#include <iostream>
#include <vector>
#include <set>

using namespace std;

const int N = 1e6 + 228;
const int K = 20;

int up[N][K];
int tin[N], h[N];
int timer = 0;

vector<int> G[N];

void dfs(int v) {
    tin[v] = timer++;
    for (int i : G[v])
        dfs(i);
}

int la(int a, int level) {
    for (int i = K - 1; i >= 0; --i) {
        if (level >= (1 << i))
            level -= (1 << i), a = up[a][i];
    }
    return a;
}

int lca(int a, int b) {
    if (h[a] > h[b])
        swap(a, b);
    b = la(b, h[b] - h[a]);
    if (a == b)
        return a;
    for (int i = K - 1; i >= 0; --i) {
        if (up[a][i] != up[b][i])
            a = up[a][i], b = up[b][i];
    }
    return up[a][0];
}

void solve() {
    int n;
    cin >> n;
    timer = 0;
    for (int i = 0; i <= n; ++i)
        G[i].clear();

    G[0].push_back(1);
    up[1][0] = 0, h[1] = 1;
    for (int i = 2; i <= n; ++i) {
        int a;
        cin >> a;
        G[a].push_back(i);
        up[i][0] = a, h[i] = h[a] + 1;
    }

    dfs(0);
    for (int k = 1; k < K; ++k) {
        for (int i = 0; i <= n; ++i) {
            up[i][k] = up[up[i][k - 1]][k - 1];
        }
    }
    vector<set<pair<int, int>>> who(n + 1);
    for (int i = 0; i <= n; ++i) {
        who[i].emplace(-1, 0);
        who[i].emplace(n + 3, 0);
    }

    cout << 0 << ' ';
    int cnt_leaf = 0;
    long long val = 0;
    vector<int> leaf(n + 1);
    for (int i = 2; i <= n; ++i) {
        auto z = who[h[i]].lower_bound(make_pair(tin[i], i));
        int v = lca(z->second, i), _v = lca((--z)->second, i);
        if (h[_v] > h[v])
            swap(_v, v);

        val += 2 * (h[i] - h[v] - 1);
        ++cnt_leaf;
        if (leaf[up[i][0]]) {
            leaf[up[i][0]] = 0;
            --cnt_leaf;
        }
        leaf[i] = 1;
        who[h[i]].emplace(tin[i], i);
        cout << val - i + cnt_leaf << ' ';
    }
    cout << '\n';
}

int main() {
    int t;
    cin >> t;
    while (t--)
        solve();
}