



'''simple docstring'''





import heapq
import sys

import numpy as np

_lowerCAmelCase 		=      tuple[int, int]






class 			lowerCAmelCase_:
  '''simple docstring'''




  def __init__(       self )       ->						Any:
      lowerCAmelCase__					:    Optional[Any]				 =   []
      lowerCAmelCase__					:    int				 =   set()




  def 				UpperCAmelCase_      (       self )       ->						str:
      if not self.empty():
          return self.elements[0][0]
      else:
          return float("""inf""" )




  def 				UpperCAmelCase_      (       self )       ->						Any:
      return len(self.elements ) == 0




  def 				UpperCAmelCase_      (       self    ,__UpperCAmelCase    ,__UpperCAmelCase )       ->						Union[str, Any]:
      if item not in self.set:
          heapq.heappush(self.elements    ,(priority, item) )
          self.set.add(__SCREAMING_SNAKE_CASE )
      else:
          # update
          # print("update", item)
          lowerCAmelCase__					:    Any				 =   []
          (lowerCAmelCase__)					:    Any				 =   heapq.heappop(self.elements )
          while x != item:
              temp.append((pri, x) )
              (lowerCAmelCase__)					:    Optional[Any]				 =   heapq.heappop(self.elements )
          temp.append((priority, item) )
          for pro, xxx in temp:
              heapq.heappush(self.elements    ,(pro, xxx) )




  def 				UpperCAmelCase_      (       self    ,__UpperCAmelCase )       ->						Dict:
      if item in self.set:
          self.set.remove(__SCREAMING_SNAKE_CASE )
          lowerCAmelCase__					:    str				 =   []
          (lowerCAmelCase__)					:    Union[str, Any]				 =   heapq.heappop(self.elements )
          while x != item:
              temp.append((pro, x) )
              (lowerCAmelCase__)					:    Dict				 =   heapq.heappop(self.elements )
          for prito, yyy in temp:
              heapq.heappush(self.elements    ,(prito, yyy) )




  def 				UpperCAmelCase_      (       self )       ->						List[Any]:
      return self.elements[0][1]






  def 				UpperCAmelCase_      (       self )       ->						List[Any]:
      (lowerCAmelCase__)					:    Union[str, Any]				 =   heapq.heappop(self.elements )
      self.set.remove(__SCREAMING_SNAKE_CASE )
      return (priority, item)







def   _SCREAMING_SNAKE_CASE    (			UpperCamelCase				,       UpperCamelCase     ):



    """simple docstring"""





    lowerCAmelCase__					:    List[str]				 =   np.array(__A     )
    lowerCAmelCase__					:    Tuple				 =   np.array(__A     )
    return np.linalg.norm(a - b     )
def   _SCREAMING_SNAKE_CASE    (			UpperCamelCase				,       UpperCamelCase     ):



    """simple docstring"""





    return consistent_heuristic(__A				,       __A     ) // t
def   _SCREAMING_SNAKE_CASE    (			UpperCamelCase				,       UpperCamelCase     ):



    """simple docstring"""





    return abs(p[0] - goal[0]     ) + abs(p[1] - goal[1]     )
def   _SCREAMING_SNAKE_CASE    (			UpperCamelCase				,       UpperCamelCase				,       UpperCamelCase				,       UpperCamelCase     ):



    """simple docstring"""





    lowerCAmelCase__					:    Tuple				 =   g_function[start] + Wa * heuristics[i](__A				,       __A     )
    return ans
def   _SCREAMING_SNAKE_CASE    (			UpperCamelCase				,       UpperCamelCase				,       UpperCamelCase     ):



    """simple docstring"""





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

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

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

    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__					:    List[Any]				 =   back_pointer[goal]
    while x != start:
        print(__A				,       end=""" """     )
        lowerCAmelCase__					:    Dict				 =   back_pointer[x]
    print(__A     )
    sys.exit()
def   _SCREAMING_SNAKE_CASE    (			UpperCamelCase     ):



    """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   _SCREAMING_SNAKE_CASE    (			UpperCamelCase				,       UpperCamelCase				,       UpperCamelCase				,       UpperCamelCase				,       UpperCamelCase				,       UpperCamelCase				,       UpperCamelCase				,       UpperCamelCase				,       ):



    """simple docstring"""





    for itera in range(__A     ):
        open_list[itera].remove_element(__A     )
    # print("s", s)
    # print("j", j)
    (lowerCAmelCase__)					:    List[Any]				 =   s
    lowerCAmelCase__					:    List[Any]				 =   (x - 1, y)
    lowerCAmelCase__					:    Optional[Any]				 =   (x + 1, y)
    lowerCAmelCase__					:    Dict				 =   (x, y + 1)
    lowerCAmelCase__					:    Optional[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__					:    List[Any]				 =   -1
                lowerCAmelCase__					:    List[str]				 =   float("""inf"""     )

            if valid(__A     ) and g_function[neighbours] > g_function[s] + 1:
                lowerCAmelCase__					:    Dict				 =   g_function[s] + 1
                lowerCAmelCase__					:    List[str]				 =   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    (			):



    """simple docstring"""





    lowerCAmelCase__					:    str				 =   []
    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 		=      {0: consistent_heuristic, 1: heuristic_a, 2: heuristic_a}

_lowerCAmelCase 		=      [
    (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 		=      make_common_ground()


_lowerCAmelCase 		=      blocks_blk
# hyper parameters
_lowerCAmelCase 		=      1
_lowerCAmelCase 		=      1
_lowerCAmelCase 		=      20
_lowerCAmelCase 		=      3  # one consistent and two other inconsistent

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

_lowerCAmelCase 		=      1
def   _SCREAMING_SNAKE_CASE    (			UpperCamelCase				,       UpperCamelCase				,       UpperCamelCase     ):



    """simple docstring"""





    lowerCAmelCase__					:    List[str]				 =   {start: 0, goal: float("""inf"""     )}
    lowerCAmelCase__					:    Union[str, Any]				 =   {start: -1, goal: -1}
    lowerCAmelCase__					:    int				 =   []
    lowerCAmelCase__					:    List[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__					:    Optional[Any]				 =   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__					:    List[str]				 =   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'''







import math





def 		_UpperCAmelCase (				__A				: int   ):
				a_		:	str									=   []
				a_		:	Tuple									=   2
				a_		:	Optional[Any]									=   int(math.sqrt(__A   )   )  # Size of every segment
				a_		:	Optional[Any]									=   [True] * (end + 1)
				a_		:	Union[str, Any]									=   []

				while start <= end:
								if temp[start] is True:
												in_prime.append(__A   )
												for i in range(start * start    ,		end + 1    ,		__A   ):
																a_		:	List[Any]									=   False
								start += 1
				prime += in_prime

				a_		:	Any									=   end + 1
				a_		:	Optional[Any]									=   min(2 * end    ,		__A   )

				while low <= n:
								a_		:	Optional[Any]									=   [True] * (high - low + 1)
								for each in in_prime:
												a_		:	Any									=   math.floor(low / each   ) * each
												if t < low:
																t += each

												for j in range(__A    ,		high + 1    ,		__A   ):
																a_		:	Union[str, Any]									=   False

								for j in range(len(__A   )   ):
												if temp[j] is True:
																prime.append(j + low   )

								a_		:	Tuple									=   high + 1
								a_		:	str									=   min(high + end    ,		__A   )

				return prime




print(sieve(10**6))




