Hello, coding enthusiast! On our journey to master coding and problem-solving, we've arrived at an interesting challenge today. We're going to focus heavily on combinatorial problems. Specifically, we're examining combinatorial problems that involve working with large datasets and multiple pairs of numbers. We'll learn how to solve significant problems efficiently by implementing smart use of data structures like dictionaries and sidestepping expensive operations, such as iterating over large arrays. Are you ready? Let's dive in!

In this unit's task, you'll be given a large list composed of pairs of distinct, positive integers, including up to 1,000,000 elements. Your challenge is to write a C# method to count the number of indices (i, j) ($i \ne j$) where the i-th pair does not share a common element with the pair. A crucial point to remember is that a pair is considered identical to , meaning the order of elements in a pair is irrelevant in this case. It is guaranteed that no two pairs are element-wise equal.