A chessboard n × m in size is given. During the zero minute we repaint all the black squares to the 0 color. During the i-th minute we repaint to the i color the initially black squares that have exactly four corner-adjacent squares painted i - 1 (all such squares are repainted simultaneously). This process continues ad infinitum. You have to figure out how many squares we repainted exactly x times.

The upper left square of the board has to be assumed to be always black. Two squares are called corner-adjacent, if they have exactly one common point.

Input

The first line contains integers n and m (1 ≤ n, m ≤ 5000). The second line contains integer x (1 ≤ x ≤ 109).

Output

Print how many squares will be painted exactly x times.

Examples

Input

3 3
1


Output

4


Input

3 3
2


Output

1


Input

1 1
1


Output

1
#include <bits/stdc++.h>
using namespace std;
const long double EPS = 1e-9;
const int MAXN = 1000;
int main() {
  int n, m;
  cin >> n >> m;
  int k, ans = 0;
  cin >> k;
  for (int x = 0; x < (int)(n); ++x) {
    for (int y = 0; y < (int)(m); ++y) {
      if ((x + y) & 1) continue;
      int t = min(x + 1, y + 1);
      t = min(t, n - x);
      t = min(t, m - y);
      if (t == k) ++ans;
    }
  }
  cout << ans << endl;
  return 0;
}
