





'''simple docstring'''


_lowerCamelCase :		dict[tuple[int, int, int], int] 			=				{}




def       __a       (   UpperCAmelCase				,	UpperCAmelCase				,	UpperCAmelCase			)					->int:



	"""simple docstring"""







	if late == 3 or absent == 2:
		return 0

	# if we have no days left, and have not failed any other rules,
	# we have a prize string
	if days == 0:
		return 1

	# No easy solution, so now we need to do the recursive calculation

	# First, check if the combination is already in the cache, and
	# if yes, return the stored value from there since we already
	# know the number of possible prize strings from this point on
	A							     =					(days, absent, late)
	if key in cache:
		return cache[key]

	# now we calculate the three possible ways that can unfold from
	# this point on, depending on our attendance today

	# 1) if we are late (but not absent), the "absent" counter stays as
	# it is, but the "late" counter increases by one
	A							     =					_calculate(days - 1				,	UpperCAmelCase				,	late + 1			)

	# 2) if we are absent, the "absent" counter increases by 1, and the
	# "late" counter resets to 0
	A							     =					_calculate(days - 1				,	absent + 1				,	0			)

	# 3) if we are on time, this resets the "late" counter and keeps the
	# absent counter
	A							     =					_calculate(days - 1				,	UpperCAmelCase				,	0			)

	A							     =					state_late + state_absent + state_ontime

	A							     =					prizestrings
	return prizestrings




def       __a       (   UpperCAmelCase = 30			)					->int:



	"""simple docstring"""







	return _calculate(UpperCAmelCase				,	absent=0				,	late=0			)


if __name__ == "__main__":
				print(solution())









import math

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

def    SCREAMING_SNAKE_CASE_							(							__magic_name__					:  int = 3					)		->			qiskit.result.counts.Counts:






	"""simple docstring"""



	if isinstance(__magic_name__	,			__magic_name__					):
		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(__magic_name__					) != 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)."""					)

	UpperCamelCase     :int          =	QuantumRegister(__magic_name__	,			"""qr"""					)
	UpperCamelCase     :str          =	ClassicalRegister(__magic_name__	,			"""cr"""					)

	UpperCamelCase     :str          =	QuantumCircuit(__magic_name__	,			__magic_name__					)

	UpperCamelCase     :List[Any]          =	number_of_qubits

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

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

	# measure all the qubits
	quantum_circuit.measure(__magic_name__	,			__magic_name__					)
	# simulate with 10000 shots
	UpperCamelCase     :str          =	Aer.get_backend("""qasm_simulator"""					)
	UpperCamelCase     :Dict          =	execute(__magic_name__	,			__magic_name__	,			shots=1_0000					)

	return job.result().get_counts(__magic_name__					)


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