Return the required sample size per group to detect an absolute lift of mde over a baseline conversion rate, at significance alpha and statistical power, for a two-sided test.

$$n = \frac{\bigl(z_{1-\alpha/2} + z_{\text{power}}\bigr)^2\bigl(p_1(1-p_1) + p_2(1-p_2)\bigr)}{\text{mde}^2}$$

Round up. The $\text{mde}^2$ in the denominator is the thing worth internalising: halving the effect you want to detect costs four times the traffic.

Input

baseline = 0.1
mde = 0.02
alpha = 0.05
power = 0.8

Output

3839