#include <bits/stdc++.h>
#include <cassert>

using namespace std;
using ll = long long;

#define all(x) (x).begin(), (x).end()
#define sz(x) (int)(x).size()
#define pb push_back
#define ff first
#define sc second

void solve() {
    int n; cin >> n;
    vector<vector<int>> g(n);
    for (int i = 0; i < n - 1; i++) {
        int u, v; cin >> u >> v;
        u--; v--;
        g[u].pb(v);
        g[v].pb(u);
    }

    auto check = [&](int k) {
        bool bad = false;
        auto dfs = [&](int v, int p, auto&&self) -> int {
            vector<int> paths;
            for (int u : g[v]) {
                if (u != p) {
                    paths.pb(1 + self(u, v, self));
                }
            }
            if (paths.empty()) return 0;
            sort(all(paths));
            int ind_last = -1;
            for (int i = 0; i < sz(paths); i++) {
                if (paths[i] < (k + 1) / 2) ind_last = i;
            }
            int sec_hf = paths.size() - ind_last - 1;
            int big = 0;
            for (int i = 0; i < sz(paths); i++) big += (paths[i] >= k); 
            auto check2 = [&](int wi) {
                int i2 = ind_last + 1;
                int big_ost = big, so = sec_hf - big;
                for (int i = ind_last; i >= 0; i--) {
                    if (wi == i) continue;
                    while (i2 < sz(paths) && (paths[i2] + paths[i] < k || wi == i2)) i2++;
                    if (i2 == sz(paths)) return false;
                    if (paths[i2] >= k) big_ost--;
                    else so--;
                    i2++;
                }
                if (wi != -1) {
                    if (paths[wi] >= k) big_ost--;
                    else if (paths[wi] >= (k + 1) / 2) so--;
                }
                if ((big_ost + so) % 2 == 0 || big_ost) return true;
                return false;
            };
            if (v == 0) {
                return check2(-1);
            } else {
                int L = -1, R = sz(paths);
                while (R - L > 1) {
                    int M = (L + R) / 2;
                    if (check2(M)) L = M;
                    else R = M;
                }
                if (L == -1) {
                    if (check2(-1)) {
                        bad = true;
                    }
                    return 0;
                }
                return (L == -1 ? 0 : paths[L]);
            }
        };      
        return (dfs(0, 0, dfs) && !bad);
    };

    int L = 1, R = n;
    while (R - L > 1) {
        int M = (L + R) / 2;
        if (check(M)) L = M;
        else R = M;
    }
    cout << L << '\n';
}

signed main() {
    int tt = 1;
    #ifdef LOCAL 
        freopen("in.txt", "r", stdin);
        freopen("out.txt", "w", stdout);
        cin >> tt;
    #else
        freopen("deleg.in", "r", stdin);
        freopen("deleg.out", "w", stdout);
        ios::sync_with_stdio(false); 
        cin.tie(0); cout.tie(0);
    #endif

    while (tt--) {
        solve();
    }

    return 0;
}