





from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE				)							-> bool:




    """simple docstring"""




    _A     =							int(number**0.5				)
    return number == sq * sq





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)							-> tuple[int, int]:




    """simple docstring"""




    _A     =							x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
    _A     =							x_den * y_den * z_den
    _A     =							gcd(_SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)
    top //= hcf
    bottom //= hcf
    return top, bottom





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE = 35				)							-> int:




    """simple docstring"""




    _A     =							set()
    _A     =							42
    _A     =							Fraction(0				)
    _A     =							42

    for x_num in range(1							,     order + 1				):
        for x_den in range(x_num + 1							,     order + 1				):
            for y_num in range(1							,     order + 1				):
                for y_den in range(y_num + 1							,     order + 1				):
                    # n=1
                    _A     =							x_num * y_den + x_den * y_num
                    _A     =							x_den * y_den
                    _A     =							gcd(_SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)
                    z_num //= hcf
                    z_den //= hcf
                    if 0 < z_num < z_den <= order:
                        _A     =							add_three(
                            _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)
                        unique_s.add(_SCREAMING_SNAKE_CASE				)

                    # n=2
                    _A     =							(
                        x_num * x_num * y_den * y_den + x_den * x_den * y_num * y_num
                    )
                    _A     =							x_den * x_den * y_den * y_den
                    if is_sq(_SCREAMING_SNAKE_CASE				) and is_sq(_SCREAMING_SNAKE_CASE				):
                        _A     =							int(sqrt(_SCREAMING_SNAKE_CASE				)				)
                        _A     =							int(sqrt(_SCREAMING_SNAKE_CASE				)				)
                        _A     =							gcd(_SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)
                        z_num //= hcf
                        z_den //= hcf
                        if 0 < z_num < z_den <= order:
                            _A     =							add_three(
                                _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)
                            unique_s.add(_SCREAMING_SNAKE_CASE				)

                    # n=-1
                    _A     =							x_num * y_num
                    _A     =							x_den * y_num + x_num * y_den
                    _A     =							gcd(_SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)
                    z_num //= hcf
                    z_den //= hcf
                    if 0 < z_num < z_den <= order:
                        _A     =							add_three(
                            _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)
                        unique_s.add(_SCREAMING_SNAKE_CASE				)

                    # n=2
                    _A     =							x_num * x_num * y_num * y_num
                    _A     =							(
                        x_den * x_den * y_num * y_num + x_num * x_num * y_den * y_den
                    )
                    if is_sq(_SCREAMING_SNAKE_CASE				) and is_sq(_SCREAMING_SNAKE_CASE				):
                        _A     =							int(sqrt(_SCREAMING_SNAKE_CASE				)				)
                        _A     =							int(sqrt(_SCREAMING_SNAKE_CASE				)				)
                        _A     =							gcd(_SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)
                        z_num //= hcf
                        z_den //= hcf
                        if 0 < z_num < z_den <= order:
                            _A     =							add_three(
                                _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)
                            unique_s.add(_SCREAMING_SNAKE_CASE				)

    for num, den in unique_s:
        total += Fraction(_SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)

    return total.denominator + total.numerator


if __name__ == "__main__":
 print(f"{solution() = }")










'''simple docstring'''





import random
import unittest

import torch

from diffusers import IFInpaintingSuperResolutionPipeline
from diffusers.utils import floats_tensor
from diffusers.utils.import_utils import is_xformers_available
from diffusers.utils.testing_utils import skip_mps, torch_device

from ..pipeline_params import (
    TEXT_GUIDED_IMAGE_INPAINTING_BATCH_PARAMS,
    TEXT_GUIDED_IMAGE_INPAINTING_PARAMS,
)
from ..test_pipelines_common import PipelineTesterMixin
from . import IFPipelineTesterMixin






@skip_mps
class __A     (    A  ,  A  ,  unittest.TestCase		):



 '''simple docstring'''







 __lowerCamelCase       :			List[Any]		=			IFInpaintingSuperResolutionPipeline
 __lowerCamelCase       :			Tuple		=			TEXT_GUIDED_IMAGE_INPAINTING_PARAMS - {'width', 'height'}
 __lowerCamelCase       :			Optional[Any]		=			TEXT_GUIDED_IMAGE_INPAINTING_BATCH_PARAMS.union({'original_image'}		)
 __lowerCamelCase       :			str		=			PipelineTesterMixin.required_optional_params - {'latents'}



 def    a__    (self			)       ->	List[Any]:


      """simple docstring"""



      return self._get_superresolution_dummy_components()



 def    a__    (self					,  A					,  A=0			)       ->	List[Any]:


      """simple docstring"""



      if str(A			).startswith('''mps'''			):
           _a           =    torch.manual_seed(A			)
      else:
           _a           =    torch.Generator(device=A			).manual_seed(A			)

      _a           =    floats_tensor((1, 3, 16, 16)					,  rng=random.Random(A			)			).to(A			)
      _a           =    floats_tensor((1, 3, 32, 32)					,  rng=random.Random(A			)			).to(A			)
      _a           =    floats_tensor((1, 3, 32, 32)					,  rng=random.Random(A			)			).to(A			)

      _a           =    {
          '''prompt''': '''A painting of a squirrel eating a burger''',
          '''image''': image,
          '''original_image''': original_image,
          '''mask_image''': mask_image,
          '''generator''': generator,
          '''num_inference_steps''': 2,
          '''output_type''': '''numpy''',
      }

      return inputs



 @unittest.skipIf(
     torch_device != '''cuda''' or not is_xformers_available()					,  reason='''XFormers attention is only available with CUDA and `xformers` installed'''					,  )
 def    a__    (self			)       ->	Optional[int]:


      """simple docstring"""



      self._test_xformers_attention_forwardGenerator_pass(expected_max_diff=1E-3			)



 def    a__    (self			)       ->	str:


      """simple docstring"""



      self._test_save_load_optional_components()



 @unittest.skipIf(torch_device != '''cuda'''					,  reason='''float16 requires CUDA'''			)
 def    a__    (self			)       ->	str:


      """simple docstring"""



      super().test_save_load_floataa(expected_max_diff=1E-1			)



 def    a__    (self			)       ->	Tuple:


      """simple docstring"""



      self._test_attention_slicing_forward_pass(expected_max_diff=1E-2			)



 def    a__    (self			)       ->	Union[str, Any]:


      """simple docstring"""



      self._test_save_load_local()



 def    a__    (self			)       ->	Any:


      """simple docstring"""



      self._test_inference_batch_single_identical(
          expected_max_diff=1E-2					,  )



