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:

<image>

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).

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.
#include <bits/stdc++.h>
using namespace std;
int main(int argc, char** argv) {
  int a, b, c, ans = 0;
  cin >> a >> b >> c;
  int D[1000001] = {1, 1};
  for (int i = 1; i < a + 1; i++) {
    for (int j = 1; j < b + 1; j++) {
      for (int k = 1; k < c + 1; k++) {
        int l = i * j * k;
        if (!D[l]) {
          long double sqi = sqrtl(l);
          int sum = 0;
          for (int m = 2; m < (int)sqi + 1; m++) {
            if (!(l % m)) {
              if (sqi == m) {
                sum++;
                continue;
              }
              sum += 2;
            }
          }
          D[l] = sum + 2;
        }
        ans += D[l];
      }
    }
  }
  cout << ans % (1 << 31) << endl;
  return 0;
}
