





import itertools
from dataclasses import dataclass
from typing import Optional

import pandas as pd
import pyarrow as pa

import datasets
from datasets.table import table_cast
@dataclass
class     UpperCamelCase__					(     datasets.BuilderConfig				):






		'''simple docstring'''






		__a       :       Optional[datasets.Features]       =	None




class     UpperCamelCase__					(     datasets.ArrowBasedBuilder				):






		'''simple docstring'''






		__a       :       Any       =	PandasConfig






		def 						snake_case__				(							self  )       -> Union[str, Any]:






									"""simple docstring"""
									return datasets.DatasetInfo(features=self.config.features  )






		def 						snake_case__				(							self,   snake_case__  )       -> Union[str, Any]:






									"""simple docstring"""
									if not self.config.data_files:
																raise ValueError(f"""At least one data file must be specified, but got data_files={self.config.data_files}"""  )
									lowercase_	:   str  				=     dl_manager.download_and_extract(self.config.data_files  )
									if isinstance(snake_case__,   (str, list, tuple)  ):
																lowercase_	:   Tuple  				=     data_files
																if isinstance(snake_case__,   snake_case__  ):
																							lowercase_	:   str  				=     [files]
																# Use `dl_manager.iter_files` to skip hidden files in an extracted archive
																lowercase_	:   Dict  				=     [dl_manager.iter_files(snake_case__  ) for file in files]
																return [datasets.SplitGenerator(name=datasets.Split.TRAIN,   gen_kwargs={"""files""": files}  )]
									lowercase_	:   Optional[Any]  				=     []
									for split_name, files in data_files.items():
																if isinstance(snake_case__,   snake_case__  ):
																							lowercase_	:   str  				=     [files]
																# Use `dl_manager.iter_files` to skip hidden files in an extracted archive
																lowercase_	:   Optional[Any]  				=     [dl_manager.iter_files(snake_case__  ) for file in files]
																splits.append(datasets.SplitGenerator(name=snake_case__,   gen_kwargs={"""files""": files}  )  )
									return splits






		def 						snake_case__				(							self,   snake_case__  )       -> pa.Table:






									"""simple docstring"""
									if self.config.features is not None:
																# more expensive cast to support nested features with keys in a different order
																# allows str <-> int/float or str to Audio for example
																lowercase_	:   Dict  				=     table_cast(snake_case__,   self.config.features.arrow_schema  )
									return pa_table






		def 						snake_case__				(							self,   snake_case__  )       -> int:






									"""simple docstring"""
									for i, file in enumerate(itertools.chain.from_iterable(snake_case__  )  ):
																with open(snake_case__,   """rb"""  ) as f:
																							lowercase_	:   List[Any]  				=     pa.Table.from_pandas(pd.read_pickle(snake_case__  )  )
																							yield i, self._cast_table(snake_case__  )






def  __magic_name__  (				lowercase				)				-> list[list]:

							"""simple docstring"""



							lowercase_	:   int  				=     current_set.copy()
							for row_index, row in enumerate(lowercase				):
														lowercase_	:   Tuple  				=     row[0]
														for column_index, column in enumerate(lowercase				):
																					if magnitude == 0:
																												lowercase_	:   Optional[int]  				=     column
																												continue
																					lowercase_	:   List[str]  				=     column / magnitude
    # Subtract to cancel term
							lowercase_	:   List[str]  				=     current_set[0]
							lowercase_	:   Optional[int]  				=     [first_row]
							lowercase_	:   Optional[Any]  				=     current_set[1::]
							for row in current_set:
														lowercase_	:   Union[str, Any]  				=     []
														# If first term is 0, it is already in form we want, so we preserve it
														if row[0] == 0:
																					final_set.append(lowercase				)
																					continue
														for column_index in range(len(lowercase				)				):
																					temp_row.append(first_row[column_index] - row[column_index]				)
														final_set.append(lowercase				)
							# Create next recursion iteration set
							if len(final_set[0]				) != 3:
														lowercase_	:   Tuple  				=     final_set[0]
														lowercase_	:   Dict  				=     []
														lowercase_	:   Any  				=     []
														for row in final_set[1::]:
																					current_first_column.append(row[0]				)
																					next_iteration.append(row[1::]				)
														lowercase_	:   Optional[Any]  				=     simplify(lowercase				)
														for i in range(len(lowercase				)				):
																					resultant[i].insert(0				,       current_first_column[i]				)
														resultant.insert(0				,       lowercase				)
														lowercase_	:   Tuple  				=     resultant
							return final_set





def  __magic_name__  (				lowercase				)				-> list:

							"""simple docstring"""



							if len(lowercase				) == 0:
														raise IndexError("""solve_simultaneous() requires n lists of length n+1"""				)
							lowercase_	:   Tuple  				=     len(lowercase				) + 1
							if any(len(lowercase				) != _length for item in equations				):
														raise IndexError("""solve_simultaneous() requires n lists of length n+1"""				)
							for row in equations:
														if any(not isinstance(lowercase				,       (int, float)				) for column in row				):
																					raise ValueError("""solve_simultaneous() requires lists of integers"""				)
							if len(lowercase				) == 1:
														return [equations[0][-1] / equations[0][0]]
							lowercase_	:   List[str]  				=     equations.copy()
							if any(0 in row for row in data_set				):
														lowercase_	:   int  				=     data_set.copy()
														lowercase_	:   Dict  				=     []
														for row_index, row in enumerate(lowercase				):
																					if 0 not in row:
																												lowercase_	:   Dict  				=     data_set.pop(lowercase				)
																												break
														if not full_row:
																					raise ValueError("""solve_simultaneous() requires at least 1 full equation"""				)
														data_set.insert(0				,       lowercase				)
							lowercase_	:   Tuple  				=     data_set.copy()
							lowercase_	:   List[Any]  				=     simplify(lowercase				)
							lowercase_	:   Dict  				=     simplified[::-1]
							lowercase_	:   list  				=     []
							for row in simplified:
														lowercase_	:   Union[str, Any]  				=     row[-1]
														if not solutions:
																					if row[-2] == 0:
																												solutions.append(0				)
																												continue
																					solutions.append(current_solution / row[-2]				)
																					continue
														lowercase_	:   Any  				=     row.copy()[: len(lowercase				) - 1 :]
														while temp_row[0] == 0:
																					temp_row.pop(0				)
														if len(lowercase				) == 0:
																					solutions.append(0				)
																					continue
														lowercase_	:   Any  				=     temp_row[1::]
														lowercase_	:   Union[str, Any]  				=     temp_row[::-1]
														for column_index, column in enumerate(lowercase				):
																					current_solution -= column * solutions[column_index]
														solutions.append(lowercase				)
							lowercase_	:   Any  				=     []
							for item in solutions:
														final.append(float(round(lowercase				,       5				)				)				)
							return final[::-1]


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							UpperCAmelCase_							=				[
							    [2, 1, 1, 1, 1, 4],
							    [1, 2, 1, 1, 1, 5],
							    [1, 1, 2, 1, 1, 6],
							    [1, 1, 1, 2, 1, 7],
							    [1, 1, 1, 1, 2, 8],
							]
							print(solve_simultaneous(eq))
							print(solve_simultaneous([[4, 2]]))