#include <bits/stdc++.h>

const int N = 1e6 + 5;

int q, n, x;
int head[N], cnt;
struct edge{ 
    int nxt, to;
} e[N];
int w[N], hson[N], d[N];
int a[N], m;

int read() {
    int res = 0, i = 1;
    char c = getchar();
    while (c < '0' || c > '9') {
        if (c == '-') i = -i;
        c = getchar();
    }
    while (c >= '0' && c <= '9') {
        res = res * 10 + c - '0';
        c = getchar();
    }
    return res * i;
}

void write(int x) {
    if (x < 0) {
        putchar('-');
        x = -x;
    }
    if (x > 9) write(x / 10);
    putchar(x % 10 + '0');
}

void add(int u, int v) {
    e[++cnt].to = v;
    e[cnt].nxt = head[u];
    head[u] = cnt;
}

void dfs1(int k, int dep) {
    w[k] = 0, d[k] = dep, hson[k] = 0;
    if (!head[k]) {
        w[k] = dep;
        return;
    }
    for (int i = head[k]; i; i = e[i].nxt) {
        dfs1(e[i].to, dep + 1);
        w[k] = std::max(w[k], w[e[i].to]);
        if (w[k] == w[e[i].to])
            hson[k] = e[i].to;
    }
}

void dfs2(int k, int top) {
    if (!head[k]) {
        a[++m] = d[k] - d[top] + 1;
        return;
    }
    if (hson[k]) dfs2(hson[k], top);
    for (int i = head[k]; i; i = e[i].nxt)
        if (e[i].to != hson[k])
            dfs2(e[i].to, e[i].to);
}

void Main() {
    n = read();
    for (int i = 1; i <= n; ++i) head[i] = 0;
    cnt = 0;
    for (int i = 2; i <= n; ++i) {
        x = read();
        add(x, i);
    }
    m = 0;
    dfs1(1, 1);
    // for (int i = 1; i <= n; ++i) write(d[i]), putchar(' ');
    // puts("");
    // for (int i = 1; i <= n; ++i) write(w[i]), putchar(' ');
    // puts("");
    dfs2(1, 1);
    std::sort(a + 1, a + m + 1, [](int x, int y) {return x > y;});
    // for (int i = 0; i <= m; ++i) write(a[i]), putchar(' ');
    // puts("");
    int ans = m;
    for (int i = 0; i < m; ++i)
        ans = std::min(ans, i + a[i + 1]);
    write(ans), puts("");
}

int main() {
    q = read();
    while (q--) Main();
    return 0;
}