


'''simple docstring'''




def   _a		(lowercase__			:   list[list]						)			->			List[str]:






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





def   _a		(lowercase__			:   list[list]						)			->			Tuple:






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


if __name__ == "__main__":
       import doctest

       doctest.testmod()
       _a   :   str												=   [
           [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]]))





'''simple docstring'''






import math





def  _SCREAMING_SNAKE_CASE		(      __snake_case							:			int				):
     _A    		=  []
     _A    		=  2
     _A    		=  int(math.sqrt(__snake_case				)				)  # Size of every segment
     _A    		=  [True] * (end + 1)
     _A    		=  []

     while start <= end:
          if temp[start] is True:
               in_prime.append(__snake_case				)
               for i in range(start * start   ,		end + 1   ,		__snake_case				):
                    _A    		=  False
          start += 1
     prime += in_prime

     _A    		=  end + 1
     _A    		=  min(2 * end   ,		__snake_case				)

     while low <= n:
          _A    		=  [True] * (high - low + 1)
          for each in in_prime:
               _A    		=  math.floor(low / each				) * each
               if t < low:
                    t += each

               for j in range(__snake_case   ,		high + 1   ,		__snake_case				):
                    _A    		=  False

          for j in range(len(__snake_case				)				):
               if temp[j] is True:
                    prime.append(j + low				)

          _A    		=  high + 1
          _A    		=  min(high + end   ,		__snake_case				)

     return prime
print(sieve(10**6))



