

def  UpperCAmelCase__      ( UpperCAmelCase__ = 10_00			)     ->     int:
       A_		   = -1
       A_		   = 0
       for a in range(1,    n // 3			):
              # Solving the two equations a**2+b**2=c**2 and a+b+c=N eliminating c
              A_		   = (n * n - 2 * a * n) // (2 * n - 2 * a)
              A_		   = n - a - b
              if c * c == (a * a + b * b):
                     A_		   = a * b * c
                     if candidate >= product:
                            A_		   = candidate
       return product


if __name__ == "__main__":
      print(f"""{solution() = }""")



'''simple docstring'''







import json
import logging
import os
import socket

import git
import numpy as np
import torch


logging.basicConfig(
    format='''%(asctime)s - %(levelname)s - %(name)s - PID: %(process)d -  %(message)s''',
    datefmt='''%m/%d/%Y %H:%M:%S''',
    level=logging.INFO,
)
__lowerCamelCase						    =      logging.getLogger(__name__)
def  UpperCAmelCase__      ( UpperCAmelCase__			)     ->     int:
       A_		   = git.Repo(search_parent_directories=UpperCAmelCase__			)
       A_		   = {
           """repo_id""": str(UpperCAmelCase__			),
           """repo_sha""": str(repo.head.object.hexsha			),
           """repo_branch""": str(repo.active_branch			),
       }

       with open(os.path.join(UpperCAmelCase__,    """git_log.json"""			),    """w"""			) as f:
              json.dump(UpperCAmelCase__,    UpperCAmelCase__,    indent=4			)
def  UpperCAmelCase__      ( UpperCAmelCase__			)     ->     Dict:
       if params.n_gpu <= 0:
              A_		   = 0
              A_		   = -1
              A_		   = True
              A_		   = False
              return

       assert torch.cuda.is_available()

       logger.info("""Initializing GPUs"""			)
       if params.n_gpu > 1:
              assert params.local_rank != -1

              A_		   = int(os.environ["""WORLD_SIZE"""]			)
              A_		   = int(os.environ["""N_GPU_NODE"""]			)
              A_		   = int(os.environ["""RANK"""]			)

              # number of nodes / node ID
              A_		   = params.world_size // params.n_gpu_per_node
              A_		   = params.global_rank // params.n_gpu_per_node
              A_		   = True

              assert params.n_nodes == int(os.environ["""N_NODES"""]			)
              assert params.node_id == int(os.environ["""NODE_RANK"""]			)

       # local job (single GPU)
       else:
              assert params.local_rank == -1

              A_		   = 1
              A_		   = 0
              A_		   = 0
              A_		   = 0
              A_		   = 1
              A_		   = 1
              A_		   = False

       # sanity checks
       assert params.n_nodes >= 1
       assert 0 <= params.node_id < params.n_nodes
       assert 0 <= params.local_rank <= params.global_rank < params.world_size
       assert params.world_size == params.n_nodes * params.n_gpu_per_node

       # define whether this is the master process / if we are in multi-node distributed mode
       A_		   = params.node_id == 0 and params.local_rank == 0
       A_		   = params.n_nodes > 1

       # summary
       A_		   = F'''--- Global rank: {params.global_rank} - '''
       logger.info(PREFIX + """Number of nodes: %i""" % params.n_nodes			)
       logger.info(PREFIX + """Node ID        : %i""" % params.node_id			)
       logger.info(PREFIX + """Local rank     : %i""" % params.local_rank			)
       logger.info(PREFIX + """World size     : %i""" % params.world_size			)
       logger.info(PREFIX + """GPUs per node  : %i""" % params.n_gpu_per_node			)
       logger.info(PREFIX + """Master         : %s""" % str(params.is_master			)			)
       logger.info(PREFIX + """Multi-node     : %s""" % str(params.multi_node			)			)
       logger.info(PREFIX + """Multi-GPU      : %s""" % str(params.multi_gpu			)			)
       logger.info(PREFIX + """Hostname       : %s""" % socket.gethostname()			)

       # set GPU device
       torch.cuda.set_device(params.local_rank			)

       # initialize multi-GPU
       if params.multi_gpu:
              logger.info("""Initializing PyTorch distributed"""			)
              torch.distributed.init_process_group(
                  init_method="""env://""",    backend="""nccl""",    )







def  UpperCAmelCase__      ( UpperCAmelCase__			)     ->     Tuple:
       np.random.seed(args.seed			)
       torch.manual_seed(args.seed			)
       if args.n_gpu > 0:
              torch.cuda.manual_seed_all(args.seed			)
