Description: 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! Input Format: The first line contains one integer number n (2 ≤ n ≤ 2·105) — the number of vertices in the tree. Next n - 1 lines describe the edges of the tree in form ai, bi (1 ≤ ai, bi ≤ n, ai ≠ bi). It is guaranteed that given graph is a tree. Output Format: 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 ai, bi, ci, where ai, bi — pair of the leaves that are chosen in the current operation (1 ≤ ai, bi ≤ n), ci (1 ≤ ci ≤ n, ci = ai or ci = bi) — choosen leaf that is removed from the tree in the current operation. See the examples for better understanding. Note: None