





"""simple docstring"""



import operator as op


a_			=      """scaler.pt"""
a_			=      """pytorch_model"""
a_			=      """random_states"""
a_			=      """optimizer"""
a_			=      """scheduler"""
a_			=      """pytorch_model.bin"""
a_			=      """pytorch_model.bin.index.json"""
a_			=      """model.safetensors"""
a_			=      """model.safetensors.index.json"""
a_			=      """1.10.2"""
a_			=      """py38"""
a_			=      """4.17.0"""
a_			=      ["""ml.p3.16xlarge""", """ml.p3dn.24xlarge""", """ml.p4dn.24xlarge"""]
a_			=      ["""FULL_SHARD""", """SHARD_GRAD_OP""", """NO_SHARD""", """HYBRID_SHARD""", """HYBRID_SHARD_ZERO2"""]
a_			=      ["""TRANSFORMER_BASED_WRAP""", """SIZE_BASED_WRAP""", """NO_WRAP"""]
a_			=      ["""BACKWARD_PRE""", """BACKWARD_POST""", """NO_PREFETCH"""]
a_			=      ["""FULL_STATE_DICT""", """LOCAL_STATE_DICT""", """SHARDED_STATE_DICT"""]
a_			=      """2.0.1"""
a_			=      ["""pdsh""", """standard""", """openmpi""", """mvapich"""]
a_			=      ["""default""", """reduce-overhead""", """max-autotune"""]

a_			=      {""">""": op.gt, """>=""": op.ge, """==""": op.eq, """!=""": op.ne, """<=""": op.le, """<""": op.lt}

# These are the args for `torch.distributed.launch` for pytorch < 1.9
a_			=      [
    """nnodes""",
    """nproc_per_node""",
    """rdzv_backend""",
    """rdzv_endpoint""",
    """rdzv_id""",
    """rdzv_conf""",
    """standalone""",
    """max_restarts""",
    """monitor_interval""",
    """start_method""",
    """role""",
    """module""",
    """m""",
    """no_python""",
    """run_path""",
    """log_dir""",
    """r""",
    """redirects""",
    """t""",
    """tee""",
    """node_rank""",
    """master_addr""",
    """master_port""",
]

a_			=      ["""DEEPSPEED""", """MULTI_GPU""", """FSDP""", """MEGATRON_LM"""]
a_			=      ["""DEEPSPEED""", """MULTI_XPU""", """FSDP"""]











"""simple docstring"""



from decimal import Decimal, getcontext
from math import ceil, factorial







def 		__lowercase					(       snake_case_  :  int						)       ->str:



    '''simple docstring'''







    if not isinstance(snake_case_    ,snake_case_						):
        raise TypeError('''Undefined for non-integers'''						)
    elif precision < 1:
        raise ValueError('''Undefined for non-natural numbers'''						)

    __A   :						int									=					precision
    __A   :						Tuple									=					ceil(precision / 14						)
    __A   :						Dict									=					426880 * Decimal(10005						).sqrt()
    __A   :						Optional[Any]									=					1
    __A   :						int									=					13591409
    __A   :						Optional[int]									=					Decimal(snake_case_						)
    for k in range(1    ,snake_case_						):
        __A   :						int									=					factorial(6 * k						) // (factorial(3 * k						) * factorial(snake_case_						) ** 3)
        linear_term += 545140134
        exponential_term *= -262537412640768000
        partial_sum += Decimal(multinomial_term * linear_term						) / exponential_term
    return str(constant_term / partial_sum						)[:-1]


if __name__ == "__main__":
       a_			=      50
       print(f'''The first {n} digits of pi is: {pi(n)}''')




