Problem Statement

We have two figures S and T on a two-dimensional grid with square cells.
S lies within a grid with N rows and N columns, and consists of the cells where S_{i,j} is #.
T lies within the same grid with N rows and N columns, and consists of the cells where T_{i,j} is #.
Determine whether it is possible to exactly match S and T by 90-degree rotations and translations.

Input

Input is given from Standard Input in the following format:
N
$S_{1,1}S_{1,2}\ldots S_{1,N}$
$\vdots$
$S_{N,1}S_{N,2}\ldots S_{N,N}$
$T_{1,1}T_{1,2}\ldots T_{1,N}$
$\vdots$
$T_{N,1}T_{N,2}\ldots T_{N,N}$

Output

Print Yes if it is possible to exactly match S and T by 90-degree rotations and translations, and No otherwise.

Constraints

• $1 \leq N \leq 200$
• Each of S and T consists of # and ..
• Each of S and T contains at least one #.

Sample Input 1

5
.....
..#..
.###.
.....
.....
.....
.....
....#
...##
....#

Sample Output 1

Yes

We can match S to T by rotating it 90-degrees counter-clockwise and translating it.

Sample Input 2

5

..

..

.....

..

..

.....

Sample Output 2

No

It is impossible to match them by 90-degree rotations and translations.

Sample Input 3

4

...

..#.
..#.
....

...

...

..#.
....

Sample Output 3

Yes

Each of S and T may not be connected.

Sample Input 4

4

...

.##.
..#.
....

..

...

..#.
....

Sample Output 4

No

Note that it is not allowed to rotate or translate just a part of a figure; it is only allowed to rotate or translate a whole figure.

见题面 Input 部分

见题面 Output 部分