"""simple docstring"""



from __future__ import annotations



def 					_lowerCamelCase(					a ,  a ,  a ,  a ,  a ,  ):
       __a     				=  len(a							)

       # If row is equal to the size of the board it means there are a queen in each row in
       # the current board (possible_board)
       if row == n:
              # We convert the variable possible_board that looks like this: [1, 3, 0, 2] to
              # this: ['. Q . . ', '. . . Q ', 'Q . . . ', '. . Q . ']
              boards.append([". " * i + "Q " + ". " * (n - 1 - i) for i in possible_board]							)
              return

       # We iterate each column in the row to find all possible results in each row
       for col in range(a							):
              # We apply that we learned previously. First we check that in the current board
              # (possible_board) there are not other same value because if there is it means
              # that there are a collision in vertical. Then we apply the two formulas we
              # learned before:
              #
              # 45º: y - x = b or 45: row - col = b
              # 135º: y + x = b or row + col = b.
              #
              # And we verify if the results of this two formulas not exist in their variables
              # respectively.  (diagonal_right_collisions, diagonal_left_collisions)
              #
              # If any or these are True it means there is a collision so we continue to the
              # next value in the for loop.
              if (
                  col in possible_board
                  or row - col in diagonal_right_collisions
                  or row + col in diagonal_left_collisions
              ):
                     continue

              # If it is False we call dfs function again and we update the inputs
              depth_first_search(
                  [*possible_board, col] ,  [*diagonal_right_collisions, row - col] ,  [*diagonal_left_collisions, row + col] ,  a ,  a ,  )



def 					_lowerCamelCase(					a							):
       __a     				=  []
       depth_first_search([] ,  [] ,  [] ,  a ,  a							)

       # Print all the boards
       for board in boards:
              for column in board:
                     print(a							)
              print(""							)

       print(len(a							) ,  "solutions were found."							)


if __name__ == "__main__":
   import doctest

   doctest.testmod()
   n_queens_solution(4)

"""simple docstring"""



import string

# frequency taken from https://en.wikipedia.org/wiki/Letter_frequency
SCREAMING_SNAKE_CASE__:Any			=	{
    """E""": 12.70,
    """T""": 9.06,
    """A""": 8.17,
    """O""": 7.51,
    """I""": 6.97,
    """N""": 6.75,
    """S""": 6.33,
    """H""": 6.09,
    """R""": 5.99,
    """D""": 4.25,
    """L""": 4.03,
    """C""": 2.78,
    """U""": 2.76,
    """M""": 2.41,
    """W""": 2.36,
    """F""": 2.23,
    """G""": 2.02,
    """Y""": 1.97,
    """P""": 1.93,
    """B""": 1.29,
    """V""": 0.98,
    """K""": 0.77,
    """J""": 0.15,
    """X""": 0.15,
    """Q""": 0.10,
    """Z""": 0.07,
}
SCREAMING_SNAKE_CASE__:Optional[int]			=	"""ETAOINSHRDLCUMWFGYPBVKJXQZ"""
SCREAMING_SNAKE_CASE__:Tuple			=	"""ABCDEFGHIJKLMNOPQRSTUVWXYZ"""



def 					_lowerCamelCase(					a							):
       __a     				=  {letter: 0 for letter in string.ascii_uppercase}
       for letter in message.upper():
              if letter in LETTERS:
                     letter_count[letter] += 1

       return letter_count



def 					_lowerCamelCase(					a							):
       return x[0]



def 					_lowerCamelCase(					a							):
       __a     				=  get_letter_count(a							)
       __a     				=  {
           freq: [] for letter, freq in letter_to_freq.items()
       }
       for letter in LETTERS:
              freq_to_letter[letter_to_freq[letter]].append(a							)

       __a     				=  {}

       for freq in freq_to_letter:
              freq_to_letter[freq].sort(key=ETAOIN.find ,  reverse=a							)
              __a     				=  "".join(freq_to_letter[freq]							)

       __a     				=  list(freq_to_letter_str.items()							)
       freq_pairs.sort(key=a ,  reverse=a							)

       __a     				=  [freq_pair[1] for freq_pair in freq_pairs]

       return "".join(a							)



def 					_lowerCamelCase(					a							):
       __a     				=  get_frequency_order(a							)
       __a     				=  0
       for common_letter in ETAOIN[:6]:
              if common_letter in freq_order[:6]:
                     match_score += 1

       for uncommon_letter in ETAOIN[-6:]:
              if uncommon_letter in freq_order[-6:]:
                     match_score += 1

       return match_score


if __name__ == "__main__":
   import doctest

   doctest.testmod()
