Signal basics, fft, and aliasing in Matlab
This lab explores basic aspects of sin/cos waves and plotting in Matlab. It then explores the Fourier Transform (FFT) a bit. The FFT is probably the most important transformation in signal processing.
More detailed explanations can be found on Michael X. Cohen's excellent Youtube channel. Here is a screen shot that shows the relationship between time domain signals (top row) and frequency domain signals (bottom row) for some simple sine waves:
Signal basics
First, let's create a sine wave. The formula for this is:
Fs = 1000; % Sampling frequency, e.g., Hz (samples/sec)
T = 1/Fs; % Sampling period (time between samples, e.g., sec)
L = 1000; % Length of signal (in samples)
t = (0:L-1)*T; % Time vector
theta = 0; % Phase, in radians
F = 10; % Frequency of sin wave (cycles/sec)
y = sin(2 * pi * F * t + theta);
create_figure('sin wave');
Try changing F to 20. What would you expect to happen? What happens?
Theta (θ) is often used to reference an angle, as it is here. θ in the equation above is the offset, or phase shift. The other part of the equation,
, provides the angle based on frequency (F) and time (t). Try changing theta, θ. What happens with positive θ? Negative θ?
θ is specified in radians, with
radians equal to 360 degrees (a full circle), or πequal to 180 degrees, a semicircle. Try replacing sin with cos above, to generate a cosine wave. What is the value of cos(θ), where theta is the angle, at time 0 (0 radians?)
Try typing sin(0) and cos(0).
What theta would shift the sin wave by 90 degrees, so it looks like the cosine wave?
The FFT
The function fft( ) estimates the coefficients of the Fourier transform, transforming a time-domain signal (i.e., an observed fMRI time series) into a series of sine waves with different amplitudes and phases.
Fourier coefficients are complex numbers, with values in the real and imaginary planes. If you are intrigued, check out this video for a great walk-through. The magnitude of this signal is what we're mainly interested in plotting here, and it relates to the power at a particular frequency. That's the length of the coefficient in complex space, as shown in the image below, and is extracted using abs(yf), where yf are the estimated Fourier coefficients. The phase is the angle of the vector as it moves through the complex plane. ![Cohen_complex_numbers.png](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAtgAAAGsCAYAAADniNBPAACAAElEQVR42uydB5hURfa3+fa/q7u6KihpGCZ19/QwgYySk6gYARFzAkVFJYoKAoIZc8SMWRRzzhkMYFwDYkBQMay6qGuOe7771nDamkunGWZwBk4/z+/pmb6pqm7dqrfOPXWqUSwWE5PJZDKZTCaTyVQ7amSFYDKZTCaTyWQyGWCbTCaTyWQymUwG2CaTyWQymUwmkwG2yWQymUwmk8lkMsA2mUwmk8lkMpkMsE0mk8lkMplMJgNsk8lkMplMJpPJZIBtMplMJpPJZDIZYJtMJpPJZDKZTAbYJpPJZDJJPB63cjCZTAbYJlNtKxqNOq2NkLA25M1k+rMA254da9NNJgNskykLFRYWSl5eXqIRjkQiUlJSIkVFRQ2yQQYOfGnHgsgrso7GZEr/DPH85+fnJ9oB/3myMmpYYE2bjriXDbVdN5kMsE0NtgHmb77pVPluqCCqMA0MMHBo0aKFtG7d2uVH82kdjMmUXl26dJH+/ftLx44d3XNjgN2w23fAunPnzrLVVltJt27dEvfTyshkgG2FYKrjRhirNZ1pmzZtXMPL/w0RrFV0Kr1795Zhw4bJlltumYAD8lWfIWF1X+X6ZVBXZdvQ6kNDLsvazkem87AdGDv44IPl0ksvlX322UdycnKqDE7TnaMhAXhDrNfVzYe+kcTAsO+++8pVV10lRxxxRMKI0pDLYW25fyYDbNNaLDpU4HrKlClyww03yK677uqsvg2todVXoWpxO+GEE+Tll1+WWbNmufypFbu+NsZ+HmrSafjlUFudTrhsG0JHVhtprquy9OtoNrC7ummo7jXVjWrChAkyd+5cGTFihHsLRBuRDLCTDWwbYptRH+p1uCyzHYClu7/aFnL/DjnkELn33ntduxiuVw3p+W6o7ZLJANu0jmrnnXeWp556Sj7++GM599xzE37ZDc1q7QM2HcoVV1wh48ePd5Z5dX+pT5aPVHmortUxfI7VzWO6dDWk+rA6FuM/qyxrPR+R5PUqE2DPmXODDB8+XFq2bJnw3c2k+vZ8NZR6nU3Z1iQfOuBJAPY9lYAdPkdDAdVs2kvrz00G2KZ60VjR8JaXl7vXhgsXLpRHHnlYHn74YeenV9+t2Jk6ow4dOkiPHj2c9dqf4FPfAMBPR6q/a7Nzro2ybQhuIfWtLLN1+aiNNKS6Zk0AGxcRfXYyAXSybfWp3tTXep0qDZnKORsXkVSAnexeNhTAjkVjDa59Mhlgm9bBKCJ9+/aVyy67TG699VYH2liyx4wZI02aNKkT/9M11WnSqZA/hWsfsOuLT+7qviLOphxW5x5le77aKpvaPEdtDzDW9P1dnTSkg+tsXUQAbFxEfMCuSf1oCJbsuh4MrM79zva5q8+AvbrlXNN2yWQywDb9OZ1MpLJhOuCAA+See+5xPth9+vRxvpfXX399wqWivgB2eNa7P0OetCIFBAVr321kdV+D+ha82i4THQz4+ch2QOCXg3+OmoTkCvtlatniMpTunP7r2j+rjqg7RLKyzPa+papTWpdqCut+mrQsU50v3f3M1nc72fHZlEUywG7VqlVKGNPIQ5qn8DXqG/xkqterk95UkTn8cKGZ6kg4TVqO4edKf0tXp/yoL2EfbH3WUz0rdVXutQHY4ecz3F5a324ywDb96aKhIhzXySef7Brebbfd1v0+ffp0eeaZZ9z/OrmppmIGO+GhcNPQWNRcl//79esnAwYMcFBPOtiGWwrHJOuo8KPeYostpG3btu5/dWHp3r27OxeW+Hbt2iWuU1ZW5q5dUVFRBbA5huvjPqIz7Omg2Na1a1eXpm222cadk/Mlg3Xdn/NwXY5hf9JH2sOddrgjZR+OB144Py45RDvhPOSHdJG/MPDqOSgDykzzxr6ckzxxnp49eya2pbN++fdJ06bXpezIG/nivLjc+NEH/Pvkx9nF5Yhy5Fs7fz9t1CsivJC+ZHCTrWVKr63fpIs0cR3SzTUoV66DFVbTnQqMdDIYonwpQ+4H4eq4r5xbO/MwTOn94TiuT945j9YTjuc8lCX1nXrFNk2zpkOvz3bSzzHkhXuh9c6PTe3ng3xSd3hO2Ic88ztlwDk4l9Z58qHRgthf77/mLxVg+yH7fLAjf6SX8tJraN32y4pzsK+Gikt1fzVtmk/qeqdOnZIOtFOJZ5N6SDvA/zqvhN+4B5QJ374LWbLnhetR97kHfhmkqkdsZ3+te34EI+oF+Scvuq/uT1pUHKttXPjZ13unzxOi7PW+ZwPYOjDS+0G9RNR56rDWs2zBmb/Jk7bpvXtWPt9+26nf4chV2p7r80m+OA/1NVmZ63Ojba+2/bqvhmVNZZgxmQywTWskesiOO+7orNVXXnml64hovIYOHSrz5s2T4447LtFB1tSqQaOH28m4ceMcNNCYjx49Wi688EK5+uqr5fLLL3fhwC6++GKZOHGia1y1U/A7WNJKB3LGGWc4v1C2E9P1+OOPdxMZSf8ll1wiI0eOdNehkSVvxxxzjOy+++5V3ERo0A888EA555xzXIdCR0Mnxb64ypAe0sc5iUBCyDKO8a1MdIKk96KLLpLZs2e7Y0gH+Zl09CTX4CdzS9FzaP522GEHlwfKgvNwPNdloinppkP2LYJaFkxK5f5wrygX/megdOUVV7p0UE4cn8lPFl9G7by00yVNvM0gb5xL80bZTJo0yXWg4TqhljDqEOHATj31VFcG/MZ9OvbYY13+uM+aR8qYfTlG465nC9g+sCmQkt/TTjvNlaWml+tccP4F7jqUU6p6rOACoOIexX3nHKRZ7wvlyzWoC+EBm96fPfbYw+UROCD6BjB39NFHJ9JDnjkfdXXUqFGJgaceDyyMGT1GLrjggsqyv+RSdxz3YvLkyW7gp9Ci6dZnlJCU5513nrsmv++2226uHlAGHE8errnmGpcPng0FMgV8fzGmdBZsfzA2ePBgmTFjhgv/pmVFe3LWWWe5slC49eGI0H88e3vvvbfbntK/eKWfLXWc/TlOoTAb17eDDjrI1Qeebf6n3lKvKXt9zkk3ZU27AeSSPs2bfgOKhx56qMunpi8dYNP2cO0TTzzR1X0FXcqQtHCeww47zJUj9Zb2jPKi7LR+cM84nmfRH7xSXnvttZfMnDkzUc/1eTr//PPduXQg7A+iFbB5U3ncjOPctakDtCEcr22Ye16C8uA8XIvyTmdx5zoDBw50badrL2ZfkUg/bRjXZLCgefDbQdp62pPDDz/c/c8zA/xTR/UZodzDb8iGDBni2kz2If/sx/W4p+SHtjDds24yGWCvY5MN18SrrTC40MgCEw888IDrUOlIaVCBYhqs+++/X9q3bZfYtybXwrJCJ0ajSacDeN1yyy1y7bXXuk4FazkdPg3l3Xff7falgfTdU9RaBtg899xzctJJJ7kOkXPcddddroPgNyAOqKBjIPIBri9z5sxxIOwDNvk78YQTnZWexpoOnHPhg37hhRe5NAFFwAmwwKTPU045xR1HeoA1rnn77be7fLHftGnTXBrIxx133OEAjc7RtwL5ZU8nyKCDc7A/56PTAAA4lo6Q69IB6WIfCuWUBR0PeWd/znPjjTe6c9HJ0oEfddRRDn4y1QO1SPMNSFAfbrvtNncuOizyRN7OPPNMVxbUFfIMePkWch14kC/y8eijjzrg436wP+ejA546daoDxbPPPltuv+12l0fSqiCW7VsRH/LowCkH7t/NN9/srkMa6GwpS36nbtF5YwkNd/R6HuoCkEHZE66SNFIXAB06cfKAph873cEBIOVb56in5OWNN95wdQrw0HqiaSL/1CXOz/PF3zqopKzYj/RSH6lX7E8aAC+9J9xX3x1Ar80z/NJLL8kuu+zi0nHnnXc6dy+An/MgzR/lxPOhIKLlkM6C7UMSYMgAgbSSLvJJ+XIfSCO/cW+5pl/mnJ9yps5fd911CYBMZhVlXwYcPFMPPvigK1Mt80x1hOf/9NNPd/WQ44B9gIy2hzLmGaFe0wbpswMkUn91kKFvhnj+eK4eeuihRP1L9yaENweAPc8K91S3kx/uDeUPfAL8XJMypJ0ivZQXzxxpJE1s23///V06KEfqIvWGNHNfqRucg2PZl3MTNckfBOrACUMB5Q6cA748zzzrnId7x3mo85TRfffd554fyiPcblBndBADiFNXSSt9Bu07xzHQIz2UAWXMwNDv5ziW54N6SJuv7QT7cx5tz6l/ek2NDHXTTTe5fFAvKA/qHNflfyz0pIU2n/a6rlxeGsI8A5MBtulPBGzgl4aeBomOTF8p05hhZaazxmJHB1vd12zaSWLppeF84oknXMNN4whg0bjSCXBe4Ir9gFo6RBpmoElfhSIaSl5BPvvss65zoZOhcQY0OVZfdatllbzQ+AMyRx55ZBXApqOiQ1mwYIHrVNiHjgZox8KuVjXORzrp7P71yiuucaezo3EnDUAIFip1S1F3FfJHB0XZquuLWjn5m3zTCVImdKxY5tQFgfOQT4CAdDEIoLMAZhUsuB/kG+hQ6KNzIb9cTwdEqe6ZX9+0vPgm3fPnz3fXxapEuWqZkkc6SYCfThyRBtLl+xjTIdPBPvnkk+6bcgLyKFt1C9BX4jvttJPr5Lmn1DN/UlY2gK33ElAi+s1FF13sYrjrq2KuRVkC+nTy3G+g1X91rgAC+CgUUjew7gFWWq9IO+VLObMPkMK1fZcN9uVevfXWW65ecW8ZBFGW7Mt1ORf3f7vttnNQpPeXc7M/ZcVzgBuNvjVRFxPqjA7GqGfqXqMuONTzRYsWOcClbnB+YBaA1zcfnIe3NzyL5Jd65pdHMgu276bANbnnY8eOdWWOFZVnQq3mHEteuQ88908//bRLl76l0PvLoJBnnTSSl2Rv16gjACTPCfVOAT2bOsLbAwaFej/JL3WNQQH3Up8B6jUDeiCTQRj3yncVoWypB2x/5JFHEnUvVRrYxjHki3ugb5G07CgXnh3SAoTT7uh9Ii16Du4TzwxpYqCEdZfBGAYGBluchzLXe8abLs4B7NL20KboM6L3BQMHAIp4xgFZ6h3Xol6yj5YHA0qupVZ7fVb8t11Y0skLbToDc3VT0faC85x33vnuPvMGgvbEfwtHe0Jbz3Z9Vrg/6mLEvv4gnrKkTKlXDA7VlY7tXJfz82aAe81953nRvqOu+1cDbANsUz0E62R/1/X1tDGgEaYxAjoUkBSWsK7QSGG58X0pqwPXupoijf57773nGnYaUH316L9epxOnkaShfvHFF50FI+xDCCwBJEuWLHGdCFDkW5v8ZdIBbDr+ZIANgGFNBIQAdTo5rFxqwdfrkiYsYXSwlAXXRHQGWFx8X2uFZ/anU6DzJL90YOrT7LsR0FHQwTGw0eXcFaA5J//jvsL9eeyxx1z69BzkDWsUwLh48WJnlaSz4hg/PdVZoGTPPfd0i/Jwrxg0KBDoPVI/db55tU/HCqBRDlqu2kHTKb/22muuzABsrJTqi+z7hpIPOkUAm0EMx2bjAqDHU1+oT5QzQECHSxloOhU+OScAwoCHew4Y+O4QHMdgjcEF9U99x33rtE6mwu0F6xwDCCxsPqQrYC97f5mDMeoKcO9PJNN9FVS5LunHckdZadrUj1TzQL3iWpMnTXZAAjxoPnVgjNX6k08+keeff94NOrQu+W8qdH8GN6QPcCRPmv5MgK31l/tPXaHsOJ+rv4V/PGOkl+eMfdSK7PvhAs9AF1ZhXMh0MKHlqfeW55M0ci4tk2zqM2liEMQzQv3imQVK9b6HJxdTR0kr8AaA+2DK80/95Jml7VJwTdbu6TYsqtxToFDzzf0iDdxvjBf33VtpJVZ//PAETP6nDVu4YKFLP/WTdsX3kfbvLe3X9ttv79oL3Dy4N3peBWzK4+2333bbaXsoUy1XFcfQ9jCYJJ0MNv02jL95bgHim+be5Nph0kI7pn2Ftp3AO/0L95lBku+ORJvFgHHZsmWuPlE2OlciHOOa32gvuQfcK71GeMIqv/OGh/PybNGPpZt/sbpzmFJN/jU1HDWyQlg3tCZXv6JzBxCwkODyoJ2obxHhdSEWKCwlOomuujP1aeQBByxrdPr6etF/paqNrk6sozPDeqI+vD5gv/DCC/LRRx/JuHHjV+ksswVszsOrxS+++MJ1vkCN32H5eSDfzZo1c5a0zz77zMHLnnvsuYpLg59nzgVY08hjdfLDBVKWWKDocOjg6JDCE5P8SWQALAMOOlbSrRMjAWzKlPQzUOKa2lFmu/iCghz3GpDnXMC1wr7vQ67nVBcC3nAATtQROnzdl3oFYLNgEUBA+klvsugBCmJ09kAB/qnZWCjVAsbgjcEFFj7Awu9ww1Fj2Eb5Eesd66EO8ig3wPSVV15x95i8+GXoT3rTCaBYl7HaMYAAPvwJYUDEihUr3AADoCHvCl3hyV7UUeDynXfecYMb7qk/gdb3vdVrA8YMbMi31n/1k+XaX375pXO98AfM/rnUoke6eP4ZCPAmQl1F0rmI6GRc7hfwCCABVeF7q9fgueG+6JsDyt+3YHK/SStWTAZ4PvBijVVXAHUjqc7rftLMIP3TTz9195xBoZ++8P48A7RPtIf61k7Ll8FATQCbZ5zBiD+oAkYZnNGGcQ8BWW17k02apb0AyP/73/8m5smkiwTDtXmDwfNMuekzwbWpj9Rz2nTKVwdm4bqu1+YtC/WS9or7rPeAc1K2PN+0nXq/U4nnhQECwKv+8JyL+sMAavny5e6tjb+gUThf5Jvr8VaCv8Oud+HnhXvJc6JhJusasMPPaqoIVqb6p0bhG2da+7QmXy/p6zkabGADCNbrq3sE+wDeWDB47UYDW1PABnKxUGiDnw6w+Z/OFnik49eOzgdsXk3zyjRV2KdMgI1Fig7i888/d36Zfogn30KmsEOa6UiARjpF9dNMNfGHYwALLGJYVjUiCMdgpQHMgDn2Q75Pp18PNH9ACKBBR8X/lAnWPTo/0k8nrJDnv97OJpwb5QQkYtWiU1KQS0R8KVrVP5bfsUzNnn2Fs2JhpVUwA9QA7Pfffz8BgX4EAH9ylFq9cDfgvqolLBNEKTAwsKBceMXu+weHnyd9pU0Z4ZPNQIIy04EmAEPn379f/1WgOpm/OuerdJF4xFkg9d5yH4H1r776ysGhHqOv38ODHo6j7N58801XVxgw6PPhT4xTcQ7qPS4ipFfroVopqedYAwEpyrW0pE3SFRYV7qmjPEsMktTdJQHY4yc4KFLAVvBlwARck29/AlwYDjW/7KM+1Lhb+ZFf2EYbw/nIkw44uTekibTRBqhlsjphEskfg1sGxdxznnmNIpIs7B35Ux9lBo8+UFLOQObqAjbXx7oK4P7rX/9yrjr+wD5ZHH/aPNppBk48H5SPumGkGlgwcGLQybV1wMp1cDl5/PHHXV4UUpP5k/vRZYB1BigMQLQt5P5wbxg0Ua7htQbC4nz4lnOf6Us0zwzmSSflQd3XgVyyfClg4+pFWsKRXMLPCuXMs8ibk7r2w/bDHZoanhrRAZrWLg3acScHnPxNR6f+dHUp3y+Xhs7NKA86St9Cp9DLb1iraAABPO3EqwvYNJwcD8jTgYY7ZT+ElzaO7IcrCB2BNro+YGNBo2FPZ+HMBNj4ZeIuAIzo63eFO78M1F0DMMb6g49mqqgqPmCTB+CXCTxAHPmgY8DPGcDmFasu4KGWcj+uq4JOk02auEk8dIz6iptzkQ4WBKIzVT/E6sb61k6fssDVxH9j4LvnhO+T3ivcIbBA4W9MPkgXHSGDB8qKQYC++fAnKvmDKcqewcurr76asDJm6gy1nlIu1GHAQeHJjx7gp1utbCNGHOCARX3j8ROlTmH9DVvGUtVr7g0DVKCY+qX3l+Pp1BmIUeeAtHRxkEkzlkTqOmWo/uz+gNOXDlhxUSHfWD99wMYazgRLLI/8pm+LksWu1jcXQDTPJoO3wvw/Oh1cUHzA1rdapJOBBftz75JZ7hQ22LbJJpu4c/FGSq2d2hZpVAzqCzBKXea+HHnkUYmJxRrKsbqARNnz1geQpX5ovUn1VofyAvaxelIXNG8K2EB6NoCt9ey0U09bBbD1DQRva7Aw60TZVBZkLXPaO54njQ7Cb+kGFjyXADB+ynofFLAZEFPe6eJG61wB/mawwaCNPopzIwYGQDHAz3mpH+pqkkzcC+49rni8OdRnCMBmoIi0TU01oZ7fcd+h7gHN+hYk1ToHmgf15a7LxYN468rgkf6ccjI1LDXCd9C09gkrDX6INDo0VmvK77tL5y7O+kBnAmD4k/B8uKQhpzHGRQH4onGt7mIdQAANI5CN9S2Z5de3buprURpjLIs+XChgA4R0vKsD2FhZcffA0qGA7fIfiycGIgqgdBLAH9emE04VvzcM2FjlAGzcDuiEgCN82tW1gAaZDpdvgCU8CAO+ADmsYViR6KTUSkXHp/6rvhWlOr7Xug9lDSj7A4cwnPpvGxRisWZyLHUY8KCc+MYSzmtw6rT/xsIHE00bZQ+EANjkj3NnSrfGHwegcC+grBQk/IGAn27SpXGqdVIs9wn4w4VB4V7fYKRaNMR3ZeIZotyo1+SD5wXA5m0AeeI3PyxjWFyfMlI3DYUBhcEwEGrEFNoO/KeTATZAqYCdbHlz/3miHmERTOZLnwywqb+4SjCww41CgYI6jHiWEPUWsR0fWAbx/3rlD9D145ZrDG0G08AfdYk6RZuhoS5rAkhNmzZ19YN6yFuCTANP0kFeSQPWVgXf6gC21nEH2KclB2zKhTrD+TQsaqpX1/pGiAEVAxTSoddN5YsOzALYQDzlHQZsDCZqVEm3OqduA2aZP4MhQo0NRH1iUIgbHPeXtos6l0q0YaQJCzb3lzwpYDOpl4my4WcvnC+ui2seVmwGtkA+9UOjpejbwNpeXCxT+6nuTPSTtAe+cGcx1X814sEwrV2iwcLCQCNFI4yld01YsPmm0QR4gT2d0JXMEkUDwsgcNxEsVxtvvHGNAJsGNB1ghxt2Oh7cC4ge4LsTJAPsVCBYXcD2O5naAmyNw6yATf6BFgCMToIySSWsiviu8zdArqCggM1kPDpwOq7wACXbTkUt9Jyb+NnhhTZSla1a6eg4yQ/55N6Qb/Xtf+KJJ13ZktZ0q9xxn6j/+Czz7UNmuhjHCntYAsO+28nSGy4b9WUHpng7AAgk84VP9TqYe0o+uTf66p56q1FEAFAdkKYDbO4p12fApO5ZqaysNQFsH6jDzzhp5lnCGo5bllo1+SbKRxiwARp+I38MHKmb1GMVUJxMDJQBI56h8FsQTQd1Bfj78MMP3f46OAu7+qQb+PjC/xvIBTQBoEzzEigv2gvSQFvn+51XB7ATFuzg2g8/9PAqgI1BQwHbj3GfDrC53z5gp3u+STeDPOoUfUwmwE52Lr98aMdor6jX1GeeM4B/ybtLEgMh2nfE33598IVvO/cC1zx1NwHOFbD9OQPp/J114isWeia/klfqFW0Ak0X9xZrWBGDrWyWeY9KB2xp9BHWJvp3nR0V/b6p/amR+MmuftEFRv8c15YNNA8SEEqwJvGKn0ea1bDJhpaPxuPOOO12j5k8orEvAJo10QFhJMlmwaxuwwz7htQXYOjmOTolFfAAqICaVsCDyDUjjDgIAcU/CFuzVBWz2wyeZziq8FHoyoPEXDOHe6gIPPmBXhlarCtjpfMCrC9ikESs0151749zEYkHVBWyurYCt/u3plr32zwEk4EpAR4/lnTpU24CdLN/ZADZ5qSvABqw1vbiZUTf5Rljhk4k6zPOjoQrDgM29Yxu+2kxKpK3gGdXyS3Y/awrYqSI/VAewFeJSta/kh3kBALZGEUkG2Bp6szqAnen5zhawfZe4ZOdSV41+ffu5+uwDNsBMW8gAk3vLfASUrj2jvmB1ZlBOGfmATZ1KNkchXPfVkk29x9VOQxLSl1FnsKwDTBirdBBUXd/96val/kTj8LLt4QmPFsihnkYRsZmea5fCkSrW1ORGXUQG32A6YuAIP0de2/GqGJcVX/zGKxQ6BGa901H5/qSZ4iyTt5oCNq+M8fNbUxbsZGBVG4B91ZV/uIhUWnwr489uuummCZ/GVCJdgALfOuNfoRSwocOvDcBmIMMbAx38ZbLiKhwCuXSOCtgaei5bwFbIrQlgawQROmj+Tra0s+8qkgmwcXUIDySSAbYfhafSH7nSSsm5gKH6BNjhjl6hrbqArZM4AWzuNc+zRglJJ9wVqLtI60HY5UUHdVgmGTDiQ069BtwUZOsCsMOqDmCni9fuAzb5SQfY4RVBkwE211PA1nj76Ywc1QFsPwJGeHCZAOyQBZvz8HYNizSDTNox/z6nkz+JkfOoiwhtSCaLs8Z6p2w5D9fkecNyDbjjRofxgrdxgLeuRKkuOHVlwPJXcw270umbUN+1zlT/ZIC9FgJ2eEJGdRdyqYlobHmFxYgfv09cRHjNjvUymXQbnSqNLNCtE+qyWd1RF7NRH2wa60zhkhReaHTpoLSDWBOAnWzSZW34YOvS7Wp1pSOgc0rWECeDOgUfhc/aBGzOSzkDU+EoKqnqpS4HjSsC0TKoIxqlQf32FbBThXf0FwSqCWDjt6urxTFw8eNsZ4rN7ruIYAnDp5i0ZgvYuggK9ZB7gA+4RneoDcBOl+9MgI0vuw/YWnd8aPPD/jHATgfYWAQ1bCP1V1empE77C66kcydiH63nOtHVD8nH4IZ6xLOKJZxnRldB1Ld79QGweU4UsJMZGPR59heaIQ+1CdjZhCfMBrB9Q0kY2H3A5tkijCRv1Dg35+G5o1yZpBmOu59sYq5vSfajAHFu7jsDNqIVpWq7wiFYw/dNo9zo6qKUO8+0DtLqCrD9N53ZhN5N94yY/jwZYK+FgL0m41/7DYJarBjhN2nSxFkCUkmtDnRWwDZASiPmr1yXCeB0kiPSmK8ZJ2F26eIaSY1esjYANuVIvpj8gm85ZeGHyQpHeQjXFQ0PV9uAzXmxBGPFJp3ZWrDJD4M1OmxezerrWwCqLgFby5jrAArAHnMKFDJTRezw345w/9WCi/WLOQZ8+xMs07mYAAe4TgFJWPK0XtcHwH7t1dcSiw6lsmBr3aaseZtFaDrAT19vJ3MR0VUzAUcNk6l1MpVStUG+kYFnmrYFX3bC5HEtoJQ2iucfiEt2nTUB2Gph57nQpdL9twzpJljrUuncX32magLYDFgBWty42L+2ADtd263PIN+cg0mOlI2eh0EpbSHPXTILeLI3Pj5s1wSw9fdwHHB/+XYN+8mAFz9+nk3+rksXzHT5NzWQlRwNStdeF5E1+WDqpDReoWlItmSvtXyrqh5Lp/fBBx+4DlcBJ91y3Jo/Okh8K+nI1eKRya+NiZVELgGk/cVDGiJg03koYHMcVhWiVmBp0TB9Ggs7WTi18HLmfJNeLH21AdjcD2Dq3XffdZ2RH0862b3VusHfgDSwQFoc0OUXruIiUleArRDI9f1VDX2LVdgVi+MYWDLY01XueA64rwBReIARnrimbigaDYIOnGcJCKovgI2LBa/edVXSsC+ob3EEmBmg8Hz6ceXZHgZsjSpEWTMYI73pfKRTwbD+pvcQP3byD/Tp4j8aT5zX/ay46lsvs33TVxuArfUGCzah8hhY6NLdqSIh6X3ibV8ywAZK/wzAzs/Ld4DNYGra1GlJ66TfD2jeuS9vv/W2qx9ap4gOQz0jWpAuMpVuMavws6j1MFvA1oWAuA96fLKISf5cg6lTpjrIxhARnixrgG2qAtjmiL52rtq4pgGb1dmwFNEwhidjpGvkdWEROlYiW/iRJDLBEBAAhBDtAXDWeMWpRIPNhBlcUuiM/Agn1QFsOgNgivQmW8mRjkMBW/2bw1CwOlFE6JAYVNB56IIgGpUFS9hdd96VsKSmeqPhr7ynln+21yZgk1bAkkVrAC3KJt19VT9I8kfniD8m91gnwulKjtkCNsf5gJ2qbMNuRJyXjp77i9uNvpoPTyry7wvCnYXBG/nk2ojjWZVSw/0lAwZ/sRquhe828OYvhMLvQK4Ctr9IUrowfdUFbIArGWAr3GMlBTD9EHBhACFtuIWQByarURf9fcKArfeF+guUA2oMKPT+pgLr8HV99xDuN9dnwOMvNKL5BEKJPsIzp89Ctm1dbQE256JO02byjKhhIpUFmGN43rk/TGbm/urzpPe7LgGbtkwBmzcCvsUY4GaQoKHy0g0UuK+0C4QtxKVNfZ/VuEI5MQDCHSndREm/TdLJgJoe6hIxsLn/mQCb+khbyqDQbzNTxQ+nD9GJ/JmMOrURC9sAuwEDthWCaXUbARrOs84623WOLFjiw0gmaQc0c+ZMN4kKC1l41cFU16WjBMQAZhq7VDGa/bBQNOqk0w+Xlwqww/7LaoGhgwAOUgE2ljEAm/i9qQBbJ4b6gE0nnC1gA6xqwVbLIR0mcLZ06VL3qtWBc7RqPsITU5nIQzkqgPkuIhoHOzzppjqLzdBxMkmIJYsZlIQX5Qj7H/O/LpXMPfXdWEhjJWA/kRGw1apXXcDWjpTOlkm4QBTuKgpFyV4va5QPrgNQ+6+UAVJ+xw1AJ6Qms+CrxZ+oIQA5cEDMdj+8458J2EQH+u6775xrhR9FwY+H7S8RzyqjuGJoLHwfhgEUf5KjAiXH8xbm9ddfdyCqi+mk8l3nOKCUtOozS7kw2Rr/eWBTVwL1YYU6DoAB8sCcLrNenYVmcGepDmBT98M+2Op+sP+++7s6gpECeE9mNFFwZEDA4iwM5GoDsKmXAHY2PtiZAJsFazCUUCY8E8lixmsdIB+syErd1OdYB/s8b7z1ok/A+BL2kw63GTyr1ANdJKe6gM1zpauU+ovMJHOr4xrMLaB9pJ1MtWKlyWSAbVqtGc7akWPto7MiOod2Vn7M0HRwra/oaCCXvb/MdUD+5I5MFmyiZhDfVl8tayOtVikFFzpgOh4m1WC9VkChgyMPwAydFnBH56QxaZNZzzg/frXAfTLABtJZvCUcqzlZ5BWuDVQB5AC2TnRKB9hAMYBN3nU1OnUvwFqIJZUOQ1+1+/6vCkRAAp0k5caree3g6BhxMeEVKB2+/5qyJlFE1CqFywNwSOfJb+rCohYtrsv1cQEBsABVBUy9j0AAgE0Hz+BFZ/+nspSxHRil4+e7OtYg0qSrwXE96jgrB/p+xvzN/aW+sB/LknNvwmlioMAgEJhR67YPnRoJAVcprIBMotI6qn7FfHM/mGjIfr4FOdWk46FDd3HnAmgzATb7A9i4KwBpWH3DFuxPPvlEln+43D3nbPMBWO8hv5FOypx861sJzSt54g0JoA5kaR4V2ilLFwt5yRIHPmzXyDfsw7m4BnM8AHQm6B115FGJsHRsP+P0M1y9BoBSRVViXyZZPvN0ZZSbMFClKysFbKys1MN0b+l8CzZtJO2btk8q2jHaEtof3IsoR327pW8wiKiB2wPXZLBK/jSKiEIudYbnVgdz2QI2EZWol9kMLABs3lQqjGq7wQCCye3UcwwP+vbOf87JC+sd8Fxx30irWs51dUSNIEMbSh0g2hQDJnUh0Xun83eYDM31eKMHjOv8AJ5Xoojwexiww88N12WQQdlihNHIStr+62CZ65FPnimuqW9G0q3QajLAtoIw1WhSozZUWGxpdHnV5jf42VqwFaKwnAEY2SztzjFEHsBCwXFYxGi08Yum48QnWztsOjfcSAAgOggaT42XqmkA3oACfFA5Jl0Hy3GHHHKIOyfn8/ODNYXXx1iksN6p20o4Rq8/451Ge9GiRQ4YUoXp8gGbGK+4T5BnOgffIsZ1KD8H2cGABRcarLcaJ5iOFChg8hdLmJNfwEqt8xoHm/sAVIVXcazu4go6IOG6lBfWddJOXkkTnTzXpwywOgLXdPqAhh/lQV+PMwACCLCSpQJsv5zJO2DPdzZvRrQc9JpAC2DEK3zADVcP0gHQAQqUERZ16g7gm2pFUqxx1D+eEwZlHMs5qHfkhVfrnANIwb0ibD3TpdKx7PHGQ1+HpwJs0jFkcOVS6QAv5ZwNYFMvsKCru4IC9oQJR7g6yqRT6rZaxhlQUAfJB39T7yhvIFknEfpWbv4nPdQFIM1/C6EWTuoFEM8gkYEZIE5ZqWsBUHXhrAudr67WFQV0oJzBKs8gg00dECVzKeCc1CcGLfhra14z1WkADPBjEI2FPFkUmTBgU98BStxBON5vMzgnzyTpRjwLPMOUK2Wh9YPy53nmOaH8dXEobZN4e8i9Y3BKOaVLk7aN3G/eHGYD2AAmb8Z4u8Qgyfer53/c02h/aZcAVt4AkUbyQF6AVwZd1HMglTdx+uZCB4DaXvBNXeOZwVpMnaF+cc/02WOVYuo3byQpI+1z+CZ6DM8tbU0qwNZnh/vBc06aeZOIhZrzaRlSj2jLMdDQPuEewjOq5Wg8YDLANtWJewiwgVURgKDBDIfwygaw9RvrJo0zr/eqE6bv6quvcZ0uYE3ngyWIhhIQo8N64/U3XCOs/pY+IKq/IA081g46Cj8aQaqYwTTI5Bvrs5+fivIKZ91mEiLl4c8yD08wxH1DrS1Yo+kUfMt+MsDmfHS+WMLwb1Wrnr+4hk6KIy906gARgw9AkE6EjhqQA5DUguRDPx01EUl0ie9kIawygkg0ViUajC4UM3nSZAcBdJzcJzpIOlwETJFmXY3Nn4ip94p7fN6557nOmnyn9Z0N0kBdwpUGf85s3owkc0lgIIebC2kF6ihDypLO9uWXXnb1hnvtLwMdBn3SDjgBluSV+okfLZNSOSfnxirqR9DwX41TP7kfAAN58gc9qeLSAyRAAfczk3uMgsT4cePdvddJmeE42FhRtUwZdFC3yAdlwvZng3wAq+p3HZ48yjdwwrMDVOo99ENG8j9WS3VV4q0TdYUypx4DxAwAcVuh/upgmTSTdsqRvPv3wncpUOjW+R9ANhMHw4vVpHOVwD8euKc8MgE212FgBrgB2mrV9cPM6QQ/dXmj3QJkgXgGLNQZrLqAMM8IA2PaPL/s+B+o5V7xDGVyXaHs2BcLfqo3Z+F804Zybdo/LV++AVJdjIWBFW0TEM0zQjvM30TU4T4yeNIBnB+STttK0qLgSvsKtPOMUAbUNZ4VzkUbxr2jLdD9tTzpGzD84DKXCbD1rSfHqMsM6dY+hHrOPeF/BlZcT/s58482GWCb6mzlRoUoXYXMj5KRrfxYpoBItnBfCdjXus5eQ9PRsdNRMasdgMTSjPWB39XqR1o1VrQfeYAOmm0+bCYLK6d5BhjVchZeBt6P45vMly8MX2rBSReWyg9HxfnJgx+Kz3+zoPcGUMGKRHnQMWM1xJqrVms/eoc/sAhb26vrg60dr/OxjZck8slvdMC83mYgwj0CVvAfVUtXAupj8SqrX6o7kZ/nTEDE+RTCajorXzt94BfAAPxGHjjSvRkBsLTOZLp3GjoO2AK2ybfeD95KUJ/CUS18f3XywoBWB4XpAFtdczinH185U17ZV6NZ6ICO37HUA9OUQdOmTd09AGLJB/cRtyIGyJqP8BwGf/lsTVc4go0/uPSjbPD8UlY8y9Rj4I56rW90fF90rcfhSDnhFR79uN1s913Cson5r3Ur1UJDYZcTzk09VDeIcJuhv7Gd55Uy9Z9X2jq9f6RV67TmR+OA+21btlGndP9MLoE66NW3IZoevaf6bGr91WW+yQvuaAyseF7841NFhNFz6cAclxMGJ5QHdYAyYeDLPmrQCa8sqvcz3ZLxvruXWs7pS0g3gwV9RgF9wFr9vE0mA2xTnVqvw1EUUsVbzhaww8vPZvLBptPhlakCtloUFD7phGicFdrSzWxPFYkl0+zuZHlVMNGl6lP5MFfHvzkcMSHZJMFwusOQ4ec1maVcO2W1qPkLOIRBMZuycftFoqsAjt4jXe1KgdmPBuGn14e0bCYqZrpf1Z2dH55k5Yc91Puc6s1DeICVLApJsnrhh/BLdY/T5cGlJRqrVlShcNn41l4FbABa/eXDK9mFBzD+wCjZ4MbPZ7K6pXVRBxe+tG745VOdZ7YmdSHdsZkAO9v1C3SgEDZW+BCZ7LrJ/s/2etksZpKx7KKxpHUnfA6/r0g2CTIM2n57QZtOe863P2hMF+c/lYtbsnIKG0h0sILU8GNRPUwG2KY1BtipGt/qAnbYbSSbSY7JALsuwiRlM5kvXb5qGsu8OnFRU6U11WIM6c4T3q86gJ3MFSbVqoXpViTLVOf+jNBXycoy2TLMqSLZhOtKqpi7yQB7detudfPs+0yHATvs4pBqKeqwm0uqVfTCdTvToMCHsXD5pKs7q7sIVzbP2OqsXZDsXKnmPzhForW26m912qFMZZKqrmc69+quOpysfVrde5PNs20yGWCb1ih81wSyq9PA/wHY1yVi3dYFYFenUa/txYKqC4eZjssGtpJZxaoL2NmWn3aoasVOtghRTQFxde5pdY9PVgdShYpMB2nJBiarA9irU34+YJMOJmbil8rkMgXsVLGp01l5Uw3MU5Wb1g/fcu1fL1vArou6VNM2IBPsp/utpkaM2myHsh10VOf32gLsZG96/oxyMZkMsE11Ctl12ZApYBPuq64Ae03lc0014NWxPqfq5GsrjdVZoa++vZpN9Sq6JmEMU7kSaBnVVpSCugDsdAtcJQPJmgJ2OggLl8/qANqaBOzqPK91ZZFdE+1QqrkndQHYDb19Nhlgm0yr7feayRKTrWsGk1yIOoL4O9NKjn92Pqu7GmddpXV1rVK1lcZkQJ3pFX99rNs1KZt0z0GqSaZ/BmDrM0WIQKLPqA92Nj7HNfXrrUk8/obS1tXU9z+VK01drwhcF8/K2tBGWx9vMsA2NUgYz/Y4IgkQexsRncFikprWtmfgz+zMFbBJA1FeCFVIpBeiLdQXS9+6BjsGeSaTAbbJtEbCBALWqCbRJUwmU+ZQi4iIChonOtuJu/Y8mkwmA2yTqYEq7J9oZWIy1b611A+7lin0mQG2yWQyGWCbTCaTKYu3RWHLtgG2yWQyGWCbTCaTqRYAOxzhwgDbZDKZDLBNJpPJVAuuWQbYJpPJZIBtMplMplr0zzbANplMJgNsk8lkMtXRJMhkMe0NsE0mkwG2yWQymUy1aNU2wDaZTAbYJpPJZDIZYJtMJpMBtslkMpkMsE0mk8kA22QymUwG2CaTyWSAbTKZTCaTAbbJZDIZYJtMJpPJANtkMpkMsE0mk8lkgG0ymUwG2CaTyWRaxwE7LCsXk8lkgG0ymUwmk8lkMpkMsE0mk8lkMplMJgNsk8lkMplMJpPJANtkMplMJpPJZDIZYJtMJpPJZDKZTAbYJpPJtLYrulJWFiaTyWSAbTKZTKaaKxqvCtjRlb+prIxMJpPJANtkMpnWLUBOowzHRqOoRKKxeKCoUxW4jlr5mkwmkwG2yWQyrWNwHU+jTIDswDoA7EhxiRQWxySy0qIdd8KiHTG3EZPJZDLANplMpnVH8RoCdjSheADXpQFcl0hBcTz4rgRuILvYA2zd38rcZDKZDLBNJpPJADslYAPXcWe9rlR8pSW7LFC5A2/9vdKFxMrbZDKZDLBNJpPJXERSAnYlUP8B2M4XO1rq4LqguMJ9A9tumwG2yWQyGWCbTCbTuqBoFkp3XGSlWwguIhEAO1IixZEApgMVBVBdgJU7GjMXEZPJZDLANplMpnUHriNpFM1wPPsUKGDHSt3kxvJIkbQriUmbNgFkR4sCwI4kva7dA5PJZDLANplMpnUbsL2we74PdgKwi0ulNNjeLVogQ3p3lm37bi4lJa2D/YtSWsztPphMJpMBtslkMjVQRSUejUiJU5H7rgyjF/WAN1oFrjXsXjQB1yWJhWN8H2zgujCO73WpVATn3qG8UKYPHyJHHjRMulTkSSySuwpYRwy2TSaTyQDbZDKZGp6FOgDoeADQ0XxpU5gjXUtyZevSHBlQuIn0yt1INm/RREpbtpCinFZSUlAobQKVlgQAXVoi+YFaxGOS68LulQbnKgvgurwSsmOR4P+iAJKLHIS7qCHxMokEx3Quairje+XJAyceLDeeNEF27lEhxUU5K/dLDu8G2SaTyWSAbTKZTA0GsKPxiJTEW0uX4hYycmAXuWzMMLn8gG3k9GH95eiBvWXPnl2lf/uO0rusXLaIRKS0qEBiJTFpVpQvGwRg3iJWLPGStsG5KgK1CwC7VOIBWEdj+QFU5wWKSl6szEF2NDiuZ+Hf5eJdovLxFRPllctOlCN33kpKA7jPDWC9IB5LgHYYuCMG2CaTyWSAbTKZTPUesAHaAHpLSgqkT1mOTN+jn7x60dHy2TXT5b1Lpsvr5x8r80+bKHdNO0TmjN1DLh2+g5yyS0+ZtF0H2b97vgzp0kL6t20pHYtbBpAegHRxuwCoy1e6eEQCYI5IXrxEWkXbSUGsVIqjubJzu03loQlbyk+3TJNP5p4ml47ZS3qUFvwB1fFKKWwbYJtMJpMBtslkMjUYReJxyY3HnYtI72hjmdC7UBZM3VlkziT5+uLx8uHpo+Sz8w+X/142Tv576Xj5Kvjti4vGydIzD5AXj9tdnpi+i1xy+LYycscO0qV9RJrGyiW/rIPzty4oLnFwnVtcIbklXaQgUiplBc1l3MBSWXzG3iK3TZHvbpspj8wcLbv27ZTwuy5cCf15Btgmk8lkgG0ymUwNDrAD5RXHpTiSLz1abyCHd28tj07dXd4851C5ZJ8+Mrl/qZwUwPPF+/aTaw/eSe46cm9ZdM5Y+eXWk+WL66bIh1dNkveunSHPXzhJThgxSLqUxiTurM8lbmKjW1jGuYe0l5L8XNkysqFcPLy7rLh0lMjcifLbLdPkzUuPkql77igdYsTHjkpBLCKFpXHnMgJgmw+2yWQyGWCbTCZTwwFsF0KvREqiBdKvsLEcP6yXLLxkitx41G7SP9ZYojmbSlluY9m8qKn0ibSUIWVFcuI2beS9cw+WDy4ZJ3cfGuw/ZWf5/trj5M3ZJ8uEnQdIp1hrB+2E5CuPlEhppMT5ZXds1VhGtN9QnjhmR5HrxwcaLXLjePnP9cfIVUceJFtWdJI2BUVSFI1IUVkbaVVSCdh2n1ZP/fr1kwkTJsjkyZMT2muvvaS4uHiVfZP9VhcqKyuTESNGVEnTmDFjpFu3bnbPTCYDbJPJZGr4gJ0XgHA8UiDbRDaTc/ffTl6ffYJcdegg6ZXfWGJFEYlECoU41aWRiHQO/t+xxV/l+n26yAfXnyjn7FQi40v+ItcP7yXvzDld7j5lrAzpFABUNB5AOwvKRKUiOK5dAM29W/09gPMcWXLWviJzjxKZMy4A7LHy3c0z5OEzpss+/beV8vwiicfjzkWkVUm0ErCjnuyeVUtHHnmk/PLLL5Ls89xzz0mbNm3cfkOGDJEnnnhCfvjhB3nnnXdkv/32q7M0de7c2V0j2efbb7+VffbZx+6dyWSAbTKZTA0bsFs5wC6SgQWN5ezd+8vbs0+Sh44dJTu3L5ei/FK3vUXbCmlV1lFiJR2le9P1ZUa/PPnwjkvkisOHyfZNGsng3EZy/8kHydvXHCfjtmwr3SJxaRuJSWk0X9pGc6RzYXMZXLSe3HRAB/n2ikMCsJ5YacW+Yaz8ePN0eXn2uTJ9+CEBwMekOBqV1rHCALAjDrDjLr52vMoiNqbMwhoNsKb7nH766XLzzTfL//73vyq///TTT7L55pvXSbouvPDCtGl66623JOrir9s9NJkMsE0mk6khRhGJxaUwViqlAdj2KWgpE/t1lOdmTpCllx0vs0YMkt06RaV3cQvpEGsh3aOtpV/rHNmt+f/JlUPaymd3XyZzJo+UwS0byVb/bCTXjB0kS+acJhO37SGbF5c515CSAJQ6FOXKFq3+KYdvkSMvzdg5gOqJlYDtLNhj5OcbJ8mH158tN08/Rrbr0FGi+ZHK5dXjlQvcKGCTVvPBzvK+BuXet29fB6y//P6bDHj6Lun99J1Oh73wWFKw/T2A7Ic/Wpr4f/To0bUOupzvkUcecee/4/23E2lCd39QadX+/fff3X4G2SaTAbbJZDI1TAXgGo+USduiUuleVCI7lxTJpbv0kk8uniSfXTtdnjx2N7lgn+5yzPYVMrlHTE7qHpfrgr+Xzxwp39x5sZw7YrAMatpIBm/WSO6Ysq+8ceVpctg2PaVdnAVnygI4LpWOhfnSs/k/5Iwhm8un52G9PjqA7CMCjQl0uPxv7kT58dbT5ZULT5RDtx0okZwAqiNxZ8mOR2NOUYsiUm2QxffauV388rP89em5CbWdd+sqcA3cxufdIhvPm5v4bdKkSbUKuZwrEonIo48+6s5/wmvPVknXzNcXJK5dVFRkgG0yGWCbTCZTQwbsEikJVBGJSbf8PNmnTY5cutcAefXiybL8plNk2Q2nyhuXHy8vnXmULDprknw8+3j5cu7p8uipE2TPrnHZocVfZGq/1rLwsuPlgTMmy7At2klJrCyA4XI3ubFrYQvZNfJ3ufPwgfL97PEicyYGYD1hJWAf5qzY/7v9OPl4zily6sF7SXlRkK4itV5XKhatWRSR9u3byxlnnCF33nmn3H333U433XSTnHbaafL444/L0qVL5d///re88sorcskll8iWW24pw4YNkxtvvFEWLVokn3/+uSxevFjuv/9+Oeigg1aZBNihQwc5+eST5aGHHpJXX33Vneujjz6SN954Q+677z6ZOHGiS0M4XUOHDpVrr73W7ffZZ5/Je++958CTtN5yyy2JtN5xxx1y6qmnOr9k9tff0aWXXur2X7BggSxfvlw++eQTefnll+X888+X3r17JyzYmQB7yLP3Jbb5gP3www87dw7/mqQN8CYPTEicNWtWle233nqrHHPMMYlyKi0tlaOOOspZrckj5fn9999nBOyCggLp0qWLK9v58+fL+++/747FfeSee+5xkzY5tz3DJpMBtslkMtVDFxEsizGJRCstjG0iRdIxt5X0L2ghh23VVi4fv7M8OXO0vHHu0fLWrGNk8QVHy7PnHClXHrGH7NunTMrym8ig2CZy/7QDZdGNF8hJBwySXm0KXGi+SHG58/HuVbChTOmxiSyauUcA1ExuPKLSgn3j2ECHiswNdMt4WXHzNJl78hjp17WDFBbmSWFxpc91iWfFrg5gA2BvvvmmVOfz66+/pt2+cOHChG8y/svffPNNxnN++umncuCBB7pj2rVr52C/rj/4UM+ePdv9/fNvv0nhvJsld95NTjs8c0+VfVsGvyUD7HQf8sBgItUHEGegsmzZspT7pAPsqVOnZixboHv//fe359hkMsA2mUym+gbYUYk4RaQwXuCWN28bKZAu+S2ka8u/ypYtG8nuhf8nh1dsIOM7NZXRnZrLHuWbSZ/CDaU05x9SHGspPfL/KRccvIucesgw2aZjrltMBsDGPaQ0APbtC9aTOXuVyn8uGh6AdeXERpmLRlfC9dxDAh0uv9w8WRZeOlUOHzZQ2hS0coCN33W8hlFEDjjggLSABng++ckH8uLnn6wyyY/P6ys+k8c+XiY//Fo1Cse77767ykS9FT/+IC8E57nng3fkiY/flze//KLKOfErHjt2rLz22murHPfQ8vdk8Vdf1BimfwwGBVxz4Wcfya+//1bt42sC2Fml68cfE39TFq988anz8f7m558yArb/ofy5T/MChe8FAyLeEtizbDIZYJtMJlM9A+yIFETzJT/WIvi/uXQozpHeJTmyXXlj2T6+nmwT+asMKPyr9Gj2F+na7O/SofmGUpKzmRQXNZeCYP+K6KbSrWgT6RBpLPF40+C8+VISrwhAPS6dclvIgWUbysIj+8j/rj7Q+VxXuoUc/IduGFX5+9yj5aNrj5dLxu8r3eP5EikucRZwN7mxmlFEsMZPmTLFQRjQ+4/5cxO64b1FMvCZe2SD+X/AXZMALI95Zb7b/5TXn5PmHnRyzObzb5fl3/53FfgDGLcItv3VO5eqWXCOU1NA49Offigl826pchyge8Ybz8s2z9ydSGss2Ec/TE7U3wHhtwIo7zb/Dve/noM87bPgQQfdPoCzvx7bIziGz6zFL1U51s8vAog//u4b+ad37HYh6/cXP3xfZTuTKcODmAMWPuz20fOvF+zXM0gD+UkH2AxY2s+7ze3vH0u53f/hksR+hCHcaaed7Hk2mQywTSaTqZ4pki9FBY2lTf56slP7zWTm/gPkthNGyp0nHCA3Thom5+zXXaYPbi9HDWwr+3TMkUFtGstWFS1li9Jc6RDPkXal+VJakiux4O9otEAKC4ulXQDEHVtsJpO3rpB3zx5RGfvahecbXekachOgjRX7iEBHBv9Pk69vP0seOmuSDOnRrnLZ9OLSQGVu0ZpEqL4s8sNkOhYv4QNQhyEyldoAvSm2Vcy7Vb73LKhYVX1wTKWjXn6qCjiSnr/Pzy49QLd+9l34UJVtm6W59o7P3vtHbOkUPtgAbbprYzFe8vWKKr/1Wgnn+gHA/e0MNhLW5d9/c4Ccbdn7gH3VO68lhX/V34JtM159JrE//u82KdJkMsA2mUymejPJsTTKiosRqSjYSAZ13FSuH7eNrLhlunx/7+ny1a0nyC+3HSdy6xT56eap8u+rJsh7Fx4sL5+2tyy8eKqcOWpf6V7SWmLlUYnHi6QigOvi4FzReLnEg+8OeTlywj47yquzJsu/rzlWPp99pHw1e7T8eM0o+f2GMfLrnEny/XWT5Murj5ZPrpkiS244SR67+FgZOXSARHFbCeA6r7hD8F2eNWADWkShYDJeOsAG4P6WJeiqLn7rlQTUdQ9gs8r24Fw5ARCHwbCZB8lYdPM867hq03nJ05IOsP18hC3oWHqB33SAfWoGwMbKvjqAnez8pHWjeekB+8uffpCmWQxcOBfp08/gwYPteTaZDLBNJpOpnkQRiZVKuwBme0c3kcmD2smrF46WZZceJnNHbC5z9uksy87aX36YfZgsnrmbLL1sjPwcwLbcNU2+vvcCmXPsOOmU10QKS6MSi0cDwI5UTkgsKZNYANjlhbkyqEsbOaxfhRzZq0im9GghZ/RrLM+M6yrfXTNGPpk9UW4/bKBM75cnE/rmy5it43LYoC4ysHtFArALittLJPjO1kVEAfvoo49OCdjjX3rCxYfGCr1eCE6xDL/6n3/LB99+LV1x/wgdp9DqW5BxMXlnJewt++arVSzUgDWfsxe9UOV3YPOu99+utMIG18yfd3PWgA2QA/xYioHhDULXxC87HWDjC/3Mv5c79xEfzPnt2UD4Ta8OYLcKDSRwH+GanHfMi4+nBOzRoW2lQXrJCy46uz73QJVtuy94IHG9Cy64wKzYJpMBtslkMtUDH+x4TCKlcWlbnCPbFq4v5+3bW165dJJcul832XaDRrJ/fGN5ePKesmDGHrJHXiMZWPAXuWqf9vLz1WNkwRmHyP59Y1KRs4Hz48afOw7gOAgudbBTHCmQ0kielOW3kIoWG0rHTf4iOzdrJHfvXyHfzTlallw1XU7Zo790z/mHVORt5lRe2FTikVx3Pvyv8cXmO+s8BdctLCxMacEu8fya+RSGoPacAIL1c04IiEc+/0jVSBYBTN+89E15Y8Xn7n8mK+JHvWnIAvvJ95XW5BELH67yOzDpf+a+92bWgL3nggerHLv9M/dU2c65sgnTl26SY00B+6uffqzyO+f9/IfvqhwbC7njKGB3C70ZuHDxS39EZPn+W1nfG0i09srnsccec65B9lybTAbYJpPJ9KeKCCLRNlGpiDWX7fP/Jhft21deumiynL9nN9m+6V/kgC7F8tDxh8nTMw+VbWMbSJv8DWXfWCN5dlxvWXbjKTJqm3Jp32pDKY56YBOttIxXrsYXcRBfEA9AOVIoZa2byaAA5O8e2UW+nTNZFl91kkzbawcpK2glBUxqdOfgXDW3RCpgp7Jg7/Lc/VVAD99qfzvRQ/Rz3ZLXq2xjwp7/AZyPf/VZ6f/0XWl9otVdg/383+/94N1K15Gff074Lf9tfnaAfdHil6ukJQzv17z7ep0D9off/jcpYGMF93/v6lm2iajC54BQehWww5ZvIJpBkSrsJqKft99+2xaoMZkMsE0mk6k+TG4skqLCXClpuZFs2Wp9OW1YN3n14iPlwUk7yz75/ycHVOTI3ZP3l+fOnigD27WQnKImslVOIzlrQDP55J6L5bJxe0un5htUBWwPdJ0CuC4sKXHgXFHQQoYGoH7vyM2TAHbpGgHs4SFI7hCaiKfWZj5Yp1MB9uMfL0sL1b6wvPIJT/pTwP7uuz+su76PcjrAJl/+55AXHq1zwO4WAux3QtsVsG9Ztjil64jmlcmfyQC7un7xWrYstsN9N8A2mQywTSaT6U9VSaCyAGg7FuVKz9x/yiHdo/L4KQfK0qumyMX7byWHdsqTa0buGED3dDlsu44SzVlPtm7RSGb2ay6f3nu53DpjnPTM39Qta76qf7e6ocSlIF4ikQDm1YJ9zwGd/zTADrt5hAGbSXaZAFtD34UnM7Iq4nlvvuiWHfe3Ec6Oz4CQBVshWD+f/fBd1i4id6703dbPoaGwd3UB2J3n3b5KKL1kIE1Mbv/3LqHjklncFbDD7jUMSrCAJxMhB3FH4cNKkawAaYBtMhlgm0wm0580uTG2cpXEqJRGI9I2ki8dC3Okf1FjOWFoJ3nj6hky7+ITZGzfCjl+yzJZcvnxsuCscXLyjsVyev+msmDKEPnP/ZfJBWP3ls6tNkpqwf7Dz1sBW11E1mvwgM3ERP/3onk3JyYy8ikNuZ2woAyf4SGo7PN01VUdw7Gh1zRg/zME2GEf60iQT/+Df3QywHbXnF/VlcP3wf79f/+TgpDvuwJ2WajsfB9sjsPHHfcYJmL68b5Zzj4/P98A22QywDaZTKY/D7DjCcCuhOySaJF0iLSQwW03lRm7dpfTRu0ue3YpluElm8ith+8s/7n5NPnqhuPk09lHyTdzT5YXL5she/cpl7atmzgLti5lvopwEQkAO5YCsI9tgIB92usLq/zeMTiHfmaFoNP3wb5t2VurbBv07L0Ohh18z5+7xgG7is/zygVmHly+JDEo2GRe1VCENy2tnDzJCpjhcHq+K0hRCKCxYuN+AxTvteDBlFFE9g/lk/TqGwBiX4cjvvjLsxtgm0wG2CaTyVQPIDsegDWLuJRIYQC2RdFWUlG4iWweaSxdSwukY1FL6VWwkezduZXMGrmtPH3OeHn2/GPkvhPHydhBvaVDLFfikbyVET9SAzaRQBxg5zeVQUWVkxy/u36yvBUA9vQAsMvzGxZgs5JgGBDzAqAMRyRRLfjso5TW7ZouNFNbgB1LsbjOrcsWu+3tkiwWs2kK33MfsC9965VV95k/d5WwiGHAfvfrFVUihaDGwfVaJYkf7kdhGT58uAG2yWSAbTKZTPUBsuMBZJcHIFwmufFIoDwpjrSSNgEIx3ObuSXR2+duJF3z1pftYxvI8E5NZd8uhTKsY0y6xQskEo26SCQRF5EkuQDsaKwkOG9RANjNZXDk7ysB+xh5OwDs4/ZseIBNDO3qgPLkV+ZVmRiYCsTDELkmADuZNRmdvTJc4flvvph0KXhdmj0VYPPp/fSdNVrJkfCImVa7BPzV//rll1+WFi1amA+2yWSAbTKZTH++oiwKE2Fp8ajkR/Ilmt9MeuT+U/Yqz5Ej+3eSKVtvLmN7Fsq+FX+XnfMayY4tG0nfzRpJ12b/J2U5G0lBUWElZBfH06jELXXOCo/lBTkyOAD1uw/quhKwTw4Ae8c6AewJEyYk9ZceE4o97cddxnLKYij6IcqHfyw+0vp566sv3CS78OIv/HZH6Jp9Q77WuEoAzCzNjkUXf+Rhz93vFqnZ0APLAs/n+eBQlJCHP1pa5ZxHvPRkle23rLRA//DrL1UswuEJh1iMw37PgPOZbzyf2OeE156t4g5CPkn7Yx8vqzKhs3con/hMA/5+nkgL+z20/L0q12RyqP/h3KQrDNr4ie8XlJ3C9TfffCMDBgyQli1bWhQRk8kA22QymeoDYEfd5MNotMAt7tKzJFdmDOohT804XN6ZdZwsveh4ee38ifLUqSPk7ml7ytXjBsvpIwbIxF26yu5bdZFOFZXg/AdIp1CsNDh/VCoKWsmQ4g0DwO4WAPaUALBPqTPA7tOnTyLmcl1+WGzmng/ecX7L//XgPNnnqU8+cAvCHPj8Iw5a5yx5o8r2z0NRRMpC1uZkHwCzpp9vv/028febX37hoBzfasA42Qf/bAYP6hOd6vPFF1/I3Ll/+EcT33tekPe7g3L6JkMZvfvuu7JixYoqy8sTV5u0EbXk+2DAoJ+vvvpKttxyS2natKnk5uZaHGyTyQDbZDKZ6gFgByBbEAB2STRPuhU1lcP6t5OnTxknn193qrx+4bHy3HnHyAsXTpU3rjhe3rv2BPnwuuPkvauny1tXTpP5l8yUE0ceIO0L8h1gFwYgnUxuJcZoqZQEgF1e2EoGA9gHB4A9Z6q8feXJcvwedQPYrVq1kmOOOUZ++eWXVSDu+++/d9tefPHFpJD33HPPyYknnphYACZ87OGHHy5Tp06tEr9aPywF/uOPPyY97w0BUIddHaa/+oyzImPRDYfxYwJkug/p79Chgzz55JNJty9atEg+//zzpNsuvvhid+wjjzySdDt5uO666+Soo46Sjz/+OGk+f/ppVVj+z3/+I4MGDZKNN95YDj74YPnoo49W2YeBT7LBz5IlS6Rz587u/l155ZUpBw/cg4suukjKysqkSZMmzj0E/2tbydFkMsA2mUym+gHY0SIpj7SUbQo2knN27yMfzZ4hr510oJywbRsZ2bNAJvQvlVMGd5cr9+opdx/UW+YftaMsmjlc/nX+DLnqiPHSLT8vI2DHVgJ2RWGuDIlvJPcc0l2+v2GqvHNFANi77yAVtQzYWDKxaG622Wbuu3fv3tK3b1+nnj17OiADAFG7du0S21BFRUViG5Ce7li29+/fXw499FCZMmWKHHDAAVJSUiI5OTluXz3ukksuSbiGrF+NhVR0IZqFCxe6dPnpbN++vUvDJpts4r6BTX878Mzvm266qXTt2rXKNnyV/WPZlzwce+yxMm7cOBk6dKhzudB8Nm7cWLbffnsZPXq0yycTCtu2bSvNmzevks9u3bq5Mue8HKPn33rrrWXMmDFuUDJixAgpLS2VvLw895ZBj+3UqVPiGBXn2nHHHV3apk2b5oB94MCB7li2A9fNmjWT1q1bm/XaZDLANplMpvoC2IECIGxbnC8DI41l1n7bynuzT5DbDttRBrZeX9rlbSyd8hpL96JmsmVsM9mpTVPZu2MrObR3TA4b2Fv26j9A2hZGqg3Y9x7SIwDsafL2FSfJcbttHwB2bq0CNpZMIAwABMJ8aFP44/cw0PnbVamOTXd8WMCoWntPfu25rOCaRWsSExz33TdlOgDoVGlJl79sjq1uPhV6AWPAl++aHItIW7r0s537ywDKfK9NJgNsk8lkqjcCaItK2khZrEC2jzeVs/YaIC+dP0XmTthTukeaSsuiImlVHJUWxTFpGi2RzSKlkltYJEUFrSSG73WEBWTiUhSrJmCP6iE/ANizT5IZu20n7QpqD7DDbiJAGD66Cm78DfxhiWYbf+t23cbvbPe36Xa2Yd1F/rkBPt1HpccBjliH9fP0px/Krs89IC3m3ZSwaPOdF/zPpMvL3/6Xc8Hgc+eddyaAMlkeSEc4rXp9fkuWB37jOCzteqzmQa+j59dyyiaf/M3+lDtW5XD5h/MQLnc9FmgmfX7a/etq+hlEKVwbYJtMBtgmk8lUTyzYARjHKicqdguA+qC+Mblt8h7y2MkHyZgBpdKt9QbSLndjKSvIkVhRoRQUFUsRQBMAdoT/I8H/0ZhTYQortgJ2aQDY7QLA3jkA7PtG9ZIfbjxW3pp9okzfdaBU1AFgY8UGvvDNBfaANsTfgBm/I/7W7em2+dtxsUD8ze9AoYIh+6h0m1rS8ev+1Vt9MDFR8eefkk4svOmmm9zxACUwnCwPpCNZPnSfdHnwy0fzoPnwzx/OpwK0n089N8dwXlw2Up0/fKz+7R+b6rqaNrarW4jBtclkgG0ymUz1KIpISQDZ7dx3cUET6RFdX04cViELzz44gOyRcvYevWT0lm1l9x5tZWDn9tIpXhaAcoFE81sFIBSAWyQAoQCcawLYP86dLosDwD62DgBbIVtBGwFjSP9Pty3Tdv/cuk3B0N9PfwcKgWQs0d27d5err77aTf5LNtGPiX333XefDB482O2PxRawVKD0r6HpyJSXdHnw80FaNR/VzWemc2dzrH9cpmMNrGtfuDIddNBBMnny5KxFvHl89utzvnbffXeZNGlSIs0TJ050oR3tnhtgm0wmU92IhWZiZVIWgEqHwn/KoPJ/yGX7bSHLZ0+Ur249U9694nhZcO5Rct/xo+TWyfvKFYcOknP26ivTd+goh27dTQZ17S7lBQHwRCvD9CUDbBaZUcBuHwD2LmrBDgB7UQDYU3bdNjhH7QN2MthOBmXhbZm2Zzp3Mqm7CrDsT/7Dqs3kRDp7Jksy2VC3sR8uEbhCaISMmuajpnmobj5TAW9tH2vPbu2LyaoffvhhjUM+slR9fctTcXGxPProo0nT+9tvv8mMGTPs3htgm0wmU+0rHqg0FpcOsXzpFdlAjhwYl9fPPkR+vH6qLDv7cHn95INlyflj5KPLjpAVlx0u380+VP57+eHyyfmHyCvnTJNzRx4i3fJ4TZ86DjbW8XgIsO9fCdhvXHGiTN6t7gH7z31LUGmJxQKNmweW7EwT+ABvYDwM11ZnTXWlOXPmrHZM+F133bVe5WnUqFFp00sYTqz2dv8NsE0mk6mWATsuZQH8di4kisgmcu4+W8rya46X12YeJKds21YO6xaVI7dpKyfv3ksuHN5f5o7bUR47bn9ZePph8tIVZ8v5Y8dJl/yCrAG7QwDSw1YC9vcBYL8eAPakALDL1mLADkM2vsY6QTLdBETcStjf4Nq0Jurn889Xrtx51TuvuZU2s9XI5/+Io04YxvpSV0nH2Wef7dJ10eKXq6SZxZT0QxhIe74MsE0mk6l2ATuA39KicuncKl8G528il4/YXt65/Hi5/qDtpWfLDSSan+cihuTlbiblkRbSq7xABncqlP03z5exO/WTffv3lnYFeVkBdnlRVDoGIL2rB9ivBoB9dADYpYVrN2D7rg7+5L9UExPV39rg2rSmBn+66NK4l57IOk47Kpl3SwJWiVVeX+oreTrnnHNculg51U/zTUvfTKR5p512smfMANtkMplqf5JjJNJOOkRKZMdIMzl95x7y0hlHyC2HDpGt8zeVNgVFUhovqwzDF6uE5WirZlKRu5GUFzSX0ki+iy7ifLBVBthZ+4NnmiRoddS0JuojA74XXnhhtQGbRYiox8wpYKXQp59+WpYuXSqfffaZLF682IWcHD9+vFtoSK/fq1cvtyrn3XffnRD+3KwgynYmBc+aNavK9ltvvdVNVmThoRtvvDHx+1133SVXXXWVvPzyy/Lvf/9bvvzyy4yAvcMOO7gyYBEljn/77bfliy++cOkm/TNnznT+6Zrefv36uYWj/PRce+21ztcbH/b3339fnnrqKTf5k/kVBtgmk8m0DqowgNpWxR0kHiuX/oVNZXz3Qnl00r7yzHEHy6ju7aRLANhto+UB9HWQ3Ghn2ayggzTOjUizgtbSvDgizctKpGVxzAG4ikVnDLBrZwKmybQm6h9vTFIBdrOVsdlTaf+FDyVglVjvjzzySEZf7eXLlzv/aFb+XLFiRcr9br/9dvn8889X2zd8+qvPSG6QD9XjHy9LbBs7dqyD/3SfH3/8Uc4991w3EZkoP9l+PvjgA7dKqQG2yWQyrTXRQTwl2+YBdm5xR4kGgN0vliNTt+sgz580Uj6+9Gh5YOoImT64t4zq01727lYhO3UokX5tiqRnSY50LtpISiNNAyDOCxRZBarDgB1L4YP92krAXtt9sE2m+gzYuCupD3YYsEe/+HjWQAmI6oe47u98vUIeXL5Env33cvn5t9+q7MtCSosWLZK6+Hzxw/fywIdL5Kuffsy4r66wqp8lQZrvD45d+t8vV9lXLeLVuSYWbgNsk8lkWosAOx6NuzB8q27jt8rfI8VlAWR3llikXHpFc+SUvfrJ+5ceIb9cP0m+u/FY+fTqKfLOrDHy0hkj5YHJQ+XqA/vIhfv1kBk7lcqoAaWybcci6RBp7RasSQnYsT9WciSKSBiw6/skxxZ7DpZW21nMXNPaDdipLNjZALa/eBJgzTlYpdQ/DyuVtpl3i9zx/turHI8V/B/BdtXCzz6qsv3gFx6tsn3eJx8ktg1+9r7E70XzbpZ9g3Ot562OuuXTd8n4ID3+8QC0/yHN7LPZvKruL5sG/++z4EH5/tdfquyfzTX18/rrr69Tb6YMsE0m07oD2FWs2cBuicSD7xImOUZiUharkI4lFbJ5UWsZ1jkip+/WVeYetpU8dPx+Mv/s0fLyJUfLW9dMlw9umikf3nK6LJs7UxZfc7w8d+Wpcsbhw2WL4oK0gF1pxV4VsH9oIFFENj52jDQZO8LqlMks2Bk+WKWHPnd/er/tAED39dxK+ISP8V04+Oyx4IEq231ABmbTXa/v03em9cH+MRgcdJ5/e9pzRIOBwfvffFWta+oHH3FdcdQA22QymdYiN5E/QDteCdfAbvB3RdDgt40USMfCAtki2L8j+7ZsIfGm/5D2uX8PYPifskV8U9m5e0TGDu4qpwzfVmZP2E3uOm6kzDt9nDx/5VlyxbSjpEth+igiTrHSAOb/AOwHGkAcbPWJbjJmuDQeN8L8o03rpAU7nQ/25FfmVQHh3Z57IOvJkRe8+eIaAexL3nolLWAf/fJTWaWXvFXnmoky2W03N4nUANtkMpnWOsiOOwsy7iDOJSSA3TaRiHQpbi17bdlVjt1nmBy2TT/pV5gvW+S2kF7RZtKjcEPZPG99adf8L9IxUKdAPXP+Jv1a/FW2b/VX2SP+DxnevUz27N0tAPNIRgt2pLgSsNt5gP3jSsA+Ztf6C9hE9Nhsz8HS5OC9LGSeaZ0E7HQa4LlCPLT8vVW2j1j4sLP8vvLFpw7I/W1N5s2VFT/+UCeAjUsJLh9cE/eOVIDN9TcKuYUwaMCP+pZli6XpvKouLou/+iLra/L59NNP3eJSTCI1wDaZTKa1qfN0ftZxKQzAOq+4nVOr4O/iSJ70bdNEZk3YV96++XK5Z9p4OaR9RI7s31GuGbOrXLJ/XzlzaIVM7ttc9uuwkQyuaCzbFG8sfSObSPecv0uX5utJRYsNpSS3lcSL0k9yrFxCvVSKgw6mYuVKjgnAnn2iTB62jZTlt6qXgM2r3dx4sbQqL12nXvOaDLCrC9h7LXiwyratn7m7CiT/EEBnTsgv+7Zlb9U6YPtp0k8qwGYCpv974bybV/ENT2Z1z+aaLnrJ9Olu0SizYJtMJtNapkq4LgngtSxQRQDYFQ6wI5F86VK0kRwxtI/cdsJEufDAYbJfeSs5a7+d5P1bL5Iv7pklK+44W/59y6ny2pUz5JGzjpAbp42QWaOGyIxhvWRUn7gM6VAkvcpi0iY/L2n863SAff9KwF7kAHvreg3Ym+66g2xwwngDbNM6CdgtAyhOtYrjtH89nYDJsIX65pUQ+/3337u41nwOfeGxKvvo8ZkAO+x6kg6wWbWRz3fffSdff/11WsA+e9ELVX7/+/zKuN6q9edXHVAc8dKTaa/J56OPPnLxsM8880y3KiuLSJkPtslkMq11gF0J11iw8b+OOEt2hRTESqRNpEDaF7aUzQs3lS3yNpLOuY1l6OZt5OR9tpVrx+0m908/UF4570h5b/Y0+XzuyfL9nWfKr/eeLd/dcbp8fuMJ8urlJ8l5o/aWzfNbZPTBXsWCfWhvB9ivX3a8HD10K2nTOqfeAnazIQPlH6cdbYBtskmOaT5hwH7ko6UJNwkWa+Fz/KvPVtlHY2iHARt3E/8z5Nn7sgZsPXbhwoWJ66YC7OouqjMsSGe6a/Jp27atbLzxxtK4cWNp3ry5W5kV9zKLImIymUxrmQW7wPleM7kx6nyyC4rLJS8W/BYAN9BbFs+Xslhr5zZSkp8jHZv/Xbo3/n+yfe56snfxBjK240Zy2jZFctGQNvLghO3kX6ePlMXnjZblt10s1x0zTroX5KwWYB81ZICU5Laotz7YLfr3lH9OG22AbVonLdg+YLPCISskqrDW6sIrvUKAfeuyxYnIIsuWLUtqwWYBmGSAffcH71QBbNxNsgVsYm7zefLJJ+XUU09NC9gnvPbsKhDddf7tKTXx5SfTXpNPcXGxNGnSRJo2bSqtWrVap9xDDLBNJtO6A9gxFpOJu8Vg4rH84LeiBPAWuOgeMSlvE5eykmCfeJkUlpRJQV4AzLmbSjy3sZS13kja520gnXP/Id1a/0P65v1dts5bT4bGNpDhfTrKsJ7dpX1hUcZJjmHAfjAA7J+Igx0A9pFDtgyu1bzeAnZeNCKtOrYzwDat8xbskpISZ531ddttt7ltu4f8pLd75p6qi9D8+qu0Cvlga0zssI/15W//q0roP3yjswVsJlTyeeyxxzIC9g1L3qjye0HIBxtwPum155yv+Afffp3xmgrYWK6BayY3rmuTow2wTSbTOjPJsbAY0C6S4lhe8FvByt/iUhCPu23F0crXl0Wl7SW3pJ3kBH/nl8SkoCQaKFKpeHBcvEhK4hFpG82VzkXNpUNhnpQXRFx0kGhiifRkqgTsqAfYDx3SMwDsY+XVy46TI3auv4ANVLfssbn87cpT1zlLlMks2GHAbtOmjWyyySbO/QHx90EHHeS2AaHheNdYrFnh8N2vV7jY0OFFXL78qTKKCL7Y/rZO825zKz8C5SNDcJwJsN9Y8VkCsE877bS0gP3ht/91i8UkC7FH2sIDghNfezbtNfmUlZU5txDai3Ux8pABtslkWneiiLjvqMQduEbcb3/8HnOWZVxHovESNyGyKFq5LRIc84ci7hwcXxItkvJovpQG3yV6bCy1Kt1UWGwmIuWRnACwN5SHD+khP984Tf512QyZsHN/idVjC3arLh3kr3PONgu2aZ23YJeXl7uJeyp1g8BNhNUQ+4QgOp38iYFMiAxv3zAA3w3mJz82G8B+/PHHMwJ2Msu7WrLD1944GBB8/sN3GQEbH2xtK9bF9sIA22QyrTOArfpjNUdPbiGaSvkdbm27qWAtjwRAXhpp6QD7EQD7hmnyyuUzZOzQvvUasPPKS2X9C6YbYJvWecDu0KGDtG7d2u2PlZYIGbhDTJo0yW3/5fffZJuQv3QyhVdy/O/PP7moHdnCeW0C9ifffyMd592W9nosg+4vHpMJsNelSY0G2CaTyQA7GWCn+70WATsPd5RYkbSJtKgE7FE95BcPsKP1GLDzCwqk5eYdzUXEtFYD9jPPVE44ZKEVHx6PevmpBDxWVFS4gSbPBeKZwIK92WabyZ13Vi4P/msA2UB623m3Vglz97f5LDl+s1vAxQ9ppxCMuwauIevNr7oYDTCOT7afpic/+SBxju2fuafKNZZ8vcL9/sADD8hJJ53k/maQ4B9/T2gSJe4oRDRpFnIJQWVBPvw0p7umutEYYJtMJpNpjUy0VMAuKQoAu80G8uiong6wXw4Ae8zQfvUesBs9fJUBtmmtBuxzzz03bRi+9957z1mvFR4Tb3jy8pwVG82aNctNStTPt7/87KzND3+01Fmp/c+rr77qYJSJkjfddFPid1ZRvOv9t2XhZx9VOVd1PyeccIIMGjQo7T4rVqyQBQsWVPkN0L8zuD6L0Cz75qsq2+bNm5f2fIsXL65SRgbYJpPJZKo7wA7gOg//7gCci4uay87xDRsEYLu0Bx0lkQAa3XeZ5MeiBtimtRawsUwT2i7Z55NPPpGBAweuAo8c61uxmfS4/fbby4MPPii//vpr0nNhtT766KOd/7Y/WXLixIny8ccfr7I/kP3TTz+t8jshA999992k18B6TZq4xllnnSW///57UrgeOnSou/YRRxwhS5cuTQnOjzzyiMsX+86ZMyfpPsuXL5cBAwasc3GvDbBNJpOpPgB2QSVgP3ZowwBsBYj1LzxO8tqUGGCb1krAZhDJkt7EbyYKRt++fRPaYostZNNNN3WTGsPwmHjLEwA6xwPZCswA+y677CLjxo2TqVOnysEHHyy9evVyFmu2a6xozsv5FbYB2TFjxsiUKVNk+PDhzi2lRYsW0rNnz0SaunXr5o7hPJ06daqSXkIJcm6diMl+5K9Pnz6Jfbp3754YEKhIF78fcMABMnnyZAfdADjX1zSryLN/zc0339ydL1kZGWCbTCaTqc4BO1bQdCVg964E7Mum13vAdvDRub3k2yRH01oK2L4VWgHZF5AK5PIshJ8BH7JzcnIcNAO4yc6jIf64DudjkiRW8TCcr470/JyT9AC9yc5LGtmP9Ka7Nr/7++pgIFkZcc1kZWSAbTKZTKa6Bez8Zg6wnzisj/x647Hy0qXHyuid+0ksr34D9l+vPk1yunVepy1TprUXsH1A1vB7AKVCJTAMCKeKpKPn4FkBmgFNzsPxgCfSc+kiLOqWgvib39im1/aPUflp8kMF6jb9nXxgSU52Xj9PbCO97B++tl6f8/n7at78a2ZTRgbYJpPJZKpzwH7y8L7y69xj5cVLpsnoIX0CwG5Rr11E1rvsJMnp18Ms2Ka1GrIBZMAUUAQm1cKsMJyu/mvcZ/bT83A8YKrSc/mLsOi1+Y1tyY5R+Wni/JpW3aa/c32NdsJ5U+WJbeyn1+Z3/9q6L+fTfVenjAywTSaTyVSngP3U6H7y29zp8sIlU+Xwwb3rNWDTaW547GjJ6WuAbaq/arXDVqtd1xV2kVqX9f9s675/HoVXhVM9X3gRlvAxelw4DeH/06XVVzb7+fv4ac72fOvqwjIG2P+fvfMAj6Lc/jByBQSlh7TNtpnZmWxJDySUQOih9947ofdOaIHQi3RFEKR3Ua+KelVUsFw7ghUEFAXELore+//9v/Ptzmaz2RSaJt5vn+d9dtmZ+XZmdhLeOTnfOQKBQFCUBHuUR7DXT8OwNnWKfAQ7LMbFjsH2P9n6WFD0qTKiD0pvXXLbrnl/btc4hRkrr+3yGqew4xdmvRvZ59txjoRgCwQCgeA2C3Z9Ltivr59aLAS7bOY4VO3QXAi2oMgRNKALSm1fBkuUs1jIHlUpoSohDz74IB599FHs378fGzduxIgRI5CYmBhw+YYNG/h7Y8eO5RU+dLp37w6bzXZT+5GampprvB49etz0eLeTorAPQrAFAoGgGAr2sdFMsPdkC7bNVLQF+96MkajSva0QbEGRwhwfg9A2TXmNdt+85qK6v+np6fj222/zrDd97do1fP/99zfUUIY6UFJpvhvZD6q5/fvvvwccjxrPUAOcv+L8tGnThrd4p/NANb6pTKEQbIFAIBD8LQWbciwrDemOoE4thGALigyGRnVx9yNLEZ6c6K2YUZQn2VGE+E49JkyYcEPR4R9//DHf8SZPnvynnhuqNU7dLP0b4lCDHVomBFsgEAgEf0vBNrgcMDgihWALigTGOkkoeWANQtPqc7HWK2cU1euTGsP89NNP7ojz1xfQ8vjjMB/bi9Iv7Ub4sT2o+dIh7DlzqsDlDV9+FCkvH+YMe+M5r4hSiklh87up4Qw9fv/vf/Ic76GHHvrTzmPPnj1zCP9//+//eGt5/TFq1Khi9TtHCLZAIBAIwS50ikjF9J6oMLqfKMMl+Muxsp+nsJaNYIyN4lJNgq2XpSuK1ybtU0ZGBpfFf1++iArHduPul3Oz5vSbBS73/XfUsf05BLswNxe0nDov0uOn36/nOR4J9p9xs0JdIikdRH8cOfcx1GP7+DnQH9TRUgi2QCAQCP6eKSL9O6P8pCFCsAV/rVy7HCizMRNV+3UOGLmmdIL58+fjxRdfxGeffYYrV67g5MmTeOqpp7B06VIkJCQEHLdRo0ZYv349Xn75ZZw5cwaXL1/G6dOn+SRDmghot9sDbteqVSs+GfGdd97BxYsXOfR68+bN6NSpE1+H2qO/++67XBZnvftKQHkm3mRyXdDyvISYJkHSzya1LM/MzMQLL7yQ6/iXLVvGj1+PYOcn2HRMNB61bSd59z0+OpYtW7agS5cuOc4FpZXQhMwjR45wDh06hEWLFuGRRx7Be++9h0uXLuHzzz/H888/z1vH0zmlduz6o+3xJ7z74ivYzzzzDOrXr19sfu8IwRYIBAIh2IUSbJKXam2bouLw3iJFRPDXXYuRGu5ZPxcV2Y2e3uzEN++aBPrnn3/ON7eYlq9bt85bpYKqdpDAFfT44osvMGzYMO++REdH4+DBg/i///u/fLejCXu+kxp7vvpUDqntdOJJvMHE+Z/nP+WpEfktv/6f/8BybC8Mx/ZwWrzymHfcFStWYOHChYU6fsp1pkd+423atAn79u0r8PhI5OkGYseOHTecN/7VV1/lyLkOZfsQSLD1/W7QoIEQbIFAIBDkIdjmIHSILFfsItgRmorwWJeIYAv+MiJSa8PiiPR2HdTTQkiWH3vssRxCRtHZFy+e47m8Z3/8LpcokmS2bduWR2R9c38//v4qnrrwKY5/fYELqP9j5cqVPEpMUWHfx6dsO5LgMz98m69UpjGJ9RVo31zjwizPT1Zv5PgLetDkwhzVTf74HS+w8Y4x6LXvg86h/+RE/wednyfZ+fnql5/yXCc/wabHAw88UCx+9wjBFggEgr9AsG3mYHS0l2eC3aBYCXZQq0a4Z/FkIdiCv4SKEwej7LJpMLHrzz9yvWbNGq+E7fj0JKzH9qLUSznTK6oxeZvy9jH88d//5JJIEuvRbz6PEB/BI8qwMSKP7cOhzz/KIXrnzp3zbjeGbVfVL2e6Cvs3RaJ/8RFRSv0o+1Lg1A96vwdbv6Dlv/7xBxdP+jdR66VDuST0Ro6/MONR9Dzm2AE+2VIfi15r7LzQDYXv44frv6G8z3gT33oRc949zidp+u4L7d/TFz7zbke55YGOXR/n7SvumwdKOxGCLRAIBILAgm0NRidHBbw0pkGxShEJbpqKMqtmCsEW/OlUGdoTpR9eBJNd8+Zd6zWvKTdXj572ee3pPPOXddocfyJHNJdetz/xz/y3Y5LXi43t+yA5TXjpYL7byUxCP//xO77+uDdfyHfd1scfL3B5fjnTN3P8BY235eP38pR+giSebhz0x5VrvxT4+b6Srotz1vuv5rsuRc3pQfnwxSFFTQi2QCAQ/FmCTWXFmGSTYGsk2C4S7IbFSrDDa1XHvXPGCMEW/KmY46IR1qQezOzngVJCCF2uie3bt7vl6/OPAopxIGF75NP3vVLY+cSThZbC1af+7d1u0lsvFmobGp8e49/KX7B9J/jltTw/Ib6Z489vvG9/u4agYwUfHwk4pX/kK9hsnXsC7AtF+emxsADBfvmr83w9ynmn714ItkAgEAhyCLbEBTsEnV2V8PLYnIKtFHHBNrHnsOpxxeI/OMHfg7BmDfCPPatgSErIlRaic/68W74cTA59pazpK49xSaQIMtV69l1Wn/2bHpSm4C9z/V47yreh6GryS4dyLKvMhPPqr9c45f3kk9IvvvvtV+w7ezqHmFKayenvruDH67/hnW++RpJf1Pvhj9/j71++9nOBy/MT4ps5/vzGG/Hvf+VYZmfLnv/yc1z46Qc+8dJ3WZdXn8xTsCnKT/tAqSmt/KL0VHubHnRuqPa3b3lCinDTe5QLr0fcqToM3WAJwRYIBAKBV7DNPoLdJSpbsF9jgp1eDAQ7PD4a/9i5XAi24M+Z0FivFkoeWoewRnUDluMjqOSc3jDFN0e4gkeE9ceHTHApl5qkk1I19Nzh7n4VOxq/ciTXxL4wv/zhA2c/5JMgfd+jShz5pWr4Rr79JzFSjnN+kxx9l+clxDd7/PkJtv/NxdrTb2ZPqPzlJ37joC+LOLYnoGDTPukpMvR4l90o+C53+aWk5DfJkUoD0ncuBFsgEAgEOQXbpkJm4myXQtE1ujIT7MbFSrAjnHaUPLhWCLbgjkONZMKb1IMpyultJKOnhejXHj03btyYyxdFm33FLe7YAa+Y/SdAJZC8JHKvp5Pir7/+6i1ll/7GcznWmfHOy1j+wRs53rvHM+lPp4xfOgRJ7Z0U7Js9/vwE239iIkm07zH6p4kEEmz/Gw+aBOm7nMYpjGCvWrUKwcHBCA0NFYItEAgEgpyCbfEVbFcVLth/MME+wQR7aNuiK9h8/z0pIqXXzRE52II7K9fRLpR6ZCmq9u6Qbwt0et2iRQsuYIf88o/r+FTD8K1BXZBgP+MpiUdNZigdgR5UBcN3HYpOU8WRwuZtEx1P/POOCvbNHn9+gl3qpd03dIwU1fYXbKdfhJoi7Tcj2KNHj0bVqlURHh4ucrAFAoFA4BMF9gg2ibPTR7B/Z4J9fMNUDCkGgk2SE1KruohgC+7cdRapocwD81Fp7ICAjWT8r0lqcKK3H/cVN4ef2NGD0iJIVn/3KVNXx0+w95897a0scvbs2YAR7Ix3X8Hc947nEkzKnc4LmuB4JwX7Zo8/P8Gu4pdjTqX68jo+Ku9H+ef+gh3vE0nXyxrejGBTnj11fKRrQVQREQgEAkEOwZaYYKuyBLslBF2jq+KV8U24YL+yfgoGtakN2Vj0Bfuuxx6A0aYIwRbcmbzrOkkwqzZ+E6dXDPGd1OiftkTP169f5w1hfCOuZXwqW9Dj5NXL3uW0TPWIHU3O8xW+Zq88lqsUn3+qBEWLd356Msd7Zr9UCJqYl/neCZ6vfe6n7wst0Dcr2Dd7/DcyadI3B5tEecnJ17Hu9Fv8WOk8BUoRuRXBvi9Ao5levXqJOtgCgUAgyFuwu8cE4ZUJTd2CvW4KBrauDakICzb9p0bSU3L/akREOYVgC2475TNGoeyKGTCx6yxQxZCA8wIiInDixAkuX/55wQnHDvLJfTSxLtWvigZFXelBAuxfTo4i1iSKnzBBrffy4VwNZKgyx/mffshVH3rDh297y9v5S/m8947fUcG+2ePPbzz/iZq0jM6L3jTHd1nVY7tvi2DnOG+eOtk0oVSfsEl58UKwBQKBQJAtA9QNUVaYYFsRaQ5GNybYxyemccF+ae0k9G9Zkwl2cJEX7LKLJyMiNkoItuC2UnlkX5R+KAsmVcnRSCaQXPsL9tixY7l8UXm8wuYL6zJMwlfXT6LzgyK2+sM/+q1Hssv5iTelOlCJvTst2Ddz/PmNRzcY/pM1K7Fj8b95IKik3+0QbMXvJsE/deeVV14Rgi0QCASCPATbFIwescE4MamZW7DXTEK/lknFQrBDa8TxyY5CsAW3C3NMFMIb1IHZk4akp4UUlGtLy0nEaeKbni9dmKYx7Y4/kWviXZNXjhS4nX8nx4u//MirdRTUrVCX2Tst2Ddz/AWNt+KDNwI2iPElmp0Dyr++HYLtXzZRh6q20OPMmTPFYpK1EGyBQCD4SwQ7yC3Yk5vj+r4MvLh6Ivq2qAGLoVqRFmwSn9Lr5yKkfm0uN0X6vMtqYMT1+JdgSYhF2VUZud4Pbd0EJfevgaF6XIFpIXldkyEhIbxd+m+//cYljIQ2LECUlZq/0ATF656ydVevXsXRo0f5a2qCQpVBSDB9o7aUtywf28ujw16xvngRK1as8OY+UypFtQCfRznMvtvpjxwdG9n4J69eKvRyqsvtu3+Jxw7mGr+wx1/Y8Z778iw/Fn/Rphzp3uzYdbnWy/D5jlfTp5qJPnnUN7Umxk/AKWrun/tNfxFYevJ1vvzChQuiiohAIBAIAgu2I6IaeuYQ7Ano27zoCzb9x3bPqpkIadagaAu2rAu25kdxk2z5NvHX729E/Tq4b8HEHGJkaFCHN5IJT62dbzm+gq5JimBTCTcq2edbku7StZ/x+LlPcOTcx/iYidt/Pd0A6fH999/zGtpBQUG4//77vZ0C9aguVdw4+sUZLoy+j/feew8OhwMVKlTgZfz++9//Zle6+OkHHP78I54zfNanuQo9Xn31Vaxbtw75Pa5du4ZbeSxbtozfNBTm+H/44QdeijC/B918+B4fiTl1VqSbBoqq/8LkXH+8/vrr/MYjv8ePP/6Y7/JffvnF+/rUt1f451B1FN/93rJli6iDLRAIBIKcgm1Wcgv2bx7B7lcMBJsii+XHD0Rok3pFV7C90WoSarsfWjGLaMuwyRKfGHsz2OTbJNgB/xqQl1xLflAkWkK1rq1QbslUrzxTIxlD43owOSK9aSH+jWQK9XPlSROhKHblypWhaRo2b97MG8XkJXHLly/nn1exYkUvzZo1w5NPPok/PNUw/B9ffvklJk+ejGrVqqFSpUoc2o4i5y+++GIOEfV9UOoK5YjTdrSPzzzzTMD1Tp06heTkZDz77LMBl3/wwQcYOnRoQCmmmwOSd5J+lZ1XOv68ZJ3ep+g7HX9aWhouXboUcL0NGzbw8erVq4fnn38+z2Y1n3/+OcaPH8+bwNA5zEva169fz88VncdAj61btyImJsb7FwX/B/11YseOHfwaoZsxIdgCgUAgcAuFR7BtTLCdEUFcsI97BPuYR7ClYhDBDouNQoRdK5q1aHNErkmoHX7YA0S0i+51Q4Ks3oJgE7d8DeX314Bcgi0FRJLYjdnUdJRbOInfpFHO9d07VyCoR7ubilwHuvEzGAxcYkmySXxJ+Nq2bcsblMyYMQN9+/ZF3bp1ebSbltN6FPWmCHaVKlW8wkxjtW/f3rvdkCFDkJKSwmVT3462oc+i7X2369atG5fpadOm8XJytJ2+3FfK7XY7F1eduLg47/j07L88NjaWv0/QviYlJeVYrt8s+H5GQcevE2g8+jn3XYc+N6/j0893fuPR/vmevxo1auRYTt+77/GTaKenp2PmzJl8/zt06MA7ONK2dJMiBFsgEAgEuQRb9Qh2bxLsKc3xK0Ww79cFu+hPcrx3+nBU7tlOCHaA83O7z8ffQbBldr1bGWXuz0C5zHEwqTZeLaTyiD4FNpK50WuTJJvE0leY/aH3aTmtR7JJ25C8kTSTwOW3HQk1CR5tQ9VLwsLCCr0dCTmR177RGLQsr7HovfyW6Z/hf8OQ1/HT+oS/IPuuQ2Pp6xQ0nu+6ee17Xvvlu7ygY6RzLnKwBQKBQBBQsKNIsGOyBfsFj2DLRbyKCE8RmTgYlQd2FYJdBARbU3KiKndYsBUfbkCwjbEulNqyCGXnjkFYreow27UcjWTotdUeeUuCrUs2iS8Jsx5hJnShJAkksSZJ08sA8og62wddtPXtaBv/7UjI9ZuBG92O9st333Qh1aPhJO60jJ79l+vj0DJ61pf5HxON778/gY6fltM+ETSm/3i0LY1HY9E6BR2f77p5jUdjEPr++x8/LaNx9OP3/yx9n0QnR4FAIBAUQrBb4rf9s5hgj0ffZtWLdCdHXbCr9GqPqj2KXwRbVZz8PYuJiacaiaioWP4syzcvdP6dBQO9f0cj2ErBkn27BVtV7NA0BxwOF3uteq8D9zEHFuywejVx1+H1KLl7JcqszkC1tHqo3KMtyo/tj3uzJnJCurS6LTc4uviSQOvSp0MCqou1737T64K2I7Hz364wn+e7ne+6ugzr+0Tr0TI9ZcZ3uT6Ovlxf5ru9frNQmOPXyyDq+cyBxtPXKezxFWa8/PZfv9HSl/t+Dq13K2lEQrAFAoHgf12wTUVfsA0uB8KjHEWzFm0BEWyZvZdStz7GjZuA0aPHwumMYv9hyzd1Lug/+pxyqXglyv/92y/YVp7LnwOJMHNoec6JjoWbUCkHmhTpnyLCJDs1tQHGjR2PoUPT+cQ8/VxomoLISDWXYFdhMl3imYdR8uBaXjWkxBMP4u6HF6Hc/PEI7tgCpsTY23Zj4i/Nuvjpr/P6bvy3o21u93a+6/run/86gZbr6+S3zH+Mgo7/ZsYr6PgKGq8wnxfos27Xz5QQbIFAIPib52DzKiJMsK+TYK8iwU6EUgwEu1KfDrhvytBiINi+ku2EqkYjLa0V1qxej7fffgeHDj2KevXqw2qx8rJreVXPoBb3OoEE21cGKPqWbx1n2Qff/b1BwVYkJh2mCJiN4TAbwmBhz1aTEYrVwmXbV7BV2odcn+keO6dEsWORzew4c1537mNn54GdT9lzXgcOHIxnn3kWJ068hszMBahVK4WdR/rLgMarePiW56MJjvfOHIES/2RSvWkBys4ahaotGyLMZfdGLf0jw7fzmr3RvywE2uZObFfQevktv9nPyGvdm1nnVsa70eVyMWxsJQRbIBAI/oIqIt4yfV7BHusR7LCinyLSrTXuZZJUfATbyZa50KRxK6xd+wA++eQMvrr4Nfbu3e8WbHYckZGReZSm07hcSj6SLefIt1YRExeHmrVq8coJNWokITGxBlxRUXw9io77irkqu8mWXTXfPHAu2Ep21JqwqxJimJzWrZWMtMYN0TytMZo1bYTUlNpIiIuCQ1NyCbbqJ9iqj2DTNRbPjiE6mt2EaPSd5qwxzI/DRjca2YLds1cfPHP0OVz6+greeec9ZM7LQnIySTYds+JNu9GvmYr9O6NCoxRUVqw5cnb1FAE9zUAWHUIFfxOEYAsEAsGfJKcBG80wwf593yw8v2oc+jSrDsVctAWboozBTVNRYUz/otuumMud6ommOiBZ7aiZnIpFC1fi1Aef4OKXl/D0U0cxcOAgREVF58rBln2k0mLTGKoHjX0vDoTI0QiLToGjQUfU7pSOdkMz0GvsAnQfk4kuo+ahw4g5aDxgMpI7DIarXmtYXDVgkGywKO4IrVts3RLKI8OKmkPCc6VtMKGOlsNQK+I+dIoKxuy2idg0vDUOZvTH0SVj8PzKCfjX8gl4Yu5QbBrZEZM71UbrGjKiJAM7dnf6iKqY3ekanuuJpDvGEoY6lkoY28iOvWNaY83IrujTvCGiVXYjqKow8mcmvqo1l2DHxydi3LiJeOml4/j662/w5r/fwdQpM9n5jGeSbfNOgpTpuM3uRjD6pDZ9Qp8u2b75vkKuBUKwBQKBQHBLgk2t0l8tZoJNEhSh2RCWGFsshEhmkudyxmH8uGlMAk/i0tff49iLxzFi+EifdIYAcs0gqTaydXTMNifMUgzC4xohvut4tJy0Hj0XHcTgVU8hfeVTGLLiSQxc+ST6rnoS3Vc/iS5L9qHj+BVIbtkX4Q62nY3K1elpEO590z8rL8GWmeRaFCuSpSoYXMOAPUPq44sVffH7I2OAvZOAfZOBA1MZ09nrabi2YzLeXTsM68e2Q4f6SUys2fFJRvZsYJ9hZp8l8c+yM4GuaaqIrlpZvDq1JbB9EL7fnYXtGZNQL9aFUM2OYLuEUHsojBqTbJviEWyVYzJZERsdjzlz5uPddz7gkv3M0X+hb59B/C8GsqdaiyyxGxOzBEO4wVsBg6pF+It1ccuvFQiEYAsEAkERFOxIU5BXsP8oZoId3CgFZdbMLvK1aC0mC4+mduncG088/hwuX/oB77/3EebNnY+oqCi+/wGP05NzLFHEmn0XRka46kCwlghTfBpSek5Gj/nbMXjFIaQv349+mVvRadJKtB6zDC3HrkT7GZvQc+lhDF79FIaveBQ9pqxGYsvuCHPFsLE0Tz6zmmd+ty8u2YgEUyUMqRmOZ6e2wjePTMY1dr1c2T4dpzZOxMsLBuGFOf3wxoL+OL96GH7cxpbvmYHzW2dg+7RB6FKvOlxmgzsPm8u1xKP7DnbDUNscgn6xRpxcPpwJ+hT88NhqHFgxD6kJDibVMgyqFRbV5JFyPQdb9aSAqOxasKFhgzQ8tGkbzp79Euc+/woPP7wL9VObsXNv8wq21SLDZLTkqk7hP7FN/J4QCMEWCAQCwU0LNv3JXvMI9mvFTLBJikLrJqP0gwuKfLZw8l4AAIAASURBVATbaDQhOSkFa1ZvwudnvsYXF77Bzh37mRQ2hskUAVVV8pzYqOdvqzIJthNBkdG4N7IOqneegJ5zt6Pf/U+iV9YudBi3CHW6psPRsA1MtZoholYbSI37o/aAReg2dz8GrXoag5c/ig7jFyMytRXCbS53uoVPDW45n2NIMgejrVIej45uAuwZARycinMPTcDhab0wo2sT9KwTjc7xGoYkyVje0oFXJrXAbxuGArvZelsysHZoR6RqNmhSNDsWjQs2Rc9tVhm12TnobDNh58A0fLVuOF5fNxkZQzqihsPAxNrI1rV6csazW8/rEWyOpDGRVtGv7xC8+MKr+O67X/Heu59g8qTZ0NRob81xkmw3NoaQaYEQbIFAIBAIwc4l2Ib4GF5erSgKtjf1gokd5V4P6D8MLx/7N7779jrefvsUJkyYyr4H2m8jtMj8J0qSXNqpeYnmYoIdi8qJLdFywkYMWHoIA1YcRusxixHVsD3CHAkIVzUY7E4ER8ahnLU6qsV1QL3+i9Br0WMYtPoZ9F+wDfV7jkSEI96dEuKVeDXf46lrLI8ZqTI+XT8aODwVV/fMxJ4pvdAzWUWiMRjRBqIq4qqVRkrVEphUqzLem9YK2D4JP+2bh+cXD0e31Br8s9x1s838HFmtGuLYZycbwtHFFYG5LeMwumUdJDsVOGVKKSGsPhMkVR80j2xrCA+zIiG+Dlbf/wDOn7uCr7/+AQf2PY60tDZMvhVv1FsuYDKnQCAEWyAQCAT/04JtkqwIqZlYJFNEdLm2WjQkxtfF/Ss34exnl5n4/YSDBx5Hs2bNYbKEQFHDmGDnv+8a+55csgkSE+fQ6CS42o5AlwVH0G/5Y+ibtR0JbfpDdsVDVWXYVQM0NYKNKyNCdqKaXBO2+gPQZOJW9L7/Xxi07CDajJwHKaEOLDaZ76fKI7z5C3YT4z3Y078urm6fgT8enYd3H8rAoBapcJktUIw22CR2PUkGWM2VYGTr1rXcjc2dnLi6fhh+3z8LJzeOxfjujdn1ZOZ52Haei00TNmOhajFQrDbYKV2jahVIYVRvOBqqpMEpmdnNhTnnNRigQgvdxMiSE0OHjMWJE+/g26vX8O67H2PK5FkwCcEWCMEWCAQCgRDsQkawI1XcdWhdEc3Bdgu2McKGju0p9/pFXL70C06fPo+sBct41RCLNYxJZhgTYymfcWSPYBthpnzsGnXReMgc9F32FIatOIzukxfBltyQVxahsnkuxQQHQ2OvLYrGK40ExzVD8sAl6LPiKQxZuh/tR2VCrV4Hkmr2lMorWLDrGyti/9juOLNzCc7vX4b9C8aiWQ0mxuFG2IwqNCbDGq+LHQaj+V7EhpRAVoMgnF3aG38wwT6/ZSoWDOnojkaz/dMj2BLbLp691zDSiCYOKxpHmlHLwa47JsuUzqE3q/Fegzmi2NmCLUtUpcWBtCZtsWP7AXYj8yO+/OJb7NxxALVrp/I0khzReiHYAiHYAoFAILjtgi25BZtPcozLKdi9qQ52cYhgM6Er8c9NRU6waV9UlSbfUe1oF2bMyMJ7757Bt99cx8svv4VBA4exfbay7yCcC7aiWgsUbCdFsGmyY0ItpPaejG6ZBzB4/sNo2zcdsjOGf6d2PhlR5tg9VUHCGCGxdVCz32z0W3oIw5fsRrcxc+FIqsUE28jHL4xgJ5sNmN66KdaOGojlI3tjWNsmqONQEWO2MlREWxyIkuxsP6kcXyUkhJfA7LrlcTqrM/67bzYub5uNVcN7wSW5Uz0kz3mKNBuRJlVBVtsa2DK8Ex4e2Q3jOrVgNwnuYzfziiNWXoObd4LMJdc5a4y7nNUxa9YifPbpRXa+f8Xx42/xiiLh4RZeG1tEsAVCsAUCgUBwxwTbLMnuRjPmEPRKDMXrU1u5BXvlOPRKiy/SrdL14yCxLr12NiyStcgJNkWwaXJjUo0UbH5oNy6c/5anh+zf9ziaNmnOhC+MCbaB52Dz8yvnlGpfKGeZ0iS0SCcMWjQi67ZBbOthSGk3EEn1GkLRNF5XWqWa2zJFklWes037EUH7kVAftQdmYsDSwxi5ZCe6j5gBe/Vknq7hTrnIFmw5D6LZOa5jikCqJiHREgK7IRhOiSLmkbAzsdYkB/tsFzQu+UFINZbE8rQgnFnWA7/tm4OzD83C/P5dmGBrvHSehV1bdP25zEHo66qIN+b0wfeHV+Obxx/Auqnp7Po0shsAiV2DEttP2SPXSgC5ztkl02K2Y2D/kXj91ZO4+s1vOHXyMyyYvxSa5nLf1FilAm8mBAIh2AKBQCC4cQFkmK1uwXZaQtG3ugH/nt4G/9k3u1gJNpVZC6mTxI6l6EWwNS2SSbQRrVp3xNNPvYQrl67h7NmvcP/96xEfl8BkjwmkZGLrWn0qhvjKteSForcUxaacZbPNAaPNxYjmr92NV2RelYO+K/6d2TREMiG2MZk0Sk5EprRH49FrMGD54xg2fzOadxsKo+rKNcnRt/a2PzTJ0MlFn8H3SWUC7ISViatRccCgOBGmxkJWNcRYqqKTVhaH+sfiuweH4uruWTi2fByGNEtlMs72WXHxY7Cxm4ZY032YGFce3yzvj+sHFuD7I6swvXcThKhGto/UMt036hxIrnNKtsmoomWLTjjy6HO4euU3nDt3GTu270Nycm1vO3nxO0AgBFsgEAgEd0ywKbfVJYWiXw0jF2yKYD+3Ygx6NIqFZAwuFoJdcs8qGKKdRUqw3VVNFN4EZeCAdLx64iS+vfo7Pjj5KWZMn83XkXgbcKtfXrGSS669ki1Lnq6Omkeq/WXcyiO9ZpvKl1MDF5nE15aMxFZD0XX2I0hf9Th6T1qK2DppqGKQ+Fgk7f7R60CCnbtGNqXpWPh14jRXRYw1GHGSATXNFdHaWgZZrVScXtwbv+2fg7M75mPThD5o6FR4pNuiRHPBVtkNRpL5PsxPqYbf1w1lN3iZ+Hr/IqS3TkQFNp5Bk31qdWsF4BZsi0lD/dQW2LbtIK5c/hUXv/wOjx05ioYNmsBoMvLUHfE7QCAEWyAQCAR3VLCjLaHo7xHs3z2C3b1RDMzhVYtFisjdjyyFoUZ8ka1pPDMjE6c/OI/vv/sDb7/9AcaPn8DPp8wFW/KJXucv2LxVeS7RzZZrhU8aNDFxN/FxJSadpsjqcDToiTajlyN92UEMytqJtF5jYLZXR5hZ5c1ruGD7XBeFFWy7bES0uTyaOCuie9y9GJhQDkNj78OcBgY8OiwFZ9am48c9c3BxeyYOzhmBHnWrI5oJLhds6kRpc8DOhLyupTweaOcCdk7G9f2ZOPngNHRMtqK8HIZw1T0ZV28oUzjBVhEdlYxFC9fi/Llv8c3lX/Daq++gV+++PC2nqF3HAoEQbIFAIPibCTalHcQwwR7ABPsNj2A/u3wMujWMLjaCfe/s0UVOsF0ul7f1edaCpfj4oy/xzZXf8PIrr2PgwIEwmsK5ELvPa2EEW85zAqS7K6LV3X6cC7aRfW8KguVomBJbIG3IAgzO2oPhi3eh2/hFSKjfBmaFWq3Td+vOveb5zT4CH1iu3evYeD1qGbHWUDRQKmJVejO8umoITq0bjs/Wj8XVrVPw371T8Z89U3Bp8yQcGd8JfWsoSLSEwSVJPEfcYnPwqid07aVZymFXj+rAwQxc278Qzy8bj2YJZoRoEkJtEttXt2RnN5bRPM1x8k4RidQSMHPGInzy8UV8e/VX3jVzzOixTLBDYbVaxO8AgRBsgUAgENwZwaYKF5SnG+OJYJNgX98/C88UM8EOZXJtVG1FMrc2Li4OG9Zvwtmz33DBfubZF9G1azfevfF2CzalnJglC8zsOYiJZlBsU6T0nonec3dh+LKDSM9Yg9RWPWCy2mExUQUTlU82pM/k5fUo5SPfyLV7sqXmycNONgejtbUcDk/pim93zcT/HZrHJHk+sG82sGci/nhkLD5c1Bcr28WgkfVeOMxB7HozcVG3UBoLG7OGMQgdzOXw0vhWwN7J+GH/YuyeNQoxxkoIZscVwo4rwmZlku3OL5c86S+yEkiydcG2sX2NwYQJc/D+u2d5JZEPPzyDjIxZiIgIy/6rgUAgBFsgEAgEtxXZLdh2Jtixngj260ywf2OCfXTFGHQpRoJdZtk0BDdvyAW7qESx9TKC8fHxeOCBLTj3+dVbEmzZE13Wv7vcgs1QZRio8Y5kQ1VnLcTzVuo7MHzF4xixeDc6DhgP1RED2WSBS3V/JuVgu7tEukvg5SXY9Fl65JoEm0rxUev0NlpVrBnQBC/P74M3s/rgrax+OLN6OH7cNhH/2Z+BPw5k4tyWmXhwfA+0SI7kNdfpZoA3uGH7XMdUBQPUKnhnVlcm2JPwzb4lWDt+KJwRQUyuZYSz9UiwTTcg2JQiotpiMX78bF4a8eqVazh1+jPMnj2XR7AlySp+/gVCsAUCgUBwZwU7ziPYr81og18PFD/BLps1EUFt04qkYCclJWHrwztw4fx3uHL5Go4+8wIT7K63JNjuduG+gi3zyY2SpiKUfV+VmVzGthmEdjO2YOCyx5C+aB/aDp4NV0JdyEYjXFS5Q6UqIG5hJWkmwabnQCkivmKveqLddtmEKDkE0eZyqCWXQ0OlNOob70Ld4BJoY/0HpjUMx9EprfHLIxN5DexPt87Glsn90CSePsPEa1vT8Te0BGFqTQVfrRnNBHsivtqzBBO7tYNmCIZJpQmaChNsiQm27JVr98TMvAXbarVzwR4zaibeJcH+hgn2qU8xf/4CkSIiEIItEAgEgjsr2FTlgsquxRpDMJAi2DPb4RoT7KeXj+aCbTFUK/KCTdU6Kqb3RHCLohnBTk5OxvZHduPLC9/fomC7ZdgtubLn+8v+N+Uzh9pcuFdJgD2tBzpMXo0By49g0LLDaDdyEVx127LtnbyWtt1i4BMUVfUGBNun/rTKP9MKje2/XY2AXQlFpFwVNksFKObyiLGWQw1DSfSNKoN/jayD61vH4Nr+TLyzYTom9kiDTTF6BbuZpRIWNtDw88NTeYrI+T3L0LdlU8iGcC7YRlVjKOz4FK9cFyTYkkewR42cjnff+YwL9mkm2IsWLuYpIkKwBUKwBQKBQHCHcE8YczGZizeHYFCSCW9ktPcI9shiI9gUwQ6Li0KEy1EkBFv2NHfR6y0nJibioc3bcO7cVV4HmwS7W7duvAb2jQk2E0vFyUVS4zKsItIRwyTXXe/aoESjlDEZctogtJ28kYn1QQxdcQhtxy5BZL1WTL6dsGga74ho5VVGzLxcnayo3rSPnFVK1Gw8Akv52pGRUZDZNaFqTmhMgF1MaO18mcTGZeLMRNsqV4YiVUYtU2nMqVsR78xui193TcVX22bggSkDERdt56ksJqsJaYbS2NwhCr/umM4Eeype3zgLKUkJ7AbExAXbzATb7CPYuljnN8mRItiS1YXh6VPwztuf4Zsrv3DBXjA/C+FMsC0Wk/j5FwjBFggEAsGdFew4YzAGJ5vx79kdfCLYMcVGsMuPG4hKg7p5ak8XDcHWo+uxsbFYv34Tzpy5wiPYzxx9Hp06dUJ4ePBNCrbKK7+QFKvsPRJsVZIRbKsBc4NBaDnpQQxY8QSGrDiMduOXIa5FT1hjE5hcyzBp1IRGdndGpBxszVMD25vHLXsi1oE7JWrUaMZigBIWDFNwNWgmBS4pmr3vgkWx8zxpsxKKCEaYYoHLXBlDYsrhX+Ma4j+7JuHHHVOxY/YwVI9zIYIJtoUJdntzKTwxuDb+s5cmRs7EYwvHwBnlZMslXsbPbNPcEyLzzb3OLdg0yXHM6Jl8kuM3l3/Gyfc/RkbGbB7BFoItEIItEAgEgjsm2AqTlSgmVTERVblgvzmnIxPs2Xhq6Si3YBeDRjM8RWREb1Qc2adIpYgQJP9Uqm/JkpX4+OOLvKvgsRdPoFevPjAaC1+mz92hUeaRXJogqComnuLhlA285X2I7IQhqQ2ajVmLwUuPYOSqI+g0YQWiGnWGMao6rHYmn0ywFS2SibDGJFh1S6uquSPDeg43r+6Rl2BrqG6thKENrBjXMh7DmiSieYIDUTwqzsSdOi6y41EVA5N/E6ySHfHmcAywl8OTw+vij92T8POeGdi7YDRqV4/lcm2zhqOP8z68Nq0N/ntwPv7YOxdbp/SDVbby/aBrz+LpSpl3WkgAwbZocDqq8zJ9H330Jbux+Rlvv3USo0eNQVhYiEgREQjBFggEAsGdE2yVCVaUSoJdmQm2ySvYTy6lCHYcE+yQYiHYQZ1aoHKfjkVKsCn9ggSb9i9z3mKcOnWBC/brr72NkSNHseXSjQm2amUSa2bPJp7DbFfC4JKDYWSibExOQ+Oh89Bv0SEMW/Youk9Zi7hmPWFyxPFIsVkyeGpkq1x8KdpMDWa4YNN+2pQc5CXYqebSOJrZBR9um47TD8/DypHdkJIUzcYww6iZITPs7HMclHIiuZBkMmJkdAX8a0wjXN81CT/sno4d80aibs0EyEy+XeaqGBFfEZ8t6w8cWcKWZ2L5kPZMsOk4VU+tbGoF7+DpKXIhOzmSYFOjmczMVTjz6SUu2G+8/i4GDhwsqogIhGALBAKB4E4LtsoEW/IIdgTenNvBE8GmKiIJxUawDU47wuNjikSKiK9gE5RLPGrkBLzx2iku2B+c/BjTp0+Hpik3GMFmx6bJMMsmqJqESAdFoGUYE1JRf8hs9M58BCNXPIo+MzaiRsv+MDqS3LWjpXAm2GFcsq0S5V+7m7bw7ohyzpzmvHOb3TQylcKxzA746dAc/P7oAjyzaBia1GCSbgmHya4xoddgptbmqoJIq4yaIfcio0ZFvJvRBtd3TsRXj0zGumkDEROl8XJ9NQxlMateKK6uH47rh5bgi+1ZGNO6No9gy6p204JNZfqSkxpgzf1bePWWixe/x9GjL6JVq7ZikqNACLZAIBAI7rwERtmsTLArYXDNcCbY7kmOTy0diy4NEplghxULwa7apRXKzRlTpASboIh6REQEunbtjWeOnsClSz/j7JkLWL5sOWLiouBub17YHGzJI56UyiEhnImxJSYZqX0moMfCPRi0/BB6ztyM+FZDEepMQZjsZEJtYRgQoZhgUGgipIwISeWYJI0tY0ItOWCT7FCZmKqynZOXwDY2lsbOQQn4fvtYYM84fL51Gqb3TEOSwwyjKYKNb0GINRwWczAcoRXQ2lQWu7vH4tsNQ3F97wycemA8pvZrDTVSgstYCfXDS2NVMwuuPTQaP+9fgg82Z6FPapyPYOspIvYbEmw6pubNOmDXjiO49PUvOH/uG+zcsR9JSck8NUcItkAItkAgEAjuvGAbKvgINkWwxzHBrlFsBLtauzSUXTipyAk2pYiQYNeunYqtW/fjAhO9ixcvY+fOXWjSpJFHsOVCCLbMJyBambBrkU6YrTYm0bWR0mMiBi7chYErnkC/xYdQP30ZlGbDYa3bA3LdjrDVbc1oCaleK1jqtmHvd4Sc0glaSns46rSGo3pDWNVYdiPg9MipPV+BrWmuhOE1I/DW0gH4764x+G1/Bt5ePR6r+qWhVy0FjdSKqG0qjTRLaQxPDMWOPim4sKw/W3cGLu/JwoE56WhdLx6SakaspSJaK/dgZ89EYMdkfL93MY6tnIEW0WaPYKu89KClMPnXCuGWa32SY48eA/Cv517F1W9+w8cfs5ua5WvgdLh47rdVpIgIhGALBAJBcUS+DfxZgm1mgl2eCXaYj2CPLzaCTVHi0Ho1UX7CoCIn2PoNgN0Rg6wFK7noffftj3juuX+hV6+eOc9pLsGWcy2nqi+aFgWTxQ57ahd0mbUNQ1b8E4OWP4FByx5H93m70XnGFnSashGdpq5Hp2nr0HHaWrTnbECHqQ+h85SH0H3KBvSesgqdh05FfEoak9lYT8t0XVrVgMRazagrGbCkQwLO3d8Df+yZhOu7MnD+gYl4ZdEQHJrSCbvGtsaR8W3w1txe+O7BccDeDPy+Zy5eXDoJw9s0hoM3mTEh0VIeXRzl8cTwhsD+WUzAF+PIgomoaQ3yEWzVW0FE9lS9ceOX0kKVVEiwFbdgR9pjMX7CDLz/3me8i+Nrr76LESPGsu+CcvStvP63+B0lEIItEAgExVKwpVvgz5HsbMG+lwl2iJ9gJzHBDi8Wgh1hUxBaM7HICba+jxRdHTxoFF55+Q0u2O+//wEyMjLgcETy5ZoaycQ5Mld3xhzXARNLKssn25wwSE7ENOyGoQt28rzr4Ssew4hVj2Pk/Y9h5KpHMXLlIfZ8kHGAM+J+Bv/3oxi98lGMW7kfk1fswojpy1C7cTsY5WiYrXoU2Ef0/dCoMZEkI00LwaLOiXgpqz8u7ZiJXw5l4tqj8/ATE+Wfds/GtT3zcH3fQvx6YCkubp+Pp+cNw4R2DVDHISNSMvIqKFSRpHtcGJ6d3Rv/98RynD+0GuunDEGMsRIkLtiBW7Zn1+fWvCiqnaOqTijs/NSqXR+rVz+Ac+ev4Msvv8X+/UfQsGFTXiWFqrAoqix+RwmEYAsEAkHxjF5Lt0Gy/2zBbucR7AlMsJNhMYQXixSR0No1UOqhLJ6SUdQEW5fjenUbYdODD+Pzzy/giy++xLZt25CSUpdHVTXNAXfZxPzH0JgA2+yxCFdiYEtugWb9ZqBFehbS0peg6bDFaDJsISPL8+yL+73Gwxax9RaieXom2g6dhRY9RiIqqTEimGDzGts8Aqz6iL5fygu7Fgy2aFhNJtS0m5HeIBJbBtbByxktcP7+rvhh4wBcW5eOnzaMwbmVI/D8jL5YOaAt+rCbtZp2JtdWC+xMnl2ykQl2ENpEhWLtoCY4OrsHHpk5AIM71ocW4RZsRc1ZPjCHbPt2dFR1qPmNi23nQqcuvfD4E8/i8pUfcfqjs5iftQSRDqcnf93M89nF7ymBEGyBQCD4HxFs+vO1mz+n3NzfQbApgh1ePQ53b19WJCPY3vQPJsejRo7FiROv4/Llb3D8+Amkpw9jNwUSTCZrjgY1Ou5tPXLNOzjaEanF8Jxpq5YIW3x9yAmNYE1oCnNiU1gSG8OUB5bERhxrYkPIifWhJNaFLZZ9x2w8i+qEZnd5IsKe1ug59t8NRY7NEpNbdiPjMIejuqECmsn3oX/1MExuqmFuq1hktkrEvNZJmNQ0Ab1rRqI+E/EYyQBVMkNiNxM0jp1dd9E2GdXlCLSONaF7Yhja1LAh2WVjx2jyRLBlP8H2EW0fwSZMVgVW2i92jl1RCZg2Yy7eO/kxvrr0HY4++yJ69O7nkXP3BFFZERFsgRBsgUAg+J8QbF2uJaoBLFuFYN+AYBsdkSi7aFIRFmwmgFYZDRs2wZYtW/HFhYs4d+4CNj24GTVqJCMiwgh3Z81Agk2tzJlcS3bYJWpL7uCvSbgp+k3HTJg9mDgSl043En/PbLW4J/hZjQwDe22ESbLw7ovuro5qjlQM//1XOWyf2Hg2irpLMtsXBZrJApvRgkizFRpDJYm2sH1iEs73R2LXNBtbsTt4PrWsOthnuaBq1HKdKpgYoZqqulu1WykNRnVf/7w0oT95CzZN/DRZbGjeoh127zmILy9+g1MfnsGSpauQwM6x7JdqIn5PCYRgCwQCwd9YsLOj1kKwb1awTRYzguvVLMIpIop7giKTy/Shw/DKK8dx5cpVnDj+GoYPG8nlW/akZdDx6DcKbhQ+8dA9oc/umYzo4PnG+r/dy1S+rpucoi4xec2BYuUTCQl6rb8ve6qV5IrweiLYNjYWQa3ZqW06RaIJm0Rt2z3fCR0DW2am4+Djyrwluxapp8G4oUmJquLgEw5l2QRN0ycwevb3BgSbIu8miwJXVDwyZmfivfc/wpdfXcWRx55G+47d2b7IQrAFQrAFAoHgf1KwFatIEblZwTabUeLoliIt2FTpgkS6Vq0UrFixCp99ehZfXfwa+/YeQLNmLWAyWbw55XpHSl/BplrQZsUNb76iMMFWotm4hMst3Ww9d6RZysanjrbsEVTesZGEVTbzDo+ybC5c/r83ku3GnTai8OY1Fpu7lTthZK8pMm5W3GLrGwFXqYoHu9Y1xZ1TTrnTFk1v2e6LXGjBpoY59Nyn3yAcfe5FfHXpW7z62ju8kkikI5YJti3XZEnxe0ogBFsgEAiKrWTLOaKCcn6inYdg587HzZabOyXYTy7xVBEp4oKtR3xJrEs88SBMvufqJr6r7IodSr7VNAqPZwwetXWXwKMJje3adcD27Ttx4fyX+OSTz7Bu3Qakptb3irWmaTlSRPwj2BzFwaC8aaen/rO7zF4uwWbYZL2WdnYVDol3cgxUuUYuvGB78qIpUk3CTpLNRdsj2PRa9t5smplYmz3Sr/BJjFQphLpTSmp2brSs6NHmwgs21QZv17Ezdu3Zj3PnL+LUh5/y1JCkmvV42ghfXwi2oJhRZXQ/hLdoJARbIBAIcoqI7BUQnUCSrYu1VTLxHFmLxcgwMdmyBpzwpvIJb6pHcO6AYO+fjX8uGYfO9YuHYNO5IcG+Z8kUmCLVmxRsv8htrhrQPmKp+OGNzCp+qD7ozVCoc6Jbtrt26Y6Dhw7jwoUvcfr0h1i8eAkSE92lBul78RdstzxnQ0ItKYFaiOcWbH3/Ah3XDdVgDyjY7pQTN24J1iXbLdhuubYpBg7/uaCIvKbAZKf8bDOTbZM7ku6VbMUTbS+cYLdo2QYPb9uOT898jo8+/gwbNz2MtGat3S3WGbwtvBBsQTEivGl9lNkwD2XvzxCCLRAIBF5x9dQMVvT/2FX3n+VJDBRVQ5RsRoKxElKk8mjhCkL3ZAl9ajnQp6YD3WtoSLMbEGcJhlMK41UVVLa+nQmInZ4pwqkL9i1GsgMJ9i9MsJ9YPBadUmtAMhYPwTabzQiukwTTTaXW+Aq2f/Ra9Uwy1KWSJhdGe4hhOPj7PC/ZR2R1qc4pxO4cY0mS+eRElysK/fr2x+HDj+Kzz87g8ccfR2r9+jCajLxjo+STIqI3WfHtXijLumCq2bWhvTcDsp9c+wq2fzMZ3yoh+aOfHz0X23uD6CfYehpKdtUOkmcjw+Q535q7zrXGljFUlTorWuHfuVL2prbkjG5n18J2kz5sOF45fgIfffQJHtqyFa3bdmBiTbWx2fejMcGW5MDHIhAUQejnvsLMkfjH/jW4b95YWJ32W059E4ItEAj+poKtwcxr9dKf8p2obglFe+VeTG5oweZBtfDczG54LTMdr2eOwkuz0rFlaDsMT6uOBrEWJuMhTKrDEK2EIcYaBieXJjVHHuxtE+w5TLD3zcLji8aiY73qTLAjio1g3/3wYoQlJdwGwfapA+0TteY5w0yqVWsSR5OSoUrR3gi2TbbCxsTYJikeqbZ7cAt2dhdC2Zs7HhnpQNeuXbF+/XosXrIE0XGxMFL1DT5BUOaQaAfMOw6Q9iD7/PUkJ9lRdW+6iaJ5hFz1yr+s5G7uEjjyq58zq0eezbkEOzuP2sprT0seEfdOoFRVniaieqDxVFkKINmyn1z74JnQ2bZtW6xZuxZLlixFs7QWfAKlJCkc/biEXAuKk2DTX+VMJhPndlRHEoItEAj+VoJNcsPLjTGZMDG5dqgy4oxV0dlRBQ/1qYk3VwzFl3sz8fX+pbi4axW+2rEC3+xdhq/2LcVr66ZiyYBmaBHHBNgaDJcUwuTayMuZ3UnB/pkJ9mMLR6NDSkKxEWz6z6jUxkyE1at1A/8RyTlEMZtswdPlVFPctZvt1JJbysZmtbFnd5RY89SqVqmEHi+jZ/fUrta8qSKKT4UPOvcE5VsnJSWhdkoKL5XHS+p5BDuX5Hrahucl13KANA7/tBXFI9d69Q1vy3FFzVeuc0i837kLHGVWfKLQ1hzL9WsvG/eYNvnGGi1l36hEokaNGoiOjuXSTX8lcKN4q7MIBMVFrnnpUaMR4eHhMBgMt2XythBsgUDwNxFsPfdW5hO76M/l4TYHYpkot7Hdgy39a+K7raOYzGbg5IYJODylJx4c0gGb+jfH4xPa4KM1w/H9vjk4vWkyFvZtjrqREYi0hLnbPJN4+FVy+F8XbIrwlJ80BGF1km5QsHW5pioaJtgUI8f9b8mT+uFOt7BZTUywDXBFhiLGZUBslBEuuwWRlCtvsrqlWnJCs1KdakJzwyU78A2Rvu8UpTISFlPO6HUBwivlkcKRl2C7I9XZgp1fRLxwgh1oMq/iJ9iyX/m/QIKt3lguuJ+M0DmMiIjwiIgSuJ64QFBMBJuuZ12ws69rIdgCgeB//RekJ0fUHSGUubhRXWtqhlE9pDTG166K91cPw++H5uDDDeOwsEtdJt1BqB1WHvXY8k6Wu7C+sx3n1/TDz/tn4fEFI9AlJRaR5jA+NomS3VfWhGDz/4BCk+IRYde8lThuVrDpmW9PUkzLpCBo7KYoLrY0WrU0YNCgBIwbm4oJExpg6JBaaJ5mRrSjPJPvEN6tULXauWDbmVzraPn8xYGXGTSZfGpHF16upUBpD3+KYN+eCbY5BfvmvntdsukaoGfxO0jwd4li69yOm0Qh2AKB4G8h2GYmLAbVDrNKsmSAjVI7zEbUrVoSD/VIwIVHZuLqgSw8mN4GjSMVOM1MriyUcmBEDeM96OsoiRdHROPXnaPx5gMzMK5LGlxse1V2wMWELUpSuWTf9ioixViwy2aOR9X2zW5BsHVkd+k7xQVNo0l5pdGwUSksWpKEZ58fg3fen4cPP1nKOXlqMZ56egSyslpw0Y5UKkIx0Q2Qk5G/YPtKpV6W7kbEWgh2biER0WqBQAi2QCD4Gwu2W1jsHmmi0mRhUAxVUS+8FO7vWQsv3z8Bx9ZOxahWKYhlAmaI0FCNCXYE5ZOaKqNlRAkc6WHCjw8NxvubMjC7X0fEylY+QZLaZTsld16vb1rAzUmOwgTbhBhjOSbYwR7BzmCCPYoJdnyxqSJCf1K9N2MUqnZve4OC7SvZ2ZMcqcOgprHzo5VCk7R7sGPXQHx6Zg1eOTEHGzd1Qeb8upg9pxY2PNgWx1+biXMXHsGRI1PRvq2LibXEvyN3yojqqfoi55vSIwT71gVbpIMIBEKwBQLB3xlK4WAC7KJUAV4FgiLPVAmkChIt5dAqqgo61bKibU0N1TX6E6ATRsUFI1UaIYk2h6OVXA7/7BOFXx4ahQ8enIM5fTog1mr2NBdxep41r+zcVC62ShPtJCbYBibY9zDBDvKU6cvA4wtHMsGOvXHBlt3VNhT5zxfsyv06o1rbpjch2L4NZtxtyG28s2E5NG56N/Yc6IRPzz6ADRv7QFNLoGSJEijhQ2x8CWzd1gNnz6/Fju0T0DClBuRwCTaT6hFsM7sOzD6TDPNKK1JuWK6FYAsEAiHYAoHgf0iwVURZNB69lGUTE7YwRMpBTLorIU6qCEdEBSiGKtCsJihUiYJKwGlWtl0QEkzl0MtZDs+Pqodru2fh1fVzMKJdGhwmA4+KW2xOhsstRR45VD1R0mwkD1Yud1RLOxcKe181I9oWinhDaQyrWQVvz22La0ywn8hKR+cUF9SIajyPXOVjGD3bmn3GNPtgdX+mojfZ+XMFOzw+GuExrkILdq7SbVx+nbzKhk0uj+qJpTE/qzY+PbMQu3aPRFBVt1D7CzYRElICW7a1xscfbcecmf0Q6zDzVBH3JEf393A7BLvAGtWKkqPbp39b8+xyfHlRyFrYt1mwxe8NgUAItkAgEBSiioh7IiJPDVCsvJKIppi4pNq5qJq5eLmYpCbaIhBnZfJtuBc1w0qis1QCG7pH4vONw/DV3vnYNH0o6iVGQzIbuVSTXFuUaI9gu0uaUZULqo8dxz47ymJGlEQY4ZLC4JSoYU0Qo2oO7Ox9TQpBtLkSqgeXxNjaVXFyfkdcZ4L9dNZg9KrLbhLYjYBmZmOY2f6ZKzOqMoI8zz7/toQg1mZClI1Jtlr4KhC3Mwe7wtAeqDCqb6FrxgYWbGocY+WR6jZtyuCFF6bijX9nom5KFa9M/+OuUuz5Lu+/SbhL3lUCDRqUwInjC/Gvo3PQrqWNnV8m1pKLl+vLbjhz84J9Q9KbV+v2PI79RhA/3wKBEGyBQCD4S/At7+aL4hVimcmXjARLMLokWzGiiQujmjiQ1d6FpyfVx5cPj8A3+2fjyaxB6JlWE1bJgghqo26jDnkOTxRb4c07KH+YIqTRkhXVrRKSmdg1S0hA03gnGifYGDJDYlhz0LC6gtTqdjSJs6K1vSIy0yR8trgr/rN/Jo4tGYrRzaLRNDocDeIkto4ZTWOMDJObOBPS4s1IY+M2ZeM3qWFHbZeFd5600/H5lGv7syLYlfp3RvmJg28ogp2jgQqfiGhnN0JGxMXehTGjI3Dy5HLs2D4Apf5BMl2ayXU5JtNl2Ot/MEoySuGuEmW4ZJe9pwR27xyAD04uxdBB8YiOpBSRGHczGsnpaTpza4ItfrYEAoEQbIFA8D+K7NM624Pi20DDnTLgNJvQSKqELSNb4LNtM3F572z8sGsq/m/PBPy8YzyOzuyEQSkWqBFVESLZEK7KMKgSr0xCqSEW1QpJdVe+oDzfWIsJ1cPCMbBZczw8bwG2Zc3G9sVTsX1JYLYtnYHNS2Zjy4LJ2Jc5Cq8uTse1h0YB+2bgk83T8c+l47Bv6RTsWjETe5ZPw/5lUxhTGdM4+xg72fubF03CI6vmYNyATrzrJEXnqWGIb8rBnyHY1Vo2QuVB3W5SsN0NWNyCHYYaiSUwbaqEk+8vR+a8+vhHyRK4u6Qu1yV9BFt/7Y5mZ86rg48/XIEpExshISqKCXYsk2uSbBevAONumS4EWyAQCMEWCASCWxZsxV+w2TqU0lHHdB/WD22KD7dMxcVtU3B50xhce2Qcru2dhU+2zMD6UZ3RuHo0TEywDaoKg6YywZbc7ad9BJuklqqMJDHRTNUi0almLbSt7kKXOvY86VgnCu1S4tA52Y4+8eFY2dKBLxb1APZk4ETWEExrFYdO1c1oW1NBhyQLOiWZGPRs9ULLWtWKRJt6cUhN0HgEm24ebLyDZXZe7504zyHd2kKyR3oF2+CMRFhSvDdFxOpyoOzqWTDWrVmwYMu6YGvsuwlFYlwJTJpgwukPViFrQUMuz3eVuJs93+0R6lJMtonSKFWiNEqXpOUlsHRJY3x4aiXGjExBrNPpEexoIdgCgUAItkAgENxRwVaZfGoaTJqdTzJMiTKifaIRfRJDMTS+CjLTFDw/uxe+2TkPn2+bjwcmDkFaUgKXQIPqdFf14BUfsttQk2SrHuwMF5Nvl2LiFULyhi1nMpxoCUVqeDlMqyvh46x++GPPAjw1ZzB6JtvgMlbm++hQDXDZQhlhDAMf20WfpdJESSs0TXa3u6bosScirE+mu1PnObhLG5SfNw4Wp4NLdVCrxrhn0WT+WlJtqDBzJKoM751nNDunYGsewaYqKMGIjS6BEelGnPpgJfbvH4IypUt45Lo0l2v3szuK/Q/+ugTKlSuB3bsH4J23VmFQv2REa5QioqeHOESKiEAgEIItEAgEt56DHViwHQ4NWkwUwuwOBLFlIWYjZHM4Yi3BqGEoh1RjOYyuGY6XJ7TCjzvm4t8bMzGxc0s4mJgZbNFMsJ2eLpF6K2omlNSOncmu2QdKIbGoUp5wQWdjUgObpPAKGF9Pxamsgbi2dxGOzB6G9klOWExhCFXtMDJ5NnvSU8z0mgk+NdMxEtRQx0Y4YFbc5d7cKRce7lRaCHu+L3M87ps7Fma7huCmqSizcoZbtvt3QZmN82CKzruqSI7Je7pgUz67EsRuKO5C+zbl8MzT4/HvN+ehWbNwTxrIXR7Bvht3MbkuedddKHO3e8Jjs+Yl8NZbS/HPx2ejeVMFkZKZd3RUfSY5KkKwBQKBEGyBQCC4Sbzl0eTsiY0UbZaZ9FqMMDGMDKp7bWHCauUiboVdNiHSEoampjLY3l7Bdw+OwZcHVmLNuH5IdOgRbKokIvtEsN1R7Gz092ROvtLG9s9pMaBG+H0YV0/BB1n98cveBTg8eygXbMkYxgXaPaHSLeX5VbeQZJ/JjXeoFrZva2xDYixKbVmE8tOHIzQlCeWnpiOkeQPcvXslqvTtyFuQ51VVJLdgU4MZEzS1CjS5FBJiSiAjIwqnP5qDAwfHsGPNXZ5Px+EqgUOPdsFHH23EjOntEeOqBsVq4hFrnfza2gvBFggEQrAFAoGgAEioNMmdcqALtsUUgbhICS1TEtCteSo6N62D5Fg71EgmzCpJs53LcwTbvlZEWWxsEoyvV/TDpX1LsW36EKQmuJhgU8RY9kSnrVx6ZcW3OomO7JU5iibzlBK/xiL8fbae3RKOBEM5jE2VcHJhX/y8bx4OMcFuV9MJmQm22VtvW280I+eIyPtG6m1/Qv1rXbDNZjOMRiOq9GiLko9uwH1Th6Jq2zSU2rQApdfPRbhm48sLLNvHxdedG60qBmhKFdiV8nDa7kaTJiWwbXsjfPLZ/di1ezAaNiqPe+8tgVKlSuBuRpWgEujYqRQOHu6Pz8/fjy2bB6JRAxscmoGXK1QV3xrU+U+4FIItEAiEYAsEAkE+wkatzKMtDt5whqLWhNVqQl3jfdg5qgPe2pSJoyumoVcDmpQXApMkw6bFQVVjYJWYYIeVwfqmBlxanY5Lu5dj89j+qOOK9Ag2pWqYAgp2Dnwbi1D3Pn88gh1pNSDeUB5jUhW8v7AXE+y5ODgnHW1rungE28zzvX3bifuKdiCUP0WyKYIdERGBMIsZZRdORIknHkTJ/atR4p+bUKlTCxgMBh7BLrCqiEew3fnXJNghcPD89TC41BJo3pRJ9sMd8cnHS/HaiTk4cnAsHt7UA5sf6IwjhwfivXcy8Oknm9g649GiuQa7Wo1HwqlUoVIIuc4VTVdEDWqBQCAEWyAQCHIJm0uyI87sZM/UFdCTusGem0eUwhMDa+PHPQvw9a6FWNYvDdW1apBNYbBb7XCaVTgiQtBKvg8H+9fCDw9Pw/mty7B2cE8kaYpHsK1MsI085zpfwVaU7DzoALgFm0klE+w4QwWM9gj2T0ywD8wZhjY1Y9yCreqCbfaRbPkvPcd65RAS6PDwcATViMM/ti9FiWceRun7MxAiWbl8k4QXWLLP02GRC7Zs4o2AnOzGiIi0lEFidAlkza2Dfz09BI/u74bjL4zFW69Owsm3puPtN6bg8MHOmJPRFE0axiPaKUFi51NiN1OyLIufBYFAIARbIBAIblfutZ0JdpTVySPZ+iRH1akhxVwGsxqE4sMNY3Ht8EL8e+VIzOucjA6R5dHCXA6tjWXR114Oa9vH4ZNlw3DtwHK8vGI6RjVPRTQTdJ5/zScpmtyl+jx51nlGkuW8oci2xIhkMhgTUQmjmGCf9ESwD8wZzgQ7lgl2hE+KiNUveq385ZLN87ANBoSGhuLe/p1w15ENqNCqEcLCwgqOXsu+cu0p0cclW+JNgOjGI1IuiU4dDNi2ZQKGDkpGWqMgdOtsR/rgmhgxtCZ693SgRVpVxEaXgyIFsc8Lh9XCBFuy8Amk2Tc04mdDIBAIwRYIBIJbEmxqj22XnLAzubKTYDMplu0KYq3l0MpWEpsH1cLlh8fjx72z8eH68XhmelccHNMaR0Y3w/GpbXB+7Sj8smcRPnpgNpb0bY1GLgtcTLAlj+xS1RD3pMNbSB2gKDa7AYi0WphgV2aCbfMI9jwm2CPQJjmeCbbRXRZQUYpE5DpQLjaJNAl1VaMB94zozZ9JuguMXvvItbuduZ2JNXu2qkyuTex1ZdSpXRErVvRC1oKRcEQq7LMi2E2JFZGRTMA1M6zmMJ4OYrGEsPeZXEsGWK1Gtl9WLtiyJ0XnTlVTEQgEAiHYAoHgf6h6CJM0T0TU7olgU+SZSsDFSWXQJb48Ng6og9eWDcGFrTNweU8mLu9bgEu7M3FlVybOb52LlxePx6IezdA82oxYxQCH5sml9kwylG+1HXkxF2zfVBFKBwkODkZQUBBCQkIKnXvtG71WJbdo22kb632Ii7kXo0c3xcYHx6F+gygYTRaYrApv+mNm58EkMbGmVBD6S4JsZM9GLtiSZPTk3bs/Xy5EDrZAIBAIwRYIBIICBVuPZMs85UAXbAvPnQ5FtHIfWkaVw6RGRmztEY+nx6XhhZkd8MzU9jgypg3W9W6MEQ0T0dBuRqQ5GApv6OKOhOpj37K05SHYvxQjwfZNFaFcbEoVyT96Lech2CpsEvs3E2iVSbJmK42OHRVseGA8+g+qz8S6EsPOpNoBg+JAhOKu9kKiTSUWrbIZVnYTZJUNHtkuOvnqAoFAIARbIBD8rQTbtw627K3EYeXtuO3yfagu34tGtopoF2VA5wQJneIltI82oVFkOOKkMNglI29YwsvgKXdOsOMMlTGaCfYHWW7BPjhnZLESbN+yffQcOHrtk5/uyY/21qmW2Lm1suMzhzPRLo8GqVUxf357zJvXBw5nJTZeCEPhOetm9j1QHXIzSTVDkk0ejB5Mnu6a+kRTzVsGUPyMCAQCIdgCgUBwi4Kt8Hxpt1yTJGu8hJ+7cUtYtIRqdhkVmdxVNttRzRSFMLMDERYbIiQZoTaqGuKWair3p3cCvFOCPYYLdk9c2+sW7NbJccVCsHXJ9iewXHuOQc55s6IyeVbYeZBNlZEQWxVjRqdgzbpeaNkiEmZjFXZDZObVYKjOtyS7b5QkHq32xegRbTNPD3F/Dn1nDg8iD1sgEAjBFggEgpsS7Jy1j7OrfLjbp1PaiMrzpq1OEmgZ4YrKhNoOs+SAlT1THWwrW89ooxQEhefwcgH07QZ4GwTbPQHPDrvVingm2GNTqVU6CfZcHJg9Aq2SYouNYOcP7bcJ2WUGdcF2R5VtnqY8NGFRkcuiS6dYrF49EsOGN0RsdAhs9BcEn/KHskewZYpU/z977wHexnXl7Sdxl4tkFTYQwDQAJMDei9g7RUlsYu+qlGRZvUukerG6ZFmSe5dLnLrJxmm72c2Xsv9kN9WxncTJOuVLNtn0ZL9sdn//c+8MQLBTvfjged5nwMHMYAYc3Hnn4NxzB+EcyL0ORMrdHMFmGIYFm2EY5qpFXY2xBxIZGMZbvyI1lc0RHkW1ExXJ9mlYXeDGG5Zgv0qCXZkWf5MINom1OwwuI9ySbH1Aev0dRkUet3MGcnLDsXtPC/buXYS0VAd8UYqsLmIEjcg5PpxzzTAMCzbDMMx7VPCDBNvmF+x2Kdiv9C9DBQm26riZIth+xCiX0QOpGyKNR5+GhKTpWP5gJY6dWI6qOQkk5VNIyu2BXyImLtcs2AzDsGAzDMO8ZwVbIXmO0jSZIrImSLBf7lt6Ewm2X3pVS7BVU7CNOBhaokzj8PjuRmNrPI6SXC9ZXgJVv5M+nxASbBsGj2DJkWuGYViwGYZhmHEEW9TpFoItItjf298xRLAdN75g+/Og5b6bgu02zOi1pulQtekoKHagf3cTduyZj5T0cJo3hV63mRHsQP42CzbDMCzYDMMwzHgpIm6vFOzEiClYnT8g2C8JwU6Ph6bcDILtCariYUaj3W6f7DzqcE6BN3YSlj1YiIeOLkB5ZYyseS2kWnRYFMubks2CzTAMCzbDMAxzIYIdfp8U7DcPdJqCvb0X5Wk3i2C7rZxrdyDVQ1RQ0fQw6J5b0dASg8PHetH7QCUd52RZZk8VJft0f91yThFhGIYFm2EYhrkgwdYRfzMLtpTswfnYYiAah3o38ksmYc/Buejf3Y7E5AgSaxst64OmuqzKLfoFdnDk84phGBZshmGY97xge0kMZQS7wI23DnbJgWaEYJspIsrNIdgSt4xci2i0qt2PmPhJWLW+EIeOdWDWnFiaNw1RUVFwGz5axjNCJ0muHsIwDAs2wzAMw4ItcbvdhIcEm8TZbZOpIY2tsThyfJGsGmJ4ptLrmlzOMMwBfQbXHtcnAJ9TDMOwYDMMw7BgW4IdP0iwd+K8EOy0m0OwhSiLaiEiLUQMWa8Z9yC3cAr2HepA/+4upKTZZT62KdcD61yJwX0YhmFYsBmGYW5ywfaX6ROCvaYgCm89ZAn2tiVmDrZ6M0SwPfB4fIiKcsuSfFG+O7BqfR4OHetG1ZwkRNrN6PVQKWfBZhiGBZthGIa5oE5/mmskwe6WKSIvkmCLCLahqjdBFRFDluRze2zQ3LejvikOR08uwMLeXLrJmCaPye02WLAZhmHBZhiGYS4tbUIl6VQMT6AO9trCaLx9qFtGsF/cuvjmEWwp0OJ470JOwSQZud60pdGqGhIhOz6K/GwWbIZhWLAZhmGYSxZsJwl2lKbKTo7rirwk2PPxJxLsF0iwy9PibhLBdsDuuA+65zZs7qvAidNLMLcmHaoWCk3XzI6PhpsFm2EYFmyGYRjmCgj24QVSsJ/fskhGsF30mkgjEekk1321DFHrWncH1by2cIci3PZ+1NZ78fDZpZi/OB9uT6g1kIwxfHkWbIZhWLAZhmGYixdsNwm2E0kk2OuLokmwe/DHgGDHwR0k2HpAYoO4SikeEyqNJ+XaY+G/IXDA8NyDlMxJOHqiF5u3z0NS6gwoSnjQcizYDMOwYDMMwzCXAZH2YSdx9uhOJEfchw3F0XjrcDf+8FI/nt+8ABUpPnhUB8m1xxJstxRSdxBXXrLHGuRFHxK59lhDonuha4TugO6eDCPqFmzum4PDx5airDJeDigjhz7X3QOwYN8UNDU1YcOGDdi4caNk9erVKCws5M+GYcHmD4FhGOZqCrZBgu1AasS9pmAf6cLvX+ojwZ5Pgu1FlGqXcm0Kthkddge4WoKtXYBgey3BjoamhyDC8T40tyfi8afXoGeBSA0JI8F2WOsbQRFvFuwbGZfLhc9//vMY6fG3v/0N27Zt48+JYcFmGIZhrpZg64jW7UiLmIRNxR68eaQTv395Owl2D8qTPfA4bXK561qwA5It9s8nS/JpdNOg6nciOf12nD67Ctv62pCSZkOkfRo0TRlY34p4D41is2DfWCxfvhxjPf7rv/4LXq+XPyuGBZthGIa52oLtNgX7FRLsLX7BjggSbH+KiGfUFBF9BK6sYJsS7DasCLbLJ1NDNGMa7Or7sGZjMY6c6EVZeTwJ93QZvTY7N6qWYHullMt1WbBv2P4Ex48flyJ98ttfRfZnXw7w9V/+LCDZFRUV/D9lWLAZhmGYqy/Yb5Fg/+GVPjy3uQtlSW64SLAVl7msJmUmKG95hI6O+mWX7LEE20LugwcxMfFywBhNnwaHdgsaWxNx9vEH0d6ZDa8vEhrJtVmWT6V9clrr+vO2OYJ9o8q1pmk4ceKElOiOf/4E3vfppwK88v3vsGAzDAs2wzDMNRbsoyTYr5Jgb+lCaaILhjN8sGAb7pFL4QUJtmYEL3+5BFsdQ7DdZiRaLu+QA8okJN+O46cewIYtNUhLt5lyrdE+aSRkQrB1p7VNgzs5XkdERUWhv78fr732Gj760Y9KPvjBD+LAgQP4+Mc/jjfeeAO//OUv5fT8+fNobGyEqqqBCPZYgv3Tn/5Urvud73wHzz77LOrq6oa9f2JiIvbv349PfepT+OY3v4lf/OIXePfdd/Gtb30LH/vYx7By5UrExsYOWmfmzJl46KGH8KEPfQhf+9rX8POf/xzvvPMOvvzlL8t5CxYskDniQ98rJSUFu3btwhe+8AX86Ec/kvv2ve99Tx6n6JzJKS0MCzbDMMwNKtjOMQS7OFGXgj1YmK+lYI8i2SICrZnRa1HzWjVuw6r1FThyYgWKSkhS3NNpGZJskmoh16ZgD+kkyYJ9XfDZz34WF/r45Cc/iSeeeGJcwR7pIUTeL7LHjh3DH//4x3HfT4h6Z2cnnW9uGTn/7//+73HX+fGPf4zm5ubAcW7duhW/+93vxl2nq6uLzwuGBZthGOaG+nndEmzfUMH+YD+eJcEuIsF2XReCLcTaGZR3PUS4ZfQ6WUal7c47UTsvAeeeWIOunkJERYu0EDvtAx2HlGyHJdh60PaH19Vmwb76FBUVjSuq/98vfop/+Mk7+Mt//3XQ/P/93/8dU7D/9Ne/4jPv/kCu71/W//jc5z6HM2fODJr367/8Gf/yi5/go++8ic+9+0N899e/HLSeqEwiIs/Bj1/86Y/4p5/9GH/3o7fk+4htBD/+/Oc/o7W1FefOnRs8n45FHNMXfvoj+XxoBZR169bx+cGwYDMMw9xwgq3Zke7v5BgQ7J4RBXtY/vXV7ORoVQkR81yGXaaD+OtZ65pP1rdOSL4bj5zbhE1bW5CTGyXXEzm6uoxeOwNRbFOeh9bYHpBsFuyrn0st5FM8fvi7/8Qdrz+F2y36vv4FdH/xk7j/9acD4nwrzS/8/Ael1AY/hgr2sW99BRmffVku7593Fz1f8H/+Hv/9P38bJvCf+vfvI/kz5/G+oOX9iPff+29fHLbOQ9/4EsJef3bY8mIbSbQtIfb+x1//OiDQQuBjPv0iPhD0XuK58ennpaT7HyJCPnfuXD5PGBZshmGYG02wM8MnYbMl2L8fRbB1S7DNCiKGZLBgXwkhDRbhGBhaonxPlxEeEGzRaVFItKLdhTUbqnD67EaUVsTL6LVOUq5pHiv3WgtKERltABsW7Gsl2CKFQjy+/atfDJfVUQh5/Rn8+Pe/HVWwx6LhCx8bJMoiinzn6+Ovt/arnwusI56Pt/x02sdf/nnwjcATb/yrvHkYbR0h2tu+9o+B5UUOOJ+PDAs2wzDMDSLYqi4E24b0MH8Eu0sK9jOBFJGIQNqHf6h0dxADgj3K8OWXgh7UATHQkTHGmue05vlov+x0HJMwa04snnp+Ozq68uGNCYGqhUrxlnKtmdUmTMnWhkSwh6eJsGBf/UogYhTGcQV7BCmt+cePjCvYIiL+/iHrCsENFt+0z7w07L2EwN82ZL2prz8dSDsJjoyL5W2vP4uoT78wbJ2yz78WeJ///MufMSUoGj8aYhtv/+ZXgfVqa2v5fGFYsBmGYW4EwdZIbmIUEuxQM4L91jFTsJ/e3I1CEmyPJdj6mIIdHA2+nILtDhpp0V9OLzqQoqJrIqKdKjs2JqbehaMnVqBvVzsSk6fTcQkiBjo2atogxpNnFuyrK9iiEkhDQ8Oogi1SKd4i2RQ5yj1f/OSwaO9blogOFWwh1ee++3WZP/3NX/1f3DtEbD9hpWL84f/91yDpFcv5tylSVm4dIsz/729/w2ff/eGgeZmffRl//ZuZdvKD3/4n7qZtvN+S7qLPfzCQkrL0S68PWs/96edlnve7v/8t6r7w0UGvzQuKsj/88MN8TjIs2AzDMDeEYJMQx2jBgt2N378mBLvTFGw1YlDHRd0wBudfDxFsnaaXLQdbD875dg8It+GBx+2V6R+iLreIXq9YXYIz5zYhr0Ds5xTZsdHs0Ohgwb5BBFuU3BtJsG8NEmj/Q0hp8DLPvvXNEQU7OLotHnP+8cODXn/eWs//eIdk+qW3vy33QTze+PUvcfAbX8J9Q8T8Z3/8Pf71lz8bdiMgJL38H17DgW/8H/zjT9/B70nchz5Sh0TKT337XwKv/Zy2e0uQzIvc7kAKyz/8gzx3+ZxhWLAZhmGuZ9ymAAcL9tvHTcF+alMHChI0EmzbsKogo+dJm4J9eauIjCTeQqyjZf61ok5DabkHz53fhM7ufCtybYcua15rlmA7zdQQFuwbMoId/ekXBg15Lh4rvvzpQctstfKVhwr29q8NrvTRPST6/dSb/zbodSHOolNl7udeGTON46e0nHjMeP2ZMdNZXHQjcOSbXx5UgSRkyDpConVazs/QNBb/4wc/+IH8nPi8ZFiwGYZhbiDB3lLiIcHukSkiT14LwR4xYj0cGbVWSZSNyYhLmoRDx1bgoSNLERMXYnVgdFuCrQc6NXIE+8YVbA9Jp//hr1O961//edAyoirISIL99JvfGCTQi7/0qVEFW6R8TJ5AbrTg55Zgi7J8d09gHVHxxP/4wOtPTbgjZvB7/exnP4OiKHxeMizYDMMwN5pgf98v2Bvbr4FgjyXWQ3KwxXt5bsUDazLw7As7kFfgljnXuhYnO0Lqmntg5MYhcs2CfWOliGivPzcszWLlVz4zaBkRdZ7IQDOjCbaoqz1phM6MIqXk6Le+Ap32Ifi1/wjqHCnqXYsIuoi0jyXPH3vnTbn80HQTH62X8pnzI5L+2ZfxG6uethjt0el08nnJsGAzDMNc34Lthu4eItgnhGD34QkS7Pw4VeZga1Ka9csv2INyuYd2aPRYqSCDkZ0s3ZG035NRWqni/KtbsGRZJcIj77beX1QV8Q4RbD0gzMGwYF9FiXa5YM/LwpQNS3DbMw/h7gPrJ97JkaT1yz9/d5Aox376xRFzqS9WsD/8wzcGzXe8/qzsyDhazreQatEp8UO0noimd37xE3IfRYWQZ978Buq/8FFZbzt4nf6v/5PclmfItoJzsP/nf/9X5nyLeV/82Y8HDagjhm93OBx8XjIs2AzDMNczbg8Jq8eNWN0uy/RtLY0aQbBFHWztCgn2aBHqAUSutVnH2iOFWdS8NjyTkZJ+Hw4cXowTp5eRbE8KKsfntjAGoev8/77aUWklJRFTl3fizlP9CGmpls8FtqKcQTcw40WwBSI3WYymKCpxDK09/YGgcnYXK9j7/u2Lg+bHkcD7Hye//dURc7Bb/unjw9YJlvL8z706bNAb8Wj7578bNN/76RcCEXGRMx782mSrJKB/WHcWbIYFm2EY5noXbLdbRrGFYGeSYG8r95Jgz8fvXiXB3tAmBdt1pQR7xKh1tFnrOghTsEm0BSTXqjYdRtTtWLg0C8+9sAdllTFQtGkkaLpkqFizYF89tBgvps9vxN2HNkmRnt7dgMnrFiF8dql5/ojBgBRF4u+s52e8Mn1+bhkhBSO4lN3FCrYYOXHodiNefxb2kUZoJL7083fxyR+/PWy+GKhGpHwMzeUWNwGiIol4iIooQ8v+3UPLh4zQYVKU9PM/enp6WLAZFmyGYZgbI0XEEuzwAcH+7avb8fj6VuTGKtdesGW6h4/wygFlNGMSyqscePSp5Vi2Yi4cihhMRoHGgn31o9R07oQ2V+PeHSsxecsyhM6rwr19KxDSMBtqlEcKtRBnv1SL/GG73S4Rz/258Bci2CON5PjvY4zkOFHBFvWrh6aBjMWGf/n8iNsbjfXW8v6HqCxy6zidHYWo+/Ovv/GNbyA0NJRzsBkWbIZhmBtJsLNIsLdX+K47wR6IYovt34vE1Eno292G4w8vQ5RvqtxGQKRVFwv2FU77CK8ux+QNS3DPnjWwFefi7gMbML17HpwJcSMKtYi4CqEW02DE6xMV7OzPviIHlwkWUhERFqX0fvGnP44p0P6BZEbrHPlykIB/7z//Q3YqHDpQjZj32pAc7Rx67+AUEn0UOXe+/pwc6Mb/+OUvf4nf/ta8IfjMuz+Q+dhDRVtEwUUaiV+u//CHP6C0tBRhYWEs2AwLNsMwzA0hTVYVkUxLsH9w8noT7GizLJ8WASP6VnTOj8EzL+xEUYmPbhAi5WiOmuoZkOtRJJsF++KILMnD1BXdmHRoE5TkBNx1sg9Tl7bDnp0WEOpgqR5LqP3LBov1RDo55loyKzr8vf7v35fpHMEDuPzP//wPnntueKWR4IeQ1Ik+xGAzH33nTZkC8rsRBooZ7SHyssXgMuff/racDpX/n/zkJ8jIyEBxcTF+9auBgXNE3vY//+zHUvb/5Rc/kUOw+x9CxsXy06ZNg81m4zrYDAs2wzDMjSDX2nUv2KL8XpgcrbG8SsXpc8vQu3w2DE+YOYCM5g10gBwdrggyUZzpKZi+oFkKtebz4o6zuzFl3SJElBcGRPhChXpovvXQ/8VEBXukx1e/+lUUFBTgvvvuw9GjRwcN6BIoo/frX6O6uhp79+6VMj708Zvf/AZtbW3o7+/Hn/70p2Gvi23+5S9/GTb/z3/+M9atW4ctW7ZIeR7tIbZ/8uRJ+TlNnjxZIiLRjz32GH73u9+NuI7Yj0ceeQQ+nw/333+/TA8Rn+tESkwyDAs2wzAMC/bYgi3rXd+DrJyp2L2/GydPr4YnegptU7VGZxxZpi+0LN97FTXWJyt83LtrNewz03HXie24d9sDCG2oCtQMD5bq0YRaCONoUeqJlEScqGB/5CMfwdatW7Fo0SIkJCRIsRbCOmXKlIC45ubmIi8vTyIixiL6K14Ty4p9D349MzMT06dPl68JRJS4sLAQS5cuxaZNm9Dd3S33MSIiAjNnzgysJ54Hrzd16lRkZWXJSihr166V0r1s2TIp//73F6IslhP491e8VlVVhd7eXnlcixcvRllZWUDGxTozZszg6DXDgs0wDHPj5GBfwxQRI1iwvQMDyMiRGqPNmtdukjN3KGITJqFnYSqefn43Zs1JRXjEvQMDyOhWdFSkgWgs0+PeVHncZh71pl5EVJXgnj1rcff+9ZjeWQ/N7Rom1P6OiX6J9gv2eEJ9If+DCxFsIb3+KLBfQIWkCtkNFtdgxDzxmlh2tNfFa6O9PhoTXc///iEhIQgPD5eI56Pt79B1hFzzCI4MCzbDMMwN2slx29Xs5BiQbBJrwxx9UaxvGKop3Yao0R1O3ImK2Xace3IFVq5pgkL7o8uhz92WYDus9fj/OZq82srycf+KboQ2z8XktYtklHpqbxsUn3dQGofAL9FXUqhHE+zy8nIp0WJo8NTPvITkz5yXrPnqZwOCvXz5cimefqkWqRMiuiwk1C+uYr543b+MmCc6CApENHis14PXD34fPxNdL3hdv1iLz9GfWiOei3nB++NfRyDmi+1GRkYG5JoFm2HBZhiGucEEO7gO9tUVbI8p11Y6iCnYoj63BlW/E4kpd2BLfx0eOrpQ5mELMTEMq3KIEG0p2GrQPozGe+f/KlI9pi9sxoyeRqIBdzy2D1PWLIQjJZE+Q31CQu3Po/ZL9eUU6tEEW7z/D3/4w1Fzmf/4xz8iLi5OiqeQaiGfYj+DI+5i38V8IdwC/zJi2/5o/Hivi/li+35xF8v4CV7Pf+Ph/9z8r/vX9a/vF+vgz1A8H+n9gtcRrwfnr3ObxbBgMwzD3ICCvbXUK0dyvKqCbQQNS64PbE83QhEVcyu6FybiyWf7UDk7QQ6H7nbrhHgfp5TrAcHWxuDmlmxR3SOktQbTlrbLtI9bXziC+7avQGReFjSPe8Q86mCGCvVIA8FcScHzC7YQy7S0NLz++uuyyoaooCEQnQS/8pWvyFxlIdcjCWuwuAYfr//vC3k9+LMKXmai2w3+DEeqmhJ8zo/0fqOtwzAs2AzDMDcAwUOlX33BHlhHVgPRrcg1vebxkDR77kFVtYKHz/Zi5ZoGRETeS8vY6DVDCrbbLaTaacn1eIKt3VSCLUZMDKspl+XzHBkp+MCHTuPuvesQNrsE6iUI9ZWMUo8n2OK9RQRYpEv4OyQG4+8QKCK846VMjHcMF/r6RDvNXmznWu6Qy7BgMwzDsGBfRsHWAoItpnLodsMhR2vMzAlB/54WHD2xDDFxkTQ/Gm7DQ8tYQ7wbbjPSLTs5aoO2d7MJtu5ywVZegPsf7JadFN//sbO46/g2zOish0qfRXDKR/AAL0OF2p9Hfa2FesSbBtoXsY8iQu3v/OfvABjc4U8cC5eqYxgWbIZhmOtYsN1jCHbbVRNsIciKIiKqYij0EPji7sLCpbk4dWYN5tYkwaFEkFTFE9FQNZFO4CF8cCrugdJ8Mq1EC3Cjp4jYczMxfVELlMR43PbcYdzx6B5MWTWfbkbo+N2uUfOo/UId3DHxehTq0dJExH77Ow2Kjn4Cf2fC4A5//P1lGBZshmGY61iwjeGC/YpfsNWrINhGoESfbthk9Lq6wYujp3rx4Jpm2j8b7WcUorzJRAJc0bFEGlyemXC7U2G444hoWdJPlvUT23TfeB0dnSmJCGmvlR0U7z60GbeSVN+3dTnUaA8Ub9SgtI+hHRNHEurRcpSv94onwcfnPy7/cXKHP4ZhwWYYhrlBBFsnwTbrYG8tjcLbx3vwm5e347F1bciJUWE4r7BgywFnvHIoc4c6BZkzI7F9dyv2H+1Fek48yXQiYhKykZhagITUPMQm5xJliE2qQlxiMZFDZEBzuwPvKTpvSq7jz14VedS1lbCV5mPKmgX4wAdP4Z69a+FMioczPnZCQj2RPOobLh3mAvOeGYZhwWYYhrluhMWsImJIwY4zbMiyWWX6js8nwe4jwe64fIJtDSAzGCMoqiyGOrchJm4aVqyuw9GHt6KupRIxSRkk0xVISqtGUkYtEjJqkJBZjcRM8bwWiRlzkZhWiYS0EsSQaLu9qdA8CTKq7XZ74TaizVxt/Tr4P9DNjBhuPGJ2CULa68w86qNbEZmTAUdKQkCOh3ZMvFChZgllGIYFm2EY5ipVaBiKFDGRSuHREOcKNwW7IliwO0mwtcso2J4huAet6/aEo6FlJo6e3Ii1m1ciZWYR4kmgk7LakJrTieTsLiTTNCmnA0m5bUQTkmY2IDGrzpTu9CqS7GKS7Gy4PCkk2CTZhlfK+8B7Xd3P3Z6XhfCaCkRUFOL9Hz2DO87uRnhVsVmP2mUMEmp/lHpoLeobKY+aYRgWbIZhGBZsKdiqJdh3ScF+69h8/Pp8H86t7cRMHwm24woJtlUFRJTYi/IqKCxOw7b+5di9fzMqa+YhLbceGQVdyCrsRVbxUmRKepFevBjpJQuRVtyD1AIS7txWku5GJGXXk2TPJskugcebhShPIjxSsqNNyb4aedSpiQgjoXZkpsqUD9E5cUZHncyvdnqjxxXqG61jIsMwLNgMwzAs2MMEmwQ6Sgh2WJBg95iCvYYE20tCd4UFWzccSE5x48FVC3Dw0G60d/cgq6ABuaVLkVf2IPLK1yCHmFm+mliFrIqVxApkVyxHZmkvifYCEu0uJOe1kWTPk2kjIjc7xpeBqOgEeDw+uN2mYAfvu+bxILI4F7rrUvKofTJCrfm8UqZv+eDDmLKyB0p8rJTq4MFHJiLU/o6JN3oeNcMwLNgMwzAs2JZgby334s1j3fjV+e04t7rjigm2iCp7PFHwRHnh8RqY1zQbBw7vw6r125Ff0oackmXIrdyI/MotKKzqQ/GcfhTN7UPBXHp97jYUVG9B3twNyKki8RbCXfaAjGyn5XchJacZyZnViE8uQnRMOgxPLEl0dKCzpW7J9ZQNS2TVjgv6LKM8Mt1Do+mdD++QedR3718Plf4WudRD86iDh9EeWhHDL9Y3Q8dEhmFYsBmGYViwR4tgBwv2mssn2MYQwRbC7fGQXEf5UFhShC39G7F9927MbViB7OIVyCnfhvyqfSiqeQgl9UdQ1nAE5Q2HUdpwCCWNB4l9KG7YjcLaPhLuLcit2oiZlWuRWbIc6QXzkZrThOSsKsQk58HlS4bm9kJzueW+CBmeTHJ99751cpCWsYRW5lHnZ8ta1KJknhDqO87skqMlRpTkQTWMEYV6aMfE8YSapZphGBZshmGYmygHW/doiDXCkGm7kwTbg7eOduPXL27HGRLsLN/lEWw3CbU7INceElP62xeLpIxMrFi9FvsfOoKOhWuRV7YcBbO2omAuyXXdERLqYyhvPmFxHGUtx4ijKG8l6W4l+W46QKK9FwW1O5A3ZxuySLLTi5chLb+TJLse8enl8CZkwYiOh+72mHK9dhFuf+ogbOnJpuyqtM+aHpRHnQRnegqmLWmVQ5Df9sxDslOiqADir0ctGEmoxUAoowk1R6kZhmHBZhiGeQ8Itu4W6RK6FOys8DuwvcyDty+zYIsSeR7NEmyDBFvgiUJ0fAKaurqx/8gprNqwByVVvciv3ICSmgNSrMuaTpFIP4yKttMoJ0olD6O8/RTKOk6ivOM4zTdlu7TpIIrq9yJv7laS7NWyE2R6YQuSZs5BXGohvVcqtNhYkuuFUpqntlYPiLAvBvbMDITVV+HW54/IPGpbca5MBRE1qS9EqP2DobBQMwxz3Qn2eEXmGYZhmIkzklwH0Am3hhhdpIjcju0Vhoxg/+qFPpxZ3Yksf4qIbi0rtjfi+2gBgpeTy2o63BpJtu6jaTzcnlgYXjdySgqwde8ebN5zDOX1K5FeuhL5c3egeN4RkuZTJNaPoLLtLKrazqGi/QxJ9SMWp006Sb47TqFS0HachPwQiup2IW/2JswsX4bM4g6k5tchMbMMUSkzMWVDL97/d49i0t41mJGRhBm5Gbj90b2yfF4IyXV4SR4iZ6YHBncJrkXtz6EWQu1P+wiuU+1fZ9gNDMMwzHUCCzbDMMzVFGxDg08LJcG+jQRbI8Huwa+e78eZVV0k2AYJdsQlC7aMYKsxMNQUeDwJ8CVFY/HKXuw+egQNC9choXgF0mbtRO68wyhqO4my9tNSqme1PYrZrY/R83MoJbn2U9Z5RlJOVHbQciTc5c3HUDbvgOwMmVu5Ctll3UgvbETCzCpM37JayvUHXj2F93/8HO5d2IQQkunQoplQVB2qog0qnRcs1P4o9UhCzVLNMAwLNsMwzHtUsIOFcBAkww4SbK8SgqzwW9FXruKtI11SsB9Z3YkMEmzNHkHLmcuq4wq2KgVbLOfHJaLXTjcMO6F45ciRVQ0F2Hl4N5as78fM2geQXL8dGc0PYWbLURS2n0J5x1kp1RUk2IKy9rMobX9EUtb+SCCaXUFU0t9VQshbTqCs6SEU1+5Cwex1yClfiMyiFsSWN+DOpw5LsX7fp5/CLc88hLsf7EZYchwJsx0Ou5Bq55hC7c+lZqFmGIYFm2EYhhlHsHVEGjqilFBkh9+CHZUqvm8J9mkS7PTLIthuuGwueBy0LacdWTlx2Lx3CTbs2YTShqXIatyK8lWPonLDc6hY8TRmLX4ClT2Po7z9URR3PIbCzkdR2nGOxPqMKdgdgwW7gubN6hCS/TAqm0XFkX0oqt6MnMpeZBR1IL6gDkZOKUJKCnH30nbcdmQzbnnuEG599iHcs3YBQpPiSa5ZqBmGYcFmGIZhLoNgOzW/YIcEBFt0cvzVc304vcov2OGXHMGO0TzwOEPhcd2DZSubse/4DtT3LERycQ9m1m9HxcrHULftFTT1fxiNWz+M2nWvYtay51HQ9Tjy2s6gsE1EsAVnUN51luT6zKCIdmXHWZLsszKKXd54EMU1W5FX+QAyi7uQkDkbrug0RERqmD4jFNNmzMD0uGhMrcrHpO3LcOdDG3H3rjUjCjVLNcMwLNgMwzDMBQq2hkiS7CjndFOwZ2n4/mUXbA2xuhsu592YPceJwyc2YMnqlcgsa0F87iLEl61FQu1OpHYcQe4Dj6Ny0yuYt+MTaO7/e8xZ9TIKux5DQesjKCHRLpERbCHZVk42/V1Of1e0C8F+jAT7FMobDpFgb0d+Jb0HCXxCRg2MqHRE2g2EhEZgxowQhIaGICIihOaFw+5SEDqriD4nlYWaYRgWbIZhGObyCvbOWbqMYP8HCfbDFyTYekCw9SGdHF1aBIzIe5GaOAW7drdhc99SFFQ2IC67BcmFy5BeuRHpJNiZLQeR0XEUqV2nkL/0KdRs/gjadr2Ops0fxezeZ6VM59QdRW79UXp+mgT7NCq7zqBSdHgk+Z7V/hhmtTyMisbDKKrpR37VKmSVLEByViO88QXQXXGwOzQS6wiEhYUiPDwENlso7Hab1XFRYcFmGIYFm2EYhrl8gj0z4hbsqvIL9nY8vFIItj5hwTZoWyJaHai97RdsfRoM5wewbEkZjh59UA6LHpdahYTMTqQVPYCsWZuQU7MTOfX7kNv4EHLbjiOz/WES7bMoXPkSmnb9PXp2fBJ1vc8hlwS7/YHzKG45Scuboj1LpIxIwX4cla2nSbCPoJiEvWD2GuSU9iIjtw0JqZXwxWTAcPvkcdvtojNjOBFG2GRnx9FGWGQYhmHBZhiGYYYJ9mgEBFuZjmzbrdhZ5ZKC/Ytnt+Hkg21Ii6bl7KEk1s6AZGtBJflECT4/LlnvWpcDyrg0MaiMCpcRBkO/E7MqbHjk9HosWlyDpJQUxKVUITmnG+nFK5BVuRG5c/uQV7sbufP2o6D1GPLaHyHJPoP0rnPI630aTZtfw8LtH8GiTc/ho//47+g/+jEU1m1F4bwDqBTVRlrNkn4VzadQ1ngIRTV9MoKdXboY6XntSE4nqU/MRrQvHm63x9p/pwVLNcMwLNgMwzDMZcKsImKYnRwjb8HO2STYx3rwf5/ZiuMPtCDVo5Bgh9ByjoBkazINRLUi1mYnRoHbwqN7aRoDj9sBl3sSYmJvw/4DTdi1eyGyslIQ5U0lwa5ESnYbMgqXIatsPfLnbCdh3o2ChgMoJsEu7jiDgo5zyO14FDNJtPN6HkHVA2ewau9j+OYPf4af/Oov6Nt7FuWNO1DcdAaVJNeVbWdQ1nwcxULS525BTsWDJNiLkJbXhuSsOYhPyhpFsMUNgsHnA8MwLNgMwzDM5RFsu8tAtBaCmZG3YleVG28f7cHPnt6Co8uakeKeiGDrlmC7EaW6SbA95rDo2r1Q1Pdh/oKZOPfYOlRWJcMguY3ypiEusQTx6fVIzl2EjJJVyJu9BUW1u1A0bx+KRam9jkdQ0vkoijsfR0EniXb7UWQ170Dbyl341vffwV/+8he88+6vsGXvS8iecxgVIjWk7RRKGw+hgLaTU7WOxH0JMou6SbAbkZw5CzEJ6fTeMSTYbhZshmFYsBmGYZjrXbB1S7BJrjUVbsMGVb0FRcWT8NgTm9G7tAaeqEjoLh+8cVmISSxEbPJcxGV2ITX/AeRUbkBhdT+K5+1FcdMhlLSeRHH7WVkHu6TrUZLtY8ht2o7G3i34tzfeloL92z/+BZ/+px+hsvkYiuoOoozEXAh6ztxtyKp4EOnFJNcFzUjMpvdJLUZMfDLtg8/KEVdZsBmGYcFmGIZhrrxgixzst45046dPb74IwRZDooscbJF3fRdc7vdj7/5GHDi4FGnp0TJ3W3QydHuT4U3IgTe5Ar6UZiTNXISs0lXIF1Hsup0oaTyAYpLmwpZTKGp7RJbmK+04TuK9E02L+vHPX38Ln/vit/Dq3/0TZrdsQf7cnSTXB1HYsBf51STXleuQWbqY5LoFKTnViE8vRUxSDqJjEuD2RNG+s2AzDMOCzTAMw1z3gm2QWGuI0hxw6ZMQGvo+dM/PxnPPb0FxscdMyzC80FxeKC6SbF8qohOK4UuuldVEUvOXIrtsDfKqNqNgbh8K6/ahYN4RFDWeQAmJdkXLcZQ1HUB54zYsXHsUOVWLsffUq5i/9hEklaxHZdt+FNb3IW/OBtrOA0gv7EJqTh0S08sRl5QLn0wPiZUpKuaxs2AzDMOCzTAMw1xBwY4KEuw3SbB/8tRmHFnWhBSXOsFOjh7E+UTuNS2r3orY+Fvw7HM7sGhxMVzGZGii0ojuIcF2k2BHw4hOQFR8LmKSZyEurRHJOfORWbQCOSTZubM2I3fOTuRWkzTXHkbRvGMoazyO8qajNK8fqeWrkNewBfXLj2DL8U8gbe425NZvR87cjcgufxCZxQuRUdCM1KxKJCQXICYxQ6aHuD0+knyDBZthGBZshmEY5ioL9uEuvPvkJhxZ2mRGsB2hIwq2HpDraLhUH00diCKZjrS9Hw8d6saRY6sQExMOTQ0hsSWRNWhdQyMMEm1a3pcJX0IxYpOrkZDRjtTcXmQXrURu+QbkV/Uhb/YeEu39yJsryu4dR2HdCWTXHERB22FktexDetMu1K5+Ah19LyO9egtyZq9BVulSpBd0IiOnDilphYhLILmOSUKUV1QP8aeHsGAzDPMeFOyxarYyDMMwlw+VcBi6LNMnBHsHCfb3DpFgP7ERR3r9gh1Oy6mDkMOKqxoM1UWYgq05psFp+wDa2tLxwQ8dQG4uybcUWFNmtUAtbR2KEQ0tOhlR8TMRk1yOuNQ6JGV1ICN/EbJLVyC3cj3yZm1BXtV25M/eSZJNol19EJm1e5FSsxOxc7Yhvm47Chcdw/Ijn0Bh2y5kVDyIjOIFSMuj/c6ahZSUmVKuvVGxiPL44BbvSSJtHrs4BsWC/lZ1Ph8YhrmpYcFmGIa5hoL9hl+wlzYh1aNDdThoOXcQ2hDBdslUEcVxJ9JS78BLLz2EhQvLoTnvhVt3D8irFTFXDTcJtsjFjpOS7YnPRkxKKeLSZyMhqw6pua0kyvORXb4EM8uXy4ogmbNWI33WWmRUrUU6kTJ7DZLmrEFM5QrMW3USPRvPICZ3PhKy2xCfUYPouBx4PLGEj/DK6LUh9kXTWbAZhmHBZhiGYa4cziDBzhaCPcuF7x7qxL8/vgGHewcE20li7VQ9hBBs3RJsneRa4IChhZLA3o79+ztw+uFNcOn3QHWGyHrYbj0aupBbwpRr2o4RTXjhdPmgeRNJsrMQnZwHX6oQ7Vkk2jVIzmtAemEbyXYXUku6kVI6H+llC4lFSKZpHP0dVdiFpKperN77LHJr18AROwtabBE0T6rM+RYl+cyyfCYDgi3E2mHBgs0wDAs2wzAMc4UEe2eV2xTsxzbg0JJGOZKj7oig5RRCJUi4VRcJqZvE2i0FW1Pvh9PxAXR2ZOGVl/eipJhEWp0iR3L0RrkR7fGYcksIwR6QbFO0FXeMjGS7Y9IRlZADX3IRYlMrkZBahcSMaiRm1iEpuwFJuc1IymuV0/i8ZvhymxCV2wh7WjVaVh5A25ojUJJmwe7KoO3GycFkXLoqEc8HHzsLNsMwLNgMwzDMFRLsSL9g227DjtlCsLvw40fXk2DPMwXbGQ6nbqNl7XCoDiiKC6oSbQm2ORx6du5kPPHEFizvFakhd9D8cLh1O+EkwdVkB5tgwfZjSrZIFyHJ9iTA5U2FJy4b3oQCxCQUmyM+JpYjLrkCcSmzpHTHEb70KrgzquDKmAVnagViSluwuP80YgvrYfMkS3E3DDHgjRqQbBZshmFYsBmGYZirJtgeZwiywm/FzrEEW0q2A6pIEyHBVhyRcDruRUzsHdjWV4fDhx+A130vyeo0uDQSa001kYJtjCjYwRFticsL3R0PlycFbm86vDEk23Ez4YvLQYwo60f4iKiEXBgJOVBIxm2xmZgeOxPzVvahvG0JQnUfbKomO1UOdLJkwWYYhgWbPwjmhu0wFgx/JswNIdhasGB78N3DXXjn0XU4uKgeycME207reaBrPijOGbDbb0FTSzIee2ItKst8CJ82CYo93CrfZwTqZOvaQA72IOg1kdMtOj865f7osiOlZvigu+LgJtmOik5EtDcJMYTPIsqXBM2bAEd0PMLdcZjsiUdyTRu6122FMy4BYYpDlhbUA4I99NhVFmyGYViwGebGkGt9CPy5MNe7YOtwaC5EOUKlYO+aE403jvSQYG/AASnYOgynYp3fiowK65roPBgNu+Mu5ObPwMmTq7H8gTkk0lOg2xW4VCHV7nEFW/7tF2yxfVWFU6KbnSlVUVbPC90QJfa88LgJw8Rwe+WANXbDg0ja1lRXDKYl5WDhpj5klFUhTGxHyLMl16MLtiKrobBgMwzDgs0w12nkWsiKk2TFRB8hkm3VD+bPjLluzl0h2G4p2Nnht5Fge/HG4QX44bmN2L+oAclRJMqKiwQ52qrAoVpTBxIS7sfGzVU4eHAZ4uNCodhD4FZIgHXvCIJtSKEOlmz5t5hvya0QbEVRCDEl8VZEiT+P7FAp1nfpegA9EPE2mU6yfbszGpUdC1HbvQhOXwwchr9m90jH7i/Tpw4Itnphv1AF31TzucQwDAs2w1yByLUp1+5AZQSB+RO4PlA3WF7MWbKZ60ywSWC9jnDkRNyBPdXxeOPIYvyABHvfokYkkWBHkXyKqLEYDt0QA82o95Mc34m2tkycfXQD5s5Ng902BaojAi7VBfcguTbRLIJ/4fHP84utEGxTsgWaVa3Ejy6HZjeCvnfOING10b7d7/QgNrcUPeu2IiorBzaXuHlQgyQ6GDUIbVxGkutIuulwyA6VXrl/Oos2wzAs2Axz+QTbH7mOJBHwJaYhM68EvqR0EpeBSLa4yBuqIjElmz875jo4f8U5qnpIsCOQF3kn9tUk4Xsk2N8/uxF7F5Jguz3wkCx7dA9Uu4gqO6A4b0VB0TQcPrIM69bNg8czHYo9EprTLs9vF203WK5dFyCepmRrFroVWR4cXVaHCHbgOITwelPRs2kXEosrYPN44DA0a0CciydYsIOj5mFGDHKq2pGQVihvAvTAKJEMwzAs2AxzWQRb/Mwe7jSQnJGLiuoGmubR3xoLNnP9C7bigc8S7P21JNhHl+BtS7AT3G64nLocrVFItNNxH+IT7sTa9SU4eGgFkpNpO44ZdE47zAFnpGCrlmRb6Bexb0OjyGOka/gj8RrdBNyvRKPhwc3Ir2+Bw+eFzfrV6HILtkMKdhwaFq5DVn4VVAfncTMMw4LNMFdAsF0Ic7qQnJmPyromJGcXsmAz1z+qS+Y6C8HOt5Ng1yThDRLst85txG4S7DiXAcNOyykGnPapcBl3oaE5GoeOtqO2NgOR4eH0mmKV5bPQ1SFcnVQX0WHyHocbpd0rMKe7F0p8LAm2IqPixiVI9lDBdsj0EFOw581fg6zCKrr5oNcVbdw8boZhGBZshrkYwSaxnlXXYgm2wYLNXOcYsq51jNNmCnZtsoxgC8HetaABsYYuK4Noqg2KehsKimagf2c7li6vQHRUmIzcCgkdLtVXT7BlWonMJddwn9OD5Op2dKzeBE9aCiIN7YoKdn3PahLs2fJzUBxqII/cD59fDMOwYDPMRQu2Zgm2gaTsfMyqbZFTM4KtDXRylHLNgs1cT+iyUodfsPeRYMsI9pkN2Dl/HmKEHNsiSR7vR2LS7Vi+MgO7di9ESopLpoVoisfMcRY3kKNyNQSbvmuWYNtzZqF32y4k5udBcRtBnRq1i2YkwQ7XzQj2zHwWbIZhbhbBHiM378JQx0G7pEaZeW8gOmM5/YKdlY/K2mY5DbObF33z4uwvC6ZwFRHmuhPsOBLsAhLsAzKCvZgEez12za9HjBgePXwSDOMuNLXEY//BTsxryKP17CTXmiyhNyDYyoiM385eKgPVfCYrbtwTmyUFO6u0FJrXe1na8eGCrZJgxwwSbFVROUWEYZgJBAVMN3BaHbpvYsEOlp4RJChQI5VhRsMlf2YPtxsyB3tWzWDBNjtGqeZAHSzYzHUo2PEk2MX2SXioLgVvHhOCvQ67eoRgh8Ju+wAKimzYtacTa9bWwuMOMyPXsk61KyDYA7/QDEG7kgy002IwGyHYk6KSsXDjduTNngPdF4PgUoCX8kvVgGCrsKkqQi3Bzi5kwWYYZuI4qP2IVDWZ1nZVBXvoT2wjogxBNQcUMAcpMBteVfEPIqDDoRgIdboQrngRYcTDHpOOqIxSJMwshTc2ji4UDhhOO1x0kXHJqSIxaNuGQhcPWp9hRkKTiEoMbkSQUCdn5qKytgFJNA2zK7Kerzk6nTIElWGuAso4aPLcjXeGkWDfhkN1cSTYC/HmmZXY2V0Jn3IXkhMmYeWqWdi3dxlyc3xQHOGmXNN5L6PYitm/QLSjI6GqVxLFROyD7sZUp4G7PfHoWrMBBTU1UKKjZOdDQ9TRDir5N+waMg6iNrf4vBxEJGEjQnQf6uevQnZRlfyei2uPOiYTuLYxDHPDMlZbHNyG2Kk9CKc2I0SMcJuQgdicMrgzi2GPS0OYy4sQ1UAYvW6T7Yop4boseapZba1JoP0LMPb+TVCwtQCaYg2xawm26v9ZUpSMkoMiCLGOxnQtHs7EQsQXzkNWfS8qluxE7ZKtmJlXJqVajGTmc4TA67ARCrwk2FFOldAIfUQ8hIt5T2NYgq1KwVZJsHMCgh1Kgu0IjEw3IDUOOj9F+TCGudJEaub5Nhpmw28g3j4NJbb340h9FN4+3oO3zq7Aju48JLhvR0tjHPYfWIiGhiI4beGWVA/ItdnYO2QdbM1pG4aqEKr9CmFJtqxkotNFycB9uhddq9aipLEBTq9PXifMUoOWZMvvrDZhVOsiJ77LNno/QRgxXY9GzYKVyCqqtL7jjsCFb2RUlmyGuanl2vzV2jECdvru24RYi/aDpkKgJ2s+xFU0ovqB7Shbuh0p8xbCUzAL9uR0zIjykbe6ECn9woBbMxCt64gWlZrEmAOivQ1uAy9FsJ2DDkBEpc2ooYOIFD/PExFGNCLI/sMML2yeOIR6EumOIAdqVhUSZs9HQdcmzFt/BJ07zqFn15NoXbdfNo6qg2TcEU7CHEGICLZDYkj8kewBXE512DzmvYkpGOYFOJzOl+TMLBLsOhLsLIRGRsLmsMNBKIopBIqsxkDz6EvBMFcaZbwIsBA+h2YKdvgHSLB9ePvEfLx1bil296SjujgS2zc3YPXKWnhdYXBGUPvoEMKqyXbQ31bKBt9hGxHdYcm2ar/8WFFy+aujQwRY3Ahz+TCvewGKqmtgeGNovkHtuitwQ3xxv1SJToz0mdL3WCC+1yGKB3XdK5FN1xCd3lt3OII+j6EofN1gmJveB8ySpuoIKA5xky7akFASbRtCSbInabHwzu5Cw5ZTaN37DBr6zqFu9T6U96xD6pwOGFnlUOKyYDN8smiCEHXN5R7118lLFGzxBoYc2tehekisowmvzIUTMj1JjcUkPQlTYnOg5c5FVEUnZnZuQMWDB9HQ/wRa9j6Pxn3n0bj7WXTveRrN6/YitbBcipHdESnFR7EuSib2cS9ao/0syrx3EOeBOLnD6aKbnJlJgl1Dgp2BkMgwRNhDSLDDoTrDSQj8RMBgmCsJCa0RFCwYkLwhOFQppkn26SgOuw2H6xPw9sML8N0z83F85Uz0ryrD7i0dKMh0Q7dNg4eWj7J+4fPSNqPonI+i94oSwQkSaQ/9PRSXmE/7cmVwyP0X++SxOeRQ7eL6IH5J8iYkw9Cj4XW46XWSbLrAeeT0whE3FQYJtE7Ho1o3zTanB41dK5FfMIuWofd3iM9jNMQ+qgzD3MT42xjXCBgiMOGIgNsxhdqPEISRO0zS4qHNWoCKTWdRvecVzNv3Grr3vooFu19E+9azmLt8FwpalyK5vBpGWiYivDGIcPvIeaMRrongsmFFyC+LYKtyYzJirXkRongxXY/H1Kh0hCaVYGpiOfTidiQ3rkbVykOo33IG7XueQ/u+l9Cy/1WS61dRSwdRv+tFdOx+AQ1rjyOusAFT1ARM1ZJopxMRYSTIPO0IVzzCLEJdCQHChhDBvKfxnwfi3JhK540vrxwF8zrgpekU3Ufnp/WLCn0pbB6BF3Z67nDHMMwVJI6Ih8OVCMWVTKQQqcNwEHbCo8cgVY3ElqZifOn0CnzliZV44eSDOLDvQTQ0z6FlREDDh0glATY9QW5Xbl++VzycdP47jUQieRh2mm93jwOtb7sYaNs2arfterLEZqQg1EinNj0J9zriEaImQ/Vk0mt0nAbhSRuMK00ev82PYX4eg/Evkxx4X3F9mO7Jwpz5W5Fe3AyFjlOhfRGfi/wsgqFrivwMBPoA4nNkGObmwB5oh1IGMPwkm8sZPmpL3OQLXkylNuS2qGxEzlqE4rUPY+6u89JPW4iO3S+hY8+L6NzzDDp3nkPz5kOoWLwJ6fUL4S2qhz2lCOExmbQdclTFLXO67SLYJ1EuLgfbL9g2zUMbjiGhoR1OKoKrqAlJ81ajeMl+NG9/Ch17X5I72bz7FTQSDbteRf3u11C3+0Oo3fVhzNv5Glp2fhANG55ETuMmePK6YeR2w53bieicVvhym+HJbYKR56d5TLR85r2OIqZFbUiufwAFPVuQ0vAA3CXt8Ja2IoaIK22xaEY8TeNLGOZK0kq0I6GkE4nF3Ugo7iHmD6ZkAS2zALGlC5Fc2oWMolosW9CNZw+txKee3Y3XXjuHTXt3IHVWM2JKuohOC//zFjq3m2jaTvSYFI9ASTctNzJeIpq25SnugLuoHa7CNhiFrRNCp2Vd+W2IKqTvWVEnfHScMXRc3pL5tO0FktgAYl5PgNgy+pvw0vPo4i645ft30LWkQz73FHfK+V7ad6/cf7FeF31/O2jdDlq3E1EVi1HxwAnMbNqIeFo+obTT+izaaV/a4C1uQZSgqBUe2l+3uF6I6wrhymmEzjDMTYP53W4hjxTfdRNPXptJPj3Pb0R0QSO1BQ1wFdM6dGNupzYlZX4/avqewDwS6rrdxJ7zaCCHbdj7spw27n2ReAHNe15A6+7n0LrtLCp6dyCtdjG1I3Ngi0lDpOaC3W6H4oiw0lEvspOjkOwIwwNnbDISiuZi7qL1aNt0HF27nkPzzvOo3/Ey6ne+jNqdL6Fmh+C8NX2J5r0sqd9J8k2C3U7PF/Q/h64tT6Blw+NoIzo2nEb3hlNo3/Aw/f3IyGw8jZYgmi8Csd6o22euKcH/J/+8djovRsJ/PrRuegQtm8+iaQvdbW59FG3bH0NX/2Po6XsU8/vOYWHfWSzqF5yxpucY5gryKPGYZHH/41hMDXgwi4iF/U9Q+/ckOrY9Ic/Txf0nsXb7dhzcuRznn9qPR597Ait2H0XnlhPoovO5k87hrr4z5vPtT9Df5+jvR2j6qPn3WPSPTEff42in7bVtexStW8+hdctZ+h6dmTCtRBut007fuY5tj6F7++PoIebT8fnpseiiz6HTomsHTYkO+nzat9P7bqVtbaHvsGDzI/SctksXsvbttN0+87vcTZ9rD313/bTveAZNdF1p3/4UFm47hwXbz9Cxnpa0b6Prx9ZTktYtNN1EbLSmFi0bGYa5GQh8tzcKb3wY7eQEgyGn3HgC7ZtPEmab0EptRCO1nfN2PE1O+hzxAup3nSfJfokkW/CyjGjXSV6VNNC8VhLunj3PoGM7tVXr9mNu53Jk5RfBGxsLVQi24xIF2+bywJ2Sjdy6DsxbuYMax0fQ0P885pE0z+7/MJr2fZSM/xXiZRPa2Uba6YbddGdAdwhNu14iwaYdJfnu2vE8NaDPomnbs2je9gxdTKjxJUlq2/o4bfeJK0YbSX3XZroAbGKuBxZYdG4Z/H/q3Dzw2miI9bs2P0n/06fQuv1Zumg/TxdxunHre5ou7E/RRf5J82Lfb9IjeZJhrgrmeffkIMT8rh1PkmQ+gxY6Z1vp/Oze8TCW9u/EydP9eOnls9hziqSSBLF7B7VXtI22HWcJEk9at43O8bb+Z4mng3jGmjeYVjF/x8i00sWlpf8ptNB3pJlEvIm+c43U9k6UJqKFbhBaaF1xDB20b9194vjoe0f71EN003t07ngKHXS8bX52mrTSsbWQcDeTRAtaSPjF3y00X7zWZtFBdEopfyxA6w66KPa/RMf4HLpJ7jtI1FvoJqSFbkJatwsekTRvM8VdSHwbLSOkvkPIPcMwNz7BN+7b6YZ9y6N04392CCIYcFreuIsggggmNG0luaZ2q160IzvPYx55af2ul0mwBaZU10g+iOo9r9H0QzTvNem0MppNbVLXNpL65ZtRWlWDlLR0EuzIyyDYqoFQ3Y3pRhzCk/IRVdyMvI4tmLPyKBq3UcO5+wW0kOW37H0JTXvFjtOdwc7nUUMHUtP3DGpJqOf1vYj6jY+jpKcP6XUPIKX2QUlmzVJk1/Qio2YZ0mqWDyJjGA9cAsuRXb0cM5nrgpy5y5E71/yfBP+Pxd+5c8cmZ+4KZFbT+TPnQeS3bcXs3n0obNuC9DlLkTW312IJMqoFi61pMOJ8sxj2GsNcGdJrliCV2ruU2lXyvCyobsXKlb342FP78PFnDmPl2o3Iq6Nl5XJE7QJiPj3vRSqd76nVK4jl9PcyuR05FX8PIVnMrx0Z8VpS9VIk0nckYc4SxM0WLJ4wCUQirZdE368UcUziu0SIdlyQ4ad2KdJqeyWpYlrXixQiuZbWpfUS5i5C3JyFiJ+9QE7F34n0mSRZx55Wu0T+JJtRu4gQ0yVIrl+FqpWnUDZ/J7Jpmylz6POpWSRJIZKqFyJ57gLavwVImm2SWDWfYZjLTo8k/hqRWNmDJAm1j1ULRmYWvUZtQOrshdQWUNs1dymi565C1oL9qNr8JOqsLAu/ZNfv8fMSGkTayK4X0dD/DJpJ4hs3Hkd+x1pEF8yDEjcTkZpHFgAR+deKY/Sa+xMSbLOjo4tE2yXL84Vq0Zhic0OLy0L+7GZUzt+ImvWn0S7SRnYImSap7n8B1f0vYnb/edT00w7vfAW1a04iLm8OJtsMTLG7MZUIoe2E2jxyOt0ixOafbxL4OzJaEmb3IswZg+nh7gkzlZhM27jH7mKuAybbXHQOueh/40JoEOJvMX/yqLhxL50v99i8uDM0Gp6UchTM6UE0Te8NpRvBcAMhcjviXDIw1abJ6XRa1zyH3LJOu+i0G0bTUKcHM+g8nM4wl4EZkeI8Gxnx2lS7B5MdsbBHGkiOuB999Xn42slV+Mojm/BgZz1smhtTwnXZNpq45HS6PVque7WYTkxzRA9jxiA8AULtJsHz/Ey7QALriuOO1MzP1haDex0pqKSLXFJBHaZEuOR8c53R93O6dSwMw1xeptL1dCq1axfLlEtkqs01jvdRu0tTwZQI8gVbAm6zZ0GrXI65m56QfQVr+kmud4hMC9GP8Dzad7+Ajl3PoL3vcTSuP4HyBduQVtEGV1I+7J4U8k4vebAXDnJgJ7XVYkwDRZYF1EaU7PdNfKQcTRb3dzgcMrnbPw0LC5OVRSIyq5FY3YuK3l1oFDl14ufIfefRvO8VNO86jxZxN7D2MFLyShEuy6mFIzIygi40djgjHYSYRgZQbESEBT3X7A4odrpTcKgSOSCB9XwiiLsMm+KQRceZ6wD6X4j/h6h1a9gHEH/blLEwR2QKV4S0GEjKKMasmg4kZxQhMsJulfVSJIqsh20zf8Kh7QqCB6JQg0ZmEoNWMMwlY51no+FwqDJQ4XNGoMR2J47Wp+OtY0vxrVOrsb59FjTNhoiIcLnctURRBg8wdi2Qg0TR99ch6tnSBT1ciUddhxhoZjZC6bseQdeNyEiFUIdhF9g1ua7iMBiGueyI75Z60TiojbFfJI6g7Yznfjphd5JoK7G4S8tETFUvatafQdOOF9Gy+zw697yA+Xufk/1EmjceR8WiPqRWL4SSMQv36knyRt7uFCLtkgMpOkX0Wgq2iGK7LMG2JPtiRnIMHnpSiLUYJU/Xdfk8IiKChMnA3REq7qI7ivtdyXBkVCKvYw3mrjyAlm2nZS5dD90VtK0/iMzCMthlz8sIKT9qkPyoVt3TkXGYI3NZ8mQOF6xdEFKkBtXdZq4VsryN9b81gvDXvVVHOQ/EOaLIL4yBUBEFzCpGVW0HUjOL5M2aIUdc8g9rKnKjzFHtRqunrYlRSBnmcjJGDXfRjooe6DHU/pXa78Sxeel4+7gQ7FWWYEdQmxpGbatyTVEU5ZqP1CbaCVOw6brjdEvBru9cheziOQin77pd7qs2Jsoog1AwDHOJiEFYtItH1TQrQ+LCcarWKK2BwefGRgyUGKr5MFlPRUzFfDRuOCH7kLT2PYqOLcdRv7wP2bXz4UgpxmQjEXc7ozHV6UK44YHm9tG+egLRaiHVl1WwhzV8ogag3S4PTjbIYr6ukWhrmEFvNE3z4j49AdNishFVWI9SahS7txxFz9rdmFlQJiM9qjUyWKCOoEVgGOBhKIEP1I/iUC4AS+pU5npgIgPKGM7hmOeHJu8mhWAnZRSisrZdTiMiImWnA1PCrYuzdSNnltIZvh+KNVIcw1wOxK8l4wm26NPic4ajxHYHjtal4c2jvfjmyZVY115pCnZk6LC27ppw3Ql2HOq7ViGHBDvC7pARMOUaR9kZ5r2K4ve/i0VRLkquJy7YWiDTQQTkREroVDUBSaUtaF97EM1rD6GwbRV8+XTDHp2KKQ43ptjIYWnZcE2H07BuAjRzNPOBYdmFYIsotptec9EyumyHlEsVbCHWg3CYDZxD8Y//biDSGkrdpoqpGUoXgwQ4k/IRm1OGmPjkwXcxavBdjDLicJQmA+POXxyq+Q+VQ2cyDQWaxwAALdVJREFU1xr7KPhfVwb9qjGAakWt7E4zRSQ+owjltR00LZQ/Gyty1Dfzy2sXQyzTBdou5Wfw+w8MdcowlxERCLiQFJG6dBLspSTYqyzBNlNELuWn18uCuDip1w41+BdHZSBFZF7naswsnkuCrcjrzngRannhczAMc9m5ZEHXLjpNZPwUES2AYvlCuNMj00Q8KYXwZVbCGZePGXoyQhUfeYIbdrGchfnrlz91VLHEWiWn1WSAxCb7JBryb0eQZ15yBNsv16rqz9Pzh80NK4Tusho38y5C/Fwv5FZEtkNVMaa7S64nkDttfWCRqsnYdy7aJTAg8cz1QeQI+F9zqtZ5NgxVnmfiJm56pAtxmUUorW1HHAl2SKTTkndFnlNmzrZdTu3K0Pe37oIZ5nIi20RlVES75xfsYhLsIyTY3yPB/gYJ9tq2WfKXPZF2528jrxWm4OrXEM26aXGY1xfngGDnSsFWA4LNMMy1YDyJHvsXMudFRq6dAfccC23gJlsKM0mx+BWM2pFQxUttiVcWOxDz7FYuuT/9WA3Iu5n5YAq2ajmLaL/VgFxHDo2qX44UkcEXk8EflHMIZmcVU55FBzWbiDw4/A35gGCP9kE6hwzbfumCzVxLBp0bY3aqHX6eqdbF3xEQbEOKdWltW0CwzUi4/07XIaPX9oBgj/AzE8NcEckeGXHeiT4rXmc4Cm134HB9Gt442ot/OyEEuwqqJjruRV77n4CvK8HWZCelQIpI0Ry6KJqdpC7tV02GYS6WKyHYg51PGfT3gFQrY6aHqDI1xP/cjGg7gqPT4oY90E9jILNBFkWQqaVmgG4g42FwNoUjKBjsHMdp3jcs7eMicIyAuYPWwcjn1s/z1s+k4kOQB6ioQxjYxvDtq5cIp4hcL4xWbcG8Yxwd83+oyVSk6XaXTBEprSHBzirEDLsj8IUY+r+2OxwjnqeXdk4olxHeh+tnHy5+P8arMiLaIdFXxesINQW7Lg3fPdKLrx9fiTUk2E4S7AgS7GtfReTaX7wHrhnmT7zip9y6rhXILqoa2FdFG6fN1xiGuSKM0X441DH7w/mv88PacIdqOd8I8yX+tFFFVgcxp/4UUrs11YLmK5Zgq1anaH+FMVVGtU3pFn4g2txIszqe5a/2Ma8Dgx11NK6YYA8W4qB5DiXQgDscI7w+pmBfq4s3c1Xle0xBMbEpZk3h2PQSFFe3ITYjP0iwR/oyqGPczLFY8j5cnnZivFJ98txVVRLsEBT7BfvwEnz92INSsFXdgUh75BW4YbgY1GuIEgjI2K1OStM1D+Z0LUJWcVngYj32NcR6bZxKIwzDXCDKOO5mfT/VEfG3h3aozgiospqcwxJff/vr7zjub1tVKy/aFGkXPfc4XDCkSJNYO8OJ6fTcRvPUgHD7q44NCLbZ2dxud8OIzUd2cS2ycwvgjnKbkh1IMR3pWhC8T1dRsINF2D6qIKuD7niUQARi6PJjidWlXjS5ysENUYlhDBwy5UPkVRtSsOOzy1DR0EnTIoRE2q2UkKFfhIFIlrwzdfhRRvjyTJQrcXPB+3Dj7sPAuas6RkcsY1MdJNjTURx+Ow7XpuE7lmCvba2Cdl0J9rXDf5Gz+wXbrmGabqB60QIS7BJ5YfVHohTHKNeOwOsMw1xuxvr+mkUwRg4yDESbbaYYOyICBQz8gi2v46otKMVTk4j2VQo2tQdRQpLtIhtCiHoIVPV+uS0xT27Pqh6mBF/vrRLPYY5YJBZ2om1pH2bVNsLtEYJtR6TqCKSUmjjkfCHfory0QyD36RoJ9khmPzyCPcLPBv4G0n9nE4Q/N+bCyvIN3b5jTHFjri/UUVAsoRJftjC7C76kbOSUzkZMcqZVumvg/zxwV6wG9X6mhkH0A5DwOcFc5vN21Dr+JmKZSNUOn30aSkiwj9Sm4LuHFuPrRx/EOhJsQxMlUCMvra27SRDXCbvdj4oQVUNedTUSMzLloFS63TEkKjb0hsYxSgSNYZhLYbzv7ujfyYFxT5RBAZKBdC8hr6KNtJFgiypgNvFcztesIEaE1Z4qgSoh5rZM+XVYf5tjrdjNKiJ2VRKpuAgPpmsZyKxeje71h1FZ0wzN0KRIS3mWQu2wsAcEW8i14oiw3usaCPaEJHyUnw4CEjxq9OdSG0vHmJEl5sbAHJ3R/EJGioo0bi+M6Hg5dajaoHMoOAcruGzPQCkfPieYy4s+AcEWlW1i7PdLwT5Mgv2dhxbha0dWYG3LbLg0VY5kyxdxZeBXTod5cQwTnZzjYqG73TBs9N22OSbQtrNkM8y1wTGoXRy4hjsskdbkL9Hhiltik7gIUQpPQRiJdRhJdhg9D1UNOXqzTbFGd/Uj0lWcHtlHwyYrh/mXU63ot2g/XPIXMHGjLt5jmjMGU///9s78O47rTM9JZIvaSQLopaqrqquru9HYAWIhdhAgSAAksRD7QoAAwQUkSHDfF1AUKXEnrdWyFJ3JnJyTyTie42Ri+8Rjeyxb0iwee+KZTPLvvLn3VnWjsZAiLYmgiPeH51R3o7twUOhb96mvvvt9iSbUjsxi7MR9NG3pUQsUXYk21R1EwzQVst9LMj/bNnU4AvdO5KP57pMT7CVvMywRwfai2Iv5qrf77Afsl3yrWLTYMaYGleEtpp3fsjoyd4VrLtUyOcLjSb5WFtZtX4itcrAtFcHelBLsKSHYR3BipAvRqKM6kvIWdDJ3OpZajCQnXr+sQRsWPxeTpZ28E6UWzrtNyxbPH0wTIWQ5iHgLDWOCuBincmuHhKyKi2VVMi9aBC23EqHCegQStdATdYiJx3Z2OfxCkjPFfL5avO81Kxf+eDnCBXUI51YjFC9W662CtoGQ47hCHc9HMJyLNWYusqKl0HNrYBU0wkpUImAKcQ87SpRDThyvRvKQWdKMlqmrGDp2HVWNW7zMCvecYZpW2p0za+78YrmN7OxUxD3ZM2C5BXvebfolxPeRBf2rFEaP4ElH68k3eCfEy61OFZ5PdZWy0pDpILEUiwXb4bEkX/u57mFRHfm91SK2ysHeqK/CnZ71+Lfb+/H7u0c9wY4KwbZWfBOLpFwb9hxudEogBDvkpY+4EW5vcpy3jmfhvEMIeZLIAJdcKyFzohOCmBivUbm+RMzFQbMAvlglSreOo2HgMNa17kN91zT6dp5CS9ck7MIKrDbjCOTXIHdDL5p6p9G96xx6xk+juWsP4mW1yBCCHcyOCaEW+4sVIZSoRk5VO+q792Hb+AV0TV5D2+ARlDV1wk4UCE/QEXCieNHJQ1ZlG9oPX0PvoVmU1mycSxlV24gX8Y7MpTPbVto6GttLV/lyt3zCgv0l5VsWfSYdCjZZ+P1YXOIvbJopLG+wWKazWLCTXd54LMkTFmx5mzNfLXJc5S5yFIL9ByHYJynY8wU7VeY1llrkpG4rW+7iR2tB6S8ZwY7YS0WvKTuEPGmiSwh2LGypPOhMsxD+/GY0T1zB4Ml30H/kBoYOX8HEsctoH5mCVdSArOxaVHfuQ8+Ba+g7dAM9U29h8MBNjB++jW07phAuK8VrsWxkxAoQSFShoWM3hg7OonfmMrbuncVW8f6ho7exQ4h0xaZu1X9grZ2N550iOE196D1+He27T6KgtDZNsK1vuWA/YDJaSrAX5uNRsImdtkI5tRJZrUIOufldpsTwkAMmKdgLrq5Vx1EKNlkewS4ws7DZE+z/d2sKv797BCeGuxBzHAp2umB7jcLSJ7TkrVvbmp+D7SjBnp97TcEm5JuKUD+cZJ3qdMGWY1TmW68OF0Mv78bmA29j8PzH2HboMtb3TaBgUzucqmZohZtQ2rIb/Yduo3P/TRRsmUFw/U5E6vZg48hFjB67gsrtvXgxkouXnGJEyrdi5+EbGD76Jgo6xrG6shuv1gyjoPMwxk6/j969F+EUVuFVp1AIdjkK2scwfPomNo9MI55fpgTb/hLBtpcU7MhTINj2A6LUj/L6oij2V8jBpgA8ZTLykP/XYwl2aIFgu4sRHE+yk5HseflhEbdbHf8P5Bs5zz2wMoas4W4pwW4JrcL9vioVwZ4v2M9uDvZc3eq0hhUPrLXrpJXXnJPsuXxJO9WlzV0YFUmV6Eyvq8t8WEKeNG6KiJJsMffKsnqyPrUjzpGyYdSLZgWchlH0HH8X24UYF7cMwJe7Hi/peXg5VIZ47Si6976FsYNvoHzjoBDjGjwfqsTzViOMymEMH74spPkI9HgJMoMxxEs2YWPPNPIbB7AqWonnIjX493YDXijZjs4j9zB+4joKKuqwxinCqkQDqgYPYujEm6jvGkMkUaCi1ylS6z88wV5Qgc566nKwCXkcuX4UyfaiVtF5K5QtJdiuXGuLJDv9IivZypT/C/IkMT3BlikiLeYL+F5/tRDsafzTHU+wZbTWMJ7ptRNm2toJ06smkJ5rbaRSQiJL4i5mtr2FVG4lAr8TV2X8ghG3hu48web3jpBlmdsjnmDLKHbMa18esIuFLNejsG0fhs/eR+vEcdiF1QiEcuHXC+GzN6Ci/RTGjn+AgZ2HUVpahUh2Cey8amTlb0Soth/9+y9i1+FLyBevhTPF73TKoeVthLluM6LV2xBvHkR0007kdOxHx4nvYcexN1BQuh6rIwV4Jb8VmybOCkl/HRWbuxGOJdLWbdkLgrJLlfK1HvlYULDJUy7YC5sOPbyIvT0vB9u9IlW3lL3C+Mn9ULDJ0yDYb/fX4P/eObDiBTu0YDFj6KGCbaelh7gToalSbyxVO9eyQ3MX3JbF7x0hyzS/R9IkW0azI+JnvnAxVtlNqOg+gpEzd1HfPwUzsQ5BI4GgWYxwXgsahy5h7PTHGJy+gm3D02gdmkbb6BE07jiF5l2XMHrsOkYPXkS0oEmIeSnCRW0o37IXW8dPomPyOFomTmDTngvYMn0VwxfeR8/+s8gtLsWr4TysLt2G9qlZDM1cREl9mzhnxB6SVfGgXhkP8BIKNnl6bqU/SkqPtfSV45K34OeEWi6ECslyQKZXccDr5vm4V6CEfLMR7Br82+1p/O7OYSHYnStEsOdLdsgT7NCSgm0vwlrUL0GHY2li/0lkQwgjVTOf3ztClm+OTwp2cp5eaxVhVUxI9MgZjJy6JcR4GAEnV8h1NgJWIZySNmze+QZGzn6CnqP30DF9TXBVbdsO3lB0TV3GpoFpVc86I7sFNT3HMHj8bXTum0Vtz27ktY4g1jKGmtGTGL30HrbunEEsrxAvWeL31PZh+8wV9Ow7gbz1G1RVogf/HY/SjI6CTb5lgm2lT6ZeRybZtlROvEFbDERHrhwuRyBnPfyJCrXVcytVXc1AbrV4LrY5FQjlrIMZz/ciX3JfoVQNbdtmBJtQsJ8uwY6rurZBuRWTbiCcgN/OhU9s9VgBQtlFsBLFakyrBhWyBKc6l+iIhCWaJ9cPqVBFCFmWdSly/K+2ivFaXju27L6MwaNXUdTYKca57MwcEdtcREvb0Dp5Bf3H30Fd7zRyazuQqGlHrLoDkZpeOPUDSFS3I17SiBfsWth1OzF24h4Gpi8jp3oLAtECPB8qUTnYBR17MX7hPpr7dyGSyFGC7TSPol/83o6x/UiUlEE37W9OsOfXDSbkSWGnurQthUzpCKn3mCo6JTsphcTnfOFsrIkUQy9pRm7LOEo696OoY0ptS7sPumyX7Mf6rr2obt+J8g1bYEXi6vfKaJf83bKjk7tgiv8L8uRQgm15gh1yc7BlHezf3T6M40Nzgv1sHwM3ZSuJbAIRCicFOxtBMcalUPudImTGymCXNIlJth0VrQNiPI+goWsM5Zv7kFO5GYa4iA6G46r7mqwgEhXnCrdbXLLagXdnixCyDGPdnPdczukvC8H2retDz8Hr6J06h7zqjUJy3c6JAXkeKKrHhtFz6D1yC1WbeqAZQrwFmVoUr5iFyEpUIxQrRpYWwwuxBhT3ncaB2fewqXNUvC8G0x/Ei1oBnivoQOPOM5g8fxPVrd0wIjG8ZCaQu3USQ8euoq13REm3bphf8neYX8KDP0vBJk+vYIcjaVJsqsHpsxN4ySlFomkQnYfexNjFDxWjF7+P0Qtz7LzwgbhyfRfjZ25i++gUIrFslZcdpWCTp1Gwb80IwW5fUYJtLZJsV7Q1Icx+Mc7lnaiClhG07TqF0ZM3sPP0bUxeuIc9F7+HHaduoOfAZVRtn4JR0qjOC8GwTB1JCnay5j0Fm5Dlw5w352thW0huMey6CQwcvoWuXceQU1abek9QnAMy4+XIa59C5+Hb2DJ2FLkVm6DnrIcvVoHwus2o3jaGxtYemOIi/LXsBlQMnMK+2ffRMnQQRm4N7EQZAkUtyO06hpFTd7Hn9DWUb2hBwLTwcrgA6/sOYUQIdlP7dtjxWFq3Rgo2eVZIdkyyHowUbCkkjrdoURcDYW04F6ucCiQ2j2H7sTsYvfQRek+9g44jd9EuBuQct9AxcxPbpmbRtH0HokKw5QLImKmr3y9vRZsUbPKk5dKUF4om8g1XsO/3CcG+dQD/eOsQjg22w5Gl5p5hwTbTI9hmErlewhbjO6JuE+umEO14AcrFRLr9+H3snP0Iw+fex+apax5Xxdi/ix0XPkT/2Q/QMHocemkDMsNystTU+cI24x62V0WI3z1CnnT0OknywlqmY7yoF6Og7RBGT9zHlqEpRAvKvECapdZMvWYV4tXSTlSMXkCvmONbJy6gcvt+dTHduvM0hmeuomt4D2LZRXg1XI7sTeMYPnUfQyfuoXnkJBr7DqJu9By2HHsPuy69i6lTs1hX2ygE2xQX7RVo3n0eO4RgV2zY5KarfSW5frhkU7DJssi12ywiXahtb/J1B6JapOgJdrIyiJyEV5vZqs5lcfte9Jx4WwzAe6js3ododQfClR0wK7tgCezKdkSrtiG7qgXR/DI4TtQt62dqaiC79XUjabUvCVlmwR7YpspYrQzBTpuATTmxWuoCOiDGeJZdiLy6Dgwdu46x2Y/Rd+QtlG8dQ3DdJmQUNWNt0SbkNO8QE+Xr6Dv7CQbPvofirTvhzykR+zM8wY6lBJvjm5DlE+v0O1dSsNeE8rC+dRwj+8+juWMITqJQVReJ2O6Fd6aVjReccoSru7B5xwxGpi9i4shlTBydxciBM2jp2YXCinqY4bg4VxTBl1+H+u7dGBDvmzxxTQj1NfTuO4/K3mmxPY2x6aMoqapVDb4iRRXYNnEYvXuPin1UqrSUOe+gYJNnSa5ltyQriZ02MN1crWRL5LBpKMGWE/EaKdixapT1zGDg9PfRfegtlNa2QDNMZBkxZImf+4w4tFAMhi4+r5swDPlZuQ8tlaOZ6hBKwSbLJNibPcH+P7cP4B9uHMSR3i3qO/nsp4gkJ2G5tkJTx0SObTnZ+eRCp9w6bBg+hfELH6D/xPdQ0tyDoCk7wDkI2DG12HFNqABWdT/ajnyAkdlP0LpvFvq6enVsbVWiM+Zh83tHyBNMCVlKsJNjXF5EW5FsFKyrQkV1IwpKKxF24m7pXNud84PqTpYY6wInOx9lVfWoa2xGdW0j8opLYcdyYcn1Goal7nYFZd52JIHc4gps3tqFqoZmRHKLEYzlI7dUuEJ9I5y8fLE/A0YsiuLqWhRVViMs00Nsy+WBgm1RsMm3SbCTdantBdFrWSVETw3MkCfZrmCb3udcwX45XoPqviMYPvkuuvZcxLrKBvUeIxIXJFQb9JgYgLKwfSxseS2UxTYcUoKd7PqYXjeb/xtCwX7SuZm6ize2pWAHZUpHWTO2T13B7vNvo238JIycMnGx7FfnBSNiu6X8zARWxxtRs/sGdlz6j+g6/Kb4XBMFm5CnKYKd6kXhCrbpdUrUdRMBzUA4EhU43jqJuQtt00PX9Xlomia2Rmp/oRSeU4g53xcIImCYKt9b5l37BH55bgmbKk0ky9DVVtXNT5Nr8xs4FhRssmwRrFASW6ILAt425P3M+9Kr27xu5DtDTKyvJerROHQUk2fexvaJU8gTV8P+kCEGjqOi2IYRgSMGsGw5bQhZkYTFoLJlBNsMqKokEdmMQmB70XH+X8iTwEgJdqYS7Hu91fjXW1P4u+vTmOlpUxONsSIEe8FaDMNWf7cmq4GU1KJr8jjGDl1Ac/sIwrE8VV5TF2NYCrZcOxGxs/GSVYnK0dex4+KH6D16DZHyDSnBtk1H7NehYBOyTIItxdpdA2GL+dfytnZqPldzuuWWuEsGHwxjDvMh83JyXnffaymUaHuSLe9oq7teQrI121JyLbfh7CjMeBR2trj4dhx1PgnZFGzyDA7AkCq9Z7hCrfDk2ruydCPYbjqJ5S2GkoK9Nm8DNo6ewtjpd9Ayegaxijbo+dUw1jUpIoUNiOZVw8peB8PJQ9iJwolYiEVkBDugItmyfqUs6yUF+8tWAhNCwf5mKom4Y9sR4zCi0rg0U4cWTcAuqkKiYD0S2UVinAqhjshby7IKgaVuHweNbGTmNGLj3jcxftHt1BYuqVLlvtyoGQWbkOW+eJbjeikc2UjK8CRc5l6bZpo0LyYp4DKKnf66rjAVyWi2lO2kYCvJtqRci+eq06s4h0ipTmJTsMkzHMFOfvnlxKkpsRYTbiSmala6CxEddUvJ8iQ7y8xVi53a9ryOwXM/QMuB22icnEXX4evoP30f/SfvY/vhW0LAzyKnoRevOUVYG5QDU4Md8iMuBDuSajZjP1KpHUK+TsGW3/m8NMH+l5v78cVbB+YEW9dXwDoMt0qQKsXpTbpSsHVTc88JYRuOmByzQ6bYGuqCWL4uS/FlmHGsNovhVHaj+/BdTJy5g8auHQhlF6gJVV2Yy/UdCgo2IU+DYMuOjvNFe24B8sME20xLGUmJtUoZ8eTay+1OPU57zZVsed4whGDLOtsSIxXRlt4RYooIefYEe24ho7qNIydbO+Z2cTMcaKEI/EHZJSmuJmPZdVGK9hpdPF+/FVv2XcGOC59gRDB+6UOMnX8Xw2fvY+TcexgW4j128WMMHLmO0s0DyLAS6mrZMXVPsE2vs2OE/w9CwV4mwdaWEGzD1FRethyrsZCBRMiYE2w5GTpRrNJy8KLTgI07zmD0zLsYPHgJxbXN0CIxb8KUZf+cVAlAfu8Ieboi2I8j2A/GTFUfejimSj2Tkh3wkM/dC3kKNnkmF3vNRbG0sBDqcDYCoWxkBqLIyHIEYWT6w/AFxMAI6mpRhBTs1cEYnKp2dO6/gokLP0D/0dvYODiNdZv6kFu7DSUtw2jbdQmDp95TjWYGDl1GfmWzkHUNYV1DTOVfU7DJ8gv2ptAq3O2twh9vTuHzNw/gUHfryhFsa75gO6btVSBIyrXERDRkq7J7svyenAzXahpecioQbT3ojnEh2PVdu2DEctVt4aRgJ2tsM0WEEAq2EuqFpIopULDJMxvFiqnWyMFwIaqbelHTPICazcNoaBO0DmBDSzcamrcgO68QumEjQ4vBl70e8drtWL9tEvkNvQjGy5ARigtiWCNTSAqaUN07g5HT9zF29j66RqcRy86HaehumT4h2EqubU6+ZHkEOze01hXsvir8y4oUbDt1B0tOtDIdJOyJdNR0I9fRkAXHcAVcirjfjuMVK4FowwC6jn8oLqA/Uo0nQvk1qpVy0Mtvl/tOppSxzj0hy1cxLLnIcSmsr0GwDdP8Url2WSzYIQo2eZbLdMkvtKxh6Qvn4rVIOTrHz2PfuQ+w5/xHmBTbyXNv49CltzF95hoqGloRjiTEFWtMRbplvetMK1dtA6GIW/PadFRdTJ94LVK2ERsnzmPHhR9g5OBFVFRvgKabqhqBrLkp5dqmYJMnetdm7kSfCK7BRu0F3Ourxb/cOoDPVpJgW3MNZyyv06LbHMaVb0dcSGeHbBW9tlV1gDiytGys0gvhq+zC9pmb2HXpz9GxZxY51S3wO3kIqIt1OyXUdhqUbEKWR7C/lK8h1fRRCS1gqfdQsMkzI9iWyoESwuwJdmPvDDomX8e23W+iZeIy2vddQc/ec+gZn0HR+g3i/TEYWhihYBia2AZCLqYeFhOxjIK55b78QR3+aD6KOvZjSOZpz7yByvrN6r2Wil5TsMnyCnZ2UrAHavGvK1Cwk5Fsy5NrlWedJtgqNSQkjpkQ7IC4kM5wKhEob0frwRuYuPQh+mZuIFHTLsa5uMD26t3KSdMt0bcQCjYhXPdlfeMRawo2eYquat2os4xQBYVkh+JlgvUIxCrhi5YJSqFHixCLFyBiOQgL8QjL+ta6Dd2QnZ5iqttTyJyrMmJIwRYinSE+l926G72nf4Adh6+iunELAob9xAYWIQ8V7MAaNCnBdhc5fnZtPw5ub1HjYsUItnc+kHItSZ4Xwqr5kyzHpSOgG3g1UoI1JVvQfuAqdl/+WK2ryK1rRZYTF3KtIWgFxHENqM/Y3r5ckk1nKNiEULC/+Yg1BZsss2S4Cxwtr/5tEje9I6LyrC07Dk3WslQyLSbJkIGY+GxMNpGQtXOFjAfDeSryHQjHVcUAy3JLcsnPy9d88XLktO1F76kPMXrkGmqbO1wZty1KNnk6Itj6Ktwf8FJEPMFWHUlXkGCHPQl20kTYVPXxdTHGbazRosgs2IC68fPYdfF9DM1cR0H9VmSETWQJqQ5aPugCw/SLfQXUAsmohxsVNz1hZylOQsiT5d+l1xgk5JvHFWwZdQ6p6LODoBRrT65DavW/4y5MMPyqdJdtuEIuf27GSlDTugNdIzNqEWQkt0TJeHL/spJAQOZl51SjoP0AeoRgDx16HeV1rfDJ37mgNSr/H+RJYniLbrI1KdjPC8Guwx9v7cdvrk7hQGezapMuBXslHZOkYKtFjmK8yzbGmeEIsiIlMPM2oXnoGMYvvivkWozjjT3Qo3nwawH49QACRlCM+aCKYJsCW0m2RFOynezUyu8eIeRJQ8EmT1yw3Y5LtpLqoIcSbO91iSFvEZs+8X5dRbjl4kafJFqBxu4ZTBy9jd7x48heV4+sUBhGJKIqEvjEZ33hAoTXtaJu9CL6znykBLuoogF+w6Zgk2VHCnZigWB/KgR7/4oV7OSCRPd5lhjvL5gJ+BIbsbH3LHadeRfDJ26hvG0IeqwAWZqJYFAItqaJsW+KcW0qKdcNTXxeRrL9SrTDQrJl2oiUdn7vCCEUbPLMR/BCaZI9J9SmantqyG5ulq4iUjKCLZ+bhgND5lwLMs1ilG/chZGDtzF69BZquvYgWFCDl8O5eEVMyi+YeXg1WoPC1j3oPPI2uo6/h82DhxDJLlY52ItWEfN/QpYhgq0EW3se94Rg/++b+/HrK/sw1bHRFWxjBQihYaoFjGGFmwZmq9ci8FkFqg36+u6j6Dv+IYaPv4vKrkNYk6jDS04hVtsJZNriXGDnIjMsxnW0BAEnD2uDBvx6UBzjgBjffrU1TCMFv3+EEAo2WQETrDUPw+vipssFS2JylNvUBOkJtiYm34xQHpySdrTtOIex0+9i4Nht1A8cRM7GPoRrOhCu7UZRxxS27r+O3pPvo1Vs82o7VXfIUNihYJOnR7BVDnYd/pgS7KYVJdhhccHrkhRsS11MB6KVKGnZjb5j76H77J+h98h7aB29hLreadT07UJ9/zga+3eiqX8PmvoOoG3oINrE44Yt3XDy8hC0NHUOcSXbUMfc4HePEELBJitHsudIjzTJBU4hMUlKXMGOKDRZIUSKdrgI0ZJmNAixHjx+A4On7qD7yA10HrqGLkH/0evYceIGevadxfrWQRg5ZSoFRTaroGCTp0OwM5Rgqwj2jf342yt7sa+9aYVFsF3BVnIdctdaGKE4tEQ1GvpmMHbuAwyc/QhDp7+P4RPvCO5h6ORNDJ+8gRHFTYyevIWJ07cweeotjOw/gYKyKrWQ1PBysinYhBAKNlnx4jEfN6LtCrbtCbYlcAXEF47BWFeP4q3j2LDzHNr2v4X2mTvYfvgmtuw+jQ29O1HZsAk5OXmuWIcjXuc4CjahYD8tgm16gu1IwdbFhXQoW62zSDQNoLrvCCr7TzyYvmOoHDiMmsFDaBicRtXWIYTz1qm1HG7+tcb8a0IIBZtQPBYLtu7lYLs527rh5WkL5CQqKw0E4gWwSpoQr2xHbm0X8mrbESutg5nIhxVx1L6TOd+yc9yiWpg89mSZBfufpWC/LgW7EaaurzjBlhcVYUMXf7sY11oYPisX/kSFaoFu5NYuIpRfCy2/DkGxDeRXw5e/HsHCSvhi+eLCW1yIW8lzh84INiGEgk3Il8qJJ9cK1YjCB133q+i2Gc5WqEi3HoCmrVE/k8KiJnPTfGBtYkIo2MuxBsN2704pEdbEY02MWU11XPWHZLnOCJyQuYiwt0BSXmT7xb4yQzqywhYyhKT7xb6Clotu6l66CAWbEELBJuQRkeW3NLhl/GzYVkxsY96kLSZWPajKdsnH6beJKdhkuQU7KMgOuoJ9t68Of7g+hV+9vgd7V4pgGwsWOXtjeU6yxTHQDa8+trEIWdvatgwxft2KQwFDS0l1Ei0l1xRsQggFm5A/abK2pWCbyYoElnpNl5JtuFEsg4JNKNhPWfQ6Ofbc9JBwUrAFdkiDE3K3trkUsqGMP4VhZELWvw5ZAVVBRGPkmhBCwSbkq4lKUD1P1tN1J275mua1pF5YA5eCTZ4WwW4Sgn2nvxa/F4L9SynY21ZQioiHKtEncHT52B2rYSMdId9CtBdiyjtT8jilWGodBwWbEELBJuSxkJLiC5sIhN1FjEnBNgTyNfmz4BKfo2CT5RdsyxPs53FnoFZFsJOCbTzzgm14KSG6F702EdMtxDQLtm6nLXy0U2M6Jdoe6g6V6VYWknWzTSOWIqxes1LrLgghhIJNyGMgF4oFPNE2UnmdcxHCgPceHivyNAp2PLAGjdrzuDtQrQT7F0Kw92wRgq2tBMFOIy2CvSg3O1Un31gUrZYX1Ya3UNIl4m3TPsfvGyGEgk3I44vKg24B8/YweVqRYhgQMhjzr0Zj4Du4O1iFf765Xwj2Xk+wV0IdbGPewuP0hlOLF0MuJdn8HhFCKNiEEELmCbajBHtD4DncG6xUZfr+5vIe7EoKtm6sqDzshy1gfiD8LhFCKNiEEEKSgh1Ugr0GG7T/MF+wWzcgFNTdMnUUbEII+XYL9rzmHYQQQr5B5gS7UXsO94Yq8YebQrBnFws2IYSQby8UbEIIoWATQgihYBNCyLcPXQi2FvIEWy1yrMTvb7iCPdE2J9iUbEIIoWATQgh5RMFOj2DLKiK/v74fP7+0GxMtDdAClGtCCKFgE0IIeSzB1o0Y4oEMNOrfwd2hKvzT9Sn8r4uTGKdgE0IIBZsQQsjXLdgaBZsQQijYhBBCHi9FJE2wB6vwu7em8LPzuzC2qR5BXxCapvFYEUIIBZsQQggFmxBCCAWbEEKeuGCb7iJHT7DvCMH+xzf3eYJdR8EmhBAKNiGEEAo2IYQQCjYhhDwFgr1BCXYl/kEI9k/PTcwJdpCCTQghFGxCCCFfTbDPe4IdCELXWEWEEEIo2IQQQr6yYI8216gINgWbEEIo2IQQQv4Uwda+i9sDlfj7N/fiJ+cmsIOCTQghFGxCCCFfXbBlBHueYLPRDCGEfPsFW57MCSGEPAlMaCEh2P4MNGrfwe3BSvz9tb3467PjGGmqQsAX4DEihJBnAAo2IYQsh2Dr38WdwWol2P/jzE4MU7AJIYSCTQgh5PEFO6AEe40S7NtDVfg7Idj//fQYhhorKdiEEELBJoQQ8viCHUFcCnboedwdqlaC/eNToxjasJ6CTQghFGxCCCGPgyYFW4uoCHaTEuwafH51D/7q5A4MCsH2ScHWeJwIIYSCTQgh5LEEW0awNwnBvucJ9o+EYPdvqKBgE0IIBZsQQshjCbZmCjzB1twI9mdXd+OHJ0Yo2IQQQsEmhBDypwp2dppg/1YI9l8Kwe6jYBNCCAWbEELI4wq2oVJE0gX70zd2478Kwe6tr0BWFgWbEEIo2IQQQv4kwW7R3BxsKdh/QcEmhBAKNiGEkD9VsG0l2Js1t0zfr9+YFII9nBJsTZPv0+bBY0cIIRRsQgghX0Gwg8FgCgo2IYRQsAkhZGWjPeDxUoI9WIW/vbIL/+X4IHoayh4s2EwbIYQQCjYhhKxYudbSxFpsjS8V7PFFgj0vPWThPgkhhFCwCSFkZQm24cmwlGMNpng9EfShMSeMrtJs9JXFsKNEw6Hytfhkog6/uTyCH5/swdn2MnQXGegtd7C9Igcb1uUi27FgpO+Tok0IIRRsQghZeYJtehIcVIId1k2UBV7F5a4a/NXpEfzNhSH84lw3fnW+C7+91IsvZvvx2aU+/PJ8D352phs/OdOPH53biWv7BlBXnAPT75vbJwWbEEK+HYK9cLU6IYSQPxXDayYj0zxcwbaFYBetXoUjtTH8z1OD+OLaCL54vQ9fXO7B51cGxPNhfHF1SDzuF6/147dXRvHT1/fg8kQn1jkGrEAgTbB5jAkh5NsABZsQQr5WwQ57Wy+CLeQ479UX0G2/iD/b0yokeghfzPbgi/Nd+OLCdvG4b47LA/j0yi78xelRTG6ugONfIz6vUbAJIYSCTQghKzuCHRDboPeaIcj1rUZt5vO42rEOvzqzHZ8Lwf5cCLZLNz6/1Ou+JuT752/swzvTA2jKDSPkyxKCbYh9mF4utkbJJoQQCjYhhKwMpFAHhAT7hRBLfLLcnvpZENFgBor8L2NXqYYfz7QIke7D5xeFWJ/fPk+wP50dwQ8v7sXJoXbkaj6VamLqJqyglGwjFcWmZBNCCAWbEEKeeblOF+wsSUiKtnw9CCvgQzyQga3RV/CfJqvx2Ww3PruYhhDszy734FdXxvDJ6UkMNFVDz1wLnxDrsGHDkIItCAV1D/F7gzzuhBBCwSaEkGdZsIX4SsEOeBHsLC9NRAp2KBhQixXX+76Dqy0afn5ys5DqdMEWXO7Gz2aHcW2yG+vjDvwZGVgbNFTayZxgz0k2BZsQQijYhBDy7KIiynOCnZTspGBrSrKDKPE9j+myl/DD/fX47YUe/FaW6jvXKR534dPZfvy3s4OY6WpCwjRUekhWyITPFxRyrStCaVCwCSGEgk0IIc9+JDso25zPCXYyRSQp2XmBl7BF+w7eG6wQYt3rCvaFTrX91ewoPp7pR3d1EcKy66PYj9yXFGnDI5UawhQRQgihYBNCyEqLZPsVmiCQkuy4fzXKXnsO55sT+OXhdvzmTCd+c05sL/XhJ7OTeGN0G6qyLSHWQswDuiKZcx1KF2wea0IIoWATQshKXPQYXBDBjvgzkbvmRYwVBPCXk834zfk+Idid+PWlEfznUxPYvblaLYYMBoMIBIJKtDVGrQkhhIJNCCFkaeRCx1hWBhq1F3CnvRC/PtONTy/14xeXx3H/wBBa1uVCX/OKEuwkPG6EEELBJoQQ8gBkNZGIkOySNd/FiaoA/vroVnx6bSd+emknTvVvQpHpR2DNaxRrQgihYBNCCHm0HO2g29lxzSqM5HwXH0824Jev78SfH+nBYF0eLN8r0AJZFGxCCKFgE0IIeXQMxLJeQYP/OVzsXIcfnRvHrfE21OWE4M94BQEKNiGEULAJIYQ8GrK6SJZmwvJnoDDjeYxVx/G9qT6c6W/BurgBXzALgaCPgk0IIRRsQgghj4KsKuITkm36fcjOeAXNORHs2dqM7poyOCF/quIIBZsQQr7lgp2+Wp0QQsg3iJBnvyzZJx6HfUEUhR1U5xehMBpTP/fxGBFCyDPB/wfZ49dVMvduhwAAAABJRU5ErkJggg==)
We can think of sine waves as projections onto one axis of a vector traveling around a circle, like the hand of a clock. If we're looking at the position of the clock hand only on one axis, it will make a sine wave-type pattern. In the case of the Fourier transform, the two dimensions are the real and imaginary number lines. We can think of Fourier coefficients describing a 3-d sine wave that spirals through time (t) with frequency f. The higher the frequency, the tighter the spiral. The larger the magnitude, the larger the spiral's radius is (its path is farther from the origin).
Image credits: Michael X. Cohen
create_figure('sin wave', 1, 2);
yf = fft(y); % Fourier transform
yf = abs(yf/L); % When X is complex, ABS(X) is the complex modulus (magnitude) of the elements of X
f = Fs*(0:(L-1))/L; % define frequencies for each element of yf
nyquist = Fs ./ 2; % Any signal faster than Nyquist freq will be aliased
h = plot_vertical_line(nyquist);
Aliasing
When a signal is sampled too slowly, it produces a phenomenon known as aliasing, in which an underlying higher-frequency signal appears to be a lower-frequency one. This occurs because the sample points capture values of the true high-frequency signal at systematic points in the phase of the true signal, as illustrated in the figure below.
Let's say we have a true signal that consists of a sine wave at F = 10 Hz, originally sampled at Fs = 1,000 Hz. This is shown in blue. What happens if we sample the signal at Fs = 20 Hz? We observe a sample every 1/2 cycle of the original wave, resulting in a constant value for every sample! This is shown by the black line in the figure. The 10 Hz signal has been aliased to a constant value.
Let's say we sample the signal at 15 Hz, shown in the center panel in the figure. Now, we have still not captured the frequency of the actual signal -- the observed samples appear to be moving more slowly in time. They are still aliased to a lower temporal frequency.
Finally, let's sample at 40 Hz. Now we capture the underlying waveform and its frequency very accurately, without aliasing.
What is happening is that the frequency of the signal is being reflected around a particuar value -- 1/2 the sampling frequency. This is called the Nyquist frequency, or "folding frequency". If we sample at 15 Hz, for example, the Nyquist frequency is 1/15 = 7.5 Hz. Any signal faster than that, e.g., our 10 Hz signal, will be reflected back to a lower frequency. As the 10 Hz signal is 2.5 Hz above the Nyquist, the aliased signal will have a frequency of 2.5 Hz below the Nyquist, or 5 Hz.
Fs = 1000; % Sampling frequency, e.g., Hz (samples/sec)
T = 1/Fs; % Sampling period (time between samples, e.g., sec)
L = Fs * 5; % Length of signal (in samples) for 5 sec signal
t = (0:L-1)*T; % Time vector
y = sin(2 * pi * F * t + theta);
Fs = 20; % New sampling frequency
downsample_by = round(1000/Fs);
plot(t(1:downsample_by:end), y(1:downsample_by:end), 'k.-', 'LineWidth', 2);
title(sprintf('Sampling rate = %3.1f, Nyquist limit = %3.2f', Fs, Nyquist))
Fs = 12; % New sampling frequency
downsample_by = round(1000/Fs);
plot(t(1:downsample_by:end), y(1:downsample_by:end), 'k.-', 'LineWidth', 2);
title(sprintf('Sampling rate = %3.1f, Nyquist limit = %3.2f', Fs, Nyquist))
Fs = 40; % New sampling frequency
downsample_by = round(1000/Fs);
plot(t(1:downsample_by:end), y(1:downsample_by:end), 'k.-', 'LineWidth', 2);
title(sprintf('Sampling rate = %3.1f, Nyquist limit = %3.2f', Fs, Nyquist))
This example shows aliasing in time, but aliasing can occur in space as well. For example, when a moving wheel on a car is sampled at a lower frame rate in a movie, the spokes of the wheel sometimes appear to be moving backwards. Another example is the Moire effect. When gratings of parallel lines and spaces are offset from one another, a lower-frequency pattern of light and dark bars appears due to spatial aliasing.
Spatial aliasing produces ghosting or 'wrap-around' artifacts in MRI.
Explore: Effects of sampling rate on aliasing
Now let's look at the effect of down-sampling the signal to a new, lower-frequency sampling rate Fs.
You can change the slider values and it will re-generate plots with the new sampling rate.
Fs_high = 1000; % Sampling frequency, e.g., Hz (samples/sec)
T = 1/Fs_high; % Sampling period (time between samples, e.g., sec)
L = Fs_high * 5; % Length of signal (in samples) for 5 sec signal
t = (0:L-1)*T; % Time vector
y = sin(2 * pi * F * t + theta);
Fs = 20; % New sampling frequency
plot_signals_with_downsampling(y, t, Fs, F)
The top panel shows the original signal at 1000 Hz (black) and signal sampled at the new, downsampled rate (pink). If the lines are on top of one another, there's no aliasing due to the reduced sampling rate. But if the pink line appears to be moving at a slower frequency, it is aliased.
Explore: Effects of phase on aliasing
Now let's look at the effect of changing the phase (theta).
You can change the slider values and it will re-generate plots with the new phase.
Fs_high = 1000; % Sampling frequency, e.g., Hz (samples/sec)
T = 1/Fs_high; % Sampling period (time between samples, e.g., sec)
% length of signal in sec
L = Fs_high * num_sec; % Length of signal (in samples)
t = (0:L-1)*T; % Time vector
y = sin(2 * pi * F * t + theta);
plot_signals_with_downsampling(y, t, Fs, F)
What do you notice about the aliasing effects as you change the phase (theta)? Why?
Which of the values that you can adjust in the sliders impact aliasing? Describe the impact of each.
What happens as you truncate the timeseries to make it short, as opposed to very long? Why does this happen?
More Exercises
The Nyquist frequency is 1/2 the sampling rate. Any signal with frequencies higher than that (faster oscillation) will be aliased back into the low frequency range.
In these examples, the sampling frequency is very high (e.g., 1000 Hz), and the underlying frequency of the sin wave is very low. So there is no problem with aliasing. Now let's look at a case where we're sampling a faster-moving underlying frequency with a lower sampling rate.
Fs = 50; % Rate we're sampling at: Sampling frequency, e.g., Hz (samples/sec)
T = 1/Fs; % Sampling period (time between samples, e.g., sec)
L = 150; % Length of signal (in samples)
t = (0:L-1)*T; % Time vector
F = 20; % Frequency of underlying signal we're detecting (cycles/sec, e.g., Hz)
y = sin(2 * pi * F * t + theta);
create_figure('sin wave', 1, 2)
ans =
Figure (sin wave) with properties:
Number: 7
Name: 'sin wave'
Color: [1 1 1]
Position: [680 558 560 420]
Units: 'pixels'
Show all properties
yf = fft(y); % Fourier transform
yf = abs(yf/L); % When X is complex, ABS(X) is the complex modulus (magnitude) of the elements of X
yf = 2 * yf(1:L/2+1); % Take only the half of frequencies below the nyquist
f = Fs*(0:(L/2))/L; % define frequencies for each element of yf
title('Frequency domain')
nyquist = Fs ./ 2; % Any signal faster than Nyquist freq will be aliased
h = plot_vertical_line(nyquist);
What is the frequency of the underlying signal?
What is the sampling rate for this signal?
What is the Nyquist frequency?
Would we expect aliasing?
How can I tell from the FFT plot that the signal is/is not aliased?
What signal frequencies (Fs) would you expect to produce aliasing based on the Nyquist frequency? 10, 15, 20, 25, 30, 40...?
At what sampling frequency would the ability to detect a 30 Hz signal break down and start to produced aliased lower-frequency signals? Modify the code to try it and test your answer.
Subfunctions
These functions simplify the code above, making some specialized plots, etc. You can run them by running code blocks in the Live Script editor.
function plot_signals_with_downsampling(y, t, Fs, F)
downsample_by = round(1000/Fs);
plot(t, y, 'k-'); hold on
set(gcf, 'Position', [0 644 1358 231])
plot(t(1:downsample_by:end), y(1:downsample_by:end), '.-', 'Color', [1 .3 .6], 'LineWidth', 2);
title(sprintf('Sampling rate = %3.1f, Nyquist limit = %3.2f', Fs, Nyquist))
[myfft, freq, line_han] = fft_calc(y, 1/1000);
set(line_han, 'Color', 'k', 'LineWidth', 2, 'LineStyle', '-');
[myfft, freq, line_han] = fft_calc(y(1:downsample_by:end), 1/Fs);
set(line_han, 'Color', [1 .3 .6], 'LineWidth', 2, 'LineStyle', '-');
set(gca, 'XLim', [0 (max(Fs, 1.2 * F))]);