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 N 15

int n,m,swp[N];
bool used[N];
char s[N][N];

void dfs(int x){
	if (x>=n){
		memset(used,0,sizeof used);
		for (int i=1;i<=m;++i)
			if (!used[i]){
				for (int j=i+1;j<=m;++j)
					if (!used[j]){
						bool fl=1;
						for (int k=1;k<=n;++k)
							if (s[k][i]!=s[swp[k]][j]){
								fl=0; break;
							}
						if (fl){used[i]=used[j]=1; break;}
					}
			}
		int tmp=0;
		for (int i=1;i<=m;++i) if (!used[i]){if (tmp) return; tmp=i;}
		if (!tmp){puts("YES"); exit(0);}
		if (tmp&&(m&1)){
			for (int i=1;i<=n;++i)
				if (s[i][tmp]!=s[swp[i]][tmp]) return;
			puts("YES"); exit(0);
		}
		return;
	}
	if (n&1){
		bool fl=1;
		for (int i=1;i<=n;++i) if (swp[i]==i) fl=0;
		for (int i=1;i<=n;++i)
			if (!swp[i]){
				if (fl){swp[i]=i; dfs(x+1); swp[i]=0;}
				for (int j=i+1;j<=n;++j)
					if (!swp[j]){
						swp[i]=j; swp[j]=i;
						dfs(x+2);
						swp[i]=swp[j]=0;
					}
				break;
			}
	}
	else{
		for (int i=1;i<=n;++i)
			if (!swp[i]){
				for (int j=i+1;j<=n;++j)
					if (!swp[j]){
						swp[i]=j; swp[j]=i;
						dfs(x+2);
						swp[i]=swp[j]=0;
					}
			}
	}
}

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