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;
template <class T> inline void read(T &x) {
	x = 0; int c = getchar(), f = 1;
	for (; !isdigit(c); c = getchar()) if (c == 45) f = -1;
	for (; isdigit(c); c = getchar()) (x *= 10) += f*(c-'0');
}
int n, m, l, p[13];
char s[13][13]; bool flag;
bool IsMat(int u, int v) {
	for (int i = 1; i <= m; i++)
		if (s[u][i] ^ s[v][p[i]]) return false;
	return true;
}
bool chk() {
	bool used[13], pal = n&1;
	memset(used, false, sizeof used);
	for (int u = 1, v; u <= n; u++) if (!used[u]) {
		for (v = u+1; v <= n; v++)
			if (!used[v] && IsMat(u, v)) break;
		if (v <= n) used[u] = used[v] = true;
		else if (!IsMat(u, u)) return false;
		else if (!pal) return false;
		else used[u] = true, pal = false;
	}
	return true;
}
void DFS(int u, bool odd) {
	if (u > m) {flag |= chk(); return;}
	if (p[u]) {DFS(u+1, odd); return;}
	if (odd) p[u] = u, DFS(u+1, odd^1), p[u] = 0;
	for (int v = u+1; !flag && v <= m; v++) if (!p[v])
		p[u] = v, p[v] = u, DFS(u+1, odd), p[u] = p[v] = 0;
}
int main() {
	read(n), read(m);
	for (int i = 1; i <= n; i++) scanf("%s", s[i]+1);
	return DFS(1, m&1), puts(flag ? "YES" : "NO"), 0;
}
