"""simple docstring"""






def   a_						(					lowerCamelCase					,			lowerCamelCase					,			lowerCamelCase       ):
				return not any(
				    neighbour == 1 and colored_vertices[i] == color
				    for i, neighbour in enumerate(lowerCamelCase       )       )



def   a_						(					lowerCamelCase					,			lowerCamelCase					,			lowerCamelCase					,			lowerCamelCase       ):

				# Base Case
				if index == len(lowerCamelCase       ):
								return True

				# Recursive Step
				for i in range(lowerCamelCase       ):
								if valid_coloring(graph[index]					,			lowerCamelCase					,			lowerCamelCase       ):
												# Color current vertex
												UpperCAmelCase__             =							i
												# Validate coloring
												if util_color(lowerCamelCase					,			lowerCamelCase					,			lowerCamelCase					,			index + 1       ):
																return True
												# Backtrack
												UpperCAmelCase__             =							-1
				return False







def   a_						(					lowerCamelCase					,			lowerCamelCase       ):
				UpperCAmelCase__             =							[-1] * len(lowerCamelCase       )

				if util_color(lowerCamelCase					,			lowerCamelCase					,			lowerCamelCase					,			0       ):
								return colored_vertices

				return []








'''simple docstring'''





__a          =		frozenset(
    [
        "prompt",
        "height",
        "width",
        "guidance_scale",
        "negative_prompt",
        "prompt_embeds",
        "negative_prompt_embeds",
        "cross_attention_kwargs",
    ]
)

__a          =		frozenset(["prompt", "negative_prompt"])

__a          =		frozenset([])

__a          =		frozenset(["image"])

__a          =		frozenset(
    [
        "image",
        "height",
        "width",
        "guidance_scale",
    ]
)

__a          =		frozenset(["image"])

__a          =		frozenset(
    [
        "prompt",
        "image",
        "height",
        "width",
        "guidance_scale",
        "negative_prompt",
        "prompt_embeds",
        "negative_prompt_embeds",
    ]
)

__a          =		frozenset(["prompt", "image", "negative_prompt"])

__a          =		frozenset(
    [
        # Text guided image variation with an image mask
        "prompt",
        "image",
        "mask_image",
        "height",
        "width",
        "guidance_scale",
        "negative_prompt",
        "prompt_embeds",
        "negative_prompt_embeds",
    ]
)

__a          =		frozenset(["prompt", "image", "mask_image", "negative_prompt"])

__a          =		frozenset(
    [
        # image variation with an image mask
        "image",
        "mask_image",
        "height",
        "width",
        "guidance_scale",
    ]
)

__a          =		frozenset(["image", "mask_image"])

__a          =		frozenset(
    [
        "example_image",
        "image",
        "mask_image",
        "height",
        "width",
        "guidance_scale",
    ]
)

__a          =		frozenset(["example_image", "image", "mask_image"])

__a          =		frozenset(["class_labels"])

__a          =		frozenset(["class_labels"])

__a          =		frozenset(["batch_size"])

__a          =		frozenset([])

__a          =		frozenset(["batch_size"])

__a          =		frozenset([])

__a          =		frozenset(
    [
        "prompt",
        "audio_length_in_s",
        "guidance_scale",
        "negative_prompt",
        "prompt_embeds",
        "negative_prompt_embeds",
        "cross_attention_kwargs",
    ]
)

__a          =		frozenset(["prompt", "negative_prompt"])
__a          =		frozenset(["input_tokens"])

__a          =		frozenset(["input_tokens"])
