Physics-
General
Easy
Question
The graph shows how the magnification m produced by a convex thin lens varies with image distance v. What was the focal length of the used
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)
The correct answer is: ![fraction numerator c over denominator b end fraction](data:image/png;base64,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)
For a lens ![m equals fraction numerator f minus v over denominator f end fraction equals negative fraction numerator 1 over denominator f end fraction v plus 1](data:image/png;base64,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)
Comparing it with y = mx + c
Slope ![equals m equals negative fraction numerator 1 over denominator f end fraction](data:image/png;base64,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)
From graph, slope of the line ![equals fraction numerator b over denominator c end fraction](data:image/png;base64,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)
Hence
Þ ![vertical line f vertical line equals fraction numerator c over denominator b end fraction](data:image/png;base64,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)
Related Questions to study
physics-
The graph shows variation of v with change in u for a mirror. Points plotted above the point P on the curve are for values of v
![](data:image/png;base64,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)
The graph shows variation of v with change in u for a mirror. Points plotted above the point P on the curve are for values of v
![](data:image/png;base64,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)
physics-General
physics-
When light is incident on a medium at angle i and refracted into a second medium at an angle r, the graph of sin i vs sin r is as shown in the graph. From this, one can conclude that
![](data:image/png;base64,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)
When light is incident on a medium at angle i and refracted into a second medium at an angle r, the graph of sin i vs sin r is as shown in the graph. From this, one can conclude that
![](data:image/png;base64,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)
physics-General
Maths-
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means
Maths-General
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means
Maths-
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means
Maths-General
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means
maths-
The value of on using simpson's 3rd rule by taking h=1 is [Given
The value of on using simpson's 3rd rule by taking h=1 is [Given
maths-General
physics-
Which of the following statement is correct
Which of the following statement is correct
physics-General
Maths-
α is a solution of the equation
where n
2,
. Then the probability that
lies on the real axis is
α is a solution of the equation
where n
2,
. Then the probability that
lies on the real axis is
Maths-General
maths-
maths-General
maths-
If
then K=
If
then K=
maths-General
maths-
maths-General
maths-
maths-General
maths-
If
then k=
If
then k=
maths-General
physics-
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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)
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