

"""simple docstring"""





import heapq
import sys

import numpy as np

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







class 							SCREAMING_SNAKE_CASE   :






					"""simple docstring"""



					def __init__(			self     :							Any						):
						lowerCAmelCase__      :		List[str]    							=      []
						lowerCAmelCase__      :		Any    							=      set()







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







					def 			__lowerCAmelCase					(			self     :							str						):
						return len(self.elements						) == 0







					def 			__lowerCAmelCase					(			self     :							Any  ,lowercase_     :							int  ,lowercase_     :							Optional[Any]						):
						if item not in self.set:
							heapq.heappush(self.elements  ,(priority, item)						)
							self.set.add(lowercase_						)
						else:
							# update
							# print("update", item)
							lowerCAmelCase__      :		Tuple    							=      []
							((lowerCAmelCase__)							,(lowerCAmelCase__))      :		Dict    							=      heapq.heappop(self.elements						)
							while x != item:
								temp.append((pri, x)						)
								((lowerCAmelCase__)							,(lowerCAmelCase__))      :		Any    							=      heapq.heappop(self.elements						)
							temp.append((priority, item)						)
							for pro, xxx in temp:
								heapq.heappush(self.elements  ,(pro, xxx)						)







					def 			__lowerCAmelCase					(			self     :							Optional[int]  ,lowercase_     :							Union[str, Any]						):
						if item in self.set:
							self.set.remove(lowercase_						)
							lowerCAmelCase__      :		List[str]    							=      []
							((lowerCAmelCase__)							,(lowerCAmelCase__))      :		List[Any]    							=      heapq.heappop(self.elements						)
							while x != item:
								temp.append((pro, x)						)
								((lowerCAmelCase__)							,(lowerCAmelCase__))      :		str    							=      heapq.heappop(self.elements						)
							for prito, yyy in temp:
								heapq.heappush(self.elements  ,(prito, yyy)						)







					def 			__lowerCAmelCase					(			self     :							Optional[Any]						):
						return self.elements[0][1]







					def 			__lowerCAmelCase					(			self     :							Any						):
						((lowerCAmelCase__)							,(lowerCAmelCase__))      :		Optional[Any]    							=      heapq.heappop(self.elements						)
						self.set.remove(lowercase_						)
						return (priority, item)

def     __SCREAMING_SNAKE_CASE    ( A_		,	A_					):
	# euclidean distance
	lowerCAmelCase__      :		Dict    							=      np.array(A_					)
	lowerCAmelCase__      :		Optional[int]    							=      np.array(A_					)
	return np.linalg.norm(a - b					)

def     __SCREAMING_SNAKE_CASE    ( A_		,	A_					):
	# integer division by time variable
	return consistent_heuristic(A_		,	A_					) // t

def     __SCREAMING_SNAKE_CASE    ( A_		,	A_					):
	# manhattan distance
	return abs(p[0] - goal[0]					) + abs(p[1] - goal[1]					)

def     __SCREAMING_SNAKE_CASE    ( A_		,	A_		,	A_		,	A_					):
	lowerCAmelCase__      :		Optional[int]    							=      g_function[start] + Wa * heuristics[i](A_		,	A_					)
	return ans

def     __SCREAMING_SNAKE_CASE    ( A_		,	A_		,	A_					):
	lowerCAmelCase__      :		Tuple    							=      np.chararray((n, n)					)
	for i in range(A_					):
		for j in range(A_					):
			lowerCAmelCase__      :		Any    							=      '''*'''

	for i in range(A_					):
		for j in range(A_					):
			if (j, (n - 1) - i) in blocks:
				lowerCAmelCase__      :		Any    							=      '''#'''

	lowerCAmelCase__      :		Optional[Any]    							=      '''-'''
	lowerCAmelCase__      :		str    							=      back_pointer[goal]
	while x != start:
		((lowerCAmelCase__)							,(lowerCAmelCase__))      :		List[Any]    							=      x
		# print(x)
		lowerCAmelCase__      :		Optional[Any]    							=      '''-'''
		lowerCAmelCase__      :		Optional[Any]    							=      back_pointer[x]
	lowerCAmelCase__      :		Optional[int]    							=      '''-'''

	for i in range(A_					):
		for j in range(A_					):
			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:-'''					)
	lowerCAmelCase__      :		str    							=      back_pointer[goal]
	while x != start:
		print(A_		,	end=''' '''					)
		lowerCAmelCase__      :		str    							=      back_pointer[x]
	print(A_					)
	sys.exit()

def     __SCREAMING_SNAKE_CASE    ( A_					):
	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     __SCREAMING_SNAKE_CASE    ( A_		,	A_		,	A_		,	A_		,	A_		,	A_		,	A_		,	A_		,	):
	for itera in range(A_					):
		open_list[itera].remove_element(A_					)
	# print("s", s)
	# print("j", j)
	((lowerCAmelCase__)							,(lowerCAmelCase__))      :		Optional[int]    							=      s
	lowerCAmelCase__      :		str    							=      (x - 1, y)
	lowerCAmelCase__      :		List[Any]    							=      (x + 1, y)
	lowerCAmelCase__      :		Optional[Any]    							=      (x, y + 1)
	lowerCAmelCase__      :		Union[str, Any]    							=      (x, y - 1)

	for neighbours in [left, right, up, down]:
		if neighbours not in blocks:
			if valid(A_					) and neighbours not in visited:
				# print("neighbour", neighbours)
				visited.add(A_					)
				lowerCAmelCase__      :		Union[str, Any]    							=      -1
				lowerCAmelCase__      :		Tuple    							=      float('''inf'''					)

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

def     __SCREAMING_SNAKE_CASE    ( ):
	lowerCAmelCase__      :		Tuple    							=      []
	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


__UpperCamelCase    : List[Any]				 =						{0: consistent_heuristic, 1: heuristic_a, 2: heuristic_a}

__UpperCamelCase    : Dict				 =						[
    (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),
]
__UpperCamelCase    : Optional[int]				 =						make_common_ground()


__UpperCamelCase    : List[str]				 =						blocks_blk
# hyper parameters
__UpperCamelCase    : Optional[int]				 =						1
__UpperCamelCase    : Tuple				 =						1
__UpperCamelCase    : Union[str, Any]				 =						2_0
__UpperCamelCase    : Optional[int]				 =						3  # one consistent and two other inconsistent

# start and end destination
__UpperCamelCase    : Tuple				 =						(0, 0)
__UpperCamelCase    : Optional[Any]				 =						(n - 1, n - 1)

__UpperCamelCase    : Union[str, Any]				 =						1

def     __SCREAMING_SNAKE_CASE    ( A_		,	A_		,	A_					):
	lowerCAmelCase__      :		str    							=      {start: 0, goal: float('''inf'''					)}
	lowerCAmelCase__      :		Tuple    							=      {start: -1, goal: -1}
	lowerCAmelCase__      :		Optional[Any]    							=      []
	lowerCAmelCase__      :		Optional[Any]    							=      set()

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

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







"""simple docstring"""





def     __SCREAMING_SNAKE_CASE    ( A_					):
	for i in range(len(A_					) - 1		,	0		,	-1					):
		lowerCAmelCase__      :		Optional[Any]    							=      False

		for j in range(A_		,	0		,	-1					):
			if unsorted[j] < unsorted[j - 1]:
				lowerCAmelCase__							,lowerCAmelCase__      :		Union[str, Any]    							=      unsorted[j - 1], unsorted[j]
				lowerCAmelCase__      :		Dict    							=      True

		for j in range(A_					):
			if unsorted[j] > unsorted[j + 1]:
				lowerCAmelCase__							,lowerCAmelCase__      :		Union[str, Any]    							=      unsorted[j + 1], unsorted[j]
				lowerCAmelCase__      :		Any    							=      True

		if not swapped:
			break
	return unsorted


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							__UpperCamelCase    : int				 =						input('''Enter numbers separated by a comma:\n''').strip()
							__UpperCamelCase    : Optional[Any]				 =						[int(item) for item in user_input.split(''',''')]
							print(F'''{cocktail_shaker_sort(unsorted) = }''')




