



from __future__ import annotations

from typing import Generic, TypeVar

UpperCamelCase__			=    TypeVar("T")
class       _lowerCAmelCase (			Generic[T]      ):






			"""simple docstring"""





			def __init__(					self						:							int      ,  lowercase						:							T )    ->       Union[str, Any]:
									"""simple docstring"""







									__lowercase											=					data  # Assign data
									__lowercase											=					None  # Initialize next as null
									__lowercase											=					None  # Initialize prev as null





class       _lowerCAmelCase (			Generic[T]      ):






			"""simple docstring"""





			def __init__(					self						:							Any )    ->       None:
									"""simple docstring"""







									__lowercase											=					None





			def 		snake_case__      (					self						:							str      ,  lowercase						:							T )    ->       None:
									"""simple docstring"""







									if self.head is None:
															__lowercase											=					Node(lowercase )
									else:
															__lowercase											=					Node(lowercase )
															__lowercase											=					new_node
															__lowercase											=					self.head
															__lowercase											=					None
															__lowercase											=					new_node





			def 		snake_case__      (					self						:							Optional[Any] )    ->       T | None:
									"""simple docstring"""







									if self.head is None:
															return None
									else:
															assert self.head is not None
															__lowercase											=					self.head.data
															__lowercase											=					self.head.next
															if self.head is not None:
																					__lowercase											=					None
															return temp





			def 		snake_case__      (					self						:							Optional[Any] )    ->       T | None:
									"""simple docstring"""







									return self.head.data if self.head is not None else None





			def __len__(					self						:							List[str] )    ->       int:
									"""simple docstring"""







									__lowercase											=					self.head
									__lowercase											=					0
									while temp is not None:
															count += 1
															__lowercase											=					temp.next
									return count





			def 		snake_case__      (					self						:							Optional[Any] )    ->       bool:
									"""simple docstring"""







									return self.head is None







			def 		snake_case__      (					self						:							Optional[Any] )    ->       None:
									"""simple docstring"""







									print("""stack elements are:""" )
									__lowercase											=					self.head
									while temp is not None:
															print(temp.data      ,  end="""->""" )
															__lowercase											=					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())










from __future__ import annotations






def 			UpperCAmelCase__     (     lowercase__ )			->   list[int]:
						if not list_of_ints:
												return []

						if min(lowercase__ ) < 0:
												raise ValueError("""All numbers must be positive""" )

						__lowercase											=					max(len(bin(lowercase__ )[2:] ) for x in list_of_ints )
						return _msd_radix_sort(lowercase__    ,							lowercase__ )






def 			UpperCAmelCase__     (     lowercase__    ,							lowercase__ )			->   list[int]:
						if bit_position == 0 or len(lowercase__ ) in [0, 1]:
												return list_of_ints

						__lowercase											=					[]
						__lowercase											=					[]
						# Split numbers based on bit at bit_position from the right
						for number in list_of_ints:
												if (number >> (bit_position - 1)) & 1:
																		# number has a one at bit bit_position
																		ones.append(lowercase__ )
												else:
																		# number has a zero at bit bit_position
																		zeros.append(lowercase__ )

    # recursively split both lists further
						__lowercase											=					_msd_radix_sort(lowercase__    ,							bit_position - 1 )
						__lowercase											=					_msd_radix_sort(lowercase__    ,							bit_position - 1 )

						# recombine lists
						__lowercase											=					zeros
						res.extend(lowercase__ )

						return res






def 			UpperCAmelCase__     (     lowercase__ )			->   List[Any]:
						__lowercase											=					len(lowercase__ )
						if not list_of_ints or length == 1:
												return

						if min(lowercase__ ) < 0:
												raise ValueError("""All numbers must be positive""" )

						__lowercase											=					max(len(bin(lowercase__ )[2:] ) for x in list_of_ints )
						_msd_radix_sort_inplace(lowercase__    ,							lowercase__    ,							0    ,							lowercase__ )






def 			UpperCAmelCase__     (     lowercase__    ,							lowercase__    ,							lowercase__    ,							lowercase__ )			->   Optional[Any]:
						if bit_position == 0 or end_index - begin_index <= 1:
												return

						bit_position -= 1

						__lowercase											=					begin_index
						__lowercase											=					end_index - 1
						while i <= j:
												__lowercase											=					False
												if not (list_of_ints[i] >> bit_position) & 1:
																		# found zero at the beginning
																		i += 1
																		__lowercase											=					True
												if (list_of_ints[j] >> bit_position) & 1:
																		# found one at the end
																		j -= 1
																		__lowercase											=					True

												if changed:
																		continue

												__lowercase						,      __lowercase											=					list_of_ints[j], list_of_ints[i]
												j -= 1
												if j != i:
																		i += 1

						_msd_radix_sort_inplace(lowercase__    ,							lowercase__    ,							lowercase__    ,							lowercase__ )
						_msd_radix_sort_inplace(lowercase__    ,							lowercase__    ,							lowercase__    ,							lowercase__ )


if __name__ == "__main__":
			import doctest

			doctest.testmod()





