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

void solve(){
    int n;
    cin >> n;
    vector<int> a(n);
    vector<vector<int> > G(n + 1);
    for(auto &it : a) cin >> it;
    if(n == 2) {
        cout << 1 << '\n';
        return;
    }
    for(int i = 1 ; i < n ; ++i) {
        auto x = a[i] , y = i + 1;
        G[y].emplace_back(x);
        G[x].emplace_back(y);
    }
    vector<bool> buff(n + 1 , false);
    function<void(int , int)> pre = [&](int now , int fa) {
        if(G[now].size() >= 3 && now != 1) buff[now] = true;
        if(G[now].size() >= 2 && now == 1) buff[now] = true;
        //cerr <<"w"<< now << ' ' << buff[now] << endl;
        for(auto it : G[now]) {
            if(it == fa) continue;
            pre(it , now);
            if(buff[it]) buff[now] = true;
        }
    };
    int ans = 0;
    function<void(int , int , int)> dfs = [&](int now , int fa , int m) {
        ans = max(ans , m);
        int cnt = 0;
        for(auto it : G[now]) {
            if(it == fa) continue;
            if(buff[it]) ++cnt;
        }
        for(auto it : G[now]) {
            if(it == fa) continue;
            //cerr << it << ' ' << fa << ' ' << ans << endl;
            if(cnt >= 2) {
                dfs(it , now , m + 1);
            }
            else {
                if(cnt == 0) {
                    ans = max(ans , m + 1);
                    return;
                }
                if(buff[it])    dfs(it , now , m);
                else dfs(it , now , m + 1);
            }
        }
    };
    pre(1 , -1);
    bool ok = true;
    for(int j = 2 ; j < n ; ++j) {
        if(buff[j] == true) {
            ok = false;
            break;
        }
    }
    if(ok) {
        cout << 1 << '\n';
        return;
    }
    dfs(1 , -1 , 1);
    cout << ans << '\n';
}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    int t=1;
    cin>>t;
    while(t--){
        solve();
    }

    return 0;
}