

import qiskit






def    SCREAMING_SNAKE_CASE__       (  lowerCamelCase__	, lowerCamelCase__			)  ->     qiskit.result.counts.Counts:
	__lowerCamelCase				:				Optional[int]					       = qiskit.Aer.get_backend('aer_simulator'			)

	# Create a Quantum Circuit acting on the q register
	__lowerCamelCase				:				List[str]					       = qiskit.QuantumCircuit(lowerCamelCase__	, lowerCamelCase__			)

	# Map the quantum measurement to the classical bits
	circuit.measure([0]	, [0]			)

	# Execute the circuit on the simulator
	__lowerCamelCase				:				List[Any]					       = qiskit.execute(lowerCamelCase__	, lowerCamelCase__	, shots=1_0_0_0			)

	# Return the histogram data of the results of the experiment.
	return job.result().get_counts(lowerCamelCase__			)


if __name__ == "__main__":
					print(F"""Total count for various states are: {single_qubit_measure(1, 1)}""")











from math import factorial

lowerCAmelCase_    =				{str(digit): factorial(digit) for digit in range(1_0)}






def      lowerCamelCase_						(				_UpperCamelCase )		->						int:






				"""simple docstring"""


				if not isinstance(_UpperCamelCase ,				_UpperCamelCase ):
								raise TypeError('''Parameter number must be int''' )

				if number < 0:
								raise ValueError('''Parameter number must be greater than or equal to 0''' )

				# Converts number in string to iterate on its digits and adds its factorial.
				return sum(DIGIT_FACTORIAL[digit] for digit in str(_UpperCamelCase ) )






def      lowerCamelCase_						(				_UpperCamelCase = 60 ,				_UpperCamelCase = 1_000_000 )		->						int:






				"""simple docstring"""


				if not isinstance(_UpperCamelCase ,				_UpperCamelCase ) or not isinstance(_UpperCamelCase ,				_UpperCamelCase ):
								raise TypeError('''Parameters chain_length and number_limit must be int''' )

				if chain_length <= 0 or number_limit <= 0:
								raise ValueError(
								    '''Parameters chain_length and number_limit must be greater than 0''' )

				# the counter for the chains with the exact desired length
				snake_case_						:    Optional[Any]				=  0
				# the cached sizes of the previous chains
				snake_case_						:    dict[int, int]				=  {}

				for start_chain_element in range(1 ,				_UpperCamelCase ):
								# The temporary set will contain the elements of the chain
								snake_case_						:    List[str]				=  set()
								snake_case_						:    List[Any]				=  0

								# Stop computing the chain when you find a cached size, a repeating item or the
								# length is greater then the desired one.
								snake_case_						:    Any				=  start_chain_element
								while (
								    chain_element not in chain_sets_lengths
								    and chain_element not in chain_set
								    and chain_set_length <= chain_length
								):
												chain_set.add(_UpperCamelCase )
												chain_set_length += 1
												snake_case_						:    List[Any]				=  digit_factorial_sum(_UpperCamelCase )

								if chain_element in chain_sets_lengths:
												chain_set_length += chain_sets_lengths[chain_element]

								snake_case_						:    List[str]				=  chain_set_length

								# If chain contains the exact amount of elements increase the counter
								if chain_set_length == chain_length:
												chains_counter += 1

				return chains_counter


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	print(F'''{solution()}''')
