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;

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 canK = false;

		outer:
		for (int row = 0; row <= n; row++) {
			for (int clm = 0; clm <= m ; clm++) {
				int black = (m - clm) * row + (n - row) * clm;
				if (black == k) {
					canK = true;
					break outer;
				}
			}
		}

		System.out.println(canK ? "Yes" : "No");
		sc.close();
	}

}
