#include <bits/stdc++.h>

using namespace std;

int main() {
  int n, m, k; cin >> n >> m >> k; for (int a = 0; a <= n; a++) for (int b = 0; b <= m; b++) if (a * b + (n - a) * (m - b) == k) { cout << "Yes" << endl; return 0; } cout << "No" << endl;
  return 0;
}

### Prompt

Please create a solution in Cpp 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 <bits/stdc++.h>

using namespace std;

int main() {
  int n, m, k; cin >> n >> m >> k; for (int a = 0; a <= n; a++) for (int b = 0; b <= m; b++) if (a * b + (n - a) * (m - b) == k) { cout << "Yes" << endl; return 0; } cout << "No" << endl;
  return 0;
}

```