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;

#define ll long long
#define mp make_pair
#define pb push_back

#define eprintf(...) fprintf(stderr, __VA_ARGS__)
#define rep(i, n) for (int i = 0; i < (int)(n); ++ i)

int h, w;
char s[15][15];
int pos[15];
bool can[15][15];
bool dp[1 << 12];

int main() {
	scanf("%d %d", &h, &w);
	rep(i, h) scanf("%s", s[i]);
	rep(i, h) pos[i] = i;
	srand(1278007);
	rep(tme, 300000) {
		rep(i, w) rep(j, w) {
			bool ok = 1;
			rep(k, h) if (s[pos[k]][i] != s[pos[h - 1 - k]][j]) {
				ok = 0; break;
			}
			can[i][j] = ok;
		}
		memset(dp, 0, sizeof(dp));
		dp[0] = 1;
		rep(mask, 1 << w) if (dp[mask]) {
			rep(i, w) if (!(mask >> i & 1)) {
				rep(j, w) if (i != j && !(mask >> j & 1)) {
					dp[mask | 1 << i | 1 << j] |= can[i][j];
				}
			}
		}
		if (w & 1) {
			rep(i, w) if (dp[((1 << w) - 1) ^ 1 << i] && can[i][i]) {
				puts("YES"); return 0;
			}
		} else {
			if (dp[(1 << w) - 1]) {
				puts("YES"); return 0;
			}
		}
		random_shuffle(pos, pos + h);
	}
	puts("NO");
	return 0;
}
