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;
bool sortbysec(const pair<long long, long long> &a,
               const pair<long long, long long> &b) {
  return (a.second < b.second);
}
double pi = 3.141592653589793238;
void my_ans_is() {
  long long d[1000001] = {0};
  for (long long i = 1; i < 1000001; i++) d[i] = 1;
  long long s = 0, m = 1073741824;
  for (long long i = 2; i <= 1000000; i++) {
    for (long long j = i; j <= 1000000; j += i) d[j]++;
  }
  long long a, b, c;
  cin >> a >> b >> c;
  for (long long i = 1; i < a + 1; i++) {
    for (long long j = 1; j < b + 1; j++) {
      for (long long k = 1; k < c + 1; k++) {
        s = s % m + d[i * j * k] % m;
        s %= m;
      }
    }
  }
  cout << s;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  ;
  { my_ans_is(); }
  return 0;
}