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 ≤ 2·10⁵) — 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.

Tree Destruction

Examples