Symmetric Grid
Problem Statement
There is an H × 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 Si.
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 ≤ i ≤ H and 1 ≤ j ≤ 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 ≤ H ≤ 12
- 1 ≤ W ≤ 12
- |Si| = W
- Si consists of lowercase English letters.
Input
Input is given from Standard Input in the following format:
H W
S1
S2
:
SH
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