#include <bits/stdc++.h>
#include "jumps.h"
using namespace std;
template<typename T> void ono_min(T &MIN, T CMP) { if(MIN > CMP) MIN = CMP; }
template<typename T> void ono_max(T &MAX, T CMP) { if(MAX < CMP) MAX = CMP; }
typedef pair<int, int> pii;
#define ff first
#define ss second
#define MP make_pair
const int mxk = 32;
const int mxn = 2e5 + 10;
const int inf = 1e9 + 10;
int L[mxn], h[mxn];
int R[mxn], n;
vector<int> adj[mxn];
int mx[mxk][mxn], mn[mxk][mxn];
pii ll[mxk][mxn], rr[mxk][mxn];
pii str[mxn * 4];
void build(int id, int tl, int tr) {
if(tl == tr) {
str[id] = MP(h[tl], tl);
return;
}
int tm = (tl + tr) / 2;
build(id * 2 + 1, tl, tm);
build(id * 2 + 2, tm + 1, tr);
str[id] = max(str[id * 2 + 1], str[id * 2 + 2]);
}
pii query(int id, int tl, int tr, int l, int r) {
if(l > r) return MP(0, -1);
if(tl == l && r == tr) return str[id];
int tm = (tl + tr) / 2;
if(r <= tm) return query(id * 2 + 1, tl, tm, l, r);
if(tm < l) return query(id * 2 + 2, tm + 1, tr, l, r);
pii LQ = query(id * 2 + 1, tl, tm, l, tm);
pii RQ = query(id * 2 + 2, tm + 1, tr, tm + 1, r);
return max(LQ, RQ);
}
void init(int N, vector<int> H) {
memset(L, -1, sizeof L);
memset(R, -1, sizeof R);
n = N;
for(int i = 0; i <= N; i++)
for(int k = 0; k <= mxk; k++) {
mn[k][i] = mx[k][i] = 0;
ll[k][i] = rr[k][i] = MP(0, 0);
}
stack<int> st;
for(int i = 1; i < N; i++) {
while(st.size() && H[st.top()] <= H[i])
st.pop();
if(st.size()) L[i] = st.top();
else L[i] = -1;
st.push(i);
}
stack<int> en;
for(int i = N - 1; i >= 0; i--) {
while(en.size() && H[en.top()] <= H[i])
en.pop();
if(en.size()) R[i] = en.top();
else R[i] = -1;
en.push(i);
}
for(int i = 0; i < N; i++) {
h[i] = H[i];
if(L[i] > -1) {
adj[i].push_back(L[i]);
if(mn[0][H[i]] == 0)
mn[0][H[i]] = H[L[i]];
ono_min(mn[0][H[i]], H[L[i]]);
ono_max(mx[0][H[i]], H[L[i]]);
ll[0][i] = MP(H[L[i]], L[i]);
}
if(R[i] > -1) {
adj[i].push_back(R[i]);
if(mn[0][H[i]] == 0)
mn[0][H[i]] = H[R[i]];
ono_min(mn[0][H[i]], H[R[i]]);
ono_max(mx[0][H[i]], H[R[i]]);
rr[0][i] = MP(H[R[i]], R[i]);
}
}
build(0, 0, n - 1);
for(int k = 1; k < mxk; k++)
for(int i = 1; i <= n; i++) {
int mnj = mn[k - 1][i];
int mxj = mx[k - 1][i];
if(mnj) mn[k][i] = mn[k - 1][mnj];
if(mxj) mx[k][i] = mx[k - 1][mxj];
}
for(int k = 1; k < mxk; k++)
for(int i = 0; i < n; i++) {
pii pl = ll[k - 1][i];
pii pr = rr[k - 1][i];
if(pl.ss) ll[k][i] = ll[k - 1][pl.ss];
if(pr.ss) rr[k][i] = rr[k - 1][pr.ss];
}
}
int solve(int s, int f) {
if(s == f) return 0;
int ans = 0;
for(int k = mxk - 1; k >= 0; k--)
if(mx[k][s] && mx[k][s] <= f) {
s = mx[k][s];
ans += (1 << k);
}
for(int k = mxk - 1; k >= 0; k--)
if(mn[k][s] && mn[k][s] <= f) {
s = mn[k][s];
ans += (1 << k);
}
if(s == f) return ans;
return inf;
}
int minimum_jumps(int A, int B, int C, int D) {
pii bet = query(0, 0, n - 1, B + 1, C - 1);
int bet_mx = bet.ff;
int bet_id = bet.ss;
// cout << endl;
// cout << "min jump: " << A << ' ' << B << ' ' << C << ' ' << D << endl;
// cout << "mid = " << bet_id << ' ' << bet_mx << endl;
int l = B;
for(int i = mxk - 1; i >= 0; i--) {
pii p = ll[i][l];
int hi = p.ff;
int id = p.ss;
if(hi == 0) continue;
if(hi > bet_mx) continue;
if(id < A) continue;
l = id;
}
auto think = [&](int i) -> int {
if(i == -1) return inf;
if(i < A) return inf;
int cur = C, cmp = max(h[i], bet_mx);
if(cmp < h[C]) return solve(h[i], h[C]);
for(int k = mxk - 1; k >= 0; k--) {
pii p = rr[k][cur];
int hi = p.ff;
int id = p.ss;
if(hi == 0) continue;
if(hi > cmp) continue;
if(id > D) continue;
cur = id;
}
if(R[cur] == -1) return inf;
if(R[cur] > D) return inf;
if(cmp > h[R[cur]]) return inf;
// cout << " think " << i << ' ' << R[cur] << endl;
return solve(h[i], h[R[cur]]);
};
int AL = think(l);
int PL = think(L[l]);
pii GL = query(0, 0, n - 1, A, B);
int L_mx = GL.ff;
int L_id = GL.ss;
int LL = INT_MAX;
auto go_left = [&](int ML) -> int {
int ret = 0;
int L_most = ML;
for(int k = mxk - 1; k >= 0; k--) {
pii p = ll[k][L_most];
int hi = p.ff;
int id = p.ss;
if(hi == 0) continue;
if(hi > bet_mx) continue;
L_most = id;
ret += (1 << k);
}
if(L[L_most] != -1) {
L_most = L[L_most];
ret++;
}
int R_most = L_most;
for(int k = mxk - 1; k >= 0; k--) {
if(C <= R_most && R_most <= D)
return ret;
pii p = rr[k][R_most];
int hi = p.ff;
int id = p.ss;
if(hi == 0) continue;
if(id > D) continue;
R_most = id;
ret += (1 << k);
}
return INT_MAX;
};
LL = go_left(L_id);
int L_most = B, sus = 0;
for(int k = mxk - 1; k >= 0; k--) {
pii p = ll[k][L_most];
int hi = p.ff;
int id = p.ss;
if(hi == 0) continue;
if(hi > bet_mx) continue;
sus += (1 << k);
L_most = id;
}
L_most = L[L_most];
int gay = inf;
if(L_most != -1 && L_most < A) {
int R_most = C;
for(int k = mxk - 1; k >= 0; k--) {
pii p = ll[k][R_most];
int hi = p.ff;
int id = p.ss;
if(hi == 0) continue;
if(hi > h[L_most]) continue;
if(id > D) continue;
R_most = id;
}
R_most = R[R_most];
// cout << A << ' ' << B << ' ' << C << ' ' << D << endl;
// cout << L_most << ' ' << R_most << endl;
if(R_most != -1 && C <= R_most && R_most <= D)
gay = solve(h[L_most], h[R_most]) + solve(L_mx, h[L_most]);
}
if(min({AL, PL, LL, gay}) != inf) return min({AL, PL, LL, gay});
return -1;
}
// 7 4 1 2 5 3 6 9 8
// 9 8 7 6 5 4 3 2 1
