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

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