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: Wrong Answer)

from collections import defaultdict


def main():
    h, w = map(int, input().split())
    s = []
    for _ in range(h):
        row = []
        s.append(row)
        for c in input().strip():
            row.append(ord(c))
    c_row = defaultdict(int)
    for row in s:
        c_row[tuple(sorted(row))] += 1
    if sum(c % 2 for c in c_row.values()) > h % 2:
        print('NO')
        return
    for row, c in c_row.items():
        if c % 2:
            count = defaultdict(int)
            for ch in row:
                count[ch] += 1
            if sum(cc % 2 for cc in count) > w % 2:
                print('NO')
                return

    c_col = defaultdict(int)
    for col in zip(*s):
        c_col[tuple(sorted(col))] += 1
    if sum(c % 2 for c in c_col.values()) > w % 2:
        print('NO')
        return

    for row, c in c_col.items():
        if c % 2:
            count = defaultdict(int)
            for ch in row:
                count[ch] += 1
            if sum(cc % 2 for cc in count) > h % 2:
                print('NO')
                return

    print('YES')


main()