#include "friend.h"
#include <bits/stdc++.h>
using namespace std;
namespace sub1{
bool adj[30][30];
bool check(int n,int confidence[],int host[],int protocol[]){
return n<=20;
}
int solve(int n,int confidence[],int host[],int protocol[]){
for (int i=1; i<n; ++i){
if (protocol[i]==0){
adj[i][host[i]]=1;
adj[host[i]][i]=1;
}else if (protocol[i]==1){
for (int j=0; j<i; ++j) if (adj[host[i]][j]){
adj[i][j]=1;
adj[j][i]=1;
}
}else{
for (int j=0; j<i; ++j) if (adj[host[i]][j] || j==host[i]){
adj[i][j]=1;
adj[j][i]=1;
}
}
}
int ans=0;
for (int i=0; i<(1<<n); ++i){
int cur=0;
bool check=1;
for (int j=0; j<n; ++j) if (i>>j&1){
cur+=confidence[j];
for (int k=j+1; k<n; ++k) if (i>>k&1){
check&=!adj[j][k];
}
}
if (check) ans=max(ans, cur);
}
return ans;
}
}
namespace sub2{
bool check(int n,int confidence[],int host[],int protocol[]){
return *min_element(protocol+1, protocol+n)==1 && *max_element(protocol+1, protocol+n)==1;
}
int solve(int n,int confidence[],int host[],int protocol[]){
return accumulate(confidence, confidence+n, 0);
}
}
namespace sub3{
bool check(int n,int confidence[],int host[],int protocol[]){
return *min_element(protocol+1, protocol+n)==2 && *max_element(protocol+1, protocol+n)==2;
}
struct DSU{
vector<int> lab, val;
void init(int n, int confidence[]){
lab.assign(n, -1);
vector<int>(confidence, confidence+n).swap(val);
}
int find_set(int u){
return lab[u]<0?u:lab[u]=find_set(lab[u]);
}
void union_sets(int u, int v){
u=find_set(u); v=find_set(v);
if (u!=v){
if (lab[u]>lab[v]) swap(u, v);
lab[u]+=lab[v];
lab[v]=u;
val[u]=max(val[u], val[v]);
val[v]=0;
}
}
} dsu;
int solve(int n,int confidence[],int host[],int protocol[]){
dsu.init(n, confidence);
for (int i=1; i<n; ++i) dsu.union_sets(i, host[i]);
return accumulate(dsu.val.begin(), dsu.val.end(), 0);
}
}
namespace sub4{
bool check(int n,int confidence[],int host[],int protocol[]){
return *min_element(protocol+1, protocol+n)==0 && *max_element(protocol+1, protocol+n)==0;
}
const int N=1e3;
vector<int> g[N];
int f[N][2];
int *a;
void dfs(int u){
f[u][0]=0; f[u][1]=a[u];
for (int v:g[u]) dfs(v), f[u][0]+=max(f[v][0], f[v][1]), f[u][1]+=f[v][0];
}
int solve(int n,int confidence[],int host[],int protocol[]){
for (int i=1; i<n; ++i) g[host[i]].push_back(i);
a=confidence;
dfs(0);
return max(f[0][0], f[0][1]);
}
}
namespace sub5{
const int N=1e5+10;
vector<int> g[N];
int f[N][2][2], ff[N][2][2];
int *a, *par, *w;
void dfs(int u){
for (int v:g[u]) dfs(v);
int sz=g[u].size();
vector<vector<int>> cur(2, vector<int>(2)), nxt(2, vector<int>(2));
for (int i=0; i<sz; ++i){
int v=g[u][i];
if (w[v]==0){
for (int du=0; du<2; ++du) for (int dp=0; dp<2; ++dp) for (int dv=0; dv<2; ++dv){
if (du && dv) continue;
nxt[du][dp]=max(nxt[du][dp], cur[du][dp]+f[v][dv][du]);
}
}else if (w[v]==1){
for (int du=0; du<2; ++du) for (int dp=0; dp<2; ++dp) for (int dv=0; dv<2; ++dv){
if (dp && dv) continue;
nxt[du][dp]=max(nxt[du][dp], (!dv)*cur[du][dp]+f[v][dv][du]);
}
}else{
for (int du=0; du<2; ++du) for (int dp=0; dp<2; ++dp) for (int dv=0; dv<2; ++dv){
if ((du && dv) || (dp && dv)) continue;
nxt[du][dp]=max(nxt[du][dp], (!dv)*cur[du][dp]+f[v][dv][du]);
}
}
cur.swap(nxt);
vector<vector<int>>(2, vector<int>(2)).swap(nxt);
}
for (int du=0; du<2; ++du) for (int dp=0; dp<2; ++dp){
f[u][du][dp]=cur[du][dp]+du*a[u];
}
}
int solve(int n,int confidence[],int host[],int protocol[]){
for (int i=1; i<n; ++i) g[host[i]].push_back(i);
a=confidence; par=host; w=protocol;
dfs(0);
return max(f[0][0][0], f[0][1][0]);
}
}
// Find out best sample
int findSample(int n,int confidence[],int host[],int protocol[]){
return sub5::solve(n, confidence, host, protocol);
// if (sub1::check(n, confidence, host, protocol)) return sub1::solve(n, confidence, host, protocol);
// if (sub2::check(n, confidence, host, protocol)) return sub2::solve(n, confidence, host, protocol);
// if (sub3::check(n, confidence, host, protocol)) return sub3::solve(n, confidence, host, protocol);
// if (sub4::check(n, confidence, host, protocol)) return sub4::solve(n, confidence, host, protocol);
// return -1;
}
