





from __future__ import annotations

from collections.abc import Iterator
from typing import Any

class     __SCREAMING_SNAKE_CASE   :






							def __init__(  self					,	__lowerCAmelCase					):
														UpperCamelCase__			       =     data
														UpperCamelCase__			       =     None






class     __SCREAMING_SNAKE_CASE   :






							def __init__(  self					):
														UpperCamelCase__			       =     None
														UpperCamelCase__			       =     None






							def __iter__(  self					):
														UpperCamelCase__			       =     self.head
														while self.head:
																					yield node.data
																					UpperCamelCase__			       =     node.next
																					if node == self.head:
																												break






							def __len__(  self					):
														return sum(1 for _ in self					)






							def __repr__(  self					):
														return "->".join(str(__lowerCamelCase					) for item in iter(self					)					)






							def 			_lowerCamelCase						(  self					,	__lowerCAmelCase					):
														self.insert_nth(len(self					)					,	__lowerCamelCase					)






							def 			_lowerCamelCase						(  self					,	__lowerCAmelCase					):
														self.insert_nth(0					,	__lowerCamelCase					)






							def 			_lowerCamelCase						(  self					,	__lowerCAmelCase					,	__lowerCAmelCase					):
														if index < 0 or index > len(self					):
																					raise IndexError("""list index out of range."""					)
														UpperCamelCase__			       =     Node(__lowerCamelCase					)
														if self.head is None:
																					UpperCamelCase__			       =     new_node  # first node points itself
																					UpperCamelCase__			       =     UpperCamelCase__			       =     new_node
														elif index == 0:  # insert at head
																					UpperCamelCase__			       =     self.head
																					UpperCamelCase__			       =     UpperCamelCase__			       =     new_node
														else:
																					UpperCamelCase__			       =     self.head
																					for _ in range(index - 1					):
																												UpperCamelCase__			       =     temp.next
																					UpperCamelCase__			       =     temp.next
																					UpperCamelCase__			       =     new_node
																					if index == len(self					) - 1:  # insert at tail
																												UpperCamelCase__			       =     new_node






							def 			_lowerCamelCase						(  self					):
														return self.delete_nth(0					)






							def 			_lowerCamelCase						(  self					):
														return self.delete_nth(len(self					) - 1					)






							def 			_lowerCamelCase						(  self					,	__lowerCAmelCase = 0					):
														if not 0 <= index < len(self					):
																					raise IndexError("""list index out of range."""					)
														UpperCamelCase__			       =     self.head
														if self.head == self.tail:  # just one node
																					UpperCamelCase__			       =     UpperCamelCase__			       =     None
														elif index == 0:  # delete head node
																					UpperCamelCase__			       =     self.tail.next.next
																					UpperCamelCase__			       =     self.head.next
														else:
																					UpperCamelCase__			       =     self.head
																					for _ in range(index - 1					):
																												UpperCamelCase__			       =     temp.next
																					UpperCamelCase__			       =     temp.next
																					UpperCamelCase__			       =     temp.next.next
																					if index == len(self					) - 1:  # delete at tail
																												UpperCamelCase__			       =     temp
														return delete_node.data







							def 			_lowerCamelCase						(  self					):
														return len(self					) == 0






def       _UpperCamelCase       ():






							"""simple docstring"""





							UpperCamelCase__			       =     CircularLinkedList()
							assert len(UpperCamelCase__    ) == 0
							assert circular_linked_list.is_empty() is True
							assert str(UpperCamelCase__    ) == ""

							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(UpperCamelCase__    ) == i
														circular_linked_list.insert_nth(UpperCamelCase__				,     i + 1    )
							assert str(UpperCamelCase__    ) == "->".join(str(UpperCamelCase__    ) for i in range(1				,     6    )    )

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

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

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

							assert circular_linked_list.is_empty() is False


if __name__ == "__main__":
					import doctest

					doctest.testmod()









def       _UpperCamelCase       (a__				:str    ):






							"""simple docstring"""





							UpperCamelCase__			       =     0

							# if input_string is "aba" than new_input_string become "a|b|a"
							UpperCamelCase__			       =     """"""
							UpperCamelCase__			       =     """"""

							# append each character + "|" in new_string for range(0, length-1)
							for i in input_string[: len(a__    ) - 1]:
														new_input_string += i + "|"
							# append last character
							new_input_string += input_string[-1]

							# we will store the starting and ending of previous furthest ending palindromic
							# substring
							UpperCamelCase__       ,       UpperCamelCase__			       =     0, 0

							# length[i] shows the length of palindromic substring with center i
							UpperCamelCase__			       =     [1 for i in range(len(a__    )    )]

							# for each character in new_string find corresponding palindromic string
							UpperCamelCase__			       =     0
							for j in range(len(a__    )    ):
														UpperCamelCase__			       =     1 if j > r else min(length[l + r - j] // 2				,     r - j + 1    )
														while (
														    j - k >= 0
														    and j + k < len(a__    )
														    and new_input_string[k + j] == new_input_string[j - k]
														):
																					k += 1

														UpperCamelCase__			       =     2 * k - 1

														# does this string is ending after the previously explored end (that is r) ?
														# if yes the update the new r to the last index of this
														if j + k - 1 > r:
																					UpperCamelCase__			       =     j - k + 1  # noqa: E741
																					UpperCamelCase__			       =     j + k - 1

														# update max_length and start position
														if max_length < length[j]:
																					UpperCamelCase__			       =     length[j]
																					UpperCamelCase__			       =     j

    # create that string
							UpperCamelCase__			       =     new_input_string[start - max_length // 2 : start + max_length // 2 + 1]
							for i in s:
														if i != "|":
																					output_string += i

							return output_string


if __name__ == "__main__":
					import doctest

					doctest.testmod()




