#include<bits/stdc++.h>
#define INF 0x3f3f3f3f
using namespace std;
const int N=200005;
vector<int>e[N];
int dep[N],mx[N],mn[N];
int t,n,k,ans;
void dfs(int x,int depth){
    dep[x]=depth;if(!e[x].size())mx[x]=mn[x]=depth;
    for(int y:e[x])dfs(y,depth+1);
}
void dfs(int x){
    for(int y:e[x])dfs(y);
    for(int y:e[x]){
        mx[x]=max(mx[x],mx[y]);
        mn[x]=min(mn[x],mn[y]);
    }
    // cerr<<x<<" "<<mx[x]<<" "<<mn[x]<<"\n";
    ans=max(ans,max(mx[x]-dep[x],mn[x]));
}
int main(){
    // freopen("1.in","r",stdin);
    cin>>t;
    while(t--){
        ans=0;cin>>n;
        for(int i=1;i<=n;++i)
            dep[i]=0,mx[i]=0,mn[i]=INF,e[i].clear();
        for(int i=2,x;i<=n;++i)cin>>x,e[x].push_back(i);
        dfs(1,0);
        dfs(1);
        cout<<ans<<"\n";
    }
    return 0;
}