Problem:
Score : 700 points

Problem Statement

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.

Sample Input 1

2 3
arc
rac

Sample Output 1

YES

If the second and third columns from the left are swapped, the grid becomes symmetric, as shown in the image below:

Sample Input 2

3 7
atcoder
regular
contest

Sample Output 2

NO

Sample Input 3

12 12
bimonigaloaf
faurwlkbleht
dexwimqxzxbb
lxdgyoifcxid
ydxiliocfdgx
nfoabgilamoi
ibxbdqmzxxwe
pqirylfrcrnf
wtehfkllbura
yfrnpflcrirq
wvcclwgiubrk
lkbrwgwuiccv

Sample Output 3

YES

Solution in Python (3.4.3) (judge verdict: Accepted)

H, W = map(int, input().split())
S = [input() for i in range(H)]
 
def check(l):
    u = [0]*W
    mid = W % 2
    for i in range(W):
        if u[i]:
            continue
        for j in range(i+1, W):
            for p, q in l:
                sp = S[p]; sq = S[q]
                if sp[i] != sq[j] or sp[j] != sq[i]:
                    break
            else:
                u[j] = 1
                break
        else:
            if mid:
                for p, q in l:
                    sp = S[p]; sq = S[q]
                    if sp[i] != sq[i]:
                        break
                else:
                    mid = 0
                    continue
            break
    else:
        return 1
    return 0
 
def make(c, l, u, p):
    while c in u:
        c += 1
    if c == H:
        if check(l):
            print("YES")
            exit(0)
        return
    if p:
        l.append((c, c))
        make(c+1, l, u, 0)
        l.pop()
    for i in range(c+1, H):
        if i in u:
            continue
        u.add(i)
        l.append((c, i))
        make(c+1, l, u, p)
        l.pop()
        u.remove(i)
 
make(0, [], set(), H%2)
print("NO")