Physics
Fluid-Mechanics
Easy
Question
An open tank 10 m long and 2 m deep is filled up to 1.5 m height of oil of specific gravity 0.82. The tank is uniformly accelerated along its length from rest to a speed of 20 m/s horizontally. The shortest time in which the speed may be attained without spilling any oil is
- 20s
- 18s
- 10s
- 5s
The correct answer is: 20s
Related Questions to study
Physics
An ideal fluid flows in the pipe as shown in the figure. The pressure in the fluid at the bottom
is the same as it is at the top
. If the velocity of the top
. Then the ratio of areas
is
![](data:image/png;base64,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)
An ideal fluid flows in the pipe as shown in the figure. The pressure in the fluid at the bottom
is the same as it is at the top
. If the velocity of the top
. Then the ratio of areas
is
![](data:image/png;base64,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)
PhysicsFluid-Mechanics
Physics
PhysicsFluid-Mechanics
Physics
Figure shows a capillary tube C dipped in a liquid that wets it. The liquid rises to a point A. If we blow air through the horizontal tube H, what will happen to the liquid column in the capillary, tube?
![](data:image/png;base64,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)
Figure shows a capillary tube C dipped in a liquid that wets it. The liquid rises to a point A. If we blow air through the horizontal tube H, what will happen to the liquid column in the capillary, tube?
![](data:image/png;base64,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)
PhysicsFluid-Mechanics
Physics
PhysicsFluid-Mechanics
Physics
We have two different liquids A and B whose relative densities are 0.75 and 1.0, respectively.
If we dip solid objects P and Q having relative densities 0.6 and 0.9 in these liquids, then
We have two different liquids A and B whose relative densities are 0.75 and 1.0, respectively.
If we dip solid objects P and Q having relative densities 0.6 and 0.9 in these liquids, then
PhysicsFluid-Mechanics
Physics
In a U-tube in which the cross-sectional area of the limb on the left is one-quarter, the limb on the right contains mercury (density 13.6 g/cm3), and the level of mercury in the narrow limb is at a distance of 36 cm from the upper end of the tube. What will be the rise in the level of mercury in the right limb if the left limb is filled to the top with water?
![](data:image/png;base64,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)
In a U-tube in which the cross-sectional area of the limb on the left is one-quarter, the limb on the right contains mercury (density 13.6 g/cm3), and the level of mercury in the narrow limb is at a distance of 36 cm from the upper end of the tube. What will be the rise in the level of mercury in the right limb if the left limb is filled to the top with water?
![](data:image/png;base64,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)
PhysicsFluid-Mechanics
Physics
A solid cone of height H and base radius H/2 floats in a liquid of density
.
It is hanging from the ceiling with the help of a string.The force by the fluid on the curved surface of the cone is (
atmospheric pressure)
![](data:image/png;base64,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)
A solid cone of height H and base radius H/2 floats in a liquid of density
.
It is hanging from the ceiling with the help of a string.The force by the fluid on the curved surface of the cone is (
atmospheric pressure)
![](data:image/png;base64,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)
PhysicsFluid-Mechanics
Physics
The minimum horizontal acceleration of the container, so that the pressure at point . A of the container becomes atmospheric is (the tank is of sufficient height)
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)
The minimum horizontal acceleration of the container, so that the pressure at point . A of the container becomes atmospheric is (the tank is of sufficient height)
![](data:image/png;base64,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)
PhysicsFluid-Mechanics
Physics
A tank is filled up to a height 2 H with a liquid and is placed on a platform of height H from the ground.
The distance x from the ground where a small hole is punched to get the maximum range R is
![](data:image/png;base64,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)
A tank is filled up to a height 2 H with a liquid and is placed on a platform of height H from the ground.
The distance x from the ground where a small hole is punched to get the maximum range R is
![](data:image/png;base64,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)
PhysicsFluid-Mechanics
Physics
A cylinder containing water up to a height of 25 cm has a hole of cross-section
in its bottom. It is counterpoised in a balance. What is the initial change in the balancing weight when water begins to flow out?
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gbpKam4mzqWZy/cB7nz5/HuXPn5J7hBeMZn1+8eFHm/K9du4Y7d27j4cOHePjwAe7fuydSFDswnpz7p0aaGuunT58iJztbhTnZSlOdlYWC/HzRVuvfqak2mwphMZtkyk3bBJDDUtLgyWeMl5+fL6e2JeAzdphMi9eU9Kjk69u7t8TT89gk2OIAfJ378gcvxQOZeKdiSM05MhQlFRVZegxkgJtxKeawgD6eHli7Zo0DlHaO3cxUCHE8qayCKH65Wg9pEU1P/DusnYrMzzmS/FFc0GiAc7Y0JOHUBomFHRANUUggQpiZmaKRJqE+evRIzrSHDyXkdAuNYOKiW+HGjRu4f+8+rl25gtOnTuHUiRM4cPAg9uzZg507d2L79u0Scq555cqVWLJkiUgG48aNAxUvY8aMkZPTYcnJyejevTu6dOkiUg6vBw0aJMBmBxEbFwuCn6cGf5s2bcCTHUH79u1kKorTUW0SWiMqOgJh4cEIDgmS+X5qqv38fODp5QH/AD8EBPqJVrlZ86Zo1qwJGjepjwYN66JZ80Zw92gOT293tGjRBE0a1IVb08Zo2rAe6n9XU+4DWnrLs7CgAMRFR8LHww2Bvt7w9/FCS083BPn5yDXjN21YH4wfHR6Kju0S0KtHkkynseNq27atlIXXMTExaNmypdgc0N6AmmVO8QX6B8DXpyV8vLwR4OcPDzd3JPfsJYAnwYkxSzkaZ2jAlz94qZEgcF50wi6EmZOb4xi/eHq6i5UVezuT2YSnOdlibKCsXZRBmjZMKy184XeNfJX2/us8L/ptil7GKcoel3vHZL/LmOuZZ6/ez1BZQkOYZk2aYtPGTa+e0Ft7U5l4Us/AudjCwnyxqDJbTMjLz0UONdA5T2WaLC3tIe7fv4cbN66L1CRTZefOIfXMGZxOOYWT1CofPybnkcOHcOL4cZw6eQKHDx3CoYMHZPaDz/fu2S33nOvfs3s39u3dK/P++/ftxWFqqg8dwtq1a1G3bl3RJHPqhx0ejWgY7t+/X4xoeH/gwAFwOHPk8GExtrl7546z5gxLNI6/NejKK3wj4C1r5qjhNBtzs7fv3EGNWjWxZetWKbiJ859WK/ILChzKgbKkq5UVLwrLktbLxnnRN4v+XkIHRymkrGexzpHcmse9e/cwevRokHPSAKN3797CsUk8rG+taHnpshnkWNJ7upPSpoRKMhJjSWVXLdN4JN7inZWRqO7k9G0lCSl2t2rV6pVyw3qilSEPrVArqe5e51mFgpfiBI9NGzbCz9cPH3z4gYglu3buUoU27FBfptcqChClRSzp2etUWmnvlk02UCReUp6Kcm4FbhL8s2cxhYrDkseEIUOHILFTRyT1SEK7Dh3Qpm0CJkycqGy5xd632LtS0yX/K62czzwvvgjCWBChhzTUOPNkOShFiSTlECNdOZJTy621zM5vOeOJFpn1wj+R9LS2WNktEyy6ftW10WmIllrZSfM9ZdNs1K/xjnQwIilBDGNohksQ89B5ke8b2m0HMGW4qL7vsPk2bL9d39VplEdYoeBlBd+4dh1ffPo5Dh84KBV05fJl1K9VBzu3bpN7cwGNK8puVqYb7UVheVRe8TReCrykpzKcJUVxFcA5z2vlPwAXLl6Et19LhEaEIyomBm0TE9E6IQHhUZFYtnyFxOG/4vl+mXtHIi4XqjsyAKKBTMMUTg1RV6FDudYAJXjU+fzvKxwqbLnQgfEu07ASiJzkcA5UJHesF/1MxWE8zkMzDzRdVKGsJpI0VPrUM/BIz0gXE1JdVIKWkovMiQv4bbBRcnTpQHhNQFOHo5kTw5dhQM+vD2cdVCx4ASyYPReeTZvr+pFw0oQJ6Nezl1zbzBbYLc5e90UFK16Rpd2/KJ1X+b3M4GVjl4TKEp6V8EiMNCwkQBqVGsC1WKzo0r0bgsPDEN+uDYaNHo6efXqhU7dO6JLUFV17dMcGl2kLririKURVCqCLNIpxU1K9aJ2EFp+F44rEoFYsEdwiSouS0gCMkzkW+YwL0yzWdBroCit8SWNGA9c11B0c64gWufxNAMw+s8i1yp3EI9hVP4jc7BxZ/VazZk1ZSELlIQ+uVuJBELPu5NAZMULh9kadChc2gF5S3b3OswoH75aNGxDk76cqwfjfjqLe+AlGvbDRyg7e16mMSvmuYfigFWmkWPbqBQWFDusmTlkM6D8Qbs3dZQFEVEwYErslILJ1EEKjfdF/UC8MGTpApqL27t4j9UrgFloKYbZbYSI3oThrAEJ3LJWyPhzitpMDvU4+NQCZhqazB/fuIzosHCOHDsO4seMQ4O+PLl27isRC8DIup45eVX/wOvl1fbdiwSuG+SZ8Ve1zhAYEYMPadbLMrvrnn4kmURMqF/bzcM34z/maREazRHb0PLiCycvNEx3bJ6J9+wQMHNwbbTu2QmLXWIydNASjxgzCoEF9EBEajL49eyAzM1PeK+SqGqsFJgttsAmGoqL8z6WOWRm6rLweP2oM2rSKlTriP84JR7WKxpGjR+QZxW4e+p2KCiscvFs2roefpzumTJqEdq3jMKBfXxw/dkwqR8YTP2euK1zGKR4qqczJIVhJCxfNh3+gL+JjYtC9c0ckdUvEkiWz0KFTNKJifdGrT3t0S0pAUrf26NwhHoE+ntiwWs2l5+fmosBwUqAI0Pktct+KIsq3+V0hNPZZhgKK913aJ2LNUqUjMJtovw5MmjwJP8z4Qa6ZP82l32Zei3+rwsArtQAgMjQY69c6DTP0c7IBMfIo5lKleAF++vdOQLmCl8SzafMGNGxUBwFBvhjQtycig/3Qp1cnrFk9H716t0Pf/omITwhCXFwgeiW1xbDvk9G5bWskteuA1FOnpKrNdJzgWCzu/NbPBbykHx465PWyhYsRFxktFlW8p6eWqOgoxzRmRYvLmuYrHLxcw3n8xAmpQBvHEdTeUVtnjCnY81WGXk5X2FsP1YyRmkUyZr5YWfkFebKWtaWvBzp37YDkHp3QrWMbdO8Ujy6dWiEgsCm+H9IdgwZ3Ra8ebTBkYDcB8IDkrmheqy7qfvU1Uk+fVvXuWKzgBK/uKN56ect5TPui/JO2eDCevn50/wG+/qwaaJvcrUtX+LZsiSFDhsg4V9zruMyZ63df9J038XuFgZeF4dEnuZd4p5AbKk2oEDBEmNcxKngTlVUhaZYAXtbL8uXLxESwUeM64lkjNjoUwwf1Rrv4cHTuGIOoaF+0cK+N+vW/gJdHXcRF+6Fpo28Q1LIFov2CULd6dfh5eODqlSuCWFW2nyd4XduVdDht4mSMGz4K51PPYtSIkdi1a5cD2HRKx/iVgaFUOHhTTh6Hl1tzMVETAFMdb7i14X1lEVFcG/jtXj8LKNo979u3FxcvXsC+fXtw/PgxWWB+YO9OpJ45gbOpx3Hy1FEcOrQPm7eswYpl87Fx/Qrs2r4Bu7Zuxt7tO7Fm6TJZbrl5w3pV7cXG1z8XsZmFJxBJZzxIexGhobh04aKqF5f/eirw7bZ/6Vr1CgWv3eCyu3ftkpUxwUEBOHr0iHKNavRulaGHq9jGKgpe1gcJrLwO8aJI4BraZiUuK61zxZa7dKItz3xp4DLkQWsqj+YtcPXyZbk3m8zQSqsq8LqMaWxWrjxS9p/UevbsmQQfb08hJNYc59LYUFXctyghE7xcnkZLIE4ZcdURn1kN17Ycl9HbBrf4MlnogC0fVks+7Da68zHDUlgoy99oCkj7cS4C+TlPFWkakzq0WtG7ew9sXL1WwCsGF2QkMg+uZtvLs/N4nbQqmPOaYbMogmJNcQF6WGiwVBr/sWBizmaMM16noD/ad4sZaUid2GziEZGdmtlsRUGBScBLQiMBss4KuAaV8Qw3sMqeWPkPK+DKHc7x2iwwWc3IN9NNz8/TSIP1qZmD5r6Xzl+An5sntmxQC+lJi2JCaSyzqCy09NbAq8UT18pSALWJ90RecwmWr5+vGNFrIuVzJdpxTKLsZCniaaP3ylKRbzMfrEueqi6VuaGqSxcOLQRnKFccnR/v1TOqC+V9pmNcv80yVKZv6brUeWJdHtx/AFER0WjcqAmWLl7JR6wlyoPG2nRl4qrfqYjwrYFXcQnlv1aLfbQX5XN90GUIHarzdx4Um2mzS4Kjszd6m1TbiKj1nyLEuIjhFVGBVd906TB+Im2hFxSQBocNGYWYyDaaRAHQKymXbv5MwKu5LmtAuxch0Rc/li5dKi5bij+XJWV0zWq4iOVyMbVm1OAiPxGiqeoIKkdHwEl1DeCVK1YjKsxpKvmzBS9BrA9y3SNHjmD48OHiWoWe/L29vfHpp5/KMqx+/fphy5Yt4tZFv2O2FKg1mKIZNXR/VcAV8bcK+OUIfHqHNJwnLlu6Eu3iO2oS/HlyXg1cisTLly93eJenUzM6cTt27JgsRqCTMbocoUULfQS5u7ujX7++4tRL16DdWCOqlpmVY6NVdQRVHYFIhGoTNdLbwgWLERedoEnvpw9ejmO1EkCDlqWnT2W6FQkICBDHZy41UuolvTsm9eiOho3qYviIoZIuI3McTK0pOwPX71VxoKrO7PVpgOa5Su+ya+cetE/o5NDDiMKKe/VQiKzgxRvlqrAiqAgmejkkoHjNk8fs2bPRtGlT8U4oD1z+Fa9sDXyXKLh46QK4Dw19K9+9e1d+oqWRnuNkGvxm8bSq7qvA/LI0oBbQqyHe1s070LhBCxQWcnURjcsNhRVVNj8l8LKSeFApRU0xDxoS0PUn3WZyf119lAY0/q4rW8clSPUxctQI2TyKW17yINA5fmYnobm8fr8qrALuK9EAdTPiLA/omdQPH7//BbZu2alI0E63TMr+nkrnV0q/nIZn5cp5WRBXrklPhp6enujUySl2ELQENgFeUsFZQ67p8JraZYulQERl/r55y2Y0bdoYe/YqrxD8JtPV3y4p3apnVUAuMw1w7ttmxbWr1xAT3QY7t+1B2zbtDeZAkVntPf2TAy8riAe9xlNMptZYHwQXOTE5JcH7IrDxd3Wq3fgs3OlPJsohuxfUqPGNw7sBv/ui9MrceOXUM1Z978fZYShjDGDcmAno23ugkG+LZm44rZdQcldIi+1HLDbTo6OrV0fjmiWlF383NzfZFkMDl2ItQUuA8bo0wtYA5HuOODI1RADT1llto8LfuX9Pi2bNZRsMiW815n1dLJAcaVQB0lmfVXVRYl0oRqGs0AryC9AqMg6nTqQICQ8e9D2Gjxgu12IoZHierEj6egmxmWBynqJtswIWk0Xtf221w2axwma1yRiX22DoQ4OV969aWNcVHQ7nTfT5vGYd6taohdu3bsvn7LTYogmgiD7GUi8xhtEu3CqXcfmr1kfVe+XH1TXD0HVKQtq7Zx8CfALF0R/vL1w8L5vPcS8iHlzXq53R6ffedvjq4CUgzPRbyy09iWopExLbdpCdwjVgOb7VyqvXKZxa9aIaTPciFpNSik0YPQax4ZHIMpxjy7aL5C56nWYVeF+503ydNvuxvEvwagWqomIgPjYBo0eMkVvuk8wjPDwUi5cskmvu9EG/0BVZxlcHryjk7LAUWmAx5sSGDRmG2t/UQlZWlhRKV4oG8usU9FnwApZCGolLXWLogEEYN2KUuiFwhQM7K1dzbh2+Tl6q3nXW64+9LkijPAhe0imPzIxMNGnQDLduamlOxVm+bCnCw8MNPUzF18Grg5fM1kJRWRVs146d+PKzLxweCHRlsEKKiyWv0uBckqXfE84r6nzZLoBbBqCwoBDdOnbGru07pAFkHaax8obvadDqUKdVFTrr9edYF6RTHqRRDeQfps9EVISxRxHp3GAElOy4feq58+fkHS7HrMg6eynwcosIx7jXSu6m2B4VVF98Vg1rVikvkCwQK0KLIuXBeV0rSWdCAMosGL0n99zlHrUZGRmqQYyeVPLj3PLKWHj+8yZa1/qsulb0qkHM7TuXLVkuNKS3LRFaAzB65ChMnzZd0dePRWx27itDrDg5LkHq7xuAbp27SYGKaKBduOWbIBANYkcIYMkt51YAACAASURBVO6cOWgdG6f2RHWZ/9UcV4dvIj9Vaf74OkTNbXVI2/ratb7Dw4dpCqAc7xoKUD7gVqFt49ujIF9tf1KRbV5mzqu4ruK83KCJIOWxcvlKNGrQSMRWsR4jR37DoC0tfQExgKCAQIwfO1byp+Nq0OpQP68KK669KkPdE7Q8tVJ12rRp6N9/gIN2eGGzKHdM8hBAdHgrrFq+yhGnospRZvAyg/SXRBBbjHHuwwcPUOe7Ojiw/4AqiMUGaoArqjAcF/O4cuUKvqtVG+fPqbEJ86NBq8OKymPVdytXZ6GBy5B2CDTl5YbdPJxbgCqHEPIQwKL5SxAVFq1vK4zeywxejl8JXCvncw2uGxwULKaPqqSAzaTmeSuMQLkwwrCpnjZ1Kpo0aiwVKw1RNeatMCKrMHoogwRI0Gql1apVq2SpqtALpxfJlbn81K52VNTS5uNHj/Ft9dq4eP6SkH5Fla/M4GUGqXgi9+Wxd89eVP+iOtLS1NiA5mJWkwVWcVvz9npXzUkZMo966w6CmJ7uf/jB2F+mCrxV4C0BzHTMp4/u3btj5MiRcit6UNhhttAVk1nMcukClvTNo0un7hg3epJ6VQPdZXbjbQC6RPBKj+OSEdU7kesqZ2dchte0aXOsWrVaMs/fmVk5GDhU0i4mWSU8Y7WV5ZSkxWcQa6n0UyvL9HwdPXXUqFHD4Y1DysF9aasWMfxMgaxJk129BXbQtRIVT3ZkZWXLWnMOuXho8LlOUcozY2bjxIkTyhiJhkKcsTS26iGNub6v03kTYZnBq0VmZozcrEmTJpJJ/tPg1RksEbyO2M4LcafJ8ajLWQLGjeRezM3Fty47EhcFRFJSEoYNGyYfZf4IXH3q/FaFL67bn0YdPQte8UlFt8ObNqJr165KVHZhXLrcJCBea8bAa0p2WzZtVrRFe32b1WGWq997k2GZwctM8Lh16w7q1q2Hw4cPyz07mmfAK7+8+J9yQ6oMwfV1ScDX/ST7yuedVnEJ65xjZg4uXbqEOnXqSKgrsnh+9fOq8KcOYlfwklpoXqvE4H79+4r7JdJMafTBTp80wt95TJo4ER3atZNrLuCXIVsxy743SVNlBq9WUkVFRaN3774qw8aa5SIZZMFKYp8K5c7fVAqG4KxGGEqIFrlbPed4hMoC7t5O7/9y2ijsyMmRiOtJYHPjY2W8oQiRnxk6dChiY5weANXYXdlFF8l7CWOiqt9/SoBW3FPaVOYflP7mytUr8PDwkGWqpJeS2lwPtRhq7nvjxg1EhoQh7cFDoWbSHd8l/ZeURnk/KzN4mbtjR47j4w8/wZOsJ5JZq9nw5aPBagBUm5NJpDf0zwp6+C/2pyfTjQ7EYmyMzCmtb7/+BidPnJTcMH+l9a7lXcFV6b0dQn6lehaNCzBmzGgMGOCc2y0tLdIMgauHXSSmnt26Y87MWYrKNQ4qErw6c5rANf58vf0xcbzSsHEpIE8uAdSLA3Q8Hebl5uH8+fPYuXOnuHGdP28eRg4fgeFDh6FDu/aIaxWN2KhItG0di64dE5HYNgExURHokBCPpC5dMHniBGzcuB47duzAkcOHZd42/fFjnXzJISuOKn7uwePi1H3UyJEIDgpS7xDcLgcbi2XV5S2t8aqeV2IglgEwSm/j7LhJAnl5uWjQoIFjGEjaL62dXelDc1/a0gf4+Qk1Cd25mOSWlk55PS+R8zJxFoKZ1ceK5Svx9dffgIDkKiK9koi/M/7jtDTs2bUbw4cNR48ePZDQpg28PT3h19IXkeHh6Na1K3r37o0+vftg+LBhco4cPgxTJ0/E8qVLsGHdWqxeuUIAO2zIYPTt0xu9k5PRp08f9OnZE706d0H7uDhEBAQgNjISPbp1w+hhw7Bh9WrcuHJFJth1XiVP3KeHi/9ZDrreMZng6+ODgweUQYmI9sVEJNfGKa8Krkqn8gBeKzTZzpw54bF37z54eHjJSjje0zBDjDNe0BloWqFRUucOHXHsyFFJz3XI9qbbvlTwMieaAzOsX68+5s6ZKxnU/44eOYr5c+chyD9ANG9enl4YNXwEdu3ciX3794Pq9Edpj3T01w6zs57g8sWLAsDtW7bgh4kT0TYmBkH+/mjWqCF83Fpg5owZuHb1quNbBK4Wn1euXCmdiZ7be9OVW5V+JQKuANbVg4sikd7J/TFlilpoQG4qC+wNm4HntR/By5PHD9Ono2dSkoPmKnTMy1ywIDpzdNvavGlzyVxebi7GjB6D0KBQhPgFY/CgwVi6ZAky0tOdmS/limNNR8/kWDSgGpjf0p0FK40HQ4o6NG7UWsGSkqaK/uSxo5g0YTz6JPdGoK8foqOi0Ld3b1y66NwkmfPTYUHB2LFtuySjG4Dh8xqq6rfKA8LXaws1s6EFyvT0TMTFtsXDh48NHauxgd0LuK6iS5tol0lIV2mOW7MW6HBRjjK8/3rlUO1RKufVMj0z07hJY0ybMg2zps9GkwZNERkWgZ07dyE3J1dllv9FYcxlgvSsYYWN815abc7aYoEIXg1gMT2zw0zOSOMPTnRTXDdOgavN+N1mgQ1m2MDQAovdBJO1AIWWAljt1BorsOvM3L9/H1s2b0Z4SChaNG+O1jGxItLz9xPHjqFNXJxEVY3gHAOVR4VWpVGZgU4GQU+kimMuXrwE4YaNMpmEMBDSWhk6c4lrtYjrJxJTVEQkqNMxCOutMINnwMuP6zEir0+npOCj9z9Aw/oNkBCfgIMHDqoMGv9p1UTfVa5EK4V3qQBHZRQbY7q+w2ttrEH3Is9YtnDzJ8POVM8Jyzaf8tz4zZgkd83gk4xMzPjhBwFxdHS0LFro1LEjthvcl2MfPf6RfHIKwdFzSp/jcl+ZCbMqb852K60uaKOswMm2DgwIxooVanUQbfYVDZZtzKvpVZtLrl27Hglt1JwvBUemr8RwLtQpio8X57O0/Bd9/ix4uXrIZJJxIsVMKps+/Nv72L17twMTGowUc8srI28qHZ3p7Oxs0NqK261Uq1YNYaGR+ifZoFrZbCsR3ZmXKvA666Io4fzYnlPys9nJdZUD/wsXLsLfLwSZmU9EZFbCYfH2L0uZFRmZTBZ06NAFJ46r6Uhyci4zVAyGY21XplCWdF8cp0TwapF55fLl+OPvf+8YNxK0GrAawJW5EXV+uf2KPq5du4b2HdrjX/+ff8ORI8flscnEiXd2RMYyhyrOW+k75VejO6eSacKESUhOVj7FbbLzgdKxyOJRR/u/GEAkIC25jRs7Eb169RGaUtNSNAIhaF0VZS9Os6xlKxG8Mj612xEeFoYTR49JZrhKR4NBK7MqO4CZP51nuuzkek19JHVPhp+fmvdlZam4YmDpQrhVnLeshFTZ42laYPuTDgICgnDy5CkhB0Ml49LuZQOYTtNsVmPoM6dTUbduA8e0k7LZoC292ueovOuoZPACOHXiJHy8vBWtk7iNeV9yXmaaGdEcurwzVV7p6crVeWZheM3j0aN0uLXwwunTZ+ReOK8s/HIVb6rAW15tUVnSYWNv374DjRs3FeUV743JDVF8vkw+NX3p9/luSHAY5syeLzTFf5wzlnH22xKb+dHFixbB16elZMJuMYyuDQ7FTGpAvExh33Zc3ckwr3pvJP2MBZswfjJiY1s7AE2tdVGxqQq8b7vN3tT3lDZZzUr06pmMyZOnCm3zuZ6seNVvk6Y0U1i5YjUC/J0SHce9nDvWdPeq3yjpvVI57+6du9DSyxv5ubkyN8sVE8wguS0VWUzsTWSopEy+7jPmU+dVl4Ett2TxErz37h8d4rRY1lRpm19afHzd9nkT7+v21mnznkda2iM0b+4ue0XznuDVcV42pLGP0iQ7x9LERuNGzXDGkOik09Db8LzEWLoseSkVvLdu3sQf3n1PLKZYSBpXcJMwVyAQyGX5SEXH0Q1J4OoekmWiePOnP/5FwKvyWKWwqui2Kq/v6zbX6WnwLlywBPGt1U73/E20wbLCyHW4VDZAK/A67QyEiwNI6t4DgwYNJok5RPLi+dH5ep2wVPCuX7ce/r5+GNCnL+bNmi0Z4T8CmB/Um4a9zsff1rusOA1a3Yj5efkyQf/1VzWkTCxboamg2LinSmx+W230Jr/DNtftHhvTFtu27RJ6Fq6rgavDl+aOFpmCYoIavDQb9vbyQ34+6Uk/L1uH8DL1UCp4V61YiaTuSXiS+QQD+/bD0CFDkJ6unJnzAyaTWQDxMh+r6LgawKzQPn0GwNPDF16ePsjKeio9JK1vqsa85U9kFdHughrhfGp4x/sL56/ArYWftLf6nToOzjDo82W5L5ekqrlcx8DZUIpyNmPLFmWGK1NJL90pvLgdXMDLjBsL6cUf8yrQOyQPcttJkyYhMjIMWzZvxKO0B6rsIk67bPVp7Kgg1lFGDDactpbS4cs2phJPSijM8wzImRdjPOPKee/dvYfkXslo3ToBO3fsxrff1ERmZqbObRV43wCRvWx7l0d8NqjQHmdGjPHu2DFTMKC/0yWSmtfXwC0+TVgCvRWrGz3mZc9PxqDoTZHS5i3b0KVrd7kRi6ti75ZHGX8hNv8yIcWZaotDSN+4fisa1leLEQzKxoJ501Dt0z9j/JjvUZCvtjrUv1FjZzPZYM5Xu6eZLFaYzOqa3i0IXAt9PtN9rIQ2WPlneMpgaLaZYbFb1PMS/uul94zLeGaris/n8sxGe2q1m4NUpIWZcuQQeTl5iAqPQr3v6snDgwcP4/2/fYynT5/KvVSDOEJ4ccOVR+VXpfFm6lnARLsEen007OvZwPHx8diwYb20te7QVZu/ej7Eiw5nH0lndAlleKO8c/cOomNjkGtsCWpxMRcur3YvFbwL5i1B00ZeqqBWesgzIS/3KY4fO4ReSV3QtnUMxo4e7VwfKzFpF628z7MnshjaaSq2eGoQiwaOXFF7wtC+cRmKCGMojoxxiICW9qH81WaF2WKC2WySa0nFeJ/KB3E9a+yhZGQJ5LZcCVWzRk10aJ8o9/xt+/ad+PCDTx3gfdXJ+vJqjKp0Xh1ErnVH8ApoKZkZrlpv3rgB7kH08OFDB0fWY2HXd1/2WoPW8Z7BLXLzcuHu4YGdu9X42vF7OXLgUsE7dfJMeLr5G+A1AVy9Y1N+n/jw9MkTSE7uhQb16iI0JATjx40FN/pyHVcyHo076BZTedYz7NBYqSJmUNRQJ/eDUXvCOJ/p3xiq3cgpGYjHO7Vqyc5lWWaYCpRiQDJr/KNj7DWr1yI+PgE+nj7iBGDXTlWROt6+/QdRr24jaPPJKvCWD3jeBKGWNU0BLhvSaEyb4YR/yODB6NChgzQ9aVSfZU33hfE0o6FUaHjTGDlilGOxAiXTF6bxksAuFbzTp86Gj6fhNobiNPkeV+AYLi41AJ5kZuDQoQNoE98aAf5+aB3bCpMnTcQPP0zHyeM0rSy6XE+/V95hxuPHOHhgP6ZMmYLkXr0RHxePiLBIDB44GFcuK1+8quW4q4JyPHbo0BG4u3kjN1ctbawC748fvASIBq7WeXBmJDoiCjt37BQS0CIzw9cFlB4xi6LTkBqZLo9rV2+gcb0WyMxQPt9e91vF3y8VvHNnL0JLLyd46Y2Ce/GSk8qaXU3pkk31z2IpxLZtW/DDDzMwacI4DB3UH+3atEZcXBwiI8KR2C4BQwcPxOwZ07Fz+zZcuHABly9fxs2bN2XnBYo0mRkZYhvKbUMfPXqE9PR0PEpLA+ed6SHjyMGDWLtqJebPnYNh3w9GDP1gxcaifZt4dE7sgHHjxmHJkiXOhdFG/pQYr8R3Xbn79x1AwwZNHeuS1bKw8u8hi1d61f2b7SSUY36lwmHzc3cPfy8/2QyPrERLh+XBfdVAT7Quar05dTfk9gbPah/fCUsWqu1CSXfl0WFo+ikVvEsWrYS/b5iQvp1rIMmtjEE5OKaUnQvU4nqK03YbRVfF0Qy8SCHu3rkj4Dxy+BCmTpqI7l06oU1cDIIC/BAVHo6W3t6ICg9DfEwrNK5fD25Nm8C9WVPU/Por1PiqOpo2bABfL0/5LdC3JXp164bWcbFoHReH0SNHYMvGjeBKIQK8MD9ff1pCqSzDuoUP2BPryuP9vr37UbtWXXC5IA/2R+pUlawruyqs3PWhiVmHpFP6lrIaCwYmjJmAGVNnGG3sBFB5tCvVq0rFqq6odzGZFaPjB7dv2YXQ4AiYCk1K72OI7OXx7VLBO3fOIrRo6iMFpgsaGX8ql7QcVjjFDZH1KTxoD8oEObW+zvGxkUiJQWFBAbKfZuHu7ds4f/YsTh4/jqNHjsh5/NgxnDp5AhfOn8ftWzfBnclfdBTXYFMLrbXUriHTIXi/q13PAd4qbfOb5YgaXOUekgZdxosEr6lAWf/lPM1Fl8RualMwemtxWVhDALm+9yrXWrXqKjaTtqyUUu122cfXq4U/OLPBg99wzcOrfFO/Uzp4Zy+EW3NjYQKncGRhsd4qSM3dMnNUjatT7abGBc9OP1UGZ2Yc2eNUzSPLSguK31q2kGKV7Z/y7EeLKXqwNMNGwwpDoUVNdEl/rqDV1/zanj37UOPb2lXgdSF8TRg/qrAYeNV0oZJblyxYhuTuao2tFpM1aHVYPmVVdhLkvEKjNjsKDb/hY0ZNQNeuavN5fpP5KA/T4tLBO2cRmjcxlgQanLcsYqVyK6OW3bH6CHDJrIgLyjUIK0tNHWnAU/tnQWFhgUwByZSPy/SP6tU4TURTNPWOrNSgtpnAlbliC6ylzBFrwLqGAt7de4uAtyzlY+VXnZWoDoo7UJDhnJqUsJit8PUOwNpVam63JPC+blvKSFEmQYw14QZ4dbqkszOpZ1G3nlPC0yvcuAxVx3uVsFTwLlu6GoH+EYodyuqJkhtM9VoUB5wnh8TiSI7ig+FEzuziZE47mzNTvKZxGtXrNoJPcWOXGWBlxEFVgM0iJwFIAw0x8SBoocRi/c7LcN59+w48IzZXjXlLbudXIa638o4Gr+a+Wi8jw6IDCA2MciokubRVpDQlLpdH/jR4aaxBjk88iGTJTp70bxhtdOvWDWPHjhM8CeOi5ClxX72+fyGgEwgRSCYxhOAX5s9bjLDQVgq8aqJIftNc8Lmhi0mkgFtkfeq7iliRirgtBTA4qMQtgwinzNKUyO76jojxZcwlC0axWY15lZscMVR3Hc8Xz0vxEsjvzk7LNS9V129r/EyqUlOZ5Kysd3bAPDomdsHaNU6LqrfdJnpYybxwieDf/vYBbt28JXm0mCmXCutSqCAtKVMH+b0seS0VvDN+mIPAgHBVCwSEYeH0XNAKcZeuBGBh9B+rvCwZfNk4WoHwopAF27F9p4jNep6XLkGLKONKBa/rAoYq8L5sG5VvfA6duM+uqzNE4Pr1GwgJjnAY4GjDifL9dtlpmPQWEhKCxYuWCKYIVA4xFTszltaWF3inTp2Blj7GPK+jh3gRJIzfixN9CfeM+SYqsow5lArcuHEzPv2kmsNIwyn6F88bAaoEc0dlazHNZbjwJspTlWbxtih6T+5lsRa6uHRViqoRw0ejb9+B0s7kyA6T3BJo8W3UMTOycMEip59oitliIsyh4hsAr29LtaqIhVNCbxmhUUEVxHyWMYfSqJs2bRHzSHo/4EFxq2TOW+y5/oqUU/9mALwCy/42iLDyfcMGi1UN94RMDQdzCQkdkJKi/JPRrW9lyPfTrKeoV7cJUlPVLh7itVJoqZzBO2vmPERGqp0F1EoJQxPgEMw1j382LAlCToHeGV/HU7L/C2D3MqAoA1cnWAleT4+Wjn1ZSwKvoNoYszsIoAh4NSeoAq+jfl6mrV47LhVDhqJTMV2cO3sePXr0AUFLpRTFU4YVkz9FH1SU8Rg8aDj69Rkq10JvItXqvGlGoGnq+WGpY9758xcjLs7Y9Vs+bNSMpubSQkP7p6d0ikQTTQKts5wLFDj9k5ObLWomeceY+uG1yVwoXgoIclY+zc5cG0CJQ0o7oX/nM6ritbdL3WjiAJsaQGOOjfmieWTtWk4VPrOnTu15w47s7Fw8yVRLBnUPLgozArgI4VWBt2h9PJ/wyjMu25jtrrcx6dmjN2bOUN5fnAvhi7fX28sfy6rcvwIpp1LxdfX6yMzMEmiIkpR6acPBxcvUS6ngXb5sNbw81aoifoULEObNnYOlS5eAG4/NnDkTM2bMwOLFi7Fm9WrMnTsXBw7sl0okIJVKXnmd5KKBe3fvyOqiImB2uRGFA4fvVovM9br89NxLGp1TGaHD50Yu9uOxYyfw+WdfOhbja7GLxMCTx/ZtO7F48VK5JiFoAhGpoQq8xTqwtwsITeh0FkEaYPtlPXmK+vUa4Nq169JmBId4SCmi0KqIfFIKsCI3Nx/NmrbExAnKXJPLZLnE1WKlwZGSEnS5XhSWCt5Zs+YhOEhtCcJErl+7Cm8vTzRt0gjvv/831K9fD54e7qjx7Td4753/xt///d/j008+BnehJ2eiEQWPrVs2w93NDY0bNkRocLDYJLdu3Ro8Y2JiZNFC//791dwYFQt2JV7s2bML/v5+CAsLxaBBA5GYmAjOlQ0dOhTjx4+Xncz37dsnXFZPerP3PXXyJE4cP46LFy/KoocrV66I7fP1a9ckb9zJTW/QffTIsSLgVVNFxmS7Ad5evZIxbvx4gxCUhlBz86KVW8V5i9bH2wEIG0ZxXUU3Cxcshoe7Mi5SXI3OHyixEdwVx325aMdsVk7/Z81ciKaGAZTSsSgjJVWWsuexVPDOnjXfAV6zRfmrEgou4R8rjye5n7KCssBsKYTVakZOTjYePX6Mx+npeJiWhnv37suKnzt37+Ly5Uu4ceM6TqecEudv+QW5at2u3YIrVy9hztxZ6NsvGcnJPdGuXTtwo7Dw8HBERkYiLCwMU6dOlZ6f39aA4v688a1bIzAgAO4t3NC4USN8+823+PSTT/HF59Xw3rvvYfw4Bcbjx0/KVNETw2aaFakBLIQIOz75+HNMGD9NSq05M1cfFYlXhAO/HaKtCKBU5m+y/dmJx7SKx5rV64z2UgYTlJIotmoaqYhy2OwmterIZkd6ehbq1mmKK5dvSD65Vl1LcnxQ1vyVCt5Vq9YhOipeEuc/Lh44efwETpw8iRXLl2Pzxo04dSoFKadP49y5c7L7Hpf3EcCcTuHWmzwpElBskd7RWBjtSNTlgjbR1GhLIW1FVye5RHvmUluraAC7RijIz5flhQ/u38f169dxnIsejh6VZYeMR/DWrlUHruBVorFaVMFy/dM//TPee/dvsipE0nZMDVWBtKxE9qbjsSPlwc3DggLDDA+neiqGJrocxhWWGRRvIr+ka85Ha3P+Pr2HYtoUtVk9h5gEr8WmNyYrG20Z4KWmt6iF1dIlK13Aa5dVPW3btUF0VDhax0Wjffu2iIwIQXhYINzcm6FRw3p4/8O/4sYN1ZuYrQSxDadTTsLXyx1BPl6oX6c23Jo1gUezZogMCUHv5J7o3r0LdmzZItYmIveL2GzD6tWr8P3gwRg8eDDGjRyFZQuXYsHs+Vi1dCWWLlyClctW4EzKaWk0V+DevXEXKUdPIeNhOgpynHsTScRi/06dOo1aNes+A1724Dwoov/iF7+Qc8uWrfKsoMBkTCeVXbx5E8RQlaYicJmpMCyqRo4YjS6d9QIAZVPPRqMEyJNHRdWblZyXDM1w0UR9S80aTmWpVqi+jGivvEeKqp1L+pzmkatXr4eXl1JYEdiOLkOqoPg/OzKfZODeg3soNOfDZjPDZM6F2ZSPnOynOLB/Hw7u34edO3dgy5Ytcm7ctAlr167D2lWrcfvGTbELLbTQsRyNIYC1a1Zj+PeDMDA5Cf26dsOC6fPQq2MSGtZugG+//BqBPv4YP3qciEIUh3TDTBk9Ff4t/BDcMgghgcGIDAtHRHgkIsIjEBToj9DQQMyaPVPip6aewzdf10JGhnJpy2REO2nMFdarV88BXm9vtTySGmc1xi4O3pckDD3d9KKwSiQvHXCU8WhmaIDXr6U/dhjeMsSl0jMzAmXjaG8C4MwkRXcyGh6k2ebNPLFooVKGauu+lxHtSwXv8uWr4ecbIh/ihzltQ03zhg3rsHXLJhw9cgDnz53BqRPHkHrmFAoK8pGRkY7c3ByYOb6wq02FZVrISOV5AY26zZzmkaWCz4tZ9DfuJcwliBSfuUTQtZOhkqAgP0fyxhVL9+/fxMNHt5DxhK5r7Tidkoovv6gu+WaqhYV0bKdE9g0bNjiAS+7761/9Gg8fPpKPswH0GMXZ0FXgddbFWwIJwUsPoQCOHDqKkMBQmeWQB3rBQqXp/Dh0pNSmNMrM49gxE8WEU/JrAPpl6rAYeNU8KhNbtGgZ/P2VJw3eP8nKQuPGjVCnzneoX68uWjRvipbeHvD2aA539xaIiIhASx8f3Lp1W/Kitca7tm1DfHQ0BiX3RnxkFBrVqYMa1aujbs2aGJjUE/2798DIIWrSms1gEhtqzsHuxdSJE7Bk7hysW7USyxcvweply7Fh3Trh3ATX8SNHiRjpmdljUdVOUTrl5GmcP3sJN6/fwYP7j0DFd052HgrylehkMGpwS8bq1b9ycF6Cl5VHTvz+++/jT3/6I375y1/i97//PX7/+z+gU6cuxpSEYSpZhDCqwPsyhFdecTXh9+yajKmTlGJRjWsMo58ibfSWOpUSvkmxncAlLmyG6PzwYRrq12ssY3WWg9yXkl9Z68YArx7zKjMtJjR37kL4+4UadUMFlCGb6NoqFgrwqG2mKZruRWx23L9zF2dOnMT927exd+dOTBo/HoP698f3Awdi7oyZmDphIhbNna+MJ2w2FFKzbbNh8+ZN6NunD/r17Yt+ffqiX79+6NKpI7p16YzOHRMREx2FubONiXjDWx8VF+3i2qLuN9/hs/c/w4d/+QjVPvkSPp7++K5WfdSv2xgtfQIxeLByvE2F1DfffCN+slgczsPx2LtvL4YMGYLMzAz4+vrIfPbjx+no0CER9K0los0zaktl7gAAIABJREFUItnLgtdYoiENzQYr7aw4gisrEVVkPLZXVmYWYiNb48b1m9J+NtJDpeO8CrhqPlpJC8xsl87dMXTICJVvvVihBPCXVMcu2mangTRTmj17Ppy2zWre9uDBgzh8+DCOHD0C+qZKf/RIdhEszMuDKb8AaQ/SYCk0yyhOlEhSiZKvF/4jYE0WMyz0hmGMC174EiOoiTLxaklQmQoL8CQzE3fv3saVK5dw8eJ5pJw+hdOnU5CScgonThyTZ3w1JSUFX3zxhYPzUpSm0qzQ5FR01a9fx7EOk+9w/xlpgOeAt/i4Rd9LnRhmenymn5fUMFXPSu60dJ3pkG2yctkadG6vFFU09lcWfJWL85IxcMpVtyvzz2Pbtu346qtvHftlKXIuuez6XR2WCt45sxfCyyNAPsB/t+/ewR/+/Bf86c9/wSeffoyvqn+J9q3j0DoiAu7NmyPQyxehvkHiCI6JayONfbv3iGEGjSx4tk1IQLs2CejVrTt6dU9C58SOWDh/gRAyiZsg5rF582ZMmzwV2zdvxZ5du7Fj61YcOnBA3MmeOZ0ifq0ePHgg410Tp6cM08eM9HSkpz9C1tMnKCjMl46ADtpLOg4dOoTPP//cRdtM7qfGszp+RGQYxowZo28FuOId8Bn7ad2PKC8huoIZatC6hlq7yEbktWv8quvSiVeDVtclG6Zbxx7YukntC0TzV7XCpHKBt6Q2Zd65KMbLq6VsAMB75cG09PK7puMCXl1YRadTp8xEM4cbHCC/oAAZmZnCpTgveuvWLTx+9Ah3bt/GlatXcf3adTy4/0A0sYXmQmPHPQh3PnP6NFJTU2VB8tYNG/HDlClYtmgRli1aii6JnTF10mQBLzleXn6euM4ZN2483Fq4IcA/AEGBQWJ0ERIcjLDQUESEhyMsNAzjxiptM31J86A/5h5d+6BJo+YI8AvB19Vr4p3//iO++LwG6tZqjk8+/BrVv/gOw4coI42DBw/JmDcrS9mZyphEc0bD0is5ORnjx09UlWIMB0qzbeYcN08SGImLHJrXPF2twDi25viGJ0V9/q7EKd0BuIZla0jXRv2pXrMRdNl0g5w+eQbBvuHgro/yu+xPpRa/PKtUrMi61G1q5EEkN8Wo5s2bj4iIKJX/5zmDKCZOK/DqcZckqKpl0sTp8HBzcl4uWL944QLI7WhimPboEe4/eCjWU+kZGQJqGkXYLFbRNtM4w1SYr3KsknzufxJ7galATCs1933uC8aP5LjckYE7J1CEzsrMxqOHmSjMt+BMynlsWLcVRw+fwtYtOzF1ynRMmTIVmzaqOdvDh4+ievVvkJWlvFKK1ZQ0PhNX4xJack2YoMBrNqt1odLrP2Mryw3ZFHhd862BrEFM4tNGBbymHyN9GiMAPRIwwookuMr3bda9qkNF+H379MP3A4zNw+iGhqcsfNHMqLKUQYOXlKXyppW6aWmP8fXXNZFyStkt6A7qRWGp4J04YTr8/Zy2zbRZjo+LQ3BAAGKiIuHt4Q4/by80bdQQ9evWQa2aNRDo5yd2wzSRlDWWdht27tiG72rWEF/MgS19EBESjLDgIHTp2AGjRozE+LHjxGJLE7de0HD48BFMmzYdM2bMxvx5C2Thw+ZNO7B3z0EcP5YCAu/69ZtqKxUqJ6zkcmo+Os/YF9UVRCVdnzyRgmrVvnSMeTV49EQ636lfv4FDbOa2pqpCnyUMApLckwdFof3794s1F+PzINFRPCYH1tNR8oPLP/39omFlIb7KlQ9WW0ZmBjq0S1RuXSkVyZyvUvxVPoXVs+AlTrTFVe/kfvhh+iyhhheBVv9eKngnT5qBkOBYSUxrYV3oDIX5eTAX5ONJxmOkPbiPWzdvIPXMGeVwGlwlkS8rFW/evI4FCxZg3vz5mDdvnoCQK5DmzJmDWbNmYfr06di0cYP6jsyBKQAQsPFxbREZFoe//ukTfPD+l+jcsS9Cg+NRu1YDfPD+R+jVo7eRP5dtHMeOh7u7J0JCwhAdrRY+REZFwt/fH25uHnBzc8O4sYqTnjl9Fl9V/xqPHqUb6SiuqA01+DA6upUDvEVsmosprBiX4OT4+KuvquOvf/0rPvzwQzRr2gznzp2X9Pnv0qXLqF3rO9SoURP169VDrVq10KhRE5w2rMUUcJ1A4TuEP0V1tgM7OT7RDag7PX3PUMR6FxFL3A+53LvG/TFdy24dhg6B9TJz5iz06pksdZubk6eUpRz2vATnlZfL8V/p9fkseMl5tXL0/PmLCA9r5aK40m3MzkhfFw1/QVIwmLjyeawYBZYsWY2oqLZSLBKDyWTB5SvXcOfOPWRlPsXTJ9kw5ZuQn5Pv8EzPyHzdigIBr8ni1Nq+sH5kUQC12k6lVWnvkHvl5eUJh6PIKRt9C+ez4knWE9y7fxf37t2RHeHu37+P06dPYfXqlRg9erSAa9GixZI0bZs/+6waMjLU/rxKG8jxkvPLnTp2wQRjVRHBq+fhpNZEBFbjW76xYf16Mezo1rWLLDOkDqBRvYao821d3L93XxJdOHepxAkN9keXTh2kU/Hz88P58wQ4p4/YedHarRA2FCKrMBe5ZudGahZLAcyWfNnUmcYwhWYTCswmmMWTph0F5kKYbVYUcvtT8bTJ6TcTTFaLGMD8WIBsyDaGw3xOP6od6EVsNmyZI8LisGq56vi5O6Tq2FTblUjwBqi524ee+czPK8DD+2nIy3VuWZubnY2nmU+Q8/QpzIWFeJqVhSuXLuHC2bO4dOECLp0/j6uXLuHWjRsyzUj9D5WfTt1JUZCVmBcDkKRlHvTxTDo4e/as3Es5KWDLogXnwgVXqax08C5eBT9fw/UrgEeP0+HvH4hmTZvDx9Nbdt4LCghCkH8gBvTqJ/vekrvdun1TFiZYbAXSYxw5fBShoeGIjW2DFs3dERkehUEDvkfXzt3Qq1syZkyegW0btymRspCWWUr85FI+umZNPXMOFy9dkkKdv3BeFhhwuR/H3tnZOYaXBM0xuV4yBwX5BUr7bMzbquZ89j83GqMPK70wQbiYMZbVsZs3d8OwoSP1raE5dlpYac7HCEuXLMIHH/xNOhb9wvZt2wWsK1eskkctvf3wzVdf6J+LhQSvMWUnpqpmAaaO9OSJ3gQcMJsKHPa6+vfnhaI8k72myk5YzyO6N/1bUfCyTpR7YNIHj3t378OjhR8e3E+Te7YD88SjtLwRsdSN6HiMGx+bgMYNmyAkKFgcxHHFmo+XF6LDQtE+Ph5dOnRAm7hYNG5QH03q10O92rXh5+MNPy9PxERGyDuNGjXCRx99hEWLFj33+8XzpYdZOuRS1x49ekgaBK9eoSfLGR2SnpODlwreaVNnw9dXeY+UDa+NDZQoGmY/eYK8nBxx3JaTm4PbN29h7+494PYkefk5sNmpeOIqDpssVODGY8m9+ogImtAmAb179UG7du3RrXN3dE3sikXzFwm3k3GhoaGdM3sO2rfvgC6duqNevYZo3rwFvvrqG3z44ceoU6eecMwuXbo5/E6xxDSVjAiLwCcff4x6deqgbp3vEODvi549uqNnjyT079cPvZN7Y8XylVJBhw8dQf16jRw7JlBDxHleZ+Pa8cUX1dG/3/dGhSouS/HVocl0zNfSRzXnqLUBvFKoDB82TMC7Y/sOSeODDz5Aw/p1MWnCeIwfOxYH9u+X585/rgBWRiOnT51GaHAIan9bA/GxsVi6dJlEz8vJxrq165B6JhWjho9Er+49sW7Favkt83EGpk2ailk/zES6Ydap9pgqnbiLE1dF3hcFr3Fnt8Ns6BVGDh+Nbl0UoTOfGrzPyzPBSwMOxtFHsyYtsHD+IqSeTsXZ1LNIS3uI61ev4ub162LL8OD+PTGf5WZ4N29cx/27d+X3w4cOyr7OlOy4Wq1r166yyR3TfV4eiv/G+Jr7Xr16FT4+LZGZqRSonOIUWjOmL9W7JYLXcFdulGvmjHlo0sRTykgvQbn5ubh65SpOnzkjgFSL2tORk53jUNOrCuHiZ67LJfdT41f1/Pn/rWal0KGITq2t65GTnSscj+ItXXqSU3IcycIqzqc4L69TTqVg165d2L59u5xbt24VcXb9unWYyu0/e/bCKoMLHj18TDYaKyLuGD2c/v4339TEuHFqjKyndYRQHD2h5mSsVDUepUjNY+/evfjHf/y/ERYWIlNI1Gr/6le/EjD/4d138O477+B3v/0dfHx8HC5KFWGxEVRDHD1yEv/57/+FgJaBOLD/AIYO/l7epxeTJxkZ+O1v/hO/+c1v0KReI8RHxODPv30PXRM7Iyo8Ep999Cnee+c9VP/8S1y9dPWliKo4kb3teyd42U2qOxElCWCTGTW+ro0tm9WsQXHgFr/XeRdZmUC3qqER9xMKD43EpQtX8MTYhpPb5/Dg/tGcgqRNvMlhtMM2UW3LcXVBfp5jjMq9f+lUQt4tZYyq8+Eakhny0Hnu1i1JDKRUOuq563rfImKz3MhYi14szI5xw7Sps9C0iZckzH93btyCRxM3/Nu//n/4z3/7D3z5UTXU/PJbuDdpAa9mHmjWsAmiQ6PwOO2hjHrBtYsAjh05joT4tiIO9OszECOGjMHEMVMwf/YizJw+CxPHTcLmjVtEbGZByHd47N61G9u2bkdqyllcu3JVtvi8d/cu8nIVkFmxdH+iC83wZY+jR47jk08+E60l31WKOdWL67SCg0MwduxYuZUpHjttUNW2K66NwAguHTpWrVqN3/72d2IXfVz2KYbMi9PscuqUqcYiCsj0FRc+jBg+Sr6hx2K84fja3zcc//Gr/5INqyQCgFHDR2D+vHk4ceIE/u7/+jt8W6OmY1+c4YPUMsbZs5Tm8u6du/jdr3+LsBAlRanG1x1O5Q2LglflU7fx5UuX0b5toqNOXNuB15omij/XnSv1JDzS0zPg7eWL1NTzYjlH+ssvyBNxVUlgyrKQSiVKVWxgApnToNSP5Bfky5iX9PD99987RN5nv1tyPTOfQkuGXQDzdObMOfROHuDoaGX2pQjn1WkBLkYaxljLoMA5cxagqea8suufTaaBbt64gbNnUnHh3HmcSTkjCwGoKT108CCOHD6Cgrw8cTkCu+pRbt28jfmzF2DuzPmYN3MRRgwagwkjp2DGpDmYMHoSEtsmYqLB2Zh5auBY+L59+6FB/QbwcPeEj7c3/Hx9ZUBPIw161AgKCsKwIUOkEdgj6yOpa0/8/t3fo+ZXNfGn3/9RuNLf/vIXfFejJgJ8/dG7Z28sXqAUVqmpZ0UUp90yDzaubnydHrXWGryu2mbNGdV7JBj9BjBv7mL8w//6F9Sr2xAXL16WH1yyqCIaShfe1K1TD99+XdORgE7ryZOn+NOfPkRoiJqyo0G7mP8ZMekY4R9++UsEBuvVX8DkCVPw3799R3QDjMbmbNCgMWrX/k7e+nGCV5VDz49PnjAZmzZsUrXwEkYNqs0U8fNliqe1atWRXRVo9kqOnvU0SxgIub3i+Irzq614bGprHlncbwWNkah7odg8YMAA9O6tZj/KCl7G4yHjW8MbDO87JnbH8WOn5DeWmQB2DNMcXF3Ay8KQaCkucN5JJbho4TI0a+IhCdBkkHudPridhuwnebCY1JpWcj/dG0pEEotYDXF1zsvZKLPXk96sMB+FBUX32dVpu4bUNqelpUkvKYCTqRQb9uzah9Ejx2Bg/0Ho26evLG4gpxrQvz/69u0rY17d8PTr++WXX0GDV41llQiuv+Xp6e0AL5/xW+y5WZn6UI2l7ubNWoR//qd/QbfOPfXPjvDm9dtYs2ID8nOd2mNy12++/hbVqlWTeKx+DV4OE955589o2sRNflOrTpwdVcrpM/jlv/8a4a3UlB4jrV61TtaJPnhACUgdQaERCAhSAOfeUSq/lTssynkN2NntYtkXGhSKtIeGoopt4SDo55eJLmL1NBprhgrPpk2bi0eVBw/TQP0NzXoVXFUOtMgu4OEvxkZ3vH/w8L5sEM95/fbt26NPH7UbIdMuS56M5nHE1VhK6t4HfXorEZxadD1cKJom8AsBK00BhVPSTYciyqWLV8DD2OKTVXf35l2E+EbA290P/n5BCA4Jhae3Dxo2aozmzdzRrJEH2rfuhCfpTw0rKW69acf5sxfQvWsPjB8zERvWbsLWTdswddJUTJ/yA9asXoM5c+Zi/4H9Ij4wkwWFBTLWuH3rlrjdST19Bndu3caDe/dwjxt1X7+OtIcPZQECCy+7BRruYrXIrSvlReHxYyfw2aefO4w0tCJKVyLfd3f3cICXoHJwrmJjXsbdtnk7fv3//ie83L1x7kwqMtPTRSK5e+uu7Mp+5tQZ/Os//R8MH6xWkfCd1DNn8b/+/n/B19dPsusKXva6/n4BqP6ZArZEADByxEjExMRh9559+Jd//Xd07qYUN/x91ao1cHPzwv37XLOsDnLu4CBjhdhLcKqixPJ8YJR3XM35FIQcPAXTp88Qk1n5nmiYS58HLZ4nBUQ1NcqaycnJQ5269bF16w6hv6zsp0JPdEejwFq0C9HPNIAfPnwgjg6ZFp0pavAW/25p90bzSKDj8Oby5atoHddBxHo+Jz3q313DX0g3T8WS+NcpVCsyAKxbvRFB/nqvIgLRgkcPH+HhgzSkp2eCVkz3H6bhwsXLSD17DqdOpiD19FmpBO7oRxCSm169eh3jx08QQ42NGzdh9arVGD9hPIYNG4opk6eiU8dOGDVKjfcomihfzTasX7cWdb75Fl99+iW+/OhT/O299/DXd97FX957D7/7z//E5598jOHDlNisQUvtXM+krmjSuCG8vT3h4d4CAf7+MpcaEhwi9tCJbTthzQq1+RSttD7+6BMX16+sJGVvrCs2LCwco0erhQkKWCRitbxLV6SO26RhA1EmcQz7y3/833j3d/8l97/59W+wa+dOiTZm1Bj83f/4nwgJCUZ8fDyqff4Ffvfb/xLbcEagaK6+ozrRYwcO4d3/82t0atcOp48cxYkDB/Gn372D5B49cfHCZfzxvQ8wZsxknQWMHTMef/79X3H58hXHsx6J3dC/h8EV2NSGhrwyh47dHjm9o4RBKY9vywBMnqTKq/Z8VvO7ZSkL6YRJaZnpaXYOatWug61b1aKG3Pw88bem3TFpkJYY0r2x1SIzFVz/3bZtW4wYoTplDbgX5UnTj2uobQyiolpj3Vo1h63HxcXTKxW869dsQmSYEsfs5MoiVjvoodQLVg+NBMgRKQa/6KBmOT0jHWYaFdhMchIcNMf8YfJUjB0+Gl3bd0RUSAhiIyLRtnVrNGvSBI3q18e4sWOkR6IoxD6S4O2cmCBrdL/66mt8+eWX+PyTD/DpRx/gD+++h9/9x+/wD7/43+jSIUmyxd3KP/jgQwd4KWGQ+7KS9JGY2NFhYaXBW0RhZYihjP/9wH5o3ry5cnXbuDHqfFcbjerXw5fVqmHvzl2SZMajx+LQQPvG+uU//TOGDVG2uWw4Lq5g+S0W5XWh4Gk2fBs1wb/8j/+JQM6xN2qCr//8IS6dO4+nmdl49zd/QJ+eak8efmDcqPH471+9g2tXr6ki2IAwz0Akte2s7tk//0jBm5WVLd4+Dx08JGWxi69jpWQtS5nUlCc7XtUbZD3NQc1adbBk2XLQPj87J1vs60VIp4KqyGkBv6eXG7LjsJhNMnQjPXB+Vmuby5KX0uJozyBjx0xBv76DpZyUwEqKb4BXZ1S6ZXnhxPGTaB0Xb8grdjzJfILRo8Zj1cp12LRxO/bs2o+jh0/gxLEUnD1zHudTL+La5RvIyysETUypoOH4igsEsjJy8PhRBjLSn8g0EAtbUFh0Okg7xha76DKAXlEiYC00qbW8NFh3UQLp33VoKijA44ePsHvHbly6oJRI+/YdxEcf0kjD8F4v43RNDKqBk5J6OsRmi0WNhwXg3CNYxj+0ulLcUn/rmZBgMQzq9W+HDx7A/PnzkXJKKSakt+a2HLI1B8c5qmdnZ2jKycW2desxetQoTJg0EccOHpZksrOzMXbkGBzcr4iZD7du2Qb35h7g/CPTpDVRmH8IEhPaq46OOglDP1ASQVSaZ7JJNeuAdaLaYsL4KXBv4a06V9YpOzhDmWqnB4oXnHQCZyaDMIaG+QUmeHq2xK7d+3D37j1hIlnZGSIyy5w95+1lSKYkMqVYYrvTUbpZpEuuaz939izi41qjfYLaYYSsXRZIkC4kT9YX5k3nnbolHlevXEd0ZDwK8pXHSdI28UTpVDaRt5thgNexz4dDW0IuRi3v6ZQUSSw3twDduvVEeHgEEtokypgrNiYWMa1iERwYhtDgMCR16Ym0B49ghQkmw5/U+ZTT6N89GU3rNMCnf/sYX3z2Nb6tUQ9/+6AaWnDJX4A/Bn8/yCHTU9wm0dFR3YCBAzBp8iRMmTJZfDRPmzZNwnlz5mDxggU4cugQbGYLrAUmIVK2yZnTp7Bq5XIcOXQQnEin2eGd23dk0C8FkXGyqqDly1ah2me1jElywkT7m3YqhTp37uoQm/m+4r5UatBNJxuSgFbV9izhKzFNvafW9Za0YorvkTCefV8BTefbNdSinX5GsLNTZDpUoDDksIVpPs1+Klwl5/9v7+qjqqqyeP9Ma2m1xmnKWTo5ran+qDATPwBTmRIEQ1FyVAwSkVBBeDy+NBDQUqxxZrJlRpqWk61RQARDERDT+Hj40iamLE0USwtzRBJQ+XjvAb9Zv33uETJUXGJZy7PWeee9e8+799xz9z57n/153hDIXGYl7/L+PxuVdghyirsncbcdCJg+A6vTjBja1NXKdo9bOmXbfrW2DXbaacHO/sbEhTwfgQ9LrDhbV4+6hjowdji3bkwOz8AQEhxCWHey74pqMyl8U0szmmzNOFNzGvQhN0eakbxQ2VkTDlWldkDZWl9tbB3nO0w35zwfAcqeWMgEcA1jKnk+QytaukZeXojl7bXrkLwwWb4TMLpTSI3s7Q2wt52Fo/U8ztXXourIIRz8vALllmJkZ29GevomSZNChwVWIqoGNs3/U/xOwUx8fDyWLH0JJlMEpvtPQ3SUCbEmE/x8xuO1v3fsMdTbaIcpIgx97/09hjk/DudBj8HN1RUeYzxk3zs7dDYmTpyE115T/rxvpq1GlCnOeCxa7ygp8JdfHkLNGRVsbtmyVy6yzex4+nSNSk1BnfhVkVf58naFFHzezrWrPjxGIQkRVTxQuCeWLQnvzePKAkeohFBqJdjgOOnCybnU743ficz8fbl73VTHmQLEbkOL4SH29bHjcB/pgW9OfCvvixxKu0F5iVTdqW1i7c34yGpR5Zz4Tw+Gdd8nyi2TiQNstB03zHQ7IS+jvLDyjbAV5G1pQsMFlccqPNKEuPgFMjZeXxCNThQcm8Qx//EYyQFcWoVFNnabmek5iI9NVISNIXJYf4C8JCWXVJoZstTX1WNBXDwOHTwov0tKSsU0LysrC9lbspGTnYP8HTuQk50NS5kFRyuPwNZsg52sDimSg6ujWjXlAlf4oIkYgVm3V+j6g1PKEkbtsbnoUIlOVQ4NOEiByFrSgqqmpgZagn30SJVcY5zXRFk8+IOAKwHi21qxa1cRxk+YAJpPzp0TjrVvvY2qqq9BFrqszCJ7a4mO2Sk7naLIl0fW7iCGXrh0y/8o+1Y+X4cElAukUAeqNS7GauoIAMA55H81wooazqDCnGN9/Zu7VUJS+oezvLJsOcLmqiQAZCEFebnnbXeIGwdn52qVkhEH59Qgu83Ndvj7z8BH+/6D78/W49yFC2iS6CsOQTpNee3kaoR9NpCRSMffaEdD43mhG/OiTTDHxchYuW0k/qnxkN6z/nh8zKFwaWXoYxiMX83/zsBzjDcqKyvluhy3Ws65HNhppNGFCqCTxcfH+z8W5XN1dbVsyN3dR2PQoIEY6OSEJ91Hw+lRJzz04IMYPmw4zBGRoEcG4z/bHBeEZTj0xafi/+vnOxG+vuPh7e2FcU97YbT7KLi5umGspxfee/c9YTOo06KinKW0pBQr/rkCaavSkJWVg/TN2dhZtAelpRbs37cfzDNEbw7ZIxqeSFwRmRCtsvIwTpw4ju9OnpSwPLVnamUscmHjY8+eMgwbMgqVh49cpFAEeK68BHBuGXr3vgO9e/XGww8/gv79ByBEoh2QmtH+2VCcczplDrkGdjGX13lMIyGvrb+zVSoytRcjAhNBOW5NXdlfU9nOi6K+xo0Ya09ekxDc3qZgwdZih8eTnsjJUc4dJApixigyB7KQosG9Qku3BvWeKBYhfrDYbK3w938O5eVWnDp1WkL/0kiD+1nN8XCRZOXiyTnn94Zz9WhsboTNYcPJ09UKeU0RMEWb5bqkV4QOVTWby1YfU62mup2PC89LJlcxv5gTGobXV76hrktYElrI/zu6Rl79gjXLlZmZCT+/Sdi7t1wu0tUHXfkkfpCsSk1obWeuIgZrs6G29hQsZXuwLXcLNm58Fxs3bcDyf7yM2NhYRJnMKMgvEMAn4hIAWJiJ0BxlRrQ5Wvqxrzk6FmFh8wSJvL3GISUpRfoLlVd8Mwq25eLJJ0ZgpMswuA1xRuDUKfB/ZjL+6jsRQYHPITx0DtasSpOQm+sM52cKRbi34j6fe0cWpm7p06fPRdXPnXfeKXbTPCcpXWQi1TqogPbGIC+vzffBwlZX/tbIoo9pJNV99X/ZsvA8++r/3cwtxPZAkaD8HfnwHOMprp/yIAbyqY0l+xCouXAaEG/8Zl/hTMTwQi2sBBOyphqBfX39UFBQBJu9VdSatLpj4SLOGGgs5MgYl5yFXM+58w2oPlmNqqpKfH9Wba8Y3fRZ/46smtK5Bz4slnI8Oz1QFmI+NmFdcA1tl0Few0yQqzhfNktBYT7GenkgLi4ae617UVFhxYnjx3DqVDVqvz+Nhvo6MZS/rvEaVEoFT7/ylahSaTEcGAiE3FtQv0wkZFTLr499JWF76HNZRffC0lKUWSzIz8vDIw88hIRKNjkgAAAGXklEQVQFCXIDFUdK2Stfeke6h2mVjt8zykmD8ae6RoAOZPo5kYLP8HPev8fuTbgzMMxsMiE+bv6lr6dHfk+fFgjtrklnm2+/5Z6a8o+OoIXULtAJgXb19XV1YLgnhgX+7mQ16mrPoPFcA5YtfgnJCxLkXO3pGjEqogcSA1WcYYK96moxNvriwAHsL7fiI6sV1jILSj/Yg8yNm7B29RqsSUvDGytXITlpEcxR0YiPjUdAQADuu++PIhfiA1PiTPhjgoLbDNph8NLKhoSIQD6fmM7WZgir6Ku7NPVFeHj+BX3/8FvcffcduP/+e+D06AMY/NijGDTQCWmvr8KunSX4rOJLHDxwFGvf3ABfn2mYGRiOmQHhmD5lFmYGhiHenIJlqS8jJTkJmzb+W1y99ELBQTJeVkZGOnJz35d9aXbOVnDPTYuko5VHxWDkWt+e1WJBcEAA5oaEyEvg/wlsutVIyUWLZevWrZK6lAhcUKBsacmN9BiAdoulVjDMYV659jzL/tM+5w/HL1yckRfazWU4Ro0ciciICMyZPRvzwsMQxHBKQTMwL2wu5sfEIOmFBCTEz0d0ZCSS4uORsuAFzI+OQdLChUhOSUFyQgJios1ITEhAcnLyxXr/gD9h+NChCJoRiFmzgiWhAN1ITZHzEGOOgv+0KfCfNlXS23qNZeST0Rg71hPeXmMxetRIuA0ZjEnjvOH6+ON4wnkopk7ww/gxY/GU2wj4jHkKwdOnIfjZqZg363ksXpCIKT6+cj40MAihATMwZ0YwZgeHIHJuGKLC5iEuOgYJCQlITExEUmKSpLVd/OIifHZAaX2U9FupjW7rSkpH0qwoGW1B2ZHCEM2SAI2NF2C1WpCTk4GVK5dj6ZJkpCQlIi4mBtFRUZgfH4vwsDmYNXMG/Cb54Gmfp+Dh6Y4RI5zh4uIEV9eBcHV1whDnx+AydDDchjkjLDQEIUHPIfWlxTCFz4Xr0MH484D+eGBAf9zd5y7cfvtv0Pfee9Cvb1/c1as37u3zO7g/MRLvbXgXubm52L59u9SgoCAJP8PMDi7Dh2KQkxNcXYZh4gQfjPf2xpbMTBFkKYSlYE3tE/mbyKsRWANuv3790LtXL5He6j48p4059H9uXMtxdaeqFfnGjaODZf8p7kGhKRGYcbipR2WkClqp7dm9G8XFxbKQFxeXYGchrfaykft+DnYVFaKosAAf7t6ND4oK5XhOdhZyt+ZgR942CbeUty0XmenpyMzYhK05WcjanC7nSoqLUVpaJvmkt2/LRWlpsWTtyM/PQ0F+HkpKilFeXg7GLmerv1ute8UEtuKTT/BpRQX27bXis//S2vAADjPixpEjOHL4MKq/+UbMZZlo/sK58+qFGoSDcNWdYmcWQRG6ESeBLpG32cYQLAppSXmJvOSzKc1VQd46EPnyN+VKeqV+ZEscEgvr+FfHcPDzA7CUlqAwPw8b/rUeWzIzUJi/A+9nb0HW5gysW7cW77zzNt5asxorV6yQmrp0KVKXLMWy1FRxQkhdkopFixdhaWoqwsLDEBw8EynJC7F8+d+wq2gnWpo6HB6ohtCSXIWMyj2LIXUInNwfskyePBmzZ4deRGqe455XjAc67UFvHEB3B3HZ59eGvHZxnOd7+jUX8n1ShQtTWwX6tivi0QaHnUEtKEBzgBZi5IKV1PkyyEu9oUJaRXmVRY6xUaaFBx3twWyA1CU2olUyA1JgRYW0YkM54R3IS0RWggUlRuuM1B39f4qX5OCKTl2npFWhzlPpW9X+XhlSdN7rr1+/HqtWvS5Do5SZahgtsLpxCNuZyhEpu1s7/+8X/t0QIlKAyDlnVnmHjQY86t2RkFC+QQmwZL7XOaFpiEGXvXZlbita1nYCPs1NO9U2+oI3oZ0RX5i7t40ugY2w25uU1VabA23a/JJqOlpy0WFB5CpEKPWbVluSi5r9GeuNUn/ClOAJj7Gyj4rNJlxsJ720YoOValXUTyQIVLUyJpcIGGl4w4CONB1WOnpHq1J53XZ9AHjzrPaazdWtXgg0Ve3uc7I/qa6mvBkZGXj1VRXDSl9Lt9295q1+v5SF5OaB5+7AzHUi7y/lpXR/nBoxNfJSQV5RUSFrAY9xUnXbnQm+1af7c39rrq5trm4hb6d9qzZq0NSXwKSLYt3Uflgj+C1guzZguzVfPTtf/we/sKWh9v7LfAAAAABJRU5ErkJggg==)
A cylinder containing water up to a height of 25 cm has a hole of cross-section
in its bottom. It is counterpoised in a balance. What is the initial change in the balancing weight when water begins to flow out?
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gbpKam4mzqWZy/cB7nz5/HuXPn5J7hBeMZn1+8eFHm/K9du4Y7d27j4cOHePjwAe7fuydSFDswnpz7p0aaGuunT58iJztbhTnZSlOdlYWC/HzRVuvfqak2mwphMZtkyk3bBJDDUtLgyWeMl5+fL6e2JeAzdphMi9eU9Kjk69u7t8TT89gk2OIAfJ378gcvxQOZeKdiSM05MhQlFRVZegxkgJtxKeawgD6eHli7Zo0DlHaO3cxUCHE8qayCKH65Wg9pEU1P/DusnYrMzzmS/FFc0GiAc7Y0JOHUBomFHRANUUggQpiZmaKRJqE+evRIzrSHDyXkdAuNYOKiW+HGjRu4f+8+rl25gtOnTuHUiRM4cPAg9uzZg507d2L79u0Scq555cqVWLJkiUgG48aNAxUvY8aMkZPTYcnJyejevTu6dOkiUg6vBw0aJMBmBxEbFwuCn6cGf5s2bcCTHUH79u1kKorTUW0SWiMqOgJh4cEIDgmS+X5qqv38fODp5QH/AD8EBPqJVrlZ86Zo1qwJGjepjwYN66JZ80Zw92gOT293tGjRBE0a1IVb08Zo2rAe6n9XU+4DWnrLs7CgAMRFR8LHww2Bvt7w9/FCS083BPn5yDXjN21YH4wfHR6Kju0S0KtHkkynseNq27atlIXXMTExaNmypdgc0N6AmmVO8QX6B8DXpyV8vLwR4OcPDzd3JPfsJYAnwYkxSzkaZ2jAlz94qZEgcF50wi6EmZOb4xi/eHq6i5UVezuT2YSnOdlibKCsXZRBmjZMKy184XeNfJX2/us8L/ptil7GKcoel3vHZL/LmOuZZ6/ez1BZQkOYZk2aYtPGTa+e0Ft7U5l4Us/AudjCwnyxqDJbTMjLz0UONdA5T2WaLC3tIe7fv4cbN66L1CRTZefOIfXMGZxOOYWT1CofPybnkcOHcOL4cZw6eQKHDx3CoYMHZPaDz/fu2S33nOvfs3s39u3dK/P++/ftxWFqqg8dwtq1a1G3bl3RJHPqhx0ejWgY7t+/X4xoeH/gwAFwOHPk8GExtrl7546z5gxLNI6/NejKK3wj4C1r5qjhNBtzs7fv3EGNWjWxZetWKbiJ859WK/ILChzKgbKkq5UVLwrLktbLxnnRN4v+XkIHRymkrGexzpHcmse9e/cwevRokHPSAKN3797CsUk8rG+taHnpshnkWNJ7upPSpoRKMhJjSWVXLdN4JN7inZWRqO7k9G0lCSl2t2rV6pVyw3qilSEPrVArqe5e51mFgpfiBI9NGzbCz9cPH3z4gYglu3buUoU27FBfptcqChClRSzp2etUWmnvlk02UCReUp6Kcm4FbhL8s2cxhYrDkseEIUOHILFTRyT1SEK7Dh3Qpm0CJkycqGy5xd632LtS0yX/K62czzwvvgjCWBChhzTUOPNkOShFiSTlECNdOZJTy621zM5vOeOJFpn1wj+R9LS2WNktEyy6ftW10WmIllrZSfM9ZdNs1K/xjnQwIilBDGNohksQ89B5ke8b2m0HMGW4qL7vsPk2bL9d39VplEdYoeBlBd+4dh1ffPo5Dh84KBV05fJl1K9VBzu3bpN7cwGNK8puVqYb7UVheVRe8TReCrykpzKcJUVxFcA5z2vlPwAXLl6Et19LhEaEIyomBm0TE9E6IQHhUZFYtnyFxOG/4vl+mXtHIi4XqjsyAKKBTMMUTg1RV6FDudYAJXjU+fzvKxwqbLnQgfEu07ASiJzkcA5UJHesF/1MxWE8zkMzDzRdVKGsJpI0VPrUM/BIz0gXE1JdVIKWkovMiQv4bbBRcnTpQHhNQFOHo5kTw5dhQM+vD2cdVCx4ASyYPReeTZvr+pFw0oQJ6Nezl1zbzBbYLc5e90UFK16Rpd2/KJ1X+b3M4GVjl4TKEp6V8EiMNCwkQBqVGsC1WKzo0r0bgsPDEN+uDYaNHo6efXqhU7dO6JLUFV17dMcGl2kLririKURVCqCLNIpxU1K9aJ2EFp+F44rEoFYsEdwiSouS0gCMkzkW+YwL0yzWdBroCit8SWNGA9c11B0c64gWufxNAMw+s8i1yp3EI9hVP4jc7BxZ/VazZk1ZSELlIQ+uVuJBELPu5NAZMULh9kadChc2gF5S3b3OswoH75aNGxDk76cqwfjfjqLe+AlGvbDRyg7e16mMSvmuYfigFWmkWPbqBQWFDusmTlkM6D8Qbs3dZQFEVEwYErslILJ1EEKjfdF/UC8MGTpApqL27t4j9UrgFloKYbZbYSI3oThrAEJ3LJWyPhzitpMDvU4+NQCZhqazB/fuIzosHCOHDsO4seMQ4O+PLl27isRC8DIup45eVX/wOvl1fbdiwSuG+SZ8Ve1zhAYEYMPadbLMrvrnn4kmURMqF/bzcM34z/maREazRHb0PLiCycvNEx3bJ6J9+wQMHNwbbTu2QmLXWIydNASjxgzCoEF9EBEajL49eyAzM1PeK+SqGqsFJgttsAmGoqL8z6WOWRm6rLweP2oM2rSKlTriP84JR7WKxpGjR+QZxW4e+p2KCiscvFs2roefpzumTJqEdq3jMKBfXxw/dkwqR8YTP2euK1zGKR4qqczJIVhJCxfNh3+gL+JjYtC9c0ckdUvEkiWz0KFTNKJifdGrT3t0S0pAUrf26NwhHoE+ntiwWs2l5+fmosBwUqAI0Pktct+KIsq3+V0hNPZZhgKK913aJ2LNUqUjMJtovw5MmjwJP8z4Qa6ZP82l32Zei3+rwsArtQAgMjQY69c6DTP0c7IBMfIo5lKleAF++vdOQLmCl8SzafMGNGxUBwFBvhjQtycig/3Qp1cnrFk9H716t0Pf/omITwhCXFwgeiW1xbDvk9G5bWskteuA1FOnpKrNdJzgWCzu/NbPBbykHx465PWyhYsRFxktFlW8p6eWqOgoxzRmRYvLmuYrHLxcw3n8xAmpQBvHEdTeUVtnjCnY81WGXk5X2FsP1YyRmkUyZr5YWfkFebKWtaWvBzp37YDkHp3QrWMbdO8Ujy6dWiEgsCm+H9IdgwZ3Ra8ebTBkYDcB8IDkrmheqy7qfvU1Uk+fVvXuWKzgBK/uKN56ect5TPui/JO2eDCevn50/wG+/qwaaJvcrUtX+LZsiSFDhsg4V9zruMyZ63df9J038XuFgZeF4dEnuZd4p5AbKk2oEDBEmNcxKngTlVUhaZYAXtbL8uXLxESwUeM64lkjNjoUwwf1Rrv4cHTuGIOoaF+0cK+N+vW/gJdHXcRF+6Fpo28Q1LIFov2CULd6dfh5eODqlSuCWFW2nyd4XduVdDht4mSMGz4K51PPYtSIkdi1a5cD2HRKx/iVgaFUOHhTTh6Hl1tzMVETAFMdb7i14X1lEVFcG/jtXj8LKNo979u3FxcvXsC+fXtw/PgxWWB+YO9OpJ45gbOpx3Hy1FEcOrQPm7eswYpl87Fx/Qrs2r4Bu7Zuxt7tO7Fm6TJZbrl5w3pV7cXG1z8XsZmFJxBJZzxIexGhobh04aKqF5f/eirw7bZ/6Vr1CgWv3eCyu3ftkpUxwUEBOHr0iHKNavRulaGHq9jGKgpe1gcJrLwO8aJI4BraZiUuK61zxZa7dKItz3xp4DLkQWsqj+YtcPXyZbk3m8zQSqsq8LqMaWxWrjxS9p/UevbsmQQfb08hJNYc59LYUFXctyghE7xcnkZLIE4ZcdURn1kN17Ycl9HbBrf4MlnogC0fVks+7Da68zHDUlgoy99oCkj7cS4C+TlPFWkakzq0WtG7ew9sXL1WwCsGF2QkMg+uZtvLs/N4nbQqmPOaYbMogmJNcQF6WGiwVBr/sWBizmaMM16noD/ad4sZaUid2GziEZGdmtlsRUGBScBLQiMBss4KuAaV8Qw3sMqeWPkPK+DKHc7x2iwwWc3IN9NNz8/TSIP1qZmD5r6Xzl+An5sntmxQC+lJi2JCaSyzqCy09NbAq8UT18pSALWJ90RecwmWr5+vGNFrIuVzJdpxTKLsZCniaaP3ylKRbzMfrEueqi6VuaGqSxcOLQRnKFccnR/v1TOqC+V9pmNcv80yVKZv6brUeWJdHtx/AFER0WjcqAmWLl7JR6wlyoPG2nRl4qrfqYjwrYFXcQnlv1aLfbQX5XN90GUIHarzdx4Um2mzS4Kjszd6m1TbiKj1nyLEuIjhFVGBVd906TB+Im2hFxSQBocNGYWYyDaaRAHQKymXbv5MwKu5LmtAuxch0Rc/li5dKi5bij+XJWV0zWq4iOVyMbVm1OAiPxGiqeoIKkdHwEl1DeCVK1YjKsxpKvmzBS9BrA9y3SNHjmD48OHiWoWe/L29vfHpp5/KMqx+/fphy5Yt4tZFv2O2FKg1mKIZNXR/VcAV8bcK+OUIfHqHNJwnLlu6Eu3iO2oS/HlyXg1cisTLly93eJenUzM6cTt27JgsRqCTMbocoUULfQS5u7ujX7++4tRL16DdWCOqlpmVY6NVdQRVHYFIhGoTNdLbwgWLERedoEnvpw9ejmO1EkCDlqWnT2W6FQkICBDHZy41UuolvTsm9eiOho3qYviIoZIuI3McTK0pOwPX71VxoKrO7PVpgOa5Su+ya+cetE/o5NDDiMKKe/VQiKzgxRvlqrAiqAgmejkkoHjNk8fs2bPRtGlT8U4oD1z+Fa9sDXyXKLh46QK4Dw19K9+9e1d+oqWRnuNkGvxm8bSq7qvA/LI0oBbQqyHe1s070LhBCxQWcnURjcsNhRVVNj8l8LKSeFApRU0xDxoS0PUn3WZyf119lAY0/q4rW8clSPUxctQI2TyKW17yINA5fmYnobm8fr8qrALuK9EAdTPiLA/omdQPH7//BbZu2alI0E63TMr+nkrnV0q/nIZn5cp5WRBXrklPhp6enujUySl2ELQENgFeUsFZQ67p8JraZYulQERl/r55y2Y0bdoYe/YqrxD8JtPV3y4p3apnVUAuMw1w7ttmxbWr1xAT3QY7t+1B2zbtDeZAkVntPf2TAy8riAe9xlNMptZYHwQXOTE5JcH7IrDxd3Wq3fgs3OlPJsohuxfUqPGNw7sBv/ui9MrceOXUM1Z978fZYShjDGDcmAno23ugkG+LZm44rZdQcldIi+1HLDbTo6OrV0fjmiWlF383NzfZFkMDl2ItQUuA8bo0wtYA5HuOODI1RADT1llto8LfuX9Pi2bNZRsMiW815n1dLJAcaVQB0lmfVXVRYl0oRqGs0AryC9AqMg6nTqQICQ8e9D2Gjxgu12IoZHierEj6egmxmWBynqJtswIWk0Xtf221w2axwma1yRiX22DoQ4OV969aWNcVHQ7nTfT5vGYd6taohdu3bsvn7LTYogmgiD7GUi8xhtEu3CqXcfmr1kfVe+XH1TXD0HVKQtq7Zx8CfALF0R/vL1w8L5vPcS8iHlzXq53R6ffedvjq4CUgzPRbyy09iWopExLbdpCdwjVgOb7VyqvXKZxa9aIaTPciFpNSik0YPQax4ZHIMpxjy7aL5C56nWYVeF+503ydNvuxvEvwagWqomIgPjYBo0eMkVvuk8wjPDwUi5cskmvu9EG/0BVZxlcHryjk7LAUWmAx5sSGDRmG2t/UQlZWlhRKV4oG8usU9FnwApZCGolLXWLogEEYN2KUuiFwhQM7K1dzbh2+Tl6q3nXW64+9LkijPAhe0imPzIxMNGnQDLduamlOxVm+bCnCw8MNPUzF18Grg5fM1kJRWRVs146d+PKzLxweCHRlsEKKiyWv0uBckqXfE84r6nzZLoBbBqCwoBDdOnbGru07pAFkHaax8obvadDqUKdVFTrr9edYF6RTHqRRDeQfps9EVISxRxHp3GAElOy4feq58+fkHS7HrMg6eynwcosIx7jXSu6m2B4VVF98Vg1rVikvkCwQK0KLIuXBeV0rSWdCAMosGL0n99zlHrUZGRmqQYyeVPLj3PLKWHj+8yZa1/qsulb0qkHM7TuXLVkuNKS3LRFaAzB65ChMnzZd0dePRWx27itDrDg5LkHq7xuAbp27SYGKaKBduOWbIBANYkcIYMkt51YAACAASURBVO6cOWgdG6f2RHWZ/9UcV4dvIj9Vaf74OkTNbXVI2/ratb7Dw4dpCqAc7xoKUD7gVqFt49ujIF9tf1KRbV5mzqu4ruK83KCJIOWxcvlKNGrQSMRWsR4jR37DoC0tfQExgKCAQIwfO1byp+Nq0OpQP68KK669KkPdE7Q8tVJ12rRp6N9/gIN2eGGzKHdM8hBAdHgrrFq+yhGnospRZvAyg/SXRBBbjHHuwwcPUOe7Ojiw/4AqiMUGaoArqjAcF/O4cuUKvqtVG+fPqbEJ86NBq8OKymPVdytXZ6GBy5B2CDTl5YbdPJxbgCqHEPIQwKL5SxAVFq1vK4zeywxejl8JXCvncw2uGxwULKaPqqSAzaTmeSuMQLkwwrCpnjZ1Kpo0aiwVKw1RNeatMCKrMHoogwRI0Gql1apVq2SpqtALpxfJlbn81K52VNTS5uNHj/Ft9dq4eP6SkH5Fla/M4GUGqXgi9+Wxd89eVP+iOtLS1NiA5mJWkwVWcVvz9npXzUkZMo966w6CmJ7uf/jB2F+mCrxV4C0BzHTMp4/u3btj5MiRcit6UNhhttAVk1nMcukClvTNo0un7hg3epJ6VQPdZXbjbQC6RPBKj+OSEdU7kesqZ2dchte0aXOsWrVaMs/fmVk5GDhU0i4mWSU8Y7WV5ZSkxWcQa6n0UyvL9HwdPXXUqFHD4Y1DysF9aasWMfxMgaxJk129BXbQtRIVT3ZkZWXLWnMOuXho8LlOUcozY2bjxIkTyhiJhkKcsTS26iGNub6v03kTYZnBq0VmZozcrEmTJpJJ/tPg1RksEbyO2M4LcafJ8ajLWQLGjeRezM3Fty47EhcFRFJSEoYNGyYfZf4IXH3q/FaFL67bn0YdPQte8UlFt8ObNqJr165KVHZhXLrcJCBea8bAa0p2WzZtVrRFe32b1WGWq997k2GZwctM8Lh16w7q1q2Hw4cPyz07mmfAK7+8+J9yQ6oMwfV1ScDX/ST7yuedVnEJ65xjZg4uXbqEOnXqSKgrsnh+9fOq8KcOYlfwklpoXqvE4H79+4r7JdJMafTBTp80wt95TJo4ER3atZNrLuCXIVsxy743SVNlBq9WUkVFRaN3774qw8aa5SIZZMFKYp8K5c7fVAqG4KxGGEqIFrlbPed4hMoC7t5O7/9y2ijsyMmRiOtJYHPjY2W8oQiRnxk6dChiY5weANXYXdlFF8l7CWOiqt9/SoBW3FPaVOYflP7mytUr8PDwkGWqpJeS2lwPtRhq7nvjxg1EhoQh7cFDoWbSHd8l/ZeURnk/KzN4mbtjR47j4w8/wZOsJ5JZq9nw5aPBagBUm5NJpDf0zwp6+C/2pyfTjQ7EYmyMzCmtb7/+BidPnJTcMH+l9a7lXcFV6b0dQn6lehaNCzBmzGgMGOCc2y0tLdIMgauHXSSmnt26Y87MWYrKNQ4qErw6c5rANf58vf0xcbzSsHEpIE8uAdSLA3Q8Hebl5uH8+fPYuXOnuHGdP28eRg4fgeFDh6FDu/aIaxWN2KhItG0di64dE5HYNgExURHokBCPpC5dMHniBGzcuB47duzAkcOHZd42/fFjnXzJISuOKn7uwePi1H3UyJEIDgpS7xDcLgcbi2XV5S2t8aqeV2IglgEwSm/j7LhJAnl5uWjQoIFjGEjaL62dXelDc1/a0gf4+Qk1Cd25mOSWlk55PS+R8zJxFoKZ1ceK5Svx9dffgIDkKiK9koi/M/7jtDTs2bUbw4cNR48ePZDQpg28PT3h19IXkeHh6Na1K3r37o0+vftg+LBhco4cPgxTJ0/E8qVLsGHdWqxeuUIAO2zIYPTt0xu9k5PRp08f9OnZE706d0H7uDhEBAQgNjISPbp1w+hhw7Bh9WrcuHJFJth1XiVP3KeHi/9ZDrreMZng6+ODgweUQYmI9sVEJNfGKa8Krkqn8gBeKzTZzpw54bF37z54eHjJSjje0zBDjDNe0BloWqFRUucOHXHsyFFJz3XI9qbbvlTwMieaAzOsX68+5s6ZKxnU/44eOYr5c+chyD9ANG9enl4YNXwEdu3ciX3794Pq9Edpj3T01w6zs57g8sWLAsDtW7bgh4kT0TYmBkH+/mjWqCF83Fpg5owZuHb1quNbBK4Wn1euXCmdiZ7be9OVW5V+JQKuANbVg4sikd7J/TFlilpoQG4qC+wNm4HntR/By5PHD9Ono2dSkoPmKnTMy1ywIDpzdNvavGlzyVxebi7GjB6D0KBQhPgFY/CgwVi6ZAky0tOdmS/limNNR8/kWDSgGpjf0p0FK40HQ4o6NG7UWsGSkqaK/uSxo5g0YTz6JPdGoK8foqOi0Ld3b1y66NwkmfPTYUHB2LFtuySjG4Dh8xqq6rfKA8LXaws1s6EFyvT0TMTFtsXDh48NHauxgd0LuK6iS5tol0lIV2mOW7MW6HBRjjK8/3rlUO1RKufVMj0z07hJY0ybMg2zps9GkwZNERkWgZ07dyE3J1dllv9FYcxlgvSsYYWN815abc7aYoEIXg1gMT2zw0zOSOMPTnRTXDdOgavN+N1mgQ1m2MDQAovdBJO1AIWWAljt1BorsOvM3L9/H1s2b0Z4SChaNG+O1jGxItLz9xPHjqFNXJxEVY3gHAOVR4VWpVGZgU4GQU+kimMuXrwE4YaNMpmEMBDSWhk6c4lrtYjrJxJTVEQkqNMxCOutMINnwMuP6zEir0+npOCj9z9Aw/oNkBCfgIMHDqoMGv9p1UTfVa5EK4V3qQBHZRQbY7q+w2ttrEH3Is9YtnDzJ8POVM8Jyzaf8tz4zZgkd83gk4xMzPjhBwFxdHS0LFro1LEjthvcl2MfPf6RfHIKwdFzSp/jcl+ZCbMqb852K60uaKOswMm2DgwIxooVanUQbfYVDZZtzKvpVZtLrl27Hglt1JwvBUemr8RwLtQpio8X57O0/Bd9/ix4uXrIZJJxIsVMKps+/Nv72L17twMTGowUc8srI28qHZ3p7Oxs0NqK261Uq1YNYaGR+ifZoFrZbCsR3ZmXKvA666Io4fzYnlPys9nJdZUD/wsXLsLfLwSZmU9EZFbCYfH2L0uZFRmZTBZ06NAFJ46r6Uhyci4zVAyGY21XplCWdF8cp0TwapF55fLl+OPvf+8YNxK0GrAawJW5EXV+uf2KPq5du4b2HdrjX/+ff8ORI8flscnEiXd2RMYyhyrOW+k75VejO6eSacKESUhOVj7FbbLzgdKxyOJRR/u/GEAkIC25jRs7Eb169RGaUtNSNAIhaF0VZS9Os6xlKxG8Mj612xEeFoYTR49JZrhKR4NBK7MqO4CZP51nuuzkek19JHVPhp+fmvdlZam4YmDpQrhVnLeshFTZ42laYPuTDgICgnDy5CkhB0Ml49LuZQOYTtNsVmPoM6dTUbduA8e0k7LZoC292ueovOuoZPACOHXiJHy8vBWtk7iNeV9yXmaaGdEcurwzVV7p6crVeWZheM3j0aN0uLXwwunTZ+ReOK8s/HIVb6rAW15tUVnSYWNv374DjRs3FeUV743JDVF8vkw+NX3p9/luSHAY5syeLzTFf5wzlnH22xKb+dHFixbB16elZMJuMYyuDQ7FTGpAvExh33Zc3ckwr3pvJP2MBZswfjJiY1s7AE2tdVGxqQq8b7vN3tT3lDZZzUr06pmMyZOnCm3zuZ6seNVvk6Y0U1i5YjUC/J0SHce9nDvWdPeq3yjpvVI57+6du9DSyxv5ubkyN8sVE8wguS0VWUzsTWSopEy+7jPmU+dVl4Ett2TxErz37h8d4rRY1lRpm19afHzd9nkT7+v21mnznkda2iM0b+4ue0XznuDVcV42pLGP0iQ7x9LERuNGzXDGkOik09Db8LzEWLoseSkVvLdu3sQf3n1PLKZYSBpXcJMwVyAQyGX5SEXH0Q1J4OoekmWiePOnP/5FwKvyWKWwqui2Kq/v6zbX6WnwLlywBPGt1U73/E20wbLCyHW4VDZAK/A67QyEiwNI6t4DgwYNJok5RPLi+dH5ep2wVPCuX7ce/r5+GNCnL+bNmi0Z4T8CmB/Um4a9zsff1rusOA1a3Yj5efkyQf/1VzWkTCxboamg2LinSmx+W230Jr/DNtftHhvTFtu27RJ6Fq6rgavDl+aOFpmCYoIavDQb9vbyQ34+6Uk/L1uH8DL1UCp4V61YiaTuSXiS+QQD+/bD0CFDkJ6unJnzAyaTWQDxMh+r6LgawKzQPn0GwNPDF16ePsjKeio9JK1vqsa85U9kFdHughrhfGp4x/sL56/ArYWftLf6nToOzjDo82W5L5ekqrlcx8DZUIpyNmPLFmWGK1NJL90pvLgdXMDLjBsL6cUf8yrQOyQPcttJkyYhMjIMWzZvxKO0B6rsIk67bPVp7Kgg1lFGDDactpbS4cs2phJPSijM8wzImRdjPOPKee/dvYfkXslo3ToBO3fsxrff1ERmZqbObRV43wCRvWx7l0d8NqjQHmdGjPHu2DFTMKC/0yWSmtfXwC0+TVgCvRWrGz3mZc9PxqDoTZHS5i3b0KVrd7kRi6ti75ZHGX8hNv8yIcWZaotDSN+4fisa1leLEQzKxoJ501Dt0z9j/JjvUZCvtjrUv1FjZzPZYM5Xu6eZLFaYzOqa3i0IXAt9PtN9rIQ2WPlneMpgaLaZYbFb1PMS/uul94zLeGaris/n8sxGe2q1m4NUpIWZcuQQeTl5iAqPQr3v6snDgwcP4/2/fYynT5/KvVSDOEJ4ccOVR+VXpfFm6lnARLsEen007OvZwPHx8diwYb20te7QVZu/ej7Eiw5nH0lndAlleKO8c/cOomNjkGtsCWpxMRcur3YvFbwL5i1B00ZeqqBWesgzIS/3KY4fO4ReSV3QtnUMxo4e7VwfKzFpF628z7MnshjaaSq2eGoQiwaOXFF7wtC+cRmKCGMojoxxiICW9qH81WaF2WKC2WySa0nFeJ/KB3E9a+yhZGQJ5LZcCVWzRk10aJ8o9/xt+/ad+PCDTx3gfdXJ+vJqjKp0Xh1ErnVH8ApoKZkZrlpv3rgB7kH08OFDB0fWY2HXd1/2WoPW8Z7BLXLzcuHu4YGdu9X42vF7OXLgUsE7dfJMeLr5G+A1AVy9Y1N+n/jw9MkTSE7uhQb16iI0JATjx40FN/pyHVcyHo076BZTedYz7NBYqSJmUNRQJ/eDUXvCOJ/p3xiq3cgpGYjHO7Vqyc5lWWaYCpRiQDJr/KNj7DWr1yI+PgE+nj7iBGDXTlWROt6+/QdRr24jaPPJKvCWD3jeBKGWNU0BLhvSaEyb4YR/yODB6NChgzQ9aVSfZU33hfE0o6FUaHjTGDlilGOxAiXTF6bxksAuFbzTp86Gj6fhNobiNPkeV+AYLi41AJ5kZuDQoQNoE98aAf5+aB3bCpMnTcQPP0zHyeM0rSy6XE+/V95hxuPHOHhgP6ZMmYLkXr0RHxePiLBIDB44GFcuK1+8quW4q4JyPHbo0BG4u3kjN1ctbawC748fvASIBq7WeXBmJDoiCjt37BQS0CIzw9cFlB4xi6LTkBqZLo9rV2+gcb0WyMxQPt9e91vF3y8VvHNnL0JLLyd46Y2Ce/GSk8qaXU3pkk31z2IpxLZtW/DDDzMwacI4DB3UH+3atEZcXBwiI8KR2C4BQwcPxOwZ07Fz+zZcuHABly9fxs2bN2XnBYo0mRkZYhvKbUMfPXqE9PR0PEpLA+ed6SHjyMGDWLtqJebPnYNh3w9GDP1gxcaifZt4dE7sgHHjxmHJkiXOhdFG/pQYr8R3Xbn79x1AwwZNHeuS1bKw8u8hi1d61f2b7SSUY36lwmHzc3cPfy8/2QyPrERLh+XBfdVAT7Quar05dTfk9gbPah/fCUsWqu1CSXfl0WFo+ikVvEsWrYS/b5iQvp1rIMmtjEE5OKaUnQvU4nqK03YbRVfF0Qy8SCHu3rkj4Dxy+BCmTpqI7l06oU1cDIIC/BAVHo6W3t6ICg9DfEwrNK5fD25Nm8C9WVPU/Por1PiqOpo2bABfL0/5LdC3JXp164bWcbFoHReH0SNHYMvGjeBKIQK8MD9ff1pCqSzDuoUP2BPryuP9vr37UbtWXXC5IA/2R+pUlawruyqs3PWhiVmHpFP6lrIaCwYmjJmAGVNnGG3sBFB5tCvVq0rFqq6odzGZFaPjB7dv2YXQ4AiYCk1K72OI7OXx7VLBO3fOIrRo6iMFpgsaGX8ql7QcVjjFDZH1KTxoD8oEObW+zvGxkUiJQWFBAbKfZuHu7ds4f/YsTh4/jqNHjsh5/NgxnDp5AhfOn8ftWzfBnclfdBTXYFMLrbXUriHTIXi/q13PAd4qbfOb5YgaXOUekgZdxosEr6lAWf/lPM1Fl8RualMwemtxWVhDALm+9yrXWrXqKjaTtqyUUu122cfXq4U/OLPBg99wzcOrfFO/Uzp4Zy+EW3NjYQKncGRhsd4qSM3dMnNUjatT7abGBc9OP1UGZ2Yc2eNUzSPLSguK31q2kGKV7Z/y7EeLKXqwNMNGwwpDoUVNdEl/rqDV1/zanj37UOPb2lXgdSF8TRg/qrAYeNV0oZJblyxYhuTuao2tFpM1aHVYPmVVdhLkvEKjNjsKDb/hY0ZNQNeuavN5fpP5KA/T4tLBO2cRmjcxlgQanLcsYqVyK6OW3bH6CHDJrIgLyjUIK0tNHWnAU/tnQWFhgUwByZSPy/SP6tU4TURTNPWOrNSgtpnAlbliC6ylzBFrwLqGAt7de4uAtyzlY+VXnZWoDoo7UJDhnJqUsJit8PUOwNpVam63JPC+blvKSFEmQYw14QZ4dbqkszOpZ1G3nlPC0yvcuAxVx3uVsFTwLlu6GoH+EYodyuqJkhtM9VoUB5wnh8TiSI7ig+FEzuziZE47mzNTvKZxGtXrNoJPcWOXGWBlxEFVgM0iJwFIAw0x8SBoocRi/c7LcN59+w48IzZXjXlLbudXIa638o4Gr+a+Wi8jw6IDCA2MciokubRVpDQlLpdH/jR4aaxBjk88iGTJTp70bxhtdOvWDWPHjhM8CeOi5ClxX72+fyGgEwgRSCYxhOAX5s9bjLDQVgq8aqJIftNc8Lmhi0mkgFtkfeq7iliRirgtBTA4qMQtgwinzNKUyO76jojxZcwlC0axWY15lZscMVR3Hc8Xz0vxEsjvzk7LNS9V129r/EyqUlOZ5Kysd3bAPDomdsHaNU6LqrfdJnpYybxwieDf/vYBbt28JXm0mCmXCutSqCAtKVMH+b0seS0VvDN+mIPAgHBVCwSEYeH0XNAKcZeuBGBh9B+rvCwZfNk4WoHwopAF27F9p4jNep6XLkGLKONKBa/rAoYq8L5sG5VvfA6duM+uqzNE4Pr1GwgJjnAY4GjDifL9dtlpmPQWEhKCxYuWCKYIVA4xFTszltaWF3inTp2Blj7GPK+jh3gRJIzfixN9CfeM+SYqsow5lArcuHEzPv2kmsNIwyn6F88bAaoEc0dlazHNZbjwJspTlWbxtih6T+5lsRa6uHRViqoRw0ejb9+B0s7kyA6T3BJo8W3UMTOycMEip59oitliIsyh4hsAr29LtaqIhVNCbxmhUUEVxHyWMYfSqJs2bRHzSHo/4EFxq2TOW+y5/oqUU/9mALwCy/42iLDyfcMGi1UN94RMDQdzCQkdkJKi/JPRrW9lyPfTrKeoV7cJUlPVLh7itVJoqZzBO2vmPERGqp0F1EoJQxPgEMw1j382LAlCToHeGV/HU7L/C2D3MqAoA1cnWAleT4+Wjn1ZSwKvoNoYszsIoAh4NSeoAq+jfl6mrV47LhVDhqJTMV2cO3sePXr0AUFLpRTFU4YVkz9FH1SU8Rg8aDj69Rkq10JvItXqvGlGoGnq+WGpY9758xcjLs7Y9Vs+bNSMpubSQkP7p6d0ikQTTQKts5wLFDj9k5ObLWomeceY+uG1yVwoXgoIclY+zc5cG0CJQ0o7oX/nM6ritbdL3WjiAJsaQGOOjfmieWTtWk4VPrOnTu15w47s7Fw8yVRLBnUPLgozArgI4VWBt2h9PJ/wyjMu25jtrrcx6dmjN2bOUN5fnAvhi7fX28sfy6rcvwIpp1LxdfX6yMzMEmiIkpR6acPBxcvUS6ngXb5sNbw81aoifoULEObNnYOlS5eAG4/NnDkTM2bMwOLFi7Fm9WrMnTsXBw7sl0okIJVKXnmd5KKBe3fvyOqiImB2uRGFA4fvVovM9br89NxLGp1TGaHD50Yu9uOxYyfw+WdfOhbja7GLxMCTx/ZtO7F48VK5JiFoAhGpoQq8xTqwtwsITeh0FkEaYPtlPXmK+vUa4Nq169JmBId4SCmi0KqIfFIKsCI3Nx/NmrbExAnKXJPLZLnE1WKlwZGSEnS5XhSWCt5Zs+YhOEhtCcJErl+7Cm8vTzRt0gjvv/831K9fD54e7qjx7Td4753/xt///d/j008+BnehJ2eiEQWPrVs2w93NDY0bNkRocLDYJLdu3Ro8Y2JiZNFC//791dwYFQt2JV7s2bML/v5+CAsLxaBBA5GYmAjOlQ0dOhTjx4+Xncz37dsnXFZPerP3PXXyJE4cP46LFy/KoocrV66I7fP1a9ckb9zJTW/QffTIsSLgVVNFxmS7Ad5evZIxbvx4gxCUhlBz86KVW8V5i9bH2wEIG0ZxXUU3Cxcshoe7Mi5SXI3OHyixEdwVx325aMdsVk7/Z81ciKaGAZTSsSgjJVWWsuexVPDOnjXfAV6zRfmrEgou4R8rjye5n7KCssBsKYTVakZOTjYePX6Mx+npeJiWhnv37suKnzt37+Ly5Uu4ceM6TqecEudv+QW5at2u3YIrVy9hztxZ6NsvGcnJPdGuXTtwo7Dw8HBERkYiLCwMU6dOlZ6f39aA4v688a1bIzAgAO4t3NC4USN8+823+PSTT/HF59Xw3rvvYfw4Bcbjx0/KVNETw2aaFakBLIQIOz75+HNMGD9NSq05M1cfFYlXhAO/HaKtCKBU5m+y/dmJx7SKx5rV64z2UgYTlJIotmoaqYhy2OwmterIZkd6ehbq1mmKK5dvSD65Vl1LcnxQ1vyVCt5Vq9YhOipeEuc/Lh44efwETpw8iRXLl2Pzxo04dSoFKadP49y5c7L7Hpf3EcCcTuHWmzwpElBskd7RWBjtSNTlgjbR1GhLIW1FVye5RHvmUluraAC7RijIz5flhQ/u38f169dxnIsejh6VZYeMR/DWrlUHruBVorFaVMFy/dM//TPee/dvsipE0nZMDVWBtKxE9qbjsSPlwc3DggLDDA+neiqGJrocxhWWGRRvIr+ka85Ha3P+Pr2HYtoUtVk9h5gEr8WmNyYrG20Z4KWmt6iF1dIlK13Aa5dVPW3btUF0VDhax0Wjffu2iIwIQXhYINzcm6FRw3p4/8O/4sYN1ZuYrQSxDadTTsLXyx1BPl6oX6c23Jo1gUezZogMCUHv5J7o3r0LdmzZItYmIveL2GzD6tWr8P3gwRg8eDDGjRyFZQuXYsHs+Vi1dCWWLlyClctW4EzKaWk0V+DevXEXKUdPIeNhOgpynHsTScRi/06dOo1aNes+A1724Dwoov/iF7+Qc8uWrfKsoMBkTCeVXbx5E8RQlaYicJmpMCyqRo4YjS6d9QIAZVPPRqMEyJNHRdWblZyXDM1w0UR9S80aTmWpVqi+jGivvEeKqp1L+pzmkatXr4eXl1JYEdiOLkOqoPg/OzKfZODeg3soNOfDZjPDZM6F2ZSPnOynOLB/Hw7u34edO3dgy5Ytcm7ctAlr167D2lWrcfvGTbELLbTQsRyNIYC1a1Zj+PeDMDA5Cf26dsOC6fPQq2MSGtZugG+//BqBPv4YP3qciEIUh3TDTBk9Ff4t/BDcMgghgcGIDAtHRHgkIsIjEBToj9DQQMyaPVPip6aewzdf10JGhnJpy2REO2nMFdarV88BXm9vtTySGmc1xi4O3pckDD3d9KKwSiQvHXCU8WhmaIDXr6U/dhjeMsSl0jMzAmXjaG8C4MwkRXcyGh6k2ebNPLFooVKGauu+lxHtSwXv8uWr4ecbIh/ihzltQ03zhg3rsHXLJhw9cgDnz53BqRPHkHrmFAoK8pGRkY7c3ByYOb6wq02FZVrISOV5AY26zZzmkaWCz4tZ9DfuJcwliBSfuUTQtZOhkqAgP0fyxhVL9+/fxMNHt5DxhK5r7Tidkoovv6gu+WaqhYV0bKdE9g0bNjiAS+7761/9Gg8fPpKPswH0GMXZ0FXgddbFWwIJwUsPoQCOHDqKkMBQmeWQB3rBQqXp/Dh0pNSmNMrM49gxE8WEU/JrAPpl6rAYeNU8KhNbtGgZ/P2VJw3eP8nKQuPGjVCnzneoX68uWjRvipbeHvD2aA539xaIiIhASx8f3Lp1W/Kitca7tm1DfHQ0BiX3RnxkFBrVqYMa1aujbs2aGJjUE/2798DIIWrSms1gEhtqzsHuxdSJE7Bk7hysW7USyxcvweply7Fh3Trh3ATX8SNHiRjpmdljUdVOUTrl5GmcP3sJN6/fwYP7j0DFd052HgrylehkMGpwS8bq1b9ycF6Cl5VHTvz+++/jT3/6I375y1/i97//PX7/+z+gU6cuxpSEYSpZhDCqwPsyhFdecTXh9+yajKmTlGJRjWsMo58ibfSWOpUSvkmxncAlLmyG6PzwYRrq12ssY3WWg9yXkl9Z68YArx7zKjMtJjR37kL4+4UadUMFlCGb6NoqFgrwqG2mKZruRWx23L9zF2dOnMT927exd+dOTBo/HoP698f3Awdi7oyZmDphIhbNna+MJ2w2FFKzbbNh8+ZN6NunD/r17Yt+ffqiX79+6NKpI7p16YzOHRMREx2FubONiXjDWx8VF+3i2qLuN9/hs/c/w4d/+QjVPvkSPp7++K5WfdSv2xgtfQIxeLByvE2F1DfffCN+slgczsPx2LtvL4YMGYLMzAz4+vrIfPbjx+no0CER9K0los0zaktl7gAAIABJREFUItnLgtdYoiENzQYr7aw4gisrEVVkPLZXVmYWYiNb48b1m9J+NtJDpeO8CrhqPlpJC8xsl87dMXTICJVvvVihBPCXVMcu2mangTRTmj17Ppy2zWre9uDBgzh8+DCOHD0C+qZKf/RIdhEszMuDKb8AaQ/SYCk0yyhOlEhSiZKvF/4jYE0WMyz0hmGMC174EiOoiTLxaklQmQoL8CQzE3fv3saVK5dw8eJ5pJw+hdOnU5CScgonThyTZ3w1JSUFX3zxhYPzUpSm0qzQ5FR01a9fx7EOk+9w/xlpgOeAt/i4Rd9LnRhmenymn5fUMFXPSu60dJ3pkG2yctkadG6vFFU09lcWfJWL85IxcMpVtyvzz2Pbtu346qtvHftlKXIuuez6XR2WCt45sxfCyyNAPsB/t+/ewR/+/Bf86c9/wSeffoyvqn+J9q3j0DoiAu7NmyPQyxehvkHiCI6JayONfbv3iGEGjSx4tk1IQLs2CejVrTt6dU9C58SOWDh/gRAyiZsg5rF582ZMmzwV2zdvxZ5du7Fj61YcOnBA3MmeOZ0ifq0ePHgg410Tp6cM08eM9HSkpz9C1tMnKCjMl46ADtpLOg4dOoTPP//cRdtM7qfGszp+RGQYxowZo28FuOId8Bn7ad2PKC8huoIZatC6hlq7yEbktWv8quvSiVeDVtclG6Zbxx7YukntC0TzV7XCpHKBt6Q2Zd65KMbLq6VsAMB75cG09PK7puMCXl1YRadTp8xEM4cbHCC/oAAZmZnCpTgveuvWLTx+9Ah3bt/GlatXcf3adTy4/0A0sYXmQmPHPQh3PnP6NFJTU2VB8tYNG/HDlClYtmgRli1aii6JnTF10mQBLzleXn6euM4ZN2483Fq4IcA/AEGBQWJ0ERIcjLDQUESEhyMsNAzjxiptM31J86A/5h5d+6BJo+YI8AvB19Vr4p3//iO++LwG6tZqjk8+/BrVv/gOw4coI42DBw/JmDcrS9mZyphEc0bD0is5ORnjx09UlWIMB0qzbeYcN08SGImLHJrXPF2twDi25viGJ0V9/q7EKd0BuIZla0jXRv2pXrMRdNl0g5w+eQbBvuHgro/yu+xPpRa/PKtUrMi61G1q5EEkN8Wo5s2bj4iIKJX/5zmDKCZOK/DqcZckqKpl0sTp8HBzcl4uWL944QLI7WhimPboEe4/eCjWU+kZGQJqGkXYLFbRNtM4w1SYr3KsknzufxJ7galATCs1933uC8aP5LjckYE7J1CEzsrMxqOHmSjMt+BMynlsWLcVRw+fwtYtOzF1ynRMmTIVmzaqOdvDh4+ievVvkJWlvFKK1ZQ0PhNX4xJack2YoMBrNqt1odLrP2Mryw3ZFHhd862BrEFM4tNGBbymHyN9GiMAPRIwwookuMr3bda9qkNF+H379MP3A4zNw+iGhqcsfNHMqLKUQYOXlKXyppW6aWmP8fXXNZFyStkt6A7qRWGp4J04YTr8/Zy2zbRZjo+LQ3BAAGKiIuHt4Q4/by80bdQQ9evWQa2aNRDo5yd2wzSRlDWWdht27tiG72rWEF/MgS19EBESjLDgIHTp2AGjRozE+LHjxGJLE7de0HD48BFMmzYdM2bMxvx5C2Thw+ZNO7B3z0EcP5YCAu/69ZtqKxUqJ6zkcmo+Os/YF9UVRCVdnzyRgmrVvnSMeTV49EQ636lfv4FDbOa2pqpCnyUMApLckwdFof3794s1F+PzINFRPCYH1tNR8oPLP/39omFlIb7KlQ9WW0ZmBjq0S1RuXSkVyZyvUvxVPoXVs+AlTrTFVe/kfvhh+iyhhheBVv9eKngnT5qBkOBYSUxrYV3oDIX5eTAX5ONJxmOkPbiPWzdvIPXMGeVwGlwlkS8rFW/evI4FCxZg3vz5mDdvnoCQK5DmzJmDWbNmYfr06di0cYP6jsyBKQAQsPFxbREZFoe//ukTfPD+l+jcsS9Cg+NRu1YDfPD+R+jVo7eRP5dtHMeOh7u7J0JCwhAdrRY+REZFwt/fH25uHnBzc8O4sYqTnjl9Fl9V/xqPHqUb6SiuqA01+DA6upUDvEVsmosprBiX4OT4+KuvquOvf/0rPvzwQzRr2gznzp2X9Pnv0qXLqF3rO9SoURP169VDrVq10KhRE5w2rMUUcJ1A4TuEP0V1tgM7OT7RDag7PX3PUMR6FxFL3A+53LvG/TFdy24dhg6B9TJz5iz06pksdZubk6eUpRz2vATnlZfL8V/p9fkseMl5tXL0/PmLCA9r5aK40m3MzkhfFw1/QVIwmLjyeawYBZYsWY2oqLZSLBKDyWTB5SvXcOfOPWRlPsXTJ9kw5ZuQn5Pv8EzPyHzdigIBr8ni1Nq+sH5kUQC12k6lVWnvkHvl5eUJh6PIKRt9C+ez4knWE9y7fxf37t2RHeHu37+P06dPYfXqlRg9erSAa9GixZI0bZs/+6waMjLU/rxKG8jxkvPLnTp2wQRjVRHBq+fhpNZEBFbjW76xYf16Mezo1rWLLDOkDqBRvYao821d3L93XxJdOHepxAkN9keXTh2kU/Hz88P58wQ4p4/YedHarRA2FCKrMBe5ZudGahZLAcyWfNnUmcYwhWYTCswmmMWTph0F5kKYbVYUcvtT8bTJ6TcTTFaLGMD8WIBsyDaGw3xOP6od6EVsNmyZI8LisGq56vi5O6Tq2FTblUjwBqi524ee+czPK8DD+2nIy3VuWZubnY2nmU+Q8/QpzIWFeJqVhSuXLuHC2bO4dOECLp0/j6uXLuHWjRsyzUj9D5WfTt1JUZCVmBcDkKRlHvTxTDo4e/as3Es5KWDLogXnwgVXqax08C5eBT9fw/UrgEeP0+HvH4hmTZvDx9Nbdt4LCghCkH8gBvTqJ/vekrvdun1TFiZYbAXSYxw5fBShoeGIjW2DFs3dERkehUEDvkfXzt3Qq1syZkyegW0btymRspCWWUr85FI+umZNPXMOFy9dkkKdv3BeFhhwuR/H3tnZOYaXBM0xuV4yBwX5BUr7bMzbquZ89j83GqMPK70wQbiYMZbVsZs3d8OwoSP1raE5dlpYac7HCEuXLMIHH/xNOhb9wvZt2wWsK1eskkctvf3wzVdf6J+LhQSvMWUnpqpmAaaO9OSJ3gQcMJsKHPa6+vfnhaI8k72myk5YzyO6N/1bUfCyTpR7YNIHj3t378OjhR8e3E+Te7YD88SjtLwRsdSN6HiMGx+bgMYNmyAkKFgcxHHFmo+XF6LDQtE+Ph5dOnRAm7hYNG5QH03q10O92rXh5+MNPy9PxERGyDuNGjXCRx99hEWLFj33+8XzpYdZOuRS1x49ekgaBK9eoSfLGR2SnpODlwreaVNnw9dXeY+UDa+NDZQoGmY/eYK8nBxx3JaTm4PbN29h7+494PYkefk5sNmpeOIqDpssVODGY8m9+ogImtAmAb179UG7du3RrXN3dE3sikXzFwm3k3GhoaGdM3sO2rfvgC6duqNevYZo3rwFvvrqG3z44ceoU6eecMwuXbo5/E6xxDSVjAiLwCcff4x6deqgbp3vEODvi549uqNnjyT079cPvZN7Y8XylVJBhw8dQf16jRw7JlBDxHleZ+Pa8cUX1dG/3/dGhSouS/HVocl0zNfSRzXnqLUBvFKoDB82TMC7Y/sOSeODDz5Aw/p1MWnCeIwfOxYH9u+X585/rgBWRiOnT51GaHAIan9bA/GxsVi6dJlEz8vJxrq165B6JhWjho9Er+49sW7Favkt83EGpk2ailk/zES6Ydap9pgqnbiLE1dF3hcFr3Fnt8Ns6BVGDh+Nbl0UoTOfGrzPyzPBSwMOxtFHsyYtsHD+IqSeTsXZ1LNIS3uI61ev4ub162LL8OD+PTGf5WZ4N29cx/27d+X3w4cOyr7OlOy4Wq1r166yyR3TfV4eiv/G+Jr7Xr16FT4+LZGZqRSonOIUWjOmL9W7JYLXcFdulGvmjHlo0sRTykgvQbn5ubh65SpOnzkjgFSL2tORk53jUNOrCuHiZ67LJfdT41f1/Pn/rWal0KGITq2t65GTnSscj+ItXXqSU3IcycIqzqc4L69TTqVg165d2L59u5xbt24VcXb9unWYyu0/e/bCKoMLHj18TDYaKyLuGD2c/v4339TEuHFqjKyndYRQHD2h5mSsVDUepUjNY+/evfjHf/y/ERYWIlNI1Gr/6le/EjD/4d138O477+B3v/0dfHx8HC5KFWGxEVRDHD1yEv/57/+FgJaBOLD/AIYO/l7epxeTJxkZ+O1v/hO/+c1v0KReI8RHxODPv30PXRM7Iyo8Ep999Cnee+c9VP/8S1y9dPWliKo4kb3teyd42U2qOxElCWCTGTW+ro0tm9WsQXHgFr/XeRdZmUC3qqER9xMKD43EpQtX8MTYhpPb5/Dg/tGcgqRNvMlhtMM2UW3LcXVBfp5jjMq9f+lUQt4tZYyq8+Eakhny0Hnu1i1JDKRUOuq563rfImKz3MhYi14szI5xw7Sps9C0iZckzH93btyCRxM3/Nu//n/4z3/7D3z5UTXU/PJbuDdpAa9mHmjWsAmiQ6PwOO2hjHrBtYsAjh05joT4tiIO9OszECOGjMHEMVMwf/YizJw+CxPHTcLmjVtEbGZByHd47N61G9u2bkdqyllcu3JVtvi8d/cu8nIVkFmxdH+iC83wZY+jR47jk08+E60l31WKOdWL67SCg0MwduxYuZUpHjttUNW2K66NwAguHTpWrVqN3/72d2IXfVz2KYbMi9PscuqUqcYiCsj0FRc+jBg+Sr6hx2K84fja3zcc//Gr/5INqyQCgFHDR2D+vHk4ceIE/u7/+jt8W6OmY1+c4YPUMsbZs5Tm8u6du/jdr3+LsBAlRanG1x1O5Q2LglflU7fx5UuX0b5toqNOXNuB15omij/XnSv1JDzS0zPg7eWL1NTzYjlH+ssvyBNxVUlgyrKQSiVKVWxgApnToNSP5Bfky5iX9PD99987RN5nv1tyPTOfQkuGXQDzdObMOfROHuDoaGX2pQjn1WkBLkYaxljLoMA5cxagqea8suufTaaBbt64gbNnUnHh3HmcSTkjCwGoKT108CCOHD6Cgrw8cTkCu+pRbt28jfmzF2DuzPmYN3MRRgwagwkjp2DGpDmYMHoSEtsmYqLB2Zh5auBY+L59+6FB/QbwcPeEj7c3/Hx9ZUBPIw161AgKCsKwIUOkEdgj6yOpa0/8/t3fo+ZXNfGn3/9RuNLf/vIXfFejJgJ8/dG7Z28sXqAUVqmpZ0UUp90yDzaubnydHrXWGryu2mbNGdV7JBj9BjBv7mL8w//6F9Sr2xAXL16WH1yyqCIaShfe1K1TD99+XdORgE7ryZOn+NOfPkRoiJqyo0G7mP8ZMekY4R9++UsEBuvVX8DkCVPw3799R3QDjMbmbNCgMWrX/k7e+nGCV5VDz49PnjAZmzZsUrXwEkYNqs0U8fNliqe1atWRXRVo9kqOnvU0SxgIub3i+Irzq614bGprHlncbwWNkah7odg8YMAA9O6tZj/KCl7G4yHjW8MbDO87JnbH8WOn5DeWmQB2DNMcXF3Ay8KQaCkucN5JJbho4TI0a+IhCdBkkHudPridhuwnebCY1JpWcj/dG0pEEotYDXF1zsvZKLPXk96sMB+FBUX32dVpu4bUNqelpUkvKYCTqRQb9uzah9Ejx2Bg/0Ho26evLG4gpxrQvz/69u0rY17d8PTr++WXX0GDV41llQiuv+Xp6e0AL5/xW+y5WZn6UI2l7ubNWoR//qd/QbfOPfXPjvDm9dtYs2ID8nOd2mNy12++/hbVqlWTeKx+DV4OE955589o2sRNflOrTpwdVcrpM/jlv/8a4a3UlB4jrV61TtaJPnhACUgdQaERCAhSAOfeUSq/lTssynkN2NntYtkXGhSKtIeGoopt4SDo55eJLmL1NBprhgrPpk2bi0eVBw/TQP0NzXoVXFUOtMgu4OEvxkZ3vH/w8L5sEM95/fbt26NPH7UbIdMuS56M5nHE1VhK6t4HfXorEZxadD1cKJom8AsBK00BhVPSTYciyqWLV8DD2OKTVXf35l2E+EbA290P/n5BCA4Jhae3Dxo2aozmzdzRrJEH2rfuhCfpTw0rKW69acf5sxfQvWsPjB8zERvWbsLWTdswddJUTJ/yA9asXoM5c+Zi/4H9Ij4wkwWFBTLWuH3rlrjdST19Bndu3caDe/dwjxt1X7+OtIcPZQECCy+7BRruYrXIrSvlReHxYyfw2aefO4w0tCJKVyLfd3f3cICXoHJwrmJjXsbdtnk7fv3//ie83L1x7kwqMtPTRSK5e+uu7Mp+5tQZ/Os//R8MH6xWkfCd1DNn8b/+/n/B19dPsusKXva6/n4BqP6ZArZEADByxEjExMRh9559+Jd//Xd07qYUN/x91ao1cHPzwv37XLOsDnLu4CBjhdhLcKqixPJ8YJR3XM35FIQcPAXTp88Qk1n5nmiYS58HLZ4nBUQ1NcqaycnJQ5269bF16w6hv6zsp0JPdEejwFq0C9HPNIAfPnwgjg6ZFp0pavAW/25p90bzSKDj8Oby5atoHddBxHo+Jz3q313DX0g3T8WS+NcpVCsyAKxbvRFB/nqvIgLRgkcPH+HhgzSkp2eCVkz3H6bhwsXLSD17DqdOpiD19FmpBO7oRxCSm169eh3jx08QQ42NGzdh9arVGD9hPIYNG4opk6eiU8dOGDVKjfcomihfzTasX7cWdb75Fl99+iW+/OhT/O299/DXd97FX957D7/7z//E5598jOHDlNisQUvtXM+krmjSuCG8vT3h4d4CAf7+MpcaEhwi9tCJbTthzQq1+RSttD7+6BMX16+sJGVvrCs2LCwco0erhQkKWCRitbxLV6SO26RhA1EmcQz7y3/833j3d/8l97/59W+wa+dOiTZm1Bj83f/4nwgJCUZ8fDyqff4Ffvfb/xLbcEagaK6+ozrRYwcO4d3/82t0atcOp48cxYkDB/Gn372D5B49cfHCZfzxvQ8wZsxknQWMHTMef/79X3H58hXHsx6J3dC/h8EV2NSGhrwyh47dHjm9o4RBKY9vywBMnqTKq/Z8VvO7ZSkL6YRJaZnpaXYOatWug61b1aKG3Pw88bem3TFpkJYY0r2x1SIzFVz/3bZtW4wYoTplDbgX5UnTj2uobQyiolpj3Vo1h63HxcXTKxW869dsQmSYEsfs5MoiVjvoodQLVg+NBMgRKQa/6KBmOT0jHWYaFdhMchIcNMf8YfJUjB0+Gl3bd0RUSAhiIyLRtnVrNGvSBI3q18e4sWOkR6IoxD6S4O2cmCBrdL/66mt8+eWX+PyTD/DpRx/gD+++h9/9x+/wD7/43+jSIUmyxd3KP/jgQwd4KWGQ+7KS9JGY2NFhYaXBW0RhZYihjP/9wH5o3ry5cnXbuDHqfFcbjerXw5fVqmHvzl2SZMajx+LQQPvG+uU//TOGDVG2uWw4Lq5g+S0W5XWh4Gk2fBs1wb/8j/+JQM6xN2qCr//8IS6dO4+nmdl49zd/QJ+eak8efmDcqPH471+9g2tXr6ki2IAwz0Akte2s7tk//0jBm5WVLd4+Dx08JGWxi69jpWQtS5nUlCc7XtUbZD3NQc1adbBk2XLQPj87J1vs60VIp4KqyGkBv6eXG7LjsJhNMnQjPXB+Vmuby5KX0uJozyBjx0xBv76DpZyUwEqKb4BXZ1S6ZXnhxPGTaB0Xb8grdjzJfILRo8Zj1cp12LRxO/bs2o+jh0/gxLEUnD1zHudTL+La5RvIyysETUypoOH4igsEsjJy8PhRBjLSn8g0EAtbUFh0Okg7xha76DKAXlEiYC00qbW8NFh3UQLp33VoKijA44ePsHvHbly6oJRI+/YdxEcf0kjD8F4v43RNDKqBk5J6OsRmi0WNhwXg3CNYxj+0ulLcUn/rmZBgMQzq9W+HDx7A/PnzkXJKKSakt+a2HLI1B8c5qmdnZ2jKycW2desxetQoTJg0EccOHpZksrOzMXbkGBzcr4iZD7du2Qb35h7g/CPTpDVRmH8IEhPaq46OOglDP1ASQVSaZ7JJNeuAdaLaYsL4KXBv4a06V9YpOzhDmWqnB4oXnHQCZyaDMIaG+QUmeHq2xK7d+3D37j1hIlnZGSIyy5w95+1lSKYkMqVYYrvTUbpZpEuuaz939izi41qjfYLaYYSsXRZIkC4kT9YX5k3nnbolHlevXEd0ZDwK8pXHSdI28UTpVDaRt5thgNexz4dDW0IuRi3v6ZQUSSw3twDduvVEeHgEEtokypgrNiYWMa1iERwYhtDgMCR16Ym0B49ghQkmw5/U+ZTT6N89GU3rNMCnf/sYX3z2Nb6tUQ9/+6AaWnDJX4A/Bn8/yCHTU9wm0dFR3YCBAzBp8iRMmTJZfDRPmzZNwnlz5mDxggU4cugQbGYLrAUmIVK2yZnTp7Bq5XIcOXQQnEin2eGd23dk0C8FkXGyqqDly1ah2me1jElywkT7m3YqhTp37uoQm/m+4r5UatBNJxuSgFbV9izhKzFNvafW9Za0YorvkTCefV8BTefbNdSinX5GsLNTZDpUoDDksIVpPs1+Klwl5/9v7+qjqqqyeP9Ma2m1xmnKWTo5ran+qDATPwBTmRIEQ1FyVAwSkVBBeDy+NBDQUqxxZrJlRpqWk61RQARDERDT+Hj40iamLE0USwtzRBJQ+XjvAb9Zv33uETJUXGJZy7PWeee9e8+799xz9z57n/153hDIXGYl7/L+PxuVdghyirsncbcdCJg+A6vTjBja1NXKdo9bOmXbfrW2DXbaacHO/sbEhTwfgQ9LrDhbV4+6hjowdji3bkwOz8AQEhxCWHey74pqMyl8U0szmmzNOFNzGvQhN0eakbxQ2VkTDlWldkDZWl9tbB3nO0w35zwfAcqeWMgEcA1jKnk+QytaukZeXojl7bXrkLwwWb4TMLpTSI3s7Q2wt52Fo/U8ztXXourIIRz8vALllmJkZ29GevomSZNChwVWIqoGNs3/U/xOwUx8fDyWLH0JJlMEpvtPQ3SUCbEmE/x8xuO1v3fsMdTbaIcpIgx97/09hjk/DudBj8HN1RUeYzxk3zs7dDYmTpyE115T/rxvpq1GlCnOeCxa7ygp8JdfHkLNGRVsbtmyVy6yzex4+nSNSk1BnfhVkVf58naFFHzezrWrPjxGIQkRVTxQuCeWLQnvzePKAkeohFBqJdjgOOnCybnU743ficz8fbl73VTHmQLEbkOL4SH29bHjcB/pgW9OfCvvixxKu0F5iVTdqW1i7c34yGpR5Zz4Tw+Gdd8nyi2TiQNstB03zHQ7IS+jvLDyjbAV5G1pQsMFlccqPNKEuPgFMjZeXxCNThQcm8Qx//EYyQFcWoVFNnabmek5iI9NVISNIXJYf4C8JCWXVJoZstTX1WNBXDwOHTwov0tKSsU0LysrC9lbspGTnYP8HTuQk50NS5kFRyuPwNZsg52sDimSg6ujWjXlAlf4oIkYgVm3V+j6g1PKEkbtsbnoUIlOVQ4NOEiByFrSgqqmpgZagn30SJVcY5zXRFk8+IOAKwHi21qxa1cRxk+YAJpPzp0TjrVvvY2qqq9BFrqszCJ7a4mO2Sk7naLIl0fW7iCGXrh0y/8o+1Y+X4cElAukUAeqNS7GauoIAMA55H81wooazqDCnGN9/Zu7VUJS+oezvLJsOcLmqiQAZCEFebnnbXeIGwdn52qVkhEH59Qgu83Ndvj7z8BH+/6D78/W49yFC2iS6CsOQTpNee3kaoR9NpCRSMffaEdD43mhG/OiTTDHxchYuW0k/qnxkN6z/nh8zKFwaWXoYxiMX83/zsBzjDcqKyvluhy3Ws65HNhppNGFCqCTxcfH+z8W5XN1dbVsyN3dR2PQoIEY6OSEJ91Hw+lRJzz04IMYPmw4zBGRoEcG4z/bHBeEZTj0xafi/+vnOxG+vuPh7e2FcU97YbT7KLi5umGspxfee/c9YTOo06KinKW0pBQr/rkCaavSkJWVg/TN2dhZtAelpRbs37cfzDNEbw7ZIxqeSFwRmRCtsvIwTpw4ju9OnpSwPLVnamUscmHjY8+eMgwbMgqVh49cpFAEeK68BHBuGXr3vgO9e/XGww8/gv79ByBEoh2QmtH+2VCcczplDrkGdjGX13lMIyGvrb+zVSoytRcjAhNBOW5NXdlfU9nOi6K+xo0Ya09ekxDc3qZgwdZih8eTnsjJUc4dJApixigyB7KQosG9Qku3BvWeKBYhfrDYbK3w938O5eVWnDp1WkL/0kiD+1nN8XCRZOXiyTnn94Zz9WhsboTNYcPJ09UKeU0RMEWb5bqkV4QOVTWby1YfU62mup2PC89LJlcxv5gTGobXV76hrktYElrI/zu6Rl79gjXLlZmZCT+/Sdi7t1wu0tUHXfkkfpCsSk1obWeuIgZrs6G29hQsZXuwLXcLNm58Fxs3bcDyf7yM2NhYRJnMKMgvEMAn4hIAWJiJ0BxlRrQ5Wvqxrzk6FmFh8wSJvL3GISUpRfoLlVd8Mwq25eLJJ0ZgpMswuA1xRuDUKfB/ZjL+6jsRQYHPITx0DtasSpOQm+sM52cKRbi34j6fe0cWpm7p06fPRdXPnXfeKXbTPCcpXWQi1TqogPbGIC+vzffBwlZX/tbIoo9pJNV99X/ZsvA8++r/3cwtxPZAkaD8HfnwHOMprp/yIAbyqY0l+xCouXAaEG/8Zl/hTMTwQi2sBBOyphqBfX39UFBQBJu9VdSatLpj4SLOGGgs5MgYl5yFXM+58w2oPlmNqqpKfH9Wba8Y3fRZ/46smtK5Bz4slnI8Oz1QFmI+NmFdcA1tl0Few0yQqzhfNktBYT7GenkgLi4ae617UVFhxYnjx3DqVDVqvz+Nhvo6MZS/rvEaVEoFT7/ylahSaTEcGAiE3FtQv0wkZFTLr499JWF76HNZRffC0lKUWSzIz8vDIw88hIRKNjkgAAAGXklEQVQFCXIDFUdK2Stfeke6h2mVjt8zykmD8ae6RoAOZPo5kYLP8HPev8fuTbgzMMxsMiE+bv6lr6dHfk+fFgjtrklnm2+/5Z6a8o+OoIXULtAJgXb19XV1YLgnhgX+7mQ16mrPoPFcA5YtfgnJCxLkXO3pGjEqogcSA1WcYYK96moxNvriwAHsL7fiI6sV1jILSj/Yg8yNm7B29RqsSUvDGytXITlpEcxR0YiPjUdAQADuu++PIhfiA1PiTPhjgoLbDNph8NLKhoSIQD6fmM7WZgir6Ku7NPVFeHj+BX3/8FvcffcduP/+e+D06AMY/NijGDTQCWmvr8KunSX4rOJLHDxwFGvf3ABfn2mYGRiOmQHhmD5lFmYGhiHenIJlqS8jJTkJmzb+W1y99ELBQTJeVkZGOnJz35d9aXbOVnDPTYuko5VHxWDkWt+e1WJBcEAA5oaEyEvg/wlsutVIyUWLZevWrZK6lAhcUKBsacmN9BiAdoulVjDMYV659jzL/tM+5w/HL1yckRfazWU4Ro0ciciICMyZPRvzwsMQxHBKQTMwL2wu5sfEIOmFBCTEz0d0ZCSS4uORsuAFzI+OQdLChUhOSUFyQgJios1ITEhAcnLyxXr/gD9h+NChCJoRiFmzgiWhAN1ITZHzEGOOgv+0KfCfNlXS23qNZeST0Rg71hPeXmMxetRIuA0ZjEnjvOH6+ON4wnkopk7ww/gxY/GU2wj4jHkKwdOnIfjZqZg363ksXpCIKT6+cj40MAihATMwZ0YwZgeHIHJuGKLC5iEuOgYJCQlITExEUmKSpLVd/OIifHZAaX2U9FupjW7rSkpH0qwoGW1B2ZHCEM2SAI2NF2C1WpCTk4GVK5dj6ZJkpCQlIi4mBtFRUZgfH4vwsDmYNXMG/Cb54Gmfp+Dh6Y4RI5zh4uIEV9eBcHV1whDnx+AydDDchjkjLDQEIUHPIfWlxTCFz4Xr0MH484D+eGBAf9zd5y7cfvtv0Pfee9Cvb1/c1as37u3zO7g/MRLvbXgXubm52L59u9SgoCAJP8PMDi7Dh2KQkxNcXYZh4gQfjPf2xpbMTBFkKYSlYE3tE/mbyKsRWANuv3790LtXL5He6j48p4059H9uXMtxdaeqFfnGjaODZf8p7kGhKRGYcbipR2WkClqp7dm9G8XFxbKQFxeXYGchrfaykft+DnYVFaKosAAf7t6ND4oK5XhOdhZyt+ZgR942CbeUty0XmenpyMzYhK05WcjanC7nSoqLUVpaJvmkt2/LRWlpsWTtyM/PQ0F+HkpKilFeXg7GLmerv1ute8UEtuKTT/BpRQX27bXis//S2vAADjPixpEjOHL4MKq/+UbMZZlo/sK58+qFGoSDcNWdYmcWQRG6ESeBLpG32cYQLAppSXmJvOSzKc1VQd46EPnyN+VKeqV+ZEscEgvr+FfHcPDzA7CUlqAwPw8b/rUeWzIzUJi/A+9nb0HW5gysW7cW77zzNt5asxorV6yQmrp0KVKXLMWy1FRxQkhdkopFixdhaWoqwsLDEBw8EynJC7F8+d+wq2gnWpo6HB6ohtCSXIWMyj2LIXUInNwfskyePBmzZ4deRGqe455XjAc67UFvHEB3B3HZ59eGvHZxnOd7+jUX8n1ShQtTWwX6tivi0QaHnUEtKEBzgBZi5IKV1PkyyEu9oUJaRXmVRY6xUaaFBx3twWyA1CU2olUyA1JgRYW0YkM54R3IS0RWggUlRuuM1B39f4qX5OCKTl2npFWhzlPpW9X+XhlSdN7rr1+/HqtWvS5Do5SZahgtsLpxCNuZyhEpu1s7/+8X/t0QIlKAyDlnVnmHjQY86t2RkFC+QQmwZL7XOaFpiEGXvXZlbita1nYCPs1NO9U2+oI3oZ0RX5i7t40ugY2w25uU1VabA23a/JJqOlpy0WFB5CpEKPWbVluSi5r9GeuNUn/ClOAJj7Gyj4rNJlxsJ720YoOValXUTyQIVLUyJpcIGGl4w4CONB1WOnpHq1J53XZ9AHjzrPaazdWtXgg0Ve3uc7I/qa6mvBkZGXj1VRXDSl9Lt9295q1+v5SF5OaB5+7AzHUi7y/lpXR/nBoxNfJSQV5RUSFrAY9xUnXbnQm+1af7c39rrq5trm4hb6d9qzZq0NSXwKSLYt3Uflgj+C1guzZguzVfPTtf/we/sKWh9v7LfAAAAABJRU5ErkJggg==)
PhysicsFluid-Mechanics
Physics
In figure, block A hangs by a cord from spring balance D and it submerged in a liquid C contained in a beaker B. The mass of the beaker is 1 kg. The mass of the liquid is 1.5 kq. Balance D reads 7.5 kg. The volume of block A is 0.003 m3. The mass per unit volume of the liquid is
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)
In figure, block A hangs by a cord from spring balance D and it submerged in a liquid C contained in a beaker B. The mass of the beaker is 1 kg. The mass of the liquid is 1.5 kq. Balance D reads 7.5 kg. The volume of block A is 0.003 m3. The mass per unit volume of the liquid is
![](data:image/png;base64,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)
PhysicsFluid-Mechanics
Physics
There is a hole of area
in the bottom of a cylindrical vessel containing fluid up to height h. The liquid flows out in time t. If the liquid were filled in the vessel up to height 4 h, then it would flow out in time
There is a hole of area
in the bottom of a cylindrical vessel containing fluid up to height h. The liquid flows out in time t. If the liquid were filled in the vessel up to height 4 h, then it would flow out in time
PhysicsFluid-Mechanics
Physics
A water tank placed on the floor has two small holes, pinched in the vertical wall, one above the other. The holes are 3.3 cm and 4.7 cm above the floor. If the jets of water issuing out from the holes hit the floor at the same point on the floor, then the height of water in the tank is
A water tank placed on the floor has two small holes, pinched in the vertical wall, one above the other. The holes are 3.3 cm and 4.7 cm above the floor. If the jets of water issuing out from the holes hit the floor at the same point on the floor, then the height of water in the tank is
PhysicsFluid-Mechanics
Physics
A water tank of height H, completely filled with water is placed on a level ground. It has two holes one at a depth h from ton and the other at height h form its base. The water ejecting from both holes
A water tank of height H, completely filled with water is placed on a level ground. It has two holes one at a depth h from ton and the other at height h form its base. The water ejecting from both holes
PhysicsFluid-Mechanics
Physics
A large open tank has two small holes in its vertical wall as shown in figure. One is a square hole of side ‘L’ at a depth ‘4y’ from the top and the other is a circular hole of radius 'R' at a depth 'y’ from the top. When the tank is completely filled with water, the quantities of water flowing out per second from both holes are the same. Then, ‘R’ is equal to:
![](data:image/png;base64,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)
A large open tank has two small holes in its vertical wall as shown in figure. One is a square hole of side ‘L’ at a depth ‘4y’ from the top and the other is a circular hole of radius 'R' at a depth 'y’ from the top. When the tank is completely filled with water, the quantities of water flowing out per second from both holes are the same. Then, ‘R’ is equal to:
![](data:image/png;base64,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)
PhysicsFluid-Mechanics