
"""simple docstring"""


import math
from collections import defaultdict
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

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






def      lowerCAmelCase_     (	snake_case_	:    Dict							,					snake_case_	:    Dict=0.999							,					snake_case_	:    Any="cosine"							,					)     ->Union[str, Any]:
			if alpha_transform_type == "cosine":

						def alpha_bar_fn(snake_case_	:    List[Any]    ):
									return math.cos((t + 0.008) / 1.008 * math.pi / 2    ) ** 2

			elif alpha_transform_type == "exp":

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

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

			lowerCamelCase__			:  Union[str, Any]  =[]
			for i in range(snake_case_    ):
						lowerCamelCase__			:  Any  =i / num_diffusion_timesteps
						lowerCamelCase__			:  List[Any]  =(i + 1) / num_diffusion_timesteps
						betas.append(min(1 - alpha_bar_fn(snake_case_    ) / alpha_bar_fn(snake_case_    )							,					snake_case_    )    )
			return torch.tensor(snake_case_							,					dtype=torch.floataa    )

class 					A_			(  A__   ,      A__     ):



							"""simple docstring"""






							SCREAMING_SNAKE_CASE_			   =     [e.name for e in KarrasDiffusionSchedulers]
							SCREAMING_SNAKE_CASE_			   =     2





							@register_to_config
							def __init__(						self						:Union[str, Any]  ,							lowerCamelCase_						:int = 1_000  ,							lowerCamelCase_						:float = 0.0_00_85  ,							lowerCamelCase_						:float = 0.0_12  ,							lowerCamelCase_						:str = "linear"  ,							lowerCamelCase_						:Optional[Union[np.ndarray, List[float]]] = None  ,							lowerCamelCase_						:str = "epsilon"  ,							lowerCamelCase_						:str = "linspace"  ,							lowerCamelCase_						:int = 0  ,							):





										"""simple docstring"""

										if trained_betas is not None:
													lowerCamelCase__			:  Any  =torch.tensor(lowerCamelCase_  ,							dtype=torch.floataa )
										elif beta_schedule == "linear":
													lowerCamelCase__			:  List[Any]  =torch.linspace(lowerCamelCase_  ,							lowerCamelCase_  ,							lowerCamelCase_  ,							dtype=torch.floataa )
										elif beta_schedule == "scaled_linear":
													# this schedule is very specific to the latent diffusion model.
													lowerCamelCase__			:  Union[str, Any]  =(
													    torch.linspace(beta_start**0.5  ,							beta_end**0.5  ,							lowerCamelCase_  ,							dtype=torch.floataa ) ** 2
													)
										elif beta_schedule == "squaredcos_cap_v2":
													# Glide cosine schedule
													lowerCamelCase__			:  List[str]  =betas_for_alpha_bar(lowerCamelCase_ )
										else:
													raise NotImplementedError(f"""{beta_schedule} does is not implemented for {self.__class__}""" )

										lowerCamelCase__			:  Tuple  =1.0 - self.betas
										lowerCamelCase__			:  List[str]  =torch.cumprod(self.alphas  ,							dim=0 )

										#  set all values
										self.set_timesteps(lowerCamelCase_  ,							lowerCamelCase_  ,							lowerCamelCase_ )





							def    UpperCAmelCase__							(						self						:Union[str, Any]  ,							lowerCamelCase_						:int  ,							lowerCamelCase_						:Any=None ):





										"""simple docstring"""

										if schedule_timesteps is None:
													lowerCamelCase__			:  Union[str, Any]  =self.timesteps

										lowerCamelCase__			:  int  =(schedule_timesteps == timestep).nonzero()

										# The sigma index that is taken for the **very** first `step`
										# is always the second index (or the last index if there is only 1)
										# This way we can ensure we don't accidentally skip a sigma in
										# case we start in the middle of the denoising schedule (e.g. for image-to-image)
										if len(self._index_counter ) == 0:
													lowerCamelCase__			:  Union[str, Any]  =1 if len(lowerCamelCase_ ) > 1 else 0
										else:
													lowerCamelCase__			:  Optional[Any]  =timestep.cpu().item() if torch.is_tensor(lowerCamelCase_ ) else timestep
													lowerCamelCase__			:  Dict  =self._index_counter[timestep_int]

										return indices[pos].item()





							@property
							def    UpperCAmelCase__							(						self						:Dict ):





										"""simple docstring"""

										if self.config.timestep_spacing in ["linspace", "trailing"]:
													return self.sigmas.max()

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





							def    UpperCAmelCase__							(						self						:Union[str, Any]  ,							lowerCamelCase_						:torch.FloatTensor  ,							lowerCamelCase_						:Union[float, torch.FloatTensor]  ,							):





										"""simple docstring"""

										lowerCamelCase__			:  List[str]  =self.index_for_timestep(lowerCamelCase_ )

										if self.state_in_first_order:
													lowerCamelCase__			:  Dict  =self.sigmas[step_index]
										else:
													lowerCamelCase__			:  Dict  =self.sigmas_interpol[step_index - 1]

										lowerCamelCase__			:  Union[str, Any]  =sample / ((sigma**2 + 1) ** 0.5)
										return sample





							def    UpperCAmelCase__							(						self						:Tuple  ,							lowerCamelCase_						:int  ,							lowerCamelCase_						:Union[str, torch.device] = None  ,							lowerCamelCase_						:Optional[int] = None  ,							):





										"""simple docstring"""

										lowerCamelCase__			:  Tuple  =num_inference_steps

										lowerCamelCase__			:  Union[str, Any]  =num_train_timesteps or self.config.num_train_timesteps

										# "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
										if self.config.timestep_spacing == "linspace":
													lowerCamelCase__			:  List[Any]  =np.linspace(0  ,							num_train_timesteps - 1  ,							lowerCamelCase_  ,							dtype=lowerCamelCase_ )[::-1].copy()
										elif self.config.timestep_spacing == "leading":
													lowerCamelCase__			:  List[Any]  =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
													lowerCamelCase__			:  Union[str, Any]  =(np.arange(0  ,							lowerCamelCase_ ) * step_ratio).round()[::-1].copy().astype(lowerCamelCase_ )
													timesteps += self.config.steps_offset
										elif self.config.timestep_spacing == "trailing":
													lowerCamelCase__			:  str  =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
													lowerCamelCase__			:  List[str]  =(np.arange(lowerCamelCase_  ,							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'.""" )

										lowerCamelCase__			:  Optional[int]  =np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5 )
										lowerCamelCase__			:  Optional[int]  =torch.from_numpy(np.log(lowerCamelCase_ ) ).to(lowerCamelCase_ )

										lowerCamelCase__			:  int  =np.interp(lowerCamelCase_  ,							np.arange(0  ,							len(lowerCamelCase_ ) )  ,							lowerCamelCase_ )
										lowerCamelCase__			:  str  =np.concatenate([sigmas, [0.0]] ).astype(np.floataa )
										lowerCamelCase__			:  int  =torch.from_numpy(lowerCamelCase_ ).to(device=lowerCamelCase_ )

										# compute up and down sigmas
										lowerCamelCase__			:  Optional[Any]  =sigmas.roll(-1 )
										lowerCamelCase__			:  Any  =0.0
										lowerCamelCase__			:  Optional[Any]  =(sigmas_next**2 * (sigmas**2 - sigmas_next**2) / sigmas**2) ** 0.5
										lowerCamelCase__			:  List[str]  =(sigmas_next**2 - sigmas_up**2) ** 0.5
										lowerCamelCase__			:  Optional[Any]  =0.0

										# compute interpolated sigmas
										lowerCamelCase__			:  int  =sigmas.log().lerp(sigmas_down.log()  ,							0.5 ).exp()
										lowerCamelCase__			:  List[str]  =0.0

										# set sigmas
										lowerCamelCase__			:  Tuple  =torch.cat([sigmas[:1], sigmas[1:].repeat_interleave(2 ), sigmas[-1:]] )
										lowerCamelCase__			:  Optional[Any]  =torch.cat(
										    [sigmas_interpol[:1], sigmas_interpol[1:].repeat_interleave(2 ), sigmas_interpol[-1:]] )
										lowerCamelCase__			:  int  =torch.cat([sigmas_up[:1], sigmas_up[1:].repeat_interleave(2 ), sigmas_up[-1:]] )
										lowerCamelCase__			:  List[str]  =torch.cat([sigmas_down[:1], sigmas_down[1:].repeat_interleave(2 ), sigmas_down[-1:]] )

										if str(lowerCamelCase_ ).startswith('mps' ):
													# mps does not support float64
													lowerCamelCase__			:  Union[str, Any]  =torch.from_numpy(lowerCamelCase_ ).to(lowerCamelCase_  ,							dtype=torch.floataa )
										else:
													lowerCamelCase__			:  List[Any]  =torch.from_numpy(lowerCamelCase_ ).to(lowerCamelCase_ )

										lowerCamelCase__			:  Any  =self.sigma_to_t(lowerCamelCase_ ).to(lowerCamelCase_  ,							dtype=timesteps.dtype )
										lowerCamelCase__			:  Optional[Any]  =torch.stack((timesteps_interpol[:-2, None], timesteps[1:, None])  ,							dim=-1 ).flatten()

										lowerCamelCase__			:  List[Any]  =torch.cat([timesteps[:1], interleaved_timesteps] )

										lowerCamelCase__			:  Dict  =None

										# for exp beta schedules, such as the one for `pipeline_shap_e.py`
										# we need an index counter
										lowerCamelCase__			:  int  =defaultdict(lowerCamelCase_ )





							def    UpperCAmelCase__							(						self						:Dict  ,							lowerCamelCase_						:List[str] ):





										"""simple docstring"""

										lowerCamelCase__			:  Optional[int]  =sigma.log()

										# get distribution
										lowerCamelCase__			:  Dict  =log_sigma - self.log_sigmas[:, None]

										# get sigmas range
										lowerCamelCase__			:  Union[str, Any]  =dists.ge(0 ).cumsum(dim=0 ).argmax(dim=0 ).clamp(max=self.log_sigmas.shape[0] - 2 )
										lowerCamelCase__			:  Any  =low_idx + 1

										lowerCamelCase__			:  List[str]  =self.log_sigmas[low_idx]
										lowerCamelCase__			:  Union[str, Any]  =self.log_sigmas[high_idx]

										# interpolate sigmas
										lowerCamelCase__			:  List[str]  =(low - log_sigma) / (low - high)
										lowerCamelCase__			:  List[str]  =w.clamp(0  ,							1 )

										# transform interpolation to time range
										lowerCamelCase__			:  Optional[Any]  =(1 - w) * low_idx + w * high_idx
										lowerCamelCase__			:  Dict  =t.view(sigma.shape )
										return t





							@property
							def    UpperCAmelCase__							(						self						:str ):





										"""simple docstring"""

										return self.sample is None





							def    UpperCAmelCase__							(						self						:Optional[int]  ,							lowerCamelCase_						:Union[torch.FloatTensor, np.ndarray]  ,							lowerCamelCase_						:Union[float, torch.FloatTensor]  ,							lowerCamelCase_						:Union[torch.FloatTensor, np.ndarray]  ,							lowerCamelCase_						:Optional[torch.Generator] = None  ,							lowerCamelCase_						:bool = True  ,							):





										"""simple docstring"""

										lowerCamelCase__			:  str  =self.index_for_timestep(lowerCamelCase_ )

										# advance index counter by 1
										lowerCamelCase__			:  int  =timestep.cpu().item() if torch.is_tensor(lowerCamelCase_ ) else timestep
										self._index_counter[timestep_int] += 1

										if self.state_in_first_order:
													lowerCamelCase__			:  Optional[int]  =self.sigmas[step_index]
													lowerCamelCase__			:  Dict  =self.sigmas_interpol[step_index]
													lowerCamelCase__			:  str  =self.sigmas_up[step_index]
													lowerCamelCase__			:  str  =self.sigmas_down[step_index - 1]
										else:
													# 2nd order / KPDM2's method
													lowerCamelCase__			:  int  =self.sigmas[step_index - 1]
													lowerCamelCase__			:  Tuple  =self.sigmas_interpol[step_index - 1]
													lowerCamelCase__			:  Tuple  =self.sigmas_up[step_index - 1]
													lowerCamelCase__			:  List[Any]  =self.sigmas_down[step_index - 1]

										# currently only gamma=0 is supported. This usually works best anyways.
										# We can support gamma in the future but then need to scale the timestep before
										# passing it to the model which requires a change in API
										lowerCamelCase__			:  Optional[Any]  =0
										lowerCamelCase__			:  Any  =sigma * (gamma + 1)  # Note: sigma_hat == sigma for now

										lowerCamelCase__			:  Any  =model_output.device
										lowerCamelCase__			:  Union[str, Any]  =randn_tensor(model_output.shape  ,							dtype=model_output.dtype  ,							device=lowerCamelCase_  ,							generator=lowerCamelCase_ )

										# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
										if self.config.prediction_type == "epsilon":
													lowerCamelCase__			:  int  =sigma_hat if self.state_in_first_order else sigma_interpol
													lowerCamelCase__			:  Optional[Any]  =sample - sigma_input * model_output
										elif self.config.prediction_type == "v_prediction":
													lowerCamelCase__			:  Union[str, Any]  =sigma_hat if self.state_in_first_order else sigma_interpol
													lowerCamelCase__			:  str  =model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + (
													    sample / (sigma_input**2 + 1)
													)
										elif self.config.prediction_type == "sample":
													raise NotImplementedError('prediction_type not implemented yet: sample' )
										else:
													raise ValueError(
													    f"""prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`""" )

										if self.state_in_first_order:
													# 2. Convert to an ODE derivative for 1st order
													lowerCamelCase__			:  Any  =(sample - pred_original_sample) / sigma_hat
													# 3. delta timestep
													lowerCamelCase__			:  str  =sigma_interpol - sigma_hat

													# store for 2nd order step
													lowerCamelCase__			:  str  =sample
													lowerCamelCase__			:  List[Any]  =dt
													lowerCamelCase__			:  Tuple  =sample + derivative * dt
										else:
													# DPM-Solver-2
													# 2. Convert to an ODE derivative for 2nd order
													lowerCamelCase__			:  Any  =(sample - pred_original_sample) / sigma_interpol
													# 3. delta timestep
													lowerCamelCase__			:  Optional[int]  =sigma_down - sigma_hat

													lowerCamelCase__			:  Optional[Any]  =self.sample
													lowerCamelCase__			:  str  =None

													lowerCamelCase__			:  Optional[int]  =sample + derivative * dt
													lowerCamelCase__			:  Dict  =prev_sample + noise * sigma_up

										if not return_dict:
													return (prev_sample,)

										return SchedulerOutput(prev_sample=lowerCamelCase_ )





							def    UpperCAmelCase__							(						self						:Dict  ,							lowerCamelCase_						:torch.FloatTensor  ,							lowerCamelCase_						:torch.FloatTensor  ,							lowerCamelCase_						:torch.FloatTensor  ,							):





										"""simple docstring"""

										lowerCamelCase__			:  Union[str, Any]  =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
													lowerCamelCase__			:  str  =self.timesteps.to(original_samples.device  ,							dtype=torch.floataa )
													lowerCamelCase__			:  Any  =timesteps.to(original_samples.device  ,							dtype=torch.floataa )
										else:
													lowerCamelCase__			:  Optional[Any]  =self.timesteps.to(original_samples.device )
													lowerCamelCase__			:  List[str]  =timesteps.to(original_samples.device )

										lowerCamelCase__			:  Any  =[self.index_for_timestep(lowerCamelCase_  ,							lowerCamelCase_ ) for t in timesteps]

										lowerCamelCase__			:  int  =sigmas[step_indices].flatten()
										while len(sigma.shape ) < len(original_samples.shape ):
													lowerCamelCase__			:  List[str]  =sigma.unsqueeze(-1 )

										lowerCamelCase__			:  str  =original_samples + noise * sigma
										return noisy_samples





							def __len__(						self						:str ):





										"""simple docstring"""

										return self.config.num_train_timesteps

"""simple docstring"""


def      lowerCAmelCase_     (	snake_case_	:    str    )     ->int:
			lowerCamelCase__			:  Optional[Any]  =len(snake_case_    )
			lowerCamelCase__			:  Any  =[0] * length
			lowerCamelCase__			:  str  =[[False for i in range(snake_case_    )] for j in range(snake_case_    )]
			for i, c in enumerate(snake_case_    ):
						lowerCamelCase__			:  Optional[Any]  =i
						for j in range(i + 1    ):
									if c == string[j] and (i - j < 2 or is_palindromic[j + 1][i - 1]):
												lowerCamelCase__			:  int  =True
												lowerCamelCase__			:  Tuple  =min(snake_case_							,					0 if j == 0 else (cut[j - 1] + 1)    )
						lowerCamelCase__			:  Any  =mincut
			return cut[length - 1]


if __name__ == "__main__":
							lowerCAmelCase			=		input("""Enter the string: """).strip()
							lowerCAmelCase			=		find_minimum_partitions(s)
							print(f"""Minimum number of partitions required for the '{s}' is {ans}""")