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) {
		Scanner sc = new Scanner(System.in);

		int n = sc.nextInt();
		int m = sc.nextInt();
		int k = sc.nextInt();

		boolean[] flg = new boolean[n * m + 1];
		for (int i = 0; i < flg.length; i++) {
			flg[i] = false;
		}

		for (int i = 0; i <= m; i ++) {
			if (m - 2 * i == 0) {
				flg[i * n] = true;
			} else if (m - 2 * i > 0) {
				for (int j = 0; i * n + j < n * m -i * n; j += (m - 2 * i)) {
					flg[i * n + j] = true;
				}
			} else {
				for (int j = 0; i * n + j >= n * m - i * n; j += (m - 2 * i)) {
					flg[i * n + j] = true;
				}
			}
		}

		if (flg[k] == true) {
			System.out.print("Yes");
		} else {
			System.out.print("No");
		}
	}
}
