#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define pii pair<int, int>
#define inf 0x3f3f3f3f
#define db double
#define il inline
#define endl '\n'
const int N = 2e5 + 5;
const int mod = 998244353;
vector<int> g[N];
int in[N], fa[N];
int find(int x) { return x == fa[x] ? x : fa[x] = find(fa[x]); }
void merge(int x, int y) { fa[find(x)] = find(y); }
void dfs(int u, int f)
{
    int s = 0;
    for (auto v: g[u])
    {
        if (v == f) continue;
        if (in[v] == 1)
        {
            if (s) merge(s, v);
            else s = v;
        } 
        dfs(v, u);
    }
}
void solve()
{
    int n;
    cin >> n;
    for (int i = 1; i <= n; i++) 
    {
        g[i].clear();
        in[i] = 0;
        fa[i] = i;
    }
    for (int i = 1; i < n; i++) 
    {
        int u, v;
        cin >> u >> v;
        g[u].push_back(v), g[v].push_back(u);
        in[u]++, in[v]++;
    }
    vector<int> v;
    int s = 0;
    for (int i = 1; i <= n; i++)
    {
        if (in[i] != 1) s = i;
        else v.push_back(i);
    }
    if (!s)
    {
        cout << -1 << '\n';
        return;
    }
    dfs(s, 0);
    map<int, int> mp;
    for (auto i: v) mp[find(i)]++;
    auto [x, w] = *mp.rbegin();
    int vs = v.size();
    if (w > vs / 2)
    {
        if (w == vs) cout << -1 << '\n';
        else cout << w << '\n';
    }
    else cout << (vs + 1) / 2 << '\n';
}   
signed main()
{
    // freopen("D:\\3022244240\\vscode\\txt\\in.txt", "r", stdin);
    // freopen("D:\\3022244240\\vscode\\txt\\out.txt", "w", stdout);
    ios::sync_with_stdio(false);
    cin.tie(0); cout.tie(0);
    int T = 1;
    cin >> T;
    while (T--) solve();
    return 0;
}