



from __future__ import annotations







def       lowerCamelCase_  (    _a       :						int    ):



    '''simple docstring'''




    UpperCAmelCase_     :       Optional[Any]  		=					[0] * max_one

    for i in range(0   ,		_a    ):
        UpperCAmelCase_     :       List[Any]  		=					i

    for i in range(2   ,		_a    ):
        if totients[i] == i:
            for j in range(_a   ,		_a   ,		_a    ):
                totients[j] -= totients[j] // i

    return totients







def       lowerCamelCase_  (    _a       :						int   ,		_a       :						int    ):



    '''simple docstring'''




    return sorted(str(_a    )    ) == sorted(str(_a    )    )







def       lowerCamelCase_  (    _a       :						int = 1000_0000    ):



    '''simple docstring'''




    UpperCAmelCase_     :       Optional[Any]  		=					1  # i
    UpperCAmelCase_     :       Optional[int]  		=					0  # φ(i)
    UpperCAmelCase_     :       List[str]  		=					get_totients(max_n + 1    )

    for i in range(2   ,		max_n + 1    ):
        UpperCAmelCase_     :       Dict  		=					totients[i]

        if i * min_denominator < min_numerator * t and has_same_digits(_a   ,		_a    ):
            UpperCAmelCase_     :       List[Any]  		=					i
            UpperCAmelCase_     :       Union[str, Any]  		=					t

    return min_numerator


if __name__ == "__main__":
      print(F"{solution() = }")




"""simple docstring"""






class       lowerCamelCase_		:





				"""simple docstring"""







				def __init__(    self  ):
								SCREAMING_SNAKE_CASE__  				=					[0]
								SCREAMING_SNAKE_CASE__  				=					0



				def 	lowerCAmelCase__		(    self							,		UpperCAmelCase__  ):
								SCREAMING_SNAKE_CASE__  				=					self.__heap[i]
								while i // 2 > 0:
												if self.__heap[i] > self.__heap[i // 2]:
																SCREAMING_SNAKE_CASE__  				=					self.__heap[i // 2]
																SCREAMING_SNAKE_CASE__  				=					temporary
												i //= 2



				def 	lowerCAmelCase__		(    self							,		UpperCAmelCase__  ):
								self.__heap.append(UpperCAmelCase__  )
								self.__size += 1
								self.__swap_up(self.__size  )



				def 	lowerCAmelCase__		(    self							,		UpperCAmelCase__  ):
								while self.__size >= 2 * i:
												if 2 * i + 1 > self.__size:
																SCREAMING_SNAKE_CASE__  				=					2 * i
												else:
																if self.__heap[2 * i] > self.__heap[2 * i + 1]:
																				SCREAMING_SNAKE_CASE__  				=					2 * i
																else:
																				SCREAMING_SNAKE_CASE__  				=					2 * i + 1
												SCREAMING_SNAKE_CASE__  				=					self.__heap[i]
												if self.__heap[i] < self.__heap[bigger_child]:
																SCREAMING_SNAKE_CASE__  				=					self.__heap[bigger_child]
																SCREAMING_SNAKE_CASE__  				=					temporary
												SCREAMING_SNAKE_CASE__  				=					bigger_child



				def 	lowerCAmelCase__		(    self  ):
								SCREAMING_SNAKE_CASE__  				=					self.__heap[1]
								SCREAMING_SNAKE_CASE__  				=					self.__heap[self.__size]
								self.__size -= 1
								self.__heap.pop()
								self.__swap_down(1  )
								return max_value



				@property
				def 	lowerCAmelCase__		(    self  ):
								return self.__heap[1:]






				def __len__(    self  ):
								return self.__size


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	# create an instance of BinaryHeap
	_lowerCamelCase  =	BinaryHeap()
	binary_heap.insert(6)
	binary_heap.insert(10)
	binary_heap.insert(15)
	binary_heap.insert(12)
	# pop root(max-values because it is max heap)
	print(binary_heap.pop())  # 15
	print(binary_heap.pop())  # 12
	# get the list and size after operations
	print(binary_heap.get_list)
	print(len(binary_heap))
