RANDOM

AtCoder

IDabc279_c

Time2000ms

Memory256MB

Difficulty—

You are given patterns $S$ and $T$ consisting of `#` and `.`, each with $H$ rows and $W$ columns. The pattern $S$ is given as $H$ strings, and the $j$\-th character of $S_i$ represents the element at the $i$\-th row and $j$\-th column. The same goes for $T$. Determine whether $S$ can be made equal to $T$ by rearranging the columns of $S$. Here, rearranging the columns of a pattern $X$ is done as follows. * Choose a permutation $P=(P_1,P_2,\dots,P_W)$ of $(1,2,\dots,W)$. * Then, for every integer $i$ such that $1 \le i \le H$, simultaneously do the following. * For every integer $j$ such that $1 \le j \le W$, simultaneously replace the element at the $i$\-th row and $j$\-th column of $X$ with the element at the $i$\-th row and $P_j$\-th column. ## Constraints * $H$ and $W$ are integers. * $1 \le H,W$ * $1 \le H \times W \le 4 \times 10^5$ * $S_i$ and $T_i$ are strings of length $W$ consisting of `#` and `.`. ## Input The input is given from Standard Input in the following format: $H$ $W$ $S_1$ $S_2$ $\vdots$ $S_H$ $T_1$ $T_2$ $\vdots$ $T_H$ [samples]

Samples

Input #1

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

Output #1

Yes

If you, for instance, arrange the $3$\-rd, $4$\-th, $2$\-nd, and $1$\-st columns of $S$ in this order from left to right, $S$ will be equal to $T$.

Input #2

3 3
#.#
.#.
#.#
##.
##.
.#.

Output #2

No

In this input, $S$ cannot be made equal to $T$.

Input #3

2 1
#
.
#
.

Output #3

Yes

It is possible that $S=T$.

Input #4

8 7
#..#..#
.##.##.
#..#..#
.##.##.
#..#..#
.##.##.
#..#..#
.##.##.
....###
####...
....###
####...
....###
####...
....###
####...

Output #4

Yes

API Response (JSON)

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    "name": "RANDOM",
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      "content": "You are given patterns $S$ and $T$ consisting of `#` and `.`, each with $H$ rows and $W$ columns.   The pattern $S$ is given as $H$ strings, and the $j$\\-th character of $S_i$ represents the element a",
      "description_type": "Markdown"
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    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
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    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc279_c"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given patterns $S$ and $T$ consisting of `#` and `.`, each with $H$ rows and $W$ columns.  \nThe pattern $S$ is given as $H$ strings, and the $j$\\-th character of $S_i$ represents the element a...",
      "is_translate": false,
      "language": "English"
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Full JSON Raw Segments