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;
long long int mod = 1073741824;
int sieve[4000000] = {0};
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long int a, b, c;
  for (int i = 1; i < 3000000; i++) {
    for (int j = i; j < 3000000; j += i) sieve[j]++;
  }
  cin >> a >> b >> c;
  long long int s = 0;
  for (long long int i = 1; i <= a; i++) {
    for (long long int j = 1; j <= b; j++) {
      for (long long int k = 1; k <= c; k++) {
        s += sieve[i * j * k];
        s %= mod;
      }
    }
  }
  double x = floor(s / mod);
  long long int ans = s - x;
  cout << ans;
  return 0;
}