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;

int h, w, mat[15];

char a[15][15];

bool vis[15], v2[15];

void solve () {
	int M = 0;
	for(int i=1;i<=h;i++) v2[i] = false;
	for(int i=1;i<=h;i++) {
		if(v2[i]) continue;
		for(int j=i+1;j<=h;j++) {
			if(v2[j]) continue;
			int flag = false;
			for(int k=1;k<=w;k++) {
				if(a[i][k] != a[j][mat[k]]) {flag = true; break;}
			}
			if(!flag) {v2[i] = true; v2[j] = true; M++; break;}
		}
	}
	if(h%2) {
		for(int i=1;i<=h;i++) {
			if(v2[i]) continue;
			bool flag = false;
			for(int j=1;j<=w;j++) {
				if(a[i][j] != a[i][mat[j]]) {flag = true; break;}
			}
			if(!flag) {v2[i] = true; M++; break;}
		}
	}
	if(M == (h+1)/2) {puts("YES"); exit(0);}
}

void Try (int X, bool F) {
	if(X == (w+1)/2) {solve(); return;}
	int I = 1;
	for(;I<=w;I++) {
		if(!vis[I]) break;
	}
	vis[I] = true;
	if(!F && w%2==1) {mat[I] = I; Try(X+1, true);}
	for(int i=1;i<=w;i++) {
		if(!vis[i]) {
			mat[I] = i; mat[i] = I;
			vis[i] = true;
			Try(X+1, F);
			vis[i] = false;
		}
	}
	vis[I] = false;
}

int main()
{
	scanf("%d%d",&h,&w);
	for(int i=1;i<=h;i++) {
		scanf("%s",a[i]+1);
	}
	Try(0, false);
	puts("NO");
}
