





def        __lowerCamelCase (							__a       :int = 1_0_0_0   )		->    int:






		"""simple docstring"""

		A__  				=       2**power
		A__  				=       str(__a   )
		A__  				=       list(__a   )
		A__  				=       0

		for i in list_num:
				sum_of_num += int(__a   )

		return sum_of_num


if __name__ == "__main__":
					A   : str			=				int(input('''Enter the power of 2: ''').strip())
					print('''2 ^ ''', power, ''' = ''', 2**power)
					A   : Any			=				solution(power)
					print('''Sum of the digits is: ''', result)










import unittest

import numpy as np







def        __lowerCamelCase (							__a       :np.ndarray   ,					__a       :np.ndarray   ,					__a       :np.ndarray   ,					__a       :np.ndarray | None = None   ,					)		->    np.ndarray:






		"""simple docstring"""

		A__  				=       np.shape(__a   )
		A__  				=       np.shape(__a   )
		A__  				=       np.shape(__a   )

		if shape_a[0] != shape_b[0]:
				A__  				=       (
				    """Expected the same number of rows for A and B. """
				    F'Instead found A of size {shape_a} and B of size {shape_b}'
				)
				raise ValueError(__a   )

		if shape_b[1] != shape_c[1]:
				A__  				=       (
				    """Expected the same number of columns for B and C. """
				    F'Instead found B of size {shape_b} and C of size {shape_c}'
				)
				raise ValueError(__a   )

		A__  				=       pseudo_inv
		if a_inv is None:
				try:
						A__  				=       np.linalg.inv(__a   )
				except np.linalg.LinAlgError:
						raise ValueError(
						    """Input matrix A is not invertible. Cannot compute Schur complement."""   )

		return mat_c - mat_b.T @ a_inv @ mat_b


class   A      (unittest.TestCase   ):
			'''simple docstring'''




			def        a_	(      self       :   Union[str, Any]       )     ->     None:







					"""simple docstring"""






					A__  				=       np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]       )
					A__  				=       np.array([[0, 3], [3, 0], [2, 3]]       )
					A__  				=       np.array([[2, 1], [6, 3]]       )

					A__  				=       schur_complement(__lowerCAmelCase							,     __lowerCAmelCase							,     __lowerCAmelCase       )

					A__  				=       np.block([[a, b], [b.T, c]]       )

					A__  				=       np.linalg.det(__lowerCAmelCase       )
					A__  				=       np.linalg.det(__lowerCAmelCase       )
					A__  				=       np.linalg.det(__lowerCAmelCase       )

					self.assertAlmostEqual(__lowerCAmelCase							,     det_a * det_s       )






			def        a_	(      self       :   str       )     ->     None:







					"""simple docstring"""






					A__  				=       np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]       )
					A__  				=       np.array([[0, 3], [3, 0], [2, 3]]       )
					A__  				=       np.array([[2, 1], [6, 3]]       )

					with self.assertRaises(__lowerCAmelCase       ):
							schur_complement(__lowerCAmelCase							,     __lowerCAmelCase							,     __lowerCAmelCase       )







			def        a_	(      self       :   List[str]       )     ->     None:







					"""simple docstring"""






					A__  				=       np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]       )
					A__  				=       np.array([[0, 3], [3, 0], [2, 3]]       )
					A__  				=       np.array([[2, 1, 3], [6, 3, 5]]       )

					with self.assertRaises(__lowerCAmelCase       ):
							schur_complement(__lowerCAmelCase							,     __lowerCAmelCase							,     __lowerCAmelCase       )


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					unittest.main()



