Count Pairs in Two Arrays

Given two integer arrays, count how many index pairs (usually i < j) satisfy a given relation that involves elements from both arrays (e.g., equality of sums/XORs or a bitwise condition). The goal is to avoid brute-force O(n^2) by reducing the problem to frequency counting, hashing, sorting + two‑pointers, or a bitwise/trie-based approach to achieve subquadratic time.