#include <bits/stdc++.h>
#define int long long
using namespace std;
int n;
vector<vector<int>> con;
vector<int> leafs;
vector<int> fa;
vector<int> dep;
bool cmp(int a, int b)
{
  return dep[a] < dep[b];
}
void dfs(int u, int f)
{
  bool flag = 0;
  fa[u] = f;
  dep[u] = dep[f] + 1;
  for (auto v : con[u])
  {
    if (v == f)
      continue;
    flag = 1;
    dfs(v, u);
  }
  if (!flag)
    leafs.push_back(u);
}
bool judge(int mid)
{
  vector<bool> vis(n + 1, 0);
  for (auto lf : leafs)
  {
    int nowpos = lf;
    int cnt = mid;
    while (cnt--)
    {
      vis[nowpos] = 1;
      nowpos = fa[nowpos];
      if (vis[nowpos])
        break;
    }
  }
  for (int i = 2; i <= n; i++)
  {
    if (vis[i])
      continue;
    else
      return 0;
  }
  return 1;
}
void solve()
{
  cin >> n;
  con.assign(n + 1, vector<int>());
  fa.assign(n + 1, 0);
  leafs.clear();
  dep.assign(n + 1, 0);
  for (int i = 2; i <= n; i++)
  {
    int f;
    cin >> f;
    fa[i] = f;
    con[f].push_back(i);
    con[i].push_back(f);
  }
  dfs(1, 1);
  sort(leafs.begin(), leafs.end(), cmp);
  int l = 0, r = n - 1;
  while (l + 1 < r)
  {
    int mid = (l + r) / 2;
    if (judge(mid))
      r = mid;
    else
      l = mid;
  }
  cout << r << endl;
}
signed main()
{
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int T = 1;
  cin >> T;
  while (T--)
  {
    solve();
  }
  return 0;
}