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;
class Main{
	public static void main(String[]args) {
		Scanner scan=new Scanner(System.in);
		int a=scan.nextInt();
		int b=scan.nextInt();
		int c=scan.nextInt();
		boolean bool=false;
		for(int i=0;i<=a;i++) {
			for(int j=0;j<=b;j++) {
				int bla=(a-i)*j+(b-j)*i;
				if(bla==c) {
					bool=true;
				}
			}
		}
		if(bool==true) {
			pl("Yes");
		}
		else {
			pl("No");
		}
	}
	public static void pl(String str) {
		System.out.println(str);
	}
}
