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.*;
import java.util.*;

public class Main {
    public static void main(String args[]) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String[] ips = br.readLine().split(" ");
        int n = Integer.parseInt(ips[0]);
        int m = Integer.parseInt(ips[1]);
        int k = Integer.parseInt(ips[2]);
        for(int i = 0; i <= n; ++i){
            int num = (k-m*i);
            int den = (n-2*i);
            if(den==0)
                continue;
            if(num%den == 0 && num/den <= m && num/den >= 0){
                System.out.println("Yes");
                return;
            }
        }
        System.out.println("No");
    }
}