# include <cstdio>

int main ( )  {
	int n, m, k ;
	scanf ( "%d%d%d", & n, & m, & k ) ;

	for ( int a = 0 ; a <= n ; ++ a )
		for ( int b = 0 ; b <= m ; ++ b )
			if ( a * m + ( n - a ) * b - a * b == k )  {
				return ! puts ( "Yes" ) ;
			}
	return ! puts ( "No" ) ;
}

### Prompt

Please create a solution in cpp to the following problem:

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

### Response

```cpp
# include <cstdio>

int main ( )  {
	int n, m, k ;
	scanf ( "%d%d%d", & n, & m, & k ) ;

	for ( int a = 0 ; a <= n ; ++ a )
		for ( int b = 0 ; b <= m ; ++ b )
			if ( a * m + ( n - a ) * b - a * b == k )  {
				return ! puts ( "Yes" ) ;
			}
	return ! puts ( "No" ) ;
}

```