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.*;

public class Main {
    public static boolean find_k(int a, int b,int x){
        if (x==0)
            return true;
        else{for(int i=1;i<=a;i++){
            for(int j=1; j<=b;j++){
                int y=i*j+(a-i)*(b-j);
                if(y==x){
                    return true;
                }
                if(y>x){
                    break;
                }

            }
        }
        return false;}
    }

    public static void main(String[] args) {
        Scanner r=new Scanner(System.in);
        int m=r.nextInt();
        int n=r.nextInt();
        int k=r.nextInt();
        if (find_k(m,n,k))
            System.out.println("Yes");
        else
            System.out.println("No");


    }
}
