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;
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  vector<long long> div(1000000 + 1, 2);
  div[1] = 1;
  for (int i = 2; i < 1000000; i++) {
    for (int j = 2 * i; j <= 1000000; j += i)
      div[j] = (div[j] + 1) % 1073741824;
  }
  int a, b, c;
  cin >> a >> b >> c;
  long long s = 0;
  for (int i = 1, Wub = a + 1; i < Wub; ++i)
    for (int j = 1, Wub = b + 1; j < Wub; ++j)
      for (int k = 1, Wub = c + 1; k < Wub; ++k) {
        s = (s % 1073741824 + div[i * j * k] % 1073741824) % 1073741824;
      }
  cout << s << "\n";
  return 0;
}