FYS-STK4155/doc/Programs/ANN/perceptron.ipynb

Day 16 In-Class Assignment: Introduction to Machine Learning

Image from: https://goo.gl/ypY9G2

1. Scientific motivation
   • Classifying data (iris types)
2. Modeling tools
   • Machine Learning (Perceptron)
3. Programming concepts
   • Creating Classes and re-usable code
   • Pulling in data from outside sources
   • Using external libraries

Agenda for today's class

1. Review of pre-class assignment
2. Problem Statement
3. Basics of the perceptron model
4. Loading and inspecting the data
5. Building the perceptron model
6. Plotting the decision boundary

---

1. Review of pre-class assignment

Were there any specific questions that came up in the pre-class assignment?

2. Problem Statement

We want to build a model that can accurately classifying two types of flowers based off of measurements we have collected. Building this model will allow us to understand how basic machine learning models learn and what exactly is happening 'under the hood'. It will provide a slightly more intuitive view of machine learning and make it seem as less of a black box and more of a tool that we understand.

3. The Basics of the Perceptron Model

The perceptron is a what is known as a basic binary classifier. It takes in a set of training data that is linerally separable and then computes a set of weights and a bias term to apply to input data as to properly classify it. Perceptrons only works for data that contains two classes and is linearly separable. For data that does not have these properties, the classifier cannot properly learn the weights and bias term.

Since the perceptron is based on linearly separable data, we can think of the model as trying to learn the slope of a line, y = m~x + b. However in machine learning, we usually define X to be an input vector, which is a 1 by N matrix, where N is the number of measurements or "features" for a given sample. Then, we can create a similar matrix of weights, W, also of length N, and re-write our equation to be:

Y = W \cdot X + B

where Y represents the resulting classification, consisting of either -1 or 1, depending on the output of W \cdot X, the dot product of W and X, and B represents the bias term. More explicitly, we can look at this in a matrix format:

Y = \begin{bmatrix} w_1 & w_2 & \dots & w_n \end{bmatrix} \cdot \begin{bmatrix} x_1 \\ x_2 \\ \vdots \\ x_n \end{bmatrix} + B

But, how do we go about learning the weights of the model?

We learn the model weights by attempting to predict the class of our input data using an initial guess for the weights, and then update our weight values based on our prediction. We can define a "step size" for how much we change our weight between subsequent guess in the following way:

step_size = eta * (target class - predicted class)

Then, using our "step size", we then update all of our weights by multiplying our step size times the corresponding feature values:

w_{1,new} = w_{1,old} + (\mathrm{step~size} \times x_{1,i}) w_{2,new} = w_{2,old} + (\mathrm{step~size} \times x_{2,i}) \vdots w_{N,new} = w_{N,old} + (\mathrm{step~size} \times x_{N,i})

We also have to update our bias term, but just use the step size for this update: B_{new} = B_{old} + \mathrm{step~size}).

In this model, we use eta to represent our "learning_rate", which takes on a value between 0 and 1.

The step size should always be a positive or negative decimal value depending on eta. For example, if we set the learning rate, eta, to be .1 and our target is -1 and we predict 1 then the we get the following equation.

step_size = .1 * (-1-1) = -.2

Alternativey, if our target is 1 and we predict it as -1 then we will get the following.

step_size = .1 * (1 - -1) = .2

This process occurs iteratively. So, for a set number of iterations we calculate a step size and adjust the weights accordingly.

But, how do we handle the "learning" process when we have multiple samples?

In this case, we need to update the weights based on all of the sample features. So our original equation above becomes:

w_{1,new} = w_{1,old} + \sum_{i=0}^{M} (\mathrm{step~size} \times x_{1,i}) w_{2,new} = w_{2,old} + \sum_{i=0}^{M} (\mathrm{step~size} \times x_{2,i}) \vdots w_{N,new} = w_{N,old} + \sum_{i=0}^{M} (\mathrm{step~size} \times x_{N,i})

where M is our total number of samples and we compute new weights for every features value.

4. Loading and inspecting the data

Before we build a machine learning model, we need data to base it off of. The data set we are going to use has been provided for you in the directory for this assignment, irsi.csv. This dataset contains measurements for the properties of two different iris varieties.

Load the data into python and visualize (with a plot) to get a sense for what it looks like. Use different colors to represent the two different iris classifications.

In [35]:

# Do This: Load in the iris.csv file and plot the data based on the iris classifications
import csv
import matplotlib.pyplot as plt
import numpy as np

sepal_length = []
sepal_width = []
label = []
with open('iris.csv', 'r') as data:
    datareader = csv.reader(data, delimiter=',', quotechar='|')
    for i,row in enumerate(datareader):
        if i == 0:
            continue
        sepal_length.append(float(row[0]))
        sepal_width.append(float(row[1]))
        label.append(row[2])

colors = []
for i in label:
    if i == 'Iris-setosa':
        colors.append(-1)
    elif i == 'Iris-versicolor':
        colors.append(1)
    else:
        colors.append(2)

dataset = np.vstack((np.asarray(sepal_length), np.asarray(sepal_width)))
dataset = dataset.T

plt.scatter(sepal_length, sepal_width, c=colors)
plt.show()
print(len(colors))

100

Questions: Is the data linearly separable? How many data points do we have? How many of each class?

Put your answers in the cell below

Yes it is! There are exactly 100 data points.

5. Building the perceptron model

Now that we have some data to work with, we want to start building a model, Part 3 outlines how to use the perceptron model to fit the data and properly update weights. Your job is to create a Python perceptron class that matches the following specifications:

• Define the perceptron class with an __init__ method
  • The class should be initialized with the following attributes:
    • user defined input value for eta, the learning rate for the perceptron.
    • a number of interations to be used by the model, n_iter. This should also be an input parameter.
    • an initial values for the bias (you can choose whether or not the user can set this values or if you want a standard default).
• Create two methods for the perceptron clas, a fit method that does the learning and a predict method that outputs the predicted class
  • The fit method should:
    • define an array of weights the same length as the input vector. You can choose how to initialize the weight values.
    • go through a set number of iterations (based on n_iter) where it makes predictions and updates the weights vector accordingly for each subsequent round of predictions.
  • The predict method should:
    • take in a feature vector and return the predicted class based on the current weights
    • hint: The prediction is just a dot product of the weights and the features plus the bias term. The resulting ouput should be in the range (-1,1), depending on the value of the dot product. If the prediction is less than 0 it should return -1, otherwise it should return 1.

In [60]:

import numpy as np

class perceptron():
    def __init__(self, eta, n_iter, bias=0):
        self.eta = eta
        self.n_iter = n_iter
        self.bias = bias
    
    def fit(self, data):
        '''does the learning'''
        self.weights = np.zeros(data.shape[1])
        
        for i in range(self.n_iter):
            for j in range(len(self.weights)):
                change = 0
                for k in range(len(data)):
                    target = float(colors[k])
                    predicted = self.predict(data[k])
                    print(predicted)
                    ss = self.eta * (target - predicted)
                    change += ss*data[k][j]
                    self.bias += ss
                self.weights[j] += change
       
    
    def predict(self, values):
        '''outputs the predicted class'''
        prediction = np.dot(self.weights, values) + self.bias
        if prediction >= 0:
            return 1.0
        else:
            return -1.0

In [61]:

A = perceptron(0.1,100)
A.fit(dataset[0:80])
A.weights

Out [61]:

1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
-1.0
1.0
-1.0
1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
-1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0

array([ 57.44, -92.64])

In [62]:

for i in range(20):
    a = A.predict(dataset[i+80])
    b = colors[i+80]
    if int(a) == b:
        print("true")
    else:
        print("false")

true
true
true
true
true
true
true
true
true
true
true
true
true
true
true
true
true
true
true
true

Testing the new perceptron class

Now that we have a classifier built, we need to test it on data, but first we need to make sure our data is in the right format so we can properly train a classifier on it. This means, if you haven't already, that you need to make sure that you classes are either -1 or 1. You'll also need to make sure the features vectors can be fed into your perceptron class correctly.

Also, remember, for a good model, we want the training data to have an even sample of both classes so it knows what to look for and doesn't end up biased towards a particular classifications.

As a rule of thumb, you should use ~75% of your sample data as your training data and reserve the remaining ~25% as testing data.

Using your new perceptron class, train the model using your training and then test the results on your testing data. You may want to come up with a method for computing how many predictions are right versus wrong.

In [ ]:

# First, make sure you data is in the right format to be fed into your perceptron class and split your data into a training set and a testing set


# Then, train your model using your `fit` method.


# Finally, test your trained model on the testing data.

6. Plotting the decision boundary

Finally, to better understand our classifier, it might help to plot what is known as the "decision boundary". The decision boundary is the line that seperates the classes in the classifier. The line is defined by the weights and the bias term that we calculated for our model.

The slope of the decision boundary is defined as:

m = -\frac{w_1}{w_2}

And the $y$-intercept, b, is defined as:

b = -\frac{B}{w_2}

You should be able to generate a set of evenly spaced $x$-axis values and then used the equation for a line (y = mx + b) to compute the decision boundary for making a plot of the line. You should get something that looks like this:

In [63]:

# Compute the decision boundary and make a plot of it, along with the data
m = -A.weights[0]/A.weights[1]
b = -A.bias/A.weights[1]

def line(x,m,b):
    return m*x + b
x = np.linspace(4,7,num=50)
plt.plot(x,line(x,m,b))
plt.scatter(sepal_length, sepal_width, c=colors)

plt.show()

---

Assignment Wrap-up

Fill out the following Google Form before submitting your assignment to D2L!

In [59]:

from IPython.display import HTML
HTML(
"""
<iframe 
	src="https://goo.gl/forms/sxPAah1RyU3bCk0z1" 
	width="80%" 
	height="500px" 
	frameborder="0" 
	marginheight="0" 
	marginwidth="0">
	Loading...
</iframe>
"""
)

Out [59]:

---

Congratulations, we're done!

Now, you just need to submit this assignment by uploading it to the course Desire2Learn web page for today's dropbox (Don't forget to add your names in the first cell).