Easy Number Challenge

Time Limit: 2 seconds

Memory Limit: 256 megabytes

Description

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).

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 (230).

Sample Input

Input
2 2 2
Output
20
Input
5 6 7
Output
1520

Sample Output

None

Hint

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.

Source

None

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