





from __future__ import annotations

from math import ceil, floor, sqrt


def 							__snake_case							(    lowerCAmelCase_ = 2_0_0_0_0_0_0	)				->						int:
    SCREAMING_SNAKE_CASE__											=			[0]
    SCREAMING_SNAKE_CASE__											=			42

    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
    SCREAMING_SNAKE_CASE__											=			0
    # the area corresponding to the grid that gives the product closest to target
    SCREAMING_SNAKE_CASE__											=			0
    # an estimate of b, using the quadratic formula
    SCREAMING_SNAKE_CASE__											=			42
    # the largest integer less than b_estimate
    SCREAMING_SNAKE_CASE__											=			42
    # the largest integer less than b_estimate
    SCREAMING_SNAKE_CASE__											=			42
    # the triangle number corresponding to b_floor
    SCREAMING_SNAKE_CASE__											=			42
    # the triangle number corresponding to b_ceil
    SCREAMING_SNAKE_CASE__											=			42

    for idx_a, triangle_a in enumerate(triangle_numbers[1:] ,							1	):
        SCREAMING_SNAKE_CASE__											=			(-1 + sqrt(1 + 8 * target / triangle_a	)) / 2
        SCREAMING_SNAKE_CASE__											=			floor(lowerCAmelCase_	)
        SCREAMING_SNAKE_CASE__											=			ceil(lowerCAmelCase_	)
        SCREAMING_SNAKE_CASE__											=			triangle_numbers[b_floor]
        SCREAMING_SNAKE_CASE__											=			triangle_numbers[b_ceil]

        if abs(target - triangle_b_first_guess * triangle_a	) < abs(
            target - best_product	):
            SCREAMING_SNAKE_CASE__											=			triangle_b_first_guess * triangle_a
            SCREAMING_SNAKE_CASE__											=			idx_a * b_floor

        if abs(target - triangle_b_second_guess * triangle_a	) < abs(
            target - best_product	):
            SCREAMING_SNAKE_CASE__											=			triangle_b_second_guess * triangle_a
            SCREAMING_SNAKE_CASE__											=			idx_a * b_ceil

    return area


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

"""simple docstring"""


import pytest

from datasets.utils.sharding import _distribute_shards, _number_of_shards_in_gen_kwargs, _split_gen_kwargs






@pytest.mark.parametrize(
    """kwargs, expected""" ,[
        ({"""num_shards""": 0, """max_num_jobs""": 1}, []),
        ({"""num_shards""": 10, """max_num_jobs""": 1}, [range(10		)]),
        ({"""num_shards""": 10, """max_num_jobs""": 10}, [range(lowercase ,i + 1		) for i in range(10		)]),
        ({"""num_shards""": 1, """max_num_jobs""": 10}, [range(1		)]),
        ({"""num_shards""": 10, """max_num_jobs""": 3}, [range(0 ,4		), range(4 ,7		), range(7 ,10		)]),
        ({"""num_shards""": 3, """max_num_jobs""": 10}, [range(0 ,1		), range(1 ,2		), range(2 ,3		)]),
    ] ,)
def      __UpperCAmelCase       (      lowercase ,lowercase		):







  """simple docstring"""
  _UpperCAmelCase    			=   _distribute_shards(**lowercase		)
  assert out == expected






@pytest.mark.parametrize(
    """gen_kwargs, max_num_jobs, expected""" ,[
        ({"""foo""": 0}, 10, [{"""foo""": 0}]),
        ({"""shards""": [0, 1, 2, 3]}, 1, [{"""shards""": [0, 1, 2, 3]}]),
        ({"""shards""": [0, 1, 2, 3]}, 4, [{"""shards""": [0]}, {"""shards""": [1]}, {"""shards""": [2]}, {"""shards""": [3]}]),
        ({"""shards""": [0, 1]}, 4, [{"""shards""": [0]}, {"""shards""": [1]}]),
        ({"""shards""": [0, 1, 2, 3]}, 2, [{"""shards""": [0, 1]}, {"""shards""": [2, 3]}]),
    ] ,)
def      __UpperCAmelCase       (      lowercase ,lowercase ,lowercase		):







  """simple docstring"""
  _UpperCAmelCase    			=   _split_gen_kwargs(lowercase ,lowercase		)
  assert out == expected






@pytest.mark.parametrize(
    """gen_kwargs, expected""" ,[
        ({"""foo""": 0}, 1),
        ({"""shards""": [0]}, 1),
        ({"""shards""": [0, 1, 2, 3]}, 4),
        ({"""shards""": [0, 1, 2, 3], """foo""": 0}, 4),
        ({"""shards""": [0, 1, 2, 3], """other""": (0, 1)}, 4),
        ({"""shards""": [0, 1, 2, 3], """shards2""": [0, 1]}, RuntimeError),
    ] ,)
def      __UpperCAmelCase       (      lowercase ,lowercase		):







  """simple docstring"""
  if expected is RuntimeError:
    with pytest.raises(lowercase		):
      _number_of_shards_in_gen_kwargs(lowercase		)
  else:
    _UpperCAmelCase    			=   _number_of_shards_in_gen_kwargs(lowercase		)
    assert out == expected
