
import qiskit
from qiskit.providers import Backend
def 					lowerCAmelCase__     (    SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_	)							->						tuple[qiskit.QuantumCircuit, str, str]:
			lowerCAmelCase__ ,							lowerCAmelCase__ : int   =						bin(SCREAMING_SNAKE_CASE_	)[2:], bin(SCREAMING_SNAKE_CASE_	)[2:]  # Remove leading '0b'

			# Ensure that both strings are of the same length
			if len(SCREAMING_SNAKE_CASE_	) > len(SCREAMING_SNAKE_CASE_	):
						lowerCAmelCase__ : Optional[int]   =						y.zfill(len(SCREAMING_SNAKE_CASE_	)	)
			else:
						lowerCAmelCase__ : Any   =						x.zfill(len(SCREAMING_SNAKE_CASE_	)	)

			# We need (3 * number of bits in the larger number)+1 qBits
			# The second parameter is the number of classical registers, to measure the result
			lowerCAmelCase__ : Optional[Any]   =						qiskit.QuantumCircuit((len(SCREAMING_SNAKE_CASE_	) * 3) + 1			,				len(SCREAMING_SNAKE_CASE_	) + 1	)

			# We are essentially "not-ing" the bits that are 1
			# Reversed because it's easier to perform ops on more significant bits
			for i in range(len(SCREAMING_SNAKE_CASE_	)	):
						if x[::-1][i] == "1":
									circuit.x(SCREAMING_SNAKE_CASE_	)
			for j in range(len(SCREAMING_SNAKE_CASE_	)	):
						if y[::-1][j] == "1":
									circuit.x(len(SCREAMING_SNAKE_CASE_	) + j	)

			return circuit, x, y
def 					lowerCAmelCase__     (    SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_			,				)							->						Union[str, Any]:
			circuit.ccx(SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_	)
			circuit.cx(SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_	)
			circuit.ccx(SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_	)
			circuit.cx(SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_	)
			circuit.cx(SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_	)
def 					lowerCAmelCase__     (    SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_ = qiskit.Aer.get_backend('aer_simulator'	)			,				)							->						int:

			if vala < 0 or vala < 0:
						raise ValueError('Both Integers must be positive!'	)

			# Store the Integers
			lowerCAmelCase__ ,							lowerCAmelCase__ ,							lowerCAmelCase__ : List[Any]   =						store_two_classics(SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_	)
			for i in range(len(SCREAMING_SNAKE_CASE_	)	):
						full_adder(SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_			,				len(SCREAMING_SNAKE_CASE_	) + i			,				len(SCREAMING_SNAKE_CASE_	) + len(SCREAMING_SNAKE_CASE_	) + i			,				len(SCREAMING_SNAKE_CASE_	) + len(SCREAMING_SNAKE_CASE_	) + i + 1	)
						circuit.barrier()  # Optional, just for aesthetics

			# Measure the resultant qBits
			for i in range(len(SCREAMING_SNAKE_CASE_	) + 1	):
						circuit.measure([(len(SCREAMING_SNAKE_CASE_	) * 2) + i]			,				[i]	)

			lowerCAmelCase__ : List[Any]   =						qiskit.execute(SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_			,				shots=1	).result()

			# The result is in binary. Convert it back to int
			return int(list(res.get_counts()	)[0]			,				2	)


if __name__ == "__main__":
					import doctest

					doctest.testmod()

import math
from decimal import Decimal, getcontext
def 					lowerCAmelCase__     (    SCREAMING_SNAKE_CASE_ = 4_000_000	)							->						int:

			try:
						lowerCAmelCase__ : str   =						int(SCREAMING_SNAKE_CASE_	)
			except (TypeError, ValueError):
						raise TypeError('Parameter n must be int or castable to int.'	)
			if n <= 0:
						raise ValueError('Parameter n must be greater than or equal to one.'	)
			lowerCAmelCase__ : Union[str, Any]   =						100
			lowerCAmelCase__ : List[Any]   =						(Decimal(5	) ** Decimal(0.5	) + 1) / Decimal(2	)

			lowerCAmelCase__ : Tuple   =						(math.floor(math.log(n * (phi + 2)			,				SCREAMING_SNAKE_CASE_	) - 1	) // 3) * 3 + 2
			lowerCAmelCase__ : Optional[int]   =						Decimal(round(phi ** Decimal(index + 1	)	)	) / (phi + 2)
			lowerCAmelCase__ : Tuple   =						num // 2
			return int(SCREAMING_SNAKE_CASE_	)


if __name__ == "__main__":
					print(F"""{solution() = }""")