'''simple docstring'''

from queue import PriorityQueue
from typing import Any

import numpy as np



def 							UpperCamelCase__			(			a__			,      a__			,      a__			,      a__			,      a__			,      a__			,      a__			,      a__			,      a__			,      ):


						'''simple docstring'''






						for nxt, d in graph[v]:
												if nxt in visited_forward:
																		continue
												_lowerCAmelCase										=cst_fwd.get(a__			,      np.inf      )
												_lowerCAmelCase										=cst_fwd[v] + d
												if new_cost_f < old_cost_f:
																		queue.put((new_cost_f, nxt)      )
																		_lowerCAmelCase										=new_cost_f
																		_lowerCAmelCase										=v
												if nxt in visited_backward:
																		if cst_fwd[v] + d + cst_bwd[nxt] < shortest_distance:
																								_lowerCAmelCase										=cst_fwd[v] + d + cst_bwd[nxt]
						return shortest_distance



def 							UpperCamelCase__			(			a__			,      a__			,      a__			,      a__      ):


						'''simple docstring'''






						_lowerCAmelCase										=-1

						_lowerCAmelCase										=set()
						_lowerCAmelCase										=set()
						_lowerCAmelCase										={source: 0}
						_lowerCAmelCase										={destination: 0}
						_lowerCAmelCase										={source: None}
						_lowerCAmelCase										={destination: None}
						_lowerCAmelCase										=PriorityQueue()
						_lowerCAmelCase										=PriorityQueue()

						_lowerCAmelCase										=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():
												_lowerCAmelCase						,				_lowerCAmelCase										=queue_forward.get()
												visited_forward.add(a__      )

												_lowerCAmelCase						,				_lowerCAmelCase										=queue_backward.get()
												visited_backward.add(a__      )

												_lowerCAmelCase										=pass_and_relaxation(
												    a__			,      a__			,      a__			,      a__			,      a__			,      a__			,      a__			,      a__			,      a__			,      )

												_lowerCAmelCase										=pass_and_relaxation(
												    a__			,      a__			,      a__			,      a__			,      a__			,      a__			,      a__			,      a__			,      a__			,      )

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

						if shortest_distance != np.inf:
												_lowerCAmelCase										=shortest_distance
						return shortest_path_distance


lowercase_     		= {
    '''B''': [['''C''', 1]],
    '''C''': [['''D''', 1]],
    '''D''': [['''F''', 1]],
    '''E''': [['''B''', 1], ['''G''', 2]],
    '''F''': [],
    '''G''': [['''F''', 1]],
}
lowercase_     		= {
    '''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()






'''simple docstring'''

from __future__ import annotations

lowercase_     		= 10



def 							UpperCamelCase__			(			a__      ):


						'''simple docstring'''






						_lowerCAmelCase										=1
						_lowerCAmelCase										=max(a__      )
						while placement <= max_digit:
												# declare and initialize empty buckets
												_lowerCAmelCase										=[[] for _ in range(a__      )]
												# split list_of_ints between the buckets
												for i in list_of_ints:
																		_lowerCAmelCase										=int((i / placement) % RADIX      )
																		buckets[tmp].append(a__      )
												# put each buckets' contents into list_of_ints
												_lowerCAmelCase										=0
												for b in range(a__      ):
																		for i in buckets[b]:
																								_lowerCAmelCase										=i
																								a += 1
        # move to next
												placement *= RADIX
						return list_of_ints


if __name__ == "__main__":
							import doctest

							doctest.testmod()





