



import argparse
import json
import re
import string
import sys
from collections import Counter






def 						_lowerCAmelCase    (					__lowerCamelCase :  Tuple  ):



 """simple docstring"""





 def remove_articles(__lowerCamelCase :  Optional[Any]  ):
  return re.sub(r"\b(a|an|the)\b"		,						" "		,						__snake_case  )

 def white_space_fix(__lowerCamelCase :  int  ):
  return " ".join(text.split()  )

 def remove_punc(__lowerCamelCase :  Union[str, Any]  ):
  __SCREAMING_SNAKE_CASE							:     Dict							=						set(string.punctuation  )
  return "".join(ch for ch in text if ch not in exclude  )

 def lower(__lowerCamelCase :  Dict  ):
  return text.lower()

 return white_space_fix(remove_articles(remove_punc(lower(__snake_case  )  )  )  )






def 						_lowerCAmelCase    (					__lowerCamelCase :  Union[str, Any]		,						__lowerCamelCase :  Optional[int]  ):



 """simple docstring"""





 __SCREAMING_SNAKE_CASE							:     Optional[int]							=						normalize_answer(__snake_case  ).split()
 __SCREAMING_SNAKE_CASE							:     int							=						normalize_answer(__snake_case  ).split()
 __SCREAMING_SNAKE_CASE							:     Union[str, Any]							=						Counter(__snake_case  ) & Counter(__snake_case  )
 __SCREAMING_SNAKE_CASE							:     int							=						sum(common.values()  )
 if num_same == 0:
  return 0
 __SCREAMING_SNAKE_CASE							:     Tuple							=						1.0 * num_same / len(__snake_case  )
 __SCREAMING_SNAKE_CASE							:     Dict							=						1.0 * num_same / len(__snake_case  )
 __SCREAMING_SNAKE_CASE							:     Optional[Any]							=						(2 * precision * recall) / (precision + recall)
 return fa






def 						_lowerCAmelCase    (					__lowerCamelCase :  Optional[Any]		,						__lowerCamelCase :  Optional[Any]  ):



 """simple docstring"""





 return normalize_answer(__snake_case  ) == normalize_answer(__snake_case  )






def 						_lowerCAmelCase    (					__lowerCamelCase :  Dict		,						__lowerCamelCase :  Tuple		,						__lowerCamelCase :  Optional[Any]  ):



 """simple docstring"""





 __SCREAMING_SNAKE_CASE							:     Tuple							=						[]
 for ground_truth in ground_truths:
  __SCREAMING_SNAKE_CASE							:     int							=						metric_fn(__snake_case		,						__snake_case  )
  scores_for_ground_truths.append(__snake_case  )
 return max(__snake_case  )






def 						_lowerCAmelCase    (					__lowerCamelCase :  Optional[Any]		,						__lowerCamelCase :  Union[str, Any]  ):



 """simple docstring"""





 __SCREAMING_SNAKE_CASE							:     int							=						0
 __SCREAMING_SNAKE_CASE							:     Optional[Any]							=						[]
 for passage in dataset:
  for qa in passage["qas"]:
   total += 1
   if qa["id"] not in predictions:
    __SCREAMING_SNAKE_CASE							:     Dict							=						F"""Unanswered question {qa["id"]} will receive score 0."""
    print(__snake_case		,						file=sys.stderr  )
    continue

   __SCREAMING_SNAKE_CASE							:     List[Any]							=						[x["text"] for x in qa["answers"]]
   __SCREAMING_SNAKE_CASE							:     List[Any]							=						predictions[qa["id"]]

   __SCREAMING_SNAKE_CASE							:     Optional[Any]							=						metric_max_over_ground_truths(__snake_case		,						__snake_case		,						__snake_case  )
   if int(_exact_match  ) == 1:
    correct_ids.append(qa["id"]  )
   exact_match += _exact_match

   fa += metric_max_over_ground_truths(__snake_case		,						__snake_case		,						__snake_case  )

 __SCREAMING_SNAKE_CASE							:     List[Any]							=						exact_match / total
 __SCREAMING_SNAKE_CASE							:     Union[str, Any]							=						fa / total

 return {"exact_match": exact_match, "f1": fa}, correct_ids


if __name__ == "__main__":
      _lowerCamelCase         =	'''1.0'''
      _lowerCamelCase         =	argparse.ArgumentParser("""Official evaluation script for ReCoRD v1.0.""")
      parser.add_argument("""data_file""", help="""The dataset file in JSON format.""")
      parser.add_argument("""pred_file""", help="""The model prediction file in JSON format.""")
      parser.add_argument("""--output_correct_ids""", action="""store_true""", help="""Output the correctly answered query IDs.""")
      _lowerCamelCase         =	parser.parse_args()

      with open(args.data_file) as data_file:
            _lowerCamelCase         =	json.load(data_file)
            if dataset_json["version"] != expected_version:
                  print(
                      f'''Evaluation expects v-{expected_version}, but got dataset with v-{dataset_json['version']}''',
                      file=sys.stderr,
                  )
            _lowerCamelCase         =	dataset_json['''data''']

      with open(args.pred_file) as pred_file:
            _lowerCamelCase         =	json.load(pred_file)

      _lowerCamelCase         =	evaluate(dataset, predictions)

      if args.output_correct_ids:
            print(f'''Output {len(correct_ids)} correctly answered question IDs.''')
            with open("""correct_ids.json""", """w""") as f:
                  json.dump(correct_ids, f)










from itertools import count
from math import asin, pi, sqrt
def 				UpperCamelCase_	(					__snake_case      :    float  )->   float:




						'''simple docstring'''
						return (
						    (1 - 2 * point) * sqrt(point - point**2  ) + 2 * point + asin(sqrt(1 - point  )  )
						) / 4
def 				UpperCamelCase_	(					__snake_case      :    int  )->   float:




						'''simple docstring'''
						__magic_name__					=      (circles_number + 1 - sqrt(2 * circles_number  )) / (
						    2 * (circles_number**2 + 1)
						)
						__magic_name__					=      circles_number * intersection_y

						__magic_name__					=      intersection_x * intersection_y / 2
						__magic_name__					=      circle_bottom_arc_integral(
						    1 / 2  ) - circle_bottom_arc_integral(__snake_case  )

						return triangle_area + concave_region_area
def 				UpperCamelCase_	(					__snake_case      :    float = 1 / 10_00  )->   int:




						'''simple docstring'''
						__magic_name__					=      (1 - pi / 4) / 4

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

						return -1


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

