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 <stdio.h>
#include <iostream>
#include <string>
#include <string.h>
using namespace std;
int n,m;
string s[20];
int swaped[20];
int used[20];
int ans = 0;
bool check()
{
	memset(used,0,sizeof used);
	for(int i=0;i<m;i++){
		for(int j=0;j<m;j++){
			if(used[i]||used[j]||i==j) continue;
			int cur=1;
			for(int k=0;k<n;k++){
				if(s[swaped[k]][i]!=s[k][j]){
					cur=0;
					break;
				}
			}
			if(cur){
				used[i]=used[j]=1;
			}
		}
	}
	int cnt=0,to=0;
	for(int i=0;i<m;i++){
		if(!used[i]){
			cnt++;to=i;
		}
	}
	if(cnt>=2||(m%2==0&&cnt)){
		return false;
	}
	if(!cnt) return true;
	for(int i=0;i<n;i++){
		if(s[swaped[i]][to]!=s[i][to]){
			return false;
		}
	}
	return true;
}


void dfs(int now,bool ji)
{
	if(now==(n+1)/2){
		if(check()){
			ans=1;
		}
		return;
	}
	for(int i=now;i<n;i++){
		for(int j=i+1;j<n;j++){
			if(swaped[i]==-1&&swaped[j]==-1){
				swaped[i]=j;
				swaped[j]=i;
				dfs(now+1,ji);
				swaped[i]=-1;
				swaped[j]=-1;
			}
		}
		if(ji&&swaped[i]==-1){
			swaped[i]=i;
			dfs(now+1,false);
			swaped[i]=-1;
		}
	}

}

int main()
{
	cin>>n>>m;
	for(int i=0;i<n;i++)
	{
		cin>>s[i];
		swaped[i]=-1;
	}
	if(n&1)
	{
		dfs(0,true);
	}
	else
	{
		dfs(0,false);
	}
	if(ans) cout<<"YES";
	else cout<<"NO";
}