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!

-----Input-----

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.

-----Output-----

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.

-----Examples-----

Input 3 1 2 1 3

Output 3 2 3 3 2 1 1

Input 5 1 2 1 3 2 4 2 5

Output 9 3 5 5 4 3 3 4 1 1 4 2 2