
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__     (    SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_ = False	)							->						List[str]:
			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__     (    SCREAMING_SNAKE_CASE_ = None			,				SCREAMING_SNAKE_CASE_ = None	)							->						Union[str, Any]:
			# Get the proper rng state
			if rng_type == RNGType.TORCH:
						lowerCAmelCase__ : str   =						torch.get_rng_state()
			elif rng_type == RNGType.CUDA:
						lowerCAmelCase__ : Optional[int]   =						torch.cuda.get_rng_state()
			elif rng_type == RNGType.XLA:
						assert is_tpu_available(), "Can't synchronize XLA seeds on an environment without TPUs."
						lowerCAmelCase__ : List[str]   =						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."
						lowerCAmelCase__ : Optional[Any]   =						torch.npu.get_rng_state()
			elif rng_type == RNGType.XPU:
						assert is_xpu_available(), "Can't synchronize XPU seeds on an environment without XPUs."
						lowerCAmelCase__ : Union[str, Any]   =						torch.xpu.get_rng_state()
			elif rng_type == RNGType.GENERATOR:
						assert generator is not None, "Need a generator to synchronize its seed."
						lowerCAmelCase__ : int   =						generator.get_state()

			# Broadcast the rng state from device 0 to other devices
			lowerCAmelCase__ : str   =						AcceleratorState()
			if state.distributed_type == DistributedType.TPU:
						lowerCAmelCase__ : Dict   =						rng_state.to(xm.xla_device()	)
						xm.collective_broadcast([rng_state]	)
						xm.mark_step()
						lowerCAmelCase__ : Dict   =						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
			):
						lowerCAmelCase__ : Any   =						rng_state.to(state.device	)
						torch.distributed.broadcast(UpperCAmelCase_			,				0	)
						lowerCAmelCase__ : str   =						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__     (    SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_ = None	)							->						Optional[int]:
			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()} = ")






