#include <iostream>
#include <algorithm>
#include <cstring>
#include <vector>
const int maxn=1e6+10;
using namespace std;
vector<int> v[maxn],lp;
int son[maxn],len[maxn];
void dfs1(int x)
{
	for(auto i:v[x])
	{
		dfs1(i);
		if(len[i]>len[son[x]]) son[x]=i;
	}
	len[x]=len[son[x]]+1;
}
void dfs2(int x,int l)
{
	if(son[x]==0) lp.push_back(l);
	else{
       dfs2(son[x],l+1);
       for(auto u:v[x]) 
       {
       	   if(u!=son[x]) dfs2(u,1);
       } 
	} 
}
void solve()
{

	int n;
	cin>>n;
	for(int i=0;i<=n;i++)
	{
        son[i]=0,len[i]=0;
        v[i].clear();
	}
	lp.clear();
	for(int i=2;i<=n;i++)
	{
        int tmp;
        cin>>tmp;
        v[tmp].push_back(i); 
	}
    dfs1(1);
    dfs2(1,1);
    sort(lp.begin(),lp.end(),greater<int>());
    int ans=lp.size();
    	//cout<<ans<<"++++"<<endl;
    	int cnt=0;
        for(auto u:lp)
        {
        	ans=min(cnt+u,ans);
        	cnt++;
        	//cout<<cnt<<" "<<u<<"----"<<endl;
        }
    cout<<ans<<endl;
    return ;
}
int main()
{
	int t;
	cin>>t;
	while(t--)
	{
		solve();
	}
   
   return 0;
}