

def    SCREAMING_SNAKE_CASE__       (  lowerCamelCase__			)  ->     str:
	__lowerCamelCase				:				Dict					       = 0

	# if input_string is "aba" than new_input_string become "a|b|a"
	__lowerCamelCase				:				Dict					       = ''
	__lowerCamelCase				:				List[Any]					       = ''

	# append each character + "|" in new_string for range(0, length-1)
	for i in input_string[: len(__snake_case			) - 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
	__lowerCamelCase       , __lowerCamelCase				:				List[str]					       = 0, 0

	# length[i] shows the length of palindromic substring with center i
	__lowerCamelCase				:				Optional[int]					       = [1 for i in range(len(__snake_case			)			)]

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

		__lowerCamelCase				:				Any					       = 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:
			__lowerCamelCase				:				Optional[int]					       = j - k + 1  # noqa: E741
			__lowerCamelCase				:				List[Any]					       = j + k - 1

		# update max_length and start position
		if max_length < length[j]:
			__lowerCamelCase				:				int					       = length[j]
			__lowerCamelCase				:				Optional[Any]					       = j

			 # create that string
	__lowerCamelCase				:				Dict					       = 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()








import heapq as hq
import math
from collections.abc import Iterator







class       lowerCamelCase__   :





     def __init__(self		,     UpperCAmelCase       )     ->   Any:
      _lowercase							      =str(id_       )
      _lowercase							      =None
      _lowercase							      =None
      _lowercase							      =[]
      _lowercase							      ={}  # {vertex:distance}





     def __lt__(self		,     UpperCAmelCase       )     ->   List[str]:
      return self.key < other.key





     def __repr__(self       )     ->   str:
      return self.id





     def      __A					(self		,     UpperCAmelCase       )     ->   Dict:
      self.neighbors.append(UpperCAmelCase       )





     def      __A					(self		,     UpperCAmelCase		,     UpperCAmelCase       )     ->   Optional[Any]:
      _lowercase							      =weight



def 				UpperCAmelCase_					(							__snake_case     ,						__snake_case     ,						__snake_case     ,						__snake_case						)     ->			List[str]:







 """simple docstring"""


 graph[a - 1].add_neighbor(graph[b - 1]						)
 graph[b - 1].add_neighbor(graph[a - 1]						)
 # add the edges:
 graph[a - 1].add_edge(graph[b - 1]     ,						__snake_case						)
 graph[b - 1].add_edge(graph[a - 1]     ,						__snake_case						)
def 				UpperCAmelCase_					(							__snake_case     ,						__snake_case						)     ->			list:







 """simple docstring"""


 _lowercase							      =[]
 for u in graph:
  _lowercase							      =math.inf
  _lowercase							      =None
 _lowercase							      =0
 _lowercase							      =graph[:]
 while q:
  _lowercase							      =min(__snake_case						)
  q.remove(__snake_case						)
  for v in u.neighbors:
   if (v in q) and (u.edges[v.id] < v.key):
    _lowercase							      =u
    _lowercase							      =u.edges[v.id]
 for i in range(1     ,						len(__snake_case						)						):
  a.append((int(graph[i].id						) + 1, int(graph[i].pi.id						) + 1)						)
 return a
def 				UpperCAmelCase_					(							__snake_case     ,						__snake_case						)     ->			Iterator[tuple]:







 """simple docstring"""


 for u in graph:
  _lowercase							      =math.inf
  _lowercase							      =None
 _lowercase							      =0

 _lowercase							      =list(__snake_case						)
 hq.heapify(__snake_case						)

 while h:
  _lowercase							      =hq.heappop(__snake_case						)
  for v in u.neighbors:
   if (v in h) and (u.edges[v.id] < v.key):
    _lowercase							      =u
    _lowercase							      =u.edges[v.id]
    hq.heapify(__snake_case						)

 for i in range(1     ,						len(__snake_case						)						):
  yield (int(graph[i].id						) + 1, int(graph[i].pi.id						) + 1)
def 				UpperCAmelCase_					(							)     ->			None:







 """simple docstring"""




if __name__ == "__main__":
  import doctest

  doctest.testmod()

