Problem Statement

You are given figures $S$ and $T$ with $H$ rows and $W$ columns consisting of # and ..
The figure $S$ is given as $H$ strings $S _ 1,S _ 2,\ldots,S _ H$; the $j$-th character of $S _ i$ represents the element at the $i$-th row and $j$-th column of $S$. The figure $T$ is given similarly.

Determine whether one can rearrange each row of $S$ to make $S$ equal $T$.

Here, rearranging each row of a figure $X$ is the following operation.

• For each $i=1,2,\ldots,H$, perform the following procedure independently.
  • Choose a permutation $P=(P _ 1,P _ 2,\ldots,P _ W)$ of $(1,2,\ldots,W)$.
  • For all integers $j$ such that $1 \leq j \leq W$, simultaneously replace the element at the $i$-th row and $j$-th column of $X$ with the one at the $i$-th row and $P_j$-th column.

Note that you may choose different permutations $P$ for different $i$.

Constraints

• $H$ and $W$ are integers.
• $1 \leq H,W$
• $1 \leq H \times W \leq 4 \times 10 ^ 5$
• $S_i$ and $T_i$ are strings of length $W$ consisting of # and ..

Sample Input 1Copy

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

Sample Output 1Copy

Yes

For example, if you choose $(4,2,1,3),(1,3,4,2),(4,1,3,2)$ for $i=1,2,3$, respectively, you can make $S$ equal $T$.

Sample Input 2Copy

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

Sample Output 2Copy

No

Sample Input 3Copy

2 1
#
.
#
.

Sample Output 3Copy

Yes

$S=T$ may hold.

Sample Input 4Copy

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

Sample Output 4Copy

Yes