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;
char c[14][14];
bool ok,vis[14];
void dfs(int now)
{
	bool o=true;
	if(ok)
	{
		return;
	}
	for(int i=now+1;i<n-now;i++)
	{
		o=false;
		for(int j=0;j<m;j++)
		{
			swap(c[i][j],c[n-now-1][j]);
		}
		dfs(now+1);
		for(int j=0;j<m;j++)
		{
			swap(c[i][j],c[n-now-1][j]);
		}
	}
	if(o)
	{
		for(int i=0;i<m;i++)
		{
			vis[i]=false;
		}
		int cnt=0;
		for(int i=0;i<m;i++)
		{
			if(!vis[i])
			{
				for(int j=i+1;j<m;j++)
				{
					if(!vis[j])
					{
						bool t=true;
						for(int k=0;k<n;k++)
						{
							t&=(c[k][i]==c[n-k-1][j]);
						}
						if(t)
						{
							vis[i]=true;
							vis[j]=true;
							cnt+=2;
							break;
						}
					}
				}
			}
		}
		for(int i=0;i<m;i++)
		{
			if(!vis[i])
			{
				bool t=true;
				for(int j=0;j<n;j++)
				{
					t&=(c[j][i]==c[n-j-1][i]);
				}
				if(t)
				{
					cnt++;
				}
				break;
			}
		}
		if(cnt==m)
		{
			ok=true;
		}
	}
}
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++)
	{
		if(!ok)
		{
			for(int j=0;j<m;j++)
			{
				swap(c[i][j],c[n/2][j]);
			}
			dfs(0);
			for(int j=0;j<m;j++)
			{
				swap(c[i][j],c[n/2][j]);
			}
		}
	}
	if(ok)
	{
		cout<<"YES"<<endl;
	}
	else
	{
		cout<<"NO"<<endl;
	}
	return 0;
}