#include <bits/stdc++.h>
using namespace std;
#define all(x) x.begin(), x.end()
// #define int long long
int solve()
{
    int n;
    cin >> n;
    vector<int> son(n + 1);
    vector<vector<int>> g(n + 1);
    vector<int> cnt(n + 1);
    for (int i = 0; i < n - 1; i++)
    {
        int x, y;
        cin >> x >> y;
        cnt[x]++;
        cnt[y]++;
        g[x].emplace_back(y);
        g[y].emplace_back(x);
    }
    int fa = 0;
    for (int i = 1; i <= n; i++)
    {
        if (cnt[i] != 1)
        {
            fa = i;
            break;
        }
    }
    if (fa == 0)
    {
        cout << -1 << "\n";
        return 0;
    }
    auto dfs = [&](int x, int fa, auto self) -> void {
        for (auto it : g[x])
        {
            if (it == fa)
            {
                continue;
            }
            self(it, x, self);
            if (son[it] == 0)
            {
                son[x]++;
            }
        }
    };
    dfs(fa, 0, dfs);
    vector<int> nums;
    for (auto it : son)
    {
        if (it > 0)
        {
            nums.emplace_back(it);
        }
    }
    sort(all(nums), greater<int>());
    if (nums.size() == 1)
    {
        cout << -1 << "\n";
        return 0;
    }
    if (nums[0] >= accumulate(nums.begin() + 1, nums.end(), 0))
    {
        cout << nums[0] << "\n";
    }
    else
    {
        cout << (accumulate(all(nums), 0) + 1) / 2 << "\n";
    }
    return 0;
}
signed main()
{
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);
    int test = 1;
    cin >> test;
    while (test--)
    {
        solve();
    }

    return 0;
}