





'''simple docstring'''




import math
import os
import re
import sys
import unittest
from pathlib import Path
from typing import Tuple
from unittest.mock import patch

from parameterized import parameterized

from transformers.testing_utils import (
    CaptureStderr,
    ExtendSysPath,
    TestCasePlus,
    execute_subprocess_async,
    get_gpu_count,
    get_torch_dist_unique_port,
    require_apex,
    require_bitsandbytes,
    require_fairscale,
    require_torch,
    require_torch_gpu,
    require_torch_multi_gpu,
    require_torch_non_multi_gpu,
    slow,
)
from transformers.trainer_callback import TrainerState
from transformers.trainer_utils import set_seed


__UpperCAmelCase            =       os.path.abspath(os.path.dirname(__file__))
with ExtendSysPath(f'''{bindir}/../../examples/pytorch/translation'''):
							from run_translation import main  # noqa


set_seed(42)
__UpperCAmelCase            =       """sshleifer/student_marian_en_ro_6_1"""
__UpperCAmelCase            =       """sshleifer/tiny-mbart"""




@require_torch
class      UpperCamelCase__					(					lowercase_			):




					"""simple docstring"""


					def lowerCamelCase_			(						self				:			List[Any]      ,						lowerCamelCase_				:			List[Any]=False      ,						lowerCamelCase_				:			Tuple=None      ,						lowerCamelCase_				:			Optional[Any]=True      ,						lowerCamelCase_				:			Dict=True      ,						lowerCamelCase_				:			Optional[int]=True      ,						lowerCamelCase_				:			List[Any]=True      ,						):

							'''simple docstring'''



							SCREAMING_SNAKE_CASE :				List[Any]		=			self.run_trainer(
							    eval_steps=1      ,						max_len=12      ,						model_name=lowerCamelCase_      ,						num_train_epochs=1      ,						distributed=lowerCamelCase_      ,						extra_args_str=lowerCamelCase_      ,						predict_with_generate=lowerCamelCase_      ,						do_train=lowerCamelCase_      ,						do_eval=lowerCamelCase_      ,						do_predict=lowerCamelCase_      ,						)
							SCREAMING_SNAKE_CASE :				Tuple		=			TrainerState.load_from_json(os.path.join(lowerCamelCase_      ,						"""trainer_state.json"""						)						).log_history

							if not do_eval:
									return

							SCREAMING_SNAKE_CASE :				List[Any]		=			[log for log in logs if """eval_loss""" in log.keys()]

							SCREAMING_SNAKE_CASE :				List[Any]		=			eval_metrics[0]
							if predict_with_generate:
									assert "eval_bleu" in first_step_stats

									SCREAMING_SNAKE_CASE :				Any		=			eval_metrics[-1]
									assert isinstance(last_step_stats["""eval_bleu"""]      ,						lowerCamelCase_						)
									assert not math.isnan(float(last_step_stats["""eval_loss"""]						)						), "eval_loss must not be `nan`"


					@require_torch_non_multi_gpu
					def lowerCamelCase_			(						self				:			Union[str, Any]						):

							'''simple docstring'''



							self.run_seqaseq_quick()


					@require_torch_multi_gpu
					def lowerCamelCase_			(						self				:			Tuple						):

							'''simple docstring'''



							self.run_seqaseq_quick(distributed=lowerCamelCase_						)


					@require_torch_multi_gpu
					def lowerCamelCase_			(						self				:			Any						):

							'''simple docstring'''



							self.run_seqaseq_quick(distributed=lowerCamelCase_						)


					@unittest.skip("""Requires an update of the env running those tests"""						)
					@require_torch_multi_gpu
					@require_fairscale
					def lowerCamelCase_			(						self				:			List[str]						):

							'''simple docstring'''



							self.run_seqaseq_quick(distributed=lowerCamelCase_      ,						extra_args_str="""--sharded_ddp simple"""						)


					@unittest.skip("""Requires an update of the env running those tests"""						)
					@require_torch_multi_gpu
					@require_fairscale
					def lowerCamelCase_			(						self				:			str						):

							'''simple docstring'''



							self.run_seqaseq_quick(distributed=lowerCamelCase_      ,						extra_args_str="""--sharded_ddp simple --fp16"""						)


					@unittest.skip("""Requires an update of the env running those tests"""						)
					@require_torch_multi_gpu
					@require_fairscale
					def lowerCamelCase_			(						self				:			Union[str, Any]						):

							'''simple docstring'''



							self.run_seqaseq_quick(distributed=lowerCamelCase_      ,						extra_args_str="""--sharded_ddp zero_dp_2"""      ,						predict_with_generate=lowerCamelCase_						)


					@unittest.skip("""Requires an update of the env running those tests"""						)
					@require_torch_multi_gpu
					@require_fairscale
					def lowerCamelCase_			(						self				:			Union[str, Any]						):

							'''simple docstring'''



							self.run_seqaseq_quick(
							    distributed=lowerCamelCase_      ,						extra_args_str="""--sharded_ddp zero_dp_2 --fp16"""      ,						predict_with_generate=lowerCamelCase_						)


					@require_apex
					@require_torch_gpu
					def lowerCamelCase_			(						self				:			List[Any]						):

							'''simple docstring'''



							self.run_seqaseq_quick(distributed=lowerCamelCase_      ,						extra_args_str="""--fp16 --fp16_backend=apex"""						)
							# test 2nd time - was getting eval_loss': nan'
							# to reproduce the problem set distributed=False
							self.run_seqaseq_quick(distributed=lowerCamelCase_      ,						extra_args_str="""--fp16 --fp16_backend=apex"""						)


					@parameterized.expand(["""base""", """low""", """high""", """mixed"""]						)
					@require_torch_multi_gpu
					def lowerCamelCase_			(						self				:			Tuple      ,						lowerCamelCase_				:			Union[str, Any]						):

							'''simple docstring'''



							SCREAMING_SNAKE_CASE :				Optional[int]		=			{
							    # test with the default log_level - should be info and thus log info once
							    """base""": {"""extra_args_str""": """""", """n_matches""": 1},
							    # test with low log_level and log_level_replica - should be noisy on all processes
							    # now the info string should appear twice on 2 processes
							    """low""": {"""extra_args_str""": """--log_level debug --log_level_replica debug""", """n_matches""": 2},
							    # test with high log_level and low log_level_replica
							    # now the info string should appear once only on the replica
							    """high""": {"""extra_args_str""": """--log_level error --log_level_replica debug""", """n_matches""": 1},
							    # test with high log_level and log_level_replica - should be quiet on all processes
							    """mixed""": {"""extra_args_str""": """--log_level error --log_level_replica error""", """n_matches""": 0},
							}

							SCREAMING_SNAKE_CASE :				List[Any]		=			experiments[experiment_id]
							SCREAMING_SNAKE_CASE :				Dict		=			{"""distributed""": True, """predict_with_generate""": False, """do_eval""": False, """do_predict""": False}
							SCREAMING_SNAKE_CASE :				Optional[int]		=			"""Running training"""
							with CaptureStderr() as cl:
									self.run_seqaseq_quick(**lowerCamelCase_      ,						extra_args_str=data["""extra_args_str"""]						)
							SCREAMING_SNAKE_CASE :				Dict		=			len(re.findall(lowerCamelCase_      ,						cl.err						)						)
							self.assertEqual(lowerCamelCase_      ,						data["""n_matches"""]						)


					@slow
					def lowerCamelCase_			(						self				:			List[Any]						):

							'''simple docstring'''



							SCREAMING_SNAKE_CASE :				Dict		=			self.run_trainer(
							    eval_steps=2      ,						max_len=1_28      ,						model_name=lowerCamelCase_      ,						learning_rate=3e-4      ,						num_train_epochs=10      ,						distributed=lowerCamelCase_      ,						)

							# Check metrics
							SCREAMING_SNAKE_CASE :				Union[str, Any]		=			TrainerState.load_from_json(os.path.join(lowerCamelCase_      ,						"""trainer_state.json"""						)						).log_history
							SCREAMING_SNAKE_CASE :				Union[str, Any]		=			[log for log in logs if """eval_loss""" in log.keys()]
							SCREAMING_SNAKE_CASE :				int		=			eval_metrics[0]
							SCREAMING_SNAKE_CASE :				List[str]		=			eval_metrics[-1]

							assert first_step_stats["eval_loss"] > last_step_stats["eval_loss"], "model learned nothing"
							assert isinstance(last_step_stats["""eval_bleu"""]      ,						lowerCamelCase_						)

							# test if do_predict saves generations and metrics
							SCREAMING_SNAKE_CASE :				Optional[int]		=			os.listdir(lowerCamelCase_						)
							SCREAMING_SNAKE_CASE :				List[str]		=			{os.path.basename(lowerCamelCase_						) for p in contents}
							assert "generated_predictions.txt" in contents
							assert "predict_results.json" in contents


					@slow
					@require_bitsandbytes
					def lowerCamelCase_			(						self				:			List[Any]						):

							'''simple docstring'''



							from transformers.training_args import OptimizerNames

							def train_and_return_metrics(lowerCamelCase_				:			str						) -> Tuple[int, float]:
									SCREAMING_SNAKE_CASE :				Optional[int]		=			"""--skip_memory_metrics 0"""

									SCREAMING_SNAKE_CASE :				Tuple		=			self.run_trainer(
									    max_len=1_28      ,						model_name=lowerCamelCase_      ,						learning_rate=3e-4      ,						num_train_epochs=1      ,						optim=lowerCamelCase_      ,						distributed=lowerCamelCase_      ,						extra_args_str=lowerCamelCase_      ,						do_eval=lowerCamelCase_      ,						do_predict=lowerCamelCase_      ,						n_gpus_to_use=1      ,						)

									# Check metrics
									SCREAMING_SNAKE_CASE :				str		=			TrainerState.load_from_json(Path(lowerCamelCase_      ,						"""trainer_state.json"""						)						).log_history
									SCREAMING_SNAKE_CASE :				Any		=			int(logs[0]["""train_mem_gpu_peaked_delta"""] / 2**20						)
									SCREAMING_SNAKE_CASE :				str		=			int(logs[0]["""train_mem_gpu_alloc_delta"""] / 2**20						)

									SCREAMING_SNAKE_CASE :				Optional[int]		=			logs[0]["""train_loss"""]
									return gpu_peak_mem_mb, gpu_alloc_mem_mb, loss

							SCREAMING_SNAKE_CASE,							SCREAMING_SNAKE_CASE,							SCREAMING_SNAKE_CASE :				Tuple		=			train_and_return_metrics(OptimizerNames.ADAMW_TORCH.value						)
							SCREAMING_SNAKE_CASE,							SCREAMING_SNAKE_CASE,							SCREAMING_SNAKE_CASE :				Optional[int]		=			train_and_return_metrics(OptimizerNames.ADAMW_BNB.value						)

							SCREAMING_SNAKE_CASE :				Optional[Any]		=			gpu_alloc_mem_orig - gpu_alloc_mem_bnb

							SCREAMING_SNAKE_CASE :				int		=			gpu_peak_mem_orig + gpu_alloc_mem_orig
							SCREAMING_SNAKE_CASE :				Optional[Any]		=			gpu_peak_mem_bnb + gpu_alloc_mem_bnb
							SCREAMING_SNAKE_CASE :				Optional[int]		=			gpu_total_mem_orig - gpu_total_mem_bnb

							# sshleifer/student_marian_en_ro_6_1 has 54M parameter, 29M of which is `nn.Embedding` which
							# doesn't get quantized and remains in fp32. Therefore we only have 25M parameters quantized
							# in 2 bytes and the diff in optim memory usage is derived as so:
							#
							# - normal 25*8=~200MB (8 bytes per param)
							# - bnb    25*2= ~50MB (2 bytes per param)
							#
							# Thus we should expect ~150MB total memory saved.
							#
							# Peak memory should be the same - the total should be different by about that same margin
							#
							# After leaving a small margin to accommodate for differences between gpus let's check
							# that we have at least 120MB in savings
							SCREAMING_SNAKE_CASE :				Tuple		=			1_20

							# uncomment the following if this test starts failing - requires py38 for a new print feature
							# gpu_peak_mem_diff = gpu_peak_mem_orig - gpu_peak_mem_bnb
							# print(f"{gpu_alloc_mem_orig=}MB {gpu_peak_mem_orig=}MB {gpu_alloc_mem_orig+gpu_peak_mem_orig=}MB")
							# print(f" {gpu_alloc_mem_bnb=}MB  {gpu_peak_mem_bnb=}MB  {gpu_alloc_mem_bnb+gpu_peak_mem_bnb=}MB")
							# print(f"{gpu_alloc_mem_diff=}MB")
							# print(f"{gpu_peak_mem_diff=}MB")
							# print(f"{gpu_total_mem_orig=}MB, {gpu_total_mem_bnb=}MB")
							# print(f"{gpu_total_mem_diff=}MB, {gpu_total_mem_diff=}MB")

							self.assertGreater(
							    lowerCamelCase_      ,						lowerCamelCase_      ,						"""should use ~150MB less alloc gpu memory with BNB, compared to without it for this model but got"""
							    f''' a difference of {gpu_alloc_mem_diff}MB, with gpu_alloc_mem_orig={gpu_alloc_mem_orig}MB and'''
							    f''' gpu_alloc_mem_bnb={gpu_alloc_mem_bnb}MB'''      ,						)

							self.assertGreater(
							    lowerCamelCase_      ,						lowerCamelCase_      ,						"""should use ~150MB less total gpu memory with BNB, compared to without it for this model but got"""
							    f''' a difference of {gpu_total_mem_diff}MB, with gpu_total_mem_orig={gpu_total_mem_orig}MB and'''
							    f''' gpu_total_mem_bnb={gpu_total_mem_bnb}MB'''      ,						)

							self.assertEqual(
							    lowerCamelCase_      ,						lowerCamelCase_      ,						f'''loss should be the same, but got loss_orig={loss_orig}, loss_bnb={loss_bnb}'''						)



					def lowerCamelCase_			(						self				:			List[str]      ,						lowerCamelCase_				:			int      ,						lowerCamelCase_				:			str      ,						lowerCamelCase_				:			int      ,						lowerCamelCase_				:			float = 3e-3      ,						lowerCamelCase_				:			str = "adafactor"      ,						lowerCamelCase_				:			bool = False      ,						lowerCamelCase_				:			str = None      ,						lowerCamelCase_				:			int = 0      ,						lowerCamelCase_				:			bool = True      ,						lowerCamelCase_				:			bool = True      ,						lowerCamelCase_				:			bool = True      ,						lowerCamelCase_				:			bool = True      ,						lowerCamelCase_				:			int = None      ,						):

							'''simple docstring'''



							SCREAMING_SNAKE_CASE :				int		=			self.test_file_dir / """../fixtures/tests_samples/wmt_en_ro"""
							SCREAMING_SNAKE_CASE :				Any		=			self.get_auto_remove_tmp_dir()
							SCREAMING_SNAKE_CASE :				Optional[Any]		=			f'''
            --model_name_or_path {model_name}
            --train_file {data_dir}/train.json
            --validation_file {data_dir}/val.json
            --test_file {data_dir}/test.json
            --output_dir {output_dir}
            --overwrite_output_dir
            --max_train_samples 8
            --max_source_length {max_len}
            --max_target_length {max_len}
            --do_train
            --num_train_epochs {str(lowerCamelCase_						)}
            --per_device_train_batch_size 4
            --learning_rate {learning_rate}
            --warmup_steps 8
            --logging_steps 0
            --logging_strategy no
            --save_steps {str(lowerCamelCase_						)}
            --group_by_length
            --label_smoothing_factor 0.1
            --target_lang ro_RO
            --source_lang en_XX
        '''.split()

							SCREAMING_SNAKE_CASE :				List[Any]		=			f'''
            --do_eval
            --per_device_eval_batch_size 4
            --max_eval_samples 8
            --val_max_target_length {max_len}
            --evaluation_strategy steps
            --eval_steps {str(lowerCamelCase_						)}
        '''.split()

							SCREAMING_SNAKE_CASE :				List[Any]		=			"""
            --do_predict
        """.split()

							SCREAMING_SNAKE_CASE :				Union[str, Any]		=			[]
							if do_train:
									args += args_train

							if do_eval:
									args += args_eval

							if do_predict:
									args += args_predict

							if predict_with_generate:
									args += "--predict_with_generate".split()

							if do_train:
									if optim == "adafactor":
											args += "--adafactor".split()
									else:
											args += f'''--optim {optim}'''.split()

							if extra_args_str is not None:
									args += extra_args_str.split()

							if distributed:
									if n_gpus_to_use is None:
											SCREAMING_SNAKE_CASE :				Optional[Any]		=			get_gpu_count()
									SCREAMING_SNAKE_CASE :				int		=			get_torch_dist_unique_port()
									SCREAMING_SNAKE_CASE :				List[str]		=			f'''
                -m torch.distributed.run
                --nproc_per_node={n_gpus_to_use}
                --master_port={master_port}
                {self.examples_dir_str}/pytorch/translation/run_translation.py
            '''.split()
									SCREAMING_SNAKE_CASE :				Dict		=			[sys.executable] + distributed_args + args
									# keep for quick debug
									# print(" ".join([f"\nPYTHONPATH={self.src_dir_str}"] +cmd)); die
									execute_subprocess_async(lowerCamelCase_      ,						env=self.get_env()						)
							else:
									SCREAMING_SNAKE_CASE :				List[Any]		=			["""run_translation.py"""] + args
									with patch.object(lowerCamelCase_      ,						"""argv"""      ,						lowerCamelCase_						):
											main()

							return output_dir










'''simple docstring'''




from math import sqrt



def 		__A		(  lowerCamelCase_	):


		"""simple docstring"""



		SCREAMING_SNAKE_CASE :				str		=			0
		for i in range(1			,			int(sqrt(lowerCamelCase_	) + 1	)	):
				if n % i == 0 and i != sqrt(lowerCamelCase_	):
						total += i + n // i
				elif i == sqrt(lowerCamelCase_	):
						total += i
		return total - n



def 		__A		(  lowerCamelCase_ = 1_00_00	):


		"""simple docstring"""



		SCREAMING_SNAKE_CASE :				str		=			sum(
		    i
		    for i in range(1			,			lowerCamelCase_	)
		    if sum_of_divisors(sum_of_divisors(lowerCamelCase_	)	) == i and sum_of_divisors(lowerCamelCase_	) != i	)
		return total


if __name__ == "__main__":
							print(solution(int(str(input()).strip())))



