






from queue import PriorityQueue
from typing import Any

import numpy as np

def      _lowerCamelCase	(						__A    :							dict		,		__A    :							str		,		__A    :							set		,		__A    :							set		,		__A    :							dict		,		__A    :							dict		,		__A    :							PriorityQueue		,		__A    :							dict		,		__A    :							float | int		,		)      ->					float | int:
    for nxt, d in graph[v]:
        if nxt in visited_forward:
            continue
        _UpperCAmelCase				:      int			  =				cst_fwd.get(__A		,		np.inf )
        _UpperCAmelCase				:      int			  =				cst_fwd[v] + d
        if new_cost_f < old_cost_f:
            queue.put((new_cost_f, nxt) )
            _UpperCAmelCase				:      Union[str, Any]			  =				new_cost_f
            _UpperCAmelCase				:      Union[str, Any]			  =				v
        if nxt in visited_backward:
            if cst_fwd[v] + d + cst_bwd[nxt] < shortest_distance:
                _UpperCAmelCase				:      Tuple			  =				cst_fwd[v] + d + cst_bwd[nxt]
    return shortest_distance

def      _lowerCamelCase	(						__A    :							str		,		__A    :							str		,		__A    :							dict		,		__A    :							dict )      ->					int:
    _UpperCAmelCase				:      List[str]			  =				-1

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

    _UpperCAmelCase				:      int			  =				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():
        _UpperCAmelCase  , _UpperCAmelCase				:      Dict			  =				queue_forward.get()
        visited_forward.add(__A )

        _UpperCAmelCase  , _UpperCAmelCase				:      Union[str, Any]			  =				queue_backward.get()
        visited_backward.add(__A )

        _UpperCAmelCase				:      List[str]			  =				pass_and_relaxation(
            __A		,		__A		,		__A		,		__A		,		__A		,		__A		,		__A		,		__A		,		__A		,		)

        _UpperCAmelCase				:      Tuple			  =				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:
        _UpperCAmelCase				:      int			  =				shortest_distance
    return shortest_path_distance


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












from math import pow, sqrt

def      _lowerCamelCase	(						*__A    :							float )      ->					bool:
    _UpperCAmelCase				:      str			  =				len(__A ) > 0 and all(value > 0.0 for value in values )
    return result

def      _lowerCamelCase	(						__A    :							float		,		__A    :							float )      ->					float | ValueError:
    return (
        round(sqrt(molar_mass_a / molar_mass_a )		,		6 )
        if validate(__A		,		__A )
        else ValueError('''Input Error: Molar mass values must greater than 0.''' )
    )

def      _lowerCamelCase	(						__A    :							float		,		__A    :							float		,		__A    :							float )      ->					float | ValueError:
    return (
        round(effusion_rate * sqrt(molar_mass_a / molar_mass_a )		,		6 )
        if validate(__A		,		__A		,		__A )
        else ValueError(
            '''Input Error: Molar mass and effusion rate values must greater than 0.''' )
    )

def      _lowerCamelCase	(						__A    :							float		,		__A    :							float		,		__A    :							float )      ->					float | ValueError:
    return (
        round(effusion_rate / sqrt(molar_mass_a / molar_mass_a )		,		6 )
        if validate(__A		,		__A		,		__A )
        else ValueError(
            '''Input Error: Molar mass and effusion rate values must greater than 0.''' )
    )

def      _lowerCamelCase	(						__A    :							float		,		__A    :							float		,		__A    :							float )      ->					float | ValueError:
    return (
        round(molar_mass / pow(effusion_rate_a / effusion_rate_a		,		2 )		,		6 )
        if validate(__A		,		__A		,		__A )
        else ValueError(
            '''Input Error: Molar mass and effusion rate values must greater than 0.''' )
    )


def      _lowerCamelCase	(						__A    :							float		,		__A    :							float		,		__A    :							float )      ->					float | ValueError:
    return (
        round(pow(effusion_rate_a / effusion_rate_a		,		2 ) / molar_mass		,		6 )
        if validate(__A		,		__A		,		__A )
        else ValueError(
            '''Input Error: Molar mass and effusion rate values must greater than 0.''' )
    )




