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<iostream>
#include<algorithm>
#include<cstdio>
#include<cstdlib>
#include<cstring>
using namespace std;

const int maxn=12+10;
int n,m,cnt[maxn][26],other[maxn];
char a[maxn][maxn];
bool cmp[maxn][maxn],cmpp[maxn],done[maxn];

void dfs2(int rest){
	if(!rest){
		puts("YES");
		exit(0);
	}
	if(rest&1){
		for(int i=0;i<m;++i){
			for(int j=0;j<n;++j)
				if(a[j][i]!=a[other[j]][i])
					goto door1;
			done[i]=true;
			dfs2(rest-1);
door1:
			;
		}
	}
	else{
		for(int i=0;i<m;++i)
			if(!done[i]){
				for(int j=i+1;j<m;++j)
					if(!done[j]){
						for(int k=0;k<n;++k)
							if(a[k][i]!=a[other[k]][j])
								goto door2;
						done[i]=done[j]=true;
						dfs2(rest-2);
						done[i]=done[j]=false;
door2:
						;
					}
				return;
			}
	}
}
void dfs1(int rest){
	if(!rest){
		dfs2(m);
		return;
	}
	if(rest&1){
		for(int i=0;i<n;++i)
			if(cmpp[i]){
				other[i]=i;
				dfs1(rest-1);
				other[i]=-1;
			}
	}
	else{
		for(int i=0;i<n;++i)
			if(other[i]==-1){
				for(int j=i+1;j<n;++j)
					if(other[j]==-1&&cmp[i][j]){
						other[i]=j;other[j]=i;
						dfs1(rest-2);
						other[i]=other[j]=-1;
					}
				return;
			}
	}
}

int main(){
	cin>>n>>m;
	for(int i=0;i<n;++i){
		cin>>a[i];
		for(int j=0;j<m;++j)
			++cnt[i][a[i][j]-'a'];
	}
	for(int i=0;i<n;++i)
		for(int j=i+1;j<n;++j){
			cmp[i][j]=cmp[j][i]=true;
			for(int k=0;k<26;++k)
				if(cnt[i][k]!=cnt[j][k]){
					cmp[i][j]=cmp[j][i]=false;
					break;
				}
		}
	for(int i=0;i<n;++i){
		int x=0;
		for(int j=0;j<26;++j)
			if(cnt[i][j]&1)
				++x;
		if(x!=m%2)
			cmpp[i]=false;
		else
			cmpp[i]=true;
		other[i]=-1;
	}
	dfs1(n);
	puts("NO");
	return 0;
}