






from math import sqrt


def 				snake_case__							(							UpperCAmelCase							:  int = 1_0_0_0_0_0_0       ):
    lowerCAmelCase__   :int      							=				0
    lowerCAmelCase__   :int      							=				0
    lowerCAmelCase__   :int

    while num_cuboids <= limit:
        max_cuboid_size += 1
        for sum_shortest_sides in range(2    ,			2 * max_cuboid_size + 1       ):
            if sqrt(sum_shortest_sides**2 + max_cuboid_size**2       ).is_integer():
                num_cuboids += (
                    min(UpperCAmelCase    ,			sum_shortest_sides // 2       )
                    - max(1    ,			sum_shortest_sides - max_cuboid_size       )
                    + 1
                )

    return max_cuboid_size


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











import gc
import random
import unittest

import numpy as np
import torch

from diffusers import DDIMScheduler, KandinskyVaaPipeline, KandinskyVaaPriorPipeline, UNetaDConditionModel, VQModel
from diffusers.utils import floats_tensor, load_numpy, slow, torch_device
from diffusers.utils.testing_utils import enable_full_determinism, require_torch_gpu

from ..test_pipelines_common import PipelineTesterMixin, assert_mean_pixel_difference


enable_full_determinism()







class 	_UpperCAmelCase  (  _A				,							unittest.TestCase		):




      """simple docstring"""



      A          =    KandinskyVaaPipeline
      A          =    [
          '''image_embeds''',
          '''negative_image_embeds''',
      ]
      A          =    ['''image_embeds''', '''negative_image_embeds''']
      A          =    [
          '''generator''',
          '''height''',
          '''width''',
          '''latents''',
          '''guidance_scale''',
          '''num_inference_steps''',
          '''return_dict''',
          '''guidance_scale''',
          '''num_images_per_prompt''',
          '''output_type''',
          '''return_dict''',
      ]
      A          =    False
      @property
      def 			snake_case_      (   self		):



          '''simple docstring'''
          return 32
      @property
      def 			snake_case_      (   self		):



          '''simple docstring'''
          return 32
      @property
      def 			snake_case_      (   self		):



          '''simple docstring'''
          return self.time_input_dim
      @property
      def 			snake_case_      (   self		):



          '''simple docstring'''
          return self.time_input_dim * 4
      @property
      def 			snake_case_      (   self		):



          '''simple docstring'''
          return 100
      @property
      def 			snake_case_      (   self		):



          '''simple docstring'''
          torch.manual_seed(0		)

          lowerCAmelCase__   :List[str]      							=				{
              "in_channels": 4,
              # Out channels is double in channels because predicts mean and variance
              "out_channels": 8,
              "addition_embed_type": "image",
              "down_block_types": ("ResnetDownsampleBlock2D", "SimpleCrossAttnDownBlock2D"),
              "up_block_types": ("SimpleCrossAttnUpBlock2D", "ResnetUpsampleBlock2D"),
              "mid_block_type": "UNetMidBlock2DSimpleCrossAttn",
              "block_out_channels": (self.block_out_channels_a, self.block_out_channels_a * 2),
              "layers_per_block": 1,
              "encoder_hid_dim": self.text_embedder_hidden_size,
              "encoder_hid_dim_type": "image_proj",
              "cross_attention_dim": self.cross_attention_dim,
              "attention_head_dim": 4,
              "resnet_time_scale_shift": "scale_shift",
              "class_embed_type": None,
          }

          lowerCAmelCase__   :List[str]      							=				UNetaDConditionModel(**_lowerCAmelCase		)
          return model
      @property
      def 			snake_case_      (   self		):



          '''simple docstring'''
          return {
              "block_out_channels": [32, 64],
              "down_block_types": ["DownEncoderBlock2D", "AttnDownEncoderBlock2D"],
              "in_channels": 3,
              "latent_channels": 4,
              "layers_per_block": 1,
              "norm_num_groups": 8,
              "norm_type": "spatial",
              "num_vq_embeddings": 12,
              "out_channels": 3,
              "up_block_types": [
                  "AttnUpDecoderBlock2D",
                  "UpDecoderBlock2D",
              ],
              "vq_embed_dim": 4,
          }
      @property
      def 			snake_case_      (   self		):



          '''simple docstring'''
          torch.manual_seed(0		)
          lowerCAmelCase__   :Optional[Any]      							=				VQModel(**self.dummy_movq_kwargs		)
          return model
      def 			snake_case_      (   self		):



          '''simple docstring'''
          lowerCAmelCase__   :int      							=				self.dummy_unet
          lowerCAmelCase__   :List[str]      							=				self.dummy_movq

          lowerCAmelCase__   :List[Any]      							=				DDIMScheduler(
              num_train_timesteps=1_000    ,	beta_schedule="linear"    ,	beta_start=0.0_0085    ,	beta_end=0.012    ,	clip_sample=_lowerCAmelCase    ,	set_alpha_to_one=_lowerCAmelCase    ,	steps_offset=1    ,	prediction_type="epsilon"    ,	thresholding=_lowerCAmelCase    ,	)

          lowerCAmelCase__   :Optional[Any]      							=				{
              "unet": unet,
              "scheduler": scheduler,
              "movq": movq,
          }
          return components
      def 			snake_case_      (   self    ,	_lowerCAmelCase    ,	_lowerCAmelCase=0		):



          '''simple docstring'''
          lowerCAmelCase__   :List[Any]      							=				floats_tensor((1, self.text_embedder_hidden_size)    ,	rng=random.Random(_lowerCAmelCase		)		).to(_lowerCAmelCase		)
          lowerCAmelCase__   :Any      							=				floats_tensor((1, self.text_embedder_hidden_size)    ,	rng=random.Random(seed + 1		)		).to(
              _lowerCAmelCase		)
          if str(_lowerCAmelCase		).startswith("mps"		):
              lowerCAmelCase__   :List[Any]      							=				torch.manual_seed(_lowerCAmelCase		)
          else:
              lowerCAmelCase__   :Optional[int]      							=				torch.Generator(device=_lowerCAmelCase		).manual_seed(_lowerCAmelCase		)
          lowerCAmelCase__   :Optional[int]      							=				{
              "image_embeds": image_embeds,
              "negative_image_embeds": negative_image_embeds,
              "generator": generator,
              "height": 64,
              "width": 64,
              "guidance_scale": 4.0,
              "num_inference_steps": 2,
              "output_type": "np",
          }
          return inputs



      def 			snake_case_      (   self		):



          '''simple docstring'''
          lowerCAmelCase__   :int      							=				"cpu"

          lowerCAmelCase__   :Dict      							=				self.get_dummy_components()

          lowerCAmelCase__   :Tuple      							=				self.pipeline_class(**_lowerCAmelCase		)
          lowerCAmelCase__   :List[Any]      							=				pipe.to(_lowerCAmelCase		)

          pipe.set_progress_bar_config(disable=_lowerCAmelCase		)

          lowerCAmelCase__   :str      							=				pipe(**self.get_dummy_inputs(_lowerCAmelCase		)		)
          lowerCAmelCase__   :Dict      							=				output.images

          lowerCAmelCase__   :str      							=				pipe(
              **self.get_dummy_inputs(_lowerCAmelCase		)    ,	return_dict=_lowerCAmelCase    ,	)[0]

          lowerCAmelCase__   :Tuple      							=				image[0, -3:, -3:, -1]
          lowerCAmelCase__   :List[Any]      							=				image_from_tuple[0, -3:, -3:, -1]

          assert image.shape == (1, 64, 64, 3)

          lowerCAmelCase__   :Tuple      							=				np.array(
              [0.623_7976, 1.0, 0.3644_1332, 1.0, 0.7063_9634, 0.2987_7186, 0.8565_2125, 0.521_6843, 0.5445_4046]		)

          assert (
              np.abs(image_slice.flatten() - expected_slice		).max() < 1e-2
          ), f''' expected_slice {expected_slice}, but got {image_slice.flatten()}'''

          assert (
              np.abs(image_from_tuple_slice.flatten() - expected_slice		).max() < 1e-2
          ), f''' expected_slice {expected_slice}, but got {image_from_tuple_slice.flatten()}'''







@slow
@require_torch_gpu
class 	_UpperCAmelCase  (  unittest.TestCase		):




      """simple docstring"""



      def 			snake_case_      (   self		):



          '''simple docstring'''
          # clean up the VRAM after each test
          super().tearDown()
          gc.collect()
          torch.cuda.empty_cache()



      def 			snake_case_      (   self		):



          '''simple docstring'''
          lowerCAmelCase__   :int      							=				load_numpy(
              "https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main"
              "/kandinskyv22/kandinskyv22_text2img_cat_fp16.npy"		)

          lowerCAmelCase__   :str      							=				KandinskyVaaPriorPipeline.from_pretrained(
              "kandinsky-community/kandinsky-2-2-prior"    ,	torch_dtype=torch.floataa		)
          pipe_prior.to(_lowerCAmelCase		)

          lowerCAmelCase__   :str      							=				KandinskyVaaPipeline.from_pretrained(
              "kandinsky-community/kandinsky-2-2-decoder"    ,	torch_dtype=torch.floataa		)
          lowerCAmelCase__   :Union[str, Any]      							=				pipeline.to(_lowerCAmelCase		)
          pipeline.set_progress_bar_config(disable=_lowerCAmelCase		)

          lowerCAmelCase__   :Optional[int]      							=				"red cat, 4k photo"

          lowerCAmelCase__   :Tuple      							=				torch.Generator(device="cuda"		).manual_seed(0		)
          lowerCAmelCase__							,lowerCAmelCase__   :Dict      							=				pipe_prior(
              _lowerCAmelCase    ,	generator=_lowerCAmelCase    ,	num_inference_steps=5    ,	negative_prompt=""    ,	).to_tuple()

          lowerCAmelCase__   :List[Any]      							=				torch.Generator(device="cuda"		).manual_seed(0		)
          lowerCAmelCase__   :List[str]      							=				pipeline(
              image_embeds=_lowerCAmelCase    ,	negative_image_embeds=_lowerCAmelCase    ,	generator=_lowerCAmelCase    ,	num_inference_steps=100    ,	output_type="np"    ,	)

          lowerCAmelCase__   :int      							=				output.images[0]

          assert image.shape == (512, 512, 3)

          assert_mean_pixel_difference(_lowerCAmelCase    ,	_lowerCAmelCase		)



