FKMO 2010 Problem 3

There are $n$ websites $1,2,\ldots,n$ ( $n \geq 2$ ). If there is a link from website $i$ to $j$ , we can use this link so we can move website $i$ to $j$ . For all $i \in \left\{1,2,\ldots,n - 1 \right\}$ , there is a link from website $i$ to $i+1$ . Prove that we can add less or equal than $3(n - 1)\log_{2}(\log_{2} n)$ links so that for all integers $1 \leq i < j \leq n$ , starting with website $i$ , and using at most three links to website $j$ . (If we use a link, website's number should increase. For example, No.7 to 4 is impossible).

Sorry for my bad English.