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) {

    	Main main=new Main();

    	main.run();

    }

    void run() {
    	Scanner sc=new Scanner(System.in);
    	int N=sc.nextInt();
    	int M=sc.nextInt();
    	int K=sc.nextInt();

    	int num=0;
    	for(int k=0;k<=N;k++) {
    		for(int l=0;l<=M;l++) {

    			num=k*(M-l)+l*(N-k);

    			if(num==K) {
    				System.out.println("Yes");
    				return;
    			}

    		}
    	}

    	System.out.println("No");

    }

}

