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;

class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);

        int N = Integer.parseInt(scanner.next());
        int M = Integer.parseInt(scanner.next());
        int K = Integer.parseInt(scanner.next());

        if (K % N == 0 || K % M == 0) {
            System.out.println("Yes");
            return;
        }
        
        if (K < N || K < M) {
            System.out.println("No");
            return;
        }


        for (int n = 0; n <= N; n++) {
            for (int m = 0; m <= M; m++) {
                int sum = n * m + (N - n) * (M - m);
                if (sum == K) {
                    System.out.println("Yes");
                    return;
                }
            }
        }

        System.out.println("No");

    }
}
