




import importlib
import importlib.metadata
import os
import warnings
from distutils.util import strtobool
from functools import lru_cache

import torch
from packaging import version
from packaging.version import parse

from .environment import parse_flag_from_env
from .versions import compare_versions, is_torch_version


try:
 import torch_xla.core.xla_model as xm  # noqa: F401

 SCREAMING_SNAKE_CASE_    :       str       =							True
except ImportError:
 SCREAMING_SNAKE_CASE_    :       Optional[int]       =							False


# Cache this result has it's a C FFI call which can be pretty time-consuming
SCREAMING_SNAKE_CASE_    :       List[Any]       =							torch.distributed.is_available()
def 							__lowerCAmelCase			(UpperCAmelCase_		):
    # Check we're not importing a "pkg_name" directory somewhere but the actual library by trying to grab the version
    a__  			=							importlib.util.find_spec(UpperCAmelCase_		) is not None
    if package_exists:
        try:
            a__  			=							importlib.metadata.metadata(UpperCAmelCase_		)
            return True
        except importlib.metadata.PackageNotFoundError:
            return False
def 							__lowerCAmelCase			():
    return _torch_distributed_available
def 							__lowerCAmelCase			():
    try:
        pass
    except ImportError:
        print(
            """Intel(R) oneCCL Bindings for PyTorch* is required to run DDP on Intel(R) GPUs, but it is not"""
            """ detected. If you see \"ValueError: Invalid backend: 'ccl'\" error, please install Intel(R) oneCCL"""
            """ Bindings for PyTorch*."""		)
    return (
        importlib.util.find_spec("""torch_ccl"""		) is not None
        or importlib.util.find_spec("""oneccl_bindings_for_pytorch"""		) is not None
    )
def 							__lowerCAmelCase			():
    return importlib.metadata.version("""oneccl_bind_pt"""		)
def 							__lowerCAmelCase			():
    return _is_package_available("""transformer_engine"""		)
@lru_cache
def 							__lowerCAmelCase			(UpperCAmelCase_=True		):
    # Due to bugs on the amp series GPUs, we disable torch-xla on them
    if torch.cuda.is_available():
        return False
    if _tpu_available and check_device:
        try:
            # Will raise a RuntimeError if no XLA configuration is found
            a__  			=							xm.xla_device()
            return True
        except RuntimeError:
            return False
    return _tpu_available
def 							__lowerCAmelCase			():
    return _is_package_available("""deepspeed"""		)
def 							__lowerCAmelCase			(UpperCAmelCase_=False		):
    if is_tpu_available():
        return not ignore_tpu
    if torch.cuda.is_available():
        return torch.cuda.is_bfaa_supported()
    if is_npu_available():
        return False
    return True
def 							__lowerCAmelCase			():
    a__  			=							_is_package_available("""bitsandbytes"""		)
    if package_exists:
        a__  			=							version.parse(importlib.metadata.version("""bitsandbytes"""		)		)
        return compare_versions(UpperCAmelCase_ ,     """>=""" ,     """0.39.0"""		)
    return False
def 							__lowerCAmelCase			():
    a__  			=							_is_package_available("""bitsandbytes"""		)
    if package_exists:
        a__  			=							version.parse(importlib.metadata.version("""bitsandbytes"""		)		)
        return compare_versions(UpperCAmelCase_ ,     """>=""" ,     """0.37.2"""		)
    return False
def 							__lowerCAmelCase			():
    return _is_package_available("""bitsandbytes"""		)
def 							__lowerCAmelCase			():
    if strtobool(os.environ.get("""ACCELERATE_USE_MEGATRON_LM""" ,     """False"""		)		) == 1:
        a__  			=							importlib.util.find_spec("""megatron"""		) is not None
        if package_exists:
            try:
                a__  			=							parse(importlib.metadata.version("""megatron-lm"""		)		)
                return compare_versions(UpperCAmelCase_ ,     """>=""" ,     """2.2.0"""		)
            except Exception as e:
                warnings.warn(F"""Parse Megatron version failed. Exception:{e}"""		)
                return False
def 							__lowerCAmelCase			():
    return _is_package_available("""safetensors"""		)
def 							__lowerCAmelCase			():
    return _is_package_available("""transformers"""		)
def 							__lowerCAmelCase			():
    return _is_package_available("""datasets"""		)
def 							__lowerCAmelCase			():
    return _is_package_available("""aim"""		)
def 							__lowerCAmelCase			():
    return _is_package_available("""tensorboard"""		) or _is_package_available("""tensorboardX"""		)
def 							__lowerCAmelCase			():
    return _is_package_available("""wandb"""		)
def 							__lowerCAmelCase			():
    return _is_package_available("""comet_ml"""		)
def 							__lowerCAmelCase			():
    return _is_package_available("""boto3"""		)
def 							__lowerCAmelCase			():
    if _is_package_available("""rich"""		):
        if "ACCELERATE_DISABLE_RICH" in os.environ:
            warnings.warn(
                """`ACCELERATE_DISABLE_RICH` is deprecated and will be removed in v0.22.0 and deactivated by default. Please use `ACCELERATE_ENABLE_RICH` if you wish to use `rich`."""		)
            return not parse_flag_from_env("""ACCELERATE_DISABLE_RICH""" ,     UpperCAmelCase_		)
        return parse_flag_from_env("""ACCELERATE_ENABLE_RICH""" ,     UpperCAmelCase_		)
    return False
def 							__lowerCAmelCase			():
    return _is_package_available("""sagemaker"""		)
def 							__lowerCAmelCase			():
    return _is_package_available("""tqdm"""		)
def 							__lowerCAmelCase			():
    return _is_package_available("""mlflow"""		)
def 							__lowerCAmelCase			():
    return is_torch_version(""">=""" ,     """1.12"""		) and torch.backends.mps.is_available() and torch.backends.mps.is_built()
def 							__lowerCAmelCase			():
    def get_major_and_minor_from_version(UpperCAmelCase_		):
        return str(version.parse(UpperCAmelCase_		).major		) + "." + str(version.parse(UpperCAmelCase_		).minor		)

    a__  			=							importlib.metadata.version("""torch"""		)
    if importlib.util.find_spec("""intel_extension_for_pytorch"""		) is None:
        return False
    a__  			=							"""N/A"""
    try:
        a__  			=							importlib.metadata.version("""intel_extension_for_pytorch"""		)
    except importlib.metadata.PackageNotFoundError:
        return False
    a__  			=							get_major_and_minor_from_version(_torch_version		)
    a__  			=							get_major_and_minor_from_version(_ipex_version		)
    if torch_major_and_minor != ipex_major_and_minor:
        warnings.warn(
            F"""Intel Extension for PyTorch {ipex_major_and_minor} needs to work with PyTorch {ipex_major_and_minor}.*,"""
            F""" but PyTorch {_torch_version} is found. Please switch to the matching version and run again."""		)
        return False
    return True
@lru_cache
def 							__lowerCAmelCase			(UpperCAmelCase_=False		):
    if importlib.util.find_spec("""torch"""		) is None or importlib.util.find_spec("""torch_npu"""		) is None:
        return False

    import torch
    import torch_npu  # noqa: F401

    if check_device:
        try:
            # Will raise a RuntimeError if no NPU is found
            a__  			=							torch.npu.device_count()
            return torch.npu.is_available()
        except RuntimeError:
            return False
    return hasattr(UpperCAmelCase_ ,     """npu"""		) and torch.npu.is_available()







@lru_cache
def 							__lowerCAmelCase			(UpperCAmelCase_=False		):
    if not parse_flag_from_env("""ACCELERATE_USE_XPU""" ,     default=UpperCAmelCase_		):
        return False
    if is_ipex_available():
        import torch

        if is_torch_version("""<=""" ,     """1.12"""		):
            return False
    else:
        return False

    import intel_extension_for_pytorch  # noqa: F401

    if check_device:
        try:
            # Will raise a RuntimeError if no XPU  is found
            a__  			=							torch.xpu.device_count()
            return torch.xpu.is_available()
        except RuntimeError:
            return False
    return hasattr(UpperCAmelCase_ ,     """xpu"""		) and torch.xpu.is_available()












from itertools import count
from math import asin, pi, sqrt
def 							__lowerCAmelCase			(UpperCAmelCase_		):
    return (
        (1 - 2 * point) * sqrt(point - point**2		) + 2 * point + asin(sqrt(1 - point		)		)
    ) / 4
def 							__lowerCAmelCase			(UpperCAmelCase_		):
    a__  			=							(circles_number + 1 - sqrt(2 * circles_number		)) / (
        2 * (circles_number**2 + 1)
    )
    a__  			=							circles_number * intersection_y

    a__  			=							intersection_x * intersection_y / 2
    a__  			=							circle_bottom_arc_integral(
        1 / 2		) - circle_bottom_arc_integral(UpperCAmelCase_		)

    return triangle_area + concave_region_area
def 							__lowerCAmelCase			(UpperCAmelCase_ = 1 / 1_000		):
    a__  			=							(1 - pi / 4) / 4

    for n in count(1		):
        if concave_triangle_area(UpperCAmelCase_		) / l_section_area < fraction:
            return n

    return -1


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






