Question about calculation of H-statistic (j vs. k)

As said in book ,"we need 2n2 calls to the machine learning models predict function to compute the two-way H-statistic (j vs. k) and 3n2 for the total H-statistic (j vs. all)", i am curious why is different?

Illustrated by the formula, we should calculate the PD of Xi and Xj, PD of Xi, and PD of Xj, which each need n predictions. So ,for each instance we need 3n, and then 3n*n for all instances.