#include <bits/stdc++.h>
using namespace std;
template <class T>
void max_self(T &a, const T &b) {
  if (a < b) a = b;
}
template <class T>
void min_self(T &a, const T &b) {
  if (a > b) a = b;
}
void err(istream_iterator<string> it) {}
template <typename T, typename... Args>
void err(istream_iterator<string> it, T a, Args... args) {
  cerr << *it << " = " << a << endl;
  err(++it, args...);
}
template <typename... Args>
void read(Args &...args) {
  ((cin >> args), ...);
}
template <typename... Args>
void write(Args... args) {
  ((cout << args), ...);
}
const int INF = 1e9 + 7;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long a, b, c, mod = (1 << 30), total = 0, maxV;
  read(a, b, c);
  maxV = a * b * c;
  vector<int> divC(maxV + 1, 0);
  for (long long num = 1; num <= maxV; ++num) {
    for (long long d = num; d <= maxV; d += num) {
      divC[d]++;
    }
  }
  for (long long o = 1; o <= a; ++o) {
    for (long long p = 1; p <= b; ++p) {
      for (long long q = 1; q <= c; ++q) {
        total += divC[o * p * q];
        if (total >= mod) total -= mod;
      }
    }
  }
  write(total, "\n");
}

### 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;
template <class T>
void max_self(T &a, const T &b) {
  if (a < b) a = b;
}
template <class T>
void min_self(T &a, const T &b) {
  if (a > b) a = b;
}
void err(istream_iterator<string> it) {}
template <typename T, typename... Args>
void err(istream_iterator<string> it, T a, Args... args) {
  cerr << *it << " = " << a << endl;
  err(++it, args...);
}
template <typename... Args>
void read(Args &...args) {
  ((cin >> args), ...);
}
template <typename... Args>
void write(Args... args) {
  ((cout << args), ...);
}
const int INF = 1e9 + 7;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long a, b, c, mod = (1 << 30), total = 0, maxV;
  read(a, b, c);
  maxV = a * b * c;
  vector<int> divC(maxV + 1, 0);
  for (long long num = 1; num <= maxV; ++num) {
    for (long long d = num; d <= maxV; d += num) {
      divC[d]++;
    }
  }
  for (long long o = 1; o <= a; ++o) {
    for (long long p = 1; p <= b; ++p) {
      for (long long q = 1; q <= c; ++q) {
        total += divC[o * p * q];
        if (total >= mod) total -= mod;
      }
    }
  }
  write(total, "\n");
}

```