/**
 * @author: XiaFan
 * @date: 2023-04-13 19:58
 */
#include <bits/stdc++.h>

using i64 = long long;

void solve() {
    int n;
    std::cin >> n;
    std::vector<std::vector<int>> adj(n);
    std::vector<int> deg(n);
    for (int i = 0; i < n - 1; i++) {
        int u, v;
        std::cin >> u >> v;
        u--, v--;
        adj[u].push_back(v);
        adj[v].push_back(u);
        deg[u]++;
        deg[v]++;
    }

    if (n <= 3) {
        std::cout << -1 << "\n";
        return;
    }
    
    int one = 0;
    std::map<int, int> mp;
    for (int i = 0; i < n; i++) {
        if (deg[i] == 1) {
            one++;
            mp[adj[i][0]]++;
        }
    }
    if (one == n - 1) {
        std::cout << -1 << "\n";
        return;
    }

    int max = 0;
    for (auto v : mp) {
        max = std::max(max, v.second);
    }
    if (max * 2 <= one) {
        std::cout << (one + 1) / 2 << "\n";
    } else {
        // std::cerr << one << " " << max << "\n";
        std::cout << 2 * max - one + (one - max + 1) / 2 << "\n";
    }
}

int main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);

    int t = 1;
    std::cin >> t;
    while (t--) {
        solve();
    }

    return 0;
}