200952: [AtCoder]ARC095 E - Symmetric Grid

Problem Statement

There is an $H \times W$ grid ($H$ vertical, $W$ horizontal), where each square contains a lowercase English letter. Specifically, the letter in the square at the $i$-th row and $j$-th column is equal to the $j$-th character in the string $S_i$.

Snuke can apply the following operation to this grid any number of times:

• Choose two different rows and swap them. Or, choose two different columns and swap them.

Snuke wants this grid to be symmetric. That is, for any $1 \leq i \leq H$ and $1 \leq j \leq W$, the letter in the square at the $i$-th row and $j$-th column and the letter in the square at the $(H + 1 - i)$-th row and $(W + 1 - j)$-th column should be equal.

Determine if Snuke can achieve this objective.

Constraints

• $1 \leq H \leq 12$
• $1 \leq W \leq 12$
• $|S_i| = W$
• $S_i$ consists of lowercase English letters.

Input

Input is given from Standard Input in the following format:

$H$ $W$
$S_1$
$S_2$
$:$
$S_H$

Output

If Snuke can make the grid symmetric, print YES; if he cannot, print NO.

Sample Input 1

2 3
arc
rac

Sample Output 1

YES

If the second and third columns from the left are swapped, the grid becomes symmetric, as shown in the image below:

Sample Input 2

3 7
atcoder
regular
contest

Sample Output 2

NO

Sample Input 3

12 12
bimonigaloaf
faurwlkbleht
dexwimqxzxbb
lxdgyoifcxid
ydxiliocfdgx
nfoabgilamoi
ibxbdqmzxxwe
pqirylfrcrnf
wtehfkllbura
yfrnpflcrirq
wvcclwgiubrk
lkbrwgwuiccv

Sample Output 3

YES