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 ≤ 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() {
  long long a, b, c, i, j, k, d, s = 0, t, l, n;
  cin >> a >> b >> c;
  map<int, int> m;
  for (i = 1; i <= a; i++) {
    for (j = 1; j <= b; j++) {
      for (k = 1; k <= c; k++) {
        m[i * j * k]++;
      }
    }
  }
  for (auto it : m) {
    if (it.first == 1)
      t = 1;
    else {
      i = it.first;
      n = sqrt(i);
      t = 2;
      for (j = 2; j <= n; j++) {
        if (i % j == 0 && j * j != i)
          t += 2;
        else if (i % j == 0)
          t += 1;
      }
      t *= (it.second);
    }
    s += t;
    s %= 1073741824;
  }
  cout << s;
}
