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 {
    static int N;
    static int M;
    static int K;
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        N = sc.nextInt();
        M = sc.nextInt();
        K = sc.nextInt();
        int[][] black = new int[N+1][M+1];
        int v;
        for (int i = 0; i < N + 1; i++) {
            v  = M * i;
            if (v == K) {
                System.out.println("Yes");
                return;
            }
            black[i][0] = v;
            black[i][0] = M * i;
            for (int j = 1; j < M + 1; j++) {
                v = black[i][j - 1] + N - i - i;
                if (v == K) {
                    System.out.println("Yes");
                    return;
                }
                black[i][j] = v;
            }
        }
        System.out.println("No");
        return;
    }
}