output_description: If it is possible to turn all the squares black, print the minimum necessary
  number of operations to achieve the objective. If it is impossible, print `-1`
  instead.
  
  * * *
input_description: The input is given from Standard Input in the following format:
  
      
      
      N
      a_{11}...a_{1N}
      :
      a_{N1}...a_{NN}
attempt: from sys import exit, setrecursionlimit
  from functools import reduce
  from itertools import *
  from collections import defaultdict, deque
  from bisect import bisect
  
  
  def read():
      return int(input())
  
  
  def reads():
      return [int(x) for x in input().split()]
  
  
  setrecursionlimit(1000000)
  
  N = read()
  L = N * N
  
  assert N <= 3
  
  a = ""
  for _ in range(N):
      a += input()
  
  queue = deque()
  queue.append((a, 0))
  visited = set()
  visited.add(a)
  
  while len(queue) != 0:
      (a, k) = queue.popleft()
      if a == "#" * L:
          print(k)
          exit()
      for i, j in product(range(N), range(N)):
          b = list(a)
          b[j:L:N] = b[N * i : N * (i + 1)]
          b = "".join(b)
          if not b in visited:
              visited.add(b)
              queue.append((b, k + 1))
  
  print("-1")
  
problem_description: Statement
  
  There is a square-shaped grid with N vertical rows and N horizontal columns.
  We will denote the square at the i-th row from the top and the j-th column
  from the left as (i,\ j).
  
  Initially, each square is either white or black. The initial color of the grid
  is given to you as characters a_{ij}, arranged in a square shape. If the
  square (i,\ j) is white, a_{ij} is `.`. If it is black, a_{ij} is `#`.
  
  You are developing a robot that repaints the grid. It can repeatedly perform
  the following operation:
  
    * Select two integers i, j (1 ≤ i,\ j ≤ N). Memorize the colors of the squares (i,\ 1), (i,\ 2), ..., (i,\ N) as c_1, c_2, ..., c_N, respectively. Then, repaint the squares (1,\ j), (2,\ j), ..., (N,\ j) with the colors c_1, c_2, ..., c_N, respectively.
  
  Your objective is to turn all the squares black. Determine whether it is
  possible, and find the minimum necessary number of operations to achieve it if
  the answer is positive.
samples: [{"input": "2\n    #.\n    .#", "output": "3\n    \n\nFor example, perform the operation as follows:\n\n  * Select i = 1, j = 2.\n  * Select i = 1, j = 1.\n  * Select i = 1, j = 2.\n\nThe transition of the colors of the squares is shown in the figure below:\n\n![6a0314bb2b1073694a7ef5a062e77b13.png](https://atcoder.jp/img/mujin/6a0314bb2b1073694a7ef5a062e77b13.png)\n\n* * *"}, {"input": "2\n    ..\n    ..", "output": "-1\n    \n\n* * *"}, {"input": "2\n    ##\n    ##", "output": "0\n    \n\n* * *"}, {"input": "3\n    .#.\n    ###\n    .#.", "output": "2\n    \n\n* * *"}, {"input": "3\n    ...\n    .#.\n    ...", "output": "5"}]