#include<bits/stdc++.h>
#define int long long
using namespace std;
using ll = long long;
using PII = pair<int,int>;

constexpr ll INF = 2E18 + 10;
constexpr int N = 2E6 + 10;

int p[N],ans;
vector <int>g[N];

int dfs(int u,int fa)
{
    ll res = 0;
    if(g[u].size() >= 3) res = 1;
    vector<ll> a;
    for(auto v : g[u]) {
        if(fa == v) continue;
        a.push_back(dfs(v, u));
    }
    sort(a.begin(), a.end());
    if(a.size() >= 2) {
        // cout << u << " " << a[a.size() - 2] << "\n";
        ans = max(ans, a[a.size() - 2] + 1);
    }

    if(a.size() != 0) {
        // cout << u << " res = " << res  << ", a.back() = " << a.back() << "\n";
        return res + a.back();
    }
        
    else {
        // cout << u << " res = " << res << "\n";
        return res;
    }
     
}

void solve()
{
    int n;
    cin>>n;
    for(int i=1;i<=n;i++){
        cin>>p[i];
        g[i].clear();
    }
    for(int i=2;i<=n;i++){
        g[i].push_back(p[i]);
        g[p[i]].push_back(i);
    }
    ans=0;
    dfs(1, 0);
    cout<<ans+1<<'\n';
}

signed main(){
    ios::sync_with_stdio(false);
    cin.tie(nullptr),cout.tie(nullptr);

    int T=1;
    cin>>T;
    while(T--){
        solve();
    }
}