



from collections.abc import Sequence
from queue import Queue


class   lowerCamelCase					:
  """simple docstring"""







  def __init__(							self :       Optional[Any]  ,     __magic_name__ :       List[str]  ,     __magic_name__ :       int  ,     __magic_name__ :       Optional[Any]  ,     __magic_name__ :       str=None  ,     __magic_name__ :       List[str]=None   )  ->	Union[str, Any]:
        SCREAMING_SNAKE_CASE_          =  start
        SCREAMING_SNAKE_CASE_          =  end
        SCREAMING_SNAKE_CASE_          =  val
        SCREAMING_SNAKE_CASE_          =  (start + end) // 2
        SCREAMING_SNAKE_CASE_          =  left
        SCREAMING_SNAKE_CASE_          =  right







  def __repr__(							self :       Optional[Any]   )  ->	Optional[Any]:
        return F'''SegmentTreeNode(start={self.start}, end={self.end}, val={self.val})'''



class   lowerCamelCase					:
  """simple docstring"""







  def __init__(							self :       int  ,     __magic_name__ :       Sequence  ,     __magic_name__ :       List[str]   )  ->	str:
        SCREAMING_SNAKE_CASE_          =  collection
        SCREAMING_SNAKE_CASE_          =  function
        if self.collection:
              SCREAMING_SNAKE_CASE_          =  self._build_tree(0  ,     len(__magic_name__   ) - 1   )







  def    __A     (							self :       str  ,     __magic_name__ :       List[str]  ,     __magic_name__ :       List[Any]   )  ->	List[str]:
        self._update_tree(self.root  ,     __magic_name__  ,     __magic_name__   )







  def    __A     (							self :       Optional[Any]  ,     __magic_name__ :       Tuple  ,     __magic_name__ :       Dict   )  ->	List[Any]:
        return self._query_range(self.root  ,     __magic_name__  ,     __magic_name__   )







  def    __A     (							self :       Union[str, Any]  ,     __magic_name__ :       Tuple  ,     __magic_name__ :       Optional[Any]   )  ->	Optional[Any]:
        if start == end:
              return SegmentTreeNode(__magic_name__  ,     __magic_name__  ,     self.collection[start]   )
        SCREAMING_SNAKE_CASE_          =  (start + end) // 2
        SCREAMING_SNAKE_CASE_          =  self._build_tree(__magic_name__  ,     __magic_name__   )
        SCREAMING_SNAKE_CASE_          =  self._build_tree(mid + 1  ,     __magic_name__   )
        return SegmentTreeNode(__magic_name__  ,     __magic_name__  ,     self.fn(left.val  ,     right.val   )  ,     __magic_name__  ,     __magic_name__   )







  def    __A     (							self :       List[str]  ,     __magic_name__ :       List[Any]  ,     __magic_name__ :       int  ,     __magic_name__ :       List[str]   )  ->	Optional[Any]:
        if node.start == i and node.end == i:
              SCREAMING_SNAKE_CASE_          =  val
              return
        if i <= node.mid:
              self._update_tree(node.left  ,     __magic_name__  ,     __magic_name__   )
        else:
              self._update_tree(node.right  ,     __magic_name__  ,     __magic_name__   )
        SCREAMING_SNAKE_CASE_          =  self.fn(node.left.val  ,     node.right.val   )







  def    __A     (							self :       List[str]  ,     __magic_name__ :       Optional[Any]  ,     __magic_name__ :       Any  ,     __magic_name__ :       Any   )  ->	int:
        if node.start == i and node.end == j:
              return node.val

        if i <= node.mid:
              if j <= node.mid:
                    # range in left child tree
                    return self._query_range(node.left  ,     __magic_name__  ,     __magic_name__   )
              else:
                    # range in left child tree and right child tree
                    return self.fn(
                        self._query_range(node.left  ,     __magic_name__  ,     node.mid   )  ,     self._query_range(node.right  ,     node.mid + 1  ,     __magic_name__   )  ,     )
        else:
              # range in right child tree
              return self._query_range(node.right  ,     __magic_name__  ,     __magic_name__   )







  def    __A     (							self :       Optional[int]   )  ->	str:
        if self.root is not None:
              SCREAMING_SNAKE_CASE_          =  Queue()
              queue.put(self.root   )
              while not queue.empty():
                    SCREAMING_SNAKE_CASE_          =  queue.get()
                    yield node

                    if node.left is not None:
                          queue.put(node.left   )

                    if node.right is not None:
                          queue.put(node.right   )


if __name__ == "__main__":
      import operator

      for fn in [operator.add, max, min]:
            print("*" * 50)
            A     :  Tuple					     =       SegmentTree([2, 1, 5, 3, 4], fn)
            for node in arr.traverse():
                  print(node)
            print()

            arr.update(1, 5)
            for node in arr.traverse():
                  print(node)
            print()

            print(arr.query_range(3, 4))  # 7
            print(arr.query_range(2, 2))  # 5
            print(arr.query_range(1, 3))  # 13
            print()



from __future__ import annotations


def      a__ (		__UpperCamelCase				):

      # preprocessing the first row
      for i in range(1     ,      len(matrix[0]				)				):
            matrix[0][i] += matrix[0][i - 1]

      # preprocessing the first column
      for i in range(1     ,      len(__UpperCamelCase				)				):
            matrix[i][0] += matrix[i - 1][0]

      # updating the path cost for current position
      for i in range(1     ,      len(__UpperCamelCase				)				):
            for j in range(1     ,      len(matrix[0]				)				):
                  matrix[i][j] += min(matrix[i - 1][j]     ,      matrix[i][j - 1]				)

      return matrix[-1][-1]


if __name__ == "__main__":
      import doctest

      doctest.testmod()


