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 answ[1000005];
int div(int n) {
  if (answ[n] != -1) {
    return answ[n];
  }
  int sqr = (int)sqrt((double)n);
  int ans = 0;
  for (int i = 1; i <= sqr; i++) {
    if (n % i == 0) {
      ans++;
      if (i * i != n) {
        ans++;
      }
    }
  }
  answ[n] = ans;
  return ans;
}
int main() {
  memset(answ, -1, sizeof(answ));
  int a, b, c;
  unsigned long long sum = 0;
  cin >> a >> b >> c;
  for (int i = 1; i <= a; i++) {
    for (int j = 1; j <= b; j++) {
      for (int k = 1; k <= c; k++) {
        sum += div(i * j * k);
        sum %= 1073741824;
      }
    }
  }
  cout << sum % 1073741824 << endl;
  return 0;
}
