#include<bits/stdc++.h>
using namespace std;
#define endl "\n"
#define debug(x) cout<<#x<<": "<<x<<endl
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
using ll=long long;
using ull=unsigned long long;
#define int long long
void solve(){
    int n;
    cin>>n;
    vector<vector<int>> adj(n+1);
    vector<int> du(n+1);
    for(int i=0;i<n-1;i++){
        int u,v;
        cin>>u>>v;
        adj[u].push_back(v);
        adj[v].push_back(u);
        du[u]++;
        du[v]++;
    }
    int le=0;
    for(int i=1;i<=n;i++){
        if(du[i]==1)
            le++;
    }
    int dep=0;

    int ed=1;
    vector<bool> vis1(n+1),vis2(n+1);
    queue<int> q;
    q.push(1);
    vis1[1]=1;
    while(!q.empty()){
        int u=q.front();
        q.pop();
        ed=u;
        for(auto x:adj[u]){
            if(vis1[x])
                continue;
            vis1[x]=1;
            q.push(x);
        }
    }

    q.push(ed);
    vis2[ed]=1;
    while(!q.empty()){
        int cn=q.size();
        for(int i=0;i<cn;i++){
            int u=q.front();
            q.pop();
            for(auto x:adj[u]){
                if(vis2[x])
                    continue;
                vis2[x]=1;
                q.push(x);
            }
        }
        dep++;
    }
    // debug(dep);
    vector<int> lv(n+1);
    auto dfs=[&](auto self,int u,int la)->void{
        for(auto x:adj[u]){
            if(x==la)
                continue;
            if(adj[x].size()==1)
                lv[u]++;
            self(self,x,u);
        }
    };
    int res=(le+1)/2;
    for(int i=1;i<=n;i++){
        if(lv[i]>(le+1)/2){
            res=lv[i];
            break;
        }
    }
    dfs(dfs,ed,0);
    if(dep<=3){
        cout<<-1<<endl;
    }
    else{
        cout<<res<<endl;
    }
}
signed main(){
    ios::sync_with_stdio(0);
    cout.tie(0);
    cin.tie(0);
    int t;
    cin>>t;
    while(t--){
        solve();
    }
}