Problem: 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

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

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.

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

Solution (in PYTHON3):

Solution:
import sys


def main():
    n = int(input())

    edges = list(map(int, sys.stdin.read().split()))
    tree_edges = dict()
    for i in range(n):
        tree_edges[i + 1] = set()

    for i in range(0, len(edges) - 1, 2):
        tree_edges[edges[i]].add(edges[i + 1])
        tree_edges[edges[i + 1]].add(edges[i])

    init_distants = [-1] * (n + 1)

    queue = [1]
    init_distants[1] = 0

    while queue:
        next_queue = []
        for process in queue:
            for next_vertex in tree_edges[process]:
                if init_distants[next_vertex] == -1:
                    init_distants[next_vertex] = init_distants[process] + 1
                    next_queue.append(next_vertex)
        queue = next_queue

    head = init_distants.index(max(init_distants))
    distants_from_head = [-1] * (n + 1)
    queue = [head]

    distants_from_head[head] = 0

    while queue:
        next_queue = []
        for process in queue:
            for next_vertex in tree_edges[process]:
                if distants_from_head[next_vertex] == -1:
                    distants_from_head[next_vertex] = distants_from_head[process] + 1
                    next_queue.append(next_vertex)
        queue = next_queue

    tail = distants_from_head.index(max(distants_from_head))
    distants_from_tail = [-1] * (n + 1)
    queue = [tail]

    distants_from_tail[tail] = 0

    while queue:
        next_queue = []
        for process in queue:
            for next_vertex in tree_edges[process]:
                if distants_from_tail[next_vertex] == -1:
                    distants_from_tail[next_vertex] = distants_from_tail[process] + 1
                    next_queue.append(next_vertex)
        queue = next_queue

    path_len_sum = 0
    removal_history = list()

    process_queue = []

    for vertex, adj in tree_edges.items():
        if len(adj) == 1:
            process_queue.append(vertex)

    while process_queue:
        next_queue = []

        for leaf in process_queue:

            if leaf == head or leaf == tail:
                continue

            if distants_from_tail[leaf] > distants_from_head[leaf]:
                path_len_sum += distants_from_tail[leaf]
                new_leaves = []

                for w in tree_edges[leaf]:
                    tree_edges[w].remove(leaf)
                    if len(tree_edges[w]) == 1:
                        new_leaves.append(w)
                next_queue.extend(new_leaves)
                removal_history.append("{0} {1} {0}".format(leaf, tail))
            else:
                path_len_sum += distants_from_head[leaf]
                new_leaves = []

                for w in tree_edges[leaf]:
                    tree_edges[w].remove(leaf)
                    if len(tree_edges[w]) == 1:
                        new_leaves.append(w)
                next_queue.extend(new_leaves)
                removal_history.append("{0} {1} {0}".format(leaf, head))
        process_queue = next_queue

    process_queue = [tail]

    while process_queue:
        leaf = process_queue[0]

        if leaf == head:
            continue

        path_len_sum += distants_from_head[leaf]
        new_leaves = []

        for w in tree_edges[leaf]:
            tree_edges[w].remove(leaf)
            if len(tree_edges[w]) == 1:
                new_leaves.append(w)
        process_queue = new_leaves
        removal_history.append("{0} {1} {0}".format(leaf, head))

    print(str(path_len_sum))
    sys.stdout.write("\n".join(removal_history))
    sys.stdout.write("\n")


main()