Score : $200$ points

Problem Statement

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.

2 2 2

Yes

Press the buttons in the order of the first row, the first column.

2 2 1

No

3 5 8

Yes

Press the buttons in the order of the first column, third column, second row, fifth column.

7 9 20

No