# include <iostream>
# include <cstdio>
using namespace std;
int main()
{
    int x, y, k;
    scanf("%d%d%d",&x,&y,&k);
    for(int i=0; i<=x; ++i)
        for(int j=0; j<=y; ++j)
        if(i*y+j*x-i*j*2 == k) return 0*puts("Yes");
    puts("No");
    return 0;
}

### Prompt

Develop a solution in Cpp to the problem described below:

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 x, y, k;
    scanf("%d%d%d",&x,&y,&k);
    for(int i=0; i<=x; ++i)
        for(int j=0; j<=y; ++j)
        if(i*y+j*x-i*j*2 == k) return 0*puts("Yes");
    puts("No");
    return 0;
}

```