






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






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










from decimal import Decimal, getcontext
from math import ceil, factorial







def lowerCamelCase__  (     _lowercase ):

     '''simple docstring'''


     if not isinstance(_lowercase					,		_lowercase ):
          raise TypeError('''Undefined for non-integers''' )
     elif precision < 1:
          raise ValueError('''Undefined for non-natural numbers''' )

     UpperCAmelCase_     :				Tuple  =     precision
     UpperCAmelCase_     :				Optional[Any]  =     ceil(precision / 14 )
     UpperCAmelCase_     :				int  =     426880 * Decimal(10005 ).sqrt()
     UpperCAmelCase_     :				Tuple  =     1
     UpperCAmelCase_     :				List[Any]  =     13591409
     UpperCAmelCase_     :				Optional[Any]  =     Decimal(_lowercase )
     for k in range(1					,		_lowercase ):
          UpperCAmelCase_     :				List[str]  =     factorial(6 * k ) // (factorial(3 * k ) * factorial(_lowercase ) ** 3)
          linear_term += 545140134
          exponential_term *= -262537412640768000
          partial_sum += Decimal(multinomial_term * linear_term ) / exponential_term
     return str(constant_term / partial_sum )[:-1]


if __name__ == "__main__":
     __a							     =					50
     print(F"""The first {n} digits of pi is: {pi(n)}""")