
'''simple docstring'''
def    _UpperCamelCase						(       SCREAMING_SNAKE_CASE__ ,       SCREAMING_SNAKE_CASE__			)  ->							float:


		'''simple docstring'''


		def get_matched_characters(SCREAMING_SNAKE_CASE__ ,       SCREAMING_SNAKE_CASE__			) -> str:
				snake_case  :       Dict     			=						[]
				snake_case  :       List[str]     			=						min(len(_stra			) ,       len(_stra			)			) // 2
				for i, l in enumerate(_stra			):
						snake_case  :       Optional[int]     			=						int(max(0 ,       i - limit			)			)
						snake_case  :       Union[str, Any]     			=						int(min(i + limit + 1 ,       len(_stra			)			)			)
						if l in _stra[left:right]:
								matched.append(SCREAMING_SNAKE_CASE__			)
								snake_case  :       Tuple     			=						F'{_stra[0:_stra.index(SCREAMING_SNAKE_CASE__			)]} {_stra[_stra.index(SCREAMING_SNAKE_CASE__			) + 1:]}'

				return "".join(SCREAMING_SNAKE_CASE__			)

		# matching characters
		snake_case  :       Union[str, Any]     			=						get_matched_characters(SCREAMING_SNAKE_CASE__ ,       SCREAMING_SNAKE_CASE__			)
		snake_case  :       List[str]     			=						get_matched_characters(SCREAMING_SNAKE_CASE__ ,       SCREAMING_SNAKE_CASE__			)
		snake_case  :       Tuple     			=						len(SCREAMING_SNAKE_CASE__			)

		# transposition
		snake_case  :       List[Any]     			=						(
		    len([(ca, ca) for ca, ca in zip(SCREAMING_SNAKE_CASE__ ,       SCREAMING_SNAKE_CASE__			) if ca != ca]			) // 2
		)

		if not match_count:
				snake_case  :       str     			=						0.0
		else:
				snake_case  :       Dict     			=						(
				    1
				    / 3
				    * (
				        match_count / len(SCREAMING_SNAKE_CASE__			)
				        + match_count / len(SCREAMING_SNAKE_CASE__			)
				        + (match_count - transpositions) / match_count
				    )
				)

		# common prefix up to 4 characters
		snake_case  :       Tuple     			=						0
		for ca, ca in zip(stra[:4] ,       stra[:4]			):
				if ca == ca:
						prefix_len += 1
				else:
						break

		return jaro + 0.1 * prefix_len * (1 - jaro)


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						print(jaro_winkler("hello", "world"))




'''simple docstring'''
from __future__ import annotations

from math import ceil, floor, sqrt




def    _UpperCamelCase						(       SCREAMING_SNAKE_CASE__ = 200_0000			)  ->							int:


		'''simple docstring'''


		snake_case  :       list[int]     			=						[0]
		snake_case  :       int

		for idx in range(1 ,       ceil(sqrt(target * 2			) * 1.1			)			):
				triangle_numbers.append(triangle_numbers[-1] + idx			)

		# we want this to be as close as possible to target
		snake_case  :       int     			=						0
		# the area corresponding to the grid that gives the product closest to target
		snake_case  :       int     			=						0
		# an estimate of b, using the quadratic formula
		snake_case  :       float
		# the largest integer less than b_estimate
		snake_case  :       int
		# the largest integer less than b_estimate
		snake_case  :       int
		# the triangle number corresponding to b_floor
		snake_case  :       int
		# the triangle number corresponding to b_ceil
		snake_case  :       int

		for idx_a, triangle_a in enumerate(triangle_numbers[1:] ,       1			):
				snake_case  :       int     			=						(-1 + sqrt(1 + 8 * target / triangle_a			)) / 2
				snake_case  :       Optional[int]     			=						floor(SCREAMING_SNAKE_CASE__			)
				snake_case  :       int     			=						ceil(SCREAMING_SNAKE_CASE__			)
				snake_case  :       Optional[Any]     			=						triangle_numbers[b_floor]
				snake_case  :       Union[str, Any]     			=						triangle_numbers[b_ceil]

				if abs(target - triangle_b_first_guess * triangle_a			) < abs(
				    target - best_product			):
						snake_case  :       str     			=						triangle_b_first_guess * triangle_a
						snake_case  :       int     			=						idx_a * b_floor

				if abs(target - triangle_b_second_guess * triangle_a			) < abs(
				    target - best_product			):
						snake_case  :       List[Any]     			=						triangle_b_second_guess * triangle_a
						snake_case  :       Any     			=						idx_a * b_ceil

		return area


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


