





'''simple docstring'''

import math
from itertools import permutations





def lowerCamelCase		(  __lowerCamelCase				:					int					)		->bool:

    if 1 < number < 4:
        # 2 and 3 are primes
        return True
    elif number < 2 or number % 2 == 0 or number % 3 == 0:
        # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
        return False

    # All primes number are in format of 6k +/- 1
    for i in range(5      , int(math.sqrt(__lowerCamelCase					) + 1					)      , 6					):
        if number % i == 0 or number % (i + 2) == 0:
            return False
    return True





def lowerCamelCase		(  __lowerCamelCase				:					int      , __lowerCamelCase				:					list					)		->bool:
    _SCREAMING_SNAKE_CASE       , _SCREAMING_SNAKE_CASE             =    0, len(__lowerCamelCase					) - 1
    while left <= right:
        _SCREAMING_SNAKE_CASE             =    (left + right) // 2
        if prime_list[middle] == target:
            return True
        elif prime_list[middle] < target:
            _SCREAMING_SNAKE_CASE             =    middle + 1
        else:
            _SCREAMING_SNAKE_CASE             =    middle - 1

    return False





def lowerCamelCase		(  )		->List[Any]:
    _SCREAMING_SNAKE_CASE             =    [n for n in range(1001      , 1_0000      , 2					) if is_prime(__lowerCamelCase					)]
    _SCREAMING_SNAKE_CASE             =    []

    for number in prime_list:
        _SCREAMING_SNAKE_CASE             =    []

        for prime_member in permutations(list(str(__lowerCamelCase					)					)					):
            _SCREAMING_SNAKE_CASE             =    int("""""".join(__lowerCamelCase					)					)

            if prime % 2 == 0:
                continue

            if search(__lowerCamelCase      , __lowerCamelCase					):
                tmp_numbers.append(__lowerCamelCase					)

        tmp_numbers.sort()
        if len(__lowerCamelCase					) >= 3:
            candidates.append(__lowerCamelCase					)

    _SCREAMING_SNAKE_CASE             =    []
    for candidate in candidates:
        _SCREAMING_SNAKE_CASE             =    len(__lowerCamelCase					)
        _SCREAMING_SNAKE_CASE             =    False

        for i in range(__lowerCamelCase					):
            for j in range(i + 1      , __lowerCamelCase					):
                for k in range(j + 1      , __lowerCamelCase					):
                    if (
                        abs(candidate[i] - candidate[j]					)
                        == abs(candidate[j] - candidate[k]					)
                        and len({candidate[i], candidate[j], candidate[k]}					) == 3
                    ):
                        passed.append(
                            sorted([candidate[i], candidate[j], candidate[k]]					)					)
                        _SCREAMING_SNAKE_CASE             =    True

                    if found:
                        break
                if found:
                    break
            if found:
                break

    _SCREAMING_SNAKE_CASE             =    set()
    for seq in passed:
        answer.add("""""".join([str(__lowerCamelCase					) for i in seq]					)					)

    return max(int(__lowerCamelCase					) for x in answer					)


if __name__ == "__main__":
      print(solution())










'''simple docstring'''

# DISCLAIMER: This code is strongly influenced by https://github.com/pesser/pytorch_diffusion
# and https://github.com/hojonathanho/diffusion

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

import flax
import jax.numpy as jnp

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils_flax import (
    CommonSchedulerState,
    FlaxKarrasDiffusionSchedulers,
    FlaxSchedulerMixin,
    FlaxSchedulerOutput,
    add_noise_common,
    get_velocity_common,
)


@flax.struct.dataclass
class       a_  :

    '''simple docstring'''
    UpperCamelCase									=				42
    UpperCamelCase									=				42

    # setable values
    UpperCamelCase									=				42
    UpperCamelCase									=				42
    UpperCamelCase									=				None


    @classmethod
    def     snake_case_(	cls				,	A				,	A				,	A				,	A				,	)	->     List[Any]:
        return cls(
            common=A				,	final_alpha_cumprod=A				,	init_noise_sigma=A				,	timesteps=A				,	)




@dataclass
class       a_  (       snake_case_ ):

    '''simple docstring'''
    UpperCamelCase									=				42




class       a_  (       snake_case_   ,					snake_case_ ):

    '''simple docstring'''
    UpperCamelCase									=				[e.name for e in FlaxKarrasDiffusionSchedulers]

    UpperCamelCase									=				42


    @property
    def     snake_case_(	self )	->     List[Any]:
        return True


    @register_to_config
    def __init__(	self				,	A = 1000				,	A = 0.0001				,	A = 0.02				,	A = "linear"				,	A = None				,	A = True				,	A = 0				,	A = "epsilon"				,	A = jnp.floataa				,	)	->     int:
        _SCREAMING_SNAKE_CASE             =    dtype


    def     snake_case_(	self				,	A = None )	->     DDIMSchedulerState:
        if common is None:
            _SCREAMING_SNAKE_CASE             =    CommonSchedulerState.create(self )

        # At every step in ddim, we are looking into the previous alphas_cumprod
        # For the final step, there is no previous alphas_cumprod because we are already at 0
        # `set_alpha_to_one` decides whether we set this parameter simply to one or
        # whether we use the final alpha of the "non-previous" one.
        _SCREAMING_SNAKE_CASE             =    (
            jnp.array(1.0				,	dtype=self.dtype ) if self.config.set_alpha_to_one else common.alphas_cumprod[0]
        )

        # standard deviation of the initial noise distribution
        _SCREAMING_SNAKE_CASE             =    jnp.array(1.0				,	dtype=self.dtype )

        _SCREAMING_SNAKE_CASE             =    jnp.arange(0				,	self.config.num_train_timesteps ).round()[::-1]

        return DDIMSchedulerState.create(
            common=A				,	final_alpha_cumprod=A				,	init_noise_sigma=A				,	timesteps=A				,	)


    def     snake_case_(	self				,	A				,	A				,	A = None )	->     jnp.ndarray:
        return sample


    def     snake_case_(	self				,	A				,	A				,	A = () )	->     DDIMSchedulerState:
        _SCREAMING_SNAKE_CASE             =    self.config.num_train_timesteps // num_inference_steps
        # creates integer timesteps by multiplying by ratio
        # rounding to avoid issues when num_inference_step is power of 3
        _SCREAMING_SNAKE_CASE             =    (jnp.arange(0				,	A ) * step_ratio).round()[::-1] + self.config.steps_offset

        return state.replace(
            num_inference_steps=A				,	timesteps=A				,	)


    def     snake_case_(	self				,	A				,	A				,	A )	->     int:
        _SCREAMING_SNAKE_CASE             =    state.common.alphas_cumprod[timestep]
        _SCREAMING_SNAKE_CASE             =    jnp.where(
            prev_timestep >= 0				,	state.common.alphas_cumprod[prev_timestep]				,	state.final_alpha_cumprod )
        _SCREAMING_SNAKE_CASE             =    1 - alpha_prod_t
        _SCREAMING_SNAKE_CASE             =    1 - alpha_prod_t_prev

        _SCREAMING_SNAKE_CASE             =    (beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev)

        return variance


    def     snake_case_(	self				,	A				,	A				,	A				,	A				,	A = 0.0				,	A = True				,	)	->     Union[FlaxDDIMSchedulerOutput, Tuple]:
        if state.num_inference_steps is None:
            raise ValueError(
                """Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler""" )

        # See formulas (12) and (16) of DDIM paper https://arxiv.org/pdf/2010.02502.pdf
        # Ideally, read DDIM paper in-detail understanding

        # Notation (<variable name> -> <name in paper>
        # - pred_noise_t -> e_theta(x_t, t)
        # - pred_original_sample -> f_theta(x_t, t) or x_0
        # - std_dev_t -> sigma_t
        # - eta -> η
        # - pred_sample_direction -> "direction pointing to x_t"
        # - pred_prev_sample -> "x_t-1"

        # 1. get previous step value (=t-1)
        _SCREAMING_SNAKE_CASE             =    timestep - self.config.num_train_timesteps // state.num_inference_steps

        _SCREAMING_SNAKE_CASE             =    state.common.alphas_cumprod
        _SCREAMING_SNAKE_CASE             =    state.final_alpha_cumprod

        # 2. compute alphas, betas
        _SCREAMING_SNAKE_CASE             =    alphas_cumprod[timestep]
        _SCREAMING_SNAKE_CASE             =    jnp.where(prev_timestep >= 0				,	alphas_cumprod[prev_timestep]				,	A )

        _SCREAMING_SNAKE_CASE             =    1 - alpha_prod_t

        # 3. compute predicted original sample from predicted noise also called
        # "predicted x_0" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
        if self.config.prediction_type == "epsilon":
            _SCREAMING_SNAKE_CASE             =    (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
            _SCREAMING_SNAKE_CASE             =    model_output
        elif self.config.prediction_type == "sample":
            _SCREAMING_SNAKE_CASE             =    model_output
            _SCREAMING_SNAKE_CASE             =    (sample - alpha_prod_t ** 0.5 * pred_original_sample) / beta_prod_t ** 0.5
        elif self.config.prediction_type == "v_prediction":
            _SCREAMING_SNAKE_CASE             =    (alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
            _SCREAMING_SNAKE_CASE             =    (alpha_prod_t**0.5) * model_output + (beta_prod_t**0.5) * sample
        else:
            raise ValueError(
                f'prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or'
                """ `v_prediction`""" )

        # 4. compute variance: "sigma_t(η)" -> see formula (16)
        # σ_t = sqrt((1 − α_t−1)/(1 − α_t)) * sqrt(1 − α_t/α_t−1)
        _SCREAMING_SNAKE_CASE             =    self._get_variance(A				,	A				,	A )
        _SCREAMING_SNAKE_CASE             =    eta * variance ** 0.5

        # 5. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
        _SCREAMING_SNAKE_CASE             =    (1 - alpha_prod_t_prev - std_dev_t**2) ** 0.5 * pred_epsilon

        # 6. compute x_t without "random noise" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
        _SCREAMING_SNAKE_CASE             =    alpha_prod_t_prev ** 0.5 * pred_original_sample + pred_sample_direction

        if not return_dict:
            return (prev_sample, state)

        return FlaxDDIMSchedulerOutput(prev_sample=A				,	state=A )


    def     snake_case_(	self				,	A				,	A				,	A				,	A				,	)	->     jnp.ndarray:
        return add_noise_common(state.common				,	A				,	A				,	A )


    def     snake_case_(	self				,	A				,	A				,	A				,	A				,	)	->     jnp.ndarray:
        return get_velocity_common(state.common				,	A				,	A				,	A )





    def __len__(	self )	->     Any:
        return self.config.num_train_timesteps



