



'''simple docstring'''






class 				lowercase			:


 """simple docstring"""


 def __init__(				self    ,a_				)						->  Optional[int]:
        _UpperCAmelCase    :		Optional[Any]     	=					val
        # Number of nodes in left subtree
        _UpperCAmelCase    :		str     	=					0
        _UpperCAmelCase    :		List[str]     	=					None
        _UpperCAmelCase    :		Union[str, Any]     	=					None
        _UpperCAmelCase    :		int     	=					None







 def _snake_case					(				self    ,a_				)						->  int:
        assert self.left_tree_size == other.left_tree_size, "Unequal Sizes of Blocks"

        if self.val < other.val:
               _UpperCAmelCase    :		Optional[int]     	=					self.right
               _UpperCAmelCase    :		str     	=					None
               if self.right:
                      _UpperCAmelCase    :		Tuple     	=					other
               _UpperCAmelCase    :		List[Any]     	=					other
               _UpperCAmelCase    :		Optional[int]     	=					self.left_tree_size * 2 + 1
               return self
        else:
               _UpperCAmelCase    :		Any     	=					other.right
               _UpperCAmelCase    :		int     	=					None
               if other.right:
                      _UpperCAmelCase    :		Any     	=					self
               _UpperCAmelCase    :		Optional[int]     	=					self
               _UpperCAmelCase    :		Optional[Any]     	=					other.left_tree_size * 2 + 1
               return other







class 				lowercase			:


 """simple docstring"""


 def __init__(				self    ,a_=None    ,a_=None    ,a_=0				)						->  Dict:
        _UpperCAmelCase    :		List[Any]     	=					heap_size
        _UpperCAmelCase    :		Tuple     	=					bottom_root
        _UpperCAmelCase    :		List[str]     	=					min_node







 def _snake_case					(				self    ,a_				)						->  List[str]:

        # Empty heaps corner cases
        if other.size == 0:
               return None
        if self.size == 0:
               _UpperCAmelCase    :		Any     	=					other.size
               _UpperCAmelCase    :		Optional[int]     	=					other.bottom_root
               _UpperCAmelCase    :		List[Any]     	=					other.min_node
               return None
        # Update size
        _UpperCAmelCase    :		str     	=					self.size + other.size

        # Update min.node
        if self.min_node.val > other.min_node.val:
               _UpperCAmelCase    :		Optional[Any]     	=					other.min_node
        # Merge

        # Order roots by left_subtree_size
        _UpperCAmelCase    :		Union[str, Any]     	=					[]
        _UpperCAmelCase	,_UpperCAmelCase    :		int     	=					self.bottom_root, other.bottom_root
        while i or j:
               if i and ((not j) or i.left_tree_size < j.left_tree_size):
                      combined_roots_list.append((i, True)				)
                      _UpperCAmelCase    :		Union[str, Any]     	=					i.parent
               else:
                      combined_roots_list.append((j, False)				)
                      _UpperCAmelCase    :		List[str]     	=					j.parent
        # Insert links between them
        for i in range(len(a_				) - 1				):
               if combined_roots_list[i][1] != combined_roots_list[i + 1][1]:
                      _UpperCAmelCase    :		List[str]     	=					combined_roots_list[i + 1][0]
                      _UpperCAmelCase    :		Optional[int]     	=					combined_roots_list[i][0]
        # Consecutively merge roots with same left_tree_size
        _UpperCAmelCase    :		List[Any]     	=					combined_roots_list[0][0]
        while i.parent:
               if (
                   (i.left_tree_size == i.parent.left_tree_size) and (not i.parent.parent)
               ) or (
                   i.left_tree_size == i.parent.left_tree_size
                   and i.left_tree_size != i.parent.parent.left_tree_size
               ):
                      # Neighbouring Nodes
                      _UpperCAmelCase    :		List[str]     	=					i.left
                      _UpperCAmelCase    :		List[Any]     	=					i.parent.parent

                      # Merging trees
                      _UpperCAmelCase    :		Optional[int]     	=					i.merge_trees(i.parent				)

                      # Updating links
                      _UpperCAmelCase    :		Union[str, Any]     	=					previous_node
                      _UpperCAmelCase    :		List[str]     	=					next_node
                      if previous_node:
                             _UpperCAmelCase    :		int     	=					i
                      if next_node:
                             _UpperCAmelCase    :		List[str]     	=					i
               else:
                      _UpperCAmelCase    :		Dict     	=					i.parent
        # Updating self.bottom_root
        while i.left:
               _UpperCAmelCase    :		Union[str, Any]     	=					i.left
        _UpperCAmelCase    :		Tuple     	=					i

        # Update other
        _UpperCAmelCase    :		Optional[Any]     	=					self.size
        _UpperCAmelCase    :		int     	=					self.bottom_root
        _UpperCAmelCase    :		Any     	=					self.min_node

        # Return the merged heap
        return self







 def _snake_case					(				self    ,a_				)						->  List[Any]:
        if self.size == 0:
               _UpperCAmelCase    :		Dict     	=					Node(a_				)
               _UpperCAmelCase    :		Optional[int]     	=					1
               _UpperCAmelCase    :		Optional[Any]     	=					self.bottom_root
        else:
               # Create new node
               _UpperCAmelCase    :		Tuple     	=					Node(a_				)

               # Update size
               self.size += 1

               # update min_node
               if val < self.min_node.val:
                      _UpperCAmelCase    :		int     	=					new_node
               # Put new_node as a bottom_root in heap
               _UpperCAmelCase    :		Dict     	=					new_node
               _UpperCAmelCase    :		int     	=					self.bottom_root
               _UpperCAmelCase    :		List[Any]     	=					new_node

               # Consecutively merge roots with same left_tree_size
               while (
                   self.bottom_root.parent
                   and self.bottom_root.left_tree_size
                   == self.bottom_root.parent.left_tree_size
               ):
                      # Next node
                      _UpperCAmelCase    :		Tuple     	=					self.bottom_root.parent.parent

                      # Merge
                      _UpperCAmelCase    :		Optional[int]     	=					self.bottom_root.merge_trees(self.bottom_root.parent				)

                      # Update Links
                      _UpperCAmelCase    :		Union[str, Any]     	=					next_node
                      _UpperCAmelCase    :		Any     	=					None
                      if next_node:
                             _UpperCAmelCase    :		List[Any]     	=					self.bottom_root







 def _snake_case					(				self				)						->  Dict:
        return self.min_node.val







 def _snake_case					(				self				)						->  List[Any]:
        return self.size == 0







 def _snake_case					(				self				)						->  Dict:
        _UpperCAmelCase    :		Optional[Any]     	=					self.min_node.val

        # Last element in heap corner case
        if self.size == 1:
               # Update size
               _UpperCAmelCase    :		Any     	=					0

               # Update bottom root
               _UpperCAmelCase    :		Optional[Any]     	=					None

               # Update min_node
               _UpperCAmelCase    :		int     	=					None

               return min_value
        # No right subtree corner case
        # The structure of the tree implies that this should be the bottom root
        # and there is at least one other root
        if self.min_node.right is None:
               # Update size
               self.size -= 1

               # Update bottom root
               _UpperCAmelCase    :		Dict     	=					self.bottom_root.parent
               _UpperCAmelCase    :		Optional[int]     	=					None

               # Update min_node
               _UpperCAmelCase    :		Any     	=					self.bottom_root
               _UpperCAmelCase    :		Tuple     	=					self.bottom_root.parent
               while i:
                      if i.val < self.min_node.val:
                             _UpperCAmelCase    :		str     	=					i
                      _UpperCAmelCase    :		int     	=					i.parent
               return min_value
        # General case
        # Find the BinomialHeap of the right subtree of min_node
        _UpperCAmelCase    :		List[str]     	=					self.min_node.right
        _UpperCAmelCase    :		Union[str, Any]     	=					None
        _UpperCAmelCase    :		List[Any]     	=					bottom_of_new
        _UpperCAmelCase    :		Dict     	=					1

        # Size, min_node and bottom_root
        while bottom_of_new.left:
               _UpperCAmelCase    :		Optional[int]     	=					size_of_new * 2 + 1
               _UpperCAmelCase    :		Tuple     	=					bottom_of_new.left
               if bottom_of_new.val < min_of_new.val:
                      _UpperCAmelCase    :		Optional[Any]     	=					bottom_of_new
        # Corner case of single root on top left path
        if (not self.min_node.left) and (not self.min_node.parent):
               _UpperCAmelCase    :		Any     	=					size_of_new
               _UpperCAmelCase    :		str     	=					bottom_of_new
               _UpperCAmelCase    :		int     	=					min_of_new
               # print("Single root, multiple nodes case")
               return min_value
        # Remaining cases
        # Construct heap of right subtree
        _UpperCAmelCase    :		List[str]     	=					BinomialHeap(
            bottom_root=a_    ,min_node=a_    ,heap_size=a_				)

        # Update size
        _UpperCAmelCase    :		int     	=					self.size - 1 - size_of_new

        # Neighbour nodes
        _UpperCAmelCase    :		Optional[int]     	=					self.min_node.left
        _UpperCAmelCase    :		Dict     	=					self.min_node.parent

        # Initialize new bottom_root and min_node
        _UpperCAmelCase    :		Dict     	=					previous_node or next_node
        _UpperCAmelCase    :		Tuple     	=					next_node

        # Update links of previous_node and search below for new min_node and
        # bottom_root
        if previous_node:
               _UpperCAmelCase    :		str     	=					next_node

               # Update bottom_root and search for min_node below
               _UpperCAmelCase    :		List[str]     	=					previous_node
               _UpperCAmelCase    :		Union[str, Any]     	=					previous_node
               while self.bottom_root.left:
                      _UpperCAmelCase    :		Tuple     	=					self.bottom_root.left
                      if self.bottom_root.val < self.min_node.val:
                             _UpperCAmelCase    :		Union[str, Any]     	=					self.bottom_root
        if next_node:
               _UpperCAmelCase    :		Tuple     	=					previous_node

               # Search for new min_node above min_node
               _UpperCAmelCase    :		Optional[int]     	=					next_node
               while i:
                      if i.val < self.min_node.val:
                             _UpperCAmelCase    :		Dict     	=					i
                      _UpperCAmelCase    :		int     	=					i.parent
        # Merge heaps
        self.merge_heaps(a_				)

        return min_value







 def _snake_case					(				self				)						->  Union[str, Any]:
        _UpperCAmelCase    :		Tuple     	=					self.bottom_root
        while top_root.parent:
               _UpperCAmelCase    :		List[Any]     	=					top_root.parent
        # preorder
        _UpperCAmelCase    :		str     	=					[]
        self.__traversal(a_    ,a_				)
        return heap_pre_order







 def _snake_case					(				self    ,a_    ,a_    ,a_=0				)						->  Dict:
        if curr_node:
               preorder.append((curr_node.val, level)				)
               self.__traversal(curr_node.left    ,a_    ,level + 1				)
               self.__traversal(curr_node.right    ,a_    ,level + 1				)
        else:
               preorder.append(("""#""", level)				)







 def __str__(				self				)						->  List[str]:
        if self.is_empty():
               return ""
        _UpperCAmelCase    :		Dict     	=					self.pre_order()

        return "\n".join(("""-""" * level + str(a_				)) for value, level in preorder_heap				)


# Unit Tests
if __name__ == "__main__":
   import doctest

   doctest.testmod()









'''simple docstring'''




import os




def     snake_case__     (			) -> int:
					A_			:  List[str]			=				os.path.dirname(os.path.realpath(lowerCamelCase__      )      )
					A_			:  str			=				os.path.join(lowerCamelCase__      ,		'''triangle.txt'''      )

					with open(lowerCamelCase__      ) as in_file:
										A_			:  List[str]			=				[[int(lowerCamelCase__      ) for i in line.split()] for line in in_file]

					while len(lowerCamelCase__      ) != 1:
										A_			:  List[str]			=				triangle.pop()
										A_			:  Optional[Any]			=				triangle[-1]
										for j in range(len(lowerCamelCase__      ) - 1      ):
															curr_row[j] += max(last_row[j]      ,		last_row[j + 1]      )
					return triangle[0][0]


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



