fLIP

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

inputFormat

Input

Input is given from Standard Input in the following format:

N M K

outputFormat

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

样例

2 2 2

Yes