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;

/**
 * http://code-festival-2017-quala.contest.atcoder.jp/tasks/code_festival_2017_quala_b
 */
public class Main {

	public static void main(String[] args) {
		
		Scanner sc = new Scanner(System.in);
		final int N = sc.nextInt();
		final int M = sc.nextInt();
		final int K = sc.nextInt();
		sc.close();
		
		boolean[] dp = new boolean[N*M+1];
		
		for(int i=0; i<=N; i++){
			for(int j=0; j<=M; j++){
				dp[i*M+j*N-i*j*2]=true;
			}
		}		
		System.out.println(dp[K] ? "Yes" : "No");
	}

}
