\n", "\n", "

\n",
"Following Section 8.3.1 [Müller, FMP, Springer 2015], we cover in this notebook a technique known as nonnegative matrix factorization (NMF). The formal definition of the NMF problem and an iterative learning procedure for computing a factorization in practice was first described by Lee and Seoung. Implementations and applications for NMF can also be found in the **NMF Toolbox**. \n",
"\n",
"

- \n",
"
- \n",
"Daniel D. Lee, H. Sebastian Seung:
**Algorithms for Non-negative Matrix Factorization.**Proceedings of the Neural Information Processing Systems (NIPS), Denver, CO, USA, pp. 556–562, 2000.\n", "

\n", " Bibtex \n", " \n",
" - \n",
"Patricio López-Serrano, Christian Dittmar, Yigitcan Özer, and Meinard Müller:
**NMF Toolbox: Music processing applications of nonnegative matrix factorization.**Proceedings of the International Conference on Digital Audio Effects (DAFx), Birmingham, UK, 2019.\n", "

\n", " Bibtex \n", "MATLAB and Python Toolbox\n", " \n",
"

\n", "\n", "\n", "\n", "As for the original data matrix $V$, we use the [magnitude STFT](../C2/C2_STFT-Basic.html), which is a sequence of spectral vectors. Using NMF, this matrix can be factorized into a product of two nonnegative matrices $W$ and $H$. In the ideal case, the first matrix $W$ represents the spectral patterns of the notes' pitches that occur in the piece of music, while the second matrix $H$ exhibits the time positions where these spectral patterns are active in the audio recording. The following figure shows such a factorization for our Chopin example.\n", "\n", "\n", "\n", "In this case, each template specified by the matrix $W$ reflects how a note of a certain pitch is spectrally realized in $V$, and the activation matrix $H$ looks similar to the piano-roll representation of the score. In practice, however, it is often hard to predict which of the signal's properties are ultimately captured by the learned factors. \n", "To better control this factorization, we will show how additional score information can be used to [constrain NMF](../C8/C8S3_NMFAudioDecomp.html) to yield a musically meaningful decomposition. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Formal Definition of NMF\n", "\n", "A matrix with real-valued coefficients is called **nonnegative** if all the coefficients are either zero or positive. Let $V \\in \\mathbb{R}_{\\ge 0}^{K \\times N}$ be such a nonnegative matrix having $K\\in\\mathbb{N}$ rows and $N\\in\\mathbb{N}$ columns. The dimensions $K$ and $N$ of the matrix $V$ are usually thought to be large. Given a number $R\\in\\mathbb{N}$ smaller than both $K$ and $N$, the goal of NMF is to find two nonnegative matrices $W \\in \\mathbb{R}_{\\ge 0}^{K \\times R}$ and $H \\in \\mathbb{R}_{\\ge 0}^{R \\times N}$ such that \n", "\n", "\\begin{equation}\n", " V \\approx W \\cdot H.\n", "\\end{equation}\n", "\n", "As said above, the columns of $V$ are regarded as $K$-dimensional data vectors, where $N$ is the number of data vectors. This matrix is then approximately factorized into a $(K \\times R)$ matrix $W$ and an $(R \\times N)$ matrix $H$. The parameter $R$, which is referred to as the **rank** of the factorization, is usually chosen to be much smaller than $K$ and $N$. Therefore, the number of coefficients in $W$ and $H$ is typically much smaller than the total number in $V$ (i.e., $KR+RN \\ll KN$), and the product $WH$ can be thought of as a compressed version of the original matrix $V$. As already mentioned before, the column vectors of $W$ are also referred to as **template vectors**, whereas the weights specified by $H$ are called **activations**. As opposed to arbitrary linear combinations as known from linear algebra, the linear combinations occurring in the NMF context only involve nonnegative weights of nonnegative template vectors. As a result, there are no effects such as destructive interferences, where a (positive) component can be canceled out by adding a kind of inverse (negative) component. Instead, the data vectors need to be explained in a purely constructive fashion only involving positive components.\n", "\n", "To find an approximate factorization $V \\approx W \\cdot H$, we need to specify a distance function that quantifies the \n", "quality of the approximation. There are many ways for defining such a distance function, leading to different NMF variants. In the following, we only consider one of these variants, which is based on the **Euclidean distance**. Let $A,B\\in\\mathbb{R}^{K \\times N}$ be two matrices with coefficients $A_{kn}$ and $B_{kn}$\n", "for $k\\in[1:K]$ and $n\\in[1:N]$. Then, the square of the Euclidean distance between $A$ and $B$ is defined by\n", "\n", "\\begin{equation}\n", " \\|A-B\\|^2:= \\sum_{k=1}^{K}\\sum_{n=1}^{N}(A_{kn}-B_{kn})^2.\n", "\\end{equation}\n", "\n", "Based on this distance measure, we can formalize our NMF problem as follows: Given a nonnegative matrix $V\\in\\mathbb{R}_{\\ge 0}^{K \\times N}$ and a rank parameter $R$, minimize\n", "\n", "\\begin{equation}\n", " \\|V-WH\\|^2\n", "\\end{equation}\n", "\n", "with respect to $W \\in \\mathbb{R}_{\\ge 0}^{K \\times R}$ and $H \\in \\mathbb{R}_{\\ge 0}^{R \\times N}$. In other words, regarding $\\|V-WH\\|^2$ as a joint function of $W$ and $H$, the objective is to find a minimum under the nonnegativity constraint for $W$ and $H$. For general matrices, this is a hard computational problem due to several reasons. First, it is in general difficult to enforce hard constraints such as nonnegativity on the solution of an optimization problem. Second, the joint optimization over both matrices $W$ and $H$ leads to computational challenges. In fact, when regarding $\\|V-WH\\|^2$ as a function of $W$ only or $H$ only, one can show that the resulting functions satisfy a strong property referred to as **convexity**. This property, which implies that any local minimum must be a global minimum, makes it possible to apply powerful tools from the field of convex analysis. However, $\\|V-WH\\|^2$ is **not convex** in both matrices together. Therefore, it is unrealistic to expect an algorithm that can solve this problem in the sense of finding a global minimum. However, there are many techniques from numerical optimization that can be applied to find local minima." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Multiplicative Update Rules\n", "\n", "Lee and Seung introduced in their seminal paper a powerful algorithm based on multiplicative update rules to iteratively learn a nonnegative matrix factorization. In the following, we only summarize their algorithm and refer to their paper or Section 8.3.1 of [Müller, FMP, Springer 2015] for a proof. The idea is based on the standard gradient descent approach, which is applied to our problem of minimizing $\\|V-WH\\|^2$ as a function of $W$ and $H$. Since the joint optimization is a very hard problem, one idea is to first fix the factor $W$ and to optimize with regard to $H$, and then to fix the learned factor $H$ and to optimize with regard to $W$. This process is then iterated, where the role of $W$ and $H$ is interchanged after each step. In standard gradient descent the update rules are additive, where a parameter needs to be chosen to control the **step size** towards the direction of the negative gradient. The main trick in the NMF optimization algorithm is that this step size parameter can be set in a specific way so that the **additive** update rules become **multiplicative** update rules. The following table shows the iterative algorithm for learning an NMF decomposition., where the multiplicative update rules are given in matrix notation. The operator $\\odot$ denotes pointwise multiplication and the operator $\\oslash$ pointwise division. \n", "\n", "\n", "\n", "The multiplicative update rules and their properties have a number of remarkable implications.\n", "\n", "* The first implication is that the matrix sequences $W^{(0)},W^{(1)},W^{(2)},\\ldots$ and $H^{(0)},H^{(1)},H^{(2)},\\ldots$ converge. Denoting the limit matrices by $W^{(\\infty)}$ and $H^{(\\infty)}$, the stationarity property implies that these matrices form a local minimum of the distance function $\\|V-WH\\|^2$.\n", "* Second, the multiplicative update rules are extremely easy to implement. \n", "* Third, in practice, the convergence turns out to be relatively fast in comparison with many other methods.\n", "* Fourth, one major benefit of using multiplicative update rules is that the nonnegativity constraints are enforced automatically.\n", "\n", "Indeed, starting with nonnegative matrices $V$, $W^{(0)}$, and $H^{(0)}$, all entries in the equations (1) and (2) of the above table are also nonnegative. Since all operations are multiplicative (either multiplication or division), also the matrices $W^{(\\ell)}$ and $H^{(\\ell)}$ remain nonnegative throughout the iteration.\n", "\n", "In practice, the iteration is performed until a specified stop criterion is fulfilled. For example, one may perform a certain number of iterations $\\ell=0,1,2,\\ldots, L$ for some user-specified parameter $L\\in\\mathbb{N}$. As another stop criterion, one may look at the distances between two subsequently computed template matrices and activation matrices. Specifying a threshold $\\varepsilon>0$, the iteration may be stopped when $\\|H^{(\\ell+1)}-H^{(\\ell)}\\|^2\\leq \\varepsilon$ and $\\|W^{(\\ell+1)}-W^{(\\ell)}\\|^2\\leq \\varepsilon$. Note that this stop criterion does not say anything about the quality of the approximation $V\\approx WH$ achieved by the procedure. Even in the limit case and even when converging to the global minimum (and not to a local one), the distance $\\|V-WH\\|^2$ may still be large. In particular, this may happen if the rank parameter $R$ is chosen too small." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Implementation\n", "\n", "In the following code cell, we provide a basic implementation that closely follows the NMF procedure described above. Here are some important notes:\n", "\n", "* All operation are performed using matrix-based operations.\n", "* To avoid devision by zero, a small value (machine epsilon) is added to the denominators in the multiplicative update rules.\n", "* In the factorization $V\\approx WH$, there is a degree of freedom with regard to columns and rows of $W$ and $H$, respectively. For example, one may divide a column of $W$ by a factor $\\alpha\\in\\mathbb{R}$ and multiply the correspond row of $H$ by the same factor without changing the product $WH$. In the following code, setting the parameter `norm=True`, we use this fact to enforce that all columns of the final template matrix $W$ are normalized with regard to the [maximum norm](../C3/C3S1_FeatureNormalization.html).\n", "* If not specified, the matrices $W$ and $H$ are initialized randomly. The power of NMF lies in the possibility of guiding the decomposition process by [initializing the matrices in a musically informed way](../C8/C8S3_NMFAudioDecomp.html)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import os, sys\n", "import numpy as np\n", "import scipy\n", "#import scipy.spatial\n", "import matplotlib.pyplot as plt\n", "import IPython.display as ipd\n", "import librosa, librosa.display\n", "#from matplotlib import gridspec\n", "from numba import jit\n", "\n", "sys.path.append('..')\n", "import LibFMP.B\n", "import LibFMP.C2\n", "import LibFMP.C6\n", "%matplotlib inline\n", "\n", "@jit(nopython=True)\n", "def NMF(V, R, thresh=0.001, L=1000, W=None, H=None, norm=False, report=False):\n", " \"\"\"NMF algorithm with Euclidean distance\n", " \n", " Notebook: C8/C8S3_NMFbasic.ipynb\n", " \n", " Args: \n", " V: Nonnegative matrix of size K x N\n", " R: Rank parameter\n", " thresh: Threshold used as stop criterion\n", " L: Maximal number of iteration\n", " W: Nonnegative matrix of size K x R used for initialization\n", " H: Nonnegative matrix of size R x N used for initialization\n", " norm (bool): Applies max-normalization of columns of final W\n", " report (bool): Reports errors during runtime\n", " \n", " Returns: \n", " W: Nonnegative matrix of size K x R\n", " H: Nonnegative matrix of size R x N\n", " V_approx: Nonnegative matrix W*H of size K x N\n", " V_approx_err: Error between V and V_approx\n", " H_W_error: History of errors of subsequent H and W matrices\n", " \"\"\" \n", " K = V.shape[0]\n", " N = V.shape[1]\n", " if W is None:\n", " W = np.random.rand(K,R)\n", " if H is None:\n", " H = np.random.rand(R,N)\n", " V = V.astype(np.float64)\n", " W = W.astype(np.float64)\n", " H = H.astype(np.float64) \n", " H_W_error = np.zeros((2,L))\n", " ell = 1\n", " below_thresh = False\n", " eps_machine = np.finfo(np.float32).eps\n", " while not below_thresh and ell <= L:\n", " H_ell = H\n", " W_ell = W \n", " H = H * ( W.transpose().dot(V) / (W.transpose().dot(W).dot(H)+ eps_machine) )\n", " W = W * ( V.dot(H.transpose()) / (W.dot(H).dot(H.transpose())+ eps_machine) )\n", " #H = np.multiply( H, np.divide( np.matmul(np.transpose(W), V), np.matmul(np.matmul(np.transpose(W), W), H))) #H+1 = H *p ((W^T * V) /p (W^T * W * H))\n", " #W = np.multiply( W, np.divide( np.matmul(V, np.transpose(H)), np.matmul(np.matmul(W, H), np.transpose(H)))) # W+1 = W *p ((V * H^T) /p (W * H * H^T)) \n", " H_error = np.linalg.norm(H-H_ell, ord=2)\n", " W_error = np.linalg.norm(W - W_ell, ord=2) \n", " H_W_error[:, ell-1] = [H_error, W_error]\n", " if report:\n", " print('Iteration: ',ell,', H_error: ',H_error,', W_error: ',W_error) \n", " if H_error < thresh and W_error < thresh:\n", " below_thresh = True\n", " H_W_error = H_W_error[:,0:ell]\n", " ell += 1 \n", " if norm: \n", " for r in range(R):\n", " v_max = np.max(W[:,r])\n", " if v_max > 0:\n", " W[:,r] = W[:,r] / v_max\n", " H[r,:] = H[r,:] * v_max \n", " V_approx = W.dot(H)\n", " V_approx_err = np.linalg.norm(V-V_approx, ord=2)\n", " return W, H, V_approx, V_approx_err, H_W_error " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Toy Example\n", "\n", "We illustrate the functioning of the NMF procedure by means of a small toy example $V \\in \\mathbb{R}_{\\ge 0}^{K \\times N}$ with $K=4$ and $N=8$. The rank parameter is set to $R=2$." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Matrix V and randomly initialized matrices W and H\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "

"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Matrix V and matrices W and H after training\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
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},
"metadata": {
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},
"output_type": "display_data"
},
{
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\n",
"text/plain": [
"

"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
" def plot_NMF(V, W, H, V_approx, error, figsize=(10,2), aspect='auto', wr=[1, 0.5, 1, 1]): \n",
" fig, ax = plt.subplots(1, 4, gridspec_kw={'width_ratios': wr},\n",
" figsize=figsize) \n",
" cmap = 'gray_r'\n",
" im = ax[0].imshow(V, aspect=aspect, origin='lower', cmap=cmap, clim=[0, np.max(V)])\n",
" ax[0].set_title(r'$V$')\n",
" plt.sca(ax[0])\n",
" plt.colorbar(im) \n",
" im = ax[1].imshow(W, aspect=aspect, origin='lower', cmap=cmap, clim=[0, np.max(W)])\n",
" ax[1].set_title(r'$W$')\n",
" plt.sca(ax[1])\n",
" plt.colorbar(im)\n",
" im = ax[2].imshow(H, aspect=aspect, origin='lower', cmap=cmap, clim=[0, np.max(H)])\n",
" ax[2].set_title(r'$H$')\n",
" plt.sca(ax[2]) \n",
" plt.colorbar(im)\n",
" im = ax[3].imshow(V_approx, aspect=aspect, origin='lower', cmap=cmap, clim=[0, np.max(V_approx)])\n",
" ax[3].set_title(r'$WH$ (error = %0.2f)'%error)\n",
" plt.sca(ax[3]) \n",
" plt.colorbar(im)\n",
" plt.tight_layout() \n",
" plt.show() \n",
" \n",
"V = np.array([ \n",
" [0, 1, 2, 3, 4, 5, 6, 7], \n",
" [0, 1, 2, 3, 3, 2, 1, 0],\n",
" [0, 0, 0, 0, 0, 0, 0, 0], \n",
" [7, 0, 0, 0, 0, 0, 0, 0], \n",
" [7, 6, 5, 4, 3, 2, 1, 0] \n",
" ],dtype=float)\n",
"\n",
"K = V.shape[0]\n",
"N = V.shape[1]\n",
"R = 2\n",
"thresh = 0.001\n",
"L = 100\n",
"\n",
"W_init = np.random.rand(K,R) \n",
"W_init = W_init/np.max(W_init)\n",
"H_init = np.random.rand(R,N) \n",
"\n",
"print('Matrix V and randomly initialized matrices W and H')\n",
"V_approx = W_init.dot(H_init)\n",
"error = np.linalg.norm(V-V_approx, ord=2)\n",
"plot_NMF(V, W_init, H_init, V_approx, error, figsize=(12,2), \n",
" aspect='equal', wr=[1, 0.3, 1, 1])\n",
"\n",
"print('Matrix V and matrices W and H after training')\n",
"W, H, V_approx, V_approx_err, H_W_error = NMF(V, R, thresh=thresh, \n",
" L=L, W=W_init, H=H_init, norm=1, report=0)\n",
"plot_NMF(V, W, H, V_approx, V_approx_err, figsize=(12,2), \n",
" aspect='equal', wr=[1, 0.3, 1, 1])\n",
"\n",
"plt.figure(figsize=(5,2))\n",
"num_iter = H_W_error.shape[1]\n",
"plt.plot(np.arange(num_iter)+1, H_W_error[0,:], 'r', label='W error')\n",
"plt.plot(np.arange(num_iter)+1, H_W_error[1,:], 'b', label='H error')\n",
"plt.yscale('log')\n",
"plt.xlabel('Iteration index')\n",
"plt.ylabel('Error (log axis)')\n",
"plt.title('Required number of iterations: %d'%num_iter)\n",
"plt.xlim([1, num_iter])\n",
"plt.legend()\n",
"plt.tight_layout()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Dependency on Rank Parameter\n",
"\n",
"In the last example, the two templates (columns of $W$) learned by NMF mainly capture characteristics of the dominating (in terms of coefficient values) first and last column of $V$, respectively. The example shows that the error between $V$ and the learned product $WH$ may still be large. This may hold even in the case that the NMF algorithm converges to a global optimum. In the following example, we show different decomposition using different parameters $R$. Obviously, using $R=1$ is the most restrictive case, where only a single template vector is used to \"explain\" the entire matrix $V$. Increasing $R$, one obtains better approximations of $V\\approx WH$. However, the matrices $W$ and $H$ are less structured and become harder to interpret."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"R = 1\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"

"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"R = 2\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"

"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"R = 3\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"

"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"R = 4\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"

"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"thresh = 0.00001\n",
"L = 100\n",
"R_set = np.array([1, 2, 3, 4])\n",
"for R in R_set: \n",
" print('R = %d'%R)\n",
" W_init = np.random.rand(K,R) \n",
" W_init = W_init/np.max(W_init)\n",
" H_init = np.random.rand(R,N) \n",
" W, H, V_approx, V_approx_err, H_W_error = NMF(V, R, thresh=thresh, \n",
" L=L, W=W_init, H=H_init, norm=1, report=0)\n",
" plot_NMF(V, W, H, V_approx, V_approx_err, figsize=(12,2), \n",
" aspect='equal', wr=[1, 0.7, 1, 1])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example: C-Major Scale\n",
"\n",
"We close this notebook with a first music scenario, where we apply NMF to the **magnitude spectrogram** of a real audio signal. As example, we use a recording of the C-major scale played on a piano starting with $\\mathrm{C4}$ ($261.6~\\mathrm{Hz}$) and ending with $\\mathrm{C5}$ ($523.2~\\mathrm{Hz}$). \n",
"\n",
"\n",
"\n",
"

\n", "\n", "\n", "\n", "As input matrix $V$, we only consider the lower-frequency part of the STFT (for better visibility). In a first experiment, we use $R=7$." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Matrix V and randomly initialized matrices W and H\n" ] }, { "data": { "image/png": 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\n", 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\n", "\n", "\n", "\n", "As input matrix $V$, we only consider the lower-frequency part of the STFT (for better visibility). In a first experiment, we use $R=7$." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Matrix V and randomly initialized matrices W and H\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "

"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Matrix V and matrices W and H after training\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"

"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"Fs = 22050\n",
"fn_wav = os.path.join('..', 'data', 'C3', 'FMP_C3_F08_C-major-scale.wav')\n",
"\n",
"x, Fs = librosa.load(fn_wav, sr=Fs)\n",
"N, H = 1024, 512\n",
"X = librosa.stft(x, n_fft=N, hop_length=H, win_length=N, window='hann', center=True, pad_mode='constant')\n",
"V = np.log(1 + 10 * np.abs(X))\n",
"V = V[0:60,:]\n",
"\n",
"K = V.shape[0]\n",
"N = V.shape[1]\n",
"R = 7\n",
"thresh = 0.0001\n",
"L = 200\n",
"\n",
"W_init = np.random.rand(K,R) \n",
"W_init = W_init/np.max(W_init)\n",
"H_init = np.random.rand(R,N) \n",
"V_approx = W_init.dot(H_init)\n",
"error = np.linalg.norm(V-V_approx, ord=2)\n",
"print('Matrix V and randomly initialized matrices W and H')\n",
"plot_NMF(V, W_init, H_init, V_approx, error, figsize=(12,2), wr=[1, 1, 1, 1])\n",
"\n",
"W, H, V_approx, V_approx_err, H_W_error = NMF(V, R, thresh=thresh, \n",
" L=L, W=W_init, H=H_init, norm=1, report=0)\n",
"print('Matrix V and matrices W and H after training')\n",
"plot_NMF(V, W, H, V_approx, V_approx_err, figsize=(12,2), wr=[1, 1, 1, 1])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The figure implies that, at least visually, one obtains a good overall approximation $V\\approx WH$. The seven templates encoded by $W$ correspond to prototypical spectral vectors of the C-major scale's notes, where the first (C4) and last note (C5) share a template. This example also shows that the order of the template columns in $W$ (and the same with the activation rows of $H$) do not have any semantics. Indeed, the NMF decomposition does not favor any order. When increasing the rank parameter, one usually obtains a better overall approximation quality, as illustrated by the next figure. For examples, details such as onset-related (vertical) structures are better reconstructed compared to using a small $R$. However, as a downside, the musical interpretation of $W$ and $H$ may get lost. We will discuss in the [FMP notebook on NMF-based spectrogram factorization](../C8/C8S3_NMFSpecFac.html) how semantics may be preserved by introducing musically informed constraints."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Matrix V and matrices W and H after training using R = 4\n"
]
},
{
"data": {
"image/png": 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WS6USnU6HYDBIuVwmk8nQ7XbpdDqEQiFCoRDNZrNvFWB1dZV4PM7hw4fNKrLWmlgsZsKZkUjEhO8laiafzc7O0mw2ueOOO1BKcfDgQebn56lUKoyMjBjqk1x3q9UyoWpZmZMVR7nuTCbD8vIy0WjUPCxaaxqNBkops7KnVI+KIqsRiUSCaDRKt9ulUqmYa7AjgX6/30Sk5P60221e9apXUa/XzWpGJpOhXq/33UO5v/bqh/SHRAXhSmqffL/0n6y2bGe1QtosaLfbO31c9wW81zkIGLT2DGI5hlJpoxqDe4ft0Ag3etauw7j6LPCzSqlP0xOHKGitLymlHgX+nbosEvE24Fe+2y9zcBg03CpzFVymMwJ9UZaNIiyCjeZ7sQcAWq2WiZAAfVGPzaJZjUbDvPOERmtHWrxpCnbkSWxDifxsRf+zWVQ2bNqft3/sttpUWC9bR/4WVpW9n8AbeZK2iD0p55DvsumAV4PYZdJXdh9t1nbBZt+x2faN0je2wg2aq/qwq86T1ppMJkOz2aTRaJgbLw97s9k0+8mD22w2+x4AeeBLpRIzMzM8//zzJJPJK0KY3tCnOE8Snq1Wq2SzWTqdDufOnWNqaoqxsTHK5TLlcpnx8XHq9box4OX84kR1u12Gh4dJJpOGv1qr1cz3x2Ix4/QJLc0eMJcuXUJrzZ//+Z+jlOKJJ54gnU5TqVT46le/atosYVC4zAFPpVJUq1WeeuopgsEg4XCYF154wVxjrVYzVIgDBw7Qbrcpl8t0u13i8bh5AMvlMtPT0ywvLzM+Pm76x87pUqrHj61Wq30evAycL33pS7zlLW8x98WmKorDJg+t15kSeAe2DBRxlMWBFs7/dgbQIDoVNwqDdp3PPffcXjehD+9617v2uglX4OGHH97rJvShWCxedZ9rGVNKqT8CvgfIKaXO01PQCwJorX8P+DzwDuA0UAX+wfpnq0qpfw08vn6qX9dabyU84eCwL3GN4yoDfBy4lx6d9R9qrQeLv+1Bu91mZmaGUChEJpMxC9N+v59oNHoFZQ76HRKbtjc3N8cLL7xgFs4ln09rbfLIbfqZbQtCj7aXSqWMTSopC9ImoW2KzSO2m9iO58+fJ5fLEQqFTNqG7QB6HQeB2Lnf+MY3SKVSpFIpoEdZFfvX7/eb77ftWrGpTp8+zblz50in0zSbTUP5jUQixmaLx+MAJogg22XhfHV1lVKpRCKRoNVqkclkSCaTpFIpIpFI333x+/3UajWzTRysUqnE3Nwc8XicTCaD3+8nmUz29YWdKnM97JR2u23swq2wG/bf4GVSOzhcJwyaU+HgsN+x0zGltX7fVT7XwM9s8tnvA7+/oy90cNiHuIa56reAv9Ra/6hSKgTErn+rHBz2L24652l2dpbJyUkTZUilUhSLRePtivctEQZZNRCVIkG9XmdmZobz58+bVQc7Yc6b8Gcn1AUCATqdDqurq4RCIRKJBIlEgrGxMer1uokUiZcu0apGo2FWRFqtFvl8nnq9zsGDB4HLEZJAIGA8dflfqZ7ogtDwqtUqMzMzQG9VQMQcAHOMnYhnJ9/J90ejUcLhMEePHjWRodXVVaPGApiVA9lfVml8Ph+tVovl5WUikYj5qdfrBINB6vU69Xrd9FWj0SAQCBhBCFlVWFtb45vf/CaZTMaIX8j9E5Ukb0KnROSkjfIs2OpN0FtlCIVC1Ot107/1et1FngYcq6uDFSAYRNqejP1Bgbx3t4IbUw4O1x87HVdKqRTwZuCnAbTWTeDqA3iPITZXOBzG7/cbW8K2sWymkJcGZ0ee1tbWOHfunBEosZUkJQXBtvns3wBLS0tUq1WTfiCCJ5FIxIhc2Sqtkl4ikaeVlRUikYgRWAD6rsErXmFHoZrNJufPn2d4eNi8d6PRKI1Gw7BrotEocFlERYS6lFLMz88zOzvL0NCQsRsjkQjxeNzYmnZEC+izIyORCIuLi+TzeRO9EvvapiyK/Sk0P4nAyf2o1+usrq6aeyhCIGJjC2vpes2/Yl9vBzdd5Ek6PB6PmwGztrZmBkaj0TB5QqK6Y8uI25xHGRyZTKZP7cSWYvVS9+zB1Ol0zAM3PDzMxMQEhw8fJhwOm8/8fr8Jm0oOjtDaAoGACXuurKwAvRDp5OSkGZAyiG1ubavVMspAjUaDV7ziFbTbbebm5ky42L52cXZsyhv0OLvRaJRoNMqxY8eMIyhOmqgpRaNROp2OGeSiqpJKpYhGozSbTaNGFgwGqVarhk9rP4AyIAOBANVq1fTP0NAQcJnDWywWSafTFItFEomEud9yTntf22mS/20HU/pMZG6DweC2jDzBrUCFGERsV8nrVkY2O1j1Xrc7Vpzz5OBw/bHDcXUEWAL+QCl1P/At4Oe11pUb0bbrBVFPDIfDZuFXlBm9zpM3T8brPAlVTPLkxWAH+mh7ttNk2zONRoNEImHy1MPhMOFw2Dgptq3o/QkGg8TjcbPgLzaifQ32YrdttyrVU8IbGhoydEHAOGLitIjSs6g22xL7osyczWZNHng4HDblCJRSJBIJc7y3baLMKRoErVbLOI7SB/aCt92P9v0IBALE43Gi0WifA2v3gZe2eD2eoe3iRs9VTm3P4aaE12HeJoQKcRdwP3DyhjXQwWGfwTum9osjpZSKKKW+qZR6Rin1nFLqf9vrNjk4CDaYq3JKqSesnw97DgkADwC/q7V+JVABfnmXm+3gMLDYjblqVyNPPp+vrxaE0L+EWibKHRJ5kTCi0Lz8fr8RHwiHwwwPD/PGN76Ro0ePMjc3Z7zyZrNJIpEwoVaJ/EhNDegJNnQ6HY4dO8by8jIjIyOsrKyQyWRMqDIej9NoNEw0yFZxkTZL/QrorbgvLi4yNjaGz+ejUCgQCARMW+RcSile+cpX0mq1SCQShEIh7r//fpLJJOl0mkajwfj4OMVi0STgNZtN48XPzs6aJL6pqSkTWQqFQhw5coR4PG7aKZQ9+VvOkUqliMfjJJNJIpGIWcGQ2lgSgrVXghqNhvlbVkPuuusuyuUy6XQan89nQvLSzxIGtxMi5d5KW+T+2EmNtsqerDbYiZxXw61ChdBa7ygatxt44IEH9roJfRAq6SBhu3WVdguf+cxnrrrPPqbtNYC3aq3LSqkg8DWl1F9orR/b64Y5OGwwrpavUjvtPHBea/2N9f//lH3gPAUCAe644w4TWbEjGvbc74042ZD/b7vtNhO1saNC8j0C2+aR45VSrK2tmc9s4QovQ8kWqxL7VFSWReTCq7pnR5lsypp8Hg6HedOb3mREHiSKI/vYxr6dviJtTyaT3H333VfURbOViKVNNnPItgnHxsZMKgZg2iKMMO99kWu1z5VKpbjtttsIBoOGridRQJtiJ6yjjSh3m0WlvNu9DKWr4Vrmqp0yj3bVeZIOloeh0+kYRT3pGHkYarVaH3dV6HvSIUNDQ6RSKaampmg2m9x3331GIc6WXBQuq1KKSqVinIxIJMK3v/1tCoUCExMThkbXbDaNoS/5NXLeTqdj6GPxeJzTp09zzz33GNlhocZJQT8JAS8tLZlwdTAYJJVKcfz4cQ4cOEAgEODSpUvkcjkTTpWCtqLYJzQ/aYcUFl5eXqZQKDA5OWmUVoQaKLDDxjb1MZPJkMlkKJfL5sEWOp04RtKPNldYitUKN/fixYusrKxw8OBB2u02ExMTRhpd2iPOlAy+ZrNpjpcXUiAQMJxfoTaKQ12v1ymXy+Y821FbgSvCtjml1BPW/x/TWn/M+n9fUiGkfwYJwtceFAyacwm9guGDBJlsr4b96Dyti1KU1/8Nrv8MXiKcwy2LnYwrrfW8UuqcUuqY1vpF4PuA529Y464TxFGx6V8yn9t55l5Hx3sO6NmS2Wx2Q1rZZmp99m+7BIvYKvax9vfaqr/Qs6nsUjh2HpD3+zbKV+92u6RSqT5nw3bY7ONsR1DOnUgkjL0HGFvJXty3naaN+sFWKZTv89Inpa1iE0o/2G20bXq7L+wcLwlibHQf7X7e7F7L+Wza5nZwo0VYnNqew02Ja1jNEyrEz2mtv6GU+i16q3n/4gY208Fh32AfR55QSvnpLYjcDvyOtWpv7/Nh4MMA4+Pju9tAh1sW1ziufg74w3Ujb4Z1iX8HB4fdYR7tqvPUbDZZWlpibGyM1dVVkskklUqFarVKPB7vi2j4/X6Wl5fN3+Ipi/cfCASIRqMsLi6SSqVIJBKcO3cOv99v1PwkchEOhykWiwwPD5uIVz6fp1ar0Ww2qVarQG/1VRRgNirGKtEkWcleXl7m5Zdf5vbbbwfg5MmTJuwp0S6fz0c6nWZ1dRWtdV9i3ezsLPfddx+ZTAattaEARqNRlFKmKK2sTkhELJFImDZIaDUcDlMul02kSlaSxeu3ozWinjcyMsLq6iq1Ws0IPzQaDVqtllnZkBUHiUy1223i8biJKDWbTSYnJ2k0GibilEqlKBQKrK6uEgwGaTQaRvRD7p3f76dSqZh+FTUXWQmp1Wrm4Zf2FwoFE6XcDnaSXMg+pUJ0u13z/A4KdtjvNxzynA0SpA7boGC792zQ7u12obXuACfWqRn/VSl1r9b6Wc8+HwM+BnD33Xe7yJTDrmGn40pr/TSw1WLgwEHUcu30C7luO+KzFXVP/hZFPDlWbAqx+7ziBt7jverNEtXwRopkmx31aLVafWwPuQY7kmNfk/c8rVbL2FJ2iop93V6FOm8kzO4rsUvtbXbkbaM+kFqeNgvM7k+7L2z70e5b6Qe7HRJFk6iYV3XQez1Xu892e+V821Xv22BMbcU+2jHzaFedp3a7zcsvv4zf7yefz/OVr3zFOEvSWTIIbJluO6wpNyWZTFKr1ahUKgQCAV566SU6nQ5Hjhwxzo9QwkqlErFYzEiNd7tdLly4QDAYZGJigoWFBbLZrHmoh4eHabfbxhGRh1xygvx+P3/5l3/JzMwMc3Nz5kUgD6C03VYtEV6o/BZnR/KbhCIoL5Z2u00kEqHb7VIul8lkMtRqNbTWRKNRFhYWUEoZhTy7nbFYrI93C1cWor1w4YKhAbbbbZaWlkgmk0YZzx5MttJgs9k0/Vuv13nmmWcol8uUSiXjgMngkpCuFxvxgO0Xx0b33O/3k81mjdz61bDTlYf9SoVYW1vjT//0T/e6GX14z3ves9dN6MPs7OxeN+EKHDlyZK+b0IftjJX9HHkSaK3zSqkvA28Hnr3K7g4ONxw3w7jaDhqNBl/+8pcNvUvSMMROs50Pe963DWzpp0AgQCaTIRKJkEgkTO52LBbrU4qz6WP232K3ZTIZs0ht0/c6nY6h5nkpcMVikdnZWSqVimk39OjqsVjMLPKLrWIXnG21WqysrNBqtcwCcSqVIhgMMjIyQjwev8J58ToX58+fN6knorIn6sdeB3Azx+TMmTOcO3eOQCBAOp2mUqkYiXTpKzvnXe6R5MIHAgGKxSKnTp2iUqnQaDSMjR2JREwfRCIRk5NvO6u2iqDcJzvvTfpcrklSOeLx+LbSFDYZU1uxj3bMPHK0PYebFo4K4eBwfbEfjTyl1AjQWnecosD3A/9+j5vl4GCwH8eVg8MgY4djasfMo111nrrdLvl8nueff556vW6oYDY9S1YN7CQ4+8eu4xSNRikUCsTjccrlMt1ul+XlZcLhMOl02tSMEoU78b7D4TCzs7McPXrUeMBnz54lGo2SSCQMPUyU+/x+P+FwmHq9TrvdNgVuL1y4YGo8AUaowV5tEC9dIlGi7BIOhw0tbm1tjVwuh1KK8fFxSqWSqeMkKxFCMex0OpRKJVNHKhKJUK1WjXdvq6JIn9sCGhL1mZ2dJZ1O4/f3itWVy2XK5TKTk5Ok02lqtZqJ2HW7XUKhEN1u10TAut0uzWaT+fl51tbWaDabRihDvH4J40J/tGmj5D9vuF5WJOSeS/+PjY3dsIKe+5EK0Ww2OXfu3F43ow+DRiMcRLW9/Yh9vEI+AXxyPe/JB/yJ1vpze9wmBwdgX4+rHaHT6XD27FlDXfNGnmy2kV3j0qa+ST+FQiE6nY6xT8TukCiQbXfYVC/5f2Vlxag912o1U1dJvl9sHris3if2SqFQ4NKlS5RKpb4IVTKZJJlMGltJlJQlBaLT6dBsNllZWaHRaBgRLFGfFqEl2/yKceMAACAASURBVIbaiN4mhYZjsRixWE/TQCJPdvTJPs5ra62trXHx4kVCoRDNZpNisWgEy8ROFLs5GAzS6XQM+0qEz9bW1jh//jyFQoFGo0E8HjdCb6KKHIvFjK1qq+1JTSu7jqkw0Oz7KNcjQmViA18Nu8E82vXIUywWM5WRvaFb20GyC5V5fwDq9Trf+73fy8mTJ0kkEmQyGXODQ6GQoa51Op0rBpTf72dpaYlSqUQqlSIUChlqnHBpx8bGWF5eNjdyYWHB5PoIVzSTyRjnCC6reomDFAgE+qQfZbsM0Gg0ysTEhKHoJRIJ4whK/pU8rIBxwObm5igWizQaDUKhEFNTU4bGJ2FSW/VErtkOY8/Pz/Pyyy9z+PBh873ZbJZ8Pk+xWKRarTI0NIRSing8bipqr6ysmJwrkTXP5XK0221T6VpehHafe/nFm1H37Lba9zwYDJLNZhkZGdmW4sqtMiEFAoGBK7gqE9GgYNDUCPcr9uuY0lp/G3jlXrfDwWEj7NdxtVP4fD5TekXsKFtBV2wlWTy1aXs2lQ0wdpksUntVhb0qcbbNYDtSYoPaCsWSYyO2kthSti0jdqq01f7cew7Jr5K0CrhcdsVO47AL9Nq5TF7qXiQSMZQ9+1hvjpXsL7/tPhAbWexLcXhEOt12niQnS/Kz5PvEgZN7F4/HjRMoNms0Gt3SeZJ7bFP44HLZGrkWSYERWuHVcI1jakfMI0fbc7hpcStMSA4Ouwk3phwcrj/cuHJwuL640cyjXXee7rjjDrLZLN///d/P6dOnDb1uYWHB1E+SaJEozAnsiMazzz7Lk08+yWtf+1oTEo3H4yQSCRqNBtVq1axISKRIPFitNbVaDYDPf/7zAJRKpb5oh00980ZC0uk0iUSC1772tYyMjLC0tATAfffdRz6fZ2hoyKxupNNp48VL5CeRSPDcc8+ZIrmpVIpYLMbExIQpMitRLglVigBGMBikUqkY1RqAlZUVhoaGzDWJ2IX0mfy2xRiKxSInT55kbm6OWCxGvV43xczsVQGbPikRQYmoxWIxMpmMqXUlwhfhcJipqSmKxSLHjh2jVCoZaiD0wtsicqHXi7xKqNyOLooKTCwWY35+nmQyaVZLroZbZTUvlUrxtre9ba+b0YdDhw7tdRP68PDDD+91E67AxYsX97oJfbBXXjfDrTKmHBx2E7fKuAoEAtx3330mcgKXUzVEXMArHLWZ8MHc3BylUolAIEC9XqdUKlGtVk29IrGj5Dts4Syfz0e5XDYsGxESkzZ6UwekfWIXyt+JRAK4XCNPomBSv1RYTPK/MCBESCscDpPNZo3dm8lkCIfDfREfsR/taMvQ0JCh+EkkyhZd26geks328fl8xGIxDh06ZNSok8mkqTEq9q4dCZLoEFymCIZCIQ4dOmRqdErkKhKJ9BUQFvtXom5ybTZVT+iU9n2y77f0pUTbrobdGFO76jz5fD5e8YpXMDY2xvz8PBMTE2bQ3H333X1hV3kAJOdIlD8E3W7X0MhEGjwajZLP5xkeHqZWqxlp71AoRL1eNw5Zo9EwuVaLi4umIK7cUDsMu1ERs2KxyMGDB7nnnnsIBALG8HjggQfI5/OsrKwQi8WMkyWKfzJIqtUqqVTKFOTN5XJG0lucLDvULMp34nxJAd2DBw8arura2hqRSISlpaW+8LEo9omKnwxMCVXPz8/3Ufts9Rhb8cbORRPqoQyMM2fOAJj2B4NBpqenicfjlEolc1/S6bS5nmw2S61Ww+fzMTIyYnK85IUoyoahUIharcbk5KRp33alKm+FCUlehA6bY7sFYHcT+Xx+r5vQh+3wyGHnY0op9XZ6xQf9wMe11h/xfP4fge9d/zcGjGqtM+ufdYDvrH92Vmv9Qzv6cgeHfYJbYa4Sg1ZsCHFkxN7yOk9eupr3t9httoqenE9UkeFy3ozdBlENlt/iNNnnss/pVe2z6XEyv4hTAfTla8u5bdU+WTC2FfXE0ZI8ddsWttHtdk1ZGKUUjUbjCufJqxBo286yKC20QilnI+ezF8ttKXmBbLfvn/SDOE/SF3JvRVvAvge2ren9Dq/zJE7pRiWENsNN5Tw5OOwWbpXVPAeH3cJOx5TqCTT8DvD36KkZPa6U+qzW2iTiaq3/ibX/z9Gfm1TTWp/4rhvu4DDAcHOVg8P1xU0XefL7e4VRFxYWiEajDA8PG5odYIrlircvNDWvpw+XlftyuRzFYpHbbruNYrFIIpEw9DARNbBDgxL+8/v9TE1NEYlETMh3aGiIarVqojUSdbE9bL+/V9D1ne98J9VqlVAoxMGDBwE4deqUoaxJiFFqQGUyGYLBILVazdDWgsGgKdw7MjJi1OoSiQSdTqcvzCsJiH6/n3q9bpQFO50O8/Pz5HI5s5og9ZikD6Rgr6z2SDTvJ3/yJ3n00UcpFotEIhETDZLrt4+xKXwSEg8EAoyNjeHz+bh06RJjY2MmuVDqJ8h9T6fTZpUhmUxSLpdNgmG32yUajZr+DIVCJkomdEyhLnY6HScYYcHn8xGPx/e6GQMNGZ+DhEETsdhO4elrGFMPAqe11jPrx38aeA+bqxi9D/i1nXyBg8N+x60yVymlTD0mUaATCpfYGl6BA3uut/9OJBLGXrApX3akSGwYieTIOTqdjrHH7HQIr0iVHYGRc0gaiC1U4aXtyffYNqMtdiG1OwOBAKlUyoiHiWCGHdmxI09y/ZJWYV+nbRdtJcZln0Pe+fJ9sVjMMIe8kSf7XohNGI1GSafTfTWbRCxCbETpDy/7QyJPNhXSK7hh/5bUHHlWtvOs3XTOUzQaJZVKUa1WDZ1NHjpRipMHWmQg7Ydf6CXiPLzyla80spNTU1M0Gg3jfEgRMjuHSpwZcZre/OY39zlUo6OjdLtdxsfHqVQq5gEIh8PGETt9+jR//dd/zbFjxxgbGzPO2uTkpFEfkZeBLaEphdOazSaFQoHR0VGjlpbP50kkEleoD0q/yYBVSpn8ptOnT3PkyBFDfwuFQjQaDfM9cFlmE3oPlFxDIpHgb/7mbzh27JiR10wmkxw/fpxarcbQ0BCJRIKzZ8+SzWZNeDiTyVAul0mlUpw6dYqvfvWrHDp0iOPHj5NIJBgbGyOfz/epx3S7XbLZrHHobPUVeblJrhX057bZLyahVg5K2HYQYHOvBwWDJg3++te/fq+bcAWKxeJeN+GasMGY2qpq+xRg6+ifB1670XmVUoeA24AvWZsj6+duAx/RWv+376btO4EYRVK6ATDv12azSTqd3vZ7KJfL8f73v58jR45Qr9cZGRkBMNRyWVgSI87OqwgEAvzSL/0Sp0+fJhqNmuKekvMq7075kXeovCdFCfWTn/zkFWVBADMfACZ3wr7+oaEhpqeneeKJJ1hYWDDUcFn4VEpRqVSIRCKmSLqN++67jx/+4R+mWCzi8/mYnp7e8fvq0UcfNTkkzWaTQCDA0NCQKS4qRqoUkY9EIlQqFTPviFEs13Xu3DnTz7VazRjSkUiEYrFoFG9lfzHcZE69Guw0gO3iVpirfD4fQ0NDhrZn55bb9+hqjhNgnjVbwtzOVRJnZSMaoFKKI0eOGCqe3R67LbYzZY+zRqNBoVAwx9i2ijdvx3aa7DE3Pz9v8sbhskMiNDqxW6UQr33eSCRini9R8RNbV+BVALSdEZ/PRyaTMXlJcp22A2dfv+2AyvE+n490Os3k5GRfXrzkxNsqgbK/91nYzGGyYQdL7Lz97eCmcp6gx/WXej3hcNgIO8gAEKfB9rjlQZKcJOh1ZqVS4dKlSwwPD9Ptdnnuuec4fPgwnU6HxcXFPk/fdiYCgQCjo6Ok02njxB06dIhUKsXKygqHDx828osiBWnXIchkMsRiMXw+n8mvEjSbTVKpFO122zxAkl8k20Qes1qt0mg0WFtbM1GqQqFALBYjkUiYFQCRJJfExkgkwt/+7d9y7Ngxzp8/z+23387Zs2dJp9NmsrCTA1utlvl++Z5cLsfS0hKZTIZsNsv4+Dirq6tGsEOOS6VSRuwhlUrRaDTM9UnkSPKVVlZWyOVypiaTDMhWq9U3cdviHXafSHvtug/i7NqRx+3kPN0qq3kweBOvPR4GAalUaq+bcAUGTTDiu4g8bVW1fSPvYrPB+xPAn2qt7eSrg1rri0qpI8CXlFLf0Vq/fNWGOjjsI9xKc5VIXtt57XClpPZG2+39xcmQz2z7wLugYBvctoFuL2zbUZ+NRMLknGJbiWS35OPDlc6T7cB5r0VYQvLetXNOhT0k8EbWWq2WWbCQIEOr1epbWLbz1r3Ol1yP5HrJQo03YuV1VLxOqn093kid9J8dXdrIGd7KQfbut505ytvWGwmX8+Rw0+JWmZAcHHYLOxxT54ED1v/TwGZe408AP2Nv0FpfXP89o5T6Mr18KOc8Odx0cHOVg8P1xU3lPEnIs16vMzo62ldATMLxooYn4dRarWa8aO/Kw+LiIp/97GdN9Eg8bDtE71XKk7+11iwtLXH27FnGxsZYXFzk2LFj1Go1ut0uqVQKv99PMpk0MpMSPZmammJoaMgUo5VVAlm5kJWDer1ONBrtk6uUv+WYsbExSqWS6SNR7iuXy4ayKFWaZRVgeXmZZ555hhdeeMEcZ4dVvX1u/7Z5uolEgq985StkMhn8fj8PPPAAjz32mFEAFPn0brdrokeVSsUo4QG86lWv4vHHH+fAgQOGdiIrMYlEgtXVVZOHJhEAW0rdG1qXbfJc2LxcyYXa7rN2K0xIg6i2N4iRnkHDBz/4wb1uQh/Onz9/1X2uYUw9DtyhlLoNuEDPQfr7G5z3GJAF/s7algWqWuuGUioHvAH4jZ18uYPDfsCtMle1221TkmZsbIxUKoXW2qQN2PP/1XD69GkeeeQR6vU6jUaDWq1mIimRSMTYgnZ+tp2fJCVPms0mo6Oj5HI5hoeHiUQiJBIJksmkUUeORqOG9RMIBFheXubcuXPccccdRKNRU6ReaKzeKJkX5XKZb33rW9x1112k02kKhQLZbLZPSVnsSLG1bNW+5557jscff9zk+6dSKUNhlUiUzMGSj2Tn7kejUU6dOmWUjQOBACMjI0xOThKJRIxKtN9/uWROq9UyrCToPbNLS0u8+OKLZDIZhoaGUEoZW1LSSFqtlmFubUdi3Avb3hcbdFCYR9t2nlRPOekJ4ILW+l3rE+KngSHgSeCntNbNrc4hoU8RBzh//jwjIyNGRMEOt0JvsMViMeOkSL0mwOQ0LS0t9VVu9kou2vxVefjlxkp4sdPpMDo6yuzsLJlMhmazSblcJpFIGCdB6IWlUol8Po/f7zf7Dg8Pm+vrdDomn0pylRqNhhFt6HQ6hjcfjUYpFouGN16tVikWi0xNTRnHQSllalDJ/2NjY6yurl6RB7YVf9TuV3EgI5EIzWbTCG/Mzc0Rj8dNEmOz2SSTyfQ5tZKnJtf1zDPPEA6HKRQKBAIBLl68SDqdNjQ+4fLKtUMvWVGoXfbLRih84lyFw2FD3RNRke3yXXe6717geowp2B7lymGwMDMzs9dNuCbsZExprdtKqZ8FHqUnVf77WuvnlFK/Djyhtf7s+q7vAz6t+2fF48B/Vkp1AR+9nKfNhCYcHPY1boW5SmtNpVIx9Yui0aixmezSLFs5HoJSqcSlS5eo1WrU63XK5bLJC5fz2rlMkgIhBnwsFiMUCtFsNvvynmSBXHLUpSyLLX1eq9UolUqmpqUs6Eq75TXmFXoQdDod8vk85XLZ5MdJO0R2XGxa6R+bOlgsFpmfnwdgbW2NZrPZpw8gOfxwWRjCFq7odrusrKwYu1KuMZVKGbtL+k1EuyTtw85VqtfrFAoFY0uKbW87q1Juxl4Iv8pzdsUzY/fbdktqwI0fUzs5+88DJ63//z3wH7XWdwBrwIeuZ8McHL4beHm4Awo3phz2DbxjajvjSmv9ea31nVrro1rrf7u+7V9ajhNa63+ltf5lz3Ff11q/Qmt9//rvT1z3C3JwGAC4ucrB4friWuaqnWJbkSel1DTwTuDfAv+L6rmHb+UyBeOTwL8Cfner87TbbfL5PMePHwdgenqaUqlEOp2m1Wrh8/moVqtGSEIiVLbijagJdbtdhoaG+iIyXklzm64nqwsSibLlGIeGhpiYmDAVloeGhshkMoRCISKRiGmThFLFUz9w4AArKyum4KWEoSWZT46zFZSgF/mZn5/nzjvvBGBlZYVUKkW32yWRSJhVaVEAksQ9abMITExPT9NsNjcskrZZ8p0tmzk6OsrFixcZGRlhdHSU4eFhhoeHCYfDptq1KBVKlErulazGKKV48MEHTcRJIm9+v59YLIbW2hQDligeXFaDspMVpX+lj0Q8xO/3m+ejVqtddVXKvtZBxfUaU8C2wti7iUFT2xO1tEHCPffcs9dN6MPLL189lWjQx5SDw37EoI+r6zVXiTiD2CoSRZC53atKJ8dshFgsxuTkJI1Gg1arZcq3iFy2pDEI88W29wAj+NButw1tL5PJEIlEiMfjJjIltp6cT84fi8X6IjlAX2qF3XbvNXS7XeLxOH5/r1ivRIsAE+WR7aIQLekeSikikYhpr6SWCPVRIjxXo+0NDQ2Ze+H3+0mlUua6xNYVe1mu0b5HSvWUPcVmDofDpn9sgQh7/40k1L3w2jJem3Y7tp8cNyi0vf8E/CKQXP9/GMhrrSUB5Tw9WdoroJT6MPBhgNHRUebn57ntttsYHR3l0qVL5PN5w/kU2pbI+EpIEDBOi+QHierdXXfdxfT0NCdOnODixYvcfvvtplZToVAwD4uEhsVxmpmZYXh4mIWFBVqtFgcOHDADRilFvV7v06+3+Zv1ep3p6Wmq1WqfstjExASrq6ukUikjwS4hXVtqUSRRC4UC585dVvIVmUc7Z0RCp3a+1sLCAtPT03zf930fgUCA6elp0uk06XSahYUF/H5/Hw+30WgY7qoo2z311FN8/etf50d+5Ec4vK4uODQ0ZLirq6urBINB4/xJ+NWWoVxdXSUUCjEzM8P09LRxumxJ+EKhYBwyod7ZaorywrEVYOyXqJ3LJVW5t0tTG+QJies0pqanpwdO3e6rX/3qXjehD+94xzv2uglX4E/+5E/2ugl9+PEf//Ft7TfgY8rBYV9iwMfVdZmrJicnSSaTJp0hn88TDAapVCqEw+Er0i28im62tPXhw4f50Ic+ZHLCxdEBDOXOzqX2OjIXL14kHo+bHCmR7ZZFXdvZsNWL7c8kZ2ptbQ24nNrhTR3xfne1WuX2229HKcXFixcJhUIsLS2ZXHjJRYLLkuP2eQ8cOGAUnwXiDIrDI0EGW8nabv/U1JSpi9put03dLcl1soMMtkMkfSzpI0IpjEajxjaUNotDKJREm3JnO0Eb5Yht5CRtRoPcDDd6TF2VtqeUehewqLX+lr15g103XP7WWn9Ma/1qrfWrM5nMNTbTwWFnGGQqxPUcU7lc7oa00cHBi92gQtwIKKUOKKX+Ril1Uin1nFLq5/e6TQ4OgltlrtqoDpiDw43AoND23gD8kFLqHUAESNFbicgopQLrqw9bSdAadLtdzpw5YyhcUsvI9uxtChdcDuHaHjxghBSOHTtGpVKhXC4bGl0kEjEiDeFw2BQVsyl/oi7V7Xa5/fbbjbedz+dNGLJarfatHoin32w2WVpaIhKJcOzYMZO8VygUqNVqlMtlo8FvJ/0BRnXP5/Pxuc99rk8IwQ7nSnKjhE/Fo5d2JZNJ06ZyucyZM2c4cOAA2Wy2rz7S2toaWmtDtxPVEmnjyMgI+XyeoaEhSqWSiQjZFaKlFoCsLohKIsDi4iKBQIBMJmOieOl0uu86pN+lTXYkS1ahJDQuoV67Oris4thRr6thwKkQ121MdTodU9BxUPDII4/sdRP68O53v3uvm3AFpqen97oJffBWgN8IAz6mtkIb+Kda6yeVUkngW0qpLzgBCodBwLWOK6+Iw3VvWA/Xba5qt9ucOnXKMFo6nQ7JZNIwYyTa4a21ZNsE0k+rq6vGFhHWTTKZvELVbTNbYXZ2lqGhIRN1spk5cpwdQfIqPS8tLfUp4sFlBT87ciPXItQ56Nlkzz//PNVqlWazSTabpdvtGptV7CGvWrRExaRGaDqdJhAIGNpjMpkkEokYmxcwTCrbbvL7/VQqFZaWlvD7/dRqNaMm6E1zkbQRSZ+xI1iNRoPl5WWUUqRSKWMzSrFt6TO7DwRXozd6t8mxOxGe2HPantb6V4BfWW/Q9wD/q9b6/UqpzwA/Sk9x5YPA/7udL1xaWjJy4DYnVR5WmyNpP7z2Z4DJKSoUCgSDQUNdSqVSrK2t0Wq1iEajJJNJk3PT6XRMCLFYLLK4uEgymaRYLKK1ZmRkxISPpdI4YLimYqR2Oh1TlNaWio7FYjSbTZaXl5mamjLfJ8p1gGnr6uoqJ0+eZG1trU9RRRwUcRTEaRLqYCgUYmhoiGKxyNNPP22qQrfbbQ4fPszKyorJNwLM93Y6HeLxOLVazSil3H333SacKv0ig9wenLJPqVQyaipCJYzFYuRyOUZGRswAFAfM7/ebSuDiNEqbvEXcJCQvv2XQyAsyEAhQrVb78qKuhkE19K7nmBJneJDwxS9+ca+bMPCwiyAOAgaFCnEjoLW+BFxa/7uklDpJj2bknCeHgcA1jisRcbhhtSGu51zVbreZmZkhHA4Ti8VotVoMDw8bW8NebBXnwXZE7BIvCwsLJrdJFILtPGnBZu+11dVVstmsobh56YHe/Br772azyfz8vFHFs0uzSNtt+pzXeVpdXeXZZ58ln89TqVQYHx+n2+1SqVRIJpMmPcR2msQeFBupUqmQy+UIhULGphseHjbS6mK7RiKRvmsUp6JcLnPx4kWj+Cz7x+Nxs5/Y5vIdfr+/7/N6vc7S0pLpMwk6yOK69KPkotm0O7kO2zndyqGSY23F7athz2l7W+CX6CUPnqbHgXVqSA4Dg2ulQiil/Eqpp5RSn7uBzdsMbkw5DCz2K23PhlLqML1iu9/Y4LMPK6WeUEo9IXkMDg43GtcyV6nLIg4fv6GN2xxurnIYWAwKbc9Aa/1l4Mvrf88AD+74C9fVStrttglPQn9CnMBWhvMqsTSbTcbHx+l0OkblTTzesbExQ6UDjPcr3q1EkqSekawMiBc9NDRkCoJJVMhOwJPVj9HRUVZWVlhZWTHfMzk5iVKKs2fP9tHMtNZmpUKoahKNsSM+3rC1XL+dwCjhXVGCkYS/UqlkxCokvywSiRg1Gin4K6Hmixcvcs8993Dq1CnC4TCVSsUkUa6srPTVYAgEAiwsLHDHHXdQKBT6IkPtdpvZ2VlGR0cNHTAcDpu/m80msVjM3LtwOGzUZOzVELm/do0r2S7Rp52EYwd1Nc/G9RhTg4ZBU/8bRAya43EzR54ESqkE8GfAL2iti97PtdYfAz4GcO+997qH2GHX4BlXOaXUE9b/H1t/Nm14RRxuOK7HXCXz/XbfN5vtZ9uEtm0kn13t/F6200bt2igaZV/DVu27Guw2biWCZc+lduTG/vG23z63t832PhvRIje7P5v1z1bb7f836qvNInubfbaZivRmuNFU2F3ljiilOHr0KG9729soFAosLS0xOjpKpVIx+T3i5Ng8yY2cp7W1NY4ePcrhw4fx+XwsLi4yOjpKs9lEa00ulyMSiRiVPJHVBohGo4bnmU6nqdfrfdvn5+eN4yNOj7fY19LSEq1Wi2QyyeTkJADz8/OcOXPGKMoInUoMfgmFdjodpqenUUqZ0HW5XDZcVfktD7U4SbbCS71e541vfCMXLlwgEAgwPDxsKncvLi6aMKzkOlWrVUKhkCk6LHSvJ598kk6nw/Hjx03ouFqtMjo6apzRRqNhuLUrKyvmWDuEevHiRRqNBu12m6mpKZaWlvqkRG1IqFscSVHds3O1pO+FCqjWebvi/G7nWdvp4FEeSdYdHbxHkFD6IOHHfuzH9roJfTh58uTVd9plSLmGQcF2JqVrGVODAqVUkJ7j9Ida68FKynO4pbHBuFrWWr96i/2NiMM6lW5fIBAIcOeddxKJRIhEInQ6HRKJhFlcFaqbVybbNu5tapfYiPF43FDnxGbxOlBeB0gWizudDrVajWKxaGyQzZT65DzFYtHkFNl5QCInLr/tPC07HUEpxT333EOpVKLT6Rhl5Ha7bXKv5NokL9xWzZMUFekzWXgX2qBXeVBsJ4HP5zPpIlKSRtIwbFqepIoo1cut9zpnkkISCASMvoCU95Fgg9jum9H2NpOl9zpc4hfYxZS3wncxV2178Xywy1o7OFwjNqBC5ISSs/7z4Q0Ok9W87SVVOTjcQtivtD3Vm20/AZzUWv8fe90eBwcb10DbExGHM/Ryjt6qlPrUjWyjg8N+wrXMVTulwu5q5Mnn8/HmN7/ZFIV98MEHicfj1Ot1crmcESSQiIzQy2wRAsGZM2coFos8++yzRuhBIjPyXe12m3q93uf5ilhCpVJhbm7O1AkYGhoyKnPitbfbbfO/hFWDwSD1ep3Tp0+TyWRoNpsmEiIRIvlfbphNNxOPXtTo7r33XkqlEvfffz/1et2sykibDxw4QKPRMKsE3W6XCxcucO7cOVMHS2pZHThwwKxyVKtV0yatNdls1qyoJBIJfD4fmUzGrFo8++yzHD161CgVAibq1mw2abfbphaCrEB0u12y2Sx33nknJ0+eNAXeEokElUrFrBLI98m9kfaFQiEjaCFUPri8SmRH7mTlQf7fDm6F1TxR2RkkPPTQQ3vdhD48+uije92EKzBokaftYr84TB68Afgp4DtKqafXt/0zrfXn97BNDg4GOxlXm4g4/OSNadn1g8/nI5vNkkwmSSQSaK2JRCJGIU9suM2odHakYm1tjXq9TiqVotlsGptFGEIidrBRdMPn87GwsMD8/DzhcNhEqlqtFoFAoE8RGS7fG2mL1pr5+XkTYZLP7e8Um0/sV7l+2VfELsLhMMlk0qj0SfFdsZekF5ZHVwAAIABJREFU7pId8ZmfnzcRIlvdzi5ua9eH2uga8vk8iUTiikiS3f9yDXJ/JPJjp6KIjdjpdEzkTCJWcr1ybrGh7cjTZsJJXhtPzr/RZ5thgzF1NTrsjqiwu+48AYyPjxslN+gp5JXLZXK5nFFUkbClOCKSHyUG9MLCAsvLy2SzWaPCdunSJYLBINFo1NxwoZvJgJBzjI6OEo/HeeGFFxgfH+fMmTMmx0coc3Z+k52/JOf5+te/3kfP894s+8G0ebkSYq1UKly4cIF4PM6FCxfIZrPEYjHe+ta3srq6SiwWIx6Pk0wmicfjlMtlkskkzzzzDIlEgtnZWeP4RSIRVldXUUoZNRtpk8iBSghZqZ70pNaaI0eOUKlUWFxcNM7m2NiYaW+n0yEajfYNNnnx1Wo1EokE586dIxAIsLa2xvDwsAkJB4NBI/der9f7Bko0GqVer5vfQuFrtVomT0u+XwrnymDeDq4hbHuFJKtS6lODPimJ4zxI2AkveTfwjW9coQ3gcA3Yr7Q9rfXX2Lg2jYPDnmO/jqtrQb1eN7LkQF9qhCyci41iO05e2l2tViOfzxv7TmiAsgAtdqRXvVfOf/bsWarVKtFo1KR0SHqCGPn24jdczlMKBoPMz8/3qSTLfmKziOqcODS2bHcoFGJtbc3Yc6IMLYvLthMmsOfUarVqrlHUCXeKSqVCvV5HKUWlUjE0RDuVQuxV6Q87F10UpIvFoukXoWHKsWI/b+Q8iTLidkpkSLt2kku9yZjadAH9WhbPB0sv18HhOuJWWM1zcNhN3CpGnoPDbuJax5Ut4uDg4HAZN3rxfNedp9XVVSKRCKlUisXFRe6//35T9MtO1KvX66aIrk0TkyjPmTNnOHPmDPfccw9+v5+FhQUOHjxIsVg0KwrirdqRjEajgVKKv/iLv+Dpp582RclEmMGm2MkKiIRU5Ueof81mk1QqZdokIV+5Dq/6i736YXv4ounv8/mIRCKcOXOGeDxOu92mVqtx6NAh2u02ExMT+Hw+KpUKJ06c4IknniCRSBgaYjqdNsXKhLYHPWVCO/LVarXI5/Mkk0m++c1vMjk5acQZRPRhbGzMrMhIW6EXJZQIVqlU4uzZs2SzWZaXl3nLW95CpVKhVqtx4MABU4tBah9Im6TPARM1FFU/oVvaSoSyglGpVMyKxdVg97/D7uLgwYN73YQ+fP7zjp11PeDGlIPD9cetMq601oaabwsgCKvEFsnyCgZ4I0+VSsWwcwBTH1OiMkKFk7QEOU6+6/Tp08Y+kRQDYcfY0RXApHGIbZhMJlldXTWpJd79JN2j2+32RZTElkwkEgQCgT41YhE3i0QiRpk4EokwOjp6hf04MzNjanYKs0joctKftnqx/VvaUS6XabfbtFotarWasfWkDyTyJbaf2GXdbtdExiqVCisrK+azUChk6IhepWkRCJO2SKRqu5Gnbrdr7PTtYKdj6loWz3fVeRI1t6mpKVZWVshms8zNzZFKpUzeRqvVMlWj5cZJoVmttRksly5dYmlpifn5eVKpFJFIhBdffJHXve51vPTSS7TbbROGFW5lMBg0OU5nz55lZmbGOD7yQIijZDtQst1WggF4y1veQigUYnFxEYCJiQnzAAqH16tyYuckyfW94x3vMHlg+XzeKJiMjIyQyWQolUpEIhH8/l5xs2azyaVLlwgEAiZPTB7ExcVFo9ACvVwieaBlkHa7XUqlEhcvXuSBBx5gdnaW6elpqtWqofhBL6ReqVTw+XrFcPP5PLVazYSMK5UKzz33HG9605uoVqt87Wtf48iRI9TrdUMnrNfrpqibPMyFQoFut2tellI0OZFIAD1nLxqN0mg0zP0vlUqUSiWmp6dveJG0/baat92iwbuFu+++e6+b0IdBjJa8+OKLe92EPoji6NVwDQqWbwd+C/ADH9daf8Tz+U8D/wG4sL7p/9Raf3z9sw8Cv7q+/d9orT+5oy93cNgnGMR31PWGUqpPTViKyYq9IrS9jWjfXucJenaEqPWJYd5oNIhGo2bhHS7T6eCy81SpVMjn89TrdbOo22q1+krn2E6E5PsAxmESurxNtxOHQ/4Wu02uIRQKGUcnEokwPT1NMBgkm82SyWSIxWKmpEw4HGZqasocK9cuyne2mp+dW7WRIp1tM8niv9AO2+22CU40m82+YIUsnovN2+l0TIBAFrmlb+QzWQiX7bYKobRPtsu2q8mQ70RpT3Cjx5Sj7TnclLiVeOQODruBnY4p1auZ8TvA3wPOA48rpT6rtX7es+sfa61/1nPsEPBrwKsBDXxr/VhXvdbhpoKbqxwcri++mzG13cXzXXWehKJ28uRJ3vSmNxEKhXjhhReoVComjDg0NIRSPS19EVWQIrCi5gawvLxMPp9nYWGBYrHIPffcQ6vV4s/+7M9IJpNG+MErNCAedKVSIZVKUalUjAiCra9v09xkm/1bVh5SqRRjY2MAnDhxgkOHDpHP54lEIly4cIFOp2M08KF3UwuFAo899pgJLz/zzDO87nWvIxKJGA1/2Vc87lKpZCJorVaLhYUFQqEQtVqNqakpo//faDRIJBJmNUVEN0TdrtPp0Gw2qdVq+Hw+ZmZmGB8fp1armZWgWq1Gs9k0UUDR+pckSGlbvV6nVCqxsLBgIna1Wo3JyUmy2Sxnz541D7GEsQGTRCkh/EwmY1aAJMq3trZmkgzb7TaFQoFOp0OhUNhW5OlWmZC63W7fMzMIkAjioOC1r33tXjfhCjzzzDN73YQ+bOcZuoYx9SBwWvcKaqKU+jTwHsDrPG2EHwC+oLVeXT/2C8DbgT/aSQMcHAYdt8pcJfN2s9k0EQ5bcc2OesDWwkNiC4RCIRqNBuVyGcCoAguNT+w3OwVAfoRSJykbYuMIS0lYRsLWsc8ljB47AiVqgSJWITQ9+Vu+X+ybSCRCLpcDejZQKpUytThlP6Ee2jS0TqfD0tKSiegI88iOkgmFULbZAhxCb2w2m30qxq1Wy6S1yLFyj+R+SMRJrlP6XI6RyJPQAKXfbGaDbPcyZja730qpvrqig2L/7TptT27y2toaKysrZDIZJiYmyOfzZDIZo+rWarUoFotEo1EikQiVSqUvtFcul3nppZdMAdsnn3zS8D/hspPkpd/Jg9xqtfjABz7A1772NQ4ePMhtt93G3Nwcw8PDZkDYso02bW9lZYVnn32WO++8k2AwyKtf3RPwKJVKLC4uks1mWVlZYWJigm63a2h48iC/+OKLXLp0ienpaV7/+tezsLDAxMQE586dQ6leQbJEIsH09DSNRsPIeQrFrVKpsLy8zPHjx1ldXaXT6ZBKpYxzJ5xboI9jLDlfsViMVqvFoUOHmJubw+/389BDDxEOh83gEflJOX55eZlUKmWO9fv91Ot1Go0GMzMzTE1N0W63OXr0KOVymaeeeso4wuIoyUMfDocNFbHVapmXoNAl5Zrlu6Ut8pLY7qC4FSYkocIOEgataO973/vevW7CFXjsscf2ugl9EOPjatih/OsUcM767DywkSf7XqXUm4FTwD/RWp/b5NipbTXyOqDRaPD4448Tj8dJpVI0Gg3Gx8eNKqzMKVLKwp4rJAfAXqgbGxujVCpx2223MTU1xfDwMI1GY1tKWe9973s5fvw40WiUTCZDMpmk2WyaxaWtuP3z8/P81V/9FeFw2Mg4Q4/6Y9OmZGHTpuv4/X7W1tb46Ec/ytLSEqVSiampKZrNJsvLy6TTaWq1Wp+8sm18+v1+UqkUtVrNFHGXRdKxsTFSqRTxeNwstti5Hrax6ff7uXDhAseOHWN+ft5Qy0X91c4lSSaTXLp0iXA4zOjoqOmHyclJLly4QDgc5siRI2bhUkqDiFEm+cffDSR3eieLWrfCXAWXF/vsvhG7SpR5befJa1DbRrosrNtpHWI/2YrN8ltsEaUU8Xic8fFx4zglk0mzyG3TCuVvO/enXC5z6dIlcrkc4XDYPL+2iqA4O7bjJr+bzSZPPvkkuVyOXC5Hq9UyYwF6z4K8U4RWZyv2NZtNFhcXTWpDp9OhXC6blBBZsJdz2cp5Qh2sVqvmnS991Wq1TM5TIBDoy8sXtWuxnWW7/JYyPbLYLw6V3Xa7b8QREgfMvrf2Pbfvt+Rc3ei0je1i152ndDqN3+/nscce48SJE5w+fZpLly4ZEYFYLGa81HA4TD6f7/PY5QY0Gg1eeuklzp8/b6Su7QREb+RIHhzbifniF79obvTCwgKJRIJEIsFDDz1kBCzC4TDZbJZarWZWBb71rW/x/PPPs7KyQrfbNXVkTpw4weTkJEtLS0xPTxuxhLW1NbOKIIO30+mQy+U4efKkiVTFYjHjUDSbTc6fP8/IyAjVarVvQFSrVSMzWa1WuXTpEtls1kTS/H6/GYjNZpN0Ok21WqVarZqXidaaxx57jDvvvJOVlRWeeOIJHnjgAZrNJvF43Dh0IiIh1bBl4IiTUygUeM1rXsPb3/52/viP/5i5uTlqtRqZTIZarUahUCAej9Nqtfry1SQqKI5yvV43bbMFPGTCj0QizM7OMjExYfjNW+FWWc1rt9usrq7udTP6YBstg4C77rprr5twBX77t397r5vQh1KpdNV9NhlTW9VP22gp0Tvz/Xfgj7TWDaXUPwI+Cbx1m8c6OOx73CpzlURMisWiWfCVeo5iH9kRls2EIwCWlpZM3qjU2hTJc3FixAkRZ8BeBF9YWKDT6aCUIp1OE4/HjZ2RSCSIx+NEIhGi0SixWMyIbol90ul0jD2YzWYBTPkdr+Nvl6jRWpPP502Ou1y/RGJk4Vvy81utlmEAyWLMwsIC/397bxoj55VdCZ4X+74vua9M7hJFUpvLVWV5pmRLA8MawNVw2e4ez0wNXBjY6G5P/7CnDXR7PIBR0wO00YY9g65pCy4P2jbKY7laMOSiJatUcpVKEkmJEncmk0xG7rHve8SbH5n38kUwSWZyyYhMvgMkYskvvnjf8uK9+8655168eBGBQADlchnpdBqRSITNLujcAret4NV22O12xGIxpFIpCCF4UYYUWI1GA06nkxetVYaLAh+j0Yh8Po94PN5h7gasK0/UvK/uGqwAOoIvgroIpAZadO+Q6dtWDcMed5/a+xYvGk8sVIpeQ0Pj4aH2qS30q0UAo8rrEQDL6gZSypSUsrbx8v8BcHKrn9XQ2CvQY5WGxqPFNseqbWNHmadWq4X5+Xk4HA7MzMzgzJkz8Pl8WFtb4wOk6JRWIWjFQKU+ATB9R9Ixov+6Wae7MU+Ug0PULDnDTUxMoFAoYGJiApVKBU6nE9VqFTMzM0w5h0Ih+P1+joCJUYlGo3A6nezkQrbgVOgWWL+gtNKyuLiIYDAIl8sFu92OqakppFIpzm+i1Y1arQaz2Yx6vd5R9Hd2dhY+nw+lUolZoMnJSczOzmJwcBDAuo41kUiwvjafz3NRNmB9FcNms3Hukt1ux8zMDMsqKQ/L6XTCbrcjk8kgFAqxFM/n8+Hy5cu4dOkSfuEXfgHf//73MTAwwPleLpeLnQDV86XqakkuQtdItaenPKtsNoupqSnOxbofnpTVvFqthps3b/a6GR3oN6an35gwAFu6h3cSj0lHfhrAjBBiEutuel8D8Mtd+xyUUq5svPx5AJc3np8C8PtCCP/G65/BhpWshsZewpMyVrXbbaRSKc7DJjULMTbqvI3OiSrdU5mofD7P8z5iWwDwXKLbyU19TQ51au4TST7J7Y7mOw6HAw6Hg51/TSYT0un0ptIyk8nEsk+SsqlsF9l1F4tFngupbnUqG0PPVaiyvVKpxPJdYsLouCnvCLjN8KjtJVv2TCbTIesjRpCkeaT8AdAhj6TzUCqVkMvluFSOzWZDuVxm5k51IaTPENS0GprTq66E3RbrdJ3VeeS9sCdznpaXl5HP5/Hee+8hEAjwCVFNBVSJHp0AugD0ularYd++ffD5fJwbQ9QqcNuTX+0kakDl9/tZt+p2uzE2NoZIJAKn04mDBw+i0WggHA4jEAjA6/VidXWVO/rly5cRCoWQzWYxMTGB0dH1BdKlpSWk02k0m01MTEwgGAwik8lw0Eb0a71eZzOMiYkJlubNz89DSokDBw6g1Wp1/ECQ9I2CC5IzHjt2DPF4HNlsli0vvV4vS7lIiiiEQCqVgpQSbreb82RyuRyGh4cRDocRj8fhdDqRyWQ4bwtYn3ymUinWtZLlObUrHo/DYDDgD//wD2E2m/H555+zVXt3oiTQWam725SjW3ZJjzabDR999BGCwWCHTvZueFIGpHw+j7//+7/vdTM68Oqrr/a6CR0YGRnpdRPuwPHjx3vdhA5QuYV7Ybt9SkrZFEL8BtYDISOA16WUF4UQvwfgjJTyTQD/XAjx8wCaANIA/vuNz6aFEP871gMwAPg9Mo/Q0NhLeFLGqlarheXlZVSrVSwsLLCBlcPh4Ak8LW7TfIECKHXuBqyPe+FwGI1Gg3PWLBYLQqEQbDYbgNt2493zClqUNRgMXBdzYGAAgUAAdrsdTqcTVquVH+12O88tjUYjcrkc536T+RawPiclmWCj0eBAimR4tBC/urqKYDAIq9XakVdEi8p2u51zE7sDKmA9QHS73VzX0+/3Y2BgoCPnidI2SLanBqWU11WpVGAymVj+l8lkmIygbeg80ZyPzqPFYkE6nUYmk0G5XObjo1xEkvipckn1HidJnxoo0qI5/R+4PY9vNBowmUxwu919s3iurco19iyehAFJQ2Mnsd0+JaV8C8BbXe/9G+U5Fyfc5LOvA3h9+63U0Nhd0GOVhsajxZ4KntrtNi5cuIDr16+jXq93VF5WVwnUFQi1MK0afTudTni9XrTbbczMzKBYLOLLX/4y1tbW4PP50Gq14Ha7UalUOIHN5XKhWq3CarUiHo8jGo2iXq8jFAohGo1iaGiII3WyOm+321hdXe1og5QSw8PDCIVCuHLlCgYGBgCsJzEeP34c1WoV6XQaqVQKgUCAZW/kEFOv1xGNRjE6OoorV65geHgY8/PzOHnyJLvptVotBINBXpGgQrNWq5VdZoLBID777DMMDAzA7XYjk8mgUChgdXWV2bDl5WV2ViJXpHg8joWFBVy9ehV+vx/ZbBZerxczMzOwWq3I5/P44IMPcPjwYXZyIStxn8+HQCCARCIBAMhkMnj33XdRrVZht9vZ7IOuJ60c0LkD0HF973XNVYccWr0IBoMPk9y+55DNZvHGG2/0uhkd+P3f//1eN6EDJFHtJ3zpS1/qdRM68KMf/ei+2zwpfUpDYyfxpPSrZrOJK1euIJvNsk02lYchwy+SupFypZs5IrmX3++H3+9Ho9FgFoccitU0gLsxV7VaDSaTiR2RBwYG4PV6WapH5glkVU4mVqSCIcc7kq/RPsPhMNxuNxtgEeOiGnVls1kuM5NIJOByuTpYIWozgI7CvMBtm29yAbVarfD5fMw8AbdLAgGbS+FI8ZNOp5l1S6VSbOpF7BnZvZPaiEw96BykUiksLi5iYWEBjUYDgUAAq6urcLlcrExyOBxsNkFQ57Q0R+wuKEzsIX0fuUQPDAygVqvhfthzzJOUEmtra5yzQxpNACzjohuNLM3JQYSsEtUJODmDVCoVtpF9+eWXcePGDa5kffToUVy9ehXhcBirq6ucz/P+++/DaDRi3759qNfrKJfLKBQKiEajsNvt7ICXy+XYZhW4TSfOzc2hWCzC7/ezRM7j8cBsNmN4eBi3bt3CyMgI8vk8zGYzqtUqOw1KKXHx4kUsLS0hGo1idnYWoVAIxWKR6dTR0VHcunULHo+H9adk5Uo1rrxeL1OqzzzzDAKBAAqFAgKBALeJgg2yeiQnvkKhgHPnzsFsNuPVV1/FW2+9hWg02nEjqzI76nhqgGO1WvnHEABCoRA7C5I2lz6vao7pHNAPIdHKKnVP26sOLGrdg63gSRiQ6vU6YrFYr5vRga38uO0k+jF42q335m5tt4ZGP+NJ6FftdhvxeBypVAqVSoVzc0jmpsrpLBYLy9fUuaGaN+P1etFoNOB2uzvmD2p+fPdzNXiivHnKO1LnFd21kdTcKyqjQ1Iyep9yp8xmM9fKbLfbHXlQlDdPC+BqCkKtVuuY71CbKJWF/kd1UclxmdwGqY2qnbc6v6ayBrQQT8FTPp/nkjdUAsFoNHKuPc1fLRYL/4/OQSKRwMrKCtfuWlxc5BIAdG1Up2Vqk8vl4jkgzensdjv3AxqzKZiuVqtwu92wWq1bStsA9hjzpKGxU3hSVvM0NHYKu7VPCSFeB/BzAOJSyqO9bo+Ghord2q80NPoVe455AtaL1Y2Pj3cYF1B0THSh6ou/WdIfsE4Bh0IhJJNJDA8P49ChQ4jH43A4HBgbG4PJZILX68Xi4iKeeuoprK2t4dixYyiXy5wIZ7fbUS6X4ff7ceDAAZhMJiSTSRQKBU7mM5vNsFgs7G5SLpfRbrcRjUZZDkdStf379yOTyWBoaAhCCHZVoZUHqnlUrVZhs9lYdkivFxYWmAmrVqvsaU9sztDQECqVCjNC2WwW4XAYg4OD+Ou//mu43W4u/EbRuRCCV2YoSY8oYKKb33//feRyOU5ypCrdRB/TeVepcKJbi8UiotEowuEwXnzxRbz77ruYnJzk1Q0q3tvtoKLSynQ8aj2GbkkfrUy8+OKL+N73vnff++xJGZAcDgcOHz7c62Z0oN+YMCpiqPFw2MV96k8B/BGAP+txOzQ07sAu7lfbgsFg4MKyxI4QW0KsEc0ByQVZNZVSmSeaU5HDnc1m46LRd4PKLhGbRewHzU1ofkRzKIPBwAwRtZdMIEhWSOYMNpuN5zqqQoZqFBEbZTKZUKvVeH+k1CFXZDp+oLNOE90j1B5S9pjNZmQyGWZp6DuB2652qnOh2WyG3W5HKBTiItVSSng8HjZ7MBqNfE5JDUXXhI5fCIGBgQFm3nw+H/x+P8v2aM5GSib1OhCzpMoZiXUkBpKOjdg1u92OYDDYwT7eDXsueBJC4Nlnn4XBsF6l+cSJE6jVasjn83C73Vw4luRlAJi2VTsNAJw7dw5SSgwMDCCZTLIV+MLCAiYnJ5HJZNg9rlKpIBAI8H7NZjNGR0fx1FNPoVqt4rPPPoPL5UKxWOTq1KR9LRaLKBQKqNVq8Hg87LJy4sQJxGIxVKtVLpJmMBgwMjKCVCrFHYqc7uiGSafTkFJicHAQg4ODKBQKHDS4XC7Oabp06RLbZFIhtuvXr3MgVKlUcO3aNSwuLiKbzaJcLqNWq+HixYtot9t8s5KmmM4ndUqHw8FBLFGxfr+fA1qv1wsAHYFPd1BLnz18+DAcDgcymQx+7ud+DlarFRMTE9yZE4kEa3QBsOsgtVHVOquOMuTAIqVEOp2G1+uF2WxGIBDY0v32JAxIgUAAv/iLv9jrZnTgxo0bvW5CB55++uleN+EOJJPJXjehA1spPA3szj4lpXxfCDHR63ZoaNwNu7FfbRcmk4mdjO12e8cCaXduEAUQ6gIucPs8ra6ucp4Oza+azSYKhQK7sW1WtkaVxZEVt9Pp7Agu6Hu65XrA+lzFZrMhEAiwRI/mSvQeBYe0uE7HQXldXq+Xc6KA9d/eRqOBlZUVmM1mDgi7Azyai7XbbdRqNZRKJZ73tdttDnoMBkOH2x49UmBisVjgcrkwNjYGr9cLr9eLUCgEr9cLn88Hu93OgRJJJymlRHXRczqdOHToECYnJ2G321miRwEYnUd1UZzQ7QJI9wedbzXoA9aDQQro1EDsXnjcfeq+RXKFEKNCiO8LIS4LIS4KIf7FxvsBIcTbQojZjUf//falobFT2Ezn3C/QfUpjN6K7T/Vbv3pYCCF+TQhxRghxJp/P97o5Gk8I9FilofFosRNj1VaYpyaAfyWl/EQI4QZwVgjxNtbrcfyDlPKbQojfBvDbAH7rXjuiFQRyyltYWEAkEsHTTz8NKSUOHjyICxcuIBwOdxwssRxUhAtABwV66NAh3Lx5Ew6HA0NDQ7xqQasAjUaDk/toVSAWi/F24XAYly5dgtPp7ChoW6lUYDQaUalUuNgsJax99NFHePbZZ9FoNJDJZAAA169fBwCUy2V4PB7YbDa4XC6srq4iEAiwyUOz2cTS0hK3a2xsDMlkEpFIBLFYDJVKBRMTEzAajUilUqjValheXobb7UYul0MsFsOVK1dY8nfx4sU7DBYocleZIjWB0uFwYHJyEhaLBYlEAkajEUNDQ3jxxRfh9/tx8uRJnD59Gs8++ywKhQIqlQqzZZVKBel0Gjdu3MDs7CxqtRqy2Syef/55ljo6nU4uCvfCCy+gUqnwaoTP52N2zuPxoFQq8UpHsVhktxpVQvj8889jdnYWIyMje2GV/JH1KZfLhZ/6qZ967A3eDv7qr/6q103owGuvvdbrJtyBfpucb6XwINDXfeqhIaX8FoBvAcDMzMzWXGk0NB4B+rhfPdL5H7Exfr+f2QtiSmieQuxLN2tExgkAUCgUsLy8zLWWyGSMzLFUSVy3agZY//11Op0ol8vsqtxsNrngrtlsZraDXAG7zRdIVkhqKFU2p5qe1et1CCHQbDZ5HwsLCzzXtNvtsNlsiMVi3F5ijlT5Gv1vbW0Ni4uLzLZZLBbE43E2VDAajfD5fADWpYTENlFAQcyNzWaD3+9nyZ7X60UkEoHD4YDVamWGymq1soEazY2NRiPq9Tr8fj/PoW02GxwOR4f0j1RQasoNfZ5A76ssX/d7dA0AbEm21/0djwP3bcVG9feVjecFIcRlAMMAXgPw0sZm3wbwHu7TecgpDgAOHz6MUqkEp9PJ1t23bt3C/v37+YYmvaPP50OhUIDH4+lw8kqn02i325iammKnkmKxyLQt0Y9SSnb8sNlssNvtSCaTMJlMGBkZwdTUFLuEkGNdMBjEyMgIbt68ydQl2S7Sje50OhGJRBCJRACsd2in0wmfz4fr16/j4MGDuHXrFpxOJwdexWIRBoMBp0+fxte//nW888554x7JAAAgAElEQVQ7KJfL+MY3voHvfOc7sNlsyOfzmJubYyqUgkeSu5Fe1ufzIZlM8o+Fep7pRtss4qZ91et1lsa5XC4Eg0EYjUaEw2FkMhkunEtF4kiTXKlUOAgdGxvD/Pw8Dhw4gKNHjyKbzbLUkNrq9Xrhdrs7ZHtjY2MwGAzsyEKU7cjICGq1GqLRKAdQwHp+1tjYGAeq90M/68gfZZ8ym80YHBx8bG19EJw7d67XTeiAKrvoF2xVerBT2Mo56uc+paGxW9HP/epRjlUAOJ+IUgVoQdXlcrFUrjvXif5oYRZAx0KwmmYB3Jb8d8v2VDkYzXsomKBgoTu/nj5HgQc9p0CLgi3gdm4T5SipVuz0HrAu00skEsjn88jlciz/o/mOEAJOp7PDfZBy7w0GA7LZLDKZDJxOJ1uoUwkcmvOq3gDqfmhuSJJJyvunc+5wODiYo+DJbrejVqt1BE8Gg6FjXuzz+TiP3+VycVkcsitX2R81SOqWRHY/p0dyRWw0GltikXaiT22Ly9rQjR8H8BGA6EbHog4WuctnWApRLBYfrrUaGlsEdR410bIf8bB9iizpNTQeN7r7VD/3Kw2N3YLtjlV3k9I9bjzsWNVvbLvG3sVOjFVbNowQQrgA/DWAfymlzG91NVeVQkxMTMhAIMCuKyaTCUNDQ6hWq4hGo0in06jX6xgaGoKUEuVyGQ6HA/l8Hh6PB6lUCuFwmNqD8fFxFAoFCCEwPDzMzh7ke2+1WlGtVhGJRGCxWHDjxg243W5YLBbU63VMTEygXC4jk8ng+PHjWFlZwdjYGJaXl1EsFrG8vIyxsTHMzc1haGgIV65cQSQSYYOGSqWCubk5VCoVAOsJgx9++CEGBwfhdrvxySefsMGE2Wxm+rLRaGBpaQm/+7u/y8zbb/7mbyIej/MqBkX/RMMCYOq4Wq3iueeeQ61Ww9TUFPvsm81mRCIRRKNRXqEhqpj2SzQzJSkePHgQFy9exMGDB+FyuRCJRDA4OIhGo4FnnnkGyWQSo6OjSKfT8Pl8KBaLGBoaYpnhj3/8Y67bNTs7i2g0ymyhxWLB6uoqxsbGEI/H2d3PYrHwyjvRu0TVN5tNNq1wOBxcd4BWV2j1ZyvYTocRQoxi3Y1rAEAbwLeklP9hyzt4ADyKPvXss8/KoaGhx9fIB8Dbb7/d6yZ0oN8MLAD0ndTyL/7iL7a03W4MmIQQf4H1VfKQEGIRwL+VUv5Jb1uloXEb2+xXm0rppJSXHk/rHs1YNT09Lev1OjMRxMqQ7I6MFYgFogkwPTabTWaOSCoGAMPDwxgcHEQgEECtVmPWRnUIJraD/j799FNWIpGUsNlsspMdSfbor91u874qlQry+Ty7AJMaJpfL8fbEftH8jSR8RqMR6XQaq6urqFQqEEIgEokwo+R2u9FsNpmJUwvV0r6y2SyfD3IFpNQS2kaVD6ryRToGt9sNv9+PwcFBxONxeL1e2Gw2nrfR95EbX7lcZoUS7cfpdHJqCskPVQc/usZ0DPdilja537rvI3Ys3Gr+0uOe/20peBJCmLHecf6zlPKNjbfXhBCDUsoVIcQggPj99mM0GnH06FHMzs5idnYWQggMDg5ifn4eTqcTgUAArVaL85osFguq1Srf2F6vt8OC2+v1IpfL4caNGwgGg5iYmMD58+cRCoUwNTUFu92OlZUVnpBHo1Hk83l23Zubm0Or1UKpVMLq6ioymQwWFha4SnU+n8e1a9c4b2lwcBCxWAyZTIbzlhYXF7G0tAQATK2ePXsWY2NjKBaLHfQ0aV9Jj1soFAAAhw4dwunTp1EqldBqtZjubbfb/BnqgMB6LtbKygr8fj/TrEQ3E31K9Krf72fnu1wuh1qtxsFOOBzG2toahoeHAawXXB0fH4fdbke73YbX60U0GsXi4iKGh4exsrICj8eDTCbD1CzR35VKBZlMBsPDw8jlcnjqqadw69YtDA0NoVQqdRTdJQoZALsb1ut1zosiZ0LqxM1mE8FgEKurqyiXy4+Ltt3RAelR9Slgc2lmL9FvkrQf/vCHvW7CHThx4kSvm9CBfrF/fRyQUv5Sr9ugoXE3bLdf3UNK19djFeXoAODAg4INmuCrC6lq0j+lLtDvFOWLk2sfBVxUdLc7WCBQYJFIJFhyls/nueAuzT/o8+QWR1I3AEilUojFYkilUixLAwCPx8P7V6261eDLaDSiVCqhVCohn8/DaDRyoKQWuyXZIcnpVNc+AFyIlr7PaDSy1TjlHQHr8yshBLvk0XmmtA6SHVLQqEoRKQ9MXYCnHCtgfWGeJH+lUgntdhsej4evg3rd6Zg27qeOY9wKVJt5NUXlbtiJ+d9W3PYEgD8BcFlK+e+Vf70J4Fc3nv8qgP+ynZZqaDxubIeylVKuSCk/2XheAEAD0iOH7lMauxVatqeh8ejR1adCJHXb+Pu1u32uS0r3yKHHKo3diu2MVQ8y/9sK8/STAP4ZgPNCCMoE/9cAvgngO0KIrwOIAfgn99uRwWDAhQsX4Ha7MT09zWxPvV7H2toaBgYGeGWCTAvIbQ24XbMIWI8sr127hlarBY/Hg4GBAVy4cAHZbJZrO50+fRrRaJQj/UqlwsYI5CA3Pj6OK1euYN++fVhaWkIymcT8/DyazSb8fj9H4N2Ji/F4HC6XC59++mlH+3w+HzKZDBsdqImK6j5GR0fh9/tRqVTwgx/8APv37+cEvXQ6jWg0ikgkgkajwUV0yQijVCrBZDIhFArxKn84HEalUsHU1BT8fj8mJycBgCWFjUYDoVAI7XYbLpcLN2/exOeff47Dhw8jl8uxUwsZchQKBa73ZDKZUCqVMDAwwD7+xHRR8qTP50Oz2YTT6cTk5CTOnTvHDJPH44Hf7+dVhkqlgmq1ytJEonbtdjuvgNBKDK2sNJtN1Ot1Lix8P2yy8hASQpxRXn9rQ1Kw2Wcn8BgHJDzCPtWPOHnyZK+b0IE///M/73UT7sDP/MzP9LoJHdjLzJOGRj9jk36VlFI+u4XPdUjpHlPzHtlYJZQaQ263G1JKOJ1Orh9E5lhk3NAtvSMVD3BbxkWucsRkkeROTXdQJWPE0qysrLDjr8lkgs1m43kWue3RXE2tSSSEQKPRwOzsLEwmE38XcNv0guYzdHxkGEHHT/NJKSUcDgenMVA9TypMa7PZEI1G76iVVK1W4XQ6mY0i+RwpkUhuB9xW+ZAMku61WCzGDBGlutCxE/tFpmKVSoVZQ5LNCSFQqVS4Nmomk0GtVuM6pKQaonkcsXd0HwDocE+8H9rtNptxbAUPM1Ztdf63Fbe9HwK4m8D1v95mo1AulxEOh3HmzBnO2/H5fJBS4urVq2yZSJShy+VCvV7ngIhMJ1qtFkvwKHfH7/djeXkZ9Xodn3/+OUZGRjA3N8fSL7vdjlQqhaWlJcTjcSwvLyOXy2FtbY01sKpzijqhoBuGcpY8Hg/+8R//EcVikQMYag/ZqAO3O66q3QVuWwOTVWQ8HkcgEMCLL76IWCzGHWZwcBDHjx9na8xqtYof/OAHSKVScDgccLvdePbZZ1kiZ7PZ8Morr2BxcRHAelAVi8U4uLJYLKjVarhw4QKazSbOnj3LAaLFYsHzzz+PdrvNFauFENi3bx8uXrzInYTklbVajR/D4TDnrC0uLiIQCLCbX71eZ4oaWJd1eTweDogKhQICgQDT53TeyFmF7D4jkQiKxeKWrMr7eUB6lH2KHA37CT//8z/f6yZ04Ld+674mUDuOfrtmj0kKASHEKwD+AwAjgP8kpfxm1///FwD/E9ZlEwkA/6OU8tbG/1oAzm9sGpNS9teNpaHxCPCA/WozKd0jx6Oe/9GcxePxsCU3vU/vUZCgSu5Ulzhgff5UKpV43kApCbRI7vF4OE2A9kcyQZPJxHM/l8vF8wxylCN5IM3Z1PeofYuLiyw9o+CJJHrkyAyAgxwKviwWCywWC9xuN6et+P1+Lk4bCAQ44HI4HOxKTEGfEIKdkGmReWBgAG63uyOgUi3OafGeghaaw5I7dbPZ5ICsWq1yEEoBkpoLVigUeEG7VCpxaZl6vY5yucxBsclk4iCQUk9obk3nUJX20f1xN9RqNVSrVbont3SvbdKn7ruAvp3535YNIzQ0dhv6dUDS0Nit2GYSrhHAHwN4GcAigNNCiDe7dOSfAnhWSlkWQvzPAP4dgF/c+F9FSvnMo2m5hkb/Ypv96m5SOg0NjQ1s0qfuuYC+3fnfjgZPUkrk83lUKhU2aWi1WohGo4hGo+wNn8/n2Vlvfn4eIyMjKBaLbLBA+7p8+TJ+4id+Ah988AEzLTabDZcuXeqgR9WkNIrELRYLSqUSstks6vU6qtUqJyUSRUgRdrdTC632t9ttRCIRHDlyBACwsrICt9uNSqXCkjxyXVFrBxiNRmZ2XnzxRVy7do3rSpXLZXzlK1+BEAKlUgkHDhxAsVjEvn37WNr41ltv4cSJE7h58yYSiQS++tWvYmRkBJlMBpVKhVk3AOykUiwWmSKnQr0vvPACzp8/j1gsxpK++fl5TE9Pw2AwoFwuY2RkBGfOnMHw8DAymQyvYpDzzYEDBzh50uPxIJ1OM208PDyMYrHIrJZ6M9N5JfMOKWUHjWw0GlGtVtlNRgiBW7duwWazPRaJ0W4dkKhQcj+h35inP/iDP+h1E+7A3/zN3/S6CR3YSv20B1ghfx7AdSnljY3P/yXW68Nw8CSl/L6y/YcA/ul2vkBDY7fjAfrVplI6KeVbj7xxjxAk4SdDA6olZLfbYbVaWfKlzrmAzev/SCmxsLDA5ldLS0tcN9LlcvFcRzWiAMBmFNlsFvF4HLlcDlJKLiZL29A1ofaRxIwkeCrTQ+YMLpeLGRYyVaBjpOOnthSLRYyNjWH//v3sHEjsk9frZdZmdHT0DmONTz/9lOs3kcKJVEKq7A64rXCiz9L5yGazPKem7T0eDyu71LmZatKmzpWr1SozUsBtE496vc5sE303MVp0HsiYQpVhqte8+3qrxZC3gp2Y/+0482Q0GnHmzBn87M/+LD7++GM4HA44nU7EYjHUajXOgxkeHsbZs2dhs9mwtraGRqPBRb0IhUIBb7zxBkqlEpLJZIeDiFooTL2IdBPRzSqlRCgUghACBw8eBACUy2Xk83kuGkY5N+SYYjKZOEDyer346le/CgC4ePEims0mJiYmsLa2Br/fDwBsARmPx1mudurUKRw5cgQej4e1r06nk+V10WgUTqcTpVIJtVoNV69exdDQELLZLNtaPvPMM/jggw/wve99DwAwMTEBt9uNXC7HhVOllBycNZtNlEolDA4OQkqJ2dlZjI+PI5fLsVtNOp3GxMQEKpUKjEYjUqkUisUiW7r7fD7cunWLf3A+++wzDA8Pw2AwYGlpCRaLBQMDAwDWJYPZbBbDw8MQQmBlZQXAuiSScqSIul9eXobf70exWORzXKvVuLAw/SButbo0Xe9tYFcOSPV6HQsLC71uRgfo+vcLvvGNb/S6CXfg7/7u73rdhA5stQbLNqUQwwDUm3MRwAv32P3XAagnxrax7yaAb0opv7ulRj4C1Ot1/PCHP0Q8Hsfa2hoqlQq7TdFiBU3OKGeDJkY0SaLfqp/+6Z/GCy+sH3YymUS1WuXfWVWKdDf4/X6sra1hamoKt27dgt/v50mZ2WxmWTtw5/WhBbUbN26g3W6zM1gwGMTg4CAcDgfK5TIGBgZYTmSz2RAKhZDL5fDhhx/i13/917kIZzgchtlsxokTJ3jSeC/87d/+LZrNJgYGBuD3++F0Onlhb6v49re/jXfeeQfvvfcenn76abz99tucAwKAJfkkoSJZN0mv7HY7Go0Gzp49i4sXLyKTySAYDOLq1atwOp0wGo2cPlCpVOBwOHguQXkrNIG1WCzsokZSKHIyo5IaNDcYGxtDIpHY0jFu023vXlK6vgXlzWSzWZ7vUEBF6QTqYjfN1YA7ra1rtRoymQxP4BcWFjgwcDqdLI9TLdDpuRCiI7/KbrfD7/dzYGe32zmPiIrvUikYo9GIRCIBm82GgYEB/iwA+Hw+vifV7yP5ID0Wi0Wsrq5iaGgI09PTaLVaiEQiLFv0eDwsAbTb7ZxCQvdbu93GrVu34PV6eYGZSroAYB8A+k5VcgisywtzuRwSiQQ7+hkMBvh8PmSzWSYQaCEbQMcCeLFY5FwmqZQUolQauk7UHywWCwqFwh0kBrkaEiGhlqFRHyn/qlardeRO3Q+Pe/63o8GT0WjE7Ows5ubmkM/n2eL7Bz/4AW9Dg46a7KfekPScLBmJWbHb7VwbCECHvhW4XdmagqpcLoexsTHYbDYcPHgQ+XwegUCAVw/I8pusJcn+MhqNolar4bvf/S5eeuklrK6u4tSpU9ymyclJrmN19OhRVCoVjI2N4fTp0/jSl76Ea9eucQegQKZYLKJYLOLYsWP8YwCAf4ir1SrbslMHv3btGgd7sVgMkUgEUkpmv8juPZvNolarIZ/P8woD6VRnZ2d534VCAaFQCGNjY7hw4QIcDgeCwSDbry8vL7N3fz6fZ6asUqlgaWkJbrcbmUyGPxcOh7kG1szMDNLpNJLJJF/TUCiEer3OK0eUsEmmGGRKQYFdOp3mIO4Bc57uid06IBHT2E9QGeJ+wFe+8pVeN+EOnDlz5v4b7SDupTdXt9mmFGKznW4qWBdC/FMAzwJQC2CNSSmXhRBTAN4VQpyXUs7dt6EaGrsIT4oRS7PZRCwWg9lsRiqVgs1m48VTmmfQnE1V6qhMFE3As9ksMyHE0litVg7Kuk0WaN5HAQjV/qQcrGg02mH1TQZWZORArIfJZML169c75p1kWhEKhXgRBQDbjFMQYbVa0Wq1sLi4yLngdBzEHBErU6vVmP0hAws6lkwmg5WVFTbNSKVSbHqh5nYB6Ajc1MC00Wiw6RkpwtLpNM9Nq9UqK4iIOaK6o+VymU3EcrkcKpUK3G43L8TQeVRVXir7R+2hoE4lN1RTC+C2QqnRaHDef7/M/3TOk8aexJMyIGlo7BQeoE8tAhhVXo8AWN5kv18B8DsAfkpKyU4aUsrljccbQoj3sO6ApIMnjT0FPVZpaDxa7ESf2nHmKZfLodlssh040YMUfVKUrlp8q051dEKy2SzMZjMikQi++MUv4ty5cwgEAgiFQviVX/kVvPnmmzCZTJiamuL8oXq9Dp/PB6fTievXr2N0dBT5fB4ejwfZbBavvfYabt68yc5wVDF5ZmYGV65c4e8eGBjAxMQEEokErFYrpqamAKzL86anp1GpVDA0NMSsVzqdxgsvvIB6vY5gMAiTyYRoNIp6vY7l5WVMTU2hVCrB4/GwNC0SicBmsyGfz8NkMsHpdDJ9GwgEsLq6imQyye50ExMTeOmll3D27NmOgmIHDhyA3W5HrVZDIBCA3W5HMBjExYsXYTKZMDExgZs3b2JgYKCjOvTQ0BC8Xi8cDgccDgeWlpZw5MgRtNttLiR88eJFBINBuFwuLCwsYHR0FO12GwcOHIDJZMLIyAgSiQRqtRrMZjPT21TZm9rl8XggxHrRYKKQq9Uq3G43CoUC6vU6arUaarUajhw5smW7yn4rHvs4QCtY/YR+Y56mp6d73YQ78MUvfrHXTejAuXPn7r8Rtt2nTgOYEUJMAlgC8DUAv6xuIIQ4DuA/AnhFShlX3vcDKEspa0KIENZlFf9uO1+uobFb8CSMVQaDAV6vl+dypAYi+ZeqDiKWRy3vQvsA1mWnzzzzDOcfqRI7klF255mrE2rKAXc6nTwnIqmezWZjxzpitSjFgOYmExMTzK6QRI5YK2JVaD80p7XZbOwgPTY21mFTTvbsxBRRDpBqz03vhUIhVKtVRCIR/t5AINCRD06SWtVxkFgdq9WK8fFx1Ot1zt0ymUwdrn/EFhHjRc5+6p/b7eYUEJvNxsok1d2Qcta7Axn6P22jHh/J+Gg7yuXaLAfufvfb48SOBk9UBykSibA1IiWN0Ykji0W6CeiiqzaRADg50Gg0wuv14uDBgzyRn52dZamO1+tFKpVCKBTC4cOHcf36dRSLRZ7UHz16FLOzszhx4gQuXbqEYDAIj8eDlZUVzuWp1+scULTbbZTLZYyPj+Ozzz6Dz+dDOBwGAHzta1/D22+/jXa7jcXFRXi9Xvbqb7VaLFWrVCo4ceIErl69ikqlggMHDsDn82F+fp4pYpLyUcciSZvZbMb4+DiA9YrWPp8PL7zwAtbW1vDjH/8Yg4ODiMVinAC+urqKYDCIyclJJBIJ5HI5lMtlDA0Nwe/3o1qt4tixY/D7/fD7/cjn89yBYrEY64NtNhuuXbvGNHu5XEYgEMDTTz+N8+fPIxAIYGhoCADYEj2Xy7G5BNWSAsB2l7VaDX6/H+l0GmazmaV7VAOK8guIDi6Xy/joo48em63yboQQgm1R+wVbDW53Cv14H+zfv7/XTejAVu6hB5BCNIUQvwHgFNatyl+XUl4UQvwegDNSyjcB/J8AXAD+amNQJEvyQwD+oxCijfVi7t+U96j2rqGxW/GkjFUGgwF+v5/neZSjpAZM6t9mluV0ngKBAM8FKUeI/mgBVl2E797P6Ogo7HY7XC4XLBYLvF4vS/8oYFADGrUtbrcbwWCQZYb020kyQXXuSov/anssFgvnDlKwR/M8+k41cKTjpvYHAgG0220EAgEYDAY2maA0EwrUgDuDJ3ovEomgVCpxwEfH5fV6OWiiAIpyqUwmE9fPMhqNcLlcCIfDaDabHHQC4CCU7mu6vmrQo87jKZDqlvDR/+lRlTfeD3uOedLQ2Ek8CQOShsZOYrt9aiPh9q2u9/6N8nzThDQp5QcAnnqAJmpo7DrosUpD49FiTwVPrVYLL7zwAgqFAo4dO4ZoNIrZ2VlMTU2xY87hw4dx4cIFGAwGLrhVLBZ5RYAkQZcuXUKz2cTS0hIqlQqef/55ZmdOnjyJw4cP49q1a3A4HHjqqadgNptx9epVhMNhRKNRvP/++6jX63j77bfZEr1QKKBUKjG9nMvlOIJuNBpYWVmB1+tFq9XCysoKuyYRE/T6669z0uDa2hqbMAwODiKbzSKVSnEh3cuXL7Pbyc2bN9l9qVwuY3V1FbVaDeVymaWA6XSaVzmazSbcbje+973vYXp6GhcuXOCq1vF4nGWJAHDo0CHEYjG43W5mzYxGI3w+HxfqnJtbTyMgetnr9aJSqSCZTOLkyZNIp9NIJBIdtPaNGzdgNBqZKST79WKxiHq9jlAoxLaZKysrCAQC7ACYTqfZtMPtdsNsNmNpaQnT09Ps+EduLkTvCyHgdDpRq9U086SAKPh+wvz8fK+b0IHZ2dleN+EObMWpbCexFYnDk9KnNDR2Ek9KvyLmwGq1sjEXsRUkketmn1TWCLj9O0XmU8RYEWtETMbdJH+0r0KhgFqtxmqeer3ewawQ40SOeSQpFEIgmUwik8l0pBgAYMUQtZsYHGJdSM6XyWSQy+UAAG63m4vzkruwap6humjSfuv1OhtLkNyRjCXoPKlSP/VRdbYjMwxiw8hww2q18vHTc/p+kiIajUZOnSHmTJVO0n7pj+aJBLJ8J2ZKle/R8arXm4zEVNfA+91reyp4EkJwfhG5ukWjUdy4cQP79++Hx+PBRx99hImJCQSDQbbLdjgcCIfDuHbtGp56an0xMpvNolqtYn5+HsFgEHNzc6zdDIfDiMViHEg0Gg2USiXYbDYMDg5y3lWpVEIkEkGtVkM6nQawLl9pt9tMzcbjcZYHkrc+3TSNRgMTExOcc0Laz3w+z3aKdJNXKhUIIeD1etlKPZVK4eDBg1xrwOPxoFqtotVqIZVKoVAoYHBwkI8jHA6jWq1iaWkJS0tLKBQKiMViWFpawokTJ9But1Gv19Fut/lHaWlpifOlisUiLBYLnE4nVldXkU6nkc/n2RI9Eolw0Eg/JFevXoXJZEK1WoXf74fD4WBXFqvViitXrrD7SjKZxPDwMEqlEtu7njx5EqdOnYLD4eAfPLvdjuHhYT6vFMSRJbnD4WDpntvtRjabRbPZ5OvxmKwqdy22qgHeKXRXDu81+vE+iMfj999oB7EVByOgP8+lhsZux5PQr8gdjmoHqeka9Afgjuf0SNsC65PpYrHIAQm9R7nqarBBE3Q1ECuXy7woS4EXcFseR4GJ2gYCBStq/SZ6vNsffTcdA9VKovIHlPvfarU4TwhAR40l+qvVaigWix1lW+hcqh4B6udJvkfzUUqPoAVzOn9UEojaql677tdUD5XOiXrOCN3Bb/f17f4ftaX7+lO7t4PH3af2fpaixhMJNWH0SRiYNDQeN7r71G7qV0KIV4QQV4UQ14UQv93r9mhoEPRYpaHxaLETY9WOMk+UhBeJRHDq1CmmQ2dmZrC4uIi1tTVmRZxOJwYGBpDJZFhuRgwHsC57mZubw5EjR1AqlVAoFPD0008jkUjgu9/9LqanpzE2NoZms4nFxUW8+OKLMBqNuHTpEicJkn/+8vIyvvGNb+Dzzz/vkLIR40I1pNrtNsLhMJLJJMrlMoLBIMrlMpaX1913f/mX142kCoUCpJRwuVwoFotYWlpi+Z/L5UKpVEI8Hoff7+faBxMTEzCZTOyX7/P5cPnyZczMzKBQKKBSqaBcLiMajUJKibW1NYyMjLABxb59+7C2toYvfelLeOutt9hhTEqJgwcPcr0noliz2SwqlQrGx8cxOjqKTz/9FMFgEEePHsXc3BxarRZqtRparRbGxsZgMBgwODjIFHc0GkU+n8fCwgKOHDmCarWKzz//HPv374fP50M+n2d63mq14uDBg8w8eb1erK6uYmRkBHa7HdeuXeP6AW63m+sLEFtnsVjQaDSQTCaRSCS2VCj3SZFCAP23akm11voF/ehk1W9t6pck3McBIYQRwB8DeBnr9umnhRBvagMKjX7Abu1X2wWxPCQRU40iSN5GznjdNZ6IeaDz1G2uoLrqdX+uu04UzSlUg4fu71X3A9xmSGib7sbcr0AAABi6SURBVCK8QGeNUpIOdrtFt9ttrslkMpk6JG9q4Wvat8qI0X5oW6vVCiklt4U+oxqrqTVS6RxQm0kiSNeB/rrPQfejel5VVz71+NXPqJ8jqKyjem275Znd1617P/e61/aUbK/dbmN5eZnzbWq1GtxuNy5fvox6vQ673Y56vY6hoSGWxlGeTS6Xg9lsRiwWA7DulvLee+/B6/Wy5aLBYEAikUCr1UK5XIbZbEY+n4fL5eLCY1JKDA0Nwefzcf6U3+/H559/zlJAsi+/du0aDhw4AIPBgEKhALPZjPn5eaaKBwYGOqoqGwwGXLp0CaVSiW/CoaEhpNNphMNhBINBuN1upNNp1Ot1DA4OIhQKodFowOfzcS7SiRMn8M477yASicDv97N0kKrcUxB2/PhxnD59Gh6PB0tLSzAajXjvvfdgNps5j2lgYABra2sAwMGex+NBs9nkAHVpaYkrZX/88cfYt28fd9pGo8GdgPKeKpUKB3SNRgPz8/NcIbtUKmFiYgJzc3NwOBzI5/OIRCJoNBpMc2cyGUSjUWSzWayursJqtaLdbsPhcGBtbQ0Oh4Od9qxWK/x+P3K5HHK5HFPzW8GTMCBJKTng7xf0Wz5PsVjsdRP2DHZpn3oewHUp5Q0AEEL8JYDXAOjgSaMvsEv71bZB8i6Sk5FcmORr6nkgqRjJ6FQ0m022Dye5G82N6JE+p7rs0WsqukrfTa7AtKBO8xVa8Cc5ncFgQK1W47wjldVQZXzdOUmqHXej0egIZNSArDvnidIvunPAKEgB0BEIqe7UwN2DJzpfJNNrNBr8mrZVrwddLzVFpdlsss18d2DUHUCpcj5VFqkGTHRtaBvaF11vuh+26ua7p4InDY2dwpOymqehsVPYxX1qGMCC8noRwAvdGwkhfg3ArwHrVsgaGjuBXdyvNDT6EnuOeQLWmZADBw4wmzA9Pc2Mgt/vh8ViwczMDIrFInK5HBsLUCEwYkQ++OADTExMMLtDRb7Ir39sbAyFQoF960nuNTY2hvn5edhsNoTDYbz66quwWCxYW1tDPp/Hvn37cP78eUxMTKBSqaBSqeDatWvctng8jvHxcS4A63A4sG/fPgDrhSallOxYUqlUMDAwgEqlAqvVinq9jnq9DqvVikAggFqtBofDgd/5nd/BqVOnsLy8jFAohDNnzgBY98unek1TU1NwuVyo1+totVp4/vnnkc1mcezYMWYf9u3bh1wuh4GBAZRKJT7f+XyeC/RGIhGsrKzAbrdjenoabrcbw8PDuHr1Kl8jp9OJZDKJYDAIKSXy+TxGR0dx69YthEIhluMFAgGcOnUKNpuNa1gZjUacO3cOrVYLlUoFi4uLEEJgZWWF60DRqgUxjSMjI1hcXOTaD61Wiw007HY7u/VRomO/rDz0A6jOQz+h3wwj+k0iB6DvrtlWpLDAru1Tm+k87vgRkVJ+C8C3AGB8fLy/ipVp7Gns0n61LVCNIjKtIrmYKhvbTCLWbTAAAD6fD81mk93eaM5FUrdupqZbfhcOh3nsNJlMcDgczDJ1u+2RMxzty+Fw8HGo46/T6ewwYFClbMQG0fwwFAqxozS51HUXpyWZo+pKR8dOqiwhBBwOB6dH0H1EbVKZJ4LZbIbf70ej0YDD4WAZn8vlgtvt7qhvReeDghH6Hxm5Ub0tYs3oWKjmFLWbpI0Eas9mUj31ucqWdZ+H+2FPBU8mkwkvv/wyTp06heHhYRw6dAiVSoVPrMvlgtfr5Twnp9OJeDwOk8nE7iiUT/H000/D5XLhwoULKBQKmJ6extraGttdu91ueDweNBoNlMtlLjTr8/kwMDDAznKzs7MolUp47rnnMDg4iP3796NcLuO5555DqVTC4uIiSqUSS/SsVisajQaGhoZQLpdhtVrx5S9/GQDw8ccfo9FoIBgMIhgMIhaLwePx4MiRI/jRj36EkZERZDIZCCEwMDDAcsM33niD3WSq1SrLC8mdz2QyIZfLoVKpwOl0YmpqCouLi9i3bx+Wl5cxOTmJarWKSqUCj8eDSCTCnYfsLymfqtVqsT7WbrdzftbAwACq1Sq8Xi9u3bqF5557Dul0mv9nMpkwNDSEUqnExYhXVlYwPj4Og8GAZrOJp59+GjabDVevXoXf7+cfi6GhIS7OC4DbS05/jUaD22az2ZBKpWCz2eDxeJgipx+4mZmZOzriZnhSVvPoB7afQHLYfoHP5+t1E+4A2dv2C/pFR/6YsAhgVHk9AmC5R23R0OjALu5X2wJN9GnuAaCjWG633Guz4IkenU4nzwvIcpsm+hTAdOc+AbeDJ5/P15F7REGEapdOuVBq8ESLuz6fj7+Hxl+Hw8HBIP3RcanBU6vVgsvl4sCLcp02y5FSj5lAjtCUR68GNGrwCWwepFDgQ/n1dP4dDge3hY6fntPn1LwqmqOpkkOLxcI5WXTeaV8q1GCI5r5qPlO386JqZ94vY5WW7WnsSTwpA5KGxk5hF/ep0wBmhBCTAJYAfA3AL/e2SRoa69jF/UpDoy+x54Ing8GAVCqFQCAAs9mMGzduIBQKoVarwWAwIBKJIJFIwOPxsDyNPkNRscpSWa1W2O12lMtlZnlIMkRFxyhBkb6DkuKi0SgKhQIzNufOnYPdbsfs7Cy+8IUvoFQqIZ/P48iRI2wY0Ww2EQ6HmckJBoPI5/N49913AYCj+HK5jMHBwQ7WyGAwIBgMYnFxEU6nE8FgkJP1yGDC5XIhmUzii1/8Ii5fvox8Po9UKoXV1VVe6Wg0GgiFQmi324jFYuzWNz4+jng8jiNHjiCRSODw4cMAgOXlZRiNRrjdbmQyGeTzeYTDYXg8Hpb0AbdrLJFEklixfD6PtbU1uFwudtqjulWJRIKllK1WC5lMpqNOwfHjx5FKpVCv15kmB4BEIgGv18vJlLQaQ3UD6P6Ym5uD1+tl44np6Wmsrq5u+X57UgakrcoYdwr9JpPbqiRtJ9Fv52ir2I19SkrZFEL8BoBTAIwAXpdSXuxxszQ0GLuxX20Xm7mlEaOjFnO9lzGAykh0O7Dd648+o7IvxNaojI/KOKlMmCrb62bIVGmcWsRVlf2pk/ludm0zh8Fuh7rN2LPNHtVzcbfzpu7jfp9T0X1NNjvH6rb0uFn9J9qXahKh7l8dH7vvh35J29jxWUWz2cT4+DiklJwLZDKZ2PHkueeew+eff45yuQyn04lisYhEIsGFzMjto1qtwul0IhAI4OjRo7h06RJarRYGBwfhdDpRq9WQTCY7aMhEIsFBlNVqZUe9SCSCXC6HyclJNJtN3Lx5kwOzW7duMa1LuTgku6M2UMFL0rN6vV4sLS3B7/ejUqlASgmz2czFZ4PBIGZmZpBMJnHs2DHUajWkUimMj49j3759+PDDDznwOnbsGG7cuIHBwUFEIhEkk0lEIhFkMhlMT0+j0WhgYWGBtb7JZBKHDx/mHCaTyYR4PI7JyUnk83nk83kOeL7whS/gk08+gcPhwMLCAkqlEsbGxtjtzuv1slSQirI99dRTSCQSqFQqyOfz8Hq9CAaDsNvtWF1dxY0bN+BwODA5OYmFhQW2ex8cHGR3mxs3brD1e7FYhN/vRzabZdqX6Nx0Oo1KpQKHw4Hl5WUkk0mEw+Etucs9Kat5/ei2Fw6He92EDvRbDhbQf5OlfpFCPC5IKd8C8Fav26Gh0Y3d3K+2i+58JHXi3T2ZBsByre7fJ3KYU4Mg9Xm3ZK87b8put/M8UJWWbRZEmUwmdswj+R3lSpFdNwDOV1Jd8NTgifZjsVjg8/m4HTS3tdvtd9idkyRQPQa3283SOwCc80WSQWoLcHucUQMxktmpVuuq1I+uBQCes1HwQk6G9H86Nvp/s9lkh2a6r9XtCZu1a7PcNlUquR3sOeZJQ2MnsVtX9zU0+hW6T2loPHrofqWh8WjxuPvUQwVPQohXAPwHrEsh/pOU8pv32p4kdGQiUKvVMDw8jFwuB7vdjnQ6jVgsxoXE2u02VldXOfqs1WpIp9MAbkesk5OTSCaTmJqa4v1T7aB6vY5QKIRCoYBSqcRMUKvVgsPhQKFQwNDQEPx+P5LJJFqtFvx+P5aXlzE8PAyDwYDZ2VnYbDa0Wi3Y7XYkk0kudBuJRJiVAsCrB8FgEBcvXoTT6US1WkWpVMLo6CgWFxfh9/vRarUQDoeRy+Vw7tw5HD16FLOzs6jX6/jhD38IAJxw98477yAQCLCRRiaT4cK4LpcLRqMRBw8ehNvtRq1Wg9PpxCeffMIrFiSBi8ViiEQiqFarCAaDOHfuHMbGxthc4+WXX8YHH3yAkydP4vz58/B6vSiXywiFQti/fz8+/fRT1Ot1xONxLCwsYHR0FO12G9PT00gkEkgmk7BYLAiHw3A6nZiensaPfvQjDA4OsllEpVLh+6BQKLBUj+SVJB0kJqXRaKBUKnFNMCEEYrHYlmjb3byat51+tZ26BzuFRqPR6yZ0wO/397oJd0AbRmhoaAC7t19td/6nSs9o3KJ6SKqEbDOWofv3idgTMkxSC7WSU123zE39I5aHXOGISVKL5qoslGoY0Wg0OIVEZYdon93Mkyrva7fbbHSxmTyP2DcC1cFSHQNVJkdlfdTz2C1xU7cHcIdkcTODDfWaqM8JZIhBSiF1P5vJ+DZ7T62BtVm7N2OttoK+Zp7EA1ZtP3DgAE+AyfGjXq+zFXalUuFghYKPkZERFAoFzsEBbjuOqPTl9PQ0VlZW4HA4EIlEkM1m2Q6dcmUikQjy+TwXpqVir1Tg1efzdRTLJSt1utFbrRaq1SoKhQKee+45XLp0iTWvJD8rlUo4dOgQgPXcrHw+j8XFRT4Hc3NziEajqNVqGBsbQ7PZxMsvv8wudWRZaTQasbCwAKfTibW1NYyOjqJYLDI9HI/H4ff74XK54PF4YLFYsLi4CI/Hw3VKUqkU53eRS+Da2hosFgsuX74Mv9+PgwcPYmFhAQMDAyiXy5y7RQFkqVSC2+1GLpfD4uIiO6uQTeVTTz2Fa9euwWKxYGRkBEajEaurqzCZTCgWi3yt6UeBaGZySaTCdGQDarfbOT+L8qz8fj/8fj+uXr26pRWFB+k82x0MHge226+MRiOcTudONvG+6Df3v+4Ci/2Afisk3Ks+JYSwAvgzACcBpAD8opRyfuN//yuArwNoAfjnUspT2/pyDY1dgN04Vj3I/E9suNypQYNqJ64+32ziTvsAwPniJJtT3ero/XvlPbndbv6s+qi63d1tQYny02k7VbanOsupuVHq8ZBsjz5LbVftvekzlOOvBi4011Pd9sg1kL6n26JcPR6j0QiXy4Vms8nfTUEo7ac7D0t1DKQAidz2aJ/q9aB9qvI9FRSQ3k221/0eyQW3alW+E33qYXgtrtoupawDoKrtGhp9AfWH6H5QBoNXARwG8EtCiMOPuYmbQfcrjb6F2qfu16+22Ke+DiAjpdwH4A8A/B8bnz2MdVe8IwBeAfB/bexPQ2PPYReOVXqc0uhrPIaxqgMPI9vbdtX24eFhJBIJ2O12DAwMIJfLsYTOYrEwI+TxeJDNZrmuk8ViQS6XY1YDWKf1XC4Xy/BmZmbY5MDv97NZwdraGkfHVEB2ZGQEKysrCAaDSCaTcDgcXODV4XDAYDCgWCxyEbFgMIjl5WWO5kulEqampnD+/HmUSiXefyaTQbVaRbVaxcTEBKLRKO/Hbrcjl8uxPNBsNqNSqSCbzWJychJXrlzB3NwcJicnmeEiSpuYp/HxceRyOTSbTa6tNDQ0hGq1inq9zizX0aNHmerMZDJIpVJM/46Pj3NtqPn5eezbt4/NH8hNcGVlhYvzkiyQirqZTCYcPHgQt27dwvT0NDKZDH+OJIDxeBzDw8Pw+Xw4e/YspJRcrBgAkskkpJSo1+soFosolUowmUwIBAKIx+NIpVJwuVwIhUJcmNhms8HtdnNhvPvhAVYeeDDY+DwNBvdkUh8D7tuv1D41NDTEK1/9ApJn9guIme4n9FuR3Me0mreVPvUagN/deP7/Afgjsb7s+BqAv5RS1gDcFEJc39jfj7fTAA2NfscuHau2Pf8bGhpiFoPGcJUhuZt0bGM/HY+q5IzYG7VG072YJ/p8t9TsbnKzzaTx6naquQLNy7p/T7tleaoBA7EqjUaDU082M87oZo82c8i72/Gq0jg671QEV3X4U80qugMPlfmhuSBdP9Vso1s6udn9TUYgm13jzdqrSjC3gp3oUw8TPG27arsQonD8+PGrD/Gd/YQQgGSvG/EIsZuOZ/x+G5w9e/aU0WgMKW/ZhBBnlNff2rg3CVsaDHYA9+1XXX0qMTMzc+sRfG8/Xn/dpvvjUbXnQfoUcO9+tZU+xdtsWIrnAAQ33v+w67PD9z2KR4RYLFaMxWL3HKsoN7NarSKXy911u4sXL+KP/uiPHm0Dt4d+u2cfBo/kWJLJ9V2USiV+b21tDQA4NYCQSCQe5qv26lj1QPO/l156aa/M/wDdr3qFXo1VHXiY4OlBqrZflVI++xDf2TcQQpzZK8cC7L3jkVK+ss2PbGkw2AFsq19JKR+JL3g/Xn/dpvtjJ9vzmPrU3bbpdX/UY1UfYi8dC2GXjlVP9PwP2Fv34l46FmBn+tTD5Dxx1XYhhAXr+vQ3H2J/Ghq9xIMMBo8Dul9p7BVspU/xNkIIEwAvgPQWP6uh8SSiH/qGHqc09hK23aceOHiSUjYBUNX2ywC+o6u2a+xi9MVgoPuVxh7CVvrUmwB+deP5VwG8K9eTCN4E8DUhhFUIMQlgBsDHO9RuDY1+Rs/HKj1OaewxbLtPPVSdpweo2v6t+2+ya7CXjgXYe8ezLWzkW9BgYATweq8GgwfoV48C/Xj9dZvuj35rD+NufUoI8XsAzkgp3wTwJwD+3w1DiDTWBy1sbPcdrCfsNgH8upRye2XmHw59e14fAPpY9hD6Zax6wud/wN46nr10LNvGg/Qp0W8FNjU0NDQ0NDQ0NDQ0NPoRD5PzpKGhoaGhoaGhoaGh8cRAB08aGhoaGhoaGhoaGhpbwI4FT0KIV4QQV4UQ14UQv71T3/uoIISYF0KcF0KcI694IURACPG2EGJ249Hf63ZuBiHE60KIuBDigvLepm0X6/jDjev0uRDiRO9arrET6Le+udn92ksIIUaFEN8XQlwWQlwUQvyLPmiTTQjxsRDis402/W+9btNeQb/1h+1Cj1Ua/Qbdp3oH3aceD3YkeBJCGAH8MYBXARwG8EtCiMM78d2PGD8tpXxG8cP/bQD/IKWcAfAPG6/7EX8KoNv3/m5tfxXrzlYzWK8M/n/vUBs1eoA+7Zt/ijvv116iCeBfSSkPAXgRwK/3wTmqAfivpJTHADwD4BUhxIs9btOuR5/2hweBHqs0+gK6T/Ucfwrdpx45dop5eh7AdSnlDSllHcBfAnhth777ceI1AN/eeP5tAP9tD9tyV0gp38e6k5WKu7X9NQB/JtfxIQCfEGJwZ1qq0QP0Xd+8y/3aM0gpV6SUn2w8L2Ddmne4x22SUsrixkvzxp92/3l49F1/eETQY5VGr6D7VA+h+9TjwU4FT8MAFpTXi+jx5OMBIAH8vRDirBDi1zbei0opV4D1CRaASM9at33cre174VppbB36em8DQogJAMcBfNTblqyv6AohzgGIA3hbStnzNu0B7IX+oMcqjX7CXrhOuk9pdOCh6jxtA2KT93bbKulPSimXhRARAG8LIa70ukGPCXvhWmlsHfp6bxFCCBeAvwbwL6WU+V63Z6Pu0TNCCB+AvxFCHJVS9kWe2C7GXugPeqzS6Cfsheuk+5RGB3aKeVoEMKq8HgGwvEPf/UggpVzeeIwD+BusU9FrRGluPMZ718Jt425t3/XXSmNb0Nd7CxBCmLEeOP1nKeUbvW6PCillFsB76K88sd2KXd8f9Fil0WfY9ddJ9ymNbuxU8HQawIwQYlIIYcF6Ffk3d+i7HxpCCKcQwk3PAfwMgAtYP4Zf3djsVwH8l9608IFwt7a/CeC/23BdeRFAjuhdjT2JXd03dwJCCAHgTwBcllL++163BwCEEOENxglCCDuArwDYq6uhO4ld3R/0WKXHqj6E7lP9B92nHhI7ItuTUjaFEL8B4BQAI4DXpZQXd+K7HxGiWJfFAOvn7M+llN8TQpwG8B0hxNcBxAD8kx628a4QQvwFgJcAhIQQiwD+LYBvYvO2vwXgvwFwHUAZwP+w4w3W2DH0Y9/c7H6VUv5JD5v0kwD+GYDzGzlGAPCvpZRv9bBNgwC+veFkZQDwHSnl3/awPXsC/dgftgk9Vmn0FXSf6i10n3o8EFJqOaOGhoaGhoaGhoaGhsb9sGNFcjU0NDQ0NDQ0NDQ0NHYzdPCkoaGhoaGhoaGhoaGxBejgSUNDQ0NDQ0NDQ0NDYwvQwZOGhoaGhoaGhoaGhsYWoIMnDQ0NDQ0NDQ0NDQ2NLUAHTxoaGhoaGhoaGhoaGluADp40NDQ0NDQ0NDQ0NDS2gP8fwJEJnPbeUU4AAAAASUVORK5CYII=\n",
"text/plain": [
"

"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Matrix V and matrices W and H after training using R = 10\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"

"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Matrix V and matrices W and H after training using R = 15\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"

"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"R = 4\n",
"W, H, V_approx, V_approx_err, H_W_error = NMF(V, R, thresh=thresh, L=L, norm=1)\n",
"print('Matrix V and matrices W and H after training using R = %d'%R)\n",
"plot_NMF(V, W, H, V_approx, V_approx_err, figsize=(12,2), wr=[1, 1, 1, 1])\n",
"\n",
"R = 10\n",
"W, H, V_approx, V_approx_err, H_W_error = NMF(V, R, thresh=thresh, L=L, norm=1)\n",
"print('Matrix V and matrices W and H after training using R = %d'%R)\n",
"plot_NMF(V, W, H, V_approx, V_approx_err, figsize=(12,2), wr=[1, 1, 1, 1])\n",
"\n",
"R = 15\n",
"W, H, V_approx, V_approx_err, H_W_error = NMF(V, R, thresh=thresh, L=L, norm=1)\n",
"print('Matrix V and matrices W and H after training using R = %d'%R)\n",
"plot_NMF(V, W, H, V_approx, V_approx_err, figsize=(12,2), wr=[1, 1, 1, 1])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Further Notes\n",
"\n",
"* An application of NMF can be found in the [FMP notebook on NMF-based audio decomposition](../C8/C8S3_NMFAudioDecomp.html), where score information is used to guide the decomposition. \n",
"\n",
"* Further extensions, implementations, and applications of NMF can be found in the \n",
"**NMF Toolbox**."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" "
]
},
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"\n",
"\n",
" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
"\n",
"

"
]
}
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