



'''simple docstring'''




from multiprocessing import Lock, Pipe, Process

# lock used to ensure that two processes do not access a pipe at the same time
lowerCamelCase							:Optional[int]       = Lock()



def      a      (			lowerCamelCase__						,				lowerCamelCase__						,				lowerCamelCase__						,				lowerCamelCase__						,				lowerCamelCase__						,				lowerCamelCase__						,				lowerCamelCase__   ):
			'''simple docstring'''





			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						,				10   ):
						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(_lowerCAmelCase   )
									process_lock.release()

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

									# take the lower value since you are on the left
									A_     :						Optional[int]     =					min(_lowerCAmelCase						,				_lowerCAmelCase   )
						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(_lowerCAmelCase   )
									process_lock.release()

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

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



def      a      (			lowerCamelCase__   ):
			'''simple docstring'''





			A_     :						List[Any]     =					[]
			A_     :						int     =					[]
			# 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
			A_     :						str     =					Pipe()
			A_     :						int     =					Pipe()
			process_array_.append(
			    Process(
			        target=_lowerCAmelCase						,				args=(0, arr[0], None, temp_rs, None, temp_rr, result_pipe[0])						,				)   )
			A_     :						List[str]     =					temp_rs
			A_     :						List[str]     =					temp_rr

			for i in range(1						,				len(_lowerCAmelCase   ) - 1   ):
						A_     :						str     =					Pipe()
						A_     :						Optional[int]     =					Pipe()
						process_array_.append(
						    Process(
						        target=_lowerCAmelCase						,				args=(i, arr[i], temp_ls, temp_rs, temp_lr, temp_rr, result_pipe[i])						,				)   )
						A_     :						Dict     =					temp_rs
						A_     :						List[Any]     =					temp_rr

			process_array_.append(
			    Process(
			        target=_lowerCAmelCase						,				args=(
			            len(_lowerCAmelCase   ) - 1,
			            arr[len(_lowerCAmelCase   ) - 1],
			            temp_ls,
			            None,
			            temp_lr,
			            None,
			            result_pipe[len(_lowerCAmelCase   ) - 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(_lowerCAmelCase   )   ):
						A_     :						List[str]     =					result_pipe[p][0].recv()
						process_array_[p].join()
			return arr



def      a      (			):
			'''simple docstring'''





			A_     :						Any     =					list(range(10						,				0						,				-1   )   )
			print("""Initial List"""   )
			print(*_lowerCAmelCase   )
			A_     :						Tuple     =					odd_even_transposition(_lowerCAmelCase   )
			print("""Sorted List\n"""   )
			print(*_lowerCAmelCase   )


if __name__ == "__main__":
						main()








'''simple docstring'''




from __future__ import annotations

from collections.abc import Callable

lowerCamelCase							:List[Any]       = list[list[float | int]]



def      a      (			lowerCamelCase__						,				lowerCamelCase__   ):
			'''simple docstring'''





			A_     :						int     =					len(lowerCamelCase__   )
			A_     :						Matrix     =					[[0 for _ in range(size + 1   )] for _ in range(lowerCamelCase__   )]
			A_     :						int
			A_     :						int
			A_     :						int
			A_     :						int
			A_     :						int
			A_     :						float

			for row in range(lowerCamelCase__   ):
						for col in range(lowerCamelCase__   ):
									A_     :						List[str]     =					matrix[row][col]

						A_     :						Optional[int]     =					vector[row][0]

			A_     :						Tuple     =					0
			A_     :						Tuple     =					0
			while row < size and col < size:
						# pivoting
						A_     :						Dict     =					max((abs(augmented[rowa][col]   ), rowa) for rowa in range(lowerCamelCase__						,				lowerCamelCase__   )   )[
						    1
						]
						if augmented[pivot_row][col] == 0:
									col += 1
									continue
						else:
									A_,   A_     :						Optional[Any]     =					augmented[pivot_row], augmented[row]

						for rowa in range(row + 1						,				lowerCamelCase__   ):
									A_     :						int     =					augmented[rowa][col] / augmented[row][col]
									A_     :						Union[str, Any]     =					0
									for cola in range(col + 1						,				size + 1   ):
												augmented[rowa][cola] -= augmented[row][cola] * ratio

						row += 1
						col += 1

			# back substitution
			for col in range(1						,				lowerCamelCase__   ):
						for row in range(lowerCamelCase__   ):
									A_     :						Tuple     =					augmented[row][col] / augmented[col][col]
									for cola in range(lowerCamelCase__						,				size + 1   ):
												augmented[row][cola] -= augmented[col][cola] * ratio

    # round to get rid of numbers like 2.000000000000004
			return [
			    [round(augmented[row][size] / augmented[row][row]						,				10   )] for row in range(lowerCamelCase__   )
			]



def      a      (			lowerCamelCase__   ):
			'''simple docstring'''





			A_     :						int     =					len(lowerCamelCase__   )
			A_     :						Matrix     =					[[0 for _ in range(lowerCamelCase__   )] for _ in range(lowerCamelCase__   )]
			A_     :						Matrix     =					[[0] for _ in range(lowerCamelCase__   )]
			A_     :						Matrix
			A_     :						int
			A_     :						int
			A_     :						int

			for x_val, y_val in enumerate(lowerCamelCase__   ):
						for col in range(lowerCamelCase__   ):
									A_     :						Dict     =					(x_val + 1) ** (size - col - 1)
						A_     :						Any     =					y_val

			A_     :						Dict     =					solve(lowerCamelCase__						,				lowerCamelCase__   )

			def interpolated_func(lowerCamelCase__   ) -> int:
						return sum(
						    round(coeffs[x_val][0]   ) * (var ** (size - x_val - 1))
						    for x_val in range(lowerCamelCase__   )   )

			return interpolated_func



def      a      (			lowerCamelCase__   ):
			'''simple docstring'''





			return (
			    1
			    - variable
			    + variable**2
			    - variable**3
			    + variable**4
			    - variable**5
			    + variable**6
			    - variable**7
			    + variable**8
			    - variable**9
			    + variable**10
			)



def      a      (			lowerCamelCase__ = question_function						,				lowerCamelCase__ = 10   ):
			'''simple docstring'''





			A_     :						list[int]     =					[func(lowerCamelCase__   ) for x_val in range(1						,				order + 1   )]

			A_     :						list[Callable[[int], int]]     =					[
			    interpolate(data_points[:max_coeff]   ) for max_coeff in range(1						,				order + 1   )
			]

			A_     :						int     =					0
			A_     :						Callable[[int], int]
			A_     :						int

			for poly in polynomials:
						A_     :						int     =					1
						while func(lowerCamelCase__   ) == poly(lowerCamelCase__   ):
									x_val += 1

						ret += poly(lowerCamelCase__   )

			return ret


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