#include <bits/stdc++.h>
using namespace std;
vector<vector<long long> > adj;
vector<bool> visited;
long long longest(long long v, long long &ans) {
  visited[v] = true;
  long long maxDist = 0;
  ans = v;
  for (long long i = 0; i < adj[v].size(); i++) {
    long long v1 = adj[v][i];
    if (!visited[v1]) {
      long long tempDist, tempV;
      tempDist = 1 + longest(v1, tempV);
      if (tempDist > maxDist) {
        maxDist = tempDist;
        ans = tempV;
      }
    }
  }
  return maxDist;
}
bool trace(long long v, long long target, vector<bool> &arr) {
  visited[v] = true;
  if (v == target) {
    arr[v] = true;
  } else {
    arr[v] = false;
    for (long long i = 0; i < adj[v].size(); i++) {
      long long v1 = adj[v][i];
      if (!visited[v1]) {
        arr[v] = arr[v] || trace(v1, target, arr);
      }
    }
  }
  return arr[v];
}
void dist(long long v, vector<long long> &arr) {
  visited[v] = true;
  for (long long i = 0; i < adj[v].size(); i++) {
    long long v1 = adj[v][i];
    if (!visited[v1]) {
      arr[v1] = 1 + arr[v];
      dist(v1, arr);
    }
  }
}
int main() {
  long long n;
  cin >> n;
  adj.clear();
  adj.resize(n);
  for (long long i = 0; i < n - 1; i++) {
    long long a, b;
    cin >> a >> b;
    a--;
    b--;
    adj[a].push_back(b);
    adj[b].push_back(a);
  }
  visited.clear();
  visited.resize(n, false);
  long long v1;
  longest(0, v1);
  visited.clear();
  visited.resize(n, false);
  long long v2;
  longest(v1, v2);
  vector<bool> mark(n, false);
  visited.clear();
  visited.resize(n, false);
  trace(v1, v2, mark);
  vector<long long> dist1(n, 0);
  visited.clear();
  visited.resize(n, false);
  dist1[v1] = 0;
  dist(v1, dist1);
  vector<long long> dist2(n, 0);
  visited.clear();
  visited.resize(n, false);
  dist2[v2] = 0;
  dist(v2, dist2);
  long long ans = 0;
  vector<pair<long long, pair<long long, long long> > > arr1;
  vector<pair<long long, pair<long long, long long> > > arr2;
  for (long long i = 0; i < n; i++) {
    if (!mark[i]) {
      if (dist1[i] >= dist2[i]) {
        ans += dist1[i];
        arr1.push_back(make_pair(dist1[i], make_pair(i, v1)));
      } else {
        ans += dist2[i];
        arr1.push_back(make_pair(dist2[i], make_pair(i, v2)));
      }
    } else {
      if (i != v1) arr2.push_back(make_pair(dist1[i], make_pair(i, v1)));
      ans += dist1[i];
    }
  }
  cout << ans << endl;
  sort(arr1.begin(), arr1.end());
  reverse(arr1.begin(), arr1.end());
  sort(arr2.begin(), arr2.end());
  reverse(arr2.begin(), arr2.end());
  for (long long i = 0; i < arr1.size(); i++) {
    cout << arr1[i].second.first + 1 << " " << arr1[i].second.second + 1 << " "
         << arr1[i].second.first + 1 << endl;
  }
  for (long long i = 0; i < arr2.size(); i++) {
    cout << arr2[i].second.first + 1 << " " << arr2[i].second.second + 1 << " "
         << arr2[i].second.first + 1 << endl;
  }
  return 0;
}

### Prompt

Generate a CPP solution to the following 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

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
vector<vector<long long> > adj;
vector<bool> visited;
long long longest(long long v, long long &ans) {
  visited[v] = true;
  long long maxDist = 0;
  ans = v;
  for (long long i = 0; i < adj[v].size(); i++) {
    long long v1 = adj[v][i];
    if (!visited[v1]) {
      long long tempDist, tempV;
      tempDist = 1 + longest(v1, tempV);
      if (tempDist > maxDist) {
        maxDist = tempDist;
        ans = tempV;
      }
    }
  }
  return maxDist;
}
bool trace(long long v, long long target, vector<bool> &arr) {
  visited[v] = true;
  if (v == target) {
    arr[v] = true;
  } else {
    arr[v] = false;
    for (long long i = 0; i < adj[v].size(); i++) {
      long long v1 = adj[v][i];
      if (!visited[v1]) {
        arr[v] = arr[v] || trace(v1, target, arr);
      }
    }
  }
  return arr[v];
}
void dist(long long v, vector<long long> &arr) {
  visited[v] = true;
  for (long long i = 0; i < adj[v].size(); i++) {
    long long v1 = adj[v][i];
    if (!visited[v1]) {
      arr[v1] = 1 + arr[v];
      dist(v1, arr);
    }
  }
}
int main() {
  long long n;
  cin >> n;
  adj.clear();
  adj.resize(n);
  for (long long i = 0; i < n - 1; i++) {
    long long a, b;
    cin >> a >> b;
    a--;
    b--;
    adj[a].push_back(b);
    adj[b].push_back(a);
  }
  visited.clear();
  visited.resize(n, false);
  long long v1;
  longest(0, v1);
  visited.clear();
  visited.resize(n, false);
  long long v2;
  longest(v1, v2);
  vector<bool> mark(n, false);
  visited.clear();
  visited.resize(n, false);
  trace(v1, v2, mark);
  vector<long long> dist1(n, 0);
  visited.clear();
  visited.resize(n, false);
  dist1[v1] = 0;
  dist(v1, dist1);
  vector<long long> dist2(n, 0);
  visited.clear();
  visited.resize(n, false);
  dist2[v2] = 0;
  dist(v2, dist2);
  long long ans = 0;
  vector<pair<long long, pair<long long, long long> > > arr1;
  vector<pair<long long, pair<long long, long long> > > arr2;
  for (long long i = 0; i < n; i++) {
    if (!mark[i]) {
      if (dist1[i] >= dist2[i]) {
        ans += dist1[i];
        arr1.push_back(make_pair(dist1[i], make_pair(i, v1)));
      } else {
        ans += dist2[i];
        arr1.push_back(make_pair(dist2[i], make_pair(i, v2)));
      }
    } else {
      if (i != v1) arr2.push_back(make_pair(dist1[i], make_pair(i, v1)));
      ans += dist1[i];
    }
  }
  cout << ans << endl;
  sort(arr1.begin(), arr1.end());
  reverse(arr1.begin(), arr1.end());
  sort(arr2.begin(), arr2.end());
  reverse(arr2.begin(), arr2.end());
  for (long long i = 0; i < arr1.size(); i++) {
    cout << arr1[i].second.first + 1 << " " << arr1[i].second.second + 1 << " "
         << arr1[i].second.first + 1 << endl;
  }
  for (long long i = 0; i < arr2.size(); i++) {
    cout << arr2[i].second.first + 1 << " " << arr2[i].second.second + 1 << " "
         << arr2[i].second.first + 1 << endl;
  }
  return 0;
}

```