#include<bits/stdc++.h>
#define gt getchar
#define pt putchar
#define ll long long
#define ull unsigned long long
#define fst first
#define snd second
#define L(x) x<<1
#define R(x) x<<1|1
using namespace std;
typedef pair<int,int> pii;
const double eps=1e-8;
inline bool pts(char ch){return ch>=48&&ch<=57;}
inline int read(){
	bool f=0;int x=0;char ch;
	ch=gt();
	while(!pts(ch)&&ch!=EOF){if(ch=='-')f=1;ch=gt();}
	while(pts(ch)){x*=10;x+=(ch-48);ch=gt();}
	if(f)return -x;
	else return x;
}
template<class T>
inline void print(T x){
	char s[114];
	int top=0;
	if(x<0)pt('-');
	do{
		top++;
		if(x>=0)s[top]=(x%10)+48;
		else s[top]=(-(x%10)+48);
		x/=10;
	}while(x);
	while(top){pt(s[top]);top--;}
}
const int MAXN=2e5+10;
vector<int>g[MAXN];
void add_edge(int u,int v){
	g[u].push_back(v);
}
int dp[MAXN],ans=-1;
int outd[MAXN];
void dfs(int u,int fa){
	if(!outd[u]){
		dp[u]=0;
		return;
	}
	for(int v:g[u]){
		if(v==fa)continue;
		dfs(v,u);
		dp[u]=min(dp[u],dp[v]+1);
		ans=max(ans,dp[v]+1);
	}
}
void solve(){
	ans=-1;
	memset(dp,0x3f,sizeof(dp));
	int n=read();
	for(int i=2;i<=n;i++){
		int p=read();
		add_edge(p,i);
		outd[p]++;
	}
	add_edge(1,0); 
	dfs(1,0);
	cout<<ans<<'\n';for(int i=0;i<=n;i++)g[i].clear();
}
signed main(){
	int T=read();
	while(T--)solve();
	return 0;
}