// Author: Chuanhua Yu
// Time: 2024-11-26.
#include<bits/stdc++.h>
using namespace std;
using ll = long long;
const int N = 2e5 + 5;

int n, tot;
int head[N], ver[N], nxt[N], h[N], th[N];

void add(int x, int y){
    ver[++tot] = y; nxt[tot] = head[x]; head[x] = tot;
}
void dfs(int x){
    for(int i = head[x]; i; i = nxt[i]){
        int y = ver[i];
        dfs(y);
        if(th[x]) th[x] = min(th[x], th[y] + 1);
        else th[x] = th[y] + 1;
    }
    for(int i = head[x]; i; i = nxt[i])
        h[x] = max(h[x], th[ver[i]] + 1);
}
void solve(){
    tot = 1;
    cin >> n;
    memset(head, 0, (n + 1) * sizeof(int));
    memset(h, 0, (n + 1) * sizeof(int));
    memset(th, 0, (n + 1) * sizeof(int));
    for(int i = 2; i <= n; i++){
        int p; cin >> p;
        add(p, i);
    }
    dfs(1);
    int ans = 0;
    for(int i = 1; i <= n; i++) ans = max(ans, h[i]);
    cout << ans << '\n';
}

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