#include<iostream>
#include<queue>
#include<cstring>
using namespace std;

const int N = 2e6 + 20;

int head[N],cnt,t, n, dis[N], dicnt[N];
bool vis[N];

struct edge{
    int u, v, nxt;
}es[N];

void add_edge(int u, int v){
    es[++cnt] = edge{u, v, head[u]};
    head[u] = cnt;
    es[++cnt] = edge{v, u, head[v]};
    head[v] = cnt;
}

void dfs(int u, int v){
    bool vis = 0;
    dis[v] = -1;
    for(int i = head[v]; i; i = es[i].nxt){
        int to = es[i].v;
        if(to == u)continue;
        dfs(v, to);
        vis = 1;
        dis[v] = max(dis[v], dis[to] + 1);
    }
    if(!vis)dis[v] = 0;
    dicnt[dis[v]] ++;
}

void solve(){
    long long ans = 1e9+10;
    cnt = 0;
    cin>>n;
    for(int i = 0; i <= n;i++){
        vis[i] = 0;
        dicnt[i] = 0;
        dis[i] = 0;
        head[i] = 0;
    }
    for(int i = 2;i<=n;i++){
        int x;
        cin>>x;
        add_edge(i, x);
    }
    dfs(0, 1);
    for(int i = 0; i <= n;i++){
        //cout<<dicnt[i]<<" ";
        ans = ans > dicnt[i] + i? dicnt[i] + i: ans;
    }
    cout<<ans<<endl;

}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);cout.tie(0);
    cin>>t;
    while(t--){
        solve();
    }
    return 0;
}