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() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  long long a, b, c;
  cin >> a >> b >> c;
  long long final = 0;
  unordered_map<long long, long long> mp;
  for (long long i = 1; i <= a; ++i) {
    for (long long j = 1; j <= b; ++j) {
      for (long long k = 1; k <= c; ++k) {
        long long temp = i * j * k;
        long long count = 0;
        if (mp[temp]) {
          final += mp[temp] % (1 << 30);
        } else {
          for (long long x = 1; x <= sqrt(temp); ++x) {
            if (temp % x == 0) {
              if (x * x != temp) {
                count += 2;
              } else {
                count++;
              }
            }
          }
          mp[temp] = count % (1 << 30);
          final += mp[temp];
        }
      }
    }
  }
  cout << final % (1 << 30);
}
