#include <bits/stdc++.h>
using namespace std;
const int N = 2e5+10;
int fa[N];
vector<int>e[N];
int dep[N];
void dfs(int r,int f){
    dep[r] = dep[f] + 1;
    if(e[r].size() == 1 && r != 1){
        return;
    }
    for(int i = 0;i<e[r].size();i++){
        if(e[r][i] == f) continue;
        dfs(e[r][i],r);
    }
}
bool cmp(int a,int b){
    return dep[a] < dep[b];
}

void solve(){
   set<pair<int,int>>st;
    int n;
    cin >> n;
    for(int i = 1;i<n;i++){
        cin >> fa[i + 1];
        e[i + 1].push_back(fa[i]);
        e[fa[i]].push_back(i + 1);
    }
    dfs(1,0);
    vector<int>leaf;
    for(int i = 2;i<=n;i++){
        if(e[i].size() == 1){
            leaf.push_back(i);
        }
    }
    sort(leaf.begin(),leaf.end(),cmp);
    int ans = 0;
    for(auto x : leaf){
        int te = x;
        int cnt = 0;
        while(te != 1 && st.find(make_pair(te,fa[te])) == st.end()){
            st.insert(make_pair(te,fa[te]));
            te = fa[te];
            cnt++;
        }
        ans = max(ans,cnt);
    }
    cout << ans << endl;
    for(int i = 1;i<=n;i++){
        e[i].clear();
        dep[i] = 0;
    }
}
int main(){
    int t;
    cin >> t;
    while(t--){
        solve();
    }
    return 0;
}