
"""simple docstring"""




import heapq
import sys

import numpy as np

_A			:       Dict   		=       tuple[int, int]

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

   def 			__magic_name__			(			self				):
          ((lowercase)		,    (lowercase))    :				int       		=							heapq.heappop(self.elements				)
          self.set.remove(_a				)
          return (priority, item)


def   __magic_name__	(      __snake_case				:       TPos     , __snake_case				:       TPos  ) ->				List[Any]:
       # euclidean distance
       lowercase    :				Optional[Any]       		=							np.array(__snake_case  )
       lowercase    :				List[Any]       		=							np.array(__snake_case  )
       return np.linalg.norm(a - b  )


def   __magic_name__	(      __snake_case				:       TPos     , __snake_case				:       TPos  ) ->				Union[str, Any]:
       # integer division by time variable
       return consistent_heuristic(__snake_case     , __snake_case  ) // t


def   __magic_name__	(      __snake_case				:       TPos     , __snake_case				:       TPos  ) ->				List[str]:
       # manhattan distance
       return abs(p[0] - goal[0]  ) + abs(p[1] - goal[1]  )


def   __magic_name__	(      __snake_case				:       TPos     , __snake_case				:       int     , __snake_case				:       TPos     , __snake_case				:       dict[TPos, float]  ) ->				List[str]:
       lowercase    :				Tuple       		=							g_function[start] + Wa * heuristics[i](__snake_case     , __snake_case  )
       return ans


def   __magic_name__	(      __snake_case				:       Any     , __snake_case				:       str     , __snake_case				:       Tuple  ) ->				Optional[int]:
       lowercase    :				Union[str, Any]       		=							np.chararray((n, n)  )
       for i in range(__snake_case  ):
              for j in range(__snake_case  ):
                     lowercase    :				str       		=							"*"

       for i in range(__snake_case  ):
              for j in range(__snake_case  ):
                     if (j, (n - 1) - i) in blocks:
                            lowercase    :				Any       		=							"#"

       lowercase    :				str       		=							"-"
       lowercase    :				str       		=							back_pointer[goal]
       while x != start:
              ((lowercase)		,    (lowercase))    :				Any       		=							x
              # print(x)
              lowercase    :				Union[str, Any]       		=							"-"
              lowercase    :				Union[str, Any]       		=							back_pointer[x]
       lowercase    :				Any       		=							"-"

       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:-"  )
       lowercase    :				Tuple       		=							back_pointer[goal]
       while x != start:
              print(__snake_case     , end=" "  )
              lowercase    :				int       		=							back_pointer[x]
       print(__snake_case  )
       sys.exit()


def   __magic_name__	(      __snake_case				:       TPos  ) ->				str:
       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   __magic_name__	(      __snake_case				:       List[str]     , __snake_case				:       List[str]     , __snake_case				:       Any     , __snake_case				:       Optional[int]     , __snake_case				:       int     , __snake_case				:       List[Any]     , __snake_case				:       Optional[Any]     , __snake_case				:       Optional[Any]     , ) ->				Any:
       for itera in range(__snake_case  ):
              open_list[itera].remove_element(__snake_case  )
       # print("s", s)
       # print("j", j)
       ((lowercase)		,    (lowercase))    :				Optional[int]       		=							s
       lowercase    :				Tuple       		=							(x - 1, y)
       lowercase    :				List[Any]       		=							(x + 1, y)
       lowercase    :				Union[str, Any]       		=							(x, y + 1)
       lowercase    :				Any       		=							(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  )
                            lowercase    :				List[Any]       		=							-1
                            lowercase    :				Dict       		=							float("inf"  )

                     if valid(__snake_case  ) and g_function[neighbours] > g_function[s] + 1:
                            lowercase    :				Optional[int]       		=							g_function[s] + 1
                            lowercase    :				Tuple       		=							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   __magic_name__	(      ) ->				int:
       lowercase    :				int       		=							[]
       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			:       int   		=       {0: consistent_heuristic, 1: heuristic_a, 2: heuristic_a}

_A			:       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),
]
_A			:       Any   		=       make_common_ground()


_A			:       List[Any]   		=       blocks_blk
# hyper parameters
_A			:       Tuple   		=       1
_A			:       Dict   		=       1
_A			:       Dict   		=       20
_A			:       List[str]   		=       3  # one consistent and two other inconsistent

# start and end destination
_A			:       int   		=       (0, 0)
_A			:       int   		=       (n - 1, n - 1)

_A			:       List[Any]   		=       1


def   __magic_name__	(      __snake_case				:       TPos     , __snake_case				:       TPos     , __snake_case				:       int  ) ->				List[str]:
       lowercase    :				str       		=							{start: 0, goal: float("inf"  )}
       lowercase    :				str       		=							{start: -1, goal: -1}
       lowercase    :				List[str]       		=							[]
       lowercase    :				Tuple       		=							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  )  )

       lowercase    :				list[int]       		=							[]
       lowercase    :				list[int]       		=							[]
       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:
                                   lowercase		,    lowercase    :				List[Any]       		=							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:
                                   lowercase    :				Dict       		=							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 __future__ import annotations

from functools import lru_cache
from math import ceil

_A			:       Optional[Any]   		=       1_00

_A			:       Optional[int]   		=       set(range(3, NUM_PRIMES, 2))
primes.add(2)
_A			:       int

for prime in range(3, ceil(NUM_PRIMES**0.5), 2):
   if prime not in primes:
      continue
   primes.difference_update(set(range(prime * prime, NUM_PRIMES, prime)))


@lru_cache(maxsize=100  )
def   __magic_name__	(      __snake_case				:       int  ) ->				set[int]:
       if number_to_partition < 0:
              return set()
       elif number_to_partition == 0:
              return {1}

       lowercase    :				set[int]       		=							set()
       lowercase    :				int
       lowercase    :				int

       for prime in primes:
              if prime > number_to_partition:
                     continue
              for sub in partition(number_to_partition - prime  ):
                     ret.add(sub * prime  )

       return ret


def   __magic_name__	(      __snake_case				:       int = 5000  ) ->				int | None:
       for number_to_partition in range(1     , __snake_case  ):
              if len(partition(__snake_case  )  ) > number_unique_partitions:
                     return number_to_partition
       return None


if __name__ == "__main__":
   print(F"{solution() = }")


