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;
 
#define ll long long
#define mod 1000000007
#define pb push_back
#define pi pair<int,int>
#define vi vector<int>
#define vpi vector< pi >
const int N=200010;
char s[20][20];
void swp(int y1,int y2,int h)
{
	for(int i=1;i<=h;i++)
		swap(s[i][y1],s[i][y2]);
}
bool hh(int h,int w)
{
	for(int i=1;i<=(h+1)/2;i++)
	{
		for(int j=1;j<=w;j++)
			if(s[i][j]!=s[h-i+1][w-j+1])
				return false;
	}
return true;
}
int main()
{
	int h,w;
	cin>>h>>w;
	for(int i=1;i<=h;i++)
		scanf("%s",s[i]+1);
	int a[30]={0},b[h+10][30];
	memset(b,0,sizeof b);
	for(int i=1;i<=h;i++)
	{
		for(int j=1;j<=w;j++)
		{
			if(h%2)
			b[i][s[i][j]-'a']++;
			a[s[i][j]-'a']++;
		}
	}
	int g=0;
	for(int j=1;j<=h;j++)
	{
		int f=0;
		for(int i=0;i<26;i++)
		if((a[i]-b[j][i])%2)
			f=1;
		if(!f)
			g=1;
	}
	if(!g)
	return !printf("NO");
	return !printf("YES");
	
	return 0;
}