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<algorithm>
#include<iostream>
#include<cstring>
#include<cstdio>
using namespace std;
int bon[1111],gut[1111],cb,cg,n,m;
char s[20][20],*z[20];
bool viz[20];
bool chk()
{
	int i,j,k,l,a,b,c,d;
	for(i=0;i<m;i++)viz[i]=0;
	for(i=0;i<m;i++)if(!viz[i])
	{
		for(j=i+1;j<m;j++)if(!viz[j])
		{
			for(a=1;a<=n;a++)if(z[a][i]!=z[n-a+1][j])goto fail;
			viz[i]=1;viz[j]=1;break;
			fail:;
		}
	}
	int fl=1;
	for(i=0;i<m;i++)
	{
		if(!viz[i])
		{
			if(m&1)
			{
				if(fl==1)
				{
					for(j=1;j<=n;j++)if(z[j][i]!=z[n-j+1][i])return 0;
					fl=0;
				}
				else return 0;
			}
			else return 0;
		}
	}
	return 1;
}
void DFS(int S,int d)
{
	if(d>n)
	{
		if(chk())
		{
			puts("YES");
			exit(0);
		}
	}
	for(int i=1;i<=n;i++)
	{
		if(S&(1<<i-1))
		{
			z[d]=s[i];
			DFS(S-(1<<i-1),d+1);
		}
	}
}
int main()
{
	int N,M,i,j,c;
	scanf("%d%d",&n,&m);
	for(i=1;i<=n;i++)scanf("%s",s[i]);
	N=1<<n;
	for(i=0;i<N;i++)
	{
		for(j=i,c=0;j;j>>=1)if(j&1)c++;
		if(c==n/2)
		{
			int r=0;
			for(j=i,c=0;j;j>>=1)
			{
				c++;
				if(j&1)z[++r]=s[c];
			}
			DFS(N-1-i,n/2+1);
		}
	}
	puts("NO");
	return 0;
}