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)

//set many funcs template
//Ver.20181225
#include<stdio.h>
#include<string.h>
#include<stdlib.h>
#include<stdbool.h>
#include<time.h>
#define inf 1072114514
#define llinf 4154118101919364364
#define mod 1000000007
#define pi 3.1415926535897932384

int max(int a,int b){if(a>b){return a;}return b;}
int min(int a,int b){if(a<b){return a;}return b;}
int zt(int a,int b){return max(a,b)-min(a,b);}
int round(int a,int b){if((a%b)*2 >= b){return (a/b)+1;}return a/b;}
int ceil(int a,int b){if(a%b==0){return a/b;}return (a/b)+1;}
int gcd(int a,int b){int c;while(b!=0){c=a%b;a=b;b=c;}return a;}
int lcm(int a,int b){int c=gcd(a,b);a/=c;return a*b;}
int nCr(int a,int b){int i,r=1;for(i=1;i<=b;i++){r*=(a+1-i);r/=i;}return r;}
int nHr(int a,int b){return nCr(a+b-1,b);}
int fact(int a){int i,r=1;for(i=1;i<=a;i++){r*=i;}return r;}
int pow(int a,int b){int i,r=1;for(i=1;i<=b;i++){r*=a;}return r;}
int dsum(int x){int r=0;while(x){r+=(x%10);x/=10;}return r;}
int dsumb(int x,int b){int r=0;while(x){r+=(x%b);x/=b;}return r;}
int sankaku(int x){return ((1+x)*x)/2;}
long long llmax(long long a,long long b){if(a>b){return a;}return b;}
long long llmin(long long a,long long b){if(a<b){return a;}return b;}
long long llzt(long long a,long long b){return llmax(a,b)-llmin(a,b);}
long long llround(long long a,long long b){if((a%b)*2 >= b){return (a/b)+1;}return a/b;}
long long llceil(long long a,long long b){if(a%b==0){return a/b;}return (a/b)+1;}
long long llgcd(long long a,long long b){long long c;while(b!=0){c=a%b;a=b;b=c;}return a;}
long long lllcm(long long a,long long b){long long c=llgcd(a,b);a/=c;return a*b;}
long long llnCr(long long a,long long b){long long i,r=1;for(i=1;i<=b;i++){r*=(a+1-i);r/=i;}return r;}
long long llnHr(long long a,long long b){return llnCr(a+b-1,b);}
long long llfact(long long a){long long i,r=1;for(i=1;i<=a;i++){r*=i;}return r;}
long long llpow(long long a,long long b){long long i,r=1;for(i=1;i<=b;i++){r*=a;}return r;}
long long lldsum(long long x){long long r=0;while(x){r+=(x%10);x/=10;}return r;}
long long lldsumb(long long x,long long b){long long r=0;while(x){r+=(x%b);x/=b;}return r;}
long long llsankaku(long long x){return ((1+x)*x)/2;}
double dbmax(double a,double b){if(a>b){return a;}return b;}
double dbmin(double a,double b){if(a<b){return a;}return b;}
double dbzt(double a,double b){return dbmax(a,b)-dbmin(a,b);}
int sortfncsj(const void *a,const void *b){if(*(int *)a>*(int *)b){return 1;}if(*(int *)a==*(int *)b){return 0;}return -1;}
int sortfnckj(const void *a,const void *b){if(*(int *)a<*(int *)b){return 1;}if(*(int *)a==*(int *)b){return 0;}return -1;}
int llsortfncsj(const void *a,const void *b){if(*(long long *)a>*(long long *)b){return 1;}if(*(long long *)a==*(long long *)b){return 0;}return -1;}
int llsortfnckj(const void *a,const void *b){if(*(long long *)a<*(long long *)b){return 1;}if(*(long long *)a==*(long long *)b){return 0;}return -1;}
int dbsortfncsj(const void *a,const void *b){if(*(double *)a>*(double *)b){return 1;}if(*(double *)a==*(double *)b){return 0;}return -1;}
int dbsortfnckj(const void *a,const void *b){if(*(double *)a<*(double *)b){return 1;}if(*(double *)a==*(double *)b){return 0;}return -1;}
int strsortfncsj(const void *a,const void *b){return strcmp((char *)a,(char *)b);}
int strsortfnckj(const void *a,const void *b){return strcmp((char *)b,(char *)a);}

int chsortfncsj(const void *a,const void *b){if(*(char *)a>*(char *)b){return 1;}if(*(char *)a==*(char *)b){return 0;}return -1;}

void shuffledget(int x[],int n){
    srand(time(0));
    int i,b[524288],p,c;
    for(i=0;i<n;i++){
        b[i]=i;
    }
    for(i=n;i>=1;i--){
        p=rand()%i;
        c=b[i-1];b[i-1]=b[p];b[p]=c;
    }
    for(i=0;i<n;i++){
        scanf("%d",&x[b[i]]);
    }
}

int dx4[4]={1,-1,0,0};
int dy4[4]={0,0,1,-1};
int dx8[8]={-1,-1,-1,0,0,1,1,1};
int dy8[8]={-1,0,1,-1,1,-1,0,1};

int search(int x,int a[],int n){
    int st=0,fi=n-1,te;
    while(st<=fi){
        te=(st+fi)/2;
        if(a[te]<x){st=te+1;}else{fi=te-1;}
    }
    return st;
}

void prarr(int arr[],int n){
  int i;
  for(i=0;i<n;i++){
    if(i){printf(" ");}
    printf("%d",arr[i]);
  }
  printf("\n");
  return;
}

typedef struct{
int val;
int node;
}sd;

int sdsortfnc(const void *a,const void *b){
if(((sd*)a)->val < ((sd*)b)->val){return -1;}
if(((sd*)a)->val > ((sd*)b)->val){return 1;}
return 0;
}

int isrev(char a[],char b[],int n){
  int i;
  for(i=0;i<n;i++){
    if(a[i]!=b[n-1-i]){return 0;}
  }
  return 1;
}

int res=0;

char s[16][16];
char map[16][16]={0};

int n,m;
int pair[16];

void rep(int pod,int sk){
  if(res==1){return;}
  //printf("[%d %d]\n",pod,sk);
  int i;
  if(pod==m){
    int j,c=0,sz[16],ssk=-1;
    char sm[16][16]={0};
    bool usf[16]={0};
    if(m%2==0){
      if(sk!=-1){return;}
      for(i=0;i<m;i++){
        if(pair[i]<i){continue;}
        sz[c]=i;
        sz[m-c-1]=pair[i];
        c++;
      }
    }
    else{
      if(sk==-1){return;}
      for(i=0;i<m;i++){
        if(pair[i]<i){continue;}
        sz[c]=i;
        sz[m-c-1]=pair[i];
        c++;
      }
      sz[c]=sk;
    }
    //for(i=0;i<m;i++){printf("[%d]",sz[i]);}printf("\n");
    for(i=0;i<n;i++){
      for(j=0;j<m;j++){
        sm[i][j]=s[i][sz[j]];
      }
      //printf("<%s>\n",sm[i]);
    }//printf("\n");
    for(i=0;i<n;i++){
      if(usf[i]==1){continue;}
      for(j=i+1;j<n;j++){
        if(usf[j]==1){continue;}
        if(isrev(sm[i],sm[j],m)==1){
          //printf("Match %d %d\n",i,j);
          usf[i]=1;
          usf[j]=1;
          break;
        }
      }
      if(usf[i]==0){
        if(ssk!=-1 || n%2==0){
          return;
        }
        ssk=i;
      }
    }
    if(n%2==0){if(ssk==-1){res=1;return;}}
    else if(ssk==-1){return;}
    else if(isrev(sm[ssk],sm[ssk],m)==1){res=1;return;}
    return;
  }
  else{
    if(pair[pod]!=-1){
      rep(pod+1,sk);
      return;
    }
    for(i=pod+1;i<m;i++){
      if(strcmp(map[pod],map[i])==0){
        pair[pod]=i;
        pair[i]=pod;
        //printf("Pairing %d %d\n",pod,i);
        rep(pod+1,sk);
        //printf("Break %d %d\n",pod,i);
        pair[pod]=-1;
        pair[i]=-1;
      }
    }
    if(sk==-1){
      rep(pod+1,pod);
    }
  }
}

int main(void){
    int i,j,k,a,b,c,h,w,r,l,t;
    scanf("%d%d",&n,&m);
    for(i=0;i<n;i++){scanf("%s",s[i]);}

    for(i=0;i<m;i++){
      for(j=0;j<n;j++){
        map[i][j]=s[j][i];
      }
      pair[i]=-1;
    }

    for(i=0;i<m;i++){
      qsort(map[i],n,sizeof(char),chsortfncsj);
      //printf("<%d:%s>\n",i,map[i]);
    }

    rep(0,-1);
    if(res==1){printf("YES\n");}
    else{printf("NO\n");}
    return 0;
}