Maths-
General
Easy
Question
- 0
- 1
![open parentheses pi over 180 close parentheses cubed](data:image/png;base64,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)
![4 open parentheses pi over 180 close parentheses cubed](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEYAAAAoCAYAAABD0IyuAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAaPUZr5AAAA1hJREFUeNrtWk9kHFEcftaqigixqqIil4qqilI9RETlElFREap6yCHKqqrqoVRFVUXJoYdaEVZEVUUv0VNVqageeggV0cPKpaKqaoWoijVW2P5++g2zL/Nm3sy8N2btfHxkJrPvvfnmN79/b4TobrTAJnGHOClyHMM54g9Tg90hLmf4ZitYow4KxAMTk47D/IoZFobX9o14JeS6Eh7wfNIJe4h7xIsd8IpcwFp7Q/zMnInJFokrHeQ/KlizCn3EZ8RykklOEf8Qz3SQMAPEv1h7EJwkkywQXxteODvIhses/fgw4RxrxMchPvNrkglqGMQkXhEHiRvEGc95Pp42NMcYcVfhX9hSPhCH4g4+TNy3aPLfIZALdpqnDY5fR75iHBzO1i2G1oZ0fGh4jnUTIVll8rctCTNK/CQdbxqe4xbuwTjeEa9aEuYm8aXn+IaFm5givrex+H2NkBcXK5KZL1ooN3qT+shpeGsZDdQUthyvN5PmhOsj8SwybRMoSH4ssqo1hTAtS6JwiN6Wzl1GUmY6Z2rG/WEVTipNYdLuwcRKgjYDBuhKYU6gRB/KhWnHEvFuyABdJ8wI8YvGAC2NSbNAY8JsISyK3GKiPemuj0q5xeTC5MKkcg9HMX7DzS1uKe4EXMO1UAX9F7eb5tdT7kOxuQVWcS6VkiAIcYpIrnXKIU9qDUVjEYnmEm5cBmfl16RiN0rPppikiAzCL2K/BRN2fKpg+cleh1XJeIFejg5KwlJrlhtVUxaEORTtG2IszE/pGm6M+226T+B/OuAmm5VGFXfY5i0Iw5Zwz3PMbc3n0jUHeM38ary65hrKor1LaAxzCfojrZCSpAl+Jv4Wx7dojgw41DfCUjN8OMLT0RWGq3nu3g94LOKS+N/RG9EURncHkf2Lle0TgdbEqEFh3koCeH2Hd9egrniVTmo+LB5v12aC9ADh1ZQwjqYlbCgc/6Sm82UX8MimMBzy4mzqq4Sp+VT2jPPwNS5miauKgBAWrgcR+Uq20+onIvrWhkqYWYgzgTBdwN/sY+TNPX617nsSwQU46zCwoE/TqDd6fJxjlJaG8EnethFdHNzsjM91/XiNHWSwVaH+IMgFb8nsaVxnDGMi+5+auX3s8bQnLotsf1m1LGLutf8DG77+mvNqYWEAAACtdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1uPjQ8L21uPjxtc3VwPjxtZmVuY2VkIHNlcGFyYXRvcnM9InwiPjxtZnJhYz48bWk+JiN4M0MwOzwvbWk+PG1uPjE4MDwvbW4+PC9tZnJhYz48L21mZW5jZWQ+PG1uPjM8L21uPjwvbXN1cD48L21hdGg+9R8B2QAAAABJRU5ErkJggg==)
Hint:
We can apply L'Hopital's rule, also commonly spelled L'Hospital's rule, whenever direct substitution of a limit yields an indeterminate form. This means that the limit of a quotient of functions (i.e., an algebraic fraction) is equal to the limit of their derivatives.
In this question, we have to find value of
.
The correct answer is: ![4 open parentheses pi over 180 close parentheses cubed](data:image/png;base64,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)
![L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator 3 sin space x minus sin space 3 x to the power of blank over denominator x cubed end fraction](data:image/png;base64,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)
We first try substitution:
= ![L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator 3 sin space 0 minus sin space 0 to the power of blank over denominator 0 end fraction equals space 0 over 0](data:image/png;base64,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)
Since the limit is in the form 0 over 0, it is indeterminate—we don’t yet know what is it. We need to do some work to put it in a form where we can determine the limit.
( sin 3x = 3sin x - 4sin3 x )
![L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator space 4 sin cubed space x over denominator x cubed end fraction space equals space 4 space L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator space sin cubed space x over denominator x cubed end fraction](data:image/png;base64,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)
so,![4 space L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator space sin cubed space x over denominator x cubed end fraction space equals space 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
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are fixed together using an optical glue as shown in figure. If a ray passes through the prisms without suffering any deviation, then
![](data:image/png;base64,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)
Three right angled prisms of refractive indices
and
are fixed together using an optical glue as shown in figure. If a ray passes through the prisms without suffering any deviation, then
![](data:image/png;base64,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)
physics-General
physics-
The distance between a convex lens and a plane mirror is 10 cm. The parallel rays incident on the convex lens after reflection from the mirror form image at the optical centre of the lens. Focal length of lens will be
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)
The distance between a convex lens and a plane mirror is 10 cm. The parallel rays incident on the convex lens after reflection from the mirror form image at the optical centre of the lens. Focal length of lens will be
![](data:image/png;base64,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)
physics-General
physics-
A double convex lens, lens made of a material of refractive index
, is placed inside two liquids or refractive indices
and
, as shown.
. A wide, parallel beam of light is incident on the lens from the left. The lens will give rise to
![](data:image/png;base64,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)
A double convex lens, lens made of a material of refractive index
, is placed inside two liquids or refractive indices
and
, as shown.
. A wide, parallel beam of light is incident on the lens from the left. The lens will give rise to
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAARYAAACkCAYAAABSOAGFAAAgAElEQVR4nOx9Z3Bc13X/721fbO/AopddEgAJgp0UKZKSBUqWZPUytuWMpSQez2SSDxlPJvmS5EuKP2Q8k0wmyX/8IR7Hsi2PKYmWWERSEjvBXtHboiwWuwC29933/h8492oX3IZe/H4zOyCBfe/dd8+955577u+cw3Acx4EHDx48lhCC1W4ADx48Nh54xcKDB48lB69YePDgseTgFQsPHjyWHLxi4cGDx5JDtNoN4MGDgOM4sCwLlmUBACKRCAzDrHKreCwEvGLhsWYQi8XgdDrR398PuVyO/fv3QyQSQSDgDev1Bl6x8FgzmJmZwfHjx3H69GnU1NSgsrISVVVVkMlkq900HvMEvxTwWHWwLItwOIzu7m589dVXmJmZgd/vxx/+8AdMTEzQrRGP9QPeYuGxquA4Dul0Gi6XC+fOnYNYLEZHRweSySROnjyJqqoqmEwmKJVKfku0jsBLiseqgmVZzMzM4OLFi3A4HGhvb8fTTz+N5uZmlJWV4cKFC+jt7UUqlVrtpvKYB3jFwmPVwHEcwuEwLl++jDNnzsBkMqGlpQV6vR5VVVXYt28fpqam0NnZCY/HwyuXdQResfBYFXAch1Qqhb6+Ppw/fx4TExNoaWmB1WoFwzDQaDRoa2tDXV0drl+/jnPnziEUCq12s3mUCF6x8FgVsCwLn8+Hr776CpOTkzhy5Ajq6+shFovBMAwEAgH0ej12796NVCqFr7/+Gg8fPkQ0GgUfkL/2wSsWHisOjuMQiURw+/Zt9PX1wWw2Y//+/dBqtWAYhpLiJBIJLBYL2traEAwGcfr0aUxPTyOdTvPKZY2DVyw8Vhwcx8HpdOLYsWPgOA7bt2+H2WyGRCIBAAgEAgiFQgCAXC7Hjh07UF1djf7+fvT29iISifCM3DWODadYOI5DIpGAx+NBIBAAx3H86raGwHEcZmZmcPfuXQwNDaGqqgp2ux0A6BaIWC0Mw0AkEsFsNqOtrQ1qtRp/+MMfMDAwgFQqxct1DWNDKpZYLIaenh4MDAwgEAggHo+DZVl+IK4yCGelq6sLFy5cQH19PTZv3ky3QACylApRNAKBADabDY2Njbh69Sru3buHUCjEy3MNY8MpFoFAAJlMBrlcji+//BI//elPcfXqVYRCIaRSKZ7FuYpIpVJwuVzo7OzE8PAwnnrqKTQ0NAB4UqFk+loAQK1Ww263o6WlBbdu3cL169eRTqdX61V4FEFB5m06naaf9bQ6pNNpWK1WWK1WdHd34+c//zlu3bqF9vZ22O12WCwWiMXiRTM5yQqcS2EJhUIaQJfLH0C2aKlU6on+JVsAoVBYsI0kGpi0IRPET1EoQjjz+XPbLxKJ6LWF/BmZz5/7DnOfH41G0dnZie7ubjQ0NKCurg4KhQIsyxb1mQgEAlitVhw6dAhnzpzBtWvX0NraCqPRCKFQmFcG5JPv/vnG+HxlQPpxbpuLyYD0Xz4ZkOcvVgYrzVrOq1g4jkMwGMTIyAgcDgcSicRKtmtJEAwGkUwm8dlnn+HcuXPYvn07jh49isOHD8Nut0OhUCzKCZhIJDAxMYHh4WHMzMxk3ctqtaKxsRFGoxEiUe5u9vv9GBoagtPpRCwWA/B4MEgkEthsNtTU1KCsrKygYpiensbw8DCcTicd2BzHQavVorGxEZWVlZBKpU/cg2wZHQ4HHA4H/H5/lhKprq5GU1MTtFotdaTmQigUgsPhwMjICH0HjuMglUpRW1uLuro6qNVqsCwLp9OJzs5OJJNJHDhwABqNhr5zMXAcB6VSia1bt+L+/fvo6+vDlStXcPjwYcRiMfT19cHr9WZdU1FRgcbGRphMppwy4DgOfr8fw8PDGB8fRzweB8Mw4DgOMpkMdrsdVVVVUCqVeduVTqcxOzuLwcFBOJ1Oqhw4joNGo0FTU1NBGSSTSQwPD2N0dBQ+ny9rS1hTU4PGxkbodLqCYyAcDmNkZOQJGchkMtTU1KC+vh5qtXpFHd4FLRafz4dr167hq6++QjAYXFeeeIFAgGAwiMnJSSSTSSQSCdy9exdCoRByuRwVFRVQKBSLekYikUBfXx9OnDiB3t5eiEQiaons3bsXcrkcOp0u54rJcRy8Xi8uX76MK1eu0IkNABqNBq+++ioMBgPKysryPp/jOLhcLnz55Zd0wgKPB3t9fT1effVVGI1GSKXSnNdHo1E8ePAAZ86cwejoaNbKePjwYWg0GqjV6oKKxe/34+bNmzh79ixmZ2chEAjAsiwUCgWOHj0KnU4HpVIJv9+Pq1evwu12Y9OmTbDZbJDJZOA4ruRxxTAMZDIZ9uzZg7Nnz+LSpUuw2WyYmprCH/7wBwwODkIgEFBLcs+ePXjttdeg1+sLyuDKlSu4cOECQqEQBAIB0uk0NBoN3nrrLWg0moKKhWVZTE5O4ssvv8S1a9eoLy+dTqOmpgZvvvkm9Hp9XhnE43E8ePAA586dw8jICLUsBAIBjhw5ArVaDZ1Ol/f5RLHcuHED586do8qVZVmo1Wp0dHRAr9dDpVKt6Pxl8pX/IA12u93rjk7NcRwEAgEGBwdx6tQpfPHFFygrK0N7ezs6OjrwzDPPoL6+HnK5fNEWy+zsLNxuN4LBIP09wzDQ6/Uwm83QaDQ5JybLsohEInC5XPB6vXS1JCa41WqlSqGQGe33++F2uzE7O5u1WqpUKpjNZhgMBko6m9tH5PRsenoa4XA4q/1GoxEVFRUoKysrqFjC4TCmp6fhdruzrFqxWAyTyQSTyQSxWAyHw4Gf/vSnAIA333wTdXV1EAqFC9piRyIRnDhxAg8fPsQrr7yCnTt3Ih6PZzl0GYaBTqeDxWKBRqPJuZ3gOA6hUIj239z2W61WGAwGyOXyvG1Jp9MIhUJUjplWo1KphMViWbAMTCYTLBZLwQBMjuMQjUbpPE0mk3Rxk0qlMBqNMJvNBS3f5UBBxTI3o9d6AXESnjt3DleuXAHHcWhvb8e2bdvQ1NREfSyL7ejM/pnbjeQ0o9CAINfnOhIvZW8NgD5/rowyT1QKmdGF2l/IN5H5fLJCz30++czOzuLUqVM4c+YMWlpa8MILL9DJOl/FQiwSYmmpVCq8//77qK+vf2K7sxIyKDRPismAPG+hY2juPfLJoBQ5LjXyboUyj/vWE1KpFKLRKPr7+xGNRrF9+3a0tLSgpaUFBoOhoEN1viBCK7SiF7p2Kfq32MAr1oaFtj/z+QDy3iORSMDhcOD06dMoLy/Hli1b6PZuPtuguairq4PdbsedO3fQ19eHiooKaLXaefXFUshgMfcg774YGSzFPZYDGy4fSzKZhM/ng1AoxFNPPYXa2loolUpIpdJ1pyQ3Avx+P7q6utDf34+dO3eivr6eWh0LVSoCgQBarRZ2ux0OhwOXL19GTU0N2traeBmvEWw4xSKVSlFdXQ2LxQKRSESPldeT43mjgGVZ3LlzB7du3cLu3btht9shl8tLOl4uBoZhUFlZCZvNhuPHj2PHjh3YvHkzn4B7jWDDqXeBQACJRAKlUgmZTLYq+0sej52agUAA169fR3d3Nw4ePIjq6uonKPsL/QCPT88aGxtRXl6O3t5edHd386S5NYINp1h4rA2QsIqJiQnodDrYbDao1Wq6BVrsRyAQQCQSoaKiAnv27MHQ0BAuXLhAT0V4rC423FZoLYEQoMbHxzE0NISZmZmsQW82m9Hc3AyDwUAje3MhGAzC7XbDbDZDoVCsuB8hmUxiamoKg4ODcLlcAL45DTGZTGhqaoLVas06afP7/Th37hwYhsGzzz5Lj0zJNmixk588R6lUoq2tDdeuXUN/fz+mp6dRXl4OsVhM25lKpTA6OoqRkRF4PJ6s+5SXl2PTpk0wGo30mpUCadv09DRUKlVBvgw5lu7v78fU1FRW/+n1etjt9idksJrgFcsyIxaL4d69e/joo4/w8OHDLJ7Fjh078Od//udQKpUFFYvP58OtW7ewZ8+eRZP6FoJUKoXe3l789re/RWdnJ91usCyLbdu24Qc/+AH0ej2dmOl0Gl6vFzdv3kR1dTV27doFsVic5bBdqsEvk8lQVVWFuro6TE5O4vbt2zh48CAMBgP9Tjwex927d3Hs2DHcvXsXwDenWXv27MEPf/hDqNXqFVcspG39/f2or68vqlh6enrw61//Gp2dnVl+Krvdjg8++CBLBquNvDwWHosH4Xe43W44nU74/f6sv+t0OtTW1kKj0eSl/QOPCWFerxc6nW7RpL6FgNDWJyYmMDMzQ39PaOvV1dX0KJ+wWU+ePIkTJ05g//79+M53vlM05mihYBgGLMvi+vXruHr1KgDgRz/6ETZv3ky/k0qlcsqA4zgYDAbU1NQUlcFyIZVKwe/3o6ysrCARL5VKwev1Ynx8HLOzs1l/U6lUqKmpoXFTvMWywUF4IhaLBSaTKYuENR/yklwuh0wmW7UBIxAIYDAYoNVqnyCBzSVxkZST169fh8Vigd1uh1gsXjaSJenH5uZmjI+P4/Lly5iYmEBtbS3ts0wZ5Gr/ak5GoVBYMBYo83tEBrnGUTEy5EqDVyzLjKUgoS3Xaj/f5xfz7ZDAxuHhYUxOTuKpp55CZWXlsrdfIBDAbDbTxNuPHj1CU1MTqqqqqNJYawQyglL7Zr0RVtdHK3msC6RSKTgcDnR2dsJoNKKpqSkrgnk5PxzHoaKiAps3b0Z3dzeGh4f5o+dVBK9YNghIQFsoFKJJrYiPJxKJwOfzIZFILOtRbCqVQn9/P27dugW73Y6amhpqMWRumZbjw7IsysvL0draSk/hlvvomZz6+f1+hMNh2uepVArhcBjBYBDxePyP8vibVywbBMRa+PnPf45jx47RfL/hcBifffYZ/vu//5vWQc4X9LYYkNwmDocDkUgENpsNZrN5xUx3hnmcUqG8vBwWiwVjY2NwOBzLGpVPcsz84he/wO9+9zsEg0GwLItgMIiTJ0/if/7nfzA6OkqTUK23YN7FgPexLAHIBCVZyOZm8SolyphYFwuJcGVZFqFQCPfu3cPt27fR3t5OV87BwUHcunULXq8XDocDt27dgsfjQWNjI3bu3JkVuLeY9icSCQwNDWFychLV1dUoLy+HVCpFMplcEt5KMZBnaDQaNDc3o7e3F48ePUJVVRUALEgGhd6d4zjE43F0d3fj7t27sNlsNJPcxMQEbt26BZfLhf3796OnpwculwtmsxkHDhyAVqvNm3hqoTIgKBTtTqzHlfDX8YpliRCNRuFyuTAzM0PzehBhlpeXw2w25z3ZSaVS8Pl8cLlcCAaDWYNKrVbDarUWzORG8rLcunULFRUV2LlzJ6RSKVKpFO7cuQMAsNlsGBsbw8WLF/HgwQPs2rULWq0WbW1tkEgkCIfDcLlcmJ6ezhqUxAowGo2QSCQ52585yaanp7Fz504olcqs+6zEYGYYBmq1mibdvnLlCoxGI5RKJX2HfEe6LMtidnYWLpcLoVCI8kRqa2thtVqf+D5xVD948AAqlQrt7e1UkQ4NDSGRSMBut2NychKXL1/G3bt3aYH7tra2JzgrLMtSGczMzGT5hyQSCSoqKmA2mwsS4MiJ3NTUFLxeb9Y4UigUsFqt0Ol0K8J14RXLEoDjOExMTODDDz/E6dOn4Xa7qRWg0+nw7rvv4s0330R1dXXOQRGJRHD16lX83//9H+7evUsHhEAgQHt7O/70T/8UBw4cyJush+M4BAIB9PX1YevWraitrYVYLKa0+nQ6DYVCAY/Hgx/96EdwOp0YGhrCwMAAWlpawDAMBgcH8atf/QonTpygSacAwGKx4P3338dLL70Es9mc9/nRaBQ9PT3w+Xxob2+HUqlcVATzQsBxHMrKymhE+0cffYTf//73MJlM+JM/+RO8+uqrqK2tzdmmRCKBa9eu4Ve/+hXu3buHZDIJiUSCn/zkJ3j//fdzPi8ej2NwcBBKpRKVlZUQi8WIRCIYGxtDIpGASqVCd3c3XnnlFXR0dKCnpwddXV2orq7OqVgGBgboGMqsnWQwGPDBBx/g1Vdfhclkytun6XQad+7cwW9/+1ucP38e6XSa+p9sNht+9KMf4ciRIwUz0i0VeMWyRDAYDHjuuefQ1NSEcDhMhS+VStHc3AytVpv3WqlUipaWFrz33ns4evQoXekZhkF5eTmampoKMnMjkQgmJiYQi8VQWVkJi8UChmEwPT2Nhw8fYuvWrfjWt76FVCqFyspKyGQyRKNRer1QKERFRQVeeuklNDc3ZzFr1Wo1WlpaCqY2JHlbyfPJykoUy0o4LzPbJpfL0dTUhNHRUZhMJhw6dAh79+4tKAORSITm5mZ873vfQ0dHB9LpNIRCIXbt2vXEd8nWb2RkBIFAADabDRUVFTQdan9/P1iWxb59+yAQCFBXVwePx4NQKIRIJJK3/VarFS+99BJaW1uzstkpFAq0trYWZOYCj+XY2NiIN998E3v27KFWF8uyMBqNaG1thUwmK9aVSwJesSwBSJ3hAwcO4MCBA/O+XiaToampCU1NTfO+luM4eDwe9Pb20sTJEokEfr8fAwMDEIlEqKqqwqZNmwA8XpkDgQDEYjGqq6tpNn6LxQKLxYIjR47Muw3xeBw3btyAQCBAc3NzVjrNldrTZ2ZSE4lEsNvtGB4eRmVlJV5//XVYLJaCPBaxWFyyDFiWxfT0NO7fvw+9Xg+bzYaysjJ6KpZMJlFVVYXa2lqYTCak02k4HA6k02ls2rQJKpXqiXsSEp/FYllwHxAlVldXt+B7LBV4xbLOwXEcpqam0NXVRbPykwTNp06dgt1uh8FgQH9/P7RaLbxeLzweD3Q6HZqamha93+a4x3WYb926BbPZTBUYyTucyTNZbhCnJ1GaUqkUDocDXq+X0t2XAizLwuPx4M6dOzCbzaipqQHLshgZGcHJkychFotRXl4Ol8sFoVBIfTdarRatra0FE6RvFPDHzesY5OSHRL36fD6EQiGMjY3h7Nmz+OyzzyAWi2kW+b6+PnzxxRcQCASw2+1LEiaQSqUwOzuLkZERqNVq1NfX07ZlYrkJcpl9IhQKYbVaUVNTA47jMDw8jEgksmTKjcRO9fT0wO12IxAIYGxsDOfPn8fx48fh8/kwMzNDM+9fvnwZsVgMLS0tayb6eLnBWyzrGCzLwuv1wul0YnZ2FseOHcO5c+doLWSpVIqPP/4YTz31FA4ePIiRkRGYzWZUVVVhfHwcDx48wKFDhxa1gs7MzKCrqwtmsxlmszlnBreVOhGa+3+r1Qqn04nu7m60tbVRFvBiQBzlk5OTCIfD+OKLL3D9+nXYbDaajf/atWu0dlJ3dzfkcjmsViu8Xi/u3LmDPXv25Dxp2kjgFcs6Rjqdxq1btxAKhfDjH/8YsVgMyWQSZrMZWq0WHR0dmJ2dRX19PTiOw8cff4xEIgGNRgOtVovm5uZFkbY4joPT6cT9+/dhtVphNpufOAlaya3Q3LaRBNvd3d30GH8xSo4wbfv6+jA+Po4/+7M/QywWQywWg9FoRHl5Ofbu3YtgMIjKykqIRCL87ne/QywWg1qthlarRX19/boqpbNQ8IplhUAmFikVkfn7zACzUgd+JikOAN5++216cjN3MqfTaXR3d8NoNGJiYgKzs7MwmUyora2lfodMUlihd8hk7HLc44Jpd+/exdNPP00juHNhuZy4ucp2kN+Xl5dDr9fj2rVrlBtC+iWXQi0mA3KsTqou/vCHP4TRaKSnL5l9zjAMent7YTabMT4+jmAwCLVajaamJnq6kymfUp5PrpnLmiZjKNOntdrgFcsKIhaLwefzwev10lWL4zhIJBJoNBrodLqS/R6RSAR9fX0IBAL0xCPf/l0oFKK1tRX/8A//QKslisViSKVSSCQSsCyLeDwO4DEZK9/gDofD8Pl88Pv9YFkWEokEXV1dGBoawjvvvAO9Xp9zki/nQM9lDRFlo1arYTKZIBAI4HQ6EQgEoFAo4PV64fP5aF8Aj/tDo9HQqoW52pxOpzEwMACPxwOlUgmxWFwwarqpqQl///d/T58jFAohk8myHObRaJTS/hUKBYxGY94sgcRR7vP54PP5soqjyWQy6HQ6aDSavETGlcSGUyxEoycSCQiFwoL8j5UEx3GYnZ3F559/jnPnztE6vSzLQqPR4Pnnn8cLL7wAq9Va0qCIxWLo7e2FXq/Htm3b6GTIdS3DPK4Hna8vUqkUJicnEYlEYLfb8w7q8fFxnDp1Cl999RXC4TA4joPb7YZarS5YRpS0YTlQbHujVqtRVVWFsbExOJ1OGAwGnDhxAl988QV8Ph8tqapUKvHSSy/h+eefp6kecmF4eBgSiQRbtmwpWKUSeOzjKtQnAOD1evFP//RPlP7/xhtvoLW1NW8IB5HB119/jXA4TNtvNBrxyiuv4JlnnlnUkfVSYUMqlmg0ioGBAWi1WtTU1KyJHBYMw0CpVKK9vR0KhSKreLdcLofNZoNSqSx5ApaVlWHXrl1gGAYWi6XoIC/WNq1WWzSfrl6vx65du6DX6xEMBtHb24tYLAaVSrUmVsm5IDWkrVYrJicnMTExgZqaGmzbtg1yufyJIvb5OCYEAoEAW7duRXNzM8xmc8GMb6VCoVDg5ZdfRigUQnV1ddHATZ1OR2VASHQc97ic6+bNm1cldWkubLjUlESx3LlzByMjIxCLxWhra0NdXR0d/KsxAYgllU6nqWmcSd0XCoXzqtKYGWhGYpIW07a5GclyIZ1OI5VK0dIeZ86cwdmzZ2EymfD666/DarXS7Plki0A+uY6GF4O5Pqt0Ok0/qVSKpjBwu924efMmrly5gqNHj+L73/8+PabPfG8iA7KdzBe6MB9/SCnvkLkNzey7YjIg7Scg/UzG0GqjoMWS6ShaT/qHUOGvX7+Omzdvor+/HwcPHkRDQwO0Wi3KyspWPI0fmfxLtT1bTGnVuSh1wmf6E6LRKKanpwEAu3fvpqU9VgqkvYWeSaxBs9kMj8dDM/QX2hYWe+ZS5sUlY2I+x/1EBsW2WKuNvL1E4iGCwSBCodC6y8bFsix27tyJyclJ/Pd//zeOHTuGw4cP44UXXkB7ezu0Wu0fDVlpOUBKgkSjUZoioRiW2lospsiIYjEajYjH4/B6vUgmk3y1xBVAQfXrdrvx9ddf48qVK1mBdesBAoEAoVAIIyMjmJ2dxezsLPx+P6ampuDxeNDR0QGTybTazVyXSKfT8Pv9iMVi0Gg01AIsFYvhtZRiqcz9vkQigcFgQCKRgMvlQlVV1Zpx6m9UFLRYRCIR9Ho9qqqqsqJh1wOEQiHcbjcmJiZo/IhMJoNSqaQTYaXD+jcCiH/C5XIhnU7DYDDMy7+TGZy4GJSqnAjFv6KiAqlUCmNjYzCZTLxiWWbkVSwMw8BkMuHIkSPYv3//uvKxkDyvN2/eRDKZhFgsRkNDA3bv3k2LkysUCl6pLACEfTo5OYlUKgW9Xg+hUDiv8UGU+mLbUSpIKVaXy4XR0VGaBoLH8qGgYiEh9WvlCKsUEC97d3c3urq6IJPJ8N5772Hfvn201sxS+lYIaSkQCCASiWSVEJVKpdRZXMjpl0qlEI1G6fYi84RGLpdDrVYXPAqOx+PUF5aZClIoFEKj0UCpVBb0gRDeD0kKncnslEgkUKvVUKlUVIFkKhaDwTDvbVDmz4VgvkqJpIWYmJjA2NgYPYXJBFmM/H4/4vE4PXETCARZciwmg2AwiFQqlVMGhY7k58og8/RJJBJBo9FQGeS6B0ngHQgEEIvF6PMJzUGlUuVNFLYc2HA8lng8DqfTCZ/Phx07dtD8qyQl31I7D9PpNO7du4fPPvsMV65cQSqVgkAgQDKZRENDA77//e9j37590Ov1ee8TDodx/fp1fPzxx3j48GFWgp729na8/fbb2LNnT84qiCR7HSF9TU9PQyQS0axxb731Fp577jnU19fnffdkMonBwUF88skn+Oqrr+jES6fTqKiowFtvvYVvfetbMBqN9Psulwssy1LFMt/JvlKKhUzu8vJypNNpTExMZCVRIojH47h27Ro++eQTdHV1UQUtEAjQ2tqKd955B/v27cvLFxobG8Pp06dx8uRJeL1eCIVCKoPXX38dzz//fFYIxVyk02kqgwsXLiAUCtF+NRqNePvtt3H06FFqIc5FIBDAhQsXcPz4cfT09EAkElHleOjQIbz22mvYtm3bivGNNpxiEYlE0Gq12Lp1KxQKBU1cvBzHy+SUo7KyEocPH0ZdXR1VCul0Gnq9Ho2NjUWzdkmlUtTV1eHo0aPYtm1bFkeDhP8Xypui1WqxY8cOqFQqRCIRmo5QIpFg69at0Gq1Bd9dKBTCaDTiqaeegsViyQo3UKlUaGlpoVtHlmURi8UwMzMDkUgEg8Ewr34leVpKwVIFL5L3E4vF8Pl81CrMbLdYLEZ9fT2OHj2K9vb2LIvBYrGgpqamoNWp0+mwY8cOKBQKRKPRLBm0trZmJS3PBYFAAKPRiP3796OioiIrPahCoUBLS0tBi0Mmk8Fut+PFF1/Erl27srandXV1qKioWNGKjxuOIAd8Q/haCTIceVY6nc6bGb2UwLJ89yDErXyDMjOQbW5wGllxiw0o8vxcZUEy3wF4vLJ3dXXh3//932EwGPDd734XSqUyi9yVjyBHuDdzV1yyMmcWOp9rBWX+m7QxMyN9LoJc5u/i8Th+85vfwOFw4C//8i+xZ8+erGPnTBnM5W0VkwFpU77+K7WMa+YYyCeDQgGS+TL0l9L+pcaGs1iAlS1JWoxRWko7FnMP8rdCwXDF2pD5/Fz3INezLItIJILh4WHIZDJqrWRaWKWC3DMajcLr9SIWi8FisUCpVNKqBR6PB0ajETqdjk6KxayDWq0WLpeL8m8yQygWK0cy6Qv1XzFkkijne4+5C8BC27BUWH3u7wZB5sBcKH19MffId+182lDseo57XACNhEpkTviFgGVZjI+P4xe/+AV+9rOfYWZmBgzDIBwO4/z58/jXf7XPP4kAACAASURBVP1X3L9/H7FYDOFwGNFodMH5YxiGoZG/Lpcry0k+nz4o9ozVHANL1YalwIa0WHgsD4hiGRoaglQqhV6vX/CgJadLXV1dcDqdtKwFx3EYGhpCb28vDX+YnJzE6OgolEolWltbIZVKF2S5KBQKiMVievKzAb0Aawa8xcKjZHDc4yJdLpeLHkMvxsEaj8fR19cHjuNohUCGYTA0NASPx4P29nakUil0d3fjwYMHcDgcOU90Smk38NjBKRKJaJ1lHssH3mJZQWQ62Mj/gdJLaOaruUyuL2b2Zjppc0U0FwtsJFaG3++HSCRaFC+CZMCbmJgAwzBobGxEWVkZEokEBgcH4Xa78cILL0AoFCIWi4FlWVrkfSFH2wzDQCqVQigUUr5PIpHIcvSXWoY1Vwa3zGuXWwZzHbTk+ZnjYLXBK5YVAgnqJNnLMrN/kexlOp0uL8+AFBsnmfgz76tQKKDX66FUKgvS60m6A+IszUwZoFAoYDAYCjKS4/E4zV4mFApz8mpKgUAgQCQSweDgIOLxOGpra1FVVQWhUIipqSkMDAwgGo1i165dkMvlcDgcS1IDWiqVQiQSYWpqCoODg4jFYvRYltAUCsmA47hFy4CUwyUyINdnyqAQES8ajWZl8SPXSySSrAxyqw1esawQOO5xBrmzZ8/iwoUL8Pv9dKKo1WocOXIEzz77LMrLy3MO6nQ6jUePHuHcuXN4+PAhXWVZloXdbsfLL7+M9vb2gsmHotEobt68ibNnz8LhcNBJKhaLsXXrVrz44otoaWnJW7Dc6XSis7MTfr8fEolkwaH7RLGQgl8tLS0QCATw+/24ffs2ZDIZtm7dSldfiUQy77CBuW0nFotEIsHAwAB+9rOfQaPRUL6JQqHAc889h2eeeQbl5eU5lQPLsujq6sLZs2fR1dWVdezd3NyMF198saAMSJzVzZs3cebMGYyNjVGrRSQSoa2tDS+//DI2bdqUN4uf0+nEl19+iStXrtAyrISoePToURw8eLBgGdaVAq9YVhCkuHdLSwutc0NIaOXl5UWLh5GC55kBlCzLorq6uigJDng8oQ0GA2w2G7RaLV3xxGIx6urqaOhGvuBMqVRKOSuEr7LQU5poNIr79+/DYDBQQtijR49w7NgxqFQq1NbW4sqVK7DZbFlJsBcDshUiFQkrKiqoYigrKysp/YNGo0FjYyNVdORTW1ub5XMqJAuDwQC73Q69Xk8tV5FIhLq6uqK5WWQyGaqqqrBly5Ysi0er1dLyK2sBa6MVfwRgmMfpH59++ukngjozJ2q+ASkSibBp0yY0NTU94Xgkmc+KRRnL5XK0tbU9UfaD7M3JPXK1gWEeB6XabDZoNJoFVVAkfoRUKoXp6WkMDQ1haGgIIpEIvb296O/vx40bNyhLdnZ2FlarFSqVioYpLOZ4WywWQyAQwGKx4Pvf/z7sdjvdNszNIJcLQqEQNpsNDQ0NOWVAYusKcWFIRsPm5uYnfCyZMsh3fUVFBUwmEw4fPvzEGCr2/JUEr1hWCJnkp4VsIcigXExJVOIYXOg9otEowuEwDahbiAXBMAycTif6+vpQXl6OyclJXL58Gb29vbDZbNi+fTvGx8cxNTWFjo4OqNVqTE5OYnh4mGbbr6mpWVBxc4FAQLPHxWIxlJWVzes+a0EG6z6DHA8emeA4jioWwgdZ6OkMOT5+//33odFokEqlaAkUclokkUhgNpvR09NDAzzVajUEAgG+853voK6ubkFZDSUSCcRiMT0ZWkwSch75wSsWHiWDKJaysrJ5r7hkC+T1euFwOBAIBFBdXY36+vqs7dfcEIGmpia8+uqr2L9/PyQSCaxWK3Q63YJ9O8TiCIfDC+LE8CgNvGLhUTKWQrH09/djamoK1dXVUCgUBQukAUBVVRWsVmuWL4IEGC4EmRYLYd/yFsvSg1csPEpC5laIJMua76RkWRbhcBhmsxktLS3Q6XT0+kL3yvwOOeJd6CkRsVgyFQuPpQevWHiUBIZhEI1GEQqFqKUxH8VCuBo7duxAW1sbFArFvB2n5D6LAVEs0WiU3wotI3jFsoSYm9MkH2W/GOU7V16NzHsUys2SK6fIXLr4Qp4PPK4XHQqFSuLc5LovSc6+mrRz8txC9bJIH2Syo8m1xWRA7p1PBpnF2/Ih3zgCQFMjzDc3DHleKfmBlgK8YlkikFwlnZ2duHLlCtxuNx0UJJPbkSNHUF1dnXdSchwHj8eDa9eu4caNG5idnc3KRHbo0CHs2bMnb33ndDqNrq4uXLx4EQMDA0gkEnQyWK1WPPvss9i6dWvBwvOJRAI3b95EZ2cnhoaGAHwzKGdmZpBIJFBZWblgJmxm9cZCuUOWa4tCZFJock1NTeHGjRu4evUqDV9gWRZisRgHDx7E3r17UVlZ+UT7CbO2q6sLly5dQn9/P+W7MMzjTIMdHR3YtGkTlEpl3jYSVvLly5fpMTtp95YtW3Do0CHYbLacnBuWZeFyuXDhwgXcv3+fMrwZhkFZWRkOHz6MPXv2UAW/XOAVyxKBsGB9Ph8cDgfGxsbo78jRKWFKFkImecztdtNBLZPJ0NzcXNR8D4fDmJiYyFIs5L6hUKjohCXxMKOjo+jv788auKlUCmq1Ouud54P5BBAul3KZq1hyvUMymcTMzAwGBwcxOztL2boSiQSbNm2iwYv57h+JRDAxMYH+/v4sqyedTiMUChU90eI4DoFAAGNjY+jv789SLDqdjiZtz4dEIgGPx4PBwUF4vV6qQFQqFbZu3boikd0bMjXlaoE4J0lYfmaQH6lpVCiZMRl84XAYkUgkawAwDENrIuULMiNpDcLhcFameULsUqlUkMlkRc1o4qQlSbXJBPz666/x5Zdforq6Gjt37kRNTU0WaziTfVosNWWuiOy5PzMp8+T/mduMUlNTkn8nEgncv38fN2/eRENDA1599VU0NDQ8wXRNJpOIRCJZ2fKJHBUKBT0VyxeoGIvFEAqFkEgklkwGBHK5nFZdyPd8sohEo9Gs3L0Mw9Bs/ctN/d+QFgsZaLnyqy4nBAIBnfxzQQRbaJUne3CVSpXTVC7leplMljcRUil7a4FAgLKyMsjl8qx7sCwLjUZDLaj1uh5lWiz5JrdIJCoqg0L9uFwyKOX5DPNNuZBM63Lu9cuNDadYyIoxPDwMtVpNA7NWymFIlMNirl9MO5di4OS6R+aAXq+KhWyvivlYFtOHc62uhWKxbVhtbs6GUyzA49XV7Xajq6sLWq0WdrsdVqt1UTEePL5ZbefjK1lLyNxSrZWESBsVRRXLehxEUqkUNTU16O/vx/nz51FbW4vdu3ejpqYGJpOpYFVBHvlBtpb5LJZi27R8UdOl3iPzOwtlzGb6vfgxsHwoqFhSqRTi8fi6ZCiq1Wq0tLSgv78f//u//4uTJ0/iyJEj+Na3voVt27ZBLpfzA2seyPRLLHQrRO5R6O+F/j8f5FNic7dC63HhXA/Iq1hYlsXY2BhOnjyJ8+fPIxqNrivTkWEYeuw3PDwMh8OB4eFh3Lt3Dy+++CJefPFFqFSqdfVOawEkudNcslhmztVcvyeTl9Q1JphP/2duZTKR6f8hbSDKg/xkWTarLcTvRuoc81g6MAxT2GIh6QcnJyfR29ubtxbLWgIZOJlHkMBj03dqagoXL16Ex+OBw+GYd3nQP1aQPurr60NXVxcYhoHX66UpEHMpk7mKJdeH3LuYDOYqlMxjaPKZyzbNPJYmP1OpFEZHRzExMYFQKISpqSlotdo1P6bXGwQCQWEeC8d9k6f11KlTGB0dXcn2LQhEsXi9XrjdbkQiEej1+qKJonkUh8/nw8zMDFiWhVqtpqksS1Uc+X7OB7mUDPk5l/eSmWyaKJtAIIBQKASNRgO9Xr/mEyatR4hEouIEuWQyCZ/Ph9nZWZq8d61r+FQqhfv37+P27dsIhULYtm0b2tvbodPpAHxDtOIxPzx8+BCXLl1CNBrFzp07UVdXl0V6m/vJJMPlUioLYe5m/jsXcY7UPs4kzGUS5e7evYuHDx/i6aefxr59+womH+exMBTdCgGPo0FNJhNMJtNKtGnRSCQScDqdsFgs+Pa3vw2r1UqTA/Gr08JBJu/IyAhmZ2dRU1ODzZs3P8G8zce+zfR/ZG6PSnGgz7VKMoPz5jJvCcs2F/M2Ho/D6XRCo9GgpaUFO3fuLJq8msfCsOF4LCTYym63Q61WQ6/XFyyWzaN0SCQSyOVyhEIhxGIxah3M3YIA2VsT4jjNjHnJpVTyUdTnWia5fClzLZNc/06n04hEIohEIkXr//BYHDacYhGJRDAajTR6k1coSwelUgm1Wk2TJAFPTvxC25VcR7sL4aPke97c78z9HqFPcBxH/UM8lgcbTrHMx8TmMT8oFAqoVCoEAgHE4/El87etlEM9FoshkUhAJpMVDAblsXhsOMXCY3nAMAwUCgXUajUCgUBJKSBKxUocBnDc49SayWQSSqWyYP0gHosHv6zzKBlSqRQKhQI+n++JcP71gGg0ilQqRRULj+UDr1h4lAyGYWgekHg8jmQyudpNKglky0YUC6msyFssywd+K7REKGTOlzqAF3OPlXq+WCyGXq9HKpVCOBzOmfOjVBDH7UrxoshJllqtzutjydeWUvpwtcdAoetXWonyimUJkEgk6AqeKViRSERLZRTLGJZKpRCLxbIyz5GkPeQe+QZHKpVCIpFAIpF4IuOZVCqFRCIpmDGM0N6JczPzHUg5T2KpSCQSqlgikQhUKlXJ/ZTv2Ss16ElGNWKxzG1HMplctAwyM/cBC5NBMpl8IjcwkUG+ccSyLJLJJOLx+BPtJ6E5K2ml8YplkUgmk7h58yYtA5pKpSAQCJBMJlFfX4/33nsP+/btg16vz3uPUCiEzs5OfPzxx3j48CEdFOl0Gtu3b8c777yD3bt3Qy6XPzEwOI7D2NgYPv/8c5w+fRozMzO0gHpZWRnefvttdHR0oK6uLu+gSiaT6O/vx8cff4yvvvqK5tVNp9MoLy/HO++8g2effRZarRYSiQQGg4FyQoCVXw0XApIAjIQjzLVYYrEYLl26hE8++QSPHj2iwZIMw2DLli149913sW/fvryWjsPhwOnTp3HixAl4vV6aJ7esrAxvvPEGnn/+edTW1ublzqTTafT29uKTTz7B+fPnEQ6HKe/HYDDg3XffRUdHBwwGQ07l4vf7cf78eXz66afo6emBWCymyunpp5/GG2+8gba2thU7DeMVyyIhEAig0WjQ2NhITW2GYeikNBgMRR2FpCzGpk2bsur1sCyLxsZGaLXagmQumUyGqqoqtLW1IRgM0mhemUwGq9VaMCs/8M2JT319PXw+H5LJJH0Hg8EAi8VCB+RcxbLWwzsyEYlEkEwmodFonrA+BAIBlYFUKs0KXq2rq4NWqy3Yh3K5HJWVlWhra0MoFMqSQWVlZc5FYS4UCgXq6uoQCAQQjUapYtFoNDCbzXlzHQOPx5DJZEJLSwsl/xHZNDY20rrXK7UI8Mm0lwCZNPNMEDO21L3xQu+RyXCdi1JJgqXcI51OY2JiAh9++CEmJyexZcsW7Nq1CzKZrCCdP18y7fkM8szcKfNNpk22GB9++CHGxsbw13/919i5c2fO7dByyaDUKO58uW5KuUe+WknzGYdLBd5iWQIwzOLy3C72HktBCizlHgzzOFl3eXk5xsbGEAgEVsxiWexz4vE4ba9arc7Z12tBBosZR2uJFLp2WsJjzYNhGMjlctTU1CAej8Pn8y1qwufKq1LKZ75IpVLweDzgOA5mszlv6QweSwdesfAoGcRiqa6uBsuytDIi+dtanKzEV+RyuSASiVBVVcVHua8AeMXCY15gmG8Kp8VisQVvh1bqGuCxxTI1NcUrlhUEr1h4zAsM87iin8ViAcMwNKPcQrDcWyCCVCoFl8sFoVDIK5YVAq9YeMwL5MjZarVCJBJhZmYmi5RXClb6IDKdTsPtdkMsFqOqqqrgsS2PpQGvWHjMC8RiKS8vh0gkwuzs7LzYs+R7C3XczlcpcRyHeDwOt9sNiUSCiooKPgBxBcAfN/OYN8RiMSoqKiAUCue9FVpJa4VhGCQSCfh8PgCPE1VJJJI1dSy7UcH38ApjKX0HqwWBQEArSgaDwTVb0I5hHteWcrvdMJvNMJvNeS2m1cJCn79W2p8PvMWyAshMi5hKpXIGmK3WSprJFi3Gzkwmk0gmk0gkEpT2H4lEMDMzA41GUxK5a6UtlkgkgqmpKRpeQeKFUqkU/c5Ky4CMBRK0SvxWEomEspILXUuCHYFv+lMoFGbdY7XBK5YVQCqVwsOHD/Hpp5+is7Mzq6qk1WrFW2+9hSNHjkCj0ayociEKr6+vD2KxGHV1dXkdmxzHob+/HydPnsS5c+fg9/vhdDpRWVmJsbExVFVVQSaTlfzclYBAIEAwGMT4+Dg2bdoEv9+Pf/u3f8ONGzcQDoezZPD222/j0KFDRWOClgJerxe//OUvcfLkSaRSKchkMrz44ot4+eWXUV1dnTcKmuM49PX14dSpU/jyyy/pO6TTaZjNZrz66qt49tlnUVFRseqcog2pWMgqvFZy35JAxc2bN0MoFNJ8sQCg1+thtVpXJQcr6R+SRqBYX6lUKjQ1NSEajSIcDmNmZgaBQADDw8PYtm0bNBpNSc9drGIppZ9IbJHf78fo6Cg6OjrQ1NQEqVQKoVBIS6syDAOdTreiTl2JRIKmpiYcOHAA6XQaYrEYDQ0NJRXUIzKIRCL0HUigYnV1dcnKfbmx4YIQSV6NmZkZyOVyqNXqNcEKzQyYywSZ3IsxX8k+O/M9c/2u0PWkLcW+RwIAk8kkxsfH8dFHH+HmzZv4i7/4CzQ1NUEgEOQNQiSfpRhymUGJ+UqARKNRfPHFF/jd736Hf/7nf8b+/fuz3jfzXpn1jkpB5j3m2+ekH+fmbSm2Dcp3LQEpc7PaYx3YoBZLLBZDT08PRCIRamtrodPpUFZWtqp7z8y6OnOx0IFABpnP50MgEEBFRQXkcjk4joPP54PP54Nery9aQ2c+R8UikQgcx0EoFKK6uhoGgwETExMIBAJIp9NFrZ6lWsfIffLdj2EYuFwueL1e1NfXQ6fTFYz0no8MkskkgsEggsEgNBoNNBoNOO5xvpepqSkolcq8eVPIs0g/zvf5ua5dyDssN1Z/n7AMkMlk0Ol0uHnzJv7zP/8TX3/9NaamphAMBp/I8rbSyFy5F2tJsSyL6elpfPLJJ/iXf/kXuN1usCyLeDyOy5cv42//9m9x9epVBAIBTE1NYWZmBpFIZNHlZTMdnmazGVqtFk6nE16vt6TUAkv5KQSXywWfzwe73Q6VSlW0QH0pYFkWXq8Xn3/+Of7mb/4GPT091ILr6enB3/3d3+HTTz+F1+uFx+OBx+NBJBLJSSJczBhYynG0HChqsazHnZJQKITNZoPb7cbIyAj+67/+C83Nzdi/fz927NiBmpqakszOtQ6WZdHb24v+/n7qdE2n05icnERfXx/dh589exYXLlyAXq/HCy+8gK1bt5a0ny8GhmFQXl4Ou90Op9OJ6elplJeX5/zuco6jXFsbhmEwOTmJQCCAp556atEpNMlzSJnZR48eQaFQUEtwamoK9+/fp/6nK1eu4NKlS0ilUnjxxRexfft26HS6dT/mSkVexcJxHKanp/Hw4UN0d3evy3IPs7OzGBwcxNWrV3Hnzh3cvn0bhw4dwjPPPIP29nZoNJp1Leh0Oo2enh6EQiEcPHgQKpUKqVQK4+Pj8Pl82L59OzweD8LhMIRCITweD7q7u+mWaSm2huXl5di6dSuuXbuG6enpnP250osTy7KIRqPweDxIJBKor69HWVnZksg6nU5jbGwMbrcbR44cgdVqBcMwcDqd6OvrQ3t7O0QiEUZHR5FKpeD3+9HT0wOr1VrykfxGQEHF4vP5cPv2bZw6dQqBQGBdTUKGYRCNRjE9PY1oNIpIJIJ79+4BADQaDZqamqhjdz2CHBU7HA5Eo1E0NTVBLpfT383OzmLv3r3wer1oampCR0cHenp6MD09jXA4vGQOVIvFgpaWFpw4cQLT09NIp9OrOnnI8avH40EgEIBKpYJer1+SEx+O45BIJDA5OQmv14vGxkbodDpwHIfJyUkMDAzgO9/5DlKpFPR6PQ4fPoyBgQHa56SG9Xodc/NBXsXCMAxqa2vxwQcf4N133130vnwlQTzzjx49wieffIKTJ09CrVZjz549eP7553HgwIEsFuZ6RDweh8PhwMzMDLRaLSorKyESiRAKhdDX14fZ2Vns2LEDVqsV0WgUQ0NDiEajsNvtsFgsS3YMX1ZWhvr6ehrp7PV6YTQa6d9XmhnKMAySySRGRkYAAA0NDUtmrbAsi8nJSbjdbmi1WtTX10MqlSISiWBgYAAjIyPYtm0bamtrEY/HMTo6Cq/Xi+rqahoCsZ7H3HxQULGIxWJotdqS+QlrAWQlHx0dxfj4OIRCIV577TVs27YNra2tqK2thdFoXPcFq4LBIG7fvg2JRIKWlhYoFAokEgn09vYiFAqhoaGBlqy4cOECfv3rX8NkMuG1114rWIZivmAYBmVlZWhsbKSTyWAwZPXtaiiWwcFBAEBTU9OSboPu37+PRCKBtrY2SKVS2ueBQACtra1QqVQQCoV48OABfvnLX0IoFOLll19e0j5fDyj4tkQY62kCJpNJzM7O4tGjR0gkEti9eze2bNkCu92+rhRkMYRCIdy9exepVArV1dWQSqUYHh7GqVOnMDs7i4aGBsqolUgkMJlMkEql6OvrQ3V1NZRK5ZJYLWQB2rJlC+7du4ehoSHs2LFjxRVL5vFzMBjEwMAADAYDNm/eDIVCsSTvShjUfr8f+/fvh1gshsvlwokTJ+ByudDe3o6HDx+iqakJQqEQFosF8XgcY2NjcLlcVOGup/m0UGw4NUoKN5nNZjQ1NaGiogJlZWUbKgcHx3EIBAIYHByEy+WCUqmEx+PB9PQ0vv76awSDQahUKrjdbjgcDmzfvh0/+clPcP/+fVy5cgWTk5Ooq6tbsvZIpVK0tbVRxRKNRilJbiWtFY57XEZ1cnISsVgMlZWVdAuyWLAsi0gkAofDQev2+P1+BINBXLx4ETMzMxCLxXC73RgbG8OOHTvw4x//GMPDw7h48SImJiYo8/qPARtOsYjFYlRWVqK8vJyyQFcC5CgyHo/T+kJkUgkEAojFYpSVleXdghEuBLme4zgIBALIZDLIZDL6HizLIhQKYXx8nCZaOnbsGC5evIgdO3bAYrFgenoa/f39eOWVV3D27Fn4fD68+eabkEgkBasykuA4EqiXGeBGKvHlar9IJEJNTQ3UajUGBgYwPj6OxsZGlJWVrfg2KBgMoqenB2VlZdBqtQgEAjRgUiKR0NOwXH2QKQNSPJ68L/FdkTCBzz77DF9++SX27t1LeTxXr17FBx98gO7ubrjdbrz11lsQi8U0jKAUFJKBRCKhYyGf1UNcAaSqJeHPEEtJLpfT9iyn5bThKP1Abrr1coNlWQSDQZw+fRqff/45xsbGqONSKpXiwIEDeOONN2C323NaT+l0Go8ePcJnn32GCxcu0IH18ssv44MPPqAO0UQige7ubpw+fRo2mw1arRbJZBIikQgGgwEsy8Lv90Mul8NkMuHChQu4cuUKRkdHUV5ejqNHj+LIkSOwWCxPDPaxsTGcO3cOJ0+ehNvtBsM8Lpoml8vx/PPP49vf/jY18+e+ezgcxieffIJLly5h8+bNeP7552GxWOadXW4x4DgOQ0ND+I//+A90dnZCoVBAr9fTk5inn34ab731FhobGyGXy5+4npDcPv74YwwMDOAf//EfUVdXB4FAgK6uLnz44Ydobm6G1Wqlyopsb4LBIDiOQ21tLW7fvo2zZ89idHQUCoUCHR0deOaZZ1BXV1dQwbAsi6mpKZw6dQqnTp2Cx+Ohv1epVHj22Wfx0ksvobGxsWBFRYfDgU8//RSXLl3CzMwMVaIqlQqvv/46jh49Shfe5cKGs1iA1fEJkRWxvr4ehw4dwuzsLIDHg10kEqGpqYnSyvNdr9PpsG3bNsjlcsoQbmtro4FlHMchHA5jeHgY09PT+Pa3v42GhgZqzZBViRxrchyH5557DmazGQMDAzCZTNi7dy+MRmPOdigUCthsNpokm8TjiMVitLa25uX9MAwDqVSK5uZmdHV14datWzhw4AAqKiqyLLflBKEXTExMIBgM4rnnnsOmTZuyVmybzQadTpfXihUIBNDpdGhvb4fVaoVKpQLHcYhEIhgbG8Po6CieffZZ7N69mx5fZ8Y/kdNIqVQKhUKBgYEBlJWVYc+ePaioqCg6kYkj3GazIR6PIxgMAngsd5lMhubm5qLcK4ZhoFKpsGXLFkgkkqwobplMBpvNtmTO7ILvshEtltUCid3JNZlIMF6x4vDk+szrMrdBPT09OHnyJBKJBN56660sxVLoniTau1AU82LaTwiVv/nNb3D8+HH81V/9FXbt2rVi0eVCoRBjY2M4c+YMurq68IMf/AD79u3LiquZGxCZ6x0yg/xI/ePR0VGcOnUKg4OD+O53v4tt27YV5MVkVmdkGGZewYGLHUNz32Gu9Z7ZB8uJDWmxrBbIxM1nphYTJhl8cxVF5nV+vx8cx2HHjh15LY9c9yylDZkDb77tZ5jHZUHq6uqg1+sxMDCAmpqaFeMLMQwDj8eD4eFh2O12VFRU5PRtFHuHTKVDyHZ+vx+pVAoHDx5EVVVVyX1Onj2f91+MDHK9w0LusRTgFcsyYDGCKzYgWlpaYLVaoVaroVKpSnrWfAf2QiESiVBfX48tW7ZgcHAQzc3NMBqNy346RBznHo8HTqeTJjtaKMs18xqBQICGhgZ6XF9qMq7lGgMreY/FgFcs6wgCgQBarRZarXa1m5ITIpEI1dXV2Lp1K27cuAGHwwG73U5TOSyHciE+JafTSU/Kampqliwbn1AoocwmBQAADU5JREFUpKkReJSODZk2gcfqIJOFq1arMTo6CpfLRS2K5UibQFbmBw8ewOVyoa2traQtIo/lBd/7PJYUAoEABoMBu3btwuTkJKXWL9dWiHCH7t+/D7/fj6eeegoGg2FZnsWjdPCKhceSQiAQQK/XY+fOnfB6vRgeHkY8Hs9KzblUH5K1bWJiAkNDQxCLxdi+ffuS5F7hsTjwioXHkoLwOGpqamCz2TA7O4u7d+9SQtlSb4MCgQDu3r0LjUaDbdu2LVkMFI/FgXferjDIpJjLMQC+OaYsJW9sps+CgBwzFjoNyZyY+RJ7lxIol2k15LqHWq3G/v37cfbsWVy+fBnNzc2QyWRLuiXiOA5erxednZ2w2+14+umnswiCxfogF88jsw+LPXsxMgC+6cNMkGtLeX6+cTQfOS4XeMWywohGoxgfH8fAwADNEUvigqqrq9HY2Aiz2ZyXx0Cyow0ODmJoaAjhcJj+TSQSoa6uDna7HWq1Ouc90uk0pqamMDg4iImJiSxFYzQaYbPZUFlZCalUmpdElkqlMDY2hoGBAczOzlJCn0AggNFoREtLC/R6PXbt2oXr16+ju7sbHo+nIMdnIYhEIhgdHcWjR4/AsiyuX7+OwcFBbNq0CbW1tZDL5TnfIRKJYGJiAgMDA7T8KpFBVVUVmpqaYDab8yoHEpA4ODgIh8NBGbKEg1JMBslkksZzOZ3OLOWi0+lgt9tRXV2dtyQMiWkaHx/H4OAgPB5PliPbZDKhpaUFRqMRUql0YZ27SPCKZYURjUZx//59HDt2DENDQ1kr7OHDh/H222/DYDAUnIDBYBCdnZ04fvw4pqen6YolEonw8ssvF83M73A4cPz4cVy/fp2GDrAsi+bmZrzzzjtFByTJtfv73/8evb29SCaTAB4rlm3btkGhUECr1aKiogI2mw1DQ0O4d+8eJBIJLBbLkiQNEwgEcLvd6O3thVQqRVdXFwYHB2G1WvHuu+/CZDLljAcCsmUwPDycxcw9cOAA3nnnnYJZ9gEgEAjg+vXr+Pzzz+FyuejvpVIpXnjhBeh0urwyIPE8x48fx9WrV7P6o76+Hu+99x6MRmPBiPxEIoGenh4cO3YMjx49ou/AMAy2bNmCH/7wh9BoNKumWHhK/wojHo/D7XbTkhmZK5LFYkFVVRW0Wm1B6nw8HofT6cTExARisRj9m1AoREVFBaqqqvLmIGFZFrOzs5iYmKBKiXxI0SuTyVSQsp5Op+F2uzE+Pk6ZwMDjQa3ValFXVwetVguRSITr16/jxIkTcDgcNOHWYuOHiIl/48YNfP7552hoaMCOHTugUCggkUhQU1OD8vLyvCt+LBaDx+PB+Ph4VppOhmFgMplQXV1dVAaxWAxOpxOTk5OIRCL0OQKBAFartaAMSC7csbGxrIWB4zioVCrU1tbCZDIVjIQn6TdJfuNMkOx2Go1mxYqwzQWvWFYYxDrIVXSKxIEU2y7kiyche+ti8TCZsSyZINcWY6xmvkOmj4E8M/MeXq8XFy5cwP/7f/8Pzz33HA4fPkwZwwsZeuQ6j8eDr776CkNDQ/je976H3bt3U0VSLB4mnwwy/RulymCun6RUGeSL58l8fqkymDuOSLoQ3sfyR4RisSCl3kMkEi0o10zm8xe6ms3nHVQqFex2O6xWK4aGhlBXV4ctW7YsmIlLJkp/fz/6+/tht9tpXttS+2MpZbDQa0txEBe7x2LfYTnBn8vxWFYIBAKYzWZ0dHQgFAqht7eXFk1byBEzyXszMDCAcDiMnTt3LmlycB5LA14aPJYV5Oh5+/btMJvNcDgcGBgYoNuwzK1ZKYS4RCKBhw8fYmpqCg0NDTRpE69Y1hZ4afBYdgiFQpjNZmzfvh2hUAj37t2jJ0nztVji8Tju3LmDVCqFAwcOPFERgMfaAK9YeCw7GIaBQqHA9u3bUV5ejtHRUQwPD2fldS32AUDrIzmdTlitVuzatQtKpXKV345HLmxIxTJ3QPJYXRBHZ3l5ObZv3w6GYXDt2jV4vd6SFQs5Ybp16xaUSiWNYl6t41QehbHhFAvZs0ciESQSidVuDo8MlJWVYd++faipqcGdO3fgdDqRSCRK8rMQxvD9+/exdetW7N69e82eiPDYoIolGo2iu7sbQ0NDCAaDdPDyWF2IRCJYrVbs3r0bFRUVuHPnDg0rKOSwBYDh4WF0dXXRhOOlJKfmsXrYcDwWwg+IxWK4e/cuBAIBdu3aBZvNRmvqLNeAXAxxDcidTBvAE6StUohfxYhr+Z6fef1821+I+EWeT1IbeDwefPTRRzCZTLBYLJTcNvcacs+uri48fPgQR44cQVNTU8FYprVCXJu7HS9GQMw8Ui8kAz6Z9iqAhO3bbDb09/fj0qVLePToEfbu3YvW1lZUVlZCrVYvuXIhNO/h4WH09/fTOjMcx9Eiaps3b4Zer89JrGJZFm63mwa2ZR7HarVa2Gw21NTUoKysLG8b0uk0Jicn0dvbC4/HQ1MVEKp9S0sLqqqqIBaLcw6sYDCIkZERDA4O0uBGjuNoWZPGxkbo9fqCisXn86G/vx+jo6OIRqP0u1KpFHa7HY2NjTCZTNizZw9OnTqF4eFh1NTUYNOmTTn9YqlUClNTU+ju7kYikaDlS/JNTCKDwcHBLKo7CfJsbm6GVqvN6ZthWRbT09MYGBjA6OholnKYK4NCSs3pdKK/vx9utxupVArAN+EOra2tqKiooCVd5iIcDmNoaAgDAwOIRCL0vjKZDLW1tUXLyGTKYGxsjIYbMMzj8jSbNm1CfX39sqeXyKtYOO5xPRWPxwOPx7OihacWC6L11Wo1xGIxfv3rX+PMmTPYt28fOjo6sGvXLpSXl0Mmky2p5k4mk+jq6sLnn3+O8fFx2haxWIyDBw/CaDRCp9Plvd7j8eDixf/f3rm8pNOFcfw7DVHpqOWQTiNCmAsjyK50ISihy6aSrEVtgv6A/p82LVvVIiioaBFdRBdB0qqiCEpUsrCBtJJ03oXMeeet32gXe38Z57NWz5nzjM9zznOeyz78fj+en58B5JSF3W6H1+uF1WrNq1iAf5uOKc3LgdxL7XA4UFVVBUEQNB2eylXwxsYGbm9vSYJkZWUlhoaGYDab884fACljsLu7C0mSSH8jg8EAr9cLQRCg0+kgCAJGR0exs7ODUCgEm832Rh4Mk2sEFggEkEgk0N3dTbJ+tXh8fCQyuL6+JuMzDIO+vj7wPA+j0fjH7yqpAnt7e/D7/WT9FBlMTEzAYrHklUE2m0U4HMb29jaOj4/JtTqQa1BvMBjA87ymYkmlUgiFQtja2iINywCA4zh4PB7wPF9QBpIkIRgM4uDgAIlEgigQk8mE8fFxWK3Wb79N08wVymazuLi4wNraGjY3N98kzP10ysrKkE6nEY/HyTneaDSira0NY2NjmJychCiKRdPaspwrJxCLxRCLxYi1UebC8zxsNhsMBoNme09JkhCLxRCPx8k2XpZl6HQ6iKJIKsVroSQYRiIRSJL0n6OAXq+H3W4Hz/OaoeiKIYlGo0SxybIMlmUhCAIEQQDHcXl3LMlkEtFoFPF4HOl0mny2vLwcoiiS5EDFsi8sLODi4gIejwdNTU3Q6/Vk3plMBicnJ1hZWYEgCJifn0djY6PmjkuWc+UEbm5uSHKgmtraWthsNs2sYyWqNxKJ4Pb29o0MbDYbyTrOd5zUkgHHcbDb7aipqfmjclfidJR3SJEBkPNPWSyWd8lAKQtxd3eH5+fnNzKwWq1FN6qv0VQsypbq/Pwcl5eXJXfDwrIsrq6u4Pf7sb+/j4qKCrhcLgwMDGBwcBDNzc3vbp/xXvL5OD7iY1G/0MDHkgMVBfdVH4t6fPV3Cyli9fMrz6GMp85tUY4tu7u7WF5ehiRJmJ6eRn19PRn3/v4e29vbiEQiGBkZgc/ng16vL7gGav/CR2Tw2j+hXoOP+lheO5+/KgN1r6JiyOCv+lhMJhPa2trgdru/dRLFRFnMZDKJQCCA6+tr9PT0oKGhAZ2dnejo6IDD4chrdT7LVxPDvupYVp+lvzL+Z5Pr1L9RCIbJNShvb2/H6ekp1tfXcXp6iurqaphMJlJIKRwOo7W1Ff39/e+ysqWeHPh/yuA70Zy9ssiyLP/1SX6ETCaDp6cnHB4eIhQKQa/XY25ujlxxKi1GS+lY91thmFy/ao/Hg0QigbOzM5jNZjQ1NSEajSIYDMJoNKKrqwuCINC4lRKioFostT9gJpMhJR97e3tRV1eH2tpamEymT1tyyvfBsiycTieGh4exuLiIo6MjyHKuD3Q4HMbMzAxcLpdm0SPKz+TXFXp6eXlBKpVCMpmETqeD0WikL+QPRzEGq6urWFpaAsMwxFk9OzsLt9tdUrtmyi+MvGVZFhzHwWKxFN05S/kelNaxfX19aGlpQSwWw/39PaampuB0OqlSKUF+ZYAcVSalheJwFUURPp8PFRUVMBgMcLvdBeN2KD+TX3cUopQu2WwW6XQaDw8PYBgmb5Qv5WdDFQvlR6GOPaFHoNKFKhYKhVJ0qEmgUChFhyoWCoVSdKhioVAoRecffjnPejC7/vsAAAAASUVORK5CYII=)
physics-General
physics-
The slab of a material of refractive index 2 shown in figure has curved surface APB of radius of curvature 10 cm and a plane surface CD. On the left of APB is air and on the right of CD is water with refractive indices as given in figure. An object O is placed at a distance of 15 cm from pole P as shown. The distance of the final image of O from P, as viewed from the left is
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)
The slab of a material of refractive index 2 shown in figure has curved surface APB of radius of curvature 10 cm and a plane surface CD. On the left of APB is air and on the right of CD is water with refractive indices as given in figure. An object O is placed at a distance of 15 cm from pole P as shown. The distance of the final image of O from P, as viewed from the left is
![](data:image/png;base64,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)
physics-General
physics-
.A rod of glass (
= 1.5) and of square cross section is bent into the shape shown in the figure. A parallel beam of light falls on the plane flat surface A as shown in the figure. If d is the width of a side and R is the radius of circular arc then for what maximum value of
light entering the glass slab through surface A emerges from the glass through B
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAARcAAAEJCAYAAAC+D2M/AAAgAElEQVR4nOy9eXRU93n//5p9RjOaGc2MRrvQghYkIcS+yoABg1nsGJN6gdR23SV16qSLT7r5pN8kTU/b+KTpOW3d7aSNkzh4w3ZsjMxuQAaEQSALCdC+7xrNSJp9+f3h370FrywjZiTd1zkcgzTW/QzMfd/n83ye5/3IIpFIBAkJCYkoI4/1AiQkJGYmkrhISEhMCZK4SEhITAmSuEhISEwJkrhISEhMCZK4SEhITAmSuEhISEwJkrhISEhMCZK4SEhITAmSuEhISEwJkrhISEhMCZK4SEhITAmSuEhISEwJkrhISEhMCZK4SEhITAmSuEhISEwJkrhISEhMCZK4SMx6gsEgXq+XYDAY66XMKJSxXoCExN0kEokwOTlJIBBAJpPh9XqZmJhgfHwcq9VKdnZ2rJc4Y5DERWLa4Ha76e/vZ2xsTPzlcDhwuVz4fD68Xi8+nw+Px0MwGEQmk4lf93q9hMNhAAKBAKFQCJlMhlKpJBQKMTIywj333MOTTz5JTk4OGo0mxu92+iOJi0RMCYVCBAIBAoEAPp8Pn89HIBDA7/ff8Huv18vw8DBDQ0NMTk4yMTGBy+XC5XIxOTkpvl74JYjH9V8Ph8PIZDIUCgUymQwAg8GA3+/n4sWLaDQaNm/eTFpamiQuUUASF4mYEQwGGRkZYWhoiJGREbq6uujs7GRkZITe3l46OzsZGBhgYmKCSCRCQkICFouFtLQ0rFYrRqORtLQ0EhMT0Wg0aDQatFotWq0WhUIBcMPX5PJPUowJCQmoVCoikQh6vZ6Ojg7+/u//ntTUVPH/k7hzJHGRmFIikQiDg4P09fWJkUd7ezsOh4NgMChuVcLhMOFwmFAoRCQSwWg0UlJSQnFxMXK5HJVKhV6vJzExkaSkJBITE9Hr9RgMBnQ6HSqVCpVKhVqtRq1Wo1AoiEQiN3xNEBeVSiV+32AwEAqFMBqNqFQqcc0Sd44kLhJRIRwOEwwGCYVChEIhwuEwPp+Pvr4+WltbuXr1Kr29vXR1dXH+/HlGR0fR6XRYLBasVitJSUmkp6eTlpaGxWIhJSWFjIwMkpOTMRqNaLVaZDIZ4XCYSCQi/gJu+L3w5+uJRCLiugD8fv8N6xYSvMK2SSI6SOIiERWGh4dpaWmhpaWF7u5uGhoaaGxsRKlUipFFZmYm5eXlLF++HKvVSmpqqhhlKJVKNBoNarUapVKJWq1Go9GgUqmQy+XiMfH1gnL9fwW+KOqQopG7jyQuErfE+Pi4eELjcrkYHh5mZGQEp9NJf38/o6OjhEIhxsbGkMvl2O12UlNTMRqN5OTkkJubS0pKCna7HYvFAiBuhYSt0ef9Xog6JKYPkrhI3DSDg4O0tLRw+fJl2tra6Ojo4MyZM4yMjJCWlobJZCI1NZWKigrWrl1Lamoq2dnZmEwmMbdyPWNjYzF4FxJ3C0lcJL4Qj8dDXV0ddXV1XL16lZ6eHiYmJpDJZJjNZpKTk9m6dSsGg4E5c+ag1+tJSEjAZrNhNpsxGAzo9XpUKtVnIpFP50kk/g+Px0N3dzfnz5+npKSE8vLyG74fiUSmRW5IEhcJEZ/Ph8vlwuFw4HA46O/vp66ujsbGRrq7u5mcnESr1ZKZmUlOTg7FxcVkZGSQlpaG3W5HoVCISd3rT3+ksvpbIxKJ4PF46O/vx+PxEA6HMZlMWCwWTCbTtBAWkMRF4v8nHA7T3NzMyZMn2b9/P83NzUQiEVJSUpg/fz7btm0jJSVFjEY0Gg1KpRKFQoFCocDtdiOTyb701Ebi5khISKCoqAiLxcKLL77I888/T2VlJY899hgPPvjgDa+N5yhGEpdZSjAYpL+/n4aGBlpaWhgYGGBgYACn04larWbhwoXYbDYyMjKYO3cuRUVFJCUliac5kUiEYDD4meSrRHTQaDRkZmayY8cOXC4XdXV1vPjii1y4cIGioiJKSkqoqKiIW2EBSVxmDcJ2xefzMT4+zuDgIM3NzRw6dIiLFy8yMjKCTqejsLCQTZs2sWDBAjIzM8X6EkFI/H7/DXUiMxHhhvV4PPh8vphs62QyGXK5nOLiYp566imee+453n//fd5//33mzZvHzp07SUhIYO7cuQBigWA8IYnLLKG1tZX6+npqa2s5d+4ck5OTGI1GrFYrW7Zsobi4WEzCWiwWDAaDWCI/26ISrVbL6Ogob731Fu+++y61tbXi9u9ucP1WR6FQEAgE6O3tFb9/5coV/vVf/5VXXnmF3bt388wzz2Cz2eJOYCRxmcEMDw/T3NxMW1sb3d3d9Pb2MjAwQCQSwWq1kpWVRUFBAaWlpZSUlKDX64lEIgQCAbE0fzYmYyORCAqFAoPBgN1uJzMzE4VCcddvXqHJ0uv14nQ6cbvdAGKPldVqxWAw3NCIGU9I4jJDGR4epqamhv/6r/+ioaEBm81GVlYWZWVlrFixguzsbPR6PYAYnYyPj8d41fGBz+fDZDLx9a9/nV27dsVkDTKZTNyOXrt2jeeff54DBw6gVCpZtWoVO3bsYNu2bWRnZ8dts6UkLjOI0dFR6urqOHz4MD09Pfj9ftFGoLi4mNTUVOx2O+np6eITTzgunm1bny9D+HsQbvBYcuLECV555RUAvvGNb7BkyRIKCwvJzc0lOzs75uv7MiRxmeYIJfj9/f10dXVRX19PdXU1Pp+PrKwsli9fzsKFC5k7dy4JCQniKU8wGCQQCMR6+RJfgNfrpaenhwsXLtDe3s7SpUvZuHEja9eujWtBuR5JXKYxExMTHDlyhKqqKqqrqwmHwxQWFvLYY49RXFyM1WoV61Hkcjk+nw+Q6k/inWAwyODgIDU1NRQXF7Nz507MZjN6vX7aCAtI4jLt8Pv9XL58mcuXL9PY2EhTUxOTk5OUlZWRkpJCUVERS5YsISMjA61WK0YpQnOgRPwjl8sxGAwUFBRgs9nIycmJ9ZJuC0lcpgGCN4rP56O5uZmqqiqOHTtGU1MTFouFe+65h4cffpi8vDz0ej1+v59QKMTExESsl37H3MyTeqaJplwux2KxiF3j0xVJXKYB7e3tvPPOO5w+fZquri40Gg0FBQXs3LmTrKws0tLSsNlsqFQqsdhtut9wQq2HTqdDq9V+5j0JoiN47EpmT/GHJC5xitfrpa+vjytXrlBXV0d9fT2jo6OYTCby8/NZsWIFS5cuxWazoVAoxAa3meJ7olQqCYfDnDp1ivb2dnQ6HaFQSKwOjkQiyOVysrOzmTNnDhaLBZVKNWPe/0xAEpc4xOPxcPXqVT744ANeeuklPB4Pq1ev5oknnqC8vFz0exW6Z2ciarUan8/HL37xC1577TWAzzRGAmzatImHHnqIDRs2iAIkER9I4hJH+Hw+Ll68yDvvvENTUxN+v5/Fixczd+5cSktLycnJwWq13tA4+HkmTDMBIQG9Zs0a2tvbOXfuHPPnz2f37t3AJzOMnE4nZ86c4ZVXXqGgoACDwSBui6bzttDj8dDT00NtbS3FxcXMnz//hu/Hcyf09UjiEgcEAgEGBwdpaGjg5MmTHDx4kFAoRFlZGdu3b2fBggUkJiaKM36EI+WZjBCBVFRU0NfXR2NjI2vXruXP/uzPgE+EeGhoiKeeeorTp08zNDREIBAQHfynM+FwGLfbTVdXF263G7lcjtFoxGQyYTQap4WwgCQucUFDQwOvvvoqhw8fxu12s3LlStatW8fChQvR6XQolUq8Xi8wvZ/It4JwAw0PDzM+Pk5hYSHJyck4nU7C4TBqtRqj0Yher4/b3prbRa/XU1hYiNls5j/+4z/43ve+R2VlJY8++ijbt2+/4bXxHMVI4hIjXC4Xzc3NnD59mra2NiYmJigpKSElJYUlS5ZQVlZGenq6OHVwtoiKgHDDdHV1MTg4SGlpKQUFBSQkJKBUKunu7qampoaxsTGys7OxWq1otdoZk3PRarVkZ2dz//33Mzw8zJUrV/j3f/93Ll26RGFhIUVFRZSXl8etsIAkLncdn8+Hw+GgsbGRU6dO8corr2Aymfja177GmjVryMnJQS6Xz/pGQrlcjkwmE2cdVVRUEA6H6ezsRKvVUldXx3vvvYdKpWLVqlWkpqai0WiYnJy842sLN6zP58Pv98fUz6W8vJxvfvObPPfcc+zfv5/9+/dTWlrKww8/jF6vJz8/n3A4HHd2CyCJy11lYmKC6upqXn75ZTo6OkhISOCBBx5gwYIFFBYWYrVakcvlM6JO5U6Ry+XI5XL8fj8tLS00NDTw5ptvYjKZCAQCFBQUcN999/HQQw+Rnp6OyWQSt453ikajYXR0lN/85je899571NbWii0UdxPBciEQCNDZ2Sl+vaGhgb6+Pl599VUef/xxvvnNb4qfnXhCEpe7wOTkJC0tLZw9e5aPPvqItrY2EhISKC0tZePGjRQWFooh/Wz0T/k0MpmMUCiEx+NhcHAQj8dDSUkJarUaj8fD5OQkLpeLpqYmysvLKSwsxO12R3VLJJfL0Wq1JCYmYrFYYubnIgisVqsVozKdTkdiYiIJCQmo1eq46N7+PCRxmWLC4TAXL17k1Vdf5e2330apVPKNb3yDdevWUVhYKB4lz4YToJtFJpOJp0FtbW2YTCZ++tOfUlJSwujoKD6fj1//+tf86Ec/QqPRMGfOHBISEkQLiTvF5/NhNpv5rd/6LXbt2hWTKPJ6P5fm5mbRz0WhUIh+Llu3bmXOnDlxe0ImiUsUuT5zHw6HuXz5Mnv37qW5uRmFQsEDDzxAQUEBFRUVZGdno9VqxT6g2b4Nuh65XI7L5aKrq4tgMIjZbMZsNmMymYhEIqjVarKysjAYDIyMjNDR0cHcuXPF+Uh3ivBvIWzNYsmpU6d47bXXkMlk7N69m0WLFlFUVER+fj45OTlxGbEISOISRYR/6LGxMRobGzl58iQHDhxAo9GwadMmtm7dSlFRkdilLNgWSvwfwlZgfHyctrY2NBoNZrMZn88nWj1qtVr0ej0mkwmPx8PQ0BC5ubkxF4JoIrR/nDt3jitXrrB06VI2bdrEunXrps37lMQlyjgcDt544w327dtHZ2cn9913H6tXr6a0tBSDwYDX65UStl+BQqHA6XTS0tKCyWQiNzdX7BuSyWRig2Z/fz+Tk5PT5ma7WUKhEIODg5w9e5bCwkJ27NiBxWIhMTFxWr1XSVyiyEcffcSJEyeorq5GLpezfv167r33XkpKSjCbzZL7200gdEK73W6uXLlCWloaFRUVWCwWzGYzDoeD48ePc+DAAfx+PykpKRQWFqJWq2dMjQt8UkiXm5tLcnIyeXl5sV7ObSGJyx0i9Ph0d3fz6quvcvLkSRQKBQ8//DA7duwgISEBuVw+YxsMo00kEsHtdtPb20tTUxM2mw2NRsPg4CCRSIT+/n5++ctfcuTIEXQ6HRUVFRQXF+NyuWaMuCgUCqxWK1arNdZLuSMkcblDBgcHee+993j33XfRaDSsX7+e8vJyioqKRFtCaQt0c2g0GpxOJ7/5zW947bXX6O7uZt++fZw+fRq9Xo9SqSQQCNDf309FRQV/+Id/SEVFBZOTkzO2gXM6I4nLbeJwOGhqaqKmpoYzZ84wPDzMunXrqKyspLi4GI1GIyZuJW4OQYQjkQhz5sxh/fr1eL1esf4nFAqh1WrJzMxky5YtbNu2DZlMxtjYWFyfmsxWJHG5DTweD8ePH+ett97i5MmTFBYW8uSTT7J48WJSUlIIBoMzfuTpVCAUi23fvp2tW7d+JuK7/qhfOK6Gm7PClLj7SOJyi/T09PD6669z4sQJRkZG2Lp1K0uWLGHhwoViCba0FbozhIkFXzTsS8hz+Xy+qHUFX1+fJBEdJHG5SYRS9JMnT3L06FFGR0cpLCzk0UcfpaCgQCxZlyKWOycQCNz0qdqdCovwIBDaLpRKZcwjIcGQfWJigoSEBHEy5nRDEpebwOfzcenSJX7yk5/Q3t7OypUr2bVrF8XFxSQnJ4vTCqVoZXoinFCFw2EMBkPMy+ndbjfNzc0cOXKERYsWsX79+piu53aRxOUraG9v59SpU5w4cYLR0VHmzZtHZWUlpaWl2Gw2aRTqNEeIXIQWjHgwnlKpVJhMJrKysqitreXChQvMnTuX8vJycnNzb3htPJtFTZ9yvxgwODjIoUOH+PWvf83Ro0dZvnw5Tz/9NKtWrcJqtUp9QTMA4eaMJ+9djUZDbm4u27ZtY2Jigh/+8If89Kc/5cCBAzgcDsLhsLhtjFdhAUlcbuD6D1ZbWxv79u3jV7/6FQkJCfzFX/wFO3bsIDs7WzRzkpiZxIPAwCdVut/61rf4z//8T1QqFT/+8Y/52te+xnPPPcf7778f6+V9JdK26DqEELmzs5P9+/dz8uRJEhISWLFiBZs3b0an093w1JCYmQjFeu3t7XR3dzMyMnLXPVOEBk6VSoXb7WZwcJD29nba29tpbGwU17Vs2TJyc3PRaDRxF8VI4vIpOjo62Lt3L/v37wfgT/7kTygvLxdNe+LlqSYxdahUKgYGBnjnnXfYu3cv586dA4hp0+D1kfLQ0BCvvfYa+/bt43d/93f53ve+R2pqqiQu8UooFKK6upqqqipOnDhBfn4+99xzDyUlJRiNRim3MosIBoMYjUYqKyuxWq309PSI9Ut3CyFyUSgUjI2NsW/fPurr6wFIT09nwYIFlJWVsX79eoxGY1x2S0viwic2lFeuXOH111/n3LlzKJVKNmzYwI4dO/D5fOL8ZYnZQSAQQKfTsXTpUpYuXRrTtQSDQT766COuXLnC+Pg4JpOJlStXsnnzZjZu3EhiYmJM1/dlSOICnDhxgl/84hc0NjZSXFzM7/zO75CXl4fP55OOmSVihjDO9n//939JSUnhW9/6Fvfeey8ZGRmih248M6vFxe1288EHH3Do0CGGh4dZtGgRlZWVlJWVibOKJWGZfcRD7mJsbIwrV67g9/tZvXo1ZWVlLFmyhHnz5sV6aTfNrBQXoWjq448/5qWXXmJsbIzy8nLR41Yov5aEZeYTD0LyaYLBIE6nk9bWVkpLS3n66afRaDSxXtYtMyvFxefz8W//9m/s378ftVrN6tWrue+++0hJSZHmBk1zhCPjTydgP32ULPxZp9Oh1WpvqMyN9b+9QqHAbrezdu1a9Hr9tBQWmIXi0tfXR3V1NadOnWJiYoKtW7eyceNGFixYgN/vx+/3o1TOur+WGUE4HBabR/1+v1iPJESqQqvG9U2mCQkJtLe3MzY2RkpKSlyU0wuil5GREdN13Cmz6i7y+XwcPnyYv/u7v6OoqIinn36ae++9F6vVyvj4eMyfWBK3hyAGwWCQyclJRkdHGRkZweFwEIlECIfDeDwe3G43Pp9PtB0dGRlBoVAwOjpKe3s7OTk5MX4nM4tZIy4+n4+XXnqJ119/nb6+PoLBIG63m+PHjwNEbRSoxO0hbGWE2g7hv9dvVYSTu3A4/Lm/FwzQPR4PHo/nhkkLwveECQLC6+CTo2eXy4VGo8FqtU7bbUi8MSvExe12c+nSJfbv309tbS0Azc3NNDc3o9Pp0Gg0YhGSFL1MLYJYfPq/kUiEQCAgbmm+qndLoVCgUChQqVSisZQgTkI+5atyLgkJCYTDYfR6PZmZmcyfPx+LxRLzbdFMYVaIy/79+/nFL36BRqNh7ty51NTUAGAymfjud7/LokWLMBgM4lNQ+nBFn+u7jwURkMvlKJVKIpEIfr+frq4url27Rnt7uyj+/f39RCIRrFYrFosFm81GZmYmKSkpJCUlkZmZSVpaGhaLBYPBIPbY3EruRFiT2WyWopYoMqPFZXx8nA8//JBjx47hcrnYuXMnLS0tnD59mpycHMrKymhoaCA7O5tly5bd8MGUuHOuL2EXRMTr9TIyMsLo6Cijo6MMDw8zOjqK0+kUq6EtFguLFy9m8eLFBINBVCoVNpsNo9FIYmIiycnJmM1mDAYDNpsNi8WCVquN9duV+BQzVlzC4TANDQ38z//8D06nk+XLl7N9+3Y++OADZDIZDz30EPPmzeNP//RPcbvdLFiwgKSkpKgNM5f4BCEfEgqFCAQCOJ1OmpubaW1tFSOUrq4uHA4HGRkZlJWVkZmZSXl5OYsXLyY1NRWj0RhzdziJW2dGicv1ofCxY8fYv38/IyMjLFy4kG3btmGz2USPW6vVyj333MMPfvAD0tPTxVGZMplMFBgpgrl5hC2PQqFArVYjk8nweDx0dXVx8eJFPvzwQ/r7+wmFQiQmJpKYmIjRaGTz5s3Y7Xa0Wi02mw2bzUZCQgImk4mkpCQpIpnGzChxEeoX2tra2L9/P+fPn6e8vJxVq1ZRVFQklvTDJ54d2dnZPPzwwwDiLOJAIEAkEhGThFIU8/lcnz8BxLyJw+EQtzoOh4POzk7RFyUQCGAymcjIyCAzM1NMoubn58d1A57E7TGjxAXg6tWr/PznP+fYsWNYrVYefvhhsaT/eqEQhmypVCqx+Mrn8+FyuXC5XNjtdiwWi1StexNcn0u5du0ahw8fpq6ujuHhYXQ6HaWlpezevZuKigqys7PF6YnXJ3clZh4zSlza2to4cOAAx44do7y8nHvvvZfs7Gw0Go0YkVzP9WXiQt1DdXU1b731Fjt27BBnPctkMnH0xGxGON3RarWMj4/T09NDZ2cnzc3NNDU14fV6xWhv1apVZGZmYjabycjIoLi4mPT0dGmbM4uYMeLS19fH/v37qa6uRq1Ws3nzZu6//368Xu8XzhISirCuZ2hoiDNnzqDT6bDZbFRUVJCUlHQ33kLcIoiwUHjY19dHb2+vmJhtaWmhra0NvV5Pfn4+ixcvZvXq1SxdulQ61p/FzAhxaW1tpaqqip/97GfY7Xb+9E//lJKSEtGW8qtqHsLhMHK5HIvFwtatWzGbzbz00ks8//zz/NVf/RWrVq3CYrGIr50tCHkVtVqNSqVicHCQCxcu8Prrr9Pc3IxKpSIvL48VK1bwh3/4h2KkotPpxIhPYvYyrcUlEokwODhIVVUV+/fvx2azsWbNGhYuXIher79lBzmFQkFWVhYbNmygqamJy5cvEwqFbmgNmOl1MDKZTMyHBINBvF4vzc3N1NfXMzg4yMDAAGNjY2RlZVFUVERxcTFlZWWUlZXFvXmRxN1lWovLyMiIeOTc0tLCn/zJn7B27Vo0Gs1ted4Gg0HkcjnJycns2bOHgYEBtFrtDYIyk4UF/u/Ux+/343K5GB0d5cyZM7zxxhv4/X5ycnJYs2YN99xzD8uWLZMEReILmbbiEg6Hqa+v52c/+xnhcJhdu3aJ+ZE7MdMWtlDp6elYrVYikYjYe3T9seunT5+mM0KiVqlU4nQ6+fjjjzl37hwff/wxPp8Pq9XKzp07KSwsJCcnRyzDl4RF4suYluISiUS4cOECH3zwAQMDA6xevZr777+ftLS0O962CDkarVaLTqcDPhEyl8vFxYsXkclklJeXi0V301VghHyKMKNnYGCAnp4eWlpauHLlCj09Pfh8PgwGAyUlJezYsYOSkhLp2FjippmW4jIxMcEbb7zB6dOnWbduHffeey95eXkAURtYJrTmC7mH3t5eXnjhBYLBIM8//zzz58/HZDJN+zoYlUrFyMgINTU1vPnmm9TW1mKxWNi8eTO/9Vu/RV5enji6QhIWiVth2onL0NAQx48fp6OjA7vdzoYNGygpKUGpVEa9FkUQDYVCQVJSEhs2bODMmTP85Cc/4aGHHmLr1q0YDAaUSuW0iWCE8nyPx0N3dzenT5+moaGBkZERrFYrTzzxBDk5OZSXl1NaWiptfSRum2knLhcvXuStt95CqVSyfPlyKioqSExMxO12T8n1IpEICoUCm83G7t270el0/PjHPyYlJYWCggJKS0vRaDRxLy7XR2ETExNiz8/+/fvp7e0lNzeXBx98kO3bt8/6uh6J6DBtxCUYDPLxxx/z3nvvUV1dze///u+zefNmFAqF2C80VQjCYbVa2bRpEwaDgWvXrlFdXU1ubi5JSUlxPT9asD1QqVT09vZSVVXF0aNHaWlpoaKigq997WusXLmS3NxczGZzrJcrMUOYNuLicDh48803aWhoEEdZpqSk4PF4CIVCU3rt67dHWVlZJCQkYLfbcbvdohWAEL0IJtCxRqiq1Wg0eDwecYD5lStXaG1tRavVsnHjRrGSdu7cubFessQMY1qIi8/n49q1a1RVVWE0Gnn66acpLi6+64PhA4EAMpmM5ORkNmzYAHwiPG63W3Sw+7SdYqwQfGMBent7OX36NL/5zW9obW2loqKCr3/96zz88MOS85rElDEtxKWqqoo333yTtLQ0li9fzrx58zAYDFMesXwen7ZqlMlknD17lg8//JDFixdTUlKC2WyOWbOjXC5HpVIRCATo6urirbfe4tKlSwQCAUpLS9mzZw9FRUXMnTtXEhaJKSWuxSUYDNLW1sbJkydpbGzkgQceoLKyUjwCjsXNKxw9C/1IwslLZ2cnQ0ND9PX1ce+994oCczcjK6VSSSgUYnR0lObmZi5cuMDZs2dxu92UlZWxZcsW1q9fL9bvSEhMJXEtLv39/ezdu5fW1lYKCwtZt24dRUVFU57AvVkEgSsqKmLdunX86Ec/4tixY9jtdhYsWIDRaLyrjnYqlYrJyUlqa2vZt28fH330Effccw87duxg48aNGI3GaV2TIzG9iNuqKLfbzblz53jvvfdISEjggQceID09Pa4KuQRvWLPZTHl5OTt37iQ9PZ0XX3yR48ePi4ndqczBCNGTUqmkvr6effv2sXfvXgKBAI888giPPPIIlZWVGI3GKV+LhMT1xGXkEgwGOXfuHCdPnsThcFBcXMzatWvFyXnxRCQSQa1Wk5mZyZNPPklycjL/8i//QkdHh7h1guh3UwsiEQ6HcTqd9Pf3c+LECWpqahgaGmL79u08/fTTpKamRu2aEhK3QlyKi8Ph4Be/+AUff/wxe/bs4Z577gHityNZSCybzWY2b95McVpHWzEAACAASURBVHExaWlpNyR9hddF6z0I86zHx8f54IMPeOWVV/D5fJSWlvKd73yHsrIybDZbVK4lIXE7xJ249PX1cfjwYTo6OkhOTqayspLc3Nyo3pjRRliXUqkkPT2djIwMwuGwOCY0GAyiVCrR6/WiEfjtIhTDjY2N0dbWxkcffURdXR2BQIBFixaxceNGKisrUavV0Xp7EhK3RdyJS21tLb/+9a+x2+2sXLmS7OxsdDpd3CRxv4xQKCQKh0KhIBgMMjAwwNDQEKFQiOLi4jvepghjT5uamjh06BBVVVWYTCYeeeQRduzYITZwSkjEmrgRF7/fT0NDA6dOnWJwcJDNmzezceNGNBrNtDPHFmphBCE4evQoR48e5ZlnnmH79u23Zfotk8nQaDT09fVx9OhRPvjgA/r6+rj//vtZvXo1CxcuJCsrawrflYTErRE34jI+Ps7bb7/Nxx9/TG5uLvPnzyc7O5uxsbGYFMvdCUItjFwux2g0otVqcTqdHDt2DLVazcqVK7Farcjl8pva6gmO+h0dHXz00UccPHgQh8NBUVERO3fuZPny5SgUCvHa0omQRDwQN+IyNDTEvn37SEhI4NlnnyU1NZWJiYm4zbN8FaFQCKVSSWZmJnv27KG4uJh//Md/pLa2lu9///ssWbIEq9X6lXUwQhTk9Xp57733OHToEOPj4zzyyCM8/fTTmM1mUViE10tIxANxIS7d3d3U1NSQkJBAaWkp5eXlmEymabcd+jTCeFOhbeH+++9nbGwMm82GSqW6Icr4oplKWq2WpqYmjh49Sn19PXa7nQcffJBNmzZJp0EScU1ciMuZM2c4efIkixYtYuXKldjtdiB6rnKxQqjgVSgU2O12Hn/8cbxeL2lpaWi12hsE5dN1MDKZDJ/Px+DgIKdPn+bw4cOkpaWxdu1aHn74YckaQSLuiam4hMNhhoeH+eCDD6ipqeG73/0uy5cvn3Y5lq9CqNRNS0sT51AL9S/Xd1EL71vwX+nq6uLHP/4xra2tlJSU8Oijj7Ju3TqpN0hiWhBTcRkZGWH//v10dXWRmppKXl4eycnJTExMxHJZUUeISIQxJcLkgL6+Pg4dOoTZbGbdunWYTCbkcjler5eLFy9y6tQp0SVu27ZtrFixQrKdlJg2xFRc2tra+NWvfoXJZGL79u2YzeZpvxX6MgTTb/gkmunq6uKnP/0pdrsdq9XKggUL0Gg0tLe388Ybb3DixAkefPBBdu7cKVYpS0hMF2ImLiMjIzQ2NjIyMsKCBQtYsWKFOCVxJnN9NW9WVhZ/8Ad/wMmTJ/n+97/PE088QUpKCq+88gqhUIhdu3bx0EMPUVFREeNVS0jcOjERl0AgwPHjxzl37hxz5syhrKyM7Oxs0SZyNiCTyUhJSeHRRx8lHA7z4osvcuTIEWw2G93d3dx777088sgjLFy48IajZgmJ6UJMxGV8fJxXX32V1tZWfvd3f5cFCxZM+/k/t4qwRRJmBKlUKl5++WVaWlr4oz/6IzZt2kRxcbFUtyIxbbnr4jI8PMyZM2eYnJwkKyuLBQsWkJKSMquEBf6vOE6hUDAyMsLVq1fJycmhpKSEDRs2MG/evFgvUULijrjr4tLQ0EBVVRVpaWmUl5eTkZGBVqvF6/Xe7aXEFLlcjs/no7Ozk5qaGhoaGkTT7MLCQvx+P06nE4PBIM6qlpCYTtz1T2xdXR2HDx+muLiYjRs3IpfLZ/QJ0echk8nQarW4XC5efPFFampq2LBhAxs3bqSwsBCAX/7yl/zBH/wBx48fZ3JyMsYrlpC4de6auHg8Hg4ePEh9fT1Wq5X8/HzS09MBZk0SFz5pQlQoFFy+fJmqqiqam5tJSUkRB70LaDQafD4fv/zlL3nllVcYGxuL4aolJG6du7YtGhkZ4b//+78ZHx9nx44dZGZmzsqIRbDqPHjwIFVVVeTn57Njx47P1LFs3rwZtVrNs88+S2NjI/n5+SxevFj0wpWQiHfuSuTi8/m4evUqV65cQaPRsHr1amw224yvafk0Go2G3t5e0cIzPz+fPXv2sGnTps+81mazsWrVKv78z/+cOXPm8Ld/+7fU1NTEYNUSErfHXRGXlpYW6urqUCgUZGdnk5eXR0JCwqzZDikUCuRyOb29vVy4cIHq6mp0Oh333Xcf69at+8LB7xkZGTzxxBNs3boVuVw+68RYYnpzV7ZFdXV1XLhwgfnz5zN//nwUCsWsOnpWq9X4fD4OHTpEdXU1BoOB++67jwcffPArmxDNZjO7d+9m586d6PX6u7RiCYk7Z8ojl2AwSH19PdeuXWPJkiVUVFSIEwtnOjKZDLVajcPhoLa2lhMnTjA6OirmWISpjF+GXC4nISEBq9WKVqtlYmKCS5cuceXKFRwOx116JxISt86URi5+v5+Ojg46OzsJBAKUl5eTl5c3q2pawuEwTU1NHDx4kOHhYUpKSnjggQdu2+jJ6/Vy+fJlxsfHSU1NvcH/RkIinpjSyKW/v593330XgBUrVtzUk3qmoFAoCIVC4rCyAwcOcN999/Gd73znjoyetFotmZmZHD16lO985zscO3YMt9sdxZVLSESHKRWXjo4ODh06hF6vZ/369SQmJs6aJK5arcbtdnPgwAHxKPmee+6htLRUHGh2O2i1WvLz8yktLcVkMvHaa6/x8ssvMzw8PKvyWBLxz5RsiyKRCF6vl9bWVhobG1m6dCkrV66cVdW4wWCQnp4eXnvtNWw2G88++yzz58+/45+rVCrJyMjgmWeeobS0lGeffZb29nYWLlyIwWBAq9VGYfUSEnfOlIhLOBzm/PnztLW1UVJSQm5uLgkJCfh8vhmdyBXmRqvVak6cOMGhQ4dITExk1apVrFq1CovFErVr2Ww21qxZw/e+9z2USiVWq3XWbDklpgdTIi6BQIDq6mra2tpYtWoVeXl5XzlCYyYgTFl0OBycPHmSmpoa1q5dy4YNG6IqLAIpKSk89dRTBAIBcVqA4Ikj1NZISMSKKfn0TUxM8OGHH9Le3s7SpUtnTam/Wq1mdHSUo0ePcvHiRRQKBTt27GDlypVTek29Xk9CQgLhcJixsTG6urqkXiSJmBN1cRkeHubs2bO43W7sdjuZmZkkJibOaDMowZvF7/dz7do13nrrLfR6Pbt27WLevHlT6iR3/QQBv9/PpUuX+MEPfsDLL7/M+Pj4lF1XQuKriLq4NDQ0cODAASwWi5hkvNmxpdMVuVxOKBSira2NS5cu0d7ezqJFi9izZ8+UbIe+iEgkQn9/P++88w5vvPEG1dXVjIyM3LXrS0hcT9TFpa6ujnfffZfs7GxWrVo1K3pilEolXq+Xl19+mbNnz7J79262bt2K3W6/q3kPo9FIZWUlL7zwAmq1mm9+85u89dZbDA0NzWhxl4hPopbQDQQCdHZ20tTUhM/nIz8/n/z8fGQy2YytbRFsKkdHR7ly5QptbW3o9Xq2bt0alWPn2yEzM5OdO3fS39/P4OAgw8PDDAwMSKNfJe46URMXl8vFgQMH6O/vZ+nSpeTl5ZGYmMjk5OSMfWoK4tLS0sLx48dJSUlh8eLFzJ8/H41GE7N1mUwm9uzZw5IlS3A6nYyPj98wl1pC4m4QNXHxeDycPn0av9/P2rVrsdvtM7qmRZjtHAqFaGxs5IMPPuAb3/gGW7dujamwCKSlpZGYmMj4+DgajUYSFom7TtTEZWxsjJaWFnJzc1m+fDlmsxm/3x+tH/8Z5HK5OG9ZuMnvZoSkVCpxu920tLRw9epVAoEAZWVl5Obm3rU1fBlKpRKz2XxDH1NbWxvj4+Pk5OSQmJgoCY7ElBKVbOPk5CRdXV0EAgFsNhv5+flTbgYll8tRqVRoNJobBrvfLQSD7Z///Oe0t7ezZcsWsrKy7tr1b4cXXniBxx9/nJMnT864edwS8UdUIpe2tjZaWlpIS0sjKysLjUYzZcIiVMFeuHCBy5cv09/fT05ODgsWLCAjI2PKRU2oKXE4HLS0tFBfX09eXh7bt28XDcfjlbKyMq5du8a//Mu/0N7ezu7duzGZTFIEIzElREVcGhsbaWxspLCwkJycnCndDgni0trayjvvvMOJEyeorKwkKSkJu90uWh1MFULNzrVr17h48SIajYb58+ezcuVKVCrVlF03Gjz66KOYTCa+/e1v4/F4KCwsZNmyZZhMplgvTWIGEpVtUV1dHefOnSMvL4/c3NwprcYV+mi2bNnC448/Tnp6OllZWcyZM2dKIyYBwcH/5MmTVFdXs2PHDrZu3Rr3wgKQlJTEunXr+Id/+AfS0tJ44YUXuHbtWqyXJTFDuePIZWRkhI6ODlwuF3PmzCEtLS3qwiKXy1EoFCiVSjGBm5ycTGZmJnK5HKPRSEZGBmq1ekpPqIQkbltbG1evXsXj8bBmzRoWLFgwZdeMNunp6Tz00EOo1Wpqamq+0sNXQuJ2uSNxGRkZ4ezZszidTlJTU8Xjz2gnC4WO6lAoJHb+jo+P09bWxsDAAPDJU9nv909pg6RSqaS/v58jR47gdrspKSlh7ty5qNXqKbvmVJCUlMTu3bvZvXu3lG+RmDLuSFxGR0f56KOPUCqVFBcXo9Ppoha1RCIRVCoVarWajo4Ozp07x8GDB+nu7iYxMZENGzYQCATIzs4mJSUlKtf8Iq4/7m5ra+PgwYMsWbKEr3/963e1dyhaCElpgZ6eHk6fPk16ejrFxcXT8j1JxB93JC6Dg4OcO3cOi8XCokWLUKlUUYscBNc6p9PJuXPneP/997l06RIjIyPodDrREb+wsJD09HRCodCUbYmE/qiuri5aW1sZHx+ntLSUdevWzQjPFI/Hw9WrV6mvr6etrY1NmzZJpt8Sd8wd3Rnd3d2cPXsWk8nEsmXL0Gq1UUuoqlQqHA4HR44cYe/evVy9epW/+7u/4/z587z55ptotVrOnDlDdnY2qampU55rCYVCVFdX09HRwcaNGykvL58RwgKQnJzM8uXLOXbsGN/97neprq6W7Bok7pjbujvC4TCjo6MMDw+j1+tJT08nLS0NpVIZtZtcp9MxNDTE66+/zsTEBGvXrqW8vJzc3FyKiopE/5I5c+ZgtVqn1OkuEokwMTHBmTNnGBwcZMuWLcybN29KrhULDAYDpaWl3H///RQUFPDiiy/yq1/9asZ3s0tMLbclLqFQiMuXLzM8PMyCBQvEY2AhNxEthLEc6enp7N69W6yKdblc+P1+EhISmDNnDhaLZUrERbCOnJiYoKenh87OThQKBatWrSI5OTmq14olCoWCtLQ0vvnNb/LMM89QW1vLyZMnZ4V7oMTUcVs5l1AodIONZUZGBsFgMCo3t2C81NnZSW9vL0lJScydO1esn5HJZGg0GkZGRhgfHycvLw+73Y7P55sScVEqlXR1dXHhwgXy8vIoKyvDYDBE9TrxgtlsZv369bz00kskJyfHRQOmxPTltsTF7/dTX1/P2NgYDz30ECkpKVELoYVTjMHBQZxOJ3a7Hbvdjl6vJxAI4HK5aG9vJxAIkJSUhNlsRqPRTNkUR7lcTktLC2fOnGHx4sWsWrXqjuYOxTvJycncf//94p8Fw+9wOIxKpZoxeSaJqee2PilOp5Pe3l78fj85OTmYTKaobUsEcZmcnMTv92OxWNBqtQSDQeRyOa2trVRVVaHVaiktLQWYkvBd2OJ5vV5aWlqoq6sjNzeXRYsWzaraEJ/Px/DwMNeuXZMsMyVuiVsWl76+PmpqaohEItjtdhITE1GpVFHdkkQiEbEgTqVSkZSUhF6vp62tjePHj3P48GEikQg5OTlTFrqrVCrcbjdnz56lv7+fOXPmMGfOHBISEmaNuITDYRwOB1VVVXz7299m7969Uje1xE1zy/F9W1sbNTU1WK1WCgoKUCqVURcWmUxGUlISRqMRh8PBxx9/TGpqKs3NzTQ2NjIwMIDRaGRsbAyn0yne8NFch0KhwOVycezYMSYmJqisrCQzMzNqP3+6EIlEcDqdNDQ0YDAYSElJobKykrS0tFgvTSLOueXIpb+/n9bWVgoKCigvL4+6R24oFEImk1FRUUFhYSENDQ384z/+I7t376aqqkrsQm5qauLtt9+mrq6O0dHRKfFzcTgcVFdXI5fL2b59+6wrLJPL5WRkZPDII4/w4osvMjY2xre//W0OHjzI4OBgrJcnEefccuQyOjpKW1sbK1euJDs7G2BKCtjkcjkFBQX8/u//Pr29vSQmJlJWVobdbicUCpGXlyceoUYzehIsFVpbW6mvrycQCJCZmUlpaSl6vT4q15hupKWlsWHDBhobG0lKSiIxMXFGW5hKRIdbFpexsTFGRkZITEwU5xNPRfGay+UiMzOTv/mbvxGvcX3SeMeOHUQiEYLBIOFw+KY+7DcT2Qh+MHV1dZw/f568vLxZLSwCJpOJb3zjG2zatElMsktIfBk3LS7CqFCn04lOp8NisWA0GnG73Z8RF6E+BLjt+hdBCMLh8A3icv16gJv2jhFsMb/qGFmhUCCTyWhqaqKjo4MHHniARYsW3fL6ZyJpaWnYbDbx71JC4su4aXHxer00NzczPj6OzWYjMTHxhhtVGLMhk8kIBoP09PQQDoexWCyoVKrbyoeEw+GouNoJR8qdnZ309/cTiURQKpXieq9/D8FgkMnJSfr6+vB4PCxZsoSCgoI7XsNMQKVS3SAq4+PjnDp1ikAgwJo1a6RuaokbuOmErsfjoaGhAbfb/YU+ucI2ZWxsjNraWi5duiTOLYrV8a3gHOdyuTh//jwNDQ3i1z8d9cjlciYnJ+no6GBychKz2Ux+fr60BfgcwuEw/f39vPDCC/zVX/0VZ86cYWxsLNbLkogjbllcwuEw8+fPJzExEfjEBd9gMBAIBKipqeE///M/+clPfsLk5CR5eXnodLqYzooWohStVotOpxPrYjo6Omhubkar1WI0GlGr1SiVSsbGxrhy5YrYzJeQkBCTdcc7crkcm83G17/+dQoLC/n+97/Pz372M4aGhmbshE2JW+Omt0U+n4+mpiaSkpKYN28eRqMRj8eDw+HA5XLR1tbGqVOnaGhoQC6Xs3nzZgoLC8WtRyynLioUChITE8nJySEjIwOZTEZtbS1VVVUsXboUu92ORqPBarUyNjbG+fPnSUpKYvny5VJu4UtISkri8ccfR6PR8Jd/+Zd8+OGHVFRUsGzZshnbfyVx89y0uAQCATo6OjAYDGRmZmIwGOjt7eXIkSMcOXKExsZGIpEI27Zt47d/+7fJzc3FYDDExZGl0OyYkpJCcXExcrmc06dP09bWRm5uLkuXLmXNmjVs2LBBzCM8/vjjVFZWSpHLV2A0GtmyZQsGg4Ha2lqOHz9OUVGRJC4SNy8uw8PD+P1+EhMTUavVvPLKK5w+fZqmpiauXr3K5OQkAOfPn0er1aJSqW76iPhuIJPJSEhIoL6+XlxTf38/w8PD9PX10dzcTHd3Nx0dHTidTpKTk+N+DlG8INTB2O12xsbGJEGWAG5SXAYHB+nu7iYhIUH0MTlw4ADvv/++aJgtcP78eWprawHiagC9kFD+dBI3GAzS3t5Od3c37e3tqNVqkpOTSU1NjdVSpyUWi4W1a9eKfw4GgwQCAfFUTuqmnn3clLh0dnbS0dEh1rZYLBb+8i//ks2bN1NTU8P777+Pw+EA4KGHHuKxxx4Tj5HjRWDkcjkmk4ljx47xT//0T4TDYZRKJTqdjsLCQvLz83E4HEQiETIzM2ddqX+0OXfuHPv27WPt2rWsWrVKOqaehdyUuLS3t9PZ2cmcOXNISUlBo9GwcuVKcnNzyczMxGQyUVdXh8/nw2KxoFAoWL58OXa7PS6sEoXTqmAwSEtLC/BJrqCkpIQ5c+awePFi7HY7e/fuBWDNmjVkZGTEcsnTnlAoxPDwMG+//Tbd3d3s3LlTEuxZxk2JS0dHB319faxZs4bs7GyCwSAjIyMoFApWrFjBmjVrGBgY4OjRo7z77rs899xz/L//9/+47777xAmJsYxg1Go1brebCxcu8OGHHxKJRFi0aBEPP/wwy5YtIyMjg+7ubvr6+jCZTKxevXpWdkBHk9LSUh599FGee+453n//fTIyMqisrMRsNsd6aRJ3iZsSl76+Pnp7e0lNTSU5OVnMWwinMFqtVvzw2O12+vr6CIVC1NfXk5mZiU6nQ6FQ3HWBEfIsY2Nj9Pf3Mzo6KrYrVFRUsGHDBpKSkvB6vQwODmKxWMjJySEzM3NGu83dDcxmMwsXLuT3fu/3OHLkCC+88AKDg4P8zu/8zqzxw5ntfOUdFAwGcTgceDwebDYbRqNRFIlIJEIgEBCjkzlz5lBcXEwgEODMmTM4HA5SU1NjGrXIZDJ8Ph8ej0e0xQTIzMykoKAAp9PJ1atXaWhoIDk5maKiolnfpBgNZDIZdrudJ598kuTkZH70ox/R29tLOBxGoVDEenkSd4EvFZdAIEB7ezterxeTyYTFYkGv14vHztcj5DSEcv/i4mLC4TAajSZmFbpChGU0GtHr9ej1epqbm4FPfIAF68y+vj7RDEkQQ+npGh0SExPZsmULJSUlWK1WSVhmEV8qLuPj47S3tyOXy0lNTUWr1X7pTSeMPAXEp38oFIr5iZFQ/p+UlITBYBD7jeCT6t2BgQGam5vZtm0b8+fPj+laZxqCq2BSUhLwf852fr8flUqF0WiUBGeG8qXiMjk5SU9PDxqNhqSkpFtynYuHUyIBIaoSopVPf29oaIje3l6Kiopm1CTFeCQUCjEwMEBPTw9er5f58+eTlZUV62VJTAFfeheFQiG8Xi8ymey2bRPiFWE+ktPpZHh4mPHxcUwmk5TInWKE6PbIkSM8++yzvP3229Lo2BnKl95Jbreb3t5eVCoVdrsdhUIRN+X8d4pMJiMQCDA4OEgwGMRqtUr9MHcBuVyO2WwW8y+HDx9Gq9Wybds2yfR7hvGlkcvo6CiXL19Gp9NRUFAg9gvNBORyOX6/n66uLtH0WzolmnoUCgXp6ek88cQT/PM//zPt7e384Ac/4OOPP/7cgwKJ6ctXnha5XC7kcjl6vT7mxXDRRKFQ4PF4aGxsZHJykqysLHQ6XayXNWuwWq2sXLmSxx57jL6+PlJSUqRc1wzjS8VFOFqWy+UxN32KNkqlEo/HQ319PTKZjHnz5kmRy13GbDbz+OOPMzk5SVpamuidI3zGZlKObzbypY8KoXJVqVRisVhmlLgoFAq8Xi/Xrl3DYDCwfv16rFZrrJc160hLSyMvL+8GT+bJyckpm/0tcff40sjF5XLh9XrR6/VYLJabdtq/XYRTKbVaLR4bT1WOx+/343Q6GRgYQK1Wk5+fL4XlMeDTp3O9vb38/Oc/x2AwsHv3bqmbehrzueISDoeZnJzE6XSiVCpJTEwkMTGRiYmJKU3oRiIR3G63eF2lUhn10Fj4eU6nk9HRUUKhEFqtVhKWOCAcDtPX18fPfvYzlEolubm5rFixApvNFuulSdwGn3tHRSIRRkdHxX4crVY75RELfPLhevvtt3nqqad48803GR0dJRwOR/XGF641ODiIw+Fg7ty5kr1CnCCXy8nJyeGv//qvmTdvHn/8x3/M//zP/9Df3y+Zfk9DPveuDYfDjIyM4PV6sVqt6HS6KY1YlEolwWCQpqYmTp48yalTp7h8+TKjo6NEIpEpEZfR0VEmJibIzMyUnoxxhNVqZdeuXWzZsgWZTEZnZydtbW1xVfEtcXN84bbo8yKXqYpeVCoVIyMjHDt2jK6uLrKyslCpVLhcrqg3EQo/a3x8XJxNJBXPxRcGg4EHHniA7Oxsenp66OvrIxgMimNhJKYHnysuwrZoYmICjUYT1UHv13N9/qOvr4+hoSEAUlJS0Gq1UxItyWQyZDIZvb29DAwMkJubKxlxxyF2u53ly5czPDwMII14mYZ8YeQyNDTExMQEZrN5ynIuwnanvb2d+vp6jEYjmZmZjI6OiqNVo31dQdAEMVu2bJlkvxiHyOXyG7qpARwOB06nE4vFgsFgkJLwcc7n/uuEQiG6u7vxer0UFhaSlJQ0JVGEQqFAo9FQU1PDsWPHWLJkCcuXLycYDDI6OorT6ZyybdHExAQul+sz848l4pdXX32Vxx57jP379+N0OmO9HImv4HMjl1AoRGdnJ5OTk+Tk5GAymaLuyyKXy/F6vTgcDhwOB2q1mtzcXABxVGwgEIja9T6Nx+PB5/ORmJgozdmZJthsNsxmM3v37qWvr489e/aQnJwsVfLGKV+4LRoYGBCtCvV6fdS3J0qlkv7+fqqrq8VpAVarleHhYaxWK2q1espyLvBJXikcDovWnRLxz4YNG0hISOBb3/oW165do6ioiBUrVkiV1XHKF25ar689mYq8h9FopKenh3//939HoVCwZ88ecnNz0el0qNVqXC4XDoeDcDg8ZU8mYZi65IQ2PTCbzSxdupS//uu/ZunSpfzzP/8zp0+fjvWyJL6ALyz/93q9oj1kNE+LhAmNw8PDXLlyhcuXL5OTk8NHH32E1+vl/PnztLa2olarxW1RNMXl+vch+OpKTB9sNhu7du0iKSmJN954QzL3imO+cFs0PDyMyWQSi+jcbnd0LqhU4vV6OX36NOfPnwdg//79vP/++wCiafayZctQq9VRueb1COKSmJiIzWaT9uvTEKPRyI4dO9iyZYuUjI9jPldcvF4vcrkctVqNQqGI2g0o+MG4XC5effVV2traeP7555HJZLjdbhQKBf39/XR0dIiFfFPlxC9MM5COM6cfQoOrICwTExPU1tai1WrJzc3FarVKD4044HPFxePxoNVq0el0UavMlclkKBQKxsfHaWlp4fLly1gsFr71rW+RmprKxMQEarWaS5cu8d5773Hs2DEGBwcBoioAwnsxGAyYTCZJXGYAPp+PK1eu4HA4aGpqorKyUjL9jgM+c2eFw2E8Hg8qlQqtVhuViwj9QXq9nra2No4dO8aqVavYtWuX+yOZ/QAAF41JREFUOGrC7XaLg+tlMhlOp/OG7uhoo1arv3JUisT0QKfTUVJSwqVLl/jOd77DgQMHcLlcsV7WrOczd63f78ftdos3H3DHkYtKpWJycpJLly7xzjvvUFVVhcFgQKfT0dbWRnZ2NvCJl8epU6c4ePAg9fX1+Hw+zp49S0VFBSaTKSonV0IklpSURHJysnRSNAPQaDQUFhayfPlyWltbeeutt3C5XDz22GOkpaVJ0WmM+FxxEU6KopVQFcTl2LFjnDp1itbWVvEmX7VqFXa7HaVSSUtLC2fOnKG6uhr4xJHszJkzWCwWKioqorJFE2pnbDYb6enpkrjMABQKBcnJyTz55JMUFxfzzDPP0NnZyZo1a7BYLJI3coz4jLgIjX3R7IL2+/0YDAbuv/9+Fi9ezPj4OIFAAIvFQkFBAWq1GplMRkFBAU899RSbN28mEolgMBhISUkhNTU16n1GWq0WvV4vPdVmEEajkaVLl/LDH/4QgLlz50Ztay9x63xGXEKhkHgcHK2nutAuX1ZWhkqlEh3mAoEA3v+vvXOPaeu64/j3+v0CG2ww4Dg2GAyEJkBZHpSEvJpE0zaaZd2ydk21TVuqVm21TloVTdrWadWkSem0RfuvijZN69pEW9REK01DmoaaAA0CAgECjGeggAGD47cvvpz9EfkszqMxEIcEzkfKH/G9595zse/3nnPu7/f9hUJUOIxGI9auXUvFRhAE8DwPnucfuFmQWCxmo5YVSEpKCp599lkA/8+kjtqlsu/84XLPNRe5XP7A1lyiI6FQKIRwOByz7dZjRyIRRCKRmJiaRHnIJNoPmLF83GqPyvM8vF4vZmZmkJycDKPRuMy9Wz3cMSfgef6Bvy26lehN/VU39/22L/X8wM23RXK5nL0tWoHc+p3yPI/Ozk78+te/xrvvvovZ2dll7Nnq4q4jl6i4RJ2/VuITXi6XQ6VSMXFZBdy4cQN1dXUYHByE3W5HRUUF801+CNwxcgmHwwgEAgkbuTwqyOVyKJVKJi4rHI1Gg/Lycvz5z39GRkYGXn31VZw8eRLj4+MrpjTxo8odI5f5+XnquL8S36RER2HRCOSVeI2MWAwGA/bt2wen04nJyUn4/X5MTEwwB8IEs2pTSlmE7upCrVbjwIEDKCoqgsvlQiAQoA+aqBHarXlsK/Xh+jC5ZxCdXC6HWq2GXC6HTCaLe93lUb1ZRSIRFApFTD3ilbiWxLg3BoMBKpUKfr+fWol0dHSgrq4ObW1tmJmZgUqlQm5uLjZv3owdO3YwS4clcFdxiQa5BQIBjI+PQy6Xg+f5uA4YnVY9anAch6SkJExOToIQAqVSedeSIonKwn7YxHsd8ez3II8VLw+6/8DN2KZo9VBCCFpaWlBdXY2zZ8+itbUVgUCABnOOjIyA4ziUlJQwp7tFcoe4zM3Nwe/3Y3Z2Fv39/bh06RKkUmlcRak4jkMoFEIwGKT/f1TgOA4KhQJtbW0AwGoVLSPLIeC3n6+/vx9Hjx6Fw+HAl19+SQWIEILe3l5MT0+jr68Pr7/+Oqqqqh5qX1cKd4iLRqOBwWCAQqHA7Owsrly5ApFIdM8pRHRbdHs0feB+RH9g0fbR0c5CfnTRc4pEInAcRxMb73UMuVwOt9sNAPj73/+Ojo4OEEIQDAap/UNeXh4AYHR0FK2trfjss88wMzMDmUyGQCCAsrIy/PjHP4ZWq8Xc3ByuX7+Ouro6OByOmL9DVVUV9u3bB6VSiVAohMHBQZw+fRpdXV1QKBQIh8PQ6/XYv38/iouLodVqEQwG0draipMnT2J2dhZyuRzhcBjr1q3Dvn37kJeXR/2MT58+jQ8//JBGnIrFYmzZsgXl5eXIzc2FVCpFMBjEX/7yF1y5cgVqtRo8z0Ov16OiogJPPvkkrFYrOI5Dd3c3jh8/jpmZGYhEIgiCgDVr1qC0tBQVFRV04bO6uhrnzp1DMBjE3NwcZDIZrFYrysrKsH37dshkMni9Xpw4cQIdHR0IBAKIRCLQaDSwWq3YtWsXSkpKwHEc+vv7ce7cOfT19WF2dhYikQjJycmw2+3Yv38/MjIyAACNjY1oaGhAf38//H4/na6Xl5fjwIEDEIlE8Hq9uHTpElpaWjAwMEC/b4VCgeeeew4VFRX0O21qakJbWxuamppw+fJlWhfpdmZmZuBwOPDMM8/E/XtkxHKHuOj1eqxbtw6hUAhTU1P3DZeOetxGo3AVCgV1049nTePW9oslelPfbwFOKpXCbrfD4/FgdHQU3d3d4DgOHo8HZrMZBw8epOLidrvR0dGBU6dO4csvv4RKpYLH44HH48Hzzz9Ps7RdLhe++OILvP/++zFZ29nZ2di9ezeAm6PBiYkJnD9/HhcuXIBGo4Hf74fFYsH69euRn59PxWpwcJCeU61WIxAIYOfOnSgqKsLatWupuLS3t+O9996jawJSqRQcxyEnJwfZ2dmQSqXgeR4XLlzA2bNnkZycjGAwCLPZjKSkJFitVlitVgCA0+nE6dOnMTIyAolEgrm5OTzxxBMQiUQoLi6m4tLV1YV///vf8Hq9CIVCUCqVePLJJ6HRaLB161YAN0MZGhoaUFNTgxs3blARLSsrg91uR0lJCQDA5XKhrq4ODQ0NGB8fh1gsRnp6Op566ins2rWLisvQ0BAuXryIxsZGuN1uqFQq6o64f/9+iEQi6udSU1ODpqYm+oDRaDTYvHkzFRe32422tjacOnUKnZ2d9/1dRWO+GIuDI7cpQPQPGn3q3AuRSERTBRQKBeRyecxo5H6IRCK6riOXyxcVsBcVpWAwCJ7noVKpvtLvN5rPFAgEEA6Hab6SIAiQyWSw2Wx0uhQMBuF2uzE1NQWe5+kTXafTwWq1QiqVUu+b6enpO56AmZmZMBqNEIvFEAQBgUAAY2Nj8Hq91EdYJpMhKysLWq0WUqkUgiDA7XZjdHQUc3NzdL+kpCQYjUZoNBoqJmNjYxgbG6OizHEcUlNTodfraUKmIAjo7+/HjRs3IBaL6Tn1ej1SUlLoQ8Dr9WJoaAg8z9OHhFKphE6ng16vp9/NxMQEnE4nfbsiEomgUqmQkpICg8EAkUiESCSCkZEReDweup9EIoFKpUJaWhp0Oh2AmxnvTqcTPp+PeiVLpVJoNBpkZWXRGKuZmRm4XC74/X5EIhGaH6TX65GVlUWL57lcLrjdbvh8PvodiMVimM1mumYSDAYxOzsLnufhcDjwpz/9CVevXr1nCZv09HS8/fbb+OlPfxr3b5Lxf+4Ql4UwPj6O8+fPo7KyEhaLZcHtp6amcPbsWWzevBl2u32x3UBzczN6e3tx4MCBJdcTjsb43I/lWviN97zxXkc8+9065X1Yx0rEgu6t+3k8Hvz1r39FdXU1mpub4XK56Lbk5GQUFBRg+/bt+O53v4uNGzfetx+MOxG/9dZbby228ZkzZ/DLX/4Sa9asQVlZ2YLb19TU4MiRI9Dr9diyZcui+hAOh3Hs2DG8++672Lp165LrPscrGMu1WP2g+xfPfvFOWx/2sZZyTrlcjuLiYmo+HwqFMD8/D71ej+LiYjzzzDN4+eWXl/TQW+0s6iW+IAhobW1FfX09xsbG4HA4sGHDBhQXF8eVMjA/P4/29nY4HA6Mjo6ivr4eGzduRGlp6YKqH3q9XtTX1+PKlSsYHh6mDnf5+fmLuSzGKkOpVGLnzp3Izc3FzMwMwuEwpFIpkpOTkZWVhbS0tOXu4mPNosQlHA7j4sWLaGhogCAI+OKLL2C1WpGfnx+XuEQiETgcDjgcDkQiETQ3N+PMmTOw2+0LEpfp6WlUV1ejp6cHwWAQH3/8MTIzM5m4MOLGaDQyG4YEsaj4Zo/Hg9raWrS2tgIAent7cfHixTu8Wu6Fz+dDXV0dmpqaAAADAwO4cOEC/H7/gvoxNjaGc+fOYWRkBABw6dIlWguJwWAsLwsWl8nJSdTV1eH69esxn7tcLnz22WdwOp1f2T76CnJoaCjm89nZWdTW1mJ8fDyufgwMDKCxsRFTU1Mxnw8NDaG2tpa5vzMYy8yCxeXatWs4f/489Ho9rQ2Tm5uL3NxcfPrpp3Q0ci96e3vxySefICkpib5hslqtKCwsRG1tLerr6+/bB0EQaNBUfn4+UlJSIBaLUVZWBoVCgQ8//BCDg4MLvTQGg/EAWbC4tLe3o6mpCT/84Q/x0ksvAQC+//3v42c/+xmGh4fR3d39le2vXbuG+vp6HDx4EK+//jpEIhG+/e1v48iRI3A6nejq6rpvH8LhMOrq6jA1NYVf/epX2LNnD+RyOd58801UVVWhubn5viOo1QxL2GQ8DOJe0A2HwxgaGgLHcdi6dSuefvppNDY2AgDMZjMqKytx+fJl6HQ6jI6Owmg0xtTx5Xkew8PDmJubQ0VFBfbs2YP//ve/4DgOJpMJFRUVePrpp6FUKjE8PIzMzMy7ljbxeDzo7e1Feno6srOzsXPnTtTU1EAkEmHdunXQarXo7e0Fz/NwuVxISUlhqfO3wXEcrl69SvPGolGu0WhpQgg2bNiA8vJyZmjNWDRxi4vP50NLSwtycnLwne98B5mZmTTC1e/3QywW44033kBnZydaWlqwefPmmFX4UCiElpYWZGVl4Zvf/CZMJhMNv48acr/22mvo6upCa2srJBLJXa0Ix8fH0dHRga9//evYsGED5HI5rR7g9/vxxBNP4M0330RraytaWlqwbdu2JTnqxRv09bjx6aef4o033rjn9ueeew4WiwUmk2lFiPNKyXZ/nIhbXFQqFdavX4/k5GRkZmYC+P+Nd6vpdW5uLgwGA5KTk2PaR0uLqNVq2j6arBhtL5FIkJOTA51Oh5SUlLv2Q6/Xo7S0FCaTiYbq394PrVaLoqIizM3NxYyeFkogEMDly5dpxOZKssUsKyvDiy++iI8++ggmkwmvvfYa9Ho9xsbG8Pnnn4PneRw/fhwvvPACcnNzl7u7i0YQBLhcLrS3t8NsNt8RpsBEJ3HELS4KhQJ5eXkx5jl3822J+mXcjkwmQ15eHsRiMX0S3s3lX6PRfKUdQkpKCpKSkmKmTLeLC4BFB0DNzc3B5XLRPJrp6WlIpdIVt06RnZ2Nffv2oa+vD4WFhfjJT35Ct9lsNpw4cQKffPIJdu/e/ViLCwCa29Xb24tAIACNRkPzsJiwJI64x7scx0Emky16Ds5xHKRS6ZLn8GKxmBZNSwTDw8M4ceIEjhw5gmPHjsFsNqOkpARqtXpF/RBnZ2dx/fp1qFQqmpEN3BRXs9kMrVZLk/weZ8RiMYxGI/bs2YPx8XEcPnwYv/nNb1BTU7PcXVvxLChCd6k314O6OR/0Te5yuXD16lW0tbWhs7MTIyMjsFgsqKysxMaNG2NqDSc6oW6xx1rIfsDN6OaBgQEYDAZqvRDtS/RBoFAoVsR6i0gkglKpxN69exEIBNDY2IgPPvgAbW1tsNvtWL9+Pb72ta8tdzdXHKvaIJTneTidTjQ0NODs2bP4+OOPMTExAYPBgB07dmDbtm1wu93UU1gul9ORl8fjoRHF0Zs6WqUyujYjCAL1NInuFx15qVQqmsEdDoep9UB0qimRSCCXy6HRaOg5/X4/NWqKnlMsFkOlUkGj0SxIdMfHx9HV1YWysjLk5+fTc/h8PrS3t8Pv96OwsBBarfa+x5qfnwfP8/D7/TFR2hzHQafTUXEWBCHmWm+1ntDpdDHlV4PBIHw+X8x0NGpNGq2oGIlE4PV6qT1l9JwajQZKpZJO4efm5uB2u5GUlIRvfOMbaGtrw5kzZ3D69Gnk5OTQbHq73U4tHVbSKHXZIEvg/fffJwDIO++8s6j2//nPf4hYLCZvvfXWUrpBXn31VaJWq0l9ff2C2jU3N5OdO3cSnU5HVCoVAUAAEI7jiF6vJxaLhWRlZZEDBw6Qf/7zn8TpdNK2v//974nFYqH72Gw2cujQIXLy5EnC8zwhhJCJiQly6NAhYrPZiNVqJZmZmaSkpIS88sorxOFw0GM5HA7yve99jxQVFZGsrCxiNpvJU089RY4cOUKuX79O9/vb3/5GvvWtb5G8vDySkZFBbDYb2bFjBzl27BgRBGFB13706FGSlJRE/vCHP5DJyUn6eWtrK8nLyyPl5eXk1KlTZHp6+r7Hmp2dJdXV1eSFF14gmZmZxGw2k/T0dGKz2ci//vUvut/Y2Bj54IMPyLZt20haWhqxWq0kNTWV7N27l1y5coUQQoggCGRoaIi88847JCcnh2RkZBCz2UyMRiN55ZVXSFtbG+F5ngiCQHp6esjhw4eJwWAga9euJRkZGSQ/P58cPXqU9PT00L/J1atXSWVlJTEYDCQ7O5toNBr6XQMgWq2WWK1W8vOf/5z09PSQUCi0oL8l4+6s6pGLSqVCfn4+AoEAnE4nTUngOA4WiwUWiwU+nw8WiwU6nS5mMTs9PR2FhYUghCASiUChUNC1iuhTTyKRwGw2o6CgAIIgUJvJrKwsqNVqeiy1Wo21a9ciEonA4/FAJBIhIyMDGRkZMW+7UlNT6RTG7/dDqVTCaDTCYDAs6LojkQimp6fh9Xrx+eefg+M4pKSkQBAETExMoLCwEFu2bMGWLVuoudNXETW+NpvNKCwshEQioeZdt458JBIJtFotbDYbnar4/X7k5OTEhAvIZDIYDAYUFBQgFApRdzyTyUTLwURHiiaTCUVFRVAoFOB5HklJSUhLS4tZ8FcoFDHnlMvlGB0dhc/ng0KhgE6nQ3p6OlJTUyGXy1fEVPCRYCnK9LiPXKJ0dHSQ3/3ud2Tt2rUEAFmzZg05fvz4kvr0qBIOh0lnZyd5+eWXY57e0X82m4309fUtdzcThtPpJL/97W9JaWkp0el0ZOvWreTtt98mLS0txOfzLXf3VhSreuQSxW634+DBg9i0aRO6urrQ2dmJjz76CAMDA/jFL34R8/QlD3hxNZ794j1WPEQiEbjdbgQCAej1ehw+fBgFBQXo7OzE8ePH4fP5VmxlhO7ublRXV2NkZASbNm3Cj370I+Tn58Nms9FREePBwcQFN71b8/LykJeXh+3bt+PcuXM4ceIEurq60N3djQ0bNtDX8MvlBPegiEQiGB8fB8/zsNvtePHFF1FQUICxsTG0t7fj8uXLGBwcXFEeJ/Pz87hx4wa6u7sxNDQEo9GI0tJS7N69O65pH2NxMHG5DZlMhj179mDXrl2Ynp5GR0cH2traUFRURI2vH2eCwSCuXbuG+fl5FBcX08+zsrKQmpoKr9eLhoYGpKenIycnZxl7+uAIh8Po6elBamoqXnrpJaSnp0Or1bJqigmG/XVvITr9iA6P1Wo1QqEQZDJZQgP3HjadnZ2Yn5/Hpk2bYtIsTCYT1qxZE/OaHXj8Q+QlEgldHDcYDEs2cWfEBxOXW7jbDbTSLDNHR0fR2dmJ1NRUWh4litVqRUFBASYnJ9HX1webzQaVSvVYCwtwc9p7a6Ag4+HAxGUVUVNTg3/84x+00mR/fz/++Mc/4tlnn6UF1fR6Pd577z3U1taiq6sLzz//PLKzs5e764zHECYuqwi5XA6bzYYf/OAHmJiYQHJyMlJTUyEIAiQSCex2O/bu3UtLter1+iVllTNWN0xcVhGVlZWorKy85/acnBzk5OTg0KFDD7FXjJXK4/3qg8FgPLIwcWEwGAmBiQuDwUgITFwYDEZCYOLCYDASAhMXBoOREJi4MBiMhMDEhcFgJAQmLgwGIyEwcWEwGAmBiQuDwUgITFwYDEZCWDHiQlZYuVUG43FnSeISNRqKRCKLbi8IAgRBWEo3EIlEEA6HmcAwGI8QSxKXpKQkWCwWpKamLqq9Wq1Gdnb2ottHSU9PR15eHnNvZzAeIZbk52IymVBVVQWbzbao9kajEVVVVSgoKFhKN7B+/Xr4/f4lixSDwXhwcGQJcwm3242hoSGYTCakpaUtuL3H46FlLDIyMhbbDYyOjmJmZgY2my2mkiGDwVg+Fi0utzvCL9Qhfqnt4z0ug8FYHpY0cmEwGIx7sWJeRTMYjEcLJi4MBiMhMHFhMBgJgYkLg8FICExcGAxGQmDiwmAwEgITFwaDkRCYuDAYjITwP8cdyqwTO4tYAAAAAElFTkSuQmCC)
.A rod of glass (
= 1.5) and of square cross section is bent into the shape shown in the figure. A parallel beam of light falls on the plane flat surface A as shown in the figure. If d is the width of a side and R is the radius of circular arc then for what maximum value of
light entering the glass slab through surface A emerges from the glass through B
![](data:image/png;base64,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)
physics-General
physics-
An optical fibre consists of core of
surrounded by a cladding of
. A beam of light enters from air at an angle
with axis of fibre. The highest
for which ray can be travelled through fibre is
![](data:image/png;base64,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)
An optical fibre consists of core of
surrounded by a cladding of
. A beam of light enters from air at an angle
with axis of fibre. The highest
for which ray can be travelled through fibre is
![](data:image/png;base64,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)
physics-General
physics-
A prism having an apex angle
and refraction index 1.5 is located in front of a vertical plane mirror as shown in figure. Through what total angle is the ray deviated after reflection from the mirror
![](data:image/png;base64,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)
A prism having an apex angle
and refraction index 1.5 is located in front of a vertical plane mirror as shown in figure. Through what total angle is the ray deviated after reflection from the mirror
![](data:image/png;base64,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)
physics-General