#include <bits/stdc++.h>

using namespace std;
using ll = long long;

int main() {
    cin.tie(0)->sync_with_stdio(0);

    int t; cin >> t;
    for (int ti = 0; ti < t; ti++) {
        int n; cin >> n;
        vector<vector<int>> adj(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);
        }

        // special case n=2
        if (n <= 2) {
            cout << "-1" << '\n';
            continue;
        }

        vector<int> bunches;
        function<int(int, int)> dp = [&](int x, int p) -> bool { 
            int nleaves = 0;
            for (int v : adj[x]) {
                if (v == p) continue;
                if (dp(v, x)) nleaves++;
            }
            if (p == 1 && adj[p].size() == 1) nleaves++;
            if (nleaves) bunches.push_back(nleaves);
            return adj[x].size() == 1;
        };

        dp(1, -1);
        if (bunches.size() == 1) {
            cout << -1 << '\n';
            continue;
        }

        sort(bunches.begin(), bunches.end());
        int bsum = 0;
        for (int i = 0; i < bunches.size(); i++) bsum += bunches[i];
        if (bunches[0] > bsum - bunches[0]) {
            cout << bunches[0] << '\n';
        } else {
            cout << (bsum+1)/2 << '\n';
        }
    }
}