'''simple docstring'''
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 			_UpperCamelCase			(  _a						:						int					,  _a						:						bool = False      ):




    """simple docstring"""



    if device_specific:
        seed += AcceleratorState().process_index
    random.seed(_A      )
    np.random.seed(_A      )
    torch.manual_seed(_A      )
    if is_xpu_available():
        torch.xpu.manual_seed_all(_A      )
    elif is_npu_available():
        torch.npu.manual_seed_all(_A      )
    else:
        torch.cuda.manual_seed_all(_A      )
    # ^^ safe to call this function even if cuda is not available
    if is_tpu_available():
        xm.set_rng_state(_A      )







def 			_UpperCamelCase			(  _a						:						Optional[RNGType] = None					,  _a						:						Optional[torch.Generator] = None      ):




    """simple docstring"""



    if rng_type == RNGType.TORCH:
        __UpperCamelCase						:						Optional[int]		     =	torch.get_rng_state()
    elif rng_type == RNGType.CUDA:
        __UpperCamelCase						:						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."
        __UpperCamelCase						:						Any		     =	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."
        __UpperCamelCase						:						str		     =	torch.npu.get_rng_state()
    elif rng_type == RNGType.XPU:
        assert is_xpu_available(), "Can't synchronize XPU seeds on an environment without XPUs."
        __UpperCamelCase						:						Any		     =	torch.xpu.get_rng_state()
    elif rng_type == RNGType.GENERATOR:
        assert generator is not None, "Need a generator to synchronize its seed."
        __UpperCamelCase						:						Union[str, Any]		     =	generator.get_state()

    # Broadcast the rng state from device 0 to other devices
    __UpperCamelCase						:						Dict		     =	AcceleratorState()
    if state.distributed_type == DistributedType.TPU:
        __UpperCamelCase						:						Union[str, Any]		     =	rng_state.to(xm.xla_device()      )
        xm.collective_broadcast([rng_state]      )
        xm.mark_step()
        __UpperCamelCase						:						int		     =	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
    ):
        __UpperCamelCase						:						Optional[int]		     =	rng_state.to(state.device      )
        torch.distributed.broadcast(_A					,  0      )
        __UpperCamelCase						:						List[Any]		     =	rng_state.cpu()
    elif state.distributed_type == DistributedType.MULTI_CPU:
        torch.distributed.broadcast(_A					,  0      )

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







def 			_UpperCamelCase			(  _a						:						List[Union[str, RNGType]]					,  _a						:						Optional[torch.Generator] = None      ):




    """simple docstring"""



    for rng_type in rng_types:
        synchronize_rng_state(RNGType(_A      )					,  generator=_A      )






from math import factorial




def        __UpperCamelCase     (      _A					:							Union[str, Any]      ,  _A					:							Tuple		)				->Any:



							"""simple docstring"""
							return factorial(_A		) / (factorial(_A		) * factorial(n - r		))




def        __UpperCamelCase     (      )				->Any:



							"""simple docstring"""
							lowerCamelCase_								=0

							for i in range(1      ,  101		):
														for j in range(1      ,  i + 1		):
																					if combinations(_A      ,  _A		) > 1E6:
																												total += 1
							return total


if __name__ == "__main__":
	print(solution())
