



'''simple docstring'''





def 			a_	(				_lowerCAmelCase = 1000			) -> int:
  return sum(2 * a * ((a - 1) // 2) for a in range(3			,n + 1			)			)


if __name__ == "__main__":
   print(solution())














class 					A__     :

     '''simple docstring'''






     def __init__( self      :    Optional[int]   ,						_SCREAMING_SNAKE_CASE      :    str = ""   ,						_SCREAMING_SNAKE_CASE      :    bool = False ):






           """simple docstring"""




           UpperCamelCase					       =  {}

           # A node will be a leaf if the tree contains its word
           UpperCamelCase					       =  is_leaf

           UpperCamelCase					       =  prefix







     def   _SCREAMING_SNAKE_CASE     ( self      :    Optional[int]   ,						_SCREAMING_SNAKE_CASE      :    str ):






           """simple docstring"""




           UpperCamelCase					       =  0
           for q, w in zip(self.prefix   ,						_SCREAMING_SNAKE_CASE ):
                 if q != w:
                       break

                 x += 1

           return self.prefix[:x], self.prefix[x:], word[x:]







     def   _SCREAMING_SNAKE_CASE     ( self      :    Any   ,						_SCREAMING_SNAKE_CASE      :    list[str] ):






           """simple docstring"""




           for word in words:
                 self.insert(_SCREAMING_SNAKE_CASE )







     def   _SCREAMING_SNAKE_CASE     ( self      :    Union[str, Any]   ,						_SCREAMING_SNAKE_CASE      :    str ):






           """simple docstring"""




           if self.prefix == word:
                 UpperCamelCase					       =  True

           # Case 2: The node has no edges that have a prefix to the word
           # Solution: We create an edge from the current node to a new one
           # containing the word
           elif word[0] not in self.nodes:
                 UpperCamelCase					       =  RadixNode(prefix=_SCREAMING_SNAKE_CASE   ,						is_leaf=_SCREAMING_SNAKE_CASE )

           else:
                 UpperCamelCase					       =  self.nodes[word[0]]
                 UpperCamelCase       ,  UpperCamelCase       ,  UpperCamelCase					       =  incoming_node.match(
                     _SCREAMING_SNAKE_CASE )

                 # Case 3: The node prefix is equal to the matching
                 # Solution: We insert remaining word on the next node
                 if remaining_prefix == "":
                       self.nodes[matching_string[0]].insert(_SCREAMING_SNAKE_CASE )

                 # Case 4: The word is greater equal to the matching
                 # Solution: Create a node in between both nodes, change
                 # prefixes and add the new node for the remaining word
                 else:
                       UpperCamelCase					       =  remaining_prefix

                       UpperCamelCase					       =  self.nodes[matching_string[0]]
                       UpperCamelCase					       =  RadixNode(_SCREAMING_SNAKE_CASE   ,						_SCREAMING_SNAKE_CASE )
                       UpperCamelCase					       =  aux_node

                       if remaining_word == "":
                             UpperCamelCase					       =  True
                       else:
                             self.nodes[matching_string[0]].insert(_SCREAMING_SNAKE_CASE )







     def   _SCREAMING_SNAKE_CASE     ( self      :    Any   ,						_SCREAMING_SNAKE_CASE      :    str ):






           """simple docstring"""




           UpperCamelCase					       =  self.nodes.get(word[0]   ,						_SCREAMING_SNAKE_CASE )
           if not incoming_node:
                 return False
           else:
                 UpperCamelCase       ,  UpperCamelCase       ,  UpperCamelCase					       =  incoming_node.match(
                     _SCREAMING_SNAKE_CASE )
                 # If there is remaining prefix, the word can't be on the tree
                 if remaining_prefix != "":
                       return False
                 # This applies when the word and the prefix are equal
                 elif remaining_word == "":
                       return incoming_node.is_leaf
                 # We have word remaining so we check the next node
                 else:
                       return incoming_node.find(_SCREAMING_SNAKE_CASE )







     def   _SCREAMING_SNAKE_CASE     ( self      :    List[Any]   ,						_SCREAMING_SNAKE_CASE      :    str ):






           """simple docstring"""




           UpperCamelCase					       =  self.nodes.get(word[0]   ,						_SCREAMING_SNAKE_CASE )
           if not incoming_node:
                 return False
           else:
                 UpperCamelCase       ,  UpperCamelCase       ,  UpperCamelCase					       =  incoming_node.match(
                     _SCREAMING_SNAKE_CASE )
                 # If there is remaining prefix, the word can't be on the tree
                 if remaining_prefix != "":
                       return False
                 # We have word remaining so we check the next node
                 elif remaining_word != "":
                       return incoming_node.delete(_SCREAMING_SNAKE_CASE )
                 else:
                       # If it is not a leaf, we don't have to delete
                       if not incoming_node.is_leaf:
                             return False
                       else:
                             # We delete the nodes if no edges go from it
                             if len(incoming_node.nodes ) == 0:
                                   del self.nodes[word[0]]
                                   # We merge the current node with its only child
                                   if len(self.nodes ) == 1 and not self.is_leaf:
                                         UpperCamelCase					       =  list(self.nodes.values() )[0]
                                         UpperCamelCase					       =  merging_node.is_leaf
                                         self.prefix += merging_node.prefix
                                         UpperCamelCase					       =  merging_node.nodes
                    # If there is more than 1 edge, we just mark it as non-leaf
                             elif len(incoming_node.nodes ) > 1:
                                   UpperCamelCase					       =  False
                             # If there is 1 edge, we merge it with its child
                             else:
                                   UpperCamelCase					       =  list(incoming_node.nodes.values() )[0]
                                   UpperCamelCase					       =  merging_node.is_leaf
                                   incoming_node.prefix += merging_node.prefix
                                   UpperCamelCase					       =  merging_node.nodes

                             return True







     def   _SCREAMING_SNAKE_CASE     ( self      :    Tuple   ,						_SCREAMING_SNAKE_CASE      :    int = 0 ):






           """simple docstring"""




           if self.prefix != "":
                 print('-' * height   ,						self.prefix   ,						'  (leaf)' if self.is_leaf else '' )

           for value in self.nodes.values():
                 value.print_tree(height + 1 )

def 		lowercase__  (				) ->			bool:
      """simple docstring"""

      UpperCamelCase					       =  'banana bananas bandana band apple all beast'.split()
      UpperCamelCase					       =  RadixNode()
      root.insert_many(_UpperCamelCase)

      assert all(root.find(_UpperCamelCase) for word in words)
      assert not root.find('bandanas')
      assert not root.find('apps')
      root.delete('all')
      assert not root.find('all')
      root.delete('banana')
      assert not root.find('banana')
      assert root.find('bananas')

      return True
def 		lowercase__  (				) ->			None:
      """simple docstring"""

      assert test_trie()
def 		lowercase__  (				) ->			None:
      """simple docstring"""

      UpperCamelCase					       =  RadixNode()
      UpperCamelCase					       =  'banana bananas bandanas bandana band apple all beast'.split()
      root.insert_many(_UpperCamelCase)

      print('Words:'       ,							_UpperCamelCase)
      print('Tree:')
      root.print_tree()


if __name__ == "__main__":
       main()



