//# pragma GCC optimize(2)
#include <bits/stdc++.h>
//#define int long long
#define SZ(x) (int)(x).size()
#define fs first
#define sc second
#define PII pair<int,int>
#define ls(u) (u)<<1
#define rs(u) (u)<<1|1
#define pb push_back
#define eb emplace_back
#define vi vector<int>
#define vvi vector<vi >
#define vI vector<PII>
#define db double
#define all(a) (a).begin(),(a).end()
#define die cout << "???" << endl
//#define endl '\n'
using namespace std;
const int mod = 998244353;
//const int mod = 1169996969;
//const int mod = 1e9+7;
//const int inf = LLONG_MAX;
const int inf = 0x3f3f3f3f;
//const int inf = 1e9;
//const db PI = acos(-1.0);
const db eps = 1e-5;
typedef long long ll;
typedef unsigned long long  ull;
const int N = 1e6+5,M = 3e5+5,K = 30;

inline int rd() {
    int f = 0; int x = 0; char ch = getchar();
    for (; !isdigit(ch); ch = getchar()) f |= (ch == '-');
    for (; isdigit(ch); ch = getchar()) x = (x << 1) + (x << 3) + ch - '0';
    if (f) x = -x;
    return x;
}

void write(int a) {if(a>=10)write(a/10);putchar(a%10+'0');}
void wt(int a) {if(a < 0) {putchar('-');a = -a;}write(a);}
void wwt(int a){wt(a);putchar('\n');}

// void write(ll a) {if(a>=10)write(a/10);putchar(a%10+'0');}
// void wt(ll a) {if(a < 0) {putchar('-');a = -a;}write(a);}
// void wwt(ll a){wt(a);putchar('\n');}

int lowbit(int x) {return (x&(-x));}
int n,m,k;

int h[N],e[N],ne[N],tot;

void add(int u,int v)
{
    e[tot] = v,ne[tot] = h[u],h[u] = tot++;
}

int f[N];
int out[N];
int dep[N];

void dfs(int u)
{
    dep[u] = dep[f[u]] + 1;

    for(int i = h[u];~i;i = ne[i])
    {
        int v = e[i];
        dfs(v);
    }
}

bool vis[N];

void dfs2(int u)
{
    for(int i = h[u];~i;i = ne[i])
    {
        int v = e[i];
        dep[v] = dep[u] + 1;
        if(!vis[v])
            dfs2(v);
    }
}


signed main()
{
    ios::sync_with_stdio(0);
    cin.tie(0),cout.tie(0);
    #ifndef ONLINE_JUDGE
    freopen("in.txt", "r+", stdin);
    freopen("out.txt", "w+", stdout);
    #endif
    
    int _;
    for(cin >> _;_;_--)
    {
        cin >> n;

        for(int i = 1;i<=n;i++)
        {
            h[i] = -1;
            out[i] = 0;
            vis[i] = 0;
        }


        tot = 0;

        for(int i = 2;i<=n;i++)
        {
            cin >> f[i];
            add(f[i],i);
            out[f[i]]++;
        }

        dfs(1);    

        int cnt = 0;
        int ans = 0;

        for(int i = 1;i<=n;i++)
        {
            if(out[i] == 0)
            {
                cnt++;
            }

            ans = max(ans,dep[i]);
        }

        ans = min(ans,cnt);

        int id = 0,mx = 0;
        int tmp = 0;

        m = sqrt(n*2);

        for(int j = 0;j<m;j++)
        {
            mx = -1;
            id = 0;
            for(int i = 1;i<=n;i++)
            {
                if(out[i] == 0 && !vis[i])
                {
                    if(dep[i] > mx)
                    {
                        mx = dep[i];
                        id = i;
                    }
                }
            }

            if(mx == -1) break;
            tmp++;
            cnt--;

            ans = min(ans,tmp + mx);


            while(!vis[id] && id)
            {
                vis[id] = 1;
                dep[id] = 0;
                dfs2(id);
                id = f[id];
            }

            mx = -1;
            id = 0;
            for(int i = 1;i<=n;i++)
            {
                if(out[i] == 0 && !vis[i])
                {
                    if(dep[i] > mx)
                    {
                        mx = dep[i];
                        id = i;
                    }
                }
            }

            if(mx < 0) continue;
            ans = min(ans,tmp + mx);
        }

        cout << ans << endl;

    }
    
    
    return 0;

}