


from __future__ import annotations



def  _a			(						__UpperCamelCase  ,  __UpperCamelCase ):
     # Checks if the entire collection has been sorted
     if len(__UpperCamelCase ) <= 1 or n <= 1:
          return

     insert_next(__UpperCamelCase  ,  n - 1 )
     rec_insertion_sort(__UpperCamelCase  ,  n - 1 )



def  _a			(						__UpperCamelCase  ,  __UpperCamelCase ):
     # Checks order between adjacent elements
     if index >= len(__UpperCamelCase ) or collection[index - 1] <= collection[index]:
          return

     # Swaps adjacent elements since they are not in ascending order
     a_			,			a_    :     List[Any]										=    (
         collection[index],
         collection[index - 1],
     )

     insert_next(__UpperCamelCase  ,  index + 1 )


if __name__ == "__main__":
       __lowerCamelCase        =     input('''Enter integers separated by spaces: ''')
       __lowerCamelCase        =     [int(num) for num in numbers.split()]
       rec_insertion_sort(number_list, len(number_list))
       print(number_list)







from math import acos, sin
from typing import List, Tuple, Union

import numpy as np
import torch
from PIL import Image

from ...models import AutoencoderKL, UNetaDConditionModel
from ...schedulers import DDIMScheduler, DDPMScheduler
from ...utils import randn_tensor
from ..pipeline_utils import AudioPipelineOutput, BaseOutput, DiffusionPipeline, ImagePipelineOutput
from .mel import Mel


class   a__	(						lowerCAmelCase_    ):
       lowerCamelCase__:     List[str]							    =     ["""vqvae"""]

       def __init__(   self      :     str      ,							lowerCamelCase_      :     AutoencoderKL      ,							lowerCamelCase_      :     UNetaDConditionModel      ,							lowerCamelCase_      :     Mel      ,							lowerCamelCase_      :     Union[DDIMScheduler, DDPMScheduler]      ,							):
            super().__init__()
            self.register_modules(unet=lowerCamelCase_      ,							scheduler=lowerCamelCase_      ,							mel=lowerCamelCase_      ,							vqvae=lowerCamelCase_    )

       def 						UpperCAmelCase(   self      :     Any    ):
            return 5_0 if isinstance(self.scheduler      ,							lowerCamelCase_    ) else 1_0_0_0

       @torch.no_grad()
       def __call__(   self      :     List[str]      ,							lowerCamelCase_      :     int = 1      ,							lowerCamelCase_      :     str = None      ,							lowerCamelCase_      :     np.ndarray = None      ,							lowerCamelCase_      :     int = 0      ,							lowerCamelCase_      :     int = 0      ,							lowerCamelCase_      :     int = None      ,							lowerCamelCase_      :     torch.Generator = None      ,							lowerCamelCase_      :     float = 0      ,							lowerCamelCase_      :     float = 0      ,							lowerCamelCase_      :     torch.Generator = None      ,							lowerCamelCase_      :     float = 0      ,							lowerCamelCase_      :     torch.Tensor = None      ,							lowerCamelCase_      :     torch.Tensor = None      ,							lowerCamelCase_      :     List[Any]=True      ,							):
            a_    :     Optional[Any]										=    steps or self.get_default_steps()
            self.scheduler.set_timesteps(lowerCamelCase_    )
            a_    :     Optional[int]										=    step_generator or generator
            # For backwards compatibility
            if type(self.unet.config.sample_size    ) == int:
                 a_    :     str										=    (self.unet.config.sample_size, self.unet.config.sample_size)
            if noise is None:
                 a_    :     Dict										=    randn_tensor(
                     (
                         batch_size,
                         self.unet.config.in_channels,
                         self.unet.config.sample_size[0],
                         self.unet.config.sample_size[1],
                     )      ,							generator=lowerCamelCase_      ,							device=self.device      ,							)
            a_    :     Tuple										=    noise
            a_    :     Union[str, Any]										=    None

            if audio_file is not None or raw_audio is not None:
                 self.mel.load_audio(lowerCamelCase_      ,							lowerCamelCase_    )
                 a_    :     Union[str, Any]										=    self.mel.audio_slice_to_image(lowerCamelCase_    )
                 a_    :     Union[str, Any]										=    np.frombuffer(input_image.tobytes()      ,							dtype="""uint8"""    ).reshape(
                     (input_image.height, input_image.width)    )
                 a_    :     Union[str, Any]										=    (input_image / 2_5_5) * 2 - 1
                 a_    :     Tuple										=    torch.tensor(input_image[np.newaxis, :, :]      ,							dtype=torch.float    ).to(self.device    )

                 if self.vqvae is not None:
                      a_    :     Dict										=    self.vqvae.encode(torch.unsqueeze(lowerCamelCase_      ,							0    )    ).latent_dist.sample(
                          generator=lowerCamelCase_    )[0]
                      a_    :     List[Any]										=    self.vqvae.config.scaling_factor * input_images

                 if start_step > 0:
                      a_    :     Tuple										=    self.scheduler.add_noise(lowerCamelCase_      ,							lowerCamelCase_      ,							self.scheduler.timesteps[start_step - 1]    )

                 a_    :     Union[str, Any]										=    (
                     self.unet.config.sample_size[1] * self.mel.get_sample_rate() / self.mel.x_res / self.mel.hop_length
                 )
                 a_    :     int										=    int(mask_start_secs * pixels_per_second    )
                 a_    :     Tuple										=    int(mask_end_secs * pixels_per_second    )
                 a_    :     Tuple										=    self.scheduler.add_noise(lowerCamelCase_      ,							lowerCamelCase_      ,							torch.tensor(self.scheduler.timesteps[start_step:]    )    )

            for step, t in enumerate(self.progress_bar(self.scheduler.timesteps[start_step:]    )    ):
                 if isinstance(self.unet      ,							lowerCamelCase_    ):
                      a_    :     Dict										=    self.unet(lowerCamelCase_      ,							lowerCamelCase_      ,							lowerCamelCase_    )["""sample"""]
                 else:
                      a_    :     Dict										=    self.unet(lowerCamelCase_      ,							lowerCamelCase_    )["""sample"""]

                 if isinstance(self.scheduler      ,							lowerCamelCase_    ):
                      a_    :     Any										=    self.scheduler.step(
                          model_output=lowerCamelCase_      ,							timestep=lowerCamelCase_      ,							sample=lowerCamelCase_      ,							eta=lowerCamelCase_      ,							generator=lowerCamelCase_      ,							)["""prev_sample"""]
                 else:
                      a_    :     Optional[Any]										=    self.scheduler.step(
                          model_output=lowerCamelCase_      ,							timestep=lowerCamelCase_      ,							sample=lowerCamelCase_      ,							generator=lowerCamelCase_      ,							)["""prev_sample"""]

                 if mask is not None:
                      if mask_start > 0:
                           a_    :     Any										=    mask[:, step, :, :mask_start]
                      if mask_end > 0:
                           a_    :     Dict										=    mask[:, step, :, -mask_end:]

            if self.vqvae is not None:
                 # 0.18215 was scaling factor used in training to ensure unit variance
                 a_    :     str										=    1 / self.vqvae.config.scaling_factor * images
                 a_    :     List[Any]										=    self.vqvae.decode(lowerCamelCase_    )["""sample"""]

            a_    :     Union[str, Any]										=    (images / 2 + 0.5).clamp(0      ,							1    )
            a_    :     Dict										=    images.cpu().permute(0      ,							2      ,							3      ,							1    ).numpy()
            a_    :     Any										=    (images * 2_5_5).round().astype("""uint8"""    )
            a_    :     int										=    list(
                (Image.fromarray(_[:, :, 0]    ) for _ in images)
                if images.shape[3] == 1
                else (Image.fromarray(lowerCamelCase_      ,							mode="""RGB"""    ).convert("""L"""    ) for _ in images)    )

            a_    :     str										=    [self.mel.image_to_audio(lowerCamelCase_    ) for _ in images]
            if not return_dict:
                 return images, (self.mel.get_sample_rate(), audios)

            return BaseOutput(**AudioPipelineOutput(np.array(lowerCamelCase_    )[:, np.newaxis, :]    )      ,							**ImagePipelineOutput(lowerCamelCase_    )    )

       @torch.no_grad()
       def 						UpperCAmelCase(   self      :     List[str]      ,							lowerCamelCase_      :     List[Image.Image]      ,							lowerCamelCase_      :     int = 5_0    ):
            assert isinstance(self.scheduler      ,							lowerCamelCase_    )
            self.scheduler.set_timesteps(lowerCamelCase_    )
            a_    :     Any										=    np.array(
                [np.frombuffer(image.tobytes()      ,							dtype="""uint8"""    ).reshape((1, image.height, image.width)    ) for image in images]    )
            a_    :     Union[str, Any]										=    (sample / 2_5_5) * 2 - 1
            a_    :     Optional[Any]										=    torch.Tensor(lowerCamelCase_    ).to(self.device    )

            for t in self.progress_bar(torch.flip(self.scheduler.timesteps      ,							(0,)    )    ):
                 a_    :     str										=    t - self.scheduler.config.num_train_timesteps // self.scheduler.num_inference_steps
                 a_    :     Any										=    self.scheduler.alphas_cumprod[t]
                 a_    :     Dict										=    (
                     self.scheduler.alphas_cumprod[prev_timestep]
                     if prev_timestep >= 0
                     else self.scheduler.final_alpha_cumprod
                 )
                 a_    :     Optional[Any]										=    1 - alpha_prod_t
                 a_    :     Optional[int]										=    self.unet(lowerCamelCase_      ,							lowerCamelCase_    )["""sample"""]
                 a_    :     Tuple										=    (1 - alpha_prod_t_prev) ** 0.5 * model_output
                 a_    :     Tuple										=    (sample - pred_sample_direction) * alpha_prod_t_prev ** (-0.5)
                 a_    :     Tuple										=    sample * alpha_prod_t ** 0.5 + beta_prod_t ** 0.5 * model_output

            return sample

       @staticmethod
       def 						UpperCAmelCase(   lowerCamelCase_      :     torch.Tensor      ,							lowerCamelCase_      :     torch.Tensor      ,							lowerCamelCase_      :     float    ):
            a_    :     Dict										=    acos(torch.dot(torch.flatten(lowerCamelCase_    )      ,							torch.flatten(lowerCamelCase_    )    ) / torch.norm(lowerCamelCase_    ) / torch.norm(lowerCamelCase_    )    )
            return sin((1 - alpha) * theta    ) * xa / sin(lowerCamelCase_    ) + sin(alpha * theta    ) * xa / sin(lowerCamelCase_    )



