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 n=sc.nextInt(),m=sc.nextInt(),k=sc.nextInt();
    for(int i=0;i<=n;i++) {
    	for(int j=0;j<=m;j++) {
    		int buff=Math.max(0,(m-j)*i)+Math.max(0,(n-i)*j);
    		//System.out.println(buff);
    		if(buff==k) {
    			System.out.println("Yes");
    			System.exit(0);
    		}
    	}
    }
    System.out.println("No");
  }
}
