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>
#define max_n 12
#define max_m 12
using namespace std;
char c[max_n+1][max_m+1],d[max_n+1],e[max_m+1];
int m,n;
bool dfs2(int x){
	if(x>m)
		return 1;
	if(e[x])
		return dfs2(x+1);
	int t=0,r=0;
	for(int i=x-1; ++i<=m; !e[i]&&(++t));
	for(int i=x-1; ++i<=m; )
		if(!e[i]){
			e[x]=i,e[i]=x,r=1;
			for(int j=0; ++j<=n&&(c[j][x]==c[d[j]][i]&&c[d[j]][x]==c[j][i]||(r=0)); );
			if(i==x){
				if(r&&(t&1)&&dfs2(x+1))
					return 1;
			}
			else
				if(r)
					return dfs2(x+1);
			e[x]=e[i]=0;
		}
	return 0;
}
bool dfs1(int x){
	if(x>n)
		return dfs2(1);
	if(d[x])
		return dfs1(x+1);
	int t=0;
	for(int i=x-1; ++i<=n; !d[i]&&(++t));
	for(int i=x-1; ++i<=n; )
		if(!d[i]){
			d[x]=i,d[i]=x;
			if(((t&1)||(i!=x))&&dfs1(x+1))
				return 1;
			d[x]=0,d[i]=0;
		}
	return false;
}
int main(){
	scanf("%d%d",&n,&m);
	for(int i=0; ++i<=n; scanf("%s",c[i]+1));
	puts(dfs1(1)?"YES":"NO");
	return 0;
}