#include <bits/stdc++.h>
using namespace std;
long long a, b, c, i, j, t, z[2222], p[2222], q[2222], g[2222], h[2222],
    s[2222 * 2222], f[2222 * 2222];
inline void inc(long long &a, long long b) {
  a += b;
  if (a > 1073741824) a -= 1073741824;
}
int main() {
  scanf("%lld%lld%lld", &a, &b, &c);
  q[1] = 1;
  for (i = 2; i <= c; i++) {
    if (!z[i]) p[++t] = i, q[i] = -1;
    for (j = 1; j <= t && i * p[j] <= c; j++) {
      z[i * p[j]] = 1;
      if (!(i % p[j])) {
        q[i * p[j]] = 0;
        break;
      } else
        q[i * p[j]] = -q[i];
    }
  }
  t = 0;
  for (i = 1; i <= a; i++)
    for (j = 1; j <= b; j++) f[i * j]++;
  for (i = 1; i <= a * b; i++)
    for (j = 1; j <= a * b / i; j++) inc(s[i], f[i * j]);
  for (i = 1; i <= c; i++)
    for (j = 1; j <= a * b / i; j++) inc(g[i], s[i * j]);
  for (i = 1; i <= c; i++)
    for (j = 1; j <= i; j++) inc(h[i], i / j);
  for (i = 1; i <= c; i++)
    (t += q[i] * g[i] * h[c / i] % 1073741824) %= 1073741824;
  printf("%lld", (t + 1073741824) % 1073741824);
  return 0;
}

### Prompt

Generate a CPP solution to the following 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:

<image>

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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
long long a, b, c, i, j, t, z[2222], p[2222], q[2222], g[2222], h[2222],
    s[2222 * 2222], f[2222 * 2222];
inline void inc(long long &a, long long b) {
  a += b;
  if (a > 1073741824) a -= 1073741824;
}
int main() {
  scanf("%lld%lld%lld", &a, &b, &c);
  q[1] = 1;
  for (i = 2; i <= c; i++) {
    if (!z[i]) p[++t] = i, q[i] = -1;
    for (j = 1; j <= t && i * p[j] <= c; j++) {
      z[i * p[j]] = 1;
      if (!(i % p[j])) {
        q[i * p[j]] = 0;
        break;
      } else
        q[i * p[j]] = -q[i];
    }
  }
  t = 0;
  for (i = 1; i <= a; i++)
    for (j = 1; j <= b; j++) f[i * j]++;
  for (i = 1; i <= a * b; i++)
    for (j = 1; j <= a * b / i; j++) inc(s[i], f[i * j]);
  for (i = 1; i <= c; i++)
    for (j = 1; j <= a * b / i; j++) inc(g[i], s[i * j]);
  for (i = 1; i <= c; i++)
    for (j = 1; j <= i; j++) inc(h[i], i / j);
  for (i = 1; i <= c; i++)
    (t += q[i] * g[i] * h[c / i] % 1073741824) %= 1073741824;
  printf("%lld", (t + 1073741824) % 1073741824);
  return 0;
}

```