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<cstring>
#include<string>
#include<cstdio>
#include<cmath>
#include<vector>
#include<queue>
#include<map>
#include<algorithm>
using namespace std;
//const int maxn=200000+10;
const int INF=int(1e9)+10;
#define LL long long
const int maxn = 20;
int n, m, swaped[maxn];
bool used[maxn], ans;

string s[20];

bool check() {
	memset(used, false, sizeof(used));
	for(int i = 0; i < m; i ++) {
		if(used[i])
			continue;
		for(int j = 0; j < m; j ++) {
			bool cur = true;
			if(i == j || used[j])
				continue;
			for(int k = 0; k < n; k ++) {
				if(s[swaped[k]][i] != s[k][j]) {
					cur = false;
					break;
				}
			}
			if(cur) {
				used[i] = used[j] = true;
				break;
			}
		}
	}

	int cnt = 0, noused = -1;
	for(int i = 0; i < m; i ++)
		if(!used[i])
			cnt ++, noused = i;
	if((cnt >= 2 ) || (cnt && (m % 2 == 0)))
		return false;
	for(int i = 0; i < n; i ++)
		if(s[swaped[i]][noused] != s[i][noused])
			return false;
	return true;
}

void dfs(int u, int flag) {
	if(u == (n + 1) / 2) {
		if(check())
			ans = true;
		return;
	}

	for(int i = u; i < n; i ++) {
		if(swaped[i] == -1) {
			for(int j = i + 1; j < n; j ++) {
				if(swaped[j] >= 0)
					continue;
				swaped[i] = j;
				swaped[j] = i;
				dfs(u + 1, flag);
				swaped[i] = swaped[j] = -1;
			}
			if(flag) {
				swaped[i] = i;
				dfs(u + 1, false);
				swaped[i] = -1;
			}
			break;
		}
	}
}

int main() {
	scanf("%d%d", &n, &m);
	memset(swaped, -1, sizeof(swaped));
	for(int i = 0; i < n; i ++)
		cin >> s[i];
	if(n & 1)
		dfs(0, true);
	else
		dfs(0, false);
	printf(ans ? "YES" : "NO");
	return 0;
}