Number Challenge

Description:

Input:

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

Output:

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

Sample Input:

2 2 2

Sample Output:

20

Sample Input:

4 4 4

Sample Output:

328

Sample Input:

10 10 10

Sample Output:

11536

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.