

'''simple docstring'''







import math
import sys
def       UpperCAmelCase__    (      UpperCAmelCase__				)			->			int:
       if number != int(UpperCAmelCase__				):
              raise ValueError("""the value of input must be a natural number"""				)
       if number < 0:
              raise ValueError("""the value of input must not be a negative number"""				)
       if number == 0:
              return 1
       A_						=      [-1] * (number + 1)
       A_						=      0
       for i in range(1,       number + 1				):
              A_						=      sys.maxsize
              A_						=      int(math.sqrt(UpperCAmelCase__				)				)
              for j in range(1,       root + 1				):
                     A_						=      1 + answers[i - (j**2)]
                     A_						=      min(UpperCAmelCase__,       UpperCAmelCase__				)
              A_						=      answer
       return answers[number]


if __name__ == "__main__":
      import doctest

      doctest.testmod()



'''simple docstring'''







from queue import PriorityQueue
from typing import Any

import numpy as np
def       UpperCAmelCase__    (      UpperCAmelCase__,       UpperCAmelCase__,       UpperCAmelCase__,       UpperCAmelCase__,       UpperCAmelCase__,       UpperCAmelCase__,       UpperCAmelCase__,       UpperCAmelCase__,       UpperCAmelCase__,       )			->			float | int:
       for nxt, d in graph[v]:
              if nxt in visited_forward:
                     continue
              A_						=      cst_fwd.get(UpperCAmelCase__,       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       UpperCAmelCase__    (      UpperCAmelCase__,       UpperCAmelCase__,       UpperCAmelCase__,       UpperCAmelCase__				)			->			int:
       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(UpperCAmelCase__				)

              A_					,			A_						=      queue_backward.get()
              visited_backward.add(UpperCAmelCase__				)

              A_						=      pass_and_relaxation(
                  UpperCAmelCase__,       UpperCAmelCase__,       UpperCAmelCase__,       UpperCAmelCase__,       UpperCAmelCase__,       UpperCAmelCase__,       UpperCAmelCase__,       UpperCAmelCase__,       UpperCAmelCase__,       )

              A_						=      pass_and_relaxation(
                  UpperCAmelCase__,       UpperCAmelCase__,       UpperCAmelCase__,       UpperCAmelCase__,       UpperCAmelCase__,       UpperCAmelCase__,       UpperCAmelCase__,       UpperCAmelCase__,       UpperCAmelCase__,       )

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

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


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