#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));
stack<int> decreasing_height;
for (int i = 0; i < N; ++i) {
while (!decreasing_height.empty() && H[decreasing_height.top()] <= H[i]) {
decreasing_height.pop();
}
L[0][i] = decreasing_height.empty() ? i : decreasing_height.top();
decreasing_height.push(i);
}
while (!decreasing_height.empty()) {
decreasing_height.pop();
}
for (int i = N - 1; i >= 0; --i) {
while (!decreasing_height.empty() && H[decreasing_height.top()] <= H[i]) {
decreasing_height.pop();
}
R[0][i] = decreasing_height.empty() ? i : decreasing_height.top();
decreasing_height.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 s, int e) {
int jumps = 0;
for (int j = kMaxLogN - 1; j >= 0; --j) {
if (H[higher[j][s]] <= H[e]) {
s = higher[j][s];
jumps |= (1 << j);
}
}
if (H[L[0][s]] > H[e]) {
for (int j = kMaxLogN - 1; j >= 0; --j) {
if (H[R[j][s]] <= H[e]) {
s = R[j][s];
jumps += (1 << j);
}
}
} else {
for (int j = kMaxLogN - 1; j >= 0; --j) {
if (H[L[j][s]] <= H[e]) {
s = L[j][s];
jumps += (1 << j);
}
}
}
return s == e ? jumps : -1;
}
int minimum_jumps(int A, int B, int C, int D) {
++A; ++B; ++C; ++D;
int s = B;
int e = C;
if (B + 1 < C) {
int middle_tallest_index = maximum_height_index(B + 1, C - 1);
if (H[e] < H[middle_tallest_index]) {
for (int j = kMaxLogN - 1; j >= 0; --j) {
if (H[R[j][e]] < H[middle_tallest_index]) {
e = R[j][e];
}
}
e = R[0][e];
}
}
if (e > D) {
return -1;
}
int jumps = INT_MAX;
while (s >= A) {
if (H[e] > H[s]) {
jumps = min(jumps, minimum_jumps(s, e));
} else {
for (int j = kMaxLogN - 1; j >= 0; --j) {
if (H[R[j][e]] < H[s]) {
e = R[j][e];
}
}
e = R[0][e];
if (e > D) {
break;
}
jumps = min(jumps, minimum_jumps(s, e));
}
s = L[0][s];
}
return jumps == INT_MAX ? -1 : jumps;
}
