#include "beechtree.h"
#include<bits/stdc++.h>
#define int long long
#define f0r(i,n) for(int i = 0; i<n; i++)
#define pb push_back
#define mp make_pair
#define vi vector<int>
#define mii map<int,int>
#define pii pair<int,int>
#define vpii vector<pii>
#define FOR(i, k, n) for(int i = k; i<n; i++)
#define vb vector<bool>
using namespace std;
vector<vi>adj, colset;
vi dep, sts, die, diesum;
int dfs(int node){
	int cur = 1;
	for(auto u : adj[node]){
		dep[u] = dep[node] + 1;
		cur += dfs(u);
	}
	sts[node] = cur;
	return cur;
}
int d2(int node){
	int cur = die[node];
	for(auto u : adj[node]){
		cur += d2(u);
	}
	diesum[node] = cur;
	return cur;
}
std::vector<signed> beechtree(signed N, signed M, std::vector<signed> P, std::vector<signed> C)
{
	vector<signed>ans(N);
	FOR(i, 1, N)ans[i] = 1;
	colset.clear(); colset.resize(N); adj.clear(); adj.resize(N); 
	dep.clear(); dep.resize(N); sts.clear(); sts.resize(N); die.clear(); die.resize(N); diesum.clear(); diesum.resize(N);
	FOR(i, 1, N){
		adj[P[i]].pb(i);
	}
	
	f0r(i, N){
		set<int>tmp;
		for(auto u : adj[i]){
			tmp.insert(u); colset[i].pb(u);
		}
		if(tmp.size() != colset[i].size()){
			die[i] = 1;
		}
	}
	dfs(0);
	d2(0);
	vpii w;
	f0r(i, N){
		w.pb(mp(colset[i].size(), i));
	}
	sort(w.rbegin(), w.rend());
	bool ok = 1;
	if(w[0].second != 0)ok = 0;
	set<int>vis;
	
	f0r(i, N){
		set<int>ne;
		for(auto u : colset[i]){
			if(!vis.count(u))ok = 0;
			ne.insert(u);
		}
		
		
		if(!ok)break;
		vis = ne;
	}
	if(ok)ans[0] = 1;
	f0r(i, N){
		if(diesum[i] != 0)ans[i] = 0;
	}
    return ans;
}
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