






from itertools import count
from math import asin, pi, sqrt


def 						_A     (       SCREAMING_SNAKE_CASE__						:			float ):
    return (
        (1 - 2 * point) * sqrt(point - point**2 ) + 2 * point + asin(sqrt(1 - point ) )
    ) / 4


def 						_A     (       SCREAMING_SNAKE_CASE__						:			int ):
    UpperCamelCase :str										=     (circles_number + 1 - sqrt(2 * circles_number )) / (
        2 * (circles_number**2 + 1)
    )
    UpperCamelCase :List[Any]										=     circles_number * intersection_y

    UpperCamelCase :List[str]										=     intersection_x * intersection_y / 2
    UpperCamelCase :Optional[int]										=     circle_bottom_arc_integral(
        1 / 2 ) - circle_bottom_arc_integral(SCREAMING_SNAKE_CASE__ )

    return triangle_area + concave_region_area


def 						_A     (       SCREAMING_SNAKE_CASE__						:			float = 1 / 1000 ):
    UpperCamelCase :Union[str, Any]										=     (1 - pi / 4) / 4

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

    return -1


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













# as due to their complexity multi-gpu tests could impact other tests, and to aid debug we have those in a separate module.

import os
import sys

from transformers.testing_utils import TestCasePlus, execute_subprocess_async, get_gpu_count, require_torch_gpu, slow

from .utils import load_json







class     UpperCAmelCase_		(      lowercase				):



      """simple docstring"""
      @classmethod
      def 					UpperCAmelCase		(       cls				)       ->   List[Any]:
          return cls




      @slow
      @require_torch_gpu
      def 					UpperCAmelCase		(       self				)       ->   int:
          UpperCamelCase :int										=     self.get_auto_remove_tmp_dir()
          UpperCamelCase :List[str]										=     F'''
            --model_name Helsinki-NLP/opus-mt-en-ro
            --save_dir {output_dir}
            --data_dir {self.test_file_dir_str}/test_data/wmt_en_ro
            --num_beams 2
            --task translation
        '''.split()

          # we want this test to run even if there is only one GPU, but if there are more we use them all
          UpperCamelCase :List[str]										=     get_gpu_count()
          UpperCamelCase :Optional[Any]										=     F'''
            -m torch.distributed.launch
            --nproc_per_node={n_gpu}
            {self.test_file_dir}/run_distributed_eval.py
        '''.split()
          UpperCamelCase :List[Any]										=     [sys.executable] + distributed_args + args
          execute_subprocess_async(SCREAMING_SNAKE_CASE_					,       env=self.get_env()				)

          UpperCamelCase :Tuple										=     os.path.join(SCREAMING_SNAKE_CASE_					,       '''test_bleu.json'''				)
          UpperCamelCase :str										=     load_json(SCREAMING_SNAKE_CASE_				)
          # print(metrics)
          self.assertGreaterEqual(metrics['''bleu''']					,       25				)





