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.PrintWriter;
import java.util.Arrays;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        try (InputReader in = new InputReader(); PrintWriter out = new PrintWriter(System.out)) {
            new Main().solve(in, out);
            out.flush();
        }
    }

    private void solve(InputReader in, PrintWriter out) {
        int n = in.nextInt();
        int m = in.nextInt();
        int k = in.nextInt();

        for (int i = 0; i <= n; i++) {
            for (int j = 0; j <= m; j++) {
                int tmp = m * i + n * j - i * j * 2;
                if (tmp == k) {
                    out.println("Yes");
                    return;
                }
            }
        }

        out.println("No");
    }
}

class InputReader implements AutoCloseable {
    private final Scanner sc = new Scanner(System.in);

    String next() {
        return this.sc.next();
    }

    int nextInt() {
        return Integer.parseInt(this.sc.next());
    }

    long nextLong() {
        return Long.parseLong(this.sc.next());
    }

    double nextDouble() {
        return Double.parseDouble(this.sc.next());

    }

    @Override
    public void close() {
        this.sc.close();
    }
}
