/*************************************
* author: marvinthang *
* created: 21.01.2024 19:34:55 *
*************************************/
#include "beechtree.h"
#include <bits/stdc++.h>
using namespace std;
#define fi first
#define se second
#define left ___left
#define right ___right
#define TIME (1.0 * clock() / CLOCKS_PER_SEC)
#define MASK(i) (1LL << (i))
#define BIT(x, i) ((x) >> (i) & 1)
#define __builtin_popcount __builtin_popcountll
#define ALL(v) (v).begin(), (v).end()
#define REP(i, n) for (int i = 0, _n = (n); i < _n; ++i)
#define REPD(i, n) for (int i = (n); i-- > 0; )
#define FOR(i, a, b) for (int i = (a), _b = (b); i < _b; ++i)
#define FORD(i, b, a) for (int i = (b), _a = (a); --i >= _a; )
#define FORE(i, a, b) for (int i = (a), _b = (b); i <= _b; ++i)
#define FORDE(i, b, a) for (int i = (b), _a = (a); i >= _a; --i)
#define scan_op(...) istream & operator >> (istream &in, __VA_ARGS__ &u)
#define print_op(...) ostream & operator << (ostream &out, const __VA_ARGS__ &u)
#ifdef LOCAL
#include "debug.h"
#else
#define file(name) if (fopen(name".inp", "r")) { freopen(name".inp", "r", stdin); freopen(name".out", "w", stdout); }
#define DB(...) 23
#define db(...) 23
#define debug(...) 23
#endif
template <class U, class V> scan_op(pair <U, V>) { return in >> u.first >> u.second; }
template <class T> scan_op(vector <T>) { for (size_t i = 0; i < u.size(); ++i) in >> u[i]; return in; }
template <class U, class V> print_op(pair <U, V>) { return out << '(' << u.first << ", " << u.second << ')'; }
template <size_t i, class T> ostream & print_tuple_utils(ostream &out, const T &tup) { if constexpr(i == tuple_size<T>::value) return out << ")"; else return print_tuple_utils<i + 1, T>(out << (i ? ", " : "(") << get<i>(tup), tup); }
template <class ...U> print_op(tuple<U...>) { return print_tuple_utils<0, tuple<U...>>(out, u); }
template <class Con, class = decltype(begin(declval<Con>()))> typename enable_if <!is_same<Con, string>::value, ostream&>::type operator << (ostream &out, const Con &con) { out << '{'; for (__typeof(con.begin()) it = con.begin(); it != con.end(); ++it) out << (it == con.begin() ? "" : ", ") << *it; return out << '}'; }
// end of template
vector <int> beechtree(int N, int M, vector <int> P, vector <int> C) {
vector <int> sz(N, 1);
vector <vector <int>> adj(N), subtree(N);
REPD(i, N) {
--C[i];
subtree[i].push_back(i);
if (i) {
sz[P[i]] += sz[i];
adj[P[i]].push_back(i);
subtree[P[i]].insert(subtree[P[i]].end(), ALL(subtree[i]));
}
}
vector <int> has_color(M);
vector <int> res(N, 1);
REPD(u, N) {
if (res[u]) {
for (int v: adj[u]) {
if (has_color[C[v]]) {
res[u] = 0;
break;
}
has_color[C[v]] = 1;
}
for (int v: adj[u]) has_color[C[v]] = 0;
}
if (!res[u]) res[P[u]] = 0;
}
vector is_subtree(N, vector<bool>(N));
REP(i, N) {
for (int v: adj[i]) has_color[C[v]] = sz[v];
REP(j, N) if (sz[i] >= sz[j]) {
is_subtree[i][j] = true;
for (int v: adj[j]) if (has_color[C[v]] < sz[v]) {
is_subtree[i][j] = false;
break;
}
}
for (int v: adj[i]) has_color[C[v]] = 0;
}
REPD(r, N) if (res[r]) {
sort(ALL(subtree[r]), [&] (int x, int y) { return sz[x] > sz[y]; });
FOR(i, 1, sz[r]) if (!is_subtree[subtree[r][i - 1]][subtree[r][i]]) {
res[r] = 0;
if (P[r]) res[P[r]] = 0;
break;
}
}
return res;
}
