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 File1{
	static long dp[][];
	public static void main(String[] args){
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		int m = in.nextInt();
		int x = in.nextInt();
		if(x*2>Math.min(n,m)+1){
			System.out.println(0);
			return;
		}
		int y = solve(n,m,x);
		System.out.println(y);
	}
	private static int solve(int n,int m,int x){
		if(x==1){
			if(n==1) return (m+1)/2;
			if(m==1) return (n+1)/2;
			return (n*m-(n-2)*(m-2))/2;
		}
		return solve(n-2,m-2,x-1);
	}
}