CF911F Tree Destruction

You are given an unweighted tree with $ n $ vertices. Then $ n-1 $ following operations are applied to the tree. A single operation consists of the following steps: 1. choose two leaves; 2. add the length of the simple path between them to the answer; 3. remove one of the chosen leaves from the tree. Initial answer (before applying operations) is $ 0 $ . Obviously after $ n-1 $ such operations the tree will consist of a single vertex. Calculate the maximal possible answer you can achieve, and construct a sequence of operations that allows you to achieve this answer!

The first line contains one integer number $ n $ ( $ 2

In the first line print one integer number — maximal possible answer. In the next $ n-1 $ lines print the operations in order of their applying in format $ a_{i},b_{i},c_{i} $ , where $ a_{i},b_{i} $ — pair of the leaves that are chosen in the current operation ( $ 1