#include<bits/stdc++.h>
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
#define pii pair<ll,ll>
#define rep(i,a,b) for(ll i=(a);i<=(b);++i)
#define per(i,a,b) for(ll i=(a);i>=(b);--i)
using namespace std;
bool Mbe;
ll read(){
    ll x=0,f=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
    while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
    return x*f;
}
void write(ll x){
    if(x<0)putchar('-'),x=-x;
    if(x>9)write(x/10);
    putchar(x%10+'0');
}
const ll N=1e6+9;
ll T,n,dp[N];
vector<ll>to[N];
void dfs(ll x,ll f){
    vector<ll>g;
    for(ll y:to[x]){
        if(y==f)continue;
        dfs(y,x);
        g.push_back(dp[y]);
    }
    sort(g.begin(),g.end());
    dp[x]=1;
    rep(i,0,(ll)g.size()-1){
        if(i==1)dp[x]=max(dp[x],g[i]+1);
        else dp[x]=max(dp[x],g[i]);
    }
}
void solve(){
    n=read();
    rep(i,0,n)to[i].clear();
    rep(i,1,n){
        ll x=read();
        to[x].push_back(i);
    }
    dfs(0,-1);
    write(dp[0]),putchar('\n');
}
bool Med;
int main(){
    cerr<<fabs(&Med-&Mbe)/1048576.0<<"MB\n";
    T=read();
    while(T--)solve();
    return 0;
}