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


import java.util.Scanner;

public class B {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int m = in.nextInt();
        int x = in.nextInt();
        while (n > 0 && m > 0 && x > 1) {
            n -= 2;
            m -= 2;
            x--;
        }
        if (n <= 0 | m <= 0) {
            System.out.println(0);
            return;
        }
        int ans = 0;
        ans += (m + 1) / 2; // first row
        if (n > 1)
            ans += (m + n % 2) / 2; // last row
        n = Math.max(0, n - 2 - m % 2); // remove the 2 rows
        ans += (n + 1) / 2; // last column
        if (m > 1)
            ans += (n + m % 2) / 2; // first column
        System.out.println(ans);
    }
}
