#include "dungeons.h"
#pragma GCC optimize("Ofast", "unroll-loops")
#include <bits/stdc++.h>
using namespace std;
#define int long long
// #define double long double
using pii = pair<int, int>;
template<typename T>
using Prior = std::priority_queue<T>;
template<typename T>
using prior = std::priority_queue<T, vector<T>, greater<T>>;
#define X first
#define Y second
#define eb emplace_back
#define pb pop_back
#define pf pop_front
#define ALL(x) begin(x), end(x)
#define RALL(x) rbegin(x), rend(x)
namespace {
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
// const int maxn = 4E5 + 5;
const int maxn = 5E4 + 5;
// const int lgmx = 19;
const int lgmx = 16;
int N;
vector<int> S, P, W, L;
int win_anc[lgmx][maxn], win_sum[lgmx][maxn], win_val[lgmx][maxn];
int los_anc[lgmx][maxn], los_sum[lgmx][maxn];
} /// end of namespace
void init(int32_t _N, vector<int32_t> _S, vector<int32_t> _P, vector<int32_t> _W, vector<int32_t> _L) {
N = _N;
for (auto &x : _S) S.eb(x);
for (auto &x : _P) P.eb(x);
for (auto &x : _W) W.eb(x);
for (auto &x : _L) L.eb(x);
memset(win_anc, 0x00, sizeof(win_anc));
memset(win_sum, 0x00, sizeof(win_sum));
// memset(win_val, 0x00, sizeof(win_val));
memset(los_anc, 0x00, sizeof(los_anc));
memset(los_sum, 0x00, sizeof(los_sum));
for (int i = 0; i < N; ++i) {
win_anc[0][i] = W[i];
win_sum[0][i] = S[i];
// win_val[0][i] = S[i];
los_anc[0][i] = L[i];
los_sum[0][i] = P[i];
}
win_anc[0][N] = los_anc[0][N] = N;
for (int lay = 1; lay < lgmx; ++lay) {
for (int i = 0; i <= N; ++i) {
int win_par = win_anc[lay-1][i];
win_anc[lay][i] = win_anc[lay-1][win_par];
win_sum[lay][i] = win_sum[lay-1][i] + win_sum[lay-1][win_par];
// win_val[lay][i] = max(win_val[lay-1][i], win_val[lay-1][win_par]);
int los_par = los_anc[lay-1][i];
los_anc[lay][i] = los_anc[lay-1][los_par];
los_sum[lay][i] = los_sum[lay-1][i] + los_sum[lay-1][los_par];
}
}
}
int simulate(int32_t now, int32_t _Z) {
/// s[i] = s[j] ///
int Z = _Z;
for (int lay = lgmx-1; lay >= 0; --lay) {
if (los_anc[lay][now] != N and Z + los_sum[lay][now] < S[0]) {
Z += los_sum[lay][now];
now = los_anc[lay][now];
}
// cerr << "(Z, now): " << Z << "," << now << "\n";
}
if (Z < S[0]) Z += P[now], now = L[now];
return Z + win_sum[lgmx-1][now];
}
