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();
		for (int i=0;i<=N;i++) {
			for (int j=0;j<=M;j++) {
				if (i*M+j*N-2*i*j==K) {
					System.out.println("Yes");
					return ;
				}
			}
		}
		System.out.println("No");
		return ;
	}

	public class People implements Comparable<People> {
		int a;
		int b;
		@Override
		public int compareTo(People o) {
			return this.a - o.a;
		}

	}
}