'''simple docstring'''
def  __lowerCamelCase       (      _UpperCamelCase  :  Tuple					):


      '''simple docstring'''


      UpperCAmelCase_            =  0
      UpperCAmelCase_            =  len(__A					)

      for i in range(n - 1					):
            for j in range(i + 1							,    __A					):
                  if arr[i] > arr[j]:
                        num_inversions += 1

      return num_inversions



def  __lowerCamelCase       (      _UpperCamelCase  :  Dict					):


      '''simple docstring'''


      if len(__A					) <= 1:
            return arr, 0
      UpperCAmelCase_            =  len(__A					) // 2
      UpperCAmelCase_            =  arr[0:mid]
      UpperCAmelCase_            =  arr[mid:]

      UpperCAmelCase_            =  count_inversions_recursive(__A					)
      UpperCAmelCase_            =  count_inversions_recursive(__A					)
      UpperCAmelCase_            =  _count_cross_inversions(__A							,    __A					)

      UpperCAmelCase_            =  inversion_p + inversions_q + cross_inversions
      return c, num_inversions



def  __lowerCamelCase       (      _UpperCamelCase  :  List[Any]							,    _UpperCamelCase  :  Dict					):


      '''simple docstring'''


      UpperCAmelCase_            =  []
      UpperCAmelCase_            =  0
      while i < len(__A					) and j < len(__A					):
            if p[i] > q[j]:
                  # if P[1] > Q[j], then P[k] > Q[k] for all  i < k <= len(P)
                  # These are all inversions. The claim emerges from the
                  # property that P is sorted.
                  num_inversion += len(__A					) - i
                  r.append(q[j]					)
                  j += 1
            else:
                  r.append(p[i]					)
                  i += 1

      if i < len(__A					):
            r.extend(p[i:]					)
      else:
            r.extend(q[j:]					)

      return r, num_inversion



def  __lowerCamelCase       (      ):


      '''simple docstring'''


      UpperCAmelCase_            =  [10, 2, 1, 5, 5, 2, 11]

      # this arr has 8 inversions:
      # (10, 2), (10, 1), (10, 5), (10, 5), (10, 2), (2, 1), (5, 2), (5, 2)

      UpperCAmelCase_            =  count_inversions_bf(__A					)
      UpperCAmelCase_            =  count_inversions_recursive(__A					)

      assert num_inversions_bf == num_inversions_recursive == 8

      print('''number of inversions = '''							,    __A					)

      # testing an array with zero inversion (a sorted arr_1)

      arr_a.sort()
      UpperCAmelCase_            =  count_inversions_bf(__A					)
      UpperCAmelCase_            =  count_inversions_recursive(__A					)

      assert num_inversions_bf == num_inversions_recursive == 0
      print('''number of inversions = '''							,    __A					)

      # an empty list should also have zero inversions
      UpperCAmelCase_            =  []
      UpperCAmelCase_            =  count_inversions_bf(__A					)
      UpperCAmelCase_            =  count_inversions_recursive(__A					)

      assert num_inversions_bf == num_inversions_recursive == 0
      print('''number of inversions = '''							,    __A					)


if __name__ == "__main__":
      main()






'''simple docstring'''
import re



def  __lowerCamelCase       (      _UpperCamelCase  :  str					):


      '''simple docstring'''


      return [char.split() for char in re.split(R'''[^ a-z A-Z 0-9 \s]'''							,    str_					)]



def  __lowerCamelCase       (      _UpperCamelCase  :  str					):


      '''simple docstring'''


      UpperCAmelCase_            =  split_input(str_					)
      return "".join(
          [''''''.join([char.capitalize() for char in sub_str]					) for sub_str in string_split]					)



def  __lowerCamelCase       (      _UpperCamelCase  :  str							,    _UpperCamelCase  :  bool							,    _UpperCamelCase  :  str					):


      '''simple docstring'''


      try:
            UpperCAmelCase_            =  split_input(_UpperCamelCase					)
            if upper:
                  UpperCAmelCase_            =  ''''''.join(
                      [
                          separator.join([char.upper() for char in sub_str]					)
                          for sub_str in string_split
                      ]					)
            else:
                  UpperCAmelCase_            =  ''''''.join(
                      [
                          separator.join([char.lower() for char in sub_str]					)
                          for sub_str in string_split
                      ]					)
            return res_str
      except IndexError:
            return "not valid string"



def  __lowerCamelCase       (      _UpperCamelCase  :  str					):


      '''simple docstring'''


      return to_simple_case(_UpperCamelCase					)



def  __lowerCamelCase       (      _UpperCamelCase  :  str					):


      '''simple docstring'''


      try:
            UpperCAmelCase_            =  to_simple_case(_UpperCamelCase					)
            return res_str[0].lower() + res_str[1:]
      except IndexError:
            return "not valid string"



def  __lowerCamelCase       (      _UpperCamelCase  :  str							,    _UpperCamelCase  :  bool					):


      '''simple docstring'''


      return to_complex_case(_UpperCamelCase							,    _UpperCamelCase							,    '''_'''					)



def  __lowerCamelCase       (      _UpperCamelCase  :  str							,    _UpperCamelCase  :  bool					):


      '''simple docstring'''


      return to_complex_case(_UpperCamelCase							,    _UpperCamelCase							,    '''-'''					)


if __name__ == "__main__":
      __import__("doctest").testmod()





