class: center, middle, inverse, title-slide # Statistical Workshop ## Advanced R for Bioinformatics. Visby, 2018. ### Bengt Sennblad ### 20 Juni, 2018 --- class: spaced ## Statistical workshop * Aim + to make you aware of some of the problems in statistic analysis + to give a survey of selected methods, and their implementation in R, to solve these problems and provide an intuition of - how and why the methods work - the connection between methods + to familiarize you with math/stat notation so you can extend your knowledge by self-studies .pull-left-50[ * Problems covered + Overfitting + Ill-posed problems + Feature selection + Data integration ] .pull-right-50[ * Methods covered + Regularization + Model selection + Dimensionality reduction ] --- name: toydata ## Toy example data We will use a simulated toy data set for demonstration examples^*. ```r N=100 # no samples P=10 # no variables # Draw variables, x_1,...,x_2, from a uniform distribution X=matrix(runif(N*(P+1)), nrow=N, ncol=P) # Draw effects b from a uniform distribution b=c(runif(P, min=1.5, max=3.5)) # intercept b0=3 # generate a y1 variable from alm of 3 first X variables only y1 <- b0 + X[,seq(1,3)] %*% b [seq(1,3)] + rnorm(N) # Store in the Y matrix (really just a vector here) Y = as.matrix(y1) ``` <br><br><br><br> *.small[In this r code, and also in some of the coming slides, we make use of matrix notation of linear models to simplify notation, see the associated "extended_reading" document]. --- name: overfit1 ## Overfitting | `Likelihood example` * Consider the two models `\begin{aligned} y & \sim \beta_0 + \beta_1 x_1 & (1) \\ y & \sim \beta_0 + \beta_1 x_1 + \beta_2 x_2 & (2) \end{aligned}` with log likelihoods `\begin{aligned} \log L[\beta_0, \beta_1 | x_1, y] & \propto \log Pr[y | x_1, \beta_0, \beta_1] & (1) \\ \log L[\beta_0, \beta_1, \beta_2 | x_1, x_2, y] & \propto \log Pr[y | x_1, x_2, \beta_0, \beta_1, \beta_2] & (2) \end{aligned}` * What are the maximum likelihood estimates (ML) of the two models? Let's plot them! -- 2 variables are clearly better than 1 variable <br><br><br> <img src="data:image/png;base64,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" style="display: block; margin: auto auto auto 0;" /> --- name: overfit2 ## Overfitting | `Likelihood example` * Consider the two models `\begin{aligned} y & \sim \beta_0 + \beta_1 x_1 & (1) \\ y & \sim \beta_0 + \beta_1 x_1 + \beta_2 x_2 & (2) \end{aligned}` with log likelihoods `\begin{aligned} \log L[\beta_0, \beta_1 | x_1, y] & \propto \log Pr[y | x_1, \beta_0, \beta_1] & (1) \\ \log L[\beta_0, \beta_1, \beta_2 | x_1, x_2, y] & \propto \log Pr[y | x_1, x_2, \beta_0, \beta_1,\beta_2] & (2) \end{aligned}` * What are the maximum likelihood estimates (ML) of the two models? Let's plot them! -- 2 variables are clearly better than 1 variable * In fact, as we include more parameters, ML will increase monotonically * Why is this? Why could this be a problem? <img 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lZma2trYGBQX19fVlbm4uKSlJTUrVs3Mhk4oK6ubvPmzRcuXKAdBACUCaE1+uDgYB8fH5FIdO3atZycnCtXrtTU1Li4uEyZMoVMAG7YuHHj8OHD8ZsQALwTQjP6/Pz8tLS01qcDamtrR0REYAni7TU1Na1fvz4tLY12EABQMoRm9HZ2dsnJyW02pqenW1tbkwnAATt27ODz+Xw+n3YQAFAyhGb0CQkJvr6+sbGxfD6fx+M1NjZevXpVKBSmpqaSCaDsJBLJmjVrtmzZQjsIACgfQkXv5uYmFArT0tIEAkFtba2VlZW3t7ePj4+BgQGZAMouJSXFxMTk888/px0EAJQPudMr9fX1AwMDAwMD7927l52dbWBg0KEDvq71tqKjo3/55RfaKQBAKREqejMzs8ePHzMMk52dPW7cuC5dujx//ryxsfHkyZNOTk5kMiivU6dO1dfXjx49mnYQAFBKhObU1dXV7IN58+b99ttvxcXFt27dmjt37uzZs8kEUGpRUVFLlizBL0AA8H5Id0dpaWloaCj7+LvvvisoKCAcQOlcunSptLT0yy+/pB0EAJQVuaK/deuWRCJxdnbOzc1lt9y/f19XV5dYACUVFRU1f/58TU1N2kEAQFkRWqP38/Pz8/OrqKhobm729fWtra1lGCYgIGDy5Mmv+xHcM5ZhmJKSkrNnz27fvp12EABQYoSK/uDBg+yDR48e3bp1i30cHBz8/fffv+5HhELhyxtV7XbYq1evnjVrlr6+Pu0gAKDESF+m2Nzc3NzcnH38ww8/EB5dudy7dy8lJaW0tJR2EABQbjiRQ3GtW7du6tSpZmZmtIMAgHIjNKOPi4t73UuzZs0ik0G51NbW7tixIz8/n3YQAFB6hIq+qKhox44d9fX17u7ubV5C0b/Sn3/+OW7cOFysHwA+HKGij4+P9/Dw8Pf3z87OJjOiUnv27NmGDRsyMjJoBwEALnjbNfoxY8Z84EheXl79+vX7wJ2oiMTExIEDBzo6OtIOAgBc8LYz+vT09A8cicfj5eXlfeBOVIFEIvnjjz927txJOwgAcASds26wLv8GycnJ3bp1GzRoEO0gAMARdIo+Pj6eyriKTyqVxsTEqNSXwgBA3tou3Vy7do1KDmClp6dLpdIvvviCdhAA4I62RU/m6vAREREERlFG7BWJ1dTUaAcBAO5oW/R1dXUERl26dCmBUZTOxYsX79+/P2HCBNpBAIBT2hY9rp9F0e+//75w4UJ1ddIXIAIAbkOnKIqioqK8vLy9e/fSDgIAXIOLmimKyMjIH374QUdHh3YQAOCaV8/oKyoq2r5PXd3Y2FhLS0v+kVTR3bt3jx49GhsbSzsIAHDQq4u+f//+VVVVampqRkZGtbW1L1680NDQePHixbBhw7Zu3dq1a1fCKTlv9erVISEhRkZGtIMAAAe9eukmNDT0+++/F4vFNTU1jx8/njJlyi+//PLw4UNra+vp06cTjsh51dXVSUlJc+bMoR0EALhJTSqVvrzVyMjo7t27BgYG7FORSNSjRw+RSPTo0aMePXrU19cTSPaGe8a+MrPy+uWXXx49erRx40baQQCAGi8vryVLlnh6espj56+e0ZuZmRUWFsqelpSU6OnpMQzz9OlTYudfCoVC6UuioqLIjE5MfX39pk2b5s2bRzsIAHDWq9fo16xZM3bs2HHjxnXt2rWysvLAgQPLly9nGGbw4MHBwcFkE3Lcpk2bPDw87OzsaAcBAM56ddH7+vr27dt3z5495eXlPB5v37597NVXEhMTR4wYQTYhlzU3N69fvz41NZV2EADgstd+YcrIyMje3t7IyKhHjx5Dhw5lN44cOZJQLtWwc+dOR0dHFxcX2kEAgMteXfSXLl0aPXp0586dLSwsSktLpVJpamoq7g/VvtgrEuOKzQAgb6/+MDY8PPy3334rLCw8derUnTt3Zs+eHRYWRjgZ56Wmpurp6cl+WwIAkJNXF31hYWFQUJDsaWhoaOuTcKBdrFmzZsmSJbRTAAD3vXrpxs7O7uzZs7Ibgl+8eLFHjx4fPlhBQUFJSUldXZ2xsTGfz7exsfnwfSqpzMzMmpoaHx8f2kEAgPtee3rlhAkTRowYYWdnd/fu3ZSUlK1bt37IMMXFxf7+/mVlZba2tgYGBvX19WVlZS4uLklJSd26dfuQPSupqKioRYsWdeiAi8oBgNy9umg8PT0LCwudnJyqqqo++uij8+fP+/v7f8gwwcHBPj4+IpHo2rVrOTk5V65cqampcXFxmTJlyofsVkkVFhbeuHGj9eIYAID8vPb0yu7du//000/tNUx+fn5aWpq2trZsi7a2dkREhKWlZXsNoUQiIyPnzZunqalJOwgAqIS2Rf+GCyiKRKL3HsbOzi45ObnNqTvp6enW1tbvvU8ldevWrczMzMTERNpBAEBVtC36CxcuyGOYhIQEX1/f2NhYPp/P4/EaGxuvXr0qFApV8Euh0dHRYWFhuGUjABDTtuh79+4tj2Hc3NyEQmFaWppAIKitrbWysvL29vbx8ZFdIFNFVFVVHThwoKioiHYQAFAh5O4Ze+/evcDAwMDAwOLi4jNnzjAM09zcTGx0BbFu3bqgoCBzc3PaQQBAhRA6vY9dtGEYZv/+/c7Oztu2bVu/fn2vXr1yc3PJBFAEYrF4y5YtuCIxABBGqOhXr16dmZnJMMxPP/2UnJx84cKFS5cuxcXFzZo1i0wARRAfHz9q1Kju3bvTDgIAqoVQ0VdXVzs4ODAM8+jRo+HDh7MbR48erTqr1U1NTXFxcQsWLKAdBABUDqGid3V1/f333yUSiZeX1549e9iN27dvd3Z2JhOAuq1bt/bv379Pnz60gwCAyiH0YeyWLVv8/Py6d+/eq1evkJCQP/74o6Wlpaqqil3PeaU33DNW6UgkkrVr127fvp12EABQRYSKvnv37vn5+bm5ubm5uUOGDGEYpmfPnmPGjDExMXndjwiFwpc3RkdHL1q0SI5B5SMjI6Nz585ubm60gwCAKiJ3eiXDMAMGDBgwYADJERXE0KFD+/fvTzsFAKgookWvsrS0tLS0tGinAAAVRajo4+LiXvcSV8+wvHnzZmZmZktLy+DBg52cnGjHAQDVRajoi4qKduzYUV9f7+7u3uYlThb9unXroqKixo4dq6GhERkZ6e/vv3btWtqhAEBFESr6+Ph4Dw8Pf3//7OxsMiNSlJOTs379+sLCwk6dOjEMs3r16sGDB+/du/fLL7+kHQ0AVBG5Oxx5eXn169eP2HAU7d+/PywsjG15hmH09PSWLFmyd+9euqkAQGWRK3oej5eXl0dsOIqePn3a5rL+xsbGdXV1tPIAgIqjc89STq7Ly/D5/LS0tNZb/vnnHxX5bQYAFBCdoo+Pj6cyLhnBwcEPHjwICQkpKCi4fv36Tz/9lJaWtnjxYtq5AEBF0Sl6btPU1Dx9+rSpqWlwcPCXX34pEolycnLecI9GAAC5ovOFqYiICCrjytujR4+0tbUNDAwMDQ1XrVq1atUq2okAACjN6JcuXUplXLkqKSnp16+fSt1KBQCUApZu2kdxcbG3t/fy5cs9PT1pZwEA+P/gWjftoKio6Isvvli5cuXXX39NOwsAQFuY0X8ogUDg4eGxatUqtDwAKCbM6D/I5cuXx4wZEx8f7+fnRzsLAMCroejfX35+/pgxYzZu3Ojr60s7CwDAa2Hp5j2dP39+5MiRmzZtQssDgIJT3Bm9It8z9r///a+/v//u3bu9vb1pZwEA+BeKO6MXCoXSl0RFRdHOxZw9exYtDwBKRHGLXjGdPHlywoQJycnJOF8eAJSF4i7dKKBjx45NnTr1yJEjgwYNop0FAOBtYUb/ttLT06dOnXr48GG0PAAoFxT9W/nnn3+mT59+5MiRzz77jHYWAIB3g6L/d/v27ZsxY8bx48cHDBhAOwsAwDtD0f+LPXv2zJ0798SJE87OzrSzAAC8D6IfxhYUFJSUlNTV1RkbG/P5fBsbG5Kjv4ekpKSFCxeePHny448/pp0FAOA9ESr64uJif3//srIyW1tbAwOD+vr6srIyFxeXpKSkbt26kcnwrhITE5ctW3bq1ClHR0faWQAA3h+hpZvg4GAfHx+RSHTt2rWcnJwrV67U1NS4uLhMmTKFTIB3tXnz5hUrVpw5cwYtDwDKjtCMPj8/Py0tTVtbW7ZFW1s7IiLC0tKSTIB3kpCQEBUVlZmZ2bNnT9pZAAA+FKEZvZ2dXXJycpuN6enp1tbWZAK8vZiYmOjoaLQ8AHAGoRl9QkKCr69vbGwsn8/n8XiNjY1Xr14VCoWpqalkAryl6OjoLVu2nDt3zsrKinYWAID2Qajo3dzchEJhWlqaQCCora21srLy9vb28fExMDAgE+BtREVFbd++PSsrq0uXLrSzAAC0G0JF/+OPP06fPj0wMDAwMJDMiO9q2bJl+/fvz8zM7Ny5M+0sAADtidAafWRk5JAhQ+Li4lpaWsiM+E5+/vnnI0eOnD17Fi0PANxD7pux586d27dvn6Oj4969eyUSCbFx30wqlc6dOzc9PT0jI8PMzIx2HACA9keu6K2trc+ePbts2bKIiIiPPvpo/vz5Z86caWhoIBbgZVKpNDw8/Ny5cxkZGaamphSTAADID+lr3QQFBV27dm3nzp13794NCAgwNDQkHEBGKpXOmTMnLy8vMzPTxMSEVgwAAHmjc+MRLy8vLy8vqVR6/fr1173ndfeM7dChHf5zevHiRUhISGlp6fHjxxXqzB8AgHZHqOj/85//vLxRTU2tT58+r/sRoVD48sbo6Ojq6uoPDCORSIKDg4VC4bFjx/T19T9wbwAACo5Q0a9Zs4bMQP9KIpFMnTq1qqrq+PHjOjo6tOMAAMidat0zViKRfPvtt9XV1YcOHULLA4CKIFT0cXFxr3tp1qxZZDIwDDN58uRnz54dOnRIS0uL2KAAAHQRKvqioqIdO3bU19e7u7u3eYlk0U+aNGnUqFGamprERgQAoI5Q0cfHx3t4ePj7+2dnZ5MZ8erVq9u2bauoqOjdu3dYWBh7PWRfX18yowMAKA5y59F7eXn169ePzFh79+4dPny4ubl5QEBAQ0ODs7Pz1atXyQwNAKBoyH0Yy+Px8vLyCAwkFotnz56dlZXF3ug1ICDAxcUlODg4NzeXwOgAAIqG9DdjWXJdl8/Pz3dwcGh9O+/AwMCioiKxWCy/QQEAFBadoo+Pj5ffztXU1KRS6Su3y29QAACFRafo5ap///6lpaUCgUC2ZdeuXX379sWlDgBANdH5wlRERIT8dq6vr79x48YRI0bMnDnT1tb2woULBw8ezMrKkt+IAACKjM6MfunSpXLd//jx48+cOdPU1HTixIkuXbpcu3atd+/ech0RAEBhcfYSCPb29pGRkbRTAADQx8E1egAAaA1FDwDAcSh6AACOe/Up5worPj5+/vz5SnSF4SdPntCOAADUGBsbv+U76+rqzp07N3DgQHnEULKif/HiRW1tLe0U78DExKSmpoZ2Cmpw+Kp8+IzK/wm80+GrqakZGRnJKYmSFb3Sed3XdFUEDl+VD59R+T8BxTl8rNEDAHAcih4AgONQ9AAAHIeiBwDgOBS9fPXo0YN2BJpw+LQjUKbifwKKc/iK8qEwAADICWb0AAAch6IHAOA4FD0AAMeh6AEAOA5FDwDAcSh6AACOQ9EDAHAcih4AgONQ9AAAHIeiBwDgOBS9vBw+fNjBwUFHR8fBweHAgQO049BRVVVlZmaWnZ1NOwhpd+7c8fb21tPT69atW2xsLO04FJw8ebJPnz56enqDBg0qLCykHYecsLCwuLg42dPz5887OTnp6Oi4ubkVFxfTSoWil4vKysrJkycvW7bs0aNHERERX331VWlpKe1QFISEhKjmneQmTJjA5/Pv3bu3b9++xYsXl5SU0E5EVHV1dUBAQGRk5MOHDz09Pf38/GgnIkEsFqempu7cuVO25enTp76+vjNmzLh//767u3tAQAC1cFKQg3379g0YMED29OOPP05MTKSYh4qtW7eOGjWqe8o3nfkAAAakSURBVPfuWVlZtLMQdfHixS5durS0tNAOQk1WVlbnzp3ZxxUVFQzD1NTU0I1EQL9+/dhS/fPPP9ktSUlJ9vb27OPGxkYtLa3Lly9TyYYZvVwEBARcvHiRfXzz5s1bt245ODjQjURYeXn58uXLExMTaQehIDc3197eftKkScbGxvb29ikpKbQTkda7d++6urqDBw/W19dv2LDBycnJ2NiYdii5y8vLk0ql7u7usi2FhYV8Pp99rK2tbWtrS+t3O3Uqo6qO1NTUmTNnhoWFubq60s5CjlQqnTp16sqVKzt37kw7CwWPHz/OysravHnz1q1bjx8/PnnyZIFA0Lt3b9q5yLG0tAwPD/f392efJicn081DS21tLY/Hkz01MDCoq6ujkgQzenmpra2dMGHCnDlzNm3atGbNGtpxiIqLizMxMZk0aRLtINT06dMnJCREX1/f39//k08+OXPmDO1ERKWkpCQkJOTk5DQ0NKSmpk6bNu3GjRu0Q1FgbGzc2Ngoe1pfX0/rNxsUvVxIJJIRI0aoq6vfuHHD19eXdhzSTp8+feDAATU1NTU1tTt37gwbNmzx4sW0Q5HTs2fPlpYW2VOJRKKnp0cxD3nnz5/39PQcOHCgjo6Or69vr169CgoKaIeiwNHR8erVq+zjpqammzdvylZyCEPRy0VaWlpdXd3u3bsNDAxoZ6Hg0KFDsk+B7O3ts7KyVq1aRTsUOWPGjKmsrNywYcPTp0/37Nlz8+bNkSNH0g5F1MCBAzMyMi5evPjs2bMTJ04IhcKBAwfSDkWBj4+PUChMTk4Wi8WLFi3i8/k2NjZUkqDo5eL8+fPXr1/X0NBQ+39U82NJ1WRiYnL69Oldu3ZZWlrGxMSkp6ebmprSDkVUQEDA0qVLg4KCTExMFixYkJSURKvg6DIwMEhJSYmIiLCwsCgsLExKSqKVBPeMBQDgOMzoAQA4DkUPAMBxKHoAAI5D0QMAcByKHgCA41D0AAAch6IHAOA4FD0AAMeh6AEAOA5FDwDAcSh6AACOQ9EDAHAcih4AgONQ9AAAHIeiBwDgOBQ9AADHoegBADgORQ8AwHEoegAAjkPRA7yWmZlZWVnZK18qLi42MjJ6ebtYLO7duzfDMK6urrdv35ZrPIC3hKIHaE/Z2dnu7u5isVgkEvXo0YN2HACGQdEDhwkEgo8++ujXX3/l8Xg2NjZHjx4dOXIkj8fz9vYWiUQMw2RmZvL5fAMDAzc3t7y8PPantm3bZmVlZWBgMH/+fNmuCgsLBw8erK+v/+mnn+bk5LxyuLKyMjU1NR8fn82bN/N4vKKiIgcHBwKHCfCvUPTAZffu3WtpaamoqPDy8hozZkxoaOjdu3ebmpo2bNhQXl4+fvz43377raKiIigoaPTo0U+ePCktLf3+++83b95cUVHx/Pnz6upqhmFEIpG3t/eMGTPu378/Y8aMMWPGNDY2vjyWra2tVCq1t7d//PjxzJkzU1NTi4qKiB8xwCuoSaVS2hkA5EIgEPTv37+xsVFDQ+Pvv/9eu3atQCBgGGb+/PkNDQ1WVlZXrlzZu3cv+2ZnZ+dffvnlypUrpaWlycnJDMM0NjbyeLwbN25kZWUlJydnZmay7/zkk09WrFhha2s7cOBA9jcDmfLycn9//9zcXEdHxwsXLhgaGpI9YoBXU6cdAECOTE1NNTQ0GIbp0KFD689OX7x4cefOnV69esm2WFhYVFVVlZeXyxbWdXR0TE1NGYYRCoVZWVlqamqyN1dWVtra2rYZy9LSsqqqimEY9p08Hu/x48fsHgDoQtEDl7Vu5zYsLCzu3r0re/q///2vR48eFRUVd+7cYbfU1dU9evSIYRhLS8tRo0alp6e3/vHi4uI2O6ysrJw0aVJoaOitW7fu3r3766+/ttdRAHwgrNGDipo4cWJKSsqpU6fEYnFMTIxEIvHy8goMDDxy5MjJkydra2sXLVrEvnP8+PHnz58/duxYY2PjqVOnTExMysvLX96hVCrNyclxdXU9deqUt7c32aMBeBMUPaiovn37/vXXX7NmzTI3N9+7d29KSoqmpmbfvn03bdoUEhJibW1tZWXFLuN07dr14MGDixcvNjY2Dg8P//vvv7t16/byDgUCgb29vaam5qVLlz777DPSxwPwevgwFgCA4zCjBwDgOBQ9AADHoegBADgORQ8AwHEoegAAjkPRAwBwHIoeAIDjUPQAAByHogcA4DgUPQAAx6HoAQA4DkUPAMBxKHoAAI5D0QMAcByKHgCA41D0AAAc93+9O7jWe9VmXwAAAABJRU5ErkJggg==" style="display: block; margin: auto auto auto 0;" /> --- name: overfit3 ## Overfitting | `Likelihood example` ### Why is this? -- #### Nested models * Model (1) can be described as a special case of Model (2) with the constraints on `\(\beta_2=0\)` * Therefore Model (2) will always have equal or better ML than Model (1) -- ### Why could this be a problem? -- #### Overfitting * In the example, the simulated data was generated from the 3 first variables + thus, the subsequent variables increase ML by modeling noise in data * This is difficult to detect by just looking at the likelihoods -- ### Solution: -- * Seek the simplest model that is "good enough" + Regularization/Bayesian priors + Model comparison + Cross-validation --- name: regularization ## Regularization * Regularization is a frequentist concept that adds auxiliary criteria, so-called *regularization terms*, to probabilistic models. + We will examplify this with a *penalized likelihood*, which attempts to balance the model's log likelihood against the number of parameters in the model + We will later cover other regularization applications when we discuss feature selection --- name: pen1 ## Regularization | `Penalized likelihood` * A very simplified penalized likelihood of our full model is `\begin{aligned} \log pL[\boldsymbol{\beta} | X, Y] & = \log Pr[Y | X, \boldsymbol{\beta}] - \#(\boldsymbol{\beta}\neq 0), \\ \end{aligned}` where, in the regularization term, `\(\#(\boldsymbol{\beta}\neq 0)\)` denote the number of non-zero elements in `\(\boldsymbol\beta\)` - We then choose the model and parameters that maximize the penalized likelihood - Applying this pL to our example, solves the overfitting problem <img 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" style="display: block; margin: auto auto auto 0;" /> --- name: pen2 ## Regularization | `Penalized likelihood` * More generally, we might want to penalize each `\(\beta_i\)` to be close to some expected value `\(m_i\)`, i.e., `\begin{aligned} \log pL[\boldsymbol{\beta} | X, Y] & = \log Pr[Y | X, \boldsymbol{\beta}] - w||\beta-m||_2^2 \\ \end{aligned}` where + `\(w\)` is some weight factor for the regularization term + `\(||\beta-m||_2^2=(||\beta-m||_2)^2=\sum_{i=1}^n (\beta_i-m_i)^2\)` is the squared `\(L_2\)` *norm*^*. * This is a more typical and formally correct pL model -- * As a parenthesis, we make a note that *norms* (typically the `\(L_2\)` and the `\(L_1\)` norm)^* features frequently in statistics, and particularly in regularization models + For example, the least squares method (which, for linear models, estimates ML) can be written as a minimization of the squared `\(L_2\)` norm of residuals: `$$\min_{\boldsymbol{\beta}}\left\{\sum_{i=1}^n (y_i-x_{i,\cdot}\boldsymbol{\beta})^2\right\} = \min_{\boldsymbol{\beta}}\left\{||Y-X\boldsymbol{\beta}||_2^2\right\}$$` *.small[See "extended_reading" document.] --- name: pen3 ## Regularization | `Bayesian interpretation` -- * Exponentiating (removing the logarithm) of the `\(\log pL\)` for the general penalized likelihood model yields `$$pL[\boldsymbol{\beta} | X, Y] = Pr[y | X, \boldsymbol{\beta}] e^{-w||\boldsymbol{\beta}-m||_2^2}$$` -- * The penalizing term can, then, be viewed as a Bayesian prior on the values of `\(\boldsymbol{\beta}\)` with `\(\Pr[\boldsymbol{\beta}] = e^{w||\boldsymbol{\beta}-m||_2^2}\)`, i.e., we obtain the Bayesian model `$$Pr[Y | X, \boldsymbol{\beta}] Pr[\boldsymbol{\beta}]$$` + In fact, setting `\(w=2\sigma^2\)` and adding a constant `\(-\log\sqrt{2\sigma^2\pi}\)` to the `\(\log pL\)` equation would make the prior on each `\(\beta_i \sim N(m,\sigma^2)\)`. -- * The corresponding penalized likelihood formula for our first very simple toy pL example is `\begin{aligned} pL[\boldsymbol{\beta} | X, Y] = Pr[Y | X, \boldsymbol{\beta}] e^{-\#(\boldsymbol{\beta}\neq 0)}, \end{aligned}` + Here, the prior on `\(\boldsymbol{\beta}\)` becomes `\(Pr[\boldsymbol{\beta}]=e^{-\#(\boldsymbol{\beta}\neq 0)}\)`. --- name: modcomp ## Model comparison Compare two models and decide which one is the best. Approaches include * Likelihood ratio test - based on likelihood only * AIC (Akaike information criterion) - Based on information theory/regularization * Bayesian information criterion - Bayesian version of AIC --- name: lrt ## Model comparison | `Likelihood ratio test (LRT)` * Method -- uses likelihoods, only + Define the likelihood ratio, `\(LR\)`, for our original models (1) and (2) as `$$LR = \frac{ML[\beta_0, \beta_1 | x_1, y]}{ML[\beta_0, \beta_1, \beta_2 | x_1, x_2, y]}$$` + Then, for nested models, the *deviance* `\(2 \log LR \sim \chi^2(\delta)\)`, (where `\(\delta\)` is the difference in dimensionality between models), which provides a significance test for rejecting the simpler model (1) * Applied to our example data set, LRT correctly discards the simpler model when sequentially adding 3 first variables, but subsequent addition of variables does not improve the model significantly. <table class="table table-striped" style="font-size: 14px; width: auto !important; margin-left: auto; margin-right: auto;"> <thead> <tr> <th style="text-align:left;"> Compared models </th> <th style="text-align:right;"> logL 1st model </th> <th style="text-align:right;"> logL 2nd model </th> <th style="text-align:left;"> logLR </th> <th style="text-align:left;"> P-value </th> <th style="text-align:left;"> Significance </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;"> 1 vs 2 variables </td> <td style="text-align:right;"> -172.30 </td> <td style="text-align:right;"> -161.85 </td> <td style="text-align:left;"> -10.44 </td> <td style="text-align:left;"> 4.87e-06 </td> <td style="text-align:left;"> *** </td> </tr> <tr> <td style="text-align:left;"> 2 vs 3 variables </td> <td style="text-align:right;"> -161.85 </td> <td style="text-align:right;"> -139.08 </td> <td style="text-align:left;"> -22.78 </td> <td style="text-align:left;"> 1.49e-11 </td> <td style="text-align:left;"> *** </td> </tr> <tr> <td style="text-align:left;"> 3 vs 4 variables </td> <td style="text-align:right;"> -139.08 </td> <td style="text-align:right;"> -138.97 </td> <td style="text-align:left;"> -0.1104 </td> <td style="text-align:left;"> 0.638 </td> <td style="text-align:left;"> - </td> </tr> <tr> <td style="text-align:left;"> 4 vs 5 variables </td> <td style="text-align:right;"> -138.97 </td> <td style="text-align:right;"> -138.30 </td> <td style="text-align:left;"> -0.6655 </td> <td style="text-align:left;"> 0.249 </td> <td style="text-align:left;"> - </td> </tr> <tr> <td style="text-align:left;"> 5 vs 6 variables </td> <td style="text-align:right;"> -138.30 </td> <td style="text-align:right;"> -138.26 </td> <td style="text-align:left;"> -0.04381 </td> <td style="text-align:left;"> 0.767 </td> <td style="text-align:left;"> - </td> </tr> <tr> <td style="text-align:left;"> 6 vs 7 variables </td> <td style="text-align:right;"> -138.26 </td> <td style="text-align:right;"> -137.84 </td> <td style="text-align:left;"> -0.4136 </td> <td style="text-align:left;"> 0.363 </td> <td style="text-align:left;"> - </td> </tr> <tr> <td style="text-align:left;"> 7 vs 8 variables </td> <td style="text-align:right;"> -137.84 </td> <td style="text-align:right;"> -137.82 </td> <td style="text-align:left;"> -0.02251 </td> <td style="text-align:left;"> 0.832 </td> <td style="text-align:left;"> - </td> </tr> <tr> <td style="text-align:left;"> 8 vs 9 variables </td> <td style="text-align:right;"> -137.82 </td> <td style="text-align:right;"> -137.82 </td> <td style="text-align:left;"> -0.0001522 </td> <td style="text-align:left;"> 0.986 </td> <td style="text-align:left;"> - </td> </tr> <tr> <td style="text-align:left;"> 9 vs 10 variables </td> <td style="text-align:right;"> -137.82 </td> <td style="text-align:right;"> -137.62 </td> <td style="text-align:left;"> -0.1968 </td> <td style="text-align:left;"> 0.53 </td> <td style="text-align:left;"> - </td> </tr> </tbody> </table> --- name: aic1 ## Model comparison | `AIC` * Method -- uses likelihood and number of parameters to estimate the information lost by selecting a model + Define, for a model `\(m\)` with estimated parameters `\(\boldsymbol{\beta}\)`, `$$AIC_m = 2\#(\boldsymbol{\beta}\neq 0)-2\log ML[\boldsymbol{\beta}|X,Y]$$` + Let `\(AIC_{min}\)` be the minimum AIC among a set of compared models + Let the *relative likelihood* for model `\(m\)` is `$$rL = e^\frac{ AIC_{min} - AIC_{m} }{2}$$` - `\(rL\)` can be interpreted as proportional to the probability that the model `\(m\)` minimizes the information loss. <!-- and can be interpreted as --> <!-- `\(rL \propto Pr[m\textrm{ minimizes estimated information loss}]\)`. --> * Notice that `$$rL = \frac{ML[\boldsymbol{\beta}_{m}|X,Y]e^{-\#(\boldsymbol{\beta}_m\neq 0])}}{ML[\boldsymbol{\beta}_{min}|X,Y]e^{-\#(\boldsymbol{\beta}_{min}\neq 0))}}$$` we see that `\(rL\)` can be viewed as a penalized likelihood ratio under our very simple pL toy model. --- name: aic1 ## Model comparison | `AIC` * Evaluation + Typical strategy is to select the model, `\(m\)` with `\(AIC_m=AIC_{min}\)` + In theory, in analogy with LRT, significance test could possibly be devised, but this is not done in practice. * AIC applied to our example data results in <table class="table" style="font-size: 14px; margin-left: auto; margin-right: auto;"> <thead> <tr> <th style="text-align:left;"> Compared models </th> <th style="text-align:right;"> AIC </th> <th style="text-align:left;"> Minimum AIC </th> <th style="text-align:left;"> rL </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;"> 1 variable </td> <td style="text-align:right;"> 350.59 </td> <td style="text-align:left;"> - </td> <td style="text-align:left;"> 2.763e-14 </td> </tr> <tr> <td style="text-align:left;"> 2 variables </td> <td style="text-align:right;"> 331.71 </td> <td style="text-align:left;"> - </td> <td style="text-align:left;"> 3.476e-10 </td> </tr> <tr> <td style="text-align:left;"> 3 variables </td> <td style="text-align:right;"> 288.15 </td> <td style="text-align:left;"> Yes </td> <td style="text-align:left;"> 1.000e+00 </td> </tr> <tr> <td style="text-align:left;"> 4 variables </td> <td style="text-align:right;"> 289.93 </td> <td style="text-align:left;"> - </td> <td style="text-align:left;"> 4.107e-01 </td> </tr> <tr> <td style="text-align:left;"> 5 variables </td> <td style="text-align:right;"> 290.60 </td> <td style="text-align:left;"> - </td> <td style="text-align:left;"> 2.938e-01 </td> </tr> <tr> <td style="text-align:left;"> 6 variables </td> <td style="text-align:right;"> 292.52 </td> <td style="text-align:left;"> - </td> <td style="text-align:left;"> 1.125e-01 </td> </tr> <tr> <td style="text-align:left;"> 7 variables </td> <td style="text-align:right;"> 293.69 </td> <td style="text-align:left;"> - </td> <td style="text-align:left;"> 6.266e-02 </td> </tr> <tr> <td style="text-align:left;"> 8 variables </td> <td style="text-align:right;"> 295.64 </td> <td style="text-align:left;"> - </td> <td style="text-align:left;"> 2.364e-02 </td> </tr> <tr> <td style="text-align:left;"> 9 variables </td> <td style="text-align:right;"> 297.64 </td> <td style="text-align:left;"> - </td> <td style="text-align:left;"> 8.695e-03 </td> </tr> <tr> <td style="text-align:left;"> 10 variables </td> <td style="text-align:right;"> 299.25 </td> <td style="text-align:left;"> - </td> <td style="text-align:left;"> 3.887e-03 </td> </tr> </tbody> </table> --- name: illposed1 ## Ill-posed problems aka overparameterization * A *well-posed problem* fulfills requirements 1. solution exists 2. unique solution 3. stable solution (small changes in input does not give huge changes in result) * Otherwise the problem is *ill-posed* + specifically if it fails 3., it is *ill-conditioned* (multi-collinearity) * Examples + Least squares regression with more parameters `\(\beta_i\)` than observations has multiple solutions + SNPs in LD may give rise to multi-collinearity * How can we solve this? -- * Solution: Add additional assumptions (constraints), implemented through, e.g., + prior distributions (Bayesian), e.g. `\(\boldsymbol{\beta}\sim N(m,\sigma^2)\)` + add a regularization term (frequentists), e.g., `\(-w(\boldsymbol{\beta}-m)^2\)` --- name: featsel ## Feature selection * Aim: Simplifying the (full) model without compromising explanatory power - balance between "simplicity" (number of variables) and "bestness" (likelihood) * methods + model comparison - As described above + regularized methods - LASSO (Least Absolute Shrinkage and Selection Operator) - Ridge regression - Elastic-net + dimensionality reduction to obtain fewer summary variables - PLS - CCA --- name: lasso1 ## Feature selection | `LASSO` * Builds on a regression model `\(Y \sim X\boldsymbol{\beta}\)` with regularization + The variables Y and X must be centered and standardized to ensure that all variables are given equal weight in the model selection. * Most common notation for lasso is *Least Squares* with an auxiliary criterion/constraint: `$$min_{\boldsymbol{\beta}}\left\{\frac{1}{N} ||Y-X\boldsymbol{\beta}||_2^2\right\} \textrm{subject to} ||\boldsymbol{\beta}||_1\leq \lambda$$` where `\(||\boldsymbol{\beta}||_1=\sum_{i=1}^n \beta_i\)` is the `\(L_1\)` norm of `\(\boldsymbol{\beta}\)`. * Other ways of viewing LASSO: + pL with regularization term `\(-\lambda\boldsymbol{\beta}\)` + Bayesian prior on `\(\beta_j ∼ LaPlace(0, 1/\lambda)\)` * Alternatives to LASSO, differing mainly in the auxiliary criterion - *Elastic-net*, which uses a squared `\(L_1\)` norm - *Ridge regression* which uses a `\(L_2\)` norm --- name: lasso2 ## Feature selection | `LASSO` * There are two main R-packages for performing LASSO, *lars* and *glmnet* + The packages may produce somewhat different results + The difference between the packages lies in - the models supported * lars: LASSO on linear model and selected GLMs * glmnet: LASSO, ridge regression or Elastic net on a larger selection of GLMs - methods for optimization- and standardization * Lasso is often visualized with the following plot (lars on our toy data) <img src="data:image/png;base64,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" style="display: block; margin: auto auto auto 0;" /> --- name: lasso3 ## Feature selection | `LASSO` * A problem is to decide `\(\lambda\)` to use as the cutoff. The two methods provide different methods for this .pull-left-50[ * glmnet ues cross-validation to obtain an estimate of the minimum `\(\lambda\)` attainable, and then view the estimated `\(\beta_i\)` under this `\(\lambda\)`. <table> <thead> <tr> <th style="text-align:right;"> Variable </th> <th style="text-align:right;"> beta(lambda=0.11) </th> </tr> </thead> <tbody> <tr> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 3.392205 </td> </tr> <tr> <td style="text-align:right;"> 1 </td> <td style="text-align:right;"> 2.075677 </td> </tr> <tr> <td style="text-align:right;"> 2 </td> <td style="text-align:right;"> 1.625815 </td> </tr> <tr> <td style="text-align:right;"> 3 </td> <td style="text-align:right;"> 2.267262 </td> </tr> <tr> <td style="text-align:right;"> 4 </td> <td style="text-align:right;"> 0.000000 </td> </tr> <tr> <td style="text-align:right;"> 5 </td> <td style="text-align:right;"> 0.000000 </td> </tr> <tr> <td style="text-align:right;"> 6 </td> <td style="text-align:right;"> 0.000000 </td> </tr> <tr> <td style="text-align:right;"> 7 </td> <td style="text-align:right;"> 0.000000 </td> </tr> <tr> <td style="text-align:right;"> 8 </td> <td style="text-align:right;"> 0.000000 </td> </tr> <tr> <td style="text-align:right;"> 9 </td> <td style="text-align:right;"> 0.000000 </td> </tr> <tr> <td style="text-align:right;"> 10 </td> <td style="text-align:right;"> 0.000000 </td> </tr> </tbody> </table> ] .pull-right-50[ * There also exists a fairly new significance test on `\(\lambda\)`, implemented in the package covTest (works only with lars on linear models) <table> <thead> <tr> <th style="text-align:left;"> </th> <th style="text-align:left;"> Variable </th> <th style="text-align:left;"> P-value </th> <th style="text-align:left;"> Significance </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;"> </td> <td style="text-align:left;"> 1 </td> <td style="text-align:left;"> 0.042 </td> <td style="text-align:left;"> * </td> </tr> <tr> <td style="text-align:left;"> </td> <td style="text-align:left;"> 3 </td> <td style="text-align:left;"> 0.0026 </td> <td style="text-align:left;"> ** </td> </tr> <tr> <td style="text-align:left;"> </td> <td style="text-align:left;"> 2 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> *** </td> </tr> <tr> <td style="text-align:left;"> </td> <td style="text-align:left;"> 5 </td> <td style="text-align:left;"> 0.8026 </td> <td style="text-align:left;"> - </td> </tr> <tr> <td style="text-align:left;"> </td> <td style="text-align:left;"> 7 </td> <td style="text-align:left;"> 0.8853 </td> <td style="text-align:left;"> - </td> </tr> <tr> <td style="text-align:left;"> </td> <td style="text-align:left;"> 10 </td> <td style="text-align:left;"> 0.8268 </td> <td style="text-align:left;"> - </td> </tr> <tr> <td style="text-align:left;"> </td> <td style="text-align:left;"> 4 </td> <td style="text-align:left;"> 0.9654 </td> <td style="text-align:left;"> - </td> </tr> <tr> <td style="text-align:left;"> </td> <td style="text-align:left;"> 8 </td> <td style="text-align:left;"> 0.9752 </td> <td style="text-align:left;"> - </td> </tr> <tr> <td style="text-align:left;"> </td> <td style="text-align:left;"> 6 </td> <td style="text-align:left;"> 0.9879 </td> <td style="text-align:left;"> - </td> </tr> <tr> <td style="text-align:left;"> </td> <td style="text-align:left;"> 9 </td> <td style="text-align:left;"> 0.9852 </td> <td style="text-align:left;"> - </td> </tr> </tbody> </table> ] --- name: dimred ## Feature selection | `Dimensionality reduction` * Recall how PCA projects `\(X\)` onto a new basis of lower dimensionality <br><br><br><br><br><br><br><br> <img 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width="2667" style="display: block; margin: auto auto auto 0;" /> --- name: dimred ## Feature selection | `Dimensionality reduction` * Recall how PCA projects `\(X\)` onto a new basis of lower dimensionality + extend to project 2 matrices `\(X\)` and `\(Y\)` onto a *common* basis using projection matrices `\(V\)` and `\(W\)` - `\(T=XV\)` and `\(U=YW\)` are "components" that captures the *joint* variation in `\(X\)` and `\(Y\)` - `\(V\)` and `\(W\)` are "loadings" that describes the contribution from original variables and defines the common basis <img 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" width="2667" style="display: block; margin: auto auto auto 0;" /> --- name: dimred2 ## Feature selection | `Dimensionality reduction` * How do we best define an appropriate common basis? + select `\(V\)` and `\(W\)` so that - PLS: the *covariance* between `\(T=XV\)` and `\(U=YW\)` is maximized - CCA: the *correlation* between `\(T=XV\)` and `\(U=YW\)` is maximized -- * PLS (Partial least squares) vs CCA (Canonical correlation analysis) + Similarities - uses regularization to limit choices of `\(V\)` and `\(W\)` for high-dimensional data - solutions connected to singular value decomposition (SVD) theory^* + Differences - relative constraints on `\(W\)` and `\(V\)` - motivation/use areas + In practice, quite equivalent behaviour when it comes to prediction, but differs in details .small[^* see "extended_reading" document] --- name: pls1 ## Feature selection | `Dimensionality reduction` ### PLS (Partial least squares or Projection to latent structures) * Components are often called *latent variables* * 2 "modes": + Regression mode: - builds on a *'multivariate regression'*, `$$YW = U ≈ T = XV \Rightarrow XVW^{-1} ≈ Y \sim X\boldsymbol{\beta} \Rightarrow \boldsymbol{\beta}=VW^{-1}$$` - this regression relation is used in an iterative estimation of the column vectors `\((v_i,w_i)\)`, where `\(v_i\in V\)` and `\(w_i \in W\)` - Can use a multivariate `\(Y\)` and handles co-linear, missing, noisy, correlated data better than standard multivariate regression + Canonical mode -- similar to CCA - column vectors `\((v_i,w_i)\)` are estimated in a single SVD - identifying similarities between data sets * Variants + several variants(OPLS, O2PLS, OnPLS) + MixOmics sPLS combines PLS with lasso. --- name: pls2 ## Feature selection | `PLS Example` * Apply MixOmics PLS in regression mode to our toy data with an additional `\(y2\)` variable, generated using `\(x_8,x_9,x_{10}\)` ```r y2 = b0 + X[,seq(8,10)] %*% b[seq(8,10)] + rnorm(N) # Y2 ~ x_8, x_9 and x_10 Y = matrix(c(y1, y2), ncol=2) # save Y-vars in Y Z = cut( y1+y2, 2 ) # bogus classification of Y based on sum of y1 and y2 ``` -- .pull-left-50[ .small[ * Find significant components <img src="data:image/png;base64,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" style="display: block; margin: auto auto auto 0;" /> ] ] -- .pull-left-50[ .small[ * Plot our samples on components from `\(X\)` and `\(Y\)` <img 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" style="display: block; margin: auto auto auto 0;" /> ] ] -- .pull-right-50[ .small[ * compare to PCA on `\(X\)` alone <img src="data:image/png;base64,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" style="display: block; margin: auto auto auto 0;" /> ] ] --- name: integration1 ## Integrative analysis * Simultaneous analysis of several data sets `\(\{X_1, \ldots, X_k\}, k\geq 2\)`, e.g., from different omics, possibly including response data `\(Y\)` ("*supervised*") or not ("*unsupervised*") * Approaches + Methods based on dimensionality reduction - Joint variation, only - Joint + unique variation + Machine learning - e.g., deep learning + Network-based methods - Multilevel network - often rather specialized, e.g., for cancer - different network learning methods, network fusion - Path modeling - for time series, causal relations, etc - variants: ML-based, PLS-based, Bayesian networks --- name: integration2 ## Integrative analysis | `Dimensionality reduction` #### Estimating joint variation only * Aims to identify common patterns of variation among `\(\{X_i\}\)` (and `\(Y\)`) * Approach: + simultaneous component analysis (SCA) = generalized PCA for 2 matrices + PLS + CCA - For all, generalization to `\(>2\)` matrices through averaging over pairwise comparisons of matrices * MixOmics package - MINT: when `\(\{X_i\}\)` share variables (e.g., integrating RNAseq data for different samples) - DIABLO: when `\(\{X_i\}\)` share samples (e.g., integrating RNAseq, metabolomics, epigenetic data for same sample) --- name: integration3 ## Integrative analysis | `Dimensionality reduction` #### Estimating joint + unique variation * Aims to identify joint variation among `\(\{X_i\}\)` (and `\(Y\)`), as well as unique variation in each `\(X_i\)` * PLS-based approach + identify `\(v_p,w_p\)` for the joint variation as described above, e.g., using SVD of `\(XY^T\)` - the unique variation is *orthogonal* to `\(Y\)`, so not included in `\(v_p,w_p\)` - remove joint variation from `\(X\)` and estimate unique variation `\(v_o,w_o\)`. + variants - OPLS: PLS-regression mode for two matrices - O2PLS: PLS canonical mode for two matrices. - OnPLS: PLS canonical mode for multiple matrices. * Other approaches + JIVE, DISCO uses SCA --- name: integration3 ## Integrative analysis | `MINT example` * MINT PLS applied to our toy data, with `\(X\)` split into 4 sub matrices `\(\{X_1, \ldots, X_4\}\)`, representing different studies, and using outcome `\(Y\)`. ```r # the vector indicating X membership in each independent study study = as.factor(c(rep(1,25), rep(2,25), rep(3,25), rep(4,25))) ## 1 2 3 4 ## 25 25 25 25 ``` -- .pull-left-50[ <img 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MRcIR6GUDSYCFrIfWj6aSIoAOBxWnIjL9fhGkPNjUWhwoiTdMcM3Ql05q0aKX2hv+/a04VXCzUAcLdCt2Jfzuho1/kDfTumzSz/WdiEKRvAeLSW+bU2Q2UkjmcoDqXL71Y8tBfHQWv8+9DQpvp3CxEeoiKlKTlHOSrKtXb7mWwlAER6NHurIKtKv2hnltpETunhnlqsuZiventfzueTQjus3wx2E2x4MuJUVvWGs8VlarNch/9+teJqoebDccG1b4ZYOgharVYikdy4cSM2NrYtz+vn53fgwIE2PmltWEdvA8Z1cRNy0YRw21eXbT0UDVcK1HtvV53PU9UOfkcRiPWVjO3iOjTUucUCL090dz+ZWb32VJFUzI27n4J04l71tivlXAyZ2LV50aWMl1cZCWZdXqHHF+7M7Pi+HgASwl0GBjv9fKls+9VymoZ7lfq5v999IyFgQkyTNudZWOxNh56EPi4Iuei4jpcepTISv1+rmLEtbem/WaezlRYv7+vMf3mAz84Xum2aHjEhRtoaGa/e/pJZvb1URuK1fzKnb01buDNz8g+3Vx3KxQlqaby/v3MzdsxIil68K0tlJJ7tXbMu7yrifjM1IsBFcDFf9dOl0hYb2TbwOeiCwb4bpkUwegkGnPrkWP43Z4upFopysrQpN2/eHDx4sFgs7tWrV3JyMtO4f//+iIgIJyenlStXBgYGZmRk1NszNTU1LCzsk08+kUqlLi4uX3zxBXP4r7/+6ufnJxaLFy9eTDestdc2dCzfxGIT0sp0Hx7Nn/TD7Y1niy07og48bGJX6ZYZkf883/WF/t7ejrYJ7nxtiO//xgaHSoWlKtO1Io1cj3f1dlg/NXxKM/ObMBRJCHd5ZZDvwiEPdl+lYu6maRHxYc7dfB4dptkRiPOT/DarS+L9e7s/r1WsOpjLqt11cJRK5YgRI1566aWysrLFixdPnDhRo9Hk5eXNmjXr+++/LyoqMhgMhYWFDfUEgNzc3MrKyvz8/K1bt65cuVKpVGZnZ8+fP3/z5s2lpaV8Pr+0tJ1nKuzSTecBJ+lj95Q7UqtyFQ9lOUV5iqZ2dx8Z5Sqwzy4Ck0pqJKhKjdnbkd/iNZa3hgfUbZSKuZ9NDG2dgW2KRIB9MiHklyvl350voQGSsqqrdPhXk8NYLcwOyz///BMdHT137lwAmDNnzpYtWw4ePJiXlzdu3Lj4+HgAWL169ebNmxvqGRUVxeVyP//8c4FAMHnyZC6XW1xcvHPnzgkTJkyaNAkAPvnkE+bwdoR19J0BrYn891bVP6mVtcUj+Rx0RKTL1O7uXdok4E/AQdntRwtz+np5OfI+OZaPk/TtUu0be7K+eTKioy3usTDk5eUlJyfXTlwoLy8vKCgICKiZeQgEAqlU2lDPqKgoiUTCpPIgCMLn8wmCKCgosAg78ng8D49mZInbA9bRP96Uqc07blTsT5PrzQ9ynfyd+VO6u4+PcWPLaLQjo6Nc3cXct/flaE1kWpluxf6cLyeHdeQt5f8sXl5e48aNO3jwYO3GN998s6Kignms1WplMllDPVNTU+uO6e3tnZOTwzw2GAzl5eV2Mb3JsFOMx5VsmeG9Q3nTt6btuF5p8fI9fBxWJXj8NbfrzF6erJdvd+L8JF9ODmNWzK4UqN8/nNdIASyW9mLKlCnnz58/dOiQwWA4deqUm5tbZmbmqFGjdu/effHiRbVavWzZMkZMu96e9Y759NNPHzx48PDhw2q1+p133mljLe66sI7+8SOrSr9yf85zv6Ufv6cgKRoAMBQZEeny8zPR6ycH9fUT2iQRn8Um9PAVfzIhhIMiAHAqq/qHi2XtbREL9OzZE7nP4MGD/f39d+3atXLlShcXl1dfffXHH3+MiIgYPXr0J598Mn36dD8/Pzc3N0dHRw6HU2/Pek/RvXv3H3744dVXXw0ICHBwcOjatWsbv0YrkLaJ+1m2bNmMGTP69u1r85Htp3Wj0+nMZrOLi+2j4xmtGweHZi+dZ1Tot14uS85RWj4zEQ+b2NXtqZ6eTBSN0WjUarXMeqLNUavV9hCgxnFcpVLZqsKUFXaymaIohULh6OjYRGW64/cU7x/KowFQBNZPDe8T0JhJarVaIpHYQ+tGLpeLRCJ7aN3odDo7ad0olUoOhyMWPxR2defOnTlz5vzyyy8xMTE2P2NddDqdk5OTXC53cnJqg9PZA3ZG/3hwt0K3bG/2C3/cPXvfy4v52Iv9vfe82O31Yf62ipVksRMjI12f6eUJABQN/zuSr9C38408yyM5evQos84ul8tXrFgxYMCAx9fLA7sZ2/EpUBi3nC85m/1gFu8o4DwV5zEj1qPpJbObhQGn6o0PMRI0W2qjfggTbVDSOjltUIJZD2YdTZrBrKfNeiDNYNIBwMs0RPOVCgMBGrizndefKVPFFwOHh3CFwHNAOHzgChGhE1B8GvNDHFwfcVIWezJ69OiXXnpp0KBBKpVq4MCBv/76a3tb1CpYR99xqdLiP10qPXBHTt5Pr3QWcp6O85we6y7i2Sso+065bt5f96Z0l76ZGGBZO6AB1p0q2nWz8tsZkXbNXTLg1Kms6oRwlw4YiUjr5LS6jPlHKUsFiiIK1xoN1bS+GvC6yp71MNDySA3ErQa7cQFMAIByEJEL4uCGOLghTr6Isx/iEoA6+yNOPoCxpWvbgo8++uijjz5qbytsA+voOyJaE/lbSvnfNyqN95MqxXxsVm+vGT097O0B3cVcZyFn180qGmBZYgACQAOsPVW0M7XSSYB5SOy7RnQoXf5lUqEBp57s0RaFAxuCNqppRT4lz6Xl+bQ8l1KV0upSIB5KQ8MA7Lu7RRG0torWVlm3Iyji6IVKQxGPKNQzCvWMQiQtrMrC8t+hTR29PTZ+6fvYfGTL+HYas96RCYredbNq6+Vyi0Y8F0OmxXo818fTScB5pD2NjNxE3B24m6eHL9yZtftmFUHSy4cHfHOmeGdqpbOQs3qMj4eYa/M3xGIzTdMmnAQAE07a8CyPHooiKFkuXZFBV92j5Hm0PJfWNbn6IMpBhM6I0BlErojIBRG5AE8EXBFwhcDhITwxcAUIxgOBxGLMB0fyi5QmAHg2RpQYIgLCRJs0QJiAMIFZCwY1rirHcC2tk9E6ORB1NP1pilaVkqpSyKmRZEFELqhHFOIdg/rFoT49gNPYxdh+P5a2/Bm2u3TMY0cbOXqm8KNWq7X5yBRFAQBBEI/s2VwIgqAoyh42M+8GY3ltrpfotlyqKrhfphVFIDHMcW4vqYeYA4SxKYaQJAkArbTZlQtrxvkuP1i8L012s1hdoDQ7CbDPx/r6SVD7fYJ6vR5BELPZDABms9lWJyIIop6hKAIUeagsC5FlQtU9RJFrNVu3BkFB5EZLPGmxJ0i8mAc4zwVz9ECFzd6gGzNIuvxgMQCsyUJ79gkVcKyja3Ac53A4TNQNghtAWwnqUkRdgqhKaFUxoi5FtBVAPciPo/XVZP5FyL8IAMDh0Z4xtHcs7duT9ogG9KEfOE3TTIHM5tr8SAiCIAjCHqUEKYrCcdzqQzQYmrRWxmKhjRw9giAYhkkkEpuPbO/wSnvYXDe8slRl+uZsMSPjzjAo2GnBYN9QafMi4ZjwytbbHC2BTTMcnv/9boHSzMPQDdMiw92FTNhf0wdp4oI7E17p4OCAYRifrwcAPp9vq7f9gc24nipNI0tSqeIbVFlaY6vqGA91DULcglC3YMQ1GHELQl0CrZbFmfBKcZPDK2szWCIZfFdzLlelM1NnC011F6keDq+UgKsHwMNR2BRByXLoigyqIoOquEtVZT2Y+BNmpOQGUnIDrm5F+BI0dAgWkYgFDQAOHwDMZjOfz+8E4ZW2qj5dUG1cd7ooV2bUmgiJgBPt4fBmop+7uBPGsLFr9O2MkaC2p5T/drXConEY4CJYMsxvYHB7xnLRALtSqww4hSJgJqldNyvfGh7Y3EGasuBuwKm9t2RKjV4oNKMoerNECwDXijRELXlfBx42tkUq0LRRjeSfw+UZVEkqVXmv9iy4NojIFfWMQjyjUc8o1D0McfIFxL4bIU/HeZ7LVQHA3zcqp/Zwb3bAPMpBPSLBIxLrNhkAgCIpeS5VfIMqTKGKrtFGNdOLNmnI9ENk+iHgCrHggVjEcMS1G4BtXGQnYM+tqjVJhZZFIANurtSYk3OVn0wIiQ9zblfTbA/r6NuTc7mqL5MKKzQ16wZMaPy0WA9Ou+a2MjE2/6RWOgs574wMXHOycO9tGQC80qd5uWPMpatxkd6TmYqvzzIKrg/uZs7nqc7nqWp343GQCTFNywKjSKr8Dpl/icq/RJWlcWiq7qIewpegvt0Rz2jUMxr1jEYkbS041ctfEioV5sgMhdXGKwXqfoGtC1tFMdQ9HHUPh54zgKaoqiyq8CpVcJksTAESBwDADWTmSTLzpJAnhshRVNx01D3cJi/k8SVXrq/t5S1QNP3uwdx9L3d3FdXjG1966aXly5dv2LBh06ZNlkYEQXAct0r3Cw8Pv3jxolQqXbhwYdM76/X6RYsW7d+/32g0Dhs2bNu2bW5u1rVrLJ1HjBhx8uTJDRs2LFy48JGvl3X07YNCT3x6Ojcps5r5E0VgfIx0wSBfl/q+Xm0ME2PjLORsnBYRKhX6OvMX7szce1tGEfjKMY62vQQNj3DVGnGlRi8UCpkZ/fk81aBgpx6+D27VHXjY8IhHBJXT6jIy7yKVf4kqTKFNmrodELEH6heL+sai/nGoW4i95+yPZFqsx+cnCgDg6F1Fax19bRAU9YhEPSKh97O0SUvlJpOZp8j8C4AbAQDMWri923R7N+rdldN9ChY1Grj/UcHR1cfr8fIMJEV/fiL/80lhVu2nT5/GcTwyMnLjxo0bN25kGletWoWiaG3HLZPJfvrpp+zsbObPZnXeunVrQUFBWloal8udNWvW119//eGHHzbU+cSJE8uWLWvi621/t/JfgwbYlybfdK5EZ66Z6nbxcliWGBDt2SHuqVMK1bW9PACEuAk3TotYuDNz/13V8OhWTz8fRshFn+wutUggcNCK83mqXv6Smb0eHTKIk3TSxcvmzNNhqitBZGHdDojYg/TtJQjpj/r1RJx8bGh26xkZ6bL2VCFO0hfzVRRNo3YQPED4Yix6LBY9FnAjmX+BTDtA5p1n1q+osjRzWRqSvInT6xlOz+nAawsh6w5FVpWxkWdvl+nrNn788ccffPBB7ZaLFy8ePHgwJSWldmPXrl0tspfN7fzaa6+99tprAFBVVUWSpJW4cUMjNwXW0bcpxUrT5ycLrhbWTDkFHPSF/t7P9va0x++8ZUR7Ojzby3N8jDTY7cFcL8RNuHl65O7rpTFtIm3/CGiKKkk13jstv3ViKFlp9SSB8ngBvbCg/mhQf1QaqlarsVZr3aSWaPenyXJkBp2ZDHETDghyHNeltWmrDjysh6/4aqFGaSDSy/Vdve35xnIFWHgiFp6oKMoU5ichGYdoVSkA0HoFnryRSPkV6/kUJ+5ppPkRRI8vRJ2Yt9oYzNbP6nS6S5cu9evXr3bjq6+++uWXX1qtwzCKxHWlipreecWKFZ9//rm/v/8PP/zQlJGbAuvo2wiKhj+ulX9/odRSu3VQiNPyxABPO6cgNRcxH1s41K9ue5Cr4KW+0kZEFww49e+tqvRyXYibkFFdr7uz2uJtVQAAoKmSm+Tdo2TmCVpfjQA8tGbv5Ffp0f+nsqAzhuD5wUHPNOGGoIlsOV/y25Vyy11+sdJ0Nkd54I783aGurbyADAp2Yi755/NU9nX096FFbtB7jmDwPLLgMnn1DzL/IgDQRjVx8Qfi6u/cvrM5fZ5j4nM6PVwMIRqu5yvkWX9Fi4qKnJycuNwHwVeHDx92dHQcPnx4U07XrM6rV69evnz5ihUr5s2bd/jw4aYc8khYR98WlKhMHx/NTy2piQV2c+C+NsBjbDev9rXKtpzMVGw4WwwAJ6G6drvVzmoztlXvQ8myybtHyLtHaXUdjV+PKG54PBoej0rDAgGelxuTtqdvv1r+dJxHc2+SNEbSRAM7sJwAACAASURBVFJSh4fCKA/flf96pdxJwFk8zG9gsJOQi2ZU6DcmF6eV6dZfpNdMalVsxsBgp6/PFANAanE9mwp2BEGxoAFY0ACqPJ249DOZfQaABlyPn/+OuL2PO2wJFjmiTe1pD4LdROnlDeZqxHhZr6PWTT5Yu3btiy++2MTTNbHzzJkz4+Pj58+f7+bmNmfOnJdffrmJ4z8S1tHbnX1psq/PFFtqg0yIcVs42IdDdzb9wuERrudyVWeylZat1Lo7q4/cVuVxUMt/aU0lmX6QvHuEkuU81AlBq127/V4d5d59+NwRcbWfCXYTdPN2SC3RFlabglybsc2Ik/TLOzLkOvyvOTFutXz9tsvlALB6Umjs/ZfQw1f8zZMRs7enXy7S58qNUd4tvyHzdxE48DCdmcyWtU/6D+rVhffEl5Qsh7j0E5lxHICm1WXm/SvQ1DjeiJWIW3C7WNU2vD3Cf+7vd+vdj0XResoXh4WFMYk1TOaEWq0+d+7c7t27m3KupnceOXLkhg0bxowZIxaLN27cmJCQ0JTxm0KHk47qTFTribf35Xx2vIDx8s5CzueTQv9vVJCdVCfbFyEX7eEjBoBe/pLZfbxm9/Hq5S+p/efsPl5Te7g3vm4zrovbe6MCxolzzftXGH+YiCdvqu3lEbcQ7tBFglcOnYv9bDeSyHXxrTsC46Y1xuZlSv+dWlmgMGpN5LfnSyyNch1eWG0McRPG+j6UrSPkomOjXAEgtVTXrLNYgQAwGyFaE1m72G8bg0pDeRM+5c/6BfXpzrRQxammHfPwC98D3dhC9mNNhLvo9WF+dW/6UAQ+HBtcN2eKz+cPGjTo4sWLzJ+nT5+OiYmxpPURBIEgSEZGRr3nsuqs1Wob6vzcc8/Fx8f36dMnMjJSIBCsXr268ZGbDjujtxcX8lQfHc1XGmo8ztBQ5xUjAjtC9GSHha4u5Nzek5B2gNYrat8nI65BnOgxWPRoxNmfaXFzqAaAYmUdHRgARkbGzaEZ+o4KPb71UhkHRUQ87FC6fGoPDyYCSmMiAUAqvj8Uriczk7CIROCKmEa1sbVaAqFSYVqZDgByZAZ3cXtqUqJeXfgzfyTvHMSTN9I6Oa2vJi58TxVc4Y37sKMFLNmKGT09ewdI1p4qzpMZtGbKUYCFuQtXDA/0bKC6w/Lly3/88cdhw4YBwKRJkyZNmmR5isPhNKLGY9VZLBYvWbKkdq6vpTOHw1m3bt26desaGqrun02E9Tu2h6Tob8+X/n61ZgfPgYctjfcfH2Od+MBSA4lzck/hucfo4tTaipCI0BnrMg6LGY96RFod0ctfwsWQYxmKWb09fZ0ebB6ez1NlVuoDXQU+Ts3YUdxyrlRnJp+K8whyEXx+snDtqcLvn45CAFxEHASgVFVzOSHuHMRPfM7FDZzY6SUqEwC4Clt7Z2ZZXypSGvtDe6v9IyjWdSIWMRw/s564+S8ATZWkGn95mjdiBdZlXDvbZh9C3EQbp9VfC7Au8fHxO3bsSE9P79KlS2tOqtPpCgsL/fzqCXloFpaEqaZ0Zh29janQmN87lHertGafJ9ZX/P6YYK9OWgHKgFMH7siMeM0NvlWYDTNXTa/QN1TJhNYryJu7ydSdfJ2sloNH0YDenG5PYOHxgNX/vjkLOc/08vzlSvm8v+7N7efV1VtsxMmUQs3v1yoQgFcH17Ok0xCZlfpD6TJHAef5ft4SPmdvmiytTHc8QzEqytVJwInyFN2t0CdlVSeGu9QInxHmaj1x8I4CRaB3QGsFeZyFNbN4TatvDmwGT8Qd+Q4aOhQ/8iGtV4BZbz70Hqf8LjdhabtnmbU7W7Zsaf0gDg4OTVzcb5wTJ040vTPr6G1JSqH6g8M1heIQgOk9PRYN9WtfPQO7cjJTsfZUkVWjVZjNiXuKfoESq0gbqjKTuP4nefcokA9kIxGxO9Z1IqfbZMTp0Z563kAfjYncfbOqtgFcDFmWGDA0tBnBMOtOF1E0vDLIh1GBXhrv/8qOexuTi4eEOgu56LyBvm/8m/W/I/m5MsNYo9kVIKNC98GtDIUeHx0u9mn19dvhfhifZa++g4CFDEbn/oUf/ZjMOQsAxPU/aWUhb8Kn/8HUqs4B6+htA0XT354v3Z5Ss1zjLOR8MDbYtkmkrSSryvD3jYp7lYYqrdnPmd/TT/J0nIerqFXrwsMjXA04VXtG/wgBA5ois88Q1/+kiq7XHof0juX3eZYbPqzpc0YUQZYnBkyIkZ7LUebKDTwOGiYVjoh0bVb53OP3FKkl2hA34aSuNdeh7j7ihHCXpKzq7VfLXx7g0z/I8e0RgV+dKvzpUpmarlwAcOxedQliig9zfqWvDdKLLNvy2g7m6AEAEbnypqwlrvyCJ28CmiJzz5v+eIE3ZV1nXbLv3NjS0avV6u+++47ZNbbhsB0frYl871DexfyaaWxPP8mHY4Ol7bq3ZsWBO/LPTxQwKyo8DppWpksr0x24I1v7RHhUK6QXhFx0euyDLO3GBAwogrx7FL+yjZbnPWjEeFjkCOg5U8d1F7q4tGBlINpT1GLpCBNBbT5XAgBLhvlhte66Fg/zu5Cn2n214En6tCMHHw8wJJa4V2kQV+WCDsZL8qYEXPNz5unv6CmJK/SYBNyWv4GWkpD6OqmYHQRO3zmINMx8YCWY9ZQsx/TXS/ynvkecW7u+zNLG2MzRy2SyF154AQDi4+NtNeZjQWG1cfnenMJqIwAgAHP6eb88wLvjSBoAwL1K/WfHCzAUXh/mP6aLq5OAU6oy/ZpSvve27O19OX/NjbFveULCRNzeS6T8VjvdCRF7cHpOw7pPRYTOOI6DStXIAHZi+9WKcrU51lfs68wvUT0UwDMyypW4tU944Rcm5lEIEHv/qQDVVbh9lQDgAdAAJF+EdZsELcWSJs3BOtAXxgosZBD/qe/N/75BaytpTaXp7wX8p79HHL3b2y6WZmAzRy+VSvft2/fdd9/ZasDHgkv56lWHcrUmEgCEXHTV6KCE8OZp+bYBv1+toGh66bCAafd14X2c+CtGBGpMZFJm9dG78ie6t7xAa2G10c9ZYLUNQdF0sdIU4EASqTuJq7/TeoXlKVQaxuk3F4scYVX8qI0x4NT2lHIASC3RTvs5rW4HIRonoExz4pwtkZpU8Q0y9xwWMhj160nTtF6v50tcsahWJZHq7q/YONit2rtNQD2j+DN/NO2Yz9RGN/29gP/U920v72wPiIzjVG4yrSpFnQOwiAQ0dEh7W2QX7PtjO3ny5LZt2wCAy+USBKFUKh91RLNhKlUajY1p0bUMiqJomm7E5p23lVuvKSiaBgBvCfe94V5BLkhTXiNjM47bPkeGibG1siG1WI0iyGBfjlV7YpAgKROu5CniA5q0ykSSpNUIN0r17xwtGxwkfnuYBwdFSNwEAGaT6Z1dt3wLDjzPOY7hD7LMKfdosuczVEB/AATUD9oZmzUau8gA1LW5pp2i+/iLyjWNfAT8fN54Y7SHVlDjgjETzsk9Z3LvSkZMBqbSJIYZdWaARssQNopMWZNyhZJmi50kSarsc4tD07TBYDCZ6sk/aAIiZMzn3INvIDoZrSw27JhvnrQBeDWbMRRFmc3mlultNQ5TdNPqQ7TJt4WqLjD/8SJtqBmZKkkl7uxDHL0Ez/wC4s4WDG1fR+/i4hIdHQ0A+fn5CILYo9IY446tNOFsAkEQJEnWazNJ0d+crziUcX9R3kf07ggfxybnuzI1Y+3xbpAkWXdkrZkSchGxwNqbu0v4AKAnoImWUBRl1TPc3cFbwj2Xr0UQ5J1E7zFRLkKUJtP2LlL86wpquO9Fab9edM9nad84tL5UbIqiSJLEMMwebqKuzQwcgPdGNCkKE8k5hdw9iChyaaMGALCSa2jXSRRHSBAEhmGtrJJqImteskTAtdjZkM2th3mfW/5jcQ2gJ61H9i4BvRxRFvHPrCbHfMrsrDAFY+1UM7au67DB+2PWm399lsatJ4i0utywbYZw4fF6VQOYwiORkTWJHS0rGFJ32NpPrVq16scffzQYDLNnz163bl3dV9oRC4/ExcXFxcUBwLJlyzAMsyr8aBPsWjOWpum6Nhtw6oNDuedza7z89FgPq928R1K3ZqytMBqNOI5b2ewu5hVVG3FUYJWXKy/DAcDTUdDEz0WtVlv1FIthy1NRr+3MTM7TfHEGWRWYPvDit854laUDFjqU0/9F1DumkWFxHDebzSKR6JEO6MS9ak8Jt5tPM75FdW1uBjRlPvYxeXsfAADGQzGMpnCkOAXdNV8wfYsJOAKBoAU1Y2ujwmtmpp7OIoudarXawcHBHpc9k8nE4/FaVTNWHEXN2GT6/QXA9VBwiX/rD+6gV6DNa8a2vuyt+dhHdb18DUYVfuYb7rDXrZothUegdQVDamP11K5du/bu3Xvx4kUHB4dZs2Z9//33r776akOd2cIjdkRtJJbvzWHyoRCA14b6PWs7RVw70T/IsbDauO1K2dJ4f0sjTtLbr1YAwIDWFaf1lPA2TYvY9scfT9zbSd8rt0SwowF9uENeRb27tWbw2lwv1qw6lOso4Pz9fAwT825viNSd5O19iMSTN+Y91L83cf0v/PQ61C2EkucSh96FkZ+1/hQFihpfE+Dy2FR6QqVhvDHvmfevBKCJiz+hntFY2LD2NqrZkPmXG3v23om6jr524RFbFQyxeurixYvTpk0LCgoCgBkzZvz999+1HX1rCo/Y+FZr/vz5nTi2slRlevmve4yX52LIR+NDOr6XB4DZvb0cBZy/b1S+ezD3fJ4qq0p//J5i/o6M9HJdV2+HZqUX1YWqyHA+uHCxZmMAlDMtpEcMf8Zm/owtNvTyFE2vP10EAGoj8cOF0ppWXE/eOQB4PcWAbAJxdTsAwpuyDg3sBygGHB4AYLFPou7hVEkqWtVanSkAYIK1ACCwOVqb7Q4WOYLT9zkAAKDxox/W3mx/bDA39rWhDdZ7JFaFR8rLy+tqzqxYscLDwyM9PX3y5Mm12+vtXO9T0dHRhw8fLisrq6qq+ueff8rKyhrp3CzYGX1TyaoyLNmdWa0nAMBRwFkzKbSHr+1XouyBVMxdOyVs5f6ck5nVJzMfiMV38xF/PjG0xXm7tE6On9tMpu23aBzmg+9P6GSuy7CP/EJsO4PYd1uWVWWI9hQVKU17bsumdHcPlQpri8+0ZnCCos9mK9MrdGUqs48Tv6u3w5BQJ0Qvp1WlqHsE6lGjhcKJGY9whVhEIuBGqioLq7wLof0aGNFEZp5EQ4ci/Ie+IbROTt49Ahw+rcgHvhh1Dy+sdgMARwHHWfiY/RK5Q16jytOpwhTaoMJPr4dhb7e3Rc0DQdDGXCZm/XHULTxSl9YXDJk7d+61a9diYmKcnJxGjRplwwiFx+zr1V5kVOhf352lMhIA4OXIWzclvFly5+1OjJfDjrldj99T3K3QV2nNAS6CWF/x4BDnFnp5wkxc+wO//LNlWiQHp3/F00c8MavgcH5xtnLVwdyPxofYSvtBayK/u1CKIrB8eMCtEt36M0XrTxdtmBZhEZ9pzeDFStPb+3Jy5Q8pwkd4iL4cyhMDQO3qelwRFjMBABChCwA0cidBZp82H3oP9erCm74J4dfo4dDqcuMvM6FW4fJSkOqwT6CWtNnjBILyRq8ybpsBuJFMP4SEDofQQe1tU3OQeICyuKEnUedAq5a6hUdqY6uCIRiGbd68efPmzQDw8ccf23Bzm3X0j+ZOue713VlMsHyIm/DrJ8OlzVHB7SAIueikrtJJXVs7DplzFk/6kik6CgAEyt1BjzzrOumr6T3cxdyN0yJe25l5Olv53qG8j8YFN2uPuiF+vFSqNBATYqTRng4R7qJ9abKrRZoz2crW+xUDTi3ZnVWqMsX5SZ7oLvV25JeoTLtvVt0q1b59UrcJQenqAgAa4KFXQclzgSnL1wBY6DDUN5YqSTX/8xrj62lNZY2Xx7icvs+hntFgUN++WQJVAAAxzs1Tz+8gIE4+3AHz8LPfAACc+QqC+oB9goXsAaff8/jRjxp6ljv4FasWq8IjVtiqYMiPP/64bdu2PXv2FBQUbNq0ySbaZwz/dTm6R3KrVLtkV42XD3cXbpoe8Th6edugqzLvfcv87xv3vTxS7Rc/G/nfMdcZjJeH+3uzvs78U1nVVwrVrT9ngcK4K7VKxMPmD/IBAAxFXo/3A4ANZ4vJhmt+NpHdt6pKVaahoc4bpkUMd1N0lSKjo1y3zIjoF+h4txqRO3elNZVE6q7ah9CqUvL2XkAx0rd3g+NyBfxpG1D/XlR5unnHK5Qs1/Tni2DSIChH8Nzv3EELsLB4rNukW9KxTPcesiOtfCHtBaf3s6h7BAAg6lLq9p72NqcZcLpNxoIG1PsU1nU8GtTfqtGq8IgVzSoY0kjhkdmzZwcGBoaGhk6YMOH9998fMGAAW3ikLbhVbvjfyXwDTgFAlKfo66nhjm0S79HhoCnixt+c5M3k/fUK1DOam/imm2f3WWmyhHCX2oU+PCW8b6dHns6u7uXXWhVfAPj6TDFB0fP7eUkduIDridv7exLGFc7ygmpjSVqRNwBVmEJQtWbEPAdOzDiaK9p6qSzYTdDL86GQTbWR+Ply2dhot0gPEQBcyFUBwIv9vaE01fTXPDSwL3/aRhRBXujvfblAvVM8fb76Ln5yDV2RgYYMRPgSquwOce132qTBes+mHRpNJ+YK+VPXm3a/ThVdM/32LJA4AGC9ZyJuIZYu14s1AIACHVN5EIhFzGbvYwaKcRPfNO2YDwDUte3Qc1pDytIdEN60Dfi5b4nrf4DZAEADAsB35A6Yx+n1dL39axceYWhZwZBGCo/w+fzff/+99lGNlzRpOv9Jt9U00isMH5woNxI0AMR4OayfGt4pSwA+EqoqEz/2KVWWVrN+wRVyB7zE6TMbEJQPMC22njx4qZhbb3tzOZ+rupiv8nXmP9XTEwDIjBN40hcAMIp5WgEAQOaeI3PP1T4KwXjmqAnbrpSRFP36YM/pvWs0RNVGYtGurMxKvQMXYxy9TIcDgL8zD9/xJdAUlX+JzD6DhQ1jgh2v40G8SZ/jh94nbu+BB9NVhNNzBjbkNah+VAo0V8gb9X/GX2YCYUIwLk3izOSXoUhpqtCYASCCW+VgVNN6+WOqHoP690L9elLFN2hNJXHnAKf71Pa2qBlwB7/CHfwKEGZKno26RzQuy9GpCo8UFRUtWrTo5s2bo0aNWrdunUgkAoCgoKD8/PxWmvV4kSMz/N+RYsbL9/AVf/VEWAdXI7ELhBk//y1xdbslruauuN9Jn+c9Eb9RGqIZ1VRqFeFr+slxkv7mbDEAdPF0OJguBwAO2dMn6lWMMgJAernOS3O3P32LEZ95cBjPAYsaIeSiH44LWXUwd/25CqFQOCHGzeLl4/wks/p4MX2ZK7c+dY+oIgMRe9DaSvz0Oix4gNJAMc9ioUPRl/eSWUl0VRZt1qOuwWjIQFQaRlGPFpukNZWmXUuAMIHAiTaqAIDSVFm+Q6fuhz/FYTkA0BoJzHaH0/8F885FAEBc/oXTdTKgj9svhcNDPZvkuztP4ZEXX3zR19d327ZtP//888KFC3/++WcAKCgoaL1ZjxElStPru7M099flv5z8X/TyVMVd/PD7lCyX+bMC3L5Bn7po6AE5ADklP10qW5bgP7FrPfncdWlZHGRqiYYJMz9+T3H8niVSu4elw3SE6k/fov16c/rOqnt4fJjz6kmhK/fnfHosX2sijmUoMiv1PXzFXz4RZlHr7O4jzi9XoJe+A0B4Ez8lLv1M5l0grv15wDgcAJjwWUTgyOn2RNPNZqA1laYd82llERYymDfuf8Ydr9BVWeTFHzjdJyMCJwA4dv8VJehOIi4BiNAG6vbtBRY0ADyioDKDVpWQBZex4IHtbRGLNdaO/sKFC6WlpY6OjoMHD+7Tp09KSkonToCqF5kWX7w7i7mp93Xk2mnFhqLpsznK26W6EpXJ25EX5SmKD3PhdhCtWorAL/1MXPoZKAIAaEB3IomHHKc90cNzfpCbAacuF6h/v1q++kSBVMwdENQED9WiOMhYX8nSeH8T0eDcOaLYCXKgkcCeQcFOq4Z7f3Sy7OszxQDQw1e8bkp4bU3m6bHubtc3C8zVBR4Jvm7dxMOXk1tn6M//eBTxF3JdprZU1JPWK2q8fHgCb+JngHIEM38wbB5D4wbTT0/yZ/9eQDjlyAwAEIDKQskiTtxbLTtRx4HuMhmpzAAAMuMY6+g7INaO3tnZOS0tbeDAgRiGrVmzZtGiRefOnav3yE6J1kQy8XYA4CnhfjbGu5U1mOqlUmteub/gXtVDUhuBrmVrJoW2eyo8Lc81H/6AKk9n/qQk3sv0z+YKon+bGS2gjI6OIgCI9RVHuAvfOZD77fnSJjn6FsHFkBk9G1voJxAJnvOIQbp6Cj0lvGKlCQASw12EXDRfYTyZWf1sb08BB/Wmq6bQp40I723ZqMotqWI+9hw1dBp98mVsr3T8h+4tLR1DFafW9vIAADyx4Jkfjdvn0gal8YcJhwTPAgwBgATyEtZlHCd2WstO1IEIi4dz64Awk1lJMHIlcJpRnJ2lDbAOr3zvvfcmTpz43HPPAcCIESPi4uJGjGiV4vZjBEnR7xzIZXJnXEXcNeMDpCKbbVZTNHx0NH/L+RKcpN/ck3uvytjV2+H9McE/PB310biQPgGOBQrj4l1ZuvYsKUcT1/4w/jbrvpdHOD1nJA/4NhXCx3Vx8xA/tCKfEO4S6CrIrNTLdbYXW7YVWhO54nBxsdIU7CbgYsj600W7b1a+dyjvx4ulWy+XAQB+6iuUMpNxc/p1iwhxE5IUnew+Q891Hkld7C9oMJvmkWARCfxnt/Imrq69uYd4RAle2otFjqScAo6aa9IZRg/pxxv3v05QdJvmitDAAQAAZj2Ze769zWGxxtqRzZs3Lz4+3jKL37x58+7du7t3797mhrUDX50qSilUA4CIh62fGuYjos3mVmVd1ubIXfmhdDkAUDTkKYw9fUQbpkcyyw5dvR2GR7q8ezA3KbN6Z2rVnL5etjppvaQUqt/ckz1voM+s3g9ORBlU97avCFKlMH8ijl680e+hgX2rUsoBwNe5ngmanzO/QGFU6HG3uokFuJ64vR+ImlsWqvgGNBAH2apNSCYesYGoRK2JXLwrM1NmivUVr50Sfr1Ys3J/zpdJRUxs2p/XKqa65DvmJCMST+ngOe9wH9xIETdfxY9/ip/6iv/MT1apUk0GqVfnB3H05E38LDmzuvJgLgB09xEH9+nVovE7IkjECMg5AwBkbjIWkdje5rA8RD0z1oiIiIiIB3FgU6dOnTr1cQqZahk7blT+e6sKAFAE3h8TFO4u0ul0thpcbya3nCthHu+5VQUAz8RJay8uIwAv9fdJyqw+n6eyt6N3FXE5KLIpuYSmYXYfLwAgS27Kd74VhMuZDljMBG7iMkanRcLHAEDx8LT9dql2zclCgqQAQMKvT6//fhzkQ431xUG2rA4fDTB/xz13XvSqUe9zoodb2jMr9SsP5E7pLp0Z57loV2ZGhb67l3DtlHAhFx0U7PR/I4M+OJIHAN18xOmlatOJLwCAE/c0rZfXHhwL6E04+VClt8i7R7HoMS0wr3H+ul4jQPhUXGeo0GQBCewHgADQVOmt9raFxRo2jh4A4HKBesPZmlv1hUP8WinoWJdtV8plOnxUlGuFxnyzRAsAfk7Ws+AAFz4AyLQ2u4doiFCpcN2U8Df2ZG8+V0JQ1CzuGfOp9RKaBACKKxKMWolFjwUAgqK/PlMc6MIHgKMZiufuX35Iil59opBZ4PJ25HnWF2SJRY3g4gYgjDId/s+Nyq50dkNxkC17CQgASdFJ+SYVGflll5paBJmV+kW7stRGAkEQgqKrtHifAMd3Ezwsu68ZlXoAQFFkWJhzeHWyu7YYAPAzX+Nnvq73LPiF7xtx9AjVkjWruxX6tDIdAHg58obZ+mvWviACR8Q1kFbk04pC2qBEhJ3q1T3usI4eipWm/zuQy+TTT+oqnWlr5eESlWnHjUo+B311sK/SQDz/+10aoFyNBz08n2N0MdsmJ6uHr3jtE2Ef/Jsadm4lQd9hHCHhGiaesgZxCWD6/H2jcmdqpZiPDQhyupivWrIr68XeLnFiyT83Ki0SYF19xPUvbXBFnLinAODDfzJvIJrpgPWnb5m8ekn6zm6KeTSAEacaL1n+9dTwxbsyrxVplu7OWjslvFhpXLwrS20kno7zZLSj/32xGwdDNOoaGYZipWnXzUoRD9s+K9rbiX+e7n3lTIyYCzFeDg1V+EB9GlyxpCrvCf96ieo1C4YsaMorsvDHtRox52k9PGwiBNShQH27k4p8AJoqvY110uKrjyn1O/qsrKzXX389PT09Ly/v5Zdf/uKLL5ydW3V9Zorn2aMSJpO60tIymGAmqBUHS5gt0B7ewnm9nSxGkiRJ03Trbf7qRJmZoGb3dBVQBi8+hLjxc+SmjRcqot0fmgvvTFUAQLSU15ozMu9GU0YINuduRT/j0zXLCPuQeEG31+JRJ1CpAEBpIH+6WAoAWhPpyKMipIJbpdol+7QcpJi4n4GNAHIxT1lUqWiohmJynvZGsSbQhRfNEUA5JOcoBsXUY5ilZqylptK3l2UHM1RfjfeNkDYWg/TxSK+VR0pSS7Tz/kyv1BJqEzklxnlurKT2y7d869YcL8NJenZPZxEYVSpj1/DgZZlvpVUYFwa4T4huOHCo/neS5hz/HCVM9NVf1YFDaaempjjmV5uTMqsBQMBB4gMa/KAJglCpVPaoMMVUV7bhzpMFkiRxHMdcwhmHYii4QUpts7HH1Iy1eq+0Wm1D/VnqpX5Hv2DBgoSEhEOHDgEAj8d78cUXd+3aVW/PJoIgCIZhTk62D8VrZSnBL5IKc+QmAPAQ81ZPjqgtC86I1bXS5qtFmouFOk8J74XBgQIOCgAfImuurwAAIABJREFUjufO+vVujtz03VXlvIG+zkKOxkjuuV21PbWaiyGz+vs7ObU8NM1oNGq12kfaTGYmmQ+/D7gBAHQg/AKdk4zGIeereQ6OY7u4AcC6C3l6nAIADoocz9L+9ExUWpnuTKYsvcJE4KSvE3/58ICkzOp9abKd6brahassmAnq52uFALA0IbBrmSuUw70qY7CRG+1pvfuK47hKpZJIJEwpwawqw750FUXT312p/mFmVCPezglg0wzHeTsysuVGAJgW6/FmgrUlarXa0dHxSoE6pVjn68SfOzDQkqywfAT3+T8yfr1RPSHWp1klq8iMY+aKNBrjIiQuuPYTb8raJh64/XQ2o8P2dC8vXw+Xhrqp1WqJRGIPRy+XywUCQevr8NWFKSWI+kYzEy6eScGz0Y+93lKC9ihK2rmp/+44JSVl6dKlzOPPPvvsyJHHVV2vcU5mVu++WQUAGIp8OC7Y5sUfLHWRFg31Y7w8AIS4icZ3cQOAf2/Jxn57c8Sm1FFbUjefK0EReH9MsP/D8S0UTV/IUzWSNNR8aOLKL+b9KxgvX4Z6pg/9JoXXi5lWf3ws/1C6PKVQfTRDAQB9Ax0XDPajaHrj2eJpPdzn93M3ERQXQ9dPDesX6PjKIF8xH9t1s4rJ/bFi+7WKMrV5aKhzv0BHPgcFABpg/emiRwoyrT9dRNG0kIveKdcduStvvHOZ2qTQ1UTyZFfpGfk5KwiK/upUEQAsHuZXOyUtwkM0PsZNbSS2Xiqre1SDECb87AYAMMW/C05+ZM5ZMu9CU45LL9cxdYbFfOyZuMegMFkLQMQ1y5G0trJ9LWGxon5H7+7uLpPJmMd5eXl1K5p3AoqUps+O10g7zB/oY49yUbtvyXJkhu4+4sSIh6Zvbyb4eYm5AODrzKdoOsRNOCFG+suzXYZHWM/ytqdUvLknm0nstAG43rxnOX52A6Ndc43THZn5y9C+PZl8UYqmAZBPjuW/sScbAELchF9ODnuqp3uIm/BakeZ0tnLD+UqSpnGS2nGjCgBcRJy5/bxJil5/psjqPFVafHtKORdDXhviC1ATAekoFt4q1SbVKnFVl6Ss6uvFmiBXwdop4QjApuSSRhILsqr0i3ZmqYzEkz08oj1FqSXaN/7Nquvrd6ZWFlYbHQWcAoXxt5Ty2v8YZYtdN6vy5A3Uia77Fl75hVaXoeEJpH8/dNACAMBPrwPq0YLym5JLmIvc7D5eEkHnVNRAxO5MTgCtYR19x6L+Oez777//9NNPA8CSJUt27Njx3nvvta1Vdoei6Q+P5DFOZGCwk0XlyoZoTeSPF0oBQG0kluzKqv0UTdNMfDYXRU68Fos2cJMu0+LbrpQBwN7bsind3cPdW3XHTWurzLuXUJWZAEADsoc/duAzK4LcRADAKMAs25PNeEmKpAGgm48DB0MQgKXx/ot2ZX5+okBpqHFnu29WPdFNGioVzoj12HdbdrVQk5yjHFIrhmRTcrEBp2b38WISfZkifHGivj/tKdpwtnhQiJPl/qY2ZoLalFwCAEuG+cf6iodHupy4V739asX8gT51OzNe3mzUvheQM3ZItJbyWbwrk/H1ax/WOTiWUQ0AaiOx+X6EqxUERSdlVb/o9mjxSFpTSaT8BhiPM2QhUICEJaCB/aiCy0TqTk5c/dq2DMk5SkaUWOrAbTzd9/EG4yJCZ1qvYB19R6N+Rz979uzo6Oj9+/fjOP7XX3/Fx8e3rVV258/rlUyUm1TMXTU6yB7RDxUas9pIAEC+wpivqH/CWKo2a01kQxr3m8+VGHAq0FVQoDCuP120aXpEvd2aAi3PM+1aTKvLAIDmCk74vTYoYUrtgtRxfpIPxwV/dDRfbayZQe+9LcNQZFliQO8ASU8/yY3imhp4/QIdLxeovz5T/M2T4VwMWTzUb9ne7K/PFvcPcmIWRtLKdMcyFK4i7nOWyydXhMVMiAMYGqo5m6P841rFC/3q8aq/X6soVZmGhDr3D3IEgEVD/c7nqn6/Wj6+i5vfwytaNMAb/2arjMRH/umD8r4j7gjFsdPXTQ1ftDMrtUT77fmS2tsGK0cG3ilvLCUCRSA+rEmxBviZ9YAbOP1fQJz9QaEAAG7Cm6ZfZxIXvseixzQUUGjAqbWna256XhzgU+9Frp3BjWTmCTRsmKXwIQOtraIKU7DoMc3I3RU6gV4BuL5uZS6WdqR+FyOVSmUyWe/evQFAo9G4u7tXVVW1rWF2pLDa+MOFmkp4yxMD7FSXOVQq/OeFrhpjPSsPFEWZTCahUOjmwG3Iy6eV6Y7clbuION89FfnaP5nXizVJWdWJ4Q3u4DUCVXLT/O9S2qgGAETkyp+6fpKXtSirQo9vPlfCePkunqLMKgNJ0btvVin1xOgubvcqahylhI8RFAg4aEqhevb2dBchFwA4KFKiNO1MrWQiU5mFeAyFdw7kWp2lWo8DwPaU8kkxUunDSjJVWvy3lHIUgbD7kTYeYt4zvTx/ulT21akiLobMjPPoeb+SCQIwKsrVUcCJRzPw/Bq5NCcBZ8O08LWnivoE1AjQXy/WXMiWvzosqIU3Qw+rK1Olt8iM44jIldt3jmV5CJWGcLpNJm7uJi58zx1evzbZz5fKytVmAIjyFE3q2hFXQcns0+bDH6CeUbzpmxFBzbtHq8tNO+bRqlK+kw/qG9u+FrK0Emsvw4SvmEwmSxwLSZJ9+/Zta7vsBkXDp8cLmO3NsV3cbJ4bVRtfJz7UF3pAkqTRiDg4NJj9b9m3XDDI10nAeX2Y/6Jdmd+cKR4YXP+iRyOQ2WfMB94BwgQAiJMvf9oGS6S8BZkOf+2fzMJqI4YiJEU7CbndfdDrxVoASMqqTsp6sKquMZHXimoi07OrDAAPtmEZJTicpAuqjQBQpcWrtPWnFBlwqlhlsnL0314oNeAUF0O3Xi4XcDAmP2t2H699abJL+SoAiPMT96xVsmrRUD8AIK4+NLKTgPO/scHMY62JXHUwT6HHfVzEU3u0RIfyIXVlmsKTvgSgucOWAM8BaunRc4YsJO+dIFJ3Yt2noO7hVoPkyg1MKiyKwLLEgIaW6doXLCwe9Yujiq//P3vnHd5U+cXxc1dGm3TvvVtKKVj2KpW9twiioigiIKI/wIELAQcKylRxICCj7D0LlFWg0EJp6aB07z2SZt35++OG0JHulLbo5/HxSS43975Jk3Pfe95zvl/y4EI+1uuiPOY7vIF+Aj089T/qiO/0X0vtQF9QUAAAPXr0iImJ4bcgCKJbmH0OOBRTxPemWhkTHwxprclLG3EuoTS+QOFjYzSuqxUA9HKRDvY0u55aERpd+Ia+pEd90LFHqLDv+aVX1L6rYMoGxEjPPcGOyPyscrWfrVFSoRIAbmXUW4YvEaI7ZvsDwDcXMu/nyF/tZTv5iZavvYkQAAgMOfBGAO+dVP9BsFqpmKRizYWkcnMj/KvR7itOpf0akctw3Jt97YuqKP6SLBHi07pbA0CJgorOlo/wtWi02ejvyPwyJQUA227mDfM1b1YBpZZq6spM0gVe6426vI4KXw8AxhzHIgifkuNIJXAsfX2rYOqG6gdgOfjhUhbNcgAwrbtNVzvjZo+hLWELEjhFCeYZDIRIOG2T5ugHbFYUeeBdYswq8vgyrjIP8xkmGLfmOdBc+w89MsUAEBcXt2PHDr5JgSTJ9evXG1D4pR0pV9J/3HqStBnm0jENYFUU+0tELgB8GOKsC2dLgp1uZ1TuvFMwxt/SVipQUWz44/IXvc0baB+l7x+gLv0IwAEA5jFQMOF7IPRnMKb3sLE3FU4LtI7Olmto9sD9ogd5VV7WRnkVGiXF4ChCsxyCAMeBjUToYCpEAFaMcH1lV/yR2JKXg2xruaWbG+Hmjal+amj25MOSoT7mvAr0PzEVHEC5kv7giHbV+vebeb8/Sa8BQJWGvphcPqaL5benE+2yL9gkibs5SKB+ubQCp2EHY4rEBPqCg9HNzKrtt/P1Fvs3A0KEiE2hHrtORGAEAFDHPGT/vULtrEJC8ObmHQdOLSMPL+bUcuHsHaidPxAi4ZQNfKzX7H4NGArzGSYY/03D7np6YBkA+O/a0NHQ/1ecO3cuwzBxcXFDhgwJDw//7bffnvGw2ojfb+ZWaRgACPEya9OkTWvYeSe/pIoa4WvRo1rFp6OZcMYLNnuiCrdF5H052u1MQum6y1kqip1WT1KCjt5Lhf+sjfIBEwQjP2/A4M3NQuRmIQKAgR6mVRrmq7PpJiK8UkkrKWaEr0WRXPMgT8FxYCLC0kpVv1zPKZRT+TKNnYkwu1y95Vr2yjEe9R25PhPB7bfzd90tuJ0pWzfJCwCcTIlS1dMYSjJsiYLmS/uNCMzcCEcRsDImLieXm2VfXcyFQgpQKU+PVlcu7bpNBcW88HY/hxBXYWyB6vCD4kndrDwsW162hHmFYF4huqcsy5aVlZmYmAgE9fopPi5W/RqhrfNZ9qJLRzMpoyN+41SVAEBd+lE4ezsAAoRIMPxT9a5XgNYgQgkx7KNmR3kATlEKAHpvHP+jHdH/hzx37lx+fv769etNTEzmzZu3Zs2a115rkkpJR+ZxserEw1IAIDBk0eAOmrTJq9Tsu1eEAPRxlfKayToC7CUEVnQusXRqd2uSZgGArKeRio7aTV3R5hDwwCnEiE+bPsPKKFPTLKehWZmaHuNvOdjDbMWpVAJDCAzhl2p3RxVW3/9CUnkvl9LxXfWvMeo1Ecyt1Oy7VwgAEWmVtzNkPR3FC/pYmJub852xAJBdoXknNImv5pzdy2ZuPwf+zc7cGV+BBrlLuHJ5VTd7yWBPUzbnPpN2o5ZcWmYV9scDdwdT4cwgG7Wy6o0+9luu5/x8JXvztMbKlpqurow10olNMdyqc+kUwwHA+K5WQxqs6qGj97LFKYJhy2vccjEkdWkdYmqP932zkWE3H7YkjX5wGBFKEKkNmx/HJJ7DuozhZAWaw+8DrQEjC05ZRh5eLHjp12Z5HHIaOVBKAECkz2dHWOdFf6AXi8VlZWXOzs4RERFz5869dOnSMx5WW7Dleg7LcQAwK8jWSZ/AekfgwP0iPnx/c6Fen97dUQXdHept7yIeHqSi/uIf44FTiRGfNOs+mhd309DsGH/Lz0e6fXQ8BQAohuNjVl04gB8uZw5wN9FvxaXPRHDT1RyK4YKcpPdy5BuvZm+fWWMBM7tCs/Tgg77KOwqXIfcKmT9u5SMI8mZf+yettnYTRix86e+H+wvZXSO6uKI4k3YDdemN95qtG/+XuxNVoPoy2EmAo2qAGS/YnHhYEpUlv5FWOcijobDVdHVlpOv4Bo4DAFuu56SUqADA0VT4YUgjswo2K4pJvaapzBVO3aCN9TRJnljOpN9EXXq1RaCnr/wMLIMPeAe166rZ9zZ1dTNq20VzeAlXmYv5DBOM+lJzfBmbdZc8uKBZsZ6Ta2vzEEkLXRj/o43QH+jff//9/v37X7t2bdmyZTKZLCAg4BkPy+DcSKu8kykDAAsj4vU2FnxvDUN9zEsUVMM6AWO6WGaX19PJGRMq0EX5oJnE0KXNLX5wNBMiABZGxIoRrigC8wc68j3DcXlV19MqAWBSNyvHamo819Mq4vIUofeKFg5ybMrxo7Ll11IrbKWC9VO8Pj6ReidTdjSudKSb9iKRXaFZdPDRAPn1Jew+3NMmccDYD4+m/H4zT0EyRx4U8622ZmJ8bl/7TddyNlzJ/tmt9vEPPShOK1X1dJbqSuMJDFkc7LT8eMqGq9l9XU0aMObVqSvzT/XeLvDqyg1LUkSkVx68XwQAGIqsHONu1FjShhj7NXdwEZsdrTm0WDh9EzAUdWolk34TsXAVjFvT8GtbAJNyhcm4hZg54z2mAybAfIcxjy6q97wJGjnmO0Iwbg2gmHDKT5ojS9jse+ShRcKZvzfVH0bxX6DvoOgP9J9//vkrr7zi4eGxf//+W7du/fRTU2WbOizbb2tX9uYPdOho2dLqBDpIAmvO1itU9KarOeMDLIOqFRfui1YDwIVHZcN8zXUmf0z8Ke7GVv4x3ms2EfJhCwZgZUwEOUujs+Xbb+fPG+DgbS3mi9Dn7EkEAHMjYvlQl+r6usN8zKdtf3gzvXJad2tbab0Ja55a4j9Lhji9vjtxx93CfvYO5gBqml18KLm4iupuK4B8QBgq0EGyfrLX/44+PhKVGczdd+w12sVcBJRymvDOOXOHqGx5mlRVfY2VF65BEeSDmkuvgzxM+7mZ3M6QHYgpmt2ADPUTdWUeus7tQrV3Um+oz67QrDybzl+q3+xrH2BfX6UNxySHMylXuJJUwHCwcENJBZsbozm4GMdFTFYkYuEqfHkbYmxV72hbBkNRVzcBADF0GWACACBCPmRSroFGjnkM4qM8AAAhFk7dyMd6tjQDrdN4oRe2ROvhi5g26ar/H8+MehdbPDw8AGDEiBEjRox4huNpEyIzZYmFSgBwNBPygmKdiJwKzdnE0rBHZWOrNYjeSKsEgKRC5Z8385zNRQDgXnm3Z+wafvUVD3pZF+U5gPh8hZ+tEV6zIJFiuORipd6Cv/+96PxO6KO/I/NvZ8h6uUhxFHmYr0guUgLA4mDH6lG+TEn9eTsfAFJLVJP/jLMWUgstYga7CIVPiv1rpbnj8qr6FFeONDUd6t4FADwsxZO6WR15ULznQcUKO0sEwESEDXC3Hm5iQT/RGTMWYASGvkjeXsLuY42sAbzo+NPMxbVfBC15rdz/emrlK9VGvu1mXqWadjYT3kqvvJVeCQAajUYoVAKAlbEAAHZE5o/pYmFAw3e2IAERGCEWbvxTFcV+ciKVX/Dv6Sx9o757R4YkT65gUq483ZIfDwCIkQWb9wABQCyc2yTKA8CDA1x5FuraF/MYyG9ApLZ4n9foW38BIaqxYk+IhdO3sCVpqK1fE4/NFiTyD1BbX4MO+j9aS+1AP2jQoBs3bgwaNKjWdp2LbH0wDLNu3bq7d+926dLl008/NTJqhReoodkRqQ0br/Wy63RuDwH2xiN8LcIelZ14qKeb4WR8KQD4Q9o4ZgMAAwC0e4j4xaW6HSLSKpcfTxnobvrdBE9d1kJFscuOpdzLkf86w7dHHTU3D0vx1pd81pzPSCxUJD7piRXiqIZmnc2eLkIWyMh3DzziS+bFBOZpJfIsvDgkZwfkQK1GKV2a2w/ADwDKgU1y5k0E5w9wuPSo/Fxy1cu91D42xrte9YdqbVAcwLrLWTI1LQAaAIRAA2gz/m4maH830+J0AHhqG8srpmVXaOqTtanSMJGZsjFdDHSxr8jW7HsLEUqFbx1GhFIO4JsLGbwri61UsGacR31fNurqRiblCmLuQoR8gDoEAkOx2VHU5XWcsky7h0bFlaUbPNAj6gqI/gdQjKj2DQEAou9cJv408+gi2+Me6hz09B8wQdOjPACwBfH8eRDbLgYZcFuQk5OzbNmy8PBwlUrVo0ePlStXDh06FABEIlFMTIyfX5Per5OT06lTp3r06DQNw7UD/cqVK3X/bxZXr14FgB07duzZs+fMmTPTp083wOgMwf0ceUxuFQDYSARjO9t0nufTEa4Uw11JKcdRpL+7SWSGnGRYABjobtrdUWKqSA+J2UKABgAQ136awcuk1VZfuzkYu1qIItIrPz2Zysd6XZT3sTHyqUcbwNfGaNdr/qklqtQSFUmznlbimFz55mu5B+4XBdhrW0+/v5hZKCfdLEQZZeopgVaLg50UVY5njyA5JZWeluJRXSygZpr7emplXH6Vv51RiL+TzkTQRITPDZJm3Dhy//ilGyTbxdaot4uJ7j7gcaGsa255VwBfLgMAUopVecnlDsUqV4CUYlU3B+N/MvqxAvG77iMtAADgx0leKTU1k9VqdXWvAiGGDPfh9wVOU0UeWox5DcH7vlH9Jczjq9TlH1B7f05eCgCcut72MfbaRmAoTllG3/qTCPnwnzsFl5LLAUCAo99N8KhPWoNTVdAxhxCRiXDmH4ix9gvJyQp4jQrtU0WJZv8CvNskYuRnBqxJJ6K3A6lAHQK50jSmtIZABeoUxCScocLXCV/b3bIzcpoqriIHABBz51qaOR2Kl156qXfv3vHx8SiK7t+/f8KECXfu3OnatWt7j6ttqf1dHD58OAD8+uuvBw8eRNFm/L0fPnw4cuRIiUQybNiwvXv3GnKMrWNPtLYccHYv2wYW4joyYgL9boLH/ntFG65mX0+thCfKYj2dpTO7EJp/1nC0AgBQh0Bu9GrQ1FDXMRXhv77k+96h5Ij0yo9OpHw9xv2zU2n3cuTe1kabpnk3sE6IAHhZib2stFcCNwvR3ujCsEdlGAozg2wJDInMlEkEWGaZ2liAzQyyBQBjiXTcKwum//1wfznVPyDQwojQpbmz3ad9cSuBQbh3PB1OYQQkKQGU/JGdiyMmcKHAh9MMoDK0A2DSbrjBjXnVhnQmsfRgUtpLXOkC/jGSByA6yfR1eqR6vY8pAATYG9fKifPGI/rfIUNyZenU9TiOIYkB7/Db6Bu/ULf/BuAYufZrQ0f+jWAE3n9erVdjuVFcxk3ExJ5TVdL3D0SYjd92U6v79vEwly629TbBsjn3gWUw76G6KM/En6KubwUAwHBgaHrIcuL+bk6WT8cdB7EpEfx+fYdqHpQSfxwGAGxeLFmPfzdblMzmxqBOQXr/tREK4rU92B14Oq9UKm/fvr17924rKysAWLBgwbFjx86ePTtp0iSNRtOlS5e7d+/SND1+/HheDoCmaYIg8vPz7ezsdu3atWLFioqKirlz5/JNHqNGjerRo8fatWsBICIiYtSoUcXFxW3h69J69E86aJo+d+7c2LFjm34gnbGRVCpVqbSzqmvXroWGhgKARqNpFyvBEiV9K10GAFIh9qJr81z6DGUlWBeO41iWpenGRcyr4yrlBChKsiyGInz4pVRy1eHViLwQADhzN/XwVXzBd60xowDfjrT7+Gzu7QzZ9O1xcg3rYSH8ZqQtaBSVzXFg/OpFm5WXC88llp1L1GYYqkhGIkQ/H2onYJS6c/awE11MoR5klAQ5GmFqNQagVqsPRufyhZvV+115xOAxGpkpQkhrY1ymZjQMN1qS6ix7UELYy2m0EqSOuFzEVkmZyklwY7xxipQsAjXMEtwcI8osFruzKO6tNJeVjuZwPT8w3pavnjeEIWN/JM58RN/8XaOQMX3mobH78cjtAMDZ+DPdZwAA+vgCknuPitimZlCmW7WbVJYRRv0BAFS/BUh5RmLU1ZVXylkOA4CJ/mYDHfEGvjZoeQEOoCFMnnxkHHFxLQLASexY2y5YajgjsmQn/0qcWIJUZNJ3dyv9poKBJshcv0WYoqgh7ypCLBc712Og2BAMw3DJV/hZg8bKX2W4X41hrQSNjIwCAwNfffXV+fPnDx482NPT8/z58wCwbNkyXerm9u3bdV+YkpIyf/78/fv3h4SErF69Oi8vDwAmT568efNmPtCfOnVqzJgxHTPKQ32BvrS0dNKkSQEBAUKhdvVP75uvjkQi4T99uVwulXaUG7fzyTK+dn6Yp0TQOafzPIlF6s/O55Es28vRKCpXeT5ZDgA90/9CCuMBAIRSeuQqEErrqwYxE2OrRznMP5wl17BiAl090r4+o9cG8LAQ/D7F9XRSZUKxOrVEU6Kku9iIvhhqZ/FE8IDlgGE5fiW2et09w3Hj/EwEOFKPggCw7GQGRd1djAkM+fRcnrd8mzOAFZWvTVE/Sfk7sPkg0y63mKlzzdS5bhV3AABygTESM76jm/uOOCsfauwPxJmPsAehiKIYTQkHANZzKD30M+3A3AYjpanE8ffQqB2s3zjuSUMTlnAMKc9kHV5gXQfmmb7wxf0ADYcBQB9n4/l9GksPis0BAJ54MCEV2QilAsKYmrwFv7QaAFiRKSaUUhM3EofeQpSlaP4D1q32mlnLoH3HcRjWrDv1poNm3QIAAIRz6dcWxzcUYWFhmzZt2rJly7x588zNzadNm7Zu3Tpj40ZkiHbv3j1+/PiJEycCwDfffPPLL78AwKRJkxYtWpSWlubh4XHq1KkVK1Y8izfQIvQH+u+//173mOO4tLTaerN1CQgIOHv2rIeHx/nz57t168ZvDA4ODg4OBoBly5Y9e89YDuBymlYHfGqQo6lp8y62BvGM1QvDMGq1utHvlo6H+YrPL+QrKfbt/g5v9bPnczjTuIsehWEAACgmnLRW7OwP9XvGqml2U1iKimaFGKqi2M23y9ZO8BQ0UwhTJpNZWpq8Y2MOAImFyrl7E4UE7m7/NK59cSbtXnYVb5/k42hhaiqiRSIK4EBsRVxRxaZptZUdeXjPWF1n7ObpkvC9zkDfzUTsXbn8u0hXBiH6mFSgFRlZiH0Fbt1dKuPKMlALN8TCDbX1A4wAgbG461i9td4NpW54THuzM34h97+LplwCAMTY2njKDzV3CCJ9hzMJZ4wrkzHPYADg1DLN/d0cguIhH6pwo88uZlVyxgDgi+V9N7SnkXntJli2OBk1dQSB9s/NeQ9QXySwjGvGIYsQE3tWRmkAMK9gKafQFMQhxla4jbfUxARBTOmeL1PXfxFzKtxAX8I29IzNjkPkBQCA2nUxcfA04JEN7hlrY2OzZs2aNWvWKBSKsLCw5cuXf/TRR1u3btW7M8NoE6GZmZlubm78Y4FAYGNjAwAODg69evU6derU5MmTHz9+PG7cuBaPqq3R/1Pv3r37/fv3r1y5cuXKlbCwsIULFzZ6oODgYJZl58yZU1paOmrUKEOPsyXczZTlVmgAoKudcSvtmdqR3ErNB0ceK0jmrX72b/WzB4CXg2zedMh+l9XatRMh/0NdGtKRVtPs8mMpUdlyb2ujHa/5eViKb2fIPj6ZWp+CQlPwtTFyNBPG5FadTXhq6+piJipTUpllahczIS+eU0GhAFCqQVzMm9qK/LhYqWIxAMgFGwCIQvxXIAsuC4MB4KHF8A/YRbHmwwEAC5wimLwO7/9rdMaRAAAgAElEQVQ23mcO3mN6Uzt69EJrOPbJwoZITwRBLT0AgJMVaHe/voVTy2i/8Qqp+9JjKfkyEgAccdl35M/oPy+zxTXcxOiYQ5qds8nL63VbEJEJ3vMVIJWa0HlMwhmOUgIAW5BAHl4MHIsPfEe3FspVlfD7t/ytPSuQDK1xLuZhmJuPNuLkyZN84TgAGBsbT548edGiRffv36++D4qiFKW9i8zO1s4U7e3ts7Ky+McqlYpX+QWAyZMnnzp16uTJkyNGjGhkStGu6A/0c+fODQ8P37lzZ0ZGxp49e5oiaobj+Keffnr48OEvv/yyAaWnZ8nFJ/akEwLaoB75WUHSHIrCOwMc3u6vlT/klGWvlf2KAQsAVV7jq/f46Hs5u/RoSlS23MfGaPN0bzdz8cZp3q4WotsZshWn0ngF3RaAIsB3Tq0+n7HsWMo/dwt23Sl4+MTIqUxFp5SoCmTk+wlea9E3KJ8xTRSPPBVfojPy5aXbjQWYtYR4XKwCgGBPMxxFImtKALUSNjdGc+h9oNWY7wgA4ErTee/v6nCqCgBAhBLgVWLijiMik8qusz86lcG3F5iJ8Z/GO5shco5Skfvf1cV6OuYQdXEtYATepcbUhxi0EOs6jpMVkGe+JI98AABceSanluN95+KBU7UnVcuYRxcBQWv05XZUkMdalRTUM7h9R9IwwcHBFEUtWbIkMzNToVBERkbu3LmTzzrgOM7bKzk5OclksrCwMJlMtmrVKj7TNXPmzNOnT589e1Ymk61YsUJ3JZg0adLVq1dDQ0NnzJjRju+rUfQH+nPnzu3atevVV1/t2rXr3r17Dxw48IyH1XpYDviWGRRBQrw7kFClgmQSCpUPC1R6zafq4m4purCgx5tPZeg56uxKUJQCAGofYD3hs4ZffjNDpqux4TXZrYyJLdN9+JrLmJwWLmoBQF9Xkx8melpJiIj0yl9u5P4akXsnU2ZvIgjxMqvSMIsOJs/bn5QuQxm/sSvGdmlK+8K52OzE8ztmsue7cY8BwI4rBgAfTcJY5ekXuEcAkBF7fRJ3FZiGxO6bhTbKU0pi0ELB2FWIQAwIQt/ZWSPW0xom+RIA8P4b1OUfgGXUbkNWhpfEFygBwAiHH/tpnNAy3oaJU1eS++ezhYl07FHq0g+A4YKJ36OufWucGMUEY74WzvgFf2EG6twTMXcGAMTYDLXrwmmqgNawWVHk/nc5ZRkWML7jywmw+XFQlgYAiKVHs+runz2mpqYXL17Mycnp27evtbX1vHnzZs2atXr1agCYNGlSSEhIVFSUg4PDunXr5syZ4+3t3b9/fz7FGhgY+McffyxcuNDFxcXY2FinCtO1a1cXF5d79+5NmjSpPd9YYzy3omZJhYoSBQUAgQ7GLTGdaAMK5eS6y1kRaZVPZtGZPZ2lS190cbdsRAqxOnT0Pib9JgAAYSQYuwqwRpo8B7qbfjnabZC7GZ8657EyJn6b4RuZKQtybnmuEwAGuJsentstLr8qrVSNAnhYiQPsjTEU+fZCxqn4UgDo52aycrR7U6J8epk66uKxpWyobosblwsA/bjYfpS2FjBAHRMAMeHQuzVj1sEpSrVRPngx3mcOAGBBs+jb2wFB6Ts7URtfzG8kV55Fhn3HyfIxrxDEzIktSGCzotSI4LNk73gEBwARR64hN3teTK5WvoRwahkZ+g5HqwHFBRPXYvVMclGXPtqcG8eSF75h4o6Tx5cDAIGgJF+n6NJHMFS/PWGHgn5wlH+AB05u35E0BV9f38OHD9fdvmfPnj179vCPly5dunSptqdswYIF/INZs2bNmjWLf7xmzVMNogkTJpSWlnbkvA08x6JmEWnaeqxBHh1iOp9XqXln/6NSBWUlIbrZGQPHPirRRGfL54Um/TrDx9u6SSlmtiSFur6FfywY+WldU8C6EBiitxHUTIyP8rNo+LUcwIWksvOJZWmlKorhXMzwYb5WkwOtq6spEBgS5CStrsNTICOjs7UV5UmFyvQyta4YvwGsjAjGe1i2SOphihTJySOxxYGQ0puJrXLof1Pj3pPIsCy4GYm/ENhv2BCg4MZdXTdsi0EIMerQDfMchAdpf71E/3lc8WMm9ToAkOdWI5fW8ortqLU3MeoLAEAt3bmgV1eldrlfZQUAQoT9zi22p3EAwNMfCCKxZHJi2Ky7AAgR/F59Ub7mUFDBqC8YrxAm8SxXksKQatzGG/MKwbqO6/gOHpyminkUBgCACTD/ZhRkPwdQFKVWq69fv75ly5b2HksjPLeiZjef+OENbFCZ9pnxU3h2qYKaEGC1fKgLCqxarUYF4nXhWWfiS1ecSvt1hm8tnyY90CR54hNeAADrOh7rMqZNB8yw3Jdn0nnDWBxFEARi8qiYvOwLj8p/nuJVnzBcgYxcePBRvowc7mtuLiYOxhQtPpS8ebpPo7FeKsK+muAP4A8APx59fBtkfdwtICXW3KffpF6zgVIePXJgc573FNJ1cX8LRmqO+Qxt7TsUGAlfqllrgRGCyevpuONM/GmuJJWjNaidP+YVgveaDbgQAJSc4OOysVFVcgAQYMh34z37edS+vaBjj7LZ0YCgwLH0rb9Qp6AmNhBhnoMxz8EAIJPJxFJpQ9XuHQkm4QxQKgBAvV9ExB1iUvXMuHbt2vjx4998882+ffs2vne7oj/Qb9y4cfbs2dBpRc3UNMsv39lKBXz5R/tSqqBuZVTaSATLh7oQGMIwcCKhYkdUikxNA0BOhWbSH7HDfCyWDnVuIMtE3f6LK8sAAMTcRTDccHf09ZhA/R2Zf/lxuZOZ8ONhrt0dJRgK99JLfossjcurWnc566vR7nWPlFuhWXQouVBOju5i8cUoNz5U8bF+y3QfzybM6wHgemrF7QyZo5mwu4OE1dlIEUZDJsze+nf8gftFk7pZuTQmB99yEBQPnIIHTgEAAK66yHOlmv7wSAov/kNgyGchNj2daie+6NijVNh3gGKCid+zmVH0vX3kwUWCl7Z25GbRVsHSdNRu/iEa0AnyNoZl2LBhuubQDo7+G8Nbt275+PhMmzbt5MmTzW3gNAgVKjq7ojldmzV5XKTk+zC72HYIbbXMcjXLwQtOEl6DYeedgk03CpQkM9jTLMBeAgDGQizsUdniQ8kqSn/JI1uSRt/dBQCAoIIxK1tVTVgTOv40eXYlHX+6+kaK4fbfLxLg6Map3r1cpASGoAjiYyXcOM3bypg4n1hWVKVnRfSHy1m6KI8iCALw4YvOL/WwqVDRq89nNGUwFMNtvpYDAO4WIl6hKDpb/s/dgn/uFpyOL3W1ENEst+lqjgHedpN4GuWLq6gFBx7xUV6Eoz9M9AxyqD2BoB8coS58CygumPQj5jmEGPo/PGgmp5aRhxbr9HufM5j4M1xlHgCAbRekM1QH/WvRH+hDQ0NzcnJmzJixfft2Ly+v5cuXP8sx0Sy36GDya/8k5LY01icUanVUGpAceZbwRYwoigBAboXm7zuFYgL97WXfHyZ68suhiwY79XKRPi5W7Y0u1PN6jqXCvgWGAgC8+zS+/MNg6DOBSi1RVWmYICeJg2mN+ndjARbibc4BxObqMYuf1t363YGOfJTnt/CxfskQp1kNqMBXI7FQwV/gb6RVRqRXAgBf0sP/l1CgAICb6ZVVmiYVLBmKvErNgoOP0kvVACARYhunefdx0dP7TV3dCBghmPTDk1pyhBi6FA+ayakq6Mgdz3LAzwiOpe7s4B+yQa+361D+oxHqTRQYGRmNGDFCoVCUlJTs27fvxx9rW6y1HYcfFPNar5uu5ayd2JIuu0dF2kDv1zFm9K7mIgQgNreK5bhLyeU0y83qYclrwd/LlgOAj7W4t7Pr9O0PzyeW8l1R1aFjj7K5MQCAGFvhgxtvXms9CpIBAHN9uu284EGVRs99XrCnWXCdPxcCwEueNYUAe8mqse4KkgUA52wbSIAhfjYezq7V97GREJLm6ze0mEdFyv8dTSlTUgBgaUxsmOrtZSVm9UlNCKf8BIS4pkcHQgxdijq98FymbpiEs1x5FgCgNr6sW/+WHYRTy9i0G2xJKgCHWnqiHgP/bYn+Z4P+QP/7778fOnQoMjJy/PjxX3zxBS9p+WyoUNF/3c5DEcTcCL+WWhGVJe+lb/bUMOml2sSZb8cI9NYSrW3TL9dzK9Q0AATYiQFgb3Thw3yFm4XIz9YYAbCRCnIrNQzLVa9H5FQV9HXtmiEx7KNnIAC77WZekYwEgOqGhVUaZu2Vgj7uZHa5BgCsJG3SE4ciMML3SS2Q38uMq3VPn6E9DZen0lLPskRdrqdWfHU2nc+nOZgKN071bsBtGHXuqW8zgvkMa9VoOyYMRd1+YlrZ/226mY6V2mPEnyYvruX9xLUQYsHQ5bxXwTOApuk1a9ZcuXIlNzfX1dV19OjR//vf/9pIC6h90R/o9+zZM2fOnMOHDz97ebLfb+bJ1cy07tY9HKVfnEn76UrWP6/6N9ctpEhOAYCxAOsgFfQAsGyoyzv7k/ZEF/L17McTyrdHlT4qUgpwdMUIV/7tMRyHILWrLejb23mlcswz2AClJk3gVnrloyKlmEDj8xWRmbK+riZVGuaDI4/jCxQkh97JkosJNKjOOqThIYywtll0peNPUxfXEpQK7/FSA7vtiy7ccj2HT7t5WIo3TPW2lrTamqrJ15gODn0vVDedx7xDQKFs9CW1YB6Hk2dXAorigVNR5yBAEDbnPh17jDy/WkCIML+RbTDqGly7dm306NG61dSUlJRLly6tWbPmxo0bnbGgvGH0x0HeReTUqVPjx7dZeYM+0kpVJx6WSEXY2/0dzMT4kVjp/Rz50biS6d2b0RxIs1yFigIAA/wsDYebhei3Gb7fhWU+zFcAwM2MKgDwshJ/PNyVl1BPKVGVVFFeVmK0WqTnKvPomEMAAChGBC82wDgoJR13Uud/DXXc/gDgJ0/h+6RXagWLAHx0InV6d5ub6RUZZWobCR6TV0XS7MJBjo0aXndo9C1LVIfluJ/Dsw890Fpd93E1+Wach0HyRU28xnRwOGUZ/WQ6TwQvbq4BPQAAx1LhPwFwgkk/6loNML9RqGcweXgJdeVnzHd4m/YQFBUVDR8+nKIoqVQ6ZcoUf3//Bw8eHDt2rLKysm/fvrz6m94Xent737p1i5ez70Q0NOGdMGECV5+wbNuw8WoOw3Jv93Pg3Xk+DHF6Y0/S7zdzR/iaN31uXqqg+FlY45XpzxYPS/EfM/3i8xULDyUzLLtkiPP0Hjb8T6RQTq46lw51ZHmoiN/4jn88cApiqaeisbkwSRepy3qWW3RufwAgBtg8ZMW8hz65FRqa5vZGa/WbiqpoBOC13nav9q7HCvW5oErDfHY67U6mVlFnWnfrD0OcDeZA2dg1plNAXdvMaaoAAPMZhrq1RJSYLUrmZPmoU1CthjLMfQDq1pfNuM3mPzRw0UFN3nzzTYqibG1ts7KydNpcMpnM2dlZJpMtXrz4jz/+qPWSkpKSv/76KyUlpc7BOgEdJbMBAOGPy+9kytwsRFOfzN+9rY0mBFgejyv561b+/15skioWAPDKBwBg1ZFm9Dq62hsvf9Hp27Csn8Kzj8eVeFqJy5RUbJ6CpNk+riZTq927sCUpTOI5AABciPeba5CzY37DCUpVa0avc/vTbhIYi7uO3uqHLziYnF+pAQAzMd7DSeJmgo3oauth2Uwd0E6VrEgtUX16MpWv/EER5P0hTi+/YNPeg+pYsIWJDF+MiwuJIUtadhCuqggAUGuvuv+EWnmxGbc5WQG0ZaCPiIgAgM2bN1dXYDQxMfnss88+/vjjM2fO1H1JQEBAYaG+orjOQEOB/rPPGhHMMiAUw/GGzkuGOFfvsJ8/wPFScvmR2OJJ3aya2HGjU98VER00vTCmi4Uxzv55p5Q3ZQUAIwE2q4/dW/0cqr93OmIb782G95qNSAwUbgijWmqXOrc/vNfs6tuNWUYqwHibj0AHyeqxHsoquYlJs9We2z9Z0YRsFQiM8a5jL6Sqv7+YyS+9GgmwVWPcO0hbdQeCpanza7Rfy96vI6YOLTsMQogAgFPL6/4Tp5EDAAjadlqgVCoBoK6C/IgRIz7++GO9BmG8NHFn6ViuRe1Af+7cudGjtU491YV72pq90YU5FZoAe2Nnc2FuTYO78V2tQu8Vbr6Ws2GqfueKzkgfZ8mLfrYVKjqjTG1hhDuZCdGaXyCuIptJuQoAiFCK937WRcr86mtysdLXxkimYa6lVnx1Jn3poBZZq7d3sqIp2SoasN9TbA5la7sunM2E30/0bPa9y78A6tafbNEjAEBMHYg+c1p8HMTGD1CczbjJaeQ1CslIJZt6HRC0ZpWq4cEwjKKotLS0Wuuu6enpAKBz1ntuqB3oZ82aNXLkyA0bNtjb167mbg0cxzXgGUsx3M47+QDwMF8xfftDvftEZspuJRf429b+7dX1jFUotMvoJEm2xvG1TT1jOY6jaRoBcJcAACOX1W4Nw2/tRDkWAGi/sRo1A+omDYP/NJo1Zp2tK/PkVQqS/ex8XlKxuouN6JtRdgqS/ehs7uXH5SRJfvIihzczW133+LXg14HkcnlbzJUYhlE49EH6v4cwTz9hpCAOzbrNuvTj7LoBQCkpWJXhnZCt/Wr1dTH+KNjWGCcrKxu5OCmVykY74BFahSSd050dKYhDATRpt9TKpwLRHGHE+YzQed7yPrdt8WlwHKdWq0myhRddpDSF0HZ+IdSAJRqlBkD7vhiGoSiqWWPGvIdjj84pDyxmQj7mTBwAAJEXYFd/QJVlrNdwGYXx1rWG9YzV4eHhkZCQ8Omnn548ebL6dt4AtmvXrq08fkejdqBPSkr68MMP/fz8vvnmm4ULFxqqpBRBkAasBDmAUX4WuQ3+rsQE6uNoaVpnfbWulaCkSpuxERBEa4wA29FKkNPI1ckXAABQzLjva4hJU8dQn5VgA4lyWmJCAYgkJjq/ui+PPE4qVgfYG2+Y6s2Ll/3yknTRoeQbmYp/Hsg/aJqFyNPji0QUgEgkqs8Pj7cSlEqlvJWgYZHJZCYmFjDwjRpDitpDZd0WevTHe82+lVG5+nxGuZIGABRB5g9weK2PXaPhimXZsrIyIyOjRj12mLir5K3a0oZo1m3IqmHCLJCY6orHZTKZtG1EzVplJciQmqM/sCwNAHjQDHHXGs0BCoVCKBTieHPW/EZ9qqnMgoKH6P7XEKkNAMLJCwEAtfERjV6h89UyuJUgz7fffsubQ82aNevXX381MzMrKip6/fXX79y5gyDIzz//3MrjdzRq/2FsbW337t178eLFhQsX7ty5c9q0afz2Tz75pO0GgQB8PNy18f2ahhDX/kL4BsvOCPPgKN9FUmg3yFZs0/oMQgOJcrzrOIQQV6/Qlwqxvq4m34z30ElU2pkItk73WXo0uT7Ryqc0OSHe7muzJItsuZJ94H4RX1hmJsZXjXXv7WJgVfFaq996lr4BQGCM+T27nsSWQd34lVfsQcxdiMHvGeCIAmPhzD/pqN1M0gW2PBM4DrXywHxH4L1f57VC25RJkybNnTt3+/btoaGhoaGhGIbp7GFXrFjRs6fe3rdOjP4rsI+Pj7e3d1RU1MOH+hMpHRmbJ02bhfJOWsTG0bFH+EdfFwwYn1A6rTltBPppIFFepy9pzTiPunvZmQh+neLSqLtCUxLiAIBggmfW/aiXDHD4JsYtVVHEPw10kKwa624rbYN235qr3/UtfXdwmLQbdNQeAAAEFYz+CggDrV7gArzfXLzfXOAnAegzLQL866+/goODP//884KCApqmCYJwcnLauHHjhAkTGnjVM644NxS1P1mapn/++efVq1fPmjVr9+7d5ubm7TKs1mBhTBAYQjFcJw30bP5DriIHACqkXklKt5GtsPB+9jSxfLN9J7DnCk1/wj5RKYQAgCLI7F627wxwaO7aw78HrjKPOvOlttKmzxzUsbvhz/FsQ7yOOXPmzJkzBwBomm5e3qmzUfu9BQUFIQhy/vz5/v1bqFLU7iAA1hJBXqWmREGxHId2tnIobe08QLbdi5DWvmNpPk0u32wXSqqo7y9lRqRpCw3sTQQrx7gHOrS9nEPnhSHJk5/wIhyoc09i4LvtPaA24fmO8lBXpvi1116Ljo7uvFGex9FUCAAMy2WUqRvduWPBscyjiwAACJprPai9R9OGcFXF9L19QLfcdaC5nI4vnbUrXucxOcLbdNer/s86yvMOiK32QXxmUJd+ZAsSAAAxthSM/wbQDtqb8h8NU/s69sYbb9S9uCUkJPj7t21Zq2HxtzO6myUDgNg8RUeohqYY7sD9ovDH5ellahQBdwtRiKd0Zi+j6ncbKoo9FV9iWhQ9WFEKAEWmARFFQgB1dLacZrVpQWMBNsbfUkw0VgrVGVZEyXNfsxm3uapi6L+grc9VKCfXXsy69cRdUiLEPgxxHuvforaA1lF36bsjw8Qdp2OPAgDvco4YdzKBl//QUTumBwYG/v3337qeKQDYunXrRx99pFDoMZrosOimabF5VZO7tfO3s0rDLDnymDfNkAgxjoO4fEVcvuJWlmLdJC8hro3al5LLfgrPfo8N55/ulnWLkGudN3gLDh4Bjozv2sg76vgrovTd3WzGbQCgo/fhXcYDol3jZTNuI9beiLEhQ/Dl5PK1l7J410YA6Odm8slw1zZZd20KbSbJaXDYzEgy7Dv+MRG8GHXs0b7j+Y/WUDvQb968+fXXX585c+YPP/wgk8nmzp2bkJBw+vRpvS/usHSzl6AIsBzE5rW2saL1rA/PSihQBDpIPh7uwt9eJORXfRuWEZUl/zUi94Mh2rL0YT4WKooNvpUGCgAAvz4jyktEEemVA91Nuztqr1vGAmyYj0VaqSoqS55ZrpYKMR9ro0EepgK8xhy/Y62I1k1WMCR1bSMAoHZd2IJE5vpmCP4MAKjrW+jIHVjARMHoLw1y5qxy9Xfnc2LytT1NUhH2wZD2mch3OtiSVPLEx3wxDNZlNN7rlfYeURsyf/7833///fPPP1+9enV7j6WtqB3op0+fPnjw4Hnz5gUFBZWVlU2ZMiU0NLT17QnPGKkI87AUp5Socis0qSWqJorktAWlCupCUpmFEfHTFC9dEbqvjfj7sc5z9qcfiy2ZP8CRT8WICXS6r1B9KQsAEDPnaYMCyOjCiPTKns5SnQ8fw3LrwrOPxxZXr/CykQhWj6u5otiRVkTrJivo6FDgOABgSzMRiRWXdh3zimYSkpk7OxGhtNbIW4aaZnfeKdgTVUAx2o9qkIfpx0NszHOvAdU55NXaEU5RQh5ZwutTok4vCEZ/2RIh4k5CZmbmn3/+CQDff//90qVLzcyeT38rPdlec3Nzf3//zMxMjUYzcuTIThfleV700RaGnkssa8dhxBcoWA6CPU1rtRqZi/G+riYamtW5HgIAmx3FF7FhLr30Hu2nK9nHYovNjYh5AxzWTfL6YpTbEC+zoiryw6MpWeUdddmZT1Y8ia2csoyO3A4ohveaDZSSU8kAQHhtLXNnJyKUCKZvQW18W3nCG2mVr+yM3xGZz0d5cyN85Rj3Hyd5mWWcr2uD/h+1odTksaWcrAAAEDMnwcQfAOs0S8ctYOrUqbxwCE3TM2bMaO/htBW1A31sbGzv3r0vX74cExNz9OjR999//80335TL9YjMdXBG+Vnwk5ALSWVs+7U4KEkWAEz0iembinF44s7Kw2ZH8w/0mtJllKmPxRabG+HbX/Gb29d+oIfpWH/L7yd4zu1rrySZbTfz2uQNNMgvN3LH/PaAX37QIVPTc/cmzdmTqPcl1PUtnKYK7/ESEfIhMeR9YEhAEEQtQ3ChYPpW1L5VGiP5MvKjE6nLj6fky0gAQBEY38V0/5yAUX4WAA11jdEPjpCnv+Cl///V0KTm2P/Y/HgAQIwshC9tRYw6XydN0zlz5sy9e/cQBNm6dSsAhIWFRUZG1rfzH3/84ezsLJFIRo4cmZ2d/QyHaQBqB/p+/fpNmDDh5s2b3t7eISEhDx48qKys7N69DVok2hhHU2E3BwkAFFWRfAVOu8C7XOmt8swoVQFA9VVBtiiZf6C3JyUirZLlYHoPm1oLiW/0tTcWYDfTKtkGevbapqrPwgivUNG6pWYAkKnpxYcfJxYqeA/xWrBFj5iHpxCRCd5/HgDgvV9HXXvzaRxAEMTMsemn5jRVTOp1+s5O+v4BNjtaqaF+i8idtTP+emoFv4OfrdGfs/wWD7DhvRsbOlRFDnV5HZN4lo7e1/QBPIcwFHniIzbzDgAALhRM+QkxbcZfpDPyxhtvAMCYMWMWLlzYu3dvAJg9W39uMzk5+ZNPPgkNDc3Ly7O3t1+82BB2b8+Q2r/GCxcuDBr0tHzbwsLiyJEjv/3227MdlWEY62/JL8buiMzv62pgDZMmEuggMRHhEemVD/MVvGUgz53sqge5VfYmgurrB1xZOgAAIUZM7ACAX2LVLbQWVZEAULdalMAQZ3NhUqGyQkUb1VN42UZVfTODbOVqZntk/pIjjzdM9XY1F31w5HFykbK7o+Tb8Z61dqYfHKFubgOOxQe+i4hNAYC68QubeRfBBRxNcpSauvCNYJKeYqG6MHHHyfCfgFQAAAvIWWTQdmxKOaf9eCVCbP5Ax6mBViiCyGSNX+OpKz/zc3nq1l9Y13H/0iJCjiXPfqUtysIIwYTvUfvnzTe1FitXriwuLiYIYt++fQBw/PhxJyen1NTUX375ZeHChbV2vnHjxtixYwcOHAgAc+fO5a8QnYjagaF6lNfx7rudsh1uTBcLfkIdk1sVld0+2ScCQxYMcmRYbvGh5F8jciPSK6+nVmy+nvfVhVwAWBzspFvk4lSVnKoSAFALN37ta6y/5Rej3HRVIrxNq/xJmWB1ZGpGt0M946iRKDcg8wY4zO1rz5eQzgtNSixUdneU/DzFu1axP1eRQ136ARSlgOGAIHTsEc2R9+nb2+MLvMoAACAASURBVBFcCD1mMo49AYB5HM48PNXoGZm44+T51UBrMP+x91/46h3phvXoq3yURxEY39Vy/xtdp3e3bmJHNJt1h0m5ipjY492nAaWkrm9t0cfQyeFY8sxXTNIFAAAEFYxdjXkObu8xtS1KpfK7774DgGXLlvEKTvb29q+++ioALF++nKZr/8rmzp37zz//AADDMNu3bx85ss29yw3L89z4K8DR13vbrQ/PBoC/buX1cm7tKl/LmNzNSkEyv93I3XWnQLdRiKMfD3d50ftpApQry+AfIOYu/AMxgVavBexqZwwAF5LKxgdYVY9hcXlVeZUab2uxCEfrXgV4v6S6PVYyNW0kwAwi8DJvgAPJcLujChQaxsvaqG6UBwAq/CetcBVDUxfX6rZztAaidukuUOSFb4SWrqh9t3pPRiqpKxsAxbJHbPktxezWo6cdBi9wjxbaJAWMXPXklEo67iSmqKSfmEjo6RojjJgHBwGAGPI+5j6ASbnCxJ9mu09v5VJBJ4NjyfOrmcSzAAAIKhi3BvPt6FKarWfmzJkkSZqbm3/77be6jX/99dfhw4cVCsWiRYu2bdtW91WXLl1avnx59+7dO52OsSEDvUwm27ZtW0hICJ/t6ghMDLDadbeguIqKya26lFw+zKd9VpZm97Qd7mN+Pa0ytUSFIuBhIezjKHK2rqHPzlVol3dQSze9B+nnZuJmIYrKln8flrlwsKOpCOcA7mbKVl/IAICZQbZ6X/Xm3kQ1xW6d7uNo9lT6NTJT9vGJ1GE+5l+M0n+uZlGlYaKztRmSfJkmtURVPUkFAGzmHSb1GmJsBVJrriARtQ9gC5MRFMG6TUKktrw6v1gshpx7TMYtOvaYoP5Az2RGZmqMd5l9cOUSwnLaKO9iLnpvkEPvS19yBcWcehkvZc53jaEAVK0j1OwaAwDUsTvmOxwAwQfMp8K+pcLXC1/56zkuKKwBQ5FnvmQehQHwypRfYn6dbK7aApKSkk6dOgUAfGGlDhzH169f/+677/75559ffvmlo2ONJYr33nvv7t2727Zt6zjxrekYLNCXlJTMnTsXAEJCQgx1zNYjwNF5/R2+DcsEgPXhWT2dpWbi9rmJsZUKpj9RG+ZDW60deN0oAAAjC71HwFHkm/Ee7x1KPvGw5OTDEhupQK5hlCQDAJMDrcfU0wfUw1FyPK5k0aFkXayPzJR9dCKVotkejgYonK3SMO8fTk4sVPZwlAQ6SnbdKfjw6OOfp3g/jfUcS4X/BADEsOWoS2/NX1PYggRi3GrMPoBf6+MoiqqslJibY/3eZLPvIVa1k/s68io1f97lzmMrWbk2CpuK8Ln97Kd2t8ZRhIzzZeSFXGUeH+j5rjGNolJYbUZfvWuMozX03X+A1hAvLuXDOh44mYk9yubFMonnsS6j6xnFcwSlJk98xKTfBABAUGLEJ52la7eVzJo1i1cbnj59ut4dWJZ9/fXXL126pNty7NixuLi4iIiITip/ZrBBW1lZnThxotb9zr17986dOwcAMpmMYZjWG4DVhWVZ3pavvh1C3ESn7Y0e5CvLlfQPYekrhjbVIpGmaZZl22LMvLFirSOj8jI+emlYTF3PSW2E8NsU170xZdE5ijwZZSRAutsbTfQ3C/aQKqqqAIA3T6h+5IV9LZQaKiy5csGBR+vGO+fJyJVheRTNLuhv86KbqFnvjqbpWvsrSPbjM9mPitXd7MSrRzqIcISlqd33Sj84kvzdGOcuNiIAQOKOoCUpnF2AyqEP0AgS9DoasZmMCmUnb4KqKnhif6hUKhEEAXMfYADqjKpYQe25X3b+USXNam+DxAQ6NcD8pUALYwGqVioAAFUrEAAVSXO6l/uMI0mSe2IChVAMmnaDsg3k/KcBABqxCaFUXJcJSomL7oxI/0XoscXklY2sfS8OF0E98GGiNbZ8DUDTdNspjpAkyX9JEFqFnP0Myb0HAICgXMhytcfIup98E6FpmmEYQxnSVYdlWYqian3xGnVwbBgTE5MGDLz4f6pl03b58uVr164RhNbhztXVNSMjozVjeMa07dWpvLw8MTERAAiCaDgctxjuCQ3ss2SA1YJj2RqGC0+V9XUWD3Fv0kxW10ZhmIFWQ+cZW30jrlHwqWoGE7L1n9REAO/2sYA+FhTDEZj2y6o7FP851DryBwMsWZa9lCJ//1imkmZphpvf12qCn7S5b63umLfeLHpUrA60E389wh4HhqZhdnczmmFDH5R/HZaz+2U30MiF0TsAQal+CzmaAQDwHS9IOIUUxLGPw1n3YN2Ydf4+AIAlnwNAGJ9RAJAvow7FV4Y9lul6XIVATRI9mDplmqkIB2BpXq9fVS4oiAOBMWVkC9UGWX3MGMuiACzLMjSNVmRh8Sc4QkwFvc5Vf1NWfoT7YDT9Ghu9h+nZiPk1b2farM+wKbTRLwWezDA4jgONXHB+BVKUCACACagXP2XdBkMrTsrPt9ro04A6X+lWfj5Xr15t7ks2bdq0adOm1py0fWltoN+8eXNYWNiAAQP0eg0OGzZs2LBhALBs2TIcx9uivbiuZ2xdzMxgwSBuw9VsAPj5RrGPg3kX23r9WnXwnrFtMWa9nrEUov3ySsxt0ZaelPeMrTvmVePNZEdT7mbKAODNvvZzBji04OAymayWw9TYANTMWLxgkGP11dclQ83szYtIhjUzM6Mu/U6rZXj3qWKvProd2BHLNQcWCu5sEwWMBEJU1zNWff8fTl6YWwV71X0uJZfr+gMIoMebZryKhZsXR+FxZUTIB7zVEScrIMNXswyJvzBDbFnDjav6mGmxmAIQi8W4mRl58QuGpVGJlTiq9pobR8lZADzugKTPTESqf+WD94w1NjZu1DO2BbSpZ6xYLBapizWnPuDKswAABEbCyevFLq1NOrfEM7Zp6PWMlUqlBj/R801r/zCLFy/uFL0DL71gcy9Hfi21QkOz7x9+PKeP/au99P+G2wtOVwqCGf7XcjdLHpurvfk9HV861t/SycwAtpz93Ez6uelpUJjxgg0AcKVp9IMjIDDGB8yv/q+oSx/MM5hJvUZH78X7za378sQ+q3ddiY984MmBVr6CQJhRbMSrxjEuL/0AZB/N/nfoB4fpxLOopSfQGrY0FVgGte9GDJxf92hPedo1xrEF8QDAyQoYWYH+nWkNW/wYqyfQd2JyYzTnP+cLeRGRiWDa5n9XidG/lU65sNACUARWjnGfvz/pcbGqSsNsvZ7Txda4p3MHkvFBBE/UYEgD52f5GhuSZj8IcXpUpDqbULroYPLWl3wMEusbgAz/CVgaEVnX1UzmVBUAQEXuwAImgFB7/8Gw3NXUiv33imLzOACt/4EYZSaapk0v+dPKRCx8eRs/xRa+toe6tplNu87mxwEAIrHGAiYS/d5quPW3WtcYInxjP6coaWj0mACtf1m4k4KnhMHNjRxDAQBi6iCcugGx1OMP/B/PHwYO9PPnNzilalfEBLp2oteMvx/yPh7Ljj8+8lY383YqwtGD4EkmR2PIQK+rsfkgxHnGCzYsx3Ecdy6x7L1DyVtf8uGtuNoEjmXz4gCAk+Uzsnz9+1BKtvgxOPWWa5jTUYVH40qr2/yaCWEyeW4KdV5aokRM7IUvb0NMtRknRGojGLcaADh5IRBivsymcappwSMSa0TSasv1zgRH3fxDcPMPAA4AUPtuginrkXrqu/7j+aPDhLlnQkyOnGY5DEUYllNT7Bu7E/+e7WdhRLT3uAAAEF2gJ5UN7tg8vrmQoYvyAIAiCF87fy6xbOv13G/Ht9mEDkFFb4Ry5Q1qPwklGYR7aHjOhaRyDfN0Od1WKpgVZDsxwAI9/hebqQQAzGeYLsrXOMnzl1ppCygleW6V1qISAPMbKRi9shPZGf5H6/kXBXoVxf4SkQsAy4c5b7qaoyTZoiry3f3J6yZ7upg3tJb7jBBq80icurLhHZvF+8HOKAJDq3WK8bHez8a4q33jK9KtATGxR0z0F7OSNHslpeL4nZJ7OQnVt3d3lMzoYTPEywxDOPL0F0zmHcTYkiOVdNRuRCTF+73VpgN+LuHKMjTHP+JKeZt5BHq9Lgh579/SDtY0CgsLP//88zVr1tjaPrfzhn9RoN9xJ7+kihrhazEpwNrf1vitfUkUw2VXqOfuTfpqtNtgz3Y2HECfKAVyZZkGPOxwXz3NwCiCvBxkY8CzNJ3UEtWJhyXnEstk1eQacBRG+Fq8HGTra2MEAMCx5OkvmKTzfMaGqyrWHF5M3fgVAP6L9c2CSb5Envtae4+IC8gBHwi6TfgvytdiyZIl+/fvl8vloaGh7T2WtuLfEuhzKzWh94qEOLpwkCMAeFsb/TTZ+/3DyRyAgmQ+PpH6Rl/7t/s7GEL6pYXolsVY7eTruUJFsRcflR2PK4mvKV5vJSEm+lu86Eq421vpyivJsyuZpPOIqaNw5u+I1JZfNtQcXkLd+BWEUvyF59YdwpCwDHXjF/rOLj4pj0htBRPXKgX2/+Vr6sK3X7WyCauDY/hOto7J5ms5JM2+1tvOzkT7Ve/lIp35xKKPA/g7Mn/RwUft6NOESG0QoQQAuNL09hqDwaFZLiK98quz6eO2Pfg2LFMX5VEEGehhunai57G3ur3Rx9aspmQ8V5SMmDnzUV67v1OQcNpGEBhxTyT7OwSUkok/BZQh11QMAqco0RxYQN/ZyUd5zH2AcM6+5152uE1RKpVvvfWWjY2NiYnJhAkTSktL23tEzeNfMaOPzpZfTamwkQhe6VkjB/fOAIfLyeWFchIB4ABicqte3534Vj/7V3raYu0xt0csPbi8WE4j5+SFnXqZkQOIza0Ke1R2Kbm8QlWjidFeSozvZj2hqxWvIA0ALFP75cLX/gEEAbTGlxN1ChIvDAOsQ6yc87CJZ5kr6wlKhfd4qb3H8hQm5Sp1fjVfwAoIivd/m+j/NiD/lildG/H3339nZmY+fPiQIIhXX31148aNq1atavxlHYbnP9CzHLfhSjYA2JkI/o6sXednIxUUykkHM6GKZMuUlIZmf7mReym5fOmLzh6mzzrWo3b+bF4sALCZkVjAxLY7EaeRs5l3uJJUwHDE0hNz7QuEAZajOYDEAsWVlIqwR2UFshoiMEIcHWwhG1HwV7+eEwUvBDZyoPqiOd62hf/NBWEoDvR7E7YPlJq68hP94Aj/DBGZEOPWYO4D2ndQzweLFi1atGgRABQXFzMMY2PTPktcLeb5D/Q5FZqUEhUAxOZV8YZTdcmt0OyY7bf/fvHZhFIAeFSkfGf/owFu0td6mJo/Q2Fj1K0f3AsFACb9VtsFeib+FHnpR6jWloUYmROjvsA8g1t4QJa7lyO/llJxLbWSt8HSgSJIH1fpSF+LIV5mgthQKj8BZUa1avT/UQ9sSQp16nO2JIV/ijoECsatfu69AFtAYWHhe++9V102Ljo6GgBu3749duxYfoupqemGDRvqFuF88skna9eudXZ2/uOPP57ZgA3C8x/oXcxFm6Z5y9V1EgTVMBHjvjbGX44yHuVn8f3FTH42ejNDfjtTPqqL6q2+9o5t1kSaVa6OzpZPDLDCUARz7gW4AGiSzYyMyaoo13DVnUkMApN0gTz7NaAoFjARdQwElmGzo5mkMPL4cuH0LWhzNE8UJHM3S34tpSIivVJWx/EkwN54pJ/FMB9zXZtCm8h0dU7om78zmXeE0zaBwBCeXxxL3/2HivgNGAoAAMWJge/ifV7/L12jl08//fTQoUN1txcVFZ09e1b3VCwWb9++vdY+33///fLlyz/55JN33nmn+s4dn+c/0ANAb5emGsb2dTXZN6frwftF/0QVyNUMy8HZhNLziaUDPcxmvGDTy9nwUkr7oguPxZVEZ8u/HuOOESLMqSeTcYtTy/44fC4O8xniZW7IxQKWpsLXA4IIpvz89I6++zTGrT957mvq8o/CNw40cgAOkouUkZmy2xmVD/MVfI+xDhSBAHtJsNf/2zvz+Caq9f8/Z2aytukaKN03KC207BVkKSJU9rLDF0FQwQWx7qjXy72vexWvcHuvKOhPAQEpqFdBEcqiUEApmwhSaAu2FOgCLV2StEmaJpnl/P6YUko3uiRNU877D17NZM7MM5Phk5NznvN8PB7p6WH7Nbesic85Skc8ag9DxI5EKLvKnv4CsMCe2SyJa2+dKKy5bv3pPbEUBAAgzyDp5FVUjz7tDrPL8sEHHxgMhno9+tLS0u7duw8ePFjc4u7uLhoN1jJ//vxHHnnkueee8/b2Xrx48TPPPNOhQbebB0LoW4WcoZ6I7TE9ptvW04U/ZGgtPBYwpF2rSLtWEa5WzBnQfVxvT5dm3FlbyZNDfX/L1x/J0SEE/5gQSoWP4vNOA8AEfGLS2HjbTgkLty7hKg0dNqLeuC0dPZW68J1QcgVr85FXcMOGpUbr+QJDWq7mQtGNepOrACCh0eBA1eienqPC3L1d7gyvsyYuIwW4u1lMjTj5SV2YvpMAWjS/ymXtZ1PXOHLms84VYYwlJhPWZEOjV9TsVxF77L+ABQDEnf+G6TcDeQS0MR6B485uY09vFp3NAYDpN0My5jWxoiehKXx8fHbu3Fl3y7Rp0/bu3Tts2LA9e/Y01So+Pn79+vUTJkxwdXX95JNPxowZY/9IbQkR+sZRyeklD3WbHOF68Lp5b2a5OPJzrbx6dWr+h78Ujgx1j4/0Gh7iJmXa++vYRyX9bG7v5TtzUrN1ggCTew2PQlI5tj4K55WhNv7pjfXFAIC6NeKdi7pHQMkVofIWfUfoC3Tmi7eMF24ZL94yFlVaGjbxVDIPBbmNCHN/OMTdVVb/m0908mvYqp6TH6KlEDmxRdGLc56Om/msd0VSMXWxsSuiY5qcX+FzjggF55B3KB0xjju9if1lrXT6f9sQjFByhf3pPaGsJtkUuXaXxL/d5lkWwn1ZtGhRRkZGbGysIAhTpkxZvXq1oyNqHUTom8NLSb84KmDJML+frmi+u1CapzUDgJUTjl7VHb2qc5XRo3t6DA91jw10U8nb3sf3UUk/nROxfGfO0au6X3LRa/DQJDhBCSyfsYcZ+qTNLgagJrWGbaxomtVkAtmVSnn2+ZLM4qqLRUZNFdtwL4ZCMX6uw4Ldhoa49eqmbOYHh+jkV69HX9fJDwBA6kJHjrO9V4V9qHtFGGOTySTTZOO8kw2vqMlD8Fb2+CcAIHnkVTpwCH95P5/7K593mg55uBVxcBb21Ebu3I47eamIiZnGPPIKknWiUqxdD4Zh1q5d63Se4LUQob8/Cgk1o1+36f26nSvQ78/SHL9WUc0KAGC08PuzNPuzNBRCfXoohwa7DQ12i+rhwrR+wMVHJX1qmO/7P+cJGKd7T5hUfgIAuIu7mCGPA22zxYyUTxQA8NfSJKNfBlpazQq5ZaYrJaY/iyqvXBtVQM8UjmGAm/VbIQhXKwb4q/qo6bjePsoWDltJlMygeXU3cBTDXz9BBcUyQxbcsyfbyDdKZ6TOFQmCwGq18msHcN7JRq6oCbjfd+CKQjo8Thw6k8S9ZE15mz22ll4cW2/RQFPwub+wxz7ElUXiS+TuLx3/VyrooeZbEZpHoVDU/ttV6SChFz3MDAaDzY8supexdhAL0TO2bsyRnihypDpxmNcfRdWpufrT+UbR307AOLO4KrO4avOZYoZC/u6SaB9FXx9FT7UsyEPWUPbFu1HXd+23wqo1qUUA4C6nU3XdFsojgsw5WH+76nSy0H9e/fZNIxryNXqfWR7f0ktvdvu//HJj3hf78iRhhXq+zmTqPZlkNIXCvKR9fRTRPoqB/kqVjAYAlmV5i8nQyChOi6AsFgrAYrFU3xueeB+qqqqa91RqqnnzcBxnj6dO9LdjWZZueUgmLf3bl4iWWGOfsYj7+w2l/fpD0cWqs98IfafXi7ne3UCVN6mT61Hh2TuvKSF6Jn5oCcvIocUXiDG2WCz28CnkOI7jOPt5xtb7EE0mW65G/vjjj1Uq1apVq2x4zM5GBwk9QoimaXsYgLXESrBtiFaCjcYc7+ke37eHwcyfya88m6//LV9fZqz5puEEnK+z5uus+/+sBABXGR3kKQ/ylAV7yoM85YGe8gAPmZTCda0ET96ofDe1iOPxirFBw0Pdl+/M+bBi6kfwXwCg079WDp6DFO4NY2gUs9lcoTeaeWmx3lKst97WW4v1lqJKa7HecifCMUABmACgfr6pv7skqodrZHeXqB7KPj1c5A2mH0SLuxZG0hBOJmMBZDIZc+9BRCtBFxeX2lo3AI3N5ZZc4gEkJZeoK3d2a8HMZztjbgrRSlAikQiNXVGjWNOSeNbExC5SBETdPc64tyzbF9Lntir7T0UKj7ox3xV6tpo9s5U7t6N20pXyiZKMe6sNJQ2sVqtMJrNH17WDrQSVSltmXvn4+DhdXnxrIUM3bUclp+N7e8X39gKA65rqM3n6PwoNl0uqdKa7PSajhb98u+ryvZW8FBJK7cJ4u0i7uUotvHDyWqUAeHJftbucydOal4/y//CYcNIwYAROx2Z92ZHPtbE1SXgsL5g5wWjhrTyuZoUqK2+y8FoTqzVxFdVcRTWnqWKrrM2tGKiFBsEPl4VCUW9ZRWSoX0zcdJVrJ0pbbPlcbjMzn/YGiyt4W1DYXSjO4C8fREqvetaJVPcIJmY6d+kH7tRGydg3G56B//Mwe3wdvuN3iORuzKjlTL8ZJEee0CqI0NuGMG9FmLdCrKVTrLeK4n75dlVuebXRUl95q1mhsMJaWHFPAsm+rPJ9WXfN7TaimUNxBgO84s8fVuf0zEYh7QlPylAB7rIQb3molzzUWxHiJQ/ylDNcFaLoDsvGE7R5ANDAwA8Lxz+W38qAeZ8DfTeSls/l2j3upqGiJtIKFR3x6H33ZI+tBcCAeet3y+q9JTpHche/ZwbORV4htduFwj/Y4x8LxVk1rxHFxExnRi1v+c87AqEWIvS2x9dN6usmHXvH60Nn4vJ15gKduUBnLtRZivUWrYnTmdh7FxvVpxD57EFjZuFUBvh3hM3P0yur4T5LkCgE7nLGTUb1cJf7ukl93WS+7lJfN1kPN6napbFcdbpD8zTo7r15AP7SD3TE2DvDDpg9/IFw8QdK4QX43q/Dls/l2gehLEe4mY61eci1G+remw4Z1kgnuo43YbNgbCwFAFxdKbpyN7oLNpaJQo90eeyRrfy1tNo3Kd++krFvkWVQhDZDhN7ueCoZT6XrAP+7qsrzvKm62gIyjYktN7K6atbMCtWsYLTwZk4Qx2QAIFdYrMm77G0pCoTSVaq9+32fdZHSMhoppLRSQkkZSimlXaSUt4vEQ8F4KBgPhcRqMRuNRrVa7bjLbRJ6wGymSsOd3mTZuVw25xPKN5pN/Td38Qek9DLFfyDrPMt8WLP10Pv8lXsWuFPqcGnCmro97taA5E/twqZmC9tKFEjphY1l3MkNTOZeHtdM1CM3X8nIZXTUBDJWQ2gPROgdA4WQ2kWidpX0brYKnlCyxvL108CzAytSh8Y91pJRgs6MZMRzAMCd3mTZ+SIdMpTPOYqUXtTMTzDTiVyqrQf+zl89ilQ+zIBZyDsMG8v5P38Wbl6wfLdMtuhrpGxT9SGJvPn6YtikZX/9mEvfCWzNaBWSuzFDn2IGziPmrvbAarWuXbt22bJlbm731EcpLS1NTk5+4403HBWYnSBC36mhfKIkw59j0z4BAOvBv8tU3SjfGEcH1S5qtZ7POYrkbtK5n/PugVDZAptcUe/srHpC4R/81aPII0C24MvaNBhmwCzrwX/wWfu5s9skj7xi2zNik5b7fTuXvgvYOw5HjJQZOI8Z+hSSt7RGE6G1rFy5MikpKSkpKScnx8urpp9RWFjYp08fo9Eok8kSE9tbhqhTQX4PdnaYhxbVlKZhzdbdr+GKQkdH1E4w1LqfC1zjy3Qbg+k7WTrxH0zfyfaKCwAA+NxfAIAZ+mStygMAAJLEvQSIEt+1FdikZX/5yLxpGvf79hqVRxTdZxI3dxsT9xJRebuybNkyuVyu0WgiIiK0Wi3UUXmVSjV//vymGn722WfR0c7n1UWEvtODKGnCasonEgCwSWfZlYhNWkfH1GYweySJu/AdUnrR/Wdjq8m6KxHfzmxRU3Hm086lK7GhBAAodXi97cjFGyk8atMc23sWYyn7y0fmTQncuR11JV7+1E7ppHexqxObizkLoaGhFy5cELU+LCwsPT29VuWvXLnS1CxXenr6e++918Gh2gQi9M6ARCmd+TFy9wMAXHHT8u1z2FDq6JjawF2Vl879TBr/NvPwM9hiFH58lSq74ujY7iBRAAC2NDCoEXjMmlC7Z4yF8lzrwX+YN03jzu2oGY4XJf7pXdJJ7zZaOpRgJyIjI0Wtr6ysHDRoUK3K+/s3PptiMBiWLFnyn//8p4PjtAlE6J0D5OItm7VOzKHGmhuWb5ZgXYGjg2od3B/fiSovm/e52GWWjHiOGbYEW4yK1L+DtVNYbIt5n/yfh+pt56/9CqyZ8mv7BIlQcNb6/UuWL+fzWftqHELqSrxnUDuiJrSRyMjIAwcOAADGGCF04sSJplQeAJ555pk33ngjIiKiAwO0GUTonQbkFSKdtwG5qAEA64st3ywVSrMdHVQroLxDqaAhsnmfI++w2o2Skcuo4ct4n5hOkltCR41HSk8+M4U9tfFOAgzmrx1nf14FAPSg/2v1EXmWv/KTZftCy3cv8DdO1dQ2lsiZAXPkS74nEu9YCgsLExJqVlZjjOPi4kpLG/+tvGHDBg8Pj2bG7js5JOvGmaDUPWWPb7HsXI4rCrFJa/nmGen4v9KRzuHCSgU/JAtupM4iFbvIHFGpaFn5RnuDZCrplA8su1/lTm3kzmxB7n64SiP66zLDlrTKaBsby/jLB7gL39YdZ0NKTzo6gRk8X/zCJjiQurOvKSkpEyZMqKysjIiIyMnJaej9nZKSsn///g0bNogvEUIsy9qjto+dcJpADzKLHQAAELhJREFUCSLI3U82f5N154tCeS6wJuu+vzK3LkoeeaV11YytVUJpNq64iVQ+qFsvpOxEaewOhwoaIl/0FXtqk3DzD6wrQDIVChrCDF5Ah49qUXss8Hln+PRd/PUTgO8WKEWeQcyQhUzfycDYy3+Y0HJKSkrqzr76+/tfuHBh4MCBlZWVffr0ycvLq1dGbd++feIf6enpCxcuzMxsWQZBp4EIvfOBXNTS+V+wB/4mrpLnLnwnFGdKE9YgN9/7N8YCd2YLe3bb3axtimb6TpU8+pqze7HaEOQZJJ38HgAAa65xa2kB2KTls/ZxF3/AFXVr+iMqOJYZOJcOjyOrWzsPSUlJ9WZfxbnZgQMHajSaL7744pVXbLxgwrEQoXdKkMxVOuND7rdt7In/B1gQbl82fzlPMnI5RE1tviF7JIlL3wmMjO4dj7xCsKFEuHacy/hRqCiQzfkMKJt54XYRWqLyvJW/doLP2sffOHnH9QkAAMnd6L5TmAGzySh8J+Tdd9+Vy+WJiYk+PneTWSMjIy9fvrxly5YXX3yxqYYDBgxwuu482FDoDQbDhx9+mJWV5ePj8/rrr4eEhNjqyIQmQMzQJyn/ftaUd3BVOVhN7NEkyNhDDXsJmsgCFoozuPRdyMVbNm9jbSYfrq607npRKPyDy9jD9J/ZgfE7PVhzg716iM/ci026utspnyi6/wwmaiLx6e60KJXKRp1GQkNDnTRTvnls9lvy0KFDwcHB27dvnzZt2o4dO2x1WELzUAGDZIu+ulsDpyxHsf8VNu1Tcf6wHvyVnwAwM/zZuvnaSOEuGfcmANQr40VoCqzN43/bovjxWeGrBdzZbbUqj+RuzIDZsoXJsie2M/1mEpUndB5s1qOfNWuW+IcgCLV1grKzs8+cOQMAVVVVgiBUV1c32b6t8DyPMRat3WwLx3EYY3vELAgCx3E2OzKlhPh/Qs94+PVDqCoDgeN+28pd/B4GPwHRM+9JWyzPAwBWHcXWO7VHONASQZPXfEj2+wQBwGw228mIzmYx6/Ih9xjkHgPtdajbRaJoCHwIIifi0BEcLeUAoH1nFGNu3lixzdjDdBMARHtCexxcEASe5+t9iBZLWw0tH1RsOUZvNpu3bt1aVFT05ps1XjnZ2dnbtm0DgMDAQJ7nbev0WAvG2Gq13n+/Nh3ZfjHb2LrTZxCasVFybguTvR+wAGY9nPwUp39rHbCQ7/mYOPguEzANYDZVCfJ7L0rglVjAiKpu9mJFq1tbxlwHs9l8/51aT/tjpiry6bw0Ju8E0t2of3DPULZnPB/+KFZ4AgBYOAAbfKb2u88YY5Zl7SHHtn+e6xy54cHt9LR0Ydor9OvXrz98+PDw4cNfeeWVlStXjho16vnnn6/tjCQkJIjrEd544w2JROLt7d3eeBtgb89YT882laVtFp7n63rG2g5v87i3TBETXTN28DdOAQCqKped/Ahl/I8ZMJfuN53z78PdPKvSZjG9Yu+J58Ypq8AzPr2b/4D0en29mq42QfSM9fDwuMcz1ka0MWbOyt88L1w/wV87gStv1XsTeQVTvcYafR9yDeqnlNp+nVd9z1jbodFolEplF/CMdXcnNluto70fTGJioljPc/fu3aNHj5469T5ZHwR7I3iFSWetE27+wR7/RCi6BABYf5s9vo49vYkJHwWIZs9soXr0oe6sXcKaG2zqagCgY6Y5Mu5OADaW8tdPCtdP8Pln76af3gF5hdC9x9ERY6luvQRBELTOW1qO8MBhs2/g3NzctLQ00Uw9Ojr6X//6l62OTGgDVMAg2eNb+GvHubPbhFsXAQDYau7PQwAIWJNl5wuoey/KKwwbSoTiDBB4OmoiHTHW0VE7AFxdKRSeFwrP8QXnsOZ6g/cR5dObCo+jIx6l1D0dEB+BYAtsJvQrVqxYsWKFrY5GsAl0eBwdHifcvsyd/5rPTgWBq6m1AoBLr/KlVwEAKT2Y2EXMkIUOjbRDwRajcPMPoeCcUHhOKMutu361BomSDhlKhY2gQ0cg126OiJFAsCVkwVTXh+rRRzp5FR79Mpe+k89Mwcayuu9i1ircusTJfqRDRyBVF62EjgWh/JpQnCkUZQjFmVib14i4i4MzIQ/T4SOpgIGtKylBIHRuiNA/KCDXbpKRL0hGPC/kn+WuHOSvHqupDMya+Nxf+NxfWABK3ZMKG04FDqF8o53b4QgLuOKmUJpDFV6yaHOE25ebKoOM3P2ooFg6aAgVOIR03gldFSL0DxiIokKGSUOGwbi/8Nd+5f88VHfiUSjPFcpz4WwyAELeoZRfDO3Xn/KLQV7BnbxOCzbpsOa6UHYVl+UKZTmC5rpYZJgGaNh1Rx6BlF9Mjbi7+3V8tARCB0OE/kFFIqcjx9OR44G3Cjcv8NdP8tdP1DEzwVhznddc5zP2AAAwUsorlHYL5HwjkTqM8g5Dbr6OKoyDq8pxxU2sKxQqCsU/cEVhI55QdZG6UL59Kd8Yyjea8o1GStunzBIInRki9A88tJQKHkoFD5WMeQ1X3OQLzgq3LglFl+5xsOKsQmk2VZrN5qbWbKFo5KJGbj2Qqgdy80GqHkjlg+QqkLsjuQrJ3Fpe9PEeOCu2GMBiwBYDNhugugIby7CxDBtLsbEcG0txlabGnqlZkNITqXtR3XpaXAOUoYMp79BO/ouEQLArROgJd0EeAYxHAPSbCQDYpBOKM4SiS0LxZay5hqs09+wq8NhQgg0lABcbPxYjRTI3YGTASBEjBwCgGJDWWapjMQLGACBYjAqOZTFrtRiAa8sKZyR3Qx4ByCuE6taT6haBuvWstfWo1uspOyzyIhCcCyL0hMZBSk8xO1N8ic16Y/5FhbkUl18TNDdwZRE2ljbXueasmCuvaXu/c1Et2AcAgJYgFzVSdUdufsgzkPIMRB6ByCNQtNIlEAhNQYSe0CKQ3A379mfu6R1jXKXB+tti1x4by8GsxxY9NuvBrMdmAzZXttzyG8lcQaZCMhXIXZFMJf6N5CpQdUcuaqTyQS7exAmLQGgbROgJbQYhFzVyUYNv9H125K1YNNoWuJoMH6krIAQASOrC8kJlZaWnp6c9at0QCAQgQk/oCGgpamb9Ed/I2iUCgWBDSCoCgUAgdHGI0BMIBEIXhwg9gUAgdHGI0BMIBEIXp4MmYzHGeXl59jCgEQQBAOxhN8pxnCAIUjtYCIlecXa6GyzLFhQU3H/X1sOyrEQisflhRSdIqVRqD08lu8YskUjs8eCxLMswjD3uhtVqpWnaHtlNHMfRNG2nTxAhVO8/S15ens1P1LXpIKEvLS3997//3THnIhAIDwL28ETsqnSQ0CsUioEDB7722msdczqbsGPHjosXLyYlJTk6kFZw+PDh5OTk5ORke/St7ERWVtbq1avXrFnj5+c0hSS1Wu3LL7/86quvDho0yNGxtIIlS5bMnDlz8uTJjg6kFaxcuTIkJGTp0qX1tstksrCwMIeE5Ix0kNDL5XKapqOiojrmdDbBy8tLKpU6V8wZGRkAEBUV5URCbzAYACA8PDwkJMTRsbSUkpISAAgICHCux4OiqO7duztXzHK53MPDw7li7oQgjFtUZaSdFBQUIIQCAwM74Fy2oqSkxGg0hoeHOzqQVqDT6W7fvu1c/yuqqqoKCgrCw8PtMR1iJ1iWzc3NDQgIUKlUjo6lFWRnZ6vVam9vb0cH0gpu3Lghl8t9fX0dHYhz00FCTyAQCARH0UHplTqd7u23354zZ85f/vIX8ad658dgMPzzn/+cO3duYmKiE83y6/X6pKSk33//3dGBtAie59esWTN79uy//e1vJlNLK6A5HOe6yeCcD7MzikanpYOEPiUlZdiwYV999VV4ePiRI0c65qTt5NChQ8HBwdu3b582bdqOHTscHU6LKC8vX7hwYVpamqMDaSm//vorAHz55ZcBAQEHDhxwdDgtwuluMjjnw+yMotFp6aDJ2EWLFgGA1WrFGLu6unbMSdvJrFmzxD8EQXBzEvMKtVq9d+/eDRs2ODqQlpKZmfnYY4+5urqOHTv266+/dnQ4LcLpbjI458PsjKLRaenQ6pWzZ892dXWdOHFiR560PZjN5q1btxYVFb355puOjqVrYjQa3d3dAUClUlVXVzs6nK6Mkz7MTicanRP7Dt2sX78+ISFh9erV4svdu3cvXbo0OTnZridtJ7Uxm83mlStX+vn5vfvuu508uaLefXYiXF1djUYjABgMhk5+k50aJ3qY6+EUotH5sW+PPjExMTExEQDef//9kSNHDh8+nGVZubxNttEdRW3Mu3fvHj169NSpUx0d0f2pjdnpiI6OPnjwYFhY2M8//xwTE+PocLosBw8edJaHuRYnEo3OTwdNxs6fP3/Xrl3z588/evToggULOuak7SQ3N3fTpk0JCQkJCQnvvPOOo8PpmsTFxQmCsHjxYo1GM378eEeH02VxxofZGUWj00Ly6AkEAqGLQ8oUEwgEQheHCD2BQCB0cYjQEwgEQheHCD2BQCB0cYjQE1pNWlqaUqm8dOmS+PL777/39fUtKytLSkrq378/x3Hi9pKSEk9Pz59++qk950pNTR05cmSjb1VUVLQ8665Xr17l5eXtiYRAcF5I1g2hLaxcuTIlJeX333/X6XQxMTHJyckTJkzgOG7w4MELFy5csWIFADz++OM8z3/77bd2iqGioqJHjx5ms7n53crLyzdv3vz222+XlZWp1Wo7BUMgdGowgdB6WJaNjY196623EhISEhMTa7efOnVKpVLl5+cfPnzYzc2tqKioXsO4uLiNGzeKf8+bN++jjz7CGK9atap79+4qlWr27Nl6vT4tLW3EiBHTp0+fNWvW4cOHR4wYIe5fb7fg4GAA8Pb2xhh/9dVXPXv2dHd3Hz9+fE5OTt0z+vj4iI96WVmZ/W4IgdCZIUJPaCM5OTlKpTIqKqq6urru9meffXbSpEm9evVav359w1abN2+Oj4/HGFdVVXl6epaVlV2/ft3Pzy8/P99gMMyYMWPdunVpaWkMw+zfv5/n+Vqhb7ibTqeTyWQY4/Pnzz/88MP5+flGo3HVqlWTJk1qeF4i9IQHmQ4takboSty6dUsqlWq1Wr1eX3esfPXq1ZGRkUFBQS+88IK4ZeXKle+//z4ApKSkzJkz59VXX9VqtYcPHx4zZoxarVar1WlpaUeOHCksLMzMzBRdWKOjoydNmlT3dKGhoQ13E9mzZ8/p06fFDj4A1P5BIBBEyGQsoS1otdonnnhi8+bNM2bMePrpp+u+5enpGR8fP2vWLIqqebpWrVoldiumTJmiUqmmTJny448//u9//3vyyScBIDU1NTY29sSJEyqVKi4uTmwik8nqnbHR3URYln355ZdrOy/OYqxBIHQYROgJbWHp0qXjxo2bOXNmUlLS5cuXP/3005a3Xbx48datWy9cuCDWnj116tTYsWPXrl07YsSIY8eOsSzbaKuGu1EUxfO8wWCIj4//5ptvLl26pNfrly9f/uyzz9rmIgmELoODhowITsxnn30WEhKi1+vFl8eOHVMqlVlZWbU7LFiw4IMPPmiqOc/z/v7+r7/+uviyoKBgyJAhcrl8ypQpycnJCoVi69atQ4cOFd+tHaNvuNvVq1eHDx+uVqsxxuvWrfP391cqlTNnztTpdA1PCmSMnvAAQ9IrCQQCoYtDhm4IBAKhi0OEnkAgELo4ROgJBAKhi0OEnkAgELo4ROgJBAKhi/P/AfMdD2pDYY6hAAAAAElFTkSuQmCC" 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" 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" style="display: block; margin: auto auto auto 0;" /> ] --- name: integration5 ### What can we use the results for? -- * Prediction + Apply the model to new data `\(X'\)` and predict the outcome `\(Y'\)` -- * Classification + Cluster on the latent variables `\(\{T,U\}\)` and identify, e.g., disease subtypes -- * Identification of "drivers" and "biomarkers" + Look at the loadings and see which original variables `\(X\)` and `\(Y\)` contribute most to the projected variabels in `\(T\)` and `\(U\)`. - However, remember that these drivers are not working alone -- it is a multivariate model we have estimated! --- name: end-slide class: end-slide # Thank you