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)
ss = Array.new(H){Array.new(W)}
chars = {}
('a'..'z').each do |ch|
    chars[ch] = 0
end

H.times do |i|
    ss[i] = gets.chomp.split('')
    ss[i].each do |ch|
        chars[ch] += 1
    end
end

odd = 0
chars.each do |key, val|
    odd += 1 if val % 2 == 1
end

if H % 2 == 1 && W % 2 == 1
    if odd > 1
        print 'NO'
        exit
    end
else
    if odd > 0
        print 'NO'
        exit
    end
end

hash = {}
ss.each do |arr|
    sorted = arr.sort.join
    hash[sorted] ||= []
    hash[sorted].push(arr)
end
odd = 0
hash.each do |key, val|
    odd += 1 if val.length % 2 == 1
end

if H % 2 == 1
    if odd > 1
        print 'NO'
        exit
    end
else
    if odd > 0
        print 'NO'
        exit
    end
end    

hash.each do |key, val|
    next if val.length > 2
    ('a'..'z').each do |ch|
        pos = []
        if val.flatten.count(ch) == 2
            val.each do |arr|
                pos.push(arr.find_index(ch))
            end
        end
        t = pos.length - pos.uniq.length
        if t > H % 2
            print 'NO'
            exit
        end
    end
end

sss = Array.new(W){Array.new(H)}
H.times do |i|
    W.times do |j|
        sss[j][i] = ss[i][j]
    end
end



hash = {}
sss.each do |arr|
    sorted = arr.sort.join
    hash[sorted] ||= []
    hash[sorted].push(arr)
end
odd = 0
hash.each do |key, val|
    odd += 1 if val.length % 2 == 1
end

if W % 2 == 1
    if odd > 1
        print 'NO'
        exit
    end
else
    if odd > 0
        print 'NO'
        exit
    end
end

hash.each do |key, val|
    next if val.length > 2
    ('a'..'z').each do |ch|
        pos = []
        if val.flatten.count(ch) == 2
            val.each do |arr|
                pos.push(arr.find_index(ch))
            end
        end
        t = pos.length - pos.uniq.length
        if t > W % 2
            print 'NO'
            exit
        end
    end
end

print 'YES'