#include<iostream>
using namespace std;

int main() {
	int N, M, K;
	cin >> N >> M >> K;
	for (int i = 0;i <= N;i ++) {
		 for (int j = 0;j <= M;j ++) {
		 	if (i * M + j * N - i * j * 2 == K) {
				cout << "Yes";
				return 0;
		 	}
		 }
	}
	cout << "No";
	return 0;
}
### 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>
using namespace std;

int main() {
	int N, M, K;
	cin >> N >> M >> K;
	for (int i = 0;i <= N;i ++) {
		 for (int j = 0;j <= M;j ++) {
		 	if (i * M + j * N - i * j * 2 == K) {
				cout << "Yes";
				return 0;
		 	}
		 }
	}
	cout << "No";
	return 0;
}
```