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Grade 11Mechanics

The “mechanical arm” on the space shuttle can handle a 2200-kg satellite when extended to 12 m; see Fig. 3-22. Yet, on the ground, this remote manipulator system (RMS) cannot support its own weight. In the “weightlessness” of an orbiting shuttle, why does the RMS have to be able to exert any force at all?
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++zLL78Eo0CzdevWEow7duzYvn17IvGXX34JtWjZsiURmmDcsWNHhBFiMPQA2BEUARnsQk1NTUVFBbJLUIRkcwHh5YiD8JBu3bp16NCBB7t27crHEYNhF5IagksitHLMBsciLKqpqfXp0wdVDv6AoKGnpyf6oL29/eTJkzdu3HjmzJm8vLyGhobnz58jFKAPgGZE3+bm5mfPniEI3LlzB8iWl5cXFxeXlZVVVlaCCa7d5eXlRUVF5eXlhD1iJAiD0T558gRiAGkGnZIXoqxxDjH40aNHDQ0NkroBTaG59fX10AYJwLW1tQCXJVRTUwOR4OrBkuAr1dXVAeiqqqonT558VBxnZ2cPHz4c1EKLgR2PwIy/+OILME1klegLaRYRo1OnTpBgeHbr1q3hzcTmjh07CoXgTBE00Ozat28vYZKgyA2u5gCOuAvsWAyCY4IrSZ5EYkKvnMN7qqqqkpmhXWhoaEBvOB8QA1wNDQ0yYDRs9AoDAwMLCwtzc3N0N0dHx2nTpm3evPn8+fOlpaWPHj16/fq1cg0MEe3Nmzeif8El7t27V1VVJfClGlpZWUkgBMrl5eWFhYVlZWWlpaXFxcXl5eWAnos7bASaAUOAQkAtyCCprpHeNTQ0AGhCMlAmlUSC4EFZJA8ePIBIEHd5hJwPSkP459PltZzwsXF88+bNUaNG/ROOicpQiJYtW7Zs2ZKozLPoymSE3Gjbti0X7rZt2xL/4BjgmwjNbZ7t3r07wpwwUaAMFgExpRl0N3V1ddQDDQ0NoapQAmWaizgNc5DyTVfFgeYNRrW0tNA9KNMgs5DeqaiooAYK1lGmIQ8mJiampqaWlpa2trbDhw9fsGDB3r17ExMT79y5gz4glTMp6vJTBIqmpiYJnFQQoMLK4ishkCB969at2traysrK8vLyqqoqidOCY8BE7gj/bmpqgrcQpyEYQsdJ6UAeqgWRlVQSTANTBDXgCw+pr6/nLkSFkM9nPXny5P79+1w0ysrKGhoaPiqO8/Pzx44dS7gVyEIz5Da5nVALEStatWolAgU5GXjt2LFj69atocKAFSiL+oakIIUSZAQ0ZrgEnBgwAU34qLq6OsAV/QG4cw7kFXUZaVneHzoBtZUiCzUXJDloSR/FgY5G1QMJ2dDQkAKelZXVyJEjFyxYEBAQkJ6e/uDBg+bmZrwKv/3222+//favUG5ubhbtFng1NjYSGuHHgIM0C3IMqmAdwpu5oHO5r6urI74iEkNXYBEIcFBnuDgkhyogTBooc0PiOpQDHePJkyd8MQRmUlVWi+jTaCNPnz6VPBUcl5aWPnz48KPiWOKxkODPP/+8VatWxF04BokdaIYwgFEUYsAKSUBRBtz8hHUgIAhwlQslJGpQhe6KAxyDJ4CFCgbgCK7gWE1NrW/fvpJ+AWjUMUBPdCcFBOKqqqqUSwj2nC8rp2/fvhT2KE0bGRlBgk1MTOzs7MaMGbN8+fJjx45dv3798ePHv/zyy/v378XN8/79+7dv32Jp4Ibg+Pnz5wROeIWICSKBiT+hpqamuroasba0tLSwsLC0tLSioqK8vByWTCR+/PgxSaSsE7HpQMebmppEQobqiNLHmlEm1sJJJHLLN6SOLe9MLVB0vefPnwN9liK/CLanj43j0aNHC6/gAKmtWrX65ptvWrVqJYAmEsOSYb3CKKQyAjkG4qAcEJPDcbmHYECmO3bsKESid+/eaLqQBKoeampqlC1AG5wBLP6rjCBFaWrUhHOkOoiv5HC8Cn2alSALoF+/flpaWmKxMDIysrS0HDVq1MqVK0NCQnJzc58+ffru3TvlP+Off/75559/guN37969e/dO3DmvFYeUgkUXI9Xjal5fX9/Y2FhXV1dZWVlWVlZUVJSbm3vjxo2bN2+WlZVVVFSA5pqaGknvAJawcHH/gGn5IClNc8KTJ0+gwqJy8B3QQFDopPQN9KUqTtFbPBhEdL45N1CjGxoaPjaOi4qKxo8fD45RKv72t78hqyHGgWAOEIwwh46GMiA0lGIK7EJcGe3bt+dZdDQJqALorl27EizFVKSmpkZNgTxMasUoEr179+a6T5ECaBKJobM4HDAqSZAmAIsGzMkgG/QT8rFz6OvrQ4WHDBkyadKkFStWHDlypKio6Pnz5wTg/9RfC7X4/fffcUKS4QEjbkiAxEpGgl9TUwOXqKqqKioqunnz5rVr1/CR3rhxIzc3t7CwsKKiAlLx4MEDImhTU5P43fjQd+/eUYJm2fz666/gGAQL8RAlDoACR3DZpDhYDGgscCGpmJA1SiGGBQAhYXnw+Meu55WUlLi5uQk//uqrryh8wCKo7X3xxRfoa6hpoqMRiVEqgKa4KUQYJuIigSkfyoUJKC9ygdScBWpUj2G0kFokZF4Iu2UBQIsJ3oCYZcCbUEzmJdBi1kyvXr3khXjxTE1NbW1tnZycZs+e7evre/78+cLCwidPnmDn/a/+uH/++ScIJhI3Kx3Kl2OwRR347t275eXl+fn5WVlZV65cuXz5cmJiYnJyMm7my5cvZ2Rk5OTkFBQUgGMYBeREbJnEfqHjYgvmczlNTHPCEPgmYuqQKM5XZaVBHgjP1F9gDkh7gl24PkCHKNfU1HxsvQIco0tIlEWsQKCAMUMhWrdu3apVK9hz69atwTFQ5oDUwneFKItqIbVfoAwzBlV9+vSBxQJHYjOwJo6Kvwd2wYdCSAioABpygo0TIwQWCJaBCGrU3oj08om9e/fW0tIyNjYeMmTI3Llz9+zZk5aW9uDBg9evX//xxx///i/74cMHyfAEuGJeww+Ex5dUDLGioqIiLy8vJSUlOjr63LlzERERJ0+ejIyMvHTpUkpKSmpq6uXLl7OysgoLC1G+Hj58SFYnQp4yjpVXDlcDYR1i5hQEywJ7qTiESFA5hxzDm588eSJJIY+LeHfv3j0KjagZhOTq6uqPXQcBxy1atED3JZ+T0div3YRpUMcTPCbIhvtAJynKEXlAr9Q4oslSeOcAichjxVZgrihtyrxSHceSJvMASomiCakGdD2sE1lBxQmtoaPApLBt1dXWWkGh54NvS0nL06NFr166Ni4u7e/fu27dv/ysKIQe0GFSBG1okxKwj3kuEqidPnty9e7ekpCQ7OzslJSUxMTE6Ojo0NDQkJOT48ePBwcGnT58+d+5cYmIinS+5ublVVVXQiRcvXogSgldTWDjrB5mPb6LMDSDQyqjl4Fm+Kikd7Bb1jbgLmgm6chCe79+/T82cUK3sGfo0OG7ZsiVZFyAWqRjVAimDGp6oFsogxgCENEEkpqhBGYIVwsn8BL5iVUN5kKoHqhzEF1yCZgp7/OzRowergtdijsMPjTdD2dgp4RbSAgkh2Itk0a9fPysrqzlz5hw5cqSwsPDly5e///77/8rf9M8///ztt9/goxyQY9AMdoHI48ePkSCuX7+enJx8/vz56Ojos2fPnjp16tixY/v37w8MDAwNDY2KioqJiUlOToZU1NTUUNoQmL558+bdu3e//fab2O2VW0iEiEvoFQO+YJfoC/F98eIFijIq8r179yDiSBBAtrGxEUauLHGgslETQWkWdivxpaWl9ff3/BwD+f45/xyu+VBxS/iDoCkVu0aIFngqkN4ivsoETf4/Y1rp06ULsJJkTHGNjAFjiARKxAm1B6szAFMGOWgm3yRFpRRGvD6Qc55DUU0TC6927N6IepBkOA7UwMjIaN27chg0bLl68eP/+fcLw//qf9cOHD+/fv5cmuffv38tFnNIAqllBQQHZW0JCwrlz58LCwk6fPn3q1Knjx48fOXLkwIEDAQEBoaGhFy5ciIuLu3r1alFRUW1tLfIZwhlrgzBMvggV5uCa8E+tH2Kcl9ALyREhub6+vrq6+tatW2VlZdRZKisr79+/D5dAGCGTg0uIRQl/BWLL7du3qdegeRcWFj548OD/KnT/w/Hv8jxKHmLaJBgLx6D8IW0jpH3IEdADgi7FDvE/ACaQDYIF9+SFYJHoS5WO4oV4LDmH+A1YwTcONZJF7vJZXAEI29KBgdivZWAoxmKqeubn5uHHjVq9effr0aeQIGjz/t9t9IcoguKampri4OCMjIzExMTY2NiIiIjw8PCoqKiwsLCQk5MiRI8HBwUePHg0ICNi/f//BgwePHj165syZy5cvX79+vby8HJMGChoxFRZB0FWmMVIDF+YgDSYcEBsYMBRCuZpIrRvNBJ6A7EBIBrscohPjo6D6yEItLS0litfW1paUlHzsOoiyXgFkEeDEnyk0g2gtzjWictu2bSHBFD7gDxT2eAqo9ejRA3wDa16Cr5KET6xnMA2pUUtroLjgOcShxrOsHErKokYThvErw0bENKehoaGjo+Pk5LRixYrjx49fv369oaGhubn5f5rP/ZsDovzLL780NTXV1tZiw7127drFixdhDocPHz527NjJkyePHj168ODBgICAoKCgAwcO+Pn5+fv7HzlyJCIiIjk5ubCwsK6uDl0MEItCLGII+hqAFrIhaSUBWDpNJI0TSeHhw4c1NTVoINg5qIrzSdiv9PcxBmj6odIi9E8cF7jaqjLwPTv8HDx7cvn37Y/c1CY4Fu5RCUCqkHE2o5jb4BsTAF8FY8jllKyZVaC76WIKgGbBbOaF3794SLxHCACvglgKemHiES4g5TmgxJWuxUogSgh5H2mdhYeHm5ubj43PlyhWacN69e/f/iksoHx8+fEA0aG5ubmxsrK6uLi4uzs7OvnLlSkJCQlRUFEF33759hw8fPn78eGBg4N69e/fv379///7du3fv2rXL19f3yJEjly5dys3NxfL74MGDp0+f0oIvtFtao6XijRBBI/TLly+FnaM5PHv2TGQ+HB1iyySIAkeMHOXl5ZK0QR6EclRUVGCoR+oGvmL5uHv3LmU8YR11dXUfu18aHKNIkNXBj8WxCcQBNBBHnoMfo8QhUwBKqiHgGFFCqKpy0JVYS8Cm8AbQUQ+gBPiBpL1PuYohHk7RNGj2BtYoGOJXpjqora09YMCAsWPHrl+//uzZs8XFxXTb/3th+N8fv//++9u3byXgVVVVFRYWZmdnp6amXrp06fz58ydOnNi3b5+fn9+uXbv27dt36NChffv2+fr67t+//8CBAwcOHNi3b9/evXtDQkKSkpKKiooETK9evYJ2A1wALRqFeCpAuYhxcAxisDieaWTCqCk+fbAIoCsqKiorKyX64nSrra29detWaWlpaWnprVu3AHFVVRUBGEdeTU0NEjLoZ8FUVFR8bJ+Q6G7oaOIb/ie6TE2EGyR5QLZDhw4URAiNkueBcuG1oqyJy0da6/BIUFUGmpKZgWYATXDFEkQzLI8DWXQJZYkDcgyOyed0dHQcHR2XL18eEhKSn5/f2NjIVfvXX3/9X5Qm/vX48OEDqHr27Bm6aWFh4c2bNzMzM5OTk2NiYsLDwwMDA3fu3Llr164dO3bs3Llz3759/v7+O3fu3LNnz6FDh0JDQ0+ePHnixImoqKi0tLTCwsKampqmpibiLjim1q1c9BY6IXEalEt9RKQ3nGiPHj0Cx4RYlgqEGGemPCgN0hidYR10iAiT5mTRN4C+dK02NDRA7v+P4fpfHv8ljr/44gtyOCl2iOjWsmXLr7/+unXr1srtTJSapUNObMHYGCDByqQWQzq3xfCu7L2UfmYACrKl1CwuH3RlWv+pjyhzDARm3o2TKenp6ura2NjMmDFj//796enp9+/flx5jmZ3zv0cq3r9/L6Z4GjqKi4vz8/Ozs7OTkpJiY2PDw8ODgoL27du3c+fO7du379q1a8+ePfv27duzZ8/BgwdPnDgRHh5+5syZqKioxMTE7OzsoqKi+vp6vtW7d+/QQBgCxJwh5YFD7969k+8vErIMviCfk26/WsUBkUBhEHYrFnjpJAW+0qWH5ELY5lXgWKYCUC5B3Kiurv4E9Tx3d/cWLVrgX5N+O6RiqnfYhuj+VxYlpMcOqkAXNOiUzgsOoixXfFEnCKhSmga4eNxk0gXisbjpiWvpNwcAACAASURBVMpi5iSKcyYeDC0tLZaBQF9DQ8PAwGDw4MGzZs3y8fEJDg5GoL106VJCQkJaWppM+iLFEZvYu3fv/qdk4+3bt9jH+GcLa8zKyrp06dKFCxfOnj0LId66dauPjw8x+MSJE8HBwceOHTt79mxkZGRUVFRqampeXl5FRcXdu3dfvHjx9u1bYArhERAj6hGSucHFhEKMBGkZXtHY2Ah26+rqiKPgUro2kCnoxqM1GgFYfh0gC4iFGXMbDzTMWOQ5CiI1NTWfwF/h7u7eunVrlDLaPYAyvR6CY+UCXseOHWG9oBbRgOyNCoU0EYmCq2yhlIIwV3wOYipTI3AF4XZXBr208itXsBkWwUwgQEywF3ebDDGysLBwcHAYPXq0m5sbc7q8vLxWrFixatWqZcuWrVmzZseOHQcPHjx79mx6enpVVdXz58//jYLx9u3b+vr6/Pz8tLS0hISE2NjYCxcuJCUlJSUlhYWFBQUF7d27Nygo6OTJkwcPHty+fbufn19gYGB4ePjFixcjIyPDw8Ojo6NjYmJSUlIqKysbGxvx9Lx9+5YwTOgV6oK5WarQ0AxEDKiFtJyIGQiBTKobePBhC/wE0Ldv38ZG9+TJEwnYtOiBY9RlojViRVVVVV1dnTQBUK+W6QK1tbWfQK9wd3dv06YNTJd4DEWGUXz99df0fjKMAsmsS5cuQJDLuqRiyv3GohtwAqFRuUkTx480FxFx+/XrR88mvgisEdjWiMT04mOt1NbWtrGxmTVrlouLCyyZZhBu48QQoz3rh8E/tra2o0aNmjx58ujRo62srCwsLPAGDR8+fMqUKStWrDhw4EBqauqDBw/ev3//X/01m5qaCgoKzp49+/PPPy9fvnzp0qVLly799ttvv//++++++27RokXTp0/nrQ4cOLB79+49e/YEBgZGR0enpqYmJCTAnk+dOpWamgo4cnNzuSw8f/5cSioyyo0MD9TCm39THDxO5ifjgtANpNlEmEN1dTUlDG5z9969e9REpJGJ+E2opv+KdhUROnjD0tLS8vJyjHhQi8ePH9fW1n6CurTEY2py0upMGKbNDihTkujUqZPQAIivDFUR/Ys4LbU6NTU1GuUhrAwHwh+MlYehEECTPmRmt3EC5xCeeRBX54ABA2bPnr1jx45x48b17NkTvFJAEROc0GVp2dfR0TEzMxs/fvzq1avd3NyYBGdkZGRjYzN8+PCpU6euWLHi4MGDOTk5/z4ev379uqKiIjIyctOmTXPnzp00aZKrq+uECRN++OGHgwcPLlq0yMLCwsnJydvbe9GiRYsXL16wYMGSJUu2bt16/vz5nJyc8PDwdevW/fDDDzt27Dh58uSBAwfWr18fGRl5586d58+fMycTwiD1DjG1Se2DCC2cWJRjdFyiL4AT+FZXV0s/thBlxAdp0q6qqsIGjRhHnserYMkEbEa5VVVVyYwLaWP5NDju0KEDBWFpCxUQc/ebb75hdhu0QVVVVSZWSZolLALgojnwtshe9GiwAMCipqYms9uUTcPKLh+Bu4w/FBGjX79+enp6EydOnDZtmra2NhRCUkzpc0ZI4VuBbOZWzZw584cffnBychowYABjUxwdHV1cXBYuXLh79+74+Pj79+//e1H5jz/+eP78+c2bNyMjI/ft2/ftt996eHjMnj07IiLizp0769at09PTMzExsbS0HDJkyNixY93d3ceNG+fq6rpp06bs7Ozo6Ohly5YtXrzYx8cnJiYmMDDQ09MzJCRExBOSSOlUFdFN5hfiuJCALQ5jmlhlGgZ8t6qqqqSkhLAKwRWklpWVoa8VFhYCU+HBhF5ADGT/qRNWWT+ur6+X3thPoFdMnDixY8eOmMVo2RdzBcUOStCwXmQ1rJIiKRD2VBQdmuRY0i1Hw4WWlpZ0KCnbgkEq7Rsgm0s/+KY3DuwCQeXbdN5ra2uLoQJWw3UAooKQwkWjd+/eRP0BAwYwN9bCwoIpbObm5oMHDx49evScOXN8fX0zMzOfPn36740WHz58aG5uLikpuXDhwoEDB1auXOnl5bVq1apr165VVlbOnz+f0Vj6+voWFhbz58/funXr5MmToTQbNmz4+eefmb27fv36xMTEtLS0hQsX7tmz5/3793/++ee7d++gB2jAYteUurTyZGKKIMzXam5uFvVX0jjIQHFxcWlpaUlJSVFRUXFxcUFBQU5ODoOrS0pK8vPzb968WVxcfOvWLUZWA+iysjLgjoRMLivBGFfGrVu3SkpKSktL8/Lyrl+/npub29jY+LFx7O7uTrcw3BcJGWohAgWlOxnlpkwYiMSIa2KTAFhSn4NJ0+WB+ivzeGALgFumccIixPzOy+EkIiejsmGfEC+yeN9IK/G14ViSKK6pqWlubu7s7Gxra4uEp6Wlpaura2RkZG9vP2LECC8vL3pIa2pqmpub/yuK/ObNm6qqqrNnz27evHnBggXu7u6jR4/etGlTTU3N5cuXXV1dmTPElLf9+/fHx8dPmjRJX1+f2O/o6Ghvbz9s2DBvb+9169adOXNm7dq1mzZtevXq1R9//EF9m4MOfvG7UXkW+4TQCRnLST0ZsYwIyhCMvLw8xqrn5uZmZ2czw1xGuOfk5DCzvbi4uLCwEHwzcgASzGyN8vJyyiLEdRnwfuPGDVYFi+TT4Pibb77B9oD6JjPapDGJfjup0qFLdO/eHeuPjIZAIxP/Q7du3URqkCxNepU1NTWJu8rDkqXFCC0ZwVhSQ/zH0jXNF8CrybVCuI2YQvlJbJZOPlDLdDa+EnzGwMDA0tKS2ZgbN26MiYmpqqp6+vTpf1ooefLkSWJi4vr1693c3EaOHOno6GhmZrZ9+/bnz58fO3bMxsaGDr8BAwZMmTIlKSkpOTl5zJgx/fv3t7KycnBwcHZ2njp16urVq7dv3+7t7f33v//9xx9//PHHHxsbGz98+MAcWDRgGkCY1E3zkohcjDyUkh59StiCQbAES5Can59fUFAAjrOysq5du5adnZ2dnQ2Ui4qK8vPzc3JyCK4FBQUgmLtFRUXSKQg/qaqqKisrKykpYRxWaWkpal1BQcEn8G26u7vTLqrsjuDA+gOCZcaKTOghEIrjTGZEKPflS3ZFcEWvAMp01TMwmJY4xrlKJOaAE8Ok6cmDl4uVnuI2jaskeQgmUCBpBJSCH/KzNDIxXlamjBoaGtrY2AwbNmzq1Kk///xzTExMRUVFc3PzvxKMBw8enDlzZuHChc7OzoMGDbKysjI1NfX39793796GDRtgR0x/mzx58tGjRzdt2mRpaamtrW1nZ+fm5rZgwYIVK1Zs3Lhx27ZtU6dOnT17NncrKyv/8Y9/vH//nkBLSxyXBRgz1Q0yqqdPn4r1meodZQioMAy4oKDg5s2bN27cuH79OntlAN8bN25kZGSwm8T169dv3rxJSM7Ly4OB5Ofn8z6E5KKiIiKx0AxxaECLyReLi4tv3rz5Cfixu7s7MZXYJsZi8jxYMiEZTOORxzjxT+xCMiqCoiBbGDMoxOpAMz3MmNCIlQemQaMyo6iI5Yyiok9EfBpSi8H+JsZ86RmRuySdUGSWFmtDpl2xwHR1dY2Nja2trZ2dnT09PX/++efExERMyfJHY8eNR48enT17ds6cOUOGDGHuvJOT065du8LCwiZNmtRfcQBcFxeXgQMHMk5g0KBB33//fURERGhoaFBQ0IkTJ5YvXz527Fhvb+/Vq1dnZGT84x//+PPPP3/99VeYA8QX5ZiyC9Yz5C1phKYZ6e7du8RgjsLCQhDMrihEXzpNsrKyrl69yo4n2dnZ169fB835+fmQCnizRFyiNaOPiL6SOCpXVTjzE/g2J06c2L59ewpvWNHRicn5GEkvTUrEYwErVFWGq0rDs7JTQqZaMX2V4WhMb2d3BVBLIqipOGTvBfI/DQ0NNkPQ0NCQMRcyNJbaOF4l2IWywah79+4yqxOyLmqJst4nmiBj6C0tLZ2cnLy8vPz8/DIyMp49e0ZF7R8K4/yjR48uXLiwYMECGxsbY2NjOPeCBQvmzp1rZ2dHZVFDQ4OozHI1NDRkjEtwcHBdXV1mZmZ4eHhqaqq/v//IkSNdXFymT58eExPzD0U8FjqBLvH69WsGwdPLWVVV1djYiHeeRiOZtoagVlFRcePGDaIvm/Skp6enpqbGxcUlJSXRypqZmcl0gevXr0s8LiwsLC4uhkIQiYF1fn4+yZ9ybMYNJ0IelPoT1KWnTJnSqVMnIitRrX379gwU5DawFju8OC1RkUmVlFvnQa3YeiingRgQzJAeZrtraWnJnh2Mv+ZfztYe5Ps6OjqSmSGlgVox04n1Xnq2pe+aKCtcnGSUBcMmDFxPZH+Tfv36ATvltG/fvn35+fnPnj0j58Ms39jYeOnSpSVLlgwcOJANRMzNzR0cHBwcHAYMGMDGDpK2IssYGBhYWVlNnjw5ISGhubk5MzMTjS8qKmratGlDhw51cnIKDQ39/fffpX+JxYOlrqGhgVYiruNMpG1W7AwikwjZ/YA878aNGzShpKSkJCUlxcXFnT9/PjIy8uLFi8nJyZcvX05PT7927VpeXp4QD3hwUVFRUVFRSUlJRUUFtysqKrgrdb7q6mrBsbjniNOfBsdc/dkngWJH27ZtpX2DbmdCnXRwUO+1s7Nzd3cfO3bs8OHDBw8ebGNjY2Njw94wRFPgSxEOoQ0cy24asjUBKRE3GOxuZGRkamrKEIlZs2YtXLjQwcFBkjzlOqKM0xS1GL1CU1NzyJAhw4YNGzt27Pz588eNG4fiAamAGfNC2kNAGyvK1NTU3Nzc2tp65MiR8+fPP3bsWGVlJSZPcAY/nj9/vqOjI/v0sNuNqakpdAU2D5OBKENapkyZkpKS8vLly5ycnNOnT2dnZ+fk5KxatWro0KFDhgwJCAiA8gJi6MSLFy8aGhrw7tBwkZ+fzzYc0rOExEGJ+P79+5WVlQUFBRkZGZcvX46Li4uJiYmOjg4PD4+IiKAenpiYCL4vX76M2nDt2jXGDLB/HJhGeC4oKCDQlpSUwIxlrK0MuoVUkAV+7PnH8Ar0B/QKJAt+oh/LUFcALUafvn372tnZTZ06lS233NzcXF1d2eTLw8Nj/Pjx1tbWXK/JzMQHLLwCvHLAkuVBfX19KysrJyenGTNmrF69euXKlVOmTBkwYID0mQJlcjiYsfg2USeQ+Zgp6ODgMHHiRAcHB6mncPXAvy9VG3QSVhqLasCAAba2tqNHj/7uu++ioqLKy8sJgc3NzZWVlRQvBg4cKEO0zMzM2N6GXxxSjtiiq6tLMXLq1KmRkZFZWVlxcXEhISEpKSnV1dU7d+50dHQcOHDg3r17mbEiDuNXr14hQaCmMaslLy+vvLy8sbFRNgeRjkAmrOXk5KSmpl68eDE6OvrkyZPHjx8/fvz4sWPHwsLCMCfFxsbKxAy2CczKyoIi5+bmytaJhGHGc4n6BgXH/lZRUVGmOEpLS6mqfAJ/xcSJE7FM4D+WZlKcFTLhig5+yfBEw9LR0WHvMC6sgwYNcnZ2Hj16tLOzs5mZGWEJAiqm4b59+wIRNu0S8YsUEKHNzs7O29t706ZNJ0+e9PX1HTNmjLGxMU4gMdMR4/lKyoqbDL6A4YBpWDIZngh8MsAFrs9Hs0RZV4w3tra2dnV1Xbp0aWBgYFpaGj2V169f9/HxGT16tLGxMUuRTZx0dXXhVyxgZBDIFfzby8vryJEjp0+fzsjIQI+rra09cuSIg4ODtbX1xo0bb926JR1Kz549q6+vLysrKywsJAzDaClYMGPu5cuXDHZ58ODBrVu38vLy0tPTmShw8uTJI0eO7N27d+/evQcOHAgKCjpy5MiJEyfOnj0bFRUVFxeXmprKVpmpqanp6ek3btygIILZA+GCn6JGSzlazJ8waSAOL/8EdemJEycyLUXMFVL1EK4sLaU9evSQ2a9wU4gHlAPfJhKv/AsFoFLRgDVCKnAM81aiNvTu3Xvq1KmnTp1KSUlJTk5euXKlkZERiSAxWMYZoiLzZaR1j9sIxoCbFBbPkCAYEVByU3gzegjrk1xTX1/fzMxs4MCBcOWtW7eGhoaeO3fuxIkTq1atcnZ2Zr8mDHf8vjLWSJYKEjgFl3nz5u3fvz84OJgWjJs3b9bU1Jw8eXLo0KFWVlZTpkyJjo6mH4mkraCggLIFc4Zu3LhRVlZWW1tLK8DLly/R2oiL+fn5qampMTExZ86cOXToEP6kXbt2+fj4+Pr67tu3LyAgIDg4+MyZMxEREbDk5ORk9oGlMpKTk5OTk0O8B6CUABknLqgVCxG8Ao5BMP5kOKYnFByDaViElPeU++2k51kmsMgEN/EwyAAr/n/8g+UpFGLZW0l5hGHXrl179+5tbW29Y8eO/Pz83NzciIgIDw8P8c6LU5QvwJhD8SeJDog+LZY3oSJ9lDallLI5LxF5TmQ+WC9M3dzcfMiQIaNGjZo0adK8efNWrVq1atWq6dOnOzs7m5qacs2RZLef4iCtlGl0pJuzZ8/evHmzj49Pfn7+7du3r1+/XlNTk5CQMHXqVEQSHx+fW7du3bt3r6SkJDc3F4UhPj6e+SxsmcNgTMyZDBWA0V6/fj0+Pv7UqVNHjhzZvXv3jh07du3atX379p9//tnHx+fAgQOBgYFBQUGhoaEYR9knmGFcKHFXrlwh4aNQB6Pgf4HQpjwkQBqteVCGjX+aPI/aGxUQqXSgJdMbIvuIyYBNZlZIkY+iGoDo06cP11nlzbmghnK1lTkVYFGkMRUVFT09vYULF8bExFy/fj09PT08PHzZsmWOjo4icfTp00dmBiiPmpWeEU1NTfY6MDExUW5/4lCeMCvKIIFcuQWQDfbIPuHKlpaWAwcOZDtHV1dXV1fXUaNGDRo0yMTEBGokCje/LFcPFpWAu3///tOmTVu1apWXl9e2bduCg4MTExNra2uzs7OXLFnCdpHe3t6RkZGgJyUlJTw8PCQkJCQkJDw8/MqVK0yNwFuMFpaTkwOvzcrKYsoWXGL37t2+vr5AmU6qw4cPBwUFHT16NDQ09NSpU1FRUfQTiHaBuHH9+nXellIfohshubS0tLKyElaDbCKlb2HJ5eXln4AfT5s2DVxSzwOdZHikeriTYc/M7paaH7166HFS29PQ0CBPYmCmbEtqaWnp6urq7u5ubGwsHf/sjoqAgGteV1d35syZISEhbFAeFxd38ODBlStXOjs7g6fevXt3VWyvJC2ovRUzZEGzpqYmJ5Nf0kkFqmRMFiQb7P6TARXmo7wjE6GULYStra0HDx48cOBAOzs7CwsLvNTqis0khU3JdqtI7FyX+vTp4+7uvnTpUkdHR4hKSEhIdXX1tWvXli1bZmZmZmlp6eDgsHnz5sTExPj4+LCwsL179/r7+wcGBkZERGRmZhYUFEBhs7KyEhISRAy+cuVKYmJiVFTUoUOHaAHctm2bj4/Pzp07d+/e7e/vT5drYGAg4wdgybGxsfHx8WzsDpQzMzNlO/js7OzCwkJoBjYgeDPgxiVHwY9aCS2rpaWln4BXTJkyRRm+smuY8g5OgmwZwkKEbtWqFfmfUJGePXvSlozywMXd0tLS29t77dq1GzZsmDVrlp6eHvyb9aOhoTFo0CB7e3stLS2gZmtr6+vre/Pmzezs7Pj4+GPHjuGxNDU1NTAwQFoREHdX7AAJCZahbz0UByiHmst0LAnAKoqxs3APTpa6ozhIubCQybGJtJmZGTtUy86+8AopFoqULdivWqOmTJ09etGiRnZ2dnZ3diBEj/Pz8Kisrb968uWHDBnt7e3Nzc3t7+1WrVgUHB9NUsmPHDn9//9OnT6Mt0C515syZM2fOhISEHD169PTp0/Hx8bQDHj9+3N/fHy6xefNmmgJ3795NV/bevXsZPwCOT506de7cuQsXLly6dCkuLi4hIYH5iIhxV65cyc7Ozs/Pv379OvmfUOfc3FwohLBnCihIzllZWbdv3/7YOJ46dSq5Wps2baQjGsgSgMX+BusgBqMxg2N2cZRIxv9YMhsrK6vp06d///33S5YsGTNmjJ6eHgRXBm8aGBisXLly06ZNLi4ulpaWgwYNmj9//okTJ+ibOH/+fGBg4IIFC2xtbdnMWUzGypOHSOagQ90UO4OghUuLq3KbYG/FzPBeikPeB/YMwSAz4xeRrbBlN3ZjY2MLCwszMzMpRsKD0VKIx1LvpMrYr1+/KVOmLFq0yNbW1sDAwMTE5McffwQQu3btGjp0qImJiZWV1bx583x9fX19fQHiqVOnrl69mpmZmZiYeOLEiYMHDzL7gn7VyMjI5OTkM2fOHDly5NChQyR227Zt27ZtG22tAQEBjN4C0AcPHgwODj516hQUOTo6+sKFC1ALfiYlJSUkJBDmqVffuHGDQklubm5ubm5+fr4guLCwEGTj9gT3tbW1HxvH8IqePXu2b9+ediaAC/eFE0MhxDwEPmRmPftLczHV0tKysbGxtramhIGdYPjw4ebm5iqKrR1lahvFal1d3dWrV58/fz4gIMDT05NhgYzxi4yMDAsL2759+9SpU62srMzNzVkGguDOSkd3pS0fucIgKlPKFvou/lKZHC793sRyBBOZJItiSEiGJ1BaxyLC7wiOlXM7+axeiq34kKj79+/v5ua2evXqoUOHampqGhkZLV++/MaNG6WlpX5+fg4ODlCyMWPGrFq1atu2bf7+/sHBwSkpKdiFExMTQ0JC9u3b5+Pjs2XLlr179zKeubi4OCoqKigo6NChQ3v37t25c6ePj4+Pjw/BmDDs6+u7d+/egwcPBgUFBQcHE4+joqKYWguIExISCB9JSUnEZqTljIyMa9euMVf85s2bBQUF5KAgOCcnp7S0lMrI7du379+//+rVq4+K41u3bnl7e2PV7dy5szRLy7a7UhaROVdS5xMDBkYzcS8QZiZNmrR58+ZFixaZmpqqKIYIircTgzL40NXVnTBhQlBQUEhIiLe398KFC0NDQ6Ojo6OiokJCQnbt2rV8+fJx48ZZW1vb2NgYGRmpKKa8de3aFVbDlwSFMliDbwV0SOnEKgQ5FpwJuGXTBnXF5tLwCrmBACKqHOK3sh8VUsGG7CqKfUkozZBfamlpubi4/Pjjj2PGjNHV1bW1tV22bFlycnJBQcG+fftGjRplZmbGDOZ58+b5+flFRkbCU7Ozs9PS0mJjY2n2Pnv27NGjR48fP56SkgJhTUpKYugWKN++ffvWrVuRKXx9fbds2bJt2zZU5KNHj544ceLEiROnT58+f/48pT4kkUuXLoHj5ORkiHJ6enpycjKqXHZ2Nta5Gzdu5CkOvKAyZYudnZqbmz8qjisrK2fNmsV/rnv37gRgwMFPUCKz2HA1QE9lXyZ4hWw8o66ubmZmtmTJkoCAgKVLl+rp6Un4FH0AkQvdQEdHZ+TIkT/++OPGjRu//fZbf3//sLCwU6dOHT58eMeOHWvXrl24cKGrq+ugQYOsra0NDAxwx6N1IPmxqGAUXRWbRXdT7IWq3E3YRzF4k08XbxBJmHjtZXCyiC3IEYgwGD4JyVJ7F8cpr1VXHL0VE/Ml5R0zZsy6detcXV1NTU0dHR2XLVt26dKlnJycoKCgyZMnc82xtLT87rvvkpKS6MvIy8sDxykpKWlpadeuXbt582ZycvLOnTt9fX39/f03bdp09OjRCxcuXLhwITQ01M/Pb9u2bdu3b9++ffvOnTv9/f3J+Xbv3o10TTw+ffp0VFTUxYsXochkjTgxkpOT09PT09LSMjMzMcfduHGDEjrUAkmusLCQbA/rBV1PNTU1L168+Kg4rqmpmT17dvfu3fv27auqqirKg+x1J9EXpIJjUEhqqFznk+u4nZ3duHHjHBwcdHR0wFwPxY7NBELUYsmHLC0tx4wZM3HixLVr14aEhAQHBx84cGDnzp0///zzli1b1q1bN2HCBJI8ruBIDZ2V9peGsUh6J12D0pkHjknFSPuofhsaGlLCQA0kEiujkxwOQZqtIMV3jwEINYYzISG8D6q5CHm8m46OzogRI1avXu3i4mJqajpo0KB58+bFxsYWFhYmJSX98MMP8GYjI6ONGzfSQM+kosrKyqKiooSEhMOHD+/fvz8mJubcuXNLlixxd3d3cXEZNGjQ1KlTg4KCKJeEhoaite3YsWPbtm2+vr4wDX9/f6p6gYGBwcHBR44cOXXqFBMLwHF8fHx8fDykgmB85coV0IxvTgrXUh7Hp88mltIt8rF1t7q6unnz5nXv3p3spLPSto1crIXO4o3kKkxEhGkwMEC2HoMo41wTvMoEWOXhmYzBJHkihhkbG0+YMGHlypVbtmxBKjp8+HB4eDdivacQBcCx2Z/EtkdUJtWC1SI1DRbGLWW+lzZ1kg0fpPQF85HY6ikN5cwZsEkRxQrJ8+b5KW/bKpBjZiIR1AtsePnz4d999N27cOEtLyxEjRixduvTy5ct1dXUPHjw4ffq0s7Mz+02tW7eO0TAMwKyrq8vLyztw4MDcuXPnz5//ww8/rF27dsqUKYMGDTIzM2NjnmXLliUmJrIkAgICADEjYHbs2OHn5+fn57d7926gHBwcjHARGRl57tw59DuoRVJSUmpqKurblStXrl69Svk6KysL/+e1a9ek8oI/DjmZrXquX79+9+7dj4rj6urqWbNmEclAMMmcbAomezUzf5srr5qaGtyUE0gKpb9I5gPhipQLPdd9Zln06dOHKncvxW4gOM6MjY2dnZ3nzJmzfv36Xbt2nTlzJjIycvHixTY2NvPmzfP09EQ1U1GM21JRbMQLdeEnhxQ+ADTXdHQDKTRyrZdaIyFWWIRYl1AnkJD19fUR12RzJ21tbf4sEnSJ/VKcl2G1/KYjRozYsGGDq6urnp6enZ3dvHnzYmJiaDoKDAwcOHAgC2nRokWxsbHHjh2Li4t79OhRdXV1XFzcypUrx40bN27cuJEjR44YMcLW1tbQJUSskQAAIABJREFU0JBlZmho6OLisn//fgbMHTt2zN/ff8eOHaCZ0XK7du3y8/Nj9v2hQ4eOHDkSFhYWFRV14cIFwjBRGWtyamoqIklGRgYgzsrKIjZTKEGsKCoqogX19u3bJSUl8fHxoaGhRUVFHxXHd+7cmTFjhtTkGCkkylrnzp1FjmDoILGQKIuLiNI053dT7O3cVbFrNO8pbg3xBFOTU1GakyKzrfT19a2trYcNGzZ+/Pj58+fPmTNn4MCBNjY2+/fvX7NmjdgqxBXUqVOntm3bYj0lTpPVQSfkEQ3Fvuc9e/aEJMAQ+ij20cFgSb8gdRBx/UMbpP+ZEzQU+zsBfel+lX2ixPoMmsWwP2LEiPXr148fPx6vs6urq4+PT0BAQEBAwPz58zG1Ghoajhs3bsmSJYsWLYqKimJH9eDg4HHjxtna2tra2trZ2Tk5OdnZ2XFBw/s/dOjQ2bNnx8TE3Lp169KlS4cOHWLOpwgXSBb79+8/cuTIsWPHQkNDIyIikJAvXryIipycnAyvyMzMBMfXrl2DVFAc4S6dI1St6f6/detWRkZGeHh4QEDAjRs3PiqOa2pqZs6cSbZE1BSXBb16kuQxVJMQi4xF/Q+kKu9nCmcV0UBaU7noq6ioSI2A+ARilD0PcukXbw1xa/z48WAUeQEKIZoxsbbbf9zunG+LcEHKJZmfVN2U+5r4JhQsRKYgnyM2y05QUgOHSUsjLe/2TymjCHaGhoZDhgxZvHixm5sbno1x48YtW7Zs3bp1CxcuHDZsGKtLR0fHxsbG09Nzy5YtGRkZDAbfvXv34MGD2R7Y2tp66NCh9vb2rCJ8V5aWlkOHDv3pp5/y8vLKyspOnDiBkcPHx8fPz2/Pnj2+vr6MNQoJCTl79mxERERkZGRkZCSbOVy8eJFgLAIFUklOTk5mZmZaWhoEAygjKtNffefOnYcPdivZWVtLzFx0dXVBQ8FFxfP/+/blz51IcFsVKXG8yXx5o9lGaEUhzv1iT6XqSDjmQJIYeQCZlYXyeFHv79++PaZ3qbt9/OTDs8xIDAwOUL0Av7y/7hkizE7UPIRj46VgdivCakm1DMFZwAImVaFxgVOEpzoaamJqkC7ynXE1LGPorN/KiAyMg5BLtBgwYtXLhw6tSptra2Y8eOdXFxcXNz8/T0HD58uImJieSRw4YN27FjR2JiIls2lZeXHzlyZNasWdOmTZs3b966des2bdrk7u5OxRS+bmxs7OTk5OHhsX///oKCgosXL0IqSPX8/f39/f337Nmzf/9+VM7Q0NAzZ86cO3fu/PnzCQkJiYmJVPVkDz9YREZGxpUrV9gHjVEbhOecnBwKeOSjtbW1WVlZWO2Ki4s/Ko4bGxsXLVqEWR40QAOYJCSkQqYUS6cdhJISmswpZAMlDoBOFCfPA8R6enpmZmYWFhaGhoaUxGxsbKysrOgqBcr0MolYBtnABimyA5/eQ7EtCJcIvqo8Tt7WR7FvJIkX/3JILUBUVYxIlCUqCJY0lE+HexACwa5ygiiMAmARhpUL4ywPR0fH77//ftasWcOGDZszZ467u/ugQYOGDRtma2trYmKCl7V///6DBw/+7rvvTp06FRcXh/VnxYoVc+bM2bFjR2Bg4MmTJ5OSkpYuXSpLCCO4o6PjqFGjvL296TQJDg7eunUr8hwI3rNnD663I0eOiOuN9hBCMuwCRoH0dvXq1bS0NLSL1NRUCcYURIj9OP0zMzMR8j52Pe/x48dLly7t1KkTV2p0NwKt7OJINsYFXfZDkFYo2cwU/tBNaUcPoiNRnLBEpBkwYICNjQ0eDFNTUycnp9GjRw8ePBgJTNqYBRMGBgb29vaWlpZIYCKiieFYepzEeUzCJwGSyzpPwWsNDQ37K8YX8Z6kfb0Vu/dJ6AXKsAtWlHxPnhIFmtsaijFLwsjVFPv2waBsbW2//fbbBQsWjBkzZsaMGRMmTHB0dHRycgLH8hcguE6ePHnu3LkeHh5Dhw41MzMjli9evNjLywvxjjXGp9PpPXDgQGdn502bNqWnp0dGRuITYhsHBDhAfPz4ccgx7s3ExMSLFy/Gx8fj4sD7Rm6HRoHpQoIxGhzdUAUFBYx4q62traioKCgo+Nj90uC4ffv2/N3J3tCtpLorl+muXbuSsfGgstpFuU7aUdHUiJqkOMplXmNjYwwxZCczZ8708fHx8vKiUc/ExMTY2JhphQRmIyOjMWPGjB8/3tjYmBVF8sQhBgapNrNsMP4CrH+y9iOoCTMmzEsMFhDLsAHyP3I+OkSUjZrSKCW+TehQf8U+7yw5LiP9+/c3MTEZM2bM6NGj7e3thwwZ4ujoaGtra2lpaWZmZmRkxNuy1O3s7Lh20SxoampK65S5uTk3pBVSulFMTU1JAT08PA4ePHj+/Pndu3dv3749MDCQasiuXbsOHToUEhISFhaGuYLekEuXLiUmJuKsELGCYIyZE0EjIyODGS6URTIyMm7evEnHK9tA3b9/n616PgGO27Vrdiv5GlQ4ZSzpPhfV26tSJkjXxGLFZwrNEYvix+CdJm0ReJffHJgZGV65cee7cuR9++MHV1XXSpEkjRowYOHDg0KFDhw8fbm9vb2tra2FhYW1tbW1tjfkYLHKJBzGgWYgB+O6t2FQBUoF8S/QSCQLMEc/6K8aBwm55HKGNoSrcwMdHVU90D0Iyp8k2wHwKHEP6Teg5dXBwGDlypL29PUZQYAoujYyMjI2NraysHB0dhwwZguPZwsKC+baGhoa47aiVgGBDQ0NImqGhIQ2FI0eOdHZ2njZt2oYNG5glx/58GC2OHj0aEhLCHPywsDB2Q4uNjYUiY+BENqbFWrgyjIJJLqjL169fLy4urq6uli1NYRcf2+/2+PHjZcuWde3aldKGIJIYjHYmwRgpA58Q+rHslk6aJXszyqhWyKgARZp/5K9vaGi4adOmmJiY9evX+/v7BwUFeXh4ODg4uLq6UhEcNmyYk5OTiYlJP8UO6ZI2SZsTvELSNYm+ougpC8ZcE8Tgr6nYhpqiBo/0UWwRKYobOEavkKZDzgev8uZ6enpaigG4nIz2zBvCTMaMGcOvCRBNTEyIvvScW1tbDxkyxMnJydnZefjw4SNGjHBycqIsb2FhYWtrCytj4i2LhyyZCiUCnIODg52d3fDhwz08PFauXOnn53fo0KEDBw7s2bMnKCjo2LFjaPNnz56Fdiv+6dAnxODExMTExMTU1FdtQfHz81atXs7OzcQjhsmAORmZmJmVqhhDcunWL/SHj4+NLSko+DY6ZNIWRt7tiqy/ZCYHsHrVYNmICvqLjyk+hof2VOv4RCqS3B8O4iYnJ2LFjDx8+vG/fvhkzZhw8ePD48eMzZswYOXLk0KFDbW1tuarinjMwMECm7a7Y20aECJRjAbeGYq4hsVDQRjxWThb7KvbllQYQKs/SKAoJBpRC3CWig1TlPpd+ihG3Mp1DEM9TSM729vYDBw60trZGDLa0tLSyshoyZAiymrm5uY2NDaR56NChY8aMYbLCwIEDrays7OzsrKysTExMaBQAu3xnfgX+vIMHD4a0jBo1asaMGTt27GAPP/btO3HiRGRkJGasmJgYsSAnJSWxayUIlm7qnJyctLQ0OlKJzRkZGbDn9PR0zEP5+fnsTZaRkcF0r4+K46VLlzIiSKoSMoJb7Dj0HYFvIQ9iYCfHB0B4gAA08JXoDtREiIUlb9iwITIy8rvvvqM6sHXr1kmTJo0aNcrCwgIc9FOM8iaiowD0VGxkxvfkBh8nJWjAKpKZ5ENqidivMpNghBBocS1QmhHMNke/AwTehqsfjXIIAPRwdjiG+OZYQlwIYi62trbu7+5QpU4YMGYLxmqWLvxkqZWNjQ+lu6NChCMbm5uZSK+FPJFN3ZZiYoaGhg4PDuHHjRo8e7eTkNHbs2A0bNrAbe2BgIA1O+I8jIyPPnz8fGxt7/vz5CxcuAN9Lly5htEhMTGQXlYyMjISEhKtXr9I6BfFIS0tLTk5OTExMSUlJSUm5efMmjXq5ubkfuy4t/FhFaTMl8fSI+UayKJI/ocsqKiqwNBG2VBTD17orhnDClcW9TmDu27evgYGBo6Pj4sWLf/rpJ09PTycnpx9++MHf33/+/PkuLi4WFhbEchlpxfsLeVD+CCo1UA7UN6kGA0fp4oY+gX6sdlqKMbWcLM4K4MvFWjQ4Elap4PARrDR+L05TV1dHZGQJyUfwDiSg5ubmDI2dPXu2k5OTtbW1vb29jY0NWR2BVktLy9nZecaMGWPGjCFhGDp0qLm5OSuE9UMHoZ6eHjoMH2RsbDx48GBPT09PT89BgwbhRtq5c+fevXv37Nnj5+e3d+/e4ODg0NDQsLCwM2fOnD17Njw8/OzZszExMXFxcWgXsbGxGC3I87BY4Oe8cuUK2lxycvLFixfDwsKonzOQ4MaNG3fu3PnYOF62bBkbOUqnENU7mR6krq5OOmxubq6lpSU2ia5du6qpqYFj5T5NWKy8m+BbMnekNHNzczs7u0GDBg0ePNja2trOzu7vf//75cuXAwMDZ86caWdnR0lCCnIqiu3OEYl5c74GtL6n0hxvaX4Wgi56RR/F5jrKfEDYhbiCRPjrr5iDr6bYM0qmL4uETKyVOYii9KkrxoKRU0proLa2trW1Nds4TJ48mYTPysrK0tKSVI8ikYaGxoQJE7Zu3bpt27Zvv/3W1dXV2dnZzs5Ohn7wheEV/8SCLCws3N3dZ82aNXr06CFDhkyaNOn7779HS2bjMwYAHDt2LCQkBE99REQEShyGITz1KMeXL1+Oj48XG0ZERERMTAyDD69evRoZGRkUFBQREcHJFy5c+NdivkMePH3/77beoE8qlEDxABDb4nLOz8/jx452dnfX19YmvPZXGvv9TkwUpozjgoB+oAQQwdKVBgwZJVj506FBfX9/i4uLo6OilS5fa2dlpKPbSkwDMRYNlRilRUCumPGH5xPK+ffuSDxG6RPdVjrvKQ9+E5moqxgxIS5/44sWSoaw6E55VFSMypJIni4TLWi/FHlNsHuXm5ubm5oavGsoL4qEx6urqlpaWP//8c15eXlpa2t69e//+97/PnDnT2NhYWagWdUUkbbp60acnTpw4YsSIKVOmrF27duvWrVu3bqVjavfu3Wx5jR8f1YIy9cWLF2HJ8fHxV65cwUqPhT8lJSUqKiowMDAmJoahWykpKVevXr106VJ0dHRYWFhYWNiJEydyc3M/No4lzwMZwiVUVFR0dHSsra3JFdzc3Dw8PDw9Pd3c3AYOHCiilXLzJn/Q3ordDBg7JO3KEv+0tbVNTU3t7e2HDh3q4uIyZ84cWlBDQ0PT0tJOnz69fv16jJoaisZmqdhx3aC9TwxJFFwIzz0Uc/C5RPCV+JcLG9bU1OTCLeqEsqBBcJWaHDFVgMtddcWIUU1FF7SUZojrZBcsA4F4b8UETlNTUwsLC0x8y5YtY7IWA5ZgU6wxwu20adMSExNLS0uTkpIuXLgQEBAwduxYubaIkYMvyfXE3Nx8zJgxXl5e3t7enp6e48ePd3Nz+/bbb3/88ceffvpp8+bNW7Zs8fX1pW+PSQBnzpwh7YuIiKBJRAYOpaamih6XmpoaGxt78uTJ6OjoS5cuhYWFnTt3jhTw4sWLBw8ePHr0aHh4+Mf2V4Djjh07qiqGyFMEwQ3s5OTk5uY2YcIEQOzl5TVnzpz58+d7eXm5uLhYW1sj+4tjAdMPfFQ6IMRULi0VRkZGVlZW9O0tW7YsIiKCFvbo6OjQ0FD6yY4ePfr999+bmpoCU7wQkkEKpmXcm5iHRGORMrWKYuMSwSK6r3L5rb9iKLL0LyGtAFnlcUGaihFeYlYWgxF4lSkCPRWj+fsoto0CfOzkZ25ubmlpuXz58i1btjBci1lhGO4oAwFKS0vLmTNnrlmzZtWqVcuXL1+yZMnw4cPFEcoVQKz9enp6VlZWo0ePnj179vLlyxcvXrxixQo2QZs7d+7SpUvXrFnz008/bdq0if2u8XCGhIQgIUdHR5P2sRdgSkpKXFzchQsXMGCwv2VISMipU6dQ6+jcTk1Npb00Ojr6wIEDfn5+2dnZHxvH3377LeU30St0dHT4W0yfPn3WrFkzZszgxvz585ctW7Z8+XL+mu7u7s7OzoMHD5YxDpTfRGTQVoyPl9YJY2NjMzMzYjxEZdeuXWVlZeypcfDgwY0bN+7YsePy5cuPHj3Ky8ubMWMGV+duiv3QeygGxSoTmz6KoctgvbtiC1QZziK+NmHGsFvlMCbWC6inslMCBUC59UNZQiF/YElDIZR9zyqKCdASm/X19QHxwIED16xZ4+fn5+LiIrOL+ENR70BNMzIyMjExsbCwsLe3pxTCF9DU1BQ3CH9hoMyMUBcXl0mTJk2fPn316tXbtm3bvHkzK2Ht2rUbN27ctGnTzp072aWdHYKJryhuV65cobDHKCPmGF27di05OTkgIGD37t1hYWGxsbGYilA5sA2lp6dHREQEBAR8GhwT7Xr06EEeTRj28vJasGAB2xsuWLBg8eLFS5YsWbFixZo1azZs2LBmzZrVq1evXr164cKFS5cuXbVqlXT229raUrxlCiWVJ9qAbW1tR4wYMXPmzJ9++mn//v2hoaGpqanl5eXFxcWxsbE7d+5cv359cHBwWVnZ48eP7969e+LEiXHjxmlqagpb6KaYMg8mBKn8RyVaUw1RtjT1U0wKFGG7n2Jgs6CctQdeWYoiBvMbiSlZR7FNJRKEgYEB07FEeRRmzJeEUUAA8PdZWlra2dlt2LDh0KFDkydPJhIrG0QlHrP4yYltbGwY7kjHDWtPWSDX0tJiihe8xdHR0cvLa8eOHYcPH967dy9oXr9+/c8//7xr1669e/ceOnTo9OnTZ8+epbcvNjYWgSI1NZWQfOHChRMnTqSnp5eUlISHhx84cCA8PDwmJiY+Pp7xcLGxsREREeHh4XSXsADKyso+AY5pXdbV1R0yZMiECROmT5/u7e09f/785cuXw1zZsXDZsmULFixYtWrVxo0bfXx8mFuzefPmw4cPnz9/Pi0tLSkp6fDhw+vXr/fy8nJ1dR0/fryHhweEZOnSpcuWLaMh59SpU2VlZezR8ssvvzQ2Nt67dy87O3vfvn0bNmw4efIk/im2MTx69Ki9vT3ohDwgXwjxlZ5ndEORLKTnvpdilx3x9Iizp79iWpeY0cAuZFpGlJM/SRSUTmkp9QFNXV1dcWmKwU3Z8obiRhWaY/Hixdu2bXN1dRU1TbaQ4uOYEG5hYUFZhCqdmZmZZK5SkcbjjykF6FtaWg4ePNjDw2PLli2MeyMAbdiwYdu2bX5+fgEBAeHh4RcuXJBJssnJydHR0WfOnLl06RJ+TqbNXrt2raSkhAofKEe+SEhIOHfu3MmTJ/38/LZu3bpv376oqKhPg+MVK1b06dPHwsJi5MiRnp6es2bNmj179uzZs4Hs3//+d9oVV69ePW3atGnTps2fP3/Lli2RkZEJCQnHjx9nYEpubm5FRUV+fn5ycvLx48fXrFkze/bsdevWBQUFMbSGXCEyMjI1NfXevXtsschGG+z6XVZWFhAQsH///tTU1Nra2qamJmZTJyYmjh07VlUxx4QLNORBVTFUs7diW2n4sapiEzR1RbOnWPVBrZTlJPSKH6Of0pYL0kYqd7GPsnMwjBn/NMYmiiMsG1aRcoWcu9ra2pAKLD4TJkzw9vZ2dHS0tLQUuw/LhkyUR2xtbZ2dnZ2cnOzt7SnmIQuKOgEnISRj4KRG6ODgMHny5KVLly5fvnzRokWkej4+PswAOHPmTGxsbGxsbFRUVFRUVFJS0uXLl0NCQg4dOnTy5Mnw8PDz58+fOnXq5MmTcXFx2dnZpaWltG1fu3YtNjaWDd/PnDkTFhbm6+sbHBxMOTA0NPTatWsfG8dr1qxh2P/MmTPnzp27YMGCefPmsZXsihUr1q9fv2nTprVr13p4eIwaNcrDw2P9+vWnT5/OzMz8H8R9Z1xbd5ru151M+pTM7kwmN3ESO86kODbBYIzpHVGEqBISIBBFEiBAmF4EiN577yCKANNswGBMMb0YMMZ0DKYbsDHgEs/98Pw4l93NTtnd65wP/hmbIuA973n/z/uUmpqa+Pj44uLijo6Ovr6+5ubm9PT04OBgZ2dnGo3GYDB8fHyysrKam5sRNjE6OopEuv8cdntwcNDZ2VlUVHTr1q3Z2dnd3V0U98HBAbLoiGI9iX8BEEDR4Dj16bG/BKE3wQR8+sT12bHymaAl4P2JAZpgGxM1jTeJIsNeGp379OnThA4Ah8g/HSdWEZj32bNnL1y4ICkpiYUFjKJBkJCTk+NwOO7u7qqqqrg9vvvuO2J6wR0oISGhrKysqKh46dKlH3/8ER9IYIj/5zgcFgcbhFFgaLl48SIISSoqKgoKCurq6nZ2dsHBwViFJCcnA5FAXlNHR0djY2NxcbFIJBKJRLBoqaioKCkpyc7OLisrgyaP0DVVVVWBUICih58LSBq5ublvWte0vr4eFhZmaGhoZ2dnaWlpa2trb2+PicLZ2ZnD4djZ2TGZTBMTE11dXTqdHh4e3tjYiDiJuLg4Ozu7mJgYbCyTkpKYTKaRkRF0dfCjSE5Obmtrg6Po1NTUf2Uz8/TpU9iHPXz4cHd3F3l1yMVobm7W09MD2kCMCgTljaBtfHLsSIvyJRbLGA8wABDOAQRHAk305OkNh0LiDIeOe3ItRywa8GkxquJMhsmBoJr84djt/KuvvpKRkdHX19fX18dUgOURpt7o6Ojm5mYGg/GXv/wF/4VHBDru119/LSMjA56QpKQkTJVwKMTrITjTuBu/+eYb0JRR+qDn42ytqKhoa2sbHBycmJiIVpqTk1NdXY0lc1NTE9xmEb9QWFhYXl4OFzm8G2huYHI2NTU1NDSUlpbGxcXBjra4uDgjIyMqKioxMTEvL+8XmCsyMzPZbLajo6ODgwOHwwFMY2try2KxzM3NTUxMDAwMKBSKk5NTcnJyS0sLjJrr6+vd3d3d3NzKy8tBgCouLob3j6ura1ZWVnFxcUJCQmFh4Z07d2DGuLKy8vz58599ZS9evNjZ2dnZ2Xn+/Pnr16/xj8+ePVtaWqqurjY0NPz02EQeK19iGYFqO1lhJ63hMTUS3EhJSUmCZIfKJqiPXxxHHxCHv9MntKWoWsILGTxpCDeALZw+TlEgVkKEgoY422lqatrY2Nja2pqammKBdiv10cnLyyMgIh8M5f/48XiFo/nCOAzqpoqICyrKysrKysrKkpCT4FRC9AtkkIEIMITo6OsbGxrq6ulJSUhcuXJCWliaTyXw+PywsDP7H5eXl0ICUlJRkZWVhG1JQUJCbm4t3yMnJyc3NhTsZ7ASGh4ebm5thWVZVVVVVVZWQkBAREQFHOfT4pKSk2NjYwcHBN13HxcXFXl5egYGBAoHAz88vODiYz+ebm5ubm5tbWlpaW1vb29v7+vqKRKKBgQHkQbS3t+fl5UVGRlZVVcFKHx23q6urpqamtbV1ZGSks7MTyPnt27dHRkbW19ePjo6IGv2719HR0dzcXG9vb3l5ubm5OZorQV3ARTQt/IUAUJFQhrUC2p6EhAQovDDBwEkLgk0YtH3//fcwpELcNBH7AOqZpKQk/vzuu++g8cSHg9KOE94Xx4LTkxs+7NUxyfzwww9kMpnNZrNYLD09PUTzqqurp6enDw0N8Xi8H3/8UUpKCq/2ypUr4G0aGxubm5sbGxszGAycW3g8HoVCAQJ9+vRpnCPxjALFQkpKikQiGRsbGxsb6+joqKioyMnJycnJGRsbAx4pLCwsLCwEx00kEuXn52dmZhIzMThxaWlpCQkJhEcRnLtGRkawiAZCV1FRkZOTAyZ+fn5+bm5uQUFBUVFRcnJyX1/f/3b1/r/r5+u4pKREIBBERkZCDp6RkSEUCl1dXT09Pb28vPz8/OLj469duzY+Pr64uDg9Pd3S0pKZmZmdnd3S0gJ3/7W1NdjeLCwsIGRzdXUVoa1dXV2tra2zs7P/VUrzz16Hh4ePHj0aGxvr6+urr69ns9nooGiBxDoDj3UcvABCoROjAZ88tiOnEc/lH3/8UUJCAtWMSQPND6MnCdivljevixYuSkpL4E58NF/hoiDEltoMnD5RETeN1njlzRkZGRltbW0tLC/IWQ0NDMpmckZExMDDg7OyMhwaKWF1dHWiPk5OTp6cnn893c3O7evVqaGhoSkoKl8uVk5P79ttvsUrECRgPh2+//RZmTsbGxpqamhoaGqampiYmJjo6OgiFyMjIKC8vh7s9lnmYhmNiYjIyMnJzc+HMCSJRRUVFW1sb8DVE5iAl7caNG21tbWKxGPE5KSkpMAyPioqKiYlJS0sbHh7+36zcf3/9TB1vbm7W1tamp6efXNIUFhZCOxAVFQXDdOQUra+vT05O1tTUACacmppCjObW1hY8/onA7qdPn25sbCwtLfX397e3t/9TKa0HBwdwglpYWHj48OH9+/fT0tLgTnlSbYH2jPpA9wVjHc9rogpRu+isaKsYNIlwMWLkQLl/f3wRDscgoKH7oh+jnYObhlsIozbx2gDbYaQGSIdR5PvvvyduCWVlZSCSkZGRDQ0NPB4PLxhUFkNDQzab7evri9VmRkYGvGKTkpIiIyOtrKwuX74MIt5JjQI2hZcuXbp8+bK8vPyVK1c0NTXRyG1sbHx8fBISEoqKigoLC/Py8tBBkUSWmZkJa4u4uDiYdmZnZ0O6h4G4p6enqqoKxRoSEoKElPLy8pycHNjRBgQE+Pr6+vj4hIeHl5aWTkxM/K+W7r+7fqaOd3d3W1tbgRfW1NSIxWKIAvASKyoqOjs7R0dH5+fnsZgYGBjo6OgYHR1dWlqCtBCBbbu7u8+ePTs6Ojo6Ojo8PHz69CnCVyYnJ2dmZv62+yLiQZ8/f/7q1auDgwOka+GuODw8PDw8HB4etrCwAHf59HH5GqNbAAAgAElEQVQo3WfHNvdgLHz//feYaLFiwJ+oS8TgSUtLg84L6ArNGKWJUiaGBOK/8Oy+cOEC4k0hxwAOgFoB6EvElRIE5c+PcxXw2jBY4yZEy0SHhiDUzs4uISGBxWLhdaL4bGxswsLCcNjKyspCAQkEAn9/f3d3dwqFIiMjA2cjfE6cCrApxHMDM7GSkpKhoaG9vb2Hhwe2ISKRCDTLzMzMsrKyGzdulJSUJCcnx8XFAVROS0sDD664uBhhewUFBc3NzW1tbbGxsb6+vn5+ftHR0RCrlpaWoq/l5uamp6fHxsaKRKKGhoY3fc7b39/v6uqqrKy8ceNGbW0thISIOYGn/tzc3MLCwuLiIqIFBwcHJycnHz58uLCwMDs7++jRIwC9h4eHr169evXq1YsXL46OjnZ3d6HW2traOjg4+NlX8/r165cvXyL7e3FxEZk/8IheX19/+fLlq1evEIS4sLDA5XL/9V//FQ9roGwQcuIhDgQNDRuDAUZkECCJLoiiRJWjQxPjB1zm8SEYOVAK+Dv+hIgDsiI0Y3wgvgphLISu/MlxugKAEWJ0Pn36NAE2Y1NIpVIjIyOpVOq5c+ekpaXl5OQoFIqXl1dqaipOYH5+fg4ODg4ODtbW1jgpGhgYyMnJwc0DOzysQvC4gJIP37KCgoK5uTmfzw8MDExMTMzNzYXoH0e6urq66upqwGdwf4P2KTExMS0tDah/fn5+VFRUamoqDOPwbunp6Xl5eeB8wioO47JIJEIHHBgYeKN1/OLFi6GhoYaGBthtDA8PIyV4bm7uwYMH09PTq6ur6+vra2try8vLqF1E9MzOzm5sbADlxZ+oY4Qh7+3t7ezsHBwc/PTTTz97tvvpp59QxE+ePJmbm7t169b169dh83H//v0XL16gSR8dHT1+/PjBgwd8Pp9AJ7DpBdcM+zY81r86jpEkzOIhvUYhYrRFr0W94t/BZEDpA4XA/+LfcT/gQ1Ai+BOaIrwbgZMQUCCWMgT7Av9OUJkJPjSoSAYGBrGxsTweD/ItBQUFKpXq5+cXFRUVGhoK21xra2srKysajWZkZGRiYmJoaKioqPj1118TJkYYYJBdcvny5cuXL+McaWBgwOVyr169GhMTU1BQgJaJERZU44KCAkQ3gJGMPg0cDTTOtLS0+Pj44OBgJyen6OhogMqVlZWNjY1lZWUpKSmxsbFpaWmw2KqpqSksLMzPz3/Tc8VPP/109+7dxsbG3t7e4eFhUHYePHiAHB54Mq+srCBmcGFhYXx8fGBgYGpqamdnBwHIL168ODw8fPHiBdYW+/v7COJ88uTJ0dHRz9bxq1ev9vf3Dw8P9/f3JyYmamtrRSKRWCxua2ubnJzc3d3FO6yurj569GhjY2NlZSUuLk5CQgLQEkHtRXvGIf30sWHKqWNXbeJZjxMYgFUiCZiAfnE0JNA6/IXAnsH3x6wsKSkJOR1IDoRNFsFwIJStoHyc+vfhNwSrjjgF4rUpKCjEx8cnJiYqKipCSm1lZeXv7x8YGOjm5ubi4uLg4GBmZmZoaAgMFJeysjKCMYmtHh5KsLCAwpRCodjb22OBV15enpeXFxISAnwXdAsQ6jGxAFTOz89PTU2Nj48vLCxMS0sLDg6Oi4srLi7OycnB/g/r6IqKChyiALBmZWUlJSXl5+dXVFSIxeLa2tp79+696Tp+8OBBR0fH4ODgxMTE7Ozs/Pw87GwxE6MTr66uggWBeXdra+vw8PDo6Ahhy0dHR+id+/v7z549Ozg4wFHv8PDw5cuXP1vHBwcHL1682NzcbGlpSUtLS0pKEolEo6OjyJfd2NiYmJjo6+tbWFjAF2psbCSRSARAi13DF8dGxai8k74+OAielND9B1ExsagjhhPQfQheNZYLWNfh5EdoPHH+I2SkOGARa+pTx9mPfz528CY225hlibsOCMzFixejo6Nzc3M1NTW//fZbJSUle3t7ECF4PB6bzWYwGIaGhhQKBXVMJpPhjgCyMkFawn2LyQqiKSaTKRAIsMW4ceNGUVFRSEiIQCCAeSE8soKCghBMlpSUVFhYmJiYCIMLkOJRu11dXdXV1fHx8Tk5OZgccDTEm+jfQI6x+ROJRG8ar/jrX/+6vLyMqMq5ubnl5eXZ2VlkpD18+HB5eXllZWVxcXFhYeHRo0fr6+sg9xwdX5gNcKGa0Z739/dxbvvpp5/+xgva39+fnJwUiUR5eXm9vb3b29svX7589uzZysrK4ODg+Pg4DoivXr2an593dXU9dWw2BZ02wa4EY5jgNnx+nCiKjnhS7UNsmwk7KYIER3TK/3PsY0soPiDWwDwNohnheESUIxhLuJ3ABiFEUBhh0YCJFSMh/vvmm294PF5GRoaRkdF3332nra1tb28PfiyPx7O1tTUzMzM1NTUyMjIwMNDX1zcwMDA0NNTW1v7xxx/R4E+dOkUscQjekqKiopOTU2FhIXbFZWVlSH/y9fXlcrne3t4FBQW1tbXZ2dkAKBDZC9shHPKIFByEQREQVmpqKhbaLS0tcPXEwqukpKSurg4KkaWlpf9fVfxf1THQtLm5OVDMpqenZ2dnFxcXV1ZWVldXl5aWgH+tr6/v7u7u7+8fHR09f/4cf6J8cSbDsezZs2dPnz599uwZdst/9zo8PERG8f7+PngXr1+/RsL94eHhX//611evXq2trd27dy87O1tJSenT4wxJwq8IjRMsHJTvF8duQwSygVoH8fLzf38Rqmy8SahHib5O+JtgXMYRDZ0YMww6IsHTIDQsMF1GnRGlhhsDnwf7wtOnT+vp6Xl4eJDJ5B9//JFMJtvZ2YEXYGNjA0EHZHxoxkZGRlQq1dDQUFZWFjptQr5AcP+/+uorJSWlgICAioqK7Ozs/Px8DG95eXlhYWGOjo4eHh4gzdbV1WEqwHENJ8v4+PisrCxQ24gdNVwvcnJy0tLSqqurOzo6GhoaCgoKUPTNzc0gEs3Nza2trf1T64J/9vr5OsbO4uHDh4DSHj16tLy8DJhiZWXl0aNHa2trW1tbjx8/3tnZefLkycHBAZ716L7Pnz9HV37+/PnBwcH29jZK8G934pMXboCfPQ6+fPlyfX0dLJauri4XF5ezZ8/++dg6ljAQIp7jhO6DEFwRQwKhjz99HB+GZoZfPDG/opsSnA10XIzOJw298Sgn2HME4+L0cRg6cTOA3vTnP/+ZoMZjigVqgb23tLS0srKyjIzMpUuXDA0NuVwuh8OxtrY2NTU1MzOj0WimpqagXjGZTBsbGxsbGzqdrqysfObMGbzsU6dOgZ9E6G4uX77s4+MDIXRtbW1nZ2dra2thYWF4eLi3t3dkZGR2dnZJSUlzc7NIJIqJiYmMjAwJCUlOTkZnBaDW398P60G4BQCGy8/Pb2xs7OnpaW5uxgkPK9vFxUUgsEdHR/+jOv1718/X8d7e3tLS0tzc3MzMzNLS0urq6smujF3d48eP9/b2dnd39/b2nj59in5MjMXAKLa3tzc3N3H+I054//gi+j9fr1+/3t3dhR8CULmcnBxDQ8NvvvkGxQrG+ifHqQUnOW4nqReoaYJsjloETnf6OBf682Nbt5MiPEwFGH8BrgGpJUhChJoISzt8TuLzEEJrvAnGDyKniM9AcDxQ5ZcvX6bRaN7e3k5OTihfc3NzKpVqbGxsYmLCYDDYbLaDg4Otra2FhYWmpub3339PSLNwb+NbxmmPyWQWFhbiQd/X13fnzp2cnBykpaekpEA/Bol/RESEn5+fh4dHUFBQcXFxd3d3Y2NjUlLStWvXOjo68vLy4uLioKkGeAfALjk52d3dvbS0dHNz8/Dw8Pnz53t7e9vb27Ozs2tra/+DQv0718/X8dHR0crKClKCZ2dnEVw8NTU1Pz+/tLT06NGjzc1NVPCTJ0/29/cPDg5QxKhmHOyePn26srLy8OHDJ0+eEEuNn05c/+xrffny5dOnT1dXVx8+fLi2traysjIyMtLc3BwWFqatrS0hIYFHOaqEoFDigmgedUwU61fHOQkEY5NYdH/66adECZ46NvQ+c2xiC3kFVBjE2e7k4uPLE7ZxxHCCO+fzE3ZyysrKPB7P3d2dRqNduXIFSPZJMifkG4aGhs7Ozo6OjgwGw9LS0tLS0sTExMzMzNzcHMRaSCTpdLqenp60tPQXX3wBGRXuZ7yqb7/99uLFixYWFgB6y8rKkBENyAJ66ZiYmJSUFHAnYmNjAwICwsLChEJhVlZWT09PZ2dnampqTEwMePRIKwNMkZ6eHhUVdfXqVQcHBx6P19bW9urVq62traGhoc7Oztra2tjY2Nu3b/9vVOzPX/9lP8bibWpqCi15dnZ2enoaoBv68fb29uPHjzH4Eku758+fHx4eEnW8vr6+vr6OwePo6IiYmP/G2IDrP/zXTz/9hHXggwcP7t27hyfDyMgIHMcKCgoEAgGXy8VZR11dXUlJSU5ODos6QjEB0x1gbQSnAjAwwbgg2BRYHRMkOEIhB3ERYGagywQB/yTmcPbERfCSCWktsc9jMBiFhYXXr1/Pysri8/kWFhb6+vrq6uowyILzgbq6uqmpKdizbDbb1taWTqebmJhQqVQGg4FStrKysra2hseKurr6V199RcwwhMb79OnT586ds7S0zMnJgZYOzPeUlJSIiAh/f39vb++4uDi40iPcCcwNMImhz0tKSoqIiMjIyLh582Zvb29bW1t1dTViR7y9vSMiIvLz8wsKCiDpS09P5/F4eGEUCqW6uvp/v36Pr5+v4ydPnszPz6MZLywszM/PP3jwYHZ2dnV1lahguIICFEMdAzjDRAGAArMHav358+eocpwCT7bnvx5v8vDmkydP9vb2TjLrX716tbOzg7yJu3fvDg8PDw0NEYa7SI2tqKjAryQgIMDDwwMgK5vNRqCGpaWlmZmZsbGxvr4+WHvGxsaYNdHbTE1NDQ0NdXR0QG6kUCgAZUkkEng8mpqaKioqyCW5ePEi1ijnz5//5ptvMAZgm41bhQidxtoFHA/Cgg0bchKJFBYW1tTUNDg42NzcnJOTIxAI6HQ6jNtUVFRUVFSUlZU1NDQYDAb6saOjo42NDTQ4JiYm+EZOLvbQm+Xl5QnJCSGkRUs2NDRMT0+vq6sDsAB/t7i4OB8fH0AWWHdfvXrV09MzKioKymfo7VpaWuB8NTQ0tLS09Pz5893d3Zs3b1ZVVV2/fdivqU5wOExMTuVyuurr6hQsXzpw5c+7cOU1NTbFY/Kbr+OnTp5iPFxYWsMYbGxu7d+/ew4cPNzc3QQPa3NwkShkNGKc9oBOAjYEZ478wb6CmiXEZ50Ls/Ahd08k6Jgr9xYsXz549293d3dzcxB5xfn5+eXl5ZmZmYGDgzp07TU1N5eXlBQUFqamp2JQCzAcDwdPT08PDw93d3dXV1dfXVyAQgLgHnbCfnx84/jBziImJyczMTE1NRWQiLK/T0tKio6O9vLwcHBysrKwAeGlra5PJZMRGqampqaqqKisrQ/iNKoShjJycnJGREfQHFArF1NTUw8MjLS2NSNxoamoqKioKDQ01NTXV1NTU1tbGZ9DQ0NDS0jI2NoYSB4c5CwsLGxsbDBhsNpvL5drb2wPQgEMpg8Eg0DeAiZh2vv76aw0NDU9Pz5ycHETXQKEUFxcHjTCfzwdE7eLignQscIaKi4ubmpqmp6dx1Hnx4gUeqk+fPp2fnwcOGxkZiSehgYEBRnZ5eXmCF6ChoVFVVfWm63h/f39lZQXlgrzB0dFRJLehdtfX1zc2NgBZAHpDsT579mx/fx/nPxQxYGPsQfb29vBfxIIaXRzFTcwSJ8+C/3mSfvXqFe4QfDYAcdiv9fQCMKisrs7KyiFg4RC4HBgaiWdiv8fLy9veGgA/9q0AMwHaamppaWllZVVTU0NMCED0lyhPsvbpXMzEyoudiv9fXEMSktLCwoKsrW1tbW1BXqAAYDFYrFYLBsbGycnJ39/f19fXxcXF2dn57CwsGvXriESpqWlBVrOGzduxMXFYZ2hpaUFf1hNTU0SiUShUBgMhoODg7m5uaGhoZmZGb4Kk8m0tbVFNaOVIhXdzs7u66+/JmThaMaALOTk5CwsLDDyFhYWIl0zJCTE19cX6Zru7u4BAQH4mUAIXVVVNTAwsL29DXIBYNaNjY3h4WE8EmGKHBcXh9y0L774Ap4vFy9ePHXqFA7EKioqv0AdHxwcbG1tra2twfQTMauzs7Mgsq2tra2vr29tbe3s7BBjw+HhIUp5f39/+/gCKocGjHPh3t4egdY9ffoU7/b06dN/ClyEFhUd+vHjx0tLS5OTkz09PSA25ebmIjEyISEhJiYmODg4ICAAKagoJtRxUFAQZAvJycnJycnp6emVlZXA8sDrgH4dXEQgpsXFxWj5sbGxcXFxEEfk5eUlJSWhwV+9epXP58MoG6kzcIRIT0+PiIhwdXX18PCIi4srLy9H0i0xZY6MjHR1dSFCD/bG6urq6urqGhoaurq6ANqAGWPlYWZmRjCEHB0d/fz80tPTq6urMzMzBQIBm82WlpaGnxOxDwd6IyEhoa+vz+FwcCDDjQ0qs6enJ9pwVFRUTk5ObW1tb2/v5OTko0eP8Jt99OjR1NTU0NDQtWvXYmNjnZyc7OzssFyk0Wg2NjaamppfHJu0E8EROB8rKyv/AvPx8+fPHz9+vLy8PD09jaDg8fHx6enplZUVzBWoYFAm8JenT5/izZ2dHaJnb29vP3nyhKhpFDEm7JmZmZGRkZmZmZ2dnf8sMv0Hr5cvX+K2WV5eHh0dhUI9IyMD/RUtWSgUBgYGBgQEBAQEwP0JUZ7h4eHQQRQUFBQUFFRVVSFR6+bNm2KxuKysDF35+vXrGRkZcLrG8aiioqKoqKi+vr61tfX69esVFRVQz6OZubu7Y4aB53t0dDQib+Pi4oKDg2NiYqqqqpAHA+FQT0/P+Pj4/Px8TU2Nvb29jo6OhoaGhoaGuro6TI51dXVBAzIwMDAyMtLX16dQKHQ6HUUcEBAQExMTHx8P46XQ0NDAwEBnZ2c1NbXPP/8cwlvYQKKOv/32W1VVVQjguVyuh4cHn8/n8XhA7rhcrr+/f3R0dEZGxtDQEPYAOPDMzMzU1NTExsZyuVwNDQ0ZGRlQUwjmCcFswU4KGnWAoWfPnlVXV/8F+vHLly8R+zoxMQGq0NTUFBA3bEB2dnZwhkPhoivv7u7u7u4+fvwYA9OjR48wdYDcA8gZNdfV1ZWTk9PQ0LC8vPw/RMhRygsLC11dXWKxODs7GwFEYWFhAQEBKNng4GB0Yn9/f3jyoSiRf1FdXV1VVdXS0oJsC1gRlJSUXL9+vaenp76+PiUlJSUlpaKiAkGICNvCEfP69eu5ubnh4eFBQUG+vr7Qy8AOQiAQIL05Li4OHF+oKsrKymBwnZSU5OXlVVxcPDk5OTo6Gh4ezmAw9PT0SCSSjo4OJgqcMuH7oa+vb2hoaGpqSqfTORyOh4eHl5dXfHw8nhX4/Ph+ESmJ9RBki58cm+mfOXPm8uXLFAoFaigvLy9nZ2c2m83j8VxdXZ2dnbG3KyoqWlpaevny5cHBwe7ubkdHh0AgoNFoCJkEcEms6wm9+scffwynUyQ3E4ukL7/8UkFBoaKi4n/yi/7b19+p4+np6ZmZGRz4UI4rKyuYLojGDMji6dOnKO7NzU24pYCIvLq6CibGxsbG9vb2+vp6W1ubj4+Pr69vT08PFihAKl6/fg1g7p/6BkAt6uvrA4sFfAAIG5Fnj5x7dGJMFzExMcXFxXBBbWhogJUTIobu3LnT2tpaVVWFsbixsbGkpCQvL6+urq6vr290dBQ4CXK1bt68mZWVFRoaKhAIMGJ6enp6enri/kFJCYVC0COhNK6pqbl+/frt27crKirc3Ny4XG5paen8/HxXV5eHh4eenp6GhgakR0BINDQ0CMBES0vLwMAAsvPAwMDw8HDojmC4jdMY+BLR0dFIQcVogU0klvanT58+f/68rq6utbW1o6MjBPAcDgcH3ICAgMrKytTU1MrKSvBqFhYW+vr6rl69CmSG4EwT3BXCsQlfCBtEuFriTaDpMjIyIpHof7IC+9vXz9fx4eEhEqOw0puZmZmenl5aWsJeA2sIKJd2TlxAMHA6BEcZN8PMzAz+/ujRo/b2dk9PTxaLBYsguKsAeN7Z2VlfX3/8+PE/3qFfv369s7MzOjoqFoth2QtqLA5w4eHhIf/+wpkvISGhurqaGH9hhDoyMvLgwYP+/v5bt27V1NRgFAaNq6qq6ubNmz09PQMDA/39/QMDA2NjY729vSUlJSEhIZiDYejh4+Pj5+eH+0coFAqFwqCgoOTk5PLycthGNTc3i8XitLQ0Dw8PFosVHR09Nja2t7c3PT2dk5NDo9FUVVW1tbW1tbVhHK91fOno6JBIJBqN5uHhgVNsVlYW5h/4VjU0NKSlpSEPD639m2++QbMkco4//fTTM2fOnD9/3sDAAD4sDg4ONjY2Dg4O3t7eAQEBUHM4OjoGBQWlp6cLhcLo6Gg+n6+iokKQYAmC3qeffnoyQA0ca4B9J+M1wIKSlpYuLCz8byy//sHr5+t4Z2dnamoKjE2klUxNTYFZsbi4CNQCUwR68Pb29tbWFrhvoMJtbW1tbGzgpDg/Pw+GRmdnp7+/P4vFysjI6O3t7e7uHhwc3NrawgR27969lpaWnp6ejY2Nf/DVHx4eTk1NVVVVgTEIBnd0dHTY8RUUFARoIiAgwN/fPyAgICgoKCsr6+bNmwCe6+rqbt682dnZeffu3enp6f7+/qamppqaGkjbCwoKYD7S0NDQ3t4Ocfj9+/dbW1szMjLCwsKgPwsODgZmh64WHBwcERGRkJCQkpIC9ikEbfX19aWlpbGxsUAefdiv9m5qaNjc3X7x4sba2Vlpaam1traenp6urq6uri2asp6eno6MDzJvL5UZGRubk5IDXC/eTsrKy3NzclpaWmpqagIAANze3kJAQNpt98eJFLHFQwYQUBUm9xsbGLi4uLi4uHA6HzWZ7enoi2FQoFDo5OWlqagJHRzSOlJQUjGDwqbAcxeoH4y/8Bj755BOYncI7HaUMpuHnn38uISGRmZn53z4I/d3r5+t4d3d3enp6bm5uenp6dHQUqTubm5tra2uguWEyBoiGmRhTB5bGmIbX1tZQvktLS0tLS93d3UKhkMvlZmRkdHV1IeRnZWUFq5Pt7e3W1tbs7Ozm5uaVlZV/5Bs+PDycmZmprq4G+zs5ORmGYjjJwehJKBRiqMBc4e/vHxMTA2ZWW1sbHAj6+/uHh4cnJyfhVYA9KqQ4SJWrqanp6uoaGRm5d+/e+Ph4a2trbm5uREQEppSIiAihUBgQEABcD+nNSAgFmlFcXIwgI9jqoM6cnZ0h7kcj6OnpCQoKAhyhp6enqamppqamqamJmqZSqQEBATDArK2tzc/Pz87Orq2txY9RJBLV19eLRCImk6mpqWloaKigoIC9I8H3IOglYOqpqalxuVzibAqTQj6fr6+vTyj5IBcHFwoiA2IyxnBMqGihM/jsOHsYTRr+SQSnSkJCIjU19R8kPP43rp+v462trampqenp6fHx8bt372JOAOK2urq6t7f37NkzHO8wTmxubmJvsry8TEwX4NqjjgcHB+Pj43k8Xnp6emtrKxxrlpeXQbqHHLqxsbGiomJiYmJnZ+dvf8MvXrxYX1/v6+srKSmJiIgIDg4ODQ1FBRMbDT8/P+gf/fz8iGRwaBwATdy6dau/v39+fn5ubg5ddnR0dGBgABpb6COys7MbGhpGRkYg0m5ra4NfTlRUVHh4OBIJIAHC8B0aGoqU5qKioqysrIyMjPT0dKx2YekQHR3t4uLi6OgYFxfX1ta2sLCwsbHR1NQUGBhoY2Ojr69PIpF0dXWJgVhXV5dMJltZWSUmJt64caO6ujo/Px94ItZyN2/eLCoqAkeCRCIR60Pi6U+wRwhZ6xdffCElJWVubg7bYw8PD1tbWxMTE2VlZYTw4Z1hZYTlPLReWFjiS0CeCDLTSRUMLniRgWb91VdfQQCWnJz8/4+6+fN13NvbW1xc3NnZOTEx8fDhQ2JIOHm2e/z4MY5xqNSRkZG+vr6ZmRkwPEEqwnK7v7+/qqoqOTk5Ly/v2rVrAGInJiagfH769Onjx48fPnyIvcD29vZJA6H/fD1//nx+fr6+vj4hIUEgEPj4+GAl4e3t7enp6e3tjb2dh4cHmg1+W76+vl5eXhj7ysvLoTvEgmp9fX16ehrQhFgszsvLg4s1BGf379/f2dnZ3t7u6enJyMiIiYmBTU5ERAS0xBhjwsPDU1JSsrOzi4qKoDCvra3Fqgw6i7i4uISEBH9/fzTj/Px8UMBGRkZiY2NB/SGTySQSCUYWGDCsra09PDy8vb3B1GlsbMR3HRMTk5iYCFkozgZsNhvRODCRIXj9sDvCJEBU86VLl/T19ZlMpouLC5vN1tbWvnTpEgS2IJagjgm2CSYHCBmhvkaqH2r6u+++u3z58rlz5wjpDUzAAFZAFikhIZGSkvJG6/j169fFxcUCgeDOnTuLi4uYfYlTHaiY+BeQzqanp6EUb25uHhkZQQufnp6en58fHR29detWfX19XV0dzlWQhmMsJoaTzc3NhYWFiYkJ2GT9V6cBQGwPHjwQi8Xh4eFYL4Nb6OXl5eLiwuPxsImADTOKGIAuSjwuLq6ysrKlpWVgYGBkZGRwcBDK2d7eXggkEVUbFRVVVFQEJ2poXmD0C5fRsLCw6Ojo6Ojo8PDwpKQktG2RSAQdfG1tbXV1dXV1dXFxcXp6enR0dGBgIPBsLy8vzKOA23p6em7dupWcnGxvb49MaSg7dHR0gL4ZGxtfvXo1KCgoMTERJq0ikSg8PNzHx8fV1dXNzS01NbW9vX1sbAw7FEVFRRQx4fZ5UpVIEKPRaK9cuaKiooIFOKJ/Ib8lpLVQicMFAXZb+Mznz5+HZFVKSkpaWksHFZkAACAASURBVJpEItnY2LBYLBkZGbiIw/r/z3/+M6HXQqHn5OS80fn4p59+am1traysRBGDPwr0F9UM+AzCkAcPHtTX1+MQ3d7e3t/fj1IG57O9vV0kEkHZUlFRgS7S1dW1trYG+BmTyczMzPDw8MzMDA49/+divEFr/hw8f3r59Oz093cfHx83NDesxQLZ8Pp/D4fB4PB6P5+joCIYAiDXOzs6urq7+/v6AWm/cuEFkGCKXs62traioKDg4WCAQpKWl5efnQxhcXFyMybilpaWoqAgDMXaBcXFxycnJiYmJWVlZ6O6jo6NjY2NDQ0Mww62trYUk08/Pz9XVFbeTlZUVlUrl8Xjh4eFRUVECgSAgIIDD4YCThMAOfX19PT09IyMjMzMzDoeDc2RBQcHdu3f7+/vLysqCg4NdXV1hupeQkNDc3AxKbU5OjpGREYh4hPEA0ANMsQRkhsaMOQFTAVjRkBtKSEiADI3WS3jiE0oZuB3IyckpKyuTyWQnJ6fw8PCrV6/Ky8t/+eWXf/7znxE4BGwEfKnz58+rqqqWlpa+abwCehCgYCBRnCxiMHUePHjQ19dXVlbG5/NpNFpCQgKyWicmJghWWk1NDawPQkNDXVxcBALBjRs3YGGxsbEBoGNoaKimpqazs3NlZWVvb4+wLQQDDlDGzs7OxMREWVlZSEgInMPR2AjVGofDcXR0dHNzQ8KDo6Mjl8tls9mwxXdzc8MiDUkt2MnB0zcrKys5OVkgELi6ugqFQuC7IpEIhuQpKSlpaWmwI/Hy8oJhrlAoTExMzMjIgAdwV1cX4WfX0dFRVVUFHBdbDxjmUqlUMNQYDAZyDKytrU1MTMCLRxHr6uqiJVtYWNja2lpbW4OJAdp7R0dHT09PeXm5p6ennZ0dIgbDw8MrKysnJibGx8crKiqYTCbMNDAJID8PESQAFrAQIeQqhL8oRghZWVkcLlVVVREsi7EY74PSP3/+vJycnIaGBoVCsbW1BUsJ1EJNTc2zZ8/Ckgsm8NCWS0lJycvLUyiU2traXwA/Bo6Gsx2erahjuLZNTU11dHQkJyczGAxQnAQCQVlZWX9//9TU1N27d0dHR4eHh2/cuBEfH29nZ4dprKSkZGpqanV1FRUMmUBBQUFaWlp/f//GxgZ4cFiLYIrA1DEyMpKamgqJJYvFAiPn5F+w6Acg6uDgAKNb4qfs5+dXWFjY1NQEpmxaWhoYnlAgY+rw8/NLSUmpra0tKirCci46Ohp+Dunp6aD4IH9AKBQmJSVhOdLV1QU8Z3BwsLu7GyZ/BDM9LCzMxsYGwmYdHR0TExOo9s3MzIAHEwMxjnSWlpZ2dnaQMLHZ7KCgILFYPDg4ODQ0hKRbkUhkb29vZmZma2sbGxtbWFhYX1/f1NQEyZ2Pj4+BgQFABswAhEYQXtFElAQxOktKSiopKRFsJDqdTqfTTU1N1dXVYWQoIyMDQyMlJSUtLS19fX0TExOYCBMRO5aWlggb+OGHHz777DMYRmKukJGRQWIfm82+fv36m65jkEJgGjQ9PT0xMbG4uAjKBGx+uru7k5OTKRQKzg2qqqp+fn6NjY1jY2NjY2P9/f1DQ0PDw8NdXV1hYWEkEsnMzCwjI+P+/fugXuCkuLW1NTExUVVVJRaLx8bGdnZ2CEnf4eHhkydP0LYnJiaysrJYLBboMhYWFszji8ViWR9f4JLT6XS8D95EUomvr296enpmZia2IThyBQUF8fl8X1/f+Ph4RN3X1NTk5eUFBwd7eHiEhIRUVlaOjY0BKhYKhW5ubj4+PjDOgQwYiPLIyMjdu3fBHa2pqSktLa2vr6+srIyPj7e3tye4wkZGRjhXubi40Ol0ony1tLTw8+FyuYGBgR4eHhwOx9XV1cfHp7i4uLe3t7e3t6+vD7nN+fn5Dg4OVCrVw8OjoqKiu7u7ubkZgmehUBgaGkqj0QgRAATYhDyRcC8nrIYuXLigra1Np9PhoWphYQFWnaWlJSLpNTQ0EP2LoyfkgJaWljwej8Ph4LlhZ2cHTYqZmdmVK1fOnDmDHfi5c+eUlZVNTEy4XK6Xl5e3t/f169ff9Fzx+PFjWBrfvXu3u7v77t27cKtYWloaGxurr6+PioqiUCinTp363e9+95e//IXJZIrFYvRgkGDQQjIzM6lUqr6+fkxMTE9Pz8rKCqYUkIcWFxdRAUNDQ/Pz8wcHBxBXP3nyBCSNhYWFoaGhnJwcJycneJ5anLhQqebm5qhsCwsL9BJjY2OQdJEIYWtr6+rqGhoaClJbdHQ01m8+Pj5CobCgoAARWhiIo6OjXV1deTxeQEAAul1OTk5qampkZCSMpGAsgnXgrVu3BgcHx8bGOjs729ra+vv74VdZV1fX29t77do1Ho8H4YaJiQnY+iAfUygULJw1NTWNjIx4PF5wcLBQKAwLC/Pz8xMIBIifSU9Pb2tra29vb29vR7yXv7+/lZUVi8UKDw/Pzs5OTk6GsBmBpElJSQwGg3AmB08IfDfMqcTAeunSJWT6MplM3Gz4QSGGC0GReHnKysrq6uqwuzY1NbWwsEDXYDAYVCqVyWRaWVlZWFiw2Wwmk6mlpXXhwgU8AZSUlMBfdXNz8/b29vHxaWpqetP9eG9v78GDB4ODgxjLZmZmsMkbGRnJz89nsVhXrlz56quvEBFApVJFItHIyMjo6Ghvb29/f39vb29TU1N0dDQweW9v787Ozvn5+dXVVTA2sTeZn58fHx+fmJjA/m//+Nrb29vY2Hj48OHg4GBKSgrsGuCdAyUP8eNGF6HRaHQ6HepLIyMjGAMTdQwPqLi4OAghQ0NDfX19ESMQHx+PYPv8/Py4uDgQx9zd3VksFmbT7Ozs0tJSREP4+vqCV44JGw7sTU1N7e3tLS0tN2/e7OvrKy8vj4yMLCkpaWhoyMzMdHJygt4Epzd9fX1NTU3sOFRUVPAot7e3Dw8PDw8PxyFVKBRitwx+SE5Ozu3btwGuFRUVubi4WFlZoThwoi0pKUHeK/h0ZDIZgiuczMDUOYlFXLhwQV5eXl9fn0qlOjg4CAQCR0dHMplsbGwMiy0tLS24uoBYBzzb2NjYyMgImlZEEZiZmdHpdPyc0UoYDIa+vr60tDTgERkZGYCGEPmFhIS0tbX9AnU8PDycn5+fkZEBSi6oXoWFhVQq9csvv4QpIGwWcJqGO1ZXV1dfX19jY2NgYKCenp6srKytre21a9dgOASU7fHjx3AkAp1oaWlpY2MDDA2QlXd2dh4+fHjnzp309HQ7Ozv8lCE9wjOaSqXiTWgiiDcZDAbcSSwsLBwdHVGvMEJtbW29d+8eXHCqqqpKSkqioqK8vLxCQ0MBoqFJI7zHyclJIBCUlpb29vZWVFR4eXmFhITk5ubm5OQUFRXV1dV1dnbeuXOnra2tq6sLNo1jY2PQ9giFQqjZYmJimEwmwV/D/ACOPBgU1tbWAFvc3d29vb2BEgYGBsJBPTIy0tXVNSgoqLGxsaioSCgU+vr62tjY4ClkaWnp7e2dkpKChIrk5GQajaahoQFMV0JCAkAy1m8//PCDtLT0lStXZGVl4UqP0IzU1NScnBw2m43CJZPJGOLRj3V1dQkUhTikIpYATxj8tME8ximFSqUqKCggrERSUhLb74CAACDrvb29b7qOp6amoqKidHV1raysYPiVlpaWlpbGYrG+/fZbJPX+6U9/UlNTy8jIwP5iYGCgs7Pz1q1bpaWlfD4fDFpnZ+eioiJE30EhAsxubW1tYWGhu7u7v78fVnHLy8tQpD558mRtbe327dtCodDa2ho/UNSxiYkJIaozNjbG+Qm8ciMjI7DLLSwsXFxcUlNT6+vrOzs7QZseGxtD6vzs7Ozo6CioCBDKU6lU5FCBlu7m5obnYE5OzsjIyOTkZGpqqqura0REBBLDMYfgMTUwMDA5OQnCSX19va+vL4/HEwgE2OcFBASYmpoSLB+C66Ojo6OtrW1hYYEdJCRJ8I5ITEzEojskJMTe3t7CwsLNzS0jIyMzM/Pq1avofw4ODpBmVVdXT09PT09P19TUsFgsZWVlqFPhKA4TW8DJUlJSOGwZGRkZGRlhPAgKCkKCmL29PYVCgaULQGsELevp6eHHi3+BZtHExATmiObm5lZWVviBOzg4YO5nsVgGBgaKiooKCgr6+vp0Ot3e3p5oFh0dHW96Pi4pKZGQkPjTn/506dIlOp0OxJRGo/3lL3/57W9/+84773zwwQenTp3i8XhYjI2MjMCdu6CgwMLCAvJjR0fHhoaGsbGxlZUVFCjGCez/BgYGKioqbt26NT09PTk5OT4+vrCwgLG4ra0tKCgIqwH0A0NDQyBT+LHiolAo+vr6GIgJ0WVAQEBdXd3S0hKopLu7u+Pj4yKRCNydvLy81NRUDw8PqEoR1QN2L+4WePglJCR0dHRsbm52d3cHBwe7ubkFBwfn5+fDSCo1NRU8z/7+fpjv9/b2AiuwsLCAqtnKyopMJmO9DFkH/sQX0tPTs7W15fP50NvZ2tr6+/sjvDY1NfXGjRtpaWl0Oh30IESDWVlZmZqaWllZoeih+gQztry83MbGRk1NTVZWVklJSUFB4crxBZtNCwsLf39/LpcL7rKbm1tKSkppaWl8fDyfzwfUgJIFImFkZEShUGBThI5LpVJxJiHexOkQP3MbGxtnZ2d3d3fAF5D3urm5YaiIjY0NDAzkcDjV1dVvmicUFhb29ttvv//++19//bWNjU1cXByDwfj444/ffvvt995777333vvNb35z7tw5oVBI2Bn29/eXlJRYWVnhpEyhUHJzc6empra2tgipyNbWFlitWKG1traOj4/DYABUJMgiPD09IXwgCAbgMWJWw9yG/mFgYABNuYmJiaOjY1JSUldX1/LyMmSCq6urQ0ND6enp6OtQa7q4uJibm+vp6WHm09fXR5sECsZisbKysjo7O4eGhrq6uvCb9vDwEAgE2I+AkFRTU9Pe3j40NIQ5vqSkhMlkGhsbQ8ysra0NWYe6ujqJRFJWVlZRUYEGE6R4CoWCx4ufn19qaqq7uzuTyeRwOD4+PpWVlW1tbQkJCba2tnhPvEIjIyNLS0sOh+Pm5iYWi3t7e0UiUW9v7/379ysrK6Ojo9lsNugZkKlCFkUikYyMjECDplAoVCoVuCHkLd7e3oaGhlpaWmpqaiQSCfwkvDYDAwMTExPMvrhOHqNx5kMXQMotQInAwEBockNDQ2G8CZ8Ab29vDocjFovfdB2Hhoa+/fbbH3zwwXfffYeR6PPPP//1r3/99ttvv/vuux9++OHp06cZDEZBQQF2H62trSkpKQwG4/z582fPnlVVVQ0NDR0YGICaGmPx9vb26urq7Owstgao3cXFRfjP4qqtrYUNxX+QQmhqahKUAzKZTDRRFDRaSGBgYFdX19TU1MjICLRYd+7cqa6u9vT0xC8J/ZLH41lZWVEoFJQIfvH6+vo2NjYg4IrFYpFIFBER4ejoCBkcMGYolBBieePGjYmJibW1tb6+vszMTG9vb+KIqaOjA+E0NHYEvqanp4dvB5RIMpns4OAgFourq6tdXFwQWR4eHl5eXh4XF8dms2k0GtYiOjo6qC07OzvolxAXBE7V+Pj4tWvXSktLIyIi6HQ6hhZ8UUNDQ4AJdnZ2NjY2enp6WGV7enpaWVmBxU8QRHV0dPDa0PItLCywQmIymRgegK+RyWSM0Xgkqqura2tr02g0Pp8fEhISHh6ekJCA8wZErAKBwNnZGb2gtrb2F6jjX//61++9996XX36ppKQkJSX1u9/97q233vrVr3719ttvf/rppzQaLT8/divHDhYWFvr6+6urqyEeSkpK6evXqzZs3l5aWYA8AtBgLlMnJyYmJifn5+cXFxcXFRRhirK6uwk4zODgYbC+c6wnjCNQxfj1Q2+Nf8DQ0NTV1cXGpqqpaWFgYHR1taGhoaWkBp7GoqIjNZpNIJAMDA2x63dzcrKys8Oik0WhMJtPOzs7Pzy8/Px9WIwKBAHkwqqqqGhoaiCCwt7d3dXVNSkoqKCgQi8UDAwOPHj26f/9+Xl4eZPe2trYUCkVVVVVeXh4PdwBb2traGO4ZDAadTsezG3E1bDYbsLSxsTGHw4mOjs7Pz4fzAx4y+FHo6emhjHx8fLBuFIvFJSUlt27d2tjYmJycFIvFuOtMTU0JYERfXx8QBIVC0dTUNDY2ZjKZ3t7emLyRE25iYoIiJu43WHwjbI7P57NYLLRkBoPBYrGYTCaVSjUwMNDW1saX0NbWNjMzc3d3j46ODgkJcXV1xRoVsi4+n+/g4ODk5OTj4+Ph4dHQ0PCm5+PQ0NC33nrr3XffhT3Up59++vvf//7tt9/+l3/5lw8++MDAwADYanx8PE67kND86U9/Onv2rJ2dXVNTE/R52GwTQ8XKygo0JvgvJDOsra1tbGyMj4+npaVZW1traGioqKioqalhRwoqt7KyMroaUdDQSmDi5PP55eXlyDxdWloCu2N6erq+vt7LywveKwgmqqury8/P53K55ubmPB4vKSkJhunl5eVYasTGxuro6Fy5coWITNTT08NTlcvlJicni8XiGzduTE5O3rlzB+gE1oE8Hs/IyEhdXV1WVlZWVhaJMvLy8hoaGnhcYKzEuA9RJ8EzVlVV9ff3b2xszMvL8/T0pNPpGE/xgebm5kwm09nZOTY2Fi+1tra2p6cHm//i4mJfX19zc3PMYDir6erq8vl8Pp+vq6uL6jQ3N4cjEY1Gw7EYK0Z0BPxs1dXVyWSyhYUF9k3AglDHNBoN7CUajYYxD12ZSqXGxsY2NDRUV1cHBgZaW1sjiRXB4ywWi0ajQc7t4uJy7dq1X6CO33vvvT/+8Y8//PDD119//dvf/vb999//4IMP3n//fUlJyfj4+Lq6OoFAoKamdubMmY8//vj999//6KOPTp8+raGhkZWVBadkyJ+ePHkC2Qh0TeB/Li8vT01N9fX1Iblsbm6utLTUysoK9CtlZWUlJSVskpSUlNDelJSUVFVVCQ0mnmimpqaenp7Xrl1bWFiA4QsB6t2+fdvf39/S0hK2UYmJiX19fffu3aurq4OIuqCgoKenB5aHiMrKzc2lUqmSkpI4HsnIyCgqKuJ20tfXt7a2BnkSCqiqqio4vHC5XFg/qampycvLw55eXl4ebixwZoGmA3AbjUaLjY318/NDr9XS0lJSUnJ0dAR0DTgcSCIkzfAQYrPZ/v7+WVlZDQ0NOF8+ePCgvLzc0dGRQqFoa2tjjEFpOjg4YE3j4uJC7OEw9WJLh0Mn5ngAKfgLMbYZGhpaW1s7ODigxxsaGmpoaKiqqmLuB1ufTqfz+fzY2Njy8vLW1tawsDA6nW5nZwds28bGBqlQzs7OTk5OFhYWJSUlv8Bc8f7773/yyScXLlz46quvfvOb37z77rvvvvvuqVOn+Hx+UVERn8+/dOkSSCH/9m//BlGhrKws1jZ3794FGrW2tgaCL2j1aL2waevr6+vo6IDIora21snJSVlZGa1XQUFBXl4exYTjkby8POr7pLeDvb19dnZ2T0/P6uoqDnY7Oztra2uzs7N9fX2JiYlgDnE4HD8/v66urs3NzYmJia6uLtQiOMegv2VmZoLQo6SkJC0tLSsrKyMjIyEhcfnyZXxRQ0PD4ODgO3fuTExMwB44ICAA1jsImAFBBzavly5dQkeHKgn3G/yHTE1NqVSqp6eno6Mj6tjIyIjgNgDENTU1hfs8nuxgiYCLV1RUdP369b6+vgcPHtTV1bm4uKCIVVVVcc+rqqoaGRllZmYuLi5ubGyUlpZaWFjgS+vp6eFwhltLVVWVcP/G2QPTAoVCwXuyWCxLS0uUtb6+Plq7urq6pqYmgRlzOBxzc/OAgICysjI/Pz9sowDJ4e8gvdjY2JiZmf1idfzRRx998sknmCjeeeedzz77zNLSMi0tzd3d/cKFCyjf3//+97BZ/+677ywsLJC5i1Qy4GvQq+LsNT09jfBTRD/hz4KCAi6Xq6WlhcIlnsiXL1++dOkSLAZlZWUR7Y3pU01NzdTUNDMzc2ZmBivApaWl3t5eRMN2d3c3NDSkp6fHxMSA3yMQCEpKSpqamnp7e+EqguCSkpISoVDY2dkZExOjqqp66dIlxC5dvnxZVlYWuXry8vIGBgY+Pj51dXUjIyN4gGLFCHwNLsXS0tKoYCQtYD7G7gMUNkCHOAhi7ieTyTweLzQ0FDOJvr4+zIcoFAqXy4V839ramsvlRkVFgRLY2dl5+/btjo6O2tpaLy8vzANYEwJuU1FRcXBwaG5ufvTo0fT0dFlZmbu7u729vbGxsYaGBqAGzEsKCgoUCsXS0tLAwACDOKYF1DGZTAbEaWhoiKcfod82MjJyd3cPDQ11c3MDbA89gZ2dHUYsJpOJfgyCAFbfFhYWIpHoF6jjd955Bzjx22+//atf/eoPf/gDjUZDxqWioiLkhL/97W8//PDD3//+92fPnmUwGCkpKQ0NDRjdcJKbmJgAaJCamgo23ODgYE9PT3d3d2dn540bN2JjY83MzFC7qAZpaWkUNFJvsYVCWpaqqiqK2MjIKCIiYnh4eHd39+DgYGxsLCsry8fHh81mx8TE3Lp1q729vbq6OjExEdY+4MHx+fy8vDxE98EtIDMzMzY2ViwW29jYoBDhQSgjI3PlyhU5OTktLS1LS8vY2Nja2tqOjo7KysqgoCCw5BCIa2BggAkErxniNtSxnJycoqIiBgmw3pCGe+XKFUVFRR0dHQ6Hgx9LSEgINsAIpgdszOFwPD09w8LCcnJympub4Z4NuoVIJHJzcwNWw2QyAYfBiMjAwMDV1bWurm5mZmZsbCwlJQXh3mZmZsTTTEVFRUFBAexhGG3B6gULUQaDgcmBaMN4AOIDtbW1LS0tIRFns9mwchMIBLDsKCoqSk9PFwgEERER+F8ymYzNn5GRUWFh4S9Qx2+99dZbb72FIv7oo480NTXj4uLKysq8vLwkJSXBn/rDH/6A8YNCoeAM1NjY2N/fPzExAc+1srKy0NBQbMsSExMhhywvL7927VpaWpqbmxsUNTIyMrCzRhGjF0pJSYHOAgdY/DSVlJTMzc2TkpKGh4cfP3787Nmzzc3N6upqDodjYmLi4uJSXl6OROvQ0FAWi8VgMDgcDgAKwBo3b97c2dnZ2toaHR0tKCgQCoUcDkdNTQ3tX0ZGBsswRUVFCoXi4+OD1SDstry8vJycnIKDg7lcLjocciAhycQqGEvgy5cvA5fQ1NSkUqnW1tbGxsYKCgrgQKK+bW1toVKh0+nwhyUwOxUVFRMTE9x4eHA1NjbCc+P27dtpaWlUKlVHRweGhYDGQadEtdivZWRkgzvj4eMDkJBIJGDaeBnhWYGYAXIjFPkZzbM4JYy41NTV8FI1Gc3Jy4nK5DAaDaNt+fn5wCoVzvZ+fX0ZGRkREhJmZmZmZGXhzADcKCgretM4U+PE777zzm9/85o9//COZTE5OTi4qKsKSFqiqtbW1jIzMhx9++N133/H5fEjT6urquru7u7q6RCKRr68vjUYjDknQGrFYLFhHGhgYIOGeiBbFQhWDJsoCAbpEZhay31JTU+/du7e/vw97uP7+/oSEhMjIyKSkJOBiSUlJXC6XTCarqKigYrBlRUnV19dvbm7W1dUFBQU5Ozvr6urKyspi9YVQclShoqIil8uFYEkkEuFupNPpgYGBsbGxONVBR4RkX3wgQqolJSXBHDc2Nsam18zMTF9fX0lJCZOSqqqqlpaWqakpQFklJSU8AUDzBZSrr6/v4uKC4BmorBMSEmBFcPXqVWCOeEkYr21sbMD6DwwM7OzsfP78+eDgoKenJxBfGB+CvKampgbOMb4Q+rGamhooeMR2E3WMmRvDMZvNDgkJsbOzw6cCwO/k5FRXV5eZmclkMpHkB1dSbW1tAjqEYqC4uPiX2YO8++67n332GYlESk5OrqurKy8vT09P9/f3j42NhfjM3Nz8k08+UVBQcHV1RXh6UVFRZmZmYGCgubk52puamhpuR4y8cEElkUgXL1789vj6/vvvkdWMhzKezkjAxYpbUlJSTk5OT08vPj5+bm4OgwFMCnt6esDTvXv3bkFBAXaBAIkAAKurq6uqqqK1eHl5DQ0N3bp1y97eHo9+YiRAGimGCk1NTTqdDqIWeJuw4rO3t/f09HRycsJj5OLFixDtoB//+OOPyNUD4oEWi/2LmpqanJycrKwsZmgqlXr16lUI9fz8/KhUKuBFwOHYMhgYGDg7O0OGiJsfIZDW1tZYWIDKB2gMnKH29nbQ+ZeXl588eXL79m0Oh4M9JdAGBQWFy5cvX7lyBYsP/C7IZDI2jgBYsKMB301dXR2IDWAKgIBkMhk/T/RsLpdbV1cXGxsLiMnIyAghJkBIccTE5JOfn//L9OOPPvpITU0tICAgJycHEWiwfS4uLi4sLAwICFBTUzt79izyinFoYDKZJBJJSkrq7NmzX375JaLDUYuXLl1SVlYGZ0pLSwt0bwgYkeEFVSOycuF0ja58/vz5H374QVdXNzw8fGxsDOZDSHACYAyRNsBUHBlJJBLKFwUNHi2dTheJRIODg6Ghoerq6leuXME9c/HiRdBr0IllZGTIZDKfz0fYd2BgILAFY2Njc3NzU1NTMpmMcxV8uSGCxz2AZwvqVUpKSk5ODtUDHANfS1FR0dPTs6ysDExRPz8/Eol0+fJlTU1NZ2dnYpdmb2+PiQiPe6gPGQwGWiZ4wHQ63djY2MPD4/r164ODg3NzczBjgL9ea2srm80mBgl5eXmcQxQUFLAuxToa8IWWlhYgcxQoAGxi1Uej0XAYQEcH9Kmjo8NkMtHUADdpa2tjS4IujvmYTCabmZmRSKSsrKw3rfsPDQ398MMPL1265OXlFRYWFhkZCQ4XMkZLS0uDgoK0tbWhLPjxxx/hY4BgC6QhwX8JBghSUlKqqqr6+vrwmiaTyRcuAhwxUgAACGxJREFUXIDOEYxvBN8ivhxBB0SAM1qdtrZ2VFTU0NAQvO9h/Q37n9nZ2bm5uf7+/oaGhtTUVHt7eyMjI21tbTk5OTKZDABfTU2NTqdHR0e3traKRCILCws5OTmEpMNwBL1fSkpKSUkJant7e3s4GuLghWpQVVUlk8lUKpVEIsnKyuK7JgJp8OKR6IH2BgdvNHv0b2lpaS0tLQgBk5OTPTw8DA0NMZOoqqoClYNDM+iRxAYeUAPWyHQ63c/PD8ZW/v7+BQUFMzMzcH7q6em5ffu2WCyuqqoSiUR2dnb49sFBI/B4PKZQuMAWgUCrqakBS4FyG4ghuB/gb6ioqBAyFnt7e6Q+Xr16FeCGqakpOjecm7FZxL9rampmZma+6TqOioq6cOECnmuwLUtKSqqsrKyvry8rK4uNjaVQKIhCIrLqiUyXU6dOnTt3jkQioXmQSCQLCwsWi2Vvb89kMnV0dH744Qci4wi2ILA4QLwzPBPOnz+PeQNZLz4+PqOjoxA+wdn7xYsX4+Pj3d3dU1NTd+7cAW3Azs6OSqVi7wqs3tjYWFdX19zcHL4n165dc3NzU1RURKy0pKQkMQlgONbT04NS1cHBwdHR0cLCAgtbTIqamppAl/T09M4dX/8hSF1aWhonKuyoEemsqKgIsEJLSwtshPDwcEdHR7RDNEslJSUSiWRra4voZmNjYywscf/o6uryeDwPDw8ajRYcHNza2lpSUiIWi3EKHBsba2xsjI+Pj4mJqa+vz87OhqLb0tISqLyCgoKmpiYGDEVFRWzd5eXlcYzGy8MiHbtSTBegDeEppKOjg/0UUCNbW9uYmBgY6lGpVEwd4KtAtmNlZYVNqrGxMf6enZ39pueKoqIiBwcHxKq5ubkFBQVlZmbW1NRkZGQ4OTnp6up+8803H3/88alTp9CGiXTlzz//XFJS0szMDMa6bDbb1dXV0dERFg1QkcDrDp6NcAeDsRJiNeAbgllCQkJCSkqKRqM1NjbC1x6LTWQvINtvbGwsNzeXyWRiyNPS0gLTHG7BLi4uWVlZ9fX1bW1tFRUVLi4uKioqiLQh0m7QLGVkZFRUVBgMhr+/P5/PRzvEhE0MEvAb9vPzMzc3xxkU0xERmH7x4kWscmRlZRUUFLDUQNGgjp2cnLKzs319ffHv2MBjN4aRNCQkpLm5OS8vD/ZCQGF1dXV9fHwaGhpKSkoEAsdiv69fX1taGh4cHBgbAqC4rKwsICDA3N09ISFheXm5tbRWLxfHx8bq6utiGArVERwcYjBeJHRMeIJgZcNMaGhqyWCwYFZiYmADuwIUXDHANxrhMJhMUKC0tLTjSQjcJSRv4IVQqNScn503XcVtbW0hISHBwMJglaWlpxcXFycnJdDr9+++/R4AXKhhcRDk5OTQkVVVVDoeDsAJXV1f0YD09PWQQEXobxGvC/xluHYgWJWZlZCgpKio6Ojpev359d3eXeG2vXr1aWFiorq5uaWmZnJwsKChgMpmKiooyMjI4f+jp6Xl7excWFlZVVY2MjOzt7S0sLBQWFlpbW8vJyeHpj3H24sWLUlJSgKgBS1tZWV29etXJyYlCoRAKYayOlZSUnJ2dAwMDnZyc6HS6nJwcxPFwNkFgOipATU0NBU2hUAAby8rKamlp0en05OTk1tbW4OBg3BiQH7u5uQmFQhaLRSKRMjIylpaWGhsbPT09hUJhXV1deHh4QEDAnTt3RkZG2trabt68OTk5ub29jdSf7u5uCKiQhdPW1ra/v489pVAoRBEjLEdFRUVTUxNpZcQWWltbG8MPQAw1NTVMCO7u7kFBQeBq2tnZGRoaYghBZAkWdSwWC/RiBwcHEomE0sfDEPcegHPwCrW0tNLT09/0XNHU1OTm5ubn54fIiZycnLCwMCqVKiEhgcYJIxnQAEgkEiAnXV1df3//3NzciooKzNAmJiaysrJEpBd8bkBQxjEf2y+ABugZBDBEJpMFAkF3d/ezZ8/wqrC3Ax3C19c3Ozu7vLwcWyXCpZ3JZDo4ONTU1BwcHCAPanNzs6Kiws7OjpA8ADACv1FbWxvbBOJoxWazCVYXzlhYL1MoFEhF7O3tnZ2dwWkm+Pg4eLm6usIZGz3JwcEBhgT29vZIvW1paamsrIyMjIT7UXx8PGwPUlNTU1JSMjIyhoeHj46O+vr6srOzb9++vbOzc/fu3cHBwaWlpfb29uHhYega4Ra5vb3d3t4eEhICO4Hk5OTZ2dn9/f179+7V19eHhYUhoAQkd9gJwOHA2dmZx+N5enq6urrCDQNvBgUFgWAtEolKS0uFQiES0hGeHhQUBN9HeP1Dw4IGB39RhI7BfD8iIgL2YvHx8bBAuHXr1pvG3SYnJ+Gq29vbC/PqxsZGWJakpqamp6cXFhbW1NQ0NjZWV1cXFBRkZGRAJzw0NIRg6rm5ud7e3vLy8ozjC+Rd/M7S0tIyMzOhnCs7vqBDrq6uFovFYrG4qalpbm7u5B2MOkY2DH6pMLGsr69vaGhoaGhArkd7e/vDhw/xIa9fv97c3MRmpO74qq+vr6mpEYvFNTU11dXV8FK5ffs2dKMQdeKCChXvdu3atVu3brW0tFRXV0PD3NjYePPmTURxwT70zp073d3dWFiCyNHT09Pf39/f39/X1wey9f3798fHx0dGRoaHdivdWViBNHxoaWlxc3Nvbg/czcpDW19eRZHVwcLC2tvbgwYONjQ0khEIDhpxtpLANDg7eu3fv8ePHeIfZ2dmBgYH/294dowAMg1AA7f1PZhZ3JwcVr9Hh0xJ6gELkv8kIgQx/jeIBqqqqay0RwSCBt8C/YEwcNTOsDY+IzMRW5njsNY6fDm7h4t5BUVVYcP9rjonOwhzTBMwxTcAc0wTufjnR4br7BiYtkvrmHbzGAAAAAElFTkSuQmCC

Profile image of Radhika Batra
11 Years agoGrade 11
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1 Answer

Profile image of Kevin Nash
11 Years ago
True weightlessness can be achieved only in deep space. In a space shuttle drifting with its engines off, the remote manipulator system (RMS) would float freely. If the engines fire, the resulting acceleration would cause the shuttle to be a non- inertial frame; in the RMS frame of reference, the floor of the accelerating shuttle would exert an upward force that would be perceived by the remote manipulator system (RMS) as similar to its weight. That is why; in the weightlessness of an orbiting shuttle, although the remote manipulator system (RMS) cannot support its own weight, RMS has to be able to exert any force at all.