






"""simple docstring"""



import functools
import math

import flax.linen as nn
import jax
import jax.numpy as jnp


def      SCREAMING_SNAKE_CASE__    (   snake_case    :      int       , snake_case    :      Optional[Any]       , snake_case    :      Union[str, Any]       , snake_case    :      str       , snake_case    :      int = 4096							)->						str:






     '''simple docstring'''



     UpperCAmelCase__				,							UpperCAmelCase__				,							UpperCAmelCase__		:  Optional[Any]				=				key.shape[-3:]
     UpperCAmelCase__		:  Tuple				=				value.shape[-1]
     UpperCAmelCase__		:  Optional[Any]				=				min(snake_case       , snake_case							)
     UpperCAmelCase__		:  Dict				=				query / jnp.sqrt(snake_case							)

     @functools.partial(jax.checkpoint       , prevent_cse=snake_case							)
     def summarize_chunk(snake_case    :      Any       , snake_case    :      int       , snake_case    :      int							):
          UpperCAmelCase__		:  List[str]				=				jnp.einsum("...qhd,...khd->...qhk"       , snake_case       , snake_case       , precision=snake_case							)

          UpperCAmelCase__		:  Optional[int]				=				jnp.max(snake_case       , axis=-1       , keepdims=snake_case							)
          UpperCAmelCase__		:  List[str]				=				jax.lax.stop_gradient(snake_case							)
          UpperCAmelCase__		:  Dict				=				jnp.exp(attn_weights - max_score							)

          UpperCAmelCase__		:  List[Any]				=				jnp.einsum("...vhf,...qhv->...qhf"       , snake_case       , snake_case       , precision=snake_case							)
          UpperCAmelCase__		:  Union[str, Any]				=				jnp.einsum("...qhk->...qh"       , snake_case							)

          return (exp_values, exp_weights.sum(axis=-1							), max_score)

     def chunk_scanner(snake_case    :      Dict							):
          # julienne key array
          UpperCAmelCase__		:  Any				=				jax.lax.dynamic_slice(
              operand=snake_case       , start_indices=[0] * (key.ndim - 3) + [chunk_idx, 0, 0]       , slice_sizes=list(key.shape[:-3]							) + [key_chunk_size, num_heads, k_features]       , )

          # julienne value array
          UpperCAmelCase__		:  int				=				jax.lax.dynamic_slice(
              operand=snake_case       , start_indices=[0] * (value.ndim - 3) + [chunk_idx, 0, 0]       , slice_sizes=list(value.shape[:-3]							) + [key_chunk_size, num_heads, v_features]       , )

          return summarize_chunk(snake_case       , snake_case       , snake_case							)

     UpperCAmelCase__				,							UpperCAmelCase__				,							UpperCAmelCase__		:  Union[str, Any]				=				jax.lax.map(f=snake_case       , xs=jnp.arange(0       , snake_case       , snake_case							)							)

     UpperCAmelCase__		:  List[Any]				=				jnp.max(snake_case       , axis=0       , keepdims=snake_case							)
     UpperCAmelCase__		:  Union[str, Any]				=				jnp.exp(chunk_max - global_max							)

     chunk_values *= jnp.expand_dims(snake_case       , axis=-1							)
     chunk_weights *= max_diffs

     UpperCAmelCase__		:  str				=				chunk_values.sum(axis=0							)
     UpperCAmelCase__		:  List[str]				=				jnp.expand_dims(snake_case       , -1							).sum(axis=0							)

     return all_values / all_weights


def      SCREAMING_SNAKE_CASE__    (   snake_case    :      Union[str, Any]       , snake_case    :      Dict       , snake_case    :      Tuple       , snake_case    :      List[str]=jax.lax.Precision.HIGHEST       , snake_case    :      int = 1024       , snake_case    :      int = 4096							)->						Union[str, Any]:






     '''simple docstring'''



     UpperCAmelCase__				,							UpperCAmelCase__				,							UpperCAmelCase__		:  str				=				query.shape[-3:]

     def chunk_scanner(snake_case    :      Tuple       , snake_case    :      Any							):
          # julienne query array
          UpperCAmelCase__		:  Dict				=				jax.lax.dynamic_slice(
              operand=snake_case       , start_indices=([0] * (query.ndim - 3)) + [chunk_idx, 0, 0]       , slice_sizes=list(query.shape[:-3]							) + [min(snake_case       , snake_case							), num_heads, q_features]       , )

          return (
              chunk_idx + query_chunk_size,  # unused ignore it
              _query_chunk_attention(
                  query=snake_case       , key=snake_case       , value=snake_case       , precision=snake_case       , key_chunk_size=snake_case							),
          )

     UpperCAmelCase__				,							UpperCAmelCase__		:  List[str]				=				jax.lax.scan(
         f=snake_case       , init=0       , xs=snake_case       , length=math.ceil(num_q / query_chunk_size							)							)

     return jnp.concatenate(snake_case       , axis=-3							)  # fuse the chunked result back




class        lowerCAmelCase__       (  nn.Module					):
   SCREAMING_SNAKE_CASE_					      =42
   SCREAMING_SNAKE_CASE_					      =8
   SCREAMING_SNAKE_CASE_					      =64
   SCREAMING_SNAKE_CASE_					      =0.0
   SCREAMING_SNAKE_CASE_					      =False
   SCREAMING_SNAKE_CASE_					      =jnp.floataa
   def 	__a				(						self	:     Any				):


        '''simple docstring'''
        UpperCAmelCase__		:  Optional[int]				=				self.dim_head * self.heads
        UpperCAmelCase__		:  Tuple				=				self.dim_head**-0.5

        # Weights were exported with old names {to_q, to_k, to_v, to_out}
        UpperCAmelCase__		:  Dict				=				nn.Dense(snake_case__				,       use_bias=snake_case__				,       dtype=self.dtype				,       name="to_q"				)
        UpperCAmelCase__		:  List[str]				=				nn.Dense(snake_case__				,       use_bias=snake_case__				,       dtype=self.dtype				,       name="to_k"				)
        UpperCAmelCase__		:  Dict				=				nn.Dense(snake_case__				,       use_bias=snake_case__				,       dtype=self.dtype				,       name="to_v"				)

        UpperCAmelCase__		:  Tuple				=				nn.Dense(self.query_dim				,       dtype=self.dtype				,       name="to_out_0"				)
        UpperCAmelCase__		:  List[Any]				=				nn.Dropout(rate=self.dropout				)
   def 	__a				(						self	:     str				,       snake_case__	:     List[Any]				):


        '''simple docstring'''
        UpperCAmelCase__				,							UpperCAmelCase__				,							UpperCAmelCase__		:  List[Any]				=				tensor.shape
        UpperCAmelCase__		:  Any				=				self.heads
        UpperCAmelCase__		:  Union[str, Any]				=				tensor.reshape(snake_case__				,       snake_case__				,       snake_case__				,       dim // head_size				)
        UpperCAmelCase__		:  str				=				jnp.transpose(snake_case__				,       (0, 2, 1, 3)				)
        UpperCAmelCase__		:  int				=				tensor.reshape(batch_size * head_size				,       snake_case__				,       dim // head_size				)
        return tensor
   def 	__a				(						self	:     Union[str, Any]				,       snake_case__	:     Any				):


        '''simple docstring'''
        UpperCAmelCase__				,							UpperCAmelCase__				,							UpperCAmelCase__		:  List[str]				=				tensor.shape
        UpperCAmelCase__		:  List[Any]				=				self.heads
        UpperCAmelCase__		:  Optional[int]				=				tensor.reshape(batch_size // head_size				,       snake_case__				,       snake_case__				,       snake_case__				)
        UpperCAmelCase__		:  Optional[Any]				=				jnp.transpose(snake_case__				,       (0, 2, 1, 3)				)
        UpperCAmelCase__		:  Tuple				=				tensor.reshape(batch_size // head_size				,       snake_case__				,       dim * head_size				)
        return tensor




   def __call__(						self	:     str				,       snake_case__	:     Dict				,       snake_case__	:     Any=None				,       snake_case__	:     int=True				):


        '''simple docstring'''
        UpperCAmelCase__		:  str				=				hidden_states if context is None else context

        UpperCAmelCase__		:  Dict				=				self.query(snake_case__				)
        UpperCAmelCase__		:  List[str]				=				self.key(snake_case__				)
        UpperCAmelCase__		:  Union[str, Any]				=				self.value(snake_case__				)

        UpperCAmelCase__		:  int				=				self.reshape_heads_to_batch_dim(snake_case__				)
        UpperCAmelCase__		:  List[Any]				=				self.reshape_heads_to_batch_dim(snake_case__				)
        UpperCAmelCase__		:  int				=				self.reshape_heads_to_batch_dim(snake_case__				)

        if self.use_memory_efficient_attention:
             UpperCAmelCase__		:  Union[str, Any]				=				query_states.transpose(1				,       0				,       2				)
             UpperCAmelCase__		:  Optional[Any]				=				key_states.transpose(1				,       0				,       2				)
             UpperCAmelCase__		:  Tuple				=				value_states.transpose(1				,       0				,       2				)

             # this if statement create a chunk size for each layer of the unet
             # the chunk size is equal to the query_length dimension of the deepest layer of the unet

             UpperCAmelCase__		:  Union[str, Any]				=				query_states.shape[-3]
             if flatten_latent_dim % 6_4 == 0:
                  UpperCAmelCase__		:  List[str]				=				int(flatten_latent_dim / 6_4				)
             elif flatten_latent_dim % 1_6 == 0:
                  UpperCAmelCase__		:  Optional[Any]				=				int(flatten_latent_dim / 1_6				)
             elif flatten_latent_dim % 4 == 0:
                  UpperCAmelCase__		:  Union[str, Any]				=				int(flatten_latent_dim / 4				)
             else:
                  UpperCAmelCase__		:  List[Any]				=				int(snake_case__				)

             UpperCAmelCase__		:  int				=				jax_memory_efficient_attention(
                 snake_case__				,       snake_case__				,       snake_case__				,       query_chunk_size=snake_case__				,       key_chunk_size=4_0_9_6 * 4				)

             UpperCAmelCase__		:  Tuple				=				hidden_states.transpose(1				,       0				,       2				)
        else:
             # compute attentions
             UpperCAmelCase__		:  Any				=				jnp.einsum("b i d, b j d->b i j"				,       snake_case__				,       snake_case__				)
             UpperCAmelCase__		:  str				=				attention_scores * self.scale
             UpperCAmelCase__		:  int				=				nn.softmax(snake_case__				,       axis=2				)

             # attend to values
             UpperCAmelCase__		:  Optional[int]				=				jnp.einsum("b i j, b j d -> b i d"				,       snake_case__				,       snake_case__				)

        UpperCAmelCase__		:  List[Any]				=				self.reshape_batch_dim_to_heads(snake_case__				)
        UpperCAmelCase__		:  List[str]				=				self.proj_attn(snake_case__				)
        return self.dropout_layer(snake_case__				,       deterministic=snake_case__				)




class        lowerCAmelCase__       (  nn.Module					):
   SCREAMING_SNAKE_CASE_					      =42
   SCREAMING_SNAKE_CASE_					      =42
   SCREAMING_SNAKE_CASE_					      =42
   SCREAMING_SNAKE_CASE_					      =0.0
   SCREAMING_SNAKE_CASE_					      =False
   SCREAMING_SNAKE_CASE_					      =jnp.floataa
   SCREAMING_SNAKE_CASE_					      =False
   def 	__a				(						self	:     List[Any]				):


        '''simple docstring'''
        # self attention (or cross_attention if only_cross_attention is True)
        UpperCAmelCase__		:  Optional[Any]				=				FlaxAttention(
            self.dim				,       self.n_heads				,       self.d_head				,       self.dropout				,       self.use_memory_efficient_attention				,       dtype=self.dtype				)
        # cross attention
        UpperCAmelCase__		:  Tuple				=				FlaxAttention(
            self.dim				,       self.n_heads				,       self.d_head				,       self.dropout				,       self.use_memory_efficient_attention				,       dtype=self.dtype				)
        UpperCAmelCase__		:  Union[str, Any]				=				FlaxFeedForward(dim=self.dim				,       dropout=self.dropout				,       dtype=self.dtype				)
        UpperCAmelCase__		:  List[Any]				=				nn.LayerNorm(epsilon=1e-5				,       dtype=self.dtype				)
        UpperCAmelCase__		:  List[Any]				=				nn.LayerNorm(epsilon=1e-5				,       dtype=self.dtype				)
        UpperCAmelCase__		:  List[Any]				=				nn.LayerNorm(epsilon=1e-5				,       dtype=self.dtype				)
        UpperCAmelCase__		:  Tuple				=				nn.Dropout(rate=self.dropout				)




   def __call__(						self	:     Any				,       snake_case__	:     Dict				,       snake_case__	:     Optional[Any]				,       snake_case__	:     str=True				):


        '''simple docstring'''
        # self attention
        UpperCAmelCase__		:  Any				=				hidden_states
        if self.only_cross_attention:
             UpperCAmelCase__		:  List[Any]				=				self.attna(self.norma(snake_case__				)				,       snake_case__				,       deterministic=snake_case__				)
        else:
             UpperCAmelCase__		:  Any				=				self.attna(self.norma(snake_case__				)				,       deterministic=snake_case__				)
        UpperCAmelCase__		:  int				=				hidden_states + residual

        # cross attention
        UpperCAmelCase__		:  Tuple				=				hidden_states
        UpperCAmelCase__		:  str				=				self.attna(self.norma(snake_case__				)				,       snake_case__				,       deterministic=snake_case__				)
        UpperCAmelCase__		:  Optional[int]				=				hidden_states + residual

        # feed forward
        UpperCAmelCase__		:  int				=				hidden_states
        UpperCAmelCase__		:  Optional[Any]				=				self.ff(self.norma(snake_case__				)				,       deterministic=snake_case__				)
        UpperCAmelCase__		:  int				=				hidden_states + residual

        return self.dropout_layer(snake_case__				,       deterministic=snake_case__				)




class        lowerCAmelCase__       (  nn.Module					):
   SCREAMING_SNAKE_CASE_					      =42
   SCREAMING_SNAKE_CASE_					      =42
   SCREAMING_SNAKE_CASE_					      =42
   SCREAMING_SNAKE_CASE_					      =1
   SCREAMING_SNAKE_CASE_					      =0.0
   SCREAMING_SNAKE_CASE_					      =False
   SCREAMING_SNAKE_CASE_					      =False
   SCREAMING_SNAKE_CASE_					      =jnp.floataa
   SCREAMING_SNAKE_CASE_					      =False
   def 	__a				(						self	:     List[str]				):


        '''simple docstring'''
        UpperCAmelCase__		:  Optional[int]				=				nn.GroupNorm(num_groups=3_2				,       epsilon=1e-5				)

        UpperCAmelCase__		:  Tuple				=				self.n_heads * self.d_head
        if self.use_linear_projection:
             UpperCAmelCase__		:  Tuple				=				nn.Dense(snake_case__				,       dtype=self.dtype				)
        else:
             UpperCAmelCase__		:  Any				=				nn.Conv(
                 snake_case__				,       kernel_size=(1, 1)				,       strides=(1, 1)				,       padding="VALID"				,       dtype=self.dtype				,       )

        UpperCAmelCase__		:  List[str]				=				[
            FlaxBasicTransformerBlock(
                snake_case__				,       self.n_heads				,       self.d_head				,       dropout=self.dropout				,       only_cross_attention=self.only_cross_attention				,       dtype=self.dtype				,       use_memory_efficient_attention=self.use_memory_efficient_attention				,       )
            for _ in range(self.depth				)
        ]

        if self.use_linear_projection:
             UpperCAmelCase__		:  Tuple				=				nn.Dense(snake_case__				,       dtype=self.dtype				)
        else:
             UpperCAmelCase__		:  List[str]				=				nn.Conv(
                 snake_case__				,       kernel_size=(1, 1)				,       strides=(1, 1)				,       padding="VALID"				,       dtype=self.dtype				,       )

        UpperCAmelCase__		:  Union[str, Any]				=				nn.Dropout(rate=self.dropout				)




   def __call__(						self	:     str				,       snake_case__	:     Tuple				,       snake_case__	:     Tuple				,       snake_case__	:     int=True				):


        '''simple docstring'''
        UpperCAmelCase__				,							UpperCAmelCase__				,							UpperCAmelCase__				,							UpperCAmelCase__		:  Optional[Any]				=				hidden_states.shape
        UpperCAmelCase__		:  str				=				hidden_states
        UpperCAmelCase__		:  List[str]				=				self.norm(snake_case__				)
        if self.use_linear_projection:
             UpperCAmelCase__		:  Optional[int]				=				hidden_states.reshape(snake_case__				,       height * width				,       snake_case__				)
             UpperCAmelCase__		:  Optional[int]				=				self.proj_in(snake_case__				)
        else:
             UpperCAmelCase__		:  List[str]				=				self.proj_in(snake_case__				)
             UpperCAmelCase__		:  Optional[int]				=				hidden_states.reshape(snake_case__				,       height * width				,       snake_case__				)

        for transformer_block in self.transformer_blocks:
             UpperCAmelCase__		:  Optional[int]				=				transformer_block(snake_case__				,       snake_case__				,       deterministic=snake_case__				)

        if self.use_linear_projection:
             UpperCAmelCase__		:  Tuple				=				self.proj_out(snake_case__				)
             UpperCAmelCase__		:  List[str]				=				hidden_states.reshape(snake_case__				,       snake_case__				,       snake_case__				,       snake_case__				)
        else:
             UpperCAmelCase__		:  int				=				hidden_states.reshape(snake_case__				,       snake_case__				,       snake_case__				,       snake_case__				)
             UpperCAmelCase__		:  Tuple				=				self.proj_out(snake_case__				)

        UpperCAmelCase__		:  List[str]				=				hidden_states + residual
        return self.dropout_layer(snake_case__				,       deterministic=snake_case__				)




class        lowerCAmelCase__       (  nn.Module					):
   SCREAMING_SNAKE_CASE_					      =42
   SCREAMING_SNAKE_CASE_					      =0.0
   SCREAMING_SNAKE_CASE_					      =jnp.floataa
   def 	__a				(						self	:     Tuple				):


        '''simple docstring'''
        # The second linear layer needs to be called
        # net_2 for now to match the index of the Sequential layer
        UpperCAmelCase__		:  Union[str, Any]				=				FlaxGEGLU(self.dim				,       self.dropout				,       self.dtype				)
        UpperCAmelCase__		:  Optional[Any]				=				nn.Dense(self.dim				,       dtype=self.dtype				)




   def __call__(						self	:     int				,       snake_case__	:     str				,       snake_case__	:     Union[str, Any]=True				):


        '''simple docstring'''
        UpperCAmelCase__		:  Optional[Any]				=				self.net_a(snake_case__				,       deterministic=snake_case__				)
        UpperCAmelCase__		:  List[str]				=				self.net_a(snake_case__				)
        return hidden_states




class        lowerCAmelCase__       (  nn.Module					):
   SCREAMING_SNAKE_CASE_					      =42
   SCREAMING_SNAKE_CASE_					      =0.0
   SCREAMING_SNAKE_CASE_					      =jnp.floataa
   def 	__a				(						self	:     Optional[int]				):


        '''simple docstring'''
        UpperCAmelCase__		:  List[Any]				=				self.dim * 4
        UpperCAmelCase__		:  Any				=				nn.Dense(inner_dim * 2				,       dtype=self.dtype				)
        UpperCAmelCase__		:  Any				=				nn.Dropout(rate=self.dropout				)




   def __call__(						self	:     int				,       snake_case__	:     Tuple				,       snake_case__	:     Any=True				):


        '''simple docstring'''
        UpperCAmelCase__		:  Union[str, Any]				=				self.proj(snake_case__				)
        UpperCAmelCase__				,							UpperCAmelCase__		:  List[str]				=				jnp.split(snake_case__				,       2				,       axis=2				)
        return self.dropout_layer(hidden_linear * nn.gelu(snake_case__				)				,       deterministic=snake_case__				)










"""simple docstring"""



def      SCREAMING_SNAKE_CASE__    (   snake_case    :      list       , snake_case    :      int       , snake_case    :      int							)->						None:






     '''simple docstring'''



     if right <= left:
          return
     UpperCAmelCase__		:  str				=				left
     UpperCAmelCase__		:  List[str]				=				right
     UpperCAmelCase__		:  List[Any]				=				sorting[left]
     while i <= b:
          if sorting[i] < pivot:
               UpperCAmelCase__				,							UpperCAmelCase__		:  List[str]				=				sorting[i], sorting[a]
               a += 1
               i += 1
          elif sorting[i] > pivot:
               UpperCAmelCase__				,							UpperCAmelCase__		:  Optional[int]				=				sorting[i], sorting[b]
               b -= 1
          else:
               i += 1
     quick_sort_apartition(snake_case       , snake_case       , a - 1							)
     quick_sort_apartition(snake_case       , b + 1       , snake_case							)


def      SCREAMING_SNAKE_CASE__    (   snake_case    :      list       , snake_case    :      int       , snake_case    :      int							)->						None:






     '''simple docstring'''



     if left < right:
          UpperCAmelCase__		:  int				=				lomuto_partition(snake_case       , snake_case       , snake_case							)
          quick_sort_lomuto_partition(snake_case       , snake_case       , pivot_index - 1							)
          quick_sort_lomuto_partition(snake_case       , pivot_index + 1       , snake_case							)


def      SCREAMING_SNAKE_CASE__    (   snake_case    :      list       , snake_case    :      int       , snake_case    :      int							)->						int:






     '''simple docstring'''



     UpperCAmelCase__		:  Union[str, Any]				=				sorting[right]
     UpperCAmelCase__		:  Optional[Any]				=				left
     for i in range(snake_case       , snake_case							):
          if sorting[i] < pivot:
               UpperCAmelCase__				,							UpperCAmelCase__		:  List[Any]				=				sorting[i], sorting[store_index]
               store_index += 1
     UpperCAmelCase__				,							UpperCAmelCase__		:  List[Any]				=				sorting[store_index], sorting[right]
     return store_index


def      SCREAMING_SNAKE_CASE__    (   snake_case    :      list							)->						list:






     '''simple docstring'''



     if len(snake_case							) <= 1:
          return sorting
     return (
         three_way_radix_quicksort([i for i in sorting if i < sorting[0]]							)
         + [i for i in sorting if i == sorting[0]]
         + three_way_radix_quicksort([i for i in sorting if i > sorting[0]]							)
     )


if __name__ == "__main__":
 import doctest

 doctest.testmod(verbose=True)

 _lowerCAmelCase     :     Optional[int]            =	input("""Enter numbers separated by a comma:\n""").strip()
 _lowerCAmelCase     :     str            =	[int(item) for item in user_input.split(""",""")]
 quick_sort_apartition(unsorted, 0, len(unsorted) - 1)
 print(unsorted)


