




"""simple docstring"""

def 		lowercase_      (		_UpperCAmelCase	):




	"""simple docstring"""






	if not head:
		return True
	# split the list to two parts
	A_   , A_  :				str	   =		head.next, head
	while fast and fast.next:
		A_  :				List[Any]	   =		fast.next.next
		A_  :				Dict	   =		slow.next
	A_  :				List[str]	   =		slow.next
	A_  :				List[Any]	   =		None  # Don't forget here! But forget still works!
	# reverse the second part
	A_  :				int	   =		None
	while second:
		A_  :				List[str]	   =		second.next
		A_  :				List[Any]	   =		node
		A_  :				Tuple	   =		second
		A_  :				List[Any]	   =		nxt
	# compare two parts
	# second part has the same or one less node
	while node:
		if node.val != head.val:
			return False
		A_  :				Union[str, Any]	   =		node.next
		A_  :				Any	   =		head.next
	return True

def 		lowercase_      (		_UpperCAmelCase	):




	"""simple docstring"""






	if not head or not head.next:
		return True

	# 1. Get the midpoint (slow)
	A_  :				List[Any]	   =		head
	while fast and fast.next:
		A_   , A_  :				List[str]	   =		fast.next.next, slow.next

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

	# 3. Comparison
	while stack:
		if stack.pop() != cur.val:
			return False
		A_  :				Union[str, Any]	   =		cur.next

	return True

def 		lowercase_      (		_UpperCAmelCase	):




	"""simple docstring"""






	if not head or not head.next:
		return True
	A_  :				Tuple	   =		{}
	A_  :				Union[str, Any]	   =		0
	while head:
		if head.val in d:
			d[head.val].append(_UpperCAmelCase	)
		else:
			A_  :				List[str]	   =		[pos]
		A_  :				Union[str, Any]	   =		head.next
		pos += 1
	A_  :				List[str]	   =		pos - 1
	A_  :				List[Any]	   =		0
	for v in d.values():
		if len(_UpperCAmelCase	) % 2 != 0:
			middle += 1
		else:
			A_  :				int	   =		0
			for i in range(0  ,      len(_UpperCAmelCase	)	):
				if v[i] + v[len(_UpperCAmelCase	) - 1 - step] != checksum:
					return False
				step += 1
		if middle > 1:
			return False
	return True











"""simple docstring"""

from queue import PriorityQueue
from typing import Any

import numpy as np

def 		lowercase_      (		_UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      ):




	"""simple docstring"""






	for nxt, d in graph[v]:
		if nxt in visited_forward:
			continue
		A_  :				Tuple	   =		cst_fwd.get(_UpperCAmelCase  ,      np.inf	)
		A_  :				Any	   =		cst_fwd[v] + d
		if new_cost_f < old_cost_f:
			queue.put((new_cost_f, nxt)	)
			A_  :				Tuple	   =		new_cost_f
			A_  :				Dict	   =		v
		if nxt in visited_backward:
			if cst_fwd[v] + d + cst_bwd[nxt] < shortest_distance:
				A_  :				Optional[Any]	   =		cst_fwd[v] + d + cst_bwd[nxt]
	return shortest_distance

def 		lowercase_      (		_UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase	):




	"""simple docstring"""






	A_  :				Tuple	   =		-1

	A_  :				Any	   =		set()
	A_  :				Tuple	   =		set()
	A_  :				Optional[int]	   =		{source: 0}
	A_  :				Dict	   =		{destination: 0}
	A_  :				Any	   =		{source: None}
	A_  :				Optional[Any]	   =		{destination: None}
	A_  :				PriorityQueue[Any]	   =		PriorityQueue()
	A_  :				PriorityQueue[Any]	   =		PriorityQueue()

	A_  :				Union[str, Any]	   =		np.inf

	queue_forward.put((0, source)	)
	queue_backward.put((0, destination)	)

	if source == destination:
		return 0

	while not queue_forward.empty() and not queue_backward.empty():
		A_   , A_  :				Union[str, Any]	   =		queue_forward.get()
		visited_forward.add(_UpperCAmelCase	)

		A_   , A_  :				Optional[int]	   =		queue_backward.get()
		visited_backward.add(_UpperCAmelCase	)

		A_  :				Any	   =		pass_and_relaxation(
		    _UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      )

		A_  :				Dict	   =		pass_and_relaxation(
		    _UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      )

		if cst_fwd[v_fwd] + cst_bwd[v_bwd] >= shortest_distance:
			break

	if shortest_distance != np.inf:
		A_  :				Optional[Any]	   =		shortest_distance
	return shortest_path_distance


_lowerCamelCase  :			Optional[Any]        =       {
    'B': [['C', 1]],
    'C': [['D', 1]],
    'D': [['F', 1]],
    'E': [['B', 1], ['G', 2]],
    'F': [],
    'G': [['F', 1]],
}
_lowerCamelCase  :			Any        =       {
    'B': [['E', 1]],
    'C': [['B', 1]],
    'D': [['C', 1]],
    'F': [['D', 1], ['G', 1]],
    'E': [[None, np.inf]],
    'G': [['E', 2]],
}

if __name__ == "__main__":
		import doctest

		doctest.testmod()





