class PartialOrderPlanner:\n",
+ "\n",
+ " def __init__(self, planningproblem):\n",
+ " self.planningproblem = planningproblem\n",
+ " self.initialize()\n",
+ "\n",
+ " def initialize(self):\n",
+ " """Initialize all variables"""\n",
+ " self.causal_links = []\n",
+ " self.start = Action('Start', [], self.planningproblem.init)\n",
+ " self.finish = Action('Finish', self.planningproblem.goals, [])\n",
+ " self.actions = set()\n",
+ " self.actions.add(self.start)\n",
+ " self.actions.add(self.finish)\n",
+ " self.constraints = set()\n",
+ " self.constraints.add((self.start, self.finish))\n",
+ " self.agenda = set()\n",
+ " for precond in self.finish.precond:\n",
+ " self.agenda.add((precond, self.finish))\n",
+ " self.expanded_actions = self.expand_actions()\n",
+ "\n",
+ " def expand_actions(self, name=None):\n",
+ " """Generate all possible actions with variable bindings for precondition selection heuristic"""\n",
+ "\n",
+ " objects = set(arg for clause in self.planningproblem.init for arg in clause.args)\n",
+ " expansions = []\n",
+ " action_list = []\n",
+ " if name is not None:\n",
+ " for action in self.planningproblem.actions:\n",
+ " if str(action.name) == name:\n",
+ " action_list.append(action)\n",
+ " else:\n",
+ " action_list = self.planningproblem.actions\n",
+ "\n",
+ " for action in action_list:\n",
+ " for permutation in itertools.permutations(objects, len(action.args)):\n",
+ " bindings = unify(Expr(action.name, *action.args), Expr(action.name, *permutation))\n",
+ " if bindings is not None:\n",
+ " new_args = []\n",
+ " for arg in action.args:\n",
+ " if arg in bindings:\n",
+ " new_args.append(bindings[arg])\n",
+ " else:\n",
+ " new_args.append(arg)\n",
+ " new_expr = Expr(str(action.name), *new_args)\n",
+ " new_preconds = []\n",
+ " for precond in action.precond:\n",
+ " new_precond_args = []\n",
+ " for arg in precond.args:\n",
+ " if arg in bindings:\n",
+ " new_precond_args.append(bindings[arg])\n",
+ " else:\n",
+ " new_precond_args.append(arg)\n",
+ " new_precond = Expr(str(precond.op), *new_precond_args)\n",
+ " new_preconds.append(new_precond)\n",
+ " new_effects = []\n",
+ " for effect in action.effect:\n",
+ " new_effect_args = []\n",
+ " for arg in effect.args:\n",
+ " if arg in bindings:\n",
+ " new_effect_args.append(bindings[arg])\n",
+ " else:\n",
+ " new_effect_args.append(arg)\n",
+ " new_effect = Expr(str(effect.op), *new_effect_args)\n",
+ " new_effects.append(new_effect)\n",
+ " expansions.append(Action(new_expr, new_preconds, new_effects))\n",
+ "\n",
+ " return expansions\n",
+ "\n",
+ " def find_open_precondition(self):\n",
+ " """Find open precondition with the least number of possible actions"""\n",
+ "\n",
+ " number_of_ways = dict()\n",
+ " actions_for_precondition = dict()\n",
+ " for element in self.agenda:\n",
+ " open_precondition = element[0]\n",
+ " possible_actions = list(self.actions) + self.expanded_actions\n",
+ " for action in possible_actions:\n",
+ " for effect in action.effect:\n",
+ " if effect == open_precondition:\n",
+ " if open_precondition in number_of_ways:\n",
+ " number_of_ways[open_precondition] += 1\n",
+ " actions_for_precondition[open_precondition].append(action)\n",
+ " else:\n",
+ " number_of_ways[open_precondition] = 1\n",
+ " actions_for_precondition[open_precondition] = [action]\n",
+ "\n",
+ " number = sorted(number_of_ways, key=number_of_ways.__getitem__)\n",
+ " \n",
+ " for k, v in number_of_ways.items():\n",
+ " if v == 0:\n",
+ " return None, None, None\n",
+ "\n",
+ " act1 = None\n",
+ " for element in self.agenda:\n",
+ " if element[0] == number[0]:\n",
+ " act1 = element[1]\n",
+ " break\n",
+ "\n",
+ " if number[0] in self.expanded_actions:\n",
+ " self.expanded_actions.remove(number[0])\n",
+ "\n",
+ " return number[0], act1, actions_for_precondition[number[0]]\n",
+ "\n",
+ " def find_action_for_precondition(self, oprec):\n",
+ " """Find action for a given precondition"""\n",
+ "\n",
+ " # either\n",
+ " # choose act0 E Actions such that act0 achieves G\n",
+ " for action in self.actions:\n",
+ " for effect in action.effect:\n",
+ " if effect == oprec:\n",
+ " return action, 0\n",
+ "\n",
+ " # or\n",
+ " # choose act0 E Actions such that act0 achieves G\n",
+ " for action in self.planningproblem.actions:\n",
+ " for effect in action.effect:\n",
+ " if effect.op == oprec.op:\n",
+ " bindings = unify(effect, oprec)\n",
+ " if bindings is None:\n",
+ " break\n",
+ " return action, bindings\n",
+ "\n",
+ " def generate_expr(self, clause, bindings):\n",
+ " """Generate atomic expression from generic expression given variable bindings"""\n",
+ "\n",
+ " new_args = []\n",
+ " for arg in clause.args:\n",
+ " if arg in bindings:\n",
+ " new_args.append(bindings[arg])\n",
+ " else:\n",
+ " new_args.append(arg)\n",
+ "\n",
+ " try:\n",
+ " return Expr(str(clause.name), *new_args)\n",
+ " except:\n",
+ " return Expr(str(clause.op), *new_args)\n",
+ " \n",
+ " def generate_action_object(self, action, bindings):\n",
+ " """Generate action object given a generic action andvariable bindings"""\n",
+ "\n",
+ " # if bindings is 0, it means the action already exists in self.actions\n",
+ " if bindings == 0:\n",
+ " return action\n",
+ "\n",
+ " # bindings cannot be None\n",
+ " else:\n",
+ " new_expr = self.generate_expr(action, bindings)\n",
+ " new_preconds = []\n",
+ " for precond in action.precond:\n",
+ " new_precond = self.generate_expr(precond, bindings)\n",
+ " new_preconds.append(new_precond)\n",
+ " new_effects = []\n",
+ " for effect in action.effect:\n",
+ " new_effect = self.generate_expr(effect, bindings)\n",
+ " new_effects.append(new_effect)\n",
+ " return Action(new_expr, new_preconds, new_effects)\n",
+ "\n",
+ " def cyclic(self, graph):\n",
+ " """Check cyclicity of a directed graph"""\n",
+ "\n",
+ " new_graph = dict()\n",
+ " for element in graph:\n",
+ " if element[0] in new_graph:\n",
+ " new_graph[element[0]].append(element[1])\n",
+ " else:\n",
+ " new_graph[element[0]] = [element[1]]\n",
+ "\n",
+ " path = set()\n",
+ "\n",
+ " def visit(vertex):\n",
+ " path.add(vertex)\n",
+ " for neighbor in new_graph.get(vertex, ()):\n",
+ " if neighbor in path or visit(neighbor):\n",
+ " return True\n",
+ " path.remove(vertex)\n",
+ " return False\n",
+ "\n",
+ " value = any(visit(v) for v in new_graph)\n",
+ " return value\n",
+ "\n",
+ " def add_const(self, constraint, constraints):\n",
+ " """Add the constraint to constraints if the resulting graph is acyclic"""\n",
+ "\n",
+ " if constraint[0] == self.finish or constraint[1] == self.start:\n",
+ " return constraints\n",
+ "\n",
+ " new_constraints = set(constraints)\n",
+ " new_constraints.add(constraint)\n",
+ "\n",
+ " if self.cyclic(new_constraints):\n",
+ " return constraints\n",
+ " return new_constraints\n",
+ "\n",
+ " def is_a_threat(self, precondition, effect):\n",
+ " """Check if effect is a threat to precondition"""\n",
+ "\n",
+ " if (str(effect.op) == 'Not' + str(precondition.op)) or ('Not' + str(effect.op) == str(precondition.op)):\n",
+ " if effect.args == precondition.args:\n",
+ " return True\n",
+ " return False\n",
+ "\n",
+ " def protect(self, causal_link, action, constraints):\n",
+ " """Check and resolve threats by promotion or demotion"""\n",
+ "\n",
+ " threat = False\n",
+ " for effect in action.effect:\n",
+ " if self.is_a_threat(causal_link[1], effect):\n",
+ " threat = True\n",
+ " break\n",
+ "\n",
+ " if action != causal_link[0] and action != causal_link[2] and threat:\n",
+ " # try promotion\n",
+ " new_constraints = set(constraints)\n",
+ " new_constraints.add((action, causal_link[0]))\n",
+ " if not self.cyclic(new_constraints):\n",
+ " constraints = self.add_const((action, causal_link[0]), constraints)\n",
+ " else:\n",
+ " # try demotion\n",
+ " new_constraints = set(constraints)\n",
+ " new_constraints.add((causal_link[2], action))\n",
+ " if not self.cyclic(new_constraints):\n",
+ " constraints = self.add_const((causal_link[2], action), constraints)\n",
+ " else:\n",
+ " # both promotion and demotion fail\n",
+ " print('Unable to resolve a threat caused by', action, 'onto', causal_link)\n",
+ " return\n",
+ " return constraints\n",
+ "\n",
+ " def convert(self, constraints):\n",
+ " """Convert constraints into a dict of Action to set orderings"""\n",
+ "\n",
+ " graph = dict()\n",
+ " for constraint in constraints:\n",
+ " if constraint[0] in graph:\n",
+ " graph[constraint[0]].add(constraint[1])\n",
+ " else:\n",
+ " graph[constraint[0]] = set()\n",
+ " graph[constraint[0]].add(constraint[1])\n",
+ " return graph\n",
+ "\n",
+ " def toposort(self, graph):\n",
+ " """Generate topological ordering of constraints"""\n",
+ "\n",
+ " if len(graph) == 0:\n",
+ " return\n",
+ "\n",
+ " graph = graph.copy()\n",
+ "\n",
+ " for k, v in graph.items():\n",
+ " v.discard(k)\n",
+ "\n",
+ " extra_elements_in_dependencies = _reduce(set.union, graph.values()) - set(graph.keys())\n",
+ "\n",
+ " graph.update({element:set() for element in extra_elements_in_dependencies})\n",
+ " while True:\n",
+ " ordered = set(element for element, dependency in graph.items() if len(dependency) == 0)\n",
+ " if not ordered:\n",
+ " break\n",
+ " yield ordered\n",
+ " graph = {element: (dependency - ordered) for element, dependency in graph.items() if element not in ordered}\n",
+ " if len(graph) != 0:\n",
+ " raise ValueError('The graph is not acyclic and cannot be linearly ordered')\n",
+ "\n",
+ " def display_plan(self):\n",
+ " """Display causal links, constraints and the plan"""\n",
+ "\n",
+ " print('Causal Links')\n",
+ " for causal_link in self.causal_links:\n",
+ " print(causal_link)\n",
+ "\n",
+ " print('\\nConstraints')\n",
+ " for constraint in self.constraints:\n",
+ " print(constraint[0], '<', constraint[1])\n",
+ "\n",
+ " print('\\nPartial Order Plan')\n",
+ " print(list(reversed(list(self.toposort(self.convert(self.constraints))))))\n",
+ "\n",
+ " def execute(self, display=True):\n",
+ " """Execute the algorithm"""\n",
+ "\n",
+ " step = 1\n",
+ " self.tries = 1\n",
+ " while len(self.agenda) > 0:\n",
+ " step += 1\n",
+ " # select <G, act1> from Agenda\n",
+ " try:\n",
+ " G, act1, possible_actions = self.find_open_precondition()\n",
+ " except IndexError:\n",
+ " print('Probably Wrong')\n",
+ " break\n",
+ "\n",
+ " act0 = possible_actions[0]\n",
+ " # remove <G, act1> from Agenda\n",
+ " self.agenda.remove((G, act1))\n",
+ "\n",
+ " # For actions with variable number of arguments, use least commitment principle\n",
+ " # act0_temp, bindings = self.find_action_for_precondition(G)\n",
+ " # act0 = self.generate_action_object(act0_temp, bindings)\n",
+ "\n",
+ " # Actions = Actions U {act0}\n",
+ " self.actions.add(act0)\n",
+ "\n",
+ " # Constraints = add_const(start < act0, Constraints)\n",
+ " self.constraints = self.add_const((self.start, act0), self.constraints)\n",
+ "\n",
+ " # for each CL E CausalLinks do\n",
+ " # Constraints = protect(CL, act0, Constraints)\n",
+ " for causal_link in self.causal_links:\n",
+ " self.constraints = self.protect(causal_link, act0, self.constraints)\n",
+ "\n",
+ " # Agenda = Agenda U {<P, act0>: P is a precondition of act0}\n",
+ " for precondition in act0.precond:\n",
+ " self.agenda.add((precondition, act0))\n",
+ "\n",
+ " # Constraints = add_const(act0 < act1, Constraints)\n",
+ " self.constraints = self.add_const((act0, act1), self.constraints)\n",
+ "\n",
+ " # CausalLinks U {<act0, G, act1>}\n",
+ " if (act0, G, act1) not in self.causal_links:\n",
+ " self.causal_links.append((act0, G, act1))\n",
+ "\n",
+ " # for each A E Actions do\n",
+ " # Constraints = protect(<act0, G, act1>, A, Constraints)\n",
+ " for action in self.actions:\n",
+ " self.constraints = self.protect((act0, G, act1), action, self.constraints)\n",
+ "\n",
+ " if step > 200:\n",
+ " print('Couldn\\'t find a solution')\n",
+ " return None, None\n",
+ "\n",
+ " if display:\n",
+ " self.display_plan()\n",
+ " else:\n",
+ " return self.constraints, self.causal_links \n",
+ "
![](\"images/fig_5_2.png\")
\n",
"\n",
- "The states are represented wih capital letters inside the triangles (eg. \"A\") while moves are the labels on the edges between states (eg. \"a1\"). Terminal nodes carry utility values. Note that the terminal nodes are named in this example 'B1', 'B2' and 'B2' for the nodes below 'B', and so forth.\n",
+ "The states are represented with capital letters inside the triangles (eg. \"A\") while moves are the labels on the edges between states (eg. \"a1\"). Terminal nodes carry utility values. Note that the terminal nodes are named in this example 'B1', 'B2' and 'B2' for the nodes below 'B', and so forth.\n",
"\n",
"We will model the moves, utilities and initial state like this:"
]
@@ -285,7 +292,9 @@
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": true
+ },
"outputs": [],
"source": [
"psource(Fig52Game.actions)"
@@ -318,7 +327,9 @@
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": true
+ },
"outputs": [],
"source": [
"psource(Fig52Game.result)"
@@ -351,7 +362,9 @@
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": true
+ },
"outputs": [],
"source": [
"psource(Fig52Game.utility)"
@@ -386,7 +399,9 @@
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": true
+ },
"outputs": [],
"source": [
"psource(Fig52Game.terminal_test)"
@@ -419,7 +434,9 @@
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": true
+ },
"outputs": [],
"source": [
"psource(Fig52Game.to_move)"
@@ -452,7 +469,9 @@
{
"cell_type": "code",
"execution_count": null,
- "metadata": {},
+ "metadata": {
+ "collapsed": true
+ },
"outputs": [],
"source": [
"psource(Fig52Game)"
@@ -473,7 +492,7 @@
},
{
"cell_type": "code",
- "execution_count": 9,
+ "execution_count": 2,
"metadata": {},
"outputs": [
{
@@ -506,7 +525,7 @@
"![](\"images/nn.png\")
\n",
+ "\n",
+ "In our code, we implemented it as:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# initialize the network\n",
+ "raw_net = [InputLayer(input_size)]\n",
+ "# add hidden layers\n",
+ "hidden_input_size = input_size\n",
+ "for h_size in hidden_layer_sizes:\n",
+ " raw_net.append(DenseLayer(hidden_input_size, h_size))\n",
+ " hidden_input_size = h_size\n",
+ "raw_net.append(DenseLayer(hidden_input_size, output_size))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Where hidden_layer_sizes are the sizes of each hidden layer in a list which can be specified by user. Neural network learner uses gradient descent as default optimizer but user can specify any optimizer when calling `neural_net_learner`. The other special attribute that can be changed in `neural_net_learner` is `batch_size` which controls the number of examples used in each round of update. `neural_net_learner` also returns a `predict` function which calculates prediction by multiplying weight to inputs and applying activation functions.\n",
+ "\n",
+ "### Example\n",
+ "\n",
+ "Let's also try `neural_net_learner` on the `iris` dataset:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "epoch:10, total_loss:15.931817841643683\n",
+ "epoch:20, total_loss:8.248422285412149\n",
+ "epoch:30, total_loss:6.102968668275\n",
+ "epoch:40, total_loss:5.463915043272969\n",
+ "epoch:50, total_loss:5.298986288420822\n",
+ "epoch:60, total_loss:4.032928400456889\n",
+ "epoch:70, total_loss:3.2628899927346855\n",
+ "epoch:80, total_loss:6.01336701367312\n",
+ "epoch:90, total_loss:5.412020420311795\n",
+ "epoch:100, total_loss:3.1044027319850773\n"
+ ]
+ }
+ ],
+ "source": [
+ "nn = neural_net_learner(iris, epochs=100, learning_rate=0.15, optimizer=gradient_descent, verbose=10)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Similarly we check the model's accuracy on both training and test dataset:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "error ration on training set: 0.033333333333333326\n"
+ ]
+ }
+ ],
+ "source": [
+ "print(\"error ration on training set:\",err_ratio(nn, iris))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "accuracy on test set: 1\n"
+ ]
+ }
+ ],
+ "source": [
+ "tests = [([5.0, 3.1, 0.9, 0.1], 0),\n",
+ " ([5.1, 3.5, 1.0, 0.0], 0),\n",
+ " ([4.9, 3.3, 1.1, 0.1], 0),\n",
+ " ([6.0, 3.0, 4.0, 1.1], 1),\n",
+ " ([6.1, 2.2, 3.5, 1.0], 1),\n",
+ " ([5.9, 2.5, 3.3, 1.1], 1),\n",
+ " ([7.5, 4.1, 6.2, 2.3], 2),\n",
+ " ([7.3, 4.0, 6.1, 2.4], 2),\n",
+ " ([7.0, 3.3, 6.1, 2.5], 2)]\n",
+ "print(\"accuracy on test set:\",grade_learner(nn, tests))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We can see that the error ratio on the training set is smaller than the perceptron learner. As the error ratio is relatively small, let's try the model on the MNIST dataset to see whether there will be a larger difference. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "epoch:10, total_loss:89.0002153455983\n",
+ "epoch:20, total_loss:87.29675663038348\n",
+ "epoch:30, total_loss:86.29591779319225\n",
+ "epoch:40, total_loss:83.78091780128402\n",
+ "epoch:50, total_loss:82.17091581738829\n",
+ "epoch:60, total_loss:83.8434277386084\n",
+ "epoch:70, total_loss:83.55209905561495\n",
+ "epoch:80, total_loss:83.106898191118\n",
+ "epoch:90, total_loss:83.37041170165992\n",
+ "epoch:100, total_loss:82.57013813500876\n"
+ ]
+ }
+ ],
+ "source": [
+ "nn = neural_net_learner(mnist, epochs=100, verbose=10)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "0.784\n"
+ ]
+ }
+ ],
+ "source": [
+ "print(err_ratio(nn, mnist))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "After the model converging, the model's error ratio on the training set is still high. We will introduce the convolutional network in the following chapters to see how it helps improve accuracy on learning this dataset."
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.6.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/notebooks/chapter19/Loss Functions and Layers.ipynb b/notebooks/chapter19/Loss Functions and Layers.ipynb
new file mode 100644
index 000000000..25676e899
--- /dev/null
+++ b/notebooks/chapter19/Loss Functions and Layers.ipynb
@@ -0,0 +1,398 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Loss Function\n",
+ "\n",
+ "Loss functions evaluate how well specific algorithm models the given data. Commonly loss functions are used to compare the target data and model's prediction. If predictions deviate too much from actual targets, loss function would output a large value. Usually, loss functions can help other optimization functions to improve the accuracy of the model.\n",
+ "\n",
+ "However, there’s no one-size-fits-all loss function to algorithms in machine learning. For each algorithm and machine learning projects, specifying certain loss functions could assist the user in getting better model performance. Here we will demonstrate two loss functions: `mse_loss` and `cross_entropy_loss`."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Min Square Error\n",
+ "\n",
+ "Min square error(MSE) is the most commonly used loss function in machine learning. The intuition of MSE is straight forward: the distance between two points represents the difference between them. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "$$MSE = -\\sum_i{(y_i-t_i)^2/n}$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Where $y_i$ is the prediction of the ith example and $t_i$ is the target of the ith example. And n is the total number of examples.\n",
+ "\n",
+ "Below is a plot of an MSE function where the true target value is 100, and the predicted values range between -10,000 to 10,000. The MSE loss (Y-axis) reaches its minimum value at prediction (X-axis) = 100."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "![](\"images/mse_plot.png\")
"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Cross-Entropy\n",
+ "\n",
+ "For most deep learning applications, we can get away with just one loss function: cross-entropy loss function. We can think of most deep learning algorithms as learning probability distributions and what we are learning is a distribution of predictions $P(y|x)$ given a series of inputs. \n",
+ "\n",
+ "To associate input examples x with output examples y, the parameters that maximize the likelihood of the training set should be:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "$$\\theta^* = argmax_\\theta \\prod_{i=0}^n p(y^{(i)}/x^{(i)})$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Maxmizing the above formula equals to minimizing the negative log form of it:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "$$\\theta^* = argmin_\\theta -\\sum_{i=0}^n logp(y^{(i)}/x^{(i)})$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "It can be proven that the above formula equals to minimizing MSE loss.\n",
+ "\n",
+ "The majority of deep learning algorithms use cross-entropy in some way. Classifiers that use deep learning calculate the cross-entropy between categorical distributions over the output class. For a given class, its contribution to the loss is dependent on its probability in the following trend:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "![](\"images/corss_entropy_plot.png\")
"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Examples\n",
+ "\n",
+ "First let's import necessary packages."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "Using TensorFlow backend.\n"
+ ]
+ }
+ ],
+ "source": [
+ "import os, sys\n",
+ "sys.path = [os.path.abspath(\"../../\")] + sys.path\n",
+ "from deep_learning4e import *\n",
+ "from notebook4e import *"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Neural Network Layers\n",
+ "\n",
+ "Neural networks may be conveniently described using data structures of computational graphs. A computational graph is a directed graph describing how many variables should be computed, with each variable by computed by applying a specific operation to a set of other variables. \n",
+ "\n",
+ "In our code, we provide class `NNUnit` as the basic structure of a neural network. The structure of `NNUnit` is simple, it only stores the following information:\n",
+ "\n",
+ "- **val**: the value of the current node.\n",
+ "- **parent**: parents of the current node.\n",
+ "- **weights**: weights between parent nodes and current node. It should be in the same size as parents.\n",
+ "\n",
+ "There is another class `Layer` inheriting from `NNUnit`. A `Layer` object holds a list of nodes that represents all the nodes in a layer. It also has a method `forward` to pass a value through the current layer. Here we will demonstrate several pre-defined types of layers in a Neural Network."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Output Layers\n",
+ "\n",
+ "Neural networks need specialized output layers for each type of data we might ask them to produce. For many problems, we need to model discrete variables that have k distinct values instead of just binary variables. For example, models of natural language may predict a single word from among of vocabulary of tens of thousands or even more choices. To represent these distributions, we use a softmax layer:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "$$P(y=i|x)=softmax(h(x)^TW+b)_i$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "where $W$ is matrix of learned weights of output layer $b$ is a vector of learned biases, and the softmax function is:\n",
+ "\n",
+ "$$softmax(z_i)=exp(z_i)/\\sum_i exp(z_i)$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "It is simple to create a output layer and feed an example into it:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[0.03205860328008499, 0.08714431874203257, 0.23688281808991013, 0.6439142598879722]\n"
+ ]
+ }
+ ],
+ "source": [
+ "layer = OutputLayer(size=4)\n",
+ "example = [1,2,3,4]\n",
+ "print(layer.forward(example))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The output can be treated like normalized probability when the input of output layer is calculated by probability."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Input Layers\n",
+ "\n",
+ "Input layers can be treated like a mapping layer that maps each element of the input vector to each input layer node. The input layer acts as a storage of input vector information which can be used when doing forward propagation.\n",
+ "\n",
+ "In our realization of input layers, the size of the input vector and input layer should match."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[1, 2, 3]\n"
+ ]
+ }
+ ],
+ "source": [
+ "layer = InputLayer(size=3)\n",
+ "example = [1,2,3]\n",
+ "print(layer.forward(example))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Hidden Layers\n",
+ "\n",
+ "While processing an input vector x of the neural network, it performs several intermediate computations before producing the output y. We can think of these intermediate computations as the state of memory during the execution of a multi-step program. We call the intermediate computations hidden because the data does not specify the values of these variables.\n",
+ "\n",
+ "Most neural network hidden layers are based on a linear transformation followed by the application of an elementwise nonlinear function called the activation function g:\n",
+ "\n",
+ "$$h=g(W+b)$$\n",
+ "\n",
+ "where W is a learned matrix of weights and b is a learned set of bias parameters.\n",
+ "\n",
+ "Here we pre-defined several activation functions in `utils.py`: `sigmoid`, `relu`, `elu`, `tanh` and `leaky_relu`. They are all inherited from the `Activation` class. You can get the value of the function or its derivative at a certain point of x:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Sigmoid at 0: 0.5\n",
+ "Deriavation of sigmoid at 0: 0\n"
+ ]
+ }
+ ],
+ "source": [
+ "s = sigmoid()\n",
+ "print(\"Sigmoid at 0:\", s.f(0))\n",
+ "print(\"Deriavation of sigmoid at 0:\", s.derivative(0))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "To create a hidden layer object, there are several attributes need to be specified:\n",
+ "\n",
+ "- **in_size**: the input vector size of each hidden layer node.\n",
+ "- **out_size**: the size of the output vector of the hidden layer. Thus each node will hide the weight of the size of (in_size). The weights will be initialized randomly.\n",
+ "- **activation**: the activation function used for this layer.\n",
+ "\n",
+ "Now let's demonstrate how a dense hidden layer works briefly:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[0.21990266877137224, 0.2038864498984756, 0.5543443697256466]\n"
+ ]
+ }
+ ],
+ "source": [
+ "layer = DenseLayer(in_size=4, out_size=3, activation=sigmoid())\n",
+ "example = [1,2,3,4]\n",
+ "print(layer.forward(example))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "This layer mapped input of size 4 to output of size 3. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Convolutional Layers\n",
+ "\n",
+ "The convolutional layer is similar to the hidden layer except they use a different forward strategy. The convolutional layer takes an input of multiple channels and does convolution on each channel with a pre-defined kernel function. Thus the output of the convolutional layer will still be with the same number of channels. If we image each input as an image, then channels represent its color model such as RGB. The output will still have the same color model as the input.\n",
+ "\n",
+ "Now let's try the one-dimensional convolution layer:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[array([3.9894228, 3.9894228, 3.9894228]), array([3.9894228, 3.9894228, 3.9894228]), array([3.9894228, 3.9894228, 3.9894228])]\n"
+ ]
+ }
+ ],
+ "source": [
+ "layer = ConvLayer1D(size=3, kernel_size=3)\n",
+ "example = [[1]*3 for _ in range(3)]\n",
+ "print(layer.forward(example))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Which can be deemed as a one-dimensional image with three channels."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Pooling Layers\n",
+ "\n",
+ "Pooling layers can be treated as a special kind of convolutional layer that uses a special kind of kernel to extract a certain value in the kernel region. Here we use max-pooling to report the maximum value in each group."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[[3, 4], [4, 4], [4, 4]]\n"
+ ]
+ }
+ ],
+ "source": [
+ "layer = MaxPoolingLayer1D(size=3, kernel_size=3)\n",
+ "example = [[1,2,3,4], [2,3,4,1],[3,4,1,2]]\n",
+ "print(layer.forward(example))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We can see that each time kernel picks up the maximum value in its region."
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.6.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/notebooks/chapter19/Optimizer and Backpropagation.ipynb b/notebooks/chapter19/Optimizer and Backpropagation.ipynb
new file mode 100644
index 000000000..5194adc7a
--- /dev/null
+++ b/notebooks/chapter19/Optimizer and Backpropagation.ipynb
@@ -0,0 +1,311 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Optimization Algorithms\n",
+ "\n",
+ "Training a neural network consists of modifying the network’s parameters to minimize the cost function on the training set. In principle, any kind of optimization algorithm could be used. In practice, modern neural networks are almost always trained with some variant of stochastic gradient descent(SGD). Here we will provide two optimization algorithms: SGD and Adam optimizer.\n",
+ "\n",
+ "## Stochastic Gradient Descent\n",
+ "\n",
+ "The goal of an optimization algorithm is to find the value of the parameter to make loss function very low. For some types of models, an optimization algorithm might find the global minimum value of loss function, but for neural network, the most efficient way to converge loss function to a local minimum is to minimize loss function according to each example.\n",
+ "\n",
+ "Gradient descent uses the following update rule to minimize loss function:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "$$\\theta^{(t+1)} = \\theta^{(t)}-\\alpha\\nabla_\\theta L(\\theta^{(t)})$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "where t is the time step of the algorithm and $\\alpha$ is the learning rate. But this rule could be very costly when $L(\\theta)$ is defined as a sum across the entire training set. Using SGD can accelerate the learning process as we can use only a batch of examples to update the parameters. \n",
+ "\n",
+ "We implemented the gradient descent algorithm, which can be viewed with the following code:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "Using TensorFlow backend.\n"
+ ]
+ }
+ ],
+ "source": [
+ "import os, sys\n",
+ "sys.path = [os.path.abspath(\"../../\")] + sys.path\n",
+ "from deep_learning4e import *\n",
+ "from notebook4e import *"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ " ![](\"images/backprop.png\")
"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Applying optimizers and back-propagation algorithm together, we can update the weights of a neural network to minimize the loss function with alternatively doing forward and back-propagation process. Here is a figure form [here](https://medium.com/datathings/neural-networks-and-backpropagation-explained-in-a-simple-way-f540a3611f5e) describing how a neural network updates its weights:\n",
+ "\n",
+ "![](\"images/nn_steps.png\")
"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In our implementation, all the steps are integrated into the optimizer objects. The forward-backward process of passing information through the whole neural network is put into the method `BackPropagation`. You can view the code with:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "psource(BackPropagation)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The demonstration of optimizers and back-propagation algorithm will be made together with neural network learners."
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.6.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/notebooks/chapter19/RNN.ipynb b/notebooks/chapter19/RNN.ipynb
new file mode 100644
index 000000000..b6971b36a
--- /dev/null
+++ b/notebooks/chapter19/RNN.ipynb
@@ -0,0 +1,487 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# RNN\n",
+ "\n",
+ "## Overview\n",
+ "\n",
+ "When human is thinking, they are thinking based on the understanding of previous time steps but not from scratch. Traditional neural networks can’t do this, and it seems like a major shortcoming. For example, imagine you want to do sentimental analysis of some texts. It will be unclear if the traditional network cannot recognize the short phrase and sentences.\n",
+ "\n",
+ "Recurrent neural networks address this issue. They are networks with loops in them, allowing information to persist.\n",
+ "\n",
+ "![](\"images/rnn_unit.png\")
"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "A recurrent neural network can be thought of as multiple copies of the same network, each passing a message to a successor. Consider what happens if we unroll the above loop:\n",
+ " \n",
+ "![](\"images/rnn_units.png\")
"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "As demonstrated in the book, recurrent neural networks may be connected in many different ways: sequences in the input, the output, or in the most general case both.\n",
+ "\n",
+ "![](\"images/rnn_connections.png\")
"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Implementation\n",
+ "\n",
+ "In our case, we implemented rnn with modules offered by the package of `keras`. To use `keras` and our module, you must have both `tensorflow` and `keras` installed as a prerequisite. `keras` offered very well defined high-level neural networks API which allows for easy and fast prototyping. `keras` supports many different types of networks such as convolutional and recurrent neural networks as well as user-defined networks. About how to get started with `keras`, please read the [tutorial](https://keras.io/).\n",
+ "\n",
+ "To view our implementation of a simple rnn, please use the following code:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "Using TensorFlow backend.\n"
+ ]
+ }
+ ],
+ "source": [
+ "import warnings\n",
+ "warnings.filterwarnings(\"ignore\", category=FutureWarning)\n",
+ "import os, sys\n",
+ "sys.path = [os.path.abspath(\"../../\")] + sys.path\n",
+ "from deep_learning4e import *\n",
+ "from notebook4e import *"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ " ![](\"images/autoencoder.png\")
"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Autoencoders are learned automatically from data examples. It means that it is easy to train specialized instances of the algorithm that will perform well on a specific type of input and that it does not require any new engineering, only the appropriate training data.\n",
+ "\n",
+ "Autoencoders have different architectures for different kinds of data. Here we only provide a simple example of a vanilla encoder, which means they're only one hidden layer in the network:\n",
+ "\n",
+ "![](\"images/vanilla.png\")
\n",
+ "\n",
+ "You can view the source code by:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ " ![](\"images/mdp.png\")
Now we define actions and a policy similar to **Fig 21.1** in the book."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Action Directions\n",
+ "north = (0, 1)\n",
+ "south = (0,-1)\n",
+ "west = (-1, 0)\n",
+ "east = (1, 0)\n",
+ "\n",
+ "policy = {\n",
+ " (0, 2): east, (1, 2): east, (2, 2): east, (3, 2): None,\n",
+ " (0, 1): north, (2, 1): north, (3, 1): None,\n",
+ " (0, 0): north, (1, 0): west, (2, 0): west, (3, 0): west, \n",
+ "}"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "This enviroment will be extensively used in the following demonstrations."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Direct Utility Estimation (DUE)\n",
+ " \n",
+ " The first, most naive method of estimating utility comes from the simplest interpretation of the above definition. We construct an agent that follows the policy until it reaches the terminal state. At each step, it logs its current state, reward. Once it reaches the terminal state, it can estimate the utility for each state for *that* iteration, by simply summing the discounted rewards from that state to the terminal one.\n",
+ "\n",
+ " It can now run this 'simulation' $n$ times and calculate the average utility of each state. If a state occurs more than once in a simulation, both its utility values are counted separately.\n",
+ " \n",
+ " Note that this method may be prohibitively slow for very large state-spaces. Besides, **it pays no attention to the transition probability $P(s'\\ |\\ s, a)$.** It misses out on information that it is capable of collecting (say, by recording the number of times an action from one state led to another state). The next method addresses this issue.\n",
+ " \n",
+ "### Examples\n",
+ "\n",
+ "The `PassiveDEUAgent` class in the `rl` module implements the Agent Program described in **Fig 21.2** of the AIMA Book. `PassiveDEUAgent` sums over rewards to find the estimated utility for each state. It thus requires the running of several iterations."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "%psource PassiveDUEAgent"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now let's try the `PassiveDEUAgent` on the newly defined `sequential_decision_environment`:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "DUEagent = PassiveDUEAgent(policy, sequential_decision_environment)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We can try passing information through the markove model for 200 times in order to get the converged utility value:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "for i in range(200):\n",
+ " run_single_trial(DUEagent, sequential_decision_environment)\n",
+ " DUEagent.estimate_U()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now let's print our estimated utility for each position:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "(0, 1):0.7956939931414414\n",
+ "(1, 2):0.9162054322837863\n",
+ "(3, 2):1.0\n",
+ "(0, 0):0.734717308253083\n",
+ "(2, 2):0.9595117143816332\n",
+ "(0, 2):0.8481387156375687\n",
+ "(1, 0):0.4355860415209706\n",
+ "(2, 1):-0.550079982553143\n",
+ "(3, 1):-1.0\n"
+ ]
+ }
+ ],
+ "source": [
+ "print('\\n'.join([str(k)+':'+str(v) for k, v in DUEagent.U.items()]))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Adaptive Dynamic Programming (ADP)\n",
+ " \n",
+ " This method makes use of knowledge of the past state $s$, the action $a$, and the new perceived state $s'$ to estimate the transition probability $P(s'\\ |\\ s,a)$. It does this by the simple counting of new states resulting from previous states and actions.![](\"images/gradients.png\")
"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Implementation\n",
+ "\n",
+ "We implemented an edge detector using a gradient method as `gradient_edge_detector` in `perceptron.py`. There are two filters defined as $[[1, -1]], [[1], [-1]]$ to extract edges in x and y directions respectively. The filters are applied to an image using `convolve2d` method in `scipy.single` package. The image passed into the function needs to be in the form of `numpy.ndarray` or an iterable object that can be transformed into a `ndarray`.\n",
+ "\n",
+ "To view the detailed implementation, please execute the following block"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "psource(gradient_edge_detector)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Example\n",
+ "\n",
+ "Now let's try the detector for real case pictures. First, we will show the original picture before edge detection:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "![](\"images/stapler.png\")
\n",
+ "\n",
+ "We will use `matplotlib` to read the image as a numpy ndarray:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "image height: 590\n",
+ "image width: 787\n"
+ ]
+ }
+ ],
+ "source": [
+ "import matplotlib.pyplot as plt\n",
+ "import numpy as np\n",
+ "import matplotlib.image as mpimg\n",
+ "\n",
+ "im =mpimg.imread('images/stapler.png')\n",
+ "print(\"image height:\", len(im))\n",
+ "print(\"image width:\", len(im[0]))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The code shows we get an image with a size of $787*590$. `gaussian_derivative_edge_detector` can extract images in both x and y direction and then put them together in a ndarray:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "image height: 590\n",
+ "image width: 787\n"
+ ]
+ }
+ ],
+ "source": [
+ "edges = gradient_edge_detector(im)\n",
+ "print(\"image height:\", len(edges))\n",
+ "print(\"image width:\", len(edges[0]))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The edges are in the same shape of the original image. Now we will try print out the image, we implemented a `show_edges` function to do this:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "![](\"images/derivative_of_gaussian.png\")
"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Implementation\n",
+ "\n",
+ "In our implementation, we initialize Gaussian filters by applying the 2D Gaussian function on a given size of the grid which is the same as the kernel size. Then the x and y direction image filters are calculated as the convolution of the Gaussian filter and the gradient filter:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "x_filter = scipy.signal.convolve2d(gaussian_filter, np.asarray([[1, -1]]), 'same')\n",
+ "y_filter = scipy.signal.convolve2d(gaussian_filter, np.asarray([[1], [-1]]), 'same')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Then both of the filters are applied to the input image to extract the x and y direction edges. For detailed implementation, please view by:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "psource(gaussian_derivative_edge_detector)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Example\n",
+ "\n",
+ "Now let's try again on the stapler image and plot the extracted edges:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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zaf73KkXevoNQnPaZCfJ/KotzAEgMzcDH+PnMqRsA19uMSP/+2wqxY7o5WveiEi1Tjh7r9F4fX9OO1gsUgJ9TIssNoLejePw4eM7TAczXzBTK10+ZZUqXjNX9OqjY5pAxn2eNxd/5xnOPIdmv58VxXom3nWJHZnYO9paXZUq/qTeDv5mlATvtyPPwthZvm+A4fA1Z+treymT59gDXtogN2qd61/VxPs+481Q5pOozAHZ8fDwSooGAWlXVw2M7UDTRgtt9vL8HRmSQQsjU0kwjzQoccfmevr03zcyolzIx5p6DpKPzOzfg2fmsIMbuFR0DQc8Ze0ZU9VCjMrsxC3SKwbE5NgMe/QDsBiEfS2riFJPzM5iY6XCOU9DVajV6kkmmBJ4X87DOneI5YFpmGH2mre4rm0E/WZB1ZTlhB07/bWtcv3edXqM/Mhb68FMZvEjjsfknZZqpY4/FOnBlQM55uObpzw1c3mmQQcgLRWZVBndfP1cs/9cp5Hw+b7vbGbipuj87ODgYDY4o54n0Il5GUJQKE4PyOg1JI3HBMBlR7jJm7CgVA0zB2jAc9WwUHJsRyuDisTDOHghxjNmTUww7stmiQZm5UeezA3Mdr2J5Xh47f2PMrkHxGSvJHAvAGFSdyjMHAAZgyBIAnydLR5fM18BO/+jRunTtKFtPp4yJIrLZpPXglMvf4Yypk7xGBljOQY5O4xw0HZCtP+vJDJMfkwH7GkV7jsn6H3rknkzGwW+uf3t7O5qrdYKNMN9kzLnhlz7/bgA7ODhoE8IpMEoKes6NF4tFu1fSAEKB2BM/PDxskZ5CP8+oonFbjydpCktfBiAziaT1vv8LQTqycA4G5J3Hdsxe2mRQQwGZxhFd/F3WVczcemluT9Gu5xiYq8YbEx2Jmb+B2mwDfXG85VE1LmjP5/MRezQop3G6tojzuPjLsSwg9Awa/ZmJeY7YgR3JTsw4uH724wK4g4htgU28vqYZO2MA0MySXcvlOC8g8Zn1y+8ERsvEK4TJmlxbxC5sh4wfvfoWIsDUwIlteA6QE/pg/PSB/J1iuznwcOcL43qq7QQw5/cMHMF564QLwTAMJuJVDhRhJuInVtrYN5tN20+GEMxGnG44sqQBcwyfOdoZfCxA03j6yRw/f9NnRjiPN5kZ83JqgKGl8yVgJyA8peg0Eo8JWdhJbIjM34ZvtohOuYXMY6T1NjB6HvRjoHDNtFf/yDk50PR+qsY1GYOQ5WKGyJiSjVSNGWemcAa7ZJjM0U9bQMbWhefpwNmTFde2fvIzp9EpY9tMruZyvOtmPj51Zr9MpuqyAr6cpCZLMdbdU+2zDAyGZENar9eNQTF4Iip7uJggT2N1rQTh4iywtun04a55JuUagI2J761QG7wVkTTaoMSYLExfwwzASnGUpQ+ajc4Rvqq6Rp/G6d8JigYvB4MExtQXfTm19PgdQPy4YcveK1YGPJqB23KzUyGD3vEGx95xlpNl42BlOZjt2fESiJ7SKc3f+TOz5dShQSNTTo/TZZgcp8flQIe+eiw0yw62W8smgyv2b7tKfViHll9mDMMwjGTDZ+m/XL/qgeyYiTKeXauRn2Vgm83DY3GM7CBpsrPJZDJ6QCHpJGDlpXHS0uvr6/a3H0joCef1rHSPwcZjZ7OQU5BQfQSGgzu9wYBMx6v6t1kkyDq9yaKwlWsnzLTJRuQ5VY1XlgAaU/RMr/hsl8PmvGDajDFZie3DINtLsWm5k91zy3m50b9ZS9aVnE4/Fcn9vR2Ghh7cB5/b0R0wbCMOQgn01r0L7AYy25CZIWNwn8zFnydrtmw9XsDY4Jf67QVS26jBK7/rgabT9aqHnfq5+t1j7247b+Z2Cgfi8zuL5k41XEcBja+ururZs2cj1OZ7lph5/phT0owyKJx+MbLZ7OH5YbAJanSTyWT0FAwbq4VkxmeFAIim2F4QsGHaKOnbdSEDcjIQA61B2IZkMOfc5XLZnhZSNX5Olft2FHb65BTXCzRERdcMPV6nBwYNG3sv4ia4pmzNajNYGNx9voNoBgb0ju1m0d+AZBn12KU3aOZCDHq3jAzoBhfrw1sGMig4WFi+2JUBxM8T8zFe8IEouH7FOWZbfp+E5+MV6iQK+AWpc6aYrmNbBtY3W1N6jLTXdjKw09PTkSFst9v26BuiBhf043BobEydTCb17Nmzlnoa6GBsTq3YNNuL9jyuJLdQIFBviEMAXPfg4KBFG54xZnruiGmgRcn+DDDnOyvCxxronDKgyKT7VY+jXzIixs54kb036HIs4yFNpi8vJiST9QKHHdkOttlsGtM2qCT79I5yp03IxP04YK3X67bXMBdUiNzWG2NC7r4jBHZCkduOSp/exkBfBiBkgA3lijZ9OX1KxuH+sGHLi7G7pOH+nSojL4/TKSJ/uyadWQf9JWNmfMwz2TPH+j5nxsRGZ9u4wct2aR9PZlj18DjtXe2zT6NAYavV/cs9eL7X8fFxE/T+/n59+vSpTdpgBpAwGK9YQRkxBvp0zQ2hg9qkoUQurmOluRaAgNfrdXuaBQ6Uhd2qx9sYrDAzJy/3c60sxDpqojgzBs8ro00aVNYUemzEwOAXdRik7SyOsE4RDQLIlWMMaN4Z3mMrnJMszHO0cyN77/Zm7gYkxsB1WOLHWWAGzhCcqt3e3tZ8Pm8voWFV3UwV2Tv1ytU1ZGO24NqibYInUDhg5aqe60EJMJY7/RiMnS7yO4Ojx2oWZf15O5TPR1/oAv1jS6ljMzGDEnaGHpgvzfdwGvSfajtTyOPj4/Z6MrY42NG8E9k3XvPbObejS1J5HI5I7OVtKz2jnp3b9JyIu8t5bBj87wjm61iAKD7TZUd/xsDfXqHx5x6XHdLjszHxf9J/j4PmiEd/7t+1PAMF35lpMT6DJ306wic78G/PO1fx0CsOzfV8fs7FvzMAJROkP/dpXTvdJ0D2mvs2o+6xlKxReRwp0x74JKu0bCwf24fHYLDytQDSlBfNd9K4+Zg8xxkGNpoppAmFAyHkxtkWx9ufnmp/061ETof427R/s9mMbu7lczsXEyL1QgDe6+PCfjK0qvF9XF7lwVkxPCvb4zZrqRrXfuxgBhPfuFr1+OkTdkrmkEaT4JHKdgqHQh19bQhZdyOiue+qx3UNg76Pca0xAdfXsEx8fA/UaHyWaZvtgf/v7u5aKQEwy9QG0E2wsAN5tc7OSF85H659e3tbt7e37R2oBG76z7cC5eJAysggh2Oa9fIdP5a5mZlZjnWcgdUsKetqyKIX7L1PkH4MrAn8HoOzHV/L4IVf0K/7cyZFWYdzfI0Mzm47AcxMyPtnEASAksjvG1tRHK9Pg2kBTp44fWZxkOZl7xSkv8/akql8AkOCh43B5/dYUwrWffv7NBLkyd8JFkQwp78GjwQNpzT528aSsvOc/T+LKJaxj3Uhm/PsVHbiHvBnaoAevHnSunXEtu6sdzuPZekxcbyd3amft9g4VXKKmXp2CaFnE7bh1LOL6y5p8J39zT+ue6VdmBlyzQwqtqGnUr9k9bmVwd/nmBiP02n7JHqy/xG4bDOWx1NtJ4AxINiVEXQ6nY523Bt4zHiS7mdx2ALNKOPr8T+CSlCxcgFRb7vopXw9YTqae3wumrulQbh+wfFOfVGGC5iWDwzVDmuwM3MYhqGx1pRzKj2dyOM26FFHyvcJZv/0lX2wQm255aZJsy+DCKzn7u6uPTzz5uamrq+vGwPy+N2n++F/O3Ev8AA+2B02Q6MgfXNzM1pQoJbam3um2rYj7DMZTjJFmu0wdZsA5jQ2QSTLG2kXBuLUjQHRPseY/ex/PyAgQZkGm82sh+9o9tveuNv4n/ymqhmyX0oLm2Flz06N89n4fTyO7HTOtZxkFEzcj/RAmMkk7Ez8dvTyUyucZmStwNHc5+d+oarH+1ro30BqcE5K7z64hmsFmWoBWAbZvIMh6zcJUDZOjNvRGACyXpPhIUszlGQkCc5PFXLT4bEHg4sZmY+1syeTwHkdCBIQEtjMeq0bGFjKNcfhwPIUO/GxfEfdzY9rpw9sIJl96jrnkpmLx1L1+Pl0zMOgMQxDW1DLQr2ZauqMsTMGj8UlKc+J822jri8+1XYC2O3tbXu6qot/+Swts68sHrMA4KgAcvMo3aqHVzSZViZb4AWoZiUGtAQvFwxRkGmthW4jtyJwoFwtZE7JrJL5GIwYrw0ABboG4LnDrjJVMdBmFPU4ONcOx/mkit7EaKBxBHa09EoRgG3AMIO0A2ZKkkwa8ExnZAV7sVjU7e1tXV9f183NTYvmTj8s9wSXrJHaln1eApfrU67H5vYOs8DUr4M2srUM7Dt+/A3n+H2leb4bx7hkYobo8dg26Td9wYBsG0pbcW3LQOssAqzwmDabzQgzfHO5a6FPtZ0A5khp5aKkXMbt1ahgZKA4A+JG8adSGjsejmBnTppsttADiaSijmIowyzLCwN2KubGuwFs0PSbMnRa0ktdzfDSIA1odqKntmykAXuOBiP0wfcGQa6RkdmO3XNMfjjHAQld8dt6ppkh+XOXEKbT6aMnI2Q66vFm/4zZ9+LaQbwY5eK9WUGvlOCA6dSV5mt43nZyZIW9eX5sR7IN2E7TXyw7Wm8RweUTxmN7NKCkjmxT/G/f9bUyi/B4XW/NBanUYbadAIaiqSnRqUHLF2bvUQKHBZSrI5vNZvTYHBSAQCwEO4cnxTh9nhEcYTlFyKLiZDJprKpnDKbrpMqM30JOA7IyDKLIxQrLVVaO8++k8mZhZmhJzc1qDfB+6oTn7OfPI0OzXubo1eiM1DmWBFunqskisw7D3wZkHuGyWCxqPp/XfD4f1dGoD/JQPvZ9ZU2R5k3Zh4eHdXx83MASZmm7ZKxOpf1OAOZpUPULMhycnXnYxvEJUrnMTlIu6RsOzJznOiVj8TkOZMgtMwMIRdqu7d12kKup+BDpc/pMLwD12k4Aq3rY5pCT86uh+O3H1SDIFGCme1yDSTsSuAaAsjP1wPncp4HQgGGDcVTl+1z54/OMILkiY7DIVCnHz/EJaBTPiUhOfdKJvbWklyIYAPjcoNUzrAwqnmeCuVlDPsguU1vPwf9jvHZWM2Cn3J6L5WHG70UWs7W9vb26vr6u29vb9oiWHmPnehyzXq/bRkvm53sNPS6XEQw0jNfjtpzp13LNYEjzYoj1mNmIwZI+vOHYNWAznCQlvXQ/s55svTkyp9zqlAyS67GDIUsAT7WdG1mpUSUi+34lWARRbjp9ePZPsikoO5teeVIFBoMh+J4pKymdgAlCr71QYOWQxqbDoNC8A97Xgd310p2MXHaKXmTzd+6PvhyBzcQyLfUbXtJozN6Yd9V41zvzctoCECGDvJE6jYkn61p/HmvWQtlG4+tnMPn2229rf3+/bm5u6ubmZsTmqh7uzzOIGeicMWCTf/rTn+ri4qLOz89bf7zbwfLAFpbLZT179mwEqsjz8PBwBLBHR0ftntuqB/Db29trt9GZvX78+LGur6/buEnP8KWsVRqkDJLWuedgXdAgG2aRtg3s/ykGh48yHo4hkOYz1czUM3txOSUXm5hXZhz5d7adAPbhw4f69ttvR9Ge90NikAglHxVNgRijNvoDgvyPYXv/mA2VSTg1BACdezsVQhimvgYV7zHJ1NS/mSPGxTyTRRmsMEqc1ODMXPI6NDOZZJoGZQzg7u6uzs7O2nVxzKoapeXJ7Dx3rsvfPN6b6/QeF4wxWn8OMhg61/TN43nfrI15sVhU1f1dIFdXV6NVUZ47lozWDspnfpY7AWo+n7d5oEevMGLXnz59ansWOX82m9XNzc2I6QNe5+fn7ZFQ9L1YLBrzOz09bYD3zTff1I8//ljD8LDC59u+DFjI6qnAbAbNOLOUgv56YMcxmU5WjVM9lxeyJaPCNpxZmCTYfowT9t9kuL2STJvzk9/U/c3Yl5eXzQB5UsQw3N9wfX19PRK8H2BISuTGwLwszFMiZrP7F4VQc7BgzPYAJfqmyOqVG7MZBMGenixSZ8rLeS40oiinZlmvoLmeAYglqHoFyPUQs5GnQAGjROnoJNMWp5UYX6ZnXpzIVV07iFNWp2+cy9xw6KyPIO8em92VavEYJ4ya+xczzQK82JuEUzDOw8PDEVtk1QZIOCsAACAASURBVJJx2Xb4jHsCM5Bhc9PptO1T495g2wD9PHv2rE5PT2uxWNQf//jHev78ef3www+1v79f//zP/9zmdX193V456PtemZMzCezCAcmgjq171z12gC3yeT7i3XZA3/v7+yMCQfNeRmzBPuSgaHaVcrJNZmbRS1XddgIYBulIihEsFouRUfOZ0zXTzaS5Rtqk6gYFRwanfPTt2lHm/tm350Dzo259XdN1MwQbDQKnmalxLIr28b5GppL8cFymlY6ymSrk+PncBpH1McvbIJtMwHO0EZtFcnzOyUvoNAexnD868hK6V8WclmXKk0HHgcINObh+ljVB92tb8Dai6XTamKGd0Cn1xcVFffz4sU5PT+vs7KwFDhgbm2QZR6/1nD9rZ/YBvmM++XYh+0nvGgarTOXRj/WF7DOg9/q2rJ6yGY7LxYFsOwHMVI4VHRogNAxDi0CkSmY1rLrwghAEYIBJp+PapCdEdKd/CS4GK85Pp8yaVwrYAG2W5GsZJK0AK8VzSQVZuRg5feNkOQeDvSMrzMlpsMdmJmLZ0Y+jL+w5AaCqRk5tQOEzgwNzNJNwqskxmb7SB/LH4YZhaIExgYLVa1gK+k1WlyybJ86SPvHcu2EY6vLysumMjdoEB2pdDsIA7Wq1Gr3o5Lvvvmv6mE6n9fXXX9fZ2Vn99NNPdX19XbPZ/YucKcUcHh6OHgHFtX7++eeWVkMkshziQGDGw1hdGkhfcGBzP7Yp94eP2Ab9Xa85aGem4RTSY3fp4O8CMJSEQOnc6SFFeYNMOuzBwcGovuVCK8boR+WQOg7Dw6Nh8lVu7q/qfuMtWyHs6Bxj1oKR8j1CxnFcEO0p1umEI0cyQC/ZJ+NwxOVavmOAeWR0d/QyODEGzjezoHlxJRmH2Z73F/UKrpyT16RfA7MjqYu1ZnNZ3/E1Dw8P26qgU3hWMuljsViMnIXarIGdrAIdWzdO/WFGMHdsh3kwB+xqOp3W0dFRu9YPP/xQV1dXdXx8XK9fv67Dw8P69OlTHR0d1T/+4z+2wE6pABkxrvl83lLQ58+f19XVVWNqdmjXsghEDurWF3+bfCTo8Bn6h/EDntafGaDPRS70vYs99hgYzfXcp9pOAOMCRnPyZiI4wONCIBNZLBZ1fHw8AhMizmw2a899qnpMSzEoPyyR5+ZnPu5H+vhzM7XN5uH5SVYQ4GdnI6ryeVJoxsuYHSX43M5tkE0qDSMwi3GqlBHIqUbS/F6Nw8ZhluexbLfbVrT3rUoOYG4GU+ZoALTxOg11pPVxdkrm5OgLSABIGf1hZjwogEyAv81syRhydQ17gS2aSXIeNk8fyBn7AxiZB8X7v/zlL3V8fFxHR0d1dHTUxoaM7u7u6uLioqrunwAzDEN98803o1LN8+fP68WLF411vn///lHQ8RzzrUkGCKeYWULxgkmWZXo2YJBBZjBvs2HrluOMLW6MD59+itlV/Q2PlMaAbm9v6/z8fFT7MhWn9uVCIw8/5HgKlhSeWXZ2VHNkREAYiCdsgzfTQnneuWy094KBGSDNtD9TQoOG+zXoZsPoM331fB0JzWCZfxacncoa+D0eF4LNMCwHj5fnvXkuZjLIxiUCF4bRL79xbIOB93khBz8D3foz0JJ6Yhs4f26fwUa8wIOu0ZcDGrLAaQFby8IBjSe6unZGult1zwAZA2wMVr3ZbOr9+/e12Wzqq6++aosLOOkvf/nLury8rJOTk+a0q9Wq3r17V8+ePRsF8+l0Wm/fvq1hGOrDhw/NT+3oDiLI1Wze99Bid7lSbrt3YHZQghU7LSS7guz4abdm49ZJBkmz9dyS4/ZZBuZn1OM0GJJ3ozNY0k2ilPNZHnnMAKvG+4Wy6OooyDI1q0NO/7Ke5gctonjXdegTI0OgMJuMWB4rArcSnRIhIy8c4KgYTa+gjJzW6/Wo/sNmSq6HQ/A3BuV6AmPKCGrGasaGvgzeyA8nSCbDylTOw4aeWwD47bqc65H5Gdf3HjU7BLUkv5/UwM6+LYMScvIWDqedfI/deAwG5M1m09gSDKaq2s5/p1JV9+API7u8vKxhGOrdu3e1XC7r1atXzbb39/fr4OCgjo+Pa7lc1tHRUZ2entaPP/5Ynz59qoODg7q4uGhpKds4ZrNZSzP9OOosmwBsXiBBDta37Z80FzvLYGDZmYVZvujPmUr6AZ/hLw6oT7XPbqO4uLioo6OjZtQM4vDwsBUtnSeT12+32/aIaNNqp3eueVU95NuODtyhDzCaVXE90h4iWjoEwjFT8RNkze44Pumuo9l2u22pjMHBzuclbLMrMyMzMCvaWyiyoG5ANigwbvYymT3glIyBMRlMXMNkTPTJeLJew3iqHr+ooapGoE0/rkWalSJDflu/NIIM84eNoScHIDsNxXjXw5yiw5KTkbgvGJeBAXvE/vARbBuwMPDm+ewvY7vS6elpnZyctD1rk8mkAdfbt29rtVrV2dlZK82wOXZ/f79OTk7q+Pi4gdzV1VVdX1+PanWwWfpmjGZeZkS+A2C73T5izLZ9znXtmPNMRhywDXo+z0FuV9sJYFdXV/UP//APLdIdHx+3aOQagCO5gYbVE0coJnFyclLX19cjtAYE/axs00/vITIjcGRxsdVFRxpGRj8GLCvQ9aSsl9mxnFbSn/N7FO6UDZBwAZr+vCXEaSbzc2rrAiggCZuyQTEPpz++KwGdmLWiV9f47JCurxn4MkLDZrxJmbH61jMbu42eBoAfHR21uTFGakoHBwcNOBgLTjubzdp+MN+g7eCCrj1Ws28vslhvyJAAhd2TUuamWp+DbCeTSdv8enFx0VYlT09Pm+xdGvnhhx/aOyo2m039+OOP9erVqwZoe3t79Ytf/KI+fvxY8/m8Pn782IKJ972ZgQIc+GSv9uvA6e/Tvw08BqZeuok8sRXOcbB/qu0EsLOzs7q5uXn05mX+dormHJ3Cb7IaK5HobIpLnxgaRmNWYzqcubWdgdeMZb7PHFC8HcWFYzsw83D/jj5mDK73MDb6Npuwo6fCPQY7t2WdBVI7Ps2prdnnarWq+XzeAgf1GBu1U1YDCfP1TvVkbQkgzJ/xeYUUufF4JesEmRnMr6+v27gODw9bUONFy1dXV3V0dDR6DA6rmNhCProYMM97TGlZq7E8HLCcxnuzrIPiZrMZZRV2/JOTk3bOer2uT58+1dXVVZ2entbx8fHodqw3b960LSSHh4f1m9/8pj0hhfTr48eP7ZYsxrG3t1eLxeLR28Hc7JNOBV1X47fLKlwjg7t91pkEzf26+YECT7WdAEY9BsUzANgXEWm1WrXVlaTM1NAANaM7BmomAUglwMHwkolZmE7rKC7a6Lhm0liamUQvtWGMBrMERv62A8NSkI2VbFaEAfTqWTYCF0ETQNlTlICIoRmADZ5ebTRbY96ZUuXiR9YzDGLJGJ2K5XfJ/FyDw25gOF7c4djT09PGuhaLRZ2eno507LphgqzZE5/5YZ4OHPTheiJ2z5jNYqjrVD2sFGKDvkWKhZq7u7tWM+M5aK4rAmAGm++//7751DAMo9qmg7RrdC6RbLfbR3rFLjjOoGf7NntifmZqtnXvLOBz+xCZixftnmo7AQzFoYScgGnt7e1tGxQC4jjf9+i6FxTRiwSkkKbdAKXpKRGXyNa7WTujJd8jeM738ZxvAbtWRX+9p3FkDYw+AVQAyY5gWVY93KfX23Fv6u0aG30mS3VaZOBz7cf1DRd4TfUNJq5XmP5nAPKYXOfwuOnbgMb5jviWE3rM53hhr3zOlgsclgBsNoLtOT2GiWJn2KGL+Ni4a3ouOzjtyRLGer1uK/n2E8bv+4uxadJL2vX1dWPNV1dXNQxDe9DjwcFBq61hs17UMljZ5mkAtu3KunKzbbhea7k6A+L6vrc2a8UGMca1C8Q+eyuRC6M0O6DrII6g6/X9ex57Gwl7Cvb+JTt/1jQwMpRg9OYzRyGzRMbBdXA0mBfnJ1U2MPGZ01aub3lwHM5oJ2bezI8GQPZSTR+DHBPc0gAMoBxjZ5tMJm2D8unp6ei+SoAgQcwvZOnNx6Bm5zAL5n+a5eSW/7sUsd1u28ZVv4EdUGBM2+223a94dnbW9OsaFsd5QQVg5x5H33NrVuLyhDMDBwfbjOugvPWLHfmulwGk9ImNzmazOj8/r9VqVVdXV00mrv9VVSMBNJ6c4ccFMWbGYx155dElDNsl+ve8TDKG4eEOD9uAgd51PeyN/nspe7bPbqNw6lL1YJiHh4etSMnAKbxhAN4X42Vr+sMQLRi+M3MhCqWQMjLjBCwm+DqMn1uTZrNZMxbXyugH40nWCEAnqBr8AFUvLgCYzCNTWAMwyua301Yr2ADFMWaKPpaxoYvJZFK/+tWv6uXLl218BwcHdXV11V5xZr15E2o25siKmufcW+ww8PMdc/ViBee6+O95uaxgQ7escBQWjTabTT1//nwEMPSfhehkpGy7AUyoOTF2s0/qc16hd8pf9XB3is+Ddd3c3FTVPdPjurYH21+PqZrlbDabBpLYNduReDFPvi/SaaYDie+ocfBGL7Y5rm9987fl4NVfB0LfyP5U++ytRDaOpKGuvfC3ayeudbULxsqgWYSdjyiG0vjMqZUF4H1qNhYzPIzUQES/FDdd65tMHpbbMRpapnXMzWwU5VY9fvVX0mPP0SkW5zo6wpQ8PrMhswmcx3ufvArnms9isWjghXPDhh0IvIpGS+Zr/VgWXuVzTdFOmYsn6BXgIM0irTs7O2tPZ3VKY0eGnQ3DUB8/fqyjo6NRMDFbzBU41wSdBjkYcH3qV2xncTptndsuHDxJB52WU3P2vaD04aBicLctcB2eXLu3t9d2EphY2L5dOsIv1ut1XV5eVlXV8+fP27alTBfN2O3b9hczuyxZMG4v4DzVPptCYgB3d3ejGtJ2u211AO8cdiRysdI1BxzQxfIERFa5fEtEbki1AaJIfnuFygrKFJXfXvFywdgKtsNaqJkGMwYUaKUmi/DxbmaVCQQJ4GZejBP5OwV0X0RSpzzMhVW7TAGQfRoqf/s2MR+PfRCAevpzemHDxwaxFRu4WZMdiOZb3qx39ideXV21epFBM9Nxsy7mZfYDkDFOAAK5ARbICPB33RKA5BjbDVtEzIZIMx1IzIwAOAOnt3CQfuKj+PJyuRzdjpWB9ujoqOHB2dlZXV1djVaUuab9lPPtP7lKb+bmsscu8Kr6DICdnJy0aDeZPNyL5tUkFOwVRQaCIfaOrarR8rYZDiyjqlp9A+MHnBA0Bs9k7XR2cm/uzDTWmzmTPQAGGHCmPhiuFzF6YOSUESW5FkFzam3GyXiyuI8jEBC43QXnxjidrjKvTGNxRBu6n4NlVpgG53l+7m+uVfV4g67naSd1NAbwXf9E78yNvjl+Nps1HRkoq6ptBKUe2GPHvTGbTWBDw/CwyZtAzbnYEPbthQjbG77GNUjnAMHlclnHx8f16dOn5nMwTM5BVhlo+Q57YaHDfkudjLa/v99ux7q+vm7bnKhBMj8/tJK+bM8GdTNIl4ws65R/r+0EsO+//77evHnTnPv09LSqHvY0sbKGsiys7Xb7iK6u1+vRSxJgb0wkC48WtFka1Jec3lE5ncasA+PxKpady6mRQcQ3idvgYDkGJafPXNPG6VQyI7znQP8ev+cDqPHoYgyMVMNGVPXgdI7YZmzJ5ojcTlHNcAx6lr9Xlawbmtkn51sGWQ9Dlqkr25prdrAZF+cZr5+wipyXy2ULktyLaF2aKWRpwgtSBl6yExwYwGGMaau9bAKbdzoMC6Pwb5BKX8gyDjLF7j9+/NjqYIeHh83+DDjL5bLevXtXt7e3dXJyUsMw1KtXr2o2m7W7A/JuGuzb2Q8Bw3sBrVPbFw286NmQ204Ae/PmTauRnJ6eNmpp2r9arUYbT512sYLDsnGmAoARrMJMAeMiGniyXuYFRABFpyN2AuoIRA4Q3quVAAyRBCaSt+44V7dynFrY8M18cAzYDTLJ9LPXsn6wWq1arcXsFyNxVHN90SySMTJOy4yW6bb79Vj5HsfKupGvb6flXObo9NCyM7DgeDTX5rhe1pw8B4ISjsuGUFgOqSaOhkw9T2yEMTv44MSTyaSOj4/bvY5mzHb+lIMZv4OxbQRGw4/3V2G7DphXV1c1n8/r4OCgnj171uyG+azX67q6umpBkA3B3GAOO3P24OcAVj2khvZ1Bznm2JsLcjEL3QVeVX/DrUS/+c1varVajZ4hXlU1n8/b0izH5uOEnUPbgZKJZCERhmR2ZgBhoplmYIiO0hiI06JkR3YS0kX647amnmNjKIwP4/OmPsDBgIZBulbkWkFGUoM6RkG9ItN2Agjz5d63dEQDBnLxahZj4Xg/+SGDBNc28Di1ckGY79OouY7H52BAKpzjRX4Jyg4wLlG4hpuBKsdPcAAwE8joxw6HA/o63gOIw2KzXnEkEGLz7t92QmmBMVDvBfS4HrYzm93f6D2ZTOr169fNJnkNHT43nU7rxYsXI/tjTs+ePWtyxZ8yuFSNbw+rGr//wAtiBGDbke+19dgzNXX77FuJQGQuArCQurgQicBhT46WueLEpMyETHFdTIWdkQK4DjeZjG9Q9ebYXj4N2/GtJhnhHDkcxcxkcA7XOBiPU72sD5nBslDh9M51LWRkA+FpA7y3EIA1czMrsKE7LbWBIGPvSaNP5gaDzXQpa3j0zXnehmFGgVxh1NiCU0/rDRnaVvJ9hU5BAT7qpb6vFpChDmXnZ45szubm7PV6XS9evBiBrhkZjBpQNeukT1gYsuF80jNqgOyddMD03A3wZrXMnUxmGO4ft3N0dNQeqEhN7ezsrLFM+yV9mBSgN1Lh1WrVbjF0EPZDCGwPZsS5rSTl7ubyzFPt6W+q2ltYLCAUYGQ03Z9MJm0ZGNBBMM6VneIZvYnaGCHCRBiO5ozJhUyDAH35M8bumoZZFA5FfzghhoxhAJT0x2cGTTc/VdardgAAn6Uxut4C60I+Lu4boK0T5OjVK+RFsOBaflhg9olBZz3Oesi0z9tnDOTog7EAXtSNSFW4jtmbzyWAUBPFSQABxt6L7tS8HFi4np8+nDW+ZIlmY/7fdUSA3gyyVwvE7ghOs9ms1ZDRkeWXDNDBydd++fJlO//Vq1cNtOjH10/bQy+M2aDNM/Vgq7Yx692lGT++241+0JcXBRPY3D77OB2UxSQ98clk/MAyp0YI1I/c8VLwMAztyQJ2gru7u5ZX85YiG62fBmBHw4AcyTkvU1evrDn/p7FsTXTGQG3spIlmDzi0jQyj9THZH9c0AHgVdbVaNSbsTbqAr2+poiVzcYBhk7GPz9uwnM44fadl9DfbdmBzwdy3ySB3p0w0O5a35tiJzPy9agbTmUzu97VdXV2NUsWqavbl24YMNMgeIOMmazbCbjabOjk5afMw+yXYAHyuBSJTb5PwPEkHXScDHDJbgCQ4UzH7QZ4soE0mkzo9Pa2jo6O6urpq5RnGYIDMmqV92DXEy8vL9vSLZKYG/txGQ7/pe1laQK4Jdm6f3Ynv1INO7TR+LRqD8U3R7Dfix4KA1fihiQDien3/wEFABLA0KLi2RCNyp0OQTrh4iFGZwnq+rjVkbcrOZGCyAszSckxZ3ESheXP33d1dffr0qT1WxWluj8VmKst1zcxcU0i25TF6C0cvapqdug+nyujHmx3Nfp89e9YWIy4uLkZMLvcdegneKQkrVjc3N6MUnRqTswDXvnKnt+unaVfeX7bdbtt2gqyfMT+zI2zEvw3+yZ6ZK1kMQWC73bY7HSwbN5dlbB/DMDT2z90LWV6w/fL/s2fPWjmINgxDe8BoVTXmnI8pAlgBW+zZxOIpGaMPlyF6bSeAffr0qV3EgjDLQeBmNdB5106YOFEkGQ97zKrGaRbXzpdt0I/fWef9ZVnv8SZLol/V+DYS03+ie0ZTfp4SKv35cT1mjsir1wyObIu4u7trb4pGhgm0djrXTsx2YUYcC8N0ncnpkJ0bxsYGUK5F0GHeTgezJXNaLBbtnr7pdNpefmGb+umnn5peN5v7bQRkBVXVtvXwyGVSSQCKgGlgQLa91gtifM4Y+I4nfrCd4ejoaGSzZg+2+wQX24TtDV34/8lkUmdnZ6Ogjw5Ikb2Axrj9FnUH4awzbjabOj4+blnKdnt/3/GvfvWrVg8007dfZNDkeweIZFMORHxP8KPOe3d314Cy13YCGFHfkQxFsnPX6ZkNFOFUPdScvFGRBiuyAFz3MEtCKEzIr2mremBfXN/Cqxo/Vsbf29j8lnDO8fkujjvquk7jdMlposGEc2im21XVdjj3CrkoH2B0TYjoZzZXNWZAMGiPDTn6NiWnLRg1x1l2Pp9rpNHaHugfpkGK5JrLbDart2/fVlXVxcVFu81puVy2RyjzzDfmYsZMgOFzs2TAx8HUTmimy7wc9OiX7OL29vbRhl/bi3WYrMlyMpv3MSlP7Mf2jrNn+lb1sErrVWvAkuwJ9juZTFpKCGvzwxCsZ48bGXtrkO3LrJR5gxnYpJm+meeuthPA6DjrEQgnaSAKszNxHIKlNuF8lwhB6omzZX2FCWM4LsxyXRAcQ8w+cqk7o6Gf9e40tbfiZgUY3FyrMBAY0BxtnDJ9+vSprq+vW/DYbDajyJdGQb+WddY1MBhvaWBsLAr0UnJ041Q4mV8PhB3EcNh8AYdTKvROkZdnzRsAeDop9rNcLuvDhw+tD4M9fWJ37BhHNpa9deNFImRDc42TOWHHBGE/GywfGOjgkjUn+s/g6M8Zb5Yc/HQJZw22PY5nX+Zkcn9j+ocPH0Y1RmRxcnLSbGmz2bS3hrO6yebftCPmjlwT8FyD7dVJuaZr2Jz/VNsJYMfHx/Xx48cR2oL2fv4WF+U4BrTZPDwOx6kAxoxzABrUvnxLDsbOVgqAyuzMTuoHIRqkTFMdlR0BMHRTecAui/AoJCOjvzcTMgA4zTBr+emnn0abEZlrGgSNiOc0OlkRzfKnIWsDOWNkHsjSzuEU1XP2/AyyVY/rTVW1k+3SvxmyX3BiYKiqthoJeLgMQb8UrtmQ3dsr5zkmg8WmPE6AC/tnbDzx1rLCLpwmZxrl+fp6GaiwSYLVdrttwMO+MH54o9h8Pq+ff/65rq+vq+p+kY7Ntdg6jNJ2ykIA13dmhQzwJZcwHLB9143rv16sMo64frir7dxG8f79+5YTOzIjMP4m2lFwB9SIaAzE6ZtfUupm2o7SuDb9u/5W9ZAeUaB0+oBzEU0QmlMEjHpvb68plHOsKIzJzMlGBgC7ltQEPRlvSnRhcxiG+vTpU00mk3r27Nlob06OyUAGs3EkdNQyUPo5Wa5tGdCqHnaAI/cEL+SC7JKVmr1a7rlSyPeLxaJubm7q6uqq2ZD7dd3RbNm6oE8zu0+fPjW74DhAbRiGtsuc8oiDHk8yJfhyrhk+4zPrBjBYTLi9vR1tL3gquNjRXSvMAMwckYOZFzLzEyZYZXXhntrSN998M7qB++rqqo0fMNlut+1uGNcDzR7zMTx8n7Uu5O5tULY3xmnmjR1m2cltJwP7+uuvW0emmC44ujietSuci4FTgL29vW2Fdr9k1EohQnpVxStvXMPpYjK8qvEGShtHvoSUYwG3qvHO9oyk/j5rXfmZa2t8xxL9fD4fsQGYqKk18k7Hyccd04dv4aHZGFx8R79+Nprn52LwU5+jt6rHgJZFYvQL89ls7gvh19fXTfbs+vaN/DSDsJuDCc+h415cxn58fFzDMLSVT2TgzarOIkipncoSsAmOZqDoz4X0YRhaScAszPNxiuUCvtkec7O8sw7FPaHc/rNYLNqr2tDZ2dlZe3mI33zk0o3rebPZ/ctQuF3Q76A0sHl/on3V9sln9O10PIEappf2lG0ngLGR1U7L4OxMTiWJdigfw/I9f9QMiH5EO4yCibu+xaTMWvidk+Z419xc3CUFNsg5/cT4mJtBLOVho8PIs+blVA2DIVImmJox0J/l0hSnPTnclGsgTrBwHcW/XYesekg/PE8zMKcb1oNlVlWP2AGf2Y4IirPZrL37cDabtYcq4vTffPPNCBgSvFwewKYoOWBnwzDUzc3NyFaQWwYzxp3bB5AX8uEz7/BH/k7teZoDsj45OXnkvIyb8SJz5Gq/Ys7oA7n827/9W/3TP/1TA4nDw8O2SuqXtuAT+HKyZmzQhXXS06oalWmwS78NCxtJv80FCj5HhsjX51i+vbYTwPb39+v6+nqUe/u2DDMdWMLd3V2dnJyMHNSDdjHcKxVMNiOua09M0A+LM1IbaJzmcG2YDhEXg3B+jgGnoaDgTF0BboONU7eqxy/JgD2RrthJmL9l588xWG8ehgUzV9dr3JI9M1+Dpu/9pD/6RK7YgAEr62C9yNk7PlcmOR8g4/P9/f168eLFiJE6rWSM9FX18EZvR3wa7A+Gwooecs3n1bsOmgEhU3HYtlNu+t5sNnV0dDTa2gCbym0wXNd2Y//IVMt74th862Bj1n15edmCB3NwiouuATlAnnsq0f98Pm/jN2C5D9ufa2XMwXOyHHfVdGk7Aezy8rLevn1bJycnLSIwcLMoBLler1u0qarR27Sz1gKK44xMzKkXE7YzskseRyZPz7qOC7agOUbCd7AuCwgDclQ3gGdERvCu7xBBHV1JB9nV7F3gnJ+ggczNopiDr5spIaDOeJJJ2aHSWTw3GtcC2M1S8lgfjyzNQNOg0el0Oq2XL1+OygUXFxc1nU7r5uam7u7u6uLiom5vb+vFixdVVfXVV181XTvo0LiWX9eGDLmXl20YyPTs7Gxk48iXoGO5Y1/efO0MxYHVQHtxcVFVD2/xJsA5C7FN+IZofATHtt+cn5/Xdnu/J+38/Lx+/vnnka8ul8vG/vAZmBM2BCDO5/NRWcbsj89dj0s2if7xkUyPe/bplHMXaLl9dhWSPSI83DBzcddDyMO93EokYsIAXNYJXB8iYtC3wx/sPgAAIABJREFUi34ImKjhp2SgSK7ZA0AXaxEk486UizFgPPyfTMxprBXn+lLVfUrOErSBg3nxO+sgXMPXxii8H80sxikp83a0Zi6kW2a9Xvm1o2RKaBnwvfdK8XeuVrvG6LqIAebg4KABGq/su7m5qb29vXYPHmzgF7/4RavJkDo6PbYNcZ1kjDjjYrFoL4E9OztrNusaG0GPVU/XAHtObb35uuwfI/Dn00WcVtoG6Nulgqqq169f11dffVXT6bQBkPWHHQ/D0Jj26elps12yAvu2bSjLRrbdDHI0ZJ7g5Tk5czG79lyfajsBzHm6FYGwUT5AYhrKAJ2ukL75LSTOlxGw9x25CMj17FCepA2U8QKkBjLAyNTVTIfWAyunFBauWYdZJDm8nx4L+JjBuf/PpV92xty3hQFknz7OYOtalp0ha25PNcbhVNclgl1zs2xtpKRartdVPTCWDCY8wwtATqDP4rkBnObVXRYRtttte1orYOBg6vqoAcoO7Xnxues8h4eHdXJyUpeXl49KMsjVaZmb7Ri9OzU0yDF+MgBeblv1cHuPSwUGSViqSw3ol/SScXhuzMUBy7Zi/zGzNBb0mLXbZ98LCTA5MsCsXOvxs7syb4d1QbfNNnyzKT8AGgpyWgEIGJQcCbN+RXMqYHAxy7DwGJ/pNkpwSyCzsWAwPESOcdgJ3I/BxzKyLPNvgxO3B2XfTwERQYDrOkgAYMkEc8y0jNbu/6lImgyO47wvzKUC30Y0mUzaC18vLy9rtbp/EzXX29/fr9evX7cyRQYa/nZt0gGNtI5jPE5W5ViUqnr8VFj6o09AwnUibBi9LRaLdouVA7xtvxc0XRohJeRzg7gZKSklm4JhZLe3t3V8fNzsireD84SMtJlk67aLp4J7b+WWz13M90rrU+2zbyVyhPELark4QuJx0CgFQfE9kdMbYK0YszCzFfp0aufI4l3HRnwr0TeL079TX9e5nJr53XgYOWDJ9anlJViy/2c2m7UaYtX4wYhmIwa97Aulul5ApMvietWYxRLFbDwOQGl0rhFm3c9BizE7VeZY5EFfrj851QQgsg7naGzWY+Dn2icnJ+3FHAAaJYs///nPNZlMmuOdnZ2NQBI7SdafjC1ZNY69Xq8bqHKnAOBwfX09qgnlPYowNZ5qQTD3M8o2m01jSVlWsM0aABhn1mAJbNj0zz//XJPJ/b5D7jfcbO5fdPLhw4c6Pz9vvvDmzZsR68xm+8RffIcHY/bnztSsc2clPRab7bPbKH75y1+2wbFTHeNksEQ95+wYCUDBwDDWrBu5FkIzMHkflNPDXNkgssF4XLdBkQcHB60gm07qAjfzw5gYk8dMgdiG7mf2M1c7f6bXNObRAwm+x9DNCjIt8x6mBGbAA8PJGhhj7rEmxuVxZ23Jhul9fJmiGBSsc4OHdZNpdxbGCXY8JZj0j5dWzOfzev/+fS2Xy/r222/ba9XMmHoprceG3M1UYVbe/DoMQz1//rzJAaaDvAGYk5OT2t/fr6urq3KDNVY9vCnbLAsde6UwmVkGxLTB1er+Ju+PHz+O7gAhKJyfn9fl5WUjALngg/xZVPPnpPJOJTnXsvYeTa/ouwa2C7yq/oYnshq0GLDvqWIiCBwm5giRq5Wca0PBIZi4GZb3xyCIdAbadvuwwY4xAAoIhzECxFXjfUuOAgkOBgDXZ5DPxcVF7e/vjyKVjd4tr80409ByHNB9A5sBg3E6lc/CucfgucI2DaLImAjaq73YWayn1I9XQb2wwNh6tRD68/9mF4yd6yN7xsuGTa797t27qqpWf4KZ0SxX686LFAZegpa3spydnbX/WQyDDXsLhQEbOVo/7JZn/6LlRGbiDMAB0AHdtuC5X15e1mQyqefPn7fzDg4OGjDzFFoHT2dWtjOvpFpH/HZ5x/qzfg20ucu/13YC2MePH+vXv/5129zI6o53lbuOhTH70bq+fw2hVj0sCcMAAA2noAAmDkoxlVTUk2M8Zh5WqPNuDNCrp+7PtZCqGjEWPybHwufxN0TiXG17quW4mAcGj8NkmurG58nczL5gkl4QMcvJAIMsk21ZJh4f4O/UzPMxS+b8bNSUcsOq9Wxwo2/GznUtdz+zCwC5vLxsY/n48WO9e/eujo6O6vT0tM7Pz0cZBeyuZ0OWg8F7tVrV5eVlC5S+R3EY7l+s6zKK2Sg+BCAMw1Cnp6eNxeUKneXIeM1QnbJantgTK+KwUZc43BcN5k86atDNe5g9Lgc1jnEQ4H/Ih/1vVx1sJ4Cdn5/Xcrmsm5ub9vRUF48RNsYFHbdiXNDMepELmQjHf7OaUlUj5LfSkwlZYVZC1fgFHDZSjkNYKTDA1g7uOfZqOVzfaQnXMeNIUPU1uU5vVbIHNslYMpp7ngZv5u3ree9Rz4FzVdNzzHTF9TuO8/luZq4GBeZkhtFL67N+BUvxSqEBjfsduQZ2x+1u1kmuiGXg4frMgYB/eXnZ9kSakZDGuaEzQNFZAUSBVC9tcpejex6wG4LuMAxtqwrAyr26uQveYLter1s2lj5sJu2x9eyN4/BPszWPu9d2ApiXTjOiGjxQHpM324IRoQADEDeWshfm9PS0sSsmeXBw0GoEZmCmrozNqRjnIxDqF67Z9Bwgd1XzWGvGDVObTCbNABK0nQI7LfJYMSSu7xSW1gM4H+valltGTbME953HMm5qZU4t/UwojA0H9LYYF9rt7AZZxs21ub7vW6QBNLY7O4XZcNZ9sA+YBeNxwd4lhsViUT/88ENVPTywkTRqb2+vXr58OUpVASGDuwOEa5X0ZwLARtlcQAAcLOfJZNI2cBPUWd3uyTL9FZmTQTE3jj89Pa2bm5t207cDBqDpYOIaMfNDtmlXCazWTQY3ZJm18qfaTgCjBoBge3uyuECvHoSwTHMBIADNO+X95EUmyWde2YLyOu/HaBCmazDU0hgzqY9ZUkYz+nBUsIP4WWRuWb+xPJ6KJsko8nNa1rMYp+fi6/mY/Nws1udlfYP5eLUzZUxD1pnuJigbuHusM2WQRsxnCWgGBx+T9pEO47SI883+ARoveLgm5/E5fTKwmUUhKzNL+1naKmNHH1ljMgO276Xd2Y69VaXq4UWy+CZBKc/ls2RQDuI0B4dkYAlcybaRRfaZbSeAed+W2YMNhlSF2lfVAxMjyqB057k+FgGC6BgPxkXx0imoDdjCsmKz/uKVN88h01rn4ln3GIah3SBrg8400ds7HAW5JqzOlDkN0EHD6RNj6tV8kElvuwIyM/vimjZ4O5xBJpleL13POgefZYrnvw2Wnof7thG7RuqAmKlr2qod26tiDkS5YsotTJvNpt6/f992/282m/rVr35VVdVeNWZ/sD2YnfHbqSOMazK5f9Agj6c2owVcvKiFH3HPsu8RZiGJ8znv97//fZ2dndWbN29GQYzH6vgJE1X3LzRxHZF3WF5fX7cVVtsGAOzSUbKx9AeaiRG29bn22X1gRncP1rUKT9ibBmFQftV91fjhcAiXqOctC0Q9hOItDdQBXMsxqJlJeNUOI8u6FoZusE3mtdls2qY+A0xGCSvHjpkgZjabdNtMMGXcc+pevcCg5Ov7N3J2H4AzASdB3P/nQoWZUrICy9vXT5bluWfK6AjNb4NOr0TQk4evBQha3tgWKRsZwsuXL5veb25u2tu8/Y5EMxeDN+PrpZz8tr4B2kzL3X9mNMx7Pp/XarWqk5OTBtCsZPJYIet0Nps1P7WcsVM/624YHl4Q8v3337d7U92X9W39ucRjxmWfs1/tSh+r/gYAA0RQ5Hr9cGe6nR+jhzERLUj3sugLa4MlICiE41Ujb/QjuqBcogBC8yooxVhv8LPwcFwrxkvlNCLU3d1di0Y29HSIFLojkp3ThmjlZ8qTcuuBQB5DH960amfBOHxrDgbn+p3ZAeP3NgjPA3309rN57MlW+W0mZRlShsgUuDd398nf1qnl4udk+Q4Rro/tsxGZW4xIt9hH5frW6elpvXjxor0ABfm7vpeg5lRrs3l48iysixSWG9AZf2YGjB+d3t7e1ocPH2oymdTLly/bFp9nz561BQHGgI8DYs5AzBi96jwMD4+gyjTcgd+pr8sdxoVe6aXnS9k+WwPDcSnumTZmHgzI8T2KQsEAH+cBHGZYXDONyQZgGu60wEbhIr+/cxTwWDjW6SbXZjzeO2bnzpTNYG0DfSqXz9rbUy1TeOspV22YpwHCaSHG6e0jmT64/pGUP9P0bAbAHJ/7MSNm/rmQ4sIw55htZ582en/n4OWHaGaKY11ttw8buJPdAfaZhs7n83Y7jj+3nzgQmKVYRgRh5AeQu2zBHLyCz3n7+/tt68Yw3G+upS82cnuPnwOZ2bHtncfnQBJOTk5GK6Zpm87grLve35aVwf7veh6YU4qkwtBXFy1hQb7Z26mSVxdwnmEY2goLINAThGsTZneTyeRRBLAh2lB87Gz28ILXVCCK/fDhQ3ttF9/ZgFE0CjUt9tzzvOxrV3Mq0asx0QykT606WnecT+DxfqbccNprvZqYa3ZmtlkH87hzO0I6syN3sjDr2kHKdShHcss7UzGaZezr0tdms2llBHSMU2+39yt0f/rTn5o9XV1d1fn5eZ2entbJyUm3TgaT9XiRG2PihSc4tbMhXlqLPOfzectahmEYPaHDCxFOQZEFAAfIshHWfg4j5m4CgC33cfqcZOTeoG798/9Tdue284j5fF5v3rxpdSTfdc5vhODc1dsvMufP6ObfRmR/nswDo00khx1lfSFzbM5lkYJjHP1QLGkDLWtdNBu9j4FN9Obwt7ZcZXRzrcWFzwwABlzLgEbh3vr0d09dl0bfmY5mem1HyfpfXs91TI+blsDlebuGk6l3Ljx4DDlejsMpDX7IjIDhm/6rqm1xOD09rdls1p7D7/1crvNxrhmo7ZjvqmoESIyLp0ZUPawSMyavKDP+nizxE66bT/ewfyDjHKMJQK9k0/P3TDcJDH93CslNnt664DqHPwOVMzLl/XW+SXo6nTb0ZlXFBm6Ki6LI8bPew0qLx8hvLw5k/75ZfDqd1uXlZYuyZlPIxOllAoVXY/IGXhSVY8DJHJVoyMy3org5lWXe/tyAkUCRqVNGS2+bcb3wqQZz4zj+Rz/o0g7K3JgDdpaAYuDIsWeKaJswG8OZM5Wm0V/eLlM1XpEnZXQKulqt2mokdTMam0avrq5ajYtd9W/fvm1FcIAAeWetyH7FHNjbOAwPj8rhlp7pdNpeRedVa2TAKissi4wLP8hSUcrKpMD2mFlBMn5k6LkZ1LAHfOKp0kvVZwCMZwb16hy5+sdFXcB1+ja66OzhXkIUTp+eQEZegCSXoN1vsjAf4/TEKD8MQzNansvUYwqM0dH8qeaicI9tmZ36s5SX0/SsISVj7bHDZBw+Dh14pYvruH/+f2ol0tfrXYeWaRjzzbTWYJXzs9MQPA0kHreZeY8lZEaQLMtsxZu0rQfXWmGfrtkwBq/ETyb3T4HAD66vr0d7zjLVcu3XY0uQ9TwYG31n6uwHgTpAebHJAc39e3zekpR69vz9nTHCtoBseoHoqbYTwNhoaidgMAwcoSJI351udAbRcWyvDNqwvHsZNCeqIOAe7Xd0xdgAQ54EYAXDZlDi+/fva7O5X2lK0OzRbo6h8O36UYIbwMr1rLSeszhlzN805mlnsVxcc0pH9QZis1RH9QwqfmyzndVAZqbIXOjn5uZmtLzeG6fH4jE5WPYagcmARXN2kOla2h4y8qqn007maLBGV2Z61rHtiPsOOQ825lfArdfrtlVnf3+/vvrqq9ELMwygMBSDucdj3dA/1/VDSS3vDBicn8HE6aPHxnkcbz3aJ61768Zjxtd3gdhnbyXKWws8oYwABiachsG72ZkzemCQbmY8RnRfz7Ulpxw4k2809dhcjyD6ub+cn8e42WxGNNvn+Tgc38ZPfwl2VnquLNIHn/fYGt9l3cnGmKs6dmbvg7NezGZ3Mc+sR5lBJCNlDk5Pc5Eij88g4vEzh16dNaO8dWKgn81mo5JH3nHgmk4CiZlqpr1mjqRusGuApapa+uniPc2+5OzFdTrbRA98XHLw+K0Dl4UykFvGk8mk3TOKTJ9iW+mfDphuXN+3p+1qn30iKwMlEgMamaey/A1bwvEdHWBhvHzWqZ4nw6Tdp3NrM77tdlvz+byNkeVxb+5zbYjGU2J//PHHOj8/b/l/KtxsqOc82Qw8WY/iexSVss7UiutkZDPoO3pmkLG8cBBWsygge878nfvccr7IgXEBBDikAZP6Rq4ocb2cqxt69v2ZuXJlsHVtje8Zi69jR3O0dzZh5lb1+KZ2sw4HLjuca4gOIGY6fvsRY+DJE+v1uv7617/Wer1ujwR6+/ZtTSaTevXq1ajPtKdM77PkYxsxQegFVOa0WCzqw4cPtVrdv4/g9PS0ZSyZrWQ67+zH+ncq7PH6Mde72k4Aw1CWy2UdHR2NDNa3p6AsHCgjuJXrgiKg4aX36XTa9t0wYcCO55Pl7TV+6YJTzaoaASXC2t/fr++//76GYRjtIkYBGBO1AtNzBOxIZoO0M9IXQMEKrZWSTDH7d72gx+LQh89zUMD4clWK4NB7a5TB1rUjg6NTIWTngIPtZAT1PNwvLQE4A4HTVf+2ffVKDHZggxNytj3Z2ZyOOcgafJOxoy9SaAOdGZz/94ZOv+ZtsVjUfD5vcv348WN7zPPJyUlbJUSHZqDYHvJm3A7I3uJkooKd3dzc1Lt37xprZDP3wcFB217k+aVMssSQ+k89JpBlRpPts/vAvPoB8DBxorgHb7bjQSUroA7jnfMsA7smgsD39vbam1YAEzNC1zdSiI4us9ms/vjHP9arV68e1T/cXOOhoVxTeQzUVN4OQz9emMgo12Nl/t6pldMdjJ29NxwDkCSDwKFcy7KD9WTIWKhfpcOiQ4yN6zwFtp5bD4gBGLOgZJ2WAbrIiJ+69MLRMAyj+3Wd3iFjBwP+T2ekv8wY0HcCFMf5mk5nU7akUqzOw8xev35dd3d37b2Z+/v79fLly3r9+vVIZ4AbPsY4GL+vhS5YIb28vKy7u7t69+5dTaf3z+0/Oztrcnjx4kU9f/68rq+vH9X6HJwMkDTruJdFID8D3FNtJ4AZvalXoUweg4MjGLjSmZ2OOJdmoM7JOccFSkf7jFh8l0VGj9XHXV1d1ddffz1Kbbzp0w7g/pICJwh5I22yMfr13wazpP9ZgO/VhQAswMVsp7cI4A2Z9MdtVpne2hFzzMzdOvXnPQBJWfX+99ws654+HOB8vu2G5npLMqCsXXls6MVycF8ca/Cz3hKcbfNmSiYDfIdj+zYw9Owf31qErUMyeL7XZDJpG2CPj49HvmkZXFxc1Gw2a7cbTafTtjkW/7esuFXJIOhm37XO/J1LDi70u7/ckJ3ts0+jYEWRfSI0pzcoARrrDX2kfpvNpqWGfmmEd8I7TfMLQ3F0JgtL860vGJwNtOregU9OTuoPf/hDe+EnfaPskUBm4yeK0lcKEfDuveTADpBRm/ZUbSnvmdzVPEf67KV/Zhd2pASIZBfu0wzEdSYbdY7ZtbTpdNrSVacpHk+vdueGXhL06StXeN1g+GZMABrH2n48/l4mYdaJIzrltM1guw5EsOZhGEaB2fVOB3wY3dHR0aNtPlX3m87/8pe/tPoRe8940cj5+XlNJvcv1b2+vq7/+Z//abXo/f39Bm5kVQBX790SjI+FiAwCZpkGK2SRaTrnuC/rNB/66LYTwE5PT+v6+rqBEMDkpdjtdttWImA1VpQLsNwIDXLbSOy43veCIOjb0Y9+HQVt/NPptI6Pj+vPf/5zPX/+vD0V08Knue6UqY9rBHZ+oqTPN6tyrclOmkqj5SqSr++tCVlv4Vz+7hU+XXswK07ATKBOgLUMHP1Tn06fqx6ncT2Q8sqbdY3MnmJKBmAzU7Nqbjr2Nc2okukZnJ9i1O4n02fLnDkzJ8DIpQazPfdrMHb5hv6QJfdekgkBXrDs+XxeP/zwQ9si8+rVq0ZIWI1nBdYyyWDDXFwSMWjbLnpBuFcD9BzN6Ho11GyffSb+d9991x7yD5rzxInt9uHJjKw4eXUShuRnZxPRQP4cPEyOOwBsMH4qpAvSdiqnuOv1un766ae2RcJ7bUz5ASIDi0EnW47XOT9j9aJG7xjO99g5z6m7QYnvd6Wm2SyXqvHSuo/pscycsx8XzPhzDrRkxhksGIMXV3wdZGXQdIDpAYXTO8bXA3h/7xoufWYaaGaVTIIxJtiZuTpdpF+CpOtAyRCr6lGd2XPl9iXfXsR4sHcyHL73ajSMK+eYhXxIi1Ndy8BAxLVYsOIzM07Xv6xP7NCZyOdAbCeAPX/+vD1o0DdboyTYB6le3hLCLTpQXgZpup1F0Kr7TY+uvfnFHq6JYTQuglZVHR0d1bt371otACNwOuMovV4/3n7h4mMWIi2DZCEc68jqiGbjxpjdzG7o0+e62Jn1sTRCX8cvT8GoPN9mELPxzdi9hr4N+BhnLn48VSOxXDz+Xj3MaXCmIBi7ncJycx9mdWZZfObgi/15FZJ+bWtZmLc8zVqyTmkwol9vbSFgu1SDndqhvZEaUIMh5YMRqW1VVUsf6bd3TbNlg61Bq8dgTS7Mqpm3bd26MaPspeK99jdvoyAfzqKic2MjMMBkpZhCs0PehsR5AIijEEDmdNHKWa1W9eLFi/rpp5/qr3/9a3399dftODs647cz+6mzR0dHDTBN8e1IZlPJXvL5WnZGf5YMz6mwjSeVnsVlO5JrWJlSWkdOd/m+qh7tC+N4SgW+8b0HkvTTAz8DJ//3AoOPd+rMmL1S6qDhmpTZEfLynM0kfPuZ2YCZGzqm5WZfZJIOnYDn1Ar/cH3MzMM2YL1CFFxT84tJrD+eKGF50hf3TXqOXqE2+CTjtg34lW3Wj4HZtUvkZJt2JsV4LNddbecuMRyXwSeLAOAYUKKsFZkU3EaEAHpMBaUYkf2Z09XLy8taLpf16tWrUaTlepnqZAQm3XXkpI8810DQS4/4u5c2Mh7PNaOMU6hkWj3QQIYunDvtyjHYAT2OHE8v/XHL1Ugz4t547Qwpm6oasYHePNImq8YFdcZqFpZz8HiyxmOHSabhaztzsL37/3R4y5/xGLQtY8/d35vx5UqzQdqssKc7Ew/82LLygobnYDkaoDmPUpHHbBtN+aM/A55LPbvYV9VnAMwO6FzZq4NmRgwMSktkcwpAv5vNpr0k1UCXTIw6GUqlcO807fz8vC4uLmq9vn/NkyOZBe15OTVIw8tm5Zq5GPyear0UDUfMdIl5Ox2CbRkUPH7OxeCdbrtv1xkYu69pZpzfp6O4qE7dhfNTXi72ehx23Nyy0QM2Pk/2lfLLFNLB02NwbTLZQaY9zMlAxhw5lzoR9tFbqEnGCyAaGC23HLP/TmD2fs3ZbNbqXdS58FvuseQHnRuIPBeDbQKZg4Zlb9nl+T6P1gv0+Ege+8gmnvymHnJU6kcIjC0EoDhpk9M+p115v6CXohG4B42QWE3x9b0xk9fD/+53vxvdAO5aQNXDZlPoLnQZY7TwrKRe3u50xEaVTshY8vus//k8s7lUusFrOn14W5KBnj78OZ+t1+u2sZF+POdeas24kVmuEtpgnV7bqb1x0oyafpwm8pnnn4bt2if9GtQyGBogzCoAXAcMxsw8sBfryLafgAiQ+AEIZqZ85mCTgQYboV+PN4Osx8z1ez+9NN2BLFlj1cMjqy0f+7aDSaaVPfaUNTWfn8Et+9iVRn72kYekZ45qfjor2yKM2Ln5zAVMGwvGCguz01nQNgQEe3h4WJeXl/Xu3bv2tEueOoHRmYa75uQFiarHK0aZ8jBnR4NMueyE2ZyiMTevNjqiG+hms4fHCZu5caxB1tsiDN5mqnYMN3/v6M64PWeul2kt/dqxvZDRA+M0TKdFPcaYKQ2fp6M4yidbcTNT5H9sGMAfhoe3w9sOM31kfLaT1BH90pfLKsmI/ahv1+kMSj2ZMJdkl5ZVjt8poetx9uWebxhwptNpw4FM5bGdBEMzWNdTMwjuap+tgQEaNk4EOJvNaj6fj+4c9ws2sjhXVW1VcrO5f5QIaWHVw+qW6yCus3Hcy5cvq6rq06dP9c0339Th4WG7zQgl9sDJOX9vKwLnm2VhyK45JStItoPsdgkfwzajsOFkxEtHTeUyBvrKFK03ltRLApKbV8Kc1u5qKZOqMfC7DpOpOb+TiWZqYjkYTJBnpq/JYKrGixdmabnqbXtErk6nPL9MqwAHvrPNOYD3ZOcUMRmPA6/lRfDLDbeZFibQeJw0+ktG7bKQMzSzRbN72wBytc/62Ax8T7WdDIxB8l5Gp4MMlPu0cBqAq+rhTnsbCIZhwWOUpt5MlJ3bd3d37d6r3/72t3VyclIvXrwY1cRgLUmLjez0m58hMDslYGuQcT3F/dC8NL2rGZzS+HuUP5ujoaOunyaaNN6slPvjzEzZg+fnRBGQ3Bfz84qZmUEvDcb4LS/r2d/zWW7LMRD5d7KoHtCb4ThAZCnAKWQGEWwT2TrIcYwDJ2Ox7Nw/tuLN3pnO2SZwegDAdwrkxmyIAQ86SBactpR/G5jzPli+s/48xiwFAaaM1QzSMvQCBRvOd6WPVZ9hYFdXV21TadXD7Q8eFH8zEde+GAwT9K0KVdUKiEZybvKG+cDiXr9+Xd9//3396U9/qjdv3jx6Vv16vW77XrwUjCFktKIxXsbIC0FRvGtB/E7Q6aUntLzVyPWUHgu0QxmAzVDMfly3yXpS1fiJA4yR4/jtz9m5bT1aV66DGSjdchsFizrogmslkFkO7iNrkXYe+jKL8NzNvg2ynMc1qf/ZSZOt9dJa13WG4aH47dIH57kMALi4f47v1ZjIeAwCnosXYNCfHxFlG3AAZg53d3et1uysyAyQ/9NnMgA4jeTzxWLR5opPWKYZzLiW59BrOxnYixcv6ubmZmS7DVtOAAAgAElEQVQYd3d3dXx8PHphLdGI2ph3DrMbl0H7diSE5pUskBfn2mw2dXZ2Vn/84x9rsVjUd9991wAuqXFuosTIXMNgvK5ncFwP6GzkGELSYgsdxaAA79vhWMaRhfik2Vk7cXT0LVjJfGgG8mS2zQDEwMwMOJenXWTdArZnXXMdmB1jdyTNmk2Oxey1x4CQgRmQA4p1iYPmewZS3wYW5megyj7NSuyAGVSwF993a8DBLtktb12ZDHgsBgrLCYZlQuB0M1NM5Mc8epkLfee1sbteZgMQ2waSUDhops0yX/Ai6+nZdjKwd+/e1enp6cjx/QTT7XbbdupXjXfmm+Wcnp5WVbWbMieTSXsIodNMFx4RxtnZWf3ud7+r1WpVX3/9dXuwG07vPLpXAHbURsg9dsj3sEyDiqO3QSBXELM2xjF2QsbZc2D/z7EeK/OC0TzlmLlS5+v6f59DvQT5s8KbEZs2DEPTPbL2yhW6ZCXPzmQGadZBuujmAOU5VNUoPXIzGOSmT+br/pFXriwms+DHq5f0lwza9uIgZVmyEn5wcDDaguKyCsf7fDNm6zgZnRvs2bJmHp6fFysc+Gx7XhDq1cBMSiwT6ylZs/3TY/+7UsiTk5O2slD1YDDURnKVyQjN4Pb29urq6mqUbqzX61Fti0ECZpvNpo6Pj+vm5qb+8Ic/1OvXr9ubjn1tRwDXGzIH9zPyJ5OHp2EMwzB6fDAKXa/XjTnaAOyEGIENN483M0iDBBQts6ypOEo5qmJkudmxV1dD3mYY6cBEzCzE8v1ThuQ0287O+NyH64u+jovjyDFZr23KgOP3ilrGvbdW9yK5GTwA3gt8yTCQq+3OYOXVxQySDoY5Tv72Oxn5zfEOwE7Tttv7nff5whsHYffpWt5TbNNzx/5dNmLOZqL87S1L1MjzxclZ10Re9r9d7KvqMwC2Wq3aTaEusGb6BvpT7DdLsYCrHtCYnBjnqbo3vNvb2zo6Oqrlclnv3r1rT0z1Xi4bWtJ2HACGgvECwj7Oz4a34QJ6diYAM9MyQM+1J4wGOZm6o6w0Lq8YGcTox7UnO5eZYoIojLnqIT3z3Q8GkDQm+vZbqbNG4zkxVrMry8qs3GmU5+V+kIebt+oMw8OjXmjYEU7mWoud3nbCGD0PsyanYAQ5O6zfyoOuzXjRnf0FX0Im2B71nqOjo5HdcH2XWsxo0Pnh4eFIvwS5XokC3fcWZ+wLyCIXpzKgwSYdTGCrtkeXQYwjZmLJAnexsM++FxKgIWe30yB8P1IGuu6aEc2rUAlqPLb68PCw/uu//qtOT0/b/YywvMlk0p4ygXMCHnY++jQzJCdHaBzDb6O9Adi1sGQEXCNTMhsXBkBztHNNB2NNMDLDrRo/oNC1tTy+x2IYF8aVxXY3zvPLjB2RPUenzvnOT2QEuBFMckOvr5nytz4ZS9Xjl5NgU9ifbc+ypi8DGce7dmfZpT1jd1kcN9vKtDcZsnXN92ZzTltd83OGwXm2VevLdUXL2Trjf5iT/Zdzfb8w5MDX8fjN9O3rKSMA1umj+2FO/+saGFEio7QN07mwU0oGmIqpqkfspqrq7Oys7u7u6j/+4z/qm2++qefPn7drWaH0gRPgGEbyBMiqao//MdOgbwsuU0M/PC4djWtaIe47ATPPRcb+n7l5Dr1jzPDcchXSaZyfIFH19Bu3rRfkwndmkz4ugdXnJGB7zE6nOd8FaZ5TZXsxc7OenbbbkfnOc3Q6V/WgL4/dAGdWynwzDbMj91Jb25cB2UwqGQfysw/Y96wTA13K32Bo5m8ikmzROnImZR832JiJ2rbQpV9gYv0hawNpyvCp9tkUEhBj4nYAK7hX3M48FtCB6pvR/fa3v631el2//vWvm1IzfXI+jWHzuQVBlCAacIwpbqZ9jMeOSFR29Koapzt2jKxxJEg1oSsV8ZYSlJiMEhmmnLPo7JS2Z0TUHX3NqmqPWcnaleeRTM5zye+8749aiHeok1rkudYl13QNLx3fQFP1kLL1ADg/d1qJXfGb/gheyVacQpo106/BA3k4uAGSjMF3umTQyjTXwdIsLbcj2fm9xcI+6w3O9jP7ja/rcWBvLlEY3M26yLC8SOf0NQlFL0A+1T57BPuCmIQHkaiOoDK1QLDenIZRHx8f11/+8pf23C4bGoJ2LYXHU7OLP+mnz7MwaYCqb5GgsfJWNX5aBlSXYw0MXuECJHsposfGd6437GJkVY9vvvZxCVYc41oVDKzqYR8OKRMFfAAcY/cqZ6bRPSbpOqNTSD9jirlQerB8Mgj5d9XjRxCl/visV1Jww3Fcg+rdJ8qKN2N3Xcb9ulaU13QtyjUkznGAotbkQEtQMrt7qiSBDA046B27d4DcbDYjm3CgzOCYTIvPmA8LEmaZLjcwpiy32PYNfA7C/+sU8ubmpm0mRZDcuM1g6TydwANMtjMMQ3v8ze9///v66quv6sWLF23wvX1EWWzkc0ciFOgo5adZMBYM0QK1MunH/fn/LC47ZTYN30WBHXUMtsyPvtxf1fhZVMmIOderk5mG0wfX9QZTf0/QsSP5Gh6vX0hBfx47hs7YnIrAHjIN8XWe0pdBw2PyyvJTMmelizmSDZgFJfAYPAA8O3KyLwf+6XQ62tTcC14c488ydYXp8MTiDCyepzMnMzPmj84zW+G6PQbn62VAsizM5qxD1xC9AJLptetpBuxsOwHs5cuXDbxgPr077e343s+CI2C0UOWzs7P66aef6vb2tr7++utmSDc3N23TJGmmC9i+lqMMzC7ZyK6UwsLFQDLC2+lpdtJsrgG6kOmWrMHA68hlA/O1k43k+TCLHlOCXZlpuK7ptMHskxqGQZnfzDdTdOvOAE9/Tl2QtW+pyfl6DozTQY2+Waq3jA16/ozz1+uH+3O94OAMo6pGgWE+n492xafz2fFgNFwvF7rMbgxW2LhBDJkeHByMrpF26zQc2XJtBw+XFjx+fI1xZzAzeDkj8Fgzq8BuGTO4YHtyEPhb0sjPMjA69kZTdmfbULwL38LDMDj++Pi4fvvb39bt7W29fPmyGQvCcz3GzAfHtID439GBsfh/11WSodkJqK9xrgHThWP3nZ/TnhK+Uwhfy3vbaO6Xv0nrcCY/RsisgnPsgMzJRmKG63kZfDjed164pVytNzulAZ7+mTs2xhgcXBgnc8p02tfpLUwwB9uO2SuPV55Op+2pw2amOK/TLLIRA7CZQ6Z6uTjg8XCOa30Oqswr39Dl420rTivpg+t5QyupM4GN4zjH7N1j5Bqea6b/XjByqQemawKEjpxCem672k4A460mZiLr9cNTSx11vdEwFc6tEtvttv77v/+73rx5017Oaafi78zrmZCNPtPSqnoEfBbAZrMZUfhkUgk2Xl3NNIjz/dvyqeo/Q4zjHOX4nbv6uTbnw3Zy64DlNplMGlN2HcNplcfoaxisGI8jq1NTy9vR3fUz5mFmh7ycThG0+Nty8RhTFlzfcu4FDDMH99EDqFwBTV0ydrNkB4lk1iwCkFF4Xukr6Mgy53hs3mQgFwI4hv89zrQ1+xIBb7VajepYZoVOG82UmIf1i805zXRAOjg4GLFNgznBbTKZtLsT/i4Au7i4aDdgc/uQc1sE4Ojh+gkAcnJyUh8/fqybm5v65ptvRkzBu6k9IYTgyTkvNv23sdrQqvqrhAjV9Syzxen0YROlnbNqXLOycyN4A9RI0JPxdgFHyJyHHYVrZkRPZ8UoCCQGWMsrjZF+Pe4MJHkXgseUdRA7km2F6zq9xz7M5p3iZh2F5tqa5cH/1in72MwQGI9ZrMsWfG5g5beDpFMx5mu26wUjPyE15WVGjEx6DA2deh+d7cLszemqQcjzH4ahbX5lVd9gnWPz52aTLtukzrFH10bpx+eayWF3n7sPsuozAIbyYWFOC1ECv22kDPTg4KCOjo7qz3/+cx0cHIzeHWljfUqRjpJG8YzC2fzIazuV6Srn9upZGf1Ji9NAaU4HewyMMfZSQqcLBsCqxw+C5Lwe+NowSBMMLpa703bPBYPKdCudghJCFv298x1ZMHaAyoVt64RxOIgl2FnmfOZ587dTUZhPpijIEjZoAId95a1a2bfZTaY7mcJxHlkHYHZ0dNR0TbDJYIU8bWcZYG0TDkgGVuuWseWN1ZyT90karK2jtGdapsu2ZdtwytIA6jT/qbYTwFC4GdBkMhndq4Vhc1GM/fj4uC4uLurf//3f69tvv20TMGtJ50XAVrxzZwuGY/hNPxiKUzo7cm9+NBtsT9BZYHY/WYuwM+UeHVoaP06LzDNqZb9WctYBTfEpUpsBeauBUwsf43naiRwImHPPuB1lLRsHg8lkvKePzzwG+jfIW8cG+QT8vJ4ZNoHODMFzsfNk6m5ZMC5k7e0nyK2nn9vb2xZozX6SKdkefL7tEV2RxnuFlYyHY5J4pK75m2saVFIu7jNBt3ctf+6HO/A7x/B3pZA83M7CclQ2K0KBt7e39ezZs5rP5/X+/fv67rvvaj6fj6KgjYTJ0TCCjLhp4E6xUtiMs5eKZZ9ch/4diYnCdsAeezCA0LJAnDJDDgYg16Ac8cy03L/rB5ma+jaXYXh4rBEG6Foh1/DtIq7bGdxwdhe0uTa2Yp0afNySOTmgJVhgN+jBiwHYBKyTYrQBIXWCQ/dYo8/5f+2dS28kx7FGk90zQ3IsSzIM////5YW98MKAF5auLGhIDh93oXuap05HNQV7cw0wAYLd9chHZMQXX0RmVVsGMKUWOziPvY7RfW1q4HA4nN6558UUX8u8NYqgnQl8DLDoi7d/lHnTd+qFjVoHDWZ2SMaBpljsnGmD8ZgR166cCtkrF5+F9K/62oPRIGh/dfXrw9kfP35c33333frLX/6yvvvuu/WnP/3pFDbYe7hzsCwbbQGp8bbrcCg2TWgZk72HGZcNdyoObwxGvq9GagAwy3Q/3Uf33Z8LNrSF/MweWpdzJVY6lNO0viBoam+Zk98xq3ZfHOZ44cM5nSq5c2cNXajf/SqI2bHYWDwXZgEOiV1qZFzrdIZlbWMzU3e9lSP2UB0qW2lOiHMUO83Ok9mwj0+LF2Vivp6+2VaYo69fv24eNXQbnlfLwfpWG6V+Lw7Vplre3InvjYdsUjUtRrhXV1frm2++WT/88MO6vb09S7RPVLX5FXukKtCE8A5PEFZj87W2+aYKywLq9z3hGZiYCIeJbsfA9vz8fGJGsArv8DfT8XinsNVMy4ZTQOc4dcFwzDKRHZTeitMnFuzRJwa8t8Gz8+M5dh02Vo+7gFewtuz9SmzrSxmDWYCLN/p64crg2wfFKXY2ZjNmzHz3j+OYRRroHfVMYWV1vrpPP8oS/bkgx7E6E39H580svf+w7SNT9NvbQJCHo7IJN6ZyEcD4lWoeRYBtGbm/fv26bm5u1t3d3frzn/98mnQbqHdqW1ksOCYTY0G5mv/xCpA91hQ6UTBMK8xa6wzhq3yuE6AsG7m/v9/kGKiX+jz2tX4NKdnrxsqUJxDAKgA6z+LrXTfzsQd4djweC8DqJy0skwIJymemM4V1V1dXmxfbtZ/WJa9eeTO0i6+Z8laVuRkP88h/zvWpBcvn4eHh7PnYRgFrbUMonEOB3xuzDfxOMXz9+vXUnlfn22ZX8ih19naCJiK+tiGrnQtt7AFJgdsryT7ulEV/Y8LO187UC3yXykUA+8c//nEyNjqM0a7166R8/Phx/fTTT+vLly/rj3/840kZ7eH80PZeSGOgApwQkB86xqCdd7Ki2qMjIJLEJLM9Ad0IataAoRlkPJGAkGW01mvins/UzzgBQ7fNmC03K4PHhVI1TMILIl8UB4M0EJu5WsYoejc/mgVYXgZrpwIAGPpZ1tUHiWkbp0cfWmB6z8+vPzbjvJhZkkHFLMSbOf3cp0GsOnw4HDavCuIadGxvocjOhrlHNs/Pz6cXhiIjFlua9GecBRgDEv8bGiJvz3mjoJ7DFnyv27NDtR5h440QAGE/tmSmyb2Mw4sHl0DsIoB9++23J2/FD10g3Lu7u/Xtt9+ul5eX9dNPP60//OEPGwEYYR0KOnHuvAvCcnLbjGytreexEdMOYOGkN39d0auXLrtCyfml74afVo561UkGnSB7Jd8HKDiUxGhRpg8fPpweJSkbwzic34IFA2YGW+cqzH4NPpwz0E45L8bl/I3ns16ctpxIJwStvJGN60OPnBP0mMwkvbXEBsf8deEHQOF6swfvG+N+7x2bmIXZjeVD/82mfA19RLbI36kbg0jrMGiWXDQUtR40ldLIaa11Gr9tD71w6Nm8rOef/9UPh8+XwsiLSXwYC5PmV9r+8Y9/XH/961/X4XBY33///SbXYw9YGs+D2hWY98H4uIVoI2/IZQOz4jtmd66E35FkjF6kuLp6fXeWV9aoz8yhk+K+2vPUs9j4r66uTr/+NOWWYFOM7dOnTycW3HbXOn+cg3s9H82JmL67YMw2ZCutQ07mz2003Pfc1gEA3NRj4Kcvrsf64r5SGhIZ4Gz4ZisO/8zKDWqc2wuvLKfJWUACIAc4oQJN5d0UjEFrDxBhlnaIEAm3zw+0VD9sT9xHKUOu7dTGrV+MpRvZGY/7cKlcvOLTp0+nPV+m2Dc3N+uvf/3r+uabb9Y333xzlhNoOOHOkYdqvskMwIbguqzIa73uzanX8TUomNnY09Ovm2w/fvx4CkNsZL5n8hoO3zr2lhqu2YND4OaQDM4TReezx8p1AC9joY6GyJx3ewDKFKo4LHdux/J3/Yxx8qDul8fVUGWt+bU5bs9sp+crP+TkUN7XA1AtTgtQx2RoXa10P+2Auxo49bFEwKzajsE2VibGdU3VNJrgnoK7AcfOpv21QzTTq3ymhZXJxvbmvOUigPGrM09PT+tf//rX+vz583p4eFh///vf17fffnsWVjgO57+Ny5PC/064QwgKe5QcLnLcbdi4PCmOp3kioIqN0Cx0JsH5No73mb96I+euDORmhOQD19qucKEoZSCuzzuwyzoKSg4zPWfuD69DogBENggzSq/OWQ78L7shlPW1VVyHwp0T55DoT4HGdQK2DpktF4c5Tl9M/TE7p57qO063n9eaf4qv/W44ZWdsuVe3XQo67p9ZbwHQTqv315HQR9qz87A8/Syx+2d5tbi9zsVeuQhgDw8P68uXL+vz58/r+++/X3/729/W169fTz+T1klH6R1SQEv9x7U2WgTZX8eBSUwbal0/15QhOObnGkJhC9dgaoV3LO5zfryI7z7vuh0WOk/Hjmn6YkaK/BiLldcLEU5GN29BHYyF/2U5h8PhlLuxwdrjd75ZffVSOteYVTnt4NykQyKvbpfZFixoz3PSOh2CmbGY1Tp0M2PAqVgHygiIIqy7HCvw0Ac/+tN+m/HCnie2RqhXtsNxrrG+23nWGR0Oh9PjggU56xfycbrHoArDwxYdLvrtKXZCDnvt5CxT17VXLubADofDur29XT///PP6xz/+cXp3VxWbCXLsa+/OQLx07pASASKwtbZgRB1G/HoZBHh3d7dhQ1NYAViRB3CeZ0oIO7RzQtJ5m4YxZlLOQ5WRuu/8d1/7Hvvj8XhaDeM89XmBhL7YoPZydlamJlwBF/JzBUnaBSTIpZQJNbShbsvBzsey874sh2722AZEz6HD9mmcFPTNKYvqDTI08GK0AI+BkPEcDq8rmICVbYQxeYXOMpmYEfbmX+uybCfmBDh5bH6/nvvH34cPH07v2ysDo+/0Fz13xGNmZ330HE862cWmvXIRwD58+LB+/PHH9fj4uL777rtNoxYIAqBBTxDK4ESgO9yQwArZ857YxtcTA5rQ2wZTmlvmw7HmnNZaG+PqBPhejLQg0jbMemz03e1uwHJbVgobh412yrN0XD6HJ3x6en2+j+MN9Sh2YjA05t+JXYfPnRvaNbvZA5S9fl8a11TK3Pfqdjjr9AcGXOdtgKpOV9ena/fGa7B2qX51jmsXdtpmTFwL8E56NDknz59ttDpf+7U8PJYea7kYQv7444/reDyengNzGGOjpDHK9GMedLoewANqZ/GcZi1OUCMUwhkL5q3XCpvdNVwx4+J7aX8ZYz0mfWm46j01ZiDOlxAaNxRp/+sRnXeZktc4ACsa9+Apva/LckL2ZrcOzyjMcQG+OSyU3HPmduvxJ51xqsL/fZ3rmLx9wYP5Zqz8IS/3m+LFmDpN11m22ZwfIZ03RXsbRENsMyV0lDHzv/k7y8jhq2XpebFOUI/H0NXr5rysH0Q+U92eL4e9/xGAGSzcKA07P2FFIJ/iAZh52cBtvBUewrKQYAMcJ2S8vb3dxPZVbo4XFGyoZoEFZwNVQ1uXCn9SaO53uOaVTY5ZfpORNy83rRBNsjWVL2ibSVR+/l4PSzGrcIjk41ZU19W+2inVMXjck1Na63XHvT1/rzeLsEyaZ6VfdcAG6b0QDtn6mBmcjz08PKzr6+tNisW6uRdW7bFry88yK0P3anHZ2pSGsTyoz/ZkrGiUZjBuntnXu6298uY2Cq/cuEEaajjRifIgzDZ8PwOavMUkfHbWH4/H9f33359+yZh7DofXpOZaW6ZjoPCD0BVWP08Mi/asLChClXMK+cwI8MaTcthT8rlh6WTcBR2zKDuGyYnUY3fcgG6va/rAhtLQznktK7Hfx9+0AnIrmPg4ZW+VtHnOfneyf62to7Axk4dy/XbYnnsbpgGp8u0LDw3Cnp+WttGogTptU9WZgq51og57AhbLcMrBTazROUTnxn9rDuwigH358mWzyuaVLgvUeaA9L2Qq7fMeFAZmwRbQDofXl9Q9P//6uuq7u7sNcL68bF/J4nzL8Xg8bb5sItXeuJPrUsUoA8GjcW6SWxPsZhxO+ttJwGIdykyMqDKnHxil5eG63Meyk8lwzKb2PCXy8L19ENpzYxmVxXZ7iGWIbhWYzFoculO8Sj0ZqQ2+DNlhuPXYc17Zls04r0TkQO7QDr6pg4az1YcyMsuz/UD3GnVQzwTmHUdD/AkUC3CdMzNz5NA6Wt4MIe39PUiMFGNzktaggOCsaKWKXmK+RPcR1MT8XE+Fa6ZlwdBn2tzztHvKgPG5b80fWGmq5O4rSt/rKd2qYCVGwVBEzwfj8Zwyf76f9ixXOxO3zf0dH8eb4DeITPV5Pp6fnzevYi5TLIjwfwpnbXjug4GQ/9UZ2nt+3v6Wgs+1DTsG7jVTRF/sqK1/3j40PQZl/ZpAxzbFVhuP2zk3b+e4uro6vU7dkRBs2KwY+XY7CNcbdMoaDcRTLpXPnsvJMbtcBLAqppW1MSwTWa/B5LUTRt8pgYhQbIgWQnNG7i9gwGfvFq8xN4yjHnvj5lZ6jfNaFMbiSTDQTJPi8ND3mqU45K6D4Lyva8hvj884zD4tR89tPSr1dQ44ZmfAfQU7jmMwzJsfnrdM+e4+rPX6sHbHMcnBMio7tJx9//Q2VtpvrmnarFuWhGxpk747irERoxcN+8pu7HC6lYG2KNOYHKLTRn8xioKtey4Ae8bUaIxrHCHZNjqvv6W8mQNrKAWi29O40y8vL6e3T1gwXplk4FxnJSrlR3goYA3DA29Yy2ezijKZadWL7wYI57p8rgZZwPZ9LgZGxmggKjjZcXg+PCazsYZL9o7ID8NoCGSw53jzS4+PjxvgMKOcHNb0iI1lwbhgMdN1nbuGlHZclj36Wjbk6xymc34K/dtvZLxnfJWn+0qbzfc4XWA9a/rFc2vG5/HVoVHaZlf2qz914NZP+uDtLiYvXs21Hhvk7Fzdj0vh41q/IQeG4OxBERgNwnBMiz1oMxR7I0+uQcFJdgupBu4cxSTktbb5JNdRAVVQza/0HntL+uP7NkI+nO/XoU3X7wktGywDKlAYvA2ME9uz56RvZioTC2yo7Nft2NDKmmirBuo59V83SdPHSXaWkZ2dZehtK44M9sJqy695nRbAcZo3MyeKV4k5NzEy67b1zNfX2XIvbSN3Mzzf493+raORhP+XxVqGXrmdoiXbVNkZfZiii0sg9mYOrBOJ4ImZ3Ygnn9DQnp3PFij3mErSjgXhYiWwoGzkZlxmD845VAmsRM3j2JszgZaLwyDadVjtPIRZjRW/IYblNlFy8hMA/UTzGVsZm8dig6EvHfe0RQOG4mP0c1oi9zzacTgcKZC7717qd5887wWNGmTDKue/7HzcTnOTrq/Odm+jse3CfZkchGXq/jPWPVbo42WxE+B4PhoON53A/OEUCjTth3WX+j2v1U3rh22z89dycSe+B1eAmVaAGJATlVPYZ4Uzi/KA7Tmpr0Kirg7QYMS1ZUjT4y7+7MmdlqS530pfRoXyT32n365nz4NyzPU2zKjX7FaAyqH5P8vU4+48I1+H7VOYYgcw3W/5+76Hh4czVtMUwVTnNEY7yrJQ2vAWChu9HXL1sMddT/tgOVJwOk9PT2ePAFHQGzOaMq0WRwa9pt+tq5ciGDsS6rE8DNjTOCbbeXp63cvp+TFWOFKaohfKRQZGpV4dMYtyxz2BMC+EM4UL9iau0/VyvxXFhlxPu7dC1clrIr3G5kmawiEbrRWNsbsOvwWVMZh5YjQGbi9QHI/HzSqYQa3hQdnIWmvz8K8ZcpXNMjKT86Zh582sF9RnJ9FQ18zMrMYOEabqlSyz1BoJ7RI2Wq5cb7aAXM1+JydZGRcUDHgTmLROL4Ywx330jTnu86G2na6GToyO4+7HBCzI3mSjzLKAaDaG3MviK7+JwfEKK/pRG7ccL4WPa70BYAzCm+tKLe1NrUj2kFVeT75DGbOXqVhoFvolJZpocUMCU1cb+Vrbd471Ouo3IDhEpY49EGr73Ybiayt31+VxVX5N8Pc+Aynj8XzbKfQ3DL1pd8+TO3GNAtsouc86YEAsQ7RTRD8NUp6bPfbLdV7ocR6wrNKsiz4i248fP2767DJtfeG45Y1s19r+SEv77felce8l3S8rX+scIBhXF2nsWDtuz7NxgPr2cOLq6mrzm2CwfwgAACAASURBVA1llJZRdWWvXAQwlLV7O6qANzc3G0rKtf5so2ag/iEP2rMioKRmSJNSesBWPJ9DUA69LBzGZa/q82V3zZFV0EyGf+CE4wWJtbZPOhjcLXvLyfmfOgfaMbvtSiP9hqEZ6Ch9HpN6+96wMtg6Lzs3xuo59pyZ7ft4AYD+W4Zl1HaoAJ11BBC2Xq51/mMvlDry4/F1JzkydD11Gvywh/ve8pZDtkzsLE0ELANK9225Pf57vuoEK4+JIbLZvZGKQYn9aWbW1k/30RiyV94EMJ5Gd2f76lnv/6Iz9pYoLIPkWUm2UZSN2EC8QsS1puBmEA1P6F83zTWc8zgMmPawBgCHNg1vy5b6Opy1tmGiJ9chJcvOBnmDJMyG/tDG9fX1Cfhgq/TXzohxfv369ex1NfTFbyYo6CIvzy3X+e0dXOdnZ53gb6jZbRBNLaBnBc6J1ZlBui7/qC19Nfg8Pv76y1b9RSkzFoMifed+vyLKYDSxiY7XDquFOek8mcU5vN+bKztg98k26jYnZl1nUCD1PBkU/dOMnaduE/kt5SKA+VUaFD9cSseZqKKnabLZlCccz2BP6boBKwvRIcda2zcv1IOZHXV7hxmj8xZepfNPtNOW++G6zPB6z8T4KNxLfYzXeSZkipx83vLiLboAnPtrZfYL+DxPfrcX8kBZ+3P1fc2N81h2dtRtZ2RZ0A/PBfXYk0/bCKawjT7x1tjWxXcnoFlVt5ECdBgq9sC+RHTeuS6Pyey6rIZiVjaFoRz386tNj1gmdSjWLW9zsDPxPNFej9fx21H5PuTW0ldoW2cLkpzfY6mbNi+dbGLTwrAHMJOgU/w3qJWt2TOsdU5Vnadg8M/P5y9va9tVJnvZvXyS+8NnlHPvvj3QbDjtHI1ZJH3HkxsEC5S+3214lQewYazUO/UZGZbheENtnZT1wvPr9j0mh+oOAytHK/S0g5xrplXsgqHlbUO1HtiRNQltQ7Ie+D6f93fPR59l3CsTqHmMfN7bCMz4C35NpZTFTzo6tQ/wTfZmkOlrcezYO+dlbVw3yWkCdJc3VyHpjMMVH/eklZG4837PlDvafArXWBhWqks0s6xure3PaTXXwT1up4qAMjo8dPwPYDJWe+a11ikEbXvUZeMqIFDMfJqDdCnD8PUONQE6wMJjsPctyF1fX2/m1zrh+XBYaM/vflunpvGY2RTQyqgN7jYk+ri3HWTP6fT9V5U7dZYJ2fEQJk/XeN73AMz9mhZSPOaClR0xIW0Bxvc75HS7vt6g48Jxp5U8567LfWVurBt7dV8qb+bAyAd0lYLJdl6gDMGfPUAfa36q7MMoXW/WUBIh2IvzuTkr6rNnMPhUmJOicKyMwsZZFrqXeyi49j4bz941LlaMCWRgenUgZVoGoz5cjUypv84BuXSryMvLax6qelKlrbFbpgUH6mAcDZMcRvt65FsdJzqYDHHqq68xg7MsvD2Gdi+V5k+nPFPlwPnmxihmm/6b2sPG7Oin4jpcig+WkRl62ZjHe5HB7p5Zvxo/Pz9WxSwL8+DKIq6uXld7+I5HtyL0/UpdWeOzw4m9nJTL3d3dRmAUG0EBpb/gXVC1kpSK872Jatrkf/uLnCqvidX6uxWyoNHwHEP1vDmBT8LdjIF6qLu/Y+Ck7NRGHYd/h2BSzuZfqtiWuVmW5QKTYkyHw+vzuM7fOL826UW3oXi+uHdPdl595tqJVTrMNwO0zKs/7u9UDPKTTUws0GBveyg7m+RkIuKFCMbch7f3HJCJxyUHfRrHpZM01LyIcwtuwINnUrmf1S4LyUlFjjuHQz1uo/mYtbZeo4nNtdbpl1c6md506k15DsUYj8MKlHZSIiuOH/GxIgN+lsHV1dUpVDSt93i6D8iyJNyzLLln2luEfBqu853//IAu/QOc6ly4BnbVpHm96sSeuQbwNrvzfPYZWesQMvb8sjLrpP7EFgDCSTYOs7mGH6qZdAqdaW4JMG10Qurj6up1XyWsl754fmobE0gVAP3Zea1pjsokret8t+PmHX1rvaZNPD9uH92cFtXAGr/V+VIoeRHAbm9vTwZA5YBMJ7cxsr2xJ9SejEFMq1Ze/rdgUQqv3vjBVPqGorHMTX8dXlL/xHT63jDH6f6jnw6T8LLIxbvhnT+xMU1bEuh/vVwZyfF43LBk5+rs9f2TdZQafdkkbMvhvsHHc9OQkLbsfS1fh3o4RetP86VmZjagMrkyvpeXl837rmA5ZtNuwwzKuoGjo46yd37hvWzTzJjcYyMJM9g+gO5ramvUwWeztzrsyoT+0I5JR4HS+juFe9UD9xubtB0B3A7HwRYvWFgfp3IRwPg5JQMQHakHdsc6IM7jUcwyzOYQpBXDObG1XnMxZgr1gAYee2P3Za1XhaMe5zwMtGw5sOewsjBpnggnuD0e52W8x84ASB3c65Wy5+fnTSL3cDhsDNpeDmVDXgDSFOI0IW/52UjKiNwmCvfp06eNfBiPGQNAzjyg8P6l9OZpOO6Q1w7CoRCO7unpaX3+/Hnd3Nxs3uTLvbRNMWABJGWHlgPhEfPQcKwbSJ+fn096Z2NFr61jDk2ttwYQyxbHYH33WD0+gz91EDW4Ho8DZzQ5F87brtEzyIb7gHwpJgjItLsSpvJmmt+VoPAOK22kptd0iuNlYw7LMD6MZPrhViaD6znnbQ8os4VVZmGva+ZGX703iL9uozA4TOyhQOV+cN6gyPX02wrpMTLmtc73V9GHbhVYaxtydZOwjdOGYmZoQJ8ofWVsWdnT2/A9Zr8/zszMYTwhm0HQ7WE46Cgs53g8rh9//HH985//XLe3t6dxlE1Tr1lsnQlzYVCzgwHEpmJGZaDyvNaoucft8t3tVr8859YFxs35RgPoAPKnXhyB2ZbtmmLbdv6yDNEyrtPEPtufvXIRwEy96fhESTtgT6xpqY3A9zfR7PDQgnNoaO9hgXh3vwse2cKZkqSTcRZ8uM/9mibKoGxmh5GZIaHYNVozSHtjezOz4+PxeHoRZZP1DqU5byC1ogIkzH/Dj8qXOjtWgIfzXOMwweyvim8n6DZxVg5xaJNcF/2G7TRPiDzr7CzfghjzXYZydXV1prcGxbISM0izN3SjUYeLHU1DSved/tqJNjrxOTsGg6PrsRO3zprceHyNfCbGjy5aZ92vRnMuv2kbRVdO1vo1MQ49RtGKpDU2rjH9ZpIdFnKtwc6DN5szS7IHoJiqe/IclrmP7r/zFo79qcftMCY/fuL43srh1bGCqJWdcUPPCQH7JgfL1izAAGk257wd84FRGtxfXs4fhUJRG7JMyjflNOijQ2b6j6yRAy/K5K8M0IZs1gj42tEwBjtP98HynIDGeUzrCGC51utTKt535XbszMr0mltCRtVBlwK7++eoxjri68qe3E+DZu2J/wZgZO8IyDbEPSYdDc2ZA4esHXPLxfeBsf2goZsT4RQPBiM0k3BohKD8GluM2gZv0LTAPPkevENEg1YN1WOheHJtCABCvRDnDAo2BhuS8yAGT9iNjRTDoyALOwk7AcsDmZiWmxljKPQBGWBsfvYR+fkXuWF4HgPAZ2CxV23Y6D7x2QzR5xxueLx2apZFAbIhfB2fZd18jnWMNg3Ma50/MmMdmxhU7aCs0/PonKb1rcXjsQ5QvFnZulAZUL/TQ3YUsHXnX0tqug2q+mlWankbJ9Y63+t4qbz5QkOzDoPJWtu9JPWmZUP27s6fuSBMK33ZX0EMwdCv5nmaRC1QcX+9V0OIGiHny4Q6FhtW8xbI1OzB8kOZDofDSXFsTPbOTgY7lMWLM4YC95SToJ6mA8yAu31gYpsuNVo+ex4NJpzzPPgheMuWfnoLA8cmD24H52NlJHXKHDcjbI4GR2FwhMFZdz0XLHq4Heu7++Sow23uFeusv6N7yKrpFSIE63v11UBzOBzW/f39ZtXa7Oru7u4U8pvIID+Hw43kLpWLZz98+LBubm7Wly9fNsaFAfVXu6d3IxEj+w0RNlYrbWP/siCK43XXh3DZ90X7fb7On80cqNssA4Vx2NjcFMWTYZBxQrmsoGyCOjiHTL3sj9yYcO8PQwG658lhpdnTSRECRgXmhrs17LZjkGELBrIDPKZnWs06uqG2/WqO1dczN8iXvKCdosf9WzaPMmcY/f39/UYXbIANj5ojcptOb7i0H+jyW6zEBQdOv7xa6GLArK73GjsG5urp6WljdwY4Ox87yebHqo+186lcBLDj8bgeHh42+7esUH2+yiEgwvBDyl2CtbAQbr1yWUOpq/uEInSljTapH0E6X7PW9hd8LHDawUCnnECZKIZm5sR5A0iBwkn2MjJkaplYVnYSTbg6/0BxmGLwNEg3j+E+INcyaUDSgGPdYPuImWKNxQzK/aFN65BXrf3iSL/+xzpRBt/8U0Mo7uHapiMKuDicygzgRu/ok1eJkVGd6ltMhOsoyNL5tbXmHfy1A9vWlNZwPbRjuZM3tY0hn7JB5+rc7t5q7lnfL51sjqRxqT2KhexEr72jPc7UaUon38o9xeb1DBYS/eBJAOq3QgI6HksVaZrIKRdnsDAld+wPQ1rr/Pk6j6vH3CcSxRiT81fur/Nz9MsyNCigYAAk40FO1NtC35pbY8yVoefPQIaSc41/is/Xo0MFRK6pPK2bBi8DTn/YlfvKAroFAt3hz47OfQH4Oo7j8fwxGwPO8XjcsHDniaw/jI3/ZpReRKk8+O46LSfmhxVWxtEUisNa2L/n39c7PWA9tA5Q/iMGttb5b0OatpvyuxMYl5eazUo4Nikb1zKpZgW0wdK/DdN9mMKAThh98YrVtDpJcfxvA61ReYKt4A4rME7LzAppgLVym7XWsMp+aZt+YFBcx/iow8zS/TETNJjVIxt8zJocUrm+T58+na6nbb++m6SxAYI2+0iT5eMcTdmQHS7gZefscAjZOSrAcVim1GWb8AKP5eY8oOVvmzJrLytFv9x2HQr1tM2ySesJc8p3629lzxi9d6+65OKneAzgjTAY68vLy7q/v9+w0slpnsaye+b/BnV3d7cxtjIeGzRMoMbkibThXV9fnz3aw+fb29u11mtYZGBw7sRhYduZjMyCdd6EiXY9tAFbMt113c11ICsfLyNoGGmHgKLa+Ax+ZpmeeI/dLIExmQUbKBlXc5pVSMsXj0wfDYz8Nfz3OO/u7jb5M8CEuT0cDqccEwVdYww3Nzcbh2iQdyF35HlkHvjzKl8XX3wOkGEOOe/cX0Gkq5IGLZc6RIf1nLdsqXuKClxH9cHXOP3iJzq6E74gwhMTHoN1BvZMXqxpAsa6xyD3QLzlzUeJLCB7IJTMgLbW9j1Ips2m13SU/Npa56/xcNK5oGW2Yg/enFXjfRuMAaAeqWyQB5oZH/1jTGYxjBHQclK+rMSTaBBCbmZtFFPwssHTpAaoud8JYO6vo6k39OcqmwGr7U8Mzn1rMtmysbHRBzMl6uTRIOvVFLajw87Beq4Yu+eIPgGYjBX2Y6dH8Zi76GIdQ6ctFzOdhpBmxm6rYbOLdd06yb2OKCiOZqpnk1Nw2NgIB/ZqEK9TYFy0B3aY9V5iX2u9AWCfP3/exPwvLy8nZIYpOG9idG3IMHUEBbMHc7GBMrFOhOIp3G7zdVYGA9Nar4zKntgTYgEzsXhxvlcpmxdrzoD2620twz3wMGC3X5Y3/2tgXcaeZFIgMvugPx07MvTKo8MQAwLMt+2ZHTgMtGJ7U/Wka5ORUTBOA1bDKHTC4OzFDy8WTBtLXYeBvU6eaww8lqW3qFh3Pd/UWQfWPFYZD/d4Li0f2rQTsEN2vSY37SfHTGA6Bjs6zjm8tpPdKxcB7OHhYd3e3m5yGg4XrGCT0FBGo7iRldUKT15XN6pcKLEfEO1kkyMDAEuDnbuoB+mKTb1cmZHDLrNOew8zFMbonBT1OhR3W2YZrtN5BYOiv7s0Ie9+c75eEofhuaH/niOcB/NPv82k0B+DteVvZfVY8eTe5W0jpM/MffWnc8bnKZ9Y3cZQWQR6fp5/TYs+Wx8re4NaWatLF7dqwA77qvveHG5nYHD3Pe6P9RFd8Dx7LLRf4lGnVRCanj/mOrO+5tr3ypv7wL58+XL6jgelkwYjhGGFpZOeWJ+fdlqjHCjiL7/8chamUF/bQhBNEjopbgXrfTCOeh8L0+xtrbVhBM5XTYoHSHllacqFFMg8rq5s2UDdB8+Zw2vXzTEzRzOPhrqWm0MCwLRhrUHMYIOcO0aDgoGmRlJQnEIh5q91u88O2bh+j1VNoRx9c/jaHNkUPptJ2oC5vuzMbZbldqwGJ+dZm/fiOvSlzJvx2c6pz3npCVwMOg5bp9XU9pvjDfH3ykUA+/r16+YNABaWcwAYiemtBVwUrofjOLkJKwbJQrOdhkkUMwQKCxEI1gpWz4TgTfmd8DXD8TgwSIOm7zdAoHywT8ba8Md5INNt/3Vl1MzHygfgkMSnXoMd57oIYVkY0Kmf663ULp5n+ugFE2Ti8Rv40A0/aO6xWd6txw6WYl1GhgZEJ9y5zoBinfVjNTZYjN1bKRyKOTeMrD1uO1zrLH2mn58+fToBGvdVh1z/pI+T7pUdVufN1DjGGC1n6kIWyMvJezNgM7v7+/v18PCwCdun8uY+ML9Pu3GqQ0uooVfxJm9mUHOd1MGgJ1rPRHmZ2spY8DC6l8F11zbFK23uM/fZW3OdvShK20l2WOjPjKUvPbSc+fMKEePxRtnn5+fNw9dQfJSmISeMzYDunAR9gRGbeTBWr2p6DrluUmpkwL2kA1BigwufnW+tPLxQUsDwf+dvPUbGwmfk31yfdcC6YGbn+W2ivX2knzgT+jAlyG3k1gnrqqMjz93EzCkFn+Zyy3B9vfchIjvaM+ADrtRjZuWw0fp1c3OzPn36dLZxvOUigHUPGOXh4eHM0JvbMNIaaBp2Gmx4uZw9EApnquuJswE1H4By16M5Du9zkwZgezVPCqUAOHkirpvA2Nc6H9h2AG4MuS/w88Zgv0qHAqj4wWyucR7D/XeI5hDSDqMG7L1VZl0FNebAK81VUnJe7pPDVO6zc7m6ujr9WC2g5M/tVwHW4apBws6SvqFX1jXPhcdqtmjgY14Zm+fezLvX9jvsGjkaSCbbmRwr7fp3A3yea5xWsLN07tf39Zjnrjhwc3NzCjXdh6ZiXC4+zG2jM7U2sjtnwufmuFxPB+cwwMli7reAS9PdT4cCnRSUl6fp2W/kxx+4zuN0TsxxO2OhLdPyghf1TJ9rtPbOAIEn3PkPG5vH6vpr4L4fIOuPl6BMgCwKjcwbcrs9jLDHfa/ZjUM+OyD6PrG5AhZjNvt3mOz6uM+sv/qHLOsMDeqMg+011If+2tl5FbNzzXnLrVs2anv0hbEaVFwMnhOL8Wp+iYRLWbMjKDND5qo44JC795e5equU5X2pXGRgKI0ZQPMMZQ0OG00vqacsDMNyGFZKabbX0Mz1wLSa85jqKwBQphDEuRjXyxgdqlpuNgKO7YU/tM1TDPawbtthSBOw9dIei5kUfeJXoRzKmn1aKQ1ATgE01GH8E+Ps3JiBGZgMEmWCDekYL2G4AalOrvpiXUS3qcvMYmK6XOMopdHDXgrF8ui82WYKOmaqZeqeD64F4LzlY3pG08U6ZRm4T46CKCUOZfHWdVISBjfnVanP5GevXAQw6LdDQ3sTe4IirZGY3IsH4AH63oldeWe6laIAxzErko0Yg/QO7z0B2QgvleYjyqI8Dht6wYY+G+CYQIdw/HeyGBmgCBz3UxE2VMvDzMwMhOfZzFy6i98LA83/+B6zMivzWuuU3DUomqFXoa3U/o987cn9rCPzUUPqsaYuDKzU8fLycnr+kvvQUWzGTLdMnfqp13Uz9w3b+d4FKutYgaOLPGZ7Zre2Hz9j6tw3xUyR7567tV5TMRwjrPfbanhZpR2S533q21Te3EbhpKFfDWzF6hsXrGgYgUHLSo6C45HYXW3l4npyIrRj4ymIOBdQj+a+18tRyhKneNwMteMpuPp9UFPo6H67LgqyazK0St361toai+W61mvYx1zZ4MwybfRVWMu5SXIDt5nslAeiXTN1xj5tpWBMDTsArj4ZYYMqw+Z7V5OptxEGsrI+2A56Pdf1aQjydE1RUA/X2Plwnn4b+N1vszz6UACyfhhIaM+AWkLQvpqIoO9d2Tbb5lrrpHXT9+6ViwB2d3e3of5O2hVkakgWlnNEVui1Xn81mEGZwjt8MiBSCHNQAAvVG/oQvHfptx/0efqMVzLbahhoZXOh3W4B8WKBx+OwyquGZrIFKAzRytu8S0MzyxIAgXlZRtzrl+61WHkrO/piR1I5o6gOjwvmXrhwyG3m1Tn1WLxianZL/ydHZ+ftbSYNP9d6dTZmxma3Lnz3LyJ5PxmAbWB3HmwK31wvfZ/kSJ3WM/e784Y8GCvjNFsvuNop2ZFbJxvGuz2z7UnfNmO/dPLz588bT2YjomGU1+GdJ89MoejrlSCUzzkFztP+4+Pjenh42EzklBOwUgNy1AMjnN5x7omeXnHi3IfvaRh4Eu5h+2iTx+8QoYzHit9QlnG4Hj8EDWCa8Xk3Pe1abg5tPT8Oh71S2RzOBPwNAwqmVlzrQEM1PrfP1r0yfifTJ3CfwrbJMRQ0qd8A6nzqxMpYjKAfZlrMj3WLes0KK0/Ph8Nz7rXMab+huHNkHjPF1zsU7mJCwcegbn028LWt6kSd9l6UtNZvYGB+75RXBZunacM+ZkUz+JlyMmBi47VeQ0a8w+Hw668s1xsgGCbFynA4bJ9fLG11KYVnLPTf46WNMi5/t2GgLJafJxuP6WRmcxB2ENRhT0Vd3ovGd2+hqLJ7u4IZtUPWysqsx3pBOwYbrllrnSnpWtul+4b3BiGHsa7b6QmHqwYk7kUufKbYIXtsyI++ePWPdjo/U8hMG762Ty8gAwNs62Dcnn+PsZ9h1Q7PTEbqkD2/FOtGWZ774nunaAT7czTg+iewtsOYyps5MH7N2Rvt7B1p2KBg5mAPUfA6dUIMjAHY6zZnYGVtLI7xeuWE/tpw7cE8jk6Sx+d2bUQWPu05BOZ/PbQfpyFp7tCh9Zb5NkHOnFFM5afwn/oxarPAblB1OoB7fL8dA7L/+vXrhv3Wk3osOBo7DDsOy7HADmunHsuO/jjE47wf57JeeqXVBm9HTJ1mG37pn/Wp80gBlKcQzIWtLh6bx2oW19VGZOaFMNuoichUOm/9IR7PjW284T5bTuygGwXUUb4VPq71BoA5BIGNWXj1EighhultDR4YddcjudNWuoYODS9coKv9xZi1tquqrdvjbf7Inq2exjIwkNSrUE8T/ihQV84ccnLcCWHXD1ABFBOIwYxsAO6fV40bunEdhgIoINPKn3o+fvx4yvMAPPS97Pvl5eX0kjyzBwOAZWEQ9f+9BYuJ+bltO9A6jeaRkF+dOP/dzocPH05vezXL5j/gZBCwnVgO1j8DrOfMqRqu92pkS8HS+tuQ1+cdiVAaFVmG1nXPf+fR4LcHqpv+Xjx5eE0wAgoYhEM2OgnSN5a3EjkJaq9KZ/uzTGttPZnDUIqNCRZmD2Sw9QqVDZRzjMlssHktg+20SlLPYS9dwG6dKAXjJN8Fs7TReZWt3oyCQnvu2g4yNmNDPg4vWwyyzKVlX6Cply5rQv715DUi999MtMwLuVZursMyrnEWtD23nLfz4DrbAMBMXZZnGT8A1y0OXGOHxnwa+HBQHqMZlO2WNprMt6wa1k/zX8AuY5vsyW+LcbTiOTRgT+yV8uZGVocGDLCg5UloHGumZcS2J17rlV15MyLC9iAueSjTca/YWcBmOhaMPcTk+U8CO5yvjPJ5mugqq8dmcDR7sJw476V/s6auqNFHxuI8IvWZFft6O4kqXsfesAPw8jWPj4+nt5kwJ14McHvIxh7ax6uHNhzAlrm1jKmzaQT6TN/o9wSU7o/zigY+rvOqs/vteXMqhjY4z2onxYtJzS2amRk0kY/1x8VM3KkCF2xsz3kV1D9+/HjSNeuFox6cDfswyxT9ea1Xnb/ExC4CmL1Mjc2hjge6R6VrZAjBnTMdNr00g6I0D9WJssJ44jleYGsoNLEoC5PvDX33hG3vWCB3m80D1BvaaXQ1FplNjxhNTx0gDxfnDj0PBQ/YkoEFcLTx4pCcMG744/bqMGAbBibLwWNof8xQLM86WeQzsSzkW9bvUNzGx3evhvKZuuir57D64XYKuh6TQXgKKSlu1/dNEYQZW2Xl+5hXnAebe2s71eGu4ttWPf9OB+yVN3fiUwEob4G4YRp04r3epx0zrcfDGIyo217InqYI7lyLldrGX6W2R3OxkL2NxJMw0dtpRceTY1ZRBmPA5j9tVdHsQQ0MDntoE2brxQvanpbRkaGvqTcug+a7XzHjYs/qOpCvdaOAY8O2zrSu6VxlbpnYEdiwzb691cXjBcSdHOde2jTIuI7WZblMDrB6Qvuuv0DYiKD6bR2ZjlU/kGttt86t4G+2b7xgAcBza303Ifi3AYyJhSIaXRtKIdB6hA6gRmADcOhjA7+9vT1de319fQJTG+MEqIyBvqGQNnRKFWcKL1sv/Z48les0QJ8EL0V03qlKVDCzzDlnhuNQbFJs5FiQs3zsJflshZzGwr3ex9e+eN7RFXtgs0UfL2ujzQnUm5cBYMqeXbfnwec4b+fthLhBgu/ThmoDq2VjJu552AO0guvkdL3laALDaasF3wvyLy8vp0WYMiXrhMHJxMXzaUBEnmX4nQfGvBfGrvUGgP3ud79b9/f34yoIAqhXKrX3OXdoz6NaOWjny5cvJ6X3A8ZlUS71ANxjwy8rsPIBCH6cYfJabW9iVfUqa72+PscLD1xr6tzJ5HhDUOTakNxjXWttmNges6J/yKwAOYW4Xixwn8xQuJ76zLyYX89B9cRzaUApmBbkpygAOZfpWod9bUOv6jWy6kZNA+0U8lonCpq0a/nZKdKW27NTn3S1DGsvIkhsWgAAGKRJREFU9UG7Zu2U6ovr8LYK53HtKBwtMDfe8G1deYuBXXydzsPDw/r9739/VgHe04M20yl6Fl2N3vWsFgoo7p/DmrxOVz782V7Syuqx+Np6v0ve0McmhdhjCZyv4dmImFzLyvKhPc6bLSM/hz9W/GmrxlrbFSQUkHN9tY/nDXBzbpR58OqWgal7qLgewCs7rwFP17hdrumik+fSoRZj8TXMT1Mak+zMoB1NuFQX7FjsHLzi6HsMeG53Cvc8/2a37UPnoCkFAxTFc97jlmHnraH4lBqwA2K8U57uNM7dM2udnn/zRBpluxWAxvGipomTd3MIxCALgkZmA4o9vz2zz7n0gVgLjf7vhTpTnQYcvndRwpNW5afebtHAs045jbZvZaCPZUdWUBTZsnC4zkoS11O4pkZQ42POGSO601SD++B69hZsrDN1Tvb4PdZxOFTmfx2g22BurTOAjg3NjtltGYiYL8977/Gc0I639hjwrENTmGUwn5xoc6G9j7rd/6ltsyTGbIdwOLw+CeM59BxZZhTqRY/2ypuPEpnymcabuje08CTXA1ix8I4NQRlckdz9mDaiToKg8EiUBTddN1F6X4vCeTvAWtvd/g4Zuc+yqud3/WYYlC6euH9uFyqO8ninPoZtI5oWDPyDohSU2Abt7ygqIaDl6LH213walpUtOkVhgOF/xzexiQIx8rIRNfy2c0Rn7MSbU0OG1OuIwjkzitka381IcIYlAZPuTKGsy8ReAEbfNwE+xYzL/ZjsqCuH1qnJtqb0heW0l7I5XXPppGmsN1KSvzEj8wS4UYTv5DmT7Guc+zJY1cDXOk+qlyWZCdlg6H/3gK31yg4IYfaKvSD30YfSZHuPvdC19L+TjKIZPAxI1GHDpJ6yM+q0ArvNhoCcm2i8x+U2DKYoYENbA1eBoMzCsrGxOn9S5mlGBADUWVqWBoOuLvupEsvZ7fEDzTZ05/cIvw20Dq3dXnW5Ye8UlvaY62mp02jO0fW6z2VcjMFzYdZVNjWxMzv8yUExl5fKm9so7C35IxFccKoH8ncbwQReKEZDTX9mQPaQZif01b/4jacFdL31oobiejk+0X8rB3WaXtcYprIXErr+PYbg/lghefaQjZQOk2CgHZeNAiOctrFcX19vnJBDHT/szH185/lAhyyACWNyiGbH0+Q/pbrnzZ/NGZrp0187NB59Q+bIb61X1o5umm3Tb5yB+1L98Hx7Pm1bhNTeumTmyfzsAVML7WGrlh3nbZNluXWGlqfBnOL57yuyPFetj2LnR32/ZawXr+gv0ZhVOIxgAv1nRXE8vWlcwEFdDjVtaBUQ9Tks3EPtsojuJUMZvaeK66tULfbua23zGPWeBYz2sbmYtc4TvV097SpaVza5hlU/h1VmjO6fw3gn1b1r2z8L11yRAez6+nojZ4NfQ6CmBszs7RCdmuB/tzkU5Bs+W//o2wR8vs7MznU6UnB4yBh4vIq+lEH7cR76AIOzTD3vAKfHM+nV/f392eNgZf+uty85wLbdNy+s2YaRWR2rSYhtvGTHerDWq51fYmEXAaw/2UVhYkypXerdO8kON82GUI7SSNNTe76pXQvGx3ocYdfIrVj0008g7HmFerm9cKhsjsK19vK+jn57JcoKWOdgBuh6ylDMJrx4gOJyn3N+VmSDlWVAu31/m8Mq60DZzcRUaL8pCNqysXN8Wi1riI9hUY/l4Otoo2M1S/dbP5oj9pw5vPb1zWlNoST3d8uGWTbFOVHLq8WAZfbDvONcDcxrne9zaxvd02fb8Bxzv53C9AzsWb8vnTTqlz3AWLhuSt75R3E517jZwuqydMNIBOwEuZWfe2zkExuCWZohOtyi/zYWAyf3+Pv0BgiX5qscilGs5BOQWc6nCTwcNkrniXffDehWJOrgPudrOMe1ZsMOx71HzAyIvju8qyE1Z+Kxmg26vwVQ6iozsIFYV60vdlrTc4P9rVLkbx3rXFV+Hq9ZE3oJgzeY2d6sM+hddYexmUFNNrvngPdA3uyTMVAc5vdRsTpjs3rq8zW0aec0LUCc9fvNK/6vmD0xkaWNDIrr7LV7nwHCCuk2LEhAwStCbsv1lGpzvnR3rW1S3AKdAKMMw+Oenj+s3KjX/ajyc02T9h5vix+YtVcm/LNhtK9eLJm2Nrh/VS7nLQy0Dg/tZLxS5/9m4mX69HHP8OoErV/U4e8AroG0jNbfy5i9IDGxQDvGyZH14WY+ozMlAvRnYio18LbV8ewl/Kd7/RNne6kTh5Z9w0QJwgS4TZm8xbamchHA3AmHgs35MEhf6wny+cbyZiacN+20wKiH77CG3u97bJATjbdH9XEb+STYaUHCxYnpjpH77V0nb9q223/Ax4lmA5KTy82VUY+VzswMpuDEdJWyffUcuP/Vl47JTMpys6Pp/DE++tzw5pL8kD/9ar1lLb63xsx3nos0i5v0hjH5rSjuE6W5KPpbkC/DK9iXWNhBu/i7galy4Ttybv7ZusS1U8ht8gNDNpO7lPDf9PvSSb+ccK1Xo7u5uVmPj4+nF9A5obnW9hUd9nwNCWEGBbauRFKPJ9OMzhPTjZRdeaNwL/1jtaxsjH5OsrGAHSYVGG309J0691aWCpBmA76GMVxiqF4pNcV3XQ61+64o5N+lfxS1ITznrYT9xR7L1szTcwIrdOqBcwZts/Sycs+3S/XWffAf+ur7ahMYHg6je7xo3yAI4NVRTgBgXaI0PCzL6nGzqYa4ZZO0i7wtH+cu/bN91iuHuLZ1+tYICDCsrAu+U7kIYL/88ssGjBwKXF1dnR7cpQFe3EZC3B21oSHIJoGncMkD5XtXRDxAv9wOJsVkd48TQraA7Sk8Nq5ryIiyYPQFDwNvWSdgUeVxHsgycB2WB3U631SPSt8ZE9cbbMiBNXnKPFnWXalFXu5bx2S2wpw0DWHjYyx9ooNjDscsAy9IWLaWTcM7G07B0jmqp6ens1dYc0/lUObC/DjE9hz5x15tvBx3sV7xvfJGTtNx20/1bIqS6JN/9pDjXQACEJ34r6MwybCzwWadgrpULj4LeXt7e1IeK91a24R7wxIUxGGHlcwC5HwBwiyIgR2Px43BG/ych/HkMhlXV1ebuL7hbcfU+lyXJ5vPDs+sFJZPc4U2dJ8ziNeTG7B8re/1UvXeWLw8bllPMvR8UR+Kh8ycWjDIdWw2bq41i7Is6YNZg+Xg+y1vh6zMWftpJ2FAdz6q47cxcg1MqsV5ub1inenceazkMqektuf0t5TqpsteaFrn4+tsG9YLzwnzYVvsdQVtMKdAfzb+S4P1GxnsBelU3+OEcApORtW9AYHGDTP5/Pz8vO7u7kbhGegKEs6NWEGdNKV/TIQVGkNpKa11uNUwhHotE3/3eAqqLvaMrX+SyVrbH1Fo/507goXVSVnh3b7Zk/NNHbOB2mE+QODj1R+Px2PwiqLbxklRN17cjs6657YdGnmslqMB2iyuaYpPnz6dvSnCKQ+nDcr8Wzdy5lo/G9n53mNkHZeP28583KU2zVwVdAw2nhuniNqnOgnq4HcE/iMA86NCftWzBdbvRt69eNYbX43Cvt6I7mvdRhGb+xpWFiQmcPQvv1TgZTMeW0Ndt+F2mzcpo7AMqbchTmk4bTU34j5VOSuTht/+bCYz9XGt131AhDo4Njsns0WU1nmihjCeSxvZFEb5uMGKsQM4jRw8x3agntemKsyO7IDs/PjeEN9ypj/YFtfZOTSHync/GlVZ7DGxPdZlcJ2283QuWiw3rrWs/dl2xznG3PvWes1Jv7UX7E0GhmFTIcKssKwIDmem0GKtrbetQTOg5sios6EWiG1wtND9IwlmLkZ6rutqyRQeeByeWOdBbLR9ntF97zhap43TcuO+GqhLDc3/ndifru8bK+w4vHrH6pHZmUufevCYzB6q4FwHiyqTaXhJ8aq0E8OMxX1tysJg7/u7UsmWgYaaBnzas0zt5JEHOcc6IkpzstPLNd2H6XtTI77G43ffKAac/nfYbRDcY3l2SHVK2K7TPHt6vRnnxZOHw/ry5cuJoeBdndBEQDTocGyteZtEqebk5TlXGt5BmUk1z2T26OL2zBb4bUZKWVRpMlTfCjx5i/5cGHXRR495otluswnTevAWszaDf0MAt40MHDYZzDz3DZ3RDcbHDxET1hVA11pnCyDuT1MCyMP5L+thDdXG5Pqb+6vOcA06Z0Zqhzhtfm1I3bDUDMUrkdNPAVKwK9tW2XDHwTUFa/o96faeLVKnQWqKMuyIGumY+eKI3c+vX7+ebTJ/q1wEMHeWRySsGAiQhh1Sco0Fa5ZVr8ZxKxkeHmbkNs34Hh8fN8l959y6vcB5O/+fjJ98BnV2cqmTvIbHXE/XCZkmqHKyolvueO6J3gMSBqtSeReuZW7NQnqfd6VbF+qV3X8eJfLcIDMU2ivHZVoUy7566JVy/69jrUxxBh4jc1W2VMeCDOxMPLYyGwMj1/qz27vEOsriywzbT+yiD2B7dR5ZrDVv38H2eKDf/bDsyc9Z3h6b7cWAZnLTBZ+3gOwigJUiUvAcKOz0gxFG2z3DmGiugQAhwIwaXriN5kvKpAAgPCnCN7X1xHGfQ8Iqltus9/ytHsSloSSfJ4Ay/XbfJioPc5iMykZe5V/rlYVZEZtnc998f70338sayloZn+vpeJ30bthXZtF2AU+3a5lUFwy+lpPtw8XOuXV2LJO8Gw66D23H93ZPmcPm3s95g8ha52kMO6s+92gAdD8LTpVVQ0zLxMza8torbzIwwKodZRB0ti88YzAWFMBiT049/m5PQTH9br0+V8rquj0Ge4KWCtBeuddZVv5fFnASeIyXUo9HqUdsXQaKhk1TPfRpCtes7JeW23uuYXAV1Xmh3mfQsbHUqRiUDRAOZeyk2kbZnNmfw1nLz2+JcF1T2A3DwCmSG3Sk4DEwZlhcd95T/OwvsmecEzh7DNbJ2u6Ub1trC0xuv29kcXTl7+5HU0YlILbR4ovTA5fIwEUA++GHH9aHDx9OYVRjeIdnhG1eimeyPXh+O84My0yrg3XnvSXgcHj9JWcLpfF2BeZj/rk2C87t2wDKUK6uXn+gtue7TaMhwyUvzFin45a7++eXNNYYUIYqF2zUYUA9ZYGO9glNPH8UlNHJ/8qlhuliZXZu08zL+tax9S0NZhPPz+e/yk70YAdoffRcdaweF/pAH5w789gBri6QMCZvs4D1VL5eDTX4U5qO4VjZZR2znVvnkfOMhXYnp9Q2pucezboMaJ73CXw3Y9o9s9b6wx/+sO7u7s7Y1WRQ9jpmH8/Pz5uf2sJ7MBAEDUU1wjvUrPezAOoNCg7OF6GYxPRlMBVyWQ3FQNrVJtqcqH2ZhsvEmAquPmdD76twCqjs5au8HQbYCGyoE8hQHIqarU6GYVlVKS2rKvTUD0Dbcza163Fz3O/mYm5w0sjOjrfz0D6vtU4rk1MY2lDPq5jWIcbBbneuvST/PZbt6MastXpMP+yEuR7ZTk78+vr6bO+c89S1y+aI20/3z3Y3OfrNHOyeWWv9/PPP6+bmZgMgRkQ6XO9TIPFAuN5MZ48Gd5C06Xo9KQUgT5AF7Wf9proRKMdMY12Hc34oob0thuofNTibgLDJyTlQ9hhb2V3fgYXMDUoAQL038mIMnnvPhRdtkG1B03NvGfohc8boENY5KrNAriGnV7mYSVHssCgTeDJWr7q6b056T3ra7Tbug/eFNXw06JpdUti+NIV87ovnqfkjy9q5WtsRdmhH5jGYbLy8vGz0nzE2ZHY/qj+eB1JQDrvfAi7KmxtZvWq31jkNnoDIArDwoL4Ngaz8/PkeA5SF7PwXguCYAcvCsMIQRtFe6+Jae8H2ZQobO1EGQY/b+8489peXl3Vzc3MKYVxXFcvgBHg5h+dS45tWfCdF7JjsPBjbxJB9rsrfXJadT9vzkr/nlOI9azYa2kbOzScatKZ5tEPyuKyzLlOuCzk6hHJfYc6Xnvubnus027UulzV5PE2POAfV0NKyctRUnfQc0S870DJop3Ka4kGfjBtvgdibG1ldeRmPz1lxEIAVtF5hCs0mcPB1BiiEV4X2da6ztJQJ8gOna80JT09YWU/ZX+XgYz5OW8ioY8Xg2hfnI5yvch0oc3NDjGWvTJtOp/L09LTx5A4f19rO9cRWOic2sLLQKX+3145DGF/rcKilgDP1d1qEuGRYBsbqSfNibtP/3/psoDGgTvo3/bk07bMX0Tils8f+zeToZx0Yx80Q7Syru/92Dmx6ZUmRncaZlMnACnp4THul5jxQZlPg5oWa85iW0C14My0rggGvINlJMvBNxwtYa52/idRj6KRyzvt3qMP3EnZOSXbLZpKly2SwHr/nc8rrGID3wHECwxqw2VzHYVZtOdmRte0yhIndOZGOjpVFwigqH3bQU7pah7zcN8/5FFY1GuGe5lDdjx6vrKfQzWUKrZugn2yi93J/AcrOwXP58vKy7u/vN7rlfWQGtH87B7bW1viOx+NpZ7W9jDu8x1ScQ0DpoaNsRC3a21uYflqAHuRbFHWt7YPATJANY6LdDdmopxSXCSuTpB6+17O5Dq+00g/LmT5Mhu3xeSwYqVcqYSUFYu7xSmaNwHM7AY7bt+PzIzNOMTQ0cuF82/GxCWDNJHs/xmIZTvOBjkxPcuy9ywsjLGs3mFlv3XfkYpk3OvA90xYd1308HjeLC5Vpx4Q8zFid4K/8KXaUzXvZ3usQWNw7Ho/r/v5+rbVOuxQOh8Pp8cBL5SKAsYTrRx1YuUIQVZAq5+Pj40kBSpfLhhCa9yNNjMaMzpNdj+TvZhRmaggZhfZqme87CSzMzUzi+fn5lHR13VbaspUarBcGXM8U2tI3g5BBoeG86y3boBjk9sIuj22trdw7p/QFoz8ej6f3xnWcBUv0qADgfEsNyQzGjKhbDMgVMufOH5mJlFW1zy7oTcHWsp4MEsZNLgynxZx7UcMyKYBjr2a0zb3Z6VlXuLepi4mImKwY3JpTdfTD5z4hA6YgZ88zj+BdKm+GkEyijZoGjbgGHfIjeKPmcroQwP3el1XvwrGnp9dnGx0S2nNO+TBPCH33mFzfFGrZMOxN3H9/9/1TfdMzdPTZxauhBQb+/AgJTMv3X11dnRS0e+cYN8VjqKG2Xo6hkM7v2Mg4x/zxuhkzUrNy6nOOz/2rIVNYyfIzrfSZfhhILUPrsce9F6JXJhhnV0jXWqf+2PEiX/rs/k59Ri4GU7Ntxo1MsBHPWZ0cYNGcVl9XZMBDz52W8H3OvXGcFBP98d7Jkpb29z96G8X9/f1GIc2ySnMdIpnh2Jv4fjrrhYLD4XD2W3AOObr9wWBR8JrCPoczje2dzDezIBfl+j3xXNs3WTR87UR0pWYqBV7GZYWz7Av8ToY2HzO1gXHvGa0Bwxs2HU5Pr8nxKpsByQ7By/zNhU0hTJmvQx7GwJ9zXU0NWBe4nzKFap4rh0PuX7cqTKEyYA/r6Vs0LHPX0UiC/hDSAqSTHXj+HSY3jEYm08PlE9u2HU12x7VgA2+AMSP15mKz4Ia/LRcB7Lvvvlv39/cbAa61/WFZdwTBmTWs9SsQOjSYkvFMJOBmim/6XA9WwTbPZIOx0nN/QaIgQB2d5Bprww/61K0DJ8En/HGxXKYcBCy34SAKhFGxIXLP+M0efdyyxbt3tdRj8T4nb3loKIKSGoSnv8rIwOnx0UaBxvMHcE3PCboO53UtA0AdZmSHcSmUpJ2G+QYQGCf923vtkhmZ9dX24XbrhP3n/KmT9XbU6Lt/E6P6zxhqoz3X3JtTRx4r43SYWUAcZX3p5P/8z/9sNgFSoR+CXuv1J5is2Cgj1NYC9oT4OHU35JyEUy9vukup12r41TDOXovPZhdNvk4Mir4xtuvr67PEfBmXcwIeE+1PYaUVoOc7Xoq/V85TQthysbzor4tDRerjz4C81jaHyXcDJox9b/VtLy9ZNtQH961/zSk6rVGmbMdgeU/6M+kFdlFj5LhTIsfjcd3d3Z2NDZn5j/Yq1z3W5pCMKIpHBR0alv24jmlczEmZZCMerkNGPsdiA9HKpVX9jQx3z6y1Pn/+fGJbBgwQHq8yLZPTOZDdRg0LQ2jQYbxRH58oPTWjqqfxO4nsTeizBdhJKItDeA3LfG0/Mz766ZCY482zIAMnpxlPx9hiJ1AmUjbj/35Wj3psgO4L/bc3bmIbhmUAN5iVZeEUyixpr2zIfXE/zTZshIyR7/b67lvnnHrM5jxfZlKVAeyT4w4RzVA9rq5kPz4+ruvr682Yp5AefXEUYec6bWhGHz1XhJ5mXfTTqQ+zv0Yi/DexMStrusNzbXa4t+J5qVxdQrf38l7ey3v5/1ze3Af2Xt7Le3kv/1/LO4C9l/fyXv5ryzuAvZf38l7+a8s7gL2X9/Je/mvLO4C9l/fyXv5ryzuAvZf38l7+a8v/As0toE27V8j6AAAAAElFTkSuQmCC\n",
+ "text/plain": [
+ "![](\"images/laplacian.png\")
"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Implementation\n",
+ "\n",
+ "There are two commonly used small Laplacian kernels:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "![](\"images/laplacian_kernels.png\")
"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In our implementation, we used the first one as the default kernel and convolve it with the original image using packages provided by `scipy`."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Example\n",
+ "\n",
+ "Now let's use the Laplacian edge detector to extract edges of the staple example:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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bpbE6KrOA8BI0vjoN9f8dZbiHOQXLKe9ByvksKy9GBLIgGBCBHfkPcRTIBCN0asT/jXJw4hih21GYm1NIdAAZMnaiqBXWcuNZcJxWYPMldoJUMRn3ZrOJ4XD4AZmP7DFIZOZSfalUislkkr6DfPkucmo2mx/oD4UO6wCB1QjHa4O+mWw38uZCH9yblyM8HAnoj90P6Brj4ZnYgDlZrvV63xhMqus1IqXE2WALDmLb7TZxopVKJSaTSVpHbMyIFH3xWAlCIE4C2ng8Tj8jo/CWrUPXUQf23//933F2dhYXFxcxHo8LvVmkZ65CQuCaRKRBjgVfLpcJcSHAyWSS4OR4PI5WqxXX19cR8eiJvfju9j7EFcHN4WRwBKSR7rFizCZ0HYFJtXB4Rmi5I8sbHUEBVh6UC+dvzgMZrVarmM1mSZauAjHOQ+nKZrOJ6XRa4IxQPtYLCI9zNQeHornYYaQTsW8uJGqa2+JzGD3Pw/jdbMxcjRQPcTo4VlIfZGCeCkeBYeDASINx2lAcrA9jjYik1yAlHDI8IONuNpsFHgt5kVlERMEWGAc6YyTNWtpxee2MxEgz+T/PYl3cWhKxb1cyl5cjRGcU5oNxbk6l/TlSc9/DgYz/M5bZbFaojKMP5rQte4KcC3jHrh9FYO/fv0+bfnkwyKJW2+9xIkKUSqUUURAI13w+j06nkyAmC4jxUAmibQLvzj28qAjNXdH87SZCBIPQp9NpWmCnZFT8HF3zlKZcLm7r4QLKO+XkMl+DI2U83MdR3cbBvV0UaDabBYKYiNVsNqPT6RQQBmjMZepms5kaY0GUVFShAnJ0ikMyckMZc77KXBqNmFZW/saoeRapx3a7b1YlEM1msxREiMgggohI9IENCF2Ac/HzncrlfXsR++Zi5gHqAdn4qtVqqafOgSgvRLCLxDrD+rjR03sEkT96cSiN9DOcziMHo0B0yQUe7onDsvMEyTKOiEeHxLMjHgEGsuEeBA2cN87ZRQPW2e0U3kvJARDH0FfEjziwq6ur6PV6sVqtYjgcRsS+/DuZTFKPGJG2Wq3GaDSKbrebFoAOYQu60WhEqVRKnt6l7X6/n5wMDbIorI2BezFBoiHC55k5Z+QUx1HPFUX2d0bs00l/lohrzoIFsiKadyHlYgsVDXx59QgngRNG0ani0teDHPkem8YxeBAGToQx8PO8X4/xm2w1OW5DYE5cGKI3pXvNuYzAjIBwzjyLVAUagjUnwBBU7Cgj9nwf36fqzXPthHm2kZkREvfk3zhUowkoDuSEI6TQQZ8cduBqI/KBGwZ9WKagMXQul71Rv50j4+D3rq7jnL1W1mPkh45CAfneRkWmXRiH19+y9NgBD4PB4ING6nK5nA5tOJRx+DrqwM7OzmK5XKYuXrzkfD5PEC/ikUimhwMeodvtpmoCUL7VasXDw0NSBhyQIaj3/TmXtqNCAOZzut1uodoYsc+/Scdyghrj5jmgSiKXU5VckVAYb3MyckI++cJgrERUkAdR2xVRvkMKlCMbp7bNZrOgKNwPZwXSoRXGkTxPe1B8xkkqaSNxmoIhmrh3wALduHjgi/uD7pgz6IQgwucwUOaC8wSF4QztsJzy5z9HD41iuMgskLv7k/w9I3YQk5GGLzt50lQCNM9oNpupIZZA7JYHgq5Pb+HiuS5SUYlG38gYXMVEf3kmFAQ0kNE39ofONZvNQrBzQIQi8tyd7rqBFRsmc3CT8qHrqAO7vb2NXq+X0hUTt4bYTMA8kXuEECRREcOLiFR9dO8JTiTfa8dl/ogxPDw8FDaWOpKan3AEYPHcg0VENRfE54n+vnCSfh4oiN/bmOEEMNLZbFZoXjVkd+pFA7B5NjhFkCcpN0bmJloUkjEZDSETHLFhO+O0wzKR7+/lAYLU0w3RbNEyB8S6kHYwHhwo4/CG/EqlkqpsLpycnJwU+sCcGhphRexbEBykrGOH0k+QMI4jR3VGg274NQrMkbqRFM8ARfM7xkJwZ22RAX/cIO7KNrxlRLFS7sDO2Nx4ut1uo9PpFO5rR8+a+gQJ246dpYslrkz7GCWn5Hm6fug66sCePn0at7e3cXd3F6enp8m4WUAWixSEMit9LZVKJSk3itBsNtPRIiAuDAKkh3DOz88L6ASB2zgMj/Pob16M1IvfY/iMHeUg6jhtRMiu0Pn+jnREXsZkREXaZ47CPFK5XE5FC8vMz7STJ+WcTCbp36wHzySiRuxTsIh9oYHnMgdQD2gMWXpLionrcrmcqtSslcfrbSw4TgczH5eTV+pYY77PxZgwJvcDWrY5d2QU02g04vT0NKEQ7uPP2/mBSkB7i8Ui8Zp5iuO0DuLffZQ4RzuUHPV7LubD8qOeGJOLRH6Osxn0hmDCOFizWq2WdpwQyBqNRkwmk0LKz72928SICX0DSRml73a7FLSRlVsucO74F2zyY1fpWI/F3/3d3+1+9atfxVdffZUcEV3T7gmhx8kGEVEsA0dEGjipGigDKA5SsIJaMUkTECRR1ydh4HQcGa1YVJXyvhOPm7H7b+6VozjPxc/j3z6yJL/foefY2Vmx3D/G2BuNRozH42QAbr3wnBz1UbK3b9/GfD6Pp0+fpnXd7Xbx6tWrmEwmafuX19AEuhsx83l7zSOKp4163sjTPVs4Gm+C597mvaw7PNdpov/NHPIepFxOEXtOx8bEhf4RpI3c8zk5+BGgzb+iu/4sPzOdgA4x9hzl+rJTY944WVdTbSO2Fd8DPfMaIycKKA7AjIUgzty8n5g+sIh9YHWrj2XRbDZjNpvF73//+6jX63F9ff0/P5H15cuX6SwvJtbtdmM8Hsf5+XkatM912m636TwwEAVVR2Cpy7SNRiO63W6aWK/XO+gMDYutpDiQXBHsGIzgHImt4DlB7fSI7zulPQTHDeFtjHaiJk/9PcbG/ZCPx+6UBEWaz+cpjbDjN8/Fv/m5e7FMFkfsj4bBKTNHEJObWvm+52A+xoR2/rOIfarr9Ip7REShBSf/rlE265HvNfUeQzcmmzR2ZS9PY/l5nmISLPOtPozLvI7Xlmf7Zx6HUTH6mbcdcE8+7+Dgi++6kdyf8/3gnshQttttYZO9HR/3IBjaYZrQBz05w7DDo6GZ9ev1egX+jXsfAhqFeX70N/F4nA7leYjAh4eHaDabiW/B+EkJIx65M5rSKIG7cjSdTtO+ydlsFtfX1wkCTyaTAhJjsXOPbuUwx3ToMp9EOsnP+Z1PTTV/Qfmb6IGBMn5HsYj9QXKOdN5Dap6OORBlGZ8V0/1ujJVeJZTC24IwIKNRrxPjyJWCaqbnyfj4A9ImHcidMM4AFGinYiVmrJTKufLeI86u8lpzufxOOu0WkxxRmLvBmWF8XnePx3ykMwPk53Sce2CYtBUQ3Nl2Z2cAlXGo/YP0Lnf+DkqMgYCL7iBzV8FNBeRpuVNnbA75glzdAUCQRkdbrVZqNeGopRwpem7ICjS7Wq3i7u4uHbPj9o//1XE6FowjA44HRWBwCMHGMZvNCqkOzsJw2CTsZrNJHA5H8LIAh1Ijvgu6w0jNvZTL5VQW5jK/YRK+XC6e404vCwuxXC7ThnO+B2rB2LzRfblcpv2Khu05SZwf3cPl7moUl61Y5t6YI45mtdqf3U50NDfh0wp4Jm0aXnNkCdoldYCHjNgjcOblVNGVs4Li6f/MCzlZ2W0o3pfJGiIPHLRPv/X7CFarVepBdCc+DsEFEhsY46NlhTXmmUbzoKLcsbEmNl4T9w6ufN/onc+5pcc8pAn0vKrvrMTP8t5KttnZ0fNd92vyPQco5IVMaZEy/0zAQx8d+Bkzgc8nYThIfOw66sBevHjxQaUJ7otWCAbJxUQh+kFdFxcXsVgsotfrJWNwAx9GWCqVotvtRrVaLRy65+qn822jAPqsqtVqgcPYbh/bLHCc/J5/s5+Qz7rRMwlKykYqBcphAZwGEcHyVM1bPMyfeC6uoqF8riDmp2aw6N1ut4B6chQGb0NliOjmdAOHCMpzNEYxMUQqrUYglpsVP0+bqRhGFDu4jdhwaKQidkhumcERY/heD9Zqs9nEZDJJzt3ku52g5Zf38WEHpjO8duiC02/vfPDJH+6U52c4Q7cZ5ZxVHghyfcEBkYa5nSRHpcgnR53YgFG1K5UugBnZVSqPp884rcVeDvGNlqH1i/GAJn/yVqL3798nQ8f5tFqtGA6HyVGMx+N48uRJDAaDFMloZF0sFunFEexFu7u7SxNzeX82m6UUwOgI4ZkYBLk4DWBhUEoEb96ESgqIhn+7wuKKFPeMKPa2ROybL3kOn7GC+Myn9XpdKISgLB/L77mHv+v52aEjQ9BTRBT2oDJGOwhvB2ItkLvPuWKcyJTiAdGTcThtMArBSdp5OQ1ibd1ywZhBNjhbxs18WA8qVkbj/Dyi2Obh3jXG1Gw208GCvEwGrhAZErBcJAEx0QNlJ8E6s9ZG0Pzf63+o55F75W0WrIm3A5kQ9/ec6qPXTpX5LLICPNhx2pFa332AgflpZIrtgfa5r7Mk+t5Ae+7zRB+OXUcd2JMnT2I8HsdkMknlVDz7arWKXq8XZ2dnMRwOC2nTYDBIUR5n4z2TOERXZdrtdmFTK0J1pYazrPIKl4/1ySEnSp0TwlY0R3BvZbDD4js5Me7UCUNlsd03xZxNUPJ7nmv04gZGNryCaI0IjGSQS6lUSq0sVjwqvXzPTYl83ymbU2fm7GKGnV6pVEr8Xu6UXTCJiIKxs56W3SG6IJc338WIMBan21z0btkRcoESQU5U7XIU7tM4WE9ONXEV1fqAwyeDcFrKv12g8Vr5fvBEvtAd1hwExOXKpfUA1MS87aDL5ce9y+gDDskFLmTG2KAjcidHvyM6bCDgI45wxOg0fgRf8b9yYN999116ywt5csQe+vFSgfV6nTw3F8pMGogBWrl2u12hAZaufy6iHRM2sY3RViqVlGrQsmDejOjgrSEoDf08eHpzDkRb0jMQBpHckBpnBR/hi14gjB6FthMGzRGVjHh4Bq0iOQkL8cnlaGguMGLfF8SYzXmYJ/FeQKcbGAjyQF5GpcwZdA0Ssbzc9W7+lLExB+5PdCalcDU2Yp/2YKzoKbwrDb/cx6Q1cuEgAaMa0xWsX6PRKFTsqtV98zFcGf9G73BCzInLwS03chwa93NGYCTHGXkO3NvtNlX/8855gwj01cEFO3ABwYcc8F3G6pQf9EwaSMuVCwuWAQi2VqvF+fl52k2DLTHeYzzYUQf2/Pnz5AyI3obiwMN2u51SyNVqlU58gDitVB73hZEm5uc5OR93kxuL5P1ikH7mMSqVxy0yKKtTI8bB521ApFE4P0d9lIbPk+bAq6EAKGLOX/liTkYFH2uApDwPEc34nULjmJGf00icvFPFnNvz9hwrIP/21h7k4DFSUeblxMwL1MfnKcJEFDlAN/NS4WUtarXaBzJk3fljXs1pJ5cRu1GTix2W/6H0j7/ReRdT2u12Wg8HYGSAPFk7ZMaYCcjmrCi6MA7rrAOmv4fN5PJijibB7QQO8ZHWfXPPeVrL511ZR6d4BrZk1I6d2UmztvCTVKWRB/7lJ7dRDIfD1KfFTUzymvNhkQ2ZI4q5uSMVykjPEZHFQsKgcwjN4rkkfWiTcsR+yw0I0txSjoIQHsppgTuyMAanvKSg7j1i4cntMSqewYKDYlzdMQ/hcr7TPBQEdEmFzemr1wLFSItf3p8AAZLISWjmZkTm3yEz1ipHfUY6EfsDDanqIbeISDsK/Fo+7uc0iH97fcwPMrfJZFKoCLpVxqf3ohd+OzXtDbPZLI3LqTS6x3l1jCXfD8ozWH+CkeVj3sd2gH7ahpzBuCqac7b8zfocao1hParV/RvNQT2Mn5/nhQ3aiMicnPKax+SeBIn1ep129OSOKadfkPFPJvF/8YtfxGg0infv3iXnNBqN4uTkJKbTaUJaGDYLsVgs0tnt9FHNZrPodDqFtAhuwo7BJCCL5BYIw+d88uYciLgIlZMBnKY4OufKwxEzVjxzBrQWsKDIJ99ywZhwKKSA+XnyJkHz6hYOyumiORsiN3vo+HfEHn1ygWAJEJ4zxsd62MFZrjiqfD/gZDIptJ0gL1IF5or83LhpBGj5eYO60wobGn9Il9AP3rbkVI7nMEH0x8IAACAASURBVCacWUQkZ8SpE6yZCx44WHq8QBCgIDeDkvYaMTE3DN68Dxv2HUSxJ+uZiwhGs8jWAdCkvR2tq+EPDw+F3kgQYrlcjvv7+5SSoleeC/f2JnwuxknHAbp86PRi9NvBFLv/yQ7sD3/4Qzx58iQuLy/j5uYmRXhXA4Hp5Pnu4KXS0mq1otvtFjis0WiUoLjRBEpGQ6hT2LyvhwVwCmiEYGLdkcqeHijsqIRygypweE5tT05OUs7OfSP2jo97wVEYLRy6OE0iV8bcSYBYnEqxJvCQLhQ4pbZMWL9qdd/Pxb0dIPg+vBaOAgRq9N3pdFIXNvfFWeQkt9M+jNJprdE16GE6naajjiaTScH50UwdUXx5qlG/m4VBlHwWROisws6Nz4MMhsNhSqHd5IncvZfPa2RESHBzzx3zdioJgnfwNvLPHSMcXU78W8/RNTIU7IY+LvY0evuVgx2Iyk6Hz7HWOVJkPtgc9u2DAYza8qLRoevomfhPnz6N+/v7mEwm6bA8Jo3xLpfLgnPi/C826XK+FoPCGTQajQRD7VQcVVgYJkW5FcE4AvBZnAvjcZrIZZ7GfW0myFlYKlT5IoLeUFh6ooyQyuVygQ9EBtzTvWS8vclONB+/USZOhM/BH/I7H5OCXByFiWw4GO6LIiKPpCjVasF5OUqbp/D68PP8d/474pEj7Ha7KVKzRtaJiD1CrNX2B2my/lQP+ZmLPNvttnAoogOFdYJUyPdjPUFJUA+eU0Rxl4T5WRPWnjNBwSmldYvf49wZs/dj+rnMgUDDxXhAdegla4tMyEKM3HFijInnsb7QP0b1XhP3edpGjbx3u/2hhjkPhz38ZARGdCAy8MDcK65Wq7TFKKJYXrfH5j6bzabwIgdKuiwAjsSoB9jripvzfO6H54YMxuma/GfMJscj9mfRRxSNJWL/9maehVPL08WIfUQ2YnIlzOmA50oJGwW2E0FxfPZYRPFt3yg9MuUzfIc1pLLaarXSvDAMHBMtH1Zey9iVXFJZOxvWCx3I/1gH8oKBAxprZEfAM0jv1+t1ejep0zcMvlwupyIPa+/n0SXuog7n7/O86XSajNSVPVdqQTAEN+TPZ43UfPy30y8jTheYxuNxQoDMAb0wR2rngPPG8aLnbNwHLSMH7NppKJwVc2BOtM3gD5iDm6yRDYHXXBlOmbP5GTdzceZz7DqKwFBwFM6TheAH7YC0XNHg9NGcaDyEihCwOQ9zQUROUidKtCymT6mw0QHJ7YidGuRRHv4DJ5IrIj8jQueIwfwScyCCeG7ufEdZD8mFexv1ReydpY8CppxOVQ8E5Fe1gQDNtSAHHLPTZyJxXqWlN41Ii6OlYAKHxPq4Cst88qjNFi0HLZfmuS/I3pwkz8I4XcwAPXFfPxvUys8JMqS/BNzVapV6IZ1S8xkCGu97wPhxFDR2cpkrcm8Y8sOhclHtRIfRKfaLsrY4DAIwMjOl4QBoFGyqwXaBQ7XugTbZ9occXMBhvPgG0nh8CTrnKjEHoaJvh/jugm0c+yULaQPOy6MIE4PGQDAc9uCxYOPx+IP8PPe08/k8hsPhB+dP2RGaNAUBMF7GdXKyf1ckXc9ETaMKQ3sWm3O5SFuJCChKXpnL0VFejUSeyAYSnvk74oI46CHjuzgB3gJtB+FeIHqd3FPnOUbsESaku+dnfooWEiPuPN0GpfAMnAxjcnAArTuIoFcvX74sBA22ePHMnCJAJ0BcXKVSKR02sF6v09FBjMH7+Rg/usA42JaFsZ2fn0e9Xk9b0pBZtfrY0DqdTgt9kRGRTmXp9/up1Wg0GqV1BOnwXDsMV6lBQ+iLtyRRMEM2plIYu9eGdUavKEA4LTSX7DYR5out+kBJH2IA+kUO+bYo+Ow8ja9WqymgoF8GJoeuowjs22+/jb/927+NarUanU4n8V23t7fx5MmTmM1miaQfj8epOgVJF/F4LDWDRVibzSYdL00krNfrhR4xFozIbgLfipxDaldsgM7uqgZ15N7dqZ7huVFbuVxO80SRGDvKlH8uj3yH9nuh0EZKoAQ7ioji0TLMl+1ajor39/cFxTRKJQDl5D6pUS4D0AORFqfN85gbUZRxuoKE495sNum47bzKhMGyZe3169cFfqXf7xd4MmToQGe+1HKERPf2KH+ewNtqteL29jZGo1GqXOOkJpNJcua1Wi21V6zX6+h0OtFsNpPzIbDizOv1elxeXkaz2Yz/+I//iHa7nZxDzsmRSlWr1fQ+xkqlknjWiD1Zb76O7AQ0hE7WarV0D2yAJl/zfKBmdBpHb8oE++N5dBjAg7M+Rnk5T8cf7JDvOoMCkOQZUH4ddWCvXr2KN2/epJ6YanW/mRtldnm83W7HcDj8oM+FQRF12fDJ7yqVSnKCCDlif7IozyaFZFMyikjUR0gIjDy90WjEw8NDAT7zh1TIaRIGDAGdoz9DYBCqnZ17f2h9wJnB+6AETrlAEigiz8GJEDAoRTt1RyEwWuQxn8/Ty1FIKZz2uSGRCweBIqP8OD8UNGKfIoN6ut1uImD5vCuikOnoBGk48oCPssNdrR63rdGSA6pwRZxxc7/lchnNZjMd9UIgtMMkXUSWNrLT09M0//V6nVpEvH8Xw2u321Gv1+P29jYiHvsnQbGTySR+/etfR6fTie+//z5RHycnJ/HFF1/EfD6P77//vpARcMjker1OzZ3oqwOvz8xyRXqxWMR0Oo1ms5n0Bd31/1kT5AICcs8YrzijWoge5NVCnB2VS2dqXNYz855+0xGBhN/9r7YSXV9fx7Nnz6LVaiXoaycBETwejxMyi3jcC0kEmkwmqQzM4PJ3vhEh+FnO9xjJoNigAIjAHKWgkNw7T7m43E2O4wGl2YEArZ3W8B0jQlCjDYtIjjF7UTEgb0ECNTBenFe1Wk2kJ87O/TWG9+YfQCgoqZWOn6OURlEYDsZIMOD/kK9ES+bBXF3IAA3k3IsdPlQAa4TykmaBBFB4HCRzBhW4OMQLUk9PT5M+VKuPJ5C0Wq2o1+vRbrfT/12FNYpwjxw8oVPBSuVxtwkpI5uUeVEz68e4eAkODq3X6yW6hZdg+Ngp7IE1x0EYBGy325TttNvtVOEjHUfm1n8CBJkBTprPuJcTWcAPEhQjiu/WNKeVUw/WC+ucdcK652ccuo4isPPz84SWUMS8fFyrPb4aCacEbxTx2FJAf81kMol+v1+oqmGQdlbmRvJSMc80AnLVwtGJzxNxQDn5ZvC8yoHzg1RnIeFdTAZjQCiI2w5AUlSl+LwrOW4PsOHn82CLDhcHTILSjFLzUyuQo0vzGAGpJ4Y4GAwKXIubMEEuFAbykreRDQbmvizmkcvEFVDGyXehE0BCOQcEUuP3bMGyIwYh+3w2AhRGaB0zj+S/PV/WdjQaJdTNoZzL5TJ6vV58+eWXMRgMUoC7u7uL8/PzuLu7S47zhx9+iO12G4PBIKWYIKhutxvL5TLevXuXUlMcq/sm0SscoavAIK6ISFRP3iyKw3L6hr3sdrsULLgv623U61SeMebkO9yXdxTwc3ogObGGViBA0rEU8igCu7+/T0fjdDqdRBjCF1Wr1RgOh3F6epo4H++AJ3+OeKyW3N/fp9QMjsIkL07DZVtXVyDkIcCJQCAfw3OjN/M1XgjG6Gqne3xQPhPJLK5TMsZJdCF9xRmiYLkhgB5BlcjKB+kxJjfqsrgEDZSI73nPJjIF1oN4vNma+8KlgJYYQ8S+r80RlLnyHBxJxL5nDyVEX0y8R0RCQyg18qZHkM/MZrPEgzI2qq088/7+Pn2ehsnFYpEQOI4ApMSzOGUFZ4V8803yrJErqjhN0Ck0x9dffx3ffPNNrFarePbsWUrFT09Po9frRafTibOzs+h2u/Hs2bP42c9+Fs1mM8kJ1Pby5csolUrx8PAQV1dXqf2CtfGZbeiK1w26wWmkC1NUbU2roKNG2uiKewVtU9wPOwJtud2IIAeSRo6r1arQmIw92uF97DrqwD777LPCK80ZCE2sVLpIVYhMCMpKhCGdnJyk43YgEM0/wAvZ8LgfztNQFcXHgdowiNAWlFPgiEjpKNyO+8TYs+XPg0AwYKIFSuN+OSua95NiwPwew0H5KZYQjZwWumfIzYgR++qgeSXv1yQq8x33A7EPkiBlAha5UMFDJ0zYo+BGhKwbnwXx+dyyiH1PFCkaz3WJnfckmmLAwdDj5XPoIJcj9rwQ/BvGgr50Op0PAgi8LGPASEkzsQlvXwLhwEnxVq0//elPMZ/P4+LiIqWwcLnI5u7uLu7v7xPvBbUBQf7ixYv45S9/mdDr1dVVQT/dRwXyIrAi1/V6nSrBXt98ozZzc0B0hkPQc1EkpwQI4nzWqAqdMcrN74Ef8O8PXUcd2J/+9KdoNBpxfn4eV1dXKafnLC/OvbfxYDCQmygZlcfhcJjeuusTCKzsfB+hI3gT1VQ8mCi5PguMghL9jR5MspvXwynimHEgRnBEFQzUhshlp+O+GIzbVRqUyfwEjiAi0g4IFtgn2jr9zU9UII3Hubg4AvKzQ6VaRoTlQpGpqLGFimeCDAlwbmFhDZEbuoCMXcAwyjXRXK0+vu2dAg9OeLfbpXFAPJvjM5dn8hhEgj65bQN+EtkgF2TorS/cDwTofarVajU+++yzpFu0s3z33Xfx5z//OZ4/fx69Xi/a7XbSzX6/H+VyOZ3Ycn5+Hqenp3F2dlY4RaRer8fZ2Vk8e/Ys8WWkqoyHebp6CNAwIIgobhR3xQ8ddlDmMsobjUZJR9DL9Xqd3mvJOkDwd7vdlOoSFOyocGpuHcnTUV9HOTCIyIeHh7RT3z0lTCJi76Dy84ccoTAAtyv4/B8jCnguDMGtGodK9+YH3PflyotRzyHOAGWlodLbUyL2XA8wnOhm5Afv4ndosjcNefj9l3zPvBBparVaTYURFG0ymSSZuJ0ARGZ+z86Fz8G54ExRLNbL1ULu4QDjSihj5zk+ugfOxTsuWB+cE3yVuUTGYUTmfjYCJ6kISu42G4wYrpCKJD1GPA99IyAxTtYOHoiCCuvIBnp+h4NzgOSMOusJhxl88803SW/n83n86le/SuN4eHiIVquVOMD7+/vodDoxGAxiPB6nqvHp6WlqMSElpppJQHfRCrSE7iAvOycjafO53JM02r2MyNqVZa+hbZN72TZdgEHH0A2KCz95K9GrV6/i+vo6SqVSPHv2LB4eHgpbIICF5gyIggzQJVsW2WQrqRKGZB4L74yzc45NlQUH+vDwkBwjxup/YxAYs6syroCZTwDpWQkYj3tyzB/hFPr9fgG9gWxw1iwWY/Bx15DD5XI5vYKOBYbfgnjFEBgfr8Fzp3jEPqVl0zPfYWwoFfdljKVSKZ1OOx6Pk3wcLc1zuEfMBLIJYebNQY9OM5gj60wEXq1WKTU0SrUzRm8c+SM+PN7YztFozikq62oSmUCB/lD5dfc+jo2UlmKBx8PFeG9ubuLdu3fpjVzsE6YZly552iKQKQ6TSv+zZ8/il7/8ZXzxxRcR8dgNAF2DPfKSWuac0zRcBCW/lTvnBbkANtgJaMxNqHQiYMetVismk0lhf6n1inVBjz92HXVgf/nLX+Lp06exXq/jzZs3hQV1o55PUmy1WslrOirifGgI5D1ww+EwOUCcGhGCkwcM272AQM/dbpeiNIpK71q+dYIKCaVh0hyclaMGwjcKwwjghfxcmhj5P8bntARnnCNY/m3Hi7xxEKBSnCGOx7xFq9VK6QIOAH6L75fL5XRqBs7B3JYrzibqXfklvTcCRW7Myc7AaQJpM6mfq9z+PakrrRsQwf1+P92PN73jXNvtdjo11esVEWkNkA3OZT6fx/39feofM7rACK2foLc8YHqrE0gOvs0bxT2OPHWeTCbptYS1Wi0uLi6SfpbL5Tg7O4uzs7PUqFyr1eLJkyfxhz/8IVqtVgwGg3j//n10u9348ssv4/z8PI2fv1lL7Apdw+k4DacyiC66QMb3zJl5XymOHVvyXuPxeJx8BffjJBt0hwzpGAd2NIX8/PPP4927dykqoDQ4I4z14eGhQNAeKjsjKFIgogaK6pSKnprtdpuUnMXiMximu9oh/8rlcpyfn8fDw0NSHDe/RkTiH3yZ8EcpQWDmtWyg/O1UGkW2gtpp8R2qV6QsTqW4cD6kck5r4ESYMykLVbeI+MBIIh4jOs2pOMxOp5POw3JVlNTDiMttKTyDy602oDPSDuuCtxExL3SIy1tTGM9kMomLi4vo9XoxGo0SomAP3fv376PRaMTp6Wm6DyQ+c0HWdo6VyuMROaRPLiqxJqenp2k9WCO3beDcORnE+o8srEfICnSMzqOz4/E4rq+v4+XLl0kX6f5/8eJFAW3/4he/+AB5LpfLODs7S3oHNUJLEwiLLMrca8SeVsH5sb8WJ4jDhzrwqTOsv52mT0zBgTqoGzR4/Y8hsKMObDqdRr/fLwwI2G6oDqlvQ3IuzP/peMcAQAQsJsq2Wq0+6H1yhYrqGsbhNIwICenLuIyMgKYR+96ViH1q42gUUTz5kufzHb6PcUdEYUw5wnLEYtFNmqPkdpw8E8dlUhrjAr3BodiAUH5HfVehXDBBDgQi1s99Xiiz5+x5uvpkxc6bg/m/+VJHbPr20A/kNJvN4unTp/H111+nVI6Uw/waOyDcCI08/Gyus7OzRHzTrwaaMhrnkALu6abOHKFE7PcXon84VLf+mH/CuHG2t7e3hb455k9qig59//33CWyAKt2fyNjM/QIs0A1vLCeYYT/MgfUBdWGPLo5Zx7gfOgk/il0BLtxH6NTzJ6eQ/X4/tTpE7F/2QMqIknY6nQRxqR74pEj6TuAF8jyaCWGI7sqn0uXTIyDKUSjGkUd1RxP3i/F/kIbHyxj47KH+J/gBowrzAOXyfmM33yedpkSPE3KLBFwNe+5QGC8m0Rlewn1XzJt0CoMg3XZBxfeiSmTS18oH5+Z5mi9hjN4mheOxo3WA82UnCMdnfs1Erp0UDs1pPQgFJ0TK1ul0EifltJKiBJuRaZ9gDLRdODvgtGGcME4Dgt2kNXpD9Q0jb7fbcXp6mjIL1t+pP06MajrIstVqRbPZjOfPn0ez2YyLi4vkyOkxwym6j8pFjjxDgicjiHDlvC22w/1o2WF9yuVyOhOQ/0NX8D2KWAYPH7t+jMQ/+u23b9/GF198kY7V8WZjJokXJfeNeDSm8XicHJsb09jB7q0iQEt+TuQhpYvYp6aQ0CApkBifx0BQJLY5GcGhhPBe/X6/EOHyCorRC9+HXMybG0nxqNj4mBkT2xg5/XNcOEtkQ4Tld3BBNkAXRXBuIF2QDJcJXc6Y4pnIrd1uJ+QREYn0Z/z5SZ0gAfQAx23EdogL89YVnKNTCf547lSo3QcIsqBfiXHhDO/u7mI+n8eTJ0/SfJMBKHBgUPC57BVFB1arx21w0+k0/Z+2IsbDvafTaeJHKWCYT9xuH7vz0X3SMKM9k/buw+r1ejEej1NQpDrP/E1PeEM/usu8jbgj9hvusQOcDjLhO06FQblOq+FUmevd3V3h9GLvlZzP56kdBr/C/L0/+GPXUQf2/PnzuLq6Sk14lPJRhsFgkBwYhkiqCO+B4gNd3RfFRUpnhISg+D5K6S51LwzOjr9dLYootikA21kYoi/PYSFBWkYbNng7B4Sebx1CLu6E32w2qYhhBzebzQr9XZZdXqkjurrlBCeLEwD1kDIgX8b37NmzAtSHP8v5GxyoSfe8UrnZbFLgQo4OBibpTRK7VG6E5vUGQbqyxRojL7eU2CEz9svLyxiPx/Hw8BAvXrxIqMrtOzZ2UBaOCg4YHokgAtp1+mi+DAeHLjEHCkAODASrfr+fCG0jM2/Dy3eboKek/wQSUxysGbZFr5jbJNBb97+xbnCsFFoc0LFB7IAxlUqllB0c4p2RNTK0TTtwf+z60bcSUYWcz+cxGAxSJzqog4fgSR2F2F5BRANddbvdtCmaaI3C23i4r4UFf8DlxTP0dRoSUaxwGE1F7B0NlUvuRWsH9+NewF//7ZQjj3xuMgWV4Mj5OTyDq20YSn7WO8hit9ul37nkzD0pTRsJubs9LxqAFECR5jyMqkgrcnjvk0iQBw7A6SqRFwIe/SI4Wq44W2gGjNBv0KaaBalNDxY9dzjKarUa5+fn8fbt25SugtpB9xizW2Xc1+U1oOjAGqDn2IqzFR88ib553UDP/X4/ta2wxYnOfKr+OHM3HeOMuZdTefSPai0tGdhnv99Pm8AZK+Ol/5NtT6A+0yQAAFeuWU9zbW5LwjH7pdTmoI1Ej13HE9DY72uaTCZxenpa8KBwRUSx4XCYBoIy8H/ug4I4ZXAf0SG4Cyx2pzPKYu6GyEx0MwLk9yy0o+Zq9bgtxY2YRHenncwnIj5wUJTB2byenyfPwnDiAPIwJ2QH5KjnBXWaxZyMzkBmIBFkwLPdmGmob2UBGbiJFcfBeJ12kCr1er24u7srNLniSDFkUAaICQSLPD0v+BXmRKsDDoLxUbBhnUC7jCNHr/1+PyIibm9vPyD4WWe+h76CHnCYHFfjNY6IVF3v9Xqp1YImbHTZLThGfAQQqAc+a94PRAT/iU6aAmBt2G+IrAlobsjdbB6Py768vExyd1sNbTqj0ShRD6BPtko5aFr2EfsTjqmWk7EBFmh7oc8PvTUqO3YddWCnp6fJaXS73QJXQQREGV2Zci7N/jo+G7E//wdYjmfOjYUuY9IkHCGKA79m/sAEKM8gKtmYjEKIuDgSnBzCM8TOlX2xWKTGQ58LjwGg9CZ2USj3wNhx+mfuyuf/jAek4gIHgcPIAsdg5xBRrMbB5+UnYeZI1tU4k9oeP87HaMytA8gOJM/caKaN2O9GYL52bqSMrCtr7UDmwACRDF/Dz9rtdpRKpRiNRkm2zIN7GBUQnAgg8LDIkrF5JwBO2L1soGpQj5tJ0QvWFPmASEFSTv9MjiPvQ4bPWuN0/BJeTkB2es/9SIcrlUq8fv06Go1G2hbo/ZLz+bxwaIH11UGTsbADwqk3c2QXxY85saMp5O9///tk3IPBIDqdTkI29KlUq/vjXowUgPAY+Hw+j+l0muArBCVOC4V1KkQkxGAhlvl5qVRK8N3wGTQUsTcYFC3fqJxvfeLnGI2NKs/9WYzFYlHo7I8ovmqLy8Q34zQ6yNOBiOIZ5ia/GUOn00lbVLjHyclJqnb6tAZ4JkdkyweZIl87F3NaGC9BBefuRk+itR1JtfrhiSBGsmw1w2nYmeUokX+TurgdgN+5p49udu/7Qy69Xq9ARXjrEmhks9kkVEL6dKigACriZ7wCjm1CDorVajUFDQwaPcZhkabhUBqNRtoPyxyRG5V0Aq2LBg5IfosY+gLKQ3dII8vlclxdXcVyuUyct7dH+eQTgqA7EEyVsO5uqMaufXQ96TM9d8euow7sd7/7XeqI//nPfx6j0ajw2jCqU5xISVMmUabZbEa73U6enhaK2WwWw+EwarVa3NzcRLlcTt4c48BQjZosEEdfFAmjoYiAMEx84wC5nO6wEMB0oDCGaqN05Q0DsWMAXTmCM37G4P4cE7T+vJ0Xc8Wg+TkG4gqT+2qQD6SqDdtOyOS87+emXKcpoGt3iuPky+VygYhmLZxG8n/Pl2rgdrtNnBeKz32QHTwOAYd141l5BRjZwtcyTrdljMfjGAwG6f84CPg+kBH35twu1setNfRG8co4B06f2c/lVgT00pV60nqvM/Lg5bTOELBNnAuZC2f8cVF0AFQ8PDzE/f19cr69Xi9lQ9iHe8rgwbAH1gZ9yHvu+L9tza05+Xr/5D6wr776Kl68eBHlcjlev36dlAGviSBrtVoiHBE+6ROdtygPyuQo50qJq2bASAzGFTMbmNMCUAACMxGMcIyEXDFECU18EwU4QZPnEJGdpvGdvBCBEhF1QZ5GaMzLc4yIFJkwaKdm7uViDhiqq1AYEimPHQZKRMCBz8DRcYGaXWHk4l7cG6ft/iGiP+kcMjFKAOlw+U3Z6IDXlZMbzs7O4vT09AOi3ByZdYztbKQ8Rrn8DXnudUE/eT4pMJ8xHWJnQvXWLR7wjFT24cAcbOycTUl4FwQB3rKmMLLb7WI4HEa5XI5er1c4L+3zzz9P7Qvz+Txubm5iPB6nVgzWutPpxGg0SojTugHix9G7qGf+G3txFoH+OAOCJwTlUTg6VLnkOsqBffbZZ/H+/fukwCiT+7QwTFIBohV5b97B7WohToqfOxUgpUSxKWVThbTX94mg9trmZHCK7kHJ+Rp3HJO24hy5XI10ZAFVsDAoGYaGMbmogCyNAPk9z3CXMs51MpkUXrN1aFykgO4Bw2j4ec5Z5V3PjAVnHVE8nSJHVvz+UKS1U86JZx9JTXrmdJF+QtoD8oMXMYi8CAOSIzVCt5iLCxnoLTKFo2JNJ5NJPH/+PI0dwzIvasRt5J2vd7VaLbTb8PYiuGKfS29USwbgthyn90YufGYwGESv1ys0yaIDu92u8LJo7BnC3dVXPkPhgSDpdQKs5HypsyB0kzlxhhvj9lgoYORUjK+jCOz29jYd98pN4LP8MgiUnj1Vo9Eo9QUxIRyDS7Amo3GO8AL+rHkFFMWOwPm1kYUnjqK76sZCWhn5vR0X0RxlBq3YkPPxuMJEhOLfGBfPcCMsXIbJd28fArnhdFwBwtn7u3zHvVTwTKRxKJc3HiNjSHo33NpJ24iIwowN1JpHXRAFDoW2AZCH71+tVtO4GD9r7UIG8jENALLBASFjOtXhXM25USSiOdUcj3XCe35zB03QYj3gZL3FjJTXHNt8Pk/naDFW1ttVX1L2iD23y/O9GR09vri4SOk42Q8bzafTaTrscb1eJ4qHcaHXeYsDetBoNFIxpNlspsMh86zk5OQkpblGk74Xa4Ze88dOMr9+9Ex8JsXmWHJwvLX5KefG5XI5HXCIMP3qJcrL3Ac0tVqtCmjvEArI+7hwchgKC2l0w8UzWRCf+CK1QAAAIABJREFUZ0S0ZmFQMJ7p3+enfaI0TjGstF54FtTEr8lOowKnQwQIxsM8XIny88xJuFufyOqCgpXFzp+UHnQRsUdc3ivq6qJ/T/CqVCqJAHfhxqmSiw1U7vg5yu41hVci5bEewlPiFKh40TuHfvB5EAupTLVajV6vFxGR+r04En06ncbp6WkhJTLqtP64JYJn+dDNnLoA9VNlxDaYH+uEc3f1PC8SuS+Nl5rAg3ltTOg7cwKJ3t3dJbtnVw62fHV1lYAAMjffFREJNRJkkBFtIzyTOThIucP/0HUUgUHgkbYYBWA8OKhms5lOlXQ0MHdluG94CTJy86bf+IsQXLmI2PND5iFyHoTLSMDwm/u55A/iQxkqlUriBpwSsNmYhcPIURLG4BSHBckdBbwCFRlvlgbOYwROh5ENLSlGtP4dhlOtVlNKy7hBKZYZyu6igjlAy5qtNSieFTmieEKHyXtO9KWplfeEMkfzPKSm6BSGzKZg0g0CC6/Ri3hsA+j3+2k/pJ2lUS48lbknWh3Qj2azGZeXlwnREmy5l3uZWFvGjswdfPmeq7+LxeNr0bzRn8DvXQOgR+vQfD5PdACZAfbrObNOPNPZiP+/Wq1iOBwWzttjPag6ViqVdMIsxT32ebrP7+TkJDWwH6JUsLN6vZ4oElMgh67SsX1Gv/vd73ZffvllfPPNN4XqF97TA8BoUFw8Nj9HaZzXRxT5CAoDjvQYKhHIqMM/57MR8QFSwFExVhCLf5YjSS8086C65zYGX8gGp0gkyrkSE5x2sii50ZzlZs7LvIrTUjcb2lgckZEhRs9cjSQi9nwX6Ml7SnN+BwX0kS65DmAAoNPtdn9G1Hq9Tigf4+Q0Wg7KRGZEf29fw+n4jc/WM+RL0OUiTaaqnXO2Rt3m2fjubrdLPYB+obP5PyPGQ3yOkS/66J4tMpBKpVIIXgACy501JZhy1FBExGg0il6vl5yh+U70A9oHB82Z/PV6PVFK2A/PMf3ji7nnPYB5yn1oqx3yvbq6ioiI77///mAp8igCoyeGFMkDdC+JB+e/baBeXCMEdtE7L3a7gvm1iCJEB+nwDBAIkzfEx4Hg+KzkEVGI3BiLK352SigZEQJSlnnVarXCiypAXczf97FDx2HkzbdwhsyfOa/Xjz09OAxvM+HzyMnOhjQAx4+82CjPvHxYY6VSSS9gcZQ3onZFF/lhxEaM5iFBZyAxaIf1el04nBHkSMEobwzl7DeeTbe5X8qLjJ2WR+x5JNaGih5oDJRPKsvz4EFdUDL348AHyuPCAfA34wb9u60GXYFXnM/nMRqNYrFYpP5Kt1kwBjeYcy9fVGCRfX6xdxQ0yIXO2qZAWBQGcj2I2PO/Bi9G6rl/Qa+PtVEc5cDI1YGhnjgKiRd2Vzl/s9j2ruy+j9gjnLwDGMMyEY2yulJkwtoErvmInDB0v5ORFotN64YdnA2Iy07O90HRiCTusSJSYSDMn7lyoiaHPlp2GBCRNSfEcXqMFR7HCARymj452gl4FijYRQNSPyNITgMxie3LyDViX0rPCwLcm/vAUTF2dAl5vXz5MsrlcuG4ZTtvDNV0A9xho9FIXFjEfgsTnKirlnzO72iwHpLGkvJSSXe3POmysxMjaMZhhGz0zgUIwBatU/yeOURE4dSH7XbfS0fLCRdtFbme8wxz1hH7tyNZF0Fy6CMpKNuhXPU3yjS/Z94OeVj/8DEfu44iMN5GZPQwn8/j8vIyRRx3k0dEqlp6iwHKUCqVUl8K96RREMeD8HE6LBItFeaVQCZOAXBU/NukYUTx3YNETBSZnQNEZzgFFidXQJo4WRyjVDgVFh8HYKKaZ282m6R4KAUR206JxSXqU9lhrkaPpBNEzuVymTZqg1Qmk0mqKjsQMSZHbyM1/k+VzqmnK582NJAbn4E/Ya1AfTgfk9EYA++GZL1YPwIVaxWxL4ZQZcPhIgM+S0WP0ykwGDeLUrGFQ2R8rIMDKa9/Q7bQAUbbRtFOR7nYK+ktZzhH1oc+tkrl8QW7cMbYiZHbbDaLTqeT9Gs+n8ft7W2akzlet+BY1rvdLumX38tgPpeAYa4ZcMK4mCvzYDxGgbbxY84r4kc4sL/5m7/Z/eY3v4lvvvkmdrtdAc478ubKDWfA58zXADGZGAvsASNESH2TzEzQCpBHLhbWaZmjPYICSeB8THzaieWLlPM/jM1IMueqzJ2BIthjVq3uX+RqRJJHJuTB/HAe7oInQjNHkIB5HAzf6IyxWtn8vRzNfQx92SitG14z/w3aWa8fD8b0epkPzcdgXi1ij2jQp9lslhyOnVGpVEpv2UJ26F/eiGskna8zso0opsR5JRp7QGbojWXJd8xh8TMjHJ7JuE1vOB027YAuoxfD4TC22238/Oc/T+koDgt+1Pcdj8fx+eefx/X1dUREOsqbixM/zCtbZsgTJEebR94/h04CaghYP/zwQ1QqlZ/Ggf31X/91ROwP4EcJgPUm42x8LJIrJJCuZ2dnaSEcPfMIzkT8soa8goPTMp9C4yf38P39M8hQLm9IdroJimGu5o1YIJ7vPXt2YtvtvuKGgjEfnpE7K6exyIWFxcB4MYnl5c3f3kCPvNyywQWHkc8NhT7kOJya5xHYl1Eu34/Yb+YGsbdarTg7O4vLy8vo9/vpLUEuNrA2HosrYzgo9NOcGEGQtR0Oh8l58sJb2lT8wg6f5eVCCXrFXKrVaiLAT05O0vixG79ExcjK+gYysV46nSSosNa2FXTNXCntD+Xy4ympUAegMbYFOhgTPJCdd19EPBYCeJuUgy3yIw2FenLRhIBg+3QPH880EiMt/dj1oyeyPnny5ANEwMMcge2BEYT7rRAy5+kbvQFj3RjplgEm75/zXYwOpYDP4bNU0Nw06h4slJ1+Lj6Hw0NRnDq6Gx0+AOdmhTtUvSKqsuhUd0EOLFx+MKKdRMT+mG6+Txk+Yo8MvNWD75P2oUw8E6UxJwGisNNibVH+vPPaVUd+ZgRrpAInutk8nijy/v37hJDYRrRcLuPZs2fpuRHFtzrbKTA+1hIOh1QIJ+Y007JkKxV6BbK1TOBImZsLMuaEqExiN/Blq9UqHc1Dip4jeuiJnHzP1wZbIRD+27/9W3zxxRdJxryxCVtAns1mM66urhJ9w8Vz0HmeNx6P037n8Xhc6HtEX/kbZ4TdI0OvlTMZ98c5iINGke/HrqMI7PLyMu7u7pJh5Nt7mEB+xDBbP2jI9FEzDJiUzZUtK6e9stM2UEFE8WWYwF4TmFTLnDJ5R0DEvonUAs7TEyA9bRs0/3kcRGZ3MHO5uTdij3gYmxsJ+QxVTKIh43L/nc9rAuHB18HtGBHhONhTyditYL6nf0egYfzIm/vmHA4/N2LKHTJjRG5s3anX62lz8enpaWrshPfKX8eGDjB/Ir6LQTzXPCStAhjyer2O4XAYk8kkIQqcU76TBLTgwgB0A9kGfCXpPnpPW0NEsWXHXCvfh1IB7Vp3I/aVRKNnZwDIiQZeUmo7aL7j55h3Yz7lcjm9Zg3ODMftIG906nQaJ2XbQf4GFM4+jqGviB9BYK9fv44XL14UzsIH4fgt3KAKFIL9U6Aw0jVHTgwIaJvzAwg234vIiZJMPmJ/GByfN1/kLt80aUFiBMnf5hJQIIQJucrYiHxEHC5XZ7mfUZGdsaOv/83v8ooflTzuiYL5wD3PDyfh1ArC18flGCHlUZLLuyVcWTYKY12MPJ3meW1xxlTIQPsYy+3tbUIAm80m3r59G5PJJDqdTgyHw/jiiy8KG5stz4h9MAOJ8XPmWak8vkoNI18sFnFxcZGiPimsN8MjFyqzfI5g6yo3a0pKCqq5vr5O67TZbNKbg5AVBuxTQNw/54ZU70x4+vRpcvCXl5cpCFH15cRc1t72wIGe6IjfTk4ApU8vD7qMjfnmbSkRe4SFXaGfoGPzlMwfp3aMpz/qwF68eBGlUilubm6i1+slz2sOxZ4eItpbO9zZu91u4/z8PB2l420HNmAbBm0HOFCMgdeHOXUlimAcpCE4Qcbqz/Nzn1ZgYyQCOuVDKfLobgMhShviR0Q6NsgpIgvshY7Yvxcv76nLnQU/g6v0WHCYENrMF7n5WGU/v1wuvh4L+XuLlrdh5f1nPMfjzYl485BweoyNNMZ9WdVqNXGojUYjyef8/Dxms1nae4kDZ11xKKwXOuWeQzv9H374IT0LpBgRqYWCizPGcHLoCHM1ikAHmZt5oHK5nMhxHCvByfsyI6LgOJ1Ogoh4+xG6TwBjxwJzZj8kF9umWCvvZ0R/jaBZ84j9wQVw1k4FvcMB+3UmZ1oEWeDofBz4x66jDuz9+/fx8uXLZPAoMacxwh1wDliv10uDQTg0wjIJzq5ylGTyGIgdjVEU9wDxmKTnuSgQDhDlQqjeKcCzuC+oEdRlWGzUh/FbAc1huJrlZkJHTyMbIzpkjBIzF6difB9EiKKYqzT3ZLLdcwb+82yiL8aeb+MwAZunKSAuBwMQmJGeoyr3IECAQFwZ4/7MHcdASglZ3e1245e//GWiDTjTC341Ys9XGtWDthyk2AO82WzSUermA0EnyA9HihMEzXwM/SM/O/u7u7s4Pz9PaA2ZOQ1Gh+z0GTstEaPRKBHsXi/kzBltVME5EJRtQ25rQq/Ql1arFaPRqAA4VqtV6g/j8FKca+7QHVSsczzfNkgV0tTLoeuoA/vyyy/j9evXUSqV0ivK6a1hQyxGZ6NAMSIiwW/gLxtWWZjz8/P0codarZYE5iNq80oW6MYEP87BEyYCrdfrQhOnS80+jwhDj9hDWhxe7hiMWnLFxKGDRNkE7MoRabOb/SKKaZAJ6nK5nEhNO0tkuV7vX4fGZcfutNrPclRE6fJtJiiUUStIBjLXL4JgvZwG2+hAtQ463mYGOmKsvi9jbLfbMZlM0nsgp9NpKvUPh8N49epVasHhcqAsl8vJoH36CRfHhBMAWYt2u51eIkInOYEMRIYD4MBP1teoCWdEI2pExM3NTdze3sZvfvObwvl6Efu9kG6jYW2gFUjTkSUVTbgrjtWmn4t+OGdOb9++jU6nExcXF6mgQtsE53VxdTqdQpEnotjOwr7evJLNGhK0sBk7NN7MZKR36DrqwOCbIDcRNKQ9h7ExWAbGYEE65g3YyY4iAZtRbpwD0Ys3oWA0hwydpsiI/d42k8zmffr9fmGbRo5++D/K7XQk4hFZktZsNpvCSZQsEL0xKArO3sjFnJYdkheYn9Mdn5fuTYZGREK6DhTePeC0HKMlYCBHp5A2HmTkyxVbpxf5rgD/zhybkUVEcXeDZeFWFv5mbUgpaTZlnQeDQaGxdbfbRafTScaA4YBeXBHl+XnPFagQvaYYAyI8OztL60qlLk+XaZkpl8vJhswvv3r1KkajUUJa/J7ARUB3HyX6bAdveyJgcu12u5Ry9/v9tEZujGXM3j+7Xq8L54HhoIyeADOsjwOf+VN+lm9RsiPLqZ5D19Eq5M3NTZyfnycF8w5/zi3CUWEEzp1ZLOe7EVGYBBHMkR1UErFHQnn64WhpB0K0h5vgvhgHMNfVRjtQjMGNr+7MzlGeXw9Xqz2eTkBhgrTETad5lPccOLaFcYESvEWmXC6nNgH3gDFHHCYOzuvA/DEmHAyKAupB3sw5L2ObmHUKhR743tyL+RpRgeLY08ezcofJvXAefvZms4nxeBzT6TTt8iBN5I3cFxcXcXZ2Fuv1Om5ubuLZs2dxeXmZDhLE2bvJ0nv00FUIcrIN9sGSAYAqXOzAVuic3+126fwtEOL9/X2h4hnxiEDOzs5iPp8nJIfe7Xa76Ha7qe2Do7WRi1Eu3KcRNY6I0zkoclSr1XTP8/Pz1EtHMcPbs1jv4XBYCL4uWiGfarVa0GHW2eDAfX7WuWPOK+JHOvH/6Z/+abdcLuPNmzdp4yoIajqdpmobaAjU4pSBCGEHxs+t6KQuRiR5CoRSE+Xdge7J2qH53qQqGCqKhxHnbQP8fejfng8OtVarpb2F/A4HY+7LcvAYrQieE8gD4/K/LROn5sz3UPrNPJwq4mxRMAcV942Zk2EcOcQ/NEee7bX0yar8n21XH9sryH18f+aB46HRkhQKIh+Hx+ZkgiLFKp5pVE4g87rn8onYB2U+xysISfvp7SKgO81zMHWK661ooDzzoawhgTpvgjXi3m63cXl5GYPBIJrNZrx79y45SKfrpJvn5+cRsacoIvYnyqJb3Afum3PLGJuLDW4GxgHmes6FHaxWq/juu+8iIuLt27cH+ymOppDfffdd/NVf/VUBNpKOucGMVISoQvc8EBQBmU8gB3fbgwl5DIN3/hkdbLf7ipWdVkSk1M2CsRIRMV3qjti/iRlojFM2mnNPWo4OOMcIJchTJByAfxex32CNwjEWHDQKkXfh54GHiOjoS4rCOrmKi2xAjj4LCqWlxO/vI2s7T5Q7Yr91ybsycA5eK6fqXPSyEfGdbpvUzp0I80Um3m8bsSfvoUNwdqTYy+Uyzs7Okn7d3d2lceWEP3pDUAINe08oesO5a/CgzOX+/r5Q9eN+ODccFaiMVprJZBL9fj/JlDFhTybPcfagR/cS8r1KpRJPnjxJOo8OkRJCP3AvV50JZm6PcXM3js6FLfQAZ0bGhv0DhuxQnYYfuo46sOfPn8d2u43RaJR4KyMFhAYyQ2FcvUJQ6/U68UAImdzaKQmLah4CRQKx8ZxDfArlY+7DhRDgiYyK/BkL1YiITuq885zNu4PB4IPvsJguXxMI7DgZP1xXRPGVbZ7feDwuOHI+m1dHc/4qn6dPFDB3sV6vE7HN+uROO2LfBMozmCNrZe4I5eSZXoccfVI1xEjzijCG7R0e3gmB/Bgv0Z45o4sYES0FjLXdbsevf/3rdJTMcDhMxmTnb0To56HXzIXvPXv2LIbDYQGpwf86iPM7AjftSfV6PZ1WwjHOrE2eslsHGSPjIK3zqw2RBWm5q53ujwSRkvY5oCIPc+ERxXPRcurHCNdy5D6MO+defR11YPf39+lkRZPDDJIBMiGXUFFsQ1M8Msd6DIfD9Frz1WqVohKLR8sGhCNVPRBLvqkWodhhsqBsq0CYfAZOCcHlVZOHh4dE/oIgSWFbrVbc3t6m88+53LtGJMd58X/zVjh5O2iiEHs7CRJOI7if0QxOFRmRllClckoGSmE94VOMYBkr97SToiSfb/dCKY2ukLOdAL9H9rxImTm44ZY5umDjFgmcOI4Aw3L6D5o0+jGivbm5iaurq9RLBx3w7Nmz5LCperoB2sEJWfjtWJDydM1fXFzEdvu4oRoOMHc+Xh8HectiMpnExcVFcnSsGUicrIO2CveS0WaCbHjlIYjS6ItMwOPCqfKH442wdxfyGJ95bBw96+wMjGq9q+8fu446sIuLi3Q+FS9PxduaZ8J7e48gzouFZGDb7f5NMvSIoYygAVcraHtgYblfzr0YibllAQMgonNvtmpwT5eoMQSMDkcJGkCB6HUzr8EiMiYQg6umThmoZPpAxIh9lRGFABkyv4h9scHODZSGvLyhOecRI6Kwnjh4NyjiIHDSTnPdksH4vFvDvJFTa1Alc0SGlicHEYIIGL85Hp8CAQJ1tdZ8HwR8jsqNGtwLViqV4vLyMsm5VCrFxcVF4WDD3HmZ67OseE65XE6FGgIGa+b5ErRASKwp98a+IiIFdsbOvZ3FOO2mzcP6TFUyX1OcV552I08COY7e+sS/I4oHg3IdSnXh8Jwt5cg/v446sDdv3sRvfvOb1NmLsM3/sFA+MM6keN6xvlwuU9UDR8N3MR7uR4WLvWOr1SptuwCZIQg+b2IUPsZ7+PKKjCM3iI+Ig3KQekTsN/6ywRXHnfM6RCg4MJTHShcR6R6gFxTT6bX7lnIkReS1Apl/4sXC/j3K7uoewYb0AW7skCLaIaKsrLWVzRyl03qnvqx5nv5iLEZ0DpDm+XBk+TNzrjLnJo3m0FnOdWdcs9ks/vjHP6Yeqbu7u6RDv/3tb9M7J51uORixrk6F+DcoiHVEd16+fJkaSwm4pmlAw/T9GcWwzjg/9GQwGMQXX3wRg8EgFotF4RVxBGBsYLVaxeXlZXKAzWYzneLrvbIEPusWVAi8uVN5924yNxfO+Bw2cYz7Sjp27JfPnz9PaYIdF7wGxDKVR3iUiP32EvgP4KCPbTECitifPolxwcP4eBPGg+CN2FBK7gvcpqPXXeGka9zXCA+FgAuL2Kd6OE3mwSKiDAjeaTTwGbRkhGYS11EbGeX9RDkf5XUBhXGxPi5IVCqVGI/HhX4bywXZ5309OBgXb7icTnExTlfmmKc/gxyMoLhwvO7ZYi1MBtsJ2VDcaGvnh5wh2o0ieQ76gY6wVYi3EUHMl8vlePLkSWy321QQwPmwBiBO/9vz4GKNSflYIxqhaWY1zUCWYroB1N/v91MzKgCE4OWX3HJRsbR9oAc4Lz6Hfd3d3cWLFy8KhS9sgwDEGrMm9JGyLqAudAS+2YH9Y9dRBzYajeJXv/pV6pdhIAgITgPh0XTK+feUkev1elpcR1kTtzgalItSOAKFuDVJmvMcGCDGZiP0a7dQFrgxBIYBgMDMSbXb7bSFxA7FFTlHXSMDUJp5N6dWdkiu6vhkDRcs8gXl+66CYoigF8N4qq15lZLvwAH53Z3c1zLEII26KaWzlq6M5QUO0w7u2bMcIiLtezWy8lE1NnwjXrhbUnSeWa1W075RI2fWDc4FZMvLVwnc8/k8IZ7NZhM3NzeJj2o0GvH8+fMYDAapP819dtAS6Gh+bNJyuYzhcJjGwwt1d7td9Pv9FNj8smQ7c7KW4XAY19fXqWfs8vIyZTmVSiVt9iZo0J8GYl+tVslpE/QI1gThJ0+exHfffZf0w3tnvZbMdb1ep0MgrMeuqAJWOLYod/L5dbQP7J//+Z93y+Uyvv7663j69GlCICaiXVkzOmBw/J/+MfcR8TepBK0IPqqHCXhyefXKqMECMwHIQvN894J5nO5bi4i022AymRTISMbv8fAceIOI+MCB2Vm5ggvK4HPcFxn7uzkKysfu59pRIiPPkTHkRL05i7wtIqJY4bVz8r+Rjx1gfg/zVyC0vDrtOWJwXv+PodNDTvPQZV7S3fggBQcZ9BEDL5fLaRsWRYVarRYXFxdRrT6+7ANnZp1ATy0b5mC95vO0Y6AHFL6oXKM3Lj5RyMrTvOVymU6/dZDzDg1sw1xypVJJQQE06HcqOKgzJ2dE6LLTxnwrn+WwWq3i22+/jUqlEm/evPmf94GRGxOZGbRJdkM8FItesBypmNMBTkbsjwGml8yLDJw1YQo6MYLD4ODQrMCr1Sr1riEsxk2UcSmbMTcajbi+vk5Vq4gotAPYUbOQeaWPNIax20BNmPvzXnTPy04HA+CZtFeYz2BO+SGOKAgpnreLsI52Fu4FswOy43DRg6oayklPEIoP2iLQUKjBQLjQOcZvzsaB91B6aj2ws+ce9AvSA2dkDSLkPszVbSe0IVBwYA242JeJblxcXMSrV69iPB7H/f19IsWtqyBIIw/bAfsSOVEV51kqlRJicXDy71lr+GxXbNkUT7XdPZKVSiW9R4BMymvUarWi2Wymo48IwqxHu91OSBWUx4Xjw3Hl6M10yMeuow7M79gzf2MjN8fhwZlvcApkb48yL5fLgpE4ghvZWZm85YWIGREJvTkl5DIScoXUXcI4zJOTk/QOPY8JBMQ4IvYENgvImBinkQCfsQN3BMsJUVduzd1g/N6Ia8UwJ8cY+AwFBsuCNc6LEcyP8RhJGqk5mjJHNz6iJ+ZZmIvpCa81+sT4vKZu1+H/9DnhHI2Sc4dEgGX+Rm6MJaL4Dk+qtKAyno3uQ5/QMtHpdKJer8erV68SLdHr9aJer8fd3V2SjZ0YOsD4nbqXSqV0MgbVTLIi7s8mcE4+5ufo+ng8Luw4cDbk9hR4yYh9s7XRPJQMJ7w6E2PsDrp2iOa/HNywd+yQ1oxj11EHhvEbhm82m0LKgyBM4jFBFhQlgnPKS/IgE6cGTJRnUwVBoESJQ7CVZ5hjMVIk4mKsRCNHjLu7u0LjLZGJQgLVSVfeIFo5bsikc17a96kRNN+SfviARuTLz+3IkJ0bET2n7XZ/IKKDjquijMVkuZGTN4ZHRGHcKB3zY6y5TuTpNHtF+RnOjxTO8/Pl+0A18H/vD835NNIh5uZmTusRc6Pb3UgbhI2TNFIC9bDf8vT0NM2lVCrF7e1tbDabdDBjuVyOu7u7+NnPfhaXl5dRqezfLLRerwtv2jIXaceOLroIgUyXy2Wcn59Hu92OdrtdOK2Xfi4cB/dFB0ejUaqiQtrDUTtjMhcKuEHHDUAc1OHY8At2uk7RkW1EFALVoesoB/YP//APuxcvXsS///u/R6vVSpHQBsnVbDYLXeJOF0njaIEgogDVIfh5fZMhLGiGaqQ5pYgPkZ4rhR5fzi3kQkGYQGY7JTsfOz9+h6BJvRgXjugQZ2fOiDnmMs3HaAdoBeHf/jvnpHJuyjJzOpkTpoe+x3dzPsqRNn9GRKSGRwh5c0A+wSIngbmfe65M7jot9fz5v/+dFy28O6DRaKT2GPdOISN3oec8FZ9ztoETYqyj0ajwchyOqLq8vEzBZjAYpDO34LhAUi4WeR0YG4jSSJLUMKJ43Lqr9qyjU82I4rsrHZhy1MbxUZY/c8xtje84ELL+PJ/PPDw8xLfffhuNRiNev379P38r0dOnT+Pdu3epJAv/BSLhMDSgqRcUY2QRyZ8RBI6O7zlNgB/A85N2WDAQ+wiAJkjux2KjsAjY3Nlq9bi/jDldXV2lqMNCUA3jO7SLcNHvwjhYZCItlb78915o95nlDgNl4/M2LCOIiOIOf8+B6MvPcCCgXhwAMmXdQHcEBozF7wV0as3a+Go0GomfcTrrC94uovhaMAKYT6rAeTmtNVrLZR2xRwjr9fqDky94BuOv1+sxnU4LTsFO0fMF0fB95MHpqP5/tVrvRPBoAAAgAElEQVSNp0+fRqfTiUajEd1uN0ajUQwGg/jP//zP+Oqrr+KPf/xjfP/993Fzc5MQ0atXrwpVWuTvrT0UyJCPdWu1WsVwOIy3b98mSohewuVymQAFKCiiaIMOkrkTozPADdXWAWcGpMe0mDhboHDCz6j0UnDyfPLrKAL7+7//+92rV6/iz3/+c5TL5cJxxU7zMFg3kHpRnXoxYHfXeyuFy7ou8xuyOt+m8uLobWFzT2Bxzr9EPL68BGI1v9xbZY7I9/fnjBQcjQ2lDyHAfJGcophwBarnVUi+g5zylBUn4ec69eP7vheyQ96sPfP3fPLnRETa7Fwul9OxK0ZTEcXXhuXyMIdlZ5lXNDE4CiOmN3B26KR1Alnmuxmcqhplcn/km1fXcjSObdFK5P2ndsAcggCF0O/3E5fbarXSW7QXi0Xq54qI1LKyWCwSnXFIN4wkXcFGNpZljlhNu1iu6Ah7pHmjVF45PoTIsG3bkVsr8DWj0Si+/vrrqNfr8cMPP/zPq5AvX75MR48AfR1pMES3VxiFuYuc/BzPTveySXQW342eefXRx+igRBy8CP8Euc0GWAQUUXzX4cnJSdzf38f19fUHgmeu5oWc0uYNivACTmmdbtoR2pmASpgXP4dbwkjseEA/PNOtCkYa8I8R+6NVPJb1el0wNkd49xlZEZkXYzYCItC4oABCzNsw3GBrZ+n58n92RyBfEAiOzHoIme/eIgzL/Vbok2WJ3JH1oeCFLJGzix7MxWmcv+fnuQJnQr5er8fNzU1yfnd3d3FychK3t7fR6/Xi888/T2+sQt7OEEy2H1o3ZwugQ9bD9hWxR8MREWdnZ0mHarVa3NzcxHq9jtvb28QpGulz4STzYlZEFDoDkCPywXbyAxfy62gK+fXXX8fZ2VlUq/t9ajgwHgpnhCPyYPzSAH7ulggmbW/c7XYLWyBQQKodLtEzjlarFd1uNyk6OwPYp0XJmef5cDscHgpmI65UKoW9hBybbAU1l2NyE+V0ShZR3IBuxQPe04fjjfGMi/vAFbBXjMuoD8Xg2GO2X3l8vP6OdWQNIP1dDUPOvrxh3FVlnpEXWhhPxOESuauMRkHIBuSQO6mI4lvh3buEHDxWj4OUlN+bH/M+VBue50ibilNefu7KL2tuOSAXAuRms0l63uv1CocNcnLqN998E3/4wx+iUqnEz3/+84S68oIbaAsnhH461d9ut4WtQVASoLJWqxX9fj851sViEdfX1/H69esYDAYFrtlpP7qIs+NneTaC88z1m/X3CTcfu46mkP/yL/+yu7m5ie+//z6Vgpko21HcbMmgvPeOBXe3OxfRGrQE0vKeKVcoybnzEjqKjCK4WdOIECHf3NzE6elpQaCG3nYgFrCNylFus9kUnANzy9stcA4YgBUKFOt03EjA5DHRFD4r30JkhIVDYLsJ88NJe8z5z/P7gDpZZ3roKM6AmniWEVdOePvi/hiQlZw1QB4Yi1tf3CXPDhGjh8lkEmdnZyn9cqWSz7gFKOLjzbs5YjRyN40AZ8i9nZqB0vL3IoB43bxdLpcL7wjNnSkvHeHoK95pabRjJ27d8lz4XLfbTRlSo9GIv/zlLwmI0L3PeqIDvnIZeccOl6vzDiAuEuIwv/3229jtdh9NIX+0Cvmzn/0s/uu//isuLi7Slgx3qmPYwMjpdJqUJZ8Ihm/uxEQ0nAwNshYKf+NcXIb35SZJ7oMT5OhdFgQHSvqUL6h3D3BZAfMufu6Z9zUduuykrWyuqPnezJ3P59VePouc7Ehy8ty8oru4CQ55Vc/7CCOKp+zaoHIEytzd4uDKHCjHvJ3XnPtZBl4HuC8bVb5O/M7pML83P5Y/02tEYORQRDuInBPyOlg2eXHGKR72Y53xesEbsaYcDVWtVlMRqVKpxG9/+9t0vNNut0vvvEQfvLWNijvB//T0NDqdTtzd3UWpVEqHOhLIfEYYMu/1eikbsqNnLRxATRfxfX+GC3/U6/ViOBzGn//856hUfmInPohgPp+nvWP5YqzX63SWULn8+H67wWBQUAoqFY5EEfuKD4oLaU965AiIMhIdjFDMq/io4G63W9jDNRgMUiMgz/H3I4rGWa1WE0GaH7rGq7MMg2307sgHLWEMvo8dn/k/HEtuAHZeGLGdr4lYlNeIxKkTY0Qp3eeTp0BGjhgZqZz5PnOEoEo6v73LgO+BrkFPlomLQSAQjBvny2d3u10yFLcwIEvGXiqVCkETxx0Rhf4q1itvT0BGRnDMk0IVvGlu1CBKuvapYDJWZxak8cyvVCqllgWqmNgnsvnXf/3XNA9SW7r/5/N5PHv2LNEGNzc3UalU0okYdNKzlhQdWq1W2jvrTfO0PvF/xoj8qVQbdaPDbk2yHbhQxdxcdDh0/eiLba+urmK9XqdUxdEBTsj9PBHFA+4YsI1hMpkUNtzSRkBEg/NwXwr3tnE5ArKQJgXZ9kATIuX8iP0Jq0Qmxm1UFREHnRdvYgFxMgejBL+VxQ4HOeCMbLD0umGIyBZ5M3bPOSe9zWU5tYbz8rlrOGnkaMVlzjzLXB4RHcNzusXPKMC42OC00vdn/nkzLM/mPu4jRLYm65EDDo5obrRp9I6jRwfszHiuq4sRxWNvcP55ddJIMc9YuBeycHUP/o5jqSDWQS3m6uBicSy1Wi0dW+22FV72u1wu4+rqKqrVx5anfr+fqA/0g7mxA4Vxudo/n88LlXEQmAMGyA6/4UDi7/JZ/Ad66AILAe5j11GG7I9//GP0+/3UZkC3trkH99UYEVGaLpVKySFxIiVd7Jx9/v9I+7ceu5Ijv/9O1oFk8dAkW2q1NJbGsA3DV77whTEYwHPhAXxhwG/BL9qABXtgW+PWwfKoW+qmWMVTnf4XfD5rf3dws/pxTwJEFXfttVZmZGTEL34RmasT683VRWw8UXmRbvjtW4b6/GfPnu15Dd+h+D1GZq21ZxgdFT0XGoXHs1UhS17fv39/exGKcLpvITJBHRNCHWlq8RdpzBdhzN36JUT7b621vX+zqKDXlHfs3zREs4W71tqoA/LTWsDb7TLGWrSsJklDKkM8LWOoUtdI894Mpzku6jk6Ovpo/DgjiNW9DiHMmXVsyImD80yGGl1BXuU86xAYAiee0Nn+7idjw0CjTB4+/HByhmOoIP6HDx+uH//4x5vjVDgLjJydna3nz5+vtdbeC1GMVSTA2PqbdUwfSgGphQMUoFvypTdNzOD4Li4utvIbyPpT7U4D9q/+1b/alMbplASmHR8f750ywepb3LIqrLmOQRuMEasMtvsc2qlXhkh4KcrfCt8f/ehH6+XLl+vNmzfb1hCe6PT0dDsux6J9+vTpBmMvLy/X69evN8WXyWMAPa9/t2h6iikoT1llbWYWdsrVApqLWGamBLGFcnt7u/e6Mn11zxK6FswsEK7TOTo6+mjDOkW1HUU46DuT67IAGs4yWBwIQ4EUpvj6a4FZtM2EMjhz+5GFYnGYYwR5WxdkE0NFiX2G+9B3zqalFRpnROcaUpb28LtEFgfse/SHvtIbztfrDlUEcDLdHlbEfX19ve3TJH9Z/bnhmpytt/KR5pje0YfHjx9vRwJBmnTg5ORkkxdkx5iRt/Vtbn4wAvv666+37NrLly/3BF0ICEJ28y1l6ndxSrJBFj5ysgRmF7r7TeUgCPzJ06dP15dffrn+9Kc/bSEcD2krFGVGdLoXNPf555/vLcCGSuXutB6a5/41LmRUI3B8fLyNycKvQZvkJqWzINwbGrG4GdamrtsP4zlUid5MbEMgRnqtD29iJk+LrYikBqPHpPDOe4o3khJC/u4smLV5t7e32zEx7rvWBxQFJVkQFmfR+dxfenR0tPFQr1+/3jN8/k6ORZ9QHGfX+5bnND/VlzomKKZGjf44hRgKkWwoF2mhP378eFvsa+0yqp5vLNUDxrSo8vj4eK8ivw2POHnnoi8hprdCcaCoJ8bSeWp06fXr13uRkPHZmH6XAfveM/G9Xdrhb8fHx3vp6JLCjuOFwBoWMSJrrb2tAs3Ute5mZm0YFI3yW0hOAHj37t3eQsNzKHZ1PwLt89da29iEsCaP4ashYmzds8anylKSvSStvjEojGER2DZRuQ6aKYKrk0CaV9HW2lWIN5xrfycxrk2jUmfCUcxFAg2XAJ+y59G1SXo3JJ/z0JDxyZMn2wIQcsiY1zGUMysNwjj0hS6eKyJoQqkhaTOV+lSk0nKTtXa7H6bxns0Z+WTWjDqniofGl/ZdCJMzrg5B8j4rf0VWU/dmZtpY9E9ipGvWHLf0yXcdhAnBCrdLDX2f8VrrexCYKtvyFJeXl3unm3aPo6xiyfXGuLgwoUs3hddDEurMQiiWFIpCXp9//vn6F//iX2wGp0S29HMX9L1797asqdjehOj3hNENBed3D/Vf86aXTvRau7f0aBOVFT30nYMMAq83DZj6nfJ5ntfvtd9k8OjRo70+8coMnPk3xxCEe/nZM+TojdC74e2s6etzy2n6DNqxyBiRjolBkvXE0ay1T/RblPrBEKA8hGDl0nyPEZ9hJoRcpIzANxed37Ozs+3N7q2NAhgmEqphpLMQtbpMkUlrqnxWbvfx48fbi3rq1MimyLwcrTVF1r43gYCz0sxHW9dWd4BM4+v6HxxCOsL27du3e2/OoaAU5NmzZ3ulFsK6o6Oj7QhZHVprP7NHCLwnLyit31olfAgh3Lv34c0xv/nNb9b/+B//Y621y4A0TS6D6jMozcQ1jc2TUta1duFGa5x8bmFWabugcH1CFen2KidOyD3dg0drZpQBxudwMNCtTcRFhxTMwjPOQnahfjNm9YRClW6D2ZQoaLZckmubXaSsWhMGs0Ec5fHevXu3bcBn5LrQen99oWvl+ziM9okcEOl9E5D/I+Xt63Vd10ar2ckFyiATnGh3ADAU/t7wvPVw1a/yd8h8rWU4HCzqpPs0i5rJDQ/NyTDmdRzVITpL3j1LkPzYDc65yY4ias1YfjCJ/8c//nGdnZ2tzz//fM+L1avz3iy5B1t06qW2B6bzvILspL9beK3DITzGdK0PVv7Xv/71un///vr5z3++N/girpubD++9UwPUEKFnGbmesWr21CRLQrj/LJPoYvV70adFeHR0tE3oWvuV6v5GMcmw6KPJhLV2W2NKzLt3+YW5G4LSU8pyFxyB+eume2FRDZljaBoy0guZKX1oKCJRVMPueo5TvxDTx8fH2ykPa328lcjYoJW5jQf32vmGMFAZjx492itcVaXOIPm8svYd4+KEGk0gvmeoTv7Hx8db9T0E7hQUTncCALJVf1d5io4axpHRzIYaB8fecFVSzbw3aQa1di78bFKBo4d2q1/ty8y+f6rd+ddf/OIX6+XLl+sPf/jD3qbWtT4oJoWVJbK4zs7ONiK35x+ZVB1zfHShaBVprf2aMkL5yU9+sl68eLH+8Ic/rBcvXmxvLPb8HgBXY+SZNRad5HorBqQcB6/pO2utPRSH6KUAJgl/N/kx4VX5PIrcMFwhYQ1PjZJrkKRk7/pyNPXqrqvnngak/YHE3r59ux4/frwng6Ojow0VQx91KIjo/v2QY6inFibjgywcaKIZvI6rIYgxF5lNJDgzsb7THQJv3rzZQxXVTToL3R/iC8nN75Nzqs53POYUKpxZOf0spdCXmEDwjRLcU1+urq72nGH7N/mzFvJWl52e2sQSSqSRCRlB9Naf9VEj79k/OIR0gx/96EebsGolGYO+BslE4XuagSopN6F+Pb/n9O8s+C9+8Yv11Vdfrd/85jfr2bNnmzC61QGpT8BQ48z0eZ5QhQK4zlaiOcFVYvdF+JJT66Rc08Xh2Yc2+FI2RqdKX6QxSW/IdL5o1L/uPlCf1qY2b1OOcC1k3O82za2vZNKkS3mSzn/3DV5fX+9lsfFr5ZIa4jTkbihZLpIBWGufsyx353meI+SnNxyWk3qdhb/WzvH2ZJWW3Mi+6U8XIud1fn6+d4ZZax8ZpmYc19rftO9erUWjuzKKDflqKDkMWUyfqX80pzX09Bqy7JhaFMuwQoKojhZeG5v1Rcfv37+/dzjqXe1OA/brX/96vXjxYr18+XK9fft2e5ecB/udgaDkIK7OlNyuAdEa/xP+DFdM4C9/+cv1+eefr5/+9Kd7fX3/fncGOY7EAmHQ/NSEIUIl/I6jeJWG4JrWWhsJ6pkN08oPFv77/8ykTq+31k6p1tonnfV3rY9LUyxUi6nlB57T71Gulju4r+vxOjUa7Zt5JDt9t/CL6JrVqnGZIWiNIJlULvTE4plckUVQI2Zeyvkg+H1uAeF0D2Xu1lrbWCGxm5ubvVftrbUrIeJwheLNkuLTlN10DbkXoyqU0pfSM3SkRoqsTk9P15MnTzaZlq6ovNfaGSZjMnfWUPlYYXt3yXRdK6YtYEBruE6VAJmWp6yxn4b7ULvTgP3zf/7P1x/+8Ietg1988cVa64OlbSp/rR0/wmCYZMfZEKyfBgAtgI8WPQX/7rvv1meffbYeP368fv/7369/8k/+yVpr7WU+1/p4/57JbpwtO0NpC81b//T27YeXeJYngOyEEp5dbqYKb/Kc/21SLJpJsttcWzKzNUaUpRtjeXuKd3p6uleD18wXZa2R1YeGKmutrTbHIYSHPD/qoNyIeWs6v4uy894tOfpqcUyFpWscwDSQRXxFiRIInBRjUBR6ff2hMPfevXtb7ZVFZQ58HzXBCJFfIwjzqR+ymkVJa63trdr0rWU11kWNd+dYUz/JIdV51UA3oulRVdYL2dXI1di1H4wxWTaspluMPIPlvpzl69evt8ipDkIzThX8d/Fg33se2Oeff749xKui1IYd2rBpG1C5L8dRK0J05M5aa/MSJmStXSr8/fv368svv1z/8A//sL766qv1s5/9bMsMzT1wJo2gfaccmglca5ehoThNOuC0KtByFoxGXzTSZ1hsrYGzkD3bdwq3uz2GtysKa/kE79QMZdPbwlPefK1dSt+ug1lnBXlReN4daukJIMfHx5uBE/55wUS3ihWl6ptrZMMsohLrXczlDNtXaNgWKdeRoYUgCSIi6DFLJycn26Gd9rW2lRfl9CanwyjUYPg7WUw0Zf6g3CaFJJu6E6LhcB1KSXlHvK+1v/ugPyXO1LbJjsvyCyFL+7TmkyzRRjWY5W4/++yzPZ65ZRo18OQ60WHlfle78zid//Af/sPt/+9A/b3snQng1XAzPGDJ2ZK1freYKWwLEQkNfP0//+f/rOfPn6/Xr1/vQeK52djP7uOCZuYWj55P1LICi1qI0UxIiV9GWEjK2DCGPX7G4mz6vB7VZPX/7Zc+tP+f+v4Mz8i7xYGzgNg8ddfDPAds1tG138bYxsjrd1FV5WixqgecbZbbNCs15VyZzfPRuuD1q/PvPg2j5gJqISkHNsfVvvnM8/vdRirN2EJo5UD9dN8mVCZ6MYddGwppW3NZx1DjYQyTI57r0s/ajvLLRaMihm5Ud+8i/xYYm5fLy8v193//9+vk5OST54HdicDOz8+3424nhwFtNBz67LPPNq6nStK0rgkDd8/OzjY0VuLzxz/+8fruu++28gcKaXLB0daYdQErIJ2V7T3CpLUuPZGCIrXkoOQnL+L782C3Lp7yBSatymXcPJ9ryLdHEDVkr5GiBC36paz1xMfHx3vZw/IdJWP7shae1jWzeJGTgFq7UDkuBl4/KfhMl8+F1HozZRg1FD1Nd60dArf9DWLT34aDE5W2HouR6iLu6Sk1LGRVZAy5kk+TJ3ahkIs1dHl5uSHWx48fb7xcnw8hFR1pUFhrGk9OTrZxVTdcC1W1uNo9GdieXgK5+V4dEDSsv9bZBA/00rPtwWy/oFJz/YPrwF68eLGdfS0bR2HL/4DR3U/mzScmjWcv7HS/etEvvvhi/eEPf1j/83/+z7XW+mhwJebXWh+l8y02SkwIILN3K7b+ZG4faSglfq9SrrW2UJYRbJxuwsmimc3WabXosN/vRM+9ckKuk5OT9fTp071F/+7duz0erWEqmXWfXAnWwvqS5baQeb656ni7cFoTCLXLrjFglJuTK7ldnkw/3bP9omM+g5iLnLszg9HRNyi+G4jpp7HIQK61tt/71qurq6ttVwJnOWVjnsu7MX76UXTUuZGUOjs723gj48IXNltpHOrXOEmGBx+41s7hM5qzcTA1hvQRb2xuzaMQvC/CrbH3Xkx6zBm0vMQ8l076wRzYt99+u372s5+t29vbjcxv1fZMV+uArKHwQ6vyi8WbPXn+/Pn6+7//+/Xll1+uL774YtufNrfonJycbAQyL3GIM+nAnUjRvx2qnK8XMWEWVb1Ji22LroQox8fH21uaNUYKPOZZi8rIpN6y4yiXN4tGPaP3k1mDQKCYLpjyPodI3MqjnEWfI6EwQzx9cJ0izdbMNXGx1j6BLSvcViOw1u7kVEmMomXPmAmCIhyEsZ0ePrdIG6rhfTlE/WgZAI6NQS5ynsa5W2msn4ZT9vc2qlHqwXkyNGutbaM02ZQsL+9pLoV4PmspBhlOvmoeRd69zRzMPFjg6Ohoe08FxzHXa9chu1Bq5FC704AZ3Onp6ZahIRSCZmWbBrW4Fbc1PLi5udkObHv79sM77c7OztY333yzzs/P109+8pO11n5ZQuP+VpyXS9Aar3cRQlld8H3RA6OgNqqclWdMfsGEd7Genp5u5HQ3AbdvjFshuQmVwamiGx85FInMGqOpbPfu3dvbxkLxW3ndKvzJUdVQVVb9f8PWWXDao470E79ZBZ6hdY1GS1PqRMopkVMXgQXQQtM6MCU+To29urraKxgVWrVBI6UFWlIwT6MoaierGl/lKozG5IfMRyMRxrW1WzhL9++cQoieNwn10hHl5UoFMLbTwNLvlvYwZrPA1vyoDMAfM3KtQWzZy13t7jr9tdvEXIPAu/AKFUjLGkrw46W6OZzgGToks1DQMyChVvVWGBMdlF+YFc74tqaTKYF33K31weDZvsHQWATlnlrfUk9GHh8JPN6mCk5BLIYaZTyDZ1Iwxqxopg167CZqxqOJF166By+SOThfRe8Y6ySEhZo5Rj+QCcM7ZWCum7Toc8pVlc/rPEK5+C/y7JlcPi/HaRFxrKenp+v8/HyvJmytfbRqbuh9w/uG9lNuvt+QnZNpwqt/a7lJDdxa+7V1DHadDyAAsUHiRcezJrC0ylo7rrkke20CPsuato4b6ZBr+WrAgENumU1171Pte0n8KbR2dmYPoAf1KQ0ZG9r4/vn5+To/P1+np6fryy+/XGvtCiTLi6k3aXaRIjAyRTldVK0ONlG+x8gSXreBFFlAmC1vKMIxqSWNa7g1fWjTnxaENhz2O4TnFI21dkXEUJ/vV9ksFmixfaXcrrWgelZaZdRWw1jEVCUU+nRLTve2utb1RTdTRuVT5tzw9sYoBJ+7OcjEnDXxMmvjGNRZh0QO5fG8N0G/m6V0TSMGz4ZORCXQSI32zPZBrn/+85+3PjbJwjBPKkFkxPl1b64+lDhvnd7jx4/3Eib0SakUg4lCgcAk2yrXJt3U31nPdu7Qbett6t6eHn7yL2utf/kv/+WGPIpOLAyT1ZqsGq2SnWut9fnnn6/z8/P17NmzrSj2yZMnG09EEdZaWxjFI9/e3m58QBWBZ5lhqt+LHqqATafXg030U0Pq7xcXF3thnZ81vDME1aps5UbW2lXYUwTf12/wfq0dCcsYlKBu9TIj4/qZFKBYrqeIDe8OVfLrg79bTGvt71tlmI+Pj/cyaa6f4T9UxvAxRp1fPBRn0d0D9o2WoyHPzgOjbwE5NcW/yc/QY/d+9erV3pg5r+5cKCKDMuhkeU6GhK6Tw+3t7d47EhoJqGZHV0wivtwc9M5wmveChZaQGCfSXdSiza1uZCVJ1qQdHTFOOq7uzub86kL7d6i8pu3OOrC//uu/vv2n//Sfrv/6X//rdvyMzjp8TBjVhUHZDE5R47t379aLFy/W7373u3V0dLSdfrrWfhGoRsFM4NyfNY1SFa6I0e8Up9fXMPDauJbyJg39GA6Q3eS3yHEarSIkk88zq27mPacS+ryp9jYwvXvPJgowFw1T+7yGG7P/+gKRdI6LphpGt2+994MHD7bwQqPYNfYl3Ofva+2QnvsaK97RXDS75dnmuH2SZezWmfKZjTQmDzTHWuJ56kTHN//fYuZeZwylRhgH4+gzO3cTaDRT+ubNm72ayM5H10tl7ffK7xBKmocgzKhhorMiLn19+/bt+uqrr9bJyQ+sA3M8s3CwNSGtdRJmFI3YviHOfvXq1frFL36xvv322/XkyZP15ZdfbpxY+Q+TVaK28byJLClZBXKNSS5vNav2ZeiEGp1I17Uo9+3b3RtZ2jfPLvKoIS4JbQyF/FLK+tGwobxP69Xabm5utlDHYZOebxE3a+v5DaGur6/3kKwMcJ/RGqC1djVu5QCLXBhnxrTGQLiCk2MIEcWd02bRtKJ995566HoIk6Oa82MsXmhBV3B1DH0RW9GV5whnfd+cXl1dba8hc61r/M7JG6f7NwNvrTBeJf79XpTaZt5lSUUykjqMtuu7JivT0glNmnDy0BkEPeUsGQidl8czvpbglKY61O5EYP/23/7b25///Ofr17/+9WbAyid5sHKBhj31mmvtQqCeG1TlaTxPIIcWK0G1apmlJ4xD22xcO5GGzJz7UkpoowimfEOf5xmfQoX6OInsepw52RDNXDj9e/tAJpSySRb9rzdufU3lMcdS5LbWLjyc2TJOh1ExNuPUyJHyCwfLudQQTjlb1HVGdIHR8RMy7RHbHSODNtGEAu4uQnOuxsnC6q6GLv6GU2ofIfuiWLsNqiNTr2Yj185nxzCR9NHR0YZwiyYb0lUv/N513LAWiiv66q6J9sO13c1RfSxCLvo6Pf3wjs1/VCX+F198sS4vd2/o8eBHjx5tFr/ZHCRkrf+XX365vv766z0UQJBi3xLG3eA6J7Zx5AwAACAASURBVK2hqUlo6Ooe3QrUcEHrwmvBXcNCE7HWjkfzzFlcV0PQ++sXJWlMX5QhPOYM6vFaDAtNKEhsGMK7qouDBPSrxs/RNMZRrpFSVvkorgUvjIUYORr1Wp4rLKakjo6hS94ZWONFNshgrcRwM2Dlobq3s3yT7/fv5hNqVR/39u3brQi6YdxaH1CNMptmy6CihnqVI+TMeEF7Jycn2za6+/fvb0aJcZ3Io84Cb9WdAfTD/92LzOaa6oGE1pT7eOO3xtnQEcivRcI14I1mimjds2sBci7Fw7h2nRxqdxqwV69ebWd2l1P505/+tFdl30P5bm5uNtLv6Oho/fKXv1x/+Zd/+dFZTjxwLX2teENU8brnlQugMAQ2t07I7hCkVt7EM6rgNVIETUkPFY/O+5e8bW2W0KDZl8pWHwqfmwnDH3V/G2Vtur2GTWHxWvtbsfAmZFayt7+vtUs+mDvyauZQyOXfRA89mBF6XmtXZFp04L7GLdNoriZ6nP/ayLYoiKPt6QlCQMatBcdql4peioSKhlrC0cr3Ih1yf/PmzVZAy6Ca05YS0Qe67z7Vb2E+Y6WPCHn30I+iuPavjl242tC7un+ofMcYej8AociQ8WzW2PP079D995511x9/8YtfrO+++24rddBm2hpkfvTo0Xr9+vX64osv1o9//ON1cXGxfvrTn26LrfCfcs7QqDxYLbBtM4wHZSzRXa+71uFNtJNH4R2ExxCC4kdClMGrh+0CpKjQpO9aJJSnyqA0QyammbNm7njDLk7It16act67d297VyDE1pM6mtI/Pj7eO85ord2bnrQmUciVvMyfejRz2oXSBdakjTF3e5PvHdIH82IcDVUsbP8Y35amFKn1oMIWfZKHa8l31pxNbqf1iebH2HCtNc7lytZa2xl2ypPKVWp1eo1iyhm7fxMNRUvV1TodjrnOCxUjBG1pirXV/lnbjXoa3pa0lyCpAb293X8nBr79B3Ng//pf/+vbf/Nv/s36u7/7u21x44Z4UNkdaMeCBJunJ19rx3NcXV19dGDZDNXqmYuaLIYWZRLEWh9nJicP1v/7fiek6Gzei1ErBO5Cash6SOHJg1LMDGzHcohDkGlD/Epy1ChBEOVbhJfGfyjrqfavXh+f454zwzn5n87DlIFFamwNi9oqy87VlO/knZo9PsQRWlwQaMsgWurgOQzS5NBmlrqc6USAkDTk5VkWcLPgmpooci+HSb6HqJH+rCyLxubn5tt663yVkytCZpCca2Z8QEHpjUZZ5sqWrbXW9qIbf8eBXV5err/7u7/74RzYz3/+8/WnP/1p7zwlXv3o6GjjPB4+fLi++eab9eLFi/XTn/50e1GlhVml5hlMHgMKzlpUJXJngSmDgVM4RHRS9k5wkwL6NUlpSEJoTElnNTEjTRnnHkMLg1fp4pvZvHpaPye0LxdVQ+X/5TsY+yofpbi62r2dvNty1lp7J9l2QTF2lV0XU+WqL/o6DVPnVV99p6E5D1wDVARGZ/QPEnn16tV69erVxm3VCBYZ4EfNy8XFxXa/i4uLzfH2hNVuSVIHxjDa1N0w1XOPj483brNGX8jEaXfbGb0WVh7aO9iiV7I+tBbW2tXO1WhX12aG1tz00IZyZGvtXuICTfWt6V2vBRh0jPw4SPwae2A8E+nOdudfZVxAYTyLSaTgFxcX6/nz5+u3v/3t+uabbzZjd3Nzs1fc19Cu9S6e1Ti5cN/EMYizXIGV91lj/Mba5VEoPW6IYpu0hmh4JMIujG/SgUx6vA4jCw4j2I+OdqUm5VDmGHoAo7E3VPJ9MvCcGsjKbK39F0n0eba3dH56n3J4/VdZk+NcAJ13z4ZI6tjKG5VHY4CLGj2zr79zpHHHx5AxFg1RSmwzaM6/f/v27Z6DFPaVg9U35LnTeluicnR0tJ1eAnm5FolPT+o824pEGQQGvpk788tIW0c9IbVOpDpSA8UBKeydhLq1rU/6z9kaXzdv39zcbIXrM9zHLzNi08h+qt1pwH75y1+up0+frqdPn27KpKM2oF5eXq4vvvhivX//4Ux6ghPi3Lu3e+W9UKipW8pHqQi4Ropna7jZs+lNZhe1vlJqoRMvQcDdQlJD6Jkmr7yb+9dDzxqzEq0zLHaPTjiFgaJ8No+q9uyixxoCUBxStNjIqE6gsL7ndVWxZip9ekSoqaivW5naTwvDwnKNJJBTKIRN5N70PudwdXW1JQV6f4uqRZ2vXr3aDBW9gDS9Bk0o1ORC0cjJycmm96435z05t6i64VhpE4sfkd8z6Mi39ETnndygpupYnVTnEoLjcIvayrtNh1Yd13zeGr9Jk1xdXW36p4SFUeco8b7Vl0Zn8+W3n2p3cmD/8T/+x9vj4+P1v//3/17Pnj3brCer/OzZs7XWh6OmvQS3YdvkleYgTXDj71kBPbmlTqY4vJti11oHDU2fz2tDVYX7BNYtQQjfyfWY2ENIsKUYxtViw8l3USZyqZdca+0R8vpcDsZY19qvgu48tJV/mp9PPqbzxGDUyJYXo9juLzSpISo/Qj79/5RJedTJU87+VxZ1Pne1zl/He3t7+1H20331qxuXEeWcFGQxTwhp6cNaa9ONzlGRkrVQB1DDWAc8yzva9M28Q251EH3e5FPpmznwwubKmu5VH6eO6iM06rntC8P6q1/9ap2env4wDuzy8nJ99tlna60PYaKNxG/evFl/+Zd/uS4vL9fXX3+9nj9/vnlMi4+XKuyFDDqgepSrq483cfMgRVbudXp6umWHSoQ2/p6Lw08nLzSMsChbR1ZPsNYu5V+vaXwgMKWqkRV6CDHW2hmLk5MP9UCtg/F3Dfq8uLjYtr4wJkVvNzc3Gz/XOq/JJ3TBus7/6/XNGcUuahOG4w2baSP7lqMUMTREtSuiNWMNd3w+5VrOqcavnKtxQqAW0NzBIXSjh1BlOVD3rVEsd0QP/by8vPzoLDP0ATBAZxw6YOyeoV/6osBWOF2HQB5NEMg6lj89OjraajmNyWnK+n56errnmITSPb31yZMnezoqMdKMdxsZQmIc3KHymUZTPzgL+Z/+03+6XWut//W//tf62c9+tiGRZ8+erTdv3mxvFCpRSnEOoQzbXOpJi6JY/pYstO6m9zuU2SgRz5j5TjNQlK0IqoiqC9t92yZ/YJEfyqjyJG1FPhMJzedRBinwTxG19ex3NYu8YXwN0uyjBTRrdKp0TVhAoTVQGm4DF+U5Fh8agcFYa5/0rxM6hL54/1bQk40xfEo+RRZF/d2fCPXqd7mcOmqGltG1cFsjttbaCzv77KKoylk0UFl1/uqkXOv/rT9shFGKZtZMWkPWJf571jbWmBtr951Wt4rE6OJcN/oEgd2/f3/97ne/+39HYP/wD/+wzs7O1meffbZ+85vfrJ/+9Kfryy+/XP/3//7fDS3pRFHSDEEI0ELuNVW0FurhwWTL8B0VGMHPwlLPKB/UhTGTChBVwz79gLjsIsC7QU4Qziy87aLTvwcPHmyQW+xfo9OwAgJsjRZuSJ/rpSba8VkVQj8awljs5+fney+6vbraHe7X8MLfZllBnw2FMn6UE+KYfSz61sciseqMRT75OGjQc2oIOs7WMrWkAm8jtHJvOtSsuho7qLSV9kJ3SKUV6JzAWrtjnvSvyZqi+NIO5YWLSrquWg9ZB9JwdK3d28T18fXr15uOkzuH5FlFcfqDW4a+6DXj5Tn6MndvlDLo7/3sB3Ngf/M3f3P79OnT9fvf/359+eWX66uvvtogbLMEk59qPUg/o9Syb5TN4oe+6iHKcRXlGdzksBTCVbm7aMpzTQ82Y/V65UPeYnI202Bo7XO9e/tWZV5rfRROal3wZGCxkt2hLNO8N0PRcdbQ9V6T7+sYex1dKgIuUp6G2nX4yDm/s99F7BPdMWCHrp/0wRynzxm4SVrPcHGir7X2nXbn36J/9OjRVt3ee1r4a62PkFojjTneidzRHWTQ0Nn3qgsy7TWOk//s/Xv9rB+kq5zu7G8N5XRMHFHXFN14//79+u1vf7uOj49/+FuJHj9+vF68eLF++9vfrp/97Gfb4WayVmutzVOXO9A5/549e7YXKjZsq9JRaB7R9pgS1v1H2fx/clbbQIPaWpNTIU94S8l75r5+Tx5vKowJafVx0Zh7TOOKq2kWTf/JsidkqFXrW3XW2oUMMsKtEyrHRSbtN46Ct0VUF2lP42URdN8nHkt/5kKixBcXF9u9e6Kv+8xyh+rXXGD9d3OzK3OBvsmfzOb3Jo1Qwyf8FYJzlk46Lb+LKmGMutuAY6C/rdGbYSY9hcboqkJQL83tS1MsfugFh6jPEBMZkH+TA+bGu0/La6k+MJ4afOPofOhT9aLzMFH5Wrv3y94FsNb6HgT2n//zf769uLhY/+W//Jf1i1/8YiuJ8GACVpFbfmB6oZLBFL8Zq3IABOiEi55N7jsQXQdOyLIhnYhDXrS8xfQaRQtVYp93Mvx/rR3SrNLNSmvGhDK5r6r6QwiuC7+oZn63JRUTFRvrId6QjCh3jYP+ty/1wH2JxURRHTeUZvHiY8qb9Rr3syiKcKD4iUQPUQkdXx1njRbj4fnVAYaBHA5luefP6txaO5TimhqkOpTytoeim0P3L3dmXfk/w/n06dOtzqxJjKJw+l/H6tnk1fKXynQ6/3m6Rr83w8a2SaP86le/Wg8fPvxhHNh/+2//bd2/f3/9xV/8xbq4uNg2vEIIhHB8fLxt4Pb3GWocMmhVbIawoZW3mLhvBVZe6fb2dp2fn++dM/748eO9M6c0Mbjr53lglJoBbDaowvV5CexDMT4FwmsYK26PHPzkPTmDps/JhRwsgG4yp1xeUuEaC6PFofXQzcLh3SibBWGu3ctP7VBYY2ytr6ox7TNc05KCm5ubvfOr1lp7NYju1+ynBQm9+7/FZWE9fPjwo3Pt2icnRtANaKkFnHRKX429n9V4lZejA/TtwYMH28mwniFbjoOD8qbxpj+tBri9vd043IuLi63P9+7d28qhIH46xHj5na4zuJzvNErTecjSNztOV2ssHQnf66eu/2AO7N//+39/e3Z2tr799tsN3kuVHx8f720xmts0evJlBdHB40gmh2OiqyTd80dwkwCfHq+ebXqrcmXlGtwXypwLQ2vY1cV9dbUrpbDoymN8Cp2YsBpb32HEWq9TQ+H/nlekYkH02ZeXu9er1XtORZpK5e/QQY2uMRvrrGGaaKb9nKiiMur/6drJyclHxyDNRIM+T7Q6ERnDVJlVvg0Jm7mrLCCTGveZJadLZNcjiBhiyHc6/Pa3Y2sf11p7KLFocXJ97tlop+toytH1h0K9+fzagYk6q0vk/PDhwy37OdfrP/pEVidAXF1dbSQd5WTQjo6Otu/xNlMxIQ9CcE+Leq1dzZfvmWRepAv39PR0+8zvU7DN8kxDOj0INAl9FJIfWszlCmqALAYLbBojW0607usrr9TPLH6LRH9rjCgEI6KP5DI99pMnT/bCBPPgHlUw81XuomFCCd0ar85rES/UrI/mu0iv8+nZrr93797ecU2dg4kcGio1s2jcrsMBTQTpGRbiDB1PTk42J14k2kQKOVYOnW99kB1vlAIZ1eA5/qfkt37hO8l1ht7v37/fSqEO6VvHXmPt8Ab9te60rjOgoM7feuoRP9AvWone+S70+33tTgT2V3/1V7cOJDRoE1RSlufQ2QkFO5GsfRW9fFW9QS365GFKHK+1j2YmSc2wHCLq28+1dpNojFWCKdDyOQT/+PHjjWeAfA5xQ2vtsjlHRx9S832JL4Ws4en/J6cwxzUXUT2l8Gl68f597mH0bP+f3NlEJfri/+0Pg1C96BwUdVbf3E8Rp0XS0LmITBhZfZvconloCQCDOUsYypPSsU9xlhC+BJQC074/onyUeWuo2/sVoU5DSyY9AXYiTd/tzoDq/Kzxk5DBb1tbxtJ6sBr5ysJn5mNeU93yOcdKT/7+7/9+HR0drd///vf/7wjs+fPnm9W2KCzmKkoVsfH7bJSkROX19fV6/vz5dnDiWrvsUonGTnK9RDNLk1PQh4cPH+69D/IQXKYYmjHyOF1MUBBP2BeTNrtVg1yU1EXh86dPn+4ZQyEhuelTq6mbMYPE9Hse7SKsqdcltyLNIqTKybMZ5KI3Y70rDGyb58MxGkWVlRnPbO5bmU8P9BMaaijGQJljhqoRQDlO6AxXxGAWDVuMNdztE77YfEBTRbAPHz7c6huNWx+bvdYn97FuGEifc350suNhGBmvGbU4q77RCCK+NV1kXZ6ULHqsPKdxc3OzbWQ/Pj7eeyuVz1xjnou26e6n2p0GDDy+vd293mmikMk92Djts6nsvKVO37t3b52fn+8ZFvCZsjQMMMl9YYfJd+3R0dHe+yIvLi72yP3p5dzHpDRkImTXWBxS31X2tXY8Bm+EG+kCPZSNoYAgflFmvSPCvaESchlhi8i1EHhlcuTdzJ0arKJaygeNeX7R8vS4Dc2gS0ru99vb3ZvbGVz98pyWYhjzRJoNxRDQ7d9a+yFma8fmUeZ1ChOdlA6wsCfC7/O6LW1uV+ox3/rb+Z7hZR0JfW0yoKiyDtz66ckpNRrv37/fnKx2c7PLBDOSULojtjseutOC67U+PtiRTD2rR29D1jPULC0xE0UfyfyTf1kfzrOf1ctXV1fb21sKiSGAy8vLraK7YSOBlVBtlmGmjlU34xkYKILpizxq7XmEGjTKdH29e8ddQ+ca5iK3tXbkK+/LKBXtNDSxANyfskzOo97VxFog+l1Z1OjNUBsJWgKX4VJ4rO/u3RDOC0eL0GYIZ261t2/frj//+c97+lID2Fo/zqbPL6qFZKCU29vbzXHWyJNJD0SEQiz+vnfBc9X9cQTqtsikoVYzpXSyKKdb0nyP0aaHk5sjl/KAjTZOTk72SoUa0XCuwkS6o7/mQqusjH2t/Qwr42hXiHtwtL0PZ6cvfQ5nY80xYo8ePdrsxdu3bzfHSufIvTrQ9VNj+4+qA/vrv/7r2xcvXqw//vGPG79jcfR44XIejF3htHZ9vTsrqwQko2grh7Cm/ALlK3Lpgmlt1+QGwO2pANq8jnfAnR1K+5cnsFDB7hoBHm2t9RFiadaS8rcuysszJqc0+85g4BAaGmvlo/Ay3RVRb9x784bz2cZKZhSvi2n2uxzZIY5urbWhx24MJ7PJo3aeG250rBxhn0UGzcyVEpick8Xp+1MO+kg3auT839x2TeDK2o9D8+u7h+an2faiqKurD2VIfXdCG73C1TVryWi21tL4etKJ9TETVpMT7HjNS0l+cmzfrflf//rXP5wDcxCcwbYGRlZyKimLX9RVI+m19QZycXGxLeSiDSc2Ekh5IBZcX+r11tr3Wj3Z0v1qiPS92bfWa/l+s43gOUUoPzNDrRLWlM0it7exaKyLm4KTQUs66kRqhCiecbVejyI6Rsii1NdZg2XcrRnqQponntYIQl76wRgy+LNsYa3doYWM10QBM6xq6Kivwubqm/msHray3Pc7Fy3WnBX30GX730MTy3NpM6T07PK5xlGjO9FhQ2m62jkh16dPn26nxLq+Drzn/vsblGl9FGmutb+tj+O8uLjY+26pCHOED2yIXkqq+gapNuv5qZB9rbXuzFO+efNmff7559vvNjzXW7W+pVzDJHYPdeTmZndCo0lWqgGGvnr16qPtRmvtQjUCa6sC1euvtf+arUOkc4VvK8P0gsLaWe/TZ661C9XmIq1x9DeTTRn0sbIpilAmUkWuXDtPzb4WgTQcrrKQTRFl72/c3d5FDs1Wdnx0oGOgwM2s4gJL7NYAUXwbp2fIP8slWnIyEV1RYMP89rt6UrTYmjeIVptIqoagCJ2D7byJGBiYnrNVpFXd9RnE1PGQe59xe3u7d3hjD45sqFr5Tae21gcaxysXe0xUdag7Htzz+vp6vXjxYiu2Nhc11sCNOf1UuxOBvXjxYp2fn297rnilTrKw8O3bt9tpp1VOHSqRWytOcDV2JteroHy3ZRd+Tq5gG1iQQbN9a63tunrITnA9uOfXSPVUiI7Z3/osp4xCUF3QFLkGvwgFOSq5MPtZ4zf7TVZ2JFCC7h31PePqvOpDFVc4/ebNm72w59Ci50V59c6NsQpP6+xkJbtIkdXuX7TJyM5xa7Jx7Z/vtUyixmkiG1lI90OWi0KKlNzH/JSPs6BnqF2j0c9OTnZ1iRBcxzANZbnAzkt3JDC+zoyT/RY+0oW524axIQuRxKNHj/aywRB7x9HyiAcPHqzPPvtsj7sUFZQXVHv2fe1OA/b1119vD3RgXTNyBHxxcbEePny4/vznP28CqpL5iXdhECG2Q0Vrc3IatvJOPdP+kAJ0Yk18Mya+U46m+wCVRFAGC60nUvA8PB/CUnMGfl+NttbaXrfl+SarxaBkOLmI1kTVWbQId60dkbvWx+hjrbXnSOoFHQ0+5XhxcbEV407jqwnnm9JvcqLohUGcyKLPriybpeu8NUtaY9x5n/domF4Z6ENpBlHG5ASvrq7WkydP1lofZ+M1Mm3E4Hs1nocOIZh9M39r7ZcD1WB3Phry15n3/61Ra6Kl4WbLk9ru37+/GWYOr/WdpXvoS59xdLQ7ZrpJOX2kNz8YgSmJADObGiXUy8vL9fnnn29EfIU0M32qjddaewezEfYUFHRTb9gjfjtJTQDMZ/MwVZqZ7XBtjVtDoVmmQeD6Jtwsr3B8fLzV+eDioCETWu7v7du3m+dpGURr0ZDPeAWes8XFJr73rwHRGj5UqdwHvzFDJvKBMKCp2Shw0+gMIEPCm3s2x9R556lbcGps/b2Gmcw7ZkaNUW2YCvWZ9775fKIqzgTlsdYuQSNEOznZnXpibmp0qkt1OmRrIRfNNJnw+PHjdXZ2tl6/fr0XsjXErcOcut5yDDrUOfR/eiBkJw/66LP+jdw8q0YdWJH15tzL2zYROMn+2b6XxG8Y56eyhpLR7QBDQQCFv1CcI3OEn50kijDDmtZrSeF7VtFHDaHfm50qQqm3nyEoQ9Kx9zBEHsT/CbpGGIlcXgFJ62/Co25eJzdoqEXEDS2hNEYO4dwQs2R4kRtFKi9GgW5uPmSdzYV7QyStKSM/rYjWM5oQcSpCjaZ6qBZY1pO3Nqi0g+cX8RV1dQuOe9Il3t3Y6Sh0zBF4q9Tz58+3e5Aljsd4W6oh4lhrh4D10xirKw4CbH+L3CQ5ZAovLy+3Gi3zLMLpAYlFevPVZ+az89fSn7V2JUtKI25ubvbus9baxnpzc7O9cAeyKwf38uXL7bV3DLvi9xq6XnNXu9OAvXr1ag8y88CyXhZfM0qNW8X7JWV5azxSi1513O9OivDmlq3TR0frs88+24O9tfgd/Hy9lZ8mtAt68kr6U4LRJPHkRRNrrY9CBTLqGPXB/1teMavM8X0tCi13YOItRg7nU9zU5LuEcDi0orY6IH2RIZyV/tP4NwxnAJu4qMwmei8KY7hxLjVqWrOWPYL76dOnm974WSTJMK71Ae0XVci4M0gPHjxY33333YZyaiSh2Ovr670DPxm4IuKizbXWtpiPjo6201TMceVZ51EHbN40b/sxdw2T1WiW47q8vNycntIdReCuIeP5ex1QebSXL1/uncJCPxpK+6z8d8dtPlv0fqh972butfZfDVYyWlpcRmOt/QXfg9BaS3V7e7tBycvLy41HaB3OWrv0eZV4rV318iR3K6iGFCab8AmrnMuEvvra9PwkuT3Hd5pe7/UTJbhXM3Ldb9aSjrX2ObzWXpnwGZ7N8K4h4tym01CK/BoSWjSV5aHTWcmxWUB9Mtd1YmRaHs/v5qaIUxa8PKBF1OfVmEMiNbLCk6K3WeRpoTZcmoZ6cksQknEpq5jZtV7DaNUBk+c0dJ23hsTq/8pn6reQUz8YmDqU8rz37t3baIz2x/5J/TT/UyeAjUOcZ8dW2XcsHIrv15h9qt1pwN68ebOePHmyx2F0wROmTMbJyclm/T0cWnvy5Mm2MCifNG4hOK6sFrl1Xq1p0uoBxfeMiX2KFvY8gqfhlXuV4/A3Fd6b4I72RVf01MnviRBrHTZia30gyLtb/xCKpNiMRMNN11HUclvl/4QhXtDQvpGNaviimbV27+LsXE/k2/op98fX1dPimKacNQultWkMmtM6y5H6WQRs3tUm1qO3BIKxI6+GsS0UbT/LXR3qvxo1z6nROjraPxO+P30HyoeYuj7W2kdEDef1p1vwyl9Vv/qvp0L4u/uXAhGBlIdea+2dPzez7QUM5k5/OdLj4+OP6BhjvQuB3VmJ/7d/+7e3Jycn6+uvv14nJyfr6dOne/F2j7mpkEt8dgANTXimGsObm5u9e7Z5ngEWQa21e5lsiWbtEBKrABk9NWht5ZRc07Ea+ySVZz1UZUQmhzKDDcfVerXWrminnnpWoE9jd4hTbL9wVTKDLW8g86bijUHrQm0mqtyVZ3k+B9WQzn272Pvsyo4eFcnSgeoQNCJUV1fV8VlADP9ETeXMWv5RiqD3cO1EiL03NDj1ot+FarQmXmbYPpv7Novd+ZsZalz1fF8qzm3qUWVqXbQgl21R+A0R1pFAgtUB/Xjz5s361a9+tY6OfmAl/ps3b9bz58+38+xL1h8yXjyTzwjl6OjDe+imh+1RJ67vJtOrq6vNsvPwjIkJ0codUHzGcW5vqQctKvTz+Ph4ex/mrCvSd3u81tovnAWvm2qnRIcUrh5PSG48ri0BXAPESJr0ohl/ayX/NLLti35Q6h7SV55iZrfcuyHn/L1h37179zaurcWwxlelFsoIg8ydzGydr/HQq+Pj4w154cjqfJsEIOvqlH6X84ReW/pRnVcrRxe6U6BjbKRAt0UMDFRR7KHWnQS+12vKJ7YQ3NzN2jbrBD3TsM9prnUqnfO26+tddT6dJgu62tqvJv86jz0a6K72vVnI169fr2+++WYLOyhOjZcHNxxrDdPbt2/Xd999t5HAXczCAouncXP9JwAAIABJREFUZCWSvM8pYbk3kBiZm5uPic2SjoyCvsiMdVHbhtExlYS1B6wGuAu7nldGqsaghHYntai1nplxN6mUnoE/VO1MSSzqtfbroHokimeaO55S7VeznSWPi+Q8+/z8fI/TqgGYHIdnMwqMRJFbn0n2a60NKaAiXG87DB3wctkaX/rg37179/Yya7NkiI4KYcnIYqUfynn0E49chM3hTZ5TzaBwthSHdWEeGfUZRtawdM1O/q3vgOzxT56L92ufXMuId7y2m631gTvv9jQURstbRHQt18DBHR0drWfPnn1yT3XbnQbM26IpU1O7c5+URtGk3eu9CRTS4B002S3Cb9apSnFysjvj++rqas/7UKYiskLbcgmNu016UQ0jxBAbXxMSjNyhze2eAX1WecHvetCixumRyMoz9bdH0EyURx7GgKCdc2UsjDEkdHZ2tkfY19iVp2xhrT7TFwR8jdAMd2vs2rciEfJroqTHYvte+093yLahkjmpzJrR7nUMML6WUy5qM9edu7V2WcY5DqjcOijnw2AWWR/aqmSd+Tt5CsEmzVH91ya6Zbi7XnBgXYe93ne0nuCK0y4Y4AwnsqPjylbW2j8v7FC704AVDay1tleJy1xUMNrkYYpq1IqYQKEY5a0HIJxyDGvtKpAtrAcPHmzfmV6tC4JA+mwL1ATOmhnKiRdyvxlGMErTOLZ8ZPJAiFMhHsNco9l71ZAqQel3J4fSe5+fn29Gjjcln5Z4NDQw3mlUmp5vWFny3vYSzoqhmYaZg2NMyHpybOa14TI5mI8a9YaHFpdseZGEPvRZFvHp6eneW6OM2wLjsFpiVJ6WvNyj/8ijvB+DRU8fPXq0t+ODHPzU3zrorp3u8ihHVYfWjdvWFcPV/bPKmBhF/++9Hz58uJ3v3/KUm5ubdX5+vierGtmuW98/PT3dIot/VBlFvRGh1MhQSp3QqWYPes4QpZhGAmRmiHpOUV+CSxlNNMLRtScnu3OVTNI81bTI0T5FY72+vl6vXr3aM4SQi0Xv2RS66MLi0kcKarGVXFcAeXFxse12IJNuZ5ohAFgNalsQDe/WWttRKjc3H7YGQRqMNHmR8fSE5pYM5nYdMvMTh7bW2ja6WzT6Xw7PIrm9vd08MSRR423ePZd8mlnWR2FtS1/o4Pn5+Xrx4sWevuKc+gwLjezwdJzRoajDNcJXMvR514oiZp81Iyd8Jhvh6exf0WEdcmkddW30w3Xm+vHjx3tFtEXaDUMvLy/3jroie88vshJhPHjwYDsTkHEzr3am9DktvSE7TmpSFLPdacDevXu3vQDCzXE1wqDp+WdYZQFeXe1eHd8TDhCfhHV8fLzBbp918TbEE6Z24TmGhzGYxlZGhHEo+a2Qr+ipntmiL9leQ9BK7sLn6+vrDb2Sx7t37zYlqqKutQuNJE7Ioa2GgOIYC4NWRawna7mEtxaRkUWAt8MLWczlliZS4hzwPmQvIdKsaw12s2rm7sGDBxsZT851qCrS1Zh1K8vcqsTwvXr1ai9DaFzu30avyrHNZJPrObQiPEbY/fGFE1H5HsTkOy0zmte0RIIuVH9mJrD86HwBckP/kv4FAmq78NI1wnPngXUI8UJ2paGOjj4UorfMo8mLrv3vI/K/dy/ky5cvN8PlphY/5FBexyQ0XKjhY3QsLjD59evXH3FCU7hIW0pvQroVQSWy58qw8AAWYFHdWvsV2pSiY/GsyZvUY/TUDvf2t6KV3o8MGKw3b95s/Eo5sWb2ZrU2R9CQkie05cT36nR4xiIbyJIH50kPwfjW+0A/UCnlfvDgwbq4uNjjEMnXM3t/Sv3mzZvtOBXjp2fm4Pb2w8kYNQynp6dbEkHjqMy9edaHop8aEM+uUdZX8+HN2J6z1i6rxwD2OZ/KatchVRbmuhzUPLjSjoHJQ+GqOX764f/0SX+sndPT0w0IFEBIshnrzc0uOaTWzPP0c+45di0uETDggCTXXDsLrWe704D96U9/2tCAyfdwgtcYsk+FF+C1392HUB89erTtQUNWtxFK62agAvsC2whaWtj9cE3gtVZFs1jKFxgP78c7WEytdZF5KUotLCaXp0+ffmTYKEIRQnkDfS4fVFlVCSyWhrhVJt69sllrv1gZAhMSGxflKnfIKBSZtSix3FRLVtbaz442fBYuMxqSFaUhyO/+/fubk2khr9emdVEYM8RNdkVzdVLd6wfZQMhQxqH5qGNBgZQ+0ffyQJOHKjKezXh6Yqzwt/fs3OOppl7T1devX2/rRF/ovQNIi5Z7HwT8IT7OfFv3bErr/OiQOac/n2p3HmjYt+1U2UpUNgshNKToTfeDmiUim2GoF7i52Z0YWc/kOpPqXgTo/ofO85oJgnqeiRjbH7/j4hhNqMd4jbNhUiFxjdhaHxSvh8D1ma2f8bzyQA2RzcdMqjR0Lo+IFzKvxj0XFSWfIZw+VMZdiA3d5pimXHtPz2qJjs98r9tgijTdC6IVkhStkhmnwtnMAzgPtRpk/2Zf9aHzVbQ09aMy6RYpetL56rNLfHeeOw8Nw3y3xqtozPfnOXENn805GeGdm2Q4OjrajtVqWI1vU5bEcTFULWMqd16Z/mAE9u7du/Xo0aO9bQItdCwnAQaWO2C4hI1d7MIP3+dpK+xOIKvOCzoJElIqD9U3EtWTNsyZyqExTnOCeSxjmNxFkVrrpnxORj6Hfibxy8CUkIds26/WLNXrrbW2WqWinXpJSuEn48UD+tkFN1FeF7FFW2RbjoXzKvq4vr7ezo8zXobp+Ph4yxAfSut7Zo/SljkkR5/ra7O8xloqgn7SI32d4U9Pt5CsqI5wbHSSEYMmqmc+76GIdaxduNaImq2J0P1efWbwjIeMhMptTW65f8td8MOa3837+/fvtxdc0xd1pFO//X0ayTo/Cbp/VCHrj370o3V+fr6RpTIIJd7rMUDt7k1kTEyUrAal7eDm6aaua4P0Hj16tKXoC4fxAfrm7xRqxv49kE3af61dOOX5ru3OAN8r/J1GU1+aMrdQeLCe7lGe5FAq3wJs+YnvtpwAX4En4u0a4pm38jXuN9FCEV/74zNjK69RT0tvhBBF2Wvtv01In/GDc89ldzsIxT2bDJoRxrFqFiudgd7meV3TeFUvlGaYD+FW/7/WflW82kbyYgydh1V07Rnmif6Wc9RKQ9CdeVxREdEhZ4SDpp9+WhulTWqMi7Ks5YuLi/XkyZNtA/7V1dVG8zQZZp2UehCZ2Xbk759qdxqwb7/9diPm3r9/v16/fr23qVmas2GjRUDhhTZFYI7paZapxGRLLeq1bm5uNmKTAjZlb7LqTTy/2zraatRMZscwhWcS+n3JhRqbGZa1tqre130on+u6S2Ct3VE2nt26HF7eC1PWWlsB6bt37zZvOTNXJeFPTk4+OourSKXIZCIEi2vSBOrnKKdnlsD33Pfv32+H9Al7Efnmoouf83nw4MF69erVJuOWP2i4W/2X0DEmhtJcuNda+yePXF5ebkkWKNt3uhg5a/LQGjY1YqA/HEr5XI6Ow53Z8Y4NH3Z8fLz3ouhZEF7Kx//JTtKnCPThw4dbeVG3IJnncoqePddNv8so+n/BB96137mr3bmZ+9/9u393+xd/8Rfr17/+9fawtXa7xSkr62whmoCGa53IIpS1Puab1E2plTLphK7GqVD50P0OhYjzOyarPEjrvMpNyIhQAGFyjXdDABPSwkfPLrFLPjUm/l6jNb/fBTPHXYdQZSiSmuUsrSfjJetpyzmVgyp/1f51vt2Dx24yqI3Hhkw9X7+hBQW5zRo35CGLGpq5IbvhS0N+aIksy8OUpGfk19pxcJ1H925pEXlNvWxSpv3v7w1/9f1QmDvXw/xsfn/yf/1/11BDXC+9blg+G0dsTiFkcjBfHT85Pn36dL169Wp99dVX6/T0dP3ud7/7f9/MXU+ihmMOVCbm6Oho4y0ak9fbzKyX2qhJWh8fH2/xNMTjZAYDNAmySH0mb9mXhZqEho5r7TyCfjJUhNr6qoaiFsUk9CGneun5NnATWGNi8TBaTVMbtzHObUMUpRwaUrTPazEq2RrXWruyDuFhQ40an4auHBnZzAVVpXd95U+Ga+3eSrXWh5CyR1rf3t6u8/PzbeGstTZPjz8rX7PWrg6Kd4cezNFaa89AcmRNLhTpQRozg9qdKY0YoKrez1x3Hnx3rV3WXL/Nq7610n1GK5V9ERqqpnPUvpSfqo5O9N2I4dmzZ3uhZu9XGme+FlCtnHloZrfrsI7zLpB1ZxayyGOt3cIp/O2m0G6YXmtXZ9QCyoZFPCmB18PMheDs77nob25uNoPWibEdobUxM6zr52utPaNAmBRqQnbGvPCZwTF2hqVEqjEW7RUFIODrpcu1UIQaHWEG5MjLFVVI+3csM9tTlNVQxWKarUgashHCz7R/qYaZQKgzKA9UJNrQxeI1N+X1itQmaijCZbCKmMoz1cBAgp0D/Z0lGVBEjX15QPSBqGUio4ZY5r4GZWaPK+deV93p3/u9iZqm8TP+ltCU2nHQoWv0r5zWHMfJyckWhjfJwXFbQ+7xjyLxf/KTn6z379+v8/PzPcvMu8+K4CoBw1diuYugKWebjKeHr0E8Pj7ekgkW/cnJyXr58uUeydnTLCzm8kjliKo4PFUNqL81LIQEkffG1SORm8FrYsCibYg3YfRau1KHGQq3hkzfus/QpAuViup8t9xH0/HQivsUcVV59ePkZJfBIzPGFJ0wEU836NdAH5oTMoLQr66uNo5vZj79n46SY6vA3R+iqDEtgYx4VmLRkA+irxGq3mt1aIcMpyQL1FNOqRniGjf60MLQItnylV1jU39xgGTeJFiNfrcfWcPQoPXFgXe9WEP607lpGdbR0dEeqV8DTW4Kou9qdxqwb775Zr148WI9f/58G0AJb62Gqe/hm6c3ts7Dwm/WCMQ0If1pwdnWgFR0YmyLCRGZNWRr7b+Qg5CKLlvz0nDWeMufUEQv5tBH32lldGG6Ce82IZPdDNY0bhbcRE+tiSpC6zMbRkF4NdDmrydVyDRZJEVhFmCNkIwwWZH98fHxll1+8+bNtvWnMm4Yql9Q5MOHD7fs99OnT9e9e/e2/8tods6cZ2++Ss6Ti3H4vZ9VZ9SKQUsW8HwxRou9J9qrQe7WGDKqgSTb8sszsjDnqB1G3lx5j6v+zKiIbPFS1lOTG0dHu8RUk1+ds+vr63V+fr53fNBauyytz7v29bnhNj2jz5wKubILn2p3GrBnz56t7777btuuQVg8ueyRhzsQjSL34SaupGo9ncl++vTppohrrfXdd99t925TI8Qg1DNNaN4Qw2SVAykUbwlGUc1a+2d36TOU0c219+59OAe+L7mdkFoWca39dDneo+Ufhe360JKM3oNxgA5n1qh1X35n0HxGkci2h/TpZ8l7CwGKa2u9GyPIIJAF5DXDTv3lJHx/bsAuHdC/9b76Tz4WpVKV8oNFdmRQZGM9NJHT5zdcbKP7xqFvddbdT9sxVvbVm6JA5U0cNRRcTsl9PLeHcs5tO2o7y1G658OHD9eTJ08+iUJFKOTKwbln5eH3Jj1alHwXB3anAXv58uU6OzvbXkJbgUq79mwwkLCevCii4YJQYCIm1+KvPvvss00ZGZsuHjzIWmtLAfNIjEbT7xR5LpZmszpZ0/vNFLwFAXGpvaryd3O1PrVSfJ6YUTm0f0pIPNMYhFdgOIPR0P34+PgjhW+yohkli68hvf41/Cp532OJqied88pQaFkD2jC1mT6yrD55Xs9h615azxXW1qFxNsbbGrZGEJ5dakATMuuPvkOH5TEruyJ9rWit/S2vVwNs/EJy89G5neS8vjBk1lL3yhr3dFYdB8RUR1802XCxe3Bvb2+3WrMiQvraOXc/6PCudqcBe/DgwfrjH/+4FbN2MlqwenV1tVeZb8FOklAni1TW2oVHLcWYmaV6LwOrMIo09LG/Nxxca0ey6zPBzYQExbdwW+zXui5jo/QND+tpGAbP84xu96lxrEExViijfFcVTt/61uMqauVTDqLcy+THis58VkpBP2eleDkpTf8ZIZu2m2jQJ4jfQm0NYMPnjrfEf7PI5nTyNkJ6DpXxq0MpCpmvAiSPhoaNIqoPE2l2rnuSRRc2HaxTaORQzrOclnm5vb396Gyxoh33rCOaznsamYlY9UVmUQhJRyEvBdZkOo3ZfHYrDg61Ow3Y9fX13stWLQ5v6uUxeB4PFwI1dq6gyguwzhRjGopmXXhcAlOta8GVmK1Q6pltHsWZQUIVdjNw2uQShDf62DCTN7LI6oko+iFvDv73OeXEKG4TCJyJZxaRaJSp9TiU/OpqV6XesLQZoBbMmjPfabNghR0UlLcun1jPzohyFJ1P97TAGYIiRH1sn8jUHM9N9r7jJx1gGMioXCmZdj71zYLs6RrGT15aryt32bmfHHAjAjoNvdZQ1zi655w/rWjXHHEmXRfGQ/cYeXrVzDcZkzN5apB3eW99dbBl5/wQB9h2pwFzWkLrvxqDF3n4WRLZxFDMub3BgNyPYPqc7oZ33YSVBFXCsQiCwjnf2/X+Tyk80+IhPM+sJ/a3EuJFHkV7DFbraGr0anQsuoYAjFOzqhAr5FCuB3qYBqaEa+fVK+8qtyJo8isy6O/k19e/FU26D8Wtk+oCmckQfaZX3WFhkZQ0N/8We+Xd+rYuiC62GtWJkiuPogOOSt9cp8915MbZZEJLZG5ubrbz+62Z6sFsRZYTXTdRovaqIXGTJEVT5c+KylA2khprfajDM36y757VtXbJmIbDs5n3Ho3UhNBd7c46MGGimqr79++vs7OzLb1JEL57797uxapNUVMkh+dNq4o/sgh7TeNrELVbLRqvT+G1JqeL0HaoZiO1GfrW61kAPOshj9aJmiQv3qgnrl5dXe2dcqlMpJ6qCt4QfPJCvuOaGgyLRV3a9fX19nbzclEWXuE9JcRFWYAWY4noQ2HAWvsvnCUr47JtqDKZqLZbr9x/OsoWUZPLbP7eZ621W7juRabTQTUSKFqC2KtLoovyQ/reOrgaKkhxJsCmblXvJs/c7zqeqki9/S5CagjaNVZkr0+9bqJFme4+CxJmrBj8OqfOUZ3YD85C8n4eeHJysveSgsbdFlw7YFGWmK/wqiyutYCbgQNdGUithZnTUqucbraQl5ivbtsTSBSw9+znk9+poOutjWH+ffJ3/uazchhkZRwloOtAGJYWy5b36CLR7CNlgJo4kP3Rdyi0RqPKOPnM1o71iHCL0Xiurq72soxTN4q0yLooxjyVkOd4a1R7f8aZ4Z7lFZVh65Jcd3Nzs7c5fK1dQXHnrOuEkWm00fEwcKIU+tNQvn0s5aEZTyMK4290g1Os7Kw1OgC56WvHwii6V/VzrbX33gX/FyJeX19vIIjeyE4y9PScvt6VhbwTgfHUDJHjpWvhj4+PN5KfEmk3N/sZOANpaMZgmXSv8aIUzVBCEATeDc0z1jaBLQisp6wnbSv0bWu/24o+/F7laajZNyBR4NYBUeQmSSxWMhd2kd/kl2afa7gYgaLMhvz61WwgLqhjqWctcmaAycBYq8zGXWRjjEVoLblp6QEZ1xjP5Mda+85N5u/169d7CMVCn0i9C7oylGVu1o7M8F+uFV6Wc1tr7R3B03KYhpJzDotIioobzhk/edUwae7juiJCsvK9tdYevTKRPF0kC1y0/9uvPBHto0ePtoLkyq1z0tCV8/lUuxOBOUO8k1KLCAZTsHIs5b1svxEqdVJwV+7ZbQSu92zWugbCDnpJhKI2Fr2K36zZNEb+X/5krX1vgEtwj7mYJsrhdVv42TBym4ij3am3NQYlZSlHwzz3E9oyiu/evdtC5RrfenVGBNIynpYGdF4oovH57tHR0UHOwr07hoYDDf3pRdP9NWjd0VAjyYCUq6KbXYBC5/J1natZx8c5VH5HR0d7ZTv+/+DBg624FV80DbD5KeF+dna2ya2GrYbAc2u8psFpCGfuZjTUM/fX2u1S6Ekl1f8a+K4F31f3Z23MQ04nart3b/eaPc/zs06/z/7/B4HdacC++OKL7UYtOyhpX6PRFyt0EizYKuFauyLHWT1tAN2awoh5g43JqLGgbMIDBgGv0O87p2xPGEEdDXdbfHdoC0nv0zoiE9Q4v8aVl9ZKYlvAzdzx6H0xAw5pcnI84MOHH153Ve8+620auvm8WThzRZE+xRN+6v+Qn9+70LT+vWGd56kLbEgONRVFFCEVgUPe+lbutk6YLG9vd697q1zU+dEzYZGEyOvXr/dCb/1oSN0sejPwLW0oEvXsNske89f7rrWP6KB58sVRlTaYdZGauSLTWZ/Y+k062uytvpOj9yPUGJNBQ0jfsVY+1b73PLBHjx5taIC11G5ubjbUBVL6O8JuhitzsbhPSUyDf/78+SYUn/X43SouYycml81pGrkG4dCEeUYriKcA8QwlgQ8hP5PQEGFyLkVvNdiTzK7HnQuhxZrau3fv9hQNQd6wlpE/Pj7eDBwZQGrmicxaU9Xwr9635HZD0VkdXkcmi9Zwn6FiePq255avlMtScA2VrbXjHX3H2P1DWJdU7rxNntdBi3WiZMpBlWtr63X6xbm13KYotxFL7znDLQ7b/5sR1i9/b8HpIQSK51prl8BpmN7wuqGfNg/b1HoYZI1bHSqdNtYZgs9253lgf/u3f3u71gdD9uTJk+0h80FdPMKfcgsEbkAlmycP4rszg+Zn0eCM2U9PT/cOUGwRHKNjUhvLV0CynJ3g+Z05rrYu3oZ1DJfdCya4W6BAf+OetU6T1G1oDYaTc8c6ZVhZM9LmZGZ8zHPnqTVb1Ylm1tZaG9cynVXlUmNeHWmbWdup2GTVULT9b3hfQ16ZVSZzzFq5sGajZ1jc8dUQVgYannf2q3KofpTjajuEUg7p9aFsZPV7rikyI1+60lCysmxyos7Z9YyjdVX06/y/Gshf/epX6+Tk5IedB/bq1avtDcGIehbcthbelCI8evRo8ySPHj3aTm+ooIRoXUStcF9r7b1pqLE0QTVM6UTjY/quxWmEILnZSsI3W9SJLiHdyTau6TllF9dae4W3t7e7F7MKc/XLIoUGeGT8SfmCen1hCYUrqoWMQPyJFGS9unDrHXlNY5le+NCis3G7zm6tHcJoqEEn1to/faNOrw5zhoXCOCelIMihzGkkyLDOxRzq36ec+xzLWjvqwPowh6ICz6sRPT093YBB71laYvJS5qgIrGuhxpu+om9KV7Twt2urzz45OdnLKHJSc46rMxNl6a/QvpvvhdA+KxduvUzdme17N3O/e/dufffdd1utzlr7r4riEbTyOs79MSBCYMFnKLDWh7dls8g8bSeykzP/zxvgfj7VKLtxCC9Mqnt1Itfar2xuKNL7HurfrDejMCanYe7V1dXGX3lmq+aLWkv06vdc6MYFxTRMmUWW6sCMrQZ9Gra19mkCC5KM6gSqhDWczZr5f40hVAjZVZFrdFwzs26cmUTP1JfyfOWtyNg9fe47+qt/mjmEdjyjB0UWqXhWx0cfGaYZbTCwHJW/tWC0Dt440D0cZd9AT66+4zPzBLm1XV9ff8R7dd30zUX0jx431L+5udl7CU8Lxju/n2p3GjC1Gi0itOAoUGF1lWNCVEphEnlIi8aEP3nyZK+MYsb89RJzsspP9U0vDTcsDBwZJNSXSqhc7iLsT0inY6R0a+0fAVSv63km+Pp6d4yz/iI6TSq5Nhs8F7p/5Mao2Hfms9vb221rWA3HLAC2EOactuSkDqWhfps9ceSoT0WRlJ8u1EBLHHiuRVJj0LDSnFQvmyFnXLVmBGe5x6eMDP3qrpKrq6vNSHEUL1++3OZ78mRd9HX+9+7d24wFnXnz5s1ets+ctLQE0qF/6gwZQHNU7qs62jIZTclI1+1cD70OV14ZOT7H+O/fv78ePny4Efnmex5IenPzoeyovOmn2p0G7MmTJ9vxrzc3u9dY8TAgOiF0awhh83w8DONFCEUTk6tox01UN3zjWAp7OwEUufc2cfZzep53NDKms5JYSGo8JrAvVNDPhniTi+I9+94ABqBIpIvVJHbBNGS1CFsjxUApF2jmuB63oaP+l9sqB9JMZHk6/ZpFjS2H8Z2O5/j4eM9ouG+97tHR7mC7GqyGgPrRN77PUMi1Laep4dO/WW5Tfo9Ra1aP7N3Pz9Y3qm73LIagCGhyf+YARXNIDybSqjEju7V2Z3FVvn2Bi/DSOD27hdgQn8+sPfd9/fr1BnhcT6cbqnqe8JbOGH+zj2zL5GXb7jRgf/rTn9bjx4+3VyZ5QwxYPGGqkLGTeagGyD1Ya4rRavx+v0peYpgA2wdK0spe8LV9cU49hSV0nq3n6V9eXu59H4lfg02htHq8Tl6NCYNeZMrYtvL+7Ozsozoez20dTwsnIQYKSUkqr2kUKVENxAznGjZNgtwcnpyc7CGdtXbhdV8hxxh6HhRdhNm5nOMvMV49EYa1n9XBEvYcdO/ZLGTDMvNqoZ2cfCibcI3FNpFrHZM5aYlK55NjmsmIzrfQuCiqzh1wKPpu8WkdVNdfkZsIZO5kacG4NeD9Dz4TxeD/jo6O9rYL1tC3XAZPZm3r1w82YCU5z87O9rZnFApTEPVSUAyE0kVe/qNe3z0p31q7Km4G9Obmw4GH0u71RDzDTNErMWj2pt69b+/xt5l1q6dByncyZ0jruvJJRUz1UIX/PVPMdcLN7vMrurAA/YQOZIssFCF/n1sFp+ST/2n4W7kyWP0uspjiU+KSwK27Mg7XNyw3Pn1ba3+zf/vg3vrpGv3r7oUaJ4a2iL/cn4Xk/vrgp1CniFZNozGWmO615rEcY2vaZqLF94WqdR76hu4pH2XufW8i8uotZ0E2+ClNeOu57t8z6qBOpyS/e/duq+Gr7L2puw6i3F+3zP1gEv/nP//5Oj8//4jbWGtXnV6inWA/5VkIpgiOsE0gJawntr2UaDJ9AAAgAElEQVSoZRJzC0Wf1ed5z6AFS0iMT5EfwyH0Oj093cui1uvN5EWVZK39UgvX1tsUencLDmPEg07+gVczXvIv/zBT9+UxhK7dGVAjoH89dVR/eU1zMKvjhU2da4roH6dYB6Df9+7d2+M9OJyiQwulVfINw/WlIRdZQSZ+kkEztEVYa+2Okamu1aiutX/eXPdINrSvQa5j6Ib8GnWL3bhqnH2/i3/SC+Q+F/+kWzjQ1pDVKckcStLQBfrUqKZ2gjH3prKGwtXhtXZHXDNypQo6l4fanXVgf/M3f3N7dna2Xr58uVlaiiCj4PNDB85NHqtektIV+QhRKFNruqCLuYfLQCGl/q01KZ5/qJlAKEe9y6wJ6318p4u1z2DAmm2ZZ32ttUsi9FRWiiwMwp+0oJfy9gC7bg3qAihvORFi54ATaW0OZSry5IRqvLSGxEV9LceAHlxnjBb2LDae92xYXurAPSqfmUBhLJvl6h7djt21Dc3nWCujUgPkUsOlf0Ui1eOpS1O2dKOoqtfVMHH284DD2e+5TttfBv5QXWfXVvdkWov+Zp0IDYsyJzLVj+vr6/Xo0aP17t279d//+39fZ2dn67e//e3/ex3Y06dPN2EfHx9vx+XKIvAm0IJwAVJ4/fr1XjbPAmZlCyE7EJ5e1gJcV/4AQa212zNX48X7EKr71RNOTqxK7Bklbik0j89bQXjd4KsxQELVNpNloiyCtXZvEbcAz87ONu/VeizyqyK3NMAYa3whZ3NaL25vnvlpogFq0qfj4+M9T1zerGR/ZbfWjhYolWAeoNKGU80gux4/VALc9y8vL7cawxpDfTEXFpgdEr0/eZojRqPzO9GNvljYntN71HjhWBuilverfPwjyxoqfWkSwjwX9U4U3PdPdkx99wQ9u7ra7UTQui2uRrXn7TUK0jd1aXSwtoD8UR9dn59qd55G8e23364XL15sXkjWwMBN4oMHDzYyU8PFIOZm2QHF4SE0fy+vMGEtOFsFnXVmnRQK07CxGUQe1rPL79Uj6YeTJcob1PhSFIrcEK7jrLE1eUVNmgmfz6nxqow0NVBkAfWST1GP67thv5yZn0080IVmmrSpfPPvh8bQ+dU3RqdIXbhcA14DWTnN6vwagLmhfqL2ojMyfPz48bboGT4hbQ0Qx1tH5LknJyd7We/OX/WuIS4ZaRO5zXWAj2yJQsGI7WMz1H78+PGWafW8s7Oz9erVq02uRWGHSnCguu5JNe4i4iZv5r09u5UKh9qdCOz58+cb2moHeV4PA1VL2Lfux2Qj+Zs+L0paa2e43KvZGkJRs6XNbCckWOH4XSg1YfMkTRvWTo8HgZV785boQ2FODZr+TQQqNNNXSMNmYeRwQyTzgTMzHtuVKEQXermTytu4yi0yErM+y+8NrcjMfOA5JofTgtHKAP/FMFah67yKoA/RFOX5ytm1JKDzyiGZMwbPta9fv976dHR0tGXaa7x6GCMZytjXMHtGw05jMc6WN5Qf01q7N8PwtsePH299bIKrRPzJyckWQWilhuiUU2kawupDkZ817vw31IgoiY2gQ+USZ6KmJ1f84Czkq1evtvKBFqj1PXj1WgbWUyjW2iltiX9NR+sxS+BNiwzRQQktWNWUPdQjdqtOoatWHqjPK1ehTYVfa3+XfhMTXdw1kjUIxoWj8azyDr0XPmqt/SppxuzJkydbiGDyuzWrJRYzI9Z5a6mBhEKNaCmCGpImB2QdZ4jTZ5uT6hM5z1ILTrGouaUBDeebBCDPSQyfnJxsBdPmho49efJkOyZnhm/k5fnG2JNda6QmAuzcNznVl7nSUX2jU4xyUf1EKSKgFpwWxWp98/yMEBi6uavFuA8hwMvLy/Xq1auP0Oft7e26uLjY47usw6kXU59+cBby+fPn2wDViHShetBM8RMAoZhghq/eq4ZwcmLCS9+rB+NFKVi9kVBstnI3DICFCS10/yXD19Mr24rumqHsFhqtyjxDqbXWHiqlqIpHmyWivMbajdgWlcyxhW7ReulpeQbPmuEA+RXy9x2BvGq9aENMc9nXrUFm7ltnVk/cMKgGowulWeAmRyZZfXR0tM3x7IPv1PhZmE4tLRpiEA/NpcXYI6U4FDxm+bcai5YM6D/HbF6bqdVX66kUwWwXFxcfnZCKoNf/hsOyqAxxuWVr8e3bt+uzzz7b/l45inBEDnXIa60tdC1FZD47Z8Yzs/2z3WnAfve7321v5Z7nHE3rX+82i1R1kNAeP368KbvrWkpQT97SjGbGTPqh+Lh97O523tbkXF5eblxE0+oT6dSotYShiwu6bHj1KQ/Zz423YQVlUZzKWPtOU9BNvVN0hlgGqImELtgSzM28Qll1JjUMJc0pWMsOmq2EbswFlHJ6erolJ9zPfJe3I18yZazLnc2QvtlRTou+kWsN3uT7Li93x6DXURwf77bX+Dd3eZyfn2/z4LOiQjLr+MwPg7/WrqTHWPWvIeTcY/vw4cP14MGDPV5ZDaWo4fp693Z76xNFcXm5Oxi0BxBAU/Tx/v372+m26rkYQM+xroo4cXLVrUYPngdRP3r0aG9uDrU7DdgXX3yxXr58ua6urrYMZLOMQhEKbHEITxgq7fT0dG9iWufiegu/Rw53wt2zpyLIbNRQEYyJmW81Kt9RRZoCna01QUdHu2LBmdyYB78VXfk3M5P1SgxhwzEFqhNdNmy5d2/3YhUK5PvdUCv0a2shpHC6yFbFNUNYQ8EQCRvna/XMeVFGCyHJv98vioFqGMOGGnWEsmUTlVXHPKuonhFgJFsiYN45Fn2kh/pTRNuwVR+mE5u60bXSUhqNwxF+FdnoC6csYqrh7JqtfpvHSde0oJysPLfyL3Fv3dY5ciIXFxd75ULkSc/olAgD/XBXu9OA/fnPf/5oT6CaL8rqX8lfg+7LPHljpF7DpBLTsiZTaSl534ikdeMnwXeCJQ+01rbUExEoYVbB+6/Iz0S1wLbhtN+bJeX1q9RFmpOPIgfoaPIwDXGFneTPK/uu5+pbF83c3VADL2QkP8rMWWnQTRXVGegN/7X+3nolzm2tte1NPcRdyrY1NCWDot/yMT2U8BDqZyCgDuOY3G55OeEeFMlY1yi7hiw9c75Nqc3irlObc9UIonN66CQYAGTyau7jGRcXFwezn5rici/P8QrGGmz9UEZhN4/mO7O2Dfqi6z+YA3ODvqnEDQtvCdrPQl5WvOUFthjg1Eq0Wqi+SzkYpSqM71OKCsFk1YP2bzM0mkfLNDlgsXZLTE9aqOGDkGqUKY3v9gQK1xYmVwmnJ6+sGvboS5XDM7tHrjJrPVX/3zBT+AHR+F4XfMPuetMiw6KvQ6F3k0T0RbhZeoJMje/29nbjaZvJqpGDFvp+04az5TqrQxwsudd5dA6MFbda+mQW+3YnQJGMMfZsrBaI0v/yrMJ1+gmBet7x8fFe9Tz91U86MbPJa32oAeXERDgNv4WDQlJzMMNqYzZ3OEHPppuAElvz5z//eY8r+1S704D13B4LEYF3fX2999IPyEkadSp7vUhflInkbSshPluJQsJaa6e0BK3Gx/1xLPVgBH5zc7Nevny554GULRR613sUFdzc3GzcgQMgKYrsH+VqdbMM4oTuNVI+L6GrXxCJEJZhFwKReevRalQod+v19NtPcitH1xC2pPgkrlvQ6jML3aK1kNpHDvD29nbbaiXkrvHyPQuh+2DJpUi399dfBmVu5/KTIWBc6sRub3fbjN6/f78hjdZeFZUwOGgM95zoCyclBCTv8sjV4+vr623PIkDQdWeOGdomSYqm6bqIgkGhw6WK1lobrSRB13Pg/Ox89ngsKJdOVVe6FsqvHmp3GrCvv/56Iy6b7gTBnz17timmgROe1ord6+v9CuS+eso9OkH1yFU+hsOEtbnftOglSGcI1nu2Cr/kZPclUhwCvrq62g6I6zswjYtM/K2GoqllC6snYXQiy1VAqL5DlhRD6+IomV1+SF8gLfs/8UEtXq2ym5MaiyY9GKaGVLztNIyer0+uWWt39FF3NiDaeXb3aDrffTxXJhDCNBZj5WhKAzCOJycf3mDO2HE+9HuendXnrLULIdVITaPVkIvsRAGeVaPa0iXGoTpxqLynTms6q667AgHfgar8/v79++3FN48ePVoXFxebznuWMHRy3M24F1UaK8dZvvlT7XvPxL+9vd24MJXdFXSNSjmjLhTw1LNYZgqPO/Dd1iY1kwElWHStjyo57L6e0exlDRllU4oAXejTFGArtyd3U68zD2gzoRR8osvG/pWB8ddwUljyMuHdBM1wNpwrX8IoldtkrLpH1fctlo6pxrMhkJR9kzCdP4c1MrjmpuPv86Hh8jmlD2oMqg+4uTpKC77zWMNXB1F+r/NDn5rdLVpuYqvJpxo2+uaen2oN02dFuiik+4PbZv2XOeEE6AADX32H9kuPzP62b4wrWujo6Gidn5/vHYRwiBYh5yb01lp7+22/+uqrdXR09MPOxP/222+33eTn5+d7e/Z69Gw5hk7S5ILAYh3kDRra1Xi5f2HmIf6qC1SoRmCIRtlLk16P0n2QDRdAfWNqHRSl8B2hQMfc2jd9c68ap8pI6+Kc3J5nzIwP2SiLaPhLyfRrhgOI7y4oxohB972SvtOgHx8fb4rLqPZNUhS9RLnrGO9ZI9R6rOvr670yEnNm3DNz5k3yDZt6PVm3GLb9IS+0CBla0E1ukM/9+/fXxcXFXiLBHOGfKruGmW3lXY21pDlnVeM4IwR/M34hJL21dmbNW+9XAFAHeXS02wvcc9U4nfZ7AgxgSClNHfT9+/fXs2fPtvFPiqntexHYycmH43EL70FjN693r4fuYuEpSuIyVo8ePdo7VsaEm4gS3DPk0ywKtT6M0vTmWsfNC2k4pZub/aOjFSpaeDVAUNBETBSp0J3xaAZ0ZvOKKqvoHQ8595rva0VMlenbt2+34sOJ/iC+osh68In0yLaorWOprFoz2HDZz3JXjNs09tULujHr0zjJ8mTGouK/4279UXWS41KuMREGpNM1cWiu3HfqYZFt57WOit5XXw4hdeNuGA3x9Dtrra1wd61dhDQ5QmtsolgGjY4U2UG3pTY6j3hEv3dM79+/X7///e/X7e3tD0NgFxcX68WLF5vnMFBkvkmYsNLbaHAQJfYoSKHsmzdv9rgG93J9kYTnNUxa68OuAcLXL5M5a7B43Hv37m0nbhwfH++9zPby8nLzolUMC4En9qwarypdEUlDkSJNSHEqbw0W1IofmFnL6cWLyCp7fYdGNYuvi5aRbRmLe1M05G0RCgRYDtEzbm5utu1prSubHn6Oba1dNlGTlq+DefLkyRb2tNxnrbXtVy2CFC00077W2vSy/WZonz59upeh1qdZouC6GhXjMZ8I8nKEHGcTDsZPb2cxrPtrE0w0otAnOtzwr06jVEa5tGkkOQz6ZPz0g74bbyOOhuHe/Vm5TgAz250G7PPPP1+/+93vtt31R0dH6+XLl5uBmm/uMQndz1WE0a0PFkTDmLkoixbqqWS4CLPX1TMgGrtQy5fwMGt9MEzexOy587VuNTpaXw/vmV20NzcfMpwNbQr9Pd8G5sqzXpXB7mvX6limd3eNUL73sjB6PE5bw6TyeXP7FUdEjpIPveeTJ0+2sMW8UXBZrDdv3uzxM4eQ5HyW+jJhRjkuhskcdyN2naH7+U51i6HVnNLw8OHDLSytrPSRAa8DORSh0C2GVgFw0V9DQvxvX348w3drhDOTkJi6wYF3jR1KIFn3zTSXb6MPNryfn59v97dmIXpOiUMhe+uCXDmk7jf+wQZM1hA6YWVbBiAt/ujRo72KaoapxKiaD167BbBVzoYvtkL0Ba4l/XhZwmsoA/1QyhoXnM8MjVrSwGBALY6zNoGqnt++fbspWHf7UxByqrJ5TvnDkq79bmE4xdE/E07xyxs0SVIkAiVQtC6IIooin/fv36+Li4tNduXUzFnrfVzf19fpLwNhzvEo9AbyrmEt91LOqjpJ5uYVUmkdXEsScHyTpK7jtBChMY7N83Cf5NnMqOshlHK6E1np66zKbyjYUJzRIVu61+jg6dOnW9aQ4zMvrdVimNfavWi3xu3i4mLb3M6RM+jsA3vAAEJdHLPx+1fDPkl9DrKntH6q3XkemMVDuPUK79+/32Dl48eP9wxILW7rs3Ta/xm1mcKu0uIbTL57t+hyeqxZrV1v1Xt7KWczbw0leg0k1/7VoOLw6jGm55vPr+dW82MMJfxN5CE+rgbDcyUqKLti1FZrHx8fbwkM/ZnZJ/fs/tGGxv5PWVvMXA7JYu8R1BAe4110MrmdhszCmUNeuQanzrMIWt/ItmHkpzKOzZDVwNC/Gf7OjF3De+UgEIbfFYZ27G0twi36K43Sou179+7tZVftc4Tg8JDWoetaEWCd6yukVRLf39+8ebPOzs42Q69/dKd6CvSU0unco5QOcb6zfW8lfssRTIRFeigcab0KwwANrfWBsPeig+kVTXC9Uzm0KuBa+1X/NRaNwfUdOuiue96yXAXFbcUw71K43XKOJihaM1cDdej3FkU2VGMUypl0xwIuAZLqZJuDmZpuoWersDVo2JxyOM0sFZmVg4EEfLfyopQztOYAy6cYS41TkSR5F020HR8fb1k6iMU8Vi/pyL179/Zqw8i/hp8MGf9mY7WeRjyJ/UmzuL8Gzamh6vFIa+3e6eB4KIZAyMuBFjDQi74TkiMij6I1TrmlF2Tv757rXrjL29vbLbNaDnuOuWF1eXP6M7ONtTl3AYE7DdhXX321Hj58uJ1C2Th2rd15TTgMC83kNdYWVuEhGjr6jlNTG5YwLNBOicfugetich2lLXLDa1QZupfQQm+IdCidbZE29COXbqL9VKNE/f9HkxMPZVF5tj2lvCsov9baC2v0r4Wh2ty/qpFrZVQZ86Cz1dj1EEFzVwTeHQrTYXEOENHp6emmNzVudSJr7bY1+Yz+NYPu56H3ZZYLurq62o5qIqsmABrmM3ZQbUNLaLjjLJdaPYEuyzO9evVqG6t+kS/ZTPRKh3tsFKfuOJsaJOMpx8opGpt1Qw4SeYeykfpSIw/59b50WalWI5DpbD/V7jRg/+yf/bONgMZZ6UQRi2MvSmgSyuvXr7drdbwnN7TjhZ9NwfPChwj/eiyLtAKcz6No9+/f3yalZx/VCMxzwLpYKEZr20rMu5eJLkHvurV2IXcTCkU7rejvhnYIFp/UTfIWXjNDLUJuGOF5rcXTrzoDn2nlCt2/Bt+ROQ3JGMbJ/5TXRCPw9L1f+9frJnruM+7du7fxt3SH8YSarq6u9k4RRVv0jP5puMwnowpJ2dRM7nShiLRo8vT0dG/3wlofsv+e8/jx4z3HM9dYObfq5tu3bzdjhaMyX+oZGS1Gp8ABipMx9hzh3bNnz7aDAtb6sDboaus7yY7utqqggMff9PHBgwdbP38wAvvmm2/W559/vil7QzmxPA5DzF1isPxNs2iEQcEPbfGZJB9BNPykIA09QNVa/8vLy726Hd5rnjtVEv358+d7mbOpgC9fvlyvX7/ejM48f4shgzbWWnsGo89Ffh7KGOEtZmuxYeWx1m4vHhlyEhYl5RFGIHH1C9qc5Sf9vcWYFJ8+1OuXB1prZ1QtHE4H0QzRm2dOp+OjDzWiSOImjeiB7LJMeIlx15MZY+Zv+tTTNXB+7Uv5p/7fZzM5VKM0SeqW5Lx8+XKveLfGWfRiDoTp7s8hNCyE6HpdnVWpAPwfIGDerq+vtzny3W4NamPQCgIKMBqtSACY7373U+1OA/ajH/1oy/JZwA3xeEBWWhhZ6Co97O8lhNfahW2TY5nbPdbaWeaJFkrQCl0bY5eMbSi61u7U1z6XUH2XcbKIjcEG1xpaCjFLKSzQGrHXr1/vpdCNCQIw8c0QMljlg8iI520msgiqmSp9WGu32M/OzvZI26LZyhu6pGQMl6Zv+tmEwtHR0fYCGEkU6Mw1EAmyvoilaBu3wnBxtDUY19fXWxZNWNvxqGucYV3Ddk6WoWOk3INu0X+ois6Yl/Ky+j1PPSk6LcFdB2FezT2AgO5hiDof/glzOWeymJyUnxyfM/afPXu2RSfuVb6tIazxtphb3wGOrj2h9tu3b7f3kt5VQrHW91Ti/9Vf/dXt559/vr799tttV3o9aif46GhXu9F9YpMrWGttIaVJ7ELDVcmOzGyX32e4Y8FNEpJC8vQN13jSSXivtTN6nqe/NXgl3MkEMuhzKRSjPvtuwt2D0vN2vSeFaLU0+deL9u+HnukaY+hnPe1jZoE4ln6/WefO+bzvDAGnty5f2b4K9eZ3O67pqT8VdkBlUz+F6JUlg8jxNOt7SJ79XVlNEUa5xNm/SWx3TDi1WSx9SO79rM8qumy5C13pnsoZ/Qj9qyvTQZY+WGuHKumL+W6ENiv+G0LiPX/729+utdYPq8R//vz5XgU+D8NYWLCMVy1z0dpa+3H/zABCFSwzYyJMJZBJjHtu0/UlcGtMZZT0uWHAXEi8irHypicnH3bY8zwlwY1F/8nI+Jo5q/L6rEoOkZEJFFLiHPlZctf1zZTxaA0xagwZCL/rt3s4IrlOivL3TeZFMWvtG5TOsWdZaC0CZrAtVNf67kTWE2H2sy4GfZ3yIYciSH+HVtQhNhqAkNt3ffMWr7V2vGNlU8NNv+oEO8f6BjnTK4t/opOjow/8Z5HORHQtEzLXa+3zT+0D5Fnjg0M2T3UmDJH1UD7WXLofOuP4+EO9pgL5ho9z18lsdxqwP/7xj9smaDwJpe2GXJ3volhrf1f7mzdv9lK3a+1exlAuqTCboAhgGgzCrtdpuNWJKelOmBMtgdnKKIp43F8Y/PTp03VxcfER4ugrwXiStXZZGK18EwM5DYt/lT8Falq/ix167dhdh7xWkLrWbsG4x6wpmhufez8LqkZBOz4+3sJBYy2qM6YaYIaupQd1SuVEGrqSURHlIV6Q3E9PT7dxFT1cXv5/7d1bbhs5EIVhZgDlwVEuC8j+N5Yl2EDg2AnmYfC1flUUzWsMsIAgsmyp2WRdTx2yX66OsPFeMTtwirJ0ZlJt6mhKCbLNkHq/t+bW+panN0vSmX3PexV0Z3aqHO31y8BX0tMlgaVYHN1tGbrWxTGy9VsHBNC5QjN8gGDx/v37gzh7T+4SWSmPCRFdgMGzjJRqilIMrcCj7tJal6fOMPLWz67f0sgiFvDlBFsK9/VMXUs9KH7y6dOn4/l+6vNpADVm3ZgC/HCtlop/evyV1LzgeXGeifGJ5uawkVx54zNVbNeiRJOw2e5eywmGPcfR/wsDFDPyORiH7+LEkR77HVVyc6+0aPZOz2YJ47rdjqQEBCRXT9roKP9pUkE4sYnbzq7orDRKrG7553XXiKEXWpklbvV5QgikSUAPSqzuteFV4mpLZI7WZzsOHfDSo9pUcF8lNtNBVVQ7ro+Pj1c+AVVFMLlVblfuZmB1PD19VDbVL9aGbslSIK9YWbtqOj6UrYowjafcFpNk0ijMxMy6EL7DolvIlji3ukjmAlPafQKbLaR7LkZXY690Efu7mTlwmpzwxElankrh63g40wKpzWQ7TqWj02UnhjWPselOBOvXErNYUukN5RqVflFH6G85s2ajNRTjV9aL6uYJVUbjoIC6OZtgdhsqUwfpXOekOo6T18+oXDi+4lXtVNOf6m35UGutI+s3d+ZAF5tefvny5bc165jMT3cWmGP8zpaVxlRox+4O4ylvbq1L2djrnU6ng9Ffx27OYMwqkgbmW3LXgYk8ohFFEY1EKBfF3Xh9fT2ejDIjPQUuZiDFplxTaXSselKjyawy+F9WUGyje//mViOKwRBbVswsseXXWut4vJRxz6hnUaTOFH9un/H3kyxZbliFgvt9FeRY3H8uHLPpeH2ngGOcLX163WYkrssJdMNvQdkaNoJmx8oZTFwVQdI93GJxtwRTKchO/N3r6+txmqsdIBXzXJih1ICW8w1Eri87m9kzqoK/t47deQE68Hu24nvQkjzhuxia+Wwi0GeF6sR6v2stEJav1Yqnc9yDBa2byquMAtl2pT9bO+vjdJY6p8fHx6NTbF4bvP4kdx3Y169fj6cvW7SfPy/PlTufz1el4vPz87Gx+XS6nEw6Faf1usylXJO11pUB+FlG1zT/VtuZABpFD4aCXzRb6i2HvJbRzQd+yjREnVuM4ToIDxj1fjtexu5fDWhiDBShStHsdirgFMqx1uU4ms+fP19lmGtdIvOPHz8OHlWNoDwr+IimAydJ2UV1D2oo49q/W91mv1vr+uRS9wUzEa0LbPvshw8fjuZSsTvS7mY77cbZUk22KGNyb5NsKavgpIxZ6Vs9QpxlU+6z5E/jlpF67T45Jfrfknhua2NvBdEFVutaUi9MsHuPbZcri6D67poyqep4qRddV0nKXJPy0m7JXQf27du39fDwsM7n85FhUc46GHvATqfTkX6SpoETMKQka13jHiazxluQeCpL32+DgAF1LI3oLc8YooXivIppMNouyFrXWRBFkll8/Pjxt9RaZlgntNY1A7ugaTOyGvVa66qEmRmDwNKNsy2lv3//fnS5ZplWjIfzZrxVym79KYF1rUvTgMOxZWRmVda75b6svtiJzLkNgkodZiEHY+HsbzkynzVfXZMaXrdszSdZtXSuUddOXNdr9tHxmG/jnlibNTLnhVTa2Zx0Jusxn+LknDSZM5IqG7Fesmx8Os6+2XG5kYJlEyCwSwN+78c9dy7vUb3+l8jqkD9ZCQXWPaSQf3IkQGzYRd+D3yhbHh4ejpttK306CotRRfD+09PTVaQooCtFLjdrRm6L1izMvdjA2jFRhCoykWY/Pz9f7cG0xaN438vLy/EUdMfsKiPm9TrP82EOa13O6xKJi7ettQ6nVWOGSRBOquuw1mWfJYPvxnqf5zjMi5KBg5DFtQtWPpPrNNtop7mvZ0NC4AJPwPVkEsUkhCUAAACcSURBVNayTmHumGBgpXS4N8bbkpqT4PS7D7I0iH737OS2IYMKMaXZlLUrp8sc/Pr1XzOpeB2HVmjn3bt3h7NCYtYcO5/PR0LSTeASlzbvev+lQ1m/VhtK3Y5pYpFz29Y9uUtk3bJly5a/We5mYFu2bNnyN8t2YFu2bHmzsh3Yli1b3qxsB7Zly5Y3K9uBbdmy5c3KdmBbtmx5s/IvSjj13Upl9AQAAAAASUVORK5CYII=\n",
+ "text/plain": [
+ "![](\"images/stapler_bbox.png\")
"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Some of the bounding boxes do have the stapler or at least most of it in the box, which can assist the classification process."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### R-CNN and Faster R-CNN\n",
+ "\n",
+ "[Ross Girshick et al.](https://arxiv.org/pdf/1311.2524.pdf) proposed a method where they use selective search to extract just 2000 regions from the image. Then the regions in bounding boxes are feed into a convolutional neural network to perform classification. The brief architecture can be shown as:\n",
+ "\n",
+ "![](\"images/RCNN.png\")
"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The problem with R-CNN is that one must pass each box independently through an image classifier thus it takes a huge amount of time to train the network. And meanwhile, the selective search is not that stable and sometimes may generate bad examples.\n",
+ "\n",
+ "Faster R-CNN solved the drawbacks of R-CNN by applying a faster object detection algorithm. Instead of feeding the region proposals to the CNN, we feed the input image to the CNN to generate a convolutional feature map. Then we identify the region of interests on the feature map and then reshape them into a fixed size with an ROI pooling layer so it can be put into another classifier. \n",
+ "\n",
+ "This algorithm is faster than R-CNN as the image is not frequently fed into the CNN to extract feature maps."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### Implementation\n",
+ "\n",
+ "For an ROI pooling layer, we implemented a simple demo of it as `pool_rois`. We can fake a simple feature map with `numpy`:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "\n",
+ "feature_maps_shape = (200, 100, 1)\n",
+ "feature_map = np.ones(feature_maps_shape, dtype='float32')\n",
+ "feature_map[200 - 1, 100 - 3, 0] = 50"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Note that the fake feature map is all 1 except for one spot with a value of 50. Now let's generate some regio of interests:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "roiss = np.asarray([[0.5, 0.2, 0.7, 0.4], [0.0, 0.0, 1.0, 1.0]])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Here we only made up two regions of interest. The first only crops some part of the image where all pixels are '1' which ranges from 0.5-0.7 of the length of the horizontal edge and 0.2-0.4 of verticle edge. The range of the second region is the whole image. Now let's pool a 3x7 area out of each region of interest."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "[array([[1., 1., 1., 1., 1., 1., 1.],\n",
+ " [1., 1., 1., 1., 1., 1., 1.],\n",
+ " [1., 1., 1., 1., 1., 1., 1.]], dtype=float32),\n",
+ " array([[ 1., 1., 1., 1., 1., 1., 1.],\n",
+ " [ 1., 1., 1., 1., 1., 1., 1.],\n",
+ " [ 1., 1., 1., 1., 1., 1., 50.]], dtype=float32)]"
+ ]
+ },
+ "execution_count": 14,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "pool_rois(feature_map, roiss, 3, 7)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "What we are expecting is that the second pooled region is different from the first one as there is an artificial feature-the '50' in its input. The printed result is exactly the same as we expected."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In order to try the whole algorithm of the Faster R-CNN, you can refer to [this GitHub repository](https://github.com/endernewton/tf-faster-rcnn) for more detailed guidance."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.6.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/notebooks/chapter24/images/RCNN.png b/notebooks/chapter24/images/RCNN.png
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diff --git a/obsolete_search4e.ipynb b/obsolete_search4e.ipynb
new file mode 100644
index 000000000..72981d49b
--- /dev/null
+++ b/obsolete_search4e.ipynb
@@ -0,0 +1,3835 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "button": false,
+ "new_sheet": false,
+ "run_control": {
+ "read_only": false
+ }
+ },
+ "source": [
+ "*Note: This is not yet ready, but shows the direction I'm leaning in for Fourth Edition Search.*\n",
+ "\n",
+ "# State-Space Search\n",
+ "\n",
+ "This notebook describes several state-space search algorithms, and how they can be used to solve a variety of problems. We start with a simple algorithm and a simple domain: finding a route from city to city. Later we will explore other algorithms and domains.\n",
+ "\n",
+ "## The Route-Finding Domain\n",
+ "\n",
+ "Like all state-space search problems, in a route-finding problem you will be given:\n",
+ "- A start state (for example, `'A'` for the city Arad).\n",
+ "- A goal state (for example, `'B'` for the city Bucharest).\n",
+ "- Actions that can change state (for example, driving from `'A'` to `'S'`).\n",
+ "\n",
+ "You will be asked to find:\n",
+ "- A path from the start state, through intermediate states, to the goal state.\n",
+ "\n",
+ "We'll use this map:\n",
+ "\n",
+ "![](\"http://robotics.cs.tamu.edu/dshell/cs625/images/map.jpg\")
\n",
+ "\n",
+ "A state-space search problem can be represented by a *graph*, where the vertices of the graph are the states of the problem (in this case, cities) and the edges of the graph are the actions (in this case, driving along a road).\n",
+ "\n",
+ "We'll represent a city by its single initial letter. \n",
+ "We'll represent the graph of connections as a `dict` that maps each city to a list of the neighboring cities (connected by a road). For now we don't explicitly represent the actions, nor the distances\n",
+ "between cities."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "button": false,
+ "collapsed": true,
+ "new_sheet": false,
+ "run_control": {
+ "read_only": false
+ }
+ },
+ "outputs": [],
+ "source": [
+ "romania = {\n",
+ " 'A': ['Z', 'T', 'S'],\n",
+ " 'B': ['F', 'P', 'G', 'U'],\n",
+ " 'C': ['D', 'R', 'P'],\n",
+ " 'D': ['M', 'C'],\n",
+ " 'E': ['H'],\n",
+ " 'F': ['S', 'B'],\n",
+ " 'G': ['B'],\n",
+ " 'H': ['U', 'E'],\n",
+ " 'I': ['N', 'V'],\n",
+ " 'L': ['T', 'M'],\n",
+ " 'M': ['L', 'D'],\n",
+ " 'N': ['I'],\n",
+ " 'O': ['Z', 'S'],\n",
+ " 'P': ['R', 'C', 'B'],\n",
+ " 'R': ['S', 'C', 'P'],\n",
+ " 'S': ['A', 'O', 'F', 'R'],\n",
+ " 'T': ['A', 'L'],\n",
+ " 'U': ['B', 'V', 'H'],\n",
+ " 'V': ['U', 'I'],\n",
+ " 'Z': ['O', 'A']}"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "button": false,
+ "new_sheet": false,
+ "run_control": {
+ "read_only": false
+ }
+ },
+ "source": [
+ "Suppose we want to get from `A` to `B`. Where can we go from the start state, `A`?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "button": false,
+ "new_sheet": false,
+ "run_control": {
+ "read_only": false
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "['Z', 'T', 'S']"
+ ]
+ },
+ "execution_count": 2,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "romania['A']"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "button": false,
+ "new_sheet": false,
+ "run_control": {
+ "read_only": false
+ }
+ },
+ "source": [
+ "We see that from `A` we can get to any of the three cities `['Z', 'T', 'S']`. Which should we choose? *We don't know.* That's the whole point of *search*: we don't know which immediate action is best, so we'll have to explore, until we find a *path* that leads to the goal. \n",
+ "\n",
+ "How do we explore? We'll start with a simple algorithm that will get us from `A` to `B`. We'll keep a *frontier*—a collection of not-yet-explored states—and expand the frontier outward until it reaches the goal. To be more precise:\n",
+ "\n",
+ "- Initially, the only state in the frontier is the start state, `'A'`.\n",
+ "- Until we reach the goal, or run out of states in the frontier to explore, do the following:\n",
+ " - Remove the first state from the frontier. Call it `s`.\n",
+ " - If `s` is the goal, we're done. Return the path to `s`.\n",
+ " - Otherwise, consider all the neighboring states of `s`. For each one:\n",
+ " - If we have not previously explored the state, add it to the end of the frontier.\n",
+ " - Also keep track of the previous state that led to this new neighboring state; we'll need this to reconstruct the path to the goal, and to keep us from re-visiting previously explored states.\n",
+ " \n",
+ "# A Simple Search Algorithm: `breadth_first`\n",
+ " \n",
+ "The function `breadth_first` implements this strategy:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "button": false,
+ "collapsed": true,
+ "new_sheet": false,
+ "run_control": {
+ "read_only": false
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from collections import deque # Doubly-ended queue: pop from left, append to right.\n",
+ "\n",
+ "def breadth_first(start, goal, neighbors):\n",
+ " \"Find a shortest sequence of states from start to the goal.\"\n",
+ " frontier = deque([start]) # A queue of states\n",
+ " previous = {start: None} # start has no previous state; other states will\n",
+ " while frontier:\n",
+ " s = frontier.popleft()\n",
+ " if s == goal:\n",
+ " return path(previous, s)\n",
+ " for s2 in neighbors[s]:\n",
+ " if s2 not in previous:\n",
+ " frontier.append(s2)\n",
+ " previous[s2] = s\n",
+ " \n",
+ "def path(previous, s): \n",
+ " \"Return a list of states that lead to state s, according to the previous dict.\"\n",
+ " return [] if (s is None) else path(previous, previous[s]) + [s]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "button": false,
+ "new_sheet": false,
+ "run_control": {
+ "read_only": false
+ }
+ },
+ "source": [
+ "A couple of things to note: \n",
+ "\n",
+ "1. We always add new states to the end of the frontier queue. That means that all the states that are adjacent to the start state will come first in the queue, then all the states that are two steps away, then three steps, etc.\n",
+ "That's what we mean by *breadth-first* search.\n",
+ "2. We recover the path to an `end` state by following the trail of `previous[end]` pointers, all the way back to `start`.\n",
+ "The dict `previous` is a map of `{state: previous_state}`. \n",
+ "3. When we finally get an `s` that is the goal state, we know we have found a shortest path, because any other state in the queue must correspond to a path that is as long or longer.\n",
+ "3. Note that `previous` contains all the states that are currently in `frontier` as well as all the states that were in `frontier` in the past.\n",
+ "4. If no path to the goal is found, then `breadth_first` returns `None`. If a path is found, it returns the sequence of states on the path.\n",
+ "\n",
+ "Some examples:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "button": false,
+ "new_sheet": false,
+ "run_control": {
+ "read_only": false
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "['A', 'S', 'F', 'B']"
+ ]
+ },
+ "execution_count": 4,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "breadth_first('A', 'B', romania)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "button": false,
+ "new_sheet": false,
+ "run_control": {
+ "read_only": false
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "['L', 'T', 'A', 'S', 'F', 'B', 'U', 'V', 'I', 'N']"
+ ]
+ },
+ "execution_count": 5,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "breadth_first('L', 'N', romania)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "button": false,
+ "new_sheet": false,
+ "run_control": {
+ "read_only": false
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "['N', 'I', 'V', 'U', 'B', 'F', 'S', 'A', 'T', 'L']"
+ ]
+ },
+ "execution_count": 6,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "breadth_first('N', 'L', romania)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "['E']"
+ ]
+ },
+ "execution_count": 7,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "breadth_first('E', 'E', romania)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "button": false,
+ "new_sheet": false,
+ "run_control": {
+ "read_only": false
+ }
+ },
+ "source": [
+ "Now let's try a different kind of problem that can be solved with the same search function.\n",
+ "\n",
+ "## Word Ladders Problem\n",
+ "\n",
+ "A *word ladder* problem is this: given a start word and a goal word, find the shortest way to transform the start word into the goal word by changing one letter at a time, such that each change results in a word. For example starting with `green` we can reach `grass` in 7 steps:\n",
+ "\n",
+ "`green` → `greed` → `treed` → `trees` → `tress` → `cress` → `crass` → `grass`\n",
+ "\n",
+ "We will need a dictionary of words. We'll use 5-letter words from the [Stanford GraphBase](http://www-cs-faculty.stanford.edu/~uno/sgb.html) project for this purpose. Let's get that file from aimadata."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "button": false,
+ "collapsed": true,
+ "new_sheet": false,
+ "run_control": {
+ "read_only": false
+ }
+ },
+ "outputs": [],
+ "source": [
+ "from search import *\n",
+ "sgb_words = open_data(\"EN-text/sgb-words.txt\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "button": false,
+ "new_sheet": false,
+ "run_control": {
+ "read_only": false
+ }
+ },
+ "source": [
+ "We can assign `WORDS` to be the set of all the words in this file:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "button": false,
+ "new_sheet": false,
+ "run_control": {
+ "read_only": false
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "5757"
+ ]
+ },
+ "execution_count": 9,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "WORDS = set(sgb_words.read().split())\n",
+ "len(WORDS)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "button": false,
+ "new_sheet": false,
+ "run_control": {
+ "read_only": false
+ }
+ },
+ "source": [
+ "And define `neighboring_words` to return the set of all words that are a one-letter change away from a given `word`:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "button": false,
+ "collapsed": true,
+ "new_sheet": false,
+ "run_control": {
+ "read_only": false
+ }
+ },
+ "outputs": [],
+ "source": [
+ "def neighboring_words(word):\n",
+ " \"All words that are one letter away from this word.\"\n",
+ " neighbors = {word[:i] + c + word[i+1:]\n",
+ " for i in range(len(word))\n",
+ " for c in 'abcdefghijklmnopqrstuvwxyz'\n",
+ " if c != word[i]}\n",
+ " return neighbors & WORDS"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "For example:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "button": false,
+ "new_sheet": false,
+ "run_control": {
+ "read_only": false
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "{'cello', 'hallo', 'hells', 'hullo', 'jello'}"
+ ]
+ },
+ "execution_count": 11,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "neighboring_words('hello')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "{'would'}"
+ ]
+ },
+ "execution_count": 12,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "neighboring_words('world')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "button": false,
+ "new_sheet": false,
+ "run_control": {
+ "read_only": false
+ }
+ },
+ "source": [
+ "Now we can create `word_neighbors` as a dict of `{word: {neighboring_word, ...}}`: "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {
+ "button": false,
+ "collapsed": true,
+ "new_sheet": false,
+ "run_control": {
+ "read_only": false
+ }
+ },
+ "outputs": [],
+ "source": [
+ "word_neighbors = {word: neighboring_words(word)\n",
+ " for word in WORDS}"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "button": false,
+ "new_sheet": false,
+ "run_control": {
+ "read_only": false
+ }
+ },
+ "source": [
+ "Now the `breadth_first` function can be used to solve a word ladder problem:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {
+ "button": false,
+ "new_sheet": false,
+ "run_control": {
+ "read_only": false
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "['green', 'greed', 'treed', 'trees', 'treys', 'trays', 'grays', 'grass']"
+ ]
+ },
+ "execution_count": 14,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "breadth_first('green', 'grass', word_neighbors)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {
+ "button": false,
+ "new_sheet": false,
+ "run_control": {
+ "read_only": false
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "['smart',\n",
+ " 'start',\n",
+ " 'stars',\n",
+ " 'sears',\n",
+ " 'bears',\n",
+ " 'beans',\n",
+ " 'brans',\n",
+ " 'brand',\n",
+ " 'braid',\n",
+ " 'brain']"
+ ]
+ },
+ "execution_count": 15,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "breadth_first('smart', 'brain', word_neighbors)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {
+ "button": false,
+ "new_sheet": false,
+ "run_control": {
+ "read_only": false
+ }
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "['frown',\n",
+ " 'flown',\n",
+ " 'flows',\n",
+ " 'slows',\n",
+ " 'slots',\n",
+ " 'slits',\n",
+ " 'spits',\n",
+ " 'spite',\n",
+ " 'smite',\n",
+ " 'smile']"
+ ]
+ },
+ "execution_count": 16,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "breadth_first('frown', 'smile', word_neighbors)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "button": false,
+ "new_sheet": false,
+ "run_control": {
+ "read_only": false
+ }
+ },
+ "source": [
+ "# More General Search Algorithms\n",
+ "\n",
+ "Now we'll embelish the `breadth_first` algorithm to make a family of search algorithms with more capabilities:\n",
+ "\n",
+ "1. We distinguish between an *action* and the *result* of an action.\n",
+ "3. We allow different measures of the cost of a solution (not just the number of steps in the sequence).\n",
+ "4. We search through the state space in an order that is more likely to lead to an optimal solution quickly.\n",
+ "\n",
+ "Here's how we do these things:\n",
+ "\n",
+ "1. Instead of having a graph of neighboring states, we instead have an object of type *Problem*. A Problem\n",
+ "has one method, `Problem.actions(state)` to return a collection of the actions that are allowed in a state,\n",
+ "and another method, `Problem.result(state, action)` that says what happens when you take an action.\n",
+ "2. We keep a set, `explored` of states that have already been explored. We also have a class, `Frontier`, that makes it efficient to ask if a state is on the frontier.\n",
+ "3. Each action has a cost associated with it (in fact, the cost can vary with both the state and the action).\n",
+ "4. The `Frontier` class acts as a priority queue, allowing the \"best\" state to be explored next.\n",
+ "We represent a sequence of actions and resulting states as a linked list of `Node` objects.\n",
+ "\n",
+ "The algorithm `breadth_first_search` is basically the same as `breadth_first`, but using our new conventions:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {
+ "button": false,
+ "collapsed": true,
+ "new_sheet": false,
+ "run_control": {
+ "read_only": false
+ }
+ },
+ "outputs": [],
+ "source": [
+ "def breadth_first_search(problem):\n",
+ " \"Search for goal; paths with least number of steps first.\"\n",
+ " if problem.is_goal(problem.initial): \n",
+ " return Node(problem.initial)\n",
+ " frontier = FrontierQ(Node(problem.initial), LIFO=False)\n",
+ " explored = set()\n",
+ " while frontier:\n",
+ " node = frontier.pop()\n",
+ " explored.add(node.state)\n",
+ " for action in problem.actions(node.state):\n",
+ " child = node.child(problem, action)\n",
+ " if child.state not in explored and child.state not in frontier:\n",
+ " if problem.is_goal(child.state):\n",
+ " return child\n",
+ " frontier.add(child)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Next is `uniform_cost_search`, in which each step can have a different cost, and we still consider first one os the states with minimum cost so far."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {
+ "button": false,
+ "collapsed": true,
+ "new_sheet": false,
+ "run_control": {
+ "read_only": false
+ }
+ },
+ "outputs": [],
+ "source": [
+ "def uniform_cost_search(problem, costfn=lambda node: node.path_cost):\n",
+ " frontier = FrontierPQ(Node(problem.initial), costfn)\n",
+ " explored = set()\n",
+ " while frontier:\n",
+ " node = frontier.pop()\n",
+ " if problem.is_goal(node.state):\n",
+ " return node\n",
+ " explored.add(node.state)\n",
+ " for action in problem.actions(node.state):\n",
+ " child = node.child(problem, action)\n",
+ " if child.state not in explored and child not in frontier:\n",
+ " frontier.add(child)\n",
+ " elif child in frontier and frontier.cost[child] < child.path_cost:\n",
+ " frontier.replace(child)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Finally, `astar_search` in which the cost includes an estimate of the distance to the goal as well as the distance travelled so far."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "metadata": {
+ "button": false,
+ "collapsed": true,
+ "new_sheet": false,
+ "run_control": {
+ "read_only": false
+ }
+ },
+ "outputs": [],
+ "source": [
+ "def astar_search(problem, heuristic):\n",
+ " costfn = lambda node: node.path_cost + heuristic(node.state)\n",
+ " return uniform_cost_search(problem, costfn)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "button": false,
+ "new_sheet": false,
+ "run_control": {
+ "read_only": false
+ }
+ },
+ "source": [
+ "# Search Tree Nodes\n",
+ "\n",
+ "The solution to a search problem is now a linked list of `Node`s, where each `Node`\n",
+ "includes a `state` and the `path_cost` of getting to the state. In addition, for every `Node` except for the first (root) `Node`, there is a previous `Node` (indicating the state that lead to this `Node`) and an `action` (indicating the action taken to get here)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 20,
+ "metadata": {
+ "button": false,
+ "collapsed": true,
+ "new_sheet": false,
+ "run_control": {
+ "read_only": false
+ }
+ },
+ "outputs": [],
+ "source": [
+ "class Node(object):\n",
+ " \"\"\"A node in a search tree. A search tree is spanning tree over states.\n",
+ " A Node contains a state, the previous node in the tree, the action that\n",
+ " takes us from the previous state to this state, and the path cost to get to \n",
+ " this state. If a state is arrived at by two paths, then there are two nodes \n",
+ " with the same state.\"\"\"\n",
+ "\n",
+ " def __init__(self, state, previous=None, action=None, step_cost=1):\n",
+ " \"Create a search tree Node, derived from a previous Node by an action.\"\n",
+ " self.state = state\n",
+ " self.previous = previous\n",
+ " self.action = action\n",
+ " self.path_cost = 0 if previous is None else (previous.path_cost + step_cost)\n",
+ "\n",
+ " def __repr__(self): return \"![](\"files/images/sprinklernet.jpg\")
\n",
"\n",
- "We store the samples on the observations. Let us find **P(Rain=True)**"
+ "Traversing the graph in topological order is important.\n",
+ "There are two possible topological orderings for this particular directed acyclic graph.\n",
+ "