


import os
import random
from pathlib import Path
from typing import List

import numpy as np
import torch
from torch.cuda.amp import GradScaler

from .utils import (
    MODEL_NAME,
    OPTIMIZER_NAME,
    RNG_STATE_NAME,
    SCALER_NAME,
    SCHEDULER_NAME,
    get_pretty_name,
    is_tpu_available,
    is_xpu_available,
    save,
)


if is_tpu_available(check_device=False):
   import torch_xla.core.xla_model as xm

from .logging import get_logger
from .state import PartialState


SCREAMING_SNAKE_CASE				:						List[Any]			   = get_logger(__name__)




def 			UpperCamelCase			(					_a				,						_a				,						_a				,						_a				,						_a				,						_a = None				,						)    ->							Any:
     '''simple docstring'''





     for i, state in enumerate(_a						):
          lowercase_				:List[Any]       			=				f"{MODEL_NAME}.bin" if i == 0 else f"{MODEL_NAME}_{i}.bin"
          lowercase_				:List[Any]       			=				os.path.join(_a				,						_a						)
          save(_a				,						_a						)
          logger.info(f"Model weights saved in {output_model_file}"						)
     # Optimizer states
     for i, opt in enumerate(_a						):
          lowercase_				:Tuple       			=				opt.state_dict()
          lowercase_				:Optional[int]       			=				f"{OPTIMIZER_NAME}.bin" if i == 0 else f"{OPTIMIZER_NAME}_{i}.bin"
          lowercase_				:Tuple       			=				os.path.join(_a				,						_a						)
          save(_a				,						_a						)
          logger.info(f"Optimizer state saved in {output_optimizer_file}"						)
     # Scheduler states
     for i, scheduler in enumerate(_a						):
          lowercase_				:Optional[int]       			=				scheduler.state_dict()
          lowercase_				:int       			=				f"{SCHEDULER_NAME}.bin" if i == 0 else f"{SCHEDULER_NAME}_{i}.bin"
          lowercase_				:Optional[int]       			=				os.path.join(_a				,						_a						)
          save(_a				,						_a						)
          logger.info(f"Scheduler state saved in {output_scheduler_file}"						)
     # GradScaler state
     if scaler is not None:
          lowercase_				:Tuple       			=				scaler.state_dict()
          lowercase_				:Optional[int]       			=				os.path.join(_a				,						_a						)
          torch.save(_a				,						_a						)
          logger.info(f"Gradient scaler state saved in {output_scaler_file}"						)
     # Random number generator states
     lowercase_				:Tuple       			=				{}
     lowercase_				:Optional[Any]       			=				f"{RNG_STATE_NAME}_{process_index}.pkl"
     lowercase_				:Union[str, Any]       			=				random.getstate()
     lowercase_				:Optional[Any]       			=				np.random.get_state()
     lowercase_				:List[Any]       			=				torch.get_rng_state()
     if is_xpu_available():
          lowercase_				:List[Any]       			=				torch.xpu.get_rng_state_all()
     else:
          lowercase_				:Optional[Any]       			=				torch.cuda.get_rng_state_all()
     if is_tpu_available():
          lowercase_				:str       			=				xm.get_rng_state()
     lowercase_				:int       			=				os.path.join(_a				,						_a						)
     torch.save(_a				,						_a						)
     logger.info(f"Random states saved in {output_states_file}"						)
     return output_dir




def 			UpperCamelCase			(					_a				,						_a				,						_a				,						_a				,						_a				,						_a=None				,						_a=None				,						**_a				,						)    ->							Union[str, Any]:
     '''simple docstring'''





     if map_location not in [None, "cpu", "on_device"]:
          raise TypeError(
              '''Unsupported optimizer map location passed, please choose one of `None`, `\'cpu\'`, or `\'on_device\'`'''						)
     if map_location is None:
          lowercase_				:str       			=				'''cpu'''
     elif map_location == "on_device":
          lowercase_				:Tuple       			=				PartialState().device
     # Model states
     for i, model in enumerate(_a						):
          lowercase_				:Optional[int]       			=				f"{MODEL_NAME}.bin" if i == 0 else f"{MODEL_NAME}_{i}.bin"
          lowercase_				:Union[str, Any]       			=				os.path.join(_a				,						_a						)
          models[i].load_state_dict(torch.load(_a				,						map_location=_a						)				,						**_a						)
     logger.info('''All model weights loaded successfully'''						)

     # Optimizer states
     for i, opt in enumerate(_a						):
          lowercase_				:int       			=				f"{OPTIMIZER_NAME}.bin" if i == 0 else f"{OPTIMIZER_NAME}_{i}.bin"
          lowercase_				:int       			=				os.path.join(_a				,						_a						)
          lowercase_				:int       			=				torch.load(_a				,						map_location=_a						)
          optimizers[i].load_state_dict(_a						)
     logger.info('''All optimizer states loaded successfully'''						)

     # Scheduler states
     for i, scheduler in enumerate(_a						):
          lowercase_				:Optional[int]       			=				f"{SCHEDULER_NAME}.bin" if i == 0 else f"{SCHEDULER_NAME}_{i}.bin"
          lowercase_				:str       			=				os.path.join(_a				,						_a						)
          scheduler.load_state_dict(torch.load(_a						)						)
     logger.info('''All scheduler states loaded successfully'''						)

     # GradScaler state
     if scaler is not None:
          lowercase_				:Dict       			=				os.path.join(_a				,						_a						)
          scaler.load_state_dict(torch.load(_a						)						)
          logger.info('''GradScaler state loaded successfully'''						)

     # Random states
     try:
          lowercase_				:Dict       			=				torch.load(os.path.join(_a				,						f"{RNG_STATE_NAME}_{process_index}.pkl"						)						)
          random.setstate(states['''random_state''']						)
          np.random.set_state(states['''numpy_random_seed''']						)
          torch.set_rng_state(states['''torch_manual_seed''']						)
          if is_xpu_available():
               torch.xpu.set_rng_state_all(states['''torch_xpu_manual_seed''']						)
          else:
               torch.cuda.set_rng_state_all(states['''torch_cuda_manual_seed''']						)
          if is_tpu_available():
               xm.set_rng_state(states['''xm_seed''']						)
          logger.info('''All random states loaded successfully'''						)
     except Exception:
          logger.info('''Could not load random states'''						)




def 			UpperCamelCase			(					_a				,						_a				,						_a = 0						)    ->							Optional[int]:
     '''simple docstring'''





     lowercase_				:Tuple       			=				Path(_a						) / f"custom_checkpoint_{index}.pkl"
     logger.info(f"Saving the state of {get_pretty_name(_a						)} to {save_location}"						)
     torch.save(obj.state_dict()				,						_a						)




def 			UpperCamelCase			(					_a				,						_a				,						_a = 0						)    ->							Union[str, Any]:
     '''simple docstring'''





     lowercase_				:int       			=				f"{path}/custom_checkpoint_{index}.pkl"
     logger.info(f"Loading the state of {get_pretty_name(_a						)} from {load_location}"						)
     obj.load_state_dict(torch.load(_a				,						map_location='''cpu'''						)						)



"""simple docstring"""

from math import floor, sqrt




def 			lowercase__  (    lowerCAmelCase :    int       )       ->					int:






    """simple docstring"""




    UpperCAmelCase  	=    0.0
    UpperCAmelCase  	=    1.0
    UpperCAmelCase  	=    int(sqrt(lowerCAmelCase       )       )
    UpperCAmelCase  	=    root
    UpperCAmelCase  	=    0
    while integer_part != 2 * root:
        UpperCAmelCase  	=    denominator * integer_part - numerator
        UpperCAmelCase  	=    (n - numerator**2) / denominator
        UpperCAmelCase  	=    int((root + numerator) / denominator       )
        period += 1
    return period




def 			lowercase__  (    lowerCAmelCase :    int = 10_000       )       ->					int:






    """simple docstring"""




    UpperCAmelCase  	=    0
    for i in range(2       , n + 1       ):
        UpperCAmelCase  	=    sqrt(lowerCAmelCase       )
        if sr - floor(lowerCAmelCase       ) != 0 and continuous_fraction_period(lowerCAmelCase       ) % 2 == 1:
            count_odd_periods += 1
    return count_odd_periods


if __name__ == "__main__":
   print(F'{solution(int(input().strip()))}')



