

from multiprocessing import Lock, Pipe, Process

# lock used to ensure that two processes do not access a pipe at the same time
snake_case_							=			Lock()


def 					A__	(       SCREAMING_SNAKE_CASE_							,       SCREAMING_SNAKE_CASE_							,       SCREAMING_SNAKE_CASE_							,       SCREAMING_SNAKE_CASE_							,       SCREAMING_SNAKE_CASE_							,       SCREAMING_SNAKE_CASE_							,       SCREAMING_SNAKE_CASE_		)   ->     Any:
		global process_lock

		# we perform n swaps since after n swaps we know we are sorted
		# we *could* stop early if we are sorted already, but it takes as long to
		# find out we are sorted as it does to sort the list with this algorithm
		for i in range(0							,       1_0		):
				if (i + position) % 2 == 0 and r_send is not None:
						# send your value to your right neighbor
						process_lock.acquire()
						r_send[1].send(SCREAMING_SNAKE_CASE_		)
						process_lock.release()

						# receive your right neighbor's value
						process_lock.acquire()
						lowerCamelCase   : str								=rr_cv[0].recv()
						process_lock.release()

						# take the lower value since you are on the left
						lowerCamelCase   : List[Any]								=min(SCREAMING_SNAKE_CASE_							,       SCREAMING_SNAKE_CASE_		)
				elif (i + position) % 2 != 0 and l_send is not None:
						# send your value to your left neighbor
						process_lock.acquire()
						l_send[1].send(SCREAMING_SNAKE_CASE_		)
						process_lock.release()

						# receive your left neighbor's value
						process_lock.acquire()
						lowerCamelCase   : Optional[int]								=lr_cv[0].recv()
						process_lock.release()

						# take the higher value since you are on the right
						lowerCamelCase   : str								=max(SCREAMING_SNAKE_CASE_							,       SCREAMING_SNAKE_CASE_		)
    # after all swaps are performed, send the values back to main
		result_pipe[1].send(SCREAMING_SNAKE_CASE_		)


def 					A__	(       SCREAMING_SNAKE_CASE_		)   ->     Optional[Any]:
		lowerCamelCase   : Optional[Any]								=[]
		lowerCamelCase   : List[Any]								=[]
		# initialize the list of pipes where the values will be retrieved
		for _ in arr:
				result_pipe.append(Pipe()		)
		# creates the processes
		# the first and last process only have one neighbor so they are made outside
		# of the loop
		lowerCamelCase   : str								=Pipe()
		lowerCamelCase   : Union[str, Any]								=Pipe()
		process_array_.append(
		    Process(
		        target=SCREAMING_SNAKE_CASE_							,       args=(0, arr[0], None, temp_rs, None, temp_rr, result_pipe[0])							,       )		)
		lowerCamelCase   : str								=temp_rs
		lowerCamelCase   : Union[str, Any]								=temp_rr

		for i in range(1							,       len(SCREAMING_SNAKE_CASE_		) - 1		):
				lowerCamelCase   : int								=Pipe()
				lowerCamelCase   : int								=Pipe()
				process_array_.append(
				    Process(
				        target=SCREAMING_SNAKE_CASE_							,       args=(i, arr[i], temp_ls, temp_rs, temp_lr, temp_rr, result_pipe[i])							,       )		)
				lowerCamelCase   : Dict								=temp_rs
				lowerCamelCase   : int								=temp_rr

		process_array_.append(
		    Process(
		        target=SCREAMING_SNAKE_CASE_							,       args=(
		            len(SCREAMING_SNAKE_CASE_		) - 1,
		            arr[len(SCREAMING_SNAKE_CASE_		) - 1],
		            temp_ls,
		            None,
		            temp_lr,
		            None,
		            result_pipe[len(SCREAMING_SNAKE_CASE_		) - 1],
		        )							,       )		)

		# start the processes
		for p in process_array_:
				p.start()

		# wait for the processes to end and write their values to the list
		for p in range(0							,       len(SCREAMING_SNAKE_CASE_		)		):
				lowerCamelCase   : int								=result_pipe[p][0].recv()
				process_array_[p].join()
		return arr


def 					A__	(       )   ->     Optional[Any]:
		lowerCamelCase   : Tuple								=list(range(1_0							,       0							,       -1		)		)
		print('''Initial List'''		)
		print(*SCREAMING_SNAKE_CASE_		)
		lowerCamelCase   : Dict								=odd_even_transposition(SCREAMING_SNAKE_CASE_		)
		print('''Sorted List\n'''		)
		print(*SCREAMING_SNAKE_CASE_		)


if __name__ == "__main__":
				main()








from collections import defaultdict
from math import ceil, sqrt


def 					A__	(       SCREAMING_SNAKE_CASE_ = 1_0_0_0_0_0_0							,       SCREAMING_SNAKE_CASE_ = 1_0		)   ->     int:
		lowerCamelCase   : defaultdict								=defaultdict(SCREAMING_SNAKE_CASE_		)

		for outer_width in range(3							,       (t_limit // 4) + 2		):
				if outer_width * outer_width > t_limit:
						lowerCamelCase   : Any								=max(
						    ceil(sqrt(outer_width * outer_width - t_limit		)		)							,       1		)
				else:
						lowerCamelCase   : str								=1

				hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

				for hole_width in range(SCREAMING_SNAKE_CASE_							,       outer_width - 1							,       2		):
						count[outer_width * outer_width - hole_width * hole_width] += 1

		return sum(1 for n in count.values() if 1 <= n <= 1_0		)


if __name__ == "__main__":
				print(F"""{solution() = }""")

