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:

<image>

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>
using namespace std;
long long a[10000001], i, j;
void divisor() {
  for (i = 1; i <= 1000000; i++) {
    for (j = i; j <= 1000000; j += i) a[j]++;
  }
}
int main() {
  divisor();
  long aa, b, c;
  while (cin >> aa >> b >> c) {
    long long ans = 0, i, j, k, d;
    for (i = 1; i <= aa; i++) {
      for (j = 1; j <= b; j++) {
        for (k = 1; k <= c; k++) {
          d = i * j * k;
          ans += a[d];
          ans = ans % 1073741824;
        }
      }
    }
    cout << ans << endl;
  }
  return 0;
}