Physics-
General
Easy
Question
Block B of mass 100 kg rests on a rough surface of friction coefficient m = 1/3. A rope is tied to block B as shown in figure. The maximum acceleration with which boy A of 25 kg can climbs on rope without making block move is :
![](data:image/png;base64,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)
The correct answer is: ![fraction numerator g over denominator 3 end fraction](data:image/png;base64,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)
Related Questions to study
physics-
In the arrangement shown in the figure, mass of the block B and A is 2m and m respectively. Surface between B and floor is smooth. The block B is connected to the block C by means of a string pulley system. If the whole system is released, then find the minimum value of mass of block C so that block A remains stationary w.r.t. B. Coefficient of friction between A and B is m :
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)
In the arrangement shown in the figure, mass of the block B and A is 2m and m respectively. Surface between B and floor is smooth. The block B is connected to the block C by means of a string pulley system. If the whole system is released, then find the minimum value of mass of block C so that block A remains stationary w.r.t. B. Coefficient of friction between A and B is m :
![](data:image/png;base64,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)
physics-General
physics-
If force F is increasing with time and at t = 0 , F = 0 where will slipping first start?
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+P77//HhKJBEqlEn5+fkhMTMTYsWORmJgIX19fqn01gSMcdDoddu7cidjY2BZ9Pzv7t2rs33TUqFHYvHkzCgoKkJubW+33Op0O6enp4DgOwcHB+Otf/9rkaR73nz8nJwdGoxGPPfYY/P39XbecTkBAgFNDoPQBal6zZ8/G0KFDcePGDXAcB4ZhEBQUhOjoaMTHx6N79+4ICQlpt18cgiDg0qVLOHToUI0jfP7+/hg+fDgefvjhehfrczTlTCYT9u/fjxkzZohfCoIgwGAw4MyZM2IflON4q9WKrKwst9vcNzo6GtHR0cjLy0NGRgbsdnuVaRw5OTnYvHkzFAoFxowZg549e1ZZTsdutyM/Px+bNm1CYGCgeH+jg0ajQWZmJuRyObp06VLlsSaTCampqVi6dCn8/f0xceLERi3V46x6A4yCyTWGDx+OQYMGwWw2iwHmuDWkPSyp7YyAgADYbDYcOHAAV65cqbJena+vL/744w+8+eabePDBBxEWFlZvM9tms+HmzZv47bff0L9/f8jlclRUVCAtLQ1HjhwRJ69WVFQgOzsbSqUSW7ZswVtvveVWARYcHIzJkycjNzcX165dw9mzZ5GUlCRuSnzw4EFcuXIF3bt3x6xZs6BWq8XHCoIAnU6H5cuXY+3atWAYBv/1X/+FefPmie+7ffv2Yfny5fD19cVzzz2HxMREyOVyWCwWXL16FVu3bkVhYSGee+45xMfHt+hm0O17SnsD8TzfqrPdpVJptc5PnuedWliypdx7bcfr4ao7ACIjIzFjxgwkJiZi1qxZyMvLg8lkAs/z0Ov1OH78OC5evIjp06fjxRdfRFxcHHx8fKptTuPo9xIEAXfu3MGbb74pDvvn5ubC29sbf//733H58mVcvXoVN2/exOLFixESEoL8/HzMnDnTJc+/NlKpFJMmTQIAfPLJJ/j000+xaNEiKJVKHD16FJs3b4a/vz9effVV9O3bt8rkcJ7nUVBQgK+//lpc2r2oqAg8z4sBtmbNGpw9exZGoxEnT55EQkICgoODodFocPv2bQQHB+P999/H2LFjW7yFQAHmJMeKBHl5ea4uikuVl5eLTSiNRoOCggKXb1wcHx+PDRs2YPHixfj999/FqQOOv9myZcuwa9cufPDBB3j22WerNKfsdjuKi4vBsiwiIyNx584daDQaHDhwQNxZfunSpeL6WdOnT0daWhouXboEtVqN559/3i133VIoFJg0aRKio6OxcOFCDBw4EFFRUSgoKMCgQYPwySef4KGHHqr2OIlEgqCgIHTo0AFZWVngeR4KhaJKrX/evHl46623cPz4cZSWluLQoUMAgAEDBuCtt97CmDFj0LFjx1Z5nozQxidzbdy4EStXrkRlZWWjVpQoKChAeXk5eJ6Ht7d3u1973mAwQKPRgGEY+Pn5wdvb2y2atI77AB1N7vvJZDIEBwfj0UcfxUsvvYTBgwcDuLsSw+uvv44dO3YgJSUFSUlJsNvtYBgGHTt2RPfu3REcHAyZTAaz2YwzZ84gOzsbgiAgNDQUSUlJUKvVbnmLmyAIsFgsqKioQHp6OoqLixETE4NOnTpBrVbX2uy1Wq04e/YsLl26BC8vLwwdOrTKWmFms1lcOv7WrVtgGAZRUVGIj48Xp3G01v3Kbb4GVlZWhvT0dJSXl9e4XVt97p0j1NBlR9oyRw1Mo9G4uihOsdlsKCkpQUZGBioqKsSfO7bzY1kW/v7+GDdunPg7uVxeZXUKLy8vDBgwAH379gUAcVTYXTn6TcPDwxEYGAi73Q65XA6pVFrvoqP9+/dHr169wLJstT4sLy8vREREIDg4GP379wdQ/bVqLW0+wBz3fMlkMvTo0QMRERENapfzPE+7XteiIZOYrVYrjh8/DoPBAJVKhaSkJHTr1q3ZymG1WnHo0CFkZ2fX2CcXHh6OAQMGYPr06Xj44YdrfA4SiaTeCZeOm5c9yb03XTt7vFwur7Pz3ZljWkObDzAA4pr206dPx+OPP97gb026barp9Ho9xo8fjxs3bsDf3x9TpkzBxIkTm3xeq9WKkpIS7N+/H7///nu1v5NUKkXPnj0xduxYTJkyBV27dq3SvCkoKEBRURE4jqPNgT1QuwgwAGITISwsrEXnpZCaVVZWik0Xx03HTb3/zmg0Ii8vD99//z2++uorWCwWMcCkUilUKhViYmLwzTffIDExscYvrrNnz6KgoAAmkwk5OTlNKg9pfe0mwEjbIggC9uzZg4ULF+Ls2bPVppZERETg1VdfxcyZM+Hj41PrQENAQAC8vLxgs9lQXFzcGkUnzYgCjHisBx54AP/6179qXKXBz88PHTp0qPc2q/79+yMpKQkdOnTA7NmzW7K4pAVQgLmxO3fu4Nq1a8jNzRWngMjlcvTs2RPdu3dv11M6GIZBhw4dqmzrd//vnZnaEBQUhP/5n/+BxWKpdzd54n4owNzU8ePH8f333+PMmTMoKCgQb2ORyWSIj4/Hn/70Jzz99NPiMHZ71Bxzr6RSqdO7CxH3QwHmZmw2G7KysrBgwQIcO3YMUqkUYWFhkEqlKCwsRElJCQoKCnDhwgVkZWXh888/R0REBN2zStol10+hJlXo9Xp8+OGHOHfuHHx8fDBhwgSsWrUKmzZtwrRp09C5c2coFApUVlbi0KFD+Pbbbxu0Qw4hbQkFmJvR6/XYv38/kpKSsGXLFixfvhwDBw5E9+7d8cknn2DNmjXo2bMngLs32a5duxaVlZUuvcGbEFehAHMjdrsder0e/fv3x4IFC/DAAw9ALpeLC+5JJBI8+OCDeOONNxAfHw9BEGA2m1FRUUEBRtolCjA3wjAMAgMD8Y9//APdunWrto0dcHfbrJEjRyI5ORlAy2yPRYinoE58NyKRSBASEoKQkJA6V3iIjIxEWFhYlccR0twsFgvS0tJw48YN2Gw2BAQEICEhAREREU26B1IQBOj1ely6dElcejo0NBRqtRrdunUTV/9wBgWYm3FmaRrHChmOm3R9fX3dYkkb0jZwHIeKigocP34c69evR35+PmQyGQwGA5KTkzF9+nR069atUbfk2Ww2lJaW4rfffsPSpUtx+/ZtcZWMkJAQjB07FpMnT0bXrl2d2smIAswDlZeXo7y8HF5eXoiLi0NgYCAFGGkWjtVst2zZgsWLF6NPnz74+OOPERQUhO+//x7Lli1Deno6/vnPfyIxMbHBK7uUlJTgm2++wfLly8EwDGQyGSQSCUwmE65fv4709HQcP34cX375JR544IF6pwfRu94D7d69GwcOHEDXrl3x9ddfu3xJE9J2GI1GHDhwAO+++y6io6PxwQcfIDk5GfHx8Xj99dcxfvx4nDlzBitWrMCdO3cadG6NRoNNmzbhyy+/RFxcHJYvX45du3Zh8+bNePbZZwHcbV6eOnUKx48fd2r9PgowD7R37174+fnhlVdeQZcuXaj2RZqFzWbDhQsX8N5770Gv1+ONN95A9+7dIZFIwLIs/Pz88OSTT0KhUGD79u3YtWtXg85/8+ZNHDlyBHPmzMFPP/2EMWPGICEhAcnJyZg/fz62bNkCHx8f2O127N69G5mZmfWek975Hmb9+vU4deoUBgwYgKeeeopqX6TZ3L59GytXrhS3TIuLi6uy3r9CocDAgQPh6+uLsrIy/Pzzz7h48aLT5/fy8sLo0aPx8ssvo3PnzlCpVJDL5VAqlQgLC8PQoUMxePBgKJVK6HQ6p/ZaoADzEDzPo6KiAqtWrUJERASmTp1aZSSSkKa6du0aTpw4AZ7n4efnV22JaIlEgsjISISGhkIikeDatWs4evSo0+fv2rUrJk2ahMjIyGqtBsfy13FxcZDL5QgPD0dQUFC956QA8xAmkwk//vgjzGYzZs6ciYceeojuf3QDjm3u7t074X6CILh8OzxnFBUVITc3V5zOU1MHPcuyeOCBB+Dr64vS0lLs2LHD6dWKvby86lzEUhAE2Gw2qNVqPProo4iIiKj3nDQK6QGsVivS0tLw2WefYe7cuRgxYoRbbaTaXjluvOd5HjKZDBERETVOLdDpdCgqKoIgCAgPD3d62otjV6GSkpJG78vAsixUKhUCAgLqPM6xuYnRaISXlxeio6Nr7Z5ISkrCzp07UVZWhrKyMpjN5iZvbsJxHAwGA27cuIEBAwYgOTnZqXNSgHmAM2fO4LXXXsPixYvx2GOPOTU/hrS8O3fuIDk5GRaLBVFRUfjmm28wcuTIasft2LED7777LgBg/vz5eOaZZ5yaQ2WxWHDq1Ck8//zzKCoqalQZAwMD8cILL+DDDz+sMzS1Wq24pLajOVfb8R07dhS/QCsrK3HmzBkMGjSoSROqKyoqsH79egQGBmLhwoXo0qWLU4+jAHNzf/zxB1avXo0ZM2bg0UcfrbazNHEtx45IdTWjHEFgtVobtKORXC4Xb+JvzJaA956jvveMyWRCaWmpU+dkWVY8n81mQ1lZWaPK5nDu3DksWbIEe/bsgUKhwK+//opnnnmGmpCe7uDBg9i6dSsGDx6MiRMnws/Pr9ob0WazIT09HWFhYQgICGi1DUXJXY6+r7r6wO7t/2rIfassyyIkJATjxo1r9K5Yjk1U6gsws9lcZY/PhnxJchzXoPLxPC+OYqalpeHUqVPIyMiARqMBy7JYvny5uEdnYGBgneeid7ub2r9/P7777jv07NkTAwYMEPsn7qXT6XD9+nVs2bIFr7zySpX9DknLcwQXgHoDzPEhr+u4mrAs2yr7UHIcV6WW5+zcwsYGq1wuR2xsLKRSKex2OyQSCS5fvgy9Xo+srCysWbMGCQkJSEpKqvM8FGBuxmKx4Ny5c3j33XdhsVgglUpRUlJS47H5+fk4ePAgQkJCEBERQRNaG4DjOBQWFtZaIwoKCoK3t3e9r6mjc70lamCOjvXbt2+LeyI0lEwmg1qtRocOHerdjdvZvtV7zyOVSuHt7d2gGhvLslCr1Rg5ciR4nkdKSgoyMzOxePFibNu2DXq9HleuXMGOHTvQt2/fOuc6UoC5EZvNhrS0NEyaNEncbPXq1at1Psbf3x//+Mc/0KFDBwowJznWUVuzZg2ys7NhsViqTHFgGAZjx47FkCFDxG3XXMFms+H8+fN46aWXav0Sq09AQACmTZuGefPm1RkyarUanTt3Fo+pa9Tz3sUEvL290a1bt0a/9xx7hCYkJODLL79EZWUl9u3bh4qKCqSlpaG8vBzh4eG1Pp4CzI1kZ2djzpw5sNvtCAgIcKp6HhkZieHDh1eZMU3q5vjgzZo1C/PmzcOOHTtQUVFR5Zht27YhKSkJb7/9NsaMGVPreaRSKaxWq3i7TU1YlgXLsuB5vkE1FUEQwHEcdDodtFqt80/wHo4bpet7L/n6+qJDhw5iH2pd5bxx4waMRiMkEgnCwsKqBF9jMQwDPz8/fPbZZxg9ejQyMjJgMpnqnY1PAeZGOnbsiFWrVjVoxEkqldJqFI3AMAxUKhXee+89JCcn47vvvsPBgwfF39vtdpw+fRqzZs3Cvn37MHfuXPj7+1d5ne9dTJLjuFonqgqCIAZIQ/qM5HI5BgwYgMOHDzd63wPHDuX1vT+kUimCg4Ph4+MDo9GIO3fu1NpsPXDgAMrLy6FUKhEVFdVs69FJJBJ06tQJoaGhyM7OrtLHWGu5m+XKzUQQBGRlZcFoNDa4s7M2eXl5sNvtsFgs2L9/PyoqKhq0BAhpHhaLRXztOY7DnTt3kJqaitLSUuTm5jZ6oibw/3tANvbvqtVq0bt3b2RkZCA/P1/8udFoxK1bt7Bu3TpkZmYiJSUFw4cPR2hoaJVr3/v/2jTmvcyyLHx8fBAfH9/gxzYUwzDo2bMn+vTpgyNHjiAzM7PaF6kgCOKyN0ajETExMXj88cebtRxSqRQKhUKcgOtRo5Acx2H16tW4desWNBpNk97UDrdu3YLZbIbdbsfmzZuxfft2mkflAoIgQKvVQiaTQavV4ocffsDevXtRWlqK/Pz8JgcYy7LV7t1rCI7jatzh2zHkv3PnTkk6dhcAABPVSURBVKSnp+PSpUt46aWXEBsbKz6ve/9fE8fvOI5r8nNtSZ07d0ZSUhIOHTqEiooKaLVa2Gw28YuB4zjk5OSgoqICDMOgd+/e6NevX7Nd33ErkdlshlqtRvfu3aFWq+t8jFsFGM/zSE1NRVpaGoqLi5t9uzC9Xt+s5yMN5wiKq1ev1jtA0RCOAGuKuporPM+joKAAR44cwcMPPywGWE0ctwAVFhbCbDbj+vXrsNvtsNlsuHbtGmw2G3Q6HaxWq1M3LLcWtVqNUaNG4fvvv0dJSQnOnz+PmJgYsYxWqxUXLlyA0WhEx44dMW7cOMTExFQ5h9FoRG5uLvLy8hAUFISEhIQam5iOQYB72e12XL58GUVFRejRowcef/zxepunbhVgDjzPQy6Xw9/fv10vF2Oz2cSOYlKdwWCAVqsFy7IICgpCXFxco/pjOI6DyWRCUVERCgoKqtWmpFIp/P39MWTIEHz44Yfo0aNHtXPYbDaUlJSgvLwcdrsd2dnZWLRoEby8vHDlyhXYbDZx0rFGo0FOTg40Gg0mTpzY6Off3ORyOXr06IFnn30WK1aswI8//oj+/ftDrVaDZVno9Xr88ssvsNvtePHFFzF69OhqfWsZGRl4//33cfjwYfTo0QM7duwQV68wGo0oLy+HIAji+mKO97bdbkdBQQE+//xz2O12PPfcc+jTp0+9ZXbLT4ZWq0VCQgL+93//Fw8++KCri+Myp06dgr+/P7p16+bqoril1atXY/78+WAYBiNHjsRnn31W52oHtcnNzcXSpUuxYsWKauHFsizi4+OxcuVK9OrVCz4+PjV2iBcXF+ONN97A2rVrMWjQIPz6668oKChAv3798Oqrr2Lbtm3Yt28f0tLS8NFHHyEjIwNTp05t9HNvKeHh4Xj77bdRUFCA3bt3Y+XKlXj77bcRGBiIHTt24LfffsNTTz2FiRMn1lh73Lt3Ly5cuACTyYT09HR8/PHH+OCDDxASEoLNmzdj9uzZ4HkeSqUSTz31lPj5Tk1NxX/+8x+EhISIwenMBF63DDBBEMTRk/ruom9rdDodVq9ejd9//x03b97E7NmzkZSURKOMNbh3AqVUKoVSqWzQdBJBEPDTTz9h7dq1OHfuXLVJph06dMCECRMwY8YMdO3aVdyj8/5z+Pj4wGKxQKPR4MSJE7h+/ToiIiKwaNEiPPTQQ1Cr1ZBKpTh+/DgMBgO2bduG6dOnN3sHeHNgWRahoaFYtGgRRo0ahe3bt2PSpElQKpVQqVRYs2YNBg0ahODg4Br7G6OiohAQEIDCwkLIZDI88sgj4gTZTp06oXv37jh58iR0Oh02btyIHTt2ICYmBkOGDME333yDbt26ibvPO9Of6ZYB5uDY0LU9cGxhtXTpUuzbtw9FRUWwWq3i/J/28jq0BscN2Nu3b8eGDRtQWFgIf39/+Pv7A7j7Wvft2xdPPfUUkpOTER0dXevrL5FIEBoaijfffBOCICAvLw+xsbFITExEYmKiGKhPPPGEOMquUqmQkpJS5wRNV5JKpejcuTOefvpp9O3bF7m5uTAYDOjUqVOVzZZrMnToUGi1WmRnZ6Nz584YMmSIWJPq06cPli9fjhs3bsBqtYJhGPj6+iI4OBhRUVHilIyGvNfdOsDaE71ej7Nnz8JsNleZN0RaBsMw8Pf3x/PPP1/ttWYYBomJiejUqVO9zRjHZNOkpCT0799f7Jy+vy8uMjISM2bMAMdx4sRWd/9SUqlU6Nu3r9gX5Ux5IyIiMGPGjBpfh8DAQAQGBlYZuWzqa0AB5iZ8fX3x7LPPYty4cXjttdfw+++/N/soLLmLYRjI5XI8+uijjT4Hz/PQarViLVmn09U7gOAILk/TkJCpKbybcr76UIC5Ccc3vdlsrrWjmLgPi8WCzMxMccI11Zhdgz4lbshut4sfCHdvZrRXFoulyqx9+ju5BgWYG7p3QiV9s7sns9mMvLw88d/0d3INakK6GY7jxPs3ATR4VIa0DpVKhYEDByI2NhaDBg1qlfsVSXUUYG6G53no9XqxFiaVSinA3JC3tzeGDRuGhQsXom/fvrRHp4tQgLk5Txhub48YhkFAQAAmTZrk6qK0a9QHRgjxWBRghBCPRQFGCPFYFGCEEI9FAUYI8VgUYIQQj0UB5uaaa3MTQtoiCjA3564bQBDiDijA3IxEIkF0dLS4VjjHcVQDI6QWFGBuhmEYcV88ALRUCyF1oABzE4IgwGAw4M6dOygsLBRv5i4qKkJWVla19doJIRRgbkOj0eDYsWPYuHEjCgsLERUVhbi4OFy6dAlbtmxBRkZGrVu9E9Je0c3cbqK8vBzl5eVITk7GqFGj4O/vX2WnaUefWE0bghJaj6u9ogBzE9HR0YiKigJQ8woUDMPQyhR1cGyu0dhRW8frSzyL2wZYYWEhdu7cibS0NFcXhbipkydPwmq1guM4HDhwAM8880yjduZmWRaDBw/Ge++91wKlJC2pUQGm0Wig1+ubfY6SzWYT94qrrKzE2rVrndqdl7RP5eXlsNls4HkeeXl5VZZ4dpZjFx2GYXDr1i2nH+Pr64vAwMAGX480L0ZoROfBzz//jD179kCv1zdrYXiex6lTp6DRaGAymWCxWKqsD09Ic3M0HaOjo/HQQw859RiZTIY///nPmDZtWguXjtSnUTWwixcvYtu2bSgpKWnu8lRD/RKkJfE8D47jkJWVhezsbKce4+XlBZVKRQHmBhoVYD4+PggJCaFwIR7LMUHY0QxVKBQICAhw6rEKhQIqlaqFS0ic0agmpE6ng9FopOYd8ViCIKCyshJTpkzBpUuXMGbMGKxYscKpxzIMA29vb/j5+bVwKUl9GlUDU6lU9A1EPJogCFAqlZDL5WAYBkqlEhEREa4uFmkgagMSQjwWBRghxGNRgBFCPBYFGCHEY1GAEUI8FgUYIcRjUYARQjwWBRghxGNRgBFCPBYFGCHEY1GAEUI8FgUYIcRjUYARQjwWBRghxGNRgBFCPBYFGCHEY1GAEUI8FgUYIcRjUYARcp9GbBNBXIQCjLQbHMfh9u3bKCoqqvUYnueRlZWF0tLSViwZaSwKMNJu2Gw2nDp1Clu3boXdbq9W0+J5HlqtFh9//LHTe0QS16IAI+1KTk4Oli9fjtzcXHAcV+V3RqMRe/bswa5du6DRaFxUQtIQFGCk3cnKysIzzzyD0tJSsRZmtVpx/vx5zJo1C1qt1sUlJM6iACPtiiAIsFgsuHTpEj777DPk5+cDANLT07FgwQKUlJRUq5kR99WojW0J8WSOENuyZQvMZjN4nkdOTg71e3kgCjDSLgmCUKWpaDKZXFga0ljUhCTtBsuyUCqVkMvltR7DMAx8fHzqPIa4Dwow0m7I5XIMGDAA3bp1q/UYlmUxZswYREdHt2LJSGMxAk07Ju2IXq/Hzp078dxzz4HjuCpzwaRSKTp27Ihff/0V8fHxkMlkLiwpcQbVwEi74uPjg6FDh2LmzJnw9vYWf84wDMLCwvDRRx8hJiaGwstDUICRdoVhGAQGBuKVV15Bly5dxL4utVqNESNGYNy4cfDy8nJxKYmzKMBIuyOXyxEbG4u//vWvCAkJgUwmQ0xMDF544QV4e3uDYRhXF5E4iQKMtEsymQwvv/wyhg8fjujoaDz//PMYNmyYq4tFGog68Um7dv78edy8eRMjR45EQECAq4tDGogCjLRrFosFgiBAJpNBIpG4ujikgSjACPEAVqsVeXl52L17N86cOQOJRILY2FiMGTMGsbGxzTbwYDKZcOvWLWzYsAHe3t549tlnERUV1SznbgkUYIS4OZvNht27d2PTpk2orKxEXFwcJBIJMjMz4eXlhfHjx2Po0KEICQlp9DV0Oh3S09Nx7Ngx7Nq1C6mpqejRowe++eYb9OrVqxmfTfOieyEJcWOCIODatWtYuHAh9Ho95s2bhwkTJoBhGBw5cgTz5s3DwoULwbIsRo8eDaVS2eBrWK1WpKamYv369Th+/DiuX78O4G5wujsahSTETfE8D71ej/feew8ZGRl47LHH8MQTT4BlWTAMg8GDB2PkyJHIz8/HggULcPHixUat528ymaDRaDBq1CikpKR4VF8gBRghbspiseDIkSM4d+4c/P39MXTo0Cp9XQzDYPz48UhISEBWVha+/fbbRgWYWq3GU089hb/85S8YNWpUlTsU3B0FGCFuyrE+v1arRXR0NMLDw6sdEx4ejvj4eBgMBhw9ehQmk6lRIcYwjPgfz/MAPGN3JgowQtyQIAgwGo04c+YMrFYrYmJioFarqx3n5+eH+Ph4MAyDsrIybNy4EXq9vtHX5TgOFoulKUVvVdSJT9oMQRBw8uRJFBcXIyoqCv379692DM/zKC4uxsmTJ8EwDJKSkhAREeH0NUpLS2E2m5tUzvDwcEildX/0bDYbbt++DaPRCABQKpVQKBTVjpPL5QgKCoJKpYLZbMaePXvw5JNPQqVSNapsgiDAbrc36rGuQAFG2gye57Fy5UocOnQII0aMwIoVK6odY7fbcebMGbz11ltgGAZLlizBmDFjnL7Gli1bcPz48UaXkWEYfPrpp/VOebDZbCgpKRH/rVAoal0hQ61Ww8/PD4WFhcjLy/OI0cPmQgFG2gxBEFBQUICsrCwkJCTUeAzP89DpdOL69waDoUHXuHz5Mvbv39/oMrIsK9aq6mK326tsrhsZGQlfX98aj5XJZFAoFOB5HuXl5R5Vg2oqCjDSprDs3W7d2ppoDMOI0wQcndYNsWTJEnz11VdNKqMz0xQ4jhODjmEYhIaG1hpg93J0wLcXFGCkTXGMnNX1QW7K6FprzZGyWq0oLi4GcDeM6+sza69LANEoJGmT6gopx+/ceZqATCZDUFCQ+O/6gtOdn0tLohoYaZNq+0A39YO+a9cuZGZmNvrxDMMgJSUF/v7+dR4nlUrFJiPP83V2zNtsNlitVvFx7ak2RgFG2p17Q6yhgbZ161b88ssvDXrsvTU+xz2L9QUYy7Jis9ExN8tut9fYlNTpdNDpdGBZFmq12qNuBWoqCjDSJtVVC7n3dw2prQiCgD//+c8IDg4Gz/PgOA48z9cbZDzPi/8BcKozXiqVIjIyEgzDQBAE5ObmorKyEoGBgdXKpNPpUFlZCZlMhk6dOrWrDUkowEib1BJ9QgzDYPLkyZg0aVKTrlFfhzxwd4JqVFQUpFIp7HY7MjIyUFpaWi3ArFYrysvLYbPZ4OPjgwcffLDGCa9tFQUYaXMEQRBrSDU1p5rShGyt5hnLsggNDUW/fv1w8eJFZGRkoKysrNpxer0e+fn5YFkWfn5+mDhxInx8fBp9XYlEAqVSCZPJ1JTitxoahSRtUl5eHk6fPl3t5/d3iDuakGazGRUVFa1WvvowDAMfHx88/fTT8Pb2RkVFRY0TYPPy8pCeng61Wo3Ro0cjMjKySsjyPA+DwYDMzEyn7nG8f56cu6MAI21SYWEhDhw4gPLycrH/qbS0FKmpqdizZ494nF6vh8lkQl5eHjZs2ODCElenVCoxatQoREVFwWQyobCwsEr4WiwW7Ny5Ezk5OejSpQtSUlKqjELyPI+ioiL88MMPePvtt7Fy5UrcunXLVU+nRVATkrQZgiCITUKNRoPNmzcjJCQE/fr1g81mw8GDB3HhwgUUFxeDZVnwPI/Dhw8jJiYGp0+fxuXLl/Haa6+5+Fn8P7lcjl69emHmzJlYsmQJfvvtN/Tu3RtdunSBRCLB1atX8Z///Acsy+K///u/MWTIkCqPd6wntmjRIty5cwcHDx5EZGQkOnfuXOP1HE1vB8cghTujACNtBs/zMJvN8PLyAsMwuHTpEmbOnImQkBCYTCaEh4dj1qxZGDRoEEaPHo2SkhL8+9//xs6dOxEYGIhp06a5+ilUI5FI8MILL8BoNGLdunX45z//ieeffx7e3t6YO3cuNBoNXnvtNYwbN67aY81mM7KyspCXlwdBEMBxHDiOq3acIAgwmUwwm83Iz88X+8FsNhtKS0tRWVkJqVTqlgsd0qYepE0QBAEGgwHDhw9HQEAAQkJCsHPnTjAMA6VSieTkZMycORNDhgyByWTCL7/8gvnz56OiogJKpRKjR4/G4sWL3XZvSJvNhnPnzmH16tU4dOgQOI7DiBEj8NJLL6FPnz6QyWTV+qx4nsfJkycxadIk5OfnY+DAgfjiiy+QlJRU5TiLxYLvvvsO586dA8dxYjPVMReNZVnExMRg7ty5rfZ8nUUBRtoEx3yoYcOGoWvXrnj//ffF6QQsy8LHxwcBAQHw9vYGx3EwGAwoLi6G3W4XJ4CGhISIN4O7I5PJhMrKSuh0OgiCAD8/P6jV6jq3VDMYDMjPz4fVaoWvry9CQkKq1aR4nodWq61znTOFQlFtCoc7oCYkaTMck0olEgmCgoJq3c9QIpHAz88Pfn5+rVzCplEqlVAqlQgLC3P6MT4+PoiPj6/zGJZl3bbmWR/3/bohpAE4jsPZs2eh0+nEOWCk7aMAI20Cx3H49ttvUVJSgpKSEnEpGtK2UYCRNoHneWRmZsJkMuHy5cu4cOGCq4tEWgEFGGkTGIZBdHQ0FAoFfHx8nLphmng+GoUkbQLP80hPT8f69evRv39/DB061C1HzUjzogAjbYbdbkdZWRm8vb0bva0Y8SwUYIQQj0V9YIQQj0UBRgjxWBRghBCPRQFGCPFYFGCEEI9FAUYI8VgUYIQQj0UBRgjxWBRghBCPRQFGCPFYFGCEEI9FAUYI8VgUYIQQj0UBRgjxWBRghBCPRQFGCPFYFGCEEI9FAUYI8Vj/B9YwmX8n2BvGAAAAAElFTkSuQmCC)
If force F is increasing with time and at t = 0 , F = 0 where will slipping first start?
![](data:image/png;base64,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)
physics-General
physics-
A force
acts on block shown. The force of friction acting on the block is :
![](data:image/png;base64,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)
A force
acts on block shown. The force of friction acting on the block is :
![](data:image/png;base64,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)
physics-General
physics-
Two blocks are connected by a spring. The combination is suspended, at rest, from a string attached to the ceiling, as shown in the figure. The string breaks suddenly. Immediately after the string breaks, what is the initial downward acceleration of the upper block of mass 2m ?
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)
Two blocks are connected by a spring. The combination is suspended, at rest, from a string attached to the ceiling, as shown in the figure. The string breaks suddenly. Immediately after the string breaks, what is the initial downward acceleration of the upper block of mass 2m ?
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJMAAADbCAYAAABp7qMUAAAgAElEQVR4nO2de3Ac9X3AP3t779Pp9LzT6fyQJVm2qAP4gU1jg00hEBoTWoiTljEZ2oYkkwzQaZo2TNOWdpI+puljknTcTGmaMpN0QggwYQqh2ICJnNhBtiyQ/NDDep8lne6l0+neu/3DvUVr8bTPOt/m95nxH7da//a3u5/9/h77299PUlVVRSAoAaZyZ0BgHIRMgpIhZBKUDCGToGQImQQlQ8gkKBlCJkHJEDIJSoaQSVAyhEyCkiFkEpQMIZOgZAiZBCVDyCQoGUImQckQMglKhpBJUDKETIKS8Z4yKYpCLBZjbm6OfD5PcZRvNptlZmaGfD6v7Ts5OUkymdTtMzQ0RDKZ1PZZWFhgaGgIRVEAUFWVhYUFpqenKRQKuv0SiYS2XzH9WCympZ9Op+np6WFxcVHbJxqNMjk5qe2Tz+eZnJwkkUiwdIRyOBzWHQ9gZmaGXC6n/U4mk3R3d5NKpbRt4+PjnD9/XvtdKBQIh8MsLCzortnk5KT2W1VV7Xql02lteyqVoq+vj0wmo+03MjLC/Py8Lv1oNKrLQy6XY2RkhKttxPX7ikyFQoGzZ8/qLnQqlWJsbEx3Q2ZmZjh37px2koVCgf7+fp1MhUKBc+fOkclktP0kSeLYsWMUCgVtWzgcJhQK6dIPh8MMDQ1pv/P5PMeOHdPlK5PJMDU1RS6X00k9MjKiO6exsTGy2azuhpw7d465uTld+gcPHiSbzWrbQqEQ09PTurRyuRxTU1Pab1VVOXXqFJlMRnsYCoUCQ0NDxONxbb9sNktPT4/2QKqqSiQSYWxsTJdWOBwmEolov1VVpa+vb9nDVm7eUyaTyURtbS2JREJ38SVJIp/P6yJTY2Mjg4OD2j6KopDL5XQ322Kx0NDQQDQaRVEUJEnC5XKRSqV0F8ZqtRIOh3XpOxwOgsGglr6qqsiyrIuGbrcbm82mPe2yLLNmzRri8bhOHIvFwvz8vO6YhUJBF1Hy+TypVGrZOS59OEwmEy6XS7cPgMfjYXx8nEKhgCRJWK1WYrGYTiZFUbRrVLymgUCAiYkJbR9VVVEURXfdJUnC7/dz7ty5ZcctJ+8rMplMJu2JWLotk8noihibzaa7sWazmebmZuLxuHbSNpuNhoaGZU+VLMu6IsDhcDA+Pq4TsZiPIlarleuvv55QKKRtt9vtmM1mLcpJkoQsyxQKBd3xqqqqOH78uO6YkiTpihOr1Up7e7smJoDX6112AyVJIpfLaRHMZDLR1NTE8ePHtW2SJC27rlarlTVr1ujyUF1dvUxWu91OPB7X9jObzQQCAUZHR5cV1eXkfVfAq6qqdDdNlmVyuZzuQsuyjNVq1W6k2WymtbWVYDCobZNlGbPZrKt/ATQ3NzMxMaETcX5+Xnex7HY7TqdTK8LMZjMbN25kZmZGE0WWZUwmk67IlCQJk8mkiwrV1dX09/frijCz2YzJ9NYlsVqtbN26lVgsptt2cfpms5l0Oq3tJ0kSVVVVTE1N6cRzu93LonQgENAJXMx/sYiUJAmPx8PMzIy2X/EBSafTlVXMFWlqamJgYEAnQDFMF7HZbPj9fq0Ik2UZn8/HwsKC7qLKsqyrTxTTHx0d1aUvSZJuH4/HQ11dnRb9ZFnG7XbrigFAK1IuLjbHx8d1gl1czNXV1ekiiNVqZf369boHRpIk7HY7kUhEu9kWi4VEIkEoFFp23ZYeb82aNVrdp3gdHA7HMum9Xi8TExMUCgWtGA2HwzrpJEnCbDZXpkw1NTXMzMy89R9NJqqqqsjn81r0sNvttLS0MDc3p51kUYiLb/bMzIzuJtntdl24N5vNtLS06FpdTqcTl8ulq7wXSaVS2jan06lVgItYLBbC4bD2W5Zl6uvrdZGvubkZs9ms/S7e3KXnCBekO3bsmJZ+MVItjXJWq5W1a9fqijmfz0cikdDlu/hgFfeTZZmWlhZOnTqlq0tdLI3NZqO+vl4X6crN+5apWPEriiHLMqtWrSIUCmlFltlsxuFwLIs6tbW1zMzMaDfbarXq6lHw9kXkxo0bmZiY0BVhxeJ1qUw1NTW6irPT6WR8fHxZ3eZiobds2UIkEtFJKMvysuiYz+d1RVhtbS1nzpzR3Uir1ao7lsVioaOjQyeP2WxGkiRdfc7pdBKJRLR6UjESFSPf0mu4NC2r1YrH49EJXG7et0xms5n6+noWFhY0mQKBALFYTLu5xSf54spuIBBgaGhI1wrL5/O6fRwOBw0NDVr6ZrOZpqYmksmkbj+LxUIsFtNFCpfLxdTUlE6CVCql26coSjEtm83Gli1bdH06xbrIxd0W2WxW17dUTH9pvnw+n64xYrVa8fv9OuGKLdeiKEuLsKX5KO67NA9tbW26B8ZkMi0TuNy8b5kcDgcbNmxgenqafD6vldlLK6JwIXosLCzoipjq6upldYW6ujrdDXE6nXi93mWtvGK9bGn0GBwcXFbxX/qEmkwmnE6nLv8+n09rwi+NChdHL5fLRU9Pj1bkFiPJ0pttNptpaGjQFeWrV6/W1WmK+VharzSZTPj9fnp7e3Utv1wupxPfYrHg9Xp1xZzP59MV08W6WjqdvmqKuvctk8ViwefzEY/HKRQKWvSRZVmLFMUKYyKRYHFxUbcfXOjcK4q4bt06rfOyuK0YFYp1lEKhQHV1NcFgUNtmsVg4f/48mUxG22dp8ZfP5zGZTHR0dGg92oVCAZfLhclkIpvNanlSVZVcLkcikdDScrvdvP7666TTaQqFgiZf8e/F4/3ar/2aVp/L5/PYbDby+byWh6XXonjNFEWhpqaGkZERLR+FQgGr1ao7H5PJRGNjIwsLC9o2uNAPVrw+qqpSXV3N5OTkMonLhfm9d7mAyWRClmUArWgrbn/99dfZvHkzsiyTSqU4f/48k5OT2lMfjUbJ5XIMDw9TVVUFXJDzzJkzNDc3Y7PZkCSJUCjE4uIisixjsViAC0Vid3e31mQutpqCwaB2EZPJJIuLi4yMjOBwOFAUhYaGBs6cOYPT6dSa+3NzcwSDQex2u9Zqi0ajvPHGG6xZs0Y7t4GBASYmJqipqQEuFGmRSETr5S5KMTY2ht1uBy7c6FgsxsjICDabDbjw8Jw7d45CocCqVau09GdmZpiamqKqqgpFUbBYLPT39+NyuYC3OkuDwaB2DbLZLLlcjtOnT1NTU6P1bQ0MDNDW1kZ1dfUHue9XBOmDTKmTy+WIRqP87d/+Lc8884z2VBYvSLFIyGQyWCwWTYhcLqfbp0ixaV282cUIIMuytl+x191qtWqV4VQqhd1u19JfmoeL0y7+K6avnfj/bys+FEvzuri4iNPp1LYVi7yiOMUO3IvTLm4rpl+UoNgDXkw/k8lonavF6AhvVeKLvd4mk0lLrxhJl56TJEm0t7fz+OOP09ra+n5v4xXjfUcmeKuu4PV6WbNmzbImf6UwMjJCJBIhEAjg9/t1ElYSsizT0dGhSV5uPlBkKjI5OUk4HK5IkQD+5V/+heeee47PfvazfOxjH9OK3kqj2DpctWrVVSHUB4pMRfx+P16vt9R5WTHq6+u1rocNGzbg8XjKnaVLxmQy6V4BlZNLkqnYeqpUinUys9mM1Wq96vprKpWrQ2mBIRAyCUqGkElQMoRMgpIhZBKUDCGToGQImQQlQ8gkKBlCJkHJEDIJSoaQSVAyhEyCkiFkEpQMIZOgZAiZBCVDyCQoGUImQckQMglKhpBJUDKETIKSIWQSlAwhk6BkCJkEJUPIJCgZQiZByRAyCUqGkElQMoRMgpIhZBKUDCGToGRc0pQ6paK4kM9KTxpWnLYwl8uRTqdXdEqd4tygS6daNApllWl4eJhIJLJsqa4rzfnz58nn84yOjtLd3a1NTLoSFBffaWpq0q2GYAQuaRrCUvEXf/EXnDx5ctmaKVea8+fPk0gkaGhooLq6esVuqsfjwe/3s2/fPvbu3btsrvJKp6yPxtTUFIODg2SzWRwOx4pNp9fc3Lwix1mKqqqcOXOGkZERbrrppqtqnbhSUVaZ0uk0yWSSf/zHf2T37t1XxSSfVwJVVUmn0zz00EMcPny4Ymcpfi/KXmhLkoTD4aCqqsqwMsGFaa+L834blbLLBG8txXW1zBpbai6egN6oGPPuCcqCkElQMq6KYu6DoqoqiUSCubk54vE4uVwOu91OdXU1jY2N2O32ip6nvFKpOJmKC9c8++yzPPvss5w6dYp4PI7P52PDhg3ce++93Hnnnbjd7nJn9VeOipMpEonwjW98g+effx6Ajo4OhoeHCYVCnDt3jhMnThAMBvnCF76wbBUpwZWlomRSFIWBgQGOHj3Krl27+O3f/m02btxIJBLh6aef5oknniAYDPKDH/yAvXv3snbt2opdsakSqSiZstksk5OTfOITn+B3f/d3qaurA2DVqlU0NTXR3NzMX//1XzM2NkZXVxc+n0/ItIJUVGtOURR8Ph979+5dtqxXXV0dn/rUp9i1axf5fJ4jR45cNcuN/qpQUZHJYrFw4403aku6L8VsNuPxeNi4cSOHDh3SrUqpqirJZJJYLMb4+DirV6/G6/USiUQIBoPMz8/jcDjo6OjA4/EgyzLhcJjJyUlmZ2eprq5m7dq1NDU1leO0K4aKk+m9KC5Zetttt2G327X3Yi+//DLPP/88r7zyCg899BB33XUXBw4c4LXXXmNycpKqqio+//nPs3//ftxuN08++SRPPvkkfX19NDc3c8899/DVr35Vt9SpQE9FyfReqKrKyMgIq1ev5sMf/jB2ux1FURgcHCQUCtHd3c3o6CinT59mdnYWp9PJ5z73OZ566in+93//l29/+9vIsszAwACRSIT77ruPxcVF/umf/on/+I//wO/386lPfaqiFzu8khhGpnQ6zblz5xgbG+POO+/E5/NhNptRFIWOjg4KhQJ+v58TJ04wPj7OHXfcwa//+q9jsVhobW3lzTffJBgM8t///d/cdNNNPPzww9TV1WEymRgfH+d73/seBw4c4M477xQyvQMVVQF/N+bn5/nWt76F3+/n4x//uLbauCzL2O12fD4fgUAAgG3btnHHHXfQ2NhITU0NnZ2d3HvvvVgsFmpqavj6179OW1sbtbW1eDwerrvuOtxuN4ODg8zMzJT5TK9eDCFTPp/n7Nmz/PKXv+TBBx9kw4YNy+o1FosFm80GgMPh0I2utFgsbNiwAYvFgt1uXzZ6oaqqCqfTiaqqLC4uXvkTqlAMIdP4+DgHDx7kD/7gD9ixY8fbjotaWnG+eDiIyWTCarW+4xCYSl+TeKWo6DqTqqrk83meeOIJ7HY7n/70p3G5XKK1VSYqWqaFhQV+8pOf4PF4eOCBB3A6nUKkMlKxMkWjUX7+858zNzfHAw88gMfj0YopVVUpFArk83ksFosoolaIiqszKYpCNpvl1Vdf5ezZs9xzzz3YbDZyuRyZTIZMJsPi4iJjY2M888wz2lcg7zb2WlXVdx3kr6qqocdul4qKi0zz8/P85Cc/4fvf/z633HILzz777LKK89TUFE899RR//ud/rrXacrkcuVzubdMsFAosLi5SKBTe9u/v9n8Fb1FRMiUSCV544QX+9V//lUgkwtDQ0Nu2wBRFweFwsH37dgAWFxcJBoOcP38et9vN7OwsExMTBAIBstkswWCQ1157DYvFwuLiImfOnGH16tVYrVbC4TBDQ0OkUimcTifj4+OEQiEaGxtX+vSveipOpmg0yu7du9+12LFarXR2duLz+VBVlbGxMfr6+mhvb6eurg6n08kvfvELPvaxjxGPxzl58iSNjY3s3bsXt9tNV1cXN954I62trRw5coR0Os3tt9+OyWQiGAzS29vLbbfdtoJnXhlUlEyNjY088MAD71nkSJKE2WzGarUiyzIdHR20tLSQz+cpFAqYzWYsFgtWqxWHw8G9997L3r17UVUVk8mk/U2SJPbu3cvtt9+uFYEWi0WMkXoHKkqmS72RsizjcDje9m/FjyPf6QNQm82m9ZwL3p2Ka80Jrl6ETIKSUfZirlAokEqlWFhYMHTzO5VKkc/nDd1DX3aZstksXV1dhMNhw1Zsi9/6TUxMGHtyjnIevKqqCqvVyn/9139RKBQM/dQWhw93dHSUOytXjLLKtHv3bmpra1d8Xsviq5hdu3axfv36FZvTUpIkGhsb2bJliyFbiGWdhjCXy5VlBrU//uM/5sc//jF/8zd/w1133bXss6krSbEPTEyQWuqD/38fTzmQZZnq6mrsdntZ6jFGEwnKLFO5LmgxGtpsNvHpUgkpe2vuSqMoCoVCgUwmQy6XQ1EUkskkuVyOWCxGKBQim81q47+NNp3ySlLWOtNKkE6nGRkZ4aWXXuLFF19kbGyM0dFRMpkMVquVmpoarr/+ej7ykY/wm7/5m6xfv15EqkvE0DIlEgmOHDnCN7/5TU6ePImiKNTX1xMOh0kmk3R2drKwsEA0GkVVVe6++27+9E//lNbW1nJnvSIx9OuUoaEhvvnNb3L48GGsViv79u3j8ccfZ+fOnXR2drJ7927uuusuNm3aRDabZWRkhKmpqXJnu2IxdAXhueeeo7u7m61bt/JXf/VX7NixA7PZzE033cTf/d3f0dXVRV9fH+l0GrPZzDXXXGPoTsUrjaFlGhwcZPXq1Tz66KNcd911mEwmkskkW7du5cEHHySdTrNp0yY8Hg9tbW3ccsst2pxPgg+OoWXyeDzE43FOnz5Ne3s7x48fp6uri6GhIbLZLMlkEq/XS21tLTfccAPNzc2GnYt8JTB0BfyHP/whjz76KNPT03g8HhKJBIVCAYfDQVNTE3NzcywsLKCqKrIs86UvfYmHH36Y+vr6cme9IjF0ZKqvr8fj8TA6OkoqlcJsNtPa2sott9xCe3s78XicoaEh+vv7yWazxONxIpGIkOkSMbRMfX19TE1NUVtbC1zocY/H47z88sucPXuW+fl5rQOzGLFEnenSMbRMhw8fxuFw8OUvf5kNGzbwwgsvMDAwoI2d8vv9uFwu6urquP7667n33ns18QQfHEPLpCgKAC0tLTQ2NvLRj34Up9PJ6dOnyeVyuN1uAoEAbW1tbNmyBbPZLCrgl4GhZdqxYwe//OUv+epXv8r27ds5cuQI8XgcVVWpr68nFouhKAoWi4Xa2lr+5E/+hLvvvvsdv2QRvDvyY4899li5M3GlsNvt9Pb2cvz4cXp6epifn6euro6dO3eya9cuWlpakCSJaDRKNBrVXrH4/f5yZ70iMXRkikQizM3NIcsy+XyeXC5HPB5neHiYbDZLNBrVpm5WVZXa2loaGhrKne2KxdAyHTp0iJmZGW677TbWrl3LoUOHiMfjDA4OMjs7SzweR5Zl3G43nZ2d/P7v/76ISpeBoWUKhUJce+21fOc736G+vp5QKMShQ4c4fvw4sVgMs9nM+vXrufHGG/nwhz+MxWIRFfDLwNA94I888ggvvPACd999N42NjXR1dREMBonFYjgcDhYXF3E4HNTU1NDW1saDDz7I9u3bV+wDA6Nh6Mi0Y8cOfvSjH/Fv//Zv2ihLi8WCx+OhuroaRVGYmZlhdHSUkydPYjKZaGlpYdWqVeXOekViaJmam5vx+/1MT0+jqio2m42WlhY++tGP0tnZSTQapbu7mzfeeINkMkk2myUcDguZLhFDy3T06FFmZ2e54YYbcLvdDA0NEQ6HefLJJ/H5fESjUTKZDGazGZ/Px1133UVbW1u5s12xGFqmvr4+Ghoa+PrXv05NTQ1jY2O89tprnDp1ilQqRVNTE2vWrOGGG27g5ptvpr29fUW/oTMahm66eDwecrkcb775JqFQiNHRUbLZLE6nk7q6Ompra5Flmenpafr6+kgkEuXOckVj6Mi0Z88eXnrpJb7xjW/gcrlIJBLk83mqqqrw+/1Eo1Gy2SyKomCz2RgYGOAP//AP8Xq95c56RWJomXw+Hz6fj2PHjjE7OwtcWDHz1ltvZdOmTaTTaQYHB+nv7yedTpNOp4lGo0KmS8TQMnV3d3PmzBkCgQCNjY1MTEwwNzfHf/7nf2rv5WZnZ0kmk9jtdn7nd35HvE65DAwt05EjR6itreU73/kOXq+XZDLJxMSEtrZcLBbD6/WyZs0atmzZwnXXXSfWkrsMDC1TcR6BbDZLLBZjdnaWgYEBRkdHMZlMrF27Fr/fz9q1a6murkaWZfE65TIwtEzbt2/n4MGDfP7znyeXy3H+/HltHqiGhgai0SiFQgG73c66det45JFHuP/++8V4pkvE0DJt2bKF9vZ2ent7tTHeN998M3v37qWmpoazZ8/S399Pf38/qVSKrq4ubrjhBjZv3lzurFckhpZpZmaGWCzG+vXricVipFIpjh8/Tj6fZ926dczMzDAwMEAoFNKWXxV1pkvH0DK98sor2Gw2vva1r2m93729vXR1dXHixAlisRi1tbVs2LCBG2+8kf3794tJKy4DQ8sUjUaJx+Ok02l27NhBU1MTDQ0N9Pf3k0gkWLVqFatWraK9vZ1du3axevXqcme5ojH0eKYDBw7w93//98iyzPXXX09vby+JRAKTyaS96M1ms8iyjMvl4itf+Qr33HOPKOouEUN/UGCxWOjr66O7u5vTp08Tj8dxuVzcdNNN7Ny5k7Vr12IymYjH49p6c9dcc40YunuJGLqYCwaDnD17Vrf6dzgc5qc//ak2dDeTyWhjnerq6kRRdxkYWqZXX32VVCrFvn37uO2223jjjTeYmJggHo9jtVpJpVI4HA48Hg+dnZ188pOfFF/0XgaGrjPdf//9TE1N8fjjj+P3+5EkiWQySTAYJBwO43A48Pl81NTU4HQ6xRe9l4mhI5PT6aS/v5/HH3+cW265hcOHD/Ozn/2M4eFhqqqqiMfjuN1u2tvbufXWW7nvvvvw+XxCqEvE0JHphz/8IX/2Z39GJBLBbreTTqdJpVL4fD4CgQCJRIJ4PE4qlUKWZfbt28ejjz4qKuCXiKEjU0tLC6tXr2ZsbIxEIoGqqkiSxPr169m+fTt2u53+/n56enq0jwnOnz8vZLpEDC3T66+/Tn9/P01NTVRXVxOPx4nH4/z85z/X5mdSVRWr1Yrb7Wb37t10dnaWO9sVi6FlOnHiBI2NjXz5y19m06ZNnD17lt7eXiYmJrQ14Gpra2lubmbz5s3s2bNHjBi4DAwtk8ViwWazUV9fj8/nY35+nqmpKW1uy0KhQH19PV6vl0AggNVqRVEUUQG/RAwt09atW3nuuef4vd/7PWpra4nFYuRyORwOB16vl2g0SiqVolAoIMsyX/ziF3nkkUdEX9MlYmiZ2tvb8fv99PT0EA6HgQtLg3V0dPChD30IRVEYGhpieHiYQqHA2NgYs7OzQqZLxNAyRaNR5ufncTqdSJKEoihIkkQ4HNbqTel0GqfTST6fp6WlRUyQehkYWqauri7sdjt/+Zd/ybZt2zh06BADAwNMT09jNptZWFjA4/GwceNGdu7cySc/+UkxYuAyMLRMmUyGhoYGNm3ahM/n4xOf+ARjY2NMTk4SiUSQZRm/309zczPr1q3DarVqL4QFHxxDy+T1ennqqaf42te+xs6dOzlz5gzT09Mkk0lcLhcLCwtYrVaqq6tpbW3ls5/9LNu3bxcLGF4ihr5qd9xxBy+//DKvv/46PT09mEwmzGYzq1evxufzYTabiUQihEIhBgYGKBQKNDY2sn79+nJnvSIxtEzJZJJMJqN9D6coijZts8/nw2KxkMvlWFhYwGaz0dDQIGaNuwwMLdNLL73E8PAwe/bs4SMf+QhHjx7l6NGj9PT0MDw8TCQSQVVV3G43W7du5dOf/jSBQKDc2a5YDD1qoFjh/t73vkdzczOyLJNOpzlx4gQnTpwgmUzS3NxMS0sLzc3N2vxMYo3eS8PQkSkQCHD06FEOHDjA5z73OdatW0djYyMLCws8/fTTeDweJiYmcLvd+P1+PvOZz3D77bfjdDrLnfWKxNAfFCiKwmuvvcbLL7/MuXPn8Hq91NXV8e///u8MDw/j9/u1aXVOnTpFLpdj27ZtYiaUS8TQbzR37drFQw89RENDA4cPH2b//v3cfffd/M///A/j4+NYrVZcLhdWqxW73Y7JZKJQKJQ72xWLoetMiqIQj8d56aWXePHFF+nt7WV+fp7p6WmtG0CWZa1j85577mHPnj24XK5yZ70iMbRMSwkGg4RCIRYWFvjKV75CX18ff/RHf0RnZyfr16/H7/dTU1MjugYuA0NXwJfi8/loaGhAVVV8Ph9jY2N8/OMfp62tDZvNhslkEuOYLpOyypTP58nn8yt+3KXBWFVVbaDcSiBJkvZRqNG6IMoq05kzZ5iZmdG+ql0pZmdnSafTHD16lLGxsRV7uStJEjabjba2NgKBABaLZUWOu1KUtc70xS9+kaNHj3L27NkVlSmbzaKqKhaLBUmSVixCSJKkjUm///77cbvdK3LclaKskWlxcZF4PM6tt95Kc3Ozod/W5/N5XnnlFeLxuLYokNEo693L5XJkMhnuu+8+du/ejc1mK2d2rijpdJpwOMyrr766olF4JSmrTKqqYjKZcLlcVFdXY7fby5mdK4rVajV05IWrpGtAkiRDN82LXxIbrfV2Mca8e4KyIGQSlAwhk6BkGFami1tMqqq+ayvKqC2slcSQMhVfkSzty1EU5R1f3SiKQjqdNmTfz0pyVbTmSkGhUCCTyTAzM8PPfvYzXnjhBb7whS+wadMmnn/+ebq6upienqajo4PPfOYztLS0oKoqx44d48c//jGDg4Ns3LiR++67j61bt5b7dCoSw8ikqipvvvkm3/72tzl8+DDBYJDf+I3fYGpqiu9+97vMzc0RCoU4ePAgs7OzPProowSDQf75n/+ZyclJYrEY3d3dTE1NceDAAaqqqgz37uxKYxiZJEmitbWV3/qt3+Lw4cMoisLBgwfZtm0b3/rWt7Db7Xz3u9/lH/7hH3j11VeBC59CPfjgg2zevFTIHWEAAAK6SURBVJmpqSkefvhhXnnlFX7wgx+wf/9+8an4B8QwdSaTyURdXR1+v1/7XOmaa65h//79tLe3EwgE2LdvH4FAgHA4zOLiIo899hh79uzB6/Vy3XXXcfPNN7O4uMjTTz9NMpks8xlVHoaRqThOqKqqitraWiRJYuPGjXi9XqxWKzabjcbGRq699lry+Tz19fV0dHRoxZnNZiMQCKAoCr/4xS9Ip9PlPqWKwzAyFSm+mln6u4gsyzidznccv1T8f6lUSrTsLgHDySQoH0ImQckQMglKhpBJUDIMJ5OiKBQKhbd916aqqjb+++14r/d3gnfHcDKlUini8bjWilsqRy6XY2xsTPusaak8qqoSj8fJ5/NIkiTEugQMI1Mul6O3t5fu7m6SySSBQIAXX3yRn/70p2SzWUZHR/nRj37E4uIiPp+PoaEhnnjiCaampojFYjz99NN0d3fj9/tZtWoV3//+9+np6Sn3aVUUhnmdAuB2u9m2bRvXXHMNiqLgcDioqanBZDLhcDjYtWsX1157LXBh9QKXy4XdbkeWZVpbW/nSl75ENpsFwOVyiWmcPyCGkclisdDa2vqOS8n7fD58Pt87/v/Nmzdfqaz9ymCYYk5QfoRMgpIhZBKUDCGToGQImQQl46ppzRm5k7B4bkY9vyJll0lRFDKZDOl02tAX+1fh65eyyiRJEqlUimeffZaTJ08adgC/qqrk83lOnz5t6DWAyyqTw+FAlmWeeeaZskxHuNKYTCY2bNiA2Ww25CQWZZ057vDhw4yOjmoL5BgdSZKw2+186EMfoqOjw3Az+5ZVpkwmQz6f/5UQqUhxmTKz2Wy4KYR+ZeYBF1x5jPVoCMqKkElQMoRMgpIhZBKUDCGToGQImQQlQ8gkKBlCJkHJEDIJSoaQSVAyhEyCkiFkEpQMIZOgZAiZBCXj/wCpkge+B1NOrAAAAABJRU5ErkJggg==)
physics-General
physics-
A particle of mass m is constrained to move on x-axis. A force F acts on the particle. F always points toward the position labeled E. For example, when the particle is to the left of E, F points to the right. The magnitude of F is a constant F except at point E where it is zero. The system is horizontal. F is the net force acting on the particle. The particle is displaced a distance A towards left from the equilibrium position E and released from rest at t = 0.
![](data:image/png;base64,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)
Find minimum time it will take to reach from
to 0.
A particle of mass m is constrained to move on x-axis. A force F acts on the particle. F always points toward the position labeled E. For example, when the particle is to the left of E, F points to the right. The magnitude of F is a constant F except at point E where it is zero. The system is horizontal. F is the net force acting on the particle. The particle is displaced a distance A towards left from the equilibrium position E and released from rest at t = 0.
![](data:image/png;base64,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)
Find minimum time it will take to reach from
to 0.
physics-General
physics-
A particle of mass m is constrained to move on x-axis. A force F acts on the particle. F always points toward the position labeled E. For example, when the particle is to the left of E, F points to the right. The magnitude of F is a constant F except at point E where it is zero. The system is horizontal. F is the net force acting on the particle. The particle is displaced a distance A towards left from the equilibrium position E and released from rest at t = 0.
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)
Velocity – time graph of the particle is
A particle of mass m is constrained to move on x-axis. A force F acts on the particle. F always points toward the position labeled E. For example, when the particle is to the left of E, F points to the right. The magnitude of F is a constant F except at point E where it is zero. The system is horizontal. F is the net force acting on the particle. The particle is displaced a distance A towards left from the equilibrium position E and released from rest at t = 0.
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)
Velocity – time graph of the particle is
physics-General
physics-
A particle of mass m is constrained to move on x-axis. A force F acts on the particle. F always points toward the position labeled E. For example, when the particle is to the left of E, F points to the right. The magnitude of F is a constant F except at point E where it is zero. The system is horizontal. F is the net force acting on the particle. The particle is displaced a distance A towards left from the equilibrium position E and released from rest at t = 0.
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)
What is the period of the motion?
A particle of mass m is constrained to move on x-axis. A force F acts on the particle. F always points toward the position labeled E. For example, when the particle is to the left of E, F points to the right. The magnitude of F is a constant F except at point E where it is zero. The system is horizontal. F is the net force acting on the particle. The particle is displaced a distance A towards left from the equilibrium position E and released from rest at t = 0.
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)
What is the period of the motion?
physics-General
physics-
A weight can be hung in any of the following four ways by string of same type. In which case is the string most likely to break?
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)
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)
A weight can be hung in any of the following four ways by string of same type. In which case is the string most likely to break?
![](data:image/png;base64,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)
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)
physics-General
physics-
A stunt man jumps his car over a crater as shown (neglect air resistance)
![](data:image/png;base64,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)
A stunt man jumps his car over a crater as shown (neglect air resistance)
![](data:image/png;base64,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)
physics-General
physics-
In the figure shown the velocity of different blocks is shown. The velocity of C is
![](data:image/png;base64,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)
In the figure shown the velocity of different blocks is shown. The velocity of C is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANYAAAEMCAYAAAC4MUjTAAAgAElEQVR4nOydeXxTVfr/P9nTZmnTNN33hW6UtUDBIoKCQBV3xUFmRlEc10GdGXVwdEb9jiP+dEbHcUNFdFiVzYVVENmptqVQutCWLmnTpm3SJM2ee+/5/cE3+aq9AYpNUup9v168BO927s35nOU5z3MeHiGEgIODY0jhh7oAHBwjEU5YHBwBgBMWB0cA4ITFwREAOGFxcAQATlgcHAGAExYHRwDghMXBEQA4YXFwBABOWBwcAYATFgdHAOCExcERADhhcXAEgGEhLIqiYDQa4XK5BhwjhMDj8cDpdMLj8Qw4zjAMDAYDbDab3/vb7XbY7fbzHqNp2u9xi8UCtiAAt9sNp9MJiqJYj9vtdvT09LDem2EYUBTl91qHwwGtVsv6TYD/+y4Mwww45vF40NnZ6fedAcDpdMLtdrOWq6+vDw6Hw++1NpvN7/emaZq1TF5MJhP0ej3rO3u/icfjuaTv6fF4YLPZQFGU3+cHi2EhLI/Hgy+//BIWi2XAMYqioNVqsWnTJlZh0TSN/fv3o7GxkfXeDMNgy5YtaG5uZj2u1Wrx9ddfg6Zp1h+zoqIChw4dYr3WbDZj165dsNvtrNdqtVp88MEHrD+00+nE999/j/b2dtaK2N/fj7/85S+sFZimaXR3d6O8vJy1kjmdTrzzzjvo6OgYcIwQAoqisH//fjidTtZ779q1C8eOHWN9Z0II9u/fj87OTtbjFosF7777Lus7EUJw9uxZbN++nfVat9uNL774AkajkfV7mkwmrF27lrXcFEWhsrISJ06c8NtIBpNhISyKotDd3c36QRwOBw4ePIjo6GjWawkhaGlpYT3GMAzsdjsaGxsRERHBek5dXR0MBgMEAgF4PN6Ae9fX1yMmJob1Wp1OhzNnzkAoFLIeb2trQ1xcHGslMRgMKC8vh0gkYr22q6sLYWFhrNdarVaUl5dDKpUOKDNwTpTV1dXg8wf+vF5R8vl8hIWFDTjudruxa9cu1ncihICmaZjNZqhUKtZyV1VVQSAQsD6bEIIzZ874/v5Tenp6oNfrERMTM+B6hmHQ2tqKpqYmVtG6XC60tLQgNzfX7+8RTEIuLKfTia6uLqhUKkgkkgHH3W43KisrMWrUKIjF4h8dI4SAYRjQNM36Q3s8HlRVVSEuLg5yuZz1+SaTCWq1mvWH1Ol0sNvtSE5OZr22r68PDMOwVnCn0wm9Xo+pU6dCIBCwPreurg5KpXLAswkhsFqtmDNnDqRSKetz9+zZw3otcK6STZ06lfWd+/v7sWXLFigUCtZy0TSNuLg4aDSaAcfcbjcqKiogEon8NlSVlZVQKpWsx2iahtVqxbhx41gbhDNnzoCmadZjNE2jo6MDRUVFrI1RT08Penp6/H6TYBPyElitVhw6dAjZ2dmswnI6neDxeJDL5QNaIpfLhaamJqjVaigUigHXejwenDhxAllZWawVlBACk8mEpKSkAT8mwzCoq6tDZGQk5HI564/d0tKCtLQ08Pn8Acc7OztBURTi4uJYK3B3dzdkMhmrKK1WK3p7e1FUVDSgMfEeb2pqQkRExIBrPR4PzGYzpkyZwvpN7HY7vvzyS6hUKtYe2u12Y/To0VCr1QOudblc2LFjB9Rqtd8ezWQyITY2dsAxhmHQ29sLu92O7Oxs1mfrdDrWXhQ4Vw/a2towZcoU1mf39PTAarWCx+Ox/lbBJuTCslgs2L9/P6uwvD90SkoK68e02Wz49ttv/QqHoii0trYiMTFxwL29w0S3243ExMQB1/5QWGyC9/Zo+fn5rO919uxZeDweVuEQQtDT04OioiLW1tU7JFKpVKyiNBgMyM7OhlgsHnBvu92O9vZ2ZGRksH4Ti8WCnp4ehIeHD7iWoij09fUhLy+PdQTgcrmwf/9+REZGDjjmHSaq1WrWoTPDMCgvL4dGoxnQk3pHHhaLxe8Qs6urC4QQZGdnD6gLDMOgu7ubdXgZKkIuLIPBAKlUCpVKNaCSURQFq9WKlJQU1u7farXi6NGjSEtLY23ZeTwelEolayVyOp04fvw4kpKSEB4eznqt3W6HWq0eULm9wxJCCJKSkljfS6fTQSAQQCQSDXi22+2G0WhEUVERa+uq0+nQ0dHhdw5lsVgwb9481nf2GjX8XWu327FgwQLWYaLZbMa3337rd5jocDiQlpbmV1gulwspKSms34SmaRw4cID1WuDcbx0eHo7c3FzW41VVVax1BDjXS1ssFuTl5Q2L3goIsbB+2nL/9KNYLBY0NDSct8eSy+WIiIhgnSN5W1A24TidThw8eBCZmZmsPRKPx4NIJIJarWYdbn333XfIzMxk7RWAc3OZhIQE1nI1NTVBKBQiOjqatSIYDAZERESwGlSMRiMMBgPGjh3L+k0sFovP8MFWbqPRiOuvv571m5jNZuzfv5+1ISKEwOFwYNasWazi8DZU3qHzT6/1eDyw2+2Ij48fcC1N0+jp6YFAIGCdzxJC0NTUhISEBNZjLpcLZrMZhYWFw2J+BYRYWE6nE729vZg0aRLrBzGbzairq0NycvKASuSd4I8ePRpCoZC1R2pubkZCQgJr5Xe73WhpaUFiYuKA3tDbU0qlUta5hsfjwcmTJ5GZmTng2h+uu6WlpQ24lhCC6upqREZGsg7lCCHQ6/XIycnxO6+jadrvJL2zsxNJSUl+DSZGoxG5ubmsvZ3FYoHFYmH9Xi6XCz09PSguLvY7d9u2bZuvQfgpDocD6enprKKkKApHjx5FdHS0X1HSNI2oqKgB1xJCfKOHlJQUrscCAL1eD4qiEBMTw/pB9Ho9jEYjYmJiBgiLpmn09/ejsLCQ9Yf0tr6pqamsw0iXy4Xk5GTWyu10OnHs2DEkJyeztuxe65ZKpWItV1dXF2QyGWvr7DXhy+Vy1nJ5zdljxowZcAwA6uvrYbfbWYeYwLke7corr2Ttzdrb26HValnfGThnbZw5cyar6LxWTLVazVru/v5+bN++ndX4wDAMHA4HJk6cyDr/crlc2LlzJ6s10dsjJSUlsX5PhmFw7Ngx1joSSkImLEIItFotGIZhHcoB5+YLOTk5rMcMBgP0ej3i4+NZP6jVavXNodh6FbfbjdzcXNZhYH9/P3bs2MF6LXBumJicnMw6T3E4HPj666+RkJDgd4gZHh6OuLg41qHayZMnERYW5ncS39/f73cI2dfXh97eXr9Dot7eXpjNZtZhN03T6OvrQ2lpKWuP1d3djYqKCtZGzDt6mDBhAqsZ3m63o6amBhqNhtVA5XK50NXVxWripygKvb29iI6OZl3LZBgGlZWVftcaQ0VIe6ze3l5ERESwTrQpikJnZycKCwtZrzUYDOju7kZ0dLRf4cXExEAmkw04brPZ0NnZibS0NFbheN2J4uLiBojW4/H45k9srbPL5cLRo0dZDS5e65dCofBbiY4cOYKUlBTWXsN7TmpqKusQ8tSpU4iMjIRMJmMVXnd3N5KTk1mPdXZ2wmq1Ii0tjbWhMpvNAMD6vRiGgdlsxs033wyZTDbgeH9/Pw4fPgyZTDZAmIQQmM1mTJ48mfVal8uFQ4cOQa1WDxC817IrkUhYv2coCamwJBIJUlJSBnxshmFgNBpBUZTfxVm9Xg+n0+l3gdVoNGLKlCmsojOZTKitrfXb21ksFmRlZUEikbCas0+dOoWkpCTWHsnhcMBms7GayimKgl6vR1RUFOt8gaIonD59mtVYwzAMXC4XGIZBZmbmgGu9wlIqlX4Xfk0mE8aPHz/gGAA0NDTA7Xb7HWJ2dXVh3LhxrPf2zr/mzZvHKg673Y6Kigq/SyJGoxEzZ870axT5+uuvWdcSGYaByWRCfn6+3x4+VIRMWDweD6mpqcjKyhpwjKZpnDlzBiqVyq/HREtLCzIyMlgtZ263GxaLBRMnTvS7DlRXV4fY2FhWYTkcDpSUlPida+zduxexsbGsrbfH48G4ceNY52ZWqxXbt29HfHy83/lVVFQUFAqF75281k2vb2F0dLRfk3VXVxciIyNZLZEmkwk0TSMvL4/12oaGBrhcLlZRea+/+uqrWcut0+mg1+shl8tZG8menh6kp6ezfk+Hw4GOjg7k5eUNEKV3iHn27FnW7+kdJhYWFrIamUJJ0Gd7J06cwKlTp+B2u+FwOCASiVgNAFVVVRAKhbBYLKw/yMaNGzFp0iT09/cPOGa1WlFVVQWdTofDhw8PqGi1tbVoaGjAmjVrBqzU0zSNU6dOITo6GjqdbkBF0uv12LdvH1JTUweYtAkhaG9vh16vx/r16wcMFa1WKzZs2IAFCxagpqZmQLmsVivOnDmDrVu3IjIyEoQQlJWVob6+HiqVCmKxGOnp6bBYLKxDqhMnTgAAWltbf3SMYRi0tLSgu7sba9euZW1s9u7dC5VKhQ8++GDAsf7+fhw9ehQej4fV8KHValFbW8tqnSWE4LvvvoPH48G6desG9FpWqxVlZWWsXheEEDQ3N0MgEGDLli0D5m9utxsnT55EUlISKisrfd8zIyMD48aNC2kvxgt2UoTXX38db7zxxnnDPAghsNlsEIlErMMtAL6QBzbRecMOBAKB36ELTdOsrSDDMD4nT7be0OVyweVyQS6X+3U0pSiK1RHVG9bA5p7lvdbj8fjK7Z1/uN1u8Hg8iMVihIeH+3XcdTqd4PP5rD6VLpcLQqHQr+XMG2Lir2fg8Xis39J7LU3TrGZ44FxjRdO038Vyj8eDsLAw1iE9wzBwOp2QSqWsC/VutxsSieRH15aWluLZZ59Famoqa3mCQdB7LI/HA4fDcd5YIQDg8/mgafqC550v9uZCcTkXurc/hEIha+jCD2ELcQHONQRut5s1FsqLt9xeNyHg3NBZKBTC4/H4vTfwfzFNbFzoucClfxOBQHDJvxWPxzvv9+TxeH7j0gAMuNY7Fw0lQe+xzGYz+vv7h0XMzHCHpmk8/fTT2LJlC8aNG4dVq1b5tfhx/B8ymQwKhcLvaCcYBL3HUiqVfsMKOH6M13+Ox+NBIpEgMTERSqWSE9ZFEOpvFHRhhfqFLyd+aljx/pv7hsOf4eGxyMExwuCExcERADhhcXAEAE5YHBwBgBMWB0cA4ITFwREAOGFxcAQATlgcHAGAExYHRwAYPpsE/IJxOBzo7++HxWKB0+mE1Wr1hdl7d4fV6/XYuHEj4uPjfTFbEokEERERUCqVfje65AgNQXfC/SXjDYOw2WxwOp3o7++H1WpFW1sbjh8/jqqqKnR0dMBkMvk80S0WC9xuNwQCgW9nJ7FYDKVSiYSEBIwZMwbFxcVIT0+HQqGAQqFAWFgY65YEHMGDE1YQoWkaRqMR27dvx5EjR1BTU4Pm5mb09PSwpvPh8Xjg8/mgKMq3AQxbOIRIJIJGo0FGRgYKCwsxffp0zJ8//0eRyBzBhRNWEGAYBvX19di+fTtWr14Ng8EAu90Oj8cDPp+PhIQEJCUlYezYsUhOTkZcXBxiY2OhVqvxwgsvYOvWrRg3bhz+85//wOFwQK/XQ6/Xo729HZWVldBqtdBqtQDOiUwmkyExMRGLFy/G1VdfjdzcXE5gQYabYwWQ/v5+dHZ24uDBg/j8889RVlaGvr4+xMfHIysrC1lZWcjMzER+fj5yc3Oh0WggFot/FOmrUCjA5/MhlUqRk5OD8PBw0DTtC3g0GAyora1FdXU1GhoacObMGbS3t6Oqqgrt7e3Yu3cvSktLMXXqVCQnJ3MhO8GCcAwpDMMQiqKI2Wwme/bsIddccw2JiIggcrmcqNVqkp+fT/773/+SlpYWYrFYCE3Tfu/l8XjI3XffTcRiMSkpKSEmk4kwDOP3uWazmTQ3N5MPP/yQ5OXlkaioKCKXy4lCoSCzZs0i27dvJyaTidA07fc+HEMD12MNMV4L3uuvv44NGzb4krzNmTMHt956K2bPng2FQgGRSAQ+nz9kBgZvqqPw8HAsXLgQc+fOxTfffIMtW7Zg+/btOHz4MKqrq3Hbbbfh2WefRVRU1LDaOXakwX3ZIaS3txcnTpzAq6++ivLycggEAkybNg333HMPJk2a5EuAFyhrnVeoQqEQEokE119/PSZPnoxFixbh448/RllZGTZs2IDTp0/jz3/+MyZMmDDstg0bKXDCGgIYhkFbWxu++uorrFq1CqdPn0Z8fDwWLFiApUuXIiMjg3Xzz0DC5/OhUCggl8uRmpqKgoICvP/++9i8eTMOHTqEZ555BkuWLMHcuXORmJjodwcmjksk1GPRyx2aponVaiUPPfQQiY2NJVKplCQnJ5O1a9cSg8Hws+49mDnWxWAymcjatWtJVFQUEYlEJC4ujvz+97/3zbs4hg5uBfFnotfr8c9//hOffvophEIhbrnlFmzZsgWlpaV+8/SGCrlcjuuuuw5ff/015s6dC4qisHnzZmzcuBFGozHUxRtRcML6GRiNRuzatQsrV64EANxyyy1Yvnw5xowZ4zcrYigRCASQy+UoLCzE888/j5KSEvT19eG1117DkSNHLnlPQY6BcMK6BMj/pgE6ffo0Vq5cia6uLkydOhX33HMPcnNz/SYWGA54N/4cN24cli9fjry8PDQ2NuKtt95CTU3NsMrjeznDCesSoGkabW1teP7551FRUYHo6Gg8+eSTyM/PH7aCYmPs2LF4+eWXoVKpsG/fPrzyyitwOp2cuIYATliXgNVqxYoVK1BRUYGEhAS8++67vpStlxNCoRBFRUX461//ioSEBOzduxd//OMfYTKZQl20yx5OWIPEbDbjm2++wVdffQWJRIJFixbhqquuYk2IPdzxZpdctGgRbrzxRgDA5s2bcfz48fMmreC4MJywBgHDMGhubsbf/vY3GI1G5OXl4Te/+Q1rXqjLBYFAgIiICNx6663Iy8uD0WjE6tWr0dPTE+qiXdZwwhoEFosFmzZtQkNDA2QyGR5++GG/GScvN4qKirBw4UJ4PB5s27YN27Zt4+ZaPwNOWIPg0KFD2Lx5M/h8Pu666y5MnjzZb66qyw2pVIrrr78eN998M/h8Pj744APs3Lkz1MW6bOGEdRF4zeurVq1Ce3s74uPj8atf/cpv9vrLFY1Gg8ceewzR0dFoamrCpk2bQl2kyxZOWBcBRVHQarWorq6GUCjEnDlzkJeXF9L8S4EgLCwMBQUFyM3N9a3TMQzDDQkvAU5YF4HNZsOWLVtgMpkQGxuLX/3qVyNOVF6kUiluuOEGxMXFQafTobKy8oLZKzkGwgnrIrDZbNi/fz/sdjsyMzORm5t72VoBL4RQKMS1116LuLg4mM1mrFy5kjWBOsf54YR1AQghMBgMqK+vByEEhYWFAY2pCjUCgQDp6ekoKiqCzWbDhg0bOAfdS2Bk1o4hhBCCnp4edHZ2QqPRoLCwEGKxeEQZLX4Kj8dDUVERgHML4t6NajguHk5YF8BisaCyshIulwt5eXkYM2ZMqIsUFEaPHo2JEyeCEIKOjg7OgDFIOGFdAKvViubmZhBCkJycjPj4+FAXKSjExsYiPz8fAGAwGOByuUJcossLTlgXwOFw+Frs2NjYEbMgfCEiIyN9XiV6vR5WqzXEJbq84IR1ARwOB9rb2wGcW0AdqdbAnyKXyxEbGwsA6OzshMViCXGJLi84YV0Au92Ozs5OEEIQHR0ddGHRNB2S+Y1QKPRtLdDa2gqDwRD0MlzOcMK6AKdPn/aFUERFRQVNWB6PB11dXTh58iQYhoHT6Qx6ECJFUQCA5uZmLkZrkHDCugAWi8WXsCAqKipo61cOhwN79+5Ff3+/L0OJzWYLqrC8SwoOhwNutztozx0JcMK6AN4da3k8nq+SBwOxWIycnBzf88RicdD3JvQ+m/MXHDyXVyx5CJDJZL7KbDAYgiYskUiEvLw8TJ8+HTabDYmJiZDL5UEVFk3TAM455/5SrKFDBSesCyAUCn2Vube311fZAo1AIIBCoUBpaSmSkpKQlJQU1B6LYRh4PB4A5xoXsVgclOeOFDhhDYJgCgs4t030zTffjBtvvBE8Hi+ovYbD4UBfXx8ATliXAiesQRBsYQEI2c5PZrMZHR0dAIDw8HBOWIOEM14MAq1W+4tZz+nq6kJtbS0AQCKRXHZbu4UaTliDoKGh4RezW2xzczPKysoAwGcV5bh4OGENgqamJlRWVobMGyKYHDt2jNvL/WfACWsQOJ1OnDx5Ena7fcQKi2EYdHZ24tChQ0FbWhiJcMIaBIQQ1NbWoqGhwefuM9KgKAq7du1CZ2dnqItyWcMJa5Do9XqsX79+xLr4OJ1OfPbZZ+jo6PjFePIHAk5YgyAtLQ0OhwOff/45WltbfQuoIwWPx4PW1lacOXPGlyyc49LghDUI7rrrLiQmJqKzsxPr168fcab3np4evPHGG+js7ERWVhbmzp0b6iJdtnDCGgRXXnklZs+eDYqi8N///hdNTU0jZq7ldrtx4MABfPLJJ2AYBrfeeivmzZsX6mJdtnDCGgQxMTG46aaboNFooNPp8NFHH8FsNoe6WENCW1sbtm3bBoZhMHHiRNx8882c4+3PgBPWIODz+Rg/fjyWL18OmUyGXbt24bPPPvPFa12uEEKwY8cO7N+/H2FhYXjggQeQkZHBLQr/DDhhDZLIyEgsWLAA06dPh9VqxYcffoiysjI4HI5QF+2ScDgc2L59O9577z04nU7Mnj0bM2fOhFKpDHXRLms4YQ0SPp+PyMhIPPTQQ4iNjUVtbS0eeughaLXay85K6PF4UFNTg0cffRRnz55FQUEBXnnlFajV6lAX7bKHE9YlIJFIcOWVV+LJJ59EYmIi6uvrsWLFCpw9ezbURRsU1dXVeOaZZ9De3o7CwkI89dRTSE5O5hxuhwBOWJcAj8eDVCrFvHnzsGTJEoSFhWHHjh34+OOP0dbWNuxdgQghqKurwz/+8Q8cPXoUUVFRuO+++3DFFVf8KLCT49LhhPUziI2NxW233Ybbb78dTqcTq1evxquvvorq6uqgb/xysTgcDlRXV+Oll17C/v37IZFIcP/996O0tBQqlSrUxRsxcML6maSkpGDFihWYPXs2jEYj3nvvPSxevBhVVVVBD4q8EIQQnDhxAjfddBPWr18Pq9WKWbNm4bHHHkNcXFyoizei4IT1M+HxeAgPD8dLL72EZcuWITExEWfOnMG9996LlStXwmKxhHxoSAiBw+HAmjVr8MADD0Cr1SIzMxNPPvkkVqxYwbkuBQBuljoECAQCpKWl4cEHH0Rubi7eeecd1NfX49VXX0V9fT1uuukm5OfnQ61WBzWvFiEERqMRjY2N2L59OzZs2AC9Xo/CwkIsW7YMV199NeLi4rg5VQDghDVE8Pl8JCUl4fbbb0dubi6ef/55HDt2DO+99x62b9+O++67D6WlpYiNjYVSqQyYkYAQAoqiYDab0dPTg927d+Ott96CVquFRCLBlClT8PLLL2PUqFEICwsb8udznIMT1hAjkUgwYcIEvPvuu/jkk0/wz3/+Ey0tLfjrX/+KDz/8ECUlJXjiiSeQnZ0dkLAMhmHQ2NiIl19+GceOHUN7eztcLhciIiLwwAMP4J577kFKSsqIzUg5XOCENcTweDwIhULExsZiyZIlmDFjBj777DNs374dra2t6OzsxHfffYfCwkKMHz8eubm5GDVqFBISEhAeHj7o5zkcDuh0OtTX16Ourg7fffcdqqur0dbWBo/Hg9TUVMydOxc33HAD8vLyoFaruTirIMAJK0AIhUJoNBpERUUhNzcXxcXF2Lp1K8rKytDS0oL6+nps27YNCQkJGDduHPLz85GdnY2IiAgoFAoolUpIpVJIpVLw+XwQQuB0OuFyuWCxWNDf3w+TyYTGxkbU1NSgvLwcnZ2doCgKEokEiYmJmDx5Mq677jrMmTMHMpmME1QQ4YQVYAQCAVQqFW699VbMnTsX5eXl+M9//oPjx4/DYrGgo6MDra2t2Lp1q+98Pp8PiUSCmJgYZGdnIy0tDTqdDmfOnIFOp4PL5QJN07491b29pEAgQExMDGbMmIHHHnsMOTk5kEqlnHEiBHDCChJes3xxcTEKCwthsVig0+nQ3t6O8vJyHD9+HKdOnfIlXnA6nejv70draysSExPR1dUFl8v1owQFMpkMBQUFKC4uxuTJk5GcnIykpCQoFArI5XLOiyKEcMIKIgKBAAKBAFKpFFFRUUhOTkZRURFmzJiB3t5e9PX1wWKxwGAwwGg0+v7L5/NB0zRUKhWioqKgVquhVquhVCoRFRWF6OhoX+4ugUDAiWkYwAkrRHiHb0KhEHFxcT7PB0KIr1diGOZHwz3vxpl8Pp/bRHOYwwlrmMHj8TgjwwiAW8zg4AgAnLA4OAIAJywOjgDACYuDIwBwwuLgCACcsDg4AgAnLA6OAMAJi4MjAHALxCy43W709/fDZrPBYDD4drptbm6GUCiETCaDXC6HTCaDRCIJdXGHDIqi4HA4YLVaYbPZ0NraCgAwmUxoa2uDQqGATCZDREQE59x7AXhkOG4lFEQIIbDZbOjr60Nvby8MBgM6OjrQ2NgInU6HEydO4NSpU/B4PMjNzUVqaioSEhKQlJSEzMxMJCYmQq1WIzo6GpGRkZDL5ZdNhfM6+vb09MBgMECv16OlpcUXN1ZfX4/q6mrI5XLk5OQgKysL8fHxyM7ORmpqKtRqNaKiohATEwOlUskFT/4Q8guHoiiydetWMnbsWBIdHU3Cw8OJUCgkfD6f8Pl8wuPxCAACgPB4PMLj8XzHhEIhkclkJDo6mpSUlJCvvvqK0DQd6le6aOrq6sh9991HEhISiEKhIGKx+Efv7e/dBQIBkUgkJCIigiQkJJAXX3yRWCyWUL/OsOIX22P19fVh3759+OKLL7B//37o9Xp4PB4oFArk5ORg/PjxiI+PR319PbZu3Qq73Y4XX3wRERERMBqN0Gq1OHHiBBoaGtDf3+/zWJ89ezZuueUWXHHFFYiMjAz1aw7A6XSipaUF69ev92VutFqt4PP5SE5OxgMUEOcAACAASURBVPjx45GdnQ21Wo26ujq8//77GD16NBYsWICIiAj09vbi1KlTqK6uhk6nA4/Hg1qtxujRo3HttdfijjvuQGpqaqhfM+T84oRFURTa2trw/vvvY+vWrWhra0N4eDjS09NRUlKCcePGIS0tDZmZmVCpVNiwYQOWLVsGi8WCiooKFBQUgKIoGAwGNDY24uzZszh9+jQOHTqElpYW2O12X9K23/72t8jKyho2TrUdHR3Yu3cv1q9fj7KyMlAUhZiYGEybNg1jx45FVlYWsrOzkZiYCKlUig0bNmDx4sWYNWsWVqxYgcLCQtjtdjQ3N6OlpQWnT59GeXk5ysvL0dPTg7CwMMybNw+PPfYY8vLyEB4eftkMi4ec0HaYwYOiKGK320lVVRW57bbbiEwmI0qlkuTk5JA//vGPpLW1lbjdbsIwzI+u+/jjj0lERATh8Xjk5MmTA+7LMAxxu93k9OnT5PHHHyfZ2dlELpcTmUxGFi1aROrq6ojT6Rxw32BC0zTR6XTkxRdfJHFxcUQkEpH4+Hhy0003kc8//5zY7XbW8q1du5YAIFdffTWprKxkva/NZiPvvfcemTp1KomJiSESiYSMHz+ebNu2jfT29hK32x2MVxx2/GKEZTabyebNm8mECRNIWFgYiY2NJc899xypqqoi/f39hKIo1sp1IWERck5cHo+H9Pf3k/LycvK73/2OqNVqIpVKycSJE8m3335LHA5HoF/RL93d3eTGG28kCoWChIWFkYKCAvLll18Sg8FwXtFfSFiEnHt3u91OtFot2bVrFykoKCBisZikpKSQJ554gmi12kC+2rDlFyEsu91OduzYQfLz80lYWBgZO3Yseeutt0hXVxdxuVznvfZihPVDnE4n0Wq15M033yTjx48nYWFhZOrUqeT48eMhab0bGxvJXXfdReRyOUlNTSVLly4lVVVVxGKxXLAXvRhheaFpmjgcDrJv3z5y9dVXk/DwcBIdHU3+53/+h+h0uqF8pcuCES8smqZJRUUFmTdvHhEKhaSoqIhs2rSJ2Gy2i7p+sMLy4u0hx44dSyQSCZkzZw45fvw4oWk6aMPC1tZW8vjjjxOpVEqSkpLI3//+d9LU1HTR1w9GWF5omibff/89WbhwIZFKpSQ/P5988MEHxOFwXFYW05/LiBYWTdOkt7eXzJ49m0gkEhIVFUV27tw5qGHZpQqLEEIcDgc5fPgwSU5OJiKRiCxYsID09fURiqIG+yqDgmEYQlEUefHFF0lERARRKBTk+eefJ93d3YO6z6UIy/v85uZmMmbMGCISiUhubi45duwYcTqdg32Vy5YRvaJnsVjw0ksvobKyEsnJyfjXv/6FqVOnQiwWB+X5YrEYo0ePxh/+8AfExcXhyJEjePXVVwOeENzpdOLgwYNYt24deDweZs6ciTvvvDNo5n8ej4eEhAR8/PHHmDJlCtra2rBs2TK0t7cH5fnDgRErLJvNhqamJmzatAl8Ph/z5s3D9ddfD5lMFjQPAT6fD5lMhjvvvBNXXXUV3G433n//fTQ0NAQ0rarFYsGrr74KrVaLlJQUvPDCC0hKSoJIJArYM3+KSCTC6NGj8fvf/x4pKSmoqqrCli1boNfrg1aGUDJihdXd3Y1//etf6OrqQkJCAm6++WZERkYGfU1JIBBAo9FgyZIlSE1NRW9vL9avX4/u7u6APM9ms+HAgQM4dOgQhEIh7rzzTowePRpSqTQgz/OHd1OckpISzJo1y9eo1NbWBrUcoWLECuvgwYP44osv4Ha7sXDhQhQVFYW0PJMnT8Zvf/tbMAyDDz74AEeOHAlIxsfm5ma8/vrr6O/vR0lJCRYsWBBSH76YmBjccMMNIISgsbERmzZtCllZgsmIFJbZbEZVVRU8Hg/GjBmDefPmhTxljUQiQVFREVQqFZxOJyorK+F2u4f8OWfPnsWpU6fAMAxmzpyJtLS0IX/GYODz+SgsLMSDDz4ImUyGEydO4MSJE8MyjexQMiKF1dbWhtOnT0MgEODqq6+GRqMJuVsRn89Heno6pk2bBrFYjLKyMphMpiGtYAzD4Pjx43C5XIiOjsb06dND3qAAQGRkJG6//XbI5XK0tLQErLceToxIYdXV1aG2thZSqRQzZsxAREREqIsE4FwFW7JkCRQKBTo6OlBeXj6kaVTNZjNqamogEokwf/58xMbGDgtfPalU6gs56e7uRllZGSesy5GamhpYLBaIxWIUFhYOm2BEmUyGmTNnIj4+HkajEYcOHRoyYRFCUFVVBa1WC4VCgXvuuQcajWZI7v1z4fF4UCqVyMjIgFAohE6nC3WRAs6IFJbXpBsVFQWVSjVsAvD4fD6kUimio6NhtVpx+vRpOJ3OIWm9CSHo6OiA2WxGWFgY4uPjIRQOnwBxgUCA5ORkiMVidHV1obu7GxRFhbpYAWN41Lghpr6+HoQQXzLt4TAc8uJtvSmKgk6ng91uH7JhUXNzM0wmky/ZwnB777i4OEilUphMJnR1dYGm6VAXK2CMSGF5MxsqFIphVbm8eMPYKYqCx+MZ8h7Lm4RuOMHn8xEfH4+wsDBfdsqRPM8akcIi/5v2JtiLoheLd85H/jdVz1DhvZc3zc9wIzw83Jf21WazDem7DzeGzyB8COHxeKBpGn19fT/7XpmZmbjhhhvgcrkQExMzBKUDrFYrCCEQCARDOg/yiomiqCGZvyQmJuKOO+5Afn7+z353QggMBgPcbrdvODwcRxNDxYgVFkVR6Onp+dmt4rRp0zBt2rQhKtm5CmYymcAwjE9YQ13B3G73kAjryiuvxJVXXjkEJTr33lqtFg6HA2FhYZBIJMOyVx0qRuSbeYXV19fn2xNwOOEVVqDweDxDNncbKhiGgVarhd1uD3VRgsKIFRZwruVubGwMqCf5YHC5XGhtbUV7e3tAhWW1WrFnz56Ah6dcLF5jRUtLC1wuV6iLExRGpLC8QwyXy4WKioph00parVZs3LgRFosloL2Jw+HA+vXrh2SOORQwDAOj0YjOzs4RbWL/ISNSWF5cLhcOHz48bFru3t5erFmzBjabLaDPcTqdOHr0KBoaGoaF5c3pdOL06dPDRujBYEQLy+l0YufOnWhtbR0WFezs2bNob28P2tC0rKwsIB70g6WzsxP/7//9v2HTwAWDESssr8XNaDRi7dq1AQssvFhaWlqwefPmIfW0OB88Hg/btm3Dt99+G/BnnQ+KolBWVobvv/8eNE2PaBP7DxmxwpJKpRg7diyEQiG++eYbHDhwIGQWQpqmcfz4cezatcvnahVIzwiFQoHIyEjU1NT4tscOVY/d2NiILVu2wO12o6CgYNhEGgSaESsspVKJGTNmIDMzEy0tLVi9ejUMBkPQJ88Mw8BgMOD999+HXq+HWq0O+IY2Go0GxcXFEIlE2L9/P8rLy4M+JCSEwO12Y82aNfjqq68gk8mwdOnSkAdeBouQC8vr1kPTNBiGGdIeRalU4sEHH0RcXBwOHTqEhx56CO3t7UETFyEEvb29ePTRR/Hdd98hJSUF7777LhITEwM6JIqIiMDf/vY3jB8/Hu3t7Xj00UdRXl4eVFO32WzGihUrsGrVKkgkEsyePRs5OTmX7VBwsHU0KJ4XZrPZF4MjFAqhVCoRGxsLh8OBuro6rF27Fg0NDUhMTMT999+P0aNHD8mqvEQiwY033gi9Xo9Vq1Zh+/btiI6Oxh/+8AekpaUFNKyCpml0dHTg73//u++5999/P2bNmoWDBw8G7LnAuR2S0tPT8dxzz+HPf/4zqqqq8Je//AWvvfYacnJyAhpVTAhBd3c3vvzyS7z99ttwOByYNGkSnn32WVAUNSyFxTAMnE4ndDodPB4PBAIBpFIpYmNjQQhBV1cX/vvf/6KyshJyuRyLFy/GFVdccd7vGBRh1dTU4NVXX4VYLEZWVhZmzpyJmJgYnD17Fs888wy+/vprxMbGoqqqCjRN46WXXoJSqfzZ8xCBQAC1Wo2lS5fC5XJh5cqVWLduHWiaxiOPPIKcnByIRKIhda1hGAYulwtNTU1444038Mknn0CpVGLJkiW4++67fY6owWDGjBlYvnw5Hn/8cRw+fBiPP/44HnvsMZSUlEAulw/5dmheD/u1a9fi7bffhtFoRHFxMZ588kmMHj0a9fX1Q/q8oYIQgs7OTjzzzDOgKAoZGRkoKirC3Llz0dPTg3/84x/45JNPEBkZCZVKhe7ubuTm5iI+Pt5vHQ3KL+yNGs3Ly8OSJUswffp0EELw1ltv4ciRI4iKisKqVavw/vvvw+PxDPmcIDExEQ888IBvt6DVq1fj7rvvxsmTJ4d8eORdQ1q8eDFWr14NiUSCRx99FPfddx+ioqKG9FkXgs/nY86cOVi9erVvOPzAAw/gtddeC8h+G263G48//jiee+456HQ6JCUl4YUXXsCMGTOG7DmBQCAQQKVSoaqqCiqVCvfffz9uvPFGSKVS7NixA2vWrIFEIsHLL7+M9evXIyEhAceOHYPVavV7z6D0WBRFISUlBb/+9a8RFxcHp9OJQ4cO4auvvkJMTAyefvppTJkyBR6PB11dXTh8+DCmTJkyZM/3xgK98MILKCwsxKpVq1BfX48lS5Zg9uzZKC0txbRp0yCRSC5pqEIIgcPhwJEjR7Blyxbs27cP7e3tyMvLw/333+/b0zAUwyCxWIwJEybg/fffxyuvvIKjR4/inXfeQWVlJRYuXIg5c+b8LCslTdOor6/H7t278eWXX6KsrAwRERGYP38+7r//fuTl5UEoFA6LdUR/0DQNq9UKjUaDO++8E0lJSRAKhThx4gTWrVuHsLAwPPHEE5g/fz7EYjEWLFiAL774ApMmTfJr5QyKsAwGA1JTUxEREQGxWAy9Xo/Vq1fD7Xbjuuuuw/z58xEeHg6GYRAREQGz2TzkBgapVIqkpCTcfffdyMzMxIoVK3Dq1Cl88MEHOHjwIObNm4errroKSUlJUKlUiIyM9A3ZfigIbytP0zTMZjP6+vqg0+mwd+9e7Ny5EzU1NRAKhSgsLMQf//hHzJ07N6SJsL1xabNnz0ZERATefPNN7N27F3v37kV9fT327duH+fPnIy8vDyqVClFRURCJRODxeAPK7H13q9WKvr4+9PT0oKqqCp9++ilOnjyJ7u5uZGdn4+6778aNN97o2+NiuMMwDHQ6HRISEhAfHw+xWAyXy4WPP/4YWq0WEydOxD333AOVSgWPx4Po6GiYTKbzjqqC8tYMw6C+vt5n7q6ursaBAwcQHR2N0tJSxMTEgBACi8WCM2fOBCwTII/HQ1RUFBYsWIC8vDz89a9/xfHjx1FdXY3y8nK88sorKC4uxrXXXovp06dDLpdDKpVCIpEgLCwMTqcTLpcLDocDZrMZBw8exO7du3HkyBHQNA2JRIKEhATMmDEDf/jDH5CTkzOsQiMmT56MV199FWvWrMG6detQW1uLjz/+GB999BFGjRqF2bNn49prr0VCQoIvtEMikYAQApfLBZfLBafTiZMnT+Lrr7/G7t27YTQaIRAIoFAoMG7cOLzwwguYNWvWsNnA52Ig55KDoKOjA93d3dBoNNBqtdi7dy94PB5uvfVWX69utVrR0NAAuVx+3l4+KMLKzMwEj8fDvffeC4/HA51Oh56eHtx8880YN24cCCGgaRoHDx7Ejh07sGjRooAuoPL5fGRkZODf//43GhsbsWrVKqxZswZutxtHjx5FeXm5r2KJRCLIZDKkp6ejtbUVVqsVbrfbJzC32w1CCORyORYtWoT77rsPKSkpwzaLfFRUFO69917cdNNN2Lx5M/7973+jo6MDzc3N+Oijj7Bu3TpIpVKIxWKIxWKIRCJIpVJYLBa43W643W7Y7Xbf3/l8PoqLi/HQQw/hiiuuQHR0dNCSTgwVIpEIWVlZyMzMxPLlyyEUCtHZ2QmtVos5c+Zg/vz5EAgEoCjKV19mzJgReqtgSkoKnn/+eXz00UeorKxESkoKFixYgMceewwREREwGAzYunUrdu3aBYVCgaioqIDv2SASiRAdHQ2lUomkpCSUlpaisbER9fX16OjoQEdHB0wmE4xGo2/Xp+bmZggEAkRERCAhIQFJSUlISUlBZmYmRo0ahTFjxgy73ZF+ikAggFwuh1wux1133YUpU6agpqYGTU1NaG5uRltbGwwGA0wmky/huUwm8yU+V6lUPovYqFGjkJ6ejilTpiA+Ph4KhSLUr3dJ8Hg8REZG4plnnsGGDRtw4MABREVFobi4GMuWLfMtDe3cuRNffPEFBAIB4uPjz2tVHbIaQNM0nE4n+Hz+gF2CFAoFCgoK8OSTT6KlpQUAUFBQ4NtYxG63IzMzE0uXLoVYLEZMTEzQNkMRi8VISkpCUlISgHNWvfb2djQ0NKC7uxs9PT2wWCyQSCRwOp1QKpXQaDSIi4vDqFGjkJSUdNm10F40Gg00Gg2mTZsGQgh6enpw5swZ6HQ6dHd3w2g0oq+vDyKRCEqlEmq1GjExMcjIyEBaWhpUKlWoX2FQeI1MPB5vQB319loPPvggSktLYbFYkJ+f/yNLblJSkm80FRERcd7h7pAJy5uTiaIojBkzBhqNxmdl4/F44PP5iImJYd07ITo6GjNnzhyqovwsvLu2ZmVlhbooQYXH4/n9fUYKhBBUV1ejra0NEydORExMDKRS6Y+2yFOpVKwNhkwmG5SlesiEJZVKUVhYiPLycqxcuRKtra3IzMzE3LlzUVBQENSFUQ4ONvh8PrKzs2EymbBx40acOHECGRkZmDFjBqZNm4awsLAh24dyyIQlEAiQmJiIiIgI5Ofno62tDRUVFVi9ejU0Gg3y8vKQl5eH2NjYH5l0hzsMw/j8xIbaS4Mj+KhUKpSUlCAvLw+TJ09GbW0ttm3bhgMHDiA9PR3jxo1DTEwM4uLiIBAIWJcdLoYhn2XL5XLfUGrWrFnQ6XTYv38/9uzZg3379iEvLw9jx45FQkKCryv2rvOEUmjeRUK73e4bQ/N4POj1epw6dQomkwlTpkzxmaI5Ll/Cw8MRHh6O5ORkzJw5E0ajEUePHsVXX32FI0eOID09HcXFxYiLi0NsbCzCw8MHDBkvRMDNV3Fxcbjttttw4403gmEY1NXV4dNPP8XmzZsxdepULF68GNOmTRt0wYcah8OB1atXY+XKlYiPj8fLL78MpVKJ5cuXY9euXRCJRJgwYQKeffbZId0OjSP0REZGYs6cOZg1axYoikJXVxc2b96MjRs3Ii4uDosXL0ZpaSnCwsJ8vdiFCLiwvLuyek2T+fn5WLZsGW699Vbo9XrU1NTgwIEDcLvdGDduHCZMmOBbsQ+2yORyOebMmYPFixcjLS0NH330EZqamnD77bfjnnvuQVVVFc6ePYtJkyYNu73ROS6dn9ZRsViMu+++G6WlpWhvb0dbWxtWrFgBmqaRnp6OSZMmYdSoUb7OgI2gL7h4u+H4+HhfvFJjYyMqKipQU1ODU6dOYc6cOSgpKQnqehAhBG1tbfjNb36DzMxM334ZIpEIDz74IAoLC2EwGNDU1ASapof1WhXHz0MikfgspAUFBbBaraivr0dtbS0aGhpw9uxZ5OTk4Pbbb0d4eDjrPUJSO37oVR0dHY3o6GgUFxeDYRg0NDSgubkZFEUFXVgikQh1dXUQCAQoKytDdXU17rzzTmRkZICmaZw+fdq3DsIxsvlhHZXL5Zg4cSImTpwImqbR29uLL774AlardXgI64fRwmwhC97tl/0dDyQymQy/+93v8M477+Df//43tFotCgsLccstt4DH4+HAgQPYuHEj7rjjjsvGoskxeC5URz0eD0wmE/r7+8/rKB4UYdE0jf7+fuzevRt1dXVoaWnxG0bgcrlwww03BDzMwBs/5E154w2K/PWvf42JEyfC5XL5XHcYhoFMJsNTTz2F5ORkzuQ+AmEYBg6HA0ePHkVZWRlaW1tZY/Vomobdbkd+fv557xcUYRmNRnz88cf417/+5Uthyuay5HXJLy0tDXiZ7HY7Dh48iPDwcKSkpEAul0OhUPh8AH/aIxUXFwe8TByhweu9v2nTJrz++uuora2FTCZjtVJTFAU+n4/MzMzz3jMowiorK8Mrr7wCm82GkpISzJo1izVArLe3FydPngxKjxAWFoaioiJ8+OGHeP3115Gbm4vbbrsNqampUCqVnHHiFwTDMGhtbcXTTz8No9GIMWPGoLS0FNHR0QPqgcViwXfffXfBsJig1J6+vj44nU48/PDD+M1vfuPXydbj8aClpcU3RAskfD4fUVFRuO+++7Bo0SIYjUbf5p4GgwGZmZm48sorERMTA7FYzA3/RjAMw6C3txeEENx2221Yvnw5oqOjWdesPB4PrrvuOhw+fDg43u3nQ6PRID4+HtOmTUNCQgKUSqXfc5VKJRwOR8CFxePxIBAIEBUVhaioKCQmJsLtdiMlJQV6vR719fVYu3YtYmNjMWrUKMTExECj0UAmkw35JiwcoYXP5yM2NhYqlQoTJkxAZmam3/pHCEFERASioqJCH4+Vm5uLWbNmoaGhAVOmTIFcLvd7rtPp9GX9CyY8Hg8SiQQZGRnIyMhAcXExzGYzDh06hN27d0MikSA9PR1FRUXIysrirIIjCIFAgISEBNx6660wGAzo6+uDWq32ez7DMDCZTOfd1Tco45vExEQ8++yz0Gq1OHXqFFwuly852g//uN1uNDQ04MSJEyHfzJ/H4yEiIgLXXnstnnrqKSxbtgzjx48P2XIAR2AJCwvD448/jsjISGzdupW1fno8HjgcDrS3t2Pnzp0wmUx+7xe0Gbp3U5MXX3wRGo3G73kUReGOO+4I2a4+DocDXV1daGtrG1CGxsZGxMfHh9SnkSNw8Pl8hIWF4e2338aePXtYz/EG5o4fP/68dXTQwvKGUXiDFy+mgvX19eGtt97C2rVrYbFYfNGbP8XtdkOtVuOWW24Jeo9AURSMRiO++OIL7NixA729vQPO0ev1+N3vfscZMoY53joK4KKcZr0ZJzdv3oy33noLZ8+eRVtbG6s/qHc334KCgvPec1DC8m7w39nZCYlEgtTU1Ivai++7777De++9B5fLhWnTpmHy5Mms+yP09fWhpaUlJJ4NLpcLmzdvxmuvvQaRSITU1FSIxeIflcPlcgVtywCOS8disaC9vR2EEOTk5Fxw6wSvuf25556DwWBAUVERpk+fjsjIyAG/t9dvUCqVnveegxKW3W7Hrl278MYbbyA1NRUvv/wyUlJSLmjB6+/vB0VReOihh7B48WJoNBrWVp+mabS2tsJmswW9AtM0jbNnz+Kaa67B0qVLkZCQMEDcOp2OW9+6DDh69Cj+8Y9/wOl0YsuWLUhISDjv+QzDoL+/Hx6PB7fccgueeeYZREdH+62jJpMJO3fuPG9dGHSP1d/fj46ODkil0ovOzJ6QkIDk5GRfdOb5rCkymSwo5vafIhaLceWVV/p26NFoNAOE9UtKnHY5Y7PZ0NnZCbvdflEbv3qj3zUaDUaPHo3k5GS/C8Dere5uueUWvw64QJCMF2lpabjuuuvQ0NCAkpKS8076rFYrHA7HeU3ygcArLJfLhT179qCkpGRAi9XW1gaRSITY2Niglo0jsPD5fKhUKixevBh9fX3o7e1FfHw867mEEHg8HnR2dmLUqFH+7xmowv6Q+Ph4PProo2AYBjU1NbDZbHA4HAP+2O121NbWhsTc7l0wJoTg7bffRl5eHnJycn70Z/bs2edNPUpR1LDeo5zDPxKJBPfeey9SU1OxZ88e2O121jra39+Ps2fPYs+ePaE3t3/77bd45ZVX0N3djXXr1vltDbz89re/DXoFtdvtWLVqFVauXAmxWIylS5f6du3xUl9fz7o9mNcEu2bNGqjVatxwww3cXOwygqIo1NbW4sUXX0RzczN6enqwdu1a1mG/12H3iiuuOO89gxY2Ultbi+7ubl9SBLaJocfjQVRUVNDTmXrL2NraitTUVDzxxBPIyMgYYJ1sbW1ltTDRNI19+/bho48+glKpxJQpUxAbG8u5Pl0m8Hg8hIWF4eTJk2htbQWfz/cb0OqdZ19oj8GgCCs7OxslJSWora3F1KlTkZyczFrpbDYbdDpdSLJzCIVCjB8/HjKZDAUFBay5rEQi0YCelKIo9PX14c0330RFRQUiIiKwZcsW3HXXXSFL3cMxOAQCAeLi4nDddddh3759GDNmDHJzc1nXwFwuF9ra2i64U1dQhBUbG4tHHnkEp06dwnXXXefbWuynEELQ3NwMk8kU9KGURCLB/PnzERYWhtraWowfP35AGb0BmtHR0b7/5138/v777+F2u2EwGLB8+XIUFhYGfd8OjktHKpXikUceQUFBAUpLS/0azxiGgcViwebNm0OfbUQikWDcuHHIy8tDeHj4eYdI2dnZcLlcQa+QLpcLn332Gb788ksYDAZWtyuj0Yg77rgDRUVFAM4NXauqqrBq1SpYrVZf1pT+/n688cYbUKvVKCwsDOp7cFwaAoEAsbGxuOOOO/wG4nqRSCRYuHAhZDKZ33OCUnu9oe8XWq0G4EsfE2wIIeDxeGhvbwfDMKwtlsFgAEVRvn93dnZizZo10Gq1A4aIR44cwc6dO5GVlRXSxHMcF4c3uuFiEAqF5/V+B0K0S9NwRCqVYv78+XC73bjhhhtYV+srKip8+bAYhsG6deuwadMmVgumXq/Hhg0bcM0112D06NGcIeMXBudN+r94s6Hceeedfr3v8/LyMGbMGDAMA61Wi82bN8Nut/u955kzZ/C3v/3tvOdwjEy4Hut/8S4QR0ZG+j3HawmiKApOp/NHLjN8Pt+XcpPH4/k8pjs6OrhF418gnLB+Jt5kDjKZzJc6NCwsDBaLJdRF4wgh3FDwZ8Lj8RAeHo6rrroK4eHhUKvVmDdv3mWbNpRjaBjyHssbBOnPCkbTNFwuF6xWK5xOJwQCAWQyGcLDwyEUCi+7IMLE+sdktwAAGjhJREFUxEQ8/fTT6OzsxLFjx6BQKPDggw/C5XLh66+/DnXxOH4G3r0tnE4nNBrNoBJhDLmwqqurkZWVNcClnhACt9uNM2fO4NNPP8Xx48dhs9nA5/Oh0WgwZ84clJaWBs0ViKIoWCwWKBSKAc/zeDzo7++HTqeDx+NBeHi4Ly/WD9fXVCoViouLcfPNN+Ojjz4Cj8eDSCRCQkICHnnkERiNRthstoC/C0dgcLvdeO+993DgwAGsXLnSl4zuYhhSYRFC8M0330CtVg8QFk3TaGhowPLly7F7924wDAOJROJrBb799lt0dHTg/vvvZw0yHGpcLhf27duHOXPm/KglcrlcaG9vx9atW/H555/DbDYjNTUVt912G6699lpffloej4e8vDwsXrwYUVFRAxa0p0yZgqVLl2LVqlWXXS88kvEalZxO5wXPtdlsqK+vR0VFBbq6uiAWi311RSqVQiQS+RXakPdYbrcbzc3NSExM/NH/d7lcePPNN3HkyBEIBAIkJSXhV7/6FQoKCkAIwd69e7F+/XrYbDa8+OKLkEgkAa2QHo8HTU1NqKmpwYQJE3yL0s3NzfjLX/6CPXv2QCgUQiKRoK+vDxUVFaiqqsKyZcsQFxeHsLAw/OlPfxrwnl4EAgGuueYayGQyLgPkMIKiKGzduhUbN268qHOrq6thNpvx1FNP+fJoSyQSXH/99SgtLfVrRR5yYeXl5aG6uhqFhYVQKpXg8Xhwu91ob2/Ht99+i+zsbNxxxx244oorkJycjLCwMBBCMG3aNEyfPh379u1DfX098vPzA+qBIZFIMGnSJBw5cgTJyck+gWzYsAFtbW14+OGHMX78eGRkZEAgEKClpQVffvkl9u3bh4ULFyI2NtbnUfJDb4wfolQqMXPmTM5fcBjB4/FgtVpRWVkJo9H4o17op3gTIFAUhRMnTviccqVSKcaOHRvcbCPp6enYt28fampqMH78eIjFYtA07QuVfvjhh/HrX/96gNUsMjIS8+bNAyEEp0+fRnZ2dkCFJRaLUVRUhB07duDAgQO49tproVQqodPpcPXVV+NPf/oTZDKZr6sfM2YMnE6nzxH3pxvNsCESiTiPi2EGn8/H9OnTsWjRIqxbtw4ajQZjxoxhNU643W7s3r0b9fX1WLhwISIjI32ZHydPnhy8LaZ5PB4yMzMRGxuLp556Cm+88Qb+f3tnHxTFff/x191xwAF3cAhyQDxACSCYGJRUiSFaq9UQx7RWS5NStWOZqfEhMbbTjFrHZqYzncZMyINpYjM6TVofMlOt2ohVK2jtAwWNCQJVkQcheKBwwHEccA/7+yOz+xPl4YBbIO2+ZviHvdv93O6+d7/f7+cpKSkJQRAICgoiISGBtLS0AZeiJ02aRFRUFP/85z9lz8nSaDQYDAaefPJJPvzwQ9rb28nOziY1NRVBEKRuE6LTVxAE9Ho9wcHBSrHOrzBqtZqUlBS2b9/OggUL+M1vfoPRaCQvL4+HHnpIEpcgCHR2dmK1WrFYLGzevJn4+HivH5Q+n8T4+/uTnZ2NwWBg7dq1HD58GLvdTmJiInFxcdLN2h9Wq5WqqqoBh1ZysGDBAhYsWEB+fj4rV66koqKCxsZGqquraWlpobW1FYvFwuXLl3n33XdxOp1K47n/AgIDA5k3bx67d+8mOjqarVu3cv78eZ859n0+FFSr1cTHx/PKK6+wadMmdu/ezaVLl8jMzCQsLIzy8nISExPR6/WSyJxOJ+3t7Zw6dYq//vWvbNiwYcyGUKGhoaxatQqn08mBAwcoKChAq9VSVFSEyWTC39+flpYWPB4PDz/8MFlZWUptwf8C1Go1QUFBxMXF8dxzzxEVFcWRI0eorq7mqaeeIjExcVQjE1lm1Xq9nkcffZSf/OQn5Ofnc/jwYf70pz8RGRlJaWkp//nPf4iJiSEyMpK2tjbprVBcXExWVlafVbqxwGQy8eMf/5jk5GSOHDlCZWUlLS0t3LlzB4PBgNlsJj09neeee46HH354zOxSkB8xe3jlypUkJiZy6tQp9u7dS25uLtHR0SOeksi2XBUSEkJOTg6zZs0iPz+fo0ePcvXqVTweD8XFxVJ0hiAIaDQaIiIi+N73vsdLL72E0Wgc86FWUFAQS5cuZcmSJXg8HpxOJ93d3dIChlhSW/FJ/XciLmalpaXxySefsGnTJjZs2EBnZ+eI9iebsMRo8bi4OHbu3MmqVauorq6moqKC8vJy7t69S0REBImJiVKNgbS0tAHT9seCe4d4Wq0WnU43aHjWvd9bvHgx4eHhUrygMlz86iEGUC9dupS4uDgKCgqorq5+oFqXN8juYNHpdOh0OqKjo3nyySexWq20tbVht9sJCgoiLCyMsLCwCZdl642gRNRqNampqaSkpAAoixtfYdRqNQaDgccff5zJkyeTmJhIS0sLRqNxWOIa0zY+AQEBmEwmTCaT9H+xM4S35aq9wePxSPUnxFSO+xH9EcPZp9gXayg7Bys26nQ6++ynt7eXnp6eAS+aVqt9YJvH48HlcvWx494OG/fu11cC12g0gzq6+7Pp/u33/nbRvtEw3Gs43H0nJCSQkJAwou+Pe0iAw+GgtrYWm83ms4ZunZ2dUszfpUuXHlgIEVukJiUleXXjud1u7HY7tbW1kid+pLjdbpqbm/F4PNjtdq5cuTLg8FdsF3P/9qamJurq6vqcL7GPrrjfTz/9dNAa+cMlMjKS5OTkfrcJgkBra6vUP7q/xE6Px0NDQwM2m43u7m7Ky8vp7OwcsTBUKhVGo5HU1NQRfV9uxl1YbW1t7Nq1i/r6eqxWq0+ybe/cuYPL5eLAgQN88skn0hNfvBh6vZ6srCx+/vOfey0sMc3+7t27/fbO8hZBEGhqasLlclFTU8PmzZsfmI/5+/tLw+Nf/epXzJ49u4+df/7zn9m/f7/kBhC5ffs2Ho+HmzdvsmnTplHP88RRhtFo5LHHHuOtt94a8DedOXOGjz/+mOvXrw/4xu7p6aGtrQ2n08nOnTv7fRt7Y1NISAh6vZ7HHnuMN998c9i/aywYd2F1dXVhsVi4efMmarWa4ODgUcfWDdS2RRAE6uvr0Wg0TJ061ev9ud1uHA6HJH5BELzqC9YfKpVqyBLbbW1tNDc34+fnR1dX1wNv8Y6ODmpqanA4HOj1einId6h2NcPF7XZjtVq5c+fOoF04xRLbVVVV3L17l4CAgH4rcgUGBvaZBowEj8dDU1MTFoulT33Hica4Cwu+vDAdHR288MIL5ObmytZppKenh5dffpnS0lJsNtuwv9/R0YFOp2PPnj1ER0fLtvL397//na1bt0pP9/txu910dHSQmZnJz372M8xmsyx2dHR0cPToUd5///0hz5fT6eTatWssW7aMjRs3Dhj1P1rsdjvvvPMOx48fH9E1HCsmjLAEQcBoNBIfH4/BYJDlOA6Hg6CgoBFP6AVBwM/PjylTpjBlyhTZotarq6uHFK0Yf2k2m4f19h0ObW1tTJo0yevhmtvtJjg4mClTphAfHy+LTTabjdDQ0AnvTxzyzhBT7Yf6DDDqHyuu8ngzoRVXmMTVKm/EIvaPHSliBSY/Pz+0Wi1+fn5SxabBEHsue9MPF/BKVPfbMthnXS4XDodDmvtotVqpFILH46Grq0tK3Lvfbm9tvtd2sSPHUAzneouIyYX32iSei8EQa0GOVWP2QYUldnC02+1S5mx/2Gw2bt++LflxxoLW1lZOnz4t5XWNV3pGY2MjV65cobW1le7ubjweDxqNhoCAAClfy2g0EhwcjNlsJiwsTCqzLfcFttvt2Gw2qqqquHz5Mm1tbWi1WsLDw5k9ezaxsbG4XC7OnTvHwoULmTJlik+O63a7+dvf/kZ7ezs2m43e3l6pbIG/vz9qtRqn04nBYCAmJgaz2SzVPfEmHae/4zU2NjJ58uR+53Zi1nB9fT2xsbGDlob2FYMKS5y85ufns379+n4n3YIgcPHiRak38VhRXFxMfn4+9fX1bNiwwadLy8PhoYceIjg4mJ/+9KecOHECh8NBdHQ0jzzyCCkpKXg8Hj799FMqKysJDAxkzZo15OTkYDabZY2HdLvdnD9/nj179nDp0iXS0tL4zne+Q1JSEg6Hg9dffx2LxYIgCFy5coWPP/7YZ8ISI8fFZunV1dUEBASQnJzM9OnTiYyMpKKigubmZlpaWggNDeXZZ59l1apVJCUleV3qGf5fNAcPHmTJkiU8+uij/X6murqaXbt2sXv37vEXFnx5gS5cuIDRaGTt2rV9VqjEpgB79+4d1skYDWI0/B//+Eeqq6v58MMPWbVqlU9WE0eCSqXCYDCQm5vLZ599Rk1NDXl5eXzrW9+SxN7Z2Ul5eTmHDh1iz549nD59ml27dvHUU0/JsgBitVp57733OHjwIDExMXzwwQckJiYSERFBYGAggiAwY8YMzp49y/vvv4/dbpeaOvjqLRoUFMTy5cs5c+YM169fJzY2ljfeeIOEhAQ0Gg09PT3S2/TYsWN89NFHFBQUsGbNGtatWzes0gyCIHD16lVu3LjBG2+80SdwVhAEbt68ydtvv01tbe2YpSR5dSe2tLRw4MABkpOTpdrlLpeLtrY2Dh06RElJCbNnz5bbVuBLMX/++edUVFTgdDq5desWFy5cICoqSrZFj8EQYyITEhKIiIigoaGB2NhYTCaTZE9UVBQxMTEYjUYuXrxISUkJH3zwATNnzvR5wHFHRwcXL17kvffeIzg4mLVr15Kdnf3ATarX66XOk6+88opXxVWGg5+fH2FhYZhMJlQqFf7+/n1KIIhMnTqV6dOnS+Xifv3rX6PX61mxYoXXtRkFQcBqtVJSUkJGRoZ0PkVn+V/+8hfOnDlDSEjImCWper3aUFtby44dOyTVOxwOTp8+ze9///tROUyHi8Ph4MSJE1I8lyAInD17FovFMmY23I84fxjs7aPT6YiPj2f27Nmo1WrKysooLy/3+YVuaGjgnXfeobGxkWeeeYZFixYN+OSfPHkyzzzzDPPmzZOlDLY3D4ygoCASExPZvXs3mZmZ3Llzh1dffZUbN24MK2VDjP7YuXMnpaWluN1uXC4XJSUl/O53v6OhoWE0P2XYeC0s8e1w6NAhOjo6qKurY+/evSMOqx8p3d3dFBUVsXr1anJzcwkICKCwsJDy8vIJXyNd7J0lxh3a7XafC6usrIx//OMfuN1uvva1rw1aix6+TPTcunXrkJ+TE7VaLfWmiomJobGxkRMnTtDS0jKs/bjdblpbWzl79iytra3YbDZefvllKisrZbJ8YLwWljj8u3v3Lr29vbS3t0uxaWOFzWajoqICvV7PnDlzyMjIIDU1lc7OTs6dOzdoF/Pxxul00tjYSGVlJR6PB7PZzIwZM3zqj3E6nfzrX/+iu7ubwMBA4uLihpzDabVaZs2aRWZm5rhF5IvD6RkzZpCUlITT6eTIkSN88cUXw9qPGHj9xRdfYLfb6enpobW1VVr6H8vfN+gcS61W4+/vL/k4RN8R0OdJq9PpxqRWudVq5eDBg3z9618nIiIClUpFTk4O165d4/z581RWVvLEE0+Ma8pGb28vFouFxsZG6e3U3d1NZ2cn+/btw2q1Mm3aNPLy8oiKivKprc3NzVy7dg2VSkVCQoJUfm4wxBykiVD7MCYmhpiYGDweD1VVVVRVVZGenj7k90RfplqtlqLo70er1RIWFjZmC1yDHkWj0RAdHc3SpUv56KOPsFqt/X7ObDaTk5Mji4H3cvXqVS5fvszGjRsxGAz4+fmRm5vLvn37aGho4A9/+ANz5swZtlPTl9hsNl577TUuXryIXq+nq6uLy5cv09LSQldXFyEhIbz22mssXLjQp743QRC4desWra2taLVaqZPkVwm9Xi/FEno8HhwOx5DfEQOFv/nNb1JUVITNZut3eG0wGFi5cuWg/lhfMqR8NRoN69evp6amhpMnT/aZUIqdNp5//nnmz58vq6F2u53KykpmzZpFfHy89ITS6XQ8/fTT7Nu3j9LSUurq6jCbzePmMDYYDGzcuJElS5ag1+vp6enh0qVLFBQUcPHiRaxWK2+99RYajYYFCxb41E1xb/TEcBI1JxLiG0W8t7xBo9GwbNkyysvL+e1vf/vAknpwcDCLFy/m+eefHxMfFnghLJVKRVxcHN/97nf57LPPpB698GV6w/z586VyZ3JSVVVFcXEx06dPp6ioSLqBnE4nGo0GrVYrVdtdsWLFuE3GtVotCQkJJCcnYzAY8Hg8xMfHk5WVRUFBAfv376e0tJRt27axY8cOli1bNqwuFgOhUqmIiYnBYDBIk/j+hkQTGYfDQXNzs+QbHCoLQESlUmEymcjNzeXMmTM0NDRI7gO1Wk16ejp5eXmEh4fLaX4fvBpw6nQ65s+fT05ODnv27JHa70yaNInNmzczbdo0WYMixegOi8WCXq+nqampz43ocrmIiYnh5s2bHDp0iEWLFmEwGCZEoKZarSY0NJTQ0FAiIyMxm8288MILlJWVkZ+fz7x586T54miJjIwkKioKt9tNRUXFV67TSXNzMxaLBbVazcyZM4dsoH0vAQEBpKam8uKLL/LLX/5Sukf0ej3f//73ycjIkNHyB/F6JhcbG8umTZsoKiqirKxMKsg5d+5cWV+vYqRFQUEBixcvZuvWrf2udB0/fpwXX3yRwsJCPv/8c6KiosYsGsRbQkNDWbJkCbNmzeL06dM0NTVhtVoJDw/3yUNArVYzbdo0ACmj95FHHpkQDxhvuHr1KpWVlfj5+bF8+fJh55fp9XpWr15NUVERx48fx8/Pj6VLl7J06dIxvxe8PuNqtRqj0ciWLVuIj48nIyODNWvWjCoNwxvsdrvUwO2JJ55Ap9MREBDwwF96ejqPP/44brebo0ePjqnT2lvEaPTg4GCpnJqvQ5qysrIwm82o1WouXLgw5Hlwu910dnby73//e9zym9xuN21tbZw6dYqmpibi4+PJzMz0eo4lolarCQkJYf369aSnpzNt2jS2bt3K5MmTx3y+OaxHmU6nIzs7mxUrVrBu3TqmTp0q+/Kl3W7n6NGjpKSkkJqaOuAJioyMZPny5Wg0Gi5fvizVMBwLRB/fYJEC4g1cV1dHVVUVwcHBpKWlERER4dM3SmJiIj/4wQ8IDQ3l3LlzFBYW0t7e3m+hF7H53smTJ0dVf2IghnJ+i5nH9fX17N+/n3PnzhEREcGGDRtITEwc9r0lPqzmzJnDSy+9xOrVq0lNTR22QH3BsCzXaDSEhoayfft2qf2JXIhVf2pra7lw4QKvvvqqFOt1v7gEQSAkJITk5GSCgoK4efMmhYWFzJs3j8DAQFmX30VR3blzB7vdLvmturq60Gg0Uhlth8NBSUkJhw8fpr6+nunTp5OXlyeV2vYVMTEx/OhHP6K2tpaTJ0/y+uuvY7fbycrKwmQySddMEATsdjuFhYXU19eTlZXls+V58Zy4XC7a29ulXKiuri7sdjsqlUqKPikrK+PQoUMcPnwYk8nExo0bycvLG9U5CQkJYeXKlfT09IyLqGCEGcRyOxPF4Mnr16/z5ptvUlNTg8VioaWlhYCAgD65TOIczGq1SiuWDoeDY8eOMXfuXObMmUN4eLhsY+zu7m6ampooLCykpqYGm83G22+/zbFjx0hLSyMyMpKOjg5KSkqorKxEEAQyMjLYsWMH6enpssx/TCYT+fn5ZGdn8+677/KLX/wCjUbDwoULSUlJQaVScePGDW7fvs3ixYv54Q9/6NNVXYfDQVNTE01NTZSVlSEIAhaLhS1btpCUlERERATXrl2jqqoKm81GUFAQq1atYt26daSkpPjknIwkSdOXjEhYchurUqno6enh1q1bZGVlkZaWhsFgoK6ujilTpvQ5vvj0q6mpweVysW3bNjweD8HBwVIC5mCFUEZLe3s71dXVhIWFsWXLFqkbiVarJSAgAH9/f0JCQnj22WfJyckhLCyMlJQUqSukHIiR5YsWLWL69OmUlpZy69YtXC4XNpsNnU5HVlYWqampREdHExoa6tO5nlar5datWzQ2NpKbm8vy5ctRq9UEBgai0+mk5M9vfOMbREVFERsbS2RkJOHh4T47J+Ptx5sQNS/uR6VSERERwbe//W2vPh8YGMjcuXOZO3euzJY9iFiAdOHChWN+7KEIDw8nPDycGTNm4HQ6pZqIWq1W1vw1rVZLZmamLPv+qjAhhaXgW8R8qLHs4PK/zlfDwaGg8BVDEZaCggxMqKFgV1cXra2tgzYVGA3d3d1S/NxIJ7a9vb20tbVJ5cPkQFy2H8rGe/Pi5KCjo0MKi/J2pc7hcMhqk91ux+FweHV+xpMJJawTJ05QXl7+gKNysCInA/m1xKZ2924T/SZiCa6RYLFY2L59e5+eSQMdbyTbBEGgubkZl8s1qI0ul4uysjK2b98uNRy/d1/373Mk23p7e6mrq0Or1Xrt4youLmbbtm0EBQX1cRD399sH+/9A21wuF5WVlbjd7nEpHuQt426Z6HSeNGmSlCAopzO3p6eH8PDwYV0U0aNvNBpxOBwUFxfLGn/X29srLTT0dxydTkd4eDi9vb2y2iI66SMiIgb1A6pUKgIDA5k0aRJ2u13q2CkHYgugib4YM+7CMhgMzJkzB5PJJLWAkbuSjsFgYObMmV5ffLGV6/z582lpafFZu6HBCAgIwOPx9BvnNnXqVJ5++mncbnefvlhyYTQaBy1jrVKpiI2NJTs7G5fLNSbXUIxmn6iohLGqB6Wg8D+EsiqooCADirAUFGRAEZaCggwowlJQkAFFWAoKMqAIS0FBBhRhKSjIgCIsBQUZUISloCADirAUFGRAEZaCggwowlJQkAFFWAoKMqAIS0FBBhRhKSjIgCIsBQUZUISloCADirAUFGRAEZaCggwowlJQkAFFWAoKMqAIS0FBBhRhKSjIgCIsBQUZUISloCADirAUFGRAEZaCggwowlJQkAFFWAoKMvB/qSdokfiSMygAAAAASUVORK5CYII=)
physics-General
physics-
Two masses m and M are attached to the strings as shown in the figure. If the system is in equilibrium, then
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)
Two masses m and M are attached to the strings as shown in the figure. If the system is in equilibrium, then
![](data:image/png;base64,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)
physics-General
physics-
Block of 1 kg is initially in equilibrium and is hanging by two identical springs A and B as shown in figures. If spring A is cut from lower point at t=0 then, find acceleration of block in ms–2 at t = 0.
![](data:image/png;base64,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)
Block of 1 kg is initially in equilibrium and is hanging by two identical springs A and B as shown in figures. If spring A is cut from lower point at t=0 then, find acceleration of block in ms–2 at t = 0.
![](data:image/png;base64,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)
physics-General
physics-
Find the acceleration of 3 kg mass when acceleration of 2 kg mass is 2 ms–2 as shown in figure.
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)
Find the acceleration of 3 kg mass when acceleration of 2 kg mass is 2 ms–2 as shown in figure.
![](data:image/png;base64,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)
physics-General
physics-
Both the blocks shown here are of mass m and are moving with constant velocity in direction shown in a resistive medium which exerts equal constant force on both blocks in direction opposite to the velocity. The tension in the string connecting both of them will be : (Neglect friction)
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)
Both the blocks shown here are of mass m and are moving with constant velocity in direction shown in a resistive medium which exerts equal constant force on both blocks in direction opposite to the velocity. The tension in the string connecting both of them will be : (Neglect friction)
![](data:image/png;base64,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)
physics-General
physics-
What should be the minimum force P to be applied to the string so that block of mass m just begins to move up the frictionless plane.
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)
What should be the minimum force P to be applied to the string so that block of mass m just begins to move up the frictionless plane.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANgAAADwCAYAAABi36q2AAAgAElEQVR4nOydd3SUZfr+r+klyUwmhYSEVHogIAhSAgFpCiqw1EVcKTbEjqyw33UtrCuCsCqKLsoiRZCOqAiI9J5gMBAIKQQS0usk0+v1+2Od+a0rQkgH3885czgnzLzzPHPe633u537uIiJJCAgINAri5h6AgMCdjCAwAYFGRBCYgEAjIghMQKAREQQmINCICAITEGhEBIEJCDQigsAEBBoRQWACAo2IIDABgUZEEJiAQCMibe4BCLQcSKKyshIVFRWw2WxwOp1wu90AALFYDJFIBKlUCrVaDZVKBa1WC7lcDqlUuI1+C+GXEfDidrtRWlqK8+fPY9++fcjMzITD4QAAaDQaBAQEwGg0wtfXF4GBgRgxYgQGDRoEPz8/iESiZh59y0QkRNMLeCAJu90Os9mMlJQUzJkzBzk5OYiOjsa7776LqKgo6PV6bNiwAXv37oVIJEKXLl3w9ttvIzo6Gkqlsrmn0OIQVjABLyKRCAqFAjKZDHFxcYiIiEBGRga0Wi26deuG1q1bw+12o02bNtBqtfj4449x8OBBvPPOO1iyZIkgsOsgODkEfoVnr6VQKCASibzmn0gkgkQiQVhYGB577DF06NABBoMBR44cQWpqajOPumUiCEygVvz3HksikSAoKAgdOnSATCZDcXEx0tPTvfs1gf+PIDCBOiESiRAaGgqJRAKXywWbzeb1OAr8fwSBCdQJh8OBwsJCOJ1OSKVSaDQawV1/HYRf5HcMSTidThiNRqjVaigUiuu+539fer0eBw4cQHJyMuRyObp164a77roLYrHwvP5fhF/kdwhJuFwumEwmHD16FJ999hnMZvNvvtdoNCI3Nxdmsxk1NTXYuXMnFi9ejLKyMrRt2xbz589Hp06dhLOw6yCsYL9D7HY7KioqsHr1aqxcuRJKpRKTJk2CTqf71XtJIi8vD7Nnz4ZMJgNJuN1uhISE4I9//CMmTJiA4OBgyOXyZphJy0cQ2O8It9uNiooKpKSkYO3atdi9ezeMRiMkEgkKCgoQHR39q8+IRCK0b98eH3zwAVwuF9xuN2QyGUJDQxEYGAiFQiGI6wYIAvsd4Fl1KisrsWrVKqxfvx7nz58H8B8BkUR6ejoSEhJ+9VmxWAy5XI6oqCi0bt26qYd+2yMI7A7H7XbDZrMhPT0dr7/+OpKTk6HX63/1noyMjGYa4Z2NILA7HIfDgQMHDmDevHnIysr6RYQ88J/VDQAuXboEq9V6XU+iQN0RvIh3OAaDAWvXrkVWVhbsdvt1D4NJory8HHl5eXC5XM0wyjsXQWB3MCRRVFSE7OxsOJ3OG763srISaWlpcDqdIAmr1QqDwQCXy4WysjLY7fYmGvWdhSCwOxi73Y5Lly7h2rVrEIlE3uTI651XVVdXIz09HVarFRaLBVevXkVhYSEUCgUMBgMqKyu94VBChlPtEfZgdzAVFRU4evQoTCYTlEolOnXqBKPRiOzsbLhcLm8cIfCfvVpNTQ0uXLiAjIwM/PDDD2jTpg1at24NiUSCL7/8EnfddRcGDBiA8PBwSCSSZp7d7YEgsDuYwsJCHD58GOHh4Rg1ahT69u2LJUuWQCKRIDw8HDKZDJcvXwYAtG7dGkOGDEG7du0QERGBAQMGeEOjRCIRZDIZFAoFdDqdELFxCwgCu0MhidTUVIjFYvztb3/DwIEDkZ6ejoKCAm/kxpUrV5CTkwORSISuXbtiwIABUKlUQkxhAyL8kncwMpkMa9euxbhx4yCVSrF+/XoYDAbodDo8++yzuPvuuyGTySCVSnH//fcL4moEhBXsDmby5MkQi8WQSCRIT0/Hvn374HQ60b9/f4SHh6NDhw6IjY2FWq3GwIEDBXE1AoLA7lA89TU8YVLfffcdysrK4Ovri8GDB0MikSAmJsbruAgKCmruId+RCAK7w/GUYtu1axckEgn69OmDu+++GwAQHR2NxMREjBw5Emq1uplHemciCOwOx+FwYO/evSgqKoJUKkX//v0RGxsLkUgErVaLP/zhDwgMDIRMJmvuod6RCAK7w6mpqcE333yDkpISBAQEoE+fPt68L4lEgtDQ0GYe4Z2NsKu9g3G73bh27Rqys7MhFosRExODuLi45h7W7wpBYHcwVqsV586dw7Vr16BSqTBy5MjrZi0LNB6CwO5gioqK8N1338FisSA0NBRTp06Fj49Pcw/rd4UgsDsUkrh8+TKOHTsGl8uFhIQEREZG3jExhFarFQUFBbBarc09lBsiCOwOxFM16vvvv0dpaSnkcrk3muN2jyP0nOsVFhZix44dqKqqau4h3RDBi3gH4nK5UFVVhX379kEmkyExMREdO3Zs7mE1CG63GxaLBYcPH4afnx+0Wm1zD+mGCCvYHYjVasXWrVtRVFQEpVKJUaNG3RGRGiRhs9mwZ88eFBYWYujQoS3+/E4Q2B1IdXU11q9fj5qaGoSFhaFPnz7QaDTNPax643A4kJaWhk2bNuHBBx9EmzZtBIEJNC0kkZGRgStXrkAkEqFjx46IjIxs7mE1CLm5uVi9ejXmzZuHDh06NPdwaoWwB7vDMBqNOHXqFPR6PQICAnDvvffCz8+vuYdVLzz18/ft24fOnTsjLi7utql+Jaxgdxg5OTk4efIkHA4HYmJi8NBDD902N+NvYbfbcezYMZSUlGD48OGQy+W3TWrN7TFKgVpz7tw5JCUlwe12o0+fPggPD79tbsbr4XA4cO3aNaxatQqDBg1CdHT0Dc/y3G437HZ7iyk/J5iIdwies68jR46gsrISKpUKDz300HXrxntqbZjNZlitVjidTm/VKR8fH0il0mYTpacGCPAfsZSVleG9995D37590aNHjxv2gXa73bBarTh16hR69erVIhw7gsDuENxuN/R6PZKSkrxnX7/lCPCI66uvvsKPP/4Ii8UCl8uFiIgIjB49GnFxcc3S0MHjhpdIJJBIJDCbzVi9ejWkUilmz55905w1u92OQ4cOYevWrYiNjRUEJtBwGI1GrF+/Hvn5+VCr1Zg2bdp1bzCSqKqqwtKlS3H27FkMHjwYCQkJKC0txbfffovXXnsNb775Ju66664mi/rwrKhXr17Fhg0bEBAQgFGjRiEtLQ0FBQWYOXMm1Gr1b66qnuiOlJQUbN++HU8//TRCQkKaZOw3hQJ3BNeuXWP79u2pVCrZu3dv5ubm0u12/+p9DoeDX375JbVaLefNm8fy8nK6XC6azWbu2bOHnTt35pgxY1hdXU2Hw9EkY3e73XQ6nXz77bcZHh7OqKgofvzxx5wwYQK3bNlCo9F43bn895yKior40ksvcfv27XQ6nU0y7tpw++5+BX7BmTNncOXKFbjdbvTo0QNarfZXKxBJGAwGfPfdd3C73bj//vvh7+8PsVgMhUKBXr16oXv37khOTsa//vUvmEymJhm7SCSCWCzGoEGDEB4ejoqKCrzxxhuQyWTo27cvVCrVDVdTo9GIXbt2eUsgtCSnTssZiUCdIImamhocOHAATqfTWzRUpVL96r0ulwuHDx9GWloawsLCEBsb6/XIicViqNVqJCQkQCKR4Ouvv0ZpaWmTzUMkEqFTp06YMWMG/P39YTKZYDQaYbFYfvMz/HnPlpGRgQsXLmDYsGHQaDQtKqBZENhtjtvtRnp6OlJTUwEAXbt2RUJCAqTSX2+v7XY7Dh8+jJycHERGRv7KkSGVStGrVy+oVCpkZmYiLS2tSebgwd/fH+PGjcOwYcMgFotx/PhxHDhwAGaz+br18F0uF4qLi/H5559j0KBBiIyMbHGhU4LAbnOcTicOHTqEtLQ0iEQi3HPPPYiIiLiueWixWJCfnw+SaNOmza9EKBaL0aFDB6hUKhgMBhQXFzflVCAWi6HT6fDaa6+hU6dOqK6uxrJly5CamvorgXlc8suWLUPHjh0xYsSI667azY0gsNsYj3mYlJQEo9EIPz8/DBo0CDKZ7LpmktPphM1m8/Zd9vzN83K5XFAoFAgLC4Pb7YbJZILNZmvSOUmlUoSHh+Ott95CdHQ0CgoKsHDhQuTl5f1iLAaDAbt374ZcLseUKVOgUql+8wCaP3sZrVZrk7dhEgR2G0MSpaWlSEtLg0Qi8ZZk+y1sNhv0ej1EIhHsdjsKCwuRl5fnfeXn56OgoMB77aKiItTU1DTVdADAe+Ddu3dv79nXsWPHsHz5clRVVXld+hkZGTh27BimTp2K4ODgG16TJPR6Pb7//nsYjcYmmsl/EM7BbmOqq6uxc+dOlJSUwM/PDy+//PINExCdTifMZjOcTie2bt2KY8eO/SoywuVyefs1m83mZmu85+PjgwkTJiA5ORl79+7Fxo0b0bVrV4wbNw4OhwP79u1D3759ERMTc1OvYXV1NbZu3YpLly4hMTGxiWbwHwSB3cbo9Xps3LgRVqsV3bp1Q2Ji4nWdG/8LSYwbNw5//OMffxEdwZ/DrWbNmoVr165BIpE0m8tbLpcjPDwcjz/+OC5duoQLFy5g3bp1iIyMREZGBux2O0aMGAGFQvGbXkOScDqdSEtLw6FDh/DCCy80eYSKILDbmBMnTuDChQsQiURITEz8zb2XB4lEAqVSCYlEAqvViuDgYAQEBHj/3+12w+l0Qi6XQyQSISQkpFlTXcRiMQYMGIAXXngBL7zwAk6ePIlFixZBIpFg0aJFCAgIuOF8XS4XKisr8c0336BHjx5eB05TIuzBbkPcbjfMZjN27tzpTapMSEi46fmPUqmEv78/XC4XMjMz4Xa7IRaLvS+RSITKykoUFhZCJBLB39+/WT1znsZ/DzzwAGbPng2VSoUTJ06gVatW8Pf3v+F8Pb/RJ598ArfbjYkTJ8LX17fJz8gEgd2GOJ1OnD17FhcvXoRYLEa/fv1qVbHXs4KRhNFohNvt/sX/e4RnNBqhUqmg0+mavcybWCyGVqvFk08+iYSEBJDE999/j3PnzsFut/9qDh6sViuOHj2KPXv2YNq0aYiOjm6WMzJBYLchVqsV27Zt81bs9fT7uhEikQgqlQphYWGQyWTXvTldLhfOnj0Lo9GI0NDQFlOJSiaTITIyEtOnT0dsbCyqqqrw4YcfIjs7G06n81fvJ4kLFy5g06ZNWLRoEdq1a9cMo/4PgsBuQ8rLy5GSkgKTyQS3241jx45h1apVOHjwIK5duwaDwXDdJ7tCoUBiYiIiIyNx5cqVX9UUdDqdyM7OhkQiwciRI2/pxvSELZWWljZ4MVCRSASJRIIBAwbg4YcfhlwuR2pqKlatWoXKyspfzNXpdKKsrAw//PADevXqhV69et3UseF2u+Fyua4bLVJfJG+88cYbDX5VgUbD5XLhxx9/xOeffw6j0eh9Wp84cQJHjx7FqVOnUF1d/YuwIZFI5N17tGrVClevXsWpU6cQERGB7t27gyQcDgcuX76M1atXQ6PR4O2330ZwcPBNTUTPIa7NZkNaWhoWL16MNm3aoHXr1g2+31GpVIiNjcXFixeRkZGBzMxMdO3aFbGxsZDJZCAJq9WKffv24dq1a5g4cSKCgoJ+07PqyX4uLS0FyRt6JOtME0XtCzQQJSUlnD9/PtVqNf39/RkfH8/Y2Fi2atWKCoXC+/cuXbpw1apVLCgooM1m837e4XAwIyODI0eOZP/+/fnxxx/z4sWLPHnyJGfOnMm+ffvyxIkTtNvtN0wR8WC321lWVsaPP/6Y7du3p5+fHx977DEWFBTQ5XI16NzdbjetViuvXLnC3r17Uy6Xs0uXLkxNTfWOxTO3o0eP0maz3XAOZrOZSUlJnDVrFk+fPt0o6TnCCnabkZWVhaVLl6K4uBg9e/bE5s2bMWLECHTu3Bl+fn6Qy+WwWCwoLy/H8ePHcfHiRQCAn58fVCoVpFIpfHx8kJiYiIqKCpw9exbnz59HRkYGNBoNnn32WcTHx0OtVtfqaW4ymfDRRx/ho48+QkVFBVq1aoVBgwahZ8+eDe6186S1qNVqaLVapKSkoKioCPn5+bjnnntQVlaG5cuXY/DgwRgyZMgN5+B0OlFRUYHly5ejffv2SExMvGFSZ51pcMkKNCofffQRxWIxxWIxP/jgA+/f3W43bTYbk5OTuWLFCj7yyCOMiIigTCZjWFgYH3nkESYnJ9NqtXqf6mazmVevXuWZM2eYn59fqye4JznSarXS4XCwuLiYzzzzDAMDAzl48GBu3ryZZWVljTZ/D4WFhXz11VcZGBjI4OBg/uUvf+HcuXO5YMECms3mG65cbrebNTU1fO+99zh58mSmp6c32jgFgd0muFwu2mw23n///ZTJZIyLi2NKSsov3uMxoaqrq5mfn88jR45wwoQJ1Ol09Pf3Z0JCAo8ePUqLxeK9psPhoM1mo8PhuKlJ6HQ6aTabeerUKT722GPcs2cPy8vLeenSJW7cuJEXLlyg0Whskkxom83GzMxMDhkyhP7+/gwNDeXUqVN54cKFG2Y0u91uOhwObt68mffddx/Pnz/v/T0aA0FgtwkWi4WHDx9mmzZtqFarOWfOHBYVFd3wM2azmZcvX+bcuXPZunVrKhQKjho1iqdOnaLT6azVHsuD3W5nQUEBV69ezbi4OAYGBnLChAksLS31CrWpSgx4sFqt3L17N9u1a0epVMoRI0YwJSXlhgKzWq1MS0vjjBkzuGPHjlrvNeuKILDbhLKyMj766KP08fFheHg49+zZUysngsvlYk1NDd966y1qtVrKZDL+4Q9/YFlZ2S3VrigqKuLrr79OjUZDqVTKqKgo/u1vf7upyBsTz4r90Ucf0dfXl2q1ms888wxNJtNviqaoqIh//etfuWzZMlZVVTWquEihJsdtQ2FhIZKTk+FwOBAdHY3Y2NhabcjFYjF8fHzwxBNPYN68edBoNDh48CBeeeWVG5YE4M/nWnq9HiaTCQqFAoGBgdBqtRgyZAjee+89zJ49u1lb0npCqcaMGYNp06ZBoVBg+/btWL169a/SbDz5bSdOnEBFRQXuv/9++Pj4NH7oVKPKV6BBsNvt/Pzzz6nVaqnRaPj888+zpqbmlq7hdDpZXFzMadOm0c/Pj2q1msuWLaPFYvnVU9xut7OmpoZJSUn805/+xBUrVrC6uprl5eX88MMPmZeX1+im1a1gMpmYlJTEPn36UKlUsnPnzvzhhx+8bnqPAyg1NZUPPvggDxw4QJPJdMNrej5X3zkKArsNyM/P56xZsyiXy9m5c2cePHjwF2dbtcXhcDA5OZn3338/xWIxhwwZwqSkpF/sndxuN/Py8rh8+XJ26dLFa5KeOHHC62ipjUOkKTEajTx9+jTvu+8+SqVSymQyPvLII8zMzKTD4aDT6WR+fj6nT5/OTz/9lHa7/Ybmtdvtpt1uZ1FR0XUfQLeCYCLeBly8eNHbazkuLg49e/asVd7X/yKRSNClSxc88cQTaNWqFS5duoSvv/4aVqvVG5Hhcrmwbt06LFy4EAUFBYiMjMSsWbMQEhICsVgMuVzeIlrR8ufok6KiImzYsAHz58/H6dOnvTlshw4dwqZNm2CxWFBaWorNmzcjLi4OY8eOhUwmu6F57XK5kJWVhRUrVsBsNtdrnILAWjgkceLECWRmZkIkEuGhhx6CRqOp04GoJ+A3MTERzz33HCwWC3bs2OEtDVBZWQmXy4XOnTvDarWiV69eWLx4MebMmYPo6OhGmN2tw/+qr3H58mW88cYb+Mc//oHjx49DJpPhkUceweDBg1FdXY1PP/0USUlJSEpKQk5ODiZMmIDAwMAbXt/lcsFgMGD58uVo3bo1fH196z1ggRaKx1QZOnQoFQoF27dvz5ycnHpf1263s7y8nH369KFareZLL73EBx54gE899RRLSkpYU1PDvXv38urVqzc9tG1qnE4n9Xo9d+7cyb59+9LPz486nY69e/fmpk2bWFxczOTkZPbo0YMKhYIxMTGcOnUq9+7dWytzr7Kykp9++innz5/P8vLyes9dyGhuwVgsFiQlJeHChQtQKBSYOnVqgzT9lkql0Gg06NatG3788Uf8+9//hlgsRnR0NHJyctCrVy9vdaqWUiWXJEwmE7KysvD1119j/fr1KC4uRlBQEIYMGYLp06fjrrvuglKphJ+fH2bMmIElS5agsLAQZWVl3nSe3zJt3W43HA4HUlNTkZqailmzZjWIl1EQWAvGaDRi2bJlMBgMCAsLw9ixY+stMLfbDZLeREbgP8Vt2rRpg/HjxyM8PBwSiaROe7zGgD+bhHa7HQcOHMBnn32G/fv3w+12o1OnTnjuuecwatQotG7d2vsZqVSKMWPG4NKlS1i9ejUyMjLwww8/IDw8/Dcj5v+7vEC3bt0QGRl5w1ZJtzIBgRbK6dOnqdFoKJPJOHr0aJaUlNTLZHE6nbx69SoLCwvpdru5f/9+DhkyhCNGjODhw4dZUVHR5NEYN8Nms7GkpISvvfYaY2JiqNVqGRAQwD/+8Y88c+YM9Xo97Xb7dT+Xnp7OuLg46nQ6dunShadPn75uWJTL5WJ1dTXnzJnjNQ0b6ncQBNYC8ZzbLF68mCKRiAEBAXz77bdptVrrdC2Hw8GKigru37+fEydO5BNPPMHKykpWVlby9OnTzM3Nvem5UFNjs9lYXl7OgwcPcvz48dRqtQwMDGR8fDz/8Y9/sKCg4KbHBSaTibt27WK7du2oVqs5ceJE5uTk/OozVVVV3LBhA4cPH860tLQG3XMKAmuBuFwu5uXlcdKkSQTAhIQEHjt2rE5teTxnQIsXL2a7du0ok8kYHh7O3bt302w2N8Lo64/b7WZhYSH/+c9/Mi4ujlKplEqlkpMmTeK+fftqfQbocrlotVr51ltveQ/XX3nllV9kFLjdbu7du5fjxo3joUOHGjzwt2UY2gK/wOVy4ejRozh79iwAoFu3bujatWudHA5OpxPffvstPv/8cxQUFKBjx4548skn0aNHj2bpYnkjPO735ORkLFu2DKdPn4bRaERkZCSeeeYZjBo1ChEREbXeH3pCqSZMmICMjAzs3LkTW7ZsQefOnTF+/HgoFArk5+fj22+/xcCBA9GzZ8+bFsYxmUw4e/YsunbtWrvjkgaVq0CDYDAY+Oyzz1KhUFAmk3Hr1q21Nls8rv3Kykrq9XoajUampaUxMTGR/fr14969e6nX6xt5BreGZ6UpKSnhmjVrGBcXR39/f2q1Wg4aNMgb2lTXxnoWi4VHjx5l165dqdVq2a9fPx4/fpylpaV89913+fTTT/PSpUvX3ct58OTB/fTTT5w+fTqvXbtWq2BrQWAtkPz8fPbr149yuZyxsbG8fPlyrT/rcDh48eJFzp07lzNmzGB2djYtFgszMjK85QMaOpW/vlgsFiYnJ3P27NnU6XSUy+Vs27YtX3nlFWZmZtY77tHtdtNsNnPJkiUMCQmhXC7n448/zk8//ZR9+vTh7t27b5q+43A4WFJSwgULFnDlypW1NiUFE7GFYTKZcPr0aWRnZ8PX1xdPP/30TaMPAMDhcMBiseD777/HmjVrvAU69+zZg5kzZ6J9+/beQqPNHeYE/H/3e1FREb777jts2LAB58+fB0kMHz4cf/rTnzBo0CAEBATUq54hf2747imSY7FY4HA4sHPnTpw6dQrTp09Hr169bljchz8X09m5cyckEgmGDx9e+2OMOj8WBBqFoqIijh8/nmq1mp06dWJpaWmtXMZms5mffPIJO3bsSKVSSV9fX06cONFbJqAl4cmMzsvL43PPPceoqCiq1WqGhobymWeeYVpaWr2dDR5T2WAwcO/evbzvvvuo0+moVCrp4+NDqVTKwMBA7tq1iwaD4YbXslqtPHPmDMeOHcsff/zxllZTQWAtjOPHj9PHx4cSiYTTp0+/qSv6v2tkfPfdd+zYsSPbt2/PZcuWsby8nFartUWZhG63m2VlZdy1axd79uxJPz8/arVa9ujRg2vWrGF1dfVNo91rg81m45UrV/j3v//dmwXeqlUr3nfffVy6dCnbtWtHlUrFgQMHMi0t7YbjvXjxIidMmMDt27ff8nGGYCK2EPhzZ5NvvvkGVqsVgYGBSExMhEQiuW63Sk9VpIMHD0KhUCAhIQGDBg3Cn//8ZwQFBWHQoEHw8fFpMS1V+bOpdvnyZWzduhWbNm1Cfn4+QkNDMWzYMMyYMQNdunSpd7MJu92OmpoaHD9+HOvXr8cPP/wAsViMuLg4/OEPf8CkSZPg7++PmpoarFixAufPn8e6devw/PPPIyQk5BemosPhQGVlJTZu3IgePXpg+PDht+55rddjQqDBcDqdzM3NZWJiImUyGe+77z6eOXPmV+/zHEJnZmby2WefZZs2bdinTx/u2bOH5H88ci0pONezwlosFu7evZsjR45kQEAAlUol27dvz3/9618sKCios4fwv7/HbrezsLCQCxYsYJcuXbx1IsePH8/vv//eawq63W7m5ORwypQplMvlbN++PdeuXfuLUgNut5vV1dVct24d586dy8zMzDqtqoLAWggmk4nLly9neHg4VSoVFyxYcN29gclk4sGDB5mQkECNRkOVSsWEhATu27evGUZ9c6xWKwsKCvjqq68yLCyMvr6+DA4O5qRJk3jp0iVWV1fXO4HTI+CDBw9y0KBB1Ol01Gg0jIiI4Pvvv8/CwkKazeZfCMRms/HSpUvs1KmTt4BrTk6ON+Lebrfz3LlzHDt2rPcAui5jFATWQigpKeGkSZOoUqnYunVr7t279xdPU7fbTZfLRb1ezzfffJMhISEMCwvjpEmTePTo0VsuIdDYeM7i9u/fz0ceeYRBQUH09/dn9+7duXDhQubm5t5yZav/xeVy0WQyMSsrix9++CG7detGnU7HVq1a8aGHHuI333zjFfD1qKmp4RdffMHY2Fj6+flxypQpzMnJod1u55UrV/jcc89x8eLFrKysrPMYBYG1EM6cOcO4uDjKZDL26dOHubm53v9zOBzMyclhWVkZHQ4Hz507x6lTp/K9995jRUVFi3JikJe4NNMAACAASURBVP+58QsKCrhkyRJ269aNIpGISqWS48aN4759+27qtasNbrebFouF+/bt45QpU6hWqymVShkTE8MFCxYwIyOjVuPU6/WcM2cO/fz86Ovry7feeoslJSWcN28en3zyyVuuvvW/CAJrAdTU1HDFihXUarUMDg7msmXLaDAYaLPZqNfruXr1at57772cNm0aCwsLabVamZOTw8rKyha15/KYakeOHOGkSZPYunVr6nQ6dujQgUuXLmVmZibNZnO9blhP8HJubi4XLlzIu+66i/7+/tRoNBw7diz37dvH0tLSWsUrevaHqampHDVqlPdo5IknnuCECROYlpZW71VWEFgL4MqVKxw7diyVSiU7dOjAq1evsqKigllZWZw/fz6DgoIol8vp6+vLTz75hEVFRayoqKDRaGwRbnjPalJUVMStW7eye/fu1Gg0DAgI4IABA/j111+zpqam3uO02+3U6/W8ePGi1+zUaDSMioriSy+95I1auVVBmM1mfv/99wwLC6OPjw87duzIgwcP1ss09CC46VsAFy9exIEDB2C325GYmIiCggKkpaVhw4YNOHHiBFwuF2QyGTQaDbZu3Ypjx44hNjYWcXFx6NChAzp27AgfH59mG7/T6URqairWrFmDNWvWwOl0Ijw8HBMnTsTjjz+OmJiY6x433CpFRUXYtWsX3nvvPeTl5UEul6N///54/PHH8eCDD3ozsG/1e5RKJfr164c5c+bgn//8J3Jzc7F792506tSpXuMFhIzmZoU/hwvt2rXLW9wzOzsbc+bMQUFBAfR6PQB4i37a7XZvhD1J+Pn5ITo6GsOGDcOkSZMQGxvrrarUFGN3uVyorq7Gjh07sGHDBqSlpUEqlSIxMRHTpk3DkCFDoNVq65Ud7SkY+tNPP2HVqlU4dOgQysvLERkZicmTJ2P8+PFo165dvbKPRSKRtyRDVlYW1q9fjy+//BIxMTGYOXMmpFJpnX9TEdkIbf0EaoXD4UBJSQmGDh2KrKws7yGn2+2GSqWCSqVCTEwMOnTogDZt2gAAiouLceXKFWRkZMBkMsHlcsHX1xc9evTAm2++ibi4OCiVSshkskaLOXQ6nbDb7SgrK8OiRYuwc+dOGAwGyOVyjBs3Di+99BJiY2Mhl8vrPAa32w2n0wmTyYQdO3ZgyZIlKC4uhtPpRHR0NP7+979j4MCB0Gg0DVLegP/ZLuHkyZOYP38+zp49i3bt2uGTTz5Bjx496i7gehuZAnWmqqqKb731Fv39/QmAIpGIAKjRaPjqq68yLS2NNTU1NBgMNBqN3pder+e5c+e4ePFi9u3blzqdjgqFgv7+/nzttdeYkZHRqKn/ZWVl3LFjB/v160cfHx+q1Wr269ePX3zxBQ0GQ4NU/TWZTPzxxx85c+ZMBgYGUqFQMDY2ls8//zzz8/NpsVjq7YC4HkajkevXr2dERAT9/Pw4btw4ZmVl1fl6gsCaCafTyaSkJHbr1o0KhYJisZgqlYrt27fnn//8Z168ePE3PWGeg1C9Xs+UlBS+/vrr7Nq1K6VSKUNCQjhz5kzm5ubeML/pVvGkfJw7d46vvfYau3btSj8/P4aFhfGpp57i4cOHqdfr651WYrPZmJeXx88++4xDhgyhTqejTqfj8OHDuWrVqlr3MasrTqeT5eXlfPnllxkVFcV77733uhE1tUUQWDNRVVXFv//971Sr1ZRIJPTx8eGQIUO4Y8eOW/K4eZrJffXVV2zbti3lcjmDg4P5zjvvNEhipceVbTQauXv3bo4YMYKBgYFUKpXs0qUL//3vf7O4uLheN73nEN1isfDcuXN8/PHHvc0DW7VqxRdffJHnzp1rshIHTqeTOTk5XLBgAXft2sWqqqo6X0sQWDPgdru5Z88eduzYkRKJhKGhoZw1axZzcnJoMplu+WzLE9GQmZnJ+Ph4KhQK6nQ67tmzp94mlNVqZXFxMd9++21GRkZ6o9InTpzIn376iQaDod6mmsPhYFVVldfF7ykm2rNnT27ZsoUVFRVNmijqWUktFku9z+0EgTUxNpuNBQUFHDt2LH19fRkdHc3169ezrKysXiadZ6XZunUr4+PjKZVKOXToUGZlZdXpui6Xi2VlZdy/fz+nTp3KoKAg+vn5sXv37lywYAEvX75cpwYU/ztmvV7P5ORkzps3jxEREfTx8WFsbCynTZvGEydO0Gg0tpiD9LogCKyJqaio4F//+lfqdDoGBgZy0aJF9TJB/heDwcClS5fSz8+PgYGBfPXVV2/JVPSYa+Xl5Vy6dCm7d+9OsVjsjZT44YcfGqTEm8vlotls5hdffMEhQ4ZQoVBQoVDw7rvv5sqVK5ukz3NTIAisiTlz5gzDw8OpVCo5bNgwZmZm1nsl+G+cTifPnj3rTSi89957mZmZWavPulwuGo1Gnj17luPHj2dYWBh1Oh0jIiL4zjvvMDs7u0FCncxmM7OysvjUU08xJiaG/v7+DA4O5uOPP37DYqK3I8JBcxNz8eJFlJWVwcfHB4MHD0ZkZGSDlk+TSCSIiopCYmIitmzZgtzcXJSWlqJdu3Y3PJOyWq2orKzE/v37sXDhQuTm5sLHxwddu3bF//3f/6Ffv37QaDR1Ptci6U2GPH36NN59912kpKRALpcjIiICTz/9tLf7iUgkahF1QxoCQWBNCElkZ2d7D0vvvvvuGxZbqSsqlQrjxo3D3r17UVVVhaKiIjidzt/MbiaJtLQ0fP7559iyZQv0ej2CgoLw6KOP4rHHHvO2q63PTU8SV65cwRdffIH169ejoKAASqUSo0ePxhNPPIG77767RTWbaCgEgTURJGGxWFBUVASSaNOmzU2LiXoa4uXn58Nms3lXu5tFLkilUvTt2xf+/v6orq5Gbm4urFbrrwTmcDig1+u9oU4XLlyA2+3GwIED8fTTT6N///4IDAys10PA4XDAYDBg7969WLNmDVJSUuB0OhEfH4+nnnoKQ4YMQXh4+B0pLkAQWJNBEgaDASaTCWKxGIGBgWjVqtV1VwX+XHPDYrEgIyMDf/3rX+FyuTBjxgyMGTPmpnUrJBIJdDodWrdujdzcXJSXl8Nms3k/53K5YLfbUVhYiI8//hgbNmyAyWSCSqXCpEmTvA336rNqeb6jrKwMq1evxqpVq1BZWQmJRIJhw4Zh3rx5iI+Pv2OF5UEQWBNiNBrhdrvh5+eHoKCg34wwd7lcyM3NxaZNm7B06VKYzWaIxWKcP38egYGBGDlyZK2+r3Xr1vDx8YHZbIbT6fT+Xa/XIykpCe+++y5OnToFl8uFnj174sknn8To0aOh0WjqtWp5HibJycl4//33cejQIbhcLrRv3x6PPvooHn74YQQHBzdqvGRLQRBYEyIWi6FQKCCXyyEWi8H/ibN2u90wGAw4duwYvvjiCxw9ehRWqxUBAQHQaDTQ6XRQq9W1/j5PlLhcLgdJ2Gw2XLp0Cdu2bcPGjRtRXl6OoKAgjBo1Cg8//DB69OgBtVpdZ3F5mthlZ2dj+/bt2LhxI4qLi6HVajFkyBA8/PDD6N+/f4uqdtXYCAJrQnx8fOB0OlFWVobCwkI4nU5IJBKvSVhTU4NVq1ZhzZo1yMvLg0gkwsCBAzF9+nS43W4EBgaiW7dutfout9vtNQ/FYjEcDgeSkpLwzjvveJsqtG/fHrNnz8aECRMQEBBQZ2Hx59QVq9WKtLQ0LFy4ECdOnIDJZEJYWBiefPJJTJ48GeHh4S2msV9T8fuabTMiEomg0Wi8TbUrKipQVFSEqKgomM1mpKenY+HChTh06BCsVivCw8MxY8YMPP3005DJZF5zsjY3qMvl8noP3W43AGDlypVYsWIFjEYjfHx8MHz4cLzxxhvo1KkTlEplvfZBnhLY69evxz//+U+YzWZvrcY333wT3bp1g1KpbBSPaUtHEFgT4THX2rRpA7FYjCtXruD48ePeVkX//ve/kZqaCoVCgcGDB2P69Om49957odPpbvm7bDYbvvnmG+j1erhcLuzcuRPl5eWwWq3o2LEjxo8fj+nTpyMwMLDOeU78OVnUYDAgKSkJ69atw4EDB2A2mxEbG4sxY8Zg5syZCAkJuSWz9o6jOU63f89s27aNCoWCKpWK9913H6dOncrQ0FBKpVK2bt2af/nLX27aSudGeJrXDR8+nAqFgiKRiGKxmD4+PnzggQe4b98+Go3Ges3BU3imuLiYixcvZteuXb013++//35+++23NBgMt3UMYUMhCKyJycjIYFRUFBUKhbdJQ2BgIAcMGMCdO3eytLS0XrXZa2pquH79eoaEhFAsFlMulzMmJoZLlizh1atXf1WAsy5UV1fzyJEjfOihh9iqVSuq1Wq2a9eO77zzDq9cueLNCBAQBNZkuFwu1tTU8PTp097y2Pg5i3ns2LFMSUn5RWvTW8VqtbKwsJDr1q1j7969KZVKqdFoOHjwYH711Vf1rpDkydfKy8vjqlWrvI0bAgICOHjwYG7bto3l5eXCqvU/CAJrIsxmMzdv3sxhw4ZRLBYTAAFQKpXy3XffpdlsrvPN6XK5+OOPP3L27NnelUskEnHkyJH86aefaLPZ6n3jWywWnjhxgo8++ih1Oh2lUimjo6P5yiuv8PLlyw1SJuBORBBYI+JpjZqdnc25c+eyc+fODAgIYEBAAMeOHcv+/ft7b9T333+fFRUVtxypbrVauWHDBg4ZMoQajYYymYxKpZJxcXE8ePBgvesmehIu33//ffbp04darZatWrXiqFGjuG3bNpaUlNS7tvydjCCwRsJms7G6uppHjx7l4MGD6efnRz8/P8bGxnLFihXMy8vjihUrGBoa6q1H/8EHH7C4uJhms7lWN63D4WBlZSX/9re/UaPREADlcjnDw8O5efPmOpcM8CRvGgwGZmRkeBMuVSoVAwICOHv2bGZlZbW4xn4tEUFgjUROTg6XLl3Ktm3bUqFQUKPRcPLkyTx8+DAtFgsdDgcLCws5d+5cRkVFUSqVUqvVctq0adyzZw8LCgpuWOfC6XQyLy+P33zzDSdNmuQVWNu2bblw4UJWVVXVeeXyJFyuXLmSPXr0oEKhoFar5YABA7h169YG6Yjye0Goi9iAuFwuGI1GnDhxAhs2bMDBgwdhMBgQHR2Nhx9+GKNHj0ZUVJT3XMhut6OyshJ79+7F+vXrkZycDAAICQnB3Xffjc6dOyMuLg4BAQHw8/ODSCSC0WhEeXk5Ll68iLS0NPz0008oKiqCWCxG586d8dRTT2H48OEIDQ295cNjl8sFs9mMCxcuYO3atd50Fz8/P0ycOBETJ05E165df7eHxnVBEFgD4CmSWV1djS1btuCTTz5Bbm4uRCIRBgwYgJdffhn9+vWDQqG47k1vsViQlZWFzz//HBs3bkR1dTVcLhdUKhWCgoK8/9psNphMJphMJpSWlsJut0MikSAgIADjx4/HjBkz0K5du1suo00SDocDRqMRX3/9NZYvX460tDRvZ8j58+djwIABCAkJaaif7HeDILAGwGg0Ii8vD4sWLcLXX38Ns9mM8PBwTJ48GbNmzUJISAgUCsVvRo57BGqz2ZCSkoJPP/0UFy5cQHV1NcxmMxwOB/z8/GAymeB2uyGTyaBSqaDVatG7d2/MnDnTu7Lcapln/hyRcenSJXzyySfYunUrjEYj1Go1xo8fjxdffBERERG1ykMT+DV3pMA8U2rMVAj+HKBbVFSE/fv3Y+XKlUhPT4dEIsHdd9+NRx99FCNGjIC/v/8t3ZgWiwVGoxFlZWXIzMxEbm4uampq4HA4YLPZoFar4e/vj4iICMTFxSE4OBh+fn51KjtgtVpRXl6Oo0eP4vPPP8eZM2e8q9bkyZMxZswYBAcHQ6FQ3PK1BX6mebZ+DY+nGpKnO2F9Dm1vhsvlos1mY3Z2NmfPnu11UoSGhnLOnDn1CnVqClwuFx0OB9PS0jhnzhyGhIR4C5bOmjWLp06dEhwYDcQdIzCr1cpr165x4cKF7NOnD7dt29YobmRPkcwtW7YwPj6e/v7+1Ol0jI+P544dO+od6tTYeGoRfvPNN+zbty8DAgKoUqkYFxfHNWvWsLCwkBaLpbmHecdw25uIdrsd1dXVSEtLw8qVK3HgwAGEhoYiODgYH3/8MaKiohokuY8kzGYzrl69is2bN2Pt2rUoLS1FUFAQhg4dijlz5iAmJgZqtbpFZul69nhXr17Fpk2b8Nlnn8FqtcLX1xd9+/bF3LlzBQ9hY9DMAq8XbrebFy9e5Ouvv862bdtSKpXS39+fEomEwcHBXLJkCcvLyxvkexwOB3fu3MkHH3yQPj4+lMvljI+P56effsri4uIWb1IZDAZ+9dVXHDZsGFUqFUUiEXv27MkPPviAVVVVLX78tyu3pcBsNhsrKir4xRdfcMSIEQwODqZOp2P37t35/vvvMyEhgT4+PoyPj+f+/fvrVTvdYrEwMzOT8+fPZ+fOnanVahkaGsonnniCJ0+eZFVVVaN2+6gvNpuN6enpfPHFF9mxY0f6+voyKCiI06dP55EjR1pkE/U7idtGYJ5VpKamhpmZmXzhhRfYqlUrajQaBgYGcuTIkTx69CjNZjMPHTrE8PBwKhQKTpkyhRUVFbfsdLDb7ayurmZycjL/8Ic/0NfXlxqNhu3bt+fSpUtZWFjYYm9MT3ujqqoqHjp0iEOHDmVgYCB9fHzYrl07b9yjEOrU+Nw2AnO5XCwqKuJnn33Ge+65h0qlkmq1mn369OHy5cu9zRPcbjerq6u5aNEib0nmZcuWsaam5pa+7+rVq/zwww/ZsWNHKhQK+vn5ccyYMd7a7PUpH93Y2O12Zmdn8+233/bmngUHB3P8+PE8fPiwNydMMAsbnxbv5HA4HLBYLDh16hS+/PJLHD58GNXV1VCr1ZgwYQLGjRuHbt26Qa1We50ZnspGc+bMwenTpxESEoKVK1eid+/eNzwv8tQiTE5Oxrp167B3717YbDa0adMGU6ZMwbhx4xAREfGbERktAc+51vr163HkyBFYLBZ06tQJU6ZMwQMPPICoqKgbHnoLNDDNrfDr8d8N2a5du8Z3332XXbp0oY+PD319fdmvXz+vS/y3VhKDwcDVq1ezXbt2VKvVfPLJJ3nt2rXrPrU951qVlZVcs2YN4+PjqdFo6OPjw8TERO7atYtGo7HFmoSetBi9Xs+3336bnTt3pkqlokaj4ciRI3ngwIEGacYncOu0SIE5nU7W1NTwwIEDHD16NDUaDX19fdm2bVvOmzePWVlZ3i4fv2XmeK7x1FNPUalUMjw8nCtWrLhuFLjZbObZs2f52GOPUaPRUKlUMjo6mn/+85+Zl5dHi8XSYsXlMYmPHj3KoUOHUqPR0M/Pj+3ateObb77J4uJibz9jgaanRQnMk1Z/5swZvvnmm+zUqRN1Oh1bt27NcePGcePGjSwtLa11ux+3280zZ86wV69e9PX15ZAhQ3jx4kVvlIencMuaNWs4bNgwrzdyxIgRXLt2LcvKyhq0tVBDYzabmZmZySVLlrBHjx5UKpUMCwvjuHHjuGPHjnqlrAg0DC1CYJ6b3Wg08ssvv+SIESOoVqupUCjYqVMnvvvuu8zKyqrTzWIwGLh9+3aGhIQwMDCQL774IsvLy2mxWJidnc1nnnmG0dHRXkfA888/z3PnzrVYYXnMZ5vNxqNHj3LixIkMDg6mXC5nQEAAFyxYwEuXLrXoo4PfE80uMM9e68KFC3zkkUcYEhJCrVZLnU7H8ePHMzk5mXq9vs51JTxd45944glqtVpqtVquW7eO27dvZ+/evanVaunn58devXpx27Zt3n7ALdXDZrfbWVJSwsWLFzMmJsbbz3jIkCE8c+YMKysrW/T4f280qxfRbDajpKQEhw8fxqeffor09HTIZDK0bdsWkydPxpQpU+Dv71/vaG673Y7jx4/jr3/9K5KSkhAREQGJRIKioiIEBARg0KBBmD17NuLj4+Hr69siPWxOpxNGo9GbDPnVV1/BZrMhJCQEo0ePxsyZM9GhQ4d69/ESaGCaQ9Wemg/79+/n9OnTGRgYSIlEQp1Ox+eee44nT56sd+f6//0+q9XKDz74gD4+Pt56gfHx8Vy+fDlLS0tb9F7F7XazqKiIH374IXv06EGRSESpVMoRI0Zw69atgoewBdOkGXQkYbVaUVhYiLVr12Lnzp3Iy8sDAAwdOhTPP/88unfvjsDAwAZ9EotEIsjlcowePRr79u3DoUOHoFAo8Nhjj2HcuHHQ6XQt8qnv6VZy9uxZfPTRRzh06BBMJhOioqIwffp0jB8/HjExMXUufy3QBDSFij0rSHl5OY8fP+51vWu1WsbExPCll15iRkYGbTZbrVYSz0bfZDKxpqam1qudyWTi6dOnGRUVRa1Wy8mTJzM/P7/FrV5ut5sWi4VFRUXcvn2791xOp9OxR48e/PLLL1ldXS243m8DmkRgDoeD586d46uvvuqNEdRoNBwzZgx37txJg8FwSyahy+WiXq/nt99+y3Xr1rGysrLWwrTb7VywYAF1Oh3lcjk//PDDFucUsNvtPHnyJGfNmkWlUkmpVMrIyEi+8MILTE9PFyo63UY0qolotVphNBqxc+dObNmyBSkpKXC5XOjatSsefvhhjBw5EpGRkVCpVLUKPXI6nTCZTEhKSsLWrVvh7++Pxx9/3Ftx6WZ42v9MmjQJaWlp2LFjBz7++GN06tQJAwcObNbUeP7cY6uystLbvO7ixYuQSqVISEjAtGnTMHToUAQEBAi1MW4nGlqx/32mdf78eU6fPp1hYWH09fWlVqvluHHjeOLEiTo1CLBYLNy0aRN79OhBrVbLuXPn1qnmus1m486dOxkdHU2tVsuxY8eysLCw2Uwuh8NBk8nEjIwMzpw5k6Ghod6mEI8//jgvXbrUqCUQBBqPBheYw+Fgfn4+V6xYwe7du9PHx4cajYb33HMP//3vf7OysrLON4vBYOB7773HsLAwyuVyJiQk8NixY7d8HbfbzdLSUj733HMMCAhgeHg4V65cyerq6lu+VkNQUlLCTZs2sVevXlSr1VSpVOzfvz/Xrl1Lg8Eg1H2/jWkwW8PhcMBgMODUqVPYvn079u7dC7PZjFatWuHBBx/ExIkT0b17d6jV6jqbOCKRCD4+Pl5TLj09Hbt370Z8fDx8fHxqneru6Tb55JNPIjk5GWlpaVi3bh26du2K3r17QyQSNbpX0e12w2KxIC0tDdu2bcPOnTtRWFiIwMBAPPDAA3j44YfRrVs3b0dMgduU+qjzv8N2rly5wrfeeovdunWjUqmkSqXi0KFDuXXr1gY7ZzKZTNy8eTN79erF+Ph4SqVSdunShceOHaPZbK7TNbds2cKgoCAqFAo+88wzjZ7r5TGh9Xo9N2/ezMTERGo0GqpUKvbs2ZOrV6++YZaAwO1FvQTmyTA+fPgwBw8eTK1WS41Gw8jISL722mvMycmh0WhssENji8XC77//nvfddx83b97MgIAA+vn5cejQoSwqKqqTiCsqKjhv3jz6+PgwJCSEmzdvrncHyBthNptZUFDAl156ia1ataJSqWRISAinTp3K8+fPN+jvJdD81ElgTqeTer2eP/74I19//XVGRUXR39+f4eHhfOihh7ht2zZWVVU1eG1Am83GpKQkjh8/nt999x2ff/55BgcHU6VS8Z///Cf1ev0t35g2m40pKSns27cvdTode/bsyfPnzzfo2D2rVmFhIbdv387hw4dTp9NRq9Wyd+/eXLJkCa9du9aiaykK1I1bFpjb7fYmMw4dOpRKpZIymYxdu3blu+++yytXrtR6JXG73b943QyHw8HMzExOmTKFq1ev5uHDhzl8+HBKJBL27NmTP/zwQ51MK71ez6VLl7JNmzb08fHhq6++yrKyslu+zvXwiCsvL4/z589n27ZtKRaLqdPp+Mgjj/DkyZNCbYw7GMkbb7zxxq3s2YqLi/HnP/8Zhw8fRmpqKqRSKSZOnIg333wTw4YNQ2BgICQSSa2cBNXV1cjMzMTVq1eh0Whqncq+b98+KBQKDB8+HGKxGCdPnkRFRQXsdjsSEhKgVCpvKaVfKpUiNjYWFy5cQHp6OgoKChAbG4tOnTrVy+HhdDphMBiwb98+vPzyy/j+++9hMpkQHh6O119/HU899RTatm0LuVzeIkO1BBqAW1VkZWUlX3nlFYaHhzM0NJRPPvkk8/Lyav0U9uzbLl++zEWLFrFz587s0aMHP/nkE+bl5Xkzla+HJ+RqxowZfPrpp1ldXc38/Hxv1aeIiAhu3LjxlgvceDh+/DgjIyOpVqs5ZswYXrt2rU55YW63myaTiVlZWfzHP/7BmJgY715rzJgxTE5OpsFgEPZZvwNuWWBOp5PXrl3jwIED6efnx/j4eKalpdXKNHO73SwvL+eXX37J+++/nxqNhhKJhBKJhFqtlhMnTuQPP/xwU4HMnj2bDz30EKuqqmiz2ZiamsouXbpQpVKxX79+TEtLq9PNW1NTw08++YTBwcEMCgriokWLbjlS3ROOtWvXLo4dO5Z+fn5UKBTs0KGDd68lODF+P9yyieiJTNdqtThz5gyuXLkCm82Gvn371qpsdE1NDQoKCtCzZ09ERUXhypUrEIlEcLlcuHz5Ms6cOQO9Xo/w8HCoVCpIpdJfXfPIkSP46aef8Kc//QlqtRo6nQ4AkJSUhLy8PMhkMvTp0wcymeyWTEWxWIw2bdogIyMD2dnZOH/+PO655x60adOmVmdsFosFly9fxocffoiPPvoIqampUKlUGD16NP7v//4PI0eORGBg4HXnJHBnUieBicViBAcHo6SkBCkpKSgsLER4eDi6du16wzQTjzjbt2+P+Ph4xMXFwWQyoaqqCv3790dubi6Ki4vx008/4ezZs+jSpQu0Wq13T+e57unTp3Ho0CE89dRT8PHxgVgsRmBgIHJzc5GWloa8vDx07NgRMTExXvHWZi8lkUigVCqhUChwEnGErgAAFE9JREFU5swZ5OTkoLq6GoMGDbphIqantNz58+fx+uuvY9OmTdDr9QgMDMSzzz6LF154AXfddRfUarVQ9/13xi0LDPiPUNRqNXx9fZGSkoL8/HxUVFSgf//+0Gg0N7yJxGKx9wmuVCoRFhaGb775BnfffTf+9re/oaKiAkVFRUhPT8euXbvgdrsRFRX1i0iN1NRUHDlyBFOmTIFOp4NYLIZGo4Farcbhw4dRVlaG9PR03HPPPZBKpcjPz4evry9kMtlNReZZxfR6PU6ePImysjIolUr07t37uisPSeTl5eHLL7/EvHnzkJqaColEgoSEBLz99tsYP348dDqdIKzfKXUWmFgshr+/P2QyGY4cOYKKigrI5XJv2NKNVjHP/4nFYq/H78CBA+jZsyceeughhIeHQ6/Xo7CwECkpKcjIyIBcLkdwcDDkcjmysrKwf/9+jB07Fq1bt4ZYLIZEIoFarUZmZiays7Oh1+tRXl4Ou90OkUiE8PDwWnkpPatscHAwfvrpJ+Tn56OyshI9e/ZEUFCQN8zLExp26NAhLFu2DKtXr4bFYkFsbCwee+wxzP1/7d17TJPXGwfwb1va0kJbKFBXFEHlIqIw5nROQRYELxPEuaEmXmam0+iiGINTEqdz2dAt0SULQ2e8RYNxgvMy4y3EKfO6ISoowqwiVZD7pS209PI+vz+2vr85nUOlwub5JCaGUHJo+nDOe85znic9HUOGDIFMJmPB9TJ7ngc4h8NBTU1NfJf7gIAAys/Pf6rkVJvNRg8ePKD58+fTmDFjqLq6mj/EXrhwIfn6+pJEIqHw8HBauXIlVVRUUG5uLmm1Wjp+/PhDh7MGg4F2795NAQEB5OvrS7Nnz6aCgoJnqmtoMpno2LFj5O/vT97e3rRo0SKqr6/nU8Pq6upo48aNNGjQIPLw8CCZTEaJiYl05MgRMplMbBODIaLnTJVyHqJeu3aNIiMjSSwW04QJE6iqqqrTZcOc9TnOnj1L4eHhlJ2dTc3NzWSxWKixsZFyc3PpjTfeIB8fH/Ly8qK4uDhau3YtaTQaysnJ4Y8HOI6jxsZGysrKotGjR9Pu3bv58mzPkkJlt9upvb2dli5dyhc+dda/OHfuHCUnJ5NKpSK5XE4BAQG0evVqqqqq4uu+MwzRM+wi/plzuedc5l28eBG1tbUQi8UYOnRop555nMtNhUIBDw8PHD16FKGhoQgKCoK7uzuCgoIwbNgw2O12NDY2QqfT4ZdffoHdbseIESMQHR0NsVgMIoJOp8Pdu3eRlpaG4cOHQ6lUdmoMj+N8VtRoNLhx4wZu376N0tJS2O12bNiwAcXFxRAKhRg1ahSWL1+OGTNmwNvbm9V9Zx7WVZFaVlZGSUlJ5OnpSaGhoXTq1KmnSgHiOI6am5tp5syZlJ6e/khV2ubmZsrLy6OEhARSKBSkUChozZo1fGKusypwVy7PnAfGW7ZsIbVaTSKRiNzd3UkkElGfPn0oIyODSktLWeY787eeawb7M7lcDo1Gg3PnzuHBgwdob29HdHQ0fHx8OvV650zm7e2N/Px8+Pn5oXfv3nw3FDc3NwQFBeGtt96CSqWCTqfDgAEDEBcXx6caSSSSZ56x/sput8NiseDXX3/Ft99+C51OB47jIJFIEBMTg/Xr12PKlCnQarXsXIv5W10WYEKhEIGBgbh//z6Ki4tRWVmJfv36YdCgQZ3OTRQIBPDx8UFDQwMOHjyI+Ph4yOVyCIVCCIVCSCQSeHt7IyoqCm+++SaEQiEGDx7MB2FXXJTkOA5tbW3Q6/XIzc3Fxx9/DJ1OB4FAgF69eiEpKQlr1qxBdHQ0vLy8Ov27MS+prp4Sy8rKKDExkb/SX1JS8lT5fBzHUXFxMY0dO5Y2btxITU1Njyz5niYD/2m1t7dTXl4eTZw4kSQSCQmFQpLL5RQbG0vbt28no9HImtcxndZlM5iTTCaDVqvFmTNnUF1djZqaGowZM6bTTeuch9hyuRxbt26FVCpFUFAQjEYjdDodNBoNny3SVTOHw+GA2WzGzZs3kZmZiR07dqC4uBhWqxW9e/fGrFmzkJ6ejri4OH5GZbMW0xkuqU3f0NCAzMxM7Ny5Ew6HA9988w3efffdTteXcNZhj4uLAxEhKSkJGo0G06dP5wOsKxAROjo6YDKZcPr0aWRmZqKsrAwcx0EsFsPb2xtffvklEhMToVare2xXS6bnckmBPaVSiZkzZ+LatWs4f/48tm7dirCwMIwYMaJTr3c+bw0fPhyNjY0YPXo0YmNjO10/sTOICHa7HdeuXcOuXbuQm5uLlpYWEBF69eqFCRMmYMWKFfxGCwsu5lm4JMDc3NwQHh6O1NRUlJSUoLy8HPv370dISAhUKtU/VpUyGAwoLi5GQkICIiIi+EuJXfEhJyKYzWZUVVXh8OHD+OGHH3D9+nW0t7dDLpdjyJAhmDVrFsaNG8dn0bPlIPPMXPmAp9fracaMGeTh4UGhoaF0/Phxamtr+8fXtbS0UEVFBZnN5i4903IWRD137hylpqaSl5cXicVikkgkpFKpaN68eVRUVNSpMTJMZ7i0P5jVakVVVRUmTpyIqqoqREVFIScnB717937ibMRxHDiO67LZg/5YDt6/fx85OTnYvHkzmpqa0NHRAZlMhgEDBiAtLQ3Jycl89gdbEjJdoct3Ef/MmS0vFotRVFSEW7duwdPTE5GRkXB3d39ixn1X7dRZLBY0NTXh5MmT2LBhA77//ns0NzcDALRaLcaPH48VK1Zg3LhxnUqtIiJwHAer1QqLxQK73Q4ALGOeeSyXdhEQCAQQi8VISkpCYWEh9uzZgz179iAyMhLJycku+1DS70nM4DgOt27dwvbt2/leZBzHwc3NDWFhYViwYAEmT54Mf3//TgUz/dGgoaGhAbdu3YJOp4NCoUBERAT69+/PZj7mES6dwYD/n2vJZDJcunQJtbW1MBgMiImJcdkNX7vdjubmZuTm5mLVqlU4deoUGhsb+e33pKQkfPXVV4iPj+ezMTrDbDbj6tWrWL58OU6ePAmtVotLly5h165daGhowODBg584MzMvnxcSYCKRCD4+PjAajSgsLERNTQ00Gg0GDhzYpR9Im80Gg8GA0tJSvi5GZWUl2tvb+YNptVqNpUuXIiIi4qnrY+j1enz22Wew2+1YuXIlJkyYgGHDhqGmpgZbtmxBnz59EBwczMqwMf/3onZT7HY71dbWUkJCAsnlcgoPD6fz58932d0pjuNIr9fT119/TVFRUSQSiUggEBAAcnNzo7CwMPL29iaBQEABAQGUkZHBV3jqrE8++YT69etHBw4ceOimwJUrV2jQoEEUGxtLp06dYtn1DM/lM5iTQCCAVCqFv78/Lly4gIqKCpjNZowePbrTaVSPY7PZ0NbWhjNnzuDzzz9Hbm4u7t27x2e+h4SEYNWqVVi4cCEGDx6Me/fuob6+HiUlJdDpdHjttdegUCieuKlis9lQVVWFTz/9FJ6enliwYAF8fX35MUulUrS1teGnn36CUChETEwMm8WY373IaOY4jurr62nt2rUkk8lIq9XSpk2bnqkZn8PhIJPJRHfv3qUvvviC/P39SSqVkkAgIIlEQmq1msaOHUs///wz31DBaDRSSUkJpaSkkFqtJplMRgkJCVReXv7EnmVGo5E2btxIGo2G4uPjqbm5+aHvtVgsVFRURFqtll5//XW6efMmm8UYInpBPZr/zOFw0OXLlyk2NpY8PT0pKiqKioqKnqrxAcdxZDAYKDc3lyZMmEByuZzc3Nz4JWF4eDitXr2aKisrH+q/7HA4yGq1UmVlJS1btoy8vLz4NktPGkNNTQ2lpKSQp6cnvf3224806nM2LQ8LCyONRkNHjhwhs9n87G8S85/xwveUhUIhQkJCMG/ePKjVauj1euzcuRPV1dX/+FqHwwGTyYSLFy9i1apVWL16NQoKCmA2m/m7ZFOnTsW6deuwePFi+Pv7P3SuJRQKIRaL8corr2DRokVIS0uDUqlEYWEh1q9fj99++w0cx4H+cvZuNptRV1cHkUiEwMDAR5azzsueffv2BcdxqKmp4c/HmJdbt3TTlsvlmDJlCk6fPo28vDwcOHAAo0aNgr+//9/WHrRarTAYDDh27Biys7Nx7do1viSbVCqFWq3GvHnzMGfOHPj7+z+xoblEIkFgYCDS0tJgs9mQlZWFo0ePwtfXF+vXr+crCjtZLBZ0dHTwpeqc///rGFUqFTiOQ3V1NQswBkA3BZhQKIRcLseyZctw9epV3Lx5E9u3b8fIkSOh0Wj4G8oA+KwJ59b74cOH0dbWBqvVCiKCt7c3Bg8ejFWrVmHkyJFwd3fv1LmWSCSCSqVCWloaamtrsW/fPuzbtw/BwcGYO3culEol/71NTU0wGo3o6OhAcXEx9uzZA7FY/NDPIyLcvXsXNpsNt2/fhtVq7bo3jPnX6pa0A2cqVN++fZGWlgYvLy8UFRUhKysLJpOJX6a1tbWhvLwcmzdvxoIFC7B//360tLTAZrNBKpUiPDwc8+fPR3Z2NmJiYuDh4dHpcy3nGJRKJRYuXIjo6GjYbDZs3boVd+/efWgGco5HJBLBaDSitrYWdXV1j/zr6Ojgv59hgG6awZyUSiUSExORn5+PQ4cOYdu2bRg5ciQSEhIgFApx/vx5fPfdd8jPz4fRaAQRQSgUQiqVIjo6Gunp6YiJiYGvr+8zj8Hd3R2hoaGYPHkybt++Db1ejx9//BFBQUH8LObcwheJRIiJiUFGRgY8PDwe+jkcx6GsrAx6vR4qlYqlTDEAujnAAECtVmPu3LkoLy/H9evXsWnTJkilUuTn52PPnj1obW2F2WwGEUEsFsPX1xfvv/8+Fi9ezDfte14ymQzvvPMODh8+jPPnz+PkyZOIi4tDTEwMAEChUEAul8NqteLWrVt/O0M1NTVBJBIhLCzsoWUu8/Lq9gBz3lxOSUmBTqfDlStXsGDBArS2tqKtrQ12ux1CoRAqlQpRUVGYM2cOxo8fDz8/vy6ryyESiRAQEID4+HhcuHABOp0Od+7cwahRoyAQCODp6QmZTAaHw8Hfev4zh8OB9vZ2VFRUQCQSwc/P75FnNObl1O0B5tzwSE1NxdmzZ1FYWAiDwQCDwcAvCdVqNWbNmoXZs2cjIiLiH29EPy3n8m/YsGEQiUSor69HZWUlfydNKpXy9UT+GlzA78nFpaWlMJlM8Pb2RnBwMAswBkA3bXI8jkajwYoVK+Dl5YW2tjYQERQKBUaOHIns7Gykp6dj4MCBLr13FRISAq1WC4FAAL1ej46ODn4cY8eOhUKhgNVq5b/u1NHRgYsXL4LjOLz66qsICAhgz2AMgB4QYA6HA0ajETU1NcjLy+MPdHv16oXk5GRkZWVh0qRJ6NWrl8vrvru7uyMyMhJCoRAGgwEOhwNEBKlUipSUFPj5+aGxsRE3btzgg4zjOJhMJhQWFsLHxwdjxozhe5YxTLd+CogIra2tOHToED788ENs3boVNpsN0dHRyMzMRFZWFiIiIl7YRUaRSPRQ5SrnLCUWixEcHIylS5eC4zjk5eXhzp07fHCdOHECR48eRUpKCt57770uX8Iy/17d8klwOBywWq0oLy/H9u3bceLECTQ0NEClUmHq1KmYNm0a38jvRV/Ff9wzlnMzZcqUKXBzc0NeXh7WrVuH0NBQ2Gw2lJWVYcmSJZgzZw5UKhXLomd4LzTAiIi/XlJQUIDMzEyUl5fD4XAgMDAQGRkZfJHP7pgFnC2SOI577A6lr68vpk2bhoiICJSUlKCiogJDhgxBamoqgoKCWA9m5hEv9FPMcRx0Oh1ycnKwY8cOtLS0QKlUYvz48ViyZAnCw8O7tchnQ0MDCgsLYbfbodVqH3unSyaTITo6GpGRkfwup0gkYvUTmcdyeYDRHyXTGhoaUFBQgJycHFy6dAkWiwXR0dFITU3FpEmToNVqIZPJXD2cJ7p8+TLMZjMUCgVCQkIeW2HKWXWYYTrDpQHGcRxsNhuqq6uxZcsW7N27F7W1tZDL5UhOTsbChQsxdOjQbu8K6fwjcOnSJTgcDvTt2xf9+vVjO4HMc3NpgBkMBty4cQMrVqzA9evXYbVa4e/vj7S0NEyfPh0KhaJHXK23Wq24cuUKrly5AqFQiLCwMAQHB3frmJj/hi4PMIfDAYvFgsrKShw8eBDbtm1DY2MjFAoFhg8fjo8++ghDhw6FUqns9sByslgsOHnyJO7duwepVIrRo0ejd+/e3T0s5j+gSwPMeTHy7NmzyMrKwrlz52A0GtG/f3988MEHmD17Nnx9ffkdwsdtiXeHuro6nDp1Cq2trejXrx/fz6ynjI/5Zz3lj/VfdVmAWSwW1NbWYsuWLcjLy0NVVRU4jsOwYcOwdOlShIeHw263o66urse9Gc7kXolEgqlTp0IkEqG2tra7h8V0klQqhYeHB8RicY87Jnmu5g/0Rylpk8mE69evY/PmzThx4gSam5vBcRyUSiX8/PygUql69M5bR0cH9Ho9bDYbAgIC2HnWv4yfnx8yMjIwdOjQHpdk/VwzGMdxqK+vx969e7Fz507U1dXBYrHwN4BbW1thMBi6tN2rK9AftewBoLS0tEePlXlUYGAgmpubYbfb/1sBRkRoaWmBQqHArFmzYLPZIBQKYbfb2fML88J4eXkhNDS0xwUX8JxLROc5l8Ph6MoxMcxTcZbj64nN6Z+7AR+bqZieoKcFltNz7yL21F+MYXoClgvEMC7EAoxhXIgFGMO4EAswhnEhFmAM40IswBjGhViAMYwLsQBjGBdiAcYwLsQCjGFciAUYw7gQCzCGcSEWYAzjQizAGMaFWIAxjAuxAGMYF2IBxjAuxAKMYVyIBRjDuBALMIZxIRZgDONCLMAYxoVYgDGMC7EAYxgXYgHGMC7EAoxhXIgFGMO4EAswhnEhFmAM40IswBjGhViAMYwL/Q9BqqCjs2mJUAAAAABJRU5ErkJggg==)
physics-General