/***************************************************************************************************
 * author : Jie Chen (4th Year CS)
 * school : Rochester Institute of Technology
 * created: 11.29.2024 18:59:18
****************************************************************************************************/
#include "bits/stdc++.h"

using namespace std;

using i64 = long long;

void work(int tc) {
    int n;
    cin >> n;

    vector<vector<int>> adj(n);
    for (int i = 0; i < n; i++) {
        int p;
        cin >> p;
        if (i != 0) {
            p--;
            adj[p].push_back(i);
        }
    }

    auto dfs = [&](auto&& self, int u) -> int {
        int cur = 1;
        int add = 0;
        if (adj[u].size() > 1) {
            add = 1;
        }
        vector<int> g;
        for (int v : adj[u]) {
            g.push_back(self(self, v) + add);
        }
        if (add == 0) {
            return cur;
        }
        sort(g.rbegin(), g.rend());
        return max({cur, g[0] - 1, g[1]});
    };
    cout << dfs(dfs, 0) << "\n";
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    int T;
    cin >> T;
    for (int t = 1; T--; t++) {
        work(t);
    }
}

// ~ JustJie