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

public class Main {

    public static void main(String[] args) {
     try{
         java.util.Scanner s1 = new java.util.Scanner(System.in);
         int n=s1.nextInt();
         int m=s1.nextInt();
         int k=s1.nextInt();
         for(int i=0;i<=n;i++)
         {
             for(int j=0;j<=m;j++)
             {
                 if((i*m+j*n-2*i*j)==k)
                 {
                     System.out.println("Yes");
                     return;
                 }
             }
         }
         System.out.println("No");
     }
     catch(Exception e)
     {}
   }
}
