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 n,m;  
string s[20];  
int swaped[20];  
int used[20];  
int ans = 0;  
bool check()  
{  
    memset(used,0,sizeof used);  
    for(int i=0;i<m;i++){  
        for(int j=0;j<m;j++){  
            if(used[i]||used[j]||i==j) continue;  
            int cur=1;  
            for(int k=0;k<n;k++){  
                if(s[swaped[k]][i]!=s[k][j]){  
                    cur=0;  
                    break;  
                }  
            }  
            if(cur){  
                used[i]=used[j]=1;  
            }  
        }  
    }  
    int cnt=0,to=0;  
    for(int i=0;i<m;i++){  
        if(!used[i]){  
            cnt++;to=i;  
        }  
    }  
    if(cnt>=2||(m%2==0&&cnt)){  
        return false;  
    }  
    if(!cnt) return true;  
    for(int i=0;i<n;i++){  
        if(s[swaped[i]][to]!=s[i][to]){  
            return false;  
        }  
    }  
    return true;  
}  
  
  
void dfs(int now,bool ji)  
{  
    if(now==(n+1)/2){  
        if(check()){  
            ans=1;  
        }  
        return;  
    }  
    for(int i=now;i<n;i++){  
        for(int j=i+1;j<n;j++){  
            if(swaped[i]==-1&&swaped[j]==-1){  
                swaped[i]=j;  
                swaped[j]=i;  
                dfs(now+1,ji);  
                swaped[i]=-1;  
                swaped[j]=-1;  
            }  
        }  
        if(ji&&swaped[i]==-1){  
            swaped[i]=i;  
            dfs(now+1,false);  
            swaped[i]=-1;  
        }  
    }  
  
}  
  
int main()  
{  
    scanf("%d%d",&n,&m);  
    for(int i=0;i<n;i++){  
        cin>>s[i];  
        swaped[i]=-1;  
    }  
    if(n&1){  
        dfs(0,true);  
    }else{  
        dfs(0,false);  
    }  
    if(ans) printf("YES\n");  
    else printf("NO\n");  
}  