


def 							__lowerCamelCase		(					UpperCAmelCase_		:						int = 100		):




      """simple docstring"""





      a		:int									=			n * (n + 1) * (2 * n + 1) / 6
      a		:Union[str, Any]									=			(n * (n + 1) / 2) ** 2
      return int(square_of_sum - sum_of_squares		)


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









import unittest

import numpy as np
import torch

from diffusers import PNDMPipeline, PNDMScheduler, UNetaDModel
from diffusers.utils.testing_utils import enable_full_determinism, require_torch, slow, torch_device


enable_full_determinism()







class 						_snake_case    ( unittest.TestCase				):




 @property
 def 			SCREAMING_SNAKE_CASE__							(						self       ):
       torch.manual_seed(0       )
       a		:List[Any]									=			UNetaDModel(
           block_out_channels=(32, 64)   ,    layers_per_block=2   ,    sample_size=32   ,    in_channels=3   ,    out_channels=3   ,    down_block_types=('''DownBlock2D''', '''AttnDownBlock2D''')   ,    up_block_types=('''AttnUpBlock2D''', '''UpBlock2D''')   ,    )
       return model




 def 			SCREAMING_SNAKE_CASE__							(						self       ):
       a		:Union[str, Any]									=			self.dummy_uncond_unet
       a		:Any									=			PNDMScheduler()

       a		:Any									=			PNDMPipeline(unet=_lowerCamelCase   ,    scheduler=_lowerCamelCase       )
       pndm.to(_lowerCamelCase       )
       pndm.set_progress_bar_config(disable=_lowerCamelCase       )

       a		:Any									=			torch.manual_seed(0       )
       a		:List[str]									=			pndm(generator=_lowerCamelCase   ,    num_inference_steps=20   ,    output_type='''numpy'''       ).images

       a		:int									=			torch.manual_seed(0       )
       a		:str									=			pndm(generator=_lowerCamelCase   ,    num_inference_steps=20   ,    output_type='''numpy'''   ,    return_dict=_lowerCamelCase       )[0]

       a		:int									=			image[0, -3:, -3:, -1]
       a		:List[str]									=			image_from_tuple[0, -3:, -3:, -1]

       assert image.shape == (1, 32, 32, 3)
       a		:str									=			np.array([1.0, 1.0, 0.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0]       )

       assert np.abs(image_slice.flatten() - expected_slice       ).max() < 1e-2
       assert np.abs(image_from_tuple_slice.flatten() - expected_slice       ).max() < 1e-2







@slow
@require_torch
class 						_snake_case    ( unittest.TestCase				):




 def 			SCREAMING_SNAKE_CASE__							(						self       ):
       a		:int									=			'''google/ddpm-cifar10-32'''

       a		:str									=			UNetaDModel.from_pretrained(_lowerCamelCase       )
       a		:Optional[Any]									=			PNDMScheduler()

       a		:Union[str, Any]									=			PNDMPipeline(unet=_lowerCamelCase   ,    scheduler=_lowerCamelCase       )
       pndm.to(_lowerCamelCase       )
       pndm.set_progress_bar_config(disable=_lowerCamelCase       )
       a		:Dict									=			torch.manual_seed(0       )
       a		:List[str]									=			pndm(generator=_lowerCamelCase   ,    output_type='''numpy'''       ).images

       a		:List[Any]									=			image[0, -3:, -3:, -1]

       assert image.shape == (1, 32, 32, 3)
       a		:int									=			np.array([0.1564, 0.1_4645, 0.1406, 0.1_4715, 0.1_2425, 0.1_4045, 0.1_3115, 0.1_2175, 0.125]       )

       assert np.abs(image_slice.flatten() - expected_slice       ).max() < 1e-2





