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 is given from Standard Input in the following format:

```
$N$
$S_{1,1}S_{1,2}\ldots S_{1,N}$
$\vdots$
$S_{N,1}S_{N,2}\ldots S_{N,N}$
$T_{1,1}T_{1,2}\ldots T_{1,N}$
$\vdots$
$T_{N,1}T_{N,2}\ldots T_{N,N}$
```

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

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

Yes

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

No

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

Yes

Each of S and T may not be connected.

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.