This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
#define sz(x) int(x.size())
#define pb push_back
#define mp make_pair
#define ft first
#define sd second
using namespace std;
typedef long long ll;
const int N = 2e5 + 10;
ll f[N];
int n, d[N], pr[N];
vector <int> g[N];
set <int> se[N];
void dfs(int v, int pred = -1) {
for (int i = 0; i < sz(g[v]); ++i) {
int to = g[v][i];
if (to == pred)
continue;
d[to] = d[v] + 1;
dfs(to, v);
}
se[pr[v]].insert(v);
for (int i = 0; i < sz(g[v]); ++i) {
int to = g[v][i];
if (to == pred)
continue;
if (sz(se[pr[v]]) < sz(se[pr[to]])) {
while (!se[pr[v]].empty()) {
se[pr[to]].insert(*se[pr[v]].begin());
se[pr[v]].erase(se[pr[v]].begin());
}
pr[v] = pr[to];
} else {
while (!se[pr[to]].empty()) {
se[pr[v]].insert(*se[pr[to]].begin());
se[pr[to]].erase(se[pr[to]].begin());
}
pr[to] = pr[v];
}
}
for (set <int> :: iterator it = se[pr[v]].begin(); it != se[pr[v]].end(); ++it)
f[v] += d[*it] - d[v] + 1;
}
int main() {
ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
cin >> n;
for (int i = 0; i < n; ++i)
pr[i] = i;
for (int i = 1; i < n; ++i) {
int x;
cin >> x;
x--;
g[i].pb(x);
g[x].pb(i);
}
dfs(0);
for (int i = 0; i < n; ++i)
cout << f[i] << ' ';
}
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