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;

string s[12];
int r[12],c[12];

int n,m;
bool dfs2(int x){
	if(x==m)
		return true;
	if(c[x]!=-1)
		return dfs2(x+1);
	int parity=0;
	for(int i=x;i<m;i++)
		if(c[i]==-1)
			parity++;
	for(int i=x;i<m;i++){
		if(c[i]==-1){
			bool available=true;
			c[i]=x;c[x]=i;
			for(int j=0;j<n;j++)
				if(s[j][i]!=s[r[j]][x]||s[r[j]][i]!=s[j][x]){
					available=false;
					break;
				}
			if(available)
				if((parity&1)||i!=x)
					if(dfs2(x+1))
						return true;
			c[i]=c[x]=-1;
		}
	}
	return false;
}
bool dfs1(int x){
	if(x==n)
		return dfs2(0);
	if(r[x]!=-1)
		return dfs1(x+1);
	int parity=0;
	for(int i=x;i<n;i++)
		if(r[i]==-1)
			parity++;
	for(int i=x;i<n;i++){
		if(r[i]==-1){
			r[x]=i;r[i]=x;
			if((parity&1)||i!=x)
				if(dfs1(x+1))
					return true;
			r[x]=r[i]=-1;
		}
	}
	return false;
}

int main(){
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	cin>>n>>m;
	for(int i=0;i<n;i++)
		cin>>s[i];
	memset(r,-1,sizeof r);
	memset(c,-1,sizeof c);
	if(dfs1(0))
		cout<<"YES"<<endl;
	else
		cout<<"NO"<<endl;
}
