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,a[13],b[13];
string s[13],ss[13];
void dfs1(int x,bool allow){
	if(x==m){
		cout<<"YES"<<endl;
		exit(0);
	}
	else if(b[x]!=-1)
		dfs1(x+1,allow);
	else{
		for(int i=x+1;i<m;i++){
			if(b[i]!=-1) continue;
			bool ok=true;
			for(int j=0;j<n;j++)
				if(s[j][x]!=s[a[j]][i]){
					ok=false;
					break;
				}
			if(ok){
				b[x]=i;
				b[i]=x;
				dfs1(x+1,allow);
				b[x]=-1;
				b[i]=-1;
			}
		}
		if(allow){
			b[x]=x;
			dfs1(x+1,0);
			b[x]=-1;
		}
	}
} 
void dfs2(int x,bool allow){
	if(x==n)
		dfs1(0,(m%2));
	else if(a[x]!=-1)
		dfs2(x+1,allow);
	else{
		for(int i=x+1;i<n;i++){
			if(ss[i]==ss[x]&&a[i]==-1){
				a[x]=i;
				a[i]=x;
				dfs2(x+1,allow);
				a[x]=-1;
				a[i]=-1;
			}
		}
		if(allow){
			a[x]=x;
			dfs2(x+1,0);
			a[x]=-1;
		}
	}
}
int main(){
	#ifdef FILIN
		#ifndef DavidDesktop
			freopen(FILIN,"r",stdin);
			freopen(FILOUT,"w",stdout);
		#endif
	#endif
	ios::sync_with_stdio(0);
	cin.tie(NULL);
	cout.tie(NULL);
	cin>>n>>m;
	for(int i=0;i<n;i++)
		cin>>s[i];
	memset(a,-1,sizeof(a));
	memset(b,-1,sizeof(b));
	for(int i=0;i<n;i++){
		ss[i]=s[i];
		sort(ss[i].begin(),ss[i].end());
	}
	dfs2(0,(n%2));
	cout<<"NO"<<endl;
	return 0;
}
