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 <cstdio>

char c[15][15],d[15],e[15];
int i,m,n;

inline bool dfs2(int x)
{
	if (x>m)
		return true;
	if (e[x])
		return dfs2(x+1);
	else
	{
		int t=0,r=0;
		for (int i=x;i<=m;i++)
			if (! e[i])
				t++;
		for (int i=x;i<=m;i++)
			if (! e[i])
			{
				e[x]=i,e[i]=x,r=1;
				for (int j=1;j<=n;j++)
					if ((c[j][x]!=c[d[j]][i]) || (c[d[j]][x]!=c[j][i]))
					{
						r=0;
						break;
					}
				if ((r) && ((t&1) || (i!=x)) && (dfs2(x+1)))
					return true;
				e[x]=0,e[i]=0;
			}
	}
	return false;
}

inline bool dfs1(int x)
{
	if (x>n)
		return dfs2(1);
	if (d[x])
		return dfs1(x+1);
	else
	{
		int t=0;
		for (int i=x;i<=n;i++)
			if (! d[i])
				t++;
		for (int i=x;i<=n;i++)
			if (! d[i])
			{
				d[x]=i,d[i]=x;
				if (((t&1) || (i!=x)) && (dfs1(x+1)))
					return true;
				d[x]=0,d[i]=0;
			}
	}
	return false;
}

int main()
{
	scanf("%d%d",&n,&m);
	for (i=1;i<=n;i++)
		scanf("%s",c[i]+1);
	if (dfs1(1))
		puts("YES");
	else
		puts("NO");
	return 0;
}