


from collections.abc import Sequence
from queue import Queue

class   A__ :







    """simple docstring"""

    def __init__(	self      , __snake_case      , __snake_case      , __snake_case      , __snake_case=None      , __snake_case=None   ):
         snake_case					=    start
         snake_case					=    end
         snake_case					=    val
         snake_case					=    (start + end) // 2
         snake_case					=    left
         snake_case					=    right




    def __repr__(	self   ):
         return F'''SegmentTreeNode(start={self.start}, end={self.end}, val={self.val})'''


class   A__ :







    """simple docstring"""

    def __init__(	self      , __snake_case      , __snake_case   ):
         snake_case					=    collection
         snake_case					=    function
         if self.collection:
              snake_case					=    self._build_tree(0      , len(__snake_case   ) - 1   )
    def 		a_      (	self      , __snake_case      , __snake_case   ):
         self._update_tree(self.root      , __snake_case      , __snake_case   )
    def 		a_      (	self      , __snake_case      , __snake_case   ):
         return self._query_range(self.root      , __snake_case      , __snake_case   )
    def 		a_      (	self      , __snake_case      , __snake_case   ):
         if start == end:
              return SegmentTreeNode(__snake_case      , __snake_case      , self.collection[start]   )
         snake_case					=    (start + end) // 2
         snake_case					=    self._build_tree(__snake_case      , __snake_case   )
         snake_case					=    self._build_tree(mid + 1      , __snake_case   )
         return SegmentTreeNode(__snake_case      , __snake_case      , self.fn(left.val      , right.val   )      , __snake_case      , __snake_case   )
    def 		a_      (	self      , __snake_case      , __snake_case      , __snake_case   ):
         if node.start == i and node.end == i:
              snake_case					=    val
              return
         if i <= node.mid:
              self._update_tree(node.left      , __snake_case      , __snake_case   )
         else:
              self._update_tree(node.right      , __snake_case      , __snake_case   )
         snake_case					=    self.fn(node.left.val      , node.right.val   )
    def 		a_      (	self      , __snake_case      , __snake_case      , __snake_case   ):
         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      , __snake_case      , __snake_case   )
              else:
                   # range in left child tree and right child tree
                   return self.fn(
                       self._query_range(node.left      , __snake_case      , node.mid   )      , self._query_range(node.right      , node.mid + 1      , __snake_case   )      , )
         else:
              # range in right child tree
              return self._query_range(node.right      , __snake_case      , __snake_case   )




    def 		a_      (	self   ):
         if self.root is not None:
              snake_case					=    Queue()
              queue.put(self.root   )
              while not queue.empty():
                   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)
  _SCREAMING_SNAKE_CASE      :			Optional[Any]      				=   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()








def       UpperCAmelCase__						(UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_    ):



     """simple docstring"""






     snake_case					=    len(UpperCamelCase_    )
     snake_case					=    [[0] * n for i in range(UpperCamelCase_    )]
     for i in range(UpperCamelCase_    ):
          snake_case					=    y_points[i]

     for i in range(2							,UpperCamelCase_    ):
          for j in range(UpperCamelCase_							,UpperCamelCase_    ):
               snake_case					=    (
                   (xa - x_points[j - i + 1]) * q[j][i - 1]
                   - (xa - x_points[j]) * q[j - 1][i - 1]
               ) / (x_points[j] - x_points[j - i + 1])

     return [q[n - 1][n - 1], q]


if __name__ == "__main__":
 import doctest

 doctest.testmod()




