



import heapq
import sys

import numpy as np

__snake_case						:Tuple      		=     tuple[int, int]

class     _A       :



       def __init__(		self							:     List[str]):


           '''simple docstring'''

           __a						       =				[]
           __a						       =				set()



       def 		_lowerCamelCase			(		self							:     List[str]):


           '''simple docstring'''

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



       def 		_lowerCamelCase			(		self							:     Optional[Any]):


           '''simple docstring'''

           return len(self.elements) == 0



       def 		_lowerCamelCase			(		self							:     Optional[Any]     ,		__SCREAMING_SNAKE_CASE							:     int     ,		__SCREAMING_SNAKE_CASE							:     Any):


           '''simple docstring'''

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



       def 		_lowerCamelCase			(		self							:     List[Any]     ,		__SCREAMING_SNAKE_CASE							:     Optional[int]):


           '''simple docstring'''

           if item in self.set:
               self.set.remove(__UpperCamelCase)
               __a						       =				[]
               ((__a)       ,   (__a))						       =				heapq.heappop(self.elements)
               while x != item:
                   temp.append((pro, x))
                   ((__a)       ,   (__a))						       =				heapq.heappop(self.elements)
               for prito, yyy in temp:
                   heapq.heappush(self.elements     ,		(prito, yyy))



       def 		_lowerCamelCase			(		self							:     List[Any]):


           '''simple docstring'''

           return self.elements[0][1]





       def 		_lowerCamelCase			(		self							:     str):


           '''simple docstring'''

           ((__a)       ,   (__a))						       =				heapq.heappop(self.elements)
           self.set.remove(__UpperCamelCase)
           return (priority, item)





def      __snake_case	(			_UpperCAmelCase   , _UpperCAmelCase				):
    # euclidean distance
    __a						       =				np.array(_UpperCAmelCase				)
    __a						       =				np.array(_UpperCAmelCase				)
    return np.linalg.norm(a - b				)





def      __snake_case	(			_UpperCAmelCase   , _UpperCAmelCase				):
    # integer division by time variable
    return consistent_heuristic(_UpperCAmelCase   , _UpperCAmelCase				) // t





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





def      __snake_case	(			_UpperCAmelCase   , _UpperCAmelCase   , _UpperCAmelCase   , _UpperCAmelCase				):
    __a						       =				g_function[start] + Wa * heuristics[i](_UpperCAmelCase   , _UpperCAmelCase				)
    return ans





def      __snake_case	(			_UpperCAmelCase   , _UpperCAmelCase   , _UpperCAmelCase				):
    __a						       =				np.chararray((n, n)				)
    for i in range(_UpperCAmelCase				):
        for j in range(_UpperCAmelCase				):
            __a						       =				'''*'''

    for i in range(_UpperCAmelCase				):
        for j in range(_UpperCAmelCase				):
            if (j, (n - 1) - i) in blocks:
                __a						       =				'''#'''

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

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





def      __snake_case	(			_UpperCAmelCase				):
    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      __snake_case	(			_UpperCAmelCase   , _UpperCAmelCase   , _UpperCAmelCase   , _UpperCAmelCase   , _UpperCAmelCase   , _UpperCAmelCase   , _UpperCAmelCase   , _UpperCAmelCase   , ):
    for itera in range(_UpperCAmelCase				):
        open_list[itera].remove_element(_UpperCAmelCase				)
    # print("s", s)
    # print("j", j)
    ((__a)       ,   (__a))						       =				s
    __a						       =				(x - 1, y)
    __a						       =				(x + 1, y)
    __a						       =				(x, y + 1)
    __a						       =				(x, y - 1)

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

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





def      __snake_case	(			):
    __a						       =				[]
    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


__snake_case						:Any      		=     {0: consistent_heuristic, 1: heuristic_a, 2: heuristic_a}

__snake_case						:List[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),
]
__snake_case						:int      		=     make_common_ground()


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

# start and end destination
__snake_case						:Tuple      		=     (0, 0)
__snake_case						:Tuple      		=     (n - 1, n - 1)

__snake_case						:str      		=     1





def      __snake_case	(			_UpperCAmelCase   , _UpperCAmelCase   , _UpperCAmelCase				):
    __a						       =				{start: 0, goal: float('''inf'''				)}
    __a						       =				{start: -1, goal: -1}
    __a						       =				[]
    __a						       =				set()

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

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

import torch
from torch import nn
from torch.distributions import (
    AffineTransform,
    Distribution,
    Independent,
    NegativeBinomial,
    Normal,
    StudentT,
    TransformedDistribution,
)






class 					_UpperCAmelCase   (	lowercase_ ):


					def __init__(					self			:int     ,       __UpperCamelCase			:Distribution     ,       __UpperCamelCase			:Dict=None     ,       __UpperCamelCase			:Optional[int]=None     ,       __UpperCamelCase			:List[str]=0		):
												A		=  1.0 if scale is None else scale
												A		=  0.0 if loc is None else loc

												super().__init__(__UpperCamelCase     ,       [AffineTransform(loc=self.loc     ,       scale=self.scale     ,       event_dim=__UpperCamelCase		)]		)


					@property
					def 	lowerCamelCase       (					self			:Any		):
												return self.base_dist.mean * self.scale + self.loc


					@property
					def 	lowerCamelCase       (					self			:Optional[int]		):
												return self.base_dist.variance * self.scale**2


					@property
					def 	lowerCamelCase       (					self			:Dict		):
												return self.variance.sqrt()







class 					_UpperCAmelCase   (	nn.Module ):


					def __init__(					self			:Dict     ,       __UpperCamelCase			:int     ,       __UpperCamelCase			:Dict[str, int]     ,       __UpperCamelCase			:Callable[..., Tuple[torch.Tensor]]     ,       **__UpperCamelCase			:str		):
												super().__init__(**__UpperCamelCase		)
												A		=  args_dim
												A		=  nn.ModuleList([nn.Linear(__UpperCamelCase     ,       __UpperCamelCase		) for dim in args_dim.values()]		)
												A		=  domain_map


					def 	lowerCamelCase       (					self			:int     ,       __UpperCamelCase			:torch.Tensor		):
												A		=  [proj(__UpperCamelCase		) for proj in self.proj]

												return self.domain_map(*__UpperCamelCase		)







class 					_UpperCAmelCase   (	nn.Module ):


					def __init__(					self			:Dict     ,       __UpperCamelCase			:int		):
												super().__init__()
												A		=  function


					def 	lowerCamelCase       (					self			:List[str]     ,       __UpperCamelCase			:Any     ,       *__UpperCamelCase			:Any		):
												return self.function(__UpperCamelCase     ,       *__UpperCamelCase		)







class 					_UpperCAmelCase   :
					UpperCamelCase      =							42
					UpperCamelCase      =							42
					UpperCamelCase      =							42


					def __init__(					self			:Any     ,       __UpperCamelCase			:int = 1		):
												A		=  dim
												A		=  {k: dim * self.args_dim[k] for k in self.args_dim}


					def 	lowerCamelCase       (					self			:List[Any]     ,       __UpperCamelCase			:Dict		):
												if self.dim == 1:
																			return self.distribution_class(*__UpperCamelCase		)
												else:
																			return Independent(self.distribution_class(*__UpperCamelCase		)     ,       1		)


					def 	lowerCamelCase       (					self			:int     ,       __UpperCamelCase			:List[str]     ,       __UpperCamelCase			:Optional[torch.Tensor] = None     ,       __UpperCamelCase			:Optional[torch.Tensor] = None     ,       ):
												A		=  self._base_distribution(__UpperCamelCase		)
												if loc is None and scale is None:
																			return distr
												else:
																			return AffineTransformed(__UpperCamelCase     ,       loc=__UpperCamelCase     ,       scale=__UpperCamelCase     ,       event_dim=self.event_dim		)


					@property
					def 	lowerCamelCase       (					self			:List[Any]		):
												return () if self.dim == 1 else (self.dim,)


					@property
					def 	lowerCamelCase       (					self			:Tuple		):
												return len(self.event_shape		)


					@property
					def 	lowerCamelCase       (					self			:int		):
												return 0.0


					def 	lowerCamelCase       (					self			:str     ,       __UpperCamelCase			:int		):
												return ParameterProjection(
												    in_features=__UpperCamelCase     ,       args_dim=self.args_dim     ,       domain_map=LambdaLayer(self.domain_map		)     ,       )


					def 	lowerCamelCase       (					self			:List[Any]     ,       *__UpperCamelCase			:torch.Tensor		):
												raise NotImplementedError()


					@staticmethod
					def 	lowerCamelCase       (					__UpperCamelCase			:torch.Tensor		):
												return (x + torch.sqrt(torch.square(__UpperCamelCase		) + 4.0		)) / 2.0







class 					_UpperCAmelCase   (	lowercase_ ):
					UpperCamelCase      =							{"df": 1, "loc": 1, "scale": 1}
					UpperCamelCase      =							StudentT


					@classmethod
					def 	lowerCamelCase       (					cls			:List[str]     ,       __UpperCamelCase			:torch.Tensor     ,       __UpperCamelCase			:torch.Tensor     ,       __UpperCamelCase			:torch.Tensor		):
												A		=  cls.squareplus(__UpperCamelCase		).clamp_min(torch.finfo(scale.dtype		).eps		)
												A		=  2.0 + cls.squareplus(__UpperCamelCase		)
												return df.squeeze(-1		), loc.squeeze(-1		), scale.squeeze(-1		)







class 					_UpperCAmelCase   (	lowercase_ ):
					UpperCamelCase      =							{"loc": 1, "scale": 1}
					UpperCamelCase      =							Normal


					@classmethod
					def 	lowerCamelCase       (					cls			:List[Any]     ,       __UpperCamelCase			:torch.Tensor     ,       __UpperCamelCase			:torch.Tensor		):
												A		=  cls.squareplus(__UpperCamelCase		).clamp_min(torch.finfo(scale.dtype		).eps		)
												return loc.squeeze(-1		), scale.squeeze(-1		)







class 					_UpperCAmelCase   (	lowercase_ ):
					UpperCamelCase      =							{"total_count": 1, "logits": 1}
					UpperCamelCase      =							NegativeBinomial


					@classmethod
					def 	lowerCamelCase       (					cls			:str     ,       __UpperCamelCase			:torch.Tensor     ,       __UpperCamelCase			:torch.Tensor		):
												A		=  cls.squareplus(__UpperCamelCase		)
												return total_count.squeeze(-1		), logits.squeeze(-1		)


					def 	lowerCamelCase       (					self			:Tuple     ,       __UpperCamelCase			:List[str]		):
												A,	A		=  distr_args
												if self.dim == 1:
																			return self.distribution_class(total_count=__UpperCamelCase     ,       logits=__UpperCamelCase		)
												else:
																			return Independent(self.distribution_class(total_count=__UpperCamelCase     ,       logits=__UpperCamelCase		)     ,       1		)


					def 	lowerCamelCase       (					self			:List[str]     ,       __UpperCamelCase			:str     ,       __UpperCamelCase			:Optional[torch.Tensor] = None     ,       __UpperCamelCase			:Optional[torch.Tensor] = None		):
												A,	A		=  distr_args

												if scale is not None:
																			# See scaling property of Gamma.
																			logits += scale.log()

												return self._base_distribution((total_count, logits)		)


