'''simple docstring'''





def      __lowerCAmelCase    (							a_		)   ->						Optional[int]:





     '''simple docstring'''





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


def      __lowerCAmelCase    (							a_		)   ->						Any:





     '''simple docstring'''





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


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 _lowerCAmelCase	:Any						=     [
     [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]]))











import importlib.metadata
import operator
import re
import sys
from typing import Optional

from packaging import version


A__      :     Tuple       =					{
    '<': operator.lt,
    '<=': operator.le,
    '==': operator.eq,
    '!=': operator.ne,
    '>=': operator.ge,
    '>': operator.gt,
}






def     a     (		lowerCamelCase_						,  lowerCamelCase_						,  lowerCamelCase_						,  lowerCamelCase_						,  lowerCamelCase_						,  lowerCamelCase_							):






				'''simple docstring'''
				if got_ver is None or want_ver is None:
								raise ValueError(
								    F"""Unable to compare versions for {requirement}: need={want_ver} found={got_ver}. This is unusual. Consider"""
								    F""" reinstalling {pkg}."""							)
				if not ops[op](version.parse(lowerCamelCase_							)						,  version.parse(lowerCamelCase_							)							):
								raise ImportError(
								    F"""{requirement} is required for a normal functioning of this module, but found {pkg}=={got_ver}.{hint}"""							)






def     a     (		lowerCamelCase_						,  lowerCamelCase_ = None							):






				'''simple docstring'''
				lowercase__  					=     F"""\n{hint}""" if hint is not None else ''''''

				# non-versioned check
				if re.match(r'''^[\w_\-\d]+$'''						,  lowerCamelCase_							):
								lowercase__					,		lowercase__					,		lowercase__  					=     requirement, None, None
				else:
								lowercase__  					=     re.findall(r'''^([^!=<>\s]+)([\s!=<>]{1,2}.+)'''						,  lowerCamelCase_							)
								if not match:
												raise ValueError(
												    '''requirement needs to be in the pip package format, .e.g., package_a==1.23, or package_b>=1.23, but'''
												    F""" got {requirement}"""							)
								lowercase__					,		lowercase__  					=     match[0]
								lowercase__  					=     want_full.split(''','''							)  # there could be multiple requirements
								lowercase__  					=     {}
								for w in want_range:
												lowercase__  					=     re.findall(r'''^([\s!=<>]{1,2})(.+)'''						,  lowerCamelCase_							)
												if not match:
																raise ValueError(
																    '''requirement needs to be in the pip package format, .e.g., package_a==1.23, or package_b>=1.23,'''
																    F""" but got {requirement}"""							)
												lowercase__					,		lowercase__  					=     match[0]
												lowercase__  					=     want_ver
												if op not in ops:
																raise ValueError(F"""{requirement}: need one of {list(ops.keys()							)}, but got {op}"""							)

    # special case
				if pkg == "python":
								lowercase__  					=     '''.'''.join([str(lowerCamelCase_							) for x in sys.version_info[:3]]							)
								for op, want_ver in wanted.items():
												_compare_versions(lowerCamelCase_						,  lowerCamelCase_						,  lowerCamelCase_						,  lowerCamelCase_						,  lowerCamelCase_						,  lowerCamelCase_							)
								return

				# check if any version is installed
				try:
								lowercase__  					=     importlib.metadata.version(lowerCamelCase_							)
				except importlib.metadata.PackageNotFoundError:
								raise importlib.metadata.PackageNotFoundError(
								    F"""The '{requirement}' distribution was not found and is required by this application. {hint}"""							)

				# check that the right version is installed if version number or a range was provided
				if want_ver is not None:
								for op, want_ver in wanted.items():
												_compare_versions(lowerCamelCase_						,  lowerCamelCase_						,  lowerCamelCase_						,  lowerCamelCase_						,  lowerCamelCase_						,  lowerCamelCase_							)






def     a     (		lowerCamelCase_							):






				'''simple docstring'''
				lowercase__  					=     '''Try: pip install transformers -U or pip install -e \'.[dev]\' if you\'re working with git main'''
				return require_version(lowerCamelCase_						,  lowerCamelCase_							)




