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

		UpperCamelCase		=     [False] * len(snake_case__ )
		UpperCamelCase		=     []
		queue.append(snake_case__ )
		UpperCamelCase		=     True

		while queue:
				UpperCamelCase		=     queue.pop(0 )
				for ind in range(len(graph[u] ) ):
						if visited[ind] is False and graph[u][ind] > 0:
								queue.append(snake_case__ )
								UpperCamelCase		=     True
								UpperCamelCase		=     u

		return visited[t]


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

		UpperCamelCase		=     [-1] * (len(snake_case__ ))
		UpperCamelCase		=     0
		while bfs(snake_case__    ,       snake_case__    ,       snake_case__    ,       snake_case__ ):
				UpperCamelCase		=     float('Inf' )
				UpperCamelCase		=     sink

				while s != source:
						# Find the minimum value in select path
						UpperCamelCase		=     min(snake_case__    ,       graph[parent[s]][s] )
						UpperCamelCase		=     parent[s]

				max_flow += path_flow
				UpperCamelCase		=     sink

				while v != source:
						UpperCamelCase		=     parent[v]
						graph[u][v] -= path_flow
						graph[v][u] += path_flow
						UpperCamelCase		=     parent[v]
		return max_flow


_UpperCAmelCase					: List[Any]      =       [
    [0, 16, 13, 0, 0, 0],
    [0, 0, 10, 12, 0, 0],
    [0, 4, 0, 0, 14, 0],
    [0, 0, 9, 0, 0, 20],
    [0, 0, 0, 7, 0, 4],
    [0, 0, 0, 0, 0, 0],
]

_UpperCAmelCase					: Tuple      =       0, 5


print(ford_fulkerson(graph, source, sink))






"""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"""]



