

'''simple docstring'''







import importlib.metadata
import operator
import re
import sys
from typing import Optional

from packaging import version


__lowerCamelCase						    =      {
    '''<''': operator.lt,
    '''<=''': operator.le,
    '''==''': operator.eq,
    '''!=''': operator.ne,
    '''>=''': operator.ge,
    '''>''': operator.gt,
}
def  UpperCAmelCase__      ( UpperCAmelCase__,    UpperCAmelCase__,    UpperCAmelCase__,    UpperCAmelCase__,    UpperCAmelCase__,    UpperCAmelCase__			)     ->     Dict:
       if got_ver is None or want_ver is None:
              raise ValueError(
                  F'''Unable to compare versions for {requirement}: need={want_ver} found={got_ver}. This is unusual. Consider'''
                  F''' reinstalling {pkg}.'''			)
       if not ops[op](version.parse(UpperCAmelCase__			),    version.parse(UpperCAmelCase__			)			):
              raise ImportError(
                  F'''{requirement} is required for a normal functioning of this module, but found {pkg}=={got_ver}.{hint}'''			)
def  UpperCAmelCase__      ( UpperCAmelCase__,    UpperCAmelCase__ = None			)     ->     None:
       A_		   = F'''\n{hint}''' if hint is not None else """"""

       # non-versioned check
       if re.match(r"""^[\w_\-\d]+$""",    UpperCAmelCase__			):
              A_   ,     A_   ,     A_		   = requirement, None, None
       else:
              A_		   = re.findall(r"""^([^!=<>\s]+)([\s!=<>]{1,2}.+)""",    UpperCAmelCase__			)
              if not match:
                     raise ValueError(
                         """requirement needs to be in the pip package format, .e.g., package_a==1.23, or package_b>=1.23, but"""
                         F''' got {requirement}'''			)
              A_   ,     A_		   = match[0]
              A_		   = want_full.split(""","""			)  # there could be multiple requirements
              A_		   = {}
              for w in want_range:
                     A_		   = re.findall(r"""^([\s!=<>]{1,2})(.+)""",    UpperCAmelCase__			)
                     if not match:
                            raise ValueError(
                                """requirement needs to be in the pip package format, .e.g., package_a==1.23, or package_b>=1.23,"""
                                F''' but got {requirement}'''			)
                     A_   ,     A_		   = match[0]
                     A_		   = want_ver
                     if op not in ops:
                            raise ValueError(F'''{requirement}: need one of {list(ops.keys()			)}, but got {op}'''			)

    # special case
       if pkg == "python":
              A_		   = """.""".join([str(UpperCAmelCase__			) for x in sys.version_info[:3]]			)
              for op, want_ver in wanted.items():
                     _compare_versions(UpperCAmelCase__,    UpperCAmelCase__,    UpperCAmelCase__,    UpperCAmelCase__,    UpperCAmelCase__,    UpperCAmelCase__			)
              return

       # check if any version is installed
       try:
              A_		   = importlib.metadata.version(UpperCAmelCase__			)
       except importlib.metadata.PackageNotFoundError:
              raise importlib.metadata.PackageNotFoundError(
                  F'''The \'{requirement}\' distribution was not found and is required by this application. {hint}'''			)

       # check that the right version is installed if version number or a range was provided
       if want_ver is not None:
              for op, want_ver in wanted.items():
                     _compare_versions(UpperCAmelCase__,    UpperCAmelCase__,    UpperCAmelCase__,    UpperCAmelCase__,    UpperCAmelCase__,    UpperCAmelCase__			)







def  UpperCAmelCase__      ( UpperCAmelCase__			)     ->     int:
       A_		   = """Try: pip install transformers -U or pip install -e '.[dev]' if you're working with git main"""
       return require_version(UpperCAmelCase__,    UpperCAmelCase__			)



'''simple docstring'''







import heapq as hq
import math
from collections.abc import Iterator


class    A__ :



    def __init__(   self						,			UpperCamelCase__    )  -> Dict:





           '''simple docstring'''
           A_		   = str(id_    )
           A_		   = None
           A_		   = None
           A_		   = []
           A_		   = {}  # {vertex:distance}



    def __lt__(   self						,			UpperCamelCase__    )  -> Optional[int]:





           '''simple docstring'''
           return self.key < other.key



    def __repr__(   self    )  -> Dict:





           '''simple docstring'''
           return self.id



    def    snake_case_     (   self						,			UpperCamelCase__    )  -> Dict:





           '''simple docstring'''
           self.neighbors.append(UpperCamelCase__    )







    def    snake_case_     (   self						,			UpperCamelCase__						,			UpperCamelCase__    )  -> Optional[Any]:





           '''simple docstring'''
           A_		   = weight

def  UpperCAmelCase__      ( UpperCAmelCase__,    UpperCAmelCase__,    UpperCAmelCase__,    UpperCAmelCase__			)     ->     Optional[int]:
       # add the neighbors:
       graph[a - 1].add_neighbor(graph[b - 1]			)
       graph[b - 1].add_neighbor(graph[a - 1]			)
       # add the edges:
       graph[a - 1].add_edge(graph[b - 1],    UpperCAmelCase__			)
       graph[b - 1].add_edge(graph[a - 1],    UpperCAmelCase__			)
def  UpperCAmelCase__      ( UpperCAmelCase__,    UpperCAmelCase__			)     ->     list:
       A_		   = []
       for u in graph:
              A_		   = math.inf
              A_		   = None
       A_		   = 0
       A_		   = graph[:]
       while q:
              A_		   = min(UpperCAmelCase__			)
              q.remove(UpperCAmelCase__			)
              for v in u.neighbors:
                     if (v in q) and (u.edges[v.id] < v.key):
                            A_		   = u
                            A_		   = u.edges[v.id]
       for i in range(1,    len(UpperCAmelCase__			)			):
              a.append((int(graph[i].id			) + 1, int(graph[i].pi.id			) + 1)			)
       return a
def  UpperCAmelCase__      ( UpperCAmelCase__,    UpperCAmelCase__			)     ->     Iterator[tuple]:
       for u in graph:
              A_		   = math.inf
              A_		   = None
       A_		   = 0

       A_		   = list(UpperCAmelCase__			)
       hq.heapify(UpperCAmelCase__			)

       while h:
              A_		   = hq.heappop(UpperCAmelCase__			)
              for v in u.neighbors:
                     if (v in h) and (u.edges[v.id] < v.key):
                            A_		   = u
                            A_		   = u.edges[v.id]
                            hq.heapify(UpperCAmelCase__			)

       for i in range(1,    len(UpperCAmelCase__			)			):
              yield (int(graph[i].id			) + 1, int(graph[i].pi.id			) + 1)
def  UpperCAmelCase__      ( )     ->     None:
       pass


if __name__ == "__main__":
      import doctest

      doctest.testmod()
