#include <bits/stdc++.h>
using namespace std;

constexpr int N = 1e6 + 7;

int n;
vector<int> g[N], lp;

int len[N], son[N];

void dfs1(int x) {
    for (int y : g[x]) {
        dfs1(y);
        if (len[y] > len[son[x]]) son[x] = y;
    }
    len[x] = len[son[x]] + 1;
}
void dfs2(int x, int l = 0) {
    if (!son[x]) lp.push_back(l);
    else {
        dfs2(son[x], l + 1);
        for (int y : g[x]) if (y != son[x]) dfs2(y, 1);
    }
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    int T;
    cin >> T;
    while (T--) {
        cin >> n;

        lp.clear();
        for (int x = 1; x <= n; ++x) son[x] = len[x] = 0, g[x].clear();

        for (int i = 2, x; i <= n; ++i) cin >> x, g[x].push_back(i);
        dfs1(1);
        dfs2(1, 1);
        sort(lp.begin(), lp.end(), greater<int>());
        int p = lp.size(), ans = p;
        for (int i = 0; i < p; ++i) ans = min(ans, lp[i] + i);
        cout << ans << '\n';
    }

    return 0;
}