

"""simple docstring"""





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

def   __SCREAMING_SNAKE_CASE  (      A_ ):







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


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							__UpperCamelCase  :      List[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"""


from __future__ import annotations

from typing import Any



def 					lowerCAmelCase				(    __UpperCamelCase ):




  """simple docstring"""







  if not postfix_notation:
    return 0

  __A									= {'''+''', '''-''', '''*''', '''/'''}
  __A									= []

  for token in postfix_notation:
    if token in operations:
      __A			,    __A									= stack.pop(), stack.pop()
      if token == "+":
        stack.append(a + b )
      elif token == "-":
        stack.append(a - b )
      elif token == "*":
        stack.append(a * b )
      else:
        if a * b < 0 and a % b != 0:
          stack.append(a // b + 1 )
        else:
          stack.append(a // b )
    else:
      stack.append(int(__UpperCamelCase ) )

  return stack.pop()


if __name__ == "__main__":
       import doctest

       doctest.testmod()




