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.Arrays;
import java.util.HashSet;
import java.util.Scanner;



public class Main {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n =in.nextInt(),m=in.nextInt(),k=in.nextInt();
        if (k == 0){
            System.out.println("Yes");
            return;
        }
        for (int i = 0; i <= n ; i++) {
            for (int j = 0; j <=m ; j++) {
                if (i *(m-j) + j *(n-i) == k){
                    System.out.println("Yes");
                    return;
                }
            }
        }
        System.out.println("No");
    }
}













