#include "bits/stdc++.h"
#include <array>
using namespace std;

using ll = long long;
using pii = pair<int, int>;

void solve() {
	int n;
	cin >> n;
	vector<vector<int>> edge(n, vector<int>());
	vector<pii> deg(n);
	for (int i = 0; i < n - 1; i++) deg[i] = {0, i};
	for (int i = 0; i < n - 1; i++) {
		int u, v;
		cin >> u >> v;
		--u, --v;
		edge[u].push_back(v), edge[v].push_back(u);
		deg[u].first++;
		deg[v].first++;
	}
	sort(rbegin(deg), rend(deg));
	if (deg[0].first == n - 1) {
		cout << -1 << "\n";
		return;
	}

	int total_leaf = 0;
	vector<int> subleaf;
	function<bool(int, int)> dfs = [&](int cur, int prev) {
		bool is_leaf = true;
		int child_leaf_cnt = 0;
		for (auto nxt: edge[cur]) {
			if (nxt == prev) continue;
			is_leaf = false;
			if (dfs(nxt, cur)) {
				++child_leaf_cnt;
			};
		}
		if (is_leaf) {
			++total_leaf;
			return true;
		}
		else {
			subleaf.push_back(child_leaf_cnt);
			return false;
		}
	};
	dfs(deg[0].second, -1);
	sort(rbegin(subleaf), rend(subleaf));
	int ans = (total_leaf + 1) / 2;
	ans = max(ans, subleaf[0]);
	cout << ans << "\n";
}

int main() {
	cin.tie(0)->sync_with_stdio(0);
	int t;
	cin >> t;
	while (t--) {
		solve();
	}
}