





import math
import sys






class  __A   :

			'''simple docstring'''







			def __init__(   self							):



				'''simple docstring'''







				lowerCamelCase__        =		0
				lowerCamelCase__        =		[]
				lowerCamelCase__        =		{}  # To store the pos of node in array





			def 		__lowerCamelCase    (   self							):



				'''simple docstring'''







				return self.cur_size == 0





			def 		__lowerCamelCase    (   self	,  __lowerCAmelCase							):



				'''simple docstring'''







				lowerCamelCase__        =		self.left(_UpperCAmelCase							)
				lowerCamelCase__        =		self.right(_UpperCAmelCase							)
				if lc < self.cur_size and self.array(_UpperCAmelCase							)[0] < self.array(_UpperCAmelCase							)[0]:
					lowerCamelCase__        =		lc
				else:
					lowerCamelCase__        =		idx
				if rc < self.cur_size and self.array(_UpperCAmelCase							)[0] < self.array(_UpperCAmelCase							)[0]:
					lowerCamelCase__        =		rc
				if smallest != idx:
					self.swap(_UpperCAmelCase	,  _UpperCAmelCase							)
					self.min_heapify(_UpperCAmelCase							)





			def 		__lowerCamelCase    (   self	,  __lowerCAmelCase							):



				'''simple docstring'''







				lowerCamelCase__        =		self.cur_size
				self.cur_size += 1
				self.array.append((sys.maxsize, tup[1])							)
				self.decrease_key((sys.maxsize, tup[1])	,  tup[0]							)





			def 		__lowerCamelCase    (   self							):



				'''simple docstring'''







				lowerCamelCase__        =		self.array[0][1]
				lowerCamelCase__        =		self.array[self.cur_size - 1]
				self.cur_size -= 1
				self.min_heapify(1							)
				del self.pos[min_node]
				return min_node





			def 		__lowerCamelCase    (   self	,  __lowerCAmelCase							):



				'''simple docstring'''







				return 2 * i + 1





			def 		__lowerCamelCase    (   self	,  __lowerCAmelCase							):



				'''simple docstring'''







				return 2 * i + 2





			def 		__lowerCamelCase    (   self	,  __lowerCAmelCase							):



				'''simple docstring'''







				return math.floor(i / 2							)





			def 		__lowerCamelCase    (   self	,  __lowerCAmelCase	,  __lowerCAmelCase							):



				'''simple docstring'''







				lowerCamelCase__        =		j
				lowerCamelCase__        =		i
				lowerCamelCase__        =		self.array[i]
				lowerCamelCase__        =		self.array[j]
				lowerCamelCase__        =		temp





			def 		__lowerCamelCase    (   self	,  __lowerCAmelCase	,  __lowerCAmelCase							):



				'''simple docstring'''







				lowerCamelCase__        =		self.pos[tup[1]]
				# assuming the new_d is atmost old_d
				lowerCamelCase__        =		(new_d, tup[1])
				while idx > 0 and self.array[self.par(_UpperCAmelCase							)][0] > self.array[idx][0]:
					self.swap(_UpperCAmelCase	,  self.par(_UpperCAmelCase							)							)
					lowerCamelCase__        =		self.par(_UpperCAmelCase							)






class  __A   :

			'''simple docstring'''







			def __init__(   self	,  __lowerCAmelCase							):



				'''simple docstring'''







				lowerCamelCase__        =		{}  # To store graph: u -> (v,w)
				lowerCamelCase__        =		num  # Number of nodes in graph
				# To store the distance from source vertex
				lowerCamelCase__        =		[0] * self.num_nodes
				lowerCamelCase__        =		[-1] * self.num_nodes  # To store the path





			def 		__lowerCamelCase    (   self	,  __lowerCAmelCase	,  __lowerCAmelCase	,  __lowerCAmelCase							):



				'''simple docstring'''







				if u in self.adjList:
					self.adjList[u].append((v, w)							)
				else:
					lowerCamelCase__        =		[(v, w)]

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





			def 		__lowerCamelCase    (   self							):



				'''simple docstring'''







				for u in self.adjList:
					print(_UpperCAmelCase	,  '''->'''	,  ''' -> '''.join(str(F'{v}({w})'							) for v, w in self.adjList[u]							)							)





			def 		__lowerCamelCase    (   self	,  __lowerCAmelCase							):



				'''simple docstring'''







				lowerCamelCase__        =		[-1] * self.num_nodes
				# src is the source node
				lowerCamelCase__        =		0
				lowerCamelCase__        =		PriorityQueue()
				q.insert((0, src)							)  # (dist from src, node)
				for u in self.adjList:
					if u != src:
						lowerCamelCase__        =		sys.maxsize  # Infinity
						lowerCamelCase__        =		-1

				while not q.is_empty():
					lowerCamelCase__        =		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__        =		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)	,  _UpperCAmelCase							)
							lowerCamelCase__        =		new_dist
							lowerCamelCase__        =		u

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





			def 		__lowerCamelCase    (   self	,  __lowerCAmelCase							):



				'''simple docstring'''







				print(F'Distance from node: {src}'							)
				for u in range(self.num_nodes							):
					print(F'Node {u} has distance: {self.dist[u]}'							)





			def 		__lowerCamelCase    (   self	,  __lowerCAmelCase	,  __lowerCAmelCase							):



				'''simple docstring'''







				lowerCamelCase__        =		[]
				lowerCamelCase__        =		0
				lowerCamelCase__        =		dest
				# Backtracking from dest to src
				while self.par[temp] != -1:
					path.append(_UpperCAmelCase							)
					if temp != src:
						for v, w in self.adjList[temp]:
							if v == self.par[temp]:
								cost += w
								break
					lowerCamelCase__        =		self.par[temp]
				path.append(_UpperCAmelCase							)
				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: '''	,  _UpperCAmelCase							)


if __name__ == "__main__":
			snake_case__									=				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 ...configuration_utils import PretrainedConfig
from ...utils import logging


_a									=				logging.get_logger(__name__)

_a									=				{
    "google/pegasus-x-base": "https://huggingface.co/google/pegasus-x-base/resolve/main/config.json",
    "google/pegasus-x-large": "https://huggingface.co/google/pegasus-x-large/resolve/main/config.json",
    # See all PEGASUS-X models at https://huggingface.co/models?filter=pegasus-x
}






class  __A   (   lowerCAmelCase			):

			'''simple docstring'''







			lowerCAmelCase_												=						"""pegasus_x"""
			lowerCAmelCase_												=						["""past_key_values"""]
			lowerCAmelCase_												=						{"""num_attention_heads""": """encoder_attention_heads""", """hidden_size""": """d_model"""}





			def __init__(   self	,  __lowerCAmelCase=9_6_1_0_3	,  __lowerCAmelCase=1_6_3_8_4	,  __lowerCAmelCase=1_6	,  __lowerCAmelCase=4_0_9_6	,  __lowerCAmelCase=1_6	,  __lowerCAmelCase=1_6	,  __lowerCAmelCase=4_0_9_6	,  __lowerCAmelCase=1_6	,  __lowerCAmelCase=0.0	,  __lowerCAmelCase=0.0	,  __lowerCAmelCase=True	,  __lowerCAmelCase=True	,  __lowerCAmelCase="gelu"	,  __lowerCAmelCase=1_0_2_4	,  __lowerCAmelCase=0.1	,  __lowerCAmelCase=0.0	,  __lowerCAmelCase=0.0	,  __lowerCAmelCase=0.02	,  __lowerCAmelCase=0	,  __lowerCAmelCase=True	,  __lowerCAmelCase=0	,  __lowerCAmelCase=1	,  __lowerCAmelCase=1	,  __lowerCAmelCase=3_2	,  __lowerCAmelCase=5_1_2	,  __lowerCAmelCase=True	,  **__lowerCAmelCase	,  ):



				'''simple docstring'''







				lowerCamelCase__        =		vocab_size
				lowerCamelCase__        =		max_position_embeddings
				lowerCamelCase__        =		d_model
				lowerCamelCase__        =		encoder_ffn_dim
				lowerCamelCase__        =		encoder_layers
				lowerCamelCase__        =		encoder_attention_heads
				lowerCamelCase__        =		decoder_ffn_dim
				lowerCamelCase__        =		decoder_layers
				lowerCamelCase__        =		decoder_attention_heads
				lowerCamelCase__        =		dropout
				lowerCamelCase__        =		attention_dropout
				lowerCamelCase__        =		activation_dropout
				lowerCamelCase__        =		activation_function
				lowerCamelCase__        =		init_std
				lowerCamelCase__        =		encoder_layerdrop
				lowerCamelCase__        =		decoder_layerdrop
				lowerCamelCase__        =		use_cache
				lowerCamelCase__        =		encoder_layers
				lowerCamelCase__        =		scale_embedding  # scale factor will be sqrt(d_model) if True

				lowerCamelCase__        =		num_global_tokens
				lowerCamelCase__        =		block_size
				lowerCamelCase__        =		stagger_local_blocks

				super().__init__(
				    pad_token_id=__lowerCAmelCase	,  eos_token_id=__lowerCAmelCase	,  is_encoder_decoder=__lowerCAmelCase	,  decoder_start_token_id=__lowerCAmelCase	,  forced_eos_token_id=__lowerCAmelCase	,  **__lowerCAmelCase	,  )





			@property
			def 		__lowerCamelCase    (   self							):



				'''simple docstring'''







				return self.encoder_attention_heads





			@property
			def 		__lowerCamelCase    (   self							):



				'''simple docstring'''







				return self.d_model



