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;
const int maxn = 2e3 + 10;
const int mod = 1073741824;
int g[maxn][maxn], prime[maxn], mo[maxn];
bool vis[maxn];
int cnt = 0;
void table() {
  mo[1] = 1;
  memset(g, 0, sizeof g);
  for (int i = 2; i < maxn; i++) {
    if (!vis[i]) prime[cnt++] = i, mo[i] = -1;
    for (int j = 0; j < cnt && i * prime[j] < maxn; j++) {
      vis[i * prime[j]] = true;
      mo[i * prime[j]] = -mo[i];
      if (i % prime[j] == 0) {
        mo[i * prime[j]] = 0;
        break;
      }
    }
  }
}
int ggcd(int a, int b) {
  if (!b) return a;
  if (g[a][b]) return g[a][b];
  return g[a][b] = g[b][a] = ggcd(b, a % b);
}
int solve(int n, int d, int k) {
  long long ans = 0;
  for (int i = 1; i <= n; i++) {
    if (ggcd(i * d, k) == 1) ans += n / i;
  }
  return ans;
}
int main() {
  table();
  int n, m, t;
  cin >> n >> m >> t;
  if (n > m) swap(n, m);
  if (n > t) swap(n, t);
  if (t > m) swap(m, t);
  int ans = 0;
  for (int k = 1; k <= t; k++) {
    int tmp = 0;
    for (int d = 1; d <= n; d++) {
      if (mo[d] != 0) tmp += mo[d] * solve(n / d, d, k) * solve(m / d, d, k);
    }
    ans = (ans + t / k * tmp + mod) % mod;
  }
  cout << (ans % mod + mod) % mod << endl;
}