#include "friend.h"
#pragma GCC optimize("O3")
#include <bits/stdc++.h>
using namespace std;
#define ll long long
// #define int ll
#define fi first
#define se second
#define ld long double
#define pb push_back
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
// Find out best sample
set<int> v[100010];
vector<bool> vis(100010, 0);
vector<int> figli[100010];
void dfs(int pos, int par) {
if (vis[pos]) return;
vis[pos] = 1;
if (par != -1) figli[par].pb(pos);
for (int x : v[pos]) dfs(x, pos);
}
int memo[100010][2];
int sol(int pos, bool posso) {
if (memo[pos][posso] && pos != 100005) return memo[pos][posso];
int ans = 0;
for (int x : figli[pos]) {
for (int y : figli[x]) {
int k = sol(y, 0);
int o = 0;
for (int z : figli[y]) {
int u = 0;
if (v[pos].count(z) == 0) {
u = sol(z, 1);
}
int l = 0;
for (int w : figli[z]) {
l += sol(w, 1);
}
o += max(u, l);
}
ans += max(k, o);
}
}
if (posso) {
int k = 0;
for (int x : figli[pos]) {
k += sol(x, 1);
}
ans = max(ans, k - 1);
}
return memo[pos][posso] = ans + 1;
}
void visita(int pos) {
vis[pos] = 1;
for (int x : figli[pos]) visita(x);
}
int findSample(int N, int confidence[], int host[], int protocol[]) {
int a[3] = {0, 0, 0};
for (int i = 1; i < N; i++) {
a[protocol[i]]++;
}
if (a[1] == N - 1) {
int tot = 0;
for (int i = 0; i < N; i++) tot += confidence[i];
return tot;
}
if (a[2] == N - 1) {
int tot = 0;
for (int i = 0; i < N; i++) tot = max(confidence[i], tot);
return tot;
}
for (int i = 1; i < N; i++) {
if (protocol[i] == 0 || protocol[i] == 2) {
v[host[i]].insert(i);
v[i].insert(host[i]);
}
if (protocol[i] == 1 || protocol[i] == 2) {
for (int x : v[host[i]]) {
v[x].insert(i);
v[i].insert(x);
}
}
}
int ans = 0;
for (int i = 0; i < N; i++) {
if (!vis[i]) {
dfs(i, -1);
}
}
// cout << "figli 0: ";
// for (int u : figli[0]) cout << u << " ";
// cout << endl;
fill(vis.begin(), vis.end(), 0);
for (int i = 0; i < N; i++) {
if (!vis[i]) {
int ma = 0;
// for (int a : figli[i]) {
// ma = max(ma, sol(a));
// for (int b : figli[a]) {
// ma = max(ma, sol(b));
// for (int c : figli[b]) {
// ma = max(ma, sol(c));
// }
// }
// }
ma = max(ma, sol(i, 1));
// figli[100005].clear();
// figli[100005].pb(i);
// ma = max(ma, sol(100005) - 1);
visita(i);
// cout << i << " " << ma << endl;
ans += ma;
}
}
return ans;
}
