



"""simple docstring"""






class 	__snake_case	:




  def __init__(			self					:						Any						, __lowerCAmelCase					:						str = ""						, __lowerCAmelCase					:						bool = False		):






         """simple docstring"""






         _lowerCamelCase						:    dict[str, RadixNode]         =			{}

         # A node will be a leaf if the tree contains its word
         _lowerCamelCase						:    List[Any]         =			is_leaf

         _lowerCamelCase						:    Union[str, Any]         =			prefix




  def 						SCREAMING_SNAKE_CASE    (			self					:						Optional[int]						, __lowerCAmelCase					:						str		):






         """simple docstring"""






         _lowerCamelCase						:    str         =			0
         for q, w in zip(self.prefix						, __lowerCAmelCase		):
                if q != w:
                       break

                x += 1

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




  def 						SCREAMING_SNAKE_CASE    (			self					:						Tuple						, __lowerCAmelCase					:						list[str]		):






         """simple docstring"""






         for word in words:
                self.insert(__lowerCAmelCase		)




  def 						SCREAMING_SNAKE_CASE    (			self					:						Optional[int]						, __lowerCAmelCase					:						str		):






         """simple docstring"""






         if self.prefix == word:
                _lowerCamelCase						:    Any         =			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:
                _lowerCamelCase						:    List[Any]         =			RadixNode(prefix=__lowerCAmelCase						, is_leaf=__lowerCAmelCase		)

         else:
                _lowerCamelCase						:    int         =			self.nodes[word[0]]
                _lowerCamelCase      ,   _lowerCamelCase      ,   _lowerCamelCase						:    Tuple         =			incoming_node.match(
                    __lowerCAmelCase		)

                # 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(__lowerCAmelCase		)

                # 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:
                       _lowerCamelCase						:    Tuple         =			remaining_prefix

                       _lowerCamelCase						:    Any         =			self.nodes[matching_string[0]]
                       _lowerCamelCase						:    List[Any]         =			RadixNode(__lowerCAmelCase						, __lowerCAmelCase		)
                       _lowerCamelCase						:    Tuple         =			aux_node

                       if remaining_word == "":
                              _lowerCamelCase						:    Union[str, Any]         =			True
                       else:
                              self.nodes[matching_string[0]].insert(__lowerCAmelCase		)




  def 						SCREAMING_SNAKE_CASE    (			self					:						Any						, __lowerCAmelCase					:						str		):






         """simple docstring"""






         _lowerCamelCase						:    Any         =			self.nodes.get(word[0]						, __lowerCAmelCase		)
         if not incoming_node:
                return False
         else:
                _lowerCamelCase      ,   _lowerCamelCase      ,   _lowerCamelCase						:    Optional[Any]         =			incoming_node.match(
                    __lowerCAmelCase		)
                # 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(__lowerCAmelCase		)




  def 						SCREAMING_SNAKE_CASE    (			self					:						List[str]						, __lowerCAmelCase					:						str		):






         """simple docstring"""






         _lowerCamelCase						:    Any         =			self.nodes.get(word[0]						, __lowerCAmelCase		)
         if not incoming_node:
                return False
         else:
                _lowerCamelCase      ,   _lowerCamelCase      ,   _lowerCamelCase						:    List[Any]         =			incoming_node.match(
                    __lowerCAmelCase		)
                # 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(__lowerCAmelCase		)
                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:
                                            _lowerCamelCase						:    List[Any]         =			list(self.nodes.values()		)[0]
                                            _lowerCamelCase						:    Tuple         =			merging_node.is_leaf
                                            self.prefix += merging_node.prefix
                                            _lowerCamelCase						:    List[Any]         =			merging_node.nodes
                    # If there is more than 1 edge, we just mark it as non-leaf
                              elif len(incoming_node.nodes		) > 1:
                                     _lowerCamelCase						:    str         =			False
                              # If there is 1 edge, we merge it with its child
                              else:
                                     _lowerCamelCase						:    str         =			list(incoming_node.nodes.values()		)[0]
                                     _lowerCamelCase						:    Optional[int]         =			merging_node.is_leaf
                                     incoming_node.prefix += merging_node.prefix
                                     _lowerCamelCase						:    Optional[Any]         =			merging_node.nodes

                              return True




  def 						SCREAMING_SNAKE_CASE    (			self					:						List[str]						, __lowerCAmelCase					:						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 	snake_case_  (				):


       '''simple docstring'''





       _lowerCamelCase						:    int         =			'''banana bananas bandana band apple all beast'''.split()
       _lowerCamelCase						:    Any         =			RadixNode()
       root.insert_many(A_						)

       assert all(root.find(A_						) 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 	snake_case_  (				):


       '''simple docstring'''





       assert test_trie()






def 	snake_case_  (				):


       '''simple docstring'''





       _lowerCamelCase						:    Tuple         =			RadixNode()
       _lowerCamelCase						:    Any         =			'''banana bananas bandanas bandana band apple all beast'''.split()
       root.insert_many(A_						)

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


if __name__ == "__main__":
   main()







"""simple docstring"""






def 	snake_case_  (				A_ :		list						):


       '''simple docstring'''





       _lowerCamelCase						:    Union[str, Any]         =			len(A_						)
       for i in range(1,    A_						):
              _lowerCamelCase						:    Tuple         =			collection[i]
              _lowerCamelCase						:    Dict         =			0
              _lowerCamelCase						:    Any         =			i - 1

              while low <= high:
                     _lowerCamelCase						:    Optional[int]         =			(low + high) // 2
                     if val < collection[mid]:
                            _lowerCamelCase						:    List[str]         =			mid - 1
                     else:
                            _lowerCamelCase						:    Dict         =			mid + 1
              for j in range(A_,    A_,    -1						):
                     _lowerCamelCase						:    Optional[int]         =			collection[j - 1]
              _lowerCamelCase						:    Tuple         =			val
       return collection


if __name__ == "__main__":
   lowerCAmelCase__      =    input('''Enter numbers separated by a comma:\n''').strip()
   lowerCAmelCase__      =    [int(item) for item in user_input.split(''',''')]
   print(binary_insertion_sort(unsorted))


