#include <bits/stdc++.h>
using namespace std;
void solve() {
int t;
cin >> t;
while (t--) {
int n;
cin >> n;
vector<vector<int>> tree(n + 1);
for (int i = 2; i <= n; ++i) {
int p;
cin >> p;
tree[p].push_back(i);
}
vector<int> depth(n + 1, 0);
// Define dfs as a lambda function
function<void(int)> dfs = [&](int u) {
vector<int> child_depths;
for (int v : tree[u]) {
dfs(v);
child_depths.push_back(depth[v]);
}
if (child_depths.empty()) {
depth[u] = 1;
} else {
sort(child_depths.rbegin(), child_depths.rend()); // Sort in decreasing order
int max_temp = 0;
for (int i = 0; i < child_depths.size(); ++i) {
int temp = child_depths[i] + i;
if (temp > max_temp) {
max_temp = temp;
}
}
depth[u] = max_temp;
}
};
dfs(1);
cout << depth[1] << '\n';
}
}
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
solve();
return 0;
}
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