



'''simple docstring'''




from __future__ import annotations


def     lowerCAmelCase_       (     _lowerCamelCase:       int ):
		__SCREAMING_SNAKE_CASE	:		Dict   	=		[0] * max_one

		for i in range(0	,				_lowerCamelCase ):
				__SCREAMING_SNAKE_CASE	:		List[Any]   	=		i

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

		return totients


def     lowerCAmelCase_       (     _lowerCamelCase:       int	,				_lowerCamelCase:       int ):
		return sorted(str(_lowerCamelCase ) ) == sorted(str(_lowerCamelCase ) )


def     lowerCAmelCase_       (     _lowerCamelCase:       int = 10_00_00_00 ):
		__SCREAMING_SNAKE_CASE	:		List[Any]   	=		1  # i
		__SCREAMING_SNAKE_CASE	:		str   	=		0  # φ(i)
		__SCREAMING_SNAKE_CASE	:		List[str]   	=		get_totients(max_n + 1 )

		for i in range(2	,				max_n + 1 ):
				__SCREAMING_SNAKE_CASE	:		Optional[int]   	=		totients[i]

				if i * min_denominator < min_numerator * t and has_same_digits(_lowerCamelCase	,				_lowerCamelCase ):
						__SCREAMING_SNAKE_CASE	:		Dict   	=		i
						__SCREAMING_SNAKE_CASE	:		List[Any]   	=		t

		return min_numerator


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




'''simple docstring'''




from __future__ import annotations

import random
from collections.abc import Iterable
from typing import Any, Generic, TypeVar

UpperCamelCase__	:     str    =			TypeVar('''T''', bound=bool)






class 						_UpperCamelCase  (							Generic[T]   ):


			'''simple docstring'''

			def __init__(							self					:			str							,					lowerCAmelCase__					:			T						):





					"""simple docstring"""






					__SCREAMING_SNAKE_CASE	:		T   	=		value
					__SCREAMING_SNAKE_CASE	:		RandomizedHeapNode[T] | None   	=		None
					__SCREAMING_SNAKE_CASE	:		RandomizedHeapNode[T] | None   	=		None

			@property
			def UpperCamelCase__ (							self					:			Any						):





					"""simple docstring"""






					return self._value



			@staticmethod
			def UpperCamelCase__ (							lowerCAmelCase__					:			RandomizedHeapNode[T] | None							,					lowerCAmelCase__					:			RandomizedHeapNode[T] | None						):





					"""simple docstring"""






					if not roota:
							return roota

					if not roota:
							return roota

					if roota.value > roota.value:
							__SCREAMING_SNAKE_CASE	,						__SCREAMING_SNAKE_CASE	:		List[str]   	=		roota, roota

					if random.choice([True, False]						):
							__SCREAMING_SNAKE_CASE	,						__SCREAMING_SNAKE_CASE	:		Tuple   	=		roota.right, roota.left

					__SCREAMING_SNAKE_CASE	:		Tuple   	=		RandomizedHeapNode.merge(roota.left							,					lowerCAmelCase__						)

					return roota






class 						_UpperCamelCase  (							Generic[T]   ):


			'''simple docstring'''

			def __init__(							self					:			Optional[int]							,					lowerCAmelCase__					:			Iterable[T] | None = ()						):





					"""simple docstring"""






					__SCREAMING_SNAKE_CASE	:		RandomizedHeapNode[T] | None   	=		None

					if data:
							for item in data:
									self.insert(lowerCAmelCase__						)

			def UpperCamelCase__ (							self					:			Dict							,					lowerCAmelCase__					:			T						):





					"""simple docstring"""






					__SCREAMING_SNAKE_CASE	:		Dict   	=		RandomizedHeapNode.merge(self._root							,					RandomizedHeapNode(lowerCAmelCase__						)						)

			def UpperCamelCase__ (							self					:			Union[str, Any]						):





					"""simple docstring"""






					__SCREAMING_SNAKE_CASE	:		Tuple   	=		self.top()

					if self._root is None:
							return None

					__SCREAMING_SNAKE_CASE	:		Union[str, Any]   	=		RandomizedHeapNode.merge(self._root.left							,					self._root.right						)

					return result

			def UpperCamelCase__ (							self					:			Union[str, Any]						):





					"""simple docstring"""






					if not self._root:
							raise IndexError("""Can't get top element for the empty heap."""						)
					return self._root.value

			def UpperCamelCase__ (							self					:			List[Any]						):





					"""simple docstring"""






					__SCREAMING_SNAKE_CASE	:		List[str]   	=		None

			def UpperCamelCase__ (							self					:			Optional[Any]						):





					"""simple docstring"""






					__SCREAMING_SNAKE_CASE	:		int   	=		[]
					while self:
							result.append(self.pop()						)

					return result



			def __bool__(							self					:			List[Any]						):





					"""simple docstring"""






					return self._root is not None


if __name__ == "__main__":
						import doctest

						doctest.testmod()