
"""simple docstring"""




_lowerCamelCase	:    int          =      frozenset(
    [
        '''prompt''',
        '''height''',
        '''width''',
        '''guidance_scale''',
        '''negative_prompt''',
        '''prompt_embeds''',
        '''negative_prompt_embeds''',
        '''cross_attention_kwargs''',
    ]
)

_lowerCamelCase	:    Dict          =      frozenset(['''prompt''', '''negative_prompt'''])

_lowerCamelCase	:    List[Any]          =      frozenset([])

_lowerCamelCase	:    Union[str, Any]          =      frozenset(['''image'''])

_lowerCamelCase	:    List[str]          =      frozenset(
    [
        '''image''',
        '''height''',
        '''width''',
        '''guidance_scale''',
    ]
)

_lowerCamelCase	:    List[Any]          =      frozenset(['''image'''])

_lowerCamelCase	:    Tuple          =      frozenset(
    [
        '''prompt''',
        '''image''',
        '''height''',
        '''width''',
        '''guidance_scale''',
        '''negative_prompt''',
        '''prompt_embeds''',
        '''negative_prompt_embeds''',
    ]
)

_lowerCamelCase	:    Any          =      frozenset(['''prompt''', '''image''', '''negative_prompt'''])

_lowerCamelCase	:    List[Any]          =      frozenset(
    [
        # Text guided image variation with an image mask
        '''prompt''',
        '''image''',
        '''mask_image''',
        '''height''',
        '''width''',
        '''guidance_scale''',
        '''negative_prompt''',
        '''prompt_embeds''',
        '''negative_prompt_embeds''',
    ]
)

_lowerCamelCase	:    Tuple          =      frozenset(['''prompt''', '''image''', '''mask_image''', '''negative_prompt'''])

_lowerCamelCase	:    Union[str, Any]          =      frozenset(
    [
        # image variation with an image mask
        '''image''',
        '''mask_image''',
        '''height''',
        '''width''',
        '''guidance_scale''',
    ]
)

_lowerCamelCase	:    Any          =      frozenset(['''image''', '''mask_image'''])

_lowerCamelCase	:    Dict          =      frozenset(
    [
        '''example_image''',
        '''image''',
        '''mask_image''',
        '''height''',
        '''width''',
        '''guidance_scale''',
    ]
)

_lowerCamelCase	:    str          =      frozenset(['''example_image''', '''image''', '''mask_image'''])

_lowerCamelCase	:    int          =      frozenset(['''class_labels'''])

_lowerCamelCase	:    List[Any]          =      frozenset(['''class_labels'''])

_lowerCamelCase	:    str          =      frozenset(['''batch_size'''])

_lowerCamelCase	:    Union[str, Any]          =      frozenset([])

_lowerCamelCase	:    Any          =      frozenset(['''batch_size'''])

_lowerCamelCase	:    Union[str, Any]          =      frozenset([])

_lowerCamelCase	:    Optional[int]          =      frozenset(
    [
        '''prompt''',
        '''audio_length_in_s''',
        '''guidance_scale''',
        '''negative_prompt''',
        '''prompt_embeds''',
        '''negative_prompt_embeds''',
        '''cross_attention_kwargs''',
    ]
)

_lowerCamelCase	:    List[Any]          =      frozenset(['''prompt''', '''negative_prompt'''])
_lowerCamelCase	:    Optional[Any]          =      frozenset(['''input_tokens'''])

_lowerCamelCase	:    Optional[int]          =      frozenset(['''input_tokens'''])

def 	a_		(	__lowercase       :     list[int]	, __lowercase       :     list[int]			)			->  tuple[float, float]:

			# Check if the input is valid
			if not len(__lowercase			) == len(__lowercase			) == 3:
						raise ValueError('Please enter a valid equation.'			)
			if equationa[0] == equationa[1] == equationa[0] == equationa[1] == 0:
						raise ValueError('Both a & b of two equations can\'t be zero.'			)

			# Extract the coefficients
			_snake_case     , _snake_case     , _snake_case          =      equationa
			_snake_case     , _snake_case     , _snake_case          =      equationa

			# Calculate the determinants of the matrices
			_snake_case          =      aa * ba - aa * ba
			_snake_case          =      ca * ba - ca * ba
			_snake_case          =      aa * ca - aa * ca

			# Check if the system of linear equations has a solution (using Cramer's rule)
			if determinant == 0:
						if determinant_x == determinant_y == 0:
									raise ValueError('Infinite solutions. (Consistent system)'			)
						else:
									raise ValueError('No solution. (Inconsistent system)'			)
			else:
						if determinant_x == determinant_y == 0:
									# Trivial solution (Inconsistent system)
									return (0.0, 0.0)
						else:
									_snake_case          =      determinant_x / determinant
									_snake_case          =      determinant_y / determinant
									# Non-Trivial Solution (Consistent system)
									return (x, y)