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:
#include<bits/stdc++.h>
using namespace std;
#define INF 0x3f3f3f3f
#define swap(a,b) (a^=b^=a^=b)
const int maxn=2e5+20;
#define ll long long int
#define ull unsigned long long int
#define uint unsigned int
#define format(a) memset(a,0,sizeof(a))
#define rep(x,y,z) for(int x=y;x<=z;x++)
#define dec(x,y,z) for(int x=y;x>=z;x--)
#define mst(x) memset(x,0,sizeof(x))
inline int read()
{
    int ans=0;
    char last=' ',ch=getchar();
    while(ch<'0'|ch>'9')last=ch,ch=getchar();
    while(ch>='0' && ch<='9')ans=ans*10+ch-'0',ch=getchar();
    if(last=='-')ans=-ans;
    return ans;
}
int n,x,y,cnt,cnt2;
vector<pair<int,int> >edge; // nxt,exist
vector<int>node[maxn];
int c[maxn],ans[maxn][2],savel[maxn],saver[maxn],color[maxn],in[maxn];
void dfs1(int cur,int fa,int num) // num: the edge from fa to cur
{
    for(int i=0;i<node[cur].size();i++)
    {
        int idx=node[cur][i],nxt=edge[idx].first;
        if(nxt==fa)continue;
        dfs1(nxt,cur,idx);
        if(edge[idx].second)c[cur]++;
    }
    if(c[cur]<=1||(c[cur]==2&&!fa))return;
    if(fa)
    {
        edge[num].second=0;edge[num^1].second=0;
        ans[cnt][0]=fa,ans[cnt][1]=cur,cnt++;
        in[cur]--,in[fa]--;
    }
    for(int i=0;i<node[cur].size();i++)
    {
        if(c[cur]==2)return;
        int idx=node[cur][i],nxt=edge[idx].first;
        if(nxt==fa||!edge[idx].second)continue;
        edge[idx].second=0;edge[idx^1].second=0;
        ans[cnt][0]=cur,ans[cnt][1]=nxt,cnt++;
        c[cur]--;in[cur]--,in[nxt]--;
    }
}
void dfs2(int cur,int fa)
{
    if(in[cur]==0)savel[color[cur]]=cur,saver[color[cur]]=cur;
    else if(in[cur]==1)
    {
        if(savel[color[cur]])saver[color[cur]]=cur;
        else savel[color[cur]]=cur;
    }
    for(int i=0;i<node[cur].size();i++)
    {
        int idx=node[cur][i],nxt=edge[idx].first;
        if(nxt==fa)continue;
        if(edge[idx].second)color[nxt]=color[cur];
        else color[nxt]=++cnt2;
        dfs2(nxt,cur);
    }
}

void solve()
{
    n=read();
    edge.clear();cnt=0,cnt2=0;
    rep(i,0,n+1)node[i].clear(),c[i]=savel[i]=saver[i]=in[i]=color[i]=0;
    rep(i,1,n-1)
    {
        x=read(),y=read();in[x]++,in[y]++;
        node[x].push_back(edge.size());
        edge.push_back({y,1});
        node[y].push_back(edge.size());
        edge.push_back({x,1});
    }
    dfs1(1,0,-1);
    color[1]=0;
    dfs2(1,0);
    cout<<cnt<<"\n";

    rep(i,0,cnt-1)
    {
        rep(j,0,1)cout<<ans[i][j]<<" ";cout<<saver[i]<<" "<<savel[i+1];
        cout<<"\n";
    }
}
int main()
{
    int _t;
    _t=read();
    while(_t--)solve();
    return 0;
}
/*
1
4
1 2
1 3
3 4


1
7
1 2
1 3
2 4
2 5
3 6
3 7
*/