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;

/*
 * To change this template, choose Tools | Templates
 * and open the template in the editor.
 */
/**
 *
 * @author teacher
 */
public class Chess3 {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        long n = in.nextInt();
        long m = in.nextInt();
        long x = in.nextInt();
        if (x == 0) {
            System.out.println(n * m / 2);
        } else {
            long nx = (n - (x-1) * 2);
            long mx = (m - (x-1) * 2);
            if (nx < 0 || mx < 0) {
                System.out.println(0);
            } else if (nx == 1 && mx == 1) {
                System.out.println(1);
            } else {
                long res = (2 * nx + 2 * mx - 4) / 2;
                System.out.println(res);

            }
        }
    }
}
