Problem Statement

Takahashi is developing an RPG. He has decided to write a code that checks whether two maps are equal.

We have grids A and B with H horizontal rows and W vertical columns. Each cell in the grid has a symbol # or . written on it.
The symbols written on the cell at the i-th row from the top and j-th column from the left in A and B are denoted by A_{i, j} and B_{i, j}, respectively.
The following two operations are called a vertical shift and horizontal shift.

• For each $j=1, 2, \dots, W,$ simultaneously do the following:

• simultaneously replace $A_{1,j}, A_{2,j}, \dots, A_{H-1, j}, A_{H,j}$ with $A_{2,j}, A_{3,j}, \dots, A_{H,j}, A_{1,j}$.

• For each $i = 1, 2, \dots, H,$ simultaneously do the following:

• simultaneously replace $A_{i,1}, A_{i,2}, \dots, A_{i,W-1}, A_{i,W}$ with $A_{i, 2}, A_{i, 3}, \dots, A_{i,W}, A_{i,1}$.

Is there a pair of non-negative integers (s, t) that satisfies the following condition? Print Yes if there is, and No otherwise.

• After applying a vertical shift s times and a horizontal shift t times, A is equal to B.

Here, A is said to be equal to B if and only if A_{i, j} = B_{i, j} for all integer pairs (i, j) such that $1 \leq i \leq H$ and $1 \leq j \leq W$.

Input

The input is given from Standard Input in the following format:
H W
$A_{1,1}A_{1,2}\dots A_{1,W}$
$A_{2,1}A_{2,2}\dots A_{2,W}$
$\vdots$
$A_{H,1}A_{H,2}\dots A_{H,W}$
$B_{1,1}B_{1,2}\dots B_{1,W}$
$B_{2,1}B_{2,2}\dots B_{2,W}$
$\vdots$
$B_{H,1}B_{H,2}\dots B_{H,W}$

Output

Print Yes if there is a conforming integer pair (s, t); print No otherwise.

Constraints

• $2 \leq H, W \leq 30$
• A_{i,j} is # or ., and so is B_{i,j}.
• H and W are integers.

Sample Input 1

4 3
..#
...
.#.
...

..

...
.#.
...

Sample Output 1

Yes

By choosing (s, t) = (2, 1), the resulting A is equal to B.
We describe the procedure when (s, t) = (2, 1) is chosen. Initially, A is as follows.
..#
...
.#.
...

We first apply a vertical shift to make A as follows.
...
.#.
...
..#

Then we apply another vertical shift to make A as follows.
.#.
...
..#
...

Finally, we apply a horizontal shift to make A as follows, which equals B.

..

...
.#.
...

Sample Input 2

3 2

.

..

.

.

Sample Output 2

No

No choice of (s, t) makes A equal B.

Sample Input 3

4 5

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

...

...#.

Sample Output 3

Yes

Sample Input 4

10 30
..........##########..........
..........####....###.....##..
.....##....##......##...#####.
....####...##..#####...##...##
...##..##..##......##..##....#

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

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

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

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

....................

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

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

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

Sample Output 4

Yes

见题面 Input 部分

见题面 Output 部分