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: Wrong Answer)

#include<cstdio>
using namespace std;
int n,m;
char a[15][15];
int cnts[205];
int main(){
	scanf("%d%d",&n,&m);
	for(int i=1;i<=n;++i){
		scanf("%s",a[i]+1);
	}
	for(int i=1;i<=n;++i){
		for(int j=1;j<=m;++j){
			++cnts[a[i][j]];
		}
	}
	if(n*m%2==1){
		int cnt=0;
		for(int i='a';i<='z';++i){
			if(cnts[i]%2==1){
				++cnt;
			}
		}
		printf(cnt==1 ? "YES" : "NO");
		return 0;
	}
	bool flag=1;
	for(int i='a';i<='z';++i){
		if(cnts[i]%2==1){
			flag=0;
		}
	}
	puts(flag ? "YES" : "NO");
	return 0;
}