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

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