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;
const int N = 1e5 + 5, M = 1e8, OO = 2000000007;
long long div1[1000009], x, y, z, total;
void seive() {
  for (int i = 2; i <= 1000000; i++) {
    if (div1[i] == 1) {
      for (int j = i; j <= 1000000; j += i) {
        int c = 0, m;
        m = j;
        while (m % i == 0) {
          c++;
          m /= i;
        }
        div1[j] *= (c + 1);
      }
    }
  }
}
int main() {
  fill(div1, div1 + 1000009, 1);
  cin >> x >> y >> z;
  seive();
  for (int i = 1; i <= x; i++)
    for (int j = 1; j <= y; j++)
      for (int k = 1; k <= z; k++)
        total =
            (total % 1073741824 + div1[i * j * k] % 1073741824) % 1073741824;
  cout << total << endl;
  return 0;
}