#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define mp make_pair
#define pii pair<int,int>
const int N = 1e6 + 10;
vector <int> G[N],vec;
int n,md[N],dep[N],fa[N],hson[N],top[N],len[N];

void dfs1(int x,int f) {
	md[x] = dep[x] = dep[f] + 1;
	fa[x] = f;
	for (auto y : G[x]) {
		if (y == f) continue;
		dfs1(y,x);
		if (md[y] > md[hson[x]]) {
			hson[x] = y;
			md[x] = md[y];
		}
	}
}

void dfs2(int x,int tp) {
	top[x] = tp;
	len[x] = md[x] - dep[top[x]] + 1;
	if (hson[x]) {
		dfs2(hson[x],tp);
	} else {
		vec.push_back(len[x]);
	}
	for (auto y : G[x]) {
		if (y != fa[x] && y != hson[x]) {
			dfs2(y,y);
		}
	}
}

void solve() {
	cin >> n;
	vec.clear();
	for (int i = 1;i <= n;++i) G[i].clear(),md[i] = fa[i] = len[i] = top[i] = hson[i] = 0;
	for (int i = 2;i <= n;++i) {
		int p;cin >> p;
		G[p].push_back(i);
		G[i].push_back(p);
	}
	dfs1(1,0);
	dfs2(1,1);
	sort(vec.begin(),vec.end());reverse(vec.begin(),vec.end());
	vec.push_back(0);
	int siz = vec.size();
	int ans = 0x3f3f3f3f;
	for (int i = 0;i < siz;++i) {
		//cout <<vec[i] << "\n";
		ans = min(ans,i + vec[i]);
	}
	cout << ans << "\n";
}

int main() {
	int T;cin >> T;
	while (T--) solve();
	return 0;
}