题目描述
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
输入格式
见题面
输出格式
见题面