



from __future__ import annotations

from typing import Any


def A    (							__UpperCamelCase       )    ->   int:
			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()









from __future__ import annotations

from fractions import Fraction


def A    (							__UpperCamelCase			,						__UpperCamelCase       )    ->   bool:
			return (
			    num != den and num % 10 == den // 10 and (num // 10) / (den % 10) == num / den
			)


def A    (							__UpperCamelCase       )    ->   list[str]:
			A__	  =     []
			A__	  =     11
			A__	  =     int('1' + '0' * digit_len       )
			for num in range(__UpperCamelCase			,						__UpperCamelCase       ):
						while den <= 99:
									if (num != den) and (num % 10 == den // 10) and (den % 10 != 0):
												if is_digit_cancelling(__UpperCamelCase			,						__UpperCamelCase       ):
															solutions.append(f'''{num}/{den}'''       )
									den += 1
						num += 1
						A__	  =     10
			return solutions


def A    (							__UpperCamelCase = 2       )    ->   int:
			A__	  =     1.0
			for fraction in fraction_list(__UpperCamelCase       ):
						A__	  =     Fraction(__UpperCamelCase       )
						result *= frac.denominator / frac.numerator
			return int(__UpperCamelCase       )


if __name__ == "__main__":
							print(solution())




