#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;
int L[mxN];
int R[mxN];
int N;
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[i] = st.empty() ? -1 : st.top();
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[i] = st.empty() ? -1 : st.top();
st.push(i);
}
tree = IterativeSegmentTree<Info>(N);
for (int i = 0; i < N; i++) {
tree.update(i, {{H[i], i}, {H[i], i}});
}
}
// we answer them in O(n)
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;
std::vector<int> dp(N, -1);
std::queue<int> q;
for (int i = A; i <= B; i++) {
dp[i] = 0;
q.push(i);
}
while (q.size()) {
int u = q.front();
q.pop();
for (int v : {L[u], R[u]}) {
if (v == -1) continue;
if (dp[v] != -1) continue;
dp[v] = dp[u] + 1;
q.emplace(v);
}
}
int ans = 1e9;
for (int i = C; i <= D; i++) {
if (dp[i] != -1) ans = std::min(ans, dp[i]);
}
return ans;
}
