from __future__ import annotations

snake_case  =			[2, 1, 4, 5, 6, 0, 8, 9, 1, 2, 0, 6, 4, 2, 0, 6, 5, 3, 2, 7]





class        SCREAMING_SNAKE_CASE   :
  """simple docstring"""







  def __init__(  self   :					str					,					__lowerCAmelCase   :					int					):


        """simple docstring"""



        _lowerCAmelCase		   =   -1
        _lowerCAmelCase		   =   -1
        _lowerCAmelCase		   =   [-1] * length
        _lowerCAmelCase		   =   None
        _lowerCAmelCase		   =   None



  def __repr__(  self   :					Union[str, Any]					):


        """simple docstring"""



        return F"Node(min_value={self.minn} max_value={self.maxx})"







def 			A_   ( _lowerCamelCase			:							list[int]    ):
      _lowerCAmelCase		   =   Node(len(_lowerCamelCase    )    )
      _lowerCAmelCase   ,  _lowerCAmelCase		   =   min(_lowerCamelCase    ), max(_lowerCamelCase    )
      # Leaf node case where the node contains only one unique value
      if root.minn == root.maxx:
            return root
      _lowerCAmelCase		   =   (root.minn + root.maxx) // 2

      _lowerCAmelCase		   =   []
      _lowerCAmelCase		   =   []

      for index, num in enumerate(_lowerCamelCase    ):
            if num <= pivot:
                  left_arr.append(_lowerCamelCase    )
            else:
                  right_arr.append(_lowerCamelCase    )
            _lowerCAmelCase		   =   len(_lowerCamelCase    )
      _lowerCAmelCase		   =   build_tree(_lowerCamelCase    )
      _lowerCAmelCase		   =   build_tree(_lowerCamelCase    )
      return root







def 			A_   ( _lowerCamelCase			:							Node | None  ,  _lowerCamelCase			:							int  ,  _lowerCamelCase			:							int    ):
      if index < 0 or node is None:
            return 0
      # Leaf node cases
      if node.minn == node.maxx:
            return index + 1 if node.minn == num else 0
      _lowerCAmelCase		   =   (node.minn + node.maxx) // 2
      if num <= pivot:
            # go the left subtree and map index to the left subtree
            return rank_till_index(node.left  ,  _lowerCamelCase  ,  node.map_left[index] - 1    )
      else:
            # go to the right subtree and map index to the right subtree
            return rank_till_index(node.right  ,  _lowerCamelCase  ,  index - node.map_left[index]    )







def 			A_   ( _lowerCamelCase			:							Node | None  ,  _lowerCamelCase			:							int  ,  _lowerCamelCase			:							int  ,  _lowerCamelCase			:							int    ):
      if start > end:
            return 0
      _lowerCAmelCase		   =   rank_till_index(_lowerCamelCase  ,  _lowerCamelCase  ,  _lowerCamelCase    )
      _lowerCAmelCase		   =   rank_till_index(_lowerCamelCase  ,  _lowerCamelCase  ,  start - 1    )
      return rank_till_end - rank_before_start







def 			A_   ( _lowerCamelCase			:							Node | None  ,  _lowerCamelCase			:							int  ,  _lowerCamelCase			:							int  ,  _lowerCamelCase			:							int    ):
      if index > (end - start) or start > end or node is None:
            return -1
      # Leaf node case
      if node.minn == node.maxx:
            return node.minn
      # Number of elements in the left subtree in interval [start, end]
      _lowerCAmelCase		   =   node.map_left[end] - (
          node.map_left[start - 1] if start else 0
      )
      if num_elements_in_left_tree > index:
            return quantile(
                node.left  ,  _lowerCamelCase  ,  (node.map_left[start - 1] if start else 0)  ,  node.map_left[end] - 1  ,  )
      else:
            return quantile(
                node.right  ,  index - num_elements_in_left_tree  ,  start - (node.map_left[start - 1] if start else 0)  ,  end - node.map_left[end]  ,  )







def 			A_   ( _lowerCamelCase			:							Node | None  ,  _lowerCamelCase			:							int  ,  _lowerCamelCase			:							int  ,  _lowerCamelCase			:							int  ,  _lowerCamelCase			:							int    ):
      if (
          start > end
          or node is None
          or start_num > end_num
          or node.minn > end_num
          or node.maxx < start_num
      ):
            return 0
      if start_num <= node.minn and node.maxx <= end_num:
            return end - start + 1
      _lowerCAmelCase		   =   range_counting(
          node.left  ,  (node.map_left[start - 1] if start else 0)  ,  node.map_left[end] - 1  ,  _lowerCamelCase  ,  _lowerCamelCase  ,  )
      _lowerCAmelCase		   =   range_counting(
          node.right  ,  start - (node.map_left[start - 1] if start else 0)  ,  end - node.map_left[end]  ,  _lowerCamelCase  ,  _lowerCamelCase  ,  )
      return left + right


if __name__ == "__main__":
 import doctest

 doctest.testmod()






'''simple docstring'''




from __future__ import annotations







def 			A_   ( _lowerCamelCase			:							str  ,  _lowerCamelCase			:							dict[str, str]    ):
      _lowerCAmelCase   ,  _lowerCAmelCase   ,  _lowerCAmelCase		   =   '', '', ''
      _lowerCAmelCase		   =   []

      for character in message_part:
            tmp.append(character_to_number[character]    )

      for each in tmp:
            one += each[0]
            two += each[1]
            three += each[2]

      return one + two + three







def 			A_   ( _lowerCamelCase			:							str  ,  _lowerCamelCase			:							dict[str, str]    ):
      _lowerCAmelCase   ,  _lowerCAmelCase		   =   '', ''
      _lowerCAmelCase		   =   []

      for character in message_part:
            this_part += character_to_number[character]

      for digit in this_part:
            tmp += digit
            if len(_lowerCamelCase    ) == len(_lowerCamelCase    ):
                  result.append(_lowerCamelCase    )
                  _lowerCAmelCase		   =   ''

      return result[0], result[1], result[2]







def 			A_   ( _lowerCamelCase			:							str  ,  _lowerCamelCase			:							str    ):
      # Validate message and alphabet, set to upper and remove spaces
      _lowerCAmelCase		   =   alphabet.replace(' '  ,  ''    ).upper()
      _lowerCAmelCase		   =   message.replace(' '  ,  ''    ).upper()

      # Check length and characters
      if len(_lowerCamelCase    ) != 27:
            raise KeyError('Length of alphabet has to be 27.'    )
      for each in message:
            if each not in alphabet:
                  raise ValueError('Each message character has to be included in alphabet!'    )

    # Generate dictionares
      _lowerCAmelCase		   =   (
          '111',
          '112',
          '113',
          '121',
          '122',
          '123',
          '131',
          '132',
          '133',
          '211',
          '212',
          '213',
          '221',
          '222',
          '223',
          '231',
          '232',
          '233',
          '311',
          '312',
          '313',
          '321',
          '322',
          '323',
          '331',
          '332',
          '333',
      )
      _lowerCAmelCase		   =   {}
      _lowerCAmelCase		   =   {}
      for letter, number in zip(_lowerCamelCase  ,  _lowerCamelCase    ):
            _lowerCAmelCase		   =   number
            _lowerCAmelCase		   =   letter

      return message, alphabet, character_to_number, number_to_character







def 			A_   ( _lowerCamelCase			:							str  ,  _lowerCamelCase			:							str = "ABCDEFGHIJKLMNOPQRSTUVWXYZ."  ,  _lowerCamelCase			:							int = 5    ):
      _lowerCAmelCase   ,  _lowerCAmelCase   ,  _lowerCAmelCase   ,  _lowerCAmelCase		   =   __prepare(
          _lowerCamelCase  ,  _lowerCamelCase    )
      _lowerCAmelCase   ,  _lowerCAmelCase		   =   '', ''

      for i in range(0  ,  len(_lowerCamelCase    ) + 1  ,  _lowerCamelCase    ):
            encrypted_numeric += __encrypt_part(
                message[i : i + period]  ,  _lowerCamelCase    )

      for i in range(0  ,  len(_lowerCamelCase    )  ,  3    ):
            encrypted += number_to_character[encrypted_numeric[i : i + 3]]

      return encrypted







def 			A_   ( _lowerCamelCase			:							str  ,  _lowerCamelCase			:							str = "ABCDEFGHIJKLMNOPQRSTUVWXYZ."  ,  _lowerCamelCase			:							int = 5    ):
      _lowerCAmelCase   ,  _lowerCAmelCase   ,  _lowerCAmelCase   ,  _lowerCAmelCase		   =   __prepare(
          _lowerCamelCase  ,  _lowerCamelCase    )
      _lowerCAmelCase		   =   []
      _lowerCAmelCase		   =   ''

      for i in range(0  ,  len(_lowerCamelCase    ) + 1  ,  _lowerCamelCase    ):
            _lowerCAmelCase   ,  _lowerCAmelCase   ,  _lowerCAmelCase		   =   __decrypt_part(message[i : i + period]  ,  _lowerCamelCase    )

            for j in range(0  ,  len(_lowerCamelCase    )    ):
                  decrypted_numeric.append(a[j] + b[j] + c[j]    )

      for each in decrypted_numeric:
            decrypted += number_to_character[each]

      return decrypted


if __name__ == "__main__":
 snake_case  =			'''DEFEND THE EAST WALL OF THE CASTLE.'''
 snake_case  =			encrypt_message(msg, '''EPSDUCVWYM.ZLKXNBTFGORIJHAQ''')
 snake_case  =			decrypt_message(encrypted, '''EPSDUCVWYM.ZLKXNBTFGORIJHAQ''')
 print(f'''Encrypted: {encrypted}\nDecrypted: {decrypted}''')





