#include "jumps.h"
#pragma GCC optimize("Ofast", "unroll-loops")
#include <bits/stdc++.h>
using namespace std;
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 ALL(x) begin(x), end(x)
#define RALL(x) rbegin(x), rend(x)
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
inline int getRand(int L, int R) {
if (L > R) swap(L, R);
return (int)(rng() % (uint64_t)(R - L + 1) + L);
}
const int INF = 1E9;
const int maxn = 1 << 18;
const int lgmx = 18;
// const int maxn = 1 << 4;
// const int lgmx = 4;
int N, sparse[lgmx][maxn], inv[maxn];
pii jump[lgmx][maxn]; /// (jump lo_edge, jump hi_edge)
vector<int> H;
inline int chmin(int &x, int y) {return x <= y ? 0 : x = y, 1;}
inline int QueryMax(int L, int R) {
int lay = __lg(R - L + 1);
return max(sparse[lay][L], sparse[lay][R - (1<<lay) + 1]);
}
void init(int _N, vector<int> _H) {
N = _N + 2;
H.eb(N + 1); for (auto x : _H) H.eb(x); H.eb(N + 2);
for (int i = 0; i < N; ++i) sparse[0][i] = H[i], inv[H[i]] = i;
for (int lay = 1; lay < lgmx; ++lay) {
for (int i = 0; i < N-(1<<lay)+1; ++i) {
sparse[lay][i] = max(sparse[lay-1][i], sparse[lay-1][i+(1<<lay-1)]);
}
}
jump[0][0] = {0, N-1}, jump[0][N-1] = {N-1, N-1};
for (int i = 1, lo, mi, hi; i < N-1; ++i) {
auto &jmp = jump[0][i];
lo = 0, hi = i;
while (lo < hi) {
mi = lo + hi + 1 >> 1;
QueryMax(mi, i) > H[i] ? lo = mi : hi = mi - 1;
}
jmp.X = lo;
lo = i, hi = N-1;
while (lo < hi) {
mi = lo + hi >> 1;
QueryMax(i, mi) > H[i] ? hi = mi : lo = mi + 1;
}
jmp.Y = lo;
if (H[jmp.X] > H[jmp.Y]) swap(jmp.X, jmp.Y);
}
for (int lay = 1; lay < lgmx; ++lay) {
for (int i = 0; i < N; ++i) {
auto anc = jump[lay-1][i];
jump[lay][i].X = jump[lay-1][anc.X].X;
jump[lay][i].Y = jump[lay-1][anc.Y].Y;
}
}
}
int minimum_jumps(int A, int B, int C, int D) {
++A, ++B, ++C, ++D;
int lo = A, hi = B, mi;
while (lo < hi) {
mi = lo + hi >> 1;
if (QueryMax(mi, B) > H[C]) lo = mi + 1;
else hi = mi;
}
A = B = inv[QueryMax(lo, B)];
// cout << "start at " << A - 1 << "\n";
int ans = 0;
for (int i = lgmx-1; i >= 0; --i) {
if (H[jump[i][A].Y] <= H[C]) A = jump[i][A].Y, ans += 1 << i;
}
for (int i = lgmx-1; i >= 0; --i) {
if (H[jump[i][A].X] <= H[C]) A = jump[i][A].X, ans += 1 << i;
}
return A == C ? ans : -1;
}
