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.*;
public class Main{
        public static void main(String[] args){
                Scanner sc = new Scanner(System.in);
                int n = sc.nextInt();
                int m = sc.nextInt();
                int k = sc.nextInt();
                boolean ebishu = true;
                for(int i = 0 ; i <= n && ebishu ; i++){
                        for(int j = 0 ; j <= m && ebishu ; j++){
                                if(i * j + (n - i) * (m - j) == k){
                                        ebishu = false;
                                }
                        }
                }
                if(ebishu){
                        System.out.println("No");
                }else{
                        System.out.println("Yes");
                }
        }
}
//変に考えずに全探索でよかった