




def 		lowercase_      (		_UpperCAmelCase  ,      _UpperCAmelCase	):




	"""simple docstring"""






	_enforce_args(_A  ,      _A	)
	if n == 0:
		return 0
	A_  :				Optional[Any]	   =		float('''-inf'''	)
	for i in range(1  ,      n + 1	):
		A_  :				List[Any]	   =		max(
		    _A  ,      prices[i - 1] + naive_cut_rod_recursive(n - i  ,      _A	)	)

	return max_revue

def 		lowercase_      (		_UpperCAmelCase  ,      _UpperCAmelCase	):




	"""simple docstring"""






	_enforce_args(_A  ,      _A	)
	A_  :				Optional[Any]	   =		[float('''-inf'''	) for _ in range(n + 1	)]
	return _top_down_cut_rod_recursive(_A  ,      _A  ,      _A	)

def 		lowercase_      (		_UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase	):




	"""simple docstring"""






	if max_rev[n] >= 0:
		return max_rev[n]
	elif n == 0:
		return 0
	else:
		A_  :				int	   =		float('''-inf'''	)
		for i in range(1  ,      n + 1	):
			A_  :				Tuple	   =		max(
			    _A  ,      prices[i - 1] + _top_down_cut_rod_recursive(n - i  ,      _A  ,      _A	)  ,      )

		A_  :				List[Any]	   =		max_revenue

	return max_rev[n]

def 		lowercase_      (		_UpperCAmelCase  ,      _UpperCAmelCase	):




	"""simple docstring"""






	_enforce_args(_A  ,      _A	)

	# length(max_rev) = n + 1, to accommodate for the revenue obtainable from a rod of
	# length 0.
	A_  :				List[Any]	   =		[float('''-inf'''	) for _ in range(n + 1	)]
	A_  :				Union[str, Any]	   =		0

	for i in range(1  ,      n + 1	):
		A_  :				Optional[Any]	   =		max_rev[i]
		for j in range(1  ,      i + 1	):
			A_  :				int	   =		max(_A  ,      prices[j - 1] + max_rev[i - j]	)

		A_  :				List[str]	   =		max_revenue_i

	return max_rev[n]

def 		lowercase_      (		_UpperCAmelCase  ,      _UpperCAmelCase	):




	"""simple docstring"""






	if n < 0:
		A_  :				List[Any]	   =		f"""n must be greater than or equal to 0. Got n = {n}"""
		raise ValueError(_A	)

	if n > len(_A	):
		A_  :				int	   =		(
		    '''Each integral piece of rod must have a corresponding price. '''
		    f"""Got n = {n} but length of prices = {len(_A	)}"""
		)
		raise ValueError(_A	)

def 		lowercase_      (		):




	"""simple docstring"""






	A_  :				Tuple	   =		[6, 10, 12, 15, 20, 23]
	A_  :				Optional[Any]	   =		len(_A	)

	# the best revenue comes from cutting the rod into 6 pieces, each
	# of length 1 resulting in a revenue of 6 * 6 = 36.
	A_  :				Optional[Any]	   =		36

	A_  :				Tuple	   =		top_down_cut_rod(_A  ,      _A	)
	A_  :				List[str]	   =		bottom_up_cut_rod(_A  ,      _A	)
	A_  :				Tuple	   =		naive_cut_rod_recursive(_A  ,      _A	)

	assert expected_max_revenue == max_rev_top_down
	assert max_rev_top_down == max_rev_bottom_up
	assert max_rev_bottom_up == max_rev_naive


if __name__ == "__main__":
		main()











"""simple docstring"""

from collections.abc import Generator
from math import sin

def 		lowercase_      (		_UpperCAmelCase	):




	"""simple docstring"""






	if len(_UpperCAmelCase	) != 32:
		raise ValueError('''Input must be of length 32'''	)

	A_  :				int	   =		b''''''
	for i in [3, 2, 1, 0]:
		little_endian += string_aa[8 * i : 8 * i + 8]
	return little_endian

def 		lowercase_      (		_UpperCAmelCase	):




	"""simple docstring"""






	if i < 0:
		raise ValueError('''Input must be non-negative'''	)

	A_  :				int	   =		format(_UpperCAmelCase  ,      '''08x'''	)[-8:]
	A_  :				Optional[Any]	   =		b''''''
	for i in [3, 2, 1, 0]:
		little_endian_hex += hex_rep[2 * i : 2 * i + 2].encode('''utf-8'''	)
	return little_endian_hex

def 		lowercase_      (		_UpperCAmelCase	):




	"""simple docstring"""






	A_  :				int	   =		b''''''
	for char in message:
		bit_string += format(_UpperCAmelCase  ,      '''08b'''	).encode('''utf-8'''	)
	A_  :				Optional[Any]	   =		format(len(_UpperCAmelCase	)  ,      '''064b'''	).encode('''utf-8'''	)

	# Pad bit_string to a multiple of 512 chars
	bit_string += b"1"
	while len(_UpperCAmelCase	) % 512 != 448:
		bit_string += b"0"
	bit_string += to_little_endian(start_len[32:]	) + to_little_endian(start_len[:32]	)

	return bit_string

def 		lowercase_      (		_UpperCAmelCase	):




	"""simple docstring"""






	if len(_UpperCAmelCase	) % 512 != 0:
		raise ValueError('''Input must have length that\'s a multiple of 512'''	)

	for pos in range(0  ,      len(_UpperCAmelCase	)  ,      512	):
		A_  :				Union[str, Any]	   =		bit_string[pos : pos + 512]
		A_  :				Optional[int]	   =		[]
		for i in range(0  ,      512  ,      32	):
			block_words.append(int(to_little_endian(block[i : i + 32]	)  ,      2	)	)
		yield block_words

def 		lowercase_      (		_UpperCAmelCase	):




	"""simple docstring"""






	if i < 0:
		raise ValueError('''Input must be non-negative'''	)

	A_  :				str	   =		format(_UpperCAmelCase  ,      '''032b'''	)
	A_  :				List[str]	   =		''''''
	for c in i_str:
		new_str += "1" if c == "0" else "0"
	return int(_UpperCAmelCase  ,      2	)

def 		lowercase_      (		_UpperCAmelCase  ,      _UpperCAmelCase	):




	"""simple docstring"""






	return (a + b) % 2**32

def 		lowercase_      (		_UpperCAmelCase  ,      _UpperCAmelCase	):




	"""simple docstring"""






	if i < 0:
		raise ValueError('''Input must be non-negative'''	)
	if shift < 0:
		raise ValueError('''Shift must be non-negative'''	)
	return ((i << shift) ^ (i >> (32 - shift))) % 2**32

def 		lowercase_      (		_UpperCAmelCase	):




	"""simple docstring"""






	A_  :				Any	   =		preprocess(_UpperCAmelCase	)

	A_  :				Any	   =		[int(2**32 * abs(sin(i + 1	)	)	) for i in range(64	)]

	# Starting states
	A_  :				List[str]	   =		0x6_7_4_5_2_3_0_1
	A_  :				str	   =		0xe_f_c_d_a_b_8_9
	A_  :				Union[str, Any]	   =		0x9_8_b_a_d_c_f_e
	A_  :				Dict	   =		0x1_0_3_2_5_4_7_6

	A_  :				int	   =		[
	    7,
	    12,
	    17,
	    22,
	    7,
	    12,
	    17,
	    22,
	    7,
	    12,
	    17,
	    22,
	    7,
	    12,
	    17,
	    22,
	    5,
	    9,
	    14,
	    20,
	    5,
	    9,
	    14,
	    20,
	    5,
	    9,
	    14,
	    20,
	    5,
	    9,
	    14,
	    20,
	    4,
	    11,
	    16,
	    23,
	    4,
	    11,
	    16,
	    23,
	    4,
	    11,
	    16,
	    23,
	    4,
	    11,
	    16,
	    23,
	    6,
	    10,
	    15,
	    21,
	    6,
	    10,
	    15,
	    21,
	    6,
	    10,
	    15,
	    21,
	    6,
	    10,
	    15,
	    21,
	]

	# Process bit string in chunks, each with 16 32-char words
	for block_words in get_block_words(_UpperCAmelCase	):
		A_  :				str	   =		aa
		A_  :				Tuple	   =		ba
		A_  :				Tuple	   =		ca
		A_  :				int	   =		da

		# Hash current chunk
		for i in range(64	):
			if i <= 15:
				# f = (b & c) | (not_32(b) & d)     # Alternate definition for f
				A_  :				str	   =		d ^ (b & (c ^ d))
				A_  :				int	   =		i
			elif i <= 31:
				# f = (d & b) | (not_32(d) & c)     # Alternate definition for f
				A_  :				List[Any]	   =		c ^ (d & (b ^ c))
				A_  :				Optional[int]	   =		(5 * i + 1) % 16
			elif i <= 47:
				A_  :				Optional[Any]	   =		b ^ c ^ d
				A_  :				List[Any]	   =		(3 * i + 5) % 16
			else:
				A_  :				Dict	   =		c ^ (b | not_aa(_UpperCAmelCase	))
				A_  :				Dict	   =		(7 * i) % 16
			A_  :				Optional[int]	   =		(f + a + added_consts[i] + block_words[g]) % 2**32
			A_  :				List[str]	   =		d
			A_  :				str	   =		c
			A_  :				Tuple	   =		b
			A_  :				Tuple	   =		sum_aa(_UpperCAmelCase  ,      left_rotate_aa(_UpperCAmelCase  ,      shift_amounts[i]	)	)

		# Add hashed chunk to running total
		A_  :				str	   =		sum_aa(_UpperCAmelCase  ,      _UpperCAmelCase	)
		A_  :				int	   =		sum_aa(_UpperCAmelCase  ,      _UpperCAmelCase	)
		A_  :				int	   =		sum_aa(_UpperCAmelCase  ,      _UpperCAmelCase	)
		A_  :				Optional[Any]	   =		sum_aa(_UpperCAmelCase  ,      _UpperCAmelCase	)

	A_  :				Dict	   =		reformat_hex(_UpperCAmelCase	) + reformat_hex(_UpperCAmelCase	) + reformat_hex(_UpperCAmelCase	) + reformat_hex(_UpperCAmelCase	)
	return digest


if __name__ == "__main__":
		import doctest

		doctest.testmod()





