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;

typedef long long ll;
typedef pair<int,int> P;

#define fr first
#define sc second

int main(){
	int h,w;
	char c[15][15];
	scanf("%d%d",&h,&w);
	for(int i = 0 ; i < h ; i ++){
		scanf("\n");
		for(int j = 0 ; j < w ; j ++){
			scanf("%c",&c[i][j]);
		}
	}
	
	vector<int> v;
	for(int i = 0 ; i < w ; i ++){
		v.push_back(i);
	}
	string s[15];
	bool used[15];
	bool a[15];
	int cnt = 0;
	int x = w/2;
	do{
		if(v[0] >= 3)break;
		for(int i = 0 ; i+1 < x ; ++i){
			if(v[i] > v[i+1])goto next_loop;
		}
		for(int i = 0 ; i < x ; ++i){
			if(v[i] > v[w-1-i])goto next_loop;
		}
		for(int i = 0 ; i < h ; ++i){
			s[i] = "";
			for(int j = 0 ; j < w ; ++j){
				s[i] += c[i][v[j]];
			}
		}
		for(int i = 0 ; i < h ; ++i){
			used[i] = false;
			a[i] = false;
		}
		for(int i = 0 ; i < h ; ++i){
			if(used[i])continue;
			used[i] = true;
			string t = s[i];
			reverse(t.begin(),t.end());
			if(s[i] == t){
				a[i] = true;
			}
			else {
				bool ok = false;
				for(int j = i+1 ; j < h ; ++j){
					if(used[j])continue;
					if(s[j] == t){
						ok = true;
						used[j] = true;
						break;
					}
				}
				if(!ok){
					goto next_loop;
				}
			}
		}
		cnt = 0;
		for(int i = 0 ; i < h ; ++i){
			if(!a[i])continue;
			a[i] = false;
			bool ok = false;
			for(int j = i+1 ; j < h ; ++j){
				if(!a[j])continue;
				if(s[i] == s[j]){
					ok = true;
					a[j] = false;
					break;
				}
			}
			if(!ok)cnt ++;
		}
		if(cnt <= 1){
			puts("YES");
			return 0;
		}
		next_loop:;
	}while(next_permutation(v.begin(),v.end()));
	
	puts("NO");
}

