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;
const int N=20;
bool use[N];
string s[N];
string str[N];
map<string,int>mp;
int n,m,qwq;
int main()
{
	cin>>n>>m;
	for(int i=0;i<n;i++)cin>>s[i];
	for(int i=0;i<n;i++)
	{
		for(int j=0;j<m;j++)
		{
			str[j]+=s[i][j];
		}
	}
	for(int i=0;i<m;i++)s[i]=str[i];
	sort(s,s+m);
	do{
		random_shuffle(s,s+m);
		qwq++;
		int cnt=0;
		mp.clear();
		for(int i=0;i<n;i++)str[i]="";
		for(int i=0;i<m;i++)
		{
			for(int j=0;j<n;j++)
			{
				str[j]+=s[i][j];
			}
		}
		for(int i=0;i<n;i++)
		{
			if(mp[str[i]])
			{
				mp[str[i]]--;
				cnt--;
			}else{
				string t=str[i];
				reverse(t.begin(),t.end());
				cnt++;
				mp[t]++;
			}
		}
		if(cnt==1||cnt==0)
		{
			cout<<"YES\n";
			return 0;
		}
		if(qwq==2e5)break;
	}while(true);
	cout<<"NO\n";
	return 0;
}