






from .number_theory.prime_numbers import next_prime




class        _lowerCAmelCase:





       """simple docstring"""







       def __init__(      self						,    _lowerCamelCase						,    _lowerCamelCase = None						,    _lowerCamelCase = None						,    ):
         UpperCamelCase_:      Optional[Any]					   =       size_table
         UpperCamelCase_:      Dict					   =       [None] * self.size_table
         UpperCamelCase_:      Dict					   =       0.7_5 if lim_charge is None else lim_charge
         UpperCamelCase_:      str					   =       1 if charge_factor is None else charge_factor
         UpperCamelCase_:      list					   =       []
         UpperCamelCase_:      dict					   =       {}





       def     _a					(      self							):
         return self._keys





       def     _a					(      self							):
         return sum(1 for slot in self.values if slot is not None							) / (
             self.size_table * self.charge_factor
         )





       def     _a					(      self						,    _lowerCamelCase							):
         return key % self.size_table





       def     _a					(      self						,    _lowerCamelCase							):
         print(f'''step {step_ord}'''							)
         print(list(range(len(self.values							)							)							)							)
         print(self.values							)





       def     _a					(      self						,    _lowerCamelCase							):
         UpperCamelCase_:      List[Any]					   =       1
         UpperCamelCase_:      List[Any]					   =       values
         for value in values:
           self.insert_data(_lowerCamelCase							)
           self._step_by_step(_lowerCamelCase							)
           i += 1





       def     _a					(      self						,    _lowerCamelCase						,    _lowerCamelCase							):
         UpperCamelCase_:      Dict					   =       data
         UpperCamelCase_:      int					   =       data





       def     _a					(      self						,    _lowerCamelCase						,    _lowerCamelCase=None							):
         UpperCamelCase_:      List[Any]					   =       self.hash_function(key + 1							)

         while self.values[new_key] is not None and self.values[new_key] != key:
           if self.values.count(_lowerCamelCase							) > 0:
             UpperCamelCase_:      List[str]					   =       self.hash_function(new_key + 1							)
           else:
             UpperCamelCase_:      List[str]					   =       None
             break

         return new_key





       def     _a					(      self							):
         UpperCamelCase_:      Optional[int]					   =       [value for value in self.values if value is not None]
         UpperCamelCase_:      Dict					   =       next_prime(self.size_table						,    factor=2							)
         self._keys.clear()
         UpperCamelCase_:      Optional[Any]					   =       [None] * self.size_table  # hell's pointers D: don't DRY ;/
         for value in survivor_values:
           self.insert_data(_lowerCamelCase							)





       def     _a					(      self						,    _lowerCamelCase							):
         UpperCamelCase_:      List[Any]					   =       self.hash_function(_lowerCamelCase							)

         if self.values[key] is None:
           self._set_value(_lowerCamelCase						,    _lowerCamelCase							)

         elif self.values[key] == data:
           pass

         else:
           UpperCamelCase_:      Optional[Any]					   =       self._collision_resolution(_lowerCamelCase						,    _lowerCamelCase							)
           if collision_resolution is not None:
             self._set_value(_lowerCamelCase						,    _lowerCamelCase							)
           else:
             self.rehashing()
             self.insert_data(_lowerCamelCase							)







from collections import deque

def 						snake_case      (UpperCAmelCase__						) ->       Any:
  return input(UpperCAmelCase__						).strip().split(' '						)

def 						snake_case      (UpperCAmelCase__			,					UpperCAmelCase__						) ->       dict[int, list[int]]:
  UpperCamelCase_:      dict[int, list[int]]					   =       {}
  for i in range(UpperCAmelCase__						):
    UpperCamelCase_:      str					   =       []

  for e in range(UpperCAmelCase__						):
    UpperCamelCase_   ,UpperCamelCase_:      List[Any]					   =       (int(UpperCAmelCase__						) for i in _input(F'''Edge {e + 1}: <node1> <node2> '''						))
    graph[x].append(UpperCAmelCase__						)
  return graph

def 						snake_case      (UpperCAmelCase__			,					UpperCAmelCase__						) ->       dict[int, list[int]]:
  UpperCamelCase_:      dict[int, list[int]]					   =       {}
  for i in range(UpperCAmelCase__						):
    UpperCamelCase_:      Tuple					   =       []

  for e in range(UpperCAmelCase__						):
    UpperCamelCase_   ,UpperCamelCase_:      str					   =       (int(UpperCAmelCase__						) for i in _input(F'''Edge {e + 1}: <node1> <node2> '''						))
    graph[x].append(UpperCAmelCase__						)
    graph[y].append(UpperCAmelCase__						)
  return graph

def 						snake_case      (UpperCAmelCase__			,					UpperCAmelCase__						) ->       dict[int, list[tuple[int, int]]]:
  UpperCamelCase_:      dict[int, list[tuple[int, int]]]					   =       {}
  for i in range(UpperCAmelCase__						):
    UpperCamelCase_:      List[Any]					   =       []

  for e in range(UpperCAmelCase__						):
    UpperCamelCase_   ,UpperCamelCase_   ,UpperCamelCase_:      List[str]					   =       (int(UpperCAmelCase__						) for i in _input(F'''Edge {e + 1}: <node1> <node2> <weight> '''						))
    graph[x].append((y, w)						)
    graph[y].append((x, w)						)
  return graph


if __name__ == "__main__":
   A_			,				A_	:	str				=				(int(i) for i in _input('Number of nodes and edges: '))

   A_	:	str				=				int(
       _input(
           'Press 1 or 2 or 3 \n'
           '1. Unweighted directed \n'
           '2. Unweighted undirected \n'
           '3. Weighted undirected \n'
       )[0]
   )

   A_	:	List[str]				=				{
       1: initialize_unweighted_directed_graph,
       2: initialize_unweighted_undirected_graph,
       3: initialize_weighted_undirected_graph,
   }[graph_choice](n, m)

def 						snake_case      (UpperCAmelCase__			,					UpperCAmelCase__						) ->       Union[str, Any]:
  UpperCamelCase_   ,UpperCamelCase_:      int					   =       {s}, [s]
  print(UpperCAmelCase__						)
  while _s:
    UpperCamelCase_:      Optional[Any]					   =       0
    for i in g[_s[-1]]:
      if i not in vis:
        _s.append(UpperCAmelCase__						)
        vis.add(UpperCAmelCase__						)
        UpperCamelCase_:      Any					   =       1
        print(UpperCAmelCase__						)
        break
    if not flag:
      _s.pop()

def 						snake_case      (UpperCAmelCase__			,					UpperCAmelCase__						) ->       Dict:
  UpperCamelCase_   ,UpperCamelCase_:      int					   =       {s}, deque([s]						)
  print(UpperCAmelCase__						)
  while q:
    UpperCamelCase_:      Dict					   =       q.popleft()
    for v in g[u]:
      if v not in vis:
        vis.add(UpperCAmelCase__						)
        q.append(UpperCAmelCase__						)
        print(UpperCAmelCase__						)

def 						snake_case      (UpperCAmelCase__			,					UpperCAmelCase__						) ->       int:
  UpperCamelCase_   ,UpperCamelCase_   ,UpperCamelCase_:      Any					   =       {s: 0}, set(), {s: 0}
  while True:
    if len(UpperCAmelCase__						) == len(UpperCAmelCase__						) - 1:
      break
    UpperCamelCase_:      str					   =       1_0_0_0_0_0
    for i in dist:
      if i not in known and dist[i] < mini:
        UpperCamelCase_:      Dict					   =       dist[i]
        UpperCamelCase_:      str					   =       i
    known.add(UpperCAmelCase__						)
    for v in g[u]:
      if v[0] not in known and dist[u] + v[1] < dist.get(v[0]			,					1_0_0_0_0_0						):
        UpperCamelCase_:      Optional[Any]					   =       dist[u] + v[1]
        UpperCamelCase_:      str					   =       u
  for i in dist:
    if i != s:
      print(dist[i]						)

def 						snake_case      (UpperCAmelCase__			,					UpperCAmelCase__=None			,					UpperCAmelCase__=None						) ->       Optional[Any]:
  if q is None:
    UpperCamelCase_:      Optional[Any]					   =       [1]
  if ind is None:
    UpperCamelCase_:      Union[str, Any]					   =       [0] * (len(UpperCAmelCase__						) + 1)  # SInce oth Index is ignored
    for u in g:
      for v in g[u]:
        ind[v] += 1
    UpperCamelCase_:      Optional[int]					   =       deque()
    for i in g:
      if ind[i] == 0:
        q.append(UpperCAmelCase__						)
  if len(UpperCAmelCase__						) == 0:
    return
  UpperCamelCase_:      Dict					   =       q.popleft()
  print(UpperCAmelCase__						)
  for w in g[v]:
    ind[w] -= 1
    if ind[w] == 0:
      q.append(UpperCAmelCase__						)
  topo(UpperCAmelCase__			,					UpperCAmelCase__			,					UpperCAmelCase__						)

def 						snake_case      () ->       str:
  UpperCamelCase_:      Dict					   =       input().strip()
  UpperCamelCase_:      List[str]					   =       []
  for _ in range(UpperCAmelCase__						):
    a.append(map(UpperCAmelCase__			,					input().strip().split()						)						)
  return a, n

def 						snake_case      (UpperCAmelCase__						) ->       Union[str, Any]:
  ((UpperCamelCase_)   ,(UpperCamelCase_)):      Dict					   =       a_and_n
  UpperCamelCase_:      List[str]					   =       list(UpperCAmelCase__						)
  UpperCamelCase_:      int					   =       [[0] * n for i in range(UpperCAmelCase__						)]
  for k in range(UpperCAmelCase__						):
    for i in range(UpperCAmelCase__						):
      for j in range(UpperCAmelCase__						):
        if dist[i][j] > dist[i][k] + dist[k][j]:
          UpperCamelCase_:      Union[str, Any]					   =       dist[i][k] + dist[k][j]
          UpperCamelCase_:      Optional[int]					   =       k
  print(UpperCAmelCase__						)

def 						snake_case      (UpperCAmelCase__			,					UpperCAmelCase__						) ->       str:
  UpperCamelCase_   ,UpperCamelCase_   ,UpperCamelCase_:      Tuple					   =       {s: 0}, set(), {s: 0}
  while True:
    if len(UpperCAmelCase__						) == len(UpperCAmelCase__						) - 1:
      break
    UpperCamelCase_:      List[str]					   =       1_0_0_0_0_0
    for i in dist:
      if i not in known and dist[i] < mini:
        UpperCamelCase_:      Tuple					   =       dist[i]
        UpperCamelCase_:      Optional[Any]					   =       i
    known.add(UpperCAmelCase__						)
    for v in g[u]:
      if v[0] not in known and v[1] < dist.get(v[0]			,					1_0_0_0_0_0						):
        UpperCamelCase_:      Dict					   =       v[1]
        UpperCamelCase_:      Optional[Any]					   =       u
  return dist

def 						snake_case      () ->       Optional[int]:
  UpperCamelCase_   ,UpperCamelCase_:      Tuple					   =       map(UpperCAmelCase__			,					input().split(' '						)						)
  UpperCamelCase_:      List[str]					   =       []
  for _ in range(UpperCAmelCase__						):
    edges.append(map(UpperCAmelCase__			,					input().split(' '						)						)						)
  return edges, n

def 						snake_case      (UpperCAmelCase__						) ->       Optional[Any]:
  # Sort edges on the basis of distance
  ((UpperCamelCase_)   ,(UpperCamelCase_)):      Optional[Any]					   =       e_and_n
  e.sort(reverse=UpperCAmelCase__			,					key=lambda UpperCAmelCase__						: x[2]						)
  UpperCamelCase_:      str					   =       [{i} for i in range(1			,					n + 1						)]
  while True:
    if len(UpperCAmelCase__						) == 1:
      break
    print(UpperCAmelCase__						)
    UpperCamelCase_:      Any					   =       e.pop()
    for i in range(len(UpperCAmelCase__						)						):
      if x[0] in s[i]:
        break
    for j in range(len(UpperCAmelCase__						)						):
      if x[1] in s[j]:
        if i == j:
          break
        s[j].update(s[i]						)
        s.pop(UpperCAmelCase__						)
        break

def 						snake_case      (UpperCAmelCase__						) ->       Dict:
  UpperCamelCase_:      Tuple					   =       []
  for node in graph:
    if not graph[node]:
      isolated.append(UpperCAmelCase__						)
  return isolated