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)
fs = h.times.map{gets.chomp.split('')}

# row
a = {}
h.times{|i|
  row = w.times.map{|j|fs[i][j]}.sort.join('')
  if a[row] == nil
    a[row]=1
  else
    a[row]+=1
  end
}
o=0
a.each{|_, cx|
  o+=1 if cx.odd?
}
if h.even? or (h.odd? and o==1)
  :ok
else
  puts "NO"
  exit
end

# col
a = {}
w.times{|j|
  col = h.times.map{|i|fs[i][j]}.sort.join('')
  if a[col] == nil
    a[col]=1
  else
    a[col]+=1
  end
}
o=0
a.each{|_, cx|
  o+=1 if cx.odd?
}
if w.even? or (w.odd? and o==1)
  :ok
else
  puts "NO"
  exit
end

# char
a = {}
h.times{|i|
  w.times{|j|
    c=fs[i][j]
    if a[c] == nil
      a[c]=1
    else
      a[c]+=1
    end
  }
}
o=0
a.each{|_, cx|
  o+=1 if cx.odd?
}
if (h*w).even? or ((h*w).odd? and o==1)
  :ok
else
  puts "NO"
  exit
end

puts "YES"