Same Map in the RPG World

AtCoder

IDabc300_b

Time2000ms

Memory256MB

Difficulty—

> 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 $1 \leq j \leq W$. ## Constraints * $2 \leq H, W \leq 30$ * $A_{i,j}$ is `#` or `.`, and so is $B_{i,j}$. * $H$ and $W$ are integers. ## Input The input is given from Standard Input in the following format: $H$ $W$ $A_{1,1}A_{1,2}\dots A_{1,W}$ $A_{2,1}A_{2,2}\dots A_{2,W}$ $\vdots$ $A_{H,1}A_{H,2}\dots A_{H,W}$ $B_{1,1}B_{1,2}\dots B_{1,W}$ $B_{2,1}B_{2,2}\dots B_{2,W}$ $\vdots$ $B_{H,1}B_{H,2}\dots B_{H,W}$ [samples]

Samples

Input #1

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

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 $B$.

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

Input #2

3 2
##
##
#.
..
#.
#.

Output #2

No

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

Input #3

4 5
#####
.#...
.##..
..##.
...##
#...#
#####
...#.

Output #3

Yes

Input #4

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

Output #4

Yes

API Response (JSON)

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    "name": "Same Map in the RPG World",
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      "memory_limit": 262144
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      "content": "> Takahashi is developing an RPG. He has decided to write a code that checks whether two maps are equal.\n\nWe have grids $A$ and $B$ with $H$ horizontal rows and $W$ vertical columns. Each cell in the ...",
      "is_translate": false,
      "language": "English"
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