import math
import sys




class  _UpperCAmelCase       :



 '''simple docstring'''




 def __init__(						self							:					Tuple)		->     List[Any]:


   """simple docstring"""







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







 def 						__UpperCAmelCase							(						self							:					Optional[int])		->     Tuple:


   """simple docstring"""







   return self.cur_size == 0







 def 						__UpperCAmelCase							(						self							:					int				,      lowercase_							:					str)		->     str:


   """simple docstring"""







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







 def 						__UpperCAmelCase							(						self							:					int				,      lowercase_							:					List[Any])		->     Any:


   """simple docstring"""







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







 def 						__UpperCAmelCase							(						self							:					Tuple)		->     int:


   """simple docstring"""







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







 def 						__UpperCAmelCase							(						self							:					str				,      lowercase_							:					str)		->     Union[str, Any]:


   """simple docstring"""







   return 2 * i + 1







 def 						__UpperCAmelCase							(						self							:					Any				,      lowercase_							:					Dict)		->     Any:


   """simple docstring"""







   return 2 * i + 2







 def 						__UpperCAmelCase							(						self							:					Tuple				,      lowercase_							:					Any)		->     Optional[int]:


   """simple docstring"""







   return math.floor(i / 2)







 def 						__UpperCAmelCase							(						self							:					Optional[int]				,      lowercase_							:					Any				,      lowercase_							:					Optional[Any])		->     Any:


   """simple docstring"""







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







 def 						__UpperCAmelCase							(						self							:					List[Any]				,      lowercase_							:					Any				,      lowercase_							:					str)		->     Dict:


   """simple docstring"""







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




class  _UpperCAmelCase       :



 '''simple docstring'''




 def __init__(						self							:					int				,      lowercase_							:					Optional[Any])		->     Tuple:


   """simple docstring"""







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







 def 						__UpperCAmelCase							(						self							:					str				,      lowercase_							:					Tuple				,      lowercase_							:					Optional[int]				,      lowercase_							:					int)		->     Union[str, Any]:


   """simple docstring"""







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

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







 def 						__UpperCAmelCase							(						self							:					Optional[int])		->     int:


   """simple docstring"""







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







 def 						__UpperCAmelCase							(						self							:					Optional[Any]				,      lowercase_							:					List[str])		->     Tuple:


   """simple docstring"""







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

   while not q.is_empty():
     _UpperCamelCase				=  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]:
       _UpperCamelCase				=  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)				,      lowercase_)
         _UpperCamelCase				=  new_dist
         _UpperCamelCase				=  u

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







 def 						__UpperCAmelCase							(						self							:					Any				,      lowercase_							:					Optional[Any])		->     List[Any]:


   """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 						__UpperCAmelCase							(						self							:					int				,      lowercase_							:					int				,      lowercase_							:					str)		->     Optional[int]:


   """simple docstring"""







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


if __name__ == "__main__":
   lowerCamelCase__   = 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

# rely on isort to merge the imports
from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_sentencepiece_available, is_torch_available


lowerCamelCase__   = {
    '''configuration_ernie_m''': ['''ERNIE_M_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''ErnieMConfig'''],
}

try:
   if not is_sentencepiece_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   lowerCamelCase__   = ['''ErnieMTokenizer''']

try:
   if not is_torch_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   lowerCamelCase__   = [
       '''ERNIE_M_PRETRAINED_MODEL_ARCHIVE_LIST''',
       '''ErnieMForMultipleChoice''',
       '''ErnieMForQuestionAnswering''',
       '''ErnieMForSequenceClassification''',
       '''ErnieMForTokenClassification''',
       '''ErnieMModel''',
       '''ErnieMPreTrainedModel''',
       '''ErnieMForInformationExtraction''',
   ]


if TYPE_CHECKING:
   from .configuration_ernie_m import ERNIE_M_PRETRAINED_CONFIG_ARCHIVE_MAP, ErnieMConfig

   try:
      if not is_sentencepiece_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .tokenization_ernie_m import ErnieMTokenizer

   try:
      if not is_torch_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_ernie_m import (
          ERNIE_M_PRETRAINED_MODEL_ARCHIVE_LIST,
          ErnieMForInformationExtraction,
          ErnieMForMultipleChoice,
          ErnieMForQuestionAnswering,
          ErnieMForSequenceClassification,
          ErnieMForTokenClassification,
          ErnieMModel,
          ErnieMPreTrainedModel,
      )


else:
   import sys

   lowerCamelCase__   = _LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)




