transformer.py

# coding=utf-8
# Copyright (c) 2020, NVIDIA CORPORATION.  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.

"""Transformer."""
import math
import torch
import torch.nn.functional as F

from megatron import get_args
from megatron import mpu
from .module import MegatronModule
from megatron.model.enums import AttnMaskType, ModelType, LayerType, AttnType
from megatron.model import LayerNorm
from megatron.model.fused_softmax import FusedScaleMaskSoftmax
from megatron.model.fused_bias_gelu import bias_gelu_impl
from megatron.model.utils import attention_mask_func, openai_gelu, erf_gelu


""" We use the following notation throughout this file:
     h: hidden size
     n: number of attention heads
     p: number of model parallel partitions
     np: n/p
     hp: h/p
     hn: h/n
     b: batch size
     s: sequence length
     l: number of layers
    Transformer takes input of size [s, b, h] and returns a
    tensor of the same size. We use the following arguments:
        hyperparameters: transformer hyperparameters
"""

class ParallelMLP(MegatronModule):
    """MLP.

    MLP will take the input with h hidden state, project it to 4*h
    hidden dimension, perform nonlinear transformation, and project the
    state back into h hidden dimension.
    """

    def __init__(self, init_method, output_layer_init_method):
        super(ParallelMLP, self).__init__()
        args = get_args()

        # Project to 4h.
        self.dense_h_to_4h = mpu.ColumnParallelLinear(
            args.hidden_size,
            args.ffn_hidden_size,
            gather_output=False,
            init_method=init_method,
            skip_bias_add=True)

        self.bias_gelu_fusion = args.bias_gelu_fusion
        self.activation_func = F.gelu
        if args.openai_gelu:
            self.activation_func = openai_gelu
        elif args.onnx_safe:
            self.activation_func = erf_gelu

        # Project back to h.
        self.dense_4h_to_h = mpu.RowParallelLinear(
            args.ffn_hidden_size,
            args.hidden_size,
            input_is_parallel=True,
            init_method=output_layer_init_method,
            skip_bias_add=True)

    def forward(self, hidden_states):

        # [s, b, 4hp]
        intermediate_parallel, bias_parallel = self.dense_h_to_4h(hidden_states)

        if self.bias_gelu_fusion:
             intermediate_parallel = \
                     bias_gelu_impl(intermediate_parallel, bias_parallel)
        else:
            intermediate_parallel = \
                self.activation_func(intermediate_parallel + bias_parallel)

        # [s, b, h]
        output, output_bias = self.dense_4h_to_h(intermediate_parallel)
        return output, output_bias


class ParallelAttention(MegatronModule):
    """Parallel self-attention layer abstract class.

    Self-attention layer takes input with size [b, s, h]
    and returns output of the same size.
    """

    def __init__(self, init_method,
                 output_layer_init_method, layer_number,
                 attention_type=AttnType.self_attn,
                 attn_mask_type=AttnMaskType.padding):
        super(ParallelAttention, self).__init__()
        args = get_args()
        self.fp16 = args.fp16
        self.bf16 = args.bf16

        self.apply_query_key_layer_scaling = args.apply_query_key_layer_scaling
        self.attention_softmax_in_fp32 = args.attention_softmax_in_fp32
        if self.apply_query_key_layer_scaling:
            self.attention_softmax_in_fp32 = True
        self.layer_number = max(1, layer_number)
        self.attention_type = attention_type
        self.attn_mask_type = attn_mask_type
        self.params_dtype = args.params_dtype

        projection_size = args.kv_channels * args.num_attention_heads

        # Per attention head and per partition values.
        world_size = mpu.get_tensor_model_parallel_world_size()
        self.hidden_size_per_partition = mpu.divide(projection_size,
                                                    world_size)
        self.hidden_size_per_attention_head = mpu.divide(
            projection_size, args.num_attention_heads)
        self.num_attention_heads_per_partition = mpu.divide(
            args.num_attention_heads, world_size)

        # Strided linear layer.
        if attention_type == AttnType.self_attn:
            self.query_key_value = mpu.ColumnParallelLinear(
                args.hidden_size,
                3 * projection_size,
                gather_output=False,
                init_method=init_method)
        else:
            assert attention_type == AttnType.cross_attn
            self.query = mpu.ColumnParallelLinear(
                args.hidden_size,
                projection_size,
                gather_output=False,
                init_method=init_method)

            self.key_value = mpu.ColumnParallelLinear(
                args.hidden_size,
                2 * projection_size,
                gather_output=False,
                init_method=init_method)

        coeff = None
        self.norm_factor = math.sqrt(self.hidden_size_per_attention_head)
        if self.apply_query_key_layer_scaling:
            coeff = self.layer_number
            self.norm_factor *= coeff

        self.scale_mask_softmax = FusedScaleMaskSoftmax(
            self.fp16, self.bf16,
            self.attn_mask_type,
            args.masked_softmax_fusion,
            attention_mask_func,
            self.attention_softmax_in_fp32,
            coeff)

        # Dropout. Note that for a single iteration, this layer will generate
        # different outputs on different number of parallel partitions but
        # on average it should not be partition dependent.
        self.attention_dropout = torch.nn.Dropout(args.attention_dropout)

        # Output.
        self.dense = mpu.RowParallelLinear(
            projection_size,
            args.hidden_size,
            input_is_parallel=True,
            init_method=output_layer_init_method,
            skip_bias_add=True)


    def _allocate_memory(self, inference_max_sequence_len, batch_size):
        return torch.empty(
            inference_max_sequence_len,
            batch_size,
            self.num_attention_heads_per_partition,
            self.hidden_size_per_attention_head,
            dtype=self.params_dtype,
            device=torch.cuda.current_device())
        

    def forward(self, hidden_states, attention_mask,
                encoder_output=None, inference_params=None):
        # hidden_states: [sq, b, h]


        # =================================================
        # Pre-allocate memory for key-values for inference.
        # =================================================
        if inference_params:
            if self.layer_number not in inference_params.key_value_memory_dict:
                inf_max_seq_len = inference_params.max_sequence_len
                inf_max_batch_size = inference_params.max_batch_size
                inference_key_memory = self._allocate_memory(
                    inf_max_seq_len, inf_max_batch_size)
                inference_value_memory = self._allocate_memory(
                    inf_max_seq_len, inf_max_batch_size)
                inference_params.key_value_memory_dict[self.layer_number] = (
                    inference_key_memory, inference_value_memory)
            else:
                inference_key_memory, inference_value_memory = \
                    inference_params.key_value_memory_dict[self.layer_number]


        # =====================
        # Query, Key, and Value
        # =====================

        if self.attention_type == AttnType.self_attn:
            # Attention heads [sq, b, h] --> [sq, b, (np * 3 * hn)]
            mixed_x_layer, _ = self.query_key_value(hidden_states)

            # [sq, b, (np * 3 * hn)] --> [sq, b, np, 3 * hn]
            new_tensor_shape = mixed_x_layer.size()[:-1] + \
                (self.num_attention_heads_per_partition,
                 3 * self.hidden_size_per_attention_head)
            mixed_x_layer = mixed_x_layer.view(*new_tensor_shape)

            # [sq, b, np, 3 * hn] --> 3 [sq, b, np, hn]
            (query_layer,
             key_layer,
             value_layer) = mpu.split_tensor_along_last_dim(mixed_x_layer, 3)
        else:
            # Attention heads [sk, b, h] --> [sk, b, (np * 2 * hn)]
            mixed_kv_layer, _ = self.key_value(encoder_output)

            # [sk, b, (np * 2 * hn)] --> [sk, b, np, 2 * hn]
            new_tensor_shape = mixed_kv_layer.size()[:-1] + \
                (self.num_attention_heads_per_partition,
                 2 * self.hidden_size_per_attention_head)
            mixed_kv_layer = mixed_kv_layer.view(*new_tensor_shape)

            # [sk, b, np, 2 * hn] --> 2 [sk, b, np, hn]
            (key_layer,
             value_layer) = mpu.split_tensor_along_last_dim(mixed_kv_layer, 2)

            # Attention head [sq, b, h] --> [sq, b, hp]
            query_layer, _ = self.query(hidden_states)
            # [sq, b, hp] --> [sq, b, np, hn]
            new_tensor_shape = query_layer.size()[:-1] + \
                (self.num_attention_heads_per_partition,
                 self.hidden_size_per_attention_head)
            query_layer = query_layer.view(*new_tensor_shape)


        # ==================================
        # Adjust key and value for inference
        # ==================================

        if inference_params:
            batch_start = inference_params.batch_size_offset
            batch_end = batch_start + key_layer.size(1)
            assert batch_end <= inference_key_memory.size(1)
            sequence_start = inference_params.sequence_len_offset
            sequence_end = sequence_start + key_layer.size(0)
            assert sequence_end <= inference_key_memory.size(0)
            # Copy key and values.
            inference_key_memory[sequence_start:sequence_end,
                                 batch_start:batch_end, ...] = key_layer
            inference_value_memory[sequence_start:sequence_end,
                                   batch_start:batch_end, ...] = value_layer
            key_layer = inference_key_memory[
                :sequence_end, batch_start:batch_end, ...]
            value_layer = inference_value_memory[
                :sequence_end, batch_start:batch_end, ...]


        # ===================================
        # Raw attention scores. [b, np, s, s]
        # ===================================

        # [b, np, sq, sk]
        output_size = (query_layer.size(1),
                       query_layer.size(2),
                       query_layer.size(0),
                       key_layer.size(0))

        # [sq, b, np, hn] -> [sq, b * np, hn]
        query_layer = query_layer.view(output_size[2],
                                       output_size[0] * output_size[1], -1)
        # [sk, b, np, hn] -> [sk, b * np, hn]
        key_layer = key_layer.view(output_size[3],
                                   output_size[0] * output_size[1], -1)

        # preallocting result tensor: [b * np, sq, sk]
        matmul_result = torch.empty(
            output_size[0]*output_size[1],
            output_size[2],
            output_size[3],
            dtype=query_layer.dtype,
            device=torch.cuda.current_device())

        # Raw attention scores. [b * np, sq, sk]
        matmul_result = torch.baddbmm(
            matmul_result,
            query_layer.transpose(0, 1),   # [b * np, sq, hn]
            key_layer.transpose(0, 1).transpose(1, 2),  # [b * np, hn, sk]
            beta=0.0, alpha=(1.0/self.norm_factor))

        # change view to [b, np, sq, sk]
        attention_scores = matmul_result.view(*output_size)


        # ===========================
        # Attention probs and dropout
        # ===========================

        # attention scores and attention mask [b, np, sq, sk]
        attention_probs = self.scale_mask_softmax(attention_scores,
                                                  attention_mask)

        # This is actually dropping out entire tokens to attend to, which might
        # seem a bit unusual, but is taken from the original Transformer paper.
        with mpu.get_cuda_rng_tracker().fork():
            attention_probs = self.attention_dropout(attention_probs)

        # =========================
        # Context layer. [sq, b, hp]
        # =========================

        # value_layer -> context layer.
        # [sk, b, np, hn] --> [b, np, sq, hn]

        # context layer shape: [b, np, sq, hn]
        output_size = (value_layer.size(1),
                       value_layer.size(2),
                       query_layer.size(0),
                       value_layer.size(3))

        # change view [sk, b * np, hn]
        value_layer = value_layer.view(value_layer.size(0),
                                       output_size[0] * output_size[1], -1)

        # change view [b * np, sq, sk]
        attention_probs = attention_probs.view(output_size[0] * output_size[1],
                                               output_size[2], -1)

        # matmul: [b * np, sq, hn]
        context_layer = torch.bmm(attention_probs, value_layer.transpose(0, 1))

        # change view [b, np, sq, hn]
        context_layer = context_layer.view(*output_size)

        # [b, np, sq, hn] --> [sq, b, np, hn]
        context_layer = context_layer.permute(2, 0, 1, 3).contiguous()

        # [sq, b, np, hn] --> [sq, b, hp]
        new_context_layer_shape = context_layer.size()[:-2] + \
            (self.hidden_size_per_partition,)
        context_layer = context_layer.view(*new_context_layer_shape)

        # =================
        # Output. [sq, b, h]
        # =================

        output, bias = self.dense(context_layer)

        return output, bias


def bias_dropout_add(x, bias, residual, prob, training):
    # type: (Tensor, Tensor, Tensor, float, bool) -> Tensor
    out = torch.nn.functional.dropout(x + bias, p=prob, training=training)
    out = residual + out
    return out


def get_bias_dropout_add(training):
    def _bias_dropout_add(x, bias, residual, prob):
        return bias_dropout_add(x, bias, residual, prob, training)
    return _bias_dropout_add


@torch.jit.script
def bias_dropout_add_fused_train(x: torch.Tensor,
                                 bias: torch.Tensor,
                                 residual: torch.Tensor,
                                 prob: float) -> torch.Tensor:
    return bias_dropout_add(x, bias, residual, prob, True)


@torch.jit.script
def bias_dropout_add_fused_inference(x: torch.Tensor,
                                     bias: torch.Tensor,
                                     residual: torch.Tensor,
                                     prob: float) -> torch.Tensor:
    return bias_dropout_add(x, bias, residual, prob, False)


class ParallelTransformerLayer(MegatronModule):
    """A single transformer layer.

    Transformer layer takes input with size [b, s, h] and returns an
    output of the same size.
    """

    def __init__(self, init_method, output_layer_init_method,
                 layer_number, layer_type=LayerType.encoder,
                 self_attn_mask_type=AttnMaskType.padding):
        args = get_args()

        super(ParallelTransformerLayer, self).__init__()
        self.layer_number = layer_number
        self.layer_type = layer_type

        self.apply_residual_connection_post_layernorm \
            = args.apply_residual_connection_post_layernorm

        self.bf16 = args.bf16
        self.fp32_residual_connection = args.fp32_residual_connection

        # Layernorm on the input data.
        self.input_layernorm = LayerNorm(
            args.hidden_size,
            eps=args.layernorm_epsilon,
            no_persist_layer_norm=args.no_persist_layer_norm)

        # Self attention.
        self.self_attention = ParallelAttention(
            init_method,
            output_layer_init_method,
            layer_number,
            attention_type=AttnType.self_attn,
            attn_mask_type=self_attn_mask_type)
        self.hidden_dropout = args.hidden_dropout
        self.bias_dropout_fusion = args.bias_dropout_fusion

        # Layernorm on the attention output
        self.post_attention_layernorm = LayerNorm(
            args.hidden_size,
            eps=args.layernorm_epsilon,
            no_persist_layer_norm=args.no_persist_layer_norm)

        if self.layer_type == LayerType.decoder:
            self.inter_attention = ParallelAttention(
                init_method,
                output_layer_init_method,
                layer_number,
                attention_type=AttnType.cross_attn)
            # Layernorm on the attention output.
            self.post_inter_attention_layernorm = LayerNorm(
                args.hidden_size,
                eps=args.layernorm_epsilon,
                no_persist_layer_norm=args.no_persist_layer_norm)

        # MLP
        self.mlp = ParallelMLP(init_method,
                               output_layer_init_method)

    def forward(self, hidden_states, attention_mask,
                encoder_output=None, enc_dec_attn_mask=None,
                inference_params=None):
        # hidden_states: [b, s, h]

        # Layer norm at the beginning of the transformer layer.
        layernorm_output = self.input_layernorm(hidden_states)
        # Self attention.
        attention_output, attention_bias = \
            self.self_attention(
                layernorm_output,
                attention_mask,
                inference_params=inference_params)

        # Residual connection.
        if self.apply_residual_connection_post_layernorm:
            residual = layernorm_output
        else:
            residual = hidden_states

        # jit scripting for a nn.module (with dropout) is not
        # trigerring the fusion kernel. For now, we use two
        # different nn.functional routines to account for varying
        # dropout semantics during training and inference phases.
        if self.bias_dropout_fusion:
            if self.training:
                bias_dropout_add_func = bias_dropout_add_fused_train
            else:
                bias_dropout_add_func = bias_dropout_add_fused_inference
        else:
            bias_dropout_add_func = get_bias_dropout_add(self.training)

        # re-enable torch grad to enable fused optimization.
        with torch.enable_grad():
            layernorm_input = bias_dropout_add_func(
                attention_output,
                attention_bias.expand_as(residual),
                residual,
                self.hidden_dropout)

        # Layer norm post the self attention.
        layernorm_output = self.post_attention_layernorm(layernorm_input)

        if self.layer_type == LayerType.decoder:
            attention_output, attention_bias = \
                self.inter_attention(layernorm_output,
                                     enc_dec_attn_mask,
                                     encoder_output=encoder_output)
            # residual connection
            if self.apply_residual_connection_post_layernorm:
                residual = layernorm_output
            else:
                residual = layernorm_input

            # re-enable torch grad to enable fused optimization.
            with torch.enable_grad():
                layernorm_input = bias_dropout_add_func(
                    attention_output,
                    attention_bias.expand_as(residual),
                    residual,
                    self.hidden_dropout)

            # Layer norm post the decoder attention
            layernorm_output = self.post_inter_attention_layernorm(layernorm_input)

        # MLP.
        mlp_output, mlp_bias = self.mlp(layernorm_output)

        # Second residual connection.
        if self.apply_residual_connection_post_layernorm:
            residual = layernorm_output
        else:
            residual = layernorm_input

        # re-enable torch grad to enable fused optimization.
        with torch.enable_grad():
            output = bias_dropout_add_func(
                mlp_output,
                mlp_bias.expand_as(residual),
                residual,
                self.hidden_dropout)

        return output


class ParallelTransformer(MegatronModule):
    """Transformer class."""

    def __init__(self, init_method, output_layer_init_method,
                 layer_type=LayerType.encoder,
                 self_attn_mask_type=AttnMaskType.padding,
                 pre_process=True, post_process=True):
        super(ParallelTransformer, self).__init__()
        args = get_args()

        self.bf16 = args.bf16
        self.fp32_residual_connection = args.fp32_residual_connection
        self.pre_process = pre_process
        self.post_process = post_process
        self.input_tensor = None

        # Store activation checkpoiting flag.
        self.activations_checkpoint_method = args.activations_checkpoint_method
        self.activations_checkpoint_num_layers = args.activations_checkpoint_num_layers
        self.distribute_checkpointed_activations = args.distribute_checkpointed_activations

        # Number of layers.
        self.num_layers = mpu.get_num_layers(
            args, args.model_type == ModelType.encoder_and_decoder)

        # Transformer layers.
        def build_layer(layer_number):
            return ParallelTransformerLayer(
                init_method,
                output_layer_init_method,
                layer_number,
                layer_type=layer_type,
                self_attn_mask_type=self_attn_mask_type)
        if args.virtual_pipeline_model_parallel_size is not None:
            assert args.num_layers % args.virtual_pipeline_model_parallel_size == 0, \
                'num_layers_per_stage must be divisible by ' \
                'virtual_pipeline_model_parallel_size'
            assert args.model_type != ModelType.encoder_and_decoder
            # Number of layers in each model chunk is the number of layers in the stage,
            # divided by the number of model chunks in a stage.
            self.num_layers = self.num_layers // args.virtual_pipeline_model_parallel_size
            # With 8 layers, 2 stages, and 4 model chunks, we want an assignment of
            # layers to stages like (each list is a model chunk):
            # Stage 0: [0]  [2]  [4]  [6]
            # Stage 1: [1]  [3]  [5]  [7]
            # With 8 layers, 2 stages, and 2 virtual stages, we want an assignment of
            # layers to stages like (each list is a model chunk):
            # Stage 0: [0, 1]  [4, 5]
            # Stage 1: [2, 3]  [6, 7]
            offset = mpu.get_virtual_pipeline_model_parallel_rank() * (
                args.num_layers // args.virtual_pipeline_model_parallel_size) + \
                (mpu.get_pipeline_model_parallel_rank() * self.num_layers)
        else:
            # Each stage gets a contiguous set of layers.
            if args.model_type == ModelType.encoder_and_decoder and \
                    mpu.get_pipeline_model_parallel_world_size() > 1:
                pipeline_rank = mpu.get_pipeline_model_parallel_rank()
                if layer_type == LayerType.encoder:
                    offset = pipeline_rank * self.num_layers
                else:
                    num_ranks_in_enc = args.pipeline_model_parallel_split_rank
                    offset = (pipeline_rank - num_ranks_in_enc) * self.num_layers
            else:
                offset = mpu.get_pipeline_model_parallel_rank() * self.num_layers

        self.layers = torch.nn.ModuleList(
            [build_layer(i + 1 + offset) for i in range(self.num_layers)])

        if self.post_process:
            # Final layer norm before output.
            self.final_layernorm = LayerNorm(
                args.hidden_size,
                eps=args.layernorm_epsilon,
                no_persist_layer_norm=args.no_persist_layer_norm)

    def _get_layer(self, layer_number):
        return self.layers[layer_number]

    def _checkpointed_forward(self, hidden_states, attention_mask,
                              encoder_output, enc_dec_attn_mask):
        """Forward method with activation checkpointing."""
        def custom(start, end):
            def custom_forward(*inputs):
                x_ = inputs[0]
                attention_mask = inputs[1]
                encoder_output = inputs[2]
                enc_dec_attn_mask = inputs[3]
                for index in range(start, end):
                    layer = self._get_layer(index)
                    x_ = layer(x_, attention_mask, encoder_output, enc_dec_attn_mask)
                return x_
            return custom_forward

        if self.activations_checkpoint_method == 'uniform':
            # Uniformly divide the total number of Transformer layers and checkpoint
            # the input activation of each divided chunk.
            # A method to further reduce memory usage reducing checkpoints.
            l = 0
            while l < self.num_layers:
                hidden_states = mpu.checkpoint(
                    custom(l, l + self.activations_checkpoint_num_layers),
                    self.distribute_checkpointed_activations,
                    hidden_states, attention_mask, encoder_output, enc_dec_attn_mask)
                l += self.activations_checkpoint_num_layers
        elif self.activations_checkpoint_method == 'block':
            # Checkpoint the input activation of only a set number of individual
            # Transformer layers and skip the rest.
            # A method fully use the device memory removing redundant re-computation.
            for l in range(self.num_layers):
                if l < self.activations_checkpoint_num_layers:
                    hidden_states = mpu.checkpoint(
                        custom(l, l + 1),
                        self.distribute_checkpointed_activations,
                        hidden_states, attention_mask, encoder_output, enc_dec_attn_mask)
                else:
                    hidden_states = custom(l, l + 1)(
                        hidden_states, attention_mask, encoder_output, enc_dec_attn_mask)
        else:
            raise ValueError("Invalid activation checkpoint method.")

        return hidden_states

    def set_input_tensor(self, input_tensor):
        """Set input tensor to be used instead of forward()'s input.

        When doing pipeline parallelism the input from the previous
        stage comes from communication, not from the input, so the
        model's forward_step_func won't have it. This function is thus
        used by internal code to bypass the input provided by the
        forward_step_func"""
        self.input_tensor = input_tensor

    def forward(self, hidden_states, attention_mask,
                encoder_output=None, enc_dec_attn_mask=None,
                inference_params=None):

        # Checks.
        if inference_params:
            assert self.activations_checkpoint_method is None, \
                'inference does not work with activation checkpointing'

        if self.pre_process:
            # Data format change to avoid explicit tranposes : [b s h] --> [s b h].
            # If the input flag for fp32 residual connection is set, convert for float.
            if self.fp32_residual_connection:
                hidden_states = hidden_states.transpose(0, 1).contiguous().float()
            # Otherwise, leave it as is.
            else:
                hidden_states = hidden_states.transpose(0, 1).contiguous()
        else:
            # See set_input_tensor()
            hidden_states = self.input_tensor

        if encoder_output is not None:
             encoder_output = encoder_output.transpose(0, 1).contiguous()

        if self.activations_checkpoint_method is not None:
            hidden_states = self._checkpointed_forward(hidden_states,
                                                       attention_mask,
                                                       encoder_output,
                                                       enc_dec_attn_mask)
        else:
            for index in range(self.num_layers):
                layer = self._get_layer(index)
                hidden_states = layer(
                    hidden_states,
                    attention_mask,
                    encoder_output=encoder_output,
                    enc_dec_attn_mask=enc_dec_attn_mask,
                    inference_params=inference_params)


        # Final layer norm.
        if self.post_process:
            # Reverting data format change [s b h] --> [b s h].
            hidden_states = hidden_states.transpose(0, 1).contiguous()
            output = self.final_layernorm(hidden_states)
        else:
            output = hidden_states
        
        return output