Tree Destruction

给你一棵 $n$ 个结点组成的树，你需要对树进行 $n-1$ 次操作，一次操作包含如下的步骤： 1. 选择两个叶子结点 2. 将这两个结点之间简单路径的长度加到答案中 3. 从树上删去两个叶子结点之一 初始答案为 $0$，显然在 $n-1$ 次操作之后树上只剩下一个结点。 计算最大的答案，并构造一组操作序列。

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<=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.

3
1 2
1 3

3
2 3 3
2 1 1

5
1 2
1 3
2 4
2 5

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