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: choose two leaves; add the length of the simple path between them to the answer; 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 ≤ n ≤ 2·10 5 ) — the number of vertices in the tree. Next n - 1 lines describe the edges of the tree in form a i , b i ( 1 ≤ a i , b i ≤ n , a i ≠ b i ). It is guaranteed that given graph is a tree. 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 ≤ a i , b i ≤ n ), c i ( 1 ≤ c i ≤ n , c i = a i or c i = b i ) — choosen leaf that is removed from the tree in the current operation. See the examples for better understanding.