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:

<image>

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 primes[] = {2,  3,  5,  7,  11, 13, 17, 19, 23, 29, 31, 37, 41,
                43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97};
int divs(int num) {
  int sum = 1;
  for (int i = 0; i < 25; i++) {
    if (num == 1) break;
    int d = 1;
    while ((num % primes[i]) == 0) {
      d++;
      num /= primes[i];
    }
    sum *= (d);
  }
  return sum;
}
int main() {
  int i, j, k;
  long long total = 0;
  cin >> i >> j >> k;
  int grid[i][j][k];
  for (int a = 1; a <= i; a++)
    for (int b = 1; b <= j; b++)
      for (int c = 1; c <= k; c++) total += divs(a * b * c);
  cout << total << endl;
  return 0;
}