Imagine sorting a basket of laundry consisting of n pairs of socks, each of a different color. Randomly pulling out socks, one at a time, you will either put each on the sorting surface or match it up with its mate to make a pair and put them away in the sock drawer.

The maximum number of socks in the sorting space can then be any number from 1 to n. For example with 3 pairs, pulling them in the order AABBCC will only require one space, ABACCB requires two, and ABCABC will require three spaces.

Find the expected number of sorting spaces required in terms of n.