Maximize memory capacity with primary-backup servers

You are helping to optimize the capacity of a cloud system. There are `n` servers, where `n` is always even. The memory capacity of the *i*-th server is given by an integer array `memory` of length `n`. When there are `n = 2 * x` servers: - Exactly `x` servers will be chosen as **primary** servers. - The remaining `x` servers will be **backup** servers. For every primary server `P`, there must exist a **distinct** backup server `B` such that: > `memory[B] >= memory[P]` (Each server can be used as either primary or backup in exactly one such pair, so the `n` servers are partitioned into `x` (primary, backup) pairs.) The **system memory capacity** is defined as the sum of the memory capacities of all primary servers: > `capacity = sum(memory[P] over all primary servers P)` Your task is to determine the **maximum possible system memory capacity** that can be obtained by: - Partitioning the `n` servers into `n/2` disjoint (primary, backup) pairs, and - Respecting the constraint `memory[backup] >= memory[primary]` within each pair. ### Input - An even integer `n` (number of servers). - An integer array `memory` of length `n`, where `memory[i]` is the memory capacity of the *i*-th server. You may assume: - `2 <= n <= 2 * 10^5`, and `n` is even. - `1 <= memory[i] <= 10^9`. ### Output - Return a single integer: the **maximum possible system memory capacity**. ### Complexity requirement Design an algorithm efficient for `n` up to about `2 * 10^5` (i.e., significantly better than `O(n^2)` time).