

'''simple docstring'''
import heapq
import sys

import numpy as np

_UpperCAmelCase  :		Optional[Any]  =		tuple[int, int]

class 						__magic_name__   :







 def __init__(       self   ):
   lowercase									=[]
   lowercase									=set()







 def 						_A(       self   ):
   if not self.empty():
     return self.elements[0][0]
   else:
     return float('''inf'''   )







 def 						_A(       self   ):
   return len(self.elements   ) == 0







 def 						_A(       self  , snake_case_  , snake_case_   ):
   if item not in self.set:
     heapq.heappush(self.elements  , (priority, item)   )
     self.set.add(_UpperCamelCase   )
   else:
     # update
     # print("update", item)
     lowercase									=[]
     ((lowercase)							, (lowercase))									=heapq.heappop(self.elements   )
     while x != item:
       temp.append((pri, x)   )
       ((lowercase)							, (lowercase))									=heapq.heappop(self.elements   )
     temp.append((priority, item)   )
     for pro, xxx in temp:
       heapq.heappush(self.elements  , (pro, xxx)   )







 def 						_A(       self  , snake_case_   ):
   if item in self.set:
     self.set.remove(_UpperCamelCase   )
     lowercase									=[]
     ((lowercase)							, (lowercase))									=heapq.heappop(self.elements   )
     while x != item:
       temp.append((pro, x)   )
       ((lowercase)							, (lowercase))									=heapq.heappop(self.elements   )
     for prito, yyy in temp:
       heapq.heappush(self.elements  , (prito, yyy)   )







 def 						_A(       self   ):
   return self.elements[0][1]







 def 						_A(       self   ):
   ((lowercase)							, (lowercase))									=heapq.heappop(self.elements   )
   self.set.remove(_UpperCamelCase   )
   return (priority, item)




def 	UpperCamelCase   (       lowercase_						:    TPos     ,					lowercase_						:    TPos	)		->	Any:




  '''simple docstring'''



  lowercase									=np.array(SCREAMING_SNAKE_CASE_	)
  lowercase									=np.array(SCREAMING_SNAKE_CASE_	)
  return np.linalg.norm(a - b	)




def 	UpperCamelCase   (       lowercase_						:    TPos     ,					lowercase_						:    TPos	)		->	int:




  '''simple docstring'''



  return consistent_heuristic(SCREAMING_SNAKE_CASE_     ,					SCREAMING_SNAKE_CASE_	) // t




def 	UpperCamelCase   (       lowercase_						:    TPos     ,					lowercase_						:    TPos	)		->	Tuple:




  '''simple docstring'''



  return abs(p[0] - goal[0]	) + abs(p[1] - goal[1]	)




def 	UpperCamelCase   (       lowercase_						:    TPos     ,					lowercase_						:    int     ,					lowercase_						:    TPos     ,					lowercase_						:    dict[TPos, float]	)		->	str:




  '''simple docstring'''



  lowercase									=g_function[start] + Wa * heuristics[i](SCREAMING_SNAKE_CASE_     ,					SCREAMING_SNAKE_CASE_	)
  return ans




def 	UpperCamelCase   (       lowercase_						:    Union[str, Any]     ,					lowercase_						:    str     ,					lowercase_						:    Dict	)		->	Dict:




  '''simple docstring'''



  lowercase									=np.chararray((n, n)	)
  for i in range(SCREAMING_SNAKE_CASE_	):
    for j in range(SCREAMING_SNAKE_CASE_	):
      lowercase									='''*'''

  for i in range(SCREAMING_SNAKE_CASE_	):
    for j in range(SCREAMING_SNAKE_CASE_	):
      if (j, (n - 1) - i) in blocks:
        lowercase									='''#'''

  lowercase									='''-'''
  lowercase									=back_pointer[goal]
  while x != start:
    ((lowercase)							, (lowercase))									=x
    # print(x)
    lowercase									='''-'''
    lowercase									=back_pointer[x]
  lowercase									='''-'''

  for i in range(SCREAMING_SNAKE_CASE_	):
    for j in range(SCREAMING_SNAKE_CASE_	):
      if (i, j) == (0, n - 1):
        print(grid[i][j]     ,					end=''' '''	)
        print('''<-- End position'''     ,					end=''' '''	)
      else:
        print(grid[i][j]     ,					end=''' '''	)
    print()
  print('''^'''	)
  print('''Start position'''	)
  print()
  print('''# is an obstacle'''	)
  print('''- is the path taken by algorithm'''	)
  print('''PATH TAKEN BY THE ALGORITHM IS:-'''	)
  lowercase									=back_pointer[goal]
  while x != start:
    print(SCREAMING_SNAKE_CASE_     ,					end=''' '''	)
    lowercase									=back_pointer[x]
  print(SCREAMING_SNAKE_CASE_	)
  sys.exit()




def 	UpperCamelCase   (       lowercase_						:    TPos	)		->	Tuple:




  '''simple docstring'''



  if p[0] < 0 or p[0] > n - 1:
    return False
  if p[1] < 0 or p[1] > n - 1:
    return False
  return True




def 	UpperCamelCase   (       lowercase_						:    Dict     ,					lowercase_						:    Optional[Any]     ,					lowercase_						:    List[str]     ,					lowercase_						:    Dict     ,					lowercase_						:    Optional[int]     ,					lowercase_						:    Optional[Any]     ,					lowercase_						:    int     ,					lowercase_						:    List[Any]     ,					)		->	List[Any]:




  '''simple docstring'''



  for itera in range(SCREAMING_SNAKE_CASE_	):
    open_list[itera].remove_element(SCREAMING_SNAKE_CASE_	)
  # print("s", s)
  # print("j", j)
  ((lowercase)							, (lowercase))									=s
  lowercase									=(x - 1, y)
  lowercase									=(x + 1, y)
  lowercase									=(x, y + 1)
  lowercase									=(x, y - 1)

  for neighbours in [left, right, up, down]:
    if neighbours not in blocks:
      if valid(SCREAMING_SNAKE_CASE_	) and neighbours not in visited:
        # print("neighbour", neighbours)
        visited.add(SCREAMING_SNAKE_CASE_	)
        lowercase									=-1
        lowercase									=float('''inf'''	)

      if valid(SCREAMING_SNAKE_CASE_	) and g_function[neighbours] > g_function[s] + 1:
        lowercase									=g_function[s] + 1
        lowercase									=s
        if neighbours not in close_list_anchor:
          open_list[0].put(SCREAMING_SNAKE_CASE_     ,					key(SCREAMING_SNAKE_CASE_     ,					0     ,					SCREAMING_SNAKE_CASE_     ,					SCREAMING_SNAKE_CASE_	)	)
          if neighbours not in close_list_inad:
            for var in range(1     ,					SCREAMING_SNAKE_CASE_	):
              if key(SCREAMING_SNAKE_CASE_     ,					SCREAMING_SNAKE_CASE_     ,					SCREAMING_SNAKE_CASE_     ,					SCREAMING_SNAKE_CASE_	) <= Wa * key(
                  SCREAMING_SNAKE_CASE_     ,					0     ,					SCREAMING_SNAKE_CASE_     ,					SCREAMING_SNAKE_CASE_	):
                open_list[j].put(
                    SCREAMING_SNAKE_CASE_     ,					key(SCREAMING_SNAKE_CASE_     ,					SCREAMING_SNAKE_CASE_     ,					SCREAMING_SNAKE_CASE_     ,					SCREAMING_SNAKE_CASE_	)	)




def 	UpperCamelCase   (       )		->	Any:




  '''simple docstring'''



  lowercase									=[]
  for x in range(1     ,					5	):
    for y in range(1     ,					6	):
      some_list.append((x, y)	)

  for x in range(1_5     ,					2_0	):
    some_list.append((x, 1_7)	)

  for x in range(1_0     ,					1_9	):
    for y in range(1     ,					1_5	):
      some_list.append((x, y)	)

    # L block
  for x in range(1     ,					4	):
    for y in range(1_2     ,					1_9	):
      some_list.append((x, y)	)
  for x in range(3     ,					1_3	):
    for y in range(1_6     ,					1_9	):
      some_list.append((x, y)	)
  return some_list


_UpperCAmelCase  :		int  =		{0: consistent_heuristic, 1: heuristic_a, 2: heuristic_a}

_UpperCAmelCase  :		Tuple  =		[
    (0, 1),
    (1, 1),
    (2, 1),
    (3, 1),
    (4, 1),
    (5, 1),
    (6, 1),
    (7, 1),
    (8, 1),
    (9, 1),
    (10, 1),
    (11, 1),
    (12, 1),
    (13, 1),
    (14, 1),
    (15, 1),
    (16, 1),
    (17, 1),
    (18, 1),
    (19, 1),
]
_UpperCAmelCase  :		Dict  =		make_common_ground()


_UpperCAmelCase  :		Any  =		blocks_blk
# hyper parameters
_UpperCAmelCase  :		Any  =		1
_UpperCAmelCase  :		Optional[int]  =		1
_UpperCAmelCase  :		Optional[int]  =		20
_UpperCAmelCase  :		List[Any]  =		3  # one consistent and two other inconsistent

# start and end destination
_UpperCAmelCase  :		Dict  =		(0, 0)
_UpperCAmelCase  :		Optional[int]  =		(n - 1, n - 1)

_UpperCAmelCase  :		str  =		1




def 	UpperCamelCase   (       lowercase_						:    TPos     ,					lowercase_						:    TPos     ,					lowercase_						:    int	)		->	Union[str, Any]:




  '''simple docstring'''



  lowercase									={start: 0, goal: float('''inf'''	)}
  lowercase									={start: -1, goal: -1}
  lowercase									=[]
  lowercase									=set()

  for i in range(SCREAMING_SNAKE_CASE_	):
    open_list.append(PriorityQueue()	)
    open_list[i].put(SCREAMING_SNAKE_CASE_     ,					key(SCREAMING_SNAKE_CASE_     ,					SCREAMING_SNAKE_CASE_     ,					SCREAMING_SNAKE_CASE_     ,					SCREAMING_SNAKE_CASE_	)	)

  lowercase									=[]
  lowercase									=[]
  while open_list[0].minkey() < float('''inf'''	):
    for i in range(1     ,					SCREAMING_SNAKE_CASE_	):
      # print(open_list[0].minkey(), open_list[i].minkey())
      if open_list[i].minkey() <= Wa * open_list[0].minkey():
        global t
        t += 1
        if g_function[goal] <= open_list[i].minkey():
          if g_function[goal] < float('''inf'''	):
            do_something(SCREAMING_SNAKE_CASE_     ,					SCREAMING_SNAKE_CASE_     ,					SCREAMING_SNAKE_CASE_	)
        else:
          lowercase							, lowercase									=open_list[i].top_show()
          visited.add(SCREAMING_SNAKE_CASE_	)
          expand_state(
              SCREAMING_SNAKE_CASE_     ,					SCREAMING_SNAKE_CASE_     ,					SCREAMING_SNAKE_CASE_     ,					SCREAMING_SNAKE_CASE_     ,					SCREAMING_SNAKE_CASE_     ,					SCREAMING_SNAKE_CASE_     ,					SCREAMING_SNAKE_CASE_     ,					SCREAMING_SNAKE_CASE_     ,					)
          close_list_inad.append(SCREAMING_SNAKE_CASE_	)
      else:
        if g_function[goal] <= open_list[0].minkey():
          if g_function[goal] < float('''inf'''	):
            do_something(SCREAMING_SNAKE_CASE_     ,					SCREAMING_SNAKE_CASE_     ,					SCREAMING_SNAKE_CASE_	)
        else:
          lowercase									=open_list[0].top_show()
          visited.add(SCREAMING_SNAKE_CASE_	)
          expand_state(
              SCREAMING_SNAKE_CASE_     ,					0     ,					SCREAMING_SNAKE_CASE_     ,					SCREAMING_SNAKE_CASE_     ,					SCREAMING_SNAKE_CASE_     ,					SCREAMING_SNAKE_CASE_     ,					SCREAMING_SNAKE_CASE_     ,					SCREAMING_SNAKE_CASE_     ,					)
          close_list_anchor.append(SCREAMING_SNAKE_CASE_	)
  print('''No path found to goal'''	)
  print()
  for i in range(n - 1     ,					-1     ,					-1	):
    for j in range(SCREAMING_SNAKE_CASE_	):
      if (j, i) in blocks:
        print('''#'''     ,					end=''' '''	)
      elif (j, i) in back_pointer:
        if (j, i) == (n - 1, n - 1):
          print('''*'''     ,					end=''' '''	)
        else:
          print('''-'''     ,					end=''' '''	)
      else:
        print('''*'''     ,					end=''' '''	)
      if (j, i) == (n - 1, n - 1):
        print('''<-- End position'''     ,					end=''' '''	)
    print()
  print('''^'''	)
  print('''Start position'''	)
  print()
  print('''# is an obstacle'''	)
  print('''- is the path taken by algorithm'''	)


if __name__ == "__main__":
     multi_a_star(start, goal, n_heuristic)







import baseaa
def      A__       (    SCREAMING_SNAKE_CASE_   :      str						)  ->  bytes:






   """simple docstring"""







   return baseaa.baaencode(string.encode('''utf-8'''						)						)
def      A__       (    SCREAMING_SNAKE_CASE_   :      bytes						)  ->  str:






   """simple docstring"""







   return baseaa.baadecode(SCREAMING_SNAKE_CASE_						).decode('''utf-8'''						)


if __name__ == "__main__":
   UpperCAmelCase_           =	"Hello World!"
   UpperCAmelCase_           =	baseaa_encode(test)
   print(encoded)

   UpperCAmelCase_           =	baseaa_decode(encoded)
   print(decoded)