




import itertools
import string
from collections.abc import Generator, Iterable




def        _SCREAMING_SNAKE_CASE      (		snake_case			,     snake_case       )						->				Generator[tuple[str, ...], None, None]:
						_UpperCAmelCase      =			iter(snake_case       )
						while True:
												_UpperCAmelCase      =			tuple(itertools.islice(snake_case			,     snake_case       )       )
												if not chunk:
																		return
												yield chunk




def        _SCREAMING_SNAKE_CASE      (		snake_case       )						->				str:
						_UpperCAmelCase      =			"""""".join([c.upper() for c in dirty if c in string.ascii_letters]       )
						_UpperCAmelCase      =			""""""

						if len(snake_case       ) < 2:
												return dirty

						for i in range(len(snake_case       ) - 1       ):
												clean += dirty[i]

												if dirty[i] == dirty[i + 1]:
																		clean += "X"

						clean += dirty[-1]

						if len(snake_case       ) & 1:
												clean += "X"

						return clean




def        _SCREAMING_SNAKE_CASE      (		snake_case       )						->				list[str]:
						# I and J are used interchangeably to allow
						# us to use a 5x5 table (25 letters)
						_UpperCAmelCase      =			"""ABCDEFGHIKLMNOPQRSTUVWXYZ"""
						# we're using a list instead of a '2d' array because it makes the math
						# for setting up the table and doing the actual encoding/decoding simpler
						_UpperCAmelCase      =			[]

						# copy key chars into the table if they are in `alphabet` ignoring duplicates
						for char in key.upper():
												if char not in table and char in alphabet:
																		table.append(snake_case       )

    # fill the rest of the table in with the remaining alphabet chars
						for char in alphabet:
												if char not in table:
																		table.append(snake_case       )

						return table




def        _SCREAMING_SNAKE_CASE      (		snake_case			,     snake_case       )						->				str:
						_UpperCAmelCase      =			generate_table(snake_case       )
						_UpperCAmelCase      =			prepare_input(snake_case       )
						_UpperCAmelCase      =			""""""

						# https://en.wikipedia.org/wiki/Playfair_cipher#Description
						for chara, chara in chunker(snake_case			,     2       ):
												_UpperCAmelCase    ,					_UpperCAmelCase      =			divmod(table.index(snake_case       )			,     5       )
												_UpperCAmelCase    ,					_UpperCAmelCase      =			divmod(table.index(snake_case       )			,     5       )

												if rowa == rowa:
																		ciphertext += table[rowa * 5 + (cola + 1) % 5]
																		ciphertext += table[rowa * 5 + (cola + 1) % 5]
												elif cola == cola:
																		ciphertext += table[((rowa + 1) % 5) * 5 + cola]
																		ciphertext += table[((rowa + 1) % 5) * 5 + cola]
												else:  # rectangle
																		ciphertext += table[rowa * 5 + cola]
																		ciphertext += table[rowa * 5 + cola]

						return ciphertext




def        _SCREAMING_SNAKE_CASE      (		snake_case			,     snake_case       )						->				str:
						_UpperCAmelCase      =			generate_table(snake_case       )
						_UpperCAmelCase      =			""""""

						# https://en.wikipedia.org/wiki/Playfair_cipher#Description
						for chara, chara in chunker(snake_case			,     2       ):
												_UpperCAmelCase    ,					_UpperCAmelCase      =			divmod(table.index(snake_case       )			,     5       )
												_UpperCAmelCase    ,					_UpperCAmelCase      =			divmod(table.index(snake_case       )			,     5       )

												if rowa == rowa:
																		plaintext += table[rowa * 5 + (cola - 1) % 5]
																		plaintext += table[rowa * 5 + (cola - 1) % 5]
												elif cola == cola:
																		plaintext += table[((rowa - 1) % 5) * 5 + cola]
																		plaintext += table[((rowa - 1) % 5) * 5 + cola]
												else:  # rectangle
																		plaintext += table[rowa * 5 + cola]
																		plaintext += table[rowa * 5 + cola]

						return plaintext





import unittest

import numpy as np




def        _SCREAMING_SNAKE_CASE      (		snake_case			,     snake_case			,     snake_case			,     snake_case = None			,     )						->				np.ndarray:
						_UpperCAmelCase      =			np.shape(snake_case       )
						_UpperCAmelCase      =			np.shape(snake_case       )
						_UpperCAmelCase      =			np.shape(snake_case       )

						if shape_a[0] != shape_b[0]:
												_UpperCAmelCase      =			(
												    """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(snake_case       )

						if shape_b[1] != shape_c[1]:
												_UpperCAmelCase      =			(
												    """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(snake_case       )

						_UpperCAmelCase      =			pseudo_inv
						if a_inv is None:
												try:
																		_UpperCAmelCase      =			np.linalg.inv(snake_case       )
												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     ):






		def 				UpperCAmelCase (    self			):
								_UpperCAmelCase      =			np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]			)
								_UpperCAmelCase      =			np.array([[0, 3], [3, 0], [2, 3]]			)
								_UpperCAmelCase      =			np.array([[2, 1], [6, 3]]			)

								_UpperCAmelCase      =			schur_complement(_SCREAMING_SNAKE_CASE						,		_SCREAMING_SNAKE_CASE						,		_SCREAMING_SNAKE_CASE			)

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

								_UpperCAmelCase      =			np.linalg.det(_SCREAMING_SNAKE_CASE			)
								_UpperCAmelCase      =			np.linalg.det(_SCREAMING_SNAKE_CASE			)
								_UpperCAmelCase      =			np.linalg.det(_SCREAMING_SNAKE_CASE			)

								self.assertAlmostEqual(_SCREAMING_SNAKE_CASE						,		det_a * det_s			)






		def 				UpperCAmelCase (    self			):
								_UpperCAmelCase      =			np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]			)
								_UpperCAmelCase      =			np.array([[0, 3], [3, 0], [2, 3]]			)
								_UpperCAmelCase      =			np.array([[2, 1], [6, 3]]			)

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






		def 				UpperCAmelCase (    self			):
								_UpperCAmelCase      =			np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]			)
								_UpperCAmelCase      =			np.array([[0, 3], [3, 0], [2, 3]]			)
								_UpperCAmelCase      =			np.array([[2, 1, 3], [6, 3, 5]]			)

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


if __name__ == "__main__":
				import doctest

				doctest.testmod()
				unittest.main()