#include <bits/stdc++.h>
using namespace std;
vector mp(0,vector (0,0));
vector deep(0,0);
vector dpt(0,0);
typedef pair<int,int> pii;
int mxd=0;
vector mpt(0,vector (0,0));
void dfs(int d,int fa){
	for(auto x:mp[d]){
		if(x==fa) continue;
		deep[x]=deep[d]+1;
		if(deep[x]>deep[mxd]) mxd=x;
		dfs(x,d);
	}
}
void solve(){
	int n;
	cin>>n;
	mp.assign(n+1,vector<int>(0));
	mpt.assign(n+1,vector<int>(0));
	for(int i=2;i<=n;i++){
		int x;
		cin>>x;
		mp[x].push_back(i);
		mpt[i].push_back(x);
	}
	mxd=1;
	deep.assign(n+1,0);
	deep[1]=0;
	dfs(1,0);
//	cout<<1<<'\n';
	vector<pii> ins;
	for(int i=1;i<=n;i++) if(mp[i].size()==0) ins.push_back({deep[i],i});
	sort(ins.begin(),ins.end());
	dpt.assign(n+1,0);
	int ans=0;
	for(auto [x,y]:ins){
		int cnt=0;
//		cout<<y<<' ';
		while(1){
//			cout<<y<<'\n';
			dpt[y]=1;
			cnt++;
//			if(mpt[y].size()==0) break;
			y=mpt[y][0];
			if(dpt[y]||mpt[y].size()==0){
				cnt++;
				break;
			}
		} 
//		cout<<' '<<cnt<<'\n';
		ans=max(ans,cnt-1);
	}
	cout<<ans<<'\n';
}
int main(){
	ios::sync_with_stdio(false);
	cin.tie(0);
	int ins=1;
	cin>>ins;
	while(ins--) solve();
	return 0;
}