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 $2\times N$ hallway made of either students represented with an S or empty spaces represented with a ..

He starts walking at $(1,1)$ (the top-left corner) and wants to get to his class at $(2,N)$ (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 $8$ 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 $2$ students from the hallway.

Can Max travel from $(1,1)$ to $(2,N)$?

Constraints

$1\le N\le 2\times {10}^5$

$(1,1)$ and $(2,N)$ will always be empty space.

Input Specification

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

The next $2$ lines will contain $N$ 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 $(1,1)$ to $(2,N)$ by removing at most $2$ students; otherwise, output NO.

Sample Input 1

6
.SS.SS
.SS.S.

Sample Output 1

NO

Explanation for Sample 1

Regardless of the $2$ students removed, Max cannot travel from $(1,1)$ to $(2,N)$.

Sample Input 2

5
.S.S.
.S.S.

Sample Output 2

YES

Explanation for Sample 2

If the students at $(1,2)$ and $(1,4)$ are removed, Max can travel from $(1,1)$ to $(2,N)$.

Note that there are multiple valid solutions.