The total pressure is defined as the force exerted by a static fluid on a surface (either plane or curved) when the fluid comes in contact with the surface. This force is always normal to the surface. The center of pressure is defined as the point of application of the resultant pressure on the surface.
The total pressure and center of pressure on the immersed surfaces are as follows:
The total pressure and center of pressure on the immersed surfaces are as follows:
1. Horizontally immersed surface. The total pressure on a horizontally immersed surface, as shown in Fig. 3.2, is given by
![](data:image/png;base64,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)
where
w = Specific weight of the liquid,
A = Area of the immersed surface, and
x (bar) = Depth of the centre of gravity of the immersed surface from the liquid surface.
The above expression holds good for all surfaces whether flat or curved.
where
w = Specific weight of the liquid,
A = Area of the immersed surface, and
x (bar) = Depth of the centre of gravity of the immersed surface from the liquid surface.
The above expression holds good for all surfaces whether flat or curved.
2. Vertically immersed surface. The total pressure on a vertically immersed surface, as shown in Fig. 3.3 , is given by
![](data:image/png;base64,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)
and the depth of centre of pressure from the liquid surface,
![](data:image/png;base64,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)
and the depth of centre of pressure from the liquid surface,
where
A = Area of immersed surface,
x (bar) = Depth of centre of gravity of the immersed surface from the liquid surface, and
Ig = Moment of inertia of immersed surface about the horizontal axis through its centre of gravity.
A = Area of immersed surface,
x (bar) = Depth of centre of gravity of the immersed surface from the liquid surface, and
Ig = Moment of inertia of immersed surface about the horizontal axis through its centre of gravity.
3. Inclined immersed surface. The total pressure on an inclined surface, as shown in Fig. 3.4, is given by
![](data:image/png;base64,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)
and the depth of centre of pressure from the liquid surface,
![](data:image/png;base64,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)
and the depth of centre of pressure from the liquid surface,
where
Theeta = Angle at which the immersed surface is inclined with the liquid surface.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANEAAAChCAIAAADWes15AAAgAElEQVR4nMS99ZMdZ5Y26P9hIzYWvp3ZnW9mm8HTbbdJtpiZqcQsCy1ZlixLlkmSqe02yDKDbLcsNIvRYmaVVFyXk+FlOPvDuZUqqWfm64mJ2O9Gxo2sW3nzZt183gPPec6pu+B/xkODMqBx01YpI5WRuKOt+g82ZWT2xr9z06AsGG2VAW3B3LEZ0Hec04Kx1mijtFUGpAEpFI3TICGhUJRLkpAwYpEwnCrihBVuGFUkZlEqEm6YE1aKboEbloi47JdCEiQ8popENPRil8gU9ytBmWvmhJWYRVQRbpgbORENccdPvJhFwnI3cpywkvA4JEHByXuxyw0LSVAJykHq+4lXCcp+4uGLfuKlInHCSiUoRzQs+6WyU+CS4GUTFrt+2QsqUrMo8Qul1jD2CqXWllxjnAYtuUY/dEpOzvGLflTJl5rdoBQTP0zckpPzQydK/CByw9gLY8/1yymNosRPeOxGjhs5qUjcyKGK+InnhBU/cKLENyCV4UykFpQBKTXF233X/yzM4Ya3WWohtcDb/2/i7D/GXPtT/e2mjGyPsPZYr77L3oZFobhQXBlprcEvy1gZp0GYeABaGxEnAdVUgwpSnxvGNE1FEqR+wmMNimnqxa4wnBtWCcoJj/GYmEVB6jNN/cRzI4cbxg2LaOiElVQkiEgvdqkiIQnw/oUkKLqFkAQIqaJb8BOPyNQJK4hmL3ZxB9+er+TwVzGLSl6x6BbqGmopT7gkTKQpjUqVfJwGTKSlSr6+8YbjlcLYCyJXGR7GHuVJ2c37UUUaGiZuxSukLCQ8Kjm5lEaExXgwniGI3ISEbuyU/RLiHq+NGxakvhdUuCQpjRDuynChqLYcjcv/f5iz7R6ZRVFGalO1cxm2cEdqIRRHLEotlJXKSvyxPW5uw5BVykipxb9nGttjPbN8dzxnx6Od00ZoK+I08CMHQKPZCGkoLCcyTUUiLGeahjSQVjBNEx4HqR/RUFjuxS7TVBiuQVFNQhKgkUt4rEAyTUMSoBnzE6+11OInHtM0SH0vdoXlqUjKfilXbsXDGlrrg9RH4+fFbiqSmEVe7Aapj4CuBOWQBGhZEYWOV4oSP04DwuKEhK5fRoMdJX6xnKu4RTRdcRoIRVMSlZxcmLiER35UKbv5lIVR6lW8Qhj7KY3Q2iUkZCIlLJaKxizyEw//orJfimhIFamElZRGCQnRyEnNpGbKcG0F3tm/F3OIlf8K5kzbwxqL1uUOiCgjmaBoY/B1xFx7U3eHnct+rMLXKjSZmUnDnTvManufa8FUnW/bc/ZbA5rLVBmuDA8i1w8dC4qwmLBYglAgqSJEphJEKpJUJESmiMKYRa2lFjRpRKZM01Qm6AqlFSlPnLBCFWGaRjTMV3IxixIeV4IyOmU3cipBmWnKNC37paJbwDtacPLodr3YLXlFdOhe7GYI82IXQZCKhCpSdAsVp6AMd7xSQkIuSdkpxGlAeUJ54vplP3QSEnpBJYhcJlI/dJ2gGKVeTHw/qnhhOaGBH1VKTi4lUUojxyt5QQV9NCLJjR0/8dD1Y2zANL1Wd9UPnVyhmUuSoc2ANPCfxBzC7r+IuczOVaM3W0VJhicuGVoyC0ZqkYEvC8VuCwTRXCGe2gWFd2z/cZxXPafV1WXQ7vwWTJR4XBLKE7w92grC4jgNmGHC8phFmemiiqB5w1cQhRENiUypJgpkxEKM3rhmJa+Iv0ILhzjLV3J+4gWpX/ZLTljByA9tHvpKL3bRi5X9khs5RKZB6mMshfsRDYPUR1eLEPf8MhMpmrEgcusbbxTLOS+oVNxiS66xUGotO4V8sQVBGUZexSs4ftHxi2U3H6VeykI/qlT8QsUtun4ZXTPlSRh7FbcYJb4TVtzIwYAVLynmkRs5ZafgeCUD0oKSmiHmNAhjjTZ/B+Y451LK/yLgAMAYa3GzlgqCNzWzZNoqpeUdTtaAMaDR8uEriD9dBQ2aMaNBKyOVUbotMrsDc5mdu2Nrn0Ygyu8IEJlItRXoILgkGBQLRamm0opqQsBCYbmwnClKZOqnXsJjtGGpSBIRM02F5VwzdMQIkZAECFlhuQCeiqTkFfEVDA3R+KHVRBhhYoGRE34E4g+B64QVYTkmNKlIvNiNWMRFKhRVmmPIH6dBGHvZPmVJnAZR4lOWJCQMQjdMXDcoOX7RC8tUxEITDOmK5ZzjFkuVPGVxQkIMDf3AwWvLLlJYHpIgpCGmGhhHtrNzUmqpjbrLgDVgLYAFaL+fbVIppbUyWltzx6/+h1s7u2KM1Qg6A5oKIq1QVnLNtFXcMGkF18xYySVRmivNlRFSMaW51Fwbqa3UVmojjVUWlFBUWwy2pAWFO1JzY5UyHDGEkeK/a+esMrbq4jNAa3NHgCiFZNoqpQSuDQvaghaao4HUoKQRWTTJFROaY/QpNMcYVBmprMQAjiqS8FhYjn4ZPa8EwQ0LaYBZiLQiO4BpiikIphFEpphn4KkwY8icKaKNKiKtqFpcnghFpWLaCqkZ5QnGBphlU0WISKhMmSLCsIgERCRh6kc0SHhERJJWoR+FqR+zKOWJtBwTdmFYyuPso9G6E5EqkFRTRBveSqEowk5bIRTnkt2lwWgwFiCDFO5k+FNGK6vxGHyxbYP/4Wbb0RPa3orN8W4Jy6UVwvBUJgok00xphtZYKiYUZSKVijGRCkWzyCDbMCeSpvqWlEbWoiXn6JelFkrL9hTJHZwIl4xLhnZRGZmlLO1hp7S01kgl2mxqNf/I7CJGkLhVXbm9FV9qq7RR3DC0hcJyTFQVSPwG8EuIeRSkvgZFFdGg0BZmzxZMQPxUJn7iIfLQ8pW8Iro2dO5I1iAIEh4zwwiNCIuzLzClEeZAVFP8aHxXSEO0VeiREetoZZHHwdwZwwmEOy4hbpgEgelU9dlwYTnjqdQMfWv2LDXTVgnFb2FOGY2Ywx1tTRV81golldFSKwMWX/87bZ5uY92E5pnJUUZigOyEFT/1NKiQBFQSqggiCcN2LohQFMAQFmPEipuxEqkyZbgFxSVBr5f91liZ0S5Ky8x9tzdpGqrpC6KzmmpYhW9sM2lGKgEAhKUZm5NluNoqjibQyCxqzHYsGGPR40tjtbJVhCU8xtsjQTBDheXKSqpJzCK8qZlVwzQFExRlpTA8y4vRUsYscsIKojAVCebLGCNWrR0I0gaybGMiFZJkSXdGLuIFtH8RkYegxHNmr2SgzNZSdvFUEW549nGYRqCNUIajM7lLgzFgAcCARXtWNW9WK6MNWKFkGEdSK3Sv/ynM4ZeOFjVjfZWuLhGkr4LUVyC5YZeuX6QsAdAYqEaJH4Zec0sDgEFIoWuIEj9K/DD2MJzH5YuRShT7ynJtBOUEwIZxwATFXLg9C5M9Z1ScNFWzjxthKRMUADzfjdOIcoIbAggTam0V5YSJKs8pFGeCUkHwPHgAnk1blcpEAJcg8O9FQOBNQqPFNNWguGYYyWWOEtmThMfoRvFgN3IwXnQjB+NCP/FKXjFfySHsMHAMSYCcBZo3dHZh7AVhNe1AG0Y1yZwjng1RiCEjZkhEpjGLIhoiU41LAolJxDceiYwjVUS2GQ706cpwDIXxLtxlrJVaEUaZ4BYgSmJldJwmSmsEnzZGGZ2QlHImpIySWCgZJTGg2zXaWGvAVq2jMcpojP+k1soIJqi2Koh8vMEGtFQCg5hKUC44+YTHEQkBYOL0iXv37YwSP1do9kOHS7L9my3jJ46VmiUktKDwD/CCCuWJ0jyMPc+vCEmV4SmJPvnsw48+eR8ApGKEpQDQt38fAEhpIhTXRmGEZ8EAAL6CjjUhsTaKsJQykpGFhKUVt/y7u3/7yWcfAwBiVxuFCEbbyTj1AteATmmitExIbMF4gWusTkjMJUtpktKECUpkqkCiwUBUYdyGZgyBIiwXhhORRiz0Ew9DDnR2WN7gmmX8H5EpRmwIDqw9YKECQYORn1AUyV783pCZS0iIh+HKR9eMNJsTVjCDCUmAmXLZLyEdg7YwoiFiPTOBqUjQ3SME8UUkX7QV2ghjpTZCKCo1rWJOW8MEl1pFcWwB/DBoybWiVZNaIZ5SSpTWABAlcRCF6GSV1toaqZU2JvO/CEFrq645SkK8i4i2LIqimhjQSDulImlsbZAgXnjp+c1bN2ImFadBodQqNTt34bQBCQCbtvy1Jd947vxpzLxy+eY4DfLFlly+GVdza74piFwuSUrDq9evNLc2/fq3vwKA2rrrYRwkJBaaA0BTS+Ou3TsBbNktEZa25JoRUhW3rLRkglJG/NDTVm3Ztnn4yGEAUHZKUouKW/YDDw9GTHu+ywUDgCgJkzQGgFKlyCWTSqQ04ZIlJE5ILBRHfPiJl3Fsl65fxLJERENk4FKZoLfF0hbXDL0nIqDoFtAtoDNFVCECECiYJpe8IsIak1wvqISxJzWL0yCIXHQIKQmrJI4iTFO0nQi1hMde7OKp2ntqRBsGBghxpGPwLdlaQpY74TFlMRo5RB7WDy1IZZQy8q6UEj8MjLXaGgOWCe54bhhHSusqswEgtUJfWXXBRhuwcZqUKmULoLTGsI8KhgkHZhtSK8oJmoQoCXEH+REMcnG5CMNbis0a1DOrV3264aNCqdUPHcJiP3Q+//LTGbOmAkDP3t0mTh63cNG8X//2F5u3bgSAP9zz+yjxAeBffvZPaP9eemXNlxs3MJF27d7prXVv9u7ba9SYkXEateZbrtVeVUYCwNqX1vQf2O/e++75/MsNfugFkb98xZMAcOHS+f4D+wHAzfobHTs/0rHzI1u3b5kxa/rAwQPe++BdbdXb694aPHRQx86PrFv/tgENAF/89fPuPbv17tvryLGfkAyat2Bu957dxtSMvnb9KjrWhMRxGnHBMLRHPOUrOSJTP/bCNEDzhmE7ZqAIpoKTR2au5BWbC01u5JT9ErItePvxNiP4vNh1wkpIAgWyMddQdAtVrMgkIWGcVj0sGryURoyniDlELcILMYppBMIIgYVmDMGdZSd4DFZXMTDAmBJxGZIgJSGXJEv12jFNSlt1VxCFKSWEUXSOWQIhlUpIGqWJBShVyoQxqXVdQ33ZqQCAtoZL4QW+tsZYK5VCG0kY1aYa6kmtoiRAT4QuSWqOfBtVVIPKWHu87rmL5vx05CBymKVKPkr87374+sWXV5+7cLpPv54AYEDe/9C9586fNiDve+AeC4or8k///I+YTPz59Ze/2vzllxs3zFswGwA2fP7ZQw8/iFYK4QUA3Xt2u37jWhgFK1Y+BQC1N6/f/+B9ANDY3HD/g/cZ0DfrbzzS6eHauusAsGvvzklTJiKefvGrnwOAF7j3/OmPFqzrOw88dP+lK5cOHzn0+3/9HQDs2rOz34C+SRpv2ba5d99emHngltI0FTE31egbrQWTVYbPS7yQBhELMV2lmgoQRbeA9uaWd2NxyStmBQ+8zVhbK/ul5kJTJShjWayl1Mw0jViYyjSlURA6rl9OSBjFPhcpco0IDjwb2tosaMPPRWBh6ImEcyZiwPuVJS4ISvTUmW+N04CwKGMbqkUww5RVysi7jLUAwKUQSmpjEpIaAKUE4zRJY6mEEDwIfaWl1ioIwyiOpZRKK6UUBnDaaACw1hJK0zQ11lgLSmutdalS0lYzwR3PsWBx45JJI1OWFCsFJmnKEsevJDSeOmPKydPHDEguSXNrw8HD+w7/dGD2nBkHDu1dvmIp3vuhwwftO7gbAO5/8F5cOv/ys3+KEl9qtuLpJ3/c+d3Lr659fvUzACpXbPrZL/4JAFoLjY3NN/2oAgCPLV7Qo1fXDz56z1gJAId+OtC9Z1cAaC20du/ZDQBOnTmJHjlMgm+/+2bR4wsAQFsZhN7b77wxfuLYgYP7A8CHH7+/ZOliALCgjhw7bECuXPXUqmdXHj5ycM++nT/7xT8DQEojwpIoCcqVQiWoMM292C+6pVQQqhnXXBhBRVrxSo5fTmgoNIvSIKERl6TkFzGRpIrkKzm0YVlls33JC21VTEIqUq5oQiPHLyc0ilKfsDhIvDANwtRniiYsDhI/TIOYRgiRLAtGVKHB82IXPwgdbgajLAREA4mLB68HcwtEZ8wiqkkUB5SnyGKaaoWTayuREL0rTpOEpphJCCVLlXJCUkKSKAriOAAwWkutJdJthBCsmQohwjCUQrYrMxilFGMM99M0jaKIK8mlIIyGSdwuma2mfilNMLUM4yCKwzUvrr56/SKAxVJMlPg7d/+wZOmiG3XXuvXozEQKAGNqRv509KAB+dDD99+ou2ZB/cP//X8KRQFgzYvPf/7lp++8+9ZXm78AgOs3L/zpgbsBVJhUvLAQJmUABWDOnj81cHDfWY9OB4ADB/d27dEJAK5cvYyW7MKl8127d8G/aMu2LfMXzgGA67VX/t+f//eXXllz+uyJjp07AMCWbV8989xKAOCSABgA/dpfXhk4uN/c+bNnzp42YVINAFCRCEUpT8LIdWOfaR6zJKJxwlMiacwSopgBQVmcyzcVyzkuSZIGSEkSmaLdoopgyJsFXlnYjsjzEy9iEaER5UmcBl5QcbwSblHsu7Hrxa7bJghwwooTOUW3gC4yM3UYomHsiGhDI4rmDT8a8YdQQ5hmQV57frt6JE2VkVxyzOszpqmaQzDBuRTaGvSqQRRGaVJXd4NzikAyRnFOtZbWaiyCWWu11mmaZj+2VwBorfHZWqvBCC2lUhn510Ys6ziNCE3DOKCcOF4FwM6eM3vVsyv27Nv5/Y/fXL9xBcD+9avPx00YAwA//+W/7D+053rtlV/++md1DbUA8GCH+46d+Gn7N1v+2z/87/i5T61ctnHTFzt3/zBtxmQA+PKrz+578I8AIDXxozKAac7VDR0+CAByheb7HrgHwBw/eaRHr64A8OXGL6ZMmwwAx08eQ2+rjNyxc8fal14AgI8+eX/4yCEAcPb8qT/eezcA7N67Y9CQ/gDgeKUevbsCwIsvr163/k28komTxwHYhIRYBhCKUMWoYjFLEp5yI4SVVDFezeaYF1Qy6QdSjH7qZb4M7yvTFFUFaJ/wNmNeErOIsJjyBNmQUiVfquSxHoonQSLNjZyCk8coDROIjEZG24n4Q9eJSgLEGbLW6H9xGVBVZfgQcKjLwl/FLIpYGMYBEp8YxCNnJBTHqsxdme2pMiPWaGOMlgg4azWAwWdjFPpQYwy0lfyNMQivO8BXxVwbjVdNLKxFkg8vCBmKlCaY/a17d92MmVMmTh43euyIxUsWAsC+/btXr30OADZ88cnwkUPGTxw7aszwG3XXDMi/fvX5Aw/9acq0iZ26PAygLah169/cun0TAIwYObR7r84DBvcZPW44AGjLUxZqywH0mhef79Wn+89/+S9Hjh0CACHpvPmPTpoyfvDQwYsefwwArly7jFEggP3+x+/GTxwLABW3OHL0sCHDBo4cPazDIw8cPX4YAOYumN256yPde3Z5/8P1AJCQsE+/nuMmjOnRu+tb6/4CAMiCSs2YSBVopjnTnEgqrFRWM82ZEcYKpLIJi1MapTSSmglFIxpKEMjpZyxxto+3GcVq3DCiCH4KCkaw8IBxWypThAKGelmNAXFDFaG6yqpkZ8OPQDILZVpcM24Y5tFZLU6CyE6CkRySrHhOpCmQqtRGZdw70vJ3IRQMVFNUbY22FqAKNYQdYk5rCe1kcNDugUDM4HjL4YLNShe31zAMXoq2CsAKxSkncPsjISGeWxmevVgzfvTxE0eQPckeQlFtxa3EGoDQqGp0LRaYBdKSCCBMeIWiABpAN7XU3fo7wGDZCgsSSnOpGYAVml64eBYAkHzmkgDAzfrrZ86dBAD0+3Ea7D+45/jJI/jJmW5MGU41F1ZKq4SVCrQCjTtSU7wMTPGqrD2WjwxF4Wf7ull2jzG8w4CMKtI+Wkf4EhZzSaimWWkhIztSkUio2i20nTGLEHPtYYQZqLQiu4b2cM8srmirwGI1T4EUlnPBkGyvCnZu3+4yYKVRXAn0ehZvGuisaoru1RhlrYI2Gdwd+Mh0Sn+DuXZ1MDBVCIJtL4DDegiXjHLCeFKtz7SrnFTrYJICQN/+vVpyjcbKlEVZvQvNiQah2qouFgxW27DO266KzywoCwrZIyygAZj2Mk8AaFOyaG0FFQnmxWhIUOSNBTepGQAgEcBk2rY2LNoqVFIYKw1IBUaDUaDRsWabMhz9L34EXr/STFqRbVgBQ1uCNx7vdEwjlB9zwwiL8Q9HJ4umThlO20oFmJwiVtBToxvNIkW0hZmpyzYFsj3C0E0j8hRIZmimlM6gyW21DJPpGrOtijnbZtA03Kpr3YG5NlOn/07MVQ2hvU2ikmHOgNVGYsNBpp9TRlJODEhUIlCeGJCZlEgomtJIGV4otQpFLSj8ESOYjAGqSrVstUKFdKC+rWZ/SyJgrMQbQ1iMPGL7tgyhuNRSW64Mx8KRAdmab8o+pSpq4gkK7NAzZtUe9G63rs1IaZUEJUExzYWV3AgiqZDEglKW45WgMbagJEjVbsOICq0IM1UYYQEXGTWsNODnopo3pRHlVYlAez0pgiyDGgpDsvDujs2Aztwoutqs6o8XpkHhekBQIuYUSCZoVu1sr4G4DXMGbNWaGa2MbvNT1aDfWq2U4JzewtPtj/bBnFJKK42bMhrPqU17I2eZoELd0mK0ldslWhG8zbhYcQXjc5T4AFppTnmCdRW0hXiD8Z5VNy1FG+aUkVJnsrxbyhQuUoSOMvwOcbIBzSUTSkhNLSgmUy4JE0kYe45f0kZYUNIwpNcR7ujfhaqWNbXleNerOg7FuBHcCKa5BKVAC1CpoIwn2nAuiTZcaoq4EYpQXbUrTFNlq+VpBVJAm+lqwxDe7+x7wC4EzCdSEiVtaEt4TBTJuL1UpnjymMfonduTIAg4tGcJj5m6FU3ikVW9oKZZDFcVyGAR2TKpRGbn/lY/e5cBo4xigrVpbxBwVpksQkL0qTtgBv+Zh7b67zkMPyVTR+Kiz4T8aPzQG2ormEyDyEUTSFhsQCrLhaRxGgSRFyW+MkIZITUDMFIxqTkAaFttyWGCoDxOatHmBBVWdbWV+F5lUEuis+izWCkwTlBqJRRlPEW0YQCAhdqUxlILJmmb8ERIw4VmKYsJSwhPLGiuWJj4XLIoCaMkVFoyQZggXFKhmLQyITHhaUJj1A0kNDagYxImNGKSMEmISIRiXlCJSRhETtktRKlHRRImHuVxmHhMJn7kRGkQkzBlcUJDZQUVqdAsiF0mUiZJymLCY20FV4SKVFghLMfWCuSEkZbLKnLSCqTiMIbD9Bl3MF5ESpkpSkSqrMSaMppqBbd8qzGguaw2IiCYOnXpMGFSTdfunQYO7jd46IAp0ybWjB89fuLY6TOnjJswetqMyZOmjJ84ZdyESTUzZk0ZNmLQ3AVzFy5aMGXa5AmTxr+17s1Zc2bOnT9nydLHZ8+Z9cqrL0+ZNvnlV19a/+66zz7/9MWX1qxeu/rxJQvXv//21u2bXvnzi19u3LBx0xc/7Ph27/5de/fv2rH7+xt11/Yd2H34pwNXr186dfr4jbprp84cv3Tl/PmLZ+obb9Q11N6ou3buwun6xhs3668fPX64VM7fqLsWRl5D081ypdCSa2zJNaKcOqVR2SnESeB4JS8oR0mY0CQlSUISz3exHko5jRLfDx1CY0LjhISMpwkJKUsoJ1wyyghlhLCUC+b6Dpc8SjxtBGUJBoVB6DKRUpbEacQ41UYZq7HwSmiqjCQ0xiXEeFKN8DRrW4r2znXX9sB6HT6w4Nb2Om/3ugSAIHEANNxmF/DHf2+pm+xUhMXVCpWiWKhtKTY35hrcyMkqHwipXLkVsRiziCmKMELbhl6+EpRLXhELcUSlKAdEK8g0Zaatxm/b9N9YEqWcaKs++/yjV/784vwFc1Y8/eT8hXNeWPPs5KkTHn/iscVLFk6ZNnH2nBnTZkyeMm3inHmzpkybOKZm5MjRIwcOHjB85PCp06eMqRk9cPCA0WNHde7aacCg/t17drv3vnsWL1nUuWunLt069+7bq2PnRwYO7te9Z5eHOz44eOgARPaDHe67974//Oo3P+/SrWPvvj06PPJAtx6df/v7X/3qNz//0/1/7Ni5w+/u/nXHLh3u/sNvf/aLf+7c9ZFefbr/7u5fd+3eqUevrkOHD3q444P3/OlfBwzqe/cfftuxc4d+A3p37Nyha/dO/Qb07tu/17QZk3v27ta3f88hwwYPHDygS7fO3Xt2e+jhBydOntC1e5e+/fvUjB89aszwHr26DhrSf+Dgfl26dcQLGzJs8IhRw3v27jFsxNARo4Z37tpp2oyp/Qb2qxk/esKkmmEjBj86d+bwkUPG1IwcOLhf3/49p8+cNnbc2JGjR4ybULNk6ZLJ0yZPmzF15OgREyePm79wzuxHZyx4bO7CRfOmTp80Y9a0p1YumzRl4mOLF85fOG/R44899fRTq9e+MGHS+KVPLl3w2PxVzz49acrE+QvnrVy1Yv7CeaPHjnryqWXzFjz66NyZK1ctnz1nxit/fvHRuTOfWrls8ZKFU2dMXPzEghWrlj23+unlK59YunzxnPkzH1+68PEljy1cNG/Z8iUvvrR65arli5csXL3muZWrlr+w5tkVTz+5bv2bR44dwigQ3Tq33IvdxlxDfUtdyStWgjIWPDDyKzh57NVAk4Z65kxsh822yLzgu9ALo0wLj6z2Gmbxe0JiJmgQ+YSlyHgBgLYCF0S+2PK3qwTa+VwLGgCUEVSkcJsvzpaUsKCUEa35Zi8oS83KTqHiFhub61pzTVeuXTx15vjFS+eOHDu0/+CeYyd+OnHq6I26a0eOHTpy7NCBg3v3Hdi9Z+/OYyd+2rn7h8NHDuzdv+vg4X3vvPvWt99v/+zzj8PY2/7Nls1bN37z/bZPN3z07vvrvvjrZx989O4Tyxa/+/66Tz778Nvvt7/+xqtvv/PmW+veeOOt1196ec1Hn0Ilp0YAACAASURBVHyw4unlb7z1+kuvrP3z6y8/v/qZF19e/fQzTz39zFMvvrx65arla9Y+t+bF1SufXjF/4bynVi5/+pmVzz7/zAtrnp89Z/ZLr6x58qknnli2+KmVyx5/4rFnnls5ZdrEhYvmzZ4zc/LUiY/OmTll2qTpM6dMnT55zrzZM2ZNff2NV2fMnjp1xqTZc2dMnTFp1Njh02ZO6j+o95iaUUOHDxo+cuikKeOHDBs0ZNigGbOmTZw8vlefHi+9snbAoH49e3cfOnxQn369+vTtOXT44P4D+wwdPqhv/14jRw8bOnzQhEk1ffv3mvXo9H4De/Uf1HvE6CGja4YPGNxn4pSaUWOHjRo7rFef7sNGDO7SreOgIf379u81cHC/YSMG9+7bA91X526PvP7GqwAWW1YJqwpScuVWLLhhTQJDQCesoCwZCySkLSLMimD5Sg572LAUwRTNXLABjamGkFxqcRcCLoj8lCUY0nHJsBhMeYLxchC62lZdSULChIRxEgBYP3TaIqqw4hWYSJhMKU9i4lMRJzSkIuEqDWOXsIiJJE59LyyHiUt5EqW+45W4JNhr6fplJlIUz7Xmm/LFFtcvY/8I5oyYW7h+uVwpABguiOuXjZUY5KGizoISmiJVgfSeBVVNmkFrK7hMAYDyOCY+4VUOTxrabnW1d0a33BwT1IJBISf2vf5bB2c/agAouwUAEIoAgAURxJXq2rO0ek4ZA0BKQ7wqZZjUjMkUKSYmEyEJgA5j14DgMrUgMbtSmueLLSmNcD3XN96Iqc9lihdMRZzSUGrKZEJ5YkFhN6GQ1FiZ0LDiFFvzTQkJi6Ucik3iNEDe0U/9sl9qLbWgyAWbfbAg4UZO0S005RvdyFEgkSjGY9DbYrN3Jr5qkywQ1A6i1BnLEnehi01pEqcRakC4ZJeunPeCytFjh6PYT9IwScPWQtONumuuX07TaqtjELtB6JYqeamZ0KQl1xBEjuuXUhoKTYQiXlh2g1JKQyYTImKlWcpCZRiXqeOVGU+lYlKh/sxvbm3AiKc138RE2tza0NRSH0Qu3p7WfFPFLWa3l7IkScMo8REoynAAywWRmkWxT3lSquSx8gigg8gFMF5QiWK/5OSUZXhjtOVh7KYs9MIygMY6LwY3iCHHLxVKBamEMrL25nUhOWFpqVKM0wgpmzDytBV+6BTLOcJiQmOhSEuh0fGLBkRMfMcvFsotfuRUvFxM3Fyxoey25kuNXlgUKmnO3ZCGtRYaG1tuUhG7QSlhoR87Fa8QJp4XlgmPDIiSm/cjp1BulYZiXyATacUtOl4poSHei1yxqeIVEhqU3Xxzrv7ytfOOXwxix/FKFbfIBUEhHR7MJUlJ5IdOGHt+6MRpgL2ulCfoFlEBWs0GNEW5MkqRS14RpSXImyDIUCKf7WMVGDNftIi3aG3FlZF3ZRUxZWRKEwCob6ybM2/W3Pmzx00Y8+jcmQDw5cYNg4b0f+jh+4cOH4SFndlzZvTt36tjlw69+nQHgEtXz/7rPb8ZMrxfh45/WvvycwDw1KonRo0d2rHLA116PLz/4E4LfPCwvj37dB47fsS6d/+irfjgo3e79eg8fNSQAYP6Hj5ywPXLS5Yuqhk/esnSRbMenR5E7umzJ177yysLH5s3cvSwYyd+kpq99pdXFjw2d0zNyKVPPt7QdJNLsvbFFyZOGrf2pRe2bP0KAOobbry97o3Hn3jsnXffKlXyAGb12uc2bvrivQ/eOXR4P2XJlevnt2z761dbPv9i48enzx0DMPsO7Nj69cbNWzf+sONbqVgYe+vWv/n1N1v3H9xzrfYyl7z2xvXDRw4dPX5k46a/up5jwZw5e/ro8UMnTh0tVwqExs2tDRcvnzt7/tTZ86ccv+BHpeOnDp29cCJfarpae77stsape+L0oZv1l5paa90g7/itrYWbuWJ9a76uruEaYYEXFBuaa8tOa1PrjUKpqVhuLrs5x8uHsROlrh+W/ajc1HqDsLBcKeQLLUykTS31XlBpzTdRlpSdQsnJ3ai/ynhScnJXay825+rdoFRxC1Hslyr5OAkoT6LYj0mAgn6U/hfLuWoOFLlB5ApJsF/VjRwU7WFCUAnK6Fgbcw1lv4RS00w6j6MwsCEcu2uzjlcDOuOZq0wKYg6VbUHkx2lkrHa8ilBcaprVl5TmAOCHTuZEUhpmJkdpLhQBUFA9XnEdEx5wFTMRaaCUh46fj1IniMsp8ZVJS05znAaNzXX5YsuVaxcvXj6HnnTv/l2nzhw/eGjf3v27pGYXL5+7eOnchUtnd+/dcaPuqh86Z8+f2rd/97btm3fs+t71y55faWqp3/DFJ3v27dz+zRYL6ur1S5u2/HXjpi/+8uafvaCiDH/1tZc++/zjvft3YbX+0tUzK1Y9MXHKmBVPL9m191sA2PDlh2teWrV8xdJly5cAwOVrF5YtXzJhUs3CRfO+3PgZAHzw0QczZ89cvGTRqDEjT505BQBjx42ZPnPysBGDsdL68qtrR44eNnzkkJ59up29cJyKoGOXB/r07zq6Zkj/QT0A1OlzR3v17ThkeO+hI/ocOrLLC3Oz504eNrLv8FH977nvdwlxr9ae69G7U7+BPabNnLB85eNUhBu+/LB3vy79B/W4577fAtgz54916d6ha4+Hu3bvXDNuNAC8+PLqhzs+2G9A7249Om//ZmtCgynTJ/Qb2KtX324jxwyNib/tm01/evAPo8YM79z1ETQTzzy3snPXR0aNHX7fA/c0tdSHsYdDTLIqLeqHcSpKJSijGcM5FVj1r2+py5Vbsd8bKcOskRvbNTJpUzbJBYkShB1irupbUdHqBS6ALZTypUrRDx0A43rllEYpiYLIxaiOCxYlAWFplIZcMqGY45UTEidpEKcBVyRKfGkYEymA5ZIUKzkLUllmQYaJl5AgoSHyfwZk5jox+Q9jz/FKmaNE5SbGKEIy5MkIS+C2h8XSZ9vDEBYbK1HWEacB1qzwV3EaSE3trVqtVIZbkNnqihK/fXpkQAaRp41oC9cAAISkADbLkFBGBQDFUo7yBEAykWioviVlkdRUaGpBGBAAEMROc66+4hUArBeUAUyxkvPDCuERoaGyHGMSP3Ioj/2wAgAJDcPYZTK1IOMkwC8qV2hOCH6TEKcBDoUAAKkZgCpWcmW3YEB4fiWMPZx9AWBKlTzlScUtEhqXnQLqWZBRQmY7omHByRecfMkrlv0SGjbEUMyilmJzS7EZ0wJUPqO3xbwVYYr9BiijRxF4tSvMcGmrgxnuwnENGMkRllowURJySQiNR44etnDRvH4Deg8fOURb8cPOb3/xq5937trpgYfuf2HN8wDwzHOrxo4b06df70FDBgLAvgN7O3XpOGzE0D/e+4e31r0JALv2/PinB+4ZNmLwpCnjb9bXSs1nzp42d/7sqdMnofLn/Q/Wz5g1deLkcYsWL/BDJ0nDaTMmr1y1fOLkcU8sW2xBnTx9bPmKpc8+/+y8BXNPnDoOAB9+/MG69W+vXvvC519u8PxyodT62ecfP/Pcyi3bvjp4eJ+24uLlc998t+27H77eun1TlPhR7B878dO12st79u3cd2APAFyvvXLo8P4Dh/aePnuiUGwNY6/25tV9B3bv3rvj4OF9UjMAfeLU0UOH9584dZSwuFjOuX6pNdd0/uKZ02dP4BSja7WXb9Rda2yuw0FaZadw7sLp5tbG+sYbXlAplFpdr1ws5cpOoVjO+aEbp0EU+80tDX7g4L33/EpKo4pbSkhYKOW8oOIHTtkpCEmL5Vy+2AKgC8VW1DghaArFVj90Km4xIWFLrjEIXaQGK24RP9SAxMROaY76ftcvh7FnQaE9wzJdELlSMz90cDQT1spSEqKjLDh5TEKxlyxmEY5NQczh5AD0rUW3gK06qBhAmacXu9jhkUlasr5JLHjeFSWhH3pSiziNAKyQnHJyo+5aRpdgmB+ngTIM17TjVhISG6uD0OeSteZbXM9RWgaR39zSlCu0BqFfKOUNGC+sXL126Wbd9dqbV0uVvAV17frlcxdOnzh5tCXXyER6+uyJHTu/v3z1wtHjh6/fuAKgt27b9OOO737c8d3W7ZsAdF1j7c7dP7z7/vrPPv/0/MVzAHbd+rdffe2V5SuefPb5Z8pOQSj66NyZTz/z1PIVS1997SUAOHnq2JKli1Y+s3zm7GmlSj6K/VmPTl/65ONTpk1EB7r3wK4evbrOXzhnTM3IDz56F13V2HGjRo0ZPnX6JADYf3DPL3/9s2kzJj/w0J9QTPX5l5/+P//9H6ZMm/h//eP/kSs0l8r57j27dHjkgT/ee/fX324FgKdWLvvd3b/u1af7H++9+8ixQ1ySBzvc16nLw126dezwyAMpiU6fPfH7f/3NjFlTh48csuGLTwCgW4/Oo8YMn7fg0T/c83vsNurVp/vc+bN/9Zufv/zqWgD71rq/ICcyZNhAALhRd61z10f69u81eOiAyVMnAMA77731YIf7Bgzq26NXV1zDNeNHI5PSq293ADh4eN99D9wzf+GcAYP6vr3+DWX4c6tXjakZOXbcqAmTas5fOINow35ExpNMh4xZKjLAbuSg98S2CWwkyEq9GNWhhDNrD3MjhxmKvW3te3WrmMMJMdWpgFYLxeM0AgANAsBg0zLijwv0YlZpCQDaqnwxp7TUViGJYKuOycZJBABCcZwrAwBckGI5F0YeAKDOB3u7vaCirUAxAfZAYI284hYBdFZIRWOM9GF71VNKo7qGWgCrrUDShEtCWdLmCnWcBlyStsIxoKttE/dCSiNtRJvzrT4qbjEjIwmLLagw9vC9BiQ6VmOr018crxRELuExYTGAiRIf3RzeyJZco9QsjL2URFyQIHJdr4wckNSMsqTiFkvl/PUbV3C6W6mcr7159cq1i8VSzoJy3JIfOucvnik7Baxk+KFz+eqFU6ePX71+CeFy9vypYyd+unLtYpKGcRrkSy31DTdOnz3huCVluOuVr9deOXXm+MlTxxy3JBS9cvXi9RtXTp05fv7CmSQJM0EKl4TQKJsckPXYYuKJox2zqmtGBce8qgmlilBJ2guuUJeAwdydmDNWU04oI5nsBAAuXDxz6Kf9p8+eOHBob0LCppb6Hbu+P3v+1NFjR1rzLVKLGzdq6+pv7tqz0w88C4ZyUt9QVyjmc/nW1nyLH3me50ot6hpq/cDBMQKOWzJWBqGLcx4ZT+MkwKF8QlILyvXKOGzLgDx15jgWVQG0AUk5SWlScctYLAEAJqjSEjVnynAAXSznECioQ9FWMF6N5FC/hGQVtPHV2ooo9QF0QkIuiDKc0BipNVQiAQBCCk+Lc/yEbusWNgJblBGyqO+1oAqlVqkYTq1DWABonG6JqxenPOFMOyZSpTmXpLG5DkALRY2V2JyHTR5cEm0EgE5JhJ28+OcA6HyhxYDM9DWMp5nmAHsKcR+1YdoK7PhC9RTlCa4QHPKlDE9plGEuUy5h8UqBRHIka/1imkojFEhuWaYowWkSTFGcN8AN45ZlmEP8VTGH/e6EpSifxIFcTz71xCt/fnFMzcj+A/sAwI87v1v0+IIhwwYOGDRg5+4dAPDu++sHDRk4dfqUaTOmAsDuvbtqxo8dNGTguAk1n33+KQAMGTZ41JiRvfp0H1Mz8ur1SwDwy1//bPzEsf/0z//47ffbAWDNS88PGtIfK2Df//hNqZKf9ej0Hr26jqkZiV0Im7du7NO/5+ChA/r273X1+hUAeGLZkuUrnhw1ZuTosaOC0I/TGIs/Tyxd/PKrawHg6++2Tp855ZPPPnz9L686XgkAps+c8vobr654+sk33noNAC5fvTB85JC33v7L3Pmz9x/cAwBff7v1tddf+f7Hb5YsXQQArbmml19d++bbrz+/+pkjxw41NN3cd2D3hs8/2bpt04cfvxeErgV14NDeuobaLzduaGqpBzC1N69igfinoweL5ZwFdfjIgbqG2mu1l0+ePkZZQnly+cqFK9cu1jXUVtyituK7H78GsLU3rl6rvQygw9ira6itvXnVcUueXzEgPb9Sdgp+6LTkGjF8xKi/WM7hlEIh6YVLZwul1ubWhlIl7/rlYinX1FJ/6cr5iltEpre5tSFfbGlubUA2MYp9nOdFeaIMr7hFISna42zUQzZlB4WZ7cUjKGHHdCEzdTjdB4/PJMR/G8ZV9U6a3Kq3om1rbG7gghmr0XVmmVqb77v1wNbi7IGzCnEfHV9DUz0635Onj2EAi0V0PAYHkTCRxklAWNyab8JBOOcunD567HBTS/3FS+fC2POCyuYtGy9dOf/V5i+xYeLEqePHTxzbsm3zjl0/pjSJk2jr9k03bl777POPf9z53YVLZxub67Zu3/TJZx/+dOQgYbEblD/7/ONPN3y07evNP+78DsCcOXfy5VfXfvPdtjUvPn/qzHHE3Jtvv77i6Scxxjpz9uTrb7y66tkVa158/tKV80Hkbvjik1mPTn9hzbMjRw+7VnsZAD786L0nn3pi+Yql+JaXXllTM3706rXPjR474uz5UxbUpCnjH1s8f0zNyJrxowHg/MUzEyePW7HqyZmzpuEZBg8d8MSyxf0G9O7Tr6cyfN+B3Z26PDxoSP/RY0csX7FUavbV5i8HDu73SKeHsOvi5Oljo8YM79Wn+yOdHkLV/ocfv/fr3/5i8tQJ/+v/9r9gojNn3qwevbpOmjL+j/feDWC3bt/Ut3+vEaOGjhw97MOP3wMwk6dO6Nm72+SpEzp27nDuwmkUxOOwXyy2piRkhqGpq+JJM9amNM5aH5ABwSlHKBhBnKFsM5M5ZeqmrGGCG1bFHIrGLJgwCZigCYkpJ1Hic0n8oMJlmpAwm2+KmnIElus5CFas2AJYc7uKIYjQs0Dmm9oXi1AWG4Ru24sWB0QAWFRlckmMlSgPllpywaw1QeRj1IiC3pSEKDSPEr+uodYPHVzB6BmV4TgyB1eOsTKInMy3tpE1WiqqLW+LXG9TeQhNkZ7MRFaU3yJrKm4REyx0x6jlpLezOUpxFJ8ip2NB4UjeTBuCIWZWTCM0xqojAOC3x0RKaIxlEowmExKmJAIwWLayoLDuQmgMYChLgtBF9Qp28IexR0WircCUC/WIKYvwg7D0wiWRimJDaxa0UUXQUaIgORuwktk51Gxyy0Rb80T17bZNady2g9YOhzrchQJxLhkTFEc9uL4jJAeADo881K1Hl7HjRnfs/DAA/Pm1Vzo88tDdf/j9UyuXb/sak7XlXbp17tu/z9ia0QCwb9+e3n16zp376IKF89//4F0AWLJ00ew5MxYtXjB0+KCKW6Q8mb9wzvyFc6bNmLx3/y4LatvXmz/46N2Vq5avefH5ilOkPNn+zZavNn/5/ofrjxw9hEnGhx+9t//Q3h27vs8Vmg3Iq9cvnTl36vTZk0ePH47TMIi8m/W1p8+evHz10qGfDmgrG5vrK07x+o0rdQ21VUbALbl+2Q8qURKGsZ/SJAj9UrngB67jV7zADSLfD90oDituyYCiLG1uaYyTKKURxuaodMKbrQxH/ZzjlTAwQrU6UndxGhAax2mAYifMP5C2QK0oDsLOcIbxq1A0ScN2fR4ax2ll2EXReZszSXCZybbRabiokLHDpYtNG0pzLEa3QfY26RR+KJMpToRhop0I1HLMQLMWm/ZYbHOaUmouNMPNWMkkkYZLzaWpav2F5jhQVVmZvXgXamKxhu14FYQd5RQAzp4/Uyjlr16/cqOuFgDKTmnfgb0tueYoCV3PAbCFYv7osSNHjx85dfI4ABSL+e+///bYsSO7du24du0KAOzZt3P3nh179u3cum1T2SkYkJ9u+OjHHd99+932Qz/tBzD7DuzesvWr3Xt3PPPsylIln5AQQ7Q33nrtvQ/eAYAjxw49/sRja196YdyEMc0tDQB22fIl02ZM/vPrL4+fOIawtLm1ac68Oevfe+eFNc+vXvsCAHz97faFi+Y9sWzx8JFDmnMN+WLLxEnj1r375pRpE8dNqAGAH3Z8P3vOrKdWLh8ybPCGLz4DgLffeatrty69+vQcP3EctDXlj6kZPX7iWCTx31r3l45dOoybOKZPv56XrpyP0+DBDveNqRk5dfokvM717709ZNjAfgN6DxzcDztwn3th1eChA1Y8/eTKVcsB9KUr5ydPndBvQO+a8aPRrU+dPmnxkoXzFjy69MnHtRVnzp0cO27U9FlTZsyauuHzTyyobds39xvQe/LUCcuWL8G5+jXjR4+pGTly9LDHn3gMAD7+9IMZs6b26dfz0bkz0dEvXDTv0bkzn1i2+Nnnn6Y8OXzkwNARg5avWDp/4Zz9B/YAwOo1zz06d+bkqRNmPTq9qaUeR8KjwWMiTdqU67f1cbUJjNFLosUSwAVUVXdSURwZqI2QigpJVdvoyKoQ2FS3qmZTGkFYimSEBYOz1tqrBVFVm60P3L/DjYI1jBFsRsSHMap9I1a1h0BXu1SyYZ/o+JDLwHbi7AyommzX0AVR6me8Pz6kFlgjzh74o9Rt8SVL2moGNjvgdv2j1OY2CTRm8W0/aUxsAXQWjyJthLwJAKAyGRUfOLwH80TC4zDycDY5el7GUz9wam9exUyzUGqNkyBXaG5srhOSckEwyWjJNaJ1zBWaMfO4eu0Szse8cOlsQ9PNppb6s+dPGZDFcq6h8SZWe5HsvVZ7+Wb99avXLlGeYIZx7sLpE6eOnjx9rLGpTija0HTzyrWLPx09uGffTrxsfEYVHWnrTcy6aDEzoO107Yi56qaqenoAvXvvjm+/3w6gjRXtxzv/7fzxqp1D9suAxmzgxx0/bN6y6cSp4zgAJldoPXXm5K49Oxua6itOWVvV0FR//MSxHbt+LJYLQnHGyPnzZ3O5lsbGesYIABCSXLlyKUp97MivzhZlSRh5lCdh5KELwHITUmvIseHtDCIXU3oUixMalyp5vMGIoSjx26pSbegwistbkEUio70roTyx7ZIhbRWOV2qPtvZwFIpj8gsAAEZqFkQuV7fYQc+vZBEeujkuCIID+7gsqCQN0fchg4PLAIsE+C4kdISk+EoYecrwKPGVxuH2HCk0dNnIp4Sxh5KcjCjBRDVKfAzj8sWWfLGl7BTKTgGdcsoiIav/qgEdLj5jYyK+F2dz45AAjNtwqzJzhmcJRJupE1nCi6F5kobYEZfxbtWWzTv6vrLRfFwyxJ8BPWnKxJrxY8dPHPfY4oUAsHnrpl59ej7w0P19+/fZsnUzAMyZ92jX7l0GDOo/cvQIAPjhh+8GDuz/0EMP3H//n7Zu3QwACxbMGz++5v4H7+k3oPfe/bsMyD/c8/v7HrynZ+9ur7/xKgAsW76ka/dO3Xp07tq9087dP9ysvz5oSP9+A3qPGjscZy9s2vLXfgN644vnzp8GgGkzJg8Y1Hfm7GljakY2tdY7XmnYiKHTZ0ybPnPa86ufA4Dde3e99fabffv1mTN3puOVpGbPPv/086ufmTNv1tInHweAH3Z8/9jihXj84SOHAOCd9esWLJz/zHOrPtvwKQDU3rz++huvPfnUssVLFu07uA8ATp05/vobr77/wfpXX3vpZv11ANi46Yut2zdt3b4pl2+Wmt2ou7bt6807d//w05GDiLyTp4+dOXfy+MkjTa31ACaI3V17fjx85MCZcycTEhojT54+du7C6Wu1l8+eO4X/5OTKtYuXr144cfIoMsaExRcunr1Zd71UySNY4yS4ev3S9dorLa2NALriFkuV/IWLZ4+d+AnVX00t9a35JjRjCLWb9deL5dz1G1dKlTyXJFdobsk1BpEbRp42Alc1IgaNXJz4aOQSHlNJsjbHW1Sw4crKrAdMgcx6wo2VSDS2zd/V/+YY+1v9ENn0U5yRS8Vt7c1tnc+3HsjKtv/R3O6elLplgaLEt6AIj5lIAQyhcRC6AObGzWvXa6/EaXCz/roXVJhIr1y7ePb8qVNnjtc33HC9csUpHj5y4MixQz8dOZikoTTszLmT333/9Vebvzx+8ghWEjd88dmxk0evXL28/ZttSsv9B/edOHV8/XvvfP3tliQNCYvXrX9zz76d277evGXbVxbkpSuXPv70o48//WjNi6sPHj4AAG+te/OZ51Y9+/wzm7du0kZdvHxh+YonN27668effvTp558CwOatG5986omlyx6fNmPyiVNHDchJU8bPmTdr9pwZn33+MQA898KqaTMmT5sxeWzNqPMXzxAWP9zxwfETxs6dP7tv/14A8PU3WydOHvf4E4/1H9gnV2gGgIcevn/g4H4jRg19bPF8LsnuPTu6du80dfqkTl0efmHNswDw0itr7n/w3s5dH5kybSKAvlF3rWv3To90eqj/wD4TJ48DgKefearDIw/0HdDr4Y4Pbv9mizJ81JjhAwf36z+wz4BBfZXhR48fvu+Be3r06vpgh/u+2vwlAMyZN6v/wD4DB/e7/6F7z104jZEMhnHYIywUzZrNMtYtmxyQzQ0mMkUgquq/U5JZozGGTBbk3/rTO3qqNQ7oyyYvVyeYKsEFi+IQmZEoCTOXJCRHdLbHmdayPdQQeW2xlAYMg25pQCxmWG2ZmnG8UrGcw0wKXQyhsZBUKoZZFS7NNg+lmUgdrxSnEYoSAIBxWnHL6EzxS0TyCbM5rHDIW1doszfig7d1vgEAHqat9oIy3PawbrtXcMR929ciAMCAREOVHcNEWu0LBgkAWCHAd2FXG+Np1gCA/0wMhxNCVevPM6eMk2+kYigNhKqKxHpBBTepGKq4W/NNOPuW0NgLKrlCcxhXBTKExbjCcRSukLcGAAhJMWLLOLasXxpJ3azFCzEnQSjNsrHo7ecWZIbt38YcgCU8zTqcUbypjPRDb9jIYTXjx44YNXzm7BkA8OXGLzo88tDQ4UN/9ZtfnrtwFgDGTxo/bcbUgUMGLFwwHwB27945derkyZMmjB9fs3fPLgBY//7bS5YtevyJx0aMGur6TUbKtAAAIABJREFUZQBY9uSSd99ft/7dt0+fPQEAR48f/vDj97D1Cys5KO44cuzQ+YtnAGxdY+3lqxdOnDra2FyHgoimlvqbddev37hSKLUgv0NY2ppvaWppjNMoJYkF67jFKPGR9Mc2Y8ZT1y+nJEUOMk6jKA5TkhBGcE5PQhIsHHPBkIPkgld79EVqQHJBkBDBShHc6vkwcRq0PQOuBz902qdQSINlQETvmf0WABy3SFncVteCbJFkK/p2JgUwfkIDg+BLSFjfeAPrthZUY3Od65dRXI0RIYD2o0wEaQAgIWFMgmwsoTK8/UBqYYUAkRFy2WTtrDIhLOci5ZKgtWs3Z5xmgPt3MecFrpBZIzGXWnBFAeyRo4f27t994NC+w0cOAsDV65e3fb3lhx3fffv99nyxVUi6a8+P73+4/tMNH52/cE4qfuToTx99/MFLL699862/nD5zSml57ORPe/bt/HTDR2+/80axkpOKLXhs7iuvrl22cum3O74F+P8Ye+9vq6p0bZA/onv07z1Gf19/446+9/tuqHC1DGVWJOcMIoqSRUTMWuZQwRzKUCYMGECiCEgUFEEkpxN2TivPPOd6+4dn7Xl2UVXdl7EH43DY+5y913rnG5/3efI/v/vGzbfd9Ngzj42fOu5s/xmw0WAzChOwV19/CUtiF/3mV/t/2EtEM2dPu/yKSy657KLLr7gkjMNytXTJZb8ZPXbUv/yvf37k0YeJ6PuDB/7jl/968SW/vuTyi4yTZ8+f+u2Vl14//JrbF946Z+4sInrjzVdXrFw+fuLYX1/0y9Uff0BEd99z1/iJY6+74eppM6YQ0Y+Hf1ix8o6777nr2uuv+u7AHiJ73wOrLv3txaPG3HjNdVeePnui0apOmTrx5lvmjBpz4+dffkpEr7z24sjRw0eOHv7Iow/u/34v48kddy7BXGHlqjuFTr87sOemeTOfePrRhYvnnzl/kohGjxuxZPniKTOmLFm+JKd83/f7pkyfPH/hrQuXLgTa5e2//HnRkttvmT/3vgdWEdGZcyeXLFuweNmCx5985KlnHiPKv9mxZer0ifNunbP8zqU7vv2GiF58+U/TZ065596Vz/7+qTBuHzx04Jb5cxctuf2Jpx7FBPK9D9556OH7X3jpjy+8/EciN5SBEXbUhXHKOCmxtJsrk0uTS2WVslJqoawc0r3IdXd3+h8oUOYXakYWNgeOcJAnpCwB2bTNZRdFUmxNgqGcutQy1qkkC/2iv+tuYqP47UbeXBnuMR3orA4FJsMHav05uZxyRTKRcSKL1WjUawAVekJaxCmA+hGjmUjiJIqSsH+wDxy/SRYPlgeiJMS5hwOA1wFKrBM2leYQuRos9505dxJVWxi3q7XBM2dPSs20EXESnDx97MfD3585e7JSGwzjdqU2ePTYT7v3fvvd/j2InidOHt2ydeOGjesGy31cpgcPHdj+7dbde77dtWdHvVnJeLxpy/ov1q459NMPPx76vlTtO33u+L4Du3bv27Hmi4+kzojMhk1fbv122zffbtu2a0em+anzp19967XN32zZuHXTnr07tRXf7tr24+Hv129cu2XrRiJ79vypNV989OHH777z3p/3frczzto7927bsHnt62++/N4H75w5d5LLdOfu7Z+sWb3m84/3frfr7PlTPx7+/pvtWz5Zs3r1x+9v3PwVEX362UevvfHy+x/+5elnn0A3yudhXTp95Rmlum4+7ZUo6lVuATVHVyrNi1oNyWOgJP37NodRRCZSzFsPHj7QaFUbzWq1XrJOIS04ffYE9oWU4Z2gGcbtWr2c8bjZriVZIhTvBO0g6mCXOMlibRTjicu1JQUkD3hGwrgNlKnPEoThpfqgIwdjAs+mp5nBLUdjHe1yohy0w1jIFZIT5QOl/jAObG6UUSkLW+26NgLnGJhhDCSApJKagbU4jNuMJzZX0LACiiROA8SjIB6S+UJNCt5xKMsgAY/TAMk4zhXQU81WDT02qVmzXR+snFeO5aSlzizJIG7GWQfbQI7yswPnYp4EaajJZIplmhfaSDIFuAa/t1IbDOIGEXGVMBmnLOxEjShp21y2OvVqvdQJm9YpYyW6LbhoRIR2jA/WfuyG2SCIf9HZQYrpFURRWEjNuGQoJYfENoZMzVwgz+c1NjzD1YU2V2tUAU8CQh0uasq0CYuW3L5i5R3odz//4h9uvf3mlavunDRl/IGD+4jo7ntXTJ0+acy4kWh8fLLm47nzbho5esSNI4d/9MlqIlqybPGSZYsnTh57082zOmGTiK674eqXXnl++swpf37rNUfm1TdemnXTjPsfunfcxDF9g+d+Onpo5ao777p7+YMP3wfK/U8/++juVSse/t0DDz1yfxi3HelHHn3w2d8/9dQzjz/3+6c7UbN/4Ny8W2++595VTz3z5Lqv1trc7Nz97Tvvvv2nF/74/od/QWfrrXfe2PPdzm3bv/7yq8+I8p+O/PiHPz377vtvr/7k/ZOnj6Gv8dWGL9et/+LsuVNxGpw7f3r9xrUbN331zrtvnjh1NGXRkaOHtmzd+M32Ldt2fA2XduTooe8Pfnfy9LFSpd/m6sSpoz8fO3z85M87vv0GOKWfjx0+euynI0cPHT3+k9Ss1igfPLz/zPkTZ/tOtsN6tTEYRq2+gTPlWl8nbnPNy41StVU9fuZYtVkdrA02o5ZHIDfaVaW41KxU7i9V+qOkXakPtIJaudafsrDRqlTqA0xEQdSq1cvNdi3j8UDpvLESKED07UAnX9CEsRjHCaUJ/BnOdq8w11DTnjR0hbzuhddg+f+wOW1Vl9j1r2T7CptrtOpREoI4g4ksSkIwEHb/5HES0F/9sRge+JQWs/+eBLmgxMc/tRGAUkrNpGLAbGH2Vyr3E7lzfacRSc+eP/Xz0cMnTh0dKJ0HpGz/93u/279n3/7drXbd5mr/93t/Pnp4154dB3880GzVgqi1bv3avd/t2b1n14Hv98dp9OOhg+vWr92xc/vHn36IFu6mLet37dnxyZrVAFBt/nrDX95968mnH/ty3WdHjh4iog9Wv/vk04+99c4b6zeuzcns/37v3fes+OiTD1auuvPrrZuI6IknH128dMGy5YuX3rHop59/NE4uWbbw3vvvXrHyjo2bviKiZ5578t7771605PZZc6aHcbvRqi5ZtnD5iqW3L7x1xqypjvT6jWtX3L30toXz7n1gZaU+EGed+QtuHjdx1J13LZk+ZxoRffz56muGXzXjpukXX37R6jUfcJN99vnHo8bceNuCWyZPnWBzdfDHAzNmTR0/cczlV1785DOPWpKPPPbA8JHXLlhy62+vvmTL1+st6aV3LJo0ZfzCxbdNnT6JiD7+9EOASoaPuG7LNxuJaP7t8yZNGT9txuRf/OrfcD2BK4G1IcL22h/AfFgABV2LF1rxukK9lnShVGlXVOjv+zkMW1OWAEgnFO9uslBBruEkTM1YiRpeW8FkQkTOecsbgpDk5KIkbAdD2RuwFdRVCiSijEVhXBR3QdBUhlsHgkFHlKPnjg0R9C2B9Pf8as1WLUraQRTAN/vZHZodkCv1MaUoHkVKZBEKicgHlGarhnfIZYphF3UHXAhG3YKUMA/wsw3MfDwC2ZFOswjwNZSfUdLBEJmIEhYQ5Vgpx0Vqh/XBWn8zqDc6NUvakCKiWrsSZh2lOZFD1RlGbQzfrFNELhNRqdpnc0nklGXacpvLZqtWtEI49rRjEAv5tw1AAOKpVMzksuCosxKwg8Lh5RoJCVbCwI7FRJKwJOMpkn5ALS8gXLL/WLP07+dzmP8DxZTxNMkSJuIgal16+cUrV925YNH8l199ISfz0ivPo405bcbkTVvWE9Hv//jMqnvvmj13xkOPPEhE27/d9sBD9y+9Y8mMWdPXrV9LRMtXLHnx5T899czjS5Yt7ATNlEWLlyx45bUX33r79d27d3CR7N2387333n7zrddWf/ReHHeSLPzs80927dmxfsParzZ8KVR29PhPBw8d2Lpt88/HDiOH+3LdZ9t2fP3dgT3HThypN2vlamnPvt0nT5/YtWfnmXOnheKNVv34yZ/BlwPFsIHS+ROnjvYPnmu2a0wkjVa13qicOHX07LlTjjT2kyu1wVqjXK4OAMk4WO6L4g4EUsKkzUVarZeqjZKxEuLP2EwDth5pHBcpmg7QEEeDpn/wHBGVan1cJnHWYTJOeZjJqB3UlWHtpMFUUmkN1jplYVNDgunYkVaal6sDCHZEDrDNIGpxlQidOlJCp1HaRmoYpW3jZKU+2GhWMQzAeegfPKcMz5j3BXkvtIyIMCCWmnGVei1hEOlhpgeDS1mYssTn/ZAEAuXU33LL/ZdsznWdJNygtiqMAy4TWDpKB20FdsFr9RLas0wkxsqfjhw813d6/YYvB0r9xulWp/nzsSNHj/28YdP6YyeOEtG3u7bt2btz154dn372EUarX677bN/+3R+ufvfA93uJ3KHD37/x55fXb/hy9er30jRsNKvvffAOIJMvvfK8I/3lus/uvf/uOXNnLl+xdN/+3crw3//xmTvvWrZ8xdKbbp7V7rTOnj9zy/x502ZMHTN29IcffSAU37h5w6233Txn7kxEmWqtNHL08Hm3zpk+c8qCRbcS0SuvvThj1pQ5c2eOmzAaMff+B1b90//zfy9cfNst8+cS0cFDByZNHnfJZReNHD0cT1h1712XXn7x8BHXXXzpr3/6+cdWpz58xHW//PW/zZk7c/VH7xHR8hVLr77uiquv/e3V115x6sxxIpo5exrIhG697Wbt+JdfrZk5Z+ryu5aMGju8v3Q2Jz1u4qgbRl+z9K4F46aMCpLGlh0bxk8bPXnm+DnzZzz73FNE+Qsv/XHm7KkjRw+fOXsaUf7trm0jx1x/58ql02dNXnbnIiK65/67Zt00ddTY4Q8+dN+uPTuiuLN02aJJU8Y/89yTV197hVDZ2q8+nzVn2l13L1+4eD76L8/94emVq+588OH7ps2YXK0Nog+QsihJA6kZqLRFdzhRQBgNE4oLWdAYYjQPSS2phdIF98N/0eAsmWE55S53Lnc55dbZPM+1UVjosjko+sk4VW9Wq/Uy4ykI0myu4zSyThO5lMWYVUDMlLrYE+M0kQtjlG/COdMdmuU5OaUFRvLSSICrMpEqJ0+ePZ7wSFqunDh68siZvlO2S1YSRK2Mx75rn/GYqUxZD350RHnEQuVkTtZYZckcPX5EKI4epM1NuTJ46swJxlO/yGOcjnoSVks2FYkwwnY3WIViSRb75zCR2mJc4eI0bLTqRLlQrG/gXMYSlxtlBBOpcSpKgiBsHz951DjFRBLE7fP9Z8/3nTnXdwbl5GC5v9IsDdb6zw+ec6S5yfpKZ388cvDgkR/K9VIn6Zw8e6Jv4PzJ0yePnTqmrExYvGP39u8O7Nu+e9vpc6ekkyfPHD945Ievt309UDp/9PhPRPT9we+27fj6h4P79+zbSWQHSv3HTx7bsnXTtu1bT505QURHjh4+8MP+aqO8Zesm5USUBZlMEh5DxVVarnOpcymtEFircVJarpwsGD+dVE5KK6QVxmlhuHIyETGe4Mf/PtrCkV0Qgv9Kpxok/KBkBcU1SCcRv5E2dcK2cdqRAzeb1yzs0Wk1PoXkkkVJmJMbLA9wyWxuO1HHkbWUg9NZk800TxVjRnAjTK6r7UonaZebpXKjdOLscVAWNNs1EAfhgd0WR7qvfD5khWoWLlDC407ahsSbdQUPS8qSUmUwSkKkI52w3Yk6zXaj1Wm2Os1mq94ImlALacedeqehc8M050ZIxW1uhOSlymA3gylgOGh4+oIO80PrDHQvjDPoUBLlqM8KwmTFHVmAxxjPEplkKnVkmS5kUoXlRHnEk0SkiUiZ5oYcGGHbcUc57SgHBXuYRalkqWSNoJVkgbYCkRHqGsbJTtj0mW6YhKCoR+4fiwibNeAH9osOXZQvSLRF75bD0FqDYcCmAwNcqH2SViTx0KQYz7xT9I0921Uf/fs25zvI0NyFL0W7BYAfbIuFcWCcFrLQk8RP9MaHBxNZrVFtthuD5YFWpwkVtiCLYp6AO1xYyY1oBM12HDTDxvnSOezuhlkwWBvghrXjVtgldPGi20Su3ii3kxYuVqVZbsctYXgi4mbU8J0kvH+0uzFowb1HwYH2EJesETRPnjs1UB1shq123GGKM81lro1VOKxeI69QSewKaeJT15u1KAlxxvyvME6bXOObvkqDBeDeG6ur7UqmU6/9AChHIqKYJzo3oINlmjPNhZHNsJWIlBuRyixicSJSaOvEPEWJAGhTsayqMiaSOI2h+qKNwq/G8VAkQXUDFhzeFWn1w9ZesnaM9j2r5hBauMuh6XlnPZwTxEKeB+cCWeULbc45RzlZZ4jy3nYxbhJeU8xkuxLQnbAN4sS/zSVh4PjMXDImspQlzXYjZHEi0nqnEaRhkIaJSM8Nni83Ks2w0V/pa0VN3ANI6zGd4QRjYQloxJRFleoAM0zaYssN7AQxjxpB3TnLRBbGAd5SksUolaQScRrZ3OCieMBmtVUDtXSmWKlerncaeJw9f0ZIXq1X+gf7wjjAjlySxSjiKrUy/hlEnXK11Gw3wjgI4yBlSeFB2w2/IolQ4O863hUWj+FywGUJT5MpppxmmuP6DNZK1Vbt+JkTx04frzSr7bhTblSOnPi53mm0onalWT195ni1XsKgJYzb5/vPlKsDyjD4NryBOI2g7ZlmhTgiJOqwTegXIDyrTS82s5ev3Ts/LODA1Ao6kq6rw7EshA96eOvhm/7K5qy1WmuWMSKnjarWK0BeaKu0UwUNr+a4fKDVIaIkizORwp1g0AaUisk1gi/+y7tZoXgqs5gnJ86erLXrMU8yxTpJIK3yvMxQOwWfnrA8SgqMJyp8NCC4TFMQgRsuTIHAASO9sbo40L2/PddEOeSEtSkcGLxdPWhKqxzlIYuY5paczk0nDVudptSi1Wme6ztbrVeYyCq18qGffmy06rVGtW/gfN/AeaF4GAX9g324r61Os1QZ7Bs4f/rsqXK1BPBB/2BfypJ22EqyGNeEiSxOo0ynkAqGKCBwuTGPOnEgrSrVy/2VgcFaqRE0Y56U6uVqq9YImmEWxTyBIeLcnj574uz5U6VKf61R7h88h6/Pnj/VDlqdsF1rVAfLA/VmrRO2oyQM4wCkcWCykVZ4bHCvHjD2HvAwecHhKgwXjiO383us/lXez/XmcBfWEH9rc845zjnuUztoAWEBP5GT44qlLIEzQ4RCFQ2VUk+Pj9OMLzyUCq8SimurmOYRjxORWiQrTiYi5VZCchk+33MU1IM6FrrAxAH+DsSOelDH0cTzlSvYzqANrIzkgnl3i7chFM94iuQB1RaX7HT/GUNWWhXzRFgpnTJkuRFpFuMUwd/DVQvJtVVMZK1Ok4gWL100cvSImbNnXHvDNegZJVnsyJarJSF5xtMg6mDYM1geKFdLtUa10aqXq6VSebCdtJpho1QfrLYqzbABvo9m2Cg3KjFPmmErYnEqM8zE8HUqs0wxSOqkMguzKNO8EzQ8eUAxXdRMagbaAzyQRCLuI7bCw/Gu1jnChRcnKQIrSXzfb+dLJ/BNZHVDfIbUrTNI9mLT/06v5MLASmSt9USI0HNWulsM5xa1BRLqnBx0mKUqkiTPDotb7iEGsDmiHD8zVazeaTjKldNQ6pBWSacylXgVM8irQX4KG/AAUmNoIzXjolCmh2/A5kg7bmU6dblFTMH2g88koCSLt4e9N5dbY1XMEyRPOjcyV3hLjaCJ3B/nBzbqRdKRqhLRv//i3yDUSUTXXHf16bOnpBIgvC44EiRzXSEiJrJitM3TMArASeNXDfwmqTASxP6FLFiuM8WkU+24k8oMBpcpxjSHaB2XSe/WPgQCMh7jrQIAgfOvreKSeY4IhFFvdheqLiGrQ1nQDUHe/yEjZDpDGYvcrrA59/+Dn/s7Nue62BAuWVGNkkFsRhOkiKTODM19IS8uGbB3yoDloKhkgUTwcAPlDNPcUS6dMrnlRqjcpIrFPML4n3fF3YO0005a6BgpzfCF60rY+NU3Swb1VztuMZPllEdJhIhmcgMtCpw8nHiAcPxFgbuVVilnZF4cg1q7HkSd7qs4Th2YIeHIrTNhHPziV//hr+H//n/8b4PlQSISkisjtVFCceessRpH14NhjdNcsIiF5UYJfh00vOCbyRQXVkYsZppnmgsrM8VUrpnmMEGcUp0bbgS3shCE4HEQtdBRYiJhPPaOwK9ZARWRqgTAOCyu4oTD56EsxS60sFzmQuUSCoi+wvC8JH5nAuBhb3MIdzChv9cTptxRnlOutC70SfIch7vAouQWFoO6IeMpUS6VgD69dcY5a3Jjyepc55RLp5RTwkhLrlj1dlLnSjkpDFdWGtKqwNprYYVyykDhxXJphf8kiJjtuMUNU9gBsVxa0Ylb2kmdS+VEIhJkckxnmU5xHA0Z67S2staoSM1trpXmQjFlOAwoSYuboYyEYo7Mpc61ypUuRGc0tzzMwjDuODJdth6WpCHjqTJCGaE0t7ne+93ucRPGvP7GK08+/fiSZQuXLV9CRFykwKKBikVqrpxMRaKstGTQ31JOaqcSEVea5TALsGeA8IrWibA85nGm0uLq5YobLqyIecw0Y5oJK7jhEYuE5dJw7SRTacxCYThTaSYTrjPlJPJF/FJhuCWTiRSXN5VJqhJctGJT2kk0PpDSeZ/XKwXRK3UHSk14RKYznSuT64LD1ep/aHOWHFSRtDVExJWMktg3mpHtZjxFDRunEZxfofqtBVwdN4Jpzq3UuUFEyBRLZcYNYybTpDKdwg+DyQfOzCdhqIAgfwu6bjwZfq5XpBYZD76PwOp1q4q0wzJHjsuUyySM2wAFEVFOBmyH2ihUnV6Cx+UWhRsOPahfhOWlxiBwsIX+mOaMxwA1wenmZNZ8/tFNN8/689uvPfv7p75Yu4aIQJ4KHB7EmaXODJlUJUxnzBSygni34LWERjwyOai1gvq+K5WeepVVfGo8Gf/VjlsxD7lh+C88DV/46AmPhfyY6Yxbprq6l/jU3ua4YQXtjeGg6McV9kG/uBcmwy3zOxN+9TpTaaZTdJf+Ia5kSIMrdxDVDKKQSwZhDcRKqUU7aDVadQxkAeb222LGKhQEmWKZYmEWQRY3YgmkbZnOqq0KriyE0nD5UKu34xa6RNDjht4KeGtBVIuUDmyP7bhVbpQgCwkRDGjDQyIIMrq1Tg0C67VGOU6DerNy7MSRPXt37ty9vW+gj4i6/BhRxlNgVIuusmHQylW5zGQasQLBlrKo3qyApQFNVwxYUxatXHXnN9u3+NgqNTt2/Mj5/jPYLcLMVKoMLLv4FL49gaPSDBs4V9KJdtxqBHWdKyz8eStEGwXEgyBbBW10O24N1gaqrUqm0lJ9EGyYvXLWiJsgmC7VByvNMtfMkPYChxELG0EdPxNeFuEFAg/o4HiSV2/QENXEzfLCr3hV4QsgaliAOv/G5ryfk1pBTjOM4ySLcnLGatwe5MsZT6URYRxESQhqxCDqRElIlDPNkdgmIo1YjHw8lVmmEnC2eyKCWrsKQlpk/fj8OHDQngeHHj4GqPYKS2pX650aMh64Q7wQzq8VNYXjwvBau5qImMhiv9WRPnXm+NTpk2bOmTZh0tjRY0e9/uZrRMREhgYeWJRjHjXDBpwBolvIgiDtwJkVvFpGCJWVKv1YJsLq63U3XL1n385ao5xkIbZWd+3eAeLEOXNnbv92q9BZkgZI1zBp4IZZMrj3zbBRbVXQs4DQDD5XJ2m34xa8Xb1TE5aD49efSZzYZtgYqPZ7vl+0PyBD49dUcTIhJFLv1BIZI2ODe/NEma2oOVgbAGM1WF0TEUMQIuYRCNFh+vgaakxgfsWvwC/F2UDl7sh6RDFgdhf6OSjN5URciownqPKSLMa4Bp13nxhilT9KQkRb9MdNbmOeJCJVubbkBmulSrMEMUadKyhUwD8V6neWm1zj6qhc4trhsgJFjEspuorbeBrTGVggcYKbYQNEkHhauVHKupqCoMD56JMPHnjoXvihn34+PGP2dAxnM57WGlXEWR+1EUfAu1ZrV+Okg2QOjNhbt22++ZY527/dSuTg8P6v//5/OtKeHhWGeO31VxHRf178SyJnnUqzsNwsQzgL+UDC42qrAkcF1yVt4eR8MQFPhqoIsuZQQkJkgOJMkHYaQd0LpoMnv9Isw8/BfXo/5zvAuBdI1/BMOLBKsww35g0XNoejgpfDL8BHgGHdjyjwBOQnsLkCyN7TLoHZDfOCvtoa+DkmOBMZHKPQ3NeeXh0RzSrs6sVpJBVPVRbzRJPhRoRZhJo0UyyViSOLUIJsFO9e5RLSn5lKwUZryeDyoW7ABAKRIkg7tXa11q5CQNLHKZyzaquCA40EpdIsxyKCeglG6Y8/+bt1678AWOGjT1bf/+B9RIR5VK1RRd8EApXg/E5lkVZXWhVtONDnTCREdv3GtfPm37R+w1oiAs3H+f4zNlcgg8YvzXi8+uP3H3zkvseeeAS4tCQLO2kHbhsRCmcJttUI6hEvOosD1X5kSIO1AUgfIWCBRdVrbcFv4TZXmuVW1ERwgInAR+KqwoCg+oAr6SWpkefgf2FVYG/Fj8UL8YuYLnIDBGiYOxIkH82RZOMW1Du1IOwgvCKlK/yc36mGeKbNXcaZdU4bk7IMkyLjNObi8HlIfdAORQUeRJ2UJTY3qcy4EUUfVWaQYuamGJIkIta58ukasmD87S0M4QOJHQQxYHMIwTjTnnAPKi0+ZCAw4ac1gjrTGeNJtV4C5vG1N16+74FVy1csXbTk9suvuJzxDPwYUgvMqbhkQx5IxIUKr86aURN4FmC6bK52fPvNhEljN3+9gYhcroOoJVRWrg5AlcYb+plzJ0eNuXHHzm8g8FpvViIWwo7xYf3gEqHKU1ueHTiDc4j0F6a+GJRgAAAgAElEQVQD64G5QJIGyS5yKcRZH457gy/iRiOo1zs1PAeM+r2Lq/CCYKCGnJfPZ2BnnaQNg661q+VGCZok/oQj8sLgfFEYsgCzPtuV08RotJevpIit2hr8re3Q84TmykjtFArYoVk+Gd+jysmGLOJG4BGkIXxekIbMZLiIcNrtpJWpVOZCOI4bUG1VcL/B8Y50DVcZLtCbGli6a+0qjj5Ola/jEAKQ+XXSNjZlAJS97Le/+fCj9348fGD9hi+DKIjicObsGWs+/5SIoiTEAxHfV3y4H42wjqZXq1NvtquNVnXHzm/GjBuJooGLBJz5jVa1f/AsFnOwDl1rlB946F4mknK1vxM2m61qVyAwQcqFBBdG0F/pQ3BEbEUkrbYqtXa10iw3gnq5UYLdoHKC1hvsCf8FP+cFaBB5kfvD/mCCyMPAeo6SM8yCcqMUZkEs4lQmtXYVNo0fiMTOa2nGSNp4lIgYikohC/0tQyXXTtpB2mEm45IPYSNyW6yEdWvYYUNS0nmeE7nc5Tl55LGnt8Y0KSfIT7t8SH86t846MtYZSKM6ssaqnKw2CruQ+E0m10Jz7ZTJNb6PZUn8ryUjFEe6BrJtZAasqx+P+T0+G0wEoQF/+3oQfpTxVBspFOMy+8Wv/p2IAHnHmH/x0kXTZ06DqwPqUGgujeCK4R1qp6QRmUi1lTmB1zuyuTnww3fjJ479eutmm+ski6IkaHUazXaj2a6Hcadb1Afwo8oI/JPLrJMEMY8jhoqeMc2CNAyzKBFF3YDohrwt4iE8FoIjjgHcG6QXIN4QZSECAkorGJZ3kKhLYHawJJi4MJx3eX3CpBPE7UzETKatoNEKmxEPM52FWZCoJGRBLOOQh0yzhEdCszgLtROZiKVm0rBas9wOm3EWNNrVTtQM4nYrqEdpEKVBq9MgIqk5+pQuN8bKnKwla5z+q3mr/4MJPcYGHpXk/qEYKOXQT3c2dyZ3tvg6v7AZ2DvoHXo4Y7pS6Rjt49yLrsq7V12RXeVkxNNCnjHXwvHe1Fjl0pOB7tm3e8y40YApQAODiFZ/9OHCxQtAOZVmSTGjc2bob4wLbYE3RC5MRLv27Bw7fswPP35vnE5ZKhR3udVOJ1lcrpZQWuHlXeBaEV/QrQyzKFOcG5GIVJPhRnaSFsqCVCZFV7yLC/KNWZw6xGLYpW9YoKtCRCELfO4Lz+SbmrhKKDKCtOPIJjIhyt99/+2p0ydNnjph/ca1UEXLsjhMg+77ScMsFE604pZySsg0YzF2PTHYjZMAnchO2Kw3K0HUKug7edwJm0HUeuqZx4kIi4+OtLLc5gq4w39gc2Qyniot/4s252Bzf/NQ/wAv38vY459gXIEhQ3rh7czzPPoCFnHEM496FtJExqCs4oJhSPrJmo+ff/FPRKSMNEYDtRZGwZhxo1esvBPfB4fBBfirXkyELchr6etvtgwfccP2Hdsc2TiN0DbCLne1XkGmS5Tjs+BHcckyliQyA5RGWBmkYScJ6p0G0xxlab1Ts2R8TxVN417IGi4C7AzOD/a0Zfvm60Zce/DID+hieH3VMAtgoLBOjLYQPWIeEdF7778zcvTwPz7/3NdbN113w9Uvv/qCsTJOA0MGV5iIcBJ6W49EBNJfIjJOxhmmzM46BXJZtEXhhf79F/+LiLDsiB2LOA1wev++zRHlrU6zXC0htv4Xbc45c4HxXcA95js0vXwWvT6P2wKDillWQf9uuXd1/utUJjIXgA32DIikMNyQtrkJ4wCFNpxcTg7UPgDEP/n0E7NvmvXz8SPYUO99D73Jb+8bJqItWzfPnD1j67av0TBCmgtQGmbNQ1jXnp+Zk00VS0TaSYKIxTFPuBHVVq3SrPm+K06Xnweg4Ci6GCLxXX4UsMgoiGjc5LHDR99w6vxJVFSNoA5tON/yRSbtUWHIW4Tll1z6n+vWf0GUays2bFo3fuIYrMA9+Mj9tUY5SoMFi+efHzibk9m4Zf0TTz1296o7D/yw793338ba6Kp77wKjyh/+9Oz9D96DAUyzXSNy69Z/cfvCW9985/VLLruIiLBOG6cBMmMIgw8zpiv62/PH5gZEEJia4QZ4m8vz/G9sTns7GzI7N7SRNoQS6EGNeheCmYfLrcolEPfaqWJW2L0ZQ6yiuWQq62UK8vgInSumMpVLTFBgc9KIYgiTG6kEwuuGTevnzJ399l/eIiIParK5MblGbQ/gCTApMDsi+vjTjxYuXrBx0wYiwqwZv8KR1ab4RMbqIeS6URgVSquY5qV6uVQvo3nZSYJ23Il5mIiYa+YnmMJyOKReEi4Uicg6kKsR0Z9e/uOsm2c++fsniChIO1D5Rf8Mia8fEvjojF+0e/+uEaNukIoNlM5zmWJDDBqH//w//+lc32ki+h//9N9A8Q4Ks+df/MO6DV9AjmfTlvWwp8/Xfvrri37x3B+evvb6q/bs21kq9+/bv/vXF/3ilddevOHGaxcvXUBEgGKAAdJYqa0aKPUPU0oZYwAqwZ/c5TbXNjdJFnfCtkdrmlw752CUvZaX57m1Os8t5Gx6XR0APLjlHlqnrRKSe/8Hu/Sx1ZEFlsuRRXLDukIFBVF3roANHgpAlvklkZhHsDlT6KvkaEsWux35UKPyxpHDl96xhIgYz4qj5azHXDGRdcsmhxcS0RdrP1+2fOmWrZuJyD/5r2aL3QEuThcQo8ZppnknCfrK/anMgAphmg/WShELpRVcM0RA+Hi4PVCS4/tIZMMsqHdq5XqpFTcd2Suvu2LanKmVRhmdOehL+5EPqgpPAuwH0zm5Tds2jhw9nIiSNKzVy2BEHCz3OdL/8ct/bTQrQdi86OJfDgyeI8qfePJ3i5fcTkSnz5745//5T0T0/It/WLTkdiIaPXbEJ2tWE9Fb77xx/4P3BFHrg9Xvzpg1FbF7wqSxRMRlCmAVqDbiNGq06sOMMZxzrEEUf1yOq9k7Cy/Ck1Jaa+oBPhHhXv09m3Mm79LnYB3XL/UkLEaug7weIDNtFdNZKhJMvjtpG5gIZjK0JTETG6wNQCQZqRvKWMwHU5U0w4YhjXHqBctBWI+AeRHRI48+PGXa5M1bNyGrg0Oq1ivGaaRogJfmheieIKLt326bNGXi1m++JiJjNdY8gSCEa/SLEQAOAfg0WB7orw6EWVTvNJDSAQ9XblTRU4W2PR7oTqPv460Nfa9MpfVOLWQBEd11z4obxwz/y4fvSCvQ0cA4Gx7O4159PodmZ6oSovzo6Z9Hjh4Oqjzofj/8uwegU/Bv//4vtVrJ5eo3l/z67LmTRPmqe1Zs2vwV+PDGTRi9/dutM2ZNPdd3Oozb//HLf4W82IhRN0AJ49HHH/79H58hcqVKPxY9QR+IbW2bqyDqCMWHwV1Za4kw/8rzPDe5RsTxwTHjqcm11lopRURCCFhnnufWOneBzeGR215EsQfcooREAALqDpanjKy0ykU4UFkjqGtSOLVI7HBSPRQFLnCo1nOSqYypTJGUSoRx4JGkRaJmNfh74AL7B/tnzJoxa85MGBA+b7Ve8Thnvyenu6Te6zd+NXHyhG92bIV/xzwmyeJGq05EgD74zwJ8obaqHbRqnbrOTZhF2G/AikOtXUfHFRtrvdsG+JjoTqOqQH//zMAZZti3e3ZMnDZh1s0ziagY/bEglUksYkzMMHSGQReKgz3zFSIaN2H0p2s+gst49vdPTZ85BTQGs2ZNPXX6WL1WnjJ1QrnST5Qvu2PRX959MyejDP/w4/fGTxxz/fBrwFd55dWXb9z0FZfpl2s/AyHay6++gDHjsRNHfnPpfyK24rVCZymLgrBjrB7mnCXKU5aALdDlDv2CIjzl2FIpHJWx2jhDlFtn2p2WT2usM0IyotzlxuU+tjrjlMtNmHSgu2Cd1lYoI6QVIK1lKuO6EDTOZIqCK5VJJlMAZtABgWNLZVJtVXycRdQI0o7nhay1q524XcCpDcffmUwdWZ0rS4bLzJHhMsPW7ap777rhxmsP/3QQWZ1xGmuwvY4KQxfkc2s+/3TSlIm79+zKyWGryAuRgS6jGTYymUojcCq4ZqlIgqTDjWCKxzwBshfJXMTidtxChuoX/pDCYnbpUzquGdrFZ8+fIqLldy2dOmPS1u2biUhZceDgd7fePm/v/t1MpnEWtjr1IG51oiZXaSYSqRnXmXEqTDpcgXoxX/P5x1deffnjT/7unvtWXnLZRZu/3gCJmEsuu+h3jz60ZNnC/7zoF/0D54jo9oW3PvXM4xDN+eHg/uuHX3P3PStQfEyaMn7JsoXaipmzpyF72/z1hv/xT/8tSjo33zJn5uxpROQFT4TKtOVRHBqnh2mrsFZzrv8s1lp9Zw6ZXOGQunh0bSVSHOxBFVhnnhZJdzcBLwZtufZc7oVERq5drrjlhjQmQqlMUKiiXyC6LPEAesiuRAGMz49uUGoY0mEWYLNX5RLNeiTdEQsBXvUCe4oU2K+0FSBe2fvdrhtHXg81I5ubcrWUsQIpWK1X4KhcboFjIKLPvlgzY/Z0EBGDrxMLNR49IZ2QuUAgQ+If86gVNeqdZiozbLghn0tl1o6DcqPAQAAL2V36Sr0eDYoq4L/rQS3j8Rdffjp95pQ/Pv9cmkVPPfP4xMnjrh9+zYJF861TkJDTRnTCplQsBvKAxeiogbAszSJsv956281PPv3Yk08/tmvPDgIHvGI/HNx/9z0rHnz4vieffqzZruVk3nz79fUb12KmHKfBkmULd+7ajhFfnARL7lh40W9+dduCWwZK57F6/ODD940ac+MdK5ZAgxRbt2CcZSLRVjORDUOtgPVjtDRRohbYuFwj7jiy0DHBWjxXzLdRTK7Rl1JGRmmIl2Oma6yUhoHex/cGmUhiHgVZp+i6GQ4nhPmdX9NFJx0G58MrSjB/PzD+AiAAPg+DGuUk5mOGNMBUmHD4pQGuUugRLlu++D8v/mW70+pEbSYyxou9AbRacnKtTrMdtOD433n37ZmzZ3y9dQvWpIOogwIfLRihOOCQftzXxXe0W1E7J0pVJowMspBpHrF4oFrqJG1/3ry3Q9pagG9NppxMZaKsVLk8+OOBmbOnLVu+eMasqaC0njVn+s23zLnp5lm/verSiy/59W0Lbxk3YfTFl/x69k0zbr3t5omTxy1cfNuoMTc+8NC9r7z24py5M9//8C+gKfE6WBmLleGdsOmFT/EHvGbI2KOkAzVKIkqzKIzbJpe9hF3QHr5Ad6pgwzUcLbqUhVg0HpZ3N/KHGqG5HYqtTrc6TaRf2Psq+ia59ZspRe/DKVibBxTk5ApIreHYDgTPVJwG3rzQaWM6A2awFTXRT0JC40cRQC5hyFjg9K2ARwSkEebokREwU2G5IomeiyYlcylkBvY1rCpKxb5c99mMWVNeePkFIkKnzX+EjKdxGoH3CR2WLd9snjFrOkj+Hdkg6mQ85YpB4VMblcjYYyE9tpHprBm2sMdgyGoyWFwtN6qpLAYGqUr88QAiDecKL8dkj4imz5wyZ+5MyOjs/37v40/+btSYGydMGjt56gQhM6GyE6eOHj/587ETR+IkOHPu5MnTx8rVgZOnj50+e+KHH/dv37EV+ohYZQJdGoYH+I5QWZwEIMICsTqWO5Xm7aBRvCRqK81THknFwKaAgUSaRWkWQWZdyIzxRCoGHk8w7qQswh7aMJdbL8QEnGZPM9MZp4Gn9e0G67ocdxcMr3KDOKuMRHLtyILGDCBHsCQXO6rdrrrKJddMdNXNMD3s7WHif9GE8x7O73oAKNALwfC3HLmRJZPIGAaqcum6FGuFzimLiWjk6OFjx48hIi4Y2iJ+Po2FN2M1BNC+Wr9u8tRJqFutM3Ea4fMWW/tOC8NhbTB64A80SeWMIaucVrkGdj+VWSKK96lJ+a0OwEwwZUGvjmuGFtLGrRvHjR8NbmEsX8Ibff3NpqV3LPr0s49QhwZRS1vRDhvYO4SGSVehhTAtQJMWzFEQXsJcC3QwXKReexKk2GHcxn4nvlOA9bvKsNCZ8BzWnuIjJ6M0Rl7COGmpqMyGeXicd2BFcOzaXMZTEC9g6cv3h3vHpr4jhY3Xol/V1aPuZayFkgvgOijN/OK4hzhrUh5Ch2zMbxw1w4aPO7ivaERhViYs9wKPCKYeq5epNMgC0W0XKcNxBInosScevvb6a/bt3yu1kEogu+0xtdw4fez40cM/Hfr0808mTp5w4If969avRRnhGf5xARHWMTUGNEYUTB+FwSmnAaIGiJ+brNiwcsWWfC94vZj+WZGp1OR6wrQJ11x7Rbky0O40YAoAiiJvOd9/ptYoN1pVkLzi6yjpgD09TgNYBpiXvJ9TmsOSYHZcpH6TAzGRyxSqlu2gAWk8ZbiQmVSsuxfCgREEdbqn7jdWZiLGfR9qCzttnB42xIWTD3Hh+B4BunRDDB2ao1Pqh0JY1vdWizsEm8vJ4VcGUQsIR/AjayOYKfbqepcl0fZEGge4PesuXcILAvDj+yMewgUAY9El7t5F//CzsmbYwLkHgy4kE5Thg+W+u+5eASynsRpbbcbq3pYHE9mkKRPHjh8zd95Nk6ZMhHhByhNsxw3Njkmha+MBgtIJplMsRVtyJrfAGnaBhtorOaPyAACEd4W2EhGjabz87jumzZ76xdo16FNgfIkkAcQGtUYZqtqez7VcHYCQJnI1EJqAVU5qFsQtMH1LxUQXWQ0TBGsbXCCR3bNv5+VXXLJv/25kI4wn1imYF8wxSjrgSYG1wRdap1yu8QTkVDl1uSPAXJTxlMks4ymOODJirAskWYx+FYKxUNxPJrwj7G2DMZ6hmefI5qS5TKCYgYI5TjvYSfEG5LMxICNQbyKT871QZHge44ppWMTCRMaxiNBhwc+JRYSfGYsIWOKsuzeVqdTrgCvDQTSLCLVi5Z2/ufTijKff7tpx6KdD2iqpRJREWEoFNunLdV/cMn/eLfPnjRh147m+s0jyPKC1aG5b5ocHcNJMZ82wkcoMG6lMcbAtCSu5kf6T6rywOXzHL4sIJ4jolT+/PH7KuFsX3UJErXaNiQTiXcjNcaRhdqAUhkVW6yV4NdioJ25ShoO5EX4LXM3wbS7Xp8+eICIIaANc/fqfX3ny6ceIiAmviuE8HbHXvQWEpFei15uyNztgPoaB+QHrgwAwgiwCD78Z5XKLp/nZji9vwfwTRJ1MpGCcAL+Etso4JTVPWdxsN4RiQrFmu1FvVOtB3debHpuJB9BgsDAPTkQBCNRrL6q73qo1O40g7rTDlrISfteSYTJLWMwVS3kC68fqZZQFXGcxi8I0iLIg4XHEQiL6Yu1nY8aNvPueu66+9oqt27YoI6BhF8ZtLrOMx8qIgVLfVddcsfSORSNGDSciYXi9XYuyMJNpJlOdq1QkOEV4zzCaYq+Cx0yzMAtjHiciCbMwYlGmMj9EwUcGKrMZNpqdeibiTCSOzN7vdt26YN7Nt95Ub1abYSPK8M4jrlk7arbCRrVVaTSrrU4dzTDv0kCghggIE4GfI3L3P3jPlGkTL7/ikh8Pf09kv9rw5YMP30dEO/dsW7jktgcfuXfEqOtXrLzjqmsvP37yyMgxN0ycPmHjNxsyld6+9PbxU8ffsXJZM2xmMiXKX3rl+fGTxiy7czGXCZENouaipbfPmDX15Vde6J23Gie15eg9DQOhAVa94cm0VfVmDaWA67JfObKwzl7YD0Iqqto4jTBWuiBAe1/YDlpC8SgJq7VKvVOrd2oeWe43RzKVYsUBeNf+Sh9WkqqtCtaT2nGrVB9EudCOW612s9lu1BpVjKc8HAGOB1Gey0IGXqgiRuOH95X7uGadpP3JFx/PvmnG1OmTFiyaP3P2tG+2bwYUot6sRElHqJTLFNTvf377tekzp2zc9JUjO1gbiHiIVTHkoDg8wNljGC8MR4M3lbGHKqGHgvZNImKgc7FwVaoPBmmnHtQHBs+hhDROLlw0f9yE0aBsxyKIBwbXg3qYBcxk9Ua51ij7NhgTSTtoNFpVn/iDsZrLlMmkUh28cdT1RLR777cPPnwfkd2wcd1ddy8nor37d15/49Ur7l723odvT542fu93O4nomd8/sWzlUiJ67a1Xb1k4j4geeuKhR59+VDn51cbPr7r28mpjcOyEkfc+sJKIps+efN9Ddw+Uzo8YdcP6jWs9CzseuEHD/MQwjAP0nLRVnbANJDqTGbZUcnKtoNkOWgXjX3eNB/cVc628q5zu2drQXi56KLpIGaMkbMVNlBGYzHDDap2qh+Gj8YvFCIwrkNLBVvzyZphBPsXAN3u+gvyveRfx6WxuhOSdpI1ky5DmijXDhsolET39zBNTpk2cO2/2jFlTfzz8PZqojVY1iFpIvZFiv//hX6bPnLL9261EOZo43DIEehhTgeoj5Rco8b/Yc8Hk1M9A0RWqtaseEVhrV1G6+gWipXcsmn3TjFdff4nIBmGz3CgBJwyAPuIAtxwWhrcK3xanQatTB1MOONSGCgWZXnn15bPmTN+waR0RxWmwYdM6NMY/+vT9FXcvI6KNm9fdumAuEWnH3/3grVdef9E6yURy4tTRL9aumTx1PKSUH33ioTf/8hoRnT57/OCh/UR07Q1X7t63I4zbUJSkrmp8V23HWjLD4OFgc+VqCSPqWqPaDlquy84ktcD4K0pClGl+au43/v1umR+ND+38dN1MAS0xipkMG1wYNiD2+UU3tLWQ4hSTfifQIkGERXreSdpRHPrsU2gO0L3r4UZG1pVkMb5TaZbRhtWkmMqE4c2oIQwnck889ejM2dMmT51w8NABZEjGSTABQKvOkf5i7ZrpM6ccPfZTplJsi3kGgkTE2H0H0BxTFj/u9DYH0/T7lD6LxQuRY4QsaHXqxslFS26/7oarn/vD00QURm0uCgIh7IWgr9SOW0EWQJMEXg0NC2j9CJWhXVX0hngMaugwbn/0yQcTJ4/DzGrDpnVz580mol17tz/86P1E9PmXnyy9cyFyuI/XfPD8n54joq/WfX7FFZe88vLzzz7zxPPPP0dES5YveOOtV4hyZRgTcSdsjBo7fNZNU6fNmLxs+eJPP/sIurf47VIzmxtLZpjLLcIogIcYXaMs8AIA2ioQtqFM6w2sugcJ7IE9xhU7EHnu4PxQqaBvFyVhO2mBeg1DbmB4/PabT+Bw9FOR+JCE4IUqoZ20kiz2BPJo56Jxg9GwT/C9zWUqTWQMuJRv+gvDUUn87rGHZt8048t1n0E0Edl3lHS8JM2GzevGjBu5Z++3oCqCv/TbYphiFWP7Lr7Xwy0xvstUijoUGzewOb9EiJzBkG4HjceeeOSW+XNX3XsXEaUsancaYdTGLyrVB9FLwhZWqlII6oGlD3e3XB3A4iMyKgDHQT5+8NCBOXNnnj13auPmryCVu//7vddcd+W586fn3jLrjhWLiWj3vh2Ll91ORAkL1nzx8VNP/I6IfvfIAy++8AciunP5kscefYiI3v/wrfGTRhPlq+5bser+FUR0w4hrTp45SkTvvv/2E089SkS+h6KtsDn2+HMD51SQzZLFLcQSYRGVeuhLem2ut6Wi/5q/03VZmHJyeV6kdHh5ypJUJnASKEhRb+KK4+yis4XtS7gE+APgJjxUM04juE+huG/QDEXzLtOvJ5lvJ0VoRpdV5yrMAmYYxkH9g+dGjblx/u3z0HSVitlchXEbPo+I3v7Ln6+46rJaveT3feCqYb6WTMgCYM1BeYGP5mkcEFvRvvZgBZRNiYhTkTSDRjtuEdEdyxffdPMsSLXCmMK4XW9WBqr9ZwfOIMFoBPVSfbDeqYUsLKQBVIZWBRYcO2GzHTQglYGuJATTiOiTNasnTRl/8SW/7hs4C0KMm26edcllFz3y+AO/e/xBIvr+0L6V9ywnIuXYF2s//eTTD60RP/986KqrLrvuuisffvj+Sy75NREpw+bNn3P9jVdffd1vo6RtSOzcve3yq35zzXVXXnr5xZXaIOMJ0APGSUdFSjastxXs8eJA7fYWBD5P6v2nN7sLHq5nq7H3a8+I7UlrYXZYC0Al6yGHfgRUzOlJeVYR/3LgoGD3/rcPZZNdjml/Ejze3ZJRJIFXM6Rz0lhMfOChey+/4pJmu6aNAFwbPVIMIl98+U9jxo1UmilSYHBGj1DlUrsCUg/35tvCwGAO0QOSRiVRbpSw84fRFtNZwmOmMkf29bdfn3/7vDlzZ0J3EP0OLlPGk5CF2LBPRFxtVsI0aAT1mEVh3O6ETS/tAD16NI3RjUO0FSqTqlj6gsCccZJJ6M84KOcSkVBps10lokxECQuIrCWtrYReaKU6SOSSLMp4zGSMykM7bnMJuZWDh/d/s30LCn+ow/XqumqrhuW56x1/+UzIdRkO/Spsl/XE5kVBOuTtLngMGVxebBV4YDq+j9kiullItP0qL/xZvVNDow79YZVL1aWaw50zYBLt4fG0uZGmoIjrVabCOYEX5JYJx3t+iEa9qQ13uSIye7/bNWvO9D/+6TmMlXxjiauUiF59/aXRY0cQkcwlDFfmwlMUeE5n/NPjWQDGBN0TUgicn7Q7UCnWuqwkoo8+W71s5dJp0ydhYRb5GSYH2oqYR6zLp1S0wS3PdFHl+GGUy7UfT+FhnDRWZjwWMgW1CpAmYdxWuhhOcJEmPLC5TLLAkdKOcxkT6TjrCCs6aUdayQzLdAYmspCH2nKhU6KciTgTkcsVl4klCbBTMbRQhXSicRJ5zjCA5HrXYXJyYRIUw/6/JtUp9lsph57E330UUhPWYCbhsSd5l/AwJ1fcqlwBUSKt8Kvq2PtFOz7r8uwJK5liTHOda0UalHXCdfXOcttbrORdtW3T5YqH85NaCM3RYuSapTxRVrrc6lwpPSRSPXb86KIDp1hO1jrtcqOtJKLX//zqVddcgQG/JQPcl3ISH9DkWhqBBqHNjXYKeDDtFARShWaOtDQgwxMmVymPucrCpKOdJKJvtm9ZsHj+zbfepDTjMgUiAedaUkYAACAASURBVLESFYAlrZ2UhmciUVakPBY6i9KO1yRWhn/x5ZrzfWeKeYDOIPxgSDGVcs2iLNC5SkXsyKQysaQTHjGVZjJVVnCdgdjPkALJn86lI8M0s2S44zIXwopUpZp0KtNUJo5MkLZNLoVlwjLlhHTcOK2NhBqstsrm2uXG5hptjWFDyVluPTxkaHhFpvcxtElN1LNV3QtgoWKpIs+dLfZuip/Ts7oHpmMcVu8b4HL8To3HzaYykU6BP0pYackppxVp2+Ur9p7YR1KPi4G3I8pBxg21dyKK4tB/Rr+pBZDcu+//ZfiIG77dtcOTA8GmieiFl54fPuIGIkLTx2Nwehs0RfJghvTBbW4chn7dENMNNAoD0zgNiPL93+8dPXbEnLkzT505DmIeBCa0OQoxQkzTDcccBQkA9DCb7dq+/btnzp42fuIYJIL1RiWRScTDRMRMZb4swxX20NdiZZ2UH2Sjv+Pn4CqXSCTgvFE2IUnA7dO5ikU0NMbMhXXGFA/djZ8F2tyRHZrxw+w87td314b27cgUkjkXPhz99R+Pd3d/ra/oOyye4F12aeGR2fjZKOCWBUrWZCDXBbs0N8KSY4ZLp3vp2H1AH4q2zmAHImUJEf308+E5c2e/8NLzt8yfR0Sg9r3AVnJy9WZtxqzpkLzGaVQWhkuvvPbyiFE3EpHpyl75HUpcJa+Q4S7cJ9fdIbfEQopxErkaQC4nTh2dO2/2+Eljzpw9CZcmNUObBoEJ2ZhvsKHxC4W4c+dPr/74/dk3zViwaP7cebMXLr7txMmjqLiRbnoiuqKn092X85W1fyD4ePSo6PLziy6NMKbD6HPBWLHMIRzvtTl/Xy5I9HHBh+EmMZGVqyXAfYGocz2kJv7hLfKCR055t6rIjTPWmSSNsXkgzVBqpV2XS7oLyPbwaz949SzdWZfYUViuc6NyDemcroCOkbnWPTZXIOm7YRR/c8m0KcRr/+e//ku5MkhEL778/DvvvgXSJEfG5dp298Hg6sZPHDdh0ngcSnSVsYPz2huvXn7FZURk86ET3Dtx8TW7z1i6fk4nLISJwPLQRct4TOROnTk+//Z5Y8eP2rHzG6IccDToyiGnRBGApA1QHSIyTp4+e+K3V146dvyoBYvmz5oz/dnfPwVoHRxkxmOZS7T0/NJh79VOVeI3MLx5+TTXrzx6AmG/0AkKWPyo3u63tznsdJquPDqug3Ea25nDiPIg6qDfi61jmCD2svwLXJfmRBoBLWsfktDV81EG46Zmu6GNQrxGFwYzKOO0Ngr1AevStfrGm4+taHp5bkcI5YC7Ho9MsYgnYH7AW8WOoOnZ4lZWFhTmWnz62Sc3jrwRbnjLNxuuveFKbbkj6IALJgppeFChr9/41fXDr3vqmSfx/DiLEhYj7E6ZNhkfGTJATGR57gBe9zU7GjcekKKtSlnUaFVhahh7Q9aHiA58v2/s+FGTpoyHuSjD20ED9WbGY7QGw6gdRC2oZRK5I0cPPfrYwxMmjV22fPH0mVMef/J3EJ8lIqBCuEzxt592eIgNxm6A3mhSHlloyQDDh/CK//JerbcwQuQt4DOGA2lmcq3zQpNE52qojdDdrcGGA5K3Yfhunjvg3pCBQT0jTiPXXXsGTgnFvCPbX+4DQ7sjm8kUPf1CeizXykqMGk2XTSzjabVeQavZOoNd80ylh47+OFDtx8wert5TOqJfzw1LRFSqlw8dPVxt1TpJ0F8ZyBTLibgR7aAFkY3+wb5e9SO/twaBsiSN33jz9clTJ65d//lTzzy25I4Fi5beVm0MMhkzEYdpK2UpQjAUlInotgXzf33Rr7xiE6Alb7z5+pRpk5HncckwtslY2mjVuWBEOcSovKtLWKyN0lYzEUvNHGkQfADBQUTvvPvm6LEjdu7efvjIQSLqQm+CVqeuLFead8JmtVYiok7YPN9/5tnnnho/cQwUwh946N7NWzZAHBaZIqgb0FhxpBkvmE2YyXSuEF6x/4vLq0mhdEPHAOIk3rdxw5gq0KOyR/vLP8FbIdMZGJhlLmQuuGUe+esnBb1ZxzAMtbhgTGaIGvB5uque5nrg5l7WSTqBJjgSr1QmmGN2krYm5ciCkDsnJxQHCyzG8LBgQC/bcevswJlGUM/JVVsVsGKB+RCtOJSxYdYJs7jWrrfjDqCOpXq5FbcjHkNJDOuoni4EiCwUEELxSq2cZPHLr7606t6V8FsHD3939XWXxVm7FVQb7VInqkdxoLuSw7C5z7/8bNacmW+8+ToyP8iUbdm6ecq0yRjVAGgDC8t4Wm/W8DbQpkZtdebc6ZQl2moYUxi3jZNcpEQujNorV905Y9bUsRNGDZb7iHJwFEMmOYhbvk0Txu1333t76vRJw0dcN3fe7Okzp7zx51exAEaUA+7rIZytTr0YcGnGZbEFknW1vPyKNao0BBN0CVQ+JHxQjFhyjUVjrNmiyaB6xHHgLHu6NgUwm1vW218roiqqydxhDmEhVQiIL9p1GEvIri4slupsboo1PscznXLHUMJkJk1Uwh0TlkciTFXCTJbpNBYRsCtJFtvcutwiJCktK60yhqfAiUgn2nELw1DPkQv8Jr4ZZnG906i164lIhVWQw2qGrVJl8My500kW5+QgcYSZBDAmUgtIXTGRbd+x7dLLf0NEyqbfbN947fDfElEnqpZr54iMIyOUKFVK69avffLpJ2bNmfnUM09OmTb55lvmwuYwRHnuD89eevklMG6pBBYTbW7gI2G1ABw4csoqpJUpS7lMc7KoAIjyLVs3Llg0f8TIG1auujMIW0Q55PNQJYBfMSfz87HDjz7+8KgxN44eO+Lqa6947IlHvjuwB8cm4zHjcZpFrU69HTQwX8LIIU4D1YXWparI5BBYfRfaNz4BKShGQTyCeaFoAIS20iyDXhctVU/fIbs0Wfg5vpiFXfaWULClom+Va5ubYVIJ6KN5bXRtVBB1gGvC+B82l+dOOp7wKBWJIR3zgKlUaJbJpNGpRLxTD8oJD2IR1NqlmHVqrVKXoa0ep2GzXW+0qhlPwrhzZuD00VM/w7AGqv0RCwdrA/t+2FttVZjOPFqpFTX7yufDLIhYdOTEkVPnTzaCRiKS86VzTLOBav/p86f6Sufr7ZpyMpNpKpKEx9hpNbmOsvD84LkwDUBZsmzF0k8/Xy1UOnbCyC/XfZqTPnH6ZyL6+eihCZPGjp845vobr73zrjvuf/DejZvXP/3sk8uWL75++LXbd2yVmrWDRhi3P1j93vXDr02zqNaqCsOjLIzSMOVJJtNKo5zwuN6sJlnERJrxRCgWp+FAqY+JJGHh+YEz7bARJZ1PPlt95dWXLVpy28drPiAitEsQFhEoq43So48/PH3mlOtuuHrEqBtW3XvXR598gMWWIOmEaYfrTBrOZFptlhudeqVRirIwFXE7aiY86sSt/7ez9/62q67axfPv3PEd33Lf93r1oihgIEBCQtpJ7wnpCUkIhEAgJIggVpAiGAiIAgIqUgREUFSU3iGQcnrbbe1VPr3M+8Oz1tzrnKD3Hd+MNTJ2TvbZZa25Zn3m80AfQlUAd4wQm2kjVV3lpDAFAF1MhI1BCB4nooMlNCwaM104u0ZeiJxGgYpdO1gzj+M5wtbHoTMChZLHWWQYw7eTFqCaiBGmFCS18ORFNb9DcZQVSS6SgcEvpE5OD3zWSsaE6kw0h4bHTk+2hpK01epMtpPJrEgGh89MNsewEvLuR+9gFj7aGBltjGBtGFR+gDCBD+HM8OmB0X6QWfePnAF0BwEiKdoDo/2jjZGJ9nijO1mYXEeVm6ydt1BGAdkxND6ogyp0boIOFO6484d333vngw8dIyIf7BcnP1u2oq9v6cJfPfaLKloRgMREdGbg5HkXnHvw+mtc0GBGv+dnP71g5jeJHIjxAYsvbN4VycBo//DkEAhlsYIw0Rhttic+PfGRUPl4Y9gGeeLkx3v379q+a/OR79wwNHpG6LTTbY6OD3E79+FHHrxiy4Z58+dcePEFBw7uP/7wsSRtobHXP3hqdHxosjMx3h4fb49nOm0kk4PjgyOTw/0jZ0Djz/SuYC8VTmB+iBEw1AcylWLoDPQr/gs2h/EjpApwAoEfwzYdKGCxFslQDKATkqIDOujJzoQOqisTREU4/npJgEpiBjI7Zvxj1QcUXGg9QJTSBYv8lIv2EK1QmbbyvY/eKlSSiyQXHSJnfNFojyqbSVVyjwmVYeQsVFaIkqEDi17YCQUIUde45cE8imXPrkiAM0OSB2hns9tQXgKai3OEdDOQR9KJ3wJsqey8qAztVmxirl674k+vvsR9V6xKYF6OWfihGw/OumTmex+83e40iOh73//u3MtnE5H0EuN5LG4xPZ7UeaM1jhgnVY7lK+Ok8eKp3z6+au2yjZvXAtvYaI8JjSVT32iO33v/Xes3rpk3f872nVsO3XjwL399pYyhIp1ojFqvGq3x8cmRdt6CrWMwDfAmAwUQNzH45w4csDlJ0RkaG0yKzvufvjc4OoC7BdEW0RN6FUA0lisa0cDgUG0UFds4hpN4fSbfNVGDAB7+knWqOKtzFRGHC3YGz/VRXCAvtpUWG8wOTQT0NrG7FcnhgbbCB0PkXFCF6honAhlPutBdF6TAHpFXNij8CtbAWlkLJwtnTbgCSB7YHIPDgNlEl3i8NYYOC/g4kPnCsHDzuVgymEhfxhRQ2QMgriBclHUmGqPOaSKav3DuT+78IZHPiiTNOyFaLAr4YLAuZaw88cUnMy86//jDx4Bl+u5tN18271IiEpVADLPaZCo10aCp1uk2IzmsxhAFqfO7f3bHwiXztu284u///IsNktBgi+rXTz6668rt8xfOvWzepWvXr7rjpz868cUnxskSdmZlO2k02xOIvMYKOBuGScNE8E1xBxYmHxjth0UyeqrkZHbFwGj/WHN0olUKQuBugceyZOAsM5WqIJnYD8kc4Au8NgBBLFGJBSB8Y8iBT6iNYt9Wtzk8noHtB/STWP0OczFwVfOySaCA7rlx0pNRuvDQevNYYrW57FYUnlLqzAWFjjm66i+89NzLf3rx+Ree+fDj9yIF3BMwNbhr0DdjTRqJLeiYAWYEiqmo9FbaeUvakpwfMEmu3pHJIrZ28ra0AmpaOqiJxmghU6J4/KFji5csIIqVJJcAzQC+ILah0PFa1Df/8gVo7IWHH3nwvAvOJSLhBHAJmU4h4dXsNnKTWSc73WY7aWBaqkzxyp//uHX7FZfMufDqa/caL4hI2fyzzz+65rp9O3ZvWbt+9cyLzr/6wL6PPn7fOkXkB4fPgKUhKxIfzfjkSDdrY0qmTaErnm5kY5Bwwa2LrMNGA6QTfBVvd5e8TDoba45ibwM812xJKOlKI3YSnS/hClwm3GBgtst1BiLsQB50d5h2IB0q8zyRo/ScBlMqYytMClUqG5ytCPkRW9FxdcECuYCBDMIr/lnt2mTaykBOW5WL1DqNZYJu1n7+hWe+ed7XH3/iV4duPLh568bjvzpOFDt5e3BsAFToo42R4Ykh5Bn9I2ea3cZ4a+z00Kmh8UFwYIGvGesFLMQRKWSV2BfgAvBweUW8X0LxgkRtpa2YbI5pJ2ZedP6777/lg8G3QEUJz13KPKgULbS77rljxaqlzzz3OyK6+ZabLp0zi4jq7BAmaOg0ZCoVMh0a6UdcHp0YuuXWo1875ys3HL7utb+XsfLId2646porl6/qW7Zy8Zr1K373+6c+PfERbB3NDvBRYlMOneRme8I4iSVCBDgkHli5QGrPEkKgb4I9wdRwx3JNhr0TJlDvimRwbAA3Nv4XJxO5Cug4eCyLex4xp5FMYj8SF4KpjEuwYJGi6aad4rYwt+tmMOgIeo/lUU2p0eVCS90FWx9RA15WQd1dj+Gr4tE1zoRokY/ffe+djz7+CM77I7966Ad3fD+QF7ZoZU0YEMurQY6It6FwynB+cZ/VaYtGGuV+gKwUF6QXKNPQUsdZwOnTUZ0ZOEkUjj14387d2zAjAgdWN2sDUgsA42RzzLoSwu+CvnzBZaCYvOHwdWALhJPDucYnPzN8eqI9nueJ83p4dOCJpx6be/nsbTs2Hzi4X+rirXf/cfSWG9esX7F0xaKFffOO/+LnT/32cesl1uUhK9BsT7STBjLm0fEhDEzRb/PRoG832hjBSgQSNfTPwTkH1DFuA17iRGaCTwisKNp1eMxlEBI1LPjwTjFAqfhfPB+s2bjBRiaHkc+xjtng2ADepZFMor/rpg7EbdU8mhEio+V6s9gpyyyxXGbRViEhi+R8BMOS9RHGV0JIuCsD1nA034no2uuufvb5p2Fzh48cuu/BnyErkiUeq+DOUIlxsLkKkmd5hclVJZ6svNRRd0UifUlcUlRy6vBzOihbzWo6ebtTtMtV56gL2SWiqw/sA1+atgKoTCQMmKajlR/IGgcuGXrwoZ/Pvuzi/sFTxx8+Blo16aX0Eu+LPgLwvdapP7z07MWXXrhsRR+mUnfe9eMVq5ZePHvm177+Pz4+8f7Tzz5lnYhkA5lcJUm3hYLMeZ2LLthD0EAGVrQM+rHsKkMcEVQBje5koXM+b6zRjXgKVVJeNqsbImYPaU1CEsscvF0L5B86JqoiI8PEDO+CFylp2oLC8koiOpjDZjqtex+MSUvyP/i5QMGfBYabhj6v8BrOxyoTjM55kNjbEEMdv1nHqxWy67wmomUr+tZvXLNw8eWXzL7o6gP7AjllRSYSZYW2cmR8SOhcOeGCNl7ZoAuV2aCVFZ6s1HmhM+2kNLl2ot1tdNKm0Ll2UpoCP5e2KDfLyfpooGeqrbRBt7qNJG8bJyN54xRR/L/+7//WaE1a7MMG47wJ1W0jFKZzoCLw2gqlio8/+WDh4stvvuWmu+6545LZFxGRDRq9fhe0J5vLlIie+t0Tq1Yv+9GPb1+7ftXGTWt37tq6eu2KufMuvfbg/ieeevSDD98B6gua0iiTA4VMlA1FYYpcZdJK47WNusAJIaOcwESxPvcE8BM4UOlLqn8QeTNUoq77ixF2nboPt3cgz6N9jqeqYlvrjblimShrr0r8KdBATiorhM4LibtUmqCMl1PQOqEHY0O2NsNTcMF7CnEKIq4HAMbztFXaKaqeADW6Sm+YGCfH617wpVLl6HPOvOj8N95+/b0P3p5sjBHFNGtrI/Kii9vXeZ0VCZgvVCWZWm6rM5+Uygw7AK+sk9qKNOvgQkIkKUaLVg5WTiI5TB4hgyl1rq168Y8vrN+4johwVyBnwGIbODGxi5SLrJAF6gDj5MrVy/qWLly3YfXS5YuHRvp9MM5rbQt47n+88bd1G1avXb9q67ZN111/zeo1y/ddtXvWxd++7vpr/vHPv5b4LpAD6ZIHJBfdLO8Ip0BHB7wM6HOUN7AJSKnyVYdPxSWXlYQaOkTsnCArjZkkRwm0kOrYJIaWlF6KjI6qsKUaR0kTQyXsGRzOGIiV2V5UJSzAoC8hfQUQtE76OEWXwVbKBT2bg3IrJL9gTz6GQM7HEqcJA5JaGKeMdy54Nk3gKCNws9GV2KGqE5gVqVS5cZKZPsteiVMu6OGRAfT3h4b7Qb2RFQmRt16BsiCSQ/GYpC0hM6zNAQKETAumDG4s5PtYZDdWIjhmReKDgcnCjono2IM/f/6F54gI85WSbIUc44RDxb0ndfkrO3Zt3XXl9u07t6zbsHrZir6f3PlDKikUaHD4zIrVS+dePvvodw5fdfWe5Sv6Vq1etmz54nvuvXNw6DQRZXnHOYVVZ3SbET21FUrnjnym8kILG11XpKAyMdGKiq0RYZHBrdwIrA/a2aXJSkQaBoewy7Osus0x6zwsr3yR2KOi5x0Ufn34Nr4HYOuRLFJeUAzixnZBTbM5+DnOvkrtJRe89Y4f1xsqvGEQyCtjIAsGBUQIv8Lm8BxcSLy01AIseU889RgYrMBJI1Ueor35lptOfPEJEa3fuAbtgA8/fu/td9/44KN3P/jw3df+9uo77705PjHy4cfvNVrj73/4jlDZ8MjA0HC/1DnYhyK5ffuvXLt+1eULLlu5etnhI4fODJyEoC8RjU0Mg1YDNWnVR6Qdu7Y/+dsnqFLGISIhC4CgSmxfMIzmgg+bv3Dups3rN21ev6hv/q4rt//nV/6/rEhe+9urW7Zt2rBp7e49OzZesW7dhtWL+ub/9ndP/O31v8CxwZlZJ73XaMGkeQd7shjAK1OkMktlNjA6KK0yZC055XWm8sJkSM5QfaM9xrNOhrvpGp+/rgSDeKKK5iXaT8ypyHg42CiMrETLeQXbZVKYUjehGu0z4VXZfo8a+Qwv61ekTPpLbS5U+zEzWKTaBY8HymhlBKdlDLsL5BFPPYUQS11rWCo3U3x0ykihC7g96xQR3fOzn77w0nMYK+G2IKIf/vj2l17+A5HftmMzEX3w0bvnfOOr//0//5/zLjh3ztxLvn7u187/9jf/43/8v7MvuxjH/IVzZ150/jnf+OoFM7/17QvPO/db51x08bfXrFu5Zt3KK7ZsuOnoDZu3bly5etm8+XMWLr58y7ZN8+bP2bx146o1y/fs27V67YrNWzfu2LUFYMxFfQtXrFq+YNH8RX0LV65esXT5knnz5/YtXbxi1fI161avWLX82xdesHrtqiXL+uYvvGzWJTM3b924YtXSrduvWLVm+eq1K4CvXLt+1fadW7Zuv+LSObPmXj77l48+/PY7b2CuACGOrEhKWhpRwuCwfIqKAT3LRKRjzfHRxthkpwElUrg6cCFKJ4AvQms315n0grUxuBuC8TwqABA1ozGJepZtkdGazCIA3D+XsRBmhSvF72Ishlq4ZAx3kheLhC3SrI0qG+0eQKB91NzE4CUYxgl7cj2dauudtkZb42MECoi57rmksFVghaUiIgeKTL3LmZwLVhllg4LX8RXZIBAQmCMtW9G3YtVS0LyjafzcH37/5tv/eOD4/Y8+/shvn37yhz++/ZZbjx4+cujue+984Pj9t37vO4/9+pe33Hr06HcOf/e2m7/3/e/OXzh3ybJFMKnvff+7R79z+Lbbb7nm2qv2XX3ljTddf+TmG/detfuue+647tCBo7cc3r5zyw2HD+2/5qqbjh7ee9Weffv3btm2ef3Gddt3btu9Z9eVe3ev37huybK+latXrN+47sjNNy3qW7h0+eIf3/GDvVftXrp88Y5dWxcvWbB+45p1G1YvX7lkzfqV6zeuOXj9NX/80wvgTpQ6T0WinFBOpCIRpih0XuisWySI71iVxVAhSVuF6AojW2m7kTS/6D+ZqbyVtpvdVidPkqLNE/TC5KCWKhnQRYLZA6wEczBM4UAzj6dhDApbKSpJJ/xQVAo73OeDgWL8iubUh599AEHEXGfgi7Fkxltjnbw9mUxIJ4bGB1tZC73rjz/9AISbSH58NLx7b7xma+PI2dPS9DH4EFzwxpU9OZhOfVnQx2CchW+DnDoRuRh415q9aAl/Ctr5csuNAWHwc2vWrUTkXbdhNQZEIJ9iOak6t631qlr18bW/6dI5sx44fj8UW2DZ9F/+A7g5Aui/+fPm2/+YfdnFmzavX7p88Z59u26+5aaLLv72939426OPP9I/cCpQCX3w0eRFgqEQGhaYiJfI52rtFJklmGWlyhpJs5E0U5klRXe0MTbRnsx1IayEufSiXlRAsFb4hvIBBlyYMeCtQUMhKrJRZr4CABMuDa1ddD0xw2B9YrTiuyIBtIcnWujzSSfQQxW2wPhBqCxJW6fOfA4PV2bbUfOudB3E37M5+DlPwVeWp61xwVhfLlBNszmplTK6DLJVRAaoEz1AtGF8BPVpjt5SIVKkMjiI6Oh3Dn964iMYH5rv3aydVjSi3bTNPGr43xLgbwVauEBvoyJJsw421NtJQ5ocr4ANF+sUOr1ZniRps5CFdaXWCnDFYGNRRroABRwiokjhpZdfPHTj9X1LF57zja8euvHglm2brtiy4cJZFyxesuAfb/yNiCJZMO4yv/Nkc0xiV410ZjJLxpHriE47b2krjBVJt4kaAl9WqkxYBfZ+Sy4p0slOI1N5KjOmm8AiJuRuYUPoRSM5Y/vOKtFR5WXJ4h01t99UpZmGuQJzYcFBYmw60R5HUMayNyu3wkcCY4vBmrAFxOwylRYiHR0f+vzkp6Wf8wo7H+yzpqxEsU51bS81+uB9CDFSoGC9dcEFiqEyykDBemecNc666K13PgbjrY8Rvb4071pnlJHWmVJsxJY0s0yyiXwOCGxmzMN+uVBZO281uo1UJknRHhofxAQ2ydsSm8BBA+kPfr+sSNDEB40SwhY4slnakUVYIrmsSAqZaSudN2neETKvNgyIKBgrJxpjzzz3u0M3XAfljc1bN23dfsWuK7f/z6/954GD+5946rFOtwltoVylaChWnTMrTJ6r1JLFippwBYCr7bzZlUlhcmHyJGunoqucKHSe5G3jVa7zotSfTQtTNJJGUiTCCl6WMaTht5hEEV5HV7KieU25EIkX0OeIs1xmAicC80KKZqJmNQ5mLoPzE7ZoJJNweIjCGORDGx1I2/HWmPLSRZOrdGh0oJt3PFnjlfbSBGVdb0WfAysvSfR0DVnLK4bS5wWKnmL9cahUWiGY0+vPlZDuaKz2wdlggIbiPXIMJHhoxuxaCDRoHzivc5OnKhWuyHSWm6ydtztFp7C5qhhJUf2BrBl4kFZnEvYKC0vzDtImqXI4SGULuBZ0asooHIzSxejY0G2337LxinVbd1yxfeeWr3z1PzA/2L1nx45dWy+dM2v5yiWP/OqhTz79sArc8czASetVXhFqYy9fR1VhtUty6sLkuU51kIVNurKJIpHZMMDN05VdGAHiJrAhPLKEgzFBG9KqYrlD+gVzZOIVtOtglLA5HupjGsttl5J4tFKMHW+NcZ4nncCILK8IuFFY1JnXMGEDRTOmF+2sJUxxeugULFVWSmX1cMcQJra/L7W5np3VP3qMFQAAIABJREFUj2l941KnqfxnuSFrXblFAba5XCQIbSgd0CDwZKxTxkveUAc/rZCpcIIrrMIWuclLajBTwI2BSCHNO4itOJAOwigxp0eOhT4f/ihdBLJ/ePHZA9fuv+HwdXfe/eOvfPU/Lpj5LRjZmnUrt2zbtGbdys1bNy5dvnje/Dm/+OXxt999A78L7AyqUWBOcVH5cnKHTFgprCwMyISF8iI3iXDlnh8uOc/L8ZgRH/hfzujrC39cmfJqFmwOLytrMq91b8fgXluxq4DeD+8Oq0JQRgHByAkub/k2SGUXHi6vtPDwRgiy7338Lj4DiutcZ9oo2Nw0ahGY3RSbq3QNg59qanzUZw/WOwwwiAgkTknaCZXs5LQ/kaDd4WAHDMKL5HwoqbXBq0DkXTQuaqFz7UQrmSx0BhAlaLyZpdYFXbeq0rZsQeQbrfGRscG/vPbKj378/SNHbzx4/TWL+uZfMvuig9dfs3L1svUb1+zes+P4w8f+8OKzp/u/uOnoDZDv2Lr9ip27t/35tT/BFQLw57w2VvpQggURqcF9AbPA4p0np7yACASautIVwua5SVTIeVrATTU4PFVRkumKnS6rtOGw0yRc2aUTtsAyCkBH9aCJSSjToJigsUHIjAjo3vFyDQoIXkNEr443+/EZ8kqWGDcDFvMYs84b/CAYHRofxHN6g+9aocpNtC+xuSn6rRTY4M72duUPq9hKRAsXL5g3f+6ivoXzF12+b//e3Xt2/fTuO2+59Zbbf3Dr7T+49aGHH3jtb68+9dtfTzbHPv70g1OnP3/vg7cnGqOfnvjodP8Xo+NDJ0+faCeNQqSo7JK0laQtZIHAFbug8WBscrjVmfz0xEdvvv2Pv/79z88+9/TTz/zm9u/fetPRG7bv3HLLrUcX9c1Hl/i8C85dvXbFth2bl63ou/a6q6+97urde3b89O6fDI8O4Ps++ZvHN21ev2//lQsXX77/mr133XMHl72oPDgT8NEoXWCZORddi5UT9EurTj28iAlWeW0jCJpyG7WOhQoZ9MrQZa1vNcM4CpNLW4pL4QjkbTSg6ONZe9kZrhQQeSoFO8NPAHrgrh47YyjI4xd1JdSpo4JmFaqKXGcYauE5cOF5peaDd4F9Y54WyAtXFCYfHBsom3ZMDuQMEjggSHp1a/RTYmv9T93m6vF02s9RTxDRrx775UO/OP7gQw/ceNMNO3fv2Lp9y/yFl184a+a8+XMW9c2fe/ns+QvnLl2+eN2G1bMvu3jWJTMvmX0RuqmHjxyafdnFq9Ysv3DWBZfOmXXpnFkLFs5d1Dd/7bqVs+fM2rJt0+49O/qWLFjUN3/Zir7FSxZs3X7FeRec+63zvzHzovPnXj77a+d8ZcWqpWvWrVy7ftWVe3eu37gGQ6rDRw4de/C+Xz/5aLM9UaNXISJ6/Z9/3bNvV9/ShV8/92sbNq3ddeX2V//yMsdQ5ABl7zrqQNaTCbFs8fQwqlReeIDgq/GAAJ2KsBgxKR2UDFluOqpaXeYpgqzEeroiAQkVqNBgZ7CtOokTHjAuFVAOPOahPuM0edjAORYnADhgyjA7nnrxvj7eBfaKv3luy18WzwGoB5oLU/b4K86hUGMoZFf3/9/mAktvEsWp8RRNh26WdLrNDz9+74WXnnvrnX/++olHd+7e9sivHvrlow/fdvstP73rJxs2rb3l1qNHbr5x3/4rN2xae/mCy/ZdtfuKzev37N25YOHcpcsWrVi5ZPmKvoPXXf2t87+xYNG8iy+98OoD+w4c3H/V1XteeOm5a6696sU/Pv/Mc7978Y/PDwydbncaE41R6nXpInDnxkp8qqHh/kV98xcsmrd95xbsU2F1nihkImE+ES6uEe6RAODAT6xXOmr2QDxoN1FBbwSxVflCB6lCLn2qK4wGHxz7eivNoRw9YUcYI4RAHoBTnrHyqh9PF1DP8oFeSQkZrIwP86ueSVXLqjzLgpVzAsBcaRx5ecGC/a4KEqrgqeoG8lNmYq5H6OFrnJnTY+s0m6vncFOH+mUxWy8jfMWoCovG1nsgH3ql4ln8Tb0//PMgRHrW/wbrJBGBsZELT+jpYKSBqIdsD/oYwGDixRut8Z/df/fB669ZtWb50uWLjn7n8LEH7xsa6cergPHUB62NwFS0AggaUEN6MgyaCGQBNdBBwRR06DkwHaSJjmOrdIUOUsdc+hQXGL8incBcAQELyRPaIj46R1Y5Cb5lF6fYTel1KsY7GD3WjQFCQfkM6CG7IhQi7Jy+9BCuYIjAlGeSDuSZJpBNH54VmAPMOZBmsPuEQDz3R9j40LGb4aGGThQ5o6sKBS4XavOugMOT99Fbb623vmJzKklMKuKSEIONxgWDtMOR1V6aoB0Z7aVywkadq8xGU+hMe+UIdO7WBe28UrqIZEGBm8rUki1MJn0p/JWb3AaNLRVjZamSpgtkfrCnv7z2yt6rds++7OJ1G1Z/6/xv/PyBe9965002ZWWEMhIMcz5a64GLNs4b58uueCQfCDBBbb12wUgttJWGLHj/lNc6lIfyUjsRyGkvXdQ2KhuV9nmhu8Yp7ZSyUuiiUHmhcmmF8dqTc9F5Cp68DVZ7Y4MF6a4NRntVYg7AaUdOO4V/2mACeUfWeA3hP+O1stIGI41QVkIVgz0cB74yAZ1KSQa4ofFlXAZpeLlBHU2uM0gggV3PVaR6gTzafoy9Y4FTNrgyq5s67J/BngxAui/D0tX6I726dwrHUw9XXMnPlcPdakHBUi31qaIDYyL45xjYlRIWoQdbEq6QXmQ6E04UNgfbY6bTQnTB04YtdhhT/+CpXz768IpVS7953teXLFt0+KZDv/39kydPnyjdY7XhwW3x2krSFI7Y+g3qe4R2RiqhvMZI3pFHoaqDUcFoW7iglC2Ml8YJ6DMXMlVGQjQbfADaqGrG0zu3LgT0Pl0IoaI6xaflUHV2xwsepUyYggNZR49jlByHbMaV6KCcLw84b6a4Y/hTD7kJaGeNzRy5WkkHE1XJklvzjjoq8JWUE1He6Y8lo9wMDE8BEsF3/jJTi+gDG9+baXypzeGGq0AoAfkvut4126rn3bJuc2CHBIqupp9SFncA75dlvBPCFVmeVBqj1D94avvOLVcf2DfrkpnzF869+sC+Xz/5aKs9CUOEv9RW86JlfckyMBljnVmsdo15BVhblRVpIlLldVekYCWzVCIufdQ+Gl1xmpY4OZOD353n172JEJU9dkAlaoc7e3DEn2QazV6oiJp5yukqImVPDgJoDH8q0zXfO7c8H/JVLcxZI9sQL2Sx6wKxH6I5FzrcEppic+Ddh82QK/FzxtsYyXgLXIlxdprNueCV0bkoWDSHgY2ltDBazNHywhjuNuEK3hiAtcHgGOnFtmhIm8rnw+DqZqedNEEpW1TgdeVi2ZzrZu3fPfMU0JTfve3m9RvX/PiOH1ReLVinfDDl316B7dFXPNeAyvG5qM9neq4u9uwvkHfeClVUvV/BNIzSKeGUddpHa5zy0bpgjFPgyijJ2JjGr2T/8wDmYGw99Sbv2dx0rnCasiEFx8PPmcY02JUJq2ugD2Ki1lG7CvrKLPo4zyborkzQZOEiQwVJRD6Ugkc9bFvs6XJPK0p4Y7B+G3OQnYGWB4anaPOi8cY3nw/BRW+dU0bzoj9/vR7U0RsMy3urss7g2+aljGkvnyhsyb/HCXJJdRYMkbdBBbLQuAYsBdJBxkqpcmMFHNsbb77+gx9974otG/qWLly1ZvkPfvQ9sKIihEKlz3gJ1nMfTaAe86uPPeQVc4nCwurYrZ6JlJJ5JU+odApa09Iq5bUJNtdFboQ2koEOOEu8VsfLASWZaWkWAf2ms/1c3Y2xD64HfZxw7XrDzbM9InJ8bpRUeY51XgE/yxLiLuoQS30VSyY3GXMuKS/xdbgg4JzE1JVOq9rckpmGKJlGhj5DGa2twSC1zOdibZYfvNSK4ZxMfFJnQOG+C/IVF6wyMitSoUphP0yOeyV60NyC5yQD9RemWwhJ1ivnNaZkKCqVzomo220dufnGnbu2bty0dsWqpRs2rf3FL49PTI4SEf86b+CiDmUUa/0zl2l4mMJfyxfYV3Dq+tymTGiM7IrURNsVaSoz7o9Ip7IiK6RQRimjjDOBQiwhriX/a92MQvSuOuflGe5hGQ2uE/jsOW7WP2RJIVgrDKehu8sigzQGGGUcDNKTt17yniiKdFRvkvkPK+ZD8CJAhKNucDgM6dKPUrl1VvKShyk3wLTPNsN6ByfHpsbwOMwYCilwI7owhefV1rRvIEbTC9vBQXXT8LIa6vDKA8tKbtpWrMJlDx37NV7hAXh0Q9Ufef3113bt3rZg4dxFiy9fs3bFwYNXf/Tx+2iIAMuEfSq0PDAlY4XkUCL3azbnTS9Vn2pzZ1+8+pKR9QZ6mECWK68hlZkU3SzPCym0NYEIZlTtK/WSME52IwVftQWmzXtAJIV199K9TbsrqFcATfN/U65Rlc+4SoHYkrFkY9X6RrsbEdY4yWMVU9HkwJ44pk2zexVKpQ1HFvNf6YT04my/W/9sM1zwznvrHRyeDR4+D7YIMDCcnHHOVrBP3o/FwUD2rEhDpSzogs10qf/CMiMAR2CeyO1N9nPAN2NrTcgMrbuPPnn/8V//sm/JggUL565es3zuvEv//vqf07RNRC5obYuSuadmpoBIISLXVLK1C71SlLONKc6juoq8rcT81OznlJHCylL31xSpzLoy7YpUOInMpOxc1ppNPaOJvfLNRxeIXPQu+ljriQaKdZwjOxjWWik/Z5UGTK+v/4XNccdEuGJ0fAiIRqC/Kj/nTCwlaNkvSC8MafapbPH4OqCGwevzUM5EPc31TvdzxhnjTCRg4NAcCj44H7yP3nmrLYTOgw+968EHbC7JO1h+BM+FJ9fJ2plMsQsOrE5Rk+BIRCK8sGRkkCYaFZSJJjeZ0gVmnXBszz7/9PKVS666es/sObP27Nt5y61Hu2mLiIgcnpaJNFJQTuUqV06F6Aude/LaSxu19lI76cg4MpA9qAPocXCLvH478o10tl/BNe7m3Vzmhco7aUdooSs+l1CruupLmdCWZVfHxh2JgM2u53ORiGPrNBa3KfZUKTeztxaqELpgQ8THRi3Zi+zkXLQff/phN+sQBe47+mgjeeM1dlkCeWkEaixWwjjbrCECgwQAXUNlZaHzehrHD1huZAbO71TMyZQAxBrUgTzjP9F+Aw+69SYRHTCxlWO4oHKTQcmUwyv2l5SXhc4LULOIjo66MIWNaCo6VADdtP3Tu35y4OD+mRedv2rN8iv37nzoFw9gnQda2wi+xklDLjdFrgvltbASDQsdrK/Nm01VFKPR3+MnqHVM6l9/Ss5a17eoDk4ehMxdTUE5Us/OpmFwwlRN21rWWJlajByIXfC4Db407tfvAXwwbsGAJN7VlknPzg3YL7LX6NU3uMRW97Qh2Whqbw3kJJ8rPLmeBnCUw2mE/UypIabd0Pz2tqaUxVgoxqD7WmcykG92G1gGwWX25GBzGM8xUCeQx/+ChHAymQBvUiBPRO209bvfP3Xg4P5LZl/07QvP27f/ysd+/cszAyfh86xT1qm86DLeBLt6SOG7IsVCMiwP1T6vm3M7huNCz5iiq6hYrJuassArsM196fWrp/YumPp2Ut3m6g3zWi/Tcc5Xb4Vi1zOQN16fXd/Ur1Go8kIXbIzh7E8+RdujllPy6nu9z8KdS/S84J+AwO0Vi9Frp/gVXCnk0ktAQ1WelyezYo6v++kZXNZOCdWxFAX00QGGiewHvx8rTTp+D6RoLF3qyaWyO9YcxcKIrZaBQZcuvTBe5Sp10WA34re/f2rL9k2LlixYsmzR9p1bfv3ko+9/8A5MDXvIyhYQj9dWEHnG2wHEkam8KJWZHEpIFSRgQvUutCFNFKfV3dzuqR/1WDbN5tjB1E96qPXZq1vRWQ/3GayvsYbXftd6wzQdGCSG8pSWNwPiDzvXabmU9UZZifU847SyUqgilxlv60FY5kttblqrmXNNFyxR5N34ev+cD34RY0G+YVGlspn2Iml1Gjk2lrG1RwFWWR5e13mbidR567wF5bn1BvoeyshC5VSV9D46EzWIurBiCUws4BLY8uiK5PTQqU9PfgIpZtjTwOBp7KWuXb9qx66th48c+vvrr1UTKlOnrgEjRAn6CAbASeOkDiZQVF4XRmhvXPQmWh2si6ZsF/mS1bss4yt7AqTZBWudwRfhc1qXRQwVBS4uia+6QnX7K1t3scyrEA1A3AyhHDTS2YPijgWdt3MlpMzXdUqrfU1QW4SqJpsWZ5H2CFXgxTORClW0k1Yp4Rw9GoT1j1p3kJzU10On85Yojk+O5SKDNXezBCTxvfFmcDCJVqeZ5t2sSE988Rlbm6vGrOVktsbOxA2UGUyO7mtKLnwrsGb68OgQUyNCA5iqFgBR1KXqfCadAIc/1joGRvtB4KOdAlmQIyudfOLJR6+7/ppLLr1w9doVYDOV5WA+oIwCDLjePQLG3QVdkntG44PR0XoKOhhHXliJ8CqdgmYmwivzNQFmWOY0wbElQV2YPRyz83E9UY/CZwe72NPOiyFazCGyIonkoa3mglZGTs2YoeUi+gdPWa8DOW1lhWexPlgbrPOWiAqZI8Iie673q10lRgDrbCctdKzYf0/Lw+r+8ksfeHKQIWgnLeM1uA1guD33Fm2s9MmN051uG8Y9vV6uxYr6Y1/ndoVDZl9NFMcmRpm5DuoIUgm04pSRI2PD6E2DCzaQb6XN/pEzWM2AnC32fjt52wRNRI7syYEv9h+8auYl3z506MDefbt+cscP3nzrdSIyVpw6fUKIlNW9YVUgFPfRYLmQVYhc0NoIpXPpFAzOkZdOMdNMrlOsP03bX5dK8GjOunJoqLSsn7jxyTHoxdsAcokotYBdTm+vV/kcBOy6WZLmHeuVdSrNO9ZL+OmsSHKR+0q4m1PhyebEqTOfEwWGUUHx0jgJk2p2GmnehQtEuHRTdcammV3d2vxZvbr/yoHX6WYJ3hR6MqYmFA0bwk04PjlGRM5bZGL1VLVem9cfl34OvwDSdCI63X8qLzIXrdKSzVNZOTg8kIssRN/NEuftyNhwp9s+3X9qdHzER2ejaWetkcZwptJO0e4U7bHmaFJ0Ihpsn334xNNP7Ni747IFc/ZcfeWea/Y8/vgjzknnlXdK67zRGM3yTrfb4uIAjTpsgypTjI4PiUoQ10cz2RxL0pZxMlNFpnNDzlY2V1jZzjq5zpppQ0cFVQ3lZSOZbOctoQQ6iPDfgbyL7nT/qaxIu1mirUrSTqM1ifNeqrVogWVYpaUPDoJSjN2IFPArad6dbE70D51Ki7YNUuoszdtCpzbIQnZZZJH9KM5tO5lwXtkgXVCfnPiwlUwqW1gvxyfHIoWJxvhEY9xVIljIsQCzqOsmWm9Acs+GWO+HnZ0OTrOzs8OucVrIAlYB34kX53fEHWiczkRWuvnQm7LwDcm5YC3NtT66Gb7q5eJ2QZZdyNx5i8VBF+zAUD8YsnD2kbQKVYxNjHa6bR9ct0haSbOVNDtpW+gCkjrKymeee/qa6/ZfetmsvmWLlq9act+xe9965w2i0Om2J1vjhcqNUy64L06daHQmiaJ1spApGD2wFA3Hlsk0FQnURYXOc5VmsquskEY2Ow3jjbLQ0rOeXLPTDOSkKaTJlS2SrOWiETrv5h3ntdQF2AUDOay7FiKFsLixKiu6gZzURTtp5CJVViZ5J1LIVQZ9KehPGCe1lcoI63U36xQykzqXujh5+rNcpoFcN+8oI8qFMZl1swRulT0B4gmo+LG322xPFjKN5EfHh8cnxwJ5othsNyabE0iMBob607yLOJPmXeyEKyON1d0scdVOe88yzuov2krrZ9rPez2g6ODak7SDYsJHh3yXgzVSfOR5xskQnfWqelOPI0wN2XWbdsHOQAhneAjixcjYcJanVIlJcq5ARLizkQDhY2EtPs277aRlvWm2Gx9+/MGRm2+aN3/u+g2rl69csveq3X969SXUBpPNsbxIWlnHki+MkE6pYNp58sa7b6YyL7M0J1gUxgcjZGaiAZ+8Dooofn7mBNjKhSp4y8MFG6IzVrWTVqfb7HSbmElguZqpAuBEO93m6f4vwM/VzdqN1ngg6A6IXHQ73SYopDOdArh7Zvg0InVXJonowOnyBiRuj27WanVaSH99dIUsyorSyFxkxlcYsKryRbbOJUur02x1mqPjo5DU8cHlIut026PjI8rITKRSiTTvIpPuZkkh88nmhPUmK1KceVcDX4Va74N/wmPTus1xaYyMTajCWK20bCctuDpmruFqBpmcMkI7Aa7VUNpZD6MwLX2sD+tmeHJZkRqr+c4gopGx4f7BM6Hi5gRoDKVrVqSVtmTsdNv9g2dKQh2j0CwQqti2Y+uFs2bedPTwSy//AfMrTLTGJ0cmGqNZ3rHkdTCFEQACWXIff/5JKjNsMCCkWq9gIpEcdjCZHQ2sLdqrpNvBp9Kuh3rw0VuvxiaGsQMLxA4YxAaHz2BVkbXeADButMZBT9FOGpDPwvxROdnsNvpHz2DrWFd6uuDCBu0ISIld0EMj/VmROm8DeWBCY6XyiAf1xgQyp/HJMVxO6w2SwnbSmmiMwxCJSKjis88/xXcEzxonBmneHRwewOtkRZqLDBufU+ccgTMwBM16MXu2zcHW8ZmVlvBwqB157GS9KWTebDeEyl1QmNj64KbZ3L9KGV2wM5CTlqKGVbPA2HIPO0QPN97ptvH1Ot02ThNQJIXM8VGEKhCjIfj3xlv/5IUDXkdFUCPy2BvQwVhygeJYc3yy0zDRuaAmGqNQw5U6n2iMYr8Bfb6S8NZJG02z2/Dk0qzbzRKkFHAqkYJ2Gu8F9nE2sv7BU5989iESwYnG6AcfvYutiLGJ4W7ehr5l/+CpdtJAjSxkKmxR6BxUHSCqkU5kOovkJhqjYxPDYPCEg2wnDaGKTKQ4jbgtkZPgQ5Zep+pmwXTwGJXN0Migjy5JO432JCDNE43xbpaAIe90/ym4HOsMSjeYMowJeSeKzV7OTtUAinpdSXY8bGr8AP25Trc90RgP5JWWrU4T7RjI56EvU8g8zbs+Wh+1cXKyOXq2n/t3NtdsN4QsWKIPJwvCN8DDFTIHMIkbS+gMRQraKsj44RcBZMIz8eXhMHCZIX8LGUlL3kYHYLd0KlN5t0hHm+OQy4EyH+wGpJzYwcR2+0hjuFO0+0fOSC/GJ8bSvIs8BsWQUMVkc6LTbY5PjoxNDENqzXoFuokzAyeHRvpd0CdPnxgYOn1m4CRsBQs7nW4TlBTaiG7WLkQX65+8UdeViTBFUnQ+PfERKHl8NNYpEAk0WuPIrpBx4zaYbE6MT4412w10/PnGhgQolG1xJXKRDY8OtZPW0Mjg5ydPRAr43ULmSN2yIh0dH2l1mlmRIqpGCmwQuciQ89Rz9il5W63HNqVWdYafDyfdbDdgXvhI+HjdLMHH4C66jzaSG58cOTPwRSzt7N/ZHKeMM5y36Gf2Wp3RAQkM06nP0XBd+WaC2U37DvXihTVMEOAAm/FRq2AsOUcezJJo6ua6XNBHHxjApBCtj0ZH5aJ10SKpAmzfk5NKsLRUqPhllSkJe2HlxknoLSlbtNqTyhQYoL373lvN9sRf/vrK+x+98/EnHwwMniYKp/u/aHUm0Y4uRJrpFPz2EL8CyF460e22xiaGiSgvumneIQqdtKmdiBSw64DmKlEM0bfaTdyN3OcL5DlPYveDT86mg9OODAxygEjnhSoarUnny1fr0YJEjy7g2ain+qxv6vDNhwrXHqqBJ+NYbaXBzEMRlC/oy4Zy1mfBGvNfia3sU2egEvHk67cI06qzwfHHihTQGFS2R489rTdTGZyL5DwZTyXDfwViU8JKHcu+miOPXq4hF6JhMZoSYxMMVQtI2Jmrb27iHuAyDeE1RI9WS0X7CGZPj2VVZQtlionJ0T37di1dvvjwkUPfve3m664/8LVzvvLGW69vvGLdH19+AaSwjda4I8dJZCns5IQnh53ZW249et4F516+4LIlyxYBMWqsrkaQdOzBn3/1f/3P2Zdd+vVzz0E1Nq3RxdUP3y2+No0oEf/VThOinrLS1+BYvgYdCP8CCzjFF9RCKv+zfu1suScabTB4o9K/xJ434fmKjyWfsI881/qv2Vx98FB99N60O/KX72Gje4DjWIIpQoUG67UBXbAuOOyklEdlSdZLMDWXlOHkuJcbgoF7KxWeggareoXlV1iOLzu9XpgSROQZFo+PWjlXVW1Hl/tj1imwQhHF557//fnf/ma1LUbvvPfmO++9yTkoQHi8e8s6OzooQ8YHc/L0Zzccvo6IxidH5sy9+LW/vuq8gtFLI4jikZtvandaX5z6HI1PnK7S8QChTj3tjVBh/aUqZwmxBtkoA2X0PHpCIOLJBFR3Qw1LUtmWx1Fdlzo5V/m+kWI1W6/cSiw39/BePLf11Tof8i6hchcrLa4SCM1EXv8Hm1PYcPRRV/r0RltdYemiCw4Y6xDLv30MPvoQQ0VQF/FVEQgC1ea7+IZklVPCCOWkI2ejARjERS+dMmRNsIArmqBddCZoaWWhCxutcqrQuY1We+3Ja69d9DZaHbSlcqqIcTDf8ZECtKDK9dVofbAumEgeHFAoaN59/62vnfMVkPmPTQw/8eRjRPTjO37wp1dfAqTq5Vde2LZzyzXX7v/9s78dmxj2ZAM5G5QJSqjcB2ud7nRbRDTzoguIQi5SdEmI6L5jP1vUt3Df/r1Dw4OoBpB09voXlcFFCqZUqrD4Opy98IAy8lJF5Rr5J7EifUf85buuutLOk8Unr5gJnHFYwDE4tAX1Z+qDAYUKgCTaKRiujYYvKDs8fADrtA/WB2u9ieRr68//Mp8L5GdgE1PZwgYVyODQ1rjgXQiME562BhYoKqOV0S54bY0yAl8Y958ku9DcAAAJeUlEQVSvEFrI1WBhKBosObACgtoDj9E0EU7i58LKXBdJ0c2NwO9ikzRTufI6N4Ulb6JVYcruD+dGSENRVtf9ro+OtY4iub/+/c/zF87duv2KAwf3Q1NQmWL9xjXHHz5GRK/+5WXoC9x7312zLpn54UfvIjUsifS8zYo0RD/ZmFi6fMneq/YSEVq1SIPeeufNR371iy3bNl865xKU8OyW6tcDJmhqzLjImeqYgzq8pcR6xGnxZArDPZuFi65OfAEH76MJ0YKCrVTPCgoCVDE6SxZgM0cWtDrA5kxLrrgNxCeW83uOe18e34Er4fW+imPaBDLY72Uo2JfaHC/DutADP6KRqKzUVmmj0IQDF7h0ygSLbVAYmYkWm8lsZ7ku8PxUZoURQChJp9pZh4GZ0ilPwUbnKTAaHprHuDw2mBA90g6+eMj2tBVCZc32hAv6geP3b91+xZ9eeUmZ4vhDx+4/di8R7di19b6f30NExx68b+36VUT06OOPLFvRh3QNbOguqELkQIy98+7b9/38Z5fNm3PPz+5GO01blReZ0jKQR1a3cvUKqiRQ6mhFHhu4Spg+VNh3HmRxPgd4LGM30IiZltL5apm0dHXR14lXCpVig86Wfq687ljGKVX2yJU7eFEhe9ZBSS9CBdcNaBo7zRO8KgcL/l/ADc82uxmBXCAHqoRQ9otL/GqFzf+XNofdHGU0Qput1gh6OQo5JG1AU5bZGznswQMJkusCE3qYFFwdCCthgjoYkFeaYHUwwMmVnjI6qQV/f/YHmIuwD8BNmYsMfIlgOXn6md9845v/C6SckBIkirv37Hj2+acLmX72+cdfO+crA0Ont+/c8twffg9RFG3BRl344NC2dMES0VO/eXLbzq1wdVKJvMiUlWnWTfNuIfILZp7P5liCZquCkUHaLFrPrRN47kDeBwfMQQ+EV6OGwQQ29vROfS28ButLntOKUsNjWQnYMGYVR52urYCIGZg9sUsAdhVbW0XA50c7kJve9Vrz39tcID8jRM86m7HnAGNtH8TzrjkzbNY3gbWdQkiBGxqFD+JpoFiSAQbLsEpPIZUZjAnQS6woswSRIy+9woYVDBfPkV55Cqh2C5GhS8nTRkaw4ee9Lijko6odRKLw0CMPLFm2SOq82Z5odiYgebNl26YHjt8PJp6Vq5et27D6Dy8+S+SNlYEsUSDySdoyRkstxifH0Dh4/oXnDh+5EdVGhQ8gfKTh0aFL51xCROjp+BpctuxyBYdLwI3islURDIBrAO+gac9jceO0DQadrLKeqPBFtoJ2G6dZtsF6VchUO8HUUmgLYIpQ1vjBgMYVGwUgbsdiKOAd+DBQj+YF3jpSkHFy/8bgYHNBahkoSi2ttxWl9RS0NB8Vk7/lBdgQo/WOb1mGK8IDq8rUYDGwY2wjCyvbWQcx1JEHXz2W9uAFbXQmWGEl9/BMtIi2yAsdBYSheroDm7NTd+O4F6ArCnai8J3vHlm2ou+1v72aFcn45EghU2Pljl1bIdlz/OFj511w7l333LH7yh33H7s3K5J33nuzb+lCuMk07w4M9R84eM1kY0JpefD6az/8+AMiuvveux5+5CEiuvGmGz77/FMiOnTj9Y8/8RhcIDc4+Batz37qD9gR4id4JtJW7kQWMkeLnlMIjt26krZnZlLeJiTySExhjqzLgzG0Cgo9SE+OGTZznXEcg1njvVwFbMNpL7dLneZdm39tcxQRIj0IhXuQfM8r1nU/p53R1gSKIO23wSFZYffL04tC5pnKTbRwVCXBgpXCyma3BXkrmJengGkEZ3j8fPg5eD5PAWaHrh7yOZwOTtocy/dUwMZav9CWC9tGtDqTzz3/++f/8MwTTz0WyOZF1zp14otPnn/hmSefepyIfnb/3d//4W0P/eKB+4/du6hv/sOPPEhEL7/yoo9GqsxHL5W49roDi5cs+tFPfjg0Mlg2XN59+5U//4mIDh+5cfGSRbfdfutLf3oR54cJ2DgZ55ZvqE3iGfrB17X00Fb5ap8FVsV2hrDrKhAkJxLGaRgcRnncH4UhcsydYnNelpSalYBTKVRnypNsz1JlLWN69PU76v9gcxBSmqocF+t2Ns3mYilCF+ur1/x+vSM4642s6lZR8mdJpGiWnAoly7iAITpZGOEpcIUBPCYcGw6Yr/TaU3AUHAX0Ds62Lf7y9fLKevQIiyRtsRwPEbHmBGu5Evl58+ec6S/Xf5548tHf/O4J0GcbKwqZ4qLifyMF753QBXeDhSrB90SkjRKysN5IlrPyUzzZtGkVOxKkdOxCkLai5+yDAyYDRlCInPl7cBNWBVPF0IhupVdYAcYEvJQejaZuc2B4BZqhKxMDtnWZoD4rMXNFipEd3iUXGWbu9QbtvykgUEOESNFH74KLFdx8qpZrqB09VmEhJS9mokoqkbe1a29KorJgyha5d9Fqp3HYYHGgP+nJ22DwEx+d8cYGa7zBgV1L4w02cMGBV/8+4IIIFZ6CG6pT7wcb4E6CIQo+WuO01EVWdJUR2kofbIjOB/vyK3+cdcmF37zgG3uv3vPwr46boDpZq9CZcsJHq61CcoP1PjghjGdQwWCEkObdSAGXxFX8uuAsChXGWJeKKL0RU4lYrp7JNYGPLleZ9qrQeaFz7ZTxWphCWoEuWq4y4zX6avi59lKYPJPdQmfSCsAjbNBFqclpXDQ2al3qOmgsqGqnQISNsVvJJFSJm5cbEtUdggTOeQu0UT15+NJGSSA/gyttXLNY7nTxMWW109do1Km2G4c7ALDSKW/Ta3Z7gGRQpjl4Zs+j4t7cLNY67/UjTJ2w1WtyhmfV28L11zy7j8XWaSo+Gx73+eCULV2gJUNEXZFMdiYgi23IOOrZdOlWg2OPG2v8SKgw+MNbb7hFx3g1ntfVP/PZeV75z1jyg2CVDgT+SPZT1QUjztD4YGFy4QqOkiWlMOlSvpt0T3XOC13j/EJqpK3CqAM3wzTUXT1LdhXpmDlrC/1LbQ7fbkaoKnNb7Za5GqZ5amB20+qJ0GN4LVuUvG1bf49QKW2ituC0AJ/Y1WyuPv6r20qt5fglNsfvhZdywX7pc+q3Gm/XsWvhU1b2yZzRRikvlZPSiXbaqlOycSj00QG4aitqBf7woaYH2evlRl+3OVcxE9Znr3HKzLrmpINjgQDwSmMKDEZz5PuZTpvdBnoc+NtXKprMe1zJp5Tc7XWeOWREnCnCbwE6UH6vaKdVP71j6v75v7G5/w0NtvW3O7zo9AAAAABJRU5ErkJggg==)
Theeta = Angle at which the immersed surface is inclined with the liquid surface.
4. Curved immersed surface. The total force on the curved surface, as shown in Fig. 3.5, is given by
![](data:image/png;base64,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)
and the direction of the resultant force on the curved surface with the horizontal is given by
![](data:image/png;base64,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)
and the direction of the resultant force on the curved surface with the horizontal is given by
where
PH = Horizontal force on the curved surface and is equal to the total pressure on the projected area of the curved surface on the vertical plane, and
PH = Horizontal force on the curved surface and is equal to the total pressure on the projected area of the curved surface on the vertical plane, and
Pv = Vertical force on the curved surface and is equal to the weight of the liquid supported by the curved surface upto the liquid surface.
Also triangular, rectangular,trapezodialshapes,and circular can wrote sir
ReplyDeletewhat the practical application of total pressure?
ReplyDeleteIt's very much useful to me..
ReplyDeleteCould you please let me know is the depth of center of pressure is independent on Temperature...?
ReplyDeletethis question is asked in one of the competitive exam.
options given were 1) Density 2)temperature etc