#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 = 24 + 1;
int N;
vector<int> S, P, W, L;
int anc[lgmx][lgmx][maxn], sum[lgmx][lgmx][maxn], val[lgmx][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);
S.eb(0), P.eb(0), W.eb(N), L.eb(N);
memset(anc, 0x00, sizeof(anc));
memset(sum, 0x00, sizeof(sum));
memset(val, 0x00, sizeof(val));
for (int lvl = 0; lvl < lgmx; ++lvl) {
/// Assume you have strength \ge 2^{lvl} ///
for (int i = 0; i < N; ++i) {
anc[lvl][0][i] = S[i] <= (1LL << lvl+1) ? W[i] : L[i];
sum[lvl][0][i] = S[i] <= (1LL << lvl+1) ? S[i] : P[i];
val[lvl][0][i] = S[i];
}
anc[lvl][0][N] = N;
}
for (int lvl = 0; lvl < lgmx; ++lvl) {
for (int lay = 1; lay < lgmx; ++lay) {
for (int i = 0; i <= N; ++i) {
int par = anc[lvl][lay-1][i];
anc[lvl][lay][i] = anc[lvl][lay-1][par];
sum[lvl][lay][i] = sum[lvl][lay-1][i] + sum[lvl][lay-1][par];
val[lvl][lay][i] = max(val[lvl][lay-1][i], val[lvl][lay-1][par]);
}
}
}
}
int simulate(int32_t now, int32_t _Z) {
int Z = _Z;
for (int lvl = 0; lvl < lgmx and now != N; ++lvl) {
if (Z >= (1LL<<(lvl+1))) continue;
for (int lay = lgmx-1; lay >= 0 and now != N; --lay) {
if (Z + sum[lvl][lay][now] < min(val[lvl][lay][now], 1LL<<(lvl+1))) {
Z += sum[lvl][lay][now];
now = anc[lvl][lay][now];
}
// cerr << "(lvl, Z, now): " << lvl << "," << Z << "," << now << "\n";
}
if (Z >= S[now]) Z += S[now], now = W[now];
else Z += P[now], now = L[now];
// cerr << "(lvl, Z, now): " << lvl << "," << Z << "," << now << "\n";
}
// assert(now == N or Z >= *max_element(ALL(S)));
return Z + sum[lgmx-1][lgmx-1][now];
}
