Let's denote d(n) as the number of divisors of a positive integer n . You are given three integers a , b and c . Your task is to calculate the following sum: Find the sum modulo 1073741824 (230).

输入描述:

The first line contains three space-separated integers a, b and c (1 ≤ a, b, c ≤ 2000).

输出描述:

Print a single integer — the required sum modulo 1073741824(230).

备注:

For the first example.d(1·1·1) = d(1) = 1; d(1·1·2) = d(2) = 2; d(1·2·1) = d(2) = 2; d(1·2·2) = d(4) = 3; d(2·1·1) = d(2) = 2; d(2·1·2) = d(4) = 3; d(2·2·1) = d(4) = 3; d(2·2·2) = d(8) = 4. So the result is 1 + 2 + 2 + 3 + 2 + 3 + 3 + 4 = 20.