





'''simple docstring'''

from __future__ import annotations

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

lowerCAmelCase__	:					Optional[int]	     =       TypeVar("T", bound=bool)


class 			SCREAMING_SNAKE_CASE__	(					Generic[T]						):







					"""simple docstring"""






					def __init__(					self    :	Union[str, Any]						,     UpperCAmelCase_    :	T						):







							"""simple docstring"""
							__UpperCAmelCase     :				Dict					   =			value
							__UpperCAmelCase     :				Dict					   =			None
							__UpperCAmelCase     :				Optional[int]					   =			None
					@property
					def 						lowerCamelCase_					(					self    :	Tuple						):







							"""simple docstring"""
							return self._value






					@staticmethod
					def 						lowerCamelCase_					(					UpperCAmelCase_    :	RandomizedHeapNode[T] | None						,     UpperCAmelCase_    :	RandomizedHeapNode[T] | None						):







							"""simple docstring"""


							if not roota:
									return roota

							if not roota:
									return roota

							if roota.value > roota.value:
									__UpperCAmelCase   ,       __UpperCAmelCase     :				int					   =			roota, roota

							if random.choice([True, False]						):
									__UpperCAmelCase   ,       __UpperCAmelCase     :				List[str]					   =			roota.right, roota.left

							__UpperCAmelCase     :				Tuple					   =			RandomizedHeapNode.merge(roota.left						,     lowerCAmelCase_						)

							return roota






class 			SCREAMING_SNAKE_CASE__	(					Generic[T]						):







					"""simple docstring"""






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







							"""simple docstring"""
							__UpperCAmelCase     :				str					   =			None

							if data:
									for item in data:
											self.insert(lowerCAmelCase_						)
					def 						lowerCamelCase_					(					self    :	Union[str, Any]						,     UpperCAmelCase_    :	T						):







							"""simple docstring"""
							__UpperCAmelCase     :				Union[str, Any]					   =			RandomizedHeapNode.merge(self._root						,     RandomizedHeapNode(lowerCAmelCase_						)						)
					def 						lowerCamelCase_					(					self    :	List[str]						):







							"""simple docstring"""
							__UpperCAmelCase     :				Dict					   =			self.top()

							if self._root is None:
									return None

							__UpperCAmelCase     :				List[str]					   =			RandomizedHeapNode.merge(self._root.left						,     self._root.right						)

							return result
					def 						lowerCamelCase_					(					self    :	Tuple						):







							"""simple docstring"""


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







							"""simple docstring"""
							__UpperCAmelCase     :				List[Any]					   =			None
					def 						lowerCamelCase_					(					self    :	Tuple						):







							"""simple docstring"""
							__UpperCAmelCase     :				List[Any]					   =			[]
							while self:
									result.append(self.pop()						)

							return result






					def __bool__(					self    :	str						):







							"""simple docstring"""
							return self._root is not None


if __name__ == "__main__":
			import doctest

			doctest.testmod()










'''simple docstring'''


from __future__ import annotations
def 		snake_case_    (UpperCamelCase       :  int      ):





							'''simple docstring'''


							_a	     =				[0] * max_one

							for i in range(0 ,						UpperCamelCase      ):
														_a	     =				i

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

							return totients
def 		snake_case_    (UpperCamelCase       :  int ,						UpperCamelCase       :  int      ):





							'''simple docstring'''


							return sorted(str(UpperCamelCase      )      ) == sorted(str(UpperCamelCase      )      )
def 		snake_case_    (UpperCamelCase       :  int = 1000_0000      ):





							'''simple docstring'''


							_a	     =				1  # i
							_a	     =				0  # φ(i)
							_a	     =				get_totients(max_n + 1      )

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

														if i * min_denominator < min_numerator * t and has_same_digits(UpperCamelCase ,						UpperCamelCase      ):
																					_a	     =				i
																					_a	     =				t

							return min_numerator


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

