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) {
		solve();
	}

	private static void solve() {
		try (Scanner cin = new Scanner(System.in)) {

			int N = cin.nextInt();
			int M = cin.nextInt();
			int K = cin.nextInt();

			for (int i = 0; i <= N; i++) {
				for (int j = 0; j <= M; j++) {
					if (N * j + (M - j - j) * i == K) {
						System.out.println("Yes");
						return;
					}
				}
			}

			System.out.println("No");
		} finally {
		}
	}

}
