Physics-
General
Easy
Question
A block of mass m moving with a velocity v0 on a smooth horizontal surface strikes and compresses a spring of stiffness k till mass comes to rest as shown in the figure. This phenomenon is observed by two observers:
A: standing on the horizontal surface
B: standing on the block
![](data:image/png;base64,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)
To an observer A, the work done by the normal reaction N between the block and the spring on the block is
- zero
- none of these
The correct answer is: ![negative fraction numerator 1 over denominator 2 end fraction m v subscript 0 end subscript superscript 2 end superscript](data:image/png;base64,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)
Related Questions to study
physics-
A block of mass m moving with a velocity v0 on a smooth horizontal surface strikes and compresses a spring of stiffness k till mass comes to rest as shown in the figure. This phenomenon is observed by two observers:
A: standing on the horizontal surface
B: standing on the block
![](data:image/png;base64,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)
To an observer A, the work done by spring force is
A block of mass m moving with a velocity v0 on a smooth horizontal surface strikes and compresses a spring of stiffness k till mass comes to rest as shown in the figure. This phenomenon is observed by two observers:
A: standing on the horizontal surface
B: standing on the block
![](data:image/png;base64,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)
To an observer A, the work done by spring force is
physics-General
physics-
A 1.0 kg block collides with a horizontal weightless spring of force constant 2.75
as shown in figure. The block compresses the spring 4.0 m from the rest position. If the coefficient of kinetic friction between the block and horizontal surface is 0.25, the speed of the block at the instant of collision is
![](data:image/png;base64,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)
A 1.0 kg block collides with a horizontal weightless spring of force constant 2.75
as shown in figure. The block compresses the spring 4.0 m from the rest position. If the coefficient of kinetic friction between the block and horizontal surface is 0.25, the speed of the block at the instant of collision is
![](data:image/png;base64,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)
physics-General
physics-
In the figure shown all the surfaces are frictionless, and mass of the block, m = 1 kg. The block and wedge are held initially at rest. Now wedge is given a horizontal acceleration of 10 m/s2 by applying a force on the wedge, so that the block does not slip on the wedge. Then work done by the normal force in ground frame on the block in
seconds is
![](data:image/png;base64,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)
In the figure shown all the surfaces are frictionless, and mass of the block, m = 1 kg. The block and wedge are held initially at rest. Now wedge is given a horizontal acceleration of 10 m/s2 by applying a force on the wedge, so that the block does not slip on the wedge. Then work done by the normal force in ground frame on the block in
seconds is
![](data:image/png;base64,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)
physics-General
physics-
Equal force F (> mg) is applied to string in all the 3 cases. Starting from rest, the point of application of force moves a distance of 2 m down in all cases. In which case the block has maximum kinetic energy?
1) ![](data:image/png;base64,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)
2) ![](data:image/png;base64,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)
3) ![](data:image/png;base64,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)
Equal force F (> mg) is applied to string in all the 3 cases. Starting from rest, the point of application of force moves a distance of 2 m down in all cases. In which case the block has maximum kinetic energy?
1) ![](data:image/png;base64,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)
2) ![](data:image/png;base64,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)
3) ![](data:image/png;base64,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)
physics-General
physics-
The dumbell is placed on a frictionless horizontal table. Sphere A is attached to a frictionless pivot so that B can be made to rotate about A with constant angular velocity. If B makes one revolution in period P, the tension in the rod is
![](data:image/png;base64,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)
The dumbell is placed on a frictionless horizontal table. Sphere A is attached to a frictionless pivot so that B can be made to rotate about A with constant angular velocity. If B makes one revolution in period P, the tension in the rod is
![](data:image/png;base64,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)
physics-General
physics-
A pendulum bob is swinging in a vertical plane such that its angular amplitude is less than 900 . At its highest point, the string is cut. Which trajectory is possible for the bob afterwards.
A pendulum bob is swinging in a vertical plane such that its angular amplitude is less than 900 . At its highest point, the string is cut. Which trajectory is possible for the bob afterwards.
physics-General
physics-
A car travelling on a smooth road passes through a curved portion of the road in form of an arc of circle of radius 10 m. If the mass of car is 500 kg, the reaction on car at lowest point P where its speed is 20 m/s is
![](data:image/png;base64,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)
A car travelling on a smooth road passes through a curved portion of the road in form of an arc of circle of radius 10 m. If the mass of car is 500 kg, the reaction on car at lowest point P where its speed is 20 m/s is
![](data:image/png;base64,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)
physics-General
physics-
Tangential acceleration of a particle moving in a circle of radius 1 m varies with time t as (initial velocity of particle is zero). Time after which total acceleration of particle makes and angle of 30° with radial acceleration is
![](data:image/png;base64,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)
Tangential acceleration of a particle moving in a circle of radius 1 m varies with time t as (initial velocity of particle is zero). Time after which total acceleration of particle makes and angle of 30° with radial acceleration is
![](data:image/png;base64,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)
physics-General
physics-
A truck starting from rest moves with an acceleration of 5 m/s2 for 1 sec and then moves with constant velocity. The velocity w.r.t ground v/s time graph for block in truck is ( Assume that block does not fall off the truck)
![](data:image/png;base64,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)
A truck starting from rest moves with an acceleration of 5 m/s2 for 1 sec and then moves with constant velocity. The velocity w.r.t ground v/s time graph for block in truck is ( Assume that block does not fall off the truck)
![](data:image/png;base64,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)
physics-General
physics-
The acceleration of 10 kg block when F = 30N
![](data:image/png;base64,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)
The acceleration of 10 kg block when F = 30N
![](data:image/png;base64,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)
physics-General
physics-
The maximum acceleration of 5 kg block
![](data:image/png;base64,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)
The maximum acceleration of 5 kg block
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAATwAAADQCAYAAACa9N1LAAAgAElEQVR4nO3deXRU9f3/8eedLZPJzGQlewghKyGBEAoGoSAiKIIgyherYFuXVsXWiv2d9nTHqtVvbbH9Wttaa+uCC4hSF1ChAiIgS0UWIUREAtn3TJbZZ+7vD85MHRMgIJCEeT/O4Xice2fyucnMaz6fz/0siqqqKkIIEQY0/V0AIYS4UCTwhBBhQwJPCBE2JPCEEGFDAk8IETYk8IQQYUMCTwgRNiTwhBBhQwJPCBE2JPCEEGFDAk8IETYk8IQQYUMCTwgRNiTwhBBhQwJPCBE2dP1dABFeOjo66Ojo6O9iDAharZb4+HgMBkN/FyVsSOCJC2rTpk385S9/wel09ndR+pWiKERHR/Pb3/6W3Nzc/i5O2JDAExdUfX0927dvx263E46LbSuKglarJTo6mvj4eOx2e38XKaxI4IkLyufzYbfbycjI4Oc//zkaTXh1I/t8PiorK/nNb36Doij4fL7+LlJYkcATF5zP5yM2Npbrrrsu7ALP6/Wye/duHnjgAQm7fiCBJ/qFRqPBbDaHZeCZTKb+LkbYCq93mxAirEngCSHChgSeECJsSOAJIcKGBJ4QImxI4AkhwoYMSxFCnJLH46GyspLGxkbcbvcZPTctLY3U1FTMZvN5Kt2ZkcATQpyS3+/n008/Zd++fezatYuKigo0Gg3R0dGMHDmSiIiIkHM7Ojpobm6mtraWmTNnctddd0ngCSEGh4iICGbNmsXUqVNZsWIFa9euRVVVSktLueeeexgyZEjwXK/XS1tbG1u3buXBBx+ksrKSzs7Ofix9KAk8EZb8fj9A2M30+CpMJhNDhw4lKyuLzz//HIPBQEJCAomJiSHnpaamUlhYyKeffkpjYyMej6efStyT/LVF2FFVlfLycnbs2IHD4ejv4gwqGo0GrVZ72vMUReG2224jISFhQAWe1PDEgObxeHj77bf55JNPmDFjBl/72tdOem5LSwurVq1i586dxMfHc9VVVzFu3DgsFgtwYtGCnTt3snLlSjZu3EhZWRn5+flERkZeqMu54Px+P3V1dTz11FO0tbUFa7ZwYgHSjIwMvvOd75yXec3Dhg3j1ltvJTU19Zy+7lchgScGJLfbzVtvvcU777zDtm3biI2NpaSkpNdz/X4/FRUV/OlPf8LtdnPttdfS3d3NP/7xD6qrq5k/fz4mkwlFUYiJicFsNmOz2WhpaQkJgItRYKHRiRMn8vjjj7Nnzx5sNhvw3wUcdu3axe23387YsWOJjY09Zz/baDRSUFAwoLoNJPDEgOT3+7Hb7cFw0ul0Jw2no0eP8sc//pFdu3bxl7/8hTFjxuDxeKitrWXVqlXExsZyzTXXoNFoyMnJYd68ebz77rsX+Ir6h6IoREVFMXXqVEwmE8uXL2fNmjVUVVUBYLPZeO211zhy5Ajz589n3rx5ZGVlodfrz+rn+f1+Ojs7OXr0KIWFhQNu+XoJPDEgGY1GbrrpJqZPn86ePXtobW3t9TxVVdmxYwfr1q1j7NixjB8/HgC9Xs/VV1/Nxo0b+dOf/kRpaSlpaWno9Xqio6NDhlL0B1VVcbvdfPzxx3R1dV2wn/n1r3+dY8eO0dDQgNvtRlVVPB4P//nPfzh69CgVFRUsXLiQoqIikpKSzvhnOJ1OKioqOHjwIDk5ORJ4QvSVRqMhMTERq9V60sDz+/3s3bsXp9NJaWlpyLHs7Gxyc3N59dVXWbVqFT/4wQ9O+rP8fn9IE1ev12MymTAajcFz7HY7XV1duN1uIiIiiI6O/kof6M7OTn784x9f8FDweDy93nhoaWnhueeeY9euXSxZsoRbbrkFRVFO+joul4va2trgTQlVVamvr+ell16iqKjovJX/q5DAE4Oay+WisbERs9nMsGHDQo5ptVoSExOpra3l3XffPWngqapKR0cHP/3pT+nq6gp25s+dO5eysjLgREhs2LCB5cuXc/z4cfLz87nnnnsYOXJkMBS0Wu0Z9VcFBuleyD4uVVXx+XynXG25q6uLxsZGvF7vSZu2Ho+HgwcPcttttwUD2+Px0NLSQnd3Nw8//PB5Kf9XJYEnBrWDBw9SWVmJoijodKFvZ41GQ1xcHKqqnnKzHEVRiIiIoKGhAZ1Ox+2338748eOJjo4GTnyQH3nkEdavX89dd93FxIkT2bBhA4sWLUKv15OWlobJZOL73/8+kydP7lO5FUUhNjaWJ598ksLCwrP/BZyhjo4OnnzySV555RW6u7tDjhkMBhYsWMDixYspLi7u8fv8Ip1OR15eHr///e9JSEgATjRn9+/fz6pVq05ZM+xPEnhiUKutraWtrY2YmJhem1E6nS7YX3YybW1trFy5kuTkZG699VZGjhxJVFQUGo0Gr9dLTU0Nzz//PLfccgtTp05lyJAhzJgxg8rKSh599FEWLlzI5ZdffsbbLep0OjIzM8nLyzvj6z4bu3bt4oknnuDf//53j20yi4uLuf3227nmmmtISUkJacr3RlEUTCYTOTk5wYHHqqqSmpqKqqoDdkc6CTwxqLndbjweD1arlbi4uF7PUVUVr9fb67H6+np2795NZWUl3//+98nJyQkZl+d2u9m1axeNjY0UFRWRkJCAVqslISGBqVOn8uCDD/LOO+8wf/58rFbrGZdfq9Wesib1Vamqis1mY/Xq1Tz99NMcOHAAm82GqqpoNBpiYmK4/vrrWbhwISNHjiQuLq7PTexArfqLzd74+Hguu+wyjhw5cl6v62wNvBIJcQY0Gk3wA/rlZlTgDqSiKL02sRoaGnj11VfZu3cv999/PyNGjOj1Qxp4rK2tDZfLhU6nQ6vVYjabUVWV48eP43K5zsPVnRtutxuHw8GUKVOYOHFi8HGNRkNycjLXX389ycnJ5ySg9Ho96enpxMXFDbg7tCCBJwa52NhYzGYzbrebtra2kHmdgZsRgY2vv6yjo4MPP/yQQ4cOBW9EfJnBYKCoqAiTycR7771HWVkZeXl52O12Pv/8c3Q6HdOnTz+r2t2FoCgKCQkJ3H777b0e12g057QmpihKcOjPQDRwhkALcRby8vJIS0ujvb2dTz75JOSY3++ntbUVi8XSa//esGHD+MY3voHP5+OOO+7g4MGDPfr6tFotKSkpjB8/ni1btrB9+3bq6+s5ePAg7777LqWlpfz0pz8lOTn5vF7nV6HRaDAYDL3+G4jNzvNJAk8MaikpKYwYMYK2tjY+/vjjkGM+n4+WlhaGDh3K/PnzezxXr9dz+eWXs2zZMhobG1m0aBEVFRUhHe6Bzvnf/e53lJWVsXv3bh588EFeeOEFrrzyStavX09aWtqAmj4lTi684l1cdDQaDaWlpVitVvbt2xdybNeuXRw6dIicnBzGjh3b6/MjIyOZOnUqv/rVr3j00Uf52c9+xq9//evgvF2/309TUxOLFi3i4YcfZuzYscH+QL1eT0RExIAdgnE+OBwO2tvb+7sYZ00CTwxoHo/npHdYAyZNmsStt97Kiy++yMaNG5k0aRI+n4/XXnuNhIQE7rvvvpCpZDU1NcHpXIEFBW6++Wb+/ve/s3nzZtauXUtGRgbx8fG4XC727NnDkSNHePjhhxk2bBgxMTHBkFMUhcTERG688UZSUlLO3y9iALDb7Rw/fpympibgxN9moA4/ORkJPDEgeTwePvjgA6qrq3G5XJhMJjZt2oTBYGDGjBkh5yYkJLBo0SIsFgtr1qxh/fr1GAwGLBYLP/7xjxk9ejRworZWXl7Otm3bSEpKQqvV8sYbbzBlyhSSk5OZOHEin332GQcOHODVV19l7NixFBQUMHToUBITE2lsbKSzs5Ouri5sNhterxev14vBYKCyspJ77rmHnJyc/vh1nVder5f9+/dTXl7Ovn37mDBhQvBG0Ouvv05WVlbw9zTQSeCJASkwxishIYHFixfj8/nQ6/W97o2gKArp6el861vfory8nIqKCiwWC2PGjCE1NTVknJjRaGTSpEl87WtfC/bP6fV69Ho9d911V3BB0IiICKKiolAUBYPBwLx58yguLsZkMmGz2WhtbcXr9eJyuaisrGTPnj3s2bPnogw8gJiYGPLz8xk+fHhIrU6v12MwGDCZTP1Yur6TwBMDkk6n6/M0LTgRehaLhfHjxwdXTPkyjUZDdnY22dnZvR7/4hg1ODGspbGxkeeee4758+czYsSIHqusqKpKZ2cnv/rVr3pM1bpY6HQ6srKyyMrK6u+ifGVya0mIk/D5fBw8eJA//vGPtLe309zcTHt7Ow6HA5fLhd1up6WlhebmZmw2W3BOqRi4pIYnxEkEmrN2u525c+dSVFTErFmzuOSSSzCbzTQ1NbFmzRq2bdvG/fffz5QpU/q7yOI0JPCEOAmtVsvYsWPZvHkzL7/8MqtWreKRRx4JrpWXl5fH3Llz+X//7/+Rmpp62gn3ov9J4AlxChEREZSWljJ06FAWLVpEa2trcCiLxWIhISGB2NjYPu3kJfqfBJ4QpxBo1qamppKSkhKyn204DTi+WEjgDTKBIQHyYbvwFEWRmtwgJ4F3HrW2tnLs2DFaWlrQ6XSYzWZycnKIjo4+48Cy2WzU1NRQX19Pbm4uGRkZ56nUQly8JPDOk7a2NtasWcOKFStITU3FbrdTWVnJD3/4Q6ZNm9bn5YRUVaWlpYUNGzbwxBNP4HA4+NnPfiaBJ8RZkMA7D1RV5dFHH2XLli386Ec/YubMmWi1Wh544AGWLVuG0Wjkqquu6lMtz+fz8eCDD7Jt2zY++eSTkw6aFUKcngw8Pg/+/e9/s379ejIzMykrKwv2+3zve9/DaDTyz3/+s8fabSej0+l44IEHePbZZ89o5oEQoicJvPNg69at1NXVkZ6eTkxMTPDxmJgYhg4dGtw4OnDH73QsFgvZ2dkMGTLkfBVZiLAQNk3a2tpatm7dit1uZ/bs2cTHxwePNTQ0sG3bNmw2G7NnzyYhIQGn08mKFSuoqanp0+vr9Xry8/O54oorOHz4MG63m+jo6JAVZRVFITMzE7vdTkVFBU6ns8+TrgOr057t3Vmv14vD4eixW1XgtaOiosJu9VsRfsLmHd7c3MxLL71EU1MTX//610MCL7BN3/Hjx/n6178enBPp9XpPuWHxF2k0Gvx+Pw6Hg5qamuD4rS9LT0/HYrFgs9nOKPC+imPHjrF9+3a2bdvWI/CGDRvGZZddxrhx4857Ob6oqamJp59+OuxWCvb5fBw7dgytVitDi/pB2ASe3+/H5XLhdDp7NCV9Pl+PY0ajkW9/+9tntMChRqOhpqaGzs5OjEYjsbGxPc6JjY3FZDJht9tPuVfqueByuTh8+DDPP/88K1eu5NixY8Hr0Wq15OXlkZeXR0ZGxgWr3UVFRZGRkYHX6+Whhx66ID9zoAns32o2m6VWfYHJb/skAhvA9HX7PUVRiIyMxG634/P5iIuLO2Wfm9PpPO1KvmcrUPaDBw/yi1/8gu3btwfDVVEUjEYj6enpPPzww0ydOpWIiIgLts1gUlISl19+OT6fD5/PF7YDeRVFISoqqtf1/cT5I4F3Ep2dndx8883s37+/T+dHRkZy9dVX881vfvOU5/l8vmAt8nwsj62qKu3t7SxZsoQ33niDjo6OkON6vZ7LLruMO+64gyFDhnDgwIFzXoZTqayspK2tDb/fj0ajISEhISybdoqiYDabZcGBC0wC7yTMZjNPPvnkGdXwLBYLfr8fnU4XXDPty6qqqmhrayMvL6/HYpJflaqq/Oc//+H222/ns88+6/UGhcfjYcOGDezYsaNf+s/cbnewthkZGcm1114bsiKxEOeTBN5JaLXaM57NoCgKXq+XuLg4Dhw4QF1dXY9zGhoacLlcpKWlnfPNmxVFIScnh3vuuYdf/vKXNDQ09DhHp9NRVFTE0KFD+yVoGhsbqaqqQlVVDAZD2N20EP0r7ALP7/fj8Xj6dO7ZfBj1ej2FhYXs2bOH+vr6Hv1U9fX1xMbGMnLkyHNew4MTY/0WLFhAUlISK1euZP369dTX1weP+/1+amtrKSkp4X/+538YOnRojyblBx98QFtbGz6f75w3u9vb24PXrSgKnZ2dYdukdTqd/Pvf/z4v/XhGo5GcnBzy8vLO+WsPZmEXeF/eV9Nut3Ps2DFqampwuVy0trZit9vp6OggPj7+rGpBV1xxBZs2baKpqQmHwxF8Qzc1NXH06FFyc3O55JJLQj7oe/bswWKxkJycTFRU1FlfX6BpPWvWLAoKCigtLeWf//wnFRUVuFwufD4fdXV1vPnmm+h0OhYvXkxBQUHIEJrHHnuMPXv20NnZ2efB0X3l9/v7PNTnYqcoCh9++OE5DfzA5kcxMTHcfffdEnhfEnaB197ezhtvvEF3dzcajYa2tja2bNmC2+2mtbWVN954gwMHDlBQUEB0dPRZBd6UKVO47rrr2LdvH7t27WL06NFotVpeffVVdDodCxcuZMSIEcCJfjeXy8VvfvMbTCYTP/jBDygpKenxIeju7sbpdOLz+fpUQw00b++++26GDx/O008/TUVFRchQmA0bNmAymbjzzjvJzs4O1kSrqqqoqKggOjqalJQUaXYOIoFxfp2dnYN6w+zzJWwCz+v1otPpcLvd/OMf/2D58uUYjUYKCgq4++67SUhI4M9//jP/+Mc/iI2N5Y033uh14HBfWCwWvv3tb/O3v/2N3//+99xyyy0YDAZWrlzJN7/5TebMmRMccBwYQlJeXk5LSwuXX345xcXFIeOzAjMzAvuzNjU10d7ejtVqPW0Y6fV6rrnmGiZMmMDu3btpbm4OOa4oCjU1NQwdOjSk6W2327nrrrv40Y9+JDcVBpGOjg4WLFjAoUOH+tx1E07CJvBaWlowm83cf//9xMbGYrVaKSsrIyYmBp1Ox5QpU5g7dy5Hjx5l+vTpREREfKWmxtChQ1m6dCmNjY189NFHuN1uVq9ejdVqDXldrVZLamoq999/P3FxcZSWlvYYjFpVVYXb7WbJkiWoqoqiKBw+fJhRo0ZhMBhOW05FURgyZAhXXnnlGV1DYMrZ2Qa/uPDCeWxjX4RN4LlcLurr6+ns7OTWW28NTv0K1JACtb2cnJyvHHYBOp2OpKQkpk+fjqqqp3zdwBJSvY28z87ODhm7pyhKsK8mHDv8hThbYRN4ra2twU74yMjIHscDAXKup/potdo+feP2VqYAmX4kxLkRNr3RjY2N1NfXc/To0f4uihCin4RN4EVHR5OVlUViYmJ/F0UI0U/Cpq10xRVXkJ2dzbBhw/q7KEKIfhI2gZednS37QQgR5sKmSSuEEBJ4QoiwIYEnhAgbEnhCiLAhgSeECBsSeEKIsCGBJ4QIGxJ4QoiwIYEnBi1VVXv998Xj77//PkuWLOHFF1/sx5KKgSJsZlqIi4fH42HdunU8++yzIav6xsbG8q1vfYvp06dTX1/Pk08+yerVq1EURWbZCEACTwxCLpeLxx57jMbGxmCNTlEUIiIiKCwsRKPRYLFYuOKKK9i+fTuHDx/u5xKLgUICTwwqDoeD/fv3k5KSwq233orFYgkei42NDS4OERMTw6RJkxgzZowEngiSwBODSmtrK08++SR33HEHY8aM+Uo7vJ3OF2uP4uIggScGDY/HQ3l5Oa+88grDhw9Ho9GQkpJCfHw8Foulz8HU1NSE3W4H/rtvxxc3Re/u7qazsxO73Y5Op8NgMBAfH49Wqw3+DAnBwUnu0opBo7q6mldeeQWHw8HSpUuZNGkSo0aN4rHHHsPhcPTpNVRV5ac//SmjRo1i9OjR3Hzzzaxfvz7k+Ouvv87VV1/Ntddey8KFC5kxYwZHjx6lu7sbu90uu4ENYlLDE4NGeno6v/rVr7j77rv58MMP+cMf/sCRI0d47LHHqK6uZtmyZSF9eieTkZHBVVddxcKFC5kwYUJIs/iFF17giSeeYMGCBXzzm9/E5XKxdu1aZs+ezbRp0xgxYgRFRUVMnTpVanmDkASeGDT0ej2pqamkpKQwdOhQxo8fz44dO3j22Wf517/+hdFo5PHHHz/p891uN08//TRut5t77rmH4uLikKas0+nk5ZdfJiYmhsmTJ5OamorX62XWrFn8+te/ZtOmTcycOZNx48ZJ2A1S0qQVg46iKMTExDBmzBhuuukm7rzzTqKioli3bh3V1dXBLS2/qL29nZdeeona2lrmz59PSUlJSNipqorX66W6uhqz2UxMTAzw3602ExMTqa2txeFw9KkWKQYmCTwxqFmtViZNmsTll19OZ2cnGzduxOv1hpzjdrvZu3cvjzzyCMOHDycjI6PXu7sajQa9Xk91dTVNTU3BxwN7AWs0muA+xmJwkr+eGPSGDx/OjBkzcLlcVFRU4PP5Qo57vV66u7vp6Ojgr3/9K4cPH8blcoWcoygKer2eESNGUFVVxa5du2hvb8dut3Po0CGampooLS1l+PDhF/LSxDkmfXjioqDX6zEajYwaNarHxucmk4mysjIuueQSli1bxnPPPUdCQkJwaMsXX+OHP/whNpuNjRs3MnLkSIYMGcITTzxBTk4Oy5YtY9SoURf60sQ5JIEnBj2/3097eztWq5UZM2ag1+t7nBMXF8e3v/1t1q1bxzPPPENqair33nsvZrO5x3klJSVMmDCB3NxcPvvsM377298SFxfXI0jF4CNNWjFo2O12qqqqcLlcwVkQfr+ft99+m+eff54bbrgBq9V60juoJpOJl19+meLiYv7v//6Pxx9/PKT563a7WbJkCWazmbFjx5KSksKll16K1WrF7/fj9Xp7vSEiBg+p4YlB4+OPP+a+++4jLi6OoqIiEhMTqaqq4vjx41x//fXMmzcv2ET1+/00NzdTV1eHw+Ggrq4Ol8tFWloat912G4888ghPP/10sOan1Wrx+XxUVVWxd+9e3nrrLaKiokKavBqNhhtvvJFZs2aF3OEVg4cEnhg00tPTmT59Oh9//DHl5eX4fD5iYmKYPXs2o0aNIjk5OXiux+OhurqaSy+9lMzMTNLS0qisrCQ/P59Ro0bx3e9+l/b2drxeL5999hlJSUlER0czY8YMDh8+jNVqxel00tzcTHd3N36/n88//5y6ujp0Oh1z587FYDD0429DnA0JPDFoZGZm8pOf/IRPP/2Uzs5O0tPTSU5OJjIyskczVq/XM2rUKIqKigBC5sCWlpZSUlISPFdRFLRaLXa7naSkJObOnUtmZiZOp5OWlpZg4H322Wfs2bOHnTt3UlZWRkZGxoW7eHFOSOCJQSUqKooxY8ac9jyNRnPSGlhvj7vdbl555RWqq6uJiooiISEBRVFCQu3SSy+lsLCQTZs29RjWIgYHCTwR9lRVpbu7mwceeICCggImTpyIxWLBaDSi0+lQVRWXy4XNZmPFihWkp6fLCsqDlASeCHuKomAymZgzZw4vv/wy8+bNw2q1UlxcTFZWFl6vly1bthAREcEjjzzCnDlzZC7tICWBJwQnmrlLly7lrrvuYsWKFbz11lvU1tZiNBoZO3Ysjz/+OIWFhaSkpMh4vEFMAk8ITtTy4uLiiI2N5c4772T+/Pm43W6MRiNWq5W4uDiMRqPMpR3kJPCE+AJFUUhOTg4Z4iIuHvJ1JYQIGxJ4QoiwIYEnQqiqGpynKsTFRgJPhJAJ8uJipqjydX7GDh06xEMPPcTRo0f7uyjnjM/nw+l04nK5OHbsGA6HgyFDhjBkyBAZczaI+P1+jh07htvtJiMjg5SUlP4uUr+YOnUqS5cu7TGESO7SnoXu7m4OHjxIeXl5fxfljPn9/h41uEAzNvDdF/hvU1NTyFLnYvBQFIWqqirq6ur6uyj9IjMzs9fHJfDOQlpaGnfddRetra39XZRTUlUVt9uNzWbjyJEj7N+/n9raWjweD36/H0VRMBgMWCwWhg0bRklJCampqWg0GunHG+QCf9twHSSdl5fX65hJadJeRAKLVNrtdqqrq6msrOTzzz/nwIEDVFRUcOjQIdra2oiIiCAjI4OhQ4eSnZ3NiBEjyM/Pp7i4mMTERGnCiouWBN4gFtha0G6309bWRlNTE8ePH+fIkSN88MEHbNu2ja6uLoxGIzExMQwZMoSMjAwyMzOZPHkyEydOlIATYUUCbxBRVRW/34/H48HhcNDR0UFDQwP79+9nzZo1fPDBB7S1taHT6YiMjMRisZCUlMTIkSOZMWMGM2bMICEhob8vQ4h+I4E3iDgcDpqamti7dy/PP/88a9euxe124/f7UVUVg8FAfHw8+fn53HLLLcycOROr1YpGownuqypEOJPAG6D8fj9ut5uOjg527NjBq6++yp49e7DZbDgcDrq7u/F6vVgsFkpLS7n22mspKysjOjo6WLuLjIyUkBPiCyTwBghVVXE4HLS1tbFv3z4++OADDhw4QGtrK42NjTQ2NuLxeLBarYwYMYLLLruM4uJi4uLiSEpKIjExEavVGnZ35ZxOJw0NDSiKQlpa2oC+/sCgbtkLo/9I4PUTn88XrMEdOnSIPXv2cPToUSorKzl+/DjV1dV0dXVhMpkoKChg1KhR5OTkMGzYMDIyMsjKyiI+Pn5Q3nCoq6vjo48+wul04nA4gkNgNBpNj8Dyer3B45GRkWRnZ1NaWgqc+JJ4+eWXWb58OSaTiZtuuol58+Zd2IvpA7fbzZEjR/jwww/xer1897vf7e8ihS0Zh3cWVFXF4/Fgt9vRaDRERUWdtmbh9/txuVx0dHRQV1dHdXU1FRUVlJeXBwcxu91uoqKiSE5OZty4ceTl5ZGbm0txcTGFhYXExsZeNE1UjUZDdXU1Tz/9NB0dHfj9fsaNG8fo0aNDzuvo6KCxsZEjR47Q1dXFDTfcEAw8gNWrV7N27VrMZjNarXZABZ7P56O6upqdO3eyYsUKdu/eTUlJiQReP5LA6wNVVfH5fMF9DZqamqiqqqK1tZX8/HxKS0t7BN4X76a2trbS0NDAsWPH+OSTT9ixYwd79+7FZrNhNBqJi4sjLy+PzA8YYYEAABDKSURBVMxMRo4cybhx4xg3bhxDhgzppys+v1JSUkhJSWHy5Mm8++67vP/++zgcDu69917uu+++kFqrx+OhqqqKl156iWeffZZjx46FvFZ+fj5ZWVno9foBtc9EYJ+MzZs3s3r1ajZv3ozNZgvZLU1ceBJ4p6GqKl1dXRw9epTDhw/z3nvv8frrr9Pe3s7ChQuZOHEier0+OGTE7XbjdDqx2WxUV1ezb98+1qxZw3vvvYfP50On0wVX0c3NzSU/P585c+YwdepUrFbroGyini2dTse0adP46KOPcDgcvZ6j1+sZPnw4CxcupK6uLmSqm6IofO9732PMmDEoisKVV155oYreJ0ajkUWLFnHFFVfwne98h3fffbe/ixT2JPBOw+12s3z5cn7+85/T0dERDLYZM2Zwxx13MHz4cPx+P3a7naamJrZt28YLL7zA9u3b6erqCs5RNRgMJCcnM378eL7xjW8wZcqUYMBpNJqLpql6vmRmZnL55ZezfPnykMcTExO59tprAQbU7zAwtQsIDvoW/W/AB57P56OjowOv10tUVNRZ7ytgs9no7OxEVVVMJhNxcXGnrU15vV5efPFFli1bRnt7e3DSfV5eHosXLyYqKopXXnmFN998k//85z84nU66u7vp7u5Go9GQkpJCSUlJcMhIZGQkJpMJs9ks+yOcIUVRmDFjBuPHj+/x+ECvFQc2+hb9b8AGnt/vp76+nrfffptNmzaRlpZGU1MTM2fOZNq0acTGxvbpdbxeL2vWrGH16tV8/vnneDwe4uPjufnmm7nmmmswmUy9Pk9VVV5//XX+9Kc/cfz48WDYKYqCz+dj2bJlOJ1OmpubaW1txe12Y7VaGT9+PFOmTCE3N5ekpCTi4+NJTEwkOjp6wH8wByqn04lGo8FsNmM2m0OO+f1+bDZbcEmkLwci/PcmU0tLCw0NDdTW1mIymcjJySEpKQm9Xn+hLkX0swEbeIcPH+bFF1/k0KFDzJo1i+zsbPbt28eKFStwu91ce+21Jw2rAL/fz3vvvcf27dvJycmhsLCQjz/+mHXr1lFVVUVmZiajR48mMjIy5HmqqrJ582b+8Ic/cOjQIdxud8ix6upqGhoaiImJITc3l5kzZ5Kbm0t6ejrDhw9n2LBhwRkO4qvbuXMniYmJFBQUhDx+9OhRNmzYwIcffkhtbS1lZWU9As/r9XL48GFWr15NQ0MDc+bMQa/Xs3HjRp599lmKioqCSwkpisLEiRNJSkqSL6eL1IAMPIfDwfr163nrrbe48847ufnmm1EUhREjRrB3716eeeYZMjIymDRp0knfmH6/P3iz4cYbb2TYsGGYTCaOHDmCqqqsXr2at99+m+zs7JDA83g8HD9+nN/97nfs3bsXu93e47VVVWXcuHHMnDmTsrIyCgsLiY+PP2+/j3Clqio2m41du3YxZsyYHoFXVVXF5s2beeONN/D7/WRkZPR4jU8//ZSHHnqIrVu38qMf/YhLL70Uo9FIVFQUP/vZz/jXv/7F0KFDycrKAk70CQ4ZMkSaoBepM6qCfHmhyJMd7+38vv4DqK2tZevWrWi1WiZOnBgMtbi4OCZMmEBNTQ1/+9vfTnpnD04EXmdnJ/Pnz6ewsBCr1YpOpyMnJ4elS5ditVpxOp34fL6Q59ntdp566im2b99Od3d3r6/t9XpxuVy0t7cHVyoJ9A+Ks9fc3MyhQ4coLy+nvLyc3bt3s3LlSnbv3t3r+ZMnT2bevHm9Bh2ceA+sX7+elStXkpaWxh133EFkZCSKolBWVsZ3v/tdjEYjbW1tXHPNNdx8881kZ2dL7e4i1ucaXmBcUUdHBxaLBbPZHHxjBKZFtbe3YzabsVgsKIpCV1cXdrv9jPZIiI+P59ChQ3zyySckJiaSmJgYcjzQXPz000+pqakhNze39wvT6UhLS+vxuKIoREZGEh8fz7Rp07BarSHHPR4Pbreb4uJijh49Snt7O06nM7hoZuAu7fbt29m5cyd/+9vfmDx5MosXL2bKlCnodAOy0jwovPbaa8Fw8/v9wa6Dk/2NAZKTk4mJiekxPg9O/C0/++yz4CbbX6y1aTQaRo8ezaRJk9i8eTN+v59Zs2ZhNBrP/YWJAaPPn06n08mKFSv45S9/yX333cfixYuDTUGv18vrr7/Offfdx/e//33uvfdeTCYTTz31FCtWrKCzs/O0rx8YnvHKK69w/Phx2traSE5O7tG0CPST7dmzh+bm5lN+GHrT2dnJ3r17ufLKKxk/fnyPfsD4+Hj+93//Nzj+bv369axatYpdu3ZRV1eH2+1GURRiY2NJSUnhkksu4brrrmPixIkSdl/Rbbfdxr333hv8/8CNo9dff/2kz0lISCA6OrrXY4G5yUCvtbb4+HgyMjLo7Ozktdde44YbbpDAu8id0Sc0MLD2y81A+O/cUK/XG3zslltuYf78+WdUw0tJSeGZZ56hs7MTnU7XY6J1TEwMCQkJOJ1OqqqqmDBhQp/L3tzczPr161m3bh2/+MUviIqK6nGeoijBu3YxMTHMnj2byy67DLvdTnt7O1u3bqW4uJjk5GQiIyOJjIwkKiqKiIiIPl+j6J1Wq0Wv14eE09VXX83BgwdP+pxTNT8jIiIwGo3Bpe57o6oqkZGRlJWVyRdWGDivf+HY2Ng+Dx/5osCNAqvV2iNItFotWq0Wl8tFdXV1n16vqamJN998k/fff5+PPvqIxsZGbDYbv/3tb4PTknoTmCcbCEafz0dmZiZms7nHB1OcH2azmauuuuqsBu4aDAZGjBhBREREcOjQF/9ugfnM8fHxLFq0SL60wsB5DbwdO3Zw8ODBk367fpmiKMHJ34Ga1pe/dQO7bgVmN/SF0WhkzJgxGAwGrFYra9asYc2aNaSmpvKTn/yE9PT0PoWXVqslLi6uTz9TnDtFRUVnNcRHq9Uyc+ZM9u/fz+bNm3nqqadYsGABJpMJm83G5s2baW1t5Vvf+hbDhw+XL7AwcF4Dr6Ojg/r6elwuV5/ODwzqDby5fT4fqqqGvBEDN050Ol2fw8disTBmzBhKSkqYNm0aBQUFLF26lFWrVjFv3jySk5Nl8OkA9uXBxmeioKCAO++8k+PHj7N+/Xri4uKIjo6moaGB+vp6br31VubOnSthFybOa+BNnz6d6dOnn/Hz4uLi0Ov1dHd34/F4Qvrxmpubqa+vx2w2U1RUdEavqygKKSkpLFiwgA0bNrB27Vrq6urweDwSeBcpm81GXV0dxcXF3HjjjbS2ttLa2sqwYcOYPXv2KZvKgVVyfD4fBoNBQvEicMaBFxiW8eXHzqX8/HxiY2Pp7u7GZrOFvCkDU4OSkpLIz88/q9c3Go1MnjyZ999/n5SUFAm7fvTFBT7Pxqmeq6oqW7Zs4e9//ztz5syhpKSkx11/j8cTnI/75WN2u53PP/+czs7O4IwcmT0zuJ1x4Pl8PhoaGkJCL7D2W2A8XmDuolarPas3yOjRoxk1ahTV1dW0tbWFBF5VVRVdXV2MHDnyrHfgUhQFi8VCYWEhqampEnj9xOfzcfjw4T738fbG4/GEjAz4IrfbzXvvvccHH3yAx+MJzp/9cr+wTqcjNjaWjIyMYOh5vV7efPNNbrnlFgwGA3/5y1+YPXt2j3GbfSWD0geGMw48l8tFeXk5zc3NKIqC3W5n06ZNPPfcczidTj7++GNaWlr48MMPmThxIunp6WdcqKysrOBSQOXl5eTl5QEnxtDt3LmT9PR0vvOd74R8I2/cuJHNmzdz2WWXMWnSJDQaDW63G5vNFrzbqygKLpeLyspK/vrXv/K9733vrMonvhq/3x8cVrR169bgzafOzs7g4HWdTnfaJqTD4WD37t1UVlbi8/no6uoK1v4Dd/MNBgMOh4MtW7awd+/eXpumiqJgMpn4xS9+wdVXX01MTAxer5djx44FB50vX76ciRMnnlHgBWb71NbWUl1djaqqdHR0UFVVhdlsDss9SPqbdunSpUv7cqLX62Xfvn289dZbNDY2smPHDtasWcO6detQVZXi4mK2b99OdXU1e/fuZciQIZSWlvY61u10dDodKSkpeL1eXn31VeBEbeBf//oXR44c4aabbmLKlCkhwwgeffRRVq9ejdvtZsKECcFBq/fffz/r16+nurqaqqoqtmzZwurVq5k1axZz5swhOjpamikXWG1tLe+99x779+9Hq9VSUFBAcXExZrOZ5uZmGhsbycrKOu3fZffu3dTU1JCUlERJSQkZGRl4vV7S09MxGAxoNBpMJhPd3d1kZWUxfvx4cnNziYyMxGAwBJfp8ng8tLa2snPnTvLz84PP7+rqoqKiAqvVyuLFixk9enSfByarqorT6WTr1q18+umnGI1GRo4cSU5ODg6Hg/r6etLS0qRv8ALrcw3P4XBgt9vJyclh7Nix2O12kpOTycvLY9q0aRiNRjo6Ojh48CB5eXlceeWVWCyWsy5YSkoKN9xwAzExMTQ0NNDY2IhGo+Huu++moKCgxzft2LFj6ezspKSkhIiICHQ6HZmZmRQUFNDY2EhtbS0RERFER0ezYMECLrnkEiwWi4RdPzCbzYwaNQpVVZk2bVqP433tK8vMzCQlJSXkMUVRgqHU1dVFdXU1mZmZfOMb3yA6OjpYywrMow7Uwqqqqnj77bcpLy8PzsAZN24cv//973G5XIwfP/6M7xYbDAYKCwvJz89n8uTJJy2nuHD6vGtZTU0Njz/+OJs2bWLFihU4HI7g1oA6nQ6/34/D4aC2tpa0tLRztsCl1+ultbWVlpYWUlNTTxpSra2tdHd3ExUVFTJcpa2tjebm5uAwFgm58KCqKu+88w5//vOfueKKK/jBD35wyvO9Xi9r167FZrOd9UBnMfD1uYbncrlobW2lvb2djIyMHqERmJVwpnNbT1tAna7XRQS+LC4urtdxeWc720MMbn6/n+eee44jR46waNEiHA4HRqOxR/MxcIOto6ODw4cPc9VVV8ng8otYnwOvo6OD48ePB+/Emkwm6XsQA5bP56O7u5vq6mpefvll4uLiKCoqIioqKvhlHehnq6ysZP/+/djt9h6rqoiLS58Dr7W1lcbGRjweDzU1NWRnZ8sbQwxYer2esrIydu7cyZtvvsk777xDVFQU06dPJzExEa1WS1dXF+Xl5XR1dfHDH/6QJUuWnNVNNjF49LkPr76+njfffJOWlhaWLFkid5fEgNfS0sLhw4d57bXXeOutt+jo6MBoNBIZGYnZbCY3N5dp06YxefJkEhISQtZ4FBenPgeex+Ohq6sLl8tFcnLy+S6XEOeE0+mkpaWF2tpaurq68Pv96HQ6TCYTMTExxMfHS59dGOlz4AkhxGAn4zOEEGFDAk8IETYk8IQQYUMCTwgRNiTwhBBhQwJPCBE2JPCEEGFDAk8IETYk8IQQYUMCTwgRNiTwhBBhQwJPCBE2JPCEEGFDAk8IETYk8IQQYUMCTwgRNiTwhBBhQwJPCBE2JPCEEGFDAk8IETYk8IQQYUMCTwgRNiTwhBBhQwJPCBE2JPCEEGFDAk8IETYk8IQQYUMCTwgRNiTwhBBhQwJPCBE2JPCEEGFDAk8IETYk8IQQYUMCTwgRNiTwhBBhQwJPCBE2JPCEEGFDAk8IETYk8IQQYUMCTwgRNiTwhBBhQwJPCBE2JPCEEGFDAk8IETYk8IQQYUMCTwgRNiTwhBBhQwJPCBE2JPCEEGFDAk8IETYk8IQQYUMCTwgRNiTwhBBhQwJPCBE2/j8JpmPsH3NurgAAAABJRU5ErkJggg==)
physics-General
physics-
The maximum "F" which will not cause motion of any of the blocks.
![](data:image/png;base64,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)
The maximum "F" which will not cause motion of any of the blocks.
![](data:image/png;base64,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)
physics-General
physics-
When F = 2N, the frictional force between 10 kg block and 5 kg block is
![](data:image/png;base64,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)
When F = 2N, the frictional force between 10 kg block and 5 kg block is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAUYAAADaCAYAAADaBOt8AAAgAElEQVR4nO3deXxU9b3/8deZmcySTPY9IQnZF0KC7JsgLkhdwLpRRFBoqa292traitdqbb3UVq1VL1pu1dr2emtRELwqIksVECFAgLAYIAGykpCdkElmP78/vDM/ZxIQEMj2eT4e/EHOmZnvmTnznu/5fr/n+1VUVVURQgjhpentAgghRF8jwSiEEH4kGIUQwo8EoxBC+JFgFEIIPxKMQgjhR4JRCCH8SDAKIYQfCUYhhPAjwSiEEH4kGIUQwo8EoxBC+JFgFEIIPxKMQgjhR4JRCCH86Hq7AGJw6uzsxG6393Yx+iSNRkNQUBBarba3izJoSTCKXvHBBx+wdu1arFZrbxelT9FoNISGhvLoo48yZMiQ3i7OoCXBKHpFeXk569ev59SpU71dlD7DYDAQERFBZGQknZ2dvV2cQU2CUfQKq9VKS0sLoaGh3H777SiKgqIovV2sXuNyuSgrK2Pz5s1YrVacTmdvF2lQk2AUvcZms5GYmMjjjz+ORjO4+wEdDgcrV65kw4YNOJ1OZCmm3iXBKHqNqqpotVoiIyMHfTDa7XaCgoJ6uxji/wzus1EIIXogwSiEEH4kGIUQwo8EoxBC+JFgFEIIPxKMQgjhR4JRCCH8yDhGIcQ34nK5aG5u5siRI5w+fRq3231ej4+MjCQ1NZXY2NhLVMLzJ8EohPjGrFYrtbW1lJeX8/7779PQ0EBAQABDhgxh5MiRPgP43W43LS0t1NXVceLECeLi4vjlL38pwSiEGDi0Wi3JyckMGTIEi8XC9u3b2b17N0ajkfHjx/PTn/4Ug8EAfHm3k9vtprOzk4MHD/L73/+ehoYGmpube/kofEkwCgHee5MH80QW35RGoyE4OJjCwkKKioqw2+3eGYM8wfhVycnJNDU18T//8z90dXX1QonPTIJRDHqqqlJaWkpXVxfDhg3DaDT2dpH6NZ1Od073viuKwlVXXcXRo0clGIW4EKqq0tHRwSeffEJ7ezvXXHMN8fHxZ33Mjh072LZtG11dXRQUFDB+/HhCQ0O9M2NbLBaOHDnCqlWrWL9+PSNGjOC3v/3toApGl8vFpk2bKC0t7TZpsFarJTMzk6uvvhqDwXDOE32cT607JiaGu+++u8/N5i7BKPq8mpoaiouL2bJlC++//z6jR49m1KhRPQajqqqcOnWKFStWsH37dsLDw4mNjeXjjz9mw4YN/OxnPyMuLs4bjvX19Rw8eJCysjLi4+NxuVyX+/B6ndls5tChQ2zatIna2lrv37VaLXFxcdxxxx3MnDmTtLQ0goODL+prG41G0tLSzrsn+1KTYBR93q5du1i+fDn79u3j6NGj5ObmnvGLdPr0adasWcPPf/5zHnnkEebPn09kZCQ7d+5kwYIFJCcnM3fuXKKjozGZTEydOpXg4GD2799/mY+qb9BqtYwaNYqYmBjCw8N56623qK6uxmazAdDU1ERZWRlbt27lhz/8IRMmTCAyMvIbrUejqqp3iE9YWBgGg6HPrW8jwSj6vBtvvJFrrrmGzZs3M3v27LPue+TIEX7/+99jt9u59dZbSUhIACA/P5+HHnqIJUuWEBkZyV133YVWq8VgMBAVFdVj50BvUVUVu91+WdfDiYuL4yc/+QkTJ07khz/8IZWVlaiqiqqqWK1WPv74Y0pKSpg3bx4/+9nPiIiIQKfTXVBnlWe4zpo1a7j++uu9n1FfIsEo+ryAgAC0Wi0ZGRkEBASccT9VVdm/fz+VlZVMnjzZ57LPbDZz44038rvf/Y7//d//ZfTo0eTm5l6O4p8XT2j8+Mc/xmw2X9bX9gSyyWRCr9d7a40ejY2N/PnPf6aoqIjvfe973HbbbQQGBp7363R1dfHxxx9z6tSpPjtTuQSj6Bc0Gg063dlPV6fTSXV1NYqiMGbMGPR6vXebVqslNDQUg8HA559/TllZ2VmD0eVysXXrVhobG4EvwzklJYXMzExvGHR1dVFaWkpJSQkWi4WMjAxGjRpFdHT0BR+nJ5x27NjRa7Oau1yuHteccblctLe3c+DAAd555x2mTZuGyWQ6Y63RarVSWlrKn/70J++lssvlory8nI0bN3LnnXde0uP4JiQYxYDR1NREZWWldwnSr7ZbKYqCXq/HaDRSVVVFVVXV1z7funXr2Lp1K1lZWUydOhWNRuMNgcbGRjZu3Mi7775LQUEB4eHhrFy5ko8++oiUlBSCgoLQ6XSMGTOGgoKCcz4GRVEIDAxk9uzZREZGnv+b8A243W5sNhuff/45+/fv79aOq9VqSUxM5LrrruO2224jIiLirM+nKApdXV20tbV5Pwu73c7Jkyfp7Ozss7VFkGAUA0hNTQ1VVVXodDri4uK61TB1Oh06nQ63201bW9sZn8flclFfX09nZycZGRnMnz/fpwbqdDo5ePAgL730EtnZ2SxcuJDw8HB27NjB4sWL+etf/8p1111HcnIyycnJ53UMnkHSP/rRjy7rpb7NZqOhoYEtW7bw0UcfddseEhJCWloac+bMYe7cuSQmJn7tc+r1egoKCnjwwQd93rvGxkb+9re/XdBl+OUiwSgGjPb2dtra2jAYDEyePPmMHSqqqtLe3t7jNpfLRWtrKy+88AIGg4Ef/vCHZGZm+uzT0dHBypUrqa2tZcWKFcTExKDT6Rg5ciQLFy7k/vvvJzMzkwcffPBrx1r2RKPRYDAYMJlM5/3YC2G322lqauI///M/ee2117DZbN7anFarJTAwkKlTp/L4449TWFjo00RxNoqioNPpCAoK8vksTCYTs2bNYvfu3X12ETQJRjHgeL6QZ2r7UlUVh8PR49+/GnazZ8/usce0rq6O6upqdDodsbGx3stEk8lEVlYWLpeL5cuXc8cdd1xQMF5OTqeTVatW8eKLL1JSUuITijqdjqysLH71q18xbdo0wsLCvrad91wEBASQm5uL0WgkJCTkGz/fpSDBKAYMjUZz1vFwLpcLl8uFoig91iaPHz/O0qVL2b9/P2+++SaxsbE9BkFYWBjh4eFYrVZKSkrIy8vDaDSiKIq3BnSut8X1NkVRKCwsZMmSJd1uy9NoNMTGxpKRkUFQUNBFOx6NRkNQUBDZ2dl9bvyihwSjGDCioqKIjo6mqqqKo0ePEhUV5Q02VVVxOp04HA5MJlOPbX96vZ7Ozk4OHz7Mq6++ysMPP0xcXFy3/cLCwkhLS8PhcLBs2TKWLFmC0WikubmZHTt2YDAYuOuuu/rUNFpnotFoyMzMJCMj44zbL0XAezrD+qq+/5MmxDlKTEwkNTXV27PqP0Da4XBgt9tJT0/vsWMjLi6Ou+++m5ycHF577TXefvttmpqauu1nMBiYMWMGEyZMYN26dXz66afs3buXTZs2sW/fPm699VYWLlxITEzMJTvWi0VRFLRarbdjyv9ff6j1XgqD86jFgBQeHk5hYSFOp5PNmzf7BKPL5eLUqVNYrVYmTJhAVlZWt8frdDpGjBjBCy+8gNls5tlnn+Xjjz+ms7PTZz9FUUhPT2f27NlcccUVVFRU8Ne//pV9+/axYMECXn/9dZKSkvrsZeKl5na7+/RQnHMhl9JiwFAUhWHDhpGcnExRUZFPoLW3t/P2229js9mYOHFij5fI8GVtsLCwkKeeeopf//rXPP3002i1Wr7zne9493E4HLz77rusXLmSFStWoNPpUFXVW/vSarWDel7HpqYmrFZrv34PJBhFv+AZfPx1NZHc3Fwee+wxFi1axIYNGwgODiYiIoIjR47w5z//mfvvv5/rrrvOW5tzu91UVVV5Ox4URcFkMnHLLbewevVq/vWvf/Hmm28yYcIEkpOTURSFxsZGPvvsM4qLi7n//vuJjo7GbDb7BEFkZCQ33XQTQ4cOvXRvSh/jdrtpb2+nrKyMzs5OAgMDe+z97w8kGEWfd+LECY4cOcKOHTuIjo6mra2NtWvXYrPZGDlypM++ISEhTJ8+nT/84Q/e2Xiio6NpbGxk/vz5fPe73/XeUWK1Wjl06BD/+te/iImJwe12s3r1aqZNm0ZycjIFBQVUVFTQ0dHBG2+8wbXXXktWVhYmk4mkpCR0Oh27d+9Gp9PR0dFBZ2ent+fbaDRy8OBBfvzjH5OTk9Mbb9tl43a7aWpq4uDBgxQXF6PVar3jHTs6OvjnP/9JcnIyGRkZJCUl9XZxz4kEo+jzbDYb9fX1xMbG8vDDDwNfXvKeOnWq276KohAeHs7ChQvZv38/u3fvpr29nenTpzNhwgRMJpO3Q8HtduN0Opk4cSJjxozx3o7nqeVMnz6dkSNH4na70Wq1WK1W3G43Op2Oq666yjsBrqqqnDx5kubmZpxOJ1arlerqanbv3s2aNWsGfDDCl73XRqORkSNHMmLECO/fPWNK9Xr9RRkDebn0n5KKQSs1NZXU1NRz3t/zZbziiiu44oorzrhfYGAgo0ePPuP2K6+8stvfVFWlpKSErVu38sADD5CSktLjPqdPn+bVV1+lurr6nMvdX2k0GqKiooiKiurtolw00istxHmw2Wz8+c9/Zu/evWfswPHUPBsbGy/6jNfi8pAaoxDnQVEUTp06xZYtW5g7dy5jx45l9OjRJCYmEhAQQGtrK3v37qW4uJjIyEgWLFjQ20UWF0CCUYjzoNPp+MEPfoDVaqWsrIzPPvuMuLg4zGYzJpMJs9lMZGQkV111FVdeeWWfv1da9EyCUYjzoNVqGTduHM8//zyff/45mzdvprOzk4CAACIjI0lJSWH8+PHeSRL681i+wUyCUYjzpNfrSUlJITk5mTvvvBOn0+mdwGKw3kI30EgwCnGBvnqnixhY5OetH3G73YNy3WMhLjepMV4Cu3btYsuWLVRUVBASEkJKSgozZswgISHhgi61jh8/zo4dO9i5cye33XYbEyZMuASlFkJ4SDBeRC6Xi7Vr17Jq1Sr0ej3jxo3DYrHw9ttvc/LkSebNm3dea4BYLBY+//xz3n33XdavX4/ZbGby5MmX8AiEECDBeNE4HA5OnDjB4sWLGTVqFD//+c/JzMzE4XCg1Wr5y1/+QmRkJPPmzSMoKOhrn09VVZqamti+fTtNTU20tLT0qUXhhRjIpI3xImltbeXFF1+ksrKSKVOmkJyc7F3U6Hvf+x4hISH893//N8XFxef0fIqikJKSwuOPP84LL7wwKO63FaKvkGC8SNra2li/fj06nY6MjAyf2p1WqyU9PZ3y8nKWL19+3h0osbGxfXqpSSEGmgF7KV1bW8umTZtoaWnh9ttvJzo62juswmKxcODAATZu3OidWcVoNNLU1MTrr7+O3W4/59eJjY1l6tSpWK1WTp48iclk8pnBxSM9PR23201FRQVWq5XAwMBzHvx7MaaYdzgcdHZ2YrPZum3TarWEhIScdWU9IQaTARuMra2tvP322xw7doypU6cSGRnpDUa73c6uXbv44x//iM1mo6CgAJPJdEHj0jQaDaqq0tbWxunTp4mPj+/x8QkJCYSGhtLR0YHVavW+3uXguXVt586d3dZBiY6OZsyYMdx8882XpSz+PIuvK4oyqEPZ6XSyffv2fjU110A2YD8Ft9uN3W7HZrPhdrt9tnlWjLNarTidTlRVRaPREB0dzcMPP3xe61UoiuJdRtNutxMZGdnj6mdhYWEEBQVhtVrPq0Z6odxuN1arlSNHjvDKK6/w3nvv0djY6D02z9KYt956KwUFBej1+ssaTGazmdjYWCwWC4899thle92+SlVVVFUlLi4Oo9Eog8Z72YANxgtxpoXYz0aj0eBwOOjq6kKj0ZCamnrG9kBFUbDZbJd8uneXy4XFYqGoqIgFCxZw8uRJnE6nd7tWq8VsNvPrX/+aOXPmEBgY6P1iXi5paWnccMMNPoPWB3ON0cOz5rK0KfcuCcb/43K5qK6u5sEHH+x2uXk2KSkp3HbbbV+7n9vtxu12oyjKJQ+goqIiXnrpJTZu3Ehra6tPjdlgMDB69Gjuuecehg8fzvHjx3vl/t7Gxkba29u970VoaKjcZ8yXwWg2mzEajb1dlEFNgvH/KIpCREQECxcuPK9e4+DgYNLT02lpaUFVVex2e4+Pb2xspK2tjbi4uEu20Ljb7eaNN97glVdeoby8nPb29m77OJ1OvvjiC/7whz9gMBh6rZbW2tqKxWIBvuxcuv766yUM+P8L3EvtuXdJMP4fjUZDcHAwN99883m3Mbrdbo4fP05AQAC1tbU99vzW19djsViIiIjotqLcxeJZ4c5zyX62fYBeve/a5XJ5a7L+bcBC9LYBH4yqqp7zAuCeXunzpdVqiYqKIiwsjMrKSiwWi3edYY/a2lp0Oh2ZmZkEBQVdsmC84447CAsLY9myZezevZv6+nqfANRqtSQmJjJ16lTy8vIICwvrVpbTp0/T0tLiDaxLcelfUVHB/v37veX2dJYNdhqNhs7OTmpqaujo6Lhkr2EwGIiNjZWa6RkM+GB0Op10dHR4v9xf7ZFWVdVbc/GEx4X2BoaHh5OTk8P27dtpbGzE5XJ5h144nU5qamqIiopizJgxPm1pDofDu+/FGKoREBDAt771LcaOHcvKlSv5zW9+Q2Njo7f33WazsXPnTlpaWhg3bhzTp0/vNqayqKiI5557js7OzktWm/tqB5SqqtTU1FyS1+lvPMOWFi9efEnaXBVFwWAwMHLkSBYvXkxAQMBFf42BYMAHo81mo7q6mlGjRgHQ2dnJtm3bWL58OTabjYqKCurr66mrqyM8PJzExMQLOiFjY2N56qmnuPPOOykrK+Oqq67CbDbjdDopKSmhvLyc8ePHc/311/s8bsOGDRQXF3PTTTdRWFh4UX7BPe2l8+bNY9q0afziF79g3bp13kXl4csa2w9+8APmz5/Pr371K0JDQ73bPAvKt7e343K5Llln0eXsBe9PLlUtztOMEhoaSmhoqLz/ZzHgg7GlpYUlS5bw7rvvEhERgcViISwsjEWLFvGLX/yCLVu2sHjxYlJSUliyZMkFn5R6vZ4rrriChx56iDVr1mA0Gpk2bRpWq5Vf//rXjB07lh/96Efexd7hy0vWFStWsHbtWrZv387y5ct7vCOmoqKC9vZ2bDZbjx0qPdFoNAQGBpKens4zzzzDddddx65du3wuzzxjMN977z1uv/12b/uky+Wiq6sLp9PJAw88QHx8vPQYDwB2u521a9dSXFzM6dOnJRjPYsAGo8ViwWg0Mm7cOJxOp7fNbOLEiUyZMoWhQ4dy4MABDh06hNFo5Nprr/1GnSKeIJo3bx4xMTGUlJR4L6knTZrEzJkzGTp0qM/lckBAAAkJCWRkZJCVldXtUtput7N3715KS0vJzMxkyJAhHD58mA8++IBJkyb12D7oT6vVkpmZSWxsLDfccEO3oUiKoqDX67tdUjmdTm+bZUFBgQw4HgAsFgs1NTXs2LFDJjz+GgM2GE+fPo3VamXWrFlMnDgRvV7P0KFDCQ4ORqfToaoqzzzzDMeOHSMyMpLY2Nhv/OVXFIW4uDjmzp3Lt771LWpra9FqtWRnZ/d4Z4nRaOT73/8+s2bNIj09vds+nueLjIxk4sSJ3r9rtdrzGtqiKIr38ul8BQQEoNfrJRgHAIfDITX/czRgg9Fms9Hc3ExTUxPjxo3rtl1RFIKCghg+fPhFf22dTkdMTAwxMTFfu29SUhJJSUk9bgsICDiviW2FEBfHgP35qK2t9elsEEKIczWgg7G+vp6SkpLeLooQop8ZsMGYnJzM8OHDycrK6u2iCCH6mQHbxjh9+nRyc3NJTEzs7aIIIfqZARuMKSkppKSk9HYxhBD90IC9lBZCiAslwSiEEH4kGIUQwo8EoxBC+JFgFEIIPxKMQgjhR4JRCCH8SDAKIYSfATvAWwh/brebI0eOYLfbiYuLO6fZj8TgJMEo+jWXy0VbWxvl5eU4nU6fbVFRUaSmpqLRaGhra6OkpIRly5bhcDh49NFHJRjFGUkwin6ts7OTV199leeff56mpiafbY888ggPPPAARqORf/zjHzzxxBOcPn2ayZMn91JpRX8hwSj6LVVVaWxs5JVXXiEvL89nVnOtVsucOXOIjo5Go9Fw7733MnHiRG655ZZeLLHoLyQYRb/V0tLCtm3b+O53v8uNN95IYGCgd5uiKKSmpnrXsgkODiYtLQ29Xt9bxRX9iASj6LdOnDjBO++8w+OPP05OTk6PKyyei55Wy+vpeTz7ySL1A58Eo+iXOjo62LBhA1u2bOHvf/8748ePJy0tjaSkJOLi4s550Sen00l5eTkWi8Vn3eWvPkdXVxcNDQ3U1dWh1WrR6/XeNX08IakoigTmACLBKPqlY8eO8dlnn9HV1cWyZctYunQpBoOBOXPm8Nvf/tYntM6ms7OTRx55hE8++QSTycTo0aO55557uOWWW9Dr9bhcLr744guefPJJDh06RG5uLlVVVVx77bX86Ec/8tZSg4KCCAoKugxHLi4HCUbRL2VnZ/PCCy/w6KOPUlRUxMsvv0x5eTnLly+nsrKSd955h5CQkK9d9lWn0zF06FBmzJjBwoULGTNmDIGBgd62yeLiYpYsWYLFYmHDhg0EBQVx5MgRXnjhBWbMmMFdd91FaGgokydPZvTo0Zfj0MVlIMEo+iWDwUBSUhIJCQmkpaUxfvx4PvvsM1asWMH27dv5zne+w+uvv86QIUPO+BwNDQ0sX74cnU7HT3/6U/Ly8ggJCfFudzgcrFu3jvLychYuXEhiYiI6nQ6TycTYsWN5//332bJlC88995ysLTTASDCKfk2r1RIREUFERASZmZkkJyfz4IMPsmHDBvbs2UNUVJTPMB6P2tpaDh48SHl5Od///vdJTU316dWGLweP79+/H7vdTlpamvfSPDAwkNGjR2MwGNizZw8Gg6HbY0X/JvdKiwEjJCSEUaNGceutt+J2uykuLubUqVPd9rPZbHzwwQf84x//4Nvf/jYZGRlnDDaj0YjVauXEiRM+vdcajUaG/gxgEoxiQElKSuLuu+8GYM+ePbS2tnbbp7W1le3bt1NSUsLf/vY3Tp8+3eOQHa1WS1JSEu3t7Xz44YdYrVbcbjd2u52qqipOnz5NcnKydLoMQBKMYsDxXDqnpKT0GFoxMTH84Ac/oKCggPfee48PP/ywx5qlTqdj7ty5zJw5k/3797N69Wqam5vZuHEjr776KiNGjODDDz8kISHhkh+TuLykjVEMKKqqYrPZUBSFkSNHEh4e3m0fjUZDbm4ucXFxPPjggyxZsoSoqCiuvfZaDAaDdz9FUYiOjmb69OnY7XZiYmLYvHkznZ2dPPTQQ6SnpxMfHy/jFwcgCUbRL1mtVpxOJyaTyTskR1VVqqureffdd8nOzvYOvelJSEgII0aMYPHixTz55JM8++yzhIeHM378eO/AbpfLRXFxMRs2bOChhx5ixIgRtLa2otfrMZvNBAQEoKqqBOMAJMEo+qXS0lI++OAD8vLyyMrKwmAwYLFY+PDDD9m5cye//OUvSUpK8gk5i8WCy+XCbrdjt9uJiIhgwYIFbNq0iY0bN7JkyRKeeeYZcnJyUBQFl8vF6tWr2bt3Lzt37qS8vNxnOI+iKGi1WsaOHUtYWBg6nXydBgr5JEW/tGPHDl5++WVsNhtDhw4lOTmZuro6oqOjWbx4Mddcc413X1VVaW1tZe/evRgMBux2O2VlZeTn52M2m7nrrruoqKhg7969vPTSSzzxxBOYzWYMBgNms5nKykqeeOIJ4MuAdbvdqKqKqqo4nU6efvpp5s2bR3R0tNQeBwgJRtEvzZ8/n5EjR7J+/XqampoYP348eXl5JCcnYzKZuu1vMpkYM2YMa9euRVEU9Ho9Op0OrVbLlClTGD16NG63G51Oh8FgQKfTERAQwOzZswkPD/fO4VheXk5FRQVdXV00Nzfz0Ucf8fTTT6MoCvfff3+PYyZF/yPBKPolk8lEQUEBqampOBwOgoKCMJlM3lv5vspzL7N/YCqKgkajISoqqsfHtLW1sXXrVkaMGMHYsWMBKCgowG6343a7cTqd/OQnP6GkpIS6ujqamprOeqeN6D8kGEW/ZTAYfHqRz8bTHtiTnv7udrt5/fXXKSoqIjc3F71ej0aj8akRut1uoqOj2bZtGwEBATKecQCRYBSiB6qqsnv3bg4ePMiqVauw2+3Ex8cTGBiIVqvFZrPR1tZGVVUV27Zt47777iMsLKy3iy0uEglGIXqg0WiYNWsWdXV1rFy5kjfffJOoqChycnIwm820t7dTV1dHTk4Ov//97xk6dKh0vAwgEoxC9EBRFG6//XZmzpzJtm3beOGFF9izZw91dXVcccUV3HDDDUydOpXExEQCAgIkFAcYCUYhzsDTaz1hwgSysrLo6upCp9NhNBoJCgrymbdRDCwSjEKchaIoBAYGyrRig4xMIiGEEH4kGIUQwo8EoxBC+JFgFD7cbjdut7u3iyFEr5LOl3PU0NDAxo0bqays7O2iXBKqquJwOLDb7ezcuRObzYaqqixbtozY2FgZjjIAOJ1OioqKcDgclJeX89xzz33tKoqDQVxcHPPnz/dZi1xRe5rTXXRTWlrKv/3bv1FUVNTbRflGPLPC+H/sqqr6zBwjBjaNRoPBYJAfPCA3N5fPP//cZ+iV1BjPkcFgICUlpccp8Psyl8uFw+HAYrHQ0dFBZ2cndrsdl8sFfPkF0Wq1GAwGIiIiCAwMxGAweLeLgUej0XS773swS01N7fYDITXGAchTI3Q4HLS2tlJeXs7q1atZvXo1x44d8846rdFoCAoKIjY2lsLCQu69914mT55MaGhobx+CEL1KgnGAUFUVu92OxWKhpKSEDz/8kE8++YTTp09jsViwWCzYbDZ0Oh3BwcFMnz6dG2+8kdzcXMxmM4GBgd7JWaXdSQx2Eoz9lNvtxmaz0drayhdffOGder+mpoba2loaGxtpa2tDr9czZMgQRo0a5Z2/MD4+noSEBGJiYggKCpJ2JiH8SDD2E0r1lQ0AABS0SURBVE6nE7vdTnt7O7W1tVRWVlJaWsrevXs5fvw4R48epaurC4PBQHR0NAkJCWRlZZGXl8fw4cNJS0sjISGhx9mthRC+JBj7IFVVcbvd3k6TtrY26uvrOXr0KAcOHGDr1q3s27cPm82G0WgkODiYsLAwUlJSyMzMZPTo0YwfP56MjAypDQpxASQY+whPh4lnFbuWlhaqqqr49NNP+ec//0lZWRl2u93bixwUFER0dDQFBQXcdNNN3HLLLYSEhAz6IPS8j18dkybE+ZJg7GWe3uPTp09TXV3NqlWrWL9+PSdOnMBqtWK1Wunq6iIgIIDw8HBGjRrF7bffzqhRowgODsZkMmE0GjGZTIM+DKxWK3V1dXR0dJCbm4tWq+0XPxQ2mw2NRiNTmPUhMo7xMnO73djtdjo7Ozl48CBFRUUcOHCA2tpaGhoaOHnyJBaLBUVRiIiIYPLkyYwfP57U1FQSEhKIjo4mOjqa4ODgfh+ER48eZfPmzdhsNjo7O723IiqK0m2NZs9SpR6hoaGMGzeOgoIC7/aVK1eydOlSXC4XN9xwAw888ACRkZGX74DOg8vloqOjg88//5w1a9Zw5ZVXcuedd/Z2scT/kWA8R54vZldXF3a7ndDQUHQ63dfWSDy9x+3t7dTU1FBZWcmhQ4c4dOgQhw8fpqqqytt7HBER4V0CND8/n9zcXFJTU0lJSSEwMLBf1H7OR1BQEBkZGZSXl/Pqq69SX1+P0+kkNTWVW265xWdfl8tFfX09jY2N3vWhPSsFemzcuJHt27ej1+tpaGhg/vz5fS4YVVWlpaWFsrIyVq9ezdq1a6mqqiI+Pr63iya+QoLxDDztfTabjdOnT3vb/GprawkKCmLWrFndajXge6dJW1sbDQ0NlJWVsW/fPvbs2cOBAwdobW0lICCA0NBQwsPDGTFiBDk5OeTn53trh4NhYtS4uDji4uIYP348mzdvpry8nPb2dsaNG8cjjzzi80PgdruxWq0cO3aM3/3ud2zbto3Gxkaf58vLy2Po0KG4XC4KCgr65HvocrnYtWsXW7duZc2aNZSWlvb7mv9AJMHYA1VV6ezspKamhvLycjZu3Mh7773HiRMnGDduHM8//7x32IunB9npdOJwOGhqaqKmpobt27ezZs0aPvvsM1wuF1qtFp1OR2BgIFlZWaSkpPCtb32LGTNmkJaWNqi/HBqNhokTJ/LJJ5/Q3t5+xn0CAwPJz8/ngQceoL6+no6ODu92RVG49957yczM5OTJk8yZM6fPLmd69dVXM2XKFCZPnsxtt92G3W7v7SIJPxKMPbDb7bzyyiu8/PLLtLe3Y7fbsVqtZGdnc//995Ofnw98Obawo6ODmpoaNmzYwPLly6msrMRut2O323E4HGi1WsLCwigoKOC2227jmmuuITw8HJ1Oh8Fg8K5XLM7dFVdcwYQJE3zaHAEiIiKYMWMGLpcLk8nUJ5sePFcZiqKQmJgon30f1aeC0dOG53K5MBqN3yg0Ojo6sFqtuN1u9Ho9wcHB53Srm9Pp5K9//SuvvfYaNTU13skU4uPjWbhwIYWFhRw8eJDNmzeze/duampqaGhooLW1lZaWFm8Qjh8/nokTJ5Kfn09UVBSxsbGEh4cTEhLS4yW4OHd6vZ6FCxdis9l8/u6ZMaY/UBRFVhfsw/rEN9TtdtPQ0MD+/fvZvHkzgYGBGI1GRo8ezYgRIwgODj6n5/Fc1u7cuZMNGzawf/9+HA4HMTEx3H777YwePfqsi6J3dXWxbt06XnzxRSoqKnxmmImIiKC8vJwlS5Zw7NgxKisraWlpQaPREBkZSUZGBpmZmWRmZpKbm0tKSgqJiYlERETIyX+RqKqKzWZDr9eTmpra43ar1UpbWxvNzc1kZmb2GJSe57FYLLS3t9Pe3o7JZCIqKuqy/nDJedF39YlgrK2tZcWKFWzatImcnBxSUlLYs2cPL774IgsXLuTaa69Fr9d/7fPYbDYOHz7Ma6+9Rn19PRqNhmPHjrF27Vr27dvH888/z4gRI3qcbslisXDo0CF+85vfcPz4cZ92H0VROHbsGEePHkWn02E2m4mIiCA3N5fc3FwKCwsZPnw4w4cPlznuLiGHw8Fnn33GuHHjuv1Ynjp1itraWnbt2sWuXbuw2Wz89re/7RaMLpeLyspK9uzZQ0VFBXFxcbS2tnL8+HGioqKYMmUKMTExAN4hU+Hh4fKZDjK9Howul4u///3vrFy5kjlz5vCzn/0MjUbD1VdfzeOPP86zzz5LRkYG6enpZ70U9gyDeOONN5g5cyZXXnklZrOZvXv3ct9991FcXMyyZcv41a9+1a224XQ6OXz4MI8++ij79u3r1nblGYQ9ZMgQhg0bxsSJE7n55pvJzs4+p8AW35zb7ebUqVO8/fbbZGZm+gSjqqrs2LGDpUuX8tFHH6HRaMjPz6erq8vnOVRVpbq6mscee4zt27ezYMEC5s6di6qqvPrqqzzzzDMsXbqUYcOGYTAY0Gg0XH/99SxatEgGXw8yvdry63a7qaqq4r333iMsLIwbb7zR26YYExPD1KlTqaur4+GHH8ZqtZ71ubq6umhubuaBBx5g+vTphIaGEhAQQEFBAW+99RaJiYkcP36c+vr6bo+tqKjgv/7rv/j000+7heJXy5qdnc0999zD/PnzycnJkS/LZaKqKh0dHezatQuLxdJtu6IoTJs2jUWLFpGbm3vG57Hb7dx777289957TJo0iZ/+9Kfex999990sWLCA5uZm9u7dS0ZGBnl5ecTGxl6y4xJ9V7cao6edzjORqb+v3p3guby4kOnwFUXB5XKxZcsWGhoayMvLIyoqyrtdo9GQlpZGcHAwxcXFHDp0iPz8/DM2rhsMBjIyMtDpdD4Drz3TbiUmJpKTk8OQIUO6HW9JSQn79+/HZDJ5p/fv6bi3bdvGkSNHSE5OJi8vj+985zsUFhbKPcoX2YEDB3jwwQe9/7darZw4cYKamhrS09N7fIxOpyMmJoaoqCgOHz7cbbtnCNaJEydwu91MnTrVZziPyWTi6quv5qOPPuLAgQMMGzaMqVOnEh8fL51lg5DPJ+50OqmoqGDlypXk5+czadIkn84Ku93OW2+9hdPp5MorryQrKwuADRs2cPz4cRwOxzm/cFxcHDfffDMHDx6ko6OD4ODgbm1/0dHRZGdnc/ToUcrKysjKyjpjMGq12h6n1HI4HDQ0NBAZGckdd9zhE77wZUCPGzeO//iP/+DQoUOUlZVx4MABysrKaG5u9vaSK4qC1WqltbXV2+Fy9OhRMjMzCQkJOefjFl/PbDYzbNgw7/8dDgcGg8F7q+SZREREdPt8PdxuN62trVgsFu+YyK8+l6IoJCQkkJubS3FxMevXr2fGjBmYzeaLd2Ci3/AJRpfLRVlZGY8//jh33XUXw4cP9wajZ4bol156CZvNRlxcnDcYW1tbqa+v7zZ84kw898Kqqkp5ebn3Jnr/NsSwsDBycnJ4//33qa2tPa/g9fQ8njx5kn/84x/cdNNN5Ofn9xieQ4YMYciQIUybNg2r1UppaSmlpaXs3LmTkpISGhoaMJvN3ppiXl4e2dnZZGRkDMhb9Xrb0KFDue+++3ze17a2NrZs2cJbb711xsd5JtPoieeWzp4WAvMIDAwkNDQUVVVpbm4+r/NNDCwX5Rph9uzZF/S4rq4uampqcDgcmM3mbpcsJpOJ8PBwXC4XJ06cOOcT1el0YrFYOHr0KCtWrGDt2rU89dRTmEwm3G73GcdGKoqCyWRi5MiRjBw5krlz59LV1cXevXtJS0sjMjJSLqt6iWds6Lp16y5obKtGoyEsLAyj0Yjb7aapqcm79o2H3W73zmR0/fXXn/MwMTHw9Pq33Ol0EhAQQFhY2Bl7eN1uNydPnjxjx4i/qqoq/vjHP/Kvf/2L2tpaOjo6mDNnDkuXLuXb3/72eZ3wRqORsWPHotFopGbYy8LCwpg3bx4RERHn/ViNRkNwcDBJSUnU1dWxZ88e7Ha7T9PM8ePH2bNnD2FhYdx9990X9DpiYLgowfjKK694T7RzlZ6ezs9//nPg/w909Q8el8vlDcPz6eBJTEzkscce4/vf/z5ffPEFzz33HAcOHODZZ58lIiKCG2644ZxrHYqiyOJQfYROp6OgoOCCh0gZDAZefvllHnnkEbZv387LL7/MwoUL0Wq1nDx5kpUrV2Kz2XjqqaeIiIiQ2/UGsYsSjAUFBURGRp5zjQ7wNpIHBATgdrtxuVzdLm06Ozu9A7Xj4uLOeXiMwWDwztwydOhQYmJiePjhhzl+/Dhbtmxh2rRpfXaCAXFmiqJ8o7WQNRoNeXl5zJo1y3tf+6pVq3A6ndhsNlJTU7nuuuuYMGGCjE8d5C5KME6ePPmCHme1WomLi+PgwYO0t7fjcDh8TshTp05x7NgxdDodw4YNu6AvRXBwMJMmTeKWW25h6dKltLa2ymLyg5Tb7ebo0aOUl5czd+5cJkyYQEdHBxaLhdjYWBISEr52TW3PVYyiKBKeA9gZg/FMl66eXj3PNv9a3vnQaDQUFhaybds2mpubsVgsPidbW1sbx44dw2AwMHbs2Ate4c5TUwgPDyc+Pr7fTDQwWHjuLOpp/Oj5Ps+Zmls8oyqefvpp2tvbmTlzJsnJyd0602w2m3eMrv9ExKqqUlFRQWlpKcnJyWRnZ3+jc0lWFem7egxGVVVpbW3t1mbocDi8A8BtNpv3hL7QWUK0Wi3Tpk3jnXfeoampiY6ODsLDw73b6+rqaGtrIyoqipSUlAu+08RzCRYfH3/GiQVE7/EEjv8tfOfLMyfmmV6jra2NTz75hM7OTmJjY6mpqSE1NbXbuavRaAgNDSU5Odl7rniGf91zzz0UFRUxYsQIXnnlFcaMGXPB5ZVg7Lt6DEa32011dTUNDQ0kJCQA0NTUxLJly6irqwNg//79TJkyhU8//dR7C9750mg0jB49mrFjx1JZWUlFRQVJSUnAl5M67N69G4PBwGOPPeYzv96JEyf44IMP6OjoYN68eURFRfnMmPLVZQc8k8e+8cYbjBo1iilTplzQGyUuPs8PbFNTE7t27fJOUutZJdFsNhMQEHBOnSBWq5XDhw9TVlbm87wRERHec0en06HRaGhtbeXNN99k1apVZ/yR1Ov1LFq0iLvuuouEhATvzD1NTU04nU5OnDjBunXrzjsYPefpqVOnOHLkCE6nE7fbTXNzMydPniQwMBCz2SwjIHqZ9sknn3zS8x+n00llZSVvvfWWdxzg9u3b2bhxI5s3byY/P5/y8nJOnjxJbW0tZWVlJCYmkpube0G1ME87TVpaGsePH2fnzp0EBgbicrnYtGkTmzdv5pprruHOO+/0OVl2797Nb37zGzZt2kRhYSHJycm0t7fzz3/+k5deeol9+/bR3NxMfX09JSUlvPnmm8TGxvLd736XIUOGyFjEPqKuro6tW7dSVFREY2MjSUlJpKenEx0djd1up7a2FoPBQFhY2NcGxd69eykrK0NRFDIyMkhLSwO+bGOOjIz03kDQ3t6OzWYjOzub9PR0YmNjvZfOAQEBaLVarFYrLS0tHDp0CLPZTHZ2trd9u6ioCIvFQmZmJnPmzPG+zrlyu90cOnSIHTt2cPz4cUJCQsjNzSUqKor29nZaW1sZMmRIv1nhcKDySQiHw0FXVxdRUVEkJyfT0tKCxWIhJiaGWbNmMXPmTMxmM2+88QYWiwWdTsekSZO+8aVpXl4eixYtYvny5bz//vuEhIRw6tQpZs+ezbhx44iOjvbZPygoiJiYGEwmE8HBwT7DfZqamjh58iRVVVXExcURFBTEiBEjmDFjBtHR0dJg3ofo9XpSUlJITk7myiuv7HGfcx1LGB8fT3h4OFdddZXP3yMjI7335Xd2dtLV1cWcOXOYNGmS90e4tbUVm83mHR3R1tZGaWkpW7ZsYdeuXVx77bWEhYVhMBi8oxuSk5MZPnz4BR13fHw8RqORUaNGMXPmTJ9tnnAWvctnXenGxkb+9re/8dprr/GXv/wFrVZLeHg4iYmJ3uEtTqeTmpoaLBYL6enpF3X+Qc9kASdOnCAzM5OoqKgeTxKLxUJ1dbX3l9/za+5wOKivr6e6upqgoCDi4+OJjIyUE01w6tQpVq5cyZ/+9Cdefvllxo4d+7WP2bJlCx9++CFz5syhsLDwMpRS9BXdJpFoa2ujurqatLQ04uLiuj9Ap2Po0KGXpDBGo5G0tLSvvTwJCgoiJyen298DAgJISkrytlMKAV+265WWlnLfffexaNGiHs/rnnR0dJCVlXXWqczEwOTTqt3Z2cmRI0d8brgXor9zu93U1dXhcrnYuHEju3fvpqWlpcfhQZ7Kwd69e/n0008pLCyUeTcHIZ8aY3t7u7fXuaKigujoaBnaIvo9RVGIjo4mLi6O2tpa/v3f/53s7GxycnLIy8vzzpBktVqpqanh0KFDpKamcuONN/Y4nEcMfD7BGBwcTHp6Olartc8uPynE+dJoNOTm5vLEE0/wwQcfcPjwYTZv3sy2bduIjY3FZDJhMBgwmUyEhISQl5fHt7/9bdLS0ggMDOzt4ote4NP50tXVRVVVFVVVVUyePPmC7zQRoi9SVZWqqiq2bNnC7t27aWhoQFVVzGazd37RgoIC8vPzpVIwyPkEoxBCiF5eDEsIIfoiCUYhhPAjwSiEEH4kGIUQwo8EoxBC+JFgFEIIPxKMQgjhR4JRCCH8SDAKIYQfCUYhhPAjwSiEEH4kGIUQwo8EoxBC+JFgFEIIPxKMQgjhR4JRCCH8SDAKIYQfCUYhhPAjwSiEEH4kGIUQwo8EoxBC+JFgFEIIPxKMQgjhR4JRCCH8SDAKIYQfCUYhhPAjwSiEEH4kGIUQwo8EoxBC+JFgFEIIPxKMQgjhR4JRCCH8SDAKIYQfCUYhhPAjwSiEEH4kGIUQwo8EoxBC+JFgFEIIPxKMQgjhR4JRCCH8SDAKIYQfCUYhhPAjwSiEEH4kGIUQwo8EoxBC+JFgFEIIPxKMQgjhR4JRCCH8SDAKIYQfCUYhhPAjwSiEEH4kGIUQwo8EoxBC+JFgFEIIPxKMQgjhR4JRCCH8/D8R5MLva61ZYgAAAABJRU5ErkJggg==)
physics-General
physics-
When F = 2N, the frictional force between 5 kg block and ground is
![](data:image/png;base64,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)
When F = 2N, the frictional force between 5 kg block and ground is
![](data:image/png;base64,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)
physics-General
physics-
Block B of mass 100 kg rests on a rough surface of friction coefficient m = 1/3. A rope is tied to block B as shown in figure. The maximum acceleration with which boy A of 25 kg can climbs on rope without making block move is :
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQ8AAAD9CAYAAACiAvKYAAAgAElEQVR4nOydeXhV1dX/P3fMzU1u5jkhCRkJY1BmRZHBARHFSrWIQBlqfV8RtSq2/rROtFULilZQa9UqoLQiYJknjcigEAgQkpCEkJB5nu98zv79ofe+UEhIwhzO53nu8zDss88+957zPXutvfZaKiGEQEFBQaGTqC/3ABQUFK5OFPFQUFDoEop4KCgodAnt5R6AQvdBlmWcTidarRa1uu33khACWZYRQqBSqdBoNO3263Q6AdBq279dZVlGlmUANBoNKpXqko/1WkKZeShcEIQQFBUV8Y9//IP8/Px221osFtLT01m7di0nTpxot09Jkvjmm29Yt27dOcdQWlrK5s2b2bp1Ky0tLW22kySJoqIi/vnPf5KXl9dun1arlf3797N+/XqKi4vPOYZrCUU8FC4Isiyze/duFixYcE7xaGlpYfHixaxYsaLdh1wIgd1u5+9//ztr1qw55xgyMjJYtGgRmZmZtLeIaLfbSUtLY+HChRw/frzdPi0WC0uWLOHzzz/HYrGccwzXEop4KFwQrFYrWVlZNDU1ERQU1GY7IQSNjY2sX7+ewMBAAgMD22zrdDqpra0lNzeXyMjIds8vyzI5OTkUFRUxdOjQdk0cs9nMkSNHsNls7Z5fCEFLSwubN28mICAAX1/fdsdwraGIh8IFoaioiOPHjxMVFUVoaGib7YQQnDx5EovFQmJiImFhYW22tdlsbNq0CSEEvXr1ardPp9PJiRMn8PLyYtCgQRgMhjbbFxcXc+LECXr06NHuWJ1OJwUFBVgsFuLi4ggODm6z7bWIIh4KF4T8/HyKioqYMGECXl5ebbaTJInCwkLUajWxsbHtzhAsFgtff/01YWFhxMXFtdlOlmVsNhtFRUUkJSVhMBjadYIWFhZSXFzMmDFj8Pb2brOd3W4nNzcXT09PYmJi0Ol0bba9FlHEQ+GCUFBQQHV1NRMnTmxXPFpaWsjPz8dgMBAdHd3miogQgubmZr7//nuio6OJjY1ts09JkqisrKS8vJyUlJRzrrIUFhZSU1PDuHHj2h1ra2srx44dw2QyER0d3Wa7axVlqVbhvBFCkJubi6+v7zn9DSdPniQ3N5fo6Oh2zQBZlikqKsJms5GQkHBO82bz5s2o1WoSExPb7dNut5Ofn4+Pjw+pqantmjelpaUUFBQQHR1NSEhIm+2uVZSZh8J54VpOPX78ODExMWi12nbf/IWFhZw4cYKJEyfi4+PTZjun00lhYSEajYbY2Nh24ytsNhvr168nNDSUxMTEdmczVquVwsJCkpKS0Ol07Y7V5RsZO3Zsu2O9VlHEQ+G8cDqdnDx5kvLychISEtp9GIUQnDhxgvr6+nP6RpqamsjLy8PT05OePXu222djYyMZGRlERES021aSJE6ePEllZWW75o1LEIuKiqirq2P06NEYjcY2+71WUcwWhfPCarW6TYb2nJquB/LYsWP4+/uTmpqKXq9vs31ZWRnHjh0jISGh3aVflyBYrVbi4+PbNS8cDgc7duxAo9G0a94IIbDZbOTl5eHv70+fPn3aNW+uVZSZh8J5YbFYWLduHSEhIfTt27fNdkIIHA4H+fn5REdHnzN8vLi4mPz8fCZOnNhufIXT6aSoqAiNRkPPnj3b7dNut7Np0yYCAgJITk5uc0VGCIHFYqGgoIDExMRzjvVaRREPhfOiqamJo0ePEhER0e7b3Ol0kpOTQ3V1dbt+CfjJsXnixAkaGxu57bbb2jVvGhsbyc3NxWg0Eh8f326f9fX1HDt2jLCwsHaFRpIk8vPzqaqqonfv3opwtIEiHgpdRghBRUUFLS0tJCYmtmsy2Gw2tm7dilqtbtc34gr4ysnJISgoyB230RYVFRVkZWXRp0+fc5o3xcXF2Gw24uPjCQoKanMMTqeTtLQ0t3nTXszItYzyrSh0GVmWKS8vx+FwEB8f3+4b2mq1smXLFgICAujXr985V0Ty8/OJiYk554NbVlZGTk4Od9xxR7srIg6Hg6KionOKl6vtjh078PX1JSUlRdlJ2waKeCh0mYaGBrKzs/H09CQhIaHNdkIIGhoaKCoqIjQ0lKSkpDbbOp1Ojh49Sk1NzTnf+pIkceLECVpbWxk1atQ5zZuOjFWSJOrq6igsLCQkJIS4uLhzbtm/VlHEQ6HLVFZWcujQIQYMGNDuBjNZlqmsrKS1tZXk5GQCAwPbfPM7HA6++eYbtFotycnJ7c5QHA4HWVlZBAcHExUVhYeHR5tjqKmpITMzk/79+7c71lNXbxISEvD39293DGaz2Z1v5FpDEQ+FLlNaWsqRI0e488478fPza7OdJEmUlZXhcDjO6Sy1Wq3s2LEDk8lEampqmyaD68HNy8tzB6e1R0VFBUePHmXs2LHtrt64zBuVSkVSUlK7Y3U6nRw4cIDW1tZ2z91dUeI8FDqFa5t8ZmYmGzZsoLq62u1gbCtuw2q1sm7dOqxWK7W1tWzYsKHN/isrK8nLyyM8PJzc3FzKy8vP+gC7VmSOHTvGwIED2b59e5vnF0KwdetWamtr3bk82mrb2trKpk2baGlpoaam5rSxBgQEMGzYMOAnQaypqaG0tJSUlJQ2r6c7o1JKLyh0BqvVysaNG3n22WcpKyvDZrPh7+/frlPR4XBgs9mwWCx4eXm1Ga3pWmlpaGjA09MTLy+vdk0Gm82G1WpFCIGvr2+7cRstLS1YrVb8/f3bnaW4xmq32/H09MTT0xMAlUpFYmIi3377LfCTiGZnZ3P06FFuu+02/P392+yzu6LMPBQ6heuhra6udmcBq6qq6vDxjY2NNDY2nrNdc3Mzzc3NHe7XarV2qF11dXWH+7TZbDQ0NAA/icepS8EqlYqIiAj8/PzaddR2Z5SZh0KnkCSJlpYWiouLcTgcl20cdrudL7/8ko8++ojAwED+8Y9/tJub40Lg4+PjDkQTQrg/KpXqmowFUWYeCp1Co9Hg4+ND7969L+s4rFYru3fvxmAw4OXlRZ8+fdp12l4ITjWhVCrVNR95qoiHQqe5Eh4c1xhc41Cr1dfk2/9yonzbCgoKXUIRDwUFhS6hiIeCgkKXUMRDQUGhSyjioaCg0CUU8VBQUOgSingoKCh0CUU8FBQUuoQiHgoKCl1CEQ8FBYUuoYiHgoJCl1DEQ0FBoUso4qGgoNAlFPFQUFDoEop4KCgodAlFPBQUFLqEIh4KCgpdQhEPBQWFLqGIh4KCQpdQxENBQaFLKOKhoKDQJZTs6QpXFa4C162trVgsFhwOBw6Hg5qaGoQQeHh44OHhgVqtvuwZ3rs7ingoXNG4xEKSJGRZxuFwUFBQQFZWFnv37sVqtVJZWcnbb79NcnIy8fHxpKSkEBAQgEajQa1Wo9PpFDG5CCgV4xSuSGRZRgiBLMts376dXbt2cfToUXJycqirq8Nut7tnHgBGoxGtVotGo0Gv1xMbG0tKSgr9+/dn/PjxxMTEoNPpLvNVdS8U8VC4YnDVwT127Bhff/01kZGRZGZm8s0331BYWIjdbsfLywsfHx/8/PxoaWmhpKQEg8HAyJEjaWpqoqqqisbGRpqbm3E6nXh7e3Pddddxzz33MHr0aKKjoxURuUAo4qFwRSDLMmazmYyMDJ599lmysrKwWq1IkoTBYMDHx4fAwEDGjRvHnXfeSVxcHMuWLePtt98mODiY9evXYzQaaWhoYPfu3axdu5bMzEzq6+tpbW3F29ubUaNG8fvf/564uDj3TEWh6yjfnsJlRwhBS0uLWwwKCwtxOByo1Wr8/PyYOnUqEydOpE+fPnh5eaHT6bDb7Xh6eqLVatFqtXh7e+Pr64uvry9RUVFMmjSJ8vJy9u7dy7Jly/jhhx/4+uuvOXDgAL/5zW+YMmUKERERih/kPFDEQ+Gy0traSnFxMUuWLGHt2rWUlZUhSRLBwcGMGjWKRx99lPj4eAICAvDw8HA/7JIknfbgq9VqNBoNGo0GnU6HwWDA09OT8PBwhgwZwvfff8/SpUvJyclh8eLFZGRk8MorrxAeHo6np+fluvyrGkU8FC4LQgjq6+tJT0/ngw8+YMuWLTQ3N6PRaIiIiOC+++7jt7/9LYmJiWg0mi6dQ6vVYjKZSE5OJjw8nPDwcF577TUOHjzoNnOef/55evToocxAuoASJKZwyRFCIIRg2bJlzJ07l6+++orm5mYA/P39efnll3n++edJTk7usnCcikqlwsfHh1tvvZUPPviAcePG0dzczOeff86OHTuQJOm8z3Etosw8FC4pDoeD4uJi3n77bVauXEljYyNarRaHw0FISAjTpk1jwoQJ+Pr6XtDZgEqlQqvV0rNnT5588kkaGxv57rvv+OCDD0hOTmb48OEX7FzXCsrMQ+GSIEkSjY2N7N69mxdeeIEPP/wQIQRxcXFotVo8PDwYOXIkc+bMwd/f/6KshKhUKjw8PEhNTeXRRx8lIiKCY8eO8dFHH9Hc3KzMQDqJIh4KFx1JkmhtbWXdunU88sgj/Otf/0KSJO69917i4+OxWq1ERETw5JNPkpiYeNHjMLy9vbn55puZPXs2arWabdu2sXPnTmw220U9b3dDEQ+Fi4oQgpycHF588UWeffZZiouLSU5O5t133yU+Pp4DBw6g1+uZPXs2vXr1umTj8vLy4sEHHyQ+Pp6amhreeecdqqqqLtn5uwOKeChcFIQQWK1WvvnmG5577jmWLVuG2WzmxhtvZMGCBUyePJljx45RU1NDUFAQo0aNwsfH55KNT6/XExkZyejRo9Hr9WRkZHDy5ElkWb5kY7jaUcRD4YLjdDppbGxk586dzJs3j+3bt6PRaLj77rv529/+xh133IFGo6GgoACAhIQEYmNjL8jKSkdx+T9GjBhBWFgYtbW1FBUVYbfbL9kYrnYU8VC44Jw4cYJFixYxY8YM8vLySEhI4NVXX+Uvf/kLPXr0QAhBdXU1JSUl+Pn5ce+99+Ll5XVZxpqamkpCQgKyLLNr1y5qa2svyziuRhTxULhgNDY2snfvXv7whz/wj3/8g4aGBkaPHs3f/vY3fvGLXxAUFIRer8dut7Nz506am5vx8fFhwoQJGAyGTp1LCIHZbMZms2GxWDhx4gSNjY2dHrO/vz+DBg1CCMH+/fu71Me1iiIeCueNEIKamho2bdrErFmz2LJlC06nk4kTJ7Jw4UIGDx6Mn58favVPt5vNZuPgwYPYbDYiIyOJjY1Fr9d3+Hw2m40TJ06wa9cuLBYLxcXFzJ07l6+//pqamppOjV2j0RAaGooQgpKSEkU8OoESJKZwXgghsNvtvPnmm3z88cdUVVURFxfH3LlzmTp1Kj4+Pmf4Mux2Ozk5OTgcDkJDQzsdDFZTU8Nbb73Fzp07MZvNAOzdu5fS0lIkSWL69Okd7lOSJHJzc4GfRElZcek4ysxDocu0tLRw8OBBHnzwQf7+97/jcDi4+eabWbx4Mb/61a/w8/M7qxNUlmVKSkrQ6XT06NGj0+dtbm5m27Zt2Gw2d6i7JEnU19eTkZHRqb5cCYdcKOLRcZSZh0KncTqd1NbW8u233/LJJ5+QlpZGYGAgEyZMYO7cucTFxbXrw3Al/XHl6egszc3NmM3msy6ruvbIdAWVSoXFYuny8dcaingodAohBM3NzSxcuJBly5ZRWVmJTqfjmWeeYdq0afj6+naoD51OR319PeXl5Z0eg4eHh7ufU7HZbBiNxk735+rHlXlMoWMoZotCh5Flmf379/O///u/fPTRR1itVm644Qa++uorpk6d2uEHT6fTkZycjE6no7KystPjiIyMZN68efj6+uLh4YG3tzdqtZqBAwdy7733dsqH4kqwDD85T8PCwjo9nmsVZeahcE6cTietra3s2LGDJUuWsGfPHvz9/bn99tt56KGHGDJkyGmJes6FXq8nJSWFtLQ0ysvLsdls7gznHcHHx4dp06ZhMBg4evQosixjMBi4++67SU1N7dS1uUwo+GlGExgY2Knjr2UU8VBoF7vdTn19PRs3buT555+nurqa4OBgnnrqKaZOndqlh02v15Oamoper6eqqor8/HwSExM7vFyr0+mIiopi3rx5OJ1OZFlGo9Gg1Wo7LEAuZFmmqanJnfPDZRIpnBvFbFFolx9//JFnnnmGJ598kqqqKoYPH87777/P9OnTO+TfOBseHh7ceOONBAQEUF9fzxdffEFra2un+3HVZPHw8OjUzOVUqqqq3CssUVFRSkrCTqCIh8JZaWpqYu3atcyfP58NGzYgyzKTJ0/mtddeY8yYMfj6+nY554ZGo8HPz48ePXq4zaGWlpZO96NSqVCr1V0u6CSEID09naKiIlQqFaGhoZ0KVrvWUcRDwY0QAqfTSXV1NStXrmTOnDkcOXIEX19fHnroIf785z8zaNCgTvk3zoYrq1dKSgoajYb8/Hyys7Mv6aY0WZaxWq18++23lJaWAmAwGJRyDJ1A+aYU3EiSRFFREX/5y19YvXo19fX13HzzzcydO5dbb70Vg8HQJdPgv1GpVGg0Gm6//XbS0tI4cuQIGzZsoF+/foSHh1+AKzk3TqeToqIifvzxR3eZB4XOoXxjCgBUV1ezefNm5syZw+rVqwG4//77Wbx4MWPHjsXLy+uCb5kfPHgwY8aMQZIkVq1axbFjx86I3bgYyLJMXV0dCxcupLCw8KKfr7uiiMc1jmu2sXz5cp599ll++OEHjEYjs2bN4u233yYlJQWTyXRRzu3r68uDDz5I3759qaur46WXXuLw4cPuuIuLRV1dHatWrWLFihXIskxUVNRFPV+3RShc09TX14spU6YIk8kktFqtiI2NFV9++aUwm81CluWLfn6z2Sw2b94sevToITw8PMSdd94pysvLL9r5ZFkWK1euFHFxcUKlUokxY8aIO+64Q2g0GjFjxgxx8uTJi3bu7oYy87hGaWlpYceOHdx3332sW7cOk8nEL3/5S5YtW8aYMWMwGAyXpBCSXq9n0KBB3HHHHXh7e/Pdd9/x0ksvkZmZeUHPI4SgqamJr776itdff53KykpCQ0OZMmVKlzbnKSgO02sOq9VKXV0d//nPf/jkk084ePAgsbGxPPjgg0yePJn4+PhLWkVeo9Hg6+vLzJkzycrK4uDBgyxbtoy6ujrmzZtH//79z2sVRJyygrR69WrefvttysrKMBqNzJw5k5tuuumCC9U1w2We+ShcQhwOhzhx4oSYOXOm8Pf3F1qtVoSFhYnVq1cLs9l8WccmSZLYv3+/uOGGG4SXl5fw8PAQvXv3Fl9//bWoqakRNptNOJ3ODptSkiQJu90uzGazOHnypJg3b54wGo1Cr9eL4OBg8dRTTwmLxSKamprEE088oZgtXUCZeVxDbNy4kXfeeYe9e/eiVqu58847mT9/Pv3797/sYdlqtZqUlBQ++ugj1qxZw2effUZeXh6zZ8+mT58+3Hbbbdx000307dv3nA5cIQTFxcWkp6ezadMmvv/+e8rKytBoNIwbN46pU6dy8803o9frcTqdl+gKux+KeHRznE4nDQ0NrFq1iiVLlnDy5En8/PyYPHky06ZNo2/fvl2O0LzQGI1G4uPjmTNnDv379+fDDz9kz5497N+/n6NHj7JmzRoSEhJITU0lOjqa0NBQAgMD0Wq1tLa2UlVVRUVFBceOHePw4cOcOHGCoqIidDod4eHhTJkyhUmTJhEbG6tsvb8AKOLRTRE/7xYtLy/n888/569//SsOh4OEhATmzp3Lvffee8HrwV4INBoN/v7+jBs3juuvv56VK1eyYsUKCgoKyM7O5vDhw3z55ZfutpGRkQQHB5OVlYXNZnMnCNJqteh0OkJCQhg8eDBz585l2LBhaLXaK+6ar1YU8eim2O12duzYwdKlS/nuu+9oaWlh8uTJPP74424z5Up+iDQaDQEBAcycOZPx48eTl5dHXl4eaWlp7N+/n9LSUux2O1VVVVgsFpqbm5FlGZPJRFxcHDfddBODBg0iKSmJuLg4TCaTIhwXGEU8uiEVFRVs3LiRRYsWUVpail6v58knn+Sxxx4jJCTksvs3OopGo8FoNBIbG0tkZCQjRozgrrvuoqmpiaamJmpqaqirq8PhcODl5UVwcDABAQF4eXnh7++PyWRyh9QronHhUcSjmyB+TgJcVFTEJ598wpIlS3A6nURFRfHQQw/x8MMP4+vre1Xu4VCr1Xh4eODh4XGas1SckrxYpVK5PwqXBkU8ugmSJFFWVsbcuXP57rvvcDqdjBs3jvnz5zN48GD0en23e7BcG+wULg+KeHQDSktL2b59OwsXLuTEiROEhIRw7733MmvWLHr06HHVmCkKVxeKeFzFWK1WioqK+Oc//8lXX31FQUEBvXr14uGHH2bKlClnLbikoHChUMTjKkWWZQoKCpg1axaHDh3C6XQSGhrKe++9x5AhQ5SkNgoXnavPe3aNI34u8Lxy5UpmzJhBRkYGISEh/OY3v2Hr1q2kpqYqsw2FS4LyerqKMJvNVFRU8MUXX/Dpp59SVlZGYmIiv/3tb7n99tvp2bNnt3OKKly5nCYe4ucsTh29ATvbvqPHyLKMw+HAarViNBqv+eAeIQQWi4WcnBwWL17MqlWrkGWZ66+/njfeeIMBAwYoWb8VLjlus8WVELatGqD/jRACq9WKxWLpVOo41znaO8a1F2PevHnk5eUhSVKH+++OOJ1Oli9fzm9/+1u++uorhBD8+te/5v3332fgwIHKaorCZUErSRIlJSVkZGTw+eefc99993HnnXe2+SYzm82Ulpaybds2du3ahZ+fH/7+/tx111306dMHT0/PMwKRzGYz1dXV7Nixg2+//Raj0Yifnx/33HMPKSkp7nKBDoeDjIwMFi1axIEDB6ipqWHOnDmXJK/llYgkSVRVVfH3v/+dv//977S2thIaGsrDDz/M/fffT2RkpOLfULhsqA8fPswbb7zBI488wqpVq6ioqGgzh6TVaiUzM5M//OEPrFu3jtGjRzNt2jSam5v585//zIEDB7Db7ac97Ha7nZycHJ5//nk+/fRThg8fzpw5c5AkiVdeeYVdu3a5j5EkCY1GQ8+ePWlqasJmsyGEuObEQ5IkzGYz2dnZvPrqq/zpT3+itbWV1NRUXnrpJf7nf/6HHj16KMKhcFnRNjU10a9fPzZt2nTOh7S0tJQ33niDwsJC3n33Xfr3749GoyE8PJw//vGPPPnkk3z++efExsa6lwqrqqp4//33SUtL41//+hf9+/dHp9MRExPD/PnzeeGFF/jwww9JSUnBw8PD3efu3bvZv3//pfgOrjgsFgvbtm3jtdde49ChQwghmDZtGr/5zW9ISEhAp9Nd0z4ghSsD9ZAhQxgzZgx9+vQ5Z+OtW7eSkZHBddddR1RUlDs9XGhoKKmpqZSXl/Pee+9RW1vrPiY9PZ3vvvuO66+/ntjYWDw9PdFqtfj7+zNkyBC3uFRVVbmLAel0umv2rZqbm8vixYt55plnyMzMJDIykldffZVnn32W+Pj4bhlmrnB1ovX09MTHx4fo6Og2GwkhsNvtpKWlYTab6d27t9snolKp0Ov1xMXFYTAY2LlzJ5MmTSI0NBQhBP/5z39obW1l0KBBp5Xyc2WO0ul0bN26lYceeoiIiIg2N27JsozNZsPpdJ42Q9Lr9RgMBvffJUmipaXFbQp5eXnh4eFxRQdNuXJvZGVl8c4777Bhwwb39/y///u/PPDAA8psQ+GKo0NPlCRJVFZWUlVVhVqtJjg4+IyHMSoqCi8vL7KzsykpKXEnns3KynLv7vzvY8LDwwkJCWH//v3k5+dz/fXXt1kr1OVMzcvLc/tk1Go1vXv3ZsiQIe4Hy263s3r1atLS0hBCMHHiRMaNG3fRao9cCGRZJjMzk2nTppGXl4eHhwdjxozhjTfeICEh4arcCavQ/emQeDidToqLi6mvrwfOHqMREBBAjx49yMvLo6amBrPZTElJibuA8dmOMRqNpKamkp6eTklJCXa7vU3xUKvVaDQaVqxYgUqlYubMmSQmJpKUlOTu+8CBA7zxxhuEhYXxwAMP4HQ6+fLLL1m+fDne3t7uWchdd93F6NGjO/YNXURcK11r1qxh6dKlFBYWkpKSwtSpU/nlL39JaGioIhwKVywdEg9ZlqmsrKS5uRmdToefn98ZN7VWqyUwMBCAmpoarFYrxcXFWK1W9Ho9Pj4+ZwiITqcjKCgIlUpFZWVlm6s8kiRht9s5cuQIAQEBTJkyhTFjxuDh4YFarUaWZSoqKvjkk0/YuXMny5cvZ8iQIUiShF6v55FHHsFqtTJt2jQSExPd47ycNDU1UVhYyNKlS9mwYQM1NTUMGTKEp556ihtuuIGAgADFTFG4oumweLj8DQaDgeDg4HYdmvX19dhsNiwWC5IkuTM7tXdMbW3tWTNZu/Zy7N27lzVr1vDCCy9w/fXXnyZesiyTnp7Oli1b8PDwoG/fvm6fzLhx47jjjjtYs2YNer2eu+++m4CAgI5c9kXDarWyd+9efve733H8+HFUKhXDhg3jvffeo2fPnle0f0bh/DnVZ3c1vyA6fZe2FV7uitOAn2YKHY3NcEWz/rcj1NVnc3MzX331Fenp6bz88sv06tXrjFmPEIKGhgaam5sxmUxnjC01NZXVq1ezb98+7HZ7xy/2AiOEwOFw8NZbb/Hxxx9TXFxMWFgY06ZNY8aMGUrQVzfH5QdsaWnBZrPh5eWFt7f3VSsgHRIP1xKq66GVZfmMB93pdFJRUYEQAh8fH/R6vfuYU9PFnYrdbqe8vBwhBH5+fme8cZ1OJ2vWrGHfvn3MmDGD+Pj401ZWTh2fn58fJpOJ+vp66uvr8fHxcfcnyzIqlQqTyXTZHs7W1laKi4tZvHgxa9asweFw0KtXL373u99xyy23EB4eftXeRAr/h2vlrL6+nrq6OioqKjhy5AjZ2dlUV1djsViw2+3Isoyfnx+33XYbo0aNIjQ0FH9//8s9/E7RIfFQq9X4+1DujrUAACAASURBVPtjNBoxm800NDScIQYNDQ3U1NSg1+uJiYnB09OTkJAQ9Ho9FouFlpaWM46xWq3k5uaiVqtJTk4+Y4+GJEmUl5dTVVXFkiVLGDp0KKmpqWcIiEqlIjo6moSEBH788Ud2796Nr68vRqOR5uZmtm7d6g6hP5v4XEwkSaK1tZX9+/ezZMkSVq9eja+vL+PGjeMPf/gDvXr1UvamdCMsFgt79+5l06ZNbN26lZycnNOirlUqlfuF6gplGDFiBNOnT2fChAkEBARc0nKf50OHxEOn05GQkEBQUBB5eXlUVFSc4Z+orKzEYrGQkJBAcnIyRqOR5ORk/P39aWhooLy8/IwNbrW1tVRWVhIcHMz1119/xn4avV7P7Nmz2bJlC8uXL+ell17i9ddfp1+/fqe102g09OrVi3nz5rnbFBYWkpSU5M6w9dvf/paJEyfi5eXVle+py9TX17N06VKWL19OUVERKpWK+fPnM3XqVEJCQhT/Rjdj3759vPzyy7S0tJCbm+veYgE/3c++vr4EBwfjdDopKSnBYrHwww8/cOzYMdLS0njppZfo2bPnZb6KjtGhO1ej0RAREUGvXr0oKCigtLT0DPEoLy/HbDYzcOBAd7CXl5cXN910E6WlpRw/fvyMY4qLi7Hb7fTr14+QkJAzfBlqtZqAgAAeeeQRioqK2Lt3L++//z5PP/000dHRp03zXQWTIyIimDRpEsHBwdTX1zN27FhefPFFgoODL2mshxCC7Oxsli5dyr/+9S8cDgfJyck8/fTT3H777fj5+Sn+jW6ELMuYzWbWrVvHkSNH8PDwICkpicjISAYMGEDv3r1JSEjAw8MDvV6PJEmcPHmSbdu2sXr1asrKylizZo17z1dcXNzlvqRz0mGfh16v56677mLfvn0cPXqU1tZWt43W1NREXl4eQgjGjh1LcHCw+7iJEyfy/fffc+jQISwWi9t0MZvNHD58GI1Gw6233kpQUJD7fP/tjY6JieGVV17hN7/5DevXr8fHx4ennnoKX19fNBoNsixTVlbGxx9/THh4OJMmTTrNh+KaKrqWjS9m7IQkSVgsFjIyMli4cCFbtmzBaDRy0003MXv2bMaPH6/EbnRDJEmioaGBnTt30tTURHh4OM8++yy33XZbm5X5+vTpwy233EJsbCyvv/465eXlbNiwgQEDBvDEE09c8XlstPB/XuBzMXLkSB5++GHmz5/P7NmzCQ8PRwjB3r172bFjB6NGjXKXMXRx3XXXMWfOHJ544gnS09MZN24carWaffv2sX37dhITE5kyZcppziJXMiAXHh4eJCYmMnfuXF5++WU+//xzhgwZwtixY/H29kaSJNLT09m6dSv19fUcP36cYcOGERYWdlofCQkJDBw48KL6PcxmM5s3b+bpp5+mpKQEPz8/nnjiCWbMmKEEfXVjXDVzqqur0ev1JCQkMGTIkHZLeqrVaoxGI7NmzcJkMjFr1iwaGxvZsGEDv/zlL88alX0lod27dy+ZmZls27YNWZZZtWoVWq2WoUOH0rt379OceUajkYkTJ9LU1MR7773Hv//9b7RaLXa7nXvvvZfJkyefEQym0+m4/fbbaWhoYMWKFWzcuBEvLy8sFgu33norU6dOxd/fH7VajdlsJi8vj+3bt1NSUoLRaGT58uU4HA769euHl5cXPj4+VFRUsHjxYiorK0lJSaF///7ExcXRu3dvvvvuOzIyMjhy5AiSJLlnOmq1GoPBwMyZM3nwwQeJiYm5oF+kLMscPHiQ5cuX8+9//5uqqioGDRrEI488wh133OGeJSl0TxwOh7usp8FgYPTo0WcNjDwbnp6ejBkzhrFjx7Jnzx6OHz/OunXrmDFjxhVdkFsLPw3+kUcecb/t2/L2ajQagoODefjhhxkwYADZ2dk0Nzdzww030L9//7MuNalUKgIDA5k1axZ9+/YlOzub+vp6brvtNgYOHHiaueIiKiqK3//+98iyjFqtRqfTodVqiY6O5ne/+5075P3UL9ZkMjF8+HBuvPFGfHx83NXhXVnLmpubycnJ4euvvyYsLIzp06dfsDKETU1NpKens3DhQvbt24fVamXs2LE8+eSTjBw5UtnUdg3gcDhIS0ujtbUVX19fRo4cidFo7NCxGo0GHx8f7rvvPjIzM2lsbOTQoUOXNSapQ4hugM1mE5988ol4/fXXhcViEZIknbWd0+kUixcvFs8884wwm81ttusosiwLq9UqVq5cKfz9/YVOpxMBAQHiV7/6laioqBCyLJ9X/woXn+bmZvHEE08IjUYjZsyYIU6ePNmlfiorK0VERIRQq9UiPj5etLa2dur3t1gs4vvvvxdJSUnCaDSKX/ziF6K6urpLY7lUXLkGVQex2Wzk5eXx/vvvc/vtt7c5mxA/+3UqKirw9fU977wYDoeDsrIylixZwsqVK2lpaWHw4MHMmDGDiRMnKntTrlFcJTA7e3+5YqkMBgOyLFNXV9ehXMKXk6tePFQqFY2NjZSWlrJmzRqCg4Pp168fgYGBeHh4oFKpMJvN1NTU8OOPP1JTU8N99913Xv6Huro6jh49yjvvvMO3336L0+lk7Nix/P73v6dv375XXaSgwvnjWpFUqVTIsozT6USj0XRYQNRqNX5+fm7xaGxsVMTjYqPT6ejfvz/jx49n8+bNzJ8/H51OR3JysnuvyMmTJ5EkyR3zER4e3qVzSZJEY2MjGzduZNGiRRw5cgRvb28mT57MggULzrn5T6H7olKpCA4Opry8HIfDQXV1NeHh4R1eLVGr1Xh4eKDRaNzJt8QVnrv3qhcPlUqFl5cXr7zyCtOmTWPv3r3s3bsXs9mMj48PycnJPPDAA+6AHS8vry6ZE0IIamtrefHFF1m7di2NjY2Eh4fzwgsvuMOKFTPl2kWtVhMZGUl2djYOh4OCggKCgoI6LB7i5z0xTqcTlUqFwWC44u+nq1484KcfLigoCF9fX3r37s2kSZOQJAmdTufeudhVH4c4peDSq6++yvbt2/H09GTEiBE88cQTDB06FH9//yv+h1a4uGg0GmJiYtzRoyUlJQwcOLDDxbhcdZMkSUKlUrlN7iuZbiEeLnQ6Hb6+vqcFqZ0PdrudlpYWvvnmG9555x327NlDcHAwkyZNYtasWfTv318J+lIAfhKP5ORkDAYDVquVvLy8Ti21ip+LqLlmHleDeCh3fjtUVVXx6quv8thjj7F79278/f157bXXeOmll+jXr58iHApu9Ho9o0ePJjAwEKvVyvfff09ra2uHj5dlmYaGBmw2GyqVCk9PzytePM4587Bare7t9Fe6A+d88fDwwMvLC41GQ1paGu+//z7bt2+nsbGRmJgYt3/D29u7S45RWZbdsxmNRuPOL9LWTdJRb7tKpXL34XK2NTU1uc22q2WL99WMVqslIiKCwYMHk5ubS05ODgcOHCAwMNAdLKZSqdzPkNVqdQcxhoeHI0kSBQUFNDU1udNatOUvEUJcEcJyTvHIy8vjs88+Q5ZlWltbu6WAuKJY/f39eeihhzh06BALFy7kyJEjyLLsjnQ9ePAgMTEx9OvXD19f307NPOrr68nPz2fz5s1UVFSg1Wrp2bMnEydOJDw8/Kz7bbZu3UpmZmabfbpu2AkTJuDp6YkQgtzcXNLS0qirq3Pb4UOHDiUyMvKK3idxtaNWq/H29mbkyJFs27aNmpoaPvnkE/bv309iYqLbUe9ahi0pKXHHcvzud7/DZDKRkZGBxWLBaDSSlJTk/r3Ez1n6mpqaaGlpoaKigsTExMsfEnCuKLI1a9aI6OhoERoaKrRarQC61UelUglvb28xePBgcd9994mnn35aGI1GoVarRXBwsJg8ebIIDAwUGo1GqNVq4efnJ5YsWSJaWlo6FUH41VdfiV69egkvLy9hNBqFVqsVHh4eYubMmaKgoOCM9g6HQwwfPlyo1eo2x+7l5SUeeOABUVxcLIQQwm63i7Fjx4pbb71VHDhwQOzYsUOMHTtW3HPPPaK6ulqJeD0LFyrC1EVhYaF44IEHRP/+/YXJZGrzt9NqtSI2NlakpKSIH374QRQWFooRI0YIg8EgevfuLTZt2uSOgrZYLKK0tFT86U9/EikpKSIyMlLs2rXrAn0DXafDryJJkpg6dSq9evXq6CFXBXa7nfz8fNasWUNeXh4qlQqbzcb48eOZPXs2gwYNorS0lHXr1rFu3TpycnL44x//yMGDB3n88cfdxa7aorW1lV27dnH48GH+9Kc/ERsbC8CaNWt499132bBhA3369OHRRx9174Fpampi9erVaLVapkyZQu/evU8zTQC+/fZbMjMzefDBB/H396eurs5dznPmzJnEx8cjSRJLlizhn//8Jxs3bmTChAmX/23VzQkNDWXOnDm89957bgfoqY5T8fPMXfy8NOu631wmjWsGHBYWxvbt29m3bx/p6ekcP34cs9mM3W7HbDZjsVgu1yW66bB4qNVqfvGLXzBu3LiLOZ5LihCC8vJyli1b5l5j9/PzY/r06TzxxBPEx8fj6elJZGQksbGxjBo1io8++oitW7eyatUqysrKeO655+jXr1+bux+dTieNjY3MnDmTsLAwt//BlUXsr3/9K99++y2PPPKI+/8cDge7d+9m/vz59OrVi8jIyNN8Gk6nkyNHjhAWFka/fv0wGAzU1NTw7rvv8uabb5KUlOTuKyYmhvHjx/OPf/yDUaNGKeJxkfHw8GDo0KGEhoZSWlpKcXExRUVFNDc309DQQHV1NWVlZWRlZVFTU4PRaKS0tJSUlBReeeUVNmzYwOHDh/nLX/7C0aNHKS4uprGx0b0Co1arsVgsVFdX43A4Lqs/q1NGsFar7Rb5NsXPCZkbGhpYtWoVb731Fg6HA6PRyPTp03n55Zfx9PQ8zacREhLCqFGjuO6661iwYAGfffYZGzdupKmpiQULFjBixIiz7qvx9vbm7rvvPmNnbWRkJI8++ij//ve/6dmz52nnslgsTJkyhUGDBp2RNtHpdHLy5EmysrLo2bMnAQEBqNVq7Ha7O5fEqX1ptVqMRiNNTU1X/i7NboBKpXKn4IyLi8NsNlNXV0d2djZff/01+/fvp6amBkmS3GkoioqKMJlM3HLLLfz4448cOnSImpoa1Go1Wq0WX19fdxBiSUkJsixTWlqK1Wq9esSju+BwODh58iR//OMf2bp1K01NTciyTI8ePXjwwQfPEA4XarUaHx8fnnvuOQYMGMDzzz/PkSNH+POf/8yiRYvo2bPnGeKq0WjOujLjSsEfFBTE2LFjTxOXsLAwgoKCzlo9z2q18sUXX+B0OhkzZow7EtHHx4cJEyaQnZ3NwIED3SkXGxoaSE9PZ+DAgRcs/kWhfcxmM+np6WzcuJH09HRKS0vdVRQtFgtCCHex9xtvvJE+ffq4V91uu+02Vq5cSWNjI9HR0YwfP54xY8YQGxvLrl27WLBgAaWlpe78p5ezjOo1JR5CCGpqati3bx+vvvoqmZmZGI1GevXqRU5ODgaDAW9v73ZXUVwbmCZOnIjD4eDFF19k3759PP7443z44YeEh4efcxlX/FxnZsWKFdxzzz0MHjz4jNlCWysjra2t7NmzB6PRyNixY93nMplM/P73v+eVV15BpVJx/fXXY7fbycrK4siRIzz88MNXdGKZ7oLT6WTfvn3Mnz+f8vJy6uvraW1tdc8goqOjiY2NZeTIkdxwww1ERUURFBTk/h3j4+OZNWsWGo2GESNGEBoa6g5zr6qqwsfH5zTxuJxcM+Jhs9mora1l5cqVfPzxx+Tk5BAZGcmUKVOIjY3lscce61R/Pj4+/PrXv6ahoYGFCxeyfft2vvjiC2bPno2fn99Zj3E4HJjNZurr6/n3v//Nzp07ef3119ts/9+4Ugrk5uZyzz33nGbuGI1GevbsyT333MPatWvZunUrFouFpKQkpk+fTmJiorJUewlwOp3U1dXR1NSE0WhEp9Ph6elJTEwMQ4YM4ZZbbmHo0KFtmv8+Pj7MnDmTkpISwsPD8fT0dJsmwcHB7iVfRTwuEbIsk5+fz3PPPceuXbswm8306NGDd999l4EDB7Jr164uR4s++OCDFBUV8c4777By5Uquu+66NotoZ2dn88EHH/Djjz+Sm5uLLMu8+uqr/L//9//o3bv3Oc/V0tLCrl27qK+vZ/To0WeIgVqt5vbbb+fmm2/GYrG4C125dmsqXBpkWaagoACdTsekSZNYsGABXl5ebiFoT8SFEOzbt49nnnmG0aNH8z//8z9ER0cDEBgYiI+PDwAVFRWdimC9GHTr+GpXYNuWLVt4/PHH2b59Ox4eHkycOJGVK1cycuRITCbTeYWZ+/v7c8sttxAQEEBeXh7btm3DarWeNTo0MjKSyZMn86tf/YqhQ4cihGDz5s188MEHHUr+UlFRwZdffsnQoUNJSko6a5ShwWDA39+fiIgIwsPD8fb2VtIgXmLEz0FdQgiCg4OJjo52R5q291vIsszhw4f585//zJEjR1i+fDmff/65Ozm5h4cHkZGRwE8z6fLy8kt2TWej24qH1WqloqKC5cuX89RTT7F3716CgoKYPXs2zz//vHsl43wfKp1Ox4ABAxg2bBhOp5PvvvuO5ubmswpBYGAgN998M/PmzeO1117jl7/8JXa7nY0bN7Jt27ZzZrA/fPgwmZmZjB079qy5XxUuP3a7HZvN1unjHA4H5eXlLFq0iB9//BFJkjAYDPTp08f9ctPpdPTo0cN9nrKysgs69s7SLcVDCEFlZSWvvPIK8+bNIycnh549e/Lxxx/z9NNPk5KSckHPFxQUxMyZM/H29qa8vJzMzMx2hUCtVjNgwAD++te/MnLkSCorK1mzZk27S6myLLNr1y4MBgNDhgy5rF52hbPjqh+0YcOGTm/jaG5uZsWKFWzatImmpia8vLx48803GT169GniERUVBfwkHqWlpRf8GjpDt/J5CCFobW1l48aNfPjhhxw4cACdTscvfvELHnnkEQYOHHhRtjobDAZGjhxJUFAQlZWVrF27luuvv77dyFNX0E+fPn3c4taW+SRJEgcPHuTQoUMEBwcTExOj+DCuIGw2GwUFBaxcuZL169dTUFDQKfFoampi06ZNvPPOOzQ1NREaGsqsWbMYNmzYaY5VrVbrnnm4cuheTrqNeDidTmpra/nyyy959913qaysxNvbm5kzZzJ79mx69ux50VYbXMtwffv2paioiN27d3eoiJZKpcLf35+goCCGDRvW5vhkWWb37t3U1NRw2223KcmHrgDEz7uXq6ur2bVrF59//jk7duzAarW6i1h3pA+n0+ledSsuLsZkMnHTTTfx61//Gh8fn9NeElqtlqioKNRqNU6nk7KyMnew2eW4H6568XA5p8rLy3nrrbdYsmQJsiyTnJzM3LlzmT59+lmDrS4GoaGhyLJMZWWlu6i3a3yukpeuH9m1Pb+8vJzExERGjhzZpnhIksTOnTvRarVMnTr1ola8Uzg3rqxfubm5vP7666xfv57m5ma0Wi0hISFERESwf//+dvtwiU9JSQlvvfWWu/TqwIEDeeaZZ85aq9ZVj9nX15fGxkYaGxtpaWnBZDIp4tEVmpub2bNnD++88w579+5Fr9czadIkZs6cyYABAy5Z+K4rl6pKpXJvhhJCUFdXx9q1a4mLi6Nv377umI6SkhJWrFjB8ePHefTRR/H29j7rDeDain306FH69etHYmKiYrJcJlzbGg4dOsQXX3zB+vXrOXnyJA6Hg5CQEKZMmcLo0aMpKCggPT293T4aGhrYv38///znP9m3bx96vZ64uDiee+45kpOT2xyDVqslJiaGrKwsLBYL5eXlGI3Gy5KY6qoVD1mW3YWB//a3v1FYWIjJZOLXv/41jz32GEFBQR3OH3mhcJ3PtWMSoLS0lA8//BC73U50dDQ33HADJpOJnJwcqqqqeOKJJxg4cGCbs46WlhbWrl1LS0sLN99881WRYaq7IX5OEVhXV8eWLVv44IMPOH78OHV1dfj6+hIXF+cOxNu3bx/r168/43iHw0FjYyPV1dX8+OOPfP3112RlZbmT//j7+/P4448zdOjQM/YznYqrcmJeXh5Wq5Xy8nJiY2Mvyx6Xq048XNO90tJSli5dyooVK6itrSUuLo7HHnuMGTNmXLb8jy7zxGWiwE+mzPjx4zly5AiNjY3s2rWLuLg4hg8fzp133onBYGj3rWE2m8nJyeGWW24hNTVVmXVcQlw+iZaWFvbv38/y5cv57LPPEEKgVqsJDg5m8ODB9OnTh/T0dF5++eXTluldolNSUkJ+fj7ffvsta9euJSsrC6fT6d5ompyczD333OMOS28Pl3hotVosFgsVFRUd8q9dDK468bDb7Rw4cIBnn32WjIwMNBoNY8aM4fnnn6dv377nXQmuq4ifSzMIIfD09HSbMEFBQcybNw+Hw+G+YbRaLXq9vkMiFxQUxHPPPYcQosO1TxUuDHa7ndzcXBYsWMAPP/xAVVUVsixjMBgICwvDYrGwZ88eduzYgSzL7tmmRqNBkiScTidpaWns2bOH6upqGhsbsdlsSJKEXq8nMjKS+++/n9tvv50BAwZ06MXw3+JRXl7u9q9daq4a8XAV0tmxYweLFi0iOzubHj16cNdddzFr1ix69ux5yc2U/6a2thaNRkNUVJT7RnDlKu0qOp2OgICACzVEhXMgfi61kZ+fT1paGp999hlHjx49rSyCq7SCq73rN05OTkar1SKEID09HUmSyMnJAf7PJxYfH0/v3r256aabGDlyJFFRUfj4+HTYCa7RaAgPD0en02Gz2aiqqlLEoy1cP2ZFRQUff/wxy5cvp7KykqSkJObOncuECRMICwu77GOUZZmqqip0Oh3x8fGKeXEV4nA4qKmp4YcffmDZsmXs2rWL2traM9rJsuyeOfr6+hIbG4u3tzcmk4nS0lIyMzPdmcEMBoO7zfDhwxk+fDhjxozBz8/vrOaqa5nX9XE6nTgcDvenqamJpqYmd6qHqqoqxWxpC1e8/5NPPsnhw4eRZZmBAwfy/vvvEx8ff0UkJxJCYDabOXHiBHq9nn79+ik7WK8yhBBUVVW5tzI4HI4zthi4fFmenp5cd911/OpXv8JsNvPFF1/w/fffo1ar3QmzXTOSXr168frrr3Pdddfh5eXlTvDTVjF2SZLcJo/D4eD48eMcOnSIjIwMDh48SE5ODi0tLQDExcW5EwtdDq7oO1ySJLKzs1mwYAHZ2dn4+/tz9913M2fOHOLj491TRNeX53JWtvXDnC14R5Kk0xxcrh/OFZPRVl+n3lhNTU2sWbOGpqYm9/4VtVrdoXF1tqTFqc7YtsbU3vkUTsdqtdLU1IQQgj179iBJknur+6kV7+Pi4khJSaFnz540NDRQW1vL0qVLqaysdJcmcZkUvr6+ZGVlodVqGTFiBMOHDz+tCLbVasVsNlNdXU15eTkVFRVUVlZSWVlJbW0ttbW11NXVuRMIWa1WLBYLVqvVHQJgMBjQaDTU19cr4nE2JEmisrKShoYGrFYrN954IykpKRQWFlJUVHRGe6PRSO/evQkNDT3DbLBYLGRkZJzxZbscsJIk0dDQQFpaGrm5uQQGBtK7d++z+hsaGhrIyMigubkZgMbGRj799FPMZjMRERFkZ2dTWFiIRqNBq9USGRlJUlLSGT4ZSZI4ceIEBQUFWK3Wc34fBoOB+Pj4s9b0aGlp4bvvvkOSJLy9vd2Zw5TCVGfiWgWpra1l/fr17N+/HyEELS0tqNVq9Ho9Xl5emEwm4uLi6NWrF1FRUVRXV1NUVMS+ffsoLS3F6XSi0+kwmUzExsYyZMgQRowYQWlpKS+//DKAO81gTU0NFRUV7k95eTk1NTVUVVVRXV1NbW0tzc3Npwm/qySIXq93mz8eHh6EhoYSGRlJXFwcMTEx7S7tXuwvsl1cpRdCQkLExo0bO5SS/UJhsVjE0qVLRVBQUIfKKERHR4uvvvpKmM3mM/o6efKkGD16tDAajR3qa9iwYWLPnj1nHVdGRoZISUlptyyC62MymcTDDz8sysrKznp9b775pggPD+/QmMLDw8WiRYtES0vLGX0dO3ZMmEwmodFoRGJioti9e7ewWq3n/yN0M2RZFlarVWRkZIj7779f+Pj4CJVKJQB3aY3evXuLefPmiQ0bNogdO3aI6dOni5CQkNN+C41GI/z8/ETfvn3Fiy++KA4dOiROnDghDh48KF566SWhVquFWq0WJpNJeHp6us9x6kelUrk/arVa6PV64ePjI0JCQkR0dLTo1auXGD9+vHj66afFZ599Jg4ePHjW3/5ycUXPPFwe6pCQkA4FwbgCw872ttVqtQQEBBAaGnraW178HNDV2Njofou4VjjaCmv38PAgKCiIxsbG00wO159PNRe8vLzw8fE5qw9EpVLh7e1NSEjIOa8N/i+T1NmuT6fTERoaisViITAw8LItWV/JuLa9f/rpp/zrX/+iqKgIh8OBwWDAZrMxbNgw7r//fgB++OEHXn75ZcrLy6mrq3PfM2q1mpCQELy9vd0VBrds2cKmTZuwWCw0NjbS3NzsvhdaWlrcswjXx7U648rKHxMTQ3R0NOHh4ZhMJkwmEz4+PqetwpSVlVFSUkJVVZV7dn25KwFe0eKh0WgYOXIkKSkpmM3mc7b38fEhLCzsrCsd3t7evPDCC7S0tOBwONz/7nQ62bt3Ly+99BKBgYG8+eabhIWFERwcTGho6FnPExAQwNtvv33aTdIWer2e4ODgsy4jazQaxo4dS2pqaoeuz9vbm+Dg4LMKka+vL59++qm7fER0dLSy4vMzrtSABw4c4P3333dHZw4cOJDU1FQOHz5MWloaDoeDtWvXUlFRQWFhoTtZ8akIIWhubqa1tfW0bQguH5larXb71jQaDQEBAcTGxhIWFkZ0dDRRUVH06NGDyMhITCYTvr6++Pj44O3t3WYcj6vY2Ew/UAAAIABJREFU+hdffIFOp+OPf/wjQUFBini0h1arJTY21l0o6XwwmUz069fvjH+3WCw0NTWh1WoJDQ0lNTWVpKSkdvsKCQnp8GyhPS7k9QUEBDB8+PDz7qc7IX52gJeWlrJq1Sr+85//oNfrueeeexg1ahT9+vUjJyeHgoICZFlm3759Z/Thmr2d6odwOdQ1Gg1+fn6nzRZMJhNms5mdO3e60xAuXrz4vKKeHQ4Hx44dIz8/311LuaN1jC8mV7R4KCicDzabjaysLMrKyhg6dCjjx4/HaDTS2tpKWloar7zyCg0NDWfNi+ESClc8hVardTtQk5OTSUpKIikpidDQULy8vPDw8HCXwdi2bZs7L67RaDzv7RKyLFNdXY0kSe7ZzJUwq1TEQ6HbotFoSEhIICYmBovFQmVlJdu3b2fdunUcO3aM8vJydyi5SqXCz8+PiIgIQkJC8PX1JSwsjIiICPfHJRSujysn6ak+KKvVelpE8YVYMpdlmZqaGpxOp1s8roRVNEU8FLolLr+DJEmcPHmStLQ0vvnmGw4cOIBGoyHw/7d35lFR3uce/8w+AwyLjMg2uCAoGCCKMS5oYnI1ao2kxlxykianMSZdjIlpm+a0SXMa62mbnJM013OTm6a3Saq1dUnSqqnWonGBuAAag6CAIIJhXwYGmH25f6Tve0VABVFH8/uc4/EceHnfd2Dm+z6/5/c83ycykvHjxxMaGsrp06cpKysjIyOD5557joyMDGJjYwMm6SyJh2T8IyIPgeAa4vP5OH36NP/7v/+L1WolISGBnJwcXn31VaKjo+WxnHa7nbVr11JeXo7ZbOb222/HbDbfMHeu/vD5fLS1teH1etHpdFft+D9cCPEQ3JL4fD5MJhMvvPACCoVCHr5kMBhQq9W9TIWlr0kzVQLhqS7h8/mw2Ww4nU6USmVAWVAK8RDckmg0GnnGyaVQqVRMmDCBefPmcdttt93wzuyL8fl88ixllUpFRETEjb4lGSEegm80er2eFStW8OSTTwbME/1CfD4fnZ2dAHK+I1AQ4iH4xhPITYRS5CEVnYnIQyC4BfD/u5P5wn82m21YB1B7vV458pC2aYd6rw6HA6VSOWw2FkI8BIIrRNr+lYTC5XLR2dlJR0eH/H9DQwOFhYVyYdnVIi1brjby8Pl8fPbZZ5hMJqZNmzYskZYQD4HgCpDEwmq1UlRURF5eHl988QUdHR10d3fLEYdk4qPX64cl+SqN3oChRx7SdLnf/va3JCUlkZiYSERExFXvKgnxEAgGwP/vkQkWi4WKigoOHDjA/v37OXfuHBaLhc7Ozl5l7JLvhl6vJzg4GIPBQFhY2FXdw4UJ06FGHna7nby8PKqqqujs7OTYsWPcddddN694XM5B6+KGJIHgeiEtTWw2G2fOnOFvf/sbW7ZsobKyspe7WGRkJCaTiejoaKKjo4mJiSEqKgqdTifXjEycOPGq7kXKefj9fnQ6HaGhoYM+R2dnJ7m5uTgcDurr69m1axfTp0+/6smDN0Q8fD4fdru9lwXgxUgNSRqNBpVKFRAVdYJvBtLT/sMPP+S9996jvr4ep9OJWq3GYDAwbtw4srOzyc7OJjIyEp1OJ4/UuNi+8mrzHi6Xi+7ubvx+v+whMhi8Xi+NjY0cPnyYjIwMTp48yaeffsoLL7xASEjIVUUfN0Q8FAoFxcXFFBYWcvToUdrb2+WuxdjYWPR6PT6fD4/Hg16v57bbbiMzM5P4+Pg+jUgCwXDS09PDyZMnefPNN8nLy8NisaDRaJgxYwb33XcfaWlpJCYmYjKZ5LzBcEfGXq9XXi4dPXqUM2fO4Pf7ZRvCwVzParWyf/9+br/9dh588EF+9atfUVtby9atW3n88cevqm7khonH9OnTCQ4O5vPPP2fv3r0YjUZWrVrF1KlTMRgMWK1WTp06xfbt2/nkk0/IyMjg0UcfZfbs2Vc1B0UgGAiPx0NtbS1vvvkmO3fuxOv1Eh4ezpIlS3jyySfJyMi4JkPGpWWS1+vFZrNhsVg4dOgQBw8e5Pjx49TX1xMVFUV0dPSgk7DV1dUcOnSIBx54gDvvvJN77rmHP/7xj2zZsoW5c+fefOIBXwtIYmIiOTk5bN++nVGjRpGdnU1aWpo882LhwoUsW7aMn//852zfvp3S0lLeeecdpk+fLqIPwbDi//f4jNdee42dO3ficrkYP348zz//PI888shlx4JeDZJotLS0sHXrVtavX09VVZUsKpLFZGJi4qByHn6/n927d+N2u1myZAlGo5F77rmHrVu3UlFRQWFhIWlpaUN+XTd0t0WlUhEaGtorY33hGlGlUjF69Gi+853vkJ+fT2VlJX//+9+ZNGmS/HMCwXDh9/vlJjqlUsnTTz/N0qVLB/TFHeo1pJyfVBNSUlJCRUUF586do7a2lq6uLjweDyEhIWRmZrJo0SJmzZolWwhcCR6Ph6amJk6dOsWCBQsICwtDoVCQmppKVlYW//rXv8jPz2fBggXExsYO6fXdUPG43E6KQqFAr9djNpvl8XrFxcXyTFCBYDhRqVSEhIRgtVoJCQkhJiaGyMjIIZ/vwuWI2+3GbrfT09NDfX297DZ25swZGhsbsdvtsjERgMFgYNWqVTz44IMkJSXJs4+vFKfTyYkTJ1AqlcyZM0c+b2RkJAsWLCA3N5ejR49SXl7OqFGjbj7xuBL8fj8NDQ2yaXF4eLiIOATDjkKhkH1s4esnd3+jJvujP5NkyZXfYrHQ2trKV199xZEjR9i3bx+FhYW4XC75fSzZFY4YMYKWlhZcLheRkZH84Ac/uKLO4P6w2+18+umnJCcn4/f7qa2tBb7eSZo4cSLBwcE0NDSwdetWZs6cOSQz5YARD0mlJXw+nzw7dM+ePXR3dxMWFsaSJUvEkkVwTVCpVERHR8sOZBaLZcBjpWjC4/HIO4Nut5vKykpOnTpFaWkp1dXVtLa2yuXr0vQ3j8cjj21ISUlh/vz5pKWl4fF4ePnllzl37tyAUwCuBI/HQ3NzM5999hkpKSl89dVXvc7lcrlISEigrKyMPXv2UFVVRVJS0qC3gQNGPDo6OsjPz5cjDIvFwvnz5/nyyy/ZuXMnI0aM4Lvf/S6zZ88ecJ6KQHA1KJVKwsPDgf9PYg5EXV0dmzZtor29ncbGRtrb22lra8NisWC1Wuns7MTpdOLxeOS+lNDQUMxmM6GhoaSmprJw4UIyMjLkwrLS0lJ5lu3ViEd3dze5ubmMGTOGVatWERMT0+v7Pp+P9vZ2XnjhBc6cOcMnn3zCypUrb27x+Mtf/sLOnTvx+/20tbVRU1NDV1cXwcHBzJo1i4cffhiTyXSjb1Vwi6JUKuUyAKnCtD/8fj/19fWsXbsWrVaL1WqV/UUvdFwPCQnB6/XS1dWFVqvloYce4oEHHiAtLa3P0Kaenh7a2tpwOByoVKp+R6ZeKZJn6+LFi5kyZUqfknbptc2cOZNTp07xz3/+k/vvv3/Q+Z2AEY/Y2FjWrl0rl/O63W46Ozv5+OOP+etf/8pnn33Gww8/zNq1a5k/f37AOT4Jbn6kBL1Go5ETnNIOzMXHhYSEkJCQQGNjIxqNRnZTT0pKYsqUKUydOpXo6GjefPNNdu3aRXBwMIsXL2bu3Ln9Fjp6PB4aGhqw2WxotVri4+OHJB5+v5+CggJaWlpYtmxZvzVRUo4lMzOTTz75hFOnTlFRUUF6evqgrhkw4iGNcIyNjZW/5vV6MZlMjB49mt/97ndUVlbyyiuvoNPpmD9/vqj1EAw7Wq2WsLAwefB0Z2envM15IQaDgdGjR3P+/Hni4uL40Y9+xLRp0+TpbyEhIfKWq3TeqKioAYvMHA4Hx44dw+l0EhkZSWJi4qBL2z0eD62trXz55ZekpqYSGRk5oBgolUqSk5MZOXIkDQ0N7N27l5kzZ2I2m6/4egH96VOpVMTGxvLAAw/w7LPPolarOXPmDH/4wx/kMX8CwXBiMBjkp35bWxsNDQ399l/p9XpGjx6N3+9Ho9EQHR3NpEmTGD9+PNHR0fKSpaOjQ45ULjXN3mazcejQIRwOB5GRkaSlpQ1qB8TlcmGxWNi9ezcFBQWEh4fT2dkpi9eFSMsWtVpNUFAQWq2WvXv3smvXLtrb23uNY70UAS0eEuHh4SxYsICYmBjcbjfNzc04nU4hHoJhJzQ0lAkTJqBWq2lqaqKmpmZA8YiLi0OlUtHT04PFYunzfrRYLPKA7KioqAET/X6/n56eHsrKynC73URGRjJhwoRBiUdlZSUvvfQS7777Lm63m3379vH973+f06dP9znW7Xbz5z//mZdeeonu7m7GjRuH0Wjk/fffZ+XKlf1O0OuPgFm2XAqfz4fT6cRut6PX64mOjr7qEX4CQX8YjUZZPFpaWjh//ny/4qHRaIiIiECpVOJ0OuXO1wvp6OjA7XajUqkuKR52u12u/dDr9YwbN27Q7+/Ro0fz6quv9srTqNXqfjcY1Go1Dz74IAsXLsTlcslfl5K9I0eOvKJr3lDx8Hq98vJD2luXhgjD/4tGR0cHW7ZswWq1YjKZePTRRwNmmpfg1sJgMDBmzBg0Gg1dXV3U1dX1G+GqVCqMRiMqlQqn00lPT0+f41wuF7GxsTQ0NBAUFDRgpOxwODhw4ABKpZKQkBCysrIG/d6WRmBeCdLEvKupnoUbLB4Oh4Mvv/xSdmxqbGxk5MiRGI1GFAoFNpuNU6dOsX79ej766CP0ej0//OEPmTdvnkiWCq4JarWayMhI1Go1DoeD5ubmfo9TKBQEBQXJ4tFf5JGQkCDbCJ44cYL6+nrGjh3b51xdXV2cPXtWHqSdmpp6TV7bcHNDxENakx07dox//OMfhIWF4XK5eP311wkPD5ebfxwOh/xHeeyxx7j33nuZM2fONWmLFgjg/wvF1Gq1PJ2+v4hBoVBgMBhQqVT4/X66u7v7HBMbG8vDDz9Mfn4+1dXVbNq0iYyMDIKCgno9/LRaLWPHjuX48ePU1NRQVlZGenp6wEfWN8zPw2w2YzAYmDx58oCWhNJaMSgoiNDQUEwmExqNJuB/qYKbF2mko1qtxuv1XlI8pDZ9n8/Xb+RhMBiYO3cu6enplJaW8vnnn1NQUMCsWbN6VXOGh4eTnZ3NRx99RFdXF1u3bpW9NobDgf1acUPuTK1Wk5KSciMuLRBcEmkqm06nw+fzUV9fj9vt7lMsplAo0Ol0qFSqAatRlUolJpOJxx57jF//+tecPXuWjz76iMzMzF45O4PBwNSpU8nMzKSoqIjjx4+zY8cOcnJyCAkJuW6vfbCIxIFAcAFKpZLg4GDGjRuHVqulq6uLysrKfm0gLhSTgZKhwcHBzJ8/n+joaBwOB7t376alpaVPLUVERATPPvssUVFRNDU18Ze//KXfJGwgoZb2oQdCUl2pxbi/td3NjNPplPfipd2fy/1OBENHMrQOZNRqNZMnT6aoqAiXy0VBQQGJiYlDyrVpNBrGjh3L/fffT0NDA01NTfz3f/83L774Yq+GNYPBwD333ENWVhY7d+7kxIkTlJSUyHadgYj6wIEDlzygpKQEp9OJ0+lk3759tLa2Xqdbuz643W5KSkpkG7qjR49SV1d3o2/rliUuLo7U1NSA3i1TqVRMnTqVv/71r7S1tXHkyBGys7PljlsJqR1foVAMWMMhOZNJbniHDh1i69at3Hfffb1MeNRqNeHh4Tz++OMUFRVRU1PDn/70J9l7IxBR5+TkXPIAl8sl12K89957AZ3AGQpSfYnD4aC2tpbnnnvulnuNgcTDDz/Mf/3Xfw3bvNRrgVqtZsqUKYSEhNDY2EhRUVGfnIbP56Onp0fupr3UB1ypVDJmzBiWLVvG4cOHaW1tJTc3l1mzZsllCfC10Nxxxx3cd999vPPOO+zZs4dHHnlkyIZA1xr1xb3+F+N2u7HZbAG99hoOIiIieu3dC64NN4ORk0KhICwsjNjYWCoqKujo6KCpqYnx48fLx0g7LFJR46VelxSZzJw5k1mzZnH48GH27dvHf/zHfzB//nz5YSX1wCxatIi///3vWCwWcnNzufPOOwkLCwu4aE395ptvXvIAt9uN0+kccDjTrYI0CUzKoAuuDWPHjg3436+0k5KQkCBHGI2Njb12XCSDYbfbLU+Pu5QoKpVKxo4dS3Z2NidOnKCqqop33nmHadOmERYWJvexaDQaEhMTmTFjBjt27CAvL0/OfQSceMyfP/+SB9zqEcfFBPpT8WZHmqgWyEiRwpgxY2TxqK2txefzycJns9k4e/YsHo8Hk8lETEzMZT/cYWFhLF26lA0bNlBaWsrhw4f54IMPeOKJJ3r1oERFRXH33XeTm5tLWVkZGzZsIDMzc0g+o9cSdaA/BQSC640UhSYlJREVFUVrayslJSU0NDQQHx8PfC0e5eXluN1uRowYQXx8/GXFQ6FQYDKZeO2111i9ejVnzpzhT3/6E9OmTSMrK0sWJr1ez9SpU9Hr9XR1dbFv3z6amprkiYmBQmDFQQJBgKBUKjGbzSQmJqJQKCgpKeH8+fPy93t6eqioqMDj8RAZGUlCQsJll2PScujOO++U58FIg7Qv7KHRaDQkJSXJhkBtbW3k5ubS09NzzV7vUBDiIRAMgNlsJjU1FZVKJbuiSy7/FouFmpoavF4vUVFRxMXFXVFOQuqcXbRoERkZGfh8PjZt2sT69evlXU1p2ZSTk0N4eDgOh4PNmzfT2Nh4HV71lSPEQyAYgPDwcFJSUlAoFDgcDo4cOSIb/xw7dgyv14tGoyEhIWHQFhEpKSk89dRTBAUF0dnZybvvvssf//hHOjs7ga+jjwULFpCYmIjL5eLkyZMUFxcH1MaF6pe//OUvb/RNBApScjjQE3qC64NCocBut7NlyxZ0Oh2tra20tbVx8OBBtm3bRmtrK0FBQTz22GNkZGQM6twajYbY2Fg6OzupqKjAYrFQXV3NhAkTCAoKwm6343a7qampobCwELvdztixY7njjjsCpqv8lq2Gkjp1pZGWVyIIdrsdm83GiBEj5BDU7/fLlYTwdfWhZLEvuLWRcg8jRoxAoVDQ1tbG66+/jkKhIDg4WHa0mzBhwqDPLbX+r169mqqqKvbu3UtpaSm/+93vmDhxolyxevr0aZRKJW63mxMnTtDU1NSn0vVGccuKR09PD1arFa1WK7dYX47CwkI2b97MG2+8gV6vl02Kampq5HF9SUlJmEymgC0ZFgwfUrHY4sWLKSgoQKFQyA8RhUKBy+Vi7ty5Q64AVavVJCQk8Mwzz3Du3Dnq6+spLy+noKBAjoJdLpdsYlxaWsr58+dJTk4OiOj4lhIPp9NJZ2cnhYWF7N+/n5KSEn70ox8xe/bsS4qH1PiXn58v+0d6vV5qamrYtm0bu3fvlk2XR4wYwfLly1myZMllC4MENz9BQUE8//zzlJaW4vF45A+ylDjNyMgYciQg+YxOnz6dn/70p2zYsIHm5mZCQkL6ra8KDQ3lq6++uqrXM5zcUuLR0NDAxo0b+fTTTykrKyM4OBibzSZPCB8IyfSlsrKS733veyiVSiwWCx9//DFHjx7lrrvuQqFQsGvXLo4dO8Ybb7yBwWDgoYceQqVSCQG5hdHpdCQlJZGUlHTNrhEREUF2djZmsxmHwzFgUlSj0RAfHx8w77dbSjy0Wi2PPfYY48aNY82aNXR1dV3RzzmdTj777DPi4uLk9Wt+fj4xMTF8+OGHaDQa/H4/OTk5PPvss+Tn5/OHP/yBe++9F5PJFDB/TMHNS2hoKLNnzwYGrupWKBQBlWu7pcQjOjoal8slj/q7UvFwOBwcPnyYBQsWyLmMuLg4srKyCAkJkcUhJiaGlStXUlVV1e8wHYFgqNyMSfhhFw/JDNbtdhMUFNTH/EWavwJfl+FK207d3d04HI5B9dJotVr0er3c3q1UKuUmpaCgoCu+Xym5mpSUJJf/ZmZmAr23bdVqNWPGjCEmJoZJkyb1O4ZQIPimMKziIe1ObNmyhTNnznD//fczZcqUXkOpa2pq2LRpExqNhqVLl8rLhM2bN1NaWjqoIpioqCiWLVtGcnLykO/Z6/XS3t5OYmJiLzHoTxTcbjdHjx5l/PjxPPXUU8KMWfCNZtgjD6/XS15eHp9//jkpKSmkp6f3+n5LSws7duxAr9eTlZUli8ecOXMGXWij0+m4nB/J5WhpaeFf//oXt99++yXNZnt6ejh37hw1NTUsX76cpKQkIRy3GJKRcXd3Nz6fD7VajV6vJyQk5JJLCqkWqL8RqNI5FAoFbreb7u5ueSr97NmzGTdu3E23XJG4JjkPu91OV1cXbre7TyQh/QK9Xm8vE9hrmc2+FK2trRw5coSlS5f2qdzz+Xw4HA7q6uooKSnhrbfewul0kpyczNixY8XIy1sE6cNfWlrKrl27OHr0KN3d3ej1eu644w4WL15MUlKSPE/oYrq7uzl69CiHDx/ulQtTq9WYzWa+853voFAoOHfuHBs3bmTz5s2YzWb5fXSzEjAJU7fbfdkt1YuRqj2Haivg9/s5fvw4RqORmJiYPrUg0hbu9u3b2b17N1988QV2u52XXnqJ5557jqefflp+qghuXjweD7W1tfzsZz+joKCAsLAwAJqbm9m/fz87duzgN7/5DXfffXeflni/309tbS3/8z//w549e3rNfg0JCeHnP/85KpUKt9vNuXPnqKqqorq6mqCgINlc/GYlYMTj9ddf5/jx44POeaxatYrbbrtt0NeTDI8rKytZvHhxvz4JarWauLg4VqxYQU5ODsePH+cXv/gFNTU1rF+/ntmzZ5OamhowvQaCoWGxWPj973+PVqvlvffeIzMzE7/fz65du3j77bcpKyvjjTfewGQyMXnyZPnnpBxfcXExdrud559/vtcDaNSoUSxevFg2QZ4xYwbBwcHs2LHjRrzMYSdgxOPee+8lJSVlUEocGhp6xRO9L8bj8VBcXIzL5WL69On9Ri9SBWBYWBhGo5Hw8HAUCgUvv/wydXV1HDx4cMiW/ILAwO/3Y7fbqa6u5oUXXiAtLY2wsDD8fj8PPfQQRqORH//4xxQXF3Ps2LFe4uHz+WSD5Mcff7xPZKLVauWdQGnCXCB6kQ6VgBGP6dOnX9freTweioqKiIuLIzIy8rJ/UMmH4Vvf+hYHDx7kz3/+M+3t7X2G9whuLvx+P11dXXz7298mPT1dzmtIrl/z5s1j7ty57Nu3j4KCAlasWCH/nNvt5tNPP6Wrq4u0tDS59GCws2kkB38pXyI1cqrV6l7vS6k8Xlreq9VqecfvRiydr6l4BPJ6zu/3U1ZWxre+9a1B5S2USiXp6emEhITIbxjBzYtSqSQlJYXx48f3mb0iDbOePn06hYWFvXpYpCHY77//PmfOnOHIkSMsXryYhQsXMnHixEFVHns8Hpqbm+W+FZVKRUhICPHx8fJQbL/fT0tLC+Xl5VRUVKBSqUhLSyMlJaXX4OzrKSLXTDw8Hg+tra29ss8ulwubzYbT6ZRnpUg7Glqt9rrNS3G73VitVpRKJQkJCVccRkrNUB6Ph4iICJKSkgYc9iO4eVCpVANGCl6vl7NnzxIeHk5WVpb8dZ/Px/nz5zGZTLS0tNDU1MT777/P9u3bmTFjBt/97nfJyMi4olmzCoWC8vJyfvaznxETE0N2djbJycnExMSgUChwOp1UVVXx4Ycf0tXVxYIFC2hvb2fdunXo9XpMJhMGgwGj0ciyZcuIi4u7Lg711+zT6nQ6qa6upqWlBfj6g9fZ2cnOnTux2Wy43W7q6upobGyktLSUmTNnDpt4eL1eOfHaX/Rjs9nYv38/48aN67dOxOfz0dnZidfrRafTyaGhx+Ohrq6Of/7zn0ydOlX2mBTcmvj9flwuF0VFRaSkpPQqRlQoFKSkpPDaa69RV1dHQUEB27Zt4/z58/ztb3/j7Nmz/OY3vyE9Pf2S0amUuO/p6UGpVLJ8+XJmzpwpu6lL82HefvttSkpKWLNmDXPmzMFqtRIaGspTTz2FUqnk6aefJi4uDrVafd0i/mv2zrfb7Wzfvp3u7m6Sk5Npb2+npqaG2NhYIiIiqK6uZuPGjZw8eZJJkyYxbdq0Ybmuz+fDarXKBTuSL+SFtLS0sHHjRn7yk5/0eTJIhUIvvvgiCoWCu+++m+TkZHQ6HXV1dbz99tvExcXx/PPPExwcfMskvwR98Xg8VFRUUFVVxRNPPEFiYqL8PWk8ZFhYGLfddhvz5s1j9erVvPvuu3zwwQccOHCAdevWsXbtWsaMGdPv+aW8yY4dO9i2bRtr1qxh5syZvVorXC4XhYWFbNiwgZycHNnLIzQ0lClTprBo0SL27t1LZGQkTzzxxHUdbTHs5ekOhwO1Ws3EiRNxOp2cPHmSxsZG0tLSeOaZZ0hISGD8+PGsX7+e7u5uwsLCmD9//hX3olwKq9XK9u3bKS8vp6enh9DQULZs2cKpU6fIzs6WM+UtLS3yk+PiLVrJdl+pVHLixAmKi4uJi4sjISGB6OhoVqxYQWZmJiaTSQjHLYzP56O8vJyNGzeycuVKFi1a1CfKvDBRqVQqMRqNLF++nJiYGH7wgx9w8OBBDh061K94SA+5LVu2UFZWxk9/+lN52//CD7/X66W6uhqv14ter5eXI5KApKenk5ubS3l5ea+5MteDYRUPn89HW1sb3d3dTJkyhSeffBKv18vIkSOJiIiQP3DLly9n7ty5wNedsFFRUcMS/qtUKubOnUtmZiYPPfQQXq9XtoyLiIiQj0tISOCVV14hNDS0jwBIW2ovv/wyjY2NtLa2YjKZMBqNGI1GTCaT6Gm5xfF6vbS1tbFnzx5GjRrFM88802umbH9ID52RI0cyb9487rrrLo4dO0Z+fj6PPPJIn+OdTid5eXns2rWLV155hXHjxvXrTqdQKORrt7e395mZeyMfYMMeedhsNtmAZ+bMmf0WX0nWgMNNcHAwwcHBl7WFi4uLu+QxCoWZp2McAAAFjUlEQVSC+Ph4ecCP4JuDVPexefNmmpqaeOKJJwgPD7/iJ7pkXbh69WpWrVrFuXPn+j2uu7ubQ4cOUVlZyT/+8Q+mTZsme6VeiFarJTU1leDgYIqLizl//jxmsxn4OtI+deoUOp2OyZMnX/eBUMMqW16vl9bWVjo7O/F4PAG9VSsQ9IfVamXv3r3U1tby5JNPMnr06EE/3VUqFSaTidDQUCIjI/s9Jjw8nBUrVpCVlcXBgwf59a9/jdVq7eMTo1KpGD9+PK+//joajYbf/va3HDhwgJKSEj744ANOnDjBT37yE5YuXTrk1zxUhlU8pGWL1Wqlra0Nm80WUHMmBIKBkIrFKioqaGpq4vvf/z4xMTFy86PUPCc1dV4KqUxBoVCQmpra7zEajYbo6Ghefvll4uPjyc3N5fe//z1tbW29zi+5h40ZM4a7776bKVOmcOLECbZt24bBYGDNmjU8+uijjBgxYlh/H1fCsO+2uN1uOZEkqi8FNwM+nw+Xy0VeXh7Nzc3MmTOHkSNHolAo5ByDJAgNDQ3ccccd8ta91+tFqVSiVqtRKBR4vV6sVisff/wxZrOZiwfJXxiNGwwGZsyYwfLly3n11Vd56623iImJ4YEHHsBoNMr31tHRwbp167j33nv5z//8TwwGg2wZcGFxmDRq5HoxrOKh0+mYN2+e7Lh14fwTgSBQ6enp4fDhw2zatImUlBRyc3P75Diqq6spLy/n7bffRqlU0t3dzf79+zl9+jTz5s0jPj4enU5HU1MTmzdvpqioiFdffbVX5CGVoUtIJejf/va3aW5u5pVXXmHNmjXEx8fLGwpOp5MvvviCvLw8OfLJzMzEYDD0Mq4aOXIkcXFx19UmYljFQ6lUMmLECJYsWYLf7xfCIQh43G43x48f56233qKqqoojR470m3j0+XwsWrSI6OhoVCoVfr+fiooKNm3axPbt25k0aRLh4eF0dHSg1Wr51a9+xaxZs2QXPZ/PR319PXl5eRiNRtmVLioqCrPZTFZWFqNGjcLlcvHuu+/i8XiIj48nNjaWoKAgwsPDKS4upqqqis2bN8uFkNJyKj4+nkcffZRly5b1Kle/lgyreEjbVddzr1kguBq8Xi82m42srKxe5ecXo9PpmDNnjiwsOp2ORYsW0dPTQ1FREfX19QQFBTF58mRmz57NpEmTekUAUoV1REQEq1evxufzERoaSnt7O2azGa1Wy49//GM8Ho882lKpVDJq1ChSU1PJycnBZrNhNptxuVzU1tbS09ODz+ejrq6Oqqoq1q1bx4QJE5g8efJ16blS+MWWiOAbzIX9SpdCSlxK9UjSoLALR5FKub6BHqA+n0/+d+E5pca3C+9BqhS12+3k5+ezZ88ennvuOUaNGiVf/8L7r6ioYMOGDRiNRlauXDlkq4rBIBozBN9ohhotS0IxmMbIS41XGOhcRUVFrFu3joULF6LT6fo9RopitFotcXFx161ZU4iHQBDA1NbWysOuU1NTGT16NAaDQc67SMbL+fn5NDc3s2rVqutmEyHEQyAIYCZOnEh6ejq7d+/m8OHDJCcnM3HiRIxGIz6fj9bWVhobG5k9ezYvvvjisLV6XAki5yEQBDA2m42GhgZKS0v55JNPOHnyJACRkZGMGTOGlJQU7rrrLsxms7x0uV5btUI8BIIARypia29vx2Kx4Ha7CQ4OxmAwEBQUhNFovO59LSDEQyAQDBFRxSUQCIaEEA+BQDAkhHgIBIIhIcRDIBAMCSEeAoFgSAjxEAgEQ0KIh0AgGBJCPAQCwZAQ4iEQCIaEEA+BQDAkhHgIBIIhIcRDIBAMCSEeAoFgSAjxEAgEQ0KIh0AgGBJCPAQCwZAQ4iEQCIaEEA+BQDAkhHgIBIIhIcRDIBAMCSEeAoFgSPwfEE+PHpPjaP4AAAAASUVORK5CYII=)
Block B of mass 100 kg rests on a rough surface of friction coefficient m = 1/3. A rope is tied to block B as shown in figure. The maximum acceleration with which boy A of 25 kg can climbs on rope without making block move is :
![](data:image/png;base64,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)
physics-General