




"""simple docstring"""




import heapq
import sys

import numpy as np

lowerCAmelCase							:    Optional[int]  							=							tuple[int, int]






class 					__magic_name__							:






				'''simple docstring'''





				def __init__( self				):





							"""simple docstring"""
							lowerCamelCase       =      []
							lowerCamelCase       =      set()





				def      _lowerCAmelCase       ( self				):





							"""simple docstring"""
							if not self.empty():
										return self.elements[0][0]
							else:
										return float("""inf"""				)





				def      _lowerCAmelCase       ( self				):





							"""simple docstring"""
							return len(self.elements				) == 0





				def      _lowerCAmelCase       ( self	,				_a	,				_a				):





							"""simple docstring"""
							if item not in self.set:
										heapq.heappush(self.elements	,				(priority, item)				)
										self.set.add(_a				)
							else:
										# update
										# print("update", item)
										lowerCamelCase       =      []
										((lowerCamelCase)   ,     (lowerCamelCase))       =      heapq.heappop(self.elements				)
										while x != item:
													temp.append((pri, x)				)
													((lowerCamelCase)   ,     (lowerCamelCase))       =      heapq.heappop(self.elements				)
										temp.append((priority, item)				)
										for pro, xxx in temp:
													heapq.heappush(self.elements	,				(pro, xxx)				)





				def      _lowerCAmelCase       ( self	,				_a				):





							"""simple docstring"""
							if item in self.set:
										self.set.remove(_a				)
										lowerCamelCase       =      []
										((lowerCamelCase)   ,     (lowerCamelCase))       =      heapq.heappop(self.elements				)
										while x != item:
													temp.append((pro, x)				)
													((lowerCamelCase)   ,     (lowerCamelCase))       =      heapq.heappop(self.elements				)
										for prito, yyy in temp:
													heapq.heappush(self.elements	,				(prito, yyy)				)





				def      _lowerCAmelCase       ( self				):





							"""simple docstring"""
							return self.elements[0][1]





				def      _lowerCAmelCase       ( self				):





							"""simple docstring"""
							((lowerCamelCase)   ,     (lowerCamelCase))       =      heapq.heappop(self.elements				)
							self.set.remove(_a				)
							return (priority, item)




def 					a__				(       snake_case__ ,				snake_case__       )		->      Dict:
			# euclidean distance
			lowerCamelCase       =      np.array(snake_case__       )
			lowerCamelCase       =      np.array(snake_case__       )
			return np.linalg.norm(a - b       )



def 					a__				(       snake_case__ ,				snake_case__       )		->      Any:
			# integer division by time variable
			return consistent_heuristic(snake_case__ ,				snake_case__       ) // t



def 					a__				(       snake_case__ ,				snake_case__       )		->      Optional[int]:
			# manhattan distance
			return abs(p[0] - goal[0]       ) + abs(p[1] - goal[1]       )



def 					a__				(       snake_case__ ,				snake_case__ ,				snake_case__ ,				snake_case__       )		->      List[str]:
			lowerCamelCase       =      g_function[start] + Wa * heuristics[i](snake_case__ ,				snake_case__       )
			return ans



def 					a__				(       snake_case__ ,				snake_case__ ,				snake_case__       )		->      Union[str, Any]:
			lowerCamelCase       =      np.chararray((n, n)       )
			for i in range(snake_case__       ):
						for j in range(snake_case__       ):
									lowerCamelCase       =      """*"""

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

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

			for i in range(snake_case__       ):
						for j in range(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:-"""       )
			lowerCamelCase       =      back_pointer[goal]
			while x != start:
						print(snake_case__ ,				end=""" """       )
						lowerCamelCase       =      back_pointer[x]
			print(snake_case__       )
			sys.exit()



def 					a__				(       snake_case__       )		->      Any:
			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__ ,				snake_case__ ,				snake_case__ ,				snake_case__ ,				snake_case__ ,				snake_case__ ,				snake_case__ ,				snake_case__ ,				)		->      str:
			for itera in range(snake_case__       ):
						open_list[itera].remove_element(snake_case__       )
			# print("s", s)
			# print("j", j)
			((lowerCamelCase)   ,     (lowerCamelCase))       =      s
			lowerCamelCase       =      (x - 1, y)
			lowerCamelCase       =      (x + 1, y)
			lowerCamelCase       =      (x, y + 1)
			lowerCamelCase       =      (x, y - 1)

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

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



def 					a__				(       )		->      Optional[int]:
			lowerCamelCase       =      []
			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


lowerCAmelCase							:    Tuple  							=							{0: consistent_heuristic, 1: heuristic_a, 2: heuristic_a}

lowerCAmelCase							:    Union[str, Any]  							=							[
    (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),
]
lowerCAmelCase							:    List[Any]  							=							make_common_ground()


lowerCAmelCase							:    Union[str, Any]  							=							blocks_blk
# hyper parameters
lowerCAmelCase							:    int  							=							1
lowerCAmelCase							:    Any  							=							1
lowerCAmelCase							:    Union[str, Any]  							=							20
lowerCAmelCase							:    List[Any]  							=							3  # one consistent and two other inconsistent

# start and end destination
lowerCAmelCase							:    str  							=							(0, 0)
lowerCAmelCase							:    List[Any]  							=							(n - 1, n - 1)

lowerCAmelCase							:    Tuple  							=							1



def 					a__				(       snake_case__ ,				snake_case__ ,				snake_case__       )		->      List[Any]:
			lowerCamelCase       =      {start: 0, goal: float("""inf"""       )}
			lowerCamelCase       =      {start: -1, goal: -1}
			lowerCamelCase       =      []
			lowerCamelCase       =      set()

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

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









"""simple docstring"""




from functools import lru_cache



def 					a__				(       snake_case__       )		->      set:
			lowerCamelCase       =      2
			lowerCamelCase       =      set()
			while i * i <= n:
						if n % i:
									i += 1
						else:
									n //= i
									factors.add(snake_case__       )
			if n > 1:
						factors.add(snake_case__       )
			return factors



@lru_cache
def 					a__				(       snake_case__       )		->      int:
			return len(unique_prime_factors(snake_case__       )       )



def 					a__				(       snake_case__       )		->      bool:
			return len(set(snake_case__       )       ) in (0, 1)



def 					a__				(       snake_case__       )		->      list:
			lowerCamelCase       =      2

			while True:
						# Increment each value of a generated range
						lowerCamelCase       =      [base + i for i in range(snake_case__       )]

						# Run elements through out unique_prime_factors function
						# Append our target number to the end.
						lowerCamelCase       =      [upf_len(snake_case__       ) for x in group]
						checker.append(snake_case__       )

						# If all numbers in the list are equal, return the group variable.
						if equality(snake_case__       ):
									return group

						# Increment our base variable by 1
						base += 1



def 					a__				(       snake_case__ = 4       )		->      int:
			lowerCamelCase       =      run(snake_case__       )
			return results[0] if len(snake_case__       ) else None


if __name__ == "__main__":
					print(solution())



