Question
One circular rig and one circular disc both are having the same mass and radius. The ratio of their moment of inertia about the axes passing through their centers and perpendicular to their planes, will be,.....
- 1:1
- 2:1
- 1:2
- 4:1
The correct answer is: 2:1
Related Questions to study
A circular plate of uniform thickness has a diameter of 56 . A circular portion of diameter 42 cm . is removed from +ve x edge of the plate. Find the position of center of mass of the remaining portion with respect to center of mass of whole plate
A circular plate of uniform thickness has a diameter of 56 . A circular portion of diameter 42 cm . is removed from +ve x edge of the plate. Find the position of center of mass of the remaining portion with respect to center of mass of whole plate
If f(x) =
x then ![lim for x not stretchy rightwards arrow 1 of fraction numerator f left parenthesis x right parenthesis minus f left parenthesis 1 right parenthesis over denominator x minus 1 end fraction equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIIAAAAmCAYAAAAIjkMFAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAZpE86XgAAAyNJREFUeNrtWz1oFEEUHoIsR7hOxEIkYJHCIgRERERESCGHVboUIhIIcgSxsxILm5BCRNKEFBYp0oiFhQgSRA4JgoQUIiJYip2FhYgcrO+Rt7AsOzs/t7vz5vZ98JHLzO7my9tvZ97MvlMqbgyBG47nbNB5sWgOrZcVZoCnC20LwAPP632g82PR3IZe9rgB/EX8DDyRC86i5zUvAEeMNM8DHwKPAullDwzgj1zwztPPRQrqJBhRgDlo3gWuAdMAeqPAMnCvpH0TuD7hte955BdNa04D6I0Cj4APStrfAK+WtK9qgvWY+vK4DNxnoNnWCE3pZY+XFJiMK7m+38BEc95hIUm7A9wqOS6h63DQbGOEJvRGg6/AsyXtY0Oi9oQ+Lxmeon9MNNsYoSm9USwZ/2j6TEF9C7xGWfhJj8CmFqxbsxhBg0vAd5o+0zB7n4K20PJQO4lmmRo0wPn1ecUTf0XTh+0vaHpYaTn58tUsyWIFntHaWjksxc4BXwFngX3gp4qpYZ2uE1qzrRGa0BvNqmGg6SvbnDkFfF248Tdps6atDRpXzS5GCLKhlHokMnUDt2d7Ff0HuRwgoZtwpuS4PVpJ5NHUlq2LZlNy2oZe9kbAp/un4RhuL52a1BzspVOqwuEprcVttlPvKvdt182KeZyj5ib01joiZL8PKCn7S9l6n9qvAz9SOzp63vJv4zC4HFk+E6PmWo2wRuvm7A3bbcqcB4X2W2QWQXv3z2dDzNsIOALMFNpxBNguaR/L/ZneEaGnOa7nmXekQieyyhHUhO2CKZgaxAgyNYgRxAhiBDGCGEEgsIepPF3QEdiUpws6PsUKAsGlxF2MMOXzpm2JuxhhyudNlxL3zhsBK2Cy4gd8YYTfzJmzPBcLNvvMg2Nb4p5prGOLNkojYH1f9p09fHpc3q/vAL+p43JursGxKXGXEYFwRAHb0fQPDU/JWJkLUEIEx7bEXYxAwKISLLlKHM9D43wHXmQYHJcSdzECJVE4NXxRx4WYLuCaI7iWuHfeCPilzfd0M4e0xo49OK4l7nX/j60XkdQRsFFubk9omO9LcLqD/5++eqOhsaFaAAABfXRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtdW5kZXIgYWNjZW50dW5kZXI9ImZhbHNlIj48bW8+bGltPC9tbz48bXJvdz48bWk+eDwvbWk+PG1vIHN0cmV0Y2h5PSJmYWxzZSI+JiN4MjE5Mjs8L21vPjxtbj4xPC9tbj48L21yb3c+PC9tdW5kZXI+PG1vPiYjeDIwMEE7PC9tbz48bWZyYWM+PG1yb3c+PG1pPmY8L21pPjxtbz4oPC9tbz48bWk+eDwvbWk+PG1vPik8L21vPjxtbz4mI3gyMjEyOzwvbW8+PG1pPmY8L21pPjxtbz4oPC9tbz48bW4+MTwvbW4+PG1vPik8L21vPjwvbXJvdz48bXJvdz48bWk+eDwvbWk+PG1vPiYjeDIyMTI7PC9tbz48bW4+MTwvbW4+PC9tcm93PjwvbWZyYWM+PG1vPj08L21vPjwvbWF0aD4MTCOIAAAAAElFTkSuQmCC)
If f(x) =
x then ![lim for x not stretchy rightwards arrow 1 of fraction numerator f left parenthesis x right parenthesis minus f left parenthesis 1 right parenthesis over denominator x minus 1 end fraction equals](data:image/png;base64,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)
From a uniform circular disc of radius R, a circular disc of radius R/6 and having center at a distance +R/2 from the ceater of the disc is removed. Determine the center of mass of remaining portion of the disc.
From a uniform circular disc of radius R, a circular disc of radius R/6 and having center at a distance +R/2 from the ceater of the disc is removed. Determine the center of mass of remaining portion of the disc.
Four particles A,B,C and D of masses m,2 m,3 m and 5 m respectively are placed at corners of a square of side x as shown in figure find the coordinate of center of mass take A. at origin of x-y plane
![](data:image/png;base64,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)
Four particles A,B,C and D of masses m,2 m,3 m and 5 m respectively are placed at corners of a square of side x as shown in figure find the coordinate of center of mass take A. at origin of x-y plane
![](data:image/png;base64,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)
If
and ![f left parenthesis 5 right parenthesis equals 2 comma f to the power of straight prime left parenthesis 0 right parenthesis equals 3](data:image/png;base64,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)
If
and ![f left parenthesis 5 right parenthesis equals 2 comma f to the power of straight prime left parenthesis 0 right parenthesis equals 3](data:image/png;base64,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)
Consider a two-particle system with the particles having masses M1, and m2. If the first particle is pushed towards the center of mass through a distance d, by what distance should the second particle be moved so as to keep the center of mass at the same position?
Consider a two-particle system with the particles having masses M1, and m2. If the first particle is pushed towards the center of mass through a distance d, by what distance should the second particle be moved so as to keep the center of mass at the same position?
For ![x element of R Lt subscript x not stretchy rightwards arrow straight infinity end subscript space open parentheses fraction numerator x minus 3 over denominator x plus 2 end fraction close parentheses to the power of x equals](data:image/png;base64,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)
There are seven indeterminate forms which are typically considered in the literature:
For ![x element of R Lt subscript x not stretchy rightwards arrow straight infinity end subscript space open parentheses fraction numerator x minus 3 over denominator x plus 2 end fraction close parentheses to the power of x equals](data:image/png;base64,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)
There are seven indeterminate forms which are typically considered in the literature:
Three particles of the same mass lie in the (X,Y) plane, The (X,Y) coordinates of their positions are (1,1),(2,2) and (3,3) respectively. The (X,Y) coordinates of the center of mass are
Three particles of the same mass lie in the (X,Y) plane, The (X,Y) coordinates of their positions are (1,1),(2,2) and (3,3) respectively. The (X,Y) coordinates of the center of mass are
given that ![f to the power of † left parenthesis 2 right parenthesis equals 6 text and end text f to the power of † left parenthesis 1 right parenthesis equals 4](data:image/png;base64,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)
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 or
given that ![f to the power of † left parenthesis 2 right parenthesis equals 6 text and end text f to the power of † left parenthesis 1 right parenthesis equals 4](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKYAAAATCAYAAAAaj3axAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAA4pJREFUeNrtWl1kHFEUHhVrVZSqVbUqVEVUrFK1YlWUqqqoChHRp1iqIvrap1jVl5Wn6ltU5aGqRERUVamIWCuWqIqqKH2M6ss+VMUay/ZcvmEy7t/M3juzbe7Hx+783D33fGfOOffOel58PCHWPIdBgtOEcB90cJoMFArEouKaBWI9xph13OPgNJHiFPF85NgNYpu4DLZxLIoScTfBbzZxr4PThIs7mCDjV+JQ6FyeOEa8js+iyVwNfa8Q14m/iT7xC/EB575rxIbFeTGb12BHh/iOOJmxr3sZaRJglLgETbwMNAkwpfIFm/BhaBJXONfMCgLLw33NyLEd4hxxODRmE8eiaMAZpvEQgTiK72cwh8Y/EJg2NAnwGr6R2WFLkwAsLr6pfDFNfKsYqCZZAbJysqhhzAhxn3P8ccw+SAdMyL0BLc86gZmGJjI7bGgSxgqxqvJFDVsPMtwj3hWc+yjocXjocI5NELcsTHwu4b1sri20IN/RlvAEnSH+wJxYhbjIGWsSJdPHtfOagZmGJjI7bGgSbvO2VDZs4GRAkZjjIA+sf8tpGDQhKC85jCFynoo8HBAvJHTcm1DpnEd/F7VpBllpJHTdTuS6MZSr8VAWX9cIzLQ0kdlhQ5Ng3P2Q36S+OBA87dGeYFhwrqshdh5ZqCI47xt+KjvoLZnIRxh/T9KTyVbFPkeYmxrXvRIElU7GTEMTlR2+Zx71SIvRkzn+SLNZTeqEs8RN4u0UncAm/BmlbgjzrKA0LyQYS0fQ6PGfghVzT+NhsK1JFoFZ4lRMoQ1l4nafPygrG5cQlJdTLhtsvKJgtXqomM8SArgr+A3dwOwmDAjbmmRVylucOBDawErNap9O+CQo0azHekk8rdF7mm60PyDzxM0EK+gf8wYyZkdggyowbWqS5eInVjC/wJ5WP+BtTbC3FWve8U1hERYxhkmwcj0reFhaikxjqpRvc4LjnEZg2tIkTmDa0CSWDRuSLQdd8DZz3yMIdGBjMzeHVXI19HCUsSK8pVh0VPGZtQLP0CsWEwRmGZmriMw5BT/prMptaBInMG1vsCttaHviV1pxsOsdf7+qm7Jtvv4qoJX4g36PBapqb6+ERZOPzMqC6ynxV4LA9LAzsImyHrwiVAWmLU1k2qSliVZgFpANTK243J84zDxMJ1qT5yhbJl87PYo53rKBXup/gtME6XraxcJA4cRr8he6t0BO1nz59wAAARF0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bXN1cD48bWk+ZjwvbWk+PG1vPiYjeDIwMjA7PC9tbz48L21zdXA+PG1vPig8L21vPjxtbj4yPC9tbj48bW8+KTwvbW8+PG1vPj08L21vPjxtbj42PC9tbj48bXRleHQ+JiN4QTA7YW5kJiN4QTA7PC9tdGV4dD48bXN1cD48bWk+ZjwvbWk+PG1vPiYjeDIwMjA7PC9tbz48L21zdXA+PG1vPig8L21vPjxtbj4xPC9tbj48bW8+KTwvbW8+PG1vPj08L21vPjxtbj40PC9tbj48L21hdGg+ji5exQAAAABJRU5ErkJggg==)
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 or
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 or
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 or
If
, then the value of
is
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 or
If
, then the value of
is
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 or
Particles of 1gm,1gm,2gm,2gm are placed at the comers A,B,C,D, respectively of a square of side
as shown in figure. Find the distance of centre of mass of the system from geometrical center of square.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAaEAAAF6CAYAAACwUecuAAAgAElEQVR4nOy9+XcbR5bv+YnITOwLAS7gToqLdlmyJbvsqnJVv6p6b07PefNm/sx5c+bMOT1TXa9f9amu6iq3LZdX7btEStx3EgRBIDMj5ofMBBIkZcuWZEl2fHxggUBmIhHIjG/cG/feEFprjeHZ0eHjIEKDABBorVlZXeX69Zv86U9/5urVa5S7e/nNb3/LOxffYXiwn0I+iW15+G6NjY1Nrn59m3//62UezczT3TPAxYvvcunddxgbHyaVtgFQrQ9TCBQSjUAAFuGHGwwGwxuF/apP4MeHRghBJp2mp6ebXDbD5uYmc/ML5HJ5crkchVyGTKqMbUmajSaPHjzik48v8+nlv1Or++QLPWTzWXKFHI5jhUc1GAyGHx9GhF4ouvVvOp1idHiQt99+i7n5Ob748ivu3LlFd3cXfT0lMikHx8qyuVnlytWbfP7FV2xt7zB27Dhnzp5hanqSUrmIZYunGl8Gg8HwpmNE6EWidcsrZluSQj7H2bOnaTQb1PZ2+frLK/z904+p9JYpFrLYsp8nT5a5cuUmD2ce01cZ4p2Lb3PhwlsMDQ+SSDoxF1zb4SZCJ5xxwBkMhjcdI0IvHN16SKkZHKyQSL7L8vI8c7MzLM494e+XL+PYFjP9/dy7e48792ZxkhnOvvUW7/3sPSamjpHLZdAimAeKC45oPYwMGQyGNx8jQt+VeL+vY6+J9otaK9A+oLGsJD3dXZw7c4oHb5/j8uXPuH/vLnu1GolklrX1Laq7TY6fPM3FS5c4NjVBtpAD2fmRAt0SH6Eh2EAH7wojRgaD4c3EiNDzckT/L1CoUIiEBktqJo6N8sH7l9jaWOeLL65w9cpV9hoaJ5HlzLmzvP/zX3Lm3Ft0lUtYjoVCIQDZ+oCDs0ICtDDGkMFgeKOR376J4SAth5toPzoQAiFAa4XyXbTv0V3u4vTp45x/6xT9lW58r0mtVieTK3L67Fu8c/EiA0OD2I6DEJG4aKJw7MASCh4Gg8HwY8GI0AtCx2ZrlBYoLUGG4dVa46RSDA0NcPb0CY5PjlMs5MhkcwyMjDJ18gRjx8YpduWRloUUwYyP1BqpdUyADAaD4ceFccd9D+JB0zo2IRRIhWy9K4QEfBA+IMmk0wwN9HNsdIRbvY/wbI/K8BDd/b1k8hlsS+LrQHyE1mEyanT0tgS1Pl0cmI4yGAyGNwwjQt+ZwEUW0Z6xEeEsDmhhgRBoNEJIJBIQSATpZIJiPkshn2PLdUnlMjipBNK2ArNUBOZphwAFikYrREG0nXKaoF6CwWAwvIkYEfrexOdm4lZK+FxItFJoZNvpqQVax7YXGi0UCh0IFhx6fNunGyvIYDC8yRgR+s48Q2CA1mitUSrMFxKBRaQRaCHDo7Trv0kIw66DfFfi5fwOqIwJSzAYDD8mjAi9RKQI5o+01gjl4Xs+aHASCbK5LHkvQSadwrYstA6dfHE/W/THgTygyEoygmQwGN50jAh9Z56h+w+j24SUCK0Dy0Z5+L7CtpP0VQY4dfoMPbs+Q+Nj5HO5YBMdn2Nqf9pRny6e8r7BYDC8SRgR+t4cloHDgqBD9xpoBcKySOfyjE1NkS71UnUl6a4e+nq6kULgK40V7NV2yYmoRM/RZ2BEyGAwvMkIs57QdyUSiLirrJ1G2mpMHSqPUqA9UD7g4XkenqfwtaSJjS8dpOWQdCxsKbEFSBRCK4L6czL8iFh0XCxl1QiRwWB4kzEi9L2Ih2kHxXXiUzlRcIEQgPbRvgdaIYQKLRsJ0sYTNq6W+CrICbKEwBIgQwESAkTo2mvPCx1OWzUiZDAY3lSMO+578/RZmXCB1aD8DgJkkCckhAxL8gSroVpIEGAJATqI5LainRGIaLXWI4YJJjDBYDD8GDCW0PficI7QEeVFY9sGlk079FqEyawS/8Cckjy071FH7vxMYwkZDIY3FSNCPwgdzrrw+eGKcEfP7zxd3gwGg+FNx7jjfhDEU55/0zvf/KrBYDD8GDAi9MI5upxP8M7BFfG+PcTAuNwMBsOPGSNCrwjxDDaQwWAw/NgxIvTC0Af+FU99h9YWUYyb5vsJkbGTDAbDm40Roe/BNzncnnl/rcLK2YogNkSEId3t+DghjLgYDIYfN0aEfiBUWFnbkhIB1PcbLC7OM//kCdVqlVQ6zeDgIIODQ+TzeaS0wsTXYN5Ih4KktUaKsCCDVmHu0av8ZgaDwfD9MSL0PXiWKDatY0UOtEb7fmDxCIHneSwvLfHvf/53/vjH/8ns48f09PTw61//mt/+9rdMTx8nl8tFStNy1uloiQghWs+FUFiWWdbOYDC8mRgReqHE5oG0wvd9lFIIIbAsCyklSinm5+b46KOP+P9+/3v+9Kc/Ua1WkVKys1NFCInn+Zw+fZpsNttyyfmRiNEWIzAuO4PB8GZjROglobXG8zyUUkgpsW0b3/dZXl7mk8uX+f3vf8/f//539mp7ACiluH79OslkEs/z0Fpz4sQJioUCvgoETQqBCIVM66i4qREhg8Hw5mJE6CUQt1Isy0IIgeu6LCws8Omnn/KHP/yBy5cvs7S0BNCykDY2Nvjiiy/QWuO6Lpubm0xMTFAqlchms0jH6Th29DAYDIY3FSNCL5HIBee6Lk+ePOGjjz7ij3/8I5cvX2Z1dRUpw6W+tSaZTJLL5Ugmk8zMzOB5HgsLCxw/fpyzZ89y+vRpenp6OsTHCJDBYHjTMSL0EogEInLJbW1t8cUXX/CHP/yBzz77jI2NDYQQpNNpfN+nXq9TKBQ4f/48uVyOubk5lpaW2N7e5tatWywuLpJMJslkMiSTSZyYRRR9nsFgMLyJGBF6SQghWnNAV69e5V//9V/55JNPWFpaoru7m0qlguM4rKysMD8/Tzab5cKFC5w6dYrZ2Vnu3r3L/fv3uX79OhsbGyQSCbTWTE5O0tPTg23bRnwMBsMbjxGhl4hSivn5eT755BO+/vprarUa+Xyeqakp3nrrLZRSfPXVVywtLWFZFr29vXzwwQe899573Lt3jz/96U9sbW0xMzPDX/7yF7LZLJlMhmKxSCKRaFlbBoPB8KZiROglEbnklFI0m00cx2FsbIyRkRHef/99pqenefz4Mbdv326FXCeTSSqVCqVSiYGBAQCq1WoQRbe3x9raGvV6vRX2bTAYDG86RoReIlJKuru7OXv2LBAEIJw6dYq3336bdDrNxsYGnue1QrmVUniehxCC7u5uLly4wN7eHj09PTQaDcbHx8nlcsYCMhgMPxqMCL0EIstGa02pVOLChQsMDQ1hWRYDAwP09/ezt7eHZVkopQ7tE1GpVHj33XcZGBig0WjQ1dXVmg+KklfjYeAGg8HwpmFE6CURiUk2m2V0dJTh4WEsy8JxHKSU1Gq1lgA9jUQiwdDQED09Pa3kVMdxsCwrKN8TJsIaDAbDm4oRoZdANB8U1XSzbbtVNUFKie/7T7Vc4pZQtH0qlTpkJZmyPQaD4ceAEaGXhBACKWVLPKSULavluwhHdIy41RSV7TEYDIY3HSNCL5nnrW4QCY4RHYPB8GPEiNBL4GlVrqNAgng17Gc5zsHt4vNApoipwWB4kzEi9JI5SoS+i2gcFLOD+xoBMhgMbzJGhF4CcWE4KqfnWV100bzSwf0MBoPhx4IRoZfEQSE6+N6ziklchMy8kMFg+LFhkkzeIIwVZDAYfmwYETIYDAbDK8OIkMFgMBheGUaEDAaDwfDKMCJkMBgMhleGESGDwWAwvDKMCBkMBoPhlWFEyGAwGAyvDCNCBoPBYHhlGBEyGAwGwyvDiJDBYDAYXhlGhAwGg8HwyjAiZDAYDIZXhhEhg8FgMLwyjAgZDAaD4ZVhRMhgMBgMrwwjQgaDwWB4ZRgRMhgMBsMrw4iQwWAwGF4ZRoQMBoPB8MowImQwGAyGV4YRIYPBYDC8MowIGQwGg+GVYUTIYDAYDK8MI0IGg8FgeGUYETIYDAbDK8OIkMFgMBheGUaEDAaDwfDKMCJkMBgMhleGESGDwWAwvDKMCBkMBoPhlWG/6hMwGAxvCjr2XLyyszD8uDAiZHjt0Af+PrK704ffPLhfxzGOeFO3XmwfTEQH/ZH0t09tSx17t6MND39Z0TqKOniUI3iDG8vwSjAiZHgt0eiWJBx44ynbtx/R/wWhrHS+Gb0BaFTsTYFAtDzUr2NneoTyPs9eLSGKxEi2Xo7LjUQjUAdejT/ivI7tZnidMSJkeK0IusTgP6BTiOJCEt+nQ2cObKRB6nCjqA+VgIg+RbX2keGYX2gZHkK8Rn1qvE3a/z/KYtMdex1hDXWIcvQk2DlqJtX5KhIVClHwqkbSOaUcnVV7r46TOIrXpm0NrxIjQobXlOfvoY7oDmPviUMGUmd3/Dr2kD/sOR1ul4OSJmL/vo7tZXgTMCJkeA15ng7tsHuoJSyHDnuw83yai+l14EjnZPtU9dNfevZv87Q9jvo73k7iaWfX3vybJuwMP2mMCBlea8KpmwMvHLHNgVe+vc87qsONd9+voxB9A8/QLi3Lr+VljMSjbeG05UXEZCZ6JsPtZMe7395W+ikDAIPB5AkZDLQ72Ij41PybT9xuieTm8LeL5nueZg/KIx4c2urbMSaRoRNjCRleKw7aJUfPRRzeOj6Pc2jLzrhkEN/kcotG7YdC6V5zjmofHYami/A7x7aMfyXdlqbgZatDtA6JtBaHjvnN53UwVCLiTWhXw8vGiJDhtaTd9R8MH4gTd5s9g0voW4Ts8LbfLyT61XHg+2kdNlHgQou+hwqfaRHlT3WGZ4hWuHr8yNGrcKQwf0tT6QPPDg4fDD9djAgZXmP0EY8QEbmEOruz6K94Vkt7X5+WcGmL+Gi+M8eobRloBFoFR5fy6A5Ta43W7XOTsm01KKUQQiCeyWr4Fp4ajh2er+5sIwEgLVA+e7Vd6q4HtoOdTJJMOMiOfVWgSjJoHyEEaBF8r/B7a30g/CB+PkoHBhIghGi3SdjE7QDzdqiIkR8DGBEyvLaEnZiOZjBUa1Qv5DNGsYW7CzRoH7SP1gqkDGdALKI0zEhDBBohgpwYrQVKC5TqtCTioqKUQinVEqGoA46/L4RASvn9heio3KhDb2m0Ds4jyuJBBufsu03m556wvLFNKt9Fz0A/3aUubEugtEZoBUqFlpOFEAotRPD9lQItA2FttVHcwxlmW6nw+0tABMdVOrC5pCViScGB+EghMEJkACNChteYYGAfy+gRQeeulUejvsv6xiYb65vs7e3jKo1l2WRzBUrlbgpdJdKpJDLsnIXQIAIx0xq0kISHb+VsKq0CsRIeUmiEkIBFZBUpdbQIRQIUjf7jltAPRdBC7XkdISTaddmqbvDw7h2+/Ooqq9s1Bo5NczaZJt/VRYpA3q2ojQ9GMBCJamgNirYzrjVA0G05jNpFCNGaVgvSgUXYlm1n3FPqYRh+ghgRMrx+xEbcgTtHhJHBAlDs7VZ5eP8Rn17+lK+vXGN1dYOG62EnkgwOjnD+/Nu8c+ki4+OjpFNJbAlShiIWdpytmSQRTrkLUJ5G+R7gImwRWjBBB6oj1xS0/o0EKLJ04m656PX440W1S9wV164QEVlfAq18PLfJ2uoqV7/+mo/+/d+5cu0WfiLLOV8yND2NHx1SB0don14g2kpphLQQUqJ8HVhEloWQoFXQTlr5wdxR2IBaCNASZNh2WPhKofzAej3oztSBSnW0TdyiNPw0MCJkeANoz3Uot8nc7Cwf/fWv/Nu//YUHD2dQGhLJNFpIHj+eZ2lxlf2mhyUtRkaGyOdSgRUkNIigPpyFJCjU0/4EpEArgRQCy5Khb8lCCKt9JprApUd77ifuaou754QILJKX36FG9oXAV4padYfFuXluXb/O5598zN8//TuPHs+T6Rmkf/Ik9cZ+58yRAK0UyvfRCHwFrg9IG2EncD2N1pBwQFgSX3lorwlKIS2BUAKlQbkaLQTCsrBtO2g3LXA9F4VGComwBLZlY8l4jtIR3yg2x2YE6ceNESHDa4pou4jCaW3luuxsbnDj2jU++fgTFuYXGBwYYHRsnL7KALV6g6vXbvLgwUNyhTID/UN0dXVRyKWCiXfVDFxuwmmHKQg76oeD0btlIUU4d6TdwNskHECGHaNonU/Uf7qu27Z8iELORDAf9RL7z+hMWu0lwPNd1tfX+eqrL/ns449ZmZ/HsSwc20L5Pp7yULodRIAQoDSN/Tq729tUd2vU9ho0XI2WNjKRwsdCSot0Kk0hlyGTsvH2azT297AsiVaa2t4+9fo+vgbLcegqlekqdtH0PFbX1qjWaoGQJRN0FbsodZXIZVJYIvidW9/igJvzhVmRhtcWI0KGN4DAhVarVnnyeJYb16/zeHaWUqmLX/3qQ06dOUNfZZDtnRqeBx9/8hlra+usrKxTq+2Hk+su+/Uq9f06GgdI4QsHpW2k5ZBI2KSSFo4FnufR2N+l0fDQ2gaZQKugq7QtG9uxQhedwm267O/v47kutm2TyWRJZ9I4TqLlHntRTdARkf4UXM+jWq3yeHaWpYUF+nt7ODY6huvDcs1FSIGQolWoVKDxPI/dnR1mHjzg9u27zC+u0vQ0ynLATmIl0yQSaXKZDFOT44yPDlDdWGZ+bhZLSpqeYmlxhfWNTVxfkUimmD5+glOnT1Or17ny9RWezC/SbLqk0mmmpqY5/9ZbjI0Mkk0nEbbVds3By1Vuw2uHESHD60U8QjrWFynls7a2yvXr15mdnSWTTTM5PcmxiXFKpRKOY5PNZDg+PYXGotBVpn+gn1QqiVKK6u42szN3mZmdYWu7zn5D4msLRIp8sUSlv8LUxAg95Sxba4vcv3+XtbUN9hsK19c0Gy4aKBYKlMolHMeh0WiwubHJ5uYmzcY+yWSKkdFRTp48wdDwCLls9gfqTwObSIVuwmQqyeDgALx9npPT0zhYzC2usP5wDqRES0kr5tBzqW1t8eDOHT775DJffnmFze1dktkCStps79Zp+uAk0nR3l/E9l0IuyerCHF989inb21X29l22tnbYb7r4vmK/2eTmrdvcf/AQpMWD+w9ZWVmjWq3heh537z5ke7vKz99/l6nJMfK5bMfP35LuNyVP2PBcPL8IadWOeAmvHEnbbdHm8NV0dALbt19135IXx2E/c/xcvuk8DiOO3OqbzvGoo5k76VnRGlQYPCDRwbSM1mjfY21tmZs3r7O6vkq5p5tMNsuThQWWVjcIIq9tEk6Kn3/wHoMjowyPjlIu5mns7/F4ZoaP/vYffPLp33mysMZuzUP5EstK09c/xPGTp/jtbz/k7MlxHt69z7/8j//J3bsP2KrWqTdcmm4Dx7boKZfo7a2QSmXZqe2xsrLMztY6+3u7oAWnz57lH//r/8avUllS6QxJS6KVev7RvTj8pwqfRblCWitsadPX18svP/wl7v4luktdzN59QDqdQloSX2s8pVGhP25vd5cnMw/55JPLfPTX/2B+YYneSj99lT4QFjs7j5h/PEfDUwyNjHLm7GlqezVqtR0ezz7i+o171F1Nubub4eFBtPJZfbjE7Tu3+fzLrxkaGaevr0JPdx9CrzE7O8vnn33Gbr1GOpOiUukln821ilhEISNCiiCARGg4sI7Rt9//4bV0aLt4j2PSZV8Xnl+EVAMtJD4SFwshwNEKuxW7I2gVPHxqNvXB9Ry/WV6ewStxxFZH79WZ3hd7XR88JxW7qqMch/CGCCehW9vF6eh82omRhsNoQAnwW8vWaCwUaA/tN9jb2WZpYYGlpRUansW+P8f9x8tYlo1QPjaCQj7P5PQJuvv6kLak2aix+Pg+n/z1I/7lX/6NWw9mSRXK9PX1k7Yc3EaTenWTh/fvMDY+RF9vnpXlZe7dvMVXX91huyHIFIqMT/TTU3Sorq3wxf0H+CKPTBXIZBOUu7vZlQ0e3LnHl/t1BsdPMHbiPOW+AWy7XQLnuVun4yAHjyjQWmLbDsVCie7uHoK4P8XykydBpy6CoANfaSwRBJ9vry9z9avP+Pjyp8wsrtPVM8T5997lrXOnyCYSDA9UEP5fuf1glkZjn4bn0fCa+H6D+l6N5aVt7Ew354+d5P33zqK9XRJWk8ePZ7h7b51kvpv3Pvglx0dGWX48i93Y4/Mb17j38A4zC29TazaDHNkoEF9HgZAaIfwwZB6CrirorqI7zGpdNaL1uh/lK4l2iVVxxAq60V9RBthRLWr4YXghIoSw8EWChgwuC4HCVkF2uo5+4gPJadFCZG2izMIwn0Aftovii5e19mkR2z7MHI8sM9Dt8iSiva0+4kG0v44KlRCG9cZFKIycEtFH6TCUOMiKaOdYhJ/VmhuIfa5xNXQQtb8S4IfCLUMBQrngNxHKQ3k+y8vrzC1XyZb6qAwM0l/pI5/J0Njd4saVr7hx/Tpzqxv82vXoL6Z4eP0rPvnbR1y7che73M8vf/df+c+//RV92SQ7q8vcunOP+ZVNnKTEDX/3lLBI22nSpSHOvfsu/+3/+JDhsuYv//xP/NP/82d2Gh7jo5N88MuLvP/OMJtz1/mn//5/c39uh7XNGosbNSbrLtl0gsTz/s7i4BUaZU5FV2jwWpSeJLQf9MgyuAdFuIhfkEAabONIcICd9UVuXv+ah7OPcfKDnLr0AT/79YecOz5KbyHLseEBGrub7GxvoWwbhcbHQwgXW0hSiW76hs7y9sVf8f4vTuLVFpHuJo8fP8Gf2aAyMsqZ8+e5eOwYy7kMjeU55hYesmtrmsLHEwI/DJPXUb5s6CyU2kWoRvCGlUCJFC4OrtKgfGz8IN1YSIS08ZGhCAVh40FNjaiV2u2nkeGcWPvVztobhh+SF+CO85BCIKzA4mnV4m2NYF6HnzbmjjvKU0dMiHSQSxKTS1oCqcPLVXTuHllDbYsuFEDxdDfg0ywwA+3ILQg6IHxAIYVACslerc5Oo066PMjYxBTnzp6mv5Rjc2mO2uYqN+88wL56jd7BEeoDJR4+vM/Mo1n2Xc302DQX3nufDz78BZWMRX1zleHRQZ4sbVDo6afc082ybZOyLXLpLJWJKT78hw/5X/7L78haazy6+im5bJqGXWB4bIp33vuAX/5inIWbgq8/+huzi3tU6002d/fZa3rB5P8LmRg6eMUccUwhg7BwHeTxSN8DRwb5O+FDSoElRKtWxH51i7XVJaq7u/RXClSGxxkan2BguJ+Uk2NaK4YH+8jnMtSEHX6GQAiNJSwSTo5iYYC+/hEGBgZxd5r095boLhfIrbvkS2X6KhWG+is4G2sMdXfRlUtTFxpfaLR8+h2ifA/l1lGei49NU+9TVw7NYDKLhPaQWmFZNolkGjuVwbKDaEelArdulGLWWQT36ffk69Bb/dR4fhHyfVxPU3dhV/gIYZGUOkgsFDHb5xt+3SNzp+Ma8D3p9F6EgvAMx9Ph5gIRWEHEO5LgZtZCdGzXLhYZvPgiA6N+aohDv32QMOokEmQzOZKJJI6GkdFR3v/5B7z/3iWGuguszc+ytbLI0uoGe3t7rCyvUEhoqtVdXM8nWyhSGRykp6+HZCqBED7ZfI7pE9MMjUMiX8J1G9y1LIQQZDJJhob7OH5inN6uPHs7q2gFmUwOleumMjRAZbCPXD6LlDLIgxECz1M0XQ9fRdULfrgLIdAagVbRoImWCEV2U2AYaRAKqTUJx8GxHdCaZrPJ/n6DpuuTclxqe3vU6w08X6FtgZASIcPkXXTbpNeEZY6CEj5Ka7SUCEuGCb9gWwLHsbEtC+G7wVzZEecf3DcS5ftUd3bYWFthdXOX7T3FnnLwkFgobL+B8H0cJ0Gu2EVf/yC9lQrpbAZz8705PLcI7dd22dprslzzWfck2WyeRE+RXD4Z2yq44GmFLLTLegS03VSRJ7fl5RXtbeLWyRHOuvax4oIRO3LHZx24RsWhJzo2gorNW4X/05HwhIIjwnyLp2d8G7vnWYgMyOAqCH83IRHSIp3J0tvbR1e5TH1jj2KxyNDQEENDQwwUszjapae3h0w6Rd33aew38FwPIQSWYyNkkM9jSYklJQKFJS0STgJfSOyEg+c2UX7wWznJBPlCjq5ioXWj+D5IyyadyVLoKpDL50g4CSBI2AzcyKE7WB+YEvwBac3nRy4uTSBMno/wA/FBCNKZFKVymVwuR7Oxz+rSEkuLiwx0pVDpBE8eP2FpeYXa3j5kCzHnlmi5znQrRCL4vyYchNoSLEG0VpGQQT1VITXaa3sXBG23toZAtJB4SrG9scG1K9e4cuMu82u7uFYKO5khaUuku49yG0hp0VXqZvLECU6fPcfo+Bi5bB7HtjoclobXk+cWoSczj3g0v8atuXWW921GJyYoXTpDXyFLMDwKXCmdJvBRl8VB4WjXQQ66osBre/QFdVS4wsHh9LebJsE0rg7Lr0RZFDow6kToNY7+jQ0CW4IoD010Gb4jrZE60fxe8KqQNoWuEuMTE4yNjbG195C93V2q2zu4jSaQRWtouh5N14OEIJlKksvlKHd3UygUeLy+zOb6Klvr67j7TUTaptlwmVtY4snSOnYmTzqRoFqt4ikVJK5aFq0pcBUUM9U66CgdW2JbQdCNUqDCWjiWBFu252h+MKJp1fhF6GuUF5TOCWrBKgK1BBB09/Vy+vRpHs1tcXduh9s3r5NLC3ZXntBlCx7cvsW1azfY2NqhkOkDaYXzvDLwCOCjVXCPB94BiUIGlpBSKOWjw8RTX2s8X+H5PtrXYdHU9rnHewCBQCtFdWeHh/fu89nfv+DJyjbZngEGh0fo7iqgG/vUd3fY3t6hcfc+D2ZmWV5d54NffsipkydI5MPQ79YErLk5X0eeW4T+/vFlbt5/wpf3l1lTOd77heLiyQmCG1eh8cKLKlrFxGnte3iUKGJS0vbhio6VHI+SooMC07Zf4pbM0/aM7yWUCtwEYVa55/vs7+1R293Fcz0cJ0kqmyWZyeE4dpD4F97QwRcKl0A+0u3c/nbGW9dJvDDdLowAACAASURBVC1apS6joA+CUjDFUjfTx09w5swZ5ld3WF1Z5usvvqSUz1EbG2JlfoaZ2cfU6vuUylkq/RUGh4fIJxWjDx7xcGmLtZVlbt+4yeRQH9tdWerb61y/eZvbD2bJd/cxdWyc3d1dmr6Hp3y8sAMPTikQG8/3UF4TpdzW+Wkt8RUoX4EOqnCLl9LnidhVfQAdDaBAyPCe8X3wNclUknwuRy6dJmFZaF+BBb2VCpfefZeVLZet/a9Y2ljl66++ZH1+hhw+y08e8+jRLLV9yEkZlPKRDk4iTTabJ19oksslSThW4JKUNnYiRSqVJZtqkHGcwP1mSbRlIRyHZCpDxlGkkimkkC2LMbB/2pZLkAzcpLa7S3VnF9f16enu4cL580yOjeDt19jZWOf+/Qdcu3GTq1eusVWtUSz3MDY2Tlc+G7RX6L0QsWCno9rP3I+vhucWoX/+f/+Zx0tbzGx6NIvDTJ+p4vqRrzcIvGyHSH77x7UvhPYI9PsQXGjtox2a0o1FsEXRMRCUtRfab7kIarUaN69f58svvmRpaZGenn7Onj/PiTPn6O7pIWV1Vgc+VA/rm2Y7zcDsqQT9hghGsVogsMjlu5iYnObd937G/NoOV2/c5i//9idu37hGT1eeenWTR/fvgmUxPT3B6dPHmZocpdnfxebmFo8WN7j+cJ5/+f0feHDjKqWMjb9fY31zi6aWXHr/5ziOg+047O832anusre3h+95AGhf0Nh3qe7uokWV/cYevnIBge9r9vb3qVZ3qO1Wae7X0b73Un/jp47tRWSxS/B8nGSSgYEBdjzJ0ECFXCoJvgdKk8wXOXH6LE2Rw8r1ceXGbbY216jv75NOOhRLZYrlbbY39gJvgAbHSZLvKjM4OkqtWaR/dICuYhZLSmwnSa5QZmhkjD27zMjwELlsBmlbJDJpunp6GRmfIKM1fb19JBwniuxp/+4RoahGy2FksllGx8a49N67nDs+hWo2qO1sMTgwSMN1WVj6mJmZWZaWloJ9CIy+yL17VPsZXj3PLUKL84ts7boolcFxkkG5kg4/hEZrF43PfqPO7p5Ps+FhKYUUFrZlIxwHTwfhuZl0irQjcJtVPLcehl0KXE+gPI3UioQtSabSYCdwPZ9mo47vuaAVjp3AyeRIpFI4UmAJFZj2IpjV6XD1hLTnH2IebyHwPY+tzQ0+//xz/q//879z6/Ztxscn+S9rmzjpAqlMlmQyHxhB7XlgOiXwKZe6EaBvJrIqhQQdXE+JZIJyb5Kz5y+wvrsPls2d23e5e+sGt7wmjhQU81nOnT3D+++/y6mTUwxVeqBZol5vsLxRY19/xsLyKl99/iW2bpCwNMVSmbHJ40xPTzExcQy5v8PI+BikduirlEingttEYtNV6mZ4bAxdGKDUnSPoQzWJTJbK4BBjE3sM9PdSzCVxrBfZ0R19JHHoj8CeCJ4GRVrzpTKnz52jPHyM3uExerpySHzQGuX7NDxFOpdjYmIcJW02N9aQvkulmMVv7FP1YGnvEZa0cKygNFEuP8y5CxeoDO5T6B6mv7+bhGMj0zn6B0a58I5PpeozPDZFqVTEsm0yXUVGpie5ZAm2EUwemySdStJaM6o16RpzpYeWpm1ZpJwUxWKR7t4+ent70a5LI5uhWt1haHCQcrlE3fVJODaOE+RnKVrr9IWDmiPEzvBKeW4ReufS2zxa3OD+SoNaKhlGzrTf11rRdOvsVLe4dfsRn39xk7knC9hakXaSlEvd5Ird7NQb4Di8995Fjo1UmL1/nUcz96i7PrWGz+Z2jermDrbvUekuM3n8BNlSD8urq8w8eMD2xiqN+h6l7h7OvPMeZy+8TX9PiVzKxpKBke9Daw4nbiMFAhRNnga3sNKa/foeayurPJ6Z4cHDh2xWa3gPH9J/7Trjx08yMDxIoZjHCudfW+lxcW/cEVd7XOiiSszx1SiVUq3X49WEfxqIdn4VAoTVTiKRFlZSMjQ8zM9//gF9lX4eP37M5to6zeY+Scei1FVi9Ng4kydP0dvbTSqZRCYsjk1N8jttMXRsksWVdeq1KsJrkrAFxa4SfUPDnD57loFKhaQ+hfrf/xvbtSZ9I5P0V4oorUkk0ly49DOS5X50psTg5ElKXWmU9qn0D/K7//UfOfnO++QHxhmbmqKYTxMMwjqLdH6PJuHwFdt5YYmWS7j9XAsJlkVXdw/nLrzNZMMjmStQLBZJWBKEz872Dnfv3uPzr67zaG4VLRz6+nrp6SpSzCRYXphnv+niuopkMkU+n6fU1UV/qY9iJkt9D+xUga5SgUTCJmkXGBo5RqrQS9WzyORLlIp5LNsm29XF6NQUqf4Ke1qS7+ohlUyGrvooqCf2PbUKlpUI7wlf+9Tr+2xsbLK2sYVq1KlurPF4dpaVlRWkEPT19lIul7GdoGuL7r+D6xd9k1ve8MPy3CL0m//8n/j82j12vp5hfj8I89Sqfbs1m02Wl5a4fecWf/7rp/ztP75kfXWDYjpBxrbJpHM4qQJLm7tkiiW6St0Us0lu37zF3/72Z9Z2amztueztu6hGE7vZoJBKMDZ5gkJlgOX1DRafzFLf3mBzbRknk+PR4jqecHjnrdMk+8vIhEOYe99aP6bzoovmn9pLMXuuy+bGBo8fz7CysoJt2+QyGUpdZdbXN7hz5y6T01OUurspFjLYhGEU+lku6MgX2G6nKJru4FLRP0VE/JnoTHZGCzKZDJMTE4yMjNB0XXzXQ2s/qAIgbaxEAiuVwnbsIFcEKBaLnH/rHNMnT9P0g8l0qRQWAmnbSMchmU6RtGwyI6P09PXgI5GJDE4iiVaQSGQ4fe4C46fO4iVSiGSapG0jtKant8IvfvVrGj6QymOF773I4IRvuyrEob8kSIdsvkgqk8dHoKQVBK5ZGvBp7DdZXFji+tWr3Lo3QyKVY/rECWgOsSUVs48esrW9S6nczbGJY4wMD9BVLFDuylHM5FC+hRJOEPkmFRJBMpmiUK7QxAbpkBASqTV2JoOTSZDtq9AQwfySI8NwoFaJnnh4QrhIIEHtwOruDvfv3Sf/0ScszT5B7VfZXF3mwYO73L33AN/3GRjop7e3F2lZrXCoTtvnp31vvY48twgNDY/waGGTVGoR9jlQ7kZT26ly//Zd/vrnv/Hp59fY2W0wNDrGsYEeLLfB6soaiysLzCxs0DOk2dtv4Hke9b09VhZXeLyyQV3b9Pb1MzI6jtjbYfHRI77+8gucrh6cdI6erhJjAz3MzVo8mlvm5s1bDI5OMNjXQ393nqRjo2XgH5ZhVFsriqgjGz16+LjNOivLSzy4f4+19TXK5TIjY+Nk0nl26y4zj2a5c+c+/QODZLMjJCwZFWoIoqcsGY7C2rdBRFTCKC44R5Ws/+mJUTRabUd1aILcm7ZzU2LZgoydIJNOH3kUDXhEwShBQIydSGAnLLLhYATioS6d1ckcK00qk0Ih8bGCSC9fYwmbTK5I2pY0hYVLmHujfZxEGsdJgrTwpBOsJhr7jBfzU4ojnrX/boUrdFQn0UGujiNxEPg6KnTqtay73r5+jk1MsF2rsbq2zZPZWXY3t9HaY2d7m2KpzMnRSc6/e4nJY2Pk0hkkDjIRfEOtZbh8tx8U6BIaG4mD03KHCRV4GWwRLJRnBw5BhFLg61YAUyv6NPpOQmBbQbDP7m6V2ZlZhJ1k8fFj1H6V2tY6a6srbGxtkswWcBwHIWUQhRe2exS02hn0FLWXsYFeNc8tQrlCgWQqhSUFBGOtjjpqa8vL3Lp+g6tfXWVzY5ex6bP88oP3OTMxgK7vcOXKFeqfXUEtrqGkQElJVNa92XBxXU1Xbx8X3/2An104S3N9kb/+8X/w6Vc38JTF8dND/PwXP2N8sJsbV76k9m8fsbmzy5O5RVbXNmg0RshmUm1LgyPGQtHEaGiZaN9jf6/G8uICszMz+J7PyZMnGRufoOlqrt+8y8LCEjdv3mFiaoLh4X4y6WQQ3q2iQkXfPPISxPOewi1b0U3tx09nPZXD7aRbv9lRs3hPp721iD3a1q7k6eZJsJ8MPzX6JUWQ5hZGaYpYJx/MwERVNCwQEiv2y7bOVByOzPw2nkW3RPyJPvhqGKkpgudBrlC4xHl4j2WyeY5NTKGEpNxb5vGTRfb2PCxh4/kelf5++iqDTJ84y9jkJAMD/SQdJxZrKkLvQiS50YkE71rEpve0IFpUML51EEmoYm5Y3foaMuaatW2HTDZDuVyip7cHtZ+kmEngWIKm22SrWuXJkyfMzS+ws7NLJpvBEjJIVXpKCx8c9hh+eJ5bhCzbCsOUw9BUoZGRm0m5bKys8mTmMZvr25RKFd6+eIlffPghJ0ZK0NjBthVL6+vcW1hDOpEJHY4ihUU2W2Bi8iQ/e/8XfHDpLNuzd5i/d517M09oprqYmJzk0ruXODZYBm+fa7fuszu/xX7DZXevTqPRDK0zEU3XdNKKzGmPlTzPZWtzk/m5OdZWVijk81y8eInTZ86xsrbJysYOK7fuMzPzmNnZJ5w6dYJsOhkcIZr7PDTIOvxifE4o/lr0+GlZQod7ikhIjp5KPhTv2KIzKy0qjdku/xOPvOz85TuP17KOBEghgsgZrY+oOSaC4IlWJF97LuKgfH4X4vs97dt2HPvQYEUceq1VdBdAWCRSGXr7UiQzaSoDvezs1NivqyCyW/k4CZtSuYee3gEy2TxOwsaSUXt1Wi0t0TtwbiI6N9HZwoGjIGhJGUUPtDwTwbeWYWUSy7IpFLs4ceokv/5Pv2J6Yhy9v4eq15h7/IjLn37GXz/+lHt37zF89Qanzp4nl8+Tz6Zp+0SP+iXagml4Nby49YTCmmtBPE54+/pN9narVDeruE2f3lKZiclJRsdH6S7ZSNdiaLiPocEeisUsrhSocGkIIQSO5ZDPZhkcGGJ0fJy+vj7Uxhy5bLDCo18o0Vup0NPXR1cpT6mrQLFYwFmp0XA99hsNXM9ruQiPtIJaFlDUdUk8t8ny8hKzMzNsbm4xPjHF+fPneeedSzx6PM/dR0+4/eAxK2sbPHw0x8LiCsVCnmw6GSz1HGZ+H86YDy2t2CRsa+JUa6SUWJaFZQUd5EGB+mnxdMs17u49+Kri8Pad491OV1+rYHfHBzxFOqLJ/9ZRoty32PbhwV7mL3e0E+mIV49QMRHW3wsCJYIkYNu2KScdCsUMnquCeR4lUUIjLYGTSJOwE/HDdEjP0z70oGs1/nowzxPUd7Pic6RRsWABRPeEFNiWQzaXYmBwkJOnTnLu5BQ0XIRbZ2S4H2nZzM4t8PnXN7h77wEPHs1Q6e8jk3Igdu4/Da/Cm8Vzi5BuFfaM3Y7RCD60QAQWaIlSEq1EywIQ2kNoFykUUgR+aq2jEiACWzok7SyZbJ5EMo2vNa7bBK1JJhxIpUmlUmG9LhetFY5tY0krWJdGhf5vrdAolLKOmCg+0M1pn1qtysL8HLOzsywvr5DK5Ll/7z6W5TC/vMbS8grbu7s0m9tcv3GLY8fG6S6XODY2gCUE+nBJrKe0Xfu5Upp6vc729jaJRAIpZbAi6E+OsBMiqM+nWnWQA4JBTigfUUMLCLoySZAm2pb7YG+FhR9cb+FAQ2PjCRsVuZR0eOxwwKIkeCJMcVYC2xXYngALmglFU/r4QmFpQUJZ2EoiVGhtS9Wu4C5i3+v7t0jr37iEhp/Q/vtgafaW5R8kakaVQDQeiGCwJ4WNEBIpXAQNUBbBcuYOWihcpdhveGhlBeO16CsFN3rgSmsJYJRqKgEfqUPXnwAlrLZbVQNK4CmF0h6ObuJID8eysZNJEqk0wpIQVl0IKi8olFD4no/rerhNF+F6CNcLokmtYACntKbpujSbTbwwv6uTb3aTG354XoAlFJngOqhbElYbCI5ukclmyOfyONJma32bmZk5VlbW6MuW8XZ3WVlZZnllhWq1ilPIBpOISocrJ0gQ4ToiWiKQQSVlKVsjmiBLO/xbBzdjdBtIES6wp1Urk/zIYaSGYELUx2vus766xuL8Amura6yvb7C1U2Njc5uuUpndhsfCyiYry2soBbeu32Cg0svx6XFGhvqx7cjvrWN3a/QhAa1XwnOyLAvf91hYWOD69euUy+XghgrLnfyUEDERUkIQjZM77ZdQbloFOoGwXIxGtF2iRNdDMMgJBj06fNXGl3ER0i0RCj5b48uwlpkvcDyB5QuUBa6tcS0PRSBCjrKwtERoGeSjiaCiWtsddrQN/qzoA/+22onIkRQN+g5aQvEF4EK7RPlo7aFFEPIuhQ0KpPSwpAtaopWD1hY+Hr7wEdgI7YRLmgSVRIQIcu9EOA8czZdFQhTM84TuTyHwRSRQYXtHoapaIXUDR/jkshn6+geoDA4icNAImp5P0/Vpui51T7GyvMzdO3eh2UA091GNGnNPZvn88895+OgRluMwPDzE8NAgXcViWHbpm6zHjgb7zr+N4fl5fktIOvhaBIUfm3vo5l5YSwqQDj2VCuOTY9y5d5+Z1VW+uHyZjKNZnurF3Vvh66++5NbdR2xu7tKbE1jSRmlo+D5116XpN/BcNyi8qDS+FjR8aLgK6bkorxmMlpB4WtJ0fbxmA+01EMpD6GgiVGBFbpJo4p92NQeBBWjqe3ssLq4wN79Erb5PNl8gkUyjNVR3ayhp0dtTIp1Os7W5xc7mMvduX+fJ7EXOnTmBHVZUbvcHR/mbAxegEIG7wXEc9vb2+Prrr6nVamSz2ZYr7qdnDcU77MjuEQdEKJCbKPNGx95pD0Mg6ACjNaEUUsdG7dIG20FIK6gHp1TYIQZH9cPja8DSYPsCqSRKgmspPOmD0EgNlgoESGoZWhga1TEAERxa7PD7tExsPNNhAUGsgz9K7GRrYKSVQmkfjUJYFkLY4Guk8JDSBy1Cd5zAx0NJFUTCCad970QnIAgFKHJLWq3fQhJUHwEVDCZkVPRXhucvkNLCkhpL+CQsGOjv52cfvE/vwBASCy0cfOGAnURYFvXqHrMPH2A7Do9u30a4dbz9PVZXAtc5QnD27Gnef+8i0xNjlIp5HNle3K4TIzivC88vQnYKkUjjJBzSjiYl3dAMB3DoqfRx8uwJHs/Nsvn5DRYe3OFP1TVu9ecRus7i8hJPFjaoNwDtILUNwkLbDiJhYwtICoUTmve+sPCtBCKRIhG+H9zvNsJOYdkJHEeSsBS2aC94ZQkLm+A2EVqFYarxCglBrbv1jSoPZxd4Mr+CsFOcPneM06dPMzIyQiqTQWvwNaysrHLt2jW++OILtjeXmXl4n4W5OeyxEbLZLFq0p20785KC+SeBQsqgEKZl2dTrde7evcvy8jKJRKIjefWnRfz7RqLS+f7B6mk69k7H/AzRfF/gIo5cbVHXqcMlOQgt7CDKK1j4LZibDPaVGiwdurRE4KZTsl05Wihagx0i8eoQoYPf6/txlAgdNedymLhARdaMJirtIzSBRSMUaBEs06AFCoWWgaQIbdGxMJyIjhx3L3QuvS3CfiCM14BIhEKktIJfQns4lmR6apLB0XHeCWLqwEqSypXpHRplbGIDe3kNyxJsrizTqG6D10R5TTy3Sbm3j+nT5zh19hyX3r3IQE+ZtB3MfckoyrSjPQ62j+FV8dwiJBOZoI7U4ADSSVApB3k5AYJkJsPw+DDvvv8ODV9w9dpDqhtrzPs7OEnJvi8RiSyWDcK3wAfHSVAol6kMD4BO0N2VI20HHYWTzJLv6advcJhULkdXIUvSsbFsh3SuQE+ln+HdPQb7yhTzOZxEMnTpgRUWloxWTY1uSqWDEFPf0ywsrXH77kPml9bI5Lp46/zb/MM//JqJiQmS6RTaV/jKY2lxgXzGZnV5jvmFJe7fucPdu3fJF/Kk0ulghE072DdojVgnEPnndfvG/umEYz8rR3Xc+qnvHN5Hd073IVolpep7e+zsVNlvNkglUxSKBbKZoOBly2qJ3H2he04QdabRSr3tWLP2/+OVEV7wAOJ7H+6AQ6+V+Nt+TccEIvxqQXHR1pdWB4717Seoj/yj/apSPs39PXaqO/iuSyqTY6daJ1pVWVpJSj39nH7rIrmuvqDGn+uDsILlHrRCKx/bssjlcgwMDjF+7BiDw8PkMyms0C0rOkTI3F+vG88tQplcgbHxY/ys6bGzU2VsbJSuYgEArRWNZhPP98gXi0xPTpCw8jR9j3QxiW8pFlfX8O8vsL7hY2EhNOTzeaanj+N5DYSyGRudpFjIYAlBoavEiTPnSGTyJByHyckJCvk8yWSKvsoAb7/zDoNDQ5RKZcZHR8hkskRZ9yJapVMHiXORzz4oleOzvV3l/oNH3L57n62dKqeGR5ianub4iRMMDg4Gh9GA8shlEuxsrXPzxjVWVla5f+8uX3/1Ff0DA5S6y2StzBFJchGBECml8X0Pz3PJ5wucPXuWU6dOkclkOkK0jTC9OGS4BP3s7CzXrl5lcWmRSqWP8+fPMzY2BkKgfL9tgYpAasx09oshuBeC1vR9n8XFeW7cuMH8/AJKR2syBdtalkO5u49UJs/E1PEw2MAPl9OIBnRg2xbJVIpsJkMmmyWVSgWh3X5QiPiHX1PD8F14bhEqFLs4fvwEQ0PD+L5HJp2hEBOh2u4e83NLPLw/w+5OnbGxUYbHxyn05lnfXufvX3zJ7KMVbEuSy2VIJBMUi12UC2cYGa4gtEUmnSeXyyOloKtU5vyFtzlx4mS4+mWGXC6LZdkMDQ2RLxRoNhsknQTZXI5MJt3KYxIENag0GqklQoowMigoL7Syusbc3Dybm1skUymGhoYYHBqkWCy2qscErm+bQj7P0PAQx48f596DRzyZX+LBvfssLS4xOTVFOpXGtp4y9opZPMpXuK5HJpPh0qVL/OM//iPd3d0IIVo15H7aodovkqjdNZ999hnVnR12qjuMjAzzu9/9jg8++AAIOsdWorCMSVBsyuXHKUoH/H36ZX3P4Kie53LlyhUajSbr6xtEQ7Z20JFFJpsjk8sf8B4Ev5HvK6QU2LaNZVlBLldo8ahWJKDAiiJ4zWDuteS5RSiVTpPJZOjp6Wm91ppM14AW7FbrzM7MM/9kiXSmi7WdHbKlDKsbq1y/cYuNtXV6ekqcOnOcoaEKmWyKnJOmu1QgSir0vSBMM51KkctmO84hiiLL5/MUi8VD70FQyaAVTyQgWsMhilDzfYVlWYyOjvLrX3+IbducPXuOkeHhIHrNa1eCCKJ+BN3dPVy8dAktLB7NztFbGaBcLoeicXQ8TniE6EyAQGySySQjIyO89dZblMvl7/lrGJ6Vra0tCsUClmWRzxeYmpri1KlTr/q0fnL4vs/ly5c75kEjoqjXozwB8UK/B+dPdfg+4Syd8SS83jz/nNCBH1iFMf3RxZPJ5uju6aNYKnP71gOuXL9D/eOPEI6k4TZwlaanu58LF87x4S9/xtTUKJZFMCmKB0qhfUHs2myNUuNVpw++1xlVFqTmaR0uHRyOmLQKrDWlNJZlUan085vf/IYPPvg5Ugqy2RyZTCYMofbDfSHy++fzec6/dZ6JqRPs1RtI2yFXKJLJZVuZ3odtmMgXLw7dYAe/i+Hl4fs+XpjIHP1t+OE5aOkfdT8DrXs6+jtK7I62j/c50fbRw3gSXm9eTLIqbWukNRrRgb82lcowPDLG2xcbOHaGvsFHrG1t4qEQUpDNFxgZHefcW29z7tw5Kn1lpND4uCjPAyUQWiKEFV5MbYGJ11aLPtv3/db77Qs8dKgIgRBWh5BEFotlWeRySQqFQuf3U9Exw8wPEYb6CEEikSCZzlAst5tRAV48yvgQ8eitThHyfR/XdVsjvJ9eZNzLJ2pvz/OwLItUKkUikejYxnVd4HAHaXgxxCvGu67bGgzEHxHx/uTg+/H7PuoL4vuYQJ83gxdWtic+AgFCHy44jkNfpZ9crsj09Gl2a3X2my6+CHy0lmOTymQp5Ivk8nkSjt3K5ZBShl12MHcjhGxH9hwgfrHGR0HtizDMF4qKlIYu4kCUnm7uA8EaQ63jtc9Ho1Geh8ZH2gkQAj8UoFZmeevT2/+Ph7Pq2OcZ0fnhKBaLHD9+HCEEJ06coKurC+DwQMrw0ogPGp92/R+0bg7+PnHL6KhgHhPc8/rz3CJ01PID7YsGJAnSGYd0pkB3b+BWUzrMHYg2suQBWVEILZDCii2LqKNgttA1J8Lnhy+yqPZa53m29wlfOfL7dJ5/NAkkWpn2kQhFbrUo/yEo4BqUGmkJYMcnxT6vlTPRvomOqo5gbpyXx+DgIL/5zW84f/485XKZSqXS8Rsc7PwML4eDbXvQenla2x/c5tuqzsfva8PrxYsrYMoR1hACERQiiDYIhalNZ1aHbqUutJco/m6j0W+/0A6/f9QuUbn+Q+FQreeBIkbF/jsWcDgcTPVU4iLU+dmGl0lPTw/5fJ5m8/9n7z2f4zjS/M9PZlW1t3AND5Ag6J0kUmY0mlnd6He3c7+Nvbg3++Z3r/av2934XcRexMXG7pgdaeZWI8ORoxEdQBAkQHjXjfZVeS/KdHWjAUkzosF0fhjNRldlV1WXyW8+Tz75ZB0pJdFoNKjIjuoQ1/x4BDkkuwhR+P2odUeJmLZkjwc/ujuu8++DtEeNHbCA3A10jMwIf0e0icafW1F8n6/5fUctAjX1j8T7HBoFjjuq3pew8K8I/+rOKZq1H/vFYhgGiUSCRCKhg0FeEn+OCHWWOWq5fo6OBz+qJQRHXXhFK9G+ABVymQmFOyGeX1V7c7Pg5uJ6+aMxwvvvlJeO3h7RKVXdjr57v5bmxdMZaakrsVefoywkzfHjRxehAxzI3WHTyrjbCmLwk00GVkVnvf9cjueo7XcW7HZAh7TGvnPz+oF52XR2hGt3qEbzcnjuItRKdAjutMI2bqYqw1upXPERfjZeWh44PxKhrdI+ahDoj023WGu/56p9Eu/273SiK7VXjU63ZzgoobemVddoXi7P3xLyaI3J6TYoGZAtIQAAIABJREFU0K/svZSfqlNovk8X/6vE8zLjND82/kBHf7Bj5xgVLUQazfPlhYiQKzHu/63k/N16TvxBNsqPw+40pZ7fAbbtQ3W8whzV5xV+71x+1Hc1L5p6vU65XKZSqeDnIEwkEsH68IBnLUQazfPjhVlC301nh79G8/xYX1/n1q1brKys0N/fz8WLF0mlUoBO4aPRvEhemAi50iJxE5L6mQ+gFS3nL/MCFoKBoio0+OY5idSBTR69D28UwiHltIgeB1ZWVvjd737H3bt3OXv2LIVCgenpaaBdhLQVpNE8X567CLU/wkZIjERoZThkOyxQdAzo+REqhO+9iaMKavE57hSLRR49esTt27eJxWKUSqVgnZ8vTgcnaDTPnxdiCbVG0nS+Wmvd1Arhzwe38OI5bL+6YjruOI6DbdvU63UajYYeXa/RvCReYJ/QUWNrXuVK/VU+Ns1fQrdkpX5STX80v46Q02ieLzpPvaYncRyHRqNBrVYLps/oRGc212ieP1qEND2JlBLLsohGo5im2ZavzDCMQ/OaaTSaH5dXKERbo3lxZDLulN71ep2ZmRlSqZTOlKDRvAS0CGl6kqGhId59911mZmYYGhpiYGDAm8Jdz2ir0bxItAhpepLBwUGuX79OrVYjEomQSCRoNpuBG0674jSaF4MWIU1PEo/Hicfjwedms0mz2WxN6e7lkdNCpNE8X3RggkaDO8mdH5CglOo63bpGo/nx0ZaQpifxhcZHStkmQhqN5sWgRUjTk/ih2GHBCQ9Q9T9rNJrnixYhTU/jC02nZeSv00Kk0TxftAhpehLbtmk0GkGKHsMw2iLitPhoNC8GLUKanqRYLLK0tMTe3h7JZJKRkRFyudwBEdIRchrN80WLkKYnWVlZ4aOPPmJ+fp7JyUnef/99+vv7dWCCRvOC0SKk6UnW1tb4+OOP+eKLL7h69SoXL14M5hECtBBpNC8IPU5I05PUajW2trZYWVlhe3ubWq12oIwWIo3m+aNFSNOTGIZBLBYjkUgQi8UwzZZTQIuPRvPi0CKk6Un8iDjTNIPIOB+dLUGjeXFoEdL0LFLKQIT8gAR/vFC3Se40Gs2PjxYhTU8Si8UYHBxkfHycwcFBIpHIgem+tTWk0Tx/dHScpicpFAq88847jI+PMzo6Sl9fX9ukdr4I6XFCGs3zRYuQpicZHh7mvffeo1gsEolE2kRISqndcRrNC0KLkKYnicfjjI6O0mw2UUoFKXvC+eJ07jiN5vmjRUjTk/jRcZ2ZtMPrtQhpNM8fLUKanqdTaMKipPuENJrni46O0/Qk4cCD8DKNRvNi0ZaQpqfpjIILR8eBntJBo3neaBHS9CRKKZrNJs1mE2gNXNXuN43mxaJFSNOTFItFnj17xt7eHvF4nEKhQD6fB1qzrPrh2lqUNJrnhxYhTU+yurrKxx9/zOLiIuPj47z99tv09fUhhMC27bbMCVqENJrnhw5M0PQkm5ubfPnll/z+97/nm2++YXd3N0hiqvuDNJoXhxYhTU9Sq9XY3NxkeXmZzc1Nms1m4HrrDFJoR3W8ui0JLVXeS6PRdEW74zQ9ieM41Go1KpUK1Wq1LU2PlAau9ohAVFp/ueKiEMEnx/tbeC+UapVXCgIh05aVRtOJtoQ0PUmnpdMuQhIQYbPGo93mcQWo/aXaih60jzQaTTvaEtL0LGFXW9dBqwKE8uyXQ4yYTolpc8eFtqPRaLqjLSFNTxLOltApRn50nLteK4hG8zzRlpCmJ7Esi3Q6TT6fJ5PJEIlEgNYYIYXCkMYhGtTqDxK0WnJBn5D/SdB1jUajaaFFSNOTZLNZzpw5g5SSmZkZUqkUtm27A1SF55ILT2qnPBHx3loBC6JNXoS3LFxWC5BGczhahDQ9yeDgINevX2d6epp8Pk8+n8dxHEzTxDAMHKUQwg898AIVOsSkm7S0644WH43mu9AipOlJcrkcFy5coFqtYlkWyWQSoDXBXSBCEAiRcIUoHIhwcAlBOWi57DQaTXe0CGl6klgshmVZbVFxfsYEhBfCjQJlu0oiWzE8388mIgjhDvcbaTSadrQIaXoSf2ZVOJimRwXh1Q5KNcFRSAUYkWA8UJuDTtng2K5QCYlCtsYOKTBwjSNtEWk0B9EipOlJwglKwRMgIVppdpQNqglOk0azQaVSZL9qU3cEQgpXVJRCKhvhNBGODUJiRaNY8RQyEgPDRBoGSFeINBrNQbQIaXoS3+rxc8UFYtRWSoFyqFTK3L03z72Hi5QqdcyI5Zo4ThOpbKRjI1QTKQTJbI7B0QkGRifIDQyRSCYwpXbGaTSHoUVI07OEZ1V1HAeEwPDnDxICoVzLqFQqcuPGDf6f//dXbG/vYSXSrivObmCqpitAThMpIDMwwMz5S1x9+6dcuvoGkXgcpV1xGs2haBHS9CS1Wo1isUi1WsUwDBKJBPF4HCVcq8UPcBMoqpUyD+ce8sdPP6VabjIxc5rBgX4yiQRRHAyaVPeLbG+ts7TyjOWNbcrKIJ7Nk8pmyMTSL/fHajSvMFqEND3J7u4uDx48YGNjg2w2y8mTJ0kkEm63kOMANkLYKGWjVJNGo44QBgOjw7z3s7/hzWuvc2KiQNKSWNJmbWWJr7+4wX/98VMer23w1VffUJg6yeT0NON9WoQ0msPQIqTpSdbX1/n888+Zm5sLBqyOj4+7M6s6DlIoN3spCiHAkIJEIsHI2Divv/EG/+1//YAz04Vge/b+BgP5FGvrGyys3mBx8QmPFxfZ2y/p8GyN5gj086HpSba3t7l9+zaffvopd+/epVgstia1w0vVIyVC+oNU3SAFZTep1ars7e1RLDfcAAVVZ3d3l0ajiZAGhmG6mRekgdSzs/5A9NQXvcZfjSXUyuXV/vfBUqG1KvxOmySroGwoG9iB4e96PPxxxZ9ZdWVlhYmJCer1erBOSjcMG+GO+wGBIQTYTYq7WyzMP+SrTJKt1WUSMQNBk83VZW5/8zULT59hRqIMT04xPTlJNp16eT/ymCCCV+f8S+3P4FHSpJ/C48sxE6GD8qI63o/+rvLExd+COHjPC7eU01FWHilE3xf9qLyqtE1qJwyEaA1JFUpgSgNhN9lee8atrz5nc22ZfCaNZRlIAdtbmyw+XmBnr8ToxBSvv/UWVy+eZzCXe2m/6VigwiIUTnbkv4enUO/+/Oin6nhzrEWoUz9oW9v5PW8EfMjsEb4I+blVHFBSoYRCBSLkqo4KKqTOHf1Q14Fvq2mXw8vEn8qhv7+fbDaLaZpBxmzhh8YpwBFIITGkiXBsKsVdlh/Ps7O5TiQSRZomQkqq1RrVeo3RsXHefOcnvP3OO5w+MUU2EdOV5BEIJWj9cwcAC+U3CJwuciTaagF9bo8/x0yEDr/lvvtm/GG36/eXCf0YHEdGRkZ4//33mZ2dZWJigkKhgG3bbv44f/oGRJCGRykQQpJJpzgxNc7oxCTpXB+GaaGExFGCSCTC1PQUV65eYWbmJLlMGsuQOI5yXXwv+0e/sugz08scexH6frevbznJwLppm/NFtBXr+LNzxpgfvvfu39MP3stkcnKS/v5+arUapmm6Y4S8WVWFEEj8PiEDhaBh2ximQWFwmJ/+7D3efe9nTJ2YIRKN4QhwHIFhSGKxGIlEnEgk4hnKnk2tZNsMrpqDKNxpm1SX86TP3F8vx0yE2vmhN2a7TzkkBG0b6gxtCBwF+kH4KyIajRKNRtuWNZtN9w8BjlKuEPkvBcI0iKeSDA2PMnPqFCdPzBy6/SZgNx1AIaWh757DCLm0VeBqa7UKBa0+Ic1fJ8dahFy63Z5/qeVyUKzaO0x1hXLcUeFZUz0Mwwil8nFc7VHCs6AFjlLUGzblSo294j7lao1oLIoAbMCxHVC49rZyq1QpJYZ2xR1Ju+tbn6le41iJ0MGwBLyU+3SxZg6jPQanLfAzyLff7p9rd54dHQKhOT44jtOWyBQ6xEkIVDA1g/CmZ3DFyHbAVgrHcR28tm0jUAiFN86IYKrwVuSLvl868Z3jqu2Z6zxPKvQktj9/+qwef46VCLVQHS8Regc3zA1vkCEcNgKhdfM6QbnWYCER+t//huO9Sw679bWtdHyQHdmtHccJQrXduYbc+0EaFvFkilyun0w2RyyewLQshHAHsirHAeUGH0jpRngBCKFc6VIydC9q/nyctk+hmLofdS+dFrLm+XIsRchNu6/apEV54w2UY1OuVKlUKjRttwUqpYFhmpjRKFY0imGY7veV3wbztqNE0DIL7SwI1xahfQVjSERQLHRsgGi5YIJFOj/FK4Mfiu1fL1+AwtaRUq41FIsnmDpxgquvv05f/wAjI6MkEolAxKQUCCWRQiGFG0WHclDKcUNg9IU/HAHhARHBQu/df9bdsRFuY7O1VoZafS1L1r+uYes22HLn1B1dxOaw9Ud953v9VC1sXTl+IqQI/O0Anv/D/SwltVqFx48e8ejRAnulMkoporEE2Xye4dExhsdGSKXSNG13QjJDgutkAd8V4M9r5qC8tCwOBg5Suq1dr7PAvSllaxCroiU4vq3lz5PmFxBCaHPpFaLTDXdwvSSTyfLWW28zOjpOLB5nYmqKvr48hiGDbUhDIpTjWT/Bt//MsWS9xmEDItrDEoJnXnmCJNxGplLuq/W8tV/LThHylyml2qzhznX+er+M4zjBstZ4Mtq+IzrEsPNvLUQHOTYiFFTwSoUqcU8tcLCbDUp7Rebm5/n0k8+4fecu++UqCEkkFieVyXLqzBmuXrvGiemTxCMmlvQcLsLxsrP4ub7c6ZmV7bWMHQchbDepJRKB7Az0Dg5ShP/2vHaBEHkTy6jDnjnNC6NcLrO5uUmpVCISiZDP50mlUgcqFyEEqVSKK5cvc/HiRdfC9fLJdZYTQnruN+Wtfxm/7Hih/Icm8Cgc4l5re2h8q0iAkNi2Q7Vap1ar4zh2MN4rGo0Si8UwTfNA5R8Wmm4Wk++WbbeMW3NP+cIUXueXDVvY4e1qAerOsRGhlgXkVu4isC7c7uLq/j7ffPUlv/n1b7lx40/s7JWIJVLEEklqjSY7eyVu33vA7n4Nhcn0xAi5VBxwUKqJcgTSdPsBfGNHKonv9pPStYRamZUF0hcdv0tKeV4B/2bz37xCLded79LTvCwWFhb49a9/zfz8PNPT07z//vtcunSpa0UhhMAwDK+fyMWhs4ciKE1nj6PmcFRba8z3RITd4f4aN5mWG/Lu98u64/6q1SrrG5usr62zt7dHtVolFosxNDTE8PAwuVyOSCTSmrzQo7NPMDzle+fMu375bkIUHH1HoyQscp2NG02L4yNCPsK/2K4VpBwbu15lY22VP336GX/48CNK+2VOnj7DxNQUqUyOtY0tbnzxFY/mF8j332J8fIrBvhx9mSRCun1DzWYDp9HEUXUQFkgDIdy8YKZpYAiFshvYjSZKGSjhAKbrrfPcA4YhcQfcu1FTrvnuipBfiRmGaBlzWoheGisrK3z00Uf86U9/4tq1a1y4cCFws7gVVaivUYQDVo4SIJ+DUVyaHwMvOMh7qGy7wc5OkflHT7h//yELjxbY2dmhVqsRj8cZGRnh9OnTzM7OMjIyQiwWC4QgyJgeEolO6ygQGc+VITzrVjkKp6MV6UZCijYL2Xff+dsPW0qaFsdHhIQfDUMr8k0p7GaD3Z0dni4+Zn7uIeX9fc6ePcv/9r//d6ZOnCSaSLL0bI1INM6dew+RQrC/X6HRaKKUotls0qjus7e3S6lUpVoDYUQwrSjxeIJkPEYmFQfDYb+0x87eDnYTFFGUMmg0bRzl5iKLx2NYlolt21T84IhmE9M0SKVSZDNZUumk57bBdc9pXgqO49BsNqlWq9Tr9bbWr1tZuOUCS9cLs/Z7Jw4GEfsFBSJwE4c7//S17kZnnCsQOlW+OPjWCZ4720Gg2C+VuHf3Lv/ff33K11/dYm19HWhZOLdv3+bhw4e89dZbXL9+ncnJSWKxOI5jHwhQgO4uusDdFqz3XK+0Gpu+Z0QBRsg68i0nf9t+Ng7DMLQQhTg+InQItt1ka3OThfl5tjY3SKcSjI+PMTxcIJ1JgzTJZrOcPnOGZLaPVDbP8PAQpmlSrVUpFTdYXnzE/Nwcq2tb7O/bCCOKFYnTl+tjfHyU0zNTpJMmS0/neDj3kEqlQb1pUK3ZVGt1lIJEMkFfXx+pZIJqtcbGxiZ7e3vUajUsy2RiYoJz584xPTVFMpno+luklG0uH83zw7IsYrEY8XicWCxGJBIJ1kkpglavS0tEgojHI7cudEj298QwjNCcTYcTiBAChKJRr7G6+oyvv/6azz77jCdPlkmnM0xOTJDL59ne3ubRo0d8/fXXAOTzeQYHB0kkEoDEtm03ejHwZLQiJn2B8i0XpRSO7WA7duBul0IGBq9t28H3bTvUgOnYng797s6xEKGgpeQ2P8BrCYHCsW12drZZevqE8n4JwzTY2Njg888/x4onsR1o2Ip60yGX62d6ZpbJyXEs02BjY525B7f54sZn3LnzLaVSFWnEMYwYti2JReNMTkxQr5SZGO/j4b37fPrpH9nYLLJfh4YtME0LQ0qazQaxeJxcLo/ddCgWizQbDYrFXcqVfaZPnMR2IJ5IMmYNA4eHh2qeP52t4G4d1xCq+PDfJeEl+mr9ZSg/FNUbY6FE5zkNL2gllt0r7rLwaJ779++yvb3N4NAQr732OlevXGF4uMDS0hKffPIpc3MPqdfrFItFGt6cUbZts7e3x95ekWq1SqPRwHHcYIZ0Ok02lyMej+PYNrWq69Go1upUazWazSZKOViWSTweIxFPAIJypUKlUvEGLYNpmqRSKTKZDPF4PHDHaxE6yLEQIQi8wQilkL4IKQdH2ZQr+2xubbG7t0epXGfvzl0eLDwBaWA7CiFNzEiME7PnyA2MAAaNeoOnjx/zycef8PHHf2B9a4vh4QlmpidIxtJsrO3w5MkyW5tbJJMRBKfYWFtlcX6e+cVVyrZF/+AwZ86cJmpJbt26yaOFRRLJPENDw4wMFxgaGkLZNRYe3We3uMfgyBjD4xPk83kcxxtVH3LTNBoNqt5NL6UMOlGllG0RPt3CQ23bDlpk0D4/zmH42/X9493w3Va+f/vAdQm1Ilv9Xt2tOf84m81m4Jr4rocyfIz+frpt0z++w0KtfSzLQilFuVymVqvRaDSo1+tUKhUajQZKKer1Gm6Fp7xoSYFSDlIaSMPCME2EbP3GcBiC47WaHbvhZlNQnUJ2EP/cdYvi8nEcJ/id4b6Gw7ZnmmbXSs//nn9dw/dMJ35Z0zS/89jC2/o+LX4/I0W1UqFer3uWSXuknFcyEB5XjNyVW5vrPLx/j6WnT4nF4pw/f4G33nqb06fP0N+XY2CgH9M0mZgYJx6PMzxcQBoS22mwX95ncXGJe/fus7z8lFJpD8exMQyTqekTXLp8icnJSZr1GktPFlleWma3WGZje4/dvV3sZp1UPMLAQD8nT8yQymRYfLrEQ687AMchk8kwMzPDuXMXGBkdIWlZ4R8fhJ63n6XeFKhjJULBmAEvIg7VRDlNmnaDSq3K1m6Jrb0yZjRJvxknn88QsSzK5X1Wlx6zt1cmmugnnxtkMGsxf/ceN7/6ivmFx+SHR7ny5jv87J13SceSrC6tcfP2t2xsbZHJZTCjUXdflQq1SoNEfoizFy7z/s/fAXufzfXH3Pxml0o9wsT0AFeuXuPsqXHm7n7J2rM5nmzusrC2xvL2DqfqDSzvBpTSrYCq1Sp37tzhV7/6FZlMBsMwggcznU4zMjLC8PAw2WyWWCx2oMOzWCyyvLzMs2fP2NvbayXjDBF2MwAUCgXOnTtHoVBoneeOvpFHjx7x4MED9vb2gu+FKxh/WTabZWJigsnJSbLZ7IF9O47D7u4ujx8/ZmFhgXK53N752+U4AWKxGIVCgcnJSYaGXDdq53YrlQpPnz5lYWGBvb29I+8jP0rqiy++YGlpif39fZaXl/njH/9IpVJBCEG9XnP7HUKNBNtuEosnOD17mpMzM0TjnkvV8UTYGy+2ubXF/fv3WX32zGthH4yi8s+z/1tzuRynTp1icnISK1xZhdjY2ODevXusrq56rfH2MS7+9lKpFKOjo0xMTNDX14dhGG2NGf9eWVpaYnFxkd3d3eA6dIq34zhYlsX4+DgnT54kn88H5z98n5TLZZ48ecLTp0/Z2dlpc091I+ymejj3kIX5R1QrFXzLU7WedA/pDUz1xwk5bG+ssfDoIVtbG8RTQyAslpbX2dosYhg2jmpgNx3GxyYYHh5mfGwEy4LtnTXm5p7y2Se3+PLLr1lbfwKqjiGg6djcvX+PJ0tLXLt2jXwmyeLcPW59c4vHTzd4vLJHqVYlGRP0JQzS8RgLU/Ok+wd49GSJ+cdzYNew6zUiZpTFxfPYjkksniIRT+BfLr9BDV5CqKDr0I346zVeeRE60HEpcMOkRROcJqgmAreyLparlOoOJ6YneffnP+fyxXP0ZxI8XZjnw9/8irtzz3hwb47hwXEmCzGePppjbeUZDQfGTp7hjZ/+nDdef404kup0iQsXzrBfq5PJJFHS5tmDL5FOk2QszYnZS7z97s94463L7K49ZHwky/BgPzI5zcnZK1y+fI0z0zlEZYnhgSTLpRI7dpOdZpO6sjGV41p1wh3PUCqV+O1vf8uXX36JZVlIKQMRGhsb46233uK9997j/Pnz7jQBIavItm22trb405/+xIcffsi9e/eC6arDlZ1f0fiV2FtvvcU//uM/Mjw8HJQNl7dtmxs3bvDP//zPPH78uOt4B7+Cm52d5YMPPnADMLqIkG3bPHv2jN/85jf827/9G1tbW11FqDOSKJvNcuXKFf7u7/6Ovr6+YPK54P5QilKpxBdffMG//uu/8vDhwzbLrrNi9ZOU7uzssL6+TqVSYW5ujn/5l3/hP/7jP4KK2t1/q1O52bDp6+vjf/xf/4OR0TFi8YQbnem57SSuZfRkcZH/+3/+Tz779FMqlcp3ipBhGMzOzvIP//APjI6OHipCCwsL/NM//ROff/45jUYDaA8x9q/D5OQkv/jFL/jggw/aGjN+Wdu2WVpa4sMPP+S3v/0tjx49CqywTmu32WySTCZ5//33+fu//3sSiUQgQo7jBBbv3t4eX375Jb/+9a/59ttvqdVqXX9zcH2Dd0GptM/a+iqVasVdL0NZLPAaAcrNSCH8mETHZn9vh7WVZba2NjHLBuXqLb744i7FvR1qtR3icUlhaJjLF14jHk0yNTFOo1FmcWmBj37/OR9+eIulJyvk8pKxkRypRJTd3R3m5h4yt/CUza1drl8+R2lzicWHd7nx9QJPtyFbKHDqRD9CVlhaeMTDOw9woimqQpJIRxkZTFPeqbH8dJHt7X1iiX5GxqYoFApE3BEfra4FFI5yPM+Olz9PHBh9+FfPKy9Ch6MAG4lNxDCIRWPYjsARJidOn+ODX/53rr92mYF0lEf3brG/vcr6Vpnd7V0WHy8RVyl2t7do1GskkhlGJk8wNXuGgjcdcyaXYWhiNNhbsbZPNBYhYhikEklGRyc5cfIUwyND2JVFcpkogwN9GJlxhkdPMjw8wUCfSS4dJ5uKEk1EsU2ThpDYwaBbNwODaZrUarXAkglXGI7jsL29TaFQ4NKlS4GF0+nyaDabbG1t8eDBA7755psDIgS0iZAQgkKhQKlUaovg8StN1yKos7q6yrfffsuDBw/axkuE9+sfx9WrV4P9Hrhanlg8efKE27dvs7a2FrihwvjC5LvrcrkcyWSSra2tNhdjOD2LL8L379/n5s2bbW6ow1xzvthJKalUKiwsLLS5B1th2nguugajo6NsbGwGfn9/O62B/IrdnR3mHj7k5s2b7O/vt1XWYfzf4ru5dnZ2jnQjFotFHjx4wFdffRXcA+Ht+tZHrVbj0qVL1Gq1tu3517XZbLK3t8fi4iJ37tzh/v37SCmxLKstbZF//dPpNNPT0+zu7h7qums0GmxtbTE3N8fXX39NtVo9YLGGzzt4to1wrRvbcYjELHeIQ8gScrxheRKv9g71xNmNBtXyPnu7e9S2Fc9Wy2TTeXLZBIlklv39TebmHlIuNjBljL6+LJk+k6+++YL//PB33Lm1TV/fIBcvnuPKpRPk0jF2dve4eW+Ota0S6WwOy5Bg19nf22Zna5dUdobX33yP1y+PIfYWuVn+mD89vEVRWYyfu8jr169zemqApbl77G7tsrK6xqNHi6ytb1OrO0TMkOXqnw8c3BzsEld2tSX0yiPa/nPzwiUTKfr7+0mmUhSbFRKJBJlMBtN0XRGGaZJOZ8ik09T3DRQ2pmUQi8eIRaOU62Dbikqlxj4QaTSwFGBZQUdpcX+fhu0gDANh+E0ahW03sZtNN4llaJyAUl5F4yiEcFN/GEK6c9Q4wstF52LbNtFolKkpt8VkWRZCCBqNBrZtUygUAneIvy5stRiGQSKRYGxsjCtXrpBIJI7sH1JKYRgGV65cIZvNBhV+uLyUkkajQaFQ4Nq1a4yMjHQVoXq9HrTmp6amSCaT3a+bcDMPzMzM8M4777C2tkYkEulaQfvWiFKKZDLJuXPn6Ovr6+reEcKd0XRsbIw33niDXC53ZAewv3x3d5e1tTVKpRLpdJpCoUA+nw+EuLNvqV6vB26u4JiFO7DZn43acRwSiQTnzp2jXq9TrVaDc91JOFHqqVOnGB4ePjIyMpfLBY2Q9iSrrcYDwPT0NCdOnCCRSLRZy+H+skQiweTkJG+88Ubgig1PY+GnqqlWqySTSWZnZ8lkModaN9FolNHRUS5fvkwkEqFarbZZ692QCExpuO7QZ8vslfYwpCCc5kiFb1u/XwhASgzTxJAGjVqdulNjYHCYn//sPd5//ycMj6T49tsv+fV//I75hyt8c/NbxqfGGBlPc+vWt9y7dw+lBjh79gw//em7vHb5JOlkhEbT5o2fvEe5KcgkUqiSS273AAAgAElEQVTiJre2F0EpUukUp6+/zv/xf/49F88Msjn3BdX1dRYfrxAlypXXXue//e0vmS4kuRk3eXBvnu3dpzQaDcqVKvV6AxWNIvy8uIekKgrnC+8VXnkRarsYLX8cfhisYZhk83kmJiYZLhR4tjXPs6Ul5uYekk1G6EvFWFlZZXVtnVKphGFEyWaT9A/0Q6NANpNh7ckazxafMP9wjrF8hqTdoF7aZ31rh+39CpFEnGazyubWLvWmA9LtWPSDARxHBYNW3ZfbZ6UcsB0H22tUS1TI/+sev6MU9XqdgYEBrl27xvXr10mlUkGrtdlskkqlGB8fZ3R0NOjTCLf0/Qp+dnYWy7J47bXX2jr+O91s4FY6Y2NjDA0NBdsJTrNnXRiGwZkzZ5BSUiwWu/YJNZtNpJT09/dz8uRJ0ul01+sopWRwcJBr167R19dHsVgMBLUbvhBEo1GGhoaYnJxsG7EeJhqNMjMzwy9/+Uu2trba3HGd2/fP361bt/joo49YXFxkZGSEn/3sZ5w/fz7oZO/Etm1yuRxnz54NrIbg/OIFIzgOQ0ND/M3f/A1nz54N3GbdAjDC18M/d0eJ0MjICB988AHnz59vE4vwtsAVq4mJCbLZbHDtw6IupWRgYIDXXnuN/v5+dnd32/oXw+es0WgQjUaZnJxkeHg4COoIl1FKEYvFmJmZQQjB1atXvbFxhwcyQEuEHi8u8vvf/547d2973b2ha+uFQCvlR3C3nnszEiUaiyENg0Q0zqlTM7z707f5xS9+Tj6XoDCUZmlxhaUn22xsbrC0vIy0+ni2vMrebpHC4BTTUxOcPHmC6elpYjEThGSSKArXHllaANOycIBYPMrU9BiXr57l1Hichcoy/QMDpDJphIgzMTnJ6bNnGMtZrC08IJPNYkXWPM9Dw3OBR9vzCrZF/vUur7wI+bSP1GiFzEozQr5/gBOnTnH67Bnmljd4/HiBP3z4IaWtdYb60qw8nuf27Tvs7uwwefokMyfGmZwcJhdvMD8/ycLyBk/m57nxx0+x6jUyhmJvc5P5x0/Z2NtnaHySocEsu8UydVuhhEBIvNT9hjtzpmEhpEQKx03xYyiEFK3ORgVSuR2RUoi2sRGNRoNYLMaZM2f4+c9/Tn9/P4ZhBBFHhmEE41n8PoPO1m0sFgs67/1oo3DyxbZz6VU40Wj0UMvF75Senp6mUCi0opcOwTRNEomENw7jIFJKcrkc58+fZ3p6us2N123fYXeVO2V2Imitd2JZFmNjY/T19QXbDb/CRKNRlFJEIhFu3rzJ06dPyefzXL16lffeew+lFI1Go2sEomVZJBKJQITCIuBX8gMDA6RSKWq1WlfR7oZlWUHeusPo7+/nzTffpFqtHhn5aBgGkUiEWCzWdu19ITIMg3w+TzweZ2pqKogI7Py9/u/xpz5PJpNt5z8c5BKJRBgfH2dgYKBNeI/uF3KnUP/m5k0ePHjAvQf3sIPr7oshrUabP0DdC5OPJ5Lk+wbIZNIoM83o6DCDgwNYnssrGo2RyWRJJpPUajbVaoVmo0nEipBMJIlFI0jhDvFoNm1wDBzVpOo42NJCIqg3GjRsB0cphIRoRBCPSSzh2zGuOkrDIBIxiViWF8lpYEgTIdwck47qHlnqnY2OV9jt2BscOxEKhEi5N6M0TFLpLOOTU1y+epXHK1s8ebbOg3t32d1cI5OMUNndZvnZCplMhnPnZjl3boaJoTTlFJw/f47HKxs8Wtnhztdfs7++SsJQVIt7rG3t4ZgRYtk8I8N9xJJpIokk9WoEyzKIWBLTMJBmhGg0QTyRwIiZRC2wTIFhGm6LLR53XX8Rk6hlYpp+xuXWg29Ig3QqzfDwMIVCIegXCUcadbZUw++RSATLsshms4ElAwRCFI4462YhtZ3rUAvaH+twmGXh0y1ooXOblmWRy+XIef1uh23H7wsDt1INV/bdLDvTNN3xHd5vD3/vsOMZGhoKxm/E43EGBwcZHx9HKUWtVusqYJ0RZN0sTL/C7jzXRwnMUeLu0zkdebcwaP94wtFw/jH45aWURCIRIpFIEEDSaVl3uuXCv69zf47jBOc/k8kE6/z+viMFWMGzlRUSqRTSMNzwdm9uJncbuHkclb/I77KXpDM5xsYnGBoaYmtPUa1U2NvdZWd3l0hEUSyW2C+XqdfrCGF4jaQkI8OjDA48plGvsrG+yubGOjvbeZr1GE27yXapQrluEzEj7G9tU6s3goABQyosAwzvtzc9L4j06gFDSvcIhXffeVayn6Mr7FFsd8f1luh0cmxECMLdkv78QRIhTayoxcDgEG++9RbKiHPr2/usb6xj12uUivtETJOZU7NMTJ3krbdf59TJCTIxQTYlufra61Qck/77j9kt1dgvFmlig7LJ9eXJDw1z9uwsJ6bHSYkype1t9qsW4+PDpJJRhIBYNMHw6DhnztUx4mOMjOSJxdwIt0w2x4mZE5QTWfLT0wz25YhGTKg1D1Ro0N6C9B/ioyr4zu+FK5xwxXNYf0q38T9B57FXCR3Wou32nb8Uv/JqzdXTLkA+fkUZDm7wf4//ve86Jtu2aTQabVaZL2phwucxLDydlXW33GDP69wddj3Dx3nY+vDv6SQ8BqnbpH/hwI1wH+FhFvfRPwKk6GgsqLCfowvKdZb1Dwwye+YM0/cW2L45x9zcA/74x4+p14oUChkezt3j9p1vKZaKjI9NMTIyzMTEBI5T58njDW7eXODe3dt8WkiwX9wknYpTrVdZePqM7d2SK1bZBKX9CrYfpKIclK28FD4CWznYThOlbIQ3l5QrzN6Mu944MdVVgDQ+x0aEBAQZE5RSOAikMLy2kSSWjHDu3DnygyPMzJ5hcXGR8v4eOE3iUZNsMsno2DjjJ07Rl09jiSZE4NTsaRLZQU6eWWd5bZPKfokINpZlkMjk6B8eYWrmFNlMgr6YIhmNUrcj9BcmyGaS4CiSyQynz5wlkSkgY0MMj06QTEaQBgwUCly99jqDpTqR/ikmx0aIRSPUaxV3mmh/gB/tghQWgm4t7nCLtXO5/71uAQmHVV7h74bdM+FK60USrsw7jytcwXZadZ19ZYfhW40DAwPkcrm20Gh/bM1hlmLncRxm7XQe04uk23nq9jccbmF2lul2r3Xrf/s+ll14u+ExGG3Odq+fVdBy4bnRCoJsrp9Ts2e4cHGJ5dUiy8+2+erLL9jd3iCVtlhdW+bx46ckkynOnJkNAmey2TTLy9usrhZZX1vnTzdusLbyhFQyRrlSYX5xkf1yncuXX+PKhdPYjsCKxUgkHCKmAY7jOswM050qIh7DjphYpuGme8KzNqMRYjHXejVNs4tvEa1FHsdGhKDligtmqhReWKMQSGkSNxOcmEyTy+Y5OT1JtVoGZROxTFLxGKlMhmg8hWlIhCMQJvRFE6TyQxTGT7C5u0etWsZCYZgmsUSSRDZLMpPBEJCQJ+jP5VFYWLEk0XgU0zBIpzOcPHWa4XEbrDTRWIZUxMIUNn1DBc6nIow7EifaRyaRJWGZNEoCh5brxG8xdf3dR1QgR1VwnZbDd5XpXN4peN+H71Ph/pBKqtu2O12T3+Ui7LaNsbExfvnLX3Lp0iXGx8cZGxs7dF+dyw9zb3Yr+zLO21ENje/adjfxCW8jfF6OsoCOumfCVo/r1WgPRvBX+7EIrjCFHPJCYMUSjE1M8s5P3sUhztff3Gdzc4f19TXW1us07TrDhRFmT53lJz95h9NnZhkaypPP53n77SqlYp1vvrlFrVZidXWVnYhJ025iGQZTkxOcOnWS0dFRtiMOo+MTWIky+XwagY2twIpEyfUPMDYxTsOMk0mnMLzflkym3AHWUxVGRgqk00kMw+/v8X54j7vgwhwLEQpfLrdFZHh3qiKYM9ubMA4gk06RTMRQyvUvSwFS4gUDmLgzqUqEshBCErNMjEiCdDYDynaj2ITEkRKkETwIqVSWdDwJGO4GpXAnxDOTRCNRckrgyAhgYQAGNpFojmgqQUYYNGUCS1pYKhTZ5P2uw1qthy37rn6Gw7ZzVJmjBOnH5Idu7/sI7/c5H2EmJycpFAo0m00Mw2jrb/mh2/LpNkvnj8lfet6+T7mjzvX3uVd+0L49TQnyxYV0xt2GJz6i4wvCHSKRSme4ePESmWyBEydOMz+3wM7uFuVqiXg8ykhhgrNnz3NqdpbBwX6iUYtoNMH58+cRmIyPj7KyskStUkYIhWFKBgeHODk7y8yp00QjJqvLaRy7yfZuhRPTY1iGwnYUiWSSiekTvFZrYMso42MjnjsO8n39nL9wgVS+QHZghKGhfkzTTf0kgt/h/UDlvcLq22McCxGCDj+xLzwH5mxxWxiGBEN2/2mu1e+pkhfcgDSwpPCko+WW8eeNsb2tm4aFNKy2bbmWGSAtDCQKo9XdqECIKCbuuqa3B+/paj+uP9M60Px5+PnQNK8K7rxebt6AwywGX6G8ySZlhGQ6xvRklGQizcT4OMW9PaqNMtFohHxuiKHBYTLZtOdidR/7bDbL2TOz9Pdl2NraolarguNgmpJ8vo+hkWGy+T5sZRONSpLJBNVqg0RukFhEohyHVCrNiZmT5Pv7UUaU7OAwpnTduPm+Pi5dusTUTB0znibf149hyEM9HS01Dn3sIY7VUygOfPohV0uFcjaBCEZhy/BC/IFkDgovvgzZWtwqp0AIf8ipP9rZd6l1Nu0kyttjj91fGs0Po/sYzhAtEQIHx3bn6xoa7Kcv3+cOHldumLhhxDAMC6Sb+w9cIRJANpsilYwyMT6KG3fgekwMw8SMGmAYCAzy+QGy6aQ7bEBYYJpIlDtkYmSUoeFhlIyAGXUtYeWQSqZJTKVoKoktLRAGhvR/nP8bND7HSIT8u9Ot2MPtJQhLUucd3JqIzPHERaBQnkkvlG8R+cUVinD/jDe9N37HaPvxiOChCBvaKnDheQGdnZ6Grkeq0fQ6/tN96Erv2W81IgWGFBjSJBo13IHDyssqIVx3u9uc9OoP5Y7TMyMGWBKlYqDc59f1hjkgFE28SENTIC3cGZyRNJXEESANE9MyXI8aBjbuGCpDSUxpIYSBLUy3PK5rXggbL6yXXkzPcxjHSIS6071tERYsd63vWgtLC2FhEaGvhjUJJyQg4UKdcf6+CLVLYzgdoW7/aDR/Ge5T5zUgPaFQ0m8cuqHQ7vQbXkSaX0YFg428rdjeNkyUCFlXymtcChFaLnHzVLpjhVr7dp9wBUGItlQSGVQPbmUipZshouVO0c3PMMdEhNovnOKgDHhBvK4IqFa8p2otPbAl6S1vudq8MQB+vyG+jxrPYlLeSgWiLbGVV6rdPmt9EqFj8vuuNBrN0RxsYrY9U4RFxu9XdZ8xISXKf1aDJqj0nnWFcjzrSBkt77lSCMfzlxiglPS0xN+XQuDnWfSHLoT9MiJociqlUCLUGPYqmcNjYHuXYyJCHv54EeHPq3pYmdZacYgAKcAJxQe0WSkKN6qgzXYKl+q0gjq/rNqFT3mbC0RIo9HA92mOeZV6ZyBP0MJUbpJgBQhfNNwpEtzMBW75YHJCG1yXmz9V98EjUAocBxzRqkPczThuxK0gGLfkW0L+wFQZkhmB329Ma9Aqqr3KCKqUlmem12qI4yVCIVqxcN04eGOF42o6HWuH6cLRt4N2sh1nSqUSm5ublMtlEokEAwMDh+bR07xoDn+22v0IbiCAu0J4OX5aBVyhUK4Y+eWFa9kIIb3KoNWX64qS9IYeeiInfeebQVgmpD9UBIVQvqcjdJRCIGWrsdxy57sT9Ilgv+GaqTfrkmMiQiL01pIG2VFCeBe/tUZ0lD/YBPHvO7xoNhF074i2Mm3LhL+fg/tofQ6FIYhOQevNm+1V4tGjR/z7v/878/PznDp1ir/927/lwoULABw2cFPz4yNEezUdbiq23FidxoNXmQtwowYIXGRuAYX0lwl/Ej13N47/ZIqIJ1BG63tKgHBTZRl+hgYBEj8zi4khcEVESGSoGWzIQOYQ/vELMIRwRQ8ZCJkbcevn5GvVMqLL0I1e4JiIEISvztE2iOgo0YpMU0d8Kwi2CUrIjlZXePPhfXTbUJfjFe3LNC+X9fV1PvnkE27cuMGbb77JG2+88bIPSQO0P7+Hl3DfZaglGmpUhgt3uEuk4Zk3QSBCeKX7X0cTEj8p6cHte/kNQ23S1rpQvSNCwtSx7eAH9KgAwbESIfh+V6mzzEHxOrS4aP3RVejEgT+O3HeP3lPHAj9btz9dxlHTI2ieN53W0NGE/BPfzYHnu2NB1wf86D10W35wWbd655Cw7B6vKHSwuqYnCWfr/j6ZrjUviu8nRJq/HvTTp+lZwslIdf+PRvNy0CKk0Wg0mpeGFiFNT+LPCur3B+kEshrNy0GLkKZnCc8DpN1xGs3L4ZhFx2k0Pw6GYRCJREgkEkSj0TYR8i0j3V+k0Tx/tAhpepJMJsOpU6ewbZuZmRlSqVQwzbXjOIEQGYahRUijeY5oEdL0JKOjo/ziF7/g0qVL5PN5hoaG2sYKaeHRaF4MWoQ0PcnAwADXrl2jVqshhCAajQYi5AuQFiKN5vmjRUjTk5imSSqVIpVKBe438LIde5Fyfp+QRqN5fmgR0vQ8UspAfMKiowVIo3n+aBHS9CzhsUHhzNlafDSaF4ceJ6TpWcKCo11vGs3LQYuQpqfxMydAy/3mu+Z0FgWN5vmj3XGanqTRaFCpVKjVahiGQSwWIxqNArT1D2kLSaN5vmgR0vQk6+vrfPvtt6yvr9Pf38/p06cZGxsLghQ0Gs2LQYuQpid59uwZv/vd77h79y5nz54lk8kwMTHRFimn0WieP1qEND1JsVhkbm6OmzdvYlkWxWKxbZCqjpLTaF4MOjBB05MopWg2m9TrdRqNRtAHFO4P0kKk0Tx/tAhpeh4/AAHAtm2azSagw7Y1mheBFiFNz3LU9N5afDSaF4PuE9L0JOGxQOGxQv7UDVqENJoXg7aEND2LLz7h6b3DrjmNRvP80ZaQpicJZ0foRni5too0mueHbvJpehJfZDrfNRrNi0WLkKZn8d1wnVM42LatB6xqNC8ILUKankQIgWEYmKaJYRgYhgG4wmTbdiBQ2hWn0TxftAhpehLTNEmn0/T19ZFOpzEMA9u2g/XaTafRvBh0YIKmJ8lms8zOzmIYBjMzMySTSWzbDiwjn3DUnEaj+fHRIqTpSQqFAu+99x7nz58nl8sxODgYrNMDVzWaF4cWIU1P0tfXx5UrV6jX6wghiEajwfggP4ec/7fmuOG7UN1r5wR/gcDpKClDJTu3oejeY6G6fkPz56FFSNOTWJaFaZptUXB+Ch8/e4LOHffq48uNUsqTBYXwBEQhcbxPCJAoUHYgRAqJ42dOp11W3DIOLSESKG9vwpc15e0x+KIKbaPbfaPvpW5oEdL0NN2yZYfT+WgRerVRwUshlINUTrDEVpKmMHCERAowcDBVA5SboNYRFrYQgIEEZJvNZCOwcQXIxJMwwPGWC1ri1DqS7iLUKXGaMFqEND1Lp/B0ooXo1UZ1vFAK5bgioXCvny0EthRIJQCFoWyEUwcESgocZYBoueTcUgrXCrIRyrWElL9WOChsRGB3GaGjCbv6DhMe0TLfDqPHbjctQhoN7YITzh2nBejVRqBQSqCUACFRUoFjg3I8GVAIoQjaGK46uS9Uy5Umgv9CBTtRB/4Wh5RsldH3z3ehRUjTk/iJS/3+H6UUUsq28GzNq43AFRNXaCRCGAgMkALhNDGlQAqDBgJHue4zhQlYIBQoiVRun44rWKLDnSbxXW4iJDetUiL06Qe43A7Tuh7VKy1Cmp6k2WxSKpUol8tIKUkmkyQSCYC2bAk6OOFVRYFy3BeABCfot5FIIUAIJGDg/q2QONJ0RQsHgYEUbp+OUKJdhIThyo7wREh56zyLyz2Clvy0I7q8636hw9AipOlJNjY2uH37NisrK+TzeS5cuEAqlQJaIiSl1H1CrzQOymnQaNhUbJtipUmlUoVGjSgNDKGIxOJEk1msRBJhuAEGCAsDx21kIFAKwpdYKLxybgSdaBMPQXdRUV3Wh7+jOQwtQpqe5NmzZ3z44YfcvXuXs2fPMjQ0xNTUVLC+W9Sc5hVDOTRqFba2d1la32JhaZP1jS3s6j5R6liqSTaXY2RymqHxKTJ9A8RiMYR0LSXXnef1G0Grg0e5fTkKA+VbSoH15H+SgSWEcvudXHw3Xpgj7qGjO5V6Ai1Cmp5kb2+P+fl5bt26RSwWY39/PxAcLUDHA6UUpb095h/c57OvvuWL2/MsrW7QrOwRdypEaZLP5Tlx5hwXrr3FucuvMTo+ihX1+4RsfKeaCAkKIdkJh2C77jjAc++1CUigQQfdbu1DZzWdvBIidFja/MMqgvBgQo3mz0EpRbPZpNFo0Gw229xu4cwJmlcVQaNR59nTJ9z49FN+94cbPFjeQUTiZOIGRrNOdX+H9WfPWFpdZ7vcQERTJLNZUvF80E90QBoMgRtqLZG0hqsKIRCei86XrFZAXXg73XuIwgHcB0qIIz/+1fPSReiwKZY7X/7yzrK+396vRHTFofm+KKWwbTuYusFH9wUdD2qVCo/mH/Hln77kwYOHxAYnefOnP+O1C7PEGjs8e3iHL2/c4PHKFrdv36ZvbJKJmROMDuW9LRx2fVXbX60hrEfZNEffKwqwHeUZUIKjbq1eu+teugiF6ZxSuVu4rJQyaKmGR7brXF+aH8JhLrewGOl76VXG7c+xohGGhoe5ImJMXniND/72l7xz7TLRxh4PvvoM5TTY/MNnbGxusLy0TKlYAqDeaLC+scH62jq7u0Ua9SomNv2ZKOlMkoptUHWiJDJ9pNJxaFSpbK9T3tmlZgtqGNSaTYSyScdM8tkU0ViM/brDzt4++/tlbNsmFouRTqcYGOinv7+faCTiH31XevGOe+ki1Dk40F8mhAjmd+lWxidcaWg0fw7h+8uf1M40X/qjoTkSRTQW5/zFS2T7BihVHZIDw4xPT5ExABkhmUqRzGQxozFEvYFpGlhS0Gg0WHv6lE/++Ak3bnzJo4VFKvt7xKXN2ekhpiZGWC/Z7NpJzlx6g7PnTtHc3+Lel59x9+tb7JTr1ITJfrWCalYZyiY5O3OSXP8Aqzv7PFpcYn1jnWqlQiaT5cTJaX7603f5yU9+Qrw/0srwoAFeARHyCY/HUErRaDTY2tpibW2NYrHoTbkMlmWSSqUYHBwkn88TiUS0K07zZ3FYP6R2xR0PrGiUsYlJRsbG3TxwRgSExKbJ7voa8wuLPFlep27DYGGYiYkJMqk4GyvPuPH5Z/z2t7/l1rcP2SuWiVmClFHnYXWDpfkHPN2q0UiM4kRzZPsy2Psb3P7mGz76zX+yWayRGCyQSCVRzQrLzSrPHs0TS2bZrjQp1Ro0bZtScY9avcajhQXi8QRnzpylP5/zguf0/eXzyohQuEKoVCo8ffqUO3fucPfuXVZXV6nVagBEIhH6+vo4d+4cFy5cYHR0lHg8rluumh9Ep/vWt6gNw2jLohAuo3mVEAghkdJASANDmBhSUqvV2NzY4N6tr/n4j59xf+4xZizJ2fPnOXv2NKl4lMW5h3z2ycfcvXsfK5bitbMXmJkaIWNU2X58jwd377K1WSRqDVFrNKg16gi7TmW/SKm4hyHjnDh5klNnZpFOlSf377A8v0C5tkKif5iZcxcYHhlmZ2ebW7dusrW1xaNHC6yurjE5NYFlmRhSHLCG/Lus16LpXoma2w9OAPeBX1lZ5Q9/+AP/9V//xdLSEvv7ZUAFLrpYNMri48fsbG9z/c03OXHiBKlUCil75bJp/lKklJimiWVZGIbRJjR+AMxRbmDNK4CQCGmgbAfbsbEbDfY2N7j55ef84aMP+fLr25SbkumzF3nt2nVOnpwmIhQrTx7z6MED9stlzp65yLs/+ymvX5olY1S5/3mM0s4qC6ulYB8IsO0G1eo+piGYOnmC9977KWcunkM09/k6AmuLi1R39jk1Osa7777L5PQE62trVCoVdrZvsLm5xdb2NpVKFWkkMKQ8MESoc7hrr/BKiBC0XHD1ep2HDx/w+9//nhs3bpBOpxkbG2NoaBDLsni2/IynT57wzTffoJQincnS39/vpVzppUun+UtIJpNMTk5SKpWYnJwkkUi0ueEcx9FRcq88AqSBcqBeKbO2usqdW9/w2//4N7766iuEleD01eu89va7XLx8mb58jvrOGrtb6+wXiyRTKU7NnuLi5YucP3+StNzHLD9laeEuc0u77JiGGwhlGDhA024Si8aYnZ3l+rVrTJ2apl7eZGfpEalkgkodzp07xxvXrzE01M+TTIY7t7/lTvwO9Xqd/XKZaq1KIhF72SfuleK5i9D3jQJRyqFer7G1tcWzZ8tsbKxjmganT8/y3nvvcfHiReLxGF988QW//tWvuH37Dk+Xlnj69Ck7Ozv0D7iRJ7bTxHEUjgq7U7w0hEIgpMQRIFRr9LPjgHIXBoPV/D4mhQxF33mZeaWX2NDPLSb9vFLh9B86M+GrzODgIG+++Sbj4+MUCgX6+/sD4fHR8wq9yrjPq3IUjXqN7a0tbn31Nb/7z9/wycefghS8/tpb/OyDDzh96QrDw6PIRplSrUqtUkHZNslYiv6+HH35HIlYAoMmqVSSfD5DKp2gVPf6B1EYhvvMC2mRyeQYGhqiry9PkQoRy0RKQTKeYKhQYHhkhFQqQWJzi2gsijQktuPQaDSwvTFpXX5N23tn/u0/zzV8mMOv2/qDKYiUN/2FQDzXKuyFWULdxEh0fBDCdZMUCkO8++471Gp1Ll68yLVrbzAzcxqAiAnz979l/uEDqpUyxVKJpu2mbt/eXOPhw/ssPF5ifatIpd7ANE1SiSiZuEkiniCazJEbHKAvE6NeLbK9uUu5YrNXrLG9vcl+aRdLCrL5LIXCCMl0lp3dIk+fPqFc2iVimsRTGQZHxpmYnmr68OgAACAASURBVGZktEAqGUcKUI6DIQVBesPvGpWmeWn09/fzxhtvcPbsWWKxGP39/QfcwjrY5dWnVqmwtPiYm19/wx8+/AN37z5gaHiC62+/w0//l19w4fp18qkEEihWo0jTRElJ03FoVss0yiVo1IkgAINa3WavWKFcruFIEMqthIU0UMKdqRVpYpkmliGReOMcFQjDxIpEMSMRt7HrN2JCx3uYLIR7iMIa5QfKdDaGvtNNrPz/lJ8MDzBcYVHenEnC8dINCVCSsAQqXIF3nwEj2Kby5LE1UPcv54WI0NEhie5JEgIiUYu+vhz/f3vv+RzHmed5fp4nTVmUQcF7Qyd6J1GUqN7W9Mz2TsTFXsRd3PyP92424jamd7Z7pJZEGUqi6L0HQXhfQJk0z714MrMKICjfAnv4fBQUgMysrKp03+f52VOnTnJg/yQIQbFQoFAsAB4qaFBdX8H3mqRSLvmOPPmOHI5jsbW5zoM7N/nT//p3Ln17nRfz6zR8SLk2+bSklIJCoUypb5LDJ49zaLKb9aUpbl67y+xcjbmlTWZmX1BdWyBjQ1dXhdHJ/XT1DjG/tMqtWzfZWJ7FEeDmS0weOcUHH/4D599/m5FMGkcKgiDEUURC1F6PKrLybnugvWmW39eLbDbLwMAAQRAghMC27eSGh1a0phGi14PW7KGV6Bn6HouzM1y+dIn/+Mt/cOW767jpHGd+f4Hf/cN/Y2z/JGEQslZrIKXE9xq42Sy5zk6sdJqlhRWmHtznyd07VHI2rmhw/9Fzbt9/zou5VZxKd2ThUIRK4YfghSFBGKJCbRmRQps//BAaQUgjCPCDgECFhEpvGwYBoQqjz96677cLUNTfSLUKg8eVGuLBUXsU8A9el3G/pKTmQ/ROytLN/9oEalvJvESAdIVyKSTISKCilyjx6wrRa+ATim56AbZlYWUsctksVn8fJF0LA7Y2lnjy+CFfX/qaew+fIuwMY+OTjI0MYQmPqSd3+ezTT/jk0y94NrdKR7mHgf4KImiwMveMhacz2E6e3nWLysAQA90Oy0tzPLx/l9t351mv2aSzKSqVMo7aYm1llm8vrZApPMHKFJBOmu7ubrZWl5idmWHTcyhW+hmdGKN/oAdHartxoBRCKV1K/vu/smEPsSxrWzJ0fKPvrB9neP2IH8ab1Q3u373LFxc/46svvuTJ1AyVnn6eTL3g62+ucOv+IxpBA8ux6KwUGR0ZYqivm+HRMQaHh5ifX+TOzZsEns/dm1dxZcCTeze4eWeK5dUalWKICkPCIMT3QxqeT73p4fm+FoUw1BUVFDSDgLqn8AKfUEXrlMLzA5rNJr7noVR7+/D233a0BheKOP1xt4T8Hw6WiQUoNqnpdxNCIUSYmPqEkMk6/Qr9uWO9ESpaHs2I9DhaJM8vLZI/+fS9xG8mQjs/6845AfFNH+r2uSoAYYEKPDY313l47w5fXLzIXz/5nKnZFYbHJjl+8jSTE2N4tXVuX7vM15cuMbu4xvDkQf7LP3zIwX3jeJsrXP/mc765eJG55TpK2Nh2SkdHSUngB6ytVcmVRnjvd+c5fXyIxsZzvrv0DZe+vctK1efQqWHefe8dRroyPL13k08+/47pxS1mX7xgaXER3/ORroWQMjqdoZno/J0Q39jtZjjDa0wSUqaobdWYnZ1ldn4eLwjI5vMESnHj9i2eTs9gp1KEBKSzKcYnRnj/vXMM9nYxMT7O2TOn2VyvsjC3yPWrV3lw7y4pK6S5tcZatYESNmHUgVVKiZtK01EqUapUyOXzSDuaKUubVCZDsVxGphWZTFpHvgmBbTvax1QqUywUSadTWFLSbvh65dcU+ou2i9GP728VmeDilhTJREi3LNf71z4uFSZFw4EgEkrdvkIgUCEEhJHYCFq6JVpv9Qtvmd9EhL6/0lJ8VQmkEASxGAmB8n3WVld4+uQRl774ki8+/4LpmTkqvSOcOHuWw8eO0d3dyfTDmzx+8JDnz6dx0hmOHDvK+xfeY2J4gLC2St4KWJp5werWY+JuiUIJ3VUxCAkCRamzmxOnTnP+/CQLz66xMP2MG7ceU9sUVHq6OXH6JAeGSuTsgLsPnzG9WGVzs5qU51CAjPxBErlLrSmx25c37CHtDuJ2x+/O8lGGvWOnEz92lSulH6bZfJ6BoWH8UFBrBgiZIsQmRCIsC2Ep0tkU2Uwa17YQCMqlMseOHmNrY4sH9x6yvLyGZQlcB7ysgx8qNppVpJQ4jk02kyGVtzh85Ci5VJ7RiTEymQyWZZFKpenu7ePoseNsNhX9fb3YtoVtWeRzWUZHhjl56iTFQoHurgqO4yDjQCb9DUkCAZLvHH1XoU2PP+163G5m00dMJnsPw4Aw9AkC8DxFsxkipSCddrFctvmIlIIgCHSRX08HVFiOheu6OK5DPOT+cZ/r1bwG5rgWQuh2vJYlQClWVla4ffMWX331JVe+/YaZ2QUGR0Y48e7vePfCBcbHBsngs1Wts7Swiu8FdPd3sn//OBMTY/SVS9DIsTUxyeDAAPcezyGEpVv9Kn16LClx3TSlrm6Gx0cZHh1G1KfpLBcpdOSoIyhXOhkcGWR4sMjC0046OrLYtiQMfTzfJ/CjUXT0HbYLkOF1p93mDkZ4/i5QkM5mmTywH8d1WVvfwPMhxMLzBX6okJbAsiVOyqZU6mBooA/HslhbW2erukUuk+PAgYNkMjlKpQJKeTy4d5316tcEbOCmHDryGTo7S1SKGbK//5DVo0v09A1TKBWwbZdcLsfExD7Ef3VoBILhif1k0ilc16ZSKXPi+DF6urpwUylGR0fJpFOvMKe1qsUAycwDtvuCfjbRS4WAer3O7NwCz6dmWV2tUi4XmZwco7unEyn17Cf2Y2/V6szOzTLzYoZ6rUaxVGR4eIjevl5SrkMQmbAt6zUWoV0jlneiIjdX9GVUGLC+usqdW7e5ePEily59TXVjg+Hxfbx94XecfPd9JvfvJ+tIGqvLBCGEITiWJOvapG2JI7WzOfQdpJDYUmAJqSNcoimoQCGFxHFdUpks6XyObDZDJuOSStk6s9kWOKkUqWyGTDpNOu3g2gIptQMvjGzGoCNpkmiYH0ycNRWk9hLf92k0Gvi+n5g5bNs2QvQa0/LX6dlQNptlYt8kwyPDhIEiCC1CJfEDobtwW0JbJyTYtsCSgtBr8vjhQ25cu8bzZy/o6ellZHiM4ZEhao1N7t+/w/LaJkEI3T1d9PV101Up099TYbS/D9/zEMLBTqWwLHCsHEMjY/T1DRFiI9w0tutiWQKnVCSXzbJv3wRCCD2DcGykFYtQ/AxoNRb3fI9qtUq1WqXRaAI6iKZcLpPJZPSrdgnx3nGkkrZHyV+JqFn4fsjMi1kuXfqK+w8e0dPdzYUL5zl27DCFYgFbuggUTS/g2dRzLn/3HXfv3CEIAyYnJshkMlS6ukinXVQQtvmWfh6/3Uxot1oUybGMTHKRnXJzfZVr313hrx9/xI1bt3Wo9omTXPjwQ869d4G+rq5kF0EqhUy72GmHwGtQXVhgdXaW2voGqlLBJ2B9s8r62jrNrQbpvEBKW5/02MGmosg1EU1bwxARBtqRF+UVhdEFI2WIFAGCAKECJDrMURDZbXd+R8NrSbVa5fnz56yvr5PL5ZJcISll0i4krthuBGnv2GkeTcKUhcB2bGy3gDY3vVxx/2VC6psbSKC6scHjhw+5f/c+N2/cptTVScNrcvPmNR49m2ZgaJIjRw+zb3KCYrFIOpMm07anpvbYYwmHlJOCXOv9vejj2rZFxrYQ6OTUyFuc/L79qtJ/VatVvv32Wy5f/o6lpSWy2SynTp3iwoULUUL+Dw2QWkY4HTjQPtjV4dauk6Fc7iSTSTE784y7d66zsbFCo1bn1KmT9PT2ocKQuYU5Pr14kb/85SNWV9c4eGCSTDZDJhuLIb/K/fHbiNCPHPCHvo/v+zy4d4+//PnP/OUvf6G6ucng8DCV7h6K5QqbWzUePZvWjj/XQoUe+VKZ4YlxOm/cYG5mnttXrjAwPMbcwgK+V+fW9Zs8fTrF1sYm6W6wIhEKg5Bm06NWq9FoNAijyJbA92n6Hp7v4QUhXhCZ3fAJAg/f9/CbDUK/iVA+VtTrSkdrthJXjRq9viwtLXH58mWePXvG4OAg58+fp7e3NykNZQIV9obdGly258oky4gjuAIQPgoJOOjkCB2xFkUZAwFSKiQhruvS29vL/n37mZ2e4/ad+zx9No2PAks3yusfGub8e+c5d+5tJsa1/ycMFHUpaLc6yWjEqYVRO/QTcdExDQRtmRkvX0mtvJyYza1Nrl+/wb/+67/y6NEj8vk8c3NzFItF3nnnHTKZzA+EZrf2K5IcoSgqT1mAJJPJMTkxycb6Ms+ePeCvH33MFxc/RyqbfK4D13WpNZpcuXqFjz76mCtXbzA2Nsahw0c4euwY/f39OLZNGKpd2+38VPbWJ7QtQF3R2NzkxYsXXP72Ml9//Q23b98mCEI2qps0fMWdh0/J5LKEfhPHcRgZm+DEieOMDvZx7t0PWJmd5T/+95+5cf1bFqpbdJS7EUKwtvCC+UdTBIHUhQMFhELiK0HT86nV6jTqNQgDJDJap/CCgCAAwgChDaWEYYgfePhBkyDwUKGuvGCBrpyghE5we+lC2THu2WHjba8gHmNMQ387lpaWuHr1Kjdu3ODIkSMcPnx428OuPU/I8LdjN9NSvKw9OXO386ArmsT3DcQOedXm89UO+uifEAjLoqurm9Nvv025s4czL2ZYXV2j6fsIS2K7NsVyiYnJ/ew/cJDOShHXtvR+UYRKBwtIQRR+1HL6twKsWn/FHy4enLbCsJJv8dJ3Am0uXl1dZWFhgc8++wzHcdja2uLs2bP09PTsesz0v7aBsIw/RfQcidNhpCSbzTAxMcaFC++yND/PN99c48a16wz09REETVY21vjk0y+4d/8+HcUix06e4MSpk4yMjJDP55DJYDv6Nr/gNnltAhPisj1rKytsVDfIZLMMDw/j+wFKSmZn55hbXCUUCmGF5HN56k2fsZERCgf301M8yOr58ywsLnDr4TMWlhaYW1zDdVxEcwvP17ZLJbSYOOk0hc4KA8MjTKynGOjvIZPWDafcdJZyVy/DY+Nkt2x6uyqkbAuFIpXN0dvfz/jkJl19g5EN1WoFJWy7p378mZFSYlnWtmrg5gH4t6PRaDAzM8OjR4+oVCpJlXYhRBTBZAqX/ha0mzx33gM/bHayEVhALFYtn1Fb0g2tx5x+IHeUyxzKF9m3762o2kGUoCkif7wlcWwb27axooetQiSmtFaI9ct5GMkSsXPpq/7avqRYKHHkyBEuXLiAbdvcv3+fqakp/v3f/x3P8wA4ffo0lYqOtGsF1YRJVJ2UEoTc8Rm3z7qUCikWS5w6eYb1lSr1ms/M9DxXvrvM0tIcq9UNbt55QCqd5fTb5/jgdx8wsW+CfCGPkJYW2qSKw+7f6sfy24jQD5owdYkIKSX5QoHJ/fuxLIfjx4/hh0GUrSwIlKIRhihLks3mGB0aZrC/G1s2UUGDcmeRIyfOUByYpIGDUBJbCDaW57hzpcbcfBUpIJVy6CgW6Snvxw9TDE1s0jO4n0qpA6VCch0l9h86gm+VqTZdxg4eJJdyUaGis6uX02ffodQ7QbZQYWxkGNex276mSiZ333dudpbhiCs5/7DT0fBrEAQ6ibDRaCQBCu2YenG/DTsrAbSXTvp1ic1SCpBIx8F1fvoe4p9/qysjk81w6NAharUaUkqCIOD+/ftMT0/z5Zdfkkql8DyPY8eOUSqVoj5rCsdxSKfTSXCNECpS1KjO5bZPr+ePKTdDV1cfx4+dZH11gy8ufsHU1FOePX1EMwQPm0NHT/Pu++9z6MhbdHR0IKRFqNpml79wFgS/5UzoZfPn9uWA7bpUurs5lsmwb98+ml4zUnhdNiNQiiYCT9rYbopSJk1nzkZ568y+eMbTJ4+pbvl0943SOzxEPp3Cr1d5ePsGD++4+EAqm6KjmKOjXKKv0k9XzzDHNgVuqkh3qQBKkSuUmTx4hEr/QZqhQ7ZQopBJoVRAudLNiVNZxg/4SDtDsVTEsW2dVaxaMf4/9cQopdja2mJlZSXJ5t/NPm74ZcQ36erqKrVaLRGjtbU1VlZWAG0KiR+Mv4bN27CddtPz6uoqW1tbeJ5Ho9FgY2ODxcVFcrkczWYzmSHtjgIRFSKOH7iqbdvEORuiEzXjzE+JUJaeRbX5bEIhCBC6wDEBMvSje1poEz0ShELiY6kQqQRKSBRRUWRAxm6YbZ8h+bTJsvZN4joK8dwllUoxNjYWFXOeYWFhgZmZGR4+fJj4LFdWVpKiu7ZtMzQ4xNj4GI7rJO6NeK+td4+TVfU7SmGTdvMMDY1y4sQK87PPefb0EU+fTCGcLKP7D3Pk2DGOnzjG4FAfjrS0n0vpYCxLV4X+4RP+A/z25rjYKBr/TqTLQuC4LgXHoVAsJBnDeoPIHyMETWwawkZISYoAu7nO2twiK4vz3L93jztPlunoHkY5KUr5NPWNZV7MzLBVb9BRLjEy0k//YA/5UomOzg66Kg4idCGwEVaIoImbzlNOdVDscnStJSEQykeEAal0nt6BMt3KjjxBIIXQItQ2AU541bBJtGzflmVRr9e5d+8en332GcViMRGhuMW54dch7sT77bffMjc3R61WY2FhgStXriQj8PZZkTHL/fq0z3oePHjA8+fP2dzcxLIsbt++zccff0w2m6XRaPyAXy5OylSISIRUVIgz9gfpB64WoaSUqJKgrCS0OPaVhEISYBMKgYWHFXpIpVAIAmHhCwsViZAdBpEIaYFKhGQXEWqfg+xc1r5coBP2UYpms8nS0lIyyxFCUK1Wefz4MVJKZmZmyOfzBEFAPp/ngwsf0NffR0ehgzAMaA//bn2W6HioUB8DIbGkJJVKkc1kyGXTOI6g0agjQhvXTVMslymWS6TSDqEHoVI6yT/5zL98XvibFTCNiU1UrY/eyquRwtIRZpYEoSM5WgdTT6NdBDaxpdeCwMF1M2RzBVLpFOtrSzyYmuXWnTvYliRsbNHY2kAqyZGjhzhz5giTk4N0FAtIN42Fg42MBgm6BURouUgcnHgUrEICXxGECmE52HYKKzp0PhD6YfLtWhbYHUOgV5yn2Aexvr7OxYsXefjwIalUKunw6b+i9Lvh5xHPbBYWFpiammJra4snT57wP/+//8nnn3/+NzQHGdqJxWV9fZ3p6Wm2trbwfZ/PPvuM+/fv47ouvh8/TF9Fq95acucpq80f0j7yV4SJNUZosYr8PTISsVBYBKRQwsKiia3qSBWgkFqEpN0SocDHUqCkwBeRv0jtLkLtYdnxsl2/ldAiJCNxaDaaLCwusLKyklyTGxsbPHz4kBcvXiClpF6vUy6X6e7q5sIHF5BCImQcLCBa1Rd2OXbxezYbTVaWV1haXGZzYxO/2cRvVllcXGB5eYVao4EXHcbWLLY9qOSXCdFv3srhldaq6MuFKoAgRIggKpYXVXxVgLDwhcQPpd5c+cgQUpkifYMjHD96lM1GwK2HL1hca1Bv+ggcOnsGmBwd4MzZMxw/dZT+vm6cjKvj+cOQVChwwgBEEyUUgXIIhS7BYymF5XuI0NcXqpKEgSKUUYVZpSNl2mdBP+Z0SCnJ5rJUKhUG+geoN+qsrKywtLSUmCDimZARoV8fKbQTvFwuo5Ti2fMpnjx98pJ/4iWT6N/SIfAGEUdw6fbcglK5hECwvLzMwsJCsk17JYuX9gG7i1C8VLSLkLbYJR6RttYFFiECgcImII0SNhYNHFXDUjr82xf27iIkwBeCINq/FbaEceczT7E9iZQd60En11rS0jXmoq6uruvS1dWlG+NtbrK+vs7a2lrSGbirqwvHddoiCWVrv1EAQYv4eytQHl6jybMnj/jmm2+5d+8hluUwMTFGtR6wubnOtWvXGZnYj1IWfV2dOBkLqaSOFlbqV7kffpOmdq0gwe/bLro8krDLtj4ccS05dPizrQJE9PCXlo2TSlMqVTh27Bi9gyP8ruqz4UkaUTBD1rboKWYY6Omi2NWPTGcIpUC1vwchhL6eXkN0WRJ9pigCREqQdjRL01d0sjyZ/e5yRl4yEitcx6Wnu4e33jpMyk1Rq9cSB7lximt2u2bEtrXbhzTJTc7u94Wu6ai3iG9gISVhEOD7fiL4ccQWqCR6StekjR8ireGuUK1HYRj5IES7YzB+MPycA/CflOT6Vnpmaju2nqEq3b00Pg9JS4GEnU9vtcPyIBJznN5ci1CrbYFou2pa20kV6tQM9EwIYWFRx1F1LBWgsPCEE5njQiQedhhoEULgC+0TUgKkUsnt3j7z0X+3Qsq3fY223y0psaMgJYFAWnowWqvVmJ+fZ3p6mnq9TiqVore3l4mJCY4fP87Jkyd1RYXEVCZQhNpc+VLPIAV41OtbLM7N8N13X/PFF1+yML/E5MQ+hoYHWa5ucePuU+7fvcf//l9/RiJ4/72z5NJlXYVCRQVO41vhF1zgv7lP6OXPGt+k0U8pEG3RHAoVVW6VoKI+PXFxPiGQlgUiTVoIBnIdDI45kMqDSOGhzWVCgauayDAkwKYuJH70rlLoDZRUiFAnnVl4WPF/QoKdBlwkkt08BDrvSCfHtV9mrWIc0O4URYHruIyOjHLhwgUOHTqI53kvjfre9DyV7xehJBMRfYEIwihZUN8TqrV9tCMZ20ySQUVU8zyK9iEqey+llfgkk9DXqJ5WKEA3A4tLNcXRRzoxEUJkUrJfQOJ3MLzELidYyJZfJFA69Dgu6bV9CBI1XYMoZyWeCb3sA1FtVQNaV0VboLWKZ0qSEAeFwKKp/4UKhUUgbAIho5mQh6VChL4YouUtEXrpu7WJ0M4rYecA3WoLhomrdszPz3PlyhWmp6cJw5B8Ps/k5CRvv/02Z8+eZf/+/YyNjZFOpwnCIDEzKqKcN6GiAZRsE2vB0vIi31y+zKcXL/L4yTMG+gY5e+48x44fZnF1DSt9iY8+/ZrvLn1OqSPFUG+RfOogbrGAkDKaCLX2+nP57WrH7fJ3MkYUQBLvv3Or9mqwuicGic0zEi8pQDoIQj1LETr20o72qidSDkh9Mux4BkPkdZIQIvU0mAaEPqFq0lQuXmChkNiWwiLEVtGLlSRUlu5xL0U0EtJZ2bFr1FLxRa70qCwqDa9CiWM79Pf3UywVdbWGNgFqT1J9k0WovR0XtB4d2rEaJCLUilCyYjc08e2tTQf6HFhBlO0h9TWkosTlRLSUHgDFUVNxQzAdWCVRShDIECUDpAgj+79FbNAJpALlY6kgenBaKGHtGIwYgFYAl1JRgziiiWPctE7pvjxKF8gUsiUa8cAhDEPtQ5GSuJ/xrvOMdktE8qvcvg0KlVhhBDpOLoheqq8vRVSTjkAPNpN1ItG+ZC6+TQx3fqbt8/nWMWkz5SmF53nU63UuX77MxsYGCwsL2LbN6KgevP7hD3/g2LFjdHToKgdxSLdlWYkAhSqeDUmEUNF+m2xtbnD//mM++/wr7j14TGelhzPvvMPJs28zsW+cnvUNthoBL2ZmuHXnPg9uX+X6WD8dWQd3ch/5fB4rshaoX3h9/+atHHY1kyTT513mSbtUFWhNt0HLjNQWsmQu2vaatt9ic43Odm5tkNiJhQAVoupV1te3WFj1WNkMqIcWUoKrPNygqVt5Y2HZWbKFIvlSGTefxXIFllBYCOxov3Kb76417rEsi46OjqhrbLTJLrbvN1WE4iPVboyJH0NCBajApyU3+iERRGG0SSlAFCiJCECEClspLBGF60qFsqLqGYmhRCKURGBHplq9rQwF+DryyrdCQstDihBbCURoQRRR5QsFNLGUr8NthYMSOozm5THwm41SoIJophm139IPS6EtEy2V0j4O0TJthtEIXN/L8UBN39Gy7bEezwd2jGmTtTsXqm0nKHrv6Hmitj1z4nWt55FqX73tfdjlxO8uQnHyZ1y7cGVlhTt37nDv3j2ePn1KEASMj4/z/vvv84c//IGzZ8/S19eHEOLlACYVC73QAVVCYVkQBD5ra2s8efKIb779jmvXb4GwOX32bd7/3e+Y2L+fSqVCR6FEGITMzk5TXVtmfXmOG1e/o1TsIJ/LMzQ8TDabpjWJ+PnsWVO7n7NFst2uJ1UB8qV18ZqdHoRkxEF88cXTeUVja4Nnjx7z3c2nPHy+wmpNFzJNqTpuUIuKljqksgU6ewcYGt/H8OQY3f0VsulUVF1BbH+T9s8k0CO3Hd2t3lTB2Y0dww2gfeAQjXzjQWeUxyGFNpi2RKj1eomu+yWERaRKSYOu2I0riKMy28w7CLD0zFcosCwJ0tJDHyFA2IDUmyAAK3F0gxUZKww7iS0eYQhx75uW2U0REuglwtLRsoCK/WuqtZNdhq07lu3yQNjlNT+w6nvX7br+R570bZvFIhuGLC8vc+PGDf785z/z0UcfMT8/z8jICBcuXOAf//EfOXXqFF1dXdsqTcSdgePyPXqXIolk09G2HtXNKvMLi6xvVCmVOzl48C3+y4e/59jx45TKJWzHwXUdRkdHePfc2zRrNR48fITjWGxWN9hYX8drNiGb/nFf8gd4bcr2/HJ2uxx3X6MveLVNmNpXNrZqPHvyhC8ufsG3N56wvAmZbJaM9HDDKlIFICSWm9VVEw6+xZnz73Ly9HEG+/tw89nkhlGi/RKPAhqE+NEXqWE3dvP8Jo8xYvdOvFQKHTuSjDWS1+w8+99zUnasUrst3LaxOcE/TGyDSJ6YxHMcFZu9RTw4S+Y127qk7OY3/HunXq9z+/Zt/vSnP/HRRx8xNTVFsVjk3Llz/NM//RNnz56lUqkkOW/tidXba8iBEDKJtI2jbaWUFEsl3nrrMIODQ/T19XH06FG6e3qwbAtLastPviPPwQMHsC2L/QcO0PQVlUo3uWwWIbRJ1PrBljU/zH8iN+5q/AAAGJVJREFUEfpx7JwIt495Y3zPY3V5jedT00zPzJIq9jMyMcFAZ4aUqiGCBltbmywsLPN06iHPZl6wtLaKUiHp8+foyGZbbXCTd40WmNnOD6J2/Gwtjyt4qShS0SF+OFnRPwcdlOvFrwkBpSPWdHRltEIoXUewzRwraDOfQlJnUET7UEpoG3sUEqSUipzaglAJQtmqmiGi14dC7nqNvdnogxT7fFrD9ih3R0gse/dHU/sxDENdSQW5oxgw3zMM+D7Veg1O0ObmJleuXOF//I//wb/9278xNTXF6OgoH374If/8z//M2bNn6e3tbasZt3vDOxGJdyxE7YV58/k8oyMj9Pf1RcVMsxQKBRzHSV4LIC1JpauLTC7HxOR+6g0fKSzSmRyOHVdmMCL0k9Cj5B3ehraHBNH6ePoqbZtSpYuj757n//p//m+O7xsiRxP8LZYWXnDlylX+7d8/4usrt/nqi4vk8wVGhkYY7O0lZbvJyC0prqhoi9TRJ9C4rLez02yqf7YdsyT6KCQMfe2gVhCGWggCIJQyGtFJHRSi4ki26KVCROe9PWoqdjCL6DWtc6TabvLWqDzxUCWfXZuTdG8bFb+PYQdREECUSCpEHJAjktOrQp8gDNG9IsW20X3cfFCncmgzufwVRuOvC2tra9y4cYNr166xsbHBwMAAv//97/mXf/kXzp49Sy6XS/Kn2pOqd1Yeb891A5LZUBzAEO8nrlnZLmLJTAqB47h0WLrFQ6gEQQBKRa3T4xHc34tP6PWhzeEZ/b1TChQgpMSybLLZLP1DAxw6dphjfeVkm4mJfnJ5h42tVZY3Vrl2c4p7d+4x9fQFhw4cIO3aOPauAd0oonpXP7oZ15uLSAYM0dUuBIHvs7y0xMNHj3j05InO6t6qI6RNubOTofFxxiYm6OnuJuM6Letn9D99X6od8tEeXK/fM3rMRe8bSU4iYC2/RmJNiveVTIN3OP0MbcSzWj0bDcMQz/cIlWJ5aYW79x7w6OETNqpVPM8nDLV9qdBRYHh4iH379jE4NEC+I0e7qe7vHcfRUbPvvvsuhw8fpquri3feeYeTJ0/S0dEBsC2Bvb2sVHsPrFe1vrAsa9tr2sPBW0IGOgVCtQbRQuiUFcsCJQiJBuuhitKPfv51/oaJULuhpzX6atloEkOq3iKyoTYbDTarm6xTJqcCLFFDqZDu3k7OvH2UmcVFnr9YZXV5ldmZRVZWNigXc6TtNqe0ao0BFboenF5nHlQ7UW2/iSQfKCTufLu0tMh3313l479+wtVr11leXsZregghKJVKHDp6jHd/93vOnD7DQG8XbsqO7GyRuUcBURi2Fhud6xN7J4RoPRxFmwjpVyXdo/QnjbLaW7WKZSRoapvMGbYTDwDjey8MfTY2qiwuLXPjxi0++ugTrl27Qa3e0KKutPktl8sxOjrKuXPvcO7dt5mYHCeXz2+rGACtGcHfG4VCgXfffZdDhw4RBAHpdJpCoUA2m30peraVVP3q79te+aN9fSxkcQHU9m1jwsgaEIYhQagHZlIqLMtuWZXiyK5fcKjfMBGK2S0koTVDirO149/DQOH7AV4AfuBhCR8hFblcluGRAcZGB8nnsqyu11lb3WCzWsP3w9iYQ9st19pvtOTXKAD4nwlFKwTXimdBKtD5IjKg2Wjy8P49Pv74Y7748muqWzWKxQKFQoFmo87sixd89eWXKDtDqdxFRy5Nzu3YbrJJfm3NWET7OVIKIQLagxfiqyPJOd9pM2z7M0QQhLETvdXQzNCOah07FdL0mszPz3Hp68v89ZPPuHbtJp7n09vbR6WrC6EEtVqd5eVl7ty5w+raKuvrq7z/wXsceustyp1lbaYD7bcLdX8gGScL/50Ikuu6dHd309XV9ZLI7JY/uNP8tnN9O+3L4iCG9n3s2DqqBKNzL62oLELrPdrtB7/s2L6hIvR97AxdiB9M26UEpVvbZjJZcrk8ruNEJgUf3w+iUYThpxAb3uLCBqpNhAh9mo0miwuL3LpxnevXrtNoehw/cYLDR44w2N/L2soKH/3lL9y8c5+nT54xPf2CfaMDqFIWpC7hVA8Enh+iggBbediESMtGOGmErR2zgdcAbysKNkjpumGBDm5wpMSxpDZDqFD7NlQ8qJBg2UjbRomovqEQ7GaUNaCfZEpXLV9aXODWrZt8/PHHXP7uGo6b4e1z5zhx4iSjIyNIoatI3751i8vffseL58/5+mtBR7GDrq4u8vk8TjSiV0qX+5FRaa6/FwGCloDEjf7al+9G+8zlVRXfXw5aaLXHiMO6X95WEtfjae21LcAqGTvHycU/nzdUhHY7WbHZJb4A2urBqejikJFVp61ZVBhKglCXwUjy6UTL59Q+Soh9BnHuiDCmuIT2cI0kB7AtiESFPusrSzy+f48H9+6ztVVjcHiEU2fO8tahg3SWCqwtLzLz/BlbtQbFQgGJIPR9Qr/JltdkeW2TueVNNjYbhM0GTtjEFYp0Jke+3EWpp5d02qW+usrq3HNqDZ8GLrUQvDDEQpGxXXJuGsux8QOPrdomXrNOEIQIYZPNlyj39NBRLJBOubrNR2zmNbSIAjxUELK1ucmTx4/59pvLXL9+nabnc+L0Uf7pv/6Rw4cP09fbgyUl9VqN3p5uMuk0V69ejapI16jV6gRhgKSV3Jw8TP8ODQ0/VkxetezXeK+WFUAlf70y5tCI0M+lNa+Jf8aCISEqqa7XxI31tPDL6J9NEEq2tnw2Npo0vSAqqMqO8OzW2+kCmqJtbPGKk2ogNoXGxUKV8lmYn+Xale94PvWMQrFI/+Aglu2wuLjE2vISQbNGX28Pv//dB5T6h9l/cD/FQh7frzM3N803V2/xzfUHzM4t06hu4PgNMo6k0tXL8OQhTp0/z/jYMAvPp/n204+Zmp5jpR6y1vSp+w1cS9GZK9JVrJDOZNisb7GwNMf6+gpevYElXYbHD3Dq3fMcOX6U/p5uPWtSuiSMOdPQbuJEKZr1OksLSzx88Jj79x+wurLG4Mg45869w3vvv0dPTxdpx45eVSLlOnTk8+ybnKDpNejp66VSKem2LfFdLESSty7Y3TRl+DHsYqL7G/CGidD2gxiH0aodN4YgyjuJhEhKgW1JHAGO5eptg5CNjSZPnszz6PEM1c06mVyJXEeGdNp9ZdhoK6vl73CI9huw/YjEUXE6HHtlZYn79+4yO/OCXGWAjeomN27c1IMFr4FrQbmQZ2RskvH9+xgeGSLlKpbmp7n23WX+9KeP+PLKHWoNRdqSpMMmDopcR4mnMyu4xQodHTmmn0/z1edfcuXabRa2AjzXJVNIkUtZOIHECR0sx8UnoNasEgQ1qqvrrK1sMjz+kNDJ0tnTT2e5TCbpdGl4CSXwGh4ryyvMzs6ztrqB66YZGh5mYt8kfX29uJbADyMfhIJiqcjhw4c4dHAfUgqEZSEdG2k5BErp+7UtudXw89g5B4oRf4NL+Y0SoVh02gNx28v/A0nAXGxCkZaF4zqkUymy8Qa4NBubTD9f5NKlG3zz7U3WNrZ4a3SSgaEeSp0dOI618531q5MiU9Lo0A62X9+tQpZxwdJGvcbK8iLPn09hr9bILK6Ty3eQz2dJCUXo1XjUrDP1fIYaKVK5AnUnYOreTT7/5FMuffUlyzXF0ZNvc/rYEcquRX1tjZmZRdabisXFJZaWV1hbW2V1ZZmlxUXqVo6BkVFOv3eGSjHD3cvXufrlVepeQPdAN+P7RxkfG2BxZpbP/voV83PzTM/Ms7S6Qb3pQz6u8mzQtEV0CN0WpV732FivsrVVx3XTlMqdFDoKOFYr9FqFOpPLti3cQp72Gycg1CHcO/0Uu0SFGX4Y9YrfXxrCb1tpQrR/NLG6ix3L2j03oVIEYUDT89jcrDLzfJqbV68h1wfJqhrKrzG/sMLV63f49NNvefJkjlJnF4ePvcX4xDDFUg57Z45Q1KKcuPS/EaBd2SlEScuGMEhqGa+uLLOxsE5lQPFWVw+jY+N0dmRYW5zjyjeXePDoKatNG2GnGezM8PjWbW7duMny8jJDb53gj//HP/Pf//hHerMp1ufmuXnrHg+mZigPDJCKZi6plEOp0MHQ4D7e++N/4//8l/9OR9biX8X/y4NrD1C1BuMT4/zxjx9y4b3TPHnwkI2VKldvP6fe9Khu1Wl4OhRfmofgLggddWW7Uciv9sNalo1l2Sh05YvYaxpGFRaEUEl4YhgGeEFIgEBKG2nZbQEtkdPeCNHfkFeEiP5E3igRUtt+il0eeKLtV4EKQzbX17l55SrKC/imnCUVbkLQpLrVYHZ+nenpZSqdvRw9fZSzb59hoL+HtKtrL0EcoxBHN0R9ZtrLXZh7I2GbKzQ+TAAqRKgQ25JkMhksqcNLu7u7OHP2DGdOn6Svq8TizBSN6jpfXPqWmRdzPH38HNsrsbS0THVzg1Q2Q//QEMOjI/T29lCyJAXbwXHSDIxPki53kk45TN9xEEqQctMMDw1x7MRxDkxOUmuskUqnyGQy2KkMQ0PD7Nu3j9GREarLK2SzWRCSesOn3vDwg/DXqmzyn4zWAZHCwnXT5LI5MukMm7UmzUYT3/O3WSxCpRChLjyrgoDNzSob1SqhkKSzebLZHK7UQf1E+S87qwaIOGvZWEd/FLslsrRaVahfS4PeLBH6PlohCRbSSZMvlOjt66V7uUa12WTq4QOW7BAn3EKEAX4oEHaW0ZFR9h08xOlzpzhyYj9dlTK2JXh1JRFzB3wf7aEarURRXd06nclQKneSy3ewRZPBgX5Onz7OO2+fobdSZOFFDw9u3+LW3Uc0Gp7O2epM0fA9QhSpTIpCRwf5TBYLASpEui7dfb0UegRuPk2t3sQSglCB7abo7OpmcHCQDmmx6St8L8BxXdJuhq5KD5VyF5l0hjjvRQGBH+D7ASoMzdn+XhSWtMjnc5TKZbLZDM25eZaXl9lYX6fp+UhHP6Kk1NdAo15nZXGee/fuMf3iBdl8B/v2H2RkZJR0KqNFJ2x1lAIzBvi5tA8C/pa8USK0cxDUFhEfPfAk4JLKlhka3c/b53w6+8fZ2PKxLRsLHxk2ECpEIcnmSoyMH+DQW0cYnhimXMnhpmxsKZP0R0UcRtkK607sp+buSIgPhZX8riIhj5oU2imyHRX6Bkfo7u1j3ZvDEiGuBSlH4li6Xbe0ovYJwtIl6dNpUvk8diaDt7bF1soq9bV1/EaDIG0TBj7r1U3Wq3XczTyh36S2VcMHlONgp9Kk3IwurhRKgjAkFJCyHTJujoyTw7JsLUBxXcAAhB9HQ/7ypl//aVEh0hJ0FDro6eum0lXmwePHzM1O8+D+PQ4eOkBvby/pTDbpmfNiZo5rV65w8eKnvJiZZWxigkKxk4GBwajJGoTRDKg9V29byPZOzMnZxm6H46U43m3mTWOO+9G0pVptW9YKz9YilM53MXHAoVAZ4ky1TsPz9UBXBTpxEgBJKpWh0tVNd3cPmXxGJxhHmQpJPbrk/MQty9tyg8zFv41YfCwVmy71mVHYIDMUyj2MTh5gbHIfs0trLMy+4Mn9u+wbGyafslldXWV+aYX16ia5UpliqUBndzdBOESx0oX3ZIaZJ0958egxq0fewioX2KxucO/uYx4+eEImk6O7UmR1ZRVPKZRtE0oZ+fGAQOpkWqGDVmzpYEsXsFBCoSwV5fiJqBNrezKhOdnbUahQK3W+I8/I6DCTk+Pcu3+f+dkXfHHxM0qlIqfPnmV8bBxhSRYXFvnmu6v8x58/4ptvvsZ2HPqHRnHdFK7jaN9Re/00XnHUzan4UYjdfu6Wf2XMcT+NV6m8RguEm+qgu7eD7t7hn/EO8hVmgNi0ZO6AVxPHKoaJQzmuRCAsl45yF5OHDnP67BRz80vMzs/zyUd/Yau6zvDQMHPz81y9foOG5zPe28PY2AjD42OUOh2mnj/m0cMp5p5Pc/Hjj8H3KFcKbFSrPLj/jJnpecZHxjh57BDNZpO677PledTqTbymrz9eCE3fo9aoYYkMvucn/r0gDGn6TRrNBl7TJwxCXVUhcpObudAOlEKFAQhIZ9MMDw9x4sRxZmZn+eKrr7h65Tu2trZ48uQJBw8eBGExOzfP5StXuH3rNn4oOHTwLY4fP8ng4BCZdGZbEU6IXbs78oTMafhJ/BaH640Toe/n10kefXkP5sr/YdrLUyhoe6AIIZFALl9gbHyS8++9x+rqGp9++ik3btzg9q3bpFIp/DCkXvfoHRjjxMnjHHrrIKOjvYRega31ZWaezfD5Z1/z5cWLXLt2Fdu1otwSl+6uAU4ePUH/wAC1zQWkbWvTWxjgB1qEBHG0VajFpa0fTtIOXGkhtVBRJFcYlUg1xXsSkog13V3YsSRdXRWOHD1Ko9mk6Xl89PEnfPLpJ9y4eZNyZwWFoNHw8PyAQrHIO+fO8eE/fMjbp0/R29uDbdtJFNyr6qwZfkV+xUNqRMjwWvKS6V4ILGmRzRU5ePAQtVqNTDbDzRs3mZ2do9FskEql6e7u560jJ3nn/FlGRvopFbPYwuHEsWNsrm3QkS3x9OkLVtc38EIPy7Hp7urnwP7DnDx9ionJSSxZ4513zjK6vMH+I4coFbMEgOvaHDiwjw8++IBMusDkvjGyuTSokHK5k1OnTpPJDjE+fpyR4R5yGccMP3alzSogBITgplL09/Vz6tQp/FDhuGlu3blLs+klBbAKRZdKpcLkvn2cP3+eM2fPMjTQhyWipoVts6B2QTIi9Hoj1M764AbDnrCtepyOLEv6mUQ+NqnNpV6zwerqCouLSywvL7NZ3cQPfCzbJp3OUyxVqPT00lEuknIFlvDwttZZnF9kYX6FarVJo+njKx+kJJ3KUego09/bT2exg+rGLHPzUzQCQb7cR2d3P8VClsDzmJ15ztL8IrZMUSlX6OoukMlJVtcXeTr1grV1n3y+h86uboqlLJmMjSMEVlulbgOgAsLQQ4WBrswkJEEQUt3cZHFpmYWlJTY2NvGDIArZFwhh4bgpch0d9PT00N1VIZ9NI4g72m5/lLX33DFC9PpiRMjwmrBdhF6y77eXqgeU0Fn07S2OdepClNIqJKFQCHwEHpbysRQI4SCkS6gkQVTTDQQqlIgQpFIIaijRQNguocwQIFFCmw0kASJUCKR2XQkfIT0UAYGCUDkoUigh0WFyClsIbCNCOwgIfY8giIJ+hB5gBIGuQC8dG0s6xL29QDdSC0MVueEElpRYUkSdoNjWNyfuPgpGhF53jDnO8JrQekgkVafVznVxKZ8o/D3q1SOlzstSKq4FKAkRkQ/HgjBAKQlSIiwbonmJzq7X+wyjtxMhCGHr2n+WDhiPpVEH2Mu2ArVx4zoLKXTGv8JK+uYq1dYkzDwDd6Dzv/Qxi8+DwLJtXbPRsrQwxesVCKWQVuv1ScdcBEqF2yLj4p9mjP36Y0TI8BoRh39GAe5xJHssPNsTFZBCRd3RRbQ+LkXbmjHpvhCWNudISTyfAbRwRXuTohWJjbQQUgtQvEgl7xLvWSen6nIz8dLWf/GDNRQiadxhaEcgpIWF0E3oVOwnAiHjfjdRQ7rof0rsrHLSflRbPXJ2BiOYWdDrjTHHGV4z1EtFp/VD5KdlGar2fUV1+4SMTWJi+3Zqxx/JJnGj7vZHXZS7tM1U2Hp5sqVqGRfj/ArzKNwNHWVI2CrX1BIRsWPL7X+0a8tO0237MiNCrzdGhAxvACZh9LUnGQCYc/SmYcxxhjcA82B77dleXsTwBmEy6AwGg8GwZxgRMhgMBsOeYUTIYDAYDHuGESGDwWAw7BlGhAwGg8GwZxgRMhgMBsOeYUTIYDAYDHuGESGDwWAw7BlGhAwGg8GwZxgRMhgMBsOeYUTIYDAYDHuGESGDwWAw7BlGhAwGg8GwZxgRMhgMBsOeYUTIYDAYDHuGESGDwWAw7BlGhAwGg8GwZxgRMhgMBsOeYUTIYDAYDHuGESGDwWAw7BlGhAwGg8GwZxgRMhgMBsOeYUTIYDAYDHuGESGDwWAw7BlGhAwGg8GwZxgRMhgMBsOeYUTIYDAYDHuGESGDwWAw7BlGhAwGg8GwZxgRMhgMBsOeYUTIYDAYDHuGESGDwWAw7BlGhAwGg8GwZxgRMhgMBsOeYUTIYDAYDHuGESGDwWAw7BlGhAwGg8GwZxgRMhgMBsOeYUTIYDAYDHuGESGDwWAw7BlGhAwGg8GwZxgRMhgMBsOeYUTIYDAYDHuGESGDwWAw7BlGhAwGg8GwZxgRMhgMBsOeYUTIYDAYDHuGESGDwWAw7BlGhAwGg8GwZxgRMhgMBsOeYUTIYDAYDHuGESGDwWAw7BlGhAwGg8GwZxgRMhgMBsOeYUTIYDAYDHuGESGDwWAw7BlGhAwGg8GwZxgRMhgMBsOeYUTIYDAYDHuGESGDwWAw7Bn/PyjeeFFci+/WAAAAAElFTkSuQmCC)
Particles of 1gm,1gm,2gm,2gm are placed at the comers A,B,C,D, respectively of a square of side
as shown in figure. Find the distance of centre of mass of the system from geometrical center of square.
![](data:image/png;base64,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)
If
then
has the value
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 or
If
then
has the value
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 or