




import random
from typing import List, Optional, Union

import numpy as np
import torch

from ..state import AcceleratorState
from .constants import CUDA_DISTRIBUTED_TYPES
from .dataclasses import DistributedType, RNGType
from .imports import is_npu_available, is_tpu_available, is_xpu_available


if is_tpu_available(check_device=False):
 import torch_xla.core.xla_model as xm
def 							__lowerCAmelCase			(UpperCAmelCase_ ,     UpperCAmelCase_ = False		):
    if device_specific:
        seed += AcceleratorState().process_index
    random.seed(UpperCAmelCase_		)
    np.random.seed(UpperCAmelCase_		)
    torch.manual_seed(UpperCAmelCase_		)
    if is_xpu_available():
        torch.xpu.manual_seed_all(UpperCAmelCase_		)
    elif is_npu_available():
        torch.npu.manual_seed_all(UpperCAmelCase_		)
    else:
        torch.cuda.manual_seed_all(UpperCAmelCase_		)
    # ^^ safe to call this function even if cuda is not available
    if is_tpu_available():
        xm.set_rng_state(UpperCAmelCase_		)
def 							__lowerCAmelCase			(UpperCAmelCase_ = None ,     UpperCAmelCase_ = None		):
    # Get the proper rng state
    if rng_type == RNGType.TORCH:
        a__  			=							torch.get_rng_state()
    elif rng_type == RNGType.CUDA:
        a__  			=							torch.cuda.get_rng_state()
    elif rng_type == RNGType.XLA:
        assert is_tpu_available(), "Can't synchronize XLA seeds on an environment without TPUs."
        a__  			=							torch.tensor(xm.get_rng_state()		)
    elif rng_type == RNGType.NPU:
        assert is_npu_available(), "Can't synchronize NPU seeds on an environment without NPUs."
        a__  			=							torch.npu.get_rng_state()
    elif rng_type == RNGType.XPU:
        assert is_xpu_available(), "Can't synchronize XPU seeds on an environment without XPUs."
        a__  			=							torch.xpu.get_rng_state()
    elif rng_type == RNGType.GENERATOR:
        assert generator is not None, "Need a generator to synchronize its seed."
        a__  			=							generator.get_state()

    # Broadcast the rng state from device 0 to other devices
    a__  			=							AcceleratorState()
    if state.distributed_type == DistributedType.TPU:
        a__  			=							rng_state.to(xm.xla_device()		)
        xm.collective_broadcast([rng_state]		)
        xm.mark_step()
        a__  			=							rng_state.cpu()
    elif (
        state.distributed_type in CUDA_DISTRIBUTED_TYPES
        or state.distributed_type == DistributedType.MULTI_NPU
        or state.distributed_type == DistributedType.MULTI_XPU
    ):
        a__  			=							rng_state.to(state.device		)
        torch.distributed.broadcast(UpperCAmelCase_ ,     0		)
        a__  			=							rng_state.cpu()
    elif state.distributed_type == DistributedType.MULTI_CPU:
        torch.distributed.broadcast(UpperCAmelCase_ ,     0		)

    # Set the broadcast rng state
    if rng_type == RNGType.TORCH:
        torch.set_rng_state(UpperCAmelCase_		)
    elif rng_type == RNGType.CUDA:
        torch.cuda.set_rng_state(UpperCAmelCase_		)
    elif rng_type == RNGType.NPU:
        torch.npu.set_rng_state(UpperCAmelCase_		)
    elif rng_type == RNGType.XPU:
        torch.xpu.set_rng_state(UpperCAmelCase_		)
    elif rng_type == RNGType.XLA:
        xm.set_rng_state(rng_state.item()		)
    elif rng_type == RNGType.GENERATOR:
        generator.set_state(UpperCAmelCase_		)







def 							__lowerCAmelCase			(UpperCAmelCase_ ,     UpperCAmelCase_ = None		):
    for rng_type in rng_types:
        synchronize_rng_state(RNGType(UpperCAmelCase_		) ,     generator=UpperCAmelCase_		)












def 							__lowerCAmelCase			(UpperCAmelCase_		):
    return n * (2 * n - 1)
def 							__lowerCAmelCase			(UpperCAmelCase_		):
    a__  			=							(1 + 24 * n) ** 0.5
    return ((1 + root) / 6) % 1 == 0
def 							__lowerCAmelCase			(UpperCAmelCase_ = 144		):
    a__  			=							start
    a__  			=							hexagonal_num(UpperCAmelCase_		)
    while not is_pentagonal(UpperCAmelCase_		):
        n += 1
        a__  			=							hexagonal_num(UpperCAmelCase_		)
    return num


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






