Maths-
General
Easy
Question
Period of ![fraction numerator sin space left parenthesis x plus a right parenthesis over denominator cos space x end fraction](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFMAAAAlCAYAAAA+ydXcAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAZpE86XgAAAu9JREFUeNrtWjFoFEEUHVIEERFEgoiIkMJCwhEQkRBEBAuREIJgcYWFBEQkBFuRFGITUliIjQQLkSCIBJEQBJEjBBEhhBQiNhYWFiGdSJDjYP3fvINh+XMzszujczIPHsncn5v9927+7Oy8Uyod3CLOq3QxjxyTR4P4oQ/yfI9cg6MInORoH4h5mriespijELNfsA5Rk8QCcSbS2EWEMWd91/ZhYou4i4QKh0S77avEr8RfxDXiccu13hDPCa9PG5K+j1hoMQeI94jbxDZxi3hC6DdGfOcj5gZx0jPRAkIuaElch6C98IM4aIhtEo9obR7vUaSZuUJ8SDwEYV8Qp4R+g8jZGbsY1FfMC8K33baM0+kRu0R8gP8v+s4IDzGbEE/HU+JlQ/+2TxJTuCk0PcWs8oE6lvhb4nmU3WEH8WyU0EL56lgzlLm3mIwDxEXiZ+LJiGL2KnPGbSRfZX9XeFTiQKmifhr6epe5jjtYu2KJyTNv3BDj11+i1JsRxdwRrrtp6DtWYbmxrnuhxDRtjXhH8Zq4H1Wy4VDmVcX8TtyntefwJUqYQc6VMI01JZaY0qZ9iLhaEm+C+CySmLzdeoyJw+vkEq4fZNPeXaw7GPRoRDEVnssb2pq0TDwm9HuOO3wM3MUdfQ6zdFvYGkV7nPzfDzqG/uZBR2jcVGkfwfE6eUNlZGRkuD+KZbo/omZkZGRkZGRkZGT0BfjEmr0Utn2/Ea+V4nxGybZIG38lR9TFdi4jhE2cFPjQl+0APhPkQ1f2kZa0+Fm156+PoD2CdtnYcrGdJdS1iZMCH/vPWuITwkx9VXrNxXaWUNcmTgrs4B20xMuupOT8udjOJvjYxMkfnFSJS+adzXY2oY5NnBR2As1MHSbb2XTzq2MTJ4VFhzVzUijp5R7vcfm5TXcHUNcmTgrD2A5dgQjsNj7R4mdw9z6FdgPtccuWp2W5biibOMnt0Ue1ZxlvCTORP+QXzLZPSv7VmYvtrC8T/8Im/oPfvC4ZOtU7+YcAAADadEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1mcmFjPjxtcm93PjxtaT5zaW48L21pPjxtbz4mI3hBMDs8L21vPjxtbz4oPC9tbz48bWk+eDwvbWk+PG1vPis8L21vPjxtaT5hPC9taT48bW8+KTwvbW8+PC9tcm93Pjxtcm93PjxtaT5jb3M8L21pPjxtbz4mI3hBMDs8L21vPjxtaT54PC9taT48L21yb3c+PC9tZnJhYz48L21hdGg+YXJMmgAAAABJRU5ErkJggg==)
Hint:
In the question we have to find the period of given function. As according to the property of periodic function of the period T, f (x +T) =f (x) So, we will check from the given options which one satisfies the statement.
The correct answer is: ![pi](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAKCAYAAABv7tTEAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAHZJREFUeNpjYEAFWUD8DYj/48HlaHoYFgKxLBCvAeIAJHEQ34eBALgL1QwD94FYHJ8GFqgTkflfCNliCcT70fh7CWmKBOL5SPxwqF/xgmlAnIjEbwbiKcQEggESvxWIdwOxChBzYdMACuZzaGKmQPwJiBczUAIA0CEatBcOsq8AAABPdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPiYjeDNDMDs8L21pPjwvbWF0aD4fatH3AAAAAElFTkSuQmCC)
Related Questions to study
physics-
In a network as shown in the figure, the potential difference across the resistance 2R is (the cell has an emf of E volt and has no ingternal resistance)
![](data:image/png;base64,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)
In a network as shown in the figure, the potential difference across the resistance 2R is (the cell has an emf of E volt and has no ingternal resistance)
![](data:image/png;base64,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)
physics-General
physics-
In the adjoining figure the equivalent resistance between A and B is
![](data:image/png;base64,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)
In the adjoining figure the equivalent resistance between A and B is
![](data:image/png;base64,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)
physics-General
physics-
The charge on the capacitor of capacitance
shown in the figure below will be
![](data:image/png;base64,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)
The charge on the capacitor of capacitance
shown in the figure below will be
![](data:image/png;base64,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)
physics-General
physics-
Each resistance shown in figure is 2
. The equivalent resistance between A and B is
![](data:image/png;base64,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)
Each resistance shown in figure is 2
. The equivalent resistance between A and B is
![](data:image/png;base64,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)
physics-General
physics-
The equivalent resistance across A and B is
![](data:image/png;base64,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)
The equivalent resistance across A and B is
![](data:image/png;base64,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)
physics-General
physics-
Figures i) and ii) below show the displacement-time graphs of two particles moving along the
-axis. We can say that
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAcUAAACyCAYAAAAzkdRJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AACyrSURBVHhe7Z0JuE3lGsdv3QpFCk00KUMlU1zqahC5CSluMjSiROSWpEmDUjRRMqWBOimlusnQRIYoczJr0EylSKSk23f93rvWudtxhj2ds/da+/97nvXE3vu6jr3W9//e93vf//sXJ4QQQghDoiiEEEJ4pFwU//jjD/f77797vxNCJAOeqR07dni/E0JES8pFccqUKW7s2LHe74QQyWDUqFFuzpw53u+EENGSUlHcsGGDa9u2rTv11FPdl19+6b0qhEiEFStWuBo1argePXq4jRs3eq8KIaIhpaJIhHjkkUe60qVLuwEDBnivCiHihbRp3759XcmSJV2lSpXcxIkTvXeEENGQMlH85Zdf3GWXXeb+8pe/2HXGGWfYrvbPP//0PiGEiJU1a9a42rVrZz9X119/vfvtt9+8d4UQBZEyURw/fryrUqVK9sNbpkwZN2TIED3AQsTJzz//7O655x5XqlSp7OeqZs2abtKkSd4nhBAFkRJR3LZtm7vwwgvtod1rr72yH+CTTz7ZzhmFELGzfPlyO0vcY4893J577mnPFL/u2rWr9wkhREEUuSjSgsE5B2eJjRs3dg0aNLB0T+fOnV2JEiXciBEj3JYtW7xPCyGi4aeffrJzeTIu7du3dxUrVnStWrVyTZo0cYcffribPn26+89//uN9WgiRF0Uuij/88INr3bq1CeK8efNcz5493fnnn+8+//xz16lTJ3fSSSdZ9ZwQInpmz57t6tev76644gq3ZMkSd9ppp7n777/fzZ8/336NQLIhFULkT5GKIsU1b7zxhuvQoYP797//ba/16dPHNW3a1H792WefmTCOHj3affvtt/aaECJ/OHIYNmyYFa6tXLnSXqNw7e6777Zfv/766+7SSy91M2fOtGdQCJE3RSqK69evd48//rh75513sgtq/vWvf7l//OMf9mv46quv3JNPPuk+/PBD7xUhRH4sXrzYPfbYY27ZsmXeK879/e9/d3feeaf9mopuPsNzRaZGCJE3RSqKmzdvtoeTQhufnKIIiCeVdEKIgmEjSZFNJJGiCPQvfvPNN2779u3eK0KI3ChSUWTHmvNcIzdRFEJEDwU0OYtocoqiECI6irzQJicSRSGSj0RRiPiQKAoRQiSKQsSHRFGIECJRFCI+JIpChBCJohDxIVEUIoRIFIWID4miECFEoihEfEgURWjBIILe2Ez00pUoioKgjYcWOS76WP2LXlaeHfrJuXBB8q+tW7daDznP1a+//ur9SeFCoihCC+5JjE7CVjDTmtYliiI3ELVPPvnEzZkzx8b3Pfvss27MmDHu0UcfdQ888ID55XLf9O7d21111VVmu4lFYJs2bdwFF1zgmjVr5k499VR34okn2mfDiERRhJYbbrghe6ZgWHe1eSFRzDx27Njh1q1bZ4bwU6dOdePGjTPhuvHGG123bt1M2FhrTznlFFe9enV39NFH2wSVChUquHLlyrkDDjjAlS5d2u277767jPTL62rXrp33/xwuJIoilOCexG6Xh/ecc87JuOHVEsXwgg0mE4YYnPDwww+b8ft1113nOnbsaBOHMINnI8h4vmLFiu0mZlwlS5a08WLHHXecq1atmqtXr55NUzn99NPd2WefbVNVLr74Ynf55Zfb5JXu3bu7Hj162EaT+6p///5uypQp3t8oXEgURShBBK+++mpbANghK30qggapTiYHLViwwAQIQ/c77rjDhArxIrLLKXZcCOHBBx/sqlSpYqnO5s2b21D3Ll26WNR43333uSeeeMImFU2ePNkmF82aNcuEllFjS5cudR9//LF55X733XdmIs+5PH+fTBg/JlEUoWTjxo22c2aR4L8UEGQSEsVgsWnTpmxjdwTqhRdesAiQcWBEcOXLl99F+EhzEunVqlXL3icbQmRHxMiwaURvwoQJ7oMPPrA/l8IYER0SRRFK2OW2bdvWFhDSPpy3ZBISxfSGqk7O/xYuXOheffVVS0d27tzZIkDO9/bcc0+7d4sXL+72339/d+ihh7pjjz3W3iedOXDgQCuUYerQ999/n3H3d2EiURShhPRPy5YtbXEhZSRRFKmE+4+WBjIYRG8jRoywTRuFLvvtt58rUaKEXfy6VKlSVvxSv359d+WVV7q77rrLBJB5mQxfJ43J8UAmpDJTgURRhBKGVDdp0sQWGhaVTFtAJIrpAxu0rKwsEzgivapVq7qyZctmV3gSGZIGRSRpi5g0aZJbtGiRW7t2rUWBpD4VCRYdEkURSt5//33XoEEDK0Z46KGHdps3GHYkiqmDohTuP3r/aIXgPqQS1D8P5CIVSvHLoEGD3DvvvGMi+Omnn2ak0US6IVEUoYSFpk6dOu6ggw6yVBUtGpmERLFooUKT4pibb77ZXXTRRZb6jKwOpffvrLPOsvefeuop99Zbb7nVq1dnXAFYEJAoilBCuTm7cSr0XnzxRe/VzEGiWPhQKDNt2jSL9ih+OeKII3YRQXoFiQY5037sscesqEYimP4kLIqUENNDQ/47N+ixoTQYa6HckCiKwuC5555zhxxyiDv++OPdm2++6b2a3tAT9vbbb7u5c+fmmu6lova1116z1FxBDj0SxcLhxx9/tIrP559/3l1zzTXuhBNOyBZC7jca57FHe/DBB+27pLBGBIuERZHSYA6Ne/XqtVuD9HvvvWe7JeyE2LnnhkRRFAY0OnNfsmjRnBwE8KOsXbu2pX0pzohM+bIY01pCif5NN91k6br8kCgmD9Y1XGTY4NM8X7du3eyWiTJlyrhKlSqZv+6wYcPsexPBJmFRZNdao0YNq57CEcGH8mNy6Hvvvbe7995789zZShRFYcDZzR577GELGJFXECBS7Nmzp/WlDRkyxJ4hoHKWog2qFRs1auS+/PLLAguHJIqJwb8vVZ+rVq1yY8eOtcZ4imVYz/bZZx9rncBDdPDgweYCw+QIpUbDQcKiyI2AYwgPrO+aTvnwLbfcYrspGlK5YfJCoigKA+47dvItWrTI9/5LJ4gMOYpg0cV/EicSIGVKPxtnpJEbz/yQKMYPYkh2oWvXrmacjWUa3wlrHGfUROwTJ060qJCeQREuklJogzEtu9vzzjvP+moobMCB4Z///GeB6QSJokg2nOPQuI8oEnkFCc7eKeFnIZ4xY4Zbs2aN9VsSpbz88svepwpGohg7rFVEhZdccon1Ev71r3+1e4jvgrWMUWRkxjjbFeElKaL40UcfZT+4ffr0sd0VqQXOFAtCoiiSDY4h3H9UADJFIEgQeZBxwdWEaJdpBTxXmDjH0lYiUYwe1i/mCjIvkPoHhJCrcePG9l3QTE8aNdPaejKVpIgi6VKqrUgxUNzAGSN+ftHk2CWKItmwwB111FFWIk+VYNBgHh5Vs/S5EaVQ0o+9VyxIFAsG1yPOaokCsVVDCOlrJcvAJoTCGpF5JEUUgWo/biqKGyhywPA2GiSKItlQ2EWUeNJJJ1kTf9CgkMYv9afEnxaAWJEo5g6eob73KOfNflTIJoqofOTIkZayFplLUkSRm4gbCp/JAw880MadUEIeDRJFkWxoWeA8iDlyWGcFCcr/8b8kSiSFSnsG7iexIlHcFezTVqxYYaLHma2/gaeAqXXr1pZRiDUaF+EkYVGkbJyzD/p1cHUg9UDaCi+/aHLwEkWRTEjl+yOj8J0M0sR9Wi+oNOUIgjN6pp3TEN63b9+YDc0liv+DjBWDemmdYMI8FaQM4WXzzpR6/r2pTs40b1yRNwmLIrtyIkSGW9JQPHToUKtE5fUNGzZ4n8obiaJIJmQtSJsiio888oj3ajDAeYe2Cxr4mX7OqCCK1urVq2e9cLEgUXTuiy++sAkp/BsylJd7gv5CplVMnTrVIkONXxI5SUgUx40bZzsupj7jAwj4+5GfP+644yxaLAiJokgWLHD0j3H/kX7k/gwK2CVidkGUSLUjkGmhaZyGcb8HOFoyWRS5D3DQatOmTbYpN6JIe87kyZPd119/7X1SiN2JSxR5WNlpUWXKrpx+Kh+iQ1zi2ZFRfFNQWkKiKJIF53GjRo2yis3KlSvbAhgEiGguv/xy+3vfc889uzwz9MaxsHNmH4uPZiaKIv9us2fPtuZ6qncRw/Lly5sY0uOp/kIRDTGLIjfeu+++aykedrXPPPPMLgMw2aVxaE2hA64ceRmB+0gURbLg/JD2BdL53FNUGaY7WLtdffXV9rxQoJbzyIHzsJNPPtmVLFlSzfv5QLqZDQVDfBFDLvoMs7KyCvSJFSKSmEUR0cP9vV27dlYll9vuFXsqigR69+5dYHmzRFEkC+67hg0b2oJ4ww03uJ9++sl7J32h/YLnhCK1vI4bGDuE4TRFIdGSKaKI4NETjZuWL4ZEiddff31UxzdC5CThQptIOLjG6T8WJIoiGZDB4CyuXLlydgZHBiMMsLB//vnn3u+iJ+yiSNU7mQAqc/2p9lS9N2vWzEQyMnslRCwkTRRZlPBApZQ8lty9RFEkA6LCfv36WZqRiS3RWAymO/xMFIv079/feyV6wiqKZKqwZWNMEwYH9BqSLueohvQykaPs2EQiJE0U/QZ+2jGolKNZNhokiiIZcPZG9SaTWUhHYkwfdBiUjP0Y4684x4+FMIoitpEUTzE+y2+xYPAADlqrV69WdCiSQtJE8emnnzYHDm5UKlKjLXuWKIpkMH36dNuQIYpEDJEVnEGETSWbTApw8BSOVeDCJopEgIMGDbLpFawxVOQy2on6hmj6oYWIlqSI4tq1a23cCjcrF+kMSuOZS1YQEkWRKKQZBwwYYPdelSpV4vIKTSeIeCiq4YzMf6aoqozl5wqTKNL7jDsR7j78W9SvX9+NGTPGipSESDZJEUUEEJs3/wHmIlqMxlhXoigShTl4VB8WL17cFk/aHIIMURF+nJHPExEjacJoCYMoYr9GCpk6Bf4NKKDCzCCIJu8iOCQsilScnnvuuZbjp5mftAY7OdJYjGUpaFqGRFEkysyZM60CkXuQ1GmQz5Y4NyNKZIQRhSQ09JMyxP6NVgMMzqMpJAmyKPLzYXHHtJPDDjvMBJF/AwqpyEoJUZgkLIr4S/Lw3nbbbXYTU/nH+Q47dzwbcZjID4miSAQa9hkk7C+cDIMNMojehRdeaM8ONnWkTem5ZEYkwog7C849BRFUUeT7xAOWwQJEx0T/9J7GYlwgRCLELYrs5khT0VSMwS7nOi+88IJFi6R/2NGR9njooYespygvJIoiERBBClKYfoAjDPdeUCFKxLOTGYqkDYl46bvr06ePPW+0IZx55plRVVoGURQ3bdpk/aVsCNjkYBVJMQ39iGqzEEVF3KLIbnX8+PE2kgWLJeBBJmr0ZylyQE4kOW3aNPt9bkgURSIQVRxzzDFWmj927FgTlqDCGTzPC8+Rf+zAxrJXr172awrXXnrpJRuQu379enstL4ImivQ2Y9FHCpzeQzxLae3yBw0IUVQkJIoMP40spiHFgyhGFjow2DO/ghuJokiEBx980NJsjAf68MMPvVeDCT7BPFNbt271XnHWe8lYNh9aNebNm1dgZXeQRHHWrFnuggsuyG7p4mdmIx1N9boQySZuUaQPjHRHZD9YbqJI2gMXiryQKIp4wdmEIi8iC6ZMBH0RJTrM+TPkFEXgeSoonRgEUfTTxaSEEUOifaLFIBi5i/CScKFNJLmJYkFIFEW8cMbGPE8qT2Mxyw4SuYliNKS7KFJQg+FHzZo1s4ukhg8fnn30IkSqkCiKQMKZGhWKLKhMbAnCRIx4CKMo8l3R28zMS74/1oysrCwTSiFSjURRBBJ6YEm3cYVlIkZuhE0U6WvGfcjvP6xTp461W+R3xCJEUSJRFIGD+6tp06a2qLZt29bmKIaVMIkitmzMOcSZhqtFixZWNCREOiFRFIGC/rwnnnjCIg362BjAG2bCIopY8XXu3Nma8ekpbd++vfVbCpFuSBRFoMAIAsMIKk7POecct3LlSu+dcBIGUWSSBV6uxYoVs8Kom266ySqHhUhHJIoiMND+M2fOHJuEQeqU6tMgN+tHQ9BFkX5DrOr4vvBFvvvuu+1cUYh0RaIoAgNTExAI0m947M6fP997J7wEWRSnTp2aLYgnnniiufXEsjYIkQokiiIwzJ0711WqVMkW2bvuuisjetqCKIpUkpIyxcOV76patWpmbh72qF6EA4miCARMV7/22mttkWVaBGnUTCBooojwkTL1XWowVshSD6IIEBJFkfYQeWAHhkk0pfyMUsqUc6kgiSLfEwOA/XaZChUquJEjR+7i5SpEuiNRFGkPFaYYRrPQMsB60aJFGTNKKEiiSM8hY7wYMI6pAmbtGJgLESQkiiLtwROzRIkSVs4/evTojDqbCooo8szTh7jPPvu4MmXK2JlvWK33RLiRKIq05r333rPokOijY8eOgR4iHA9BEEVS2d27dzczBQSxX79+Ma0BQqQTEkWRtjCarGfPnpY2paSfodWZRrqL4tdff+169OhhMy3Lli3rbr31VvUhikAjURRpy/jx413FihXdvvvuay4omUg6i+L333/vevfubZuW/fff376jMPvQisxAoijSEsyjKdpgwW3SpIlbsmSJ905mka6iiJHCwIEDzbqNimCixU8++cR7V4jgIlEUaQem3/fff7+dT5UrV849/vjj3juZRzqKIt8PA4JpucCDtk2bNm7VqlXeu0IEG4miSDuWLVvm6tatawsuFY3r1q3z3sk80k0UaYWhF/HUU0+1KL5BgwZu+fLl3rtCBB+JokgrsG5DCCncOOmkk8wuLJNJN1FcvHixO//88+37Of74490rr7zivSNEOJAoirTh119/dWPGjLFpCkQhNH8zKiqTSSdR5ByRIcF+L+IDDzxg35kQYUKiKNKGmTNnutq1a5sgYhXGYNpMJ11EkbQpA50Z7kw1MH+nTE5ri/AiURRpAdWlzZs3N0GsWrWqnVsxPzHTSRdR5PuoUaOGfT8MDNaQYBFWkiqKVKQdc8wxMTXvShQFEzC6du1qCy6RyNChQ922bdu8dzOb0047zdodYiWZorh69ersDQvniK+//rr3jhDhI6mi+OKLL7pTTjnFmnqjRaKY2TBSaNCgQeaGUrJkSde3b18TSfE/6NXEJSZWkiWK69evd9dcc40JYqlSpdyoUaOsJUOIsJJUUWSaAYbNsRRHSBQzF9KjjIQiLYe3aYcOHTLO27QgcPWZPn2697voSYYoYrz+1FNPudKlS9v3c+ONN8rCTYSepIoiO0hmp8Uy1keimLnMnj07ezp7o0aNzPxb7App5HgG9CZDFKdOnWqes3w/jO5as2aN944Q4SWpohgPEsXMhH5EIkMa9CtXruzGjRtnQ2pFckhUFD/77DPXqVOn7HPEGTNmeO8IEW4kiqLIIb1ODyJniKTmsHTbvHmz965IBomKIscgnPMyDop+xEyaYSkyG4miKFJIB2ZlZbmjjjrKopArrrjCxg+J5JKIKNIe07BhQ/t+cK/55ptvvHeECD8SRVFkbN++3T3//POuVq1atuDWqVPHzZs3z3tXJJN4RRGHGp5JP2365ptveu8IkRlIFEWRwHnhlClTsgWxSpUq7uWXX1Z5fyERryjSg1itWjW311572bMZS9GcEGFAoigKHRbWWbNm2VxEBJHCmmeeeSbjfU0Lk3hEkf5Qqkz5jjANwHZPiExDoigKnQULFriWLVvaZAUs3HA+kiAWLrGKIqlt5lYeeuihVlwzfPhwe02ITEOiKAqVhQsXZo8aqlixohsxYoQEsQiIVRSZiejPSGzfvr21ZAiRiUgURaFBhIhNGQstU9qHDRvmNm3a5L0rCpNYRJGRUL169XJ77723eRdPnDhRZuwiY5EoikKByIOIA0EkJUcv4k8//eS9KwqbaEWRFOmkSZPcIYccYt9Vv3793MaNG713hcg8JIoi6TBWyJ+ej4n0HXfcEZNJvEicaEXx888/dxdeeKEJImb+bGaEyGQkiiKpfPrppzZVAQNpCjb4NQuvKFqiEUWqgidMmOAOOOAA27wwRFgju0SmI1EUSYNJ+T179jRBLFGihAniF1984b0ripJoRJHJ+d26dbMoESOFVatWee8IkblIFEVSoKjmkksucfvuu68rVqyY6969u/vqq6+8d0VRE40ocpZ4xBFHmActMxspuBEi05EoioR5++233dlnn23Vi4hinz59JIgppiBRxIC9d+/eFiVWr17dLVu2TO41QuxEoijiBou21157zZ1++um2uGLyPWDAABlIpwEFieK0adNsViLnvoijWjCE+B8SRREXjBLKysrK9jLFum3kyJEaAZUm5CeKbGaI5vneateu7ebOneu9I4SQKIqYWb9+vXv00UfN1Nsv0hg7dqwqF9OI/ERx0aJF7m9/+5sVQ9G0H89kfyHCikRRxARnhaTbOD9EELEGmz17tveuSBfyEkXODekbRRCJ8jVRX4hdkSiKqGEYMC0XiCFtF+ecc45Sb2lKXqKIp+mZZ55p3+Fll10m9xohciBRFFGxdOlSW0SJMPbYYw/Xrl07t3LlSu9dkW7kJopYutGgj+3eQQcd5MaMGeO9I4TwkSiKfGESO9PyiS4YPIv7CUUaavROb3ITRZr1GzVqZJsarN3kNCTE7kgURZ6sXbvW3XLLLVZZSrqNCQqDBg2yQhuR3uQURVouaMPA+JvUN7MT1YYhxO5IFMVu/PHHH+6tt95yF110kS2gCCLN+S+88ILbsmWL9ymRzuQURSaU3HzzzWaucPzxx7s5c+Z47wghIpEoil0gCuTciTYLxPCwww5zV111lfvggw+8T4ggkFMUifobNGhg3ynPnKJ9IXJHoiiywdCbdgu8MFk8a9as6YYOHep+/PFH7xMiKESKIm0Y06dPtw0O58IvvfSSvS6E2B2JonBbt261dCnfA2JYvHhx16xZM+thI5UqgkekKGL0fd9991lvadWqVd3ixYvtdSHE7kgUMxxGO7F4Hn300TYUuEyZMnb2RLpNBtHBJVIU6U2k2pTNTseOHa3fVAiROxLFDAX/y8mTJ7tWrVpZmwUR4llnnWV+ppqSH3wiRfH99993FSpUsCKbp59+2nxrhRC5I1HMQD766CN3++2325QExJDFskuXLm7evHkmliL4UFTTv39/+/XgwYPte6a1ZsWKFfaaECJ3JIoZBGm0J5980qJDv9WicePG7pFHHlEjd8hAFAcOHGjmCwx/5jyR/8rWTYj8kShmAJs2bXITJkyw8yTOlRBDGvFxplm4cKH3KREmEEUiRKz4qlWrZiny4cOHm0gKIfJGohhicCxZvny569evnzvyyCNNDMuVK2dnh4x6UmVpeGF6Ce5DGC7wvVN1On/+fO9dIUReSBRDCMbP3333nXv11VdNAFkUOTdkhh7RA+OfVFkabk4//XR33XXXudtuu82+//bt22vepRBRIFEMGfQcYuDdtGlTa6+gzaJ8+fLmYYorjRbGzAAD95YtW7o2bdq40qVL2/miMgNCFIxEMSRwVkT1KNEB54VEB1zMPHzjjTfcDz/84H1SZAIUUNWuXdvVq1fPelBxsZEBuBAFI1EMOBg9kya99tprLT2KjRdiSJ8aZ0rLli3zPikyCZ6pUqVKubJly7oTTjjBHIuEEAUjUQwouJKMGzfOXX311Tb1ACFkTl6tWrXcDTfc4GbNmqV0WQZD+tzPFpxyyinuk08+8d4RQuSHRDFgYL9GKuzKK6+02XgsesWKFbNUGUUVr7/+utu8ebP3aZGpRIpi27ZtlToVIkokigGASlF2+hMnTrRewxIlSthiR2qsYcOGrm/fvnZu+Msvv3j/C5Hp+KLIvXLrrbd6rwohCkKimMZQPENrBY335557brYYHnjgga5+/fruwQcfNCcaRQEiJ74o0p86cuRI71UhREFIFNMMosLffvvN2ieGDRvmmjdvbiJIAQ3tFYjhmDFj3DfffCN3EpEnvijWqFHDvfLKK96rQoiCkCimEVSSkiLlvBCz7oMOOsgWNi76zp599lm3Zs0aE00h8sMXxUaNGrkFCxZ4rwohCkKimGIQOPoLaZ84//zzzY7LF0KarnEieeqpp9yHH34oFxoRNfSncg8xR1E9qkJEj0QxRSByo0ePdtdcc435VPrnhfvss4+V0NNWQcvFxx9/7P0vhIgORBCbN+4nnIy0mRIieiSKRQhT7jnfGTJkiBXOlCxZ0hYu+gtr1qzp2rVrZ2OcZsyYYf6lQsQDhg206HBfcS4thIgeiWIhwuy61atXWyM9fqRXXHGF22+//UwIuY499lgz7L7xxhvd1KlTNetOJIXZs2fbuCgcbchGCCGiR6KYRIjuEDYa7CmYueuuu+xn8wtmqCClkhTbrdatW9tn+Pzvv//u/QlCJAbtOWQj8DvlwgJQCBE9EsUE8YVw6dKl7rnnnrOfp27dum7//fe3c0LcZhjbVLFiRSukIZ1FBSmVpuovFMlmx44dLisry1WoUMHs/3A4EkJEj0QxTrZs2WJpqjvvvNOdffbZVjV62GGHZRfMcBERdunSxVKnnPMwx1CuM6IwQRSfeeYZE0XuP5yOhBDRI1GMAoQMmzVEEHeQHj16WNRHcYxfLMN1xBFHWLEMTjNMPJ87d6778ssvVf0nigxS8RRrMUuTKuY5c+Z47wghokGimIOff/7ZimPefvtt99hjj7k77rjDXX755a5Zs2Y2monFxhdBzgjr1KnjLrvsMhPCyZMnm3gqLSpSBX2v3LOk7OlVJK0vhIiejBZFfEVJa7755pt2DoOwMZeQKLB69epu7733zhZALgQR2yzaKegvZEf+zjvvuHXr1nl/ohCpBes/ely5dynmUp+rELERWlHcunWr+/HHH923335r1aA0y8+fP9/aIxDBJ554wgQQb1FMkyPFD49RzgcRRob18hk+O2LECIsg8R0V6Q3i8NFHH2Xcd0Wqv1u3bnYfX3zxxTZ3U4hkwVi6FStW2PoaVlIuir179zafxtwgDckZiX+x0PFlcPHl4Nyxfv16mxRB2hITbRrfmTdIFHf77bebmDFPjjTnMcccY1Whvvjtueee1jfIXEIKEyiWady4sUWBWKshohTHULwgggX3xtNPP+0efvhhSyFu2rTJeyfc8Gxccskldn9fddVVsngTScMfYTd48GAr5lq5cmUohxKkVBTZ1TI5/rTTTjPxWbVqlS1gFKi89957Vk5O5SZFK/z38ccfty/koYcesnMTCl4QvHr16ln5OYUuBxxwgAkdZypckb+mMpSL1xBIqkavu+469+KLL5qYElGyeLKwqHcw2LCh4rvs37+/mSRgkEDUtG3bNu8T4YSq6FatWpkocm+r2lkkEwIE1smLLrrI1lwybgQoYVovUyqKDD9lUC4iRfk4kVqVKlVsEUO0jjrqKIvg/OvQQw915cqVswvxo/ITr1A/8iPtyWtEfnxhRH0dOnRw119/vRs+fLh5iZL+XLJkiZ21sEiycKowJryQPmcIM+bq3GMIBQ91WGGBwiWJ5+G2227zXhUiuVCLgdk8azLj7MjIhGUDllJRpGDFFzSu4sWLW0SHUOICgzji4UjqE9NsTI5JtVIJyvQIbNNIjzJhgh0L1Z9MnED0iDpphyB9FPboQOTPH3/84e655x7zAmXTxL3Us2dPu0/CBqYQJ598sj1P/MxCFBYUGFKZz71Wvnx5qw259957rYAxyKRUFN966y1LYUYKIxdnfbQ7sIAhjkR+hx9+uKVHEcrKlStbFSjOMQ0aNHAtW7a0XUvnzp1d9+7d7SIty5kKswl5nS/v0ksvteIDokddmXN16tTJKoojjRW42OEiHBs2bPDuyOCDwxI2b2RauHL799ClK9GL9ClBCUdfkc8UWT/EkTPHoKZUU15oQ2TH2aAvZFxUz3EhajjCcCFuXHwRXCx0HTt2NLGjsMAXO5rndemKvOgjPe+88yzl7j+8ZCUQRc6mwySKPgykZjOY27+HLl2JXmTqWHvPOOMMC2L854qjLQaiU+QmURQiTaE4gOIsRJFeU9psOM+mTUcIER+0OxGocCxBWxtmEVT9B70NSKIoQg1R4MCBA21iBLZ8FJ/gWCSEiB9qNsjYUWjTqFEjc//6/vvvvXeDjURRhBJ6qqgspiqOcw/GeDGdJIx9VUIUFRSt0RfOkRdiSD83Fd5qyRAizaFfD+ciHtrFixdbVaYQIjEQQFrbuHCMwms3bEgU0xh2ZZx7MZ1DEU5ssHPFECLo5eEib3gmMPlYtGiRJtEUEbS3ffbZZ7bpDCsSxTQGU4EvvvjCPfnkk9aPOWnSpFCII5NIcCaiQi3nOQQpzptuuskNGTLEBjIzqgs7KSFywsaHaOWBBx5wffr0MYEMOlhL4sKEwxab4khotcGCkn5sQJjuu+8+aysaNWqUFbm8++679p6IH4liAMDTlfYTejJ5KKZMmWLOJUGEBx1XoYMPPtj16tVrl3YIUjGIIaXdLVq0sI1ArVq1bJCzEHnBIGVabho2bGiFVMyQDOIZF44wDEigeGXChAm7iCIZD87weDY4J2fDzCYARy/6tm+++WYzpaBdQkcFiSFRDAj4seLCUqpUKVetWjXrr5s2bVqBhs8Um0yfPt0tXLgwLZx9iAyxWqMalDO/SFgU8LmlMRhTdyJEXIzwtiUVKkReYFTtGzTQO8cYOHqgeW4Kgmk6jIDj7DmVZ2R4PjMYmub3nMKGOxeCT+82UyoQxffff982yzh6YVuJoLLZnDlzpqwrE0CimAR4qIjmOPsrjIudL7vCl19+2QTCb5RFWNgh8hDkFTnyHi5ACFE0C0Rhw78TTfMsYNF4kBIt4swyfvx47xURJDjrY5INacHc7u1kXDwfCASj3Xgm/OcDe8j777/f7Pzy2xAyeKBixYrulltuSakoEgFWqlQpbns+hiZgt0b6VUbw8SNRTAJTp041H1fEp7AuUiRVq1a1SNF/6Ln4PfMeWXQiiw04b6C5lvMWxmVhis15HZEaVmCpgL/fxIkTrYGeBYgoNhLSRZw3cvk/C2JI2pgpF9r9Bg+ME3DX4TvM7b5O1sWzwX+LFSu2y/Nx4IEHuq5du+a6AeM+4xnp16+fGcYjJkScpPSL+hnh3seBiCZ4agdyglgTPfrizvOB8PGaP9qOSBfLyzZt2mjmawJIFJMANybNrFTBFcbFzU6E9dprr1mUxcOOiwRTRGigJY2asxqMIpYTTzzR0inYMDE0mYUDOzz+zFSwceNGK6LBz5aS7pyFBDTV42HLeaK/iBEhEx2TRqUcXAQLFm9EhqkKOe/rZF08G1yMlvMjRc7amJTD/ZZXWpQiLj6DNRnPCFEWzwgpSf6+Rcny5cvNyJ3NA6nQnDz33HOWWmVzC4gjxUW4M/kiSv8glpdEvSq4iR+JYkBAUGiYxRydB58iFSLUvCyVqMqjepMUEiJEBStRF+eLqfL6pJIW0UPM2UTkhAeZB5ozFR5w4Odj98vixcIhRG5wzkZKnsgQ5yJSkKRU8ztz58yalGX16tVNEDGx5hnhyIHnrSjhfJ3nGv/m3KJUxJCfjagW2IhzdsqoPf9sno0xtQaIPDNilVmJD4liAEAM2L3y8FJsQ2UaY1sKgh0nfoRMIvFTLKmE3Tdjv5hukpslFNEj01AYP0NqC6gixCSec0XK1IXICUUy/n1FpTKZk5yFKnmBmDJ3lerVVEIkyIaQ2a854dklAiTzw88GHIUwH5TMD32DQFSOWQUbZ+bHpvJ8NMhIFNMczjhoU+Bh4SC9oGrTSNgtsgNmAkk6tHBQFEH6Fxf9nE31pINY0IhqOYOKTK0SFVOmTmWqdr8iEopoOAvkzJlWpViFYMyYMXa0wPOVyh5gDOvZEN5+++3eK/+HrAntFqRPP/30U3sGXn31VRM/Uqj+BhIQVyJF/pycZ/YiOiSKaQw7RApoeACi3fn68L8l4qJEnQbfdNg10p9IwRDngzlFkcIARtGwMCCePux+qZwldUSDcjpEvCI9IIvATFauePoSuZeYlsJgczaeqby3aLdgiktuokg6l7NOolk2tzzLtGFQsDZ06NBdfvaxY8fan0NGKSwG3UWNRDGNIXqKV8w4E6GajfM7mpvTIcLiPJMUME3WOUWRFHGTJk3ccccdt9t7RIpEkOzqcxbniMyEzRItRok06XO2zhkebRCk5vkzUwVnoBTFcSaYE6I/okIyPkAESKsSosizHQmf5XUiyFiySuL/SBTTmEQeUtKuVHFSdOCfOaQaKgU5v2FqRU7ho1iA3TDCSN+nD/8GNCVTqk56LJULl0gvEr0XqHbmfiSlH80ZfWFC5Szn5rQq5YRolpSo379IwRrFaGRdclrbZWVlmbhiXpAOfclBRKIYUig+oDKNs4h0ia4Q6latWtnfK6dDDQ8z1XfscCMfZtLGl156qQnmggULvFeFSBya9rnn2IilGtqtyOp06dLFe+X/cP9TVIN5B5BVwf6QZ4kqcx+iZqppiSqppNVRQ3xIFEMKpsEU2VC2nS7QZ8ikbv5eiHbkTp+0UYUKFSz9E/kwL1261CLL2rVrp03EK8IBIkME1rRpU++V1EHEh30j1eKRWRRSvPQuEtFSKQtkTHiGOIeMbB3h+erWrZuJIoIv4kOiGFLo76MncK+99rI+P4yCqVxLJZyPMgUf9xAKBXx3jm93LgLNW7RwZcuWdTNmzrTXfFi4SJ1Scu9/XohkQBoSJypccChiob0hVR67pG/POuss68eNTImyeaTIjGeYs0QqZBmYjdnAo48+usuZKpW4FLGRifEFVMSORDHE0Lzcu3dvc73hkN5viE8l7HLpx+rcqVO2Q82G7dvd6J0R4uAhQ9y6HMYCd+6MIBHLeP0ghciPWbNmWTsGRWmcXePTmgoohKPKmg0g54s+pEoHDBhgY6M4BmFjSRRIGwoiGJltITtEewniXtTmA2FCoiiKFFKgeDNWqlzZzXz3XfefRYvc70OHYiDLysDBo/t1xAi3fdw49+2yZa5hkyZ27kORjhBhBlMOojzOCmMtkuHzWNphb4cJRiJVuZmORFEUKaR/aM5v0rSpe2OnEO4YNcptrlvX/bJzt/7n2rXu95274J93CuHW1q3dkuefdx26dLFoNx36LIUoTOjVpb+QSC9Wn18+z8QcNpykhUX8SBRFkUMaCId/K6jZKXZ/bt7s/mTUDZHizh3un0zJ2LLF/bF9u9u2U0RTNdVDiKKGe52z81j7ivk8G85UuvKEBYmiEEII4SFRFEIIITwkikIIIYSHRFEIIYTwkCgKIYQQHhJFIYQQwkOiKIQQQhjO/RdRCeWqb5oGrQAAAABJRU5ErkJggg==)
Figures i) and ii) below show the displacement-time graphs of two particles moving along the
-axis. We can say that
![](data:image/png;base64,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)
physics-General
physics-
The graph of displacement
time is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAREAAADiCAMAAABeOwO/AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAMAUExURf///zExMdbW1gAAAObe3nNzcwgZEGtja62trUpjWkoZEJxjWuZa5uYQ5ubWEOZaEBAZQr3v3rUxWrVjMXsxWntjMRlrWu/377Va77XvWkpr3krvWkparbWtWkqtWrUZ70oZrbUplLXvGUop3krvGbWtGUqtGbXvnOZ7peYxpeaUMeYZMRBrGYSc7+alY+YpY4TvnHtKlLXOWkpK3krOWrWMWkqMWrUIlLXOGUoI3krOGbWMGUqMGbXOnOaEY+YIY4TOnCEhIebWnOalnISMjEpKWr1jWubWc+Z75uZac+Yx5ubWMeZaMRAZY7WMnObWUuZaUkIIWoyljEJCQsXFxebWvea95ualveac5mtaUrUQKXsQKYRrzhlrjIQpzhkpjLUQCHsQCIRKzhlKjIQIzhkIjKUQWqVjEGsQWmtjEAhKWu/m70IpWjo6MbW1vQgACHtze7Wt70JrKeb3c3trpeb3IbVrzkprjLUpzkopjOZateYQtealEOYpEBBKKYStzkJCELWUxbWM70JrCLVKzkpKjLUIzkoIjOZalOYQlOaEEOYIEBBKCISMzlLv77VrpVKt71LvrVKtrbUxKXsxKRnv7xmt7xnvrRmtrYRr7xlrrYQp7xkprYTvaxlr7xnva4Staxmta4QppYTvKRkp7xnvKYStKRmtKYzv71LO77VKpVKM71LOrVKMrRnO7xmM7xnOrRmMrYTOaxlK7xnOa4SMaxmMa4QIpYTOKRkI7xnOKYSMKRmMKYzO71LvzrVrhFKtzlLvjFKtjLUxCHsxCBnvzhmtzhnvjBmtjIRK7xlKrYQI7xkIrYTvShlrzhnvSoStShmtSoQphITvCBkpzhnvCIStCBmtCIzvzlLOzrVKhFKMzlLOjFKMjBnOzhmMzhnOjBmMjITOShlKzhnOSoSMShmMSoQIhITOCBkIzhnOCISMCBmMCIzOzsUQWsVjEIwQWoxjEClKWub3vbWtjIStrb3O74SMpUIQMSkIEHNzWtbe7+b3/0oxMf/3/wAAAI5LJcEAAAEAdFJOU////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////wBT9wclAAAACXBIWXMAABcRAAAXEQHKJvM/AAAK4klEQVR4Xu2dbXKruBKGDRICr4D1UAV/zw/E3CrWoDJ4c95ZqlL+SOp2E5JgwDZgIcmRnjOTgzMzZxy59fbbLQk2DofD4XA4HK+AaH93fFPl7YXjC1F6RXvpaMgTtncTp4MIa+KCpMMlSgghuQuSH2gIA0K8qn3p2ESsZqQmafvSQU/HjCfB0QXJN3my9cMdzZPQKUnDOciKTeCJTcCtTTeiGwsiSmG2hDAiIsr99pu2ER26QxJhZJw8CoNTwRcbOWdJFbfXAMXhCb0zfLVVR94SlvWDAZS1vbIQkRGS9BPtFnTEVi6RBwb11AuJAHXEUiiECARJ1L5swVxjK1HC0LRvr0egyTV24pcs5F760QsSi3UEvDrde7Ty+FVQ2KsjNAjRstNNnlXdqPjyIzYSvYNDPSR0I4q8W8VYqyOiwmEIYERgSLoxYq+ONJEQeIOKzmY/AgTJQDRs9iPASIxY7EeQkSlic10DBMkgRkIXIz3s9SMNIzFysrk/0sTIpb38xulIe/VDYPmsGdMRq2Pk4HJNj6auucb2XDPiWS3PNcMYcbmmvfrB8to3CgYBYbmOUL+zyPmF5bXvCJbryAiW68gIlnvWEZyO9HE60sfyumYEy/3ICJbXNSM4HeljtR8ReXgK+nt5bdYRkXuJl5S9rXkW+xGRJmFxLrJD+7rFYh0pOMFDikVv2lisI9UHST/b6w4W1zU0YEl6tZmmwea6xg/Z0cv7mcVqP+JHIUn6xxQtr2toVvePW9nrRyj+4CJlp96IrFPXXGJKqQ9QKvpr74ZAQzxsVO362+LX0RFR5EHGwRDy7NCcazKQOMp4mX3wwWln+X7kQqMTTxgeSwDqhJ8iM6Uq55xn/QiRryMC9DvBgYD4yEq+w6Hxgmqwb8UMxt6VXD8C8ZExUjMvfCtoHMe0eA89GJPkFK0wOddBqo6IqIT4YNnb+VdPKU05fM8LBgushiJTR2gOP3uy/VdcByPoLAQO4y8SJvLqGlGcasLK0TtVFHtek91r3MRCmo6IPKtJEtz604qvfzpYdzYPWTpSBKAgPLqduPwTzJzwBe7ZIKmugTISEsrVWaY+AhXWezN+5kjxI3G1hR/2kUwIzMye8foqpa6pyhp+1McmjEIkPRw43cjQkYgzwu/OmG8o3knK8Ch53o/EEegDH9YHo9AA9MbsKHlaR0TkgUudXODixDF7SJ72Ixgh5YyKX0CaNnpIntSRONoRMj1CEJw43sRJpoMndaTipN7OtF1iz8iHuVbtqbomrkqYMrOH1IeMkxlbCj+lI0UGU2bBp00zwramDskzOlKAB50jqr8UO3K8WRRq5om6xi8Z2XVvFTUDTNmpmUOy3I/4ARizxQKZG5uDF9c1IsUkurjf8fWfmzgki3UEP+RnfiK0JUbevXCpHyk4OT4nBH5ISGiglCzTkRjyLhse1pkHuDtm4K1hl/kRDPl53n2MKjGxW7JIR2jKagk+XBzAuxonJUt05NKkzvbFM5xDVhs3JEvqGrBXSSol2kGf66s7pBrAAh2BqqSWZcFxcA17zsN8HUFVnV/v3oDCBDRs3syuaz7hZ5B483BhnCuZ60dEBFM/H9kYu5TigzCjUvDcusbPaib1M8UnPRjVZJypI+JAZLe/UJdCg/YgzfMjMXygH7I/UB9yl0EpeJ6OYCkiP1maNW/m+JELPstkhScyXA4J2RmTgufoiDis1NKAeUOM6THO0ZECDOY6bS+YjcnyfpxcZtQ1RcbYvr2WTW5OFTxdR0R+rPlaiyygUIMt+5qYrCOYeAe76qUhKpiRZqx8Tq5rQP3Yiq4BIhDmjQlSMtWPCHSWay5M4sqnEfXNxLoG54xXSSzwhmCr5F97rZOJOtIsRrTXK4FrWlsDTMk0PyICMKtrZ8eiXFWppjJNRyCiFTxiDmfm8Pytaib5EUWq97lntf55M0VHBFRi18/vWIkiM8DMT9ERqGcUVev/YOh1+7QJdQ2eAnh2jXci9ES0P2/4sY5g813VtoZLob959FhHsG+m7E2iKSmX7FaQx+O6JiX1qvb9GkhrSa413zzyIwJMgtKOH8zRD62dkkd1jc9rtdteRFBLW1VexAMdETBnpC3yTgN0a8rppdV44EcqZVbkl1z6Itks7usI7p6Ts1NkBrjHTeP+tLt+RKUV6RB59U5fxXdXR5rliPZaJeBc9e2guKcjX2vU7QuVwLw5att5dKeuUW5Ffmja0LqC5I6OYE9Lk8Lh8o2udtptHYlTjfuhmkZ3e62Y23UNrsUuPD3zPM1iiJ4guelHaMZq5VbkF19bO+1WXYMLNFoPe4AV0iPrt3QEZFXv1lvcvaNF12/4EYHFhS5Z/QJXRHTYwxs6gkv1mrt7IiBMR1tg3I/Au6m1b4Py8VNRL66jOhJDxOrfKidAXDXM3FEd8fW51S4CyxvlQzJW14i8NmP3frMQ3F4rY0xHCnCrRhx6wS0JitbOfhnRkeZ9fK66e2Yq1U59Bh6pa3T0Vm/xrn6XzdCP4Nrru+pQvcV/OIHVhuugrsHzLh8aW+HX4LvharcwDnSkWWY0JURA1EKIWKXzpu9HGltkzoA0jXm1W3/7OlJ9aC9orsGD43uVQdLzIyKFzKs0SB+i2h31dETNpsR5KG7MX+uIOGlY1XwEzWqm8E1d1TXaW4njQOAq3FJypSNN5tW9e3LIBSJXnbh1dcS4zPtNs1DSXq9Op665UFNq3j6fOZQ3qnx0x49gt9mwzPsNrt6oamF16hqlsTkPXJRXJa4dHTnVte79xjfBpXFFrfBfP4JtEfMy7ze4uUfNKvSPjtCMqfRBs1G2u+fHj0TJeqd5ZfAfnvFRESTfOqJSzRdxeQOzpOIj+9YRNGcmhwjkm1Dy3XFu0NY1UHKzt+YbxnLB1o0Cd/ClI59QcRuxZnWP5qTJ+nHc6EiM584MNWcdoMpQcICyyb5iz5imXV+zUNKsCD3IaAX8n8wPEQiSgJDVbTXqCA1Y3XtYtqFAAlj9jq5b77KJDL3j8hCR1/XaJgH8iAjJ8d2cO7TdBR/2clg3KYacQogoSGqSiLDia6/XIdzh0XSDljUf8S7jDtP3OCVBomu/9SJwR9iqhwhS4jGzljUfUd24wxSt5OgLZHhiyG23JkJTXOMb9AViP3/3ZYxJSszZUDSRczjaIRd+6ElonOOfnr9I5v0BO4x5f2sUEHGWHZ5U3fhfwvj/2hevA9Q3o2vjtIRElE961uEt4hNhgY9Pwn+hX5RWJeFR8/T+lvb7FIaqrnc5fWJM0PA0eM1fhoPvsHmXjDC8+v2FwO/4THJCjs8YFlGlwatxCIJ033/b8E0AH2NPQEzk5OG/AIY8T1+mJFmf3GM8Fy/lrlZFvHP+7rvx+EFUh/1rdHlkcr4jmbSybzw2Isrv3IXDvO1iChB5ueQ5oH8ZEbJdavzj6OUCdry9GudfQrxcStn/IpzL7kPYxUbE139f6IGQOgnscWHU6zSWixPvsGu+ZF6NtYtn8u4fiVRpSJJTGrWTothnWcmzEr9k2RYvsi3Hai4Bb/r17/xxwIZjVXvvyeP4lHGLahdRlSwEbb1jOtLkyKNnGiAvhgjv77qmgcfvubS/R5Tc3aRAo9CiLNMQsXtr8nER2db7EMH9O5GKkQ783+Z8OqavtlayLgU39ayCLiqPWdjkuEeUHF3b+Aq6Jby0pGKZSMV3XtBeOxousVtdcDgcDofD4XA4HC2bzf8BPE6GC4oImPgAAAAASUVORK5CYII=)
Its corresponding velocity-time graph will be
The graph of displacement
time is
![](data:image/png;base64,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)
Its corresponding velocity-time graph will be
physics-General
Maths-
Period of
is
Period of
is
Maths-General
physics-
The current I drawn from the 5V source will be
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)
The current I drawn from the 5V source will be
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAATAAAAErCAYAAABZ6t+rAAAgAElEQVR4nOy9WW8cSXa//VRVZu37ThZ3UpQocdgt9XT3uHv+GC89hoExbMO+MHznj2fAN76wYWMAzxjuGU/P9Kpd3Cnute97VtZ70W/EFClKrYVbkfEAgqSqrMzKqMhfnDhxzglLv9/vo1AoFEOI9aK/gEKhULwtSsAUCsXQogRMoVAMLUrAFArF0KIETKFQDC3aRX8Bxcn0+336/T5W6x/HmF6vR6vVotVqYZomuq7jcDhwOBxHjjMMg06nQ6vVotvtYrPZcDgcuN1ubDbbRdyOQnEmKAG7BJimiWEYtNtter0eVqsVXdfRdR2LxYLFYgGgUqmQyWSo1WoYhoHNZiMcDpNIJHC5XFgsFrrdLvV6nWKxSLVapdVqYbVacbvdhEIhfD4fbrcbq9Uqz6tQDCtKwC6Qfr8vraVCocDKygqVSgWPx8Ps7CyTk5MAdLtdGo0Gy8vLPH78mG63S7vdplKpcOPGDf7kT/6EaDSKzWajVquxvb3N8vKytNQajQYAXq+XO3fusLi4iNPpVAKmGHqUgF0g/X6fbrdLsVhkd3eXra0tisWitJYmJibo9/vU63WeP3/O5uYm6XQan8+HaZrk83lcLhfb29tymri3t8f29ja5XA6Xy4XL5aLT6XBwcMCDBw/o9/uMj4+jaRp2u/2im0CheCeUgF0wvV6Pw8NDdnd3sVgs6LpOq9Wi0+kgkiTy+TzfffcdhUKBSCTC4uIidrsdv99PrVZjdXUVl8uF3+/n8ePHVCoV4vE4N27cIJlMUqvV+Pzzz/nNb35DMBjk3r17eL1eJWCKoUcJ2AUiBCscDtPpdCiXy9hsNorFIvC9hWaaJoVCgUePHmG1Wrlz5w7RaJRQKIRhGGxsbJDJZMjn87RaLTY3N7Hb7dy5c4fR0VEikQgej4fR0VFGR0ex2+1Uq1U6nc4F371C8e4oAbtALBYLDoeDyclJIpEIu7u7GIZBo9GQq4X9fp9KpcL6+jqhUEhO/QKBAHNzc9TrdQ4PD6nVanQ6HXK5HIlEgkQigd/vx2KxYLVaCYfD3LlzB6/XS7fbxTCMC757heLdUXFgF4zFYsFms6FpGpqmYbPZjoREwPerlIOiY7FYpIi53W451dQ0Dbfbjcvlwm63Y7PZsFgs0pID5Arn8WsoFMOI6sWXANM0pcCI+C/xB8Bms6HrOjabTb5umia9Xo9+vy+noh6Ph3A4jNvtpt1u0+l05Lnb7TblchnDMHA6nSoeTHElUAJ2SRgULdM05b8tFou0rETog2EY1Go10um09JsJJ34kEkHXdfL5PNVqlV6vB0Cr1SKdTtNut/F6vVitVgzDQFVTUgwzygd2CRB+KjHd6/V6mKYpg1h9Ph8TExO0Wi2y2SyVSgWbzcaTJ0/I5XIEAgF0XQcgkUhQKBRYX1/H7Xbj9XqpVCq0Wi3cbje9Xo9cLofP58PhcChLTDHUKAvsEiACWtvtNq1W68jfvV6PYDDI4uIigUCAw8ND0uk0e3t7PHjwgGKxSDKZRNM0ms0mPp+PXq/H06dPOTg4oN1uk8vlaDabxONxTNNkc3OTQqEgp6AKxbCiLLALxjRNcrkcm5ubfPvtt2xvb9NsNrHZbPR6Pebn5/F4PHzwwQe43W5WVlZ48uSJ/GwqlWJ2dpZOp8Pe3h4rKyusra1RKBRoNpsAlMtl0uk06XQau90uRU44+RWKYUUJ2AUjUn2KxaKM5XK5XNJnNTo6KuO+bDYbpmmysrJCu91mcnKSubk5UqkUpVKJTCZDuVym3W4TCoXwer1yAcDhcMjIfL/frxz5iiuBRdXEv1hM06Rer1MqlcjlcrRaLZkWJFYVvV4vuq5Tq9XI5/NUKhVM08Tj8RAKhQgEArRaLcrlMplMRsaRCfFrNBqUSiWKxSI2m41AIEA4HMbn86FpmrLCFEOLErALYrDZRaiDWBUUTn3xR/x/0MF//DgRVjH4nogxE581DEN+Br6PCVNWmGKYUQJ2AQzGfQkxeZkVdPz1wfiwwVI74r3j1xmsKza40qmsLsVVQPnALgARWNrv96WPStN++KcQaUZOp/PEROzjomQYBq1WS0buO53OE49TKIYVJWAXQKfTIZvN0mg0sFqtxGIxwuHwK4Wl1+txcHBAJpMhFosRiURwuVyvTAnKZrNks1lcLhehUAi73a5SiBRXCiVgF0C5XOarr75ibW2NbrfLn//5n/Pxxx+faIWZpkmxWGRra4uvvvqKzc1NFhcXef/997lx4wYOh+PI8YPTw/v37/P73/+e6elpFhcXpYipKaTiqqAE7BwRwtFoNNjZ2WF1dZVut8vc3Bxzc3NEIpEXRKzf71MsFnn06BGrq6vk83m8Xi/RaJTJyckTBUxUeN3a2mJ9fR2AeDxOt9tVNcAUVwo1nzhHRAXWbrdLv9/H5/MRj8cplUqsra3RarVO/EylUmFrawuXy8Xdu3fRdZ1cLke73QaQCwLi34eHh3z77bc0Gg0SiQT9fp9qtUqz2TyyCKBQDDtKwM6RXq9Hs9nEMAz8fj8TExPMzMzQbDZZX1+XtesFwtkvig8mEgnm5+cJBAIYhkGz2aTb7b4gYNvb2/zP//wP3W6X9957j2QySb/fJ51OUyqVjhyvUAwzSsDOCVHTq1AoUKvViMVizM/PMz8/j8ViIZPJyNQfYSWJqWCr1SIWizE1NcX09DSJRAKbzUY6nSaXy8mKEyLW6/DwkIcPH2K32/nggw+YnZ3FarWytrbG3t7ekfCKwdgxhWLYUAJ2TlitVtrtNg8fPuTx48f4/X4mJydJpVIkk0n8fj+GYchgViF2Dx8+ZG9vj5mZGW7cuEEsFiOVSmGxWPjlL3/JF198IS00i8VCu93GbrfLc4fDYeLxOJ1Oh88//5ynT58euYao5Kqc+oph5NI48cUD1Wg05IYWF7VadprXFOdqtVrk83lyuRyGYRCJREgmk5imKS2qYrGI1+slFArRbrcpFAqsra1hsVh4//33GR0dxeFwkEwm2d3dZWVlBV3X+eSTT/B6vdJi03WdxcVFxsfHcbvdRCIR7HY7h4eHZLNZms0mFouFarXK/v6+TC86vg/leXKW13Q6nXJTXyXUV4tLI2AiNuqbb75hZ2fnhZpYr8OrjjuNc7zLdbrdLhaLhfHxcSYnJxkdHcXn89HtdgmHw9RqNdbX1+l0OiwtLdFsNimVSlQqFXw+H8FgEK/Xi2mahEIh4vE4fr8f+H7DW6fTSbPZZHt7m263y61btxgZGZGlp0dGRpicnMTj8chNPQ4ODvjiiy8ol8tyd+/Xbe/TbM8fOu6HznHS+2JKbLVamZmZ4e7du3JPAcXV4dL8mu12W8Y7ZTIZUqkUdrtdihi8mCrzppz2eU461+A1RNoOfF8W2u12MzExweTkpNzWTOyuncvlePToEa1Wi9nZWbLZLAcHB3g8HhKJBB6PR+YxOhwOYrEYd+7cwWazcXBwAHwvkjs7O9jtdm7duiWrs1qtVhKJBHfu3MHlcpFOp3E6nWQyGfb29rBarUQiEVnt4nXa6VVt8LLjfujYd7nWYIrUoH9PbABcKBRwuVx4vd43vr7i8nJpBKzT6VCr1ajX6/j9fj755BM5lRoUgsEOPJgTKP7/pq8Jjr/3smu+7PhXnaPf76PrOm63W1pSIiJe0zSCwSAej4eDgwNpiW5vb3N4eMjY2Bhzc3MyfkuIWDQa5dNPP2VnZ4etrS06nQ42m439/X2SySShUAifzyctqmg0ytLSEgcHB2xvb+N0OmVVi+npaX72s5+h67rcOOT4vZ/UHq/72vG2eZ3j3/azg6+1Wi1yuRxWq5VKpSIreyiuDpdGwHq9nqyW4Ha7GRkZIRqNnhgbBa8/kr/piH/axw9OZXRdl5tzDCJK53i9XkqlEl9++SX1eh2AyclJpqamjgSg2mw2/H4/DoeDfD7Pzs4O2WwWu91OsVhkZGRE+nzEtX0+H/1+n52dHZaXlwHQdZ1oNMr09DSpVApd1+l2u6fSNmfV7m9yXKPRwG63yxJFiqvHpREwgaZpOJ1OPB4PVqsVt9t90V/pzBGCNDc3x9raGg8fPsTv9zM7O8vIyAihUOjI8WIXIl3XcblcdDodMpkMmqbJRQBRI18gKrECcsOPWCzGBx98wNTUlGzn458bZhwOB+12m2q1qtKnriiXKoxicKpwnYItLRYLoVCI//f//h/z8/Nks1lsNhtTU1M/OOUJBoNMTU1hs9kwDIPFxUUWFhZOtDhsNhs+n49wOCxL7AiRvIoMxrspriaXzgITXKdOJ6bNk5OT5HI5nj9/ztTUFIlEQpbAeRnCUmu32xiGwfz8PMlk8sSqExaLhXA4LOvsRyIRRkdHr6SVe3x/TWV9XU0urYBdpw4nwhcA6bAXDv8fWvb3+XzMzs4SiUSwWCyMjIy8ssxOPB7n7t27/OhHP8LtdhMIBE79fhSK8+LSCdh1Eq5BxH2HQiEZk3WSw/84TqeTSCQihcjpdL5U9KxWK36/H5fLBXzvb7wu1SnUVPJqcukE7Lqj6/obWUU2m+21V9hEZdbrIlqDKPG6mlwqJ75CcdoIy/a6WvZXHSVgiiuPEq+rixIwhUIxtCgBUygUQ4sSMIVCMbRcOgF7VQK1QvE2qBCKq8ulEzDlcFUoFK/LpREwUfbloiqCKq4+ygq7elwaAVMozhIlXlcTJWAKhWJoUQKmUCiGFiVgCoViaLmUAqaWvRUKxetwKQVMrUIqFIrX4dIJmBIvhULxulw6AVMozgLllriaKAFTXHmUcF1dLpWAqemjQqF4Ey6VgCkUZ4WaQl5NlIApFIqhRQmY4sqiXBJXHyVgiiuNqm5ytbm0Aqb8FQqF4oe4tAKmUJwmakC8migBU1x5lHhdXdTO3NeYfr9Pt9slk8mQyWTQNI1gMEgikcDhcMjQg1arRSaToVAoUKvVaLVa6LrO3NwcyWQSXdcBaDab7O/vk8/n6fV69Ho9+v0+mqbh8/lIpVIEAgGs1osZN5WQXT0uvYD1+33lhD0jTNOkWq3y9OlTvvzyS1wuFzdu3OCTTz7B4XBgmibtdpt0Os3XX3/N2toa+XyeTCaD3W7n7/7u7/B4PPj9fgzDIJ1O8+WXX7KysoJpmnS7XbrdLv1+n2QyyV/+5V/idrux2+0X9puq/nS1uPQCpjg7Wq0Wh4eHZDIZ6vU6pmnSaDTo9XoA9Ho9tre3efbsGXt7ezgcDt5//302NzfZ39/n4OCAzc1NpqamyOfzPHnyhHK5TCwWI5lMYrVayefz/P73v2dvb487d+4wPj6OrutKRBSnwqUTMLXsfX4YhkGn08FutxOJRF6YYhmGwdraGt988w2apjE3N8eHH35IPB7nwYMHtNttdnd38fv9bG1t8fjxYxKJBDdv3mRubg5d19nd3eXx48dsb29TKpVoNBr4/f5zv9eLmj6Kabi4/vH+Lf7d7/cxTfPI6+K9weOPn2/w2Ov43FwaAbuIH+B4p75OHaDX66HrOmNjY9jtdkKhEOl0+oh1JATsu+++4+7du0SjUaLRKA6HA5vNxvb2NpVKhXw+z97eHvv7+9y6dYvbt28TDAal/2xycpJ6vQ5Ao9G4UDE5z2v1+316vR7dbpd2u02/38dms6Hrumxn8afdbtNqtej1elitVhwOB5qmYbPZsNlsAEem5cK/2O/30XVd/iZWq/Va9eNLI2AXQb1ep91u4/F4LtQvc1Houo7P56Pb7dJsNimXy0ceANM0KZfLZLNZer0eDocDp9OJ1+vFNE3y+TyVSoV2u02j0aDdbuNyuQgGg9jtdvr9Pi6Xi1AoRCQSQdO0I1bGVcU0TQzDoNlskk6nKZVKR8RncFHD4/HQbrfZ2Nhgd3f3iI8wHA6TSCQIh8OYpsnBwQHZbJZKpYLL5cJqtVIoFNA0jXg8TjKZJBKJYLPZrk1fvpQCdh6Jt2L1rV6vk0ql5EradUF0ctHWYlQXo71AWAhiVRG+F75wOIzT6aRWq0mLweVyYbFYMAxDChiA1WpF0zTsdjuadim73KnS7/fpdDoUi0WePn3K3t4eLpeLWq1GLpej2WwSi8X4+c9/TiKRIJvN8pvf/IZvvvmG6elpvF4vpVKJ6elp7t69i9vtptvt8uDBA1ZWVigWi6RSKdxuN0+ePMEwDCYnJ/nwww/xer3yd7gOXOneZJomlUqFTCbD1tYWhUJBPqBWqxW32000GpUPaavVYnd3l+3tbarVKu12G4BoNEoqlWJ0dBSfz3dlVrKsVqv8I6Yq4v/wR/GyWq3oun5E9Or1Ot1uF13XCQQCJBIJRkZG0HWdVqslwzC63S7ZbJb9/X0++ugjvF7vhYRRnPe0VdM0vF4vk5OTBAIBNE2jUqngcDj43e9+x+7uLnfv3kXXddbX12k0GsTjcW7cuIGu69RqNdLpNMvLy4TDYfr9PisrK5TLZcbHx5mZmcHn8+F2u9na2mJ7e5tQKCR/B5fLda73e1FcaQHr9XoUi0VWV1flSlggEMBut+NyuVhYWGBsbAybzUa73SaTyfDo0SMePXokp0TtdptIJMLs7Cw/+clPcDqd8iEfdhET1peY8nS7XWlBwfcC5vF4CAQCWCwWOp0OrVaLSqXCzs4OnU4Hp9MpB4KRkRE6nY70pVmtVur1OtlslnQ6jWEY2Gw2TNN8wdK7SgjBDwaDeL1eDMPAMAw53fvyyy/JZDK0221KpRKbm5vYbDbu3LnDvXv35PT88PCQzc1NZmdnsdvtHB4e4vV6uXPnDrOzs/j9fmZnZ/niiy/Y2Njg4OCAw8NDwuGwErBhRzhQW60WrVYLl8vF7Ows7733HrFYDLvdTjgcxu/3o+s6h4eHPHz4kO3tbXRd56OPPsLtdrO3t8fTp0/53//9X4LBIJFIBK/Xi91uv+hbfCeEcIk2qlQqFAoF7HY7tVqNUChEv99nbGyMubk5Go0Gu7u7zM7OkslkePbsGQ6HA5/PR61Wkz6bg4MDqtUqHo8Hh8NBJpORllqpVCKXy+FwOPB4POc2AJy39SWsVkD6/drtNp1Oh3K5TCQSwe/34/V6qdfrHB4eyr7l9/vp9XoEg0HS6TTlcplqtYrX68Vms+FyufB4PLjdbukH8/l8eDweDMOgWq3KAeg6cCkF7LQ6thCxXq+Hy+XC7/dLq0usAvX7fWq1GplMhvX1dUzTZHJykjt37uD3+2VH2t3dJZvNksvlsNvtV0LAms0mmUyGhw8f8vXXX7O3t4fb7cbn81Gv14lGo8zOztLpdHj27Blra2t0u10qlQr1ep3333+fcDhMuVxmZ2eHtbU1VldXCYVC3LhxA6/Xy/b2NplMhlwux9OnTwmFQvh8PhwOx7n5HS/CUj5+zWazSTab5fDwkPHxcZLJJPF4nO3tbRla4nQ6sdvtmKaJx+NB0zQ6nY4MBtZ1HbvdLqfzwrfocDhwu91omiZXJ68Ll07ATrOzCR+OzWZD07QjP7yg1+tRr9fJ5/Nks1nm5uZYWloikUjIMIP5+Xnq9Tq9Xo9MJkM0Gh16P5jFYqFer7O8vMyvfvUrfvnLX9JoNAiHw+TzefL5PJ999hk3b94kHo9TrVb57W9/y69//Wt8Ph9LS0vE43ESiQQPHjzgiy++4D/+4z/Y29tjcXGRv/mbv8E0TZ4/f8729jZbW1vY7XY57QmFQuciYJfhN2q1WqTTaXZ2dshms/z0pz/l448/xmKxcHBwcCRMAr6fgooFD+GfFKEX4lghUqZpYrFY5CKKsMquC5dOwE4Tm80mHcytVot2u83jx49ZXl7GMAwmJiaIRqM0Gg25Cme32+UUUdM0nE4nPp8Pv9+P1WrFMIwrM8I5nU5SqRQ/+clP8Pv9cuSPRqPMzc0RCATweDzous4HH3wgp9Rut5upqSnGxsYIBAJMTk7yJ3/yJ3g8HiqVilzw8Hq9/PjHP8bv95PNZgmHw8zOzl5oPuR5U61WOTg4YGNjA4vFwt27d7l9+zaBQADDMKRIwVFRarfb0mfo9/vx+/3SD9lsNmU/7HQ6mKaJy+UimUwyPj5+bfxfcIUFTFhewWCQiYkJDMNgd3eXra0tMpkMlUqFH/3oR9y+fRufzyfFSoiUCCg0TfOFUe6qPHw+n4+FhQXm5ub4xS9+AXBkRVKEPOi6znvvvcfi4iKmadLv96WVYLVamZ+fZ2Zmhl/84heYpnkkEHNsbIxPP/2UbrcrzzsYnHmeiEWL87LKTNNkf3+f1dVV9vb2GBkZ4d69ewSDQVqtlpwWejwe+v0+1WpVpnKVSiV6vR5erxen0ymFrtFokMlkSKVS+Hw+GYsnrFvh070uXFkBg+9FzO12o+s6LpeLsbExuYK2s7NDuVxmZWWFpaUlaWXZbDYZEa1pmnSMFotFpqen5QLAZZiavAvHQyR+6FiHw/HS92022wvvDwrF8divi7Bgz/OaYipYrVZ58uQJ6+vrxGIx6bRfW1ujXq9z69Yt3G43k5OTbG9v8+jRI8LhMJqmsbOzI10YYhXX5/ORy+W4f/8+4+Pj+P1+vv32W54/fy7TtgzDkOle14FLK2Cn1eFEZwoEAvh8PtrtNg6HA8Mw2NraIpfL0e12cbvdhMNhWVVBRDTXajVKpRLVahVN0/B4PFc6BOC0eJXAD7v4vwph5RmGIQfLzc1N+X42m2V9fZ1ut0s8HicSiTA3N0exWGRjY4OHDx/KwNWJiQmmp6epVCqk02kajYZM3RJuj/X1dTY2NojFYlgsFprNJnfu3LnAFjhfLpWAnXbH7vf7VCoVyuWyXMERUeXCfLdarbRaLZxOJ9FolL29PZ49eyZXKjOZDKVSSa4GCd/DsDvxFWeD6BPdblfGEuZyOVlvzW630263SSaTGIYh065EmaKHDx/Kqf3t27cZGxtjc3OTzc1N1tfXqdVqxONxueJYr9fZ398nm83KINbrNMBeKgE7TUQU+OHhIU+ePKFYLMrIeuHQHxkZIRaLUSqVyGazLC8vs7KyIn0+TqeTp0+f8uTJE7a2tnC73VgsFj766CNGRkaujC9McbqIaXkoFOLevXtEIhFarZYM4LVYLEQiEZLJJB6PB5fLxeLiIk6nk0wmg9Pp5MaNG3KaKFK4gsEg3W6XcDhMMpnE6XTy0UcfkUgkAAiFQkxMTODz+S7y9s+VKytg8H01hXw+z8rKCo8fP+bw8FBOF8fHx1laWuLWrVs8ePCAx48f87vf/Y7NzU3i8Tj1ep1Wq8Xe3h6Hh4fkcjm+/fZb7HY7c3NzxGKxa5HXp3hzhM8wFovxZ3/2Z0deP14GR3Dz5k1u3rwJvFh0cWpqiqmpqSOvi7//6q/+6kipnuPnveoM7RMoVgqBIytmg9hsNrkKduvWLWq1GoZhyPy9hYUFYrGYdKbevHmTUqmEz+djbm6OUCjEZ599xvz8PMViEYfDQSqVIhqNKutryDivnblFhoNwN7hcriNTutcRl5cdc9Lr17UOmGAoBazf78syJV6vl0AgIPP1BtE0jVQqRSKRkMnHg5URnE4nNpuNmZkZxsfHj0QxC1NfhFqIsIrBgNirhnjoRHyS0+l86cMhshzE8YM+xpcdL3IuxfnPazX3vFc9DcPg8PBQ+qVisRgOh+Olg55pmnQ6HVnFYzA27GXHd7tdTNM80hevo5BdOgF71YgiTOhOp8M333zDkydPuHnzJrdu3ZIBl4PnEZaZzWbj+fPnFAoFmXMWCATk8U6nU4YBCKf+1tYWzWaTQCBAMBiUIRbi3FeRbDbL3t4e2WyWeDzO0tLSS1OmTNOUm4EUCgUSiQQ3btx46fGGYVAul8lkMqTTaRKJBNPT0698sE+L8/y9xArk48eP+eKLL/jJT37CBx98QDgcPrFtRNHHtbU10uk0MzMzJJNJGUd3HNM0aTabPH/+nFqtxtjYGMFg8MQsk+vApROwVyFGnnw+z+bmJk+fPqXf7+P3+5mYmHghnmmwXO/Tp09ZXV1lamqKhYUFIpHIkeOOl+1dXl7m4OCAVCrFzZs3CQaDV75zHBwc8ODBA3Z2dqRV+rICeYZh8Pz5cx4/fszBwQHz8/OycOFJMWPdbpednR2Wl5fZ2dlhbm4Or9dLPB7H6XSe6X0NlmE+a2tMrDpubGzw5MkT4vE4ExMTsmjmcXq9HrVaja+//pr79+/zs5/9DJvNRjweP7HdTdOkXq/z7Nkztre3uX37NjMzMyQSCdxu95ne22VkqASs3+9TKpXY2NigUqlgmibpdJp0Ok273cbtdh9xdIqo8HK5zMOHD/nyyy8pFAp4PB6mpqbkCDcodBaLRe7Us7y8zNTUlEy5EauQVwlxz71ej3Q6LaPGAba3t9E0jVAo9MJ993o9tra2+O6772SpHFGe+iQBa7fbrK2tcf/+fXK5HKZpEg6HZaT5VUAUBtja2iKfz2OaJtlslt3dXWKxGG63+wXXgxC8+/fv8+tf/xqPx0MoFJLVPI4fLwKrV1dXefDgAeVymU6ng8/nu1YpRIKhMSmEab63t8f9+/dxu9188MEHJBIJLBaLjLkRgasijGJzc5OvvvoKp9PJzZs3cTqdNBoNSqUSrVbryDVE58jn8zgcDrxeL51Oh1KpRD6fl2EYVxGR6hMMBpmensZisfDFF1+wtbV1otUipiwej4eJiQlarRZffPEF+/v7Lz3/wcEBpVJJ5kw+ffqUcrl81rd2LgifoAhejUaj/MVf/AUOh0MK2vH+BlAsFllfXycajfLxxx9TLBa5f/8+mUzmxOMbjQbFYlGmfK2vr/Ps2TOKxSLdbvc8bvVScWkE7GW+r8HXer0euVyOzc1NwuEwH374IZOTk+i6TrFYpFarHflsp9NhfX2db7/9lmQyyaeffkoqlaLT6fD8+XNKpdIR68swDPb393n+/DnhcFgmNNfrdba3t184/1VA7A15eHiI1WplYmKC999/n0AgwJMnT9jb2ztSx15Mw2q1Gg6Hg/Hxce7evYvf71tbsPAAACAASURBVGdzc1NaV8fpdDp0Oh1cLhdTU1OyQJ/Y7OO0GQwpOGkXoLOg2WxSLBbJ5/OMjo7y2WefEQqFZDmhwXsdLGe0tbXF9PQ0f/3Xf43L5WJnZ4fDw8MX+pvwIx4eHuL3+5mamsIwDHK5HIVCgWazeWb3dlm5NFNI4WwXlU5Pqs0uCvBZLBZZZaJSqVCpVNje3sZutxMIBIA/WmCFQoFMJsPS0hJzc3Osrq6ys7PDV199hdvtZmRkRB7f6XRYXl7m4cOH3L59m/Hxcdn57t+/L3fluUr0+302Nja4f/8+TqeTRCIhAy+fPn0qV8eEf1Fspfb8+XO63S7j4+OylLRYFRMFDEUyfLvdlqkzPp+P6elp9vb2KJVKZ7qaO7irj1hBPis/psVioVgsks1mabVaeL1eRkdHCQaD5HI5qtXqEQETpZl2d3fJ5/PMzMxw584d0uk0mUyGfD5PqVSSQaqDgdmrq6skk0mZ0G2xWGRSdzgcPpP7u6y8s4D1ej06nY7cNuqk6carRj3RoXK5HKVSiWazKX8Q4ZuxWq30ej0ajQZWq1XmkPn9fiKRCOVymbW1NQKBADMzM8D3I361WpVlj0W98Hq9zu7uLpubm9y6dUvuiyjOf3BwwMHBAR9//DEzMzM4nU4KhQK7u7tyd5nBEAL4Y+cS4vqmvOlnxHcQn32bWCAxIAzuAzA/P088HiccDhOLxWS8W71eP5J2tbq6yv3795mdnWViYoJkMgkgS8Ck02m5/ZqoiZ/JZIhEIjKIWIhLo9GQfkkhgoNF/N7U8T4YLNpsNikUCtJdkM/nzyQERhQezOVytFotWQjT5/MRj8fJZrOyxtrk5CRWq1WKUaFQkHm4yWSShYUFdF2nXC6Tz+eP9E+RMVIqlbh16xa3bt2S0fvlcpliscjo6Ci6rss9PwfDVUTbikHpJER7v2vJdJvNhtPpPPNNjN9JwMQDIHZ3FmVnXsZxZzn8UcCKxaIsR2wYBhsbG3I6Mlg5wel0srCwIFMpIpEIm5ubrK2tkUqlZPkbUWVV13Wmp6dlyZx4PI7f76fdblMsFikWi4TDYbrdLtVqlVarhdVqxev1ygTZzc1Nnj9/TrVapVQqoWkajUaDcrmMpmn0+30KhQLtdvuFEf51f7wfOm6w7cQ+g61WS5Zj0TTtjTqK6NCGYVAsFmUuaDweR9d1otEo8/PzuFwuCoWCrBbaarVk0vH8/Dzj4+P4fD7ZFwqFAk+ePGFpaUlacpubm+zs7DA+Ps7k5CTxeFw+TPv7+7TbbW7duoXL5aLRaJDL5ahUKgBHdkN6nTYbFDAxiIkYQFGD/vjD+S4PmOiXYiput9uZmpqSm8WMjY1RKpXY3t7m4OBAbj3XarXY39+n0+kwMzMjq5zcuHGDXq/Hd999J0NU4vG4bKtCoYDD4SAcDsvaX8vLyzx79kxabR6PRxZR9Pv9sjinqMtfKBSoVCpHnkPDMI7sXXnSAsLrtpVhGNK9EA6Hz1TE3knABpeM0+k0qVSKUCh0JCD0+N/H/y06nMvlkkvqYtQQloZIvHa73QSDQTRNk8v1Xq8Xh8NBp9OhVqtRLpdxOBwUCgW2t7exWCwyql7sgzg9PS2nLzs7O7hcLvr9viztOzU1hd/vx+FwEAwGmZycpNlsyvpOLpeLfD7P/v4+o6OjRCIROcodD8cQ93j8vo9z/L2TjhWWqGmabG9v8/nnn5NKpfjTP/1TvF7vKz970vktFgt2u52ZmRlmZ2dlgUKr1UoikWB+fl76x0SN/GKxiGEYeDwefD6fbP9gMEg4HObzzz+nUCgcKR/z3Xff8eTJE/7hH/6BYDCIy+UiGo2SzWb5z//8T3RdJ5FI0Gw22d7elit48Xgch8NxRMBexxo7bp2K31fEVh3/PY6n+LxuGwrEanc0GsXpdMqBFSAWi5FKpdjd3aVWq1EsFrHZbLIwoc1mY2RkRBbMDIfDxONx3G43pVKJtbU1PB4PvV6PjY0NSqUSsVhM7nQUjUZJp9NyEN3d3SUSidBoNGRanIhhFK4ZsamNmDHYbDa2trb45ptvZBlxYT0NWvvH2+H466IdNzc3KZfLss1PCjI/Ld5JwISP6eDggFwux40bNxgdHT0ynRycAhz/90l/C443nCjY5vP55LK7qEQZCASIxWKYpsnh4SFut1suX6dSKaanpwkEAnJTBPEDbWxssLGxIbP7K5WKTLL1+/0AuFwuafYXi0U2Nzfx+/1kMhn29vYIhUIyFEA8aIMPxMuE+2XvHX9t8Fyi2GK9XqdWq/Hf//3f3L17l1/84hfygXnZtGvwXIPTBKfTSTgcJhgMHjk+EonQ7/f57rvv2N/fJx6P4/F4SKfTuN1ubt++TSwWk6O0y+XC6/Wyv7/P2toamUyGkZERKpUKW1tbrKysYBiGjO73er14PB5WV1dpNBr8/Oc/R9M0nj17Rr/fly6CQCBwZGX5VX1m8P6PI+79Zec6qY2O/46v+v2EmBwvKCgsIL/fT6fTYXd3l263Kyupejwe2baA3M0oGo3KfRomJyex2+0cHBzQ7Xal70tc1+1243Q6qVarbG1tSYszl8vhdrvpdDrSFSNCOcTmxAAOh4P19XXp+11cXCQSiUiRe1m7HW9DUSGjWCzKii6pVEo+S2fBOwnY8QfB7/cTCoXodDon3uDxfw++dlLA3uAIKeqCDwYDCgtifHycjz/+mGazyerqKj6fT+7mIqZDIsjPZrPh8/mIRqM8evSI/f19WTpnb29PVnAV+xdaLBZ8Ph+BQIDl5WUZRS4c1V6vl2AwKC2jV7XVq9rgVa8LhAVWrVbx+/0y3UdM/QYfvh86r2hzTdNOjB8SKVP7+/s8fPiQYDBIMBhkc3OTaDTKRx99RCqVklNmsTvO4uIiLpcLwzDIZDJ0Oh0SiQSLi4tEo1H5cIsH9caNGxwcHLC5uSkfuqWlJRYWFl66+9ObWEeCk9rmdX1rr+OHE8/A8WmXmOILQXr48CE7OztSyCORiNwkWOByuRgZGZG7OBWLRbkdoM/nY2xs7IjFLQKCd3Z2ZI27QCAgd+sWoiWSzI9bVuLZdTqdeDweaU0Ly+91BuF+vy99dSLL5STL9rR5Zyf+cbNU13XpFxKcZGq+jJfd8EmOavEAxuNxrFYrjx49Ym1tTT5UHo9H/hCiMYXoeTwerFYr1WqV3d1drFYr2WyWaDRKIpGQuxuLKYjwKxweHtJoNAiFQoyOjhIKhWTg5qsE7HXu8YfaaLAmvwh0FJaPqJn+KuvkZdd52bUGndMbGxsEAgEKhQKTk5PcunXrhcwHl8vFe++9RyAQoNVqsb6+DkAikWB8fFz+TuK6Pp+Pe/fusbKywubmJr1eD5/Px+joKBMTE/Ihe53px9u26evwOuL4qmuIQSaXy7G1tcXGxgbBYJCpqSkSiYTcMk0gKllsb2+zv7/P3t4ezWZTnicajR4ZdNxuN8lkkv39fbmKOTExwezsLLFYTJZKB478ZsL4EOcQm4KI/u7xeH6wTw+2jbgHkXVwHpkrpxZGMfggnGeGvAimFGImVrxisRiffvopk5OTR74X/PHhDAQCeL1eDg4OpBNT13Vp3YjPCP+bqF1+cHCA1+tlYmLiyNTrPH6wwd20hQN5MAfutNpdCH0sFiMWi5FOp6lUKrjdbhwOx4klpDVN4+bNm7hcLr766iv29vawWq0sLi6ytLQkd5ge9Ht++OGH6LrOv//7v+N2u1lYWJBtelVSt8QepB6PR/qm/H4/i4uLMgTl+PGhUIhQKISmaXJWIWqMHY/od7lcMpWo2WzKAVaI0GA7vkxsRbjJ8cW1t/kNznPT51MRsItOrxEbTAyGXXi9XsbGxl4aF6NpGqOjo7JeWKfTYXR0FJ/P98K0RWxSMTo6SrlcplAoMDo6yujoqPRdnBfnOTjous7U1BT5fJ7l5WXa7TbxePzI9GUQsbgifKDVahWr1SpzVY+vlNrtdtmmIyMjciHnqqXEaJqG3++Xq8Vij9JAIIDb7X5BJISvSsR6PXr0iH6/z4cffihDUQYFTNM0abnOzs5SKBSIRCIvFDh4FWIwPA3OUw8uTSDruyJWPKLRKJFIhKmpqVc+DKJWWKPRYGVlBavV+lLBE/P76elp3G43lUpFxqJdxAa3r+PjOg1sNhvT09My6LLVaskVs+MMCqvwo0QiERl0fLydhMUMkEwm+fDDD7FYLDKc4CohZgmhUIhkMkkgECCZTBIOh7FarS9Mk4XVPzo6SrPZ5NGjR5TLZQKBwIlVLYRvS1T3yOfzcrfuNw2tgXevnXbWfq9BTlXAzvOLH0fU9RIms3A6v2xUEXtGzs7O8tlnn2Gaptwn8iTEUn8gEKDb7eJ0OqWf7KI462tbrVYCgQBzc3MycPdVbSRwuVwsLS0xPj6OxWJhfHz8lcf7/X7ef/99ALmidpUQftSpqSk59fZ6vTI+62U+SJ/Px8zMDD//+c9pNpvMz8+/dPDQNE2GrrRaLTRNkwtRr/sdxZ+LfI7flFMVsIt8mEU8jXAUH5/TH0ccMzglOmkVCf7YQbxe70unT1cR4QeLRqN4vV5p5f7QQyGChycnJ+X/X4XdbieVSgEnr0gPO8KiEmlaou+9yh0g2j4SifDRRx9hmqbcIvAkbDYbbrf7rUvqnOYU8jx5JwE73vgXqdxCZAY7xutkBQh/g1iRuWoPz7swuPjhdDpfW1zEAzsYv/am17xqiNX6wcWW173Xwf55lpyFBTYUYRSXhbf9gYdx5Dlv3nTxQLXpi7zNAowQvvPgtHxggvMwaFQvUygUR6aQw+QDUwI2xJxnSIXiajPYl5SAKRSKoUP4gJWAKc6VYepwisvJ8VXIYelTpypgajqjUAwnwxoHpiywIUYNGIrTZBj706kK2DApt0KhOMpprUIeL55wligLTKFQnPoq5HlZc0rAhpTXyTZQKN6E0w5kPQ+UgCkUChUHplAohhcRRqFWIRUKxVAyjPmrw/eNFRLlA1OcJoNxYMNihSkBG0KUaClOm2GtBzZ831gBKBFTnC7XNhJfFLlTD9T5o9pccZoI8TppN+7LyjsLmHqILgfD0uEUl5NhjStUU0iFQgGcXirReaIssCFmGEdMxeXkLAJZh66k9DApt0KhOMpZbGpz1pqgppAKheIFC2xYjBElYAqFAkDlQioUiuFE7UqkuDCGqcMpLi8qlUhxrqgVSMVpoVKJFArFUHOaPrDzsuBOJZVIoVAMN6ddD0yVlFYoFOfGaQZFn6dr41Qi8ZUv5vxRba44bQZXIU9rZ6KzRqUSDTHDWsdccfkY7EumaV7wt3l91BRSoVAAZ5NKdNYoJ75CoRjaVCLtNE82LDc97Ih2HrbRUnG5Gcb+pKaQQ84wdjrF5WNYU4lO1QJTKM6bwYdtMIbpuLAffyjFsWoA+CPDuCCkBGwIucqhK0JU6vU6+/v75HI52u02c3NzjI2NyWO63S6FQoF0Os3+/j6lUgmA6elp7ty5g8fjwWq1YpomhUKBvb09Dg4OqFQqaJqGy+UiFAoxMjJCPB7H4XAMZSrNaSEssF6vpwRMcT5cVRHrdDrkcjnu37/P5uYmhmHg8XikgAnx2tjYYH19nWw2SzabpVAokMvl8Pv9jI+P43A4qFarbG9v8/TpUw4PD6nX62iaJjeuWFpa4sc//jGxWAy73X7Bd35xHN+V6F1F7LxEUAnYFWCYRswfot/vUyqV2Nzc5Ouvv2Zvb49wOEy73ZbHNBoNNjY2ePToEZlMhnv37nHz5k1+9atfsbu7y5dffommaUSjUVZWVtjY2CCTyTAxMUEqlcJisfDFF1/wr//6rxQKBUZGRvD7/ddawOD0p5Dn0S+VgCkuFRaLRU7xIpEI9XodXdePWJuVSoUnT56wsbGBruuMjo4SCATY29tjf3+f/f19stkshmHw9ddfUy6XSSaTzM7OMjMzg2maPH/+HJvNRrVaJZvNMjs7e4F3fTk4iyn0WYuYErAh5ipOIS0WC6FQiFu3buF0Onn69Cm7u7s4HA55TLlc5tGjR1SrVebm5nC73YyMjPDxxx/z6NEjnj9/TqVSoVqt8oc//IFIJMKf/umfMjU1RTAYpNvtMjk5ySeffILdbqdWq9HpdC7wri+eYc3quL5eyyvCVRUxu92O2+3G5XKhadqR++z1ejSbTSk6VqsVp9PJ2NgYkUhEOu8Nw6Db7WKxWHC5XDidTgA0TcPpdBIIBORrV7Ed34Tj+0IOi4ipXMgh5iq3fa/XwzAMDMN4ITfParWiaRo2mw3448MmREq853Q6iUQieL1eer0e3W4XQIpbu93GYrHgcDiO5AEKB/+wPMSnxbWLA7vKD5DiYhF9a7BO1eB7NpsNTdOw2+1SyJrNpnT22+12fD4fExMTOBwOOp0OrVYLn88HfL8QsLe3x9jYGMFgkH6/T61Wo1wuo2kaHo8HXdfRNG0ocwTflGG0vuAUfGDDeuOK4aDf79Pr9Y5YYbqu4/P56Ha7dDoder0enU6Hw8NDKpUKuq5jt9sJBALMz8/TbDalT0wIWK1WI5fLMTIygt1uJ5/Ps7W1xcbGBn6/n9nZWWKxGH6//9rEhw0WNByWZ/mdBex4JLRC8S6YponFYpFTvlarRaPRoNlsymOcTicjIyPU63VKpRKVSoV8Ps/a2hqFQgGXyyV9aLOzs+zu7pJOpwmHw9KJX6lUaLVa9Ho92u026+vrPHnyhN/+9reMj4/zF3/xF7z33nt4vd4LbI3zQ6USKc6VqzhY9Pt9DMOgUqmwvr7O559/zoMHD8hkMjQaDarVKktLS9jtdpaWluj1eqyvr/Nf//VfOBwOKpUK8XicmZkZrFYra2tr/OEPf2BlZYVGo4HFYsHv91Mul9na2mJvbw+73U44HGZ8fJzJyUk0TSMWizExMYHP55PT0+vAYCDrsKAEbIi5iilFhmFQLBbZ3Nzk97//PU+ePKHT6dBut+n1evj9fhYWFrhz5w7tdptMJsPvf/97ms0mU1NTzMzMMDU1RbfbZXNzk//6r/9idXWVYDDI0tIS1WqVXC5HpVIB4PDwkPX1dW7evMn777+P3+/H6XRKP9t18H/B8PYlJWCKS4XNZiMYDHLr1i3+9m//lk8//ZR+v4/X62VkZIRUKoXb7cZms3Hz5k3sdjs3b96k3W4Tj8eZnJwkGo1iGAaLi4v84z/+I4VCAY/Hw8LCAsFgkEAggNvtZmxsDE3TGB0dZW5ujkAggM/nG8oH+TQ4TV/2ebXhqTjxj/NDWf7CSXj8mOvacRR/xGaz4ff7cTgcJBIJGfpgs9mw2+14vV7sdjsWi4VkMkkwGGR+fh7TNHE6nTgcDjRNo9/v4/F4SCaTGIaBpmly1VIEvs7Pz2O1WnE4HNjtdnne68hxH9iwiNiFWGAivgf+uCQ+uFx+XTvRdUf0BZvNhq7ruN3uIwPd8ZAKEebgdrvl+4P9x+Fw4PF4TjyHw+F46eeuI8MaTXCqYRSvi2EYpNNpHj58iNVq5fbt20QiETk1ULwZw7Ts/UMcF5ofOvZVx73te9eV09wXEoYgmVvE6Iho6dfdzaTT6bCzs8O//Mu/YLfb+ed//mfcbjdOp1MJ2BtwnS0GxekzjP3pnYagTqcjazGVSiUajcZrFURrtVqUy2VKpRK9Xo9IJCKXrIexERWKYedabupRq9V4/vw5Ozs7wPdVAlqt1g9Wt2w2m9RqNTRNIxgMEovFpL9DoRhE9Anhx1ID3NlxLeLAhDpbrVaKxSIrKyusr6/j8XjI5/NSmDTt5aduNBrUajV0Xcfj8aiKAG/JdWgv0zRpt9uyz1330s9nxbD6BN/KAhMpHtlslnw+T6lUotPpsL29zcTEBB6P50j9puM0m01arRaBQIBwOKz8Xu/AVRexbrdLuVwmn89jmiYzMzOvTO8xTZNut3ukjM6rHkzTNGU60escf1U5i1Si87CY38oCa7fb7O7ucnBwQLfbxTRNGo0Ga2trJBIJJiYm8Hq9J8Z69ft9ms0m3W6XeDxOPB6/8g/haXOdplKtVot0Os2DBw9otVoEg0G8Xq/MmTzeDp1ORwoe8Mq+CN8LZLVaJZ1OY7FYGB8fx+12D61F8i6chQ/s0lVkNU1T+r62t7ep1+t0Oh1M0+Tg4IDt7W0ymQwul0sGFQ7SbrepVqs0Gg1CoRCRSOTaPIxnwTD5K96GZrPJzs4OT58+pdlscu/ePZLJJFar9UTLvVgs8vDhQ7788kusVit///d/L3MjTzq+VCqxurrKt99+i9Vq5ZNPPmFiYuJaVaGAs4kDu5RhFMInIaaOYiSE70e/Wq1GsVgkEomg6/qRka/X69FoNGQlgHg8TjQavVYd5bS56uJfr9c5PDykVCrR7XbZ2toiHA6TSCRkIOogpVKJZ8+e8Yc//AGLxcLt27fxer2yUuvx9ioUCqysrPDw4UMA/H6/DKLVdf1c7vGycC2c+BaLRTrf/X4/gUBAliVJJBLSohJO18EOYxgG9Xqder1Ov98nkUgQi8WUgL0hw9TB3pZ+v49pmtTrdVqtFrOzs1gsFh48eECtVuOv/uqvcLlcJ04hTdNkYWGBTqfD7373O1qtFp999tmJftlarUa1WiWRSNBut3n69CmBQIDJycnzutVLwbBOmd9YwKxWKy6Xi7GxMbkZgghmnZ2dZXZ2llAodOJqkbDQWq0WVqsVv99/7Uz10+QqW1+dTod8Pk+xWETTNMbHx9E0jX/7t3+j3W7z05/+9Ij13ul0ZMkdXde5c+cOzWaT//u//2NjY4N6vU4gEDji0uj1enLwHRsbk9u1FQoFKYTXqW+KexUltd+W8/TRvpUF5vV6uXnzJrqu0263abfbdLtdFhYW+NGPfkQoFDpxdOx2u9RqNQzDQNd1nE7ntU6gfVcG67j3ej35+mWz0N7097VYLNRqNVZXV0mn0wQCAaampmShQxE0LZK04XtLan19nUwmg9frZXZ2lm63y+PHj6Xftt1uy0RvsTGIYRg4HA5GR0flhroWi4Vms3kkxEc4tgfj0i47r9PuwvIavJ9huDfBW1lgdrsdh8NBOBzG5/Ph8/kwDINIJEI4HJYbKxxHhF/Y7Xa5mjS4oYLi9RCdTtM0WRMLkA/naV3jLD/7qmMsFgvpdJrHjx9jGAZzc3OEQiEsFgszMzOyH7VaLSkwuVyO//u//6Pf7zM3N8fIyAgA7733HhaLhXq9TqPRkAHTtVqNw8ND2u02sViMyclJ+v0+lUoFn89HpVKRlS/gewtPCJ7YFET4d3+o+srb8Cbne5sBYhCbzUYul6NcLmMYBk6nc2gsz7eKAxMNIEqQuFwu+v0+LpfrhU1IX7jg/79jsiib8kPHK17EarXi8XgYHR3F4/FQLBYBXtil513b9W0//7qfe9Vx6XSafD6Pz+cjGo1Kh/37779PpVKR00W/349pmhQKBR49esTIyAjJZJJQKISmaXz44YdkMhlyuRyBQAC/34/NZqNYLErrLJFIMDo6iqZpNJtNyuUyh4eH0gIzTZNqtUqhUJD5viJ86DTa603b5jSuOfg5EZRer9dxOByEQqGhWcB4p1QiERkt/FivCl4F8Hq9TE5OkkgksNlshMPhaxXTdBpYLN/vmTgzM8M//dM/ARAMBrHb7S+MmidZY6/z2kkC+ENTpzd9/VXX7vf7uN1uPvnkEwKBAOPj4zL2a2Fhgf39fXK5nFxEEuWZotEoqVSKeDyOy+XCZrMxOjrK4eEh3333HaZpEgwGCQaDHBwc8Mtf/pLZ2Vnm5uZkLbHR0VH29/dZXl7GYvl+l/BGo0E6nSabzRKNRolGo9jt9hcE7GXteFZtNfja61z7Vee3Wq2EQiGCwSCJRGJo9gJ4523VxDbwoo7TqxCbLYik7bMwva8DmqaRTCbx+/20Wq0jtdUGeVWnfpXP400elHc518uON00Tu91OKBTC4/FIP6lpmqRSKRqNBsvLy3JzWrHpx9zcHJOTk/j9frkdWiAQQNd1CoUCh4eHpNNpNE2jWCyys7NDKpXC5/OhaRq6rhMKhej3++zt7bG7u4vb7aZQKFCv14Hva4wNVm19mzZ9k0HkTdrtXa7tcrkIhUJEo1EikcjQZMecWj2wwWKELxOl4wULlXi9HcIKE9uLwZs5Xl/XEf2653yX4172WXGPVqtVWpZiwLRarRQKBbkinslk6Pf7LCwsMDo6KgVPHB8KhUilUnQ6Hba2tuTO3WNjY6RSKSl4AG63m2AwiN/vp1QqsbKyQjabZXR0lB//+MdEIhE5YL9uzNRpt/ebHPsqMRPffzBR/vgu6Jedd7bA3nQKOEyNc5n5oWJ+VxHRdzRNo9frkc1m6ff7ZDIZIpGITE07Pp2ORqPcvHmT3d1dtre3Ze26e/fucePGjSP5jzabjWQyyY0bNzg4OCCdTmO1WpmeniaZTA7N1OpNOD4TGqZVyFPp/cN0w4rhR0zj6vU6m5ubZDIZ2u02brcbt9v9wgp4OBxmYWEBj8dDJpNheXmZVqvFT37yExkONDglHB0d5b333pPpcbqu4/f7cblcF3G7Z85xo2KYjIzrM3wrrgyBQICFhQVcLhfpdBpd1wmHwzLk4Tgul4tYLCbTiVZWVtjb25OZIMdjEX0+H6lUivHxcVKpFIlE4lrvVnSZUduqKYYOj8cjp3iFQoHJyUnGx8dfufTvcrlIJpOMjY2Ry+XQNA2v1/vCFFz4gcRuRx6Ph2AwKJ37ijfj0lWjUCguGl3XiUQi3Lt3j9HRUen/etUUT5TKcTgczMzMyK3bXoamady8eZOJiQksFosssaN4fS5lNQqF4qKxWq243W4mJiaIx+NH9oN8GRaLhUAggMvlIh6PY7PZXnn8YFxUr9dT8YqXFCVgiqHEarXi9XrlquDriIvNZsPpdL5WCfPBUJ/rtNI7bCgBUwwtb2MRKSvqfDgvi1UNLQqF4lQ5z0FCCZhCoTgzzlrMs838PAAADMlJREFUlIApFIoz46xXIpWAKRSKM+E8wiiUgCkUiqFFCZhCoRhalIApFIqhRQmYQqEYWpSAKRSKoUUJmEKhGFqUgCkUiqFFCZhCoRhalIApFIqhRQmYQqEYWpSAKRSKoUUJmEKhGFqUgCkUiqFFCZhCoRhalIApFIqhRQmYQqE4E1RNfIVCMZScV118JWAKheJM6Pf7qqS0QqFQvAwlYAqFYmhRAqZQKIYWJWAKhWJoUQKmUCiGFiVgCoViaFECplAohhYlYAqFYmhRAqZQKIYWJWAKhWJoUQKmUCiGFiVgCoViaFECplAohhYlYAqF4kxQ1SgUCsXQc5YipgRMoVCcKWdZ3FAJmEKhGFqUgCkUiqFFCZhCoThVLBbLkWmj8oEpFArFCSgBUygUQ4sSMIVCMbQoAVMoFEOLEjCFQjG0KAFTKBRDixIwhUIxtCgBUygUQ4t20V/gOiEC+vr9/pFAv7PMFVMorjJKwM4RwzAoFouUy2Xa7TbBYJBkMommqZ9BoXgb1JNzDvT7fUzTpNVqkclk2N/fp1qtMjY2RigUwmq1vpB+oVAofhglYGeMaZp0u10Mw6DZbFKv16lWq1SrVWq1GvV6nX6/j6Zp2O12rFblllQoXhclYGdMt9slm82STqdJp9Ps7e2Rz+dptVpUq1WazSbRaJRYLMbY2BgOh+Oiv7JCMTQoATtjOp0OBwcHfPvttzx+/JhKpUKn08E0TXRdZ3V1lZmZGRYXF4nFYlLARDle4fAftMyOv6emn4rLxHn2SSVgZ4zdbieZTLK0tEQoFCKTyRxx4o+Pj5NIJEgmk0esL+E3MwwDi8WC3W4/0iF6vR7dbheb7f9r736eGqf/OI4/myZt2qalPym0FEFcZ1ZGxB9704ujHv0zvXhwvHrQGWcvHtaZHd3VxcW6QLtsKZRS+iP9kX4PTPItUH4spYXA+zHjOErTJE366ifvzyefePH5fDexa0IMNfgDO+458SXAxszv95PL5cjlcqyurpLP5ykUCtRqNXK5HCsrK0MDyC767+3t4fV6SafTTm+lZVk0Gg3evHlDIBBgZmYGTdOAo5PHDjf75FEUBa/Xi6qq0lITEzPu8AIJsIk62bQ+r5nd6XQolUr89ttv6LrOl19+ydTUlBNQW1tb/PTTT2SzWb755hui0Sj9fp96vc7a2hpPnjxhf38fVVVJJBI8ePCATz75BL/ff2ocmhBuNVKX11kJK1+O0+zmtK7rRKNRUqkUhmFgWdbQ13c6HarVKmtra7x8+ZJWq+W8T7fbZXd3l99//521tTVarZZzLCzLotlssru7S6lUYmdnh0qlQqPRcNYlx0fcFdICmyCv18v09DTxeNwp4nu93qEtIsuyME2Tw8ND4KjmNfi3VqtFtVqlXq/T7Xbp9/soioLf72dhYQGfz0ez2cTr9WIYBolEwrnMFGKcXFfEtzdW6ixn83g8aJp26RDxer14PB663e6xehb8v85lmibdbhdVVZ1eSr/fTyqVIhwO0+v18Hg8qKqK3++XEf9iIuyB2ZMw0hltd+/3+33a7TbVapVyuTyREDv5/oNf8NsYoPZn5fV6gaMW1bDLR3vbK5UKtVoN0zQJBoND97fX69FqtTg4OEDXdedY2O8zuK5Go+EsN/jvceznbWJvz7j3+22c9xkNHj+30TQNy7Ko1+tYloXX63V+iMdlpABTVRVd12k2m+TzeZ49e+Z8SS+z0ee95qLlr7rsVT7Mt1lm2GvtkfaGYbC4uIimaeTzeer1Oh6P51iY2ctXq1V2d3fZ2toiEokce3/7Nb1ej7/++ovvvvsOwzCcFpt9OTm4fnsZ0zQxTfPCQv5Zf3vbZUY9D0Z5zeD4Obtn1r4Uv+wxPfl0navu40WvPxm0b/PeVw2I617O/gEtFArOf+u6fqV1XNZIAaZpGrFYjHg8zvb2NsVikcPDQ+ekGUcIXaYHbZRwO+sX8KJ1XrRdmqYRiUSIRCL4fD5nKMVZAVar1Tg4ODhWfD+5Prtg//r1a3RdPxZgw/ZNURRardaxov95+3eZ/3dei+G6f8Te5pwYLGsMDi0ZrCVedjtPhstV9/W8c2TYY8jG3Qi47GsGt+syn5XX62VmZoZoNOqcl+MyUoD5/X5mZ2cJhUI8fPiQer1Op9MZaYNPHrzrbPJf1/CBq2yTXYcKh8N4PB4ePHhAu90GjreqBgNsY2ODn3/+eej67W1YXFzk22+/JRqNXngfpR3QJ0fyX8Wox2XUY3GZ9Q8Wkwf3fVwmeXk6rqEw17EPPp+PUChEMpk8NQD7uo18CRkOhwmFQszMzNDr9a79JLmt7/W267Qvre1mdjqdPtbqsg+y/ff9/X2nB/Fkj87glzIej/P++++TSqUuLJ6eDMlRPo/r+izHdUwGv+Ane8XuSojdxPrOY2+LpmlOh9G4C/ojF/GlZ2s82u22cyKcPAnsHs1gMIhhGEQiEaamplxZ+BViFDJ3yy1lh1G32z1W17JrWYZhsLCwwOzsLJqmSXiJe0maT7eUx+NB13VmZmYwDMMZEgFHzfJYLMbHH3/M7OwsqqrK7UHiXvL0b9NFtHDYI+2LxSKaprG0tEQgEACOWmWHh4eUy2UCgQCpVEpaYeJekgC7pXq9njO8wq552b2MlmUNnQ9MAkzcNxJgt5ybR2YLMW5SA7vlJLiEOJv0QgohXEsCTAjhWnIJeQNM02R/f59Go+HcemXf6jI4d5d9+dhsNqlUKgDouk4oFDr19CJ7ep1arYaiKITDYWe+MSHuKgmwG7Czs8Ovv/5KPp+nVquhqiqqqtLpdPjggw/4+uuvSSaTTqgVi0UeP35Mr9cjm82yvLxMJpM5du9jq9Via2uLJ0+eEAwG+fTTT0kmk2O/mVaImyQBNmH9fp+DgwOeP3/O/v4+mUyGUCiEpml0u11n6hx7+MTg5IWFQoHt7W2mpqaIx+MEAoFj0+Ts7Ozw9OlTUqkUq6urzvISYOKukgCbsH6/T6vV4s2bN0QiER49euTctW9ZFqFQ6NgcSpZlEQwGyWazbGxssLa2xtLSErlcDp/P59yLWq/XKZVKFAoFNE3D5/PJFNLizpMAmzB7ssFwOEw6nWZxcZFMJoOu6870OqqqOpNCKopCIpFgdXWVzc1N1tfX2dzcZGNjg3g87gRYoVAgn89jWRaGYRAMBqX+Je486YWcIHsSQvufarXKf//9x8uXL3n16hWVSgXTNI8toygKgUCAbDZLLpcjEolQLpfZ3Nyk0+kAR5ePxWKRUqlEJpPhnXfeOVXkF+IukhbYhPX7fZrNJsVikUKhwPPnz/H5fCSTSR4+fMjKygoffvjh0OlxUqkU7777Ltvb27x+/doJu0qlQqlUotvt8ujRIz766CO5fBT3ggTYBNnDJYLBIPPz8wSDQeLxOB6PB8uyePHiBR6Ph3Q6jaZphEKhYyGWSCRYWFhgd3eXer1Ou92mUqnw77//Uq1WCQaDLC4uMjc3d+HsrELcBRJgE6YoCslkks8//9x5hiNAPp/nhx9+YH19neXlZaampk49jSgajTI/P8/6+joAjUaDnZ0dnj17hmmaTE9POw/MFeI+kACbMI/HQyKR4LPPPkPTNAzDcIZJpFIpLMuiVqvRbDZPLWsYBplMhmw2S6VS4dWrVxSLRf7++29isRhzc3POnPtC3AcSYBNkWRadTod2u+08vcWeNtoe9mAX5ofx+/3E43Hm5uZoNpv88ccfbG1tUS6XmZ+fJ5PJOHOGCXEfSKFkgjqdDnt7e/z55598//33PH78mGazSb/fp16v888//7C9vU0kEnEe5nGSrutMT08D8Msvv/D06VN0XSedTpNOp/H5fJPeLSFujLTAJsh+CIplWZTLZRqNhnO/YqlUIhaLkc1mmZ6eHvo0bjgaI5ZMJonH47RaLafon06niUaj8pAVca/I2T5BqqoSj8fJ5XIsLS3x4sULfvzxR0zTJJFI8MUXX7C8vEw2mz33icaxWIyFhQWWl5fp9/u89957pNPpM0NPiLtKAmyC7JH10WjU6Wnc29uj1+sRi8VYWVlx6lhnDYOwa2ezs7N89dVXKIpCLpcjnU6jqqoEmLhXZErpCev3+3Q6HRqNBqZp0u12URQFn8+HYRjOANTzxnF1Oh2nM0BVVXRdd54dKQEm7hMJsBtg31I0+BRzRVEu/RTjweUktMR9JgEmhHAtGUYhhHAtCTAhhGtJgAkhXEsCTAjhWhJgQgjXkgATQriWBJgQwrUkwIQQriUBJoRwLQkwIYRrSYAJIVxLAkwI4VoSYEII15IAE0K4lgSYEMK1JMCEEK4lASaEcC0JMCGEa0mACSFcSwJMCOFaEmBCCNeSABNCuJYEmBDCtSTAhBCu9T8i+Z3sRKLMlAAAAABJRU5ErkJggg==)
physics-General
physics-
In the circuit given E=0.6V,
=100
,
. The equivalent resistance of the circuit, in ohm is
![](data:image/png;base64,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)
In the circuit given E=0.6V,
=100
,
. The equivalent resistance of the circuit, in ohm is
![](data:image/png;base64,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)
physics-General
physics-
Six equal resistances are connected between points P,
and R as shown in the figure. Then the net resistance will be maximum between
![](data:image/png;base64,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)
Six equal resistances are connected between points P,
and R as shown in the figure. Then the net resistance will be maximum between
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAXoAAAFbCAYAAADbUEUDAAAgAElEQVR4nOzdd1Dc953/8SfLUnaXDkvX0jtL7xJCSJYlS5ZjOXZsx06cOPHk7jLnyeWP+zt/3c3N5Mb/XCbj/OzESRy5RpZcJIwKEkV0RO+9L3Vpu+yy5feHw551LpIsYAF9HjOMZYH4fhaWF9/9lPfbwWq1WhEEQRD2LYm9ByAIgiBsLxH0giAI+5wIekEQhH1OBL0gCMI+J4JeEARhnxNBLwiCsM+JoBcEQdjnRNALgiDscyLoBUEQ9jkR9IIgCPucCHpBAO61EoioGCLsRVJ7D0AQdgMHBwcMBgP19fV0dnYyNTWFXq/H1dWVgIAAEhISyM3NRSaT2XuognDfRNALwj/o9XouXrzIRx99xNjYGEajEScnJ1QqFWfOnEGtVougF/YkEfSC8A+Ojo6sra2RkZHBf/3Xf+Hv78/8/DyffPKJmLIR9jQR9ILwD1qtlvn5eQBiYmIIDQ1lZmaG3t5eJBIJjo6Odh6hIHw3IugFAVheXqazs5OOjg46Ojq4fv06GxsbuLu7c/bsWc6cOYOLi4u9hykI34kIekEAFhYWWFpaIjMzE39/f7y8vDAajbi7u1NQUEB8fDxOTk72HqYgfCcOosOUIEBTUxPd3d14e3sTFhZGbGwsUqm4DxL2B7GPXhCAoaEhWltbcXJyIjg4WIS8sK+IoBcEQCKR4OTkhFwux9HRUeyyEfYVMXUjCMDi4iJra2t4eXkhl8uRSMQ9kLB/iKAXBEHY58RtiyAIwj4ngl4QBGGfE0EvCIKwz4mgFwRB2OdE0AuCIOxzIugFQRD2ORH0giAI+5wIekEQhH1OBL0gCMI+J4JeEARhnxNBLwiCsM+JoBcEQdjnRNALgiDscyLoBUEQ9jkR9IIgCPucCHpBEIR9TgS9IAjCPieCXhAEYZ8TQS8IgrDPiaAXBEHY50TQC4Ig7HMi6AVBEPY5EfSCIAj7nAh64aE0OzvL+++/z/Xr121/Z7Va7TgiQdg+IuiFh45Wq6W5uZm//vWvfPLJJ2i1WgAcHBzsPDJB2B4i6IWHTmVlJe+++y6Tk5O0t7fz+uuv09HRYe9hCcK2EUEvPFSmpqaorq6mu7ublJQUfHx8+Oyzz6ivr8disdh7eIKwLUTQCw+N4eFhLl++TEdHB76+vvzyl7/k8ccfZ3R0lKamJnp6elhfX7f3MAVhy4mgFx4a7e3tXLx4EYVCwcmTJ0lKSiIpKYmsrCxmZma4fPmybb5eEPYTEfTCvmc2m5mZmaGlpYW2tjYSEhI4e/YsMpmM0NBQfvCDH+Dg4EBpaSkTExP2Hq4gbDkR9MK+p9VqeeONN2hra+Pw4cPk5uYSFBQEgL+/P8XFxahUKubn52lqamJ0dBSz2WznUQvC1hFBL+x7vb293LhxA5PJxJkzZ1Cr1Xe8X6lUkpycTEhICA0NDVRWVoqgF/YVqb0HIAjbqa6ujvLycgBSU1N59NFHcXd3/8rH5ebmotfrefPNN9HpdJw9e3anhyoI20bc0Qv71uLiIlevXqWmpobk5GRyc3O/NuQBIiMjyc7Oxtvbm9nZWZqamlhdXd3hEQvC9hBBL+xLq6ur9PT0UFlZyfj4OMeOHSMnJ+cbP14qlRIVFcWhQ4fw9vbm4sWL1NfX7+CIBWH7iKkbYV9qaGjgwoULODs7c/jwYRITE/Hy8vrWf7O57VKv1/POO+8gk8koLCxEKhU/JsLeJu7ohX3FYrEwOztLfX09NTU1xMTE8PjjjxMcHHzXf+vo6EhWVhZJSUnMz8/T1dUlDlEJ+4IIemFf2ZyX7+jowM3NjUOHDlFUVISLi8s9f47ExESeffZZHB0d+fvf/y721gt7ngh6YV/p7e3ls88+Y319nZMnT5KWloZE8sXT/F7LEEdERPCDH/wALy8vysrK6Onp2c4hC8K2E0Ev7Atms5nh4WHblE1wcDCvvPIKYWFhto+51zLEnp6ePPLII4SGhjI0NERLSwv9/f1sbGxs1/AFYVuJoBf2hfX1dS5cuMCtW7coKCjg0KFDeHp6PtDnVKvV5OXl0dnZyeeffy4OUQl7lgh6Yc/bvJsvLy9ndnaWs2fPkp+f/8CfV61Wc+bMGebn56moqGBmZmYLRisIO0/sGxP2vJaWFq5evYpUKiUzM5Ps7GxbLZsHERERgVQqpbS0lLGxMWpra5FIJISGhm7BqAVh54igF/a01dVVqqqquHnzJsnJyRw9evSetlLeq9DQUNLT09HpdFy7dg1XV1cR9MKeI6ZuhD1raWmJxsZGKisr6e/vJzc3l0ceecS2y2YrWCwWjh8/Tk5ODjdu3KC6unrLPrcg7BRxRy/sWSMjI5w/f5719XWOHj1KfHw8jo6OW3oNiURCXFwck5OTeHt709zczOuvv45SqSQoKAi1Wo2bm9uWXlMQtpoIemFP2tjYoLu7m8rKSrKzs3nhhRe2ZUrFwcHBVgcnJSWFqqoq/vM//5PY2FgKCgowm83ExMTg6emJs7Pzlr6aEIStIp6Vwp5jNBq5cuUKDQ0NhIaGkpOTQ0ZGBh4eHtt2TZlMRkREBC4uLoyMjGAwGBgZGeHf/u3feOWVV3jzzTfp7OzctusLwoMQd/TCnjM+Pk5JSQlTU1McPHiQrKws5HL5tl/XxcUFNzc33NzccHZ2xmq1YjAYmJycpKGhAZ1Ox+DgIBEREQQFBeHl5SUKogm7gngWCnvK5OQktbW1lJeXo1Kp+N73vkdMTMy2X9dgMKDRaFAoFGRnZyOTyQgKCuIPf/gDq6urXLp0iT//+c/MzMxw9OhRTp48aTtdKwj2JoJe2FPKy8u5dOkS4eHhFBYWEh4eviPz4iaTiZWVFfz9/QkJCaGxsZGBgQHc3d2JjIzEaDQil8vp7e3F0dGRiooKbt++TVxcHCkpKcTFxaFUKrd9nILwdRx/85vf/MbegxCEe7G4uMgbb7xBVVUVL730Et/73vfw9va+5xo2D2J2dpYrV67g7+9Pfn4+LS0tDA4OEhISgkqlIjs7m6NHj1JQUIDFYqGlpYXz58/T09ODwWBAJpOhUChwdXXF0dERq9W6I+MWBBB39MIu9uUwHBwc5Pz580xPT5OamkpGRgYqlWrHxrK+vs7Y2BheXl5ERkZy8uRJ6uvruXnzJq6urrbiaUFBQRw7doyIiAhOnTrF6OgoExMTvPbaa7i5uVFQUEB+fj5paWliW6awY0TQC7vWZsibzWYaGhr49NNPCQ4O5pFHHiEyMnJHx2I0GpmcnCQiIgKlUsmjjz6Kq6srb731FnV1dZw6dQpvb28kEglhYWGEhYVRXFxMa2srn3/+Of39/YyPj+Pg4IBOp2Nubo7o6GiCgoJwc3O7r3r5gnC/RNALu9ra2hq1tbXcvHmTmZkZTp8+zZkzZ+7aFnCrmUwmZmdnWV5eti3EGgwGzp8/z9jYmG0/f2Bg4B3/Li4ujsDAQM6ePUt/fz/V1dWUl5fz1ltvoVarKS4u5vjx48TFxeHk5LSjj0l4eIigF3a12dlZPv30U4aGhsjOziYzM9Mui5o6nQ6pVIpMJrNt5QwNDSU/P5+2tjY+/vhjvLy8vhL0Li4u+Pv72xZxXVxccHJywtfXF6vVSltbG1NTU0RFRZGQkEBERASBgYEi9IUtJYJe2LWMRiP9/f2Ul5fj7+/Pj370I1JTU3d0DJt75VdWVvD19UWpVOLs7AyAq6srZ86cYXl5mffff5+srCwKCwu/8XPJZDKOHDlCcXExy8vL3Lhxg0uXLvHee+/h5OREfn4+x48fp6CggLCwMBH2wpYRu26EXev69euUlpaytrZGXl4eTzzxBH5+fjs6BqvVyvz8PD09PbS2tpKUlERxcTEAUqkUHx8fZmdn6ezsxN3dHW9vb3x8fL4xpDfXHVxcXPD09CQ4OBi1Wo1KpcJgMNDU1MSNGzcYGBhAp9Ph7u4uFm2FBybu6IVdaWlpiZs3b9Lc3ExeXh7FxcU7HvLwRdBrtVpWV1fx8vLC3d39jvc7OzujVqs5dOgQ4+PjfPjhh/j6+t7TYnFgYCCBgYEcPnyY8fFxLl++zMcff0xHRwfz8/PMz8+zsrJCQkICISEhyGQynJycRD0d4b6JO3ph1xkfH+fmzZtcu3YNgBdeeIHs7GzblMlOslgsDAwM0N/fz8LCAvHx8WRmZt7xMW5ubvj5+VFSUsK1a9c4dOgQ0dHR93UdmUyGSqWiuLiYI0eOIJfL6e7u5vz581RXVzM2NoazszPe3t64urpu5UMUHgLijl7Yddrb2/n0009xcnIiMzOThIQEFAqFXcZitVrR6XQYDAbkcjkymewrH+Pm5kZKSgrh4eF0dnbS2tpKeHg4sbGx93woysnJiYCAAAICAoiOjsbNzQ1HR0ckEgmrq6v09fWh1+vp7u4mPj4elUqFUqm029dF2FtE0Au7ysrKCk1NTVRUVPDTn/6UH/7wh/j6+tp1TOvr62xsbODi4vKNryoUCgUnT57E0dGRlpYWW7XL7/oqJC0tjfT0dDY2Nqirq6O0tJTLly9z/vx5EhMTKSoq4ujRoyQkJIg7fOGuRNALu8bExASffPIJ3d3dqNVqMjIyiIyMtGupAIvFwujoKBqNBpVK9a1tCg8dOoRUKuW///u/qays5OTJk0RFRX2n8W82UHFxcUGtViOVSgkPD2d4eJiZmRkaGxtpa2sjOjqa5ORkUlJSUKlUolqm8LXEs0LYFUwmEz09PXz00Ue4u7vz1FNPkZqaavd6MBaLhbGxMWZnZykoKPjKPvkv8/PzIzc3F7lczvj4OI2Njbi4uHDgwIEHGoOXlxf5+fnk5+ezvLxMaWkpn332GXV1dXR2dtLf38/S0hLp6elERETg6uqKRCLZ8m5bwt4lgl6wO6vVSnt7O7dv38ZgMJCXl8djjz2Gv7+/vYdm20e/sbGBs7PzXfe2y+VyTp06RW1tLRcvXkShUNiCfisKmXl4eFBUVERycjKTk5O0tbXR3t7On/70J9577z2SkpI4dOgQ2dnZW9okXdjbRNALdre0tER5eTnNzc3ExsaSlZVlC/ndUOVxbW2N9fV1FArFXRucODs7c+zYMXQ6He+99x7t7e0UFxejUCge+HFsfi2USiVKpZL4+HhCQ0Nxc3NjfX0djUZDb28vJpOJ6elpEhMTOXDgAN7e3nh4eNj96yjYj9heKdiVwWCgt7eXP/zhD0xOTvKTn/yEvLw82yEhe4eT0WjkvffeY3Z2ljNnzhAREfGt8+COjo74+fmh1+uprq4Gvlio9fHxeeAuWF/3tfD09CQ5OZlTp07Zprrq6+spKSmhoaGB6elp3Nzc8PHxEYXTHmLijl6wq+bmZkpKSrBarajVatRqNQEBAfYelo3BYGBpaQmDwYCPj88973CJjIykqKiIzs5Ozp8/T0RExLbsHpJKpbZfPGq1GolEgre3N729vWg0GsbGxjh37hxVVVXExcURHx9PWFiYOG37kBFBL9jNysoKVVVVXLlyhaysLI4fP77rWu+trq6yvr6Og4MDnp6e9/zv/P39eeKJJxgaGuLmzZs8/fTTxMfHb+NIv9ihk5GRQUZGBgaDgcrKSj7//HPKysqorq4mLCyMY8eOUVBQQFJSEgqFAovFIk7aPgRE0At2sbi4SGVlJe3t7UilUg4dOkRRUdGu2hNuNBrRarW4urri5OR0X7tY3NzcSEpKIjU1laGhIRoaGvD19SUtLW1HtkC6uLiQnp5OUFAQjzzyCL29vfT29nL9+nXKysoIDw8nKyuL3NxcYmNjt308gn2JoBfsYmBggJKSEtbW1sjPzycjI8M2nbAbFmABlpeX0Wg0yGQyXF1d73tMMpmMrKwspqamaGpqwmg0EhkZiY+PzzaN+E4+Pj74+PiQmJiIWq3m1q1bGAwG+vr6aGtrQ6fTsbKywuzsLCqVylZATezF33/Ed1TYURaLhZmZGerq6rhy5QqPP/44v/zlLwkKCrJ9zG4IeYCFhQXGx8dxcnLCx8fnO+1Lz8zMxGw28+qrr9LX18fTTz+9Y0H/ZUqlkhMnTlBcXMzIyAh1dXVUVVXx1ltv4eLiQmJiIidPniQ/P/9bzwoIe5MIemFH6XQ6246QmJgYMjMzd928/Ca9Xs/KygoymczWJvB+ubu7k5CQQGxsLCMjI9TU1CCXy4mKitqGEX8zqVRqe8Xk4+ODTCbD3d2d4OBgxsfH0Wq1lJaW0tPTQ0xMDHFxcXh5eaHVapFIJHh4eKBUKsXOnT1KbK8UdtTIyAi/+93vmJmZ4aWXXuLgwYM73hbwXo2NjdHf38/6+jpBQUFkZmZ+pzUEJycn26uUzs5O5HI5KSkpWz3c++Ln54darebIkSOEhYVhNBptd/m3b9/GYrGwtrZGdXU1vb29aLVaPDw87PJqRHhw4o5e2DFdXV3cuHEDs9lMYmIieXl5hIWF2XtY32hxcZHJyUnc3d0JCQn5znPXLi4unDx5EovFwm9/+1uUSiXFxcUEBATYvUyBVColPj4ed3d3kpOT6evrY3BwkO7ubmpra9Fqteh0OlxdXRkaGuL06dOkpaXZfnHtlvUU4duJoBd2hNFopKqqihs3bhAREcHhw4cJDw/f1SGxvLzMzMwMCQkJKJXK7xzKDg4O+Pr6olarUSgUjI2NUVNTw8GDB3fFmQF3d3fi4+OJj4/n4MGDtmqZGo0Gk8nEysoKMzMzVFVV4eTkhLOzM3FxcUil0l39/RP+lwh6Ydutra3R1dVFWVkZHR0dfP/73+f48eO7fv+2yWTCaDQikUhwdnZ+4FBTKpU8/fTTNDQ08MEHHxAaGrorgv7L3NzcyM3NRa1WMzExwe3bt1lYWMBgMFBfX8/HH3/M9PQ0J0+e5MSJE/YernCPRNAL225wcJDz588zPz9PcnIySUlJX2nJtxutrKwwPz+PXC7H19f3gX8x+fj4cOLECTQaDVevXqWrq4vk5GRkMtmuuTOWSCS4u7vj7u5OQEAAXl5erK2tYTabUSqVNDU1MTg4yI0bNwgODiY2NlYs0O4BIuiFbdfS0sL7779PQUEBP/rRjwgJCbH3kO7J5vZKDw8PDhw48MD7y2UyGUlJSSQlJVFVVUVrayvBwcEUFBTs2k5RERERwBdz8WlpaQwNDfHb3/6Wnp4eLl26hNlsJi0tzc6jFO5GBL2wbUwmEzU1NXR0dBAYGEh2djbZ2dn3VUrAnpaXl5menrZtRdwqycnJFBcXc/v2bYxGI5mZmbs26DdfaWz+NywsjBdeeIG2tjbGxsa4ceMGPT096PV6dDod6+vr6PX6O0o7K5VKMjMzyc/Pt+dDeaiJoBe2zcTEBJ999hljY2McPXqUgoKCXbuV8utsthDc6rIM0dHRnDx5ktraWhoaGhgfH98z2xYlEgkFBQUEBQXxl7/8ha6uLlpaWtDpdLa39fV11tbWGB8fByAhIQFnZ2cR9HYkgl7YFmNjY9y8eZPPP/+cyMhIzp49S0JCgr2HdU9MJhMzMzNYrVYiIiK2/G7bw8ODxMRE0tPTaWlp4fr161gslj01BbKxsYHFYsHDwwMPDw9cXFxsPXWVSiUA77zzDj09PYSEhOypX/D7kQh6YVvU1NRw/fp13NzcUKvVJCUlfedG2TvNaDQyPz8PgK+v77YsNnp7e1NYWIjBYKC0tBSTyURiYuKe+RrJ5XKSk5OBL1odyuVy2yKuxWJhfHwcX19fwsPDOXz48J75Jb9fiaAXttza2hrXrl2jvr6ef/qnf+L48eN7qlCWxWLBYDAA2PqvbjWr1UpRURGrq6v85S9/AeC5557bteUg/q/g4GCeeOIJ4Iv5ewcHB1ubxYqKCi5cuMDU1BTR0dGcOXPmgfvmCg9md29kFvYEq9Vq+/P4+DgffPABk5OThIeHk5OTQ1xc3K7fM/9ler2eyclJAEJCQh64M9TXcXBwsB1UysjIwGKxcO3aNcbGxrb8WlvNarUikUjumK7ZDPnR0VFbGYXU1FSeeeaZPbPLaj/bOz99wq715T3g9fX1vPvuu7i6uvLoo48SHR29a/aI3yu9Xs/Y2BgWi2Xbgn7TgQMH+OEPf4hKpeLSpUt0dnZu27W2yjd9P0dHR/nkk0+ora3FarVy9OhRDh48uKd+ye9X4jsgbAm9Xk9tbS03b95kdHSU9PR0nnjiiT25CGc0Gm2nQV1cXLa1Ho2Pjw9PPvkkMTExNDU10dTUxMzMDGazeduuuR1WVla4desWv//979nY2OCf//mfbXP4gv2JoBe2xMzMDJcvX2ZgYICoqCgyMzOJiIiwe9Gu72Iz6K1WK15eXtu2QLpZEMzHx8dWFri/v5/q6mrW1ta25ZrbQafTUV5ezs2bN9Hr9SQmJnLixAn8/f3tPTThH0TQC1ticHCQS5cuYbVaefnll+1ehvdBbO66cXZ2JiwsbNumbr48BRITE8Nzzz2HVqvlo48+QqvVbss1t4NGo+GNN96gurqan//85zz77LN4e3vbe1jCl4igFx5YdXU1FRUVuLi4oFarycvL23XFuu6HTqdjbGwMBwcHwsPDbQ07tlNYWBjHjx/H09OT/v5+Ojo6WFtbu2Ohe7f48pg6Ojr46KOPWFpaIi4ujuPHj4spm11IBL3wQHQ6HZ9//jk1NTXk5uZy9OhRgoKC9twC7Jdt7rqxWq0EBQUhk8m2/ZqbzUhiY2NxcnKipqaGxsZGLBbLtl/7fn35e3vjxg0uXLhAbGwszzzzDMnJyaLI2S60dzY3C7vO3Nwc9fX1tLa22nZZZGRk2HtYD0wikWC1Wm1vO6mgoICVlRUqKiqwWq0cPnx4R6//bb7cZGRhYYGrV69SX1+PQqHg+PHjHD16dMvLRQhbQ9zRC99ZS0sLJSUlmEwmkpOTSUtLw9fX197DemAbGxs4ODgglUrvaAO4E1JSUjh48CBLS0t0dnba6sXsBl/uKtXS0sLFixfR6/UcPnyYgoKCe5qXN5vNGAwG1tbW0Gq1LCwssLa2titfuewnIuiF+2axWJidnaW8vJzS0lIyMjJ44YUX9kxhrm9itVrZ2NhgYWEBs9mMu7s7vr6+Oxr0Xl5eJCUlkZmZCcDFixfp6urasevfzcbGBrdu3aK0tJTu7m4yMzP513/9V4KCgu76by0WCwsLCwwMDNDU1MTVq1f56KOPaG1tZXV1VYT9NhJTN8J922yc0d/fT2BgIBkZGajV6j25lfLLLBYLWq2W5eVlHB0d7TYN4e/vz6OPPsrVq1f54IMPUCgUu6JWjNlsZmBggAsXLtDb20tmZiYpKSm4uroyMzPD4uIier3eVrL46/5sNBoxmUzAF1typ6enWVxcxNnZmfj4+F1brnmvE0Ev3Leenh7effddZDIZTz/9NCkpKXs+5OGLO/rFxUVWV1eRy+V2W1R0cXHhxIkTDA0N8f/+3/8jKSmJM2fO4OPjY9dF7snJSWpra/noo4/w8/PjlVdewdfXl/Lycubm5piZmWF2dpa5uTnm5uaYnZ1ldnaWmZkZ9Ho9jo6O+Pj4EBAQQHBwMFqtlpGREZydnTlw4ABhYWEi6LeJCHrhnlksFlpbW6mtrWVxcZHU1FROnTq1Zwpx3Y3ZbGZ+fh6DwUBISIjd9oJvtvNTq9UUFhai1Wq5fPkyjz32mF3XQDo7O7l+/TqDg4OMjIzwxhtv4OPjg0QiQSqVIpVKcXR0RCaTERERQUxMjO3vXFxckMlkeHt74+DgwMTEBA0NDYyNjREZGUlOTg4eHh52e2z7nQh64Z6trKxw8+ZNWltbiYiIICcnx9Zqbj+wWq0sLS1hNBrx9/e3eyesxMREXnjhBSoqKrh06RIJCQl2Dfr19XUAkpKSWFpaYmBggIWFBfz8/FAqlXh6etr+7OfnZ3tTKpV33Kmvrq5y7tw5FAoFKSkp5Obm7qvn0W4kgl64JxaLhdHRUa5cucLa2hq//vWvyc3NtfewtpTVasVoNGI2m3F2drZ7aWWVSsVTTz1FW1sbJSUltLW1ER4ejre3t10KhRUWFpKQkIBWq8VsNuPq6mrbmfR1b5vv+3IJCavVyu3bt3n99deRy+X8+7//O9nZ2Tv+WB42IuiFe9LS0sK1a9dYWVkhMjKSzMzMfVfLxGKxMD8/j06nw8fHZ0v7xN6vzT3rvr6+xMfH09jYSHNzs22hdieD/ss1eR50Z1VdXR2lpaUYjUZSU1PJzc21daQSto8IeuGuDAYDJSUlfPjhh2RkZHDixIl9WcvEbDYzMTHB0tKS3c8EfHnRNScnh5WVFcrKygAoKira0VcbW7kA/Pnnn3P16lVOnz7N8ePH9/yW3L1C7KMXvtXy8jLV1dUMDg4il8spKiri8OHD+/IE5OY+7+XlZWQy2a55jImJiRw5cgQnJycGBgZoaWlhdXXV3sO6L4uLi5SWltLb24uHhwdFRUXk5OTYfXrsYSGCXvhWg4ODlJSUYDAYOHToEIcOHcLf339P17L5Jpv76HU6HXK5fNcE/WZ/1piYGMxmMzdu3NhVh6juRXNzMx9++CEbGxsUFBSQkZFh16mxh40IeuFrWa1WFhYWqK2t5bPPPsPf35+XXnppX7eF29xHbzAYCA0N3VXTCs7Ozpw8eZL4+HguXrxIXV2d7X27scLlJpPJxNDQEOXl5ZSXl5OYmMiPf/xj/Pz87D20h4oIeuFrra2tUV5eTnNzM25ubiQlJREfH2/rDbofGY1GZmdn0ev1BAYG7qo7TkdHR7Kzs0lJSWFpaYm+vj40Gs0dhcZ2o4WFBS5fvkx7ezsBAQGkp6fv2YY0e5kIeuFraTQa/va3vzE0NMRPf/pTDh48aO8hbbvV1VVmZ2fR6XS7rgWiRCLB29ublJQUsrOzWVhY4Pz584yOjtp7aN9qeHiYt956i4WFBX7xi1+Qnp5u7yE9lETQC18xPDzMrVu3WFlZISwsjMOHD+/7Ay1ms5nl5WUUCgXe3t7b1j7wQYWFhXH69Gk2NjZ4++23d7BrWDoAACAASURBVPVcfXNzM2VlZUgkEtRqNYcOHSI4ONjew3ooiaAX7mCxWKisrKSsrIzw8HAOHz5MTEzMvp6ygS92F2m1WpRK5a5eh/D19bVtb62traW9vZ2lpaW7Vn60WCyYTCaMRiNGo5GNjY1trRap1+u5fPkylZWV5OXl8eijj6JSqe5pysZqtWKxWLBYLJjNZsxm865eh9gLxN4mwcZgMNDf38/Vq1dpb2/nV7/6FceOHXso5lNXVlZYXFy03dHv5nlvb29v8vLy6O/vp6+vj8uXL/O9733vWzthjY+P09HRQVdXFwaDgeDgYLKzs0lMTNzy8S0sLNDY2GjrkPX000/f1ylqg8HA4uKirV69k5MT4eHh29qofb8TQS/YDAwM8NlnnzE2Noa/vz/p6ekEBgbae1g7YmVlBa1Wi0KhwMvLyy4lBu5HXl4eer3edgApJyeHyMhI4Iv2jqurq6ytrbG0tMTs7CxjY2MMDAzQ2trK+vo6kZGRBAUFbXnQW61Wmpqa+PjjjzEYDCQkJNgW8RcXF9nY2MBkMn3tf41GIzqdjpWVFdbW1lhZWWF6ehpnZ2eSkpJISkqyPUbh/oigF2xqa2v5n//5H/Ly8nj22WcfqvnU1dVVtFotcrkcLy+vXX1HDxAbG4tCoaCkpITGxkba2trw8vJCoVDQ09NDQ0MDzc3N3L59m76+PsLDw4mMjLTVnjGZTJjN5i0dk9lsZnZ2lpKSEt555x1+8pOf8OSTTzI9Pc3g4CBTU1MsLCwwPz/P3Nwc8/PzLCws2P6s0WiAL6an/P398fDwYGlpCYlEQltbG2fPnhVB/x2JoBcwGo20trbS2tqKq6srGRkZFBYW2r16407aDBpPT08CAgJ2/R09QHBwMCkpKbaCcx988AEajYa1tTVbsw+VSsWBAwdQq9V4enry6aefYrFYyM/P3/Jf5Dqdjp6eHjo7O5mfn6exsRF3d3fbXPtmwbjNO3gHBwc8PT1RKBQEBwcTHx+Pq6srvr6+ODo62ipkOjk5UVxczIEDB7Z0vA8TEfQCGo2G9957j/HxcR5//HGKi4v3XcGyu1lYWECj0RAfH09gYOCeCHqz2cyxY8cICQlBp9Px2WefcfXqVeLi4sjPzyc3N9fWBcrZ2ZmpqSneffddLBYLhYWFxMbGbul49Ho94+PjSCQSJBIJdXV1DA8P4+fnh6+vL76+vrbSxZv//+W/UyqVtmYv3d3dXLt2ja6uLnx8fHjxxReJjo7e0vE+TETQP+RmZmaoqamhtrYWlUrF2bNnd0Xbup1mNBpZX1/HyckJFxeXXT91A18cokpOTubAgQPodDpiYmJ47LHH8PPzIyQkBH9/f4KDg3F2dkan09He3o5cLicgIIDw8PBvXbz9Ltzd3cnJycHHx4cnnngCiUSCq6srMpnsrm9yudz2NTeZTJSUlPD222+jVqs5ceLEQzWNuB1E0D/EjEYjtbW1VFZWAhAXF0dOTo7dWujZ0+bin0wmw8PDY08E/f8tHZyUlPSNH1tTU0NZWZntdOp2HAiTyWTExMQQExPznT/H4uIitbW1XL16lcHBQV5++WUee+yxLf+l9LDZ/a9PhW2zuLjIxx9/zK1bt3j88cc5ffr0Q7t9bXp6mpGREXx9fVGpVHti6uZ+tLe3U1NTQ0xMDLm5ubt2y2x3dzevvfYaGxsb/PrXv+bIkSN4enruiV+8u9n+ejYL92xiYoIbN24wNTWFn58fBw8eJCkp6aH9gdrse7rZGWk/Bb1Wq2VwcJD5+Xni4uJITk7elY+vo6ODiooK5ufnSUxM5MknnxTz8ltETN08pBobG3nvvffw8fEhLy+P+Pj4h3LKZlNgYCDh4eFotVomJiaIjIzctXe992NhYYGWlhbm5ubw9PQkJiZm19XxgS/OMZw7d46WlhZyc3M5efIkycnJ9h7WvrH7fq0L28pgMNDZ2UllZSV9fX3ExcVx7NixXfnDv5Pi4+OJi4vj448/5s0332R6etreQ9oSGo2GyspKW/VLe3bN+iYTExNcvnyZ1tZWFAoFZ8+e3Xf9iO1NBP1DRqPRcPnyZXp6elAqlaSnpxMXF7cv7l4fRFxcHBkZGQwPD3PlyhWqq6uZnJy097Ae2NjYGLdu3cLT05Njx47d19kIi8ViO7m6XUwmE5WVlVy6dAlHR0eysrI4cuTIQ3/jsdVE0D9khoaGOH/+PE5OTvzyl78UZWP/ITQ0lMLCQn7+858TERHBa6+9xt///neMRqO9h/adGQwG+vr6aG5uxs/Pj6NHj95Xr1+tVkt/fz9TU1PbMr61tTUaGhq4fPkyzc3NnD59mueff160F9wG4iv6kDCZTHR2dlJbW4terycmJobi4uJd1UXJ3kJDQzl9+jRWq5W//OUv1NbWEhYWRkFBwZ7riGQwGOjq6mJiYgIPDw9CQ0Pv2hpxs4jY3Nwc4+PjTExMMDMzQ2pqKgEBAVu+I6utrY1z584xOTlJcnIyBw8eJDQ0dEuvIXxBBP1DwmAw8P7779PQ0EB+fj6FhYUi5L9GVFQUp0+fxmg0UlZWxmuvvYZCoeDYsWP2Htp9WV1dpby8nPn5eU6cOEFUVNS3frzBYKClpYXq6mrq6uro6OhgcnISg8HASy+9xLFjx7Ys6M1mM/Pz81y7do0//OEPfP/73+dXv/rVvu95YE8i6B8SOp2OhoYGRkZGePHFF0lNTbX3kHat8PBwTp06hU6no7y8nE8//ZT19XVOnz5t+5hva+HX29vLwMAACwsLqNVqUlJSdmroNqurq1y5cgWr1crLL79MXFzcHe9fX19nZGSE/v5++vv7mZycZHl5GZPJhJ+fH/n5+UxOTlJfX4/Vat3SHVnz8/O8//77th02ubm5+Pv7Mz8/j8FgsFWwdHBwQK1W4+bmtmXXfliJoN8jrFYrJpMJg8GA1WrF0dERR0dHpFLpPS2kGo1GlpaWsFqtREREoFQqd2DUe5NUKiUpKYm1tTU2NjaoqqpCq9WiVqtRqVQAd4T8ZqEuk8nE9PQ0lZWVVFRU0N3dzc9+9jO7BL1Go6Grq4vIyEgyMzPx9/fHZDJhtVrRarWMjIzQ0tJCXV2d7fFFR0eTk5NDVlYW7u7ujI6OIpVKt7xcwvT0NB9++CFLS0ucPXuW4OBgBgcH0Wq1LC8vs7a2xuzsLFKpFA8PD5KSkmyNRx7Wcx4PSgT9HmC1WllaWqKuro4///nP6PV64uPjSU1NJS0t7St3a19HoVCQlpbG8PAwfX19+Pv7P9BR9YdBWloacrkcnU5Hb28vv/vd73j00Ue/Mo3T19fHrVu3uHHjBoODgwQHBzM9PU1HRwdzc3M7Omar1UpPTw+tra1ERUVRUFBAWFgYCwsLVFVV0dTURHd3NxMTE3h6ehIeHs4LL7xAaGgoKpWKsLAwXF1dbQ29ExIStvQg3fr6OlNTU4yMjDA8PAxAVVUV7u7utgNrLi4uODo6IpfLKS0tZXR0lNTUVJRK5b7vdLZdRNDvAZvTBJOTk3z44YfAF3eR6+vrtoWzwMBA3Nzc8Pb2xs3N7SsnH11dXcnKykIikdDc3CyC/h44OzuTnJzM8ePHsVqt1NfXExAQQFFRETqdjqGhIdv0R29vL0NDQywuLuLj44NUKsXLy8suNVoaGxupqqrC09MTq9VKWVkZU1NTtLa20t/fz9zcHBKJhODgYDIyMsjJySE2NtYWolarlc7OTtra2vjxj3+MWq3+1qmq+2E2m3Fzc+PgwYMEBQXh4+NjK3zm5uZme/Pw8MDZ2ZnJyUlqa2tZX18nNTVV1KP/jkTQ7wESiQRPT08CAwNxd3cnODiYgoICBgYGOHfuHBqNhrCwMIqLizl06BApKSlfWWh1dHQkJSXF1hhicx5auLvHHnsMX19fJiYm2NjYQKPRUFZWxoULF6iursbT05Pi4mJeffVVAgICqK6uZmBggMjIyB3/ZWq1Wrl9+zbXr18nLi6OK1eu8Pvf/57AwECSkpLIzs4mNTWV5ORk3N3dcXR0xNnZ+Y475enpadra2hgfH0etVm9pGQK5XE5mZiavvfYaJpMJiUSCg4MDDg4Otj9vVr1cW1vj0qVL1NXVcf78efR6vQj670gE/R7i7+9PSkoKcrkcmUxGZmYmkZGR9PT0sL6+bms+UVpaSmRkJBEREahUKiIiInByciI7O5uJiQn++te/MjIywurqqljo+hZfvotNTEzkmWeeQSqVMjw8zOjoKE5OThw9epTw8HAyMzM5cuQIVquVd955h/n5eZ544oktr/l+L6RSqa0KZ2BgIKGhoURERJCUlERsbCwxMTHfuONqdnaW1tZWHB0diYiI2PK+BA4ODri6ut51qyd88Sq0oKCAlZUV3n77bRobGzl8+DBBQUEP/QG/+yWCfg9RKpUcPXqUkZERpqameOGFF0hOTmZqaorm5mYqKyu5du0aQ0NDqFQqUlJSyM/PZ2Njw9YbNCAgAKlUytzcHP39/cTGxiKXy+38yHanL09VuLm58cwzzzA+Ps7t27dxc3Pj+PHjnDp16o6+usPDw9TV1eHi4kJ6ejrh4eE7PubY2FgOHjxIcHAwaWlpFBQU4O/vf0/hODw8THV1NUFBQdtSs/5+RUVFcfjwYT766CMGBweprKyksLCQkJAQu45rr3H8zW9+8xt7D0K4N1KpFIVCQVdXF9euXSMnJ4fo6Gjc3d3x8vJCpVKRk5NDXl4eQUFB6PV6Ojo6uHLlCiUlJczOzqLRaNDpdCgUCiwWC4GBgfd1WvJh9OU7excXF9zd3QkLCyM2NvaOAz4zMzPU1dVx+/ZtoqKiePrpp3f8FZODgwNeXl4kJibaFurvp2NWdXU1f//734mMjKSoqIioqCi7l66WSCSYTCYmJiZoaGggMTGRsLAw4Nu3uQr/S9zR7yEKhYKUlBSuXLnCxMQEvb29HDt2DCcnJ5RK5R1bJjfrj9fV1dHW1mab3vHz80Mikdh6emZmZoqDKnfx5SBxcXH5xt6lzc3N1NTUoFKpyMjIwMPDY6eGCPxv6EVERHzn7+n4+DgjIyM89thjqNXqe94/b7Va0ev1rK6uAl98neRy+ZbsknF3d+fkyZOMjY3x4Ycf0tnZSW5u7p7pBLYbiKDfYxQKBfHx8aSnpzM+Ps7NmzfJy8v7yp1jTEwMoaGhnDp1Co1Gw+DgIN3d3TQ0NFBTU4PRaCQ5OZmVlRU7PZL9p6Ojg4aGBoqLi8nMzNzxEHqQ662vrzM8PMzk5CQymYywsLA7pqTuZrNVYUVFBY6OjsTExJCVlXVfn+ObuLi42Pb4d3d309rayvnz53n88cdxd3d/4M//MBBBvwdFR0dTUFBAf38/169fJzU11Rb0m3d1Li4uuLi44OXlRXBwMCqVCqVSiaenJ0FBQVgsFsLCwggKCrLzo9kfNpt7zM3N2Zp77KUFw5WVFRobG1lZWSEhIeGeerTOzMwwOTnJ6Ogog4ODDA0NMTk5iVwux2AwEBsbuyVBvyktLQ2NRkNJSQkXLlxArVaLmvX3SAT9HhQWFkZhYSGNjY3U1NSwvLxsm7b5prs6X19fCgsLKSwsvOOUoXjp++C0Wi3t7e3Mzc3h5uZGdHT0fZUD3g20Wq3tlV5hYeFdd9vMzc3R0NBAeXk59fX1DA4OYrFYCA4OJiAgAK1Wu+WVP6OionjiiScoKSmhpqaG9vZ2AgMD8fX1Fc/juxBBv8O2YvHI19eX5ORklEols7OzdHZ24uvre9fempvv+78fIxa0HoxGo6G6uhpnZ2eysrLuu1jc+vo68/PzrK6uEhAQYJda7DMzM1y5coWUlBQKCwu/dh1icHCQlpYWWltbGR8fZ21tDWdnZ9LS0nj++eeZnJzk/fffJzg4mPT09G1pchIQEMDhw4cxm82UlZXh4uLC2bNnt/w6+40I+h22GahLS0ssLy+zvr6OVCrF3d0dV1dXnJ2d72mXQ0BAALGxsWg0Gpqbm/H29ubgwYMPNCbhuxkdHaWyshKVSsWRI0fuOm9ssVgwGAwYjUa0Wi2jo6MMDQ2xtLREUVHRjga91WrFbDYzMTHB1NQUeXl5JCcnI5VKMRqN6PV6VlZW0Gg0tLe309DQQF1dHTqdDpVKRXZ2NocPH+bo0aM0NTXx/vvv4+PjQ05OzraUdnZycuL48eM4Ojpy8eJFW0OVnV743mtE0NuB1Wrl3Xff5YMPPkCj0aBUKsnJySE9PZ3U1FTi4+Pv6fNkZmaysrJCc3MzHh4eHDp0aJtHLnydvr4+bty4wb/8y79w5MiRu07bbDbcqK6upqWlhfHxccbHx5FIJHh5ee1oETSTyURTUxNDQ0Pk5uaSn5+PVCrFYrHQ1tZGdXU1ZWVlNDQ0EBISglqt5rnnniMmJsZWHM/JyYmxsTFaWlpsu5LCwsK2rQF5amoqZrOZK1euMDAwwM2bN8nJySEgIGBbrrcfiKC3k7m5OYaGhtBqtVgsFsbHxzGZTAwPD9PU1GSrA+Lv74+Pj8/XbnNLSUlhaWmJsrIyurq6WFhYEDXmd5DRaGR8fJypqSkUCgUhISFfeybBYrGg0WjQaDTMzMzYCnpNTk6i0+mQSqWYTCZWVlbQ6/U7+hjMZjO3b9+mt7eXyMhIzGYzFRUVDA8P09/fz/T0NHq9nsDAQBITE8nLyyMrK4uYmJg7TrdWV1fT09Nj29q5XSG/KSIigtzcXNra2rhw4QIKhUIE/bcQQW8ncXFxnDhxAoPBgI+PD4GBgXR0dHD9+nXm5uYICAjg0KFD5Obmkp6eTmRk5Ff2JAcEBJCcnIxEImFiYoKuri6Sk5P33ELgXrW6usrNmzdZXFzkxIkTX1tF1Gq1MjU1RVVVFWVlZZSXl2M0GgkLC+PQoUM88sgjWK1Wmpub6ejo2PFdUCaTiY6ODrq7u8nNzbVtXRwdHUUul1NUVMRPf/pTsrOz8fPzw9XV1VaTZtPa2hqNjY2MjY2RlZW1I2Uf5HI5Tz/9NKurq/z5z38mISGBo0ePbvt19yoR9Haw2VBhcXGRd955BwcHB55//nkyMzPJzMxkbGyMpaUl9Ho9paWlXL16FX9/f1QqFVFRUURHRxMeHo6DgwMHDhywNYnYbAItgn5nGAwGbty4wfr6OmfOnCEtLQ34IvgGBgZse76Hh4dtJXgLCwsJDAwkOjqa1NRUTCYTJSUlGI1GcnJydvxov8ViYXJyku7ubry8vPDz87OVUAgNDSUqKoqYmJhvPCQGX2zNrK2tZWFhgZdffvmepx4fhIuLC3FxcaSlpVFeXs7AwAClpaUcPHgQhUKx7dffa0TQ20lsbCyzs7OMjY3h6upKREQE3t7eHDlyhMXFRbq7u6mpqeHWrVt0dnZitVptZWVnZ2dZXl4mLCwMnU5HZmYmBoOBqqoqYmNjxd7iHTI/P09XVxdKpZLo6GgcHR2ZnZ2lu7ub27dv09DQQG1tLXNzcxQWFtqqi8bHx9vCqK+vj5qaGuRyOSdPntzxoJdIJCiVSvz8/LBarbZXGnl5efe0wGk2m5mcnGRsbAxnZ2fi4+N37EZDKpWSnp7OmTNn6Ojo4OLFi4SFhd1Tf4aHjQh6O3FwcLAVnbJYLFRWVpKXl4dSqcTb25vk5GRCQkJ45JFHmJ+fZ2RkhNHRUSYmJnjrrbeYn58nMjKSxMREoqOjbeVpDx48yNramrir2UZWq5WJiQk6Ojrw8vLC09OT4eFhrl27RktLC/Pz8ygUCqKjo3n11VcJDw8nKCgIpVKJj4/PHd+bsbEx+vr6yMzMJDc3d1u2JH4bmUzGq6++yosvvohMJsPT0xNfX9973sXS399Pc3MzKpWK0NDQHX/excTE8Oyzz/If//Ef3Lx5k6KiIgICAvDw8Nj2dYK9RAS9HXl7e5Ofn09nZyfXrl3D09PTdvDJ3d39jm16CwsLdHd309zczMbGBjqdjoWFBQYHB3F2dmZ0dNT2Njs7+5Ua48LWsVqt9Pb20tjYyMLCgm2HytjYGPPz87ZDU3l5eeTl5X3ttIfFYmFoaIi+vj5cXV0JCgra8ZDfbEm5Wdn0u+jt7aW+vt5Wqnkre8veCycnJ2JiYoiLi6Ojo4O6ujp8fHzEfP3/IYLejjbrbc/NzXH16lXS09M5fPjw136sl5cXWVlZpKam8uMf/5i1tTXa2tq4ffs2bW1ttLe3A1/UHJmfn8ff318E/TaamJigra2Njo4OFAoFnp6eZGVl8fzzz5OcnGzbQ/5NZyKsVistLS309vaSmZlpl76yW3F+or+/n6amJp566inS09ORSu0TKUeOHMFkMnH16lWsVitFRUXijv5LRNDbkaurK8nJybS0tLC0tMTIyAharfZrT7hKJJI7DlO5ubnh7OyMp6cnBw4cICkpiZWVFTIyMvD397fbD9zDwMHBgcTERJ588kmio6NxdXVFrVYTFxdHVFTUPR0UcnR0pKmpiba2Nk6fPr0n11UWFxcZHx9neXmZiIgI4uLi7Pa8S05Oxmg0UllZydDQEA0NDajVatFY5x9EGtiRg4MDbm5utoMnGo2GpqYmMjMz72lBy9vbm+zsbLKzs3dgtMImBwcH2w6pubk5nJyc7nsBUq/X09vby8TEBPHx8XbpRPUglpaW6OjoYGFhwdYLYXNfvcViwWKx3NEicLu5ubmRkpJCamoqvb29fPLJJ5jNZnGI8B/Ea5sHtFkg7EEEBQVRUFCAXq+noqKCpaWlLRiZsBP8/PzuO+SXl5dtay0hISGEhYU9UJevrXgO3q+5uTlqa2uRSCTk5ubeUQRtdnaWGzduUFtby/DwMBsbGzsyJjc3N5588kkiIyM5d+4cZWVlmEymHbn2bieC/gFtTrHMzc3R3t5OZWUlNTU1tlOv9/JECwwM5OjRo1itVqqrq9FoNNs9bMGORkdHqa2tRSaTkZycfE+LsFarlaWlJcbHx+nq6qKpqck25WePWkUajYaqqipkMhlFRUU4ODjYNgxcv36dmzdvUlNTQ19f344FvVQqJTs7G7VajU6ns51j2OnTxruRmLrZIp9//jlvvvkmfX19eHt7c+zYMQ4fPnxPh2CUSiVFRUVcuHDBdsAmLS0NqVQqCo7tQ8PDw9TW1hIQEGDrlHQ3y8vL1NbWcuvWLRoaGujs7EShUPDaa6/xyCOP7MCo7zQ9PU1FRQU/+9nPKCwspKenh7/97W9cvnwZo9FIcHAwvr6+uLi4kJeXt2Pj2txb/+KLLzI5Ock777zDL37xC6Kjo3dsDLuRCPotYjAYWFtbsx0Pn5ubsxWDioyMJDIyEpVKRUhIyB01QjZtdvUJCAhgaGiIrq4uEhMTxaLqPjQwMEBLSws/+clPyMvL+9q958vLy0xOTjI+Pk5/fz9jY2PodDqWl5dxcHBgbW2Nubk51tbWdnTsZrOZ2dlZhoeHgS+6an3wwQeMjY0xPj6OUqkkPDycyMhIBgYGGBoaora2FrVavWPlHTb79b799tvU1NTYTvk+zK0HRXPwLTI/P4/JZEKlUtmOjPf09PDpp5/S0dHB9PQ0VqsVhUKBUqnEwcHhK3Xgl5eXMZlMzM7OYrFYSE5OFlsk9xGLxcLc3ByffvoplZWVPPfccxQWFtoWKzefDzqdjra2NiorK7l06RLnzp3j6tWryOVyIiIiiI+Px9XVFYVCwWOPPUZ4ePiOPQa9Xk9tbS2tra0sLS0xODhITU0Ni4uLREdH8/zzz/Piiy9SWFjIzMwMvb29DAwM4OTkREJCwo6M0dnZmQMHDtDd3U1tbS0eHh54eHgQEBCwp7p+bSVxu7hFIiMjSUtL491338XDw4MXX3yRkydP0t7ezujoKFNTU7a6NUqlkqSkJNLT00lPT7eF+WbZ4d/97nfo9Xp+9KMf2flRCVtpaWmJhoYGjEYjubm5d0wnDAwM0NbWZpu6W11dxdnZGR8fH1566SUCAgJISEhgbW2NiooK5HI5ubm521Lz/W7MZjMWiwWZTGY72xEXF0d0dDRhYWG2evp5eXnMzc3xpz/9CVdXV5566qkdHWdWVhbj4+M0NjZiMpnIyMjY0evvJiLot8iBAwfQarVotVrW19dRqVT4+/uTnZ1NT08PFRUVVFRU0NfXR3d3NzMzM6ysrNhq1nh4eODu7k5MTAzr6+uMjY2h0Wh29G5N2F6Li4tUVVWh1+tJS0vDYDAwMTHB0NAQPT09dHR00NzcjEajISAggMTERHJzczl48KDtedDa2kp3dzdKpfKeWv5tNUdHR5RKJTExMZjNZtLS0iguLv7K89RqtRIfH8/IyAirq6sMDQ0xNjZGaGjojk2fJCcns76+TlNTE7dv32ZkZISYmJgdufZuI6ZutoijoyOOjo5UVVWh0+mIjIy0lXX19PQkKiqKwsJC8vPziYmJYWNjg/r6et58801KS0tZWFjAzc0NhULB6OgoUqkUhUKBQqH42hrnwt4zNDTEH//4RwwGA1FRUbS0tHDu3Dn++Mc/0t7ejq+vLwUFBTz77LM8//zznDhxgoSEBJRKpW16p7Kyktdff53ExEReeeWVHS+bIJFI8PHxISYmhtzcXNRqNX5+fl+ZEtkMc7PZzMjICI6OjlitVry8vHbs+SyXy/Hw8GBwcBCtVoter0cmk+14KejdQNzRbyF3d3fi4uJsx9u9vb3JycnByckJHx8ffHx8OHDgAKGhoSiVShQKBVarFYPBwOjoKJcvX8bFxYXFxUVWVla4evUqXl5eREZG2vuhCVtAr9czODiIq6srKpUKvV6PRCIhISEBlUpFeno6KSkpxMTEfOVE52ZTmuHhYTw8PAgJCbFLOWqJRGK7AbkX/7+9+wyK+74TP/7exi6dpZel9w4C0UE0S5YUy5LtxHLiOLbHmbmb5O7BPbnJg7vJg0symctMbi73z419yaVYE5cotmQVJARCSEIWCISooiNA9N63sLv/Bw57li1FQkJaWL6vGYb22/19Fvb32e9+T7/HSQAAIABJREFUy+fr5eVFSUkJ165d4+zZswQHBz/T57OXl5el5n9ZWRkymYz4+PhnXpPH2kSi30QSiYTU1FS0Wi3Nzc0EBgaSkZHxteM0Gg2BgYGUlpaysLBAW1sbly9fpqqqio6ODtRqNTKZjOHh4fveXtieZDIZdnZ2zMzMMDAwwO7du8nOziYzMxM3NzeMRqNlNelX6fV6rl+/zuDgIHv27CExMdEKj2DjnJ2d2bNnD7dv3+azzz5j//79zzyG9evsj3/8I2q1mgMHDhAaGrqjkr3outlEEokEDw8PxsfH+dOf/oS7uzvPPffc1y7c9e9lMhkODg64ubnh4eFBZGQk8fHx+Pr64uLigru7O+np6U9UXVDYOuRyOQEBAeTn55Ofn096ejoxMTGW7pf1qbn3S/QGg4H//d//pbe3l+LiYtLS0iyVTrcymUyGm5sbAwMDtLW14evri5+fH87Ozs9k6rBEIkEmk2E0GhkbG0Ov1zMzM4O/v/+2+PttFtGi30TrA1VqtZrV1VVWVlYwGo0PfUKvV6ZMT08HoLa2lp6eHtbW1nb8Qg9bYTab8fX15Y033nis28/OztLV1cXKygrJycnbapBeIpEQExNDZmYmIyMjnD9/ntdee+2ZDiQHBARw+PBhrly5wu3bt5menn5m594KRKLfRGazmRs3bjA7O8s777xDTk7OY7Va4uPjCQsLs8y7F7a/J5lpMjExwa1btwAICgoiJCQEe3v7zQrtmQgNDeW5557j/fff59y5cxw6dOiZnl+pVBIcHIxUKsVgMPzNrRFtkah1s4nGxsY4e/YsbW1tFBcXW1roG+Xk5ISXlxfe3t4i0Qt0d3dTX1+Ph4cH8fHxlnnq24mPjw9paWk4OTkxNjZGf38/JpPpmZ1fq9XS39+PTqcjMDBwx5UvFol+k8zMzHDr1i1OnjxJfX09Go0GHx8fa4cl2ICOjg4aGhqIiIggIyNjWy7jl8vlBAcHk5CQgLe3Nzdu3ODGjRvPLNmPj49z/PhxqqurmZ2d3XFVLUWi3yQtLS2Ul5fj6upKamqqVVYsCrZndXWVzs5Ouru7iYqKIiMjY9vOFpHJZOzatYvExERu3LjB9evXn3qterPZjMFgoK+vj46ODvR6PSEhIY+8J66tEH30m6SxsZHa2lpyc3PZu3fvjntrKGy+9e6GkZERjEYjERERuLm5WZKX0WhkbW3NsverVCpFKpWiUCi27DZ6SUlJzM3NUV1djaur61PfyN5oNNLT00NnZycGgwEfHx8iIyPvW1jQlolE/4TWL8b+/n7MZjO5ubkUFBRs21aXsHWMjY1Zar6XlJQQHh4OwN27d2lra6O5uZm6ujqWl5eJi4uzTF0sLi7G39/fytHfn7+/P/Hx8Xh6ejI7O0t9fT1JSUlPbbWsyWSioaGB3t5ekpOTiY+P33FJHkSif2IjIyNUVFSwsLBAYmLiPavuvlqdUhA2YmxsjEuXLgEQGxtLS0sL3d3d3L59mzt37jA4OMjg4CCAZYl/f38/Wq2WpKQkfH198fT0fKLdq54Gf39/kpKSGBgYoLq6GicnJ9LS0p7KuZaXl2lsbGRkZITS0lKSk5Ofynm2OpHon1B3dzfHjx8nLi6Ol19++Z5FGCLJC09iYmKCy5cvExQUhJubGz/72c8YHx9HLpcTHh5Oamoqr776KsHBwahUKhoaGjhz5gy//OUvsbOz4+WXX+bgwYOkpqZa+6HcQ6VSUVJSwvnz56msrCQyMvKpJfqJiQna2trQarXs2bOHpKSkp3KerU4k+se0trZGX1+fZTs3jUbzyJt6C8KjMJlMrK2tsbq6islkQqPREBoair+/P6GhoURGRhITE2MZ+JdKpZhMJtRqNYODg9y+fZv5+Xlu3LhBbGwskZGR+Pr6WvlRfZHo09PT6enp4dy5c/T29jI7O4urq+umji3cvXuX1tZW7O3tLTWmdmrjSyT6x7S0tERVVRVtbW2WzSBElUlhM6nVapKTk7Gzs8PX15eMjAwSEhIeuNgnPDyc8PBwSktLaWxs5JNPPqG6uppz586Rn5/PgQMHyMzMxMvLy6rdijKZzFIB093dnbt371JXV2ep+bNZOjo6qKurIzw8nKSkpB3ZN79O1Lp5THfv3uW9995jamqKw4cPk5WVhbu7u7XDEmyIo6MjMTEx5OXlsWvXLqKiovD29n5oq9fBwQG1Wk1ERATh4eG4ubkxMjJCbW0tjY2NjI2N4ezsjFqttmoLV6/Xs7S0xPj4OOPj4yQnJ29qoj916hRnz54lJyeHoqKie8o97zSiRf8YJicnaWtrY3R0FD8/P/Lz87dV7RFh6zObzZZN4zdqvbieh4cHCQkJREdHU1ZWxueff05bW5tlc5zk5GTCw8NRq9VWae36+vpSWlrK7373O+rr67l79+6mXEfrBcx6e3uZmppCo9EQGRm5Y7ttQLToH0tFRQXl5eU4OTmRl5fHnj17dvTbQmHzbVZSWu8mSU9PJy8vDy8vL+7evcsnn3xCbW0tY2NjuLm54e3t/cz3U13fBOTGjRvcunXLMobg4ODwRC3vkZERysvLaW5uxsnJiYMHD+642jZfJRL9Bs3NzfHxxx9TV1dHcXExRUVFaDQaa4clCA8kl8tRqVR4enri4uKCUqlEoVAgk8mYn5+nq6uLnp4e9Ho9Dg4Oz7S+kkwmY3BwkLGxMUwmE0qlkoiIiCdK9L29vRw7dgyDwUBmZibZ2dk7fvxMdN1swNzcHC0tLbS3t7O0tGRZzi0I20VYWBhhYWG89tprXL9+nU8//ZQPPviAlZUVDh06xIsvvkhxcTHOzs7PLKbk5GRmZ2e5cuUKdnZ2FBUVPdHK8omJCRoaGsjOzqa0tHRH1Z1/EJHoH+LLsxMGBgb49NNPsbOz47nnniM4ONjK0QnC44uPj0cqlRIWFkZ3dzfT09O8//77HD9+nKysLPLz85/JvPOEhASMRiNnzpyhpaWFoaEhoqOjN9yqNxqNzM3NWfaoDQkJIT4+XlSARST6h/pyX+nt27f5/PPPyc7O5tChQ6JwmbCtOTs7k5GRQUZGBn19fZw8eZIzZ85w7do15ufnMZlMyGQyNBoNCoUClUr1VGatKJVKy05b4+Pjlr71jfar6/V66uvr6e/vJzw8nOjoaJHk/0r00T+ClZUVrl+/zsWLF+nv72f//v0cOnRIDMAKNsPJyYmIiAjS0tJITk5maWmJ2tpaPvvsM9ra2rC3t8fHx+ep1XAyGo3Mzs6i0+kYHh7G3d19w7urra6u8sc//pGBgQHy8vLIyMjYEgvEtgLRon8EMzMznDx5ks7OTlJSUoiLi7PMUBD1bARboFAo8PHxwcfHh7CwMFxcXFCpVLS2ttLf38/58+cZGRkhNjaWwMBAPD09sbOz29TzFxYWotVqOX78OKGhoZSWlm5oh7bR0VGam5uRSCTs2rVLdK1+iUj0j2BkZIQzZ87g6enJD3/4Q6Kioiy/E0lesDWenp689NJLFBcX09raSmVlJRUVFVy8eJHg4GBeeukl8vLyCAsL27RzKhQKEhISGBwcZHh4mNu3bzMwMEBgYOAjvaCMj4/T1tbG+Pg4gYGBhIaGbsuduJ4W0XXzED09PVy/fp2uri5SU1P51re+9Uw3NRaEZ2298aJSqXB1dcXLywuNRoOrqys6nY62tjaampoYGRlBKpXi7u7+WHsj38/y8jJdXV3IZDLkcjn+/v6PNAOotraWS5cusbS0RHJyMs8995woFf4lItH/DWtra5w9e5YbN24QGhpKUVHRY+8DKwjbkUqlws/Pj5SUFEJCQjCZTDQ2NtLe3s7Y2Bhra2vY2dlhZ2eHUqlEKpU+0btco9GIVCplbGyM7u5uYmJiCAgIeOjtTp48yeXLl0lMTKSgoICYmJhnvgBsK9uZhR8e0cLCAleuXKGlpYWioqLHWo4uCLYiMDCQb3zjG/ziF7/gX/7lX4iNjeX8+fP84Ac/4N/+7d8oKytjdXX1ntuYzeYNncPHx4fnn38epVLJxYsX6e7ufuhtFhYW6OnpYWRkhIyMDPLy8jbtHYatEH+NB5icnKS+vp6xsTGcnJyIiYkRfX7CjqZUKvH398ff35/IyEjs7e1ZXFyksbGR/v5+Ll26xPT0NFFRUYSEhODr67vhVrVcLkej0aDRaJDL5fT399PZ2Ul4ePh9k/fi4iKdnZ0sLy/j7e1NVFSUuE7vQ3TdPEBNTQ3vv/8+dnZ25OXlkZmZKebkCsJfyeVyQkJCKCwspKioCLPZTF1dHb/97W9pbm5GoVAQFBT02Ctsl5aWMBqNzM/Po9VqiY2NvW+fe39/PxUVFWi1WuLj48nJyRF7QtyHaNF/hdlsZm5ujoaGBhoaGnj55ZcpKSnZcbvGC8KDrE8pViqVKJVK3NzcMJlMODo64u3tzdLSEjdu3GBoaIjw8HASExOJiYnZUAJOSEhgcXGRd999l7GxMQ4ePHjfF43BwUGqqqqIj4+noKBgx9e0eRCR6L9ifn6e2tpabt++jdlsJj4+npSUFGuHJQhbxv0GW5OSkkhMTOTQoUNUVVVx5swZPvnkE1QqFYcPH8ZgMJCeno5KpcJkMj10hW1gYCBra2v84he/oLe3l6GhIQICAu653foub21tbWRnZ7Nr164nqpFjy0Si/4rh4WE++ugjlpaWOHr06I7dY1IQNkoikeDj40NxcTGhoaG0trZy+/ZtWlpaaGlpISAggLy8PLKzswkKCnro/Xl6epKbm0tbWxt1dXU4OjpaNvdeWlqirq6Ozs5Oy/RP8a77wUSi/yuz2czKygrd3d20traSkJDAiy++SGhoqLVDE4RtYz3Z+/j4EBcXx82bNzlz5gytra00NTVhMBhYWloiJSWFwMBAywrc+7G3t6eoqAi5XE5NTQ1OTk6WRL+8vExVVRVDQ0OkpqaK6/QhRKL/K6PRyM2bN2lqasLV1ZX4+HgSExNRKBTWDk0QtiUnJyeysrJISUmhp6eH2tpaKioq+NWvfkVgYCB5eXl84xvfICoq6r7XmVQqJScnh6mpKY4dO4abmxtvvvkmcrkcrVbLtWvXkEqlvPbaaxuui7PTiET/V3q9nurqapqamkhPTyc9PV0keUF4AlKpFJVKhUqlIiUlBXt7e+zt7WlubmZycpKmpiaGh4ct42BfHbCVSqV4enoSERGBt7e3ZSpnVFQUd+/eZX5+nvDwcFJTU0XxsocQ0yv/anR0lPfee4/x8XHeeecd0tPTxRJqQdgkUqkUb29vUlNTycvLw8HBge7ubj777DPLPHg3Nzfc3NxQKBT3DLqaTCZmZmYwmUxMTk4yOzvL6Ogo/f39JCcnc/jw4R276fejEoke6O7uprKykp6eHkJDQzly5Ag+Pj7WDksQbJKdnR1ubm6EhoaSnJyMu7s7w8PDfPbZZ1RXV6PValGr1ZbWvb29PQqFgoGBASoqKhgYGECr1RIYGEh2djYxMTFWfkRb347vujGbzdTX11NZWUlgYCA5OTmiaJkgPGW+vr74+vqSm5vLzZs3OXnypGXTEAcHBwDS09Px9vZGpVKxe/dubt26RX9/P/39/RgMBr73ve+RkpIiSoU/gh2d6HU6HUNDQ1y7do1bt27xz//8zxw4cEBsKCIIz1B8fLylxk1LSwu1tbX8+te/Zm1tjf379/PCCy+we/duUlJSiIyMpKWlhZmZGWJiYja8C9VOtaMT/fT0NJWVlYyMjBAUFER0dLRYPi0Iz5hSqSQgIMDyoVKpkMlkdHd309HRgVQqZXx8nPb2dqRSKXq9Hp1Oh7u7u+U+RKv+b9vRiX5oaIhTp05hb2/P4cOH0Wg01g5JEHa0oKAgvvvd77J3715aW1v57LPPqKys5NSpUxgMBtbW1pBIJMhkMnQ6neV2Isn/bTsy0ZvNZubn5+nq6mJ8fJzc3FwKCgrw8vKydmiCsONJJBJ8fX2xs7OzrIZta2vj9u3b9Pf34+npiYuLC62trbi6uuLp6SkS/UPsyFk3q6urfP755zQ0NLC0tERBQQF79+7d1D0wBUF4Mvb29gQGBpKcnIyPjw9yuRyDwYCPjw/e3t4sLCygUCiIiIgQif4hdmSLfnFxkRMnTjAyMsKBAwfIzs4W83AFYYuSyWTExMTg7+/Pvn37GBoaoqmpibKyMpRKJfv377d2iFvejstuCwsLtLW10dnZCUBOTo5YPi0IW5yDgwO+vr7ExcWxZ88e4uPjWVpaoq+vj5GREWuHt+XtuER/69YtKisrUSgUxMTEEBYWJlbACsI2olKpiImJISQkhJWVFa5evcrQ0JC1w9rSdlSiNxgM1NXVUVNTQ1xcHAUFBaJ+tSBsQ+7u7uTk5ODk5MSFCxfo7++3dkhb2o5J9Hq9njt37nD79m0mJyfJyMggNzfX2mEJgvAY7O3tKSwsRKPRUF9fT29vr7VD2tJ2TKIfHBzkxIkT6HQ68vLyiIuLw9XVVQzCCsI2pFKpSEpKIiIigrW1NXp7e+np6blnbr3wf3ZMluvo6KCiogInJyeef/75R9rhRhCErUsmkxEWFkZkZCRjY2NcvXqVxcVFa4e1Jdl8ojcYDAwMDNDU1ERnZycajYaSkhLc3NysHZogCE8oMDCQ/fv3s7y8zIULF5idnbV2SFuSzSd6nU5HRUUF3d3dJCYmEh8fL/aWFAQb4e/vT35+Pg4ODnR1ddHf34/RaMRsNls7tC3F5hP91NQUFy5cYG5ujldeecWy56QgCNufUqkkJiYGjUaD0Wi0rJExmUzWDm1LsemVsePj4zQ0NDA6OkpkZCSFhYWib14QbFBSUhIjIyO0tLTg4uJCdHS0tUPaUmy2RW8ymairq+Pq1au4ubmRkJBAcHCwqIkhCDYoJSWF/Px87t69S319PfPz89YOaUux2USv1+upqKjg0qVL5OfnU1RUZO2QBEF4SsLDw8nKykKv19Pd3U1XVxfLy8vWDmvLsMlEv75b/MjICPb29uzatUvsKykINs7X15eYmBiUSiW1tbViteyX2GSi7+7u5vz589jZ2ZGbm0tUVJSoZyMINk4mk1FaWkpUVBRXr16lvb3d2iFtGTaZ6FtbWykvL8ff358XXngBDw8Pa4ckCMJTZm9vT3FxMbGxsTQ1NdHS0sLS0pK1w9oSbCrRGwwG+vr66OrqYmpqioiICLKzs7G3t7d2aIIgPGVSqRR3d3fCw8ORSCQMDQ3R3t4ukj02lujn5uY4efIkw8PD7Nmzh7i4OBQKhbXDEu5DLGgRnhYfHx+ef/55AC5cuMDk5KSVI7I+m0n0JpOJrq4uKisr0Wq17N27V2woskWYTCZ0Oh3Dw8P09fWh0+k2PM1VvDAIj8rPz4/9+/cjk8morKxkcHDQ2iFZnU0k+vUkX1tbS2dnJy4uLpSUlODn52ft0AS+KENx9+5dKioqOHny5GO1sMT6B+FReXh4UFhYiIODA42NjXR3d7O8vLyjGws2sTJWr9dz5coVGhsbSUpKIiMjA3d3d2uHJfzV2NgYZWVlnD9/Hp1OR0JCAl5eXtjZ2d03gff09HD9+nUGBwfx8fHh6NGjODo6PvD+5+fn6enpoaysDIVCwTe/+U0CAwNFt90OplKpiI2NJS4ujv7+fhoaGsjKysLOzs7aoVnFtk/0ZrOZsbExGhoaGBsb45vf/KbYUGSLGRgY4MyZMzQ1NeHm5kZraysajYaoqChkMtnXjm9ubua3v/0tbW1tJCUlkZOTQ2xs7APvf2hoiMrKSt59910cHR0JCwuz7DEq7FwpKSlMTEzQ1dVFVVUVSUlJOzbRb/uum6GhIWpra5mamsLb25u8vDyxOGoLMZlM9Pb20tjYiEajoaioiDt37lBfX4/RaLznWLPZzPz8PN3d3dy+fRuFQoG9vT21tbV0d3c/8Bzt7e1UV1fj6+uLRqPh+vXrdHR0PO2HJmxxSUlJFBYW0tHRQVlZGTMzM9YOyWq2fYu+tbWVc+fOoVAoSE1NJTg42Noh2aT1AdWlpSUUCsUj1fM3mUx0dnYyODiIo6Mjubm5ZGVl8f7772MwGDh06NA9LaylpSWam5sZGxvDy8uLqKgoNBoNV65cQSaTERkZ+bVzaLVaurq6GBgY4LnnnkOpVFJTU0NQUBCFhYUbfpwGg8FS+dBgMKDX64EvXoSMRuNjfxgMBuRyOc7Oznh6euLp6Ymjo6MYe3iKnJyciI6ORq1WMz4+TkdHB2q1GrVabe3Qnrltn+jr6+s5ffo0b731FiUlJcjl2/4hbUkLCwsMDw/T2dmJWq1+pNpBq6urXL16lcnJSUpKSjh06BD+/v785Cc/YXJykqmpKVxdXS3Hz8zMUFlZyfLyMgcPHiQzM5PFxUV+/vOfo1Qq+e53v3vP/S8tLdHZ2cmdO3ews7PjyJEjrKys8D//8z/cunWLubm5R3pBMhgMSCQS1tbWmJycZHV1FalUyszMDLOzs0gkEoxGI8vLy6yurrKyssLKygqrq6uWj/Xvv/z5y8fMzc3h6OhIfHw8eXl5lum/zs7OG/9nCI/MxcWFffv20dzczNWrV1GpVBQXF1s7rGdu22bF5eVl2tramJiYIDAwkJSUFGJjY3dsH9zTpNVqqaiooKqqCrPZjFKppLy8HKlUikQiuecDvliK7uHhwdraGk1NTTg6OpKZmUl8fDxyuZyIiAhmZ2dpamrC3t4ef39/AEZGRigrKyMsLIzXXnuN5ORkenp68PT0ZHp6mrq6OmJjYy3JcWpqisuXL6PT6UhLSyM8PJz5+Xmio6PR6XTU19eTmppqWRk9OztLa2srra2tjIyMIJPJMBqN97TatVotgGWg+Mt1zddnbZjN5ntmcJjNZhQKhaXF/uXf6fV61tbWUCgUyGQyzGYzDQ0NNDY28sYbb1BSUiKes0+RUqmksLAQnU7H6dOncXV1FYl+OxkdHeXcuXOsra3xwgsvsGvXLlQqlbXDsjmLi4t0dXVRXl7O+fPnSU1NZW1tjcuXL7O8vIxKpUIikSCVSi2JTC6XExAQgJ+fHy4uLsTGxpKeno6XlxfLy8sUFhbS0tLCtWvXUKvV+Pv7YzQa6e/vp6Ojg6ioKDIyMnB0dCQoKIjc3FwGBwf57LPPkEqlpKenAzA8PMzly5fx9vamtLQUV1dXJBIJ+/fvZ2BggIqKCnx8fCyJvqenh5MnT3Lx4kW6u7uRy+WWFyuz2YxMJsPBwQF7e3scHBzw8PBArVZjMpmQy+U4ODhYPlQq1T3Hrn9e/9rR0dGyIlsul+Pv749Op6OxsZF3332Xzz77DG9vb3x8fIiJicHBwcFq/2NbJpPJSE1Npa+vj+7ubtrb25mfn7/nneROsG0T/eDgIOfOnSM1NZVXXnmFkJAQa4dkcwwGA9XV1bz33nvY2dnx9ttvk52djbOzM2+88QZ6vd6SJNdbsUajEYlEglqtxtXVFaVSiaenJ35+fkgkEuzs7MjJyWFmZobTp08TExNDUVERjY2NdHV1kZaWRmpqqmU6paurKwcOHOCjjz7iz3/+M5GRkaSnp2Mymeju7qapqYmjR49SWlqKk5MTEomE4uJi/vCHP1BWVsa+ffuAL2byXLp0id7eXg4ePEhsbCxra2vI5XLLixV8kZTlcjkymQylUmlpbUskknt+d7/P9/savliar1QqcXJyYvfu3aysrODh4cHnn3/O4OAgP/rRj0hLS7vvDCThyUgkEhQKBWFhYWRkZGAymaiqqiI7OxsfHx9rh/fMbLtEbzQaLbM4FhYW8PPzIzEx0dph2Zz5+XkaGhqoqqpicHCQ559/nm9961uWaY7Z2dmPdb9yuZzY2FhaWlqYmppidHTU0jff0dFBfn6+pcUOX8yH3rVrF3V1dczOznLnzh0GBweZnp5maGgIOzs7NBqNZYDNwcGBxMREPDw8mJycZGxsjOHhYcrLy2lvb8fd3Z19+/aRl5f35H+kx7DedeDm5mapxXL27FmMRiO7du0SVVafkoCAAPbu3UtLSwtnz54lICBgRyV62Y9//OMfWzuIjdDpdPz617+mpqaGuLg4CgsLiYqKsnZYNkWv13Pr1i1+8pOfMDg4yOuvv84LL7xAXFzcE88SWW/VLyws0NLSglqtxmAw8Pvf/56JiQlef/110tLSLN0e6y2ylZUVZmdnkcvlDA8Pc+vWLWZnZwkNDSU3N5ewsDDL8UqlktHRUcvsnf7+fj755BPs7e158cUXSUpKsuogqJ2dHZ6envj6+mI2m/nzn//MxMQEKSkpuLm5IZVu+1nPW876TLHGxkbOnTtHdnb231ybYWu2VaI3m810dnbym9/8hpmZGY4ePUpGRsaO6297mlZWVjh37hynT59mZmaG1NRUXnrpJWJiYjZ1RpPBYGBiYoLp6Wna2tro6OggODiY73znO2g0mq8db2dnh0wmo62tjfLychobG3FwcOCFF14gNTUVFxeXe47X6XQsLy9z584dbty4QV9fH0lJSXzzm98kICDA6tMa7ezsLKuDBwYGmJ6eZmJiAmdnZzQajdXjszXrib6jo4OmpiYiIiIIDQ3F3t5+R7ywbqtH2NfXR21tLTMzM/j6+pKXlyc2+95Ey8vLdHR08NFHH1FeXs7evXt5++23iY2N3fRyAh4eHuzZswej0UhNTQ2+vr7k5uY+8O20RqOhpKQEs9lMc3MzPT09rK6ukpmZSUBAwNeODw0NJScnh7GxMW7evIlarSYqKorg4OAtc2G7urqSn5/PD37wAzQaDe+//z5lZWUMDAxYZgIJm0epVJKQkEBGRgb9/f1UVFTsmO0Gt1WL/vTp05w5c4bIyEgOHDhAenq6qGeySQwGA+fOnePXv/41a2trFBcXc/DgwU1vya9TKpW4u7szPj7O3Nwczz33HCUlJQQHBz9wUNLBwcEyrz08PJyioiL27Nlz3+eAo6Mjjo6O9Pf3I5fLLf3ygYGBm/5YnoRSqcTLywtnb2MFAAAZk0lEQVSFQoFWq7WsCg4PD8fb29va4dmc9XdKtbW1jIyMUFpa+jfrKNmKbTEYazQaGRsbo7Gxkd7eXg4dOsTzzz8vNhTZJHNzc5ZZKe3t7bz00kscPXr0gbVoNoNUKsXDw4PMzEykUim5ubnExcX9zRcVuVxOXl4efn5+rK2tERgY+DcHL/39/cnLyyM8PJzdu3dv2ZlZbm5uFBYWolAo+M1vfkNNTQ3x8fGW2SJiEeDmCQwMJCsri5MnT9Ld3c3IyAheXl7WDuup2xYt+vVZE7du3UKlUnHkyBGioqJEP+YmMBgM3Lhxw7Ja9ejRo5bph89iup+7uzsxMTEEBARgb2//0P+pi4sLGo2GkJAQfH19H7rYyNfXl+joaPz8/HBwcNgy3TZf5eDgYIlxfYHa2NgYaWlpODk5WTs8m7G+HqKtrY3Z2VlcXFxwdHS0+WS/LZoKd+/epby8HICCgoIt9/Z7u1paWuLixYtcunSJtbU1du3axd69e4mMjHxmc7rXu1gelVKpfKQpiGazGYlE8rVB2q3M1dWVgoICJBKJpdzE8ePHKSoqIi4uztrh2QxnZ2fS0tJYXFzk888/x9HR0eZn4GzN5s1XrFc79PX15cUXX8TT09PaIW17q6urdHZ28rvf/Y4LFy5w+PDhpzbwag3b9d2en58f+/bt4/XXX8fd3Z13332Xs2fPsri4aO3QbIbJZGL37t2kpqbS3NzMrVu3rB3SU7elW/QGg4G6ujra29vRaDTExcURHh4u+iyfkE6no6ysjE8++QSpVMqhQ4coLCwkMjJy2yZIW7K+qMpkMrG8vMz169fR6/V85zvfEdVZN4FUKiU8PJyRkREcHBwYGxujubmZiIgImy1FsaVb9JOTk5w5c4be3l7y8/NJTU0VSf4Jzc/Pc/PmTSoqKqirqyMpKYnXX3/dMvgnbA1+fn6UlpbyjW98A71ez6lTp7h+/Tqzs7P3FFoTHo9EIiEkJMRSCuPSpUs2vbfslh2MXV5epqGhgf/3//4fUqmUf/iHfyAhIUEk+idgMBi4evUqP/3pT1laWuLll19+pgOvwsY4OzsTFBSERCJhZmaG+vp6xsbGxLTiTbJeo2l9h7ro6GgiIiKsHdZTsWVb9K2trVy7dg2z2UxoaCixsbGiOuUTWFhY4MKFC5SXl7O0tERsbCwHDhwgLi5OJPktaL1InKenJ4WFhZSUlGA0Gqmvr+f8+fOMjo5aOcLtz9HRkaysLDQaDQMDA/T19dnsQrUt2zy+evUqly9fprCwkNLSUtGSfwJarZbOzk7+67/+i/Hxcd5++20KCwuJiYnZstMNd7ovj5WEhYWhVqvRarVcvnyZX/3qV0xPT/POO+9YMcLtT6FQEBwcTFRUFI6OjvT19dHQ0EBSUpLNLaLacl03RqORwcFBTp8+zdDQEEeOHCEnJ8dSa1zYGK1Wy5kzZ/jwww/R6XRkZGRw6NAhoqOjxYvnNmJvb4+7uzvwRSmQ6elplpaWCAgIsAwgrk8pFTZmeXmZ6elpZmZmWFxcJDEx0eYS/ZZrzt29e5dr166xsLBASEgISUlJW6II1Xa0XiHy7NmzVFdXk5mZyZtvvklcXJzo492GIiIiOHjwIAUFBczMzHDs2DFu3rxp+b24Rh5PYGAgpaWl6HQ6rl27xuTkpLVD2nRbLtG3tbXx0Ucf4erqypEjR+5bsEp4uPWB1x//+MdMT0/z9ttvc+DAASIjI0V3zTbm7+/Pd77zHfbt24dSqeTYsWP89re/xWg0Wo758laGwsP5+fmRm5uLWq1mZGSE27dvMzs7a1N/xy1zxa/Xs2ltbaW3t5fAwEDy8/MfaXNn4V7z8/NcunSJixcvMjY2RnR0NIcPH7bs2SpsT2azGalUikajoaioiJycHCYnJ6moqODatWuWSoyiZb9xnp6ehIeHo1araWlpoaWlxaYS/Za56tdnhXR0dBAQEEBMTAx+fn7WDmvb0el0tLe38+///u8sLy/z1ltvsWfPHqKjo0VLfpv7cgKPi4vD29sbk8nEtWvX+K//+i+OHDnC0aNHAdFf/zjS09NZXFykpaUFR0dHcnNzrR3SptkyiX58fJzy8nIWFhYoKioiOjra2iFtO+ubhlRWVqJQKMjJyaGoqIioqCiR5G2Qp6cn+/fvR6lUcuHCBaqqqnBzcyM7O9uyGY9I+I8uJSUFrVZLVVUVzc3NjI6O3ncTnO3I6onebDazurpKT08PLS0tREdHc/DgQUJDQ60d2raytLREZ2cnf/nLX6ivr+f73/8+Bw8eFC15G5eSkoKnpyfj4+O0trby+9//Hjs7O4qLiwHRjbMRarWapKQkVCqVpRt5fb+A7c7q0ytNJhPl5eXU1NTg6OjI3r172bt3r+hL3oC1tTXKy8v57//+b0wmEyUlJZYkL/6Ots/JyYmQkBAMBgOtra1MTEyg1WoJDQ0V//8NcnFxYW5uzrLVpbu7u03sYmf1Z4HJZKK7u5u2tjbc3d1ZWFjg1q1byOVydDodsHmtkse9n61w/vu9BZfJZOh0Oqamprh48SL19fW8+uqrfPvb3yY8PFy05HeA9QHaqKgoSktLGRsbo729ndOnTxMcHExAQAAjIyOYTKZ7nj/Wfk5vhRjWr6t1dnZ2zM/PI5FIWFlZobW1lbi4OPLy8jYlTmuyeqKXSCQ4OTmxvLzMpUuX+NOf/oRarf7aP2H92Pt9fb/vN3L84xy3mfE8yf1KpVLkcjlOTk5kZmby3HPPERkZ+bVzC7bpy8+H5ORk3N3d+Y//+A9qa2v55JNPGB0d5cyZM2i1WssmLRt5vm3k+M26dqx1TqlUislkYnV1lcnJSbRaLS+//PLXjtuOrJ7opVIpSUlJrKysEBoayszMDLDxQaQnbR08zu2t0Zr58u3WW3PrLXutVktjYyOurq5ER0eLnYl2mKmpKTo6Opifn8fBwQFPT0+cnZ2Zm5tDr9c/0SK5Z319WOucUqkUhUKBwWAAsJlJIRLzFpksul5Jbv3rL//8fl8/7HcbPX4zzrmReDbjfiUSCUajkdXVVSorK/nwww9ZWVkhNjaWN998k/T09Efank/Y/gwGA6dOneKPf/wjOp2OxMRE3nrrLWJiYp7outro8ZvxHH9a9/uw6/PLP1//7OzsbBPlELZMohcen9FoZHh4mJaWFmpra+no6GBlZYW4uDiOHDlCcnKyzW6oIHzRkj916hRXr15lZGSEgoICSkpKiI+Pt4kkJTw5q3fdCE9OJpMRFBREUFAQAQEBnDx5ko8++oihoSGcnJwwGAwkJSXh4uIiBmhtiNlsZmFhgYaGBsrKyiwFuUpLS9m9e7e1wxO2EKu06MUijqdHr9czMjLCrVu3uHr1KjU1NXh6epKXl8fRo0fFVnQ2RKvV8v7773Pp0iXm5ubIzMzklVdeISQkRLyDE+7xVFr0ZrOZyclJ6urqGB8fx87ODicnJ/z8/IiPj8fZ2flpnFbgiyliISEheHp64urqislkYmBggFu3biGTyUhNTSU2NhYfHx+x4cg2Njo6SkNDAzU1NczMzJCRkUFhYSFxcXHWDk3Ygp5Ki352dpYrV67wox/9iPb2dgA0Gg0FBQX86Ec/IiEhYbNPKXzF+rsmk8nEuXPn+Mtf/sLVq1fx8fHh7/7u78jPzycwMNDaYQqPYW1tjePHj/PRRx+h0+lITk7mzTffFJVJhQfa9ES/uLjIn/70J6qrq/Hz88PZ2RmTycTo6Cgmk4kDBw6QmZmJr6+vWLX3jExNTXHjxg0uXbpEd3c3er2e+Ph4ioqKyMvLE9Mwt5H1mlDV1dUMDw+Tn59PYWEhu3btElttCg+0qZlWr9czOjrK9evX6e/v51//9V+JiYkB4ObNm1RXVzM6Okp7ezuenp4i0T8j68WvYmJiOHfuHL/73e+YmJhgZWUFR0dHMjIykMlkyGQyMXayRZlMJlZWVrh58yYnTpxgZWWFhIQE9u/fT2pqqrXDE7a4Ta11MzY2RltbG25ubhQUFJCWloZSqQRAqVRaCpgplUrCwsLELkfPmJOTE0FBQWRlZeHs7ExnZydVVVU0Njbi7u6Ol5eX5cVXDJhvLSsrK3zwwQecPn2axcVFcnJyePXVV4mIiLCseBVsw6Neexu5Rje1SW0wGFhZWcHLy4uAgABkMhlarZa+vj66u7uZmJjA09OToKAgMRBoBQqFAj8/P/z8/HBxccFgMFBTU0NTUxN2dnYMDw+TlpaGRqMR77a2kPHxcW7evMmVK1eYmpoiLS2NwsJCEhMTrR2a8BRIJBK0Wi0DAwNMTEywsLCAyWRCJpNhZ2dHQEAAUVFRG8qhm3o1Ozo64uPjQ2dnJxMTE3h7ezM6Osp7771HXV0dTk5O/PznPyc5OXkzTys8hoSEBIKCgsjOzqasrIwPPviAiooKXn31VV5++WXCw8OtHaLA/1UmPXHiBFqtlrS0NN544w1RxtvGTU9P8+6771JeXk5PTw86nQ57e3tcXFx47bXX+OlPf4q9vf0j39+mJno3NzciIiLo7e2ltraWxsZGent7uX79Os7OziQlJeHt7b2ZpxSegIuLC6mpqUgkEmQyGf39/dy8eZP5+XnS0tLIysrC39/f2mHuWKOjo1y6dInq6mpWVlbIy8tjz549hIaGim5PG7e2tmbZ+OTQoUMolUrm5+dpbW3Fyclpw92qm5roFQoFAQEB+Pj4sLKywoULFxgfH0ehUJCdnU1RUZFl5xtha3Bzc6OwsJCsrCwuXLjABx98QGVlJU1NTej1erKysvDz87OMtQhPn9lsRqvVUl9fz8cff4xWqyUhIYFDhw6J7podwmAwYDAY2LVrFz/+8Y+xs7NjZmaG48eP4+zsvOGu76fSEZueno63tzevvPIKer0epVLJwMAA8/PzaLXap3FK4QmpVCry8vLw9fXl+vXr1NXV8bOf/YyIiAi++93vUlBQgLu7u7XD3BEWFhb4+OOPqampQafTkZ+fz/79+wkLC7N2aMIzMjo6SlNTE+fPn6eurg5nZ2dUKhUKhYL8/PwNb1z+VBK9j48PPj4+9/yspaXFMugnbE1qtZrdu3dbZt+0trZy+/ZtLl68iMlksryAi/naT8/k5CQ3b96kqqqK2dlZUlNTKSoqElModwiz2czc3Byzs7P4+PiwvLzMnTt36O3tBeDNN98kODh4w103z6zWjV6vtwwoiBkdW5vJZGJubo6+vj4uXbpEWVkZRqORhIQEvve974mCWU+JwWDg2LFjnD17lpWVFXbv3s23v/1tgoODRdfZDmEymSxjmyaTibCwMPz8/HjnnXeorq7m7Nmzlv2AN+KZ7Rkrk8lQKpVIpVIxR3uLk0gk2Nvb4+/vj4uLC3Z2dqytrTExMUFPTw9DQ0PY29vj6ur62C/a4jlwr5GRESoqKrh48SLT09NkZ2dTXFxMcnKyGHjdQcxmM5cvX+bOnTukpKSQmZmJq6srd+/eZW5ujoiICNzd3XFxcdnQ9WOVprW4wLePhIQEEhIS+Pzzz/n000/58MMPuXjxIisrK5jN5g3VLVp/8yiRSB76HPjqBisbvf/tRK/XU1tby7Fjxyybhrz88suiQNkOZDabmZ2dZWpqCqlUik6nQ6lUkp2djU6n49q1a6yurvL9739/Q93gYuMR4ZEsLS3R0dHBlStXaGpqYmRkhMDAQHJzc9m/fz9+fn4PvO3a2hqLi4t0dnaysLBAVlYWLi4uDzx+bm6OsbExZmdnUalUxMfHP/RJrdfruXz5MlKp9LHe2lrL9PQ0J06coKamhtHRUQoKCigtLSU+Pl6UGt6BzGYzHR0dLC0tERYWhlqtRiqVMj09zfj4ONPT06jVamJjY623YEqwXU5OTqSnpxMREUF1dTXHjh2jt7cXrVaLSqUiMzMTLy8vnJycvlZBcWFhgdbWViorK5mfnycgIID4+PgHnmt4eJiqqiru3LmDr68vvr6+f/OFRKvV0tvby/nz55HL5URFRaHRaDbtsT8N64Nu9fX1lJeXs7CwQFJSEsXFxWIMZIda786MjY392u88PDzw8PC47/GP4pn10Qu2wc7OjuDgYAoLC/Hw8KC/v9+yjZ1arcbLy+trLdGuri6OHTvGmTNnGBgYIDIyEj8/P1Qq1X2fqJcvX+aXv/wl586ds9Ra12g0D3xSNzU1cfr0aSoqKhgdHcXe3h5nZ+evXRhbiV6v58MPP+STTz5haWmJrKwsXn/9daKjo0Wf/A614Zk0W72PXti+pFIpDg4OODg4UFhYaJlNNTY2xqlTpxgeHiYnJ4e4uDjLTJG+vj6uXLnC8vIyISEhdHV1odFoyMnJuaf1bzabWVpa4s6dO0xMTGBnZ4dcLqe5uRlPT0+io6PvG1NraysVFRU4ODhgb2/PxYsX8fT0JCoq6pn8TTZqeHiY+vp6ampqmJ+fJysri6KiIkulV0HYbCLRC48tICCA119/nfT0dC5cuMAf/vAHGhsb6evr46233iIhIYGFhQX6+/sZHh4mOzub/Px82tvbqa2tZffu3ffM2pmfn6e2tpaxsTFiYmKIiIjAy8uL+vp6VCoVUVFR923FdHZ20trayt///d9jb2/P+++/T0JCAkeOHHmWf45HYjAYuHr1Kh988AF6vZ6UlBSOHj26ZV+UBNsgEr3wRBQKBZGRkcjlcjw9PWlqamJoaIj//M//RKPREBwczOzsLImJiezfv5+4uDg+/fRTZmZm+N73vndPYaaFhQWqq6uZnZ0lJyeH/Px8lpaW+MlPfoJEIuHIkSO4ublZjl9ZWaG3t5eZmRnLwLBUKuXjjz9meHiY7u5ugoKCtswcdJ1OR1lZGVeuXLGseC0uLn6sBTCCsBEi0QtPTKVSERsbS2xsLDdu3OCDDz6gubmZ27dvExUVhYeHB0VFRRQVFVnKI9+9e5fBwUHc3NwsM2omJyepr6/H39+fPXv2UFBQQHd3Nzqdjjt37tDd3U1cXByOjo7AF+V7L168iF6vJzMzk8TERNbW1oiJiWFpaYmrV69SWlpKYGCgZeOO5eVlDAYDJpMJ2Fg/56Mee7/j7O3t6enp4caNGywvL5OQkMDevXtJT09/5PMLwuMSiV7YVHFxcfzwhz9kbW2NO3fucPz4cYxGI3l5eQQHB6PT6cjNzWVwcJDr16/j4OBAXFwcOp2Ovr4+BgYGiIqKIicnB5VKhVqtZu/evYyPj3PhwgWUSiVJSUkATExMUFVVhaenJwUFBTg7O7O2tkZxcTGff/45FRUVJCUlERgYyNTUFBcuXODTTz+lr6+PhYUFpFKpZYxgfW7/l+f43+/zg37/sNvq9XoCAwMpLi4mPz+fgIAAgoODn8W/RBBEohc2l6Ojo6X4VlhYGMPDwygUCmJjYy3dNHl5edTU1HDlyhUCAwOJi4uju7ub3t5e1Go1QUFBln1sXV1dOXDgAGVlZZSXlxMeHm5J9ENDQ/T29hIREUFGRgYODg6YTCby8vLo7OykoqKC4eFhoqKiuHnzJo2NjQwNDSGRSPDy8gK+3vp+0GKuByXwh91WIpFYFnJ5eHiQnJxMUlKSKBAnPFMi0QtPjUwm49vf/jYSicQy6KpQKNi9ezcDAwOcOHGCnJwcAOrr6+np6SE3N/eeUrzOzs4UFRXR1NTEe++9R2FhIVNTU0xPT9Pf34/ZbCYwMNCyUYpMJiM2NhaNRsPq6ioDAwPU19dz9uxZlpeXefHFFykpKSEpKQmDwYDRaAT+b1Xtlz9/+eNBx3z12Pv9HMBoNGJvb4+np6co7Cc8cyLRC0/F+mKOrw6EyuVygoODCQsLw9HRkYmJCW7evMmpU6cYGxvjH//xH79Wc319wDcxMZG5uTlLPZjx8XESEhLuu9tSeHg4iYmJDAwM0N/fT2VlJbt372bfvn2kpKQgk8k2tEOPIGxn0ocfIggb97CBy+DgYBISEpibm6OsrIzr16+zuLhIQkLCfVe1RkVFcfjwYfR6PSdOnODs2bPMzs6yZ88eIiIivnZ8ZGQkJSUllr79u3fv4u7uTlpamtivWNhxRKIXrMLb25uCggLm5uY4ceIErq6uZGdnW/rOvyosLIwDBw6wuLjIn//8Z06fPs3U1BT5+fn3nYMeFRVFcXExs7Oz9PX1kZ6eTkpKytN+WIKwJYmuG8Eq1Go1OTk5dHZ2cvPmTXbv3k1RUZFlEPar1qdwajQaXF1dMRqN+Pv7ExYWdt9SyVKplPDwcNLS0pBIJOzbt09sSi/sWCLRC1bh6OhIcnIyOTk56PV69u3bR1ZW1t9c3KRQKNi7dy9qtZq1tTUSEhL+Zl0YuVzOP/3TP2EwGFCpVFtm4ZQgPGuiTLFgVT09PfT39xMbG0tAQMBD+/bHx8eZmprCZDKhVqsfeBuxsYkg/B+R6AVBEGycGIwVBEGwcSLRC4Ig2DiR6AVBEGycSPSCIAg2TiR6QRAEGycSvSAIgo0TiV4QBMHGiUQvCIJg40SiFwRBsHEi0QuCINg4kegFQRBsnEj0giAINk4kekEQBBsnEr0gCIKNE4leEATBxolELwiCYONEohcEQbBxItELgiDYOJHoBUEQbJxI9IIgCDZOJHpBEAQbJxK9IAiCjROJXhAEwcaJRC8IgmDjRKIXBEGwcSLRC4Ig2DiR6AVBEGycSPSCIAg2TiR6QRAEGycSvSAIgo0TiV4QBMHGiUQvCIJg40SiFwRBsHEi0QuCINg4kegFQRBsnEj0giAINk4kekEQBBsnEr0gCIKN+/+yy1GrrDXMtgAAAABJRU5ErkJggg==)
physics-General
physics-
In the circuit shown the equivalent resistance between A and B is
![](data:image/png;base64,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)
In the circuit shown the equivalent resistance between A and B is
![](data:image/png;base64,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)
physics-General
physics-
In the circuit shown, the currents
are
![](data:image/png;base64,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)
In the circuit shown, the currents
are
![](data:image/png;base64,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)
physics-General
physics-
The resistance is connected as shown in the figure below. Find the equivalent resistance between the points A and B.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZkAAAE2CAYAAACz7+/1AAAgAElEQVR4nOzdd1Bd953//+etcOm99yp6FUgIEKhLblHcYmcTJ04vm0kmyZbMbiaZ+Waz/2wmk2QnyXo3xY6dteRYtmUVowaWKAIkQEg00XsRXLjA7eX3h5fzE2pGshDt85jxTKTbPke597zO+ZT3R+ZwOBwIgiAIwjKQr3QDBEEQhPVLhIwgCIKwbETICIIgCMtGhIwgCIKwbETICIIgCMtGhIwgCIKwbETICIIgCMtGhIwgCIKwbETICIIgCMtGhIwgCIKwbETICIIgCMtGhIwgCIKwbETICIIgCMtGhIwgCIKwbETICIIgCMtGhIwgCIKwbETICBvW/ezX90n39hN7AwoblUzsjClsZK2trZSXl2MwGJDLP7rmkslkKBQKlEolAQEBFBUV4e/vv+h1g4ODdHV10dXVhU6nQy6X4+vrS0REBElJSfj4+Ejvt0Cr1VJeXo6/vz9JSUl4enqiVCof2bEKwkoQ33BhQ6usrOSb3/zmHR9TqVTk5OQQGRm5KGTMZjNVVVW89957VFRUMDg4iEwmIyYmhqKiIl544QWys7Px9fVFJpNJr6utreVHP/oRhYWFfOMb3yAxMVGEjLDuiW+4sKF5eXmRm5tLeno6OTk5OBwOJicn6e/vZ3h4GH9/fzQajfT8gYEB6urqePfdd5mcnOQrX/kKHh4e6HQ6Ojo6GB0d5Q9/+APDw8N84QtfAMBms/Gzn/2M119/nY6ODulzBGEjECEjbGhxcXG89NJL7N27l/j4eAAmJyc5efIkk5OT+Pn54ePjIz3/6tWrvPPOO3R3d5Oens5Xv/pVgoKCsFqtnDhxgrfffpujR4/i7OzM888/j0ajoa6ujg8++ICOjg4AlEolCoVi0V2OIKxXImSEDS0hIYGQkBA8PT2lv2tvb+evf/0rpaWllJSU4OvrKz3W2trKhQsX2Lt3LwcPHpRep1QqKS0txWw2c+zYMUZHR+nv7+fQoUOcO3eOL3/5y5SUlPDzn/8cg8HwyI9TEFaKCBlhw3I4HLi4uODi4iL92Ww209PTw+TkJG5uboSEhCx6zY0bN+jv78fPz4/4+HjUarX0mJubG3FxcSgUCqanp7lx4wYqlYrExET27dvHpUuXUCqVWK3WR3qcgrCSRMgIG9at3VUGg4G6ujqGhoZISUkhPDz8ttc4HA5sNhsOh0P672YKhQKFQoHJZMJsNvPlL39ZmgBgMpmk9xCEjUKEjCD8H6PRyLvvvsvMzAw7d+4kKSnptueo1Wrc3NxwcnJCoVDc9rhKpcJkMuHk5ER0dDR+fn7SY2IMRtiIxGJMQfg/ExMTVFdXMzk5SUFBAdHR0bc9x9fXl+joaNRqNQaD4ba7EoPBgIuLC8HBwURFRS16TNzBCBuRCBlBAEZGRrh69SoqlYrg4GACAgKkx24Oh6SkJAoLC5HJZIyMjGC326XnjI+PMzAwQGZmJjk5OY/8GARhNRIhIwhAfX09lZWVxMTEkJWVhbOzs/SYTCbDaDTS29uLq6srpaWlOBwOuru70ev1wEchc+3aNXp7e9m7dy+pqam0tbUxOzu7UockCKuCCBlBACoqKjh37hz5+fmUlpbe9vjAwAB//etfmZiYIDc3F71eT2trK1qtVnpOU1MTnZ2d7Nu3j8DAQP7nf/6H+vr6R3kYgrDqiIF/YUOz2+309fXR3t7O5OQk8fHx0qLMmzkcDubn5/nggw84evQo586dIygoiP379xMTE4PD4aClpYX33nsPvV6P1Wqlv7+fgoIC6T0sFgsWiwW9Xo/NZnuUhykIK0aEjLCh6XQ6hoeH0Wg0xMbG3nHaMny0BiY6OpqLFy9y+vRpANzd3ZmZmcFoNKJSqXA4HIyNjfHf//3fBAQEsHnzZlxdXaX30Gg0eHt74+Pjg0qlErPNhA1BVGEWNjSz2YxOp6O7uxuLxUJmZuaiYFhgNBoZHx+nr6+PkZERHA4Hfn5+bNq0iaCgIORyOQ0NDXR1dWG323FxccHPz4/Y2FhpEsHIyAgNDQ0EBASQkJCAq6vrHadBC8J6IkJGEG7hcDgW3WXc+ucHeT+Hw3Fb6X9B2AhEyAiCIAjLRozJCAKf/G5lpd9fWN9u/v44HA4GBwepqqqira0NpVIp3SknJyeTnp5ORETEqtmrSNzJCBuGw+HAbrdLP1a73Y5cLl9yN9bN9coWfvRyuXzJ4bHw+Quvvfk/QViq/v5+Kioq+N3vfkdVVdWix3bs2MGzzz7LU089RXBw8Aq1cDERMsKGceXKFaqrq3F1dWV2dpba2lqKiop4+eWXP/a1BoOB/v5+amtrqa+vZ2BggE2bNvG9733vtq2Z76atrY3f/e53jI2NERwczIEDB8jOzsbLy0uM1wgfS6/XU1lZyVtvvcW5c+coLS2loKAAi8WCQqHAZrPx9ttv09vbyw9/+EMOHDiAv7//in+3Vsf9lCA8Ak1NTfzlL38hPz8fh8PBW2+9hdls5plnnsHDw+Oer52ZmaGmpobz589z6dIlGhsbSU9P58CBA3h5eaFSqT7281taWjh8+DATExMkJSXh5eWFu7s7WVlZi7YMEIQ76e/v5/Dhw5w+fRqbzcZjjz3Gk08+ueg53d3dVFZWUllZSXBwMDt27Fjx75biJz/5yU9WtAWC8IgcOnSIt99+m7/7u79j9+7ddHd34+Ligre3Nx4eHnecurygu7ubP/3pTzg7O1NaWkpQUBBeXl5YrVacnJwICwu762tNJhPNzc3U19czMTFBVlYWW7duZWxsDKPRKEJGuCeHw4FOp6O8vJxf/OIXpKWl8dprr7Fly5bb7lJUKhXe3t60t7djNBopKipa8e+WuJMR1j2j0UhfXx9arRY/Pz8iIiLYtGkTW7dupbe3l8rKSoKCghYVxbyZ3W6np6eHjo4OSktL2bt3LwkJCdTV1VFeXo5GoyE/P/+un2+xWKipqaGnp4f09HQ2b95McHAwv/71r5mZmeG55567Z8AJG5vdbqetrY3Ozk78/f3Jy8sjOTkZuH1CSUpKCk5OTvj4+ODn57cq1mGJkBHWvampKc6fP4/D4WDXrl0EBgbi7OxMfn4+Wq2Wuro6tmzZQmZm5m2vtVgstLe309rais1mIyQkhLS0NOLj45mZmeGVV14hODhY2kPmTgwGA/X19UxOTvL000+ze/dulEoler2egYEB+vv78ff3X/ErTmF1stvtNDY2MjQ0xNNPP01hYaH02K2TRnx8fNi8eTO5ubnSxJSVtuFCpr29nfr6eqqqqhgfH79reY+7zfi5n5lA9/seMplMKit/r8951G1bzmO+n+fcT9sMBgN+fn58+9vfZm5ujuPHj6NWq9m1axd+fn4olUry8/NpaGjg7bffpqenB5vNdtuVn81mo7KykuvXr5OTk0NiYiIAzs7OxMXFkZiYiNFo5MKFC2RlZeHj47Po9QvTTTs7O/Hw8GDz5s0EBQVhMBhIS0ujvb2dhoYG3N3dSU1NveOxtLe3c/78eerr67lx4wZqtVp8Zz/m71f7d/bmGYYqlQqVSoXZbEahUBAWFkZGRgaFhYU4OTlht9tpb2+np6eHLVu23HGfo5vf+9bPXOnp8xsuZHp6eqioqKCsrEyqWfUwvrw3/9ge9PVLfe6tj93tS/SwfvRr8ZhnZ2cJDw+XuqKsVitRUVFkZ2fj6ekJgKenJyEhIQAMDw/T09NDRETEojuKmZkZLl68yPj4OJ/5zGcW7ZYZHh7Ozp076enp4cSJE1JdspsNDg7S1taGxWLB39+fmJgYAORyOYWFhSgUCqqrq/Hy8pJCxuFwYLVasdls6HQ6urq6aGlp4fTp0/T394vv7Cdox2o55pun0ZvNZvR6PbOzs8jlciIjI3n66afJzc3FyckJh8PB6OgoExMTeHp64uXlddfPW2qbH6UNFzILC5b27duHt7e3NCtoKTO57/Wcm6/m7va8O/39na4Cl/I5D9LWT/LaW//+Xse5lPe4eWHZ/bx+qZ9htVpxcXEhNjYWjUbDz3/+czQajdRVtiAkJISCggJmZ2e5ePEiPj4+UlDMz8/T0dFBZ2cnnp6eFBYWLtrt0tvbmz179vDqq69y9OhRCgoKyM7OXtSWlpYWGhoaSExMlLowAJRKpTT4/9ZbbxEcHMyLL74IfFRPbWBggIqKCmpqati/fz/f//73efHFF9Hr9VIXyCf9N1ogvrNLe4+H+Z1dCA+dTkdjYyOnT59mdHQUo9FId3c3zc3NWK3Wj32/m993pcPkbjZcyAwNDTE2NsYTTzxBbGzsSjdHWAZ3ulJNSUm543PDwsIoLCykurqaCxcuUFxcLIVMZ2cn9fX1ODs7ExsbK931LHB1dSUtLY3w8HBpUzOtVounp6cUBA0NDVy8eJEDBw6Ql5cnnQgWukViYmJQKpWMjY3R19dHZGQkZrOZy5cvU19fz/DwMO7u7oSGhhIaGvqw/6mEFWIwGOjt7eXGjRsAJCQkSFPrf//73zM2NrZoOwiNRoNGo8Fms90xfBa+V9evX6evr4+QkBACAwPx9vZe8XGZlR8VesQaGxs5ceIEHR0dmEymlW6OsAxu7pL4uKu70NBQ8vLy0Ol01NXVMTc3Jz3W2NhIVVUVaWlpbN++/Y5Xqq6urqSmppKbm0tPTw9lZWXSbph6vZ6mpiaampqIi4sjKyvrtjGfiIgIioqKkMvlnD59mqmpKfR6PR9++CGzs7Ps2bPnrtsPCGvXwpqpf//3f+fEiRNER0fz9a9/nX/+538mKSkJq9W66A7Kz88Pb29vZmZmmJmZuev7Hjp0iO9+97scOnSIrq6uVbFv0YYLGaPRyPz8PBaLRSoPIqw/S+06cHNzIzY2Fn9/f6xWK93d3RgMBqanp7l27Rrt7e1kZGRQVFR01wWXCQkJlJSUMDAwwMmTJ7FYLMBHdzE2m434+HjCw8NRKBS3tcvf35/i4mKUSiVlZWV0dnYyMTHBpUuXsFqt7Nixg8jIyE/2jyGsGkNDQ/zlL3/h1Vdf5cqVK2RlZfHcc8+xd+9eEhMT8fb2lmqRLZDL5aSnpxMQEMDrr7/O0aNHbwuPqakpXn31Verq6vDw8CA+Pp7IyEgxhXklqFQq1Gr1it9CCquHt7c38fHxDA0N0dHRgZOTExqNhuHhYRwOB5s2bcLPz++ur1+4Gzlx4gRXrlxBq9UyNzdHeXk57u7u0rTpO/H09GTr1q20trby4YcfcvnyZQIDA5mamiIzM5O0tLTlOmzhETKbzczNzXHhwgUOHTrExMQEUVFRvPDCC2zZskWqOKHT6bBYLIsuRhQKBdnZ2fT39/P222/j5OTErl27CA8Px9nZGScnJ6qqqnjjjTdQqVQ8/vjjlJSU3PU796htuJARhDtJTk7mxo0bdHV1MTAwgJubGy4uLuzatQtfX997vnZhV82kpCRpPGVsbIzTp0+Tnp5OUVGRNKPtVs7OziQmJkpjM2VlZQQHB5Oenn7bJAJhbTIYDNTU1PCHP/yBqakp4uPjefLJJ6X1VncqaXRzL4tcLicuLo4nnngCq9VKdXU1L774IgqFAicnJ6xWKz4+PiQkJLBz5062bdtGUFDQoz7MuxIhIwhAamoqOp2ON954g56eHnx8fCgoKGDXrl23TUu+E3d3d3Jzc5mfn+fChQvSAOzu3bvJysrCzc3trq9VKBTExsYSHx9Pe3s7ExMTPPnkk+Tk5DzMQxQesbm5OQYHB2lvb+fSpUv09/cTFhZGcXEx+fn595zIcWu3qkqlIjk5GbVajVKpZGBgAKPRKE2BjouLY/v27Wzfvl0KmNUy40yEjCAA0dHRzM3N8R//8R+0trai0Wh46qmn2LFjx5L25XA4HOTl5TE3N8fvfvc7urq6iIiIIDo6ekkl16OiotixYwc9PT3Mz8+Tl5d318WZwtpw6dIlDh06xKVLl/Dw8OArX/kKW7ZsISQkBI1Gc9fX3S0Y5HI50dHRfOtb3+KLX/yiFCIOhwOVSoWLi8uiqhOrIWBAhIwgSAIDA9m8eTMymYyAgAA2bdq05I2fZDIZkZGRpKenExUVhaurK3l5ecTHxy/p9UFBQZSUlEgnjU2bNokyM2uQ1Wqlvb2d8vJyrl27xsTEBKmpqWRkZLBt27Z7rtZfioXqAB9XNXw1ESEjCP/HxcWFgwcPUlhYiLu7+13X1tyNUqkkPj6e/fv3Y7PZyMjIWPJJxdPTk/T0dNLT0x+k6cIqYDQa6enp4dSpU7zyyitoNBr27NnDpz/9aXJyclbNncWjJkJGEP6PRqMhNzcXs9mMSqW65zjK3Xh6erJnzx4AvLy87tktIqwfbW1tlJeXc/bsWaampigqKmLz5s1SrbH7DZj1FEgbMmTW0/+BwsOjUCjuOVX54zgcDhQKBREREQ+xVcJqZbPZmJmZob+/n8rKSqqqqujv7ycyMpKnnnqKLVu24O3tfd/v+3Hla9aaDRcyS623JAj3S1y8bCw3btzgzJkzvP766+h0OmJiYvjBD35AXl4ePj4+Yo+g/7PhQsZsNmOxWKRFmYIgCPdjbGyM1tZWLl68SEtLC3a7nbS0NAoLCykuLr7r5ncb1YYLGZPJhNFoRK1Wr4qSC4IgrB2zs7NcuHCBY8eOUVlZiZ+fHy+++CI7d+5k06ZND+UzRHfZGrewklZ0bQiCsFQWi4WGhgZOnjzJpUuXmJ2d5bHHHmPz5s3k5OQs2gJCWGzDhcxCZd71cpUgCMLysdlsTE5Ocv36dSoqKigvL8dsNpOSksKLL75Ibm7uSjdx1dtwISMIgrBU169fp6ysjCNHjmC1WsnLy6O4uJicnBz8/f1XunlrgggZQRCEW2i1Wq5du0ZlZSXNzc24uroSGxvLzp07KSgouO8tkJfqbrNfl9rFvxqHAkTICIIg3KKqqoo//vGP0m6l3/3ud8nNzcXNzW3JpYY+iVs33FtqcKy2gAERMoIgCMBHg/vNzc0cPXqUnp4ePDw82L9/PxkZGWRmZi7b3ctSzc7O8otf/ILr16/j5OQk3enY7XZ2797NZz/7WWD13c2IkBEEYUOz2WzodDp6eno4d+4cb7/9NsHBwTz33HMUFxcTFxf3SNtztynMNTU1vPLKKwwNDeHi4oJcLsdkMmGxWBgbG6O4uJjw8PBVFTAgQkYQhA2uoaGBo0ePcvnyZeRyOZ///OfJyclh06ZNH7th3aNgt9v513/9V06ePEl2djZf/epXKSgowMPDg76+Pg4dOkRbWxvPP/88P/jBD/j0pz+90k1eRISMIAgbjs1mY3R0lNbWVqqrq2lubsZqtZKamsr+/ftJTk5e0fbdfDcyPDzMkSNHaG1t5fOf/zzPP/+8tDFZXl4enp6e/PrXv+b999+nvLyc/fv3r6rCrCJkBEHYcMbGxjh+/Di//e1vUSgUbNu2jSeeeIKcnJwHqr79sMlkMuRyOXa7nba2NoxGI4GBgezateu2rZX37NnDwMAAx48fp6enh+rqanJzc1fNnjMiZARB2DAGBgZoaGigqqpK2r00LS2NkpIScnJyVnxwf8FCZRK5XE54eDjf+c53kMlkiyoL3DzA7+vri1wuR6/Xo9PpsFqtK9X024iQEQRh3bNYLExPT1NZWcmJEye4ePEioaGhfPWrX6WoqIiQkJCVbuIiDocDu90OQGJiIomJiYseu3WK88zMDA6HA2dnZ1xdXVdVXUYRMoIgrGsL4fLuu+8yMjKCu7s7X//618nOziYhIWHVrdy/NUDuxeFwMDIyQnt7OzabDR8fH6KiosSYjCAIwnKbn59ncHCQpqYmqqqquHr1KoGBgeTm5vL0008THh6+0k18IDcHkFar5f3336exsZGgoCCSkpIICQlZVduYiJARBGHdsdlsVFZWcvz4ccrLy3Fzc+Pxxx9n+/btZGRkrIkNxZZSxLenp4f//M//ZGJigueee46SkpJVd2wiZARBWDdsNhvt7e1UVlZSU1PDwMAACQkJZGZmsmvXLlJTU3FxcVnpZt7TUrrKbDYbx48f56233qKnp4eMjAw+9alPkZqa+ghaeH9EyAiCsC6YTCaGhoY4efIkr732GgaDgczMTL75zW+Sl5eHs7PzSjfxobBarXR1dfH73/+eY8eOkZaWxsGDBykuLl5VA/4LRMgIgrDm9fX1ceHCBU6ePMnExASpqank5OSQn59PSkrKmguYe93NnDhxgl//+tf09PRQUlLCyy+/TElJyaoMGBAhIwjCGmY2mxkZGaG8vJzz58/T2tpKdHQ0+/fvZ9euXQQEBKx0Ex/IncZjZmZmaG9v55133uHUqVOUlpbyxS9+kWeffVYK0dVWHBNEyAiCsIZVVlby+uuv09HRgZ+fH9///vfJysoiKCho1ax4f1A3B838/Dzl5eX8+Mc/ZmxsjMcff5yXX36Zffv2LbpLW20BAyJkBEFYY3Q6Hb29vVy7do3GxkZmZmaIiYkhKyuL7du3r7qFlQ/i5rCYm5vj/fff58SJE5jNZgoLC/nCF77Arl271kQ3oAgZQRDWDJvNxrVr1zh27BhvvfUWoaGhPPXUUxQXF5OYmIiTk9NKN/ETW1iMKZfLgY9K4fz2t7/l0qVLfOlLX+Lpp5+muLh4hVu5dCJkBEFYE9rb26moqODChQtMT0+zd+9esrOzycvLW3Wr3D8puVyOXC5nYmKC8+fP097ezvz8PO+99x7Xr1/nz3/+MzabDbPZDHwUvnK5nPT0dLZs2UJ2djaenp4rfBQfESEjCMKq5XA4mJ+fZ2xsjDNnznD69GmGhoZITk7mpZdeIi0tDZVKtdLNXDZzc3PodDoSExOxWq3Mz89z8eLF2wpgWiwWFAoFBoOBkJAQUlJSVqjFtxMhIwjCqqXVaikrK+PPf/4zRqOR+Ph4nn76abKzs4mIiFiXASOTybDb7VitVqKiovjMZz7Dnj170Ov1UuHMW2efLfzZ29sbPz+/VVNNGkTICIKwCmm1Wrq7u7ly5Qp1dXXMzMyQkJBASUnJmp6avFQLYSKTyQgLCyMsLOyB3mM1zDYTISMIwqpiNpu5cOECx48fp76+Hn9/f770pS9RUFBAQkLCql10uNqshoABETKCIKwSer2eS5cucfr0abq7u7FYLOzYsYP09HTy8/OJjIzcMAGzWgLiYRAhIwjCinI4HGi1Wtrb2zl27BiHDh2Sthr+3Oc+R0JCwko38ZFaTwEDImQEQVhhFy9e5MyZM1RUVGC1Wnn88ccpLCxk8+bNDzQWIawuImQEQXjk7HY7o6OjtLa2cvbsWRoaGpifnyc9PZ0nn3yS/Px83N3dV7qZK2op+8msBSJkBEF45CYnJzl69CivvfYaU1NTJCQk8A//8A9s3rwZHx+fNVEuRVgaETKCIDwy4+PjXLlyhQsXLtDa2oq7uzs5OTls3bqVgoIC/P39V7qJwkMmQkYQhGW1sF5Dr9dTW1vLyZMnOXXqFBEREXz605/mwIEDREZGrnQzV42F2mXrhQgZQRCW1dzcHHV1dVRUVNDc3IxMJuNLX/oSGRkZJCYmisH9O1gv4zEgQkYQhGVisVgYGhriypUrVFdX09zcjM1mIysri+eee46oqKiVbuKqJZPJ1k3QiJARBGFZtLW1cezYMQ4fPoyvry/bt28nPz+fpKQkMfayBOuly0yEjCAID9Xw8DBNTU1cuHCBzs5OIiMjycrKorS0lNTU1DW/Y+VyWwgXcScjCIJwi7m5Oc6dO8c777xDW1sbmzZt4rvf/S4ZGRmrZn8T4dESISMIwic2OztLbW0tH3zwAQMDAzg7O/Piiy+Sk5NDWlqaCJgNTISMIAgPzGw2Mz4+TmtrK+fOnaOiooLQ0FC2bt3Kpz71KSIiIla6iWuW6C4TBGHDq6qqoqysjNraWlxcXHj66afJz88nJSUFb2/vlW6esAqIkBEE4b6YTCa6u7tpaGjg8uXL9Pf34+/vT1paGrt27SI5OVmUhfkExGJMQRA2LKvVSk9PD4cOHeK1117D29uboqIiPve5z5GSkoJCodgwe74sF4fDsW66ykCEjCAIS9TS0sLFixeprKzkxo0bFBQUkJWVRX5+Pps2bUKtVq90E9cFcScjCMKG4XA4MBgMDA4OUlZWxrlz52hrayMnJ4eXXnqJvLy8DV+SX7g3ETKCINzV7Owsx44d46233mJgYAB/f3+++93vkpeXR1xcnAiYZbReusxEyAiCcBudTkd/fz8NDQ18+OGHDA0NERISwrZt23jiiSdEUUthyUTICIKwiE6no7a2lrKyMo4ePUpQUBAHDx5k//79pKSkIJfLV7qJwhoiQkZYVxb2LhHun8Fg4OrVq9TV1dHY2Mj09DQlJSWkp6ezdetWkpOTxcyxR0DULhOEVcRms2GxWHA4HDg5Od31KtvhcGCxWKTnAigUCpRKJUql8o7BZLPZsFqt2Gw27HY78NEJYOF1CoVi3QTa9PQ0XV1dnDp1ig8//JCZmRmysrL4zne+Q2Ji4ro5zrViPf17i5AR1pSb71TsdjtdXV0cOXKE8fFxvvWtbxETE3PH18zOznLixAmOHDki1dZKSUlhz5497NmzR5p+e/P7d3d3U15ezocffkhPTw82m42QkBAyMzPZt28faWlpODk5rfkTQnd3N6dOneK9995DqVSSlpZGSkoKaWlpREZGrvnjE1aWCBlhTZHJZFitVm7cuIFWq2VgYICTJ0/S3d3N888/f8eQmZ2d5fLly1RXV9PQ0MD8/DwqlYqxsTE0Gg3x8fFERUVJgWGz2ZicnOT8+fOUlZUxMDDA1NQUZrMZrVaLTqdDLpdjMpnYvHkzTk5OK/Av8cnNzMzQ3d1NVVUVFy9e5MaNG+Tk5FBaWkp+fj6+vr4r3URhHRAhI6w5Wq2Ww4cPY7FYCA4ORq/XYzQapS6tWw0PD/PXv/4Vg8HAF7/4RbZt28b8/Dy//e1v6erq4ty5c+zevZvY2FgA+vv7OX78OCdOnJLp6sMAACAASURBVECn0/G9732P/Px85ufnqays5MyZMxw+fJjOzk6SkpLWZMg4HA5panJnZyfx8fH80z/9ExkZGQQHB4uyMCvk5oWYYkxGEFaIk5MTMTExKJVK/Pz8cHd3x2w23zVk+vv7OX/+PLm5uTz22GOkpaUxOTlJXV0dbW1tXLlyhfT0dClkBgYGOH78OAaDgfz8fPLy8qStgl1cXLDZbNTV1XHp0iWGhobW1BW/wWCgvb2d2tpampubUavVFBQUsHnzZrZt20ZAQMBKN1FYZ0TICGuOh4cHjz32mPTngICAO9Z7cjgcGI1GBgcH6ezspKioiLS0NABUKhVbtmxhenqa5uZmpqampNeNjo5SU1PD3r17OXjw4KKtgqOjo3n88cf505/+xMDAAAMDA0RHR6+JRYl6vZ6Ojg7ee+89jhw5QlJSEgcOHKCoqIjIyEgxNVlYFiJkhDXvbgPTdrsdnU7H9PQ0Vqt10fNUKhX+/v7Y7XauX7+OVquVHlsYe4GPAk2pXPwz8fLyQq1WY7FY0Ol0GAyGVR8yly9f5sKFC9TW1mI0GiktLaWwsJD8/HyCgoJEwKwionbZGme327HZbOumv1Pgrt1kAEajEZPJdNv6DrlcjkajwW63Mz09jdFolB6TyWQolcq7nngX3ksul+Pi4rJqC0NarVa0Wi09PT2cO3eO+vp6JiYmSEtL41Of+hSZmZl4eHisdDOFmzgcDmw227o6R224kLFYLJhMpnuemIT15W5XhQ6HA7Vajbu7+6KgcHJyws/PD1dXV2Qy2W0/drlcjtlsRqVSkZiYiJeX17K2/0GNjIxw+PBh3nzzTVQqFenp6Xz5y18mNTUVLy8vXFxcVrqJwi0WCpLq9fp1c47acCGTnJyMyWQiNDR0pZsiPCQLIXKnMFEoFMjlcux2+6I7E5vNhsFgQC6X4+XltWiGWGBgoHSVr9VqsVqti95zZGQEX19f3N3dCQ4Olv5+tVQbGBoaoqWlhbq6OpqamnB1dSU1NZWSkhK2bduGm5vbSjdRuAuNRsOzzz6L1WolKChopZvzUGy4kNm9e7c0TVNYHxbuNG6945DJZDg7O6PRaKSgWbCw1mbhx3zziTcgIICSkhLMZjO9vb3Ex8dLYy79/f00NzeTmJh42/bCqyFgJicnOXXqFMePH6euro7MzEz+/u//nvz8fEJCQla6ecLHcHV15Yc//OG6GpfZcCGTkZFBf38/b7zxBg6Hg+zsbNLT03F1dV3ppglLcKe7hYU/3zqGIpPJ8PPzIywsDA8PD0ZGRmhubiYtLQ2VSkV1dTVjY2OkpqYSGhqK3W7n/PnzmEwm9u7dS3V1NR0dHWRnZxMYGAhAV1cXDQ0N7Ny5Ez8/P8rKyoiJiSEnJ+fR/APchcFg4MMPP6SsrIyrV6+iVCr5whe+QF5eHpmZmeKiao2wWCw0NzfT1dWFVqslICCA5ORkEhISVrppD2zDhYxGo8HHx4f6+nqGhobQ6XQYjUZSUlJwcnJCrVbfswaWsLJkMhl2ux29Xo/ZbGZ0dJTJyUksFgvt7e3ExcWhVCpxdXWVxlmio6PJycnBZDJx/PhxHA4Her2eK1euoNFoyM/PJyIigrm5OWpqapDL5RQVFTEwMMC1a9coLi4mKSkJmUxGb28vVVVVpKenY7VaOXHiBHl5eSsSMg6HA5PJxOTkJF1dXZw8eZLTp0/j4uLCjh07+MY3viHWvawxNpuNzs5OqqqqGBwcJDg4mKmpKebm5ggPD0ehUKBWq1Gr1ahUqjVxtyNzrJcpDPdhfn6ekydPUltbS2dnJ2NjYzg7O1NUVERxcTF5eXnizmYV02q1HDt2jJqaGq5evUpVVRUWi4X4+Hiys7PJyMhg7969ZGdnAx8Vf6yurubo0aOcOXMGg8GAm5sbYWFhPPHEE7zwwgv4+fkxMzPDm2++yalTp7h8+TLd3d14eHjw//7f/+Ozn/0sPj4+/OxnP+Nf/uVfcHNzIyQkBBcXF774xS/yne9855H/O+j1es6cOcPZs2epra3F1dWVzMxMSkpKyMrKIjAwUFwsrTF2u53Z2Vna29upqKigra2N4eFhJiYm8PDwIC8vj+zsbNLS0oiLi0OlUgGrZzzwThQ/+clPfrLSjXjU5HI5np6euLu7I5PJMJvN6PV65ufnmZiYYGxsDLVaLa4CVymz2czAwIB0BxMZGUlCQgKBgYH4+voSGhpKTEyM1MXl5OREcHCwNKXXZrNJ4y4lJSXExcUBH/3ArVYrer2eyclJfHx8yMnJYdu2bURHR6PRaBgdHWViYgJ3d3eCgoLIyclhy5Yt0ns8quPv7++nurqakydP0tbWhpOTE7m5uezbt4/i4mK8vLxW7UlHuDOHw4FcLsfZ2Rl/f3+cnJxwdnZGoVBgsViwWq1YrVbGx8cZGBhgbm4OlUqFq6vrbWu5VpMNeScD///aCofDwdTUFC0tLbz55ptUVlai1Wr59re/zT/8wz+scCuFO3E4HFIJ/pvXEywMlt5civ/m1yyU+rfb7dJamIX/Fp6zUN7farVKP3q1Wi1tB2A2mzGbzdKV48JnLVxRLjeLxUJfXx/Hjh3j9OnTjIyMkJ6ezte//nUSExNxc3MTe76sEzabTSoIOzc3R3t7O6dOnaK8vJzr16+TlpbG/v37ef7551f1BfHqjb9lJpfLsdlstLW1cfnyZerr62lpaUGhUJCWlkZERMRKN1G4g4WTu0qluq8Tu0wmk/qy7/W+N4fOnSzlPZbL8PAw1dXVnD17Fq1WS2BgoNR9kpKSIrp41xmFQsH4+Dg9PT20tbVx9epVGhsbmZycJDw8nJycHDIzM1f9eqcNFTILq/1NJhMGg4GOjg7Onz/Phx9+SGdnJ/7+/uTn51NSUsLmzZtXurnCHSzXSfxhvO9yBszY2Bg1NTWcPHmS8vJycnJy2LlzJ0VFRYSFhS3b5wqPxs130Qv7Hw0PD9Pa2kpjYyMNDQ0MDg4il8uJiYmhoKBAKva62m2o7rIbN27Q0NBAVVUVFRUV6PV6oqOjiYiIIDo6moSEBEJDQ/H29sbDw0OUOxceyN3uaB70Tuf999/nxIkT9Pb24uPjQ35+PpmZmSQkJODr6yu6x9YBu91OR0cHTU1NXLlyhY6ODoaHh/Hw8CAyMpLg4GDCw8OJjIzEz88PT09PAgICVv1dDKzzOxmLxcLMzAxarZbBwUG6urro6emhs7OTiYkJvL29iYuLo6CggKysrHWzwlZYWTKZDKPRyMzMDHq9HqVSSWho6JJnei1MTR4bG5NmGfX29qLRaMjOzuapp54iPDx8mY9CWE56vZ6ZmRl0Oh03btxgeHiYoaEhBgYG6OvrY2pqCpVKRXBwMGlpaaSnp5OUlISfn99KN/2+res7mb6+Pmpra6moqKC+vp7h4WFSU1MpLCwkLy+P2NhYvL290Wg0tw0UC8In0dvby4ULF+js7MTd3Z2XXnppyScIk8lEX18fhw8f5n//939JSEigtLSUgoICaVuB1TybSLg3h8PBlStXqK2tpb6+nsbGRrq7u4mIiCAnJ4fU1FRSUlLYtGkT7u7uyOVyVCrVmj1HrctvakdHB1VVVfT29qLVanE4HGzevBl3d3diY2NJTk4mNTV11ZdnF9au6elprly5Qnt7u1RQMz8/n6ysrNvK0dxKr9fT2NjIyMgIYWFhbNu2jR07dhAXF7dqKz4L92Yymejv7+fq1as0NzdjMBiw2WwolUoyMjLIyckhPDychIQEYmNjiYqKWrWFV+/XugyZy5cv85vf/Ibx8XHCw8N57LHH2L17txjMFx4Zg8HA+Pg4s7OzGAwGXn/9dVpaWrDZbKSnpxMQEHDX8Rm9Xs/Vq1dRKBQ8/fTTlJaWSrt2CmuT0Wjk2rVrvPbaaxw5coTo6GhKSkrIzc0lPz9/xcsSLad1GTJeXl6EhITQ29tLa2urVDHX3d2dTZs2rXTzhA1ApVLh5eWFUqnE2dkZuVzOyMgI//iP/8j27dt59tlnycvLu2O3l91ux2QySRutiVX7a59SqcTX11daZKnVaunv7yclJQWNRrPSzVtW63LFv9lsBj76oWs0GtRqNSaTiampKWZnZ6VpzAv7iYiV0cLDNjU1xcDAAEqlkoCAALZu3YpCoaCyshKdTiet23F3d8fJyWnRd3Bubo4rV66g1+txc3MjMjJy0RbQwtq0UHdPrVbj5eWFm5sbLi4u0qJis9mM1WpFpVKtybGXu1mWkFnpOjoeHh4kJSWxb98+tm/fjpeXF+Pj41RVVfHee+9x6tQpxsfHpRPAzXuJCMLDoNPpGB0dZWhoCKvVyu7du9m+fTvZ2dno9XrOnz9PU1MTMzMzJCYmLrqaNRgMdHd3o9PpsNlsxMbGijL9a5xcLsfNzY2EhASKi4ulO5j29nbKysp48803uXbtGlarFX9/fzw9PVe6yQ/NkkLGZrMxOTlJTU0N586d4/z581y6dIne3l6USiXu7u4oFIrbNo/q7u6mrq6Os2fP8uGHH3Lp0iV6enrQ6/XSboTLEUZKpRKNRoOrqyuBgYHSFYObm5v0mRaLhf7+fi5fvkxfXx9zc3M4HA5pppkgfBIGg4HJyUmuX7+OXq9nx44dBAUFERYWhkajQSaTMTMzw8jICAMDAxiNRjw8PKTdOAcGBhgbG2N2dpakpCRRgWKNWyhBpFar8fDwICAgADc3NzQazaKLXK1WS1NTE62treh0OuCjyvGPqmzRclhSyCwsYnz11Vf505/+xFtvvcWJEydobm7G39+fiIgIXFxcFvUdT09P8/777/PGG2/wpz/9iSNHjnDq1CmuXbvG/Pw8/v7+j2zBo6+vL0lJSRQXF5Ofn090dDQ6nY7q6mrpCmJmZgYAZ2dnvL29RT+48IlYLBZ0Oh3Nzc1MTk5SWFhIQEAASqVSWrFtt9tpbW3l7bffZnR0lMDAQIKCglAoFIyNjTE0NMTo6Cipqali4H+dWVgDk5WVRWFhITk5OTg7O9Pe3s6bb77J2bNnmZubw263o9FopAvktWhJ62T+/Oc/c/jwYVJTU4mKikImk1FfX8+VK1fYunUre/bsobi4WNpd8Pr161RVVXHkyBEAtm7dilqtRqvV0tbWxuzsLP7+/jz33HM8/vjjy3uEdzA5Ocng4CA9PT10d3czMTHBzMwMs7OzqNVqQkNDycrKIjs7m6CgINGdtkE1NTVRW1tLe3s7YWFhPPPMM4tKuNyrW3h+fp7Ozk5++ctf0tXVxa9+9SsyMzMXPWdoaIjLly9TUVFBe3s7ZrOZ0tJScnJy8PDw4MKFC5w6dYpvfvObPPnkk8t6rMLKMplMDA8P093dTVtbG4ODg9JCTZPJRHR0NKmpqWRlZZGQkCCda2/9DlZVVXH27Fna29uZnp5GpVJhNptxcXFhy5YtbN26lezs7EXnNLvdTk1NDRcvXqSpqQmtVotGoyEmJobc3FyKiorw9fV94AvvJfUL3bhxA61WS3FxMQcOHAAgLi4Oo9GITCZDp9Mt2tr24sWLvP/++4yOjrJr1y6+853voNFomJub45133uFvf/sb77//PhERESsSMr6+vvj6+pKRkQFAW1sb5eXlHD9+nObmZkwmE3v27MHd3R0PDw8RMhvUwkZgFy9eJDw8HHd3d7Zs2UJ0dDQuLi737OrVaDT4+vpis9mkbZ4XLJwYQkNDCQ4OJiYmhjfffJOjR49y/vx5Zmdnyc3NRavVcuPGDYxG46M4XGEFOTk5ER0dTXR0NDt37mRoaIizZ89y5swZ2tvbGR8fly6GtVqttPr/1rubxsZGDh8+zNjYGCaTCblcjslkwsPDAy8vL+Lj47HZbNLzHQ4HnZ2dnDp1igsXLtDV1cXU1BRKpZLg4GDGx8eRy+Vs3ryZ0NDQBzq2JYXMCy+8wIEDB0hKSgJgYmKCyclJQkJCyMrKkm71Fly+fJnGxkaeffZZDhw4IJ2kXV1dOXDgANPT05w8eZKenh4GBgYICQlZ0dkUmzZtws/PT2rn6dOn6ejo4Pr16yQkJHzs4jlhfVIoFHh6epKVlcXg4CA/+tGP2LFjB5/73OfYvn37Pasey+Vy/Pz8sFgsTExMLAqZm8NJLpcTFxfH1772NXbu3MmxY8ek309PTw9TU1OYTKZlPU5h9QkMDGT//v2UlpYyMzNDW1sbTU1NnD17lmPHjhEVFcXLL7/Mtm3bFr3OaDQSFBTEP//zP5Oeni4t+lQoFHh7e+Pt7S2dqxfuYE6fPk1ZWRkJCQn80z/9Ex4eHgwNDXHmzBlaWlr45S9/yde+9jVeeOGFBzqWe4bMQk9aSEgIISEhVFVVUV9fz+joKPPz83h4eBAREUF4ePiigamRkRFptXJUVJR0myWTyfDx8SEyMhK73c709DSTk5P4+vquSKE3o9HIwMAAIyMjDA0NMT4+TkhICCUlJSQlJREZGbnu57ALd+fm5rZo0aSTkxOTk5OcOHGCubk5cnJyiImJuesdjbOzM2q1Wtru+W6cnJwIDQ0lNDQUk8mEUqmUFmMGBgauiSKIwsOlVCqlMkR+fn709PQwPj5Oc3MzRqMRpVKJwWC47XU2mw0XFxeKi4s/dkaiw+GgurqaiooKPD09yc/PZ+fOnQCkp6dL63mOHDlCQUEBzz777ANNirrnK27+8UxPT/PTn/6UsrIyAGmK8MKsiZvZ7fZF3Wd2u31Rf95CDZ6FzadWonyaw+Ggq6uLEydO8O6779La2kpKSgqFhYU888wzJCcnExQUJCYAbGA+Pj6EhYVJg+8HDx6kvLycv/3tb7S2trJ9+3a+8pWv3LOwqqenJ15eXszOzmI2mz92X/Y9e/aQnp7OyZMnuXr1KlarleDg4OU4PGENGB0dpa6ujjNnztDU1ITRaCQqKoqtW7fe8Xsnl8txOBxotdolhUxjYyPXr1/n+9//PqWlpVJXrlqtZu/evQwMDHDo0CEGBwcZGBggLCzsvme6LTmWnJ2d+exnP0tKSgo2m42hoSFaW1upqalBo9GQlJQkdTc5Ozvj6uqKWq1GLpff9qOSy+UYjUbc3d2Jjo5+pJsttbe3c/nyZWpraxkfH0etVpOQkEBeXh4pKSmkpKSILjIB+GjsLigoiJmZGTw8PIiPj8ff3x8fHx/q6uq4cuUK//Zv/8bWrVspLS2944/e3d0dT09P5ubmmJmZwdfX92On7QcFBVFUVERSUhJ2u52YmJjlOkRhFVqocdbS0kJfXx/T09M4OTlRVFTE888/L5X8v9MYibOzMzMzM/zmN7/Bzc0NrVaLr68vycnJ7Nix47bq3VqtlunpaWnM5uZlKDKZDC8vLxwOh/T9DQwMXN6Q+fznP8/nP/95jEYjf/jDH3j11VepqanBzc2NqKgoKWQCAwOJjIwEPuqSunUGhNlsxt3dndDQUHx9fe+rwfdrYSWtTqdjeHiYuro6zp8/z5kzZ3B1dWXfvn3s3r2bLVu2rOotTIUHt7AhFHx0gbPUu9OFkJmamkKhUKBQKIiOjubLX/4yfn5+vPPOO3zwwQcMDg6iVCrJzc0lPDx8UZfCQsjMz88zPT2Nj4/Pkj47NjZWTFveIKxWKyaTCbvdztTUFDU1NVy4cIHa2loMBgPBwcEUFRVRWlp62xjMrRaGNhobGxkcHOTGjRt4enqSnZ2Nt7c3Xl5euLq6Sr+BW38Pt56rF9Y/KhQKVCrVA/XsPNCqQ2dnZzIyMigqKuLatWs0NTXx+OOPS1VDMzMzmZubw2AwMDY2JgWOzWZjZGSEqakptm7dSmpq6l0P7kHd+j4jIyNUVFTwwQcfUFNTQ2hoKGlpafzoRz8iLi6OqKgoAgMD19UKW2Exg8HAyMgIarUaHx+fJd85u7q6EhISwvT0NGazGYvFIj22Y8cOQkJCSEtLo6Kigp/+9Kfs3LmTT33qU5SWlkrPW7hCnJubY3p6ekW6hoXVbXBwkPPnz1NRUUFbWxtubm6EhoZy8OBB4uPjiYmJwdfXd0m9K4WFhSQkJDA/Py/tWVNVVcXVq1c5deoUBoOBxx9/XPoNuLm54eXldc8txS0WC35+fmzatOmBJmjdM2SsVitzc3P09/czOztLcnKydKBqtRqlUomTk5P0vwE6OzsJCwujsLCQ3t5e+vr6yMzMxMnJCYvFQkNDA9PT0xw8eJDg4GC6uroICQl5aAPsC1Oqh4aG6O3tpauri87OTkZHR1Gr1VJ/ZnFx8QNPyRPWloXB+tnZWWkBXHx8/JIG1BcWDNtsNqnrYeHv8/Ly8PT0xGKxMDU1xfXr1ykrK8Nms5GTkyNdOXp7e0t3MiJkBIPBgFarZWRkhN7eXuk8OTAwgNVqJSQkRKrOnJSUdNu58V4X5P7+/rfVuXNycmJ8fJzOzk7c3NzYvXs3rq6u0sLgiYkJLBYLc3NzBAYGLnqt0WgkJCSEqKgoKWDu94bgniFjNBrp6uriv/7rv7h8+TI///nP2bVrF/BRmDQ2NhIdHc3WrVvx9PSkubmZd955h6KiIjIyMqitrcVut6PT6fD398dsNlNXV4dMJuOb3/wm9fX1vPLKK7z44oukp6cvudEf59q1a7zxxhuUlZWh1+vZuXMnL7zwAnl5eQQHB+Pm5iZKx2wgw8PDvPLKK1y5coWgoCA+97nP8cwzz5CTk/OxV2YymYzw8HDm5uYYGhq6ra5UfHw83/jGN9i7dy9vvPEGlZWVNDY28thjj/HCCy/g5uYmQkaQLJxTKysrOXfuHGfPnsXZ2Zldu3bx3HPPkZWVRXh4OJ6ensjl8jt+P++3x8fHx4eoqChGRkaYmZlZNCkrKysLh8PBzMwMo6OjUhetyWSio6MDnU7Hjh07SExMfODPv+eZ1snJicDAQKKiomhpaeH111+nrKwMg8HA6OgoKpWK9PR0MjMzUavVWCwWpqenOXz4MDMzM5SXl5OTk8P+/fvx9/fHarVy6dIlWlpa0Gq1jI+PMzc3x9zc3H01+uMMDQ1RW1tLX18ffn5+hISEkJ6eTkpKykP9HGFtsFqtzM/PExQURHp6Oi0tLfzxj3+ku7ubrVu3St25dyKXywkODmZsbIyRkREiIiIWhYxcLsfT05O0tDQOHjxIYGAgjY2NVFVV0dfXJ1XU1el0zMzMiJDZoAwGA21tbVy6dInGxkYcDgchISG88MILBAYGkpaWJi2beJA6ZSaTiYmJCS5fvsz09LR0zoWP9ie6ceMGarUab29vqfpKQ0MDwcHBFBcXU11dTU9Pj7Tm0WQyUVdXh8Vi4aWXXsLhcHD27FkyMjLuexz9niGjUqkICwvjwIEDOBwOjhw5QlNTExaLhdTUVB577DGys7Ol9PP09CQ8PJw33niDuro64KOpzgt1weCjH3xvby+//vWvCQ8Pp7Cw8KHXL5PJZDg7O5OYmEh4eDgBAQHYbDYMBgNOTk44HI51VUpbuDeVSkVgYCCxsbHs2bOHo0ePUl1dzeTkJBaLhWeeeQaNRnPHbgCFQkFwcDB6vV4aT4yOjr7tM5RKJQUFBWRkZHDkyBHeeecdXnvtNRISEti0aRM6ne6hX0wJa8fCbqfvvvsuVVVVbN68maeeeop9+/bd8ft0v0wmE4ODg7zzzju0tLTg4+PD9u3bmZubo6Ojg5GREYKDg9m0aRMajYbLly/zwQcfUFpaipubG11dXdLaxaCgIMxmM5cuXcLFxYVPf/rTnD17lurqavz9/R9uyCyIjY3lueeeIz8/n6mpKRwOB97e3oSFhREaGirNOAgKCuLJJ58kLS2NGzduSFeBCQkJwEeDTD/+8Y95+eWXkclkUpXkhz1Fs7CwED8/P65fv05nZ6e04MjX15fc3Fy2bt0qlZQR1j+lUilVOA4ICODb3/42fX19nD59mr/97W/U1NTwxBNPUFxcfNs4jUKhICgoiImJCUZHR9Fqtff8LFdXV3bv3k1gYCDJycmcO3eOEydOEBgYSHp6uriT2aA0Gg3Jycl0d3fT09NDQ0MDo6OjDA4Osm3bNpKTk4mKinrg91epVHh4eBAcHExDQwP/+q//Kl0wubm5ER0dLc1OU6lUKJVK7HY7v/zlL+ns7KSrq4u9e/dy4MABKWTq6uqoq6ujoqICm81GcHDwoskvS7WkkHFzcyMuLo64uLh7Ps/V1ZWYmJi7hoZarb7rFLyHObssMDCQwMBAEhISqKurw2Qy0draSltbG2azGb1ez9TUFOHh4Xh4eODt7b2mS2kL96ZUKvHy8pIWAG/ZsoXc3Fzm5+c5d+4cDQ0NAMzMzEjTkBdm2yzcyfT19UllXu5m4TscGBgozT6zWCwolUqioqIWVb8QNhYnJyfi4+MpKSnBZrNRV1fH5OQkbW1tmEwmenp6iI2NJSwsDA8PD6lu4lJ7XFQqFX5+fuTl5aHX66mqqmJoaAi1Wk1kZCSbN2+Wvtvw0fT81NRUqTBrTEzMosF9lUpFYmIiQ0NDTE1NERYWRnp6Oh4eHvd97EuqwrxWLeyAaTab6e/vp6mpicrKSlpaWtDpdMTFxfHYY4+xe/fuRdV1hfWltbWVX/3qVyiVSrZs2UJpaSkhISEYjUaam5s5ffo0r7/+OpOTk3z961/n4MGD0kQUi8XCtWvXOH36NB988AHPPPMMX/va15b0uWazmdnZWYxGo7RLq5ubm9iJdYOy2WxYLBbm5+el7ZevXLlCY2Mj165dw2QyERAQQF5eHgUFBeTn5y95R1SHw4HdbsdoNGIwGDAajdL23Wq1GhcXF1xcXKSLaYvFgtFoZG5uDpPJhEwmw8XFRSoIvFDY1WAwIJPJpG3EPTw8lm8x5lqkUCikf1wvLy/p6iA0NJSO/6+9+w6O+r7zP/5c1VVh1SXUQahXVJGEmi1jiiHgs01szuFyTnK+Op6bu8vln5vJzc3kP2dybS65kozjxM45cQEMBoEQIFkFNYQkVFDvbVVXbevvD5/2Z0IxYMTuat+PGc/YLjajpwAAIABJREFU3v2uPit9d1/f76e8P93drK2tUVNTw+DgIJGRkURFRREdHS1Tm7cYZ2dnvL29zR/ujZpPSqWS1NRUFAoF8/PzNDQ0cOPGDXP/9p49e/Dz82PHjh14e3szMjKCWq1+6J/r4uJyz/5rS+8cKyxjY0GvUqnEz8+PkJAQvL29CQgIYMeOHYyOjqLRaJiamqKsrIzKykpCQ0PNdzhhYWH3HQ/ZWDDp4eHxUOvAnJ2dcXZ2Ztu2bfdt6+9PZ97wqOfvpmy/bK18fHyIj49n7969JCUl4erqSkdHB+Xl5Vy5coXl5WXc3NwICQlBqVTKl8EWsbS0RG9vL0tLSzg6OhIXF2e+QnRyciIkJITs7Gyio6NpamqiubmZwcFBVCoVO3fuxNPTk66uLn73u9+RkJDAvn37vlZ75JwS8P83LktNTaWkpMRcTn9lZYWWlhZOnTpFc3MzU1NTrKysmItmurq6mqchW+JcetSfaVchs8HBwYFt27aZx23i4+OJiIhAq9XS3t5OWVkZw8PDKJVKm96RTnxhbW2NsbEx1Go1KysrJCUl3VV0UqlU4uvrS2xsLH5+foyPj9PY2EhjYyMBAQHMzs5SXl5OQkIChYWFck6IJ87T09M8Qzc5OZm9e/eSkJCAUqlkfHycpqYmLl68SFNTE2q1GpVKZROVSrZ0d9mDKJVKIiMjiYyMJCsri+bmZs6cOUNVVRUtLS0888wzBAcHExISYt6FTtguk8nE2toaWq32jr1dvszb25vc3FwiIiIwGAycP3+eK1euEBAQwPLysrlqxdjYGBEREbKZnXiiFAoF/v7++Pv7m9f0TU1NcfXqVSoqKrh+/TptbW2EhobywgsvEBkZeVfBS2tktyHzZaurq8zOzpoHy+CLee0rKyv3/UIStkOj0dDb28v4+DgqleorpxEHBwdz8uRJUlJSuHbtGh9//DF9fX24u7uztrZGf38/fn5+EjJi0wUEBJCamoparWZ8fJzbt2+ztLTE5OTkPfeTsUZ2GTLLy8vmjdUmJibMG5YZDAays7NJTk4mLS2NXbt2yYZRNmxhYYGWlhaqq6tpbW3Fy8uLzMxM82ZQ97IxDufn50deXh5KpZL5+XkcHR1ZXV1FpVJJWSKxqTQaDRMTE4yNjTE8PMzY2BiLi4uEhoaaCxGnpKTcd2De2tjdJ2VxcZHe3l5qamqorKw011LbsWMHe/bs4eDBg+zZswcfHx/zngrC9mg0Gtrb2/npT39KQ0MDXl5e5ObmcvTo0QduMvblv7eHhwd5eXkkJSVRVVXF//7v/7Jz505iY2Of6h5Iwn4YDAa6urqoqanh888/p7m5mbm5OXJyciguLua1114jJiYGf39/m1lztaXXyWzo6+ujs7OTrq4uurq6mJmZwdPT0zy9OTQ01Ny/GRERYTNXCOJuS0tLdHZ2UlFRQX19PWtra4SFhZGfn09mZiYxMTGPtfB2amqKW7duERgY+NivIcS9ZqxOT0/T2tpKW1sbvb295kKqnp6e+Pr6EhwcTEREBDt27CAyMvKOBZG2MAN2S4bM+vo6q6urGI1GJicnaWhooLm5mVu3bjEwMICLiwv5+fkUFBSQk5NDVFSUdH/YOK1Wy/z8PJ2dnVRVVXH16lUmJyc5ePAgL7zwAgUFBZZuohBm6+vrzM/PMzMzw+3bt2lqaqK2tpbBwUECAgLMW8EXFRU9sICrLdhyIWMymbh58yYVFRVUVVUxOjqKSqUiLCyMmJgYc6XTjYWZGytche0yGAx0d3dz+vRpc7mO7OxsnnvuOXbt2sX27dule0tY3JfvOioqKvjwww+pq6vDZDKRmJhIdHQ0u3btIioqiqCgILZt24a3t7fN3zVvqcv3lZUVuru7KSsro6ysjIGBATw9PcnKyiIzM5PU1FTS0tKkAvMWYTKZmJyc5MaNGzQ1NdHR0YHRaCQ+Pp6SkhL27dt3R1eCLXQtiK1ro7JEW1sbp0+fprq6Go1GQ2xsLLm5uWRnZxMXF/dY9cGs2ZYKGbVaTVlZGZ999hk9PT1kZWVx4MABDh8+LKVitqDp6WmuXbvGr371Kzo7O3nuuec4evQoOTk5BAUF3RUoEjDC0pqamnj77bfp7e3Fz8+PV199lWeffZb09PQte/G7pVb8bxRy8/DwwNPTEzc3N9RqNdevX6e1tZWZmRn0ej1OTk64uLjYzOwMcaeVlRXKyso4ffo0169fx9XVldzcXPbt22euNCtjbMIaGY1GXFxc8PLywtXVFY1GQ39/P21tbYyNjaHT6fD19X3srY6t0ZYKGVdXVyIjI4mNjTWv0m5tbeXTTz+ltbWV5eVl1tbWcHJyksV0NmijcmxrayvvvfcetbW16HQ6Dhw4wMmTJ8nIyNhyXQ1ia/H19SUzM5PQ0FAMBgMdHR1cv36d69evMzo6islkYvv27fj6+gJb4+57yw38wxdXC4uLi8zNzTE5OcnIyAjDw8OMjo7S19dHYGAg3//+95/4Zmli86yvr9Pa2spvfvMbWltbCQ8PJyEhgbS0NOLi4u7YPE8Ia7e6usrMzAyzs7OMjo7S29tLd3c3S0tLxMXFkZOTs2Vq5G3JPgUHBwe8vb3x9vY2b206NDREXV0dY2NjzMzMPNYOb+Lp0+l0jI+P097eTmNjI+3t7QBkZmZSVFRkrvEkhC1xc3MjPDyc8PBw0tLSGBwcpL6+nra2NmZmZujv7yc7O1tCxpZEREQQEBBg3itEil7ahqGhId59910qKytZWFjgxRdf5NChQ+zYscMmKtAK8TBCQ0MJDQ2lqKiIsrIyTCYTq6urbNu2zea7zOwmZOCLq4exsTGam5t58cUXLd0c8QBjY2PU1dXR1NRET08PwcHBFBYW8txzz5GamrplZ+II+7QxUcXf35/e3l4WFxfJzc3Fz8/P5iex2F0ndm1tLefPn2d+ft7STRH3YDQaGR4epr6+nl/+8pecPXsWlUrFyy+/zN///d+zZ88eCRixZS0sLFBXV0ddXR2Li4tfWTHcFth2RD4Gk8lk/kdYl5mZGS5fvsznn39Of38/AQEBFBYWkpeXR2xsLG5ubpZuohCbait+P9ldyDg5OeHs7Gzz/ZxbydLSEqOjozQ3N3P16lUGBgZwdXUlPz+fZ5991jx5Q4itTqFQ4OjoiJOT05b5jrK7kBHWZXl5maamJv71X/+V7u5uoqKiOHLkCPv27SMwMFAmaAhh4yRkhEVoNBq6urpoaGigpaUFjUZDQkIChYWFlJSUEBsba+kmCiGeALsNma3U52lrdDodbW1tfPTRR1y+fJnl5WVOnjzJwYMHSU5OtvnZNEKI/08+zeKp0el0dHZ2cvbsWdrb21ldXaWoqIi0tDSysrJkXx8htiC7/ERvlQE1W2EwGJifn6e7u5va2louXLiAVqslJyeHl156ib1791q6iUKITWKXISOertu3b3Pu3DkuXrzI9PQ0OTk5FBQUkJeXR0hIiKWbJ4TYRHYXMnIX8/RMTU1x8+ZNqquraWxsRKfTkZKSwnPPPUdeXh7BwcGWbqIQVmfjO2qrjBvbXciIp2N+fp66ujr+/d//nd7eXkJCQvjWt77F4cOH8fX13RKF/4QQX01CRjxRw8PDNDY2UldXR29vLy4uLhw6dIi8vDz27NnD9u3bLd1EIayWyWRibW0NnU6Hm5sbzs7Olm7S1yYhI54IrVbL3Nwc1dXVnDt3jubmZjw8PDh27BgHDhwgLS3N0k0UwuqZTCbW19fR6XRbZlNFuwsZhUKBQqHYMv2d1mB9fZ2WlhY+/fRTGhoaWFpa4qWXXqKwsJCoqCi5exHiEW2l7yi7Cxnx5Gi1WkZGRrh58yYtLS10dnbi7u5OcnIyL7zwAllZWZZuohDCwiRkxGPr6enhs88+43e/+x1ra2scOHCAffv2kZeXh1KptHTzhBBWQEJGPLLp6WkqKyupq6ujr6+PnTt3EhMTQ0lJCenp6VKSXwhhZrchs1X6O58Wk8mEXq9nfX2d+vp63nvvPYaHhwkODubEiRMUFRXh5+dn6WYKIayMXYaMLMh8dNPT09TV1XHq1Cmmp6cJCwujuLiYlJQUEhISJGCEEPdkdyEjAfNo1tfXGR0dpa6ujpqaGm7dusX27dvJy8tj7969sqGYEOKB7C5kxKNpbW3lvffeo7a2FkdHR06ePElBQQERERGyoZgQ4itJyIi7GAwG+vv7qaqqorOzk8XFRZKSkti1axfFxcUkJCRYuolCCBthlyEjXWb3ZzAYGBoa4sqVK/zbv/0bHh4eHD9+nOLiYhITE6XmmBDikdhlyIh76+/v59q1a9TW1jI+Pk5GRgZZWVmUlpYSGRkpASOEeGQSMnbOZDKxuLjI6OgotbW1fP755/T39xMYGMjhw4elJL8Q4mux25CRdTJfmJ+fp7y8nJ/+9Kesrq6SkpLCn/7pn5KRkUFAQIAM7gshvha7CxkZj/nC7OwsXV1dNDY2cuPGDQwGA/Hx8RQXF1NYWCh3L0KIJ8LuQgYkaNbW1rh+/TqnT5/mypUrqFQq3njjDYqLi4mNjbX7348Q4smxy5CxV6urqzQ0NHD69GkGBwdRKBQcOXKEtLQ0cnJyiIyMlIARQjxRdhsy9jQmo9frmZ2dpbOzk7KyMj799FN8fHx49tlnef3114mPj7d0E4UQW5TdhYw9Xqk3NjZSVlbGpUuXUCgUHD9+nJycHFJTU2VDMSHEprK7kLEXWq2WsbEx2tvbqayspLW1FVdXV1JTUzl06BBpaWmy54sQYtNJyGxBRqORoaEhzp07x/vvv49arSYuLo4f/OAH5Ofn4+TkhJOT/OmFEJvPLr9ptnKXWU9PD/X19VRXVzM6OkpERATPPPMMWVlZZGRkyN2LEOKpsruQ2aoBs76+zsTEBJcuXeLSpUu0trYSHR3Nyy+/zDPPPCPrXoQQFmF3IbNhK80uW1lZoaysjN/+9rf09fWhUql48803ycnJITo6msDAQEs3UQhhp+w2ZLaClZUVhoeHaW1t5cqVK9y+fRs/Pz/y8vI4evQou3btsnQThRB2TkLGht28eZOzZ89y+vRpVCoVhw8fZv/+/aSlpUnFZCGEVZCQsTHr6+v09fXR0tJCXV0do6OjZGRkkJKSQkFBAWlpabi6ulq6mUIIAdhpyNjq4L9Go6G/v5+ysjIuX77MzMwMycnJ/NVf/RUpKSk4OjpauolCCHEHuwwZsL2B/6GhISoqKjh16hR6vZ6YmBiOHDlCamoqMTExEjBCCKtkdyFja3cxy8vLDA0NUVdXR3V1NcPDwyQlJVFcXExeXp6UhRFCWDW7CxmwraDZmJo8MjJCWFgYf/M3f0NaWhrh4eG4u7tbunlCCPFAdhky1k6r1dLV1UVtbS03b97EYDCQlJREZmYmRUVFhISEWLqJQgjxUOw2ZKx1TEar1dLX18fp06f5xS9+QXx8PMeOHaOoqIidO3dKzTEhhE2xu2+sja4ya+wya2hooLKykpaWFnQ6HcePHyczM5OMjAxCQ0Nxdna2dBOFEOKR2F3IgHUFjMFgYGlpiaGhIS5dukRVVRUzMzPk5uby7W9/m5iYGKtqrxBCPAq7DBmTyWQ13WVTU1N88sknvP/++zg7O5OcnMyf/MmfkJqaSnBwsASMEMKm2WXIWIPJyUm6u7tpaWmhoaEBk8lEUlISpaWllJSUoFKpLN1EIYT42iRkLGBxcZHy8nIuXLjAzZs3iY6O5i/+4i/Izc1lx44dlm6eEEI8MXYZMpbqglpYWKCyspLy8nLGxsZwdnbmxRdfZPfu3aSnpxMaGmqRdgkhxGaxu5CxRMDo9Xqmp6dpa2vjzJkzXLx4kaioKPbv38/rr78uG4oJIbYsuwuZDU9r4F+v11NRUcGlS5eorKzE19eX7373u+Tk5JCYmCgbigkhtjS7DZnNtrq6ysjICO3t7Vy+fJmuri48PDzIycnhG9/4BomJiTg4OFi6mUIIsansMmQ2u8tMp9PR09PDBx98wLlz51hZWSE3N5e33nqL+Ph4nJycJGCEEHbBLkNmsxiNRm7dukV9fT11dXVMTU0RExNDXFwceXl5JCUlyap9IYRdsduQeZJjMiaTCa1Wy8DAAOfOnePy5cvcvn2b/Px8XnnlFYqLi/Hy8npiP08IIWyF3YbMk+wym5ub45NPPuH8+fOMjIwQHBzM3/7t35Kenk50dLQEjBDCbtldyGyEy9e9kzEajSwsLDA8PExbWxsVFRX09vYSGhpKUVERr7zyCv7+/k+iyUIIYbPsLmTgydzFzM7OcvnyZc6fP09tbS1RUVG89tpr7N+/n5iYGFxcXJ5AS4UQwrbZZch8HRqNhlu3btHY2EhtbS1zc3Ps2bOHnJwc9u7dS0pKiqWbKIQQVkNC5hHMz89z+/Ztzpw5Q01NDRqNhpKSEt58800iIiJwdHS0dBPFQzAajQAyjVyIp8DuQuZxx2QaGxspLy+nuroaV1dX0tPTiY+PJz09nfDwcAkYG1JbW8vS0hIFBQV4eHh87dczmUxf2QV7v+c8zLFC2DK7Cxl4tDEZjUZDd3c35eXlVFVVMTw8TElJCfv27WPPnj0yc8zGLC4ucvXqVcbGxvDz8yMxMRF3d/eHPl6j0bC0tISTkxNubm64u7s/1B2RQqFAr9ezsrLC+vo6JpMJb29vGbsTW55dhszDWl9f59e//jVlZWVMTU2RmJjIG2+8QXJyMiEhIbi5uVm6ieIRbIyn1dbW0tnZiYeHB4cPH6agoOChX6O+vp4LFy4QGBhIWloa+fn5D30eqNVqrl+/TkdHByaTiePHj7Nz587HfTtC2AQJmXuYnJzk9u3btLW10dTUhIODA7t376awsJDi4mJ8fHws3UTxGMbHx7l58yZ6vR6TyUR1dTU7dux46JBZXV2ltbWVsrIyPDw8WFpaIicn56F//uzsLOXl5Vy/fh03NzdycnIkZMSWZ3cho1AoHthdNjs7S3V1NR988AHXr1+nqKiIl156ifz8fIKDg3Fysrtf2ZYxNDREc3MzO3fuxMvLi6qqKnp6eh7q2OXlZbq7u+nv72diYgK1Wo23tzcrKyts27btoV5jenqa6upqWlpaCAkJoa+vj5SUFHx9fWUSgtiy7PIb816D/gaDgWvXrlFZWUlzczMuLi6cOHGCvLw8UlNTCQkJkS8CGzc4OEhNTQ0nTpxg9+7d3Lx5k5mZGfr7+wkPD3/gBcTs7CxVVVVotVpyc3Pp6urCYDBw48YNsrOz8fX1ve+xRqORlZUVhoaG0Gg0hIWFkZiYyMjICC0tLezduxelUrkZb1lsIWq1mosXL9LS0sLIyAg6nc78nWQwGFAqlbz88sscOnTIqiYi2WXIfPluRqfTsbKyQk9PD+Xl5dTX17O0tMSRI0c4efKk7Fa5hYyOjjI2NkZYWBipqanExsai1+tpaWlBqVQ+cPO4iYkJrl27RnBwMN/4xjdobm5mbm6OmpoaXF1dKSkpue+xOp2O9vZ2BgcH8ff3JyoqiqSkJLq6uqirqyMnJ0dCRnyl2dlZPvroIyorK1lcXAQwF9xdXFzEZDLh4+NDUlIS4eHhVlOM1+5CZmPK6MaMoqGhIT788EOuXbtGSEgIBw4cICUlhdjYWIKCgizcWvEkbFxEzM/PExERwfbt2wkLCyMnJ4f+/n4aGxuJiIh4YMj09/dTVVXFK6+8wvPPP09ERATXrl2juroaX1/fB4aMVqulqamJsbExMjMz2bNnDwEBAZw9e5aJiQn+8i//cjPetthidDodo6Oj7N69m5MnT7J9+3aUSiVOTk50dnZSVVXF2toaZ86c4aWXXiIsLMzSTQbsMGQcHBzQarXmvvimpia6urpQKpVkZ2dTXFxMbGyshVspnqT5+Xnz2pjk5GT8/Pzw9vYmJyeH6elpampqyM3Nveexer2ewcFBBgcHcXNzY/v27YSEhODl5cXk5CSffPIJvb29LCws3Hc6++rqKjU1NczPz/Pqq6+yd+9eDAYDLi4uzM3NMTAwQGpq6mb+CoSNUCqVGI1GdDrdXd36S0tLLC4ukpCQwB/8wR/g6upqfiwmJgYHBwcqKipobm5m3759T7vp92V3IePq6sry8jIXLlygvLycW7dukZuby2uvvUZOTg4qlcrSTRRP2MLCAk1NTRgMBnJycvD29gYgPT2dq1ev0tTUxPj4+D2PXV9fp6qqiqGhIUpLS0lOTgbAw8ODuLg4VCoV09PTNDc3k5qaes+xmcXFRRoaGvD09CQzM5Pw8HCWlpZISUmhp6eHmpoanJycSExM3LxfgrAJ91skrtVqUavVmEwmlErlHQEDsLa2hru7OwaDgcXFRfR6/dNo7kPZkiHzoFXUbm5urK2tcf78edbX11lcXGR2dpaRkRFOnTqFUqk0L5Z7kK9a0Pk4q7if9GtaQxsfZkX7gx5XKBR3/S0e5vXW1tbw8fHh29/+NgqFAoPBwK5du3jmmWcIDAwEwMfHh9DQULy9vZmammJychJ/f/87Bk0NBgNXrlxhdHSUEydO3BEE/v7+ZGdnMzU1xbVr1wgMDLwrZNRqNZ2dnXh6erJz505zF6yrqyu7d+9mbW2N+vp6AgIC7gqZ+fl5Ojs7WV1dZWZmhubmZtRqtbmv3RbPh6f9eo/zmpY6Zx0cHNDpdAQHBxMfH2++GDIajYyMjKBWq4mJiSE+Pv6u4zUaDXV1dZhMJlJSUh56xuPTYPMhYzQa0ev1rK6uolAo2LZt2wP/oBEREcTFxZlnZ6hUKiYmJhgdHcVoND7SyfGoj22cvPc6qZ/0z9qM13taj33Vh/xhHltcXCQiIoLi4mJ27dpFdHQ0qampJCQk3PH88PBwUlJSmJmZMU9Z/3K3l1qtNi+e3L179x3rWlQqFaWlpVy4cIGamhpycnLuCor29naampqIiYlh9+7d5oWbG2uvpqen+fDDD4mJibnrvfT09HD58mUUCgUzMzP89re/ZXh42Fwl4Gn83eWcfbjHnsQ5u7KyQkBAAG+88QZHjhwxh4zJZGJiYoKZmRn8/PxwdHRkbm4OFxcX9Ho9SqWSjo4OWltbSUxMpKSk5IGzHZ82mw8ZtVrNjRs3+NnPfoaXlxdvv/22+Y9zLy+++CLZ2dmsrKxgMBhwdHTEYDBgNBrvGTL38rh70TzOcY96zFc9/0E1tB7luAc9/35B/TA/Y+P5X/fvoNPp8PDwID4+Hh8fH44fP37PrtCQkBCysrIYGhqisbGRrKwsc8gMDAxQW1uLl5cXYWFhhIWF3XGX4+3tTUlJCS0tLXz88cd0d3dTVFSEm5ub+T13dnZy48YNEhMTSUtLMx/v5ORESkoKQ0NDTE9P09vby8TEBNu3b2dlZYWmpiY+//xzuru7OXDgAK+88govvPACS0tL5td4lHNDzlnrP2f1ej1ubm7m2WFfnlK/MehfVlbGqVOn+K//+i8UCoX5IjsoKIi0tDReeOEFCgoKrGo9n/W05DENDw9z5coVysrK2LFjB/Pz8/cMmY0TLjIyksjISAu0VFjS/VbWBwcHk52dTXt7O/X19bz66qvmWWbt7e1UV1cTHh5OVlbWHV0QX56lGBERgUqlYmRkhPb2dlJSUlAqlWi1Wnp7exkYGODo0aMkJyfftdYqNDSUoKAgNBoNbW1t+Pj4sLq6ytWrV+nq6sLX15fo6GjzP8L+mEwmpqamUKvV+Pj44OTkxPr6uvkxnU6HQqHAy8sLBwcHVlZW8PT0tJp1fdbRiq/h9u3b1NXVERUVRVZWFouLi+h0urueJ5Vuxb0EBgaSlZWFRqOhoaGB6elp82O3bt3i+vXrREdHs2fPnjvuYr58Pu3YsYPnn3+e2dlZrl69ysrKCvDFBdDIyAhra2vExMTcc0GvSqXimWeewcPDg6qqKtRqNWtra9TU1LCyskJpaanVTEUVlmE0Grl16xbLy8u89dZbfPDBB5SXl3PlyhWuXLlCfX09P/jBD5iZmeHMmTN88sknd5zHlmazIbO6ukpHRwcTExN4e3sTHh6On58fGo0GjUZj6eYJG+Ln50d4eDg+Pj4MDw8zPj7O2NgYo6OjrK6uEhsbS0JCwn1XUUdHR/Pss88yPj7OhQsXmJ+fZ3FxkebmZgBiY2PvuxW3r68vhYWFuLi4cOnSJVpaWhgfH2dychJ3d3d2795tnqgg7FdHRwcDAwOkpaWRlZXF9u3bCQgIIDAwEG9vb6Kjo/H392d2dpauri6Wl5ct3WQzm+0uGx0d5cyZM2i1WvLy8hgaGsLFxYX5+Xk0Go0UsRQPTaFQkJaWxsLCAv39/ZhMJtzd3VlaWiIkJISdO3c+cEV+UFAQ2dnZ/OQnP6GtrY3x8XHUajXV1dWoVCoyMjLuu2+Nl5cXmZmZlJeX09bWRnV1NbGxsbi6uhIeHk54ePhmvW1hI/R6PePj40xPT9/3e21tbc28MNNgMDz2GNxmsKmQ+fJA3vT0NKdOneLgwYMcO3aMiooKBgcHGRgYIDAwUD6c4pHExcUxPT1Nf38/3d3dqFQqXF1dKSgowM/P7yuP9/HxISsrC6PRSGdnJyMjI1RUVFBaWkp+fv59F2oqFArzuEtERAR1dXWMjIwQFxcnW3kLAHOlCj8/v/tWpRgdHeW///u/SUtL4+DBg1Z1kW1TIbMRMEajkfHxcbRaLdu3b2fXrl309vYyOjrK6OgoMzMzFm6psDWxsbHmu4/u7m58fX3Zt28fJSUlD5ytuMHFxYX8/HyMRiNNTU3cvHmTsbEx/P39SUxM/ModOKOjo8nIyKChoYHl5WVOnDghVQAES0tLDA8PA18syLx69SoRERHmcT9HR0fc3Nyoq6tjfn6e8PBwMjMzZZ3M17G2tsbly5cZGhrim9/8JpmZmQC4u7vj4eHB9PS0jMmIRxYaGkpSUhJqtZq+vj7UajV/+Id/+NB7zZhMJjIyMlhYWODtt9+mt7eX6Oho87Y5kYCIAAAL3klEQVQCXyUsLIz8/Hy6u7txdHS855obYX/m5ubo7OykpaWF1tZWKisrcXFxMXeHGY1GtFotiYmJvPXWWxw8eJCwsDCrmuhkcyEzNzdnXqD2ne98x7z6NTg4GF9fX27evMnS0pKFWylsUUBAALt370an0xEUFHTHAsmHWWwXFhZGQkICYWFhuLm5UVBQ8NDTjgMDA8nNzWVtbQ2AXbt2fb03I7YEd3d3duzYwbFjx4iLizOPt3y5V2d9fZ3MzEyOHDlCbGysVQUM2FjIrK+vMzAwQE1NDaGhoeZxF4PBYP7FzszMmMtgC/EolEolL774IgUFBahUqjuqAzzsB3fnzp0cPXoUg8FAeno6O3bseKjjVCoVqamp0kUm7uDv709xcTHFxcWWbspjs6mQ6ezspKysjPb2dhoaGnj99ddxd3dneXkZjUbDxMQEIyMjZGVlWbqpwgYplUoyMzPRarU4Ozs/Vr+2l5cXpaWlKBQK/Pz8zFtKCGGvbCpk2tvbaWxsJDQ0lNnZWSorK823jk5OTiwtLbGyssL8/LylmypskJOT09dak2IymXByciIqKuoJtkoI22YzIaPRaOjt7UWn0/FP//RPJCcns7S0ZA6Zbdu2UVVVxQ9/+ENWV1eZnp4mICDA0s0WdsTa+sKFsAY2ETK9vb1cvHiRyclJ0tPT71tl1MHBgZiYGJydnZmamsLT09Nc9VYIIcTTZxNlZZqbm/nxj38MwMsvv3zf1ddGo5GkpCSCgoJYXFw0F5ETQghhGQqTNdUfuI/29nbKy8tJTk4mOzsbDw+Pe1YYnZ+fp62tDRcXF0JDQ/Hz83tgORAhhBCby+pD5mF2qXuU5wkhhHh6rL677GGDQwJGPGlP4vrLyq/hhNh0NjHwL8Rm0+v1qNVqBgcH8fT0JD4+/p5dsiaTiZWVFfr6+sz185RKJf7+/kRGRt5VmHDj4mdqaorx8XGmpqZYW1vD0dERlUpFYGAgoaGhuLu7y4WS2JIkZITgi3JF1dXV/OQnPyElJYUf//jHuLi43PW89fV1enp6+Od//mfOnj3L3NwcQUFB5Ofn873vfc+8EPP3j6moqODTTz/l6tWrjI2N4erqSkJCAqWlpXzzm98kLi7uK4toCmGLJGSEXRsZGaG1tRVHR0fzv3t6et63m6ujo4OysjKWl5fJzMwkKCiIyclJBgcHaWhoMNc825hwMj4+TlNTE+fOnUOtVnP48GEAlpeXmZycpL29nXfffZfDhw9TWlr61N63sC22PDYtISPs2tjYGNXV1URFRaFQKNDr9ej1+vs+v7GxkbNnz5KXl8f+/fvJy8ujrKyM//zP/6SjowM/Pz9CQ0PNIVNfX88nn3xCe3s7ubm5/PCHP8Tf3x+1Ws1HH33E6dOnef/99/Hw8JCQEfelUCgwGo2sra3dUatx42LI2dkZpVJpdQEDEjLCzkVHR3P8+HGCg4Pp7OzE3d39viGj0Wjo6Oigvb2dkydPUlJSgoODA7t27aKgoIC2tjY6OzvNlZThi1Cqq6ujpKSEQ4cOmcds/Pz8OHToEIuLi1y+fJmenh7GxsYIDg62yi8KYRlfvjOZm5vjr//6r7l58ybu7u7mgNHr9Rw/fpy/+7u/Mx8D1jMZSkJG2C2TyYSvr6+5ekRYWBiurq737CrT6/XMzs4yPj7O7Ows/v7+5okBfn5+JCUlUV9fT09Pzx2LgIeHhxkcHCQmJoaUlJQ7JhNs7GEDoFarmZycxMfHR6pUCLMvTxz57LPPuHr1KuPj40RGRuLk5IRGo2FkZAR3d3fy8vJIT0+3urE9CRlht37/Sk+n0913LEan0zE/P8/6+rp5H/UNSqUST09PZmdnmZ+fR6vVmh/T6/Xm/1YoFHf1mTs7O+Pg4IDBYGB9ff2O1xUCvjj3vv/973Px4kVKS0t5/vnnKSoqwsvLi76+Pt555x3Ky8s5fvw4//iP/8j3vvc9Szf5DhIyQnzJ/ULGaDSi0+kwGo13hZOjo6N5JtrGplIbXFxccHNzM4fJ73N0dESn0+Hu7k5ISIhsDSDu0t/fb56VWFpayrFjx/D09AQgPT0dk8nE3Nwcv/zlL7l+/TpHjx69407b0qyjFUJYOYVCgaOj4z37uQ0GA3q9Hg8PD7y9vXF0dDQ/tjERwMnJCZ1Od9exOp0OJycntm/fTkREhNV8MQjrMD8/z9DQEB4eHsTFxVFUVGQOmA0ZGRns378fJycnRkZGaGxstKqNG+VORoj/o1AozCHy+2Hi4OCAs7OzeZaPs7Oz+TGtVsvKygpKpRIHB4c7QiY5OZmJiQm0Wi3T09Pm3VyNRiPz8/PMzs6SkZFBcnKy+RhrnIYqLMPNzY2EhAR+9KMfoVAoCAkJMT/25fNkYzajTqdDq9ViNBot0t57kZAR4v+YTCZzV9fvd5s5OTnh5eWFSqXC0dHxjo3xFhcX6evrQ6lUEhwcbP7Az8zMEBERwd69e5mdnWVwcJDk5GSUSiV6vZ6Wlhamp6c5cOAAO3fuZGZmBm9vb5yc5GMpvuDq6kpoaCihoaHm/7cRLl++EFGr1RgMBtzd3fHy8rKqc0juzYXd+v0g2Zi6bDKZ7hqAd3JyIiwsjMjISDw9Pblx4wbt7e3AFzN/KioqUCqVZGRk4OXlRW9vL7/61a8AKCwsZGFhge7ubpaWlsw/q76+HrVazeuvv46npyc/+9nP6Ojo2Oy3LWzcl8NFr9fT3d1Ne3s7JpOJwMBAoqKirGpsz3riToinTKFQoFar6e3tZWZmhrq6OqampgD4+c9/TlxcHEFBQURFRZn7wXNycjh48CDDw8P8x3/8B8nJyfT09KDRaCgoKCA/Px8PDw+WlpYYHh5mbm4OgPPnzxMdHc3Y2BgBAQEYDAZu3LhBd3c3KpWK4eFhenp6KCgosNjvQ9getVrNb37zGxobG0lISGD37t0EBQVZ1Z2M9bRECAsYHh7m1KlT1NTU0NHRgVarZXx8nLfffpuUlBQKCwt59dVXzSFTUFCASqXiX/7lX3jnnXfQaDTs3LmTgwcPUlRURHx8PACenp4EBwebvwDgi5lmExMTpKamYjKZmJmZobGxkcbGRgICAtizZ88dYz1CPIjBYODWrVv8/Oc/Z319nTfffJPCwkJcXV0t3bQ7SMgIuxYcHMzzzz9PYmIiCwsL5gFTJycn/Pz8CA8Px8vLy/x8lUpFSkoK3/nOd9i7dy8ajYbAwEASExOJjo42Py8gIIB9+/YRFBTE0NAQDg4OREVFERcXB3wxUPvnf/7nFBcXo1Ao8PLyIjIykqioqKf7CxA2SafT8T//8z+8//77zM3NUVxczLFjx8wXOdbE6jctE8IaPEqBQvh6JT1kdpl4kIWFBVpaWviHf/gHrl27RnFxMX/0R3/EH//xH1u6afckISOEEDbknXfe4Uc/+hEGg4GcnBy++93vkp2dzbZt2yzdtHuS7jIhhLABo6OjVFVV8fHHHzM8PMyRI0f41re+ZS7UCtZ5Fyx3MkIIYeVmZmY4d+4cP/jBD9BqtRw5coQ33niDwsJCSzftK0nICCGEFZudneUXv/gFly5dYmlpiby8PE6cOEF6evoDj7OWuxrpLhNCCCul1WoZGBjg17/+Nc3NzfzZn/0Z+/fvJzY2lpWVlTv2LoIvqnq7uLjctyCrJUjICCGElRoYGODKlSuMjo4C8O6771JeXo63tzdGo9FcmUKn0+Ho6EheXp55KwA/Pz9LNt1MQkYIIayYp6cnpaWl3L59G5PJhF6vR6PR3PGcjZDR6XR3bTdhaTImI4QQVkqv17O2tsb6+vodtfV+38b4i4uLC0ql0lwR3BpIyAghxBZkLQP/1hF1QgghnihrCBiQkBFCCLGJJGSEEEJsGgkZIYQQm0ZCRgghxKaRkBFCCLFpJGSEEEJsGgkZIYQQm0ZCRgghxKaRkBFCCLFpJGSEEEJsGgkZIYQQm0ZCRgghxKaRkBFCCLFpJGSEEEJsGgkZIYQQm0ZCRgghxKaRkBFCCLFpJGSEEEJsGgkZIYQQm0ZCRgghxKaRkBFCCLFpJGSEEEJsmv8Hne7V/P7sCh8AAAAASUVORK5CYII=)
The resistance is connected as shown in the figure below. Find the equivalent resistance between the points A and B.
![](data:image/png;base64,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)
physics-General
Maths-
The cosecant function whose period is 4 is
The cosecant function whose period is 4 is
Maths-General