class matrix:
    #you should not change this value on its own, but I'm going to let you
    array = []
    def __init__(self, arr):
        self.array = self.validate(arr)
        if(self.array == False):
            self.array = []
    def isSquare(self):
        return len(self.array) == len(self.array[0])
    def infnorm(self, v = array):
        max = 0
        for x in v:
            if abs(x) > max:
                max = x
        return max
    #row b + c times row a
    def rowAdd(self, a, b, c = 1):
        for i in range(len(self.array[b])):
            self.array[b][i] += c*self.array[a][i]
    #row a = c*row a
    def rowMul(self, a, c):
        for i in range(len(self.array[a])):
            self.array[a][i] *= c

    def validate(self, arr):
        array = []
        for i in arr:
            if (type(i) in [list]):
                for j in i:
                    if type(j) not in [int, float]:
                        return False
                if(len(i) == len(arr[0])):
                    array.append(i)
                else:
                    return False
            elif type(i) in [int, float]:
                array.append([i])
            else:
                print("input array not valid")
                return False
        return array

    def __str__(self):
        string = ""
        for i in self.array:
            string += str(i)
            string += "\n"
        return string

    def __add__(self,other):
        array = self.array
        try:
            for i in range(len(other.array)):
                for j in range(len(other.array[0])):
                    array[i][j] += other.array[i][j]
        except:
            print("arrays are probably not the same size")
            return self
        return matrix(array)

    def __sub__(self,other):
        array = self.array
        try:
            for i in range(len(other.array)):
                for j in range(len(other.array[0])):
                    array[i][j] -= other.array[i][j]
        except:
            print("arrays are probably not the same size")
            return self
        return matrix(array)


    def __mul__(self, other):
        otherA = []
        array = []
        if type(other) in {int, float}:
            for i in range(len(array)):
                otherA.append([])
                for j in range(len(array[0])):
                    otherA.append(other*array[i][j])
            return otherA


        for i in range(len(self.array)):
            array.append([])
            for j in range(len(other.array[0])):
                array[i].append(0)
        try:
            for i in range(len(self.array)):
                for j in range(len(other.array[0])):
                    for k in range(len(other.array)):
                        array[i][j] += self.array[i][k] * other.array[k][j]

        except Exception as e:
            print(e, ": arrays are probably the wrong size")
            return self
        return matrix(array)

    def __len__(self):
        return len(self.array)

    def __getitem__(self, index):
        return self.array[index]
    def __setitem__(self, key, value):
        self.array[key] = value

A = [[15,7,-7],[-1,1,1],[13,7,-5]]

def power(A, x = [[1],[0],[0]], y =[[0],[0],[0]], it = 0):
    p = 0
    z = 0
    x = matrix(x)
    A = matrix(A)
    y = A*x
    for i in range(len(y)):
        if abs(y[i][0]) > abs(z):
            z = y[i][0]
            p = i
            break
    for i in range(len(y)):
        x[i] = y[i][0]/z
    lbd = y[p]
    if(it < 5):
        return power(A, x, y, it+1)
    else:
        print(lbd)
power(A)