

import itertools
import math

def        lowerCamelCase__       (    _a):

	if 1 < number < 4:
		# 2 and 3 are primes
		return True
	elif number < 2 or number % 2 == 0 or number % 3 == 0:
		# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
		return False

	# All primes number are in format of 6k +/- 1
	for i in range(5							,	int(math.sqrt(__snake_case) + 1)							,	6):
		if number % i == 0 or number % (i + 2) == 0:
			return False
	return True

def        lowerCamelCase__       (    ):
	SCREAMING_SNAKE_CASE      :					Optional[Any]    =				2
	while True:
		if is_prime(__snake_case):
			yield num
		num += 1

def        lowerCamelCase__       (    _a = 10001):
	return next(itertools.islice(prime_generator()							,	nth - 1							,	__snake_case))


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






'''simple docstring'''




import math

import qiskit






def        _lowerCAmelCase			(  __snake_case  : int = 1 ,							__snake_case  : int = 1 ,							__snake_case  : int = 1			)     ->     qiskit.result.counts.Counts:
     if (
         isinstance(__snake_case ,							__snake_case			)
         or isinstance(__snake_case ,							__snake_case			)
         or isinstance(__snake_case ,							__snake_case			)
     ):
          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(__snake_case			) != input_a)
         or (math.floor(__snake_case			) != input_a)
         or (math.floor(__snake_case			) != 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
     __A						: int      =       qiskit.QuantumRegister(4 ,							'qr'			)
     __A						: Optional[int]      =       qiskit.ClassicalRegister(2 ,							'cr'			)
     # list the entries
     __A						: Union[str, Any]      =       [input_a, input_a, carry_in]

     __A						: Dict      =       qiskit.QuantumCircuit(__snake_case ,							__snake_case			)

     for i in range(0 ,							3			):
          if entry[i] == 2:
               quantum_circuit.h(__snake_case			)  # for hadamard entries
          elif entry[i] == 1:
               quantum_circuit.x(__snake_case			)  # for 1 entries
          elif entry[i] == 0:
               quantum_circuit.i(__snake_case			)  # 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] ,							__snake_case			)  # measure the last two qbits

     __A						: str      =       qiskit.Aer.get_backend('aer_simulator'			)
     __A						: Any      =       qiskit.execute(__snake_case ,							__snake_case ,							shots=10_00			)

     return job.result().get_counts(__snake_case			)


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