#include<bits/stdc++.h>
using namespace std;
int n,m,k;
int main(){
	scanf("%d%d%d",&n,&m,&k);
	for (int i=0;i<=n;i++){
		for (int j=0;j<=m;j++){
			if (i*m+j*n-2*i*j==k){
				printf("Yes");
				return 0;
			}
		}
	}
	printf("No");
	return 0;
}
### Prompt

Construct a cpp code solution to the problem outlined:

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<bits/stdc++.h>
using namespace std;
int n,m,k;
int main(){
	scanf("%d%d%d",&n,&m,&k);
	for (int i=0;i<=n;i++){
		for (int j=0;j<=m;j++){
			if (i*m+j*n-2*i*j==k){
				printf("Yes");
				return 0;
			}
		}
	}
	printf("No");
	return 0;
}
```