#include "beechtree.h"
#include <bits/stdc++.h>
using namespace std;
#define MAXN 200001
#define nl '\n'
#define ff first
#define ss second
#define ll long long
#define ld long double
#define terminator main
#define pll pair<ll,ll>
#define add insert
#define append push_back
#define pii pair<int,int>
#define all(x) (x).begin(),(x).end()
vector<int> a[MAXN];
map<int, bool> x[MAXN];
vector<int> beechtree(int n, int m, vector<int> p, vector<int> c){
vector<pii> vec;
vector<int> ans(n, 1);
for(int v = n - 1; v >= 0; v--){
if(v) a[p[v]].append(v);
vec = {{a[v].size(), v}};
for(auto & u : a[v]){
if(a[u].size() > a[v].size() || !ans[u] || x[v][c[u]])
ans[v] = 0;
vec.append({a[u].size(), u});
x[v][c[u]] = 1;
}
if(!ans[v]) continue;
sort(all(vec));
for(int i = 0; i < a[v].size(); i++)
for(auto & [j, k] : x[vec[i].ss])
if(!x[vec[i + 1].ss][j]) ans[v] = 0;
}
return ans;
}
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