


def 		lowercase_  (     _UpperCamelCase  ):


			'''simple docstring'''







			__lowercase 					=   current_set.copy()
			for row_index, row in enumerate(_UpperCamelCase  ):
						__lowercase 					=   row[0]
						for column_index, column in enumerate(_UpperCamelCase  ):
									if magnitude == 0:
												__lowercase 					=   column
												continue
									__lowercase 					=   column / magnitude
    # Subtract to cancel term
			__lowercase 					=   current_set[0]
			__lowercase 					=   [first_row]
			__lowercase 					=   current_set[1::]
			for row in current_set:
						__lowercase 					=   []
						# If first term is 0, it is already in form we want, so we preserve it
						if row[0] == 0:
									final_set.append(_UpperCamelCase  )
									continue
						for column_index in range(len(_UpperCamelCase  )  ):
									temp_row.append(first_row[column_index] - row[column_index]  )
						final_set.append(_UpperCamelCase  )
			# Create next recursion iteration set
			if len(final_set[0]  ) != 3:
						__lowercase 					=   final_set[0]
						__lowercase 					=   []
						__lowercase 					=   []
						for row in final_set[1::]:
									current_first_column.append(row[0]  )
									next_iteration.append(row[1::]  )
						__lowercase 					=   simplify(_UpperCamelCase  )
						for i in range(len(_UpperCamelCase  )  ):
									resultant[i].insert(0       ,			current_first_column[i]  )
						resultant.insert(0       ,			_UpperCamelCase  )
						__lowercase 					=   resultant
			return final_set


def 		lowercase_  (     _UpperCamelCase  ):


			'''simple docstring'''







			if len(_UpperCamelCase  ) == 0:
						raise IndexError('''solve_simultaneous() requires n lists of length n+1'''  )
			__lowercase 					=   len(_UpperCamelCase  ) + 1
			if any(len(_UpperCamelCase  ) != _length for item in equations  ):
						raise IndexError('''solve_simultaneous() requires n lists of length n+1'''  )
			for row in equations:
						if any(not isinstance(_UpperCamelCase       ,			(int, float)  ) for column in row  ):
									raise ValueError('''solve_simultaneous() requires lists of integers'''  )
			if len(_UpperCamelCase  ) == 1:
						return [equations[0][-1] / equations[0][0]]
			__lowercase 					=   equations.copy()
			if any(0 in row for row in data_set  ):
						__lowercase 					=   data_set.copy()
						__lowercase 					=   []
						for row_index, row in enumerate(_UpperCamelCase  ):
									if 0 not in row:
												__lowercase 					=   data_set.pop(_UpperCamelCase  )
												break
						if not full_row:
									raise ValueError('''solve_simultaneous() requires at least 1 full equation'''  )
						data_set.insert(0       ,			_UpperCamelCase  )
			__lowercase 					=   data_set.copy()
			__lowercase 					=   simplify(_UpperCamelCase  )
			__lowercase 					=   simplified[::-1]
			__lowercase 					=   []
			for row in simplified:
						__lowercase 					=   row[-1]
						if not solutions:
									if row[-2] == 0:
												solutions.append(0  )
												continue
									solutions.append(current_solution / row[-2]  )
									continue
						__lowercase 					=   row.copy()[: len(_UpperCamelCase  ) - 1 :]
						while temp_row[0] == 0:
									temp_row.pop(0  )
						if len(_UpperCamelCase  ) == 0:
									solutions.append(0  )
									continue
						__lowercase 					=   temp_row[1::]
						__lowercase 					=   temp_row[::-1]
						for column_index, column in enumerate(_UpperCamelCase  ):
									current_solution -= column * solutions[column_index]
						solutions.append(_UpperCamelCase  )
			__lowercase 					=   []
			for item in solutions:
						final.append(float(round(_UpperCamelCase       ,			5  )  )  )
			return final[::-1]


if __name__ == "__main__":
		import doctest

		doctest.testmod()
		a : Any		=				[
		    [2, 1, 1, 1, 1, 4],
		    [1, 2, 1, 1, 1, 5],
		    [1, 1, 2, 1, 1, 6],
		    [1, 1, 1, 2, 1, 7],
		    [1, 1, 1, 1, 2, 8],
		]
		print(solve_simultaneous(eq))
		print(solve_simultaneous([[4, 2]]))






from dataclasses import dataclass
from typing import List, Optional, Union

import numpy as np
import PIL

from ...utils import BaseOutput, OptionalDependencyNotAvailable, is_torch_available, is_transformers_available
from .timesteps import (
    fastaa_timesteps,
    smartaa_timesteps,
    smartaa_timesteps,
    smartaaa_timesteps,
    smartaaa_timesteps,
    superaa_timesteps,
    superaa_timesteps,
    superaaa_timesteps,
)
@dataclass
class 	lowerCamelCase_       (				lowerCAmelCase__				):



					'''simple docstring'''







					__UpperCAmelCase            =				42
					__UpperCAmelCase            =				42
					__UpperCAmelCase            =				42


try:
	if not (is_transformers_available() and is_torch_available()):
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	from ...utils.dummy_torch_and_transformers_objects import *  # noqa F403
else:
	from .pipeline_if import IFPipeline
	from .pipeline_if_imgaimg import IFImgaImgPipeline
	from .pipeline_if_imgaimg_superresolution import IFImgaImgSuperResolutionPipeline
	from .pipeline_if_inpainting import IFInpaintingPipeline
	from .pipeline_if_inpainting_superresolution import IFInpaintingSuperResolutionPipeline
	from .pipeline_if_superresolution import IFSuperResolutionPipeline
	from .safety_checker import IFSafetyChecker
	from .watermark import IFWatermarker


