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;
#define ll long long
const int MAXN=30;
char st[MAXN][MAXN];
int sp[MAXN],ans,used[MAXN];
int n,m;
bool check()
{
	memset(used,0,sizeof(used));
	for(int i=0;i<m;i++){
		if(used[i]) continue;
		for(int j=0;j<m;j++){
			bool vis=1;
			if(i==j||used[j]) continue;
			for(int k=0;k<n;k++){
				if(st[k][i]==st[sp[k]][j]) continue;
				vis=0;
				break;
			}
			if(vis){
				used[i]=used[j]=1;
				break;
			}
		}
	}
	int cnt=0,pos=-1;
	for(int i=0;i<m;i++)
		if(!used[i]) cnt++,pos=i;
	if(cnt>=2||(cnt&&(m%2==0))) return 0;
	if(cnt==1)
		for(int i=0;i<n;i++)
			if(st[i][pos]!=st[sp[i]][pos]) return 0;
	return 1;
}
void dfs(int u,int flag)
{
	if(u==(n+1)>>1){
		if(check()) ans=1;
		return;
	}
	if(ans==1) return;
	for(int i=u;i<n;i++){
		if(sp[i]==-1){
			for(int j=i+1;j<n;j++){
				if(sp[j]==-1){
					sp[i]=j;sp[j]=i;
					dfs(u+1,flag);
					sp[i]=sp[j]=-1;
				}
			}
			if(flag){
				sp[i]=i;
				dfs(u+1,0);
				sp[i]=-1;
			}
		}
	}
}
int main()
{
	while(cin>>n>>m){
		memset(sp,-1,sizeof(sp));
		ans=0;
		for(int i=0;i<n;i++) scanf("%s",st[i]);
		if(n&1) dfs(0,1);
		else dfs(0,0);
		if(ans) cout<<"YES"<<endl;
		else cout<<"NO"<<endl;
	}
}
