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 void main(String[] args){
        Scanner sc = new Scanner(System.in);
        // 整数の入力                                                           
        int N = sc.nextInt();
        int M = sc.nextInt();
        int K = sc.nextInt();
        boolean can = false;

        for(int i=0; i<= M; i++){
            for(int j=0; j <= N; j++){
                if(K == j*(M-i) + i*(N-j) && !can){
                    System.out.println("Yes");
                    can = true;
                }
            }
        }
        if(!can) System.out.println("No");

    }
}
