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 {
 
    static public void main(String[] args) {
        Scanner sc = new Scanner(System.in);
 
        int n = sc.nextInt();
        int m = sc.nextInt();
        int k = sc.nextInt();
 
        int x = Math.min(n, m);
        int y = Math.max(n, m);
 
        k = Math.min(k, x * y - k);
 
        boolean found = false;
        for (int i = 0; i < (x + 1) / 2 && !found; i++) {
            int count = i * y;
            if(count == k) {
                found = true;
                break;
            }
            for (int j = 0; j < y; j++) {
                count += x - 2 * i;
                if(count == k) {
                    found = true;
                    break;
                }
            }
        }
 
        if(found) System.out.println("Yes");
        else System.out.println("No");
    }
}