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[]) {

        // 入力
        Scanner sc = new Scanner(System.in);
        int n = Integer.parseInt(sc.next());
        int m = Integer.parseInt(sc.next());
        int k = Integer.parseInt(sc.next());

        // 主処理
        Set<Integer> set = new HashSet<>();
        for (int i = 1; i <= n; i++) {
            set.add(i * m);
            for (int j = 1; j <= m; j++) {
                set.add(j * n);
                set.add((n * j - (i * j)) + (m * i - (i * j)));
            }
        }

        String result = k == 0 || set.contains(k) ? "Yes" : "No";

        // 出力
        System.out.println(result);
        sc.close();
    }
}
