#include "friend.h"
#include <bits/stdc++.h>
using namespace std;
#ifdef LOCAL
#include <debug.h>
#include "grader.cpp"
#endif
#define ft front
#define bk back
#define st first
#define nd second
#define ins insert
#define ers erase
#define pb push_back
#define pf push_front
#define _pb pop_back
#define _pf pop_front
#define lb lower_bound
#define ub upper_bound
#define mtp make_tuple
#define bg begin
#define ed end
#define all(x) (x).bg(), (x).ed()
#define sz(x) (int)(x).size()
typedef long long ll; typedef unsigned long long ull;
typedef double db; typedef long double ldb;
typedef pair<int, int> pi; typedef pair<ll, ll> pll;
typedef vector<int> vi; typedef vector<ll> vll; typedef vector<pi> vpi; typedef vector<pll> vpll;
typedef string str;
template<typename T> T gcd(T a, T b) { return (b == 0? a : gcd(b, a % b)); }
template<typename T> T lcm(T a, T b) { return a / gcd(a, b) * b; }
#define FOR(i, l, r) for (int (i) = (l); (i) <= (r); ++(i))
#define FOS(i, r, l) for (int (i) = (r); (i) >= (l); --(i))
#define FRN(i, n) for (int (i) = 0; (i) < (n); ++(i))
#define FSN(i, n) for (int (i) = (n) - 1; (i) >= 0; --(i))
#define EACH(i, x) for (auto &(i) : (x))
#define WHILE while
#define file "TEST"
mt19937 rd(chrono::steady_clock::now().time_since_epoch().count());
ll rand(ll l, ll r) { return uniform_int_distribution<ll>(l, r)(rd); }
/*
----------------------------------------------------------------
END OF TEMPLATE
----------------------------------------------------------------
Tran The Bao - ghostwriter
Training for VOI23 gold medal
----------------------------------------------------------------
DIT ME CHUYEN BAO LOC
----------------------------------------------------------------
*/
namespace subtask1 {
const int N = 10;
int c[N], d1[N][N], rs = 0;
void brute(int n, int confidence[], int i, int s) {
if (i >= n) {
bool ok = 1;
FRN(x, n)
FRN(y, n) {
if (x == y || !c[x] || !c[y]) continue;
if (d1[x][y]) ok = 0;
}
if (ok) rs = max(rs, s);
return;
}
brute(n, confidence, i + 1, s);
c[i] = 1;
brute(n, confidence, i + 1, s + confidence[i]);
c[i] = 0;
}
int findSample(int n, int confidence[], int host[], int protocol[]) {
FOR(i, 1, n - 1) {
int h = host[i], p = protocol[i];
if (!p) d1[i][h] = d1[h][i] = 1;
else if (p == 1) {
FRN(j, n)
if (d1[h][j])
d1[i][j] = d1[j][i] = 1;
}
else {
FRN(j, n)
if (d1[h][j])
d1[i][j] = d1[j][i] = 1;
d1[i][h] = d1[h][i] = 1;
}
}
brute(n, confidence, 0, 0);
return rs;
}
}
namespace subtask2 {
int rs = 0;
int findSample(int n, int confidence[], int host[], int protocol[]) {
FRN(i, n) rs += confidence[i];
return rs;
}
}
namespace subtask3 {
int rs = 0;
int findSample(int n, int confidence[], int host[], int protocol[]) {
FRN(i, n) rs = max(rs, confidence[i]);
return rs;
}
}
namespace subtask4 {
const int N = 1e3;
int d[N][2], confidence[N];
vi adj[N];
void dfs(int u, int p) {
int s0 = 0, s1 = 0;
EACH(v, adj[u]) {
if (v == p) continue;
dfs(v, u);
s0 += d[v][0];
s1 += d[v][1];
}
d[u][0] = max(confidence[u] + s1, s0);
d[u][1] = s0;
}
int findSample(int n, int confidence[], int host[], int protocol[]) {
FRN(i, n) subtask4::confidence[i] = confidence[i];
FOR(i, 1, n - 1) {
int u = i, v = host[i];
adj[u].pb(v);
adj[v].pb(u);
}
dfs(0, -1);
return d[0][0];
}
}
namespace subtask5 {
const int oo = 1e9 + 5;
const int N = 1e3 + 2;
int n, c[N], pre[N], ptr[N], dis[N], capacity[N][N], d1[N][N], confidence[N], source, sink;
void bfs(int source) {
FRN(i, n) dis[i] = oo;
dis[source] = 0;
queue<int> q;
q.push(source);
WHILE(!q.empty()) {
int u = q.ft();
q.pop();
FRN(v, n) {
if (!capacity[u][v] || dis[v] < oo) continue;
dis[v] = dis[u] + 1;
q.push(v);
}
}
}
int findBlockingFlow(int u, int flow) {
if (!flow) return 0;
if (u == sink) return flow;
WHILE(ptr[u] < n) {
int v = ptr[u]++;
if (!capacity[u][v] || dis[v] != dis[u] + 1) continue;
int f = findBlockingFlow(v, min(flow, capacity[u][v]));
if (f) {
pre[v] = u;
return f;
}
}
return 0;
}
int dinic() {
int rs = 0;
WHILE(1) {
bfs(source);
memset(ptr, 0, sizeof ptr);
int f = findBlockingFlow(source, oo);
if (!f) break;
WHILE(f) {
rs += f;
int cur = sink;
WHILE(cur != source) {
int prev = pre[cur];
capacity[prev][cur] = 0;
capacity[cur][prev] = 1;
cur = prev;
}
f = findBlockingFlow(source, oo);
}
}
return rs;
}
int findSample(int n, int confidence[], int host[], int protocol[]) {
subtask5::n = n;
FRN(i, n) subtask4::confidence[i] = confidence[i];
FOR(i, 1, n - 1) {
int u = i, v = host[i], p = protocol[i];
if (p == 0) {
d1[u][v] = d1[v][u] = 1;
c[u] = c[v] ^ 1;
}
else {
FRN(j, n)
if (d1[v][j])
d1[u][j] = d1[j][u] = 1;
c[u] = c[v];
}
}
source = subtask5::n++;
sink = subtask5::n++;
FRN(i, n)
if (c[i]) capacity[source][i] = 1;
else capacity[i][sink] = 1;
FRN(i, n)
FRN(j, n) {
if (!d1[i][j] || !c[i]) continue;
capacity[i][j] = 1;
}
return n - dinic();
}
}
namespace solution {
int findSample(int n, int confidence[], int host[], int protocol[]) {
return 1;
}
}
int findSample(int n, int confidence[], int host[], int protocol[]) {
if (n <= 10) return subtask1::findSample(n, confidence, host, protocol);
bool sub2 = (n <= 1e3), sub3 = (n <= 1e3), sub4 = (n <= 1e3), sub5 = (n <= 1000);
FRN(i, n)
if (confidence[i] != 1)
sub5 = 0;
FOR(i, 1, n - 1) {
if (protocol[i] != 1) sub2 = 0;
if (protocol[i] != 2) sub3 = 0;
if (protocol[i] != 0) sub4 = 0;
if (protocol[i] == 2) sub5 = 0;
}
if (sub2) return subtask2::findSample(n, confidence, host, protocol);
if (sub3) return subtask3::findSample(n, confidence, host, protocol);
if (sub4) return subtask4::findSample(n, confidence, host, protocol);
if (sub5) return subtask5::findSample(n, confidence, host, protocol);
return solution::findSample(n, confidence, host, protocol);
}
/*
6
13 3 6 20 10 15
0 0 0 1 1 2 2 1 0 0
2
10 20
0 1
2
10 20
0 0
3
1 1 1
0 0 0 1
----------------------------------------------------------------
From Benq:
stuff you should look for
* int overflow, array bounds
* special cases (n=1?)
* do smth instead of nothing and stay organized
* WRITE STUFF DOWN
* DON'T GET STUCK ON ONE APPROACH
----------------------------------------------------------------
*/
