#include <bits/stdc++.h>

#define rep(i, j, k) for (int i = (j); i <= (k); ++i)
#define per(i, j, k) for (int i = (j); i >= (k); --i)
#define SZ(v) int((v).size())
#define ALL(v) (v).begin(),(v).end()
#define fi first
#define se second
using ll = long long;
using pii = std::pair<int, int>;
using pll = std::pair<ll, ll>;

template<class T>inline void chkmn(T &x, T y) { if (y < x) x = y; }
template<class T>inline void chkmx(T &x, T y) { if (y > x) x = y; }

using namespace std;

const int maxn = 200010;

int n, fa[maxn], f[maxn], mx;
vector<int> e[maxn];

void dfs(int u) {
  if (!SZ(e[u])) return f[u] = 0, void();
  f[u] = 0;
  vector<int> vec;
  for (int v : e[u]) {
    dfs(v), f[v]++;
    vec.emplace_back(f[v]);
  }
  sort(ALL(vec));
  f[u] = vec[0], chkmx(mx, f[u] + (u != 1));
}

void work() {
  cin >> n;
  rep (i, 1, n) e[i].clear();
  rep (i, 2, n) cin >> fa[i], e[fa[i]].emplace_back(i);
  mx = 0, dfs(1);
  cout << mx << '\n';
}

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