Your task is to find how many complex numbers x satisfy the following two conditions: xn = a + bi and xm = c + di.

Input

The first line contains integers a, b, n (-1018 ≤ a, b ≤ 1018, 1 ≤ n ≤ 100). The second line contains integers c, d and m (-1018 ≤ c, d ≤ 1018, 1 ≤ m ≤ 100). It is guaranteed that a2 + b2 > 0 и c2 + d2 > 0.

Output

Print one integer: the answer to the problem.