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;

char a[15][15];
int n, m;

char cu[15];
int co[15];

char ru[15];
int ro[15];

bool row_same(int r1, int r2){
	for(int j=(m&1)+1; j+1<=m; j+=2){
		if(a[r1][co[j]] != a[r2][co[j+1]] || a[r2][co[j]] != a[r1][co[j+1]]){
			return 0;
		}
	}
	if(m&1) return a[r1][co[1]] == a[r2][co[1]];
	return 1;
}

void rdfs(int p){
	if(p > n){
		puts("YES");
		exit(0);
	}
	for(int i=1; i<=n; ++i) if(!ru[i]){
		ro[p] = i;
		if((p&1) == (n&1)) if(!row_same(ro[max(1, p-1)], i)) continue;
		ru[i] = 1;
		rdfs(p+1);
		ru[i] = 0;
		if(p&1) break;
	}
}

void cdfs(int p){
	if(p > m){
		rdfs(1);
		return;
	}
	for(int i=1; i<=m; ++i) if(!cu[i]){
		cu[i] = 1;
		co[p] = i;
		cdfs(p+1);
		cu[i] = 0;
		if((p&1) != (m&1)) break;
	}
}

int main()
{
	scanf("%d%d",&n,&m);
	for(int i=1; i<=n; ++i) scanf("%s", a[i]+1);
	cdfs(1);
	puts("NO");
	return 0;
}
