def        __UpperCAmelCase    (       UpperCAmelCase       )->       str:



			"""simple docstring"""







			lowercase							=		0

			# if input_string is "aba" than new_input_string become "a|b|a"
			lowercase							=		''''''
			lowercase							=		''''''

			# append each character + "|" in new_string for range(0, length-1)
			for i in input_string[: len(UpperCAmelCase       ) - 1]:
						new_input_string += i + "|"
			# append last character
			new_input_string += input_string[-1]

			# we will store the starting and ending of previous furthest ending palindromic
			# substring
			lowercase		,lowercase							=		0, 0

			# length[i] shows the length of palindromic substring with center i
			lowercase							=		[1 for i in range(len(UpperCAmelCase       )       )]

			# for each character in new_string find corresponding palindromic string
			lowercase							=		0
			for j in range(len(UpperCAmelCase       )       ):
						lowercase							=		1 if j > r else min(length[l + r - j] // 2,		r - j + 1       )
						while (
						    j - k >= 0
						    and j + k < len(UpperCAmelCase       )
						    and new_input_string[k + j] == new_input_string[j - k]
						):
									k += 1

						lowercase							=		2 * k - 1

						# does this string is ending after the previously explored end (that is r) ?
						# if yes the update the new r to the last index of this
						if j + k - 1 > r:
									lowercase							=		j - k + 1  # noqa: E741
									lowercase							=		j + k - 1

						# update max_length and start position
						if max_length < length[j]:
									lowercase							=		length[j]
									lowercase							=		j

    # create that string
			lowercase							=		new_input_string[start - max_length // 2 : start + max_length // 2 + 1]
			for i in s:
						if i != "|":
									output_string += i

			return output_string


if __name__ == "__main__":
						import doctest

						doctest.testmod()






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

import flax
import jax.numpy as jnp
from jax import random

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput
from .scheduling_utils_flax import FlaxSchedulerMixin






@flax.struct.dataclass
class      __lowercase					:
						# setable values
						lowercase					 =     None
						lowercase					 =     None
						lowercase					 =     None  # sigma(t_i)

						@classmethod
						def        __a		(	cls				:      List[str]   )							->		Dict:


									'''simple docstring'''

									return cls()






@dataclass
class      __lowercase					(    _A    ):
						lowercase					 =     42
						lowercase					 =     42
						lowercase					 =     42






class      __lowercase					(    _A       ,     _A    ):

						@property
						def        __a		(	self				:      Union[str, Any]   )							->		Optional[Any]:


									'''simple docstring'''

									return True

						@register_to_config
						def __init__(	self				:      int							,							__lowerCamelCase				:      float = 0.02							,							__lowerCamelCase				:      float = 1_00							,							__lowerCamelCase				:      float = 1.007							,							__lowerCamelCase				:      float = 80							,							__lowerCamelCase				:      float = 0.05							,							__lowerCamelCase				:      float = 50							,							)							->		List[Any]:


									'''simple docstring'''

									pass

						def        __a		(	self				:      Dict   )							->		Optional[int]:


									'''simple docstring'''

									return KarrasVeSchedulerState.create()

						def        __a		(	self				:      str							,							__lowerCamelCase				:      KarrasVeSchedulerState							,							__lowerCamelCase				:      int							,							__lowerCamelCase				:      Tuple = ()   )							->		KarrasVeSchedulerState:


									'''simple docstring'''

									lowercase							=		jnp.arange(0							,							__lowerCamelCase   )[::-1].copy()
									lowercase							=		[
									    (
									        self.config.sigma_max**2
									        * (self.config.sigma_min**2 / self.config.sigma_max**2) ** (i / (num_inference_steps - 1))
									    )
									    for i in timesteps
									]

									return state.replace(
									    num_inference_steps=__lowerCamelCase							,							schedule=jnp.array(__lowerCamelCase							,							dtype=jnp.floataa   )							,							timesteps=__lowerCamelCase							,							)

						def        __a		(	self				:      Optional[Any]							,							__lowerCamelCase				:      KarrasVeSchedulerState							,							__lowerCamelCase				:      jnp.ndarray							,							__lowerCamelCase				:      float							,							__lowerCamelCase				:      random.KeyArray							,							)							->		Tuple[jnp.ndarray, float]:


									'''simple docstring'''

									if self.config.s_min <= sigma <= self.config.s_max:
												lowercase							=		min(self.config.s_churn / state.num_inference_steps							,							2**0.5 - 1   )
									else:
												lowercase							=		0

									# sample eps ~ N(0, S_noise^2 * I)
									lowercase							=		random.split(__lowerCamelCase							,							num=1   )
									lowercase							=		self.config.s_noise * random.normal(key=__lowerCamelCase							,							shape=sample.shape   )
									lowercase							=		sigma + gamma * sigma
									lowercase							=		sample + ((sigma_hat**2 - sigma**2) ** 0.5 * eps)

									return sample_hat, sigma_hat

						def        __a		(	self				:      str							,							__lowerCamelCase				:      KarrasVeSchedulerState							,							__lowerCamelCase				:      jnp.ndarray							,							__lowerCamelCase				:      float							,							__lowerCamelCase				:      float							,							__lowerCamelCase				:      jnp.ndarray							,							__lowerCamelCase				:      bool = True							,							)							->		Union[FlaxKarrasVeOutput, Tuple]:


									'''simple docstring'''

									lowercase							=		sample_hat + sigma_hat * model_output
									lowercase							=		(sample_hat - pred_original_sample) / sigma_hat
									lowercase							=		sample_hat + (sigma_prev - sigma_hat) * derivative

									if not return_dict:
												return (sample_prev, derivative, state)

									return FlaxKarrasVeOutput(prev_sample=__lowerCamelCase							,							derivative=__lowerCamelCase							,							state=__lowerCamelCase   )

						def        __a		(	self				:      str							,							__lowerCamelCase				:      KarrasVeSchedulerState							,							__lowerCamelCase				:      jnp.ndarray							,							__lowerCamelCase				:      float							,							__lowerCamelCase				:      float							,							__lowerCamelCase				:      jnp.ndarray							,							__lowerCamelCase				:      jnp.ndarray							,							__lowerCamelCase				:      jnp.ndarray							,							__lowerCamelCase				:      bool = True							,							)							->		Union[FlaxKarrasVeOutput, Tuple]:


									'''simple docstring'''

									lowercase							=		sample_prev + sigma_prev * model_output
									lowercase							=		(sample_prev - pred_original_sample) / sigma_prev
									lowercase							=		sample_hat + (sigma_prev - sigma_hat) * (0.5 * derivative + 0.5 * derivative_corr)

									if not return_dict:
												return (sample_prev, derivative, state)

									return FlaxKarrasVeOutput(prev_sample=__lowerCamelCase							,							derivative=__lowerCamelCase							,							state=__lowerCamelCase   )



						def        __a		(	self				:      int							,							__lowerCamelCase				:      KarrasVeSchedulerState							,							__lowerCamelCase				:      str							,							__lowerCamelCase				:      str							,							__lowerCamelCase				:      Dict   )							->		Tuple:


									'''simple docstring'''

									raise NotImplementedError()





