#include "beechtree.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N = 2e5 + 7;
int n, m;
vector<int> g[N];
int col[N], ok[N], par[N];
set<int> s[N];
int sz[N], d[N];
void dfs(int u) {
sz[u] = 1;
for (auto v : g[u]) {
dfs(v);
sz[u] += sz[v];
d[v] = s[v].size();
s[u].insert(col[v]);
if (s[u] < s[v]) swap(s[u], s[v]);
for (auto x : s[v]) s[u].insert(v);
s[v].clear();
}
set<int> children;
for (auto v : g[u]) children.insert(col[v]);
if (children.size() == s[u].size() && g[u].size() == s[u].size()) {
int rem = sz[u] - 1 - g[u].size();
if (rem == 0) ok[u] = 1;
for (auto v : g[u]) {
if (d[v] == rem) {
ok[u] = 1;
}
}
}
}
vector<int> beechtree(int N, int M, vector<int> P, vector<int> C) {
n = N;
m = M;
for (int i = 0; i < n; ++i) {
par[i] = P[i];
if (i > 0) {
g[P[i]].push_back(i);
}
}
for (int i = 0; i < n; ++i) {
col[i] = C[i];
}
dfs(0);
vector<int> ret(n);
for (int i = 0; i < n; ++i) ret[i] = ok[i];
return ret;
}
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