#include <cstdio>

int main(){
  int N, M, K; scanf("%d%d%d", &N, &M, &K);

  bool ans = false;

  for(int n = 0; n <= N; n++){
    for(int m = 0; m <= M; m++){
      int k = n * M + m * N - 2 * n * m;
      if(k == K) ans = true;
    }
  }

  puts(ans ? "Yes" : "No");
  return 0;
}
### Prompt

Your challenge is to write 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 <cstdio>

int main(){
  int N, M, K; scanf("%d%d%d", &N, &M, &K);

  bool ans = false;

  for(int n = 0; n <= N; n++){
    for(int m = 0; m <= M; m++){
      int k = n * M + m * N - 2 * n * m;
      if(k == K) ans = true;
    }
  }

  puts(ans ? "Yes" : "No");
  return 0;
}
```