#include <bits/stdc++.h>
#define ll long long
 
using namespace std;
 
const int MOD = 1e9 + 7;
 
void solve(){
	int n;
	cin >> n;
 
	vector<vector<int>> g(n + 1, vector<int>());
 
	for(int i = 2; i <= n; i++){
		int x;
		cin >> x;
		g[x].push_back(i);
	}
 
	int ans = n;
	vector<int> dp(n + 1, 0);
	auto dfs = [&](int x, auto && self) -> void {
		for(auto y: g[x]){
			self(y, self);
		}
 
		vector<int> p;
 
		for(auto y: g[x]){
			p.push_back(dp[y]);
		}
		if(!p.size())return;
		sort(p.begin(), p.end());
		dp[x] = p.back() + 1;
		int cur = 1;
		for(int i = p.size() - 2; i >= 0; i--){
			dp[x] = max(dp[x], p[i] + cur);
			if(i >= 1)cur++;
		}
	};
	dfs(1, dfs);
 
	cout << dp[1] << "\n";
}
 
int main(){
	ios_base::sync_with_stdio(false);
	cin.tie(nullptr);
 
	int t = 1;
	cin >> t;
 
	for(int i = 1; i <= t; i++){
		solve();
	}
	return 0;
}

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5
6
1 2 2 1 1
15
1 1 2 2 3 3 4 4 5 5 6 6 7 7
5
1 2 2 2
7
1 1 2 1 1 2
10
1 1 1 2 2 2 4 3 3