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<cstdio>
#include<cstring>
using namespace std;
int n, m, match[15], vis[13], ans;
char s[15][15];

bool check() {
	memset(vis, 0, sizeof(vis));
	for(int i=1; i<=m; i++)
		for(int j=1; j<=m; j++) {
			if(vis[i] || vis[j] || i==j) continue;
			bool flag = 1;
			for(int k=1; k<=n; k++) {
				if(s[match[k]][i] != s[k][j]) {
					flag = 0;
					break;
				}
			}
			if(flag) vis[i] = vis[j] = 1;
		}
	int cnt = 0, flag = 0;
	for(int i=1; i<=m; i++)
		if(!vis[i]) {
			cnt++;
			flag = i;
		}
	if((m % 2 == 0 && cnt) || cnt >= 2) return 0;
	if(!cnt) return 1;
	for(int i=1; i<=n; i++)
		if(s[match[i]][flag] != s[i][flag]) return 0;
	return 1;
}

void dfs(int step, bool flag) {
	if(ans) return;
	if(step == ((n+1) >> 1)) {
		if(check()) ans = 1;
		return;
	}
	for(int i=step; i<=n; i++) {
		for(int j=i+1; j<=n; j++)
			if(match[i] == -1 && match[j] == -1) {
				match[i] = j, match[j] = i;
				dfs(step+1, flag);
				match[i] = match[j] = -1;
			}
		if(flag && match[i] == -1) {
			match[i] = i;
			dfs(step+1, 0);
			match[i] = -1;
		}
	}
}

int main()
{
	memset(match, -1, sizeof(match));
	scanf("%d%d", &n, &m);
	for(int i=1; i<=n; i++) scanf("%s", s[i]+1);
	if(n % 2 == 1) dfs(0, 1);
		else dfs(0, 0);
	if(ans) printf("YES\n");
		else printf("NO\n");
	return 0;
}