

import math
from typing import Optional

import numpy as np
import torch
from torch import nn

from .activations import get_activation





def 				__a							(       __A			,							__A			,							__A = False			,							__A = 1			,							__A = 1			,							__A = 10000			,							):
    assert len(timesteps.shape						) == 1, "Timesteps should be a 1d-array"

    SCREAMING_SNAKE_CASE__         =    embedding_dim // 2
    SCREAMING_SNAKE_CASE__         =    -math.log(A__						) * torch.arange(
        start=0			,							end=A__			,							dtype=torch.floataa			,							device=timesteps.device						)
    SCREAMING_SNAKE_CASE__         =    exponent / (half_dim - downscale_freq_shift)

    SCREAMING_SNAKE_CASE__         =    torch.exp(A__						)
    SCREAMING_SNAKE_CASE__         =    timesteps[:, None].float() * emb[None, :]

    # scale embeddings
    SCREAMING_SNAKE_CASE__         =    scale * emb

    # concat sine and cosine embeddings
    SCREAMING_SNAKE_CASE__         =    torch.cat([torch.sin(A__						), torch.cos(A__						)]			,							dim=-1						)

    # flip sine and cosine embeddings
    if flip_sin_to_cos:
        SCREAMING_SNAKE_CASE__         =    torch.cat([emb[:, half_dim:], emb[:, :half_dim]]			,							dim=-1						)

    # zero pad
    if embedding_dim % 2 == 1:
        SCREAMING_SNAKE_CASE__         =    torch.nn.functional.pad(A__			,							(0, 1, 0, 0)						)
    return emb





def 				__a							(       __A			,							__A			,							__A=False			,							__A=0						):
    SCREAMING_SNAKE_CASE__         =    np.arange(A__			,							dtype=np.floataa						)
    SCREAMING_SNAKE_CASE__         =    np.arange(A__			,							dtype=np.floataa						)
    SCREAMING_SNAKE_CASE__         =    np.meshgrid(A__			,							A__						)  # here w goes first
    SCREAMING_SNAKE_CASE__         =    np.stack(A__			,							axis=0						)

    SCREAMING_SNAKE_CASE__         =    grid.reshape([2, 1, grid_size, grid_size]						)
    SCREAMING_SNAKE_CASE__         =    get_ad_sincos_pos_embed_from_grid(A__			,							A__						)
    if cls_token and extra_tokens > 0:
        SCREAMING_SNAKE_CASE__         =    np.concatenate([np.zeros([extra_tokens, embed_dim]						), pos_embed]			,							axis=0						)
    return pos_embed





def 				__a							(       __A			,							__A						):
    if embed_dim % 2 != 0:
        raise ValueError("embed_dim must be divisible by 2"						)

    # use half of dimensions to encode grid_h
    SCREAMING_SNAKE_CASE__         =    get_ad_sincos_pos_embed_from_grid(embed_dim // 2			,							grid[0]						)  # (H*W, D/2)
    SCREAMING_SNAKE_CASE__         =    get_ad_sincos_pos_embed_from_grid(embed_dim // 2			,							grid[1]						)  # (H*W, D/2)

    SCREAMING_SNAKE_CASE__         =    np.concatenate([emb_h, emb_w]			,							axis=1						)  # (H*W, D)
    return emb





def 				__a							(       __A			,							__A						):
    if embed_dim % 2 != 0:
        raise ValueError("embed_dim must be divisible by 2"						)

    SCREAMING_SNAKE_CASE__         =    np.arange(embed_dim // 2			,							dtype=np.floataa						)
    omega /= embed_dim / 2.0
    SCREAMING_SNAKE_CASE__         =    1.0 / 10000**omega  # (D/2,)

    SCREAMING_SNAKE_CASE__         =    pos.reshape(-1						)  # (M,)
    SCREAMING_SNAKE_CASE__         =    np.einsum("m,d->md"			,							A__			,							A__						)  # (M, D/2), outer product

    SCREAMING_SNAKE_CASE__         =    np.sin(A__						)  # (M, D/2)
    SCREAMING_SNAKE_CASE__         =    np.cos(A__						)  # (M, D/2)

    SCREAMING_SNAKE_CASE__         =    np.concatenate([emb_sin, emb_cos]			,							axis=1						)  # (M, D)
    return emb







class  UpperCamelCase_      (	nn.Module      ):


  """simple docstring"""



  def __init__(						self     :					Any  ,	A_     :					Union[str, Any]=224  ,	A_     :					str=224  ,	A_     :					Union[str, Any]=16  ,	A_     :					int=3  ,	A_     :					Tuple=768  ,	A_     :					str=False  ,	A_     :					Optional[int]=True  ,	A_     :					List[Any]=True  ,	)       ->			Union[str, Any]:
      super().__init__()

      SCREAMING_SNAKE_CASE__         =    (height // patch_size) * (width // patch_size)
      SCREAMING_SNAKE_CASE__         =    flatten
      SCREAMING_SNAKE_CASE__         =    layer_norm

      SCREAMING_SNAKE_CASE__         =    nn.Convad(
          __UpperCamelCase  ,	__UpperCamelCase  ,	kernel_size=(patch_size, patch_size)  ,	stride=__UpperCamelCase  ,	bias=__UpperCamelCase						)
      if layer_norm:
          SCREAMING_SNAKE_CASE__         =    nn.LayerNorm(__UpperCamelCase  ,	elementwise_affine=__UpperCamelCase  ,	eps=1E-6						)
      else:
          SCREAMING_SNAKE_CASE__         =    None

      SCREAMING_SNAKE_CASE__         =    get_ad_sincos_pos_embed(__UpperCamelCase  ,	int(num_patches**0.5						)						)
      self.register_buffer("pos_embed"  ,	torch.from_numpy(__UpperCamelCase						).float().unsqueeze(0						)  ,	persistent=__UpperCamelCase						)







  def   _UpperCamelCase     (						self     :					Tuple  ,	A_     :					Dict						)       ->			int:
      SCREAMING_SNAKE_CASE__         =    self.proj(__UpperCamelCase						)
      if self.flatten:
          SCREAMING_SNAKE_CASE__         =    latent.flatten(2						).transpose(1  ,	2						)  # BCHW -> BNC
      if self.layer_norm:
          SCREAMING_SNAKE_CASE__         =    self.norm(__UpperCamelCase						)
      return latent + self.pos_embed







class  UpperCamelCase_      (	nn.Module      ):


  """simple docstring"""



  def __init__(						self     :					Union[str, Any]  ,	A_     :					List[str]  ,	A_     :					Optional[Any]  ,	A_     :					Optional[int] = "silu"  ,	A_     :					Dict = None  ,	A_     :					Optional[Any] = None  ,	A_     :					Dict=None  ,	)       ->			int:
      super().__init__()

      SCREAMING_SNAKE_CASE__         =    nn.Linear(__UpperCamelCase  ,	__UpperCamelCase						)

      if cond_proj_dim is not None:
          SCREAMING_SNAKE_CASE__         =    nn.Linear(__UpperCamelCase  ,	__UpperCamelCase  ,	bias=__UpperCamelCase						)
      else:
          SCREAMING_SNAKE_CASE__         =    None

      SCREAMING_SNAKE_CASE__         =    get_activation(__UpperCamelCase						)

      if out_dim is not None:
          SCREAMING_SNAKE_CASE__         =    out_dim
      else:
          SCREAMING_SNAKE_CASE__         =    time_embed_dim
      SCREAMING_SNAKE_CASE__         =    nn.Linear(__UpperCamelCase  ,	__UpperCamelCase						)

      if post_act_fn is None:
          SCREAMING_SNAKE_CASE__         =    None
      else:
          SCREAMING_SNAKE_CASE__         =    get_activation(__UpperCamelCase						)







  def   _UpperCamelCase     (						self     :					Any  ,	A_     :					Dict  ,	A_     :					Optional[int]=None						)       ->			Any:







      if condition is not None:
          SCREAMING_SNAKE_CASE__         =    sample + self.cond_proj(__UpperCamelCase						)
      SCREAMING_SNAKE_CASE__         =    self.linear_a(__UpperCamelCase						)

      if self.act is not None:
          SCREAMING_SNAKE_CASE__         =    self.act(__UpperCamelCase						)

      SCREAMING_SNAKE_CASE__         =    self.linear_a(__UpperCamelCase						)

      if self.post_act is not None:
          SCREAMING_SNAKE_CASE__         =    self.post_act(__UpperCamelCase						)
      return sample







class  UpperCamelCase_      (	nn.Module      ):


  """simple docstring"""



  def __init__(						self     :					int  ,	A_     :					Optional[int]  ,	A_     :					Dict  ,	A_     :					Dict						)       ->			str:
      super().__init__()
      SCREAMING_SNAKE_CASE__         =    num_channels
      SCREAMING_SNAKE_CASE__         =    flip_sin_to_cos
      SCREAMING_SNAKE_CASE__         =    downscale_freq_shift







  def   _UpperCamelCase     (						self     :					Optional[Any]  ,	A_     :					Tuple						)       ->			int:
      SCREAMING_SNAKE_CASE__         =    get_timestep_embedding(
          __UpperCamelCase  ,	self.num_channels  ,	flip_sin_to_cos=self.flip_sin_to_cos  ,	downscale_freq_shift=self.downscale_freq_shift  ,	)
      return t_emb







class  UpperCamelCase_      (	nn.Module      ):


  """simple docstring"""



  def __init__(						self     :					Any  ,	A_     :					Dict = 256  ,	A_     :					Any = 1.0  ,	A_     :					int=True  ,	A_     :					int=True  ,	A_     :					str=False						)       ->			str:
      super().__init__()
      SCREAMING_SNAKE_CASE__         =    nn.Parameter(torch.randn(__UpperCamelCase						) * scale  ,	requires_grad=__UpperCamelCase						)
      SCREAMING_SNAKE_CASE__         =    log
      SCREAMING_SNAKE_CASE__         =    flip_sin_to_cos

      if set_W_to_weight:
          # to delete later
          SCREAMING_SNAKE_CASE__         =    nn.Parameter(torch.randn(__UpperCamelCase						) * scale  ,	requires_grad=__UpperCamelCase						)

          SCREAMING_SNAKE_CASE__         =    self.W







  def   _UpperCamelCase     (						self     :					Any  ,	A_     :					Optional[Any]						)       ->			Optional[int]:







      if self.log:
          SCREAMING_SNAKE_CASE__         =    torch.log(__UpperCamelCase						)

      SCREAMING_SNAKE_CASE__         =    x[:, None] * self.weight[None, :] * 2 * np.pi

      if self.flip_sin_to_cos:
          SCREAMING_SNAKE_CASE__         =    torch.cat([torch.cos(__UpperCamelCase						), torch.sin(__UpperCamelCase						)]  ,	dim=-1						)
      else:
          SCREAMING_SNAKE_CASE__         =    torch.cat([torch.sin(__UpperCamelCase						), torch.cos(__UpperCamelCase						)]  ,	dim=-1						)
      return out







class  UpperCamelCase_      (	nn.Module      ):


  """simple docstring"""



  def __init__(						self     :					List[Any]  ,	A_     :					Optional[int]  ,	A_     :					Union[str, Any]  ,	A_     :					Optional[Any]  ,	A_     :					Optional[int]  ,	)       ->			str:
      super().__init__()

      SCREAMING_SNAKE_CASE__         =    height
      SCREAMING_SNAKE_CASE__         =    width
      SCREAMING_SNAKE_CASE__         =    num_embed
      SCREAMING_SNAKE_CASE__         =    embed_dim

      SCREAMING_SNAKE_CASE__         =    nn.Embedding(self.num_embed  ,	__UpperCamelCase						)
      SCREAMING_SNAKE_CASE__         =    nn.Embedding(self.height  ,	__UpperCamelCase						)
      SCREAMING_SNAKE_CASE__         =    nn.Embedding(self.width  ,	__UpperCamelCase						)







  def   _UpperCamelCase     (						self     :					Any  ,	A_     :					Dict						)       ->			str:
      SCREAMING_SNAKE_CASE__         =    self.emb(__UpperCamelCase						)

      SCREAMING_SNAKE_CASE__         =    self.height_emb(torch.arange(self.height  ,	device=index.device						).view(1  ,	self.height						)						)

      # 1 x H x D -> 1 x H x 1 x D
      SCREAMING_SNAKE_CASE__         =    height_emb.unsqueeze(2						)

      SCREAMING_SNAKE_CASE__         =    self.width_emb(torch.arange(self.width  ,	device=index.device						).view(1  ,	self.width						)						)

      # 1 x W x D -> 1 x 1 x W x D
      SCREAMING_SNAKE_CASE__         =    width_emb.unsqueeze(1						)

      SCREAMING_SNAKE_CASE__         =    height_emb + width_emb

      # 1 x H x W x D -> 1 x L xD
      SCREAMING_SNAKE_CASE__         =    pos_emb.view(1  ,	self.height * self.width  ,	-1						)

      SCREAMING_SNAKE_CASE__         =    emb + pos_emb[:, : emb.shape[1], :]

      return emb







class  UpperCamelCase_      (	nn.Module      ):


  """simple docstring"""



  def __init__(						self     :					Optional[Any]  ,	A_     :					int  ,	A_     :					List[str]  ,	A_     :					str						)       ->			Optional[int]:
      super().__init__()
      SCREAMING_SNAKE_CASE__         =    dropout_prob > 0
      SCREAMING_SNAKE_CASE__         =    nn.Embedding(num_classes + use_cfg_embedding  ,	__UpperCamelCase						)
      SCREAMING_SNAKE_CASE__         =    num_classes
      SCREAMING_SNAKE_CASE__         =    dropout_prob



  def   _UpperCamelCase     (						self     :					Optional[Any]  ,	A_     :					List[Any]  ,	A_     :					int=None						)       ->			Any:







      if force_drop_ids is None:
          SCREAMING_SNAKE_CASE__         =    torch.rand(labels.shape[0]  ,	device=labels.device						) < self.dropout_prob
      else:
          SCREAMING_SNAKE_CASE__         =    torch.tensor(force_drop_ids == 1						)
      SCREAMING_SNAKE_CASE__         =    torch.where(__UpperCamelCase  ,	self.num_classes  ,	__UpperCamelCase						)
      return labels







  def   _UpperCamelCase     (						self     :					Optional[Any]  ,	A_     :					List[Any]  ,	A_     :					str=None						)       ->			Union[str, Any]:
      SCREAMING_SNAKE_CASE__         =    self.dropout_prob > 0
      if (self.training and use_dropout) or (force_drop_ids is not None):
          SCREAMING_SNAKE_CASE__         =    self.token_drop(__UpperCamelCase  ,	__UpperCamelCase						)
      SCREAMING_SNAKE_CASE__         =    self.embedding_table(__UpperCamelCase						)
      return embeddings







class  UpperCamelCase_      (	nn.Module      ):


  """simple docstring"""



  def __init__(						self     :					Union[str, Any]  ,	A_     :					List[str] = 1024  ,	A_     :					Optional[Any] = 768  ,	A_     :					int = 768  ,	A_     :					List[str] = 10  ,	)       ->			int:
      super().__init__()

      SCREAMING_SNAKE_CASE__         =    num_image_text_embeds
      SCREAMING_SNAKE_CASE__         =    nn.Linear(__UpperCamelCase  ,	self.num_image_text_embeds * cross_attention_dim						)
      SCREAMING_SNAKE_CASE__         =    nn.Linear(__UpperCamelCase  ,	__UpperCamelCase						)







  def   _UpperCamelCase     (						self     :					Dict  ,	A_     :					Union[str, Any]  ,	A_     :					Tuple						)       ->			Dict:
      SCREAMING_SNAKE_CASE__         =    text_embeds.shape[0]

      # image
      SCREAMING_SNAKE_CASE__         =    self.image_embeds(__UpperCamelCase						)
      SCREAMING_SNAKE_CASE__         =    image_text_embeds.reshape(__UpperCamelCase  ,	self.num_image_text_embeds  ,	-1						)

      # text
      SCREAMING_SNAKE_CASE__         =    self.text_proj(__UpperCamelCase						)

      return torch.cat([image_text_embeds, text_embeds]  ,	dim=1						)







class  UpperCamelCase_      (	nn.Module      ):


  """simple docstring"""



  def __init__(						self     :					Dict  ,	A_     :					str = 768  ,	A_     :					Tuple = 768  ,	A_     :					Dict = 32  ,	)       ->			List[Any]:
      super().__init__()

      SCREAMING_SNAKE_CASE__         =    num_image_text_embeds
      SCREAMING_SNAKE_CASE__         =    nn.Linear(__UpperCamelCase  ,	self.num_image_text_embeds * cross_attention_dim						)
      SCREAMING_SNAKE_CASE__         =    nn.LayerNorm(__UpperCamelCase						)







  def   _UpperCamelCase     (						self     :					Optional[int]  ,	A_     :					str						)       ->			Optional[Any]:
      SCREAMING_SNAKE_CASE__         =    image_embeds.shape[0]

      # image
      SCREAMING_SNAKE_CASE__         =    self.image_embeds(__UpperCamelCase						)
      SCREAMING_SNAKE_CASE__         =    image_embeds.reshape(__UpperCamelCase  ,	self.num_image_text_embeds  ,	-1						)
      SCREAMING_SNAKE_CASE__         =    self.norm(__UpperCamelCase						)
      return image_embeds







class  UpperCamelCase_      (	nn.Module      ):


  """simple docstring"""



  def __init__(						self     :					Optional[int]  ,	A_     :					List[Any]  ,	A_     :					str  ,	A_     :					int=0.1						)       ->			Any:
      super().__init__()

      SCREAMING_SNAKE_CASE__         =    Timesteps(num_channels=256  ,	flip_sin_to_cos=__UpperCamelCase  ,	downscale_freq_shift=1						)
      SCREAMING_SNAKE_CASE__         =    TimestepEmbedding(in_channels=256  ,	time_embed_dim=__UpperCamelCase						)
      SCREAMING_SNAKE_CASE__         =    LabelEmbedding(__UpperCamelCase  ,	__UpperCamelCase  ,	__UpperCamelCase						)







  def   _UpperCamelCase     (						self     :					Optional[int]  ,	A_     :					Dict  ,	A_     :					List[Any]  ,	A_     :					Tuple=None						)       ->			Dict:
      SCREAMING_SNAKE_CASE__         =    self.time_proj(__UpperCamelCase						)
      SCREAMING_SNAKE_CASE__         =    self.timestep_embedder(timesteps_proj.to(dtype=__UpperCamelCase						)						)  # (N, D)

      SCREAMING_SNAKE_CASE__         =    self.class_embedder(__UpperCamelCase						)  # (N, D)

      SCREAMING_SNAKE_CASE__         =    timesteps_emb + class_labels  # (N, D)

      return conditioning







class  UpperCamelCase_      (	nn.Module      ):


  """simple docstring"""



  def __init__(						self     :					Dict  ,	A_     :					Optional[Any]  ,	A_     :					Optional[int]  ,	A_     :					Optional[Any] = 64						)       ->			Optional[int]:
      super().__init__()
      SCREAMING_SNAKE_CASE__         =    nn.LayerNorm(__UpperCamelCase						)
      SCREAMING_SNAKE_CASE__         =    AttentionPooling(__UpperCamelCase  ,	__UpperCamelCase						)
      SCREAMING_SNAKE_CASE__         =    nn.Linear(__UpperCamelCase  ,	__UpperCamelCase						)
      SCREAMING_SNAKE_CASE__         =    nn.LayerNorm(__UpperCamelCase						)







  def   _UpperCamelCase     (						self     :					Dict  ,	A_     :					Tuple						)       ->			Optional[int]:
      SCREAMING_SNAKE_CASE__         =    self.norma(__UpperCamelCase						)
      SCREAMING_SNAKE_CASE__         =    self.pool(__UpperCamelCase						)
      SCREAMING_SNAKE_CASE__         =    self.proj(__UpperCamelCase						)
      SCREAMING_SNAKE_CASE__         =    self.norma(__UpperCamelCase						)
      return hidden_states







class  UpperCamelCase_      (	nn.Module      ):


  """simple docstring"""



  def __init__(						self     :					List[Any]  ,	A_     :					Union[str, Any] = 768  ,	A_     :					Tuple = 768  ,	A_     :					Tuple = 1536						)       ->			Any:
      super().__init__()
      SCREAMING_SNAKE_CASE__         =    nn.Linear(__UpperCamelCase  ,	__UpperCamelCase						)
      SCREAMING_SNAKE_CASE__         =    nn.LayerNorm(__UpperCamelCase						)
      SCREAMING_SNAKE_CASE__         =    nn.Linear(__UpperCamelCase  ,	__UpperCamelCase						)







  def   _UpperCamelCase     (						self     :					Union[str, Any]  ,	A_     :					int  ,	A_     :					Tuple						)       ->			Dict:
      SCREAMING_SNAKE_CASE__         =    self.text_proj(__UpperCamelCase						)
      SCREAMING_SNAKE_CASE__         =    self.text_norm(__UpperCamelCase						)

      # image
      SCREAMING_SNAKE_CASE__         =    self.image_proj(__UpperCamelCase						)

      return time_image_embeds + time_text_embeds







class  UpperCamelCase_      (	nn.Module      ):


  """simple docstring"""



  def __init__(						self     :					Tuple  ,	A_     :					Optional[int] = 768  ,	A_     :					Optional[int] = 1536						)       ->			Optional[Any]:
      super().__init__()
      SCREAMING_SNAKE_CASE__         =    nn.Linear(__UpperCamelCase  ,	__UpperCamelCase						)
      SCREAMING_SNAKE_CASE__         =    nn.LayerNorm(__UpperCamelCase						)







  def   _UpperCamelCase     (						self     :					List[Any]  ,	A_     :					List[Any]						)       ->			Optional[int]:
      SCREAMING_SNAKE_CASE__         =    self.image_proj(__UpperCamelCase						)
      SCREAMING_SNAKE_CASE__         =    self.image_norm(__UpperCamelCase						)
      return time_image_embeds







class  UpperCamelCase_      (	nn.Module      ):


  """simple docstring"""



  def __init__(						self     :					int  ,	A_     :					List[str] = 768  ,	A_     :					Union[str, Any] = 1536						)       ->			str:
      super().__init__()
      SCREAMING_SNAKE_CASE__         =    nn.Linear(__UpperCamelCase  ,	__UpperCamelCase						)
      SCREAMING_SNAKE_CASE__         =    nn.LayerNorm(__UpperCamelCase						)
      SCREAMING_SNAKE_CASE__         =    nn.Sequential(
          nn.Convad(3  ,	16  ,	3  ,	padding=1						)  ,	nn.SiLU()  ,	nn.Convad(16  ,	16  ,	3  ,	padding=1						)  ,	nn.SiLU()  ,	nn.Convad(16  ,	32  ,	3  ,	padding=1  ,	stride=2						)  ,	nn.SiLU()  ,	nn.Convad(32  ,	32  ,	3  ,	padding=1						)  ,	nn.SiLU()  ,	nn.Convad(32  ,	96  ,	3  ,	padding=1  ,	stride=2						)  ,	nn.SiLU()  ,	nn.Convad(96  ,	96  ,	3  ,	padding=1						)  ,	nn.SiLU()  ,	nn.Convad(96  ,	256  ,	3  ,	padding=1  ,	stride=2						)  ,	nn.SiLU()  ,	nn.Convad(256  ,	4  ,	3  ,	padding=1						)  ,	)







  def   _UpperCamelCase     (						self     :					Any  ,	A_     :					List[str]  ,	A_     :					int						)       ->			Any:
      SCREAMING_SNAKE_CASE__         =    self.image_proj(__UpperCamelCase						)
      SCREAMING_SNAKE_CASE__         =    self.image_norm(__UpperCamelCase						)
      SCREAMING_SNAKE_CASE__         =    self.input_hint_block(__UpperCamelCase						)
      return time_image_embeds, hint







class  UpperCamelCase_      (	nn.Module      ):


  """simple docstring"""



  def __init__(						self     :					str  ,	A_     :					str  ,	A_     :					Optional[Any]  ,	A_     :					Dict=None						)       ->			Optional[Any]:
      super().__init__()
      SCREAMING_SNAKE_CASE__         =    dtype
      SCREAMING_SNAKE_CASE__         =    nn.Parameter(torch.randn(1  ,	__UpperCamelCase						) / embed_dim**0.5						)
      SCREAMING_SNAKE_CASE__         =    nn.Linear(__UpperCamelCase  ,	__UpperCamelCase  ,	dtype=self.dtype						)
      SCREAMING_SNAKE_CASE__         =    nn.Linear(__UpperCamelCase  ,	__UpperCamelCase  ,	dtype=self.dtype						)
      SCREAMING_SNAKE_CASE__         =    nn.Linear(__UpperCamelCase  ,	__UpperCamelCase  ,	dtype=self.dtype						)
      SCREAMING_SNAKE_CASE__         =    num_heads
      SCREAMING_SNAKE_CASE__         =    embed_dim // self.num_heads







  def   _UpperCamelCase     (						self     :					List[Any]  ,	A_     :					List[Any]						)       ->			Optional[int]:
      SCREAMING_SNAKE_CASE__         =    x.size()

      def shape(A_     :					Tuple						):
          # (bs, length, width) --> (bs, length, n_heads, dim_per_head)
          SCREAMING_SNAKE_CASE__         =    x.view(__UpperCamelCase  ,	-1  ,	self.num_heads  ,	self.dim_per_head						)
          # (bs, length, n_heads, dim_per_head) --> (bs, n_heads, length, dim_per_head)
          SCREAMING_SNAKE_CASE__         =    x.transpose(1  ,	2						)
          # (bs, n_heads, length, dim_per_head) --> (bs*n_heads, length, dim_per_head)
          SCREAMING_SNAKE_CASE__         =    x.reshape(bs * self.num_heads  ,	-1  ,	self.dim_per_head						)
          # (bs*n_heads, length, dim_per_head) --> (bs*n_heads, dim_per_head, length)
          SCREAMING_SNAKE_CASE__         =    x.transpose(1  ,	2						)
          return x

      SCREAMING_SNAKE_CASE__         =    x.mean(dim=1  ,	keepdim=__UpperCamelCase						) + self.positional_embedding.to(x.dtype						)
      SCREAMING_SNAKE_CASE__         =    torch.cat([class_token, x]  ,	dim=1						)  # (bs, length+1, width)

      # (bs*n_heads, class_token_length, dim_per_head)
      SCREAMING_SNAKE_CASE__         =    shape(self.q_proj(__UpperCamelCase						)						)
      # (bs*n_heads, length+class_token_length, dim_per_head)
      SCREAMING_SNAKE_CASE__         =    shape(self.k_proj(__UpperCamelCase						)						)
      SCREAMING_SNAKE_CASE__         =    shape(self.v_proj(__UpperCamelCase						)						)

      # (bs*n_heads, class_token_length, length+class_token_length):
      SCREAMING_SNAKE_CASE__         =    1 / math.sqrt(math.sqrt(self.dim_per_head						)						)
      SCREAMING_SNAKE_CASE__         =    torch.einsum("bct,bcs->bts"  ,	q * scale  ,	k * scale						)  # More stable with f16 than dividing afterwards
      SCREAMING_SNAKE_CASE__         =    torch.softmax(weight.float()  ,	dim=-1						).type(weight.dtype						)

      # (bs*n_heads, dim_per_head, class_token_length)
      SCREAMING_SNAKE_CASE__         =    torch.einsum("bts,bcs->bct"  ,	__UpperCamelCase  ,	__UpperCamelCase						)

      # (bs, length+1, width)
      SCREAMING_SNAKE_CASE__         =    a.reshape(__UpperCamelCase  ,	-1  ,	1						).transpose(1  ,	2						)

      return a[:, 0, :]  # cls_token



import math





class 					__snake_case    :




					def __init__(  self       ,			__UpperCamelCase						)	->    Dict:



									'''simple docstring'''







									snake_case__   :      Optional[int]   				= len(__UpperCamelCase						)
									snake_case__   :      Dict   				= [0] * (
									    4 * self.N
									)  # approximate the overall size of segment tree with array N
									self.build(1       ,			0       ,			self.N - 1						)




					def      __a     (  self       ,			__UpperCamelCase						)	->    Any:



									'''simple docstring'''







									return idx * 2




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



									'''simple docstring'''







									return idx * 2 + 1




					def      __a     (  self       ,			__UpperCamelCase       ,			__UpperCamelCase       ,			__UpperCamelCase						)	->    int:  # noqa: E741



									'''simple docstring'''







									if l == r:
													snake_case__   :      Dict   				= A[l]
									else:
													snake_case__   :      Optional[Any]   				= (l + r) // 2
													self.build(self.left(__UpperCamelCase						)       ,			__UpperCamelCase       ,			__UpperCamelCase						)
													self.build(self.right(__UpperCamelCase						)       ,			mid + 1       ,			__UpperCamelCase						)
													snake_case__   :      int   				= max(self.st[self.left(__UpperCamelCase						)]       ,			self.st[self.right(__UpperCamelCase						)]						)




					def      __a     (  self       ,			__UpperCamelCase       ,			__UpperCamelCase       ,			__UpperCamelCase						)	->    int:



									'''simple docstring'''







									return self.update_recursive(1       ,			0       ,			self.N - 1       ,			a - 1       ,			b - 1       ,			__UpperCamelCase						)




					def      __a     (  self       ,			__UpperCamelCase       ,			__UpperCamelCase       ,			__UpperCamelCase       ,			__UpperCamelCase       ,			__UpperCamelCase       ,			__UpperCamelCase						)	->    Tuple:  # noqa: E741



									'''simple docstring'''







									if r < a or l > b:
													return True
									if l == r:
													snake_case__   :      List[str]   				= val
													return True
									snake_case__   :      str   				= (l + r) // 2
									self.update_recursive(self.left(__UpperCamelCase						)       ,			__UpperCamelCase       ,			__UpperCamelCase       ,			__UpperCamelCase       ,			__UpperCamelCase       ,			__UpperCamelCase						)
									self.update_recursive(self.right(__UpperCamelCase						)       ,			mid + 1       ,			__UpperCamelCase       ,			__UpperCamelCase       ,			__UpperCamelCase       ,			__UpperCamelCase						)
									snake_case__   :      Tuple   				= max(self.st[self.left(__UpperCamelCase						)]       ,			self.st[self.right(__UpperCamelCase						)]						)
									return True




					def      __a     (  self       ,			__UpperCamelCase       ,			__UpperCamelCase						)	->    List[str]:



									'''simple docstring'''







									return self.query_recursive(1       ,			0       ,			self.N - 1       ,			a - 1       ,			b - 1						)




					def      __a     (  self       ,			__UpperCamelCase       ,			__UpperCamelCase       ,			__UpperCamelCase       ,			__UpperCamelCase       ,			__UpperCamelCase						)	->    Optional[int]:  # noqa: E741



									'''simple docstring'''







									if r < a or l > b:
													return -math.inf
									if l >= a and r <= b:
													return self.st[idx]
									snake_case__   :      str   				= (l + r) // 2
									snake_case__   :      Optional[Any]   				= self.query_recursive(self.left(__UpperCamelCase						)       ,			__UpperCamelCase       ,			__UpperCamelCase       ,			__UpperCamelCase       ,			__UpperCamelCase						)
									snake_case__   :      List[str]   				= self.query_recursive(self.right(__UpperCamelCase						)       ,			mid + 1       ,			__UpperCamelCase       ,			__UpperCamelCase       ,			__UpperCamelCase						)
									return max(__UpperCamelCase       ,			__UpperCamelCase						)




					def      __a     (  self						)	->    Optional[Any]:



									'''simple docstring'''







									snake_case__   :      Tuple   				= []
									for i in range(1       ,			N + 1						):
													show_list += [self.query(__UpperCamelCase       ,			__UpperCamelCase						)]
									print(__UpperCamelCase						)


if __name__ == "__main__":
				lowerCAmelCase__	:  Optional[int]						=  [1, 2, -4, 7, 3, -5, 6, 11, -20, 9, 14, 15, 5, 2, -8]
				lowerCAmelCase__	:  Any						=  15
				lowerCAmelCase__	:  List[Any]						=  SegmentTree(A)
				print(segt.query(4, 6))
				print(segt.query(7, 11))
				print(segt.query(7, 12))
				segt.update(1, 3, 1_11)
				print(segt.query(1, 15))
				segt.update(7, 8, 2_35)
				segt.show_data()


