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(final String args[]) {
        Scanner scanner = new Scanner(System.in);
        final int rows = scanner.nextInt();
        final int columns = scanner.nextInt();
        final int targetBlack = scanner.nextInt();
        for (int rowPushes = 0; rowPushes <= rows; rowPushes++) {
            for (int columnPushes = 0; columnPushes <= columns; columnPushes++) {
                int black = rowPushes * columns + columnPushes * rows - 2 * rowPushes * columnPushes;
                if (black == targetBlack) {
                    System.out.println("Yes");
                    System.exit(0);
                }
            }
        }
        System.out.println("No");
    }
}