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 <iostream>
#include <fstream>
#include <vector>
#include <algorithm>
#include <queue>
#include <map>
#include <random>
#include <cstdio>
#include <cstring>
#include <cmath>

// for i in f..<t { as swift
#define forin(i, f, t) for(auto i = f; i < t; i++)

using namespace std;
using ll = long long;
using XY = pair<int, int>;

bool solve(vector<int> &map, bool odd = false) {
    auto num1s = 0;
    for (auto num : map) {
        if (num % 2 != 0) {
            if (!odd) return false;
            else {
                if (++num1s != 1) return false;
            }
        }
    }
    return true;
}

int main() {
    int h, w;
    cin >> h >> w;
    vector<string> s(h);
    for (auto &v: s) cin >> v;
    
    vector<int> charMap(0xff, 0);
    forin(i, 0, h) {
        forin(j, 0, w) {
            charMap[s[i][j]]++;
        }
    }
    auto able = solve(charMap, h % 2 == 1 && w % 2 == 1);
    cout << (able ? "YES" : "NO");
}