We have a grid with N rows and M columns of squares. Initially, all the squares are white.

There is a button attached to each row and each column. When a button attached to a row is pressed, the colors of all the squares in that row are inverted; that is, white squares become black and vice versa. When a button attached to a column is pressed, the colors of all the squares in that column are inverted.

Takahashi can freely press the buttons any number of times. Determine whether he can have exactly K black squares in the grid.

Constraints

* 1 \leq N,M \leq 1000
* 0 \leq K \leq NM

Input

Input is given from Standard Input in the following format:


N M K


Output

If Takahashi can have exactly K black squares in the grid, print `Yes`; otherwise, print `No`.

Examples

Input

2 2 2


Output

Yes


Input

2 2 1


Output

No


Input

3 5 8


Output

Yes


Input

7 9 20


Output

No
import java.util.Scanner;

public class Main {
	public static void main(String[]args) {
		try(Scanner scan = new Scanner(System.in)){

			int N = scan.nextInt();
			int M = scan.nextInt();
			int K = scan.nextInt();



			int goukei = 0;
			int ok = 0;
			for(int i = 0;i<=N;i++) {
				for(int j = 0;j<=M;j++) {
					goukei =  i*M+j*N-2*i*j;
					if(goukei==K) {
						ok=1;break;
					}
				}
			}

			if(ok==1)System.out.println("Yes");
			else System.out.println("No");

		}


	}


}
