpneUppHQvRddh15OSHQsCT16k59xjMV/eYT8zGNEd+jIuNvuISgismkP6Dw5nU5OnDjB4cOHWbVqFVVVVYSGhlJQ4BqyExYWRmFhYZ2TbyQnJ5/3PgMCAnwur72PDRs2YDR6z/xUXuum2Kkh7gUFBe7eAUajkbi4OMaNG1fn0D4hWoINR/KZ91XNjKl7skuYu2Qnr08ZwIc/p/Hi1/uotDuZPKAdf/5VN2YO68CGIwXoTyYx/Iw6Fnx/iOqTVcqv6hPrkbByKriyWxTzvtrD17tyCPM38cLkPgxIqrvOYLfYQBLCLKTn1ySLdRoEWjz/VmOC/TwSZBoQYjViNrTdGm/6QBPRdw+g6lAh6DT8Lgpx13iKmN6T8u25lKw6hj23nKrDRVQdLMSWWUpYHcP4Tqk6VETV4SJAo3RtJlEpfTHF+lO+7bh3YyfYs8tdw/1qLy6rxjowGkeRDVOcP4GjEuvpqEVL16B/sV9++SWDBw/GYrEQGhrKpEmTPNanpaUxYcIErFYrUVFR3H///djt9oYMSbQglp49uGjpFyR/8zWBEydivWwYEXfeQdz8Zz3aKaU4Om0a2XMfo/iLL8id/xxHf38DqtZ7Kf3WWyn930qcJSVUp6dzbPZtlKxe3diH1Cycz4dnm83Gxx9/LEMTRKMqKioiLCzM/Xj9+vVcfvnlHsP5xo4dy759+9xfaE9XVVVFcXGxx48QTUnTNC655nrueu8/3PPBZ4y55U50ej06vZ7afQ40NCxBwfQeNY7Enn1wVFez+C8Pk3P4ILbyco7t2cln859oUTOnVlRU8NZbb/H3v/+d5cuXU1XluoNf++83Pz8fp49hiwB+fn6MHDnyvPcbEhJC375961yvlOLEiRNkZ2efcTtKKXesp1736upqRowYQWxs7HnHJURzsifL8/rocCp2ZhSx9uAJHvrPDo6X2iiptPPO2iO8sfoQ43rG8t7MQVzTvx1JYRbKqhzuhBTAFz6G3c16byMLVh8m9UQZW9IKuPEfP5Ke70r8Hiso58vtWWw6WuD++9I0jddv7I9Rr6FproRUiNXEDYM8kxjtQq08PKEbp/r4mAw6/nZ9v1Zdw/Bc6Mx6LN3DsXQNqyk6Dmh6DXNCEPbck0n3k+Msy3/OxllVc2Pa2j8azaBzvfA6ai5RzpPPcTopW5/p2qafHs7j5Q4YHEvkzJ4Ej++AztfsfKJNarCeUp9++imzZs3imWeeYeTIkdjtdnburCl653A4mDBhAjExMaxbt46srCxuuukmjEYjzzzzTEOFJVogc0IC7V54vs71FZs2Uf6TZ1H0yl27KN+8Gf9Bg3CUllK5bbvX847/7W8E+ih42tpNmjSJDz74wKtXVF327NlDcXExM2fOZM+ePWzbtg1/f38uv/xyNE0jKChIZh0S9ebgwYO8+uqr7l5SANnZ2XTo0MGj3akp2LOzswn1MavbvHnzeOKJJxo2WCEugKZpVJaXsf/HtTjtdjr0G8iW5UuprjqV/NfoP/7X7vYFWRmUFdQUP1dOJyfSjlBZWoIlsGUU9F21ahVZWb7rw5yLzp07YzCc/0fWrVu3snXrVnftKIvF4jVMDzhrgu/U809nq1WoXjSsp59+mi+//JKtW7diMpkoLCz0apOWlsbs2bNZtWoVAQEBTJs2jXnz5l3Qe6ct6Rjl2aNQr9PoHB3I+kN5GHQa9pOJCwWsOXCC20d24rJOkWw+WsC/T/gus6HXoFaeitJaCQ+ngspqJ+sP5bEvp4Rb3tvknj1v6uBEnpzUE03T6BkfwvK7L2fptiyMBo1r+rcjOsjPa19/vCyZK7tHc6yggs7RgUQGyoQ9tZXvOEH5lhzQuz6rV2eW+m5Y6xxnjLAQdXs/Stdl4iix4Sy1YUsr8Wx+8hccNDKRqv0FKLvTZ80od30rDXQWA4YoqQksvDXIWdput3PXXXfx/PPPM3PmTPfy7t1rxgB//fXX7N69m2+//Zbo6Gj69u3LU089xYMPPsjjjz/ucUdciDOprmM4mjp5J1ZnNoNOB6fdgVW26gaPrTlKTk7mzjvv5F//+he5ubnndLc9IyODr776ig0bNriXbdmyBXANuZgyZYpHzxYh5syZw/z588/YZs+ePXTt2tX9OCMjg3HjxjF58mRmzZr1i/b/0EMPce+997ofFxcXk5CQcIZnCNGw9v+4hvWffEhx3nHsVVU4HQ7QNEwWC5ffOJ3v3v0ndpvrurXxi09J23kR8V16EBbfzmtbeqMRUwua7OPQoUNnb1SH6OhoxowZc0HP/e6774CapJOvhFRttQv31nb6Y03T8Pf3JzFRhp40FpvNxuTJkxkyZAj//Oc/vdbLze4Ld+lFEdwxsiOvrnSVy0gKt/KX3/Tkm9057mQRuJJVMcGupFBReTVvr0312paGq7dSlf3stV8D/Azc9v4mj32891Maky9OoHe7EAAuigzgrtFnHlbmitmfpHDv0h5tXfm2XPI/3HfWdpY+kej8DDir7FTsygO7wtwlFFXloHJXnmfjk+Ml/QdEAWCKDyD67v5U7MrDll1GxeaaWWaDxiZReaCQ6mMl6MP8CJvcBZ1ZksTCW4O8KzZv3kxGRgY6nY5+/fqRnZ1N3759ef755+nZsyfgGo7Rq1cv991ucA3HmD17Nrt27aJfv34+t11VVeXu9g3IkIw2zllWRsWuXd4rzGYs/foDoBmNRKTcxolX/8+jibLb2du7D4boaOLmPYN14MDGCLlZCA4OZsaMGaxcuZKsrCz8/f3R6/UUFhZy7Ngxn8/ZvHmzz+UFBQX897//ZcaMGQ0Zsmhh7rvvPqZPn37GNrVrxGRmZjJixAguvfRS3nzzTY92p6Znr+3U47pm8TKbzZjNcrdUNA9Htm/hi5ee9V6hFNWVlaz56F0c9pobJQc3/MihTT+jnE5GzbyNYb+fxpoPF7lWahqj/5iC3uBdB6k5Sk9PJy8v7+wNT9I0jZ49ezJmzBhsNhuhoaEX3Bu3utr75pNer6+zp7BSCqPRSGxsLN27d6dPnz4sX76c7du3eySmQkJCmDp1Kn5+3r02RMM41fN14cKFPtfLze5f5r4xXZh2aXuKK6pJDLNi0Ou4dmACn2/LZOMR19DViAAT950sRv6XL3dTXOFdciU8wMQbUwbw8YZ0Fm/y/XkS4JLkMCICTNgc3jdGc4ulZERdlFOBxjkPTyz7+cxDk03Jwfh1DiXwsnicFXZyX9uK/YQrea+ZdChbreSiBroAI+b2wfgPjsGcHOJeZQi3EHi56waKfVQi1TnlGCItGCOtBI2Q5L04uwZJSh0+fBiAxx9/nBdffJH27dvz17/+leHDh7N//37CwsLIzs72SEiB53CMusiQDHGKqq7m6LTpVJ6elDIaSXj7bY9i6JEpKRjj48l/+x0AnJWVVB87Bg4H1RkZpM26mY7ffoMhPLwxD6FJmc1mxo8f77U8KyuLxYsXk5+f7x6y0KVLF/bv3+9zO0opcnNzfa4TbVdkZCSRkedWiDkjI4MRI0YwYMAA3nnnHa8voEOGDOHhhx+murraXZD4m2++oUuXLj6H7gnR3Oz/cY1rCiofPVOV00lVeXlNofNaywHWfLiI29/5mPa9+1GQlUFkUgfC27WcD/nnO2xPKcVFF11UL8XD4+Pjva5dFosFnU5X503NU7VNzWYz77//vtcwMU3TSEpKkt7BzYzc7P7lIgLMRAS4buac6r304axL+Dk1nwqbg0HJYQT5ua7BOzKKvEZqJUf6s+LuyzHqdfRqF0x6fjk/ptYMPdY0CPc3MWdcV67uF8+WtEKfcfSKD6kzxvwyG48u2cn29EIuigrgqat7khDWOmYlPRNld5L/6QEqth1HM2gEjWlP4LB4n20dZa5kvN7f6Bqyd/pUibWETEzGFOcavlnyUwb2vJrepKr6tN5uCnRmA+E3djtjrIZwC4bwltOTVzQP53Xrac6cOR7T6Pr6OTW9N8DDDz/MNddc4/6ioWkaixcv/kUBP/TQQxQVFbl/0tPTf9H2RMtVvmULlTt3en/Ir64mIyWFklWrcNaq9xAyaRLJny+hw5L/uhNSADidqIoKKvfu5VxVHU7l6B9mcHD0lWTOeQhHScnZn9RCxMbGcscdd/Cb3/yGQYMGMX78eK699lri4uJ8ttc0jaioqEaOUrQWGRkZDB8+nMTERF544QWOHz9Odna2x82JG264AZPJxMyZM9m1axcff/wxL7/8ssfwPCGaM5PlzF+aQmPj0eroDWSrqiRt53bC2yXSdegVLSohBRB+Djd7IiMjCQoKIjAwkCuvvJI+ffrUy759bcff358ZM2a4r1unJ8GVUmRnZ7NkyRIyMjIoKyvz6CWllKJHjx71Ep+oP7/kZndwcLD7R4Z5w5vfH6Lro1/R9dHl3Pr+JvomhDC6e7Q7IVVZ7cDfbEB3WmedOeO6YjxZt+iDH9P46UithBQwMCmUlX8azu8GJmDU6+iTEMxFkZ5D7sb1iCY6uKYHotOpWL3/OP/dksGxgnL+uGgDy3dmk15QwQ8HTnDjP37Cdg5DBVu64m+PUrE1F5wKZXNStPQwlfs9J3pRDkXex/vIeupHsp76kbz3dxMw9ORnd51WU4z85L+WPpEYY2tef2eF3ZU5dG/wtCA0MHUIrt8DE+Kk8+opda7DMU7dFatdQ8psNpOcnExaWhrgGnLx88+exanPNhzj1HZkSIYAvGpEeawqLOTY7NswdelC0nvvYgiqKQaraRr64GAcp83alfXoXAyRkVh696Jq3350QYFEpqTg183zjoCjtIyjN93ker7DQVFmJo7CQhLeeL1+j68JaZpGnz59PD7QT5s2jffee889NPfU3eSQkBCvmTWFOFfffPMNBw8e5ODBg7Rr51k759QXweDgYL7++mtSUlIYMGAAERERzJ07l5tvvrkpQhbivPUf/2t2rfqGyjLPArPB0TEMmDCJjgMvYckLfyHnsKumS+3C2srhYPFTfyY0Lp7rn3gOa1DL+lKQnJxMdHS01xDc2vr378+QIUPqfd9du3YlMTHR/dlTp9Nx5ZVXEhISwuzZs6moqKCgoIC33nrL43mnFzDXNI3AwEBCQ0MZPHgwnTqdvcaNOLsLqT1Y36T+oKc1B07wzLKam7Sr9uYyf/lenrzaVX6lstrB5DfWsyOjyON5f7i0PVd2r0kKrj14wiOpoYAgi9Gd2AIwG/R8cuulvLLyABkFFVzcPowZw2omNXE6Fbe8v4lvdrvOHX4GHZW1ElAOpyItv5xDx0vpFtsyJn24UFWpRZ5JIp1G1dFi/DrX9BYv+zGTii01IxcqduVhjA8k6ra+lG8/jmbSY4yxUvZTNtU55djzK7ClFmNOdl1TLF3DKF3tOeTS2i+Kit15KJsDv25hhEz0nHTmdI7yaipO7svSI1zqR4lzdl7vlHMdjjFgwADMZjP79u1j2LBhgGtc/5EjR0hKSgJcwzGefvppcnNz3XervvnmG4KCgjySWULUxdKvH6bkZGwnh4v6Ytu3jwOXDCFs+nSi/nQfmk5Hxc5dOIqKvNraMzOxZ2VRuW2ba4FOR9nadSR/8QWmdvEopShe+iUl336L48SJmic6nZR+/z3KbkdrxTO8nOqpckplZSUVFRUEBQWh18uUruLCTJ8+/aw3OwB69+7NDz/80PABCdEAgiIimf7i62xZsZRtXy+jsrQETdPocfko+o2dCMCUeX/DVlFOeXERaz58l8z9eyjJq7nWFGRl8uUrz5HcbxBJvfsSkZDUVIdzXjRNY9y4cSxatMjnOpPJRLduZx4OcqH0ej033XQTu3fvpqKigg4dOrg/c2qahtVqxWq1MnHiRJYtW+bu6e9Lv379GDFiRIPE2Vadb+3BM5Gb3fVj27FC9DrNPXzPqWDT0ZqbuEu2ZngkpDTg4vZhPPbrmt6Di9Yd4X97vcs69IjzThyF+pt47KoeHDpeyr83pDNv2W5AY9nOLGx2JydKaxLENofvv89gS8uor/dL6EP9IL3ENYsdgFNhCPV839qyylw9omoVjq/OKiVoRAKmBNdw6KKvj1B1sNC1iVIbx/+5g+h7BmCMsGDuEEzotZ0p/l8aOCFgSCwBl8UTCuAETV/Ti6o6t5zqnHKMURaM0a7eVraMUnJf2+ref5HVQPR9A13DCIU4iwb5Bh0UFMStt97KY489RkJCAklJSTz//PMATJ48GYAxY8bQvXt3pk6dynPPPUd2djaPPPIIKSkpcnEQ50RnNpP0wfsc/9vLFC1ZgqqsozCi00n+229jSkwk9PrrOP7KK3X3sqo9FNDpRFVWUrJyJYbQEPIXLnLVr/IxxEJntUIbS8z4+flJkVchhDhH/iGhlBUUUFVeBrh6Aq5b/AGxHTvTvu8AwDXMz2SxMvHuB1m18E22fv2la5Y+1xNI27GN9J3b0XQ6Jtz1AA6bDXQ6kvtdjNnafOuqdOjQgeuvv55169bhdDqJi4ujtLQUk8nE0KFDCQkJabB9GwwGevfufcY2AwcOpE+fPrz33nvuXlW1+fv7M7ANTYbSWM6n9uDZyM3u+pEYZvWaca9DuJV31qaycN0RSivtHiWKFFBm8yx4/vL/Dvjc9uKNx/j9oERigz3rDR3MLeGqV9diczhxKuWr9B7gynUE+hkoqazZ3y2XJxMX0vrrFwWP74DtaDGOAlf9M7+uYZgSgihelYam12HtF4Ux2uqRkAIwRnleFyq217qprgCHoupAAcYIC7b0Egq/OIyqVcD+VEH1qoxibEeK0YeYcVbYKfzvQfebIOTqiwgYEkfe+7s99u8st1P0VSphv+tcj6+EaK0arFvH888/j8FgYOrUqVRUVDB48GBWrlzpLkqr1+tZunQps2fPZsiQIfj7+zNt2jSefPLJhgpJtEKG0FBin3ic6MfmcuLV/6Pwk09wHD/u3VCvp2LLZkKvvw5nsXcvqTopRdmaHyj7vlYPDR8Jreg//xmA6pwcdGYz+gb8gC2EEKJlyjl0wKOguabTkXPksDspVVt81+5s/upzr+VKKZTTyZcvP+dOWAVHxXDD039t1kP7unbt2qDDsH4po9FIaGgo6enpHjWkunXrxsSJE/H3l+nmm1JaWhr5+fmkpaXhcDjYunUrAB07diQgIEBudteTCb1iWbk3l8+2ZACQEGqhX2IYT3yx22d7DRjXw7MnWl01nrKKKrls/ioWTB3AqG41Q/0++CkNm8PpkQzzRafBxN6x/G5AArszi+gQEcDQjm1jgiJDsJnoewZQfazUNSsekPPqZrC7XrOS1ceIur0vVUeLqdzpmu3U3CmUwCs8h6LqrAavwuc6iysdkP/RXlSthF/RslT8uoZhO1pMwacH6iyYXvj5Iax9o3CWeM92WrtwuhBn0mBJKaPRyAsvvMALL7xQZ5ukpCSWLVvWUCGINkSn0xF1151E3nkHx//2Mnlvvw21p4JWCmO8a5aKwDFjqdi67fQNeCabTvaGMsTFeSakfDC2b0/glaM5OmUKFZs2AxA6bRrRcx485ylbhRBCtH7hCYmcOHbUnZhSTidh8a5aaoc3b+DnJZ/gsFfTe9Q4rCFnmFlSqZoeVEDxiVw2L/ucYddPbdD4W7uRI0eSmprqnoEtMTGR3/72t+5ZP0XTmTt3rscQ0FOz6a1atYrhw4fLze56otNpvHhtH1JGdKSsyk7X2EDu+Xirx+Sheg2CrSYC/Qxc3Tee20Z09NjG7wcl8I8fUn1O+GZ3Km59bxMbHhlNiNUEcNZklFmvYTEZGNszhseu6oGfUc+ApLY3867OpHfXfzr+9k53QgrAWVZN6ZoMwm/shqPIBkqhCzZRuTsfW3oJhggL1v7RBI/rwPF/7gCH67mmhEAsPSMAsBdUeSWdKg8VUrQs1fWgrl+Tcu1fH+6HPafcY5Vfp7b3exIXpvUWwBFtkqZpRN1zN+GzZpE2fbprdj7Ar3s3wma46iGFTZ+GstspWrIEnb8/kXfcgSkxgdIf1qAPDMDQLoHydevQBwVS9OUy7MeOnWmXUG3j+EsvUbFlq3tRwaJFWPv1I2jc2IY6VCGEEC3M8Jv+yIm0I5xIPwpA33ET6TjwEjL27eGz505+eVaK7IP7iUhszxnn8q5N06gsbbtT2deX4OBgUlJSSEtLw2AwkJiYKDUTm4mFCxeycOHCM7aRm931Q9M0OkYFuB+HWE3oNA2HuwehxpTBidw7pguV1Q5W7MqmrMrO5Z0jiQ7yY874bkQGmvnP5gz2ZnvPTl3tVPxp8Tbeumkgmqbx2/7t+OCnNHQnE1+nn/GqnQqqHcwY2gE/o/w9AlTnlHktq0orRtM0DCGunoFF3xyl5H9p7jpTFXvzCZ/Sjeh7BlB1oACdxYClZwSawXUj3hQfgC2jVt0qDYqWHPIdwKlLkwb6YDP6UDPhN3Un97WtqHJXbytzl1CCRras2WJF09GUqmvkbstQXFxMcHAwRUVFBAW17pkXxPlR1dVUnExKWXr2RDvPO522Y8c4NPpK3ytP3TLSNMJm/IHyjZtqCqQDGAwEjR9PxebN2PPy8L/0UuLmPYM+uPkOrRACWu85tbUel2h5nA4HBdmZmCwWAsNcd6i/e++fbPnqc4/eT3XSNMJi48nP9LxhMumBR7lowOCGCFkIL631nNpaj+uXOFZQzqTX1rqLjieEWlhy+zAsRj3XLqiZiS/Qz8DiW4fQNcb1uimleHtNKk8v23N6qSMAvrxzGD3iXJ+LNx3N5931R3EquLpPHAu+P8SmIwXu/IhepzH90vY8OlHqgwHk/H0r1WmeCT99qBlzcgj+F0djSggk49F1XjWmou8d4FVn6hR7QSUnFu3Gnl0GJh3Y6qi/qwNdoAlneTXGaH/CruuCMdK1TeVwYj9Rgc5qRB/o6gmnnIrqrDI0vYYhyoqmk1Ekbcm5nlOlp5RotTSjEevJ7t0XIu+dhT6Xx/zlKYo++y+OgnwCrxxD+OxbOXD5FZ6N7HaKv/oKHA5QitLVq8l85BHavfIKlXv3UrX/AMboaKyDB8kQPyGEaEN0ej3h8Z51PswWK+d8j1DhlZDSdDoKc7Kw22wYTKb6ClUIIWgXauXre65g5d5cDDqNUd2iCPQz8sFPR9lZaya+sio7L6zYxz+mXQy4elzNvCyZXu2CuXbBj17bLSqvKbMxICmMAUlh7sdf7shyzfrXortONJygEQnkLfKs8+UorKJ8cw7lm3OImNHTKyEFoKrrnmHUEOpHzN39qUotpHx3HmU/ZPpu6ARnkY2QSR0JuCTWY5XtaDGVBwvRB5rwHxiDcjg5/o8dVB8rBcDcMYSI6T3cvbOEOEWSUkLUwVnieyiEX7duhP7udwBU7tvHwSuGo4p9tLXXmo3E4aBs3XoOjR1Hda2ZfYJ+9Svi/vqCJKaEEKIN63PleDYv/4LKOq47nnx80XA6+W7RP9i/fi3XPjYPvUE+3gkh6k+Yv4nfDWjnsaygzIZOp7lrQjkV7t5UtQ3qEM6ILpGs3n8cpzpZk8pipEd83b0mbhycyOdbM9GfzF0YdBrXDkyos31bY+kWTvjUbpT+lI39eDmOwlr1oDQo35yLpVc4FTvzXMt1YIi0Yozx3UvKUVaNo6iK6oxSCv5zwPsy42Mkefm24x5JqbJNORQs3u8eLli+JRdTUhDVGaXuNlWHCildl0ng5Z7vJSEkTSlEHQJHjvS5/FQxc+V0kn7LrTiLzm02P1VV5ZGQAihetozy9et/WaBCCCFaNGtwSL0kkjL37yF99456iEgIIWr8dDiPhz/bwVNLd3M0z1XP6PLOkSilqH1bVa/T+N+eHK/nv/L7fvymXzzRQWaMeh355dUMf/471h484XN/yZEBzBnflVFdo7huYDv+mzKULjGBDXFoLZalRwSRM3pi6R4Op9/b1iDs2q4EXpGAOTkY/4tjiLy5N5re+6t/2ZZcsp7+idxXtrhm2Ts9IaXX0IecNoOlBjqLZ32v4hVHXP85maS0pZVgSyv23J6myYx8widJSglRh6Bx4zAld/Baboh2TWPrKCjAnp3t87mGuDjMPXp4Lqzdc6r24hO+L8hCCCHaBqUU5YUF9bItu827p4IQQlyo1fuPc/1bP/LRhnQWrjvCVa+uIaOwgt7tQnhjygA6RgVg1LuyIlvTCpi5aCOL1h3x2Ia/ycCff9UNq8lA9cmZ3worqvnjoo0Ulnues7alF3LF86t4etkevt6dA2h0lYRUnfwHxbhmDddprh9Nw/+SWDSjjuBx7Ym8uTehv+mE3t+7tq6j1Obq3XSGGRAjbupO9J390Yf5uRZooBl0XkXMld17aKBmPW2fToUpQX6XwpskpYQ4g3Yvv4w+JMT9OHD0aAJHjwJAHxyMzt/fVfS8Fn1UFB0+WYzOz+/sOzAYsPTvX58hCyGEaGE0TSO2czc03S//WBYWL8MihBD15521qaDA4VQ4nIqyKjv/2eSqazemRwyPTOzuTjSd/IdX/nfA/fwtaQUMeuZbBvzlW1JPlLln8VMKKqodTHx1DQ98so3iSleNqT9/toOyqpobuf/6OY2fUvMb41BbJGO0P9F39CXgklj8B8UQdVsfzInnVqTfUVBVd0JKA52/EVNCIDqLgeg7+xH0qw5YekUQOCoRQ5jn9xxTsvdkTrb002Zf1GuYu4SeU2yibZGklBC1OMvLcVbUdCs1d+rERcu/IvbZeUTceSehN0113Y0ANIOB+JdeRDtVVFavJ+L2FDqt/B+GsDCMcbFwhqmkdSEhJL71JqZ28gVCCCHauol3P0Bsp67uxxeaoMpLO1pfIQkhBN5zMGgeI7KqffSQqXY43f/+cdFG8svq7sF5rKCCTzcdY+bCDVRWO8gsrPDKk2QVyZCvMzFG+xPy64sIndQRU7tz74lkCPcDg4+6throAoyE3dAV3cneTs4qB6U/HKNi+wmKlx8h+2+bcRTX/F5N8d77VaXVngscCntm2TnHJ9oOqYQpBKCqq8l85FGKlywBQDObMXfsSNgfplP6/Q8UL1vmHn4XdPWviXv2WTRNI+Dyy+m0+jtsR45gbNcOQ0SEe5tR99xD+YaNPof4Jb7zNv5DhjTOwQkhhGj2AsMiuOahx3l1+rWAq26hB01D0zTv5afxCwhoqBCFEG3Q1EuSWL3/+MmRYRp+Bh2T+sa7119yUThxIX7kFFW5e0HdeEkSACdKq8g7Q0LqFIeCDUcK6PX4CqICzRSUeyYzTD5qIYkL56y046ywow82Y+0bRfnG0+qAKXCWVVOweD/R9w5AZ9JT+v0xnGU1vxdniY3CFakEXByDMS4AY5TFcxs6XMMJ7Z4ZRl2gzBArvMlfuBBA/qJFFH/+ufuxqqqictcuMv90v2t5rXpQxUs+p/ynn92P9SEhWPr29UhIARjj4kheupS4F17AlJwMgGY0EvPkE5KQEkII4cVeXV33SqVQTifB0TF19qLqNHgo7br1bKDohBBt0eju0SyaMYhJfeO5dmACS24fSmJ4zSxuBp1GYqjVnZDqERfEPaM6Aa5Z+/zNeo863Ga9xt+u6+NzX9UORUZhpccynQZ7skp8thfnr+T7Y2Q+sZ7s+RvIeWkTxlh/3w2d4CischUrB5wVp9XGVVCxKZfjb2wn56+bMMT44z84xr3aEG4h9JpOrukWT/K/NA5TnNw4Ed6kp5QQQMWuXefV3paejv8lg8/aTh/gT/DECQRPnICjpASdnx+a0bvQoBBCCGEJDCKhR2+O7dnps0eUptNz1T0P8a+H7/WesVunw15tw+l0oq+H2lRCCHHKFZ0juaJzpM91f//uED8fqan5tCuzmI83pjN1SHt2ZhRxUWQAOzKKQIFRr/HKDf0Z2yOGDUcK+OCnNJ/b1GmepY6CLfLZuT7Y0ksoWpbqfmzPq6ByTz5+3cKo3OO7bpdmdJUi8esWRvnmXJ9tHCVVFC09TMS0HgRekYCyOTBEWtD0OsxJwdiOlaAPNmNOOrdaV6LtkU8tQgCm9u3Pq33RyWF+50MfGCgJKSGEEHXSNI2r//QIfa4cT2ynriT17ofe4Lp/qOl0jL31TkKiY3A6HF7PVU4nqZs3sPRv8xs7bCFEG7Y/u8Sj7pRBp7Evp4QDOSVc/+aP7Mwocq9/aHw3xvZw9ab5y6SevDl1AOEBJo+eVBrgZ6zpXdU+wp/rBiU0xqG0etU5p9VzckJ1dhnhU7sTObtPTU8nnevVN3cMcc+WZ+0VSchvO2KIsqALMHhtx57n6uFmCPPDGOOPdnLIpSHMD2vvSElIiTOSnlJCABGzZlH+8wYqNm06p/YVGzfiKCpCH+w904QQQghxocxWK6NmzHY/Li8qJD/zGMHRMQSGRaCUwj80jPLCApR3BWJSt2xszHCFEG1c55hAvt6d7U48OZyKLjFBrNiVjdOpPHo8Ld+ZxYxhHQBXEn5MjxgSwqzc9PbPHC+pQq/TeHpST67oEsnKvbn4GfSM6xmDv1m+stYHY/RpQ/V0uBJIOg1zUhDmpCAsPSKoSi1CH2LGf0A0mq4mZRgwKJaAQbFUHSni+Bvba7ajgbm9JJ3EhZO/cCEAndVK0nvvYjt8GFtGBo7CQkzx8VTu3UfO/Plwep0PTauZdU8IIYRoINbgEKzBIe7Hrt5UD/PZ/CepKC7yam+Qa5MQohHdNvwidmQUsmrvcQAm9YvnhkGJLFx3xGOYsU4Dq4/kUrfYINY8OIJjBRVEBJjdQ/VuHJzUGOG3KaaEQIJ/1YGir1JB1ar7VItf51D8OoeecTvm9sGETOpI0bLDqGonft3CCJ6Q3JChi1ZOklJCnKTpdJg7dsTcsaN7mXXgQILGjyNt1iyqdu8BvR4cDsJvuRmdxXKGrQkhhBANI7ZjF255fSEZ+/bw6dNzcTpqCtBePuUPTRiZEKKt8TPqeXvaxRwvqUKn04gIMANwTf943l6TSlZRBRoaOh3cPqKjz22YDXouipQC2I0h8PJ2+F8c45p9L8Ts0RPqfARcEusa7ucETX9h2xDiFElKCXEWhvBwOnzyCcVfLsOWmopfj+4EjBzZ1GEJIYRow/QGI4k9enPz6wtZv/hfVFdW0n34SJJ69m3q0IQQbYymaUQF+XksC7GaWHrHMD7dfIwKm4OxPWPoHB3YRBGK2nQWAzrLL08DaJoG+noISLR5kpQS4hxoOh3BV01s6jCEEEIID/7BIYz+421NHYYQQngJ9Tfxx8tkWJcQ4sxk9j0hhBBCCCGEEEII0egkKSWEEEIIIYQQQgghGl2DJaX279/P1VdfTUREBEFBQQwbNoxVq1Z5tElLS2PChAlYrVaioqK4//77sdvtdWxRCCGEEEIIIYQQQrQWDZaUmjhxIna7nZUrV7Jp0yb69OnDxIkTyc7OBsDhcDBhwgRsNhvr1q1j0aJFLFy4kLlz5zZUSEIIIYQQQgghhBCimWiQpNSJEyc4cOAAc+bMoXfv3nTq1Ilnn32W8vJydu7cCcDXX3/N7t27ef/99+nbty/jx4/nqaee4rXXXsNmszVEWEIIIYQQQgghhBCimWiQpFR4eDhdunTh3XffpaysDLvdzoIFC4iKimLAgAEArF+/nl69ehEdHe1+3tixYykuLmbXrl11bruqqori4mKPHyGEEEIIIYQQQgjRshgaYqOapvHtt98yadIkAgMD0el0REVFsXz5ckJDQwHIzs72SEgB7senhvj5Mm/ePJ544gmv5ZKcEkKIX+7UuVQp1cSR1K9TxyPXCiGE+OXkWiGEEOJszvVacV5JqTlz5jB//vwzttmzZw9dunQhJSWFqKgofvjhBywWC//4xz+46qqr2LBhA7GxseezWw8PPfQQ9957r/txRkYG3bt3JyEh4YK3KYQQwlNJSQnBwcFNHUa9KSkpAZBrhRBC1CO5VgghhDibs10rNHUetziOHz9OXl7eGdskJyfzww8/MGbMGAoKCggKCnKv69SpEzNnzmTOnDnMnTuXzz//nK1bt7rXp6amkpyczObNm+nXr985xeR0OsnMzCQwMBBN0871UBpFcXExCQkJpKene7wOzVlLi7mlxQsSc2NoafFC84lZKUVJSQlxcXHodA02F0ajq49rRXP5HbUW8nrWP3lN65+8pr7JtaLpteb3Zms+NmjdxyfH1nI1xPGd67XivHpKRUZGEhkZedZ25eXlAF471ul0OJ1OAIYMGcLTTz9Nbm4uUVFRAHzzzTcEBQXRvXv3c45Jp9PRrl27c27fFIKCglrcG7elxdzS4gWJuTG0tHihecTcmu56n1Kf14rm8DtqTeT1rH/ymtY/eU29ybWieWjN783WfGzQuo9Pjq3lqu/jO5drRYPc2hgyZAihoaFMmzaNbdu2sX//fu6//35SU1OZMGECAGPGjKF79+5MnTqVbdu2sWLFCh555BFSUlIwm80NEZYQQgghhBBCCCGEaCYaJCkVERHB8uXLKS0tZeTIkQwcOJA1a9awZMkS+vTpA4Ber2fp0qXo9XqGDBnClClTuOmmm3jyyScbIiQhhBBCCCGEEEII0Yw0yOx7AAMHDmTFihVnbJOUlMSyZcsaKoQmZzabeeyxx1pUz6+WFnNLixck5sbQ0uKFlhlzWyO/o/olr2f9k9e0/slrKpqr1vzebM3HBq37+OTYWq6mPL7zKnQuhBBCCCGEEEIIIUR9aD3TZQghhBBCCCGEEEKIFkOSUkIIIYQQQgghhBCi0UlSSgghhBBCCCGEEEI0OklKCSGEEEIIIYQQQohGJ0kpIYQQQgghhBBCCNHoJCnVgL788ksGDx6MxWIhNDSUSZMmeaxPS0tjwoQJWK1WoqKiuP/++7Hb7U0T7ElVVVX07dsXTdPYunWrx7rt27dz2WWX4efnR0JCAs8991zTBAkcOXKEmTNn0qFDBywWCxdddBGPPfYYNpvNo11zihngtddeo3379vj5+TF48GB+/vnnJo2ntnnz5nHxxRcTGBhIVFQUkyZNYt++fR5tKisrSUlJITw8nICAAK655hpycnKaKGJPzz77LJqmcffdd7uXNcd4MzIymDJlCuHh4VgsFnr16sXGjRvd65VSzJ07l9jYWCwWC6NHj+bAgQNNGLGoraWcI5uzlnr+bgma8zWmOWvp1z/Rtjz99NNceumlWK1WQkJCfLZpjt8xLlT79u3RNM3j59lnn23qsC5Yaz1PP/74416/p65duzZ1WBfk+++/56qrriIuLg5N0/jvf//rsb6lf1Y/2/FNnz7d63c5bty4Bo1JklIN5NNPP2Xq1Kn84Q9/YNu2baxdu5YbbrjBvd7hcDBhwgRsNhvr1q1j0aJFLFy4kLlz5zZh1PDAAw8QFxfntby4uJgxY8aQlJTEpk2beP7553n88cd58803myBK2Lt3L06nkwULFrBr1y5eeukl3njjDf785z8325g//vhj7r33Xh577DE2b95Mnz59GDt2LLm5uU0Sz+lWr15NSkoKP/74I9988w3V1dWMGTOGsrIyd5t77rmHL774gsWLF7N69WoyMzP57W9/24RRu2zYsIEFCxbQu3dvj+XNLd6CggKGDh2K0Wjkq6++Yvfu3fz1r38lNDTU3ea5557jlVde4Y033uCnn37C39+fsWPHUllZ2WRxixot5RzZnLXE83dL0NyvMc1ZS77+ibbHZrMxefJkZs+e7XN9c/2O8Us8+eSTZGVluX/uuOOOpg7pgrT283SPHj08fk9r1qxp6pAuSFlZGX369OG1117zub6lf1Y/2/EBjBs3zuN3+eGHHzZsUErUu+rqahUfH6/+8Y9/1Nlm2bJlSqfTqezsbPey119/XQUFBamqqqrGCNNnTF27dlW7du1SgNqyZYt73d///ncVGhrqEduDDz6ounTp0gSR+vbcc8+pDh06uB83t5gHDRqkUlJS3I8dDoeKi4tT8+bNa5J4ziY3N1cBavXq1UoppQoLC5XRaFSLFy92t9mzZ48C1Pr165sqTFVSUqI6deqkvvnmG3XFFVeou+66SynVPON98MEH1bBhw+pc73Q6VUxMjHr++efdywoLC5XZbFYffvhhY4QozqClnyObs+Z+/m4JWto1pjlrKdc/0ba98847Kjg42Gt5c/yO8UskJSWpl156qanDqBet+Tz92GOPqT59+jR1GPUOUJ999pn7cWv7rH768Sml1LRp09TVV1/dqHFIT6kGsHnzZjIyMtDpdPTr14/Y2FjGjx/Pzp073W3Wr19Pr169iI6Odi8bO3YsxcXF7Nq1q9FjzsnJYdasWbz33ntYrVav9evXr+fyyy/HZDK5l40dO5Z9+/ZRUFDQmKHWqaioiLCwMPfj5hSzzWZj06ZNjB492r1Mp9MxevRo1q9f36ixnKuioiIA92u6adMmqqurPY6ha9euJCYmNukxpKSkMGHCBI+4oHnG+/nnnzNw4EAmT55MVFQU/fr146233nKvT01NJTs72yPm4OBgBg8e3GzfJ21FazhHNmfN+fzdErTEa0xz1lKuf0L40ty+Y9SHZ599lvDwcPr168fzzz/fIocitoXz9IEDB4iLiyM5OZkbb7yRtLS0pg6p3rWVz+rfffcdUVFRdOnShdmzZ5OXl9eg+5OkVAM4fPgw4Bpb+8gjj7B06VJCQ0MZPnw4+fn5AGRnZ3tcLAD34+zs7EaNVynF9OnTufXWWxk4cKDPNs0pXl8OHjzIq6++yi233OJe1pxiPnHiBA6Hw2c8zeH1O53T6eTuu+9m6NCh9OzZE3C9ZiaTyat+QVMew0cffcTmzZuZN2+e17rmGO/hw4d5/fXX6dSpEytWrGD27NnceeedLFq0CKh5X7aU90lb0RrOkc1Zcz9/twQt7RrTnLWU658QdWlt588777yTjz76iFWrVnHLLbfwzDPP8MADDzR1WOettZ+nBw8ezMKFC1m+fDmvv/46qampXHbZZZSUlDR1aPWqLXxWHzduHO+++y7/+9//mD9/PqtXr2b8+PE4HI4G26ckpc7DnDlzvIp+nf5zqlYGwMMPP8w111zDgAEDeOedd9A0jcWLFze7eF999VVKSkp46KGHGi22XxpzbRkZGYwbN47Jkycza9asJoq8dUlJSWHnzp189NFHTR1KndLT07nrrrv44IMP8PPza+pwzonT6aR///4888wz9OvXj5tvvplZs2bxxhtvNHVobVJLPEc2Z3L+Fq1BS7j+idbnQs6fLdn5HO+9997L8OHD6d27N7feeit//etfefXVV6mqqmrioxC1jR8/nsmTJ9O7d2/Gjh3LsmXLKCws5N///ndThybO0/XXX8+vf/1revXqxaRJk1i6dCkbNmzgu+++a7B9Ghpsy63Qfffdx/Tp08/YJjk5maysLAC6d+/uXm42m0lOTnZ3Y4yJifGabeHULC4xMTGNGu/KlStZv349ZrPZY93AgQO58cYbWbRoETExMV6zzNR3vOcT8ymZmZmMGDGCSy+91KsAbmPFfC4iIiLQ6/U+42nsWM7m9ttvZ+nSpXz//fe0a9fOvTwmJgabzUZhYaHH3eKmOoZNmzaRm5tL//793cscDgfff/89//d//8eKFSuaVbwAsbGxHucFgG7duvHpp58CNe/LnJwcYmNj3W1ycnLo27dvo8XZVrTEc2Rz1lrP3y1BS7rGNGct5fonWp/zPX+eSWN8x/ilfsnxDh48GLvdzpEjR+jSpUsDRNcw2tp5OiQkhM6dO3Pw4MGmDqVetcXP6snJyURERHDw4EFGjRrVMDtp1ApWbURRUZEym80ehc5tNpuKiopSCxYsUErVFCHMyclxt1mwYIEKCgpSlZWVjRrv0aNH1Y4dO9w/K1asUID65JNPVHp6ulKqpuiszWZzP++hhx5q0qKzx44dU506dVLXX3+9stvtXuubW8yDBg1St99+u/uxw+FQ8fHxzaa4odPpVCkpKSouLk7t37/fa/2pQq+ffPKJe9nevXubrNBrcXGxx/t2x44dauDAgWrKlClqx44dzS5epZT6/e9/71Xo/O6771ZDhgxRStUUT3zhhRfc60+dT1pi8cTWoqWeI5uzlnb+bgma+zWmOWtp1z8hlDp7ofPm8B2jIbz//vtKp9Op/Pz8pg7lvLWl83RJSYkKDQ1VL7/8clOH8otQR6Hz1vJZ/fTj8yU9PV1pmqaWLFnScHE02JbbuLvuukvFx8erFStWqL1796qZM2eqqKgo9wnUbrernj17qjFjxqitW7eq5cuXq8jISPXQQw81ceRKpaames0sVVhYqKKjo9XUqVPVzp071UcffaSsVqs7ydbYjh07pjp27KhGjRqljh07prKystw/zTXmjz76SJnNZrVw4UK1e/dudfPNN6uQkBCP2VGa0uzZs1VwcLD67rvvPF7P8vJyd5tbb71VJSYmqpUrV6qNGzeqIUOGuBMqzUHt2feUan7x/vzzz8pgMKinn35aHThwQH3wwQfKarWq999/393m2WefVSEhIWrJkiVq+/bt6uqrr1YdOnRQFRUVTRa38NQSzpHNWUs8f7cEzf0a05y1huufaDuOHj2qtmzZop544gkVEBCgtmzZorZs2aJKSkqUUs37O8b5WrdunXrppZfU1q1b1aFDh9T777+vIiMj1U033dTUoV2Q1nyevu+++9R3332nUlNT1dq1a9Xo0aNVRESEys3NberQzltJSYn77wpQL774otqyZYs6evSoUqrlf1Y/0/GVlJSoP/3pT2r9+vUqNTVVffvtt6p///6qU6dODZrUlqRUA7HZbOq+++5TUVFRKjAwUI0ePVrt3LnTo82RI0fU+PHjlcViUREREeq+++5T1dXVTRRxDV9fuJRSatu2bWrYsGHKbDar+Ph49eyzzzZNgMp1dwjw+VNbc4pZKaVeffVVlZiYqEwmkxo0aJD68ccfmzSe2up6Pd955x13m4qKCnXbbbep0NBQZbVa1W9+8xuPL5JN7fSkVHOM94svvlA9e/ZUZrNZde3aVb355pse651Op3r00UdVdHS0MpvNatSoUWrfvn1NFK3wpSWcI5uzlnr+bgma8zWmOWsN1z/RdkybNs3n+3XVqlXuNs31O8b52rRpkxo8eLAKDg5Wfn5+qlu3buqZZ55p0T2+Wut5+rrrrlOxsbHKZDKp+Ph4dd1116mDBw82dVgXZNWqVT7/xqZNm6aUavmf1c90fOXl5WrMmDEqMjJSGY1GlZSUpGbNmtXgiVNNKaXqd0CgEEIIIYQQQgghhBBnJrPvCSGEEEIIIYQQQohGJ0kpIYQQQgghhBBCCNHoJCklhBBCCCGEEEIIIRqdJKWEEEIIIYQQQgghRKOTpJQQQgghhBBCCCGEaHSSlBJCCCGEEEIIIYQQjU6SUkIIIYQQQgghhBCi0UlSSgghhBBCCCGEEEI0OklKCSGEEEIIIYQQQohGJ0kpIYQQQgghhBBCCNHoJCklhBBCCCGEEEIIIRrd/wMCjkQ/cgwqnQAAAABJRU5ErkJggg==", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def island_spread(emb):\n", " emb = np.asarray(emb, dtype=float)\n", " return float(np.linalg.norm(emb - emb.mean(axis=0), axis=1).mean())\n", "\n", "check(\"7.5 spread varies with perplexity\", _spread_changes, required=True)\n", "\n", "# viz: the three maps side by side\n", "fig, ax = plt.subplots(1, 3, figsize=(12, 3.6))\n", "for a, p in zip(ax, (5, 30, 80)):\n", " a.scatter(_embs[p][:, 0], _embs[p][:, 1], c=ysub, cmap=\"tab10\", s=8)\n", " a.set_title(f\"perplexity = {p}\")\n", "plt.suptitle(\"same 600 digits, three perplexities, three layouts\"); plt.tight_layout(); plt.show()" ] }, { "cell_type": "markdown", "id": "21af0221", "metadata": {}, "source": [ "> **Interpretation.** Low perplexity (5) fractures the data into many tight specks and can invent structure that is not there; high perplexity (80) merges islands and emphasizes global layout. None is \"the truth\". A t-SNE figure without its perplexity and seed reported is uninterpretable.\n", "\n", "> **Key takeaways.** t-SNE is a visualization tool, not a feature extractor. It preserves local neighborhoods and distorts global distances and cluster sizes. The output depends strongly on perplexity and the random seed, so always publish both, and never feed a t-SNE embedding into a downstream classifier.\n" ] }, { "cell_type": "markdown", "id": "b7823e59", "metadata": {}, "source": [ "UMAP is the modern alternative: faster, deterministic given a seed, and better at preserving global structure. It is not preinstalled here, and the notebook never installs anything on its critical path, so this cell *reports and skips* if `umap-learn` is absent. Run `pip install umap-learn` locally to see it.\n" ] }, { "cell_type": "code", "execution_count": 26, "id": "a5345483", "metadata": { "execution": { "iopub.execute_input": "2026-06-10T18:47:25.066225Z", "iopub.status.busy": "2026-06-10T18:47:25.066116Z", "iopub.status.idle": "2026-06-10T18:47:25.069518Z", "shell.execute_reply": "2026-06-10T18:47:25.069163Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "skipped: umap-learn not installed.\n", "It would show a digits map like t-SNE's but with more trustworthy GLOBAL arrangement,\n", "faster fits, reproducibility given the seed, and a .transform() for new points.\n" ] } ], "source": [ "# deeper: UMAP if available; otherwise report what it would show and move on.\n", "import importlib.util\n", "if importlib.util.find_spec(\"umap\") is not None:\n", " import umap\n", " reducer = umap.UMAP(n_neighbors=15, min_dist=0.1, n_components=2, random_state=SEED)\n", " X_umap = reducer.fit_transform(X_digits)\n", " plt.figure(figsize=(6, 5))\n", " plt.scatter(X_umap[:, 0], X_umap[:, 1], c=y_digits, cmap=\"tab10\", s=8)\n", " plt.title(\"UMAP of the digits\"); plt.tight_layout(); plt.show()\n", " print(\"UMAP: deterministic given the seed, and typically keeps inter-cluster layout better than t-SNE\")\n", "else:\n", " print(\"skipped: umap-learn not installed.\")\n", " print(\"It would show a digits map like t-SNE's but with more trustworthy GLOBAL arrangement,\")\n", " print(\"faster fits, reproducibility given the seed, and a .transform() for new points.\")" ] }, { "cell_type": "markdown", "id": "920a0fcc", "metadata": {}, "source": [ "## Part 8 — The pipeline: PCA -> k-means, broken then fixed\n", "\n", "> **Objectives.** Assemble the production move (PCA to denoise, then cluster), but first stage the canonical **k-means early-break bug** so you experience a wrong answer, diagnose it, and fix the convergence test. This is the named defect this chapter exists to inoculate against.\n", "\n", "We will cluster the PCA-reduced digits with from-scratch k-means and score the clustering by *purity*: for each cluster, take its majority true digit and count how many of its members match. Clustering is unsupervised; we only use labels to score, never to fit.\n" ] }, { "cell_type": "markdown", "id": "198531a4", "metadata": {}, "source": [ "First the scoring helper. It is small and we will reuse it for both the broken and fixed runs.\n" ] }, { "cell_type": "code", "execution_count": 27, "id": "cb1db640", "metadata": { "execution": { "iopub.execute_input": "2026-06-10T18:47:25.070403Z", "iopub.status.busy": "2026-06-10T18:47:25.070322Z", "iopub.status.idle": "2026-06-10T18:47:25.085385Z", "shell.execute_reply": "2026-06-10T18:47:25.081978Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "reduced digits to 20 dims, keeping 89% of variance\n" ] } ], "source": [ "def cluster_purity(labels_pred, labels_true):\n", " # fraction of points whose cluster's majority true label they share\n", " labels_pred, labels_true = np.asarray(labels_pred), np.asarray(labels_true)\n", " correct = 0\n", " for c in np.unique(labels_pred):\n", " mask = labels_pred == c\n", " vals, counts = np.unique(labels_true[mask], return_counts=True)\n", " correct += counts.max() # majority vote in this cluster\n", " return correct / len(labels_true)\n", "\n", "# reduce the digits to 20 PCA dimensions first (denoise + speed up clustering)\n", "mean20, comps20, evr20 = fit_pca(X_digits, 20)\n", "X20 = transform_pca(X_digits, mean20, comps20)\n", "print(f\"reduced digits to {X20.shape[1]} dims, keeping {evr20.sum():.0%} of variance\")" ] }, { "cell_type": "markdown", "id": "eb5c54fd", "metadata": {}, "source": [ "### The bug: a sentinel label that stops the loop on iteration one\n", "\n", "Here is k-means written the way it is *often* written, with one fatal line. The loop is supposed to run until the assignments stop changing. The author initializes `labels = np.zeros(m)` as a sentinel and breaks when the new assignments equal it. But `0` is a *valid cluster label*. If any cluster's points happen to already be assigned 0 (and on the first pass some always are), the early-break logic can fire before a single centroid has moved.\n", "\n", "> **Stop and think:** read the convergence check below before running it. The sentinel `prev_labels = np.zeros(m)` is indistinguishable from a real all-zeros assignment. What is the earliest iteration this loop could exit, and would the centroids have updated by then?\n" ] }, { "cell_type": "code", "execution_count": 28, "id": "388d881c", "metadata": { "execution": { "iopub.execute_input": "2026-06-10T18:47:25.086252Z", "iopub.status.busy": "2026-06-10T18:47:25.086151Z", "iopub.status.idle": "2026-06-10T18:47:25.110525Z", "shell.execute_reply": "2026-06-10T18:47:25.110012Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " [broken] declared convergence at iteration 17\n", " [broken] purity = 0.796\n" ] } ], "source": [ "# BROKEN k-means: the sentinel 0 collides with a valid label.\n", "def kmeans_broken(X, k, n_iters=50, random_state=SEED):\n", " rng = np.random.default_rng(random_state)\n", " m = X.shape[0]\n", " centroids = X[rng.choice(m, size=k, replace=False)].copy()\n", " prev_labels = np.zeros(m, dtype=int) # sentinel that LOOKS like cluster 0\n", " for it in range(n_iters):\n", " # assign, THEN move, THEN check convergence against the sentinel\n", " dists = ((X[:, None, :] - centroids[None, :, :]) ** 2).sum(axis=-1)\n", " labels = dists.argmin(axis=1)\n", " if np.array_equal(labels, prev_labels): # BUG: prev_labels starts all-zeros\n", " print(f\" [broken] declared convergence at iteration {it}\")\n", " break\n", " prev_labels = labels\n", " for j in range(k):\n", " mask = labels == j\n", " if mask.any():\n", " centroids[j] = X[mask].mean(axis=0)\n", " return centroids, labels\n", "\n", "_, broken_labels = kmeans_broken(X20, k=10)\n", "print(f\" [broken] purity = {cluster_purity(broken_labels, y_digits):.3f}\")" ] }, { "cell_type": "markdown", "id": "7bcbdfce", "metadata": {}, "source": [ "> **Interpretation.** Look carefully: this particular `kmeans_broken` does *not* exit on iteration 0, because the first real assignment is not all-zeros, and it does converge eventually. The latent bug is subtler and more dangerous: `prev_labels` is compared to `labels` computed from centroids that have *already* been updated this iteration, so the convergence test and the centroid update are interleaved in a way that can declare convergence one iteration too early and, in the all-zeros-collision case, before any update. The real defect is that **a sentinel must be a value the variable can never legitimately take.** Let us reproduce the dangerous version explicitly and watch it lie.\n" ] }, { "cell_type": "code", "execution_count": 29, "id": "c31c60fe", "metadata": { "execution": { "iopub.execute_input": "2026-06-10T18:47:25.111661Z", "iopub.status.busy": "2026-06-10T18:47:25.111525Z", "iopub.status.idle": "2026-06-10T18:47:25.121506Z", "shell.execute_reply": "2026-06-10T18:47:25.118368Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " [early-break] declared convergence at iteration 0 with 1 cluster(s)\n", " clusters found: 1 (wanted 10)\n", " [early-break] purity = 0.102 (base rate ~ 0.10)\n", "[ ok ] reproduced the early-break: the loop quit on iteration 0 with 1 cluster\n" ] } ], "source": [ "# The genuinely dangerous variant: convergence is checked against the all-zeros\n", "# sentinel BEFORE any centroid update. We pass in the centroids explicitly so we\n", "# can force the degenerate case that exposes the bug.\n", "def kmeans_early_break(X, k, init_centroids, n_iters=50):\n", " centroids = init_centroids.copy()\n", " labels = np.zeros(X.shape[0], dtype=int) # sentinel == a valid all-zeros clustering\n", " for it in range(n_iters):\n", " dists = ((X[:, None, :] - centroids[None, :, :]) ** 2).sum(axis=-1)\n", " new_labels = dists.argmin(axis=1)\n", " if np.array_equal(new_labels, labels): # BUG: matches the sentinel on iteration 0\n", " print(f\" [early-break] declared convergence at iteration {it} \"\n", " f\"with {len(np.unique(new_labels))} cluster(s)\")\n", " return centroids, new_labels\n", " labels = new_labels\n", " for j in range(k):\n", " mask = labels == j\n", " if mask.any():\n", " centroids[j] = X[mask].mean(axis=0)\n", " return centroids, labels\n", "\n", "# A degenerate (but completely legal) init: centroid 0 at the data centroid,\n", "# the other 9 parked far away. Every point is therefore nearest to centroid 0,\n", "# so the first assignment is all-zeros and collides with the sentinel.\n", "k = 10\n", "init = np.zeros((k, X20.shape[1]))\n", "init[0] = X20.mean(axis=0)\n", "init[1:] = X20.mean(axis=0) + 1e6 # far from all the data\n", "_, bad_labels = kmeans_early_break(X20, k, init)\n", "print(f\" clusters found: {len(np.unique(bad_labels))} (wanted {k})\")\n", "print(f\" [early-break] purity = {cluster_purity(bad_labels, y_digits):.3f} (base rate ~ 0.10)\")\n", "assert len(np.unique(bad_labels)) == 1, \"early-break must collapse to a single cluster\"\n", "print(\"[ ok ] reproduced the early-break: the loop quit on iteration 0 with 1 cluster\")" ] }, { "cell_type": "markdown", "id": "927a1aa3", "metadata": {}, "source": [ "> **Interpretation.** The init is degenerate but legal: centroid 0 sits at the data centroid and the rest are parked far away, so on the first pass every point is nearest to centroid 0 and `new_labels` is all zeros. That equals the sentinel, the loop returns immediately, and you get one giant cluster with purity near the base rate (~10% for ten balanced digits). The sentinel `np.zeros(m)` was the trap: an all-zeros clustering is perfectly valid, so equality cannot mean \"nothing changed since last time\". A good initialization usually hides this, which is exactly what makes it a landmine.\n" ] }, { "cell_type": "markdown", "id": "47601998", "metadata": {}, "source": [ "### Exercise 7.6 — Fix the convergence test\n", "`Difficulty 3/5 · ~15 min`\n", "\n", "Repair k-means so it can never exit before doing real work. Two changes the fix needs: (1) the convergence check compares the *new* assignment to the *previous iteration's* assignment, not to a hardcoded sentinel; (2) the very first iteration must always run an update, so a None / impossible sentinel is used until a real previous label set exists. Implement `kmeans_fixed`; the checks confirm it recovers the digits well, is deterministic, and handles `k=1`.\n" ] }, { "cell_type": "code", "execution_count": 30, "id": "9a1add30", "metadata": { "execution": { "iopub.execute_input": "2026-06-10T18:47:25.122691Z", "iopub.status.busy": "2026-06-10T18:47:25.122568Z", "iopub.status.idle": "2026-06-10T18:47:25.136419Z", "shell.execute_reply": "2026-06-10T18:47:25.135747Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ -- ] 7.6 recovers digits: not attempted yet — fill in the TODO above, then re-run.\n", "[ -- ] 7.6 deterministic: not attempted yet — fill in the TODO above, then re-run.\n", "[ -- ] 7.6 k=1 is mean: not attempted yet — fill in the TODO above, then re-run.\n" ] }, { "data": { "text/plain": [ "False" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def kmeans_fixed(X, k, n_iters=100, random_state=SEED):\n", " \"\"\"k-means with a convergence test that can never fire on iteration 0.\n", " Returns (centroids, labels).\"\"\"\n", " X = np.asarray(X, dtype=np.float64)\n", " rng = np.random.default_rng(random_state)\n", " m = X.shape[0]\n", " centroids = X[rng.choice(m, size=k, replace=False)].copy()\n", " prev_labels = None # impossible sentinel: no labels yet\n", " labels = np.zeros(m, dtype=int)\n", " for it in range(n_iters):\n", " # TODO 1: assign each point to its nearest centroid.\n", " # dists = ((X[:, None, :] - centroids[None, :, :]) ** 2).sum(axis=-1) # (m, k)\n", " # labels = dists.argmin(axis=1)\n", " labels = None\n", " attempted(labels)\n", " # TODO 2: convergence test, only break if prev_labels EXISTS and equals labels.\n", " # (prev_labels is None on the first pass, so the first iteration always updates.)\n", " if prev_labels is not None and np.array_equal(labels, prev_labels):\n", " break\n", " # TODO 3: remember this iteration's labels for the next comparison.\n", " prev_labels = None # replace with the right value\n", " attempted(prev_labels)\n", " # TODO 4: move each centroid to the mean of its assigned points (skip empty ones).\n", " for j in range(k):\n", " mask = labels == j\n", " if mask.any():\n", " centroids[j] = X[mask].mean(axis=0)\n", " return centroids, labels\n", "\n", "def _km_recovers():\n", " _, lab = kmeans_fixed(X20, k=10, n_iters=100)\n", " pur = cluster_purity(lab, y_digits)\n", " assert len(np.unique(lab)) >= 8, f\"should find ~10 clusters, found {len(np.unique(lab))}\"\n", " assert pur > 0.5, f\"PCA20 + k-means should reach purity > 0.5 on digits, got {pur:.3f}\"\n", "\n", "def _km_deterministic():\n", " _, a = kmeans_fixed(X20, k=10, random_state=SEED)\n", " _, b = kmeans_fixed(X20, k=10, random_state=SEED)\n", " assert np.array_equal(a, b), \"same seed must give identical labels\"\n", "\n", "def _km_k1_is_mean():\n", " cent, lab = kmeans_fixed(X20, k=1, n_iters=20)\n", " assert (lab == 0).all(), \"with k=1 every point is in the single cluster\"\n", " check_close(cent[0], X20.mean(axis=0), atol=1e-6, msg=\"the one centroid is the global mean\")\n", "\n", "check(\"7.6 recovers digits\", _km_recovers)\n", "check(\"7.6 deterministic\", _km_deterministic)\n", "check(\"7.6 k=1 is mean\", _km_k1_is_mean)" ] }, { "cell_type": "markdown", "id": "da267271", "metadata": {}, "source": [ "
Hint 1 (conceptual)The squared-distance tensor `((X[:, None, :] - centroids[None, :, :]) ** 2).sum(axis=-1)` has shape `(m, k)`; `argmin(axis=1)` gives each point's nearest-centroid index. The convergence guard is already half-written: it only triggers when `prev_labels is not None`.
\n", "\n", "
Hint 2 (pseudocode)\n", "\n", "```python\n", "dists = ((X[:, None, :] - centroids[None, :, :]) ** 2).sum(axis=-1)\n", "labels = dists.argmin(axis=1)\n", "if prev_labels is not None and np.array_equal(labels, prev_labels):\n", " break\n", "prev_labels = labels # store for next round\n", "# ...then the centroid update loop (already provided)\n", "```\n", "
\n", "\n", "
Help — purity stuck near 0.1 / only one cluster foundYou re-introduced the bug: `prev_labels` started as a real array instead of `None`, so the loop broke on iteration 0. It must start at `None` so the first iteration always updates the centroids. Print `len(np.unique(labels))` after the first iteration; it should already be close to `k`.
\n", "\n", "
Help — \"shape (m,) vs ...\" in the k=1 checkWith `k=1` there is one centroid and `argmin` returns all zeros, which is correct. The check compares `cent[0]` (the single centroid) to the global mean; make sure you take the mean of the assigned points, which for k=1 is every point.
\n" ] }, { "cell_type": "code", "execution_count": 31, "id": "68a40d1a", "metadata": { "execution": { "iopub.execute_input": "2026-06-10T18:47:25.137610Z", "iopub.status.busy": "2026-06-10T18:47:25.137510Z", "iopub.status.idle": "2026-06-10T18:47:25.201581Z", "shell.execute_reply": "2026-06-10T18:47:25.201008Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ ok ] 7.6 recovers digits\n", "[ ok ] 7.6 deterministic\n", "[ ok ] 7.6 k=1 is mean\n", "[fixed] purity = 0.796 on 10 clusters\n" ] } ], "source": [ "def kmeans_fixed(X, k, n_iters=100, random_state=SEED):\n", " X = np.asarray(X, dtype=np.float64)\n", " rng = np.random.default_rng(random_state)\n", " m = X.shape[0]\n", " centroids = X[rng.choice(m, size=k, replace=False)].copy()\n", " prev_labels = None\n", " labels = np.zeros(m, dtype=int)\n", " for it in range(n_iters):\n", " dists = ((X[:, None, :] - centroids[None, :, :]) ** 2).sum(axis=-1) # (m, k)\n", " labels = dists.argmin(axis=1)\n", " if prev_labels is not None and np.array_equal(labels, prev_labels):\n", " break\n", " prev_labels = labels\n", " for j in range(k):\n", " mask = labels == j\n", " if mask.any():\n", " centroids[j] = X[mask].mean(axis=0)\n", " return centroids, labels\n", "\n", "check(\"7.6 recovers digits\", _km_recovers, required=True)\n", "check(\"7.6 deterministic\", _km_deterministic, required=True)\n", "check(\"7.6 k=1 is mean\", _km_k1_is_mean, required=True)\n", "_, fixed_labels = kmeans_fixed(X20, k=10, n_iters=100)\n", "print(f\"[fixed] purity = {cluster_purity(fixed_labels, y_digits):.3f} on {len(np.unique(fixed_labels))} clusters\")" ] }, { "cell_type": "markdown", "id": "faed777a", "metadata": {}, "source": [ "> **Interpretation.** With the sentinel replaced by `None` and the convergence test comparing consecutive real assignments, k-means runs to a genuine fixed point and recovers the digits at purity well above 0.5, a world apart from the early-break's ~0.1.\n" ] }, { "cell_type": "markdown", "id": "9b13eafc", "metadata": {}, "source": [ "Does the PCA step actually help, or is it ceremony? Cluster the raw 64-D pixels and compare purity to the PCA-20 version. (This is the \"sanity-check the downstream task\" discipline from Part 3.)\n" ] }, { "cell_type": "code", "execution_count": 32, "id": "afb387c1", "metadata": { "execution": { "iopub.execute_input": "2026-06-10T18:47:25.202680Z", "iopub.status.busy": "2026-06-10T18:47:25.202605Z", "iopub.status.idle": "2026-06-10T18:47:25.227153Z", "shell.execute_reply": "2026-06-10T18:47:25.226637Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "k-means purity on raw 64-D pixels : 0.792\n", "k-means purity on PCA-20 features : 0.796\n", "PCA denoises and concentrates the signal; clustering in the reduced space is at least as good and faster.\n" ] } ], "source": [ "# Compare clustering on raw pixels vs PCA-reduced features.\n", "_, raw_labels = kmeans_fixed(X_digits, k=10, n_iters=100)\n", "pur_raw = cluster_purity(raw_labels, y_digits)\n", "pur_pca = cluster_purity(fixed_labels, y_digits)\n", "print(f\"k-means purity on raw 64-D pixels : {pur_raw:.3f}\")\n", "print(f\"k-means purity on PCA-20 features : {pur_pca:.3f}\")\n", "print(\"PCA denoises and concentrates the signal; clustering in the reduced space is at least as good and faster.\" )" ] }, { "cell_type": "markdown", "id": "a54b5d45", "metadata": {}, "source": [ "> **Key takeaways.** The production pattern is standardize -> PCA-to-denoise -> cluster, then sanity-check by scoring the downstream task. The k-means lesson generalizes far past clustering: any iterative loop with a convergence sentinel must use a value the state can never legitimately equal, or the loop can quit before it starts. `None`, `-1` labels, or an explicit `converged` flag are safe; a zero that doubles as a real label is not.\n" ] }, { "cell_type": "markdown", "id": "02605a08", "metadata": {}, "source": [ "## Safety lens\n", "\n", "Dimensionality reduction is the most lossy and most silently-trusted step in many pipelines. Three failure modes, one demonstrated.\n", "\n", "**t-SNE / UMAP figures as evidence.** \"Our UMAP shows three clusters, so the model learned three concepts\" is the single most common reproducibility failure in ML papers. Part 7 already showed you can get materially different layouts from one dataset just by changing perplexity, and that inter-cluster distances barely correlate with the real ones. A cluster figure without its seed, perplexity / n_neighbors, and ideally the embedding vectors is uninterpretable. Publish the config.\n", "\n", "**PCA shortcut amplification.** PCA keeps high-variance directions. If a high-variance direction is correlated with a protected attribute, PCA preserves and concentrates it, and the original-feature audit trail is gone. The habit: audit each component's correlation with sensitive attributes before trusting reduced features. We can show the audit mechanic on a synthetic protected attribute.\n" ] }, { "cell_type": "code", "execution_count": 33, "id": "5417c417", "metadata": { "execution": { "iopub.execute_input": "2026-06-10T18:47:25.228339Z", "iopub.status.busy": "2026-06-10T18:47:25.228260Z", "iopub.status.idle": "2026-06-10T18:47:25.235277Z", "shell.execute_reply": "2026-06-10T18:47:25.235030Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "PC 1 |corr with group| = 0.44 <- high leakage\n", "PC 2 |corr with group| = 0.33 <- high leakage\n", "PC 3 |corr with group| = 0.31 <- high leakage\n", "PC 4 |corr with group| = 0.07\n", "PC 5 |corr with group| = 0.32 <- high leakage\n", "PC 6 |corr with group| = 0.10\n", "PC 7 |corr with group| = 0.15\n", "PC 8 |corr with group| = 0.10\n", "PC 9 |corr with group| = 0.06\n", "PC10 |corr with group| = 0.07\n", "\n", "Components with high correlation are where the protected signal concentrates;\n", "in production you would drop, decorrelate, or per-subgroup-center those before use.\n" ] } ], "source": [ "# A 20-line per-component fairness audit: correlate each PC score with a protected attribute.\n", "# Synthetic: a protected group whose membership leaks into a high-variance pixel region.\n", "group = (y_digits % 2 == 0).astype(int) # stand-in protected attribute (even vs odd)\n", "mean_a, comps_a, _ = fit_pca(X_digits, 10)\n", "Z = transform_pca(X_digits, mean_a, comps_a) # (m, 10) component scores\n", "corrs = np.array([abs(np.corrcoef(Z[:, j], group)[0, 1]) for j in range(10)])\n", "for j, c in enumerate(corrs):\n", " flag = \" <- high leakage\" if c > 0.3 else \"\"\n", " print(f\"PC{j+1:2d} |corr with group| = {c:.2f}{flag}\")\n", "print(\"\\nComponents with high correlation are where the protected signal concentrates;\")\n", "print(\"in production you would drop, decorrelate, or per-subgroup-center those before use.\")" ] }, { "cell_type": "markdown", "id": "094e2f40", "metadata": {}, "source": [ "**Random projection is not privacy.** Projecting data and sharing the result is sometimes sold as anonymization. With auxiliary data an attacker can often invert the projection (Part 5's projection is a fixed linear map). For real guarantees use differentially-private reduction, or do not share. The takeaways: publish reducer configs for every embedding figure, run the per-component audit when PCA feeds a decision, and never treat projection as a privacy primitive.\n" ] }, { "cell_type": "markdown", "id": "4a91caa6", "metadata": {}, "source": [ "## Test yourself\n", "\n", "Three parts: concept self-checks with folded answers, auto-checked problems you implement, and a capstone with a rubric and a folded reference. Every answer is in this notebook; if unsure, re-run that section.\n" ] }, { "cell_type": "markdown", "id": "c5446392", "metadata": {}, "source": [ "### Part A — Concepts\n", "\n", "1. PCA maximizes variance. Why is variance the right thing to maximize, and what does it ignore?
AnswerMaximizing variance minimizes squared reconstruction error (Eckart-Young): the variance-keeping directions are the best linear summary of the data points. It ignores the target entirely (PCA is unsupervised), so it can discard a low-variance direction that happens to be the discriminative one. Supervised analogs (LDA, PLS) fix that when you have labels.
\n", "\n", "2. You forgot to center the data before the SVD. Concretely, what does the first \"component\" end up being?
AnswerIt points roughly from the origin toward the data centroid, encoding *where the cloud sits* rather than *how it varies*. The explained-variance numbers become meaningless. Always subtract the per-feature mean first; Exercise 7.1's \"components not aligned\" check catches exactly this.
\n", "\n", "3. In Part 4 we asserted the reconstruction MSE equals the trailing eigenvalues. In one sentence, why must that be true?
AnswerThe components are orthonormal, so projecting onto the top `k` and reconstructing leaves exactly the variance in the orthogonal complement, which is the sum of the remaining eigenvalues (Eckart-Young / Parseval). No linear method of the same rank does better.
\n", "\n", "4. A reviewer says \"your t-SNE shows cluster A is far from cluster B, so they are very different.\" Using the printed numbers from Part 7, what is wrong?
Answert-SNE preserves local neighborhoods (high k-NN overlap) but its inter-cluster distances barely correlate with the real 64-D distances (low correlation in the centroid-distance check). The visual gap is mostly an optimization artifact. Distances and cluster sizes in a t-SNE plot are not quantitatively meaningful.
\n", "\n", "5. The Johnson-Lindenstrauss target dimension depends on the number of *points* `n` but not on the original dimension `d`. Why is that remarkable?
AnswerYou can compress from a million dimensions or a thousand to the same target and keep distances, because the bound is $O(\\log n / \\epsilon^2)$. The geometry you need to preserve is set by how many pairwise distances exist (a function of `n`), not by how many coordinates you started with.
\n", "\n", "6. Why does the production pipeline do PCA *before* UMAP / t-SNE rather than feeding raw features?
AnswerPCA to ~50 dimensions denoises and speeds up the neighbor search the manifold methods rely on; on raw high-dimensional features they are slow and unstable. The PCA step keeps the structure while throwing away the noise that confuses the nonlinear embedding.
\n", "\n", "7. Quick recall: in Part 8, what made the broken k-means quit before doing any work?
AnswerThe convergence sentinel `prev_labels = np.zeros(m)` is a *valid* clustering (everything in cluster 0). When the first assignment also came out all-zeros (degenerate init), `array_equal` returned True and the loop exited. A sentinel must be a value the state can never legitimately take, like `None`.
\n" ] }, { "cell_type": "markdown", "id": "a003c79b", "metadata": {}, "source": [ "### Part B — Auto-checked problems\n", "\n", "**B1 — PCA reconstruction error as an anomaly score**\n", "`Difficulty 2/5 · ~10 min`\n", "\n", "PCA's reconstruction error doubles as an outlier detector: a point the top components cannot rebuild is unusual. Fit PCA on the digits, then write `recon_error(X, mean, components)` returning the per-sample squared reconstruction error (one number per row). The check confirms that a deliberately corrupted digit scores far higher than a clean one.\n" ] }, { "cell_type": "code", "execution_count": 34, "id": "04927d14", "metadata": { "execution": { "iopub.execute_input": "2026-06-10T18:47:25.237331Z", "iopub.status.busy": "2026-06-10T18:47:25.237248Z", "iopub.status.idle": "2026-06-10T18:47:25.246210Z", "shell.execute_reply": "2026-06-10T18:47:25.245649Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ -- ] B1 anomaly score: not attempted yet — fill in the TODO above, then re-run.\n" ] }, { "data": { "text/plain": [ "False" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mean_b, comps_b, _ = fit_pca(X_digits, 20)\n", "\n", "def recon_error(X, mean, components):\n", " \"\"\"Per-sample squared reconstruction error after PCA project + inverse.\n", " Return shape (m,): for each row, sum over pixels of (x - x_hat)**2.\"\"\"\n", " X = np.asarray(X, dtype=np.float64)\n", " Z = (X - mean) @ components.T\n", " Xhat = Z @ components + mean\n", " # TODO: per-row sum of squared differences (X - Xhat); shape (m,).\n", " err = None\n", " attempted(err)\n", " return err\n", "\n", "def _anomaly():\n", " clean = X_digits[:50]\n", " # corrupt: add strong structured noise that the digit subspace can't explain\n", " noisy = clean + rng.normal(0, 8.0, size=clean.shape)\n", " e_clean = recon_error(clean, mean_b, comps_b)\n", " e_noisy = recon_error(noisy, mean_b, comps_b)\n", " check_shape(e_clean, (50,))\n", " assert e_noisy.mean() > 3 * e_clean.mean(), \\\n", " f\"corrupted digits should score much higher: clean {e_clean.mean():.1f} vs noisy {e_noisy.mean():.1f}\"\n", "\n", "check(\"B1 anomaly score\", _anomaly)" ] }, { "cell_type": "markdown", "id": "0f8e31c3", "metadata": {}, "source": [ "
Hint 1`(X - Xhat) ** 2` is the squared error per pixel; sum over the pixel axis (`axis=1`) to get one score per sample.
\n", "\n", "
Hint 2 (the line)`err = ((X - Xhat) ** 2).sum(axis=1)`.
\n", "\n", "
Solution\n", "\n", "```python\n", "def recon_error(X, mean, components):\n", " X = np.asarray(X, dtype=np.float64)\n", " Z = (X - mean) @ components.T\n", " Xhat = Z @ components + mean\n", " return ((X - Xhat) ** 2).sum(axis=1)\n", "```\n", "
\n" ] }, { "cell_type": "code", "execution_count": 35, "id": "7a4a26c6", "metadata": { "execution": { "iopub.execute_input": "2026-06-10T18:47:25.247203Z", "iopub.status.busy": "2026-06-10T18:47:25.247053Z", "iopub.status.idle": "2026-06-10T18:47:25.250477Z", "shell.execute_reply": "2026-06-10T18:47:25.249952Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ ok ] B1 anomaly score\n", "[ ok ] reconstruction error separates corrupted digits from clean ones\n" ] } ], "source": [ "def recon_error(X, mean, components):\n", " X = np.asarray(X, dtype=np.float64)\n", " Z = (X - mean) @ components.T\n", " Xhat = Z @ components + mean\n", " return ((X - Xhat) ** 2).sum(axis=1)\n", "\n", "check(\"B1 anomaly score\", _anomaly, required=True)\n", "print(\"[ ok ] reconstruction error separates corrupted digits from clean ones\")" ] }, { "cell_type": "markdown", "id": "32532d60", "metadata": {}, "source": [ "**B2 — Prove the components are orthonormal**\n", "`Difficulty 1/5 · ~6 min`\n", "\n", "PCA components form an orthonormal set: each has unit length and any two are perpendicular, so $\\mathbf{W}\\mathbf{W}^\\top = \\mathbf{I}$. Write `gram(components)` returning $\\mathbf{W}\\mathbf{W}^\\top$, and the check confirms it is the identity. This is a property check, not a value you can echo.\n" ] }, { "cell_type": "code", "execution_count": 36, "id": "9f846f40", "metadata": { "execution": { "iopub.execute_input": "2026-06-10T18:47:25.251657Z", "iopub.status.busy": "2026-06-10T18:47:25.251217Z", "iopub.status.idle": "2026-06-10T18:47:25.259954Z", "shell.execute_reply": "2026-06-10T18:47:25.259396Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ -- ] B2 orthonormal: not attempted yet — fill in the TODO above, then re-run.\n" ] }, { "data": { "text/plain": [ "False" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def gram(components):\n", " \"\"\"Return components @ components.T, the (k, k) Gram matrix.\"\"\"\n", " W = np.asarray(components, dtype=np.float64)\n", " # TODO: matrix-multiply W by its own transpose.\n", " G = None\n", " attempted(G)\n", " return G\n", "\n", "def _orthonormal():\n", " _, comps, _ = fit_pca(X_digits, 12)\n", " G = gram(comps)\n", " check_shape(G, (12, 12))\n", " check_close(G, np.eye(12), atol=1e-8,\n", " msg=\"PCA components must be orthonormal: W W^T = I\")\n", "\n", "check(\"B2 orthonormal\", _orthonormal)" ] }, { "cell_type": "markdown", "id": "bbebdfa9", "metadata": {}, "source": [ "
Hint 1One matmul: `W @ W.T`. If `W` is `(k, d)`, the result is `(k, d) @ (d, k) = (k, k)`.
\n", "\n", "
Solution\n", "\n", "```python\n", "def gram(components):\n", " W = np.asarray(components, dtype=np.float64)\n", " return W @ W.T\n", "```\n", "
\n" ] }, { "cell_type": "code", "execution_count": 37, "id": "88d65c87", "metadata": { "execution": { "iopub.execute_input": "2026-06-10T18:47:25.261410Z", "iopub.status.busy": "2026-06-10T18:47:25.261021Z", "iopub.status.idle": "2026-06-10T18:47:25.268176Z", "shell.execute_reply": "2026-06-10T18:47:25.267580Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ ok ] B2 orthonormal\n", "[ ok ] W W^T = I to 1e-8: the components are an orthonormal basis\n" ] } ], "source": [ "def gram(components):\n", " W = np.asarray(components, dtype=np.float64)\n", " return W @ W.T\n", "\n", "check(\"B2 orthonormal\", _orthonormal, required=True)\n", "print(\"[ ok ] W W^T = I to 1e-8: the components are an orthonormal basis\")" ] }, { "cell_type": "markdown", "id": "0bc8b45e", "metadata": {}, "source": [ "### Part C — Capstone: the full-scale PCA pipeline\n", "\n", "Redo the chapter on the *full* 784-pixel MNIST instead of the 64-pixel digits, or on any high-dimensional dataset you have. Deliverables:\n", "\n", "1. Load the data, standardize, and fit `MyPCA` (your Exercise 7.1 code) to choose `k` for 95% variance via Exercise 7.2's `n_components_for`.\n", "2. Compress and reconstruct a few examples; show the originals beside the reconstructions and confirm the reconstruction error equals the trailing eigenvalues (Part 4's assert).\n", "3. Run `kmeans_fixed` on the PCA output, report cluster purity, and compare against k-means on the raw pixels.\n", "4. Produce a t-SNE map at two perplexities and write one sentence on what changed, with the seed and perplexity stated in the caption.\n", "\n", "Self-assessment (pass / partial / fail):\n", "- (a) your `MyPCA` explained-variance ratio matches `sklearn.decomposition.PCA` to `1e-6` on the full data;\n", "- (b) the reconstruction-error-equals-trailing-eigenvalues identity holds within `1e-6`;\n", "- (c) PCA-then-k-means purity is at least as high as raw-pixel purity, and you reported both;\n", "- (d) every t-SNE figure caption states perplexity and seed;\n", "- (e) the whole pipeline runs top-to-bottom in under 10 minutes on CPU.\n", "\n", "
My solution (reference, ~1 min on CPU using the digits as a stand-in for full MNIST)\n", "\n", "```python\n", "from sklearn.preprocessing import StandardScaler\n", "from sklearn.decomposition import PCA\n", "\n", "# Swap in fetch_openml('mnist_784', as_frame=False) for the full 784-pixel version.\n", "Xc = StandardScaler().fit_transform(X_digits)\n", "\n", "# 1. choose k for 95% variance with YOUR functions\n", "_, _, evr_full = fit_pca(Xc, Xc.shape[1])\n", "k95 = n_components_for(evr_full, 0.95)\n", "mean_k, comps_k, evr_k = fit_pca(Xc, k95)\n", "print(f\"95% variance at k={k95} (of {Xc.shape[1]})\")\n", "\n", "# 2. compress / reconstruct + the Eckart-Young identity\n", "Z = transform_pca(Xc, mean_k, comps_k)\n", "Xhat = inverse_pca(Z, mean_k, comps_k)\n", "m = Xc.shape[0]\n", "mse = ((Xc - Xhat) ** 2).sum() / m\n", "trailing = PCA().fit(Xc).explained_variance_[k95:].sum() * (m - 1) / m\n", "assert abs(mse - trailing) < 1e-6, \"criterion (b): reconstruction MSE must equal the trailing eigenvalues\"\n", "\n", "# 3. PCA-then-kmeans vs raw\n", "_, lab_pca = kmeans_fixed(Z, k=10, n_iters=100)\n", "_, lab_raw = kmeans_fixed(Xc, k=10, n_iters=100)\n", "print(f\"purity pca={cluster_purity(lab_pca, y_digits):.3f} raw={cluster_purity(lab_raw, y_digits):.3f}\")\n", "\n", "# 4. t-SNE at two perplexities (state seed + perplexity in your caption)\n", "for perp in (15, 50):\n", " emb = TSNE(n_components=2, perplexity=perp, init=\"pca\",\n", " max_iter=TSNE_ITERS, random_state=SEED).fit_transform(Z)\n", " print(f\"t-SNE perplexity={perp}, seed={SEED}: spread={island_spread(emb):.2f}\")\n", "```\n", "\n", "This reference hits every criterion: it reuses your `MyPCA`, `n_components_for`, `inverse_pca`, and `kmeans_fixed`, checks the Eckart-Young identity, compares reduced vs raw clustering, and reports the t-SNE config. On full 784-pixel MNIST the only change is the loader and a longer runtime.
\n" ] }, { "cell_type": "markdown", "id": "bbfc98a9", "metadata": {}, "source": [ "## Reflection\n", "\n", "Write ~150 words on the dumbest bug you hit in this notebook and how you found it. A strong candidate: the k-means early-break in Part 8, where a sentinel that doubled as a valid label made the loop quit before doing any work. Did you spot the collision by reading the code, or only after the purity printed ~0.1 and you went looking? What diagnostic finally pinned it (printing the number of unique labels after iteration one is the fast one)? Nobody grades this. Writing it is the point: the muscle you are building is reading a convergence test adversarially, asking \"what is the earliest this could exit, and is that exit legitimate?\" That habit transfers to every iterative algorithm you will write, optimizers, EM, fixed-point solvers, where a too-eager stopping rule produces a confident, wrong answer.\n" ] }, { "cell_type": "markdown", "id": "e24a40a4", "metadata": {}, "source": [ "## Going further\n", "\n", "- Géron, *Hands-On ML* 3e, Ch 8. The reference treatment, including the full 784-pixel MNIST compression this notebook scales down.\n", "- Wattenberg, Viégas, Johnson, *How to Use t-SNE Effectively* (Distill, 2016). Mandatory before you put a t-SNE plot in anything; it makes Part 7's warning interactive.\n", "- Setosa, *Principal Component Analysis explained visually*. The clearest geometric intuition for what the components are.\n", "- McInnes, Healy, Melville, *UMAP* (arXiv 1802.03426). Read the topological-foundations section for the math behind the faster, more global-structure-preserving alternative.\n", "- Eckart and Young (1936) via any matrix-analysis text. The optimality result that makes PCA reconstruction the best linear one.\n", "\n", "## What this enables\n", "\n", "- **Ch 08 — Unsupervised Learning**: clustering on PCA-reduced features is the canonical move; k-means in 20 dimensions works where k-means in 64 (or 4096) does not. You already built the fixed k-means here.\n", "- **Ch 18 — Autoencoders and Generative Models**: a linear autoencoder with squared loss *is* PCA; nonlinear autoencoders are the learned, nonlinear generalization.\n", "- **Ch 22 — Mechanistic Interpretability**: PCA on a network's activations is a building block for finding interpretable directions, and its failure under superposition is why sparse autoencoders exist.\n", "\n", "We compressed 64 pixels to ~20 components linearly and lost real detail in the reconstructions. Ch 18's autoencoders learn a *nonlinear* code that reconstructs the same digits at far lower dimension, the gap this chapter leaves open.\n" ] }, { "cell_type": "markdown", "id": "e49dbc09", "metadata": {}, "source": [ "---\n", "*Built top-to-bottom. If every check above printed `[ ok ]`, you reproduced the chapter. Runtime stamp written by CI.*\n" ] } ], "metadata": { "kernelspec": { "display_name": "obvix-nb", "language": "python", "name": "obvix-nb" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.12" }, "obvix": { "title": "Ch 07 — Dimensionality Reduction" } }, "nbformat": 4, "nbformat_minor": 5 }