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.*;

// ARC 77-C
// http://arc077.contest.atcoder.jp/tasks/arc077_a

public class Main {
	
	public static void main (String[] args) throws InterruptedException {
		Scanner in = new Scanner(System.in);
		
		int N = in.nextInt();
		int M = in.nextInt();
		int K = in.nextInt();
		
		boolean isPossible = false;
		
		for (int x = 0; x <= N && !isPossible; x++) {
			for (int y = 0; y <= M && !isPossible; y++) {
				int numBlack = (x * M - x * y) + (y * N - x * y);
//				System.out.printf("x: %d, y: %d, numBlack: %d\n", x, y, numBlack);
				if (numBlack == K) {
					isPossible = true;
				}
			}
		}
		
		System.out.println(isPossible ? "Yes" : "No");
	}
	
}
