After a difficult research, Anton decided to relax at his country house. He has a beautiful garden with many different flowers. But, oh no, upon arrival he saw a significant number of holes in the ground. It's a mole!

Now, armed with a shovel, Anton will be waiting for the mole. The mole can emerge from any hole. Anton wants to choose a position so that in the worst case, he runs to the mole in the \textbf{minimum} amount of time.

The garden can be represented as a matrix $n \times m$, where $n$ is the number of rows, and $m$ is the number of columns. Rows are numbered from top to bottom, from $1$ to $n$. Columns are numbered from left to right, from $1$ to $m$. Thus, the cell with index $(1;1)$ is located in the upper left corner.

Each cell of the garden $a_{i, j}$ describes the state of this cell:
\begin{itemize}
\item $a_{i, j}$ = ``\t{.}'' --- this cell does not contain flowers or holes;
\item $a_{i, j}$ = ``\t{F}'' --- this cell contains flowers;
\item $a_{i, j}$ = ``\t{H}'' --- this cell contains a hole.
\end{itemize}

Anton also knows that the number of holes does not exceed $100$.

As a person who has put a lot of time into these flowers, your heart cannot bear trampling on them. Therefore, you need to find a path in such a way that it does not pass through them.

At any moment in time, Anton can move from position $(x, y)$ to any of the following positions: $(x-1,y)$, $(x+1,y)$, $(x,y-1)$, $(x,y+1)$, provided that the new position does not contain flowers and is inside the garden.

Find all positions ($x;y$) from which Anton will run to the moles in the worst case in the minimum amount of time.