diff --git a/account/__init__.py b/account/__init__.py
new file mode 100644
index 0000000..e69de29
diff --git a/account/quick_deduction.py b/account/quick_deduction.py
new file mode 100644
index 0000000..a12fb64
--- /dev/null
+++ b/account/quick_deduction.py
@@ -0,0 +1,22 @@
+
+
+def deduction(x):
+    if x < 36000:
+        return x*0.03
+    if x < 144000:
+        return 36000*0.03 - 36000*0.1
+    if x < 300000:
+        return 36000*0.03 + (144000 - 36000)*0.1 - 144000*0.2
+    if x < 420000:
+        return 36000*0.03 + (144000 - 36000)*0.1 + (300000 - 144000)*0.2 - 300000*0.25
+    if x < 660000:
+        return 36000*0.03 + (144000 - 36000)*0.1 + (300000 - 144000)*0.2 + (420000 - 300000)*0.25 - 420000*0.3
+    if x < 960000:
+        return 36000 * 0.03 + (144000 - 36000) * 0.1 + (300000 - 144000) * 0.2 + (420000 - 300000) * 0.25 + (660000 - 420000) * 0.3 - 660000*0.35
+    return 36000 * 0.03 + (144000 - 36000) * 0.1 + (300000 - 144000) * 0.2 + (420000 - 300000) * 0.25 + (660000 - 420000) * 0.3 + (960000 - 660000)*0.35 - 960000*0.45
+
+
+if __name__ == '__main__':
+    for x in [10000, 100000, 200000, 300000, 400000, 500000, 600000, 700000, 800000, 900000, 10000000]:
+        print(x, deduction(x))
+
diff --git a/dl/__init__.py b/dl/__init__.py
new file mode 100644
index 0000000..e69de29
diff --git a/dl/bn/__init__.py b/dl/bn/__init__.py
new file mode 100644
index 0000000..e69de29
diff --git a/dl/bn/np_demo.py b/dl/bn/np_demo.py
new file mode 100644
index 0000000..9cd6296
--- /dev/null
+++ b/dl/bn/np_demo.py
@@ -0,0 +1,28 @@
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+
+batch = np.zeros([2, 3, 3, 3])
+batch[0, :, :, 0] = np.asarray([[2.4, 0.3, 5.6],
+                                [7.2, 0.0, 2.1],
+                                [1.9, 7.4, 4.1]])
+batch[0, :, :, 1] = np.asarray([[1.0, 2.1, 3.8],
+                                [9.6, 2.0, 4.4],
+                                [9.3, 3.9, 1.4]])
+batch[0, :, :, 2] = np.asarray([[2.6, 8.1, 9.0],
+                                [2.2, 6.6, 0.2],
+                                [6.3, 6.0, 0.1]])
+
+batch[1, :, :, 0] = np.asarray([[5.1, 9.0, 6.9],
+                                [9.7, 2.9, 2.4],
+                                [6.2, 0.7, 4.3]])
+batch[1, :, :, 1] = np.asarray([[3.3, 7.9, 4.8],
+                                [3.7, 2.0, 9.4],
+                                [4.9, 2.1, 7.8]])
+
+batch[1, :, :, 2] = np.asarray([[2.8, 5.4, 0.0],
+                                [6.4, 1.8, 6.8],
+                                [3.7, 5.6, 5.6]])
+print(batch[:, :, :, 0].mean())
+print(batch[:, :, :, 0].var())
\ No newline at end of file
diff --git a/matrix/__init__.py b/matrix/__init__.py
new file mode 100644
index 0000000..e69de29
diff --git a/matrix/rank.py b/matrix/rank.py
new file mode 100644
index 0000000..6ade71b
--- /dev/null
+++ b/matrix/rank.py
@@ -0,0 +1,7 @@
+
+import numpy as np
+from numpy.linalg import matrix_rank
+
+if __name__ == '__main__':
+    m = np.asarray([[1, 2, 3], [4, 5, 6], [5, 7, 9]])
+    matrix_rank(m)
\ No newline at end of file
diff --git a/ml/__init__.py b/ml/__init__.py
new file mode 100644
index 0000000..e69de29
diff --git a/ml/gbdt+lr/__init__.py b/ml/gbdt+lr/__init__.py
new file mode 100644
index 0000000..e69de29
diff --git a/network/__init__.py b/network/__init__.py
new file mode 100644
index 0000000..e69de29
diff --git a/network/logic_gates.py b/network/logic_gates.py
new file mode 100644
index 0000000..2a33d16
--- /dev/null
+++ b/network/logic_gates.py
@@ -0,0 +1,13 @@
+import torch
+
+
+def and_gate():
+    and_weights = torch.tensor([1, 1, -2])
+    
+
+if __name__ == '__main__':
+    # x1, x2, b
+    X = torch.tensor([(0, 0, 1), (0, 1, 1), (1, 0, 1), (1, 1, 1)], dtype=torch.double)
+
+    print(X)
+    pass
diff --git a/network/lstm_add.py b/network/lstm_add.py
new file mode 100644
index 0000000..1eeb4f9
--- /dev/null
+++ b/network/lstm_add.py
@@ -0,0 +1,138 @@
+from random import seed
+from random import randint
+from numpy import array
+from math import ceil
+from math import log10
+from math import sqrt
+from numpy import argmax
+from keras.models import Sequential
+from keras.layers import Dense
+from keras.layers import LSTM
+from keras.layers import TimeDistributed
+from keras.layers import RepeatVector
+
+
+# generate lists of random integers and their sum
+def random_sum_pairs(n_examples, n_numbers, largest):
+    X, y = list(), list()
+    for i in range(n_examples):
+        in_pattern = [randint(1, largest) for _ in range(n_numbers)]
+        out_pattern = sum(in_pattern)
+        X.append(in_pattern)
+        y.append(out_pattern)
+    return X, y
+
+
+# convert data to strings
+def to_string(X, y, n_numbers, largest):
+    max_length = n_numbers * ceil(log10(largest + 1)) + n_numbers - 1
+    Xstr = list()
+    for pattern in X:
+        strp = '+'.join([str(n) for n in pattern])
+        strp = ''.join([' ' for _ in range(max_length - len(strp))]) + strp
+        Xstr.append(strp)
+    max_length = ceil(log10(n_numbers * (largest + 1)))
+    ystr = list()
+    for pattern in y:
+        strp = str(pattern)
+        strp = ''.join([' ' for _ in range(max_length - len(strp))]) + strp
+        ystr.append(strp)
+    return Xstr, ystr
+
+
+# integer encode strings
+def integer_encode(X, y, alphabet):
+    char_to_int = dict((c, i) for i, c in enumerate(alphabet))
+    Xenc = list()
+    for pattern in X:
+        integer_encoded = [char_to_int[char] for char in pattern]
+        Xenc.append(integer_encoded)
+    yenc = list()
+    for pattern in y:
+        integer_encoded = [char_to_int[char] for char in pattern]
+        yenc.append(integer_encoded)
+    return Xenc, yenc
+
+
+# one hot encode
+def one_hot_encode(X, y, max_int):
+    Xenc = list()
+    for seq in X:
+        pattern = list()
+        for index in seq:
+            vector = [0 for _ in range(max_int)]
+            vector[index] = 1
+            pattern.append(vector)
+        Xenc.append(pattern)
+    yenc = list()
+    for seq in y:
+        pattern = list()
+        for index in seq:
+            vector = [0 for _ in range(max_int)]
+            vector[index] = 1
+            pattern.append(vector)
+        yenc.append(pattern)
+    return Xenc, yenc
+
+
+# generate an encoded dataset
+def generate_data(n_samples, n_numbers, largest, alphabet):
+    # generate pairs
+    X, y = random_sum_pairs(n_samples, n_numbers, largest)
+    # convert to strings
+    X, y = to_string(X, y, n_numbers, largest)
+    # integer encode
+    X, y = integer_encode(X, y, alphabet)
+    # one hot encode
+    X, y = one_hot_encode(X, y, len(alphabet))
+    # return as numpy arrays
+    X, y = array(X), array(y)
+    return X, y
+
+
+# invert encoding
+def invert(seq, alphabet):
+    int_to_char = dict((i, c) for i, c in enumerate(alphabet))
+    strings = list()
+    for pattern in seq:
+        string = int_to_char[argmax(pattern)]
+        strings.append(string)
+    return ''.join(strings)
+
+
+# define dataset
+seed(1)
+n_samples = 5000
+n_numbers = 2
+largest = 100
+alphabet = ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '+', ' ']
+n_chars = len(alphabet)
+n_in_seq_length = n_numbers * ceil(log10(largest + 1)) + n_numbers - 1
+n_out_seq_length = ceil(log10(n_numbers * (largest + 1)))
+# define LSTM configuration
+n_batch = 10
+n_epoch = 50
+# create LSTM
+model = Sequential()
+# n_in_seq_length: 7, n_chars: 12
+model.add(LSTM(100, input_shape=(n_in_seq_length, n_chars)))
+model.add(RepeatVector(n_out_seq_length))
+model.add(LSTM(50, return_sequences=True))
+model.add(TimeDistributed(Dense(n_chars, activation='softmax')))
+model.compile(loss='categorical_crossentropy', optimizer='adam', metrics=['accuracy'])
+print(model.summary())
+# train LSTM
+for i in range(n_epoch):
+    X, y = generate_data(n_samples, n_numbers, largest, alphabet)
+    print(i)
+    model.fit(X, y, epochs=1, batch_size=n_batch)
+
+# evaluate on some new patterns
+X, y = generate_data(n_samples, n_numbers, largest, alphabet)
+result = model.predict(X, batch_size=n_batch, verbose=0)
+# calculate error
+expected = [invert(x, alphabet) for x in y]
+predicted = [invert(x, alphabet) for x in result]
+# show some examples
+for i in range(20):
+    print('Expected=%s, Predicted=%s' % (expected[i], predicted[i]))
diff --git a/oop/MethodTest.py b/oop/MethodTest.py
new file mode 100644
index 0000000..67fdf57
--- /dev/null
+++ b/oop/MethodTest.py
@@ -0,0 +1,42 @@
+
+from datetime import datetime
+
+class Test:
+    alias = 'wudaokou nash'
+
+    @staticmethod
+    def static_mode(language):
+        print(f'static method, {Test.alias} codes in {language}')
+
+    @classmethod
+    def class_mode(cls, language):
+        print(f'class method, {cls.alias} codes in {language}')
+
+
+class Repr:
+
+    def __init__(self, name):
+        self.name = name
+
+    def __repr__(self):
+        return f'{self.__class__.__module__}.{self.__class__.__qualname__}(name={self.name})'
+
+    def __str__(self):
+        return f'{self.name}'
+
+
+if __name__ == '__main__':
+    t = Test()
+    t.static_mode('chinese')
+    t.class_mode('english')
+
+    r = Repr('zhang')
+    print(r)
+    print(repr(r))
+    print(str(r))
+
+    now = datetime.now()
+    print(now.__str__())
+    print(now.__repr__())
+
+
diff --git a/oop/TestProperrty.py b/oop/TestProperrty.py
new file mode 100644
index 0000000..de43e17
--- /dev/null
+++ b/oop/TestProperrty.py
@@ -0,0 +1,22 @@
+
+class Screen(object):
+    @property
+    def width(self):
+        return self._width
+
+    @width.setter
+    def width(self, value):
+        self._width = value
+
+    @property
+    def height(self):
+        return self._height
+
+    @height.setter
+    def height(self, value):
+        self._height = value
+
+    @property
+    def resolution(self):
+        return self._height*self._width
+
diff --git a/oop/__init__.py b/oop/__init__.py
new file mode 100644
index 0000000..e69de29
diff --git a/oop/dp/Decorator.py b/oop/dp/Decorator.py
new file mode 100644
index 0000000..390935a
--- /dev/null
+++ b/oop/dp/Decorator.py
@@ -0,0 +1,59 @@
+
+from abc import ABCMeta, abstractmethod
+
+
+class Person(metaclass=ABCMeta):
+    def __init__(self, name):
+        self._name = name
+
+    @abstractmethod
+    def wear(self):
+        print('着装: ')
+
+
+class Engineer(Person):
+
+    def __init__(self, name, skill):
+        super().__init__(name)
+        self._skill = skill
+
+    def wear(self):
+        print(f'我是 {self._name} 工程师, 我会 {self._skill}')
+        super().wear()
+
+
+class ClothingDecorator(Person):
+    def __init__(self, person: Person):
+        self._decoratored = person
+
+    def wear(self):
+        self._decoratored.wear()
+        self.decorate()
+
+    @abstractmethod
+    def decorate(self):
+        pass
+
+
+class CasualPantDecorator(ClothingDecorator):
+    def __init__(self, person: Person):
+        super().__init__(person)
+    def decorate(self):
+        print('一条卡其色裤子')
+
+
+class BeltDecorator(ClothingDecorator):
+    def __init__(self, person: Person):
+        super().__init__(person)
+
+    def decorate(self):
+        print('一条黑色腰带')
+
+if __name__ == '__main__':
+    tony = Engineer('Tony', '算法')
+    pant = CasualPantDecorator(tony)
+    belt = BeltDecorator(pant)
+    belt.wear()
+
+
+
diff --git a/oop/dp/__init__.py b/oop/dp/__init__.py
new file mode 100644
index 0000000..e69de29
diff --git a/ordemo/polygon.py b/ordemo/polygon.py
new file mode 100644
index 0000000..6a157f4
--- /dev/null
+++ b/ordemo/polygon.py
@@ -0,0 +1,45 @@
+from ortools.linear_solver import pywraplp
+
+
+def main():
+    # Create the mip solver with the SCIP backend.
+    solver = pywraplp.Solver.CreateSolver('SCIP')
+
+    infinity = solver.infinity()
+    # x and y are integer non-negative variables.
+    x = solver.IntVar(3, infinity, 'x')
+    y = solver.IntVar(0, infinity, 'y')
+    t = solver.IntVar(0, infinity, 't')
+
+    print('Number of variables =', solver.NumVariables())
+
+    solver.Add(t == x-2)
+    # x + 7 * y <= 17.5.
+    solver.Add(y == 2*x/t)
+
+    # x <= 3.5.
+    # solver.Add(x <= 3.5)
+
+    print('Number of constraints =', solver.NumConstraints())
+
+    # Maximize x + 10 * y.
+    solver.Maximize(0)
+
+    status = solver.Solve()
+
+    if status == pywraplp.Solver.OPTIMAL:
+        print('Solution:')
+        print('Objective value =', solver.Objective().Value())
+        print('x =', x.solution_value())
+        print('y =', y.solution_value())
+    else:
+        print('The problem does not have an optimal solution.')
+
+    print('\nAdvanced usage:')
+    print('Problem solved in %f milliseconds' % solver.wall_time())
+    print('Problem solved in %d iterations' % solver.iterations())
+    print('Problem solved in %d branch-and-bound nodes' % solver.nodes())
+
+
+if __name__ == '__main__':
+    main()
\ No newline at end of file
diff --git a/ordemo/send_more_money.py b/ordemo/send_more_money.py
index 77fddda..d8e10fa 100644
--- a/ordemo/send_more_money.py
+++ b/ordemo/send_more_money.py
@@ -50,5 +50,5 @@ def solution_count(self):
 
 solver.Solve(model, solution_printer)
 
-print(
-    f"  {solver.Value(S)}{solver.Value(E)}{solver.Value(N)}{solver.Value(D)}\n+ {solver.Value(M)}{solver.Value(O)}{solver.Value(R)}{solver.Value(E)}\n={solver.Value(M)}{solver.Value(O)}{solver.Value(N)}{solver.Value(E)}{solver.Value(Y)}")
+# print(
+#     f"  {solver.Value(S)}{solver.Value(E)}{solver.Value(N)}{solver.Value(D)}\n+ {solver.Value(M)}{solver.Value(O)}{solver.Value(R)}{solver.Value(E)}\n={solver.Value(M)}{solver.Value(O)}{solver.Value(N)}{solver.Value(E)}{solver.Value(Y)}")
diff --git a/ordemo/two_sum.py b/ordemo/two_sum.py
new file mode 100644
index 0000000..5652998
--- /dev/null
+++ b/ordemo/two_sum.py
@@ -0,0 +1,36 @@
+from ortools.sat.python import cp_model
+
+
+class VarArraySolutionPrinter(cp_model.CpSolverSolutionCallback):
+    """Print intermediate solutions."""
+
+    def __init__(self, variables):
+        cp_model.CpSolverSolutionCallback.__init__(self)
+        self.__variables = variables
+        self.__solution_count = 0
+
+    def on_solution_callback(self):
+        self.__solution_count += 1
+        for v in self.__variables:
+            print('%s=%i' % (v, self.Value(v)), end=' ')
+        print()
+
+    def solution_count(self):
+        return self.__solution_count
+
+
+l = [2, 7, 1, 3, 6, 9, 10, -1, 12, 22]
+target = 9
+
+model = cp_model.CpModel()
+
+xs = [model.NewBoolVar(str(i)) for i in range(len(l))]
+
+model.Add(sum(xs) == 2)
+
+model.Add(sum([xs[i]*l[i] for i in range(len(l))]) == target)
+solver = cp_model.CpSolver()
+solution_printer = VarArraySolutionPrinter(xs)
+solver.parameters.enumerate_all_solutions = True
+solver.Solve(model, solution_printer)
+
diff --git a/sat/__init__.py b/sat/__init__.py
new file mode 100644
index 0000000..e69de29
diff --git a/sat/color.py b/sat/color.py
new file mode 100644
index 0000000..094370d
--- /dev/null
+++ b/sat/color.py
@@ -0,0 +1,1561 @@
+N = 120
+# X(G) = 9
+COLORS = 8
+# M = 1276
+EDGES = [
+ [1, 16],
+ [1, 20],
+ [1, 94],
+ [1, 80],
+ [1, 57],
+ [1, 62],
+ [1, 89],
+ [1, 113],
+ [1, 5],
+ [1, 21],
+ [1, 15],
+ [2, 24],
+ [2, 30],
+ [2, 77],
+ [2, 92],
+ [2, 41],
+ [2, 55],
+ [2, 6],
+ [2, 54],
+ [3, 100],
+ [3, 44],
+ [3, 105],
+ [3, 91],
+ [3, 42],
+ [3, 103],
+ [3, 90],
+ [3, 22],
+ [3, 67],
+ [3, 31],
+ [3, 115],
+ [3, 71],
+ [4, 38],
+ [4, 85],
+ [4, 49],
+ [4, 50],
+ [4, 61],
+ [4, 63],
+ [4, 99],
+ [4, 96],
+ [4, 84],
+ [4, 107],
+ [4, 12],
+ [5, 56],
+ [5, 26],
+ [5, 72],
+ [5, 38],
+ [5, 32],
+ [5, 85],
+ [5, 76],
+ [5, 1],
+ [5, 34],
+ [5, 53],
+ [6, 11],
+ [6, 87],
+ [6, 13],
+ [6, 14],
+ [6, 41],
+ [6, 24],
+ [6, 55],
+ [6, 92],
+ [6, 2],
+ [6, 60],
+ [7, 66],
+ [7, 83],
+ [7, 21],
+ [7, 118],
+ [7, 48],
+ [7, 10],
+ [7, 120],
+ [7, 25],
+ [7, 75],
+ [7, 64],
+ [7, 28],
+ [7, 51],
+ [8, 73],
+ [8, 18],
+ [8, 53],
+ [8, 86],
+ [8, 71],
+ [8, 104],
+ [8, 98],
+ [8, 38],
+ [8, 46],
+ [8, 100],
+ [9, 33],
+ [9, 31],
+ [9, 69],
+ [9, 58],
+ [9, 116],
+ [9, 17],
+ [9, 51],
+ [9, 70],
+ [9, 101],
+ [9, 119],
+ [9, 38],
+ [10, 25],
+ [10, 75],
+ [10, 48],
+ [10, 83],
+ [10, 21],
+ [10, 7],
+ [10, 64],
+ [10, 35],
+ [10, 120],
+ [10, 36],
+ [10, 118],
+ [11, 6],
+ [11, 55],
+ [11, 14],
+ [11, 41],
+ [11, 60],
+ [11, 87],
+ [11, 30],
+ [11, 54],
+ [11, 13],
+ [12, 117],
+ [12, 19],
+ [12, 43],
+ [12, 102],
+ [12, 23],
+ [12, 88],
+ [12, 35],
+ [12, 97],
+ [12, 68],
+ [12, 29],
+ [12, 4],
+ [13, 60],
+ [13, 41],
+ [13, 6],
+ [13, 87],
+ [13, 55],
+ [13, 14],
+ [13, 54],
+ [13, 77],
+ [13, 30],
+ [13, 11],
+ [14, 55],
+ [14, 60],
+ [14, 11],
+ [14, 6],
+ [14, 87],
+ [14, 13],
+ [14, 77],
+ [14, 54],
+ [14, 24],
+ [14, 41],
+ [15, 53],
+ [15, 95],
+ [15, 52],
+ [15, 65],
+ [15, 59],
+ [15, 108],
+ [15, 39],
+ [15, 66],
+ [15, 37],
+ [15, 112],
+ [15, 88],
+ [15, 1],
+ [16, 65],
+ [16, 1],
+ [16, 62],
+ [16, 80],
+ [16, 94],
+ [16, 47],
+ [16, 57],
+ [16, 113],
+ [16, 89],
+ [16, 26],
+ [16, 27],
+ [16, 34],
+ [17, 31],
+ [17, 34],
+ [17, 28],
+ [17, 9],
+ [17, 101],
+ [17, 69],
+ [17, 33],
+ [17, 79],
+ [17, 42],
+ [17, 103],
+ [17, 115],
+ [18, 20],
+ [18, 8],
+ [18, 93],
+ [18, 100],
+ [18, 86],
+ [18, 27],
+ [18, 84],
+ [18, 73],
+ [18, 53],
+ [18, 71],
+ [18, 98],
+ [19, 61],
+ [19, 97],
+ [19, 12],
+ [19, 23],
+ [19, 35],
+ [19, 43],
+ [19, 117],
+ [19, 102],
+ [19, 29],
+ [19, 80],
+ [19, 114],
+ [19, 90],
+ [20, 18],
+ [20, 113],
+ [20, 1],
+ [20, 89],
+ [20, 62],
+ [20, 80],
+ [20, 47],
+ [20, 94],
+ [20, 57],
+ [20, 65],
+ [20, 56],
+ [20, 67],
+ [21, 83],
+ [21, 118],
+ [21, 7],
+ [21, 10],
+ [21, 120],
+ [21, 25],
+ [21, 75],
+ [21, 48],
+ [21, 1],
+ [22, 39],
+ [22, 44],
+ [22, 105],
+ [22, 91],
+ [22, 42],
+ [22, 3],
+ [22, 90],
+ [22, 103],
+ [22, 67],
+ [22, 74],
+ [23, 27],
+ [23, 102],
+ [23, 43],
+ [23, 19],
+ [23, 97],
+ [23, 12],
+ [23, 35],
+ [23, 117],
+ [23, 59],
+ [23, 44],
+ [23, 57],
+ [23, 95],
+ [23, 38],
+ [24, 2],
+ [24, 54],
+ [24, 30],
+ [24, 92],
+ [24, 6],
+ [24, 60],
+ [24, 14],
+ [24, 77],
+ [25, 10],
+ [25, 120],
+ [25, 118],
+ [25, 75],
+ [25, 83],
+ [25, 21],
+ [25, 7],
+ [25, 28],
+ [25, 31],
+ [25, 48],
+ [25, 50],
+ [26, 5],
+ [26, 109],
+ [26, 93],
+ [26, 64],
+ [26, 34],
+ [26, 72],
+ [26, 56],
+ [26, 16],
+ [26, 76],
+ [26, 92],
+ [26, 51],
+ [27, 23],
+ [27, 65],
+ [27, 76],
+ [27, 38],
+ [27, 84],
+ [27, 72],
+ [27, 88],
+ [27, 18],
+ [27, 95],
+ [27, 47],
+ [27, 16],
+ [27, 113],
+ [28, 58],
+ [28, 79],
+ [28, 68],
+ [28, 17],
+ [28, 32],
+ [28, 109],
+ [28, 120],
+ [28, 25],
+ [28, 89],
+ [28, 7],
+ [28, 75],
+ [29, 52],
+ [29, 65],
+ [29, 39],
+ [29, 108],
+ [29, 112],
+ [29, 37],
+ [29, 19],
+ [29, 95],
+ [29, 74],
+ [29, 12],
+ [30, 92],
+ [30, 2],
+ [30, 24],
+ [30, 77],
+ [30, 54],
+ [30, 55],
+ [30, 11],
+ [30, 41],
+ [30, 13],
+ [30, 93],
+ [31, 17],
+ [31, 9],
+ [31, 58],
+ [31, 33],
+ [31, 79],
+ [31, 51],
+ [31, 70],
+ [31, 3],
+ [31, 106],
+ [31, 25],
+ [31, 110],
+ [32, 114],
+ [32, 69],
+ [32, 5],
+ [32, 28],
+ [32, 78],
+ [32, 101],
+ [32, 110],
+ [32, 115],
+ [32, 85],
+ [32, 79],
+ [32, 36],
+ [33, 113],
+ [33, 9],
+ [33, 38],
+ [33, 31],
+ [33, 106],
+ [33, 110],
+ [33, 51],
+ [33, 17],
+ [33, 91],
+ [33, 116],
+ [33, 69],
+ [34, 37],
+ [34, 88],
+ [34, 109],
+ [34, 17],
+ [34, 56],
+ [34, 93],
+ [34, 26],
+ [34, 76],
+ [34, 106],
+ [34, 72],
+ [34, 16],
+ [34, 5],
+ [34, 65],
+ [35, 43],
+ [35, 117],
+ [35, 102],
+ [35, 19],
+ [35, 97],
+ [35, 23],
+ [35, 12],
+ [35, 10],
+ [35, 89],
+ [35, 80],
+ [36, 49],
+ [36, 98],
+ [36, 64],
+ [36, 111],
+ [36, 116],
+ [36, 115],
+ [36, 10],
+ [36, 32],
+ [37, 34],
+ [37, 39],
+ [37, 95],
+ [37, 59],
+ [37, 112],
+ [37, 65],
+ [37, 29],
+ [37, 108],
+ [37, 15],
+ [37, 52],
+ [37, 104],
+ [37, 57],
+ [38, 4],
+ [38, 106],
+ [38, 51],
+ [38, 33],
+ [38, 27],
+ [38, 5],
+ [38, 58],
+ [38, 70],
+ [38, 116],
+ [38, 8],
+ [38, 9],
+ [38, 81],
+ [38, 23],
+ [39, 22],
+ [39, 37],
+ [39, 112],
+ [39, 29],
+ [39, 65],
+ [39, 52],
+ [39, 15],
+ [39, 59],
+ [39, 117],
+ [39, 98],
+ [39, 90],
+ [40, 74],
+ [40, 119],
+ [40, 82],
+ [40, 66],
+ [40, 46],
+ [40, 81],
+ [40, 73],
+ [40, 45],
+ [40, 107],
+ [41, 87],
+ [41, 13],
+ [41, 55],
+ [41, 11],
+ [41, 6],
+ [41, 2],
+ [41, 60],
+ [41, 30],
+ [41, 14],
+ [42, 91],
+ [42, 67],
+ [42, 103],
+ [42, 3],
+ [42, 44],
+ [42, 22],
+ [42, 90],
+ [42, 105],
+ [42, 17],
+ [42, 106],
+ [43, 35],
+ [43, 23],
+ [43, 12],
+ [43, 117],
+ [43, 19],
+ [43, 102],
+ [43, 97],
+ [43, 105],
+ [43, 70],
+ [43, 111],
+ [44, 88],
+ [44, 3],
+ [44, 90],
+ [44, 105],
+ [44, 22],
+ [44, 67],
+ [44, 42],
+ [44, 91],
+ [44, 97],
+ [44, 103],
+ [44, 23],
+ [44, 76],
+ [45, 100],
+ [45, 81],
+ [45, 119],
+ [45, 46],
+ [45, 74],
+ [45, 66],
+ [45, 82],
+ [45, 52],
+ [45, 117],
+ [45, 40],
+ [45, 86],
+ [46, 119],
+ [46, 66],
+ [46, 45],
+ [46, 111],
+ [46, 81],
+ [46, 74],
+ [46, 40],
+ [46, 82],
+ [46, 102],
+ [46, 8],
+ [46, 104],
+ [47, 94],
+ [47, 89],
+ [47, 62],
+ [47, 113],
+ [47, 16],
+ [47, 20],
+ [47, 57],
+ [47, 80],
+ [47, 27],
+ [47, 59],
+ [48, 84],
+ [48, 10],
+ [48, 120],
+ [48, 7],
+ [48, 75],
+ [48, 118],
+ [48, 83],
+ [48, 21],
+ [48, 114],
+ [48, 25],
+ [49, 36],
+ [49, 4],
+ [49, 76],
+ [49, 50],
+ [49, 96],
+ [49, 63],
+ [49, 61],
+ [49, 113],
+ [49, 99],
+ [49, 107],
+ [49, 109],
+ [49, 85],
+ [50, 96],
+ [50, 4],
+ [50, 107],
+ [50, 49],
+ [50, 61],
+ [50, 63],
+ [50, 99],
+ [50, 51],
+ [50, 78],
+ [50, 25],
+ [51, 38],
+ [51, 70],
+ [51, 106],
+ [51, 110],
+ [51, 31],
+ [51, 9],
+ [51, 33],
+ [51, 50],
+ [51, 94],
+ [51, 26],
+ [51, 7],
+ [52, 98],
+ [52, 29],
+ [52, 15],
+ [52, 108],
+ [52, 95],
+ [52, 39],
+ [52, 59],
+ [52, 45],
+ [52, 100],
+ [52, 37],
+ [52, 73],
+ [53, 15],
+ [53, 71],
+ [53, 100],
+ [53, 98],
+ [53, 8],
+ [53, 104],
+ [53, 73],
+ [53, 86],
+ [53, 18],
+ [53, 112],
+ [53, 5],
+ [54, 77],
+ [54, 24],
+ [54, 92],
+ [54, 30],
+ [54, 13],
+ [54, 14],
+ [54, 11],
+ [54, 2],
+ [55, 14],
+ [55, 11],
+ [55, 41],
+ [55, 60],
+ [55, 13],
+ [55, 30],
+ [55, 6],
+ [55, 2],
+ [55, 87],
+ [56, 5],
+ [56, 88],
+ [56, 68],
+ [56, 34],
+ [56, 109],
+ [56, 76],
+ [56, 93],
+ [56, 26],
+ [56, 84],
+ [56, 20],
+ [56, 72],
+ [57, 107],
+ [57, 62],
+ [57, 94],
+ [57, 113],
+ [57, 89],
+ [57, 1],
+ [57, 16],
+ [57, 47],
+ [57, 20],
+ [57, 23],
+ [57, 37],
+ [58, 68],
+ [58, 116],
+ [58, 28],
+ [58, 31],
+ [58, 9],
+ [58, 76],
+ [58, 38],
+ [58, 115],
+ [58, 106],
+ [58, 110],
+ [58, 70],
+ [58, 101],
+ [59, 89],
+ [59, 112],
+ [59, 108],
+ [59, 37],
+ [59, 15],
+ [59, 95],
+ [59, 52],
+ [59, 39],
+ [59, 23],
+ [59, 65],
+ [59, 47],
+ [59, 66],
+ [60, 13],
+ [60, 14],
+ [60, 87],
+ [60, 55],
+ [60, 11],
+ [60, 77],
+ [60, 41],
+ [60, 24],
+ [60, 92],
+ [60, 6],
+ [61, 19],
+ [61, 110],
+ [61, 63],
+ [61, 85],
+ [61, 4],
+ [61, 96],
+ [61, 50],
+ [61, 107],
+ [61, 49],
+ [61, 78],
+ [61, 99],
+ [62, 57],
+ [62, 16],
+ [62, 47],
+ [62, 20],
+ [62, 89],
+ [62, 1],
+ [62, 80],
+ [62, 94],
+ [62, 114],
+ [62, 103],
+ [62, 96],
+ [63, 106],
+ [63, 61],
+ [63, 96],
+ [63, 107],
+ [63, 4],
+ [63, 49],
+ [63, 50],
+ [63, 93],
+ [63, 99],
+ [63, 103],
+ [64, 36],
+ [64, 114],
+ [64, 26],
+ [64, 70],
+ [64, 84],
+ [64, 10],
+ [64, 119],
+ [64, 7],
+ [64, 120],
+ [65, 16],
+ [65, 27],
+ [65, 108],
+ [65, 29],
+ [65, 15],
+ [65, 39],
+ [65, 37],
+ [65, 95],
+ [65, 112],
+ [65, 20],
+ [65, 59],
+ [65, 76],
+ [65, 34],
+ [66, 7],
+ [66, 82],
+ [66, 46],
+ [66, 119],
+ [66, 45],
+ [66, 40],
+ [66, 15],
+ [66, 95],
+ [66, 74],
+ [66, 81],
+ [66, 59],
+ [66, 68],
+ [67, 42],
+ [67, 105],
+ [67, 44],
+ [67, 88],
+ [67, 103],
+ [67, 91],
+ [67, 3],
+ [67, 90],
+ [67, 104],
+ [67, 22],
+ [67, 20],
+ [68, 58],
+ [68, 56],
+ [68, 28],
+ [68, 72],
+ [68, 69],
+ [68, 111],
+ [68, 101],
+ [68, 109],
+ [68, 12],
+ [68, 66],
+ [69, 79],
+ [69, 9],
+ [69, 32],
+ [69, 115],
+ [69, 101],
+ [69, 68],
+ [69, 17],
+ [69, 111],
+ [69, 33],
+ [70, 79],
+ [70, 51],
+ [70, 110],
+ [70, 116],
+ [70, 64],
+ [70, 38],
+ [70, 31],
+ [70, 9],
+ [70, 58],
+ [70, 43],
+ [71, 100],
+ [71, 98],
+ [71, 53],
+ [71, 73],
+ [71, 104],
+ [71, 81],
+ [71, 119],
+ [71, 8],
+ [71, 86],
+ [71, 18],
+ [71, 3],
+ [72, 76],
+ [72, 5],
+ [72, 88],
+ [72, 27],
+ [72, 68],
+ [72, 26],
+ [72, 109],
+ [72, 34],
+ [72, 97],
+ [72, 56],
+ [72, 83],
+ [73, 88],
+ [73, 8],
+ [73, 104],
+ [73, 71],
+ [73, 86],
+ [73, 108],
+ [73, 53],
+ [73, 18],
+ [73, 100],
+ [73, 40],
+ [73, 52],
+ [74, 40],
+ [74, 82],
+ [74, 45],
+ [74, 46],
+ [74, 119],
+ [74, 81],
+ [74, 66],
+ [74, 29],
+ [74, 22],
+ [75, 10],
+ [75, 120],
+ [75, 25],
+ [75, 118],
+ [75, 48],
+ [75, 83],
+ [75, 21],
+ [75, 7],
+ [75, 85],
+ [75, 28],
+ [76, 79],
+ [76, 72],
+ [76, 27],
+ [76, 49],
+ [76, 109],
+ [76, 58],
+ [76, 56],
+ [76, 34],
+ [76, 5],
+ [76, 26],
+ [76, 65],
+ [76, 44],
+ [77, 54],
+ [77, 92],
+ [77, 2],
+ [77, 30],
+ [77, 93],
+ [77, 60],
+ [77, 14],
+ [77, 13],
+ [77, 87],
+ [77, 24],
+ [78, 109],
+ [78, 107],
+ [78, 79],
+ [78, 99],
+ [78, 32],
+ [78, 61],
+ [78, 85],
+ [78, 50],
+ [78, 96],
+ [79, 76],
+ [79, 70],
+ [79, 69],
+ [79, 28],
+ [79, 78],
+ [79, 31],
+ [79, 116],
+ [79, 88],
+ [79, 85],
+ [79, 17],
+ [79, 32],
+ [80, 89],
+ [80, 113],
+ [80, 16],
+ [80, 1],
+ [80, 20],
+ [80, 94],
+ [80, 62],
+ [80, 47],
+ [80, 19],
+ [80, 35],
+ [80, 86],
+ [81, 45],
+ [81, 82],
+ [81, 71],
+ [81, 46],
+ [81, 119],
+ [81, 74],
+ [81, 40],
+ [81, 66],
+ [81, 38],
+ [82, 66],
+ [82, 81],
+ [82, 74],
+ [82, 40],
+ [82, 45],
+ [82, 114],
+ [82, 119],
+ [82, 46],
+ [82, 86],
+ [82, 104],
+ [82, 118],
+ [83, 21],
+ [83, 7],
+ [83, 10],
+ [83, 120],
+ [83, 25],
+ [83, 75],
+ [83, 48],
+ [83, 118],
+ [83, 72],
+ [84, 93],
+ [84, 48],
+ [84, 27],
+ [84, 64],
+ [84, 18],
+ [84, 56],
+ [84, 4],
+ [85, 4],
+ [85, 61],
+ [85, 99],
+ [85, 101],
+ [85, 5],
+ [85, 109],
+ [85, 79],
+ [85, 78],
+ [85, 32],
+ [85, 75],
+ [85, 49],
+ [86, 100],
+ [86, 104],
+ [86, 73],
+ [86, 18],
+ [86, 8],
+ [86, 98],
+ [86, 53],
+ [86, 71],
+ [86, 82],
+ [86, 80],
+ [86, 45],
+ [87, 41],
+ [87, 6],
+ [87, 60],
+ [87, 13],
+ [87, 14],
+ [87, 11],
+ [87, 92],
+ [87, 77],
+ [87, 55],
+ [88, 44],
+ [88, 73],
+ [88, 34],
+ [88, 56],
+ [88, 72],
+ [88, 67],
+ [88, 27],
+ [88, 12],
+ [88, 79],
+ [88, 89],
+ [88, 15],
+ [88, 100],
+ [89, 59],
+ [89, 80],
+ [89, 47],
+ [89, 20],
+ [89, 57],
+ [89, 62],
+ [89, 113],
+ [89, 1],
+ [89, 16],
+ [89, 88],
+ [89, 35],
+ [89, 28],
+ [90, 44],
+ [90, 103],
+ [90, 91],
+ [90, 105],
+ [90, 3],
+ [90, 42],
+ [90, 22],
+ [90, 67],
+ [90, 39],
+ [90, 19],
+ [91, 42],
+ [91, 3],
+ [91, 90],
+ [91, 103],
+ [91, 22],
+ [91, 44],
+ [91, 67],
+ [91, 105],
+ [91, 98],
+ [91, 33],
+ [91, 111],
+ [92, 30],
+ [92, 77],
+ [92, 54],
+ [92, 24],
+ [92, 2],
+ [92, 87],
+ [92, 6],
+ [92, 60],
+ [92, 26],
+ [93, 84],
+ [93, 106],
+ [93, 18],
+ [93, 26],
+ [93, 34],
+ [93, 77],
+ [93, 56],
+ [93, 96],
+ [93, 63],
+ [93, 30],
+ [94, 116],
+ [94, 47],
+ [94, 57],
+ [94, 1],
+ [94, 16],
+ [94, 113],
+ [94, 80],
+ [94, 20],
+ [94, 62],
+ [94, 118],
+ [94, 117],
+ [94, 51],
+ [95, 15],
+ [95, 37],
+ [95, 112],
+ [95, 52],
+ [95, 59],
+ [95, 65],
+ [95, 27],
+ [95, 66],
+ [95, 29],
+ [95, 108],
+ [95, 23],
+ [96, 50],
+ [96, 99],
+ [96, 63],
+ [96, 61],
+ [96, 49],
+ [96, 93],
+ [96, 107],
+ [96, 4],
+ [96, 62],
+ [96, 78],
+ [97, 19],
+ [97, 102],
+ [97, 117],
+ [97, 23],
+ [97, 35],
+ [97, 44],
+ [97, 43],
+ [97, 12],
+ [97, 111],
+ [97, 72],
+ [97, 108],
+ [98, 52],
+ [98, 71],
+ [98, 36],
+ [98, 111],
+ [98, 53],
+ [98, 104],
+ [98, 100],
+ [98, 86],
+ [98, 91],
+ [98, 8],
+ [98, 39],
+ [98, 18],
+ [99, 101],
+ [99, 96],
+ [99, 85],
+ [99, 78],
+ [99, 107],
+ [99, 4],
+ [99, 50],
+ [99, 49],
+ [99, 63],
+ [99, 61],
+ [100, 3],
+ [100, 71],
+ [100, 45],
+ [100, 86],
+ [100, 53],
+ [100, 18],
+ [100, 104],
+ [100, 98],
+ [100, 52],
+ [100, 73],
+ [100, 112],
+ [100, 88],
+ [100, 8],
+ [101, 99],
+ [101, 116],
+ [101, 115],
+ [101, 85],
+ [101, 69],
+ [101, 17],
+ [101, 32],
+ [101, 68],
+ [101, 9],
+ [101, 110],
+ [101, 58],
+ [102, 23],
+ [102, 97],
+ [102, 35],
+ [102, 12],
+ [102, 117],
+ [102, 43],
+ [102, 19],
+ [102, 104],
+ [102, 114],
+ [102, 46],
+ [103, 90],
+ [103, 42],
+ [103, 91],
+ [103, 3],
+ [103, 67],
+ [103, 105],
+ [103, 44],
+ [103, 22],
+ [103, 62],
+ [103, 17],
+ [103, 63],
+ [104, 73],
+ [104, 86],
+ [104, 71],
+ [104, 100],
+ [104, 98],
+ [104, 53],
+ [104, 8],
+ [104, 102],
+ [104, 67],
+ [104, 37],
+ [104, 82],
+ [104, 46],
+ [105, 3],
+ [105, 44],
+ [105, 67],
+ [105, 22],
+ [105, 90],
+ [105, 103],
+ [105, 91],
+ [105, 42],
+ [105, 43],
+ [105, 117],
+ [105, 112],
+ [106, 38],
+ [106, 63],
+ [106, 93],
+ [106, 51],
+ [106, 33],
+ [106, 110],
+ [106, 116],
+ [106, 34],
+ [106, 58],
+ [106, 31],
+ [106, 42],
+ [107, 57],
+ [107, 78],
+ [107, 50],
+ [107, 63],
+ [107, 99],
+ [107, 61],
+ [107, 110],
+ [107, 96],
+ [107, 49],
+ [107, 4],
+ [107, 40],
+ [108, 65],
+ [108, 59],
+ [108, 52],
+ [108, 29],
+ [108, 15],
+ [108, 73],
+ [108, 37],
+ [108, 112],
+ [108, 113],
+ [108, 95],
+ [108, 97],
+ [109, 78],
+ [109, 34],
+ [109, 26],
+ [109, 76],
+ [109, 56],
+ [109, 28],
+ [109, 85],
+ [109, 72],
+ [109, 68],
+ [109, 49],
+ [109, 120],
+ [110, 61],
+ [110, 116],
+ [110, 70],
+ [110, 51],
+ [110, 106],
+ [110, 33],
+ [110, 107],
+ [110, 32],
+ [110, 58],
+ [110, 101],
+ [110, 31],
+ [111, 98],
+ [111, 46],
+ [111, 115],
+ [111, 36],
+ [111, 68],
+ [111, 69],
+ [111, 97],
+ [111, 91],
+ [111, 43],
+ [112, 59],
+ [112, 39],
+ [112, 95],
+ [112, 37],
+ [112, 29],
+ [112, 65],
+ [112, 108],
+ [112, 15],
+ [112, 100],
+ [112, 53],
+ [112, 105],
+ [113, 33],
+ [113, 20],
+ [113, 80],
+ [113, 57],
+ [113, 47],
+ [113, 94],
+ [113, 89],
+ [113, 16],
+ [113, 1],
+ [113, 49],
+ [113, 108],
+ [113, 27],
+ [114, 115],
+ [114, 32],
+ [114, 64],
+ [114, 82],
+ [114, 62],
+ [114, 102],
+ [114, 48],
+ [114, 19],
+ [115, 114],
+ [115, 101],
+ [115, 69],
+ [115, 111],
+ [115, 58],
+ [115, 36],
+ [115, 32],
+ [115, 3],
+ [115, 17],
+ [116, 94],
+ [116, 58],
+ [116, 110],
+ [116, 101],
+ [116, 70],
+ [116, 9],
+ [116, 79],
+ [116, 106],
+ [116, 36],
+ [116, 38],
+ [116, 33],
+ [116, 119],
+ [117, 12],
+ [117, 35],
+ [117, 97],
+ [117, 43],
+ [117, 102],
+ [117, 19],
+ [117, 23],
+ [117, 39],
+ [117, 94],
+ [117, 45],
+ [117, 105],
+ [118, 120],
+ [118, 21],
+ [118, 25],
+ [118, 7],
+ [118, 75],
+ [118, 48],
+ [118, 94],
+ [118, 83],
+ [118, 10],
+ [118, 82],
+ [119, 46],
+ [119, 45],
+ [119, 66],
+ [119, 40],
+ [119, 71],
+ [119, 81],
+ [119, 74],
+ [119, 82],
+ [119, 64],
+ [119, 9],
+ [119, 116],
+ [120, 118],
+ [120, 25],
+ [120, 75],
+ [120, 48],
+ [120, 83],
+ [120, 21],
+ [120, 7],
+ [120, 28],
+ [120, 10],
+ [120, 64],
+ [120, 109],
+]
+
+# N = 47
+# # X(G) = 6
+# COLORS = 5
+# # M = 236
+# EDGES = [
+#     [1, 2],
+#     [1, 4],
+#     [1, 7],
+#     [1, 9],
+#     [1, 13],
+#     [1, 15],
+#     [1, 18],
+#     [1, 20],
+#     [1, 25],
+#     [1, 27],
+#     [1, 30],
+#     [1, 32],
+#     [1, 36],
+#     [1, 38],
+#     [1, 41],
+#     [1, 43],
+#     [2, 3],
+#     [2, 6],
+#     [2, 8],
+#     [2, 12],
+#     [2, 14],
+#     [2, 17],
+#     [2, 19],
+#     [2, 24],
+#     [2, 26],
+#     [2, 29],
+#     [2, 31],
+#     [2, 35],
+#     [2, 37],
+#     [2, 40],
+#     [2, 42],
+#     [3, 5],
+#     [3, 7],
+#     [3, 10],
+#     [3, 13],
+#     [3, 16],
+#     [3, 18],
+#     [3, 21],
+#     [3, 25],
+#     [3, 28],
+#     [3, 30],
+#     [3, 33],
+#     [3, 36],
+#     [3, 39],
+#     [3, 41],
+#     [3, 44],
+#     [4, 5],
+#     [4, 6],
+#     [4, 10],
+#     [4, 12],
+#     [4, 16],
+#     [4, 17],
+#     [4, 21],
+#     [4, 24],
+#     [4, 28],
+#     [4, 29],
+#     [4, 33],
+#     [4, 35],
+#     [4, 39],
+#     [4, 40],
+#     [4, 44],
+#     [5, 8],
+#     [5, 9],
+#     [5, 14],
+#     [5, 15],
+#     [5, 19],
+#     [5, 20],
+#     [5, 26],
+#     [5, 27],
+#     [5, 31],
+#     [5, 32],
+#     [5, 37],
+#     [5, 38],
+#     [5, 42],
+#     [5, 43],
+#     [6, 11],
+#     [6, 13],
+#     [6, 15],
+#     [6, 22],
+#     [6, 25],
+#     [6, 27],
+#     [6, 34],
+#     [6, 36],
+#     [6, 38],
+#     [6, 45],
+#     [7, 11],
+#     [7, 12],
+#     [7, 14],
+#     [7, 22],
+#     [7, 24],
+#     [7, 26],
+#     [7, 34],
+#     [7, 35],
+#     [7, 37],
+#     [7, 45],
+#     [8, 11],
+#     [8, 13],
+#     [8, 16],
+#     [8, 22],
+#     [8, 25],
+#     [8, 28],
+#     [8, 34],
+#     [8, 36],
+#     [8, 39],
+#     [8, 45],
+#     [9, 11],
+#     [9, 12],
+#     [9, 16],
+#     [9, 22],
+#     [9, 24],
+#     [9, 28],
+#     [9, 34],
+#     [9, 35],
+#     [9, 39],
+#     [9, 45],
+#     [10, 11],
+#     [10, 14],
+#     [10, 15],
+#     [10, 22],
+#     [10, 26],
+#     [10, 27],
+#     [10, 34],
+#     [10, 37],
+#     [10, 38],
+#     [10, 45],
+#     [11, 17],
+#     [11, 18],
+#     [11, 19],
+#     [11, 20],
+#     [11, 21],
+#     [11, 29],
+#     [11, 30],
+#     [11, 31],
+#     [11, 32],
+#     [11, 33],
+#     [11, 40],
+#     [11, 41],
+#     [11, 42],
+#     [11, 43],
+#     [11, 44],
+#     [12, 23],
+#     [12, 25],
+#     [12, 27],
+#     [12, 30],
+#     [12, 32],
+#     [12, 46],
+#     [13, 23],
+#     [13, 24],
+#     [13, 26],
+#     [13, 29],
+#     [13, 31],
+#     [13, 46],
+#     [14, 23],
+#     [14, 25],
+#     [14, 28],
+#     [14, 30],
+#     [14, 33],
+#     [14, 46],
+#     [15, 23],
+#     [15, 24],
+#     [15, 28],
+#     [15, 29],
+#     [15, 33],
+#     [15, 46],
+#     [16, 23],
+#     [16, 26],
+#     [16, 27],
+#     [16, 31],
+#     [16, 32],
+#     [16, 46],
+#     [17, 23],
+#     [17, 25],
+#     [17, 27],
+#     [17, 34],
+#     [17, 46],
+#     [18, 23],
+#     [18, 24],
+#     [18, 26],
+#     [18, 34],
+#     [18, 46],
+#     [19, 23],
+#     [19, 25],
+#     [19, 28],
+#     [19, 34],
+#     [19, 46],
+#     [20, 23],
+#     [20, 24],
+#     [20, 28],
+#     [20, 34],
+#     [20, 46],
+#     [21, 23],
+#     [21, 26],
+#     [21, 27],
+#     [21, 34],
+#     [21, 46],
+#     [22, 23],
+#     [22, 29],
+#     [22, 30],
+#     [22, 31],
+#     [22, 32],
+#     [22, 33],
+#     [22, 46],
+#     [23, 35],
+#     [23, 36],
+#     [23, 37],
+#     [23, 38],
+#     [23, 39],
+#     [23, 40],
+#     [23, 41],
+#     [23, 42],
+#     [23, 43],
+#     [23, 44],
+#     [23, 45],
+#     [24, 47],
+#     [25, 47],
+#     [26, 47],
+#     [27, 47],
+#     [28, 47],
+#     [29, 47],
+#     [30, 47],
+#     [31, 47],
+#     [32, 47],
+#     [33, 47],
+#     [34, 47],
+#     [35, 47],
+#     [36, 47],
+#     [37, 47],
+#     [38, 47],
+#     [39, 47],
+#     [40, 47],
+#     [41, 47],
+#     [42, 47],
+#     [43, 47],
+#     [44, 47],
+#     [45, 47],
+#     [46, 47]
+# ]
+
+import pycosat
+from timeit import default_timer as timer
+
+# x(v, c) <--> vertex v is set to color c
+def x(v, c):
+    return c*N + v
+
+# x(1,0) = 1, x(2,0) = 2, ..., x(n-1, 0) = n-1, x(1,1) = n, ...
+
+cnf = []
+
+# Constraint 1: every vertex gets a color
+for v in range(1, N+1):
+    cnf.append([x(v, c) for c in range(COLORS)])
+
+# Constraint 2: if (u, v) is an edge, then u and v have different colors
+for u, v in EDGES:
+    for c in range(COLORS):
+        cnf.append([-x(u, c), -x(v, c)])
+
+# Constraint 3: every vertex has at most one color
+for v in range(1, N+1):
+   for c1 in range(COLORS):
+       for c2 in range(c1+1, COLORS):
+           cnf.append([-x(v, c1), -x(v, c1)])
+
+# Symmetry breaking -- try solving the second graph for K=5 with and without these constraints!
+cnf.append([x(1, 0)])
+cnf.append([x(2, 1)])
+
+t = timer()
+soln = pycosat.solve(cnf)
+time = timer()-t
+print(soln)
+print(f'{COLORS} colors took {time} sec')
\ No newline at end of file