
import math
import sys


class 		__magic_name__   :





		def __init__(							self    :	Any				):
				lowerCAmelCase		:					int  	=     0
				lowerCAmelCase		:					str  	=     []
				lowerCAmelCase		:					Optional[Any]  	=     {}  # To store the pos of node in array





		def       _A							(							self    :	List[Any]				):
				return self.cur_size == 0





		def       _A							(							self    :	Tuple						,  lowerCamelCase__    :	List[str]				):
				lowerCAmelCase		:					Any  	=     self.left(lowerCamelCase__				)
				lowerCAmelCase		:					Dict  	=     self.right(lowerCamelCase__				)
				if lc < self.cur_size and self.array(lowerCamelCase__				)[0] < self.array(lowerCamelCase__				)[0]:
						lowerCAmelCase		:					List[str]  	=     lc
				else:
						lowerCAmelCase		:					Any  	=     idx
				if rc < self.cur_size and self.array(lowerCamelCase__				)[0] < self.array(lowerCamelCase__				)[0]:
						lowerCAmelCase		:					Tuple  	=     rc
				if smallest != idx:
						self.swap(lowerCamelCase__						,  lowerCamelCase__				)
						self.min_heapify(lowerCamelCase__				)





		def       _A							(							self    :	Any						,  lowerCamelCase__    :	int				):
				# Inserts a node into the Priority Queue
				lowerCAmelCase		:					int  	=     self.cur_size
				self.cur_size += 1
				self.array.append((sys.maxsize, tup[1])				)
				self.decrease_key((sys.maxsize, tup[1])						,  tup[0]				)





		def       _A							(							self    :	Tuple				):
				# Removes and returns the min element at top of priority queue
				lowerCAmelCase		:					Optional[int]  	=     self.array[0][1]
				lowerCAmelCase		:					int  	=     self.array[self.cur_size - 1]
				self.cur_size -= 1
				self.min_heapify(1				)
				del self.pos[min_node]
				return min_node





		def       _A							(							self    :	Optional[Any]						,  lowerCamelCase__    :	str				):
				# returns the index of left child
				return 2 * i + 1





		def       _A							(							self    :	Dict						,  lowerCamelCase__    :	List[str]				):
				# returns the index of right child
				return 2 * i + 2





		def       _A							(							self    :	Dict						,  lowerCamelCase__    :	Optional[Any]				):
				# returns the index of parent
				return math.floor(i / 2				)





		def       _A							(							self    :	Tuple						,  lowerCamelCase__    :	List[str]						,  lowerCamelCase__    :	Any				):
				# swaps array elements at indices i and j
				# update the pos{}
				lowerCAmelCase		:					Optional[Any]  	=     j
				lowerCAmelCase		:					str  	=     i
				lowerCAmelCase		:					List[Any]  	=     self.array[i]
				lowerCAmelCase		:					Optional[Any]  	=     self.array[j]
				lowerCAmelCase		:					Any  	=     temp





		def       _A							(							self    :	Any						,  lowerCamelCase__    :	Any						,  lowerCamelCase__    :	int				):
				lowerCAmelCase		:					Dict  	=     self.pos[tup[1]]
				# assuming the new_d is atmost old_d
				lowerCAmelCase		:					int  	=     (new_d, tup[1])
				while idx > 0 and self.array[self.par(lowerCamelCase__				)][0] > self.array[idx][0]:
						self.swap(lowerCamelCase__						,  self.par(lowerCamelCase__				)				)
						lowerCAmelCase		:					Tuple  	=     self.par(lowerCamelCase__				)



class 		__magic_name__   :





		def __init__(							self    :	Tuple						,  lowerCamelCase__    :	Any				):
				lowerCAmelCase		:					List[Any]  	=     {}  # To store graph: u -> (v,w)
				lowerCAmelCase		:					Optional[Any]  	=     num  # Number of nodes in graph
				# To store the distance from source vertex
				lowerCAmelCase		:					Union[str, Any]  	=     [0] * self.num_nodes
				lowerCAmelCase		:					Dict  	=     [-1] * self.num_nodes  # To store the path





		def       _A							(							self    :	Optional[Any]						,  lowerCamelCase__    :	int						,  lowerCamelCase__    :	Dict						,  lowerCamelCase__    :	Union[str, Any]				):
				#  Edge going from node u to v and v to u with weight w
				# u (w)-> v, v (w) -> u
				# Check if u already in graph
				if u in self.adjList:
						self.adjList[u].append((v, w)				)
				else:
						lowerCAmelCase		:					Optional[int]  	=     [(v, w)]

				# Assuming undirected graph
				if v in self.adjList:
						self.adjList[v].append((u, w)				)
				else:
						lowerCAmelCase		:					List[Any]  	=     [(u, w)]





		def       _A							(							self    :	Dict				):
				# u -> v(w)
				for u in self.adjList:
						print(lowerCamelCase__						,  '''->'''						,  ''' -> '''.join(str(f'''{v}({w})'''				) for v, w in self.adjList[u]				)				)





		def       _A							(							self    :	Optional[int]						,  lowerCamelCase__    :	Dict				):
				# Flush old junk values in par[]
				lowerCAmelCase		:					Optional[int]  	=     [-1] * self.num_nodes
				# src is the source node
				lowerCAmelCase		:					Optional[Any]  	=     0
				lowerCAmelCase		:					Any  	=     PriorityQueue()
				q.insert((0, src)				)  # (dist from src, node)
				for u in self.adjList:
						if u != src:
								lowerCAmelCase		:					Dict  	=     sys.maxsize  # Infinity
								lowerCAmelCase		:					List[Any]  	=     -1

				while not q.is_empty():
						lowerCAmelCase		:					str  	=     q.extract_min()  # Returns node with the min dist from source
						# Update the distance of all the neighbours of u and
						# if their prev dist was INFINITY then push them in Q
						for v, w in self.adjList[u]:
								lowerCAmelCase		:					Tuple  	=     self.dist[u] + w
								if self.dist[v] > new_dist:
										if self.dist[v] == sys.maxsize:
												q.insert((new_dist, v)				)
										else:
												q.decrease_key((self.dist[v], v)						,  lowerCamelCase__				)
										lowerCAmelCase		:					Tuple  	=     new_dist
										lowerCAmelCase		:					List[str]  	=     u

        # Show the shortest distances from src
				self.show_distances(lowerCamelCase__				)





		def       _A							(							self    :	str						,  lowerCamelCase__    :	Any				):
				print(f'''Distance from node: {src}'''				)
				for u in range(self.num_nodes				):
						print(f'''Node {u} has distance: {self.dist[u]}'''				)





		def       _A							(							self    :	Optional[Any]						,  lowerCamelCase__    :	int						,  lowerCamelCase__    :	Any				):
				# To show the shortest path from src to dest
				# WARNING: Use it *after* calling dijkstra
				lowerCAmelCase		:					List[Any]  	=     []
				lowerCAmelCase		:					Union[str, Any]  	=     0
				lowerCAmelCase		:					List[str]  	=     dest
				# Backtracking from dest to src
				while self.par[temp] != -1:
						path.append(lowerCamelCase__				)
						if temp != src:
								for v, w in self.adjList[temp]:
										if v == self.par[temp]:
												cost += w
												break
						lowerCAmelCase		:					str  	=     self.par[temp]
				path.append(lowerCamelCase__				)
				path.reverse()

				print(f'''----Path to reach {dest} from {src}----'''				)
				for u in path:
						print(f'''{u}'''						,  end=''' '''				)
						if u != dest:
								print('''-> '''						,  end=''''''				)

				print('''\nTotal cost of path: '''						,  lowerCamelCase__				)


if __name__ == "__main__":
		__SCREAMING_SNAKE_CASE			:   List[str]         =     Graph(9)
		graph.add_edge(0, 1, 4)
		graph.add_edge(0, 7, 8)
		graph.add_edge(1, 2, 8)
		graph.add_edge(1, 7, 11)
		graph.add_edge(2, 3, 7)
		graph.add_edge(2, 8, 2)
		graph.add_edge(2, 5, 4)
		graph.add_edge(3, 4, 9)
		graph.add_edge(3, 5, 14)
		graph.add_edge(4, 5, 10)
		graph.add_edge(5, 6, 2)
		graph.add_edge(6, 7, 1)
		graph.add_edge(6, 8, 6)
		graph.add_edge(7, 8, 7)
		graph.show_graph()
		graph.dijkstra(0)
		graph.show_path(0, 4)

# OUTPUT
# 0 -> 1(4) -> 7(8)
# 1 -> 0(4) -> 2(8) -> 7(11)
# 7 -> 0(8) -> 1(11) -> 6(1) -> 8(7)
# 2 -> 1(8) -> 3(7) -> 8(2) -> 5(4)
# 3 -> 2(7) -> 4(9) -> 5(14)
# 8 -> 2(2) -> 6(6) -> 7(7)
# 5 -> 2(4) -> 3(14) -> 4(10) -> 6(2)
# 4 -> 3(9) -> 5(10)
# 6 -> 5(2) -> 7(1) -> 8(6)
# Distance from node: 0
# Node 0 has distance: 0
# Node 1 has distance: 4
# Node 2 has distance: 12
# Node 3 has distance: 19
# Node 4 has distance: 21
# Node 5 has distance: 11
# Node 6 has distance: 9
# Node 7 has distance: 8
# Node 8 has distance: 14
# ----Path to reach 4 from 0----
# 0 -> 7 -> 6 -> 5 -> 4
# Total cost of path:  21


from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available, is_vision_available


__SCREAMING_SNAKE_CASE			:   str         =     {
    'configuration_deta': ['DETA_PRETRAINED_CONFIG_ARCHIVE_MAP', 'DetaConfig'],
}

try:
		if not is_vision_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		__SCREAMING_SNAKE_CASE			:   Optional[int]         =     ['DetaImageProcessor']

try:
		if not is_torch_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		__SCREAMING_SNAKE_CASE			:   str         =     [
		    'DETA_PRETRAINED_MODEL_ARCHIVE_LIST',
		    'DetaForObjectDetection',
		    'DetaModel',
		    'DetaPreTrainedModel',
		]


if TYPE_CHECKING:
		from .configuration_deta import DETA_PRETRAINED_CONFIG_ARCHIVE_MAP, DetaConfig

		try:
				if not is_vision_available():
						raise OptionalDependencyNotAvailable()
		except OptionalDependencyNotAvailable:
				pass
		else:
				from .image_processing_deta import DetaImageProcessor

		try:
				if not is_torch_available():
						raise OptionalDependencyNotAvailable()
		except OptionalDependencyNotAvailable:
				pass
		else:
				from .modeling_deta import (
				    DETA_PRETRAINED_MODEL_ARCHIVE_LIST,
				    DetaForObjectDetection,
				    DetaModel,
				    DetaPreTrainedModel,
				)

else:
		import sys

		__SCREAMING_SNAKE_CASE			:   Dict         =     _LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)
