Complex Root

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

Input

The first line contains integers a, b, n (-10^18 ≤ a, b ≤ 10^18, 1 ≤ n ≤ 100). The second line contains integers c, d and m (-10^18 ≤ c, d ≤ 10^18, 1 ≤ m ≤ 100). It is guaranteed that a^2 + b^2 > 0 и c^2 + d^2 > 0.

Output

Print one integer: the answer to the problem.

Examples