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.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Main main = new Main();
        main.solve();
    }
    public void solve() {
        Scanner scan = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        int N = scan.nextInt();
        int M = scan.nextInt();
        int K = scan.nextInt();
        if ( K == 0 || K == N * M) {
            System.out.println("Yes");
            return;
        }
        if ( K % M == 0 || K % N == 0) {
            System.out.println("Yes");
            return;
        }

        for (int i = 1; i <= N; i++) {
            int count = M * i;
            for (int j = 1; j <= M; j++) {
                count = count - i + (N - i);
                if (count == K) {
                    System.out.println("Yes");
                    return;
                }
            }
        }
        System.out.println("No");
    }
}
