#include "beechtree.h"
#include <bits/stdc++.h>
//#define int long long
#define pii pair<int,int> 
#define vi vector<int>
#define ff first
#define ss second
#define sp << " " << 
#define all(x) x.begin(),x.end()
using namespace std;
const int LIM = 2e5+1;
vector<pii> edges[LIM];
vi ans(LIM,0),C,P;
int N;
vi ctr(LIM,0);
bool check(int node) {
    for (auto it : edges[node]) {
        ctr[it.ss] = 0;
    }
    for (auto it : edges[node]) {
        if (ctr[it.ss]) return false;
        ctr[it.ss]++;
    }
    //hepsi farklı
    int cocu = 0;
    for (auto it : edges[node]) {
        if (edges[it.ff].size()) cocu++;
    }
    if (cocu > 1) return false;
    if (!cocu) return true;
    ctr.assign(N,0);
    for (auto it : edges[node]) ctr[it.ss]++;
    for (auto it : edges[node]) {
        for (auto itt : edges[it.ff]) {
            if (!ctr[itt.ss]) return false;
        }
    }
    return true;
}
int dfs(int node) {
    for (auto it : edges[node]) dfs(it.ff);
   return ans[node] = check(node);
}
std::vector<int> beechtree(int N_, int M, std::vector<int> P_, std::vector<int> C_)
{
    N = N_;
    P = P_,C = C_;
    ans.assign(N_,0);
    for (int i = 0;i<N;i++) edges[i].clear(); 
    vi v;
    for (auto it : C) v.push_back(it);
    sort(all(v));
    v.erase(unique(all(v)),v.end());
    for (auto& it : C) it = lower_bound(all(v),it)-v.begin();
    for (int i = 1;i<N;i++) {
        edges[P[i]].push_back({i,C[i]});
    }
    dfs(0);
    return ans;
}
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