Numerical solution of systems of linear equationsAle\305\241 N\304\233me\304\215ek & Mirko NavaraeUlweUlyPEtfVG5eVF47Rlo7cktYXjp2eVV1SkBqOkY6Ojo6Ojo6Ojo6WnlZVUBqOkBqOjo6Ojo6Ojo6Ojp2eTpVPktKSkFKW0lqOkRcXDxGXFw7VlpLRlp5YVJ5ajpOWjxWWjtGWjtGWjo+Ojs6XFxqPlhKP0xqPFRqO0RqOmhqeU1mRz88PUI7P2I6PUI7REo8WGo/WGpAUjs/cjpDYjs9cjtcXGo+QEtDSEtEUGtKVGtFXFxtdURsS0BtVlxcUVVZVUZgS1NUbWJYb3RYc1NRVWVNTFRYTXRUcXZMdUxIbVRATltEbz1dUkVBVFNddWR5WVxcZ107Rjo9Ujs9Ujo9Sjo+Olo/Rlo9XlpAdlpCTlpDdnk+RUtdSjtGWj1WWjxWWkBOWj9GW0JWOkBKO0hKPFBaQEZcXExWXFxbdlprXlxcO0dkT05eW0doS0B4Qk5gUVZeO0huO3FcXF5WYDxfZFBPZmtIdG5mYE5wbG5YdE5JdnFOaG93eVRFPUFSOkRqQkhqQjxqWXZ1XXFrclZ2Rz9hXXFrblZ0SEBBOmBNSWhweEB1b3FzVWVwZk1NPnFrVVFvRE1Vb1FUSFRKZ0B0TGBXS1VUV2FQQHV1RkVwOmxuUHRKPmh0YkBtX3FySkRUUmVwc212XkRrd3VKUmFOTnl0SlxcTl1RUGhUUVtkWWdUc0BpakVJbEtZalxccU9DcXRmbHhMZG1aRXJHVEtJTWt0eGRwX2RoYXNMb2FgWFtPSXM9bmRYQWVcXEBfXm5scl5zR0h0UnZoTk9geV5abkFeXFxXW3FiYWVGc1tZPEFpTnFiXWtjc3diZU11a3NSVkdHYV11a29SVElIQTo6WnRWXz9fbF9OYG1QZnJIZWBveVVeZWRQWmlmZnh2YmVZY1NgeDxOWlk+XltIZXlQZD1OXFxhUGN0QXBcXG9xeWVvRWY/U3Rnd3lJT3ZGWUJJQ2dHS1dbYUJsaWZOSVdiSWdCd2R1WVliQVRQZVNHTUVudWRbP3A6TFNKYXY8RVBVYVRnYFRWVFRlXVZLRVZHXFxuV1FrU0FMO01rPHFtVkl4bWFWPFlSTFVtY0lvb3RyanBvTVxcd3BQTmZBU1VITXdUcmBVTV9lbUw9cGA8cHdNVE9YTWdoUHJtUlY8bGpcXHlgWU09QHlocHRheVM/PHFTRGxfbFJSZE1UPHVcXFVKQmFSUkxxdm1OWFBybVFtclRUSDtzOjo6Ojo6Ojo6Ojo6Onh2R3VUVElWYXRtd3FSU2l2UHB0ZXVzdGBwcFRUR3FwVmhPQV1Na0lZPFVtZ11QXU1vVGlUVmRuY2xyTmFPXUFNSD15OlhMOmFtTTx2O2x3SVVUR1FySHB5cEltWEBvb2F4Z11xVm1sa0RQZ3FzYGlNZkx2dFR0TGlRcEx2S3Rtb1lWTE1udWhqW0hSb0l2RlRzalBXXkBQbkVtPkxNTExOWElwPGRXW01VVU1xPllKXl1tZmB4Y3VLT0x5XFxBU3RoU1N5U3JIUkxta3lETWhsU2xRd1FFbWVATXNIcUZpSkRZVFNkeUl1dmhET3NVWHN0dGB4VktweVVZbm1YdUppWFhETXZwck5RUWBhcGRxdXdYWWh0UEhMbTo8Ulh1VXdAeFJ0cFc8WVNpVVRcXFhxTUtkWFNTSVZAWW9rSWo9QU1OTHFzZHJgPW9PaHE/PVVNaFBndHJNXVBoRW1KYU5oWE1eVW9GVVJDRHNjcXhsUHJWTFNwaUt0PHN0SHFAQHBFPVdzQXFhWHNuTFNMYWxMVVhPXFxvdHhsa015YUB3YGFzY0h3YFl0PWR3WEFLcXBMXFxJTF5NUGpAbUZ1TE9dal5pdD9lUlhdTnVZUFQ8bEJ1U1xcQXFdWUxxbFd1eVZGRVZVYVVpZFF0YXVvbHZPRHJkZWxSZHJOYE1uaVJOPVNJWHBCXXJATUpBPXRLSG1RXFxsTnlWPEB5T0VZb3lzRXFyYVVUQ3VsS2V1RlBTV1FVaE1uXVRyYmFKc2hvbVBQOk1SX0VNZ0lNPUB2SmBOa0R3Z2FuYXF1YnBsZkxRQG1ySlVUZ0R1QXVyQVVQdTxuYnFrREV3aElzUHVZQ2V4Pzx2V0lNYERtW1VSO1B4ZkhSbnR0V0hMUUBsQmx4VGB3eUBrUmhyY2xUWUlXQ2xvakhubVF4RXVrRlRNcHhwa2R4eWdhU2B2dU5bRF9dYUZqUGlgZ25kRT9xPVFsXUllZ3BodVhlZkluPllmcmZmZ09qZnhkXFxnYGNmamFJdGZBYEpfa1FPYEZoblNQY0Q/cHBZYVRoW11RcVRPc1ZRXFxjcWNtSGdKeV48X2NkX2VcXGdsbFddaE5vX19ucGBwY0B1a1FzcFZwR0duc0BnQElld09cXEFocz5YdlNXZE13Wklxa11JbG15b3RHamJxbk5pdWdvYD1nWj1HXnFYYEhWaUdwZlhQYDtHa3J4dztxXlhJX1RhcWpIcVxcT2FmSWREeF4/Xm5QUGdxYV5aYVtWcWV4Z3hfPmVneGNYX3Q9PnJDX19jSHBSdlpIUFxcX1d3QV9dc2dkS0Bta09yQWBrSHZadElia2dzWE9hcXh2SHlZeURDZ1Nbd2hBcVdwX1RCa3JcXE1iaUlIVE11SmdJSGVlaEtndVVjTllnQENHWW9idUF4XUt5cm1kVV1kUHVCRHNHVXdzdktTS1d1SHlCQ1dIVXVyb1dHbmV5dmVHb2dlZ1lTUWdVc2FDVWNIb0NXR19TU2tkYXNiQ0diUHVIX1dYO3F4RGF0UElmU0dnYEFIZkVXYjtVdT11amtyVV1TcVFIXmFEW0lFSV1pZU1ZcHF4Wkl1UU9VQE94PmdYQ3FWclVpd1NVRXFDZG1CX1FkTk1VckVWYVlUTHVzRXNyVktDcnNnTEtyc3NVZGdVZ0tJW2VXc0lEOz9ibHVSQEFJQ2F1bjtjS1tFZW1DcjtGa2FFbENSdlN3dklIQWF1T2doUXNWVklAQFFNSXRdbXB1aHJ4dXBvVVVlcVdSSHJbPFVFTFRlWFNPdFVEbFNwaUpBRE5fRU9wPG50VFZhTHN0RVY9WVdCbVBIWUpQSWtmRVZsTVY/THdtRVhTbFlMRW1bZXNpRXJpdVNcXHBraWVvdHB1UGVXTHFxWHl1ZElreG1zcXRuZEF0aGB0VGlzRFRNWk1wd2xYXWxZZ1hyS1VNPVFxdElQZVRvZ2RUeUhMVFVSRGd1bm5xQkFjV0hqYD91bUBgY1h2cFdkZml2PV5lZ29fdnB3RHBdWEFsVG9bbkBwZVdrTXdoXFw+bmA+cXROcj5eYDtOZERWcV9vb0pIZ3F4bDxmclNvaEV2Yjphc3JhXmBGX2s/cFlQaG5ubEpxblZOdFZJbWlgXm5HWnduaVxcSHNOPltAeHJkQWpXV2NVcVxcQz9sdGdxdGZpbXByYk9kPGlrQl9uXUlnRGl0b1ZnZ29mY2d0dHhiTG91b2ZbWGhyZndaSl5rTEhoUm5meG5xPW9iP2h5SG5hYXdrVl55QmF2eF9laz9zamlhdnltX0ZiXmlgcXh1Rm94Z254eUFaQ2dxQUF1TF5vTW9mTXdvXVBaO25pYEFhXlZhdWhgVXBaYGh0dVFeQlZxRlB3bFhdYlBlR09aV1BpXkZcXGVob0NvbjpXdT14a05OaHU+ZU1wX0xfdXFpaWVgd0pva2FAZ3V3c1pfd1RYeGRfZ3Rxb3FAYlxcbmhkcXRRSG94aW1mP11PSGNwSWI7XmdQR3hPYV5IR2pqPnN0P1xcTFBkaHBwYHFyckh5UmZoSnZeQ2ZyQWhfak9wPFl2QHZteD95a1ZuUXFjY1h3VGFodF5tXWloSlZddWdvVW9hZmdxbXdmUHFoZHFob0BvPG5qYGlxcnB0QVZ1ZGleXFxgXVBJZG9hbktIZGBZck9QZXZ2Wztmbzp3d2deYlpGcFJ2c2lpd1hBczpRZU93YGNYZEJwcmtPX0R3aT93aHBHcWFmYGFIeFZ4ZlluZmdGa3Rgam5nYk1vaXlBWkNHXFxhWXN1d1tbZ19kUF1Kd3FTUF54dng7eHNabl07XnZYQGJhcXZJX2FzWXZJeV1CWHROd2tWeVlvU2FRQ3BvaUhRZlJPWVFBZ1dnSWdDVHFFR0t1QmZRY3h5Q1BndWl5ZE9Jd1R1WV1fcnBXZ09leHVjZTxlSFpFUm9Bd1pld0BPYllHRWhnVXJvdGh3eENpWHBFVz1XRUM/eVRvdUd5VG5Vck5DRXFvc05rd1hbVWlhZFRLeGhLdVBldnZlVHdXV15tWHlddmhjZWFtd0RHRGVbZFRpWVlzZVVbSU1nRHJtaD89VGdHWUprSHJjRG5vUmxNY3ZvZlk7UkRBR11FYlNTWHg/R0l3dmBBZVRxdEhdRWRVSUdNaUhBWE5LaXVdZ1xcY2dFXXdmaXVDPVVFQUdlP0hPcVVRcXQ6VXRacUJLY1RnRUViS3VkPWZoRUh0T1NCWXZnZ0JwZUd2P2dHRVJQO3lqUXVfSUZSTUhba2daUWRlb3dpaWRaV0VrTXM/SUZHU2JyQXRZeUJxd2lKcVc7YXdqZWVhP2JjTUxzWW5udFI9SU5TUXdabHg7VU9wdXZ3UEtyVU9XUVVRcEtmSXJQTUxEaVlMXXVbZHNCUXlrdVhBSVNqdXJaWFlYQHlxWVZIUHF2bG10SXFaPWpyWHZiZHBZVGpLbFBuYW9acHVGSVdVcFRWZU9pTHZiZXNlVXV4TFNkVUpRVG9DZVl5SFlVaFZOaXk+ZHFUPW86RFdRVXdXbXhYWXB3QHJoPHRjYFdMWVM6YHBjRXFrVFdKUFVxcGxtVGtsbHNVPU1XUFZ2VE5beXhTWU1hWXZoVVljcFBsTE1BSHZMdHRDSHBWXW46UXdASVJQWXlUXFx2cHhVZVhzY01PTU1YS1BzcGlrTEF4WGVvUGxtW0VRVUVQcERsUUBRUVVSXkBNTEhKbD1tPmVKYF1LXFxlbklBVWR5TFBZb0BUWHlcXHhWYU91bVZLSG51YW5YXFxPbl1zUnhsR3hTamhKSUBqZHB5XTxwZklOO0VPd1BTZHVwTk1YcmBxdHBNZkRQcnFvdEByPnBZTWRQSWhNZnFxdmRXWVFvRFxcVHdBeFFZWEFFd2R1bEVhWGZRcT95dW1kcm9dWG1gVmh0eEVwcm9sSkpkWFFwdV9VUUZ1ckdVd11ATFRsWWNJSk1AdEZMdkpQcXhlcmZgbkZFTT5dbGlhdmtzW1xcUXJBSnN5UUlYSllgTWpJc3A9WEVYdG1pUmBUd0hhbXJASmVpS1FddlNRcWF0bkhlV0dhVGtpTz1IeXVcXHdkaHNyVGxxYGtSeFRtPU9AeG8/dWtSYW1xXFx0PjxRXmluSl1VbUhsY2lWY1lwb1FWUnVqYGBybk1wXFxwd3lkbFlFdEg8ckNwTlRtdnJpWXZIVD1Vd1d4TFxcSHdvbXZlXXc7TEt2ZHA8VVY/RHJdbUxtXFxKPlxcS2BgSmNwTlppWUNscFJodl08UnRxbTpNT3NQTl9tTUxxc0R4cT9gT0ZxTUhhV2RxcXRAbm5oU1lsd1RcXFRQVVNzbGxBWXdMZGxKUFNyaHVEWVVbaG9zQFBAeHRvVHc7XFxPTHlPRkRTa2FPPHVwWV1ZTFxcU2M9eGFkWWFxbkFETWJEeUJddGFMbEl1TXhEeXh4dmVpWHF1UXl4cUN0WHRMd0FJeERpbGhEeUF0VHdVeUpIbndgTmtsWEBweE09UFtwWE10V1NRUXVZV1FpeEtMSm1MbmI8T2s8T29EeUs9TWBlTGpgWHNgb0JIUlNYVEZUTWxEWWxlVXZ0VEx0VVhsbz5oVW1sWHl1dU5deEpwT0NlTEloWXdJVU5Ma2xgU3FUVk9dTnk8Vk88VW1kbWx1alJdazpUeWJUTUJYdGtVeEtgd3V4a09sVlRlbj94VFJpd19wUXA8T3ZteXl4bGlpVnRlWXNMTWRxcmtBc01Yb3VITWZwcFhVdWlcXG5lZWx3PVFtQHZQaVJqcFZScXBTaW9GbXRdXVRBZFNPYG06eW5mUXhCRU9DQExtRHRgQFI6QVlMSWxweU5zaFBWUFBATXU+dWpSPXdpaHlqWXR0dXNuaVJKcXhEcU5kcVI+VU48RFVbWWo6UVdFaEw7dUo+VVBgXFxUUmlyZURYZEVPcGB3alVUSHRrYzxrTFxcckFATU5lWENkblZsUz9Zc0ZAT3NVeXVJd2NYT0E9Tk1tcUFRWVk9cEdBalpBdXVta3JRa09oTERoeGZsUm5wWEhNbTx0TmNBWU5ETnNUamhZcFdwb0NYT05Fa0BdTUBVTm1UVlRlS0FcXFVvYFFUXVZ2VXdrXVBoUHlrcU5WSGhuSlZmQzo6Ojo6OjpKQnlMXnlVcFhudHhMUVVvb0xNY0BZPWxwR2xRY1BrQF1xTnlsTGxzQXRTbG1NVnVQaUl5T2VvR2hSP0xzRlh2QFVQbGxTbUVrXzxQUGBseVBWQkxYUXlqQGhRclB4cl1XYGxQXWhwZmltYlBPUXVTX3F0SmhZc2VWaWFWPEBrPXVTXFxxVFtRVkBEUV5MWE9ES1BcXFdJZU1iaU5rSG9jbUtecG9BbXZybVhKbXFmeVI/PHR2VFBKeGpNdE9UeFJEdXVTWW9XSUtyPFd1RHdDaXRiaUw8WHJlSXBwWW9EdGt4VGp0aFRZVFlwQGw+XFxuPVFzYHh0UnVPTFRUXFxsVXVIcEFMUmhUd19gTVk8UD5JamdoU1dQVjxZU0RcXFFsSEtaYHJBTU1IbFNtVHRAbExNbFBrSEw+SG54XFxtZ0RNSnlWPWl4YlFQXWFxRkRWR3VxV3RUVER4c1BySmBxXVl4YUl5bkBsWUVNd2hvZlRXVHFqOl1VRGhPU0x4VXhwQGxLcmRwO0RZR3BTS2xtZXlPWW13XlRSPVFPWGFVSUhPVkFsZnhybXhyUnh3a2xOWGl4cVFwTlRzWEVQc0FtaXVsTnFrbGRWSVhUPWluaWB1VGB0TFBxWnFSXFxNSlJJblJkd3JYWWw8dUpJdU9BcWdlVGFlU2xZVGhdcExNT29NTFZEeUdtUVFNUFVkV0ppTW9xbmVteVhAcGxUdlpVTV9pdmhIc0xUb0hdUXBJTm1UU11UeVF4TGtcXG1DaFVtdFRbcHNfYEpfaFFhZGtjeGtoZFNbYE5FPExkRVRjSFZiSHRWcXB1YE9zPEtbPFNYbXJidFVLTHVDPFZAWXZMdW8+VFRdQFNiXFxRb0FqSUBWbGltd3hwa2V2W0h5cXh3UnBvZ0BXW01tSFFwdlFudXhLbGhrT2BvPExvUWVtY1V3VlFRPWhvW1RPRTxUXFxUb3g8VWdBVVVEeVpxVllAT2I8Vjp1VGtEV3BAdFpgVkZodmZpWFRZcEl1VUVtd1RxWT5ZWGxIUXFgeEx1eUNZb1U8cFJJb1VMUVZsamVxbE9oVGVgdmZtTEBgcGg9VDpAUm9UTFxceXFSTEpgXFxwSFBxbDxWaXF2X0VRSFxcblRYSkhhc0R4UG9xUFRpeXVEdVdhUWZxc0Fld15leWVQUGhwbHdAT115WTpYb3F1U1plcmhYTWNcXFBFbHN3ZW1zTU87eGxwPExVbHBjSUxdX1pwWHJddmRiYGF4VnV4b21kV2hgX2s7Xls8Vmh2V3RMaWtBcGhIcXlUR3lmYWlueXk6RnNhWGNwUHdWV25kR2lHXm5PUGxRSHlOSGR2bmxdWVxcQG90SmZab25mSlZfRl9mZFB0XVZzYFFoQj5tUFFpTGFeQEB0Z3FyZWFga0duTXdybUdtU2h0XWddYWZuSUBka190PGdcXHhHXXRvZG9GXldGa1tWbHVpdXJxdEA+cHhxZkJedEpfXnRweWxgb1s+ZURAcWdxXUhwblxccXluYGdrdmRXVmNuZ3RgeF5iYXlhd3VxX3hwP29bRmNWR3dTaHdASF1GWHNrVm5sXnRyR3hUaWdAQF1bX3BuVnNGXnBGcGBNYV9ucHVMbmpUaWdDTmNVZmdDTmNKXmpbSV9ASWBGWGZSaF11dlp1Z2BBYG1PeHRQYGVjP11ESXVib2RXUW9Fb21sSWBZcGdVV2ReZnI+TmpOaW50Z19Hd2BMWGdEYG5jdm1QWGdlVmVCeWtUYWRxaHB4bnJgZ11OP3Z1cWJrUHFMWHlkVlxcRkd1PFFlZ1Bdcl5zUU9kPXlrUWlma0BhV3BnRWF5YGdkVmhyaXBtYWZhYFhlTkdtSj51R3BsWFloWGF0ZlF2ZT9jS15jakF1cFBzWG5zQGduVFlsV3lsZWhuS15vWHlvOk5tSHduY1FqbHhgS1ZeQlZ3PV9dZD5vdnBzYmdvdFB4PndnVj5mS2hdY0duVEBhUW92dT9oQ3deOm9hZmF3dF5tPHBzZml1R19vTXlyVk5obT9ldE5oeGF5YD9pSGFvUmdgXnFvTFl1Q2F3Z0Zjc3hfU3BcXEhxblJReWJgeGRwWj9xb0tXZ15JaGtObl5edmNGbVp4Z09Yc3ZwdndAbV5gd0Rpb0BZa3h2b0heYV5xalRoc0lgdlxcb290aGNQUWZ3V29ZaXhHP2g+QGNcXFduR1ZnbWB3TWdbbFZ4R1BbYHBqVW9nR0lmSFdgXFxWXmZYY2pYc1ZPYUJ5clN4aUluYlhIZlN4WW9ycj94XmNmdVtIQGtjZEtZVmVEdkFkck1CPEtCVVtSckVGSkVVPjtHXWNiRlFDTkl2XUVWQXNXUmdnQj9EXFxBWEZBZ2ZTVlJVYkZvSD5zVlJNa1ZQeGlEeGdwcVxceG5GWE9rRFduTHhWTVNwTXhzTEpPXU5vPFc7dVBXPU9BUG9XSVFoUXVCXFxzRFFQRWVtZD1SakRQVk1UcWl3W2RrYW1sRmFsO0xKPk1tVFhWTGBKTEBQXFxtdHhgVWZMdzw9SnNRVGh5U3ZQWT9QdWFBUHVUbFFdd1R1cVZVeXY9U1J0WFVsVnlJa0xpcUdcXE87PXlAcE5mRVhiXFx3W3VUZVlQPFRTdFVWVHVYeE1PXFxwbVZwdmBkTFpnYVxcYVxcTG5wV2dlWkdeWEZeVGlnaFZobVldZ2lzQ0diWFFpbFlzZXBoYndhQUl3UEFvUj9rQFdeTT9zQWheS252V29nSldWWWRbZW5sdVBdPWs7QU0/PXJSRVJKbE1iRW1iRUxDWEtXbExecVhYXFxzaVF3UGh1dUB2b3lYZFhxanlUXWlxPzxUak1SS2hTSFVTSnByaTxQVFFQRUFvUmR5Yz11W1ByQXFSQGxRS1BySV1KaVBTVUFuPnhSPlFreHBUZnBNRm1OXWlUZmBYUXVucnlucU15ZUVOZF13a3VSVkhXYVxcbWtxclQ8a1d0V21sT0l4VHBlTFZZdHhYUnVsWD91Uj5VSltla3Z5d0ZJbXVsbzpocE5sUl15cE5kT3NoeUpsbFxcWVR4aVJdPWtbPW9oeXFWdHlPXFxrYGlrdlRMZlFWVHlqamx0aEBSSj1OUUFYO1VxYHhMa1FxT1B1OzxTP3FQc0hzZnFUeFxcUHdpbmZQcEFUcTpEeURlUEVQdmR0UFxcXFxMc2RSWkVqbkVQc0FQXFxlU2Rhc1NNWFF1d3dIV1RpUEdkeWJVd111cGlhUF9RUFdIeHhseFxcdFRKQHJBaVNTRXM6RVROSHNIeHQ9bFQ9XVJfTEtLWVZgbXhPcFZQPHFabFJdRUxLVUppeGtFbGpdSVY/YXNJSEpwdHBNdXhwSFljcVJzSVRkYFh3eVVSaXVDcVE6cHh4RG5IeU5mQXNvaFNHTHJtcE9oUHlkeVJnUE9nZHdLYVdiQGx3RXBQWE5ndFI6RVNjTE9nTFI9THhsRHBsbG5KSE87bXl1dW09XVU8PHNBeFVgPXl5dGpdTEx4YVVKeEtIPHM6ZG1vXFxLdFlTZmhwQE9mT3djcD90az5wRmZyUWlcXG1fXFx3bnRKV2hUcXNlaWg7QG9QeVtOP2xJQGdhR2VmWWRuVmF2UW1VWV5jUWRkWGFcXFdsaz5rP0BaSHlrVW9gYmZcXFhYbXRWYFNQcUNpb2dWd1NxamVpbTt2cVVPWktIb2BZc0p3dXBZcUh5dHFod0dOXjpueGNnbl0+a1tYcmFQZWdnYmZXXFxxQGxTb3BabmxgX3ZMYXduQGxOaGY8Z110QXNWSGg8aVtNQWM+Z2F1PnVneFp4aGhvPmdIYHR1cGhpcG5XcGxQeWNnP21VYXFoWXBQWXFATnE+P2pdWWlAZl09dmdTX29eUHZlZ29TSGJhcHRndmRrSGRFXl1fR29aTltjaWdgSHRDWW5WcG95ZlpNaVphcXhcXGhbdj91b1dneG5xZGl1cFhxUHF5eFBXV3ZVc3Q6bVhSSUZbdXhIcVRWaWZjTUdgcWVBP1lqUUVVQVdHXWJEbUZmX2NWd2dOYXhWUXZmV2NfYUk6V2JBX0NeX0dsY2NdY1RaSXltYFlYQHlkPXhJWVNWTUx4YFVIbHleSXd1aVl3dXl5cFlvWUw6WWVmb10/UHVNUWdrZ2ddT3FPSHRlZmxxUWVkUWRHX3FkXmBITnVNcWtIaHRVb2pvT3FtZltycFs/dnNVb1xcQVBtQHBbc1hqbWBaeGltWGlnT3ZyWV5zXlBcXFtmd3BhYFNOaWpIeEVpZW1oZkppb3Vxd1dQbU5mdXVIdUdgdVZmdkhpa1twb3FGaHlvakxneHlwY3ROdkNxWkpweEdhcVxceGNfcGhyYFpyUXBJb2lqPl1XYHF3QHdTQHNvR1trVm1vZ3g9SXFXaHJvTmlFPm9waXd4Zm5rQG9MVm5OR1xcUlF1R3BcXFZuX3JYXFx2aFs7T114eXJscGxmWHVRbmZrRnBpeWxEWGpJR3d3V3RKb3Rrb2JLR1o9b2Zvb2JDWWh0XmVyPnVvdmFdZmVfeGhlcHI/d3VZZ2dYcHVQeGZCcW1UYGNjV15CXmVucXdwSGFKX3FkZ1tAQGZAaG5QYWhFWVtuWFxcdVBeYVFdeGlod2lpV3dqTWdvUml0WGZhT3hjPFFobUBcXHV4WmhOZF5AdVhAYV5JXFxJYVprd3ZZaF15RnVBYVp5QVprVnY/YGF2cWpUQGx0dmRNP3VwaG1VaWdiR2x0b25ZUWVQUXloUGtlPnBAaXd1UXVZQVtgYXdneWpkd2BHUWhqUWs/dm52X2pDaFtuSHRAWWdbTnJLX2ZLTmJcXEZlQ09aZGdpWFZeTk95ZmZnXj9bZE94SWBreEByb3d4VEd3Q09dUEd0YGdaZXBgT05pWUlwZm9kYlltQk5qZF9aRGFcXFFwZlBYcFlfbmdBdVNxXFxPUWRfSWRvR11dWGxdQG1SWG5GT2thaGJrQFtDUWU+SHZgeFxcYW54P0FoP053R1hhdmhhXFw/dWFpWldhXmJHY1BAYmFncHlBWmJhcVRxdHl1Yj9yZXVCaVFlZFVHbHVkbmdnVm9iYFNGTVN3eUB3a0FVa1ByU1lvU0FwUURKdFhSa1l4S0hMWzxKWXVtVVlscmhOb3RKYFV5VXRRPEVqamR2eGlLbEx3RklXVGRzP1VNQk1qXk1qSkBsS2RSaFRYZVhqZVRRPkBRanFwUWBSPGhMa0B3cTx0b0l5S0xYVF1rc1xcUlFhTUZMc0h0bXhYdllddkl4VEh4c0l0bVY8bHM8VkxIamFlS3l4WTp0UXd1WHV0VGB5VHVYUV55dGRATG5AVnVEU25BV3VIa1xcdWxXPE5YPGxeVHRnaXhCWFZeYFZbRUo+cVZpbE5IWVdUbXNgWWxaUFZ0VW5GYFRHdXVwWVFPUU9bVEtrRGpQXXA9aHhUQHVeaWtvbFZ1aHhcXHh0TlRsUXRUR1FMOmVXTm1RTUFNPFVPPnRra2hPbU1Wc1RrR2hRUDx4TlFraHVwa3RXSlR0U3VMYkRPQj1UWURYR1hrQlRUcGlRXVBxZVVvdGx3QkBPR0x4WnhMXFxtcGNJVEZpdWhxVEVJamVwbj15cVhkSzxAcFBpU1dxT1BJVV5wc1VwTE5BUWd4Uj1ka2xFTURMTGh0cUl4T0RMTG9oTz1dcnZoVXdgd1VdcFhwdVFZcXN0VEpYbmllakVtVEtIclhRTTxoUjpkdkppcWRBcUI8bEBdUnF4VGpsTVU9SkxcXFVuRXBPeE5OQFA7RWxLaE1LdHNGbGxfUXFTWHhKZVN5eE9odU1JWWo7WFZYXFxZWEB5YXVteFhWRU10dWVQV3B4Y2xYaVxcdFZRdz9NUj5FTmVldUBseEhsakt1eExYcjttS1NhamtkWFZebUhZZlxcWWFAWHJRcW54SGtCR2g+cHFoXl12SGZzQFxcXXFxR2Fob1ltYndpbndyR09hS2BuRWZmSF9tVXBwPE9nZz9va0ZnWHddQ1hjZVFbTVdwQnFiamZqXWB3cGZ0QGhxTlN3YUNcXHlFPXdHc1V3WkdmQV9UcHVlVW1jSE93d1dWalVVVV1ITHdlS2tmaUtZcUVjTHVSU21TU3l2WWF3dFNXUGdVQUdIWGl0RGVoeFdnRGN3SGVVcVVVbz1EZ0tVX2VWdENoPF1DQV1Waj1ZQUFUVkNJW0FoPlt5ZWNkeE1WUl9YWWtXdUdobTtzblV4dHFXVHNZXmFYTU93TnlSTVdTVUVWO3FndUVkSldCa0VGclFUTlNTR29XT0VVYFdCRl9YbD9YZUd0THl1QFtjTnd4VFVJd3NjWXl2SXdFPEl5bVd2TXdzPWFoXW9kdnVDWXdZV3dmeXd1dWN1PWd5VT1Ec0tXXFxrVDp5Q2lndlRTVW5dRWNreHR1VVBpaFo9VD9xdTxxZHI7WVB0VGZdcW9BbUNQU3hxTFBlck9FVkNseElpUlM8U2BRcF1RUG1JdF9lU2RdcmpBdVRUbnVBd2hBeFVod0BYblBVTHFxdHRcXHV0PFVPdWxnSVRlbHRUZXR0XXZGZHhnRW5KRGpUcXI7cVBPXFxqVlR5R3lraFxcSllUbUdgTHVdV2tQcT5hVVBIbmo8a0x5VU1QWUpxUEJBdmBBVWZxbzx1dGx0Slhtb29MT29xdF88b2V4UmR1TmdNVmJQTV9xUF1EUjtATGw8TGdwVV1wVm9pdnB4VWhYTERBcEd1T09ITmtVeFdBSmVgc1lZUl5BTF9BcWt5c19peXl3aUl4eFhOXUBwXXBWbzpwb09ueXVpZGZPdlxcUW1pQGV1R2tzWHJUWFxcb0ZdbEdfO1ZwUklqVF5lUU9sVmhucldjZkBxXkh2Z2dvSF5waVhnRkBxVUFvPFd0aF9xZnhnWE5lVUlpZFFgd2hrV3ZwbmdtUEhKU3VVcWNjQ1lldVJeW0VvZ1lOU0Q9YWdEX1NQV1dfR3VhW2c9c0ZdZ2VJa2JMd2lLQWJMW2J0X2V1Y1JMRWZnX0hDbXRtTWNjc1ZWSWhATXVrc1JWbHNyOjo6Ojo6Ok5xdWdbOmhdRkdaRWlkVmBQZWNoS2hWZ3U8TWJuX2dgQ0ZFS0NGW3hhP0NQXVdEWVdkU0JLO2ZIQ1JUYWJDT1RYS2VUc2NXc1RXRVhDS2JPXVViaXZXcVc9UVNsWURSR2N1cXdaYVNvaWhIb2Z2QUJlb0Vdc2dGP0ZiW3JjT0ZETUdmaWdLWUhlZXZKX1JDdXhVYWluQUdyT1NrP0Vnb1NjW1RRdXRePWVxcUdLbUVucWRXaVVPbVRwZ2h1X1d3RVJNU1Zgc0R1d2RrdWNSdVhCT0hGc2lbWVJXWXhKPWJUXUlmUXdMTVU9dXlXSWhxWUVbZWU7ZXdmP0RfX2lAQXNNc0dQO0dIQ0hcXF9JQ3NZTnFoZ3dUQmNpdz1JTVFpVVNGbHVXRFtnT2l2UVtFRUtjREdUZltHbFd4PlNpVUtERE1jbE13dVFDPD9YRmdzZXFyQl1GXWtHc09GcU1oTU9nTnF1QT93YFFmU1VVYV1YRVV5cV1JRF9Gb2tJTWVVXztGUElYb2d2U0dJa21HQFtWR19GXU1GQV1FR11TbV9Sd09IVUVUbmFIQ1t0UD9mZz9Ubz1jQXNzZWtEVl95RXlES1dnZHNDRVNDWFtEcXdWTFNzWz1mandWTElST0NSY01jTF9EXz1ZRFdERmNWY2tja19CX0FpQWtmTF11XVN0Umtia11DXUFFQGNpa3lDRWFlbXNURTtHdGV2Wmd1eENDZUFYPHlEWl1ZPFdYYmV3aT1TVFlVblNDa0VWP3NXU01JY0lVbHFERkdEaldWX01IQj9ES0tVTnFmVkFUdT1nTnF0WGV1aGFVd29HbkV5T1llTk9iT0NVREVIY210YVl2Rk9lb0djTkN2aGd5VGdHTGtHVl1kU1t5blVmZUFEPWh5a1V3WW1UY2xrRlxcUnVobXJEcElhVFBxbVB1eFF0T3dhdWJ0bmk8bFRlbmdRckZ5UUNEa05gU0tcXF5ATmw+T3RcXElmTG9sWD5xdXlsRV55TnFgUUBgVWF4a253XFxfXlFRaExRXXFpeEdJckh4a0BGdXRIaURWXFxLUWxPTmxwSGJhR2NraXlxeHhwUHg8YXZDb2RmUGZFb2R1b2dSdmQ8UGZTTmNMSGE+YFxcX2VSU1dmT2ReTVNJS2hcXGV2X1dpXXFFUltTQVlTQk1ZXVFiPVtmbUNXeXdoTUN3bU1mQW1WTVd5bW9FZGlpZVN4T19yU3NEVG9ES3VHeHl0Sm9YS0l0SFNXW2ViSUtUeVFiSmd4XVl2TllJPGV3UV9iTVVzb0NlUFdkP09FWGt2bktjck1ZakVCQmdlPVF0YUVVcT9YdlVTUVt4WGtST2FmTGtUTGNoeFFZZ1l2XVF3amViU210VGVzTFd3eHdkbV9ERk9UQ0Vlbl1zUmNCZ2lEZ0dTbVtHP2VyTUdiUV9EPUVSbmd5Z0V0PUVDYG9mbU1oQEd0aGV3eTtiQG9IcGViRnl0VUtmOmNCZD9CO2dVSVd4aV9IY21XQFNTSXlTUWV5YXNkbmV1cl9EY3VnX3FEWUNmcnFlVkd0c2NXP3NmcmNmbFFYcEt0Sz9GXz9IXT9YcVtXXW1mZU93UHFVUXdYR0VFdll1cmNSaVFGT3VzTGNXXUFodUVoV2t0RDtTbD9TTGljQENVVz9DTU1CYFVWRElYQltCXFxBeU5JcmxBdD4/Q0ljaF9vUlZ5Y2FtdE1ldEdjclhZWUNxZ3dXaUxFeUJTc1xcZ2Roa1RTW2dnXVlfSWZUY1JsaVRfU3Q+cUJCdVNoPVV1U0dXU0lwW3ZSRUhPT3ZpWWVkSUhcXE9HeEtJZG9oWkljPHVHTVtSP11ibHdIUD94cll5ZT1UcmVybGlCV11UcVdzTGF1Yldzc1twc3hURVl1TmlVdXRSa2xzbGBLY0B0VkFNTF1OQWRQU0RvPHFRZ2FZbmlOQ11LcHlsXTxrRXlrRlRNYURsWVFTXFxhUz5JeWZ0cVdcXE9HSHZoWEpwcEpZcFVsWEtAXFxWY2xQT2xtYklZR0lWUG1NaXFRU1Bza2BZRWhWcHl0PmRRVFRURUxXRkVTQmxXRnlWVGh5YFxcdUhVV3dMWEZYb2xkWVBJbWZUUXNMdEs8UGdReXR0c3JFVHVscXdIT1FYS3hwdWNhTmd1am9UUlVITTxMWFZFVUJsVnBkXjtZXWRGW1tYcFN5XlBmYFdJX2RXZklmdnBJdE9nXWpAeD9pZjpOcHFuYWVwXFxsb3RLRl94X2VHaGRjX21FcVxcS0h3PE9kYFFlZEhlWVhzPV5vZldvc1ZpRl5rcz55Oz9lZkBwRWljT1BwSFdsZ3lnTVltST55QFh1dUdsXFxncmg/d1pYdVNJY01QcFBhZndWaXhXeGpOWzppc2VWYV1hazp4cGpudWxuZE9nXWBWeXVeX2FfY0Npd1VfaEN5bVh2d2BfXndGZkFmdW94XFxJP2w6b2U+ZnF2bltGZmlsVmhBSVxcakk7XUdyUUJQZVlFS2hLd0docXJFUVVic0RjR2k/ZWdpa0RjXUdEO3lUd3JCV2hgV0lob1dgZWV3eUhHU0l0W0ZxYVZLX3dMVWZeRWRGc2hgPVloQ2VNZ2NHbVVcXF1ybWFTaWVVQ0NWZ091dk9HdUFIbV1kVVV3S2FERl9IV11FOklZVGlUUldERkdlY2VVdl95UEtmS3NieFVpW0tzWl13YG9kQF1lVEtmb3VFP2FoYU9mZllWPG9UPnd4cXFYZ2dpdHFHPXFJR1VjUkNSO19nc1FIbmdYXkVmd2N3UUtUZk1VUGlZQmtmdWdnRGNIST13VlNSQ0lncnNDSUFyUkV1S1N0Sl1YYVl4UFNoVW90QGlTP2VWbENlQ01VVmNSZlVlX0lobEdTUHdkamllPmFCXT9mS2dlRmFiU1VIO0V3RF9GZW1GPD1pTl9UZEF1PFVSSF9lTj1IQUtkP0FobVFDcHVSQztkVWdWVnFDRDtSRE1DQXVXb3NiPlt4X19pbltiR09SdkVWb1NTV2F3ZVtITW1oW0dnR2N4cGtVW1tFaE9HS2dFbjtEQGl2Qm9Fb015XFxhRUBBWGQ7VFpZSUhbRF1JRWZpdmJraE1rQlxcR0lRT0VBc2RiTUhIQXlhbXZwWVZJeXVWSWlGbUV5c1ZhUVhocWNObXRfP2ZMQ3RjRWZbc0dRbUk+Z1RaQXVlP3JhUUM/S1Q8Q2M+b1Vzb1RuYXRlVUJUSUJNW0ViRWR4eXZgYXNBcXZIX0Jtd0VVWWRnc1ZadUNzeXJIc0RLZVhZUWhkQ3hIR3NsZXhgUWVGWXdiUXlkcXVzZ1d3SW5EQEplbFhaSEpSZE95YWpKTU9PSVhbWFFyQXZxaVlzaFNtWGNieHdAWXJMYWRecXhhSWxSYVxca1hdXFx2anB3dFBwXFxqQXhFZndAR3NFP2FISWRsSWZLcVxcSlh0O09saT9fRElsaVFyW3Fjd0dhQWdxeF53YVd0VnltWV9lPGdrXldnUFl2cm5kal5uYUldSEdoRlh2cm5zbV5rXUFhb3Fya19teEdlQEloc1l2cl55bXBreUdpRV5xb1d1ZnlseD5sb3FuX190VXBuaWloV2BmZXZkZldcXGxWXUpgdUxYeUleY0NJbWJ4b19hXlxcWGVMeWVGT25RTl07R3FsZ2lsYWZ0b3FtUWs9d3dxXmxySG9dUHNZWGhBSWxJWWpvaXk6d2FieF1KWHRIP0Fjdm5jdHVvWFRNWXB1cm9paHA/SUNrZl5vSFtRVWVvZm1rRHFHaFVjdGlLVm9PWXNvWD1lVz5PQ1dNZV8/Q2Z3aWhRaXF5Z11RVEg7RUtTWF1zU2NbY1J3Y09hSGVzdEtNc2RXV1h1SVVpaXBFWGZjVE9hYnI7dFlfd0B3ZEVxYjtreGlbRW1rSHR1U0pjeHRtWVM7RFxcd0RPZVRPY2dNVVhDX0JPU2ZlQ1NcXEdiXFx5UztRRGttVkhFaGxfeWNFWXh5dW1leXk7cmNTWDpZaF9Ld3I/dU5PRz93ZHl1UjtJVTpzVGE7dHBpVF47YnU7aD1fZ05DdTxXdWdXaWFdZ1Y7RlNNY0dJZUhrWVRBUkZraGljV09zQm1DQmZndlFZU2ddVT9zZ0dzWWdBdUdhdE9RZ09NWUc9WT9vQ1g9U0dvRmpLQk1VTjpsSz5IVjxoUjtVdlNUUktBdjtBS1VJdF1hcFZkdkRNU1VtcndsV2NsV2lMT2tNV1BFd11lc2ZQdFR0TFhZS2Y9blxcZFNQdVVhXXVmZVFfUVFRSVA6UU87WGVCZnZxR3BUb2Y+QW1BPmBCaHJmP1pwcV9LcHhOb2JCV2hLXmNSWVs/YW9oPmN2SGVRZmFydmBpcHhXX254R3JmeGdvZ2NXaGhucGdlaHc7TnBUd3dsZ3M/UXZjeXR3SWxsP2dIZ2deYHhIQHJzQGJ1cF8/WGdNXmlpaGpoXltPbnhIV3FOaWxkZ3lTUXA+TnF0UWRFYVxcPWZsTGlwcUF2c2d5dlZoYXFtckZ5cnddaW5deF9tUGhvYWZvbHB3T25zd2B3Z2hbRm9nW3hbeWd4U1lzaHlxP0BbVkhhalF3TXZzTEhjVXBnVlhxUlhzS1Z2RD9eXT5mUWdrUGFncFByaj9cXHFgZWxIc3JIYlVPa2BOYWFfbmVmbz5fd3lBWmpnZmdxc2ZwZXFuXFxOQW95cGNQSW5TTnV1XmNHV2RocGRnVmlNb3VoP1xcPWBfZ09hclhnUXdjSV5nUUZwY2B2XFxnYlNZbjpXYFtPaWc/ZVJPd1ZYa25Bb2lPdVtxZF9Yc2dnZHFAXVRpaXFAXUxHbEI/dW9Hb2I+dGFPYnBxZ1tOdWtAX09ObWg/cmhgdWVOZ1BhaGxudFFwcV9gaWBBc0FWalV2YVJmeVRGZHBxdk1pXjtvX3NIdD1wYUNOaHd5dUtHW09Jb3dHaG9YZWFebm8/aWpmcWNQdVVmbD5ZbWpGYEhOXFxtd1xccV93PHlyR1hxW0ZuPWBkX29sW3ZiSHlpVk55SHBhQF9fQF91b3d2WVFjbXlyVlZ5az92bU95SkBhYVl5c3dhW3Z2R1dmaFFvQ1hxb1FvRHl4TXdoeGF1ZGh3XVddPGZcXElAZ2NZd11gYEtPaVBoX2l5dktIbXVPcEJ4YFh3YnheaV1mXmV4YkJ5ZlxcR2NDZmRSSHBHcWRpUGxWPmtOPmRKUGBUV2ZkbmRubmx0cXQ9V2ZLaXBBQGZkPnlRWWZedmFUTm5RXmZkeWJob1xcVGhdPXddQFFrZ3hbbVhaUmFoXlF1QHZ0Tld1Oj9aZEByW05wa1d3ZUdnXFxwZkZZbFZec0NhZFVJcHV3bnJYcUI+YDtXZ3BWb09ZYWFGY1d3b29YYm5PY0NYW2ZmaVZndEBPcHZJcl9Yd3E/Z1c+akNGcGtBcGN4bHQ+blFJdVNuZ1VpW05XX04/ZFFQdHBQY2dGZEVgblRGc2x3b0Zpd19PZGNYX2pnaHBwXFw+UHdYaXZPcXBbcWxsbnBoPnJoaV1RQFxcbklvb093Wk55S190Q0FuUm9oU1lscHFmcUZdR2ZsZFdeUz9pbk5jR3FsSElba0h4T09od0d4cl9mXU9oWXZreVheQlF4dl55Q1B5ckFebEFheHZpbmhwX154Rm9tPHlcXGZxd2dZanZXdWxxZ1RXck13ZGVfZHZPWmRXa0xXbj5YX29wX1xcV3dVb1tTT29iSXhieGBlZ3J4Z25DP15OVl5MX2dRUGhESV9aR3BSUXVgV1pGRlpBcF9IX15YWV1ZUHBdVnllWW90R3JpcGBPcGVdYGNUUXk+aXBzUW5fZnhqV3drT18+UXF2WV1YYGZIVmZZSWZCTm5LSWt3QGRnX3l1Tl8+d2hbYF9OYGphXnduVnJHTnZDR3ReeWtpeGhpdmlPV2RzdnRheGVub3dHWHVSTmpfaF8+UXJKT3BVWV9ST2xYP2RNSWdJSFtDSGBlaWg/WXJWd25PXmBmYGpRVmN4RnA8RnZnRnJoZnNReXNUYWFsaHhmZ19cXG94dU9lVWhsUVlnRFB2VldnPE93QFdrRmBjeW90ZklrZ3ZyVz5paVBlZU9oS25hbXZjOndJP0RsXWVfQ1VlS2ldSWRfcXhFP3dbcUlpXUVzX3I7d1Y6QXN2X0lJc1Vod0JIVVJQV1NdaVVXUXJAXUc7WXVuO3U9YXZlU3VrQ2hOV1VyO3ZrSXdcXGtHbktUT01TOz9GP0tIQ2FWRD1Ga0FVcFdCUE91VmtGUUlpVm1JUlllcz9jYUtGd2ljYVFGX3VVZ2dnYV95VWNHV01UZT9GSldpY1lib2VHVW9Wb3dDTG9EaUdSSnlyRFh3S0xXUElLQTxrdkRyblFSR2BRXkhWaElNWUhRUE1OSUl4X0hvUUFYc2ZvSEdzZWlwTndkVmldWV9pdGhsZ3FoSVlmUWd1cT9dS3BkS0dmZWdcXHhncU5pdlVIc3NYdXJHaztfa0NWWmk+aFI/ZEA/cWpmZHBHbT9PZ3VPZlJAYm9AZT1HdERWc1hOYXJOXFxWcVxcRGZudGhiakB4PXhsQnhoWUdddFBgR1hwZklxWmdiQmhtWFdrcT9xY1F1X1FxdWFgb2dsT1lgYGdfTl5mRmBrTF51XkBcXFVvcD1JYkVXXWNHdmteY0NhZ3Y/aXRxeVZvaVp4bVlYd25hWmNnb29waT5XaWp4a3RnYXNxc2tfanVHcGhxc2pfbWk+YTxpaXdXaFZoXkNvZGtHd2VhamFJXUlpdlZ4Zk9YalZpYWlBcG54b2VPaXBvX0hudVR4Wkhfdz15eHBxeFdoYTppeGF2Yj13a2hYYk9Xc1xceWNdYWtRaW10cGBMQGRnSWdLYGB0XmNyeGptcVxcVE5uQFFlYE9eeVZed1ddTD93RHdoTGhpVUZjTWlkVG9sbmZwRUluTF9rbz5aZm9oRHZkaVFmZml2aElqV0lwVV5lZkBjP09uT29wZEBhblZoX05rd0lxQUduanhyXFxxY0JpdlJXZ1pHbmZpYHg+b0FwYV5GZjtZYHVGXVh5Z3BgXz5BW154ckRPeXRZcjtPY11fdzxPbU1JeFlAeV4+cEZxanhvZE9IeHhYc0lXXlRZdmJvZEF2az55XVl4YVlvd11ReHh5eTpWblV3ZGJxYTtBZHVmXFxkYGpoUV12RmtLTl9gZ2ZUV2VEWGpTeWo+Xm5yZ1xcZWhoRHBuPGhqW3ZgY155RXBrW2dkQ2laQWlwa25yXmBebm9seFZ0ZkdjPV93b2BtbV5tYUZdTFdwRnheUm5zbV9tYUFdQElgRlBpYUlhSHlpZlZmUl55bWFteEFlQWlgOk90T2dvdVZfZWhcXEtob1B5WmZpcWFAaGR5W1xcX19fZmBmT2VKUV1qUVtFYXBXaXNyWGVZRnVHeGxrcHk8QVtUaHBOV2dLbm1gWGdKVmc7XmdrQGtWX2Y9R1pgPm5kPnQ+T3FeWFxcVVZrXW9sZHllRWhjeEZvXFxfZ113YG9QdUdpZXJ4W3hobWJOW2FAaUdeb2lIaGVfcGd3ZXA/cEJ4Wl9vXk9BY21pbjxQa1ZoYEpoXmpvZ1o+ZTxBc2o+eXF5XnBWeGNxeVZWaXlHandxeWc/ZXBQeVVZcVR3bVhxcVJAdGVWXW5uam9vYWJxYz9ZbGFXbm5wXlpAeFNwY05PZ2lWcTxeYlVXWlp2cUNvdUNoYHNpd0lRaWV2bllAa1NIbFNPaXQ+ZFhRXWN3bWFgbEdncm5geFlIZUNeZ2d3X2xoXkthd1txZ09Pd2NpZEdWXFxOd2BTWGpmSW1Od2hcXEFzR0Fqa0ZrO3Z2P3FiUkdtQD5mUUFeRWlnSUZhT2BpU3BoZUZ4YldycmB4R2Z3Sml5b3BvZ0d0SVZkZT5kR2ldWXl4R3deQHd0YWBncD5mVEhiVWB1O0ZuR05baXBsbWh0ZHBtYGlyZl53Q0dqS05bcnBhQD5bR0Zlb3ZrRGB4cVluXVB0cVlgZVh1RGZxUFFxaV5mPVleTj90b2lyVVBlY0F4cT9cXFR4dFpvZWhXXFxxSGZMUGxZSHBRb2BvWHVBZmhvYV91b3hzaG9TYGJNWGBgTmNqUFxcU29aXnFzO0dxc1dfWz5vaHlpeW5dWXlqcVlpeHFhdkZ5TVllcnZ3d2d1Pld3YFBvb3B3V0ZsZGJUdVZMS3ZEa0Zwa1dYO2NQc2VqQ1dyR2Y+U0NPc0JIV0hDV0RCW0RbS1RtRXlvQUdrT3ZwV2ZNPWNEO0N4X1djYUd1T3dfVFlfXXE/THReQE1mTEt2PGpvRUpFYHVScU9vbGt2PFdmZHNrRW9MTHVtVXd1RW52PVlgWVNSbHVKdGpKdG9xeVBzSVFodHJaaWxhdFhhbXR2QGtpVW9gRFFJeFVnZVRpTXhLSXdQPXZBZVJReU1vTHd0PHdHZXA9aU5NRXY8PE1xVFBUaFd1ZUtgSUxScHR1XFxPQ3RxcE11a1VPcmB4SnRMTU1MRFRQdlVKd2F4UG10WHByaGVZcj1wO1FTX0xwaWRrclRRVGVUdXhUQ1F2cmh0RHRUQVBtTFlyQkBxOkBUXFxBbEpFU2VdUlt4TmB1S1hoUVBUU1h0bD9IdWZdc19NVkt0VkF0bXl4cnFZeHNta25wVEd1UWx5blVNWVlMd3lwdXR1eW1Fd3Zld3d5cWNQWHZ1cWVVd3VtcWl5T211eU9YWHVtcWl4bHJ1cXFZcWxtdj9YdHdwbFBZbUhJVnJIT25JbUxsbkNRVFF1TmJtdENVbEpcXFNARXNSPVZkVHRAdXk7cGthZExsPFhrVVBdXFxWeGFzZ2xKXFx5c1B0TFZ5TXA9TlxcYW9jXUxzVE9TWVRAQXlQRG9wPVhcXGx5aEhTUGFvXFxwd1JkdWhEU0tpVzxgdEVYTVdMdW9RdVNVbVZ0dl5VU2NoVEFIc048c3ZYdENsVm9VWGtoaltETVxcZW1vSXlpZHFRVE8+VHY7XXFSTW9PZXlXcU88aXFwYFFBeHNRaXZUbWxfTE9fbXhAdHFmVXZYZFc7cFFQUU5scFg9eVJPcUxMcW5aUVJrTEo/ZEpCUVhzWFVPSGs7TVhadFBwWFFIQHF4SXRJXXN2eXFlWVZidVlJQHhQdVVHRWxYXFx5ZkxMYF15cXRaaV9hY2h3REdmQkFlZG9hUUdrSG52THdcXFBAYFVJXWNfc3ZecXNod2VnX2lYW0RRaD9QaVBva15odXVOYXlPbFhvcmNZcVg+dGFmZk1heHdgX1BWeEo/W0xnXnA+WzpRXFxmTnhvRnJxcFxcO1FfX2FoRV5yWmBbXFw/cz4/aEN4cl94bGBidEV1RlFYPmF2W0dzaE1Cd1dIX11mS19ZPWljZHFpYFVSR29jRl15Tm9nV29zXWdYaklUPHVId1N3PFVWWl91OmdXRj1nb29WVz9UQV1nXFxbSXJnZ2o9d2tVWGRFRDxfQkxrWEtFcl1PRlBhY05vUnRNWVlBRG5Pd3VpeFVvY3lVaUtRZXhHd2VnSEhFd2RleFdVZ0dlZkZfU1ZHRlRJQl5HSVNDY2pDRT87ZEZnVkBhdkRTdEBbdWA7UmNHdD5nczpVZW1bYkljdFdZeV1BSHZ5U3l1VUl3WU1TVU5FdkNrY01bRWNJeTx5STpBQkhXWElpYnRzdmR3QnFveXk7cjxcXE1feXVReE9qSXhWdFlgZFFzcUx1RG1dVHA+VG5jT2FqcGNGQHFZaG86d2dnR2lQd14/SGNHWF9UP2BxWG1vbl1NVnhUXmxQSWZfYXJ0UGpEcVpgaG9CV2VLT2RIVmJEX2NmeWZYb2deUGQ9aXdHeGtdUWZpSGlNSGZiTl1daWJnaWBoX3NGWWdXX2w+T2xPUXNmaGF1YFs6d1pCP1tlTlt2R2hHX2o8UXdsWV48WWxRTmBkcGdoYHBsYXRTXl89WWdWZmc7WHZubnZWcHVLTl9rX25icGE+UHhGaHdRZ2VBUF5WX3BSWW5kR2o8ZmdzPnc6TnhYQG1xaGZASW1gVmtVb2lWR2tkbmhcXGduPE9oXXdncVBfXnd0XkdaOlZqQXlhO2h5eUFaQXhxWUByb1ZwSU9oaG5cXHR5XFxUd3BfdnNYZ2VYV25YSW9Ub3lBaUhXREJvWG5NZ0VtY1A/VmhXV2tbVU1DV049d3U7WF95Zl1jc2dheDtJWV1pZmBddV9vaFFbdV9xY01DR3FTd09XeGVLdUxVSG5BaGNVZz91dk5RVEg9dUddU0ZtSFltZlI9Y1J5Y0ZjRVtHaFRzQ1NxU0NpST8/SXZhWEVBc0RnVFlLd2tZd2NNQ3hXVWRlWHk/VnZNdlJVaVE9SFpRdlVcXEtMVVE9dHhvbFBqTFJOWXVuVE1cXGhuWVFvQmFPV1RvQ0BVbWV2TVVSUHVZR0xsQHRLb1BzaFRLQVxcTGVVckFsUHhYU3l0eD1QV3Vxb0tMdVRRbkpxdXNxTXl5VXB0cFhNcVdlbjxEd2d1ang8b0xsc2tNcWtcXExHTE5FQXdMTVVgVVRMXFxXUEx2UFVzOlBLX2xRVlhYPUxrTElVbWh5RER0RGh5UmlwbzxUaXBNWUluYW1rcnl2ZVFYanVZeHB5VnRNVFRXW01za2hRb1B2VFVZQEl0QmlYak1Zam1KPmBUYkhyV3BqXXlsPW10S0VPbGl1bDxYRFV1PlVQVmRPWFl2TT1sRDxRVEB2YUFzVUxrW1RNVW1LQ3RMcGxOZklxeVxcbGdRVEFxakdMeDtRcFxcTHRvYU9XdG46bXFucXZnQHBbWHdBREs/YXlGdHdfVU5WYXJmWFVpWU5AVVFmXFx1ZURVS2xORGRTZWhtbGx4Y2BXeEB4PlRQQWFuUlVTV0h3VUhzWkl4SXVrW1l2ZXlzXXlzXXVZaUxtY3VSVlBYVEhXQVd2Rz9hXXFrblZUOkx3TFxcVztUcl5FeVFQVztEV0RsdUNZa2N1bXhZTkdUV3J0d2ZcXHk+dXBJbUtmPGx5PUpyYXdjYFJDRXdqWHZsUFNUaHlWXFxZTGxWX2h3dmhKYWFvR21POnFXak1TbV10TFhXcXR3SkluS0Byb3VQYkFzO0hRQlVMbFVVQkltUGlXVkVvdHRWY21NZ0FYXXBRXFxJVVpEdVZtVFVhd1RhTl9ZblVdb2VZSmlAc0FhU051dFN1bVJsc09cXEtjSFFAWVRWVHZybHNtYEtdQVFIZXFrXU1heU1QSFhWbHlybVN5YG9ddW0+TUxOWExCPVRPeVk6RHY/SG1ycVlQbVZ5dHFeSFlzeWpyWXdBdXVvZVdVRHdPQXNMbVBvXFxzR1BUYmR0YmBSWm10W0hwQ3Rrb3FybXhXSWRORzxzPFVYVFxcWHFkeVlMSjxRb1NkTTxMU0ttblZsSl5wUEFYTGdwc1xcWW9ldVVKaHFPSXBnZU9fZHJVUHBCdVdXVGxJcU8/WExrZFNNbHdQTU47SFV3XFx3U3B2QG10Rz1yWGB5TEBYaFxcVkY8ck15U1BoWE1ZalxcbHRTYGpmRVNnbXN3RVl1WFJtPVVJRXF5PUpucGtcXGhZSFludGVnSFl0YmlpWz9xcU9kZmF5Z1hrbWl3VmhudmZrVnBqWF5fR1B3b2dfSU9lXXB4Xz9sTEdwV1dyOlBjdVheW3BseE5mTmBxPkduOmB1Zz54bmBmeVBaQHlsWj5gZnBkRkZkdj5raVBgZT5fbFZePEBbYUZyPlZacXlqRkZaUHV0eXJgdXJiZ3RjU0lQQUVXd0JlaUVDcVlBbXhcXF1zP3FmaGtEcV9WcnFjS2FZaXViXk12eTtCUV91YEFUdl1SSEtXPnF0bWVHc01iXFxpYz5hVlxcbXRYZ3hLeXVZcVRWeUk6a1Y9SXV5O2JvZ3JheXFGcVZwTE1YVXBvWVVpQFZjTXdZSVhGZVc+XVdSaE9bSXBKeWs6bVBnXVRDYHR4cEpUeXRHeWtMbHVsZHdXaFJCdVdESFlicXd2dGpWUXJObUptaWt0PHRgVExSZVFnUXFkTVVNbFVRYG9meFU/RE9sWXRHXVJjbVNgXFxNUGBscHBZU0ltSElWclRSW0VOcm14bnl4XV1SXU1rc11YYXBxXFxITmJ5V194T0lUVVFwUEN5UjpIdURgdWdgTVZBSzxMU21Uc1hhcmF0bmRAS2JsdUE8bEpQT1s8U3ZISmdMcHdZUlVsTEZEWFZdTnlIV1xceHVAWE9DSVVLYE5GbEtaeU5MZG06YVZsZXhkZXV1VXhZUXFlcXBoPFRGcXNDcFRJSGtwbHhmaE9aXFxXYWl3cHlXVmB3T1RXV1xcdT5cXFZOZU9qXW09PXBedUw9YE4+ZXRdVFZNeXNOVE1RYG9bQE9mRU9tTXBxQW14WXRFdE9tbHdhXFx0Oll2ZExMXUhSU3BNSU1xQGlSQ2xVeEVuSXlqakVzRlFNS2xVZllnS1Z5a255RUB3THBuX2B5Zml5b0dhbFluV2lveGZsZVhsZUB0Wk5fPXlsUWhnb3hja1ZpclBfPUdpX294ZnhsbE5gSW5jVG5weHZkVWhmT254YHBiaHBiY19rW2BsPnlbWT51TXFpc3hjcF50Z1llSFhePXFdcFBjUF5wX2Z3cWZ0YGd1RF9kXmhuUEF4YFlxcT9bbT9dSEFgbkhmUFltbUdbUU9vald2Ym9la253PFdoR3hebE95aUd3YFB1VVBmUGdpSGhfQ19xcWZcXEZnYUhweVxcYXVqR2NHcGtuQWtbUWo/R2xeT21UR3BGUV5rdnA6b2hJcGxKUGxSP3NRWXNfb29WVm5BUWxrbm54Xm9NQG5UZ2xXbmZqRm8+TmhraWhkPnNEQWVrXnY6eHVEeXFEWV89aGhxUWBJaXVEX3VRaHdXXlxcaVh1X1dbPHlyP0d1VHB4X3dZY2lmX3d2VVVHRVNOcURnTXJkXWJcXF9JQFdmdHlCanFEQV9lanFES1NmTEtIaWtjZ3lYaz9IeHlkbmVZcXFycnl3TGd0VEtJXFw/SXVHZGd3SGpjY0trQ3lZQllddkxHd3FzV2BJdXVJZz5DZWNjRGI9Z1Fdck9XZVZ3c2RfVHI/QlxccXlKR2ZnY1dqQXU6UVl0a1R0eUdcXE1id2lFT0tnZ1V5Y1lkQ1t1UkF2YldHP3loblVUckd2SmV4Q0VVb013X2lCRVViSTtkUllGbW90YHl0b0diYz1XcnloXT9TUVNXVXFJcFFTdWF0Y3VjRVtIZ1FZSE9Xa2NlYU93ZndYZV1YalloYVVzcFFyTmdVX09JaUNSUm1TXkNjZm1nYj1HUz1SVFFjP2d5T3VSdFdVa2lWRFdyaG9iQG1mWnVHZ09zdXN3WFVVTUFnTXVUaT9ma295W2F1VWF4aUl1R3dWbWVkX0d3RVliXm1XX2FnP3lzQl9FTFFnamd5RFtIRkFUUEFpXVFVO1NiXj1nT11VX2VSdF1DZWl4ZU9YRW14XmlSPU1XUm9Ub1FHbFlGR11Zaz9CSV1nS0VHcElCXmdCVm10PlFXY0tkVVdicV1oY0FYYGFZWW1TVkVXWWl1X3dyS2dYWUlneU1CPGN5d1t3d0NYZ3N1TUFzb3did2lWdW9UWV1ldHN2VmFWbXdzWHFSYmd5VVV2dEd3XW13dHVmbVdVTlFXeV10aFNkWj12YHFGUEF4UztCbW1CQltoOltiYmdGX1FWO21EeWdSQUNmZmVEUD1kR3V0YXdCV0NyYl95Vkl1cnFpclNjQU9XXlNJYz1DcD11XWNoTmlHPFt4bl9TaGtVVE1JV3N1UEdyW2tGaG1YU1lVUl9zUVlmOmFUXUV1XXl0cmlSW2FDXXF1Xkd4V0lmY1FWWlVnZ19zWHl1SHdCdEFoVVFoR0tzcldjZXdDVWN0ZG9VZ2NGZGVoc1FnUk1VcUN0ZmN3XFxhUnc/clhfUnc/R1pVRkN1ST1dR2dpWUJhR1BhWGZFVE5HSVxcT3hmV0JxS0ZTaXRPZVROS0hOb3NfV3Y7X0R2SWheR3JZYWZHc3JJSWZ1UVRdaUJ1c0NgXWl5UVh1XXN2S3hRWVdmR2ZZZXRjRVlYd1VgZ0lnWWZWZVh0eUZLSUlhd2ZUQWNvd0NmVXlVQWNuaWlVT0hwcWZpRXhab0N2c3VPR2ZNc1NuUUJdP2lvcWVAV0I/d2JBU3JTUVhLRWRYZXc8PUJhVVVWRXRHQ1ZLXFx2QkhOQV1Za1xcdWdJbz9MdlU9cVBESm9wbzxddHBpdFZpcUxYTWJkeF5pU0dldT9ha1ZMbm1Zb09MTVZFU0dgdUFcXEtfaFFTTVBdRUpgbUw7ZVFSTHJsPXE8bHU+RU1KWG5rSG1tQHB2cXlkXVhbcVB4dU1rYXVdVFFkcHZsVFlzRHhpTXFqRXhcXGlPTl1sXV1TXkxYTk15cWFOUEBVaUV4TmhNY3VKZHFNQlh2TjxzXFxlTD5oS0V0U3hgV0lNVHNEV0NNdVZ0anVBVmFUcF5oTU15am11WF1QS2c8bHhMU3M9VkNtVXNgampYUFlhbUNQbUhAUVlod3JxSzxRTVFVd3VhVldpVUNoS0FtV0hNb2NwV3lFVnl0UlhEeWpwTHJ0dVZITHlgTEJ0TUs9VWVRaldRSk9wcEU9eXNxTGF1WW9wdVJpbW50VXR4TWBkeVtRVz9dVTtQa2BwU1RlcWNhb2lpTUt1V1dgcE5UdzpVblVoUEVxc0xFVW88cEZMVmVYWD9cXHFmRFJlUExmcXBxXFxWaFRXakRQb0BwXVFLRmVWUGB0dkBYP0hZdWRlZllxUVhfT3BvVklwTGFgdHlaZHhzXT9geT93YFZjdWdhTEdoQWZaYFdzPnljb3BsUl9zVnhyPUlpS2h4XWF5U3FlUnZmU3FaeFlsYEFebnF2WUFvUXFnTnduTEdgQE9pcmduWGd5ZWBoaWB2ZFdmW29wTXliY25rZGBhUFBlQldua19fSWBdZ3Z0VXFfcj5zUz5vVV5fUkBvXXloeF9eTG5jSU9jXkZsPlF0UlByT2h2QklaPT9cXE5PWlhJYV1pc2xZeF5ReVhXZUluXnU+b2BPYlRIaGZeYWVJZXdvcFhQc21ualdIaD5QcUBxZT1XZ0RhZHBAcG1JYWs/YURBYGVJaUl5cVluZXNOc29mYGJYXUpxeVxcYGR0R2s/V2BYZ3lsZ1xcWVltVEd2X0ZxUWhzWGhodGh5d19mPz9Lb1VVb3RkXXRvZXRHYVdPaUhvT2VYU2VzW0NIS2NPeWRfS1RsQWdnUVZIYWZnQXNuS2ZFWUVJU0VFbXVZPWR2P0lwdXZ1TXVpQ0d3a1ldUVh4d2JqY2Jsd2NodXhMd3h3X3RyT1VUd3NtYUVgb2RGc3ZTT3JNV2dkd1k/eXdUYXlBbXdYSVd3R3ZeV3h3R1RjdVJwX0lrcWRSRUU9WXRjaXRlRWZnUWRVa3Nqd3hrTWVITVZmZVhxV3V4XXZQZVlVV1Nec2ZIS2ZeVVNMbVU+dXN2R1dTU0htZ3ROV3JTO2dGd0dcXEFUXFxXaFVvZz9pRUN5R1NVWUlBZz9FWWdnRkBFdnRnVmtJVmZbSWBlV2RneV1PVEljVmRLdWtpQ2thR0ddRjtbYkE/d2xTd0prR11lWWRTRGdJaFhleXJXREhxQ3lFVk9NeXRrVmxtSEFFZkVzdmM7RHZNdHRzclRDVUFNaWJleWVBVVddV2FlVGc9RlNFSVBjR2ZHdkJtY0BhdHJXYk9VWUdhREZTRWdRWWVLRHNlY0c/dGhbZWNtWFtRVmZneD1ZUldtd1JRcl1TZnhfdXJrVVdpRlJ3SGNdWVg7RG5veURddHR1VEtjZ3VjVElpR2NZaHBZQk9xWUJxVGVdeHRpeVhfREVneVxcbVJwZVdpRXhNV0c7TXJlZ1Nfb0NMcXc9S0l3T1lqb0V5XUNdQ0dSYVhfZ2R0SVRiPVRhX0Jua3dzeXZ5O3JrcWRJPVdSV2RoWXlsWXhrRWVoZ2lqVVlOa1hKd2JqTVVIX0hCPUlPZVVhbXVdQVliU3RhQXVvZ1RkaURIcUNLPUlmX1lTZXNEcWI6PWVYa2c+WVNLSUNPUXdbR2NFXXM7Q2VVX1dvZVhdbURlUWdAQ2dDR0M/VWdvO0RjZ2JRW2dlTWM+SUNmZ2lBW1VoQWN0T0VDa2Q+S0hQSWNMc0ZLSHBBVHJWYHdjTFRLbUw+PFNzTVdlSFRBcFZzaWpKUU1RYVlOUXlSdU5ncWxnZG9hdXFLaXB2SVZaVEpbSUpkXFxuaVlMOnVSUXBPPGF4PklMS3RVW0FMZkVQYUBRP2VXUERrR2VWSFhyUlxcVGM8TVBFTHNEcWdITDxPZmVXdmZgdmtxdGJIYlFob2tBdUFpcEtealZxbnRPaWc/YklgckBgcVtodFxceGxfWGZTSF1eP2t0QFxcVFlwTz5rYUZnTEddTG9iO1h5bV9aaG9vVnltbk5mdnZaVj5oUW9tTk94SXZaQEFucndzWE5tVE9rdHd1YEd0UGhfV0BuQmZlU0heXFxOclVeZVU/aG9hW1dxa2NXYD9HXFxdR3BKb2ddZndvVnVJXnRLR3VcXFl2UEljQWdlbz5qRD5nTk9hbmFia0hdcHlpcG9hZnB3R1FvRm5bcmh1d0BtSnhoSmdbXFxOXU9vcHNYb29WeHRPZ0l5cD5GW2N3Z2BGbW5vcFFpZ01wZlBHZ0xIc3FIWmFfamVxbmVRaGZRdlxcP2E8RmZyPl5CYGxTTmFwR3hCcW9Jd3dVYXhwaXRncWJnV11QaW89Z3ROWXVCaXREVnVfSWx3QGM/XlpfWG1jX2dlZ1paYXJ0Z3dHT2xHSXRvPnZcXG5sPFFkbE9dSXBiQGBlXWlES0h1X0Ntc3M+UWNHX3RzW3JgX3NUd2c+eXhuT2dfS0h1VXRTZUdlWVVBV3hEO3VuQ2hlaVdNRURNV2Zid0VgP2JnQ3lWW2NcXGlkck1SRk1HZW1yQ1tiYVNlR0lCPE9ESUNUamNWTEdTY0FURFFyOj9CQnNUSmF5WnFJRFF1dU1ZPWFkeVVoZ1l4RklUXFxZQnBBRVB5dWNnd0tnWVo9dXM9dGFBRWV3c2BfVHdBUnVpc1NpR2h5ZjpddVFLYjpHaD9xclZzTV1teV5sbF5odF1ZcGpNT0F0VVF5eGhBWEtJV0x4b1B0bFFIVVp1UkpRdWl1eHN4dlBkS3RVUXdtbXlMdG1pVFBpeXJId21BU0NZeT1ETlR0WW1lV2VxWFRlcF1JdW9USlV0a09RbE5VVUJkcFBYdUQ8dHU8UENBVEs9a15VV0VIeEFNUUBheDppS2poUVBBTnJUUlpIS3I8S0VwSj5FTFVAbVJQeHJVVEtBeXhYdHRQSz9xTz91bGR1d3VNbUdRd2NMeUR1dFRhcVl4dGBRV1BkU0xtVFZAcW08d2hZckBpUEg8V19EWUV1TUBcXFM+bVRmSUpERFJsbXBKRHNWZXBeTGpgRFVRYW1hYVVZeG1BPFZ5dHlpSFl3cVNfZHBRaVR5ZWx0UExpSFZPbXBaWXlJWXBGcUxOPXBecHRkXXZNQFBlVGpFdHA8dWxqRE5DUE13bXBEZHNEXFxRdGVrX0VzQV1vZ2RuPUBTQGVOTmh4QkBSUllMXFxJUHJRdD48WDxBeU9MdG9cXFFNTVRFTFhwPU9tXXg9dFBVZXFPeUtBZVBLQFFdeVNmPVE8ZFJWRXNnWFBUYVZwPFNyXFxWQj1MXWV1YlFvYVFQTkV4S2VtX11QSE14XkVzUHlNQWFtcll2cVF5dUl3ZHBPXFxAeUk8VE5QTEpEc0dIdVdQakpcXHNkaHRscWpiYUtZUVJDTE1FaXVZVW1uTExOTXZEeU9OYVJOXFxYXUxMZmluRXRuS0hrP0VsYmBWUT1LRWl4UG9aXnZhZ3dfQHFgQHheUFFxcVFlRkd1cEhvWmBMQ3NkRWZIU2lMc3huaWk8VWZaeXRxbVlWb3RLPVlcXFV3O1lXaF9mTndZa09FQEdya1VUWENIX212dmtYUFdWVXF2QEFpXXlVdDtZOmVpeHdlWXd1aWtIR2VIT2tIeUtUVHFVaj1iS2dnP19JdWdJandDSE1UPldyYG9XcUt5Vz9yVj9nYFNCXkVUYGtVZXlHUGtkPWVTPltFRlN3O0dWbnN1RmNkX0FZY093cUN2QG1ldllFV2FFWW9TVGFSRz1ieGtpeW9ZdW1kVHVCWU1nPmViRGNUXVlmT2VGT093Z3VzdV1XdkN2ZWtyb0dJO1FGYUlGUXF2X1FIXFxLZkZTRXNdRmFzSGlrR3FpRl5FWWhdZWxNZWRVeXB3UkdlaUdBeUlXRWdvaGdnZnZPdlZDRW5RRz91c2U7Uzx1RlVPYz9jWEtnQ1U/Uj9xWE1TaERlc1Q9dllRZEtNWDxzRE9NVXdrVj9dV3ZdVlF3QmA/dXJ1dV5Pc0RvWHR5STp5Qk91WUhhV2tVVXJxdW55ZXBVRXZlSXRVRU5ldGQ9V01jRFhlclxccVQ7U2U+QWNuS1ZqXVZkW2dLa1NPR0loSXNxO1NQa2Y/c2NyX2N2cWc6d1hgdVN4YXV3W3ZPeVVYTUJudWlZbWhSY1Nsc2dQVXdAO1Rmb0NoZWhPUWdKcWJ4PVl2V0VRc1U8b0ZTPVlYQVQ7ZVdBU2VsWVZCR3g7c0NNUVZVd2NsZVg7S3NRdWdGa0hZR3NSW0VxY0NWa3d4bXREUUU9Z0ZTR0ZlRU1XQFl0YFJwbE55RUtGSExRQFJtUVNDUW1tPG9gTVdqaWtDXFxXO210eGhWQ0x0UlBZPGxKbF1MUGxXdEV0QVVxa0B2ak1PQzxOWHhqPXBPZnh2SGRTPlVvaGR0UkVxZnVUblFQcFxcb2dlb1loT2xUU1F5VU9BTGhEVGB0UHhUcUthbHRscmhBS19MTmxNUENdeFZQVU9JVUxEVHltWF5Fc1hgdG10a1FAUHZhdG9VVWBvZz1vYEVuYFNxa3lWaFZRbVNpXmVPXmY+bltZamdgZ1lIaGZgc3RwdFVwaWdwX0w/Y0hRZz5paEFAdlRQbFpXYkJIYG9OZFo+Y3BnXnM/clBmZkFRXnNoeXh5eTp2ZklhdGRxeWVQW0NRdnVAZFNXckxnZkpedXc/bG1vZ0pBc2Q+aGg/ckRPdWxGW2dhaT9heGM/YGVQc2peY3Y/cV1YbzpPXFxUYW1lcGs7Plxcdj5sTG91UWhfTHhbdl5kYFFjdWldUVd2VFhqYXB3cWltS3hkWGl1SVhecj91blhoTldfX09tVVFmT3FsTWheQEZdaHdgeGFkTEBjcEhueF9odUBcXFNBbEFHbDpwZXZHa0hIcWBeWmBPW3BgY2Fvc3dWd0ZWdk54dnh5cUFId2BYb3FXZHJBc05ReWRndmBwb09oXT15cVdHbVtwdlJ3dVFRdkZhbE51SkV4QWFFWD9mdTtXXFxFU11pQz1tVjpnRWRFeWw9SEJlRz9LRWZrSXNDd0hzRERXclhdZUNHSHRZSFhRR29nYlNVWU5TaHV3ZmpVWFtjRXFtSHVVYl5BcmZjc1RbVmxVRV1DZ3RdU1NldWNjdU5tRmtzVUdFRUdPeGRNZ1FRc0VlU0hNRF51cnVNRl1pd1NzWFZNaHhNaWRlVlxcPXl2S2RdUVJSSWdcXHdYcUVXPVlXZVdjQl1VdW9lQnVJTEl2TFtTVFtkTmBPW1FTcGh4XWhQU1xcVldpdmJ0UztlWVs8TW5hbWJgV3RoTFJpTz1xbDp1d1VFUHZEVGJpTV9ock9dVGVxeDppdWxYVGJYd0xEV29VUXZUdHQ8dXdpTWRRcFhVSmZkcWpgWVJQcW9EamBFak9xVj1tWWJpSnhoTm1gT0NNT0dZdEU9bEVFTE1RTElJeWFpb1A9Tm5Qc19wTWlJd1c8WVdRVlVsVW9Qd2tYTEZFeUw9WHJkS3Jhd0xoVmFtVl5sbF5oc09keEFYUktYbmVZUkdMbk11dVl0cld0SldNVFVodEJZVkxEd11Ma1JsVVNldm5Na2JUbjxNWENZTmpgVEdETDt1VnFNVk9cXHQ8YFM+PUpDXFxxZGFKOkRLXjxKO2BuTTxSOkR5XlhMWj1qdkxsd2VwSGRYeUlSb3F5Z1BVTmlXRnFweT1qdGBrV0VvdD1vWGxud1VSdUxrTGlqVVFqUWF0QUlWTWVPa0B2PHVKcGxXU0x3QkBteT1KXUh4Q1hSX3BxSlRuX3FzZlxcc2VISz51Vkc9bWBRUkt0eGt4UlF0bHNcXFlbbHNfPW1tTWZoWV1IV2Q/eF9nTnBkeXQ+eF5kbmNOdm9pd3BTTmRrX210eXZWRmt3cGZocXhbaHdPeHBed2RvXl5VX2NLUHVYaVxcaF9ldUhgS2lnQG5dcW9gcWZzbG50PT5idFdEW0JteVRqZXhfdVJFQ3JUV1hEeUk6T2VSRVdFPXVrO3VdRURJP1VVV2ZkWUlwcWJUQWlZaWhPW0NuT2lvW1RQcXJQVXheRXNGS0NxZ1VAPWV3eUk6Y3I7P2JFbXJUP2lRd2JtQ1VSWWhUdUk+ZWZ4SUlBd1hCbVh3TXVvdUg+V0lxYVd1c2R5eEtddHdPQGp1dEtzZXdgaU51cHQ/aVBkZHVgeUtaXW5CZXJsaHVeSWxBcXI6SHhlYFJkWXZUYVhMZHBwVG48aFVlTFZDTUxlSXRGUW9PbFRxQHVFZUpkYHM6dXBtRXlCWFZwYHlKQHJkPVdbTU1GaFJPPXB2QHBDdXdbYHF0bE5beVNFSG9OYVBPRE5ERHhHQXBlWUs9PXlVPUtIeVRWRFZyUHRKYW1hZXRSbVJ1bXFkWXJaWXlweU9SeXFLcXZTaXleTFdoZXd3eFNpTFRwTVN0eVk6SHFfWXVjTGxmUU8/cXNXeFFFUHc8RExdRXdTXFxzd0VqXFw9VFdkTXZkWHF1U1FhcW5xT3hEWFNYbE5sbmc8TXVhbUJJeHBZeVdsU3Q8a1ZkWG55cml5U3F4c0lIb01ta3Jwdj1ET3dAcV1ta25YVEhAUV1lc3JYRldXPD10UldCPT9DP1tIdEdzOmtyWlNTUD1VQz9zSztDRjtnal1CcU1GSV1FQF9ycG9FRWt4Rj9FaVNZVF1FQ2NHdW1VRnVYVml2YHF0VF90VnFUR1FIcXlJOnVSTm1ib3FkZF1kdnVGRmNiYz1VdFdna1F0eElIYFFZbz11a11IO2dDYFNZVGlyUW9GVHVlSFt3dkF5VG94ZmtVTVNEdld5b3d2QGdkcGF0ZEVJWkdkZ3NIdWF4YWlTYE91Sld0a1t2bllFZnF5VEVlc3dkSnVUVEdZYVdETkFpTWdHaU1jPWdjcmNCY1VzPFdkTmN3c01jT2FDXUlJQU1NSkRUS3VWQG1LcEBMTlRqW1hrO01LRkVTa1V0XURMUjx0Zm1WS2xOS0hqTU12clxceFM9UGBtcm9FUUtoVkBpWFBdbmpMVldodj9xcG5Ub3RIc3NZc3c9Tm95TGhFeFl0VGV1U2hAbll5S1dMVWBgUmxlcWxBdXV4TmBgckRVTV9sVmtYbWZwcEppUGRJSkVFSkZxckZNbl9heG9QeWdEcG5sTl5xUWZ5V1BgV1tQTXJFcGNsd0RBbW5NbmVgTGxhbm9wb2lITVdobndISmhlWXZwbVlhdXd1bndVc3RJUVNFa2hweWBYV19wdUVJbGRRcExgS05FdV9Yb3RocTpUWFdgVGJRcGFlb2dldFphcDx1TkRJd0BgdE5dTFxcdGxmbXlZcE5MdGtMSVhpZGxTaXdrdHJfeVRvVEpRdXQ6SHRKaHhQVFB3QFl0YFQ6WG10cXNdaFRxaXR3XFxrQGx2Sj1VdUlOV1RWVzx0WHROSHh0PklYSkBRR2hNc3huOllZdkx4dj1Mc1BuUHBQc0hqdFRuXFxhdHFEbVFZdjpBT0ZxS2dYdG1Ua0ZxbFJEeDtxSlhIUz1dUGVYcEdJb15obkJRdmd1d0ZxT0VRVF9EdkZFcHFhc1BQdnloWFZVdHddTUJtSnFpTz5ocUZcXHRzQFZvZG9SXWxdZWxkYHdwYVZJeHBrYE9dZVZcXDxzVWlOUFBqbGBTO2BQSnVrbERVdGR5Xk1MakBzY2VsPV1wWTxqXzxwOkVuSWV2Pll3eGxRb3lPdUR4cElUblRTeWBqYlxcdlZIVVBIU1BFWV1VdlR4SkJcXE5PZXVTeE1hSFVjXFxTeG1xbFxcbUtMTztMaz9hUWVEUWhHdmdGdlZma3NfZ2g+W21QZUFQZkVJaGVBa1J5W0I/b1RnZl8/ZUlocGRWWlBwbEpPZ3Z2anc+XFxlQHFyTndBeF1cXFdaPG9xYHdedmhyWFhaR3Z0SUlyaHdddHB0RU5aXXFeP1deZWhrQkFlRT9cXE9Ra0g/eHFOckBpW3VvdD4+aEFhXVBHbUw+aWRhYmx4clxcT3dTR2NpcWNQUHZfeF5zdl9TXmpSVltFT2Y+RmBTSGU8R2hZb2xbX15rbmxgd2ZJcGxRZ2x0UGVyTmtsbmJEXmBjWG1zb3BobnJQYXZxeVpFcHdwUGdrYVtDUWlnb3dbWHREeHV0WF55VmFLSV5MWF5nSHVgVmNnVnlVcWNdRmtVRm1eZ3Z0WHZHYGA+QWNJYGFtaW9uUHVQaU1tV2h3WGZteEJlc0tLZHh5VVVhYz9zUlpXdU5veWJnZGBjSXBVSGxLZGtXV3ZNQ0dzSUBJZUVrZ25BRUlNc2pLdWBtVlRndE93ckhZVGRVYmhZZ0tlSGx1Y1llZ1ddRndXaXNnU0J3Y0tHZ3VxREc9ZUlfSHE/RmhnRmdDRVlBSE1LR2lzVXhBeXNNV2FTV15LaFZdR21vZVJvVUNFc1V3ckJHZURJeW1ZZjxNdHZBeXRPZ2thWVNfV2tpWGtLZVVfR09pRD5bZVBreWtZU0tRSXZjZndxYkBscFxcSF9GYWNhdnk6XmBWQWlKSWVxaG5LXnVvR3dZTl1bb2FuQGBJSGpTUWRxRm9XaV1leWtgT3lLcHRVcHJcXHluTUBwUllyZU9sb0libEl2VV9fWlFdXl9eR0dteG9fPmlmPj9bTF9bYV9lRld2PmddRnlqVFdlZFljYkhnSGdmcFhtRD9mYVltd2hlaFZxeGh4WHF0Z1djUmdrUVhiUmdgW1FnRFF4P3lqWW9zRV9iTHZtRVF1PnlmPEl1ZVZrSHB0eXdgX05gQ190Y0BlcWledVhra2VAU2RtQUZUa0ledXhqX1JzcGxSRXRZWVNIaFBAYFZ5QHhwYHA9RXFvYW5jcHRqWVVkUHNsVVZjWXRCbHJ3PFNIaVRGVHZ2dHFqeVVVeFd0SWxjbVM9ZXdfbXdKRVFlPXh2dHRsYGxmZHNQVXZYVVFVPXh3QW9sQFU8aHJTVFlQWUpPUXZJWVM/bVVqXFxZOmBKX0FzP2lvQXlsRFxcdUtEc1RwVEdMTFNkdF55a25kaztgSj9kVmRUSkhcXE5YcFFlSXBzZUtQeVdXeFA/XVJZeVRlQFReeVBDUFJAYHdhdXlJRHlOYHZCUHZXcHN5PEp0WFJzeHRkbHFxXFxVU0hwUFxcbVRRUGF0dEt0WUlhdXBgUVxcbVlYUHJVRXhYTFRWUHJKYFBuUXZ5ZEpbSFdEaXRGcHlhcGphVVRjbHRrXFxNeElVQHVZdnRZYWhwb2FXYWZ3aGBuZ2l5Zldob0hoW3hnVGZ3SFBlQkZvS1l5QHZzW1ZrUlFlbVh2TE9pZGh3YkBtcnFoOnlfQXFrRF9bdm9hW0hzckFtUlh0XXB0eEFcXGxJZVN5XnRPdWV3YElgXVVuW11ZY04+bE9XXUFnZGFmXWdIWkQ/ZUE/dlpGc2VhdEVPXUM+Y0dobEFnZzpJdFc+Z11nb2tebW5YdEtwZFRZYGdxY3N2aXBPZGdwalRxcUJIdmt4bEBJdj9pcnRgbm5YbVRAb0BgYXdXUUdpcU1lVEV4P0NYTUVVU092UGdSPlNGZFFXa19lSFNYcUtJYmt5YkFDcHVHaFNzTXlialdYVENnU3FmXl9oQlVDVkNCXT1pSmViVWVWdE1JQ3V5dTtDOlNXb0lJcmlHeUtEdXlneGFlUXllaFdDUU9nbVN2VFFoV095cUVEd1VzWWFiYmV0R3VEUWV2RWlFcD1DTUdlQkNGVGtiP29ZYXlYVEdybXV3PGFWQlVIZE9TY3FSTEVDRnV1ZTt4UkdlTGtjcmFHQEFUdW1nSXNHTVdVcWl1b3VYP29YWVVmZk9ITUNmP2VzYmd0O2NCQztTYGd5TEVmbWNIVHVla3ViVlVWSktHPE9VTFFYXz9Jbj1ETHliUVNHW1FGQz1WPE9jTnVZXUNkUnNEZGt5WD9odl95dV11bXFnX3N4VFdTVHFobF95bmtnTHV0VFFjZl9Yb2dWcT9IT2NXckNoWHF5T0NWZU1kal1HYT1lTEloY2FFZ1dZQmV4Vmt5YFtkTF1WXFxteGVLSEF5STpXYztBWDpJeWt3SHRRc21rd3d3QkpnSENJQlxcZ3lZQVlFWXd1a3VreVNwWWhIa3hBY2dgV1ldaWJMZ3VbRXVGY0Q8cVZ4V3NmVWk8U3hkb0VyX1d0c3lvQ0RuV2c+O0M7V1ZLY1hla2lCb0heT0RVRWZqQ0ZkU1lMdUV5dVdEXFxtZ2VuXFw8T3Zsa3lHbXB3a3hpcGB4aVJpd3heZVFYZ3lmZlhJc3g/dnF5XFxwSWlcXGd2cD55VnZZOkpzcG5RTW1jZXlCZHhGZXNmVHBSUFhVTHNSYFNsYFA/SE5FaE9BQFVcXFByXmlMSGRQO1R2P0VWS3ViO1Z2TXdsT3Zkakd2dEBiVlZySlhmOllaUEBga2Bea3F3Q094SUdxeE55UllhSEBhYVFaUGlyZ2BedGdoclBtS2lqcWd3Z0lxc1BqZ2dlYz91b09nTWhvdG5sX3BuV1FoeUZjZ0haT2hbZGZnVmFhcklrXj9wb29yeF9hW0lkP0ZjTF90VUFjVT9vcnhfQE51PVheY1htPUhpS2ZqZ3FpSEFnWEdxZVBzc3dwVWZoXFxWb0ZAZl9pbVJJcURBcEFIdk4+X1ZfW19XcT5IX2NGbVRHaVBgdTxZdUxwa2VHdkxnblJ2cEZ4cUlBXFxPWHFEaF1ldmBMR2xUWGNIYGFycWhnZ3B0XnQ/cWBVQWdQX2RCUF9tUGBQT2RRaHdnP2tqZl5DT2VrcWp5Z2FcXGBpal53YnBoWHFuRFFudFdiWm9vYkB1UD5gaXFiXUdfdVFoPE51V2liQkllQ0hzPFlcXFZwZktPYHBJXmtedF9AYV9QYD1WdEVOckpvbEt5d1l4ZUs/b2ZpZUlZSHFjX19TeFVUaFd2bUtYZV9Yd11VZ2NybV90RmFYc11WdXNnPD1USVNTaE1yP0tIO3dyU2d3PWF1QldUSHNHQ2VidVFET11CbG1FYztlXl1ybV1XPj9GWW1VQTtnWW9la3FyaU9oT3NYX2t4RnV3V09pT2tWQF9HVWV2ZE1iZFNnWkl2YnNmRmFnW1F3PU9kUltYYjtEOlVkPUFJOkFoSHdLclRxYlBzUmBMPnV4YU1WdUB4eFhRbHRRd2F1bHlPanhXVUFzaElrWFFZPmRXZT13W1hxQlBZTlFXdFxcUz9YclFRb0pMVm1pdGlcXG9aeUtEbVA+RVJMTFQ+VFNLYExNVExgaU9tUFNHSGpaPXlGeWtqYHJBeFR3aHNkdVZGdXhnWW9qbFJxYXNKbExVXFxXVVVWbG1KZlVVR210Wmx4U0RRVUB3VkVXalRVbF1NXXhPaFhxXWR1X0VvZEFMeHFZYGxOaFB0VnF4dExWY2l3VWRqeGl2X110P1BSTEx4Y1BvW3F5RmF0XjxLcmhuX21WSzxxTGhuQ1BrdUlUWGxzVVhzS2VOYUxQVFBVd2xRc2RrZ1xcc2FxdU1JbURJUXhUaj1Id1BRV0B1Vms9eVdxbWdhSz1dd3BVcztZUWdoclBYb0poUHNMT1tscFtNTHNlbWVdUWhMc0V3W29pZlBGaFRuaERAW2BnX1NXc0tvbGZwcGl2X3Bvc0Y/Yk5ZdmZhcWtedE1AalZwWzpIdlFxaldeYnVheGxJY2FZbzped2dXdnZXcHFhb3BXeV9Gb0ROalJJaHBweWZAcXFublhBaVVwallmYUtPaVtIbE9fZXQ+d0JncmtwXz5Bd1JnZ2tgazxeZHBgbEdfcG1OXFxUP2xJUG1neWh5QVpPWHFQdmxOUXF4X2lXYV87WF1ZUWdRb3NVT2NlWXNzVlxcS25qZU9xTlldV29sYlBda2dqQk9cXFJGdTx3Xl5AanM/eT1IXFxGVmVHZ2BSVmtJeGNyQWx3XmJld213d2l2PnFpRndDb3R5QVp2cWNneHZtWXNmd2tVcHE9V3VaTnhXVmpMdm1lWG5bUVxceHhfZ3BdPGZuR2lsW2ZsdUd4PlBmbGZtTUhfcXFpZkdveHZvdXB3SXlyYmFsblldcmhjZWhxbW9dUFB2bFltbHddPWhjPXBdXXFqbnZxSmhhZGhgY2lkPGhbeHhib19jb1FcXGVndGZZbUx3cD9Rc05ZZkRIY1RGX2F4YkRwaz9hc3ZHXWNAZm5odVBZc1RmalRBYXY/c0xZcXdObnQ+W0xOYEBJc0pBYUZIW1JmamRRW1BPZGlYc2lWZ25oc3BIblFecFd4ZztOZWZYZUFxa3NmWztQWmZoeFVWYU9IcW1OZWRHZktga1Jhb2FGdkpYbFRuYFhOYzxmc0J3aE14X2Z2cHReZW4+cVZQeHJ3eFV5cWdmaFE/ZWVXX3hecUZuW21ZZlZJa1lwYUxIeGNXYE1nZWRvcHI+Y0x4Z1NhXm54YVtRbENnamBpcllvZ25uWkJZW1ZvbmFgYWVZaFVOeWRheGh4dXNuQEV3YnVzUWVkU1FoUV1nRGdyR2d0Q0NVPl1WY2F5Pl9yRk13VmliPl9pSVNEXUl4am1pU1d0Uj15dUdVQVF4TXNpWVlZXVlITFFIcz9zTF9paGV4cmVUcFdSU0l4Pml4Q0FXQ21kal1FYV1DPVdTZ01WQHlHS0FJQGNpVGFTPWVDXUlpQVNZcmtibF9XY0llRFdYYUNGcHF2SGlVTE1pSz95YFFFTz1oQz1ZaW93VEdFdmNUY29HX1VHPXVDUUNIYF9ZbGNTaUtIWmFmPl9HbUFTdXNpSmtEVEN5dFtEZWFDdUN5dV1YQE94ZF1FdW9WXl9kXmVXYGdiRT9JWUF0b210O0tTYnFCa3hMSkx5RE14d0BTUXlwcmh5SWl1V2hsZGVNPnB2YU1UTTxXQ3lPcFhyWD1PdVxcTFpYVj1pcHddVFpQc3BEUjpMVkZ4bUFdVkllWT5IVnlMdkhcXHhvZFJkTFNzQFNDRU9ldG1DQVFGcXB2QVFKaVE6SU5NdVFUTG1ATHl0RGtIcHlnVW5kXXdEUUtAaVNqdFFXbVdVbHdSdV93YXZEP2ZDZ2h4XnFiTmRdZ3l2P3BMUWhRUHhhWXNGeHA+eF9BYHZTRl9BUWtYPmxhR1tIV2BJcHdmX3hISWBGeGZYbnlyaGVOdnFJWXR5QVpnP0Vldnk7QmlTd1JtU3dZeHNLeFlnd2lvdkpPd3k7Ym5xQlJ5dWdvSElrWFRBaXd3eHNveFhBRT5nVXdzZFdHcm1RV2BzUllTVkdRdVdVdFNPRGB1SWs9Zm53ZHZtRFpVWHBPVlBBY1tjVF1FdT1vWD5DaGpDQ2ttVWVjWGlvRWpjZ3ZtSE1TYkZVd1tXZklbZ25RRE1beU9DZ2t1WElFVEpRc21ZVEFzRGZTc1NVdkRRaHFRaHBnWXlfZEhpVmJvdjxZVFFbdj5xZXZtWEhRV0NDWFVXY2NlWWRHSEVDeFpVZDtLaF89R0ZXcl1rZm9JY111UlRVZGtpRnh4ajp0UUBUbE1lTnNlTHNhVmdxeVo9UFh5TWV1a1VBSlJFT05Icm1lS1JgeVpVbz9hT1ZRTV1NdGBcXG9zWUpoeFRmaWxbTU5fZFNZSExRdXE+eGtMeHNyXFx4Q3VVPGF0UFFudlxcUEZ1a1VQcWR0b25JWFxccGtMVFZoXFxKXWV4O2xVO3FXQFRqX2xqRURzdFVyaGFxZXVyRklOYU11b3VuREhyZmRLT2xqRUxUVEh5cFRVUUhrb3BwcFBNcHl2U2lYeVFUb1lQQV11dTx2dnFXa0V0WHRRREVsamxUcGlsUHBQU0F3clFPcGxSXjxZYz1WbUFwTlRVQkB4bl1rW0RLa2xRcWVOQml4cHBMaGlUa2lQR014UWR5aWhSX3VQcHVvVUh3RF12bVRZeXVPcHRrP2xqcV1TX1lvXlFUYGxUUlFYU1lNSVhsbXRyXFxsUmBMVUtRU3BdS0tFcjxUT0BEeUNJTUBgcT5BeEptbVZ1b2RpUWJwbD9JTU9Ydz5FeG9BUmdcXEpLbWo8XW5QSFZfbHdRSE9FPFg6VEpXeVBJdFlcXFxcT3FNbT9xT0lod2NQUmBgd3RBbFBgV1lddWZEUU08SlNRb1NVTUJgdUw9TE1UcFNMTWhAZEJwa0NAYXZ3bGBJXmZXbFduXmZ2dlBJb2ZYYmtYcXNndE9Pd3BXa2xOXmBQaGVpcE15ZktHW2lvdmRuZmI+YlNhXk1mXFxMP2hGYWtBYWNGeHI9SWF5R1xcWVlzUm9lVldyaGZ2eGZyZEd0W2ljQUlcXFVZdkNQYlBhandobmhmZ3RgbGNIY0Vnb1xcWXNAd2hCVmhSbnNqXlBoc3NgamVkVHJyUUlXaE1ibWdTWHF4SWN5T193eTtyV2l5RU9ZcldTVHdFZlVJSVdjb2VJQT9JRmVoWWlyP1dFPWVUaktUTFFzaz1iZ0d4RF1CS195SFNUZnFDa19oRG1WPFNmbE1YQGNET2VUbTtocV13V19yQ1tXeWF1QlVUQGFWYz1kVXlIXz9FOk9CUD9SOnVzSXFlXXFkXk1ER0F2TmFZRmNnR0t0YGtmbElST0dDQXdXPDtScjtZbjtEUFNyUEN2XWNySFdTSD91SVN1XU9iaEtDWztUcj9nU3FDZGN0U1tVYF9kUUN0T0Nnak9kbmdJWG93R1NoT3lYcEFCRWN5b29ldWd4anVobj9nZVd0Zk1yZFtUVz1nQ3dlO2dYdENmQWFSRGd1Ul1yQFlXXUV1dm12Xk9CU0d2XFxjd2pBSEFLVE9zeUZ1WGt3dDxrVFJxdVJxRUlnZ1BxRGxpWE9HST5PeWA/VGFBZD5TY2RzZFtfZHNQc0xZdGV1S1d0c3FgS1txa2Nsak5hUGVkT11Ibz1tdU9AdD90eD5Qbk5gSmNoc2NZbVxcWHVEWWxGaHZvYFZvSXB2ZG9TbHNtYExlaG9yVFZzTVR3WVBOZG9jaXhwVW9ydHNpaXNmdXdHRXhlUVdHPFNwZE9gVE1RWE1xVHhvYE5NWE9RTHBXdU1dUHNPVVJQRXNUVVVHcXVMTE1DYU1LZVJpaHQ+bG1tdXRNcFhUZG90bVBBZW9xQHVoRFVTSFFDZXNoYXFlQFVobGxvbEo+QVJkXUpaYVBWPHNEbUxWVG9kUFhmUFE9RHV5eEtpaG5xcXdJaVdtTFllbXdLUXdvWHJkeU9PdFFVZU9IQXZSQVVSUXl4XFx4cFBTOkxwVkRWbVBYTWRva2F2Q2FNQ3FqQnVyZ2FNSUx4PVhybFl3YkFsWHhQbmxtSW1QV1l0alhsdEl0T2VVQlVPYG1VPXFMSWBVUkBSTXFKRWxZY0RXYFlPTXVLPXRKVmVKcmBSYVhWPXRWUmB2O0htP1ROb2xsUlVUZUxYWGxSP2F3PTx0aVROYlVSeFF1Z2lvcGBqcFRVdXlMbTxrZ11QYTxLPEFsQHRPQ01zSmBMXUVLRFFUVlRWQ2xza1xcS11BTUBJUEZGYWdPdnRZaFBxcXNweExHclVZc3BGdVZQXVRxaUl5aXBgX19fdGdxZ0o+XU1weG5XbGtGc1pXYllOZFNmZHF2XFxrSXdKeFphUWBfXnlrb2E+d2E/aHZkRml3eGJvR2Z3QGFUWXFcXGFycHFoWWFyYFhiWz9kRmlnR2lvWFdfcElocHlgZ0ZzZ2dyTlZkZ3hkaVFbX0lnQHFvYUBrRXdjZmZtaGhwSF9eYj51RXFlQVFfZ2hwQFdrYWZedXdkVV5wbGhvQld5Xj9tdEFsYUBIWUI7V0ZYW0Rpd2ZNQXdTb0RZTUdVcXY7PVU7ZXltY2dIO2dFdUdnd2ZmaWdLT2ZLa1duXWZVPXJoV2heY0hOPXQ9aVRdW1ZHPVNOVUZtdVVaU3deR1ZQa2VUQ1VqWWhyQXNiQ3dpV1NFX2NXaWVYd2RXeWVVXUdoV2lYO2ddcUdoSXhFVWdjcUdlS2JMPWNaVWVFWUc6T2I7RWhZPUQ+QXljW1dyZ0lCSWhfP1hxU0JhZ0drZ0lBRVVkVVRTaWdRWVhJV0ZpZXhFd3lPQ1ZxZVd3W1ZTb2ZmUXRXZVVkPUV1ZVV0S0Zfb3NSP2haT1leYVVhQWZIb1NpV2ZkPUNUYXJCVWNzZURhP0VNaWVGRXZzYWg8WWhjX1lCc0l0XXN5O1J1V0NaeUk6Y3VubUdvZ2lbWVJVO3lXZ3NIPXNKUVVrS3ZncVdJU0NZRWl0TWRTc1lOP3lzWWdFXWN2a0R0T0VtQ2lraXdQRWNRUVNBW0hDU0d4S0ddTXM+WXhUbXc8b1VtcUdHZHJvcFJXRG9gZXJiXVZjREttSE5oQUtebHZOWXZSVHlGSXNNSXZ1XFxzWURPT1FKU3F4W1FYWHR4ST1XZ1R2b2VwYklzT2lvVWFQYVlVa3VLUD1VQ1lMO3BMY3B1Y2RNblFQZnhWYGxTQmBwPT1xa3B3Qjx2O2l3Q2BrQ0RxTnVYT2hRcHhyYXB3QEVXWEhVdVh4ZHhVWkh1cXV3VFlPPGhwSEFzQVRMT3lyQXFLcFxcdERhbWlETkthTU88UWtYbj91U0lUTmBAT2xVcmF0cE88cz1EeF9Ia111bWtBV0tAc2pMWGp4UVZET0lYT29QTWBRT1dsdV1ZcFFRaUdWYE94ZmducG5pbUdgcFVAbGRZXFx2QW1VZ3M/YWtBaFxcSWhzQ0dmdnhmdmFdbEdic3Frb1h0SEF3SHdwSXBvU1dfQGdmR0RsU0RgPUM9UVJCO3NYTWNjR3RSb0h5S2VGd2RWUVNMXVU8SVVuQ2hHU1ZFTXNVX2lOXUVdTXVIaVVUU1lUT2NYXUVBcWdAVUZrZWlER3hyYUded3ZQbVZMRVVqZXRlc2JfXUd3XXluTXZqR1RfZ0hQUVM8RWlCTWVeTWJBSVRUR2d1SVRCV2V5Q2RJc2RjP0RMd0lsT1RMX0JcXDtpOlNoXT90bENzbFtYSldTT3FWY2tTTmNIOlt0O0dyVWl1PUtIY1dFaFFZYU1CZ0tHRz10cEdUZHVXW2FiR09TSnFCQ29HZUt2Qm9UPmlERz1zdT1GXkdlZkF5bj9DcHVCVUNWUG1iXFxrWXBdQz4/SF5ReVxccUU9PVRpRWdzaUNZS1I6U3d1Y2V5Z0dqUXd0UUhjRVNzcWZFO1hPQ0ZgUVleW2VVSXRbY1VBSWRFXUNKO3NHY1I+eUVnVWNaX3JQVVNCc1hiX1JjT0ZdU2dFX2JSSVJVRUdscXZyWXhrYWRuc3ZsV2dCd2NyS1ZfRVVEV1RWd1I6a0k+P3VHS0lbSWdBU0ZrU3Zsa2NPXVVfUVM9PXlMX3RfZXZEX3M8dUdNX3ddaVJJW2JOb1JUT3NNT3l3b0hjZ0dfUXdBQVVPa2RRXVZ0c3ZSbXJrV2h0X3R0d1hgd1lHQ1hyUXV3UUNAWWhFVVV5PVZmXUNWU2VwbVg9WXdQaXNYXVNpaWldZVhnW1ZocWVCc1dvQ0hTaVM/b2VvVUJMU1dDbUNFU0NYT1lmTUd1R1RaQ3JlW3hTQ2VgWXNgbURNY1ZtW0ZYV1VHa3V0QUlkdWRdQ2NcXGFyd0lpXFxRZ2hpRlNZY25TZGV5RWB3Zlg7VEI9dE5jZndZR2BVY21VaDxldmZldUd1RF5xc1FdRlhLdUBVc3Y7VWt3Y0xVZ0R3WWZfeENzZmNldFNJYl5NcltnckddQlN1ZU5hVkNvR3lHd3JPdFA9ZkBPRE53R1BVeTpzR2dxdztPdFZzeFxca1RMO0NLT2Y8bXRwdUJNc0VfW2ZfVUhiRVVhb0hVb0R4TXhdP3dGV2R5XXZBW2RrQVhsZWZbW0RtQUVOZ3ZKU1NETUdIV3ViV1VMWXR3U1Z3Z1NZTVd3dVlSX3JPWWdjdVNZeXhldWVfWXZXWXdjWXdobUh5WXJRRWl3eUk6SXJvYWh2Q2lgS2lBRVZlZ3VQR3hWb2ZXa0hSO2lAdXliRUVQRWc+eUZRZ3VCQ3N2b1Z5a1dIS1ldPXVOP0dtT2Znc0ZgV2NFdXJMXUhxWVhmTWJsX3NbW1JbSUdRdXhYcXRua2hXW0hsdWVaW1NHZ3N1UWdnZ2VZX1R1UXNPV1dRdUdaQWdSP3hxb3ZOc2NeYUtHTUtDRE5ObXJkTXhARW9DaHd1VG5fUXR1YGxMdHZhTVZ4SU5nQXZdZFFGUFheSFg/aUxjRFRGPFZuPU93UGtBcWpeUWw6TUxzPU5laWplVFNRaFhnYEx1cXBfVW5vUXFGZEtnZFRrXFxtc1R1RkROcVRXRkBSTXBsUnBLc0xrd21uXzxKTnhLV2hLSkBtUXBNOnFyVUFLa0lUckh5ZmxWbnF2UWhMcHlQTFBydVl3XFxUcW5kWXFQU0xET2RBcUd1dkdpV1pUSkJUTFtUa1VtdGdRdVh1VFxccFFLQVc+QG5MZHRoYFFGcWpXWHJHdExiTVBTRG46XFxNc1VsVFBLRkl1bFB4UFV0U2x0SHFOblV0cWl4bHhvckRKU1xcbjxJa2xkVUhQUTtNVj5QUkZRVUNhVjpoUkA9TmBAUUBAdUlEa0JlTEFITFxcSFBqcVBtcVc/eXNDXW13aFdIWXdRcHJcXGhsWHROc3VSSGlUWWx3dGB4PEFQWWBVdUFYX1R3aE1SW1FTQHlRTURNUFFMVlRvcnhSaEB4TlR2eUhTSUhzREF1Z0hrTTxSXnVYb2lLP2xrbHBwUW1VclFLUkVrRWxWYmxRcUVMdXluRHBSQVF2a0VQcUxYUXVrc2lPcXlsY2Bqb0h2PjxxQEhzVFhySVFsQFxcU05wbkJJbVhsdnhUdFM9dlFZbFtdVz9hS01FTFFcXFJaPU9cXEBQVjxwdlRPbTxYSURTWVlMXFx1eHJ1VW9wUVtlbk51TmRRUnU8blhpdW1MV1RpeUA9cnNMdmdJUGdASnc8V1poUHVFdFB4Uj5Qb0VFcF10UndMcGRNWDxBdFJEazp1bkxEUWNZU0VIWEVIdmJ5eE1UaldpcVZVUG9EVEdscWhQSz5NcztVUXBlaz1JUUVxcWRdVUo8U05gajtdc1FUT1xcQVROblpOTndeaGlmSG92QHBOSGZfSHZGSW9Kdnc7eVtyeXNTeWFucVtqeHk6PmlXR3lYXmllbmlRcXZ5TmhxeWNlaVthTmxYWW5ab3BAeWlfVndHV3lyQFtId2ZjZ3dneW93Xl9iaHFKcHdFT2dwcV5eeXVKZnhQT3JOb2RAUF1vUWdmaGljWF5vb29fZmZoSWNbXmdmZ2NVaGxaV3VreGJfb3FYZnhlWHNmbl5yPmNOb2tuP2REaHZGXm1tVmBzaGE6T2peWVpMQVpXdng9eHdUeXFad3k6dmJVeGZwWWxjSHF5Pm5zP2VweGVwcWlpeW5jaWtZdmV0WHRuaHJxRmdmR2NxTmp1Xlo6YHBWZm5kR3ZpeXFeXnFrPnRjaHZOZmxTSXNcXD5cXGRhdl4/Y3NvY14/cnFxdmhWYUNvbGBAX11Xb3VmeVhZcWV4aVNpWnhed2VnaFF5b1Bma1c/Y0pQc15QcGZZY0ducm9xb01eXmVQXFxcXGluRHdqbmZaWmdpSFBya3Z4bG5qUD9kRj9fZXBlbUZecmZzcUFpPVh3Vk9fQXlkZ1ltSD50eUZbaT51UUBrPXljRHF1a0deV0BnT05wT0dya25xY15bW0doTmFlXlhta2ZsZ2ZuaEhfa05gZVBwbGZsW3FqT3lzeUBlaldBcXJZY3V1VVdvUUZNP1dtZ2JwcXhod0RdZ1hFZ2hdUUVtWXZSTUNXc1lDT2Z2T1hnTVdXa1JYR1VbRXdlc2NNRUdcXEtVdGlXdW9kX09DWG9oTmtmTGV3aGlFQ01yQF1CPk9DXkdIPUtWcm9Fc3dpVUlCTl9EY1tSSGNoXFxLeT9vdXFXSWlVYmFTWXl1dTt5RD5peD5PU1VPR0NRQ0lRZkFNcmpld2Y7RU9tdTxTSFo9dFZhUkZ5aGVPeFRdaDxldltbZ3V1U2xZVnZJY0Zzc0tPRGlLVmFXaT9BaWlRRXRvRF51ZU49R01XV19bZ2M/WXE/WE5tdkZbVHFLRlZbRD5ndkdjaVZDYlNDRUBRZkVdVD9RQztjZFtxVEE9U0VzdXk7UmpXaFRZVmtlaG53RV9vd1d3RGlldFU9dEJVdHR3d2ptVz5ddWlzZGM9U0FrU05bVHNJRT1xeWBxdGVbV3U/ZkpraGt1UlVrdExZdFJpWEBpVGlfcnc9WFNFQk5lZ3VpWXBZeUtHVFZBRWhnSERbR0NVVz1FaW9haE1VQkRdaUtrdlFXZ1FBZEZldFdlcl9dSV1Fc2NzZltJaHNlZ2tXeEBdeGdZeGNxeUtVdU9leVJFYztHU0JfRF1xY0RVYmB5VkBbRldNd1JlYzpTRl9deEhxdFJLdXZzSGdRRlVrSE9jVHRlVDw7WFRzY1dfVHdnZ2pDdG53UmhXREtDSTxLdGlTZ1BTSEs7RFpzdktDSWRFYzphdW15V2F5dEVzUlZZSEZRdVVhaF1rc3JVREhBaV1jc25XRkhGYWZ4XlZ4cVR5WktvaWFJXFx3cWhuWHhhb3FlR1theV9wSWpOeWVzYHJ5Z2VnYGFoeWk9eW95QVpNSHhZeXk6VmBrdnk6Vm5nV2dVeW54aXZteHk6dndZd3k6RmRYRm9lbm1sdng9V1pqSHJeSV8+YXNGYHZzX19NYFp2X2FZWHJmaGw9R3hqdnE9YU8/VnRVdWtFZGB3UmNZVz11Q1t1Yz9DdU9FZTxVQz1LZlJDcktRZHdzdVZjaUNLZVJddz5BSEdRRUVfVERNdEJbVUBtdE1rR0J3SWJxaVo9QjtbYj1tb1NJbE9IdERQUEpodDtAVjxoUUJQUUlQc1NtWEdhVD54S1hBbE5kWXhNcWxddWd1VFRFbVtQdVZAS2dFdnh5UnA9T3JAV0s+cWROdmpXdEw/W1tgXmJYbF9Yb2w+XW9uZWxfZmRfdUdfcXVHXVxcT11dT3JIQW5saHRHeGtoRmF3eWFPSWNcXHBbPFheTl5rQ0ZdSHB4eVhybD9uSz5qbUl4WVhyTEddUD9gZXlbZ0Zfb2dQaWg8R1RWVUZTbWlVdUlaaVh5SXNrVVZuVUZ0VWZleWNNWXl0R1JkUUlvcVJveWJLVVk/ZURib0hVO2lsW1RjbVRDc0hXP0NPcURPd1ZnT3ZgU1JkX2RnX2JIdXlcXF9DcztHX014Y0NpQ0NEaGFIeHlkZGtEdUtXbW9pT2VoUml3X013TXd1UklFV090dWVjZFtHZWVXamdjZWVpd29maElnRGFHcWtEc3VSSWdUVVdIbV9YPXl2PHVzVnFUR2NoTmN3ZVVWYG9laD9Ia0N5ZFt5UlFmXWVHXl1DO1NHVUtYWD9CSEFpPEFyTXdSeUN0U2NncWNTR2lUUm1oXFxdeDx1RE5VdTo7VV5jZklvc1FfZUdXRGtZdk1taFJvSGtpZW9rdnI/SVBHY0JtdUE7SWhrV2xTV0dhaWJ3U0BdZl9dZ0FxZnZ5RFFNeXNzZEh5d2RTZHRRUz91eHJvYmV1VG5heFpVZTpBcktTRklXV29rWFJbcmpbUmM7ZGFjWWhTQ0hHclhXWFJJSVJFQ1BPdEBHdFZFVmJFaEtZZ0FxaExfeXk7Qk1neVVvZEdpZVdvWXVjRD9Zd25vRV49d2BpSUxPVExtWEdVRVxcX0NVaUg8RXZmY3RXR3hlQ3J0VXhhS3NYX3NQVUZMW0ZeWUdHd2NYP0lMW2VdYXRCVXJRb1lebXhUSVVOb3dteUdvb1NcXF1nOkd2b1lTTk9kSmFYP1FCY0FVV2t5OldnZ19JWGFDU0tmVGxwQ1FQQGFYa1l2a2RVdmxLakhYXFxNVlpUeGl0S1ZpTnBkcnZUeUdwSjxVbHlwbnV1V1FeYz92X0xPYEw+dl5WcWVWdmNQbXNhZXhuZlBRXlZ4aGRgZUJPdT1fXlA+ZWdGZ2FBalJpcFZOXFxsWHNuPl9scXhhP3BNZnd2X2dLWWNgX2NWV1teX2JXcHRkcWpyb2RjX1tpP114T1tCYWFCUWs7WV5ebltORnhcXG91cXdcXGxRWmRZeVhwbVlBbEBIdVl3cFF5dE15dUleZWVWdFFZdFhucVhwcVhEYGV5eTtiQ21jdFVZSWF3bmV0eTtyQDtHVztjTkVnd0dFc01Db1t2Wll2dFVpTV9ST2tpbVdHPU9FW29YVmlVcV9zWkVVUmVVO1dDQ0VEZT9mPFNpPjtXQ2tUQEVFbGNUamd4Vk9EU3FUb1tTUnd5dm1pOnV3blFpV211cEFSVWlGPmV2a3NCbXVYWE9EYlFZaVl1YEFCbUtDc2dIU2NYZD1GQ0tCOnd5OztUU214b1FRWE1UPUVyXFw8bnVEcF9RU0pscGBNVGpRUVVQcmJkeEh5VFBlWXJxTGU8dWRpc2JgU0pFU1J1SlBpcjxockg8dVBRTW9NeEhBcm9MUFBUTkhhTGpsbGRcXFFYbHBPYVlEVU9oWHdpcFFjcFNDbXRXcHNZTFFPbXBQYXNuVW1ldXZgdU9AVHdNUHFodXZsQXF0cVRlWHVUbEp2aHZhTU1TaHZMYE9QVFZLZVF1RUtmaG54WVhLTE8+ZG8+PE5gVVRhSG5LYHNVcW9oaHRfVU5HPFdgXXhybVRTXXNdWE9fZHVPcVFlUWpnPFJ2PHl4cHN0cE5JQWt0dWtZRVVFbHdHbFF2bWxGdXVvWG5PRXh0QFlLTEw/aXZIdG5gXXVMZHRMbHJsdVFVbXhkVW9dbU8/ZEpBZVRzdVhgZXJcXFV1VGRvdmRVWElrUmhQdWlNOkRYRllvW2lKUWBVaGlzX1xccm5QVlVVdklxdU5YWUJQck5sakxVUU9JT25Ib09VVlNUU2NZVURUc2NRc21dS2NMV0RJeFZUb3JsUnZ1bld5UFE9VnZ0eHlkUW9pc1F4T0BVa1Z0UTtlTFVETEldUGJNcztsbExIU3JAbEhgUkpcXHFObVhnaFBcXEFQRz1TWEVMQFxcVlBxVmRcXE1xPHZScEs/WHM9bXBLSHZpTE91VU9TSXNSWVVFdVZOSWtMdXlEWU89SVdOSFBQPFFsaHJScU5DQFhMZGtSYVN4TE5lXVNGTU1kYHM7aFRwYUp1SE9eXFxxUVFWVWhuYFhtPFxcVENdTnRwT3NJaz1wcnRJdXJsd1U9bmtZbWRxa01Jb29gbkBkeUN1VWZIdj9deU9wTGdcXFtzT2s6cXhGZ2tPUV1tYVpMb2NXQGQ6TnlFQG5AYXN1UGheSGhEaV5BaWFAUXFURl9KPmI9b1pKX3dEWVxcaWF4ckl2Q2B2ZEBsUz5qT1FwcFlwcGllZnlsaHlba3dpYW9saFZkaUdqSUl5UUBneUFaZVFlYWd5SFh0X1F0cF9DUXVBdXRXRUlYS1J0R2c9dWZucU9SQG87SHBXbWw+RW9cXF1sXUFQQXBLO0hsTmhPY1VUYV1zd0FNS1l2bGRqdFh4aHFQTUV3TGlURnB2YlxceWhId0dpUGNAVnBZcG9pbmZ0d3R1VnBEa1RZTmpdcFdnW09hbWlGakZfd1lfck5oYG1AZFtIYWs+XFx5T1xcO0hrRUdmZVZiZG5sPHFkZkhfPll2VnhjZV9lY3hdW3B5YmBkTGh0cmd3UllzZ3FqaWhkYUlrZm9ja2h2a3BjZ2FbZk5yQ2dkT2ZdVlBuamhkUHdeOmBuR3BqXnFnbT95c09ac15iPEB4cU9bREdfYj9jSl9zQU5bQz94c1ZeTWh3ZXByXXFrc1Zyb3lhZ0hidmhkSz9eZ2lbYXFwb0dxZkZuSnZnV1hmVWlkU25bcnhtbFdmXFxYcmBOb2lOXFx3aGFkeHN4UF9fcV49T2dEX2ReQHFMYWRWaGZSd3JtdnZAWFtmaXNvR3VnaG1eYHdIUHFgZmJkaW54bmA9RnN4aV9ReV9UX3JlUHR5d1tNb19fV1tGP3FvR3lReWZXcGNNdmxMPm1IR3Zib3JNZmxdZndbWXlKZ2dkeGFlV1tUTnFkaXdFeGNGZm87d2c+UGxQUW1Hb2x4WGBtdl15ZmNVR1xca15hakBzS1hoX152bE54VFlmSF55aGheYWBcXD5YX0JuZGtneVhRXWFgZ293dER5XmVRbT1gb3BGZXRZXXVwYnFQcGBgbWFIdGZ2alpwcUBmeVBuYXBebkBmbj5YXFx4bl9eT3FseHRCV19bT19Od21HcHhQWHZSV2VSaXhxcWtnQXNKX3V1dmtOaXFIeHRjR3NQVmhaT3ZsQWljaFtiaFt5b3BqVnhUP2A8UXBvP21GWXRSd21ZVl5abl5IZ3U8T3N4RnddVm1Kb2pkZ3BqRnk7XlxcO1hvXm92QEhmSkl2eHFdQkFiRmFkSG5vT2hkTVBqO15aeXBtO190Z0d3cEFxQT9seFd2V25zd0lwUkdbP29fXFxmdmxgd0doa15eeGNXZGxGcjtGdFt5dD5Oc0tIa0RQW0xeXU1IbFVma1BOXU0+azx4WlpeZ2ZuckBRZW9vb3d3Z1VndG94Wk9QaWBXcF5wck1wW2NwY2ZpbF4+YmJWcF9GcXRWZEpWXVpmXWBRdXRXZll5ckNPZU5PeGtZeHdmbHZecXRHX09BcWBhZG9oaHd4Z2pod3luXVdwck5ocm1AZFVpb15QdWhXdGdobWdwW1ZuYmtWY1pPbl5XZlpIZ1RZYmNJXXNuWlNwbDo/YmxYWlZZalRWZV8+Xmc+d2ZAcUV5c19wdGxnbllvZXBRYVFhdmxIbHF4X1RYWl1XZFU+cGlRdXc+dHVIXFxkbmQ9aHB0QW9cXE9oPVFcXEJgcnVhZTo/dU9mXlpWcndGXFx1SFxcSWBoQkdcXGBoYl9uXj1XZl1BcGVJZGFReHBwZz0/bVZRZD9fbGFwXUBZcGNhZmtpd0RJbF4/b0FRY2VXb1Z5ZExwbHduZlNfbmJXd1JWdnBeYmBmYEhQaWphX3ZAcUdIaFpoa1RPW3c/ZEJJdU9mc2N4cF1WYl0+Y11mWnJ3W2NOZDxmeG15eEVWWk5JXXRgaW13b1BQeXhJaWp3ZUxZbGd4eTo+eVdYZUh5XVFAW0ZPbGlRaEE/Y3FpeXNfeHdJZkN2eTpma1JXY1lgW2ZAc1t3dVxcV3A/SGZlbnhydm9kT3BPWGZEXnhISWhZeGNId2hYdmJjV3lxPmJzQVp4QXdiaFxcQ152ZVFsZ05tZWBnS2lzRl9dPGdlVkdsRGBiZFZvbT9iTnZeO25uUk5mRW9gRFdyYmFsY1ZcXFRuXkpJY1xcaXZfP2U+QXlsYV1jWXE6eVtpb2hmbltDeHdXeGlRV1xcWE5eeUFaSV9tSG50bFZxRmZqQWB4eHZzZ3B4Z152Ok9qXz90UkhjUkB0VWdcXFo/aXM/aEJQc0dAbWNWbEBeZmFndm5GbTxWdU1YXXBQbVtWaUxpZUJxX0xfY0d3a0h3bGNnYmdvb1E/YnVwalRfXFxpeWI7R3RecFtfZndcXHdvW0Z2VU9uPnldSD5yRV9eRHd4Z1hvcFd4b19jTEddUXdfa2FzV3BwdmZ0aGFxYD9CO2laSUVdW1lJXWhoeUdfYVJkQXZoc1dXa0l3UXlfS3lrUXlgYWVxTXdJR3dJVWZZVVZ5U0hteUZ4eUZ0aVlyeUNdc3VZQ1Y7PVN2dXVFSVg7cWl5SVhrX1lZY0d5eXRDXXdxQ2VVX0lmZ0NcXHFSUGNJTWd0ZWVjQ0VoZUloVFFET29TTm1IXFxtVWhFc3RdVW49RFVjdHdbRnlrdE1FZ04/VWNpV0ZJdlJjc3NlR1BpWXJtVHdvVGZJWVVxdUBhR0lrdlBjWWdRdE9LdVhDZEJjVlZJeXJ3RUBtY1ZTY01ReEhnVVFldENHc2w/Q25reUI/aG9HZEVtVzprd25PZmRxQ1VJRFFtRnNFeWtBVGQ/RUVPZ3ZFV29xWGF5Y2V1SEpVSFNtdEA7VF1hUkxpdmRXd25DZEtjdkxbQ3NtU1FLZ2VlUltneEJHSG1LVnJHSU1PR3B3U3JpcnA/RT9Jc1FhUkBrZF1NV1VnQ2RzUjpRWHJpdz9Fd0p3ZXVzV1tVTndUWG5pUHZtTT1ZbkREUEFBTVlkVmBJb115dklAVlxcdGtGdHBdcUxOSHBTaG9EVUxJaW9CTG47VHZedWtkQFVAUHlTSHBHRE5MWFRITFE8VW9qVFJmTFhGWXlPaU5PdEtTSUo+XFx2QnlSX0RKT01rSU1qQ3B3dlhKeWVQSTxzeUR5ZHlZOmh4dEhXQll5cHhRVFhyZHhZOkxUVTx2eT1qcUx1dmh2Z2lvdUB1SGV0blVPP1F3RHRLVHlPTEBPdGxOZ1deUVB5cllmcHBgZ3BiZGFwTWBkZHBsPU9rPlhcXGdxYkVgW0RGc2hWdGReYUxIeFNOYD5XYExfZUlGbTxZdkl3eFVZY0dnZ3NxbWZOUVtUXFxPZ2dTdGRLVWFhWVhDY09Zb0BZUHlMVlJMcU1VeWlUV0k9bktETmRlTkhgbElAcEFFUmRcXHNgPXV1dXZhVVZrdVVkVnBqaGxIZnVAaXdGb2dUb3R0ZnFSaXlbT3NYUW10YGZjcGNvWXdTV25zcGV2cGxGVlxcQkFwU05mcm9mQ0ZeUV9iWEhcXGRebklAdGY+dWBec3FobkBIYVhvYFVBeEBnb1RJbD1PYUVHY1d3ZGN4YktvZEZ2bmFAbER3cD5Gakh5bllQZWlwcGdGZltJbWVodkBPZUFIZWVQdWl5aEJxWkNHXUhxXVBOY1B3dVJZZl1hXFxGYE53UnBBdk9Zcz49d2R3Q2RTRGRTWXNDWGVrYk5hVVF3SUZvd1ZVd1hHdk9fVVFpR2dRWUtlZmRQV1Y8bV08VXlMcF5Qal9gV2NEUWRIdz1oanlcXEthZG9KWW49ZEtYXFxcXFBwbFlgc1NZZ1R4bGpfcl5vdkZhcEB2bFJxYGlAXFxFWXRzX29WSFtrWGtlZ3FPQVxcbz9kckl5T1Z4aE9tWE90eWhtPk5fRldeZl9ycE9aSUlmak5lQmB3XnFiX19jS3ZraXZfbUhdPklzR09lcmF2ZnFkW1l3R1ZvZUdXeUk6d2RFcXdEO0VVZWdPb3Q8ZURrP1U/P1lHcVVNdWVDQVNnP3NvX0JUWVdmT0JoQ3lMT2JDbXZfZVNyS1VAc3JSV1VIT0NFTWVeSUVrZVh2WUJeeVY8UVlsbXh3UVdPdXhNT1k/bUlybWc7P1RhUVJUSXZ4b2VHX2ZqQ0lFVUQ9W3VOZWJ5XVhTW3duSUhAR2lVcXh3bVQ6U1hfQWM/Z0VudXc+dVdCT1ZcXFNUVXNiXj1jZlFDdmNiaztnX3dlZUtYdE9DWWNpdmtzc3N0ZU9ycWVXeFlGcXV3bm95ak1kc1l4YElleU9md3lkdXdZc3VJUUVTbWFFWUFUVHVWaVl3aEdFV2V2dGdEdW9EVGdXV2VDbT9lbG9YVGdiWFt5bUNYPz91Yz1JaGtFYTtFUUtzeTtSVHN4S3VVTUl0bGtWWUNIZ0dpTnlYdlFld1NZVmN3Qk1UYFVnR0NDSF1FY1NUYE9zXFxVTUVMTF1wa0R1TGRYU1o9a25cXHJiSVRSWHJJQHNKWFllVHJGQVBFVXdvdXROcExVUXJQXFxPXWFxaXlUVWlwZlBZYUx0ZG10WkRwUUhVckhwV01qUml2SURMXFxNWEFddWZZU0JdSkxIUV5NakN4eE5xb1Jpa11VUnRAc0Zoa1hZUHFldUR5UE9sVXY8bEl4bVF0dFRBWHJZb3k9Sl9oc2tZeXlcXE95QVVeVXhHPHlQaXlpXFxzeGl2aHlNUE1NSWFucWlKR2hVbTxXVXRvcGFzd1h3VWRWZERNRGRPbF1QQ3BYVGl5QERRUGB3UHhreFh3S1BOQz1QdFRNTFxcbltgb3ZNb1t1blBsd1VQclZsWHVRbGZUVk08eXhdVFVQd0lQdTxxcmhQUXVQdk1VUmU8dFVFdl5ocGBUbF95b0Zgc0F5U01xVD5dU0ldT2xcXG5WRVNzYWt2cHBSWFJ5WE9DSFc/RW5ETHJPXFxtb2lTU3F5RVBVeElORGh1YlBySE9wTElwVT9gakBwY0FrRFlvZmBdc253bFhgP2ZmSUBvY0BeSkZbVEZqXWBbW3BgcUhgQk9haF5mRU54RlBhO05tSFZbcld5WmB5Q0B2WW5sdnh1QXdxV1BxW1l5QWF3SXl5OmZqZUFtXFxYa053bVh5dV1mZmNYdVRAdHhnYnZvcjpJdWx4XmtgWkVAcXJnaVhXbFJeeDtpaHRudl9vXk1PXkFub3JGYFtvZF1pW19udlpIZnNBZ1Q/a1t5W2ReY25XdUxnd3R3eTpebEVpZXZwd2lAdTtRb0lfZ2hmckJpYmJobVRGdEBmcG9Ra3FCeV9jTllYTGNCcEdnYl9yTl1pcHlSRG1IVFlWR21ZTkFja2V1b0Vpa1VFcENoSXd1bEt5VVtmYml3XFx3U2ZhV3BrUkFdZ2dvU0tRcl1dQnhPeWljaFVLWUc7UlhvVGBnRHJNZFs/ZExJSFBHZj9NRWBVVWRVVD5ZbT49VHRsdF9VUFhIWWZob2dIUnNweTt1cEN1UHVMeWdAS0V0V0dpbVRQSkxlVVN1eEtEbGR1c11cXHg+RXdaWVZUUXZIRU9VbFhYUHhrcEtbPHZARXNUeW0+dXJaeE54PVRSVXdERVNhSHJGUEtXaU5LdVJNRU9LdU9JQWpteXg6YFZYdGtTRVFvZEtdWFJzeXBmUFdHVFhAQFVUZVZNWXhvZXNbRG5IdW1aYE5wPFhmcXdrSHBKSGlQaG5CSWxRUGNRXm1sYWRkYWxeSF4+eXBGaHZidnJsdmdLeFthSWJJeHk6Rmdud1p1cW5XcHNQbnJicGhFd2dzcVpfcHd1eWRVb2BfUFtvdnFlP3dVT18/cHZXSGdnblp5UGVQTmtKRnBocFxceD5yXndbRm92O25aSVBfQ3lqbXZcXFtOc3hhXnZeajtPbFpRYztYXFxXSXlub3RVV1xcWW9oWnFid3lcXFh3X2xGb1tHXFw7b19oPnRKeXRgQVo7eGdgSFZlWFF5VkVndz9vQkVzSUZLUlJnZHJTdE9zaWhNQz1PZ0R5RnhHU0dnYndfQ3ZpRldvdVlRdEJlVmRRVUdZZW5TZGFPQ29JeEJ3dHRtZG1td3BfZ1BJdGdDcm5FV2BFaV5lV2hTVmZNeEVzdUtDU2ZjR1pka2BgSmdgT110cj5ESzx0dlxcRW1RYHBjVVRSXVk6TXJKPG9kUG9mWEpIdEpJPU5YeEtHPHh2QHZ4aXR0WVl0YXFOeVk6YHBXWFBDWW5tXFxRa11YVVhSTklXcGh5TUFRaWBYQnF4cFlOQHVMYFhXSXBzdWFWTEhQTFRMVFRyW01qRU1zbFRUSEl2P2VPZkFwSUF4THFsa3VLVlVOS3hWdFRScXVPcGl4QGBOaD1Zd1xcclNhTkB1bV9lVFFQUXdNVFNYdmxMakhYb1ZkbFphT1NlbEE8VlN1dDx1bE9xbEBFTT5IdUZcXFdLWFdBSG1zUGxNdFhdQHFpWUxndW1jbVhxcXllTFFRZHNLXXhvaU9VZHJHYHFcXERTTlRybHlTdHBYX01xQlBXZGlNQ0hsSkRQT1xcVUVETGp0TkZZdV50dnJUVENhT3B4dnRUUltlTHRcXFVYdW1XSHFeWXVYXFxtWkl4U0hZal1wcEhWVkFRaURUZ1B2bEBxUlxcT1xccW5BUUpvbHRxTVBnbHI7dVBYYXRDTFRTSHRcXFBQTVBsakBTbWhvY2luYnBwbG14YEFvUGhObkxvSVVbUUltTGloTWh5YT5iSFdsSVljaXZhcj9cXEJ5YnRQcGV5X3NRX0VOb2VncUZHdzpmZVtGZlFYZ09BbF9mZ0BRd1BHX1l5YVRJP2FVWnNnSkFUZGFmPlFCdE9ITVBORFVNcFVPRWl3cFBUWGl5eHlVS3B5bWhxWWRza0V0WWx5VXR5Xm1QaFh4dllqb1VqX010dFhuS2VXeVh0XVxcdWl1bm9AdFVUTnFkUExVT3BUS3ZJYEA/Zk9ZY1VWY21QWkhAbUJAdF5AZWBGXWJPXWBoaWE/WzxfamVJbFNQZFxcT2NFb11xUHFUWXBhd11reU9PRmJVc1ZzVUdNdWV3dWV5c0FVVzxLR1BLcmFJQnZPdXBDck95R0BZQj1xRWtHRFlfQ1FXdUh5Z1dhc0FxcnRBdERjWVZNZE09RXZtR0VRdU5jWWFBeWxFR3BpRm91V3VBdXJXVVBZV3ZndURVdFhjRWdpYnVjaXdlSFNrZ15JdEZNeHBXdkdfZlFdREpFbVhFcEZodUY9dW9MdWxAVUZMeUJUdkE9V1FBVWRxSkR0b0FETFNkajxNSkJZa2FVdVJxeV9hWUBRdVV4WDpYU3VRWVNheW1pbHd0bWltVFhQbUxkeWZgUVphTmhZeUZlUFRIVztUWFlsTUg9TTxdcmB1bGJcXHVjSGxOeEpSRVRgREpaYXJ2cFBdTVdqRXhDYE9fcVVRUVBPaFZVcXdoSHVpPHlZaVRubWxvaHNrWVlOWVFLRUttRG9mWVRmcU9VSU5AcXVoQVU+RExgZHVvSVBEdU9QUFFaUFNFRHBpdHFHcFBPbExOeXZqYVFxSE5PeE9EeWtlcXBSZXByUUpNRFRleXVXTU5ZSW91bGxwRXJkdWtwTFBeaXliQHBycFJWVExvPHg6cXM6RHNzRE9eSXRTaU5VXVJgUXBecW4/cHFCSF1uUXZldnFvbndbUW1mSHd4Z3NBXm9ZYXJgUENDd24/VG5jcz1fRWw/Rm1PRlBNZ2RHRVRNVmA9dlpZZkV1SEFLeVJbR0NVYj5TREFVRUBdZExRY1tXckJZVmRjUlpZSFZXYllLeXh5WEpXSGZ5VlFveUxNZ0V1WTp3WEFDV2hvR1lVSHlLUz1xZkR5Vj0/Z01XUjx5ZFlvVkRTSGttZkJTQ1lFdW5hVFNZeGxfdlFjdHN3eWJTZWNxU0VBdGpLZ1hRVHF5V115U3BBZGxJRHdtVV11eWBndUB1dj9tdEhRUmhFSXdJeFdleTp3VHdvWG9bVz1XdD55ZWBFSWp3dENnZ0lQT1VAbF5VVW1xcj89T3BVcGBUU0hAUFxcZVdPcVI/YW9OVVlDTFRdZVI8ZUtsXFxYZlRScVROdnlUYmlPU3ROSXlYQWF1VkFXUU1vTmhvZ2RPZGFUWnRrVlVPQVBvYnVtWmRVWW14PFBMXmlsVVRKRVBMTGhxPT1MT2VwS21ZVmFyPkFPU3lZOkh1bWlwaUltV3l4bGB0cHh2Y1RObmVWW0F3QEF5VHVYamR0XkVzTUVQZ2hZc3BtXVlVbXRUckV3UWltX0VPQWxWc2hVTEBzXFxsTENRTmtgcERoU09VblNVTkZMcFVVUnZdTWZAbV1xV0FJVz5NcFxcVG1AaU0+QFZsUVA/cFZkPVZzYEo6RE1BbXE6dXRZRHJJQHlJRXV5XFx4SEBQeT15V0VZWFxcWWVweVFtVnlQWHF5U2Vla2FsbXl4cmhReFRlbXRcXHdmZFNgdXdPdXNOaVVzUHZbWFd1PVNlXVE9PE5IbWRPeW5kUWBnX2pobmBsP29qQWZUUGB2cWpZYGtiUHhKQG1MWW1QYHRyb3d2R3lRWXJwQW5VYWR4b3RQZmBvc3BnYmFtYlA/dnFNUkNVR0dxVkVzZVNHZUl3ZWBnZ0I/VVg9VV4/Y3NRRGxFVXNjZ2t1UnhzdExXVERLYk9bQmVBeXRvdW5vVUZvWXRldmZ1U0dFZ2hnY2djeGBNYkJzSGVVaVhvQ0BzV19RY0NLY29BVEJNSWE7QmlNYz5Bc2I9R1JvaGN1Q11JRlU/WGRZY1Z1dmxRSVNrQnFLQm1hVmtPU1dfQkhzcmRXUlhBeVpLaElHdGRRc0pNVWhxQl5ZRFJvdkBtUnBJVndXd1plY2c9ZEtRdT1NY01Xc2NdV0dDd1RXYklnQ1ZFR2ljZ25TZFBpVEF5Vl1TWEhVU0ZdWXVXVFl1clU9dXVRcnBBeD9XeGh3Rm9DQlNFY1NjWWNNVlVZZkpzaFB3ZldtVlhjRk1beV9lcl9hcl1hRkZTWT1vRFJvcWthcj5hSjtcXFdjXFxLW0h4TF12Y0B4YXFOcGV3PVFQdWxrWGFyT3lsRGVvcnVuWWlXW2RsaHR2QkFQPGxLPGFzVXFYanRYXFxweUNJUEtIbkNFTGRcXGtjcVN3XU1ncFd3bGx2dG5qUFRUaHZWeW5nVVRHaFhyTHlrXXZsVHNCcXNyRHVMYXBnUU5BSVdPeWtVSXVfUHVEdXRYYE9OWG48UG1IUXRbPU89bHVGaGxeXFxqVF10XFxlTl5FU049VGpZS1JxeV1dd19ETUVtcnlQb1E8T2lNbVhBTmdVamxhblA9eHJcXHlYSHhVeUtrQXRqbExCWU9DbWtQZU1seW1fYFZyYVhMQFFbTHJXXXdeSXNdSWw7bU9MSE9iSHNFWHFVZWxMYVNwPFdVZU1IPFFQZVZiXW5rdVJbUFlSUUxePVhQdFF4ZVBOVFFYSXV4VVFxWVR0REpSWFNoWVBtVFJmQVBJdW5yTHJtQW1VXVJKWXVhPVhPdWxrQHRSRFRfRE1lQW9xSU5pVXhrRFBUTFNWRVlocXFVcFhrZVM+cXhJTFR3QHVmQVF5QHRHTHVXUVBxaXB2aE55WFhHUE1sQExCbGtMcWxUeVRBcFlfXVVSRU9CUXR3bGtwWHVCX3JfXmNhcXRVYGlQUXRdWGpnaWVYd3NDZl91d29UUW13cGB1P2dzZ25FQWhKWV5QUF9kaXVWb2RNeWpVcGtaQWc6R2VEWHhzcGVed3FYVmdnV29McWBKZ2tSYHBnaVxcV3hlY2hoQHhwXUddckF3VG95WXhjcVlfZmZ2QWFlaHh0QUlrdFdiRXFrTkBgZklraV5ibF9iUVBtSE9cXHVxd3JueHlWcm95dnZmeGV3YUd2cUJneXFmd3JJcXNIXkBRdUJJY0NRd2pYeV1HXFxwaWdIQGJ1SW4/V3NEeXZBeWRlPl1kSXZCT2ByUGNHcV1xd19CcXloWG5ER2xIdmFOaGVZcHF5SG1ieWtJQHNXYGZ4P0F3dlBnWHNJR0FdZWtvVlZJSEFYVEhAQV9FR1dleXdWV0FYZkl5Sm10Z0dUZz9ldF9laT1Daj90Q1dXbWFlOmtnYnVEYE1ZO0F0TmVzWGtCTF9oXm12XXNzdldETUd1SlNZc0lpXlFIZFV1b1tSZFlza2FTZm1ISWdmQV9oUUNIc1llUldpa1dXXFxhVUFXVWtRQ0xfVkRNVD9TY09fVkRlRFM/VE9jSEhTQmNRZzpZYkBpR0VdRE1HVkhBZ11rTDxMVE5FdUo8TDthamVQal5MSjtgTUlcXEo8YHFkdXF5PUp3eHZKeVVtRWtRZHlbaXdpQHlxeUtpSVVueXB2TXI/dVlSVXllbXl3aFY7SHhHWUt0UXJZeXVpcXJqeVk6YHNzeE94eVdadVFHVXZ3WW1IdHlaaW55PWo/WEp5dXdPWXl3VXd4cGp5P2BLeGlQcV1UeXk6dmtyb3lveW09d2lGYV5ZZ3hBcHB5WHZYQWVRXl15P2NVV3l3QXlYeV1zeWxvdnk6ZnN2eVpjeW5TQXFpcXhEdmVyQWV5bnhveWV5cHVtPDpgdkV1dFRQdlFAT2NpTFdJeGhMUnFgdV9kdFtsTzpAamdkU15kUmpQVnVMbz51dEtJTWBtTkp0bmd0cl9RU0tITlNZbGBIc0pYdmhkT0VleFN1c3d0cVZgS0Rxd0doc1ZManRIdWdocldcXHNQTUtLXXFPUVhTYFlATHJCdHZCSHhDWG5EaHVDVE5DXXJoSVhDZGw9XUpxPVR0QVU9bHhUZGxlRVByVW9RSWpCRFdnXFxra3BSP0V5QWBOTmRUXkx4O0BWWERxOmB5blhWSERxP2BPR0BxXTtWaF5ZeEdxYl9Hd0k+cUBAZVt3blhGaWFpXFw+cHBNaWNdVl9rZ3JlRGBPRD5DVmRPZE9hVXRDdnJtc21FaV11VVhbaHB5V2tRdkFvSTtJeHh3d0tXQ0s/VkxBZUpLdD0/U0JBQ3FHQlJNckFZVmFbRHhDUnk9Ym9lYmVndXJRZ19hST5RWXdXZ2pNZW5JWTxvQ1xcQVlLRURwZURdV3hCTXNvW3JuW3RrSUhWYWZVV2RgX2lvc3ZGV2JEdURfWUl2Y3ZwT2RMaUJfS2hdTXVxY3RvY1ZQd0lFZ2lJU1hfX3RlWWdSaXRoVUU6a3NcXE9YS0FsZz1rR0x3cHRxRD1yXFxBUlU9b2Q8dkZMcVpha05dSnRZdDw8VERtUkNNTlxceFZbTExNRHlFTXhhcW5vZWtodWtPYXA+WFV1UE9uVWxGVXdVcXJVaU1mRFdnRHU+PXRTSVBOUVdfdE1pRFhkYFRyXXI+QWtvQHVAdVFoXFxWb2RMXFxZTl5ZdjpFbV9QUEhleWZweEdZVmNha1JIWVBob1dwWEBtWEJVcFNda1dQWVBBVmZoTkRcXFVOQXFjcExmVVRRYXZFRHZmaVljXFxMO3R2UmVtZnFYXFxVUmVwU0RoUGRJTTtRcFBcXHFaXFxPR1BZcFVWb3lYY1Vvc0RNdWVWUnFMZXFTRUVQZDxVbm9tPFZsZVhiTWdjY0ZjVFdtZ1djSXdub1BnPE9oXlB5YXd0WGZ0YUddSGlhbV5tYXFdU2B5bUh5XVl4YXl3T2hyak94VWh0VGBvPUBoW0hhbHhvPkZiTFlvVWZaUmFcXGRfXWxwb0RXb1Q/alBhX2pBc3FuX3ZHdFxcPnZaPmhVPmVzeXZQT2lyb2g+Tm9uPnlMbmU7cWJTV2pgdl5LYWFUWHZld2hUcGpMPm9kT3lhYWVmYWxiSWY+YGRTd3RmcHlnVl5bX113T15sYWZcXHlqQHFtZ0d0PEZzdUBtTHh2bmhldEF4TlFieE9iUk5kVXFpTU9xV3hbRXdgT1F5cXBveFBbd1FbTkhgcE9wQGBnP1hnb2ZyQlh3O2ddTnhvT1dpSGd3YF90bFdvT3dkUkduT1BkXFxnXkB2XktnbWh2ZlVWXUFBXW1gXFxpYF9DQVtSZ21WVm91XlxcaHZ5Oj5pOj5rRVlyS1hzY0Z3V25hQHdvY2ZnW2BzdV9lPF9dSFdgZWFrZz5hUEdgWWBjXXl0S0FlSGlhd1dgVlBpeUFaaW5ubW95WGdoQV9bPFhvO0ZgWz9wS2BdSHZwWV9cXDpHczxhcllwZkpGcDtvcj9RaWtPYG1edndgbGtOXU4+YUZ4cWBWZGhJb2ducEVxZ3JecVtBYUhJaUthZ3dHa0pfdE5ZZ3g+c3l4XFxiZ1t4bm1jVnhBTmN0VnRJaXlyX2tfQV89X2dAX2tVUXBgX2NRSF5ASWY6WWpPdm5fZ2NVUF52PmNHQWF1aXNbYGRHUXVpZ150WGBnZ2hxeGdlP2dvZ11ZSWJvYHdXP2VsUF1naW09eG9UWFtQbng+XnBxWV5aYlZLdVJJeXBddlBRaDpRSElNWWB5RkxRVW47Rz5DdFdDWWlfQk9ndXJnY19PeG1XeWxldT95Ql1LSHBHaEdfVGFxcm9PSUpFZV1vdm1jY0JDeFp3Zj9JdGRvdFFPVmBbdEc/ZT1Hc2FpVzxRWW9ReWdRaU5VZnBtZFJMTlNgVkR0bmplT1tkUl94Uk51Smo9bFloeFJgWGloT11xVEVIVGd1c1VtT25UcWBhdGZkd1RZanRQV0hsVndwWFNxeFBETzpZTztZU0c9WV5BeUpkTk5EUUJcXHZvTXZWVUo8SHVGXFx5b2VRUFhyTU12cFhURVl1Ymxyd2VOeXV4Y1lRR0BseFlzZ2BXZGhSPWRVUE1QQ21wdUBNZUFqU2lwOkxTR2xKa1BSQ1xcblN5UE9tSnB4cjplTFBgVlZQUWhRUEV5c2xkUHRZeU1Vd0JtSmdpVFV4cD1UVXZQd1JJS1xcdXRKWUtnTFdQYU1HQUpacW5DRFVdbFdnTHZmRWpLbW9ncE5KPXh2cVBJcVJIcWtrdGxUdExzWExSWXRERGxPXFxZXU1MY1VNUGR4eT1KR3BZeVV0bHlvQUBYRWVZbF1TQmV3dmRqckBzd2xWUVxcdVBlcnRZT3hFZEpBdklJa0hOXz1Xbz1Bb0hweXc+ZXFPXFxRcWtPaHlNVmZnX2RFSWVneGdrTmVPeVtMV29mQW9jVmVkb3BfXmltV3U6QWRmX2tMeHJUd3BzWXNScXM9X19ER3BmVl9NZnJVdlpaX2Zyd21waHZBZ2pUPmFTXl4+YV09QGM/QGxDTnFmTnNcXE5bUz95RmheYV9bP0lxXllcXEJBeG9GcFhucFVRcWVwZ0hAXkVfZFlJd3FJdjtwdlpGaXNeaG1ZakdwYldmYGBJaF8+cWxwdHd2dk1HXWFJZVFfc1RhXXBpdj5ZaU54bVlnYnRfZkhYZ09AdFhYcmVxXUxgdHV3WlRvcT15cFg+YUVXcExmaGdwXUN4bzxpYF5PcVRRa1FXZmJgYFBQWkZQbFxcX11DP11AWHddWV51TnhVWGRpUGNgbmFeZmBKeGxnXm5zSGx1eWZfUWpTZl9vX2Vdb29tbnB4bnB5SHJUSWhlWHVKZ19ZUWVJeGtiX29RT3Y/P2FOQXhsXnQ9X3hUcHBmRng8V15OYXViR2xhT286UXU/Vmw9T2dWXllrRktndEpdWGFJaElTeWFZcmdPU1Fpd1pxRVZpWGNrZ0ZdQ0dlZVBtU1RBWFNTWXBvRWZLeHQ/Um1BU29ZWWt1VGI8c1RpcnVheWJUUUhQeWJgbm1UdXJZVmpITFRQU2s8UGhQa0I9U09YamxQWD5BSndpTj1cXHhsXXVubUtvbVhPaHljaG9obVB1ZHg8VW5xYW9SZVduSE9DdG1vdU9CZE9MRHh0YVBPQVNRRExLcFM6SVY/PXNWUHheSXJSTFNLZG5HZHZlYUtwWWxlYVdJaVFUTVVjTW9MUVRVRXdUZXF3VVNEWUw/WE9RV2hocWRrXmtheXRybnJtV3dZeHN5bm15b2FlV2VQcWtpUWd3Z11ScXNycWdlZ2NlT2dPXm9ZeWc7SFtGZl1WX25jWHlCRmpJX2VnX3NmZm1wSF5cXEBmQWhkXXdiVkBoYnZyVE9gUF9fUVFbT3BqcF5eQ1dkUFZ2Z0Z1cElybFlpUVFlbkZ2XWByPVh1VWhjY1FdSnFbVnFhd0hlQldrWk9mQVBibGhbSD5mW1dxTWluZj5aamZbPmhramhaTkhiY19yQGlqXl9tUl5yV1hrbF5kcm93QW93WUdjcXFiaXZfV15beFZdbU5sY2hhRmZpPmBwT2F0PW5mRm9jcG54RFdxdGBoPz9dYVBnclFvV1ByYHhiZ2FyYEhjQ2hlWFdvVHhubm5aU193O1dbZk5wW3BleWBmVVdcXD1XW3NReHVHa0t2aVY+anR2az9gWmRpcnJpdmlPZXZOb29vYXJYdVlBY0BAcnNYYz9fXVBHckZwYVNAY05wZEY/dD93WjxBX1xcQWR2SXE9cGI6UW1UXlxccWhtanBwaD9pYkhyVj9dTF9gU2lnRGFrUGhldFFkdnBub09obXFoUWFsW1h3UlFqbU5wOz5xUmdkaGhzTG9rSE5tcF5ocld0WEltVT9fXFxHY2Z4cV5edFNWWldpXFxkZmJoZ1pAQHE9cFtwRmB1WFpMWGRbXltld3FLcXN1aVxcWFh1Z19hXFx5ZEJnbldobWJpY1M+XFw9SVtrYF5XeHBPP2xkUHJmQHY+aGFfZ11NRm9LYXRfZ2ljcGtkSVtraXB0SGtPV1p0cHFoaXVEZmFyYXZxWFpqYXZNPnJaTndBSWlJeGd1dmZTV2djZmRiWGVIRnlPZ25EP3FKQGhPZ2RVSGBiSF5OYWlNcGM9R2dCUV5taWBQWWRoTmRWRl5DUlNTV3NrRW1ndmlZU0tvZXY7QkpfWXBnWExhVnJFY3R3R3htUlB1Q0lbaWRVZHl3ZWVlRU91SVtnZGljSVRfWWtfaGE7ZlVdZXJDV2F3RVZHWU5HQkpLYkY9Z2lHRDthVT1TYllhVE1PczxleWJzZ0BJVVdleDpxc3E9QmNnaU9VaHlLaTpPQ29Fc3k7ck9RUlFfZGM9SFpvV3Q9RkI/eE07Qm5dSE5DVWptYz5DdGs/aWxTaG5VV2tnVUJfYkZDY3NvdFFhVVJFaFhVZGh3eEBtRkVXeHFXeE9JeFJTeDx1Y0xlZFhhZ0dvaHB5REtTRVlfc2JnVF5dZXdNVVZpVlBHaVxcb1RWaVdKU0ZtdVhEUWZJV2VeY1dWPWRTYXdMWXNPUVRsO1M/W2hLP3VDb2d0b1VaZUZTR2I6T3dsPUM7ZVk7c1JhT1ZYa3lOVVRETWRQcHBfeD5EPlhwZWtGckZzdnNgQ1JzW2VMX1lhZ0hEaVNUZVdoXWhHc2ZQa3R4U1hlWXVDb2VlW3Zwb3hLaUI8WHNMQFdOVFVcXFFNSmh0P2l2YGBUbHFsVGx2Sj1vUkhSeVxcdVFZeDxgVWhleGFQbGhpUWhpUVVoVFBpeGpVTWJtTHBhal1Vdm9pcmhFVkI9dlh4UVJVcGVtb3JgdVJlWG1FS3NAcF1sU2dkc2dwUExdc1JgUWtkb0Zla108Sz9gbkBhamhFcWF4bnVMdkRUeFV1TGZtdlxcZU8/cFJ1YFBnTXQ/bWt0VHdGbExeYG94aXVSQU5ESHVgWE95SVdAQE1YRVNbXVJASVZOTHBybVZfRXJsRXFxPWxAPU9eUHQ/VVM/PGppdHE/UGtkdFBXaE5CQHQ+PUxvRHZ2XFx5Z1xccHN0a2U9W01ea3RZdkVuY09ea2FXdHJmeG5xZG12a1lfY2FxXXlYc2NhbXlBWlF4bXhIYWBQakE/bHJ3YUtfb3dxaWpOdWp2a0lAW0BXXW5xc3c+bUg/YEloYnRXeWtod0BpYXhIbW95c2hoYXdWYGV5bVlndmFJeEZOcFhRaGBQdWdncGFvXVNQc1VOY21fbXRXdnhGbURJaEZQeXRXdlNeeHh5Y1ZXZnZhbXRJaERReHZHeXhmaXZ5bXl2bVFpY3JWdkhYZEc/YV1FR2lYclVCR3l4ZUd4cFV1eHVXSXdIa0VjQXdnYXRjVllmUVl0UXFhWHhxQ1l3WVB4bXl4QVVkQ2teTGx4eW5DVVRZYXFsbHNRTXhfcW5seVZoWHBpVXNjUVN3WXRjaXdJVXFydHh0WVZNcW1TaHhveVJgZHF5WExZbHNyQFZMQHleWWxBSWpDbVhZSHJgXFw9YWxvaGtneVk6WFBqbHlWaXhIXVBGaVhQRGxNXXBjTU9bQG9zUVJXSHd0PXlveXJSdXhQVU1pQVFIQVRGQXFBXW9mQVNAQXRQQFhuRVVJeXZPZW52WW9TWXNLXFxVWVl0dG1YVUh4dTx1O1BRTl14d1FSa1FQYGFtdWB2b0hsc01XXjx5TkFUP2BWd0VtYGxtSGBNRF1MQF1WZmBwSzxVYFVRSVVWa1RVW2V3bHBQXnVSdHBvdW11UmhXQ1VyXlFWa2hwaHF0X2RwcGRSVmFzXFxQdzx1S3hAdE9UeUBdVGNoSkVIa1I9cFtJakthVUFVT3E8dXJFTE9JcURwcktxbF5EbUNsbmJtdUV1cF5dbVJUc0pAUGpdaktFUF9ZdE5hTXJcXFE8QHFdbWp2PExWSFhBSXFQZW5uWVZIQFFNbXNyWFZHYHBdbTs6Ojo6Om5zQGh0eGFfUnd5Oj50YHZhV1F4c3Z1bV9vb0ZbTEleRXhbW2djW0h3XXlePGlmSGd2Q0dnaE5zRFh3R0ZvP0leSHZfR0Z2aFdmZU5zSmdwWz9hSFFkP3hmTUlddVhaP05tUFZmPGFva0hwYT51Oj52THhpWmZgPV92WT5zZVlkRHdibWlhaHldY2FrbU55TVhvcz93blBxcWZkQEh1VWlzc3dub1BbcF5xZ1ltUWldbUdjanhzTVBwZE9dc1FxQk5uVG93c1BbZ2ZrSVl0UVZeP0dwbk50VkF5am9eY0ZcXGhwYFVBXURpdmxwdGpfbkRRb1lXa2hXdkFZdGxOcUV5ZlVRZTpuWk5AcGZvdnBnbFZoaltXb0dxbm5Jd3Bgcj54WkJAdFVZYE1Pb0ZAaGU/ZDtZclBgc0Z3Y1hueEJnYFZocXM+c2lIXz5oZldocEpxc0BZZHB4WlxcX2VlYWNHT2RVR2Vwd2VSd2RvSGpSdmBtbm49b11RQWBBP1tGXltNSHhUUGZFPnhDd3J0X19DdnM6b2ltdmt1dl1rYVxcbUBsQkFyQHhhUG54V2hrbVlwR2hrO3FraUBxcGd1Q1l4c19xUHBoTnh0YHBxUlBpa3FgTWdmd2hmeVBmU0ZwTF9pXFx3YkRocUpwalZ4XFxLaGZuTmxDZm55PlxcSmhjSVlsVV5pZ0ZjVGhwcnB0dkBcXFBHbF0/ZUdxal9XalpeXT5ha214b2ZfcEthYkhJeExocTxJcjpPZGVpZXdOZlFxdFd5ZGtYaWF5b2lZYlJIXFxmZ29yT3VWSVxcR2ZbRkBmY254XFx2YVxcRmxkeF5sUHVFdnRCb2xFVmBQYV9yWHdMP25LUGxAcGxfQGBcXEFsdXFjbnhraU92WURlW3hxXXhtS3V5O2JUcXI+c2ZAaWNQaVlVUWJndUViUWk7R3ZhPURmQHNjQVhXdXhvVUxxRVViUWpHeFRpXFxMV1xcbHhEeVxcVE9gUHBqQVY9ZXdXUHBaZG9nVVRTQHRwPU47bXh2bFZYSHhAVVZoaFRLXVlqdXhdeE9hZHhXVFc7dXVubVRpRXZuaFFVcHVUcVZXbW1uQHZ0aXNIRHZcXEVxU0xtRFVxV1BRO21sRnhyaXRQZHVNWmBOPEFYWG12Oz1sSGBPP2FXSkRXc1VMaVRRb213V3RRXWlsV2RObVl4WlVvWHFVVVRXR2xwb2B3b0xrSkxwSV1wZ0xuVlVwV2lyQ0lQb2RPQ213YGBPTWRzYz1xeHVSdG9idlF1X1BkTHlzWD9lZEFlckd4cWFfQ2hsdGdmam9kdmFmQHlrd1FlR1FeQlZ1aWhuTVd1ZlBvW2BdSXdbZE5zTE9pS25xbGdsX0dhSGlgPFhoTnh2cm5zTGdvRXlvTF5udHV5O2JOYUZhRUdQd0lNSVdIR1hZXUVhQUlfXWRxeVZ5VUJueUk6cUlpZXl5O3J5O2JYZXJbaXhfSUlXUWlhX1lxdVlAXVd3cVlZU2VMRXdbb1VwQWhtc2lRc2k9WXNuS0dNb3M/QWVFUWlKP0hwaWJOT2dFa2NrSVQ8UUdba0N3T0NfbVVFPWleX2JQS2ZQR0RGc2l0dVhma2VxVWlzYVlrR2NJZ3hfRVdEXUd3WUVRa0Zub1hvW2ZvcUJFZ1lFX3hKQ1JFeWQ6d1VrT0NIbWR2RXhmW1lfTWhGX1VQTVZfVVduW0ZCSVhlRXM+S0hMVWZtdUVDc3hQUW1jUUtzaHU/QWtHPHB1VFBvdXNuRE9cXHFTWFFSYFRzaVV2alxcVGhNdj5BVD1pcERteGdQdFNEeWpkUl5oUEZYeFNNS09seT5scWRpb3VQTENIVmVEUVBAV0xldExZTmREb1t0cF9EbV15bV9ETVxcaXhHXFxUc1F2aEBWXFxUcEt0b3k9am54cVI8dWFxV2F1U3ltd05tSz1RVGNBVEVpS0Fdc3JQUk95Smt0VnZMdUBVak9wUldsdWFRcHhhUUFAb3l0VD5BeXJ1eFtVWEtodmpMdlxcRW5MXFxWXFxVb0Nhc29RcT1JeF9YdUd5c2FUbWxocl1tSlk8VFtgbVxcaHBsWHZOPXc6bUxsRVR1TGpiSFVRcHRSaXhVRUpBTGxHUW09eVZtSW1bTWpeRFBHSHlmaE5RdW5ncEpZbFZ2ZFhzSE9mTHBxdXJAXXNrTHVIeG5oYW1SaVBATVdUVHNYQXdKeWw7VUthVHY/QWpfVFJLVVBrUEtXWHVCTHF2RXA+bWpnbHQ7XFxvZlFUPlhXXlFQVVF4SjxvPXVlc09keG54eGB4VGF0ZHB3QnB3YFFfQGFfaWlfbWltXmBuc0hnRlhgZ19bSHl1WHBhTT5yd2Q7W3lPP0VPZXk7Q1I6O2luZXg8V09nXU1McE1WbHlwYFA+QHljTXdVaVhnSW9aWVk/aU1PbHhBPmFdTmxvdmV0eWxrT2dHaWd0cHBCUWxXaWlBSWZxR3VIQXhYcXVKQWJXWWBARm9YdnBbT2dWeV9EPl9lSGdgZm4+SVxcZEZlUFlvZXZqbGlbUVhcXFhJXkNpXmA+W0NIXUlGc0J4bHNxeGxucFg/dE4+cTtuZmVoZ19udUdZaHhWdFJfa0hHYXJoeHVgXUNpeV1AbGZXW0BOZltHYEVPcFZWbUx4am5wY2xGaFhOaV1ubk0/YT1xZ2FgPWFmUWFzWFFkTXdITnF5Oz10Q0tXRUxSdWRwZl1VPFBXbWBXcD1xS2BOUGlzUmVKUllSQWVPaGRWPk1ZXFx0U2VZbl9EUnNsbT5MTFJkV01QVnZMb0ZpUEFVeUVgWVVdUVFteGxtdWk8UFBRdHFlS2FUTV5hd3d1eEVxdW88VVpRU1dxbWVoeWtMWHFgTmU8VEx1b1FobkFdTV1Ib09UcEBIU2dQUVRdb0ZEU2ZhU0JpSlF5S2dNcD9xTz1UcnRNWXVRcmFNdUtsV0ZFVnNMUVI8UWdBdWtYTEJBVWtoakRJUXZQWEVtU0ZIeU9Id11JUEpoVEJ4VVBAVWNQcm1lc19IbV9VcHJoS1BBT0NJWHNFUUtUVm9kTjxIS2ZQcGRkckxYT0FlTmNRc0JRVDpsTVNNdTxFVD9MUGpcXHJSeVRbRHlGPHlESVd4eW1UeE11ZXNDcVlUXVNtQUtvSXlXXXJMaVVSTXNIeW1OSW9VcUpwdFdDUW9UYVVQXU5mUXVgZHFobWs8SFRjaFBCYXVWYVVPPFhNPXRITHBTeFhcXHlQclVqTXBKeUhuX0RWWW1ZXmxYVmVYUEx1PXhSQT1XR1F0dUByYGlyakB3clRxRXBQZ1RUQ2RrYE1vaGl4RDxwTUxOaVVwZ3hKVFhPTGBQc11yQW1LTVFMeEhKUnBtZ2ltX3FxVnRwX1xcdm9cXEtDeXQ+WGtdeVFwTFV0aVRNUXFTZFVxSHhHWHF0PXBRcE91aExNbFhFQUxwSG8+d2xNZ25TYXdaeGVKSFxcQ3BmW1BhT3FoQz9iSWlfUnhzW1Z0TD5lUWBlRVdmW05eXmdoR1d3blBkSFhpTlZgdVFodW9oSFBdVHZqW05nRFF2X1dsV25wcGhbc29uUGhyZT9hY1FlQmZnW094V25vRWhsP0hrY3FodD9zS1BkRU90XXd3U05fSUFYXXZCZ2NgV2RuPUNmUVdJU3hgP2Nkb0NNdUdNZ2ZCVUNtWUVuX2Y/QVlfQ1NKd3JoUXlQZ0dicWdXUVZRU1VOU1Vba3dvc3VXZ1lNRWNrSWRHT2JrU0hPY0Y/XVlmTUdVVUhUPUdeX0Z2O2leW2RBV0hCX3ZeS1ZwYVVGQ0NZX0Nwd3VIc0RwR2lEZVR1QWRyY1Z5d2lFSVVOPXJsU1lgUUZlU3NLU0hlU1hkU2JxQ2ZzbWhCP2lFc3JTX3NWO3NGYVJQQ0hZb2Nvd2Rsd0lJa3NdaXVoYXJ4VURYV0dxb0JdR1ZuUXQ/dUVUY1RPQXljcXlBSWQ9ZVVTVUVNWXhSQ0V1W1VNV0NXTVluXUdNY2RXTUVGU2N2T1Zna0JdbXVWV0JIVUJoX3NfeURrSXlhP3ZrR3JuP3lnbWVQY3ltYVRnaFJZXXQ6WUxfUFJpPXZRUXZGeGxxTFNcXFVSVVBWaGF0ckVxTnFYUUBzSERWYXFSQ1BOVnRzWm10ZUBLO3FMbW1tdUxUXXRWTUhZTXhXTmlRT3RYa2hLRVhRZXRNXlRwWGVvZ1hzTlhWbXhSTmh5Q2hxa2x0ZnFUZ1RvVEVwRllLU1FvSlRyPlhsU1FtdmxwW0lrYEltT1xcTnlIa0V0UVZkblBgbVpcXE8/RVReYHZRQHNDVVZfXFxUcUFURXhOb0F0QmFTOz1sdFROamRUPmRLP2lvR2xwVlBVPlxcWXhBbFxcaFhmdHlZUVlpWW1rUHhtRG9ecFJ0UGtqZHFsaWxXRG5NdWpoUUxaPWtKSXZHaU9cXElLQnBPXFxNUmFpWUBldkhVbF9IUF5tbkFJS1FUWFdkeHk9amZJblF5b3VhUkR0eWBNdUltTFNBc2t5V1ZJV09wc19AVGhUUG48b0R0S09xcGNZS0Z0blxcTVVoVXRmcXRqeE5wQW11RHVxZXFcXFhUYUlrPkFrSG1SWzxNVnRYWUFMY2RTRWVWP0R4P0BTWVlQWFFxdVB2UXFwT3FyZFFRcGhNcWRyRllUTnFRO3VWcm1KdEByd2xzV0B0XVhPSXRUPUxuZUh4W2RUQnRrW0V3b1BxOnVWeVVLTXVVWElxQGhOdV1PSFxccm95b0xkd0dpVmtET05dV2ZZTUVkSlBdUXhRdG89T09ReFF4V3ZldE9Ic2hxWGdodmlxdVhgeHBReFFUb19JcHFxT11MdV5QVW08V0FdTWVITDx4T1M8d15lbl9pTGQ8VW1dbktUTnlVVE5kVUw8bWtlWURRTkdMdk5tanFMamJVVndsTV1Ac3RVS2xJTXlsdXJQeWtNT3VJcUpZUXdUS2thU1lcXEtOcE1QRVVnTG5hRXJyQExMVE5UVXZjP2ZKaV5oVmJzQFlFR2BJVWxzV2JZaVhpV0NDWEJXZVhFR2VhaWZRWT1XU107d1hdUmVvV1txaHhTZU5pUklBRVVFU1ZNaWdFaVpnRG5PQmllZFdBSVVvRldBRXZFZmBzYkVzdWZnU0JVY2g9c2BDc0J5ZE9HaFpjdHd3WFdRUzxreVs/cktRZnldSGxBZ21PSV1BZEhzdld3VG9rWHRxY2xXcm5zVWJNeG9nRmJPV2RvRkFdZGxPd2ddYltDU15PZWVDd0xbdU5ZRmtDVnU9dmdrUmtdV2ZPR0tld1hVUktBeXRpV0BxV3dDZD91eGFRV1JRZWFJR1VRaT1HUHJIamxkTXdYd3VAbz9xU2tseEp1VFxcPGxYYEtjTE9hVFRVTGpVVFBTaEpuVWpDQU1xVExkVFhGUHB4SXFQcHNnWXdHXFxRYXVXTEVXVmxTdGFZYHBUYHBtZ0RPZV1WalB0Q3lKeEhQU111Rz1XZnFqUGxXPEFWcmF1WG1VQllxTUh0Q0lxcUB0RGxuRj1xZFB1STx2UWBXc2Bqb21MQmBuakxTWE5qU1lqd2Baa2FwXl9fandvc2lzZWdmdHFcXEJ3WmZvbF5RZ3VBcV1xa3N3WlVvclZIaEFRPUlIQV1lY0BBOjo6Ojo6Ojo6Ojo6Wl1oYllPb3RxeGFIdXdpa1VJXFxAcWdJX2dXZ21HV2pBX2FQRmc6bmtMT25Ddl1MRmtDRm08dlprZmVGcGhzZlxcb3ZvPEdvUXFuUkFzQFdkTFBrX0dcXEp2bFxcUF5OdmxdcWthb2VDcWVDaXFhd3FgV2VJb2NHYGNnb2ZOUGpbV248Z1xcaXBjbEBoQUZcXFFnalA/YTthdj9YWkx4Y1dYZUhAXVtwW1xcZmI7X15JWGA/eFlvVFBxZGRJdEldeUZfck1BeWNzUlZTWEFzdG5XRkhBWU1IaG5WdEhAQTo6Ojo6Ojo6OlpReXlTPTozOlwiXHtcfQ==LSUrQU5OT1RBVElPTkc2Jy0lKUJPVU5EU19YRzYjJCIiISEiIi0lKUJPVU5EU19ZR0YnLSUtQk9VTkRTX1dJRFRIRzYjJCIlK1hGKi0lLkJPVU5EU19IRUlHSFRHNiMkIiUrO0YqLSUpQ0hJTERSRU5HNiI=Copyright:A user can use the document without restrictions. Distribution and printing is possible only with the consent of the authors. The document may exist in differnt versions because the authors upgrade it.Contact addresses of authors: nemecek@math.feld.cvut.cznavara@cmp.felk.cvut.czrestart;Description of the programThis document allows to apply the basic numerical iterative methods for solving systems of linear equations:Jacobi iterative method (JIM),Gauss-Seidel iterative method (GSM),Successive over-relaxation method (SOR),to compose iteration matrices, compare the conditions and speed of convergence, evaluate the error vector, optimize the choice of the relaxation factor in SOR. The user may add further criteria of convergence and comparison of results.Mostly library functions are used directly (see the help pages for details), thus it is recommended to keep the notation of basic variables, following the textbook Navara, M., N\304\233me\304\215ek, A.: Numerick\303\251 metody, Nakladatelstv\303\255 \304\214VUT Praha, dotisk 2005.Global variables:
Asquare matrix of the system 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bcolumn vector of the right-hand sidesnorder and also rank of matrix Aprescolumn vector of the exact solutionxcolumn vector of the initial 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iteration matrices for particular 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 diameters of iteration matrices for particular methods maxitermaximal number of iterationsnumdigitsnumber of valid digits for computationsjim, gsm, sorarray of 0..maxiter iterations (column vectors) for particular methods\317\211 omegarelaxation factor in SORlastJIM, lastGSM, lastSORcolumn vectors of the last iterations for particular 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column vectors of the errors or the last iterations for particular methods...other variables are described in the text
Initialization (it is sufficient to run this part once at the beginning of work)with(LinearAlgebra);with(Student[NumericalAnalysis]);InputRead a task for the assessmentSolve a system of linear equations in matrix form LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2J1EiQUYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjctSSNtb0dGJDYvUSJ+RidGL0Y1RjgvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZOLUYsNidRInhGJ0YvL0YzRjEvRjZRLGJvbGQtaXRhbGljRidGOC1GOzYvUSI9RidGL0Y1RjhGPkZARkJGREZGRkhGSi9GTVEsMC4yNzc3Nzc4ZW1GJy9GUEZlbi1GLDYnUSJiRidGL0ZURlVGOEYvRjVGOA== with precision 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. For all methods, check the convergence and its speed, compare, and try to optimize the choice of the relaxation factor in SOR. Specify the filename, eventually the path (e.g. ~/nm/ulohy/uloha410.txt).read("uloha4??.txt"):A:=zadani[1..n, 1..n]: b:=zadani[1..n, n+1]:'A'=A, 'b'=b, 'n'=n;Manual inputHint: Use the palette Matrix.A:= :b:= :A, b;Evaluation of the rank (mandatory)n:=Rank(A);Exercise 6.53A:=<<1 | 2 | -2> , <1 | 1 | 1> , <2 | 2 | 1>>:b:=<1, 1, 1>:A, b;Evaluation of the rank (mandatory)n:=Rank(A);Exercise 6.54A:=<<5 | 3 | 4> , <3 | 6 | 4> , <4 | 4 | 5>>:b:=<1, -1, -1>:A, b;Evaluation of the rank (mandatory)n:=Rank(A);Exercise 6.55A:=<<8 | 1 | -1> , <2 | -1 | 10> , <1 | -5 | 1>>:
b:=<9, 19, -12>:after a transformationA:=<<8 | 1 | -1> , <1 | -5 | 1>, <2 | -1 | 10>>:
b:=<9, -12, 19>:A, b;Evaluation of the rank (mandatory)n:=Rank(A);Exercise A:=<<4 | -1 | 0> , <-1 | 4 | -1> , <0 | -1 | 4>>:b:=<2, 6, 2>:A, b;Evaluation of the rank (mandatory)n:=Rank(A);Exercise A:=<<5 | 0 | 0 | 1> , <1 | 0 | 1 | 5> , <0 | 1 | 5 | 1> , <0 | 5 | 1 | 0>>:b:=<4, -2, 7, -8>:A, b;Evaluation of the rank (mandatory)n:=Rank(A);Iterative 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 matrix form of the system of linear 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 D diagonal, L strictly lower triangular, U strictly upper triangularExact solutionas a row vectorpres:=LinearAlgebra[LinearSolve](A, b): Transpose(pres);Jacobi iterative method (JIM)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 analysis of the methodMatrix decomposition.DD:=Matrix(A, shape='diagonal'): L:= Matrix(A, shape='triangular[lower, unit]')-IdentityMatrix(n):U:= Matrix(A, shape='triangular[upper, unit]')-IdentityMatrix(n):A, DD, L, U;Composition of the iteration matrix of JIM.B[JIM]:=-MatrixInverse(DD).(L+U):C[JIM]:=MatrixInverse(DD):'B[JIM]'=B[JIM], 'C[JIM]'=C[JIM];Characteristic polynomial, eigenvalues, and spectral radius of the iteration matrix for checking the conditions of convergence.CharacteristicPolynomial(B[JIM], lambda): %=factor(%);Eigenvalues(B[JIM]): %=evalf(%);rho[JIM]:=SpectralRadius(B[JIM]): 'rho[JIM]'=rho[JIM], evalf('rho[JIM]'=rho[JIM]);Initial values.x:=Vector(1..n, 0.); x:=<1., 2., 3.>;Use of JIMDecomposition of the matrix of the system and composition of the iteration matrix.IterativeFormula(A, b, method = jacobi, showsteps = true):Computation of the spectral radius checks a necessary condition for convergence.rho[JIM]:=IterativeFormula(A, b, method = jacobi, output = ['spectralradius']):
'rho[JIM]'=evalf(rho[JIM]);Choose the maximal number of iterations maxiter, eventually the number of digits numdigits. You may supress a long output by replacing ; with : after the last statement. Iterations are saved in array jim.maxiter:=24:numdigits:=10:IterativeFormula(A, b, method = jacobi, initialapprox = x, digits=numdigits, iterations = maxiter, output = ['iterates']): jim:=%;The last iteration...lastJIM:=jim[nops(jim)];... or more.jim[nops(jim)-1..nops(jim)];Error vector after the last iteration of JIM.`po\304\215et iterac\303\255` = maxiter, `zvolen\303\241 p\305\231esnost` = numdigits*` platn\303\275ch cifer`:epsilon[JIM]:=[pres-lastJIM, %];Gauss-Seidel iterative method (GSM)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Manual analysis of the methodMatrix decomposition.DD:=Matrix(A, shape='diagonal'): L:= Matrix(A, shape='triangular[lower, unit]')-IdentityMatrix(n):U:= Matrix(A, shape='triangular[upper, unit]')-IdentityMatrix(n):A, DD, L, U;Composition of the iteration matrix of GSM.B[GSM]:=-MatrixInverse(DD+L).U:C[GSM]:=MatrixInverse(DD+L):'B[GSM]'=B[GSM], 'C[GSM]'=C[GSM];Characteristic polynomial, eigenvalues, and spectral radius of the iteration matrix for checking the conditions of convergence.CharacteristicPolynomial(B[GSM], lambda): %=factor(%);Eigenvalues(B[GSM]): %=evalf(%);rho[GSM]:=SpectralRadius(B[GSM]): 'rho[GSM]'=rho[GSM], evalf('rho[GSM]'=rho[GSM]);Initial values.x:=Vector(1..n, 0.); x:=<1., 2., 3.>;Use of GSMDecomposition of the matrix of the system and composition of the iteration matrix.IterativeFormula(A, b, method = gaussseidel, showsteps = true):Computation of the spectral radius checks a necessary condition for convergence.rho[GSM]:=IterativeFormula(A, b, method = gaussseidel, output = ['spectralradius']):
'rho[GSM]'=evalf(rho[GSM]);Choose the maximal number of iterations maxiter, eventually the number of digits numdigits. You may supress a long output by replacing ; with : after the last statement. Iterations are saved in array gsm.maxiter:=24:numdigits:=10:IterativeFormula(A, b, method = gaussseidel, initialapprox = x, digits=numdigits, iterations = maxiter, output = ['iterates']): gsm:=%;The last iteration...lastGSM:=gsm[nops(gsm)];... or more.gsm[nops(gsm)-1..nops(gsm)];Error vector after the last iteration of GSM.`po\304\215et iterac\303\255` = maxiter, `zvolen\303\241 p\305\231esnost` = numdigits*` platn\303\275ch cifer`:epsilon[GSM]:=[pres-lastGSM, %];Successive over-relaxation method (SOR)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 Relaxation factor \317\211.omega:=1.1;Manual analysis of the methodMatrix decomposition.DD:=Matrix(A, shape='diagonal'): L:= Matrix(A, shape='triangular[lower, unit]')-IdentityMatrix(n):U:= Matrix(A, shape='triangular[upper, unit]')-IdentityMatrix(n):A, DD, L, U;Composition of the iteration matrix of SOR.B[SOR, omega]:=MatrixInverse(DD+omega*L).((1-omega)*DD-omega*U):C[SOR, omega]:=omega*MatrixInverse(DD+omega*L):'B[SOR, omega]'=B[SOR, omega]; 'C[SOR, omega]'=C[SOR, omega];Characteristic polynomial, eigenvalues, and spectral radius of the iteration matrix for checking the conditions of convergence.CharacteristicPolynomial(B[SOR, omega], lambda): %=factor(%);Eigenvalues(B[SOR, omega]): %=evalf(%);rho[SOR, omega]:=SpectralRadius(B[SOR, omega]): 'rho[SOR, omega]'=rho[SOR, omega], evalf('rho[SOR, omega]'=rho[SOR, omega]);Graph of the spectral radius of the iteration matrix 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Here you may try to optimize the choice of the relaxation factor \317\211 in SOR.Initial values.x:=Vector(1..n, 0.); x:=<1., 2., 3.>;Use of SORDecomposition of the matrix of the system and composition of the iteration matrix.IterativeFormula(A, b, method = SOR(omega), showsteps = true):Computation of the spectral radius checks a necessary condition for convergence.rho[SOR, omega]:=IterativeFormula(A, b, method = SOR(omega), output = ['spectralradius']):
'rho[SOR, omega]'=evalf(rho[SOR, omega]);Choose the maximal number of iterations maxiter, eventually the number of digits numdigits. You may supress a long output by replacing ; with : after the last statement. Iterations are saved in array sor.maxiter:=24:numdigits:=10:IterativeFormula(A, b, method = SOR(omega), initialapprox = x, digits=numdigits, iterations = maxiter, output = ['iterates']): sor:=%;The last iteration...lastSOR:=sor[nops(sor)];... or more.sor[nops(sor)-1..nops(sor)];Error vector after the last iteration of SOR.`po\304\215et iterac\303\255` = maxiter, `zvolen\303\241 p\305\231esnost` = numdigits*` platn\303\275ch cifer`:epsilon[SOR, omega]:=[pres-lastSOR, %];Comparison of resultsThis is a space for your experiments. Use the previous results stored in global variables.Comparison of results for given precisions, together with the precise solution.pres, lastJIM, epsilon[JIM];pres, lastGSM, epsilon[GSM];pres, lastSOR, 'omega'=omega, epsilon[SOR, omega]; Comparison of Euclidean norm for ending condition 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 for particular methods and the last two iterations.VectorNorm(jim[nops(jim)]-jim[nops(jim)-1], 2);VectorNorm(gsm[nops(gsm)]-gsm[nops(gsm)-1], 2);VectorNorm(sor[nops(sor)]-sor[nops(sor)-1], 2);Plot of selected entries of the partial solutions (blue \342\200\223 initial value, yellow - next iterations, red - last iteration) in 2D ...plotres:=proc (met,j,k) local i,n;
n:=nops(met);
plots[pointplot]([seq([met[i][j],met[i][k]], i=1..n), [met[1][j],met[1][k]]], style=point, symbol=solidcircle, symbolsize=20, color=[blue, seq(COLOR(RGB, 1, 1-i/(n-1), 0), i=1..n-1), blue], args[4..nargs(args)]);
end:plotres(sor,2,3); # you may choose another method or entries... or 3D.plotres3d:=proc (met,j,k,l) local i,n;
n:=nops(met);
plots[pointplot3d]([seq([met[i][j],met[i][k],met[i][l]], i=1..n), [met[1][j],met[1][k],met[1][l]]], symbol=solidcircle, symbolsize=20, color=[blue, seq(COLOR(RGB, 1, 1-i/(n-1), 0), i=1..n-1), blue], axes=boxed, args[5..nargs(args)])
end:plotres3d(gsm,1,2,3); # you may choose another method or entries