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
from collections import deque as dq
n = int(input())

ind = 0
inp = [int(x)-1 for line in sys.stdin.readlines() for x in line.split()]

coupl = [[] for _ in range(n)]
for _ in range(n-1):
    a,b = inp[ind],inp[ind+1]
    ind+=2
    coupl[a].append(b)
    coupl[b].append(a)

Q = dq()
found = [False]*n
master = 0
found[master] = True

dia1 = 0
Q.append(master)
while Q:
    node = Q.popleft()
    dia1 = node
    for nei in coupl[node]:
        if not found[nei]:
            found[nei] = True
            Q.append(nei)


dia2 = 0
Q.append((dia1,0))
dist1 = [0]*n
found = [False]*n
found[dia1] = True
while Q:
    node,d = Q.popleft()
    dia2 = node
    dist1[node]=d
    for nei in coupl[node]:
        if not found[nei]:
            found[nei] = True
            Q.append((nei,d+1))

Q = []
Q.append((dia2,0))
dist2 = [0]*n
found = [False]*n
found[dia2] = True
while Q:
    node,d = Q.pop()
    dist2[node]=d
    for nei in coupl[node]:
        if not found[nei]:
            found[nei] = True
            Q.append((nei,d+1))

neigs = [0]*n

leaves = []
for i in range(n):
    if i != dia1 and i != dia2 and len(coupl[i])==1:
        leaves.append(i)
    neigs[i]=len(coupl[i])
points = 0
lista = []

while leaves:
    node = leaves.pop()
    if dist1[node]<dist2[node]:
        lista.append((dia2,node,node))
        points += dist2[node]
    else:
        lista.append((dia1,node,node))
        points += dist1[node]
    for nei in coupl[node]:
        neigs[nei]-=1
        if neigs[nei]==1:
            leaves.append(nei)
leaves.append(dia2)
while leaves:
    node = leaves.pop()
    lista.append((dia1,node,node))
    points += dist1[node]
    for nei in coupl[node]:
        neigs[nei]-=1
        if neigs[nei]==1:
            leaves.append(nei)
print(points)
for l in lista:
    a,b,c = l
    print(a+1,b+1,c+1)