Problem: 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:

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Find the sum modulo 1073741824 (230).

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).

Examples

Input

2 2 2


Output

20


Input

4 4 4


Output

328


Input

10 10 10


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.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
long long array[1000007];
int main() {
  long long k, i, j, x, y, z, sum;
  for (i = 1; i < 1000007; i++) {
    for (j = i; j < 1000007; j = j + i) {
      array[j]++;
    }
  }
  scanf("%lld %lld %lld", &x, &y, &z);
  sum = 0;
  for (i = 1; i <= x; i++) {
    for (j = 1; j <= y; j++) {
      for (k = 1; k <= z; k++) {
        sum = sum + array[i * j * k];
        sum = sum % 1073741824;
      }
    }
  }
  printf("%lld\n", sum);
  return 0;
}