#include <bits/stdc++.h>
#include "friend.h"
using namespace std;
#define FOR(a, b, c) for (int a = b; a < c; a++)
#define ll long long
#define vi vector<int>
#define pb push_back
#define mp make_pair
int memo[1000][2];
bool friends[1000][1000];
bool isLeft[1000];
bool visited[1000];
int *A;
int n;
void dfsVisited(int u, int p) {
visited[u] = true;
for (int v = 0; v < n; v++) {
if (!friends[v][u]) continue;
if (v == p || v == u) continue;
dfsVisited(v, u);
}
}
int run(int u, int canTake, int p) {
if (memo[u][canTake] != -1) return memo[u][canTake];
int ans = 0;
// Option 1: Don't take u
int opAns = 0;
for (int v = 0; v < n; v++) {
if (!friends[v][u]) continue;
if (v == p || v == u) continue;
opAns += run(v, 1, u);
}
ans = opAns;
// Option 2: Take u
if (canTake) {
opAns = A[u];
for (int v = 0; v < n; v++) {
if (!friends[v][u]) continue;
if (v == p || v == u) continue;
opAns += run(v, 0, u);
}
ans = max(ans, opAns);
}
return memo[u][canTake] = ans;
}
int match[1000];
int aug(int u) {
if (visited[u]) return 0;
visited[u] = true;
for (int v = 0; v < n; v++) {
if (!friends[u][v] || u == v || isLeft[v]) continue;
if (match[v] == -1 || aug(match[v])) {
match[v] = u; return 1;
}
}
return 0;
}
void dfsLeft(int u, int p, int l) {
isLeft[u] = l;
visited[u] = true;
for (int v = 0; v < n; v++) {
if (v == u || !friends[v][u] || visited[v]) continue;
dfsLeft(v, u, !l);
}
}
// Find out best sample
int findSample(int n2, int confidence[], int host[], int protocol[]) {
n = n2;
if (n <= 1000) {
FOR(i, 0, n) FOR(j, 0, n) friends[i][j] = false;
A = confidence;
FOR(i, 1, n) {
int h = host[i], p = protocol[i];
if (p == 0) {
// IAmYourFriend
friends[i][h] = true;
friends[h][i] = true;
} else if (p == 1) {
// MyFriendsAreYourFriends
for (int u = 0; u < n; u++) {
if (!friends[u][h]) continue;
friends[u][i] = true;
friends[i][u] = true;
}
} else {
// WeAreYourFriends
friends[i][h] = true;
friends[h][i] = true;
for (int u = 0; u < n; u++) {
if (!friends[u][h] || u == h) continue;
friends[u][i] = true;
friends[i][u] = true;
}
}
}
}
if (n <= 10) {
// Subtask 1
int ans = 0;
for (int i = 0; i < (1 << n); i++) {
int curAns = 0;
bool invalid = false;
for (int j = 0; j < n; j++) {
if (!(i & (1 << j))) continue;
for (int f = 0; f < n; f++) {
if (!friends[j][f] || j == f) continue;
if (i & (1 << f)) {
invalid = true;
break;
}
}
if (invalid) break;
curAns += confidence[j];
}
if (!invalid) ans = max(ans, curAns);
}
return ans;
} else {
bool isSubtaskTwo = true;
for (int i = 1; i < n; i++) {
if (protocol[i] != 1) isSubtaskTwo = false;
}
if (isSubtaskTwo) {
// Subtask two: Sum all confidence values
int ans = 0;
for (int i = 0; i < n; i++) ans += confidence[i];
return ans;
}
bool isSubtaskThree = true;
for (int i = 1; i < n; i++) {
if (protocol[i] != 2) isSubtaskThree = false;
}
if (isSubtaskThree) {
// Subtask Three: We Are Your Friends, entire graph is connected
int ans = 0;
for (int i = 0; i < n; i++) ans = max(ans, confidence[i]);
return ans;
}
bool isSubtaskFour = true;
for (int i = 1; i < n; i++) {
if (protocol[i] != 0) isSubtaskFour = false;
}
if (isSubtaskFour) {
// Subtask Four: Tree
// Define dp[i][0] = max confidence of subtree of i, cannot take i
// dp[i][1] = max confidence of subtree of i, can take i
for (int i = 0; i < n; i++) visited[i] = false;
for (int i = 0; i < n; i++) memo[i][0] = memo[i][1] = -1;
int ans = 0;
for (int i = 0; i < n; i++) {
if (!visited[i]) {
dfsVisited(i, i);
ans += run(i, 1, i);
}
}
return ans;
}
bool isSubtaskFive = n <= 1000;
for (int i = 1; i < n; i++) if (protocol[i] == 2 || confidence[i] != 1) isSubtaskFive = false;
if (isSubtaskFive) {
// Subtask Five: It's a bipartite graph, asking you to find maximum independent set
for (int i = 0; i < n; i++) isLeft[i] = false;
for (int i = 0; i < n; i++) visited[i] = false;
for (int i = 0; i < n; i++) {
if (!visited[i]) dfsLeft(i, i, 1);
}
int mcbm = 0;
for (int i = 0; i < n; i++) match[i] = -1;
for (int i = 0; i < n; i++) {
if (!isLeft[i]) continue;
for (int i = 0; i < n; i++) visited[i] = false;
mcbm += aug(i);
}
return n - mcbm;
}
// Subtask Six: Induction Trick
int ans = 0;
for (int i = n - 1; i >= 1; i--) {
int h = host[i];
int h_val = confidence[h];
int me_val = confidence[i];
if (protocol[i] == 0) {
if (me_val > h_val) {
confidence[h] = 0;
ans += me_val;
} else {
confidence[h] -= me_val;
ans += me_val;
}
} else if (protocol[i] == 1) {
confidence[h] += confidence[i];
} else if (protocol[i] == 2) {
confidence[h] = max(confidence[h], confidence[i]);
}
if (i == 1) ans += confidence[h];
}
return ans;
}
}
