#include "jumps.h"
#include <bits/stdc++.h>
using namespace std;
constexpr int kMaxLogN = 20;
int N;
vector<int> H;
vector<vector<int>> L, R;
vector<vector<int>> higher;
void init(int _N, std::vector<int> _H) {
N = _N;
H = _H;
H.insert(H.begin(), INT_MAX);
H.insert(H.end(), INT_MAX);
N += 2;
L = R = higher = vector<vector<int>>(kMaxLogN, vector<int>(N));
// leftward edges
stack<int> stak;
for (int i = 0; i < N; ++i) {
while (!stak.empty() && H[stak.top()] <= H[i]) {
stak.pop();
}
L[0][i] = stak.empty() ? i : stak.top();
stak.push(i);
}
// rightward edges
while (!stak.empty()) {
stak.pop();
}
for (int i = N - 1; i >= 0; --i) {
while (!stak.empty() && H[stak.top()] <= H[i]) {
stak.pop();
}
R[0][i] = stak.empty() ? i : stak.top();
stak.push(i);
}
for (int i = 0; i < N; ++i) {
higher[0][i] = H[L[0][i]] > H[R[0][i]] ? L[0][i] : R[0][i];
}
for (int j = 1; j < kMaxLogN; ++j) {
for (int i = 0; i < N; ++i) {
L[j][i] = L[j - 1][L[j - 1][i]];
R[j][i] = R[j - 1][R[j - 1][i]];
higher[j][i] = higher[j - 1][higher[j - 1][i]];
}
}
}
int maximum_height_index(int l, int r) {
for (int j = kMaxLogN - 1; j >= 0; --j) {
if (R[j][l] <= r) {
l = R[j][l];
}
}
return l;
}
int minimum_jumps(int A, int B, int C, int D) {
++A; ++B; ++C; ++D;
// touching
if (B == C - 1) {
return R[0][B] <= D ? 1 : -1;
}
int m = maximum_height_index(B + 1, C - 1);
// jump over
if (H[B] > H[m]) {
return R[0][B] <= D ? 1 : -1;
}
// starting point
int s = B;
for (int j = kMaxLogN - 1; j >= 0; --j) {
if (A <= L[j][s] && H[L[j][s]] < H[m]) {
s = L[j][s];
}
}
int jumps = 0;
if (A <= L[0][s]) {
// next maximum can jump over
if (R[0][L[0][s]] <= D) {
return 1;
}
}
else {
// limit height by a[m]
for (int j = kMaxLogN - 1; j >= 0; --j) {
if (H[higher[j][s]] <= H[m]) {
jumps |= (1 << j);
s = higher[j][s];
}
}
// stopped at m
if (s == m) {
return R[0][s]<=D ? jumps+1 : -1;
}
// if jump over
if (0 < L[0][s] && R[0][L[0][s]] <= D) {
return jumps+2;
}
}
for (int j = kMaxLogN - 1; j >= 0; --j) {
if (R[j][s] < C) {
jumps += (1 << j);
s = R[j][s];
}
}
return C<=R[0][s]&&R[0][s]<=D ? jumps+1 : -1;
}
