#include <bits/stdc++.h>

using namespace std;

int n,m,k;

int main() {
    cin>>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) {
                cout<<"Yes";
                return 0;
            }
    cout<<"No";
}

### Prompt

In cpp, your task is to solve 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 n,m,k;

int main() {
    cin>>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) {
                cout<<"Yes";
                return 0;
            }
    cout<<"No";
}

```