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 d[1010];
int f[1001001] = {0};
int main() {
  int a, b, c, sum = 0;
  cin >> a >> b >> c;
  for (int i = 1; i <= a; i++)
    for (int j = 1; j <= b; j++)
      for (int k = 1; k <= c; k++) {
        int t = i * j * k, s = 1;
        if (f[t]) {
          sum = (sum + s) % 1073741824;
          continue;
        }
        memset(d, 0, sizeof(d));
        for (int e = 2; e <= 100; e++)
          while (t % e == 0) d[e]++, t /= e;
        for (int e = 2; e <= 100; e++)
          if (d[e]) s *= (d[e] + 1);
        f[t] = s;
        sum = (sum + s) % 1073741824;
      }
  cout << sum << endl;
}