==================================================================================================== import os import sys with open(sys.argv[0]) as f: code = f.read() # read the code of this file ASAP, for logging import uuid import glob import time from dataclasses import dataclass import numpy as np import torch from torch import nn import torch.nn.functional as F import torch.distributed as dist import torch._inductor.config as config from torch.nn.parallel import DistributedDataParallel as DDP # ----------------------------------------------------------------------------- # Muon optimizer def zeropower_via_svd(G, steps=None): U, S, V = G.svd() return U @ V.T @torch.compile def zeropower_via_newtonschulz5(G, steps=10, eps=1e-7): """ Newton-Schulz iteration to compute the zeroth power / orthogonalization of G. We opt to use a quintic iteration whose coefficients are selected to maximize the slope at zero. For the purpose of minimizing steps, it turns out to be empirically effective to keep increasing the slope at zero even beyond the point where the iteration no longer converges all the way to one everywhere on the interval. This iteration therefore does not produce UV^T but rather something like US'V^T where S' is diagonal with S_{ii}' \sim Uniform(0.5, 1.5), which turns out not to hurt model performance at all relative to UV^T, where USV^T = G is the SVD. """ assert len(G.shape) == 2 a, b, c = (3.4445, -4.7750, 2.0315) X = G.bfloat16() X /= (X.norm() + eps) # ensure top singular value <= 1 if G.size(0) > G.size(1): X = X.T for _ in range(steps): A = X @ X.T B = A @ X X = a * X + b * B + c * A @ B if G.size(0) > G.size(1): X = X.T return X zeropower_backends = dict(svd=zeropower_via_svd, newtonschulz5=zeropower_via_newtonschulz5) class Muon(torch.optim.Optimizer): """ Muon - MomentUm Orthogonalized by Newton-schulz Muon internally runs standard SGD-momentum, and then performs an orthogonalization post- processing step, in which each 2D parameter's update is replaced with the nearest orthogonal matrix. To efficiently orthogonalize each update, we use a Newton-Schulz iteration, which has the advantage that it can be stably run in bfloat16 on the GPU. Some warnings: - This optimizer assumes that all parameters passed in are 2D. - It should not be used for the embedding layer, the final fully connected layer, or any {0,1}-D parameters; those should all be optimized by a standard method (e.g., AdamW). - To use it with 4D convolutional filters, it works well to just flatten their last 3 dimensions. - We believe it is unlikely to work well for training with small batch size. - We believe it may not work well for finetuning pretrained models, but we haven't tested this. - We have not yet tried this optimizer for training scenarios larger than NanoGPT (124M). Arguments: lr: The learning rate used by the internal SGD. momentum: The momentum used by the internal SGD. nesterov: Whether to use Nesterov-style momentum in the internal SGD. (recommended) backend: The chosen backend for the orthogonalization step. (recommended: 'newtonschulz5') backend_steps: The number of iteration steps to use in the backend, if it is iterative. """ def __init__(self, params, lr=3e-4, momentum=0.95, nesterov=True, backend='newtonschulz5', backend_steps=5, rank=0, world_size=1): defaults = dict(lr=lr, momentum=momentum, nesterov=nesterov, backend=backend, backend_steps=backend_steps) super().__init__(params, defaults) self.rank = rank self.world_size = world_size def step(self): for group in self.param_groups: lr = group['lr'] momentum = group['momentum'] zeropower_backend = zeropower_backends[group['backend']] # generate weight updates in distributed fashion total_params = sum(p.numel() for p in group['params']) updates_flat = torch.zeros(total_params, device='cuda', dtype=torch.bfloat16) curr_idx = 0 for i, p in enumerate(group['params']): # luckily this will perfectly distribute a transformer with multiple of 4 layers to 8 GPUs if i % self.world_size == self.rank: g = p.grad if g is None: continue state = self.state[p] if 'momentum_buffer' not in state: state['momentum_buffer'] = torch.zeros_like(g) buf = state['momentum_buffer'] buf.mul_(momentum).add_(g) if group['nesterov']: g = g.add(buf, alpha=momentum) g = zeropower_backend(g, steps=group['backend_steps']) g *= max(g.size(0), g.size(1))**0.5 # scale to have update.square().mean() == 1 updates_flat[curr_idx:curr_idx+p.numel()] = g.flatten() curr_idx += p.numel() # sync updates across devices. we are not memory-constrained so can do this simple deserialization dist.all_reduce(updates_flat, op=dist.ReduceOp.SUM) # deserialize and apply updates curr_idx = 0 for p in group['params']: g = updates_flat[curr_idx:curr_idx+p.numel()].view_as(p.data).type_as(p.data) p.data.add_(g, alpha=-lr) curr_idx += p.numel() # ----------------------------------------------------------------------------- # PyTorch nn.Module definitions for the GPT-2 model class Rotary(torch.nn.Module): def __init__(self, dim, base=10000): super().__init__() self.inv_freq = 1.0 / (base ** (torch.arange(0, dim, 2).float() / dim)) self.seq_len_cached = None self.cos_cached = None self.sin_cached = None def forward(self, x): seq_len = x.shape[1] if seq_len != self.seq_len_cached: self.seq_len_cached = seq_len t = torch.arange(seq_len, device=x.device).type_as(self.inv_freq) freqs = torch.outer(t, self.inv_freq).to(x.device) self.cos_cached = freqs.cos().bfloat16() self.sin_cached = freqs.sin().bfloat16() return self.cos_cached[None, :, None, :], self.sin_cached[None, :, None, :] def apply_rotary_emb(x, cos, sin): assert x.ndim == 4 # multihead attention d = x.shape[3]//2 x1 = x[..., :d] x2 = x[..., d:] y1 = x1 * cos + x2 * sin y2 = x1 * (-sin) + x2 * cos return torch.cat([y1, y2], 3).type_as(x) class CausalSelfAttention(nn.Module): def __init__(self, config): super().__init__() self.n_head = config.n_head self.n_embd = config.n_embd self.head_dim = self.n_embd // self.n_head assert self.n_embd % self.n_head == 0 self.c_q = nn.Linear(self.n_embd, self.n_embd, bias=False) self.c_k = nn.Linear(self.n_embd, self.n_embd, bias=False) self.c_v = nn.Linear(self.n_embd, self.n_embd, bias=False) # output projection self.c_proj = nn.Linear(self.n_embd, self.n_embd, bias=False) self.c_proj.weight.data.zero_() # zero init suggested by @Grad62304977 self.rotary = Rotary(self.head_dim) def forward(self, x): B, T, C = x.size() # batch size, sequence length, embedding dimensionality (n_embd) q = self.c_q(x).view(B, T, self.n_head, self.head_dim) k = self.c_k(x).view(B, T, self.n_head, self.head_dim) v = self.c_v(x).view(B, T, self.n_head, self.head_dim) cos, sin = self.rotary(q) q, k = F.rms_norm(q, (q.size(-1),)), F.rms_norm(k, (k.size(-1),)) # QK norm suggested by @Grad62304977 q, k = apply_rotary_emb(q, cos, sin), apply_rotary_emb(k, cos, sin) y = F.scaled_dot_product_attention(q.transpose(1, 2), k.transpose(1, 2), v.transpose(1, 2), is_causal=True) y = y.transpose(1, 2).contiguous().view_as(x) # re-assemble all head outputs side by side y = self.c_proj(y) return y class MLP(nn.Module): def __init__(self, config): super().__init__() self.c_fc = nn.Linear(config.n_embd, 4 * config.n_embd, bias=False) self.c_proj = nn.Linear(4 * config.n_embd, config.n_embd, bias=False) self.c_proj.weight.data.zero_() # zero init suggested by @Grad62304977 def forward(self, x): x = self.c_fc(x) x = F.relu(x).square() # https://arxiv.org/abs/2109.08668v2; ~1-2% better than GELU; suggested by @SKYLINEZ007 and @Grad62304977 x = self.c_proj(x) return x class Block(nn.Module): def __init__(self, config): super().__init__() self.attn = CausalSelfAttention(config) self.mlp = MLP(config) def forward(self, x): x = x + self.attn(F.rms_norm(x, (x.size(-1),))) x = x + self.mlp(F.rms_norm(x, (x.size(-1),))) return x # ----------------------------------------------------------------------------- # The main GPT-2 model @dataclass class GPTConfig: vocab_size : int = 50304 n_layer : int = 12 n_head : int = 6 # head dim 128 suggested by @Grad62304977 n_embd : int = 768 class GPT(nn.Module): def __init__(self, config): super().__init__() self.config = config self.transformer = nn.ModuleDict(dict( wte = nn.Embedding(config.vocab_size, config.n_embd), h = nn.ModuleList([Block(config) for _ in range(config.n_layer)]), )) self.lm_head = nn.Linear(config.n_embd, config.vocab_size, bias=False) self.transformer.wte.weight = self.lm_head.weight # https://paperswithcode.com/method/weight-tying def forward(self, idx, targets=None, return_logits=True): # forward the GPT model itself x = self.transformer.wte(idx) # token embeddings of shape (b, t, n_embd) for block in self.transformer.h: x = block(x) x = F.rms_norm(x, (x.size(-1),)) if targets is not None: # if we are given some desired targets also calculate the loss logits = self.lm_head(x) logits = logits.float() # use tf32/fp32 for logits loss = F.cross_entropy(logits.view(-1, logits.size(-1)), targets.view(-1), ignore_index=-1) else: # inference-time mini-optimization: only forward the lm_head on the very last position logits = self.lm_head(x[:, [-1], :]) # note: using list [-1] to preserve the time dim logits = logits.float() # use tf32/fp32 for logits loss = None # there are performance reasons why not returning logits is prudent, if not needed if not return_logits: logits = None return logits, loss # ----------------------------------------------------------------------------- # Our own simple Distributed Data Loader def _peek_data_shard(filename): # only reads the header, returns header data with open(filename, "rb") as f: # first read the header, which is 256 int32 integers (4 bytes each) header = np.frombuffer(f.read(256*4), dtype=np.int32) if header[0] != 20240520: print("ERROR: magic number mismatch in the data .bin file!") print("---> HINT: Are you passing in a correct file with --input_bin?") print("---> HINT: Dataset encoding changed recently, re-run data prepro or refer again to README") print("---> HINT: For example re-run: `python dev/data/tinyshakespeare.py`, then re-try") exit(1) assert header[1] == 1, "unsupported version" ntok = header[2] # number of tokens (claimed) return ntok # for now just return the number of tokens def _load_data_shard(filename): with open(filename, "rb") as f: # first read the header, which is 256 int32 integers (4 bytes each) header = np.frombuffer(f.read(256*4), dtype=np.int32) assert header[0] == 20240520, "magic number mismatch in the data .bin file" assert header[1] == 1, "unsupported version" ntok = header[2] # number of tokens (claimed) # the rest of it are tokens, stored as uint16 tokens = np.frombuffer(f.read(), dtype=np.uint16) assert len(tokens) == ntok, "number of tokens read does not match header?" return tokens class DistributedDataLoader: def __init__(self, filename_pattern, B, T, process_rank, num_processes): self.process_rank = process_rank self.num_processes = num_processes self.B = B self.T = T # glob files that match the pattern self.files = sorted(glob.glob(filename_pattern)) assert len(self.files) > 0, f"did not find any files that match the pattern {filename_pattern}" # load and validate all data shards, count number of tokens in total ntok_total = 0 for fname in self.files: shard_ntok = _peek_data_shard(fname) assert shard_ntok >= num_processes * B * T + 1 ntok_total += int(shard_ntok) self.ntok_total = ntok_total # kick things off self.reset() def reset(self): self.current_shard = 0 self.current_position = self.process_rank * self.B * self.T self.tokens = _load_data_shard(self.files[self.current_shard]) def advance(self): # advance to next data shard self.current_shard = (self.current_shard + 1) % len(self.files) self.current_position = self.process_rank * self.B * self.T self.tokens = _load_data_shard(self.files[self.current_shard]) def next_batch(self): B = self.B T = self.T buf = self.tokens[self.current_position : self.current_position+B*T+1] buf = torch.tensor(buf.astype(np.int32), dtype=torch.long) x = (buf[:-1]).view(B, T) # inputs y = (buf[1:]).view(B, T) # targets # advance current position and load next shard if necessary self.current_position += B * T * self.num_processes if self.current_position + (B * T * self.num_processes + 1) > len(self.tokens): self.advance() return x.cuda(), y.cuda() # ----------------------------------------------------------------------------- # int main @dataclass class Hyperparameters: # data hyperparams input_bin : str = 'data/fineweb10B/fineweb_train_*.bin' # input .bin to train on input_val_bin : str = 'data/fineweb10B/fineweb_val_*.bin' # input .bin to eval validation loss on # optimization hyperparams batch_size : int = 8*60 # batch size, in sequences, across all devices device_batch_size : int = 10 # batch size, in sequences, per device sequence_length : int = 1024 # sequence length, in tokens num_iterations : int = 2*10172 # number of iterations to run learning_rate : float = 0.0036 / 2 warmup_iters : int = 500 warmdown_iters : int = 2*2906 # number of iterations of linear warmup/warmdown for triangular or trapezoidal schedule weight_decay : float = 0 # evaluation and logging hyperparams val_loss_every : int = 125 # every how many steps to evaluate val loss? 0 for only at the end val_tokens : int = 10403840 # how many tokens of validation data? it's important to keep this fixed for consistent comparisons save_every : int = 0 # every how many steps to save the checkpoint? 0 for only at the end args = Hyperparameters() # set up DDP (distributed data parallel). torchrun sets this env variable assert torch.cuda.is_available() dist.init_process_group(backend='nccl') ddp_rank = int(os.environ['RANK']) ddp_local_rank = int(os.environ['LOCAL_RANK']) ddp_world_size = int(os.environ['WORLD_SIZE']) device = f'cuda:{ddp_local_rank}' torch.cuda.set_device(device) print(f"using device: {device}") master_process = (ddp_rank == 0) # this process will do logging, checkpointing etc. # convenience variables B, T = args.device_batch_size, args.sequence_length # calculate the number of steps to take in the val loop. assert args.val_tokens % (B * T * ddp_world_size) == 0 val_steps = args.val_tokens // (B * T * ddp_world_size) # calculate the steps of gradient accumulation required to attain the desired global batch size. assert args.batch_size % (B * ddp_world_size) == 0 train_accumulation_steps = args.batch_size // (B * ddp_world_size) # load tokens train_loader = DistributedDataLoader(args.input_bin, B, T, ddp_rank, ddp_world_size) val_loader = DistributedDataLoader(args.input_val_bin, B, T, ddp_rank, ddp_world_size) if master_process: print(f"Training DataLoader: total number of tokens: {train_loader.ntok_total} across {len(train_loader.files)} files") print(f"Validation DataLoader: total number of tokens: {val_loader.ntok_total} across {len(val_loader.files)} files") x, y = train_loader.next_batch() # there are only 50257 unique GPT-2 tokens; we extend to nearest multiple of 128 for efficiency. suggested to me by @Grad62304977. # this originates from Karpathy's experiments. num_vocab = 50304 model = GPT(GPTConfig(vocab_size=num_vocab, n_layer=52, n_head=12, n_embd=1536)) if master_process: print(sum(p.numel() for p in model.parameters())) model = model.cuda() if hasattr(config, "coordinate_descent_tuning"): config.coordinate_descent_tuning = True # suggested by @Chillee model = torch.compile(model) # here we wrap model into DDP container model = DDP(model, device_ids=[ddp_local_rank]) raw_model = model.module # always contains the "raw" unwrapped model ctx = torch.amp.autocast(device_type='cuda', dtype=torch.bfloat16) # init the optimizer(s) optimizer1 = torch.optim.AdamW(raw_model.lm_head.parameters(), lr=args.learning_rate, betas=(0.9, 0.95), weight_decay=args.weight_decay, fused=True) optimizer2 = torch.optim.AdamW(raw_model.transformer.h.parameters(), lr=0.5*args.learning_rate, betas=(0.9, 0.95), weight_decay=args.weight_decay, fused=True) optimizers = [optimizer1, optimizer2] # learning rate decay scheduler (linear warmup and warmdown) def get_lr(it): assert it <= args.num_iterations # 1) linear warmup for warmup_iters steps if it < args.warmup_iters: return (it+1) / args.warmup_iters # 2) constant lr for a while elif it < args.num_iterations - args.warmdown_iters: return 1.0 # 3) linear warmdown else: decay_ratio = (args.num_iterations - it) / args.warmdown_iters return decay_ratio schedulers = [torch.optim.lr_scheduler.LambdaLR(opt, get_lr) for opt in optimizers] # begin logging if master_process: run_id = str(uuid.uuid4()) logdir = 'logs/%s/' % run_id os.makedirs(logdir, exist_ok=True) logfile = 'logs/%s.txt' % run_id # create the log file with open(logfile, "w") as f: # begin the log by printing this file (the Python code) f.write('='*100 + '\n') f.write(code) f.write('='*100 + '\n') # log information about the hardware/software environment this is running on # and print the full `nvidia-smi` to file f.write(f"Running pytorch {torch.version.__version__} compiled for CUDA {torch.version.cuda}\nnvidia-smi:\n") import subprocess result = subprocess.run(['nvidia-smi'], stdout=subprocess.PIPE, stderr=subprocess.PIPE, text=True) f.write(f'{result.stdout}\n') f.write('='*100 + '\n') training_time_ms = 0 # start the clock torch.cuda.synchronize() t0 = time.time() # begin training train_loader.reset() for step in range(args.num_iterations + 1): last_step = (step == args.num_iterations) # This effectively ignores timing first 10 steps, which are slower for weird reasons. # Alternately, and slightly more correctly in terms of benchmarking, we could do 10 # steps with dummy data first, and then re-initialize the model and reset the loader. if step == 10: training_time_ms = 0 t0 = time.time() timed_steps = float('nan') if step <= 11 else (step - 10) + 1 # <= 11 to avoid bug in val # once in a while evaluate the validation dataset if (last_step or (args.val_loss_every > 0 and step % args.val_loss_every == 0)): # stop the clock torch.cuda.synchronize() training_time_ms += 1000 * (time.time() - t0) # run validation batches model.eval() val_loader.reset() val_loss = 0.0 for _ in range(val_steps): x_val, y_val = val_loader.next_batch() with ctx: # of course, we'd like to use no_grad() here too, but that creates a torch.compile error for some reason _, loss = model(x_val, y_val, return_logits=False) val_loss += loss.detach() del loss dist.all_reduce(val_loss, op=dist.ReduceOp.AVG) val_loss /= val_steps # log val loss to console and to logfile if master_process: print(f'step:{step}/{args.num_iterations} val_loss:{val_loss:.4f} train_time:{training_time_ms:.0f}ms step_avg:{training_time_ms/(timed_steps-1):.2f}ms') with open(logfile, "a") as f: f.write(f'step:{step}/{args.num_iterations} val_loss:{val_loss:.4f} train_time:{training_time_ms:.0f}ms step_avg:{training_time_ms/(timed_steps-1):.2f}ms\n') # start the clock again torch.cuda.synchronize() t0 = time.time() if master_process and (last_step or (args.save_every > 0 and step % args.save_every == 0)): # stop the clock torch.cuda.synchronize() training_time_ms += 1000 * (time.time() - t0) # save the state of the training process log = dict(step=step, code=code, model=raw_model.state_dict(), optimizers=[opt.state_dict() for opt in optimizers]) torch.save(log, 'logs/%s/state_step%06d.pt' % (run_id, step)) # start the clock again torch.cuda.synchronize() t0 = time.time() # bit confusing: we want to make sure to eval on 0th iteration # but also after the very last iteration. so we loop for step <= num_iterations # instead of just < num_iterations (one extra due to <=), only to do # the validation/sampling one last time, and then we break right here as we're done. if last_step: break # --------------- TRAINING SECTION BEGIN ----------------- model.train() for i in range(1, train_accumulation_steps+1): # forward pass with ctx: _, loss = model(x, y, return_logits=False) train_loss = loss.detach() # advance the dataset for the next batch x, y = train_loader.next_batch() # backward pass if i < train_accumulation_steps: with model.no_sync(): # there's no need to sync gradients every accumulation step loss.backward() else: loss.backward() # just sync on the last step for p in model.parameters(): p.grad /= train_accumulation_steps # step the optimizers and schedulers for opt, sched in zip(optimizers, schedulers): opt.step() sched.step() # null the gradients model.zero_grad(set_to_none=True) # --------------- TRAINING SECTION END ------------------- # everything that follows now is just diagnostics, prints, logging, etc. #dist.all_reduce(train_loss, op=dist.ReduceOp.AVG) # all-reducing the training loss would be more correct in terms of logging, but slower if master_process: approx_time = training_time_ms + 1000 * (time.time() - t0) print(f"step:{step+1}/{args.num_iterations} train_loss:{train_loss.item():.4f} train_time:{approx_time:.0f}ms step_avg:{approx_time/timed_steps:.2f}ms") with open(logfile, "a") as f: f.write(f"step:{step+1}/{args.num_iterations} train_loss:{train_loss.item():.4f} train_time:{approx_time:.0f}ms step_avg:{approx_time/timed_steps:.2f}ms\n") if master_process: print(f"peak memory consumption: {torch.cuda.max_memory_allocated() // 1024 // 1024} MiB") # ------------------------------------------------------------------------- # clean up nice dist.destroy_process_group() ==================================================================================================== Running pytorch 2.4.1+cu121 compiled for CUDA 12.1 nvidia-smi: Wed Oct 16 02:54:21 2024 +-----------------------------------------------------------------------------------------+ | NVIDIA-SMI 555.42.06 Driver Version: 555.42.06 CUDA Version: 12.5 | |-----------------------------------------+------------------------+----------------------+ | GPU Name Persistence-M | Bus-Id Disp.A | Volatile Uncorr. ECC | | Fan Temp Perf Pwr:Usage/Cap | Memory-Usage | GPU-Util Compute M. | | | | MIG M. | |=========================================+========================+======================| | 0 NVIDIA H100 80GB HBM3 Off | 00000000:18:00.0 Off | 0 | | N/A 29C P0 117W / 700W | 19390MiB / 81559MiB | 14% Default | | | | Disabled | +-----------------------------------------+------------------------+----------------------+ | 1 NVIDIA H100 80GB HBM3 Off | 00000000:2A:00.0 Off | 0 | | N/A 32C P0 122W / 700W | 21706MiB / 81559MiB | 22% Default | | | | Disabled | +-----------------------------------------+------------------------+----------------------+ | 2 NVIDIA H100 80GB HBM3 Off | 00000000:3A:00.0 Off | 0 | | N/A 33C P0 120W / 700W | 19438MiB / 81559MiB | 14% Default | | | | Disabled | +-----------------------------------------+------------------------+----------------------+ | 3 NVIDIA H100 80GB HBM3 Off | 00000000:5D:00.0 Off | 0 | | N/A 30C P0 121W / 700W | 19438MiB / 81559MiB | 11% Default | | | | Disabled | +-----------------------------------------+------------------------+----------------------+ | 4 NVIDIA H100 80GB HBM3 Off | 00000000:84:00.0 Off | 0 | | N/A 29C P0 119W / 700W | 19186MiB / 81559MiB | 0% Default | | | | Disabled | +-----------------------------------------+------------------------+----------------------+ | 5 NVIDIA H100 80GB HBM3 Off | 00000000:8B:00.0 Off | 0 | | N/A 33C P0 123W / 700W | 19258MiB / 81559MiB | 1% Default | | | | Disabled | +-----------------------------------------+------------------------+----------------------+ | 6 NVIDIA H100 80GB HBM3 Off | 00000000:91:00.0 Off | 0 | | N/A 31C P0 119W / 700W | 19258MiB / 81559MiB | 0% Default | | | | Disabled | +-----------------------------------------+------------------------+----------------------+ | 7 NVIDIA H100 80GB HBM3 Off | 00000000:E4:00.0 Off | 0 | | N/A 29C P0 122W / 700W | 19198MiB / 81559MiB | 0% Default | | | | Disabled | +-----------------------------------------+------------------------+----------------------+ +-----------------------------------------------------------------------------------------+ | Processes: | | GPU GI CI PID Type Process name GPU Memory | | ID ID Usage | |=========================================================================================| | 0 N/A N/A 19126 C /usr/bin/python3 0MiB | | 1 N/A N/A 19127 C /usr/bin/python3 0MiB | | 2 N/A N/A 19128 C /usr/bin/python3 0MiB | | 3 N/A N/A 19129 C /usr/bin/python3 0MiB | | 4 N/A N/A 19130 C /usr/bin/python3 0MiB | | 5 N/A N/A 19131 C /usr/bin/python3 0MiB | | 6 N/A N/A 19132 C /usr/bin/python3 0MiB | | 7 N/A N/A 19133 C /usr/bin/python3 0MiB | +-----------------------------------------------------------------------------------------+ ==================================================================================================== step:0/20344 val_loss:22.6137 train_time:278ms step_avg:nanms step:1/20344 train_loss:22.6211 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