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.HashSet;
import java.util.Scanner;
import java.util.Set;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int maxN = sc.nextInt();
		int maxM = sc.nextInt();
		int want = sc.nextInt();
		Set<Integer> set = new HashSet<Integer>();
		for(int n = 0; n <= maxM; n++) {
			for(int m = 0; m <= maxN; m++) {
				set.add(maxN * n + maxM * m - 2 * n * m);
			}
		}
		System.out.println(set.contains(want) ? "Yes" : "No");
	}
}