

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

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, logging, randn_tensor
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin


__a						:List[Any]            = logging.get_logger(__name__)  # pylint: disable=invalid-name

@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerDiscrete
class      _a				( snake_case_							):




      """simple docstring"""

      _lowerCamelCase					: torch.FloatTensor
      _lowerCamelCase					: Optional[torch.FloatTensor]					=					None




def 			__snake_case	(   __UpperCamelCase  :   List[Any]							,__UpperCamelCase  :   List[Any]=0.999							,__UpperCamelCase  :   Dict="cosine"							,):



      """simple docstring"""

      if alpha_transform_type == "cosine":

            def alpha_bar_fn(__UpperCamelCase  :   Any						):
                  return math.cos((t + 0.008) / 1.008 * math.pi / 2						) ** 2

      elif alpha_transform_type == "exp":

            def alpha_bar_fn(__UpperCamelCase  :   Any						):
                  return math.exp(t * -12.0						)

      else:
            raise ValueError(f'''Unsupported alpha_tranform_type: {alpha_transform_type}'''						)

      A_	     =							[]
      for i in range(__UpperCamelCase						):
            A_	     =							i / num_diffusion_timesteps
            A_	     =							(i + 1) / num_diffusion_timesteps
            betas.append(min(1 - alpha_bar_fn(__UpperCamelCase						) / alpha_bar_fn(__UpperCamelCase						)							,__UpperCamelCase						)						)
      return torch.tensor(__UpperCamelCase							,dtype=torch.floataa						)



class      _a				( snake_case_    ,							snake_case_							):




      """simple docstring"""

      _lowerCamelCase					: Any					=					[e.name for e in KarrasDiffusionSchedulers]
      _lowerCamelCase					: str					=					1





      @register_to_config
      def __init__(      self       :							str	, UpperCAmelCase       :							int = 1000	, UpperCAmelCase       :							float = 0.0_001	, UpperCAmelCase       :							float = 0.02	, UpperCAmelCase       :							str = "linear"	, UpperCAmelCase       :							Optional[Union[np.ndarray, List[float]]] = None	, UpperCAmelCase       :							str = "epsilon"	, UpperCAmelCase       :							str = "linear"	, UpperCAmelCase       :							Optional[bool] = False	, UpperCAmelCase       :							str = "linspace"	, UpperCAmelCase       :							int = 0	, ):
            if trained_betas is not None:
                  A_	     =							torch.tensor(UpperCAmelCase	, dtype=torch.floataa  )
            elif beta_schedule == "linear":
                  A_	     =							torch.linspace(UpperCAmelCase	, UpperCAmelCase	, UpperCAmelCase	, dtype=torch.floataa  )
            elif beta_schedule == "scaled_linear":
                  # this schedule is very specific to the latent diffusion model.
                  A_	     =							(
                      torch.linspace(beta_start**0.5	, beta_end**0.5	, UpperCAmelCase	, dtype=torch.floataa  ) ** 2
                  )
            elif beta_schedule == "squaredcos_cap_v2":
                  # Glide cosine schedule
                  A_	     =							betas_for_alpha_bar(UpperCAmelCase  )
            else:
                  raise NotImplementedError(f'''{beta_schedule} does is not implemented for {self.__class__}'''  )

            A_	     =							1.0 - self.betas
            A_	     =							torch.cumprod(self.alphas	, dim=0  )

            A_	     =							np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5  )
            A_	     =							np.concatenate([sigmas[::-1], [0.0]]  ).astype(np.floataa  )
            A_	     =							torch.from_numpy(UpperCAmelCase  )

            # setable values
            A_	     =							None
            A_	     =							np.linspace(0	, num_train_timesteps - 1	, UpperCAmelCase	, dtype=UpperCAmelCase  )[::-1].copy()
            A_	     =							torch.from_numpy(UpperCAmelCase  )
            A_	     =							False
            A_	     =							use_karras_sigmas





      @property
      def 		__A  (      self       :							Dict  ):
            # standard deviation of the initial noise distribution
            if self.config.timestep_spacing in ["linspace", "trailing"]:
                  return self.sigmas.max()

            return (self.sigmas.max() ** 2 + 1) ** 0.5





      def 		__A  (      self       :							Optional[Any]	, UpperCAmelCase       :							torch.FloatTensor	, UpperCAmelCase       :							Union[float, torch.FloatTensor]  ):
            if isinstance(UpperCAmelCase	, torch.Tensor  ):
                  A_	     =							timestep.to(self.timesteps.device  )
            A_	     =							(self.timesteps == timestep).nonzero().item()
            A_	     =							self.sigmas[step_index]

            A_	     =							sample / ((sigma**2 + 1) ** 0.5)

            A_	     =							True
            return sample





      def 		__A  (      self       :							Tuple	, UpperCAmelCase       :							int	, UpperCAmelCase       :							Union[str, torch.device] = None  ):
            A_	     =							num_inference_steps

            # "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
            if self.config.timestep_spacing == "linspace":
                  A_	     =							np.linspace(0	, self.config.num_train_timesteps - 1	, UpperCAmelCase	, dtype=UpperCAmelCase  )[
                      ::-1
                  ].copy()
            elif self.config.timestep_spacing == "leading":
                  A_	     =							self.config.num_train_timesteps // self.num_inference_steps
                  # creates integer timesteps by multiplying by ratio
                  # casting to int to avoid issues when num_inference_step is power of 3
                  A_	     =							(np.arange(0	, UpperCAmelCase  ) * step_ratio).round()[::-1].copy().astype(UpperCAmelCase  )
                  timesteps += self.config.steps_offset
            elif self.config.timestep_spacing == "trailing":
                  A_	     =							self.config.num_train_timesteps / self.num_inference_steps
                  # creates integer timesteps by multiplying by ratio
                  # casting to int to avoid issues when num_inference_step is power of 3
                  A_	     =							(np.arange(self.config.num_train_timesteps	, 0	, -step_ratio  )).round().copy().astype(UpperCAmelCase  )
                  timesteps -= 1
            else:
                  raise ValueError(
                      f'''{self.config.timestep_spacing} is not supported. Please make sure to choose one of \'linspace\', \'leading\' or \'trailing\'.'''  )

            A_	     =							np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5  )
            A_	     =							np.log(UpperCAmelCase  )

            if self.config.interpolation_type == "linear":
                  A_	     =							np.interp(UpperCAmelCase	, np.arange(0	, len(UpperCAmelCase  )  )	, UpperCAmelCase  )
            elif self.config.interpolation_type == "log_linear":
                  A_	     =							torch.linspace(np.log(sigmas[-1]  )	, np.log(sigmas[0]  )	, num_inference_steps + 1  ).exp()
            else:
                  raise ValueError(
                      f'''{self.config.interpolation_type} is not implemented. Please specify interpolation_type to either'''
                      " 'linear' or 'log_linear'"  )

            if self.use_karras_sigmas:
                  A_	     =							self._convert_to_karras(in_sigmas=UpperCAmelCase	, num_inference_steps=self.num_inference_steps  )
                  A_	     =							np.array([self._sigma_to_t(UpperCAmelCase	, UpperCAmelCase  ) for sigma in sigmas]  )

            A_	     =							np.concatenate([sigmas, [0.0]]  ).astype(np.floataa  )
            A_	     =							torch.from_numpy(UpperCAmelCase  ).to(device=UpperCAmelCase  )
            if str(UpperCAmelCase  ).startswith("mps"  ):
                  # mps does not support float64
                  A_	     =							torch.from_numpy(UpperCAmelCase  ).to(UpperCAmelCase	, dtype=torch.floataa  )
            else:
                  A_	     =							torch.from_numpy(UpperCAmelCase  ).to(device=UpperCAmelCase  )





      def 		__A  (      self       :							Tuple	, UpperCAmelCase       :							Any	, UpperCAmelCase       :							Dict  ):
            # get log sigma
            A_	     =							np.log(UpperCAmelCase  )

            # get distribution
            A_	     =							log_sigma - log_sigmas[:, np.newaxis]

            # get sigmas range
            A_	     =							np.cumsum((dists >= 0)	, axis=0  ).argmax(axis=0  ).clip(max=log_sigmas.shape[0] - 2  )
            A_	     =							low_idx + 1

            A_	     =							log_sigmas[low_idx]
            A_	     =							log_sigmas[high_idx]

            # interpolate sigmas
            A_	     =							(low - log_sigma) / (low - high)
            A_	     =							np.clip(UpperCAmelCase	, 0	, 1  )

            # transform interpolation to time range
            A_	     =							(1 - w) * low_idx + w * high_idx
            A_	     =							t.reshape(sigma.shape  )
            return t





      def 		__A  (      self       :							Union[str, Any]	, UpperCAmelCase       :							torch.FloatTensor	, UpperCAmelCase       :							Any  ):
            A_	     =							in_sigmas[-1].item()
            A_	     =							in_sigmas[0].item()

            A_	     =							7.0  # 7.0 is the value used in the paper
            A_	     =							np.linspace(0	, 1	, UpperCAmelCase  )
            A_	     =							sigma_min ** (1 / rho)
            A_	     =							sigma_max ** (1 / rho)
            A_	     =							(max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
            return sigmas





      def 		__A  (      self       :							List[Any]	, UpperCAmelCase       :							torch.FloatTensor	, UpperCAmelCase       :							Union[float, torch.FloatTensor]	, UpperCAmelCase       :							torch.FloatTensor	, UpperCAmelCase       :							float = 0.0	, UpperCAmelCase       :							float = 0.0	, UpperCAmelCase       :							float = float("inf"  )	, UpperCAmelCase       :							float = 1.0	, UpperCAmelCase       :							Optional[torch.Generator] = None	, UpperCAmelCase       :							bool = True	, ):

            if (
                isinstance(UpperCAmelCase	, UpperCAmelCase  )
                or isinstance(UpperCAmelCase	, torch.IntTensor  )
                or isinstance(UpperCAmelCase	, torch.LongTensor  )
            ):
                  raise ValueError(
                      (
                          "Passing integer indices (e.g. from `enumerate(timesteps)`) as timesteps to"
                          " `EulerDiscreteScheduler.step()` is not supported. Make sure to pass"
                          " one of the `scheduler.timesteps` as a timestep."
                      )	, )

            if not self.is_scale_input_called:
                  logger.warning(
                      "The `scale_model_input` function should be called before `step` to ensure correct denoising. "
                      "See `StableDiffusionPipeline` for a usage example."  )

            if isinstance(UpperCAmelCase	, torch.Tensor  ):
                  A_	     =							timestep.to(self.timesteps.device  )

            A_	     =							(self.timesteps == timestep).nonzero().item()
            A_	     =							self.sigmas[step_index]

            A_	     =							min(s_churn / (len(self.sigmas  ) - 1)	, 2**0.5 - 1  ) if s_tmin <= sigma <= s_tmax else 0.0

            A_	     =							randn_tensor(
                model_output.shape	, dtype=model_output.dtype	, device=model_output.device	, generator=UpperCAmelCase  )

            A_	     =							noise * s_noise
            A_	     =							sigma * (gamma + 1)

            if gamma > 0:
                  A_	     =							sample + eps * (sigma_hat**2 - sigma**2) ** 0.5

            # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
            # NOTE: "original_sample" should not be an expected prediction_type but is left in for
            # backwards compatibility
            if self.config.prediction_type == "original_sample" or self.config.prediction_type == "sample":
                  A_	     =							model_output
            elif self.config.prediction_type == "epsilon":
                  A_	     =							sample - sigma_hat * model_output
            elif self.config.prediction_type == "v_prediction":
                  # * c_out + input * c_skip
                  A_	     =							model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
            else:
                  raise ValueError(
                      f'''prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`'''  )

            # 2. Convert to an ODE derivative
            A_	     =							(sample - pred_original_sample) / sigma_hat

            A_	     =							self.sigmas[step_index + 1] - sigma_hat

            A_	     =							sample + derivative * dt

            if not return_dict:
                  return (prev_sample,)

            return EulerDiscreteSchedulerOutput(prev_sample=UpperCAmelCase	, pred_original_sample=UpperCAmelCase  )





      def 		__A  (      self       :							int	, UpperCAmelCase       :							torch.FloatTensor	, UpperCAmelCase       :							torch.FloatTensor	, UpperCAmelCase       :							torch.FloatTensor	, ):
            # Make sure sigmas and timesteps have the same device and dtype as original_samples
            A_	     =							self.sigmas.to(device=original_samples.device	, dtype=original_samples.dtype  )
            if original_samples.device.type == "mps" and torch.is_floating_point(UpperCAmelCase  ):
                  # mps does not support float64
                  A_	     =							self.timesteps.to(original_samples.device	, dtype=torch.floataa  )
                  A_	     =							timesteps.to(original_samples.device	, dtype=torch.floataa  )
            else:
                  A_	     =							self.timesteps.to(original_samples.device  )
                  A_	     =							timesteps.to(original_samples.device  )

            A_	     =							[(schedule_timesteps == t).nonzero().item() for t in timesteps]

            A_	     =							sigmas[step_indices].flatten()
            while len(sigma.shape  ) < len(original_samples.shape  ):
                  A_	     =							sigma.unsqueeze(-1  )

            A_	     =							original_samples + noise * sigma
            return noisy_samples







      def __len__(      self       :							Optional[Any]  ):
            return self.config.num_train_timesteps


def 			__snake_case	(   __UpperCamelCase  :   str						):



      """simple docstring"""

      A_	     =							len(__UpperCamelCase						)
      A_	     =							[0] * length
      A_	     =							[[False for i in range(__UpperCamelCase						)] for j in range(__UpperCamelCase						)]
      for i, c in enumerate(__UpperCamelCase						):
            A_	     =							i
            for j in range(i + 1						):
                  if c == string[j] and (i - j < 2 or is_palindromic[j + 1][i - 1]):
                        A_	     =							True
                        A_	     =							min(__UpperCamelCase							,0 if j == 0 else (cut[j - 1] + 1)						)
            A_	     =							mincut
      return cut[length - 1]


if __name__ == "__main__":
      __a						:Union[str, Any]            = input('Enter the string: ').strip()
      __a						:Tuple            = find_minimum_partitions(s)
      print(F"Minimum number of partitions required for the '{s}' is {ans}")