from math import ceil
from typing import Optional

from scipy.stats import norm

SND_QUARTILE: float = 0.674490

def suggest_iqr_to_range_to_suggest_bins_num(n: int) -> float:
    p = 1 / (n + 1)
    return (SND_QUARTILE / norm.ppf(1 - p/2))

def suggest_bins_num(n: int, iqr_to_range: Optional[float] = None, scale: float = 1.) -> int:
    if n <= 0:
        raise ValueError(f'n should be >= 1, got {n}')
    if (iqr_to_range is not None) and (iqr_to_range <= 0.):
        raise ValueError(f'iqr_to_range should be > 0 or None, got {iqr_to_range}')
    if scale <= 0.:
        raise ValueError(f'scale should be > 0, got {scale}')
    if iqr_to_range is None:
        iqr_to_range = suggest_iqr_to_range_to_suggest_bins_num(n)
    t = 0.5 * scale * (1. / iqr_to_range) * (n ** (1. / 3))
    return int(ceil(t))