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 <string>
#include <algorithm>
#include <iomanip>
#include <vector>
#include <map>
#include <cmath>
#include <queue>
#include <utility>
#include <functional>
#include <deque>
#include <cctype>
#include <stack>
#include <bitset>
#include <set>

#define MAX 100100
#define rep(i,n) for(int i=0;i<n;i++)
#define REP(i,k,n) for(int i=k;i<n;i++)
using namespace std;

string sw[12];
string sh[12];
int h,w;

bool check_sh(int j){
  rep(i,w){
    if(i==j) continue;
    if(sh[i] == sh[j]){
      return true;
    }
  }
  return false;
}
bool check_sw(int j){
  rep(i,h){
    if(i==j) continue;
    if(sw[i] == sw[j]){
      return true;
    }
  }
  return false;
}
int main(){
  cin.tie(0);
  ios::sync_with_stdio(false);
  cin >> h >> w;
  rep(i,h) cin >> sw[i];
  rep(i,w){
    rep(j,h){
      sh[i] += sw[j][i];
    }
  }
  rep(i,h) sort(sw[i].begin(),sw[i].end());
  rep(i,w) sort(sh[i].begin(),sh[i].end());
  int ct = 0;
  rep(i,h){
    if(!check_sw(i)){
      if(ct == 0){ct+=1; continue;}
      cout << "No" << endl;
      return 0;
    }
  }
  rep(i,w){
    if(!check_sh(i)){
      if(ct == 0){ct+=1; continue;}
      cout << "No" << endl;
      return 0;
    }
  }
  cout << "Yes" << endl;

  return 0;

}