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;
long long dp[1000003], dp2[1000003];
int main() {
  std::ios_base::sync_with_stdio(false);
  std::cin.tie(NULL);
  std::cout.tie(NULL);
  long long n, m, ans = 0, tmp, a;
  cin >> n >> m;
  cin >> a;
  for (long long x = 1; x <= n; x++) {
    for (long long y = 1; y <= m; y++) {
      if ((x % 2) != (y % 2)) continue;
      tmp = min(x, y);
      tmp = min(tmp, min((n - x + 1), (m - y + 1)));
      if (tmp == a) ans++;
    }
  }
  cout << ans;
  return 0;
}
