

def 	a						(				_UpperCAmelCase							: int			,       _UpperCAmelCase							: int						):







		'''simple docstring'''





		__UpperCAmelCase   :					Optional[Any]													=     1.0
		for i in range(1			,       r + 1						):
				ret *= (n + 1 - i) / i
		return round(__lowercase						)

def 	a						(				_UpperCAmelCase							: int						):







		'''simple docstring'''





		return choose(8 + n			,       __lowercase						) + choose(9 + n			,       __lowercase						) - 10

def 	a						(				_UpperCAmelCase							: int						):







		'''simple docstring'''





		return sum(non_bouncy_exact(__lowercase						) for i in range(1			,       n + 1						)						)

def 	a						(				_UpperCAmelCase							: int = 1_00						):







		'''simple docstring'''





		return non_bouncy_upto(__lowercase						)


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










from __future__ import annotations

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

__A             =TypeVar("T", bound=bool)

class 		UpperCAmelCase__      (      Generic[T]       ):




			'''simple docstring'''






			def __init__(       self							:			List[Any]	,	a_							:			T			):
					'''simple docstring'''





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




			@property
			def 			snake_case__					(       self							:			Any			):
					'''simple docstring'''





					return self._value




			@staticmethod
			def 			snake_case__					(       a_							:			RandomizedHeapNode[T] | None	,	a_							:			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   :					Union[str, Any]													=     roota.right, roota.left

					__UpperCAmelCase   :					Optional[Any]													=     RandomizedHeapNode.merge(roota.left	,	a_			)

					return roota

class 		UpperCAmelCase__      (      Generic[T]       ):




			'''simple docstring'''






			def __init__(       self							:			Tuple	,	a_							:			Iterable[T] | None = ()			):
					'''simple docstring'''





					__UpperCAmelCase   :					RandomizedHeapNode[T] | None													=     None

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




			def 			snake_case__					(       self							:			List[str]	,	a_							:			T			):
					'''simple docstring'''





					__UpperCAmelCase   :					Optional[Any]													=     RandomizedHeapNode.merge(self._root	,	RandomizedHeapNode(a_			)			)




			def 			snake_case__					(       self							:			Optional[int]			):
					'''simple docstring'''





					__UpperCAmelCase   :					Optional[Any]													=     self.top()

					if self._root is None:
							return None

					__UpperCAmelCase   :					Tuple													=     RandomizedHeapNode.merge(self._root.left	,	self._root.right			)

					return result




			def 			snake_case__					(       self							:			Any			):
					'''simple docstring'''





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




			def 			snake_case__					(       self							:			Optional[Any]			):
					'''simple docstring'''





					__UpperCAmelCase   :					str													=     None




			def 			snake_case__					(       self							:			Tuple			):
					'''simple docstring'''





					__UpperCAmelCase   :					List[Any]													=     []
					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()





