


from collections.abc import Sequence
from queue import Queue


class     lowercase__  :






  def __init__(					self      :					Any		,						_lowercase      :					str		,						_lowercase      :					str		,						_lowercase      :					int		,						_lowercase      :					Dict=None		,						_lowercase      :					Tuple=None ):




         """simple docstring"""







         UpperCAmelCase__										=     start
         UpperCAmelCase__										=     end
         UpperCAmelCase__										=     val
         UpperCAmelCase__										=     (start + end) // 2
         UpperCAmelCase__										=     left
         UpperCAmelCase__										=     right






  def __repr__(					self      :					Optional[int] ):




         """simple docstring"""







         return F"""SegmentTreeNode(start={self.start}, end={self.end}, val={self.val})"""




class     lowercase__  :






  def __init__(					self      :					Optional[Any]		,						_lowercase      :					List[Any]		,						_lowercase      :					str ):




         """simple docstring"""







         UpperCAmelCase__										=     collection
         UpperCAmelCase__										=     function
         if self.collection:
                UpperCAmelCase__										=     self._build_tree(0		,						len(snake_case__ ) - 1 )






  def 			_UpperCAmelCase  (					self      :					List[Any]		,						_lowercase      :					List[Any]		,						_lowercase      :					Dict ):




         """simple docstring"""







         self._update_tree(self.root		,						snake_case__		,						snake_case__ )






  def 			_UpperCAmelCase  (					self      :					Optional[Any]		,						_lowercase      :					Union[str, Any]		,						_lowercase      :					str ):




         """simple docstring"""







         return self._query_range(self.root		,						snake_case__		,						snake_case__ )






  def 			_UpperCAmelCase  (					self      :					Optional[int]		,						_lowercase      :					List[str]		,						_lowercase      :					str ):




         """simple docstring"""







         if start == end:
                return SegmentTreeNode(snake_case__		,						snake_case__		,						self.collection[start] )
         UpperCAmelCase__										=     (start + end) // 2
         UpperCAmelCase__										=     self._build_tree(snake_case__		,						snake_case__ )
         UpperCAmelCase__										=     self._build_tree(mid + 1		,						snake_case__ )
         return SegmentTreeNode(snake_case__		,						snake_case__		,						self.fn(left.val		,						right.val )		,						snake_case__		,						snake_case__ )






  def 			_UpperCAmelCase  (					self      :					List[str]		,						_lowercase      :					Dict		,						_lowercase      :					int		,						_lowercase      :					Optional[Any] ):




         """simple docstring"""







         if node.start == i and node.end == i:
                UpperCAmelCase__										=     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__ )
         UpperCAmelCase__										=     self.fn(node.left.val		,						node.right.val )






  def 			_UpperCAmelCase  (					self      :					Optional[Any]		,						_lowercase      :					Tuple		,						_lowercase      :					List[Any]		,						_lowercase      :					List[str] ):




         """simple docstring"""







         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 			_UpperCAmelCase  (					self      :					List[Any] ):




         """simple docstring"""







         if self.root is not None:
                UpperCAmelCase__										=     Queue()
                queue.put(self.root )
                while not queue.empty():
                       UpperCAmelCase__										=     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      = 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

import math





def __UpperCAmelCase       (		__A ,						__A			)						->					float:



       '''simple docstring'''





       UpperCAmelCase__										=     u
       for i in range(1 ,						__A			):
              UpperCAmelCase__										=     temp * (u - i)
       return temp





def __UpperCAmelCase       (		)						->					None:



       '''simple docstring'''





       UpperCAmelCase__										=     int(input("enter the numbers of values: "			)			)
       UpperCAmelCase__										=     []
       for _ in range(__A			):
              y.append([]			)
       for i in range(__A			):
              for j in range(__A			):
                     y[i].append(__A			)
                     UpperCAmelCase__										=     0

       print("enter the values of parameters in a list: "			)
       UpperCAmelCase__										=     list(map(__A ,						input().split()			)			)

       print("enter the values of corresponding parameters: "			)
       for i in range(__A			):
              UpperCAmelCase__										=     float(input()			)

       UpperCAmelCase__										=     int(input("enter the value to interpolate: "			)			)
       UpperCAmelCase__										=     (value - x[0]) / (x[1] - x[0])

       # for calculating forward difference table

       for i in range(1 ,						__A			):
              for j in range(n - i			):
                     UpperCAmelCase__										=     y[j + 1][i - 1] - y[j][i - 1]

       UpperCAmelCase__										=     y[0][0]
       for i in range(1 ,						__A			):
              summ += (ucal(__A ,						__A			) * y[0][i]) / math.factorial(__A			)

       print(F"""the value at {value} is {summ}"""			)


if __name__ == "__main__":
    main()





