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 (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <stdlib.h>
#define rep(i,l,r)for(int i=(l);i<(r);i++)
#define bit(n,m)(((n)>>(m))&1)

int h,w,a[20];
char S[20][20];

void g(int s,int m){
	if(!s){
		puts("YES");
		exit(0);
	}
	int i=__builtin_ctz(s);
	if(m){
		int b=1;
		rep(k,0,h)b&=S[k][i]==S[a[k]][i];
		if(b)g(s^(1<<i),0);
	}
	rep(j,i+1,w)if(bit(s,j)){
		int b=1;
		rep(k,0,h)b&=S[k][i]==S[a[k]][j];
		if(b)g(s^(1<<i)^(1<<j),m);
	}
}

void f(int s,int m){
	if(!s)g((1<<w)-1,w%2);
	int i=__builtin_ctz(s);
	if(m){
		a[i]=i;
		f(s^(1<<i),0);
	}
	rep(j,i+1,h)if(bit(s,j)){
		a[i]=j;
		a[j]=i;
		f(s^(1<<i)^(1<<j),m);
	}
}

int main(){
	scanf("%d%d",&h,&w);
	rep(i,0,h)scanf(" %s",S[i]);
	f((1<<h)-1,h%2);
	puts("NO");
}