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+ + Week 42 Convolutional and Recurrent Neural Networks and Autoencoders +
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Week 42 Convolutional and Recurrent Neural Networks and Autoencoders

+ +

+ + +

+Morten Hjorth-Jensen [1, 2] +
+ +

+ + +

[1] Department of Physics, University of Oslo
+
[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University
+
+

+

Oct 10, 2020

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+ + +

Read »

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+ © 1999-2020, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license +
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+ + + + +

Plan for week 42

+ + + +Reading suggestions for both days: Aurelien Geron's chapters 13 and 14. Autoencoders are discussed in chapter 15 of Geron's text. + +

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+ + + + +

Convolutional Neural Networks (recognizing images)

+ +

+Convolutional neural networks (CNNs) were developed during the last +decade of the previous century, with a focus on character recognition +tasks. Nowadays, CNNs are a central element in the spectacular success +of deep learning methods. The success in for example image +classifications have made them a central tool for most machine +learning practitioners. + +

+CNNs are very similar to ordinary Neural Networks. +They are made up of neurons that have learnable weights and +biases. Each neuron receives some inputs, performs a dot product and +optionally follows it with a non-linearity. The whole network still +expresses a single differentiable score function: from the raw image +pixels on one end to class scores at the other. And they still have a +loss function (for example Softmax) on the last (fully-connected) layer +and all the tips/tricks we developed for learning regular Neural +Networks still apply (back propagation, gradient descent etc etc). + +

+What is the difference? CNN architectures make the explicit assumption that +the inputs are images, which allows us to encode certain properties +into the architecture. These then make the forward function more +efficient to implement and vastly reduce the amount of parameters in +the network. + +

+Here we provide only a superficial overview, for the more interested, we recommend highly the course +IN5400 – Machine Learning for Image Analysis +and the slides of CS231. + +

+Another good read is the article here https://arxiv.org/pdf/1603.07285.pdf. + +

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+ + + + +

Regular NNs don’t scale well to full images

+ +

+As an example, consider +an image of size \( 32\times 32\times 3 \) (32 wide, 32 high, 3 color channels), so a +single fully-connected neuron in a first hidden layer of a regular +Neural Network would have \( 32\times 32\times 3 = 3072 \) weights. This amount still +seems manageable, but clearly this fully-connected structure does not +scale to larger images. For example, an image of more respectable +size, say \( 200\times 200\times 3 \), would lead to neurons that have +\( 200\times 200\times 3 = 120,000 \) weights. + +

+We could have +several such neurons, and the parameters would add up quickly! Clearly, +this full connectivity is wasteful and the huge number of parameters +would quickly lead to possible overfitting. + +

+

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+

Figure 1: A regular 3-layer Neural Network.

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+ + + + +

3D volumes of neurons

+ +

+Convolutional Neural Networks take advantage of the fact that the +input consists of images and they constrain the architecture in a more +sensible way. + +

+In particular, unlike a regular Neural Network, the +layers of a CNN have neurons arranged in 3 dimensions: width, +height, depth. (Note that the word depth here refers to the third +dimension of an activation volume, not to the depth of a full Neural +Network, which can refer to the total number of layers in a network.) + +

+To understand it better, the above example of an image +with an input volume of +activations has dimensions \( 32\times 32\times 3 \) (width, height, +depth respectively). + +

+The neurons in a layer will +only be connected to a small region of the layer before it, instead of +all of the neurons in a fully-connected manner. Moreover, the final +output layer could for this specific image have dimensions \( 1\times 1 \times 10 \), +because by the +end of the CNN architecture we will reduce the full image into a +single vector of class scores, arranged along the depth +dimension. + +

+

+
+

Figure 2: A CNN arranges its neurons in three dimensions (width, height, depth), as visualized in one of the layers. Every layer of a CNN transforms the 3D input volume to a 3D output volume of neuron activations. In this example, the red input layer holds the image, so its width and height would be the dimensions of the image, and the depth would be 3 (Red, Green, Blue channels).

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+ + + + +

Layers used to build CNNs

+ +

+A simple CNN is a sequence of layers, and every layer of a CNN +transforms one volume of activations to another through a +differentiable function. We use three main types of layers to build +CNN architectures: Convolutional Layer, Pooling Layer, and +Fully-Connected Layer (exactly as seen in regular Neural Networks). We +will stack these layers to form a full CNN architecture. + +

+A simple CNN for image classification could have the architecture: + +

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Transforming images

+ +

+CNNs transform the original image layer by layer from the original +pixel values to the final class scores. + +

+Observe that some layers contain +parameters and other don’t. In particular, the CNN layers perform +transformations that are a function of not only the activations in the +input volume, but also of the parameters (the weights and biases of +the neurons). On the other hand, the RELU/POOL layers will implement a +fixed function. The parameters in the CONV/FC layers will be trained +with gradient descent so that the class scores that the CNN computes +are consistent with the labels in the training set for each image. + +

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+ + + + +

CNNs in brief

+ +

+In summary: + +

+ +For more material on convolutional networks, we strongly recommend +the course +IN5400 – Machine Learning for Image Analysis +and the slides of CS231 which is taught at Stanford University (consistently ranked as one of the top computer science programs in the world). Michael Nielsen's book is a must read, in particular chapter 6 which deals with CNNs. + +

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+ + + + +

CNNs in more detail, building convolutional neural networks in Tensorflow and Keras

+ +

+As discussed above, CNNs are neural networks built from the assumption that the inputs +to the network are 2D images. This is important because the number of features or pixels in images +grows very fast with the image size, and an enormous number of weights and biases are needed in order to build an accurate network. + +

+As before, we still have our input, a hidden layer and an output. What's novel about convolutional networks +are the convolutional and pooling layers stacked in pairs between the input and the hidden layer. +In addition, the data is no longer represented as a 2D feature matrix, instead each input is a number of 2D +matrices, typically 1 for each color dimension (Red, Green, Blue). + +

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+ + + + +

Setting it up

+ +

+It means that to represent the entire +dataset of images, we require a 4D matrix or tensor. This tensor has the dimensions: +$$ +(n_{inputs},\, n_{pixels, width},\, n_{pixels, height},\, depth) . +$$ + +

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+ + + + +

The MNIST dataset again

+ +

+The MNIST dataset consists of grayscale images with a pixel size of +\( 28\times 28 \), meaning we require \( 28 \times 28 = 724 \) weights to each +neuron in the first hidden layer. + +

+If we were to analyze images of size \( 128\times 128 \) we would require +\( 128 \times 128 = 16384 \) weights to each neuron. Even worse if we were +dealing with color images, as most images are, we have an image matrix +of size \( 128\times 128 \) for each color dimension (Red, Green, Blue), +meaning 3 times the number of weights \( = 49152 \) are required for every +single neuron in the first hidden layer. + +

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+ + + + +

Strong correlations

+ +

+Images typically have strong local correlations, meaning that a small +part of the image varies little from its neighboring regions. If for +example we have an image of a blue car, we can roughly assume that a +small blue part of the image is surrounded by other blue regions. + +

+Therefore, instead of connecting every single pixel to a neuron in the +first hidden layer, as we have previously done with deep neural +networks, we can instead connect each neuron to a small part of the +image (in all 3 RGB depth dimensions). The size of each small area is +fixed, and known as a receptive. + +

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+ + + + +

Layers of a CNN

+The layers of a convolutional neural network arrange neurons in 3D: width, height and depth. +The input image is typically a square matrix of depth 3. + +

+A convolution is performed on the image which outputs +a 3D volume of neurons. The weights to the input are arranged in a number of 2D matrices, known as filters. + +

+Each filter slides along the input image, taking the dot product +between each small part of the image and the filter, in all depth +dimensions. This is then passed through a non-linear function, +typically the Rectified Linear (ReLu) function, which serves as the +activation of the neurons in the first convolutional layer. This is +further passed through a pooling layer, which reduces the size of the +convolutional layer, e.g. by taking the maximum or average across some +small regions, and this serves as input to the next convolutional +layer. + +

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+ + + + +

Systematic reduction

+ +

+By systematically reducing the size of the input volume, through +convolution and pooling, the network should create representations of +small parts of the input, and then from them assemble representations +of larger areas. The final pooling layer is flattened to serve as +input to a hidden layer, such that each neuron in the final pooling +layer is connected to every single neuron in the hidden layer. This +then serves as input to the output layer, e.g. a softmax output for +classification. + +

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+ + + + +

Prerequisites: Collect and pre-process data

+

+ + +

# import necessary packages
+import numpy as np
+import matplotlib.pyplot as plt
+from sklearn import datasets
+
+
+# ensure the same random numbers appear every time
+np.random.seed(0)
+
+# display images in notebook
+%matplotlib inline
+plt.rcParams['figure.figsize'] = (12,12)
+
+
+# download MNIST dataset
+digits = datasets.load_digits()
+
+# define inputs and labels
+inputs = digits.images
+labels = digits.target
+
+# RGB images have a depth of 3
+# our images are grayscale so they should have a depth of 1
+inputs = inputs[:,:,:,np.newaxis]
+
+print("inputs = (n_inputs, pixel_width, pixel_height, depth) = " + str(inputs.shape))
+print("labels = (n_inputs) = " + str(labels.shape))
+
+
+# choose some random images to display
+n_inputs = len(inputs)
+indices = np.arange(n_inputs)
+random_indices = np.random.choice(indices, size=5)
+
+for i, image in enumerate(digits.images[random_indices]):
+    plt.subplot(1, 5, i+1)
+    plt.axis('off')
+    plt.imshow(image, cmap=plt.cm.gray_r, interpolation='nearest')
+    plt.title("Label: %d" % digits.target[random_indices[i]])
+plt.show()
+
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+ + + + +

Importing Keras and Tensorflow

+

+ + +

from tensorflow.keras import datasets, layers, models
+from tensorflow.keras.layers import Input
+from tensorflow.keras.models import Sequential      #This allows appending layers to existing models
+from tensorflow.keras.layers import Dense           #This allows defining the characteristics of a particular layer
+from tensorflow.keras import optimizers             #This allows using whichever optimiser we want (sgd,adam,RMSprop)
+from tensorflow.keras import regularizers           #This allows using whichever regularizer we want (l1,l2,l1_l2)
+from tensorflow.keras.utils import to_categorical   #This allows using categorical cross entropy as the cost function
+#from tensorflow.keras import Conv2D
+#from tensorflow.keras import MaxPooling2D
+#from tensorflow.keras import Flatten
+
+from sklearn.model_selection import train_test_split
+
+# representation of labels
+labels = to_categorical(labels)
+
+# split into train and test data
+# one-liner from scikit-learn library
+train_size = 0.8
+test_size = 1 - train_size
+X_train, X_test, Y_train, Y_test = train_test_split(inputs, labels, train_size=train_size,
+                                                    test_size=test_size)
+
+

+

+ +

+ + +
+ + + + + + + +
+ +
+ + + + + + diff --git a/doc/pub/week42/html/._week42-bs016.html b/doc/pub/week42/html/._week42-bs016.html new file mode 100644 index 000000000..dfec01b28 --- /dev/null +++ b/doc/pub/week42/html/._week42-bs016.html @@ -0,0 +1,244 @@ + + + + + + + + +Week 42 Convolutional and Recurrent Neural Networks and Autoencoders + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + Week 42 Convolutional and Recurrent Neural Networks and Autoencoders +
+ +
+ +
+
+ + +
+ +

 

 

 

+ + + + +

Running with Keras

+ +

+ + +

def create_convolutional_neural_network_keras(input_shape, receptive_field,
+                                              n_filters, n_neurons_connected, n_categories,
+                                              eta, lmbd):
+    model = Sequential()
+    model.add(layers.Conv2D(n_filters, (receptive_field, receptive_field), input_shape=input_shape, padding='same',
+              activation='relu', kernel_regularizer=regularizers.l2(lmbd)))
+    model.add(layers.MaxPooling2D(pool_size=(2, 2)))
+    model.add(layers.Flatten())
+    model.add(layers.Dense(n_neurons_connected, activation='relu', kernel_regularizer=regularizers.l2(lmbd)))
+    model.add(layers.Dense(n_categories, activation='softmax', kernel_regularizer=regularizers.l2(lmbd)))
+    
+    sgd = optimizers.SGD(lr=eta)
+    model.compile(loss='categorical_crossentropy', optimizer=sgd, metrics=['accuracy'])
+    
+    return model
+
+epochs = 100
+batch_size = 100
+input_shape = X_train.shape[1:4]
+receptive_field = 3
+n_filters = 10
+n_neurons_connected = 50
+n_categories = 10
+
+eta_vals = np.logspace(-5, 1, 7)
+lmbd_vals = np.logspace(-5, 1, 7)
+
+

+

+ +

+ + +
+ + + + + + + +
+ +
+ + + + + + diff --git a/doc/pub/week42/html/._week42-bs017.html b/doc/pub/week42/html/._week42-bs017.html new file mode 100644 index 000000000..b0a93025f --- /dev/null +++ b/doc/pub/week42/html/._week42-bs017.html @@ -0,0 +1,233 @@ + + + + + + + + +Week 42 Convolutional and Recurrent Neural Networks and Autoencoders + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + Week 42 Convolutional and Recurrent Neural Networks and Autoencoders +
+ +
+ +
+
+ + +
+ +

 

 

 

+ + + + +

Final part

+ +

+ + +

CNN_keras = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)
+        
+for i, eta in enumerate(eta_vals):
+    for j, lmbd in enumerate(lmbd_vals):
+        CNN = create_convolutional_neural_network_keras(input_shape, receptive_field,
+                                              n_filters, n_neurons_connected, n_categories,
+                                              eta, lmbd)
+        CNN.fit(X_train, Y_train, epochs=epochs, batch_size=batch_size, verbose=0)
+        scores = CNN.evaluate(X_test, Y_test)
+        
+        CNN_keras[i][j] = CNN
+        
+        print("Learning rate = ", eta)
+        print("Lambda = ", lmbd)
+        print("Test accuracy: %.3f" % scores[1])
+        print()
+
+

+

+ +

+ + +
+ + + + + + + +
+ +
+ + + + + + diff --git a/doc/pub/week42/html/._week42-bs018.html b/doc/pub/week42/html/._week42-bs018.html new file mode 100644 index 000000000..fd562927a --- /dev/null +++ b/doc/pub/week42/html/._week42-bs018.html @@ -0,0 +1,246 @@ + + + + + + + + +Week 42 Convolutional and Recurrent Neural Networks and Autoencoders + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + Week 42 Convolutional and Recurrent Neural Networks and Autoencoders +
+ +
+ +
+
+ + +
+ +

 

 

 

+ + + + +

Final visualization

+ +

+ + +

# visual representation of grid search
+# uses seaborn heatmap, could probably do this in matplotlib
+import seaborn as sns
+
+sns.set()
+
+train_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))
+test_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))
+
+for i in range(len(eta_vals)):
+    for j in range(len(lmbd_vals)):
+        CNN = CNN_keras[i][j]
+
+        train_accuracy[i][j] = CNN.evaluate(X_train, Y_train)[1]
+        test_accuracy[i][j] = CNN.evaluate(X_test, Y_test)[1]
+
+        
+fig, ax = plt.subplots(figsize = (10, 10))
+sns.heatmap(train_accuracy, annot=True, ax=ax, cmap="viridis")
+ax.set_title("Training Accuracy")
+ax.set_ylabel("$\eta$")
+ax.set_xlabel("$\lambda$")
+plt.show()
+
+fig, ax = plt.subplots(figsize = (10, 10))
+sns.heatmap(test_accuracy, annot=True, ax=ax, cmap="viridis")
+ax.set_title("Test Accuracy")
+ax.set_ylabel("$\eta$")
+ax.set_xlabel("$\lambda$")
+plt.show()
+
+

+

+ +

+ + +
+ + + + + + + +
+ +
+ + + + + + diff --git a/doc/pub/week42/html/._week42-bs019.html b/doc/pub/week42/html/._week42-bs019.html new file mode 100644 index 000000000..8fdfb544c --- /dev/null +++ b/doc/pub/week42/html/._week42-bs019.html @@ -0,0 +1,231 @@ + + + + + + + + +Week 42 Convolutional and Recurrent Neural Networks and Autoencoders + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + Week 42 Convolutional and Recurrent Neural Networks and Autoencoders +
+ +
+ +
+
+ + +
+ +

 

 

 

+ + + + +

Recurrent neural networks: Overarching view

+ +

+Till now our focus has been, including convolutional neural networks +as well, on feedforward neural networks. The output or the activations +flow only in one direction, from the input layer to the output layer. + +

+A recurrent neural network (RNN) looks very much like a feedforward +neural network, except that it also has connections pointing +backward. + +

+RNNs are used to analyze time series data such as stock prices, and +tell you when to buy or sell. In autonomous driving systems, they can +anticipate car trajectories and help avoid accidents. More generally, +they can work on sequences of arbitrary lengths, rather than on +fixed-sized inputs like all the nets we have discussed so far. For +example, they can take sentences, documents, or audio samples as +input, making them extremely useful for natural language processing +systems such as automatic translation and speech-to-text. + +

+

+ +

+ + +
+ + + + + + + +
+ +
+ + + + + + diff --git a/doc/pub/week42/html/._week42-bs020.html b/doc/pub/week42/html/._week42-bs020.html new file mode 100644 index 000000000..ed1225536 --- /dev/null +++ b/doc/pub/week42/html/._week42-bs020.html @@ -0,0 +1,223 @@ + + + + + + + + +Week 42 Convolutional and Recurrent Neural Networks and Autoencoders + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + Week 42 Convolutional and Recurrent Neural Networks and Autoencoders +
+ +
+ +
+
+ + +
+ +

 

 

 

+ + + + +

Set up of an RNN

+ +

+The figure here displays a simple example of an RNN, with inputs \( x_t \) +at a given time \( t \) and outputs \( y_t \). Introducing time as a variable +offers an intutitive way of understanding these networks. In addition +to the inputs \( x_t \), the layer at a time \( t \) receives also as input +the output from the previous layer \( t-1 \), that is \( y_{t1} \). + +

+This means also that we need to have weights that link both the inputs +\( x_t \) to the outputs \( y_t \) as well as weights that link the output +from the previous time \( y_{t-1} \) and \( y_t \). The figure here shows an +example of a simple RNN. + +

+

+ +

+ + +
+ + + + + + + +
+ +
+ + + + + + diff --git a/doc/pub/week42/html/._week42-bs021.html b/doc/pub/week42/html/._week42-bs021.html new file mode 100644 index 000000000..d66827982 --- /dev/null +++ b/doc/pub/week42/html/._week42-bs021.html @@ -0,0 +1,220 @@ + + + + + + + + +Week 42 Convolutional and Recurrent Neural Networks and Autoencoders + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + Week 42 Convolutional and Recurrent Neural Networks and Autoencoders +
+ +
+ +
+
+ + +
+ +

 

 

 

+ + + + +

Solving differential equations and eigenvalue problems with RNNs

+ +

+In our discussions of ordinary differential equations and partial +differential equations using neural networks. Here we will discuss how +we can solve say ordinary differential equations and eigenvalue +problems using RNNs. Eigenvalue problems can be solved using RNNs by +rewriting such a problems as a non-linear differential equation. + +

+Instead of starting with a well-known ordinary differential equation, +we start directly with an eigenvaule problem. + +

+

+ +

+ + +
+ + + + + + + +
+ +
+ + + + + + diff --git a/doc/pub/week42/html/._week42-bs022.html b/doc/pub/week42/html/._week42-bs022.html new file mode 100644 index 000000000..b9642e0f8 --- /dev/null +++ b/doc/pub/week42/html/._week42-bs022.html @@ -0,0 +1,211 @@ + + + + + + + + +Week 42 Convolutional and Recurrent Neural Networks and Autoencoders + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + Week 42 Convolutional and Recurrent Neural Networks and Autoencoders +
+ +
+ +
+
+ + +
+ +

 

 

 

+ + + + +

Long-Short Time Memory

+ +

+Discussions about dynamic unrolling through time. discuss memory cells, input and output + +

+

+ +

+ + +
+ + + + + + + +
+ +
+ + + + + + diff --git a/doc/pub/week42/html/._week42-bs023.html b/doc/pub/week42/html/._week42-bs023.html new file mode 100644 index 000000000..589adfa06 --- /dev/null +++ b/doc/pub/week42/html/._week42-bs023.html @@ -0,0 +1,234 @@ + + + + + + + + +Week 42 Convolutional and Recurrent Neural Networks and Autoencoders + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + Week 42 Convolutional and Recurrent Neural Networks and Autoencoders +
+ +
+ +
+
+ + +
+ +

 

 

 

+ + + + +

Autoencoders: Overarching view

+ +

+Autoencoders are artificial neural networks capable of learning +efficient representations of the input data (these representations are called codings) without +any supervision (i.e., the training set is unlabeled). These codings +typically have a much lower dimensionality than the input data, making +autoencoders useful for dimensionality reduction. + +

+More importantly, autoencoders act as powerful feature detectors, and +they can be used for unsupervised pretraining of deep neural networks. + +

+Lastly, they are capable of randomly generating new data that looks +very similar to the training data; this is called a generative +model. For example, you could train an autoencoder on pictures of +faces, and it would then be able to generate new faces. Surprisingly, +autoencoders work by simply learning to copy their inputs to their +outputs. This may sound like a trivial task, but we will see that +constraining the network in various ways can make it rather +difficult. For example, you can limit the size of the internal +representation, or you can add noise to the inputs and train the +network to recover the original inputs. These constraints prevent the +autoencoder from trivially copying the inputs directly to the outputs, +which forces it to learn efficient ways of representing the data. In +short, the codings are byproducts of the autoencoder’s attempt to +learn the identity function under some constraints. + +

+

+ +

+ + +
+ + + + + + + +
+ +
+ + + + + + diff --git a/doc/pub/week42/html/._week42-bs024.html b/doc/pub/week42/html/._week42-bs024.html new file mode 100644 index 000000000..e4e5ca22e --- /dev/null +++ b/doc/pub/week42/html/._week42-bs024.html @@ -0,0 +1,206 @@ + + + + + + + + +Week 42 Convolutional and Recurrent Neural Networks and Autoencoders + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + Week 42 Convolutional and Recurrent Neural Networks and Autoencoders +
+ +
+ +
+
+ + +
+ +

 

 

 

+ + + + +

Simple examples of Autoencoders

+ +

+ +

+ +

+ + +
+ + + + + + + +
+ +
+ + + + + + diff --git a/doc/pub/week42/html/figslides/cnn.jpeg b/doc/pub/week42/html/figslides/cnn.jpeg new file mode 100644 index 0000000000000000000000000000000000000000..67bf3ced745f869c2069894442b02cb5c177b4c5 GIT binary patch literal 24437 zcmeFZcU)87w>Eev3R0y>6QTm5qN37k1f)w5qze&|E+En(1cLOAfPw;oQbmN&0#ZW< zLFq+8O+b1{5JG^EO#IHwz3=_qdFQ_G%x69`f6O5}IegB}Icp_*@Aa%_Jtvf3lm+0d zo|di_KtlrnG}J$Uf&rdrLS3Bzz`y{w1^@sfaEgW#prh{nbDTy1IQ7py0O-*O{@cC@ z&6R)eL(BE=`_#UFH|m-Hy-}tC4S=`b3bKiND@`+JIy|RtRWEdwZ_2fm^8K!f*eEb4p zm&LDKy(TRqD<`j@sBuqIOIt@*&-9_0xrL>bwZl_KCubK|Hy>X={{ZOA!0?F3sOXs3 zxYV>aZ__j0z0b_cFDNW3{#^2(ZT9jNIxepDNqVh)9{>c%Hl%W;!P-jS<8Db?qO|{>K~(`@iJbzd82r zexU&tIvVPiN5=txffLibxGTVaZ0dLE(?XSo039IpIYS_B%Yu-ZzVm48I*EUwe_p_K z;?7Ghx7tbXHaY{6KL6u@S3N)ENw*BylS%N;FrV>lk_bky{(2Mtvt=Ro&RgdNJ4oge zKWF@%SGDWrH>5oT4RA&Ar*n(jc%rggg~t-14 z2rb!d+&!X;i#NV!Z1o-)0|0)aTV+O}sG2fF&kYC5(Y&F;;pNdh-2j=9fhyWAL&gU~ zuQswLU%@np(SGO0|zwZjmA0!{dqN 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