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<stdio.h>

int arcmp(char a1[],char a2[]);

int main(void){
  int H,W;
  char board[12][13];
  char row[12][26]={{0}},rowset[12];
  char col[12][26]={{0}},colset[12];
  int i,j;
  int rs=0,cs=0;

  scanf("%d%d%*c",&H,&W);
  for(i=0;i<H;i++) scanf("%[a-z]%*c",board[i]);
  for(i=0;i<H;i++){
    for(j=0;j<W;j++){
      row[i][board[i][j]-'a']++;
      col[j][board[i][j]-'a']++;
    }
  }

  for(i=0;i<12;i++) rowset[i]=colset[i]=-1;

  for(i=0;i<H-1;i++){
    if(rowset[i]!=-1) continue;
    for(j=i+1;j<H;j++){
      if(rowset[j]!=-1) continue;
      if(arcmp(row[i],row[j])){
	rowset[i]=j;
	rowset[j]=i;
      }
    }
  }

  for(i=0;i<W-1;i++){
    if(colset[i]!=-1) continue;
    for(j=i+1;j<W;j++){
      if(colset[j]!=-1) continue;
      if(arcmp(col[i],col[j])){
	colset[i]=j;
	colset[j]=i;
      }
    } 
  }

  for(i=0;i<H;i++) rs+=(rowset[i]==-1);
  for(i=0;i<W;i++) cs+=(colset[i]==-1);

  puts(rs==H%2 && cs==W%2 ? "YES" : "NO");
  return 0;
}

int arcmp(char a1[],char a2[]){
  int i;
  for(i=0;i<26;i++) if(a1[i]!=a2[i]) return 0;
  return 1;
}