
import heapq
import sys

import numpy as np

__a  			=					tuple[int, int]
class  lowercase__:



	"""simple docstring"""




	def __init__(       self  :			Any       )       ->     List[str]:
					lowercase_       =					[]
					lowercase_       =					set()
	def 						_lowercase  (       self  :			int       )       ->     Tuple:
					if not self.empty():
									return self.elements[0][0]
					else:
									return float('''inf'''       )
	def 						_lowercase  (       self  :			Dict       )       ->     List[Any]:
					return len(self.elements       ) == 0
	def 						_lowercase  (       self  :			Any       ,							SCREAMING_SNAKE_CASE_  :			Optional[Any]       ,							SCREAMING_SNAKE_CASE_  :			Union[str, Any]       )       ->     Any:
					if item not in self.set:
									heapq.heappush(self.elements       ,							(priority, item)       )
									self.set.add(SCREAMING_SNAKE_CASE_       )
					else:
									# update
									# print("update", item)
									lowercase_       =					[]
									(lowercase_)       =					heapq.heappop(self.elements       )
									while x != item:
													temp.append((pri, x)       )
													(lowercase_)       =					heapq.heappop(self.elements       )
									temp.append((priority, item)       )
									for pro, xxx in temp:
													heapq.heappush(self.elements       ,							(pro, xxx)       )
	def 						_lowercase  (       self  :			Union[str, Any]       ,							SCREAMING_SNAKE_CASE_  :			int       )       ->     List[Any]:
					if item in self.set:
									self.set.remove(SCREAMING_SNAKE_CASE_       )
									lowercase_       =					[]
									(lowercase_)       =					heapq.heappop(self.elements       )
									while x != item:
													temp.append((pro, x)       )
													(lowercase_)       =					heapq.heappop(self.elements       )
									for prito, yyy in temp:
													heapq.heappush(self.elements       ,							(prito, yyy)       )
	def 						_lowercase  (       self  :			str       )       ->     Optional[int]:
					return self.elements[0][1]




	def 						_lowercase  (       self  :			Tuple       )       ->     List[Any]:
					(lowercase_)       =					heapq.heappop(self.elements       )
					self.set.remove(SCREAMING_SNAKE_CASE_       )
					return (priority, item)




def 				a						(							snake_case__:					TPos						,   snake_case__:					TPos					):


				'''simple docstring'''
				lowercase_       =					np.array(_lowerCamelCase					)
				lowercase_       =					np.array(_lowerCamelCase					)
				return np.linalg.norm(a - b					)




def 				a						(							snake_case__:					TPos						,   snake_case__:					TPos					):


				'''simple docstring'''
				return consistent_heuristic(_lowerCamelCase						,   _lowerCamelCase					) // t




def 				a						(							snake_case__:					TPos						,   snake_case__:					TPos					):


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




def 				a						(							snake_case__:					TPos						,   snake_case__:					int						,   snake_case__:					TPos						,   snake_case__:					dict[TPos, float]					):


				'''simple docstring'''
				lowercase_       =					g_function[start] + Wa * heuristics[i](_lowerCamelCase						,   _lowerCamelCase					)
				return ans




def 				a						(							snake_case__:					Optional[Any]						,   snake_case__:					List[str]						,   snake_case__:					int					):


				'''simple docstring'''
				lowercase_       =					np.chararray((n, n)					)
				for i in range(_lowerCamelCase					):
								for j in range(_lowerCamelCase					):
												lowercase_       =					"*"

				for i in range(_lowerCamelCase					):
								for j in range(_lowerCamelCase					):
												if (j, (n - 1) - i) in blocks:
																lowercase_       =					"#"

				lowercase_       =					"-"
				lowercase_       =					back_pointer[goal]
				while x != start:
								(lowercase_)       =					x
								# print(x)
								lowercase_       =					"-"
								lowercase_       =					back_pointer[x]
				lowercase_       =					"-"

				for i in range(_lowerCamelCase					):
								for j in range(_lowerCamelCase					):
												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(_lowerCamelCase						,   end=''' '''					)
								lowercase_       =					back_pointer[x]
				print(_lowerCamelCase					)
				sys.exit()




def 				a						(							snake_case__:					TPos					):


				'''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 				a						(							snake_case__:					Optional[Any]						,   snake_case__:					Dict						,   snake_case__:					Union[str, Any]						,   snake_case__:					str						,   snake_case__:					str						,   snake_case__:					Any						,   snake_case__:					Any						,   snake_case__:					Optional[int]						,   ):


				'''simple docstring'''





				for itera in range(_lowerCamelCase					):
								open_list[itera].remove_element(_lowerCamelCase					)
				# print("s", s)
				# print("j", j)
				(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(_lowerCamelCase					) and neighbours not in visited:
																# print("neighbour", neighbours)
																visited.add(_lowerCamelCase					)
																lowercase_       =					-1
																lowercase_       =					float('''inf'''					)

												if valid(_lowerCamelCase					) 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(_lowerCamelCase						,   key(_lowerCamelCase						,   0						,   _lowerCamelCase						,   _lowerCamelCase					)					)
																				if neighbours not in close_list_inad:
																								for var in range(1						,   _lowerCamelCase					):
																												if key(_lowerCamelCase						,   _lowerCamelCase						,   _lowerCamelCase						,   _lowerCamelCase					) <= Wa * key(
																												    _lowerCamelCase						,   0						,   _lowerCamelCase						,   _lowerCamelCase					):
																																open_list[j].put(
																																    _lowerCamelCase						,   key(_lowerCamelCase						,   _lowerCamelCase						,   _lowerCamelCase						,   _lowerCamelCase					)					)




def 				a						(							):


				'''simple docstring'''
				lowercase_       =					[]
				for x in range(1						,   5					):
								for y in range(1						,   6					):
												some_list.append((x, y)					)

				for x in range(15						,   20					):
								some_list.append((x, 17)					)

				for x in range(10						,   19					):
								for y in range(1						,   15					):
												some_list.append((x, y)					)

    # L block
				for x in range(1						,   4					):
								for y in range(12						,   19					):
												some_list.append((x, y)					)
				for x in range(3						,   13					):
								for y in range(16						,   19					):
												some_list.append((x, y)					)
				return some_list


__a  			=					{0: consistent_heuristic, 1: heuristic_a, 2: heuristic_a}

__a  			=					[
    (0, 1),
    (1, 1),
    (2, 1),
    (3, 1),
    (4, 1),
    (5, 1),
    (6, 1),
    (7, 1),
    (8, 1),
    (9, 1),
    (1_0, 1),
    (1_1, 1),
    (1_2, 1),
    (1_3, 1),
    (1_4, 1),
    (1_5, 1),
    (1_6, 1),
    (1_7, 1),
    (1_8, 1),
    (1_9, 1),
]
__a  			=					make_common_ground()


__a  			=					blocks_blk
# hyper parameters
__a  			=					1
__a  			=					1
__a  			=					2_0
__a  			=					3  # one consistent and two other inconsistent

# start and end destination
__a  			=					(0, 0)
__a  			=					(n - 1, n - 1)

__a  			=					1




def 				a						(							snake_case__:					TPos						,   snake_case__:					TPos						,   snake_case__:					int					):


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

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

				lowercase_       =					[]
				lowercase_       =					[]
				while open_list[0].minkey() < float('''inf'''					):
								for i in range(1						,   _lowerCamelCase					):
												# 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(_lowerCamelCase						,   _lowerCamelCase						,   _lowerCamelCase					)
																else:
																				lowercase_       =					open_list[i].top_show()
																				visited.add(_lowerCamelCase					)
																				expand_state(
																				    _lowerCamelCase						,   _lowerCamelCase						,   _lowerCamelCase						,   _lowerCamelCase						,   _lowerCamelCase						,   _lowerCamelCase						,   _lowerCamelCase						,   _lowerCamelCase						,   )
																				close_list_inad.append(_lowerCamelCase					)
												else:
																if g_function[goal] <= open_list[0].minkey():
																				if g_function[goal] < float('''inf'''					):
																								do_something(_lowerCamelCase						,   _lowerCamelCase						,   _lowerCamelCase					)
																else:
																				lowercase_       =					open_list[0].top_show()
																				visited.add(_lowerCamelCase					)
																				expand_state(
																				    _lowerCamelCase						,   0						,   _lowerCamelCase						,   _lowerCamelCase						,   _lowerCamelCase						,   _lowerCamelCase						,   _lowerCamelCase						,   _lowerCamelCase						,   )
																				close_list_anchor.append(_lowerCamelCase					)
				print('''No path found to goal'''					)
				print()
				for i in range(n - 1						,   -1						,   -1					):
								for j in range(_lowerCamelCase					):
												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)






from __future__ import annotations

import sys
from collections import deque
from typing import Generic, TypeVar

lowercase  :					Optional[Any]													=       TypeVar('T')




class  lowerCamelCase__							(				Generic[T]):




	'''simple docstring'''




	_A								=     42  # Cache store of keys
	_A								=     42  # References of the keys in cache
	_A								=     1_0  # Maximum capacity of cache







	def __init__(					self		:Optional[Any]     ,   a		:int						)		-> None:
								__UpperCamelCase	:   Union[str, Any]			   =					deque()
								__UpperCamelCase	:   str			   =					set()
								if not n:
															__UpperCamelCase	:   Union[str, Any]			   =					sys.maxsize
								elif n < 0:
															raise ValueError("n should be an integer greater than 0."						)
								else:
															__UpperCamelCase	:   Any			   =					n







	def    _lowerCamelCase				(					self		:Tuple     ,   a		:T						)		-> None:
								if x not in self.key_reference:
															if len(self.dq_store						) == LRUCache._MAX_CAPACITY:
																						__UpperCamelCase	:   int			   =					self.dq_store.pop()
																						self.key_reference.remove(a						)
								else:
															self.dq_store.remove(a						)

								self.dq_store.appendleft(a						)
								self.key_reference.add(a						)







	def    _lowerCamelCase				(					self		:Any						)		-> None:
								for k in self.dq_store:
															print(a						)







	def __repr__(					self		:Tuple						)		-> str:
								return f'LRUCache({self._MAX_CAPACITY}) => {list(self.dq_store						)}'


if __name__ == "__main__":
		import doctest

		doctest.testmod()

		lowercase  :					LRUCache[str | int]													=       LRUCache(4)
		lru_cache.refer('A')
		lru_cache.refer(2)
		lru_cache.refer(3)
		lru_cache.refer('A')
		lru_cache.refer(4)
		lru_cache.refer(5)
		lru_cache.display()

		print(lru_cache)
		assert str(lru_cache) == "LRUCache(4) => [5, 4, 'A', 3]"