Problem:
Score : 700 points

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

Solution in Ruby (2.3.3) (judge verdict: Wrong Answer)

h,w = gets.split.map(&:to_i)
s = h.times.map{gets.chomp.split('').sort}.sort{|a,b| a.sort*'' <=> b.sort*''}

a1 = s.map{|t|t*''}.uniq.size
b1 = s.each.all?{|t|
  tmp = t.group_by{|x| x}.map{|k,v| v.size}.sort
  tmp.count{|x| x%2==1}<=1
}
c1 = h/2==a1 || b1

s = s.transpose.sort{|a,b| a.sort*'' <=> b.sort*''}
a2 = s.map{|t|t*''}.uniq.size
b2 = s.each.all?{|t|
  tmp = t.group_by{|x| x}.map{|k,v| v.size}.sort
  tmp.count{|x| x%2==1}<=1
}
c2 = w/2==a2 || b2

#p [a1,b1,c1],[a2,b2,c2]

puts (c1 && c2)? "YES" : "NO"