



'''simple docstring'''


import math

_lowerCamelCase	:       int      	=	10
_lowerCamelCase	:       Union[str, Any]      	=	7
_lowerCamelCase	:       Optional[Any]      	=	BALLS_PER_COLOUR * NUM_COLOURS







def 				__lowerCamelCase				(   A__ = 20    )       ->	str:






   """simple docstring"""
   UpperCamelCase					=  math.comb(A__    ,						A__    )
   UpperCamelCase					=  math.comb(NUM_BALLS - BALLS_PER_COLOUR    ,						A__    )

   UpperCamelCase					=  NUM_COLOURS * (1 - missing_colour / total)

   return F"""{result:.9f}"""


if __name__ == "__main__":
   print(solution(20))






'''simple docstring'''


from typing import Optional, Tuple

import jax
import jax.numpy as jnp
from flax import linen as nn
from flax.core.frozen_dict import FrozenDict
from transformers import CLIPConfig, FlaxPreTrainedModel
from transformers.models.clip.modeling_flax_clip import FlaxCLIPVisionModule







def 				__lowerCamelCase				(   A__    ,						A__    ,						A__=1e-1_2    )       ->	Dict:






   """simple docstring"""
   UpperCamelCase					=  jnp.divide(emb_a.T    ,						jnp.clip(jnp.linalg.norm(A__    ,						axis=1    )    ,						a_min=A__    )    ).T
   UpperCamelCase					=  jnp.divide(emb_a.T    ,						jnp.clip(jnp.linalg.norm(A__    ,						axis=1    )    ,						a_min=A__    )    ).T
   return jnp.matmul(A__    ,						norm_emb_a.T    )

class  SCREAMING_SNAKE_CASE (  nn.Module		):






    """simple docstring"""





    _SCREAMING_SNAKE_CASE	  =  42
    _SCREAMING_SNAKE_CASE	  =  jnp.floataa






    def  A       (  self      :					List[Any] ):


       """simple docstring"""







       UpperCamelCase					=  FlaxCLIPVisionModule(self.config.vision_config )
       UpperCamelCase					=  nn.Dense(self.config.projection_dim  ,						use_bias=UpperCamelCase__  ,						dtype=self.dtype )

       UpperCamelCase					=  self.param('concept_embeds'  ,						jax.nn.initializers.ones  ,						(1_7, self.config.projection_dim) )
       UpperCamelCase					=  self.param(
           'special_care_embeds'  ,						jax.nn.initializers.ones  ,						(3, self.config.projection_dim) )

       UpperCamelCase					=  self.param('concept_embeds_weights'  ,						jax.nn.initializers.ones  ,						(1_7,) )
       UpperCamelCase					=  self.param('special_care_embeds_weights'  ,						jax.nn.initializers.ones  ,						(3,) )






    def __call__(  self      :					str  ,						UpperCamelCase__      :					List[str] ):


       """simple docstring"""







       UpperCamelCase					=  self.vision_model(UpperCamelCase__ )[1]
       UpperCamelCase					=  self.visual_projection(UpperCamelCase__ )

       UpperCamelCase					=  jax_cosine_distance(UpperCamelCase__  ,						self.special_care_embeds )
       UpperCamelCase					=  jax_cosine_distance(UpperCamelCase__  ,						self.concept_embeds )

       # increase this value to create a stronger `nfsw` filter
       # at the cost of increasing the possibility of filtering benign image inputs
       UpperCamelCase					=  0.0

       UpperCamelCase					=  special_cos_dist - self.special_care_embeds_weights[None, :] + adjustment
       UpperCamelCase					=  jnp.round(UpperCamelCase__  ,						3 )
       UpperCamelCase					=  jnp.any(special_scores > 0  ,						axis=1  ,						keepdims=UpperCamelCase__ )
       # Use a lower threshold if an image has any special care concept
       UpperCamelCase					=  is_special_care * 0.0_1

       UpperCamelCase					=  cos_dist - self.concept_embeds_weights[None, :] + special_adjustment
       UpperCamelCase					=  jnp.round(UpperCamelCase__  ,						3 )
       UpperCamelCase					=  jnp.any(concept_scores > 0  ,						axis=1 )

       return has_nsfw_concepts

class  SCREAMING_SNAKE_CASE (  _a		):






    """simple docstring"""





    _SCREAMING_SNAKE_CASE	  =  CLIPConfig
    _SCREAMING_SNAKE_CASE	  =  """clip_input"""
    _SCREAMING_SNAKE_CASE	  =  FlaxStableDiffusionSafetyCheckerModule






    def __init__(  self      :					Union[str, Any]  ,						UpperCamelCase__      :					CLIPConfig  ,						UpperCamelCase__      :					Optional[Tuple] = None  ,						UpperCamelCase__      :					int = 0  ,						UpperCamelCase__      :					jnp.dtype = jnp.floataa  ,						UpperCamelCase__      :					bool = True  ,						**UpperCamelCase__      :					List[str]  ,						):


       """simple docstring"""







       if input_shape is None:
          UpperCamelCase					=  (1, 2_2_4, 2_2_4, 3)
       UpperCamelCase					=  self.module_class(config=UpperCamelCase__  ,						dtype=UpperCamelCase__  ,						**UpperCamelCase__ )
       super().__init__(UpperCamelCase__  ,						UpperCamelCase__  ,						input_shape=UpperCamelCase__  ,						seed=UpperCamelCase__  ,						dtype=UpperCamelCase__  ,						_do_init=_do_init )






    def  A       (  self      :					int  ,						UpperCamelCase__      :					jax.random.KeyArray  ,						UpperCamelCase__      :					Tuple  ,						UpperCamelCase__      :					FrozenDict = None ):


       """simple docstring"""







       UpperCamelCase					=  jax.random.normal(UpperCamelCase__  ,						UpperCamelCase__ )

       UpperCamelCase				,      UpperCamelCase					=  jax.random.split(UpperCamelCase__ )
       UpperCamelCase					=  {'params': params_rng, 'dropout': dropout_rng}

       UpperCamelCase					=  self.module.init(UpperCamelCase__  ,						UpperCamelCase__ )['params']

       return random_params






    def __call__(  self      :					List[Any]  ,						UpperCamelCase__      :					Dict  ,						UpperCamelCase__      :					dict = None  ,						):


       """simple docstring"""







       UpperCamelCase					=  jnp.transpose(UpperCamelCase__  ,						(0, 2, 3, 1) )

       return self.module.apply(
           {'params': params or self.params}  ,						jnp.array(UpperCamelCase__  ,						dtype=jnp.floataa )  ,						rngs={}  ,						)

