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;
vector<long long> p(1000001);
bool vis[1000001];
int main() {
  long long a, b, c;
  cin >> a >> b >> c;
  vector<long long> v;
  memset(vis, false, sizeof(vis));
  for (long long i = 1; i <= a; i++) {
    for (long long j = 1; j <= b; j++) {
      for (long long k = 1; k <= c; k++) v.push_back(i * j * k);
    }
  }
  long long ans = 0;
  for (long long i = 0; i < v.size(); i++) {
    long long s = 0;
    if (vis[v[i]] == false) {
      for (long long j = 1; j * j <= v[i]; j++) {
        if (v[i] % j == 0) {
          if (j != v[i] / j)
            s = (s % 1073741824 + 2) % 1073741824;
          else
            s = (s % 1073741824 + 1) % 1073741824;
        }
      }
      p[v[i]] = s;
      vis[v[i]] = true;
      ans = (ans + s % 1073741824) % 1073741824;
    } else
      ans = (ans + p[v[i]] % 1073741824) % 1073741824;
  }
  cout << ans;
  return 0;
}
