#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[N];
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);
for (int i=0; i<n; ++i) a[i]=confidence[i];
dfs(0);
return max(f[0][0], f[0][1]);
}
}
namespace sub5{
bool check(int n,int confidence[],int host[],int protocol[]){
return *min_element(protocol+1, protocol+n)==0 && *max_element(protocol+1, protocol+n)==1;
}
struct FlowEdge{
int u, v, c, f;
FlowEdge(int _u=0, int _v=0, int _c=0, int _f=0){
u=_u, v=_v, c=_c, f=_f;
}
};
const int N=1e3+10;
vector<int> adj[N];
int a[N], color[N];
vector<FlowEdge> e;
vector<int> g[N];
int dep[N], ptr[N];
int source, sink;
void add_edge(int u, int v, int c){
g[u].push_back(e.size());
e.emplace_back(u, v, c);
g[v].push_back(e.size());
e.emplace_back(v, u, 0);
}
bool bfs(){
memset(dep, -1, sizeof dep);
dep[source]=0;
queue<int> q;
q.push(source);
while (q.size()){
int u=q.front(); q.pop();
if (u==sink) return 1;
for (int i:g[u]){
if (dep[e[i].v]!=-1 || e[i].c==e[i].f) continue;
dep[e[i].v]=dep[u]+1;
q.push(e[i].v);
}
}
return 0;
}
int dfs(int u, int pushed){
if (u==sink || !pushed) return pushed;
for (int &cid=ptr[u]; cid<(int)g[u].size(); ++cid){
int eid=g[u][cid];
if (dep[e[eid].v]!=dep[u]+1 || e[eid].c==e[eid].f) continue;
int t=dfs(e[eid].v, min(pushed, e[eid].c-e[eid].f));
if (!t) continue;
e[eid].f+=t;
e[eid^1].f-=t;
return t;
}
return 0;
}
int dinic(){
int flow=0;
while (bfs()){
memset(ptr, 0, sizeof ptr);
int pushed;
while ((pushed=dfs(source, 1e9))) flow+=pushed;
}
return flow;
}
int solve(int n,int confidence[],int host[],int protocol[]){
int sum=0;
for (int i=0; i<n; ++i) a[i]=confidence[i], sum+=a[i];
for (int i=1; i<n; ++i){
if (protocol[i]==0){
adj[host[i]].push_back(i);
adj[i].push_back(host[i]);
color[i]=color[host[i]]^1;
}else{
adj[i]=adj[host[i]];
color[i]=color[host[i]];
}
}
source=n; sink=n+1;
for (int i=0; i<n; ++i){
if (color[i]==0){
add_edge(source, i, a[i]);
for (int j:adj[i]) add_edge(i, j, 1e9);
}else{
add_edge(i, sink, a[i]);
}
}
return sum-dinic();
}
}
// Find out best sample
int findSample(int n,int confidence[],int host[],int protocol[]){
if (sub5::check(n, confidence, host, 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;
}
