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# Copyright 2022 The HuggingFace Team. All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
import math
from dataclasses import dataclass
from typing import Optional
import torch
import torch.nn.functional as F
from torch import nn
from ..configuration_utils import ConfigMixin, register_to_config
from ..modeling_utils import ModelMixin
from ..models.embeddings import ImagePositionalEmbeddings
from ..utils import BaseOutput
from ..utils.import_utils import is_xformers_available
@dataclass
class Transformer2DModelOutput(BaseOutput):
"""
Args:
sample (`torch.FloatTensor` of shape `(batch_size, num_channels, height, width)` or `(batch size, num_vector_embeds - 1, num_latent_pixels)` if [`Transformer2DModel`] is discrete):
Hidden states conditioned on `encoder_hidden_states` input. If discrete, returns probability distributions
for the unnoised latent pixels.
"""
sample: torch.FloatTensor
if is_xformers_available():
import xformers
import xformers.ops
else:
xformers = None
class Transformer2DModel(ModelMixin, ConfigMixin):
"""
Transformer model for image-like data. Takes either discrete (classes of vector embeddings) or continuous (actual
embeddings) inputs.
When input is continuous: First, project the input (aka embedding) and reshape to b, t, d. Then apply standard
transformer action. Finally, reshape to image.
When input is discrete: First, input (classes of latent pixels) is converted to embeddings and has positional
embeddings applied, see `ImagePositionalEmbeddings`. Then apply standard transformer action. Finally, predict
classes of unnoised image.
Note that it is assumed one of the input classes is the masked latent pixel. The predicted classes of the unnoised
image do not contain a prediction for the masked pixel as the unnoised image cannot be masked.
Parameters:
num_attention_heads (`int`, *optional*, defaults to 16): The number of heads to use for multi-head attention.
attention_head_dim (`int`, *optional*, defaults to 88): The number of channels in each head.
in_channels (`int`, *optional*):
Pass if the input is continuous. The number of channels in the input and output.
num_layers (`int`, *optional*, defaults to 1): The number of layers of Transformer blocks to use.
dropout (`float`, *optional*, defaults to 0.1): The dropout probability to use.
cross_attention_dim (`int`, *optional*): The number of context dimensions to use.
sample_size (`int`, *optional*): Pass if the input is discrete. The width of the latent images.
Note that this is fixed at training time as it is used for learning a number of position embeddings. See
`ImagePositionalEmbeddings`.
num_vector_embeds (`int`, *optional*):
Pass if the input is discrete. The number of classes of the vector embeddings of the latent pixels.
Includes the class for the masked latent pixel.
activation_fn (`str`, *optional*, defaults to `"geglu"`): Activation function to be used in feed-forward.
num_embeds_ada_norm ( `int`, *optional*): Pass if at least one of the norm_layers is `AdaLayerNorm`.
The number of diffusion steps used during training. Note that this is fixed at training time as it is used
to learn a number of embeddings that are added to the hidden states. During inference, you can denoise for
up to but not more than steps than `num_embeds_ada_norm`.
attention_bias (`bool`, *optional*):
Configure if the TransformerBlocks' attention should contain a bias parameter.
"""
@register_to_config
def __init__(
self,
num_attention_heads: int = 16,
attention_head_dim: int = 88,
in_channels: Optional[int] = None,
num_layers: int = 1,
dropout: float = 0.0,
norm_num_groups: int = 32,
cross_attention_dim: Optional[int] = None,
attention_bias: bool = False,
sample_size: Optional[int] = None,
num_vector_embeds: Optional[int] = None,
activation_fn: str = "geglu",
num_embeds_ada_norm: Optional[int] = None,
):
super().__init__()
self.num_attention_heads = num_attention_heads
self.attention_head_dim = attention_head_dim
inner_dim = num_attention_heads * attention_head_dim
# 1. Transformer2DModel can process both standard continous images of shape `(batch_size, num_channels, width, height)` as well as quantized image embeddings of shape `(batch_size, num_image_vectors)`
# Define whether input is continuous or discrete depending on configuration
self.is_input_continuous = in_channels is not None
self.is_input_vectorized = num_vector_embeds is not None
if self.is_input_continuous and self.is_input_vectorized:
raise ValueError(
f"Cannot define both `in_channels`: {in_channels} and `num_vector_embeds`: {num_vector_embeds}. Make"
" sure that either `in_channels` or `num_vector_embeds` is None."
)
elif not self.is_input_continuous and not self.is_input_vectorized:
raise ValueError(
f"Has to define either `in_channels`: {in_channels} or `num_vector_embeds`: {num_vector_embeds}. Make"
" sure that either `in_channels` or `num_vector_embeds` is not None."
)
# 2. Define input layers
if self.is_input_continuous:
self.in_channels = in_channels
self.norm = torch.nn.GroupNorm(num_groups=norm_num_groups, num_channels=in_channels, eps=1e-6, affine=True)
self.proj_in = nn.Conv2d(in_channels, inner_dim, kernel_size=1, stride=1, padding=0)
elif self.is_input_vectorized:
assert sample_size is not None, "Transformer2DModel over discrete input must provide sample_size"
assert num_vector_embeds is not None, "Transformer2DModel over discrete input must provide num_embed"
self.height = sample_size
self.width = sample_size
self.num_vector_embeds = num_vector_embeds
self.num_latent_pixels = self.height * self.width
self.latent_image_embedding = ImagePositionalEmbeddings(
num_embed=num_vector_embeds, embed_dim=inner_dim, height=self.height, width=self.width
)
# 3. Define transformers blocks
self.transformer_blocks = nn.ModuleList(
[
BasicTransformerBlock(
inner_dim,
num_attention_heads,
attention_head_dim,
dropout=dropout,
cross_attention_dim=cross_attention_dim,
activation_fn=activation_fn,
num_embeds_ada_norm=num_embeds_ada_norm,
attention_bias=attention_bias,
)
for d in range(num_layers)
]
)
# 4. Define output layers
if self.is_input_continuous:
self.proj_out = nn.Conv2d(inner_dim, in_channels, kernel_size=1, stride=1, padding=0)
elif self.is_input_vectorized:
self.norm_out = nn.LayerNorm(inner_dim)
self.out = nn.Linear(inner_dim, self.num_vector_embeds - 1)
def _set_attention_slice(self, slice_size):
for block in self.transformer_blocks:
block._set_attention_slice(slice_size)
def forward(self, hidden_states, encoder_hidden_states=None, timestep=None, return_dict: bool = True):
"""
Args:
hidden_states ( When discrete, `torch.LongTensor` of shape `(batch size, num latent pixels)`.
When continous, `torch.FloatTensor` of shape `(batch size, channel, height, width)`): Input
hidden_states
encoder_hidden_states ( `torch.LongTensor` of shape `(batch size, context dim)`, *optional*):
Conditional embeddings for cross attention layer. If not given, cross-attention defaults to
self-attention.
timestep ( `torch.long`, *optional*):
Optional timestep to be applied as an embedding in AdaLayerNorm's. Used to indicate denoising step.
return_dict (`bool`, *optional*, defaults to `True`):
Whether or not to return a [`models.unet_2d_condition.UNet2DConditionOutput`] instead of a plain tuple.
Returns:
[`~models.attention.Transformer2DModelOutput`] or `tuple`: [`~models.attention.Transformer2DModelOutput`]
if `return_dict` is True, otherwise a `tuple`. When returning a tuple, the first element is the sample
tensor.
"""
# 1. Input
if self.is_input_continuous:
batch, channel, height, weight = hidden_states.shape
residual = hidden_states
hidden_states = self.norm(hidden_states)
hidden_states = self.proj_in(hidden_states)
inner_dim = hidden_states.shape[1]
hidden_states = hidden_states.permute(0, 2, 3, 1).reshape(batch, height * weight, inner_dim)
elif self.is_input_vectorized:
hidden_states = self.latent_image_embedding(hidden_states)
# 2. Blocks
for block in self.transformer_blocks:
hidden_states = block(hidden_states, context=encoder_hidden_states, timestep=timestep)
# 3. Output
if self.is_input_continuous:
hidden_states = hidden_states.reshape(batch, height, weight, inner_dim).permute(0, 3, 1, 2)
hidden_states = self.proj_out(hidden_states)
output = hidden_states + residual
elif self.is_input_vectorized:
hidden_states = self.norm_out(hidden_states)
logits = self.out(hidden_states)
# (batch, self.num_vector_embeds - 1, self.num_latent_pixels)
logits = logits.permute(0, 2, 1)
# log(p(x_0))
output = F.log_softmax(logits.double(), dim=1).float()
if not return_dict:
return (output,)
return Transformer2DModelOutput(sample=output)
def _set_use_memory_efficient_attention_xformers(self, use_memory_efficient_attention_xformers: bool):
for block in self.transformer_blocks:
block._set_use_memory_efficient_attention_xformers(use_memory_efficient_attention_xformers)
class AttentionBlock(nn.Module):
"""
An attention block that allows spatial positions to attend to each other. Originally ported from here, but adapted
to the N-d case.
https://github.com/hojonathanho/diffusion/blob/1e0dceb3b3495bbe19116a5e1b3596cd0706c543/diffusion_tf/models/unet.py#L66.
Uses three q, k, v linear layers to compute attention.
Parameters:
channels (`int`): The number of channels in the input and output.
num_head_channels (`int`, *optional*):
The number of channels in each head. If None, then `num_heads` = 1.
norm_num_groups (`int`, *optional*, defaults to 32): The number of groups to use for group norm.
rescale_output_factor (`float`, *optional*, defaults to 1.0): The factor to rescale the output by.
eps (`float`, *optional*, defaults to 1e-5): The epsilon value to use for group norm.
"""
def __init__(
self,
channels: int,
num_head_channels: Optional[int] = None,
norm_num_groups: int = 32,
rescale_output_factor: float = 1.0,
eps: float = 1e-5,
):
super().__init__()
self.channels = channels
self.num_heads = channels // num_head_channels if num_head_channels is not None else 1
self.num_head_size = num_head_channels
self.group_norm = nn.GroupNorm(num_channels=channels, num_groups=norm_num_groups, eps=eps, affine=True)
# define q,k,v as linear layers
self.query = nn.Linear(channels, channels)
self.key = nn.Linear(channels, channels)
self.value = nn.Linear(channels, channels)
self.rescale_output_factor = rescale_output_factor
self.proj_attn = nn.Linear(channels, channels, 1)
def transpose_for_scores(self, projection: torch.Tensor) -> torch.Tensor:
new_projection_shape = projection.size()[:-1] + (self.num_heads, -1)
# move heads to 2nd position (B, T, H * D) -> (B, T, H, D) -> (B, H, T, D)
new_projection = projection.view(new_projection_shape).permute(0, 2, 1, 3)
return new_projection
def forward(self, hidden_states):
residual = hidden_states
batch, channel, height, width = hidden_states.shape
# norm
hidden_states = self.group_norm(hidden_states)
hidden_states = hidden_states.view(batch, channel, height * width).transpose(1, 2)
# proj to q, k, v
query_proj = self.query(hidden_states)
key_proj = self.key(hidden_states)
value_proj = self.value(hidden_states)
# transpose
query_states = self.transpose_for_scores(query_proj)
key_states = self.transpose_for_scores(key_proj)
value_states = self.transpose_for_scores(value_proj)
# get scores
scale = 1 / math.sqrt(math.sqrt(self.channels / self.num_heads))
attention_scores = torch.matmul(query_states * scale, key_states.transpose(-1, -2) * scale) # TODO: use baddmm
attention_probs = torch.softmax(attention_scores.float(), dim=-1).type(attention_scores.dtype)
# compute attention output
hidden_states = torch.matmul(attention_probs, value_states)
hidden_states = hidden_states.permute(0, 2, 1, 3).contiguous()
new_hidden_states_shape = hidden_states.size()[:-2] + (self.channels,)
hidden_states = hidden_states.view(new_hidden_states_shape)
# compute next hidden_states
hidden_states = self.proj_attn(hidden_states)
hidden_states = hidden_states.transpose(-1, -2).reshape(batch, channel, height, width)
# res connect and rescale
hidden_states = (hidden_states + residual) / self.rescale_output_factor
return hidden_states
class BasicTransformerBlock(nn.Module):
r"""
A basic Transformer block.
Parameters:
dim (`int`): The number of channels in the input and output.
num_attention_heads (`int`): The number of heads to use for multi-head attention.
attention_head_dim (`int`): The number of channels in each head.
dropout (`float`, *optional*, defaults to 0.0): The dropout probability to use.
cross_attention_dim (`int`, *optional*): The size of the context vector for cross attention.
activation_fn (`str`, *optional*, defaults to `"geglu"`): Activation function to be used in feed-forward.
num_embeds_ada_norm (:
obj: `int`, *optional*): The number of diffusion steps used during training. See `Transformer2DModel`.
attention_bias (:
obj: `bool`, *optional*, defaults to `False`): Configure if the attentions should contain a bias parameter.
"""
def __init__(
self,
dim: int,
num_attention_heads: int,
attention_head_dim: int,
dropout=0.0,
cross_attention_dim: Optional[int] = None,
activation_fn: str = "geglu",
num_embeds_ada_norm: Optional[int] = None,
attention_bias: bool = False,
):
super().__init__()
self.attn1 = CrossAttention(
query_dim=dim,
heads=num_attention_heads,
dim_head=attention_head_dim,
dropout=dropout,
bias=attention_bias,
) # is a self-attention
self.ff = FeedForward(dim, dropout=dropout, activation_fn=activation_fn)
self.attn2 = CrossAttention(
query_dim=dim,
cross_attention_dim=cross_attention_dim,
heads=num_attention_heads,
dim_head=attention_head_dim,
dropout=dropout,
bias=attention_bias,
) # is self-attn if context is none
# layer norms
self.use_ada_layer_norm = num_embeds_ada_norm is not None
if self.use_ada_layer_norm:
self.norm1 = AdaLayerNorm(dim, num_embeds_ada_norm)
self.norm2 = AdaLayerNorm(dim, num_embeds_ada_norm)
else:
self.norm1 = nn.LayerNorm(dim)
self.norm2 = nn.LayerNorm(dim)
self.norm3 = nn.LayerNorm(dim)
def _set_attention_slice(self, slice_size):
self.attn1._slice_size = slice_size
self.attn2._slice_size = slice_size
def _set_use_memory_efficient_attention_xformers(self, use_memory_efficient_attention_xformers: bool):
if not is_xformers_available():
print("Here is how to install it")
raise ModuleNotFoundError(
"Refer to https://github.com/facebookresearch/xformers for more information on how to install"
" xformers",
name="xformers",
)
elif not torch.cuda.is_available():
raise ValueError(
"torch.cuda.is_available() should be True but is False. xformers' memory efficient attention is only"
" available for GPU "
)
else:
try:
# Make sure we can run the memory efficient attention
_ = xformers.ops.memory_efficient_attention(
torch.randn((1, 2, 40), device="cuda"),
torch.randn((1, 2, 40), device="cuda"),
torch.randn((1, 2, 40), device="cuda"),
)
except Exception as e:
raise e
self.attn1._use_memory_efficient_attention_xformers = use_memory_efficient_attention_xformers
self.attn2._use_memory_efficient_attention_xformers = use_memory_efficient_attention_xformers
def forward(self, hidden_states, context=None, timestep=None):
# 1. Self-Attention
norm_hidden_states = (
self.norm1(hidden_states, timestep) if self.use_ada_layer_norm else self.norm1(hidden_states)
)
hidden_states = self.attn1(norm_hidden_states) + hidden_states
# 2. Cross-Attention
norm_hidden_states = (
self.norm2(hidden_states, timestep) if self.use_ada_layer_norm else self.norm2(hidden_states)
)
hidden_states = self.attn2(norm_hidden_states, context=context) + hidden_states
# 3. Feed-forward
hidden_states = self.ff(self.norm3(hidden_states)) + hidden_states
return hidden_states
class CrossAttention(nn.Module):
r"""
A cross attention layer.
Parameters:
query_dim (`int`): The number of channels in the query.
cross_attention_dim (`int`, *optional*):
The number of channels in the context. If not given, defaults to `query_dim`.
heads (`int`, *optional*, defaults to 8): The number of heads to use for multi-head attention.
dim_head (`int`, *optional*, defaults to 64): The number of channels in each head.
dropout (`float`, *optional*, defaults to 0.0): The dropout probability to use.
bias (`bool`, *optional*, defaults to False):
Set to `True` for the query, key, and value linear layers to contain a bias parameter.
"""
def __init__(
self,
query_dim: int,
cross_attention_dim: Optional[int] = None,
heads: int = 8,
dim_head: int = 64,
dropout: float = 0.0,
bias=False,
):
super().__init__()
inner_dim = dim_head * heads
cross_attention_dim = cross_attention_dim if cross_attention_dim is not None else query_dim
self.scale = dim_head**-0.5
self.heads = heads
# for slice_size > 0 the attention score computation
# is split across the batch axis to save memory
# You can set slice_size with `set_attention_slice`
self._slice_size = None
self._use_memory_efficient_attention_xformers = False
self.to_q = nn.Linear(query_dim, inner_dim, bias=bias)
self.to_k = nn.Linear(cross_attention_dim, inner_dim, bias=bias)
self.to_v = nn.Linear(cross_attention_dim, inner_dim, bias=bias)
self.to_out = nn.ModuleList([])
self.to_out.append(nn.Linear(inner_dim, query_dim))
self.to_out.append(nn.Dropout(dropout))
def reshape_heads_to_batch_dim(self, tensor):
batch_size, seq_len, dim = tensor.shape
head_size = self.heads
tensor = tensor.reshape(batch_size, seq_len, head_size, dim // head_size)
tensor = tensor.permute(0, 2, 1, 3).reshape(batch_size * head_size, seq_len, dim // head_size)
return tensor
def reshape_batch_dim_to_heads(self, tensor):
batch_size, seq_len, dim = tensor.shape
head_size = self.heads
tensor = tensor.reshape(batch_size // head_size, head_size, seq_len, dim)
tensor = tensor.permute(0, 2, 1, 3).reshape(batch_size // head_size, seq_len, dim * head_size)
return tensor
def forward(self, hidden_states, context=None, mask=None):
batch_size, sequence_length, _ = hidden_states.shape
query = self.to_q(hidden_states)
context = context if context is not None else hidden_states
key = self.to_k(context)
value = self.to_v(context)
dim = query.shape[-1]
query = self.reshape_heads_to_batch_dim(query)
key = self.reshape_heads_to_batch_dim(key)
value = self.reshape_heads_to_batch_dim(value)
# TODO(PVP) - mask is currently never used. Remember to re-implement when used
# attention, what we cannot get enough of
if self._use_memory_efficient_attention_xformers:
hidden_states = self._memory_efficient_attention_xformers(query, key, value)
# Some versions of xformers return output in fp32, cast it back to the dtype of the input
hidden_states = hidden_states.to(query.dtype)
else:
if self._slice_size is None or query.shape[0] // self._slice_size == 1:
hidden_states = self._attention(query, key, value)
else:
hidden_states = self._sliced_attention(query, key, value, sequence_length, dim)
# linear proj
hidden_states = self.to_out[0](hidden_states)
# dropout
hidden_states = self.to_out[1](hidden_states)
return hidden_states
def _attention(self, query, key, value):
# TODO: use baddbmm for better performance
if query.device.type == "mps":
# Better performance on mps (~20-25%)
attention_scores = torch.einsum("b i d, b j d -> b i j", query, key) * self.scale
else:
attention_scores = torch.matmul(query, key.transpose(-1, -2)) * self.scale
attention_probs = attention_scores.softmax(dim=-1)
# compute attention output
if query.device.type == "mps":
hidden_states = torch.einsum("b i j, b j d -> b i d", attention_probs, value)
else:
hidden_states = torch.matmul(attention_probs, value)
# reshape hidden_states
hidden_states = self.reshape_batch_dim_to_heads(hidden_states)
return hidden_states
def _sliced_attention(self, query, key, value, sequence_length, dim):
batch_size_attention = query.shape[0]
hidden_states = torch.zeros(
(batch_size_attention, sequence_length, dim // self.heads), device=query.device, dtype=query.dtype
)
slice_size = self._slice_size if self._slice_size is not None else hidden_states.shape[0]
for i in range(hidden_states.shape[0] // slice_size):
start_idx = i * slice_size
end_idx = (i + 1) * slice_size
if query.device.type == "mps":
# Better performance on mps (~20-25%)
attn_slice = (
torch.einsum("b i d, b j d -> b i j", query[start_idx:end_idx], key[start_idx:end_idx])
* self.scale
)
else:
attn_slice = (
torch.matmul(query[start_idx:end_idx], key[start_idx:end_idx].transpose(1, 2)) * self.scale
) # TODO: use baddbmm for better performance
attn_slice = attn_slice.softmax(dim=-1)
if query.device.type == "mps":
attn_slice = torch.einsum("b i j, b j d -> b i d", attn_slice, value[start_idx:end_idx])
else:
attn_slice = torch.matmul(attn_slice, value[start_idx:end_idx])
hidden_states[start_idx:end_idx] = attn_slice
# reshape hidden_states
hidden_states = self.reshape_batch_dim_to_heads(hidden_states)
return hidden_states
def _memory_efficient_attention_xformers(self, query, key, value):
hidden_states = xformers.ops.memory_efficient_attention(query, key, value, attn_bias=None)
hidden_states = self.reshape_batch_dim_to_heads(hidden_states)
return hidden_states
class FeedForward(nn.Module):
r"""
A feed-forward layer.
Parameters:
dim (`int`): The number of channels in the input.
dim_out (`int`, *optional*): The number of channels in the output. If not given, defaults to `dim`.
mult (`int`, *optional*, defaults to 4): The multiplier to use for the hidden dimension.
dropout (`float`, *optional*, defaults to 0.0): The dropout probability to use.
activation_fn (`str`, *optional*, defaults to `"geglu"`): Activation function to be used in feed-forward.
"""
def __init__(
self,
dim: int,
dim_out: Optional[int] = None,
mult: int = 4,
dropout: float = 0.0,
activation_fn: str = "geglu",
):
super().__init__()
inner_dim = int(dim * mult)
dim_out = dim_out if dim_out is not None else dim
if activation_fn == "geglu":
geglu = GEGLU(dim, inner_dim)
elif activation_fn == "geglu-approximate":
geglu = ApproximateGELU(dim, inner_dim)
self.net = nn.ModuleList([])
# project in
self.net.append(geglu)
# project dropout
self.net.append(nn.Dropout(dropout))
# project out
self.net.append(nn.Linear(inner_dim, dim_out))
def forward(self, hidden_states):
for module in self.net:
hidden_states = module(hidden_states)
return hidden_states
# feedforward
class GEGLU(nn.Module):
r"""
A variant of the gated linear unit activation function from https://arxiv.org/abs/2002.05202.
Parameters:
dim_in (`int`): The number of channels in the input.
dim_out (`int`): The number of channels in the output.
"""
def __init__(self, dim_in: int, dim_out: int):
super().__init__()
self.proj = nn.Linear(dim_in, dim_out * 2)
def gelu(self, gate):
if gate.device.type != "mps":
return F.gelu(gate)
# mps: gelu is not implemented for float16
return F.gelu(gate.to(dtype=torch.float32)).to(dtype=gate.dtype)
def forward(self, hidden_states):
hidden_states, gate = self.proj(hidden_states).chunk(2, dim=-1)
return hidden_states * self.gelu(gate)
class ApproximateGELU(nn.Module):
"""
The approximate form of Gaussian Error Linear Unit (GELU)
For more details, see section 2: https://arxiv.org/abs/1606.08415
"""
def __init__(self, dim_in: int, dim_out: int):
super().__init__()
self.proj = nn.Linear(dim_in, dim_out)
def forward(self, x):
x = self.proj(x)
return x * torch.sigmoid(1.702 * x)
class AdaLayerNorm(nn.Module):
"""
Norm layer modified to incorporate timestep embeddings.
"""
def __init__(self, embedding_dim, num_embeddings):
super().__init__()
self.emb = nn.Embedding(num_embeddings, embedding_dim)
self.silu = nn.SiLU()
self.linear = nn.Linear(embedding_dim, embedding_dim * 2)
self.norm = nn.LayerNorm(embedding_dim, elementwise_affine=False)
def forward(self, x, timestep):
emb = self.linear(self.silu(self.emb(timestep)))
scale, shift = torch.chunk(emb, 2)
x = self.norm(x) * (1 + scale) + shift
return x
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