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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import static java.lang.System.*;
import java.util.Arrays;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {

		Scanner sc = new Scanner(in);
		
		int h = sc.nextInt();
		int w = sc.nextInt();
		
		char[][] c = new char[h][w];
		char[][] r = new char[w][h];
		
		for(int i=0; i<h; i++) {
			c[i] = sc.next().toCharArray();
			for(int j=0; j<w; j++) r[j][i] = c[i][j];
		}
		
		out.println(check(h, w, c) && check(w, h, r) ? "YES" : "NO");
		
		return;
	}

	private static boolean check(int n, int m, char[][] array) {
		for(int i=0; i<n; i++) Arrays.sort(array[i]);
		
		boolean[] used = new boolean[n];
		Arrays.fill(used, false);
		for(int i=0; i<n-1; i++) {
			if(used[i]) continue;
			for(int j=i+1; j<n; j++) {
				if(used[j]) continue;
				
				boolean flag = true;
				for(int k=0; k<m; k++) {
					if(array[i][k] != array[j][k]) {
						flag = false;
						break;
					}
				}
				if(flag) used[i] = used[j] = true;
			}
		}
		
		int count = 0;
		for(boolean b: used) if(!b) count++;
		
		return count <= 1;
	}

}