#include <iostream>
#include <cstdio>
using namespace std;
int main()
{
    int n,m,k,g=0;
    cin>>n>>m>>k;
    for(int i=0;i<=m;i++)
        for(int j=0;j<=n;j++)
        {
            if((i*n+j*m-2*(i*j))==k){cout<<"Yes"<<endl;return 0;}
        }
    cout<<"No"<<endl;
}

### 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>
#include <cstdio>
using namespace std;
int main()
{
    int n,m,k,g=0;
    cin>>n>>m>>k;
    for(int i=0;i<=m;i++)
        for(int j=0;j<=n;j++)
        {
            if((i*n+j*m-2*(i*j))==k){cout<<"Yes"<<endl;return 0;}
        }
    cout<<"No"<<endl;
}

```