
from __future__ import annotations

from collections.abc import Iterator
from typing import Any



class       _snake_case   :


 def __init__(					self					,  SCREAMING_SNAKE_CASE_):


   '''simple docstring'''




   lowercase__  :   Any    		=      data
   lowercase__  :   Node | None    		=      None



class       _snake_case   :


 def __init__(					self):


   '''simple docstring'''




   lowercase__  :   List[Any]    		=      None
   lowercase__  :   int    		=      None


 def __iter__(					self):


   '''simple docstring'''




   lowercase__  :   List[str]    		=      self.head
   while self.head:
     yield node.data
     lowercase__  :   str    		=      node.next
     if node == self.head:
       break


 def __len__(					self):


   '''simple docstring'''




   return sum(1 for _ in self)


 def __repr__(					self):


   '''simple docstring'''




   return "->".join(str(SCREAMING_SNAKE_CASE_) for item in iter(self))


 def      lowercase__     (					self					,  SCREAMING_SNAKE_CASE_):


   '''simple docstring'''




   self.insert_nth(len(self)					,  SCREAMING_SNAKE_CASE_)


 def      lowercase__     (					self					,  SCREAMING_SNAKE_CASE_):


   '''simple docstring'''




   self.insert_nth(0					,  SCREAMING_SNAKE_CASE_)


 def      lowercase__     (					self					,  SCREAMING_SNAKE_CASE_					,  SCREAMING_SNAKE_CASE_):


   '''simple docstring'''




   if index < 0 or index > len(self):
     raise IndexError("""list index out of range.""")
   lowercase__  :   Optional[int]    		=      Node(SCREAMING_SNAKE_CASE_)
   if self.head is None:
     lowercase__  :   Union[str, Any]    		=      new_node  # first node points itself
     lowercase__  :   Dict    		=      new_node
   elif index == 0:  # insert at head
     lowercase__  :   int    		=      self.head
     lowercase__  :   int    		=      new_node
   else:
     lowercase__  :   List[str]    		=      self.head
     for _ in range(index - 1):
       lowercase__  :   Union[str, Any]    		=      temp.next
     lowercase__  :   int    		=      temp.next
     lowercase__  :   Optional[Any]    		=      new_node
     if index == len(self) - 1:  # insert at tail
       lowercase__  :   Union[str, Any]    		=      new_node


 def      lowercase__     (					self):


   '''simple docstring'''




   return self.delete_nth(0)


 def      lowercase__     (					self):


   '''simple docstring'''




   return self.delete_nth(len(self) - 1)


 def      lowercase__     (					self					,  SCREAMING_SNAKE_CASE_ = 0):


   '''simple docstring'''




   if not 0 <= index < len(self):
     raise IndexError("""list index out of range.""")
   lowercase__  :   str    		=      self.head
   if self.head == self.tail:  # just one node
     lowercase__  :   List[Any]    		=      None
   elif index == 0:  # delete head node
     lowercase__  :   str    		=      self.tail.next.next
     lowercase__  :   List[Any]    		=      self.head.next
   else:
     lowercase__  :   Optional[int]    		=      self.head
     for _ in range(index - 1):
       lowercase__  :   List[Any]    		=      temp.next
     lowercase__  :   Optional[Any]    		=      temp.next
     lowercase__  :   Dict    		=      temp.next.next
     if index == len(self) - 1:  # delete at tail
       lowercase__  :   Tuple    		=      temp
   return delete_node.data



 def      lowercase__     (					self):


   '''simple docstring'''




   return len(self) == 0

def 		UpperCamelCase	(      )		->	None:


  '''simple docstring'''






  lowercase__  :   int    		=      CircularLinkedList()
  assert len(lowercase_   ) == 0
  assert circular_linked_list.is_empty() is True
  assert str(lowercase_   ) == ""

  try:
    circular_linked_list.delete_front()
    raise AssertionError  # This should not happen
  except IndexError:
    assert True  # This should happen

  try:
    circular_linked_list.delete_tail()
    raise AssertionError  # This should not happen
  except IndexError:
    assert True  # This should happen

  try:
    circular_linked_list.delete_nth(-1   )
    raise AssertionError
  except IndexError:
    assert True

  try:
    circular_linked_list.delete_nth(0   )
    raise AssertionError
  except IndexError:
    assert True

  assert circular_linked_list.is_empty() is True
  for i in range(5   ):
    assert len(lowercase_   ) == i
    circular_linked_list.insert_nth(lowercase_ , i + 1   )
  assert str(lowercase_   ) == "->".join(str(lowercase_   ) for i in range(1 , 6   )   )

  circular_linked_list.insert_tail(6   )
  assert str(lowercase_   ) == "->".join(str(lowercase_   ) for i in range(1 , 7   )   )
  circular_linked_list.insert_head(0   )
  assert str(lowercase_   ) == "->".join(str(lowercase_   ) for i in range(0 , 7   )   )

  assert circular_linked_list.delete_front() == 0
  assert circular_linked_list.delete_tail() == 6
  assert str(lowercase_   ) == "->".join(str(lowercase_   ) for i in range(1 , 6   )   )
  assert circular_linked_list.delete_nth(2   ) == 3

  circular_linked_list.insert_nth(2 , 3   )
  assert str(lowercase_   ) == "->".join(str(lowercase_   ) for i in range(1 , 6   )   )

  assert circular_linked_list.is_empty() is False


if __name__ == "__main__":
     import doctest

     doctest.testmod()








lowerCamelCase__    :		str          =   [
    [0, 1_6, 1_3, 0, 0, 0],
    [0, 0, 1_0, 1_2, 0, 0],
    [0, 4, 0, 0, 1_4, 0],
    [0, 0, 9, 0, 0, 2_0],
    [0, 0, 0, 7, 0, 4],
    [0, 0, 0, 0, 0, 0],
]

def 		UpperCamelCase	(      lowercase_ , lowercase_ , lowercase_ , lowercase_   )		->	str:


  '''simple docstring'''






  lowercase__  :   Any    		=      [False] * len(lowercase_   )
  lowercase__  :   List[Any]    		=      [s]
  lowercase__  :   int    		=      True

  while queue:
    lowercase__  :   Dict    		=      queue.pop(0   )
    for ind in range(len(graph[u]   )   ):
      if visited[ind] is False and graph[u][ind] > 0:
        queue.append(lowercase_   )
        lowercase__  :   Optional[Any]    		=      True
        lowercase__  :   int    		=      u

  return visited[t]

def 		UpperCamelCase	(      lowercase_ , lowercase_ , lowercase_   )		->	int:


  '''simple docstring'''






  lowercase__  :   Optional[int]    		=      [-1] * (len(lowercase_   ))
  lowercase__  :   Optional[Any]    		=      0
  lowercase__  :   List[Any]    		=      []
  lowercase__  :   Optional[Any]    		=      [i[:] for i in graph]  # Record original cut, copy.
  while bfs(lowercase_ , lowercase_ , lowercase_ , lowercase_   ):
    lowercase__  :   Optional[int]    		=      float("""Inf"""   )
    lowercase__  :   Tuple    		=      sink

    while s != source:
      # Find the minimum value in select path
      lowercase__  :   List[str]    		=      min(lowercase_ , graph[parent[s]][s]   )
      lowercase__  :   List[str]    		=      parent[s]

    max_flow += path_flow
    lowercase__  :   str    		=      sink

    while v != source:
      lowercase__  :   int    		=      parent[v]
      graph[u][v] -= path_flow
      graph[v][u] += path_flow
      lowercase__  :   Union[str, Any]    		=      parent[v]

  for i in range(len(lowercase_   )   ):
    for j in range(len(graph[0]   )   ):
      if graph[i][j] == 0 and temp[i][j] > 0:
        res.append((i, j)   )

  return res


if __name__ == "__main__":
     print(mincut(test_graph, source=0, sink=5))






