

"""simple docstring"""





# A Bipartite Graph is a graph whose vertices can be divided into two independent sets,
# U and V such that every edge (u, v) either connects a vertex from U to V or a vertex
# from V to U. In other words, for every edge (u, v), either u belongs to U and v to V,
# or u belongs to V and v to U. We can also say that there is no edge that connects
# vertices of same set.
from queue import Queue



def 				_lowerCAmelCase					(  UpperCAmelCase   :							Any ):


					'''simple docstring'''






					UpperCamelCase__						:			List[str]				     =Queue()
					UpperCamelCase__						:			Dict				     =[False] * len(lowerCAmelCase_ )
					UpperCamelCase__						:			Any				     =[-1] * len(lowerCAmelCase_ )

					def bfs():
										while not queue.empty():
															UpperCamelCase__						:			List[str]				     =queue.get()
															UpperCamelCase__						:			int				     =True

															for neighbour in graph[u]:
																				if neighbour == u:
																									return False

																				if color[neighbour] == -1:
																									UpperCamelCase__						:			Union[str, Any]				     =1 - color[u]
																									queue.put(lowerCAmelCase_ )

																				elif color[neighbour] == color[u]:
																									return False

										return True

					for i in range(len(lowerCAmelCase_ ) ):
										if not visited[i]:
															queue.put(lowerCAmelCase_ )
															UpperCamelCase__						:			str				     =0
															if bfs() is False:
																				return False

					return True


if __name__ == "__main__":
				# Adjacency List of graph
				print(check_bipartite({0: [1, 3], 1: [0, 2], 2: [1, 3], 3: [0, 2]}))








from __future__ import annotations

from typing import Generic, TypeVar

UpperCamelCase								=     TypeVar('T')





class  __lowerCamelCase       (    Generic[T]    ):




    """simple docstring"""

    def __init__(       self     :     List[str]   ,	SCREAMING_SNAKE_CASE__     :     T   )      ->       List[Any]:
         lowerCAmelCase__		= data  # Assign data
         lowerCAmelCase__		= None  # Initialize next as null
         lowerCAmelCase__		= None  # Initialize prev as null






class  __lowerCamelCase       (    Generic[T]    ):




    """simple docstring"""

    def __init__(       self     :     Any   )      ->       None:
         lowerCAmelCase__		= None


    def    a      (       self     :     Tuple   ,	SCREAMING_SNAKE_CASE__     :     T   )      ->       None:
         if self.head is None:
              lowerCAmelCase__		= Node(SCREAMING_SNAKE_CASE__   )
         else:
              lowerCAmelCase__		= Node(SCREAMING_SNAKE_CASE__   )
              lowerCAmelCase__		= new_node
              lowerCAmelCase__		= self.head
              lowerCAmelCase__		= None
              lowerCAmelCase__		= new_node


    def    a      (       self     :     int   )      ->       T | None:
         if self.head is None:
              return None
         else:
              assert self.head is not None
              lowerCAmelCase__		= self.head.data
              lowerCAmelCase__		= self.head.next
              if self.head is not None:
                   lowerCAmelCase__		= None
              return temp


    def    a      (       self     :     int   )      ->       T | None:
         return self.head.data if self.head is not None else None


    def __len__(       self     :     List[str]   )      ->       int:
         lowerCAmelCase__		= self.head
         lowerCAmelCase__		= 0
         while temp is not None:
              count += 1
              lowerCAmelCase__		= temp.next
         return count


    def    a      (       self     :     Tuple   )      ->       bool:
         return self.head is None


    def    a      (       self     :     Dict   )      ->       None:
         print("stack elements are:"   )
         lowerCAmelCase__		= self.head
         while temp is not None:
              print(temp.data   ,	end="->"   )
              lowerCAmelCase__		= temp.next


# Code execution starts here
if __name__ == "__main__":
     # Start with the empty stack
     UpperCamelCase								=     Stack()

     # Insert 4 at the beginning. So stack becomes 4->None
     print('Stack operations using Doubly LinkedList')
     stack.push(4)

     # Insert 5 at the beginning. So stack becomes 4->5->None
     stack.push(5)

     # Insert 6 at the beginning. So stack becomes 4->5->6->None
     stack.push(6)

     # Insert 7 at the beginning. So stack becomes 4->5->6->7->None
     stack.push(7)

     # Print the stack
     stack.print_stack()

     # Print the top element
     print('\nTop element is ', stack.top())

     # Print the stack size
     print('Size of the stack is ', len(stack))

     # pop the top element
     stack.pop()

     # pop the top element
     stack.pop()

     # two elements have now been popped off
     stack.print_stack()

     # Print True if the stack is empty else False
     print('\nstack is empty:', stack.is_empty())
