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;
#pragma GCC target("avx2")
#pragma GCC optimization("unroll-loops")
#pragma GCC optimize("O2")
constexpr int dx[] = {-1, 0, 1, 0, 1, 1, -1, -1};
constexpr int dy[] = {0, -1, 0, 1, 1, -1, 1, -1};
constexpr long long INF = 1999999999999999997;
constexpr int inf = INT_MAX;
constexpr int MAXSIZE = int(1e6) + 5;
constexpr auto PI = 3.14159265358979323846L;
constexpr auto oo = numeric_limits<int>::max() / 2 - 2;
constexpr auto eps = 1e-6;
constexpr auto mod = 1000000007;
constexpr auto MOD = 1000000007;
constexpr auto MOD9 = 1000000009;
constexpr auto maxn = 100006;
void fastio() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
}
int d(int l) {
  int cnt = 0;
  for (int i = 1; i * i <= l; i++) {
    if (l % i == 0) cnt += 2;
    if (i * i == l) cnt--;
  }
  return cnt;
}
int m = 1073741824;
int main() {
  fastio();
  int a, b, c;
  cin >> a >> b >> c;
  int ans = 0;
  for (int i = 1; i <= a; i++) {
    for (int j = 1; j <= b; j++) {
      for (int k = 1; k <= c; k++) {
        int l = i * j * k;
        ans += d(l);
        ans % m;
      }
    }
  }
  cout << ans;
}