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;
inline void pisz(int n) { printf("%d\n", n); }
const int fx[4][2] = {{0, 1}, {-1, 0}, {0, -1}, {1, 0}};
const int fxx[9][2] = {{0, 0}, {0, 1},  {0, -1}, {1, 0},  {-1, 0},
                       {1, 1}, {1, -1}, {-1, 1}, {-1, -1}};
const int N = 500;
const long long mod = 1000000007;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long n, m, x;
  cin >> n >> m >> x;
  x--;
  long long a = n - 2 * x;
  long long b = m - 2 * x;
  long long err = 0;
  if (a > 0 && b > 0) {
    err = 1;
    if (a == 1 && b == 1) {
      cout << 1 << "\n";
    } else if (a == 1 || b == 2) {
      cout << (a + b) / 2;
    } else {
      cout << a + b - 2;
    }
  }
  if (!err) {
    cout << 0;
  }
}
