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) {
		Scanner sc = new Scanner(System.in);
		
		int h = Integer.parseInt(sc.next());
		int w = Integer.parseInt(sc.next());
		
		int k = Integer.parseInt(sc.next());
		
		int now = 0;
		boolean jdg = false;
		
		for(int i = 0 ; i <= w ;i++) {
			for(int j = 0 ; j <= h ; j++) {
				now = h * i + w * j - (i * j * 2);
				//System.out.println(now);
				if(now == k) {
					jdg = true;
					break;
				}
			}
		}
		
		
		if(jdg) {
			System.out.println("Yes");
		}
		else {
			System.out.println("No");
		}

	}

}
