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>
using namespace std;
int main() {
  cin.tie(0);
  ios_base::sync_with_stdio(false);
  int a, b, c;
  int sum = 0;
  cin >> a >> b >> c;
  vector<int> cnt(1000001);
  for (int i = 1; i <= a; i++) {
    for (int j = 1; j <= b; j++) {
      for (int k = 1; k <= c; k++) {
        int chislo = i * j * k;
        int cnt_ch = 0;
        if (cnt[chislo] == 0) {
          for (int m = 1; m <= sqrt(chislo); m++) {
            if (chislo % m == 0) {
              if (chislo / m == chislo / (chislo / m)) {
                cnt_ch++;
              } else {
                cnt_ch += 2;
              }
            }
          }
          cnt[chislo] = cnt_ch;
        }
        sum += cnt[chislo];
      }
    }
  }
  cout << sum << endl;
  return 0;
}