#include "jumps.h"
#include <bits/stdc++.h>
template <typename Info, typename Merge = std::plus<Info>>
struct IterativeSegmentTree {
int n;
std::vector<Info> T;
IterativeSegmentTree() {}
IterativeSegmentTree(int _n) : n(2 << std::__lg(_n)), T(2 * n, Info()){};
template <typename Type>
IterativeSegmentTree(const std::vector<Type>& a) : n(2 << std::__lg(a.size())), T(2 * n, Info()) {
for (int i = n; i < n + (int) a.size(); i++) {
T[i] = a[i - n];
}
for (int i = n - 1; i > 0; i--) {
T[i] = Merge()(T[i << 1], T[i << 1 | 1]);
}
}
template <typename Iterator>
IterativeSegmentTree(Iterator first, Iterator last) : n(2 << std::__lg(distance(first, last))), T(2 * n, Info()) {
int id = n;
for (Iterator it = first; it != last; it++) {
T[id++] = *it;
}
for (int i = n - 1; i > 0; i--) {
T[i] = Merge()(T[i << 1], T[i << 1 | 1]);
}
}
void update(int p, const Info& v) {
for (T[p += n] = v; p >>= 1;) {
T[p] = Merge()(T[p << 1], T[p << 1 | 1]);
}
}
Info query(int l, int r) {
Info resl = Info(), resr = Info();
for (l += n, r += n; l < r; l >>= 1, r >>= 1) {
if (l & 1) resl = Merge()(resl, T[l++]);
if (r & 1) resr = Merge()(T[--r], resr);
}
return Merge()(resl, resr);
}
};
struct Info {
std::pair<int, int> mn = {1e9, -1}, mx = {-1e9, -1};
};
Info operator+(const Info& a, const Info& b) {
return {std::min(a.mn, b.mn), std::max(a.mx, b.mx)};
}
constexpr int mxN = 200002, LOG = 20;
int L[LOG][mxN];
int cntL[LOG][mxN];
int R[LOG][mxN];
int cntR[LOG][mxN];
int N;
int prefer[LOG][mxN];
int cnt[LOG][mxN];
std::vector<int> H;
IterativeSegmentTree<Info> tree;
void init(int _N, std::vector<int> _H) {
N = _N;
H = _H;
std::stack<int> st;
for (int i = 0; i < N; i++) {
while (st.size() && H[st.top()] <= H[i]) {
st.pop();
}
L[0][i] = st.empty() ? i : st.top();
cntL[0][i] = L[0][i] != i;
st.push(i);
}
while (st.size()) st.pop();
for (int i = N - 1; i >= 0; i--) {
while (st.size() && H[st.top()] <= H[i]) {
st.pop();
}
R[0][i] = st.empty() ? i : st.top();
cntR[0][i] = R[0][i] != i;
st.push(i);
}
tree = IterativeSegmentTree<Info>(N);
for (int i = 0; i < N; i++) {
tree.update(i, {{H[i], i}, {H[i], i}});
}
for (int i = 0; i < N; i++) {
if (L[0][i] == i && R[0][i] == i) {
prefer[0][i] = i;
cnt[0][i] = 0;
continue;
}
cnt[0][i] = 1;
if (L[0][i] == i) {
prefer[0][i] = R[0][i];
} else if (R[0][i] == i) {
prefer[0][i] = L[0][i];
} else {
prefer[0][i] = H[L[0][i]] > H[R[0][i]] ? L[0][i] : R[0][i];
}
}
for (int k = 0; k + 1 < LOG; k++) {
for (int i = 0; i < N; i++) {
prefer[k + 1][i] = prefer[k][prefer[k][i]];
cnt[k + 1][i] = cnt[k][i] + cnt[k][prefer[k][i]];
L[k + 1][i] = L[k][L[k][i]];
R[k + 1][i] = R[k][R[k][i]];
cntL[k + 1][i] = cntL[k][i] + cntL[k][L[k][i]];
cntR[k + 1][i] = cntR[k][i] + cntR[k][R[k][i]];
}
}
}
int minimum_jumps(int A, int B, int C, int D) {
int sz_mid = C - B - 1;
auto bl = tree.query(A, B + 1);
auto br = tree.query(C, D + 1);
if (sz_mid > 0) {
auto bmid = tree.query(B + 1, C);
if (bmid.mx.first >= br.mx.first) {
return -1;
}
}
if (H[B] >= br.mx.first) return -1;
int jumps = 0;
int u = B;
for (int k = LOG - 1; k >= 0; k--) {
int to = prefer[k][u];
if (H[to] >= H[C]) continue;
jumps += cnt[k][u];
u = to;
}
for (int k = LOG - 1; k >= 0; k--) {
int to = R[k][u];
if (to >= C) continue;
jumps += cntR[k][u];
u = to;
}
jumps++;
return jumps;
}
