






'''simple docstring'''
def  _a(  UpperCamelCase__				:						Optional[int]							):




						'''simple docstring'''






						SCREAMING_SNAKE_CASE__     :				List[str]									=0
						SCREAMING_SNAKE_CASE__     :				str									=len(UpperCamelCase__							)

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

						return num_inversions





def  _a(  UpperCamelCase__				:						int							):




						'''simple docstring'''






						if len(UpperCamelCase__							) <= 1:
												return arr, 0
						SCREAMING_SNAKE_CASE__     :				int									=len(UpperCamelCase__							) // 2
						SCREAMING_SNAKE_CASE__     :				List[Any]									=arr[0:mid]
						SCREAMING_SNAKE_CASE__     :				List[str]									=arr[mid:]

						SCREAMING_SNAKE_CASE__     :				Dict									=count_inversions_recursive(UpperCamelCase__							)
						SCREAMING_SNAKE_CASE__     :				List[Any]									=count_inversions_recursive(UpperCamelCase__							)
						SCREAMING_SNAKE_CASE__     :				str									=_count_cross_inversions(UpperCamelCase__,	UpperCamelCase__							)

						SCREAMING_SNAKE_CASE__     :				Any									=inversion_p + inversions_q + cross_inversions
						return c, num_inversions





def  _a(  UpperCamelCase__				:						Any,	UpperCamelCase__				:						Dict							):




						'''simple docstring'''






						SCREAMING_SNAKE_CASE__     :				Optional[Any]									=[]
						SCREAMING_SNAKE_CASE__     :				Optional[Any]									=0
						while i < len(UpperCamelCase__							) and j < len(UpperCamelCase__							):
												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(UpperCamelCase__							) - i
																		r.append(q[j]							)
																		j += 1
												else:
																		r.append(p[i]							)
																		i += 1

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

						return r, num_inversion





def  _a(  ):




						'''simple docstring'''






						SCREAMING_SNAKE_CASE__     :				Optional[Any]									=[1_0, 2, 1, 5, 5, 2, 1_1]

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

						SCREAMING_SNAKE_CASE__     :				Dict									=count_inversions_bf(UpperCamelCase__							)
						SCREAMING_SNAKE_CASE__     :				Tuple									=count_inversions_recursive(UpperCamelCase__							)

						assert num_inversions_bf == num_inversions_recursive == 8

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

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

						arr_a.sort()
						SCREAMING_SNAKE_CASE__     :				Optional[Any]									=count_inversions_bf(UpperCamelCase__							)
						SCREAMING_SNAKE_CASE__     :				Optional[Any]									=count_inversions_recursive(UpperCamelCase__							)

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

						# an empty list should also have zero inversions
						SCREAMING_SNAKE_CASE__     :				Dict									=[]
						SCREAMING_SNAKE_CASE__     :				List[str]									=count_inversions_bf(UpperCamelCase__							)
						SCREAMING_SNAKE_CASE__     :				Optional[int]									=count_inversions_recursive(UpperCamelCase__							)

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


if __name__ == "__main__":
		main()







'''simple docstring'''
import inspect
import os
import sys
import unittest

import accelerate
from accelerate.test_utils import execute_subprocess_async, require_tpu






class      __SCREAMING_SNAKE_CASE      (			unittest.TestCase				):




 def      __magic_name__	(      self	:							int      )	->						Tuple:
       SCREAMING_SNAKE_CASE__     :				Optional[int]									=inspect.getfile(accelerate.test_utils      )
       SCREAMING_SNAKE_CASE__     :				Optional[Any]									=os.path.sep.join(mod_file.split(os.path.sep      )[:-1] + ['''scripts''', '''test_script.py''']      )
       SCREAMING_SNAKE_CASE__     :				Dict									=os.path.sep.join(inspect.getfile(self.__class__      ).split(os.path.sep      )[:-1]      )




 @require_tpu
 def      __magic_name__	(      self	:							int      )	->						Tuple:
       SCREAMING_SNAKE_CASE__     :				Any									=F"\n            {self.test_dir}/xla_spawn.py\n            --num_cores 8\n            {self.test_file_path}\n        ".split()
       SCREAMING_SNAKE_CASE__     :				List[str]									=[sys.executable] + distributed_args
       execute_subprocess_async(__lowercase					,      env=os.environ.copy()      )