Problem: Nastia has an unweighted tree with n vertices and wants to play with it!

The girl will perform the following operation with her tree, as long as she needs:

  1. Remove any existing edge. 
  2. Add an edge between any pair of vertices. 



What is the minimum number of operations Nastia needs to get a bamboo from a tree? A bamboo is a tree in which no node has a degree greater than 2.

Input

The first line contains a single integer t (1 ≤ t ≤ 10 000) — the number of test cases.

The first line of each test case contains a single integer n (2 ≤ n ≤ 10^5) — the number of vertices in the tree.

Next n - 1 lines of each test cases describe the edges of the tree in form a_i, b_i (1 ≤ a_i, b_i ≤ n, a_i ≠ b_i).

It's guaranteed the given graph is a tree and the sum of n in one test doesn't exceed 2 ⋅ 10^5.

Output

For each test case in the first line print a single integer k — the minimum number of operations required to obtain a bamboo from the initial tree.

In the next k lines print 4 integers x_1, y_1, x_2, y_2 (1 ≤ x_1, y_1, x_2, y_{2} ≤ n, x_1 ≠ y_1, x_2 ≠ y_2) — this way you remove the edge (x_1, y_1) and add an undirected edge (x_2, y_2).

Note that the edge (x_1, y_1) must be present in the graph at the moment of removing.

Example

Input


2
7
1 2
1 3
2 4
2 5
3 6
3 7
4
1 2
1 3
3 4


Output


2
2 5 6 7
3 6 4 5
0

Note

Note the graph can be unconnected after a certain operation.

Consider the first test case of the example: 

<image> The red edges are removed, and the green ones are added.

Solution (in CPP):

Solution:
#ifndef _MY
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,abm,mmx,tune=native")
#endif
//#define _GLIBCXX_DEBUG
#include "bits/stdc++.h"
#define F first
#define S second
#define mp make_pair
#define all(x) (x).begin(), (x).end()
using namespace std;
typedef long long ll;
typedef long double ld;
const int64_t INF = (int64_t)(2e18);
const int inf = (int)(1e9 + 7);
const int maxn = 500 * 1000 + 100;
clock_t cl;
double current_time() { return double(clock() - cl) / CLOCKS_PER_SEC; }
//------------------------------------------//


void solve(){
    int n;
    cin >> n;
    vector<vector<int>> g(n);
    for (int i = 0; i < n-1; ++i){
        int a, b;
        cin >> a >> b;
        --a; --b;
        g[a].push_back(b);
        g[b].push_back(a);
    }

    set<pair<int,int>> s;

    function<void(int, int)> dfs = [&](int v, int p){
        for (auto& it : g[v]){
            if (it == p) continue;
            dfs(it, v);
        }
        int cnt = 0;
        for (auto& it : g[v]){
            if (it == p) continue;
            if (s.count(mp(v, it))) continue;
            if (s.count(mp(it, v))) continue;
            ++cnt;
            if (cnt > 2) s.insert(mp(it, v));
        }
        if (cnt >= 2 && v != p) s.insert(mp(v, p));
    };

    dfs(0, 0);
    //for (auto& it : s) cout << it.F << " " << it.S << endl;
    //cout << endl;

    vector<int> cnts(n);
    vector<int> color(n);
    function<void(int,int,int)> dfs_color = [&](int v, int p, int c){
        color[v] = c;
        for (auto& it : g[v]){
            if (s.count(mp(v, it))) continue;
            if (s.count(mp(it, v))) continue;
            cnts[v]++;
            if (it == p) continue;
            dfs_color(it, v, c);
        }
    };

    int curcol = 0;
    for (int i = 0; i < n; ++i){
        if (color[i] != 0) continue;
        dfs_color(i, i, ++curcol);
    }
    map<int, vector<int>> ma;
    for (int i = 0; i < n; ++i){
        if (cnts[i] < 2) ma[color[i]].push_back(i);
    }

    vector<vector<int>> vv;
    for (auto& it : ma) vv.push_back(it.second);
    
    vector<pair<int,int>> v1, v2;
    for (auto& it : s) v1.push_back(it);

    for (int i = 0; i < vv.size()-1; ++i){
        v2.push_back(mp(vv[i].back(), vv[i+1][0]));
    }

    cout << v1.size() << endl;
    for (int i = 0; i < (int)v1.size(); ++i){
        cout << v1[i].first + 1 << " ";
        cout << v1[i].second + 1 << " ";
        cout << v2[i].first + 1 << " ";
        cout << v2[i].second + 1 << " ";
        cout << endl;
    }


}


int32_t main(){
    cl = clock();
    ios_base::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cin.tie(nullptr);
#ifdef _MY
    freopen("VimProject/input.txt", "r", stdin);
    freopen("VimProject/output.txt", "w", stdout);
#endif

    int t;
    cin >> t;
    while(t--) solve();


    return 0;
}