
from math import factorial


def       A       (					lowercase    ,       lowercase )   ->  int:
		'''simple docstring'''

		if n < k or k < 0:
				raise ValueError('Please enter positive integers for n and k where n >= k' )
		return factorial(snake_case__ ) // (factorial(snake_case__ ) * factorial(n - k ))


if __name__ == "__main__":
					print(
					    "The number of five-card hands possible from a standard",
					    F'''fifty-two card deck is: {combinations(52, 5)}\n''',
					)

					print(
					    "If a class of 40 students must be arranged into groups of",
					    F'''4 for group projects, there are {combinations(40, 4)} ways''',
					    "to arrange them.\n",
					)

					print(
					    "If 10 teams are competing in a Formula One race, there",
					    F'''are {combinations(10, 3)} ways that first, second and''',
					    "third place can be awarded.",
					)






"""simple docstring"""




import operator as op


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

lowerCAmelCase							:			Optional[int]     							=							{""">""": op.gt, """>=""": op.ge, """==""": op.eq, """!=""": op.ne, """<=""": op.le, """<""": op.lt}

# These are the args for `torch.distributed.launch` for pytorch < 1.9
lowerCAmelCase							:			Union[str, Any]     							=							[
    """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""",
]

lowerCAmelCase							:			List[str]     							=							["""DEEPSPEED""", """MULTI_GPU""", """FSDP""", """MEGATRON_LM"""]
lowerCAmelCase							:			Optional[Any]     							=							["""DEEPSPEED""", """MULTI_XPU""", """FSDP"""]



