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)

n,m=gets.split
n=n.to_i
m=m.to_i

arr2=[]
n.times{
    
    arr2<<gets.chomp.split("")}
    
arr3=[]
i=0
m.times{
   arr3<<arr2.transpose[i] ; i+=1}
j=0
n.times{
   arr2[j]=arr2[j].sort
    j+=1
}
   j=0
m.times{
   arr3[j]=arr3[j].sort
    j+=1
}


aa=0
loop{
    if n==1
        aa=1
        break
    end
    
   if arr2.count(arr2[0])==1
       aa+=1
       arr2.delete_at(0)
    else 
        
      
        kk=arr2[1..-1].index(arr2[0])
          arr2.delete_at(0)
          arr2.delete_at(kk)
      end
      
      if aa==2  || arr2.length<=1
          break
      end
          
    
}


bb=0
loop{
    
    if m==1
        bb=1
        break
    end
    
   if arr3.count(arr3[0])==1
       bb+=1
       arr3.delete_at(0)
    else 
        
      
        kk=arr3[1..-1].index(arr3[0])
          arr3.delete_at(0)
          arr3.delete_at(kk)
      end
      
      if bb==2  || arr3.length<=1
          break
      end
          
    
}


if aa==2 || bb==2
    puts "NO"
    elsif aa==1 && n%2==0
    puts "NO"
    elsif bb==1 && m%2==0
    puts "NO"
else 
    puts "YES"
end