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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>

using namespace std;

bool isPalindrome(string &S) {
    int chars[256];
    memset(chars, 0, sizeof(chars));
    for (int i = 0; i < S.length(); i++) {
        chars[S[i]] += 1;
    }

    int odd = 0, even = 0;
    for (int i = 0; i < 256; i++) {
        if (chars[i]%2 == 0) even += 1;
        else odd += 1;
    }

    if (S.length()%2 == 0) {
        if (odd == 0) return true;
        else return false;
    } else {
        if (odd == 1) return true;
        else return false;
    }
}

int h, w;
vector<string> S;
map<string, int> counter;

int main() {
    cin >> h >> w;
    for (int i = 0; i < h; i++) {
        string T;
        cin >> T;
        sort(T.begin(), T.end());
        counter[T] += 1;
        S.push_back(T);
    }

    int odd = 0;
    string oddString;
    for (int i = 0; i < h; i++) {
        if (counter[S[i]]%2 == 1) {
            odd += 1;
            oddString = S[i];
        }
    }

    if (h%2 == 0) {
        if (odd == 0) cout << "YES";
        else cout << "NO";
    } else {
        if (odd != 1) cout << "NO";
        else {
            if (isPalindrome(oddString)) cout << "YES";
            else cout << "NO";
        }
    }
    cout << endl;
}