#include <iostream>

int main()
{
	int n, m, k;
	std::cin >> n >> m >> k;
	
	for (int i = 0; i <= n; ++i)
	{
		for (int j = 0; j <= m; ++j)
		{
			if (j * (n - i) + i * (m - j) == k)
			{
				std::cout << "Yes";
				return 0;
			}
		}
	}
	
	std::cout << "No";
	return 0;
}
### Prompt

Create a solution in CPP for 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 n, m, k;
	std::cin >> n >> m >> k;
	
	for (int i = 0; i <= n; ++i)
	{
		for (int j = 0; j <= m; ++j)
		{
			if (j * (n - i) + i * (m - j) == k)
			{
				std::cout << "Yes";
				return 0;
			}
		}
	}
	
	std::cout << "No";
	return 0;
}
```