#include<iostream>

int main()
{
	int h,w,t;
	bool found = false;
	std::cin >> h >> w >> t;
	for(int lx=0;lx<=h;lx++)
	{
		for(int ly=0;ly<=w;ly++)
		{
			if((lx*(w-ly)+(h-lx)*ly) == t)
			{
				found = true;
				goto end;
			}
		}
	}
end:
	std::cout << (found?"Yes":"No") << std::endl;
}

### Prompt

Please formulate a cpp solution 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<iostream>

int main()
{
	int h,w,t;
	bool found = false;
	std::cin >> h >> w >> t;
	for(int lx=0;lx<=h;lx++)
	{
		for(int ly=0;ly<=w;ly++)
		{
			if((lx*(w-ly)+(h-lx)*ly) == t)
			{
				found = true;
				goto end;
			}
		}
	}
end:
	std::cout << (found?"Yes":"No") << std::endl;
}

```