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;
int n,m,i,j,k,t,c[15];
string wrd[15],wrd2[15];
map<string,int> s;
int main(){
	scanf("%d%d",&n,&m);
	for (i=0;i<n;i++){
		cin>>wrd[i];
		c[i]=i;
	}
	if (!(m&1))
	{
		for (t=0;t<(1<<m);t++)
		{
			if (__builtin_popcount(t)!=m/2) continue;
			int cnt=0,cnt2=n/2;
			for (j=0;j<m;j++)
			{
				if ((1<<j)&t) c[cnt++]=j; else c[cnt2++]=j;
			}
			do{
				s.clear();
				for (i=0;i<n;i++){
					wrd2[i]="";
					for (j=0;j<m;j++){
					wrd2[i].push_back(wrd[i][c[j]]);
				}
				s[wrd2[i]]++;
			}
			bool f=0;
			for (i=0;i<n;i++){
				reverse(wrd2[i].begin(),wrd2[i].end());
				if ((--s[wrd2[i]])<0){
					if (f)
					break;f=1;
				}
			}
			if (i==n&&((n&1)||!f)){
				cout<<"YES";
				return 0;
			}
		}while (next_permutation(c,c+m));
	}
	}
	else
	{
		for (k=0;k<m;k++)
		{
			c[n/2+1]=k;
			for (t=0;t<(1<<m);t++)
		{
			if (__builtin_popcount(t)!=m/2) continue;
			if ((1<<k)&t) continue;
			int cnt=0,cnt2=n/2+1;
			for (j=0;j<m;j++)
			{
				if ((1<<j)&i) c[cnt++]=j; else c[cnt2++]=j;
			}
			do{
				s.clear();
				for (i=0;i<n;i++){
					wrd2[i]="";
					for (j=0;j<m;j++){
					wrd2[i].push_back(wrd[i][c[j]]);
				}
				s[wrd2[i]]++;
			}
			bool f=0;
			for (i=0;i<n;i++){
				reverse(wrd2[i].begin(),wrd2[i].end());
				if ((--s[wrd2[i]])<0){
					if (f)
					break;f=1;
				}
			}
			if (i==n&&((n&1)||!f)){
				cout<<"YES";
				return 0;
			}
		}while (next_permutation(c,c+m));
	}
	}}
	cout<<"NO";
	return 0;
}