2012 IMO Shortlist C2

Let $n \geq 1$ be an integer. What is the maximum number of disjoint pairs of elements of the set $\{1,2, \ldots, n\}$ such that the sums of the different pairs are different integers not exceeding $n$ ?

令 $n \geq 1$ 为整数。集合 $\{1,2, \ldots, n\}$ 中不相交的元素对的最大数量是多少，使得不同对的总和是不超过 $n$ 的不同整数？