Flips For A Guaranteed Margin

You are estimating an unknown but fixed $p$, the probability a coin lands heads, by flipping it $n$ times and taking the sample proportion $\bar{X}_n$. Using the CLT approximation you want

$P\left(\left|\bar{X}_n - p\right| < 0.01\right) \ge 0.75.$

The script has everything except the standard deviation of a single flip:

from statistics import NormalDist

eps, q = 0.01, 0.75
z = NormalDist().inv_cdf((1 + q) / 2)     # 1.15035
sigma = ...                               # sd of one flip: depends on p, which is unknown
n_min = (z * sigma / eps) ** 2

Report the smallest integer $n$ that works for EVERY $p$ in $(0,1)$.

Answer format: enter an integer.