#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;
const int INF = 1E13;
int N;
vector<int> S, P, W, L;
vector<int> dep(maxn);
int sum[lgmx/4+1][lgmx][maxn];
int32_t anc[lgmx/4+1][lgmx][maxn], mnm[lgmx/4+1][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(mnm, 0x00, sizeof(mnm));
for (int i = N-1; i >= 0; --i) dep[i] = dep[W[i]] + S[i];
for (int lvl = 0; lvl <= lgmx/4; ++lvl) {
/**
* Assume strength is in [2^{4*lvl-4}, 2^{4*lvl}), every opponent with strength
* greater or equal to 2^{4*lvl} is ignored and you lose immediately as we
* only consider opponents with strength less than 2^{4*lvl} in this level.
**/
for (int i = 0; i <= N; ++i) {
anc[lvl][0][i] = S[i] < (1<<(4*lvl)) ? W[i] : L[i];
sum[lvl][0][i] = S[i] < (1<<(4*lvl)) ? S[i] : P[i];
mnm[lvl][0][i] = S[i] < (1<<(4*lvl)) ? INF : S[i];
}
for (int lay = 1; lay < lgmx; ++lay) {
for (int i = 0; i <= N; ++i) {
int32_t 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];
int32_t tmp = mnm[lvl][lay-1][par];
if (tmp != INF) tmp -= sum[lvl][lay-1][i];
mnm[lvl][lay][i] = min(mnm[lvl][lay-1][i], max(0, tmp));
}
}
}
}
int simulate(int32_t now, int32_t _Z) {
int Z = _Z;
for (int lvl = 0; lvl <= lgmx/4; ++lvl) {
// int lvl = __lg(Z) / 4;
for (int _ = 0; _ < 16; ++_) {
for (int lay = lgmx-1; lay >= 0; --lay) {
if (Z < mnm[lvl][lay][now]) {
Z += sum[lvl][lay][now];
now = anc[lvl][lay][now];
}
}
// cerr << "lvl = " << lvl << ", Z = " << Z << ", now = " << now << "\n";
if (Z >= S[now]) Z += S[now], now = W[now];
else Z += P[now], now = L[now];
// cerr << "lvl = " << lvl << ", Z = " << Z << ", now = " << now << "\n";
}
}
return Z + dep[now];
}
