



"""simple docstring"""





def   a__      ( lowerCAmelCase__ ):
      UpperCAmelCase_     					=				0
      UpperCAmelCase_     					=				len(lowerCAmelCase__ )

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

      return num_inversions
def   a__      ( lowerCAmelCase__ ):
      if len(lowerCAmelCase__ ) <= 1:
            return arr, 0
      UpperCAmelCase_     					=				len(lowerCAmelCase__ ) // 2
      UpperCAmelCase_     					=				arr[0:mid]
      UpperCAmelCase_     					=				arr[mid:]

      UpperCAmelCase_					,       UpperCAmelCase_     					=				count_inversions_recursive(lowerCAmelCase__ )
      UpperCAmelCase_					,       UpperCAmelCase_     					=				count_inversions_recursive(lowerCAmelCase__ )
      UpperCAmelCase_					,       UpperCAmelCase_     					=				_count_cross_inversions(lowerCAmelCase__      ,     lowerCAmelCase__ )

      UpperCAmelCase_     					=				inversion_p + inversions_q + cross_inversions
      return c, num_inversions
def   a__      ( lowerCAmelCase__      ,     lowerCAmelCase__ ):
      UpperCAmelCase_     					=				[]
      UpperCAmelCase_     					=				UpperCAmelCase_     					=				UpperCAmelCase_     					=				0
      while i < len(lowerCAmelCase__ ) and j < len(lowerCAmelCase__ ):
            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(lowerCAmelCase__ ) - i
                  r.append(q[j] )
                  j += 1
            else:
                  r.append(p[i] )
                  i += 1

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

      return r, num_inversion
def   a__      ( ):
      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(lowerCAmelCase__ )
      UpperCAmelCase_					,       UpperCAmelCase_     					=				count_inversions_recursive(lowerCAmelCase__ )

      assert num_inversions_bf == num_inversions_recursive == 8

      print("number of inversions = "      ,     lowerCAmelCase__ )

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

      arr_a.sort()
      UpperCAmelCase_     					=				count_inversions_bf(lowerCAmelCase__ )
      UpperCAmelCase_					,       UpperCAmelCase_     					=				count_inversions_recursive(lowerCAmelCase__ )

      assert num_inversions_bf == num_inversions_recursive == 0
      print("number of inversions = "      ,     lowerCAmelCase__ )

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

      assert num_inversions_bf == num_inversions_recursive == 0
      print("number of inversions = "      ,     lowerCAmelCase__ )


if __name__ == "__main__":
  main()








def 		lowercase_	(  _UpperCamelCase	):


			'''simple docstring'''







			__lowercase			       = hex_num.strip()
			if not hex_num:
						raise ValueError('''No value was passed to the function'''	)

			__lowercase			       = hex_num[0] == '''-'''
			if is_negative:
						__lowercase			       = hex_num[1:]

			try:
						__lowercase			       = int(_UpperCamelCase							,      16	)
			except ValueError:
						raise ValueError('''Invalid value was passed to the function'''	)

			__lowercase			       = ''''''
			while int_num > 0:
						__lowercase			       = str(int_num % 2	) + bin_str
						int_num >>= 1

			return int(('''-''' + bin_str) if is_negative else bin_str	)


if __name__ == "__main__":
	import doctest

	doctest.testmod()


