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>
#define fi first
#define se second
#define mp make_pair
using namespace std;

typedef pair <int, int> pii;

char a[20][20], b[20][20];
int row[20][30], col[20][30];
int to[20], vis[20], vvv[20];
int n, m;

int check(){
	memset(vvv, 0, sizeof(vvv));
	int tot = m;
	for (int i = 0; i < m; i++){
		if (vvv[i]) continue;
		for (int j = i + 1; j < m; j++){
			if (vvv[j]) continue;
			int flag = 1;
			for (int k = 0; k < n; k++){
				flag &= a[k][i] == a[n - k - 1][j];
			}
			if (flag){
				vvv[i] = 1, vvv[j] = 1, tot -= 2;
				break;
			}
		}
		if (!vvv[i] && tot != 1) return 0;
	}
	return 1;
}

int dfs(int now){
	if (now == n) return check();
	if (vis[now]) return dfs(now + 1);
	for (int i = 0; i < n; i++){
		if (vis[i]) continue;
		to[now] = i, vis[i] = 1, swap(a[now], a[i]);
		if (dfs(now + 1)) return 1;
		swap(a[now], a[i]), vis[i] = 0;
	}
	return 0;
}

int main(){
	scanf("%d%d", &n, &m);
	for (int i = 0; i < n; i++){
		scanf("%s", a[i]);
		for (int j = 0; j < m; j++){
			row[i][a[i][j] - 'a']++;
			col[j][a[i][j] - 'a']++;
		}
	}
	if (dfs(0)) printf("YES\n");
	else printf("NO\n");
	return 0;
}