#include "friend.h"
/*
* Author: Nonoze
* Created: Tuesday 28/04/2026
*/
#include <bits/stdc++.h>
using namespace std;
#ifndef DEBUG
#define dbg(...)
#else
#include "grader.cpp"
#endif
// #define cout cerr << "OUT: "
#define endl '\n'
#define endlfl '\n' << flush
#define quit(x) return (void)(cout << x << endl)
template<typename T> void read(T& x) { cin >> x; }
template<typename T1, typename T2> void read(pair<T1, T2>& p) { read(p.first), read(p.second); }
template<typename T> void read(vector<T>& v) { for (auto& x : v) read(x); }
template<typename T1, typename T2> void read(T1& x, T2& y) { read(x), read(y); }
template<typename T1, typename T2, typename T3> void read(T1& x, T2& y, T3& z) { read(x), read(y), read(z); }
template<typename T1, typename T2, typename T3, typename T4> void read(T1& x, T2& y, T3& z, T4& zz) { read(x), read(y), read(z), read(zz); }
template<typename T> void print(vector<T>& v) { for (auto& x : v) cout << x << ' '; cout << endl; }
#define sz(x) (int)(x.size())
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define make_unique(v) sort(all(v)), v.erase(unique(all(v)), (v).end())
#define pb push_back
#define mp(a, b) make_pair(a, b)
#define fi first
#define se second
#define cmin(a, b) a = min(a, b)
#define cmax(a, b) a = max(a, b)
#define YES cout << "YES" << endl
#define NO cout << "NO" << endl
#define QYES quit("YES")
#define QNO quit("NO")
// #define int long long
#define double long double
const int inf = numeric_limits<int>::max() / 4;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
const int MOD = 1e9+7, LOG=20;
int n;
vector<int> adj[100000];
vector<pair<int, bool>> adj2[100000];
// Find out best sample
int findSample(int _n, int a[], int host[], int protocol[]) { n=_n;
for (int v=1; v<n; v++) {
if (protocol[v]==0) {
adj[host[v]].pb(v);
} else {
adj2[host[v]].pb({v, protocol[v]-1});
}
}
int dp[n][2];
for (int i=n-1; i>=0; i--) {
for (int ok=0; ok<2; ok++) {
int ans=0, sm=0;
for (auto &v: adj[i]) ans+=dp[v][1];
for (auto &v: adj2[i]) ans+=dp[v.fi][0];
if (ok) {
for (auto &v: adj[i]) sm+=dp[v][1];
for (auto &v: adj2[i]) sm+=dp[v.fi][0];
int idx=0;
cmax(ans, sm);
for (auto &v: adj[i]) {
while (idx<sz(adj2[i]) && adj2[i][idx].fi<v) {
sm+=dp[adj2[i][idx].fi][1]-dp[adj2[i][idx].fi][0];
cmax(ans, sm);
if (adj2[i][idx].se==1) sm-=dp[adj2[i][idx].fi][1]-dp[adj2[i][idx].fi][0];
idx++;
}
sm+=dp[v][0]-dp[v][1];
}
while (idx<sz(adj2[i])) {
sm+=dp[adj2[i][idx].fi][1]-dp[adj2[i][idx].fi][0];
cmax(ans, sm);
if (adj2[i][idx].se==1) sm-=dp[adj2[i][idx].fi][1]-dp[adj2[i][idx].fi][0];
idx++;
}
cmax(ans, sm);
int ans2=a[i];
for (auto &j: adj[i]) ans2+=dp[j][0];
for (auto &j: adj2[i]) {
if (j.se==0) ans2+=dp[j.fi][1];
else ans2+=dp[j.fi][0];
}
cmax(ans, ans2);
}
dp[i][ok]=ans;
}
}
return dp[0][1];
}
