#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define pb push_back
const int N = 1e6 + 5, inf = 1e9;
int n;
vector<int> e[N];
vector<int> ret;
int son[N], dep[N];

void dfs(int u) {

	for (auto v : e[u]) {
		dfs(v);
		if (!son[u] || dep[v] > dep[son[u]])
			son[u] = v;
	}
	dep[u] += dep[son[u]] + 1;

}

void dfs1(int u, int depth) {
	if (!son[u])
		ret.push_back(depth);
	if (son[u])
		dfs1(son[u], depth + 1);
	for (auto v : e[u]) {
		if (v != son[u])
			dfs1(v, 1);
	}
}

void solve() {
	cin >> n;
	for (int i = 1 ; i <= n ; i++)
		dep[i] = 0, son[i] = 0;
	for (int i = 1; i <= n; i++)
		vector<int>().swap(e[i]);
	ret.clear();
	for (int i = 2; i <= n; i++) {
		int x;
		cin >> x;
		e[x].pb(i);
	}

	dfs(1);
	dfs1(1, 1);

	sort(ret.begin(), ret.end(), greater<int>());

//	for (auto x : ret)
//		cout << x << '\n';
	int ans = ret.size();
	for (int i = 0 ; i < ret.size() ; i++) {
		ans = min(ans, i + ret[i]);
	}
	cout << ans << '\n';
}

int main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	cout.tie(0);
	int t = 1;
	cin >> t;
	while (t--)
		solve();
	return 0;
}