#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }


int N;
vector<int> P;

vector<vector<int>> graph;
vector<int> dp;

void dfs(int u) {
  vector<int> fs;
  for (const int v : graph[u]) {
    dfs(v);
    fs.push_back(dp[v]);
  }
  sort(fs.begin(), fs.end());
  const int len = fs.size();
  if (len == 0) {
    dp[u] = 1;
  } else if (len == 1) {
    dp[u] = fs[len - 1];
  } else {
    dp[u] = max(1 + fs[len - 2], fs[len - 1]);
  }
}

int main() {
  for (int numCases; ~scanf("%d", &numCases); ) { for (int caseId = 1; caseId <= numCases; ++caseId) {
    scanf("%d", &N);
    P.resize(N);
    for (int u = 0; u < N; ++u) {
      scanf("%d", &P[u]);
      --P[u];
    }
    
    graph.assign(N, {});
    for (int u = 1; u < N; ++u) {
      graph[P[u]].push_back(u);
    }
    dp.assign(N, -1);
    dfs(0);
    printf("%d\n", dp[0]);
  }
#ifndef LOCAL
  break;
#endif
  }
  return 0;
}