





from __future__ import annotations

import math


def     lowerCamelCase_	(      lowerCAmelCase:	float    ,							lowerCAmelCase:	int				)->		float:
  _snake_case   :				Tuple														=	u
  for i in range(1    ,							lowerCAmelCase				):
    _snake_case   :				Optional[int]														=	temp * (u - i)
  return temp


def     lowerCamelCase_	(      )->		None:
  _snake_case   :				Optional[Any]														=	int(input('enter the numbers of values: '				)				)
  _snake_case   :				list[list[float]]														=	[]
  for _ in range(lowerCAmelCase				):
    y.append([]				)
  for i in range(lowerCAmelCase				):
    for j in range(lowerCAmelCase				):
      y[i].append(lowerCAmelCase				)
      _snake_case   :				int														=	0

  print('enter the values of parameters in a list: '				)
  _snake_case   :				Tuple														=	list(map(lowerCAmelCase    ,							input().split()				)				)

  print('enter the values of corresponding parameters: '				)
  for i in range(lowerCAmelCase				):
    _snake_case   :				Dict														=	float(input()				)

  _snake_case   :				Tuple														=	int(input('enter the value to interpolate: '				)				)
  _snake_case   :				int														=	(value - x[0]) / (x[1] - x[0])

  # for calculating forward difference table

  for i in range(1    ,							lowerCAmelCase				):
    for j in range(n - i				):
      _snake_case   :				Tuple														=	y[j + 1][i - 1] - y[j][i - 1]

  _snake_case   :				Union[str, Any]														=	y[0][0]
  for i in range(1    ,							lowerCAmelCase				):
    summ += (ucal(lowerCAmelCase    ,							lowerCAmelCase				) * y[0][i]) / math.factorial(lowerCAmelCase				)

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


if __name__ == "__main__":
      main()











from __future__ import annotations

from random import random



class        _lowerCAmelCase    :


  '''simple docstring'''







  def __init__(      self      :					Dict      ,				UpperCamelCase      :					int | None = None							):


    '''simple docstring'''





    _snake_case   :				str														=	value
    _snake_case   :				List[Any]														=	random()
    _snake_case   :				Node | None														=	None
    _snake_case   :				Node | None														=	None







  def __repr__(      self      :					Optional[Any]							):


    '''simple docstring'''





    from pprint import pformat

    if self.left is None and self.right is None:
      return f"""'{self.value}: {self.prior:.5}'"""
    else:
      return pformat(
          {f"""{self.value}: {self.prior:.5}""": (self.left, self.right)}      ,				indent=1							)







  def __str__(      self      :					Dict							):


    '''simple docstring'''





    _snake_case   :				List[str]														=	str(self.value							) + ' '
    _snake_case   :				List[Any]														=	str(self.left or ''							)
    _snake_case   :				int														=	str(self.right or ''							)
    return value + left + right




def     lowerCamelCase_	(      lowerCAmelCase:	Node | None    ,							lowerCAmelCase:	int				)->		tuple[Node | None, Node | None]:
  if root is None:  # None tree is split into 2 Nones
    return None, None
  elif root.value is None:
    return None, None
  else:
    if value < root.value:
      _snake_case							,					_snake_case   :				Optional[Any]														=	split(root.left    ,							lowerCAmelCase				)
      return left, root
    else:
      _snake_case							,					_snake_case   :				List[str]														=	split(root.right    ,							lowerCAmelCase				)
      return root, right


def     lowerCamelCase_	(      lowerCAmelCase:	Node | None    ,							lowerCAmelCase:	Node | None				)->		Node | None:
  if (not left) or (not right):  # If one node is None, return the other
    return left or right
  elif left.prior < right.prior:
    _snake_case   :				str														=	merge(left.right    ,							lowerCAmelCase				)
    return left
  else:
    _snake_case   :				Union[str, Any]														=	merge(lowerCAmelCase    ,							right.left				)
    return right


def     lowerCamelCase_	(      lowerCAmelCase:	Node | None    ,							lowerCAmelCase:	int				)->		Node | None:
  _snake_case   :				Tuple														=	Node(lowerCAmelCase				)
  _snake_case							,					_snake_case   :				Optional[int]														=	split(lowerCAmelCase    ,							lowerCAmelCase				)
  return merge(merge(lowerCAmelCase    ,							lowerCAmelCase				)    ,							lowerCAmelCase				)


def     lowerCamelCase_	(      lowerCAmelCase:	Node | None    ,							lowerCAmelCase:	int				)->		Node | None:
  _snake_case							,					_snake_case   :				Optional[int]														=	split(lowerCAmelCase    ,							value - 1				)
  _snake_case							,					_snake_case   :				List[str]														=	split(lowerCAmelCase    ,							lowerCAmelCase				)
  return merge(lowerCAmelCase    ,							lowerCAmelCase				)


def     lowerCamelCase_	(      lowerCAmelCase:	Node | None				)->		None:
  if not root:  # None
    return
  else:
    inorder(root.left				)
    print(root.value    ,							end=','				)
    inorder(root.right				)


def     lowerCamelCase_	(      lowerCAmelCase:	Node | None    ,							lowerCAmelCase:	str				)->		Node | None:
  for arg in args.split():
    if arg[0] == "+":
      _snake_case   :				List[str]														=	insert(lowerCAmelCase    ,							int(arg[1:]				)				)

    elif arg[0] == "-":
      _snake_case   :				Any														=	erase(lowerCAmelCase    ,							int(arg[1:]				)				)

    else:
      print('Unknown command'				)

  return root


def     lowerCamelCase_	(      )->		None:
  _snake_case   :				Tuple														=	None
  print(
      'enter numbers to create a tree, + value to add value into treap, '
      '- value to erase all nodes with value. \'q\' to quit. '				)

  _snake_case   :				List[Any]														=	input()
  while args != "q":
    _snake_case   :				int														=	interact_treap(lowerCAmelCase    ,							lowerCAmelCase				)
    print(lowerCAmelCase				)
    _snake_case   :				Tuple														=	input()

  print('good by!'				)


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      main()




