Input:

The input consists of two lines. The first line contains two space$-$separated integers, $m$ and $n,$ the number of rows and columns in the grid, respectively. The second line contains $m$ strings, each of length $n,$ representing the grid. Each character in the grid is either a $\text{'}$ : $\text{'}($representing good land$)$ or an $\text{'}x\text{'}($representing a hole$).$

Output:

The output consists of a single integer, the perimeter of the largest possible rectangular area that does not contain any holes. If such an area cannot be constructed, output the string "impossible".

Constraints:

$1m,n200$

samples:

Sample Input:

$45$

$....$

$.$x$.$x$.$

$.....$

$.....$

Sample Output:

$14$

$q,$

Sample Input:

$22$

$.x$

$x.$

Sample Output:

Imp

Example $2$:

$45$

$\backslash$table$[[.,.,.,.,.],[.,x,.,x,.],[.,x,.,.,.],[.,.,.,.,.]]$

In this example we can build only $7$ possible paling does not contain any holes

$P=10$

$\backslash$table$[[.,*,.,.,*$ossibleqquadImportant note: the execution time shouldn't exceed $2$ seconds and any test case that exceeds the limit will be considered a timeout.