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 <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <map>
#include <sstream>
#include <queue>
#include <deque>
#define ll long long
#define MP make_pair
#define PII pair<int, int>
#define F first
#define S second
using namespace std;
int n,m;
char c[15][15];
bool ok[15][15];
vector<PII> vv;
queue<int> qq;
void col(queue<int> q)
{
	if (q.size()<2)
	{
		cout <<"YES";
		exit(0);
	}
	int t=q.front();
	q.pop();
	for (int i=0;i<q.size();i++)
	{
		int tt=q.front();
		q.pop();
		if (ok[t][tt]) col(q);
		q.push(tt);
	}
	if (q.size()%2==0) col(q);
	q.push(t);
}
void row(vector<PII> v,queue<int> q)
{
	if (q.size()>=1)
	{
		int t=q.front();
	    q.pop();
	    for (int i=0;i<q.size();i++)
	    {
		    int tt=q.front();
		    q.pop();
		    v.push_back(MP(t,tt));
		    //cout <<t<<" "<<tt<<" ##\n";
			row(v,q);
			v.pop_back();
			q.push(tt);
		}
		if (q.size()%2==0)
		{
			v.push_back(MP(t,t));
		    //cout <<t<<" "<<t<<" ##\n";
			row(v,q);
			v.pop_back();
		}
		q.push(t);
	}
	else
	{
		for (int i=0;i<m;i++)
		{
			for (int j=0;j<=i;j++)
			{
				ok[i][j]=ok[j][i]=1;
				for (int k=0;k<v.size();k++)
				{
					int x=v[k].F,y=v[k].S;
					if (c[x][i]!=c[y][j] || c[x][j]!=c[y][i]) ok[i][j]=ok[j][i]=0;
				}
			}
		}
		for (int i=0;i<m;i++) q.push(i);
		col(q);
	}
}
int main()
{
	cin >>n>>m;
	for (int i=0;i<n;i++)
	{
		for (int j=0;j<m;j++)
		    cin >>c[i][j];
	}
	for (int i=0;i<n;i++) qq.push(i);
	row(vv,qq);
	cout <<"NO";
	return 0;
}