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`.

Examples

Input

2 3
arc
rac


Output

YES


Input

3 7
atcoder
regular
contest


Output

NO


Input

12 12
bimonigaloaf
faurwlkbleht
dexwimqxzxbb
lxdgyoifcxid
ydxiliocfdgx
nfoabgilamoi
ibxbdqmzxxwe
pqirylfrcrnf
wtehfkllbura
yfrnpflcrirq
wvcclwgiubrk
lkbrwgwuiccv


Output

YES
#include<bits/stdc++.h>
using namespace std;
int h,w;
bool solve(int id,vector<string>& s){
    if(id==h/2){
        vector<int> flag(w,false);
        for(int j=0;j<w;j++){
            if(flag[j]) continue;
            for(int k=j+1;k<w;k++){
                bool isok=true;
                for(int i=0;i<h;i++){
                    if(s[i][j]!=s[h-1-i][k]){
                        isok=false;
                        break;
                    }
                }
                if(isok){
                    flag[j]=flag[k]=true;
                    break;
                }
            }
        }
        int cnt=count(flag.begin(),flag.end(),false);
        if(cnt>=2) return false;
        if(cnt==0) return true;
        for(int j=0;j<w;j++){
            if(!flag[j]){
                for(int i=0;i<h;i++){
                    if(s[i][j]!=s[h-1-i][j]) return false;
                }
                return true;
            }
        }        
        assert(false);
    }
    for(int i=id+1;i<h-id;i++){
        if(h%2==1 && i==h/2) continue;
        assert(i<=h-id-1);
        if(i!=h-id-1) swap(s[i],s[h-id-1]);
        if(solve(id+1,s)) return true;
        if(i!=h-id-1) swap(s[i],s[h-id-1]);
    }
    return false;
}

int main(){
    cin>>h>>w;
    vector<string> s(h);
    for(int i=0;i<h;i++) cin>>s[i];
    vector<int> flag(h);
    bool isok=false;
    if(h%2==1){
        for(int i=0;i<h;i++){
            swap(s[i],s[h/2]);
            isok=isok || solve(0,s);
            swap(s[i],s[h/2]);
        }
    }else{
        isok=solve(0,s);
    }
    cout<<(isok? "YES" : "NO")<<endl;
    return 0;
}
