






def _a (  SCREAMING_SNAKE_CASE__      :  list       )	->    float:

							'''simple docstring'''






							SCREAMING_SNAKE_CASE__       :      int     =						0
							while len(SCREAMING_SNAKE_CASE__       ) > 1:
														SCREAMING_SNAKE_CASE__       :      Any     =						0
														# Consider two files with minimum cost to be merged
														for _ in range(2       ):
																					SCREAMING_SNAKE_CASE__       :      Tuple     =						files.index(min(SCREAMING_SNAKE_CASE__       )       )
																					temp += files[min_index]
																					files.pop(SCREAMING_SNAKE_CASE__       )
														files.append(SCREAMING_SNAKE_CASE__       )
														optimal_merge_cost += temp
							return optimal_merge_cost


if __name__ == "__main__":
		import doctest

		doctest.testmod()













from queue import PriorityQueue
from typing import Any

import numpy as np




def _a (  SCREAMING_SNAKE_CASE__      :  dict			,				SCREAMING_SNAKE_CASE__      :  str			,				SCREAMING_SNAKE_CASE__      :  set			,				SCREAMING_SNAKE_CASE__      :  set			,				SCREAMING_SNAKE_CASE__      :  dict			,				SCREAMING_SNAKE_CASE__      :  dict			,				SCREAMING_SNAKE_CASE__      :  PriorityQueue			,				SCREAMING_SNAKE_CASE__      :  dict			,				SCREAMING_SNAKE_CASE__      :  float | int			,				)	->    float | int:

							'''simple docstring'''






							for nxt, d in graph[v]:
														if nxt in visited_forward:
																					continue
														SCREAMING_SNAKE_CASE__       :      Union[str, Any]     =						cst_fwd.get(SCREAMING_SNAKE_CASE__			,				np.inf       )
														SCREAMING_SNAKE_CASE__       :      Optional[int]     =						cst_fwd[v] + d
														if new_cost_f < old_cost_f:
																					queue.put((new_cost_f, nxt)       )
																					SCREAMING_SNAKE_CASE__       :      List[Any]     =						new_cost_f
																					SCREAMING_SNAKE_CASE__       :      Union[str, Any]     =						v
														if nxt in visited_backward:
																					if cst_fwd[v] + d + cst_bwd[nxt] < shortest_distance:
																												SCREAMING_SNAKE_CASE__       :      Optional[int]     =						cst_fwd[v] + d + cst_bwd[nxt]
							return shortest_distance




def _a (  SCREAMING_SNAKE_CASE__      :  str			,				SCREAMING_SNAKE_CASE__      :  str			,				SCREAMING_SNAKE_CASE__      :  dict			,				SCREAMING_SNAKE_CASE__      :  dict       )	->    int:

							'''simple docstring'''






							SCREAMING_SNAKE_CASE__       :      Union[str, Any]     =						-1

							SCREAMING_SNAKE_CASE__       :      List[str]     =						set()
							SCREAMING_SNAKE_CASE__       :      List[Any]     =						set()
							SCREAMING_SNAKE_CASE__       :      int     =						{source: 0}
							SCREAMING_SNAKE_CASE__       :      Union[str, Any]     =						{destination: 0}
							SCREAMING_SNAKE_CASE__       :      List[Any]     =						{source: None}
							SCREAMING_SNAKE_CASE__       :      Union[str, Any]     =						{destination: None}
							SCREAMING_SNAKE_CASE__       :      PriorityQueue[Any]     =						PriorityQueue()
							SCREAMING_SNAKE_CASE__       :      PriorityQueue[Any]     =						PriorityQueue()

							SCREAMING_SNAKE_CASE__       :      Dict     =						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():
														SCREAMING_SNAKE_CASE__   ,SCREAMING_SNAKE_CASE__       :      List[str]     =						queue_forward.get()
														visited_forward.add(SCREAMING_SNAKE_CASE__       )

														SCREAMING_SNAKE_CASE__   ,SCREAMING_SNAKE_CASE__       :      List[Any]     =						queue_backward.get()
														visited_backward.add(SCREAMING_SNAKE_CASE__       )

														SCREAMING_SNAKE_CASE__       :      Any     =						pass_and_relaxation(
														    SCREAMING_SNAKE_CASE__			,				SCREAMING_SNAKE_CASE__			,				SCREAMING_SNAKE_CASE__			,				SCREAMING_SNAKE_CASE__			,				SCREAMING_SNAKE_CASE__			,				SCREAMING_SNAKE_CASE__			,				SCREAMING_SNAKE_CASE__			,				SCREAMING_SNAKE_CASE__			,				SCREAMING_SNAKE_CASE__			,				)

														SCREAMING_SNAKE_CASE__       :      List[Any]     =						pass_and_relaxation(
														    SCREAMING_SNAKE_CASE__			,				SCREAMING_SNAKE_CASE__			,				SCREAMING_SNAKE_CASE__			,				SCREAMING_SNAKE_CASE__			,				SCREAMING_SNAKE_CASE__			,				SCREAMING_SNAKE_CASE__			,				SCREAMING_SNAKE_CASE__			,				SCREAMING_SNAKE_CASE__			,				SCREAMING_SNAKE_CASE__			,				)

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

							if shortest_distance != np.inf:
														SCREAMING_SNAKE_CASE__       :      int     =						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 :    Tuple  							= {
    '''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()






