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 main() {
  long long sum = 0;
  int d[1000000 + 1] = {0};
  for (int i = 1; i <= 1000000; i++) {
    for (int j = i; j <= 1000000; j += i) {
      d[j]++;
    }
  }
  int a, b, c;
  cin >> a >> b >> c;
  for (auto(i) = (1); (i) < (a + 1); ++(i))
    for (auto(j) = (1); (j) < (b + 1); ++(j))
      for (auto(k) = (1); (k) < (c + 1); ++(k))
        sum = (sum + d[i * j * k]) % 1073741824;
  cout << sum % 1073741824;
  return 0;
}