

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

import numpy as np
import torch
from scipy import integrate

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

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




      """simple docstring"""

      _lowerCamelCase					: Optional[Any]					=					4_2
      _lowerCamelCase					: List[Any]					=					None




def 			__snake_case		(   __UpperCamelCase  :   List[str]							,__UpperCamelCase  :   Any=0.999							,__UpperCamelCase  :   Optional[int]="cosine"							,):



      """simple docstring"""

      if alpha_transform_type == "cosine":

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

      elif alpha_transform_type == "exp":

            def alpha_bar_fn(__UpperCamelCase  :   Union[str, 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					: Optional[Any]					=					[e.name for e in KarrasDiffusionSchedulers]
      _lowerCamelCase					: str					=					1





      @register_to_config
      def __init__(      self       :							int	, UpperCAmelCase       :							Dict = 1000	, UpperCAmelCase       :							Union[str, Any] = 0.0_001	, UpperCAmelCase       :							int = 0.02	, UpperCAmelCase       :							List[Any] = "linear"	, UpperCAmelCase       :							Any = None	, UpperCAmelCase       :							List[str] = False	, UpperCAmelCase       :							Optional[int] = "epsilon"	, UpperCAmelCase       :							Optional[Any] = "linspace"	, UpperCAmelCase       :							List[Any] = 0	, ):
            if trained_betas is not None:
                  A_	     =							torch.tensor(__lowerCamelCase	, dtype=torch.floataa  )
            elif beta_schedule == "linear":
                  A_	     =							torch.linspace(__lowerCamelCase	, __lowerCamelCase	, __lowerCamelCase	, 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	, __lowerCamelCase	, dtype=torch.floataa  ) ** 2
                  )
            elif beta_schedule == "squaredcos_cap_v2":
                  # Glide cosine schedule
                  A_	     =							betas_for_alpha_bar(__lowerCamelCase  )
            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(__lowerCamelCase  )

            # setable values
            A_	     =							None
            A_	     =							use_karras_sigmas
            self.set_timesteps(__lowerCamelCase	, __lowerCamelCase  )
            A_	     =							[]
            A_	     =							False





      @property
      def 		__A  (      self       :							List[str]  ):
            # 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       :							Any	, UpperCAmelCase       :							List[Any]	, UpperCAmelCase       :							List[str]  ):
            if isinstance(__lowerCamelCase	, 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       :							List[Any]	, UpperCAmelCase       :							List[str]	, UpperCAmelCase       :							Dict	, UpperCAmelCase       :							List[Any]  ):

            def lms_derivative(UpperCAmelCase       :							Optional[int]  ):
                  A_	     =							1.0
                  for k in range(__lowerCamelCase  ):
                        if current_order == k:
                              continue
                        prod *= (tau - self.sigmas[t - k]) / (self.sigmas[t - current_order] - self.sigmas[t - k])
                  return prod

            A_	     =							integrate.quad(__lowerCamelCase	, self.sigmas[t]	, self.sigmas[t + 1]	, epsrel=1E-4  )[0]

            return integrated_coeff





      def 		__A  (      self       :							Optional[Any]	, UpperCAmelCase       :							Optional[Any]	, UpperCAmelCase       :							Union[str, Any] = 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	, __lowerCamelCase	, dtype=__lowerCamelCase  )[
                      ::-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	, __lowerCamelCase  ) * step_ratio).round()[::-1].copy().astype(__lowerCamelCase  )
                  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(__lowerCamelCase  )
                  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(__lowerCamelCase  )
            A_	     =							np.interp(__lowerCamelCase	, np.arange(0	, len(__lowerCamelCase  )  )	, __lowerCamelCase  )

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

            A_	     =							np.concatenate([sigmas, [0.0]]  ).astype(np.floataa  )

            A_	     =							torch.from_numpy(__lowerCamelCase  ).to(device=__lowerCamelCase  )
            if str(__lowerCamelCase  ).startswith("mps"  ):
                  # mps does not support float64
                  A_	     =							torch.from_numpy(__lowerCamelCase  ).to(__lowerCamelCase	, dtype=torch.floataa  )
            else:
                  A_	     =							torch.from_numpy(__lowerCamelCase  ).to(device=__lowerCamelCase  )

            A_	     =							[]





      def 		__A  (      self       :							Any	, UpperCAmelCase       :							Optional[int]	, UpperCAmelCase       :							Optional[int]  ):
            # get log sigma
            A_	     =							np.log(__lowerCamelCase  )

            # 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(__lowerCamelCase	, 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       :							Any	, UpperCAmelCase       :							Dict  ):
            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	, self.num_inference_steps  )
            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       :							Any	, UpperCAmelCase       :							Union[str, Any]	, UpperCAmelCase       :							List[str]	, UpperCAmelCase       :							Optional[Any]	, UpperCAmelCase       :							List[str] = 4	, UpperCAmelCase       :							str = True	, ):
            if not self.is_scale_input_called:
                  warnings.warn(
                      "The `scale_model_input` function should be called before `step` to ensure correct denoising. "
                      "See `StableDiffusionPipeline` for a usage example."  )

            if isinstance(__lowerCamelCase	, torch.Tensor  ):
                  A_	     =							timestep.to(self.timesteps.device  )
            A_	     =							(self.timesteps == timestep).nonzero().item()
            A_	     =							self.sigmas[step_index]

            # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
            if self.config.prediction_type == "epsilon":
                  A_	     =							sample - sigma * 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))
            elif self.config.prediction_type == "sample":
                  A_	     =							model_output
            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
            self.derivatives.append(__lowerCamelCase  )
            if len(self.derivatives  ) > order:
                  self.derivatives.pop(0  )

            # 3. Compute linear multistep coefficients
            A_	     =							min(step_index + 1	, __lowerCamelCase  )
            A_	     =							[self.get_lms_coefficient(__lowerCamelCase	, __lowerCamelCase	, __lowerCamelCase  ) for curr_order in range(__lowerCamelCase  )]

            # 4. Compute previous sample based on the derivatives path
            A_	     =							sample + sum(
                coeff * derivative for coeff, derivative in zip(__lowerCamelCase	, reversed(self.derivatives  )  )  )

            if not return_dict:
                  return (prev_sample,)

            return LMSDiscreteSchedulerOutput(prev_sample=__lowerCamelCase	, pred_original_sample=__lowerCamelCase  )





      def 		__A  (      self       :							List[str]	, UpperCAmelCase       :							Any	, UpperCAmelCase       :							List[Any]	, UpperCAmelCase       :							Union[str, Any]	, ):
            # 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(__lowerCamelCase  ):
                  # 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       :							int  ):
            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}")