

def      a      (			A__	:   list[list]     )    ->      list[list]:





      """simple docstring"""



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





      """simple docstring"""



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


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  lowercase_									=   [
      [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 __future__ import annotations
def      a      (			A__	:   list[int]     )    ->      int:





      """simple docstring"""



      if not nums:
            return 0
      _lowercase	       =nums[0]
      _lowercase	       =0
      for num in nums[1:]:
            _lowercase       ,       _lowercase	       =(
                max_excluding + num,
                max(A__      ,   A__     ),
            )
      return max(A__      ,   A__     )


if __name__ == "__main__":
  import doctest

  doctest.testmod()


