def  __lowerCamelCase						(		lowerCAmelCase__      ,    lowerCAmelCase__      ):
       lowerCAmelCase__	      =   1.0
       for i in range(1      ,    r + 1      ):
              ret *= (n + 1 - i) / i
       return round(lowerCAmelCase__      )






def  __lowerCamelCase						(		lowerCAmelCase__      ):
       return choose(8 + n      ,    lowerCAmelCase__      ) + choose(9 + n      ,    lowerCAmelCase__      ) - 1_0






def  __lowerCamelCase						(		lowerCAmelCase__      ):
       return sum(non_bouncy_exact(lowerCAmelCase__      ) for i in range(1      ,    n + 1      )      )






def  __lowerCamelCase						(		lowerCAmelCase__ = 1_0_0      ):
       return non_bouncy_upto(lowerCAmelCase__      )


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

import importlib
import sys
from argparse import REMAINDER, ArgumentParser
from pathlib import Path

import torch_xla.distributed.xla_multiprocessing as xmp






def  __lowerCamelCase						(		):
       lowerCAmelCase__	      =   ArgumentParser(
           description=(
               'PyTorch TPU distributed training launch helper utility that will spawn up multiple distributed processes'
           )      )

       # Optional arguments for the launch helper
       parser.add_argument('--num_cores'      ,    type=lowerCAmelCase__      ,    default=1      ,    help='Number of TPU cores to use (1 or 8).'      )

       # positional
       parser.add_argument(
           'training_script'      ,    type=lowerCAmelCase__      ,    help=(
               'The full path to the single TPU training '
               'program/script to be launched in parallel, '
               'followed by all the arguments for the '
               'training script'
           )      ,    )

       # rest from the training program
       parser.add_argument('training_script_args'      ,    nargs=lowerCAmelCase__      )

       return parser.parse_args()






def  __lowerCamelCase						(		):
       lowerCAmelCase__	      =   parse_args()

       # Import training_script as a module.
       lowerCAmelCase__	      =   Path(args.training_script      )
       sys.path.append(str(script_fpath.parent.resolve()      )      )
       lowerCAmelCase__	      =   script_fpath.stem
       lowerCAmelCase__	      =   importlib.import_module(lowerCAmelCase__      )

       # Patch sys.argv
       lowerCAmelCase__	      =   [args.training_script] + args.training_script_args + ['--tpu_num_cores', str(args.num_cores      )]

       xmp.spawn(mod._mp_fn      ,    args=()      ,    nprocs=args.num_cores      )


if __name__ == "__main__":
    main()
