

def  UpperCAmelCase__      ( UpperCAmelCase__,    UpperCAmelCase__			)     ->     float:
       if mass < 0:
              raise ValueError("""The mass of a body cannot be negative"""			)
       return 0.5 * mass * abs(UpperCAmelCase__			) * abs(UpperCAmelCase__			)


if __name__ == "__main__":
      import doctest

      doctest.testmod(verbose=True)



'''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()
