






import math

import qiskit







def 	_UpperCamelCase   (    UpperCamelCase_       :					int = 1    ,       UpperCamelCase_       :					int = 1    ,       UpperCamelCase_       :					int = 1		)  ->   qiskit.result.counts.Counts:

						"""simple docstring"""



						if (
						    isinstance(UpperCamelCase_    ,       UpperCamelCase_		)
						    or isinstance(UpperCamelCase_    ,       UpperCamelCase_		)
						    or isinstance(UpperCamelCase_    ,       UpperCamelCase_		)
						):
												raise TypeError('inputs must be integers.'		)

						if (input_a < 0) or (input_a < 0) or (carry_in < 0):
												raise ValueError('inputs must be positive.'		)

						if (
						    (math.floor(UpperCamelCase_		) != input_a)
						    or (math.floor(UpperCamelCase_		) != input_a)
						    or (math.floor(UpperCamelCase_		) != carry_in)
						):
												raise ValueError('inputs must be exact integers.'		)

						if (input_a > 2) or (input_a > 2) or (carry_in > 2):
												raise ValueError('inputs must be less or equal to 2.'		)

						# build registers
						lowerCAmelCase__    						=						qiskit.QuantumRegister(4    ,       'qr'		)
						lowerCAmelCase__    						=						qiskit.ClassicalRegister(2    ,       'cr'		)
						# list the entries
						lowerCAmelCase__    						=						[input_a, input_a, carry_in]

						lowerCAmelCase__    						=						qiskit.QuantumCircuit(UpperCamelCase_    ,       UpperCamelCase_		)

						for i in range(0    ,       3		):
												if entry[i] == 2:
																		quantum_circuit.h(UpperCamelCase_		)  # for hadamard entries
												elif entry[i] == 1:
																		quantum_circuit.x(UpperCamelCase_		)  # for 1 entries
												elif entry[i] == 0:
																		quantum_circuit.i(UpperCamelCase_		)  # for 0 entries

    # build the circuit
						quantum_circuit.ccx(0    ,       1    ,       3		)  # ccx = toffoli gate
						quantum_circuit.cx(0    ,       1		)
						quantum_circuit.ccx(1    ,       2    ,       3		)
						quantum_circuit.cx(1    ,       2		)
						quantum_circuit.cx(0    ,       1		)

						quantum_circuit.measure([2, 3]    ,       UpperCamelCase_		)  # measure the last two qbits

						lowerCAmelCase__    						=						qiskit.Aer.get_backend('aer_simulator'		)
						lowerCAmelCase__    						=						qiskit.execute(UpperCamelCase_    ,       UpperCamelCase_    ,       shots=1000		)

						return job.result().get_counts(UpperCamelCase_		)


if __name__ == "__main__":
					print(f'Total sum count for state is: {quantum_full_adder(1, 1, 1)}')













from __future__ import annotations

from functools import lru_cache
from math import ceil

__snake_case    :    Union[str, Any]         =     1_00

__snake_case    :    Tuple         =     set(range(3, NUM_PRIMES, 2))
primes.add(2)
__snake_case    :    int

for prime in range(3, ceil(NUM_PRIMES**0.5), 2):
					if prime not in primes:
										continue
					primes.difference_update(set(range(prime * prime, NUM_PRIMES, prime)))







@lru_cache(maxsize=100		)
def 	_UpperCamelCase   (    UpperCamelCase_       :					int		)  ->   set[int]:

						"""simple docstring"""



						if number_to_partition < 0:
												return set()
						elif number_to_partition == 0:
												return {1}

						lowerCAmelCase__    						=						set()
						lowerCAmelCase__    						=						42
						lowerCAmelCase__    						=						42

						for prime in primes:
												if prime > number_to_partition:
																		continue
												for sub in partition(number_to_partition - prime		):
																		ret.add(sub * prime		)

						return ret







def 	_UpperCamelCase   (    UpperCamelCase_       :					int = 5000		)  ->   int | None:

						"""simple docstring"""



						for number_to_partition in range(1    ,       UpperCamelCase_		):
												if len(partition(UpperCamelCase_		)		) > number_unique_partitions:
																		return number_to_partition
						return None


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





