Physics-
General
Easy
Question
An observer can see through a pin-hole the top end of a thin rod of height h, placed as shown in the figure The beaker height is 3h and its radius h When the beaker is filled with a liquid up to height 2h, he can see the lower end of the rod Then the refractive index of the liquid is
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)
The correct answer is: ![square root of fraction numerator 5 over denominator 2 end fraction end root](data:image/png;base64,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)
Related Questions to study
physics-
A rectangular glass slab ABCD of refractive index n1 is immersed in water of refractive index
A ray of light is incident a the surface AB of the slab as shown The maximum value of the angle of incidence amax, such that the ray comes out only from the other surface CD, is given by
![](data:image/png;base64,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)
A rectangular glass slab ABCD of refractive index n1 is immersed in water of refractive index
A ray of light is incident a the surface AB of the slab as shown The maximum value of the angle of incidence amax, such that the ray comes out only from the other surface CD, is given by
![](data:image/png;base64,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)
physics-General
physics-
A light ray traveling in glass medium is incident on glass-air interface at an angle of incidence q The reflected (R) and transmitted (T) intensitites, both as function of q , are plotted The correct sketch is
A light ray traveling in glass medium is incident on glass-air interface at an angle of incidence q The reflected (R) and transmitted (T) intensitites, both as function of q , are plotted The correct sketch is
physics-General
physics-
A point source S is placed at the bottom of different layers as shown in the figure The refractive index of bottom most layer is m0 The refractive index of any other upper layer is
ray of light with angle i slightly more than 30° starts from the source S Total internal reflection takes place at the upper surface of a layer having n equal to
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)
A point source S is placed at the bottom of different layers as shown in the figure The refractive index of bottom most layer is m0 The refractive index of any other upper layer is
ray of light with angle i slightly more than 30° starts from the source S Total internal reflection takes place at the upper surface of a layer having n equal to
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)
physics-General
physics-
An insect starts moving up in a liquid from point O of variable refractive index
where y is depth of liquid from the surface If u is the speed of insect, its apparent speed to the observer E immediatly after insect start moving
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)
An insect starts moving up in a liquid from point O of variable refractive index
where y is depth of liquid from the surface If u is the speed of insect, its apparent speed to the observer E immediatly after insect start moving
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)
physics-General
maths-
If
, then
equals
If
, then
equals
maths-General
maths-
The inverse of the matrix
is
The inverse of the matrix
is
maths-General
maths-
The ad joint of
is
The ad joint of
is
maths-General
chemistry-
The reaction of ethanol with
does not give:
The reaction of ethanol with
does not give:
chemistry-General
chemistry-
An aqueous solution of ethyl alcohol:
An aqueous solution of ethyl alcohol:
chemistry-General
physics-
A reflecting surface is represented by the equation
A ray travelling horizontally as shown in figure and becomes vertical after reflection The coordinates of the point (s) where this ray is incident is
![](data:image/png;base64,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)
A reflecting surface is represented by the equation
A ray travelling horizontally as shown in figure and becomes vertical after reflection The coordinates of the point (s) where this ray is incident is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAO4AAACdCAYAAACzWERNAAAUTElEQVR4nO3deXxU5b3H8c/sk8xkspCErCSyKrJElMUFikhZRaq4REVrtYoWS21vr3qvF62ltLa1bq20eq8bKErdUKQorldulT3RoLIvCZCNZCaZyWQyc+ac+8fAhCFgiSFMTvJ7v155vTIn55z8Jsx3nuc8z3kGg6ZpGkIIXTHGuwAhRPtJcIXQIQmuEDokwRVChyS4QuiQBFcIHZLgCqFDElwhdEiCK4QOSXCF0KFOCW7N2ie4amAK6RMf5J+VCtDC3tfmcOGUX/Fxpfqtx64u39AZJQnRrXRKcDPH3MmfH5yOq6aBoMsMmNFqzVx8791cnH3iX/lZ5RZuXP1bAkpLZ5QlRLfRSV1lI1mzfsEPHa/z8OLdhIOlLP2ikGsuSvzWo/5UsozqZjcvbnu/c8oSopvovGtc6znMmTeWbxY9zsqVr1I5+lrONp949x2e/byxaw0AD29ehqp9e5daiJ6sEwenIq3uTc5XmbswwOTL8771lz1a8mr0+22eCt7Z83nnlSaEznXuqLK1iNvmjqff5GImpZx4t9pmD899sypm28Mlr3RqaULoWSdPBynsL89k1g9HYvuWvRZ9uZxAOBizbc3BMtZVfd255QmhU99y1fndqZ4vefvNrzCn7OXtxktY2N90wn2blRZKanfw+wvmkGi2MX/tszxzyd2sq/6a13b+L6OzBndGiaeEpmmgaRiMMh0uTi9DZ3x0jfL1X7mm+C9UF93Ow4/PZUzqiV/YqqZiNER+XlK7g8nLf0nNrW+1+VlX5P/8n7iffZrc/34h3qWIHqZTWlzz4Dt4/cs7TmrfbwtmVw4tQNjjRvV6412G6IG6djKEEMclwRVChyS4QuiQBFcIHZLgCqFDElwhdEiCK4QOSXCF0CEJrhA6JMEVQockuELokARXCB2S4AqhQxJcIXRIgiuEDklwhdAhCa4QOiTBFUKHJLhC6JAEVwgdkuAKoUMSXCF0SIIrhA5JcIXQIQmuEDokwRVChyS4QuiQBFcIHZLgCqFDElwhdEiCK4QOSXCF0CEJrhA6JMEVQockuELokARXCB2S4AqhQxJcIXRIgiuEDklwhdAhCa4QOiTBFUKHJLgdpAYC8S5B9EAS3A5o2foNyoGKeJcheiAJbgc0ffQ+akMDwV07412K6GEkuN9Ry9ZvCG7bCoD72afjXI3oaSS435H7maei33uXv4FSWxPHakRPI8H9DkJVlXhXvh19rIWCeJY8H8eKRE8jwf0OPC88A4oSs63h5SWofn+cKhI9jQS3ncI+L00frCZp5hXRbSk334ql8AwaX1sWx8pET2KOdwF6YzAYKVj1EQazGe9bbwCQce98AMINnniWJnoQCW47GR2OE/7MlJxyGisRPZl0lYXQIQluB2Q8uBBzXn68yxA9kAS3A0wpqZgze8e7DNEDSXCF0CEJrhA6JMEVQockuELokARXCB2S4AqhQxJcIXRIgiuEDklwhdAhCa4QOiTBFUKHJLhC6JAEVwgdkuAKoUMSXCF0SIIrhA5JcIXQIQmuEDokwRVChyS4QuiQfK6yjqiaRl1AxR0I425Ro1+NQZVgWCOkamyoaaHQZcZuMmI1gskANpMBq8mI02LAZTHgUzRGZNhItRlJTzBhNhri/dREO0lwuxBN0zgUUNnmDrGpJsCOBgVPi0qFT6HCq7DPp6BqkGg2kGozYjdBIAxF6TasJrAaDSzf3cSUgkTS7SZCqkbpoRaCKgxItuALqexpVKj0K1iNBrwhDZMB7CYDZ6VaGJBioU+SmXyniTNcFsZk2Umzm+L9ZxHHIcGNk2BYo6wuyKaaFjbWBPj0YAvV/jCeoEofpxmjAVxWI9cOdDK1IIF8p5lr3qvh5UkZjM9LBOCx0gb+rzLAa1MjHxHbrKgs+1sTz0zIoFdCJHDXr65hWC8r95wb+V8WHinxsK66hWVTehMKa1T5FfovqeC6gU5CGuxrVHi4pJFDzWF8ikaG3ciZqRYcFiOzBzkZk2Wnr8uMwSCtdDxJcE+TqiaFNZUBXt/ZREltC3u8CkkWI+dm2sh3mqnwKXx+ZQ79ky0kWoxc+141IzJs/PuISOAUVaPGH6Z/ijV6zgqfQr6ztUWs8CokmAyk2VuHLvb7FKYXJEYfl/sU8p2Rf3aLyYDDYiSowpwhLhItkeOmvF3JveemcN1AJ9s9IT6o8HPfWjd1gTC3fFiLw2JkdG8bBS4zNw5yMqq3HZN0t0+rDgfX89JitEAA1xVXYUpNPRU1dQv1gTCry5v5oKKZTw82s6tBoSjDiqJqDE6z8t7MbAqSIi3Xqn1+1lcHGJZuix5f4VWYeUbr/1NU2RTGYIDsxNag7vcpjOp91DG+MPlJsa1hhVchPyk23ONyEmLOkWYzRkMLUFYX5IGRqSRZI28sG6pbuDg3gfd/kB3tKazY08SCDR5e2e5D1WBcbgKT8hOYUZhAYXLrm4voHB0ObsJ5oyifMYm6R/6Ac8o0kouvJ2Hk6FNRm66omsbmmiCryv2s2udnXVULCWYDPx2WzBPj0rkg247LauSyd6r4fp8ECl2W6LH7fQp5zth/iiMhPKLcp5DrMMe0bBU+hVn9HDGPj26BVU1jf1PsuY89735fONoCA9Q1hznYFGZIr9bwfXKgmfG5dgCsJgPnZtpYtsPHVf0dLJ2cyZeHgnx8oJk3dzcxb00dg1MtzOrnYGZfByMyrNKt7gQnDO6OgX3adSItFMS7YjneFcux9CnAOW0GzomTMTqdJ30OQ30FfeoDBHfvatfvjpdgVRUNzSEe/LCGN3Y3oWkGJvVJ4LazXcwdCg9t8vC7C9Jijqk4qqt6xLHBDasaB5pi96vwxobyeMdVNikUJrW+IdT4w4RUyHWYY445+jzHnqOsLsgZSWaSrJEWWNM0PjkQYN7w5Og+zYrKM197eWt6FkaDgaIMG0UZNnwhjZAKPx3m4q09fi558yBhDe4Y6uKms5IYnCYt8anSKde4ofJ9uP/2F9xPLwKbDYPx5KaLEzWV/wm1UP7KpZ1R1ikTViGkaqhhhYOpeexpVOiTZGHj1bnRqZWntzS2CSicKLhh+hzVClb7w2ga5DhaA+YNqW1e+Ol2EwNSWoP6k6HJhFQt+thiNDBvmAurqbXFe+SiXhQd1SU3GeG8zNbzltUFGZbe+nibJ4Q3pHJeZusxr2xvIs9p5sLs1m3uQJg/lTSw4tLejM1J4OoBTh7e7OGprxqp8IYY+fcDFDjNXJBjZ+GYVHonyvBKR5zwrzdge/lJnUBTFHYOHwShEAAGmw3n9MtIKZ6NveicdhVTUruDyct/Sc2tb7XruNPh6/ogi7d6eeLLRhJNBm48M4kr+zuYlGVj00YP2z2hmPnQ/T4lpksK4A+p1AXUNsE90KRwwVEhSLMbeXlyZsz5fjw4iZvOTIo5bnNxXszjZFvsG2SvBBOPj0uP2VY8MLYHdMtgV8zjqQWJjM2xt/6OmiDjc+3R8GuaxpNlDcwd6orpAj9a2sCo3jbGHr5+bgqp/LHEw/MTM5lakIgvqDJheSUfVPhZstXLZWc4uHagkx/0TcQoXel26/DbXmDzJgiFsPYbQHLx9SRdPguTK/lfH6gDnkCYl7b7eO4bL9+4Q1zR14HDbODNab256KgBnorjhLTCp9Av2RKzrbo5TJIldtQXYMHoVM5KbW3l7GYjVw+IDZjBYMByGqZU+6fE1lw80MFlZ7SOSpceCrKzQeH6Qa311TWHeeyLBlbPzI5ue7KskX7JFqb0ifyddjaE+Ko+yK4b8mkOazy0ycOsVdX0dZmYOzSZWwa72rzxiBPrcHCV+kPkvfRqtxqQ2ljdwl/LGnhuq4+RmVbuHJbMrH4OEswGbIv2xAwsQaSre06Grc228bkJMdsKk8xsuS6/zWDNyN52uiqjwYDT2lrvmakWPr48G8dRo9B/Km1gbI6dMVmR5+ENqvxhs4dlk3tHn+v969z8ZKiLrMPX2w0tKnPOTmJifgJPfNHIvZ/Xc+0AJwvGpMVcNojj6/BfKGnK9FNRR9wFFJWl230sKmtkuyfErH4ONODTWbnYDncTK7xKmykZiLSux44Kn5lqiZmqgUirqfcXZYLZ2OZNqsqvsHBM6yDc4180MCTNyoS8SJDXVwf4+EAzz1ySAUDZoSAr9vrZMTufHKeZjAQTl75TRWNQZeCScmackcicIS4m5icijk/fr6JToLY5zF/LGnmk1EOu08xdw5O5doCTb9xB3i1vjoYWIlMyOQ5Tm5sNqvwKBccE8s/fi7227M6evSQz+r2qaTxa2sDy6bGt7bxhyWQcvpvrgfX1zDnbRY7TjKZpzF/r5t4RKdw3MpW9jSGmr6hi6ttVzOzr4P6RKTHz2yKixwZ3qzvIo6UNLNnq43u5dlQNXp6UGX2RVBwzvwlHpmTa/sk+uzK3zfVsT2U0GCgtzote86+vDvB5ZYClkyLh3lzTwuryZnbfGGl9P6ho5mt3kJUzsgBQVNjdqPDpFdn8fWcTY149SFGGlUcv7MXo7K57SXG69bjRgNLaFi5+8yBFL+8nrMKGq3N5fWpvvCHtX86buqxGJvVp232T0MY6eqCuMMnCikuzoosV7l/n5s5hLjITTZHWdp2be0akROeNH1zv5oZBTs7PTuDRsemsnNGb9dUtXLz8IDd9UMN+nxKX59TV9JgWd11VgN9s9PBhhZ+QBh/NzGbs4cGj7e4giWYDKUeNah5vpHhaYSLTCuW6qz0yE01kJrYO0g1Lt/JvRZFZh1X7mtnbqDB3aGRK6uv6IK/vamLr7Pzo/k+WeblzmIufD0/mv9a6GbCknGkFiTw3MROXtce1O1Hd/pmvrWxm0luVfP+tSoakWfmiOB9FJWaAZX9TmDxn7D2++U4zE44ZFRYd99vz06Irl94r97NgTGr0PukH1rm5ZXBSdACvtLaFd/f5uXdECgUuC4u/n0Ffl4UvDwXpv7icp7Y0Ej7qhpOepNu2uFvqgtz3eR0r9jZz13AXr0zOJM1uYktdkBSrEac1dgVNniO2W/yzou4xF92VPTa2V/TN8qu6IP/Y52fnDa2t7bFTSCv2+KlvUdk5O49PDrZw15pDLNzo5oWJGVyc17N6Qt2uxd3VEOKG1TWM+vsBchxmNGDh+WnRa6zIvbmxIT14uMUVp9fRPZxcp4kVl2aRfTik66oiU0h3H17WqGoa969zc995KTisJqYXJvKXcb2obVa5dEUVcz6upa45HJfnEQ/dJrg1TQrF71YzZOl+7GYD22bnc/tQF73sRhLMx7Sux4T0R2dFJv5F/KTYTEzIa700+dV6N3cNTyb9cLf6jV1N1LeEufXsyPWwpmks2OBh/sgUvro+n2p/mH5Lylmwvh5N6/7dZ903M8GwxqKyRuavqwegpDiXMw/fPvjFoZbjrsQ5erUMIDe8d0FX93dyxeEli2E10trOH5kanVd/v6KZbZ4Q7w5Lxmk18vrU3hS+UM7DpQ1sqAnyt/Hp5HTjXpRun5mmabyz188v/1mPzWRgztlJlNWFoqGFyFzssa3rdQNPfpmhiJ8fDW5dUPHm7iZawlp0kcWRmzbuGZESHat4ZYcPq8nAjmvyufuzega/VMG84ck8ODq1W64H1mVXebs7yJS3q7jlw1r+rSiZkmtySbKa2oR0/3GW0A1MtTIwVdaF6slF2XZWzsjCcri1XbnXT7lP4SeHp5EUVeNX6908MCqVzEQzz0/MZEpBIn8s8TDjnWqq/d1v7ldXwfWHVOavreecZQc4K83Cjhv6cNsQFyajoc0CcYCCJDMT82VKR++yHOaYntQjpQ38x7kp0WmkxVu9mAwGrj/cmzrUHGblPj8rL80mxWZk2Mv7+cdef1xq7yy66Sqv2NPEvE/ryHGY+OzKHIYfc/9qhU9hTFbsttuGxK41Fd3D8xMzozMDwbDGrzd4eOj8tOg95H/Y7GF8bgIT8iNfS7f5uG51DbMHOfnjhWkxg5V61eWfQYVXYebKKm7+sJb5I1NYM6ttaOHIXKxu3odEB/RJMkcX37+83UeSxcDVAyIDWdV+hUVljfx6dOsHF143yElpcS5fHApy7rIDbKkLxqVuAFVTT8l5umxwVU1jUVkDQ5ZWkG43sW12PjcPdp3w0xIWjkljXK7chN7TTCtMZOWM7Ojr4qFNHib3SWiz9LDQZeGTy7MpHuDk/NcOsHirNx7lcucnj/Pguuc54Kvt0Hm6ZBO11R3kxx/WUukP8+b0rJj5vROZ2dfxL/cR3c+RpYIAjUGVp7Z4WXdV7nH3NRkN3D8qlfOzbFy/uoY1BwM8Ma7Xae06j8sdxrXvLWDBhsVMLxzD7UNmMrlgJEZD+2owaF1otnpTzXbOW3ZbvMsQupYNVMa7iHYpTMrix2dP55bB08hy9DqpY7pUV9lqkjlW0VH6Ci3AXm8VD21aysKNL9IUaj6pY7pUiytEd7e26ivOf3Vu9HFRen9uH3IZ1w2aSJL15BdKdMlrXCG6q/f2bSDRbOOaARO4fchljMo66zudR4IrxGk0tFdfDt78Osm2jl0WSldZCB3qUoNTQoiTI8EVQofkGleI00xVAgRawmgYMNnsWNQALSEwWuzYT/ID8KTFFeI08+/5lCd/dB45uZP4XUkjtat+wfip97Bsi5uTvZNZBqeEiIeGNfzn5GLeveB33GrYSu+f/4Yr8k6+HZXgChEngZLfM3Xa4yT/ZiNv3JLTru6vdJWFiAuVxpowQyYMpvSxX/NOdfuW+0lwhYgDZftSHt88kvtfeIYFQz7i5/NeZE87Pl1WgivEaeYre5E7bnyKhqKzSDOnc97Fw1FX3cvsn73AxpqTa3nlGlcIHZIWVwgdkuAKoUMSXCF0SIIrhA5JcIXQIQmuEDokwRVChyS4QuiQBFcIHZLgCqFDElwhdEiCK4QOSXCF0CEJrhA6JMEVQockuELokARXCB36f/tJy35mvP4ZAAAAAElFTkSuQmCC)
physics-General
physics-
A particle is dropped to move along the axis of a concave mirror of focal length f from a height f/2 as shown in the figure The acceleration due to gravity is g Find the maximum speed of the image
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)
A particle is dropped to move along the axis of a concave mirror of focal length f from a height f/2 as shown in the figure The acceleration due to gravity is g Find the maximum speed of the image
![](data:image/png;base64,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)
physics-General
physics-
The co-ordinates of image of point object P formed after two successive reflection in situation as shown in figure considering first reflection at concave mirror and then at convex
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)
The co-ordinates of image of point object P formed after two successive reflection in situation as shown in figure considering first reflection at concave mirror and then at convex
![](data:image/png;base64,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)
physics-General
physics-
A beam of light strikes one mirror of a right angle mirror assembly at an angle of incidence 450 as shown in the figure The right angle mirror assembly is rotated such that the angle of incidence becomes 600 Which of the following statements is (are) correct about the emerging light beam
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4gWxNNhzATu1csYMF2O0lDRnNZnxis+1by65xl7LH4E67PY81Xb/PuwmpiB/XGZ/+3vPr4E7y6tI7QkGLWLNrJgTVf8d5SgeGThxBQV4OzfDu/7vVm1OSRpIZHEhVgbHoqtSz6sJ5ceWkitRsXsnJPDrnZB9mzdRtZhqE8NP1BRsYY0GCnbO8q1qcXUWcGQ2AUsfFRhHjoMBVuZ+uWDPKrNHiEx5Kc4IdYuptFvy1g2aIF/PLLXH75dT5LVu8kp86DhF6puOVvYtGmTOxGb3x9YogyFrFx4wHMOk+8A2JJDrKwd+0WshpA7xFMUo+R9I+2Ubh7HesyTERfNoZUrZmqOl96DE3CULSf9AOl1Om9CYuOJj4qGE/98ddSi09UMt06hyOV55GVmUedVyqj7nyQiR1qObh+CZsy7bh5+eMfHUuI4yArNxygTu+Br080iVEiR1avZ28VaDy8iElOpeegEfSM0GItPczBrEIaQi/l7nuuoV+0k8y169mWVU6N4oZ/aATxsRH4GEwUH9jEsgWLmq7LL03XJZ08syfRaeGY05ewKdOJ0ccPn5hQvAs3sfagDb2nD4FxCQQ27GHNlsOYBTe8QpPpnOZP5eblLFu9jCUL5jH351/45beFLF2zjUJ9Ep2SIvF3c+E9pbQ3pGxl5X8mKt0SRymPLzY3vVij5K98Qunnn6pc/0GmIiuKotTMU+5NDlAGvpqpOK0ZypsjEpSJ39Y0HV+trJg+URn75Bwlp8auKIqirPxXVyXuipnKimyzoig7lVfHDVEmvzBPybA0nlG7/AXlhkFDlRv/s1FpUA4qP702Vbnnkc+UvTV1SlXJbmXlF/cpQzoNVf7xTYmi2AuVtVP7K74dblTeO9h4vmnhvUqy3xDlpUNNEX9xjRKYcK8yr6FlLptLkE/x2tGdysLvv1JmLTikmKxVSnFejpKVuV/ZNPcT5Y1/TVFe2NHiUV4UOMu2KvO/+1r5enHmcddln7Lx5w+V1x5+QHk5/RwSrd+tzHrhHWXZkQqlorJcKcrNUbIOHVB2zn1SmfzPj5VVuysv+Oc4nvZXLTolEk5Fg6eHPx17JSEgY5ECCQnWst1ch7NyK8t2+dIzwQNJAY3gy/BpPzD8uBQErYAggqjTw7YFrDykJ2ZCMP5NnRcGdyNGDw9sGhGpOJeCrD3srBTZuvBXBIuEqBvIfS+PJzzZCNZKFK0nRv+O9OkAyGacgSEEadOxNsiAgENSAAWn3Y7TqG+b9ddTPBSzVs9n4a+Z+EwaiWwTMPr4Y0TCYOlMl1otUkzLh3kxkL3yNxbOLyToxhEnXBd9fBpdG4wQffZp1i59nZfWJvLm5XXIvgF4+PpjlMHHksbQSxIJC3Btw0ubvGdPi3DsjxNfU2Sk5p5kRTl2hGwyY5WqyM+vQ+7tf2xSmLW+HsHDE8Ox6kjjEHLz0SpM1nqsThn5WHIKSlOaDqcds0nGN743V0wa19h92YQkAfUVTSdJjQPuBAHlFL0ANL3X8pUh1+EbE4+PZR5zZ9xObv8eJAW7I5vraBCD6Tb+Hm4KaO0IWwe/uES8TYv5ecYdHO7Xg8QgN6SGWsy6cHqOv4tJ/mefpjayFz3rP2Hqv/fRs1syUf4GlLoyyrW9mXR3BxIiXNsN2f7kIjT+FJXj/t30Bs1yaPxbaDpcRBeaRKJ/FQu/ncOhwTeQ6K0DWzGLv91C7HVj6eZ3XAOgomAMDSfIo4xD6TnkXd6PiGCQZQnJ4cTpcKD1CyHMo44j637juy2DuL+nF7KjhsL8XLLKQri0p/YkYQhCsxOb4qKx61NRFOx2B2463Ykfp40S1Gsyz38zkkkbVrJuTzEmjS8xl4xn6OBUgtrCVF8XEdz3Vl76djST169i3d5iGrT+xA26liEDUwg8x+vi0echvlo+lk3L1pCefRSLzp+ES29jdM9IjC1wL7U/uZhMmOoaMDvsmOtqATeQHVgaGrDKDixmGZCwW8xY7E5sVgtW9yHccmMaC9+bwZ1PlHHboBDqdiwmp/tzvOTmDjgwWZ04rGZM9Q3Q/XKuHPgbL8x9j88Tgwm6uSfW3ELKissRSgop8hxD9zHD6bD4XV6ZUkH2jVfSSSylsEyhw13TwJaByWxFclgxOwHFjsVswS7ZsZgsOGV39F5euJsLyc45zEaTRO/+HfHSnSylNolbCJ1GTKLTiNYO5CLDPYzOo26k86gLmWYs/cfG0v8CJnmmtKveInt1AbsWfc/389aTXmZDdsj4BPnjRQ7LPv+epYfrkN39iIk2ULhsNt+vyKbcqicktTdX3TCWVDmbzUvnsWDdEdxGPMnMf/QkxE2hZNtXzP5hPfuO1COFxtGjc1+GDOtEQEMG87/4lFnzMzAjI/p6oLiFkhDdmUsG9aFLjI78LStZvHgth+QkRk15nNvTJHI3zOXz75dzuEbB4BdLrHshS7/+gWWZ5di0IXTs2onYKB2lG+bw9Xf7ibjiegZEe55yAF/7QEGWleOqgAqKLCMr4lksuaAgyQrCeVUjFRRZQTlWwlU5H9T1XFRaFUW2UF1cSH6hlbB+aYQAsrWWon3bOWzsy9CU0zU6NorIcXQfm4540i0tGh/jORTIFQe1JfkUFtXh3qk78cbTn6Ly17TbZ6FKG8Bcys5vnmXy8FFMmrmIPAAU6st28OHDN/GP15dhOm0iJg4tfIFJAwdx9cxF5NXa//TIP32O2qvIWvAGU64cybhHvybdcurDVM4OVS4qrYcxlJ7Dr+Xm4XFIjuZ+NwGfiIE89cMGlr86ltN3lnrR8cp/MrFPAN5u/MU0iXpysnIoLK4++S29P0lDLuPGK7rhI7l6IYK/D6pcVFoXjQaju+HEiYpaPcbQeGIDzrSbxIi7m/jX7SQFC/n252WsP/QnxRKNFq3BcNzkP5XzRZWLykXBiV6QcdTnsftgxYkHmfLYtmIxyzZlU/WHs5uHGGj1MrXZ21i/PZuj5sZBTY6C5bz51Gt8/uNi1m5cxfqMPMr/ZL1HQdAgSmDJ28nGbYeoOKmWJVGXs4Xli5ezKbv2DyKSqM7czIqFi1i1uwiT9Pu7UvkhsopqMTttVBzawdbdOZQ3NL5vKc9k56at7M2v5S/WImtztL+uaJU2iwBQl83Sz17i+Q83YB37IVtfGQKyg6rNb3PPK4WMffI2onY+x1UPFeIb7od793/wv2eHIggaDNoyFr/0bw4WZrFhbTb+N77F/6ZeRozTC3eDHqPBiSTLTT1Cp8hfo4PqDJb+52ZenLWE3AYNwf0mM+2/r3NDAjjMR1j65uusMPQize0Acx5/APO4d5k9fRShmgJ+eeh2PhOv59bBCmv/9W+e7vocnz7endol7/B/L83Dbdy99NBVUZS+lJW7TaTc/gjj4+0cWfkbS3bnUuc/iDueeYknR4WcIrq2R9ssudTmk1dYSoW58b9SbTF5h3PIrz4b7zeQv/sAFedRBrYW55BbfJTatr+u5UWBAuAdT68rJzEouJY6W+P3aa/fy6fT/0t579u5tk8ag27/F5cZMsgMmsSrDw4jSNSBAObDJfhPmMob3yzm8wdSqdm2gh3ZNfjE9aVbUhh+/pF0HjCCQV1iCT5pmR8BQWmg1m4gaODzrMrYztL/3ULI/u94YeY3FFJP4W9v8Jl8E8/edx0Tbn6UVyaHsfWdZ3l/hxU591c++OYocWOu4NLxd/PvCfGUbVpLep0/fSePoUeQhsLD0H3SY3y0aB7/uSOZsl+/Y6ezO1M+W8ayDx7mUo8jrF65iYIWvu6uom3JRalgz0/PMWnUKG57dQkZNQAKhxa/y4O33s3zP2WcPglHA/mrP+DBMZcwaspXZJyLXOqzWf7O3Vw6/Hqe+n4XJapcLiAieqM/Pl6NI6pBQbIf4VBmPYLRC6NGg8bYkeRoqCipQOOubTxOltBEptIlOhgfjZ6EuHDcbQ1UWW0ogE4rIIgiWl3jkPeT22cUZFmHd2AMnXrG4O0bTfcRN/HI1dFUbFvH2oJatixYTF7eVn6c/TWzv5vDat1o/v3w1XT20EDkdbw+71umDxU59NsnfLk+n8rqeqwSoPfDU68nLC6JqDB/NISTEBmAMTiYiPBIogzgFxFOuKeOhpqaM+ghaxu0rWqREESXMf3pPGsORVX1ND7YBBKG3sELiRPRhCWfLgUEnQdhXUZzbfdZfPWTib9a7K8h+yBHIxMId9NxwjJQXomMHNmdr2ftoqauPSzIfZGhCIhC8yKXAjpjZy7p6cmC1avJfySeaPI4nCPSdVwvvDQaQG48Uqs7tj6JVqtBVBxIktLYjnHsIfJXTxMBQdSga/pViB5+xCRF47mwntqGWqwVFtyHDmPyTXE4HHLjwlhaPW5uOkQxEL/qT5n+mJPuEycxbsB8vtwvNg4ObJpuotFqaV6lUhRFRK3u2KJO0PSZZaXdtLu0rZILgGcQfj4eHL8hgiEkibSePUgNP7NtEnRGPyKDfZtu4D/jCN+++QP76uynHvEZGIivpzs6QUFRR3O6FK0xjutefZmrpUW8/9anfPzmD9Rf9zHv3dMFX8OxlXZB+aM6lBP+JdDYYPtXCAi/ty7LcuN8scAEOoV44KF3krVyBUeMXvj4+ODj7YWnLZ2Nh5zYt7/G3c/uI+Gmm7lqcCIxAUY0goig0XB8c/Wx1Qb/RHLt6VZqWyWXZpq/geOeRub6auptboQEHje0UqrmSPo+SrSRdO4We9yK/I1b+QkIjcsn1mSzq0BPUlo0HgD1+/jxpcd5bbHAxAFL0XTpx8COIXjo/+hiBVFrxE1yUFOQT40hjNjgxvwVpbnobaE8cx/ZtUaiU1OJ9DjudKmSQ9v3US4Ek9yzIyEn3Pe15BZAbJQP9rJDHKr1p0NyUOPGZNYSDmbV4hWXTIRn23s+nIBWi1YUEdAcuxk1uqZlJcXG8qJkr2b7d3Nwjn2WByfG4+8uIrq7H7fouhadKIBGg17XeBH1Og2ioEGj1aABNIKCtcGKw5TD0SonNimQiKDjrp0iIzksmCwW7E33leXoIZatK6f/Pa8x0MeHgMv7ofzrNW67xcojtw4lVs5i0S9H6Du9D/VbN7Elq5p+bmEEOo4wd0sOtbWJmHL2UZDixCqLaDQ6msJDr9UiaiS02qZPrWu6DhpNG/1Rnkwb/hwCGh04i9bz7fvv8WWGHyPufJypY2MBG2Xpi/nh+y04+o+ik+kbHn4uHSEyjuDgXtzw8OV4CQKy00TWnJf4eW46hw8dRhr4LJ+9ehV+ZUdxmGuotBmpq66kqt6K8xSjs0StO8qRn3nz0Y/Zu2oH5YZ4Rv7jUf51+yiSPaD28EZWLFxDljYAbdF23nxJpsddM3jqsgAqdszhrXfX4zF6GFEFs3llhoFJ//kPk+PrOLDkM/77/hz2ptzLk9F7WbzjANt2FhE06TVmdM1gzuId7EnfS4HXpTz+8r+4ukswrtvayoU46jiyeTk/LtvIkSr4dck4wi7xp2Dpl8zbWEJu0Y98uyuBSR0sFGRs5ef1k9n2kQGtRove3ZOAhGFMmfYAnYp/4ueNBeTWzufbFb25rbudDcu2kbWnkoXz1zK4x83E9+lPhzkf8tYMJ+b/e5w7rgg+MRaPaDqPuJJL9//CrPvuZ09qOD4aAcP1r/LauDhEUSbx2hn858hUnpv1Fv9c9SXRaUOYOOURLgkQ8bpkPFcnPsPHky9l9+gbuCUpiQDrFn5d0Z+Aily2ZGeTbp7DsqFxeEaVsnjVVvZusWBYsZ4RCT1g8wqWbd3MHp9QFm8aQUT/iDMYQHhx04bloiBLoI3oREyIO9alB8mvaRyUIBftYMm3s/n16HDeHDOYqBw7GXNm8/auRP77xXDiRSflioRsK+Wo133c8/Bo6lbNYNIbX7PkoTHcEtmbYV0jcJ+nI/mSYQzpEIHXSaUWAZFqCqv9GHbHrdxx7UF+/eh9Zr//Lr4R8cwYVceG1evZbRjCXdd2RMnywbl3Gu+88i4p8ffh+8vHfJk1mJ/eu4LEQpl1sx5l9rKHmd/pZAMAACAASURBVHxfJBFdLyGk9lm+3noQafwN/GMYDPvkHu77/A2+fuI+xt8+ghuv+pF/PzCX+WvG0icpmHjXbkHjGjTuBPeeyGOfDuBu2ZOQmDB83Qy4D7uTN367GqshgOg4PxS9SFDSFdw7vD9xzmrq6q3YHFYaju7hi8+38MadQ3jki1Xc5jASEh1DiKeT4Q99zILJdgxB0cQaFHx73cqMDwdTZHInLD4O/5MKfN5E9bmOR14eQGmNHa27ETe9G97hMYS4AYgYgroy/rH36DyhhCqzjN47lISUJHw1QPw1zPgqhTsq7ej8Y0gOHcN3/SqQfMIJNTTQudM1NGh8CY8OI1Dvx9ipn9HrXgljUBTRwZ4wbAqvfDsBs9aX8Fi/tvmw+ANtWC40LcDtR2RUFKG+BTTPh60vL2R/Rib1ybeSaNBgjEikX6cwXv3FhjE+EE9rFaUIaAyhdOzbg67egNiTiJnzySuT0cQY8ffUI4g6PAMCCfLQn6JxSkGStPjHd6Xv0L70MPYlUSgj9/Hv2bZtNxtDLOxYu5KMqEjS15ViNZkwdr2Uqx3h6MQAOo1/lLdGp9HVvI+Fy9KpkO0cLa9BIQ7viM4kR7jj7oylS/duxLhBlxFpPPpNHh6dutG9ezhGhtLVfza7SuoxWYC2KBdRh0dwLJ2DY0942T2iIz2aN4uXGihc+j4f147k0+fG4wMosoSsgHXXyzy8wIhnYALRUQknpOHpHUjkCa8EEds5iBNzOh4BjZsPYQk+hP3FMYbAeNIC40/xWbyITO19Qp6+Ab/nFhZ9fGeDF54+QZyw6J6XF37hp++QaEu0abmcwHGNs54BQUSFGjFnZbCPK+iNncqaOgwxScd9oSKC1hNfb0CRceoMuIkSDntjz0PzFiKKJCMBJ28aoqAoOjy8PTA01aP9OqSQGu1NSd1RjhSZKa2WCRramV49jNRZofslo7nWwwu/ACOGuliMX8/m3cwOdEnuTKSnQHFzM58CgigiePjgrZEADegNaDRe+PnompqatOg0oMgy7Xleu+J0YCrcw/qfV/FEcDkDUyLw1TsxleRTYAph3LWpeLbCvk4qp6cNyqV5/MNxKCe+oonuw5gb7yD/s2XM+nAORZ4VHPIbz8xnryPxuFQap+v/nlzjqrW/t+c3dyH+5UU6bgsTZCcOvRdefoFE+pWwrrqSmiobQdFdmp6GCjTksWd/OeVLXuOTI/154tGBdPQvZrdRYYsgIh4fgyL/PhFPaYxOVo6Pr331LpwKQedJ5KjHec+6iHWZ+9l29DBGnwAiElLo3rUrfVP90Lf3i9BGaYNy0aAVQVR0NDe0a7QaBLFxHAEAliqqGmyISaOYODCNKA89PUZHEB3UfIIevbZx86jGrYBEtAYdoiCg0RnQArIATrMJuyiRl1dCWGgA7gb97z9m2Ynd2kCDHbRN3RbFOzMo1oTRY9AgBqfsYGeYldc/fI6pfv/ixgGhOPIyyDhiI7hHDNt/XUBG6iT6xgVTs+UHdpXL2G0mivOKCY8JRic29pa4/d69gICITq9rWuNXj0Zs3BRM1wa/xTNG1OIZ259r70ul7+F8KuodoPckMDqBKJ+/8bqYbYA2thKdlaq9C5j18Y+sKXEjsnNPUn0r2Dr3c2Yv2Ee9X0cGXZJGgDWTdT98wLu/7Ke2Ioutm7ewZeM6Nu0twh6YQFj1Rr755BN+SbcR1acPHY1VpM+fxUc/bcca2YveXRIJ1eWy4ucFbMmqRgjsQOe4IIzHLwWnVTAV53DwQBY5ueVUHNnB1hwnEZdcybUjOxLoH0Cgp0JZ+lJ++WUxqzenc+iojoheoxnVxUhNxioWL9vC3ooaquwGnIeWsibfSHKfLgRXrmHW/75gVWkQaT07ESoWsemnT/hoUQ6GxDQ6x/lg3juPLz76lZ2WYDqkdSEl3IMW3TOtpRHd8A4IISw8jLCQAHzc2vOHbR+0Mbk4aKi2oQ/tSFqv7nRLiSbYQ0HU+RCV0ovePVKJi43ET6ilPP8w+VY/At1s1NfXY6qvpbK8lJw8B4kDEzAYIug5sC9p8XFEBxqwOzyI7dGXXp06kBwXil9oFHFRwfh7h9Otf28SgtzRnrCPViAxSfFE+nvi6emJp4cvMd0GMXhgN6LcAdwJjOlI17Rk4uNiiU1IpffgUVw+Oo1QowfhCUlEBfvhExBFSt8RjOidQFx8B7r07UagXIsQ0o0BfbqQlBRHuKdEPYGk9O5F95QOJEb4IJgVfOK70b1HJ9I6xBDmZ2zHy2CqtEXa4TKXJg6vWcDizXWk3HsXw70dWBpsSM56Cvav58vPsrn+46l0b+0wVVTaOe2wtl5N0cGNzP0mm9zYePRxfnjoZKx1RymtgLSxl5N0Psn/PvRWpb2ifscXhHZYcmmgJH0Jsz+fw+ZSHYERwfh7e+Lh6UdIdCpDxg0n6TxHKFl2bEMbHIwuMlq9CdsJssWCoyAfQSOiTzivx49KE+1QLk04jpK1cxeHShtQ3AOJ6tCFbjFeFyTp4rtvwzhoCD7X34igP2lhEJU2iKMgj5rZX6Hx8sL//n+2djjtgnZYLWpCF0hS35HnVwX6E5ylJTiPVqA4JQR1AFe7QLZacZQUoUjBpz9Y5YxQ+xfOBY0WQdS0/xFsfyMEQUBo/l5VLgiqXFRUVFyCKhcVFRWXoMpFRUXFJahyUVFRcQmqXFRUVFyCKhcVFRWXoMpFRUXFJahyUVFRcQmqXFRUVFyCKhcVFRWXoMpFRUXFJahyUVFRcQmqXFRUVFyCKhcVFRWXoMpFRUXFJahyUVFRcQmqXFRUVFyCKhcVFRWXoMpFRUXFJahyUVFRcQmqXFRUVFyCKhcVFRWXoMpFRUXFJahyUVFRcQmqXFRUVFyCKhcVFRWXoMpFRUXFJahyUVFRcQmqXFRUVFyCKhcVFRWXoMpFRUXFJahyUVFRcQmqXFRUABBAEEBo7TjaD6pcVFQAFAUkJ4pTau1I2g3a1g5AReViQLZZcZSWIugNrR1Ku0GVi4oKIFVVYdufgcbbp7VDaTeo1SIVFcBRmI9UXIRUUYY953Brh9MuUOWi8rfHnnsE84b1CHoDjvx86uf/2tohtQtUuaj87bHty8Cyfg2iuzvS0QrMG9YhWyytHZZLqbGZsDhtLs1DlYvK3xqpphrL9i04y8pAowGNBmdRIfUL57V2aC6j3FzN9C2fs6F4r0vzuSByMdnNlJurccpqN55K28K6ZzfmdWsQ3NwAEDQanKUlmBYvaOXIXEONzcTdK9/gx4OrMJkaUCTZZXmdt1wki51Pt/zKiDmPsDR/24WISUWlRVAUBcuuHdgO7Ec0GhtLLlotiCKOIzlYtm5u7RAvKCaHmVuXvcjOskPMTL6ReJsP5RXlSJJrCgXnJReTyUReYQEdtaHEaQO5b81/VMGotBlsGXux79+P+4CBeF45Dn3HVNzSuuB9/Y2IRg/qF85v7RAvGGaHhUmLZ5JelsnMxEn09k1CEaCkuJiKctcIRlAURTmXExtMJoqLizGZTBg0Okps1bxzZD47zbl8PuJxRkb3utCxXjTkX3MFHkOH43f3vYjuxtYOR+UccZaXoTid6MIjsOccpvK9t9EGBRH05DModhuOggJ0sbEImrY9HMzqtDFh0XR2lWfyQtJNdPeOBxSaf/iKohASGkpwcDAajeaC5XtOJRfTcWIRRRGHIhFq8OOhuCvpZYzj1hUvs6JgxwULUkXFFWiDQ9CFRzT+R5YapwA0PWsFvQF9QmKbF4tdcnDtwmnsKs/kpaSb6eYdx/FiARAEgbLSUsrLypDlC9cGc9ZyMZlMFBcV0dDQgCj+frpTkQgx+PJA3BX09Uhk8rIXWFmw84IFqqKicnY4JCdXz3+aXRVZvJJ8K2nesQCcqqoiCAJlZWWUlZZeMMGclVxM9fUUFxVhNpsRhJOnj0qKTIjBl/tjL+cSzw5MWjqT1YXpFyRQFRWVM8cpOxm34Cl2VWTxavKtdPKKOu2Eb0EQKC8vv2CCOWO5mOrrKS4u/lOxNCMpMsEGH+6LvYzB3ilct2QGawp3nXegKioqZ4akSIyb/3/sKs/m9Q63keoZhXAWa0lUVFRQWlrKOTbHHuOM5HKmYmlGVhSC9T5MiRnDEO9OTFw8nbVFu88rUBUVldMjKRJj5/0fO8uzeK3DraR4RiKewW/2eBRF4WhFBSUlJeclmNPKpd5korik5IzF0oyMQpDehykxlzLUJ5UJi6apglFRcSFOWeLq+U+zszyT1zvcSopnFKJwbqNNjgmmuPicBfOXOdfX11NSXIzlLMVyLMAmwdwTM4bBPilMWDyNdcV7zilQFRWVP8chO5mwaBrbyw7yWodbSPWMQnOOYmlGURQqKyspPkfB/Gnux4vlvAI8VoIZwyCvjkxYNI31Lp7ToKLyd8IhObl+0Qy2lOzjlQ630Mkz5pxLLH9ElmWqzlEwp4ygvr6ekpISLBdoZqiCQrDelymxlzHAK5nrFk93+aSpFuH82rtUVM4bm2Rn0pKZbC7J4MWkm+niFXvWbSynQ5KkRsEUFZ2VYE6Si+kClVj+iIJCiN6X+2Ivp7dHAtctmcHG4owLmoercFaU4ywtOfZ/QRQRdLrG+SiAo7AAqbqqtcJT+Zticdq4ZelLbCjey8zEyXT3iT+rXqEzRRCERsFUVZ2VYE6Qi+kCl1j+iIJCaNM4mO7uMUxaOrNNlGA0AYGUvzCd4rtvo+r9d3BWlGHZvo2KF2ZQcN3V1C+cj6DTt3aYKn8jGhwW/rHiVdYV7WF64vX08k106fop5yKYY/E0i8V8gUssf0RWFMLd/Hko7io6GcK5edmLbCy5uEswgiiiCwvHsnUz1R9/gFRRgWXHVmq/+xrb/gy0QUGInp6tHabK34R6u5kpq95kdcEunkmYSH/fDgi4vpZ+vGCKCgtPO9lRhMY2luZxLC2BpMiEu/nzz/hxJOlCuG35y2y4yAXjM+lmRP8ApMqjKJITxdyAVHkU48AhuHXr0drhqfxNqLWZeHDN26zM38HU+PEM9EsBhBZr/msWjNlsPm3pRQTQarU4nM7zHpF3NkiKTKRbAA8njCNK9OOuFa+x4SJug9HHxePWrUdjCUUBEBB0eoyDh6KPi2/t8FT+BlRb63hk/fusyNvBY3HXMCQgDYU/TkN0LYqi4ObmRlh4+GlnUIsA7u7uRERGotfrW1QwTkUi2i2QRxOuIRgP7lvz5kXdBuN91dVoAoNQnE4UhwO37j1wS+vS2mGp/A2ostbx+MYPWZa7jX/FXsnIwK4oitLiYml2hZeX12nHvh1rc/H18SE8IqLFBeNQJGKNwTyeeC3eTgMPrn3noh0H4zFkGPr4BASNBtlqxWPUGPSJya0dlko756ilhqmbPmbpka08EH05Y4J6ILeSWMLCw/Hy8jqjc05oYPb19SU8PLzFBWOXncQbQ3kyaQJudpFH1r13cQpGFDEOHobo54cmKBi3Lt0Q3d1bOyqVdkyFpYZntnzG4pwt3Bs9hiuDeyG1oli8vb3P+LyTVsLx9fNDURRKSkux22znNOz/XLDJDhKNoTyVNJHnM7/nsQ3/49VLpjAo/OKqdnhdfiV1P32HJiQEXVTUnx/oKGH3spVsORrOqFuGEXfsDTumkl0s+nEDRWgQNQaMkf24blxXvAGUSnYvXMruSgcavzRGX96doAu3OJhKG6LMXMVz275k0eHN3B01mrEhfXDKcpsQC/zJCF0/f39CQ0MxGAwtWoKxyg6SPML5v+TrkMw2pm786KKbi6QNDUNwc8fQIQWNf+CfHCVTlv4b7097kQ/mbKXo+LdMFRyc/yFvf/EN38yezTc/zGXloQZEQJEayJo7i/nZJhQBGg4v5Mu5B6l3uG6FdpWLk3JzNTO3fcXC7M3cGTGSa0L6IbWSWELDws5aLPAXe0X7+/sDUFZaiq0FSzBW2U4HzwieTr6e5w59x9ObPuX5/ndeXCUYRUH08ETQ6U75tr1oB1tWrWFvnQFjsttxF9lBZWkO6TkR3PbyZKLsJmyCG8Gde+OJjMOazfy5h0l88V2ujxCg5GceeGIBmSPj6OZjQC3A/D0oM1fxwvavWZi9kdsihjMhbABOJOTWEEtoKD4+57Z/9l8O6vP39yekFUowFslOimcUzyTfQH1dHdM2f3bRlWCQZU45bMmWy9b1uyiRoxk4KAmdw/n7UfV57F3+FbP3SPj7hJEyeCxjrxhNvxgdoKBIZmocXoQHNIk8IBxvZw0NSks+r1RakzJzNS9s/5r52Ru4JWIY14Vd0iiWFvz9nSAWX99zTue0I4b9/f0JCQlpccGYJRupXlE82+EGqmtrmL75i4tPMCdhI2/TGtKrfEgeMpqenlbsx9VoLLU1FGXsp+Dgdzx62x3c99TbzN1TSeM4Rw0atyRG9HKwbPZcFi5axNyvFmPpPpxkN92xUku1VWJVoYU6u1pVam+Um6t5sUksN4cN5frwga0iFjc3t/MWC5zhSnT+AQGtIpgGyUZnr2ie7XADlTVVzNj8BesvYsHYctezeq8Zn9TBDOvmgcUqw7GJZDKidwTdb3iGt57/N7cNCaBswcs8/Nh7LCtpvKYafSCD/3ELKZU72bxlM9srOnDLXcMIddMgACaHzGs7a3htZw2VVlUu7YkKcw0v7pjNvOz13BQ2hBsiBuFUWkcsYWFh5y0W+Is2lz/iHxAAgkBpC/YiCYBJspHmFcuzHW/guYPfMmPLl0zrexsDw9Ncnv9ZYTvCxrXZKBE9uHRIKNQfQdRoEDVaGqc0ihi8w0gdGEYqMHbSdVz+0VQeeuFTXv5qImMeT2lMx7sLkx4/uX2pWSyzDpl4qqcvwe7qNt/thaOWGl7Y/hW/NYllUsTgNi8WOMvV//2bepFachxMo2CsdPGK5dmOkyivPtq4ifZFNhepdOUPLNq2l/3F5exfvowlv60lPa+c6qLdrFu7h6xy5x/OCKTnjVN57MpAsrdspfov0jY5ZN5Ir+WjffVM6+PHlDQfPHSqXNoDVdY6nt/+Fb9mr+Om8CHcEN6KYgkPv2BigbMouTTT3ItUWlKC3W5vwRJMo2CmdbiB5w59x7RNnzGz/530D+vk8vxPj5Nyk4PKjJVsXLmG+YAoW6irrqPWdpiPX9Fh//frPD78xJnTgsabnv274LvQ7U9X4ai3y7y1q5b39tTy0gB/7kw9+y5BlYuTGls9M7Z+wa9Z67g1YjjXhw1EaoU2FoPB0CiWc+wV+jPO6fHn7+9PaFgYOp2u5Usw3nE80+EGKmoqeXrTJ2wu3d8i+f81Wjpd8xj/XbCVbVs2sW1HOrsXv8/UsX1IHfYw78/9gMeHeiA7bVgsjt9Pc9RTWqmh+4i+/NnzYnGemff21vLygABVLO2IOnsD07Z8wdysddwWMaJJLHKriCU8IuKCiwXOYyN6f39/wsLDW0UwXb1jjzXyTt34EVtLD7RI/n+FRmvA3eiJp6cnHm5aNB5u6FFQ0KLXAWI9pQdW8f3nc1iXWURxYTZ79+xgeXEXHrwp9k/TdcgKn40I4o7UM5vPoXLxY3KYeXrzp8zJXMsdESOZGDagVcSiNxiIiIx0iVjgHKpFx9NcRSouKsLpdLZYFalBstHFO5ZnOt7AzEPf89j6//H6oPvoHdLR5fmfMaIbPqGRxBj8cQOQzFQeXManr/5M9Y/9uCQtHO/AFK567CH6GE48tcEh0+BQCDJquLGDKpX2hMVp5alNnzAncy33RI7imrD+yCgtLhadXk9kZOQ5jbw9UwTlAhQ7mpe+aynBNOMu6tlTn8cLmd/j6eXJ24Mfokew62cpF1xzBR7DRuB/933g5nYGZyg0alHGUnGYzGInvjHJxPiePOa23iHz/p5asmocfDAsCK3Yctfz74w9O5PK999FGxRE0NRnXZKHzWnn3xv+xy9Za7k3agzjQvqAQMuLRacjOjoaLxeKBc6jWnQ8/v7+RERGotWeV0HorLHIdrp4xfB08vWYTWYeXPsOuyqyXZ6vLIDFbqe2tpbq2loqq6qoqqqitq4Oi8Vyin12mwUh4h6URNeuKX8qlnd21TJtSw0jotwv+CruKq2HQ3LyyPr3+SlrNQ9EX8bYVhALNC4MFx0T43KxwHlWi47Hz88PgMKCgguyifWZYpHtdPaK5v+SJvJi1o9MWfUGHw17lC5BCS7Ls0DUsnrFSg7s3EtBURENJhMGNwMRERF079aN4cOH07lzZ9zd3U+7WlczJofM27tqeX5bDV+ODOL6ZHVN3vaCJEv8c907/Jy1lkdixjImuEdjObaFxaLRaIiJiTnj9VjOlws6WMLPz4+o6GhEsWXHYFhlB6le0TyVNBHJYufOla+SUXnEZfl9a3Hwy4FMPDw9GD/+Gu6//34m3ziZiPAI5sz5hUvHXMbYcVezaPFinM4/jm85GZOjsbt55rYavhqliqU9oSgKD6x5mx+z1vBo7DguDe6OgNCikxChSSyxsS1SYmnmgrS5HI+iKNTW1pKfl9eiUwUA9KKWA/WFvJz9E06DwNej/49U/z/viTlXiq65Ao/hI/G9+z4wGE56PyMjgzfefJOFCxcyduw4np85k5CQ4FOmZXYqvLe7lqe3VDN7dBATElWxtAauanOZsupNfspew9S48QwP6IJGEFt02QQAURSJjYtrsRLLsXwvdIKCIODj40NMTEyLNu5C44p2HT0jmJo4AZ0dblwyk4PV+Rc8HwmQZBlZPvXWCp07d+bzzz5j1qxZbN++nVtuvYX8/FPHYZcUyqwS31yqiqW9cc+qN/gxexVPxV/LsIC0VhNLXHw8nq2w9Y1L6i+CIODt40NMbGyLC8ahSCR7RvBkwrW4O7RMXDSdQy4QzJlw6ejRfPLJx9hsdqZMuReTyXTSMb4GkVcHBDA+QRVLe+KelW/wU/Zqno2/niH+ndEKmlYTi4eHR4v/DsFFcoEmwXh7t4pgnIpEkmc4TyaOx1vSM37hM2RWF7RoDM307NGDGdOnUV5RwfQZzwFQa5d5b08t7+yuBUAUcMEmnCqtxT0rX+fHw6uZFn89A/1T0P0NxQIulAu0rmAkRSbeGMZjCdfgp7gzbsH/kdVKghk4cCB333UXSxYtZNmGbbyyq4EZW6tJ8z/1SnYqbZd7Vr3OD9mrmRF/PQP8/r5iARfLBX4XTGwrtMHIyCQYQ3ksfjwBigdXLXiK7JrCFo0BGlvqBw+6hI4dO3DnSx/y9WE7n44IYliUscVjUXEd96x8gx+yVjEzYRL9/TqiFzUtvoLgxSIWaAG5QKNgvJoaeVsaBYU4YwiPJVxNoOLBVfOf4nBN0elPvMB4hsbgiOuFPWcX7wwO4Ko4jxaPQcV13LvqTX7IXsWMhEn08+uAXtT+rcUCLSQXOLGK1JIoTX/GGUN5NOEa/DFy5fypHK4tbrEYSs0SL+42szPxaj785keujmixrFVagPtX/4fvslYyI+F6Bvh1bDWxxMbFXTRigRaUC4Agio3d1K0kmHhjKI/FN7bBXDXvSXJaSDB5dQ5qbBJvjoxmXLe405+g0mZ4cM07fJO5nGfjr2OAX0qriEUQBGJjY/H09LxoxAItLBc4cRxMS/JHwfgoboyd/xRHWkAwnQP0vHZJIFfFqm0s7Yl/rX2X2YeW8nT8RAb5p7ZeiSU2Fs8z2Lu5pWmVtRIFQcDH15foVhJMgkcYj8ePx0PSMW7h0xypK7nAeUBpg5Mfs0xsK7PhoROJ8NRi0FxcX77KufPv9e/x1aGlPBk3nqEBndGLupYVi6IgiiLRMTF4e3tfdGKBVpILNArG19eX6OjoFr0wzYJJ9AjjiYRrMThExi98hpy68y/BNC+sUNzg5LGNVXy4rw537cX3paucBwo8tv5/fLF/CY/GXM2IwK7oBG2L74QoajRER0c3LvR0EYoFWlEu0CQYPz8io6JaXDAKCkkeYTyRMB7RJnP94hnn1Qbzu1gkHt9Qxd5KO1M6e5Py/+2deXxU1dmAn3vvLAlZZ18ySUhAZFOwYsQVrYKKGyLoh7bV1oXN+rMuuFBttRRE5VOqtdXPpSoBEUUQ0Sq4gKBVQ1iKSBLABcieELYss9z7/TGZFIoKIZk7C+f5hz+Y3HtyZvLMe+55z/uKXJakQdVU7v70Gf7x9T+5Le8SRjhOiolYDAYDuXl53VpMOxrEvIS8JElYLBZ8Ph+SJOl22FEDVDT6pvu4t9cYgs1+rnn/T0e1ixQRy459Qe5aXc/Xu/w8cEo2Y3qno8Tpt4qgcwTVEFM/e45/bHqXW3wjudg1RPcEuYhYfD4f2XEuFogDuUC7YKxWcnJyUBRF19PUIU2lX0Yu9/YeQ/O+Zq5bNoOtTZ0TjARsbQpw56oGyncFmDrEIs4KJRH+UJA/fP4iL256l5t9I7jMXYRR1l8sRqORHJ+P7PbaSfFOXMgFwoKx2mx4vF7dBRPUQgxsrwfTtKeJGz98hIpOZvJ+0N5i9a6fZTO6l0iQSxZag36mffkyL371Dr/x/pzR7tMwyHJMSlN6vd6OomyJQNzIBcKCsdlsuD0e3QUT0EIMyuzJfceNpXpXHZM+fuInBaMB8gH1bYvcZh481coViSiWUIjAzh20rC2N9UjiipZgGw+vmcsLXy3lF55hXOU5E4OsxEQsHq8XS3tB/EQhruQCYcHY7XbcHg8Gg0FXwfjVICdn9WLqcVfxfX0lt674y4+Wa0hT4NsmP+sagzS1qQy2mznFZcaYiAW1FQV1/34anniU+lkzaV79CVrAH+tRxZTmYCuPlL7K818t5WrXmVybMwxFVlA1/Uq4apqGyWTC4/F0dNpIJOJOLvAfwbhcLt0F06oGKMo+jt/3GcvWuu+5c9XThxScSlP9bGpWmLq2hbe+9xNQ4nIaO4XB6ULds5uG2bOomzmNuukPsXfpWwRrqmM9NF2QjCYwKJhkAy3ArLWv8fzGtxnjGMqvfOeiSHJMxOJyu8N9Ni2RvgAAFuBJREFU2hMQfcv1dwJJkrA7HGhAbU2Nrm1LWlQ/Q7P7MrXP1Uwrm889q59hxuk3088aTvrbktOPh/bnUV29l0sNdfTYZiaoSKh6p2d2F7KMumcPpoJetK4tpW39OlrXlLBv2Xv0OHUoKSeehDE3D4M3B0nnDg96IJlMtH71b6TtO6nrYeK1zYt4/t9vM8pexPW556FIMqFYiMXlwpagYoEo1NDtbjRNo66uTnfBAKQpZj5p3MS0svkMzjmemWf8GkXO5baXPqdi87fcZdjKRVINsqoSiutZPAyShBYMEvjuW/xlX0N7gXUtGERraQZJxtizAFOfvig612HVBUVBqq4muGMHb52Wy8yT07k0tT835Y+ImVicLhd2u123+0aDuJcL0BG91NXVEQwEdBfMioav+HP5PM4puJia1vNpkq3cVvsRP2/YiBQMEkrwXBZJktDa2mhdt5bWdaUgy2jBIISCKE435n79Mfh8yOYUpJTUpCubZ5aN1LfsYuGur1jmkenZ/wwm+YRYukpCyCVCTU0NdbW1ukcw6UoKy+pKmfK1n7370/i/kUXcOFD/2jRRJRSiZuoUml55EclsxphfgLlPX1KLhpL28/MxFRTGeoRRoxl4qmIJf1+7iPN69OGWnAtQZP3FYmxfCiWDWCDB5AL6C6bjrKFm4rntARZWz+X8AitTTr6avhZ9S0dEk8B337LzxuuQjAbMffuTds55pJ0/HLlHAm6td4L9gRae3LCQZzcsYYRlEBN7XhSTiCXZxAJx/ED3x3C5XND+HCbagjFKUNUmYZIhw+Dn9kIDAzIG8aeyN2gL+bm/6Dr6WvKidn/d0DTUQIDUIaeQccUYehQNjfWIdKE50MqTG97k2Q1LGG45UYilm0m4yAUATQtHMFEUjFGC7a0SL2w3cZY1yKnZIcwypBtSWVa3junlCzgzfxAPnHodxye6YFQVNRhANh3a4C1ZaQm2MXv9Gzy74a3YRixGIy63O+nEAnGa53JYJAmny4XD4YhKJq9Bgso2iYe3pvDpLiNmWetYHu0NtjDcMZh7+4xh1XfreeiLl2LWtqTbkOVjSixtQT9/Wf8Gz2xYzAjLICb0vBBDDMRiMBhwJ6lYIFEjl3Y0TaO2tpbamhpCoVC3RDCKBDVtEn/aksKWZoVpfVo4KTOEBAcdU8swpPJ+3dr2CGYwDw79Ncdl+7p8f0F08YcCPL5uAX9bv4iLbD9jfP4FGCQlJmLxeDzYklQskOByge4VjATU+cNiKd+v8EjfFk7MCLds/aFJylBSeL9+HTMqFnB63iCmnXYjvbK8R31/QXQJqkFmrX2Np9cv4mLbydyUNxyjbNBdLIqi4PV6wwlyCZ7G8FMk5rLoACRJwul04nK5kGW5S0ukNhUe3mambJ/CrH7NPykWgL2hVobbB3PfcVfx2fcbuPfTZ9m2u/tKZgq6j5Cq8tja+Ty5fiGX2mMrlpycnKQXCySBXCAsGIfTidvtPirBRN7i75pljMBTA5oZkK62V6z7afaFWjnPPoj7+ozli+0bmbL6b3y759g4j5MoaJrGo6XzeHLdQq6wn8pvcmMYseTkhE83J7lYIAmWRQcSOSpQXVXVKcG0qeHdIYMc/jeg0elzQmmKmQ/r/82MigWclHM8s8++ldwMZyd/A0E0eHjNXGave52rnKfzK9+5mGWjrmKB8Begz+fDYrXGZTHtaJAUkUuEyGlqj8dzxD+zOygxZ4eJGn/44GGb2nmxAOwPtXGOfSD39RnL2spyfrtiNjv31XX+QoJu5eE1xTyxbgHjnGfyy5wYiiU395gSCySZXCDcx8Vmt+P1Hv7BalNAYmpZKotrTYS64fPWEvJztnUg9x03lg1VFYz/aBZV+xu6fmHBUTFzzVxmlb7Gta6zuSbnbMyK/mIBwmKxWI4psUCSLYsORFVVGurr2blz5yFvqgQ0+CXur0ilfL/MswObKeyhdltFVLNsZFXjJmZseZ3jnT158fx7cPVInPKEycCMkmIeWzefGzznMcZzBqmKUdcKchHy8vPJzs4+5sQCSSwXaBdMQwM7d+zoeHMloN4vMbU8lW+aZZ49oZmeqd0nlggm2cBnu8qYXrGAXvZcXhkxFWeP+K/YngzMKJnDI6Xzudk3nCvdp5GqmIRYYkBSywUOFowsSdS2hcWyvUXi7ye0REUsEYySwhdN5Uzf8jp5Vi+vXvQA9pSsKN1NAGGxzCx9lUm+C7ncXUQP2Uz03uEfJy8vLywWOemePBwxSf+by7KMzWYjN9fH/qDGql0GjDI8HWWxQLjo95Ds47iv91i2N1Zx9bsP0ti6J4p3PLaJiGVy7kVc5ioiNQZi0TRNiKWdpI9cOtBU6hsa2fbddvyaRLpBn5pHEiBJMqW7tzJ9ywK82U4WjnwIS0qmDnc/dphRMoeHS+dxa3vDsh5Kiq59hSAslvz8fLKys5GPcbHAMRC5ANS1hFiwpZmsbAu98nNJV1TdiqlphD90J2UWcl/vMVQ21THqnftpatun0wiSn4dLiplROpff5o5kpBBL3JD0s7B1d4BfvF/LvPJ9qJKE1WrFl5uHquqYndn+QR+cWch9va+kuqmOUUunslsIpsvMXDOX6aXF3Jp7MRc7h5AWA7GgaeQJsRxCUs9EeZOfGz6oo64lxPTTrJgVGUmWsVgs5Obm6i4YCaldMGOo3l3P5Uunsse/X7cxJBuPls5j+pricMQSK7EAue27QkIsB5O0s/F1o5+bPqxnf0Dl5eFO+lpNHf+nKAoWq5Vcny9mgrm315VUNdVz+dtT2eNv1m0MycJjpfP585piJudexCXOU0iP0VIot/3hrRDLoSTljKyra2P8R3X4QxovnO9koM10yGsURcFis5ETY8FUNtUy6u2p7GkTEcyRMmvtfKateYUJORdwqfOUmEQsQiyHJ+lmZce+IC9v3kuWSeHpc+yc8ANiiaAoCrYYCuakrLBgtu+qZvQ794sl0hHwxNrXmVbyCjd7h3O5qyh2S6H2lH4hlh8n6bai9wVUtjYFMMgSA35CLAcSCoVoqK+nsrJS12xKCQkNrX2b+nUKbTm8NvKPZJnSdRtDIvGXdW/wYMlLXO8+lzGe02Mmlkg9lmM9j+VwJI1cduwNsieg0t96ZEL5b0KhEPX19VTFQDAAXzZVMH3rAvo6elJ8wf1km4VgDuSp9Qt58MuXuMZ1FuO8Z5GmpOiaIKdpGpIkCbF0gqSYoc+qWrlzdQMf7Wg56msoitJRrkFP30a+eU/JPo57eo1hU+03/GrZdJEHcwBPb3iTaSWvcLXjDMZ5zybNoL9YZFnuKE0pxHJkJPwsfV7TypRPG9ntVznLm9KlaymKgt3pxN2JejDdQUQwQ7OP555eV7KhqoIbls9kV9teXccRj/zt34v5c8kcRtmK+IXvnLBY9JR/u1jc7cW0hViOnISeqX9Vt3LXqkbMCvyxyMKJ9q63x1BkuaMmL6BbFKOhoaFyhrU/d/e6ki93fs2ED2cd02eRntm4hOklcxhpOYnrc88j3ZCCqnNpSllROtp/iIe3nSNhZ2tVZSt3rW4kRZGYfpqNU91di1oORG4XjNPpDDdp100wENJCDLMNZErv0Xy6fQO3rvwLDa27dbl/vKBpGs9uXMKML+cwPOsEbsgfQbohJSY1b10uF3aHQ4jlKEjIGSvb5efxdU1kGGWmDbVS5Or+hl6yooQbrzmdXe4q0FkCWpDz7CcypddoPvp2Dbd/8jR1LU263T+WqJrKc5uWMqOkmGGZ/Rjf80IylNiI5cD3X9B5Eq5XNIBfhXNzUjnVncIpURBLhMg3F5pGfX09qqrqtpPkV4MMd5xEUFN5dOtC7pEVZpx2E84krmgXUkP8Y/M/mVlSzOnpfZhUMJJ0JZWgFtJtDB1icTpxOBzIx2ihp+4gIeVygs30k8lx3YmiKLjcbgDdBdOmBrjYOQRVU3ms4k0MksxDQ3+Dq4dVl/vrSVAN8fLm95hZMpchPXpxa8GlpCspsROLyyXE0kUSUi56ExGMBjToLJgW1c9l7iJUNP63fBGKJHN/0XV40my63F8PAmqQOZuX8UjJPAan5PO7wsvIMKQQ0FksBoMBu90eXgoJsXQZIZcjRGnfNUDTaGho0FUwzSE/V7iHomoaj29ejCzJTD3ll0khmEAoyJzyZTyyZh4DU3zc0WsUGYZU3cWitIvF2d65U9B1hFw6gaIoHTkwjY2NXe5N3Rn2h9oY4zkdDY3Hv16MIsncPeQavGmJ28g8oAYpLl/GoyXz6Gf2clevK8gw9iCgBnUbQ0QsDiGWbkfIpZNEBKMRFoyqo2D2hVoZ6zmDEBqzNy1GkiSmnDwuIQUTUIPMLV/Oo2te5XiTh7t7jY6NWBRFiCVKCLkcBYqidHR1bNR5ibQv1Mr/eM5C1VSe3LgEGYm7Th6XUEukoBpibtlyZq6Zx/FGN/f0vjJ2YnE4hFiihJDLURJbwbRwbc4w0ODJr5YgSzJ3/OzqbhfM3r17ycjI6NZrhtQQc8uXM7NkLn2Mbu4WYklahFy6wEHPYHQWzN5gC9f6hgHw5MYlaGjcdfI43N20Tb1+wwb++e67jB07lsLCwm65ZkhTmVv+ATO+LKav0cPdx11JphBL0iLk0kUMkQimfRcpcjRfDyKC0dB4auNSAKacfE2XW8eWlq5l/IQJVFVV8dHHH/PM3/9Ofn5+l66paRpzy5Yz/ctX6GvyMqX36JiIRZZlIRadELPbDSiKgsfrDZ+a1fEsEvxHMLcUXMwrG8PZrUd7VEDTNEpLS5k4cSKZGRnMLS6mpqaWiZMmsWPHji6Ns7hsGdO+eJl+phzu6j2aLGOa7mKRJAlHJEFOiCXqJE2xqHggFAxSVVWlewQDkKakMLdyBX/dtpRx/Yfz+6JfYU898taxYbGsZcKEiWRmZfLmwjfIzMxk2zffMGrUFeTm+njmmWfw5eR0emxzypbx4Of/4MSUXG7vNQqLMT0mYnG5XDhcLhQhFl0Qs9yNKAYDHo8Hu13/reH9oVau8Z7NLYWXMG/TMv70xUtHXA8mErGMHz+ebEsWi95cSGZmuCNkYUEBixa9ybfffsekiZOorKzs1LiKNy/jD/96kcEpeWGxGPSNWICwWNxuIRadETPdzSgGQ/iD7HDoujyCcKLd/3jP4reFl/LqpuU88Nnz7PYfvqJdSUkJN908HovVypsLFx6yQ1RYUMCStxZTsXULEydOoqqq6ojGU1y2nN9//jxDehRwW+HlZBvSdM28hbA4XW43DqdTiEVnxGxHAUMMBdMcauMq7xncWngp8zd/xL2r/4+9P9EX6YsvvmD8hAk4nU4WvbmQ9PQfrt1bWFjI0rffpqy8nIkTJ1FZ+dOCKS5bxn2fPctpab25teASso1puh5ChLBYPB4PDodDiCUGiBmPEh2CcTp1bVsC0BLyM8ZzOr8rvJSFZR9z56qn2R84tL7wZ//6FzePH4/X6+WN1xeQlpb2k9ctLCjgnaVvs7msjMmTJ//oEmlu2XLu+fRZzkzvy6SeF5NtTNddLKqq4vF6sTudKIqi670FYYRcoojBYMDlcuF0uXQXTKsaYJRrKLcVXsbiik+4beVTtAT9Hf+/avVqxo+fQF5ePvNfffWwYolQWFjI20ve4uvNm5k8+ZZDlkhzy5Zz56d/49zMAUzoeWFMIhZVVfHm5GC320XEEkPEzEeZiGBcMRBMQAtymauI2wsu5+0tq7nl48cJofLJyk+YOHESvXv3Zl7xnCMWS4TevXuz5K3FbC4rY9LkW9i5cycQFsvtq59mRNaJ3Jg/AosxXdcKchAWS47XGxaLiFhiitiK1olgMEhtbS3VVVW6fuglQJZk/llbyl93vkuPba2kLamioE8hL7zwfKfFciBlZWVcMfpKBvc/gUHjhzN75ztcmDmI630/x2LK0LWYNrSLJScHmxBLXCDkoiPBYJDamhqqq6t1FoyErMgs3riCP/71Ec6yDeDl51/EZ3d3+doVZeWMu/oa1mRXcfNN47mm7/lYDWm6tv8AUEMhvD6fiFjiCLEs0hGDwYDT5cLtdhMK6VgMCQ1VVRnZ53SmTXmAr883cfea57olsvhS+p6KURmMumQUY/LPxGpM110sISGWuERELjEglhGMisaH9RuY9c0ihuWdRPGI3x91JvH8ig+ZtGI2V9pOZZz3LGzmDN07N4dCIXKEWOISEbnEAIPBgCNGEYyMxLm2E7izYBQrv1/Lte9NO6pcnPkVHzFpxROMthcxznc2tpRMIRbBQQi5xAijwYDD6YyJYBRJZphtYFgw29dx7XvTOnWN1yo+YvKKJ7jCXsQ1OcOwGTN0TxZUhVjiHrEsijGxWiLJSAS0ECsbNvLYN4s5O28Qcy944LA/93rFx0xY8Tij7Kdwbc4wbMbMjl7XenFQHosQS9wiIpcYE3nI69I5glHRMEoKZ9sGcEfB5azcvv6wEcwbW1YwaeUTXGYbElOxRA6HCrHEN0IucYDBYMDldOJyuWIgGAPDbAO4o+flfPx9Kb98/88/+NqFW1YyaeUTjLT+jF/6zo2ZWNweT/gQohBL3CPkEicYjMZwBKNzJu9/BDOQOwou54Nv13D9sofhAHEs2vYJk1fOZnjWiVznOxe7MUN3sWiahtvjwSnEkjAIucQRxnbBOByOGAhG4VzbCfyu4FLe++ZzbvzgUTQ03tq2mltWzOaczP7ckHs+dlMmagzE4nS5hFgSDPFANw4JBAJUV1dTX1enazlGCYmQprKsfh2zti3mBFchmxu/56zsftzkG4HDnKV7Sn9ELC6XS4glwRByiVMigmmoq0PSWTAqKu9Ul/Bc5XJGFBQxZcBVBOr30dLWqlvpzo6atw4HTrcbgxBLwiHkEscEAgGqqqpobGjQtR4vGlhtNrbJDfSz5eNMtbC7qYmdO3fi9/ujPpaIWOx2Oy63G4NBNKlIRIRc4pxAIEBVZSWNjY26CEbTNGw2Gx6PF4Px4D/qpqYmKqMsGCGW5EE80I1zjEYjHo8Hq9UKUfweiHzHWK1W3G73IWIByM7OxuP1YjKZovJIV9M0ZCGWpEHIJQEwmkx4PB6yreFuit0dbEaiBYvFgsfjwWgy/ehrLRZLWDBGY7eOI9KwzCrEkjQIuSQIHYLJzu7WxmsRsWRbLLgPI5YIlvbXmkymbhlHh1giUZMQS1Ig5JJAmEwmPF5vtwnmQLF42mVxpEREYDKZurRci4jFYrXi9niEWJII8U4mGBHBaMDupqaj7uzYIZbs7E6LJYLVZkMDamtq8Le1QSfHcaBYPEIsSYeIXBIQk8mE1+sl6ygjmIPE0v6A9mix2Ww4XS5MZnOnIhgRsSQ/Qi4JSodgsrI6JZjuiFj+G5vNhtPpxGg2H9EuUodYLBY8bjdGIZakRMglgemsYA4Ri9ncbWOx2e04nc7D7iIdKBa3x4PBaOy2MQjiCyGXBMdkNh+RYCJiyYqCWCLYI4L5kV2k/xaLUYglqRFySQIOJxg9xBLB7nD8oGAOzKURYjk2EIvdJMFkNuPxegHYvXt3xx/zf4vFHEWxRLA7HADU1tYSCAQ6xmC12XC73UIsxwjibFGS0dbWRlVl5UGC0VMsB1JfX09NdTXBYFCI5RhERC5JhvmACKapqSksFq8XczfsCnUWu92OqqoEAwHsDocQyzGGiFySlJaWFpr37yctLY2U1NRYD0dwDCLkIhAIooLYLRIIBFFByEUgEEQFIReBQBAVhFwEAkFUEHIRCARRQchFIBBEBSEXgUAQFYRcBAJBVBByEQgEUUHIRSAQRAUhF4FAEBWEXAQCQVQQchEIBFFByEUgEESF/wd2RU59KL6ysQAAAABJRU5ErkJggg==)
A beam of light strikes one mirror of a right angle mirror assembly at an angle of incidence 450 as shown in the figure The right angle mirror assembly is rotated such that the angle of incidence becomes 600 Which of the following statements is (are) correct about the emerging light beam
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAARcAAAD2CAYAAAD8vMNHAAAgAElEQVR4nOydZ2AU1dqAn5ltyab33gskEHqX3sQGiqAidq+K9V69NvxUQOz1qlevvaDYRZTeey+hhJaEkF5J32yfme9HEgRBqZuQOM8Pyu7MOe/Ozj5z+hEURVFQUVFRucCIrR2AiopK+0SVi4qKiktQ5aKiouISVLmoqKi4BFUuKioqLkGVi4qKiktQ5aKiouISVLmoqKi4BFUuKioqLkGVi4qKiktQ5aLiUk6aXNLqk02U1g/hQtAGPoS2tQNQaQtYyF71G2sy65AFGZtVxjd1JGNHJuF9mjMFQebwkv/x2YpKEq64nTuGRJ02N8VcwYFf3uKVDeHc8+YDDHA7j9CVGg6vnc9Pv23C3PkGbrh6ECl+55Feq6FgKt3FnHf+y5bIe3jzvj4YWjuk06CWXFT+mro9/PDcE7yzoR7v6FjiEhLokOBD1bLXeeKFn0ivlE7zEBXx8A4kIjKcAC/3M8pS0GgxBkcSGR6C7/k+/gQjgUE2Dq/+hd+W7iG/4TzTazUEtDoPQiIiiAjyQdPa4ZwBgjorWuXUKGDLZd6Mf/Ls6mDufesFbusbgh4AJ+Ub/8s/H/kOy6ineOnRMaT46P86LYSzjkBWQDz7005BOv+94V5+M9zGYy9OYVTEhUiztZBpK2WCthGlSssj2anc8Ckvfbwej6seOU4sAFqCB9zPQ8Ng8xf/YfamEuoAkGlosIPiwFxnwmx1NB0vIDlsmC2O4zKQaSjPITOnmBrp1CHIdbVYjvu/rboGG4CzmuKSGpwnnVFP6ZFMMnOPYv3DO4ogIAinb6pQzOXkHc6l+KSg7NTU2gFw1pVRUmn//S1HNUVFFSflCWCvLCTncAGVtj++Y8Vql3A6bJgbTJhszZFJmMpyyDxSQt0pr4tEba3lhHSqm+OqKj5F3I2xH83LIjO38pQxugq1zUXllEjOenb+/D3ptkT+PaoD+pMKHzr6juhP5GefMX/VPsYGFlG1cxlr7Sn09i5l76bdWHpOZsKgSBx75jE/24deI6/i6t4hSNVZ7Ni0jQN13gS6N7B+QRl232ACffyJ7TGYZPsOlixZx56SCCbMuJmE3M0sX7GaTdlBjJkYyKFlW9iTVYXf4Dt56MaehOhEbLmr+Wl5DoK3EVvhIb7RdOXyCSPoEeF1wk3+pwUhWzUF+7ex+WAVtvoy8ost+PW+komjYqjbvoSl6/aQHziCSVF5rNy8i4wiA90m3csE/z0sWLGTjAOFKKkTuO8fw0nw1CJSwe7lW8mtM1Fbkk1WuSedLpvAld19MB3cyOJF66kO7oi/XMreLYUEXXYLNw33pWTjJvbXexFgMLFuQQVOn0AC/QKJ6tSDwKJlLFp/iIroCUy7MYojm5azfPU2coIvZWLAAZZuySCrOoihdz3Ijd0D0IpA3T7m/7oTa0AoHvUrWbJIh5eHFsE/lSH9OxMbcD4NWn+NWnI5QxRrLbUNDiT5L45xWDGbrad4orY1FGRnJXsPlCLqw4mKEJFP8asUwyMJ9hQoOHQYq6mMHXM/46OPv2PFwUrqzXXU1ZuxOi0cXvMzs76ey+Z8G1DHnkVf8fGs1RT6pdEzwZ2arbN48bkPWZprwykLyPWlZC74iDe+3kyJALK1hiML3ue1j39ixa4C6gU/gk3r+O/091leZEXBwqYPnuD5n/PQR3ejb3QZi9/7L9+tz6XyjCr9Fgr2bmDh/B1Ue0fRoUMwuuJ5vPbYTD7fWoW1KosF/3udT+ZvJ7fahuDhi7L7M6ZN/4CFe4uoF/2I9Mjm+xde4ce99diB0qWzmbezBJtvLKlpUVStfJfnnv+E5ZlVOG0HWP7953zw+SLSC2toMFuxVmeyecEsPvl6HSUBXegRb6By4+e88PwnLM+1IylO6oozmPfh28zeUoaAjLkqk/nvv87HP69md2EDgm8ApjVvM+291ZTYJcDKrq9e4I1fc9GGd6RbijsHvnmFF/63gJ15dZyutex8aVclF8laS2nOATJzS6m0a/HwCSUhOYGYCL/zbFl3sv/nN/iipCe3TB5FWpjxxHfri8hMX8fyLdUE9RzKFcNTTtuLcrGjKE4czsbiivhnjyC9Dr0o4LQqhPW8nJF93uGbRV50vvp+buvqieQU8PBwJ6hvT1IPFaLR6sFxgB1rt5LRMJhJI2II1RoYfnkv5mzJJ27YVfSLBoIGcc2QjvznsA4t4N1hOBOGpzBjuwH/fv/gkU5ukGFh4aBfSc+3MSFWRPLpwaS7bmRgrA9OKYZgeS2FxbXUWSHkdO3IDZnsWLucJVmR/PO6QNwtMmmDB9Mjaz95BQIpV13DsI5vkuERSp/rJ3MVUOaxiR+mbqOsx3SeTNGDPZit3z5M+gErcr8jzH1vHoWXPUx/T3fcvbsyZGQfMteVUFyvJ3LAcAamfc+h8kSGTH6Ca5IMOPOX8OHMjey1DmfSsGjCNFqGju7Bb7sqiB92Bf3jocEwliEdP6dAqwV8SRl+LcM7vkK6IYj+d99Pih52Nyxg8PydFNjHEeWWxbwvF2Mafi99EqMI87yFq7u/xZLsNMZe1o+EgDNrYD9X2pVcFKedhuJ0ln/1GV9uEuhx3cM8HRFJBJy3XOrKC8kriKLefopyibOBnJWzef+TYrr8qwOjhqecV27NSPW1WDy88RCFc2gOPR8ERK0fMeFeyHuOUlYuIwRrTq5T1NVRa4Xg6Ai0Gh2SLKGPiifSaMDNYDx20WWF31tmRXeM7iJOSwUlpUCkgKQIIGjRNpcKJQcIWgSa2kgkB4qoQ3SPpUtKUzHe0xc/vYTTJuGU/RjxwKP47skjfct+GiqKqXfIuMGZjQcpL6X0cCZHrMFUF+VhanAiBI7koZevIyDSH5vFhOimxxAcSQiAZMPd2w+DXkdCvL6xuVpnxFMnUekAsWEPO7PMWPsepaJMg7VMwvuSu3l6uD/RKYFAEU5JR1hUGL6+jZ9H6++Ph0HBYT5KaSkQ0XRd+P26yE4FQfP7lyA5ZEStFvfYzqToAWS8/P3Qyw6ssgJo8fH1oK4gl0r7QMIBSQI3vYLdcXz7l2toV3LRegaRPPJyLt23jDmb60gePp4+yRdiNIAb/R96n16CG7pTPMW1fsmMHj2c/hsWY79gIqhjx5ylaCZNpOdfdcS4CI3Wl16jLyFo/ga2bilFSYs46XNV7NlLvjOaoYNT8TOKFEkKiiQh/VkHpGQHTSr9Lh1Gv+IdbJy3hX4D68ksNJJ67U2M7fz7oacc6qZIOBygGEBQAAQEBDSCiYz5X/DJWoXUK27nrmsVVn20mWoFBLHxuL9GwWmxoTWGkjp8NMnHvW6qtSDZFFAEFLmpsVRRkGUZkJGcCopBQJBlFAQQQJEVkGoxe3ZlxFXdCWpOzmbCLGibPp2CJMk0J4lnZy4ZM5RtX2WwccE2evWv4nCZN2nXjuGKTsfH+sfPoqBIThyA7thVE5rySOGaKeOZ+9561m9NQRdbyV5HV665djSpET6nuSbnT/trc1EkJEGLm06DVvzDDeqwYJUBnDTU1mE9xf3rNFVRXl6N+Y9tKxo3cDqQ5BNPcpprqW6QMNsVNDrdSenJtjoqj1ZRd4rMHBYrEoCzgdo667Gfk2Kr5PC6L3ntvQVk5OZTVGNFbuEBA4LWjbixU7hjgCe7vvuMDaUnPumUqi18Ovcg/oNv5+ZhMfgCCAIIIpo/1KNEUUQQRESx8UkcFNOdAT0T8bVlsj27Ac8ek5j24nV0aB68IWqa0hAax3OIIpomSWi0TT8vrYgAiBo9BsdG3n/mA7LiruemKxNwq66g2mTGKTVQW9ccA00xnOLDBkYQHeFGzYaveffrnRRUVFFZksXO9QtZmF6FVq9DFBQQNMfi02rERrFphcYfkUaDgNKYh1cKPVNsbPrqA75ZsIu8imqqSg6y8peVpOdXATq0ooAgiGiODVgxEhzXg/494vCyHGJ7lhXfPpN5dua1JDfFLGg0iELj5wAQRA2iICAImqZSggaNKAAimsYLRlCXAYzoFY618Aj704+ScPvzTL25LzGeZ3M3nBvtquQCNI43Vxr/bn6AOkxlHNmfwcHsYnRpgwkv28ymXQUoSSMZf1k3QvSAXEdexgEKyiupOFpBjSaangP6kBrujqOqkCP7NrO+LJoxw7sSHeAOcj1Fhw6SlVtMtdMNITOTojqJoOab19lAVXEOh7ILKCoqp14IILFPf3on+SOXZ5Ox7xBZhTrShoRSvnkL6fkKSSPHc1n3QOTiHfz8+lvMz+9AwtrVuKcO5ao+kbhrW/JZIKIJHMljrzxG2RM/8um33dEOi8FbJ4JiJnfZJ2zUX8Wjz9zBJRFGFFsR+WU1VBblcjivmIYULzxEAZQ6ikvKqCgtp6SkAgXYtmIJv62ppteDowlzB1FjI3dzOnWRiSRHeiFVFZOdX0pDvQdH8uupN5aTlVeOpc5Ibs5R6sO1mHKKqDRXUXQkj7I0Ba8Qb0rW/czczpVE1+dTY6ul7uAO9mSmEe8opLyyilKxiKJSM0qY8cTnv1cy3S+/htHLZvLT03dxZO1IugSIKIIfve8ag6lwEfllJurd88irsxIslZGVX06DWUdedim18Z5IxQWUNzRQmZdJXt0gxt55HQv+70temZrLpkE9STRWcjTgcu4eoIeaAoorKigmj9x8E1KQJxry2LR4CQs2NNDn/tGEuQmIGgs5m3dRG5VAUoSB6uLD5JeaqPPJo7ChG+7Fh8mrMFPnlUtOVQOhQhU5hZU0VBeSk3eUPp292fDOG6yUbuOWQD/8A9zQSkfYubmKyKQkIv3d0bmwvq2ZPn36dNcl3woo1eRuXcGSrVYSrriRUQlgyl3Ld69P5fHXl1MXEkzRmkXs3LeaWR8sgxE3MTRC4ujmz3n53XVY47vS0XsP7015kl/oxxX9wrBlLeS1++/h+R3BXDa6L/EBBqq3zuKN/y4gWxNNhzATu1csYMF2O0lDRnNZnxis+1by65xl7LH4E67PY81Xb/PuwmpiB/XGZ/+3vPr4E7y6tI7QkGLWLNrJgTVf8d5SgeGThxBQV4OzfDu/7vVm1OSRpIZHEhVgbHoqtSz6sJ5ceWkitRsXsnJPDrnZB9mzdRtZhqE8NP1BRsYY0GCnbO8q1qcXUWcGQ2AUsfFRhHjoMBVuZ+uWDPKrNHiEx5Kc4IdYuptFvy1g2aIF/PLLXH75dT5LVu8kp86DhF6puOVvYtGmTOxGb3x9YogyFrFx4wHMOk+8A2JJDrKwd+0WshpA7xFMUo+R9I+2Ubh7HesyTERfNoZUrZmqOl96DE3CULSf9AOl1Om9CYuOJj4qGE/98ddSi09UMt06hyOV55GVmUedVyqj7nyQiR1qObh+CZsy7bh5+eMfHUuI4yArNxygTu+Br080iVEiR1avZ28VaDy8iElOpeegEfSM0GItPczBrEIaQi/l7nuuoV+0k8y169mWVU6N4oZ/aATxsRH4GEwUH9jEsgWLmq7LL03XJZ08syfRaeGY05ewKdOJ0ccPn5hQvAs3sfagDb2nD4FxCQQ27GHNlsOYBTe8QpPpnOZP5eblLFu9jCUL5jH351/45beFLF2zjUJ9Ep2SIvF3c+E9pbQ3pGxl5X8mKt0SRymPLzY3vVij5K98Qunnn6pc/0GmIiuKotTMU+5NDlAGvpqpOK0ZypsjEpSJ39Y0HV+trJg+URn75Bwlp8auKIqirPxXVyXuipnKimyzoig7lVfHDVEmvzBPybA0nlG7/AXlhkFDlRv/s1FpUA4qP702Vbnnkc+UvTV1SlXJbmXlF/cpQzoNVf7xTYmi2AuVtVP7K74dblTeO9h4vmnhvUqy3xDlpUNNEX9xjRKYcK8yr6FlLptLkE/x2tGdysLvv1JmLTikmKxVSnFejpKVuV/ZNPcT5Y1/TVFe2NHiUV4UOMu2KvO/+1r5enHmcddln7Lx5w+V1x5+QHk5/RwSrd+tzHrhHWXZkQqlorJcKcrNUbIOHVB2zn1SmfzPj5VVuysv+Oc4nvZXLTolEk5Fg6eHPx17JSEgY5ECCQnWst1ch7NyK8t2+dIzwQNJAY3gy/BpPzD8uBQErYAggqjTw7YFrDykJ2ZCMP5NnRcGdyNGDw9sGhGpOJeCrD3srBTZuvBXBIuEqBvIfS+PJzzZCNZKFK0nRv+O9OkAyGacgSEEadOxNsiAgENSAAWn3Y7TqG+b9ddTPBSzVs9n4a+Z+EwaiWwTMPr4Y0TCYOlMl1otUkzLh3kxkL3yNxbOLyToxhEnXBd9fBpdG4wQffZp1i59nZfWJvLm5XXIvgF4+PpjlMHHksbQSxIJC3Btw0ubvGdPi3DsjxNfU2Sk5p5kRTl2hGwyY5WqyM+vQ+7tf2xSmLW+HsHDE8Ox6kjjEHLz0SpM1nqsThn5WHIKSlOaDqcds0nGN743V0wa19h92YQkAfUVTSdJjQPuBAHlFL0ANL3X8pUh1+EbE4+PZR5zZ9xObv8eJAW7I5vraBCD6Tb+Hm4KaO0IWwe/uES8TYv5ecYdHO7Xg8QgN6SGWsy6cHqOv4tJ/mefpjayFz3rP2Hqv/fRs1syUf4GlLoyyrW9mXR3BxIiXNsN2f7kIjT+FJXj/t30Bs1yaPxbaDpcRBeaRKJ/FQu/ncOhwTeQ6K0DWzGLv91C7HVj6eZ3XAOgomAMDSfIo4xD6TnkXd6PiGCQZQnJ4cTpcKD1CyHMo44j637juy2DuL+nF7KjhsL8XLLKQri0p/YkYQhCsxOb4qKx61NRFOx2B2463Ykfp40S1Gsyz38zkkkbVrJuTzEmjS8xl4xn6OBUgtrCVF8XEdz3Vl76djST169i3d5iGrT+xA26liEDUwg8x+vi0echvlo+lk3L1pCefRSLzp+ES29jdM9IjC1wL7U/uZhMmOoaMDvsmOtqATeQHVgaGrDKDixmGZCwW8xY7E5sVgtW9yHccmMaC9+bwZ1PlHHboBDqdiwmp/tzvOTmDjgwWZ04rGZM9Q3Q/XKuHPgbL8x9j88Tgwm6uSfW3ELKissRSgop8hxD9zHD6bD4XV6ZUkH2jVfSSSylsEyhw13TwJaByWxFclgxOwHFjsVswS7ZsZgsOGV39F5euJsLyc45zEaTRO/+HfHSnSylNolbCJ1GTKLTiNYO5CLDPYzOo26k86gLmWYs/cfG0v8CJnmmtKveInt1AbsWfc/389aTXmZDdsj4BPnjRQ7LPv+epYfrkN39iIk2ULhsNt+vyKbcqicktTdX3TCWVDmbzUvnsWDdEdxGPMnMf/QkxE2hZNtXzP5hPfuO1COFxtGjc1+GDOtEQEMG87/4lFnzMzAjI/p6oLiFkhDdmUsG9aFLjI78LStZvHgth+QkRk15nNvTJHI3zOXz75dzuEbB4BdLrHshS7/+gWWZ5di0IXTs2onYKB2lG+bw9Xf7ibjiegZEe55yAF/7QEGWleOqgAqKLCMr4lksuaAgyQrCeVUjFRRZQTlWwlU5H9T1XFRaFUW2UF1cSH6hlbB+aYQAsrWWon3bOWzsy9CU0zU6NorIcXQfm4540i0tGh/jORTIFQe1JfkUFtXh3qk78cbTn6Ly17TbZ6FKG8Bcys5vnmXy8FFMmrmIPAAU6st28OHDN/GP15dhOm0iJg4tfIFJAwdx9cxF5NXa//TIP32O2qvIWvAGU64cybhHvybdcurDVM4OVS4qrYcxlJ7Dr+Xm4XFIjuZ+NwGfiIE89cMGlr86ltN3lnrR8cp/MrFPAN5u/MU0iXpysnIoLK4++S29P0lDLuPGK7rhI7l6IYK/D6pcVFoXjQaju+HEiYpaPcbQeGIDzrSbxIi7m/jX7SQFC/n252WsP/QnxRKNFq3BcNzkP5XzRZWLykXBiV6QcdTnsftgxYkHmfLYtmIxyzZlU/WHs5uHGGj1MrXZ21i/PZuj5sZBTY6C5bz51Gt8/uNi1m5cxfqMPMr/ZL1HQdAgSmDJ28nGbYeoOKmWJVGXs4Xli5ezKbv2DyKSqM7czIqFi1i1uwiT9Pu7UvkhsopqMTttVBzawdbdOZQ3NL5vKc9k56at7M2v5S/WImtztL+uaJU2iwBQl83Sz17i+Q83YB37IVtfGQKyg6rNb3PPK4WMffI2onY+x1UPFeIb7od793/wv2eHIggaDNoyFr/0bw4WZrFhbTb+N77F/6ZeRozTC3eDHqPBiSTLTT1Cp8hfo4PqDJb+52ZenLWE3AYNwf0mM+2/r3NDAjjMR1j65uusMPQize0Acx5/APO4d5k9fRShmgJ+eeh2PhOv59bBCmv/9W+e7vocnz7endol7/B/L83Dbdy99NBVUZS+lJW7TaTc/gjj4+0cWfkbS3bnUuc/iDueeYknR4WcIrq2R9ssudTmk1dYSoW58b9SbTF5h3PIrz4b7zeQv/sAFedRBrYW55BbfJTatr+u5UWBAuAdT68rJzEouJY6W+P3aa/fy6fT/0t579u5tk8ag27/F5cZMsgMmsSrDw4jSNSBAObDJfhPmMob3yzm8wdSqdm2gh3ZNfjE9aVbUhh+/pF0HjCCQV1iCT5pmR8BQWmg1m4gaODzrMrYztL/3ULI/u94YeY3FFJP4W9v8Jl8E8/edx0Tbn6UVyaHsfWdZ3l/hxU591c++OYocWOu4NLxd/PvCfGUbVpLep0/fSePoUeQhsLD0H3SY3y0aB7/uSOZsl+/Y6ezO1M+W8ayDx7mUo8jrF65iYIWvu6uom3JRalgz0/PMWnUKG57dQkZNQAKhxa/y4O33s3zP2WcPglHA/mrP+DBMZcwaspXZJyLXOqzWf7O3Vw6/Hqe+n4XJapcLiAieqM/Pl6NI6pBQbIf4VBmPYLRC6NGg8bYkeRoqCipQOOubTxOltBEptIlOhgfjZ6EuHDcbQ1UWW0ogE4rIIgiWl3jkPeT22cUZFmHd2AMnXrG4O0bTfcRN/HI1dFUbFvH2oJatixYTF7eVn6c/TWzv5vDat1o/v3w1XT20EDkdbw+71umDxU59NsnfLk+n8rqeqwSoPfDU68nLC6JqDB/NISTEBmAMTiYiPBIogzgFxFOuKeOhpqaM+ghaxu0rWqREESXMf3pPGsORVX1ND7YBBKG3sELiRPRhCWfLgUEnQdhXUZzbfdZfPWTib9a7K8h+yBHIxMId9NxwjJQXomMHNmdr2ftoqauPSzIfZGhCIhC8yKXAjpjZy7p6cmC1avJfySeaPI4nCPSdVwvvDQaQG48Uqs7tj6JVqtBVBxIktLYjnHsIfJXTxMBQdSga/pViB5+xCRF47mwntqGWqwVFtyHDmPyTXE4HHLjwlhaPW5uOkQxEL/qT5n+mJPuEycxbsB8vtwvNg4ObJpuotFqaV6lUhRFRK3u2KJO0PSZZaXdtLu0rZILgGcQfj4eHL8hgiEkibSePUgNP7NtEnRGPyKDfZtu4D/jCN+++QP76uynHvEZGIivpzs6QUFRR3O6FK0xjutefZmrpUW8/9anfPzmD9Rf9zHv3dMFX8OxlXZB+aM6lBP+JdDYYPtXCAi/ty7LcuN8scAEOoV44KF3krVyBUeMXvj4+ODj7YWnLZ2Nh5zYt7/G3c/uI+Gmm7lqcCIxAUY0goig0XB8c/Wx1Qb/RHLt6VZqWyWXZpq/geOeRub6auptboQEHje0UqrmSPo+SrSRdO4We9yK/I1b+QkIjcsn1mSzq0BPUlo0HgD1+/jxpcd5bbHAxAFL0XTpx8COIXjo/+hiBVFrxE1yUFOQT40hjNjgxvwVpbnobaE8cx/ZtUaiU1OJ9DjudKmSQ9v3US4Ek9yzIyEn3Pe15BZAbJQP9rJDHKr1p0NyUOPGZNYSDmbV4hWXTIRn23s+nIBWi1YUEdAcuxk1uqZlJcXG8qJkr2b7d3Nwjn2WByfG4+8uIrq7H7fouhadKIBGg17XeBH1Og2ioEGj1aABNIKCtcGKw5TD0SonNimQiKDjrp0iIzksmCwW7E33leXoIZatK6f/Pa8x0MeHgMv7ofzrNW67xcojtw4lVs5i0S9H6Du9D/VbN7Elq5p+bmEEOo4wd0sOtbWJmHL2UZDixCqLaDQ6msJDr9UiaiS02qZPrWu6DhpNG/1Rnkwb/hwCGh04i9bz7fvv8WWGHyPufJypY2MBG2Xpi/nh+y04+o+ik+kbHn4uHSEyjuDgXtzw8OV4CQKy00TWnJf4eW46hw8dRhr4LJ+9ehV+ZUdxmGuotBmpq66kqt6K8xSjs0StO8qRn3nz0Y/Zu2oH5YZ4Rv7jUf51+yiSPaD28EZWLFxDljYAbdF23nxJpsddM3jqsgAqdszhrXfX4zF6GFEFs3llhoFJ//kPk+PrOLDkM/77/hz2ptzLk9F7WbzjANt2FhE06TVmdM1gzuId7EnfS4HXpTz+8r+4ukswrtvayoU46jiyeTk/LtvIkSr4dck4wi7xp2Dpl8zbWEJu0Y98uyuBSR0sFGRs5ef1k9n2kQGtRove3ZOAhGFMmfYAnYp/4ueNBeTWzufbFb25rbudDcu2kbWnkoXz1zK4x83E9+lPhzkf8tYMJ+b/e5w7rgg+MRaPaDqPuJJL9//CrPvuZ09qOD4aAcP1r/LauDhEUSbx2hn858hUnpv1Fv9c9SXRaUOYOOURLgkQ8bpkPFcnPsPHky9l9+gbuCUpiQDrFn5d0Z+Aily2ZGeTbp7DsqFxeEaVsnjVVvZusWBYsZ4RCT1g8wqWbd3MHp9QFm8aQUT/iDMYQHhx04bloiBLoI3oREyIO9alB8mvaRyUIBftYMm3s/n16HDeHDOYqBw7GXNm8/auRP77xXDiRSflioRsK+Wo133c8/Bo6lbNYNIbX7PkoTHcEtmbYV0jcJ+nI/mSYQzpEIHXSaUWAZFqCqv9GHbHrdxx7UF+/eh9Zr//Lr4R8cwYVceG1evZbRjCXdd2RMnywbl3Gu+88i4p8ffh+8vHfJk1mJ/eu4LEQpl1sx5l9rKHmd/pZAMAACAASURBVHxfJBFdLyGk9lm+3noQafwN/GMYDPvkHu77/A2+fuI+xt8+ghuv+pF/PzCX+WvG0icpmHjXbkHjGjTuBPeeyGOfDuBu2ZOQmDB83Qy4D7uTN367GqshgOg4PxS9SFDSFdw7vD9xzmrq6q3YHFYaju7hi8+38MadQ3jki1Xc5jASEh1DiKeT4Q99zILJdgxB0cQaFHx73cqMDwdTZHInLD4O/5MKfN5E9bmOR14eQGmNHa27ETe9G97hMYS4AYgYgroy/rH36DyhhCqzjN47lISUJHw1QPw1zPgqhTsq7ej8Y0gOHcN3/SqQfMIJNTTQudM1NGh8CY8OI1Dvx9ipn9HrXgljUBTRwZ4wbAqvfDsBs9aX8Fi/tvmw+ANtWC40LcDtR2RUFKG+BTTPh60vL2R/Rib1ybeSaNBgjEikX6cwXv3FhjE+EE9rFaUIaAyhdOzbg67egNiTiJnzySuT0cQY8ffUI4g6PAMCCfLQn6JxSkGStPjHd6Xv0L70MPYlUSgj9/Hv2bZtNxtDLOxYu5KMqEjS15ViNZkwdr2Uqx3h6MQAOo1/lLdGp9HVvI+Fy9KpkO0cLa9BIQ7viM4kR7jj7oylS/duxLhBlxFpPPpNHh6dutG9ezhGhtLVfza7SuoxWYC2KBdRh0dwLJ2DY0942T2iIz2aN4uXGihc+j4f147k0+fG4wMosoSsgHXXyzy8wIhnYALRUQknpOHpHUjkCa8EEds5iBNzOh4BjZsPYQk+hP3FMYbAeNIC40/xWbyITO19Qp6+Ab/nFhZ9fGeDF54+QZyw6J6XF37hp++QaEu0abmcwHGNs54BQUSFGjFnZbCPK+iNncqaOgwxScd9oSKC1hNfb0CRceoMuIkSDntjz0PzFiKKJCMBJ28aoqAoOjy8PTA01aP9OqSQGu1NSd1RjhSZKa2WCRramV49jNRZofslo7nWwwu/ACOGuliMX8/m3cwOdEnuTKSnQHFzM58CgigiePjgrZEADegNaDRe+PnompqatOg0oMgy7Xleu+J0YCrcw/qfV/FEcDkDUyLw1TsxleRTYAph3LWpeLbCvk4qp6cNyqV5/MNxKCe+oonuw5gb7yD/s2XM+nAORZ4VHPIbz8xnryPxuFQap+v/nlzjqrW/t+c3dyH+5UU6bgsTZCcOvRdefoFE+pWwrrqSmiobQdFdmp6GCjTksWd/OeVLXuOTI/154tGBdPQvZrdRYYsgIh4fgyL/PhFPaYxOVo6Pr331LpwKQedJ5KjHec+6iHWZ+9l29DBGnwAiElLo3rUrfVP90Lf3i9BGaYNy0aAVQVR0NDe0a7QaBLFxHAEAliqqGmyISaOYODCNKA89PUZHEB3UfIIevbZx86jGrYBEtAYdoiCg0RnQArIATrMJuyiRl1dCWGgA7gb97z9m2Ynd2kCDHbRN3RbFOzMo1oTRY9AgBqfsYGeYldc/fI6pfv/ixgGhOPIyyDhiI7hHDNt/XUBG6iT6xgVTs+UHdpXL2G0mivOKCY8JRic29pa4/d69gICITq9rWuNXj0Zs3BRM1wa/xTNG1OIZ259r70ul7+F8KuodoPckMDqBKJ+/8bqYbYA2thKdlaq9C5j18Y+sKXEjsnNPUn0r2Dr3c2Yv2Ee9X0cGXZJGgDWTdT98wLu/7Ke2Ioutm7ewZeM6Nu0twh6YQFj1Rr755BN+SbcR1acPHY1VpM+fxUc/bcca2YveXRIJ1eWy4ucFbMmqRgjsQOe4IIzHLwWnVTAV53DwQBY5ueVUHNnB1hwnEZdcybUjOxLoH0Cgp0JZ+lJ++WUxqzenc+iojoheoxnVxUhNxioWL9vC3ooaquwGnIeWsibfSHKfLgRXrmHW/75gVWkQaT07ESoWsemnT/hoUQ6GxDQ6x/lg3juPLz76lZ2WYDqkdSEl3IMW3TOtpRHd8A4IISw8jLCQAHzc2vOHbR+0Mbk4aKi2oQ/tSFqv7nRLiSbYQ0HU+RCV0ovePVKJi43ET6ilPP8w+VY/At1s1NfXY6qvpbK8lJw8B4kDEzAYIug5sC9p8XFEBxqwOzyI7dGXXp06kBwXil9oFHFRwfh7h9Otf28SgtzRnrCPViAxSfFE+nvi6emJp4cvMd0GMXhgN6LcAdwJjOlI17Rk4uNiiU1IpffgUVw+Oo1QowfhCUlEBfvhExBFSt8RjOidQFx8B7r07UagXIsQ0o0BfbqQlBRHuKdEPYGk9O5F95QOJEb4IJgVfOK70b1HJ9I6xBDmZ2zHy2CqtEXa4TKXJg6vWcDizXWk3HsXw70dWBpsSM56Cvav58vPsrn+46l0b+0wVVTaOe2wtl5N0cGNzP0mm9zYePRxfnjoZKx1RymtgLSxl5N0Psn/PvRWpb2ifscXhHZYcmmgJH0Jsz+fw+ZSHYERwfh7e+Lh6UdIdCpDxg0n6TxHKFl2bEMbHIwuMlq9CdsJssWCoyAfQSOiTzivx49KE+1QLk04jpK1cxeHShtQ3AOJ6tCFbjFeFyTp4rtvwzhoCD7X34igP2lhEJU2iKMgj5rZX6Hx8sL//n+2djjtgnZYLWpCF0hS35HnVwX6E5ylJTiPVqA4JQR1AFe7QLZacZQUoUjBpz9Y5YxQ+xfOBY0WQdS0/xFsfyMEQUBo/l5VLgiqXFRUVFyCKhcVFRWXoMpFRUXFJahyUVFRcQmqXFRUVFyCKhcVFRWXoMpFRUXFJahyUVFRcQmqXFRUVFyCKhcVFRWXoMpFRUXFJahyUVFRcQmqXFRUVFyCKhcVFRWXoMpFRUXFJahyUVFRcQmqXFRUVFyCKhcVFRWXoMpFRUXFJahyUVFRcQmqXFRUVFyCKhcVFRWXoMpFRUXFJahyUVFRcQmqXFRUVFyCKhcVFRWXoMpFRUXFJahyUVFRcQmqXFRUVFyCKhcVFRWXoMpFRUXFJahyUVFRcQmqXFRUABBAEEBo7TjaD6pcVFQAFAUkJ4pTau1I2g3a1g5AReViQLZZcZSWIugNrR1Ku0GVi4oKIFVVYdufgcbbp7VDaTeo1SIVFcBRmI9UXIRUUYY953Brh9MuUOWi8rfHnnsE84b1CHoDjvx86uf/2tohtQtUuaj87bHty8Cyfg2iuzvS0QrMG9YhWyytHZZLqbGZsDhtLs1DlYvK3xqpphrL9i04y8pAowGNBmdRIfUL57V2aC6j3FzN9C2fs6F4r0vzuSByMdnNlJurccpqN55K28K6ZzfmdWsQ3NwAEDQanKUlmBYvaOXIXEONzcTdK9/gx4OrMJkaUCTZZXmdt1wki51Pt/zKiDmPsDR/24WISUWlRVAUBcuuHdgO7Ec0GhtLLlotiCKOIzlYtm5u7RAvKCaHmVuXvcjOskPMTL6ReJsP5RXlSJJrCgXnJReTyUReYQEdtaHEaQO5b81/VMGotBlsGXux79+P+4CBeF45Dn3HVNzSuuB9/Y2IRg/qF85v7RAvGGaHhUmLZ5JelsnMxEn09k1CEaCkuJiKctcIRlAURTmXExtMJoqLizGZTBg0Okps1bxzZD47zbl8PuJxRkb3utCxXjTkX3MFHkOH43f3vYjuxtYOR+UccZaXoTid6MIjsOccpvK9t9EGBRH05DModhuOggJ0sbEImrY9HMzqtDFh0XR2lWfyQtJNdPeOBxSaf/iKohASGkpwcDAajeaC5XtOJRfTcWIRRRGHIhFq8OOhuCvpZYzj1hUvs6JgxwULUkXFFWiDQ9CFRzT+R5YapwA0PWsFvQF9QmKbF4tdcnDtwmnsKs/kpaSb6eYdx/FiARAEgbLSUsrLypDlC9cGc9ZyMZlMFBcV0dDQgCj+frpTkQgx+PJA3BX09Uhk8rIXWFmw84IFqqKicnY4JCdXz3+aXRVZvJJ8K2nesQCcqqoiCAJlZWWUlZZeMMGclVxM9fUUFxVhNpsRhJOnj0qKTIjBl/tjL+cSzw5MWjqT1YXpFyRQFRWVM8cpOxm34Cl2VWTxavKtdPKKOu2Eb0EQKC8vv2CCOWO5mOrrKS4u/lOxNCMpMsEGH+6LvYzB3ilct2QGawp3nXegKioqZ4akSIyb/3/sKs/m9Q63keoZhXAWa0lUVFRQWlrKOTbHHuOM5HKmYmlGVhSC9T5MiRnDEO9OTFw8nbVFu88rUBUVldMjKRJj5/0fO8uzeK3DraR4RiKewW/2eBRF4WhFBSUlJeclmNPKpd5korik5IzF0oyMQpDehykxlzLUJ5UJi6apglFRcSFOWeLq+U+zszyT1zvcSopnFKJwbqNNjgmmuPicBfOXOdfX11NSXIzlLMVyLMAmwdwTM4bBPilMWDyNdcV7zilQFRWVP8chO5mwaBrbyw7yWodbSPWMQnOOYmlGURQqKyspPkfB/Gnux4vlvAI8VoIZwyCvjkxYNI31Lp7ToKLyd8IhObl+0Qy2lOzjlQ630Mkz5pxLLH9ElmWqzlEwp4ygvr6ekpISLBdoZqiCQrDelymxlzHAK5nrFk93+aSpFuH82rtUVM4bm2Rn0pKZbC7J4MWkm+niFXvWbSynQ5KkRsEUFZ2VYE6Si+kClVj+iIJCiN6X+2Ivp7dHAtctmcHG4owLmoercFaU4ywtOfZ/QRQRdLrG+SiAo7AAqbqqtcJT+Zticdq4ZelLbCjey8zEyXT3iT+rXqEzRRCERsFUVZ2VYE6Qi+kCl1j+iIJCaNM4mO7uMUxaOrNNlGA0AYGUvzCd4rtvo+r9d3BWlGHZvo2KF2ZQcN3V1C+cj6DTt3aYKn8jGhwW/rHiVdYV7WF64vX08k106fop5yKYY/E0i8V8gUssf0RWFMLd/Hko7io6GcK5edmLbCy5uEswgiiiCwvHsnUz1R9/gFRRgWXHVmq/+xrb/gy0QUGInp6tHabK34R6u5kpq95kdcEunkmYSH/fDgi4vpZ+vGCKCgtPO9lRhMY2luZxLC2BpMiEu/nzz/hxJOlCuG35y2y4yAXjM+lmRP8ApMqjKJITxdyAVHkU48AhuHXr0drhqfxNqLWZeHDN26zM38HU+PEM9EsBhBZr/msWjNlsPm3pRQTQarU4nM7zHpF3NkiKTKRbAA8njCNK9OOuFa+x4SJug9HHxePWrUdjCUUBEBB0eoyDh6KPi2/t8FT+BlRb63hk/fusyNvBY3HXMCQgDYU/TkN0LYqi4ObmRlh4+GlnUIsA7u7uRERGotfrW1QwTkUi2i2QRxOuIRgP7lvz5kXdBuN91dVoAoNQnE4UhwO37j1wS+vS2mGp/A2ostbx+MYPWZa7jX/FXsnIwK4oitLiYml2hZeX12nHvh1rc/H18SE8IqLFBeNQJGKNwTyeeC3eTgMPrn3noh0H4zFkGPr4BASNBtlqxWPUGPSJya0dlko756ilhqmbPmbpka08EH05Y4J6ILeSWMLCw/Hy8jqjc05oYPb19SU8PLzFBWOXncQbQ3kyaQJudpFH1r13cQpGFDEOHobo54cmKBi3Lt0Q3d1bOyqVdkyFpYZntnzG4pwt3Bs9hiuDeyG1oli8vb3P+LyTVsLx9fNDURRKSkux22znNOz/XLDJDhKNoTyVNJHnM7/nsQ3/49VLpjAo/OKqdnhdfiV1P32HJiQEXVTUnx/oKGH3spVsORrOqFuGEXfsDTumkl0s+nEDRWgQNQaMkf24blxXvAGUSnYvXMruSgcavzRGX96doAu3OJhKG6LMXMVz275k0eHN3B01mrEhfXDKcpsQC/zJCF0/f39CQ0MxGAwtWoKxyg6SPML5v+TrkMw2pm786KKbi6QNDUNwc8fQIQWNf+CfHCVTlv4b7097kQ/mbKXo+LdMFRyc/yFvf/EN38yezTc/zGXloQZEQJEayJo7i/nZJhQBGg4v5Mu5B6l3uG6FdpWLk3JzNTO3fcXC7M3cGTGSa0L6IbWSWELDws5aLPAXe0X7+/sDUFZaiq0FSzBW2U4HzwieTr6e5w59x9ObPuX5/ndeXCUYRUH08ETQ6U75tr1oB1tWrWFvnQFjsttxF9lBZWkO6TkR3PbyZKLsJmyCG8Gde+OJjMOazfy5h0l88V2ujxCg5GceeGIBmSPj6OZjQC3A/D0oM1fxwvavWZi9kdsihjMhbABOJOTWEEtoKD4+57Z/9l8O6vP39yekFUowFslOimcUzyTfQH1dHdM2f3bRlWCQZU45bMmWy9b1uyiRoxk4KAmdw/n7UfV57F3+FbP3SPj7hJEyeCxjrxhNvxgdoKBIZmocXoQHNIk8IBxvZw0NSks+r1RakzJzNS9s/5r52Ru4JWIY14Vd0iiWFvz9nSAWX99zTue0I4b9/f0JCQlpccGYJRupXlE82+EGqmtrmL75i4tPMCdhI2/TGtKrfEgeMpqenlbsx9VoLLU1FGXsp+Dgdzx62x3c99TbzN1TSeM4Rw0atyRG9HKwbPZcFi5axNyvFmPpPpxkN92xUku1VWJVoYU6u1pVam+Um6t5sUksN4cN5frwga0iFjc3t/MWC5zhSnT+AQGtIpgGyUZnr2ie7XADlTVVzNj8BesvYsHYctezeq8Zn9TBDOvmgcUqw7GJZDKidwTdb3iGt57/N7cNCaBswcs8/Nh7LCtpvKYafSCD/3ELKZU72bxlM9srOnDLXcMIddMgACaHzGs7a3htZw2VVlUu7YkKcw0v7pjNvOz13BQ2hBsiBuFUWkcsYWFh5y0W+Is2lz/iHxAAgkBpC/YiCYBJspHmFcuzHW/guYPfMmPLl0zrexsDw9Ncnv9ZYTvCxrXZKBE9uHRIKNQfQdRoEDVaGqc0ihi8w0gdGEYqMHbSdVz+0VQeeuFTXv5qImMeT2lMx7sLkx4/uX2pWSyzDpl4qqcvwe7qNt/thaOWGl7Y/hW/NYllUsTgNi8WOMvV//2bepFachxMo2CsdPGK5dmOkyivPtq4ifZFNhepdOUPLNq2l/3F5exfvowlv60lPa+c6qLdrFu7h6xy5x/OCKTnjVN57MpAsrdspfov0jY5ZN5Ir+WjffVM6+PHlDQfPHSqXNoDVdY6nt/+Fb9mr+Om8CHcEN6KYgkPv2BigbMouTTT3ItUWlKC3W5vwRJMo2CmdbiB5w59x7RNnzGz/530D+vk8vxPj5Nyk4PKjJVsXLmG+YAoW6irrqPWdpiPX9Fh//frPD78xJnTgsabnv274LvQ7U9X4ai3y7y1q5b39tTy0gB/7kw9+y5BlYuTGls9M7Z+wa9Z67g1YjjXhw1EaoU2FoPB0CiWc+wV+jPO6fHn7+9PaFgYOp2u5Usw3nE80+EGKmoqeXrTJ2wu3d8i+f81Wjpd8xj/XbCVbVs2sW1HOrsXv8/UsX1IHfYw78/9gMeHeiA7bVgsjt9Pc9RTWqmh+4i+/NnzYnGemff21vLygABVLO2IOnsD07Z8wdysddwWMaJJLHKriCU8IuKCiwXOYyN6f39/wsLDW0UwXb1jjzXyTt34EVtLD7RI/n+FRmvA3eiJp6cnHm5aNB5u6FFQ0KLXAWI9pQdW8f3nc1iXWURxYTZ79+xgeXEXHrwp9k/TdcgKn40I4o7UM5vPoXLxY3KYeXrzp8zJXMsdESOZGDagVcSiNxiIiIx0iVjgHKpFx9NcRSouKsLpdLZYFalBstHFO5ZnOt7AzEPf89j6//H6oPvoHdLR5fmfMaIbPqGRxBj8cQOQzFQeXManr/5M9Y/9uCQtHO/AFK567CH6GE48tcEh0+BQCDJquLGDKpX2hMVp5alNnzAncy33RI7imrD+yCgtLhadXk9kZOQ5jbw9UwTlAhQ7mpe+aynBNOMu6tlTn8cLmd/j6eXJ24Mfokew62cpF1xzBR7DRuB/933g5nYGZyg0alHGUnGYzGInvjHJxPiePOa23iHz/p5asmocfDAsCK3Yctfz74w9O5PK999FGxRE0NRnXZKHzWnn3xv+xy9Za7k3agzjQvqAQMuLRacjOjoaLxeKBc6jWnQ8/v7+RERGotWeV0HorLHIdrp4xfB08vWYTWYeXPsOuyqyXZ6vLIDFbqe2tpbq2loqq6qoqqqitq4Oi8Vyin12mwUh4h6URNeuKX8qlnd21TJtSw0jotwv+CruKq2HQ3LyyPr3+SlrNQ9EX8bYVhALNC4MFx0T43KxwHlWi47Hz88PgMKCgguyifWZYpHtdPaK5v+SJvJi1o9MWfUGHw17lC5BCS7Ls0DUsnrFSg7s3EtBURENJhMGNwMRERF079aN4cOH07lzZ9zd3U+7WlczJofM27tqeX5bDV+ODOL6ZHVN3vaCJEv8c907/Jy1lkdixjImuEdjObaFxaLRaIiJiTnj9VjOlws6WMLPz4+o6GhEsWXHYFhlB6le0TyVNBHJYufOla+SUXnEZfl9a3Hwy4FMPDw9GD/+Gu6//34m3ziZiPAI5sz5hUvHXMbYcVezaPFinM4/jm85GZOjsbt55rYavhqliqU9oSgKD6x5mx+z1vBo7DguDe6OgNCikxChSSyxsS1SYmnmgrS5HI+iKNTW1pKfl9eiUwUA9KKWA/WFvJz9E06DwNej/49U/z/viTlXiq65Ao/hI/G9+z4wGE56PyMjgzfefJOFCxcyduw4np85k5CQ4FOmZXYqvLe7lqe3VDN7dBATElWxtAauanOZsupNfspew9S48QwP6IJGEFt02QQAURSJjYtrsRLLsXwvdIKCIODj40NMTEyLNu5C44p2HT0jmJo4AZ0dblwyk4PV+Rc8HwmQZBlZPvXWCp07d+bzzz5j1qxZbN++nVtuvYX8/FPHYZcUyqwS31yqiqW9cc+qN/gxexVPxV/LsIC0VhNLXHw8nq2w9Y1L6i+CIODt40NMbGyLC8ahSCR7RvBkwrW4O7RMXDSdQy4QzJlw6ejRfPLJx9hsdqZMuReTyXTSMb4GkVcHBDA+QRVLe+KelW/wU/Zqno2/niH+ndEKmlYTi4eHR4v/DsFFcoEmwXh7t4pgnIpEkmc4TyaOx1vSM37hM2RWF7RoDM307NGDGdOnUV5RwfQZzwFQa5d5b08t7+yuBUAUcMEmnCqtxT0rX+fHw6uZFn89A/1T0P0NxQIulAu0rmAkRSbeGMZjCdfgp7gzbsH/kdVKghk4cCB333UXSxYtZNmGbbyyq4EZW6tJ8z/1SnYqbZd7Vr3OD9mrmRF/PQP8/r5iARfLBX4XTGwrtMHIyCQYQ3ksfjwBigdXLXiK7JrCFo0BGlvqBw+6hI4dO3DnSx/y9WE7n44IYliUscVjUXEd96x8gx+yVjEzYRL9/TqiFzUtvoLgxSIWaAG5QKNgvJoaeVsaBYU4YwiPJVxNoOLBVfOf4nBN0elPvMB4hsbgiOuFPWcX7wwO4Ko4jxaPQcV13LvqTX7IXsWMhEn08+uAXtT+rcUCLSQXOLGK1JIoTX/GGUN5NOEa/DFy5fypHK4tbrEYSs0SL+42szPxaj785keujmixrFVagPtX/4fvslYyI+F6Bvh1bDWxxMbFXTRigRaUC4Agio3d1K0kmHhjKI/FN7bBXDXvSXJaSDB5dQ5qbBJvjoxmXLe405+g0mZ4cM07fJO5nGfjr2OAX0qriEUQBGJjY/H09LxoxAItLBc4cRxMS/JHwfgoboyd/xRHWkAwnQP0vHZJIFfFqm0s7Yl/rX2X2YeW8nT8RAb5p7ZeiSU2Fs8z2Lu5pWmVtRIFQcDH15foVhJMgkcYj8ePx0PSMW7h0xypK7nAeUBpg5Mfs0xsK7PhoROJ8NRi0FxcX77KufPv9e/x1aGlPBk3nqEBndGLupYVi6IgiiLRMTF4e3tfdGKBVpILNArG19eX6OjoFr0wzYJJ9AjjiYRrMThExi98hpy68y/BNC+sUNzg5LGNVXy4rw537cX3paucBwo8tv5/fLF/CY/GXM2IwK7oBG2L74QoajRER0c3LvR0EYoFWlEu0CQYPz8io6JaXDAKCkkeYTyRMB7RJnP94hnn1Qbzu1gkHt9Qxd5KO1M6e5Py/+2deXxU1dmAn3vvLAlZZ18ySUhAZFOwYsQVrYKKGyLoh7bV1oXN+rMuuFBttRRE5VOqtdXPpSoBEUUQ0Sq4gKBVQ1iKSBLABcieELYss9z7/TGZFIoKIZk7C+f5hz+Y3HtyZvLMe+55z/uKXJakQdVU7v70Gf7x9T+5Le8SRjhOiolYDAYDuXl53VpMOxrEvIS8JElYLBZ8Ph+SJOl22FEDVDT6pvu4t9cYgs1+rnn/T0e1ixQRy459Qe5aXc/Xu/w8cEo2Y3qno8Tpt4qgcwTVEFM/e45/bHqXW3wjudg1RPcEuYhYfD4f2XEuFogDuUC7YKxWcnJyUBRF19PUIU2lX0Yu9/YeQ/O+Zq5bNoOtTZ0TjARsbQpw56oGyncFmDrEIs4KJRH+UJA/fP4iL256l5t9I7jMXYRR1l8sRqORHJ+P7PbaSfFOXMgFwoKx2mx4vF7dBRPUQgxsrwfTtKeJGz98hIpOZvJ+0N5i9a6fZTO6l0iQSxZag36mffkyL371Dr/x/pzR7tMwyHJMSlN6vd6OomyJQNzIBcKCsdlsuD0e3QUT0EIMyuzJfceNpXpXHZM+fuInBaMB8gH1bYvcZh481coViSiWUIjAzh20rC2N9UjiipZgGw+vmcsLXy3lF55hXOU5E4OsxEQsHq8XS3tB/EQhruQCYcHY7XbcHg8Gg0FXwfjVICdn9WLqcVfxfX0lt674y4+Wa0hT4NsmP+sagzS1qQy2mznFZcaYiAW1FQV1/34anniU+lkzaV79CVrAH+tRxZTmYCuPlL7K818t5WrXmVybMwxFVlA1/Uq4apqGyWTC4/F0dNpIJOJOLvAfwbhcLt0F06oGKMo+jt/3GcvWuu+5c9XThxScSlP9bGpWmLq2hbe+9xNQ4nIaO4XB6ULds5uG2bOomzmNuukPsXfpWwRrqmM9NF2QjCYwKJhkAy3ArLWv8fzGtxnjGMqvfOeiSHJMxOJyu8N9Ni2RvgAAFuBJREFU2hMQfcv1dwJJkrA7HGhAbU2Nrm1LWlQ/Q7P7MrXP1Uwrm889q59hxuk3088aTvrbktOPh/bnUV29l0sNdfTYZiaoSKh6p2d2F7KMumcPpoJetK4tpW39OlrXlLBv2Xv0OHUoKSeehDE3D4M3B0nnDg96IJlMtH71b6TtO6nrYeK1zYt4/t9vM8pexPW556FIMqFYiMXlwpagYoEo1NDtbjRNo66uTnfBAKQpZj5p3MS0svkMzjmemWf8GkXO5baXPqdi87fcZdjKRVINsqoSiutZPAyShBYMEvjuW/xlX0N7gXUtGERraQZJxtizAFOfvig612HVBUVBqq4muGMHb52Wy8yT07k0tT835Y+ImVicLhd2u123+0aDuJcL0BG91NXVEQwEdBfMioav+HP5PM4puJia1vNpkq3cVvsRP2/YiBQMEkrwXBZJktDa2mhdt5bWdaUgy2jBIISCKE435n79Mfh8yOYUpJTUpCubZ5aN1LfsYuGur1jmkenZ/wwm+YRYukpCyCVCTU0NdbW1ukcw6UoKy+pKmfK1n7370/i/kUXcOFD/2jRRJRSiZuoUml55EclsxphfgLlPX1KLhpL28/MxFRTGeoRRoxl4qmIJf1+7iPN69OGWnAtQZP3FYmxfCiWDWCDB5AL6C6bjrKFm4rntARZWz+X8AitTTr6avhZ9S0dEk8B337LzxuuQjAbMffuTds55pJ0/HLlHAm6td4L9gRae3LCQZzcsYYRlEBN7XhSTiCXZxAJx/ED3x3C5XND+HCbagjFKUNUmYZIhw+Dn9kIDAzIG8aeyN2gL+bm/6Dr6WvKidn/d0DTUQIDUIaeQccUYehQNjfWIdKE50MqTG97k2Q1LGG45UYilm0m4yAUATQtHMFEUjFGC7a0SL2w3cZY1yKnZIcwypBtSWVa3junlCzgzfxAPnHodxye6YFQVNRhANh3a4C1ZaQm2MXv9Gzy74a3YRixGIy63O+nEAnGa53JYJAmny4XD4YhKJq9Bgso2iYe3pvDpLiNmWetYHu0NtjDcMZh7+4xh1XfreeiLl2LWtqTbkOVjSixtQT9/Wf8Gz2xYzAjLICb0vBBDDMRiMBhwJ6lYIFEjl3Y0TaO2tpbamhpCoVC3RDCKBDVtEn/aksKWZoVpfVo4KTOEBAcdU8swpPJ+3dr2CGYwDw79Ncdl+7p8f0F08YcCPL5uAX9bv4iLbD9jfP4FGCQlJmLxeDzYklQskOByge4VjATU+cNiKd+v8EjfFk7MCLds/aFJylBSeL9+HTMqFnB63iCmnXYjvbK8R31/QXQJqkFmrX2Np9cv4mLbydyUNxyjbNBdLIqi4PV6wwlyCZ7G8FMk5rLoACRJwul04nK5kGW5S0ukNhUe3mambJ/CrH7NPykWgL2hVobbB3PfcVfx2fcbuPfTZ9m2u/tKZgq6j5Cq8tja+Ty5fiGX2mMrlpycnKQXCySBXCAsGIfTidvtPirBRN7i75pljMBTA5oZkK62V6z7afaFWjnPPoj7+ozli+0bmbL6b3y759g4j5MoaJrGo6XzeHLdQq6wn8pvcmMYseTkhE83J7lYIAmWRQcSOSpQXVXVKcG0qeHdIYMc/jeg0elzQmmKmQ/r/82MigWclHM8s8++ldwMZyd/A0E0eHjNXGave52rnKfzK9+5mGWjrmKB8Begz+fDYrXGZTHtaJAUkUuEyGlqj8dzxD+zOygxZ4eJGn/44GGb2nmxAOwPtXGOfSD39RnL2spyfrtiNjv31XX+QoJu5eE1xTyxbgHjnGfyy5wYiiU395gSCySZXCDcx8Vmt+P1Hv7BalNAYmpZKotrTYS64fPWEvJztnUg9x03lg1VFYz/aBZV+xu6fmHBUTFzzVxmlb7Gta6zuSbnbMyK/mIBwmKxWI4psUCSLYsORFVVGurr2blz5yFvqgQ0+CXur0ilfL/MswObKeyhdltFVLNsZFXjJmZseZ3jnT158fx7cPVInPKEycCMkmIeWzefGzznMcZzBqmKUdcKchHy8vPJzs4+5sQCSSwXaBdMQwM7d+zoeHMloN4vMbU8lW+aZZ49oZmeqd0nlggm2cBnu8qYXrGAXvZcXhkxFWeP+K/YngzMKJnDI6Xzudk3nCvdp5GqmIRYYkBSywUOFowsSdS2hcWyvUXi7ye0REUsEYySwhdN5Uzf8jp5Vi+vXvQA9pSsKN1NAGGxzCx9lUm+C7ncXUQP2Uz03uEfJy8vLywWOemePBwxSf+by7KMzWYjN9fH/qDGql0GjDI8HWWxQLjo95Ds47iv91i2N1Zx9bsP0ti6J4p3PLaJiGVy7kVc5ioiNQZi0TRNiKWdpI9cOtBU6hsa2fbddvyaRLpBn5pHEiBJMqW7tzJ9ywK82U4WjnwIS0qmDnc/dphRMoeHS+dxa3vDsh5Kiq59hSAslvz8fLKys5GPcbHAMRC5ANS1hFiwpZmsbAu98nNJV1TdiqlphD90J2UWcl/vMVQ21THqnftpatun0wiSn4dLiplROpff5o5kpBBL3JD0s7B1d4BfvF/LvPJ9qJKE1WrFl5uHquqYndn+QR+cWch9va+kuqmOUUunslsIpsvMXDOX6aXF3Jp7MRc7h5AWA7GgaeQJsRxCUs9EeZOfGz6oo64lxPTTrJgVGUmWsVgs5Obm6i4YCaldMGOo3l3P5Uunsse/X7cxJBuPls5j+pricMQSK7EAue27QkIsB5O0s/F1o5+bPqxnf0Dl5eFO+lpNHf+nKAoWq5Vcny9mgrm315VUNdVz+dtT2eNv1m0MycJjpfP585piJudexCXOU0iP0VIot/3hrRDLoSTljKyra2P8R3X4QxovnO9koM10yGsURcFis5ETY8FUNtUy6u2p7GkTEcyRMmvtfKateYUJORdwqfOUmEQsQiyHJ+lmZce+IC9v3kuWSeHpc+yc8ANiiaAoCrYYCuakrLBgtu+qZvQ794sl0hHwxNrXmVbyCjd7h3O5qyh2S6H2lH4hlh8n6bai9wVUtjYFMMgSA35CLAcSCoVoqK+nsrJS12xKCQkNrX2b+nUKbTm8NvKPZJnSdRtDIvGXdW/wYMlLXO8+lzGe02Mmlkg9lmM9j+VwJI1cduwNsieg0t96ZEL5b0KhEPX19VTFQDAAXzZVMH3rAvo6elJ8wf1km4VgDuSp9Qt58MuXuMZ1FuO8Z5GmpOiaIKdpGpIkCbF0gqSYoc+qWrlzdQMf7Wg56msoitJRrkFP30a+eU/JPo57eo1hU+03/GrZdJEHcwBPb3iTaSWvcLXjDMZ5zybNoL9YZFnuKE0pxHJkJPwsfV7TypRPG9ntVznLm9KlaymKgt3pxN2JejDdQUQwQ7OP555eV7KhqoIbls9kV9teXccRj/zt34v5c8kcRtmK+IXvnLBY9JR/u1jc7cW0hViOnISeqX9Vt3LXqkbMCvyxyMKJ9q63x1BkuaMmL6BbFKOhoaFyhrU/d/e6ki93fs2ED2cd02eRntm4hOklcxhpOYnrc88j3ZCCqnNpSllROtp/iIe3nSNhZ2tVZSt3rW4kRZGYfpqNU91di1oORG4XjNPpDDdp100wENJCDLMNZErv0Xy6fQO3rvwLDa27dbl/vKBpGs9uXMKML+cwPOsEbsgfQbohJSY1b10uF3aHQ4jlKEjIGSvb5efxdU1kGGWmDbVS5Or+hl6yooQbrzmdXe4q0FkCWpDz7CcypddoPvp2Dbd/8jR1LU263T+WqJrKc5uWMqOkmGGZ/Rjf80IylNiI5cD3X9B5Eq5XNIBfhXNzUjnVncIpURBLhMg3F5pGfX09qqrqtpPkV4MMd5xEUFN5dOtC7pEVZpx2E84krmgXUkP8Y/M/mVlSzOnpfZhUMJJ0JZWgFtJtDB1icTpxOBzIx2ihp+4gIeVygs30k8lx3YmiKLjcbgDdBdOmBrjYOQRVU3ms4k0MksxDQ3+Dq4dVl/vrSVAN8fLm95hZMpchPXpxa8GlpCspsROLyyXE0kUSUi56ExGMBjToLJgW1c9l7iJUNP63fBGKJHN/0XV40my63F8PAmqQOZuX8UjJPAan5PO7wsvIMKQQ0FksBoMBu90eXgoJsXQZIZcjRGnfNUDTaGho0FUwzSE/V7iHomoaj29ejCzJTD3ll0khmEAoyJzyZTyyZh4DU3zc0WsUGYZU3cWitIvF2d65U9B1hFw6gaIoHTkwjY2NXe5N3Rn2h9oY4zkdDY3Hv16MIsncPeQavGmJ28g8oAYpLl/GoyXz6Gf2clevK8gw9iCgBnUbQ0QsDiGWbkfIpZNEBKMRFoyqo2D2hVoZ6zmDEBqzNy1GkiSmnDwuIQUTUIPMLV/Oo2te5XiTh7t7jY6NWBRFiCVKCLkcBYqidHR1bNR5ibQv1Mr/eM5C1VSe3LgEGYm7Th6XUEukoBpibtlyZq6Zx/FGN/f0vjJ2YnE4hFiihJDLURJbwbRwbc4w0ODJr5YgSzJ3/OzqbhfM3r17ycjI6NZrhtQQc8uXM7NkLn2Mbu4WYklahFy6wEHPYHQWzN5gC9f6hgHw5MYlaGjcdfI43N20Tb1+wwb++e67jB07lsLCwm65ZkhTmVv+ATO+LKav0cPdx11JphBL0iLk0kUMkQimfRcpcjRfDyKC0dB4auNSAKacfE2XW8eWlq5l/IQJVFVV8dHHH/PM3/9Ofn5+l66paRpzy5Yz/ctX6GvyMqX36JiIRZZlIRadELPbDSiKgsfrDZ+a1fEsEvxHMLcUXMwrG8PZrUd7VEDTNEpLS5k4cSKZGRnMLS6mpqaWiZMmsWPHji6Ns7hsGdO+eJl+phzu6j2aLGOa7mKRJAlHJEFOiCXqJE2xqHggFAxSVVWlewQDkKakMLdyBX/dtpRx/Yfz+6JfYU898taxYbGsZcKEiWRmZfLmwjfIzMxk2zffMGrUFeTm+njmmWfw5eR0emxzypbx4Of/4MSUXG7vNQqLMT0mYnG5XDhcLhQhFl0Qs9yNKAYDHo8Hu13/reH9oVau8Z7NLYWXMG/TMv70xUtHXA8mErGMHz+ebEsWi95cSGZmuCNkYUEBixa9ybfffsekiZOorKzs1LiKNy/jD/96kcEpeWGxGPSNWICwWNxuIRadETPdzSgGQ/iD7HDoujyCcKLd/3jP4reFl/LqpuU88Nnz7PYfvqJdSUkJN908HovVypsLFx6yQ1RYUMCStxZTsXULEydOoqqq6ojGU1y2nN9//jxDehRwW+HlZBvSdM28hbA4XW43DqdTiEVnxGxHAUMMBdMcauMq7xncWngp8zd/xL2r/4+9P9EX6YsvvmD8hAk4nU4WvbmQ9PQfrt1bWFjI0rffpqy8nIkTJ1FZ+dOCKS5bxn2fPctpab25teASso1puh5ChLBYPB4PDodDiCUGiBmPEh2CcTp1bVsC0BLyM8ZzOr8rvJSFZR9z56qn2R84tL7wZ//6FzePH4/X6+WN1xeQlpb2k9ctLCjgnaVvs7msjMmTJ//oEmlu2XLu+fRZzkzvy6SeF5NtTNddLKqq4vF6sTudKIqi670FYYRcoojBYMDlcuF0uXQXTKsaYJRrKLcVXsbiik+4beVTtAT9Hf+/avVqxo+fQF5ePvNfffWwYolQWFjI20ve4uvNm5k8+ZZDlkhzy5Zz56d/49zMAUzoeWFMIhZVVfHm5GC320XEEkPEzEeZiGBcMRBMQAtymauI2wsu5+0tq7nl48cJofLJyk+YOHESvXv3Zl7xnCMWS4TevXuz5K3FbC4rY9LkW9i5cycQFsvtq59mRNaJ3Jg/AosxXdcKchAWS47XGxaLiFhiitiK1olgMEhtbS3VVVW6fuglQJZk/llbyl93vkuPba2kLamioE8hL7zwfKfFciBlZWVcMfpKBvc/gUHjhzN75ztcmDmI630/x2LK0LWYNrSLJScHmxBLXCDkoiPBYJDamhqqq6t1FoyErMgs3riCP/71Ec6yDeDl51/EZ3d3+doVZeWMu/oa1mRXcfNN47mm7/lYDWm6tv8AUEMhvD6fiFjiCLEs0hGDwYDT5cLtdhMK6VgMCQ1VVRnZ53SmTXmAr883cfea57olsvhS+p6KURmMumQUY/LPxGpM110sISGWuERELjEglhGMisaH9RuY9c0ihuWdRPGI3x91JvH8ig+ZtGI2V9pOZZz3LGzmDN07N4dCIXKEWOISEbnEAIPBgCNGEYyMxLm2E7izYBQrv1/Lte9NO6pcnPkVHzFpxROMthcxznc2tpRMIRbBQQi5xAijwYDD6YyJYBRJZphtYFgw29dx7XvTOnWN1yo+YvKKJ7jCXsQ1OcOwGTN0TxZUhVjiHrEsijGxWiLJSAS0ECsbNvLYN4s5O28Qcy944LA/93rFx0xY8Tij7Kdwbc4wbMbMjl7XenFQHosQS9wiIpcYE3nI69I5glHRMEoKZ9sGcEfB5azcvv6wEcwbW1YwaeUTXGYbElOxRA6HCrHEN0IucYDBYMDldOJyuWIgGAPDbAO4o+flfPx9Kb98/88/+NqFW1YyaeUTjLT+jF/6zo2ZWNweT/gQohBL3CPkEicYjMZwBKNzJu9/BDOQOwou54Nv13D9sofhAHEs2vYJk1fOZnjWiVznOxe7MUN3sWiahtvjwSnEkjAIucQRxnbBOByOGAhG4VzbCfyu4FLe++ZzbvzgUTQ03tq2mltWzOaczP7ckHs+dlMmagzE4nS5hFgSDPFANw4JBAJUV1dTX1enazlGCYmQprKsfh2zti3mBFchmxu/56zsftzkG4HDnKV7Sn9ELC6XS4glwRByiVMigmmoq0PSWTAqKu9Ul/Bc5XJGFBQxZcBVBOr30dLWqlvpzo6atw4HTrcbgxBLwiHkEscEAgGqqqpobGjQtR4vGlhtNrbJDfSz5eNMtbC7qYmdO3fi9/ujPpaIWOx2Oy63G4NBNKlIRIRc4pxAIEBVZSWNjY26CEbTNGw2Gx6PF4Px4D/qpqYmKqMsGCGW5EE80I1zjEYjHo8Hq9UKUfweiHzHWK1W3G73IWIByM7OxuP1YjKZovJIV9M0ZCGWpEHIJQEwmkx4PB6yreFuit0dbEaiBYvFgsfjwWgy/ehrLRZLWDBGY7eOI9KwzCrEkjQIuSQIHYLJzu7WxmsRsWRbLLgPI5YIlvbXmkymbhlHh1giUZMQS1Ig5JJAmEwmPF5vtwnmQLF42mVxpEREYDKZurRci4jFYrXi9niEWJII8U4mGBHBaMDupqaj7uzYIZbs7E6LJYLVZkMDamtq8Le1QSfHcaBYPEIsSYeIXBIQk8mE1+sl6ygjmIPE0v6A9mix2Ww4XS5MZnOnIhgRsSQ/Qi4JSodgsrI6JZjuiFj+G5vNhtPpxGg2H9EuUodYLBY8bjdGIZakRMglgemsYA4Ri9ncbWOx2e04nc7D7iIdKBa3x4PBaOy2MQjiCyGXBMdkNh+RYCJiyYqCWCLYI4L5kV2k/xaLUYglqRFySQIOJxg9xBLB7nD8oGAOzKURYjk2EIvdJMFkNuPxegHYvXt3xx/zf4vFHEWxRLA7HADU1tYSCAQ6xmC12XC73UIsxwjibFGS0dbWRlVl5UGC0VMsB1JfX09NdTXBYFCI5RhERC5JhvmACKapqSksFq8XczfsCnUWu92OqqoEAwHsDocQyzGGiFySlJaWFpr37yctLY2U1NRYD0dwDCLkIhAIooLYLRIIBFFByEUgEEQFIReBQBAVhFwEAkFUEHIRCARRQchFIBBEBSEXgUAQFYRcBAJBVBByEQgEUUHIRSAQRAUhF4FAEBWEXAQCQVQQchEIBFFByEUgEESF/wd2RU59KL6ysQAAAABJRU5ErkJggg==)
physics-General
physics-
A boy is walking under an inclined mirror at a constant velocity V m/s along the X axis as shown in figure If the mirror is inclined at an angle q with the horizontal then what is the velocity of the image?
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)
A boy is walking under an inclined mirror at a constant velocity V m/s along the X axis as shown in figure If the mirror is inclined at an angle q with the horizontal then what is the velocity of the image?
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)
physics-General
maths-
Let
, then the ad joint of A is
Let
, then the ad joint of A is
maths-General