#include <bits/stdc++.h>
using namespace std;
#ifndef ONLINE_JUDGE
#define dbg(x) cerr << #x << ' '; print(x); cerr << endl;
#else
#define dbg(x)
#endif
void print(int x) {cerr << x;}
void print(long long x) {cerr << x;}
void print(char x) {cerr << x;}
void print(string x) {cerr << x;}
void print(double x) {cerr << x;}
template <class T> void print(vector <T> x);
template <class T> void print(set <T> x);
template <class T> void print(multiset <T> x);
template <class T, class V> void print(pair <T, V> x);
template <class T, class V> void print(map <T, V> x);
template <class T> void print(vector <T> x) {cerr << "[ "; for(auto i : x) {print(i); cerr << ' ';} cerr << "]";}
template <class T> void print(set <T> x) {cerr << "[ "; for(auto i : x) {print(i); cerr << ' ';} cerr << "]";}
template <class T> void print(multiset <T> x) {cerr << "[ "; for(auto i : x) {print(i); cerr << ' ';} cerr << "]";}
template <class T, class V> void print(pair <T, V> x) {cerr << "{"; print(x.first); cerr << ' '; print(x.second); cerr << "}";}
template <class T, class V> void print(map <T, V> x) {cerr << "[ "; for(auto i : x) {print(i); cerr << ' ';} cerr << "]";}
#define ll long long
#define pb push_back
#define ppb pop_back
#define PII pair <int, int>
#define PLL pair <ll, ll>
#define all(v) (v).begin(), (v).end()
#define OK cerr << "OK\n";
#define MP make_pair
const int N0 = 2e5 + 5;
int n, m;
vector <int> p, c, T[N0], answ;
vector <int> dfs(int node){
if(T[node].empty()){
return {};
}
//build ultimate set
set <int> ultimate;
for(int u : T[node]){
ultimate.insert(c[u]);
}
if(ultimate.size() != T[node].size()) answ[node] = 0;
//build sub
vector <pair <int, set <int>>> sub;
for(int u : T[node]){
vector <int> k = dfs(u);
answ[node] &= answ[u];
set <int> colors;
for(int i : k){
colors.insert(c[i]);
}
sub.pb({colors.size(), colors});
}
//check
sort(all(sub));
reverse(all(sub));
set <int> tmp = ultimate;
for(auto x : sub){
int sz = tmp.size();
set <int> ntmp;
for(int i : x.second){
tmp.insert(i);
ntmp.insert(i);
}
if(tmp.size() != sz){
answ[node] = 0;
}
tmp = ntmp;
}
vector <int> res;
return T[node];
}
vector <int> beechtree(int N, int M, vector <int> P, vector <int> C){
n = N, m = M, p = P, c = C;
for(int i = 1; i < n; i++){
T[p[i]].pb(i);
}
answ.assign(n, 1);
dfs(0);
return answ;
}
