





import math

import numpy as np
import qiskit
from qiskit import Aer, ClassicalRegister, QuantumCircuit, QuantumRegister, execute


def     lowerCamelCase_	(      lowerCAmelCase:	Optional[int] = 3				)->		qiskit.result.counts.Counts:



		if isinstance(lowerCAmelCase    ,							lowerCAmelCase				):
				raise TypeError('number of qubits must be a integer.'				)
		if number_of_qubits <= 0:
				raise ValueError('number of qubits must be > 0.'				)
		if math.floor(lowerCAmelCase				) != number_of_qubits:
				raise ValueError('number of qubits must be exact integer.'				)
		if number_of_qubits > 10:
				raise ValueError('number of qubits too large to simulate(>10).'				)

		_snake_case   :				str														=	QuantumRegister(lowerCAmelCase    ,							'qr'				)
		_snake_case   :				Union[str, Any]														=	ClassicalRegister(lowerCAmelCase    ,							'cr'				)

		_snake_case   :				Optional[int]														=	QuantumCircuit(lowerCAmelCase    ,							lowerCAmelCase				)

		_snake_case   :				List[str]														=	number_of_qubits

		for i in range(lowerCAmelCase				):
				quantum_circuit.h(number_of_qubits - i - 1				)
				counter -= 1
				for j in range(lowerCAmelCase				):
						quantum_circuit.cp(np.pi / 2 ** (counter - j)    ,							lowerCAmelCase    ,							lowerCAmelCase				)

		for k in range(number_of_qubits // 2				):
				quantum_circuit.swap(lowerCAmelCase    ,							number_of_qubits - k - 1				)

		# measure all the qubits
		quantum_circuit.measure(lowerCAmelCase    ,							lowerCAmelCase				)
		# simulate with 10000 shots
		_snake_case   :				List[str]														=	Aer.get_backend('qasm_simulator'				)
		_snake_case   :				Optional[int]														=	execute(lowerCAmelCase    ,							lowerCAmelCase    ,							shots=1_00_00				)

		return job.result().get_counts(lowerCAmelCase				)


if __name__ == "__main__":
						print(
						    F"""Total count for quantum fourier transform state is: \
    {quantum_fourier_transform(3)}"""
						)











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()




