# Adaptive Echo Cancellation

In this notebook we will use the adaptive LMS filter to estimate the impulse response of a communication channel that introduces multiples echos.

```python
%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np
import scipy.signal as sp
import IPython
from scipy.io import wavfile
```

```python
plt.rcParams["figure.figsize"] = (14,4)
```

We will compare the convergence properties of the LMS algorithm both for noise-like signals and for voice signals. Let's load a brief speech telephone-quality sample that we will use in the following.

```python
Fs, s = wavfile.read('speech2.wav')
s = s / 32767.0 # scale the signal to floats in [-1, 1]
print('sampling rate:', Fs, 'Hz, data length:', len(s), 'samples')
IPython.display.Audio(s, rate=Fs)
```

    sampling rate: 8000 Hz, data length: 19063 samples

<audio controls="controls" >
    <source 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WX5+gGGAYb3wArQ9MP/aQhc+7kDx/r9Bhb9CgHVB2Tziw5K+gj8Ng4e8FUOVfqbAYP/4Pr/DUzyfwcNA0T4VggI/fj8GQcX/oT+bghf+lQEIgEVBmD+HfvYCuLz/wNhB0L5lQmw+qsK+Pse+sQTtu6cCHwGUPkYC4H4GQWzAWL84giI9qEN9P0d+vgT8u36D3ABSPWBDWP7BwdV/H8BNAHABzP5pAKR/CIHqf+O++AL//2oBT8CIADaAN0J3fVSBDQBjwJzASr4bBFj+O/4xw6lAlr8aPtCDzX+WfHZIh3laf+2Fojz7fnmAi0WdOa9ArAYLPGGAGQLBPOdB2oHo/WCBI4HufwFACr4dQz9AQ/zyQiY/awJlvvwA0j8nAGxCjfylP26E3jyDPsdDcX2FgT99nkNjfcjAxoEMOyrHsbosQEWCLL2hA0X9eACKP0UBtYHZ+7J/mwXMu7Y+EEIRwtc8D35CRYl6hQHxAWt9gX+eQWGDJXmNQ0DBf30hP9a/uMJU+9QBbYE1fV2BRH7pwUN+lb+wwmH77ACSwWC9w76uwOJ+wT5oQZY/Yj9ugSx9+X/2wL5+nb4XvibBBrtfAhe/tnzDAx49/IGnPVTCbwEHftn/3gBUgO17lIL7voo9owFqvwt/6n/5AE78YsGugQG8icMHf3n+ioB7wOF7yUFgvvq93sEOADL+F/7fwuV610H6wW+4yAPM/2t+KgCPP9X/RD7DQjL+dr6ygxL+zz9phJy9a8FdgOxAxb/hPpvEDUBW/RjElkA0fzwDF8Lg/33+7cac/0h+RMP7f4+AdMDH//z/PL8dgm+7c/6VQmq9EHwSP1TAq7o1vqSANDuFO/xBbjynPMZAhL5nvYkAG0Qpe+xC7INkwoQDwUNbhicCyMY6xgEDiQiZRXqER4gShvFGCET2iKOG0YEnRAzFWn8+f/y+sb38+4S7LTorN5I7Qvjtd7x5s/ozOo252Hzze6V9JX0VvCR+vn7RfNa9t8C4Qdx+YIJJxW+CpMU7Rk6HdgZTy3HJ3kdLDaCMMklNDLbNkonGygEHaUX+Rw0/HEB0PaG9eHkx9Ug6HXXCdnI2cLfaOYF5pDwv/VN+iYG7gTlAwYPAQokAYz+Hv0y8Crn7ufZ3m/fQdkb3Jjga+GI6+vulfxnCfIKJRXjItYiJSrQJlgyDTPqMvkzUTOSMxgzaTVbKXkGQB6IIcfq+PQB8LPsY81Yy7zaqsSdzYnQzdNW4GblaPAw8dj/zguoBBgLMRYnEBYOBQQv/oH+CehV2w3UuN29zHC8p86F0b/PRc0Z4xT11Pb+BIkWCSGSLOMsJzBaOIg/Bzf8NjJAqTu+NIc1GR6W+wY0Jf2c36bt0udt30CnhNMLy/+zjsQZyTrZVNeg5/rz8fEjCXAMTgKcEJ8XHw10BZ/8Hfsx5z/VSM1YzKHNgLT8vcvHHMt+yKbRVe7F9db9BhA5IlAxuDF3OqtEbkfPRbVHTEXESVQ/NjxZCeERWTRB37zhMuHy6CS+TKHC08O2RLI6vGzJsdh52K/st/NG/OQTAA3lCXwbpxyfEaEEevOcAgLqFc4Pzv3LSc4csSa89se6yrLMSNQR8DD+GQISE3AmxDfEN707cEp5UCFNMkm4S3BVHkckNNUEuS9uJ+TXcOhV5MjqGa3BraXRKbLGt6m4IM752brccfA18kkGNBgbDJcPuiH/IfINAPTRCWHzXt7wyZDMmN0wuOa7L8QU1P/UB86/7zgCGQuvFX8kzz2tQDlCzUvKUrxaQFHyTxtbN1eFA7kxuUC98GjsK94pB/m11Kex06ywLbfCrRrIucvTzQzxW+cq8XoUaRN6CZMTuSauE1L1Fg1//froN9jo1oLgNsNmycTGxc853/3VMuhH+qAO6xMKGYY3z0CCP5BG4FPPWOVR7VTVXcZFgQ1kSq0rofNa9I7sNQFQqoa9cNDPrRq3V64FyabCk8z47W7cU/JlDqsLDgcXEjAcVAvHA1sKF/y77YrmZN8p4MDPAdOc0FDaVOaK3XrwtwDGD0gTwh4KN/E69EAYR85Qk1TEUVlVkFStG4o9TEIiAgQGq+1QDFnQRLea3M64jr8bsrXAscnzv7blEd0n4lYBTQd2Bc4FHw1qF9gIIQL+AM74OvjJ4snqHuI24QXj4t/Z8nTvXfoXB7kRAyD5JQM0Wz2fQp1OtU/GUcpXSFJGLXxC4kBKGCASmv8ADDfmedGz3s7GoMohw8LCvctKyAfhcdxK4F76/P/dADsAuQevFP0HTgNwBCwCNf4+7g/1Ku+n7uzwlvGo+yL/bga0EIEXKiaKLSM0/z0EROtLh06sT1BUvTjfN6ZL3ShbHJYMTROrBPzfH+ox3brUSNQQzCXR+Myo29ji39m66xj7ZfvO+sj9JAm0CW0BEQSv//T/2PdY9/30ie859uT1T/oS/z8G3w59FFQe4idmLTU25Ds3QC1GU0ZGR05KZzdcL2Y+MijeF94NkAp6BWbouOfs4FrWmdjA0H/QJNEV2tLihdwp58j1sfUu9YT3iAA2AHL6NfsA+Cv34fTc8V7wMvDr9ev3qfwyA1sG7RBlGOMe6SR2K+YyZzPQNxY98TlYOvw6UzcnJNknDikOEo4JtAIQAYzw2+K/4vbZEtau1c/Rh9Dp1RDfud9f3/joIu1E7e/wafDa8TjyH/K57jvtSO/E7Z3uPfA+9T34uP93BdEGeA4BF58c7x7CIy8oryhiLEAvCCqKK7Qr7Cp1KCUaMRaHGRUOYwWR+bL1XvPt5WnhF9nK16raytXO1H7Xa90j4ybeE+Fr6TrrKurL6c3sre7X7ZDrheqg69vuovAn8y33xf09AKgGRw4oDQEROBU4H+geixp2HZwhGiSgH5AWDRxDHFYYhBiCCw0Usg7MB7gErvu+/un59vEj7jnpf+vI54Lj3+AO4bPjhuFx4NTgl+K44yXoe+Zi5V3qNfB57LDxYvEa9zv8rfqkBJMGOwLrD6gHQRLIDWgJuxccCQwc5A6JCbYbHg5YGEAPdQqiGhAJOhFQBXUIDw5SAfcGTwBYAnIBVfsM+eT7hPPZ96zzDPF49A3nsu836SHtY+oH5Yftj/Jk8NPt9Pg986gHzfcl+FIGpANkCmn/JwOLB08MwwePBJECow5iBhcb0PYTDvcKHBO7A9YDsgo+BR8WAPt2Czz3+hsyAGkEGvtU//4RkPnR+wj3N/87CxnyXPwP6rIPM/T5/uzxE/TYEd7oiROC254NpPd/Ajv7w/EUBxz82QuP7BYE7vk+EdL85/YJCoEAyBaG8KIIIwIOBH0V4egkEaX1DBXN+cP8/gPh/XsOovLHBoTyOxcI9H8F8/j9+48Qo/RmCJ3vPAkJ/3n+FPp0+bQFdP/lATn4KQFp/MgDxvjU/KD+Q/qFB0Xzegfv880J4fnDA8b1xAMA//cAbgVy9QsHFveSBkj4Tv9A/VwGa/xWBbH14Qkw9wcJz/bl/KAC4/v5Ae31RAMc/GoESvdDAqL6BgPCAlD26ANC+QoINfdZAyD33gAKBGD2GgU28VENifW2BB/4KvyLBJ394voL/wL8Bgae+v/+q/xV/kMBYvwV/IYBGfuWCNX0RAZ4+qsCEQJG/Sr/+/t1BMP4GAN3+wcDTPpdBmb0mANA/GIBKf+/+4sC8vspALP/nf0mBU368wYE+vgEOv+D/M4AbP1/Alj/RAGcAfD60AHa+LQFX/VjDEzzwwzs9cUEzf1g/xsGy/vsBq35Fwh2+FwGcfn3BWr7Xf7g/QcBwvvXA6L+6QMo/bgFTP6B/gUACgBLBD36vwQl/r8BIfsw/Y8C+/0aBFH2Cglo+nUG5/xCAZz9dAPP/NsEDf2BAXEDJPstApz+PQMF/GEA4AA4/dn/ZQESAJUEh/1jAhH7/wOH+ncF6/7//g8Bfv4iA4T78QWh+isFq/3+Anj8kf/m/VIDzP2e/oQBsgAsAID78gUZ/2kC1QDd/+//HgAa/4sEGPvYAVX/WwO8+W3/mgFw/N4GqPz6/1T7KAWkAIf9fAK8+pUJ1f1nA1D9AgGd+3gBtwCfAJz9OgTfAgv/tv3YA3sBBAEo/UEC+QBOBKH91vvfAJz/HglP+3cCnPx/AhoAPP1UAXUBGwV5/7D/2f+b/y8Evf39A1P5AwpA+4YE8/jHBNsBawI5Aaj9nwRk/awD+/0FBp/8hwS0/Ij/6QDS/ugCq/+rARH9VAJxAKf+OQaG/WwC9P3QB4v4rwN/+w4F/f+K+zYCK/4WCCX5WAo2/g4A7QCkAxD/S/6nAGcCawBiAE/8HQcrAiP5rwOpANAHo/zLAYYBrP4AA+gA1PspApv+RwVd/GUD8P/3/J4Dz/xaABMA8AD0BlD8cwJq+8IG1/4xAfP8agBR/DcFsvvI/o0Ev/1tCILzGAkb+NMGdPs+Bbr5FQJU/k4FyffhAPABUAQe/Q7/A/1vAmv+zP4u+g7/+v74AIYEgPVuBL37dQZZ93ECvv1eBcX6Av/v+BkAIADH/Uv8ZvnzAy3/avwp/a3/+wBd+nr/a/n6/1v7L//i+T0A1/ss/8T76fzE/uv6owGr+Jf+4veO/sD/efob+pP/HP/G+rX8U/6X/nv9ffm2/Jf6NgA0+3/2c/r3+i4FmfcI+5P8GQX8+C/6jfej/BYAFvig/qj4LAPu+Wj+GfQE/rP5Lvxo+hL72f4cAN392/xg+e79ff5Q+1r7mvid/ob9r/l9/Lr62/92/L7/Svxp+uv+8f4U+7v7vv0LAVf8LfzR/fb+JARX9o4Dw/nt/rn5Wf6L+Tr+3/5w/dUAk/ojBfn6zwJF+sMFovpHADQCdvy7/Lz/kQBBAw/97QBC//YC8P8f/f4CDv6LAST+vwLc9iYJPgLlBtH3dgfSAcMC9gBhAFUBtgWK/sj9LgABARAGPQNEAkX+OwYPAtMEdP68BSX+0gye/cQCcQBdCloFKwKjBAAAPwYLAqACC/5BCnsBSQUsAloG7QF2CooEngU4BLsFjwMxBRcFfwUOCI8F2QYZBD8JiAK3Bq4COwbBARsI7QJ3BxMGewpLBIcJRQUIB28IRQOBBjkC6wu8Ar4J+wRWCd8HjAg+B8cDfwk9BfwHHwbXBhAI7QVUCUkEVQdnBSsJRgYsBuIIEgWpC+4GagdkCPYHhQi5BAYIkAUHCGYIRgT5CIQGdQlQBpEHegY3C7IE7QdcBZkHdAWaB8wFogloCfcFOwmdCagGbgfhB2AHYQfEBNsGdgRHCKMGWAgrBRIGigiRCBcF5AgsByMKIAnHBwIEyQgHBlIHlAQOBkkFvAjIBbEF3gUYCC4JIAi0BmAFFAdVCCEHoAUJB8oGgwZlBHoF4ga9B/AFEwYDBccFgAXqBB0GHAZRBqAI4wWDBrkFBwfWBcQJogIBB/IEBgjPBl0FYwYPA04IvQIpBVIE7AcyBn0EFQuMBQQJbgXiBlAF2AgeBYAGsgirB2IJwQbZB9AFIQrPBfcHPQbnB50FjgaRAWkFCATJBRkC3wOxAhwEWQQlAQMC0gBmBOL/pwBB/SIA4P0+/6f+1v6M/7kA4ABnA6MG5gnCDG8PmRDGEl8X6hfKGzkdex6dHaYf9h9jHkoWqBJ6DroJQwTI/Vv59/Ir80vuh+6+7ebu4fCJ8yX2b/X39V310vQf9FXzxO9O7cXs2uwk7O7t/+9A8XP45/9HBmAPihXwGbsgIykCK5EwYDY/Ozs/gkTQQfk0hQwvFrkQ2/9m82vigNtG1lPng9yi1Wjh0vD7+wEGKgmlCV8ObxmbEh4L/QJ5Aeb5fvvJ7SrgAdpi3iba4NaL4Mrg2+tN8yf5FfeYAOoEIwb/BJ0HhgrAFdkYmRU6F1sfRyg8KCAv8TGdPRdAskk0FW0IABq/C1cDw+lB4xbQkuUA6njY29Vw5kTz/v6nBR8D5AADD94UdAqlAjL/8vqy+G77CPCF5svluuoN38/q9+kP7Lbuy/U69f/2wfxn+y/5if2H/TEAqQbQDLkMcg0dFRYUNhhtG7UhbCCCKMorBi63MKYhuwGYFUUKewr7+sDxauYl4An1OuVx5aviWPDV8k39UwBi/Ir8/QLDBHIBSwA+/DP4Nfuk+qnzpu928FbrX/AB9d7wXPHw8Wn1P/NK94T5rvZl9wH/lf+e/NUDsgY8Ce8JZwsNB0kH3g5ME24TlRN1FWAXnh1PIX4lVhunEgIOLA5UDDoGvP3p8nXw3PDT8xzy3O/m75HzH/jZ+cP4U/jC+vT9r/+j/Tz7d/eM9sz1evbo9hP2//Pl8q71o/dM+O/2HPfY9uT5gPxi/Xv+tf8DARoDzwUTB34HeQivCXUKWAtpDD8N0w1TDvoOPg9oED8SPhPHExYS/hB6DU0LvQnaBwcGHAJYALv8nPrY+F73IPb29EH17vRl9f71Nvb09lj2lva+9vr26Pdc9wb4mfcy+ND4KPkL+hT7E/zU/H79A/79/r3/xwC2AXoCqwNLBLsFQAaFBhkHjAckCCYI/QjTCPsIxwjtB2cIPQisCIkIdQhkCHcIlQexBqYGzgUvBd8D0wLiAM7/sf5J/WX8rvp3+XT4QviR9032QvZ29Z71bvUZ9jb28fWx9vr2vPdb+Gj5JPpZ+6T8mP14/i3/v/9VADgBsgH2ARECRgKqAuACZgM5A5kDVgOTA+IDWQOYA4gDZANIA5kDWgNQAykD5wK7AkMC2AF7ATMBMABE/4T+uP3Q/FX8ZvuX+vH5sfgy+KL3vPZ+9jj2xfXd9Qz2WvZP9sH2UPdl+Jv4Mvla+mj6afvr+4j8gvxh/RX9vv0L/hf+T/45/iP+bf7q/k7+MP7//QD/UP6F/qD9BP6c/uz98P51/oP9Qv73/bD9pv1i/Wn8lPwt/H37f/vR+mP6svkr+sn46Pjg+F/4RfjZ9374qvcJ+Cf3Ifjq98T32fjW9+T45vgc+Q/5oPnb+Qr6Ofoa+jD6/PqR+hD74vo1+/n62vq3++L6fvvC+2f7ifve+1P7Z/vd+5v7d/t1+3/7Q/zP+6T7dvsb+8f6jfvX+iz7xfnR+aL5d/pa+r35QvlJ+R36RPkj+VP5A/mm95r5yfm4+An5jPip+LH5Jvlg+V75xfmK+Zz5yvlo+q75wvr8+VX7rvmE+lv7Pvpc/Hj6B/zX+uX7ZPve+gT8kPvJ+0b8Q/3O/Aj8dPxN+539DP5e+yH9YfyQ/MX7hPw1/Jf7bPxE+xr8bP2K+6P8efo1+of7Qfqe+9/5Zfrz+Rv6Lvui+UD6PPrh+fH7c/vs+Nz7o/qW/Kz5HvsL/Rv6Ev6B+kP7ffzD+/L8Qf1a/IH9JPyV/nL8UvwKAOD8DfxJ/lD9lQDI/YQApf4K/SAB2fwF/hz8o/wC+5D8Zv2v/Bj80fxM/WP8/P/2/zH5/f0F/xT75f84+sr4lvyp+GP8Pf7B+7L7b/rt/N35Ovpf+pn9Nf3W9rD+/PgT/Pf8b/y2/TL8pP9H+rAAhf37/MsAAP7g/aMAqgA+/1sA2AB3AcP/+wEg/2oC+/7X/Q0CVf5k/vz6CgGrAHX4Wf1V/pf3p/uU/Az4f/mJ+wD6WPYp97v81/ds9bH5+Prp9Xn2zv1f+Nb1cfpF/ST64flH++/65gB8AEH5X/ge/kgHCgHuAqsLPAIiB+EK0AU1DHkJfwcoC70JPAdSCTsK7wR5B7sFpwObB30AJQCY/lf6w/cT9xvxn+zl8yDt5eaM7qXqTOeo7eLq6+3K7c3xdPR39Bz1x/op/aD56wE/BBH9pgTVCuEF8AnZDoMKsBC/EPcQhBVQEc8VpRmpGTcbTR2FHzAXchFCDqQFVArk/nH+6fgS6h3rPOYA5lLo9Of952rqteuH7sD5F/Xd+AL7UvIV+NX4kfNw8ivxIu7m6Yfw6e5w7wb52/Nk+KsArwEyBq0K1wwxDKUNqhUEEP8XYheIFjQeoxlvHlUjMB+dI5IeWRY8EH0OVwbABbMDHfVv8+3miuUX5mzkhege6FLo0OwR8Wv31f3c/sIAFwMJAAUEfAG0/nX8L/TM8mPv+e1S7K7rCOum61Ltm+7H9Jb1kv2k/jYBPhFoDU0ROhhvEmkY4ht8G1Adfx2+IiwjmyU6KPgp+h4jEzcSqQaqCT8EFv2o8uDlTeQK3m/k3uVn5gXocOrp7eT1UP9KAQ0GUgUdBVMHdAflBZEAdvqS8yLuMuii55vlr+NE53rlnei264TwVfNp+Pn+HwGwCmAOkBNNEDsWJxnsFWYefyTfIcUrzjSGMHI9nz2/KGYeTxSmB7AKVP/39vjf6NZI0CfM/9uK2crgaeTM6Ff1nAD4C9YREhPzEHcRlRBHEIYLswJr9e7nweCh1FDWXdMw1ZTWNdtn49PnrPRg928AUgbrDIEURBkwHvcbFiD2HKwdQB+FInInyS58NnU7NENQQHEmqiAiEtQNfw0hAD3z8Nab1OrFxdDQ1hHY5d5x30vrD/iNCG8QZRScE7gRtxHWE5IQ8wrc/mXya+lb4T7YHdZp0fHRDdXb2ybj2eje8ZX1HP9lBQoMSBBgE8UWtxiSHEgbwxuyGNAegiPdLQQ5O0ArRk9P+j1dKeIjEQ4DFF8DYPwO3QPQhcX5vnPRt8s82U3YFuOS8qgDWxPRFywbjxe8FxYamhX+ENsDf/YI6RbdjtGpzoHNbc790MbTEN1e5Hfw5vZu/kEDIQlDDj4RZxStFDsUDxZME/ITPBJwGxQhtjAsOp1Ho041Xd1AQTF5JEYRZhZAAXf4s88/yiC1K74TxsfGK9Iy0cLj2fM0C/QW6BwgHg8Z4x6OHDoZ+A1K/gfsGOKf2P/K9sl8wt3GdMsg17De0ejE8If3EgOdB6gNMw0JDaENFRBTEbcQ1gxKCo8LtxTsH6UwlDoqSVhReGd6T8c5mSZjDt4RzgBE9IzNFsOBrEK2U8L3xXHS89OH5bT2sg9dGoggxh7jGdkdVBllE1EGdPOa5KfeztT4xEHDX770xsLVmN4q5Gvr6/GW93QEjQYrB18GjQXfCM0KZAg4D/oM8QyEFMkiwDYGTL9a9WE3aNRwnikJ+VLrutTJ3H3f/9HzsYfESt1y9fANRRlVD+cSkR4FHDQKAfGi0e6+t8fo0QnU/9055ZT0SgtbF4APUfBS3xPcdeB02VjQhMon0XbqVf1y/YL4EPzRAkcS2xyjG50a5iC2H6EexipVM4FEf1aJXnRhUXAMavQDyrt/rUSs+M7P6nvgs9UHAq4hvShwJzARbfYo+DL73NylwDu4m7oo2In8tAmBCWIWWRzhG6gZMAVs1omtBa2Xt7XQuuR57an7yxTeHwYUhf275Zved+eQ82r78gZBFGQigygHLdcx2UHbUu9grGgOaNFnqGqiC72WvZFgppfSXf58BuTvGxRgQws44h9+As/cJ9i85drUMLzxw9zW2PZyHK0lIhV/EPMQLQQ8+CvnUsatlS6oBtGS74YE/AvqBhcRWxvQAkbjptbb13/pIQJsC5wRsyI1MtQ0kDZAO49E2FfWZgZgbVu+YZdABsirlb+lNMSE+PQUqwf2BcMyAjY/GyQA9N+tzPTb598NzR/NW+GG9kgSPCCOEhwDmgRy+HfstNcaw16wg7Wd27T3AghaBzgIkQUEBOv23OXF22vh/Owa/FwL1RkRIn0r3i8BLwIzcEDJShdQ7lB/S+JU8EkvBVC3c7L6y2XySw8DCyf/4g/fITUSZPpA4ePSp9of6O3hLdt635rslgDDDcII0/ou9cnwA+1Z3abLW8Exu8DNru6U/v8A6wU4AeH6pfZ962XeYOEx6nL10weEFA4bliH3JkAkIyxONAY9F0lrU0FLuFEuWCwttNmzsb/A6dpa/ooJW/3c/x4ZbheMAwDt09h01mnlW+Vw2bHXqOHD8CsE8Aj2/O70D/QO73jiT9DmxKW7hMCp2cLxx/1YA3UFU/2q+CDyg+eE4OTkKO3X/vgPARk1Ghkh/COdKTcyTTfkQKtN508MT3RU/z06BDvJEcVX0azt2v38+kP5/gdiFKwI6Pjg5VTeRuMt6P3dttUX2X7jwfTAAKL+NfeL93b1lOkA27fRPMmvx3rPpt7c7Zr6OgHaACv+q/t899jwoOup6wv0hwLqDmUV7xhwHZglIyy/MCY3MEOcTJlQ2lO6WTo4CPvp02XOudoi7c70Gu988UUFnBDbCpT9UfE47GTv7u6U4fDVa9Xf4Obw3fv6+aT3mvrA/Cz2qerb3XvNx8vA1fLi8Ouv9+v+OgUiCXgIfwBV+Yb02fRh+8wDygi9Ds4UwRZFGV8b9yGyKOIwwDWJOiI50z8dRtw0tgyu9ybyTfcs+xf5+u+26RL0x/4YBNn/7vyv+Yv7Hf3l+zn0Su4u7XrxtvaS9130VfIL8s3yP/QO9PnugOtE8GT2dPlu9sHznfFS8yv2w/dn99D2BvhA+w3/eQGKA9wFPAiyCnMNSRBDEtUUZhghHfQipSq+MWk4mDsNOeU0ejKxME4pQCBuFncMpwJi/ZT5evNU7RLqVOns6AnrxO007oPtnO408Efwbe/W7YDrbuls6SPrROzV7Ortpu8x8Xfz1/bA+cT7f/5JAjYGoQlEDP4N/Q5/ENoSiRQrFVMVURXlFZYXEhrzG3YezSGNJqYrGzL5MwYvACoLKbQmvB9sGCoPLwWg/PD3FvR+723qmedm5zXoueoZ7vXuae4+8FnzovS29KnzU/GL707wv/JJ8wryN/Fw8nXzVfSk9c/2A/d7+N77uP7QACMCCQMLBPMFNwgfCpAKLwqlCtQLRQ0XDgAQdxINFWQZQyD7JdMqAC7aLBwoIyWjI5AeNxc/DpcFsv2r93DyN+7t6f3ldeQD5armj+hp6tbqcOuR7IPtx+2T7Pjqtun/6NHpvOsF7dTseOz27APv1PA08evxBvN59Jb2Vvld+l/62vqy+wT9XP6I/9z//P89AKoBJgNIBCsFLwfSCoQPtRX5Gy0hzyVxKTonCSJSH/IcGhfAD5EHOf4n9n/w++vU587jquDQ33rgTOLf5NrmFudx5wzozOjv6C3o0uZp5UvlfOaA6A3qKOto6y/sEO2Z7gvwHPGD8Uzy4PNV9aH28Pbh9rX2ZvdI+Cn5cfkD+QL53vk1+2T8ZP2+/j4B4gWFCm0Q3BZ+HNMgBydeKUYjrR0jHP8YfRI5DK0DI/nZ8TXuj+tQ6HHkQ+KM4dziZeXS6IbpT+h26Ijpoulh6UTpXOe25X/mT+kK62DsWu4k8O/v+O8u8lX0qfST9F/17vXH9in4kPjX9073pfdr+Az5y/ix+Cf5o/ni+u/8jP4VAGsDWwc6DJQS/xiiHl4jrCjeLcEp4yCvHWIdVhdkEOYJKP+g9UryXPH57brqHejz5bHmj+lU7UXu8exq60Ds6uzh7VTt8uuM6CTpduuc70fxKfO99Mj1svXC9pv5H/t0+/v5z/g07uXsie3C8Vnz+vi6+kT9I/wd/Pv7jfkp+zP+jAJDBUYKOA38E4Ee5ykBNiw/LkU5RuxMGSPaAEbzsPJk9u3w1Oyx39vq+/GhBFIE8QDG+Z7+WftL+JLxluZX39PfkuV96VjpmerM79T2IPt7//39hfaP+Lr5Xf1Z+CD3PvJ/9Y33mvzF/T37QPbi9Uz27PWz86Xv3+y77CLuZPDa8vr1HfqPAJwFmQpzDk0U1RbWHQMgLye6Kp8zWTSwNqk08ECxIIf3LvHu8Kb/f/jn9T/n5vLC+RoJ1gTu+bXwgPZW9mfzaOyE4TbeUuSe7bjx5u4D7cXzbvs0AKIBxv1D89v1j/y3Aoj/6vow+mUBHwVIBVH+7/Ye8xj2+fZD9bbwXO7G72fy6PEm8crxIvYd/SAD6gbOCfEOdhIDGScbJh40IXApdS7fN4c45Ti0N+I7JTI7CXH8DffCAe3/SP2v8ufztvuuBdMI+P6J9gH23vn+9mHzW+lb5b3nHfBe9M/00fGI9zn9rANFBD4E5ft093n6gP5W/5T8+vu6/6QGOwrZCYUERABoAEkBef8t+yb3g/Yu+m38xf0w/wsCMwcCDb8QwhPNFYYW+xqVH+AiWSa1LakxezboNU83BzsvPxQhoAUZ/hMBLQXF/4H2be/J9cb+8AaeAVP5tPZD/CX9S/t987DsRuzS8Z72nfcb86P0Jfo3AIAEfQb/Abv+OQSEBuAF1/9X/FH+LQMRBSYDvf0L+vb7/fyg+nP2fPND81L2PPZv9LnzP/ZB/CYC5ANxBw0Krg5sFF8auxldG6wfuiXqKmMwxDCMMlUzTjeHLAESdAZABUEIWQHu+2Dxku8C9J36+Pjo8sbtJ/HM9Ij08fGQ7e7qW+zE8CHyqO7x7JnvQfTJ+If7afym+sz8rwFoA73+DfvW+s78cP9cAAb+U/sG+4j8mfxn+oL3I/Yx9pj27fW59OjzRPU59+/4Avqd+xn+EgL4Bg8LWgzPDUcS9xaNGtQdux/aIQIm8igAKt8h1RpPH+MbsRPIEK8JaAAo/0D87vY/8/rtJ+x47Z3sjuzz7oHte+wV8Izwce6b7vDsuOxt8MPxdvPP9ar0DPfB+or6bvvF/Hz84P6RAc8B/gHnAbIBtgIwAzQDCAPOArQCyQO1A9cDbgMWA3kDngXIBscJPQw+DpISFxbuGF8ezSExJIUoHCwjLhkydSqEH0sleB+KFTETpgzjAWwBNv5F+Rv48vO88nT15vM39CH4vPbB9dP5fPm19/D4Nvfw9h/5Dvuz/R4A6f4KAcECaAJHA3kEvAOGBAQGnwarBoEGega8BpwGSgYYBt8FKgaaBmgGUQZZBusFZAagBggJ1AqYDOIQShQdF18bZR/DI8UmyykiLSUxhzKUNEcqXSQGKP4fmhdnFEcNZQSXA+T+ovpu+GX1wfQB9hH0bfQ49xz25PUi+Xb3L/b69uX1RPYK+Rj6Wvy9/o39mwGlBAsCsAFSBOMD/AMhBfIDxwPgA08DLgPwAfn/YgCUAJr/Vf/m/gn+A/5o/sr+uf/xALwCogVuCPULmQ9rEuoVLhqOHfUgZiS4Jrwo9SuSK5YfTR/pHgAVww/dDCcDUv17+1j1x/LJ78PsFO3z7KvqHO2n7iTtk+5x8D3uge7L7sntCu8A8Uby2/XJ9nv3Ovv/+v74fPpw+3v6B/vp+tL5Evou+mT5z/he95325vbh9qP2gfbu9f/1H/Zb9kv2Dvev+P/61fzmAIkEnwbWCZsNPBCtE0QWXhiwGvQcoh5BIXcbrxOLFR4QGAj+BL3/d/YE9Cbw+erN6Czm8eOj5GPjveIl5qbmOuZT6brpW+gz6lrq8enw64jtz+5G8pfytfPe9WT0DPQr9pP17vQy9gv1mPSQ9R/1aPQR9A3z7/Kp81XznvPj83fz0/Of9HP0fPXM9mT44/q6/fQATgQxB64KtA2FEHgTGRb5F5IaDhxTHbcYXxMWE9oNLAc8A9D9nPU/8lvu8OlQ537ll+OU42LjMeNc5bLm/OY+6Xjq9umD62nsQ+zX7c/vl/BA8obz2PR89ez0xPQM9m32cvY890r3ffea+Cj5s/i6+MP4yfgH+ez4Wfgm+Nf3nfeR9yP3bPe0+D76S/zz/tUBcARrBwMKxAwaD0oRQhMqFcQWdRikGVYaaxfqErcRvQ0JCL4DjP/T+K70V/EM7WHqFumQ5xfnSudY5wDp2eqX637tgu/f7zLxq/Kz8inztPRK9T72+Pbg9+/4QPle+Xz6jvsd/FX9Vf7M/q7/fABbAEgAFgCf/0f/uP6e/fP8RPw4+wr76/rv+r77rvyj/Wr/JAGuArUEdQYbCAsK7AsEDUkOCxAjEVEShRM6FC8U5hKrETkQ/w0SC1kInwSEAA/91Pmv9vPz8PF18Fnv2e4e76/vIfDS8APy3/K688n0zfVW9on3V/if+cf6U/wf/U7+wP7I/2UAXwG8ARkDbAO/BBMFGAbOBb4GsgWCBgIF4AWOAwYFbf918//8VvwCAo8CZQMBBNECnwOVA84EwwVLB+EHsAdTB6YIVgk1CQILOQscDEMMkgwKDf0MNg0RDGQMCAnLCJwJrwcpBowDbwLgABn/2/3E/Fr7ufpk+cj4Jvg0+PX3Yvgn+Lb3jPhb+Oz6cPmY/K3weutK9K75swDKApgDtgX+Bc8I0AcSCWkJzAsIC5YJQwcoCGoHSAeUB8AGJAYECFgFdwdjBdsEKwYVBRcENATxBhAFnQdLA4UFtAGZBGcB+QP6AHwC3QAtAeABJgGbAhwB4gLO/8ICAgHUAwkCMQLGAYoAfQFKAGD/pv9n/XH95ftK+zH7Kvpa+1f5GPuS+Rf7uPhb+4z4s/tn+tH63PqR+o78o/rN/Qz6Yf4a+5f+UP0N/l//VQAVAEj/pAABAMkAwP/+AYv+/AH0/0EB3QCl/xQAqAAy//3/hf/g/+z/9v1a/oD94vyN/eT9J/xF/On7WP0k+iH8cvpM+4n9xPtt/oH6w/wN+1L82vo+/TH8Xvvx/cz5F/6Y+H//Vflc/XH6/fpy/bP5Pf30+kD9pPrt+jb8z/qQ/ET7n/2e+jr8ivwN/sz7MPtn/Rj8z/4I/UX+Qfyg/mD8dAHC+1L//P0NAlf/jwDL/cf+LAF+/ocBYP1ZBET+ygES/fACUwC1//sAmP4RAW3/AAMnAEb/wv9y/3EBTf8sAaz/Jf+0AD7/6gHT/rYDZf/zAm/+HgKU/6sCuP/2AXMBV/+JAz4AZwLgAJMCXAAqA1n/sQPM/lkDegAGA3oACgTFAW4B1ADuAS8CHgFTBH0AvQTxAMUDvwGsA8QBYATr//sDnAC0BU0CvgJlAWQDbANeAzsDTwNtAtkDyABDAo4CtQA7BPP/YARlAL0FYf+VBOX/yAJhAT8CfQEXAfUBOv+ABDwApAAxArT/xAMQ/+sC2/14AsACaf6kAwb90gLk/q8Cuv4PAcoAFQHB/mcA1/wwAY7/pQDXAOn92wHp/LMCXPxJAfH88P/p/DkAPf1KATH7G/9n/wP/rvys+3T/T/yv//T6e/+Y/NQBs/mJ/SX7Vf/++y78kvtj/T392vwY+0j8hfu3/HL8zPr++o/7Dv5c+Vz+Dvk1/ff6Xfx/+ej60vgl+m77pfhs+4z4U/z8+BH/Lft2+vv7dPqo+8H35/sR9gb6JfnS+v353fhi+RT5e/jo+fT62vpI+UL6tvvf+sD55PcP+eH74/l3+Wv5fvs0+gr7evyI+Zj8XPiI/uD4JvwB94z82/r/+p36l/qk+//5pvsy+nT6O/pR++X6tfxo+cf/wfezAIL44AI1+PYAyPhC/d/8ZfvQ/ov52P4t+msBVft0AUT7NAIj/K8ESfuNA/n8qAMh/FMCgP8z/G4G9fhACfL2mgeb/NMEFAL9/TEFzf5nB1r+DwTk/5sB5QEkAHQCZ/+uA0IBfgJZALL9bQEK/gYDxP1oAWb9L//H/9b9kgDv/TIBUP39/wz/6gCBAJz/2QCs//QBpwGvAsQAsAAQAcsBSgNWA74CbQCjAfwCGQOJAYgBIQK7ASUCiwKXAaQAZgFrApcBMQAWAPz/lf+M/4YA9wBQAJ//OQAjADIAvgBFAMj/owCWAfQA5v5s/vD/fACMAA0BowBv/+r/EQFZASkA+v8hAIH/Rf6i/uj/OgC+/0gAfAAUADgAQQC3/6H+ov76/r3/yP9u/yb/Dv+l/6z/cf8m/7P+Wf5p/uP+Xf+r/07/0P4+/t79g/33/PH8hP0f/dX8aP0K/gP+Ev3R+1T7R/uj+d74O/md+YH5LPtO/dP8hvr4+WP7dvtj+nj6//rg+Wf5Cfu++4b7TPvh+tj6JPuh/CD+gf6N/sP+6/1K/fz9Hf+s/nL+yv6T/eX7xvv2/ED92PzT/Iv9bP45/hf+Q/7j/Gn7D/ui+kv5zvdy90X4b/ke+uT5V/ke+av48/cL+KL43ff99ib3NffF9qf2V/bj9SL2Kvdr96z3x/hU+c768vx3/sP+iv8AAfYB+gIeBOgERgWYBWwGJQgECgAL/AvVDAcN3Q10D5cPmw7KDTQMNwqsCAYHBQToAHj+d/tX+OD15fOO8XPvse1b7L7rROsb6+HqAOtq6y/s3uzK7Zzun+9q8TXzVfX493j6pvy6/10DEwcvChwNChAPExsWQhlTG9gcqh51IL8h2yK0JK4ltCUQIvEcNRmHFi4RuQreBCL+T/jC9MXx8e2B62fqkuni6S/sQu6z7xbxB/PI9NT2RvjG+N74nPls+439hP9pANIANwHbAEQAfQBiAMT+9v2A/of+n/5a//r+Ef6J/s7/ogCAASwCnAJZA7sECQetB/kH1gkxDcsQqhRGGcgczx9VI54iWB/UHEgbpheFEhAO0wiGAwn/UPxX+V32Y/Sl80/z/POB9bf2ofaA9qj2i/b69e30BfQ78yTzbfTP9Zj2o/ag9hz38vWz9bj2qveR9pD2YPgH+eH5j/vK+0n7fPzM/lMAfAFTAtICEgQLBYoGrAiKCl8M4A+DFPIZox4ZIg4kayQ3HqcZrRk0F6UOHwjWA+L7gvd+9uLzEu+t7VPt1Oy+7rrxgvJx8i7yRvJJ8mDyJ/HL71zvBu9m8GTzR/UY9Y/2lPfl9oT3nfeo9sz28/fc9jz23PeC9/b25/eD+IH46vkH/Cn8tPxd/hMAGgFxAj4E1wamCggPRBP4GL8dniH1JasqBiSqGs0bCxwnFM4LgAkIAIf3uvdo92rywu8A8Gzui+6M8uv0G/Uo9Pvy7fJF85rygPHd8L3vh+8387D2Fvf8+JD7avvj+Sv86f2j+0z7ivxW+zX61ftP/EP6pPqW+8z78fyk/qP+Gf8jAMQBFwNZBSMHBwoQDswSjBd+HcwicieeKpIvmy5AIgcfBCHmHUUSoQ3DCLj9TPpW/HD5+/Tb9NP0MvMU9UD51fn5+Jr3YfaD9iH2NfWo9J7zXvOj9CL5Jfvs+9P/+QFrAI7+8gAbAv0AawEfAeb+Gv5W/5H/Uf7p/b/9A/28/a3+ev8AADEA4gCkArsEUgcLC+MO+hH0Fuod0yNNJ0gr/C6RMfMokx5lHvMeWxgJDkAKHAMR+h36JvzU+H701fQG9b7yGPa7+iz5Hfaa8snuxesw64bvpPGZ8e3xyPOi+bb8DAOlAlr54vHE83b66Pgl+PT3d/h8/v4ERQjWAjv+Gvzd/Av/Ofxe+en4hfx6BDAM+xANEWkTKhyXJbYw/zXcMwwujy5FNjgv9u0L3cTimvX5Bo4DTwGj7oMJagwdDxEBRvDg7nbx/vkd7TXsaOce7E749gCE/yf2l/vx+Ub7IPmZ9+/tIe0m/l4D6/9H98T1/PWi/hUARfri9V3zvvOn9PDyM++c7yL1l/U59mT4vfs8/+MEIAcwC/oNERK0FkoaiSMMK58uMy59NHY0HzT8N+si8tby3+byqwDYAuL94vomAAsirwkv/Uju5fOu9Fv3GOZu1znpLfOh+Sr3avqM+GYBWghe+230ZPNt+1b1S/btACUGVwd+Ab/++v2k+3r42PSu8oHwUfTe9ID1vvRH9In1Aff59GD2ZfpIAEkGgA3bDt8QTRVeHP4grydaMkwyGTb2Ni43bj2/J3/LT+jC/MYDqvcT+nEAuQ+xKwn9uPU99+UH9fbS79TWQt/09Sv0bOiE7Lf/iwNHBvn5r/RW+9T/TPpX6bDt9wMwCwb8xeru+TYGaQbA+Evw3vflAMr7dOkx7YP16Pz89kL0hfOFAsIDGAFPAaIOsBCkEzoUWBv6IYwtICkhKKorijGmMQw6dQTuyjkJcPpn9NbjWP+R/C8cYQoR7VMAwg32AMHoS+q03sT1duoi4CTjtP81/GX3kvbl++wB3QAL9CPy6PL2+44CHPIP7qL8ov4J9DD08/gy+Fj6R/Fv7urzlfaF6mHvxvYS+QH3bvmw/HkJug4sC18Q/Bl/IxMemSZ+KhUyGS2OLekwriuY0FL86v/N7tff5vO7/KIEiRO76hMIJA6nCVToEvjg573wceUE21PgB/ji8QTr8PZtAXkAofwY9+r9EPxA8rr6Nf0u8h3p7PMd8rD2mPaH9CP4/P999n7vMPXD8/fvGvPE8MjzzPwd/QP+sQwOEt8RnBQ0I2of3yrJKqMtOirLLhEo3SoV3+T4kgsp5pXgnO8zBcL0sQvQ7+INhxArBi3uRAJb9jHqBOVp32Lmqux85xXlIfyg/QX56PpkBJIHnv8C8voCrgPg9wvj0/Ji9WjwbOus8LT9QP3W9Hby1QDJ+cLw2fFQ+0z4E/eH9yACbw/DCmQNdxs9JOskNikbM/4wizMiKyojJ+onB3cA6tqi3snxo/RN6eb+NvhnEHsLTwasA4YSIfky8VPy0+wu5ObjF+OD6pHw3O8s9b8AOAJKA6wCSwIiCgwCD/p8/dr5Febj60TskOnB6b/yMfKz+P764fjE+3//+PmP+zL/rP4b/9kDBQk/DfwSxRyNIE4ujSuPNUYuMjwo82kPKRgH4fHeBvAG9IbRQ/YK66sBVP3HBSAFWhviBVP+Vwlp/znvQuxC7s/liuRl5Czp0+8N78z07f8E/scJ9Ab+Cp0Fsgma+gb5eu/f7P3nF+iY53zq4fCs83z2lfzCAaEA6gKWB/AHNQdEBogN3AthDsgPhBs+GUEhJSBPLmcUrPvaKuT7iO9l8p8H4NjY5xzxous96f3yB/tY/YUEGfuIDM4H9P+U/C0H+feh75Lz3PSq6K3qc+4q9KPpmfZR/13+bf3tBYkL5wb4B04HIwdvARb51fTF+JTvLefQ7q/wi+Z26N/0RfFi8Ff55ABL/mkCmwcUDkcKuAzpEBYWaw4pFq0XRxq2EPoRPQyfB0YIBPnc/Wb3K/bx6Zz1ue787efuYfnv89r2Sf2z/y/9av+NAtX/W/00/c78VPmn98/1Svfk86/0e/Rs+lb3V/h9/HX/kvw1/9MDrgLLAegEOgbqAzoCaQRgAuH9CPlg+632UvD17+zxJeyu6vDvDvDN7SPzFvga91T60/9jASABkQRTBqYHkgYUCAgJRgmVBhkJfQkqCFsHwwnyCNIGmAicB3kFiQPzBFYBaP7n/tv9w/lL+TT6Vvex9YL3Nfdi9QX3T/ie94P4Pvqv+jr7cvwk/X79Zf2X/ST+D/5X/Qn+7v7M/uH+KAFNArsC2ANeBpwH6gfyCVMLsgvBC1sNxgyeDCAMSwzkCg4KoAcqB1sGHQNHAdcA1P7c+4D7Yfta+aD4EPon+uP5/foI/Vf9Uv7o//oAPgFFAhMDjwMcBNkEKwXRBVoGjAZcB+AHzgfQB2IIYQj7B/UHKgi5B0oHTwcSB7oGgQZjBuIFowVZBfgEvwRlBBwE9gPeA8kDrgP1A/8DFgRoBLEE6wQKBYIF7AUVBkoGyQYLB0sHrAf7B0wIogjsCAgJVAmoCb4J2An7CeIJ/AnyCd4JyAmzCZcJYAlGCQsJ2wjPCLAImwh+CF4IaAheCE0IRgg+CFMIbQheCHsIrQi3CNAI9wgLCUcJYAl+CZkJvAnJCeYJ9gkLChIKCwoVChEKCQr7CeQJ4QnbCcEJqgmlCYQJdglgCTIJJAkKCQYJ5AjoCNAIqQiZCJYIlAiQCF8IZghpCGIIWQhMCDQISQhLCEgIUghECDUIKQgoCP8H/gfWB9MHxQewB4sHfAddBzEHDgfqBuEGwwafBoAGUgY+Bh4GEQbiBcQFrAWPBXQFTgVBBRUFBAXTBLQEogSgBHkEYARQBEoEPAQLBAME8wPUA70DoAOIA24DXQMsAx8D6wLdAsICoQKUAloCPgIiAhIC3AHGAZYBdAE+ASwB+gDbALkArACGAHcAWwA2AD0A+f/0/9L/rf90/2r/Uf8t/y3/Kf8N/+b+6f7Z/r7+rP6i/mX+S/44/jD+C/73/d/9xf2//aX9f/14/VP9SP0m/Sn9C/3u/PX7svkH/GX+b/+M/TX7xvoN/C/+Lf6i/M/6Hvsp/BH9qPzH+8r69/rZ+4z8PvyG+9D6KPu++yv8wftB+5/6x/rN+wz8fvt2+kf6vvp0+3z7+/ow+jv6r/oW+zz72Ppg+l/6p/ry+hH76Pq7+ov6oPra+uL6yfqh+m/6efqS+sP6kfqC+oL6b/qO+nT6efpR+nT6cvrx+r/6SPo0+mL6qPqA+pn6ZfqL+o36jvpp+lX6qPoI+xf72fqe+tL69Ppa+0T71fpq+jn6fvp7+oT6KPtW++L6xvqr+lv7FPvs+ln6PfqP+h/77vX27rDtHvMJ/PoBfgGm+0b3Lfjq/PEAPwHv/d36//mo+179nvw5+q/38fe/+Qn8Sf2W/Bn7X/oF+6v88f32+0P9d/vh/dD86PzR+q35/Pn6+fv7v/sV+2f55vlH++788fww/I/6uvpo+6H9KADX/fH9Gvzx/L/9R/w//9H8ZP5y/F37Wfrd+0T9mv9U/VH7QPiO/0P+yAHo/KL7efu7/dIAJv5x/vD9Rvz4+4f/7wHM/P34s/xL/hEB2/3U+0T93v5gAVMCk/8i/Bb5pAJIBSUD8fr5+M/8Lgf+Ak8CtvaQ/c8CNwXKAkL8ivt0A+gAaAc2/4n/hgBW/ZgIH//PBUH85gSp+xwI/AGEB7P8D/8pBKoEmwi9/VIERP7bBZkD9Qf6Au0BAQJsBnAELwuv/usE5QB6BuIGYwRcA4UAnAPCBt0JqgRxB5QBXwY3BxkJlQMiB+cAcgcDBiIHsQNsCOMC6wtDBAoIOwhFBmEJigQNCAcFHwoWAxQLxwF8DIkDeQqRCE0IGQgpBdUHaQmkCG4IYQRGCWwIeQgrCrMAeA3+AykLPQfZDPkHggfUCaYHOAjTBhkHTgc1CLsHkQzgArwMgAT1CjAHxQcvCfcGyAmKB4oFkwlqBuEHHAwAAskJqwSfCzEH7AhgBNgHGQhVCBQIDQdvB/gGrAhsB7wIggWQBtgFJgp1BmQKVgOCBR4GRAbKBqMEbgMCCYsEKwr3BdQGNAWoAxIJpwSkBiAGjQPsBYsEmgaLBPcCDgUwA+MHNgOmB/IBjAQEBtYE7AS+ApcEMwWBBYsDXwMlAmIFjgGLA1sDjQMuBYMB0AQpAvwDPQI4AyABkwMbAn4C7/94BHQCdAQyAZUDJQJUAUIB2v+DAx4BKQSL/pQCeAAqBVsCVwST/pQDqP5hBCD/CQHM/+QBIgJeATYCKgCRAWsAKwIj/hYC2PwOBFT+2wPB/F4Cb//nAoD/+gCm//4A2P+s/2MCtfyzA6D9GQMU/XAAhP5zAcoA4v6qAOv+nwHE/uX/2v9o/yz/Lf73APb+9//O/r79PP8p/5X+jf6k/yD/mQC1/TgBEv1g/9j+6gG5/4r/ov5e/wL/9/1S/UD/6v8T/6H/J/0hAdf9FgGY/8UAVv8X/6//wv+r/oD/Tv6N/xP/u/+4/L3/Df65/z/+SwDf/uv/9wBZ/7QB+/zdAbT9hAL0/Mf/sP3WAqr++ABd/ekAbAAR/98AOP+kAb4A6f9o/z8BAv9cAc/+UAIo/zcBw/59/1YBTwCsAPn+5wG+/x4B5P9ZAKEBCAAjAcIAmADg/0QCvACiAfj/EwKoACYCqP94Ac4BMwK/AHr/OQCYAgEC7gFNAN0BlQJrA+IBmgJOAdABhQIPAVkBvACQAeMBGAOPACkCHAEMAk0CKAOcA0YAkwJQAAwEEQF1At0CHgHwArQBsgRyAFYDEQBKAyQC6gI+AiwC1AMVAvwDLgDaARABgQS8AWEBbgGNAVYDrABXBLIBywKBAUgCvwCcAhgBZwMqAe8C6ACqAV4BEgH8AXAB3wEDAvb/SgPd/30BbwAMAFMC/P5wAnj/8QDKAF4BCgDyAGX/4AAZAPj+qQBb/+8B0P0qABQAxv7Q/9H7fgFV/TYAG/5f/2j+B/7U/RH+gf2d/zT+Xf1q/vH8Vf8k+/z9efrP/Xn78v1x/Gv8Pfxm/BH7yvvy++b6mPyM+u778Pp2/Gv5j/se+mX7nvjO/gP3cfx89mn8mPc1+0T6+ve0+eH5RvuS9lT7Z/at+/T4V/ru9Yb6Y/ie+k73zfh09Jj43PV++iH13/j195j5EPgK9jn3J/b4+V73GvZx9gP3hPhS9iH2EvYi9uP46PMa+qLzb/p68pf6bvOh9nj4cPcR+HL0FfhW9aT6iPHy9dH2Rfv59DL0FvWZ9t/6QvQe9hz1rPo39UD2lfc+9CD38vQi+QL16fcC+JT3nPa39pH4WPU3+Yz2F/YJ9931zvhz9in3/fcl+OH6CPVx+LL6+ff9+Pz1x/na9zf4nPkj+Ab5OvcS+7D1DPqm9w76HPkW+jr3P/sU+j73KfpR+VH+ifUC/Ej5xPkX+bf6zvvb91b8Ffqn+Y35xfm7+/D6Vfxk/Fn8Nfgl+1T8Mf5c/eP5Rf6K+8T9sPkn/Xb4VPvf/B39BfvR/ZD88fwS/r78wPyy+23+nfo+AAX9jf5I/ZT9bP5v/eb+eP0c/o3+Rf73/VP9gP2J/Fr+q/67ALv+qf42/ugAZf0w/33/iv4aAZkAhf1i/B/+Bf/3ABn9gP9lAu3/Kv/dAAgByf7pAHz/bQASAFcBowDAAlH8LgEm/mID+P7dAEgB2wMbAHsCRv76/pwDMwIBAgD9vgUdAAYDSPwkBCX+7AUM/hwCTQAyBdUA8QBR/qMAFwEKA7sCAADN/+QBXgPyAIwAmgBHBSADRQZS/gMDKv+kBHkAfAOlAWgC6gJFArECmAKaAyMBowXcAl4D8QDbAOsANgDFAQICugIvBgEDQgL2/40E3QK6BEUAHQKYAToGrAH6AVf/8gR6BecCjQPm/rEEjwBLBrb/ugRMAgoFJQILBToChAM7AtgCHwLwAr4BxAGUAjwE7AOqA+YCbgONBP0D1gSVAGEBfAKrBBMGzgIGBBIB6AMZA/YCaQNGAzYDsAOkBAIEfQOoAkAHcAOkB6QDTwZHAXYElAOMAWoCLgI7AicFwgN/BVUArQhbAsYHPAKxBdIDxQFeBg0A2gfpAHwITP4mBv3/tASXAKUE1gQBBX4G3QJVBFUBewSLBFQG/AODA1kBEgXIA1oFxwLrBHEDQwSeBZEEeQN5AtQB6QPeAvcEFwGMA4IFMwQNBkIB7QbnAO8H2gC4BncCPAayAc0CvwUSBi0GywIDBmUAtAYWAesHRgB8BpcCnwXsA5kDhgSXAuoIRQPMBrwDKwYXAmsDqwQUBJwFIQUZBZMD1QXTBTgEBwXGAhMFrQUSByEEugLTBEsDtQYuA7UGGwSeB+cEXAT3BcYD/gYrBNEFdANhBaAFXQVlBFYDkAX0BdQF7wRbAzkGtAWWBU4EUQTbBGUEGQVhBI4FhQThBgYFaQUNBJwFOAXTBAcFZAQTBsEEyQSZBD4FPQWWBIgFRQSMBH0FTgWCBZYE3gSDBIwEwANXBZIEgAUdBFIEpAPnAxYEGAQWBX0EPwVzBAwFdwMIBOADKwPWAwYE3AM2AlAERwSHA9ADJwQ5A8cEQQT7AiIFSQN2A08D0gPcAegDmQNoArMD+AOiAq8B2wL8AmAC4gOLAuwCjgLnAjECwgGUA04BmQP2AVMCKAHjAmQCVwDaAWYBXwI+AV0CFgE3AYcCogGzARcBQQKqASECXAHSAFUBPQKhABQAYAHkAIMAXgHGADwAugC8ALsAv/8JAbYAmwAJAbcAHgCe/yEAHQAWAFoANgCb/2n/1f8pAPIAPP4e/3X/9f7UAC//qP8X/4X/tP5g/3H/cP7FAKf+D/9Q/S3+Tf/O/qr/C/9A/Tj+iP8E/ib9s/59/mv9jP2d/kj9Mf1g/gL9JP7n/Zz9dvw1/tH94PzQ/IX9p/wH/Lz8dP2E/Af9SPy4+3/9Ff10/Ab8ifzW+wn8TPyY++77FfqM/Cj7+fyO+K3zJfwT/CT8xvpw/AX6yPoP+yz6g/qd+mD7M/ru+r/4IPmT+F74rPnm+E35hvhn+JP47fgv+Z74oPke9xP46/kO+S345fe797339fdl99X3aff/9v/26fb59sv25vb29qr2pvaI9on2OPai9h/2XfYY9gf28vVc9a71U/WX9ST1PPUx9dv01fRO9TP15PTm9N70tfTg9IH0ifSH9HT0KfRP9PfzBfTw8xX03fMK9PPzAvSm8wL0iPP/83Hzi/T48M/ovO+q9tb1xvMK8yn0D/Np9VT0afNt9CP0j/Rd8vfyHe178v3znPM29PbzXfQn8wL17vJa9c3zM/UE87PyOvXX9Ib0XfLc80n0YvS18wr0FfTk88vzVvT686bzIfSi9Wj0e/Kx8rvz6PTK9e/02/TW9Yn0yvXI9SD13vRa9eL0ufTu9Jv1wfQk9XL17vUE9qT1+vUs9vn1KfbE9un0afOv9AT3gvah9k32tvZG91H28vZJ91L3LffY9sX3TvdP95b2ovdC96P26/e896f3x/db+HL3IfiP+Ov3g/h4+DD5E/np9+r4qfjK+AP5Sflw+ZP4vfhn+bL5zfia+QH51vma+V/52/nt+TP6z/k6+lD6yPqk+p36gvre+rb6kfpX+hb7R/sL+wX7Ovvi+hb7ZPtn+1j7mPt1+4j75vt7+xz8pPvS+//7yfsY/Fv8pPzd+7j8gvyA/H382/zh/Kn8l/xI/M784fxA/RD9aP1C/cj8Xv09/af9Jf3N/YD9kP3I/aD9Yf13/R3+DP4L/nD+6v2q/aT+u/23/tP9iv7N/nf+NP7A/iH/zP7a/h//+f5S/x7/EP9Z/5z+O/9A/9v/if8f//n+QP8ZAJ//wP/b/+L/zP/q/9n/IQA+AO7/0P/g/+QAqP/Y/4oAVwCHAN0AjgBoABgAygAXAd8AAwHIADkB8ADnANUB/wBHAXYBRAEDAXcBZAJ3ARYCZQHbAYABtgEqArIB/gERAisCSwItAigCEwKdAc4BlwJtAqMCzgGSAsQCTAJwAq0BEANeAjEDbQPzAd4BvgJcAhIDVwPAAnACWwLiAtACWAK5ArICKgK8AicDyAOUAdYCCgP8AgwC7wJ1AlsC6gJeA7cCDwKXAqQC9wIXAnADBwIXAxkCEwPyAcoC2AF0A6oB/QKjAQIEbADeA5v5m/ofBykC6QMFAbsDDQKgAwYC5AOOAGgDMQLZAosApQHGAPz/QQAQATgCRAECAYYAPwJJAHgAHQEHA8r+EAM0AuQAu/9eAc0A0//U/+EAPwGY/2ABE/9AAPb/3gBW/aL+Ov5O+nP5MwE2ALICSgOt//f/OAFaAroAzwCQADUA9gCP/wn/KPwK/+73+esj/Y0FrQRxAxADCv/3AvICiQM+/mMCmAEpApUA/QAAAsH8/fv6+gcBLQH7AfYALQN7/ggBsv50A2j/ZADVBYP/KP8XAzwDIALvAWr+LwE+AOAAjP9bACwASgQ/A8MCLvzxANACNgRdAy0ARgKFAn4CqgMPAwz/wAPb/9gBlgAgBTEEawNHAdcAh/ynAIUD7gRqBHoGvgZNBWYENgM8A10DvQV6BE0GhgfVB40EvARNAkMGXQfsCXoHQQd4BsgHUAarB2oFmwRQB4kI3AUCBr0GiQRoAwMEXARcBOUG6AXXA7ADEgXUBCAHQQUkBSUGhAeeBaYG4QaOCD4J4gqrCvkIkAgvCgoLeQ3/EIYS9BJBEyYTExSzFmsZ+BuzHRceKR3aGlgYzRXsFVIX+Ba/EncMdgTW/A/5M/nG+w7+CQAp/nr6rPbX84rxjPEe8qjzZfUa+BH63fwc/kb/rv5gABsD0AhhDawTJhe4F9gXIhugHqMjAi2yNc4+A0V5SX9J60pXR9g3TSyLAx3XFsrFzv7tyxStOgg5WSmKDb7yuOXW6+n5t/9wACT0V+ns5F3xgAHbE0sdPhfUB+v37uyt563kmeVf4pfoEPvvDuEeUyGAF/v/5PB26VHyXQFwFJ8bXBxBFvERrRLSHFkiYCONKHQq2DK6QBJOb1NkVtJULC3s1bO6X6QfxRUCEEJTVYlGEyPv623Yddzt91kMQBuHA/7sT9uT3nDxqhXtLfYt8ByQAUXn5t4q6QT9jQL6A3gC6/yp/AUAlwBk+6X5XvSW9qn64gHzAd4BtPvA+ZX+yQt6E7IWhBE5CXoGdA7tG7IwPj8JSWxOWFFGUsBdo1I14k67nIwInQTqkj/wcaNr5UQx8HPM5MYA5gIPiirdDvXvAtAnynvkHRauNvs9fSON+rrWM9G53hYBoA9qCaYGsuwA6k/1JgfvD1kQcQC175/pou0T+SsGUQveBbYEOAIQB7MK5g9pDMsMxA7eFr0hgzLeOklEoUVKTVxN3VqfPVXOwsCDire5QQNmR5tuGFjgKsDdkdVm0AX3pBtaHfj+cuSoy2vTBfsMIBo4ojNzDf7qFdZO2G7slQ3dCKoDOAHp+ID/Cge3CzH+6PZG4qfnxfP9AP0JhAmC+fvu7fD0+Y0HdRCVC2oCY/yk/RUNZx/nKWAyKDDrLrI0H0NlTrZhyEqxz1C6AYB5s6gJGkhFeAZSIx3QzavNp89A/yUkhBeL9enSyb7903cAsiBoNNUiH/XI3EHPudo89e0NKAHM9YDvBOS++EoAzwjDAj3wJ9/B4pbsrfhRBdH+UfJG7ErqMffdA10H0gMs/dn1kP7CEGAcfSUxJboeGCKfLfs920tlV9ZBO866tVeEtbe/Cnc5AWjrN5sI6scVzeHXOQOdHWwGaua+wuq7kdtAA08dEyWyCvXhUNbT0W/lrPrlBMf0ZOSC42XgbPq0/xcF2PxA5SXdBeDE7Gr21P3r8pDqwOZX6XP3Kv9G/nT7S/RG9fEAaxKkGaYbWxVhFr4dwzFfPshLp0XFRhb7ZbOGrEyh6/2vIRBN7zzzCQfh0MoU5rz0RxQyBS/k0co0wP/aq/xxESYT5QRr58zcZ+Sj6735+Pe47gbcB+Tv7gwD4wiV+Qjvt91f4Lvta/yL/WD10Oe73orl4O/R/fsCOPvs8mnx2vfnBqsWphdwEQcOPxCuIZM0QkbgRuI+lTd1MTrhVsGguQHLGxS/JWk/VB1L+encr+CY9939YAkZ7QfTpMqb1N/yEAXQBbP9dvHH5vbtbvbD85rt8ubz3f/gS/ThAOUMawML7/DkLt3Y5vn1Ev6Z+GLvouQV4hXqLfF8+P76APgX92D5Dv0qBoAN7wo0DQYU9Bt8LLQ5CUECP3Q4oTVHNIriTr0Ev37V5xkoLWQtcgw/6ffeofAdBfQAnfME20fEgNCU6Uj7tvyl72nnxu0T9+b/uvpj5rXUH9uD5V/wtQCn+T3weOwx70H2cPas74/oQek06yPvevDH6ZzjlOcC8uf9xgGA/TD21vfCBB4TIxWmEpsO7xv/LXNE90oSPqoqyTO/FQrTycuyz9v3BRlgIbAPKvoU8fTzrQE0ABXqrN9l1jvWN+VA7xvtFubj6tf3mgHQAAb1IeSM3G3hT/HD7qzrjOwn8Yz81/+M+4/xWeng68rzq/g38tfnmONF6BrzFvxD/rz6qfdB/OYFSRE6FBgIzAnbFPMnHT7PRcM4MS4UMC5FDj/97jTEcsp28jcdJiLwB6PuTPKeBycTHQZ45QPVCN+F57Pwe+sp3RPcd/DVBoYLzvsA7VLlm+3G9vr3oOms3SDpRfxtBLz95vI67/j1h/3M/ILxZOes5XPt7POs8+7wQvQM/KECLwWdBCUFZQ9BEhUSaRpZITgtLTtxQYo3dzb3Pt1D/P1z0qDkHfbVDk4Kr/cL9bUEghG6DK/0PeVv40/0ie3t3O/YgN146cj29PmV9InwTvcU/Sz2l+gR6Wrtau2B9qr72OtI6c/0/Pp5/d33n/FY83bzuux26GbmGeq98ZH5zPmD+R7+fgROCcsNKg2qEGwW/yGQLdk1YzUWNjY4Sj0wO679IuEV9FP7zwEF+X7vf/k2CxUJaP1N7Tjw3fRV8/7gIdRv3Grny+rK54jo0vC1+gb7W/Tx6jztZvTX8cHi9OM38EP7xfS67oDtyvgdAaD7sO2L6nLv4/Kv75nmAunW94wCTP//+nb9+Ak4FpcTqRGhF50mJzVvO6wxwDB0Pf5A3SJQ7RD0ffuBBJTy5+5U8xUI0wkO+Tr0dPJrABf4I+uC2dLklulY6SXeauLu7YX5+Pb171Hv/PJN+XHx5uXj5F7yVfPI8HPuhfVY/Jv/2vis9bP3V/eh9Druv+0T8bb4zvto/sz/UAZuCFgSOBUxFi8ekijeMK4zZjVLONY6ej4AKiT9bf/SA5z/je6U8Rj40gJIAQn0bPib/pb/qvUc7uDncO9f7W/lFuDv6Ovw1PH37Z3vOPa4+Nb19/ER7YzuBfRQ8kLrneyL94v8sPo1+EX7rf07+5L04/L89AH3nvdu++P+5wTgB6gIWRMiGkgbViFyLpUzNjhiOOU5djtvPWQQ6wFyBs8G+vat7tH0oPlZARrzQvVM+iICOfda81bs8PFk8IzpX+Id5hPsBu7b6tHsxfG59pHztvXs8ffwFPF565TuIe+c82Hz8/i++J/8P/tp+nb3Hvdi9QT2IfcN+/X/CgJlAyQFag3QFFsXoxt4J7wuoTGkM1w3UjoIN2odZgmsBgsIsvwr8vPwlfR7+IXzGPAk88f5W/jN8y3vGPDb8eju8ucP5c/opet16nvozupS7wT0xvSu8Gfwn/Tb88zt8euQ8e72BPdu9ej26/qg/Mv62fcr+Mz7nv5a/73/lAGKBLEENAWLCDMNqRDnFPgZtB7dIg4nfilWKasg3BUgEtMTmg4cCKUGcQMg/xn9/foT+BT3zvXT9Ef09PPM8zb08vGZ7y7vF+7N66TrjOsk673sK/DP8FDws++b74Hxr/BH79nxC/Pa8QH0+vXW9Tn3aPit+H/7q/4RAY8EiQZYB6gJtgrWC4AQdBPvFa0cUiM6J9EshDGpM4AvZSZgJE8jvBrtEi4PpweAAJb9F/lf8wjxGfAt7zTv7u6s72Lx9u+L7uruT+3a66vsFuzS6+Xu5PKW9F70rPS89Pv1cve896j45fk3+gP8Qv2Y/E39Yv6c/isAVQL+A5YGcghvCIsJTwu4Cp4MGhFKE5AXHh8mI2wmgitNL6IvWyhKIvchNh6qFXkQzQutA5D+3Pvo9q3yIvJk8ZfwkPCm8Avyn/KP8Nrvg+/S7WXtzO1Q7PHsbvCO8zz0Z/Qm9QX1rPWe9tL2Kffy92H4Pfl2+Yz5W/rb+hv7TPzU/Xb/jwHbAqgCwgPZBaMGLAZFCd8ORRJnFtQchyFhJAYpSi2MKSkhSB91Hv8WKhBTDGMFff6w+tn2UfLy7zzvUu6k7WDtdO7579LuIu287QftN+uR603rc+pb7BTwhfIe80P0HvaT9fP0uvaM99H2lveC+Cv4jPgw+TH5R/nA+Yz6FPwx/Rv+P/8gAGwA6wEAAyUDBwV4CbgNIxJNF0wchCAmJfgoNiw5Kb0hhiDaHuAXwhFADqsGx//P/KT4GfTZ8hLygfAa8AfwvfAz8m7xSvCU8NDv8u6B7/buGu727//ya/Xn9rX4TPp8+sb6efv/+wv8ZfyV/IT8f/wd/WD99vwR/XP9Sv43//3/IgCqAIsBgwJ4A1MELgUSCHsMMRAtFNEZxx5gImkmXSqRLXArmyX/IvEgGRuSFZURgAo0A8v/M/zq99v13/Q/85jy+fKO8yv06POC84fzDvMj8lXy7/Ew8Wby//Tx9gz4mvlp+/z74frk+6r98vzZ/E/9DPwO+nD6e/sF/Gn9Qv4Y/x4AKwD8/1cAKQA0ADQBXgHQAa8EnAcTCv8NkxJ5Fk8avB24IMIjFSb4JP8grh4yHBQX/RGbDSsHfQDW+4L3c/M98Zfvj+3I7NfsFO3Q7SnuwO3L7f3toe1d7S7tzOyH7YXv4fDH8bHybfPh8yT0pfRE9dn1TPbr9oP3GfhB+S36efqN+gX7SvuE+1D79fqi+nr6PfqS+YD5yfm3+vP8m/93AYUEGwiOCjANGhB9EpcUgRbOF3oXrxWLEy4RbA1eCDoEuP9K+sz1HvLi7mbs6+o06RLomefn54zo2ugU6ZbpN+pa6n7qtOpM6jTq0eo965Xrdeyk7VnuEu8u8Jnx8PKl9BP2lPdJ+cP6Efz//IP95v39/W39z/z8+xf7ffrR+ST5xPjW+N34m/ly+gv7JvyU/ej+9f8pAY8CWgM5BFcFAAZ2BgsHGwcIB7oGaAU8BA4DcwE//1L9Hvuy+IX2mfSM8v7wFfDd7tvtTu337M3s1ezR7JvsgOxW7FvsY+xF7ITsJu0A7uTuLvDE8VnzFPXI9nH4M/r/+6P9Af9AAJgBiQL2AjUDdgOkA7oDQQNKAnYBFQFvAVgBlQA3AHv/1v6p/o7/HgDw/yz/jP6D/sL+ev7k/Y/91fxy/MT8E/3K/Jf8KPxM/EH8+Pvy+zP8Dvzf+2P7VPv0+kj64vmR+Sz5x/hp+NL3hfek98H3d/dX96L3jfe19xr4ofjq+Of4BfmV+S76q/oQ+2/7Efyj/Bf9Y/2v/Xf+cv5W/Z/9pP2D/F37ePsB+6z5Qvm7+df5APpz+rv6svqp+lP6h/q8+oP6KfoL+kr6b/p/+kT6QfqC+pj6h/r1+n374fsJ/Mn8Z/02/tf+W/+5//f/PQAOANz/qv+0/0r/o/6s/cT88/tR+4L6rvnC+DL4q/dn93L3pve195z3p/fS9274EPnL+Tn60fr9+gH8Kv0g/hz/3v5A/Bz8Rf6c/9r+ev5x/1D/Iv+a/zkAOv9p/hP+qP3i/NT8FP2f/Jv7aPtY+/r6gPpk+lj6NPpO+iX7tPvx+xr9PP4+/uL9Qv9cAEYASwBhAZQCVQMWBKwEKAW9BaAG3waKBgYGJQaEBpQGFQbXBX4F6QSXBBEEEwNCAsUB+wAsABwAggCOAAMB4gHCAjIBUAB0AcsCMgPcA8cECAVtBaIG1wdyCPYIuQlACkAKPAqCCpwKNgo9CjMKJArbCcYJtglyCQsJHglACRoJRgl1CWUJaAluCbYJEwpGCkEK8gnRCacJqQnHCboJuAnCCeQJ2QnOCfsJdgqjCiwL1AuxC1ILrgtuDJcMxAwaDUQNKw0XDUYNKQ0DDRoNGw0sDQYN4Qy3DF0MCgzgC7gLuwuSC2kLYgudC94LBgwKDAkMIQwlDDcMZAyGDLIM2wwbDS0NKA0jDfoMuQyKDIUMRAwaDOkLuAubC5ALggthCywLLQv5CuQK3grlCvUKAgv+CugKwAqsCosKcgphCjwKLQqBCj4KnQmfCbwJ0wmYCacJpAliCUEJbglmCV0JUAkmCewIsQiLCH8IQggICP0H2ge0B3IHOwcRB/kG5QbUBpMGgwaNBm8GXAZKBkEGIAYRBgYG2QWuBYoFjwVgBUYFKwUXBfsE0wS2BJEEkARrBE4EQgQDBOcD5QOxA44DfwNPAzQDGAPgAtACvgKRAngCYAJBAj0CDwIPAukB4AHcAb0BrQGbAZ8BgwGLAWABUgFEASkBDgEeAe4A8gDLANQAigCvAGwAkQBaAGQAPABEAKP/IwDm/w0Ag//j/27/pP9Y/6//Uf9u/yr/MP/q/h3/9/4B/9b+2v7K/qL+vv5a/qv+vv0V/jn5aPzh6ojjNd5F3vjTruFP8b7qs+hF9dz9qP3lAWYAYwDG9+P6p/J46HDa+d4U4ozmBupv8mzzCfgj/S8EBgJS+sf7Q/2k+o/14fps9wrzyvL0+y/+Uv/A/UwAIv7E/kQAbv9v+Sr2GPkJ++772/sa/ZD9yv+CAisDbABU/4P/CgC0/3/9bPw++878Q/0M/wz/o/5vAOkBVQLg/9ABlQG0Adv/s//e+4j9jvx8+xj7Vf6F/50CoP9k/iv+agDt//D+d/3v/KADPgJ3Amn+qv2o/PH+bP1tAC3/eQDh/g0CP/9CA2j/H/3q+l/+OP/q/xH+XfyFAN8AsgWEAF/9Gvft+f/9KwK+ATIEaP/1AUf/RQHf/hcBEP5BAC/91gHvBOwDcgHI/nD/kACBBEb9/PuK/nQHLQcsB5MCy/4u/ToCtgC9/lz+UQKdA6QGNgUuBSsC9AAUAan/N/86AvIE8wPSAxoEJQMrAAIBff8KAJgFtgUUAq0BaAGqAFACBAIN/5EAYwJoCK8FOAG6/1IBBv8sAML+uQKmCOcIDwS7/oL8Kv/nAWYBpwAbAoEGuQnqBJoAwP8T/+b/CAFvACgBFAV8Be0FBgHPAOf9rQH5AzAIrwdsBZgCAQDG+/T86wCaA4UFdALmA9wFGgjIBJz/rfvG/XEAIwXDBMQEugIKBCwDBQMtAlEBiv9GAJ4CIQGgAbD/KwAvAuYFoQW5BD0D2wGtA5ADSgMhAFoAhwDkAQ0BegK5BE0ELASSBKsELQQ/BL0BcwCTACQCWASbBwgG4gTlBBUEVwEtA7wCOgT/BMgEzwBZACkE+QmFDPYIAgYfA0ADCwLnAfoD+gcxClYIaQT1AacCFAENAgsDQwbZCLQJEgZyBfYEgATfBbYEKwTuA/kJ6wqlB8QCkgBJ/78APQIdB08LzAxYB00DqQAXAAED8waLCJMI8gbqBYMG8QSIBLcCGgPBBrMM2wyYCxkIkwTHBb4IawkhC7MLNAtzDFgOiAy9CSYJ5goGDYcMnAuWCx0LaAliCDsJoQ1xD60PTAmdBLcFVQdhCTcKiggvBuYE2QRZBrcGhQSaA8wFBgZrBIUBmP/W/b7+bP76/wUBeQImBJ0DQACw/dP9Of3FAEIEwwVSBE0HIAgHCtoKrwxPDpsO1g3PDsMP+RF2F4kXkRYDFngXZRZ5FvQWrBfLF2EXkBUKFuQW4hXfFegVCxOUDyQMiQTf/Zb5rfj++rL6L/cR8T7rKupM7DLvafD67/HthuyX67Psn+//8mL1Hfih+nr8JP59ANIBHwMaBNoHtgkkDR0SiRPdE5MTqhksHQ4fTCDVIfYi4iQsJt8gGB34Gj0dLx+JIAwYMAu+/8/z1fGW9ygAHP2M+2/1R/De7mXxIvHG7xLu+Ovl6prr6Ov57EXnj+C04PjlF/BS+M/4ofNH7j3qSO3r8h/6BgCYBi0IvAYFBN0C9QPECXMOzhIIFfgTrhLCE1gVcRlFHjMiEyTfI10hex64GssWYA46BtT1NutN6lHyxv5vB1UG4vu88G/oWuY96CPtze4N8Ivuz+588WL07/Xv9UzzlvA17tLrCuvi57Hg792N4IjpCvZ7/hH+5PcT8LnrPuxt8N31HPu9/yICwgEuAET/EwAlBQsJegtyD2cS9hYQGyoerx+XI7IkIiZXH1cSY/Q62tfUv95I+NwNYRLABkP1leZb5SPpvO0o7cnmKeAv4MLmF/Dl92L4ZvN+7xfsU+vp6rXnSOO54UfjSOjK7LHvV/Ku8vPyQvK58NLtJ+wd7Kzu+fFv9WT3LvnD+kD9lf/7/lH+/P/iBH0LQhX5G8MeaCBkI9kkjCXBJGUZ6vWd1cHG9tBO8IMNdxpXENn59Ob74cblre2f8Jfsl+TU4F7kT+zG84H29PTR8eDtCe3F62To2+Nf4/Li0uWl7t34jf5I+iryKusN5inlo+m87pLzZPW29LPxDu9G7mvxPfWO+TD9zv/5AAABDAYhDTITrBo4IxkqRi/sL80uNyzyBrDRSbqSvMHh2xCOJo4fkQbp6Y7jWerB8cb2bu/k4fzbIuMa7sD4c/uC9u3xufDS8Nvyoe5f5vbhNuIZ403uwflgAGMAXPak71XtPusL6dbqhOu/8aD1Efb48cTuIO4V85z21/fq+Oj6Rf/fBQcOFREAEOAUKh0eKJkxQTPWMlgyVypj5fC9TLp20ewEQiUFIswPvPWO53D13/r0+Qvx7eC81Svg6u61+ZL7mfTx75z1jvg6/Fv3aeu04e/lHOlu7C/69QRECgsGl/6786PrVucU6sztoPCU8kXzw/KQ8DLyz/MH8znu8exB70n61wLWCJ8GTAfIBQ4O8BdaJdEp3DKAMKo1FDJaP4gMaMdiwsXOfP4KItgm3QkCACzv6wCrDHUCZe7t4izWtN+u8d32CvR+7b7tLPyDBrEFhPyk7Jfhvuah8k3wmfYW/wUFcws2CY/9/PMI7NXrKvSJ95X1JfNH76zvsfTZ93n3zfEz7Kbta/YDAEcERf4z/VgBFAutEgkZFBrVHQEjsi7WMH4xhSz0L/sauuLb2V/hLfwoC3oUVwGf/SL8sQM0CikB6O1M5JjfJt+H6+jtEOv06MfvlvpKAzYA0fmj7grrpezP9TbwDe/G9WACsAiFCb8BI/Y+8B/wR/Nx87Pvb+sW64ftIfES80zxRewT6aTrEfH69kT58vbT9xn7zAEYCYIMXwwtEcsWwB5yJq0s3CgWKXomSC1mDh7r4uP/7qL6wgJWBDz1HPQR90wA4wCI+BHorOMT4NziBOjA59/h6uIy66P03vjR+Bfzne9h75z0Q/eg8anwSvdy/0oAD/5k91L0lPXL+ZT6Z/bi75fs4uyU7q/vBe/67PXqluse76Lz8PZ+9kX11vf4/OP+bwBMA/4DdQblCjIOOBHPFiYatR1xIe4jBSTwJIAXUwXFBQAMGQe+A5YB+fct9hT5Yfj19iP0au+K8MbwUfCO8g3zie5Q7kDxWfHi8SHyUPBa8Yb0QPgd/JL7KPsj/939kPrP/fn99fpU+8b79PvH/Sj9avtX+vP4Bvp6/LD73Pm3+fH5bfss/iv/Jv+h/zACqgb4Ck0OrBEaFH8XOByBIdsk/CdWKnss+S1vMIUlCh4sIyAdCxWtEsYMnQR1BIEB3/1J+0L39PW69132S/YQ+eH32/XT+Oj4HPec9/321/Y0+jr9qQDEA0YD7wY7DLwLVwjlCS0LWgoHC34L/gmUCekI7QdgB+4FygRVBT4E+QJ3A/IDDQNqAwEEHQTFBdQHKwqLDW4Q7RKaF5wbEx5DIxwneyg7LBwxMTIyNF0w/iPIJqknkx59GUoWkw0hC+AKdAWwAib/1Pvq/Bz9yPog/GD8dPnj+hD9pvob+qP5mvhE++7+2gAmBHgEzAXOC64NrQzuC34LPgwEDsUNnwxnC/AJtgmECRMITQYuBUIEeQPsAqECdAKQAZMAZgFQA4ME4wUcCCAKAg2wEJgU0xdGGUkdhyENJPgmQiqTK6otti3/IqchpCMcHQMXvhQDDm0JggilA/z/Nf0b+r75DfpC9zP32fgY9/L2wPic9pz1FPa09eb2sfn5+jH+wP+wAE0FRAhRB/cHXQeGBhoJ+gi7BjkGHgVnBJoEhwKfABUA0v5Z/u/9Wfzh+1b81PsW/P38Y/0i/ywBkgLcBIkIIwuzDW8QWhN3Fp0Z2RtmHs8gaSI+JJwltB4CG5cbkheJEk8PKwoABccCBv/s++P4+vXH9I70jvJv8ovz3/Jc8qHz3fIW8pLyrvJf8z311PZs+er7Jf0WAOMCmAK8AQYCigJ+AxcDKgL5Aa0BNgHPACz/p/1R/Qj9lvy1+6z6vfpQ+/36pvp++lT7A/3I/ioADgOeBR0IyAuCDsAPnxOjFnoYRRu7HWseACEoHb0WCBiRFcEP8AygCXsDvgHc/vX6rvhZ9ib0TvTA8k3xFvNd8/vxB/OK8ufwzfH88Vvx5fJz9Fr2sflw+kr8X/9l//T/MgKLAHQAjQKCAZoAUgH9/+/+vP48/az8Uvy2+lz6DfqA+JP4+fjh9w/4H/nO+UH7Mv1a/4MBLAO7BTUJfArOC+gOAhGDEmgUgBZiF5cYhxa3E9ATVRL8DeMKZggeBEkBgf4x+zz48vUH9ObypPGt8NPw+vBu8Jnws/BP8Hrw0PC48GPx2vJN9Bn2DPf896f5fvr++lP7P/vO+4/8Tfxa/E386PvO+6P7BPvF+rv6o/o9+v/5NfoR+nX5cPnA+QL66fpi/M/9mv9yAUcDPwaOCEIKzAzvDk4QwRKQFHAV6RBlDfUNkwv4Bi8FJAKW/dn71fk194r15/Nr8g3y/PDE8C/yCvK48HvxRPFD8IjwU/CQ74rw3/Gt87D1P/bk90D6cvpD+0f9lf2+/GH9Cf69/YD9RP2F/In71vqU+mn6mvma+Ar4R/er9p32UPb39Tf24fbE9wH5+flW+9j8fv6TAF8CIQOQBHUGQwcWCEsJeQmqCXAKXApaCiEKJAlaCCkHQwWbA9oB9v6H/Ib6xfeD9fTzzPEF8Mnumu0M7bbsGuzd68PrwOuD7Bntmu1t7oHvivAW8sbznPWs9/n5VPzf/lMBagMuBTIHGgnOCbQKSQz7DJANcQ45D6sPYxAJEQQSgxL2EtcQ6AutCTQIKASpAD/+wPmL9rD0YfLb8Cfw5u4I76/v0e8x8TfzdvM39NT12PUz9hf3yvYk98b4EfoB/KD9df5gANQBLgKDA+wEEgXTBekG9gZpB+gHVQfrBo4GrQUmBYQELQPuAZUA/v6t/U/8k/pV+bP4E/j19+H3qPfF9xH48/cN+IT49/hb+TD6z/p6+3z8Zf1C/jP/NQAwAXMCrQPJBOwF+QZoB/0Hiwi7CNsIOAkkCfoIFAnLCJUIXAgLCMcHdAfqBqYGqAadBokGTwb+Be4FtwVKBR0FEAUSBUoFRgUrBVYFYQUxBVUFwQWYBcMFHwYOBh8GPwYnBv4F4wV6BSoFCQWSBGIEewRCBAwEJAQ2BC0ETARwBI8E+QR9BecFfQbCBgkHhgfWBxIIhQjJCPEISglBCVgJpgm2CdcJGAoBCvAJDwoDCuEJ4wmiCVUJJQmuCDMICQh9B/8G5AZhBtIFggX1BCcEtwMrA6oCIgKcASEBzwCiACUAHQAlACQAZgDtAEwBvwFlAtsCfQM4BNsEcwUKBoMGBAemByUIfwjdCDoJuAn8CfkJJgpaChUK9gkXCqYJYQk+CdEIawhDCN4HawftBjAGdAXfBPUDMAN6AocB0QAcAIT/s/5P/gX+u/2u/bf98f0e/mr+yv4o/83/YADfAD0B1wFrAhYDwgNsBDoFEQbIBloH8QeOCOsIEwleCWAJQQkrCRoJ1QitCJEIOQjxB7IHYQceB6UGQAbgBU0FhATuAywDMgJyAcQAEABl/+v+m/5Z/kT+X/6P/tT+If+A/wAAjwAOAaABOAKgAiADlQPvA2gE0QQtBZgF+AVPBoQGqgblBgcHEQf4BiEHGgfkBsQGmQZbBh8G0wVwBfoEjwRCBN4DYgMLA8ICTAIUAuEBsAGRAYwBjgFtAZMBvAHcAQACIwJxApwC1gITA04DtAPSAzEEZgSHBNIEFAUpBTgFaAVyBXYFcQVwBUEFNgUbBQUF1QSYBHUEPwQiBNwDpwNyAz8DEwPuAqgCigJxAlQCMwIiAvwB5gHzAdIB7gHhAfsBBwITAhcCBQI1Aj0COgJYAmgCZwJpAnkCcwKFAmACYAJYAjQCLQISAvQB5gG4AaEBfwFcATEBHwEQAd8AuACgAIsAUQBAACUA+f/X/9T/q/+m/5j/cf9Z/1b/Qf86/07/Lf8I/xn/C//x/u7+//7X/rf+zP7G/sT+u/60/or+cf5h/j7+Sv4m/uP95P3S/Y39bP1u/WP9P/0a/Qn99vza/MP8ovyK/Gr8Zvw4/DD8Jvwx/Bv8BfwN/OL71fvY+877r/u0+4X7iPt5+2f7RPs/+0b7G/sS+wH76PrJ+sn6vPqK+pn6mPpk+ln6Xvo0+jX6LPoM+vX59vnc+bf5xvm5+an5hvma+ZP5gvmE+YT5Xflt+WH5N/le+TH5Lvk1+Sv5E/kc+SD5JPkf+RL5/PgD+Rn56Pjc+Pz49/jO+Nf46Pj2+Pn44vjW+OD4yPjZ+M74+vja+Nf46fjg+Ob4/PgP+fL4Bfkx+e34E/k1+T/5LPlU+UL5P/kp+T75WPmf+Y/5dfmC+bL56/m8+bX5//kL+p35BPqk+cf58/kD+mH5jPlK65byNPzc7oj8/f4k9y4BdP5b+pYD7f6r+pIBxv64+lH/7/vd+CL+Qfye+eb7WPxO+wr8ofrK/LL8pvk2+1/94fqy/SD9f/mY/cH8zfpG/MP9T/to/Iz9qftN/mr+U/yz/pP93/1c/8X9Nf/V/8j+2f/D/zL+RABL/+P9VP8//7v9rP4j/tr9gP++/Qr+8f4f/hT+dP+A/Uz+Jv9b/kD9WP4f/4D95f2V/y3/z/2n/zUAPv89/58B9v5FAEEB/P+uAHoAewFoAMT/igLz/hwAwwKk/qcBKADt/7gA+P8XANgB3v5P/+wBHP72/6f/IwCW/zsAWgCQ/4QCTv09A6X+AAD1AkD97gGUAEMA2/9UAGAA7gD9/TwCSAB5/XQDH/8lABEAwAA3/0ABPgAw/jMCk/3SATn+ugCv/pX+UwAhAMf8Xf+JBDT5Gv/wAzr7Yv3iAmv+f/vzAJ4DnvqE+qEIb/nY+h4Gavol/Zb/PQIe+dL+XwOx+g79CQWB/GT3hgeZ/rf0UAYEAUrypAc8ACj0iQS4/zD8dPrMA1cA/fRxA14DOfN1AJ4FbfZr/M8DDPt1+ZgEsvuq+NICdf8G+JAAM/+K+0T8jwJV/Lv4XgaC/uL1UQEoBQT14fxZBtD4DPr1Bf/84PgLAIcB//xO+xIBOP8q+/gAwP1G/I3/3gBa+5v9jQKF/dr8F/5HA7r3DwP0/3X4cQK9/pb8DwJC/d/8oADf/aT6GQPz/Xb78wHI+gIExP3I/VoCP/uYADUDb/iaBCb+N/tZArYAtvrd/ekAPwXV9PL/Sw088xT7UAnb/rT2pgbP/2P6CP9cBNT+evh5AIMDvfqtA//57gBbA8v60ACSAeX7LAGt/1P93QEQ90oLYvot+lUIT/qnAAQASv/4AOX6CAMO/3sBZP47/jD8UgaC/nf5ugYF/2n6Tf9UBqj6h/1BBbb+f/hGB5j+C/o9A7//+feSBkD/mPibBu39Nf4yA+0AM/xN/HoCGQRN95sBhwIR/dH+B/9HBGP5q/9dA8P/Ivn5CjD9ZPbHCI4COfpe/QUExgAQ+ncCDAXk9kcBGQQI+xL9wgZz/FEBufzEBGD+yvtgAgcAB/4aA/L62QLXAvT40wiq/NH9vf97BGT7gP8vAqUC1/tO/0wCs/6BAZj+oQBJ/ioE0gGT+/sCAACGAcn/UAJZ/5wAkQR19hEGuAAf//T6ywiAAT75IgMFBNz/4v+vBrj4WQQYBCr+0wCa/nL/1gHqAMIAwfvBBuEA0/igBD4A3wAE/d7+6wSl/xoB8v67A2r2qAIiADcA6P82/PAFRP5IAIj7jwRF+m39FQOk/BD85v7qAJf/CPiKBDb/FfhWA1v+wfzf/Q/+D/t9/jj/GfzT+h4Bpft1+7L+w//l+Q76r//b+mj9Cve/AX374veTAv/6bPjT+tL8ZPln9/H6CgB/8Yb86wID9GX5NfyC+4LyXvmyAo3xvPcqAlL3vPI890P+gvXn9UD9n/xT9nvzJ/1H9LD5RvXB9i34g/da/C/0j/bD80r3lffl9sX0kPxh9MT0zvTd+Nr7Au2h9PL3Q/Z99DD2gfqf7gH1bPsX98L1tvI69NTzDwI26Db0N/mW9ujwV/JjAOXqa/aG/CnxtO2b/fn2p++H7rj9uu8r9pb7De4x8ej3cP4o7dv14vdK8gD1KPQt+/PvufCH/krv9+3v+9X4ffHh8BL6XPmp8cv5JPS59Bb6e/F787P1AvZd9b/68/J/+EP6efG3/Bzqxv+N9ob0SvyX81j4xPRg+Jn7oPKw9UIAY/I0AEPyMvxn84n1pvvE9wP5OfT5/tb5cvWK9sMC8fT88soCw/1L8Cz8ywNw943xNAWk/QPuXPtmBMr21/CUBowBFvP8+nkGa/oE+EIA2gC0+6v6OwCC/L75vACQAPT7TfnRADP9igLD+UEDUf0n+F4IUgAT/i/7YQc/AfIAyf6/AcD8jAXrAgT6+P8dBYYFcPiGBa/+jP3wA10I0gEm930Q+wa3/CQF+wf2AVX3iAtOBKv47Qb3CkMB5PtbCxoNI/puA0oSlf/R+g8LPw2a9XYEYBGoAdABXwgSDl0DbQA2CVoMSQAMBRsKKv/BBZAP3Qeg/TwIHA6ZCv/+Qw1iB2YHkAeGCDMHkANxCQ8MmARr/zoSggmtAhIB2BCABoQA4A8oCg/9bg7yD7UAUQN+DqQNxwLWBFgLhArTBiINZgdKBK0JBQ4KB6UGYQRhDhAPZgB+EMkELgwcBjUN7QUjAp0SMQOKBq8JHwaoCHcMpAUKBQgL7w6KCDgF+AkgBSELOQ+f994KHgv7Cdf8NQ7FCjn/uwwBDsMDYAReEJMINAHgAn4VLwN5/wULAA0NA6z+UAkaCXgDoQZeBrMLVAP3CGENzQGiA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type="audio/wav" />
    Your browser does not support the audio element.
</audio>

Also, a little helper function to generate a $\delta[n]$ signal:

```python
def delta(N):
    d = np.zeros(N)
    d[0] = 1
    return d
```

We will use a recursive model for the echo generation in which each reflection is flipped in sign, attenuated and lowpass filtered with a simple one-pole lowpass.

In the above block diagram, $M$ is the echo's delay, $-1 < \alpha < 0$ is the attenuation factor for each repetition and $H(z) = (1-\lambda)/(1 - \lambda z^{-1})$ is a simple leaky integrator with $\lambda$ relatively small in order to just attenuate more and more the signal with each reflection.

The CCDE governing the system turns out to be

$$
    y[n] = x[n] − \lambda x[n − 1] + \lambda y[n − 1] + \alpha (1 − \lambda)y[n − M]
$$

```python
def echo(x, M, lmb=0.6, alpha=-0.8):
    y = np.zeros(len(x))
    for n in range(0, len(x)):
        if n >= M:
            y[n] = x[n] - lmb * x[n-1] + lmb * y[n-1] + alpha * (1 - lmb) * y[n - M]
        elif n > 0:
            y[n] = x[n] - lmb * x[n-1] + lmb * y[n-1]
        else:
            y[n] = x[n]
    return y
```

Let's look at the impulse response of the echo "system" for $M$ small

```python
plt.plot(echo(delta(500), 100));
```

For audio signals, that's how the echo sounds for a delay to about 50ms

```python
IPython.display.Audio(echo(s, int(0.050 * Fs)), rate=Fs)
```

<audio controls="controls" >
    <source 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type="audio/wav" />
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Let's now implement the LMS filter for echo cancellation. Given the original signal $x[n]$ and its echo-corrupted version $d[n] = h[n] \ast x[n]$, the LMS algorithm will estimate $h[n]$ iteratively as

\begin{align}
  e[n] &= d[n] - \mathbf{h}_{n}^{T} \mathbf{x}_n \\
  \mathbf{h}_{n+1} &= \mathbf{h}_n + \alpha_n\, e[n] \, \mathbf{x}_n
\end{align}

where $\mathbf{h}_n$ is the set of estimated filter coefficients at iteration $n$:
$$\mathbf{h}_n = \begin{bmatrix} h_n[0] & h_n[1] & h_n[2] & \ldots & h_n[N-1] \end{bmatrix}$$
and where
$$\mathbf{x}_n = \begin{bmatrix} x[n] & x[n-1] & x[n-2] & \ldots & x[n - N + 1] \end{bmatrix}$$

```python
def lms(x, d, N, a=0.001):
    # Run the LMS adaptation using x as the input signal, d as the desired output signal and a as the step size
    # Will return an N-tap FIR filter
    #
    # initial guess for the filter is a delta
    h = delta(N)
    # number of iterations
    L = min(len(x), len(d))
    # let's store the error at each iteration to plot the MSE
    e = np.zeros(L)
    # run the adaptation
    for n in range(N, L):
        e[n] = d[n] - np.dot(h, x[n:n-N:-1])
        h = h + a * e[n] * x[n:n-N:-1]
    return h, e[N:]
```

Let's now test the LMS filter using unit-variance white Gaussian noise as the input signal. With this maximally decorrelated input the convergence is faster. First, let's verify that the filter converges to a good approximation of the echo's impulse response:

```python
# echo delay
delay = 100

# LMS parameters
taps = 500
step_size = 0.0008

# this function generates runs the LMS adaptation on a signal of length L and returns the filter's coefficients
def test_lms(L):
    # the input signal
    ns = np.random.randn(L)
    return lms(ns, echo(ns, delay), taps, step_size)[0]

# precision increases with length of the adaptation
plt.plot(echo(delta(taps), delay)); # original impulse response
plt.plot(test_lms(1000));
plt.plot(test_lms(5000));
plt.plot(test_lms(10000));

```

Clearly the precision depends on the number of steps in the adaptation. You can try and play with the value of the step size, for instance, and see how it affects the convergence.

To have a quantitative descrition of the convergence process we can plot the MSE, averaged over a number of independent experiments.

```python
TRIALS = 100
L = 8000

for n in range(0, TRIALS):
    ns = np.random.randn(L)
    err = np.square(lms(ns, echo(ns, delay), taps, step_size)[1])
    if n == 0:
        mse = err
    else:
        mse = mse + err
mse = mse / TRIALS
plt.plot(mse);
```

As you can see, with these parameters the error stops decreasing after about 4000 iterations.

Let's now run the LMS adaptation using a voice signal as the input. Since the voice signal is very correlated, the convergenge will be slower, but we can use a much larger step size.

```python
# let's build the echo signal with a 20ms delay
delay = int(0.020 * Fs)
es = echo(s, delay)

# now let's estimate the first 500 taps of the echo impulse response using the speech signal
taps = 500
step_size = 0.01

h, err = lms(s, es, taps, step_size)
plt.plot(echo(delta(taps), delay));
plt.plot(h);
```

You can see that, in spite of the almost 20 thousand iterations, the convergence is much less accurate than in the case of a white noise input. Nevertheless, the echo canceler does its job reasonably well, as illustrated by the magnitude of the error signal with respect to the echo signal:

```python
plt.plot(es);
plt.plot(err);
```