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 Lua (5.3.2) (judge verdict: Runtime Error)

local h, w = io.read("*n", "*n", "*l")
local map = {}
for i = 1, h do
  local str = io.read()
  for j = 1, w do
    map[(i - 1) * w + j] = str:sub(j, j)
  end
end
local vertical = {}
local vmap = {}
for i = 1, w do
  vertical[i] = {}
  for j = 1, h do
    vertical[i][j] = map[(j - 1) * w + i]
  end
  table.sort(vertical[i])
  vertical[i] = table.concat(vertical[i], "")
  local v = vertical[i]
  if vmap[v] then
    vmap[v] = nil
  else
    vmap[v] = true
  end
end
local vrem = 0
for k, v in pairs(vmap) do
  vrem = vrem + 1
end

local horizontal = {}
local hmap = {}
for i = 1, h do
  horizontal[i] = {}
  for j = 1, w do
    horizontal[i][j] = map[(i - 1) * w + j]
  end
  table.sort(horizontal[i])
  horizontal[i] = table.concat(horizontal[i], "")
  local v = vertical[i]
  if hmap[v] then
    hmap[v] = nil
  else
    hmap[v] = true
  end
end
local hrem = 0
for k, v in pairs(vmap) do
  hrem = hrem + 1
end
local f = vrem <= 1 and hrem <= 1
print(f and "YES" or "NO")