


def        snake_case_					(  snake_case					)  ->    list[list]:
       lowercase__:       Union[str, Any]        =       current_set.copy()
       for row_index, row in enumerate(_lowerCAmelCase					):
              lowercase__:       str        =       row[0]
              for column_index, column in enumerate(_lowerCAmelCase					):
                     if magnitude == 0:
                            lowercase__:       Optional[Any]        =       column
                            continue
                     lowercase__:       Tuple        =       column / magnitude
    # Subtract to cancel term
       lowercase__:       List[Any]        =       current_set[0]
       lowercase__:       Tuple        =       [first_row]
       lowercase__:       Optional[Any]        =       current_set[1::]
       for row in current_set:
              lowercase__:       int        =       []
              # 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:
              lowercase__:       str        =       final_set[0]
              lowercase__:       Any        =       []
              lowercase__:       Optional[int]        =       []
              for row in final_set[1::]:
                     current_first_column.append(row[0]					)
                     next_iteration.append(row[1::]					)
              lowercase__:       Union[str, Any]        =       simplify(_lowerCAmelCase					)
              for i in range(len(_lowerCAmelCase					)					):
                     resultant[i].insert(0      ,							current_first_column[i]					)
              resultant.insert(0      ,							_lowerCAmelCase					)
              lowercase__:       List[Any]        =       resultant
       return final_set




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


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 __lowerCAmelCase			=							[
     [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        snake_case_					(  snake_case      ,							snake_case					)  ->    list[int]:
       lowercase__:       Tuple        =       0
       lowercase__:       str        =       len(snake_case					) - 1

       while i < j:
              if nums[i] + nums[j] == target:
                     return [i, j]
              elif nums[i] + nums[j] < target:
                     lowercase__:       str        =       i + 1
              else:
                     lowercase__:       Dict        =       j - 1

       return []


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 print(F'''{two_pointer([2, 7, 11, 15], 9) = }''')


