from __future__ import annotations


def     UpperCamelCase(						__UpperCamelCase							:	int  ,__UpperCamelCase							:	int  ,__UpperCamelCase							:	int				):
		assert (
		    c % greatest_common_divisor(__UpperCamelCase  ,__UpperCamelCase				) == 0
		)  # greatest_common_divisor(a,b) function implemented below
		(lowerCAmelCase_)    :  Optional[Any]             =				extended_gcd(__UpperCamelCase  ,__UpperCamelCase				)  # extended_gcd(a,b) function implemented below
		lowerCAmelCase_    :  Optional[Any]             =				c / d
		return (r * x, r * y)


def     UpperCamelCase(						__UpperCamelCase							:	int  ,__UpperCamelCase							:	int  ,__UpperCamelCase							:	int  ,__UpperCamelCase							:	int = 2				):
		(lowerCAmelCase_)    :  Optional[int]             =				diophantine(__UpperCamelCase  ,__UpperCamelCase  ,__UpperCamelCase				)  # Initial value
		lowerCAmelCase_    :  Any             =				greatest_common_divisor(__UpperCamelCase  ,__UpperCamelCase				)
		lowerCAmelCase_    :  Optional[int]             =				a // d
		lowerCAmelCase_    :  Optional[int]             =				b // d

		for i in range(__UpperCamelCase				):
				lowerCAmelCase_    :  Dict             =				xa + i * q
				lowerCAmelCase_    :  Optional[int]             =				ya - i * p
				print(__UpperCamelCase  ,__UpperCamelCase				)


def     UpperCamelCase(						__UpperCamelCase							:	int  ,__UpperCamelCase							:	int				):
		if a < b:
				lowerCAmelCase_    :  Optional[Any]             =				b, a

		while a % b != 0:
				lowerCAmelCase_    :  Union[str, Any]             =				b, a % b

		return b


def     UpperCamelCase(						__UpperCamelCase							:	int  ,__UpperCamelCase							:	int				):
		assert a >= 0 and b >= 0

		if b == 0:
				lowerCAmelCase_    :  Tuple             =				a, 1, 0
		else:
				(lowerCAmelCase_)    :  List[str]             =				extended_gcd(__UpperCamelCase  ,a % b				)
				lowerCAmelCase_    :  List[str]             =				q
				lowerCAmelCase_    :  List[Any]             =				p - q * (a // b)

		assert a % d == 0 and b % d == 0
		assert d == a * x + b * y

		return (d, x, y)


if __name__ == "__main__":
						from doctest import testmod

						testmod(name='''diophantine''', verbose=True)
						testmod(name='''diophantine_all_soln''', verbose=True)
						testmod(name='''extended_gcd''', verbose=True)
						testmod(name='''greatest_common_divisor''', verbose=True)










from __future__ import annotations

from typing import Generic, TypeVar

A__						:						Dict          =      TypeVar('''T''')



class        __snake_case		(  Generic[T]		):




							def __init__( self  : List[Any]       ,       A_  : T):
									lowerCAmelCase_    :  Optional[Any]             =				data  # Assign data
									lowerCAmelCase_    :  Node[T] | None             =				None  # Initialize next as null
									lowerCAmelCase_    :  Node[T] | None             =				None  # Initialize prev as null





class        __snake_case		(  Generic[T]		):




							def __init__( self  : Union[str, Any]):
									lowerCAmelCase_    :  Node[T] | None             =				None




							def      UpperCAmelCase__    ( self  : List[str]       ,       A_  : T):
									if self.head is None:
											lowerCAmelCase_    :  List[Any]             =				Node(A_)
									else:
											lowerCAmelCase_    :  Tuple             =				Node(A_)
											lowerCAmelCase_    :  Optional[int]             =				new_node
											lowerCAmelCase_    :  Optional[int]             =				self.head
											lowerCAmelCase_    :  Optional[Any]             =				None
											lowerCAmelCase_    :  Dict             =				new_node




							def      UpperCAmelCase__    ( self  : List[str]):
									if self.head is None:
											return None
									else:
											assert self.head is not None
											lowerCAmelCase_    :  Tuple             =				self.head.data
											lowerCAmelCase_    :  Any             =				self.head.next
											if self.head is not None:
													lowerCAmelCase_    :  Optional[Any]             =				None
											return temp




							def      UpperCAmelCase__    ( self  : Union[str, Any]):
									return self.head.data if self.head is not None else None




							def __len__( self  : Dict):
									lowerCAmelCase_    :  List[str]             =				self.head
									lowerCAmelCase_    :  str             =				0
									while temp is not None:
											count += 1
											lowerCAmelCase_    :  Union[str, Any]             =				temp.next
									return count




							def      UpperCAmelCase__    ( self  : Dict):
									return self.head is None







							def      UpperCAmelCase__    ( self  : Dict):
									print('''stack elements are:''')
									lowerCAmelCase_    :  Optional[Any]             =				self.head
									while temp is not None:
											print(temp.data       ,       end='''->''')
											lowerCAmelCase_    :  List[str]             =				temp.next


# Code execution starts here
if __name__ == "__main__":
						# Start with the empty stack
						A__						:						Stack[int]          =      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())





