






"""simple docstring"""


import functools
import math

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




def 			snake_case  (A_      :List[str]	,			A_      :int	,			A_      :List[str]	,			A_      :Union[str, Any]	,			A_      :int = 4_0_9_6      ):







  '''simple docstring'''

  a,     a,     a     :			Dict				=   key.shape[-3:]
  a     :			str				=   value.shape[-1]
  a     :			List[str]				=   min(A_	,			A_      )
  a     :			List[Any]				=   query / jnp.sqrt(A_      )

  @functools.partial(jax.checkpoint	,			prevent_cse=A_      )
  def summarize_chunk(A_      :str	,			A_      :Any	,			A_      :Tuple      ):
    a     :			Any				=   jnp.einsum('...qhd,...khd->...qhk'	,			A_	,			A_	,			precision=A_      )

    a     :			List[str]				=   jnp.max(A_	,			axis=-1	,			keepdims=A_      )
    a     :			Optional[Any]				=   jax.lax.stop_gradient(A_      )
    a     :			Any				=   jnp.exp(attn_weights - max_score      )

    a     :			str				=   jnp.einsum('...vhf,...qhv->...qhf'	,			A_	,			A_	,			precision=A_      )
    a     :			Any				=   jnp.einsum('...qhk->...qh'	,			A_      )

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

  def chunk_scanner(A_      :int      ):
    # julienne key array
    a     :			Union[str, Any]				=   jax.lax.dynamic_slice(
        operand=A_	,			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
    a     :			Dict				=   jax.lax.dynamic_slice(
        operand=A_	,			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(A_	,			A_	,			A_      )

  a,     a,     a     :			Optional[int]				=   jax.lax.map(f=A_	,			xs=jnp.arange(0	,			A_	,			A_      )      )

  a     :			int				=   jnp.max(A_	,			axis=0	,			keepdims=A_      )
  a     :			Optional[Any]				=   jnp.exp(chunk_max - global_max      )

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

  a     :			int				=   chunk_values.sum(axis=0      )
  a     :			int				=   jnp.expand_dims(A_	,			-1      ).sum(axis=0      )

  return all_values / all_weights




def 			snake_case  (A_      :List[Any]	,			A_      :Any	,			A_      :Tuple	,			A_      :List[str]=jax.lax.Precision.HIGHEST	,			A_      :int = 1_0_2_4	,			A_      :int = 4_0_9_6      ):







  '''simple docstring'''

  a,     a,     a     :			Tuple				=   query.shape[-3:]

  def chunk_scanner(A_      :Optional[Any]	,			A_      :List[Any]      ):
    # julienne query array
    a     :			int				=   jax.lax.dynamic_slice(
        operand=A_	,			start_indices=([0] * (query.ndim - 3)) + [chunk_idx, 0, 0]	,			slice_sizes=list(query.shape[:-3]      ) + [min(A_	,			A_      ), num_heads, q_features]	,			)

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

  a,     a     :			List[Any]				=   jax.lax.scan(
      f=A_	,			init=0	,			xs=A_	,			length=math.ceil(num_q / query_chunk_size      )      )

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






class 						snake_case  (  nn.Module       ):
    __magic_name__         =     42
    __magic_name__         =     8
    __magic_name__         =     64
    __magic_name__         =     0.0
    __magic_name__         =     False
    __magic_name__         =     jnp.floataa





    def 				lowerCamelCase__      (							self	:					List[str]			):


      '''simple docstring'''




      a     :			Union[str, Any]				=   self.dim_head * self.heads
      a     :			int				=   self.dim_head**-0.5

      # Weights were exported with old names {to_q, to_k, to_v, to_out}
      a     :			Optional[Any]				=   nn.Dense(A				,		use_bias=A				,		dtype=self.dtype				,		name='to_q'			)
      a     :			List[Any]				=   nn.Dense(A				,		use_bias=A				,		dtype=self.dtype				,		name='to_k'			)
      a     :			List[Any]				=   nn.Dense(A				,		use_bias=A				,		dtype=self.dtype				,		name='to_v'			)

      a     :			Dict				=   nn.Dense(self.query_dim				,		dtype=self.dtype				,		name='to_out_0'			)
      a     :			int				=   nn.Dropout(rate=self.dropout			)





    def 				lowerCamelCase__      (							self	:					Dict				,		A	:					int			):


      '''simple docstring'''




      a,     a,     a     :			int				=   tensor.shape
      a     :			List[Any]				=   self.heads
      a     :			Optional[Any]				=   tensor.reshape(A				,		A				,		A				,		dim // head_size			)
      a     :			List[Any]				=   jnp.transpose(A				,		(0, 2, 1, 3)			)
      a     :			Tuple				=   tensor.reshape(batch_size * head_size				,		A				,		dim // head_size			)
      return tensor





    def 				lowerCamelCase__      (							self	:					List[Any]				,		A	:					Optional[int]			):


      '''simple docstring'''




      a,     a,     a     :			List[Any]				=   tensor.shape
      a     :			Optional[int]				=   self.heads
      a     :			Any				=   tensor.reshape(batch_size // head_size				,		A				,		A				,		A			)
      a     :			str				=   jnp.transpose(A				,		(0, 2, 1, 3)			)
      a     :			List[str]				=   tensor.reshape(batch_size // head_size				,		A				,		dim * head_size			)
      return tensor





    def __call__(							self	:					Dict				,		A	:					Union[str, Any]				,		A	:					Optional[int]=None				,		A	:					Optional[int]=True			):


      '''simple docstring'''




      a     :			Any				=   hidden_states if context is None else context

      a     :			List[str]				=   self.query(A			)
      a     :			List[Any]				=   self.key(A			)
      a     :			Tuple				=   self.value(A			)

      a     :			Dict				=   self.reshape_heads_to_batch_dim(A			)
      a     :			Dict				=   self.reshape_heads_to_batch_dim(A			)
      a     :			str				=   self.reshape_heads_to_batch_dim(A			)

      if self.use_memory_efficient_attention:
        a     :			int				=   query_states.transpose(1				,		0				,		2			)
        a     :			Optional[Any]				=   key_states.transpose(1				,		0				,		2			)
        a     :			int				=   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

        a     :			Dict				=   query_states.shape[-3]
        if flatten_latent_dim % 6_4 == 0:
          a     :			List[str]				=   int(flatten_latent_dim / 6_4			)
        elif flatten_latent_dim % 1_6 == 0:
          a     :			str				=   int(flatten_latent_dim / 1_6			)
        elif flatten_latent_dim % 4 == 0:
          a     :			List[str]				=   int(flatten_latent_dim / 4			)
        else:
          a     :			Dict				=   int(A			)

        a     :			str				=   jax_memory_efficient_attention(
            A				,		A				,		A				,		query_chunk_size=A				,		key_chunk_size=4_0_9_6 * 4			)

        a     :			Tuple				=   hidden_states.transpose(1				,		0				,		2			)
      else:
        # compute attentions
        a     :			int				=   jnp.einsum('b i d, b j d->b i j'				,		A				,		A			)
        a     :			int				=   attention_scores * self.scale
        a     :			List[Any]				=   nn.softmax(A				,		axis=2			)

        # attend to values
        a     :			Union[str, Any]				=   jnp.einsum('b i j, b j d -> b i d'				,		A				,		A			)

      a     :			Optional[Any]				=   self.reshape_batch_dim_to_heads(A			)
      a     :			Any				=   self.proj_attn(A			)
      return self.dropout_layer(A				,		deterministic=A			)






class 						snake_case  (  nn.Module       ):
    __magic_name__         =     42
    __magic_name__         =     42
    __magic_name__         =     42
    __magic_name__         =     0.0
    __magic_name__         =     False
    __magic_name__         =     jnp.floataa
    __magic_name__         =     False





    def 				lowerCamelCase__      (							self	:					Dict			):


      '''simple docstring'''




      a     :			List[Any]				=   FlaxAttention(
          self.dim				,		self.n_heads				,		self.d_head				,		self.dropout				,		self.use_memory_efficient_attention				,		dtype=self.dtype			)
      # cross attention
      a     :			Dict				=   FlaxAttention(
          self.dim				,		self.n_heads				,		self.d_head				,		self.dropout				,		self.use_memory_efficient_attention				,		dtype=self.dtype			)
      a     :			int				=   FlaxFeedForward(dim=self.dim				,		dropout=self.dropout				,		dtype=self.dtype			)
      a     :			Any				=   nn.LayerNorm(epsilon=1E-5				,		dtype=self.dtype			)
      a     :			Dict				=   nn.LayerNorm(epsilon=1E-5				,		dtype=self.dtype			)
      a     :			List[str]				=   nn.LayerNorm(epsilon=1E-5				,		dtype=self.dtype			)
      a     :			int				=   nn.Dropout(rate=self.dropout			)





    def __call__(							self	:					str				,		A	:					Union[str, Any]				,		A	:					Optional[Any]				,		A	:					Tuple=True			):


      '''simple docstring'''




      a     :			Union[str, Any]				=   hidden_states
      if self.only_cross_attention:
        a     :			Optional[Any]				=   self.attna(self.norma(A			)				,		A				,		deterministic=A			)
      else:
        a     :			Any				=   self.attna(self.norma(A			)				,		deterministic=A			)
      a     :			str				=   hidden_states + residual

      # cross attention
      a     :			Any				=   hidden_states
      a     :			Dict				=   self.attna(self.norma(A			)				,		A				,		deterministic=A			)
      a     :			Optional[int]				=   hidden_states + residual

      # feed forward
      a     :			Any				=   hidden_states
      a     :			List[Any]				=   self.ff(self.norma(A			)				,		deterministic=A			)
      a     :			List[Any]				=   hidden_states + residual

      return self.dropout_layer(A				,		deterministic=A			)






class 						snake_case  (  nn.Module       ):
    __magic_name__         =     42
    __magic_name__         =     42
    __magic_name__         =     42
    __magic_name__         =     1
    __magic_name__         =     0.0
    __magic_name__         =     False
    __magic_name__         =     False
    __magic_name__         =     jnp.floataa
    __magic_name__         =     False





    def 				lowerCamelCase__      (							self	:					int			):


      '''simple docstring'''




      a     :			Tuple				=   nn.GroupNorm(num_groups=3_2				,		epsilon=1E-5			)

      a     :			List[Any]				=   self.n_heads * self.d_head
      if self.use_linear_projection:
        a     :			List[Any]				=   nn.Dense(A				,		dtype=self.dtype			)
      else:
        a     :			Dict				=   nn.Conv(
            A				,		kernel_size=(1, 1)				,		strides=(1, 1)				,		padding='VALID'				,		dtype=self.dtype				,		)

      a     :			int				=   [
          FlaxBasicTransformerBlock(
              A				,		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:
        a     :			str				=   nn.Dense(A				,		dtype=self.dtype			)
      else:
        a     :			Dict				=   nn.Conv(
            A				,		kernel_size=(1, 1)				,		strides=(1, 1)				,		padding='VALID'				,		dtype=self.dtype				,		)

      a     :			str				=   nn.Dropout(rate=self.dropout			)





    def __call__(							self	:					List[str]				,		A	:					Optional[Any]				,		A	:					str				,		A	:					Tuple=True			):


      '''simple docstring'''




      a,     a,     a,     a     :			int				=   hidden_states.shape
      a     :			Optional[Any]				=   hidden_states
      a     :			int				=   self.norm(A			)
      if self.use_linear_projection:
        a     :			Optional[Any]				=   hidden_states.reshape(A				,		height * width				,		A			)
        a     :			List[Any]				=   self.proj_in(A			)
      else:
        a     :			Union[str, Any]				=   self.proj_in(A			)
        a     :			Optional[int]				=   hidden_states.reshape(A				,		height * width				,		A			)

      for transformer_block in self.transformer_blocks:
        a     :			Union[str, Any]				=   transformer_block(A				,		A				,		deterministic=A			)

      if self.use_linear_projection:
        a     :			Union[str, Any]				=   self.proj_out(A			)
        a     :			List[Any]				=   hidden_states.reshape(A				,		A				,		A				,		A			)
      else:
        a     :			int				=   hidden_states.reshape(A				,		A				,		A				,		A			)
        a     :			int				=   self.proj_out(A			)

      a     :			str				=   hidden_states + residual
      return self.dropout_layer(A				,		deterministic=A			)






class 						snake_case  (  nn.Module       ):
    __magic_name__         =     42
    __magic_name__         =     0.0
    __magic_name__         =     jnp.floataa





    def 				lowerCamelCase__      (							self	:					Dict			):


      '''simple docstring'''




      a     :			Optional[Any]				=   FlaxGEGLU(self.dim				,		self.dropout				,		self.dtype			)
      a     :			Dict				=   nn.Dense(self.dim				,		dtype=self.dtype			)





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


      '''simple docstring'''




      a     :			Dict				=   self.net_a(A				,		deterministic=A			)
      a     :			List[Any]				=   self.net_a(A			)
      return hidden_states






class 						snake_case  (  nn.Module       ):
    __magic_name__         =     42
    __magic_name__         =     0.0
    __magic_name__         =     jnp.floataa





    def 				lowerCamelCase__      (							self	:					Union[str, Any]			):


      '''simple docstring'''




      a     :			List[str]				=   self.dim * 4
      a     :			List[Any]				=   nn.Dense(inner_dim * 2				,		dtype=self.dtype			)
      a     :			int				=   nn.Dropout(rate=self.dropout			)





    def __call__(							self	:					Union[str, Any]				,		A	:					Dict				,		A	:					Tuple=True			):


      '''simple docstring'''




      a     :			int				=   self.proj(A			)
      a,     a     :			Dict				=   jnp.split(A				,		2				,		axis=2			)
      return self.dropout_layer(hidden_linear * nn.gelu(A			)				,		deterministic=A			)












"""simple docstring"""


def 			snake_case  (A_      :int = 1_0_0_0      ):







  '''simple docstring'''

  a     :			Union[str, Any]				=   0
  a     :			int				=   (n - 1) // 3
  total += ((terms) * (6 + (terms - 1) * 3)) // 2  # total of an A.P.
  a     :			Tuple				=   (n - 1) // 5
  total += ((terms) * (1_0 + (terms - 1) * 5)) // 2
  a     :			Dict				=   (n - 1) // 1_5
  total -= ((terms) * (3_0 + (terms - 1) * 1_5)) // 2
  return total


if __name__ == "__main__":
   print(f'''{solution() = }''')




