
def  UpperCamelCase					(							lowerCAmelCase__	):
					'''simple docstring'''
					assert isinstance(lowerCAmelCase__				,    lowerCAmelCase__	), f'The input value of [n={number}] is not an integer'

					if number == 1:
										return 2
					elif number < 1:
										lowercase					=		f'The input value of [n={number}] has to be > 0'
										raise ValueError(lowerCAmelCase__	)
					else:
										lowercase					=		sylvester(number - 1	)
										lowercase					=		num - 1
										lowercase					=		num
										return lower * upper + 1


if __name__ == "__main__":
							print(F'The 8th number in Sylvester\'s sequence: {sylvester(8)}')






from __future__ import annotations

from random import random







class        lowercase	:




							def __init__(       self     ,A__ = None):
												lowercase					=		value
												lowercase					=		random()
												lowercase					=		None
												lowercase					=		None




							def __repr__(       self):
												from pprint import pformat

												if self.left is None and self.right is None:
																	return f'\'{self.value}: {self.prior:.5}\''
												else:
																	return pformat(
																	    {f'{self.value}: {self.prior:.5}': (self.left, self.right)}     ,indent=1)





							def __str__(       self):
												lowercase					=		str(self.value) + ''' '''
												lowercase					=		str(self.left or '''''')
												lowercase					=		str(self.right or '''''')
												return value + left + right



def  UpperCamelCase					(							lowerCAmelCase__				,    lowerCAmelCase__	):
					'''simple docstring'''
					if root is None:  # None tree is split into 2 Nones
										return None, None
					elif root.value is None:
										return None, None
					else:
										if value < root.value:
															lowercase			,		lowercase					=		split(root.left				,    lowerCAmelCase__	)
															return left, root
										else:
															lowercase			,		lowercase					=		split(root.right				,    lowerCAmelCase__	)
															return root, right



def  UpperCamelCase					(							lowerCAmelCase__				,    lowerCAmelCase__	):
					'''simple docstring'''
					if (not left) or (not right):  # If one node is None, return the other
										return left or right
					elif left.prior < right.prior:
										lowercase					=		merge(left.right				,    lowerCAmelCase__	)
										return left
					else:
										lowercase					=		merge(lowerCAmelCase__				,    right.left	)
										return right



def  UpperCamelCase					(							lowerCAmelCase__				,    lowerCAmelCase__	):
					'''simple docstring'''
					lowercase					=		Node(lowerCAmelCase__	)
					lowercase			,		lowercase					=		split(lowerCAmelCase__				,    lowerCAmelCase__	)
					return merge(merge(lowerCAmelCase__				,    lowerCAmelCase__	)				,    lowerCAmelCase__	)



def  UpperCamelCase					(							lowerCAmelCase__				,    lowerCAmelCase__	):
					'''simple docstring'''
					lowercase			,		lowercase					=		split(lowerCAmelCase__				,    value - 1	)
					lowercase			,		lowercase					=		split(lowerCAmelCase__				,    lowerCAmelCase__	)
					return merge(lowerCAmelCase__				,    lowerCAmelCase__	)



def  UpperCamelCase					(							lowerCAmelCase__	):
					'''simple docstring'''
					if not root:  # None
										return
					else:
										inorder(root.left	)
										print(root.value				,    end=''','''	)
										inorder(root.right	)



def  UpperCamelCase					(							lowerCAmelCase__				,    lowerCAmelCase__	):
					'''simple docstring'''
					for arg in args.split():
										if arg[0] == "+":
															lowercase					=		insert(lowerCAmelCase__				,    int(arg[1:]	)	)

										elif arg[0] == "-":
															lowercase					=		erase(lowerCAmelCase__				,    int(arg[1:]	)	)

										else:
															print('''Unknown command'''	)

					return root



def  UpperCamelCase					(							):
					'''simple docstring'''
					lowercase					=		None
					print(
					    '''enter numbers to create a tree, + value to add value into treap, '''
					    '''- value to erase all nodes with value. \'q\' to quit. '''	)

					lowercase					=		input()
					while args != "q":
										lowercase					=		interact_treap(lowerCAmelCase__				,    lowerCAmelCase__	)
										print(lowerCAmelCase__	)
										lowercase					=		input()

					print('''good by!'''	)


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							main()




