After attending the lectures for all his normal courses, Max has to attend his List I Communication credit lecture.

To get to his lecture, he has to traverse through a hallway made of either students represented with an `S`

or empty spaces represented with a `.`

.

He starts walking at (the top-left corner) and wants to get to his class at (the bottom-right corner).

Max can move from one cell to another if both cells are empty space and share a corner or edge (i.e., he can move in all directions).

Since all the other students are walking to their List I Communication credit, they do not move, which enrages Max.

Because Max is enraged, he can remove at most students from the hallway.

Can Max travel from to ?

#### Constraints

and will always be empty space.

#### Input Specification

The first line will contain an integer, , the number of columns in the hallway.

The next lines will contain characters that are each either an `S`

or `.`

, the hallway filled with students or empty space, respectively.

#### Output Specification

Output `YES`

if he can travel from to by removing at most students; otherwise, output `NO`

.

#### Sample Input 1

```
6
.SS.SS
.SS.S.
```

#### Sample Output 1

`NO`

#### Explanation for Sample 1

Regardless of the students removed, Max cannot travel from to .

#### Sample Input 2

```
5
.S.S.
.S.S.
```

#### Sample Output 2

`YES`

#### Explanation for Sample 2

If the students at and are removed, Max can travel from to .

Note that there are multiple valid solutions.

## Comments

i remove u