class SquareMatrix(): def __init__(self, n, mod=1000000007): self.n = n self.mat = [[0 for j in range(n)] for i in range(n)] self.mod = mod @staticmethod def id(n, mod=1000000007): res = SquareMatrix(n, mod) for i in range(n): res.mat[i][i] = 1 return res @staticmethod def modinv(n, mod): assert n % mod != 0 c0, c1 = n, mod a0, a1 = 1, 0 b0, b1 = 0, 1 while c1: a0, a1 = a1, a0 - c0 // c1 * a1 b0, b1 = b1, b0 - c0 // c1 * b1 c0, c1 = c1, c0 % c1 return a0 % mod def set(self, arr): for i in range(self.n): for j in range(self.n): self.mat[i][j] = arr[i][j] % self.mod def operate(self, vec): assert len(vec) == self.n res = [0 for _ in range(self.n)] for i in range(self.n): for j in range(self.n): res[i] += self.mat[i][j] * vec[j] res[i] %= self.mod return res def add(self, other): assert other.n == self.n res = SquareMatrix(self.n, self.mod) for i in range(self.n): for j in range(self.n): res.mat[i][j] = self.mat[i][j] + other.mat[i][j] res.mat[i][j] %= self.mod return res def subtract(self, other): assert other.n == self.n res = SquareMatrix(self.n, self.mod) for i in range(self.n): for j in range(self.n): res.mat[i][j] = self.mat[i][j] - other.mat[i][j] res.mat[i][j] %= self.mod return res def times(self, k): res = SquareMatrix(self.n, self.mod) for i in range(self.n): for j in range(self.n): res.mat[i][j] = self.mat[i][j] * k res.mat[i][j] %= self.mod return res def multiply(self, other): assert self.n == other.n res = SquareMatrix(self.n, self.mod) for i in range(self.n): for j in range(self.n): for k in range(self.n): res.mat[i][j] += self.mat[i][k] * other.mat[k][j] res.mat[i][j] %= self.mod return res def power(self, k): tmp = SquareMatrix(self.n, self.mod) for i in range(self.n): for j in range(self.n): tmp.mat[i][j] = self.mat[i][j] res = SquareMatrix.id(self.n, self.mod) while k: if k & 1: res = res.multiply(tmp) tmp = tmp.multiply(tmp) k >>= 1 return res def trace(self): res = 0 for i in range(self.n): res += self.mat[i][i] res %= self.mod return res def determinant(self): res = 1 tmp = SquareMatrix(self.n, self.mod) for i in range(self.n): for j in range(self.n): tmp.mat[i][j] = self.mat[i][j] for j in range(self.n): if tmp.mat[j][j] == 0: for i in range(j + 1, self.n): if tmp.mat[i][j] != 0: idx = i break else: return 0 for k in range(self.n): tmp.mat[j][k], tmp.mat[idx][k] = tmp.mat[idx][k], tmp.mat[j][k] res *= -1 inv = SquareMatrix.modinv(tmp.mat[j][j], self.mod) for i in range(j + 1, self.n): c = -inv * tmp.mat[i][j] % self.mod for k in range(self.n): tmp.mat[i][k] += c * tmp.mat[j][k] tmp.mat[i][k] %= self.mod for i in range(self.n): res *= tmp.mat[i][i] res %= self.mod return res def transpose(self): res = SquareMatrix(self.n, self.mod) for i in range(self.n): for j in range(self.n): res.mat[i][j] = self.mat[j][i] return res def inverse(self): #self.determinant() != 0 res = SquareMatrix.id(self.n, self.mod) tmp = SquareMatrix(self.n, self.mod) sgn = 1 for i in range(self.n): for j in range(self.n): tmp.mat[i][j] = self.mat[i][j] for j in range(self.n): if tmp.mat[j][j] == 0: for i in range(j + 1, self.n): if tmp.mat[i][j] != 0: idx = i break else: return 0 for k in range(self.n): tmp.mat[j][k], tmp.mat[idx][k] = tmp.mat[idx][k], tmp.mat[j][k] res.mat[j][k], res.mat[idx][k] = res.mat[idx][k], res.mat[j][k] inv = SquareMatrix.modinv(tmp.mat[j][j], self.mod) for k in range(self.n): tmp.mat[j][k] *= inv tmp.mat[j][k] %= self.mod res.mat[j][k] *= inv res.mat[j][k] %= self.mod for i in range(self.n): c = tmp.mat[i][j] for k in range(self.n): if i == j: continue tmp.mat[i][k] -= tmp.mat[j][k] * c tmp.mat[i][k] %= self.mod res.mat[i][k] -= res.mat[j][k] * c res.mat[i][k] %= self.mod return res def linear_equations(self, vec): return self.inverse().operate(vec) def print(self): print(*self.mat, sep='\n') def is_same(A, B): if A.n != B.n: return False n = A.n for i in range(n): for j in range(n): if A.mat[i][j] != B.mat[i][j]: return False return True from itertools import chain def discrete_logarithm(x, y, mod): #x**k % mod == y if is_same(y, SquareMatrix.id(2, mod)): return -1 if is_same(x, SquareMatrix(2, mod)) and is_same(y, SquareMatrix(2, mod)): return 1 sqrt_mod = int(mod**0.5 + 1000) power_x = {} p = SquareMatrix.id(2, mod) for i in range(sqrt_mod): if is_same(p, y): return i #x**i % mod == y tmp = p.multiply(y) tmp = tuple(chain.from_iterable(tmp.mat)) power_x[tmp] = i p = p.multiply(x) z = x.power(sqrt_mod) g = SquareMatrix.id(2, mod) for i in range(1, sqrt_mod + 3): g = g.multiply(z) tmp = tuple(chain.from_iterable(g.mat)) if tmp in power_x: res = i * sqrt_mod - power_x[tmp] if is_same(x.power(res), y): return res return -1 MOD = int(input()) a = [tuple(map(int, input().split())) for _ in range(2)] b = [tuple(map(int, input().split())) for _ in range(2)] A = SquareMatrix(2, MOD) B = SquareMatrix(2, MOD) A.set(a) B.set(b) print(discrete_logarithm(A, B, MOD))