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 <cstdlib>
#include <cstring>
#include <cstdio>
bool vis[15];
int ano[15], n, m; 
char str[15][15]; 
inline bool chk(int x, int y)
{
	for (int i = 0; i < m; i++)
	{
		if (str[x][i] != str[y][ano[i]])
			return false; 
	}
	return true;
}
inline void work()
{
	bool flg = false; 
	memset(vis, false, sizeof(vis)); 
	for (int i = 0; i < n; i++)
	{
		if (vis[i])
			continue; 
		for (int j = i + 1; j < n && !vis[i]; j++)
		{
			if (!vis[j] && chk(i, j))
				vis[i] = vis[j] = true; 
		}
		if (!vis[i] && (n & 1) && chk(i, i) && !flg)
			vis[i] = flg = true; 
		if (!vis[i])
			return; 
	}
	puts("YES"); 
	exit(0); 
}
void dfs(int cur, bool rem)
{
	if (cur >= m / 2 && !rem)
	{
		work(); 
		return; 
	}
	int pos = -1; 
	for (int i = 0; i < m; i++)
	{
		if (-1 == ano[i])
		{
			pos = i; 
			break; 
		}
	}
	if (rem)
	{
		ano[pos] = pos; 
		dfs(cur, false); 
		ano[pos] = -1; 
	}
	for (int j = pos + 1; j < m; j++)
	{
		if (~ano[j])
			continue; 
		ano[pos] = j; 
		ano[j] = pos; 
		dfs(cur + 1, rem); 
		ano[pos] = ano[j] = -1; 
	}
}
int main()
{
	// freopen("ARC095-E.in", "r", stdin); 
	// freopen("ARC095-E.out", "wt", stdout); 
	scanf("%d%d", &n, &m); 
	for (int i = 0; i < n; i++)
		scanf("%s", str[i]); 
	memset(ano, -1, sizeof(ano)); 
	dfs(0, m & 1); 
	puts("NO"); 
	return 0; 
}
