



from __future__ import annotations

from collections import Counter
from random import random

class  __snake_case      :







							'''simple docstring'''






							def __init__(							self		):
											a__				      =		{}


							def _a      (							self  ,  a_		):
											a__				      =		{}


							def _a      (							self  ,  a_  ,  a_  ,  a_		):
											if nodea not in self.connections:
															self.add_node(_A		)
											if nodea not in self.connections:
															self.add_node(_A		)
											a__				      =		probability


							def _a      (							self		):
											return list(self.connections		)







							def _a      (							self  ,  a_		):
											a__				      =		0
											a__				      =		random()

											for dest in self.connections[node]:
															current_probability += self.connections[node][dest]
															if current_probability > random_value:
																			return dest
											return ""




def 			A_      (	__a     :				Any ,		__a     :				Dict ,		__a     :				Any		):

				"""simple docstring"""
				a__				      =		MarkovChainGraphUndirectedUnweighted()

				for nodea, nodea, probability in transitions:
								graph.add_transition_probability(__snake_case ,		__snake_case ,		__snake_case		)

				a__				      =		Counter(graph.get_nodes()		)
				a__				      =		start

				for _ in range(__snake_case		):
								a__				      =		graph.transition(__snake_case		)
								visited[node] += 1

				return visited


if __name__ == "__main__":
	import doctest

	doctest.testmod()






def 			A_      (	__a     :				Any		):

				"""simple docstring"""
				if not head:
								return True
				# split the list to two parts
				a__      ,			a__				      =		head.next, head
				while fast and fast.next:
								a__				      =		fast.next.next
								a__				      =		slow.next
				a__				      =		slow.next
				a__				      =		None  # Don't forget here! But forget still works!
				# reverse the second part
				a__				      =		None
				while second:
								a__				      =		second.next
								a__				      =		node
								a__				      =		second
								a__				      =		nxt
				# compare two parts
				# second part has the same or one less node
				while node:
								if node.val != head.val:
												return False
								a__				      =		node.next
								a__				      =		head.next
				return True

def 			A_      (	__a     :				int		):

				"""simple docstring"""
				if not head or not head.next:
								return True

				# 1. Get the midpoint (slow)
				a__				      =		a__				      =		a__				      =		head
				while fast and fast.next:
								a__      ,			a__				      =		fast.next.next, slow.next

				# 2. Push the second half into the stack
				a__				      =		[slow.val]
				while slow.next:
								a__				      =		slow.next
								stack.append(slow.val		)

				# 3. Comparison
				while stack:
								if stack.pop() != cur.val:
												return False
								a__				      =		cur.next

				return True




def 			A_      (	__a     :				Any		):

				"""simple docstring"""
				if not head or not head.next:
								return True
				a__				      =		{}
				a__				      =		0
				while head:
								if head.val in d:
												d[head.val].append(__a		)
								else:
												a__				      =		[pos]
								a__				      =		head.next
								pos += 1
				a__				      =		pos - 1
				a__				      =		0
				for v in d.values():
								if len(__a		) % 2 != 0:
												middle += 1
								else:
												a__				      =		0
												for i in range(0 ,		len(__a		)		):
																if v[i] + v[len(__a		) - 1 - step] != checksum:
																				return False
																step += 1
								if middle > 1:
												return False
				return True

