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)

def matchColumn(i,j)
  ha = {}
  (0...$h).each do |k|
    ha[$sArr[k][i]+$sArr[k][j]] = ha[$sArr[k][i]+$sArr[k][j]].to_i + 1
  end
  ha.each do |k,v|
    if ha[k.reverse] != v
      return false
    end
  end
  return true
end

def compColumn
  odd = $w%2
  match = [false] * $w 
  (0...$w).each do |i|
    if match[i]
      next
    end
    (i+1...$w).each do |j|
      if !match[j] && matchColumn(i,j)
        match[i] = true
        match[j] = true
        break
      end
    end
    if !match[i]
      odd -= 1
      if odd < 0
        return false
      end
      match[i] = true
    end
  end
  return true
end

def matchRow(i,j)
  ha = {}
  (0...$w).each do |k|
    ha[$sArr[i][k]+$sArr[j][k]] = ha[$sArr[i][k]+$sArr[j][k]].to_i + 1
  end
  ha.each do |k,v|
    if ha[k.reverse] != v
      return false
    end
  end
  return true
end

def compRow
  odd = $h%2
  match = [false] * $h 
  (0...$h).each do |i|
    if match[i]
      next
    end
    (i+1...$h).each do |j|
      if !match[j] && matchRow(i,j)
        match[i] = true
        match[j] = true
        break
      end
    end
    if !match[i]
      odd -= 1
      if odd < 0
        return false
      end
      match[i] = true
    end
  end
  return true
end

$h,$w = gets.split.map(&:to_i)
$sArr = []
(0...$h).each do |i|
  $sArr[i] = gets.chomp.split("")
end

if compRow && compColumn
  printf("YES\n")
else
  printf("NO\n")
end