
import heapq as hq
import math
from collections.abc import Iterator







class 			A_  :




	'''simple docstring'''


	def __init__(			self						,       snake_case			):
		lowercase	    =       str(id_			)
		lowercase	    =       None
		lowercase	    =       None
		lowercase	    =       []
		lowercase	    =       {}  # {vertex:distance}





	def __lt__(			self						,       snake_case			):
		return self.key < other.key





	def __repr__(			self			):
		return self.id





	def       SCREAMING_SNAKE_CASE__		(			self						,       snake_case			):
		self.neighbors.append(snake_case			)





	def       SCREAMING_SNAKE_CASE__		(			self						,       snake_case						,       snake_case			):
		lowercase	    =       weight






def 				UpperCAmelCase_						(				__SCREAMING_SNAKE_CASE					,				__SCREAMING_SNAKE_CASE					,				__SCREAMING_SNAKE_CASE					,				__SCREAMING_SNAKE_CASE				):
	# add the neighbors:
	graph[a - 1].add_neighbor(graph[b - 1]				)
	graph[b - 1].add_neighbor(graph[a - 1]				)
	# add the edges:
	graph[a - 1].add_edge(graph[b - 1]					,				__SCREAMING_SNAKE_CASE				)
	graph[b - 1].add_edge(graph[a - 1]					,				__SCREAMING_SNAKE_CASE				)






def 				UpperCAmelCase_						(				__SCREAMING_SNAKE_CASE					,				__SCREAMING_SNAKE_CASE				):
	lowercase	    =       []
	for u in graph:
		lowercase	    =       math.inf
		lowercase	    =       None
	lowercase	    =       0
	lowercase	    =       graph[:]
	while q:
		lowercase	    =       min(__SCREAMING_SNAKE_CASE				)
		q.remove(__SCREAMING_SNAKE_CASE				)
		for v in u.neighbors:
			if (v in q) and (u.edges[v.id] < v.key):
				lowercase	    =       u
				lowercase	    =       u.edges[v.id]
	for i in range(1					,				len(__SCREAMING_SNAKE_CASE				)				):
		a.append((int(graph[i].id				) + 1, int(graph[i].pi.id				) + 1)				)
	return a






def 				UpperCAmelCase_						(				__SCREAMING_SNAKE_CASE					,				__SCREAMING_SNAKE_CASE				):
	for u in graph:
		lowercase	    =       math.inf
		lowercase	    =       None
	lowercase	    =       0

	lowercase	    =       list(__SCREAMING_SNAKE_CASE				)
	hq.heapify(__SCREAMING_SNAKE_CASE				)

	while h:
		lowercase	    =       hq.heappop(__SCREAMING_SNAKE_CASE				)
		for v in u.neighbors:
			if (v in h) and (u.edges[v.id] < v.key):
				lowercase	    =       u
				lowercase	    =       u.edges[v.id]
				hq.heapify(__SCREAMING_SNAKE_CASE				)

	for i in range(1					,				len(__SCREAMING_SNAKE_CASE				)				):
		yield (int(graph[i].id				) + 1, int(graph[i].pi.id				) + 1)






def 				UpperCAmelCase_						(				):
	pass


if __name__ == "__main__":
	import doctest

	doctest.testmod()





'''simple docstring'''
from __future__ import annotations

import math


def      a (     __a					,   __a					,   __a					,   __a					,   __a  )    ->      int:



					'''simple docstring'''






					if depth < 0:
										raise ValueError('''Depth cannot be less than 0'''  )

					if len(__a  ) == 0:
										raise ValueError('''Scores cannot be empty'''  )

					if depth == height:
										return scores[node_index]

					if is_max:
										return max(
										    minimax(depth + 1					,   node_index * 2					,   __a					,   __a					,   __a  )					,   minimax(depth + 1					,   node_index * 2 + 1					,   __a					,   __a					,   __a  )					,   )

					return min(
					    minimax(depth + 1					,   node_index * 2					,   __a					,   __a					,   __a  )					,   minimax(depth + 1					,   node_index * 2 + 1					,   __a					,   __a					,   __a  )					,   )


def      a (     )    ->      None:



					'''simple docstring'''






					UpperCamelCase__  :str				   =					[90, 23, 6, 33, 21, 65, 123, 34423]
					UpperCamelCase__  :List[Any]				   =					math.log(len(__a  )					,   2  )
					print('''Optimal value : '''					,   end=''''''  )
					print(minimax(0					,   0					,   __a					,   __a					,   __a  )  )


if __name__ == "__main__":
		import doctest

		doctest.testmod()
		main()