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:

$\sum_{i = 1}^{a} \sum_{j = 1}^{b} \sum_{k = 1}^{c} d(i \cdot j \cdot k)$

Find the sum modulo 1073741824 (2^30).

-----Input-----

The first line contains three space-separated integers a, b and c (1 ≤ a, b, c ≤ 100).

-----Output-----

Print a single integer — the required sum modulo 1073741824 (2^30).

-----Examples-----

Input 2 2 2

Output 20

Input 5 6 7

Output 1520

-----Note-----

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.