





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:






		"""simple docstring"""

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







def    __lowerCamelCase					(							__a   :str    ,     __a   :str    ,     __a   :dict    ,     __a   :dict    )		->				int:






		"""simple docstring"""

		A__        =   -1

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

		A__        =   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__        =   queue_forward.get()
				visited_forward.add(__a    )

				A__      ,			A__        =   queue_backward.get()
				visited_backward.add(__a    )

				A__        =   pass_and_relaxation(
				    __a    ,     __a    ,     __a    ,     __a    ,     __a    ,     __a    ,     __a    ,     __a    ,     __a    ,     )

				A__        =   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:
				A__        =   shortest_distance
		return shortest_path_distance


A    :					Dict =      {
    '''B''': [['''C''', 1]],
    '''C''': [['''D''', 1]],
    '''D''': [['''F''', 1]],
    '''E''': [['''B''', 1], ['''G''', 2]],
    '''F''': [],
    '''G''': [['''F''', 1]],
}
A    :					Optional[int] =      {
    '''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()










def    __lowerCamelCase					(							__a   :str    )		->				list:






		"""simple docstring"""

		A__        =   [0] * len(__a    )

		for i in range(1    ,     len(__a    )    ):
				# use last results for better performance - dynamic programming
				A__        =   prefix_result[i - 1]
				while j > 0 and input_string[i] != input_string[j]:
						A__        =   prefix_result[j - 1]

				if input_string[i] == input_string[j]:
						j += 1
				A__        =   j

		return prefix_result







def    __lowerCamelCase					(							__a   :str    )		->				int:






		"""simple docstring"""

		return max(prefix_function(__a    )    )


if __name__ == "__main__":
					import doctest

					doctest.testmod()



