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.io.IOException;
import java.util.Scanner;
class Main
{

	static int n,m,k,end=0;
	public static void main(String[] args)throws IOException
	{
		Scanner sc = new Scanner(System.in);
		n=sc.nextInt();m=sc.nextInt();k=sc.nextInt();
		for(int i=0;end==0&&i<=n;i++)
		{
			for(int j=0;j<=m;j++)
			{
				if(m*i+(n-i)*j-i*j==k){end=1;break;}
			}
		}
		if(end==1){System.out.println("Yes");}
		else{System.out.println("No");}
	}

}
