题目描述
Problem Statement
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.
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
Output
If S can be made equal to T, print Yes; otherwise, print No.
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 ..
Sample Input 1
3 4
.
..
...
.###
..##
...#
Sample 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.
Sample Input 2
3 3
.
.#.
.
.
.
.#.
Sample Output 2
No
In this input, S cannot be made equal to T.
Sample Input 3
2 1
.
.
Sample Output 3
Yes
It is possible that S=T.
Sample Input 4
8 7
..#..
.##.##.
..#..
.##.##.
..#..
.##.##.
..#..
.##.##.
....###
...
....###
...
....###
...
....###
...
Sample Output 4
Yes
输入格式
见题面 Input 部分
输出格式
见题面 Output 部分