#include<bits/stdc++.h>
using namespace std;

void solve(){
	int n;
	cin >> n;
	vector<int> a(n);
	vector<vector<int> > G(n + 1);
	for(auto &it : a) cin >> it;
	if(n == 2) {
		cout << 1 << '\n';
		return;
	}
	for(int i = 1 ; i < n ; ++i) {
		auto x = a[i] , y = i + 1;
		G[y].emplace_back(x);
		G[x].emplace_back(y);
	}
	vector<bool> buff(n + 1 , false);
	function<void(int , int)> pre = [&](int now , int fa) {
		if(G[now].size() >= 3 && now != 1) buff[now] = true;
		if(G[now].size() >= 2 && now == 1) buff[now] = true;
		//cerr <<"w"<< now << ' ' << buff[now] << endl;
		for(auto it : G[now]) {
			if(it == fa) continue;
			pre(it , now);
			if(buff[it]) buff[now] = true;
		}
	};
	int ans = 0;
	function<void(int , int , int)> dfs = [&](int now , int fa , int m) {
		ans = max(ans , m);
		//cerr << now << ' ' << ans << ' ' << m << endl;
		int cnt = 0;
		for(auto it : G[now]) {
			if(it == fa) continue;
			if(buff[it]) ++cnt;
		}
		if(cnt == 0) {
			//cerr <<"w"<< now << ' '<<ans << ' ' << m << endl;
			ans = max(ans , m + 1);
			return;
		}
		for(auto it : G[now]) {
			if(it == fa) continue;
			//cerr << it << ' ' << fa << ' ' << m << endl;
			if(cnt >= 2) {
				dfs(it , now , m + 1);
			}
			else {
				
				if(buff[it])    dfs(it , now , m);
				else ans = max(ans , m + 1);
			}
		}
	};
	pre(1 , -1);
	if(!buff[1]) {
		cout << 1 << '\n';
		return; 
	}
	dfs(1 , -1 , 1);
	cout << ans << '\n';
}

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